id	sid	tid	token	lemma	pos
ejpam-5594	1	1	european	european	PROPN
ejpam-5594	1	2	journal	journal	PROPN
ejpam-5594	1	3	of	of	ADP
ejpam-5594	1	4	pure	pure	ADJ
ejpam-5594	1	5	and	and	CCONJ
ejpam-5594	1	6	applied	apply	VERB
ejpam-5594	1	7	mathematics	mathematic	NOUN
ejpam-5594	1	8	vol	vol	NOUN
ejpam-5594	1	9	.	.	PROPN
ejpam-5594	2	1	17	17	NUM
ejpam-5594	2	2	,	,	PUNCT
ejpam-5594	2	3	no	no	INTJ
ejpam-5594	2	4	.	.	NOUN
ejpam-5594	2	5	4	4	NUM
ejpam-5594	2	6	,	,	PUNCT
ejpam-5594	2	7	2024	2024	NUM
ejpam-5594	2	8	,	,	PUNCT
ejpam-5594	2	9	4014	4014	NUM
ejpam-5594	2	10	-	-	SYM
ejpam-5594	2	11	4049	4049	NUM
ejpam-5594	2	12	issn	issn	PROPN
ejpam-5594	2	13	1307	1307	NUM
ejpam-5594	2	14	-	-	SYM
ejpam-5594	2	15	5543	5543	NUM
ejpam-5594	2	16	–	–	PUNCT
ejpam-5594	2	17	ejpam.com	ejpam.com	X
ejpam-5594	2	18	published	publish	VERB
ejpam-5594	2	19	by	by	ADP
ejpam-5594	2	20	new	new	PROPN
ejpam-5594	2	21	york	york	PROPN
ejpam-5594	2	22	business	business	PROPN
ejpam-5594	2	23	global	global	VERB
ejpam-5594	2	24	some	some	DET
ejpam-5594	2	25	new	new	ADJ
ejpam-5594	2	26	fractional	fractional	ADJ
ejpam-5594	2	27	hermite	hermite	ADJ
ejpam-5594	2	28	-	-	PUNCT
ejpam-5594	2	29	hadamard	hadamard	ADJ
ejpam-5594	2	30	type	type	NOUN
ejpam-5594	2	31	inequalities	inequality	NOUN
ejpam-5594	2	32	for	for	ADP
ejpam-5594	2	33	generalized	generalized	ADJ
ejpam-5594	2	34	class	class	NOUN
ejpam-5594	2	35	of	of	ADP
ejpam-5594	2	36	godunova	godunova	PROPN
ejpam-5594	2	37	-	-	PUNCT
ejpam-5594	2	38	levin	levin	PROPN
ejpam-5594	2	39	functions	function	NOUN
ejpam-5594	2	40	by	by	ADP
ejpam-5594	2	41	means	mean	NOUN
ejpam-5594	2	42	of	of	ADP
ejpam-5594	2	43	interval	interval	NOUN
ejpam-5594	2	44	center	center	NOUN
ejpam-5594	2	45	-	-	PUNCT
ejpam-5594	2	46	radius	radius	NOUN
ejpam-5594	2	47	order	order	NOUN
ejpam-5594	2	48	relation	relation	NOUN
ejpam-5594	2	49	with	with	ADP
ejpam-5594	2	50	applications	application	NOUN
ejpam-5594	2	51	waqar	waqar	PROPN
ejpam-5594	2	52	afzal1	afzal1	PROPN
ejpam-5594	2	53	,	,	PUNCT
ejpam-5594	2	54	mehreen	mehreen	NOUN
ejpam-5594	2	55	s.	s.	PROPN
ejpam-5594	2	56	khan2	khan2	PROPN
ejpam-5594	2	57	,	,	PUNCT
ejpam-5594	2	58	mutum	mutum	PROPN
ejpam-5594	2	59	zico	zico	PROPN
ejpam-5594	2	60	meetei3	meetei3	PROPN
ejpam-5594	2	61	,	,	PUNCT
ejpam-5594	2	62	mujahid	mujahid	PROPN
ejpam-5594	2	63	abbas4,5	abbas4,5	PROPN
ejpam-5594	2	64	,	,	PUNCT
ejpam-5594	2	65	jorge	jorge	PROPN
ejpam-5594	2	66	e.	e.	PROPN
ejpam-5594	2	67	maćıas	maćıas	PROPN
ejpam-5594	2	68	-	-	PUNCT
ejpam-5594	2	69	dı́az6,7,∗	dı́az6,7,∗	PROPN
ejpam-5594	2	70	,	,	PUNCT
ejpam-5594	2	71	hector	hector	PROPN
ejpam-5594	2	72	vargas	vargas	NOUN
ejpam-5594	2	73	-	-	PUNCT
ejpam-5594	2	74	rodŕıguez8	rodŕıguez8	PROPN
ejpam-5594	2	75	1	1	NUM
ejpam-5594	2	76	department	department	NOUN
ejpam-5594	2	77	of	of	ADP
ejpam-5594	2	78	mathematics	mathematic	NOUN
ejpam-5594	2	79	,	,	PUNCT
ejpam-5594	2	80	government	government	NOUN
ejpam-5594	2	81	college	college	NOUN
ejpam-5594	2	82	university	university	PROPN
ejpam-5594	2	83	,	,	PUNCT
ejpam-5594	2	84	katchery	katchery	NOUN
ejpam-5594	2	85	road	road	NOUN
ejpam-5594	2	86	,	,	PUNCT
ejpam-5594	2	87	lahore	lahore	NOUN
ejpam-5594	2	88	54000	54000	NUM
ejpam-5594	2	89	,	,	PUNCT
ejpam-5594	2	90	pakistan	pakistan	PROPN
ejpam-5594	2	91	2	2	NUM
ejpam-5594	2	92	department	department	NOUN
ejpam-5594	2	93	of	of	ADP
ejpam-5594	2	94	mathematics	mathematic	NOUN
ejpam-5594	2	95	,	,	PUNCT
ejpam-5594	2	96	faculty	faculty	NOUN
ejpam-5594	2	97	of	of	ADP
ejpam-5594	2	98	science	science	NOUN
ejpam-5594	2	99	,	,	PUNCT
ejpam-5594	2	100	jazan	jazan	PROPN
ejpam-5594	2	101	university	university	PROPN
ejpam-5594	2	102	,	,	PUNCT
ejpam-5594	2	103	jazan	jazan	NOUN
ejpam-5594	2	104	45142	45142	NUM
ejpam-5594	2	105	,	,	PUNCT
ejpam-5594	2	106	saudi	saudi	PROPN
ejpam-5594	2	107	arabia	arabia	PROPN
ejpam-5594	2	108	3	3	NUM
ejpam-5594	2	109	department	department	NOUN
ejpam-5594	2	110	of	of	ADP
ejpam-5594	2	111	mathematics	mathematics	PROPN
ejpam-5594	2	112	,	,	PUNCT
ejpam-5594	2	113	college	college	NOUN
ejpam-5594	2	114	of	of	ADP
ejpam-5594	2	115	science	science	PROPN
ejpam-5594	2	116	,	,	PUNCT
ejpam-5594	2	117	jazan	jazan	PROPN
ejpam-5594	2	118	university	university	PROPN
ejpam-5594	2	119	,	,	PUNCT
ejpam-5594	2	120	p.o	p.o	PROPN
ejpam-5594	2	121	.	.	PROPN
ejpam-5594	2	122	box	box	PROPN
ejpam-5594	2	123	114	114	NUM
ejpam-5594	2	124	,	,	PUNCT
ejpam-5594	2	125	jazan	jazan	NOUN
ejpam-5594	2	126	45142	45142	NUM
ejpam-5594	2	127	,	,	PUNCT
ejpam-5594	2	128	saudi	saudi	PROPN
ejpam-5594	2	129	arabia	arabia	PROPN
ejpam-5594	2	130	4	4	NUM
ejpam-5594	2	131	department	department	NOUN
ejpam-5594	2	132	of	of	ADP
ejpam-5594	2	133	mechanical	mechanical	ADJ
ejpam-5594	2	134	engineering	engineering	NOUN
ejpam-5594	2	135	sciences	science	NOUN
ejpam-5594	2	136	,	,	PUNCT
ejpam-5594	2	137	faculty	faculty	NOUN
ejpam-5594	2	138	of	of	ADP
ejpam-5594	2	139	engineering	engineering	NOUN
ejpam-5594	2	140	and	and	CCONJ
ejpam-5594	2	141	the	the	DET
ejpam-5594	2	142	built	build	VERB
ejpam-5594	2	143	environment	environment	NOUN
ejpam-5594	2	144	,	,	PUNCT
ejpam-5594	2	145	doornfontein	doornfontein	ADJ
ejpam-5594	2	146	campus	campus	NOUN
ejpam-5594	2	147	,	,	PUNCT
ejpam-5594	2	148	university	university	PROPN
ejpam-5594	2	149	of	of	ADP
ejpam-5594	2	150	johannesburg	johannesburg	PROPN
ejpam-5594	2	151	,	,	PUNCT
ejpam-5594	2	152	south	south	PROPN
ejpam-5594	2	153	africa	africa	PROPN
ejpam-5594	2	154	5	5	NUM
ejpam-5594	2	155	department	department	PROPN
ejpam-5594	2	156	of	of	ADP
ejpam-5594	2	157	medical	medical	ADJ
ejpam-5594	2	158	research	research	NOUN
ejpam-5594	2	159	,	,	PUNCT
ejpam-5594	2	160	china	china	PROPN
ejpam-5594	2	161	medical	medical	PROPN
ejpam-5594	2	162	university	university	PROPN
ejpam-5594	2	163	,	,	PUNCT
ejpam-5594	2	164	taichung	taichung	PROPN
ejpam-5594	2	165	406040	406040	NUM
ejpam-5594	2	166	,	,	PUNCT
ejpam-5594	2	167	taiwan	taiwan	PROPN
ejpam-5594	2	168	6	6	NUM
ejpam-5594	2	169	department	department	NOUN
ejpam-5594	2	170	of	of	ADP
ejpam-5594	2	171	mathematics	mathematic	NOUN
ejpam-5594	2	172	,	,	PUNCT
ejpam-5594	2	173	school	school	NOUN
ejpam-5594	2	174	of	of	ADP
ejpam-5594	2	175	digital	digital	ADJ
ejpam-5594	2	176	technologies	technology	NOUN
ejpam-5594	2	177	,	,	PUNCT
ejpam-5594	2	178	tallinn	tallinn	PROPN
ejpam-5594	2	179	university	university	PROPN
ejpam-5594	2	180	,	,	PUNCT
ejpam-5594	2	181	narva	narva	PROPN
ejpam-5594	2	182	rd	rd	PROPN
ejpam-5594	2	183	.	.	PROPN
ejpam-5594	2	184	25	25	NUM
ejpam-5594	2	185	,	,	PUNCT
ejpam-5594	2	186	10120	10120	NUM
ejpam-5594	2	187	tallinn	tallinn	PROPN
ejpam-5594	2	188	,	,	PUNCT
ejpam-5594	2	189	estonia	estonia	PROPN
ejpam-5594	2	190	7	7	NUM
ejpam-5594	2	191	department	department	NOUN
ejpam-5594	2	192	of	of	ADP
ejpam-5594	2	193	mathematics	mathematics	PROPN
ejpam-5594	2	194	and	and	CCONJ
ejpam-5594	2	195	physics	physics	PROPN
ejpam-5594	2	196	,	,	PUNCT
ejpam-5594	2	197	autonomous	autonomous	ADJ
ejpam-5594	2	198	university	university	NOUN
ejpam-5594	2	199	of	of	ADP
ejpam-5594	2	200	aguascalientes	aguascaliente	NOUN
ejpam-5594	2	201	,	,	PUNCT
ejpam-5594	2	202	ave	ave	PROPN
ejpam-5594	2	203	.	.	PUNCT
ejpam-5594	3	1	universidad	universidad	PROPN
ejpam-5594	3	2	940	940	NUM
ejpam-5594	3	3	,	,	PUNCT
ejpam-5594	3	4	ciudad	ciudad	PROPN
ejpam-5594	3	5	universitaria	universitaria	PROPN
ejpam-5594	3	6	,	,	PUNCT
ejpam-5594	3	7	aguascalientes	aguascaliente	NOUN
ejpam-5594	3	8	20100	20100	NUM
ejpam-5594	3	9	,	,	PUNCT
ejpam-5594	3	10	mexico	mexico	PROPN
ejpam-5594	3	11	8	8	NUM
ejpam-5594	3	12	department	department	NOUN
ejpam-5594	3	13	of	of	ADP
ejpam-5594	3	14	exact	exact	ADJ
ejpam-5594	3	15	sciences	science	NOUN
ejpam-5594	3	16	and	and	CCONJ
ejpam-5594	3	17	technology	technology	NOUN
ejpam-5594	3	18	,	,	PUNCT
ejpam-5594	3	19	los	los	PROPN
ejpam-5594	3	20	lagos	lagos	PROPN
ejpam-5594	3	21	university	university	PROPN
ejpam-5594	3	22	center	center	NOUN
ejpam-5594	3	23	,	,	PUNCT
ejpam-5594	3	24	university	university	PROPN
ejpam-5594	3	25	of	of	ADP
ejpam-5594	3	26	guadalajara	guadalajara	PROPN
ejpam-5594	3	27	,	,	PUNCT
ejpam-5594	3	28	jalisco	jalisco	PROPN
ejpam-5594	3	29	,	,	PUNCT
ejpam-5594	3	30	mexico	mexico	PROPN
ejpam-5594	3	31	abstract	abstract	NOUN
ejpam-5594	3	32	.	.	PUNCT
ejpam-5594	4	1	the	the	DET
ejpam-5594	4	2	purpose	purpose	NOUN
ejpam-5594	4	3	of	of	ADP
ejpam-5594	4	4	this	this	DET
ejpam-5594	4	5	article	article	NOUN
ejpam-5594	4	6	is	be	AUX
ejpam-5594	4	7	to	to	PART
ejpam-5594	4	8	establish	establish	VERB
ejpam-5594	4	9	several	several	ADJ
ejpam-5594	4	10	new	new	ADJ
ejpam-5594	4	11	forms	form	NOUN
ejpam-5594	4	12	of	of	ADP
ejpam-5594	4	13	hermite	hermite	ADJ
ejpam-5594	4	14	-	-	PUNCT
ejpam-5594	4	15	hadamard	hadamard	ADJ
ejpam-5594	4	16	inequalities	inequality	NOUN
ejpam-5594	4	17	by	by	ADP
ejpam-5594	4	18	utilizing	utilize	VERB
ejpam-5594	4	19	fractional	fractional	ADJ
ejpam-5594	4	20	integral	integral	ADJ
ejpam-5594	4	21	operators	operator	NOUN
ejpam-5594	4	22	via	via	ADP
ejpam-5594	4	23	a	a	DET
ejpam-5594	4	24	totally	totally	ADV
ejpam-5594	4	25	interval	interval	NOUN
ejpam-5594	4	26	midpoint	midpoint	NOUN
ejpam-5594	4	27	-	-	PUNCT
ejpam-5594	4	28	radius	radius	NOUN
ejpam-5594	4	29	order	order	NOUN
ejpam-5594	4	30	relation	relation	NOUN
ejpam-5594	4	31	for	for	ADP
ejpam-5594	4	32	differentiable	differentiable	ADJ
ejpam-5594	4	33	godunova	godunova	PROPN
ejpam-5594	4	34	-	-	PUNCT
ejpam-5594	4	35	levin	levin	PROPN
ejpam-5594	4	36	mappings	mapping	NOUN
ejpam-5594	4	37	.	.	PUNCT
ejpam-5594	5	1	moreover	moreover	ADV
ejpam-5594	5	2	,	,	PUNCT
ejpam-5594	5	3	in	in	ADP
ejpam-5594	5	4	order	order	NOUN
ejpam-5594	5	5	to	to	PART
ejpam-5594	5	6	verify	verify	VERB
ejpam-5594	5	7	our	our	PRON
ejpam-5594	5	8	main	main	ADJ
ejpam-5594	5	9	results	result	NOUN
ejpam-5594	5	10	,	,	PUNCT
ejpam-5594	5	11	we	we	PRON
ejpam-5594	5	12	construct	construct	VERB
ejpam-5594	5	13	some	some	DET
ejpam-5594	5	14	non	non	ADJ
ejpam-5594	5	15	-	-	ADJ
ejpam-5594	5	16	trivial	trivial	ADJ
ejpam-5594	5	17	examples	example	NOUN
ejpam-5594	5	18	and	and	CCONJ
ejpam-5594	5	19	remarks	remark	NOUN
ejpam-5594	5	20	that	that	PRON
ejpam-5594	5	21	lead	lead	VERB
ejpam-5594	5	22	to	to	ADP
ejpam-5594	5	23	other	other	ADJ
ejpam-5594	5	24	generalized	generalize	VERB
ejpam-5594	5	25	convex	convex	NOUN
ejpam-5594	5	26	mappings	mapping	NOUN
ejpam-5594	5	27	with	with	ADP
ejpam-5594	5	28	different	different	ADJ
ejpam-5594	5	29	settings	setting	NOUN
ejpam-5594	5	30	.	.	PUNCT
ejpam-5594	6	1	furthermore	furthermore	ADV
ejpam-5594	6	2	,	,	PUNCT
ejpam-5594	6	3	we	we	PRON
ejpam-5594	6	4	exploit	exploit	VERB
ejpam-5594	6	5	special	special	ADJ
ejpam-5594	6	6	cases	case	NOUN
ejpam-5594	6	7	of	of	ADP
ejpam-5594	6	8	hölder	hölder	NOUN
ejpam-5594	6	9	’s	’s	PART
ejpam-5594	6	10	,	,	PUNCT
ejpam-5594	6	11	young	young	ADJ
ejpam-5594	6	12	’s	’s	ADV
ejpam-5594	6	13	,	,	PUNCT
ejpam-5594	6	14	and	and	CCONJ
ejpam-5594	6	15	minkowskitype	minkowskitype	NOUN
ejpam-5594	6	16	inequalities	inequality	NOUN
ejpam-5594	6	17	in	in	ADP
ejpam-5594	6	18	order	order	NOUN
ejpam-5594	6	19	to	to	PART
ejpam-5594	6	20	develop	develop	VERB
ejpam-5594	6	21	new	new	ADJ
ejpam-5594	6	22	bounds	bound	NOUN
ejpam-5594	6	23	of	of	ADP
ejpam-5594	6	24	hermite	hermite	ADJ
ejpam-5594	6	25	-	-	PUNCT
ejpam-5594	6	26	hadamard	hadamard	ADJ
ejpam-5594	6	27	inequality	inequality	NOUN
ejpam-5594	6	28	.	.	PUNCT
ejpam-5594	7	1	finally	finally	ADV
ejpam-5594	7	2	,	,	PUNCT
ejpam-5594	7	3	we	we	PRON
ejpam-5594	7	4	relate	relate	VERB
ejpam-5594	7	5	our	our	PRON
ejpam-5594	7	6	key	key	ADJ
ejpam-5594	7	7	results	result	NOUN
ejpam-5594	7	8	with	with	ADP
ejpam-5594	7	9	special	special	ADJ
ejpam-5594	7	10	means	mean	NOUN
ejpam-5594	7	11	and	and	CCONJ
ejpam-5594	7	12	demonstrate	demonstrate	VERB
ejpam-5594	7	13	some	some	PRON
ejpam-5594	7	14	of	of	ADP
ejpam-5594	7	15	their	their	PRON
ejpam-5594	7	16	applications	application	NOUN
ejpam-5594	7	17	.	.	PUNCT
ejpam-5594	8	1	2020	2020	NUM
ejpam-5594	8	2	mathematics	mathematic	NOUN
ejpam-5594	8	3	subject	subject	NOUN
ejpam-5594	8	4	classifications	classification	NOUN
ejpam-5594	8	5	:	:	PUNCT
ejpam-5594	8	6	11b73	11b73	NUM
ejpam-5594	8	7	,	,	PUNCT
ejpam-5594	8	8	11b83	11b83	NUM
ejpam-5594	8	9	key	key	ADJ
ejpam-5594	8	10	words	word	NOUN
ejpam-5594	8	11	and	and	CCONJ
ejpam-5594	8	12	phrases	phrase	NOUN
ejpam-5594	8	13	:	:	PUNCT
ejpam-5594	8	14	hermite	hermite	ADJ
ejpam-5594	8	15	-	-	PUNCT
ejpam-5594	8	16	hadamard	hadamard	PROPN
ejpam-5594	8	17	,	,	PUNCT
ejpam-5594	8	18	cr	cr	NOUN
ejpam-5594	8	19	-	-	PUNCT
ejpam-5594	8	20	order	order	NOUN
ejpam-5594	8	21	,	,	PUNCT
ejpam-5594	8	22	fractional	fractional	ADJ
ejpam-5594	8	23	operators	operator	NOUN
ejpam-5594	8	24	,	,	PUNCT
ejpam-5594	8	25	interval	interval	NOUN
ejpam-5594	8	26	mappings	mapping	NOUN
ejpam-5594	8	27	∗corresponding	∗corresponde	VERB
ejpam-5594	8	28	author	author	NOUN
ejpam-5594	8	29	.	.	PUNCT
ejpam-5594	9	1	doi	doi	NOUN
ejpam-5594	9	2	:	:	PUNCT
ejpam-5594	9	3	https://doi.org/10.29020/nybg.ejpam.v17i4.5594	https://doi.org/10.29020/nybg.ejpam.v17i4.5594	NUM
ejpam-5594	9	4	email	email	NOUN
ejpam-5594	9	5	addresses	address	NOUN
ejpam-5594	9	6	:	:	PUNCT
ejpam-5594	9	7	waqar2989@gmail.com	waqar2989@gmail.com	X
ejpam-5594	9	8	(	(	PUNCT
ejpam-5594	9	9	w.	w.	PROPN
ejpam-5594	9	10	afzal	afzal	PROPN
ejpam-5594	9	11	)	)	PUNCT
ejpam-5594	9	12	,	,	PUNCT
ejpam-5594	9	13	mskhan@jazanu.edu.sa	mskhan@jazanu.edu.sa	PROPN
ejpam-5594	9	14	(	(	PUNCT
ejpam-5594	9	15	m.	m.	PROPN
ejpam-5594	9	16	s.	s.	PROPN
ejpam-5594	9	17	khan	khan	PROPN
ejpam-5594	9	18	)	)	PUNCT
ejpam-5594	9	19	,	,	PUNCT
ejpam-5594	9	20	mmeetei@jazanu.edu.sa	mmeetei@jazanu.edu.sa	PROPN
ejpam-5594	9	21	(	(	PUNCT
ejpam-5594	9	22	m.	m.	NOUN
ejpam-5594	9	23	z.	z.	PROPN
ejpam-5594	9	24	meetei	meetei	PROPN
ejpam-5594	9	25	)	)	PUNCT
ejpam-5594	9	26	,	,	PUNCT
ejpam-5594	9	27	abbas.mujahid@gmail.com	abbas.mujahid@gmail.com	X
ejpam-5594	9	28	(	(	PUNCT
ejpam-5594	9	29	m.	m.	NOUN
ejpam-5594	9	30	abbas	abbas	PROPN
ejpam-5594	9	31	)	)	PUNCT
ejpam-5594	9	32	,	,	PUNCT
ejpam-5594	9	33	jemacias@correo.uaa.mx	jemacias@correo.uaa.mx	PROPN
ejpam-5594	9	34	(	(	PUNCT
ejpam-5594	9	35	j.	j.	PROPN
ejpam-5594	9	36	e.	e.	PROPN
ejpam-5594	9	37	maćıas	maćıas	PROPN
ejpam-5594	9	38	-	-	PUNCT
ejpam-5594	9	39	dı́az	dı́az	NOUN
ejpam-5594	9	40	)	)	PUNCT
ejpam-5594	9	41	,	,	PUNCT
ejpam-5594	9	42	hvargas@culagos.udg.mx	hvargas@culagos.udg.mx	NOUN
ejpam-5594	9	43	(	(	PUNCT
ejpam-5594	9	44	h.	h.	PROPN
ejpam-5594	9	45	vargas	vargas	PROPN
ejpam-5594	9	46	-	-	PUNCT
ejpam-5594	9	47	rodriguez	rodriguez	NOUN
ejpam-5594	9	48	)	)	PUNCT
ejpam-5594	9	49	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5594	9	50	4014	4014	NUM
ejpam-5594	10	1	copyright	copyright	NOUN
ejpam-5594	10	2	:	:	PUNCT
ejpam-5594	10	3	©	©	PROPN
ejpam-5594	10	4	2024	2024	NUM
ejpam-5594	10	5	the	the	DET
ejpam-5594	10	6	author(s	author(s	NOUN
ejpam-5594	10	7	)	)	PUNCT
ejpam-5594	10	8	.	.	PUNCT
ejpam-5594	11	1	(	(	PUNCT
ejpam-5594	11	2	cc	cc	NOUN
ejpam-5594	11	3	by	by	ADP
ejpam-5594	11	4	-	-	PUNCT
ejpam-5594	11	5	nc	nc	PROPN
ejpam-5594	11	6	4.0	4.0	NUM
ejpam-5594	11	7	)	)	PUNCT
ejpam-5594	11	8	j.	j.	PROPN
ejpam-5594	11	9	e.	e.	PROPN
ejpam-5594	11	10	maćıas	maćıas	PROPN
ejpam-5594	11	11	-	-	PUNCT
ejpam-5594	11	12	dı́az	dı́az	NOUN
ejpam-5594	11	13	et	et	NOUN
ejpam-5594	11	14	al	al	PROPN
ejpam-5594	11	15	.	.	PUNCT
ejpam-5594	11	16	/	/	SYM
ejpam-5594	11	17	eur	eur	PROPN
ejpam-5594	11	18	.	.	PUNCT
ejpam-5594	12	1	j.	j.	PROPN
ejpam-5594	12	2	pure	pure	PROPN
ejpam-5594	12	3	appl	appl	PROPN
ejpam-5594	12	4	.	.	PROPN
ejpam-5594	12	5	math	math	PROPN
ejpam-5594	12	6	,	,	PUNCT
ejpam-5594	12	7	17	17	NUM
ejpam-5594	12	8	(	(	PUNCT
ejpam-5594	12	9	4	4	NUM
ejpam-5594	12	10	)	)	PUNCT
ejpam-5594	12	11	(	(	PUNCT
ejpam-5594	12	12	2024	2024	NUM
ejpam-5594	12	13	)	)	PUNCT
ejpam-5594	12	14	,	,	PUNCT
ejpam-5594	12	15	4014	4014	NUM
ejpam-5594	12	16	-	-	SYM
ejpam-5594	12	17	4049	4049	NUM
ejpam-5594	12	18	4015	4015	NUM
ejpam-5594	12	19	1	1	NUM
ejpam-5594	12	20	.	.	PUNCT
ejpam-5594	13	1	introduction	introduction	NOUN
ejpam-5594	13	2	convex	convex	NOUN
ejpam-5594	13	3	analysis	analysis	NOUN
ejpam-5594	13	4	provides	provide	VERB
ejpam-5594	13	5	a	a	DET
ejpam-5594	13	6	powerful	powerful	ADJ
ejpam-5594	13	7	mathematical	mathematical	ADJ
ejpam-5594	13	8	framework	framework	NOUN
ejpam-5594	13	9	for	for	ADP
ejpam-5594	13	10	analyzing	analyze	VERB
ejpam-5594	13	11	problems	problem	NOUN
ejpam-5594	13	12	in	in	ADP
ejpam-5594	13	13	various	various	ADJ
ejpam-5594	13	14	fields	field	NOUN
ejpam-5594	13	15	,	,	PUNCT
ejpam-5594	13	16	especially	especially	ADV
ejpam-5594	13	17	due	due	ADP
ejpam-5594	13	18	to	to	ADP
ejpam-5594	13	19	the	the	DET
ejpam-5594	13	20	well	well	ADV
ejpam-5594	13	21	-	-	PUNCT
ejpam-5594	13	22	behaved	behave	VERB
ejpam-5594	13	23	properties	property	NOUN
ejpam-5594	13	24	of	of	ADP
ejpam-5594	13	25	convex	convex	NOUN
ejpam-5594	13	26	sets	set	NOUN
ejpam-5594	13	27	and	and	CCONJ
ejpam-5594	13	28	functions	function	NOUN
ejpam-5594	13	29	.	.	PUNCT
ejpam-5594	14	1	its	its	PRON
ejpam-5594	14	2	uses	use	NOUN
ejpam-5594	14	3	span	span	VERB
ejpam-5594	14	4	a	a	DET
ejpam-5594	14	5	variety	variety	NOUN
ejpam-5594	14	6	of	of	ADP
ejpam-5594	14	7	fields	field	NOUN
ejpam-5594	14	8	,	,	PUNCT
ejpam-5594	14	9	including	include	VERB
ejpam-5594	14	10	control	control	NOUN
ejpam-5594	14	11	theory	theory	NOUN
ejpam-5594	14	12	[	[	X
ejpam-5594	14	13	56	56	NUM
ejpam-5594	14	14	]	]	PUNCT
ejpam-5594	14	15	,	,	PUNCT
ejpam-5594	14	16	economics	economic	NOUN
ejpam-5594	14	17	[	[	X
ejpam-5594	14	18	54	54	NUM
ejpam-5594	14	19	]	]	PUNCT
ejpam-5594	14	20	,	,	PUNCT
ejpam-5594	14	21	machine	machine	NOUN
ejpam-5594	14	22	learning	learn	VERB
ejpam-5594	14	23	[	[	X
ejpam-5594	14	24	38	38	NUM
ejpam-5594	14	25	]	]	PUNCT
ejpam-5594	14	26	,	,	PUNCT
ejpam-5594	14	27	and	and	CCONJ
ejpam-5594	14	28	optimization	optimization	NOUN
ejpam-5594	14	29	[	[	X
ejpam-5594	14	30	53	53	NUM
ejpam-5594	14	31	]	]	PUNCT
ejpam-5594	14	32	.	.	PUNCT
ejpam-5594	15	1	in	in	ADP
ejpam-5594	15	2	control	control	NOUN
ejpam-5594	15	3	theory	theory	NOUN
ejpam-5594	15	4	[	[	X
ejpam-5594	15	5	55	55	NUM
ejpam-5594	15	6	]	]	PUNCT
ejpam-5594	15	7	,	,	PUNCT
ejpam-5594	15	8	systems	system	NOUN
ejpam-5594	15	9	are	be	AUX
ejpam-5594	15	10	often	often	ADV
ejpam-5594	15	11	formulated	formulate	VERB
ejpam-5594	15	12	as	as	ADP
ejpam-5594	15	13	convex	convex	NOUN
ejpam-5594	15	14	problems	problem	NOUN
ejpam-5594	15	15	,	,	PUNCT
ejpam-5594	15	16	where	where	SCONJ
ejpam-5594	15	17	the	the	DET
ejpam-5594	15	18	system	system	NOUN
ejpam-5594	15	19	needs	need	VERB
ejpam-5594	15	20	to	to	PART
ejpam-5594	15	21	minimize	minimize	VERB
ejpam-5594	15	22	energy	energy	NOUN
ejpam-5594	15	23	or	or	CCONJ
ejpam-5594	15	24	error	error	NOUN
ejpam-5594	15	25	subject	subject	NOUN
ejpam-5594	15	26	to	to	ADP
ejpam-5594	15	27	dynamic	dynamic	ADJ
ejpam-5594	15	28	constraints	constraint	NOUN
ejpam-5594	15	29	;	;	PUNCT
ejpam-5594	15	30	in	in	ADP
ejpam-5594	15	31	signal	signal	ADJ
ejpam-5594	15	32	processing	processing	NOUN
ejpam-5594	15	33	,	,	PUNCT
ejpam-5594	15	34	it	it	PRON
ejpam-5594	15	35	aids	aid	VERB
ejpam-5594	15	36	in	in	ADP
ejpam-5594	15	37	the	the	DET
ejpam-5594	15	38	design	design	NOUN
ejpam-5594	15	39	of	of	ADP
ejpam-5594	15	40	codes	code	NOUN
ejpam-5594	15	41	that	that	PRON
ejpam-5594	15	42	minimize	minimize	VERB
ejpam-5594	15	43	transmission	transmission	NOUN
ejpam-5594	15	44	errors	error	NOUN
ejpam-5594	15	45	,	,	PUNCT
ejpam-5594	15	46	enhancing	enhance	VERB
ejpam-5594	15	47	communication	communication	NOUN
ejpam-5594	15	48	reliability	reliability	NOUN
ejpam-5594	15	49	[	[	X
ejpam-5594	15	50	24	24	NUM
ejpam-5594	15	51	]	]	PUNCT
ejpam-5594	15	52	.	.	PUNCT
ejpam-5594	16	1	convex	convex	NOUN
ejpam-5594	16	2	analysis	analysis	NOUN
ejpam-5594	16	3	is	be	AUX
ejpam-5594	16	4	closely	closely	ADV
ejpam-5594	16	5	related	relate	VERB
ejpam-5594	16	6	to	to	ADP
ejpam-5594	16	7	economic	economic	ADJ
ejpam-5594	16	8	theory	theory	NOUN
ejpam-5594	16	9	,	,	PUNCT
ejpam-5594	16	10	particularly	particularly	ADV
ejpam-5594	16	11	in	in	ADP
ejpam-5594	16	12	the	the	DET
ejpam-5594	16	13	study	study	NOUN
ejpam-5594	16	14	of	of	ADP
ejpam-5594	16	15	utility	utility	NOUN
ejpam-5594	16	16	functions	function	NOUN
ejpam-5594	16	17	[	[	X
ejpam-5594	16	18	14	14	NUM
ejpam-5594	16	19	]	]	PUNCT
ejpam-5594	16	20	,	,	PUNCT
ejpam-5594	16	21	which	which	PRON
ejpam-5594	16	22	represent	represent	VERB
ejpam-5594	16	23	rational	rational	ADJ
ejpam-5594	16	24	consumer	consumer	NOUN
ejpam-5594	16	25	preferences	preference	NOUN
ejpam-5594	16	26	where	where	SCONJ
ejpam-5594	16	27	utility	utility	NOUN
ejpam-5594	16	28	increases	increase	VERB
ejpam-5594	16	29	with	with	ADP
ejpam-5594	16	30	consumption	consumption	NOUN
ejpam-5594	16	31	,	,	PUNCT
ejpam-5594	16	32	but	but	CCONJ
ejpam-5594	16	33	at	at	ADP
ejpam-5594	16	34	a	a	DET
ejpam-5594	16	35	diminishing	diminishing	NOUN
ejpam-5594	16	36	rate	rate	NOUN
ejpam-5594	16	37	.	.	PUNCT
ejpam-5594	17	1	for	for	ADP
ejpam-5594	17	2	more	more	ADV
ejpam-5594	17	3	recent	recent	ADJ
ejpam-5594	17	4	applications	application	NOUN
ejpam-5594	17	5	in	in	ADP
ejpam-5594	17	6	diverse	diverse	ADJ
ejpam-5594	17	7	disciplines	discipline	NOUN
ejpam-5594	17	8	of	of	ADP
ejpam-5594	17	9	applied	apply	VERB
ejpam-5594	17	10	sciences	science	NOUN
ejpam-5594	17	11	,	,	PUNCT
ejpam-5594	17	12	we	we	PRON
ejpam-5594	17	13	refer	refer	VERB
ejpam-5594	17	14	to	to	ADP
ejpam-5594	17	15	[	[	X
ejpam-5594	17	16	22	22	NUM
ejpam-5594	17	17	,	,	PUNCT
ejpam-5594	17	18	26	26	NUM
ejpam-5594	17	19	,	,	PUNCT
ejpam-5594	17	20	27	27	NUM
ejpam-5594	17	21	,	,	PUNCT
ejpam-5594	17	22	59	59	NUM
ejpam-5594	17	23	,	,	PUNCT
ejpam-5594	17	24	64	64	NUM
ejpam-5594	17	25	]	]	PUNCT
ejpam-5594	17	26	and	and	CCONJ
ejpam-5594	17	27	the	the	DET
ejpam-5594	17	28	references	reference	NOUN
ejpam-5594	17	29	therein	therein	ADV
ejpam-5594	17	30	.	.	PUNCT
ejpam-5594	18	1	interval	interval	NOUN
ejpam-5594	18	2	analysis	analysis	NOUN
ejpam-5594	18	3	is	be	AUX
ejpam-5594	18	4	a	a	DET
ejpam-5594	18	5	mathematical	mathematical	ADJ
ejpam-5594	18	6	methodology	methodology	NOUN
ejpam-5594	18	7	that	that	PRON
ejpam-5594	18	8	allows	allow	VERB
ejpam-5594	18	9	numerical	numerical	ADJ
ejpam-5594	18	10	algorithms	algorithm	NOUN
ejpam-5594	18	11	to	to	PART
ejpam-5594	18	12	address	address	VERB
ejpam-5594	18	13	uncertainty	uncertainty	NOUN
ejpam-5594	18	14	more	more	ADV
ejpam-5594	18	15	rigorously	rigorously	ADV
ejpam-5594	18	16	.	.	PUNCT
ejpam-5594	19	1	it	it	PRON
ejpam-5594	19	2	has	have	VERB
ejpam-5594	19	3	applications	application	NOUN
ejpam-5594	19	4	in	in	ADP
ejpam-5594	19	5	a	a	DET
ejpam-5594	19	6	variety	variety	NOUN
ejpam-5594	19	7	of	of	ADP
ejpam-5594	19	8	domains	domain	NOUN
ejpam-5594	19	9	,	,	PUNCT
ejpam-5594	19	10	including	include	VERB
ejpam-5594	19	11	numerical	numerical	ADJ
ejpam-5594	19	12	computation	computation	NOUN
ejpam-5594	19	13	,	,	PUNCT
ejpam-5594	19	14	global	global	ADJ
ejpam-5594	19	15	optimization	optimization	NOUN
ejpam-5594	19	16	,	,	PUNCT
ejpam-5594	19	17	control	control	NOUN
ejpam-5594	19	18	systems	system	NOUN
ejpam-5594	19	19	,	,	PUNCT
ejpam-5594	19	20	engineering	engineering	NOUN
ejpam-5594	19	21	,	,	PUNCT
ejpam-5594	19	22	and	and	CCONJ
ejpam-5594	19	23	computer	computer	NOUN
ejpam-5594	19	24	graphics	graphic	NOUN
ejpam-5594	19	25	.	.	PUNCT
ejpam-5594	20	1	borwein	borwein	PROPN
ejpam-5594	20	2	et	et	PROPN
ejpam-5594	20	3	al	al	PROPN
ejpam-5594	20	4	.	.	PUNCT
ejpam-5594	21	1	[	[	X
ejpam-5594	21	2	17	17	NUM
ejpam-5594	21	3	]	]	PUNCT
ejpam-5594	21	4	initially	initially	ADV
ejpam-5594	21	5	defined	define	VERB
ejpam-5594	21	6	convex	convex	NOUN
ejpam-5594	21	7	interval	interval	NOUN
ejpam-5594	21	8	-	-	PUNCT
ejpam-5594	21	9	valued	value	VERB
ejpam-5594	21	10	functions	function	NOUN
ejpam-5594	21	11	(	(	PUNCT
ejpam-5594	21	12	ivfs	ivfs	NOUN
ejpam-5594	21	13	)	)	PUNCT
ejpam-5594	21	14	in	in	ADP
ejpam-5594	21	15	1981	1981	NUM
ejpam-5594	21	16	,	,	PUNCT
ejpam-5594	21	17	and	and	CCONJ
ejpam-5594	21	18	since	since	SCONJ
ejpam-5594	21	19	then	then	ADV
ejpam-5594	21	20	,	,	PUNCT
ejpam-5594	21	21	several	several	ADJ
ejpam-5594	21	22	researchers	researcher	NOUN
ejpam-5594	21	23	have	have	AUX
ejpam-5594	21	24	extended	extend	VERB
ejpam-5594	21	25	and	and	CCONJ
ejpam-5594	21	26	promoted	promote	VERB
ejpam-5594	21	27	different	different	ADJ
ejpam-5594	21	28	types	type	NOUN
ejpam-5594	21	29	of	of	ADP
ejpam-5594	21	30	convexity	convexity	NOUN
ejpam-5594	21	31	by	by	ADP
ejpam-5594	21	32	using	use	VERB
ejpam-5594	21	33	ivfs	ivfs	NOUN
ejpam-5594	21	34	.	.	PUNCT
ejpam-5594	22	1	for	for	ADP
ejpam-5594	22	2	example	example	NOUN
ejpam-5594	22	3	,	,	PUNCT
ejpam-5594	22	4	include	include	VERB
ejpam-5594	22	5	preinvex	preinvex	NOUN
ejpam-5594	22	6	[	[	X
ejpam-5594	22	7	48	48	NUM
ejpam-5594	22	8	]	]	PUNCT
ejpam-5594	22	9	,	,	PUNCT
ejpam-5594	22	10	harmonic	harmonic	VERB
ejpam-5594	22	11	convex	convex	NOUN
ejpam-5594	22	12	[	[	X
ejpam-5594	22	13	41	41	NUM
ejpam-5594	22	14	]	]	PUNCT
ejpam-5594	22	15	,	,	PUNCT
ejpam-5594	22	16	godunova	godunova	PROPN
ejpam-5594	22	17	-	-	PUNCT
ejpam-5594	22	18	levin	levin	PROPN
ejpam-5594	23	1	[	[	X
ejpam-5594	23	2	5	5	NUM
ejpam-5594	23	3	]	]	PUNCT
ejpam-5594	23	4	,	,	PUNCT
ejpam-5594	23	5	(	(	PUNCT
ejpam-5594	23	6	h1	h1	NOUN
ejpam-5594	23	7	,	,	PUNCT
ejpam-5594	23	8	h2)-convex	h2)-convex	VERB
ejpam-5594	24	1	[	[	X
ejpam-5594	24	2	9	9	NUM
ejpam-5594	24	3	]	]	PUNCT
ejpam-5594	24	4	,	,	PUNCT
ejpam-5594	24	5	log	log	NOUN
ejpam-5594	24	6	-	-	PUNCT
ejpam-5594	24	7	convex	convex	NOUN
ejpam-5594	24	8	[	[	X
ejpam-5594	24	9	49	49	NUM
ejpam-5594	24	10	]	]	PUNCT
ejpam-5594	24	11	,	,	PUNCT
ejpam-5594	24	12	coordinated	coordinate	VERB
ejpam-5594	24	13	convex	convex	NOUN
ejpam-5594	24	14	[	[	X
ejpam-5594	24	15	62	62	NUM
ejpam-5594	24	16	]	]	PUNCT
ejpam-5594	24	17	,	,	PUNCT
ejpam-5594	24	18	and	and	CCONJ
ejpam-5594	24	19	various	various	ADJ
ejpam-5594	24	20	others	other	NOUN
ejpam-5594	25	1	[	[	X
ejpam-5594	25	2	21	21	NUM
ejpam-5594	25	3	,	,	PUNCT
ejpam-5594	25	4	31	31	NUM
ejpam-5594	25	5	,	,	PUNCT
ejpam-5594	25	6	34	34	NUM
ejpam-5594	25	7	,	,	PUNCT
ejpam-5594	25	8	39	39	NUM
ejpam-5594	25	9	,	,	PUNCT
ejpam-5594	25	10	40	40	NUM
ejpam-5594	25	11	,	,	PUNCT
ejpam-5594	25	12	43	43	NUM
ejpam-5594	25	13	,	,	PUNCT
ejpam-5594	25	14	51	51	NUM
ejpam-5594	25	15	,	,	PUNCT
ejpam-5594	25	16	52	52	NUM
ejpam-5594	25	17	]	]	PUNCT
ejpam-5594	25	18	and	and	CCONJ
ejpam-5594	25	19	the	the	DET
ejpam-5594	25	20	references	reference	NOUN
ejpam-5594	25	21	therein	therein	ADV
ejpam-5594	25	22	.	.	PUNCT
ejpam-5594	26	1	it	it	PRON
ejpam-5594	26	2	’s	’	VERB
ejpam-5594	26	3	important	important	ADJ
ejpam-5594	26	4	to	to	PART
ejpam-5594	26	5	remember	remember	VERB
ejpam-5594	26	6	that	that	SCONJ
ejpam-5594	26	7	the	the	DET
ejpam-5594	26	8	partial	partial	ADJ
ejpam-5594	26	9	order	order	NOUN
ejpam-5594	26	10	relation	relation	NOUN
ejpam-5594	26	11	defines	define	VERB
ejpam-5594	26	12	these	these	DET
ejpam-5594	26	13	convex	convex	PROPN
ejpam-5594	26	14	ivfs	ivfs	NOUN
ejpam-5594	26	15	,	,	PUNCT
ejpam-5594	26	16	meaning	mean	VERB
ejpam-5594	26	17	that	that	SCONJ
ejpam-5594	26	18	any	any	DET
ejpam-5594	26	19	two	two	NUM
ejpam-5594	26	20	intervals	interval	NOUN
ejpam-5594	26	21	may	may	AUX
ejpam-5594	26	22	not	not	PART
ejpam-5594	26	23	be	be	AUX
ejpam-5594	26	24	comparable	comparable	ADJ
ejpam-5594	26	25	.	.	PUNCT
ejpam-5594	27	1	this	this	PRON
ejpam-5594	27	2	indicates	indicate	VERB
ejpam-5594	27	3	that	that	SCONJ
ejpam-5594	27	4	the	the	DET
ejpam-5594	27	5	maximum	maximum	ADJ
ejpam-5594	27	6	-	-	PUNCT
ejpam-5594	27	7	minimum	minimum	ADJ
ejpam-5594	27	8	problem	problem	NOUN
ejpam-5594	27	9	can	can	AUX
ejpam-5594	27	10	not	not	PART
ejpam-5594	27	11	be	be	AUX
ejpam-5594	27	12	solved	solve	VERB
ejpam-5594	27	13	since	since	SCONJ
ejpam-5594	27	14	it	it	PRON
ejpam-5594	27	15	is	be	AUX
ejpam-5594	27	16	impossible	impossible	ADJ
ejpam-5594	27	17	to	to	PART
ejpam-5594	27	18	determine	determine	VERB
ejpam-5594	27	19	which	which	PRON
ejpam-5594	27	20	of	of	ADP
ejpam-5594	27	21	them	they	PRON
ejpam-5594	27	22	is	be	AUX
ejpam-5594	27	23	the	the	DET
ejpam-5594	27	24	greatest	great	ADJ
ejpam-5594	27	25	or	or	CCONJ
ejpam-5594	27	26	smallest	small	ADJ
ejpam-5594	27	27	interval	interval	NOUN
ejpam-5594	27	28	using	use	VERB
ejpam-5594	27	29	these	these	DET
ejpam-5594	27	30	orderings	ordering	NOUN
ejpam-5594	27	31	.	.	PUNCT
ejpam-5594	28	1	hu	hu	PROPN
ejpam-5594	28	2	and	and	CCONJ
ejpam-5594	28	3	wang	wang	PROPN
ejpam-5594	29	1	[	[	X
ejpam-5594	29	2	23	23	NUM
ejpam-5594	29	3	]	]	PUNCT
ejpam-5594	29	4	introduced	introduce	VERB
ejpam-5594	29	5	the	the	DET
ejpam-5594	29	6	cr	cr	NOUN
ejpam-5594	29	7	-	-	PUNCT
ejpam-5594	29	8	order	order	NOUN
ejpam-5594	29	9	,	,	PUNCT
ejpam-5594	29	10	which	which	PRON
ejpam-5594	29	11	takes	take	VERB
ejpam-5594	29	12	into	into	ADP
ejpam-5594	29	13	account	account	NOUN
ejpam-5594	29	14	the	the	DET
ejpam-5594	29	15	midpoint	midpoint	NOUN
ejpam-5594	29	16	and	and	CCONJ
ejpam-5594	29	17	radius	radius	NOUN
ejpam-5594	29	18	of	of	ADP
ejpam-5594	29	19	two	two	NUM
ejpam-5594	29	20	intervals	interval	NOUN
ejpam-5594	29	21	to	to	PART
ejpam-5594	29	22	address	address	VERB
ejpam-5594	29	23	this	this	DET
ejpam-5594	29	24	limitation	limitation	NOUN
ejpam-5594	29	25	.	.	PUNCT
ejpam-5594	30	1	this	this	DET
ejpam-5594	30	2	order	order	NOUN
ejpam-5594	30	3	is	be	AUX
ejpam-5594	30	4	total	total	ADJ
ejpam-5594	30	5	,	,	PUNCT
ejpam-5594	30	6	meaning	mean	VERB
ejpam-5594	30	7	that	that	SCONJ
ejpam-5594	30	8	any	any	DET
ejpam-5594	30	9	two	two	NUM
ejpam-5594	30	10	interval	interval	NOUN
ejpam-5594	30	11	numbers	number	NOUN
ejpam-5594	30	12	are	be	AUX
ejpam-5594	30	13	comparable	comparable	ADJ
ejpam-5594	30	14	.	.	PUNCT
ejpam-5594	31	1	in	in	ADP
ejpam-5594	31	2	[	[	X
ejpam-5594	31	3	61	61	NUM
ejpam-5594	31	4	]	]	PUNCT
ejpam-5594	31	5	authors	author	NOUN
ejpam-5594	31	6	provided	provide	VERB
ejpam-5594	31	7	the	the	DET
ejpam-5594	31	8	appropriate	appropriate	ADJ
ejpam-5594	31	9	optimization	optimization	NOUN
ejpam-5594	31	10	conditions	condition	NOUN
ejpam-5594	31	11	for	for	ADP
ejpam-5594	31	12	the	the	DET
ejpam-5594	31	13	constrained	constrain	VERB
ejpam-5594	31	14	optimization	optimization	NOUN
ejpam-5594	31	15	issue	issue	NOUN
ejpam-5594	31	16	of	of	ADP
ejpam-5594	31	17	interval	interval	NOUN
ejpam-5594	31	18	-	-	PUNCT
ejpam-5594	31	19	valued	value	VERB
ejpam-5594	31	20	objective	objective	ADJ
ejpam-5594	31	21	function	function	NOUN
ejpam-5594	31	22	and	and	CCONJ
ejpam-5594	31	23	provided	provide	VERB
ejpam-5594	31	24	a	a	DET
ejpam-5594	31	25	novel	novel	ADJ
ejpam-5594	31	26	definition	definition	NOUN
ejpam-5594	31	27	of	of	ADP
ejpam-5594	31	28	convex	convex	ADJ
ejpam-5594	31	29	ivf	ivf	NOUN
ejpam-5594	31	30	using	use	VERB
ejpam-5594	31	31	cr	cr	NOUN
ejpam-5594	31	32	-	-	PUNCT
ejpam-5594	31	33	order	order	NOUN
ejpam-5594	31	34	.	.	PUNCT
ejpam-5594	32	1	among	among	ADP
ejpam-5594	32	2	the	the	DET
ejpam-5594	32	3	several	several	ADJ
ejpam-5594	32	4	different	different	ADJ
ejpam-5594	32	5	types	type	NOUN
ejpam-5594	32	6	of	of	ADP
ejpam-5594	32	7	inequalities	inequality	NOUN
ejpam-5594	32	8	,	,	PUNCT
ejpam-5594	32	9	the	the	DET
ejpam-5594	32	10	hermite	hermite	PROPN
ejpam-5594	32	11	-	-	PUNCT
ejpam-5594	32	12	hadamard	hadamard	ADJ
ejpam-5594	32	13	type	type	NOUN
ejpam-5594	32	14	inequality	inequality	NOUN
ejpam-5594	32	15	is	be	AUX
ejpam-5594	32	16	a	a	DET
ejpam-5594	32	17	fundamental	fundamental	ADJ
ejpam-5594	32	18	component	component	NOUN
ejpam-5594	32	19	of	of	ADP
ejpam-5594	32	20	convex	convex	ADJ
ejpam-5594	32	21	analysis	analysis	NOUN
ejpam-5594	32	22	,	,	PUNCT
ejpam-5594	32	23	offering	offer	VERB
ejpam-5594	32	24	crucial	crucial	ADJ
ejpam-5594	32	25	perspectives	perspective	NOUN
ejpam-5594	32	26	and	and	CCONJ
ejpam-5594	32	27	instruments	instrument	NOUN
ejpam-5594	32	28	for	for	ADP
ejpam-5594	32	29	theoretical	theoretical	ADJ
ejpam-5594	32	30	investigation	investigation	NOUN
ejpam-5594	32	31	and	and	CCONJ
ejpam-5594	32	32	real	real	ADJ
ejpam-5594	32	33	-	-	PUNCT
ejpam-5594	32	34	world	world	NOUN
ejpam-5594	32	35	applications	application	NOUN
ejpam-5594	32	36	in	in	ADP
ejpam-5594	32	37	numerous	numerous	ADJ
ejpam-5594	32	38	scientific	scientific	ADJ
ejpam-5594	32	39	domains	domain	NOUN
ejpam-5594	32	40	.	.	PUNCT
ejpam-5594	33	1	the	the	DET
ejpam-5594	33	2	inequality	inequality	NOUN
ejpam-5594	33	3	is	be	AUX
ejpam-5594	33	4	defined	define	VERB
ejpam-5594	33	5	as	as	SCONJ
ejpam-5594	33	6	follows	follow	VERB
ejpam-5594	33	7	:	:	PUNCT
ejpam-5594	33	8	consider	consider	VERB
ejpam-5594	33	9	φ	φ	PROPN
ejpam-5594	33	10	:	:	PUNCT
ejpam-5594	34	1	ω	ω	NUM
ejpam-5594	34	2	⊆	⊆	NUM
ejpam-5594	34	3	r	r	NOUN
ejpam-5594	34	4	→	→	SYM
ejpam-5594	34	5	r	r	NOUN
ejpam-5594	34	6	a	a	DET
ejpam-5594	34	7	convex	convex	NOUN
ejpam-5594	34	8	mapping	mapping	NOUN
ejpam-5594	34	9	on	on	ADP
ejpam-5594	34	10	the	the	DET
ejpam-5594	34	11	interval	interval	NOUN
ejpam-5594	34	12	ω	ω	PROPN
ejpam-5594	34	13	with	with	ADP
ejpam-5594	34	14	ε1	ε1	PROPN
ejpam-5594	34	15	,	,	PUNCT
ejpam-5594	34	16	ε2	ε2	PROPN
ejpam-5594	34	17	∈	∈	PROPN
ejpam-5594	34	18	ω	ω	PROPN
ejpam-5594	34	19	.	.	PUNCT
ejpam-5594	35	1	then	then	ADV
ejpam-5594	35	2	,	,	PUNCT
ejpam-5594	35	3	the	the	DET
ejpam-5594	35	4	inequality	inequality	NOUN
ejpam-5594	35	5	listed	list	VERB
ejpam-5594	35	6	below	below	ADV
ejpam-5594	35	7	is	be	AUX
ejpam-5594	35	8	true	true	ADJ
ejpam-5594	35	9	:	:	PUNCT
ejpam-5594	35	10	φ	φ	PROPN
ejpam-5594	35	11	(	(	PUNCT
ejpam-5594	35	12	ε1	ε1	PROPN
ejpam-5594	35	13	+	+	CCONJ
ejpam-5594	35	14	ε2	ε2	ADJ
ejpam-5594	35	15	2	2	NUM
ejpam-5594	35	16	)	)	PUNCT
ejpam-5594	35	17	≤	≤	NOUN
ejpam-5594	35	18	1	1	NUM
ejpam-5594	35	19	ε2	ε2	ADJ
ejpam-5594	35	20	−	−	PROPN
ejpam-5594	35	21	ε1	ε1	PROPN
ejpam-5594	35	22	∫	∫	PROPN
ejpam-5594	35	23	ε2	ε2	PROPN
ejpam-5594	35	24	ε1	ε1	PROPN
ejpam-5594	35	25	φ(θ	φ(θ	PROPN
ejpam-5594	35	26	)	)	PUNCT
ejpam-5594	35	27	dθ	dθ	PROPN
ejpam-5594	35	28	≤	≤	PROPN
ejpam-5594	35	29	φ(ε1	φ(ε1	PROPN
ejpam-5594	35	30	)	)	PUNCT
ejpam-5594	35	31	+	+	SYM
ejpam-5594	35	32	φ(ε2	φ(ε2	NUM
ejpam-5594	35	33	)	)	PUNCT
ejpam-5594	35	34	2	2	NUM
ejpam-5594	35	35	.	.	PUNCT
ejpam-5594	36	1	(	(	PUNCT
ejpam-5594	36	2	1	1	X
ejpam-5594	36	3	)	)	PUNCT
ejpam-5594	36	4	the	the	DET
ejpam-5594	36	5	hermite	hermite	PROPN
ejpam-5594	36	6	-	-	PUNCT
ejpam-5594	36	7	hadamard	hadamard	ADJ
ejpam-5594	36	8	inequality	inequality	NOUN
ejpam-5594	36	9	is	be	AUX
ejpam-5594	36	10	frequently	frequently	ADV
ejpam-5594	36	11	employed	employ	VERB
ejpam-5594	36	12	in	in	ADP
ejpam-5594	36	13	optimization	optimization	NOUN
ejpam-5594	36	14	problems	problem	NOUN
ejpam-5594	36	15	involving	involve	VERB
ejpam-5594	36	16	convex	convex	NOUN
ejpam-5594	36	17	functions	function	NOUN
ejpam-5594	36	18	.	.	PUNCT
ejpam-5594	37	1	it	it	PRON
ejpam-5594	37	2	helps	help	VERB
ejpam-5594	37	3	establish	establish	VERB
ejpam-5594	37	4	bounds	bound	NOUN
ejpam-5594	37	5	on	on	ADP
ejpam-5594	37	6	integrals	integral	NOUN
ejpam-5594	37	7	of	of	ADP
ejpam-5594	37	8	convex	convex	NOUN
ejpam-5594	37	9	functions	function	NOUN
ejpam-5594	37	10	,	,	PUNCT
ejpam-5594	37	11	which	which	PRON
ejpam-5594	37	12	can	can	AUX
ejpam-5594	37	13	be	be	AUX
ejpam-5594	37	14	crucial	crucial	ADJ
ejpam-5594	37	15	for	for	ADP
ejpam-5594	37	16	finding	find	VERB
ejpam-5594	37	17	optimal	optimal	ADJ
ejpam-5594	37	18	solutions	solution	NOUN
ejpam-5594	37	19	in	in	ADP
ejpam-5594	37	20	various	various	ADJ
ejpam-5594	37	21	mathematical	mathematical	ADJ
ejpam-5594	37	22	models	model	NOUN
ejpam-5594	37	23	.	.	PUNCT
ejpam-5594	38	1	various	various	ADJ
ejpam-5594	38	2	authors	author	NOUN
ejpam-5594	38	3	study	study	VERB
ejpam-5594	38	4	this	this	DET
ejpam-5594	38	5	inequality	inequality	NOUN
ejpam-5594	38	6	using	use	VERB
ejpam-5594	38	7	different	different	ADJ
ejpam-5594	38	8	methodologies	methodology	NOUN
ejpam-5594	38	9	,	,	PUNCT
ejpam-5594	38	10	including	include	VERB
ejpam-5594	38	11	different	different	ADJ
ejpam-5594	38	12	kinds	kind	NOUN
ejpam-5594	38	13	of	of	ADP
ejpam-5594	38	14	intervalj	intervalj	NOUN
ejpam-5594	38	15	.	.	PUNCT
ejpam-5594	39	1	e.	e.	PROPN
ejpam-5594	39	2	maćıas	maćıas	PROPN
ejpam-5594	39	3	-	-	PUNCT
ejpam-5594	39	4	dı́az	dı́az	NOUN
ejpam-5594	39	5	et	et	NOUN
ejpam-5594	39	6	al	al	PROPN
ejpam-5594	39	7	.	.	PUNCT
ejpam-5594	39	8	/	/	SYM
ejpam-5594	39	9	eur	eur	PROPN
ejpam-5594	39	10	.	.	PUNCT
ejpam-5594	40	1	j.	j.	PROPN
ejpam-5594	40	2	pure	pure	PROPN
ejpam-5594	40	3	appl	appl	PROPN
ejpam-5594	40	4	.	.	PROPN
ejpam-5594	40	5	math	math	PROPN
ejpam-5594	40	6	,	,	PUNCT
ejpam-5594	40	7	17	17	NUM
ejpam-5594	40	8	(	(	PUNCT
ejpam-5594	40	9	4	4	NUM
ejpam-5594	40	10	)	)	PUNCT
ejpam-5594	40	11	(	(	PUNCT
ejpam-5594	40	12	2024	2024	NUM
ejpam-5594	40	13	)	)	PUNCT
ejpam-5594	40	14	,	,	PUNCT
ejpam-5594	40	15	4014	4014	NUM
ejpam-5594	40	16	-	-	SYM
ejpam-5594	40	17	4049	4049	NUM
ejpam-5594	40	18	4016	4016	NUM
ejpam-5594	40	19	valued	value	VERB
ejpam-5594	40	20	order	order	NOUN
ejpam-5594	40	21	relations	relation	NOUN
ejpam-5594	40	22	,	,	PUNCT
ejpam-5594	40	23	stochastic	stochastic	ADJ
ejpam-5594	40	24	and	and	CCONJ
ejpam-5594	40	25	fuzzy	fuzzy	ADV
ejpam-5594	40	26	-	-	PUNCT
ejpam-5594	40	27	valued	value	VERB
ejpam-5594	40	28	mappings	mapping	NOUN
ejpam-5594	40	29	,	,	PUNCT
ejpam-5594	40	30	and	and	CCONJ
ejpam-5594	40	31	various	various	ADJ
ejpam-5594	40	32	kinds	kind	NOUN
ejpam-5594	40	33	of	of	ADP
ejpam-5594	40	34	fractional	fractional	ADJ
ejpam-5594	40	35	operators	operator	NOUN
ejpam-5594	40	36	.	.	PUNCT
ejpam-5594	41	1	for	for	ADP
ejpam-5594	41	2	example	example	NOUN
ejpam-5594	41	3	,	,	PUNCT
ejpam-5594	41	4	in	in	ADP
ejpam-5594	41	5	[	[	PUNCT
ejpam-5594	41	6	50	50	NUM
ejpam-5594	41	7	]	]	PUNCT
ejpam-5594	41	8	,	,	PUNCT
ejpam-5594	41	9	authors	author	NOUN
ejpam-5594	41	10	used	use	VERB
ejpam-5594	41	11	generalized	generalized	ADJ
ejpam-5594	41	12	convex	convex	NOUN
ejpam-5594	41	13	mappings	mapping	NOUN
ejpam-5594	41	14	,	,	PUNCT
ejpam-5594	41	15	also	also	ADV
ejpam-5594	41	16	known	know	VERB
ejpam-5594	41	17	as	as	ADP
ejpam-5594	41	18	preinvex	preinvex	NOUN
ejpam-5594	41	19	functions	function	NOUN
ejpam-5594	41	20	,	,	PUNCT
ejpam-5594	41	21	and	and	CCONJ
ejpam-5594	41	22	developed	develop	VERB
ejpam-5594	41	23	various	various	ADJ
ejpam-5594	41	24	variations	variation	NOUN
ejpam-5594	41	25	of	of	ADP
ejpam-5594	41	26	hermite	hermite	ADJ
ejpam-5594	41	27	and	and	CCONJ
ejpam-5594	41	28	hadamard	hadamard	ADJ
ejpam-5594	41	29	inequalities	inequality	NOUN
ejpam-5594	41	30	for	for	ADP
ejpam-5594	41	31	interval	interval	NOUN
ejpam-5594	41	32	-	-	PUNCT
ejpam-5594	41	33	valued	value	VERB
ejpam-5594	41	34	functions	function	NOUN
ejpam-5594	41	35	;	;	PUNCT
ejpam-5594	41	36	in	in	ADP
ejpam-5594	41	37	[	[	X
ejpam-5594	41	38	63	63	NUM
ejpam-5594	41	39	]	]	PUNCT
ejpam-5594	41	40	,	,	PUNCT
ejpam-5594	41	41	authors	author	NOUN
ejpam-5594	41	42	used	use	VERB
ejpam-5594	41	43	h	h	NOUN
ejpam-5594	41	44	-	-	PUNCT
ejpam-5594	41	45	convex	convex	NOUN
ejpam-5594	41	46	mappings	mapping	NOUN
ejpam-5594	41	47	on	on	ADP
ejpam-5594	41	48	coordinates	coordinate	NOUN
ejpam-5594	41	49	in	in	ADP
ejpam-5594	41	50	the	the	DET
ejpam-5594	41	51	sense	sense	NOUN
ejpam-5594	41	52	of	of	ADP
ejpam-5594	41	53	interval	interval	NOUN
ejpam-5594	41	54	-	-	PUNCT
ejpam-5594	41	55	valued	value	VERB
ejpam-5594	41	56	functions	function	NOUN
ejpam-5594	41	57	and	and	CCONJ
ejpam-5594	41	58	developed	develop	VERB
ejpam-5594	41	59	hadamard	hadamard	NOUN
ejpam-5594	41	60	and	and	CCONJ
ejpam-5594	41	61	bullen	bullen	PROPN
ejpam-5594	41	62	type	type	NOUN
ejpam-5594	41	63	inclusions	inclusion	NOUN
ejpam-5594	41	64	;	;	PUNCT
ejpam-5594	41	65	in	in	ADP
ejpam-5594	41	66	[	[	X
ejpam-5594	41	67	10	10	NUM
ejpam-5594	41	68	]	]	PUNCT
ejpam-5594	41	69	,	,	PUNCT
ejpam-5594	41	70	authors	author	NOUN
ejpam-5594	41	71	used	use	VERB
ejpam-5594	41	72	(	(	PUNCT
ejpam-5594	41	73	h1	h1	PROPN
ejpam-5594	41	74	,	,	PUNCT
ejpam-5594	41	75	h2)-godunova	h2)-godunova	PROPN
ejpam-5594	41	76	and	and	CCONJ
ejpam-5594	41	77	levin	levin	PROPN
ejpam-5594	41	78	functions	function	NOUN
ejpam-5594	41	79	and	and	CCONJ
ejpam-5594	41	80	developed	develop	VERB
ejpam-5594	41	81	hermite	hermite	PROPN
ejpam-5594	41	82	-	-	PUNCT
ejpam-5594	41	83	hadamard	hadamard	ADJ
ejpam-5594	41	84	and	and	CCONJ
ejpam-5594	41	85	jensen	jensen	PROPN
ejpam-5594	41	86	type	type	NOUN
ejpam-5594	41	87	inequalities	inequality	NOUN
ejpam-5594	41	88	;	;	PUNCT
ejpam-5594	41	89	in	in	ADP
ejpam-5594	41	90	[	[	X
ejpam-5594	41	91	35	35	NUM
ejpam-5594	41	92	]	]	PUNCT
ejpam-5594	41	93	,	,	PUNCT
ejpam-5594	41	94	authors	author	NOUN
ejpam-5594	41	95	used	use	VERB
ejpam-5594	41	96	harmonical	harmonical	ADJ
ejpam-5594	41	97	convex	convex	NOUN
ejpam-5594	41	98	mappings	mapping	NOUN
ejpam-5594	41	99	and	and	CCONJ
ejpam-5594	41	100	developed	develop	VERB
ejpam-5594	41	101	double	double	ADJ
ejpam-5594	41	102	inequalities	inequality	NOUN
ejpam-5594	41	103	using	use	VERB
ejpam-5594	41	104	inclusion	inclusion	NOUN
ejpam-5594	41	105	relation	relation	NOUN
ejpam-5594	41	106	;	;	PUNCT
ejpam-5594	41	107	in	in	ADP
ejpam-5594	41	108	[	[	X
ejpam-5594	41	109	18	18	NUM
ejpam-5594	41	110	]	]	PUNCT
ejpam-5594	41	111	dragomir	dragomir	X
ejpam-5594	41	112	developed	develop	VERB
ejpam-5594	41	113	hermite	hermite	ADJ
ejpam-5594	41	114	–	–	PUNCT
ejpam-5594	41	115	hadamard	hadamard	NOUN
ejpam-5594	41	116	’s	’s	PART
ejpam-5594	41	117	type	type	NOUN
ejpam-5594	41	118	inequalities	inequality	NOUN
ejpam-5594	41	119	for	for	ADP
ejpam-5594	41	120	operator	operator	NOUN
ejpam-5594	41	121	convex	convex	NOUN
ejpam-5594	41	122	functions	function	NOUN
ejpam-5594	41	123	;	;	PUNCT
ejpam-5594	41	124	in	in	ADP
ejpam-5594	41	125	[	[	PUNCT
ejpam-5594	41	126	19	19	NUM
ejpam-5594	41	127	]	]	PUNCT
ejpam-5594	41	128	authors	author	NOUN
ejpam-5594	41	129	show	show	VERB
ejpam-5594	41	130	some	some	DET
ejpam-5594	41	131	new	new	ADJ
ejpam-5594	41	132	generalization	generalization	NOUN
ejpam-5594	41	133	of	of	ADP
ejpam-5594	41	134	hermite	hermite	PROPN
ejpam-5594	41	135	–	–	PUNCT
ejpam-5594	41	136	hadamard	hadamard	ADJ
ejpam-5594	41	137	and	and	CCONJ
ejpam-5594	41	138	mercer	mercer	PROPN
ejpam-5594	41	139	forms	form	NOUN
ejpam-5594	41	140	of	of	ADP
ejpam-5594	41	141	inequalities	inequality	NOUN
ejpam-5594	41	142	for	for	ADP
ejpam-5594	41	143	geometric	geometric	ADJ
ejpam-5594	41	144	–	–	PUNCT
ejpam-5594	41	145	arithmetic	arithmetic	ADJ
ejpam-5594	41	146	convexity	convexity	NOUN
ejpam-5594	41	147	by	by	ADP
ejpam-5594	41	148	using	use	VERB
ejpam-5594	41	149	interval	interval	NOUN
ejpam-5594	41	150	maps	map	NOUN
ejpam-5594	41	151	.	.	PUNCT
ejpam-5594	42	1	some	some	DET
ejpam-5594	42	2	other	other	ADJ
ejpam-5594	42	3	important	important	ADJ
ejpam-5594	42	4	results	result	NOUN
ejpam-5594	42	5	and	and	CCONJ
ejpam-5594	42	6	inequalities	inequality	NOUN
ejpam-5594	42	7	connected	connect	VERB
ejpam-5594	42	8	to	to	ADP
ejpam-5594	42	9	these	these	PRON
ejpam-5594	42	10	employing	employ	VERB
ejpam-5594	42	11	different	different	ADJ
ejpam-5594	42	12	types	type	NOUN
ejpam-5594	42	13	of	of	ADP
ejpam-5594	42	14	fractional	fractional	ADJ
ejpam-5594	42	15	operators	operator	NOUN
ejpam-5594	42	16	,	,	PUNCT
ejpam-5594	42	17	including	include	VERB
ejpam-5594	42	18	hadamard	hadamard	NOUN
ejpam-5594	42	19	,	,	PUNCT
ejpam-5594	42	20	atangana	atangana	PROPN
ejpam-5594	42	21	–	–	PUNCT
ejpam-5594	42	22	baleanu	baleanu	PROPN
ejpam-5594	42	23	,	,	PUNCT
ejpam-5594	42	24	caputo	caputo	PROPN
ejpam-5594	42	25	–	–	PUNCT
ejpam-5594	42	26	fabrizio	fabrizio	PROPN
ejpam-5594	42	27	and	and	CCONJ
ejpam-5594	42	28	riemann	riemann	PROPN
ejpam-5594	42	29	–	–	PUNCT
ejpam-5594	42	30	liouville	liouville	VERB
ejpam-5594	42	31	fractional	fractional	ADJ
ejpam-5594	42	32	integrals	integral	NOUN
ejpam-5594	42	33	(	(	PUNCT
ejpam-5594	42	34	see	see	VERB
ejpam-5594	42	35	refs	ref	NOUN
ejpam-5594	42	36	.	.	PUNCT
ejpam-5594	43	1	[	[	X
ejpam-5594	43	2	1	1	NUM
ejpam-5594	43	3	,	,	PUNCT
ejpam-5594	43	4	2	2	NUM
ejpam-5594	43	5	,	,	PUNCT
ejpam-5594	43	6	6	6	NUM
ejpam-5594	43	7	,	,	PUNCT
ejpam-5594	43	8	28	28	NUM
ejpam-5594	43	9	,	,	PUNCT
ejpam-5594	43	10	30	30	NUM
ejpam-5594	43	11	,	,	PUNCT
ejpam-5594	43	12	42	42	NUM
ejpam-5594	43	13	,	,	PUNCT
ejpam-5594	43	14	60	60	NUM
ejpam-5594	43	15	]	]	NUM
ejpam-5594	43	16	)	)	PUNCT
ejpam-5594	43	17	.	.	PUNCT
ejpam-5594	44	1	as	as	SCONJ
ejpam-5594	44	2	the	the	DET
ejpam-5594	44	3	primary	primary	ADJ
ejpam-5594	44	4	focus	focus	NOUN
ejpam-5594	44	5	of	of	ADP
ejpam-5594	44	6	this	this	DET
ejpam-5594	44	7	paper	paper	NOUN
ejpam-5594	44	8	is	be	AUX
ejpam-5594	44	9	on	on	ADP
ejpam-5594	44	10	cr	cr	NOUN
ejpam-5594	44	11	-	-	PUNCT
ejpam-5594	44	12	interval	interval	NOUN
ejpam-5594	44	13	order	order	NOUN
ejpam-5594	44	14	relations	relation	NOUN
ejpam-5594	44	15	,	,	PUNCT
ejpam-5594	44	16	recent	recent	ADJ
ejpam-5594	44	17	advances	advance	NOUN
ejpam-5594	44	18	in	in	ADP
ejpam-5594	44	19	center	center	ADJ
ejpam-5594	44	20	-	-	PUNCT
ejpam-5594	44	21	radius	radius	NOUN
ejpam-5594	44	22	order	order	NOUN
ejpam-5594	44	23	relations	relation	NOUN
ejpam-5594	44	24	should	should	AUX
ejpam-5594	44	25	be	be	AUX
ejpam-5594	44	26	recalled	recall	VERB
ejpam-5594	44	27	using	use	VERB
ejpam-5594	44	28	a	a	DET
ejpam-5594	44	29	different	different	ADJ
ejpam-5594	44	30	type	type	NOUN
ejpam-5594	44	31	of	of	ADP
ejpam-5594	44	32	convex	convex	NOUN
ejpam-5594	44	33	mapping	mapping	NOUN
ejpam-5594	44	34	.	.	PUNCT
ejpam-5594	45	1	in	in	ADP
ejpam-5594	45	2	[	[	X
ejpam-5594	45	3	58	58	NUM
ejpam-5594	45	4	]	]	PUNCT
ejpam-5594	45	5	,	,	PUNCT
ejpam-5594	45	6	the	the	DET
ejpam-5594	45	7	authors	author	NOUN
ejpam-5594	45	8	initially	initially	ADV
ejpam-5594	45	9	presented	present	VERB
ejpam-5594	45	10	the	the	DET
ejpam-5594	45	11	idea	idea	NOUN
ejpam-5594	45	12	of	of	ADP
ejpam-5594	45	13	cr	cr	NOUN
ejpam-5594	45	14	-	-	PUNCT
ejpam-5594	45	15	order	order	NOUN
ejpam-5594	45	16	in	in	ADP
ejpam-5594	45	17	covex	covex	NOUN
ejpam-5594	45	18	sense	sense	NOUN
ejpam-5594	45	19	.	.	PUNCT
ejpam-5594	46	1	in	in	ADP
ejpam-5594	46	2	comparison	comparison	NOUN
ejpam-5594	46	3	to	to	ADP
ejpam-5594	46	4	other	other	ADJ
ejpam-5594	46	5	order	order	NOUN
ejpam-5594	46	6	relations	relation	NOUN
ejpam-5594	46	7	,	,	PUNCT
ejpam-5594	46	8	this	this	DET
ejpam-5594	46	9	relation	relation	NOUN
ejpam-5594	46	10	is	be	AUX
ejpam-5594	46	11	more	more	ADV
ejpam-5594	46	12	compatible	compatible	ADJ
ejpam-5594	46	13	and	and	CCONJ
ejpam-5594	46	14	possesses	possess	VERB
ejpam-5594	46	15	a	a	DET
ejpam-5594	46	16	various	various	ADJ
ejpam-5594	46	17	additional	additional	ADJ
ejpam-5594	46	18	characteristics	characteristic	NOUN
ejpam-5594	46	19	that	that	SCONJ
ejpam-5594	46	20	other	other	ADJ
ejpam-5594	46	21	interval	interval	NOUN
ejpam-5594	46	22	order	order	NOUN
ejpam-5594	46	23	relations	relation	NOUN
ejpam-5594	46	24	lack	lack	VERB
ejpam-5594	46	25	.	.	PUNCT
ejpam-5594	47	1	in	in	ADP
ejpam-5594	47	2	[	[	X
ejpam-5594	47	3	25	25	NUM
ejpam-5594	47	4	]	]	PUNCT
ejpam-5594	47	5	authors	author	NOUN
ejpam-5594	47	6	defined	define	VERB
ejpam-5594	47	7	a	a	DET
ejpam-5594	47	8	new	new	ADJ
ejpam-5594	47	9	class	class	NOUN
ejpam-5594	47	10	of	of	ADP
ejpam-5594	47	11	convex	convex	NOUN
ejpam-5594	47	12	mapping	mapping	NOUN
ejpam-5594	47	13	for	for	ADP
ejpam-5594	47	14	convex	convex	NOUN
ejpam-5594	47	15	optimizing	optimize	VERB
ejpam-5594	47	16	problems	problem	NOUN
ejpam-5594	47	17	in	in	ADP
ejpam-5594	47	18	the	the	DET
ejpam-5594	47	19	context	context	NOUN
ejpam-5594	47	20	of	of	ADP
ejpam-5594	47	21	cr	cr	NOUN
ejpam-5594	47	22	-	-	PUNCT
ejpam-5594	47	23	order	order	NOUN
ejpam-5594	47	24	based	base	VERB
ejpam-5594	47	25	on	on	ADP
ejpam-5594	47	26	their	their	PRON
ejpam-5594	47	27	work	work	NOUN
ejpam-5594	47	28	.	.	PUNCT
ejpam-5594	48	1	in	in	ADP
ejpam-5594	48	2	response	response	NOUN
ejpam-5594	48	3	to	to	ADP
ejpam-5594	48	4	these	these	DET
ejpam-5594	48	5	discoveries	discovery	NOUN
ejpam-5594	48	6	,	,	PUNCT
ejpam-5594	48	7	liu	liu	PROPN
ejpam-5594	48	8	et	et	PROPN
ejpam-5594	48	9	al	al	PROPN
ejpam-5594	48	10	.	.	PUNCT
ejpam-5594	49	1	[	[	X
ejpam-5594	49	2	36	36	NUM
ejpam-5594	49	3	,	,	PUNCT
ejpam-5594	49	4	37	37	NUM
ejpam-5594	49	5	]	]	PUNCT
ejpam-5594	49	6	derived	derive	VERB
ejpam-5594	49	7	discrete	discrete	ADJ
ejpam-5594	49	8	versions	version	NOUN
ejpam-5594	49	9	of	of	ADP
ejpam-5594	49	10	jensen	jensen	PROPN
ejpam-5594	49	11	and	and	CCONJ
ejpam-5594	49	12	hermite	hermite	PROPN
ejpam-5594	49	13	-	-	PUNCT
ejpam-5594	49	14	hadamard	hadamard	ADJ
ejpam-5594	49	15	inequalities	inequality	NOUN
ejpam-5594	49	16	based	base	VERB
ejpam-5594	49	17	on	on	ADP
ejpam-5594	49	18	two	two	NUM
ejpam-5594	49	19	different	different	ADJ
ejpam-5594	49	20	types	type	NOUN
ejpam-5594	49	21	of	of	ADP
ejpam-5594	49	22	generalized	generalized	ADJ
ejpam-5594	49	23	convex	convex	NOUN
ejpam-5594	49	24	mappings	mapping	NOUN
ejpam-5594	49	25	by	by	ADP
ejpam-5594	49	26	using	use	VERB
ejpam-5594	49	27	cr	cr	NOUN
ejpam-5594	49	28	-	-	PUNCT
ejpam-5594	49	29	order	order	NOUN
ejpam-5594	49	30	.	.	PUNCT
ejpam-5594	50	1	as	as	ADP
ejpam-5594	50	2	a	a	DET
ejpam-5594	50	3	result	result	NOUN
ejpam-5594	50	4	of	of	ADP
ejpam-5594	50	5	using	use	VERB
ejpam-5594	50	6	superquadratic	superquadratic	ADJ
ejpam-5594	50	7	functions	function	NOUN
ejpam-5594	50	8	in	in	ADP
ejpam-5594	50	9	a	a	DET
ejpam-5594	50	10	fractional	fractional	ADJ
ejpam-5594	50	11	frame	frame	NOUN
ejpam-5594	50	12	of	of	ADP
ejpam-5594	50	13	reference	reference	NOUN
ejpam-5594	50	14	via	via	ADP
ejpam-5594	50	15	cr	cr	NOUN
ejpam-5594	50	16	-	-	PUNCT
ejpam-5594	50	17	order	order	NOUN
ejpam-5594	50	18	relations	relation	NOUN
ejpam-5594	50	19	,	,	PUNCT
ejpam-5594	50	20	khan	khan	PROPN
ejpam-5594	50	21	and	and	CCONJ
ejpam-5594	50	22	saad	saad	PROPN
ejpam-5594	50	23	[	[	X
ejpam-5594	50	24	33	33	NUM
ejpam-5594	50	25	]	]	PUNCT
ejpam-5594	50	26	developed	develop	VERB
ejpam-5594	50	27	several	several	ADJ
ejpam-5594	50	28	novel	novel	ADJ
ejpam-5594	50	29	bounds	bound	NOUN
ejpam-5594	50	30	for	for	ADP
ejpam-5594	50	31	various	various	ADJ
ejpam-5594	50	32	kinds	kind	NOUN
ejpam-5594	50	33	of	of	ADP
ejpam-5594	50	34	double	double	ADJ
ejpam-5594	50	35	inequalities	inequality	NOUN
ejpam-5594	50	36	.	.	PUNCT
ejpam-5594	51	1	to	to	PART
ejpam-5594	51	2	explore	explore	VERB
ejpam-5594	51	3	entropy	entropy	NOUN
ejpam-5594	51	4	and	and	CCONJ
ejpam-5594	51	5	mean	mean	ADJ
ejpam-5594	51	6	characteristics	characteristic	NOUN
ejpam-5594	51	7	,	,	PUNCT
ejpam-5594	51	8	fahad	fahad	VERB
ejpam-5594	51	9	et	et	PROPN
ejpam-5594	51	10	al	al	PROPN
ejpam-5594	51	11	.	.	PUNCT
ejpam-5594	52	1	[	[	X
ejpam-5594	52	2	20	20	NUM
ejpam-5594	52	3	]	]	PUNCT
ejpam-5594	52	4	used	use	VERB
ejpam-5594	52	5	geometric	geometric	ADJ
ejpam-5594	52	6	and	and	CCONJ
ejpam-5594	52	7	arithmetic	arithmetic	ADJ
ejpam-5594	52	8	-	-	PUNCT
ejpam-5594	52	9	cr	cr	NOUN
ejpam-5594	52	10	-	-	PUNCT
ejpam-5594	52	11	convex	convex	NOUN
ejpam-5594	52	12	functions	function	NOUN
ejpam-5594	52	13	.	.	PUNCT
ejpam-5594	53	1	afzal	afzal	PROPN
ejpam-5594	53	2	et	et	PROPN
ejpam-5594	53	3	al	al	PROPN
ejpam-5594	53	4	.	.	PUNCT
ejpam-5594	54	1	[	[	X
ejpam-5594	54	2	4	4	NUM
ejpam-5594	54	3	,	,	PUNCT
ejpam-5594	54	4	8	8	NUM
ejpam-5594	54	5	]	]	PUNCT
ejpam-5594	54	6	created	create	VERB
ejpam-5594	54	7	different	different	ADJ
ejpam-5594	54	8	types	type	NOUN
ejpam-5594	54	9	of	of	ADP
ejpam-5594	54	10	discrete	discrete	ADJ
ejpam-5594	54	11	jensen	jensen	PROPN
ejpam-5594	54	12	type	type	NOUN
ejpam-5594	54	13	and	and	CCONJ
ejpam-5594	54	14	hermite	hermite	ADJ
ejpam-5594	54	15	-	-	PUNCT
ejpam-5594	54	16	hadamard	hadamard	ADJ
ejpam-5594	54	17	inequality	inequality	NOUN
ejpam-5594	54	18	utilizing	utilize	VERB
ejpam-5594	54	19	the	the	DET
ejpam-5594	54	20	conventional	conventional	ADJ
ejpam-5594	54	21	riemann	riemann	PROPN
ejpam-5594	54	22	integral	integral	ADJ
ejpam-5594	54	23	operator	operator	NOUN
ejpam-5594	54	24	by	by	ADP
ejpam-5594	54	25	using	use	VERB
ejpam-5594	54	26	the	the	DET
ejpam-5594	54	27	cr	cr	PROPN
ejpam-5594	54	28	-	-	PUNCT
ejpam-5594	54	29	h	h	NOUN
ejpam-5594	54	30	-	-	PUNCT
ejpam-5594	54	31	godunovalevin	godunovalevin	ADJ
ejpam-5594	54	32	function	function	NOUN
ejpam-5594	54	33	in	in	ADP
ejpam-5594	54	34	convex	convex	NOUN
ejpam-5594	54	35	and	and	CCONJ
ejpam-5594	54	36	harmonic	harmonic	ADJ
ejpam-5594	54	37	convex	convex	NOUN
ejpam-5594	54	38	sense	sense	NOUN
ejpam-5594	54	39	.	.	PUNCT
ejpam-5594	55	1	theorem	theorem	NOUN
ejpam-5594	55	2	1	1	NUM
ejpam-5594	55	3	(	(	PUNCT
ejpam-5594	55	4	see	see	VERB
ejpam-5594	55	5	[	[	X
ejpam-5594	55	6	4	4	NUM
ejpam-5594	55	7	]	]	NUM
ejpam-5594	55	8	)	)	PUNCT
ejpam-5594	55	9	.	.	PUNCT
ejpam-5594	56	1	let	let	VERB
ejpam-5594	56	2	h	h	NOUN
ejpam-5594	56	3	:	:	PUNCT
ejpam-5594	56	4	(	(	PUNCT
ejpam-5594	56	5	0	0	NUM
ejpam-5594	56	6	,	,	PUNCT
ejpam-5594	56	7	1	1	NUM
ejpam-5594	56	8	)	)	PUNCT
ejpam-5594	56	9	→	→	NOUN
ejpam-5594	56	10	r+	r+	NOUN
ejpam-5594	56	11	such	such	ADJ
ejpam-5594	56	12	that	that	DET
ejpam-5594	56	13	h	h	NOUN
ejpam-5594	56	14	(	(	PUNCT
ejpam-5594	56	15	1	1	NUM
ejpam-5594	56	16	2	2	NUM
ejpam-5594	56	17	)	)	PUNCT
ejpam-5594	56	18	̸=	̸=	PROPN
ejpam-5594	56	19	0	0	NUM
ejpam-5594	56	20	,	,	PUNCT
ejpam-5594	56	21	and	and	CCONJ
ejpam-5594	56	22	φ	φ	PRON
ejpam-5594	56	23	:	:	PUNCT
ejpam-5594	57	1	[	[	X
ejpam-5594	57	2	ε1	ε1	NOUN
ejpam-5594	57	3	,	,	PUNCT
ejpam-5594	57	4	ε2	ε2	PROPN
ejpam-5594	57	5	]	]	PUNCT
ejpam-5594	57	6	→	→	SYM
ejpam-5594	57	7	r+	r+	PUNCT
ejpam-5594	57	8	i	i	PRON
ejpam-5594	57	9	be	be	VERB
ejpam-5594	57	10	an	an	DET
ejpam-5594	57	11	cr	cr	NOUN
ejpam-5594	57	12	-	-	PUNCT
ejpam-5594	57	13	h	h	NOUN
ejpam-5594	57	14	-	-	PUNCT
ejpam-5594	57	15	godunova	godunova	ADJ
ejpam-5594	57	16	-	-	PUNCT
ejpam-5594	57	17	levin	levin	PROPN
ejpam-5594	57	18	mapping	mapping	PROPN
ejpam-5594	57	19	,	,	PUNCT
ejpam-5594	57	20	ε1	ε1	PROPN
ejpam-5594	57	21	,	,	PUNCT
ejpam-5594	57	22	ε2	ε2	PROPN
ejpam-5594	57	23	∈	∈	PROPN
ejpam-5594	57	24	r+	r+	NOUN
ejpam-5594	57	25	,	,	PUNCT
ejpam-5594	57	26	then	then	ADV
ejpam-5594	57	27	the	the	DET
ejpam-5594	57	28	inequality	inequality	NOUN
ejpam-5594	57	29	stated	state	VERB
ejpam-5594	57	30	below	below	ADV
ejpam-5594	57	31	holds	hold	VERB
ejpam-5594	57	32	true	true	ADJ
ejpam-5594	57	33	:	:	PUNCT
ejpam-5594	57	34	h	h	NOUN
ejpam-5594	57	35	(	(	PUNCT
ejpam-5594	57	36	1	1	NUM
ejpam-5594	57	37	2	2	NUM
ejpam-5594	57	38	)	)	PUNCT
ejpam-5594	57	39	2	2	NUM
ejpam-5594	57	40	φ	φ	NOUN
ejpam-5594	57	41	(	(	PUNCT
ejpam-5594	57	42	ε2	ε2	PROPN
ejpam-5594	57	43	+	+	CCONJ
ejpam-5594	57	44	ε1	ε1	PROPN
ejpam-5594	57	45	2	2	NUM
ejpam-5594	57	46	)	)	PUNCT
ejpam-5594	57	47	⪯cr	⪯cr	VERB
ejpam-5594	57	48	1	1	NUM
ejpam-5594	57	49	ε2	ε2	NOUN
ejpam-5594	57	50	−	−	PROPN
ejpam-5594	57	51	ε1	ε1	PROPN
ejpam-5594	57	52	∫	∫	PROPN
ejpam-5594	57	53	ε2	ε2	PROPN
ejpam-5594	57	54	ε1	ε1	PROPN
ejpam-5594	57	55	φ(v)dv	φ(v)dv	NOUN
ejpam-5594	57	56	⪯cr	⪯cr	VERB
ejpam-5594	58	1	[	[	X
ejpam-5594	58	2	φ(ε1	φ(ε1	NOUN
ejpam-5594	58	3	)	)	PUNCT
ejpam-5594	58	4	+	+	NUM
ejpam-5594	58	5	φ(ε2	φ(ε2	NUM
ejpam-5594	58	6	)	)	PUNCT
ejpam-5594	58	7	]	]	PUNCT
ejpam-5594	59	1	∫	∫	PROPN
ejpam-5594	60	1	1	1	NUM
ejpam-5594	60	2	0	0	NUM
ejpam-5594	61	1	d	d	X
ejpam-5594	61	2	♭	♭	INTJ
ejpam-5594	61	3	h	h	PROPN
ejpam-5594	61	4	(	(	PUNCT
ejpam-5594	61	5	♭	♭	PROPN
ejpam-5594	61	6	)	)	PUNCT
ejpam-5594	61	7	.	.	PUNCT
ejpam-5594	62	1	sahoo	sahoo	PROPN
ejpam-5594	62	2	et	et	PROPN
ejpam-5594	62	3	al	al	PROPN
ejpam-5594	62	4	.	.	PUNCT
ejpam-5594	63	1	[	[	X
ejpam-5594	63	2	45	45	NUM
ejpam-5594	63	3	]	]	PUNCT
ejpam-5594	63	4	employed	employ	VERB
ejpam-5594	63	5	fractional	fractional	ADJ
ejpam-5594	63	6	integral	integral	ADJ
ejpam-5594	63	7	operators	operator	NOUN
ejpam-5594	63	8	to	to	PART
ejpam-5594	63	9	construct	construct	VERB
ejpam-5594	63	10	the	the	DET
ejpam-5594	63	11	following	follow	VERB
ejpam-5594	63	12	double	double	ADJ
ejpam-5594	63	13	relation	relation	NOUN
ejpam-5594	63	14	for	for	ADP
ejpam-5594	63	15	cr	cr	NOUN
ejpam-5594	63	16	-	-	PUNCT
ejpam-5594	63	17	convex	convex	NOUN
ejpam-5594	63	18	functions	function	NOUN
ejpam-5594	63	19	:	:	PUNCT
ejpam-5594	63	20	theorem	theorem	NOUN
ejpam-5594	63	21	2	2	NUM
ejpam-5594	63	22	(	(	PUNCT
ejpam-5594	63	23	see	see	VERB
ejpam-5594	63	24	[	[	X
ejpam-5594	63	25	45	45	NUM
ejpam-5594	63	26	]	]	PUNCT
ejpam-5594	63	27	)	)	PUNCT
ejpam-5594	63	28	.	.	PUNCT
ejpam-5594	64	1	let	let	VERB
ejpam-5594	64	2	φ	φ	NOUN
ejpam-5594	64	3	:	:	PUNCT
ejpam-5594	65	1	[	[	X
ejpam-5594	65	2	ε1	ε1	NOUN
ejpam-5594	65	3	,	,	PUNCT
ejpam-5594	65	4	ε2	ε2	PROPN
ejpam-5594	65	5	]	]	PUNCT
ejpam-5594	65	6	→	→	SYM
ejpam-5594	65	7	r+	r+	PUNCT
ejpam-5594	65	8	i	i	PRON
ejpam-5594	65	9	be	be	VERB
ejpam-5594	65	10	an	an	DET
ejpam-5594	65	11	cr	cr	NOUN
ejpam-5594	65	12	-	-	PUNCT
ejpam-5594	65	13	convex	convex	NOUN
ejpam-5594	65	14	function	function	NOUN
ejpam-5594	65	15	on	on	ADP
ejpam-5594	65	16	[	[	X
ejpam-5594	65	17	ε1	ε1	NOUN
ejpam-5594	65	18	,	,	PUNCT
ejpam-5594	65	19	ε2	ε2	PROPN
ejpam-5594	65	20	]	]	PUNCT
ejpam-5594	65	21	,	,	PUNCT
ejpam-5594	65	22	then	then	ADV
ejpam-5594	65	23	the	the	DET
ejpam-5594	65	24	inequality	inequality	NOUN
ejpam-5594	65	25	stated	state	VERB
ejpam-5594	65	26	below	below	ADV
ejpam-5594	65	27	holds	hold	VERB
ejpam-5594	65	28	true	true	ADJ
ejpam-5594	65	29	:	:	PUNCT
ejpam-5594	65	30	j.	j.	PROPN
ejpam-5594	65	31	e.	e.	PROPN
ejpam-5594	65	32	maćıas	maćıas	PROPN
ejpam-5594	65	33	-	-	PUNCT
ejpam-5594	65	34	dı́az	dı́az	NOUN
ejpam-5594	65	35	et	et	NOUN
ejpam-5594	65	36	al	al	PROPN
ejpam-5594	65	37	.	.	PUNCT
ejpam-5594	65	38	/	/	SYM
ejpam-5594	65	39	eur	eur	PROPN
ejpam-5594	65	40	.	.	PUNCT
ejpam-5594	66	1	j.	j.	PROPN
ejpam-5594	66	2	pure	pure	PROPN
ejpam-5594	66	3	appl	appl	PROPN
ejpam-5594	66	4	.	.	PROPN
ejpam-5594	66	5	math	math	PROPN
ejpam-5594	66	6	,	,	PUNCT
ejpam-5594	66	7	17	17	NUM
ejpam-5594	66	8	(	(	PUNCT
ejpam-5594	66	9	4	4	NUM
ejpam-5594	66	10	)	)	PUNCT
ejpam-5594	66	11	(	(	PUNCT
ejpam-5594	66	12	2024	2024	NUM
ejpam-5594	66	13	)	)	PUNCT
ejpam-5594	66	14	,	,	PUNCT
ejpam-5594	66	15	4014	4014	NUM
ejpam-5594	66	16	-	-	SYM
ejpam-5594	66	17	4049	4049	NUM
ejpam-5594	66	18	4017	4017	NUM
ejpam-5594	66	19	φ	φ	PROPN
ejpam-5594	66	20	(	(	PUNCT
ejpam-5594	66	21	ε2	ε2	PROPN
ejpam-5594	66	22	+	+	CCONJ
ejpam-5594	66	23	ε1	ε1	PROPN
ejpam-5594	66	24	2	2	NUM
ejpam-5594	66	25	)	)	PUNCT
ejpam-5594	66	26	⪯cr	⪯cr	VERB
ejpam-5594	66	27	2α−1γ(α+	2α−1γ(α+	NUM
ejpam-5594	66	28	1	1	NUM
ejpam-5594	66	29	)	)	PUNCT
ejpam-5594	66	30	(	(	PUNCT
ejpam-5594	66	31	ε2	ε2	ADJ
ejpam-5594	66	32	−	−	PROPN
ejpam-5594	66	33	ε1)α	ε1)α	NOUN
ejpam-5594	66	34	(	(	PUNCT
ejpam-5594	66	35	j	j	PROPN
ejpam-5594	66	36	(	(	PUNCT
ejpam-5594	66	37	ε1+ε2	ε1+ε2	NOUN
ejpam-5594	66	38	2	2	NUM
ejpam-5594	66	39	)	)	PUNCT
ejpam-5594	66	40	+	+	NOUN
ejpam-5594	66	41	φ(ε2	φ(ε2	NUM
ejpam-5594	66	42	)	)	PUNCT
ejpam-5594	67	1	+	+	SYM
ejpam-5594	67	2	jα	jα	X
ejpam-5594	67	3	(	(	PUNCT
ejpam-5594	67	4	ε1+ε2	ε1+ε2	NOUN
ejpam-5594	67	5	2	2	NUM
ejpam-5594	67	6	)	)	PUNCT
ejpam-5594	67	7	−φ(ε1	−φ(ε1	PROPN
ejpam-5594	67	8	)	)	PUNCT
ejpam-5594	67	9	)	)	PUNCT
ejpam-5594	67	10	⪯cr	⪯cr	VERB
ejpam-5594	67	11	φ(ε1	φ(ε1	PRON
ejpam-5594	67	12	)	)	PUNCT
ejpam-5594	68	1	+	+	SYM
ejpam-5594	68	2	φ(ε2	φ(ε2	NUM
ejpam-5594	68	3	)	)	PUNCT
ejpam-5594	68	4	2	2	NUM
ejpam-5594	68	5	shah	shah	NOUN
ejpam-5594	68	6	et	et	PROPN
ejpam-5594	68	7	al	al	PROPN
ejpam-5594	68	8	.	.	PUNCT
ejpam-5594	69	1	[	[	X
ejpam-5594	69	2	47	47	NUM
ejpam-5594	69	3	]	]	PUNCT
ejpam-5594	69	4	employed	employ	VERB
ejpam-5594	69	5	cr	cr	NOUN
ejpam-5594	69	6	-	-	PUNCT
ejpam-5594	69	7	convex	convex	NOUN
ejpam-5594	69	8	stochastic	stochastic	NOUN
ejpam-5594	69	9	processes	process	NOUN
ejpam-5594	69	10	to	to	PART
ejpam-5594	69	11	establish	establish	VERB
ejpam-5594	69	12	different	different	ADJ
ejpam-5594	69	13	variations	variation	NOUN
ejpam-5594	69	14	of	of	ADP
ejpam-5594	69	15	hermite	hermite	ADJ
ejpam-5594	69	16	-	-	PUNCT
ejpam-5594	69	17	hadamard	hadamard	ADJ
ejpam-5594	69	18	type	type	NOUN
ejpam-5594	69	19	relations	relation	NOUN
ejpam-5594	69	20	in	in	ADP
ejpam-5594	69	21	the	the	DET
ejpam-5594	69	22	mercer	mercer	PROPN
ejpam-5594	69	23	sense	sense	NOUN
ejpam-5594	69	24	.	.	PUNCT
ejpam-5594	70	1	theorem	theorem	NOUN
ejpam-5594	70	2	3	3	NUM
ejpam-5594	70	3	(	(	PUNCT
ejpam-5594	70	4	see	see	VERB
ejpam-5594	70	5	[	[	X
ejpam-5594	70	6	47	47	NUM
ejpam-5594	70	7	]	]	PUNCT
ejpam-5594	70	8	)	)	PUNCT
ejpam-5594	70	9	.	.	PUNCT
ejpam-5594	71	1	let	let	VERB
ejpam-5594	71	2	φ	φ	NOUN
ejpam-5594	71	3	:	:	PUNCT
ejpam-5594	72	1	[	[	X
ejpam-5594	72	2	ε1	ε1	NOUN
ejpam-5594	72	3	,	,	PUNCT
ejpam-5594	72	4	ε2]×ω	ε2]×ω	X
ejpam-5594	72	5	→	→	SYM
ejpam-5594	72	6	r+	r+	PUNCT
ejpam-5594	72	7	i	i	PRON
ejpam-5594	72	8	be	be	VERB
ejpam-5594	72	9	a	a	DET
ejpam-5594	72	10	γ	γ	NOUN
ejpam-5594	72	11	-	-	ADJ
ejpam-5594	72	12	convex	convex	ADJ
ejpam-5594	72	13	cr	cr	NOUN
ejpam-5594	72	14	-	-	PUNCT
ejpam-5594	72	15	interval	interval	NOUN
ejpam-5594	72	16	-	-	PUNCT
ejpam-5594	72	17	valued	value	VERB
ejpam-5594	72	18	stochastic	stochastic	NOUN
ejpam-5594	72	19	processes	process	NOUN
ejpam-5594	72	20	then	then	ADV
ejpam-5594	72	21	the	the	DET
ejpam-5594	72	22	inequality	inequality	NOUN
ejpam-5594	72	23	stated	state	VERB
ejpam-5594	72	24	below	below	ADV
ejpam-5594	72	25	holds	hold	VERB
ejpam-5594	72	26	true	true	ADJ
ejpam-5594	72	27	:(	:(	X
ejpam-5594	72	28	1−	1−	NUM
ejpam-5594	72	29	e−ζ	e−ζ	ADP
ejpam-5594	72	30	)	)	PUNCT
ejpam-5594	72	31	γ	γ	PROPN
ejpam-5594	72	32	(	(	PUNCT
ejpam-5594	72	33	1	1	NUM
ejpam-5594	72	34	2	2	NUM
ejpam-5594	72	35	)	)	PUNCT
ejpam-5594	72	36	φ	φ	PROPN
ejpam-5594	72	37	(	(	PUNCT
ejpam-5594	72	38	η1	η1	NOUN
ejpam-5594	72	39	+	+	CCONJ
ejpam-5594	72	40	η2	η2	PROPN
ejpam-5594	72	41	−	−	PROPN
ejpam-5594	72	42	ε1	ε1	PROPN
ejpam-5594	72	43	+	+	CCONJ
ejpam-5594	72	44	ε2	ε2	ADJ
ejpam-5594	72	45	2	2	NUM
ejpam-5594	72	46	,	,	PUNCT
ejpam-5594	72	47	.	.	PUNCT
ejpam-5594	72	48	)	)	PUNCT
ejpam-5594	73	1	⪯cr	⪯cr	VERB
ejpam-5594	73	2	1−	1−	NUM
ejpam-5594	73	3	β	β	X
ejpam-5594	73	4	2	2	NUM
ejpam-5594	73	5	[	[	PUNCT
ejpam-5594	73	6	jβ	jβ	X
ejpam-5594	73	7	η1+η2−ε−1	η1+η2−ε−1	PROPN
ejpam-5594	73	8	[	[	X
ejpam-5594	73	9	φ	φ	X
ejpam-5594	73	10	]	]	X
ejpam-5594	73	11	(	(	PUNCT
ejpam-5594	73	12	η1	η1	NOUN
ejpam-5594	73	13	+	+	CCONJ
ejpam-5594	73	14	η2	η2	ADJ
ejpam-5594	73	15	−	−	PROPN
ejpam-5594	73	16	ε2	ε2	PROPN
ejpam-5594	73	17	)	)	PUNCT
ejpam-5594	74	1	+	+	CCONJ
ejpam-5594	74	2	jβ	jβ	PROPN
ejpam-5594	74	3	η1+η2−ε+2	η1+η2−ε+2	PROPN
ejpam-5594	74	4	[	[	X
ejpam-5594	74	5	φ	φ	X
ejpam-5594	74	6	]	]	X
ejpam-5594	74	7	(	(	PUNCT
ejpam-5594	74	8	η1	η1	NOUN
ejpam-5594	74	9	+	+	CCONJ
ejpam-5594	74	10	η2	η2	PROPN
ejpam-5594	74	11	−	−	PROPN
ejpam-5594	74	12	ε1	ε1	PROPN
ejpam-5594	74	13	)	)	PUNCT
ejpam-5594	74	14	]	]	PUNCT
ejpam-5594	74	15	⪯cr	⪯cr	X
ejpam-5594	74	16	[	[	PUNCT
ejpam-5594	74	17	φ	φ	PROPN
ejpam-5594	74	18	(	(	PUNCT
ejpam-5594	74	19	η1	η1	NOUN
ejpam-5594	74	20	,	,	PUNCT
ejpam-5594	74	21	.	.	PUNCT
ejpam-5594	74	22	)	)	PUNCT
ejpam-5594	75	1	+	+	CCONJ
ejpam-5594	75	2	φ	φ	PROPN
ejpam-5594	75	3	(	(	PUNCT
ejpam-5594	75	4	η2	η2	X
ejpam-5594	75	5	,	,	PUNCT
ejpam-5594	75	6	.)−	.)−	PROPN
ejpam-5594	75	7	φ(ε1	φ(ε1	PROPN
ejpam-5594	75	8	,	,	PUNCT
ejpam-5594	75	9	.	.	PUNCT
ejpam-5594	75	10	)	)	PUNCT
ejpam-5594	76	1	+	+	CCONJ
ejpam-5594	77	1	φ(ε2	φ(ε2	NUM
ejpam-5594	77	2	,	,	PUNCT
ejpam-5594	77	3	.	.	PUNCT
ejpam-5594	77	4	)	)	PUNCT
ejpam-5594	78	1	2	2	X
ejpam-5594	78	2	]	]	PUNCT
ejpam-5594	78	3	∆.	∆.	NOUN
ejpam-5594	78	4	for	for	ADP
ejpam-5594	78	5	some	some	DET
ejpam-5594	78	6	additional	additional	ADJ
ejpam-5594	78	7	results	result	NOUN
ejpam-5594	78	8	and	and	CCONJ
ejpam-5594	78	9	inequalities	inequality	NOUN
ejpam-5594	78	10	obtained	obtain	VERB
ejpam-5594	78	11	using	use	VERB
ejpam-5594	78	12	other	other	ADJ
ejpam-5594	78	13	types	type	NOUN
ejpam-5594	78	14	of	of	ADP
ejpam-5594	78	15	generalized	generalized	ADJ
ejpam-5594	78	16	convex	convex	NOUN
ejpam-5594	78	17	mappings	mapping	NOUN
ejpam-5594	78	18	under	under	ADP
ejpam-5594	78	19	center	center	ADJ
ejpam-5594	78	20	radius	radius	NOUN
ejpam-5594	78	21	order	order	NOUN
ejpam-5594	78	22	relations	relation	NOUN
ejpam-5594	78	23	connected	connect	VERB
ejpam-5594	78	24	to	to	ADP
ejpam-5594	78	25	developed	develop	VERB
ejpam-5594	78	26	results	result	NOUN
ejpam-5594	78	27	,	,	PUNCT
ejpam-5594	78	28	please	please	INTJ
ejpam-5594	78	29	see	see	VERB
ejpam-5594	78	30	the	the	DET
ejpam-5594	78	31	following	follow	VERB
ejpam-5594	78	32	publications	publication	NOUN
ejpam-5594	78	33	[	[	X
ejpam-5594	78	34	7	7	NUM
ejpam-5594	78	35	,	,	PUNCT
ejpam-5594	78	36	12	12	NUM
ejpam-5594	78	37	,	,	PUNCT
ejpam-5594	78	38	44	44	NUM
ejpam-5594	78	39	,	,	PUNCT
ejpam-5594	78	40	46	46	NUM
ejpam-5594	78	41	]	]	PUNCT
ejpam-5594	78	42	and	and	CCONJ
ejpam-5594	78	43	their	their	PRON
ejpam-5594	78	44	references	reference	NOUN
ejpam-5594	78	45	.	.	PUNCT
ejpam-5594	79	1	this	this	DET
ejpam-5594	79	2	study	study	NOUN
ejpam-5594	79	3	is	be	AUX
ejpam-5594	79	4	regarded	regard	VERB
ejpam-5594	79	5	fresh	fresh	ADJ
ejpam-5594	79	6	and	and	CCONJ
ejpam-5594	79	7	significant	significant	ADJ
ejpam-5594	79	8	since	since	SCONJ
ejpam-5594	79	9	it	it	PRON
ejpam-5594	79	10	presents	present	VERB
ejpam-5594	79	11	new	new	ADJ
ejpam-5594	79	12	and	and	CCONJ
ejpam-5594	79	13	original	original	ADJ
ejpam-5594	79	14	conclusions	conclusion	NOUN
ejpam-5594	79	15	using	use	VERB
ejpam-5594	79	16	center	center	ADJ
ejpam-5594	79	17	-	-	PUNCT
ejpam-5594	79	18	radius	radius	NOUN
ejpam-5594	79	19	interval	interval	NOUN
ejpam-5594	79	20	order	order	NOUN
ejpam-5594	79	21	relations	relation	NOUN
ejpam-5594	79	22	.	.	PUNCT
ejpam-5594	80	1	furthermore	furthermore	ADV
ejpam-5594	80	2	,	,	PUNCT
ejpam-5594	80	3	this	this	PRON
ejpam-5594	80	4	is	be	AUX
ejpam-5594	80	5	the	the	DET
ejpam-5594	80	6	first	first	ADJ
ejpam-5594	80	7	time	time	NOUN
ejpam-5594	80	8	that	that	PRON
ejpam-5594	80	9	hermite	hermite	PROPN
ejpam-5594	80	10	-	-	PUNCT
ejpam-5594	80	11	hadamard	hadamard	PROPN
ejpam-5594	80	12	and	and	CCONJ
ejpam-5594	80	13	its	its	PRON
ejpam-5594	80	14	numerous	numerous	ADJ
ejpam-5594	80	15	versions	version	NOUN
ejpam-5594	80	16	,	,	PUNCT
ejpam-5594	80	17	including	include	VERB
ejpam-5594	80	18	product	product	NOUN
ejpam-5594	80	19	form	form	NOUN
ejpam-5594	80	20	,	,	PUNCT
ejpam-5594	80	21	weighted	weight	VERB
ejpam-5594	80	22	form	form	NOUN
ejpam-5594	80	23	,	,	PUNCT
ejpam-5594	80	24	and	and	CCONJ
ejpam-5594	80	25	employing	employ	VERB
ejpam-5594	80	26	symmetric	symmetric	ADJ
ejpam-5594	80	27	mappings	mapping	NOUN
ejpam-5594	80	28	,	,	PUNCT
ejpam-5594	80	29	are	be	AUX
ejpam-5594	80	30	produced	produce	VERB
ejpam-5594	80	31	by	by	ADP
ejpam-5594	80	32	atangana	atangana	PROPN
ejpam-5594	80	33	-	-	PUNCT
ejpam-5594	80	34	baleanu	baleanu	ADJ
ejpam-5594	80	35	fractional	fractional	ADJ
ejpam-5594	80	36	integral	integral	ADJ
ejpam-5594	80	37	operators	operator	NOUN
ejpam-5594	80	38	under	under	ADP
ejpam-5594	80	39	cr	cr	NOUN
ejpam-5594	80	40	-	-	PUNCT
ejpam-5594	80	41	order	order	NOUN
ejpam-5594	80	42	relation	relation	NOUN
ejpam-5594	80	43	.	.	PUNCT
ejpam-5594	81	1	additionally	additionally	ADV
ejpam-5594	81	2	,	,	PUNCT
ejpam-5594	81	3	we	we	PRON
ejpam-5594	81	4	utilize	utilize	VERB
ejpam-5594	81	5	a	a	DET
ejpam-5594	81	6	number	number	NOUN
ejpam-5594	81	7	of	of	ADP
ejpam-5594	81	8	additional	additional	ADJ
ejpam-5594	81	9	known	know	VERB
ejpam-5594	81	10	results	result	NOUN
ejpam-5594	81	11	,	,	PUNCT
ejpam-5594	81	12	such	such	ADJ
ejpam-5594	81	13	as	as	ADP
ejpam-5594	81	14	minkowski	minkowski	ADJ
ejpam-5594	81	15	,	,	PUNCT
ejpam-5594	81	16	holder	holder	NOUN
ejpam-5594	81	17	,	,	PUNCT
ejpam-5594	81	18	and	and	CCONJ
ejpam-5594	81	19	young	young	ADJ
ejpam-5594	81	20	,	,	PUNCT
ejpam-5594	81	21	in	in	ADP
ejpam-5594	81	22	the	the	DET
ejpam-5594	81	23	development	development	NOUN
ejpam-5594	81	24	of	of	ADP
ejpam-5594	81	25	these	these	DET
ejpam-5594	81	26	results	result	NOUN
ejpam-5594	81	27	.	.	PUNCT
ejpam-5594	82	1	furthermore	furthermore	ADV
ejpam-5594	82	2	,	,	PUNCT
ejpam-5594	82	3	we	we	PRON
ejpam-5594	82	4	provide	provide	VERB
ejpam-5594	82	5	bounds	bound	NOUN
ejpam-5594	82	6	of	of	ADP
ejpam-5594	82	7	these	these	DET
ejpam-5594	82	8	inequalities	inequality	NOUN
ejpam-5594	82	9	in	in	ADP
ejpam-5594	82	10	terms	term	NOUN
ejpam-5594	82	11	of	of	ADP
ejpam-5594	82	12	special	special	ADJ
ejpam-5594	82	13	functions	function	NOUN
ejpam-5594	82	14	and	and	CCONJ
ejpam-5594	82	15	many	many	ADJ
ejpam-5594	82	16	applications	application	NOUN
ejpam-5594	82	17	in	in	ADP
ejpam-5594	82	18	terms	term	NOUN
ejpam-5594	82	19	of	of	ADP
ejpam-5594	82	20	special	special	ADJ
ejpam-5594	82	21	means	mean	NOUN
ejpam-5594	82	22	.	.	PUNCT
ejpam-5594	83	1	we	we	PRON
ejpam-5594	83	2	are	be	AUX
ejpam-5594	83	3	especially	especially	ADV
ejpam-5594	83	4	inspired	inspire	VERB
ejpam-5594	83	5	by	by	ADP
ejpam-5594	83	6	the	the	DET
ejpam-5594	83	7	works	work	NOUN
ejpam-5594	83	8	of	of	ADP
ejpam-5594	83	9	these	these	DET
ejpam-5594	83	10	authors	author	NOUN
ejpam-5594	83	11	[	[	X
ejpam-5594	83	12	4	4	NUM
ejpam-5594	83	13	,	,	PUNCT
ejpam-5594	83	14	11	11	NUM
ejpam-5594	83	15	,	,	PUNCT
ejpam-5594	83	16	13	13	NUM
ejpam-5594	83	17	,	,	PUNCT
ejpam-5594	83	18	20	20	NUM
ejpam-5594	83	19	,	,	PUNCT
ejpam-5594	83	20	33	33	NUM
ejpam-5594	83	21	]	]	PUNCT
ejpam-5594	83	22	to	to	PART
ejpam-5594	83	23	introduced	introduce	VERB
ejpam-5594	83	24	a	a	DET
ejpam-5594	83	25	new	new	ADJ
ejpam-5594	83	26	and	and	CCONJ
ejpam-5594	83	27	improved	improved	ADJ
ejpam-5594	83	28	form	form	NOUN
ejpam-5594	83	29	of	of	ADP
ejpam-5594	83	30	several	several	ADJ
ejpam-5594	83	31	inequalities	inequality	NOUN
ejpam-5594	83	32	,	,	PUNCT
ejpam-5594	83	33	which	which	PRON
ejpam-5594	83	34	undergo	undergo	VERB
ejpam-5594	83	35	multiple	multiple	ADJ
ejpam-5594	83	36	improvements	improvement	NOUN
ejpam-5594	83	37	and	and	CCONJ
ejpam-5594	83	38	reverses	reverse	VERB
ejpam-5594	83	39	in	in	ADP
ejpam-5594	83	40	various	various	ADJ
ejpam-5594	83	41	circumstances	circumstance	NOUN
ejpam-5594	83	42	.	.	PUNCT
ejpam-5594	84	1	this	this	DET
ejpam-5594	84	2	note	note	NOUN
ejpam-5594	84	3	is	be	AUX
ejpam-5594	84	4	structured	structure	VERB
ejpam-5594	84	5	into	into	ADP
ejpam-5594	84	6	five	five	NUM
ejpam-5594	84	7	parts	part	NOUN
ejpam-5594	84	8	,	,	PUNCT
ejpam-5594	84	9	starting	start	VERB
ejpam-5594	84	10	with	with	ADP
ejpam-5594	84	11	an	an	DET
ejpam-5594	84	12	introduction	introduction	NOUN
ejpam-5594	84	13	and	and	CCONJ
ejpam-5594	84	14	foundational	foundational	ADJ
ejpam-5594	84	15	discussion	discussion	NOUN
ejpam-5594	84	16	of	of	ADP
ejpam-5594	84	17	the	the	DET
ejpam-5594	84	18	topic	topic	NOUN
ejpam-5594	84	19	related	relate	VERB
ejpam-5594	84	20	to	to	PART
ejpam-5594	84	21	preliminary	preliminary	VERB
ejpam-5594	84	22	.	.	PUNCT
ejpam-5594	85	1	in	in	ADP
ejpam-5594	85	2	section	section	NOUN
ejpam-5594	85	3	3	3	NUM
ejpam-5594	85	4	,	,	PUNCT
ejpam-5594	85	5	we	we	PRON
ejpam-5594	85	6	develop	develop	VERB
ejpam-5594	85	7	numerous	numerous	ADJ
ejpam-5594	85	8	innovative	innovative	ADJ
ejpam-5594	85	9	versions	version	NOUN
ejpam-5594	85	10	of	of	ADP
ejpam-5594	85	11	the	the	DET
ejpam-5594	85	12	double	double	ADJ
ejpam-5594	85	13	inequality	inequality	NOUN
ejpam-5594	85	14	,	,	PUNCT
ejpam-5594	85	15	including	include	VERB
ejpam-5594	85	16	its	its	PRON
ejpam-5594	85	17	product	product	NOUN
ejpam-5594	85	18	and	and	CCONJ
ejpam-5594	85	19	weighted	weight	VERB
ejpam-5594	85	20	forms	form	NOUN
ejpam-5594	85	21	,	,	PUNCT
ejpam-5594	85	22	using	use	VERB
ejpam-5594	85	23	various	various	ADJ
ejpam-5594	85	24	other	other	ADJ
ejpam-5594	85	25	well	well	ADV
ejpam-5594	85	26	-	-	PUNCT
ejpam-5594	85	27	known	know	VERB
ejpam-5594	85	28	inequalities	inequality	NOUN
ejpam-5594	85	29	.	.	PUNCT
ejpam-5594	86	1	in	in	ADP
ejpam-5594	86	2	section	section	NOUN
ejpam-5594	86	3	4	4	NUM
ejpam-5594	86	4	,	,	PUNCT
ejpam-5594	86	5	we	we	PRON
ejpam-5594	86	6	tie	tie	VERB
ejpam-5594	86	7	our	our	PRON
ejpam-5594	86	8	conclusions	conclusion	NOUN
ejpam-5594	86	9	to	to	ADP
ejpam-5594	86	10	special	special	ADJ
ejpam-5594	86	11	means	mean	NOUN
ejpam-5594	86	12	and	and	CCONJ
ejpam-5594	86	13	demonstrate	demonstrate	VERB
ejpam-5594	86	14	their	their	PRON
ejpam-5594	86	15	applications	application	NOUN
ejpam-5594	86	16	.	.	PUNCT
ejpam-5594	87	1	finally	finally	ADV
ejpam-5594	87	2	,	,	PUNCT
ejpam-5594	87	3	in	in	ADP
ejpam-5594	87	4	section	section	NOUN
ejpam-5594	87	5	5	5	NUM
ejpam-5594	87	6	,	,	PUNCT
ejpam-5594	87	7	we	we	PRON
ejpam-5594	87	8	provide	provide	VERB
ejpam-5594	87	9	a	a	DET
ejpam-5594	87	10	precise	precise	ADJ
ejpam-5594	87	11	conclusion	conclusion	NOUN
ejpam-5594	87	12	and	and	CCONJ
ejpam-5594	87	13	possible	possible	ADJ
ejpam-5594	87	14	future	future	ADJ
ejpam-5594	87	15	work	work	NOUN
ejpam-5594	87	16	.	.	PUNCT
ejpam-5594	88	1	2	2	X
ejpam-5594	88	2	.	.	X
ejpam-5594	88	3	preliminaries	preliminary	NOUN
ejpam-5594	88	4	in	in	ADP
ejpam-5594	88	5	this	this	DET
ejpam-5594	88	6	section	section	NOUN
ejpam-5594	88	7	,	,	PUNCT
ejpam-5594	88	8	we	we	PRON
ejpam-5594	88	9	present	present	VERB
ejpam-5594	88	10	some	some	DET
ejpam-5594	88	11	well	well	ADV
ejpam-5594	88	12	-	-	PUNCT
ejpam-5594	88	13	known	know	VERB
ejpam-5594	88	14	definitions	definition	NOUN
ejpam-5594	88	15	and	and	CCONJ
ejpam-5594	88	16	outcomes	outcome	NOUN
ejpam-5594	88	17	that	that	PRON
ejpam-5594	88	18	can	can	AUX
ejpam-5594	88	19	be	be	AUX
ejpam-5594	88	20	utilized	utilize	VERB
ejpam-5594	88	21	to	to	PART
ejpam-5594	88	22	support	support	VERB
ejpam-5594	88	23	the	the	DET
ejpam-5594	88	24	paper	paper	NOUN
ejpam-5594	88	25	’s	’s	PART
ejpam-5594	88	26	core	core	NOUN
ejpam-5594	88	27	findings	finding	NOUN
ejpam-5594	88	28	.	.	PUNCT
ejpam-5594	89	1	furthermore	furthermore	ADV
ejpam-5594	89	2	,	,	PUNCT
ejpam-5594	89	3	we	we	PRON
ejpam-5594	89	4	will	will	AUX
ejpam-5594	89	5	go	go	VERB
ejpam-5594	89	6	over	over	ADP
ejpam-5594	89	7	some	some	DET
ejpam-5594	89	8	fundamental	fundamental	ADJ
ejpam-5594	89	9	ideas	idea	NOUN
ejpam-5594	89	10	relating	relate	VERB
ejpam-5594	89	11	to	to	ADP
ejpam-5594	89	12	fractional	fractional	ADJ
ejpam-5594	89	13	and	and	CCONJ
ejpam-5594	89	14	interval	interval	NOUN
ejpam-5594	89	15	calculus	calculus	NOUN
ejpam-5594	89	16	.	.	PUNCT
ejpam-5594	90	1	some	some	DET
ejpam-5594	90	2	fundamental	fundamental	ADJ
ejpam-5594	90	3	topics	topic	NOUN
ejpam-5594	90	4	are	be	AUX
ejpam-5594	90	5	not	not	PART
ejpam-5594	90	6	fully	fully	ADV
ejpam-5594	90	7	j.	j.	PROPN
ejpam-5594	90	8	e.	e.	PROPN
ejpam-5594	90	9	maćıas	maćıas	PROPN
ejpam-5594	90	10	-	-	PUNCT
ejpam-5594	90	11	dı́az	dı́az	NOUN
ejpam-5594	90	12	et	et	NOUN
ejpam-5594	90	13	al	al	PROPN
ejpam-5594	90	14	.	.	PUNCT
ejpam-5594	90	15	/	/	SYM
ejpam-5594	90	16	eur	eur	PROPN
ejpam-5594	90	17	.	.	PUNCT
ejpam-5594	91	1	j.	j.	PROPN
ejpam-5594	91	2	pure	pure	PROPN
ejpam-5594	91	3	appl	appl	PROPN
ejpam-5594	91	4	.	.	PROPN
ejpam-5594	91	5	math	math	PROPN
ejpam-5594	91	6	,	,	PUNCT
ejpam-5594	91	7	17	17	NUM
ejpam-5594	91	8	(	(	PUNCT
ejpam-5594	91	9	4	4	NUM
ejpam-5594	91	10	)	)	PUNCT
ejpam-5594	91	11	(	(	PUNCT
ejpam-5594	91	12	2024	2024	NUM
ejpam-5594	91	13	)	)	PUNCT
ejpam-5594	91	14	,	,	PUNCT
ejpam-5594	91	15	4014	4014	NUM
ejpam-5594	91	16	-	-	SYM
ejpam-5594	91	17	4049	4049	NUM
ejpam-5594	91	18	4018	4018	NUM
ejpam-5594	91	19	covered	cover	VERB
ejpam-5594	91	20	here	here	ADV
ejpam-5594	92	1	;	;	PUNCT
ejpam-5594	92	2	thus	thus	ADV
ejpam-5594	92	3	,	,	PUNCT
ejpam-5594	92	4	we	we	PRON
ejpam-5594	92	5	refer	refer	VERB
ejpam-5594	92	6	to	to	ADP
ejpam-5594	92	7	[	[	X
ejpam-5594	92	8	20	20	NUM
ejpam-5594	92	9	]	]	PUNCT
ejpam-5594	92	10	.	.	PUNCT
ejpam-5594	93	1	prior	prior	ADV
ejpam-5594	93	2	to	to	ADP
ejpam-5594	93	3	proceeding	proceeding	NOUN
ejpam-5594	93	4	,	,	PUNCT
ejpam-5594	93	5	we	we	PRON
ejpam-5594	93	6	correct	correct	VERB
ejpam-5594	93	7	a	a	DET
ejpam-5594	93	8	few	few	ADJ
ejpam-5594	93	9	notations	notation	NOUN
ejpam-5594	93	10	that	that	PRON
ejpam-5594	93	11	are	be	AUX
ejpam-5594	93	12	utilized	utilize	VERB
ejpam-5594	93	13	in	in	ADP
ejpam-5594	93	14	the	the	DET
ejpam-5594	93	15	article	article	NOUN
ejpam-5594	93	16	.	.	PUNCT
ejpam-5594	94	1	•	•	NUM
ejpam-5594	94	2	ri	ri	PROPN
ejpam-5594	94	3	:	:	PUNCT
ejpam-5594	94	4	space	space	NOUN
ejpam-5594	94	5	of	of	ADP
ejpam-5594	94	6	intervals	interval	NOUN
ejpam-5594	94	7	in	in	ADP
ejpam-5594	94	8	r	r	NOUN
ejpam-5594	94	9	;	;	PUNCT
ejpam-5594	94	10	•	•	NUM
ejpam-5594	94	11	φ	φ	NOUN
ejpam-5594	94	12	=	=	SYM
ejpam-5594	94	13	φ	φ	PROPN
ejpam-5594	94	14	:	:	PUNCT
ejpam-5594	94	15	interval	interval	NOUN
ejpam-5594	94	16	maps	map	NOUN
ejpam-5594	94	17	become	become	VERB
ejpam-5594	94	18	dysfunctional	dysfunctional	ADJ
ejpam-5594	94	19	;	;	PUNCT
ejpam-5594	94	20	•	•	NUM
ejpam-5594	94	21	⊆	⊆	NUM
ejpam-5594	94	22	:	:	PUNCT
ejpam-5594	94	23	inclusion	inclusion	NOUN
ejpam-5594	94	24	interval	interval	NOUN
ejpam-5594	94	25	order	order	NOUN
ejpam-5594	94	26	relation	relation	NOUN
ejpam-5594	94	27	;	;	PUNCT
ejpam-5594	94	28	•	•	NUM
ejpam-5594	94	29	⪯cr	⪯cr	NUM
ejpam-5594	94	30	:	:	PUNCT
ejpam-5594	94	31	cr	cr	NOUN
ejpam-5594	94	32	-	-	PUNCT
ejpam-5594	94	33	interval	interval	NOUN
ejpam-5594	94	34	order	order	NOUN
ejpam-5594	94	35	relation	relation	NOUN
ejpam-5594	94	36	;	;	PUNCT
ejpam-5594	94	37	•	•	NUM
ejpam-5594	94	38	≤	≤	NUM
ejpam-5594	94	39	:	:	PUNCT
ejpam-5594	94	40	standard	standard	ADJ
ejpam-5594	94	41	order	order	NOUN
ejpam-5594	94	42	relation	relation	NOUN
ejpam-5594	94	43	;	;	PUNCT
ejpam-5594	94	44	•	•	NUM
ejpam-5594	94	45	ivf	ivf	NOUN
ejpam-5594	94	46	:	:	PUNCT
ejpam-5594	94	47	interval	interval	NOUN
ejpam-5594	94	48	-	-	PUNCT
ejpam-5594	94	49	valued	value	VERB
ejpam-5594	94	50	function	function	NOUN
ejpam-5594	94	51	;	;	PUNCT
ejpam-5594	94	52	2.1	2.1	NUM
ejpam-5594	94	53	.	.	PUNCT
ejpam-5594	95	1	set	set	NOUN
ejpam-5594	95	2	-	-	PUNCT
ejpam-5594	95	3	valued	value	VERB
ejpam-5594	95	4	analysis	analysis	NOUN
ejpam-5594	95	5	the	the	DET
ejpam-5594	95	6	space	space	NOUN
ejpam-5594	95	7	containing	contain	VERB
ejpam-5594	95	8	all	all	DET
ejpam-5594	95	9	subsets	subset	NOUN
ejpam-5594	95	10	of	of	ADP
ejpam-5594	95	11	r	r	NOUN
ejpam-5594	95	12	in	in	ADP
ejpam-5594	95	13	n	n	CCONJ
ejpam-5594	95	14	-	-	PUNCT
ejpam-5594	95	15	dimensional	dimensional	ADJ
ejpam-5594	95	16	interval	interval	NOUN
ejpam-5594	95	17	space	space	NOUN
ejpam-5594	95	18	ri	ri	NOUN
ejpam-5594	95	19	.	.	PUNCT
ejpam-5594	96	1	ri	ri	PROPN
ejpam-5594	97	1	=	=	PUNCT
ejpam-5594	97	2	{	{	PUNCT
ejpam-5594	97	3	[	[	X
ejpam-5594	97	4	ε1	ε1	NOUN
ejpam-5594	97	5	,	,	PUNCT
ejpam-5594	97	6	ε2	ε2	PROPN
ejpam-5594	97	7	]	]	PUNCT
ejpam-5594	97	8	:	:	PUNCT
ejpam-5594	97	9	ε1	ε1	PROPN
ejpam-5594	97	10	,	,	PUNCT
ejpam-5594	97	11	ε2	ε2	PROPN
ejpam-5594	97	12	∈	∈	PROPN
ejpam-5594	97	13	r	r	NOUN
ejpam-5594	97	14	and	and	CCONJ
ejpam-5594	97	15	ε1	ε1	VERB
ejpam-5594	97	16	≤	≤	ADV
ejpam-5594	97	17	ε2	ε2	ADJ
ejpam-5594	97	18	}	}	PUNCT
ejpam-5594	97	19	,	,	PUNCT
ejpam-5594	97	20	to	to	PART
ejpam-5594	97	21	define	define	VERB
ejpam-5594	97	22	the	the	DET
ejpam-5594	97	23	hausdorff	hausdorff	NOUN
ejpam-5594	97	24	metric	metric	ADJ
ejpam-5594	97	25	in	in	ADP
ejpam-5594	97	26	ri	ri	PROPN
ejpam-5594	97	27	,	,	PUNCT
ejpam-5594	97	28	use	use	VERB
ejpam-5594	97	29	this	this	DET
ejpam-5594	97	30	formula	formula	NOUN
ejpam-5594	97	31	:	:	PUNCT
ejpam-5594	97	32	h(ε1	h(ε1	INTJ
ejpam-5594	97	33	,	,	PUNCT
ejpam-5594	97	34	ε2	ε2	PROPN
ejpam-5594	97	35	)	)	PUNCT
ejpam-5594	97	36	=	=	SYM
ejpam-5594	97	37	max{d(ε1	max{d(ε1	NOUN
ejpam-5594	97	38	,	,	PUNCT
ejpam-5594	97	39	ε2	ε2	NOUN
ejpam-5594	97	40	)	)	PUNCT
ejpam-5594	97	41	,	,	PUNCT
ejpam-5594	97	42	d(ε2	d(ε2	NOUN
ejpam-5594	97	43	,	,	PUNCT
ejpam-5594	97	44	ε1	ε1	PROPN
ejpam-5594	97	45	)	)	PUNCT
ejpam-5594	97	46	}	}	PUNCT
ejpam-5594	97	47	,	,	PUNCT
ejpam-5594	97	48	(	(	PUNCT
ejpam-5594	97	49	2	2	X
ejpam-5594	97	50	)	)	PUNCT
ejpam-5594	98	1	where	where	SCONJ
ejpam-5594	98	2	d(ε1	d(ε1	NOUN
ejpam-5594	98	3	,	,	PUNCT
ejpam-5594	98	4	ε2	ε2	PROPN
ejpam-5594	98	5	)	)	PUNCT
ejpam-5594	98	6	=	=	SYM
ejpam-5594	98	7	supν∈ε1	supν∈ε1	ADJ
ejpam-5594	98	8	d(ν	d(ν	PROPN
ejpam-5594	98	9	,	,	PUNCT
ejpam-5594	98	10	ε2	ε2	NOUN
ejpam-5594	98	11	)	)	PUNCT
ejpam-5594	98	12	,	,	PUNCT
ejpam-5594	98	13	and	and	CCONJ
ejpam-5594	98	14	d(ν	d(ν	PROPN
ejpam-5594	98	15	,	,	PUNCT
ejpam-5594	98	16	ε2	ε2	ADJ
ejpam-5594	98	17	)	)	PUNCT
ejpam-5594	99	1	=	=	SYM
ejpam-5594	99	2	minµ∈ε2	minµ∈ε2	PROPN
ejpam-5594	99	3	d(ν	d(ν	PROPN
ejpam-5594	99	4	,	,	PUNCT
ejpam-5594	99	5	µ	µ	NOUN
ejpam-5594	99	6	)	)	PUNCT
ejpam-5594	99	7	=	=	SYM
ejpam-5594	99	8	minµ∈ε2	minµ∈ε2	PROPN
ejpam-5594	99	9	|ν	|ν	NOUN
ejpam-5594	99	10	−	−	PROPN
ejpam-5594	99	11	µ|	µ|	PROPN
ejpam-5594	99	12	.	.	PUNCT
ejpam-5594	100	1	remark	remark	NOUN
ejpam-5594	100	2	1	1	NUM
ejpam-5594	100	3	.	.	PUNCT
ejpam-5594	101	1	the	the	DET
ejpam-5594	101	2	hausdorff	hausdorff	NOUN
ejpam-5594	101	3	metric	metric	NOUN
ejpam-5594	101	4	(	(	PUNCT
ejpam-5594	101	5	2	2	NUM
ejpam-5594	101	6	)	)	PUNCT
ejpam-5594	101	7	can	can	AUX
ejpam-5594	101	8	also	also	ADV
ejpam-5594	101	9	be	be	AUX
ejpam-5594	101	10	expressed	express	VERB
ejpam-5594	101	11	as	as	SCONJ
ejpam-5594	101	12	follows	follow	VERB
ejpam-5594	101	13	:	:	PUNCT
ejpam-5594	101	14	h([ε1	h([ε1	NOUN
ejpam-5594	101	15	,	,	PUNCT
ejpam-5594	101	16	ε1	ε1	PROPN
ejpam-5594	101	17	]	]	PUNCT
ejpam-5594	101	18	,	,	PUNCT
ejpam-5594	102	1	[	[	X
ejpam-5594	102	2	ε2	ε2	ADJ
ejpam-5594	102	3	,	,	PUNCT
ejpam-5594	102	4	ε2	ε2	PROPN
ejpam-5594	102	5	]	]	PUNCT
ejpam-5594	102	6	)	)	PUNCT
ejpam-5594	103	1	=	=	SYM
ejpam-5594	103	2	max{|ε1	max{|ε1	NOUN
ejpam-5594	103	3	−	−	PROPN
ejpam-5594	103	4	ε2|	ε2|	PROPN
ejpam-5594	103	5	,	,	PUNCT
ejpam-5594	103	6	|ε1	|ε1	NOUN
ejpam-5594	103	7	−	−	ADP
ejpam-5594	103	8	ε2|	ε2|	NOUN
ejpam-5594	103	9	}	}	PUNCT
ejpam-5594	103	10	.	.	PUNCT
ejpam-5594	104	1	in	in	ADP
ejpam-5594	104	2	interval	interval	NOUN
ejpam-5594	104	3	space	space	NOUN
ejpam-5594	104	4	,	,	PUNCT
ejpam-5594	104	5	we	we	PRON
ejpam-5594	104	6	call	call	VERB
ejpam-5594	104	7	this	this	PRON
ejpam-5594	104	8	the	the	DET
ejpam-5594	104	9	moore	moore	PROPN
ejpam-5594	104	10	metric	metric	PROPN
ejpam-5594	104	11	.	.	PUNCT
ejpam-5594	105	1	for	for	ADP
ejpam-5594	105	2	instance	instance	NOUN
ejpam-5594	105	3	,	,	PUNCT
ejpam-5594	105	4	if	if	SCONJ
ejpam-5594	105	5	ζ1	ζ1	NUM
ejpam-5594	105	6	=	=	PUNCT
ejpam-5594	106	1	[	[	X
ejpam-5594	106	2	ε1	ε1	PROPN
ejpam-5594	106	3	,	,	PUNCT
ejpam-5594	106	4	ε1	ε1	PROPN
ejpam-5594	106	5	]	]	PUNCT
ejpam-5594	106	6	and	and	CCONJ
ejpam-5594	106	7	ζ2	ζ2	NOUN
ejpam-5594	106	8	=	=	SYM
ejpam-5594	107	1	[	[	X
ejpam-5594	107	2	ε2	ε2	ADJ
ejpam-5594	107	3	,	,	PUNCT
ejpam-5594	107	4	ε2	ε2	PROPN
ejpam-5594	107	5	]	]	PUNCT
ejpam-5594	107	6	are	be	AUX
ejpam-5594	107	7	two	two	NUM
ejpam-5594	107	8	closed	closed	ADJ
ejpam-5594	107	9	intervals	interval	NOUN
ejpam-5594	107	10	,	,	PUNCT
ejpam-5594	107	11	then	then	ADV
ejpam-5594	107	12	the	the	DET
ejpam-5594	107	13	minkowski	minkowski	ADJ
ejpam-5594	107	14	sum	sum	NOUN
ejpam-5594	107	15	,	,	PUNCT
ejpam-5594	107	16	scalar	scalar	ADJ
ejpam-5594	107	17	multiplication	multiplication	NOUN
ejpam-5594	107	18	,	,	PUNCT
ejpam-5594	107	19	and	and	CCONJ
ejpam-5594	107	20	difference	difference	NOUN
ejpam-5594	107	21	are	be	AUX
ejpam-5594	107	22	defined	define	VERB
ejpam-5594	107	23	as	as	SCONJ
ejpam-5594	107	24	follows	follow	VERB
ejpam-5594	107	25	:	:	PUNCT
ejpam-5594	107	26	ζ1	ζ1	NOUN
ejpam-5594	107	27	+	+	CCONJ
ejpam-5594	107	28	ζ2	ζ2	NOUN
ejpam-5594	107	29	=	=	SYM
ejpam-5594	107	30	{	{	PUNCT
ejpam-5594	107	31	ε1	ε1	NOUN
ejpam-5594	107	32	+	+	CCONJ
ejpam-5594	107	33	ε2	ε2	ADJ
ejpam-5594	107	34	|	|	ADV
ejpam-5594	107	35	ε1	ε1	PROPN
ejpam-5594	107	36	∈	∈	PROPN
ejpam-5594	107	37	ζ1	ζ1	NOUN
ejpam-5594	107	38	,	,	PUNCT
ejpam-5594	107	39	ε2	ε2	PROPN
ejpam-5594	107	40	∈	∈	NOUN
ejpam-5594	107	41	ζ2	ζ2	NOUN
ejpam-5594	107	42	}	}	PUNCT
ejpam-5594	107	43	and	and	CCONJ
ejpam-5594	107	44	γζ1	γζ1	NOUN
ejpam-5594	107	45	=	=	PUNCT
ejpam-5594	107	46	{	{	PUNCT
ejpam-5594	107	47	γε1	γε1	NOUN
ejpam-5594	107	48	|	|	ADV
ejpam-5594	107	49	ε1	ε1	PROPN
ejpam-5594	107	50	∈	∈	PROPN
ejpam-5594	107	51	ζ1	ζ1	PROPN
ejpam-5594	107	52	}	}	PUNCT
ejpam-5594	107	53	.	.	PUNCT
ejpam-5594	108	1	and	and	CCONJ
ejpam-5594	108	2	ζ1	ζ1	NOUN
ejpam-5594	108	3	−	−	NOUN
ejpam-5594	108	4	ζ2	ζ2	NOUN
ejpam-5594	108	5	=	=	PUNCT
ejpam-5594	109	1	[	[	X
ejpam-5594	109	2	ε1	ε1	NOUN
ejpam-5594	109	3	−	−	PROPN
ejpam-5594	109	4	ε2	ε2	PROPN
ejpam-5594	109	5	,	,	PUNCT
ejpam-5594	109	6	ε1	ε1	VERB
ejpam-5594	109	7	−	−	PROPN
ejpam-5594	109	8	ε2	ε2	PROPN
ejpam-5594	109	9	]	]	PUNCT
ejpam-5594	109	10	,	,	PUNCT
ejpam-5594	109	11	with	with	ADP
ejpam-5594	109	12	the	the	DET
ejpam-5594	109	13	product	product	NOUN
ejpam-5594	109	14	ζ1	ζ1	NOUN
ejpam-5594	109	15	·	·	PUNCT
ejpam-5594	109	16	ζ2	ζ2	NOUN
ejpam-5594	109	17	=	=	SYM
ejpam-5594	110	1	[	[	X
ejpam-5594	110	2	min{ε1ε2	min{ε1ε2	PROPN
ejpam-5594	110	3	,	,	PUNCT
ejpam-5594	110	4	ε1ε2	ε1ε2	NOUN
ejpam-5594	110	5	,	,	PUNCT
ejpam-5594	110	6	ε1ε2	ε1ε2	NOUN
ejpam-5594	110	7	,	,	PUNCT
ejpam-5594	110	8	ε1ε2	ε1ε2	NOUN
ejpam-5594	110	9	}	}	PUNCT
ejpam-5594	110	10	,	,	PUNCT
ejpam-5594	110	11	sup{ε1ε2	sup{ε1ε2	PROPN
ejpam-5594	110	12	,	,	PUNCT
ejpam-5594	110	13	ε1ε2	ε1ε2	NOUN
ejpam-5594	110	14	,	,	PUNCT
ejpam-5594	110	15	ε1ε2	ε1ε2	NOUN
ejpam-5594	110	16	,	,	PUNCT
ejpam-5594	110	17	ε1ε2	ε1ε2	NOUN
ejpam-5594	110	18	}	}	PUNCT
ejpam-5594	110	19	]	]	PUNCT
ejpam-5594	110	20	,	,	PUNCT
ejpam-5594	110	21	and	and	CCONJ
ejpam-5594	110	22	the	the	DET
ejpam-5594	110	23	division	division	NOUN
ejpam-5594	110	24	ζ1	ζ1	NOUN
ejpam-5594	110	25	ζ2	ζ2	NOUN
ejpam-5594	110	26	=	=	SYM
ejpam-5594	110	27	[	[	PUNCT
ejpam-5594	110	28	min	min	NOUN
ejpam-5594	110	29	{	{	PUNCT
ejpam-5594	110	30	ε1	ε1	PROPN
ejpam-5594	110	31	ε2	ε2	PROPN
ejpam-5594	110	32	,	,	PUNCT
ejpam-5594	110	33	ε1	ε1	VERB
ejpam-5594	110	34	ε2	ε2	ADV
ejpam-5594	110	35	,	,	PUNCT
ejpam-5594	110	36	ε1	ε1	VERB
ejpam-5594	110	37	ε2	ε2	ADV
ejpam-5594	110	38	,	,	PUNCT
ejpam-5594	110	39	ε1	ε1	VERB
ejpam-5594	110	40	ε2	ε2	ADV
ejpam-5594	110	41	}	}	PUNCT
ejpam-5594	110	42	,	,	PUNCT
ejpam-5594	110	43	max	max	PROPN
ejpam-5594	110	44	{	{	PUNCT
ejpam-5594	110	45	ε1	ε1	VERB
ejpam-5594	110	46	ε2	ε2	PROPN
ejpam-5594	110	47	,	,	PUNCT
ejpam-5594	110	48	ε1	ε1	VERB
ejpam-5594	110	49	ε2	ε2	ADV
ejpam-5594	110	50	,	,	PUNCT
ejpam-5594	110	51	ε1	ε1	VERB
ejpam-5594	110	52	ε2	ε2	ADV
ejpam-5594	110	53	,	,	PUNCT
ejpam-5594	110	54	ε1	ε1	VERB
ejpam-5594	110	55	ε2	ε2	ADV
ejpam-5594	110	56	}	}	PUNCT
ejpam-5594	110	57	]	]	PUNCT
ejpam-5594	110	58	,	,	PUNCT
ejpam-5594	110	59	where	where	SCONJ
ejpam-5594	110	60	0	0	NUM
ejpam-5594	110	61	/∈	/∈	NOUN
ejpam-5594	110	62	ζ2	ζ2	NOUN
ejpam-5594	110	63	.	.	PUNCT
ejpam-5594	111	1	j.	j.	PROPN
ejpam-5594	111	2	e.	e.	PROPN
ejpam-5594	111	3	maćıas	maćıas	PROPN
ejpam-5594	111	4	-	-	PUNCT
ejpam-5594	111	5	dı́az	dı́az	NOUN
ejpam-5594	111	6	et	et	NOUN
ejpam-5594	111	7	al	al	PROPN
ejpam-5594	111	8	.	.	PUNCT
ejpam-5594	111	9	/	/	SYM
ejpam-5594	111	10	eur	eur	PROPN
ejpam-5594	111	11	.	.	PUNCT
ejpam-5594	112	1	j.	j.	PROPN
ejpam-5594	112	2	pure	pure	PROPN
ejpam-5594	112	3	appl	appl	PROPN
ejpam-5594	112	4	.	.	PROPN
ejpam-5594	112	5	math	math	PROPN
ejpam-5594	112	6	,	,	PUNCT
ejpam-5594	112	7	17	17	NUM
ejpam-5594	112	8	(	(	PUNCT
ejpam-5594	112	9	4	4	NUM
ejpam-5594	112	10	)	)	PUNCT
ejpam-5594	112	11	(	(	PUNCT
ejpam-5594	112	12	2024	2024	NUM
ejpam-5594	112	13	)	)	PUNCT
ejpam-5594	112	14	,	,	PUNCT
ejpam-5594	112	15	4014	4014	NUM
ejpam-5594	112	16	-	-	SYM
ejpam-5594	112	17	4049	4049	NUM
ejpam-5594	112	18	4019	4019	NUM
ejpam-5594	112	19	definition	definition	NOUN
ejpam-5594	112	20	1	1	NUM
ejpam-5594	112	21	(	(	PUNCT
ejpam-5594	112	22	see	see	VERB
ejpam-5594	112	23	[	[	X
ejpam-5594	112	24	4	4	NUM
ejpam-5594	112	25	]	]	NUM
ejpam-5594	112	26	)	)	PUNCT
ejpam-5594	112	27	.	.	PUNCT
ejpam-5594	113	1	for	for	ADP
ejpam-5594	113	2	any	any	DET
ejpam-5594	113	3	two	two	NUM
ejpam-5594	113	4	intervals	interval	NOUN
ejpam-5594	113	5	the	the	DET
ejpam-5594	113	6	center	center	ADJ
ejpam-5594	113	7	-	-	PUNCT
ejpam-5594	113	8	radius	radius	NOUN
ejpam-5594	113	9	order	order	NOUN
ejpam-5594	113	10	relation	relation	NOUN
ejpam-5594	113	11	is	be	AUX
ejpam-5594	113	12	defined	define	VERB
ejpam-5594	113	13	as	as	ADP
ejpam-5594	113	14	ζ1	ζ1	NOUN
ejpam-5594	113	15	=	=	PUNCT
ejpam-5594	114	1	[	[	X
ejpam-5594	114	2	ε1	ε1	NOUN
ejpam-5594	114	3	,	,	PUNCT
ejpam-5594	114	4	ε2	ε2	PROPN
ejpam-5594	114	5	]	]	X
ejpam-5594	114	6	=	=	SYM
ejpam-5594	115	1	⟨ωc	⟨ωc	PROPN
ejpam-5594	115	2	,	,	PUNCT
ejpam-5594	115	3	ωr⟩	ωr⟩	NUM
ejpam-5594	115	4	=	=	SYM
ejpam-5594	115	5	〈	〈	PROPN
ejpam-5594	115	6	ε1+ε2	ε1+ε2	ADJ
ejpam-5594	115	7	2	2	NUM
ejpam-5594	115	8	,	,	PUNCT
ejpam-5594	115	9	ε2−ε1	ε2−ε1	PROPN
ejpam-5594	115	10	2	2	NUM
ejpam-5594	115	11	〉	〉	NOUN
ejpam-5594	115	12	,	,	PUNCT
ejpam-5594	115	13	ζ2	ζ2	NOUN
ejpam-5594	115	14	=	=	PUNCT
ejpam-5594	116	1	[	[	X
ejpam-5594	116	2	ε1	ε1	NOUN
ejpam-5594	116	3	,	,	PUNCT
ejpam-5594	116	4	ε2	ε2	PROPN
ejpam-5594	116	5	]	]	X
ejpam-5594	116	6	=	=	SYM
ejpam-5594	117	1	⟨ωc	⟨ωc	NUM
ejpam-5594	117	2	,	,	PUNCT
ejpam-5594	117	3	ωr⟩	ωr⟩	NUM
ejpam-5594	117	4	=	=	SYM
ejpam-5594	117	5	〈	〈	PROPN
ejpam-5594	117	6	ε1+ε2	ε1+ε2	ADJ
ejpam-5594	117	7	2	2	NUM
ejpam-5594	117	8	,	,	PUNCT
ejpam-5594	117	9	ε2−ε1	ε2−ε1	PROPN
ejpam-5594	117	10	2	2	NUM
ejpam-5594	117	11	〉	〉	NOUN
ejpam-5594	117	12	,	,	PUNCT
ejpam-5594	117	13	where	where	SCONJ
ejpam-5594	117	14	ζ1	ζ1	PROPN
ejpam-5594	117	15	⪯cr	⪯cr	VERB
ejpam-5594	117	16	ζ2	ζ2	NOUN
ejpam-5594	117	17	⇐	⇐	ADJ
ejpam-5594	117	18	⇒	⇒	NOUN
ejpam-5594	117	19	{	{	PUNCT
ejpam-5594	117	20	ωc	ωc	ADP
ejpam-5594	117	21	<	<	X
ejpam-5594	117	22	ωc	ωc	X
ejpam-5594	117	23	,	,	PUNCT
ejpam-5594	117	24	if	if	SCONJ
ejpam-5594	117	25	ωc	ωc	ADP
ejpam-5594	117	26	̸=	̸=	PROPN
ejpam-5594	117	27	ωc	ωc	NUM
ejpam-5594	117	28	;	;	PUNCT
ejpam-5594	117	29	ωr	ωr	NUM
ejpam-5594	117	30	≤	≤	NUM
ejpam-5594	117	31	ωr	ωr	VERB
ejpam-5594	117	32	,	,	PUNCT
ejpam-5594	117	33	if	if	SCONJ
ejpam-5594	117	34	ωr	ωr	VERB
ejpam-5594	117	35	=	=	PUNCT
ejpam-5594	117	36	ωr	ωr	NOUN
ejpam-5594	117	37	.	.	PUNCT
ejpam-5594	118	1	the	the	DET
ejpam-5594	118	2	relation	relation	NOUN
ejpam-5594	118	3	⪯cr	⪯cr	NUM
ejpam-5594	118	4	satisfies	satisfy	VERB
ejpam-5594	118	5	the	the	DET
ejpam-5594	118	6	following	follow	VERB
ejpam-5594	118	7	relational	relational	ADJ
ejpam-5594	118	8	properties	property	NOUN
ejpam-5594	118	9	for	for	ADP
ejpam-5594	118	10	any	any	DET
ejpam-5594	118	11	three	three	NUM
ejpam-5594	118	12	intervals	interval	NOUN
ejpam-5594	118	13	ζ1	ζ1	NOUN
ejpam-5594	118	14	=	=	PUNCT
ejpam-5594	119	1	[	[	X
ejpam-5594	119	2	ε1	ε1	NOUN
ejpam-5594	119	3	,	,	PUNCT
ejpam-5594	119	4	ε2	ε2	PROPN
ejpam-5594	119	5	]	]	X
ejpam-5594	119	6	=	=	SYM
ejpam-5594	120	1	⟨ωc	⟨ωc	NUM
ejpam-5594	120	2	,	,	PUNCT
ejpam-5594	120	3	ωr⟩	ωr⟩	NOUN
ejpam-5594	120	4	,	,	PUNCT
ejpam-5594	120	5	ζ2	ζ2	NOUN
ejpam-5594	120	6	=	=	PUNCT
ejpam-5594	121	1	[	[	X
ejpam-5594	121	2	ε1	ε1	NOUN
ejpam-5594	121	3	,	,	PUNCT
ejpam-5594	121	4	ε2	ε2	PROPN
ejpam-5594	121	5	]	]	X
ejpam-5594	121	6	=	=	SYM
ejpam-5594	122	1	⟨ωc	⟨ωc	NUM
ejpam-5594	122	2	,	,	PUNCT
ejpam-5594	122	3	ωr⟩	ωr⟩	NOUN
ejpam-5594	122	4	and	and	CCONJ
ejpam-5594	122	5	ζ3	ζ3	NOUN
ejpam-5594	122	6	=	=	PUNCT
ejpam-5594	123	1	[	[	X
ejpam-5594	123	2	η1	η1	NOUN
ejpam-5594	123	3	,	,	PUNCT
ejpam-5594	123	4	η2	η2	X
ejpam-5594	123	5	]	]	PUNCT
ejpam-5594	123	6	=	=	SYM
ejpam-5594	123	7	⟨ηc	⟨ηc	PROPN
ejpam-5594	123	8	,	,	PUNCT
ejpam-5594	123	9	ηr⟩	ηr⟩	PUNCT
ejpam-5594	123	10	:	:	PUNCT
ejpam-5594	123	11	reflexivity	reflexivity	NOUN
ejpam-5594	123	12	:	:	PUNCT
ejpam-5594	123	13	ζ1	ζ1	PROPN
ejpam-5594	123	14	⪯cr	⪯cr	NUM
ejpam-5594	123	15	ζ1	ζ1	PROPN
ejpam-5594	123	16	.	.	PUNCT
ejpam-5594	124	1	anti	anti	ADJ
ejpam-5594	124	2	-	-	NOUN
ejpam-5594	124	3	symmetry	symmetry	ADJ
ejpam-5594	124	4	:	:	PUNCT
ejpam-5594	124	5	ζ1	ζ1	PROPN
ejpam-5594	124	6	⪯cr	⪯cr	NUM
ejpam-5594	124	7	ζ2	ζ2	NOUN
ejpam-5594	124	8	and	and	CCONJ
ejpam-5594	124	9	ζ2	ζ2	NOUN
ejpam-5594	124	10	⪯cr	⪯cr	NUM
ejpam-5594	124	11	ζ1	ζ1	NOUN
ejpam-5594	124	12	.	.	PUNCT
ejpam-5594	125	1	transitivity	transitivity	NOUN
ejpam-5594	125	2	:	:	PUNCT
ejpam-5594	125	3	ζ1	ζ1	PROPN
ejpam-5594	125	4	⪯cr	⪯cr	NUM
ejpam-5594	125	5	ζ2	ζ2	NOUN
ejpam-5594	125	6	and	and	CCONJ
ejpam-5594	125	7	ζ2	ζ2	NOUN
ejpam-5594	125	8	⪯cr	⪯cr	NUM
ejpam-5594	125	9	ζ3	ζ3	NOUN
ejpam-5594	125	10	then	then	ADV
ejpam-5594	125	11	ζ1	ζ1	PROPN
ejpam-5594	125	12	⪯cr	⪯cr	VERB
ejpam-5594	125	13	ζ3	ζ3	NOUN
ejpam-5594	125	14	.	.	PUNCT
ejpam-5594	126	1	comparability	comparability	NOUN
ejpam-5594	126	2	:	:	PUNCT
ejpam-5594	126	3	ζ2	ζ2	NOUN
ejpam-5594	126	4	⪯cr	⪯cr	NUM
ejpam-5594	126	5	ζ3	ζ3	NOUN
ejpam-5594	126	6	or	or	CCONJ
ejpam-5594	126	7	ζ3	ζ3	NOUN
ejpam-5594	126	8	⪯cr	⪯cr	NUM
ejpam-5594	126	9	ζ2	ζ2	NOUN
ejpam-5594	126	10	.	.	PUNCT
ejpam-5594	127	1	theorem	theorem	NOUN
ejpam-5594	127	2	4	4	NUM
ejpam-5594	127	3	(	(	PUNCT
ejpam-5594	127	4	see	see	VERB
ejpam-5594	127	5	[	[	X
ejpam-5594	127	6	4	4	NUM
ejpam-5594	127	7	]	]	NUM
ejpam-5594	127	8	)	)	PUNCT
ejpam-5594	127	9	.	.	PUNCT
ejpam-5594	128	1	let	let	VERB
ejpam-5594	128	2	φ	φ	NOUN
ejpam-5594	128	3	:	:	PUNCT
ejpam-5594	129	1	[	[	X
ejpam-5594	129	2	ε1	ε1	NOUN
ejpam-5594	129	3	,	,	PUNCT
ejpam-5594	129	4	ε2	ε2	PROPN
ejpam-5594	129	5	]	]	PUNCT
ejpam-5594	129	6	→	→	SYM
ejpam-5594	129	7	r+	r+	PUNCT
ejpam-5594	129	8	i	i	PRON
ejpam-5594	129	9	be	be	VERB
ejpam-5594	129	10	an	an	DET
ejpam-5594	129	11	interval	interval	NOUN
ejpam-5594	129	12	set	set	NOUN
ejpam-5594	129	13	-	-	PUNCT
ejpam-5594	129	14	valued	value	VERB
ejpam-5594	129	15	map	map	NOUN
ejpam-5594	129	16	given	give	VERB
ejpam-5594	129	17	by	by	ADP
ejpam-5594	129	18	φ	φ	PROPN
ejpam-5594	129	19	=	=	PUNCT
ejpam-5594	130	1	[	[	X
ejpam-5594	130	2	φ	φ	NOUN
ejpam-5594	130	3	,	,	PUNCT
ejpam-5594	130	4	φ̄	φ̄	PROPN
ejpam-5594	130	5	]	]	PUNCT
ejpam-5594	130	6	.	.	PUNCT
ejpam-5594	131	1	then	then	ADV
ejpam-5594	131	2	the	the	DET
ejpam-5594	131	3	φ	φ	PROPN
ejpam-5594	131	4	is	be	AUX
ejpam-5594	131	5	riemann	riemann	PROPN
ejpam-5594	131	6	integrable	integrable	ADJ
ejpam-5594	131	7	on	on	ADP
ejpam-5594	131	8	[	[	X
ejpam-5594	131	9	ε1	ε1	NOUN
ejpam-5594	131	10	,	,	PUNCT
ejpam-5594	131	11	ε2	ε2	PROPN
ejpam-5594	131	12	]	]	PUNCT
ejpam-5594	131	13	iff	iff	PROPN
ejpam-5594	131	14	φ	φ	PROPN
ejpam-5594	131	15	and	and	CCONJ
ejpam-5594	131	16	φ̄	φ̄	PROPN
ejpam-5594	131	17	are	be	AUX
ejpam-5594	131	18	riemann	riemann	PROPN
ejpam-5594	131	19	integrable	integrable	ADJ
ejpam-5594	131	20	on	on	ADP
ejpam-5594	131	21	[	[	X
ejpam-5594	131	22	ε1	ε1	NOUN
ejpam-5594	131	23	,	,	PUNCT
ejpam-5594	131	24	ε2	ε2	PROPN
ejpam-5594	131	25	]	]	PUNCT
ejpam-5594	132	1	and∫	and∫	PROPN
ejpam-5594	132	2	ε2	ε2	PROPN
ejpam-5594	132	3	ε1	ε1	VERB
ejpam-5594	132	4	φ(e)de	φ(e)de	VERB
ejpam-5594	132	5	=	=	SYM
ejpam-5594	133	1	[	[	X
ejpam-5594	133	2	∫	∫	X
ejpam-5594	133	3	ε2	ε2	PROPN
ejpam-5594	133	4	ε1	ε1	VERB
ejpam-5594	133	5	φ(e)de	φ(e)de	NOUN
ejpam-5594	133	6	,	,	PUNCT
ejpam-5594	133	7	∫	∫	PROPN
ejpam-5594	133	8	ε2	ε2	PROPN
ejpam-5594	133	9	ε1	ε1	VERB
ejpam-5594	133	10	φ̄(e)de	φ̄(e)de	PROPN
ejpam-5594	133	11	]	]	PUNCT
ejpam-5594	133	12	we	we	PRON
ejpam-5594	133	13	shall	shall	AUX
ejpam-5594	133	14	refer	refer	VERB
ejpam-5594	133	15	to	to	ADP
ejpam-5594	133	16	the	the	DET
ejpam-5594	133	17	set	set	NOUN
ejpam-5594	133	18	of	of	ADP
ejpam-5594	133	19	all	all	DET
ejpam-5594	133	20	riemann	riemann	PROPN
ejpam-5594	133	21	integrable	integrable	ADJ
ejpam-5594	133	22	interval	interval	NOUN
ejpam-5594	133	23	-	-	PUNCT
ejpam-5594	133	24	valued	value	VERB
ejpam-5594	133	25	maps	map	NOUN
ejpam-5594	133	26	on	on	ADP
ejpam-5594	133	27	[	[	X
ejpam-5594	133	28	ε1	ε1	NOUN
ejpam-5594	133	29	,	,	PUNCT
ejpam-5594	133	30	ε2	ε2	PROPN
ejpam-5594	133	31	]	]	PUNCT
ejpam-5594	133	32	as	as	ADP
ejpam-5594	133	33	ir([ε1,ε2	ir([ε1,ε2	PROPN
ejpam-5594	133	34	]	]	X
ejpam-5594	133	35	)	)	PUNCT
ejpam-5594	133	36	.	.	PUNCT
ejpam-5594	134	1	theorem	theorem	NOUN
ejpam-5594	134	2	5	5	NUM
ejpam-5594	134	3	(	(	PUNCT
ejpam-5594	134	4	see	see	VERB
ejpam-5594	134	5	[	[	X
ejpam-5594	134	6	4	4	NUM
ejpam-5594	134	7	]	]	NUM
ejpam-5594	134	8	)	)	PUNCT
ejpam-5594	134	9	.	.	PUNCT
ejpam-5594	135	1	let	let	VERB
ejpam-5594	135	2	φ	φ	NUM
ejpam-5594	135	3	,	,	PUNCT
ejpam-5594	135	4	h	h	NOUN
ejpam-5594	135	5	:	:	PUNCT
ejpam-5594	136	1	[	[	X
ejpam-5594	136	2	ε1	ε1	NOUN
ejpam-5594	136	3	,	,	PUNCT
ejpam-5594	136	4	ε2	ε2	PROPN
ejpam-5594	136	5	]	]	PUNCT
ejpam-5594	136	6	→	→	SYM
ejpam-5594	136	7	r+	r+	NOUN
ejpam-5594	136	8	i	i	PRON
ejpam-5594	136	9	given	give	VERB
ejpam-5594	136	10	by	by	ADP
ejpam-5594	136	11	φ	φ	PROPN
ejpam-5594	136	12	=	=	PUNCT
ejpam-5594	137	1	[	[	X
ejpam-5594	137	2	φ	φ	NOUN
ejpam-5594	137	3	,	,	PUNCT
ejpam-5594	137	4	φ̄	φ̄	PROPN
ejpam-5594	137	5	]	]	PUNCT
ejpam-5594	137	6	,	,	PUNCT
ejpam-5594	137	7	and	and	CCONJ
ejpam-5594	137	8	h	h	NOUN
ejpam-5594	138	1	=	=	PUNCT
ejpam-5594	139	1	[	[	X
ejpam-5594	139	2	h	h	NOUN
ejpam-5594	139	3	,	,	PUNCT
ejpam-5594	139	4	h̄	h̄	X
ejpam-5594	139	5	]	]	PUNCT
ejpam-5594	139	6	.	.	PUNCT
ejpam-5594	140	1	if	if	SCONJ
ejpam-5594	140	2	φ	φ	PROPN
ejpam-5594	140	3	,	,	PUNCT
ejpam-5594	140	4	h	h	PROPN
ejpam-5594	140	5	∈	∈	PROPN
ejpam-5594	140	6	ir([ε1,ε2	ir([ε1,ε2	PROPN
ejpam-5594	140	7	]	]	PUNCT
ejpam-5594	140	8	)	)	PUNCT
ejpam-5594	140	9	,	,	PUNCT
ejpam-5594	140	10	and	and	CCONJ
ejpam-5594	140	11	φ(e	φ(e	NUM
ejpam-5594	140	12	)	)	PUNCT
ejpam-5594	140	13	⪯cr	⪯cr	NUM
ejpam-5594	140	14	h	h	NOUN
ejpam-5594	140	15	(	(	PUNCT
ejpam-5594	140	16	e	e	NOUN
ejpam-5594	140	17	)	)	PUNCT
ejpam-5594	140	18	,	,	PUNCT
ejpam-5594	140	19	∀	∀	X
ejpam-5594	140	20	e	e	X
ejpam-5594	140	21	∈	∈	PROPN
ejpam-5594	141	1	[	[	X
ejpam-5594	141	2	ε1	ε1	NOUN
ejpam-5594	141	3	,	,	PUNCT
ejpam-5594	141	4	ε2	ε2	PROPN
ejpam-5594	141	5	]	]	PUNCT
ejpam-5594	141	6	,	,	PUNCT
ejpam-5594	141	7	then∫	then∫	NOUN
ejpam-5594	141	8	ε2	ε2	PROPN
ejpam-5594	141	9	ε1	ε1	VERB
ejpam-5594	141	10	φ(e)de	φ(e)de	NOUN
ejpam-5594	141	11	⪯cr	⪯cr	NUM
ejpam-5594	141	12	∫	∫	PROPN
ejpam-5594	141	13	ε2	ε2	PROPN
ejpam-5594	141	14	ε1	ε1	PROPN
ejpam-5594	141	15	h	h	NOUN
ejpam-5594	141	16	(	(	PUNCT
ejpam-5594	141	17	e)de	e)de	PROPN
ejpam-5594	141	18	.	.	PROPN
ejpam-5594	141	19	example	example	NOUN
ejpam-5594	142	1	1	1	X
ejpam-5594	142	2	.	.	X
ejpam-5594	143	1	consider	consider	VERB
ejpam-5594	143	2	φ	φ	NOUN
ejpam-5594	143	3	=	=	PUNCT
ejpam-5594	144	1	[	[	X
ejpam-5594	144	2	v	v	X
ejpam-5594	144	3	+	+	NUM
ejpam-5594	144	4	1	1	NUM
ejpam-5594	144	5	,	,	PUNCT
ejpam-5594	144	6	2v	2v	PROPN
ejpam-5594	144	7	+	+	CCONJ
ejpam-5594	144	8	2	2	X
ejpam-5594	144	9	]	]	PUNCT
ejpam-5594	144	10	and	and	CCONJ
ejpam-5594	144	11	h	h	NOUN
ejpam-5594	144	12	=	=	PUNCT
ejpam-5594	145	1	[	[	X
ejpam-5594	145	2	v2	v2	X
ejpam-5594	145	3	+	+	NOUN
ejpam-5594	145	4	2	2	NUM
ejpam-5594	145	5	,	,	PUNCT
ejpam-5594	145	6	3v	3v	NUM
ejpam-5594	145	7	+	+	CCONJ
ejpam-5594	145	8	2	2	NUM
ejpam-5594	145	9	]	]	PUNCT
ejpam-5594	145	10	,	,	PUNCT
ejpam-5594	145	11	∀	∀	X
ejpam-5594	145	12	v	v	ADP
ejpam-5594	145	13	∈	∈	PROPN
ejpam-5594	146	1	[	[	X
ejpam-5594	146	2	0	0	NUM
ejpam-5594	146	3	,	,	PUNCT
ejpam-5594	146	4	1	1	NUM
ejpam-5594	146	5	]	]	PUNCT
ejpam-5594	146	6	.	.	PUNCT
ejpam-5594	147	1	φc	φc	NOUN
ejpam-5594	147	2	=	=	NOUN
ejpam-5594	147	3	3v	3v	NUM
ejpam-5594	148	1	+	+	CCONJ
ejpam-5594	148	2	3	3	NUM
ejpam-5594	148	3	2	2	NUM
ejpam-5594	148	4	,	,	PUNCT
ejpam-5594	148	5	φr	φr	ADP
ejpam-5594	148	6	=	=	SYM
ejpam-5594	148	7	v	v	PROPN
ejpam-5594	148	8	+	+	CCONJ
ejpam-5594	148	9	1	1	NUM
ejpam-5594	148	10	2	2	NUM
ejpam-5594	148	11	,	,	PUNCT
ejpam-5594	148	12	hc	hc	NOUN
ejpam-5594	148	13	=	=	SYM
ejpam-5594	148	14	v2	v2	PROPN
ejpam-5594	148	15	+	+	CCONJ
ejpam-5594	148	16	3v	3v	NUM
ejpam-5594	148	17	+	+	CCONJ
ejpam-5594	148	18	4	4	NUM
ejpam-5594	148	19	2	2	NUM
ejpam-5594	148	20	and	and	CCONJ
ejpam-5594	148	21	hr	hr	NOUN
ejpam-5594	148	22	=	=	SYM
ejpam-5594	148	23	3v	3v	NUM
ejpam-5594	149	1	−	−	PROPN
ejpam-5594	149	2	v2	v2	NOUN
ejpam-5594	149	3	2	2	NUM
ejpam-5594	149	4	.	.	PUNCT
ejpam-5594	150	1	from	from	ADP
ejpam-5594	150	2	definition	definition	NOUN
ejpam-5594	150	3	1	1	NUM
ejpam-5594	150	4	,	,	PUNCT
ejpam-5594	150	5	we	we	PRON
ejpam-5594	150	6	have	have	AUX
ejpam-5594	150	7	φ(v	φ(v	NOUN
ejpam-5594	150	8	)	)	PUNCT
ejpam-5594	150	9	⪯cr	⪯cr	NUM
ejpam-5594	150	10	h	h	NOUN
ejpam-5594	150	11	(	(	PUNCT
ejpam-5594	150	12	v	v	NOUN
ejpam-5594	150	13	)	)	PUNCT
ejpam-5594	150	14	,	,	PUNCT
ejpam-5594	150	15	∀	∀	X
ejpam-5594	150	16	v	v	ADP
ejpam-5594	150	17	∈	∈	PROPN
ejpam-5594	151	1	[	[	X
ejpam-5594	151	2	0	0	NUM
ejpam-5594	151	3	,	,	PUNCT
ejpam-5594	151	4	1	1	NUM
ejpam-5594	151	5	]	]	PUNCT
ejpam-5594	151	6	.	.	PUNCT
ejpam-5594	152	1	since	since	SCONJ
ejpam-5594	152	2	,	,	PUNCT
ejpam-5594	152	3	∫	∫	PROPN
ejpam-5594	152	4	1	1	NUM
ejpam-5594	152	5	0	0	NUM
ejpam-5594	153	1	[	[	X
ejpam-5594	153	2	v	v	X
ejpam-5594	153	3	+	+	NUM
ejpam-5594	153	4	1	1	NUM
ejpam-5594	153	5	,	,	PUNCT
ejpam-5594	153	6	2v	2v	PROPN
ejpam-5594	153	7	+	+	CCONJ
ejpam-5594	153	8	2]dv	2]dv	NUM
ejpam-5594	153	9	=	=	PUNCT
ejpam-5594	154	1	[	[	PUNCT
ejpam-5594	154	2	3	3	NUM
ejpam-5594	154	3	2	2	NUM
ejpam-5594	154	4	,	,	PUNCT
ejpam-5594	154	5	3	3	NUM
ejpam-5594	154	6	]	]	PUNCT
ejpam-5594	154	7	.	.	PUNCT
ejpam-5594	155	1	and	and	CCONJ
ejpam-5594	155	2	∫	∫	PROPN
ejpam-5594	155	3	1	1	NUM
ejpam-5594	155	4	0	0	NUM
ejpam-5594	156	1	[	[	X
ejpam-5594	156	2	v2	v2	X
ejpam-5594	156	3	+	+	CCONJ
ejpam-5594	156	4	2	2	NUM
ejpam-5594	156	5	,	,	PUNCT
ejpam-5594	156	6	2v	2v	PROPN
ejpam-5594	157	1	+	+	CCONJ
ejpam-5594	157	2	2]dv	2]dv	NUM
ejpam-5594	157	3	=	=	PUNCT
ejpam-5594	158	1	[	[	PUNCT
ejpam-5594	158	2	7	7	NUM
ejpam-5594	158	3	3	3	NUM
ejpam-5594	158	4	,	,	PUNCT
ejpam-5594	158	5	7	7	NUM
ejpam-5594	158	6	2	2	NUM
ejpam-5594	158	7	]	]	PUNCT
ejpam-5594	158	8	from	from	ADP
ejpam-5594	158	9	theorem	theorem	NOUN
ejpam-5594	158	10	5	5	NUM
ejpam-5594	158	11	,	,	PUNCT
ejpam-5594	158	12	we	we	PRON
ejpam-5594	158	13	have	have	VERB
ejpam-5594	158	14	∫	∫	PROPN
ejpam-5594	158	15	1	1	NUM
ejpam-5594	158	16	0	0	NUM
ejpam-5594	158	17	φ(v)dv	φ(v)dv	NOUN
ejpam-5594	158	18	⪯cr	⪯cr	NUM
ejpam-5594	158	19	∫	∫	PROPN
ejpam-5594	158	20	1	1	NUM
ejpam-5594	158	21	0	0	NUM
ejpam-5594	158	22	h	h	NOUN
ejpam-5594	158	23	(	(	PUNCT
ejpam-5594	158	24	v)dv	v)dv	PROPN
ejpam-5594	158	25	.	.	PUNCT
ejpam-5594	159	1	j.	j.	PROPN
ejpam-5594	159	2	e.	e.	PROPN
ejpam-5594	159	3	maćıas	maćıas	PROPN
ejpam-5594	159	4	-	-	PUNCT
ejpam-5594	159	5	dı́az	dı́az	NOUN
ejpam-5594	159	6	et	et	NOUN
ejpam-5594	159	7	al	al	PROPN
ejpam-5594	159	8	.	.	PUNCT
ejpam-5594	159	9	/	/	SYM
ejpam-5594	159	10	eur	eur	PROPN
ejpam-5594	159	11	.	.	PUNCT
ejpam-5594	160	1	j.	j.	PROPN
ejpam-5594	160	2	pure	pure	PROPN
ejpam-5594	160	3	appl	appl	PROPN
ejpam-5594	160	4	.	.	PROPN
ejpam-5594	160	5	math	math	PROPN
ejpam-5594	160	6	,	,	PUNCT
ejpam-5594	160	7	17	17	NUM
ejpam-5594	160	8	(	(	PUNCT
ejpam-5594	160	9	4	4	NUM
ejpam-5594	160	10	)	)	PUNCT
ejpam-5594	160	11	(	(	PUNCT
ejpam-5594	160	12	2024	2024	NUM
ejpam-5594	160	13	)	)	PUNCT
ejpam-5594	160	14	,	,	PUNCT
ejpam-5594	160	15	4014	4014	NUM
ejpam-5594	160	16	-	-	SYM
ejpam-5594	160	17	4049	4049	NUM
ejpam-5594	160	18	4020	4020	NUM
ejpam-5594	160	19	0	0	NUM
ejpam-5594	160	20	0.2	0.2	NUM
ejpam-5594	160	21	0.4	0.4	NUM
ejpam-5594	160	22	0.6	0.6	NUM
ejpam-5594	161	1	0.8	0.8	NUM
ejpam-5594	161	2	0	0	NUM
ejpam-5594	161	3	0.2	0.2	NUM
ejpam-5594	161	4	0.4	0.4	NUM
ejpam-5594	161	5	0.6	0.6	NUM
ejpam-5594	161	6	0.8	0.8	NUM
ejpam-5594	161	7	1	1	NUM
ejpam-5594	161	8	v	v	NOUN
ejpam-5594	161	9	v	v	ADP
ejpam-5594	161	10	a	a	DET
ejpam-5594	161	11	lu	lu	NOUN
ejpam-5594	161	12	es	es	X
ejpam-5594	161	13	v2	v2	PROPN
ejpam-5594	161	14	2	2	NUM
ejpam-5594	161	15	+	+	SYM
ejpam-5594	161	16	v	v	NOUN
ejpam-5594	161	17	v2	v2	PROPN
ejpam-5594	161	18	+	+	NUM
ejpam-5594	161	19	2v	2v	PROPN
ejpam-5594	161	20	v3	v3	PROPN
ejpam-5594	161	21	3	3	NUM
ejpam-5594	162	1	+	+	CCONJ
ejpam-5594	162	2	2v	2v	NUM
ejpam-5594	162	3	3v2	3v2	NUM
ejpam-5594	162	4	2	2	NUM
ejpam-5594	162	5	+	+	NUM
ejpam-5594	162	6	2v	2v	PROPN
ejpam-5594	162	7	figure	figure	VERB
ejpam-5594	162	8	1	1	NUM
ejpam-5594	162	9	:	:	PUNCT
ejpam-5594	162	10	graphical	graphical	ADJ
ejpam-5594	162	11	validation	validation	NOUN
ejpam-5594	162	12	of	of	ADP
ejpam-5594	162	13	theorem	theorem	NOUN
ejpam-5594	162	14	5	5	NUM
ejpam-5594	162	15	.	.	PUNCT
ejpam-5594	163	1	definition	definition	NOUN
ejpam-5594	163	2	2	2	NUM
ejpam-5594	163	3	(	(	PUNCT
ejpam-5594	163	4	see	see	VERB
ejpam-5594	163	5	[	[	X
ejpam-5594	163	6	4	4	NUM
ejpam-5594	163	7	]	]	NUM
ejpam-5594	163	8	)	)	PUNCT
ejpam-5594	163	9	.	.	PUNCT
ejpam-5594	164	1	let	let	VERB
ejpam-5594	164	2	φ	φ	NOUN
ejpam-5594	164	3	:	:	PUNCT
ejpam-5594	165	1	[	[	X
ejpam-5594	165	2	ε1	ε1	NOUN
ejpam-5594	165	3	,	,	PUNCT
ejpam-5594	165	4	ε2	ε2	PROPN
ejpam-5594	165	5	]	]	PUNCT
ejpam-5594	165	6	→	→	SYM
ejpam-5594	165	7	r+	r+	PUNCT
ejpam-5594	165	8	i	i	PRON
ejpam-5594	165	9	be	be	VERB
ejpam-5594	165	10	an	an	DET
ejpam-5594	165	11	cr	cr	NOUN
ejpam-5594	165	12	set	set	NOUN
ejpam-5594	165	13	-	-	PUNCT
ejpam-5594	165	14	valued	value	VERB
ejpam-5594	165	15	map	map	NOUN
ejpam-5594	165	16	given	give	VERB
ejpam-5594	165	17	by	by	ADP
ejpam-5594	165	18	φ	φ	PROPN
ejpam-5594	165	19	=	=	PUNCT
ejpam-5594	166	1	[	[	X
ejpam-5594	166	2	φ	φ	NOUN
ejpam-5594	166	3	,	,	PUNCT
ejpam-5594	166	4	φ̄	φ̄	PROPN
ejpam-5594	166	5	]	]	PUNCT
ejpam-5594	166	6	;	;	PUNCT
ejpam-5594	166	7	then	then	ADV
ejpam-5594	166	8	,	,	PUNCT
ejpam-5594	166	9	φ	φ	PROPN
ejpam-5594	166	10	is	be	AUX
ejpam-5594	166	11	said	say	VERB
ejpam-5594	166	12	to	to	PART
ejpam-5594	166	13	be	be	AUX
ejpam-5594	166	14	cr	cr	NOUN
ejpam-5594	166	15	-	-	PUNCT
ejpam-5594	166	16	convex	convex	NOUN
ejpam-5594	166	17	if	if	SCONJ
ejpam-5594	166	18	φ(	φ(	NUM
ejpam-5594	166	19	♭	♭	PRON
ejpam-5594	166	20	ε1	ε1	VERB
ejpam-5594	166	21	+	+	CCONJ
ejpam-5594	166	22	(	(	PUNCT
ejpam-5594	166	23	1−	1−	NUM
ejpam-5594	166	24	♭	♭	INTJ
ejpam-5594	166	25	)	)	PUNCT
ejpam-5594	166	26	ε2	ε2	PROPN
ejpam-5594	166	27	)	)	PUNCT
ejpam-5594	166	28	⪯cr	⪯cr	VERB
ejpam-5594	166	29	♭	♭	PROPN
ejpam-5594	166	30	φ(ε1	φ(ε1	PROPN
ejpam-5594	166	31	)	)	PUNCT
ejpam-5594	167	1	+	+	CCONJ
ejpam-5594	167	2	(	(	PUNCT
ejpam-5594	167	3	1−	1−	NUM
ejpam-5594	167	4	♭	♭	INTJ
ejpam-5594	167	5	)	)	PUNCT
ejpam-5594	167	6	φ(ε2	φ(ε2	NOUN
ejpam-5594	167	7	)	)	PUNCT
ejpam-5594	167	8	,	,	PUNCT
ejpam-5594	167	9	holds	hold	VERB
ejpam-5594	167	10	for	for	ADP
ejpam-5594	167	11	all	all	DET
ejpam-5594	167	12	ε1	ε1	PROPN
ejpam-5594	167	13	,	,	PUNCT
ejpam-5594	167	14	ε2	ε2	PROPN
ejpam-5594	167	15	∈	∈	PROPN
ejpam-5594	167	16	b	b	X
ejpam-5594	167	17	⊂	⊂	PROPN
ejpam-5594	167	18	r	r	PROPN
ejpam-5594	167	19	and	and	CCONJ
ejpam-5594	167	20	♭	♭	PROPN
ejpam-5594	167	21	∈	∈	PROPN
ejpam-5594	168	1	[	[	X
ejpam-5594	168	2	0	0	NUM
ejpam-5594	168	3	,	,	PUNCT
ejpam-5594	168	4	1	1	NUM
ejpam-5594	168	5	]	]	PUNCT
ejpam-5594	168	6	.	.	PUNCT
ejpam-5594	169	1	definition	definition	NOUN
ejpam-5594	169	2	3	3	NUM
ejpam-5594	169	3	(	(	PUNCT
ejpam-5594	169	4	see	see	VERB
ejpam-5594	169	5	[	[	X
ejpam-5594	169	6	4	4	NUM
ejpam-5594	169	7	]	]	NUM
ejpam-5594	169	8	)	)	PUNCT
ejpam-5594	169	9	.	.	PUNCT
ejpam-5594	170	1	let	let	VERB
ejpam-5594	170	2	φ	φ	NOUN
ejpam-5594	170	3	:	:	PUNCT
ejpam-5594	171	1	[	[	X
ejpam-5594	171	2	ε1	ε1	NOUN
ejpam-5594	171	3	,	,	PUNCT
ejpam-5594	171	4	ε2	ε2	PROPN
ejpam-5594	171	5	]	]	PUNCT
ejpam-5594	171	6	→	→	SYM
ejpam-5594	171	7	r+	r+	PUNCT
ejpam-5594	171	8	i	i	PRON
ejpam-5594	171	9	be	be	VERB
ejpam-5594	171	10	an	an	DET
ejpam-5594	171	11	cr	cr	NOUN
ejpam-5594	171	12	set	set	NOUN
ejpam-5594	171	13	-	-	PUNCT
ejpam-5594	171	14	valued	value	VERB
ejpam-5594	171	15	map	map	NOUN
ejpam-5594	171	16	given	give	VERB
ejpam-5594	171	17	by	by	ADP
ejpam-5594	171	18	φ	φ	PROPN
ejpam-5594	171	19	=	=	PUNCT
ejpam-5594	172	1	[	[	X
ejpam-5594	172	2	φ	φ	NOUN
ejpam-5594	172	3	,	,	PUNCT
ejpam-5594	172	4	φ̄	φ̄	X
ejpam-5594	172	5	]	]	PUNCT
ejpam-5594	172	6	and	and	CCONJ
ejpam-5594	172	7	h	h	NOUN
ejpam-5594	172	8	:	:	PUNCT
ejpam-5594	172	9	(	(	PUNCT
ejpam-5594	172	10	0	0	NUM
ejpam-5594	172	11	,	,	PUNCT
ejpam-5594	172	12	1	1	NUM
ejpam-5594	172	13	)	)	PUNCT
ejpam-5594	172	14	→	→	SYM
ejpam-5594	172	15	r	r	NOUN
ejpam-5594	172	16	be	be	VERB
ejpam-5594	172	17	non	non	ADJ
ejpam-5594	172	18	-	-	ADJ
ejpam-5594	172	19	negative	negative	ADJ
ejpam-5594	172	20	function	function	NOUN
ejpam-5594	172	21	;	;	PUNCT
ejpam-5594	172	22	then	then	ADV
ejpam-5594	172	23	,	,	PUNCT
ejpam-5594	172	24	φ	φ	PROPN
ejpam-5594	172	25	is	be	AUX
ejpam-5594	172	26	said	say	VERB
ejpam-5594	172	27	to	to	PART
ejpam-5594	172	28	be	be	AUX
ejpam-5594	172	29	cr	cr	PROPN
ejpam-5594	172	30	-	-	PUNCT
ejpam-5594	172	31	h	h	NOUN
ejpam-5594	172	32	-	-	PUNCT
ejpam-5594	172	33	convex	convex	NOUN
ejpam-5594	172	34	if	if	SCONJ
ejpam-5594	172	35	φ(	φ(	NUM
ejpam-5594	172	36	♭	♭	PRON
ejpam-5594	172	37	ε1	ε1	VERB
ejpam-5594	172	38	+	+	CCONJ
ejpam-5594	172	39	(	(	PUNCT
ejpam-5594	172	40	1−	1−	NUM
ejpam-5594	172	41	♭	♭	INTJ
ejpam-5594	172	42	)	)	PUNCT
ejpam-5594	172	43	ε2	ε2	ADJ
ejpam-5594	172	44	)	)	PUNCT
ejpam-5594	172	45	⪯cr	⪯cr	VERB
ejpam-5594	172	46	h(	h(	PROPN
ejpam-5594	172	47	♭	♭	PROPN
ejpam-5594	172	48	)φ(ε1	)φ(ε1	PUNCT
ejpam-5594	172	49	)	)	PUNCT
ejpam-5594	173	1	+	+	CCONJ
ejpam-5594	173	2	h(1−	h(1−	PROPN
ejpam-5594	173	3	♭	♭	INTJ
ejpam-5594	173	4	)	)	PUNCT
ejpam-5594	173	5	φ(ε2	φ(ε2	NOUN
ejpam-5594	173	6	)	)	PUNCT
ejpam-5594	173	7	,	,	PUNCT
ejpam-5594	173	8	holds	hold	VERB
ejpam-5594	173	9	for	for	ADP
ejpam-5594	173	10	all	all	DET
ejpam-5594	173	11	ε1	ε1	PROPN
ejpam-5594	173	12	,	,	PUNCT
ejpam-5594	173	13	ε2	ε2	PROPN
ejpam-5594	173	14	∈	∈	PROPN
ejpam-5594	173	15	b	b	X
ejpam-5594	173	16	⊂	⊂	PROPN
ejpam-5594	173	17	r	r	PROPN
ejpam-5594	173	18	and	and	CCONJ
ejpam-5594	173	19	♭	♭	PROPN
ejpam-5594	173	20	∈	∈	PROPN
ejpam-5594	173	21	(	(	PUNCT
ejpam-5594	173	22	0	0	NUM
ejpam-5594	173	23	,	,	PUNCT
ejpam-5594	173	24	1	1	NUM
ejpam-5594	173	25	)	)	PUNCT
ejpam-5594	173	26	.	.	PUNCT
ejpam-5594	174	1	definition	definition	NOUN
ejpam-5594	174	2	4	4	NUM
ejpam-5594	174	3	(	(	PUNCT
ejpam-5594	174	4	see	see	VERB
ejpam-5594	174	5	[	[	X
ejpam-5594	174	6	4	4	NUM
ejpam-5594	174	7	]	]	NUM
ejpam-5594	174	8	)	)	PUNCT
ejpam-5594	174	9	.	.	PUNCT
ejpam-5594	175	1	let	let	VERB
ejpam-5594	175	2	φ	φ	NOUN
ejpam-5594	175	3	:	:	PUNCT
ejpam-5594	176	1	[	[	X
ejpam-5594	176	2	ε1	ε1	NOUN
ejpam-5594	176	3	,	,	PUNCT
ejpam-5594	176	4	ε2	ε2	PROPN
ejpam-5594	176	5	]	]	PUNCT
ejpam-5594	176	6	→	→	SYM
ejpam-5594	176	7	r+	r+	PUNCT
ejpam-5594	176	8	i	i	PRON
ejpam-5594	176	9	be	be	VERB
ejpam-5594	176	10	an	an	DET
ejpam-5594	176	11	cr	cr	NOUN
ejpam-5594	176	12	set	set	NOUN
ejpam-5594	176	13	-	-	PUNCT
ejpam-5594	176	14	valued	value	VERB
ejpam-5594	176	15	map	map	NOUN
ejpam-5594	176	16	given	give	VERB
ejpam-5594	176	17	by	by	ADP
ejpam-5594	176	18	φ	φ	PROPN
ejpam-5594	176	19	=	=	PUNCT
ejpam-5594	177	1	[	[	X
ejpam-5594	177	2	φ	φ	NOUN
ejpam-5594	177	3	,	,	PUNCT
ejpam-5594	177	4	φ̄	φ̄	X
ejpam-5594	177	5	]	]	PUNCT
ejpam-5594	177	6	and	and	CCONJ
ejpam-5594	177	7	h	h	NOUN
ejpam-5594	177	8	:	:	PUNCT
ejpam-5594	177	9	(	(	PUNCT
ejpam-5594	177	10	0	0	NUM
ejpam-5594	177	11	,	,	PUNCT
ejpam-5594	177	12	1	1	NUM
ejpam-5594	177	13	)	)	PUNCT
ejpam-5594	177	14	→	→	SYM
ejpam-5594	177	15	r	r	NOUN
ejpam-5594	177	16	be	be	VERB
ejpam-5594	177	17	non	non	ADJ
ejpam-5594	177	18	-	-	ADJ
ejpam-5594	177	19	negative	negative	ADJ
ejpam-5594	177	20	function	function	NOUN
ejpam-5594	177	21	;	;	PUNCT
ejpam-5594	177	22	then	then	ADV
ejpam-5594	177	23	,	,	PUNCT
ejpam-5594	177	24	φ	φ	PROPN
ejpam-5594	177	25	is	be	AUX
ejpam-5594	177	26	said	say	VERB
ejpam-5594	177	27	to	to	PART
ejpam-5594	177	28	be	be	AUX
ejpam-5594	177	29	cr	cr	PROPN
ejpam-5594	177	30	-	-	PUNCT
ejpam-5594	177	31	h	h	NOUN
ejpam-5594	177	32	-	-	PUNCT
ejpam-5594	177	33	godunova	godunova	NOUN
ejpam-5594	177	34	-	-	PUNCT
ejpam-5594	177	35	levin	levin	PROPN
ejpam-5594	177	36	if	if	SCONJ
ejpam-5594	177	37	φ(	φ(	NUM
ejpam-5594	177	38	♭	♭	PRON
ejpam-5594	177	39	ε1	ε1	VERB
ejpam-5594	177	40	+	+	CCONJ
ejpam-5594	177	41	(	(	PUNCT
ejpam-5594	177	42	1−	1−	NUM
ejpam-5594	177	43	♭	♭	INTJ
ejpam-5594	177	44	)	)	PUNCT
ejpam-5594	177	45	ε2	ε2	ADJ
ejpam-5594	177	46	)	)	PUNCT
ejpam-5594	177	47	⪯cr	⪯cr	NUM
ejpam-5594	177	48	φ(ε1	φ(ε1	NOUN
ejpam-5594	177	49	)	)	PUNCT
ejpam-5594	177	50	h	h	NOUN
ejpam-5594	177	51	(	(	PUNCT
ejpam-5594	177	52	♭	♭	INTJ
ejpam-5594	177	53	)	)	PUNCT
ejpam-5594	177	54	+	+	NUM
ejpam-5594	177	55	φ(ε2	φ(ε2	NUM
ejpam-5594	177	56	)	)	PUNCT
ejpam-5594	177	57	h(1−	h(1−	NOUN
ejpam-5594	177	58	♭	♭	PROPN
ejpam-5594	177	59	)	)	PUNCT
ejpam-5594	177	60	,	,	PUNCT
ejpam-5594	177	61	holds	hold	VERB
ejpam-5594	177	62	for	for	ADP
ejpam-5594	177	63	all	all	DET
ejpam-5594	177	64	ε1	ε1	PROPN
ejpam-5594	177	65	,	,	PUNCT
ejpam-5594	177	66	ε2	ε2	PROPN
ejpam-5594	177	67	∈	∈	PROPN
ejpam-5594	177	68	b	b	X
ejpam-5594	177	69	⊂	⊂	PROPN
ejpam-5594	177	70	r	r	PROPN
ejpam-5594	177	71	and	and	CCONJ
ejpam-5594	177	72	♭	♭	PROPN
ejpam-5594	177	73	∈	∈	PROPN
ejpam-5594	177	74	(	(	PUNCT
ejpam-5594	177	75	0	0	NUM
ejpam-5594	177	76	,	,	PUNCT
ejpam-5594	177	77	1	1	NUM
ejpam-5594	177	78	)	)	PUNCT
ejpam-5594	177	79	.	.	PUNCT
ejpam-5594	178	1	the	the	DET
ejpam-5594	178	2	class	class	NOUN
ejpam-5594	178	3	of	of	ADP
ejpam-5594	178	4	all	all	DET
ejpam-5594	178	5	cr	cr	NOUN
ejpam-5594	178	6	-	-	PUNCT
ejpam-5594	178	7	h	h	NOUN
ejpam-5594	178	8	-	-	PUNCT
ejpam-5594	178	9	godunova	godunova	ADJ
ejpam-5594	178	10	-	-	PUNCT
ejpam-5594	178	11	levin	levin	PROPN
ejpam-5594	178	12	convex	convex	PROPN
ejpam-5594	178	13	mappings	mapping	NOUN
ejpam-5594	178	14	are	be	AUX
ejpam-5594	178	15	denoted	denote	VERB
ejpam-5594	178	16	by	by	ADP
ejpam-5594	178	17	sgx(h	sgx(h	PROPN
ejpam-5594	178	18	,	,	PUNCT
ejpam-5594	178	19	[	[	X
ejpam-5594	178	20	ε1	ε1	PROPN
ejpam-5594	178	21	,	,	PUNCT
ejpam-5594	178	22	ε2],r	ε2],r	NOUN
ejpam-5594	178	23	+	+	CCONJ
ejpam-5594	178	24	i	i	PROPN
ejpam-5594	178	25	)	)	PUNCT
ejpam-5594	178	26	.	.	PUNCT
ejpam-5594	179	1	remark	remark	PROPN
ejpam-5594	179	2	2	2	NUM
ejpam-5594	179	3	.	.	NOUN
ejpam-5594	179	4	•	•	NOUN
ejpam-5594	179	5	if	if	SCONJ
ejpam-5594	179	6	h	h	NOUN
ejpam-5594	179	7	(	(	PUNCT
ejpam-5594	179	8	♭	♭	INTJ
ejpam-5594	179	9	)	)	PUNCT
ejpam-5594	180	1	=	=	SYM
ejpam-5594	180	2	1	1	NUM
ejpam-5594	181	1	♭	♭	NOUN
ejpam-5594	181	2	s	s	PART
ejpam-5594	181	3	,	,	PUNCT
ejpam-5594	181	4	then	then	ADV
ejpam-5594	181	5	definition	definition	NOUN
ejpam-5594	181	6	4	4	NUM
ejpam-5594	181	7	recovers	recover	VERB
ejpam-5594	181	8	cr	cr	PRON
ejpam-5594	181	9	-	-	PUNCT
ejpam-5594	181	10	s	s	NOUN
ejpam-5594	181	11	-	-	PUNCT
ejpam-5594	181	12	convex	convex	NOUN
ejpam-5594	181	13	functions	function	NOUN
ejpam-5594	181	14	in	in	ADP
ejpam-5594	181	15	[	[	X
ejpam-5594	181	16	4	4	NUM
ejpam-5594	181	17	]	]	PUNCT
ejpam-5594	181	18	.	.	PUNCT
ejpam-5594	182	1	•	•	INTJ
ejpam-5594	182	2	if	if	SCONJ
ejpam-5594	182	3	h	h	NOUN
ejpam-5594	182	4	(	(	PUNCT
ejpam-5594	182	5	♭	♭	INTJ
ejpam-5594	182	6	)	)	PUNCT
ejpam-5594	182	7	=	=	SYM
ejpam-5594	182	8	1	1	NUM
ejpam-5594	182	9	,	,	PUNCT
ejpam-5594	182	10	then	then	ADV
ejpam-5594	182	11	definition	definition	NOUN
ejpam-5594	182	12	4	4	NUM
ejpam-5594	182	13	recovers	recover	VERB
ejpam-5594	182	14	cr	cr	DET
ejpam-5594	182	15	-	-	PUNCT
ejpam-5594	182	16	p	p	NOUN
ejpam-5594	182	17	-	-	PUNCT
ejpam-5594	182	18	functions	function	NOUN
ejpam-5594	182	19	in	in	ADP
ejpam-5594	182	20	[	[	X
ejpam-5594	182	21	4	4	NUM
ejpam-5594	182	22	]	]	PUNCT
ejpam-5594	182	23	.	.	PUNCT
ejpam-5594	183	1	•	•	INTJ
ejpam-5594	183	2	if	if	SCONJ
ejpam-5594	183	3	h	h	NOUN
ejpam-5594	183	4	(	(	PUNCT
ejpam-5594	183	5	♭	♭	INTJ
ejpam-5594	183	6	)	)	PUNCT
ejpam-5594	183	7	=	=	SYM
ejpam-5594	184	1	1	1	NUM
ejpam-5594	184	2	♭	♭	INTJ
ejpam-5594	184	3	,	,	PUNCT
ejpam-5594	184	4	then	then	ADV
ejpam-5594	184	5	definition	definition	NOUN
ejpam-5594	184	6	4	4	NUM
ejpam-5594	184	7	recovers	recover	VERB
ejpam-5594	184	8	cr	cr	NOUN
ejpam-5594	184	9	-	-	PUNCT
ejpam-5594	184	10	convex	convex	NOUN
ejpam-5594	184	11	functions	function	NOUN
ejpam-5594	184	12	in	in	ADP
ejpam-5594	184	13	[	[	X
ejpam-5594	184	14	45	45	NUM
ejpam-5594	184	15	]	]	PUNCT
ejpam-5594	184	16	definition	definition	NOUN
ejpam-5594	184	17	5	5	NUM
ejpam-5594	184	18	(	(	PUNCT
ejpam-5594	184	19	see	see	VERB
ejpam-5594	184	20	[	[	X
ejpam-5594	184	21	15	15	NUM
ejpam-5594	184	22	]	]	NUM
ejpam-5594	184	23	)	)	PUNCT
ejpam-5594	184	24	.	.	PUNCT
ejpam-5594	185	1	let	let	VERB
ejpam-5594	185	2	φ	φ	NOUN
ejpam-5594	185	3	:	:	PUNCT
ejpam-5594	186	1	[	[	X
ejpam-5594	186	2	ε1	ε1	NOUN
ejpam-5594	186	3	,	,	PUNCT
ejpam-5594	186	4	ε2	ε2	PROPN
ejpam-5594	186	5	]	]	PUNCT
ejpam-5594	186	6	→	→	SYM
ejpam-5594	186	7	r+	r+	PUNCT
ejpam-5594	186	8	i	i	PRON
ejpam-5594	186	9	be	be	VERB
ejpam-5594	186	10	an	an	DET
ejpam-5594	186	11	set	set	NOUN
ejpam-5594	186	12	-	-	PUNCT
ejpam-5594	186	13	valued	value	VERB
ejpam-5594	186	14	map	map	NOUN
ejpam-5594	186	15	given	give	VERB
ejpam-5594	186	16	by	by	ADP
ejpam-5594	186	17	φ	φ	PROPN
ejpam-5594	186	18	=	=	PUNCT
ejpam-5594	187	1	[	[	X
ejpam-5594	187	2	φ	φ	NOUN
ejpam-5594	187	3	,	,	PUNCT
ejpam-5594	187	4	φ̄	φ̄	PROPN
ejpam-5594	187	5	]	]	PUNCT
ejpam-5594	187	6	.	.	PUNCT
ejpam-5594	188	1	the	the	DET
ejpam-5594	188	2	interval	interval	NOUN
ejpam-5594	188	3	-	-	PUNCT
ejpam-5594	188	4	valued	value	VERB
ejpam-5594	188	5	left	left	NOUN
ejpam-5594	188	6	-	-	PUNCT
ejpam-5594	188	7	sided	sided	ADJ
ejpam-5594	188	8	and	and	CCONJ
ejpam-5594	188	9	right	right	ADV
ejpam-5594	188	10	-	-	PUNCT
ejpam-5594	188	11	sided	sided	ADJ
ejpam-5594	188	12	atangana	atangana	PROPN
ejpam-5594	188	13	-	-	PUNCT
ejpam-5594	188	14	baleanu	baleanu	ADJ
ejpam-5594	188	15	fractional	fractional	ADJ
ejpam-5594	188	16	integral	integral	NOUN
ejpam-5594	188	17	of	of	ADP
ejpam-5594	188	18	function	function	NOUN
ejpam-5594	188	19	φ	φ	NOUN
ejpam-5594	188	20	and	and	CCONJ
ejpam-5594	188	21	order	order	NOUN
ejpam-5594	188	22	ς	ς	PROPN
ejpam-5594	188	23	>	>	X
ejpam-5594	188	24	0	0	NUM
ejpam-5594	188	25	is	be	AUX
ejpam-5594	188	26	defined	define	VERB
ejpam-5594	188	27	by	by	ADP
ejpam-5594	188	28	j.	j.	PROPN
ejpam-5594	188	29	e.	e.	PROPN
ejpam-5594	188	30	maćıas	maćıas	PROPN
ejpam-5594	188	31	-	-	PUNCT
ejpam-5594	188	32	dı́az	dı́az	NOUN
ejpam-5594	188	33	et	et	NOUN
ejpam-5594	188	34	al	al	PROPN
ejpam-5594	188	35	.	.	PUNCT
ejpam-5594	188	36	/	/	SYM
ejpam-5594	188	37	eur	eur	PROPN
ejpam-5594	188	38	.	.	PUNCT
ejpam-5594	189	1	j.	j.	PROPN
ejpam-5594	189	2	pure	pure	PROPN
ejpam-5594	189	3	appl	appl	PROPN
ejpam-5594	189	4	.	.	PROPN
ejpam-5594	189	5	math	math	PROPN
ejpam-5594	189	6	,	,	PUNCT
ejpam-5594	189	7	17	17	NUM
ejpam-5594	189	8	(	(	PUNCT
ejpam-5594	189	9	4	4	NUM
ejpam-5594	189	10	)	)	PUNCT
ejpam-5594	189	11	(	(	PUNCT
ejpam-5594	189	12	2024	2024	NUM
ejpam-5594	189	13	)	)	PUNCT
ejpam-5594	189	14	,	,	PUNCT
ejpam-5594	189	15	4014	4014	NUM
ejpam-5594	189	16	-	-	SYM
ejpam-5594	189	17	4049	4049	NUM
ejpam-5594	189	18	4021	4021	NUM
ejpam-5594	189	19	ab	ab	PROPN
ejpam-5594	189	20	ε1i	ε1i	NUM
ejpam-5594	189	21	ς	ς	PROPN
ejpam-5594	189	22	t{φ(t	t{φ(t	NUM
ejpam-5594	189	23	)	)	PUNCT
ejpam-5594	189	24	}	}	PUNCT
ejpam-5594	189	25	=	=	SYM
ejpam-5594	190	1	1−	1−	NUM
ejpam-5594	190	2	ς	ς	PROPN
ejpam-5594	190	3	b(ς	b(ς	PROPN
ejpam-5594	190	4	)	)	PUNCT
ejpam-5594	190	5	φ(t	φ(t	PROPN
ejpam-5594	190	6	)	)	PUNCT
ejpam-5594	191	1	+	+	CCONJ
ejpam-5594	191	2	ς	ς	PROPN
ejpam-5594	191	3	b(ς)γ(ς	b(ς)γ(ς	NUM
ejpam-5594	191	4	)	)	PUNCT
ejpam-5594	191	5	∫	∫	PROPN
ejpam-5594	191	6	t	t	PROPN
ejpam-5594	191	7	ε1	ε1	VERB
ejpam-5594	191	8	φ(	φ(	NUM
ejpam-5594	191	9	♭	♭	PROPN
ejpam-5594	191	10	)(t−	)(t−	NOUN
ejpam-5594	191	11	♭	♭	INTJ
ejpam-5594	191	12	)	)	PUNCT
ejpam-5594	192	1	ς−1	ς−1	PROPN
ejpam-5594	192	2	d	d	NOUN
ejpam-5594	192	3	♭	♭	PROPN
ejpam-5594	192	4	,	,	PUNCT
ejpam-5594	192	5	abiςε2{φ(t	abiςε2{φ(t	PROPN
ejpam-5594	192	6	)	)	PUNCT
ejpam-5594	192	7	}	}	PUNCT
ejpam-5594	193	1	=	=	SYM
ejpam-5594	193	2	1−	1−	NUM
ejpam-5594	193	3	ς	ς	PROPN
ejpam-5594	193	4	b(ς	b(ς	PROPN
ejpam-5594	193	5	)	)	PUNCT
ejpam-5594	193	6	φ(t	φ(t	PROPN
ejpam-5594	193	7	)	)	PUNCT
ejpam-5594	194	1	+	+	CCONJ
ejpam-5594	194	2	ς	ς	PROPN
ejpam-5594	194	3	b(ς)γ(ς	b(ς)γ(ς	NUM
ejpam-5594	194	4	)	)	PUNCT
ejpam-5594	194	5	∫	∫	PROPN
ejpam-5594	194	6	ε2	ε2	PROPN
ejpam-5594	194	7	t	t	PROPN
ejpam-5594	194	8	φ(	φ(	NUM
ejpam-5594	194	9	♭	♭	PROPN
ejpam-5594	194	10	)(	)(	PROPN
ejpam-5594	195	1	♭	♭	PROPN
ejpam-5594	195	2	−	−	PROPN
ejpam-5594	195	3	t)ς−1	t)ς−1	INTJ
ejpam-5594	195	4	d	d	NOUN
ejpam-5594	195	5	♭	♭	PROPN
ejpam-5594	195	6	,	,	PUNCT
ejpam-5594	195	7	where	where	SCONJ
ejpam-5594	195	8	ε1	ε1	VERB
ejpam-5594	195	9	<	<	X
ejpam-5594	195	10	ε2	ε2	PROPN
ejpam-5594	195	11	,	,	PUNCT
ejpam-5594	195	12	ς	ς	PROPN
ejpam-5594	195	13	∈	∈	PROPN
ejpam-5594	195	14	(	(	PUNCT
ejpam-5594	195	15	0	0	NUM
ejpam-5594	195	16	,	,	PUNCT
ejpam-5594	195	17	1],γ	1],γ	NUM
ejpam-5594	195	18	(	(	PUNCT
ejpam-5594	195	19	♭	♭	INTJ
ejpam-5594	195	20	)	)	PUNCT
ejpam-5594	195	21	=	=	NOUN
ejpam-5594	196	1	∫∞	∫∞	NOUN
ejpam-5594	196	2	0	0	NUM
ejpam-5594	196	3	t	t	PROPN
ejpam-5594	196	4	♭	♭	PROPN
ejpam-5594	196	5	−1e−t	−1e−t	NOUN
ejpam-5594	196	6	dt	dt	NOUN
ejpam-5594	196	7	is	be	AUX
ejpam-5594	196	8	the	the	DET
ejpam-5594	196	9	special	special	ADJ
ejpam-5594	196	10	function	function	NOUN
ejpam-5594	196	11	,	,	PUNCT
ejpam-5594	196	12	b(ς	b(ς	PROPN
ejpam-5594	196	13	)	)	PUNCT
ejpam-5594	196	14	>	>	X
ejpam-5594	196	15	0	0	NUM
ejpam-5594	197	1	such	such	ADJ
ejpam-5594	197	2	that	that	PRON
ejpam-5594	197	3	b(0	b(0	NOUN
ejpam-5594	197	4	)	)	PUNCT
ejpam-5594	197	5	=	=	SYM
ejpam-5594	197	6	b(1	b(1	PROPN
ejpam-5594	197	7	)	)	PUNCT
ejpam-5594	197	8	=	=	SYM
ejpam-5594	198	1	1	1	X
ejpam-5594	198	2	,	,	PUNCT
ejpam-5594	198	3	∥b(ς)∥	∥b(ς)∥	NOUN
ejpam-5594	198	4	=	=	SYM
ejpam-5594	198	5	1	1	NUM
ejpam-5594	198	6	,	,	PUNCT
ejpam-5594	198	7	and	and	CCONJ
ejpam-5594	198	8	βa	βa	NOUN
ejpam-5594	198	9	=	=	SYM
ejpam-5594	198	10	βa(p	βa(p	ADJ
ejpam-5594	198	11	,	,	PUNCT
ejpam-5594	198	12	q	q	X
ejpam-5594	198	13	)	)	PUNCT
ejpam-5594	198	14	=	=	SYM
ejpam-5594	199	1	∫	∫	PROPN
ejpam-5594	200	1	a	a	PRON
ejpam-5594	200	2	0	0	NUM
ejpam-5594	201	1	♭	♭	INTJ
ejpam-5594	201	2	p−1(1−	p−1(1−	PROPN
ejpam-5594	201	3	♭	♭	PROPN
ejpam-5594	201	4	)	)	PUNCT
ejpam-5594	202	1	q−1	q−1	PROPN
ejpam-5594	203	1	d	d	PUNCT
ejpam-5594	203	2	♭	♭	PROPN
ejpam-5594	203	3	is	be	AUX
ejpam-5594	203	4	the	the	DET
ejpam-5594	203	5	beta	beta	NOUN
ejpam-5594	203	6	integral	integral	NOUN
ejpam-5594	203	7	in	in	ADP
ejpam-5594	203	8	incomplete	incomplete	ADJ
ejpam-5594	203	9	sense	sense	NOUN
ejpam-5594	203	10	.	.	PUNCT
ejpam-5594	204	1	theorem	theorem	NOUN
ejpam-5594	204	2	6	6	NUM
ejpam-5594	204	3	(	(	PUNCT
ejpam-5594	204	4	see	see	VERB
ejpam-5594	204	5	[	[	X
ejpam-5594	204	6	4	4	NUM
ejpam-5594	204	7	]	]	NUM
ejpam-5594	204	8	)	)	PUNCT
ejpam-5594	204	9	.	.	PUNCT
ejpam-5594	205	1	let	let	VERB
ejpam-5594	205	2	φ	φ	NOUN
ejpam-5594	205	3	:	:	PUNCT
ejpam-5594	206	1	[	[	X
ejpam-5594	206	2	ε1	ε1	NOUN
ejpam-5594	206	3	,	,	PUNCT
ejpam-5594	206	4	ε2	ε2	PROPN
ejpam-5594	206	5	]	]	PUNCT
ejpam-5594	206	6	→	→	SYM
ejpam-5594	206	7	r+	r+	PUNCT
ejpam-5594	206	8	i	i	PRON
ejpam-5594	206	9	be	be	VERB
ejpam-5594	206	10	an	an	DET
ejpam-5594	206	11	interval	interval	NOUN
ejpam-5594	206	12	set	set	NOUN
ejpam-5594	206	13	-	-	PUNCT
ejpam-5594	206	14	valued	value	VERB
ejpam-5594	206	15	map	map	NOUN
ejpam-5594	206	16	given	give	VERB
ejpam-5594	206	17	by	by	ADP
ejpam-5594	206	18	φ	φ	PROPN
ejpam-5594	206	19	=	=	PUNCT
ejpam-5594	207	1	[	[	X
ejpam-5594	207	2	φ	φ	NOUN
ejpam-5594	207	3	,	,	PUNCT
ejpam-5594	207	4	φ̄	φ̄	PROPN
ejpam-5594	207	5	]	]	PUNCT
ejpam-5594	207	6	,	,	PUNCT
ejpam-5594	207	7	then	then	ADV
ejpam-5594	207	8	we	we	PRON
ejpam-5594	207	9	have	have	VERB
ejpam-5594	207	10	ab	ab	PROPN
ejpam-5594	207	11	ε1i	ε1i	PROPN
ejpam-5594	207	12	ς	ς	PROPN
ejpam-5594	207	13	t{φ(t	t{φ(t	NUM
ejpam-5594	207	14	)	)	PUNCT
ejpam-5594	207	15	}	}	PUNCT
ejpam-5594	208	1	=	=	PUNCT
ejpam-5594	208	2	[	[	PUNCT
ejpam-5594	208	3	ab	ab	X
ejpam-5594	208	4	ε1i	ε1i	NUM
ejpam-5594	208	5	ς	ς	PROPN
ejpam-5594	208	6	t{φ(t	t{φ(t	NUM
ejpam-5594	208	7	)	)	PUNCT
ejpam-5594	208	8	}	}	PUNCT
ejpam-5594	208	9	,	,	PUNCT
ejpam-5594	208	10	abε1i	abε1i	PROPN
ejpam-5594	208	11	ς	ς	PROPN
ejpam-5594	208	12	t{φ(t	t{φ(t	NUM
ejpam-5594	208	13	)	)	PUNCT
ejpam-5594	208	14	}	}	PUNCT
ejpam-5594	208	15	]	]	PUNCT
ejpam-5594	208	16	and	and	CCONJ
ejpam-5594	208	17	abiςε2{φ(t	abiςε2{φ(t	NUM
ejpam-5594	208	18	)	)	PUNCT
ejpam-5594	208	19	}	}	PUNCT
ejpam-5594	208	20	=	=	SYM
ejpam-5594	208	21	[	[	PUNCT
ejpam-5594	208	22	abiςε2{φ(t	abiςε2{φ(t	NOUN
ejpam-5594	208	23	)	)	PUNCT
ejpam-5594	208	24	}	}	PUNCT
ejpam-5594	208	25	,	,	PUNCT
ejpam-5594	208	26	abiςε2{φ(t	abiςε2{φ(t	PROPN
ejpam-5594	208	27	)	)	PUNCT
ejpam-5594	208	28	}	}	PUNCT
ejpam-5594	208	29	]	]	PUNCT
ejpam-5594	208	30	.	.	PUNCT
ejpam-5594	209	1	the	the	DET
ejpam-5594	209	2	following	follow	VERB
ejpam-5594	209	3	inequalities	inequality	NOUN
ejpam-5594	209	4	are	be	AUX
ejpam-5594	209	5	frequently	frequently	ADV
ejpam-5594	209	6	used	use	VERB
ejpam-5594	209	7	to	to	PART
ejpam-5594	209	8	produce	produce	VERB
ejpam-5594	209	9	our	our	PRON
ejpam-5594	209	10	major	major	ADJ
ejpam-5594	209	11	results	result	NOUN
ejpam-5594	209	12	.	.	PUNCT
ejpam-5594	210	1	theorem	theorem	ADJ
ejpam-5594	210	2	7	7	NUM
ejpam-5594	210	3	(	(	PUNCT
ejpam-5594	210	4	see	see	VERB
ejpam-5594	210	5	[	[	X
ejpam-5594	210	6	3	3	NUM
ejpam-5594	210	7	]	]	NUM
ejpam-5594	210	8	)	)	PUNCT
ejpam-5594	210	9	.	.	PUNCT
ejpam-5594	211	1	(	(	PUNCT
ejpam-5594	211	2	hölder	hölder	NOUN
ejpam-5594	211	3	inequality	inequality	NOUN
ejpam-5594	211	4	)	)	PUNCT
ejpam-5594	211	5	.	.	PUNCT
ejpam-5594	212	1	let	let	VERB
ejpam-5594	212	2	1	1	NUM
ejpam-5594	212	3	<	<	X
ejpam-5594	212	4	p	p	NOUN
ejpam-5594	212	5	and	and	CCONJ
ejpam-5594	212	6	1	1	NUM
ejpam-5594	212	7	p	p	NOUN
ejpam-5594	212	8	+	+	NOUN
ejpam-5594	212	9	1	1	NUM
ejpam-5594	212	10	q	q	NOUN
ejpam-5594	212	11	=	=	NOUN
ejpam-5594	212	12	1	1	X
ejpam-5594	212	13	.	.	X
ejpam-5594	213	1	consider	consider	VERB
ejpam-5594	213	2	two	two	NUM
ejpam-5594	213	3	real	real	ADV
ejpam-5594	213	4	-	-	PUNCT
ejpam-5594	213	5	valued	value	VERB
ejpam-5594	213	6	functions	function	NOUN
ejpam-5594	213	7	φ	φ	NOUN
ejpam-5594	213	8	and	and	CCONJ
ejpam-5594	213	9	ג	ג	X
ejpam-5594	213	10	on	on	ADP
ejpam-5594	213	11	[	[	X
ejpam-5594	213	12	ε1	ε1	NOUN
ejpam-5594	213	13	,	,	PUNCT
ejpam-5594	213	14	ε2	ε2	PROPN
ejpam-5594	213	15	]	]	PUNCT
ejpam-5594	213	16	with	with	ADP
ejpam-5594	213	17	|φ|p	|φ|p	PROPN
ejpam-5594	213	18	,	,	PUNCT
ejpam-5594	213	19	q|ג|	q|ג|	NOUN
ejpam-5594	213	20	are	be	AUX
ejpam-5594	213	21	also	also	ADV
ejpam-5594	213	22	integrable	integrable	ADJ
ejpam-5594	213	23	on	on	ADP
ejpam-5594	213	24	[	[	X
ejpam-5594	213	25	ε1	ε1	NOUN
ejpam-5594	213	26	,	,	PUNCT
ejpam-5594	213	27	ε2	ε2	PROPN
ejpam-5594	213	28	]	]	PUNCT
ejpam-5594	213	29	,	,	PUNCT
ejpam-5594	213	30	then	then	ADV
ejpam-5594	213	31	one	one	PRON
ejpam-5594	213	32	has	have	AUX
ejpam-5594	213	33	∫	∫	PROPN
ejpam-5594	213	34	ε2	ε2	PROPN
ejpam-5594	213	35	ε1	ε1	VERB
ejpam-5594	213	36	|φ(	|φ(	ADV
ejpam-5594	213	37	♭	♭	PROPN
ejpam-5594	213	38	)ג(	)ג(	PUNCT
ejpam-5594	213	39	♭	♭	PROPN
ejpam-5594	213	40	)|d	)|d	PROPN
ejpam-5594	213	41	♭	♭	PROPN
ejpam-5594	213	42	≤	≤	PROPN
ejpam-5594	213	43	(	(	PUNCT
ejpam-5594	213	44	∫	∫	PROPN
ejpam-5594	213	45	ε2	ε2	PROPN
ejpam-5594	213	46	ε1	ε1	VERB
ejpam-5594	213	47	|φ(	|φ(	ADV
ejpam-5594	213	48	♭	♭	NOUN
ejpam-5594	213	49	)|pd	)|pd	PUNCT
ejpam-5594	213	50	♭	♭	PROPN
ejpam-5594	213	51	)	)	PUNCT
ejpam-5594	213	52	1	1	NUM
ejpam-5594	213	53	p	p	NOUN
ejpam-5594	213	54	(	(	PUNCT
ejpam-5594	213	55	∫	∫	PROPN
ejpam-5594	213	56	ε2	ε2	PROPN
ejpam-5594	213	57	ε1	ε1	PROPN
ejpam-5594	213	58	♭	♭	PROPN
ejpam-5594	213	59	qd|(	qd|(	NOUN
ejpam-5594	213	60	♭	♭	NOUN
ejpam-5594	213	61	)ג|	)ג|	NOUN
ejpam-5594	213	62	)	)	PUNCT
ejpam-5594	213	63	1	1	NUM
ejpam-5594	213	64	q	q	NOUN
ejpam-5594	213	65	another	another	DET
ejpam-5594	213	66	generalized	generalized	ADJ
ejpam-5594	213	67	variant	variant	NOUN
ejpam-5594	213	68	of	of	ADP
ejpam-5594	213	69	hölder	hölder	NOUN
ejpam-5594	213	70	’s	’s	PART
ejpam-5594	213	71	inequality	inequality	NOUN
ejpam-5594	213	72	is	be	AUX
ejpam-5594	213	73	defined	define	VERB
ejpam-5594	213	74	as	as	ADP
ejpam-5594	213	75	follows	follow	VERB
ejpam-5594	213	76	.	.	PUNCT
ejpam-5594	214	1	theorem	theorem	ADJ
ejpam-5594	214	2	8	8	NUM
ejpam-5594	214	3	(	(	PUNCT
ejpam-5594	214	4	see	see	VERB
ejpam-5594	214	5	[	[	X
ejpam-5594	214	6	16	16	NUM
ejpam-5594	214	7	]	]	PUNCT
ejpam-5594	214	8	)	)	PUNCT
ejpam-5594	214	9	.	.	PUNCT
ejpam-5594	215	1	let	let	VERB
ejpam-5594	215	2	two	two	NUM
ejpam-5594	215	3	real	real	ADV
ejpam-5594	215	4	-	-	PUNCT
ejpam-5594	215	5	valued	value	VERB
ejpam-5594	215	6	functions	function	NOUN
ejpam-5594	215	7	φ	φ	NOUN
ejpam-5594	215	8	and	and	CCONJ
ejpam-5594	215	9	ג	ג	X
ejpam-5594	215	10	on	on	ADP
ejpam-5594	215	11	[	[	X
ejpam-5594	215	12	ε1	ε1	NOUN
ejpam-5594	215	13	,	,	PUNCT
ejpam-5594	215	14	ε2	ε2	PROPN
ejpam-5594	215	15	]	]	PUNCT
ejpam-5594	215	16	and	and	CCONJ
ejpam-5594	215	17	|φ|	|φ|	PROPN
ejpam-5594	215	18	,	,	PUNCT
ejpam-5594	215	19	|φ||ג|q	|φ||ג|q	PUNCT
ejpam-5594	215	20	are	be	AUX
ejpam-5594	215	21	also	also	ADV
ejpam-5594	215	22	integrable	integrable	ADJ
ejpam-5594	215	23	on	on	ADP
ejpam-5594	215	24	[	[	X
ejpam-5594	215	25	ε1	ε1	NOUN
ejpam-5594	215	26	,	,	PUNCT
ejpam-5594	215	27	ε2	ε2	PROPN
ejpam-5594	215	28	]	]	PUNCT
ejpam-5594	215	29	,	,	PUNCT
ejpam-5594	215	30	then	then	ADV
ejpam-5594	215	31	one	one	NUM
ejpam-5594	215	32	has∫	has∫	NOUN
ejpam-5594	215	33	ε2	ε2	NOUN
ejpam-5594	215	34	ε1	ε1	VERB
ejpam-5594	215	35	|φ(	|φ(	ADV
ejpam-5594	215	36	♭	♭	PROPN
ejpam-5594	215	37	)ג(	)ג(	PUNCT
ejpam-5594	215	38	♭	♭	PROPN
ejpam-5594	215	39	)|d	)|d	PROPN
ejpam-5594	215	40	♭	♭	PROPN
ejpam-5594	215	41	≤	≤	PROPN
ejpam-5594	215	42	(	(	PUNCT
ejpam-5594	215	43	∫	∫	PROPN
ejpam-5594	215	44	ε2	ε2	PROPN
ejpam-5594	215	45	ε1	ε1	VERB
ejpam-5594	215	46	|φ(	|φ(	ADV
ejpam-5594	215	47	♭	♭	NOUN
ejpam-5594	215	48	)|d	)|d	NOUN
ejpam-5594	215	49	♭	♭	PROPN
ejpam-5594	215	50	)	)	PUNCT
ejpam-5594	215	51	1−	1−	PROPN
ejpam-5594	215	52	1	1	NUM
ejpam-5594	215	53	q	q	NOUN
ejpam-5594	216	1	(	(	PUNCT
ejpam-5594	216	2	∫	∫	PROPN
ejpam-5594	216	3	ε2	ε2	PROPN
ejpam-5594	216	4	ε1	ε1	VERB
ejpam-5594	216	5	|φ(	|φ(	ADV
ejpam-5594	216	6	♭	♭	PROPN
ejpam-5594	216	7	)||ג(	)||ג(	NOUN
ejpam-5594	216	8	♭	♭	INTJ
ejpam-5594	216	9	)|qd	)|qd	NOUN
ejpam-5594	216	10	♭	♭	PROPN
ejpam-5594	216	11	)	)	PUNCT
ejpam-5594	216	12	1	1	NUM
ejpam-5594	216	13	q	q	NOUN
ejpam-5594	216	14	.	.	PUNCT
ejpam-5594	217	1	theorem	theorem	NOUN
ejpam-5594	217	2	9	9	NUM
ejpam-5594	217	3	(	(	PUNCT
ejpam-5594	217	4	see	see	VERB
ejpam-5594	217	5	[	[	X
ejpam-5594	217	6	16	16	NUM
ejpam-5594	217	7	]	]	PUNCT
ejpam-5594	217	8	)	)	PUNCT
ejpam-5594	217	9	.	.	PUNCT
ejpam-5594	218	1	(	(	PUNCT
ejpam-5594	218	2	young	young	PROPN
ejpam-5594	218	3	’s	’s	PART
ejpam-5594	218	4	inequality	inequality	NOUN
ejpam-5594	218	5	)	)	PUNCT
ejpam-5594	218	6	.	.	PUNCT
ejpam-5594	219	1	consider	consider	VERB
ejpam-5594	219	2	p	p	PRON
ejpam-5594	219	3	,	,	PUNCT
ejpam-5594	219	4	q	q	ADJ
ejpam-5594	219	5	be	be	AUX
ejpam-5594	219	6	positive	positive	ADJ
ejpam-5594	219	7	real	real	ADJ
ejpam-5594	219	8	numbers	number	NOUN
ejpam-5594	219	9	satisfying	satisfy	VERB
ejpam-5594	219	10	1	1	NUM
ejpam-5594	219	11	p	p	NOUN
ejpam-5594	220	1	+	+	NOUN
ejpam-5594	220	2	1	1	NUM
ejpam-5594	220	3	q	q	NOUN
ejpam-5594	220	4	=	=	ADJ
ejpam-5594	220	5	1	1	X
ejpam-5594	220	6	.	.	PUNCT
ejpam-5594	221	1	then	then	ADV
ejpam-5594	221	2	if	if	SCONJ
ejpam-5594	221	3	φ	φ	PROPN
ejpam-5594	221	4	,	,	PUNCT
ejpam-5594	221	5	h	h	PROPN
ejpam-5594	221	6	are	be	AUX
ejpam-5594	221	7	nonnegative	nonnegative	ADJ
ejpam-5594	221	8	functions	function	NOUN
ejpam-5594	221	9	then	then	ADV
ejpam-5594	221	10	we	we	PRON
ejpam-5594	221	11	have	have	VERB
ejpam-5594	221	12	,	,	PUNCT
ejpam-5594	221	13	g	g	PROPN
ejpam-5594	221	14	h	h	NOUN
ejpam-5594	221	15	≤	≤	VERB
ejpam-5594	221	16	φp	φp	ADP
ejpam-5594	221	17	p	p	NOUN
ejpam-5594	222	1	+	+	CCONJ
ejpam-5594	222	2	h	h	NOUN
ejpam-5594	222	3	q	q	NOUN
ejpam-5594	222	4	q	q	NOUN
ejpam-5594	222	5	,	,	PUNCT
ejpam-5594	222	6	and	and	CCONJ
ejpam-5594	222	7	equality	equality	NOUN
ejpam-5594	222	8	holds	hold	VERB
ejpam-5594	222	9	iff	iff	PROPN
ejpam-5594	222	10	φp	φp	ADP
ejpam-5594	222	11	=	=	PUNCT
ejpam-5594	222	12	h	h	PROPN
ejpam-5594	222	13	q.	q.	NOUN
ejpam-5594	222	14	the	the	DET
ejpam-5594	222	15	following	follow	VERB
ejpam-5594	222	16	two	two	NUM
ejpam-5594	222	17	below	below	ADP
ejpam-5594	222	18	lemmas	lemmas	PROPN
ejpam-5594	222	19	[	[	X
ejpam-5594	222	20	29	29	NUM
ejpam-5594	222	21	]	]	PUNCT
ejpam-5594	222	22	also	also	ADV
ejpam-5594	222	23	play	play	VERB
ejpam-5594	222	24	a	a	DET
ejpam-5594	222	25	very	very	ADV
ejpam-5594	222	26	crucial	crucial	ADJ
ejpam-5594	222	27	role	role	NOUN
ejpam-5594	222	28	in	in	ADP
ejpam-5594	222	29	creating	create	VERB
ejpam-5594	222	30	our	our	PRON
ejpam-5594	222	31	main	main	ADJ
ejpam-5594	222	32	findings	finding	NOUN
ejpam-5594	222	33	.	.	PUNCT
ejpam-5594	223	1	[	[	X
ejpam-5594	223	2	see	see	VERB
ejpam-5594	223	3	[	[	X
ejpam-5594	223	4	29	29	NUM
ejpam-5594	223	5	]	]	X
ejpam-5594	223	6	]	]	X
ejpam-5594	223	7	j.	j.	PROPN
ejpam-5594	223	8	e.	e.	PROPN
ejpam-5594	223	9	maćıas	maćıas	PROPN
ejpam-5594	223	10	-	-	PUNCT
ejpam-5594	223	11	dı́az	dı́az	NOUN
ejpam-5594	223	12	et	et	NOUN
ejpam-5594	223	13	al	al	PROPN
ejpam-5594	223	14	.	.	PUNCT
ejpam-5594	223	15	/	/	SYM
ejpam-5594	223	16	eur	eur	PROPN
ejpam-5594	223	17	.	.	PUNCT
ejpam-5594	224	1	j.	j.	PROPN
ejpam-5594	224	2	pure	pure	PROPN
ejpam-5594	224	3	appl	appl	PROPN
ejpam-5594	224	4	.	.	PROPN
ejpam-5594	224	5	math	math	PROPN
ejpam-5594	224	6	,	,	PUNCT
ejpam-5594	224	7	17	17	NUM
ejpam-5594	224	8	(	(	PUNCT
ejpam-5594	224	9	4	4	NUM
ejpam-5594	224	10	)	)	PUNCT
ejpam-5594	224	11	(	(	PUNCT
ejpam-5594	224	12	2024	2024	NUM
ejpam-5594	224	13	)	)	PUNCT
ejpam-5594	224	14	,	,	PUNCT
ejpam-5594	224	15	4014	4014	NUM
ejpam-5594	224	16	-	-	SYM
ejpam-5594	224	17	4049	4049	NUM
ejpam-5594	224	18	4022	4022	NUM
ejpam-5594	224	19	let	let	VERB
ejpam-5594	224	20	φ	φ	NOUN
ejpam-5594	224	21	:	:	PUNCT
ejpam-5594	224	22	b	b	X
ejpam-5594	224	23	◦	◦	NOUN
ejpam-5594	224	24	⊂	⊂	X
ejpam-5594	224	25	r	r	NOUN
ejpam-5594	224	26	→	→	SYM
ejpam-5594	224	27	r	r	NOUN
ejpam-5594	224	28	is	be	AUX
ejpam-5594	224	29	a	a	DET
ejpam-5594	224	30	differentiable	differentiable	ADJ
ejpam-5594	224	31	mapping	mapping	NOUN
ejpam-5594	224	32	on	on	ADP
ejpam-5594	224	33	b	b	NOUN
ejpam-5594	224	34	◦	◦	NOUN
ejpam-5594	224	35	,	,	PUNCT
ejpam-5594	224	36	where	where	SCONJ
ejpam-5594	224	37	ε1	ε1	PROPN
ejpam-5594	224	38	,	,	PUNCT
ejpam-5594	224	39	ε2	ε2	PROPN
ejpam-5594	224	40	∈	∈	PROPN
ejpam-5594	224	41	b	b	X
ejpam-5594	224	42	◦	◦	NOUN
ejpam-5594	224	43	,	,	PUNCT
ejpam-5594	224	44	with	with	ADP
ejpam-5594	224	45	ε1	ε1	PROPN
ejpam-5594	224	46	<	<	X
ejpam-5594	224	47	ε2	ε2	PROPN
ejpam-5594	224	48	.	.	PUNCT
ejpam-5594	225	1	if	if	SCONJ
ejpam-5594	225	2	φ	φ	PROPN
ejpam-5594	225	3	′	′	PROPN
ejpam-5594	225	4	∈	∈	PROPN
ejpam-5594	225	5	l[ε1	l[ε1	NOUN
ejpam-5594	225	6	,	,	PUNCT
ejpam-5594	225	7	ε2	ε2	PROPN
ejpam-5594	225	8	]	]	PUNCT
ejpam-5594	225	9	(	(	PUNCT
ejpam-5594	225	10	space	space	NOUN
ejpam-5594	225	11	of	of	ADP
ejpam-5594	225	12	all	all	DET
ejpam-5594	225	13	measurable	measurable	ADJ
ejpam-5594	225	14	function	function	NOUN
ejpam-5594	225	15	)	)	PUNCT
ejpam-5594	225	16	,	,	PUNCT
ejpam-5594	225	17	then	then	ADV
ejpam-5594	225	18	one	one	NUM
ejpam-5594	225	19	has	have	VERB
ejpam-5594	225	20	bk(φ	bk(φ	NOUN
ejpam-5594	225	21	,	,	PUNCT
ejpam-5594	225	22	ε1	ε1	PROPN
ejpam-5594	225	23	,	,	PUNCT
ejpam-5594	225	24	ε2	ε2	ADJ
ejpam-5594	225	25	)	)	PUNCT
ejpam-5594	225	26	=	=	PUNCT
ejpam-5594	226	1	k−1∑	k−1∑	PROPN
ejpam-5594	226	2	ȷ=0	ȷ=0	PROPN
ejpam-5594	226	3	1	1	NUM
ejpam-5594	226	4	2k	2k	NOUN
ejpam-5594	226	5	[	[	PUNCT
ejpam-5594	226	6	φ	φ	PROPN
ejpam-5594	226	7	(	(	PUNCT
ejpam-5594	226	8	(	(	PUNCT
ejpam-5594	226	9	k−ȷ)ε1	k−ȷ)ε1	PROPN
ejpam-5594	226	10	+	+	NUM
ejpam-5594	226	11	ȷε2	ȷε2	NOUN
ejpam-5594	226	12	k	k	PROPN
ejpam-5594	226	13	)	)	PUNCT
ejpam-5594	227	1	+	+	NOUN
ejpam-5594	227	2	φ	φ	PROPN
ejpam-5594	227	3	(	(	PUNCT
ejpam-5594	227	4	(	(	PUNCT
ejpam-5594	227	5	k−ȷ−	k−ȷ−	PROPN
ejpam-5594	227	6	1)ε1	1)ε1	NUM
ejpam-5594	227	7	+	+	CCONJ
ejpam-5594	227	8	(	(	PUNCT
ejpam-5594	227	9	ȷ+	ȷ+	ADV
ejpam-5594	227	10	1)ε2	1)ε2	NUM
ejpam-5594	227	11	k	k	NOUN
ejpam-5594	227	12	)	)	PUNCT
ejpam-5594	227	13	]	]	PUNCT
ejpam-5594	227	14	−	−	PROPN
ejpam-5594	227	15	1	1	NUM
ejpam-5594	227	16	ε2	ε2	NOUN
ejpam-5594	227	17	−	−	PROPN
ejpam-5594	227	18	ε1	ε1	PROPN
ejpam-5594	227	19	∫	∫	PROPN
ejpam-5594	227	20	ε2	ε2	PROPN
ejpam-5594	227	21	ε1	ε1	PROPN
ejpam-5594	227	22	φ(ς)dς	φ(ς)dς	PRON
ejpam-5594	227	23	=	=	PUNCT
ejpam-5594	227	24	k−1∑	k−1∑	PROPN
ejpam-5594	227	25	ȷ=0	ȷ=0	PROPN
ejpam-5594	227	26	ε2	ε2	ADJ
ejpam-5594	227	27	−	−	PROPN
ejpam-5594	227	28	ε1	ε1	PROPN
ejpam-5594	227	29	2k2	2k2	NUM
ejpam-5594	228	1	[	[	X
ejpam-5594	228	2	∫	∫	PROPN
ejpam-5594	228	3	1	1	NUM
ejpam-5594	228	4	0	0	NUM
ejpam-5594	228	5	(	(	PUNCT
ejpam-5594	228	6	1−	1−	NUM
ejpam-5594	228	7	2	2	NUM
ejpam-5594	228	8	♭	♭	PROPN
ejpam-5594	228	9	)φ′	)φ′	PROPN
ejpam-5594	228	10	(	(	PUNCT
ejpam-5594	228	11	♭	♭	X
ejpam-5594	228	12	(	(	PUNCT
ejpam-5594	228	13	k−ȷ)ε1	k−ȷ)ε1	PROPN
ejpam-5594	228	14	+	+	NUM
ejpam-5594	228	15	ȷε2	ȷε2	NOUN
ejpam-5594	228	16	k	k	X
ejpam-5594	228	17	+	+	PROPN
ejpam-5594	228	18	(	(	PUNCT
ejpam-5594	228	19	1−	1−	NUM
ejpam-5594	228	20	♭	♭	INTJ
ejpam-5594	228	21	)	)	PUNCT
ejpam-5594	228	22	(	(	PUNCT
ejpam-5594	228	23	k−ȷ−	k−ȷ−	PROPN
ejpam-5594	228	24	1)ε1	1)ε1	NUM
ejpam-5594	228	25	+	+	CCONJ
ejpam-5594	228	26	(	(	PUNCT
ejpam-5594	228	27	ȷ+	ȷ+	ADV
ejpam-5594	228	28	1)ε2	1)ε2	NUM
ejpam-5594	228	29	k	k	NOUN
ejpam-5594	228	30	)	)	PUNCT
ejpam-5594	229	1	d	d	X
ejpam-5594	229	2	♭	♭	X
ejpam-5594	229	3	]	]	PUNCT
ejpam-5594	229	4	.	.	PUNCT
ejpam-5594	230	1	holds	hold	VERB
ejpam-5594	230	2	.	.	PUNCT
ejpam-5594	231	1	[	[	X
ejpam-5594	231	2	see	see	VERB
ejpam-5594	231	3	[	[	X
ejpam-5594	231	4	32	32	NUM
ejpam-5594	231	5	]	]	X
ejpam-5594	231	6	]	]	X
ejpam-5594	231	7	let	let	VERB
ejpam-5594	231	8	ε1	ε1	VERB
ejpam-5594	231	9	<	<	X
ejpam-5594	231	10	ε2	ε2	PROPN
ejpam-5594	231	11	,	,	PUNCT
ejpam-5594	231	12	ε1	ε1	PROPN
ejpam-5594	231	13	,	,	PUNCT
ejpam-5594	231	14	ε2	ε2	PROPN
ejpam-5594	231	15	∈	∈	PROPN
ejpam-5594	231	16	r+,φ	r+,φ	PROPN
ejpam-5594	231	17	:	:	PUNCT
ejpam-5594	231	18	r+	r+	NOUN
ejpam-5594	231	19	→	→	PUNCT
ejpam-5594	231	20	r+	r+	PRON
ejpam-5594	231	21	is	be	AUX
ejpam-5594	231	22	a	a	DET
ejpam-5594	231	23	differentiable	differentiable	ADJ
ejpam-5594	231	24	mapping	mapping	NOUN
ejpam-5594	231	25	.	.	PUNCT
ejpam-5594	232	1	if	if	SCONJ
ejpam-5594	232	2	φ′′	φ′′	PROPN
ejpam-5594	232	3	∈	∈	PROPN
ejpam-5594	232	4	l[ε1	l[ε1	NOUN
ejpam-5594	232	5	,	,	PUNCT
ejpam-5594	232	6	ε2	ε2	PROPN
ejpam-5594	232	7	]	]	PUNCT
ejpam-5594	232	8	,	,	PUNCT
ejpam-5594	232	9	for	for	ADP
ejpam-5594	232	10	each	each	DET
ejpam-5594	232	11	ς	ς	PROPN
ejpam-5594	232	12	∈	∈	PROPN
ejpam-5594	232	13	(	(	PUNCT
ejpam-5594	232	14	0	0	NUM
ejpam-5594	232	15	,	,	PUNCT
ejpam-5594	232	16	1	1	NUM
ejpam-5594	232	17	]	]	PUNCT
ejpam-5594	232	18	,	,	PUNCT
ejpam-5594	232	19	then	then	ADV
ejpam-5594	232	20	one	one	PRON
ejpam-5594	232	21	has	have	VERB
ejpam-5594	232	22	1	1	NUM
ejpam-5594	232	23	ε2	ε2	ADJ
ejpam-5594	232	24	−	−	PROPN
ejpam-5594	233	1	ε1	ε1	PROPN
ejpam-5594	233	2	[	[	PUNCT
ejpam-5594	233	3	abiςε2+ε1	abiςε2+ε1	PROPN
ejpam-5594	233	4	2	2	NUM
ejpam-5594	233	5	{	{	PUNCT
ejpam-5594	233	6	φ(ε1)}+	φ(ε1)}+	PROPN
ejpam-5594	233	7	ab	ab	PROPN
ejpam-5594	233	8	ε2+ε1	ε2+ε1	PROPN
ejpam-5594	233	9	2	2	NUM
ejpam-5594	233	10	iςε2{φ(ε2	iςε2{φ(ε2	NOUN
ejpam-5594	233	11	)	)	PUNCT
ejpam-5594	233	12	}	}	PUNCT
ejpam-5594	233	13	]	]	PUNCT
ejpam-5594	234	1	−	−	PROPN
ejpam-5594	234	2	1	1	NUM
ejpam-5594	234	3	(	(	PUNCT
ejpam-5594	234	4	ε2	ε2	ADJ
ejpam-5594	234	5	−	−	PROPN
ejpam-5594	234	6	ε1)b(ς	ε1)b(ς	PROPN
ejpam-5594	234	7	)	)	PUNCT
ejpam-5594	235	1	[	[	X
ejpam-5594	235	2	φ(ε1	φ(ε1	X
ejpam-5594	235	3	)	)	PUNCT
ejpam-5594	235	4	+	+	CCONJ
ejpam-5594	235	5	φ(ε2)]−	φ(ε2)]−	PROPN
ejpam-5594	235	6	(	(	PUNCT
ejpam-5594	235	7	ε2	ε2	PROPN
ejpam-5594	235	8	−	−	PROPN
ejpam-5594	235	9	ε1	ε1	PROPN
ejpam-5594	235	10	)	)	PUNCT
ejpam-5594	235	11	ς−1	ς−1	PROPN
ejpam-5594	235	12	2ς−1b(ς)γ(ς	2ς−1b(ς)γ(ς	NUM
ejpam-5594	235	13	)	)	PUNCT
ejpam-5594	235	14	φ	φ	PROPN
ejpam-5594	235	15	(	(	PUNCT
ejpam-5594	235	16	ε2	ε2	PROPN
ejpam-5594	235	17	+	+	CCONJ
ejpam-5594	235	18	ε1	ε1	PROPN
ejpam-5594	235	19	2	2	NUM
ejpam-5594	235	20	)	)	PUNCT
ejpam-5594	235	21	=	=	SYM
ejpam-5594	235	22	(	(	PUNCT
ejpam-5594	235	23	ε2	ε2	PROPN
ejpam-5594	235	24	−	−	PROPN
ejpam-5594	235	25	ε1	ε1	PROPN
ejpam-5594	235	26	)	)	PUNCT
ejpam-5594	236	1	ς−1	ς−1	PROPN
ejpam-5594	236	2	2(ς	2(ς	NUM
ejpam-5594	236	3	+	+	CCONJ
ejpam-5594	236	4	1)b(ς)γ(ς	1)b(ς)γ(ς	NUM
ejpam-5594	236	5	)	)	PUNCT
ejpam-5594	236	6	∫	∫	NOUN
ejpam-5594	237	1	1	1	NUM
ejpam-5594	237	2	0	0	NUM
ejpam-5594	237	3	wς	wς	PROPN
ejpam-5594	237	4	(	(	PUNCT
ejpam-5594	237	5	♭	♭	INTJ
ejpam-5594	237	6	)	)	PUNCT
ejpam-5594	238	1	[	[	PUNCT
ejpam-5594	238	2	φ′′(	φ′′(	NOUN
ejpam-5594	238	3	♭	♭	PRON
ejpam-5594	238	4	ε1	ε1	VERB
ejpam-5594	238	5	+	+	CCONJ
ejpam-5594	238	6	(	(	PUNCT
ejpam-5594	238	7	1−	1−	NUM
ejpam-5594	238	8	♭	♭	INTJ
ejpam-5594	238	9	)	)	PUNCT
ejpam-5594	238	10	ε2	ε2	PROPN
ejpam-5594	238	11	)	)	PUNCT
ejpam-5594	239	1	+	+	PUNCT
ejpam-5594	239	2	φ′′(	φ′′(	NOUN
ejpam-5594	239	3	♭	♭	NUM
ejpam-5594	239	4	ε2	ε2	NOUN
ejpam-5594	239	5	+	+	CCONJ
ejpam-5594	239	6	(	(	PUNCT
ejpam-5594	239	7	1−	1−	NUM
ejpam-5594	239	8	♭	♭	INTJ
ejpam-5594	239	9	)	)	PUNCT
ejpam-5594	239	10	ε1	ε1	PROPN
ejpam-5594	239	11	)	)	PUNCT
ejpam-5594	239	12	]	]	PUNCT
ejpam-5594	240	1	d	d	X
ejpam-5594	240	2	♭	♭	INTJ
ejpam-5594	240	3	,	,	PUNCT
ejpam-5594	240	4	where	where	SCONJ
ejpam-5594	240	5	wς	wς	VERB
ejpam-5594	240	6	(	(	PUNCT
ejpam-5594	240	7	♭	♭	INTJ
ejpam-5594	240	8	)	)	PUNCT
ejpam-5594	240	9	=	=	PRON
ejpam-5594	240	10	{	{	PUNCT
ejpam-5594	240	11	♭	♭	PROPN
ejpam-5594	240	12	ς+1	ς+1	NUM
ejpam-5594	240	13	,	,	PUNCT
ejpam-5594	240	14	♭	♭	PROPN
ejpam-5594	240	15	∈	∈	PROPN
ejpam-5594	240	16	[	[	PUNCT
ejpam-5594	240	17	0	0	NUM
ejpam-5594	240	18	,	,	PUNCT
ejpam-5594	240	19	12	12	NUM
ejpam-5594	240	20	)	)	PUNCT
ejpam-5594	240	21	,	,	PUNCT
ejpam-5594	240	22	(	(	PUNCT
ejpam-5594	240	23	1−	1−	NUM
ejpam-5594	240	24	♭	♭	INTJ
ejpam-5594	240	25	)	)	PUNCT
ejpam-5594	240	26	ς+1	ς+1	PROPN
ejpam-5594	240	27	,	,	PUNCT
ejpam-5594	240	28	♭	♭	PROPN
ejpam-5594	240	29	∈	∈	PROPN
ejpam-5594	240	30	[	[	PUNCT
ejpam-5594	240	31	1	1	NUM
ejpam-5594	240	32	2	2	NUM
ejpam-5594	240	33	,	,	PUNCT
ejpam-5594	240	34	1	1	NUM
ejpam-5594	240	35	]	]	PUNCT
ejpam-5594	240	36	.	.	PUNCT
ejpam-5594	241	1	in	in	ADP
ejpam-5594	241	2	[	[	X
ejpam-5594	241	3	57	57	NUM
ejpam-5594	241	4	]	]	PUNCT
ejpam-5594	241	5	,	,	PUNCT
ejpam-5594	241	6	the	the	DET
ejpam-5594	241	7	authors	author	NOUN
ejpam-5594	241	8	introduced	introduce	VERB
ejpam-5594	241	9	these	these	DET
ejpam-5594	241	10	type	type	NOUN
ejpam-5594	241	11	of	of	ADP
ejpam-5594	241	12	inequalities	inequality	NOUN
ejpam-5594	241	13	that	that	PRON
ejpam-5594	241	14	utilize	utilize	VERB
ejpam-5594	241	15	the	the	DET
ejpam-5594	241	16	s	s	NOUN
ejpam-5594	241	17	-	-	NOUN
ejpam-5594	241	18	convexity	convexity	NOUN
ejpam-5594	241	19	with	with	ADP
ejpam-5594	241	20	the	the	DET
ejpam-5594	241	21	help	help	NOUN
ejpam-5594	241	22	of	of	ADP
ejpam-5594	241	23	lemma	lemma	PROPN
ejpam-5594	241	24	2.1	2.1	NUM
ejpam-5594	241	25	.	.	PUNCT
ejpam-5594	242	1	theorem	theorem	VERB
ejpam-5594	242	2	10	10	NUM
ejpam-5594	242	3	.	.	PUNCT
ejpam-5594	243	1	let	let	VERB
ejpam-5594	243	2	φ	φ	NOUN
ejpam-5594	243	3	:	:	PUNCT
ejpam-5594	244	1	b	b	X
ejpam-5594	244	2	⊂	⊂	X
ejpam-5594	244	3	r	r	NOUN
ejpam-5594	244	4	→	→	SYM
ejpam-5594	244	5	r	r	NOUN
ejpam-5594	244	6	is	be	AUX
ejpam-5594	244	7	a	a	DET
ejpam-5594	244	8	differentiable	differentiable	ADJ
ejpam-5594	244	9	mapping	mapping	NOUN
ejpam-5594	244	10	on	on	ADP
ejpam-5594	244	11	b	b	NOUN
ejpam-5594	244	12	◦	◦	NOUN
ejpam-5594	244	13	,	,	PUNCT
ejpam-5594	244	14	where	where	SCONJ
ejpam-5594	244	15	ε1	ε1	PROPN
ejpam-5594	244	16	,	,	PUNCT
ejpam-5594	244	17	ε2	ε2	PROPN
ejpam-5594	244	18	∈	∈	PROPN
ejpam-5594	244	19	b	b	X
ejpam-5594	244	20	◦	◦	NOUN
ejpam-5594	244	21	,	,	PUNCT
ejpam-5594	244	22	with	with	ADP
ejpam-5594	244	23	ε1	ε1	PROPN
ejpam-5594	244	24	<	<	X
ejpam-5594	244	25	ε2	ε2	PROPN
ejpam-5594	244	26	.	.	PUNCT
ejpam-5594	245	1	if	if	SCONJ
ejpam-5594	245	2	|φ′|q	|φ′|q	PUNCT
ejpam-5594	245	3	is	be	AUX
ejpam-5594	245	4	s	s	NOUN
ejpam-5594	245	5	-	-	NOUN
ejpam-5594	245	6	convex	convex	NOUN
ejpam-5594	245	7	on	on	ADP
ejpam-5594	245	8	[	[	X
ejpam-5594	245	9	ε1	ε1	NOUN
ejpam-5594	245	10	,	,	PUNCT
ejpam-5594	245	11	ε2	ε2	PROPN
ejpam-5594	245	12	]	]	PUNCT
ejpam-5594	245	13	for	for	ADP
ejpam-5594	245	14	some	some	DET
ejpam-5594	245	15	q	q	NOUN
ejpam-5594	245	16	>	>	X
ejpam-5594	245	17	1	1	NUM
ejpam-5594	245	18	,	,	PUNCT
ejpam-5594	245	19	then	then	ADV
ejpam-5594	245	20	one	one	PRON
ejpam-5594	245	21	has	have	VERB
ejpam-5594	245	22	|bk(φ	|bk(φ	NUM
ejpam-5594	245	23	,	,	PUNCT
ejpam-5594	245	24	ε1	ε1	PROPN
ejpam-5594	245	25	,	,	PUNCT
ejpam-5594	245	26	ε2)|	ε2)|	PROPN
ejpam-5594	245	27	≤	≤	PROPN
ejpam-5594	245	28	k−1∑	k−1∑	PROPN
ejpam-5594	245	29	ȷ=0	ȷ=0	PROPN
ejpam-5594	245	30	ε2	ε2	ADJ
ejpam-5594	245	31	−	−	PROPN
ejpam-5594	245	32	ε1	ε1	PROPN
ejpam-5594	245	33	2k2	2k2	NUM
ejpam-5594	245	34	(	(	PUNCT
ejpam-5594	245	35	1	1	NUM
ejpam-5594	245	36	p+	p+	NOUN
ejpam-5594	245	37	1	1	NUM
ejpam-5594	245	38	)	)	PUNCT
ejpam-5594	245	39	1	1	NUM
ejpam-5594	245	40	p	p	NOUN
ejpam-5594	245	41	(	(	PUNCT
ejpam-5594	245	42	1	1	NUM
ejpam-5594	245	43	s+	s+	SYM
ejpam-5594	245	44	1	1	NUM
ejpam-5594	245	45	)	)	PUNCT
ejpam-5594	245	46	1	1	NUM
ejpam-5594	245	47	q	q	NOUN
ejpam-5594	245	48	×	×	NOUN
ejpam-5594	246	1	[	[	X
ejpam-5594	246	2	∣∣∣∣φ′	∣∣∣∣φ′	INTJ
ejpam-5594	246	3	(	(	PUNCT
ejpam-5594	246	4	(	(	PUNCT
ejpam-5594	246	5	k−ȷ)ε1	k−ȷ)ε1	X
ejpam-5594	246	6	+	+	NUM
ejpam-5594	246	7	ȷε2	ȷε2	NOUN
ejpam-5594	246	8	k	k	PROPN
ejpam-5594	246	9	)	)	PUNCT
ejpam-5594	246	10	∣∣∣∣q	∣∣∣∣q	PROPN
ejpam-5594	247	1	+	+	CCONJ
ejpam-5594	247	2	∣∣∣∣φ′	∣∣∣∣φ′	PROPN
ejpam-5594	247	3	(	(	PUNCT
ejpam-5594	247	4	(	(	PUNCT
ejpam-5594	247	5	k−ȷ−	k−ȷ−	PROPN
ejpam-5594	247	6	1)ε1	1)ε1	NUM
ejpam-5594	247	7	+	+	CCONJ
ejpam-5594	247	8	(	(	PUNCT
ejpam-5594	247	9	ȷ+	ȷ+	ADV
ejpam-5594	247	10	1)ε2	1)ε2	NUM
ejpam-5594	247	11	k	k	NOUN
ejpam-5594	247	12	)	)	PUNCT
ejpam-5594	247	13	∣∣∣∣q	∣∣∣∣q	PROPN
ejpam-5594	247	14	]	]	X
ejpam-5594	247	15	1	1	NUM
ejpam-5594	247	16	q	q	NOUN
ejpam-5594	247	17	holds	hold	NOUN
ejpam-5594	247	18	,	,	PUNCT
ejpam-5594	247	19	where	where	SCONJ
ejpam-5594	247	20	1	1	NUM
ejpam-5594	247	21	p	p	NOUN
ejpam-5594	248	1	+	+	NOUN
ejpam-5594	248	2	1	1	NUM
ejpam-5594	248	3	q	q	NOUN
ejpam-5594	248	4	=	=	ADJ
ejpam-5594	248	5	1	1	X
ejpam-5594	248	6	.	.	PUNCT
ejpam-5594	248	7	j.	j.	PROPN
ejpam-5594	248	8	e.	e.	PROPN
ejpam-5594	248	9	maćıas	maćıas	PROPN
ejpam-5594	248	10	-	-	PUNCT
ejpam-5594	248	11	dı́az	dı́az	NOUN
ejpam-5594	248	12	et	et	NOUN
ejpam-5594	248	13	al	al	PROPN
ejpam-5594	248	14	.	.	PUNCT
ejpam-5594	248	15	/	/	SYM
ejpam-5594	248	16	eur	eur	PROPN
ejpam-5594	248	17	.	.	PUNCT
ejpam-5594	249	1	j.	j.	PROPN
ejpam-5594	249	2	pure	pure	PROPN
ejpam-5594	249	3	appl	appl	PROPN
ejpam-5594	249	4	.	.	PROPN
ejpam-5594	249	5	math	math	PROPN
ejpam-5594	249	6	,	,	PUNCT
ejpam-5594	249	7	17	17	NUM
ejpam-5594	249	8	(	(	PUNCT
ejpam-5594	249	9	4	4	NUM
ejpam-5594	249	10	)	)	PUNCT
ejpam-5594	249	11	(	(	PUNCT
ejpam-5594	249	12	2024	2024	NUM
ejpam-5594	249	13	)	)	PUNCT
ejpam-5594	249	14	,	,	PUNCT
ejpam-5594	249	15	4014	4014	NUM
ejpam-5594	249	16	-	-	SYM
ejpam-5594	249	17	4049	4049	NUM
ejpam-5594	249	18	4023	4023	NUM
ejpam-5594	249	19	3	3	NUM
ejpam-5594	249	20	.	.	PUNCT
ejpam-5594	250	1	the	the	DET
ejpam-5594	250	2	main	main	ADJ
ejpam-5594	250	3	results	result	NOUN
ejpam-5594	250	4	this	this	DET
ejpam-5594	250	5	section	section	NOUN
ejpam-5594	250	6	uses	use	VERB
ejpam-5594	250	7	the	the	DET
ejpam-5594	250	8	cr	cr	PROPN
ejpam-5594	250	9	-	-	PUNCT
ejpam-5594	250	10	h	h	NOUN
ejpam-5594	250	11	-	-	PUNCT
ejpam-5594	250	12	godunova	godunova	ADJ
ejpam-5594	250	13	-	-	PUNCT
ejpam-5594	250	14	levin	levin	PROPN
ejpam-5594	250	15	function	function	NOUN
ejpam-5594	250	16	to	to	PART
ejpam-5594	250	17	build	build	VERB
ejpam-5594	250	18	multiple	multiple	ADJ
ejpam-5594	250	19	forms	form	NOUN
ejpam-5594	250	20	of	of	ADP
ejpam-5594	250	21	hermitehadamard	hermitehadamard	NOUN
ejpam-5594	250	22	inequality	inequality	NOUN
ejpam-5594	250	23	,	,	PUNCT
ejpam-5594	250	24	with	with	ADP
ejpam-5594	250	25	several	several	ADJ
ejpam-5594	250	26	particular	particular	ADJ
ejpam-5594	250	27	cases	case	NOUN
ejpam-5594	250	28	.	.	PUNCT
ejpam-5594	250	29	theorem	theorem	NOUN
ejpam-5594	250	30	11	11	NUM
ejpam-5594	250	31	.	.	PUNCT
ejpam-5594	251	1	let	let	VERB
ejpam-5594	251	2	h	h	NOUN
ejpam-5594	251	3	:	:	PUNCT
ejpam-5594	251	4	(	(	PUNCT
ejpam-5594	251	5	0	0	NUM
ejpam-5594	251	6	,	,	PUNCT
ejpam-5594	251	7	1	1	NUM
ejpam-5594	251	8	)	)	PUNCT
ejpam-5594	251	9	→	→	NOUN
ejpam-5594	251	10	r+	r+	NOUN
ejpam-5594	251	11	and	and	CCONJ
ejpam-5594	251	12	h	h	NOUN
ejpam-5594	251	13	̸=	̸=	PROPN
ejpam-5594	251	14	0	0	NUM
ejpam-5594	251	15	.	.	PUNCT
ejpam-5594	252	1	let	let	VERB
ejpam-5594	252	2	φ	φ	NOUN
ejpam-5594	252	3	:	:	PUNCT
ejpam-5594	253	1	[	[	X
ejpam-5594	253	2	ε1	ε1	NOUN
ejpam-5594	253	3	,	,	PUNCT
ejpam-5594	253	4	ε2	ε2	PROPN
ejpam-5594	253	5	]	]	PUNCT
ejpam-5594	253	6	→	→	SYM
ejpam-5594	253	7	r+	r+	NOUN
ejpam-5594	253	8	i	i	PRON
ejpam-5594	253	9	is	be	AUX
ejpam-5594	253	10	cr	cr	PROPN
ejpam-5594	253	11	-	-	PUNCT
ejpam-5594	253	12	h	h	NOUN
ejpam-5594	253	13	-	-	PUNCT
ejpam-5594	253	14	godunovalevin	godunovalevin	ADJ
ejpam-5594	253	15	mapping	mapping	NOUN
ejpam-5594	253	16	,	,	PUNCT
ejpam-5594	253	17	ε1	ε1	PROPN
ejpam-5594	253	18	,	,	PUNCT
ejpam-5594	253	19	ε2	ε2	PROPN
ejpam-5594	253	20	∈	∈	PROPN
ejpam-5594	253	21	r+	r+	NOUN
ejpam-5594	253	22	,	,	PUNCT
ejpam-5594	253	23	ε1	ε1	VERB
ejpam-5594	253	24	<	<	X
ejpam-5594	253	25	ε2	ε2	PROPN
ejpam-5594	253	26	.	.	PUNCT
ejpam-5594	254	1	if	if	SCONJ
ejpam-5594	254	2	φ	φ	PROPN
ejpam-5594	254	3	∈	∈	PROPN
ejpam-5594	254	4	l[ε1	l[ε1	NOUN
ejpam-5594	254	5	,	,	PUNCT
ejpam-5594	254	6	ε2	ε2	PROPN
ejpam-5594	254	7	]	]	PUNCT
ejpam-5594	254	8	,	,	PUNCT
ejpam-5594	254	9	then	then	ADV
ejpam-5594	254	10	the	the	DET
ejpam-5594	254	11	following	follow	VERB
ejpam-5594	254	12	relation	relation	NOUN
ejpam-5594	254	13	holds	hold	VERB
ejpam-5594	254	14	true	true	ADJ
ejpam-5594	254	15	:	:	PUNCT
ejpam-5594	254	16	h	h	NOUN
ejpam-5594	254	17	(	(	PUNCT
ejpam-5594	254	18	1	1	NUM
ejpam-5594	254	19	2	2	NUM
ejpam-5594	254	20	)	)	PUNCT
ejpam-5594	254	21	(	(	PUNCT
ejpam-5594	254	22	ε2	ε2	ADJ
ejpam-5594	254	23	−	−	PROPN
ejpam-5594	254	24	ε1	ε1	PROPN
ejpam-5594	254	25	)	)	PUNCT
ejpam-5594	254	26	ς	ς	NOUN
ejpam-5594	254	27	b(ς)γ(ς	b(ς)γ(ς	X
ejpam-5594	254	28	)	)	PUNCT
ejpam-5594	254	29	φ	φ	PROPN
ejpam-5594	254	30	(	(	PUNCT
ejpam-5594	254	31	ε2	ε2	PROPN
ejpam-5594	254	32	+	+	CCONJ
ejpam-5594	254	33	ε1	ε1	PROPN
ejpam-5594	254	34	2	2	NUM
ejpam-5594	254	35	)	)	PUNCT
ejpam-5594	254	36	+	+	NUM
ejpam-5594	254	37	1−	1−	NUM
ejpam-5594	254	38	ς	ς	X
ejpam-5594	254	39	b(ς	b(ς	PROPN
ejpam-5594	254	40	)	)	PUNCT
ejpam-5594	254	41	[	[	PUNCT
ejpam-5594	254	42	φ(ε1	φ(ε1	NOUN
ejpam-5594	254	43	)	)	PUNCT
ejpam-5594	254	44	+	+	SYM
ejpam-5594	254	45	φ(ε2	φ(ε2	NUM
ejpam-5594	254	46	)	)	PUNCT
ejpam-5594	254	47	]	]	PUNCT
ejpam-5594	254	48	⪯cr	⪯cr	VERB
ejpam-5594	254	49	ab	ab	PROPN
ejpam-5594	254	50	ε1i	ε1i	PROPN
ejpam-5594	254	51	ς	ς	PROPN
ejpam-5594	254	52	ε2{φ(ε2)}+	ε2{φ(ε2)}+	PROPN
ejpam-5594	254	53	abiςε2{φ(ε1	abiςε2{φ(ε1	PROPN
ejpam-5594	254	54	)	)	PUNCT
ejpam-5594	254	55	}	}	PUNCT
ejpam-5594	254	56	⪯cr	⪯cr	X
ejpam-5594	254	57	[	[	PUNCT
ejpam-5594	254	58	φ(ε1	φ(ε1	NOUN
ejpam-5594	254	59	)	)	PUNCT
ejpam-5594	254	60	+	+	SYM
ejpam-5594	254	61	φ(ε2	φ(ε2	NUM
ejpam-5594	254	62	)	)	PUNCT
ejpam-5594	254	63	b(ς	b(ς	PROPN
ejpam-5594	254	64	)	)	PUNCT
ejpam-5594	254	65	]	]	PUNCT
ejpam-5594	255	1	[	[	PUNCT
ejpam-5594	255	2	1−	1−	NUM
ejpam-5594	255	3	ς	ς	NOUN
ejpam-5594	255	4	+	+	NOUN
ejpam-5594	255	5	ς(ε2	ς(ε2	NOUN
ejpam-5594	255	6	−	−	PROPN
ejpam-5594	255	7	ε1	ε1	PROPN
ejpam-5594	255	8	)	)	PUNCT
ejpam-5594	255	9	ς	ς	PROPN
ejpam-5594	255	10	γ(ς	γ(ς	NOUN
ejpam-5594	255	11	)	)	PUNCT
ejpam-5594	255	12	×	×	NOUN
ejpam-5594	255	13	∫	∫	NOUN
ejpam-5594	255	14	1	1	NUM
ejpam-5594	255	15	0	0	NUM
ejpam-5594	256	1	♭	♭	INTJ
ejpam-5594	256	2	ς−1	ς−1	PROPN
ejpam-5594	256	3	(	(	PUNCT
ejpam-5594	256	4	1	1	NUM
ejpam-5594	256	5	h	h	NOUN
ejpam-5594	256	6	(	(	PUNCT
ejpam-5594	256	7	♭	♭	PROPN
ejpam-5594	256	8	)	)	PUNCT
ejpam-5594	257	1	+	+	CCONJ
ejpam-5594	257	2	1	1	NUM
ejpam-5594	257	3	h(1−	h(1−	NOUN
ejpam-5594	257	4	♭	♭	PROPN
ejpam-5594	257	5	)	)	PUNCT
ejpam-5594	257	6	)	)	PUNCT
ejpam-5594	258	1	d	d	X
ejpam-5594	258	2	♭	♭	X
ejpam-5594	258	3	]	]	PUNCT
ejpam-5594	258	4	,	,	PUNCT
ejpam-5594	258	5	(	(	PUNCT
ejpam-5594	258	6	3	3	X
ejpam-5594	258	7	)	)	PUNCT
ejpam-5594	258	8	where	where	SCONJ
ejpam-5594	258	9	ς	ς	PROPN
ejpam-5594	258	10	∈	∈	PROPN
ejpam-5594	258	11	(	(	PUNCT
ejpam-5594	258	12	0	0	NUM
ejpam-5594	258	13	,	,	PUNCT
ejpam-5594	258	14	1	1	NUM
ejpam-5594	258	15	)	)	PUNCT
ejpam-5594	258	16	.	.	PUNCT
ejpam-5594	259	1	proof	proof	NOUN
ejpam-5594	259	2	.	.	PUNCT
ejpam-5594	260	1	as	as	ADP
ejpam-5594	260	2	φ	φ	PROPN
ejpam-5594	260	3	∈	∈	PROPN
ejpam-5594	260	4	sgx(h	sgx(h	PROPN
ejpam-5594	260	5	,	,	PUNCT
ejpam-5594	260	6	[	[	X
ejpam-5594	260	7	ε1	ε1	PROPN
ejpam-5594	260	8	,	,	PUNCT
ejpam-5594	260	9	ε2],r	ε2],r	NOUN
ejpam-5594	260	10	+	+	CCONJ
ejpam-5594	260	11	i	i	PROPN
ejpam-5594	260	12	)	)	PUNCT
ejpam-5594	260	13	,	,	PUNCT
ejpam-5594	260	14	we	we	PRON
ejpam-5594	260	15	have	have	VERB
ejpam-5594	260	16	φ	φ	PROPN
ejpam-5594	260	17	(	(	PUNCT
ejpam-5594	260	18	ν1	ν1	NOUN
ejpam-5594	260	19	+	+	CCONJ
ejpam-5594	260	20	ν2	ν2	PROPN
ejpam-5594	260	21	2	2	NUM
ejpam-5594	260	22	)	)	PUNCT
ejpam-5594	260	23	⪯cr	⪯cr	VERB
ejpam-5594	260	24	1	1	NUM
ejpam-5594	260	25	[	[	PUNCT
ejpam-5594	260	26	h	h	NOUN
ejpam-5594	260	27	(	(	PUNCT
ejpam-5594	260	28	1	1	NUM
ejpam-5594	260	29	2	2	NUM
ejpam-5594	260	30	)	)	PUNCT
ejpam-5594	260	31	]	]	PUNCT
ejpam-5594	261	1	[	[	X
ejpam-5594	261	2	φ(ν1	φ(ν1	NOUN
ejpam-5594	261	3	)	)	PUNCT
ejpam-5594	261	4	+	+	NOUN
ejpam-5594	261	5	φ(ν2	φ(ν2	NOUN
ejpam-5594	261	6	)	)	PUNCT
ejpam-5594	261	7	]	]	PUNCT
ejpam-5594	261	8	,	,	PUNCT
ejpam-5594	261	9	let	let	VERB
ejpam-5594	261	10	ν1	ν1	NOUN
ejpam-5594	261	11	=	=	SYM
ejpam-5594	261	12	♭	♭	PROPN
ejpam-5594	261	13	ε1	ε1	VERB
ejpam-5594	261	14	+	+	CCONJ
ejpam-5594	261	15	(	(	PUNCT
ejpam-5594	261	16	1−	1−	NUM
ejpam-5594	261	17	♭	♭	INTJ
ejpam-5594	261	18	)	)	PUNCT
ejpam-5594	261	19	ε2	ε2	ADJ
ejpam-5594	261	20	,	,	PUNCT
ejpam-5594	261	21	ν2	ν2	NOUN
ejpam-5594	261	22	=	=	SYM
ejpam-5594	261	23	♭	♭	PROPN
ejpam-5594	261	24	ε2	ε2	ADJ
ejpam-5594	261	25	+	+	CCONJ
ejpam-5594	261	26	(	(	PUNCT
ejpam-5594	261	27	1−	1−	NUM
ejpam-5594	261	28	♭	♭	INTJ
ejpam-5594	261	29	)	)	PUNCT
ejpam-5594	261	30	ε1	ε1	PROPN
ejpam-5594	261	31	,	,	PUNCT
ejpam-5594	261	32	the	the	DET
ejpam-5594	261	33	above	above	ADJ
ejpam-5594	261	34	relation	relation	NOUN
ejpam-5594	261	35	becomes	become	VERB
ejpam-5594	261	36	as	as	SCONJ
ejpam-5594	261	37	h	h	NOUN
ejpam-5594	261	38	(	(	PUNCT
ejpam-5594	261	39	1	1	NUM
ejpam-5594	261	40	2	2	NUM
ejpam-5594	261	41	)	)	PUNCT
ejpam-5594	261	42	φ	φ	PROPN
ejpam-5594	261	43	(	(	PUNCT
ejpam-5594	261	44	ε2	ε2	PROPN
ejpam-5594	261	45	+	+	CCONJ
ejpam-5594	261	46	ε1	ε1	PROPN
ejpam-5594	261	47	2	2	NUM
ejpam-5594	261	48	)	)	PUNCT
ejpam-5594	261	49	⪯cr	⪯cr	VERB
ejpam-5594	261	50	[	[	PUNCT
ejpam-5594	261	51	φ(	φ(	NUM
ejpam-5594	261	52	♭	♭	PROPN
ejpam-5594	261	53	ε1	ε1	VERB
ejpam-5594	261	54	+	+	CCONJ
ejpam-5594	261	55	(	(	PUNCT
ejpam-5594	261	56	1−	1−	NUM
ejpam-5594	261	57	♭	♭	INTJ
ejpam-5594	261	58	)	)	PUNCT
ejpam-5594	261	59	ε2	ε2	PROPN
ejpam-5594	261	60	)	)	PUNCT
ejpam-5594	261	61	+	+	CCONJ
ejpam-5594	262	1	φ(	φ(	NUM
ejpam-5594	262	2	♭	♭	NOUN
ejpam-5594	262	3	ε2	ε2	ADJ
ejpam-5594	262	4	+	+	CCONJ
ejpam-5594	262	5	(	(	PUNCT
ejpam-5594	262	6	1−	1−	NUM
ejpam-5594	262	7	♭	♭	INTJ
ejpam-5594	262	8	)	)	PUNCT
ejpam-5594	262	9	ε1	ε1	PROPN
ejpam-5594	262	10	)	)	PUNCT
ejpam-5594	262	11	]	]	PUNCT
ejpam-5594	262	12	.	.	PUNCT
ejpam-5594	263	1	(	(	PUNCT
ejpam-5594	263	2	4	4	X
ejpam-5594	263	3	)	)	PUNCT
ejpam-5594	263	4	multiplying	multiply	VERB
ejpam-5594	263	5	by	by	ADP
ejpam-5594	263	6	♭	♭	PROPN
ejpam-5594	263	7	ς−1	ς−1	PROPN
ejpam-5594	263	8	in	in	ADP
ejpam-5594	263	9	(	(	PUNCT
ejpam-5594	263	10	4	4	NUM
ejpam-5594	263	11	)	)	PUNCT
ejpam-5594	263	12	and	and	CCONJ
ejpam-5594	263	13	integrating	integrating	NOUN
ejpam-5594	263	14	,	,	PUNCT
ejpam-5594	263	15	we	we	PRON
ejpam-5594	263	16	have	have	VERB
ejpam-5594	263	17	1	1	NUM
ejpam-5594	263	18	ς	ς	PROPN
ejpam-5594	263	19	φ	φ	X
ejpam-5594	263	20	(	(	PUNCT
ejpam-5594	263	21	ε2	ε2	PROPN
ejpam-5594	263	22	+	+	CCONJ
ejpam-5594	263	23	ε1	ε1	PROPN
ejpam-5594	263	24	2	2	NUM
ejpam-5594	263	25	)	)	PUNCT
ejpam-5594	263	26	⪯cr	⪯cr	VERB
ejpam-5594	263	27	1	1	NUM
ejpam-5594	263	28	h	h	NOUN
ejpam-5594	263	29	(	(	PUNCT
ejpam-5594	263	30	1	1	NUM
ejpam-5594	263	31	2	2	NUM
ejpam-5594	263	32	)	)	PUNCT
ejpam-5594	264	1	[	[	X
ejpam-5594	264	2	∫	∫	X
ejpam-5594	264	3	1	1	NUM
ejpam-5594	264	4	0	0	NUM
ejpam-5594	264	5	♭	♭	PROPN
ejpam-5594	264	6	ς−1φ(	ς−1φ(	NOUN
ejpam-5594	264	7	♭	♭	PROPN
ejpam-5594	264	8	ε1	ε1	VERB
ejpam-5594	264	9	+	+	CCONJ
ejpam-5594	264	10	(	(	PUNCT
ejpam-5594	264	11	1−	1−	NUM
ejpam-5594	264	12	♭	♭	NOUN
ejpam-5594	264	13	)	)	PUNCT
ejpam-5594	264	14	ε2)d	ε2)d	NOUN
ejpam-5594	264	15	♭	♭	PROPN
ejpam-5594	265	1	+	+	NUM
ejpam-5594	265	2	∫	∫	PROPN
ejpam-5594	265	3	1	1	NUM
ejpam-5594	265	4	0	0	NUM
ejpam-5594	265	5	♭	♭	PROPN
ejpam-5594	265	6	ς−1φ(	ς−1φ(	NOUN
ejpam-5594	265	7	♭	♭	NOUN
ejpam-5594	265	8	ε2	ε2	NOUN
ejpam-5594	265	9	+	+	CCONJ
ejpam-5594	265	10	(	(	PUNCT
ejpam-5594	265	11	1−	1−	NUM
ejpam-5594	265	12	♭	♭	INTJ
ejpam-5594	265	13	)	)	PUNCT
ejpam-5594	265	14	ε1)d	ε1)d	NOUN
ejpam-5594	265	15	♭	♭	PROPN
ejpam-5594	265	16	]	]	PUNCT
ejpam-5594	265	17	,	,	PUNCT
ejpam-5594	265	18	that	that	PRON
ejpam-5594	265	19	is	is	ADV
ejpam-5594	265	20	h	h	NOUN
ejpam-5594	265	21	(	(	PUNCT
ejpam-5594	265	22	1	1	NUM
ejpam-5594	265	23	2	2	NUM
ejpam-5594	265	24	)	)	PUNCT
ejpam-5594	265	25	ς	ς	PROPN
ejpam-5594	265	26	φ	φ	PROPN
ejpam-5594	265	27	(	(	PUNCT
ejpam-5594	265	28	ε2	ε2	PROPN
ejpam-5594	265	29	+	+	CCONJ
ejpam-5594	265	30	ε1	ε1	PROPN
ejpam-5594	265	31	2	2	NUM
ejpam-5594	265	32	)	)	PUNCT
ejpam-5594	265	33	⪯cr	⪯cr	VERB
ejpam-5594	265	34	∫	∫	PROPN
ejpam-5594	265	35	1	1	NUM
ejpam-5594	265	36	0	0	NUM
ejpam-5594	265	37	♭	♭	PROPN
ejpam-5594	265	38	ς−1φ(	ς−1φ(	NOUN
ejpam-5594	265	39	♭	♭	PROPN
ejpam-5594	265	40	ε1	ε1	VERB
ejpam-5594	265	41	+	+	CCONJ
ejpam-5594	265	42	(	(	PUNCT
ejpam-5594	265	43	1−	1−	NUM
ejpam-5594	265	44	♭	♭	NOUN
ejpam-5594	265	45	)	)	PUNCT
ejpam-5594	265	46	ε2)d	ε2)d	NOUN
ejpam-5594	265	47	♭	♭	PROPN
ejpam-5594	266	1	+	+	NUM
ejpam-5594	266	2	∫	∫	PROPN
ejpam-5594	266	3	1	1	NUM
ejpam-5594	266	4	0	0	NUM
ejpam-5594	266	5	♭	♭	PROPN
ejpam-5594	266	6	ς−1φ(	ς−1φ(	NOUN
ejpam-5594	266	7	♭	♭	NOUN
ejpam-5594	266	8	ε2	ε2	NOUN
ejpam-5594	266	9	+	+	CCONJ
ejpam-5594	266	10	(	(	PUNCT
ejpam-5594	266	11	1−	1−	NUM
ejpam-5594	266	12	♭	♭	INTJ
ejpam-5594	266	13	)	)	PUNCT
ejpam-5594	266	14	ε1)d	ε1)d	PROPN
ejpam-5594	266	15	♭	♭	PROPN
ejpam-5594	266	16	.	.	PUNCT
ejpam-5594	267	1	j.	j.	PROPN
ejpam-5594	267	2	e.	e.	PROPN
ejpam-5594	267	3	maćıas	maćıas	PROPN
ejpam-5594	267	4	-	-	PUNCT
ejpam-5594	267	5	dı́az	dı́az	NOUN
ejpam-5594	267	6	et	et	NOUN
ejpam-5594	267	7	al	al	PROPN
ejpam-5594	267	8	.	.	PUNCT
ejpam-5594	267	9	/	/	SYM
ejpam-5594	267	10	eur	eur	PROPN
ejpam-5594	267	11	.	.	PUNCT
ejpam-5594	268	1	j.	j.	PROPN
ejpam-5594	268	2	pure	pure	PROPN
ejpam-5594	268	3	appl	appl	PROPN
ejpam-5594	268	4	.	.	PROPN
ejpam-5594	268	5	math	math	PROPN
ejpam-5594	268	6	,	,	PUNCT
ejpam-5594	268	7	17	17	NUM
ejpam-5594	268	8	(	(	PUNCT
ejpam-5594	268	9	4	4	NUM
ejpam-5594	268	10	)	)	PUNCT
ejpam-5594	268	11	(	(	PUNCT
ejpam-5594	268	12	2024	2024	NUM
ejpam-5594	268	13	)	)	PUNCT
ejpam-5594	268	14	,	,	PUNCT
ejpam-5594	268	15	4014	4014	NUM
ejpam-5594	268	16	-	-	SYM
ejpam-5594	268	17	4049	4049	NUM
ejpam-5594	268	18	4024	4024	NUM
ejpam-5594	268	19	multiplying	multiply	VERB
ejpam-5594	268	20	the	the	DET
ejpam-5594	268	21	above	above	ADJ
ejpam-5594	268	22	relation	relation	NOUN
ejpam-5594	268	23	with	with	ADP
ejpam-5594	268	24	ς(ε2−ε1)ς	ς(ε2−ε1)ς	NOUN
ejpam-5594	268	25	b(ς)γ(ς	b(ς)γ(ς	NOUN
ejpam-5594	268	26	)	)	PUNCT
ejpam-5594	268	27	and	and	CCONJ
ejpam-5594	268	28	adding	add	VERB
ejpam-5594	268	29	the	the	DET
ejpam-5594	268	30	expression	expression	NOUN
ejpam-5594	268	31	1−ς	1−ς	NUM
ejpam-5594	268	32	b(ς	b(ς	PROPN
ejpam-5594	268	33	)	)	PUNCT
ejpam-5594	269	1	[	[	PUNCT
ejpam-5594	269	2	φ(ε1)+φ(ε2	φ(ε1)+φ(ε2	NUM
ejpam-5594	269	3	)	)	PUNCT
ejpam-5594	269	4	]	]	PUNCT
ejpam-5594	269	5	,	,	PUNCT
ejpam-5594	269	6	we	we	PRON
ejpam-5594	269	7	get	get	VERB
ejpam-5594	269	8	that	that	DET
ejpam-5594	269	9	h	h	NOUN
ejpam-5594	269	10	(	(	PUNCT
ejpam-5594	269	11	1	1	NUM
ejpam-5594	269	12	2	2	NUM
ejpam-5594	269	13	)	)	PUNCT
ejpam-5594	269	14	(	(	PUNCT
ejpam-5594	269	15	ε2	ε2	ADJ
ejpam-5594	269	16	−	−	PROPN
ejpam-5594	269	17	ε1	ε1	PROPN
ejpam-5594	269	18	)	)	PUNCT
ejpam-5594	269	19	ς	ς	NOUN
ejpam-5594	269	20	b(ς)γ(ς	b(ς)γ(ς	X
ejpam-5594	269	21	)	)	PUNCT
ejpam-5594	269	22	φ	φ	PROPN
ejpam-5594	269	23	(	(	PUNCT
ejpam-5594	269	24	ε2	ε2	PROPN
ejpam-5594	269	25	+	+	CCONJ
ejpam-5594	269	26	ε1	ε1	PROPN
ejpam-5594	269	27	2	2	NUM
ejpam-5594	269	28	)	)	PUNCT
ejpam-5594	269	29	+	+	NUM
ejpam-5594	270	1	1−	1−	NUM
ejpam-5594	270	2	ς	ς	X
ejpam-5594	270	3	b(ς	b(ς	PROPN
ejpam-5594	270	4	)	)	PUNCT
ejpam-5594	270	5	[	[	PUNCT
ejpam-5594	270	6	φ(ε1	φ(ε1	NOUN
ejpam-5594	270	7	)	)	PUNCT
ejpam-5594	270	8	+	+	SYM
ejpam-5594	270	9	φ(ε2	φ(ε2	NUM
ejpam-5594	270	10	)	)	PUNCT
ejpam-5594	270	11	]	]	PUNCT
ejpam-5594	270	12	⪯cr	⪯cr	X
ejpam-5594	270	13	ς(ε2	ς(ε2	NUM
ejpam-5594	270	14	−	−	PROPN
ejpam-5594	270	15	ε1	ε1	PROPN
ejpam-5594	270	16	)	)	PUNCT
ejpam-5594	270	17	ς	ς	NOUN
ejpam-5594	270	18	b(ς)γ(ς	b(ς)γ(ς	X
ejpam-5594	270	19	)	)	PUNCT
ejpam-5594	270	20	∫	∫	PROPN
ejpam-5594	271	1	1	1	NUM
ejpam-5594	271	2	0	0	NUM
ejpam-5594	271	3	♭	♭	PROPN
ejpam-5594	271	4	ς−1φ(	ς−1φ(	NOUN
ejpam-5594	271	5	♭	♭	PROPN
ejpam-5594	271	6	ε1	ε1	VERB
ejpam-5594	271	7	+	+	CCONJ
ejpam-5594	271	8	(	(	PUNCT
ejpam-5594	271	9	1−	1−	NUM
ejpam-5594	271	10	♭	♭	NOUN
ejpam-5594	271	11	)	)	PUNCT
ejpam-5594	271	12	ε2)d	ε2)d	NOUN
ejpam-5594	271	13	♭	♭	PROPN
ejpam-5594	272	1	+	+	NUM
ejpam-5594	272	2	ς(ε2	ς(ε2	NOUN
ejpam-5594	272	3	−	−	PROPN
ejpam-5594	272	4	ε1	ε1	PROPN
ejpam-5594	272	5	)	)	PUNCT
ejpam-5594	272	6	ς	ς	NOUN
ejpam-5594	272	7	b(ς)γ(ς	b(ς)γ(ς	X
ejpam-5594	272	8	)	)	PUNCT
ejpam-5594	272	9	∫	∫	PROPN
ejpam-5594	272	10	1	1	NUM
ejpam-5594	272	11	0	0	NUM
ejpam-5594	272	12	♭	♭	PROPN
ejpam-5594	272	13	ς−1φ(	ς−1φ(	NOUN
ejpam-5594	272	14	♭	♭	NOUN
ejpam-5594	272	15	ε2	ε2	NOUN
ejpam-5594	272	16	+	+	CCONJ
ejpam-5594	272	17	(	(	PUNCT
ejpam-5594	272	18	1−	1−	NUM
ejpam-5594	272	19	♭	♭	INTJ
ejpam-5594	272	20	)	)	PUNCT
ejpam-5594	272	21	ε1)d	ε1)d	NOUN
ejpam-5594	272	22	♭	♭	PROPN
ejpam-5594	272	23	+	+	PROPN
ejpam-5594	272	24	1−	1−	NUM
ejpam-5594	272	25	ς	ς	X
ejpam-5594	272	26	b(ς	b(ς	PROPN
ejpam-5594	272	27	)	)	PUNCT
ejpam-5594	272	28	[	[	PUNCT
ejpam-5594	272	29	φ(ε1	φ(ε1	NOUN
ejpam-5594	272	30	)	)	PUNCT
ejpam-5594	272	31	+	+	SYM
ejpam-5594	272	32	φ(ε2	φ(ε2	NUM
ejpam-5594	272	33	)	)	PUNCT
ejpam-5594	272	34	]	]	PUNCT
ejpam-5594	272	35	.	.	PUNCT
ejpam-5594	273	1	in	in	ADP
ejpam-5594	273	2	the	the	DET
ejpam-5594	273	3	final	final	ADJ
ejpam-5594	273	4	two	two	NUM
ejpam-5594	273	5	integrals	integral	NOUN
ejpam-5594	273	6	of	of	ADP
ejpam-5594	273	7	the	the	DET
ejpam-5594	273	8	preceding	precede	VERB
ejpam-5594	273	9	relation	relation	NOUN
ejpam-5594	273	10	,	,	PUNCT
ejpam-5594	273	11	let	let	VERB
ejpam-5594	273	12	a	a	DET
ejpam-5594	273	13	=	=	SYM
ejpam-5594	273	14	♭	♭	PROPN
ejpam-5594	273	15	ε1	ε1	VERB
ejpam-5594	273	16	+	+	CCONJ
ejpam-5594	273	17	(	(	PUNCT
ejpam-5594	273	18	1	1	NUM
ejpam-5594	273	19	−	−	PROPN
ejpam-5594	273	20	♭	♭	INTJ
ejpam-5594	273	21	)	)	PUNCT
ejpam-5594	273	22	ε2	ε2	PROPN
ejpam-5594	273	23	and	and	CCONJ
ejpam-5594	273	24	b	b	X
ejpam-5594	273	25	=	=	SYM
ejpam-5594	273	26	♭	♭	PROPN
ejpam-5594	273	27	ε2	ε2	PROPN
ejpam-5594	273	28	+	+	CCONJ
ejpam-5594	273	29	(	(	PUNCT
ejpam-5594	273	30	1−	1−	NUM
ejpam-5594	273	31	♭	♭	INTJ
ejpam-5594	273	32	)	)	PUNCT
ejpam-5594	273	33	ε1	ε1	VERB
ejpam-5594	273	34	respectively	respectively	ADV
ejpam-5594	273	35	,	,	PUNCT
ejpam-5594	273	36	we	we	PRON
ejpam-5594	273	37	have	have	AUX
ejpam-5594	273	38	h	h	NOUN
ejpam-5594	273	39	(	(	PUNCT
ejpam-5594	273	40	1	1	NUM
ejpam-5594	273	41	2	2	NUM
ejpam-5594	273	42	)	)	PUNCT
ejpam-5594	273	43	(	(	PUNCT
ejpam-5594	274	1	ε2	ε2	ADJ
ejpam-5594	274	2	−	−	PROPN
ejpam-5594	274	3	ε1	ε1	PROPN
ejpam-5594	274	4	)	)	PUNCT
ejpam-5594	274	5	ς	ς	NOUN
ejpam-5594	274	6	b(ς)γ(ς	b(ς)γ(ς	X
ejpam-5594	274	7	)	)	PUNCT
ejpam-5594	274	8	φ	φ	PROPN
ejpam-5594	274	9	(	(	PUNCT
ejpam-5594	274	10	ε2	ε2	PROPN
ejpam-5594	274	11	+	+	CCONJ
ejpam-5594	274	12	ε1	ε1	PROPN
ejpam-5594	274	13	2	2	NUM
ejpam-5594	274	14	)	)	PUNCT
ejpam-5594	274	15	+	+	NUM
ejpam-5594	274	16	1−	1−	NUM
ejpam-5594	274	17	ς	ς	X
ejpam-5594	274	18	b(ς	b(ς	PROPN
ejpam-5594	274	19	)	)	PUNCT
ejpam-5594	274	20	[	[	PUNCT
ejpam-5594	274	21	φ(ε1	φ(ε1	NOUN
ejpam-5594	274	22	)	)	PUNCT
ejpam-5594	274	23	+	+	SYM
ejpam-5594	274	24	φ(ε2	φ(ε2	NUM
ejpam-5594	274	25	)	)	PUNCT
ejpam-5594	274	26	]	]	PUNCT
ejpam-5594	275	1	≤	≤	NUM
ejpam-5594	275	2	ab	ab	X
ejpam-5594	275	3	ε1i	ε1i	PROPN
ejpam-5594	275	4	ς	ς	PROPN
ejpam-5594	275	5	ε2{φ(ε2)}+	ε2{φ(ε2)}+	PROPN
ejpam-5594	275	6	abiςε2{φ(ε1	abiςε2{φ(ε1	PROPN
ejpam-5594	275	7	)	)	PUNCT
ejpam-5594	275	8	}	}	PUNCT
ejpam-5594	275	9	,	,	PUNCT
ejpam-5594	275	10	so	so	CCONJ
ejpam-5594	275	11	the	the	DET
ejpam-5594	275	12	first	first	ADJ
ejpam-5594	275	13	relation	relation	NOUN
ejpam-5594	275	14	of	of	ADP
ejpam-5594	275	15	(	(	PUNCT
ejpam-5594	275	16	3	3	X
ejpam-5594	275	17	)	)	PUNCT
ejpam-5594	275	18	holds	hold	VERB
ejpam-5594	275	19	.	.	PUNCT
ejpam-5594	276	1	taking	take	VERB
ejpam-5594	276	2	into	into	ADP
ejpam-5594	276	3	account	account	NOUN
ejpam-5594	276	4	definition	definition	NOUN
ejpam-5594	276	5	4	4	NUM
ejpam-5594	276	6	,	,	PUNCT
ejpam-5594	276	7	we	we	PRON
ejpam-5594	276	8	have	have	AUX
ejpam-5594	276	9	φ(	φ(	NUM
ejpam-5594	276	10	♭	♭	PRON
ejpam-5594	276	11	ε1	ε1	VERB
ejpam-5594	276	12	+	+	SYM
ejpam-5594	276	13	(	(	PUNCT
ejpam-5594	276	14	1−	1−	NUM
ejpam-5594	276	15	♭	♭	INTJ
ejpam-5594	276	16	)	)	PUNCT
ejpam-5594	276	17	ε2	ε2	ADJ
ejpam-5594	276	18	)	)	PUNCT
ejpam-5594	276	19	⪯cr	⪯cr	NUM
ejpam-5594	276	20	φ(ε1	φ(ε1	NOUN
ejpam-5594	276	21	)	)	PUNCT
ejpam-5594	277	1	h	h	NOUN
ejpam-5594	277	2	(	(	PUNCT
ejpam-5594	277	3	♭	♭	INTJ
ejpam-5594	277	4	)	)	PUNCT
ejpam-5594	278	1	+	+	NUM
ejpam-5594	278	2	φ(ε2	φ(ε2	NUM
ejpam-5594	278	3	)	)	PUNCT
ejpam-5594	278	4	h(1−	h(1−	PROPN
ejpam-5594	278	5	♭	♭	PROPN
ejpam-5594	278	6	)	)	PUNCT
ejpam-5594	278	7	.	.	PUNCT
ejpam-5594	278	8	.	.	PUNCT
ejpam-5594	279	1	multiplying	multiply	VERB
ejpam-5594	279	2	aforementioned	aforementione	VERB
ejpam-5594	279	3	result	result	NOUN
ejpam-5594	279	4	with	with	ADP
ejpam-5594	279	5	♭	♭	PROPN
ejpam-5594	279	6	ς−1	ς−1	PROPN
ejpam-5594	279	7	,	,	PUNCT
ejpam-5594	279	8	and	and	CCONJ
ejpam-5594	279	9	integrating	integrating	NOUN
ejpam-5594	279	10	,	,	PUNCT
ejpam-5594	279	11	we	we	PRON
ejpam-5594	279	12	have∫	have∫	VERB
ejpam-5594	280	1	1	1	NUM
ejpam-5594	280	2	0	0	NUM
ejpam-5594	280	3	♭	♭	PROPN
ejpam-5594	280	4	ς−1φ(	ς−1φ(	NOUN
ejpam-5594	280	5	♭	♭	PROPN
ejpam-5594	280	6	ε1	ε1	VERB
ejpam-5594	280	7	+	+	CCONJ
ejpam-5594	280	8	(	(	PUNCT
ejpam-5594	280	9	1−	1−	NUM
ejpam-5594	280	10	♭	♭	NOUN
ejpam-5594	280	11	)	)	PUNCT
ejpam-5594	280	12	ε2)d	ε2)d	PROPN
ejpam-5594	280	13	♭	♭	PROPN
ejpam-5594	280	14	⪯cr	⪯cr	NUM
ejpam-5594	280	15	φ(ε1	φ(ε1	NOUN
ejpam-5594	280	16	)	)	PUNCT
ejpam-5594	280	17	∫	∫	PROPN
ejpam-5594	281	1	1	1	NUM
ejpam-5594	281	2	0	0	NUM
ejpam-5594	281	3	♭	♭	PROPN
ejpam-5594	281	4	ς−1d	ς−1d	PROPN
ejpam-5594	281	5	♭	♭	PROPN
ejpam-5594	281	6	h	h	PROPN
ejpam-5594	281	7	(	(	PUNCT
ejpam-5594	281	8	♭	♭	INTJ
ejpam-5594	281	9	)	)	PUNCT
ejpam-5594	282	1	+	+	NUM
ejpam-5594	282	2	φ(ε2	φ(ε2	NUM
ejpam-5594	282	3	)	)	PUNCT
ejpam-5594	282	4	∫	∫	PROPN
ejpam-5594	283	1	1	1	NUM
ejpam-5594	283	2	0	0	NUM
ejpam-5594	283	3	♭	♭	PRON
ejpam-5594	283	4	ς−1d	ς−1d	PROPN
ejpam-5594	283	5	♭	♭	INTJ
ejpam-5594	283	6	h(1−	h(1−	PROPN
ejpam-5594	283	7	♭	♭	PROPN
ejpam-5594	283	8	)	)	PUNCT
ejpam-5594	283	9	.	.	PUNCT
ejpam-5594	284	1	(	(	PUNCT
ejpam-5594	284	2	5	5	X
ejpam-5594	284	3	)	)	PUNCT
ejpam-5594	284	4	multiplying	multiply	VERB
ejpam-5594	284	5	both	both	DET
ejpam-5594	284	6	sides	side	NOUN
ejpam-5594	284	7	of	of	ADP
ejpam-5594	284	8	(	(	PUNCT
ejpam-5594	284	9	5	5	NUM
ejpam-5594	284	10	)	)	PUNCT
ejpam-5594	284	11	by	by	ADP
ejpam-5594	284	12	ς(ε2−ε1)ς	ς(ε2−ε1)ς	NOUN
ejpam-5594	284	13	b(ς)γ(ς	b(ς)γ(ς	NOUN
ejpam-5594	284	14	)	)	PUNCT
ejpam-5594	284	15	and	and	CCONJ
ejpam-5594	284	16	adding	add	VERB
ejpam-5594	284	17	the	the	DET
ejpam-5594	284	18	expression	expression	NOUN
ejpam-5594	284	19	1−ς	1−ς	NUM
ejpam-5594	284	20	b(ς)φ(ε2	b(ς)φ(ε2	NOUN
ejpam-5594	284	21	)	)	PUNCT
ejpam-5594	284	22	to	to	ADP
ejpam-5594	284	23	both	both	DET
ejpam-5594	284	24	sides	side	NOUN
ejpam-5594	284	25	of	of	ADP
ejpam-5594	284	26	the	the	DET
ejpam-5594	284	27	desired	desire	VERB
ejpam-5594	284	28	relation	relation	NOUN
ejpam-5594	284	29	,	,	PUNCT
ejpam-5594	284	30	we	we	PRON
ejpam-5594	284	31	get	get	VERB
ejpam-5594	284	32	ς(ε2	ς(ε2	ADJ
ejpam-5594	285	1	−	−	ADP
ejpam-5594	285	2	ε1	ε1	PROPN
ejpam-5594	285	3	)	)	PUNCT
ejpam-5594	285	4	ς	ς	NOUN
ejpam-5594	285	5	b(ς)γ(ς	b(ς)γ(ς	X
ejpam-5594	285	6	)	)	PUNCT
ejpam-5594	285	7	∫	∫	PROPN
ejpam-5594	286	1	1	1	NUM
ejpam-5594	286	2	0	0	NUM
ejpam-5594	286	3	♭	♭	PROPN
ejpam-5594	286	4	ς−1φ(	ς−1φ(	NOUN
ejpam-5594	286	5	♭	♭	PROPN
ejpam-5594	286	6	ε1	ε1	VERB
ejpam-5594	286	7	+	+	CCONJ
ejpam-5594	286	8	(	(	PUNCT
ejpam-5594	286	9	1−	1−	NUM
ejpam-5594	286	10	♭	♭	NOUN
ejpam-5594	286	11	)	)	PUNCT
ejpam-5594	286	12	ε2)d	ε2)d	NOUN
ejpam-5594	286	13	♭	♭	PROPN
ejpam-5594	286	14	+	+	PROPN
ejpam-5594	286	15	1−	1−	NUM
ejpam-5594	286	16	ς	ς	PROPN
ejpam-5594	286	17	b(ς	b(ς	PROPN
ejpam-5594	286	18	)	)	PUNCT
ejpam-5594	286	19	φ(ε2	φ(ε2	PROPN
ejpam-5594	286	20	)	)	PUNCT
ejpam-5594	286	21	⪯cr	⪯cr	VERB
ejpam-5594	286	22	ς(ε2	ς(ε2	NOUN
ejpam-5594	286	23	−	−	PROPN
ejpam-5594	286	24	ε1	ε1	PROPN
ejpam-5594	286	25	)	)	PUNCT
ejpam-5594	286	26	ς	ς	NOUN
ejpam-5594	286	27	b(ς)γ(ς	b(ς)γ(ς	NUM
ejpam-5594	286	28	)	)	PUNCT
ejpam-5594	286	29	[	[	PUNCT
ejpam-5594	286	30	φ(ε1	φ(ε1	NOUN
ejpam-5594	286	31	)	)	PUNCT
ejpam-5594	286	32	∫	∫	PROPN
ejpam-5594	287	1	1	1	NUM
ejpam-5594	287	2	0	0	NUM
ejpam-5594	287	3	♭	♭	PROPN
ejpam-5594	287	4	ς−1d	ς−1d	PROPN
ejpam-5594	287	5	♭	♭	PROPN
ejpam-5594	287	6	h	h	PROPN
ejpam-5594	287	7	(	(	PUNCT
ejpam-5594	287	8	♭	♭	INTJ
ejpam-5594	287	9	)	)	PUNCT
ejpam-5594	288	1	+	+	NOUN
ejpam-5594	288	2	φ(ε2	φ(ε2	NUM
ejpam-5594	288	3	)	)	PUNCT
ejpam-5594	288	4	∫	∫	PROPN
ejpam-5594	289	1	1	1	NUM
ejpam-5594	289	2	0	0	NUM
ejpam-5594	289	3	♭	♭	PRON
ejpam-5594	289	4	ς−1d	ς−1d	PROPN
ejpam-5594	289	5	♭	♭	INTJ
ejpam-5594	289	6	h(1−	h(1−	PROPN
ejpam-5594	289	7	♭	♭	PROPN
ejpam-5594	289	8	)	)	PUNCT
ejpam-5594	289	9	]	]	PUNCT
ejpam-5594	290	1	+	+	CCONJ
ejpam-5594	290	2	1−	1−	NUM
ejpam-5594	290	3	ς	ς	PROPN
ejpam-5594	290	4	b(ς	b(ς	PROPN
ejpam-5594	290	5	)	)	PUNCT
ejpam-5594	290	6	φ(ε2	φ(ε2	NOUN
ejpam-5594	290	7	)	)	PUNCT
ejpam-5594	290	8	.	.	PUNCT
ejpam-5594	291	1	(	(	PUNCT
ejpam-5594	291	2	6	6	X
ejpam-5594	291	3	)	)	PUNCT
ejpam-5594	291	4	making	make	VERB
ejpam-5594	291	5	a	a	DET
ejpam-5594	291	6	modification	modification	NOUN
ejpam-5594	291	7	in	in	ADP
ejpam-5594	291	8	the	the	DET
ejpam-5594	291	9	previous	previous	ADJ
ejpam-5594	291	10	integral	integral	NOUN
ejpam-5594	291	11	of	of	ADP
ejpam-5594	291	12	the	the	DET
ejpam-5594	291	13	preceding	precede	VERB
ejpam-5594	291	14	relation	relation	NOUN
ejpam-5594	291	15	,	,	PUNCT
ejpam-5594	291	16	a	a	DET
ejpam-5594	291	17	=	=	X
ejpam-5594	291	18	♭	♭	PROPN
ejpam-5594	291	19	ε1+(1−	ε1+(1−	PROPN
ejpam-5594	291	20	♭	♭	PROPN
ejpam-5594	291	21	)ε2	)ε2	PROPN
ejpam-5594	291	22	,	,	PUNCT
ejpam-5594	291	23	then	then	ADV
ejpam-5594	291	24	the	the	DET
ejpam-5594	291	25	above	above	ADJ
ejpam-5594	291	26	relation	relation	NOUN
ejpam-5594	291	27	become	become	VERB
ejpam-5594	291	28	as	as	SCONJ
ejpam-5594	291	29	ab	ab	X
ejpam-5594	291	30	ε1i	ε1i	NUM
ejpam-5594	291	31	ς	ς	PROPN
ejpam-5594	291	32	ε2{φ(ε2	ε2{φ(ε2	NOUN
ejpam-5594	291	33	)	)	PUNCT
ejpam-5594	291	34	}	}	PUNCT
ejpam-5594	291	35	⪯cr	⪯cr	VERB
ejpam-5594	291	36	ς(ε2	ς(ε2	NUM
ejpam-5594	292	1	−	−	PROPN
ejpam-5594	292	2	ε1	ε1	PROPN
ejpam-5594	292	3	)	)	PUNCT
ejpam-5594	292	4	ς	ς	NOUN
ejpam-5594	292	5	b(ς)γ(ς	b(ς)γ(ς	NUM
ejpam-5594	292	6	)	)	PUNCT
ejpam-5594	292	7	[	[	PUNCT
ejpam-5594	292	8	φ(ε1	φ(ε1	NOUN
ejpam-5594	292	9	)	)	PUNCT
ejpam-5594	292	10	∫	∫	PROPN
ejpam-5594	293	1	1	1	NUM
ejpam-5594	293	2	0	0	NUM
ejpam-5594	293	3	♭	♭	PROPN
ejpam-5594	293	4	ς−1d	ς−1d	PROPN
ejpam-5594	293	5	♭	♭	PROPN
ejpam-5594	293	6	h	h	PROPN
ejpam-5594	293	7	(	(	PUNCT
ejpam-5594	293	8	♭	♭	INTJ
ejpam-5594	293	9	)	)	PUNCT
ejpam-5594	294	1	+	+	NOUN
ejpam-5594	294	2	φ(ε2	φ(ε2	NUM
ejpam-5594	294	3	)	)	PUNCT
ejpam-5594	294	4	∫	∫	PROPN
ejpam-5594	295	1	1	1	NUM
ejpam-5594	295	2	0	0	NUM
ejpam-5594	295	3	♭	♭	PRON
ejpam-5594	295	4	ς−1d	ς−1d	PROPN
ejpam-5594	295	5	♭	♭	INTJ
ejpam-5594	295	6	h(1−	h(1−	PROPN
ejpam-5594	295	7	♭	♭	PROPN
ejpam-5594	295	8	)	)	PUNCT
ejpam-5594	295	9	]	]	PUNCT
ejpam-5594	296	1	+	+	CCONJ
ejpam-5594	296	2	1−	1−	NUM
ejpam-5594	296	3	ς	ς	PROPN
ejpam-5594	296	4	b(ς	b(ς	PROPN
ejpam-5594	296	5	)	)	PUNCT
ejpam-5594	296	6	φ(ε2	φ(ε2	NOUN
ejpam-5594	296	7	)	)	PUNCT
ejpam-5594	296	8	.	.	PUNCT
ejpam-5594	297	1	(	(	PUNCT
ejpam-5594	297	2	7	7	X
ejpam-5594	297	3	)	)	PUNCT
ejpam-5594	297	4	j.	j.	PROPN
ejpam-5594	297	5	e.	e.	PROPN
ejpam-5594	297	6	maćıas	maćıas	PROPN
ejpam-5594	297	7	-	-	PUNCT
ejpam-5594	297	8	dı́az	dı́az	NOUN
ejpam-5594	297	9	et	et	NOUN
ejpam-5594	297	10	al	al	PROPN
ejpam-5594	297	11	.	.	PUNCT
ejpam-5594	297	12	/	/	SYM
ejpam-5594	297	13	eur	eur	PROPN
ejpam-5594	297	14	.	.	PUNCT
ejpam-5594	298	1	j.	j.	PROPN
ejpam-5594	298	2	pure	pure	PROPN
ejpam-5594	298	3	appl	appl	PROPN
ejpam-5594	298	4	.	.	PROPN
ejpam-5594	298	5	math	math	PROPN
ejpam-5594	298	6	,	,	PUNCT
ejpam-5594	298	7	17	17	NUM
ejpam-5594	298	8	(	(	PUNCT
ejpam-5594	298	9	4	4	NUM
ejpam-5594	298	10	)	)	PUNCT
ejpam-5594	298	11	(	(	PUNCT
ejpam-5594	298	12	2024	2024	NUM
ejpam-5594	298	13	)	)	PUNCT
ejpam-5594	298	14	,	,	PUNCT
ejpam-5594	298	15	4014	4014	NUM
ejpam-5594	298	16	-	-	SYM
ejpam-5594	298	17	4049	4049	NUM
ejpam-5594	298	18	4025	4025	NUM
ejpam-5594	298	19	again	again	ADV
ejpam-5594	298	20	by	by	ADP
ejpam-5594	298	21	definition	definition	NOUN
ejpam-5594	298	22	4	4	NUM
ejpam-5594	298	23	,	,	PUNCT
ejpam-5594	298	24	we	we	PRON
ejpam-5594	298	25	have	have	AUX
ejpam-5594	298	26	φ(	φ(	NUM
ejpam-5594	298	27	♭	♭	PRON
ejpam-5594	298	28	ε1	ε1	VERB
ejpam-5594	298	29	+	+	SYM
ejpam-5594	298	30	(	(	PUNCT
ejpam-5594	298	31	1−	1−	NUM
ejpam-5594	298	32	♭	♭	INTJ
ejpam-5594	298	33	)	)	PUNCT
ejpam-5594	298	34	ε2	ε2	ADJ
ejpam-5594	298	35	)	)	PUNCT
ejpam-5594	298	36	⪯cr	⪯cr	NUM
ejpam-5594	298	37	φ(ε1	φ(ε1	NOUN
ejpam-5594	298	38	)	)	PUNCT
ejpam-5594	298	39	h	h	NOUN
ejpam-5594	298	40	(	(	PUNCT
ejpam-5594	298	41	♭	♭	INTJ
ejpam-5594	298	42	)	)	PUNCT
ejpam-5594	299	1	+	+	NUM
ejpam-5594	299	2	φ(ε2	φ(ε2	NUM
ejpam-5594	299	3	)	)	PUNCT
ejpam-5594	299	4	h(1−	h(1−	PROPN
ejpam-5594	299	5	♭	♭	PROPN
ejpam-5594	299	6	)	)	PUNCT
ejpam-5594	299	7	.	.	PUNCT
ejpam-5594	300	1	multiplying	multiply	VERB
ejpam-5594	300	2	aforementioned	aforementioned	ADJ
ejpam-5594	300	3	relation	relation	NOUN
ejpam-5594	300	4	with	with	ADP
ejpam-5594	300	5	♭	♭	PROPN
ejpam-5594	300	6	ς−1	ς−1	PROPN
ejpam-5594	300	7	,	,	PUNCT
ejpam-5594	300	8	and	and	CCONJ
ejpam-5594	300	9	integrating	integrating	NOUN
ejpam-5594	300	10	,	,	PUNCT
ejpam-5594	300	11	we	we	PRON
ejpam-5594	300	12	have	have	VERB
ejpam-5594	300	13	ς(ε2	ς(ε2	NUM
ejpam-5594	300	14	−	−	ADP
ejpam-5594	300	15	ε1	ε1	PROPN
ejpam-5594	300	16	)	)	PUNCT
ejpam-5594	300	17	ς	ς	NOUN
ejpam-5594	300	18	b(ς)γ(ς	b(ς)γ(ς	X
ejpam-5594	300	19	)	)	PUNCT
ejpam-5594	300	20	∫	∫	PROPN
ejpam-5594	300	21	1	1	NUM
ejpam-5594	300	22	0	0	NUM
ejpam-5594	300	23	♭	♭	PROPN
ejpam-5594	300	24	ς−1φ(	ς−1φ(	NOUN
ejpam-5594	300	25	♭	♭	NOUN
ejpam-5594	300	26	ε2	ε2	NOUN
ejpam-5594	300	27	+	+	CCONJ
ejpam-5594	301	1	(	(	PUNCT
ejpam-5594	301	2	1−	1−	NUM
ejpam-5594	301	3	♭	♭	INTJ
ejpam-5594	301	4	)	)	PUNCT
ejpam-5594	301	5	ε1)d	ε1)d	NOUN
ejpam-5594	301	6	♭	♭	PROPN
ejpam-5594	302	1	+	+	PROPN
ejpam-5594	303	1	1−	1−	NUM
ejpam-5594	303	2	ς	ς	PROPN
ejpam-5594	303	3	b(ς	b(ς	PROPN
ejpam-5594	303	4	)	)	PUNCT
ejpam-5594	303	5	φ(ε1	φ(ε1	PROPN
ejpam-5594	303	6	)	)	PUNCT
ejpam-5594	303	7	⪯cr	⪯cr	VERB
ejpam-5594	303	8	ς(ε2	ς(ε2	NUM
ejpam-5594	303	9	−	−	PROPN
ejpam-5594	304	1	ε1	ε1	PROPN
ejpam-5594	304	2	)	)	PUNCT
ejpam-5594	304	3	ς	ς	NOUN
ejpam-5594	304	4	b(ς)γ(ς	b(ς)γ(ς	NUM
ejpam-5594	304	5	)	)	PUNCT
ejpam-5594	304	6	[	[	PUNCT
ejpam-5594	304	7	φ(ε2	φ(ε2	NUM
ejpam-5594	304	8	)	)	PUNCT
ejpam-5594	304	9	∫	∫	PROPN
ejpam-5594	305	1	1	1	NUM
ejpam-5594	305	2	0	0	NUM
ejpam-5594	305	3	♭	♭	PROPN
ejpam-5594	305	4	ς−1d	ς−1d	PROPN
ejpam-5594	305	5	♭	♭	PROPN
ejpam-5594	305	6	h	h	PROPN
ejpam-5594	305	7	(	(	PUNCT
ejpam-5594	305	8	♭	♭	INTJ
ejpam-5594	305	9	)	)	PUNCT
ejpam-5594	305	10	+	+	NOUN
ejpam-5594	305	11	φ(ε1	φ(ε1	NOUN
ejpam-5594	305	12	)	)	PUNCT
ejpam-5594	305	13	∫	∫	PROPN
ejpam-5594	306	1	1	1	NUM
ejpam-5594	306	2	0	0	NUM
ejpam-5594	306	3	♭	♭	PRON
ejpam-5594	306	4	ς−1d	ς−1d	PROPN
ejpam-5594	306	5	♭	♭	INTJ
ejpam-5594	306	6	h(1−	h(1−	PROPN
ejpam-5594	306	7	♭	♭	PROPN
ejpam-5594	306	8	)	)	PUNCT
ejpam-5594	306	9	]	]	PUNCT
ejpam-5594	307	1	+	+	CCONJ
ejpam-5594	307	2	1−	1−	NUM
ejpam-5594	307	3	ς	ς	PROPN
ejpam-5594	307	4	b(ς	b(ς	PROPN
ejpam-5594	307	5	)	)	PUNCT
ejpam-5594	307	6	φ(ε1	φ(ε1	PROPN
ejpam-5594	307	7	)	)	PUNCT
ejpam-5594	307	8	.	.	PUNCT
ejpam-5594	308	1	making	make	VERB
ejpam-5594	308	2	a	a	DET
ejpam-5594	308	3	modification	modification	NOUN
ejpam-5594	308	4	in	in	ADP
ejpam-5594	308	5	the	the	DET
ejpam-5594	308	6	previous	previous	ADJ
ejpam-5594	308	7	integral	integral	NOUN
ejpam-5594	308	8	of	of	ADP
ejpam-5594	308	9	the	the	DET
ejpam-5594	308	10	preceding	precede	VERB
ejpam-5594	308	11	relation	relation	NOUN
ejpam-5594	308	12	with	with	ADP
ejpam-5594	308	13	some	some	DET
ejpam-5594	308	14	dummy	dummy	ADJ
ejpam-5594	308	15	variable	variable	NOUN
ejpam-5594	308	16	,	,	PUNCT
ejpam-5594	308	17	b	b	X
ejpam-5594	308	18	=	=	SYM
ejpam-5594	308	19	♭	♭	PROPN
ejpam-5594	308	20	ε2	ε2	PROPN
ejpam-5594	308	21	+	+	CCONJ
ejpam-5594	308	22	(	(	PUNCT
ejpam-5594	308	23	1−	1−	NUM
ejpam-5594	308	24	♭	♭	INTJ
ejpam-5594	308	25	)	)	PUNCT
ejpam-5594	308	26	ε1	ε1	PROPN
ejpam-5594	308	27	,	,	PUNCT
ejpam-5594	308	28	then	then	ADV
ejpam-5594	308	29	the	the	DET
ejpam-5594	308	30	above	above	ADJ
ejpam-5594	308	31	relation	relation	NOUN
ejpam-5594	308	32	becomes	become	VERB
ejpam-5594	308	33	abiςε2{φ(ε1	abiςε2{φ(ε1	PROPN
ejpam-5594	308	34	)	)	PUNCT
ejpam-5594	308	35	}	}	PUNCT
ejpam-5594	308	36	⪯cr	⪯cr	VERB
ejpam-5594	308	37	ς(ε2	ς(ε2	NUM
ejpam-5594	308	38	−	−	PROPN
ejpam-5594	309	1	ε1	ε1	PROPN
ejpam-5594	310	1	)	)	PUNCT
ejpam-5594	310	2	ς	ς	NOUN
ejpam-5594	310	3	b(ς)γ(ς	b(ς)γ(ς	NUM
ejpam-5594	310	4	)	)	PUNCT
ejpam-5594	310	5	[	[	PUNCT
ejpam-5594	310	6	φ(ε2	φ(ε2	NUM
ejpam-5594	310	7	)	)	PUNCT
ejpam-5594	310	8	∫	∫	PROPN
ejpam-5594	311	1	1	1	NUM
ejpam-5594	311	2	0	0	NUM
ejpam-5594	311	3	♭	♭	PROPN
ejpam-5594	311	4	ς−1d	ς−1d	PROPN
ejpam-5594	311	5	♭	♭	PROPN
ejpam-5594	311	6	h	h	PROPN
ejpam-5594	311	7	(	(	PUNCT
ejpam-5594	311	8	♭	♭	INTJ
ejpam-5594	311	9	)	)	PUNCT
ejpam-5594	311	10	+	+	NOUN
ejpam-5594	311	11	φ(ε1	φ(ε1	NOUN
ejpam-5594	311	12	)	)	PUNCT
ejpam-5594	311	13	∫	∫	PROPN
ejpam-5594	312	1	1	1	NUM
ejpam-5594	312	2	0	0	NUM
ejpam-5594	312	3	♭	♭	PRON
ejpam-5594	312	4	ς−1d	ς−1d	PROPN
ejpam-5594	312	5	♭	♭	INTJ
ejpam-5594	312	6	h(1−	h(1−	PROPN
ejpam-5594	312	7	♭	♭	PROPN
ejpam-5594	312	8	)	)	PUNCT
ejpam-5594	312	9	]	]	PUNCT
ejpam-5594	313	1	+	+	CCONJ
ejpam-5594	313	2	1−	1−	NUM
ejpam-5594	313	3	ς	ς	PROPN
ejpam-5594	313	4	b(ς	b(ς	PROPN
ejpam-5594	313	5	)	)	PUNCT
ejpam-5594	313	6	φ(ε1	φ(ε1	PROPN
ejpam-5594	313	7	)	)	PUNCT
ejpam-5594	313	8	.	.	PUNCT
ejpam-5594	314	1	(	(	PUNCT
ejpam-5594	314	2	8)	8)	NUM
ejpam-5594	314	3	adding	add	VERB
ejpam-5594	314	4	(	(	PUNCT
ejpam-5594	314	5	7	7	NUM
ejpam-5594	314	6	)	)	PUNCT
ejpam-5594	314	7	and	and	CCONJ
ejpam-5594	314	8	(	(	PUNCT
ejpam-5594	314	9	8)	8)	NUM
ejpam-5594	314	10	,	,	PUNCT
ejpam-5594	314	11	we	we	PRON
ejpam-5594	314	12	can	can	AUX
ejpam-5594	314	13	get	get	VERB
ejpam-5594	314	14	that	that	SCONJ
ejpam-5594	314	15	the	the	DET
ejpam-5594	314	16	second	second	ADJ
ejpam-5594	314	17	relation	relation	NOUN
ejpam-5594	314	18	of	of	ADP
ejpam-5594	314	19	(	(	PUNCT
ejpam-5594	314	20	3	3	NUM
ejpam-5594	314	21	)	)	PUNCT
ejpam-5594	314	22	.	.	PUNCT
ejpam-5594	315	1	this	this	PRON
ejpam-5594	315	2	finishes	finish	VERB
ejpam-5594	315	3	the	the	DET
ejpam-5594	315	4	proof	proof	NOUN
ejpam-5594	315	5	.	.	PUNCT
ejpam-5594	316	1	example	example	NOUN
ejpam-5594	316	2	2	2	NUM
ejpam-5594	316	3	.	.	PUNCT
ejpam-5594	317	1	let	let	VERB
ejpam-5594	317	2	φ	φ	NOUN
ejpam-5594	317	3	:	:	PUNCT
ejpam-5594	318	1	[	[	X
ejpam-5594	318	2	1	1	NUM
ejpam-5594	318	3	,	,	PUNCT
ejpam-5594	318	4	4	4	NUM
ejpam-5594	318	5	]	]	PUNCT
ejpam-5594	318	6	→	→	PUNCT
ejpam-5594	318	7	r+	r+	PUNCT
ejpam-5594	318	8	i	i	PRON
ejpam-5594	318	9	defined	define	VERB
ejpam-5594	318	10	as	as	ADP
ejpam-5594	318	11	φ(µ	φ(µ	NOUN
ejpam-5594	318	12	)	)	PUNCT
ejpam-5594	318	13	=	=	NOUN
ejpam-5594	319	1	[	[	PUNCT
ejpam-5594	319	2	2eµ	2eµ	ADJ
ejpam-5594	319	3	+	+	CCONJ
ejpam-5594	319	4	1	1	NUM
ejpam-5594	319	5	,	,	PUNCT
ejpam-5594	319	6	3eµ	3eµ	NOUN
ejpam-5594	319	7	+	+	CCONJ
ejpam-5594	319	8	√	√	PROPN
ejpam-5594	319	9	µ	µ	DET
ejpam-5594	319	10	3	3	NUM
ejpam-5594	319	11	]	]	PUNCT
ejpam-5594	319	12	with	with	ADP
ejpam-5594	319	13	h	h	PROPN
ejpam-5594	319	14	(	(	PUNCT
ejpam-5594	319	15	♭	♭	INTJ
ejpam-5594	319	16	)	)	PUNCT
ejpam-5594	319	17	=	=	SYM
ejpam-5594	319	18	1	1	NUM
ejpam-5594	319	19	♭	♭	INTJ
ejpam-5594	319	20	,	,	PUNCT
ejpam-5594	319	21	ς	ς	PROPN
ejpam-5594	319	22	=	=	NOUN
ejpam-5594	319	23	1	1	NUM
ejpam-5594	319	24	2	2	NUM
ejpam-5594	319	25	,	,	PUNCT
ejpam-5594	319	26	then	then	ADV
ejpam-5594	319	27	we	we	PRON
ejpam-5594	319	28	have	have	VERB
ejpam-5594	319	29	h	h	NOUN
ejpam-5594	319	30	(	(	PUNCT
ejpam-5594	319	31	1	1	NUM
ejpam-5594	319	32	2	2	NUM
ejpam-5594	319	33	)	)	PUNCT
ejpam-5594	319	34	(	(	PUNCT
ejpam-5594	319	35	ε2	ε2	ADJ
ejpam-5594	319	36	−	−	PROPN
ejpam-5594	319	37	ε1	ε1	PROPN
ejpam-5594	319	38	)	)	PUNCT
ejpam-5594	319	39	ς	ς	NOUN
ejpam-5594	319	40	b(ς)γ(ς	b(ς)γ(ς	X
ejpam-5594	319	41	)	)	PUNCT
ejpam-5594	319	42	φ	φ	PROPN
ejpam-5594	319	43	(	(	PUNCT
ejpam-5594	319	44	ε2	ε2	PROPN
ejpam-5594	319	45	+	+	CCONJ
ejpam-5594	319	46	ε1	ε1	PROPN
ejpam-5594	319	47	2	2	NUM
ejpam-5594	319	48	)	)	PUNCT
ejpam-5594	320	1	+	+	NUM
ejpam-5594	320	2	1−	1−	NUM
ejpam-5594	320	3	ς	ς	X
ejpam-5594	320	4	b(ς	b(ς	PROPN
ejpam-5594	320	5	)	)	PUNCT
ejpam-5594	320	6	[	[	PUNCT
ejpam-5594	320	7	φ(ε1	φ(ε1	NOUN
ejpam-5594	320	8	)	)	PUNCT
ejpam-5594	320	9	+	+	SYM
ejpam-5594	320	10	φ(ε2	φ(ε2	NUM
ejpam-5594	320	11	)	)	PUNCT
ejpam-5594	320	12	]	]	PUNCT
ejpam-5594	321	1	≈	≈	PROPN
ejpam-5594	322	1	[	[	X
ejpam-5594	322	2	81.77390	81.77390	NUM
ejpam-5594	322	3	,	,	PUNCT
ejpam-5594	322	4	103.32659	103.32659	NUM
ejpam-5594	322	5	]	]	PUNCT
ejpam-5594	322	6	,	,	PUNCT
ejpam-5594	322	7	ab	ab	PROPN
ejpam-5594	322	8	ε1i	ε1i	NUM
ejpam-5594	322	9	ς	ς	PROPN
ejpam-5594	322	10	ε2{φ(ε2)}+	ε2{φ(ε2)}+	PROPN
ejpam-5594	322	11	abiςε2{φ(ε1	abiςε2{φ(ε1	PROPN
ejpam-5594	322	12	)	)	PUNCT
ejpam-5594	322	13	}	}	PUNCT
ejpam-5594	323	1	≈	≈	PROPN
ejpam-5594	324	1	[	[	X
ejpam-5594	324	2	90.33565	90.33565	NUM
ejpam-5594	324	3	,	,	PUNCT
ejpam-5594	324	4	131.54364	131.54364	NUM
ejpam-5594	324	5	]	]	X
ejpam-5594	324	6	.	.	PUNCT
ejpam-5594	325	1	and	and	CCONJ
ejpam-5594	325	2	[	[	PUNCT
ejpam-5594	325	3	φ(ε1	φ(ε1	NOUN
ejpam-5594	325	4	)	)	PUNCT
ejpam-5594	325	5	+	+	SYM
ejpam-5594	325	6	φ(ε2	φ(ε2	NUM
ejpam-5594	325	7	)	)	PUNCT
ejpam-5594	325	8	b(ς	b(ς	PROPN
ejpam-5594	325	9	)	)	PUNCT
ejpam-5594	325	10	]	]	PUNCT
ejpam-5594	326	1	[	[	PUNCT
ejpam-5594	326	2	1−	1−	NUM
ejpam-5594	326	3	ς	ς	NOUN
ejpam-5594	326	4	+	+	NOUN
ejpam-5594	326	5	ς(ε2	ς(ε2	NOUN
ejpam-5594	326	6	−	−	PROPN
ejpam-5594	326	7	ε1	ε1	PROPN
ejpam-5594	326	8	)	)	PUNCT
ejpam-5594	326	9	ς	ς	PROPN
ejpam-5594	326	10	γ(ς	γ(ς	NOUN
ejpam-5594	326	11	)	)	PUNCT
ejpam-5594	326	12	×	×	NOUN
ejpam-5594	326	13	∫	∫	NOUN
ejpam-5594	326	14	1	1	NUM
ejpam-5594	326	15	0	0	NUM
ejpam-5594	327	1	♭	♭	INTJ
ejpam-5594	327	2	ς−1	ς−1	PROPN
ejpam-5594	327	3	(	(	PUNCT
ejpam-5594	327	4	1	1	NUM
ejpam-5594	327	5	h	h	NOUN
ejpam-5594	327	6	(	(	PUNCT
ejpam-5594	327	7	♭	♭	PROPN
ejpam-5594	327	8	)	)	PUNCT
ejpam-5594	328	1	+	+	CCONJ
ejpam-5594	328	2	1	1	NUM
ejpam-5594	328	3	h(1−	h(1−	NOUN
ejpam-5594	328	4	♭	♭	PROPN
ejpam-5594	328	5	)	)	PUNCT
ejpam-5594	328	6	)	)	PUNCT
ejpam-5594	329	1	d	d	X
ejpam-5594	329	2	♭	♭	X
ejpam-5594	329	3	]	]	X
ejpam-5594	330	1	=	=	PUNCT
ejpam-5594	330	2	[	[	PUNCT
ejpam-5594	330	3	e4	e4	PROPN
ejpam-5594	330	4	+	+	CCONJ
ejpam-5594	330	5	e+	e+	VERB
ejpam-5594	330	6	√	√	PROPN
ejpam-5594	330	7	3	3	NUM
ejpam-5594	330	8	√	√	PROPN
ejpam-5594	330	9	π	π	PROPN
ejpam-5594	330	10	(	(	PUNCT
ejpam-5594	330	11	2e4	2e4	NUM
ejpam-5594	330	12	+	+	NUM
ejpam-5594	330	13	2e+	2e+	NUM
ejpam-5594	330	14	2	2	NUM
ejpam-5594	330	15	)	)	PUNCT
ejpam-5594	330	16	3π	3π	NOUN
ejpam-5594	330	17	+	+	CCONJ
ejpam-5594	330	18	1	1	NUM
ejpam-5594	330	19	,	,	PUNCT
ejpam-5594	330	20	(	(	PUNCT
ejpam-5594	330	21	3e4	3e4	NUM
ejpam-5594	330	22	+	+	CCONJ
ejpam-5594	330	23	3e+	3e+	NUM
ejpam-5594	330	24	1	1	NUM
ejpam-5594	330	25	)	)	PUNCT
ejpam-5594	330	26	(	(	PUNCT
ejpam-5594	330	27	1	1	NUM
ejpam-5594	330	28	2	2	NUM
ejpam-5594	330	29	+	+	CCONJ
ejpam-5594	330	30	√	√	NUM
ejpam-5594	330	31	3	3	NUM
ejpam-5594	330	32	√	√	PROPN
ejpam-5594	330	33	π	π	PROPN
ejpam-5594	330	34	3π	3π	NOUN
ejpam-5594	330	35	)	)	PUNCT
ejpam-5594	330	36	]	]	PUNCT
ejpam-5594	331	1	≈	≈	PROPN
ejpam-5594	332	1	[	[	X
ejpam-5594	332	2	96.30783	96.30783	NUM
ejpam-5594	332	3	,	,	PUNCT
ejpam-5594	332	4	142.81028	142.81028	NUM
ejpam-5594	332	5	]	]	PUNCT
ejpam-5594	332	6	.	.	PUNCT
ejpam-5594	333	1	j.	j.	PROPN
ejpam-5594	333	2	e.	e.	PROPN
ejpam-5594	333	3	maćıas	maćıas	PROPN
ejpam-5594	333	4	-	-	PUNCT
ejpam-5594	333	5	dı́az	dı́az	NOUN
ejpam-5594	333	6	et	et	NOUN
ejpam-5594	333	7	al	al	PROPN
ejpam-5594	333	8	.	.	PUNCT
ejpam-5594	333	9	/	/	SYM
ejpam-5594	333	10	eur	eur	PROPN
ejpam-5594	333	11	.	.	PUNCT
ejpam-5594	334	1	j.	j.	PROPN
ejpam-5594	334	2	pure	pure	PROPN
ejpam-5594	334	3	appl	appl	PROPN
ejpam-5594	334	4	.	.	PROPN
ejpam-5594	334	5	math	math	PROPN
ejpam-5594	334	6	,	,	PUNCT
ejpam-5594	334	7	17	17	NUM
ejpam-5594	334	8	(	(	PUNCT
ejpam-5594	334	9	4	4	NUM
ejpam-5594	334	10	)	)	PUNCT
ejpam-5594	334	11	(	(	PUNCT
ejpam-5594	334	12	2024	2024	NUM
ejpam-5594	334	13	)	)	PUNCT
ejpam-5594	334	14	,	,	PUNCT
ejpam-5594	334	15	4014	4014	NUM
ejpam-5594	334	16	-	-	SYM
ejpam-5594	334	17	4049	4049	NUM
ejpam-5594	334	18	4026	4026	NUM
ejpam-5594	334	19	thus	thus	ADV
ejpam-5594	334	20	,	,	PUNCT
ejpam-5594	334	21	we	we	PRON
ejpam-5594	334	22	have	have	AUX
ejpam-5594	334	23	[	[	NOUN
ejpam-5594	334	24	81.77390	81.77390	NUM
ejpam-5594	334	25	,	,	PUNCT
ejpam-5594	334	26	103.32659	103.32659	NUM
ejpam-5594	334	27	]	]	PUNCT
ejpam-5594	334	28	⪯cr	⪯cr	X
ejpam-5594	335	1	[	[	X
ejpam-5594	335	2	90.33565	90.33565	NUM
ejpam-5594	335	3	,	,	PUNCT
ejpam-5594	335	4	131.54364	131.54364	NUM
ejpam-5594	335	5	]	]	PUNCT
ejpam-5594	335	6	⪯cr	⪯cr	NUM
ejpam-5594	335	7	[	[	X
ejpam-5594	335	8	96.30783	96.30783	NUM
ejpam-5594	335	9	,	,	PUNCT
ejpam-5594	335	10	142.81028	142.81028	NUM
ejpam-5594	335	11	]	]	PUNCT
ejpam-5594	335	12	.	.	PUNCT
ejpam-5594	336	1	consequently	consequently	ADV
ejpam-5594	336	2	,	,	PUNCT
ejpam-5594	336	3	theorem	theorem	VERB
ejpam-5594	336	4	11	11	NUM
ejpam-5594	336	5	is	be	AUX
ejpam-5594	336	6	correct	correct	ADJ
ejpam-5594	336	7	.	.	PUNCT
ejpam-5594	337	1	the	the	DET
ejpam-5594	337	2	different	different	ADJ
ejpam-5594	337	3	types	type	NOUN
ejpam-5594	337	4	of	of	ADP
ejpam-5594	337	5	settings	setting	NOUN
ejpam-5594	337	6	allow	allow	VERB
ejpam-5594	337	7	us	we	PRON
ejpam-5594	337	8	to	to	PART
ejpam-5594	337	9	get	get	VERB
ejpam-5594	337	10	results	result	NOUN
ejpam-5594	337	11	for	for	ADP
ejpam-5594	337	12	other	other	ADJ
ejpam-5594	337	13	types	type	NOUN
ejpam-5594	337	14	of	of	ADP
ejpam-5594	337	15	generalized	generalized	ADJ
ejpam-5594	337	16	convex	convex	NOUN
ejpam-5594	337	17	mappings	mapping	NOUN
ejpam-5594	337	18	,	,	PUNCT
ejpam-5594	337	19	as	as	SCONJ
ejpam-5594	337	20	described	describe	VERB
ejpam-5594	337	21	in	in	ADP
ejpam-5594	337	22	the	the	DET
ejpam-5594	337	23	remark	remark	NOUN
ejpam-5594	337	24	below	below	ADV
ejpam-5594	337	25	.	.	PUNCT
ejpam-5594	338	1	remark	remark	PROPN
ejpam-5594	338	2	3	3	NUM
ejpam-5594	338	3	.	.	PUNCT
ejpam-5594	339	1	(	(	PUNCT
ejpam-5594	339	2	i	i	NOUN
ejpam-5594	339	3	)	)	PUNCT
ejpam-5594	339	4	if	if	SCONJ
ejpam-5594	339	5	h	h	X
ejpam-5594	339	6	(	(	PUNCT
ejpam-5594	339	7	♭	♭	INTJ
ejpam-5594	339	8	)	)	PUNCT
ejpam-5594	340	1	=	=	SYM
ejpam-5594	340	2	1	1	NUM
ejpam-5594	340	3	♭	♭	NOUN
ejpam-5594	340	4	s	s	PART
ejpam-5594	340	5	,	,	PUNCT
ejpam-5594	340	6	then	then	ADV
ejpam-5594	340	7	theorem	theorem	VERB
ejpam-5594	340	8	11	11	NUM
ejpam-5594	340	9	yields	yield	NOUN
ejpam-5594	340	10	an	an	DET
ejpam-5594	340	11	outcome	outcome	NOUN
ejpam-5594	340	12	for	for	ADP
ejpam-5594	340	13	the	the	DET
ejpam-5594	340	14	cr	cr	PROPN
ejpam-5594	340	15	-	-	PUNCT
ejpam-5594	340	16	s	s	NOUN
ejpam-5594	340	17	-	-	PUNCT
ejpam-5594	340	18	convex	convex	ADJ
ejpam-5594	340	19	function	function	NOUN
ejpam-5594	340	20	for	for	ADP
ejpam-5594	340	21	ab	ab	PROPN
ejpam-5594	340	22	integral	integral	ADJ
ejpam-5594	340	23	operators	operator	NOUN
ejpam-5594	340	24	:	:	PUNCT
ejpam-5594	341	1	2s	2s	NUM
ejpam-5594	341	2	(	(	PUNCT
ejpam-5594	341	3	ε2	ε2	PROPN
ejpam-5594	341	4	−	−	PROPN
ejpam-5594	341	5	ε1	ε1	PROPN
ejpam-5594	341	6	)	)	PUNCT
ejpam-5594	341	7	ς	ς	NOUN
ejpam-5594	341	8	b(ς)γ(ς	b(ς)γ(ς	X
ejpam-5594	341	9	)	)	PUNCT
ejpam-5594	341	10	φ	φ	PROPN
ejpam-5594	341	11	(	(	PUNCT
ejpam-5594	341	12	ε2	ε2	PROPN
ejpam-5594	341	13	+	+	CCONJ
ejpam-5594	341	14	ε1	ε1	PROPN
ejpam-5594	341	15	2	2	NUM
ejpam-5594	341	16	)	)	PUNCT
ejpam-5594	341	17	+	+	NUM
ejpam-5594	341	18	1−	1−	NUM
ejpam-5594	341	19	ς	ς	X
ejpam-5594	341	20	b(ς	b(ς	PROPN
ejpam-5594	341	21	)	)	PUNCT
ejpam-5594	341	22	[	[	PUNCT
ejpam-5594	341	23	φ(ε1	φ(ε1	NOUN
ejpam-5594	341	24	)	)	PUNCT
ejpam-5594	341	25	+	+	SYM
ejpam-5594	341	26	φ(ε2	φ(ε2	NUM
ejpam-5594	341	27	)	)	PUNCT
ejpam-5594	341	28	]	]	PUNCT
ejpam-5594	341	29	≤	≤	NUM
ejpam-5594	341	30	ab	ab	X
ejpam-5594	341	31	ε1i	ε1i	PROPN
ejpam-5594	341	32	ς	ς	PROPN
ejpam-5594	341	33	ε2{φ(ε2)}+	ε2{φ(ε2)}+	PROPN
ejpam-5594	341	34	abiςε2{φ(ε1	abiςε2{φ(ε1	PROPN
ejpam-5594	341	35	)	)	PUNCT
ejpam-5594	341	36	}	}	PUNCT
ejpam-5594	341	37	≤	≤	PROPN
ejpam-5594	341	38	[	[	PUNCT
ejpam-5594	341	39	φ(ε1	φ(ε1	NOUN
ejpam-5594	341	40	)	)	PUNCT
ejpam-5594	341	41	+	+	SYM
ejpam-5594	341	42	φ(ε2	φ(ε2	NUM
ejpam-5594	341	43	)	)	PUNCT
ejpam-5594	341	44	b(ς	b(ς	PROPN
ejpam-5594	341	45	)	)	PUNCT
ejpam-5594	341	46	]	]	PUNCT
ejpam-5594	342	1	[	[	PUNCT
ejpam-5594	342	2	1−	1−	NUM
ejpam-5594	342	3	ς	ς	NOUN
ejpam-5594	342	4	+	+	NOUN
ejpam-5594	342	5	ς(ε2	ς(ε2	NOUN
ejpam-5594	342	6	−	−	PROPN
ejpam-5594	342	7	ε1	ε1	PROPN
ejpam-5594	342	8	)	)	PUNCT
ejpam-5594	342	9	ς	ς	PROPN
ejpam-5594	342	10	γ(ς)(s+ς	γ(ς)(s+ς	NOUN
ejpam-5594	342	11	)	)	PUNCT
ejpam-5594	343	1	+	+	NUM
ejpam-5594	343	2	ς(ε2	ς(ε2	NOUN
ejpam-5594	344	1	−	−	NOUN
ejpam-5594	344	2	ε1	ε1	PROPN
ejpam-5594	344	3	)	)	PUNCT
ejpam-5594	344	4	ς	ς	PROPN
ejpam-5594	344	5	γ(ς	γ(ς	NOUN
ejpam-5594	344	6	)	)	PUNCT
ejpam-5594	344	7	γ(ς)γ(s+1	γ(ς)γ(s+1	NOUN
ejpam-5594	344	8	)	)	PUNCT
ejpam-5594	344	9	γ(ς	γ(ς	NOUN
ejpam-5594	344	10	+	+	PUNCT
ejpam-5594	344	11	s+2	s+2	NOUN
ejpam-5594	344	12	)	)	PUNCT
ejpam-5594	344	13	]	]	PUNCT
ejpam-5594	344	14	.	.	PUNCT
ejpam-5594	345	1	(	(	PUNCT
ejpam-5594	345	2	9	9	NUM
ejpam-5594	345	3	)	)	PUNCT
ejpam-5594	345	4	(	(	PUNCT
ejpam-5594	345	5	ii	ii	NOUN
ejpam-5594	345	6	)	)	PUNCT
ejpam-5594	345	7	if	if	SCONJ
ejpam-5594	345	8	h	h	PROPN
ejpam-5594	345	9	(	(	PUNCT
ejpam-5594	345	10	♭	♭	INTJ
ejpam-5594	345	11	)	)	PUNCT
ejpam-5594	345	12	=	=	SYM
ejpam-5594	345	13	1	1	NUM
ejpam-5594	345	14	,	,	PUNCT
ejpam-5594	345	15	then	then	ADV
ejpam-5594	345	16	theorem	theorem	VERB
ejpam-5594	345	17	11	11	NUM
ejpam-5594	345	18	yields	yield	NOUN
ejpam-5594	345	19	an	an	DET
ejpam-5594	345	20	outcome	outcome	NOUN
ejpam-5594	345	21	for	for	ADP
ejpam-5594	345	22	the	the	DET
ejpam-5594	345	23	cr	cr	PROPN
ejpam-5594	345	24	-	-	PUNCT
ejpam-5594	345	25	p	p	NOUN
ejpam-5594	345	26	-	-	PUNCT
ejpam-5594	345	27	convex	convex	NOUN
ejpam-5594	345	28	function	function	NOUN
ejpam-5594	345	29	for	for	ADP
ejpam-5594	345	30	ab	ab	PROPN
ejpam-5594	345	31	integral	integral	ADJ
ejpam-5594	345	32	operators	operator	NOUN
ejpam-5594	345	33	:	:	PUNCT
ejpam-5594	345	34	(	(	PUNCT
ejpam-5594	345	35	ε2	ε2	ADJ
ejpam-5594	345	36	−	−	PROPN
ejpam-5594	345	37	ε1	ε1	PROPN
ejpam-5594	345	38	)	)	PUNCT
ejpam-5594	345	39	ς	ς	NOUN
ejpam-5594	345	40	b(ς)γ(ς	b(ς)γ(ς	X
ejpam-5594	345	41	)	)	PUNCT
ejpam-5594	345	42	φ	φ	PROPN
ejpam-5594	345	43	(	(	PUNCT
ejpam-5594	345	44	ε2	ε2	PROPN
ejpam-5594	345	45	+	+	CCONJ
ejpam-5594	345	46	ε1	ε1	PROPN
ejpam-5594	345	47	2	2	NUM
ejpam-5594	345	48	)	)	PUNCT
ejpam-5594	346	1	+	+	NUM
ejpam-5594	346	2	1−	1−	NUM
ejpam-5594	346	3	ς	ς	X
ejpam-5594	346	4	b(ς	b(ς	PROPN
ejpam-5594	346	5	)	)	PUNCT
ejpam-5594	346	6	[	[	PUNCT
ejpam-5594	346	7	φ(ε1	φ(ε1	NOUN
ejpam-5594	346	8	)	)	PUNCT
ejpam-5594	346	9	+	+	SYM
ejpam-5594	346	10	φ(ε2	φ(ε2	NUM
ejpam-5594	346	11	)	)	PUNCT
ejpam-5594	346	12	]	]	PUNCT
ejpam-5594	347	1	≤	≤	NUM
ejpam-5594	347	2	ab	ab	X
ejpam-5594	347	3	ε1i	ε1i	PROPN
ejpam-5594	347	4	ς	ς	PROPN
ejpam-5594	347	5	ε2{φ(ε2)}+	ε2{φ(ε2)}+	PROPN
ejpam-5594	347	6	abiςε2{φ(ε1	abiςε2{φ(ε1	PROPN
ejpam-5594	347	7	)	)	PUNCT
ejpam-5594	347	8	}	}	PUNCT
ejpam-5594	347	9	≤	≤	PROPN
ejpam-5594	347	10	[	[	PUNCT
ejpam-5594	347	11	φ(ε1	φ(ε1	NOUN
ejpam-5594	347	12	)	)	PUNCT
ejpam-5594	347	13	+	+	SYM
ejpam-5594	347	14	φ(ε2	φ(ε2	NUM
ejpam-5594	347	15	)	)	PUNCT
ejpam-5594	347	16	b(ς	b(ς	PROPN
ejpam-5594	347	17	)	)	PUNCT
ejpam-5594	347	18	]	]	PUNCT
ejpam-5594	348	1	[	[	PUNCT
ejpam-5594	348	2	1−	1−	NUM
ejpam-5594	348	3	ς	ς	PROPN
ejpam-5594	348	4	+	+	NOUN
ejpam-5594	348	5	2(ε2	2(ε2	NUM
ejpam-5594	348	6	−	−	PROPN
ejpam-5594	348	7	ε1	ε1	PROPN
ejpam-5594	348	8	)	)	PUNCT
ejpam-5594	348	9	ς	ς	NOUN
ejpam-5594	348	10	γ(ς	γ(ς	NOUN
ejpam-5594	348	11	)	)	PUNCT
ejpam-5594	348	12	]	]	PUNCT
ejpam-5594	348	13	.	.	PUNCT
ejpam-5594	349	1	(	(	PUNCT
ejpam-5594	349	2	10	10	NUM
ejpam-5594	349	3	)	)	PUNCT
ejpam-5594	349	4	theorem	theorem	NOUN
ejpam-5594	349	5	12	12	NUM
ejpam-5594	349	6	.	.	PUNCT
ejpam-5594	350	1	let	let	VERB
ejpam-5594	350	2	h	h	NOUN
ejpam-5594	350	3	:	:	PUNCT
ejpam-5594	350	4	(	(	PUNCT
ejpam-5594	350	5	0	0	NUM
ejpam-5594	350	6	,	,	PUNCT
ejpam-5594	350	7	1	1	NUM
ejpam-5594	350	8	)	)	PUNCT
ejpam-5594	350	9	→	→	NOUN
ejpam-5594	350	10	r+	r+	NOUN
ejpam-5594	350	11	and	and	CCONJ
ejpam-5594	350	12	h	h	NOUN
ejpam-5594	350	13	̸=	̸=	PROPN
ejpam-5594	350	14	0	0	NUM
ejpam-5594	350	15	.	.	PUNCT
ejpam-5594	351	1	let	let	VERB
ejpam-5594	351	2	φ	φ	NOUN
ejpam-5594	351	3	:	:	PUNCT
ejpam-5594	352	1	[	[	X
ejpam-5594	352	2	ε1	ε1	NOUN
ejpam-5594	352	3	,	,	PUNCT
ejpam-5594	352	4	ε2	ε2	PROPN
ejpam-5594	352	5	]	]	PUNCT
ejpam-5594	352	6	→	→	SYM
ejpam-5594	352	7	r+	r+	NOUN
ejpam-5594	352	8	i	i	PRON
ejpam-5594	352	9	is	be	AUX
ejpam-5594	352	10	cr	cr	PROPN
ejpam-5594	352	11	-	-	PUNCT
ejpam-5594	352	12	h	h	NOUN
ejpam-5594	352	13	-	-	PUNCT
ejpam-5594	352	14	godunovalevin	godunovalevin	ADJ
ejpam-5594	352	15	mapping	mapping	NOUN
ejpam-5594	352	16	,	,	PUNCT
ejpam-5594	352	17	ε1	ε1	PROPN
ejpam-5594	352	18	,	,	PUNCT
ejpam-5594	352	19	ε2	ε2	PROPN
ejpam-5594	352	20	∈	∈	PROPN
ejpam-5594	352	21	r+	r+	NOUN
ejpam-5594	352	22	,	,	PUNCT
ejpam-5594	352	23	ε1	ε1	VERB
ejpam-5594	352	24	<	<	X
ejpam-5594	352	25	ε2	ε2	NOUN
ejpam-5594	352	26	and	and	CCONJ
ejpam-5594	352	27	ג	ג	X
ejpam-5594	352	28	:	:	PUNCT
ejpam-5594	353	1	[	[	X
ejpam-5594	353	2	ε1	ε1	NOUN
ejpam-5594	353	3	,	,	PUNCT
ejpam-5594	353	4	ε2	ε2	PROPN
ejpam-5594	353	5	]	]	PUNCT
ejpam-5594	353	6	→	→	X
ejpam-5594	353	7	r+	r+	NOUN
ejpam-5594	353	8	is	be	AUX
ejpam-5594	353	9	symmetric	symmetric	ADJ
ejpam-5594	353	10	about	about	ADP
ejpam-5594	353	11	ε1+ε2	ε1+ε2	PROPN
ejpam-5594	353	12	2	2	NUM
ejpam-5594	353	13	.	.	PUNCT
ejpam-5594	354	1	if	if	SCONJ
ejpam-5594	354	2	φ	φ	PROPN
ejpam-5594	354	3	∈	∈	PROPN
ejpam-5594	354	4	l[ε1	l[ε1	NOUN
ejpam-5594	354	5	,	,	PUNCT
ejpam-5594	354	6	ε2	ε2	PROPN
ejpam-5594	354	7	]	]	PUNCT
ejpam-5594	354	8	,	,	PUNCT
ejpam-5594	354	9	then	then	ADV
ejpam-5594	354	10	the	the	DET
ejpam-5594	354	11	following	follow	VERB
ejpam-5594	354	12	relation	relation	NOUN
ejpam-5594	354	13	holds	hold	VERB
ejpam-5594	354	14	true	true	ADJ
ejpam-5594	354	15	:	:	PUNCT
ejpam-5594	354	16	h	h	NOUN
ejpam-5594	354	17	(	(	PUNCT
ejpam-5594	354	18	1	1	NUM
ejpam-5594	354	19	2	2	NUM
ejpam-5594	354	20	)	)	PUNCT
ejpam-5594	354	21	2	2	NUM
ejpam-5594	354	22	φ	φ	NOUN
ejpam-5594	354	23	(	(	PUNCT
ejpam-5594	354	24	ε2	ε2	PROPN
ejpam-5594	354	25	+	+	CCONJ
ejpam-5594	354	26	ε1	ε1	PROPN
ejpam-5594	354	27	2	2	NUM
ejpam-5594	354	28	)	)	PUNCT
ejpam-5594	354	29	[	[	PUNCT
ejpam-5594	354	30	ab	ab	X
ejpam-5594	354	31	ε1i	ε1i	PROPN
ejpam-5594	354	32	ς	ς	PROPN
ejpam-5594	354	33	ε2{ג(ε2)}+	ε2{ג(ε2)}+	PROPN
ejpam-5594	354	34	abiςε2{ג(ε1	abiςε2{ג(ε1	PROPN
ejpam-5594	354	35	)	)	PUNCT
ejpam-5594	354	36	}	}	PUNCT
ejpam-5594	354	37	]	]	PUNCT
ejpam-5594	355	1	−	−	PROPN
ejpam-5594	355	2	h	h	NOUN
ejpam-5594	355	3	(	(	PUNCT
ejpam-5594	355	4	1	1	NUM
ejpam-5594	355	5	2	2	NUM
ejpam-5594	355	6	)	)	PUNCT
ejpam-5594	355	7	2	2	NUM
ejpam-5594	355	8	φ	φ	NOUN
ejpam-5594	355	9	(	(	PUNCT
ejpam-5594	355	10	ε2	ε2	PROPN
ejpam-5594	355	11	+	+	CCONJ
ejpam-5594	355	12	ε1	ε1	PROPN
ejpam-5594	355	13	2	2	NUM
ejpam-5594	355	14	)	)	PUNCT
ejpam-5594	355	15	1−	1−	NUM
ejpam-5594	355	16	ς	ς	PROPN
ejpam-5594	355	17	b(ς	b(ς	PROPN
ejpam-5594	355	18	)	)	PUNCT
ejpam-5594	355	19	[	[	PUNCT
ejpam-5594	355	20	(	(	PUNCT
ejpam-5594	355	21	ε1)ג	ε1)ג	NOUN
ejpam-5594	355	22	+	+	CCONJ
ejpam-5594	355	23	(	(	PUNCT
ejpam-5594	355	24	ε2)ג	ε2)ג	PROPN
ejpam-5594	355	25	]	]	PUNCT
ejpam-5594	356	1	+	+	CCONJ
ejpam-5594	357	1	1−	1−	NUM
ejpam-5594	357	2	ς	ς	X
ejpam-5594	357	3	b(ς	b(ς	PROPN
ejpam-5594	357	4	)	)	PUNCT
ejpam-5594	357	5	[	[	PUNCT
ejpam-5594	357	6	φ(ε1)ג(ε1	φ(ε1)ג(ε1	PROPN
ejpam-5594	357	7	)	)	PUNCT
ejpam-5594	357	8	+	+	CCONJ
ejpam-5594	357	9	φ(ε2)ג(ε2	φ(ε2)ג(ε2	PROPN
ejpam-5594	357	10	)	)	PUNCT
ejpam-5594	357	11	]	]	PUNCT
ejpam-5594	357	12	≤	≤	NUM
ejpam-5594	357	13	ab	ab	X
ejpam-5594	357	14	ε1i	ε1i	PROPN
ejpam-5594	357	15	ς	ς	PROPN
ejpam-5594	357	16	ε2{(φג(ε2)}+	ε2{(φג(ε2)}+	PROPN
ejpam-5594	357	17	abiςε2{(φג(ε1	abiςε2{(φג(ε1	PROPN
ejpam-5594	357	18	)	)	PUNCT
ejpam-5594	357	19	}	}	PUNCT
ejpam-5594	357	20	⪯cr	⪯cr	VERB
ejpam-5594	357	21	ς(ε2	ς(ε2	NUM
ejpam-5594	357	22	−	−	PROPN
ejpam-5594	357	23	ε1	ε1	PROPN
ejpam-5594	357	24	)	)	PUNCT
ejpam-5594	357	25	ς	ς	NOUN
ejpam-5594	357	26	b(ς)γ(ς	b(ς)γ(ς	NUM
ejpam-5594	357	27	)	)	PUNCT
ejpam-5594	357	28	[	[	PUNCT
ejpam-5594	357	29	φ(ε1	φ(ε1	NOUN
ejpam-5594	357	30	)	)	PUNCT
ejpam-5594	357	31	+	+	SYM
ejpam-5594	357	32	φ(ε2	φ(ε2	NUM
ejpam-5594	357	33	)	)	PUNCT
ejpam-5594	357	34	]	]	PUNCT
ejpam-5594	358	1	×	×	NOUN
ejpam-5594	358	2	∫	∫	PROPN
ejpam-5594	358	3	1	1	NUM
ejpam-5594	358	4	0	0	NUM
ejpam-5594	359	1	♭	♭	NUM
ejpam-5594	359	2	ς−1	ς−1	PROPN
ejpam-5594	359	3	[	[	PUNCT
ejpam-5594	359	4	1	1	NUM
ejpam-5594	359	5	h	h	NOUN
ejpam-5594	359	6	(	(	PUNCT
ejpam-5594	359	7	♭	♭	PROPN
ejpam-5594	359	8	)	)	PUNCT
ejpam-5594	359	9	+	+	CCONJ
ejpam-5594	359	10	1	1	NUM
ejpam-5594	359	11	h(1−	h(1−	NOUN
ejpam-5594	359	12	♭	♭	PROPN
ejpam-5594	359	13	)	)	PUNCT
ejpam-5594	359	14	]	]	PUNCT
ejpam-5594	360	1	ε2	ε2	PROPN
ejpam-5594	360	2	♭	♭	NOUN
ejpam-5594	360	3	)ג	)ג	PUNCT
ejpam-5594	361	1	+	+	CCONJ
ejpam-5594	361	2	(	(	PUNCT
ejpam-5594	361	3	1−	1−	NUM
ejpam-5594	361	4	♭	♭	INTJ
ejpam-5594	361	5	)	)	PUNCT
ejpam-5594	361	6	ε1)d	ε1)d	NOUN
ejpam-5594	361	7	♭	♭	PROPN
ejpam-5594	361	8	+	+	NUM
ejpam-5594	361	9	1−	1−	NUM
ejpam-5594	361	10	ς	ς	X
ejpam-5594	361	11	b(ς	b(ς	PROPN
ejpam-5594	361	12	)	)	PUNCT
ejpam-5594	361	13	[	[	PUNCT
ejpam-5594	361	14	φ(ε1)ג(ε1	φ(ε1)ג(ε1	PROPN
ejpam-5594	361	15	)	)	PUNCT
ejpam-5594	361	16	+	+	CCONJ
ejpam-5594	361	17	φ(ε2)ג(ε2	φ(ε2)ג(ε2	PROPN
ejpam-5594	361	18	)	)	PUNCT
ejpam-5594	361	19	]	]	PUNCT
ejpam-5594	361	20	,	,	PUNCT
ejpam-5594	361	21	(	(	PUNCT
ejpam-5594	361	22	11	11	NUM
ejpam-5594	361	23	)	)	PUNCT
ejpam-5594	361	24	where	where	SCONJ
ejpam-5594	361	25	ς	ς	PROPN
ejpam-5594	361	26	∈	∈	PROPN
ejpam-5594	361	27	(	(	PUNCT
ejpam-5594	361	28	0	0	NUM
ejpam-5594	361	29	,	,	PUNCT
ejpam-5594	361	30	1	1	NUM
ejpam-5594	361	31	]	]	PUNCT
ejpam-5594	361	32	.	.	PUNCT
ejpam-5594	362	1	j.	j.	PROPN
ejpam-5594	362	2	e.	e.	PROPN
ejpam-5594	362	3	maćıas	maćıas	PROPN
ejpam-5594	362	4	-	-	PUNCT
ejpam-5594	362	5	dı́az	dı́az	NOUN
ejpam-5594	362	6	et	et	NOUN
ejpam-5594	362	7	al	al	PROPN
ejpam-5594	362	8	.	.	PUNCT
ejpam-5594	362	9	/	/	SYM
ejpam-5594	362	10	eur	eur	PROPN
ejpam-5594	362	11	.	.	PUNCT
ejpam-5594	363	1	j.	j.	PROPN
ejpam-5594	363	2	pure	pure	PROPN
ejpam-5594	363	3	appl	appl	PROPN
ejpam-5594	363	4	.	.	PROPN
ejpam-5594	363	5	math	math	PROPN
ejpam-5594	363	6	,	,	PUNCT
ejpam-5594	363	7	17	17	NUM
ejpam-5594	363	8	(	(	PUNCT
ejpam-5594	363	9	4	4	NUM
ejpam-5594	363	10	)	)	PUNCT
ejpam-5594	363	11	(	(	PUNCT
ejpam-5594	363	12	2024	2024	NUM
ejpam-5594	363	13	)	)	PUNCT
ejpam-5594	363	14	,	,	PUNCT
ejpam-5594	363	15	4014	4014	NUM
ejpam-5594	363	16	-	-	SYM
ejpam-5594	363	17	4049	4049	NUM
ejpam-5594	363	18	4027	4027	NUM
ejpam-5594	363	19	proof	proof	NOUN
ejpam-5594	363	20	.	.	PUNCT
ejpam-5594	364	1	as	as	ADP
ejpam-5594	364	2	φ	φ	PROPN
ejpam-5594	364	3	∈	∈	PROPN
ejpam-5594	364	4	sgx(h	sgx(h	PROPN
ejpam-5594	364	5	,	,	PUNCT
ejpam-5594	364	6	[	[	X
ejpam-5594	364	7	ε1	ε1	PROPN
ejpam-5594	364	8	,	,	PUNCT
ejpam-5594	364	9	ε2],r	ε2],r	NOUN
ejpam-5594	364	10	+	+	CCONJ
ejpam-5594	364	11	i	i	PROPN
ejpam-5594	364	12	)	)	PUNCT
ejpam-5594	364	13	,	,	PUNCT
ejpam-5594	364	14	we	we	PRON
ejpam-5594	364	15	have	have	VERB
ejpam-5594	364	16	φ	φ	PROPN
ejpam-5594	364	17	(	(	PUNCT
ejpam-5594	364	18	ε2	ε2	PROPN
ejpam-5594	364	19	+	+	CCONJ
ejpam-5594	364	20	ε1	ε1	PROPN
ejpam-5594	364	21	2	2	NUM
ejpam-5594	364	22	)	)	PUNCT
ejpam-5594	364	23	≤	≤	NOUN
ejpam-5594	364	24	1	1	NUM
ejpam-5594	364	25	h	h	NOUN
ejpam-5594	364	26	(	(	PUNCT
ejpam-5594	364	27	1	1	NUM
ejpam-5594	364	28	2	2	NUM
ejpam-5594	364	29	)	)	PUNCT
ejpam-5594	365	1	[	[	X
ejpam-5594	365	2	φ(	φ(	NUM
ejpam-5594	365	3	♭	♭	PRON
ejpam-5594	365	4	ε1	ε1	VERB
ejpam-5594	365	5	+	+	CCONJ
ejpam-5594	365	6	(	(	PUNCT
ejpam-5594	365	7	1−	1−	NUM
ejpam-5594	365	8	♭	♭	INTJ
ejpam-5594	365	9	)	)	PUNCT
ejpam-5594	365	10	ε2	ε2	PROPN
ejpam-5594	365	11	)	)	PUNCT
ejpam-5594	365	12	+	+	CCONJ
ejpam-5594	365	13	φ(	φ(	NUM
ejpam-5594	365	14	♭	♭	NOUN
ejpam-5594	365	15	ε2	ε2	ADJ
ejpam-5594	365	16	+	+	CCONJ
ejpam-5594	365	17	(	(	PUNCT
ejpam-5594	365	18	1−	1−	NUM
ejpam-5594	365	19	♭	♭	INTJ
ejpam-5594	365	20	)	)	PUNCT
ejpam-5594	365	21	ε1	ε1	PROPN
ejpam-5594	365	22	)	)	PUNCT
ejpam-5594	365	23	]	]	PUNCT
ejpam-5594	365	24	.	.	PUNCT
ejpam-5594	366	1	(	(	PUNCT
ejpam-5594	366	2	12	12	NUM
ejpam-5594	366	3	)	)	PUNCT
ejpam-5594	366	4	multiplying	multiply	VERB
ejpam-5594	366	5	above	above	ADP
ejpam-5594	366	6	relation	relation	NOUN
ejpam-5594	366	7	with	with	ADP
ejpam-5594	366	8	h	h	NOUN
ejpam-5594	366	9	(	(	PUNCT
ejpam-5594	366	10	1	1	NUM
ejpam-5594	366	11	2	2	NUM
ejpam-5594	366	12	)	)	PUNCT
ejpam-5594	366	13	♭	♭	PROPN
ejpam-5594	367	1	ς−1ג(	ς−1ג(	PROPN
ejpam-5594	367	2	♭	♭	PROPN
ejpam-5594	367	3	ε2	ε2	ADJ
ejpam-5594	367	4	+	+	CCONJ
ejpam-5594	367	5	(	(	PUNCT
ejpam-5594	367	6	1	1	NUM
ejpam-5594	367	7	−	−	PROPN
ejpam-5594	367	8	♭	♭	NUM
ejpam-5594	367	9	)	)	PUNCT
ejpam-5594	367	10	ε1	ε1	PROPN
ejpam-5594	367	11	)	)	PUNCT
ejpam-5594	367	12	,	,	PUNCT
ejpam-5594	367	13	and	and	CCONJ
ejpam-5594	367	14	integrating	integrate	VERB
ejpam-5594	367	15	the	the	DET
ejpam-5594	367	16	desired	desire	VERB
ejpam-5594	367	17	relation	relation	NOUN
ejpam-5594	367	18	over	over	ADP
ejpam-5594	367	19	(	(	PUNCT
ejpam-5594	367	20	0	0	NUM
ejpam-5594	367	21	,	,	PUNCT
ejpam-5594	367	22	1	1	NUM
ejpam-5594	367	23	)	)	PUNCT
ejpam-5594	367	24	,	,	PUNCT
ejpam-5594	367	25	we	we	PRON
ejpam-5594	367	26	have	have	VERB
ejpam-5594	367	27	h	h	NOUN
ejpam-5594	367	28	(	(	PUNCT
ejpam-5594	367	29	1	1	NUM
ejpam-5594	367	30	2	2	NUM
ejpam-5594	367	31	)	)	PUNCT
ejpam-5594	367	32	φ	φ	PROPN
ejpam-5594	367	33	(	(	PUNCT
ejpam-5594	367	34	ε2	ε2	PROPN
ejpam-5594	367	35	+	+	CCONJ
ejpam-5594	367	36	ε1	ε1	PROPN
ejpam-5594	367	37	2	2	NUM
ejpam-5594	367	38	)	)	PUNCT
ejpam-5594	367	39	∫	∫	PROPN
ejpam-5594	368	1	1	1	NUM
ejpam-5594	368	2	0	0	NUM
ejpam-5594	368	3	♭	♭	PROPN
ejpam-5594	368	4	ς−1ג(	ς−1ג(	PROPN
ejpam-5594	368	5	♭	♭	PROPN
ejpam-5594	368	6	ε2	ε2	ADJ
ejpam-5594	368	7	+	+	CCONJ
ejpam-5594	368	8	(	(	PUNCT
ejpam-5594	368	9	1−	1−	NUM
ejpam-5594	368	10	♭	♭	INTJ
ejpam-5594	368	11	)	)	PUNCT
ejpam-5594	368	12	ε1)d	ε1)d	NOUN
ejpam-5594	368	13	♭	♭	PROPN
ejpam-5594	368	14	≤	≤	NUM
ejpam-5594	368	15	∫	∫	PROPN
ejpam-5594	368	16	1	1	NUM
ejpam-5594	368	17	0	0	NUM
ejpam-5594	368	18	♭	♭	PROPN
ejpam-5594	368	19	ς−1	ς−1	PROPN
ejpam-5594	368	20	[	[	PUNCT
ejpam-5594	368	21	φ(	φ(	NUM
ejpam-5594	368	22	♭	♭	PROPN
ejpam-5594	368	23	ε1	ε1	VERB
ejpam-5594	368	24	+	+	CCONJ
ejpam-5594	368	25	(	(	PUNCT
ejpam-5594	368	26	1−	1−	NUM
ejpam-5594	368	27	♭	♭	INTJ
ejpam-5594	368	28	)	)	PUNCT
ejpam-5594	368	29	ε2	ε2	PROPN
ejpam-5594	368	30	)	)	PUNCT
ejpam-5594	368	31	+	+	CCONJ
ejpam-5594	368	32	φ(	φ(	NUM
ejpam-5594	368	33	♭	♭	NOUN
ejpam-5594	368	34	ε2	ε2	ADJ
ejpam-5594	368	35	+	+	CCONJ
ejpam-5594	368	36	(	(	PUNCT
ejpam-5594	368	37	1−	1−	NUM
ejpam-5594	368	38	♭	♭	INTJ
ejpam-5594	368	39	)	)	PUNCT
ejpam-5594	368	40	ε1	ε1	PROPN
ejpam-5594	368	41	)	)	PUNCT
ejpam-5594	368	42	]	]	PUNCT
ejpam-5594	369	1	ε2	ε2	PROPN
ejpam-5594	369	2	♭	♭	NOUN
ejpam-5594	369	3	)ג	)ג	PUNCT
ejpam-5594	370	1	+	+	CCONJ
ejpam-5594	370	2	(	(	PUNCT
ejpam-5594	370	3	1−	1−	NUM
ejpam-5594	370	4	♭	♭	INTJ
ejpam-5594	370	5	)	)	PUNCT
ejpam-5594	370	6	ε1)d	ε1)d	PROPN
ejpam-5594	370	7	♭	♭	PROPN
ejpam-5594	370	8	.	.	PUNCT
ejpam-5594	371	1	let	let	VERB
ejpam-5594	371	2	u	u	NOUN
ejpam-5594	371	3	=	=	NOUN
ejpam-5594	371	4	♭	♭	PROPN
ejpam-5594	371	5	ε2	ε2	PROPN
ejpam-5594	371	6	+	+	CCONJ
ejpam-5594	371	7	(	(	PUNCT
ejpam-5594	371	8	1−	1−	NUM
ejpam-5594	371	9	♭	♭	INTJ
ejpam-5594	371	10	)	)	PUNCT
ejpam-5594	371	11	ε1	ε1	PROPN
ejpam-5594	371	12	,	,	PUNCT
ejpam-5594	371	13	then	then	ADV
ejpam-5594	371	14	the	the	DET
ejpam-5594	371	15	above	above	ADJ
ejpam-5594	371	16	relation	relation	NOUN
ejpam-5594	371	17	becomes	become	VERB
ejpam-5594	371	18	h	h	NOUN
ejpam-5594	371	19	(	(	PUNCT
ejpam-5594	371	20	1	1	NUM
ejpam-5594	371	21	2	2	NUM
ejpam-5594	371	22	)	)	PUNCT
ejpam-5594	371	23	1	1	NUM
ejpam-5594	371	24	(	(	PUNCT
ejpam-5594	371	25	ε2	ε2	PROPN
ejpam-5594	371	26	−	−	PROPN
ejpam-5594	371	27	ε1)ς	ε1)ς	NOUN
ejpam-5594	371	28	φ	φ	PROPN
ejpam-5594	371	29	(	(	PUNCT
ejpam-5594	371	30	ε2	ε2	PROPN
ejpam-5594	371	31	+	+	CCONJ
ejpam-5594	371	32	ε1	ε1	PROPN
ejpam-5594	371	33	2	2	NUM
ejpam-5594	371	34	)	)	PUNCT
ejpam-5594	371	35	∫	∫	PROPN
ejpam-5594	371	36	ε2	ε2	PROPN
ejpam-5594	371	37	ε1	ε1	PROPN
ejpam-5594	371	38	(	(	PUNCT
ejpam-5594	371	39	u−	u−	PROPN
ejpam-5594	371	40	ε1	ε1	PROPN
ejpam-5594	371	41	)	)	PUNCT
ejpam-5594	371	42	ς−1ג(u)du	ς−1ג(u)du	PROPN
ejpam-5594	371	43	⪯cr	⪯cr	VERB
ejpam-5594	371	44	1	1	NUM
ejpam-5594	371	45	(	(	PUNCT
ejpam-5594	371	46	ε2	ε2	PROPN
ejpam-5594	371	47	−	−	PROPN
ejpam-5594	371	48	ε1)ς	ε1)ς	NOUN
ejpam-5594	372	1	[	[	X
ejpam-5594	372	2	∫	∫	X
ejpam-5594	372	3	ε2	ε2	PROPN
ejpam-5594	372	4	ε1	ε1	PROPN
ejpam-5594	372	5	(	(	PUNCT
ejpam-5594	372	6	u−	u−	PROPN
ejpam-5594	372	7	ε1	ε1	PROPN
ejpam-5594	372	8	)	)	PUNCT
ejpam-5594	372	9	ς−1φ(ε2	ς−1φ(ε2	PROPN
ejpam-5594	373	1	+	+	CCONJ
ejpam-5594	373	2	ε1	ε1	PROPN
ejpam-5594	373	3	−	−	PROPN
ejpam-5594	373	4	u)ג(u)du	u)ג(u)du	ADJ
ejpam-5594	373	5	+	+	CCONJ
ejpam-5594	373	6	∫	∫	PROPN
ejpam-5594	373	7	ε2	ε2	PROPN
ejpam-5594	373	8	ε1	ε1	PROPN
ejpam-5594	373	9	(	(	PUNCT
ejpam-5594	373	10	u−	u−	PROPN
ejpam-5594	373	11	ε1	ε1	PROPN
ejpam-5594	373	12	)	)	PUNCT
ejpam-5594	373	13	ς−1φ(u)ג(u)du	ς−1φ(u)ג(u)du	NOUN
ejpam-5594	373	14	]	]	PUNCT
ejpam-5594	373	15	.	.	PUNCT
ejpam-5594	374	1	making	make	VERB
ejpam-5594	374	2	a	a	DET
ejpam-5594	374	3	modification	modification	NOUN
ejpam-5594	374	4	in	in	ADP
ejpam-5594	374	5	the	the	DET
ejpam-5594	374	6	previous	previous	ADJ
ejpam-5594	374	7	integral	integral	NOUN
ejpam-5594	374	8	of	of	ADP
ejpam-5594	374	9	the	the	DET
ejpam-5594	374	10	preceding	precede	VERB
ejpam-5594	374	11	relation	relation	NOUN
ejpam-5594	374	12	,	,	PUNCT
ejpam-5594	374	13	v	v	NOUN
ejpam-5594	374	14	=	=	SYM
ejpam-5594	374	15	ε2+ε1−u	ε2+ε1−u	PROPN
ejpam-5594	374	16	,	,	PUNCT
ejpam-5594	374	17	from	from	ADP
ejpam-5594	374	18	ε2)ג	ε2)ג	NOUN
ejpam-5594	374	19	+	+	CCONJ
ejpam-5594	374	20	ε1	ε1	PROPN
ejpam-5594	374	21	−	−	PROPN
ejpam-5594	374	22	v	v	NOUN
ejpam-5594	374	23	)	)	PUNCT
ejpam-5594	374	24	=	=	PUNCT
ejpam-5594	374	25	,	,	PUNCT
ejpam-5594	374	26	(	(	PUNCT
ejpam-5594	374	27	v)ג	v)ג	ADJ
ejpam-5594	374	28	one	one	NUM
ejpam-5594	374	29	has	have	VERB
ejpam-5594	374	30	h	h	NOUN
ejpam-5594	374	31	(	(	PUNCT
ejpam-5594	374	32	1	1	NUM
ejpam-5594	374	33	2	2	NUM
ejpam-5594	374	34	)	)	PUNCT
ejpam-5594	374	35	1	1	NUM
ejpam-5594	374	36	(	(	PUNCT
ejpam-5594	374	37	ε2	ε2	PROPN
ejpam-5594	374	38	−	−	PROPN
ejpam-5594	374	39	ε1)ς	ε1)ς	NOUN
ejpam-5594	374	40	φ	φ	PROPN
ejpam-5594	374	41	(	(	PUNCT
ejpam-5594	374	42	ε2	ε2	PROPN
ejpam-5594	374	43	+	+	CCONJ
ejpam-5594	374	44	ε1	ε1	PROPN
ejpam-5594	374	45	2	2	NUM
ejpam-5594	374	46	)	)	PUNCT
ejpam-5594	374	47	∫	∫	PROPN
ejpam-5594	374	48	ε2	ε2	PROPN
ejpam-5594	374	49	ε1	ε1	PROPN
ejpam-5594	374	50	(	(	PUNCT
ejpam-5594	374	51	u−	u−	PROPN
ejpam-5594	374	52	ε1	ε1	PROPN
ejpam-5594	374	53	)	)	PUNCT
ejpam-5594	374	54	ς−1ג(u)du	ς−1ג(u)du	NOUN
ejpam-5594	374	55	≤	≤	ADV
ejpam-5594	374	56	1	1	NUM
ejpam-5594	374	57	(	(	PUNCT
ejpam-5594	374	58	ε2	ε2	PROPN
ejpam-5594	374	59	−	−	PROPN
ejpam-5594	374	60	ε1)ς	ε1)ς	NOUN
ejpam-5594	375	1	[	[	X
ejpam-5594	375	2	∫	∫	X
ejpam-5594	375	3	ε2	ε2	PROPN
ejpam-5594	375	4	ε1	ε1	PROPN
ejpam-5594	375	5	(	(	PUNCT
ejpam-5594	375	6	ε2	ε2	ADJ
ejpam-5594	375	7	−	−	PROPN
ejpam-5594	375	8	v)ς−1φ(v)ג(v)dv+	v)ς−1φ(v)ג(v)dv+	NOUN
ejpam-5594	375	9	∫	∫	PROPN
ejpam-5594	375	10	ε2	ε2	PROPN
ejpam-5594	375	11	ε1	ε1	PROPN
ejpam-5594	375	12	(	(	PUNCT
ejpam-5594	375	13	u−	u−	PROPN
ejpam-5594	375	14	ε1	ε1	PROPN
ejpam-5594	375	15	)	)	PUNCT
ejpam-5594	375	16	ς−1φ(u)ג(u)du	ς−1φ(u)ג(u)du	NOUN
ejpam-5594	375	17	]	]	PUNCT
ejpam-5594	375	18	.	.	PUNCT
ejpam-5594	376	1	multiplying	multiply	VERB
ejpam-5594	376	2	above	above	ADP
ejpam-5594	376	3	relation	relation	NOUN
ejpam-5594	376	4	with	with	ADP
ejpam-5594	376	5	ς(ε2−ε1)ς	ς(ε2−ε1)ς	NOUN
ejpam-5594	376	6	b(ς)γ(ς	b(ς)γ(ς	NOUN
ejpam-5594	376	7	)	)	PUNCT
ejpam-5594	376	8	and	and	CCONJ
ejpam-5594	376	9	adding	add	VERB
ejpam-5594	376	10	the	the	DET
ejpam-5594	376	11	expression	expression	NOUN
ejpam-5594	376	12	1−ς	1−ς	NUM
ejpam-5594	376	13	b(ς	b(ς	PROPN
ejpam-5594	376	14	)	)	PUNCT
ejpam-5594	376	15	[	[	PUNCT
ejpam-5594	376	16	φ(ε1	φ(ε1	NOUN
ejpam-5594	376	17	)	)	PUNCT
ejpam-5594	376	18	+	+	SYM
ejpam-5594	376	19	φ(ε2	φ(ε2	NUM
ejpam-5594	376	20	)	)	PUNCT
ejpam-5594	376	21	]	]	PUNCT
ejpam-5594	376	22	to	to	ADP
ejpam-5594	376	23	both	both	DET
ejpam-5594	376	24	sides	side	NOUN
ejpam-5594	376	25	of	of	ADP
ejpam-5594	376	26	the	the	DET
ejpam-5594	376	27	desired	desire	VERB
ejpam-5594	376	28	results	result	NOUN
ejpam-5594	376	29	,	,	PUNCT
ejpam-5594	376	30	we	we	PRON
ejpam-5594	376	31	get	get	VERB
ejpam-5594	376	32	that	that	DET
ejpam-5594	376	33	h	h	NOUN
ejpam-5594	376	34	(	(	PUNCT
ejpam-5594	376	35	1	1	NUM
ejpam-5594	376	36	2	2	NUM
ejpam-5594	376	37	)	)	PUNCT
ejpam-5594	376	38	ς	ς	PROPN
ejpam-5594	376	39	b(ς)γ(ς	b(ς)γ(ς	NOUN
ejpam-5594	376	40	)	)	PUNCT
ejpam-5594	376	41	φ	φ	PROPN
ejpam-5594	376	42	(	(	PUNCT
ejpam-5594	376	43	ε2	ε2	PROPN
ejpam-5594	376	44	+	+	CCONJ
ejpam-5594	376	45	ε1	ε1	PROPN
ejpam-5594	376	46	2	2	NUM
ejpam-5594	376	47	)	)	PUNCT
ejpam-5594	376	48	∫	∫	PROPN
ejpam-5594	376	49	ε2	ε2	PROPN
ejpam-5594	376	50	ε1	ε1	PROPN
ejpam-5594	376	51	(	(	PUNCT
ejpam-5594	376	52	u−	u−	PROPN
ejpam-5594	376	53	ε1	ε1	PROPN
ejpam-5594	376	54	)	)	PUNCT
ejpam-5594	376	55	ς−1ג(u)du+	ς−1ג(u)du+	NOUN
ejpam-5594	376	56	1−	1−	NUM
ejpam-5594	376	57	ς	ς	X
ejpam-5594	376	58	b(ς	b(ς	PROPN
ejpam-5594	376	59	)	)	PUNCT
ejpam-5594	376	60	[	[	PUNCT
ejpam-5594	376	61	φ(ε1)ג(ε1	φ(ε1)ג(ε1	PROPN
ejpam-5594	376	62	)	)	PUNCT
ejpam-5594	376	63	+	+	CCONJ
ejpam-5594	376	64	φ(ε2)ג(ε2	φ(ε2)ג(ε2	PROPN
ejpam-5594	376	65	)	)	PUNCT
ejpam-5594	376	66	]	]	PUNCT
ejpam-5594	376	67	⪯cr	⪯cr	VERB
ejpam-5594	376	68	ς	ς	PROPN
ejpam-5594	376	69	b(ς)γ(ς	b(ς)γ(ς	NOUN
ejpam-5594	376	70	)	)	PUNCT
ejpam-5594	377	1	[	[	X
ejpam-5594	377	2	∫	∫	X
ejpam-5594	377	3	ε2	ε2	PROPN
ejpam-5594	377	4	ε1	ε1	PROPN
ejpam-5594	377	5	(	(	PUNCT
ejpam-5594	377	6	ε2	ε2	ADJ
ejpam-5594	377	7	−	−	PROPN
ejpam-5594	377	8	v)ς−1φ(v)ג(v)dv+	v)ς−1φ(v)ג(v)dv+	NOUN
ejpam-5594	377	9	∫	∫	PROPN
ejpam-5594	377	10	ε2	ε2	PROPN
ejpam-5594	377	11	ε1	ε1	PROPN
ejpam-5594	377	12	(	(	PUNCT
ejpam-5594	377	13	u−	u−	PROPN
ejpam-5594	377	14	ε1	ε1	PROPN
ejpam-5594	377	15	)	)	PUNCT
ejpam-5594	377	16	ς−1φ(u)ג(u)du	ς−1φ(u)ג(u)du	NOUN
ejpam-5594	377	17	]	]	PUNCT
ejpam-5594	378	1	+	+	CCONJ
ejpam-5594	378	2	1−	1−	NUM
ejpam-5594	378	3	ς	ς	X
ejpam-5594	378	4	b(ς	b(ς	PROPN
ejpam-5594	378	5	)	)	PUNCT
ejpam-5594	378	6	[	[	PUNCT
ejpam-5594	378	7	φ(ε1)ג(ε1	φ(ε1)ג(ε1	PROPN
ejpam-5594	378	8	)	)	PUNCT
ejpam-5594	378	9	+	+	CCONJ
ejpam-5594	378	10	φ(ε2)ג(ε2	φ(ε2)ג(ε2	PROPN
ejpam-5594	378	11	)	)	PUNCT
ejpam-5594	378	12	]	]	PUNCT
ejpam-5594	378	13	.	.	PUNCT
ejpam-5594	379	1	from	from	ADP
ejpam-5594	379	2	this	this	PRON
ejpam-5594	379	3	,	,	PUNCT
ejpam-5594	379	4	it	it	PRON
ejpam-5594	379	5	can	can	AUX
ejpam-5594	379	6	be	be	AUX
ejpam-5594	379	7	follows	follow	VERB
ejpam-5594	379	8	as	as	ADP
ejpam-5594	379	9	h	h	NOUN
ejpam-5594	379	10	(	(	PUNCT
ejpam-5594	379	11	1	1	NUM
ejpam-5594	379	12	2	2	NUM
ejpam-5594	379	13	)	)	PUNCT
ejpam-5594	379	14	φ	φ	PROPN
ejpam-5594	379	15	(	(	PUNCT
ejpam-5594	379	16	ε2	ε2	PROPN
ejpam-5594	379	17	+	+	CCONJ
ejpam-5594	379	18	ε1	ε1	PROPN
ejpam-5594	379	19	2	2	NUM
ejpam-5594	379	20	)	)	PUNCT
ejpam-5594	379	21	abiςε2{ג(ε1	abiςε2{ג(ε1	PROPN
ejpam-5594	379	22	)	)	PUNCT
ejpam-5594	379	23	}	}	PUNCT
ejpam-5594	379	24	−	−	PROPN
ejpam-5594	379	25	h	h	NOUN
ejpam-5594	379	26	(	(	PUNCT
ejpam-5594	379	27	1	1	NUM
ejpam-5594	379	28	2	2	NUM
ejpam-5594	379	29	)	)	PUNCT
ejpam-5594	379	30	φ	φ	PROPN
ejpam-5594	379	31	(	(	PUNCT
ejpam-5594	379	32	ε2	ε2	PROPN
ejpam-5594	379	33	+	+	CCONJ
ejpam-5594	379	34	ε1	ε1	PROPN
ejpam-5594	379	35	2	2	NUM
ejpam-5594	379	36	)	)	PUNCT
ejpam-5594	379	37	1−	1−	NUM
ejpam-5594	379	38	ς	ς	PROPN
ejpam-5594	379	39	b(ς	b(ς	PROPN
ejpam-5594	379	40	)	)	PUNCT
ejpam-5594	379	41	(	(	PUNCT
ejpam-5594	379	42	ε1)ג	ε1)ג	NOUN
ejpam-5594	379	43	+	+	CCONJ
ejpam-5594	379	44	1−	1−	NUM
ejpam-5594	379	45	ς	ς	X
ejpam-5594	379	46	b(ς	b(ς	PROPN
ejpam-5594	379	47	)	)	PUNCT
ejpam-5594	379	48	[	[	PUNCT
ejpam-5594	379	49	φ(ε1)ג(ε1	φ(ε1)ג(ε1	PROPN
ejpam-5594	379	50	)	)	PUNCT
ejpam-5594	379	51	+	+	CCONJ
ejpam-5594	379	52	φ(ε2)ג(ε2	φ(ε2)ג(ε2	PROPN
ejpam-5594	379	53	)	)	PUNCT
ejpam-5594	379	54	]	]	PUNCT
ejpam-5594	379	55	⪯cr	⪯cr	VERB
ejpam-5594	379	56	ab	ab	PROPN
ejpam-5594	379	57	ε1i	ε1i	PROPN
ejpam-5594	379	58	ς	ς	PROPN
ejpam-5594	379	59	ε2{(φג(ε2)}+	ε2{(φג(ε2)}+	PROPN
ejpam-5594	379	60	abiςε2{(φג(ε1	abiςε2{(φג(ε1	PROPN
ejpam-5594	379	61	)	)	PUNCT
ejpam-5594	379	62	}	}	PUNCT
ejpam-5594	379	63	.	.	PUNCT
ejpam-5594	380	1	(	(	PUNCT
ejpam-5594	380	2	13	13	NUM
ejpam-5594	380	3	)	)	PUNCT
ejpam-5594	380	4	j.	j.	PROPN
ejpam-5594	380	5	e.	e.	PROPN
ejpam-5594	380	6	maćıas	maćıas	PROPN
ejpam-5594	380	7	-	-	PUNCT
ejpam-5594	380	8	dı́az	dı́az	NOUN
ejpam-5594	380	9	et	et	NOUN
ejpam-5594	380	10	al	al	PROPN
ejpam-5594	380	11	.	.	PUNCT
ejpam-5594	380	12	/	/	SYM
ejpam-5594	380	13	eur	eur	PROPN
ejpam-5594	380	14	.	.	PUNCT
ejpam-5594	381	1	j.	j.	PROPN
ejpam-5594	381	2	pure	pure	PROPN
ejpam-5594	381	3	appl	appl	PROPN
ejpam-5594	381	4	.	.	PROPN
ejpam-5594	381	5	math	math	PROPN
ejpam-5594	381	6	,	,	PUNCT
ejpam-5594	381	7	17	17	NUM
ejpam-5594	381	8	(	(	PUNCT
ejpam-5594	381	9	4	4	NUM
ejpam-5594	381	10	)	)	PUNCT
ejpam-5594	381	11	(	(	PUNCT
ejpam-5594	381	12	2024	2024	NUM
ejpam-5594	381	13	)	)	PUNCT
ejpam-5594	381	14	,	,	PUNCT
ejpam-5594	381	15	4014	4014	NUM
ejpam-5594	381	16	-	-	SYM
ejpam-5594	381	17	4049	4049	NUM
ejpam-5594	381	18	4028	4028	NUM
ejpam-5594	381	19	similarly	similarly	ADV
ejpam-5594	381	20	,	,	PUNCT
ejpam-5594	381	21	multiplying	multiplying	NOUN
ejpam-5594	381	22	h	h	NOUN
ejpam-5594	381	23	(	(	PUNCT
ejpam-5594	381	24	1	1	NUM
ejpam-5594	381	25	2	2	NUM
ejpam-5594	381	26	)	)	PUNCT
ejpam-5594	381	27	♭	♭	PROPN
ejpam-5594	382	1	ς−1ג(	ς−1ג(	PROPN
ejpam-5594	382	2	♭	♭	PROPN
ejpam-5594	382	3	ε1+(1−	ε1+(1−	PROPN
ejpam-5594	382	4	♭	♭	PROPN
ejpam-5594	382	5	)	)	PUNCT
ejpam-5594	382	6	ε2	ε2	PROPN
ejpam-5594	382	7	)	)	PUNCT
ejpam-5594	382	8	on	on	ADP
ejpam-5594	382	9	both	both	DET
ejpam-5594	382	10	sides	side	NOUN
ejpam-5594	382	11	of	of	ADP
ejpam-5594	382	12	(	(	PUNCT
ejpam-5594	382	13	12	12	NUM
ejpam-5594	382	14	)	)	PUNCT
ejpam-5594	382	15	and	and	CCONJ
ejpam-5594	382	16	integrating	integrating	NOUN
ejpam-5594	382	17	,	,	PUNCT
ejpam-5594	382	18	we	we	PRON
ejpam-5594	382	19	have	have	VERB
ejpam-5594	382	20	h	h	NOUN
ejpam-5594	382	21	(	(	PUNCT
ejpam-5594	382	22	1	1	NUM
ejpam-5594	382	23	2	2	NUM
ejpam-5594	382	24	)	)	PUNCT
ejpam-5594	382	25	φ	φ	PROPN
ejpam-5594	382	26	(	(	PUNCT
ejpam-5594	382	27	ε2	ε2	PROPN
ejpam-5594	382	28	+	+	CCONJ
ejpam-5594	382	29	ε1	ε1	PROPN
ejpam-5594	382	30	2	2	NUM
ejpam-5594	382	31	)	)	PUNCT
ejpam-5594	382	32	∫	∫	PROPN
ejpam-5594	383	1	1	1	NUM
ejpam-5594	383	2	0	0	NUM
ejpam-5594	383	3	♭	♭	PROPN
ejpam-5594	383	4	ς−1ג(	ς−1ג(	PROPN
ejpam-5594	383	5	♭	♭	PROPN
ejpam-5594	383	6	ε1	ε1	VERB
ejpam-5594	383	7	+	+	CCONJ
ejpam-5594	383	8	(	(	PUNCT
ejpam-5594	383	9	1−	1−	NUM
ejpam-5594	383	10	♭	♭	NOUN
ejpam-5594	383	11	)	)	PUNCT
ejpam-5594	383	12	ε2)d	ε2)d	NOUN
ejpam-5594	383	13	♭	♭	PROPN
ejpam-5594	383	14	≤	≤	NUM
ejpam-5594	383	15	∫	∫	PROPN
ejpam-5594	383	16	1	1	NUM
ejpam-5594	383	17	0	0	NUM
ejpam-5594	384	1	♭	♭	PROPN
ejpam-5594	384	2	ς−1	ς−1	PROPN
ejpam-5594	384	3	[	[	PUNCT
ejpam-5594	384	4	φ(	φ(	NUM
ejpam-5594	384	5	♭	♭	PROPN
ejpam-5594	384	6	ε1	ε1	VERB
ejpam-5594	384	7	+	+	CCONJ
ejpam-5594	384	8	(	(	PUNCT
ejpam-5594	384	9	1−	1−	NUM
ejpam-5594	384	10	♭	♭	INTJ
ejpam-5594	384	11	)	)	PUNCT
ejpam-5594	384	12	ε2	ε2	PROPN
ejpam-5594	384	13	)	)	PUNCT
ejpam-5594	384	14	+	+	CCONJ
ejpam-5594	384	15	φ(	φ(	NUM
ejpam-5594	384	16	♭	♭	NOUN
ejpam-5594	384	17	ε2	ε2	ADJ
ejpam-5594	384	18	+	+	CCONJ
ejpam-5594	384	19	(	(	PUNCT
ejpam-5594	384	20	1−	1−	NUM
ejpam-5594	384	21	♭	♭	INTJ
ejpam-5594	384	22	)	)	PUNCT
ejpam-5594	384	23	ε1	ε1	PROPN
ejpam-5594	384	24	)	)	PUNCT
ejpam-5594	384	25	]	]	PUNCT
ejpam-5594	385	1	ε1	ε1	VERB
ejpam-5594	385	2	♭	♭	PRON
ejpam-5594	385	3	)ג	)ג	PUNCT
ejpam-5594	386	1	+	+	CCONJ
ejpam-5594	386	2	(	(	PUNCT
ejpam-5594	386	3	1−	1−	NUM
ejpam-5594	386	4	♭	♭	NOUN
ejpam-5594	386	5	)	)	PUNCT
ejpam-5594	386	6	ε2)d	ε2)d	PROPN
ejpam-5594	386	7	♭	♭	PROPN
ejpam-5594	386	8	.	.	PUNCT
ejpam-5594	387	1	let	let	VERB
ejpam-5594	387	2	u	u	PRON
ejpam-5594	387	3	=	=	NOUN
ejpam-5594	388	1	♭	♭	PROPN
ejpam-5594	388	2	ε1	ε1	VERB
ejpam-5594	388	3	+	+	CCONJ
ejpam-5594	388	4	(	(	PUNCT
ejpam-5594	388	5	1−	1−	NUM
ejpam-5594	388	6	♭	♭	INTJ
ejpam-5594	388	7	)	)	PUNCT
ejpam-5594	388	8	ε2	ε2	PROPN
ejpam-5594	388	9	,	,	PUNCT
ejpam-5594	388	10	then	then	ADV
ejpam-5594	388	11	the	the	DET
ejpam-5594	388	12	above	above	ADJ
ejpam-5594	388	13	result	result	NOUN
ejpam-5594	388	14	becomes	become	VERB
ejpam-5594	388	15	h	h	NOUN
ejpam-5594	388	16	(	(	PUNCT
ejpam-5594	388	17	1	1	NUM
ejpam-5594	388	18	2	2	NUM
ejpam-5594	388	19	)	)	PUNCT
ejpam-5594	388	20	1	1	NUM
ejpam-5594	388	21	(	(	PUNCT
ejpam-5594	388	22	ε2	ε2	PROPN
ejpam-5594	388	23	−	−	PROPN
ejpam-5594	388	24	ε1)ς	ε1)ς	NOUN
ejpam-5594	388	25	φ	φ	PROPN
ejpam-5594	388	26	(	(	PUNCT
ejpam-5594	388	27	ε2	ε2	PROPN
ejpam-5594	388	28	+	+	CCONJ
ejpam-5594	388	29	ε1	ε1	PROPN
ejpam-5594	388	30	2	2	NUM
ejpam-5594	388	31	)	)	PUNCT
ejpam-5594	388	32	∫	∫	PROPN
ejpam-5594	388	33	ε2	ε2	PROPN
ejpam-5594	388	34	ε1	ε1	PROPN
ejpam-5594	388	35	(	(	PUNCT
ejpam-5594	388	36	ε2	ε2	PROPN
ejpam-5594	388	37	−	−	PROPN
ejpam-5594	388	38	u)ς−1ג(u)du	u)ς−1ג(u)du	PROPN
ejpam-5594	388	39	⪯cr	⪯cr	NUM
ejpam-5594	388	40	1	1	NUM
ejpam-5594	388	41	(	(	PUNCT
ejpam-5594	388	42	ε2	ε2	PROPN
ejpam-5594	388	43	−	−	PROPN
ejpam-5594	388	44	ε1)ς	ε1)ς	NOUN
ejpam-5594	389	1	[	[	X
ejpam-5594	389	2	∫	∫	X
ejpam-5594	389	3	ε2	ε2	PROPN
ejpam-5594	389	4	ε1	ε1	PROPN
ejpam-5594	389	5	(	(	PUNCT
ejpam-5594	389	6	ε2	ε2	NOUN
ejpam-5594	389	7	−	−	PROPN
ejpam-5594	389	8	u)ς−1φ(u)ג(u)du	u)ς−1φ(u)ג(u)du	PROPN
ejpam-5594	389	9	+	+	CCONJ
ejpam-5594	389	10	∫	∫	PROPN
ejpam-5594	389	11	ε2	ε2	PROPN
ejpam-5594	389	12	ε1	ε1	PROPN
ejpam-5594	389	13	(	(	PUNCT
ejpam-5594	389	14	ε2	ε2	PROPN
ejpam-5594	389	15	−	−	PROPN
ejpam-5594	389	16	u)ς−1φ(ε2	u)ς−1φ(ε2	ADJ
ejpam-5594	389	17	+	+	CCONJ
ejpam-5594	389	18	ε1	ε1	PROPN
ejpam-5594	389	19	−	−	PROPN
ejpam-5594	389	20	u)ג(u)du	u)ג(u)du	NOUN
ejpam-5594	389	21	]	]	PUNCT
ejpam-5594	389	22	.	.	PUNCT
ejpam-5594	390	1	making	make	VERB
ejpam-5594	390	2	a	a	DET
ejpam-5594	390	3	modification	modification	NOUN
ejpam-5594	390	4	in	in	ADP
ejpam-5594	390	5	the	the	DET
ejpam-5594	390	6	previous	previous	ADJ
ejpam-5594	390	7	integral	integral	NOUN
ejpam-5594	390	8	of	of	ADP
ejpam-5594	390	9	the	the	DET
ejpam-5594	390	10	preceding	precede	VERB
ejpam-5594	390	11	relation	relation	NOUN
ejpam-5594	390	12	,	,	PUNCT
ejpam-5594	390	13	v	v	NOUN
ejpam-5594	390	14	=	=	SYM
ejpam-5594	390	15	ε2	ε2	PROPN
ejpam-5594	390	16	+	+	CCONJ
ejpam-5594	390	17	ε1	ε1	PROPN
ejpam-5594	390	18	−	−	PROPN
ejpam-5594	390	19	u	u	PROPN
ejpam-5594	390	20	,	,	PUNCT
ejpam-5594	390	21	ε2)ג	ε2)ג	PROPN
ejpam-5594	390	22	+	+	CCONJ
ejpam-5594	390	23	ε1	ε1	PROPN
ejpam-5594	390	24	−	−	PROPN
ejpam-5594	390	25	v	v	NOUN
ejpam-5594	390	26	)	)	PUNCT
ejpam-5594	390	27	=	=	PUNCT
ejpam-5594	390	28	,	,	PUNCT
ejpam-5594	390	29	(	(	PUNCT
ejpam-5594	390	30	v)ג	v)ג	X
ejpam-5594	390	31	we	we	PRON
ejpam-5594	390	32	have	have	VERB
ejpam-5594	390	33	h	h	NOUN
ejpam-5594	390	34	(	(	PUNCT
ejpam-5594	390	35	1	1	NUM
ejpam-5594	390	36	2	2	NUM
ejpam-5594	390	37	)	)	PUNCT
ejpam-5594	390	38	1	1	NUM
ejpam-5594	390	39	(	(	PUNCT
ejpam-5594	390	40	ε2	ε2	PROPN
ejpam-5594	390	41	−	−	PROPN
ejpam-5594	390	42	ε1)ς	ε1)ς	NOUN
ejpam-5594	390	43	φ	φ	PROPN
ejpam-5594	390	44	(	(	PUNCT
ejpam-5594	390	45	ε2	ε2	PROPN
ejpam-5594	390	46	+	+	CCONJ
ejpam-5594	390	47	ε1	ε1	PROPN
ejpam-5594	390	48	2	2	NUM
ejpam-5594	390	49	)	)	PUNCT
ejpam-5594	390	50	∫	∫	PROPN
ejpam-5594	390	51	ε2	ε2	PROPN
ejpam-5594	390	52	ε1	ε1	PROPN
ejpam-5594	390	53	(	(	PUNCT
ejpam-5594	390	54	ε2	ε2	PROPN
ejpam-5594	390	55	−	−	PROPN
ejpam-5594	390	56	u)ς−1ג(u)du	u)ς−1ג(u)du	ADJ
ejpam-5594	390	57	≤	≤	ADV
ejpam-5594	390	58	1	1	NUM
ejpam-5594	390	59	(	(	PUNCT
ejpam-5594	390	60	ε2	ε2	PROPN
ejpam-5594	390	61	−	−	PROPN
ejpam-5594	390	62	ε1)ς	ε1)ς	NOUN
ejpam-5594	391	1	[	[	X
ejpam-5594	391	2	∫	∫	X
ejpam-5594	391	3	ε2	ε2	PROPN
ejpam-5594	391	4	ε1	ε1	PROPN
ejpam-5594	391	5	(	(	PUNCT
ejpam-5594	391	6	ε2	ε2	ADJ
ejpam-5594	391	7	−	−	PROPN
ejpam-5594	391	8	u)ς−1φ(u)ג(u)du+	u)ς−1φ(u)ג(u)du+	NOUN
ejpam-5594	391	9	∫	∫	PROPN
ejpam-5594	391	10	ε2	ε2	PROPN
ejpam-5594	391	11	ε1	ε1	PROPN
ejpam-5594	391	12	(	(	PUNCT
ejpam-5594	391	13	v−	v−	NOUN
ejpam-5594	391	14	ε1	ε1	PROPN
ejpam-5594	391	15	)	)	PUNCT
ejpam-5594	391	16	ς−1φ(v)ג(v)dv	ς−1φ(v)ג(v)dv	NOUN
ejpam-5594	391	17	]	]	PUNCT
ejpam-5594	391	18	.	.	PUNCT
ejpam-5594	392	1	multiplying	multiply	VERB
ejpam-5594	392	2	above	above	ADP
ejpam-5594	392	3	relation	relation	NOUN
ejpam-5594	392	4	with	with	ADP
ejpam-5594	392	5	ς(ε2−ε1)ς	ς(ε2−ε1)ς	NOUN
ejpam-5594	392	6	b(ς)γ(ς	b(ς)γ(ς	NOUN
ejpam-5594	392	7	)	)	PUNCT
ejpam-5594	392	8	and	and	CCONJ
ejpam-5594	392	9	adding	add	VERB
ejpam-5594	392	10	the	the	DET
ejpam-5594	392	11	expression	expression	NOUN
ejpam-5594	392	12	1−ς	1−ς	NUM
ejpam-5594	392	13	b(ς	b(ς	PROPN
ejpam-5594	392	14	)	)	PUNCT
ejpam-5594	392	15	[	[	PUNCT
ejpam-5594	392	16	φ(ε1	φ(ε1	NOUN
ejpam-5594	392	17	)	)	PUNCT
ejpam-5594	392	18	+	+	SYM
ejpam-5594	392	19	φ(ε2	φ(ε2	NUM
ejpam-5594	392	20	)	)	PUNCT
ejpam-5594	392	21	]	]	PUNCT
ejpam-5594	392	22	to	to	ADP
ejpam-5594	392	23	both	both	DET
ejpam-5594	392	24	sides	side	NOUN
ejpam-5594	392	25	of	of	ADP
ejpam-5594	392	26	the	the	DET
ejpam-5594	392	27	desired	desire	VERB
ejpam-5594	392	28	result	result	NOUN
ejpam-5594	392	29	,	,	PUNCT
ejpam-5594	392	30	we	we	PRON
ejpam-5594	392	31	get	get	VERB
ejpam-5594	392	32	that	that	DET
ejpam-5594	392	33	h	h	NOUN
ejpam-5594	392	34	(	(	PUNCT
ejpam-5594	392	35	1	1	NUM
ejpam-5594	392	36	2	2	NUM
ejpam-5594	392	37	)	)	PUNCT
ejpam-5594	392	38	ς	ς	PROPN
ejpam-5594	392	39	b(ς)γ(ς	b(ς)γ(ς	NOUN
ejpam-5594	392	40	)	)	PUNCT
ejpam-5594	392	41	φ	φ	PROPN
ejpam-5594	392	42	(	(	PUNCT
ejpam-5594	392	43	ε2	ε2	PROPN
ejpam-5594	392	44	+	+	CCONJ
ejpam-5594	392	45	ε1	ε1	PROPN
ejpam-5594	392	46	2	2	NUM
ejpam-5594	392	47	)	)	PUNCT
ejpam-5594	392	48	∫	∫	PROPN
ejpam-5594	392	49	ε2	ε2	PROPN
ejpam-5594	392	50	ε1	ε1	PROPN
ejpam-5594	392	51	(	(	PUNCT
ejpam-5594	392	52	ε2	ε2	PROPN
ejpam-5594	392	53	−	−	PROPN
ejpam-5594	392	54	u)ς−1ג(u)du	u)ς−1ג(u)du	PROPN
ejpam-5594	392	55	+	+	CCONJ
ejpam-5594	392	56	1−	1−	NUM
ejpam-5594	392	57	ς	ς	X
ejpam-5594	392	58	b(ς	b(ς	PROPN
ejpam-5594	392	59	)	)	PUNCT
ejpam-5594	392	60	[	[	PUNCT
ejpam-5594	392	61	φ(ε1)ג(ε1	φ(ε1)ג(ε1	PROPN
ejpam-5594	392	62	)	)	PUNCT
ejpam-5594	392	63	+	+	CCONJ
ejpam-5594	392	64	φ(ε2)ג(ε2	φ(ε2)ג(ε2	PROPN
ejpam-5594	392	65	)	)	PUNCT
ejpam-5594	392	66	]	]	PUNCT
ejpam-5594	392	67	⪯cr	⪯cr	VERB
ejpam-5594	392	68	ς	ς	PROPN
ejpam-5594	392	69	b(ς)γ(ς	b(ς)γ(ς	NOUN
ejpam-5594	392	70	)	)	PUNCT
ejpam-5594	393	1	[	[	X
ejpam-5594	393	2	∫	∫	X
ejpam-5594	393	3	ε2	ε2	PROPN
ejpam-5594	393	4	ε1	ε1	PROPN
ejpam-5594	393	5	(	(	PUNCT
ejpam-5594	393	6	ε2	ε2	ADJ
ejpam-5594	393	7	−	−	PROPN
ejpam-5594	393	8	u)ς−1φ(u)ג(u)du+	u)ς−1φ(u)ג(u)du+	NOUN
ejpam-5594	393	9	∫	∫	PROPN
ejpam-5594	393	10	ε2	ε2	PROPN
ejpam-5594	393	11	ε1	ε1	PROPN
ejpam-5594	393	12	(	(	PUNCT
ejpam-5594	393	13	v−	v−	NOUN
ejpam-5594	393	14	ε1	ε1	PROPN
ejpam-5594	393	15	)	)	PUNCT
ejpam-5594	393	16	ς−1φ(v)ג(v)dv	ς−1φ(v)ג(v)dv	NOUN
ejpam-5594	393	17	]	]	PUNCT
ejpam-5594	394	1	+	+	CCONJ
ejpam-5594	394	2	1−	1−	NUM
ejpam-5594	394	3	ς	ς	X
ejpam-5594	394	4	b(ς	b(ς	PROPN
ejpam-5594	394	5	)	)	PUNCT
ejpam-5594	394	6	[	[	PUNCT
ejpam-5594	394	7	φ(ε1)ג(ε1	φ(ε1)ג(ε1	PROPN
ejpam-5594	394	8	)	)	PUNCT
ejpam-5594	394	9	+	+	CCONJ
ejpam-5594	394	10	φ(ε2)ג(ε2	φ(ε2)ג(ε2	PROPN
ejpam-5594	394	11	)	)	PUNCT
ejpam-5594	394	12	]	]	PUNCT
ejpam-5594	394	13	.	.	PUNCT
ejpam-5594	395	1	from	from	ADP
ejpam-5594	395	2	this	this	PRON
ejpam-5594	395	3	,	,	PUNCT
ejpam-5594	395	4	it	it	PRON
ejpam-5594	395	5	can	can	AUX
ejpam-5594	395	6	be	be	AUX
ejpam-5594	395	7	follows	follow	VERB
ejpam-5594	395	8	that	that	SCONJ
ejpam-5594	395	9	h	h	NOUN
ejpam-5594	395	10	(	(	PUNCT
ejpam-5594	395	11	1	1	NUM
ejpam-5594	395	12	2	2	NUM
ejpam-5594	395	13	)	)	PUNCT
ejpam-5594	395	14	φ	φ	PROPN
ejpam-5594	395	15	(	(	PUNCT
ejpam-5594	395	16	ε2	ε2	PROPN
ejpam-5594	395	17	+	+	CCONJ
ejpam-5594	395	18	ε1	ε1	PROPN
ejpam-5594	395	19	2	2	NUM
ejpam-5594	395	20	)	)	PUNCT
ejpam-5594	395	21	ab	ab	PROPN
ejpam-5594	395	22	ε1i	ε1i	NUM
ejpam-5594	395	23	ς	ς	PROPN
ejpam-5594	395	24	ε2{ג(ε2	ε2{ג(ε2	PROPN
ejpam-5594	395	25	)	)	PUNCT
ejpam-5594	395	26	}	}	PUNCT
ejpam-5594	396	1	−	−	PROPN
ejpam-5594	396	2	h	h	NOUN
ejpam-5594	396	3	(	(	PUNCT
ejpam-5594	396	4	1	1	NUM
ejpam-5594	396	5	2	2	NUM
ejpam-5594	396	6	)	)	PUNCT
ejpam-5594	396	7	φ	φ	PROPN
ejpam-5594	396	8	(	(	PUNCT
ejpam-5594	396	9	ε2	ε2	PROPN
ejpam-5594	396	10	+	+	CCONJ
ejpam-5594	396	11	ε1	ε1	PROPN
ejpam-5594	396	12	2	2	NUM
ejpam-5594	396	13	)	)	PUNCT
ejpam-5594	396	14	1−	1−	NUM
ejpam-5594	396	15	ς	ς	PROPN
ejpam-5594	396	16	b(ς	b(ς	PROPN
ejpam-5594	396	17	)	)	PUNCT
ejpam-5594	396	18	(	(	PUNCT
ejpam-5594	396	19	ε2)ג	ε2)ג	NOUN
ejpam-5594	396	20	+	+	PROPN
ejpam-5594	396	21	1−	1−	NUM
ejpam-5594	396	22	ς	ς	X
ejpam-5594	396	23	b(ς	b(ς	PROPN
ejpam-5594	396	24	)	)	PUNCT
ejpam-5594	396	25	[	[	PUNCT
ejpam-5594	396	26	φ(ε1)ג(ε1	φ(ε1)ג(ε1	PROPN
ejpam-5594	396	27	)	)	PUNCT
ejpam-5594	396	28	+	+	CCONJ
ejpam-5594	396	29	φ(ε2)ג(ε2	φ(ε2)ג(ε2	PROPN
ejpam-5594	396	30	)	)	PUNCT
ejpam-5594	396	31	]	]	PUNCT
ejpam-5594	396	32	⪯cr	⪯cr	VERB
ejpam-5594	396	33	ab	ab	PROPN
ejpam-5594	396	34	ε1i	ε1i	PROPN
ejpam-5594	396	35	ς	ς	PROPN
ejpam-5594	396	36	ε2{(φג(ε2)}+	ε2{(φג(ε2)}+	PROPN
ejpam-5594	396	37	abiςε2{(φג(ε1	abiςε2{(φג(ε1	PROPN
ejpam-5594	396	38	)	)	PUNCT
ejpam-5594	396	39	}	}	PUNCT
ejpam-5594	396	40	.	.	PUNCT
ejpam-5594	397	1	(	(	PUNCT
ejpam-5594	397	2	14	14	NUM
ejpam-5594	397	3	)	)	PUNCT
ejpam-5594	397	4	j.	j.	PROPN
ejpam-5594	397	5	e.	e.	PROPN
ejpam-5594	397	6	maćıas	maćıas	PROPN
ejpam-5594	397	7	-	-	PUNCT
ejpam-5594	397	8	dı́az	dı́az	NOUN
ejpam-5594	397	9	et	et	NOUN
ejpam-5594	397	10	al	al	PROPN
ejpam-5594	397	11	.	.	PUNCT
ejpam-5594	397	12	/	/	SYM
ejpam-5594	397	13	eur	eur	PROPN
ejpam-5594	397	14	.	.	PUNCT
ejpam-5594	398	1	j.	j.	PROPN
ejpam-5594	398	2	pure	pure	PROPN
ejpam-5594	398	3	appl	appl	PROPN
ejpam-5594	398	4	.	.	PROPN
ejpam-5594	398	5	math	math	PROPN
ejpam-5594	398	6	,	,	PUNCT
ejpam-5594	398	7	17	17	NUM
ejpam-5594	398	8	(	(	PUNCT
ejpam-5594	398	9	4	4	NUM
ejpam-5594	398	10	)	)	PUNCT
ejpam-5594	398	11	(	(	PUNCT
ejpam-5594	398	12	2024	2024	NUM
ejpam-5594	398	13	)	)	PUNCT
ejpam-5594	398	14	,	,	PUNCT
ejpam-5594	398	15	4014	4014	NUM
ejpam-5594	398	16	-	-	SYM
ejpam-5594	398	17	4049	4049	NUM
ejpam-5594	398	18	4029	4029	NUM
ejpam-5594	398	19	adding	add	VERB
ejpam-5594	398	20	(	(	PUNCT
ejpam-5594	398	21	13	13	NUM
ejpam-5594	398	22	)	)	PUNCT
ejpam-5594	398	23	and	and	CCONJ
ejpam-5594	398	24	(	(	PUNCT
ejpam-5594	398	25	14	14	NUM
ejpam-5594	398	26	)	)	PUNCT
ejpam-5594	399	1	,	,	PUNCT
ejpam-5594	399	2	we	we	PRON
ejpam-5594	399	3	can	can	AUX
ejpam-5594	399	4	get	get	VERB
ejpam-5594	399	5	the	the	DET
ejpam-5594	399	6	first	first	ADJ
ejpam-5594	399	7	relation	relation	NOUN
ejpam-5594	399	8	in	in	ADP
ejpam-5594	399	9	(	(	PUNCT
ejpam-5594	399	10	11	11	NUM
ejpam-5594	399	11	)	)	PUNCT
ejpam-5594	399	12	.	.	PUNCT
ejpam-5594	400	1	now	now	ADV
ejpam-5594	400	2	again	again	ADV
ejpam-5594	400	3	taking	take	VERB
ejpam-5594	400	4	into	into	ADP
ejpam-5594	400	5	account	account	NOUN
ejpam-5594	400	6	definition	definition	NOUN
ejpam-5594	400	7	4	4	NUM
ejpam-5594	400	8	,	,	PUNCT
ejpam-5594	400	9	we	we	PRON
ejpam-5594	400	10	have	have	AUX
ejpam-5594	400	11	φ(	φ(	NUM
ejpam-5594	400	12	♭	♭	PRON
ejpam-5594	400	13	ε1	ε1	VERB
ejpam-5594	400	14	+	+	SYM
ejpam-5594	400	15	(	(	PUNCT
ejpam-5594	400	16	1−	1−	NUM
ejpam-5594	400	17	♭	♭	INTJ
ejpam-5594	400	18	)	)	PUNCT
ejpam-5594	400	19	ε2	ε2	ADJ
ejpam-5594	400	20	)	)	PUNCT
ejpam-5594	400	21	⪯cr	⪯cr	NUM
ejpam-5594	400	22	φ(ε1	φ(ε1	NOUN
ejpam-5594	400	23	)	)	PUNCT
ejpam-5594	401	1	h	h	NOUN
ejpam-5594	401	2	(	(	PUNCT
ejpam-5594	401	3	♭	♭	INTJ
ejpam-5594	401	4	)	)	PUNCT
ejpam-5594	402	1	+	+	NUM
ejpam-5594	402	2	φ(ε2	φ(ε2	NUM
ejpam-5594	402	3	)	)	PUNCT
ejpam-5594	402	4	h(1−	h(1−	NOUN
ejpam-5594	402	5	♭	♭	PROPN
ejpam-5594	402	6	)	)	PUNCT
ejpam-5594	402	7	,	,	PUNCT
ejpam-5594	402	8	φ(	φ(	NUM
ejpam-5594	402	9	♭	♭	NOUN
ejpam-5594	402	10	ε2	ε2	ADJ
ejpam-5594	402	11	+	+	CCONJ
ejpam-5594	402	12	(	(	PUNCT
ejpam-5594	402	13	1−	1−	NUM
ejpam-5594	402	14	♭	♭	INTJ
ejpam-5594	402	15	)	)	PUNCT
ejpam-5594	402	16	ε1	ε1	PROPN
ejpam-5594	402	17	)	)	PUNCT
ejpam-5594	402	18	⪯cr	⪯cr	NUM
ejpam-5594	402	19	φ(ε2	φ(ε2	NUM
ejpam-5594	402	20	)	)	PUNCT
ejpam-5594	402	21	h	h	NOUN
ejpam-5594	402	22	(	(	PUNCT
ejpam-5594	402	23	♭	♭	PROPN
ejpam-5594	402	24	)	)	PUNCT
ejpam-5594	402	25	+	+	NUM
ejpam-5594	402	26	φ(ε1	φ(ε1	NOUN
ejpam-5594	402	27	)	)	PUNCT
ejpam-5594	402	28	h(1−	h(1−	PROPN
ejpam-5594	402	29	♭	♭	PROPN
ejpam-5594	402	30	)	)	PUNCT
ejpam-5594	402	31	,	,	PUNCT
ejpam-5594	402	32	adding	add	VERB
ejpam-5594	402	33	the	the	DET
ejpam-5594	402	34	above	above	ADJ
ejpam-5594	402	35	two	two	NUM
ejpam-5594	402	36	relations	relation	NOUN
ejpam-5594	402	37	yields	yield	NOUN
ejpam-5594	402	38	that	that	PRON
ejpam-5594	402	39	φ(	φ(	NUM
ejpam-5594	402	40	♭	♭	PRON
ejpam-5594	402	41	ε1	ε1	VERB
ejpam-5594	402	42	+	+	SYM
ejpam-5594	402	43	(	(	PUNCT
ejpam-5594	402	44	1−	1−	NUM
ejpam-5594	402	45	♭	♭	INTJ
ejpam-5594	402	46	)	)	PUNCT
ejpam-5594	402	47	ε2	ε2	PROPN
ejpam-5594	402	48	)	)	PUNCT
ejpam-5594	402	49	+	+	CCONJ
ejpam-5594	402	50	φ(	φ(	NUM
ejpam-5594	402	51	♭	♭	NOUN
ejpam-5594	402	52	ε2	ε2	ADJ
ejpam-5594	402	53	+	+	CCONJ
ejpam-5594	402	54	(	(	PUNCT
ejpam-5594	402	55	1−	1−	NUM
ejpam-5594	402	56	♭	♭	INTJ
ejpam-5594	402	57	)	)	PUNCT
ejpam-5594	402	58	ε1	ε1	PROPN
ejpam-5594	402	59	)	)	PUNCT
ejpam-5594	402	60	≤	≤	NOUN
ejpam-5594	403	1	[	[	PUNCT
ejpam-5594	403	2	1	1	NUM
ejpam-5594	403	3	h	h	NOUN
ejpam-5594	403	4	(	(	PUNCT
ejpam-5594	403	5	♭	♭	PROPN
ejpam-5594	403	6	)	)	PUNCT
ejpam-5594	404	1	+	+	CCONJ
ejpam-5594	404	2	1	1	NUM
ejpam-5594	404	3	h(1−	h(1−	NOUN
ejpam-5594	404	4	♭	♭	PROPN
ejpam-5594	404	5	)	)	PUNCT
ejpam-5594	404	6	]	]	PUNCT
ejpam-5594	405	1	[	[	PUNCT
ejpam-5594	405	2	φ(ε1	φ(ε1	NOUN
ejpam-5594	405	3	)	)	PUNCT
ejpam-5594	405	4	+	+	SYM
ejpam-5594	405	5	φ(ε2	φ(ε2	NUM
ejpam-5594	405	6	)	)	PUNCT
ejpam-5594	405	7	]	]	PUNCT
ejpam-5594	405	8	.	.	PUNCT
ejpam-5594	406	1	multiplying	multiply	VERB
ejpam-5594	406	2	aforementioned	aforementione	VERB
ejpam-5594	406	3	result	result	NOUN
ejpam-5594	406	4	with	with	ADP
ejpam-5594	406	5	♭	♭	PROPN
ejpam-5594	406	6	ς−1ג(	ς−1ג(	PROPN
ejpam-5594	406	7	♭	♭	PROPN
ejpam-5594	406	8	ε2+(1−	ε2+(1−	PROPN
ejpam-5594	406	9	♭	♭	PROPN
ejpam-5594	406	10	)	)	PUNCT
ejpam-5594	406	11	ε1	ε1	PROPN
ejpam-5594	406	12	)	)	PUNCT
ejpam-5594	406	13	and	and	CCONJ
ejpam-5594	406	14	integrating	integrating	NOUN
ejpam-5594	406	15	,	,	PUNCT
ejpam-5594	406	16	we	we	PRON
ejpam-5594	406	17	have∫	have∫	VERB
ejpam-5594	406	18	1	1	NUM
ejpam-5594	406	19	0	0	NUM
ejpam-5594	407	1	♭	♭	PROPN
ejpam-5594	407	2	ς−1	ς−1	PROPN
ejpam-5594	407	3	[	[	PUNCT
ejpam-5594	407	4	φ(	φ(	NUM
ejpam-5594	407	5	♭	♭	PROPN
ejpam-5594	407	6	ε1	ε1	VERB
ejpam-5594	407	7	+	+	CCONJ
ejpam-5594	407	8	(	(	PUNCT
ejpam-5594	407	9	1−	1−	NUM
ejpam-5594	407	10	♭	♭	INTJ
ejpam-5594	407	11	)	)	PUNCT
ejpam-5594	407	12	ε2	ε2	PROPN
ejpam-5594	407	13	)	)	PUNCT
ejpam-5594	407	14	+	+	CCONJ
ejpam-5594	407	15	φ(	φ(	NUM
ejpam-5594	407	16	♭	♭	NOUN
ejpam-5594	407	17	ε2	ε2	ADJ
ejpam-5594	407	18	+	+	CCONJ
ejpam-5594	407	19	(	(	PUNCT
ejpam-5594	407	20	1−	1−	NUM
ejpam-5594	407	21	♭	♭	INTJ
ejpam-5594	407	22	)	)	PUNCT
ejpam-5594	407	23	ε1	ε1	PROPN
ejpam-5594	407	24	)	)	PUNCT
ejpam-5594	407	25	]	]	PUNCT
ejpam-5594	408	1	ε2	ε2	PROPN
ejpam-5594	408	2	♭	♭	NOUN
ejpam-5594	408	3	)ג	)ג	PUNCT
ejpam-5594	409	1	+	+	CCONJ
ejpam-5594	409	2	(	(	PUNCT
ejpam-5594	409	3	1−	1−	NUM
ejpam-5594	409	4	♭	♭	INTJ
ejpam-5594	409	5	)	)	PUNCT
ejpam-5594	409	6	ε1)d	ε1)d	NOUN
ejpam-5594	409	7	♭	♭	PROPN
ejpam-5594	409	8	≤	≤	PROPN
ejpam-5594	409	9	[	[	PUNCT
ejpam-5594	409	10	φ(ε1	φ(ε1	NOUN
ejpam-5594	409	11	)	)	PUNCT
ejpam-5594	409	12	+	+	SYM
ejpam-5594	409	13	φ(ε2	φ(ε2	NUM
ejpam-5594	409	14	)	)	PUNCT
ejpam-5594	409	15	]	]	PUNCT
ejpam-5594	410	1	∫	∫	PROPN
ejpam-5594	411	1	1	1	NUM
ejpam-5594	411	2	0	0	NUM
ejpam-5594	411	3	♭	♭	NUM
ejpam-5594	412	1	ς−1	ς−1	PROPN
ejpam-5594	412	2	[	[	PUNCT
ejpam-5594	412	3	1	1	NUM
ejpam-5594	412	4	h	h	NOUN
ejpam-5594	412	5	(	(	PUNCT
ejpam-5594	412	6	♭	♭	PROPN
ejpam-5594	412	7	)	)	PUNCT
ejpam-5594	413	1	+	+	CCONJ
ejpam-5594	413	2	1	1	NUM
ejpam-5594	413	3	h(1−	h(1−	NOUN
ejpam-5594	413	4	♭	♭	PROPN
ejpam-5594	413	5	)	)	PUNCT
ejpam-5594	413	6	]	]	PUNCT
ejpam-5594	414	1	ε2	ε2	PROPN
ejpam-5594	414	2	♭	♭	NOUN
ejpam-5594	414	3	)ג	)ג	PUNCT
ejpam-5594	415	1	+	+	CCONJ
ejpam-5594	415	2	(	(	PUNCT
ejpam-5594	415	3	1−	1−	NUM
ejpam-5594	415	4	♭	♭	INTJ
ejpam-5594	415	5	)	)	PUNCT
ejpam-5594	415	6	ε1)d	ε1)d	PROPN
ejpam-5594	415	7	♭	♭	PROPN
ejpam-5594	415	8	.	.	PUNCT
ejpam-5594	416	1	making	make	VERB
ejpam-5594	416	2	a	a	DET
ejpam-5594	416	3	modification	modification	NOUN
ejpam-5594	416	4	in	in	ADP
ejpam-5594	416	5	the	the	DET
ejpam-5594	416	6	previous	previous	ADJ
ejpam-5594	416	7	integral	integral	NOUN
ejpam-5594	416	8	of	of	ADP
ejpam-5594	416	9	the	the	DET
ejpam-5594	416	10	preceding	precede	VERB
ejpam-5594	416	11	relation	relation	NOUN
ejpam-5594	416	12	,	,	PUNCT
ejpam-5594	416	13	v	v	NOUN
ejpam-5594	416	14	=	=	SYM
ejpam-5594	416	15	ε2	ε2	PROPN
ejpam-5594	416	16	+	+	CCONJ
ejpam-5594	416	17	ε1	ε1	PROPN
ejpam-5594	416	18	−	−	PROPN
ejpam-5594	416	19	u	u	PROPN
ejpam-5594	416	20	,	,	PUNCT
ejpam-5594	416	21	from	from	ADP
ejpam-5594	416	22	ε2)ג	ε2)ג	PROPN
ejpam-5594	416	23	+	+	CCONJ
ejpam-5594	416	24	ε1	ε1	PROPN
ejpam-5594	416	25	−	−	PROPN
ejpam-5594	416	26	v	v	NOUN
ejpam-5594	416	27	)	)	PUNCT
ejpam-5594	416	28	=	=	PUNCT
ejpam-5594	416	29	,	,	PUNCT
ejpam-5594	416	30	(	(	PUNCT
ejpam-5594	416	31	v)ג	v)ג	X
ejpam-5594	416	32	we	we	PRON
ejpam-5594	416	33	have	have	VERB
ejpam-5594	416	34	1	1	NUM
ejpam-5594	416	35	(	(	PUNCT
ejpam-5594	416	36	ε2	ε2	PROPN
ejpam-5594	416	37	−	−	PROPN
ejpam-5594	416	38	ε1)ς	ε1)ς	NOUN
ejpam-5594	417	1	[	[	X
ejpam-5594	417	2	∫	∫	X
ejpam-5594	417	3	ε2	ε2	PROPN
ejpam-5594	417	4	ε1	ε1	PROPN
ejpam-5594	417	5	(	(	PUNCT
ejpam-5594	417	6	ε2	ε2	ADJ
ejpam-5594	417	7	−	−	PROPN
ejpam-5594	417	8	v)ς−1φ(v)ג(v)dv+	v)ς−1φ(v)ג(v)dv+	NOUN
ejpam-5594	417	9	∫	∫	PROPN
ejpam-5594	417	10	ε2	ε2	PROPN
ejpam-5594	417	11	ε1	ε1	PROPN
ejpam-5594	417	12	(	(	PUNCT
ejpam-5594	417	13	u−	u−	PROPN
ejpam-5594	417	14	ε1	ε1	PROPN
ejpam-5594	417	15	)	)	PUNCT
ejpam-5594	417	16	ς−1φ(u)ג(u)du	ς−1φ(u)ג(u)du	NOUN
ejpam-5594	417	17	]	]	PUNCT
ejpam-5594	417	18	≤	≤	PROPN
ejpam-5594	417	19	[	[	PUNCT
ejpam-5594	417	20	φ(ε1	φ(ε1	NOUN
ejpam-5594	417	21	)	)	PUNCT
ejpam-5594	417	22	+	+	SYM
ejpam-5594	417	23	φ(ε2	φ(ε2	NUM
ejpam-5594	417	24	)	)	PUNCT
ejpam-5594	417	25	]	]	PUNCT
ejpam-5594	418	1	∫	∫	PROPN
ejpam-5594	419	1	1	1	NUM
ejpam-5594	419	2	0	0	NUM
ejpam-5594	419	3	♭	♭	NUM
ejpam-5594	420	1	ς−1	ς−1	PROPN
ejpam-5594	420	2	[	[	PUNCT
ejpam-5594	420	3	1	1	NUM
ejpam-5594	420	4	h	h	NOUN
ejpam-5594	420	5	(	(	PUNCT
ejpam-5594	420	6	♭	♭	PROPN
ejpam-5594	420	7	)	)	PUNCT
ejpam-5594	421	1	+	+	CCONJ
ejpam-5594	421	2	1	1	NUM
ejpam-5594	421	3	h(1−	h(1−	NOUN
ejpam-5594	421	4	♭	♭	PROPN
ejpam-5594	421	5	)	)	PUNCT
ejpam-5594	421	6	]	]	PUNCT
ejpam-5594	422	1	ε2	ε2	PROPN
ejpam-5594	422	2	♭	♭	NOUN
ejpam-5594	422	3	)ג	)ג	PUNCT
ejpam-5594	423	1	+	+	CCONJ
ejpam-5594	423	2	(	(	PUNCT
ejpam-5594	423	3	1−	1−	NUM
ejpam-5594	423	4	♭	♭	INTJ
ejpam-5594	423	5	)	)	PUNCT
ejpam-5594	423	6	ε1)d	ε1)d	PROPN
ejpam-5594	423	7	♭	♭	PROPN
ejpam-5594	423	8	.	.	PUNCT
ejpam-5594	424	1	multiplying	multiply	VERB
ejpam-5594	424	2	above	above	ADP
ejpam-5594	424	3	relation	relation	NOUN
ejpam-5594	424	4	with	with	ADP
ejpam-5594	424	5	ς(ε2−ε1)ς	ς(ε2−ε1)ς	NOUN
ejpam-5594	424	6	b(ς)γ(ς	b(ς)γ(ς	NOUN
ejpam-5594	424	7	)	)	PUNCT
ejpam-5594	424	8	and	and	CCONJ
ejpam-5594	424	9	adding	add	VERB
ejpam-5594	424	10	the	the	DET
ejpam-5594	424	11	expression	expression	NOUN
ejpam-5594	424	12	1−ς	1−ς	NUM
ejpam-5594	424	13	b(ς	b(ς	PROPN
ejpam-5594	424	14	)	)	PUNCT
ejpam-5594	424	15	[	[	PUNCT
ejpam-5594	424	16	φ(ε1	φ(ε1	NOUN
ejpam-5594	424	17	)	)	PUNCT
ejpam-5594	424	18	+	+	SYM
ejpam-5594	424	19	φ(ε2	φ(ε2	NUM
ejpam-5594	424	20	)	)	PUNCT
ejpam-5594	424	21	]	]	PUNCT
ejpam-5594	424	22	,	,	PUNCT
ejpam-5594	424	23	we	we	PRON
ejpam-5594	424	24	have	have	VERB
ejpam-5594	424	25	ς	ς	PROPN
ejpam-5594	424	26	b(ς)γ(ς	b(ς)γ(ς	NOUN
ejpam-5594	424	27	)	)	PUNCT
ejpam-5594	425	1	[	[	X
ejpam-5594	425	2	∫	∫	X
ejpam-5594	425	3	ε2	ε2	PROPN
ejpam-5594	425	4	ε1	ε1	PROPN
ejpam-5594	425	5	(	(	PUNCT
ejpam-5594	425	6	ε2	ε2	ADJ
ejpam-5594	425	7	−	−	PROPN
ejpam-5594	425	8	v)ς−1φ(v)ג(v)dv+	v)ς−1φ(v)ג(v)dv+	NOUN
ejpam-5594	425	9	∫	∫	PROPN
ejpam-5594	425	10	ε2	ε2	PROPN
ejpam-5594	425	11	ε1	ε1	PROPN
ejpam-5594	425	12	(	(	PUNCT
ejpam-5594	425	13	u−	u−	PROPN
ejpam-5594	425	14	ε1	ε1	PROPN
ejpam-5594	425	15	)	)	PUNCT
ejpam-5594	425	16	ς−1φ(u)ג(u)du	ς−1φ(u)ג(u)du	NOUN
ejpam-5594	425	17	]	]	PUNCT
ejpam-5594	426	1	+	+	CCONJ
ejpam-5594	426	2	1−	1−	NUM
ejpam-5594	426	3	ς	ς	X
ejpam-5594	426	4	b(ς	b(ς	PROPN
ejpam-5594	426	5	)	)	PUNCT
ejpam-5594	426	6	[	[	PUNCT
ejpam-5594	426	7	φ(ε1)ג(ε1	φ(ε1)ג(ε1	PROPN
ejpam-5594	426	8	)	)	PUNCT
ejpam-5594	426	9	+	+	CCONJ
ejpam-5594	426	10	φ(ε2)ג(ε2	φ(ε2)ג(ε2	PROPN
ejpam-5594	426	11	)	)	PUNCT
ejpam-5594	426	12	]	]	PUNCT
ejpam-5594	426	13	⪯cr	⪯cr	X
ejpam-5594	426	14	ς(ε2	ς(ε2	NUM
ejpam-5594	426	15	−	−	PROPN
ejpam-5594	426	16	ε1	ε1	PROPN
ejpam-5594	426	17	)	)	PUNCT
ejpam-5594	426	18	ς	ς	NOUN
ejpam-5594	426	19	b(ς)γ(ς	b(ς)γ(ς	NUM
ejpam-5594	426	20	)	)	PUNCT
ejpam-5594	426	21	[	[	PUNCT
ejpam-5594	426	22	φ(ε1	φ(ε1	NOUN
ejpam-5594	426	23	)	)	PUNCT
ejpam-5594	426	24	+	+	SYM
ejpam-5594	426	25	φ(ε2	φ(ε2	NUM
ejpam-5594	426	26	)	)	PUNCT
ejpam-5594	426	27	]	]	PUNCT
ejpam-5594	427	1	×	×	NOUN
ejpam-5594	427	2	∫	∫	PROPN
ejpam-5594	427	3	1	1	NUM
ejpam-5594	427	4	0	0	NUM
ejpam-5594	428	1	♭	♭	NUM
ejpam-5594	428	2	ς−1	ς−1	PROPN
ejpam-5594	428	3	[	[	PUNCT
ejpam-5594	428	4	1	1	NUM
ejpam-5594	428	5	h	h	NOUN
ejpam-5594	428	6	(	(	PUNCT
ejpam-5594	428	7	♭	♭	PROPN
ejpam-5594	428	8	)	)	PUNCT
ejpam-5594	428	9	+	+	CCONJ
ejpam-5594	428	10	1	1	NUM
ejpam-5594	428	11	h(1−	h(1−	NOUN
ejpam-5594	428	12	♭	♭	PROPN
ejpam-5594	428	13	)	)	PUNCT
ejpam-5594	428	14	]	]	PUNCT
ejpam-5594	429	1	ε2	ε2	PROPN
ejpam-5594	429	2	♭	♭	NOUN
ejpam-5594	429	3	)ג	)ג	PUNCT
ejpam-5594	430	1	+	+	CCONJ
ejpam-5594	430	2	(	(	PUNCT
ejpam-5594	430	3	1−	1−	NUM
ejpam-5594	430	4	♭	♭	INTJ
ejpam-5594	430	5	)	)	PUNCT
ejpam-5594	430	6	ε1)d	ε1)d	NOUN
ejpam-5594	430	7	♭	♭	PROPN
ejpam-5594	430	8	+	+	NUM
ejpam-5594	430	9	1−	1−	NUM
ejpam-5594	430	10	ς	ς	X
ejpam-5594	430	11	b(ς	b(ς	PROPN
ejpam-5594	430	12	)	)	PUNCT
ejpam-5594	430	13	[	[	PUNCT
ejpam-5594	430	14	φ(ε1)ג(ε1	φ(ε1)ג(ε1	PROPN
ejpam-5594	430	15	)	)	PUNCT
ejpam-5594	430	16	+	+	CCONJ
ejpam-5594	430	17	φ(ε2)ג(ε2	φ(ε2)ג(ε2	PROPN
ejpam-5594	430	18	)	)	PUNCT
ejpam-5594	430	19	]	]	PUNCT
ejpam-5594	430	20	,	,	PUNCT
ejpam-5594	430	21	that	that	ADV
ejpam-5594	430	22	is	is	ADV
ejpam-5594	430	23	ab	ab	PROPN
ejpam-5594	430	24	ε1i	ε1i	PROPN
ejpam-5594	430	25	ς	ς	PROPN
ejpam-5594	430	26	ε2{(φג(ε2)}+	ε2{(φג(ε2)}+	PROPN
ejpam-5594	430	27	abiςε2{(φג(ε1	abiςε2{(φג(ε1	PROPN
ejpam-5594	430	28	)	)	PUNCT
ejpam-5594	430	29	}	}	PUNCT
ejpam-5594	431	1	j.	j.	PROPN
ejpam-5594	431	2	e.	e.	PROPN
ejpam-5594	431	3	maćıas	maćıas	PROPN
ejpam-5594	431	4	-	-	PUNCT
ejpam-5594	431	5	dı́az	dı́az	NOUN
ejpam-5594	431	6	et	et	NOUN
ejpam-5594	431	7	al	al	PROPN
ejpam-5594	431	8	.	.	PUNCT
ejpam-5594	431	9	/	/	SYM
ejpam-5594	431	10	eur	eur	PROPN
ejpam-5594	431	11	.	.	PUNCT
ejpam-5594	432	1	j.	j.	PROPN
ejpam-5594	432	2	pure	pure	PROPN
ejpam-5594	432	3	appl	appl	PROPN
ejpam-5594	432	4	.	.	PROPN
ejpam-5594	432	5	math	math	PROPN
ejpam-5594	432	6	,	,	PUNCT
ejpam-5594	432	7	17	17	NUM
ejpam-5594	432	8	(	(	PUNCT
ejpam-5594	432	9	4	4	NUM
ejpam-5594	432	10	)	)	PUNCT
ejpam-5594	432	11	(	(	PUNCT
ejpam-5594	432	12	2024	2024	NUM
ejpam-5594	432	13	)	)	PUNCT
ejpam-5594	432	14	,	,	PUNCT
ejpam-5594	432	15	4014	4014	NUM
ejpam-5594	432	16	-	-	SYM
ejpam-5594	432	17	4049	4049	NUM
ejpam-5594	432	18	4030	4030	NUM
ejpam-5594	432	19	⪯cr	⪯cr	NOUN
ejpam-5594	432	20	ς(ε2	ς(ε2	NOUN
ejpam-5594	432	21	−	−	PROPN
ejpam-5594	432	22	ε1	ε1	PROPN
ejpam-5594	432	23	)	)	PUNCT
ejpam-5594	432	24	ς	ς	NOUN
ejpam-5594	432	25	b(ς)γ(ς	b(ς)γ(ς	NUM
ejpam-5594	432	26	)	)	PUNCT
ejpam-5594	432	27	[	[	PUNCT
ejpam-5594	432	28	φ(ε1	φ(ε1	NOUN
ejpam-5594	432	29	)	)	PUNCT
ejpam-5594	432	30	+	+	SYM
ejpam-5594	432	31	φ(ε2	φ(ε2	NUM
ejpam-5594	432	32	)	)	PUNCT
ejpam-5594	432	33	]	]	PUNCT
ejpam-5594	433	1	×	×	NOUN
ejpam-5594	433	2	∫	∫	PROPN
ejpam-5594	433	3	1	1	NUM
ejpam-5594	433	4	0	0	NUM
ejpam-5594	434	1	♭	♭	NUM
ejpam-5594	434	2	ς−1	ς−1	PROPN
ejpam-5594	434	3	[	[	PUNCT
ejpam-5594	434	4	1	1	NUM
ejpam-5594	434	5	h	h	NOUN
ejpam-5594	434	6	(	(	PUNCT
ejpam-5594	434	7	♭	♭	PROPN
ejpam-5594	434	8	)	)	PUNCT
ejpam-5594	434	9	+	+	CCONJ
ejpam-5594	434	10	1	1	NUM
ejpam-5594	434	11	h(1−	h(1−	NOUN
ejpam-5594	434	12	♭	♭	PROPN
ejpam-5594	434	13	)	)	PUNCT
ejpam-5594	434	14	]	]	PUNCT
ejpam-5594	435	1	ε2	ε2	PROPN
ejpam-5594	435	2	♭	♭	NOUN
ejpam-5594	435	3	)ג	)ג	PUNCT
ejpam-5594	436	1	+	+	CCONJ
ejpam-5594	436	2	(	(	PUNCT
ejpam-5594	436	3	1−	1−	NUM
ejpam-5594	436	4	♭	♭	INTJ
ejpam-5594	436	5	)	)	PUNCT
ejpam-5594	436	6	ε1)d	ε1)d	NOUN
ejpam-5594	436	7	♭	♭	PROPN
ejpam-5594	436	8	+	+	NUM
ejpam-5594	436	9	1−	1−	NUM
ejpam-5594	436	10	ς	ς	X
ejpam-5594	436	11	b(ς	b(ς	PROPN
ejpam-5594	436	12	)	)	PUNCT
ejpam-5594	436	13	[	[	PUNCT
ejpam-5594	436	14	φ(ε1)ג(ε1	φ(ε1)ג(ε1	PROPN
ejpam-5594	436	15	)	)	PUNCT
ejpam-5594	436	16	+	+	CCONJ
ejpam-5594	436	17	φ(ε2)ג(ε2	φ(ε2)ג(ε2	PROPN
ejpam-5594	436	18	)	)	PUNCT
ejpam-5594	436	19	]	]	PUNCT
ejpam-5594	436	20	,	,	PUNCT
ejpam-5594	436	21	so	so	CCONJ
ejpam-5594	436	22	the	the	DET
ejpam-5594	436	23	second	second	ADJ
ejpam-5594	436	24	relation	relation	NOUN
ejpam-5594	436	25	holds	hold	VERB
ejpam-5594	436	26	true	true	ADJ
ejpam-5594	436	27	in	in	ADP
ejpam-5594	436	28	(	(	PUNCT
ejpam-5594	436	29	11	11	NUM
ejpam-5594	436	30	)	)	PUNCT
ejpam-5594	436	31	.	.	PUNCT
ejpam-5594	437	1	this	this	PRON
ejpam-5594	437	2	concludes	conclude	VERB
ejpam-5594	437	3	the	the	DET
ejpam-5594	437	4	proof	proof	NOUN
ejpam-5594	437	5	.	.	PUNCT
ejpam-5594	438	1	example	example	NOUN
ejpam-5594	439	1	3	3	X
ejpam-5594	439	2	.	.	PUNCT
ejpam-5594	439	3	let	let	VERB
ejpam-5594	439	4	φ	φ	NOUN
ejpam-5594	439	5	:	:	PUNCT
ejpam-5594	440	1	[	[	X
ejpam-5594	440	2	1	1	NUM
ejpam-5594	440	3	,	,	PUNCT
ejpam-5594	440	4	4	4	NUM
ejpam-5594	440	5	]	]	PUNCT
ejpam-5594	440	6	→	→	PUNCT
ejpam-5594	440	7	r+	r+	PUNCT
ejpam-5594	440	8	i	i	PRON
ejpam-5594	440	9	defined	define	VERB
ejpam-5594	440	10	as	as	ADP
ejpam-5594	440	11	φ(µ	φ(µ	NOUN
ejpam-5594	440	12	)	)	PUNCT
ejpam-5594	440	13	=	=	NOUN
ejpam-5594	441	1	[	[	PUNCT
ejpam-5594	441	2	2eµ	2eµ	ADJ
ejpam-5594	441	3	+	+	CCONJ
ejpam-5594	441	4	1	1	NUM
ejpam-5594	441	5	,	,	PUNCT
ejpam-5594	441	6	3eµ	3eµ	NOUN
ejpam-5594	441	7	+	+	CCONJ
ejpam-5594	441	8	√	√	PROPN
ejpam-5594	441	9	µ	µ	DET
ejpam-5594	441	10	3	3	NUM
ejpam-5594	441	11	]	]	PUNCT
ejpam-5594	441	12	with	with	ADP
ejpam-5594	441	13	h1	h1	PROPN
ejpam-5594	441	14	(	(	PUNCT
ejpam-5594	441	15	♭	♭	INTJ
ejpam-5594	441	16	)	)	PUNCT
ejpam-5594	441	17	=	=	SYM
ejpam-5594	441	18	1	1	NUM
ejpam-5594	441	19	♭	♭	PROPN
ejpam-5594	441	20	,	,	PUNCT
ejpam-5594	441	21	η	η	PROPN
ejpam-5594	441	22	=	=	SYM
ejpam-5594	441	23	1	1	NUM
ejpam-5594	441	24	2	2	NUM
ejpam-5594	441	25	and	and	CCONJ
ejpam-5594	441	26	a	a	DET
ejpam-5594	441	27	real	real	ADV
ejpam-5594	441	28	-	-	PUNCT
ejpam-5594	441	29	valued	value	VERB
ejpam-5594	441	30	symmetric	symmetric	ADJ
ejpam-5594	441	31	functions	function	NOUN
ejpam-5594	441	32	are	be	AUX
ejpam-5594	441	33	defined	define	VERB
ejpam-5594	441	34	as	as	ADP
ejpam-5594	441	35	(	(	PUNCT
ejpam-5594	441	36	ð)ג	ð)ג	PUNCT
ejpam-5594	441	37	=	=	SYM
ejpam-5594	441	38	ð−	ð−	PROPN
ejpam-5594	441	39	1	1	NUM
ejpam-5594	441	40	for	for	ADP
ejpam-5594	441	41	ð	ð	PROPN
ejpam-5594	441	42	∈	∈	PROPN
ejpam-5594	441	43	[	[	PUNCT
ejpam-5594	441	44	1	1	NUM
ejpam-5594	441	45	,	,	PUNCT
ejpam-5594	441	46	52	52	NUM
ejpam-5594	441	47	]	]	PUNCT
ejpam-5594	441	48	and	and	CCONJ
ejpam-5594	441	49	(	(	PUNCT
ejpam-5594	441	50	ð)ג	ð)ג	PUNCT
ejpam-5594	441	51	=	=	NOUN
ejpam-5594	441	52	−ð+	−ð+	VERB
ejpam-5594	441	53	4	4	NUM
ejpam-5594	441	54	for	for	ADP
ejpam-5594	441	55	ð	ð	PROPN
ejpam-5594	441	56	∈	∈	PROPN
ejpam-5594	441	57	[	[	PUNCT
ejpam-5594	441	58	5	5	NUM
ejpam-5594	441	59	2	2	NUM
ejpam-5594	441	60	,	,	PUNCT
ejpam-5594	441	61	4	4	NUM
ejpam-5594	441	62	]	]	PUNCT
ejpam-5594	441	63	,	,	PUNCT
ejpam-5594	441	64	then	then	ADV
ejpam-5594	441	65	we	we	PRON
ejpam-5594	441	66	consider	consider	VERB
ejpam-5594	441	67	h	h	NOUN
ejpam-5594	441	68	(	(	PUNCT
ejpam-5594	441	69	1	1	NUM
ejpam-5594	441	70	2	2	NUM
ejpam-5594	441	71	)	)	PUNCT
ejpam-5594	441	72	2	2	NUM
ejpam-5594	441	73	φ	φ	NOUN
ejpam-5594	441	74	(	(	PUNCT
ejpam-5594	441	75	ε2	ε2	PROPN
ejpam-5594	441	76	+	+	CCONJ
ejpam-5594	441	77	ε1	ε1	PROPN
ejpam-5594	441	78	2	2	NUM
ejpam-5594	441	79	)	)	PUNCT
ejpam-5594	441	80	[	[	PUNCT
ejpam-5594	441	81	ab	ab	X
ejpam-5594	441	82	ε1i	ε1i	PROPN
ejpam-5594	441	83	ς	ς	PROPN
ejpam-5594	441	84	ε2{ג(ε2)}+	ε2{ג(ε2)}+	PROPN
ejpam-5594	441	85	abiςε2{ג(ε1	abiςε2{ג(ε1	PROPN
ejpam-5594	441	86	)	)	PUNCT
ejpam-5594	441	87	}	}	PUNCT
ejpam-5594	441	88	]	]	PUNCT
ejpam-5594	442	1	−	−	PROPN
ejpam-5594	442	2	h	h	NOUN
ejpam-5594	442	3	(	(	PUNCT
ejpam-5594	442	4	1	1	NUM
ejpam-5594	442	5	2	2	NUM
ejpam-5594	442	6	)	)	PUNCT
ejpam-5594	442	7	2	2	NUM
ejpam-5594	442	8	φ	φ	NOUN
ejpam-5594	442	9	(	(	PUNCT
ejpam-5594	442	10	ε2	ε2	PROPN
ejpam-5594	442	11	+	+	CCONJ
ejpam-5594	442	12	ε1	ε1	PROPN
ejpam-5594	442	13	2	2	NUM
ejpam-5594	442	14	)	)	PUNCT
ejpam-5594	442	15	1−	1−	NUM
ejpam-5594	442	16	ς	ς	PROPN
ejpam-5594	442	17	b(ς	b(ς	PROPN
ejpam-5594	442	18	)	)	PUNCT
ejpam-5594	442	19	[	[	PUNCT
ejpam-5594	442	20	(	(	PUNCT
ejpam-5594	442	21	ε1)ג	ε1)ג	NOUN
ejpam-5594	442	22	+	+	CCONJ
ejpam-5594	442	23	(	(	PUNCT
ejpam-5594	442	24	ε2)ג	ε2)ג	PROPN
ejpam-5594	442	25	]	]	PUNCT
ejpam-5594	443	1	+	+	CCONJ
ejpam-5594	444	1	1−	1−	NUM
ejpam-5594	444	2	ς	ς	X
ejpam-5594	444	3	b(ς	b(ς	PROPN
ejpam-5594	444	4	)	)	PUNCT
ejpam-5594	444	5	[	[	PUNCT
ejpam-5594	444	6	φ(ε1)ג(ε1	φ(ε1)ג(ε1	PROPN
ejpam-5594	444	7	)	)	PUNCT
ejpam-5594	444	8	+	+	CCONJ
ejpam-5594	444	9	φ(ε2)ג(ε2	φ(ε2)ג(ε2	PROPN
ejpam-5594	444	10	)	)	PUNCT
ejpam-5594	444	11	]	]	PUNCT
ejpam-5594	445	1	=	=	PUNCT
ejpam-5594	445	2	φ	φ	X
ejpam-5594	445	3	(	(	PUNCT
ejpam-5594	445	4	5	5	NUM
ejpam-5594	445	5	2	2	NUM
ejpam-5594	445	6	)	)	PUNCT
ejpam-5594	445	7	[	[	PUNCT
ejpam-5594	445	8	1	1	NUM
ejpam-5594	445	9	2	2	NUM
ejpam-5594	445	10	ג	ג	PROPN
ejpam-5594	445	11	(	(	PUNCT
ejpam-5594	445	12	5	5	NUM
ejpam-5594	445	13	2	2	NUM
ejpam-5594	445	14	)	)	PUNCT
ejpam-5594	445	15	+	+	CCONJ
ejpam-5594	445	16	1	1	NUM
ejpam-5594	445	17	2	2	NUM
ejpam-5594	445	18	√	√	NOUN
ejpam-5594	445	19	π	π	PROPN
ejpam-5594	445	20	∫	∫	PROPN
ejpam-5594	445	21	5	5	NUM
ejpam-5594	445	22	2	2	NUM
ejpam-5594	445	23	1	1	NUM
ejpam-5594	445	24	(	(	PUNCT
ejpam-5594	445	25	µ−	µ−	NOUN
ejpam-5594	445	26	1	1	NUM
ejpam-5594	445	27	)	)	PUNCT
ejpam-5594	445	28	(	(	PUNCT
ejpam-5594	445	29	5	5	NUM
ejpam-5594	445	30	2	2	NUM
ejpam-5594	445	31	−	−	PROPN
ejpam-5594	445	32	µ	µ	X
ejpam-5594	445	33	)	)	PUNCT
ejpam-5594	445	34	−1	−1	NOUN
ejpam-5594	445	35	2	2	NUM
ejpam-5594	445	36	+	+	CCONJ
ejpam-5594	445	37	1	1	NUM
ejpam-5594	445	38	2	2	NUM
ejpam-5594	445	39	ג	ג	NOUN
ejpam-5594	445	40	(	(	PUNCT
ejpam-5594	445	41	5	5	NUM
ejpam-5594	445	42	2	2	NUM
ejpam-5594	445	43	)	)	PUNCT
ejpam-5594	445	44	+	+	CCONJ
ejpam-5594	445	45	1	1	NUM
ejpam-5594	445	46	2	2	NUM
ejpam-5594	445	47	√	√	NOUN
ejpam-5594	445	48	π	π	PROPN
ejpam-5594	445	49	∫	∫	PROPN
ejpam-5594	445	50	4	4	NUM
ejpam-5594	445	51	5	5	NUM
ejpam-5594	445	52	2	2	NUM
ejpam-5594	445	53	(	(	PUNCT
ejpam-5594	445	54	−µ+	−µ+	NOUN
ejpam-5594	445	55	4	4	NUM
ejpam-5594	445	56	)	)	PUNCT
ejpam-5594	445	57	(	(	PUNCT
ejpam-5594	445	58	µ−	µ−	PROPN
ejpam-5594	445	59	5	5	NUM
ejpam-5594	445	60	2	2	NUM
ejpam-5594	445	61	)	)	PUNCT
ejpam-5594	445	62	−1	−1	NOUN
ejpam-5594	445	63	2	2	NUM
ejpam-5594	445	64	]	]	PUNCT
ejpam-5594	445	65	dµ	dµ	ADP
ejpam-5594	446	1	≈	≈	PROPN
ejpam-5594	447	1	[	[	X
ejpam-5594	447	2	73.10130	73.10130	NUM
ejpam-5594	447	3	,	,	PUNCT
ejpam-5594	447	4	106.84792	106.84792	NUM
ejpam-5594	447	5	]	]	PUNCT
ejpam-5594	447	6	,	,	PUNCT
ejpam-5594	447	7	and	and	CCONJ
ejpam-5594	447	8	ab	ab	PROPN
ejpam-5594	447	9	ε1i	ε1i	NUM
ejpam-5594	447	10	ς	ς	PROPN
ejpam-5594	447	11	ε2{(φג(ε2)}+	ε2{(φג(ε2)}+	PROPN
ejpam-5594	447	12	abiςε2{(φג(ε1	abiςε2{(φג(ε1	PROPN
ejpam-5594	447	13	)	)	PUNCT
ejpam-5594	447	14	}	}	PUNCT
ejpam-5594	447	15	=	=	PUNCT
ejpam-5594	447	16	[	[	PUNCT
ejpam-5594	447	17	1	1	NUM
ejpam-5594	447	18	2	2	NUM
ejpam-5594	447	19	φ	φ	NOUN
ejpam-5594	447	20	(	(	PUNCT
ejpam-5594	447	21	3	3	NUM
ejpam-5594	447	22	2	2	NUM
ejpam-5594	447	23	)	)	PUNCT
ejpam-5594	447	24	+	+	CCONJ
ejpam-5594	447	25	1	1	NUM
ejpam-5594	447	26	2	2	NUM
ejpam-5594	447	27	√	√	NOUN
ejpam-5594	447	28	π	π	PROPN
ejpam-5594	447	29	∫	∫	PROPN
ejpam-5594	447	30	5	5	NUM
ejpam-5594	447	31	2	2	NUM
ejpam-5594	447	32	1	1	NUM
ejpam-5594	447	33	[	[	PUNCT
ejpam-5594	447	34	2eµ	2eµ	ADJ
ejpam-5594	447	35	+	+	CCONJ
ejpam-5594	447	36	1	1	NUM
ejpam-5594	447	37	,	,	PUNCT
ejpam-5594	447	38	3eµ	3eµ	NOUN
ejpam-5594	447	39	+	+	CCONJ
ejpam-5594	447	40	√	√	PROPN
ejpam-5594	447	41	µ	µ	PRON
ejpam-5594	447	42	3	3	NUM
ejpam-5594	447	43	]	]	PUNCT
ejpam-5594	447	44	(	(	PUNCT
ejpam-5594	447	45	µ−	µ−	NOUN
ejpam-5594	447	46	1	1	NUM
ejpam-5594	447	47	)	)	PUNCT
ejpam-5594	447	48	(	(	PUNCT
ejpam-5594	447	49	5	5	NUM
ejpam-5594	447	50	2	2	NUM
ejpam-5594	447	51	−	−	PROPN
ejpam-5594	447	52	µ	µ	X
ejpam-5594	447	53	)	)	PUNCT
ejpam-5594	447	54	−1	−1	NOUN
ejpam-5594	447	55	2	2	NUM
ejpam-5594	447	56	+	+	CCONJ
ejpam-5594	447	57	1	1	NUM
ejpam-5594	447	58	2	2	NUM
ejpam-5594	447	59	φ	φ	NOUN
ejpam-5594	447	60	(	(	PUNCT
ejpam-5594	447	61	3	3	NUM
ejpam-5594	447	62	2	2	NUM
ejpam-5594	447	63	)	)	PUNCT
ejpam-5594	447	64	+	+	CCONJ
ejpam-5594	447	65	1	1	NUM
ejpam-5594	447	66	2	2	NUM
ejpam-5594	447	67	√	√	NOUN
ejpam-5594	447	68	π	π	PROPN
ejpam-5594	447	69	∫	∫	PROPN
ejpam-5594	447	70	4	4	NUM
ejpam-5594	447	71	5	5	NUM
ejpam-5594	447	72	2	2	NUM
ejpam-5594	447	73	[	[	PUNCT
ejpam-5594	447	74	2eµ	2eµ	ADJ
ejpam-5594	447	75	+	+	CCONJ
ejpam-5594	447	76	1	1	NUM
ejpam-5594	447	77	,	,	PUNCT
ejpam-5594	447	78	3eµ	3eµ	NOUN
ejpam-5594	447	79	+	+	CCONJ
ejpam-5594	447	80	√	√	PROPN
ejpam-5594	447	81	µ	µ	PRON
ejpam-5594	447	82	3	3	NUM
ejpam-5594	447	83	]	]	PUNCT
ejpam-5594	447	84	(	(	PUNCT
ejpam-5594	447	85	−µ+	−µ+	NOUN
ejpam-5594	447	86	4	4	NUM
ejpam-5594	447	87	)	)	PUNCT
ejpam-5594	447	88	(	(	PUNCT
ejpam-5594	447	89	µ−	µ−	PROPN
ejpam-5594	447	90	5	5	NUM
ejpam-5594	447	91	2	2	NUM
ejpam-5594	447	92	)	)	PUNCT
ejpam-5594	447	93	−1	−1	NOUN
ejpam-5594	447	94	2	2	NUM
ejpam-5594	447	95	]	]	PUNCT
ejpam-5594	447	96	dµ	dµ	ADP
ejpam-5594	448	1	≈	≈	PROPN
ejpam-5594	449	1	[	[	X
ejpam-5594	449	2	81.16120	81.16120	NUM
ejpam-5594	449	3	,	,	PUNCT
ejpam-5594	449	4	111.35182	111.35182	NUM
ejpam-5594	449	5	]	]	PUNCT
ejpam-5594	449	6	.	.	PUNCT
ejpam-5594	450	1	finally	finally	ADV
ejpam-5594	450	2	,	,	PUNCT
ejpam-5594	450	3	we	we	PRON
ejpam-5594	450	4	have	have	VERB
ejpam-5594	450	5	ς(ε2	ς(ε2	NUM
ejpam-5594	450	6	−	−	ADP
ejpam-5594	450	7	ε1	ε1	PROPN
ejpam-5594	450	8	)	)	PUNCT
ejpam-5594	450	9	ς	ς	NOUN
ejpam-5594	450	10	b(ς)γ(ς	b(ς)γ(ς	NUM
ejpam-5594	450	11	)	)	PUNCT
ejpam-5594	450	12	[	[	PUNCT
ejpam-5594	450	13	φ(ε1	φ(ε1	NOUN
ejpam-5594	450	14	)	)	PUNCT
ejpam-5594	450	15	+	+	SYM
ejpam-5594	450	16	φ(ε2	φ(ε2	NUM
ejpam-5594	450	17	)	)	PUNCT
ejpam-5594	450	18	]	]	PUNCT
ejpam-5594	451	1	×	×	NOUN
ejpam-5594	451	2	∫	∫	PROPN
ejpam-5594	451	3	1	1	NUM
ejpam-5594	451	4	0	0	NUM
ejpam-5594	452	1	♭	♭	NUM
ejpam-5594	452	2	ς−1	ς−1	PROPN
ejpam-5594	452	3	[	[	PUNCT
ejpam-5594	452	4	1	1	NUM
ejpam-5594	452	5	h	h	NOUN
ejpam-5594	452	6	(	(	PUNCT
ejpam-5594	452	7	♭	♭	PROPN
ejpam-5594	452	8	)	)	PUNCT
ejpam-5594	452	9	+	+	CCONJ
ejpam-5594	452	10	1	1	NUM
ejpam-5594	452	11	h(1−	h(1−	NOUN
ejpam-5594	452	12	♭	♭	PROPN
ejpam-5594	452	13	)	)	PUNCT
ejpam-5594	452	14	]	]	PUNCT
ejpam-5594	453	1	ε2	ε2	PROPN
ejpam-5594	453	2	♭	♭	NOUN
ejpam-5594	453	3	)ג	)ג	PUNCT
ejpam-5594	454	1	+	+	CCONJ
ejpam-5594	454	2	(	(	PUNCT
ejpam-5594	454	3	1−	1−	NUM
ejpam-5594	454	4	♭	♭	INTJ
ejpam-5594	454	5	)	)	PUNCT
ejpam-5594	454	6	ε1)d	ε1)d	NOUN
ejpam-5594	454	7	♭	♭	PROPN
ejpam-5594	454	8	+	+	NUM
ejpam-5594	454	9	1−	1−	NUM
ejpam-5594	454	10	ς	ς	X
ejpam-5594	454	11	b(ς	b(ς	PROPN
ejpam-5594	454	12	)	)	PUNCT
ejpam-5594	454	13	[	[	PUNCT
ejpam-5594	454	14	φ(ε1)ג(ε1	φ(ε1)ג(ε1	PROPN
ejpam-5594	454	15	)	)	PUNCT
ejpam-5594	454	16	+	+	CCONJ
ejpam-5594	454	17	φ(ε2)ג(ε2	φ(ε2)ג(ε2	PROPN
ejpam-5594	454	18	)	)	PUNCT
ejpam-5594	454	19	]	]	PUNCT
ejpam-5594	455	1	≈	≈	PROPN
ejpam-5594	456	1	[	[	X
ejpam-5594	456	2	85.14621	85.14621	NUM
ejpam-5594	456	3	,	,	PUNCT
ejpam-5594	456	4	115.36241	115.36241	NUM
ejpam-5594	456	5	]	]	PUNCT
ejpam-5594	456	6	.	.	PUNCT
ejpam-5594	457	1	j.	j.	PROPN
ejpam-5594	457	2	e.	e.	PROPN
ejpam-5594	457	3	maćıas	maćıas	PROPN
ejpam-5594	457	4	-	-	PUNCT
ejpam-5594	457	5	dı́az	dı́az	NOUN
ejpam-5594	457	6	et	et	NOUN
ejpam-5594	457	7	al	al	PROPN
ejpam-5594	457	8	.	.	PUNCT
ejpam-5594	457	9	/	/	SYM
ejpam-5594	457	10	eur	eur	PROPN
ejpam-5594	457	11	.	.	PUNCT
ejpam-5594	458	1	j.	j.	PROPN
ejpam-5594	458	2	pure	pure	PROPN
ejpam-5594	458	3	appl	appl	PROPN
ejpam-5594	458	4	.	.	PROPN
ejpam-5594	458	5	math	math	PROPN
ejpam-5594	458	6	,	,	PUNCT
ejpam-5594	458	7	17	17	NUM
ejpam-5594	458	8	(	(	PUNCT
ejpam-5594	458	9	4	4	NUM
ejpam-5594	458	10	)	)	PUNCT
ejpam-5594	458	11	(	(	PUNCT
ejpam-5594	458	12	2024	2024	NUM
ejpam-5594	458	13	)	)	PUNCT
ejpam-5594	458	14	,	,	PUNCT
ejpam-5594	458	15	4014	4014	NUM
ejpam-5594	458	16	-	-	SYM
ejpam-5594	458	17	4049	4049	NUM
ejpam-5594	458	18	4031	4031	NUM
ejpam-5594	458	19	this	this	PRON
ejpam-5594	458	20	implies	imply	VERB
ejpam-5594	458	21	that	that	SCONJ
ejpam-5594	458	22	[	[	X
ejpam-5594	458	23	73.10130	73.10130	NUM
ejpam-5594	458	24	,	,	PUNCT
ejpam-5594	458	25	106.84792	106.84792	NUM
ejpam-5594	458	26	]	]	X
ejpam-5594	458	27	⪯cr	⪯cr	NUM
ejpam-5594	458	28	[	[	X
ejpam-5594	458	29	81.16120	81.16120	NUM
ejpam-5594	458	30	,	,	PUNCT
ejpam-5594	458	31	111.35182	111.35182	NUM
ejpam-5594	458	32	]	]	PUNCT
ejpam-5594	458	33	⪯cr	⪯cr	NUM
ejpam-5594	458	34	[	[	X
ejpam-5594	458	35	85.14621	85.14621	NUM
ejpam-5594	458	36	,	,	PUNCT
ejpam-5594	458	37	115.36241	115.36241	NUM
ejpam-5594	458	38	]	]	PUNCT
ejpam-5594	458	39	.	.	PUNCT
ejpam-5594	459	1	consequently	consequently	ADV
ejpam-5594	459	2	,	,	PUNCT
ejpam-5594	459	3	theorem	theorem	VERB
ejpam-5594	459	4	12	12	NUM
ejpam-5594	459	5	is	be	AUX
ejpam-5594	459	6	valid	valid	ADJ
ejpam-5594	459	7	.	.	PUNCT
ejpam-5594	460	1	remark	remark	PROPN
ejpam-5594	460	2	4	4	NUM
ejpam-5594	460	3	.	.	PUNCT
ejpam-5594	461	1	(	(	PUNCT
ejpam-5594	461	2	i	i	NOUN
ejpam-5594	461	3	)	)	PUNCT
ejpam-5594	461	4	if	if	SCONJ
ejpam-5594	461	5	h	h	X
ejpam-5594	461	6	(	(	PUNCT
ejpam-5594	461	7	♭	♭	INTJ
ejpam-5594	461	8	)	)	PUNCT
ejpam-5594	462	1	=	=	SYM
ejpam-5594	462	2	1	1	NUM
ejpam-5594	462	3	♭	♭	NOUN
ejpam-5594	462	4	s	s	PART
ejpam-5594	462	5	,	,	PUNCT
ejpam-5594	462	6	then	then	ADV
ejpam-5594	462	7	theorem	theorem	VERB
ejpam-5594	462	8	12	12	NUM
ejpam-5594	462	9	yields	yield	NOUN
ejpam-5594	462	10	an	an	DET
ejpam-5594	462	11	outcome	outcome	NOUN
ejpam-5594	462	12	for	for	ADP
ejpam-5594	462	13	the	the	DET
ejpam-5594	462	14	cr	cr	PROPN
ejpam-5594	462	15	-	-	PUNCT
ejpam-5594	462	16	s	s	NOUN
ejpam-5594	462	17	-	-	PUNCT
ejpam-5594	462	18	convex	convex	ADJ
ejpam-5594	462	19	function	function	NOUN
ejpam-5594	462	20	for	for	ADP
ejpam-5594	462	21	ab	ab	PROPN
ejpam-5594	462	22	integral	integral	ADJ
ejpam-5594	462	23	operators	operator	NOUN
ejpam-5594	462	24	:	:	PUNCT
ejpam-5594	462	25	2s−1φ	2s−1φ	NUM
ejpam-5594	462	26	(	(	PUNCT
ejpam-5594	462	27	ε2	ε2	PROPN
ejpam-5594	462	28	+	+	CCONJ
ejpam-5594	462	29	ε1	ε1	PROPN
ejpam-5594	462	30	2	2	NUM
ejpam-5594	462	31	)	)	PUNCT
ejpam-5594	462	32	[	[	PUNCT
ejpam-5594	462	33	ab	ab	X
ejpam-5594	462	34	ε1i	ε1i	PROPN
ejpam-5594	462	35	ς	ς	PROPN
ejpam-5594	462	36	ε2{ג(ε2)}+	ε2{ג(ε2)}+	PROPN
ejpam-5594	462	37	abiςε2{ג(ε1	abiςε2{ג(ε1	PROPN
ejpam-5594	462	38	)	)	PUNCT
ejpam-5594	462	39	}	}	PUNCT
ejpam-5594	462	40	]	]	PUNCT
ejpam-5594	462	41	−	−	PROPN
ejpam-5594	463	1	2s−1φ	2s−1φ	NUM
ejpam-5594	463	2	(	(	PUNCT
ejpam-5594	463	3	ε2	ε2	PROPN
ejpam-5594	463	4	+	+	CCONJ
ejpam-5594	463	5	ε1	ε1	PROPN
ejpam-5594	463	6	2	2	NUM
ejpam-5594	463	7	)	)	PUNCT
ejpam-5594	463	8	1−	1−	NUM
ejpam-5594	463	9	ς	ς	PROPN
ejpam-5594	463	10	b(ς	b(ς	PROPN
ejpam-5594	463	11	)	)	PUNCT
ejpam-5594	463	12	[	[	PUNCT
ejpam-5594	463	13	(	(	PUNCT
ejpam-5594	463	14	ε1)ג	ε1)ג	NOUN
ejpam-5594	463	15	+	+	CCONJ
ejpam-5594	463	16	(	(	PUNCT
ejpam-5594	463	17	ε2)ג	ε2)ג	PROPN
ejpam-5594	463	18	]	]	PUNCT
ejpam-5594	464	1	+	+	CCONJ
ejpam-5594	464	2	1−	1−	NUM
ejpam-5594	464	3	ς	ς	X
ejpam-5594	464	4	b(ς	b(ς	PROPN
ejpam-5594	464	5	)	)	PUNCT
ejpam-5594	464	6	[	[	PUNCT
ejpam-5594	464	7	φ(ε1)ג(ε1	φ(ε1)ג(ε1	PROPN
ejpam-5594	464	8	)	)	PUNCT
ejpam-5594	464	9	+	+	CCONJ
ejpam-5594	464	10	φ(ε2)ג(ε2	φ(ε2)ג(ε2	PROPN
ejpam-5594	464	11	)	)	PUNCT
ejpam-5594	464	12	]	]	PUNCT
ejpam-5594	464	13	⪯cr	⪯cr	VERB
ejpam-5594	464	14	ab	ab	PROPN
ejpam-5594	464	15	ε1i	ε1i	PROPN
ejpam-5594	464	16	ς	ς	PROPN
ejpam-5594	464	17	ε2{(φג(ε2)}+	ε2{(φג(ε2)}+	PROPN
ejpam-5594	464	18	abiςε2{(φג(ε1	abiςε2{(φג(ε1	PROPN
ejpam-5594	464	19	)	)	PUNCT
ejpam-5594	464	20	}	}	PUNCT
ejpam-5594	464	21	⪯cr	⪯cr	VERB
ejpam-5594	464	22	ς(ε2	ς(ε2	NUM
ejpam-5594	464	23	−	−	PROPN
ejpam-5594	464	24	ε1	ε1	PROPN
ejpam-5594	464	25	)	)	PUNCT
ejpam-5594	464	26	ς	ς	NOUN
ejpam-5594	464	27	b(ς)γ(ς	b(ς)γ(ς	NUM
ejpam-5594	464	28	)	)	PUNCT
ejpam-5594	464	29	[	[	PUNCT
ejpam-5594	464	30	φ(ε1	φ(ε1	NOUN
ejpam-5594	464	31	)	)	PUNCT
ejpam-5594	464	32	+	+	SYM
ejpam-5594	464	33	φ(ε2	φ(ε2	NUM
ejpam-5594	464	34	)	)	PUNCT
ejpam-5594	464	35	]	]	PUNCT
ejpam-5594	465	1	×	×	NOUN
ejpam-5594	465	2	∫	∫	PROPN
ejpam-5594	465	3	1	1	NUM
ejpam-5594	465	4	0	0	NUM
ejpam-5594	465	5	♭	♭	PROPN
ejpam-5594	465	6	ς−1	ς−1	PROPN
ejpam-5594	465	7	[	[	PUNCT
ejpam-5594	465	8	♭	♭	X
ejpam-5594	465	9	s	s	X
ejpam-5594	465	10	+	+	X
ejpam-5594	465	11	(	(	PUNCT
ejpam-5594	465	12	1−	1−	NUM
ejpam-5594	465	13	♭	♭	INTJ
ejpam-5594	465	14	)	)	PUNCT
ejpam-5594	465	15	s	s	PART
ejpam-5594	465	16	]	]	PUNCT
ejpam-5594	465	17	ε2	ε2	PROPN
ejpam-5594	465	18	♭	♭	PROPN
ejpam-5594	465	19	)ג	)ג	PUNCT
ejpam-5594	466	1	+	+	CCONJ
ejpam-5594	466	2	(	(	PUNCT
ejpam-5594	466	3	1−	1−	NUM
ejpam-5594	466	4	♭	♭	INTJ
ejpam-5594	466	5	)	)	PUNCT
ejpam-5594	466	6	ε1)d	ε1)d	NOUN
ejpam-5594	466	7	♭	♭	PROPN
ejpam-5594	466	8	+	+	NUM
ejpam-5594	466	9	1−	1−	NUM
ejpam-5594	466	10	ς	ς	X
ejpam-5594	466	11	b(ς	b(ς	PROPN
ejpam-5594	466	12	)	)	PUNCT
ejpam-5594	466	13	[	[	PUNCT
ejpam-5594	466	14	φ(ε1)ג(ε1	φ(ε1)ג(ε1	PROPN
ejpam-5594	466	15	)	)	PUNCT
ejpam-5594	466	16	+	+	CCONJ
ejpam-5594	466	17	φ(ε2)ג(ε2	φ(ε2)ג(ε2	PROPN
ejpam-5594	466	18	)	)	PUNCT
ejpam-5594	466	19	]	]	PUNCT
ejpam-5594	466	20	.	.	PUNCT
ejpam-5594	467	1	(	(	PUNCT
ejpam-5594	467	2	15	15	NUM
ejpam-5594	467	3	)	)	PUNCT
ejpam-5594	467	4	(	(	PUNCT
ejpam-5594	467	5	ii	ii	NOUN
ejpam-5594	467	6	)	)	PUNCT
ejpam-5594	467	7	if	if	SCONJ
ejpam-5594	467	8	h	h	PROPN
ejpam-5594	467	9	(	(	PUNCT
ejpam-5594	467	10	♭	♭	INTJ
ejpam-5594	467	11	)	)	PUNCT
ejpam-5594	467	12	=	=	SYM
ejpam-5594	467	13	1	1	NUM
ejpam-5594	467	14	,	,	PUNCT
ejpam-5594	467	15	then	then	ADV
ejpam-5594	467	16	theorem	theorem	VERB
ejpam-5594	467	17	12	12	NUM
ejpam-5594	467	18	yields	yield	NOUN
ejpam-5594	467	19	an	an	DET
ejpam-5594	467	20	outcome	outcome	NOUN
ejpam-5594	467	21	for	for	ADP
ejpam-5594	467	22	the	the	DET
ejpam-5594	467	23	cr	cr	PROPN
ejpam-5594	467	24	-	-	PUNCT
ejpam-5594	467	25	p	p	NOUN
ejpam-5594	467	26	-	-	PUNCT
ejpam-5594	467	27	convex	convex	NOUN
ejpam-5594	467	28	function	function	NOUN
ejpam-5594	467	29	for	for	ADP
ejpam-5594	467	30	ab	ab	PROPN
ejpam-5594	467	31	integral	integral	ADJ
ejpam-5594	467	32	operators	operator	NOUN
ejpam-5594	467	33	:	:	PUNCT
ejpam-5594	467	34	1	1	NUM
ejpam-5594	467	35	2	2	NUM
ejpam-5594	467	36	f	f	NOUN
ejpam-5594	467	37	(	(	PUNCT
ejpam-5594	467	38	ε2	ε2	PROPN
ejpam-5594	467	39	+	+	CCONJ
ejpam-5594	467	40	ε1	ε1	PROPN
ejpam-5594	467	41	2	2	NUM
ejpam-5594	467	42	)	)	PUNCT
ejpam-5594	467	43	[	[	PUNCT
ejpam-5594	467	44	ab	ab	X
ejpam-5594	467	45	ε1i	ε1i	PROPN
ejpam-5594	467	46	ς	ς	PROPN
ejpam-5594	467	47	ε2{ג(ε2)}+	ε2{ג(ε2)}+	PROPN
ejpam-5594	467	48	abiςε2{ג(ε1	abiςε2{ג(ε1	PROPN
ejpam-5594	467	49	)	)	PUNCT
ejpam-5594	467	50	}	}	PUNCT
ejpam-5594	467	51	]	]	PUNCT
ejpam-5594	468	1	−	−	PROPN
ejpam-5594	468	2	1	1	NUM
ejpam-5594	468	3	2	2	NUM
ejpam-5594	468	4	φ	φ	NOUN
ejpam-5594	468	5	(	(	PUNCT
ejpam-5594	468	6	ε2	ε2	PROPN
ejpam-5594	468	7	+	+	CCONJ
ejpam-5594	468	8	ε1	ε1	PROPN
ejpam-5594	468	9	2	2	NUM
ejpam-5594	468	10	)	)	PUNCT
ejpam-5594	468	11	1−	1−	NUM
ejpam-5594	468	12	ς	ς	PROPN
ejpam-5594	468	13	b(ς	b(ς	PROPN
ejpam-5594	468	14	)	)	PUNCT
ejpam-5594	468	15	[	[	PUNCT
ejpam-5594	468	16	(	(	PUNCT
ejpam-5594	468	17	ε1)ג	ε1)ג	NOUN
ejpam-5594	468	18	+	+	CCONJ
ejpam-5594	468	19	(	(	PUNCT
ejpam-5594	468	20	ε2)ג	ε2)ג	PROPN
ejpam-5594	468	21	]	]	PUNCT
ejpam-5594	469	1	+	+	CCONJ
ejpam-5594	469	2	1−	1−	NUM
ejpam-5594	469	3	ς	ς	X
ejpam-5594	469	4	b(ς	b(ς	PROPN
ejpam-5594	469	5	)	)	PUNCT
ejpam-5594	469	6	[	[	PUNCT
ejpam-5594	469	7	φ(ε1)ג(ε1	φ(ε1)ג(ε1	PROPN
ejpam-5594	469	8	)	)	PUNCT
ejpam-5594	469	9	+	+	CCONJ
ejpam-5594	469	10	φ(ε2)ג(ε2	φ(ε2)ג(ε2	PROPN
ejpam-5594	469	11	)	)	PUNCT
ejpam-5594	469	12	]	]	PUNCT
ejpam-5594	469	13	⪯cr	⪯cr	VERB
ejpam-5594	469	14	ab	ab	PROPN
ejpam-5594	469	15	ε1i	ε1i	PROPN
ejpam-5594	469	16	ς	ς	PROPN
ejpam-5594	469	17	ε2{(φג(ε2)}+	ε2{(φג(ε2)}+	PROPN
ejpam-5594	469	18	abiςε2{(φג(ε1	abiςε2{(φג(ε1	PROPN
ejpam-5594	469	19	)	)	PUNCT
ejpam-5594	469	20	}	}	PUNCT
ejpam-5594	469	21	⪯cr	⪯cr	VERB
ejpam-5594	469	22	2ς(ε2	2ς(ε2	NUM
ejpam-5594	469	23	−	−	NOUN
ejpam-5594	469	24	ε1	ε1	PROPN
ejpam-5594	469	25	)	)	PUNCT
ejpam-5594	469	26	ς	ς	NOUN
ejpam-5594	469	27	b(ς)γ(ς	b(ς)γ(ς	NUM
ejpam-5594	469	28	)	)	PUNCT
ejpam-5594	469	29	[	[	PUNCT
ejpam-5594	469	30	φ(ε1	φ(ε1	NOUN
ejpam-5594	469	31	)	)	PUNCT
ejpam-5594	469	32	+	+	SYM
ejpam-5594	469	33	φ(ε2	φ(ε2	NUM
ejpam-5594	469	34	)	)	PUNCT
ejpam-5594	469	35	]	]	PUNCT
ejpam-5594	470	1	×	×	NOUN
ejpam-5594	470	2	∫	∫	PROPN
ejpam-5594	470	3	1	1	NUM
ejpam-5594	470	4	0	0	NUM
ejpam-5594	470	5	♭	♭	PROPN
ejpam-5594	470	6	ς−1ג(	ς−1ג(	PROPN
ejpam-5594	470	7	♭	♭	PROPN
ejpam-5594	470	8	ε2	ε2	ADJ
ejpam-5594	470	9	+	+	CCONJ
ejpam-5594	470	10	(	(	PUNCT
ejpam-5594	470	11	1−	1−	NUM
ejpam-5594	470	12	♭	♭	INTJ
ejpam-5594	470	13	)	)	PUNCT
ejpam-5594	470	14	ε1)d	ε1)d	NOUN
ejpam-5594	470	15	♭	♭	PROPN
ejpam-5594	471	1	+	+	NUM
ejpam-5594	471	2	1−	1−	NUM
ejpam-5594	471	3	ς	ς	X
ejpam-5594	471	4	b(ς	b(ς	PROPN
ejpam-5594	471	5	)	)	PUNCT
ejpam-5594	471	6	[	[	PUNCT
ejpam-5594	471	7	φ(ε1)ג(ε1	φ(ε1)ג(ε1	PROPN
ejpam-5594	471	8	)	)	PUNCT
ejpam-5594	471	9	+	+	CCONJ
ejpam-5594	471	10	φ(ε2)ג(ε2	φ(ε2)ג(ε2	PROPN
ejpam-5594	471	11	)	)	PUNCT
ejpam-5594	471	12	]	]	PUNCT
ejpam-5594	471	13	.	.	PUNCT
ejpam-5594	472	1	using	use	VERB
ejpam-5594	472	2	holder	holder	NOUN
ejpam-5594	472	3	and	and	CCONJ
ejpam-5594	472	4	young	young	ADJ
ejpam-5594	472	5	inequalities	inequality	NOUN
ejpam-5594	472	6	,	,	PUNCT
ejpam-5594	472	7	we	we	PRON
ejpam-5594	472	8	present	present	VERB
ejpam-5594	472	9	a	a	DET
ejpam-5594	472	10	novel	novel	ADJ
ejpam-5594	472	11	refinement	refinement	NOUN
ejpam-5594	472	12	of	of	ADP
ejpam-5594	472	13	(	(	PUNCT
ejpam-5594	472	14	h	h	NOUN
ejpam-5594	472	15	-	-	PUNCT
ejpam-5594	472	16	h	h	NOUN
ejpam-5594	472	17	)	)	PUNCT
ejpam-5594	472	18	fractional	fractional	ADJ
ejpam-5594	472	19	integral	integral	ADJ
ejpam-5594	472	20	inequalities	inequality	NOUN
ejpam-5594	472	21	when	when	SCONJ
ejpam-5594	472	22	the	the	DET
ejpam-5594	472	23	function	function	NOUN
ejpam-5594	472	24	φ	φ	PROPN
ejpam-5594	472	25	is	be	AUX
ejpam-5594	472	26	twice	twice	ADV
ejpam-5594	472	27	differentiable	differentiable	ADJ
ejpam-5594	472	28	and	and	CCONJ
ejpam-5594	472	29	belongs	belong	VERB
ejpam-5594	472	30	to	to	ADP
ejpam-5594	472	31	the	the	DET
ejpam-5594	472	32	class	class	NOUN
ejpam-5594	472	33	of	of	ADP
ejpam-5594	472	34	cr	cr	PROPN
ejpam-5594	472	35	-	-	PUNCT
ejpam-5594	472	36	godunova	godunova	PROPN
ejpam-5594	472	37	-	-	PUNCT
ejpam-5594	472	38	levin	levin	PROPN
ejpam-5594	472	39	mappings	mapping	NOUN
ejpam-5594	472	40	,	,	PUNCT
ejpam-5594	472	41	based	base	VERB
ejpam-5594	472	42	on	on	ADP
ejpam-5594	472	43	the	the	DET
ejpam-5594	472	44	identity	identity	NOUN
ejpam-5594	472	45	in	in	ADP
ejpam-5594	472	46	lemma	lemma	PROPN
ejpam-5594	472	47	2.1	2.1	NUM
ejpam-5594	472	48	.	.	PUNCT
ejpam-5594	473	1	j.	j.	PROPN
ejpam-5594	473	2	e.	e.	PROPN
ejpam-5594	473	3	maćıas	maćıas	PROPN
ejpam-5594	473	4	-	-	PUNCT
ejpam-5594	473	5	dı́az	dı́az	NOUN
ejpam-5594	473	6	et	et	NOUN
ejpam-5594	473	7	al	al	PROPN
ejpam-5594	473	8	.	.	PUNCT
ejpam-5594	473	9	/	/	SYM
ejpam-5594	473	10	eur	eur	PROPN
ejpam-5594	473	11	.	.	PUNCT
ejpam-5594	474	1	j.	j.	PROPN
ejpam-5594	474	2	pure	pure	PROPN
ejpam-5594	474	3	appl	appl	PROPN
ejpam-5594	474	4	.	.	PROPN
ejpam-5594	474	5	math	math	PROPN
ejpam-5594	474	6	,	,	PUNCT
ejpam-5594	474	7	17	17	NUM
ejpam-5594	474	8	(	(	PUNCT
ejpam-5594	474	9	4	4	NUM
ejpam-5594	474	10	)	)	PUNCT
ejpam-5594	474	11	(	(	PUNCT
ejpam-5594	474	12	2024	2024	NUM
ejpam-5594	474	13	)	)	PUNCT
ejpam-5594	474	14	,	,	PUNCT
ejpam-5594	474	15	4014	4014	NUM
ejpam-5594	474	16	-	-	SYM
ejpam-5594	474	17	4049	4049	NUM
ejpam-5594	474	18	4032	4032	NUM
ejpam-5594	474	19	theorem	theorem	VERB
ejpam-5594	474	20	13	13	NUM
ejpam-5594	474	21	.	.	PUNCT
ejpam-5594	475	1	let	let	VERB
ejpam-5594	475	2	h	h	NOUN
ejpam-5594	475	3	:	:	PUNCT
ejpam-5594	475	4	(	(	PUNCT
ejpam-5594	475	5	0	0	NUM
ejpam-5594	475	6	,	,	PUNCT
ejpam-5594	475	7	1	1	NUM
ejpam-5594	475	8	)	)	PUNCT
ejpam-5594	475	9	→	→	NOUN
ejpam-5594	475	10	r+	r+	NOUN
ejpam-5594	475	11	and	and	CCONJ
ejpam-5594	475	12	h	h	NOUN
ejpam-5594	475	13	̸=	̸=	PROPN
ejpam-5594	475	14	0	0	NUM
ejpam-5594	475	15	.	.	PUNCT
ejpam-5594	476	1	let	let	VERB
ejpam-5594	476	2	φ	φ	NOUN
ejpam-5594	476	3	:	:	PUNCT
ejpam-5594	477	1	[	[	X
ejpam-5594	477	2	ε1	ε1	NOUN
ejpam-5594	477	3	,	,	PUNCT
ejpam-5594	477	4	ε2	ε2	PROPN
ejpam-5594	477	5	]	]	PUNCT
ejpam-5594	477	6	→	→	SYM
ejpam-5594	477	7	r+	r+	NOUN
ejpam-5594	477	8	i	i	PRON
ejpam-5594	477	9	is	be	AUX
ejpam-5594	477	10	cr	cr	PROPN
ejpam-5594	477	11	-	-	PUNCT
ejpam-5594	477	12	h	h	NOUN
ejpam-5594	477	13	-	-	PUNCT
ejpam-5594	477	14	godunovalevin	godunovalevin	ADJ
ejpam-5594	477	15	mapping	mapping	NOUN
ejpam-5594	477	16	,	,	PUNCT
ejpam-5594	477	17	ε1	ε1	PROPN
ejpam-5594	477	18	,	,	PUNCT
ejpam-5594	477	19	ε2	ε2	PROPN
ejpam-5594	477	20	∈	∈	PROPN
ejpam-5594	477	21	r+	r+	NOUN
ejpam-5594	477	22	,	,	PUNCT
ejpam-5594	477	23	ε1	ε1	VERB
ejpam-5594	477	24	<	<	X
ejpam-5594	477	25	ε2	ε2	PROPN
ejpam-5594	477	26	.	.	PUNCT
ejpam-5594	478	1	if	if	SCONJ
ejpam-5594	478	2	φ′′	φ′′	PROPN
ejpam-5594	478	3	∈	∈	PROPN
ejpam-5594	478	4	l[ε1	l[ε1	NOUN
ejpam-5594	478	5	,	,	PUNCT
ejpam-5594	478	6	ε2	ε2	PROPN
ejpam-5594	478	7	]	]	PUNCT
ejpam-5594	478	8	and	and	CCONJ
ejpam-5594	478	9	|φ′′|	|φ′′|	NOUN
ejpam-5594	478	10	is	be	AUX
ejpam-5594	478	11	also	also	ADV
ejpam-5594	478	12	cr	cr	NOUN
ejpam-5594	478	13	-	-	PUNCT
ejpam-5594	478	14	h	h	NOUN
ejpam-5594	478	15	-	-	PUNCT
ejpam-5594	478	16	godunovalevin	godunovalevin	ADJ
ejpam-5594	478	17	function	function	NOUN
ejpam-5594	478	18	,	,	PUNCT
ejpam-5594	478	19	then	then	ADV
ejpam-5594	478	20	the	the	DET
ejpam-5594	478	21	following	follow	VERB
ejpam-5594	478	22	double	double	ADJ
ejpam-5594	478	23	relation	relation	NOUN
ejpam-5594	478	24	hold	hold	VERB
ejpam-5594	478	25	true	true	ADJ
ejpam-5594	478	26	:	:	PUNCT
ejpam-5594	478	27	1	1	NUM
ejpam-5594	478	28	ε2	ε2	ADJ
ejpam-5594	478	29	−	−	PROPN
ejpam-5594	478	30	ε1	ε1	PROPN
ejpam-5594	478	31	[	[	PUNCT
ejpam-5594	478	32	abiςε2+ε1	abiςε2+ε1	PROPN
ejpam-5594	478	33	2	2	NUM
ejpam-5594	478	34	{	{	PUNCT
ejpam-5594	478	35	φ(ε1)}+	φ(ε1)}+	PROPN
ejpam-5594	478	36	ab	ab	PROPN
ejpam-5594	478	37	ε2+ε1	ε2+ε1	PROPN
ejpam-5594	478	38	2	2	NUM
ejpam-5594	478	39	iςε2{φ(ε2	iςε2{φ(ε2	NOUN
ejpam-5594	478	40	)	)	PUNCT
ejpam-5594	478	41	}	}	PUNCT
ejpam-5594	478	42	]	]	PUNCT
ejpam-5594	479	1	−	−	PROPN
ejpam-5594	479	2	1	1	NUM
ejpam-5594	479	3	(	(	PUNCT
ejpam-5594	479	4	ε2	ε2	ADJ
ejpam-5594	479	5	−	−	PROPN
ejpam-5594	479	6	ε1)b(ς	ε1)b(ς	PROPN
ejpam-5594	479	7	)	)	PUNCT
ejpam-5594	479	8	[	[	PUNCT
ejpam-5594	479	9	φ(ε1	φ(ε1	NOUN
ejpam-5594	479	10	)	)	PUNCT
ejpam-5594	479	11	+	+	SYM
ejpam-5594	479	12	φ(ε2	φ(ε2	NUM
ejpam-5594	479	13	)	)	PUNCT
ejpam-5594	479	14	]	]	PUNCT
ejpam-5594	480	1	−	−	PROPN
ejpam-5594	480	2	(	(	PUNCT
ejpam-5594	480	3	ε2	ε2	ADJ
ejpam-5594	480	4	−	−	PROPN
ejpam-5594	480	5	ε1	ε1	PROPN
ejpam-5594	480	6	)	)	PUNCT
ejpam-5594	480	7	ς−1	ς−1	PROPN
ejpam-5594	480	8	2ς−1b(ς)γ(ς	2ς−1b(ς)γ(ς	NUM
ejpam-5594	480	9	)	)	PUNCT
ejpam-5594	480	10	φ	φ	PROPN
ejpam-5594	480	11	(	(	PUNCT
ejpam-5594	480	12	ε2	ε2	PROPN
ejpam-5594	480	13	+	+	CCONJ
ejpam-5594	480	14	ε1	ε1	PROPN
ejpam-5594	480	15	2	2	NUM
ejpam-5594	480	16	)	)	PUNCT
ejpam-5594	480	17	⪯cr	⪯cr	NUM
ejpam-5594	480	18	(	(	PUNCT
ejpam-5594	480	19	ε2	ε2	ADJ
ejpam-5594	480	20	−	−	PROPN
ejpam-5594	480	21	ε1	ε1	PROPN
ejpam-5594	480	22	)	)	PUNCT
ejpam-5594	481	1	ς−1	ς−1	PROPN
ejpam-5594	481	2	(	(	PUNCT
ejpam-5594	481	3	ς	ς	PROPN
ejpam-5594	481	4	+	+	NOUN
ejpam-5594	481	5	1)b(ς)γ(ς	1)b(ς)γ(ς	NUM
ejpam-5594	481	6	)	)	PUNCT
ejpam-5594	481	7	[	[	PUNCT
ejpam-5594	481	8	|φ′′(ε1)|+|φ′′(ε2)|	|φ′′(ε1)|+|φ′′(ε2)|	X
ejpam-5594	481	9	]	]	PUNCT
ejpam-5594	481	10	×	×	NOUN
ejpam-5594	481	11	∫	∫	PROPN
ejpam-5594	481	12	1	1	NUM
ejpam-5594	482	1	2	2	NUM
ejpam-5594	482	2	0	0	NUM
ejpam-5594	482	3	♭	♭	NOUN
ejpam-5594	482	4	ς+1	ς+1	PRON
ejpam-5594	482	5	[	[	PUNCT
ejpam-5594	482	6	1	1	NUM
ejpam-5594	482	7	h	h	NOUN
ejpam-5594	482	8	(	(	PUNCT
ejpam-5594	482	9	♭	♭	PROPN
ejpam-5594	482	10	)	)	PUNCT
ejpam-5594	483	1	+	+	CCONJ
ejpam-5594	483	2	1	1	NUM
ejpam-5594	483	3	h(1−	h(1−	NOUN
ejpam-5594	483	4	♭	♭	PROPN
ejpam-5594	483	5	)	)	PUNCT
ejpam-5594	483	6	]	]	PUNCT
ejpam-5594	484	1	d	d	X
ejpam-5594	484	2	♭	♭	INTJ
ejpam-5594	484	3	,	,	PUNCT
ejpam-5594	484	4	(	(	PUNCT
ejpam-5594	484	5	16	16	NUM
ejpam-5594	484	6	)	)	PUNCT
ejpam-5594	484	7	where	where	SCONJ
ejpam-5594	484	8	ς	ς	PROPN
ejpam-5594	484	9	∈	∈	PROPN
ejpam-5594	484	10	(	(	PUNCT
ejpam-5594	484	11	0	0	NUM
ejpam-5594	484	12	,	,	PUNCT
ejpam-5594	484	13	1	1	NUM
ejpam-5594	484	14	]	]	PUNCT
ejpam-5594	484	15	.	.	PUNCT
ejpam-5594	484	16	proof	proof	NOUN
ejpam-5594	484	17	.	.	PUNCT
ejpam-5594	485	1	firstly	firstly	ADV
ejpam-5594	485	2	,	,	PUNCT
ejpam-5594	485	3	from	from	ADP
ejpam-5594	485	4	lemma	lemma	PROPN
ejpam-5594	485	5	2.1	2.1	NUM
ejpam-5594	485	6	,	,	PUNCT
ejpam-5594	485	7	we	we	PRON
ejpam-5594	485	8	have	have	VERB
ejpam-5594	485	9	1	1	NUM
ejpam-5594	485	10	ε2	ε2	ADJ
ejpam-5594	485	11	−	−	PROPN
ejpam-5594	485	12	ε1	ε1	PROPN
ejpam-5594	485	13	[	[	PUNCT
ejpam-5594	485	14	abiςε2+ε1	abiςε2+ε1	PROPN
ejpam-5594	485	15	2	2	NUM
ejpam-5594	485	16	{	{	PUNCT
ejpam-5594	485	17	φ(ε1)}+	φ(ε1)}+	PROPN
ejpam-5594	485	18	ab	ab	PROPN
ejpam-5594	485	19	ε2+ε1	ε2+ε1	PROPN
ejpam-5594	485	20	2	2	NUM
ejpam-5594	485	21	iςε2{φ(ε2	iςε2{φ(ε2	NOUN
ejpam-5594	485	22	)	)	PUNCT
ejpam-5594	485	23	}	}	PUNCT
ejpam-5594	485	24	]	]	PUNCT
ejpam-5594	486	1	−	−	PROPN
ejpam-5594	486	2	1	1	NUM
ejpam-5594	486	3	(	(	PUNCT
ejpam-5594	486	4	ε2	ε2	ADJ
ejpam-5594	486	5	−	−	PROPN
ejpam-5594	486	6	ε1)b(ς	ε1)b(ς	PROPN
ejpam-5594	486	7	)	)	PUNCT
ejpam-5594	486	8	[	[	PUNCT
ejpam-5594	486	9	φ(ε1	φ(ε1	NOUN
ejpam-5594	486	10	)	)	PUNCT
ejpam-5594	486	11	+	+	SYM
ejpam-5594	486	12	φ(ε2	φ(ε2	NUM
ejpam-5594	486	13	)	)	PUNCT
ejpam-5594	486	14	]	]	PUNCT
ejpam-5594	487	1	−	−	PROPN
ejpam-5594	487	2	(	(	PUNCT
ejpam-5594	487	3	ε2	ε2	ADJ
ejpam-5594	487	4	−	−	PROPN
ejpam-5594	487	5	ε1	ε1	PROPN
ejpam-5594	487	6	)	)	PUNCT
ejpam-5594	487	7	ς−1	ς−1	PROPN
ejpam-5594	487	8	2ς−1b(ς)γ(ς	2ς−1b(ς)γ(ς	NUM
ejpam-5594	487	9	)	)	PUNCT
ejpam-5594	487	10	φ	φ	PROPN
ejpam-5594	487	11	(	(	PUNCT
ejpam-5594	487	12	ε2	ε2	PROPN
ejpam-5594	487	13	+	+	CCONJ
ejpam-5594	487	14	ε1	ε1	PROPN
ejpam-5594	487	15	2	2	NUM
ejpam-5594	487	16	)	)	PUNCT
ejpam-5594	487	17	⪯cr	⪯cr	NUM
ejpam-5594	487	18	(	(	PUNCT
ejpam-5594	487	19	ε2	ε2	ADJ
ejpam-5594	487	20	−	−	PROPN
ejpam-5594	487	21	ε1	ε1	PROPN
ejpam-5594	487	22	)	)	PUNCT
ejpam-5594	488	1	ς−1	ς−1	PROPN
ejpam-5594	488	2	2(ς	2(ς	NUM
ejpam-5594	488	3	+	+	CCONJ
ejpam-5594	488	4	1)b(ς)γ(ς	1)b(ς)γ(ς	NUM
ejpam-5594	488	5	)	)	PUNCT
ejpam-5594	488	6	×	×	NOUN
ejpam-5594	488	7	∫	∫	NOUN
ejpam-5594	488	8	1	1	NUM
ejpam-5594	488	9	0	0	NUM
ejpam-5594	488	10	|wς(	|wς(	NUM
ejpam-5594	488	11	♭	♭	NUM
ejpam-5594	488	12	)|	)|	X
ejpam-5594	489	1	[	[	PUNCT
ejpam-5594	489	2	|φ′′(	|φ′′(	NOUN
ejpam-5594	489	3	♭	♭	PRON
ejpam-5594	489	4	ε1	ε1	VERB
ejpam-5594	489	5	+	+	CCONJ
ejpam-5594	489	6	(	(	PUNCT
ejpam-5594	489	7	1−	1−	NUM
ejpam-5594	489	8	♭	♭	INTJ
ejpam-5594	489	9	)	)	PUNCT
ejpam-5594	489	10	ε2)|+|φ′′(	ε2)|+|φ′′(	NOUN
ejpam-5594	489	11	♭	♭	PROPN
ejpam-5594	489	12	ε2	ε2	PROPN
ejpam-5594	489	13	+	+	CCONJ
ejpam-5594	489	14	(	(	PUNCT
ejpam-5594	489	15	1−	1−	NUM
ejpam-5594	489	16	♭	♭	INTJ
ejpam-5594	489	17	)	)	PUNCT
ejpam-5594	489	18	ε1)|	ε1)|	PROPN
ejpam-5594	489	19	]	]	PUNCT
ejpam-5594	490	1	d	d	X
ejpam-5594	490	2	♭	♭	INTJ
ejpam-5594	490	3	.	.	PUNCT
ejpam-5594	491	1	(	(	PUNCT
ejpam-5594	491	2	17	17	NUM
ejpam-5594	491	3	)	)	PUNCT
ejpam-5594	491	4	as	as	SCONJ
ejpam-5594	491	5	|φ′′|	|φ′′|	PROPN
ejpam-5594	491	6	is	be	AUX
ejpam-5594	491	7	cr	cr	PROPN
ejpam-5594	491	8	-	-	PUNCT
ejpam-5594	491	9	h	h	NOUN
ejpam-5594	491	10	-	-	PUNCT
ejpam-5594	491	11	godunova	godunova	ADJ
ejpam-5594	491	12	-	-	PUNCT
ejpam-5594	491	13	levin	levin	PROPN
ejpam-5594	491	14	function	function	PROPN
ejpam-5594	491	15	,	,	PUNCT
ejpam-5594	491	16	we	we	PRON
ejpam-5594	491	17	have	have	VERB
ejpam-5594	491	18	1	1	NUM
ejpam-5594	491	19	ε2	ε2	ADJ
ejpam-5594	491	20	−	−	PROPN
ejpam-5594	491	21	ε1	ε1	PROPN
ejpam-5594	491	22	[	[	PUNCT
ejpam-5594	491	23	abiςε2+ε1	abiςε2+ε1	PROPN
ejpam-5594	491	24	2	2	NUM
ejpam-5594	491	25	{	{	PUNCT
ejpam-5594	491	26	φ(ε1)}+	φ(ε1)}+	PROPN
ejpam-5594	491	27	ab	ab	PROPN
ejpam-5594	491	28	ε2+ε1	ε2+ε1	PROPN
ejpam-5594	491	29	2	2	NUM
ejpam-5594	491	30	iςε2{φ(ε2	iςε2{φ(ε2	NOUN
ejpam-5594	491	31	)	)	PUNCT
ejpam-5594	491	32	}	}	PUNCT
ejpam-5594	491	33	]	]	PUNCT
ejpam-5594	492	1	−	−	PROPN
ejpam-5594	492	2	1	1	NUM
ejpam-5594	492	3	(	(	PUNCT
ejpam-5594	492	4	ε2	ε2	ADJ
ejpam-5594	492	5	−	−	PROPN
ejpam-5594	492	6	ε1)b(ς	ε1)b(ς	PROPN
ejpam-5594	492	7	)	)	PUNCT
ejpam-5594	492	8	[	[	PUNCT
ejpam-5594	492	9	φ(ε1	φ(ε1	NOUN
ejpam-5594	492	10	)	)	PUNCT
ejpam-5594	492	11	+	+	SYM
ejpam-5594	492	12	φ(ε2	φ(ε2	NUM
ejpam-5594	492	13	)	)	PUNCT
ejpam-5594	492	14	]	]	PUNCT
ejpam-5594	493	1	−	−	PROPN
ejpam-5594	493	2	(	(	PUNCT
ejpam-5594	493	3	ε2	ε2	ADJ
ejpam-5594	493	4	−	−	PROPN
ejpam-5594	493	5	ε1	ε1	PROPN
ejpam-5594	493	6	)	)	PUNCT
ejpam-5594	493	7	ς−1	ς−1	PROPN
ejpam-5594	493	8	2ς−1b(ς)γ(ς	2ς−1b(ς)γ(ς	NUM
ejpam-5594	493	9	)	)	PUNCT
ejpam-5594	493	10	φ	φ	PROPN
ejpam-5594	493	11	(	(	PUNCT
ejpam-5594	493	12	ε2	ε2	PROPN
ejpam-5594	493	13	+	+	CCONJ
ejpam-5594	493	14	ε1	ε1	PROPN
ejpam-5594	493	15	2	2	NUM
ejpam-5594	493	16	)	)	PUNCT
ejpam-5594	493	17	≤	≤	NOUN
ejpam-5594	493	18	(	(	PUNCT
ejpam-5594	493	19	ε2	ε2	ADJ
ejpam-5594	493	20	−	−	PROPN
ejpam-5594	493	21	ε1	ε1	PROPN
ejpam-5594	493	22	)	)	PUNCT
ejpam-5594	494	1	ς−1	ς−1	PROPN
ejpam-5594	494	2	2(ς	2(ς	NUM
ejpam-5594	494	3	+	+	CCONJ
ejpam-5594	494	4	1)b(ς)γ(ς	1)b(ς)γ(ς	NUM
ejpam-5594	494	5	)	)	PUNCT
ejpam-5594	494	6	×	×	NOUN
ejpam-5594	494	7	{	{	PUNCT
ejpam-5594	494	8	∫	∫	PROPN
ejpam-5594	494	9	1	1	NUM
ejpam-5594	494	10	2	2	NUM
ejpam-5594	494	11	0	0	NUM
ejpam-5594	494	12	♭	♭	PRON
ejpam-5594	494	13	ς+1	ς+1	PRON
ejpam-5594	494	14	[	[	PUNCT
ejpam-5594	494	15	|φ′′(ε1)|	|φ′′(ε1)|	NUM
ejpam-5594	494	16	h	h	NOUN
ejpam-5594	494	17	(	(	PUNCT
ejpam-5594	494	18	♭	♭	INTJ
ejpam-5594	494	19	)	)	PUNCT
ejpam-5594	495	1	+	+	CCONJ
ejpam-5594	495	2	|φ′′(ε2)|	|φ′′(ε2)|	PROPN
ejpam-5594	495	3	h(1−	h(1−	PROPN
ejpam-5594	495	4	♭	♭	PROPN
ejpam-5594	495	5	)	)	PUNCT
ejpam-5594	495	6	]	]	PUNCT
ejpam-5594	496	1	d	d	X
ejpam-5594	496	2	♭	♭	PROPN
ejpam-5594	496	3	+	+	NUM
ejpam-5594	496	4	∫	∫	PROPN
ejpam-5594	496	5	1	1	NUM
ejpam-5594	496	6	1	1	NUM
ejpam-5594	496	7	2	2	NUM
ejpam-5594	496	8	(	(	PUNCT
ejpam-5594	496	9	1−	1−	NUM
ejpam-5594	496	10	♭	♭	INTJ
ejpam-5594	496	11	)	)	PUNCT
ejpam-5594	496	12	ς+1	ς+1	NOUN
ejpam-5594	496	13	[	[	PUNCT
ejpam-5594	496	14	|φ′′(ε1)|	|φ′′(ε1)|	NUM
ejpam-5594	496	15	h	h	NOUN
ejpam-5594	496	16	(	(	PUNCT
ejpam-5594	496	17	♭	♭	INTJ
ejpam-5594	496	18	)	)	PUNCT
ejpam-5594	496	19	+	+	CCONJ
ejpam-5594	496	20	|φ′′(ε2)|	|φ′′(ε2)|	PROPN
ejpam-5594	496	21	h(1−	h(1−	PROPN
ejpam-5594	496	22	♭	♭	PROPN
ejpam-5594	496	23	)	)	PUNCT
ejpam-5594	496	24	]	]	PUNCT
ejpam-5594	497	1	d	d	X
ejpam-5594	497	2	♭	♭	PROPN
ejpam-5594	498	1	+	+	NUM
ejpam-5594	498	2	∫	∫	PROPN
ejpam-5594	498	3	1	1	NUM
ejpam-5594	498	4	2	2	NUM
ejpam-5594	498	5	0	0	NUM
ejpam-5594	498	6	♭	♭	NOUN
ejpam-5594	498	7	ς+1	ς+1	PRON
ejpam-5594	498	8	[	[	PUNCT
ejpam-5594	498	9	|φ′′(ε2)|	|φ′′(ε2)|	X
ejpam-5594	498	10	h	h	PROPN
ejpam-5594	498	11	(	(	PUNCT
ejpam-5594	498	12	♭	♭	PROPN
ejpam-5594	498	13	)	)	PUNCT
ejpam-5594	499	1	+	+	CCONJ
ejpam-5594	499	2	|φ′′(ε1)|	|φ′′(ε1)|	NUM
ejpam-5594	499	3	h(1−	h(1−	NOUN
ejpam-5594	499	4	♭	♭	PROPN
ejpam-5594	499	5	)	)	PUNCT
ejpam-5594	499	6	]	]	PUNCT
ejpam-5594	500	1	d	d	X
ejpam-5594	500	2	♭	♭	PROPN
ejpam-5594	500	3	+	+	NUM
ejpam-5594	500	4	∫	∫	PROPN
ejpam-5594	500	5	1	1	NUM
ejpam-5594	500	6	1	1	NUM
ejpam-5594	500	7	2	2	NUM
ejpam-5594	500	8	(	(	PUNCT
ejpam-5594	500	9	1−	1−	NUM
ejpam-5594	500	10	♭	♭	INTJ
ejpam-5594	500	11	)	)	PUNCT
ejpam-5594	500	12	ς+1	ς+1	PROPN
ejpam-5594	500	13	[	[	PUNCT
ejpam-5594	500	14	|φ′′(ε2)|	|φ′′(ε2)|	X
ejpam-5594	500	15	h	h	PROPN
ejpam-5594	500	16	(	(	PUNCT
ejpam-5594	500	17	♭	♭	PROPN
ejpam-5594	500	18	)	)	PUNCT
ejpam-5594	500	19	+	+	CCONJ
ejpam-5594	500	20	|φ′′(ε1)|	|φ′′(ε1)|	NUM
ejpam-5594	500	21	h(1−	h(1−	NOUN
ejpam-5594	500	22	♭	♭	PROPN
ejpam-5594	500	23	)	)	PUNCT
ejpam-5594	500	24	]	]	PUNCT
ejpam-5594	501	1	d	d	X
ejpam-5594	501	2	♭	♭	PROPN
ejpam-5594	501	3	}	}	PUNCT
ejpam-5594	501	4	=	=	SYM
ejpam-5594	501	5	(	(	PUNCT
ejpam-5594	501	6	ε2	ε2	PROPN
ejpam-5594	501	7	−	−	PROPN
ejpam-5594	501	8	ε1	ε1	PROPN
ejpam-5594	501	9	)	)	PUNCT
ejpam-5594	502	1	ς−1	ς−1	PROPN
ejpam-5594	502	2	(	(	PUNCT
ejpam-5594	502	3	ς	ς	PROPN
ejpam-5594	502	4	+	+	NOUN
ejpam-5594	502	5	1)b(ς)γ(ς	1)b(ς)γ(ς	NUM
ejpam-5594	502	6	)	)	PUNCT
ejpam-5594	502	7	j.	j.	PROPN
ejpam-5594	502	8	e.	e.	PROPN
ejpam-5594	502	9	maćıas	maćıas	PROPN
ejpam-5594	502	10	-	-	PUNCT
ejpam-5594	502	11	dı́az	dı́az	NOUN
ejpam-5594	502	12	et	et	NOUN
ejpam-5594	502	13	al	al	PROPN
ejpam-5594	502	14	.	.	PUNCT
ejpam-5594	502	15	/	/	SYM
ejpam-5594	502	16	eur	eur	PROPN
ejpam-5594	502	17	.	.	PUNCT
ejpam-5594	503	1	j.	j.	PROPN
ejpam-5594	503	2	pure	pure	PROPN
ejpam-5594	503	3	appl	appl	PROPN
ejpam-5594	503	4	.	.	PROPN
ejpam-5594	503	5	math	math	PROPN
ejpam-5594	503	6	,	,	PUNCT
ejpam-5594	503	7	17	17	NUM
ejpam-5594	503	8	(	(	PUNCT
ejpam-5594	503	9	4	4	NUM
ejpam-5594	503	10	)	)	PUNCT
ejpam-5594	503	11	(	(	PUNCT
ejpam-5594	503	12	2024	2024	NUM
ejpam-5594	503	13	)	)	PUNCT
ejpam-5594	503	14	,	,	PUNCT
ejpam-5594	503	15	4014	4014	NUM
ejpam-5594	503	16	-	-	SYM
ejpam-5594	503	17	4049	4049	NUM
ejpam-5594	503	18	4033	4033	NUM
ejpam-5594	503	19	×	×	NOUN
ejpam-5594	503	20	{	{	PUNCT
ejpam-5594	503	21	∫	∫	PROPN
ejpam-5594	503	22	1	1	NUM
ejpam-5594	503	23	2	2	NUM
ejpam-5594	503	24	0	0	NUM
ejpam-5594	503	25	♭	♭	PRON
ejpam-5594	503	26	ς+1	ς+1	PRON
ejpam-5594	503	27	[	[	PUNCT
ejpam-5594	503	28	|φ′′(ε1)|	|φ′′(ε1)|	NUM
ejpam-5594	503	29	h	h	NOUN
ejpam-5594	503	30	(	(	PUNCT
ejpam-5594	503	31	♭	♭	INTJ
ejpam-5594	503	32	)	)	PUNCT
ejpam-5594	504	1	+	+	CCONJ
ejpam-5594	504	2	|φ′′(ε2)|	|φ′′(ε2)|	PROPN
ejpam-5594	504	3	h(1−	h(1−	PROPN
ejpam-5594	504	4	♭	♭	PROPN
ejpam-5594	504	5	)	)	PUNCT
ejpam-5594	504	6	]	]	PUNCT
ejpam-5594	505	1	d	d	X
ejpam-5594	505	2	♭	♭	PROPN
ejpam-5594	506	1	+	+	NUM
ejpam-5594	506	2	∫	∫	PROPN
ejpam-5594	506	3	1	1	NUM
ejpam-5594	506	4	2	2	NUM
ejpam-5594	506	5	0	0	NUM
ejpam-5594	506	6	♭	♭	NOUN
ejpam-5594	506	7	ς+1	ς+1	PRON
ejpam-5594	506	8	[	[	PUNCT
ejpam-5594	506	9	|φ′′(ε2)|	|φ′′(ε2)|	X
ejpam-5594	506	10	h	h	PROPN
ejpam-5594	506	11	(	(	PUNCT
ejpam-5594	506	12	♭	♭	PROPN
ejpam-5594	506	13	)	)	PUNCT
ejpam-5594	507	1	+	+	CCONJ
ejpam-5594	507	2	|φ′′(ε1)|	|φ′′(ε1)|	NUM
ejpam-5594	507	3	h(1−	h(1−	NOUN
ejpam-5594	507	4	♭	♭	PROPN
ejpam-5594	507	5	)	)	PUNCT
ejpam-5594	507	6	]	]	PUNCT
ejpam-5594	508	1	d	d	X
ejpam-5594	508	2	♭	♭	PROPN
ejpam-5594	508	3	}	}	PUNCT
ejpam-5594	508	4	=	=	SYM
ejpam-5594	508	5	(	(	PUNCT
ejpam-5594	508	6	ε2	ε2	PROPN
ejpam-5594	508	7	−	−	PROPN
ejpam-5594	508	8	ε1	ε1	PROPN
ejpam-5594	508	9	)	)	PUNCT
ejpam-5594	509	1	ς−1	ς−1	PROPN
ejpam-5594	509	2	(	(	PUNCT
ejpam-5594	509	3	ς	ς	PROPN
ejpam-5594	509	4	+	+	NOUN
ejpam-5594	509	5	1)b(ς)γ(ς	1)b(ς)γ(ς	NUM
ejpam-5594	509	6	)	)	PUNCT
ejpam-5594	509	7	[	[	PUNCT
ejpam-5594	509	8	|φ′′(ε1)|+|φ′′(ε2)|	|φ′′(ε1)|+|φ′′(ε2)|	X
ejpam-5594	509	9	]	]	PUNCT
ejpam-5594	509	10	∫	∫	PROPN
ejpam-5594	510	1	1	1	NUM
ejpam-5594	510	2	2	2	NUM
ejpam-5594	510	3	0	0	NUM
ejpam-5594	510	4	♭	♭	NOUN
ejpam-5594	510	5	ς+1	ς+1	PRON
ejpam-5594	510	6	[	[	PUNCT
ejpam-5594	510	7	1	1	NUM
ejpam-5594	510	8	h	h	NOUN
ejpam-5594	510	9	(	(	PUNCT
ejpam-5594	510	10	♭	♭	PROPN
ejpam-5594	510	11	)	)	PUNCT
ejpam-5594	510	12	+	+	CCONJ
ejpam-5594	510	13	1	1	NUM
ejpam-5594	510	14	h(1−	h(1−	NOUN
ejpam-5594	510	15	♭	♭	PROPN
ejpam-5594	510	16	)	)	PUNCT
ejpam-5594	510	17	]	]	PUNCT
ejpam-5594	511	1	d	d	X
ejpam-5594	511	2	♭	♭	INTJ
ejpam-5594	511	3	.	.	PUNCT
ejpam-5594	511	4	remark	remark	PROPN
ejpam-5594	511	5	5	5	NUM
ejpam-5594	511	6	.	.	PUNCT
ejpam-5594	512	1	(	(	PUNCT
ejpam-5594	512	2	i	i	NOUN
ejpam-5594	512	3	)	)	PUNCT
ejpam-5594	512	4	if	if	SCONJ
ejpam-5594	512	5	h	h	X
ejpam-5594	512	6	(	(	PUNCT
ejpam-5594	512	7	♭	♭	INTJ
ejpam-5594	512	8	)	)	PUNCT
ejpam-5594	513	1	=	=	SYM
ejpam-5594	513	2	1	1	NUM
ejpam-5594	513	3	♭	♭	NOUN
ejpam-5594	513	4	s	s	PART
ejpam-5594	513	5	,	,	PUNCT
ejpam-5594	513	6	then	then	ADV
ejpam-5594	513	7	theorem	theorem	VERB
ejpam-5594	513	8	13	13	NUM
ejpam-5594	513	9	yields	yield	NOUN
ejpam-5594	513	10	an	an	DET
ejpam-5594	513	11	outcome	outcome	NOUN
ejpam-5594	513	12	for	for	ADP
ejpam-5594	513	13	the	the	DET
ejpam-5594	513	14	cr	cr	PROPN
ejpam-5594	513	15	-	-	PUNCT
ejpam-5594	513	16	s	s	NOUN
ejpam-5594	513	17	-	-	PUNCT
ejpam-5594	513	18	convex	convex	ADJ
ejpam-5594	513	19	function	function	NOUN
ejpam-5594	513	20	for	for	ADP
ejpam-5594	513	21	ab	ab	PROPN
ejpam-5594	513	22	integral	integral	ADJ
ejpam-5594	513	23	operators	operator	NOUN
ejpam-5594	513	24	:	:	PUNCT
ejpam-5594	513	25	1	1	NUM
ejpam-5594	513	26	ε2	ε2	ADJ
ejpam-5594	513	27	−	−	PROPN
ejpam-5594	513	28	ε1	ε1	PROPN
ejpam-5594	513	29	[	[	PUNCT
ejpam-5594	513	30	abiςε2+ε1	abiςε2+ε1	PROPN
ejpam-5594	513	31	2	2	NUM
ejpam-5594	513	32	{	{	PUNCT
ejpam-5594	513	33	φ(ε1)}+	φ(ε1)}+	PROPN
ejpam-5594	513	34	ab	ab	PROPN
ejpam-5594	513	35	ε2+ε1	ε2+ε1	PROPN
ejpam-5594	513	36	2	2	NUM
ejpam-5594	513	37	iςε2{φ(ε2	iςε2{φ(ε2	NOUN
ejpam-5594	513	38	)	)	PUNCT
ejpam-5594	513	39	}	}	PUNCT
ejpam-5594	513	40	]	]	PUNCT
ejpam-5594	514	1	−	−	PROPN
ejpam-5594	514	2	1	1	NUM
ejpam-5594	514	3	(	(	PUNCT
ejpam-5594	514	4	ε2	ε2	ADJ
ejpam-5594	514	5	−	−	PROPN
ejpam-5594	514	6	ε1)b(ς	ε1)b(ς	PROPN
ejpam-5594	514	7	)	)	PUNCT
ejpam-5594	514	8	[	[	PUNCT
ejpam-5594	514	9	φ(ε1	φ(ε1	NOUN
ejpam-5594	514	10	)	)	PUNCT
ejpam-5594	514	11	+	+	SYM
ejpam-5594	514	12	φ(ε2	φ(ε2	NUM
ejpam-5594	514	13	)	)	PUNCT
ejpam-5594	514	14	]	]	PUNCT
ejpam-5594	515	1	−	−	PROPN
ejpam-5594	515	2	(	(	PUNCT
ejpam-5594	515	3	ε2	ε2	ADJ
ejpam-5594	515	4	−	−	PROPN
ejpam-5594	515	5	ε1	ε1	PROPN
ejpam-5594	515	6	)	)	PUNCT
ejpam-5594	515	7	ς−1	ς−1	PROPN
ejpam-5594	515	8	2ς−1b(ς)γ(ς	2ς−1b(ς)γ(ς	NUM
ejpam-5594	515	9	)	)	PUNCT
ejpam-5594	515	10	φ	φ	PROPN
ejpam-5594	515	11	(	(	PUNCT
ejpam-5594	515	12	ε2	ε2	PROPN
ejpam-5594	515	13	+	+	CCONJ
ejpam-5594	515	14	ε1	ε1	PROPN
ejpam-5594	515	15	2	2	NUM
ejpam-5594	515	16	)	)	PUNCT
ejpam-5594	515	17	≤	≤	NOUN
ejpam-5594	515	18	(	(	PUNCT
ejpam-5594	515	19	ε2	ε2	ADJ
ejpam-5594	515	20	−	−	PROPN
ejpam-5594	515	21	ε1	ε1	PROPN
ejpam-5594	515	22	)	)	PUNCT
ejpam-5594	516	1	ς−1	ς−1	PROPN
ejpam-5594	516	2	(	(	PUNCT
ejpam-5594	516	3	ς	ς	PROPN
ejpam-5594	516	4	+	+	NOUN
ejpam-5594	516	5	1)b(ς)γ(ς	1)b(ς)γ(ς	NUM
ejpam-5594	516	6	)	)	PUNCT
ejpam-5594	516	7	[	[	PUNCT
ejpam-5594	516	8	|φ′′(ε1)|+|φ′′(ε2)|	|φ′′(ε1)|+|φ′′(ε2)|	NOUN
ejpam-5594	516	9	]	]	PUNCT
ejpam-5594	517	1	[	[	X
ejpam-5594	517	2	(	(	PUNCT
ejpam-5594	517	3	12)ς+s+2	12)ς+s+2	NOUN
ejpam-5594	517	4	ς	ς	PROPN
ejpam-5594	517	5	+	+	PROPN
ejpam-5594	517	6	s+2	s+2	NUM
ejpam-5594	517	7	+	+	CCONJ
ejpam-5594	517	8	β	β	NOUN
ejpam-5594	517	9	1	1	NUM
ejpam-5594	517	10	2	2	NUM
ejpam-5594	517	11	(	(	PUNCT
ejpam-5594	517	12	ς	ς	PROPN
ejpam-5594	517	13	+	+	PROPN
ejpam-5594	517	14	2	2	NUM
ejpam-5594	517	15	,	,	PUNCT
ejpam-5594	517	16	s+1	s+1	NOUN
ejpam-5594	517	17	)	)	PUNCT
ejpam-5594	517	18	]	]	PUNCT
ejpam-5594	517	19	.	.	PUNCT
ejpam-5594	517	20	(	(	PUNCT
ejpam-5594	517	21	ii	ii	NOUN
ejpam-5594	517	22	)	)	PUNCT
ejpam-5594	517	23	if	if	SCONJ
ejpam-5594	517	24	h	h	PROPN
ejpam-5594	517	25	(	(	PUNCT
ejpam-5594	517	26	♭	♭	INTJ
ejpam-5594	517	27	)	)	PUNCT
ejpam-5594	517	28	=	=	SYM
ejpam-5594	517	29	1	1	NUM
ejpam-5594	517	30	,	,	PUNCT
ejpam-5594	517	31	then	then	ADV
ejpam-5594	517	32	theorem	theorem	VERB
ejpam-5594	517	33	13	13	NUM
ejpam-5594	517	34	yields	yield	NOUN
ejpam-5594	517	35	an	an	DET
ejpam-5594	517	36	outcome	outcome	NOUN
ejpam-5594	517	37	for	for	ADP
ejpam-5594	517	38	the	the	DET
ejpam-5594	517	39	cr	cr	PROPN
ejpam-5594	517	40	-	-	PUNCT
ejpam-5594	517	41	p	p	NOUN
ejpam-5594	517	42	-	-	PUNCT
ejpam-5594	517	43	convex	convex	NOUN
ejpam-5594	517	44	function	function	NOUN
ejpam-5594	517	45	for	for	ADP
ejpam-5594	517	46	ab	ab	PROPN
ejpam-5594	517	47	integral	integral	ADJ
ejpam-5594	517	48	operators	operator	NOUN
ejpam-5594	517	49	:	:	PUNCT
ejpam-5594	517	50	1	1	NUM
ejpam-5594	517	51	ε2	ε2	ADJ
ejpam-5594	517	52	−	−	PROPN
ejpam-5594	517	53	ε1	ε1	PROPN
ejpam-5594	517	54	[	[	PUNCT
ejpam-5594	517	55	abiςε2+ε1	abiςε2+ε1	PROPN
ejpam-5594	517	56	2	2	NUM
ejpam-5594	517	57	{	{	PUNCT
ejpam-5594	517	58	φ(ε1)}+	φ(ε1)}+	PROPN
ejpam-5594	517	59	ab	ab	PROPN
ejpam-5594	517	60	ε2+ε1	ε2+ε1	PROPN
ejpam-5594	517	61	2	2	NUM
ejpam-5594	517	62	iςε2{φ(ε2	iςε2{φ(ε2	NOUN
ejpam-5594	517	63	)	)	PUNCT
ejpam-5594	517	64	}	}	PUNCT
ejpam-5594	517	65	]	]	PUNCT
ejpam-5594	518	1	−	−	PROPN
ejpam-5594	518	2	1	1	NUM
ejpam-5594	518	3	(	(	PUNCT
ejpam-5594	518	4	ε2	ε2	ADJ
ejpam-5594	518	5	−	−	PROPN
ejpam-5594	518	6	ε1)b(ς	ε1)b(ς	PROPN
ejpam-5594	518	7	)	)	PUNCT
ejpam-5594	518	8	[	[	PUNCT
ejpam-5594	518	9	φ(ε1	φ(ε1	NOUN
ejpam-5594	518	10	)	)	PUNCT
ejpam-5594	518	11	+	+	SYM
ejpam-5594	518	12	φ(ε2	φ(ε2	NUM
ejpam-5594	518	13	)	)	PUNCT
ejpam-5594	518	14	]	]	PUNCT
ejpam-5594	519	1	−	−	PROPN
ejpam-5594	519	2	(	(	PUNCT
ejpam-5594	519	3	ε2	ε2	ADJ
ejpam-5594	519	4	−	−	PROPN
ejpam-5594	519	5	ε1	ε1	PROPN
ejpam-5594	519	6	)	)	PUNCT
ejpam-5594	519	7	ς−1	ς−1	PROPN
ejpam-5594	519	8	2ς−1b(ς)γ(ς	2ς−1b(ς)γ(ς	NUM
ejpam-5594	519	9	)	)	PUNCT
ejpam-5594	519	10	φ	φ	PROPN
ejpam-5594	519	11	(	(	PUNCT
ejpam-5594	519	12	ε2	ε2	PROPN
ejpam-5594	519	13	+	+	CCONJ
ejpam-5594	519	14	ε1	ε1	PROPN
ejpam-5594	519	15	2	2	NUM
ejpam-5594	519	16	)	)	PUNCT
ejpam-5594	519	17	≤	≤	NOUN
ejpam-5594	519	18	(	(	PUNCT
ejpam-5594	519	19	1	1	NUM
ejpam-5594	519	20	2	2	NUM
ejpam-5594	519	21	)	)	PUNCT
ejpam-5594	519	22	ς+1	ς+1	NUM
ejpam-5594	519	23	(	(	PUNCT
ejpam-5594	519	24	ς	ς	PROPN
ejpam-5594	519	25	+	+	X
ejpam-5594	519	26	1)(ς	1)(ς	NUM
ejpam-5594	519	27	+	+	CCONJ
ejpam-5594	519	28	2	2	NUM
ejpam-5594	519	29	)	)	PUNCT
ejpam-5594	519	30	(	(	PUNCT
ejpam-5594	519	31	ε2	ε2	ADJ
ejpam-5594	519	32	−	−	PROPN
ejpam-5594	519	33	ε1	ε1	PROPN
ejpam-5594	519	34	)	)	PUNCT
ejpam-5594	519	35	ς−1	ς−1	PROPN
ejpam-5594	519	36	b(ς)γ(ς	b(ς)γ(ς	NOUN
ejpam-5594	519	37	)	)	PUNCT
ejpam-5594	519	38	[	[	PUNCT
ejpam-5594	519	39	|φ′′(ε1)|+|φ′′(ε2)|	|φ′′(ε1)|+|φ′′(ε2)|	NOUN
ejpam-5594	519	40	]	]	PUNCT
ejpam-5594	519	41	.	.	PUNCT
ejpam-5594	520	1	theorem	theorem	ADJ
ejpam-5594	520	2	14	14	NUM
ejpam-5594	520	3	.	.	PUNCT
ejpam-5594	521	1	let	let	VERB
ejpam-5594	521	2	h	h	NOUN
ejpam-5594	521	3	:	:	PUNCT
ejpam-5594	521	4	(	(	PUNCT
ejpam-5594	521	5	0	0	NUM
ejpam-5594	521	6	,	,	PUNCT
ejpam-5594	521	7	1	1	NUM
ejpam-5594	521	8	)	)	PUNCT
ejpam-5594	521	9	→	→	NOUN
ejpam-5594	521	10	r+	r+	NOUN
ejpam-5594	521	11	and	and	CCONJ
ejpam-5594	521	12	h	h	NOUN
ejpam-5594	521	13	̸=	̸=	PROPN
ejpam-5594	521	14	0	0	NUM
ejpam-5594	521	15	.	.	PUNCT
ejpam-5594	522	1	let	let	VERB
ejpam-5594	522	2	φ	φ	NOUN
ejpam-5594	522	3	:	:	PUNCT
ejpam-5594	523	1	[	[	X
ejpam-5594	523	2	ε1	ε1	NOUN
ejpam-5594	523	3	,	,	PUNCT
ejpam-5594	523	4	ε2	ε2	PROPN
ejpam-5594	523	5	]	]	PUNCT
ejpam-5594	523	6	→	→	SYM
ejpam-5594	523	7	r+	r+	NOUN
ejpam-5594	523	8	i	i	PRON
ejpam-5594	523	9	is	be	AUX
ejpam-5594	523	10	cr	cr	PROPN
ejpam-5594	523	11	-	-	PUNCT
ejpam-5594	523	12	h	h	NOUN
ejpam-5594	523	13	-	-	PUNCT
ejpam-5594	523	14	godunovalevin	godunovalevin	ADJ
ejpam-5594	523	15	mapping	mapping	NOUN
ejpam-5594	523	16	,	,	PUNCT
ejpam-5594	523	17	ε1	ε1	PROPN
ejpam-5594	523	18	,	,	PUNCT
ejpam-5594	523	19	ε2	ε2	PROPN
ejpam-5594	523	20	∈	∈	PROPN
ejpam-5594	523	21	r+	r+	NOUN
ejpam-5594	523	22	,	,	PUNCT
ejpam-5594	523	23	ε1	ε1	VERB
ejpam-5594	523	24	<	<	X
ejpam-5594	523	25	ε2	ε2	PROPN
ejpam-5594	523	26	.	.	PUNCT
ejpam-5594	524	1	if	if	SCONJ
ejpam-5594	524	2	φ′′	φ′′	PROPN
ejpam-5594	524	3	∈	∈	PROPN
ejpam-5594	524	4	l[ε1	l[ε1	NOUN
ejpam-5594	524	5	,	,	PUNCT
ejpam-5594	524	6	ε2	ε2	PROPN
ejpam-5594	524	7	]	]	PUNCT
ejpam-5594	524	8	and	and	CCONJ
ejpam-5594	524	9	|φ′′|	|φ′′|	NOUN
ejpam-5594	524	10	is	be	AUX
ejpam-5594	524	11	also	also	ADV
ejpam-5594	524	12	cr	cr	NOUN
ejpam-5594	524	13	-	-	PUNCT
ejpam-5594	524	14	h	h	NOUN
ejpam-5594	524	15	-	-	PUNCT
ejpam-5594	524	16	godunovalevin	godunovalevin	ADJ
ejpam-5594	524	17	function	function	NOUN
ejpam-5594	524	18	,	,	PUNCT
ejpam-5594	524	19	then	then	ADV
ejpam-5594	524	20	the	the	DET
ejpam-5594	524	21	following	follow	VERB
ejpam-5594	524	22	double	double	ADJ
ejpam-5594	524	23	relation	relation	NOUN
ejpam-5594	524	24	holds	hold	VERB
ejpam-5594	524	25	true	true	ADJ
ejpam-5594	524	26	:	:	PUNCT
ejpam-5594	524	27	1	1	NUM
ejpam-5594	524	28	ε2	ε2	ADJ
ejpam-5594	524	29	−	−	PROPN
ejpam-5594	524	30	ε1	ε1	PROPN
ejpam-5594	524	31	[	[	PUNCT
ejpam-5594	524	32	abiςε2+ε1	abiςε2+ε1	PROPN
ejpam-5594	524	33	2	2	NUM
ejpam-5594	524	34	{	{	PUNCT
ejpam-5594	524	35	φ(ε1)}+	φ(ε1)}+	PROPN
ejpam-5594	524	36	ab	ab	PROPN
ejpam-5594	524	37	ε2+ε1	ε2+ε1	PROPN
ejpam-5594	524	38	2	2	NUM
ejpam-5594	524	39	iςε2{φ(ε2	iςε2{φ(ε2	NOUN
ejpam-5594	524	40	)	)	PUNCT
ejpam-5594	524	41	}	}	PUNCT
ejpam-5594	524	42	]	]	PUNCT
ejpam-5594	525	1	−	−	PROPN
ejpam-5594	525	2	1	1	NUM
ejpam-5594	525	3	(	(	PUNCT
ejpam-5594	525	4	ε2	ε2	ADJ
ejpam-5594	525	5	−	−	PROPN
ejpam-5594	525	6	ε1)b(ς	ε1)b(ς	PROPN
ejpam-5594	525	7	)	)	PUNCT
ejpam-5594	525	8	[	[	PUNCT
ejpam-5594	525	9	φ(ε1	φ(ε1	NOUN
ejpam-5594	525	10	)	)	PUNCT
ejpam-5594	525	11	+	+	SYM
ejpam-5594	525	12	φ(ε2	φ(ε2	NUM
ejpam-5594	525	13	)	)	PUNCT
ejpam-5594	525	14	]	]	PUNCT
ejpam-5594	526	1	−	−	PROPN
ejpam-5594	526	2	(	(	PUNCT
ejpam-5594	526	3	ε2	ε2	ADJ
ejpam-5594	526	4	−	−	PROPN
ejpam-5594	526	5	ε1	ε1	PROPN
ejpam-5594	526	6	)	)	PUNCT
ejpam-5594	526	7	ς−1	ς−1	PROPN
ejpam-5594	526	8	2ς−1b(ς)γ(ς	2ς−1b(ς)γ(ς	NUM
ejpam-5594	526	9	)	)	PUNCT
ejpam-5594	526	10	φ	φ	PROPN
ejpam-5594	526	11	(	(	PUNCT
ejpam-5594	526	12	ε2	ε2	PROPN
ejpam-5594	526	13	+	+	CCONJ
ejpam-5594	526	14	ε1	ε1	PROPN
ejpam-5594	526	15	2	2	NUM
ejpam-5594	526	16	)	)	PUNCT
ejpam-5594	526	17	⪯cr	⪯cr	NUM
ejpam-5594	526	18	(	(	PUNCT
ejpam-5594	526	19	ε2	ε2	ADJ
ejpam-5594	526	20	−	−	PROPN
ejpam-5594	526	21	ε1	ε1	PROPN
ejpam-5594	526	22	)	)	PUNCT
ejpam-5594	527	1	ς−1	ς−1	PROPN
ejpam-5594	527	2	(	(	PUNCT
ejpam-5594	527	3	ς	ς	PROPN
ejpam-5594	527	4	+	+	NOUN
ejpam-5594	527	5	1)b(ς)γ(ς	1)b(ς)γ(ς	NUM
ejpam-5594	527	6	)	)	PUNCT
ejpam-5594	527	7	(	(	PUNCT
ejpam-5594	527	8	(	(	PUNCT
ejpam-5594	527	9	1	1	NUM
ejpam-5594	527	10	2	2	NUM
ejpam-5594	527	11	)	)	PUNCT
ejpam-5594	527	12	ςp+2p	ςp+2p	PRON
ejpam-5594	527	13	ςp+	ςp+	NOUN
ejpam-5594	527	14	p+	p+	NOUN
ejpam-5594	527	15	1	1	NUM
ejpam-5594	527	16	)	)	PUNCT
ejpam-5594	527	17	1	1	NUM
ejpam-5594	527	18	p	p	NOUN
ejpam-5594	527	19	[	[	PUNCT
ejpam-5594	527	20	|φ′′(ε1)|+|φ′′(ε2)|	|φ′′(ε1)|+|φ′′(ε2)|	X
ejpam-5594	527	21	]	]	X
ejpam-5594	527	22	×	×	NOUN
ejpam-5594	528	1	[	[	X
ejpam-5594	528	2	(	(	PUNCT
ejpam-5594	528	3	∫	∫	PROPN
ejpam-5594	528	4	1	1	NUM
ejpam-5594	528	5	0	0	NUM
ejpam-5594	528	6	d	d	X
ejpam-5594	528	7	♭	♭	INTJ
ejpam-5594	528	8	h	h	PROPN
ejpam-5594	528	9	(	(	PUNCT
ejpam-5594	528	10	♭	♭	PROPN
ejpam-5594	528	11	)	)	PUNCT
ejpam-5594	528	12	)	)	PUNCT
ejpam-5594	528	13	1	1	NUM
ejpam-5594	528	14	q	q	NOUN
ejpam-5594	528	15	+	+	CCONJ
ejpam-5594	528	16	(	(	PUNCT
ejpam-5594	528	17	∫	∫	PROPN
ejpam-5594	528	18	1	1	NUM
ejpam-5594	528	19	0	0	NUM
ejpam-5594	528	20	d	d	X
ejpam-5594	528	21	♭	♭	PROPN
ejpam-5594	528	22	h(1−	h(1−	PROPN
ejpam-5594	528	23	♭	♭	PROPN
ejpam-5594	528	24	)	)	PUNCT
ejpam-5594	528	25	)	)	PUNCT
ejpam-5594	528	26	1	1	NUM
ejpam-5594	528	27	q	q	NOUN
ejpam-5594	528	28	]	]	PUNCT
ejpam-5594	528	29	,	,	PUNCT
ejpam-5594	528	30	(	(	PUNCT
ejpam-5594	528	31	18	18	NUM
ejpam-5594	528	32	)	)	PUNCT
ejpam-5594	528	33	j.	j.	PROPN
ejpam-5594	528	34	e.	e.	PROPN
ejpam-5594	528	35	maćıas	maćıas	PROPN
ejpam-5594	528	36	-	-	PUNCT
ejpam-5594	528	37	dı́az	dı́az	NOUN
ejpam-5594	528	38	et	et	NOUN
ejpam-5594	528	39	al	al	PROPN
ejpam-5594	528	40	.	.	PUNCT
ejpam-5594	528	41	/	/	SYM
ejpam-5594	528	42	eur	eur	PROPN
ejpam-5594	528	43	.	.	PUNCT
ejpam-5594	529	1	j.	j.	PROPN
ejpam-5594	529	2	pure	pure	PROPN
ejpam-5594	529	3	appl	appl	PROPN
ejpam-5594	529	4	.	.	PROPN
ejpam-5594	529	5	math	math	PROPN
ejpam-5594	529	6	,	,	PUNCT
ejpam-5594	529	7	17	17	NUM
ejpam-5594	529	8	(	(	PUNCT
ejpam-5594	529	9	4	4	NUM
ejpam-5594	529	10	)	)	PUNCT
ejpam-5594	529	11	(	(	PUNCT
ejpam-5594	529	12	2024	2024	NUM
ejpam-5594	529	13	)	)	PUNCT
ejpam-5594	529	14	,	,	PUNCT
ejpam-5594	529	15	4014	4014	NUM
ejpam-5594	529	16	-	-	SYM
ejpam-5594	529	17	4049	4049	NUM
ejpam-5594	529	18	4034	4034	NUM
ejpam-5594	529	19	where	where	SCONJ
ejpam-5594	529	20	ς	ς	PROPN
ejpam-5594	529	21	∈	∈	PROPN
ejpam-5594	529	22	(	(	PUNCT
ejpam-5594	529	23	0	0	NUM
ejpam-5594	529	24	,	,	PUNCT
ejpam-5594	529	25	1	1	NUM
ejpam-5594	529	26	]	]	PUNCT
ejpam-5594	529	27	,	,	PUNCT
ejpam-5594	529	28	1	1	NUM
ejpam-5594	529	29	p	p	NOUN
ejpam-5594	529	30	+	+	NOUN
ejpam-5594	529	31	1	1	NUM
ejpam-5594	529	32	q	q	NOUN
ejpam-5594	529	33	=	=	NOUN
ejpam-5594	529	34	1	1	X
ejpam-5594	529	35	.	.	PUNCT
ejpam-5594	530	1	proof	proof	NOUN
ejpam-5594	530	2	.	.	PUNCT
ejpam-5594	531	1	according	accord	VERB
ejpam-5594	531	2	to	to	ADP
ejpam-5594	531	3	lemma	lemma	PROPN
ejpam-5594	531	4	2.1	2.1	NUM
ejpam-5594	531	5	and	and	CCONJ
ejpam-5594	531	6	taking	take	VERB
ejpam-5594	531	7	into	into	ADP
ejpam-5594	531	8	account	account	NOUN
ejpam-5594	531	9	hölder	hölder	PROPN
ejpam-5594	531	10	’s	’s	PART
ejpam-5594	531	11	inequality	inequality	NOUN
ejpam-5594	531	12	and	and	CCONJ
ejpam-5594	531	13	apply	apply	VERB
ejpam-5594	531	14	it	it	PRON
ejpam-5594	531	15	to	to	ADP
ejpam-5594	531	16	relation	relation	NOUN
ejpam-5594	531	17	(	(	PUNCT
ejpam-5594	531	18	17	17	NUM
ejpam-5594	531	19	)	)	PUNCT
ejpam-5594	531	20	,	,	PUNCT
ejpam-5594	531	21	we	we	PRON
ejpam-5594	531	22	have	have	VERB
ejpam-5594	531	23	1	1	NUM
ejpam-5594	531	24	ε2	ε2	ADJ
ejpam-5594	531	25	−	−	PROPN
ejpam-5594	531	26	ε1	ε1	PROPN
ejpam-5594	531	27	[	[	PUNCT
ejpam-5594	531	28	abiςε2+ε1	abiςε2+ε1	PROPN
ejpam-5594	531	29	2	2	NUM
ejpam-5594	531	30	{	{	PUNCT
ejpam-5594	531	31	φ(ε1)}+	φ(ε1)}+	PROPN
ejpam-5594	531	32	ab	ab	PROPN
ejpam-5594	531	33	ε2+ε1	ε2+ε1	PROPN
ejpam-5594	531	34	2	2	NUM
ejpam-5594	531	35	iςε2{φ(ε2	iςε2{φ(ε2	NOUN
ejpam-5594	531	36	)	)	PUNCT
ejpam-5594	531	37	}	}	PUNCT
ejpam-5594	531	38	]	]	PUNCT
ejpam-5594	532	1	−	−	PROPN
ejpam-5594	532	2	1	1	NUM
ejpam-5594	532	3	(	(	PUNCT
ejpam-5594	532	4	ε2	ε2	ADJ
ejpam-5594	532	5	−	−	PROPN
ejpam-5594	532	6	ε1)b(ς	ε1)b(ς	PROPN
ejpam-5594	532	7	)	)	PUNCT
ejpam-5594	532	8	[	[	PUNCT
ejpam-5594	532	9	φ(ε1	φ(ε1	NOUN
ejpam-5594	532	10	)	)	PUNCT
ejpam-5594	532	11	+	+	SYM
ejpam-5594	532	12	φ(ε2	φ(ε2	NUM
ejpam-5594	532	13	)	)	PUNCT
ejpam-5594	532	14	]	]	PUNCT
ejpam-5594	533	1	−	−	PROPN
ejpam-5594	533	2	(	(	PUNCT
ejpam-5594	533	3	ε2	ε2	ADJ
ejpam-5594	533	4	−	−	PROPN
ejpam-5594	533	5	ε1	ε1	PROPN
ejpam-5594	533	6	)	)	PUNCT
ejpam-5594	533	7	ς−1	ς−1	PROPN
ejpam-5594	533	8	2ς−1b(ς)γ(ς	2ς−1b(ς)γ(ς	NUM
ejpam-5594	533	9	)	)	PUNCT
ejpam-5594	533	10	φ	φ	PROPN
ejpam-5594	533	11	(	(	PUNCT
ejpam-5594	533	12	ε2	ε2	PROPN
ejpam-5594	533	13	+	+	CCONJ
ejpam-5594	533	14	ε1	ε1	PROPN
ejpam-5594	533	15	2	2	NUM
ejpam-5594	533	16	)	)	PUNCT
ejpam-5594	533	17	⪯cr	⪯cr	NUM
ejpam-5594	533	18	(	(	PUNCT
ejpam-5594	533	19	ε2	ε2	ADJ
ejpam-5594	533	20	−	−	PROPN
ejpam-5594	533	21	ε1	ε1	PROPN
ejpam-5594	533	22	)	)	PUNCT
ejpam-5594	534	1	ς−1	ς−1	PROPN
ejpam-5594	534	2	2(ς	2(ς	NUM
ejpam-5594	534	3	+	+	CCONJ
ejpam-5594	534	4	1)b(ς)γ(ς	1)b(ς)γ(ς	NUM
ejpam-5594	534	5	)	)	PUNCT
ejpam-5594	534	6	(	(	PUNCT
ejpam-5594	534	7	∫	∫	PROPN
ejpam-5594	534	8	1	1	NUM
ejpam-5594	534	9	0	0	NUM
ejpam-5594	534	10	|wς(	|wς(	NUM
ejpam-5594	534	11	♭	♭	SYM
ejpam-5594	534	12	)|pd	)|pd	SYM
ejpam-5594	534	13	♭	♭	PROPN
ejpam-5594	534	14	)	)	PUNCT
ejpam-5594	534	15	1	1	NUM
ejpam-5594	535	1	p	p	NOUN
ejpam-5594	535	2	[	[	X
ejpam-5594	535	3	(	(	PUNCT
ejpam-5594	535	4	∫	∫	PROPN
ejpam-5594	535	5	1	1	NUM
ejpam-5594	535	6	0	0	NUM
ejpam-5594	535	7	|φ′′(	|φ′′(	NOUN
ejpam-5594	535	8	♭	♭	PRON
ejpam-5594	535	9	ε1	ε1	VERB
ejpam-5594	535	10	+	+	CCONJ
ejpam-5594	535	11	(	(	PUNCT
ejpam-5594	535	12	1−	1−	NUM
ejpam-5594	535	13	♭	♭	INTJ
ejpam-5594	535	14	)	)	PUNCT
ejpam-5594	535	15	ε2)|qd	ε2)|qd	NOUN
ejpam-5594	535	16	♭	♭	PROPN
ejpam-5594	535	17	)	)	PUNCT
ejpam-5594	535	18	1	1	NUM
ejpam-5594	535	19	q	q	NOUN
ejpam-5594	536	1	+	+	CCONJ
ejpam-5594	536	2	(	(	PUNCT
ejpam-5594	536	3	∫	∫	PROPN
ejpam-5594	536	4	1	1	NUM
ejpam-5594	536	5	0	0	NUM
ejpam-5594	536	6	|φ′′(	|φ′′(	NOUN
ejpam-5594	536	7	♭	♭	NOUN
ejpam-5594	536	8	ε2	ε2	NOUN
ejpam-5594	536	9	+	+	CCONJ
ejpam-5594	536	10	(	(	PUNCT
ejpam-5594	536	11	1−	1−	NUM
ejpam-5594	536	12	♭	♭	INTJ
ejpam-5594	536	13	)	)	PUNCT
ejpam-5594	536	14	ε1)|qd	ε1)|qd	PROPN
ejpam-5594	536	15	♭	♭	PROPN
ejpam-5594	536	16	)	)	PUNCT
ejpam-5594	536	17	1	1	NUM
ejpam-5594	536	18	q	q	NOUN
ejpam-5594	536	19	]	]	PUNCT
ejpam-5594	536	20	.	.	PUNCT
ejpam-5594	537	1	(	(	PUNCT
ejpam-5594	537	2	19	19	NUM
ejpam-5594	537	3	)	)	PUNCT
ejpam-5594	537	4	as	as	SCONJ
ejpam-5594	537	5	|φ′′|q	|φ′′|q	NOUN
ejpam-5594	537	6	is	be	AUX
ejpam-5594	537	7	an	an	DET
ejpam-5594	537	8	cr	cr	NOUN
ejpam-5594	537	9	-	-	PUNCT
ejpam-5594	537	10	h	h	NOUN
ejpam-5594	537	11	-	-	PUNCT
ejpam-5594	537	12	godunova	godunova	ADJ
ejpam-5594	537	13	-	-	PUNCT
ejpam-5594	537	14	levin	levin	PROPN
ejpam-5594	537	15	mapping	mapping	PROPN
ejpam-5594	537	16	,	,	PUNCT
ejpam-5594	537	17	we	we	PRON
ejpam-5594	537	18	have	have	VERB
ejpam-5594	537	19	1	1	NUM
ejpam-5594	537	20	ε2	ε2	ADJ
ejpam-5594	537	21	−	−	PROPN
ejpam-5594	537	22	ε1	ε1	PROPN
ejpam-5594	537	23	[	[	PUNCT
ejpam-5594	537	24	abiςε2+ε1	abiςε2+ε1	PROPN
ejpam-5594	537	25	2	2	NUM
ejpam-5594	537	26	{	{	PUNCT
ejpam-5594	537	27	φ(ε1)}+	φ(ε1)}+	PROPN
ejpam-5594	537	28	ab	ab	PROPN
ejpam-5594	537	29	ε2+ε1	ε2+ε1	PROPN
ejpam-5594	537	30	2	2	NUM
ejpam-5594	537	31	iςε2{φ(ε2	iςε2{φ(ε2	NOUN
ejpam-5594	537	32	)	)	PUNCT
ejpam-5594	537	33	}	}	PUNCT
ejpam-5594	537	34	]	]	PUNCT
ejpam-5594	538	1	−	−	PROPN
ejpam-5594	538	2	1	1	NUM
ejpam-5594	538	3	(	(	PUNCT
ejpam-5594	538	4	ε2	ε2	ADJ
ejpam-5594	538	5	−	−	PROPN
ejpam-5594	538	6	ε1)b(ς	ε1)b(ς	PROPN
ejpam-5594	538	7	)	)	PUNCT
ejpam-5594	538	8	[	[	PUNCT
ejpam-5594	538	9	φ(ε1	φ(ε1	NOUN
ejpam-5594	538	10	)	)	PUNCT
ejpam-5594	538	11	+	+	SYM
ejpam-5594	538	12	φ(ε2	φ(ε2	NUM
ejpam-5594	538	13	)	)	PUNCT
ejpam-5594	538	14	]	]	PUNCT
ejpam-5594	539	1	−	−	PROPN
ejpam-5594	539	2	(	(	PUNCT
ejpam-5594	539	3	ε2	ε2	ADJ
ejpam-5594	539	4	−	−	PROPN
ejpam-5594	539	5	ε1	ε1	PROPN
ejpam-5594	539	6	)	)	PUNCT
ejpam-5594	539	7	ς−1	ς−1	PROPN
ejpam-5594	539	8	2ς−1b(ς)γ(ς	2ς−1b(ς)γ(ς	NUM
ejpam-5594	539	9	)	)	PUNCT
ejpam-5594	539	10	φ	φ	PROPN
ejpam-5594	539	11	(	(	PUNCT
ejpam-5594	539	12	ε2	ε2	PROPN
ejpam-5594	539	13	+	+	CCONJ
ejpam-5594	539	14	ε1	ε1	PROPN
ejpam-5594	539	15	2	2	NUM
ejpam-5594	539	16	)	)	PUNCT
ejpam-5594	539	17	⪯cr	⪯cr	NUM
ejpam-5594	539	18	(	(	PUNCT
ejpam-5594	539	19	ε2	ε2	ADJ
ejpam-5594	539	20	−	−	PROPN
ejpam-5594	539	21	ε1	ε1	PROPN
ejpam-5594	539	22	)	)	PUNCT
ejpam-5594	540	1	ς−1	ς−1	PROPN
ejpam-5594	540	2	(	(	PUNCT
ejpam-5594	540	3	ς	ς	PROPN
ejpam-5594	540	4	+	+	NOUN
ejpam-5594	540	5	1)b(ς)γ(ς	1)b(ς)γ(ς	NUM
ejpam-5594	540	6	)	)	PUNCT
ejpam-5594	540	7	(	(	PUNCT
ejpam-5594	540	8	(	(	PUNCT
ejpam-5594	540	9	1	1	NUM
ejpam-5594	540	10	2	2	NUM
ejpam-5594	540	11	)	)	PUNCT
ejpam-5594	540	12	ςp+2p	ςp+2p	PRON
ejpam-5594	540	13	ςp+	ςp+	NOUN
ejpam-5594	540	14	p+	p+	NOUN
ejpam-5594	540	15	1	1	NUM
ejpam-5594	540	16	)	)	PUNCT
ejpam-5594	540	17	1	1	NUM
ejpam-5594	540	18	p	p	NOUN
ejpam-5594	540	19	×	×	NOUN
ejpam-5594	540	20	{	{	PUNCT
ejpam-5594	541	1	[	[	X
ejpam-5594	541	2	∫	∫	PROPN
ejpam-5594	541	3	1	1	NUM
ejpam-5594	541	4	0	0	NUM
ejpam-5594	541	5	(	(	PUNCT
ejpam-5594	541	6	|φ′′(ε1)|q	|φ′′(ε1)|q	NOUN
ejpam-5594	541	7	h	h	NOUN
ejpam-5594	541	8	(	(	PUNCT
ejpam-5594	541	9	♭	♭	PROPN
ejpam-5594	541	10	)	)	PUNCT
ejpam-5594	542	1	+	+	CCONJ
ejpam-5594	542	2	|φ′′(ε2)|q	|φ′′(ε2)|q	PRON
ejpam-5594	542	3	h(1−	h(1−	PROPN
ejpam-5594	542	4	♭	♭	PROPN
ejpam-5594	542	5	)	)	PUNCT
ejpam-5594	542	6	)	)	PUNCT
ejpam-5594	543	1	d	d	X
ejpam-5594	543	2	♭	♭	X
ejpam-5594	543	3	]	]	PUNCT
ejpam-5594	543	4	1	1	NUM
ejpam-5594	543	5	q	q	NOUN
ejpam-5594	544	1	+	+	CCONJ
ejpam-5594	545	1	[	[	X
ejpam-5594	545	2	∫	∫	X
ejpam-5594	545	3	1	1	NUM
ejpam-5594	545	4	0	0	NUM
ejpam-5594	545	5	(	(	PUNCT
ejpam-5594	545	6	|φ′′(ε2)|q	|φ′′(ε2)|q	NOUN
ejpam-5594	545	7	h	h	NOUN
ejpam-5594	545	8	(	(	PUNCT
ejpam-5594	545	9	♭	♭	INTJ
ejpam-5594	545	10	)	)	PUNCT
ejpam-5594	545	11	+	+	NUM
ejpam-5594	545	12	|φ′′(ε1)|q	|φ′′(ε1)|q	X
ejpam-5594	545	13	h(1−	h(1−	PROPN
ejpam-5594	545	14	♭	♭	PROPN
ejpam-5594	545	15	)	)	PUNCT
ejpam-5594	545	16	)	)	PUNCT
ejpam-5594	546	1	d	d	X
ejpam-5594	546	2	♭	♭	X
ejpam-5594	546	3	]	]	PUNCT
ejpam-5594	546	4	1	1	NUM
ejpam-5594	546	5	q	q	NOUN
ejpam-5594	546	6	}	}	PUNCT
ejpam-5594	546	7	.	.	PUNCT
ejpam-5594	547	1	then	then	ADV
ejpam-5594	547	2	,	,	PUNCT
ejpam-5594	547	3	we	we	PRON
ejpam-5594	547	4	apply	apply	VERB
ejpam-5594	547	5	the	the	DET
ejpam-5594	547	6	fact	fact	NOUN
ejpam-5594	547	7	that	that	SCONJ
ejpam-5594	547	8	ε2∑	ε2∑	PROPN
ejpam-5594	547	9	k=1	k=1	PROPN
ejpam-5594	547	10	(	(	PUNCT
ejpam-5594	547	11	uk	uk	PROPN
ejpam-5594	547	12	+	+	CCONJ
ejpam-5594	547	13	vk	vk	PROPN
ejpam-5594	547	14	)	)	PUNCT
ejpam-5594	547	15	ε1	ε1	VERB
ejpam-5594	547	16	≤	≤	NOUN
ejpam-5594	547	17	ε2∑	ε2∑	PROPN
ejpam-5594	548	1	k=1	k=1	PROPN
ejpam-5594	549	1	uk	uk	PROPN
ejpam-5594	549	2	ε1	ε1	VERB
ejpam-5594	549	3	+	+	CCONJ
ejpam-5594	549	4	ε2∑	ε2∑	PROPN
ejpam-5594	549	5	k=1	k=1	PROPN
ejpam-5594	549	6	vk	vk	PROPN
ejpam-5594	549	7	ε1	ε1	PROPN
ejpam-5594	549	8	,	,	PUNCT
ejpam-5594	549	9	for	for	ADP
ejpam-5594	549	10	0	0	NUM
ejpam-5594	549	11	<	<	X
ejpam-5594	549	12	ε1	ε1	VERB
ejpam-5594	549	13	<	<	X
ejpam-5594	549	14	1	1	NUM
ejpam-5594	549	15	,	,	PUNCT
ejpam-5594	549	16	u1	u1	NOUN
ejpam-5594	549	17	,	,	PUNCT
ejpam-5594	549	18	u2	u2	NOUN
ejpam-5594	549	19	,	,	PUNCT
ejpam-5594	549	20	·	·	PUNCT
ejpam-5594	549	21	·	·	PUNCT
ejpam-5594	549	22	·	·	PUNCT
ejpam-5594	549	23	,	,	PUNCT
ejpam-5594	549	24	uε2	uε2	VERB
ejpam-5594	549	25	≥	≥	NUM
ejpam-5594	549	26	0	0	NUM
ejpam-5594	549	27	,	,	PUNCT
ejpam-5594	549	28	v1	v1	NOUN
ejpam-5594	549	29	,	,	PUNCT
ejpam-5594	549	30	v2	v2	PROPN
ejpam-5594	549	31	,	,	PUNCT
ejpam-5594	549	32	·	·	PUNCT
ejpam-5594	549	33	·	·	PUNCT
ejpam-5594	549	34	·	·	PUNCT
ejpam-5594	549	35	,	,	PUNCT
ejpam-5594	549	36	vε2	vε2	X
ejpam-5594	549	37	≥	≥	NOUN
ejpam-5594	549	38	0	0	NUM
ejpam-5594	549	39	.	.	PUNCT
ejpam-5594	550	1	this	this	PRON
ejpam-5594	550	2	further	far	ADV
ejpam-5594	550	3	implies	imply	VERB
ejpam-5594	550	4	as	as	SCONJ
ejpam-5594	550	5	follows	follow	VERB
ejpam-5594	550	6	:	:	PUNCT
ejpam-5594	550	7	1	1	NUM
ejpam-5594	550	8	ε2	ε2	ADJ
ejpam-5594	550	9	−	−	PROPN
ejpam-5594	550	10	ε1	ε1	PROPN
ejpam-5594	550	11	[	[	PUNCT
ejpam-5594	550	12	abiςε2+ε1	abiςε2+ε1	PROPN
ejpam-5594	550	13	2	2	NUM
ejpam-5594	550	14	{	{	PUNCT
ejpam-5594	550	15	φ(ε1)}+	φ(ε1)}+	PROPN
ejpam-5594	550	16	ab	ab	PROPN
ejpam-5594	550	17	ε2+ε1	ε2+ε1	PROPN
ejpam-5594	550	18	2	2	NUM
ejpam-5594	550	19	iςε2{φ(ε2	iςε2{φ(ε2	NOUN
ejpam-5594	550	20	)	)	PUNCT
ejpam-5594	550	21	}	}	PUNCT
ejpam-5594	550	22	]	]	PUNCT
ejpam-5594	551	1	−	−	PROPN
ejpam-5594	551	2	1	1	NUM
ejpam-5594	551	3	(	(	PUNCT
ejpam-5594	551	4	ε2	ε2	ADJ
ejpam-5594	551	5	−	−	PROPN
ejpam-5594	551	6	ε1)b(ς	ε1)b(ς	PROPN
ejpam-5594	551	7	)	)	PUNCT
ejpam-5594	551	8	[	[	PUNCT
ejpam-5594	551	9	φ(ε1	φ(ε1	NOUN
ejpam-5594	551	10	)	)	PUNCT
ejpam-5594	551	11	+	+	SYM
ejpam-5594	551	12	φ(ε2	φ(ε2	NUM
ejpam-5594	551	13	)	)	PUNCT
ejpam-5594	551	14	]	]	PUNCT
ejpam-5594	552	1	−	−	PROPN
ejpam-5594	552	2	(	(	PUNCT
ejpam-5594	552	3	ε2	ε2	ADJ
ejpam-5594	552	4	−	−	PROPN
ejpam-5594	552	5	ε1	ε1	PROPN
ejpam-5594	552	6	)	)	PUNCT
ejpam-5594	552	7	ς−1	ς−1	PROPN
ejpam-5594	552	8	2ς−1b(ς)γ(ς	2ς−1b(ς)γ(ς	NUM
ejpam-5594	552	9	)	)	PUNCT
ejpam-5594	552	10	φ	φ	PROPN
ejpam-5594	552	11	(	(	PUNCT
ejpam-5594	552	12	ε2	ε2	PROPN
ejpam-5594	552	13	+	+	CCONJ
ejpam-5594	552	14	ε1	ε1	PROPN
ejpam-5594	552	15	2	2	NUM
ejpam-5594	552	16	)	)	PUNCT
ejpam-5594	552	17	⪯cr	⪯cr	NUM
ejpam-5594	552	18	(	(	PUNCT
ejpam-5594	552	19	ε2	ε2	ADJ
ejpam-5594	552	20	−	−	PROPN
ejpam-5594	552	21	ε1	ε1	PROPN
ejpam-5594	552	22	)	)	PUNCT
ejpam-5594	553	1	ς−1	ς−1	PROPN
ejpam-5594	553	2	(	(	PUNCT
ejpam-5594	553	3	ς	ς	PROPN
ejpam-5594	553	4	+	+	NOUN
ejpam-5594	553	5	1)b(ς)γ(ς	1)b(ς)γ(ς	NUM
ejpam-5594	553	6	)	)	PUNCT
ejpam-5594	553	7	(	(	PUNCT
ejpam-5594	553	8	(	(	PUNCT
ejpam-5594	553	9	1	1	NUM
ejpam-5594	553	10	2	2	NUM
ejpam-5594	553	11	)	)	PUNCT
ejpam-5594	553	12	ςp+2p	ςp+2p	PRON
ejpam-5594	553	13	ςp+	ςp+	NOUN
ejpam-5594	553	14	p+	p+	NOUN
ejpam-5594	553	15	1	1	NUM
ejpam-5594	553	16	)	)	PUNCT
ejpam-5594	553	17	1	1	NUM
ejpam-5594	554	1	p	p	PROPN
ejpam-5594	554	2	j.	j.	PROPN
ejpam-5594	554	3	e.	e.	PROPN
ejpam-5594	554	4	maćıas	maćıas	PROPN
ejpam-5594	554	5	-	-	PUNCT
ejpam-5594	554	6	dı́az	dı́az	NOUN
ejpam-5594	554	7	et	et	NOUN
ejpam-5594	554	8	al	al	PROPN
ejpam-5594	554	9	.	.	PUNCT
ejpam-5594	554	10	/	/	SYM
ejpam-5594	554	11	eur	eur	PROPN
ejpam-5594	554	12	.	.	PUNCT
ejpam-5594	555	1	j.	j.	PROPN
ejpam-5594	555	2	pure	pure	PROPN
ejpam-5594	555	3	appl	appl	PROPN
ejpam-5594	555	4	.	.	PROPN
ejpam-5594	555	5	math	math	PROPN
ejpam-5594	555	6	,	,	PUNCT
ejpam-5594	555	7	17	17	NUM
ejpam-5594	555	8	(	(	PUNCT
ejpam-5594	555	9	4	4	NUM
ejpam-5594	555	10	)	)	PUNCT
ejpam-5594	555	11	(	(	PUNCT
ejpam-5594	555	12	2024	2024	NUM
ejpam-5594	555	13	)	)	PUNCT
ejpam-5594	555	14	,	,	PUNCT
ejpam-5594	555	15	4014	4014	NUM
ejpam-5594	555	16	-	-	SYM
ejpam-5594	555	17	4049	4049	NUM
ejpam-5594	555	18	4035	4035	NUM
ejpam-5594	555	19	×	×	NOUN
ejpam-5594	556	1	[	[	X
ejpam-5594	556	2	(	(	PUNCT
ejpam-5594	556	3	∫	∫	PROPN
ejpam-5594	556	4	1	1	NUM
ejpam-5594	556	5	0	0	NUM
ejpam-5594	556	6	|φ′′(ε1)|q	|φ′′(ε1)|q	PROPN
ejpam-5594	556	7	h	h	NOUN
ejpam-5594	556	8	(	(	PUNCT
ejpam-5594	556	9	♭	♭	INTJ
ejpam-5594	556	10	)	)	PUNCT
ejpam-5594	556	11	d	d	NOUN
ejpam-5594	556	12	♭	♭	PROPN
ejpam-5594	556	13	)	)	PUNCT
ejpam-5594	556	14	1	1	NUM
ejpam-5594	556	15	q	q	NOUN
ejpam-5594	556	16	+	+	CCONJ
ejpam-5594	556	17	(	(	PUNCT
ejpam-5594	556	18	∫	∫	PROPN
ejpam-5594	556	19	1	1	NUM
ejpam-5594	556	20	0	0	NUM
ejpam-5594	556	21	|φ′′(ε2)|q	|φ′′(ε2)|q	PRON
ejpam-5594	556	22	h(1−	h(1−	PROPN
ejpam-5594	556	23	♭	♭	INTJ
ejpam-5594	556	24	)	)	PUNCT
ejpam-5594	556	25	d	d	X
ejpam-5594	556	26	♭	♭	PROPN
ejpam-5594	556	27	)	)	PUNCT
ejpam-5594	556	28	1	1	NUM
ejpam-5594	556	29	q	q	NOUN
ejpam-5594	557	1	+	+	CCONJ
ejpam-5594	557	2	(	(	PUNCT
ejpam-5594	557	3	∫	∫	PROPN
ejpam-5594	557	4	1	1	NUM
ejpam-5594	557	5	0	0	NUM
ejpam-5594	557	6	|φ′′(ε2)|q	|φ′′(ε2)|q	PRON
ejpam-5594	557	7	h	h	NOUN
ejpam-5594	557	8	(	(	PUNCT
ejpam-5594	557	9	♭	♭	INTJ
ejpam-5594	557	10	)	)	PUNCT
ejpam-5594	557	11	d	d	NOUN
ejpam-5594	557	12	♭	♭	PROPN
ejpam-5594	557	13	)	)	PUNCT
ejpam-5594	557	14	1	1	NUM
ejpam-5594	557	15	q	q	NOUN
ejpam-5594	557	16	+	+	CCONJ
ejpam-5594	557	17	(	(	PUNCT
ejpam-5594	557	18	∫	∫	PROPN
ejpam-5594	557	19	1	1	NUM
ejpam-5594	557	20	0	0	NUM
ejpam-5594	557	21	|φ′′(ε1)|q	|φ′′(ε1)|q	NOUN
ejpam-5594	557	22	h(1−	h(1−	PROPN
ejpam-5594	557	23	♭	♭	INTJ
ejpam-5594	557	24	)	)	PUNCT
ejpam-5594	558	1	d	d	X
ejpam-5594	558	2	♭	♭	PROPN
ejpam-5594	558	3	)	)	PUNCT
ejpam-5594	558	4	1	1	NUM
ejpam-5594	558	5	q	q	NOUN
ejpam-5594	558	6	]	]	X
ejpam-5594	558	7	=	=	SYM
ejpam-5594	558	8	(	(	PUNCT
ejpam-5594	558	9	ε2	ε2	PROPN
ejpam-5594	558	10	−	−	PROPN
ejpam-5594	558	11	ε1	ε1	PROPN
ejpam-5594	558	12	)	)	PUNCT
ejpam-5594	558	13	ς−1	ς−1	PROPN
ejpam-5594	558	14	(	(	PUNCT
ejpam-5594	558	15	ς	ς	PROPN
ejpam-5594	558	16	+	+	NOUN
ejpam-5594	558	17	1)b(ς)γ(ς	1)b(ς)γ(ς	NUM
ejpam-5594	558	18	)	)	PUNCT
ejpam-5594	558	19	(	(	PUNCT
ejpam-5594	558	20	(	(	PUNCT
ejpam-5594	558	21	1	1	NUM
ejpam-5594	558	22	2	2	NUM
ejpam-5594	558	23	)	)	PUNCT
ejpam-5594	558	24	ςp+2p	ςp+2p	PRON
ejpam-5594	558	25	ςp+	ςp+	NOUN
ejpam-5594	558	26	p+	p+	NOUN
ejpam-5594	558	27	1	1	NUM
ejpam-5594	558	28	)	)	PUNCT
ejpam-5594	558	29	1	1	NUM
ejpam-5594	558	30	p	p	NOUN
ejpam-5594	558	31	[	[	PUNCT
ejpam-5594	558	32	|φ′′(ε1)|+|φ′′(ε2)|	|φ′′(ε1)|+|φ′′(ε2)|	X
ejpam-5594	558	33	]	]	X
ejpam-5594	558	34	×	×	NOUN
ejpam-5594	559	1	[	[	X
ejpam-5594	559	2	(	(	PUNCT
ejpam-5594	559	3	∫	∫	PROPN
ejpam-5594	559	4	1	1	NUM
ejpam-5594	559	5	0	0	NUM
ejpam-5594	559	6	d	d	X
ejpam-5594	559	7	♭	♭	INTJ
ejpam-5594	559	8	h	h	PROPN
ejpam-5594	559	9	(	(	PUNCT
ejpam-5594	559	10	♭	♭	PROPN
ejpam-5594	559	11	)	)	PUNCT
ejpam-5594	559	12	)	)	PUNCT
ejpam-5594	559	13	1	1	NUM
ejpam-5594	559	14	q	q	NOUN
ejpam-5594	559	15	+	+	CCONJ
ejpam-5594	559	16	(	(	PUNCT
ejpam-5594	559	17	∫	∫	PROPN
ejpam-5594	559	18	1	1	NUM
ejpam-5594	559	19	0	0	NUM
ejpam-5594	559	20	d	d	X
ejpam-5594	559	21	♭	♭	PROPN
ejpam-5594	559	22	h(1−	h(1−	PROPN
ejpam-5594	559	23	♭	♭	PROPN
ejpam-5594	559	24	)	)	PUNCT
ejpam-5594	559	25	)	)	PUNCT
ejpam-5594	559	26	1	1	NUM
ejpam-5594	559	27	q	q	NOUN
ejpam-5594	559	28	]	]	PUNCT
ejpam-5594	559	29	.	.	PUNCT
ejpam-5594	560	1	the	the	DET
ejpam-5594	560	2	finishes	finish	VERB
ejpam-5594	560	3	the	the	DET
ejpam-5594	560	4	proof	proof	NOUN
ejpam-5594	560	5	.	.	PUNCT
ejpam-5594	561	1	remark	remark	VERB
ejpam-5594	561	2	6	6	NUM
ejpam-5594	561	3	.	.	PUNCT
ejpam-5594	562	1	(	(	PUNCT
ejpam-5594	562	2	i	i	NOUN
ejpam-5594	562	3	)	)	PUNCT
ejpam-5594	562	4	if	if	SCONJ
ejpam-5594	562	5	h	h	X
ejpam-5594	562	6	(	(	PUNCT
ejpam-5594	562	7	♭	♭	INTJ
ejpam-5594	562	8	)	)	PUNCT
ejpam-5594	563	1	=	=	SYM
ejpam-5594	563	2	1	1	NUM
ejpam-5594	563	3	♭	♭	NOUN
ejpam-5594	563	4	s	s	PART
ejpam-5594	563	5	,	,	PUNCT
ejpam-5594	563	6	then	then	ADV
ejpam-5594	563	7	theorem	theorem	VERB
ejpam-5594	563	8	14	14	NUM
ejpam-5594	563	9	yields	yield	NOUN
ejpam-5594	563	10	an	an	DET
ejpam-5594	563	11	outcome	outcome	NOUN
ejpam-5594	563	12	for	for	ADP
ejpam-5594	563	13	the	the	DET
ejpam-5594	563	14	cr	cr	PROPN
ejpam-5594	563	15	-	-	PUNCT
ejpam-5594	563	16	s	s	NOUN
ejpam-5594	563	17	-	-	PUNCT
ejpam-5594	563	18	convex	convex	ADJ
ejpam-5594	563	19	function	function	NOUN
ejpam-5594	563	20	for	for	ADP
ejpam-5594	563	21	ab	ab	PROPN
ejpam-5594	563	22	integral	integral	ADJ
ejpam-5594	563	23	operators	operator	NOUN
ejpam-5594	563	24	:	:	PUNCT
ejpam-5594	563	25	1	1	NUM
ejpam-5594	563	26	ε2	ε2	ADJ
ejpam-5594	563	27	−	−	PROPN
ejpam-5594	563	28	ε1	ε1	PROPN
ejpam-5594	563	29	[	[	PUNCT
ejpam-5594	563	30	abiςε2+ε1	abiςε2+ε1	PROPN
ejpam-5594	563	31	2	2	NUM
ejpam-5594	563	32	{	{	PUNCT
ejpam-5594	563	33	φ(ε1)}+	φ(ε1)}+	PROPN
ejpam-5594	563	34	ab	ab	PROPN
ejpam-5594	563	35	ε2+ε1	ε2+ε1	PROPN
ejpam-5594	563	36	2	2	NUM
ejpam-5594	563	37	iςε2{φ(ε2	iςε2{φ(ε2	NOUN
ejpam-5594	563	38	)	)	PUNCT
ejpam-5594	563	39	}	}	PUNCT
ejpam-5594	563	40	]	]	PUNCT
ejpam-5594	564	1	−	−	PROPN
ejpam-5594	564	2	1	1	NUM
ejpam-5594	564	3	(	(	PUNCT
ejpam-5594	564	4	ε2	ε2	ADJ
ejpam-5594	564	5	−	−	PROPN
ejpam-5594	564	6	ε1)b(ς	ε1)b(ς	PROPN
ejpam-5594	564	7	)	)	PUNCT
ejpam-5594	564	8	[	[	PUNCT
ejpam-5594	564	9	φ(ε1	φ(ε1	NOUN
ejpam-5594	564	10	)	)	PUNCT
ejpam-5594	564	11	+	+	SYM
ejpam-5594	564	12	φ(ε2	φ(ε2	NUM
ejpam-5594	564	13	)	)	PUNCT
ejpam-5594	564	14	]	]	PUNCT
ejpam-5594	565	1	−	−	PROPN
ejpam-5594	565	2	(	(	PUNCT
ejpam-5594	565	3	ε2	ε2	ADJ
ejpam-5594	565	4	−	−	PROPN
ejpam-5594	565	5	ε1	ε1	PROPN
ejpam-5594	565	6	)	)	PUNCT
ejpam-5594	565	7	ς−1	ς−1	PROPN
ejpam-5594	565	8	2ς−1b(ς)γ(ς	2ς−1b(ς)γ(ς	NUM
ejpam-5594	565	9	)	)	PUNCT
ejpam-5594	565	10	φ	φ	PROPN
ejpam-5594	565	11	(	(	PUNCT
ejpam-5594	565	12	ε2	ε2	PROPN
ejpam-5594	565	13	+	+	CCONJ
ejpam-5594	565	14	ε1	ε1	PROPN
ejpam-5594	565	15	2	2	NUM
ejpam-5594	565	16	)	)	PUNCT
ejpam-5594	565	17	⪯cr	⪯cr	NUM
ejpam-5594	565	18	(	(	PUNCT
ejpam-5594	565	19	ε2	ε2	ADJ
ejpam-5594	565	20	−	−	PROPN
ejpam-5594	565	21	ε1	ε1	PROPN
ejpam-5594	565	22	)	)	PUNCT
ejpam-5594	566	1	ς−1	ς−1	PROPN
ejpam-5594	566	2	(	(	PUNCT
ejpam-5594	566	3	ς	ς	PROPN
ejpam-5594	566	4	+	+	NOUN
ejpam-5594	566	5	1)b(ς)γ(ς	1)b(ς)γ(ς	NUM
ejpam-5594	566	6	)	)	PUNCT
ejpam-5594	566	7	(	(	PUNCT
ejpam-5594	566	8	(	(	PUNCT
ejpam-5594	566	9	1	1	NUM
ejpam-5594	566	10	2	2	NUM
ejpam-5594	566	11	)	)	PUNCT
ejpam-5594	566	12	ς+1	ς+1	NUM
ejpam-5594	566	13	ς	ς	PROPN
ejpam-5594	567	1	+	+	CCONJ
ejpam-5594	567	2	2	2	NUM
ejpam-5594	567	3	)	)	PUNCT
ejpam-5594	567	4	1	1	NUM
ejpam-5594	567	5	p	p	NOUN
ejpam-5594	567	6	[	[	PUNCT
ejpam-5594	567	7	|φ′′(ε1)|q+|φ′′(ε2)|q	|φ′′(ε1)|q+|φ′′(ε2)|q	NOUN
ejpam-5594	567	8	]	]	PUNCT
ejpam-5594	567	9	1	1	NUM
ejpam-5594	567	10	q	q	NOUN
ejpam-5594	567	11	×	×	NOUN
ejpam-5594	568	1	[	[	X
ejpam-5594	568	2	(	(	PUNCT
ejpam-5594	568	3	1	1	NUM
ejpam-5594	568	4	2	2	NUM
ejpam-5594	568	5	)	)	PUNCT
ejpam-5594	568	6	ς+s+2	ς+s+2	PROPN
ejpam-5594	568	7	ς	ς	PROPN
ejpam-5594	568	8	+	+	NUM
ejpam-5594	568	9	s+2	s+2	NUM
ejpam-5594	568	10	+	+	CCONJ
ejpam-5594	568	11	β	β	NOUN
ejpam-5594	568	12	1	1	NUM
ejpam-5594	568	13	2	2	NUM
ejpam-5594	568	14	(	(	PUNCT
ejpam-5594	568	15	ς	ς	PROPN
ejpam-5594	568	16	+	+	PROPN
ejpam-5594	568	17	2	2	NUM
ejpam-5594	568	18	,	,	PUNCT
ejpam-5594	568	19	s+1	s+1	NOUN
ejpam-5594	568	20	)	)	PUNCT
ejpam-5594	568	21	]	]	PUNCT
ejpam-5594	568	22	1	1	NUM
ejpam-5594	568	23	q	q	NOUN
ejpam-5594	568	24	.	.	PUNCT
ejpam-5594	569	1	(	(	PUNCT
ejpam-5594	569	2	20	20	NUM
ejpam-5594	569	3	)	)	PUNCT
ejpam-5594	569	4	(	(	PUNCT
ejpam-5594	569	5	ii	ii	NOUN
ejpam-5594	569	6	)	)	PUNCT
ejpam-5594	569	7	if	if	SCONJ
ejpam-5594	569	8	h	h	PROPN
ejpam-5594	569	9	(	(	PUNCT
ejpam-5594	569	10	♭	♭	INTJ
ejpam-5594	569	11	)	)	PUNCT
ejpam-5594	570	1	=	=	NOUN
ejpam-5594	570	2	,	,	PUNCT
ejpam-5594	570	3	then	then	ADV
ejpam-5594	570	4	theorem	theorem	VERB
ejpam-5594	570	5	14	14	NUM
ejpam-5594	570	6	yields	yield	NOUN
ejpam-5594	570	7	an	an	DET
ejpam-5594	570	8	outcome	outcome	NOUN
ejpam-5594	570	9	for	for	ADP
ejpam-5594	570	10	the	the	DET
ejpam-5594	570	11	cr	cr	PROPN
ejpam-5594	570	12	-	-	PUNCT
ejpam-5594	570	13	p	p	NOUN
ejpam-5594	570	14	-	-	PUNCT
ejpam-5594	570	15	convex	convex	NOUN
ejpam-5594	570	16	function	function	NOUN
ejpam-5594	570	17	for	for	ADP
ejpam-5594	570	18	ab	ab	PROPN
ejpam-5594	570	19	integral	integral	ADJ
ejpam-5594	570	20	operators	operator	NOUN
ejpam-5594	570	21	:	:	PUNCT
ejpam-5594	570	22	1	1	NUM
ejpam-5594	570	23	ε2	ε2	ADJ
ejpam-5594	570	24	−	−	PROPN
ejpam-5594	570	25	ε1	ε1	PROPN
ejpam-5594	570	26	[	[	PUNCT
ejpam-5594	570	27	abiςε2+ε1	abiςε2+ε1	PROPN
ejpam-5594	570	28	2	2	NUM
ejpam-5594	570	29	{	{	PUNCT
ejpam-5594	570	30	φ(ε1)}+	φ(ε1)}+	PROPN
ejpam-5594	570	31	ab	ab	PROPN
ejpam-5594	570	32	ε2+ε1	ε2+ε1	PROPN
ejpam-5594	570	33	2	2	NUM
ejpam-5594	570	34	iςε2{φ(ε2	iςε2{φ(ε2	NOUN
ejpam-5594	570	35	)	)	PUNCT
ejpam-5594	570	36	}	}	PUNCT
ejpam-5594	570	37	]	]	PUNCT
ejpam-5594	571	1	−	−	PROPN
ejpam-5594	571	2	1	1	NUM
ejpam-5594	571	3	(	(	PUNCT
ejpam-5594	571	4	ε2	ε2	ADJ
ejpam-5594	571	5	−	−	PROPN
ejpam-5594	571	6	ε1)b(ς	ε1)b(ς	PROPN
ejpam-5594	571	7	)	)	PUNCT
ejpam-5594	571	8	[	[	PUNCT
ejpam-5594	571	9	φ(ε1	φ(ε1	NOUN
ejpam-5594	571	10	)	)	PUNCT
ejpam-5594	571	11	+	+	SYM
ejpam-5594	571	12	φ(ε2	φ(ε2	NUM
ejpam-5594	571	13	)	)	PUNCT
ejpam-5594	571	14	]	]	PUNCT
ejpam-5594	572	1	−	−	PROPN
ejpam-5594	572	2	(	(	PUNCT
ejpam-5594	572	3	ε2	ε2	ADJ
ejpam-5594	572	4	−	−	PROPN
ejpam-5594	572	5	ε1	ε1	PROPN
ejpam-5594	572	6	)	)	PUNCT
ejpam-5594	572	7	ς−1	ς−1	PROPN
ejpam-5594	572	8	2ς−1b(ς)γ(ς	2ς−1b(ς)γ(ς	NUM
ejpam-5594	572	9	)	)	PUNCT
ejpam-5594	572	10	φ	φ	PROPN
ejpam-5594	572	11	(	(	PUNCT
ejpam-5594	572	12	ε2	ε2	PROPN
ejpam-5594	572	13	+	+	CCONJ
ejpam-5594	572	14	ε1	ε1	PROPN
ejpam-5594	572	15	2	2	NUM
ejpam-5594	572	16	)	)	PUNCT
ejpam-5594	572	17	⪯cr	⪯cr	NUM
ejpam-5594	572	18	(	(	PUNCT
ejpam-5594	572	19	ε2	ε2	ADJ
ejpam-5594	572	20	−	−	PROPN
ejpam-5594	572	21	ε1	ε1	PROPN
ejpam-5594	572	22	)	)	PUNCT
ejpam-5594	573	1	ς−1	ς−1	PROPN
ejpam-5594	573	2	(	(	PUNCT
ejpam-5594	573	3	ς	ς	PROPN
ejpam-5594	573	4	+	+	NOUN
ejpam-5594	573	5	1)b(ς)γ(ς	1)b(ς)γ(ς	NUM
ejpam-5594	573	6	)	)	PUNCT
ejpam-5594	573	7	(	(	PUNCT
ejpam-5594	573	8	1	1	NUM
ejpam-5594	573	9	2	2	NUM
ejpam-5594	573	10	)	)	PUNCT
ejpam-5594	573	11	ς+1	ς+1	NUM
ejpam-5594	573	12	ς	ς	PROPN
ejpam-5594	574	1	+	+	CCONJ
ejpam-5594	574	2	2	2	NUM
ejpam-5594	574	3	[	[	PUNCT
ejpam-5594	574	4	|φ′′(ε1)|q+|φ′′(ε2)|q	|φ′′(ε1)|q+|φ′′(ε2)|q	NOUN
ejpam-5594	574	5	]	]	PUNCT
ejpam-5594	574	6	1	1	NUM
ejpam-5594	574	7	q	q	NOUN
ejpam-5594	574	8	.	.	PUNCT
ejpam-5594	575	1	(	(	PUNCT
ejpam-5594	575	2	21	21	NUM
ejpam-5594	575	3	)	)	PUNCT
ejpam-5594	575	4	theorem	theorem	NOUN
ejpam-5594	575	5	15	15	NUM
ejpam-5594	575	6	.	.	PUNCT
ejpam-5594	576	1	let	let	VERB
ejpam-5594	576	2	h	h	NOUN
ejpam-5594	576	3	:	:	PUNCT
ejpam-5594	576	4	(	(	PUNCT
ejpam-5594	576	5	0	0	NUM
ejpam-5594	576	6	,	,	PUNCT
ejpam-5594	576	7	1	1	NUM
ejpam-5594	576	8	)	)	PUNCT
ejpam-5594	576	9	→	→	NOUN
ejpam-5594	576	10	r+	r+	NOUN
ejpam-5594	576	11	and	and	CCONJ
ejpam-5594	576	12	h	h	NOUN
ejpam-5594	576	13	̸=	̸=	PROPN
ejpam-5594	576	14	0	0	NUM
ejpam-5594	576	15	.	.	PUNCT
ejpam-5594	577	1	let	let	VERB
ejpam-5594	577	2	φ	φ	NOUN
ejpam-5594	577	3	:	:	PUNCT
ejpam-5594	578	1	[	[	X
ejpam-5594	578	2	ε1	ε1	NOUN
ejpam-5594	578	3	,	,	PUNCT
ejpam-5594	578	4	ε2	ε2	PROPN
ejpam-5594	578	5	]	]	PUNCT
ejpam-5594	578	6	→	→	SYM
ejpam-5594	578	7	r+	r+	NOUN
ejpam-5594	578	8	i	i	PRON
ejpam-5594	578	9	is	be	AUX
ejpam-5594	578	10	cr	cr	PROPN
ejpam-5594	578	11	-	-	PUNCT
ejpam-5594	578	12	h	h	NOUN
ejpam-5594	578	13	-	-	PUNCT
ejpam-5594	578	14	godunovalevin	godunovalevin	ADJ
ejpam-5594	578	15	mapping	mapping	NOUN
ejpam-5594	578	16	,	,	PUNCT
ejpam-5594	578	17	ε1	ε1	PROPN
ejpam-5594	578	18	,	,	PUNCT
ejpam-5594	578	19	ε2	ε2	PROPN
ejpam-5594	578	20	∈	∈	PROPN
ejpam-5594	578	21	r+	r+	NOUN
ejpam-5594	578	22	,	,	PUNCT
ejpam-5594	578	23	ε1	ε1	VERB
ejpam-5594	578	24	<	<	X
ejpam-5594	578	25	ε2	ε2	PROPN
ejpam-5594	578	26	.	.	PUNCT
ejpam-5594	579	1	if	if	SCONJ
ejpam-5594	579	2	φ′′	φ′′	PROPN
ejpam-5594	579	3	∈	∈	PROPN
ejpam-5594	579	4	l[ε1	l[ε1	NOUN
ejpam-5594	579	5	,	,	PUNCT
ejpam-5594	579	6	ε2	ε2	PROPN
ejpam-5594	579	7	]	]	PUNCT
ejpam-5594	579	8	and	and	CCONJ
ejpam-5594	579	9	|φ′′|	|φ′′|	NOUN
ejpam-5594	579	10	is	be	AUX
ejpam-5594	579	11	also	also	ADV
ejpam-5594	579	12	cr	cr	NOUN
ejpam-5594	579	13	-	-	PUNCT
ejpam-5594	579	14	h	h	NOUN
ejpam-5594	579	15	-	-	PUNCT
ejpam-5594	579	16	godunovalevin	godunovalevin	ADJ
ejpam-5594	579	17	function	function	NOUN
ejpam-5594	579	18	,	,	PUNCT
ejpam-5594	579	19	then	then	ADV
ejpam-5594	579	20	the	the	DET
ejpam-5594	579	21	following	follow	VERB
ejpam-5594	579	22	double	double	ADJ
ejpam-5594	579	23	relation	relation	NOUN
ejpam-5594	579	24	holds	hold	VERB
ejpam-5594	579	25	true	true	ADJ
ejpam-5594	579	26	:	:	PUNCT
ejpam-5594	579	27	1	1	NUM
ejpam-5594	579	28	ε2	ε2	ADJ
ejpam-5594	579	29	−	−	PROPN
ejpam-5594	579	30	ε1	ε1	PROPN
ejpam-5594	579	31	[	[	PUNCT
ejpam-5594	579	32	abiςε2+ε1	abiςε2+ε1	PROPN
ejpam-5594	579	33	2	2	NUM
ejpam-5594	579	34	{	{	PUNCT
ejpam-5594	579	35	φ(ε1)}+	φ(ε1)}+	PROPN
ejpam-5594	579	36	ab	ab	PROPN
ejpam-5594	579	37	ε2+ε1	ε2+ε1	PROPN
ejpam-5594	579	38	2	2	NUM
ejpam-5594	579	39	iςε2{φ(ε2	iςε2{φ(ε2	NOUN
ejpam-5594	579	40	)	)	PUNCT
ejpam-5594	579	41	}	}	PUNCT
ejpam-5594	579	42	]	]	PUNCT
ejpam-5594	580	1	j.	j.	PROPN
ejpam-5594	580	2	e.	e.	PROPN
ejpam-5594	580	3	maćıas	maćıas	PROPN
ejpam-5594	580	4	-	-	PUNCT
ejpam-5594	580	5	dı́az	dı́az	NOUN
ejpam-5594	580	6	et	et	NOUN
ejpam-5594	580	7	al	al	PROPN
ejpam-5594	580	8	.	.	PUNCT
ejpam-5594	580	9	/	/	SYM
ejpam-5594	580	10	eur	eur	PROPN
ejpam-5594	580	11	.	.	PUNCT
ejpam-5594	581	1	j.	j.	PROPN
ejpam-5594	581	2	pure	pure	PROPN
ejpam-5594	581	3	appl	appl	PROPN
ejpam-5594	581	4	.	.	PROPN
ejpam-5594	581	5	math	math	PROPN
ejpam-5594	581	6	,	,	PUNCT
ejpam-5594	581	7	17	17	NUM
ejpam-5594	581	8	(	(	PUNCT
ejpam-5594	581	9	4	4	NUM
ejpam-5594	581	10	)	)	PUNCT
ejpam-5594	581	11	(	(	PUNCT
ejpam-5594	581	12	2024	2024	NUM
ejpam-5594	581	13	)	)	PUNCT
ejpam-5594	581	14	,	,	PUNCT
ejpam-5594	581	15	4014	4014	NUM
ejpam-5594	581	16	-	-	SYM
ejpam-5594	581	17	4049	4049	NUM
ejpam-5594	581	18	4036	4036	NUM
ejpam-5594	581	19	−	−	NOUN
ejpam-5594	581	20	1	1	NUM
ejpam-5594	581	21	(	(	PUNCT
ejpam-5594	581	22	ε2	ε2	ADJ
ejpam-5594	581	23	−	−	PROPN
ejpam-5594	581	24	ε1)b(ς	ε1)b(ς	PROPN
ejpam-5594	581	25	)	)	PUNCT
ejpam-5594	581	26	[	[	PUNCT
ejpam-5594	581	27	φ(ε1	φ(ε1	NOUN
ejpam-5594	581	28	)	)	PUNCT
ejpam-5594	581	29	+	+	SYM
ejpam-5594	581	30	φ(ε2	φ(ε2	NUM
ejpam-5594	581	31	)	)	PUNCT
ejpam-5594	581	32	]	]	PUNCT
ejpam-5594	582	1	−	−	PROPN
ejpam-5594	582	2	(	(	PUNCT
ejpam-5594	582	3	ε2	ε2	ADJ
ejpam-5594	582	4	−	−	PROPN
ejpam-5594	582	5	ε1	ε1	PROPN
ejpam-5594	582	6	)	)	PUNCT
ejpam-5594	582	7	ς−1	ς−1	PROPN
ejpam-5594	582	8	2ς−1b(ς)γ(ς	2ς−1b(ς)γ(ς	NUM
ejpam-5594	582	9	)	)	PUNCT
ejpam-5594	582	10	φ	φ	PROPN
ejpam-5594	582	11	(	(	PUNCT
ejpam-5594	582	12	ε2	ε2	PROPN
ejpam-5594	582	13	+	+	CCONJ
ejpam-5594	582	14	ε1	ε1	PROPN
ejpam-5594	582	15	2	2	NUM
ejpam-5594	582	16	)	)	PUNCT
ejpam-5594	582	17	⪯cr	⪯cr	NUM
ejpam-5594	582	18	(	(	PUNCT
ejpam-5594	582	19	ε2	ε2	ADJ
ejpam-5594	582	20	−	−	PROPN
ejpam-5594	582	21	ε1	ε1	PROPN
ejpam-5594	582	22	)	)	PUNCT
ejpam-5594	583	1	ς−1	ς−1	PROPN
ejpam-5594	583	2	(	(	PUNCT
ejpam-5594	583	3	ς	ς	PROPN
ejpam-5594	583	4	+	+	NOUN
ejpam-5594	583	5	1)b(ς)γ(ς	1)b(ς)γ(ς	NUM
ejpam-5594	583	6	)	)	PUNCT
ejpam-5594	583	7			PROPN
ejpam-5594	583	8	(	(	PUNCT
ejpam-5594	583	9	1	1	NUM
ejpam-5594	583	10	2	2	NUM
ejpam-5594	583	11	)	)	PUNCT
ejpam-5594	583	12	(	(	PUNCT
ejpam-5594	583	13	ς+1	ς+1	NUM
ejpam-5594	583	14	)	)	PUNCT
ejpam-5594	583	15	(	(	PUNCT
ejpam-5594	583	16	q−p	q−p	X
ejpam-5594	583	17	q−1	q−1	PROPN
ejpam-5594	583	18	)	)	PUNCT
ejpam-5594	584	1	(	(	PUNCT
ejpam-5594	584	2	q−	q−	PROPN
ejpam-5594	584	3	1	1	NUM
ejpam-5594	584	4	)	)	PUNCT
ejpam-5594	584	5	(	(	PUNCT
ejpam-5594	584	6	ς	ς	PROPN
ejpam-5594	584	7	+	+	PROPN
ejpam-5594	584	8	1)(q−	1)(q−	NUM
ejpam-5594	584	9	p	p	NOUN
ejpam-5594	584	10	)	)	PUNCT
ejpam-5594	585	1	+	+	CCONJ
ejpam-5594	585	2	q−	q−	PROPN
ejpam-5594	585	3	1	1	NUM
ejpam-5594	585	4	1−	1−	SYM
ejpam-5594	585	5	1	1	NUM
ejpam-5594	585	6	q	q	NOUN
ejpam-5594	585	7	×	×	NOUN
ejpam-5594	585	8	[	[	PUNCT
ejpam-5594	585	9	|φ′′(ε1)|q+|φ′′(ε2)|q	|φ′′(ε1)|q+|φ′′(ε2)|q	NOUN
ejpam-5594	585	10	]	]	PUNCT
ejpam-5594	585	11	1	1	NUM
ejpam-5594	585	12	q	q	NOUN
ejpam-5594	586	1	[	[	X
ejpam-5594	586	2	∫	∫	X
ejpam-5594	586	3	1	1	NUM
ejpam-5594	586	4	2	2	NUM
ejpam-5594	586	5	0	0	NUM
ejpam-5594	586	6	♭	♭	NUM
ejpam-5594	586	7	ςp+pd	ςp+pd	VERB
ejpam-5594	586	8	♭	♭	PROPN
ejpam-5594	586	9	h	h	PROPN
ejpam-5594	586	10	(	(	PUNCT
ejpam-5594	586	11	♭	♭	INTJ
ejpam-5594	586	12	)	)	PUNCT
ejpam-5594	587	1	+	+	NUM
ejpam-5594	587	2	∫	∫	PROPN
ejpam-5594	587	3	1	1	NUM
ejpam-5594	587	4	2	2	NUM
ejpam-5594	587	5	0	0	NUM
ejpam-5594	587	6	♭	♭	PRON
ejpam-5594	587	7	ςp+pd	ςp+pd	VERB
ejpam-5594	587	8	♭	♭	PROPN
ejpam-5594	587	9	h(1−	h(1−	PROPN
ejpam-5594	587	10	♭	♭	PROPN
ejpam-5594	587	11	)	)	PUNCT
ejpam-5594	587	12	]	]	PUNCT
ejpam-5594	587	13	1	1	NUM
ejpam-5594	587	14	q	q	NOUN
ejpam-5594	587	15	,	,	PUNCT
ejpam-5594	587	16	(	(	PUNCT
ejpam-5594	587	17	22	22	NUM
ejpam-5594	587	18	)	)	PUNCT
ejpam-5594	587	19	where	where	SCONJ
ejpam-5594	587	20	ς	ς	PROPN
ejpam-5594	587	21	∈	∈	PROPN
ejpam-5594	587	22	(	(	PUNCT
ejpam-5594	587	23	0	0	NUM
ejpam-5594	587	24	,	,	PUNCT
ejpam-5594	587	25	1	1	NUM
ejpam-5594	587	26	]	]	PUNCT
ejpam-5594	587	27	,	,	PUNCT
ejpam-5594	587	28	q	q	X
ejpam-5594	587	29	≥	≥	X
ejpam-5594	587	30	p	p	X
ejpam-5594	587	31	>	>	X
ejpam-5594	587	32	1	1	NUM
ejpam-5594	587	33	.	.	PUNCT
ejpam-5594	587	34	proof	proof	NOUN
ejpam-5594	587	35	.	.	PUNCT
ejpam-5594	588	1	by	by	ADP
ejpam-5594	588	2	using	use	VERB
ejpam-5594	588	3	the	the	DET
ejpam-5594	588	4	holder	holder	NOUN
ejpam-5594	588	5	’s	’s	PART
ejpam-5594	588	6	inequality	inequality	NOUN
ejpam-5594	588	7	and	and	CCONJ
ejpam-5594	588	8	taking	take	VERB
ejpam-5594	588	9	into	into	ADP
ejpam-5594	588	10	account	account	NOUN
ejpam-5594	588	11	relation	relation	NOUN
ejpam-5594	588	12	(	(	PUNCT
ejpam-5594	588	13	17	17	NUM
ejpam-5594	588	14	)	)	PUNCT
ejpam-5594	588	15	,	,	PUNCT
ejpam-5594	588	16	we	we	PRON
ejpam-5594	588	17	have	have	VERB
ejpam-5594	588	18	1	1	NUM
ejpam-5594	588	19	ε2	ε2	ADJ
ejpam-5594	588	20	−	−	PROPN
ejpam-5594	588	21	ε1	ε1	PROPN
ejpam-5594	588	22	[	[	PUNCT
ejpam-5594	588	23	abiςε2+ε1	abiςε2+ε1	PROPN
ejpam-5594	588	24	2	2	NUM
ejpam-5594	588	25	{	{	PUNCT
ejpam-5594	588	26	φ(ε1)}+	φ(ε1)}+	PROPN
ejpam-5594	588	27	ab	ab	PROPN
ejpam-5594	588	28	ε2+ε1	ε2+ε1	PROPN
ejpam-5594	588	29	2	2	NUM
ejpam-5594	588	30	iςε2{φ(ε2	iςε2{φ(ε2	NOUN
ejpam-5594	588	31	)	)	PUNCT
ejpam-5594	588	32	}	}	PUNCT
ejpam-5594	588	33	]	]	PUNCT
ejpam-5594	589	1	−	−	PROPN
ejpam-5594	589	2	1	1	NUM
ejpam-5594	589	3	(	(	PUNCT
ejpam-5594	589	4	ε2	ε2	ADJ
ejpam-5594	589	5	−	−	PROPN
ejpam-5594	589	6	ε1)b(ς	ε1)b(ς	PROPN
ejpam-5594	589	7	)	)	PUNCT
ejpam-5594	589	8	[	[	PUNCT
ejpam-5594	589	9	φ(ε1	φ(ε1	NOUN
ejpam-5594	589	10	)	)	PUNCT
ejpam-5594	589	11	+	+	SYM
ejpam-5594	589	12	φ(ε2	φ(ε2	NUM
ejpam-5594	589	13	)	)	PUNCT
ejpam-5594	589	14	]	]	PUNCT
ejpam-5594	590	1	−	−	PROPN
ejpam-5594	590	2	(	(	PUNCT
ejpam-5594	590	3	ε2	ε2	ADJ
ejpam-5594	590	4	−	−	PROPN
ejpam-5594	590	5	ε1	ε1	PROPN
ejpam-5594	590	6	)	)	PUNCT
ejpam-5594	590	7	ς−1	ς−1	PROPN
ejpam-5594	590	8	2ς−1b(ς)γ(ς	2ς−1b(ς)γ(ς	NUM
ejpam-5594	590	9	)	)	PUNCT
ejpam-5594	590	10	φ	φ	PROPN
ejpam-5594	590	11	(	(	PUNCT
ejpam-5594	590	12	ε2	ε2	PROPN
ejpam-5594	590	13	+	+	CCONJ
ejpam-5594	590	14	ε1	ε1	PROPN
ejpam-5594	590	15	2	2	NUM
ejpam-5594	590	16	)	)	PUNCT
ejpam-5594	590	17	=	=	SYM
ejpam-5594	591	1	(	(	PUNCT
ejpam-5594	591	2	ε2	ε2	PROPN
ejpam-5594	591	3	−	−	PROPN
ejpam-5594	591	4	ε1	ε1	PROPN
ejpam-5594	591	5	)	)	PUNCT
ejpam-5594	592	1	ς−1	ς−1	PROPN
ejpam-5594	592	2	2(ς	2(ς	NUM
ejpam-5594	592	3	+	+	CCONJ
ejpam-5594	592	4	1)b(ς)γ(ς	1)b(ς)γ(ς	NUM
ejpam-5594	592	5	)	)	PUNCT
ejpam-5594	592	6	×	×	NOUN
ejpam-5594	592	7	∫	∫	NOUN
ejpam-5594	592	8	1	1	NUM
ejpam-5594	592	9	0	0	NUM
ejpam-5594	592	10	|wς(	|wς(	NUM
ejpam-5594	592	11	♭	♭	PRON
ejpam-5594	592	12	)|	)|	PUNCT
ejpam-5594	592	13	q−p	q−p	PROPN
ejpam-5594	592	14	q	q	X
ejpam-5594	592	15	·	·	SYM
ejpam-5594	592	16	|wς(	|wς(	NUM
ejpam-5594	592	17	♭	♭	PRON
ejpam-5594	592	18	)|	)|	NOUN
ejpam-5594	593	1	p	p	NOUN
ejpam-5594	593	2	q	q	X
ejpam-5594	593	3	[	[	PUNCT
ejpam-5594	593	4	|φ′′(	|φ′′(	NOUN
ejpam-5594	593	5	♭	♭	PRON
ejpam-5594	593	6	ε1	ε1	VERB
ejpam-5594	593	7	+	+	CCONJ
ejpam-5594	593	8	(	(	PUNCT
ejpam-5594	593	9	1−	1−	NUM
ejpam-5594	593	10	♭	♭	INTJ
ejpam-5594	593	11	)	)	PUNCT
ejpam-5594	593	12	ε2)|+|φ′′(	ε2)|+|φ′′(	NOUN
ejpam-5594	593	13	♭	♭	PROPN
ejpam-5594	593	14	ε2	ε2	PROPN
ejpam-5594	593	15	+	+	CCONJ
ejpam-5594	593	16	(	(	PUNCT
ejpam-5594	593	17	1−	1−	NUM
ejpam-5594	593	18	♭	♭	INTJ
ejpam-5594	593	19	)	)	PUNCT
ejpam-5594	593	20	ε1)|	ε1)|	PROPN
ejpam-5594	593	21	]	]	PUNCT
ejpam-5594	594	1	d	d	X
ejpam-5594	594	2	♭	♭	PROPN
ejpam-5594	594	3	⪯cr	⪯cr	NUM
ejpam-5594	594	4	(	(	PUNCT
ejpam-5594	594	5	ε2	ε2	ADJ
ejpam-5594	594	6	−	−	PROPN
ejpam-5594	594	7	ε1	ε1	PROPN
ejpam-5594	594	8	)	)	PUNCT
ejpam-5594	595	1	ς−1	ς−1	PROPN
ejpam-5594	595	2	2(ς	2(ς	NUM
ejpam-5594	595	3	+	+	CCONJ
ejpam-5594	595	4	1)b(ς)γ(ς	1)b(ς)γ(ς	NUM
ejpam-5594	595	5	)	)	PUNCT
ejpam-5594	595	6	(	(	PUNCT
ejpam-5594	595	7	∫	∫	PROPN
ejpam-5594	595	8	1	1	NUM
ejpam-5594	595	9	0	0	NUM
ejpam-5594	595	10	|wς(	|wς(	NUM
ejpam-5594	595	11	♭	♭	PRON
ejpam-5594	595	12	)|	)|	PUNCT
ejpam-5594	595	13	q−p	q−p	PROPN
ejpam-5594	595	14	q−1d	q−1d	PRON
ejpam-5594	595	15	♭	♭	PROPN
ejpam-5594	595	16	)	)	PUNCT
ejpam-5594	595	17	1−	1−	NUM
ejpam-5594	595	18	1	1	NUM
ejpam-5594	595	19	q	q	NOUN
ejpam-5594	595	20	×	×	NOUN
ejpam-5594	596	1	[	[	X
ejpam-5594	596	2	(	(	PUNCT
ejpam-5594	596	3	∫	∫	PROPN
ejpam-5594	596	4	1	1	NUM
ejpam-5594	596	5	0	0	NUM
ejpam-5594	596	6	|wς(	|wς(	NUM
ejpam-5594	596	7	♭	♭	PRON
ejpam-5594	596	8	)|p|φ′′(	)|p|φ′′(	PUNCT
ejpam-5594	596	9	♭	♭	PROPN
ejpam-5594	596	10	ε1	ε1	VERB
ejpam-5594	596	11	+	+	CCONJ
ejpam-5594	596	12	(	(	PUNCT
ejpam-5594	596	13	1−	1−	NUM
ejpam-5594	596	14	♭	♭	INTJ
ejpam-5594	596	15	)	)	PUNCT
ejpam-5594	596	16	ε2)|qd	ε2)|qd	NOUN
ejpam-5594	596	17	♭	♭	PROPN
ejpam-5594	596	18	)	)	PUNCT
ejpam-5594	596	19	1	1	NUM
ejpam-5594	596	20	q	q	NOUN
ejpam-5594	597	1	+	+	CCONJ
ejpam-5594	597	2	(	(	PUNCT
ejpam-5594	597	3	∫	∫	PROPN
ejpam-5594	597	4	1	1	NUM
ejpam-5594	597	5	0	0	NUM
ejpam-5594	597	6	|wς(	|wς(	NUM
ejpam-5594	597	7	♭	♭	NOUN
ejpam-5594	597	8	)|p|φ′′(	)|p|φ′′(	NOUN
ejpam-5594	597	9	♭	♭	PROPN
ejpam-5594	597	10	ε2	ε2	PROPN
ejpam-5594	597	11	+	+	CCONJ
ejpam-5594	597	12	(	(	PUNCT
ejpam-5594	597	13	1−	1−	NUM
ejpam-5594	597	14	♭	♭	INTJ
ejpam-5594	597	15	)	)	PUNCT
ejpam-5594	597	16	ε1)|qd	ε1)|qd	PROPN
ejpam-5594	597	17	♭	♭	PROPN
ejpam-5594	597	18	)	)	PUNCT
ejpam-5594	597	19	1	1	NUM
ejpam-5594	597	20	q	q	NOUN
ejpam-5594	597	21	]	]	PUNCT
ejpam-5594	597	22	.	.	PUNCT
ejpam-5594	598	1	as	as	SCONJ
ejpam-5594	598	2	|φ′′|q	|φ′′|q	PROPN
ejpam-5594	598	3	is	be	AUX
ejpam-5594	598	4	cr	cr	PROPN
ejpam-5594	598	5	-	-	PUNCT
ejpam-5594	598	6	h	h	NOUN
ejpam-5594	598	7	-	-	PUNCT
ejpam-5594	598	8	godunova	godunova	ADJ
ejpam-5594	598	9	-	-	PUNCT
ejpam-5594	598	10	levin	levin	PROPN
ejpam-5594	598	11	mapping	mapping	PROPN
ejpam-5594	598	12	,	,	PUNCT
ejpam-5594	598	13	one	one	PRON
ejpam-5594	598	14	has	have	VERB
ejpam-5594	598	15	1	1	NUM
ejpam-5594	598	16	ε2	ε2	ADJ
ejpam-5594	598	17	−	−	PROPN
ejpam-5594	599	1	ε1	ε1	PROPN
ejpam-5594	599	2	[	[	PUNCT
ejpam-5594	599	3	abiςε2+ε1	abiςε2+ε1	PROPN
ejpam-5594	599	4	2	2	NUM
ejpam-5594	599	5	{	{	PUNCT
ejpam-5594	599	6	φ(ε1)}+	φ(ε1)}+	PROPN
ejpam-5594	599	7	ab	ab	PROPN
ejpam-5594	599	8	ε2+ε1	ε2+ε1	PROPN
ejpam-5594	599	9	2	2	NUM
ejpam-5594	599	10	iςε2{φ(ε2	iςε2{φ(ε2	NOUN
ejpam-5594	599	11	)	)	PUNCT
ejpam-5594	599	12	}	}	PUNCT
ejpam-5594	599	13	]	]	PUNCT
ejpam-5594	600	1	−	−	PROPN
ejpam-5594	600	2	1	1	NUM
ejpam-5594	600	3	(	(	PUNCT
ejpam-5594	600	4	ε2	ε2	ADJ
ejpam-5594	600	5	−	−	PROPN
ejpam-5594	600	6	ε1)b(ς	ε1)b(ς	PROPN
ejpam-5594	600	7	)	)	PUNCT
ejpam-5594	600	8	[	[	PUNCT
ejpam-5594	600	9	φ(ε1	φ(ε1	NOUN
ejpam-5594	600	10	)	)	PUNCT
ejpam-5594	600	11	+	+	SYM
ejpam-5594	600	12	φ(ε2	φ(ε2	NUM
ejpam-5594	600	13	)	)	PUNCT
ejpam-5594	600	14	]	]	PUNCT
ejpam-5594	601	1	−	−	PROPN
ejpam-5594	601	2	(	(	PUNCT
ejpam-5594	601	3	ε2	ε2	ADJ
ejpam-5594	601	4	−	−	PROPN
ejpam-5594	601	5	ε1	ε1	PROPN
ejpam-5594	601	6	)	)	PUNCT
ejpam-5594	601	7	ς−1	ς−1	PROPN
ejpam-5594	601	8	2ς−1b(ς)γ(ς	2ς−1b(ς)γ(ς	NUM
ejpam-5594	601	9	)	)	PUNCT
ejpam-5594	601	10	φ	φ	PROPN
ejpam-5594	601	11	(	(	PUNCT
ejpam-5594	601	12	ε2	ε2	PROPN
ejpam-5594	601	13	+	+	CCONJ
ejpam-5594	601	14	ε1	ε1	PROPN
ejpam-5594	601	15	2	2	NUM
ejpam-5594	601	16	)	)	PUNCT
ejpam-5594	601	17	=	=	SYM
ejpam-5594	602	1	(	(	PUNCT
ejpam-5594	602	2	ε2	ε2	PROPN
ejpam-5594	602	3	−	−	PROPN
ejpam-5594	602	4	ε1	ε1	PROPN
ejpam-5594	602	5	)	)	PUNCT
ejpam-5594	603	1	ς−1	ς−1	PROPN
ejpam-5594	603	2	2(ς	2(ς	NUM
ejpam-5594	603	3	+	+	CCONJ
ejpam-5594	603	4	1)b(ς)γ(ς	1)b(ς)γ(ς	NUM
ejpam-5594	603	5	)	)	PUNCT
ejpam-5594	603	6	×	×	NOUN
ejpam-5594	603	7	∫	∫	NOUN
ejpam-5594	603	8	1	1	NUM
ejpam-5594	603	9	0	0	NUM
ejpam-5594	603	10	|wς(	|wς(	NUM
ejpam-5594	603	11	♭	♭	PRON
ejpam-5594	603	12	)|	)|	PUNCT
ejpam-5594	603	13	q−p	q−p	PROPN
ejpam-5594	603	14	q	q	X
ejpam-5594	603	15	·	·	SYM
ejpam-5594	603	16	|wς(	|wς(	NUM
ejpam-5594	603	17	♭	♭	PRON
ejpam-5594	603	18	)|	)|	NOUN
ejpam-5594	604	1	p	p	NOUN
ejpam-5594	604	2	q	q	X
ejpam-5594	604	3	[	[	PUNCT
ejpam-5594	604	4	|φ′′(	|φ′′(	NOUN
ejpam-5594	604	5	♭	♭	PRON
ejpam-5594	604	6	ε1	ε1	VERB
ejpam-5594	604	7	+	+	CCONJ
ejpam-5594	604	8	(	(	PUNCT
ejpam-5594	604	9	1−	1−	NUM
ejpam-5594	604	10	♭	♭	INTJ
ejpam-5594	604	11	)	)	PUNCT
ejpam-5594	604	12	ε2)|+|φ′′(	ε2)|+|φ′′(	NOUN
ejpam-5594	604	13	♭	♭	PROPN
ejpam-5594	604	14	ε2	ε2	PROPN
ejpam-5594	604	15	+	+	CCONJ
ejpam-5594	604	16	(	(	PUNCT
ejpam-5594	604	17	1−	1−	NUM
ejpam-5594	604	18	♭	♭	INTJ
ejpam-5594	604	19	)	)	PUNCT
ejpam-5594	604	20	ε1)|	ε1)|	PROPN
ejpam-5594	604	21	]	]	PUNCT
ejpam-5594	605	1	d	d	X
ejpam-5594	605	2	♭	♭	PROPN
ejpam-5594	605	3	⪯cr	⪯cr	NUM
ejpam-5594	605	4	(	(	PUNCT
ejpam-5594	605	5	ε2	ε2	ADJ
ejpam-5594	605	6	−	−	PROPN
ejpam-5594	605	7	ε1	ε1	PROPN
ejpam-5594	605	8	)	)	PUNCT
ejpam-5594	606	1	ς−1	ς−1	PROPN
ejpam-5594	606	2	2(ς	2(ς	NUM
ejpam-5594	606	3	+	+	CCONJ
ejpam-5594	606	4	1)b(ς)γ(ς	1)b(ς)γ(ς	NUM
ejpam-5594	606	5	)	)	PUNCT
ejpam-5594	606	6	(	(	PUNCT
ejpam-5594	606	7	∫	∫	PROPN
ejpam-5594	606	8	1	1	NUM
ejpam-5594	606	9	0	0	NUM
ejpam-5594	606	10	|wς(	|wς(	NUM
ejpam-5594	606	11	♭	♭	PRON
ejpam-5594	606	12	)|	)|	PUNCT
ejpam-5594	606	13	q−p	q−p	PROPN
ejpam-5594	606	14	q−1d	q−1d	PRON
ejpam-5594	606	15	♭	♭	PROPN
ejpam-5594	606	16	)	)	PUNCT
ejpam-5594	606	17	1−	1−	NUM
ejpam-5594	606	18	1	1	NUM
ejpam-5594	606	19	q	q	NOUN
ejpam-5594	606	20	×	×	NOUN
ejpam-5594	607	1	[	[	X
ejpam-5594	607	2	(	(	PUNCT
ejpam-5594	607	3	∫	∫	PROPN
ejpam-5594	607	4	1	1	NUM
ejpam-5594	607	5	0	0	NUM
ejpam-5594	607	6	|wς(	|wς(	NUM
ejpam-5594	607	7	♭	♭	X
ejpam-5594	607	8	)|p|φ′′(ε1)|qd	)|p|φ′′(ε1)|qd	PROPN
ejpam-5594	607	9	♭	♭	PROPN
ejpam-5594	607	10	h	h	PROPN
ejpam-5594	607	11	(	(	PUNCT
ejpam-5594	607	12	♭	♭	INTJ
ejpam-5594	607	13	)	)	PUNCT
ejpam-5594	608	1	+	+	CCONJ
ejpam-5594	608	2	∫	∫	PROPN
ejpam-5594	608	3	1	1	NUM
ejpam-5594	608	4	0	0	NUM
ejpam-5594	608	5	|wς(	|wς(	NUM
ejpam-5594	608	6	♭	♭	NUM
ejpam-5594	608	7	)|p|φ′′(ε2)|qd	)|p|φ′′(ε2)|qd	NOUN
ejpam-5594	608	8	♭	♭	PROPN
ejpam-5594	608	9	h(1−	h(1−	PROPN
ejpam-5594	608	10	♭	♭	PROPN
ejpam-5594	608	11	)	)	PUNCT
ejpam-5594	608	12	)	)	PUNCT
ejpam-5594	609	1	1	1	NUM
ejpam-5594	609	2	q	q	NOUN
ejpam-5594	609	3	+	+	CCONJ
ejpam-5594	609	4	(	(	PUNCT
ejpam-5594	609	5	∫	∫	PROPN
ejpam-5594	609	6	1	1	NUM
ejpam-5594	609	7	0	0	NUM
ejpam-5594	609	8	|wς(	|wς(	NUM
ejpam-5594	609	9	♭	♭	NUM
ejpam-5594	609	10	)|p|φ′′(ε2)|qd	)|p|φ′′(ε2)|qd	NOUN
ejpam-5594	609	11	♭	♭	PROPN
ejpam-5594	609	12	h	h	PROPN
ejpam-5594	609	13	(	(	PUNCT
ejpam-5594	609	14	♭	♭	INTJ
ejpam-5594	609	15	)	)	PUNCT
ejpam-5594	610	1	+	+	CCONJ
ejpam-5594	610	2	∫	∫	PROPN
ejpam-5594	610	3	1	1	NUM
ejpam-5594	610	4	0	0	NUM
ejpam-5594	610	5	|wς(	|wς(	NUM
ejpam-5594	610	6	♭	♭	X
ejpam-5594	610	7	)|p|φ′′(ε1)|qd	)|p|φ′′(ε1)|qd	PUNCT
ejpam-5594	610	8	♭	♭	PROPN
ejpam-5594	610	9	h(1−	h(1−	PROPN
ejpam-5594	610	10	♭	♭	PROPN
ejpam-5594	610	11	)	)	PUNCT
ejpam-5594	610	12	)	)	PUNCT
ejpam-5594	610	13	1	1	NUM
ejpam-5594	610	14	q	q	NOUN
ejpam-5594	610	15	]	]	PUNCT
ejpam-5594	610	16	j.	j.	PROPN
ejpam-5594	610	17	e.	e.	PROPN
ejpam-5594	610	18	maćıas	maćıas	PROPN
ejpam-5594	610	19	-	-	PUNCT
ejpam-5594	610	20	dı́az	dı́az	NOUN
ejpam-5594	610	21	et	et	NOUN
ejpam-5594	610	22	al	al	PROPN
ejpam-5594	610	23	.	.	PUNCT
ejpam-5594	610	24	/	/	SYM
ejpam-5594	610	25	eur	eur	PROPN
ejpam-5594	610	26	.	.	PUNCT
ejpam-5594	611	1	j.	j.	PROPN
ejpam-5594	611	2	pure	pure	PROPN
ejpam-5594	611	3	appl	appl	PROPN
ejpam-5594	611	4	.	.	PROPN
ejpam-5594	611	5	math	math	PROPN
ejpam-5594	611	6	,	,	PUNCT
ejpam-5594	611	7	17	17	NUM
ejpam-5594	611	8	(	(	PUNCT
ejpam-5594	611	9	4	4	NUM
ejpam-5594	611	10	)	)	PUNCT
ejpam-5594	611	11	(	(	PUNCT
ejpam-5594	611	12	2024	2024	NUM
ejpam-5594	611	13	)	)	PUNCT
ejpam-5594	611	14	,	,	PUNCT
ejpam-5594	611	15	4014	4014	NUM
ejpam-5594	611	16	-	-	SYM
ejpam-5594	611	17	4049	4049	NUM
ejpam-5594	611	18	4037	4037	NUM
ejpam-5594	611	19	=	=	SYM
ejpam-5594	611	20	(	(	PUNCT
ejpam-5594	611	21	ε2	ε2	PROPN
ejpam-5594	611	22	−	−	PROPN
ejpam-5594	611	23	ε1	ε1	PROPN
ejpam-5594	611	24	)	)	PUNCT
ejpam-5594	612	1	ς−1	ς−1	PROPN
ejpam-5594	612	2	2(ς	2(ς	NUM
ejpam-5594	612	3	+	+	CCONJ
ejpam-5594	612	4	1)b(ς)γ(ς	1)b(ς)γ(ς	NUM
ejpam-5594	612	5	)	)	PUNCT
ejpam-5594	612	6			PROPN
ejpam-5594	612	7	(	(	PUNCT
ejpam-5594	612	8	1	1	NUM
ejpam-5594	612	9	2	2	NUM
ejpam-5594	612	10	)	)	PUNCT
ejpam-5594	612	11	(	(	PUNCT
ejpam-5594	612	12	ς+1	ς+1	NUM
ejpam-5594	612	13	)	)	PUNCT
ejpam-5594	612	14	(	(	PUNCT
ejpam-5594	612	15	q−p	q−p	X
ejpam-5594	612	16	q−1	q−1	PROPN
ejpam-5594	612	17	)	)	PUNCT
ejpam-5594	612	18	(	(	PUNCT
ejpam-5594	612	19	q−	q−	PROPN
ejpam-5594	612	20	1	1	NUM
ejpam-5594	612	21	)	)	PUNCT
ejpam-5594	612	22	(	(	PUNCT
ejpam-5594	612	23	ς	ς	PROPN
ejpam-5594	612	24	+	+	PROPN
ejpam-5594	612	25	1)(q−	1)(q−	NUM
ejpam-5594	612	26	p	p	NOUN
ejpam-5594	612	27	)	)	PUNCT
ejpam-5594	613	1	+	+	CCONJ
ejpam-5594	613	2	q−	q−	PROPN
ejpam-5594	613	3	1	1	NUM
ejpam-5594	613	4	1−	1−	SYM
ejpam-5594	613	5	1	1	NUM
ejpam-5594	613	6	q	q	NOUN
ejpam-5594	613	7	{	{	PUNCT
ejpam-5594	613	8	[	[	PUNCT
ejpam-5594	613	9	|φ′′(ε1)|q	|φ′′(ε1)|q	X
ejpam-5594	613	10	(	(	PUNCT
ejpam-5594	613	11	∫	∫	PROPN
ejpam-5594	613	12	1	1	NUM
ejpam-5594	613	13	2	2	NUM
ejpam-5594	613	14	0	0	NUM
ejpam-5594	613	15	♭	♭	NUM
ejpam-5594	613	16	ςp+pd	ςp+pd	VERB
ejpam-5594	613	17	♭	♭	PROPN
ejpam-5594	613	18	h	h	PROPN
ejpam-5594	613	19	(	(	PUNCT
ejpam-5594	613	20	♭	♭	INTJ
ejpam-5594	613	21	)	)	PUNCT
ejpam-5594	614	1	+	+	CCONJ
ejpam-5594	614	2	∫	∫	PROPN
ejpam-5594	614	3	1	1	NUM
ejpam-5594	614	4	1	1	NUM
ejpam-5594	614	5	2	2	NUM
ejpam-5594	614	6	(	(	PUNCT
ejpam-5594	614	7	1−	1−	NUM
ejpam-5594	614	8	♭	♭	PROPN
ejpam-5594	614	9	)	)	PUNCT
ejpam-5594	614	10	ςp+pd	ςp+pd	VERB
ejpam-5594	614	11	♭	♭	PROPN
ejpam-5594	614	12	h	h	PROPN
ejpam-5594	614	13	(	(	PUNCT
ejpam-5594	614	14	♭	♭	PROPN
ejpam-5594	614	15	)	)	PUNCT
ejpam-5594	614	16	)	)	PUNCT
ejpam-5594	615	1	+	+	ADV
ejpam-5594	615	2	|φ′′(ε2)|q	|φ′′(ε2)|q	INTJ
ejpam-5594	615	3	(	(	PUNCT
ejpam-5594	615	4	∫	∫	PROPN
ejpam-5594	615	5	1	1	NUM
ejpam-5594	615	6	2	2	NUM
ejpam-5594	615	7	0	0	NUM
ejpam-5594	615	8	♭	♭	PRON
ejpam-5594	615	9	ςp+pd	ςp+pd	VERB
ejpam-5594	615	10	♭	♭	PROPN
ejpam-5594	615	11	h(1−	h(1−	PROPN
ejpam-5594	615	12	♭	♭	PROPN
ejpam-5594	615	13	)	)	PUNCT
ejpam-5594	616	1	+	+	CCONJ
ejpam-5594	616	2	∫	∫	PROPN
ejpam-5594	616	3	1	1	NUM
ejpam-5594	616	4	1	1	NUM
ejpam-5594	616	5	2	2	NUM
ejpam-5594	616	6	(	(	PUNCT
ejpam-5594	616	7	1−	1−	NUM
ejpam-5594	616	8	♭	♭	PROPN
ejpam-5594	616	9	)	)	PUNCT
ejpam-5594	616	10	ςp+pd	ςp+pd	NUM
ejpam-5594	616	11	♭	♭	PROPN
ejpam-5594	616	12	h(1−	h(1−	PROPN
ejpam-5594	616	13	♭	♭	PROPN
ejpam-5594	616	14	)	)	PUNCT
ejpam-5594	616	15	)	)	PUNCT
ejpam-5594	616	16	]	]	PUNCT
ejpam-5594	617	1	1	1	NUM
ejpam-5594	617	2	q	q	NOUN
ejpam-5594	617	3	+	+	X
ejpam-5594	617	4	[	[	PUNCT
ejpam-5594	617	5	|φ′′(ε2)|q	|φ′′(ε2)|q	INTJ
ejpam-5594	617	6	(	(	PUNCT
ejpam-5594	617	7	∫	∫	PROPN
ejpam-5594	617	8	1	1	NUM
ejpam-5594	617	9	2	2	NUM
ejpam-5594	617	10	0	0	NUM
ejpam-5594	617	11	♭	♭	NUM
ejpam-5594	617	12	ςp+pd	ςp+pd	VERB
ejpam-5594	617	13	♭	♭	PROPN
ejpam-5594	617	14	h	h	PROPN
ejpam-5594	617	15	(	(	PUNCT
ejpam-5594	617	16	♭	♭	INTJ
ejpam-5594	617	17	)	)	PUNCT
ejpam-5594	618	1	+	+	CCONJ
ejpam-5594	618	2	∫	∫	PROPN
ejpam-5594	618	3	1	1	NUM
ejpam-5594	618	4	1	1	NUM
ejpam-5594	618	5	2	2	NUM
ejpam-5594	618	6	(	(	PUNCT
ejpam-5594	618	7	1−	1−	NUM
ejpam-5594	618	8	♭	♭	PROPN
ejpam-5594	618	9	)	)	PUNCT
ejpam-5594	618	10	ςp+pd	ςp+pd	VERB
ejpam-5594	618	11	♭	♭	PROPN
ejpam-5594	618	12	h	h	PROPN
ejpam-5594	618	13	(	(	PUNCT
ejpam-5594	618	14	♭	♭	PROPN
ejpam-5594	618	15	)	)	PUNCT
ejpam-5594	618	16	)	)	PUNCT
ejpam-5594	619	1	+	+	X
ejpam-5594	619	2	|φ′′(ε1)|q	|φ′′(ε1)|q	X
ejpam-5594	619	3	(	(	PUNCT
ejpam-5594	619	4	∫	∫	PROPN
ejpam-5594	619	5	1	1	NUM
ejpam-5594	619	6	2	2	NUM
ejpam-5594	619	7	0	0	NUM
ejpam-5594	619	8	♭	♭	PRON
ejpam-5594	619	9	ςp+pd	ςp+pd	VERB
ejpam-5594	619	10	♭	♭	PROPN
ejpam-5594	619	11	h(1−	h(1−	PROPN
ejpam-5594	619	12	♭	♭	PROPN
ejpam-5594	619	13	)	)	PUNCT
ejpam-5594	620	1	+	+	CCONJ
ejpam-5594	620	2	∫	∫	PROPN
ejpam-5594	620	3	1	1	NUM
ejpam-5594	620	4	1	1	NUM
ejpam-5594	620	5	2	2	NUM
ejpam-5594	620	6	(	(	PUNCT
ejpam-5594	620	7	1−	1−	NUM
ejpam-5594	620	8	♭	♭	PROPN
ejpam-5594	620	9	)	)	PUNCT
ejpam-5594	620	10	ςp+pd	ςp+pd	NUM
ejpam-5594	620	11	♭	♭	PROPN
ejpam-5594	620	12	h(1−	h(1−	PROPN
ejpam-5594	620	13	♭	♭	PROPN
ejpam-5594	620	14	)	)	PUNCT
ejpam-5594	620	15	)	)	PUNCT
ejpam-5594	620	16	]	]	PUNCT
ejpam-5594	620	17	1	1	NUM
ejpam-5594	620	18	q	q	X
ejpam-5594	620	19			NOUN
ejpam-5594	620	20	=	=	PUNCT
ejpam-5594	620	21	(	(	PUNCT
ejpam-5594	620	22	ε2	ε2	PROPN
ejpam-5594	620	23	−	−	PROPN
ejpam-5594	620	24	ε1	ε1	PROPN
ejpam-5594	620	25	)	)	PUNCT
ejpam-5594	621	1	ς−1	ς−1	PROPN
ejpam-5594	621	2	(	(	PUNCT
ejpam-5594	621	3	ς	ς	PROPN
ejpam-5594	621	4	+	+	NOUN
ejpam-5594	621	5	1)b(ς)γ(ς	1)b(ς)γ(ς	NUM
ejpam-5594	621	6	)	)	PUNCT
ejpam-5594	621	7			PROPN
ejpam-5594	621	8	(	(	PUNCT
ejpam-5594	621	9	1	1	NUM
ejpam-5594	621	10	2	2	NUM
ejpam-5594	621	11	)	)	PUNCT
ejpam-5594	621	12	(	(	PUNCT
ejpam-5594	621	13	ς+1	ς+1	NUM
ejpam-5594	621	14	)	)	PUNCT
ejpam-5594	621	15	(	(	PUNCT
ejpam-5594	621	16	q−p	q−p	X
ejpam-5594	621	17	q−1	q−1	PROPN
ejpam-5594	621	18	)	)	PUNCT
ejpam-5594	622	1	(	(	PUNCT
ejpam-5594	622	2	q−	q−	PROPN
ejpam-5594	622	3	1	1	NUM
ejpam-5594	622	4	)	)	PUNCT
ejpam-5594	622	5	(	(	PUNCT
ejpam-5594	622	6	ς	ς	PROPN
ejpam-5594	622	7	+	+	PROPN
ejpam-5594	622	8	1)(q−	1)(q−	NUM
ejpam-5594	622	9	p	p	NOUN
ejpam-5594	622	10	)	)	PUNCT
ejpam-5594	623	1	+	+	CCONJ
ejpam-5594	623	2	q−	q−	PROPN
ejpam-5594	623	3	1	1	NUM
ejpam-5594	623	4	1−	1−	SYM
ejpam-5594	623	5	1	1	NUM
ejpam-5594	623	6	q	q	NOUN
ejpam-5594	623	7	×	×	NOUN
ejpam-5594	623	8	[	[	PUNCT
ejpam-5594	623	9	|φ′′(ε1)|q+|φ′′(ε2)|q	|φ′′(ε1)|q+|φ′′(ε2)|q	NOUN
ejpam-5594	623	10	]	]	PUNCT
ejpam-5594	623	11	1	1	NUM
ejpam-5594	623	12	q	q	NOUN
ejpam-5594	624	1	[	[	X
ejpam-5594	624	2	∫	∫	X
ejpam-5594	624	3	1	1	NUM
ejpam-5594	624	4	2	2	NUM
ejpam-5594	624	5	0	0	NUM
ejpam-5594	624	6	♭	♭	NUM
ejpam-5594	624	7	ςp+pd	ςp+pd	VERB
ejpam-5594	624	8	♭	♭	PROPN
ejpam-5594	624	9	h	h	PROPN
ejpam-5594	624	10	(	(	PUNCT
ejpam-5594	624	11	♭	♭	INTJ
ejpam-5594	624	12	)	)	PUNCT
ejpam-5594	625	1	+	+	NUM
ejpam-5594	625	2	∫	∫	PROPN
ejpam-5594	625	3	1	1	NUM
ejpam-5594	625	4	2	2	NUM
ejpam-5594	625	5	0	0	NUM
ejpam-5594	625	6	♭	♭	PRON
ejpam-5594	625	7	ςp+pd	ςp+pd	VERB
ejpam-5594	625	8	♭	♭	PROPN
ejpam-5594	625	9	h(1−	h(1−	PROPN
ejpam-5594	625	10	♭	♭	PROPN
ejpam-5594	625	11	)	)	PUNCT
ejpam-5594	625	12	]	]	PUNCT
ejpam-5594	625	13	1	1	NUM
ejpam-5594	625	14	q	q	NOUN
ejpam-5594	625	15	.	.	PUNCT
ejpam-5594	626	1	remark	remark	PROPN
ejpam-5594	626	2	7	7	NUM
ejpam-5594	626	3	.	.	PUNCT
ejpam-5594	627	1	(	(	PUNCT
ejpam-5594	627	2	i	i	NOUN
ejpam-5594	627	3	)	)	PUNCT
ejpam-5594	627	4	if	if	SCONJ
ejpam-5594	627	5	h	h	X
ejpam-5594	627	6	(	(	PUNCT
ejpam-5594	627	7	♭	♭	INTJ
ejpam-5594	627	8	)	)	PUNCT
ejpam-5594	628	1	=	=	SYM
ejpam-5594	628	2	1	1	NUM
ejpam-5594	628	3	♭	♭	NOUN
ejpam-5594	628	4	s	s	PART
ejpam-5594	628	5	,	,	PUNCT
ejpam-5594	628	6	then	then	ADV
ejpam-5594	628	7	theorem	theorem	VERB
ejpam-5594	628	8	15	15	NUM
ejpam-5594	628	9	yields	yield	NOUN
ejpam-5594	628	10	an	an	DET
ejpam-5594	628	11	outcome	outcome	NOUN
ejpam-5594	628	12	for	for	ADP
ejpam-5594	628	13	the	the	DET
ejpam-5594	628	14	cr	cr	PROPN
ejpam-5594	628	15	-	-	PUNCT
ejpam-5594	628	16	s	s	NOUN
ejpam-5594	628	17	-	-	PUNCT
ejpam-5594	628	18	convex	convex	ADJ
ejpam-5594	628	19	function	function	NOUN
ejpam-5594	628	20	for	for	ADP
ejpam-5594	628	21	ab	ab	PROPN
ejpam-5594	628	22	integral	integral	ADJ
ejpam-5594	628	23	operators	operator	NOUN
ejpam-5594	628	24	:	:	PUNCT
ejpam-5594	628	25	1	1	NUM
ejpam-5594	628	26	ε2	ε2	ADJ
ejpam-5594	628	27	−	−	PROPN
ejpam-5594	628	28	ε1	ε1	PROPN
ejpam-5594	628	29	[	[	PUNCT
ejpam-5594	628	30	abiςε2+ε1	abiςε2+ε1	PROPN
ejpam-5594	628	31	2	2	NUM
ejpam-5594	628	32	{	{	PUNCT
ejpam-5594	628	33	φ(ε1)}+	φ(ε1)}+	PROPN
ejpam-5594	628	34	ab	ab	PROPN
ejpam-5594	628	35	ε2+ε1	ε2+ε1	PROPN
ejpam-5594	628	36	2	2	NUM
ejpam-5594	628	37	iςε2{φ(ε2	iςε2{φ(ε2	NOUN
ejpam-5594	628	38	)	)	PUNCT
ejpam-5594	628	39	}	}	PUNCT
ejpam-5594	628	40	]	]	PUNCT
ejpam-5594	629	1	−	−	PROPN
ejpam-5594	629	2	1	1	NUM
ejpam-5594	629	3	(	(	PUNCT
ejpam-5594	629	4	ε2	ε2	ADJ
ejpam-5594	629	5	−	−	PROPN
ejpam-5594	629	6	ε1)b(ς	ε1)b(ς	PROPN
ejpam-5594	629	7	)	)	PUNCT
ejpam-5594	629	8	[	[	PUNCT
ejpam-5594	629	9	φ(ε1	φ(ε1	NOUN
ejpam-5594	629	10	)	)	PUNCT
ejpam-5594	629	11	+	+	SYM
ejpam-5594	629	12	φ(ε2	φ(ε2	NUM
ejpam-5594	629	13	)	)	PUNCT
ejpam-5594	629	14	]	]	PUNCT
ejpam-5594	630	1	−	−	PROPN
ejpam-5594	630	2	(	(	PUNCT
ejpam-5594	630	3	ε2	ε2	ADJ
ejpam-5594	630	4	−	−	PROPN
ejpam-5594	630	5	ε1	ε1	PROPN
ejpam-5594	630	6	)	)	PUNCT
ejpam-5594	630	7	ς−1	ς−1	PROPN
ejpam-5594	630	8	2ς−1b(ς)γ(ς	2ς−1b(ς)γ(ς	NUM
ejpam-5594	630	9	)	)	PUNCT
ejpam-5594	630	10	φ	φ	PROPN
ejpam-5594	630	11	(	(	PUNCT
ejpam-5594	630	12	ε2	ε2	PROPN
ejpam-5594	630	13	+	+	CCONJ
ejpam-5594	630	14	ε1	ε1	PROPN
ejpam-5594	630	15	2	2	NUM
ejpam-5594	630	16	)	)	PUNCT
ejpam-5594	630	17	⪯cr	⪯cr	NUM
ejpam-5594	630	18	(	(	PUNCT
ejpam-5594	630	19	ε2	ε2	ADJ
ejpam-5594	630	20	−	−	PROPN
ejpam-5594	630	21	ε1	ε1	PROPN
ejpam-5594	630	22	)	)	PUNCT
ejpam-5594	631	1	ς−1	ς−1	PROPN
ejpam-5594	631	2	(	(	PUNCT
ejpam-5594	631	3	ς	ς	PROPN
ejpam-5594	631	4	+	+	NOUN
ejpam-5594	631	5	1)b(ς)γ(ς	1)b(ς)γ(ς	NUM
ejpam-5594	631	6	)	)	PUNCT
ejpam-5594	631	7			PROPN
ejpam-5594	631	8	(	(	PUNCT
ejpam-5594	631	9	1	1	NUM
ejpam-5594	631	10	2	2	NUM
ejpam-5594	631	11	)	)	PUNCT
ejpam-5594	631	12	(	(	PUNCT
ejpam-5594	631	13	ς+1	ς+1	NUM
ejpam-5594	631	14	)	)	PUNCT
ejpam-5594	631	15	(	(	PUNCT
ejpam-5594	631	16	q−p	q−p	X
ejpam-5594	631	17	q−1	q−1	PROPN
ejpam-5594	631	18	)	)	PUNCT
ejpam-5594	632	1	(	(	PUNCT
ejpam-5594	632	2	q−	q−	PROPN
ejpam-5594	632	3	1	1	NUM
ejpam-5594	632	4	)	)	PUNCT
ejpam-5594	632	5	(	(	PUNCT
ejpam-5594	632	6	ς	ς	PROPN
ejpam-5594	632	7	+	+	PROPN
ejpam-5594	632	8	1)(q−	1)(q−	NUM
ejpam-5594	632	9	p	p	NOUN
ejpam-5594	632	10	)	)	PUNCT
ejpam-5594	633	1	+	+	CCONJ
ejpam-5594	633	2	q−	q−	PROPN
ejpam-5594	633	3	1	1	NUM
ejpam-5594	633	4	1−	1−	SYM
ejpam-5594	633	5	1	1	NUM
ejpam-5594	633	6	q	q	NOUN
ejpam-5594	633	7	×	×	NOUN
ejpam-5594	633	8	[	[	PUNCT
ejpam-5594	633	9	|φ′′(ε1)|q+|φ′′(ε2)|q	|φ′′(ε1)|q+|φ′′(ε2)|q	NOUN
ejpam-5594	633	10	]	]	PUNCT
ejpam-5594	633	11	1	1	NUM
ejpam-5594	633	12	q	q	NOUN
ejpam-5594	633	13	[	[	PUNCT
ejpam-5594	633	14	(	(	PUNCT
ejpam-5594	633	15	1	1	NUM
ejpam-5594	633	16	2	2	NUM
ejpam-5594	633	17	)	)	PUNCT
ejpam-5594	633	18	ςp+p+s+1	ςp+p+s+1	NUM
ejpam-5594	633	19	ςp+	ςp+	NOUN
ejpam-5594	633	20	p+	p+	VERB
ejpam-5594	633	21	s+1	s+1	PROPN
ejpam-5594	633	22	+	+	NUM
ejpam-5594	633	23	β	β	NOUN
ejpam-5594	633	24	1	1	NUM
ejpam-5594	633	25	2	2	NUM
ejpam-5594	633	26	(	(	PUNCT
ejpam-5594	633	27	ςp+	ςp+	NOUN
ejpam-5594	633	28	p+	p+	NOUN
ejpam-5594	633	29	1	1	NUM
ejpam-5594	633	30	,	,	PUNCT
ejpam-5594	633	31	s+1	s+1	NOUN
ejpam-5594	633	32	)	)	PUNCT
ejpam-5594	633	33	]	]	PUNCT
ejpam-5594	633	34	1	1	NUM
ejpam-5594	633	35	q	q	NOUN
ejpam-5594	633	36	.	.	PUNCT
ejpam-5594	634	1	(	(	PUNCT
ejpam-5594	634	2	ii	ii	NOUN
ejpam-5594	634	3	)	)	PUNCT
ejpam-5594	634	4	if	if	SCONJ
ejpam-5594	634	5	h	h	PROPN
ejpam-5594	634	6	(	(	PUNCT
ejpam-5594	634	7	♭	♭	INTJ
ejpam-5594	634	8	)	)	PUNCT
ejpam-5594	634	9	=	=	SYM
ejpam-5594	634	10	1	1	NUM
ejpam-5594	634	11	,	,	PUNCT
ejpam-5594	634	12	then	then	ADV
ejpam-5594	634	13	theorem	theorem	VERB
ejpam-5594	634	14	15	15	NUM
ejpam-5594	634	15	yields	yield	NOUN
ejpam-5594	634	16	an	an	DET
ejpam-5594	634	17	outcome	outcome	NOUN
ejpam-5594	634	18	for	for	ADP
ejpam-5594	634	19	the	the	DET
ejpam-5594	634	20	cr	cr	PROPN
ejpam-5594	634	21	-	-	PUNCT
ejpam-5594	634	22	p	p	NOUN
ejpam-5594	634	23	-	-	PUNCT
ejpam-5594	634	24	convex	convex	NOUN
ejpam-5594	634	25	function	function	NOUN
ejpam-5594	634	26	for	for	ADP
ejpam-5594	634	27	ab	ab	PROPN
ejpam-5594	634	28	integral	integral	ADJ
ejpam-5594	634	29	operators	operator	NOUN
ejpam-5594	634	30	:	:	PUNCT
ejpam-5594	634	31	1	1	NUM
ejpam-5594	634	32	ε2	ε2	ADJ
ejpam-5594	634	33	−	−	PROPN
ejpam-5594	634	34	ε1	ε1	PROPN
ejpam-5594	634	35	[	[	PUNCT
ejpam-5594	634	36	abiςε2+ε1	abiςε2+ε1	PROPN
ejpam-5594	634	37	2	2	NUM
ejpam-5594	634	38	{	{	PUNCT
ejpam-5594	634	39	φ(ε1)}+	φ(ε1)}+	PROPN
ejpam-5594	634	40	ab	ab	PROPN
ejpam-5594	634	41	ε2+ε1	ε2+ε1	PROPN
ejpam-5594	634	42	2	2	NUM
ejpam-5594	634	43	iςε2{φ(ε2	iςε2{φ(ε2	NOUN
ejpam-5594	634	44	)	)	PUNCT
ejpam-5594	634	45	}	}	PUNCT
ejpam-5594	634	46	]	]	PUNCT
ejpam-5594	635	1	−	−	PROPN
ejpam-5594	635	2	1	1	NUM
ejpam-5594	635	3	(	(	PUNCT
ejpam-5594	635	4	ε2	ε2	ADJ
ejpam-5594	635	5	−	−	PROPN
ejpam-5594	635	6	ε1)b(ς	ε1)b(ς	PROPN
ejpam-5594	635	7	)	)	PUNCT
ejpam-5594	635	8	[	[	PUNCT
ejpam-5594	635	9	φ(ε1	φ(ε1	NOUN
ejpam-5594	635	10	)	)	PUNCT
ejpam-5594	635	11	+	+	SYM
ejpam-5594	635	12	φ(ε2	φ(ε2	NUM
ejpam-5594	635	13	)	)	PUNCT
ejpam-5594	635	14	]	]	PUNCT
ejpam-5594	636	1	−	−	PROPN
ejpam-5594	636	2	(	(	PUNCT
ejpam-5594	636	3	ε2	ε2	ADJ
ejpam-5594	636	4	−	−	PROPN
ejpam-5594	636	5	ε1	ε1	PROPN
ejpam-5594	636	6	)	)	PUNCT
ejpam-5594	636	7	ς−1	ς−1	PROPN
ejpam-5594	636	8	2ς−1b(ς)γ(ς	2ς−1b(ς)γ(ς	NUM
ejpam-5594	636	9	)	)	PUNCT
ejpam-5594	636	10	φ	φ	PROPN
ejpam-5594	636	11	(	(	PUNCT
ejpam-5594	636	12	ε2	ε2	PROPN
ejpam-5594	636	13	+	+	CCONJ
ejpam-5594	636	14	ε1	ε1	PROPN
ejpam-5594	636	15	2	2	NUM
ejpam-5594	636	16	)	)	PUNCT
ejpam-5594	636	17	⪯cr	⪯cr	NUM
ejpam-5594	636	18	(	(	PUNCT
ejpam-5594	636	19	ε2	ε2	ADJ
ejpam-5594	636	20	−	−	PROPN
ejpam-5594	636	21	ε1	ε1	PROPN
ejpam-5594	636	22	)	)	PUNCT
ejpam-5594	637	1	ς−1	ς−1	PROPN
ejpam-5594	637	2	(	(	PUNCT
ejpam-5594	637	3	ς	ς	PROPN
ejpam-5594	637	4	+	+	NOUN
ejpam-5594	637	5	1)b(ς)γ(ς	1)b(ς)γ(ς	NUM
ejpam-5594	637	6	)	)	PUNCT
ejpam-5594	637	7			PROPN
ejpam-5594	637	8	(	(	PUNCT
ejpam-5594	637	9	1	1	NUM
ejpam-5594	637	10	2	2	NUM
ejpam-5594	637	11	)	)	PUNCT
ejpam-5594	637	12	(	(	PUNCT
ejpam-5594	637	13	ς+1	ς+1	NUM
ejpam-5594	637	14	)	)	PUNCT
ejpam-5594	637	15	(	(	PUNCT
ejpam-5594	637	16	q−p	q−p	X
ejpam-5594	637	17	q−1	q−1	PROPN
ejpam-5594	637	18	)	)	PUNCT
ejpam-5594	638	1	(	(	PUNCT
ejpam-5594	638	2	q−	q−	PROPN
ejpam-5594	638	3	1	1	NUM
ejpam-5594	638	4	)	)	PUNCT
ejpam-5594	638	5	(	(	PUNCT
ejpam-5594	638	6	ς	ς	PROPN
ejpam-5594	638	7	+	+	PROPN
ejpam-5594	638	8	1)(q−	1)(q−	NUM
ejpam-5594	638	9	p	p	NOUN
ejpam-5594	638	10	)	)	PUNCT
ejpam-5594	639	1	+	+	CCONJ
ejpam-5594	639	2	q−	q−	PROPN
ejpam-5594	639	3	1	1	NUM
ejpam-5594	639	4	1−	1−	SYM
ejpam-5594	639	5	1	1	NUM
ejpam-5594	639	6	q	q	NOUN
ejpam-5594	639	7	×	×	NOUN
ejpam-5594	639	8	(	(	PUNCT
ejpam-5594	639	9	(	(	PUNCT
ejpam-5594	639	10	1	1	NUM
ejpam-5594	639	11	2	2	NUM
ejpam-5594	639	12	)	)	PUNCT
ejpam-5594	639	13	ςp+p	ςp+p	PROPN
ejpam-5594	639	14	ςp+	ςp+	NOUN
ejpam-5594	639	15	p+	p+	VERB
ejpam-5594	639	16	1	1	NUM
ejpam-5594	639	17	)	)	PUNCT
ejpam-5594	639	18	1	1	NUM
ejpam-5594	639	19	q	q	NOUN
ejpam-5594	639	20	[	[	PUNCT
ejpam-5594	639	21	|φ′′(ε1)|q+|φ′′(ε2)|q	|φ′′(ε1)|q+|φ′′(ε2)|q	NOUN
ejpam-5594	639	22	]	]	PUNCT
ejpam-5594	639	23	1	1	NUM
ejpam-5594	639	24	q	q	NOUN
ejpam-5594	639	25	.	.	PUNCT
ejpam-5594	640	1	j.	j.	PROPN
ejpam-5594	640	2	e.	e.	PROPN
ejpam-5594	640	3	maćıas	maćıas	PROPN
ejpam-5594	640	4	-	-	PUNCT
ejpam-5594	640	5	dı́az	dı́az	NOUN
ejpam-5594	640	6	et	et	NOUN
ejpam-5594	640	7	al	al	PROPN
ejpam-5594	640	8	.	.	PUNCT
ejpam-5594	640	9	/	/	SYM
ejpam-5594	640	10	eur	eur	PROPN
ejpam-5594	640	11	.	.	PUNCT
ejpam-5594	641	1	j.	j.	PROPN
ejpam-5594	641	2	pure	pure	PROPN
ejpam-5594	641	3	appl	appl	PROPN
ejpam-5594	641	4	.	.	PROPN
ejpam-5594	641	5	math	math	PROPN
ejpam-5594	641	6	,	,	PUNCT
ejpam-5594	641	7	17	17	NUM
ejpam-5594	641	8	(	(	PUNCT
ejpam-5594	641	9	4	4	NUM
ejpam-5594	641	10	)	)	PUNCT
ejpam-5594	641	11	(	(	PUNCT
ejpam-5594	641	12	2024	2024	NUM
ejpam-5594	641	13	)	)	PUNCT
ejpam-5594	641	14	,	,	PUNCT
ejpam-5594	641	15	4014	4014	NUM
ejpam-5594	641	16	-	-	SYM
ejpam-5594	641	17	4049	4049	NUM
ejpam-5594	641	18	4038	4038	NUM
ejpam-5594	641	19	theorem	theorem	NOUN
ejpam-5594	641	20	16	16	NUM
ejpam-5594	641	21	.	.	PUNCT
ejpam-5594	642	1	let	let	VERB
ejpam-5594	642	2	h	h	NOUN
ejpam-5594	642	3	:	:	PUNCT
ejpam-5594	642	4	(	(	PUNCT
ejpam-5594	642	5	0	0	NUM
ejpam-5594	642	6	,	,	PUNCT
ejpam-5594	642	7	1	1	NUM
ejpam-5594	642	8	)	)	PUNCT
ejpam-5594	642	9	→	→	NOUN
ejpam-5594	642	10	r+	r+	NOUN
ejpam-5594	642	11	and	and	CCONJ
ejpam-5594	642	12	h	h	NOUN
ejpam-5594	642	13	̸=	̸=	PROPN
ejpam-5594	642	14	0	0	NUM
ejpam-5594	642	15	.	.	PUNCT
ejpam-5594	643	1	let	let	VERB
ejpam-5594	643	2	φ	φ	NOUN
ejpam-5594	643	3	:	:	PUNCT
ejpam-5594	644	1	[	[	X
ejpam-5594	644	2	ε1	ε1	NOUN
ejpam-5594	644	3	,	,	PUNCT
ejpam-5594	644	4	ε2	ε2	PROPN
ejpam-5594	644	5	]	]	PUNCT
ejpam-5594	644	6	→	→	SYM
ejpam-5594	644	7	r+	r+	NOUN
ejpam-5594	644	8	i	i	PRON
ejpam-5594	644	9	is	be	AUX
ejpam-5594	644	10	cr	cr	PROPN
ejpam-5594	644	11	-	-	PUNCT
ejpam-5594	644	12	h	h	NOUN
ejpam-5594	644	13	-	-	PUNCT
ejpam-5594	644	14	godunovalevin	godunovalevin	ADJ
ejpam-5594	644	15	mapping	mapping	NOUN
ejpam-5594	644	16	,	,	PUNCT
ejpam-5594	644	17	ε1	ε1	PROPN
ejpam-5594	644	18	,	,	PUNCT
ejpam-5594	644	19	ε2	ε2	PROPN
ejpam-5594	644	20	∈	∈	PROPN
ejpam-5594	644	21	r+	r+	NOUN
ejpam-5594	644	22	,	,	PUNCT
ejpam-5594	644	23	ε1	ε1	VERB
ejpam-5594	644	24	<	<	X
ejpam-5594	644	25	ε2	ε2	PROPN
ejpam-5594	644	26	.	.	PUNCT
ejpam-5594	645	1	if	if	SCONJ
ejpam-5594	645	2	|φ′′|∈	|φ′′|∈	NOUN
ejpam-5594	645	3	l[ε1	l[ε1	NOUN
ejpam-5594	645	4	,	,	PUNCT
ejpam-5594	645	5	ε2	ε2	PROPN
ejpam-5594	645	6	]	]	PUNCT
ejpam-5594	645	7	and	and	CCONJ
ejpam-5594	645	8	|φ′′|	|φ′′|	NOUN
ejpam-5594	645	9	is	be	AUX
ejpam-5594	645	10	also	also	ADV
ejpam-5594	645	11	cr	cr	NOUN
ejpam-5594	645	12	-	-	PUNCT
ejpam-5594	645	13	h	h	NOUN
ejpam-5594	645	14	-	-	PUNCT
ejpam-5594	645	15	godunovalevin	godunovalevin	ADJ
ejpam-5594	645	16	function	function	NOUN
ejpam-5594	645	17	,	,	PUNCT
ejpam-5594	645	18	then	then	ADV
ejpam-5594	645	19	the	the	DET
ejpam-5594	645	20	following	follow	VERB
ejpam-5594	645	21	double	double	ADJ
ejpam-5594	645	22	relation	relation	NOUN
ejpam-5594	645	23	holds	hold	VERB
ejpam-5594	645	24	true	true	ADJ
ejpam-5594	645	25	:	:	PUNCT
ejpam-5594	645	26	1	1	NUM
ejpam-5594	645	27	ε2	ε2	ADJ
ejpam-5594	645	28	−	−	PROPN
ejpam-5594	645	29	ε1	ε1	PROPN
ejpam-5594	645	30	[	[	PUNCT
ejpam-5594	645	31	abiςε2+ε1	abiςε2+ε1	PROPN
ejpam-5594	645	32	2	2	NUM
ejpam-5594	645	33	{	{	PUNCT
ejpam-5594	645	34	φ(ε1)}+	φ(ε1)}+	PROPN
ejpam-5594	645	35	ab	ab	PROPN
ejpam-5594	645	36	ε2+ε1	ε2+ε1	PROPN
ejpam-5594	645	37	2	2	NUM
ejpam-5594	645	38	iςε2{φ(ε2	iςε2{φ(ε2	NOUN
ejpam-5594	645	39	)	)	PUNCT
ejpam-5594	645	40	}	}	PUNCT
ejpam-5594	645	41	]	]	PUNCT
ejpam-5594	646	1	−	−	PROPN
ejpam-5594	646	2	1	1	NUM
ejpam-5594	646	3	(	(	PUNCT
ejpam-5594	646	4	ε2	ε2	ADJ
ejpam-5594	646	5	−	−	PROPN
ejpam-5594	646	6	ε1)b(ς	ε1)b(ς	PROPN
ejpam-5594	646	7	)	)	PUNCT
ejpam-5594	646	8	[	[	PUNCT
ejpam-5594	646	9	φ(ε1	φ(ε1	NOUN
ejpam-5594	646	10	)	)	PUNCT
ejpam-5594	646	11	+	+	SYM
ejpam-5594	646	12	φ(ε2	φ(ε2	NUM
ejpam-5594	646	13	)	)	PUNCT
ejpam-5594	646	14	]	]	PUNCT
ejpam-5594	647	1	−	−	PROPN
ejpam-5594	647	2	(	(	PUNCT
ejpam-5594	647	3	ε2	ε2	ADJ
ejpam-5594	647	4	−	−	PROPN
ejpam-5594	647	5	ε1	ε1	PROPN
ejpam-5594	647	6	)	)	PUNCT
ejpam-5594	647	7	ς−1	ς−1	PROPN
ejpam-5594	647	8	2ς−1b(ς)γ(ς	2ς−1b(ς)γ(ς	NUM
ejpam-5594	647	9	)	)	PUNCT
ejpam-5594	647	10	φ	φ	PROPN
ejpam-5594	647	11	(	(	PUNCT
ejpam-5594	647	12	ε2	ε2	PROPN
ejpam-5594	647	13	+	+	CCONJ
ejpam-5594	647	14	ε1	ε1	PROPN
ejpam-5594	647	15	2	2	NUM
ejpam-5594	647	16	)	)	PUNCT
ejpam-5594	647	17	⪯cr	⪯cr	NUM
ejpam-5594	647	18	(	(	PUNCT
ejpam-5594	647	19	ε2	ε2	ADJ
ejpam-5594	647	20	−	−	PROPN
ejpam-5594	647	21	ε1	ε1	PROPN
ejpam-5594	647	22	)	)	PUNCT
ejpam-5594	648	1	ς−1	ς−1	PROPN
ejpam-5594	648	2	2(ς	2(ς	NUM
ejpam-5594	648	3	+	+	CCONJ
ejpam-5594	648	4	1)b(ς)γ(ς	1)b(ς)γ(ς	NUM
ejpam-5594	648	5	)	)	PUNCT
ejpam-5594	648	6	{	{	PUNCT
ejpam-5594	648	7	(	(	PUNCT
ejpam-5594	648	8	1	1	NUM
ejpam-5594	648	9	2	2	NUM
ejpam-5594	648	10	)	)	PUNCT
ejpam-5594	648	11	ςp+p−1	ςp+p−1	NOUN
ejpam-5594	648	12	(	(	PUNCT
ejpam-5594	648	13	ςp+	ςp+	NOUN
ejpam-5594	648	14	p+	p+	NOUN
ejpam-5594	648	15	1)p	1)p	NUM
ejpam-5594	648	16	+	+	NOUN
ejpam-5594	648	17	1	1	NUM
ejpam-5594	648	18	q	q	NOUN
ejpam-5594	648	19	[	[	PUNCT
ejpam-5594	648	20	|φ′′(ε1)|q+|φ′′(ε2)|q	|φ′′(ε1)|q+|φ′′(ε2)|q	NOUN
ejpam-5594	648	21	]	]	PUNCT
ejpam-5594	648	22	∫	∫	PROPN
ejpam-5594	648	23	1	1	NUM
ejpam-5594	648	24	0	0	NUM
ejpam-5594	649	1	(	(	PUNCT
ejpam-5594	649	2	1	1	NUM
ejpam-5594	649	3	h	h	NOUN
ejpam-5594	649	4	(	(	PUNCT
ejpam-5594	649	5	♭	♭	PROPN
ejpam-5594	649	6	)	)	PUNCT
ejpam-5594	650	1	+	+	CCONJ
ejpam-5594	650	2	1	1	NUM
ejpam-5594	650	3	h(1−	h(1−	NOUN
ejpam-5594	650	4	♭	♭	PROPN
ejpam-5594	650	5	)	)	PUNCT
ejpam-5594	650	6	)	)	PUNCT
ejpam-5594	651	1	d	d	X
ejpam-5594	651	2	♭	♭	PROPN
ejpam-5594	651	3	}	}	PUNCT
ejpam-5594	651	4	,	,	PUNCT
ejpam-5594	651	5	where	where	SCONJ
ejpam-5594	651	6	ς	ς	PROPN
ejpam-5594	651	7	∈	∈	PROPN
ejpam-5594	651	8	(	(	PUNCT
ejpam-5594	651	9	0	0	NUM
ejpam-5594	651	10	,	,	PUNCT
ejpam-5594	651	11	1	1	NUM
ejpam-5594	651	12	]	]	PUNCT
ejpam-5594	651	13	.	.	PUNCT
ejpam-5594	651	14	proof	proof	NOUN
ejpam-5594	651	15	.	.	PUNCT
ejpam-5594	652	1	by	by	ADP
ejpam-5594	652	2	using	use	VERB
ejpam-5594	652	3	the	the	DET
ejpam-5594	652	4	holder	holder	NOUN
ejpam-5594	652	5	’s	’s	PART
ejpam-5594	652	6	inequality	inequality	NOUN
ejpam-5594	652	7	and	and	CCONJ
ejpam-5594	652	8	taking	take	VERB
ejpam-5594	652	9	into	into	ADP
ejpam-5594	652	10	account	account	NOUN
ejpam-5594	652	11	result	result	NOUN
ejpam-5594	652	12	(	(	PUNCT
ejpam-5594	652	13	17	17	NUM
ejpam-5594	652	14	)	)	PUNCT
ejpam-5594	652	15	,	,	PUNCT
ejpam-5594	652	16	based	base	VERB
ejpam-5594	652	17	on	on	ADP
ejpam-5594	652	18	the	the	DET
ejpam-5594	652	19	young	young	PROPN
ejpam-5594	652	20	’s	’s	PART
ejpam-5594	652	21	result	result	NOUN
ejpam-5594	652	22	:	:	PUNCT
ejpam-5594	652	23	ab	ab	PROPN
ejpam-5594	652	24	≤	≤	NUM
ejpam-5594	652	25	1	1	NUM
ejpam-5594	652	26	p	p	NOUN
ejpam-5594	652	27	ap	ap	PROPN
ejpam-5594	653	1	+	+	CCONJ
ejpam-5594	653	2	1	1	NUM
ejpam-5594	653	3	q	q	NOUN
ejpam-5594	653	4	bq	bq	NOUN
ejpam-5594	653	5	,	,	PUNCT
ejpam-5594	653	6	we	we	PRON
ejpam-5594	653	7	obtain	obtain	VERB
ejpam-5594	653	8	1	1	NUM
ejpam-5594	653	9	ε2	ε2	ADJ
ejpam-5594	653	10	−	−	PROPN
ejpam-5594	654	1	ε1	ε1	PROPN
ejpam-5594	654	2	[	[	PUNCT
ejpam-5594	654	3	abiςε2+ε1	abiςε2+ε1	PROPN
ejpam-5594	654	4	2	2	NUM
ejpam-5594	654	5	{	{	PUNCT
ejpam-5594	654	6	φ(ε1)}+	φ(ε1)}+	PROPN
ejpam-5594	654	7	ab	ab	PROPN
ejpam-5594	654	8	ε2+ε1	ε2+ε1	PROPN
ejpam-5594	654	9	2	2	NUM
ejpam-5594	654	10	iςε2{φ(ε2	iςε2{φ(ε2	NOUN
ejpam-5594	654	11	)	)	PUNCT
ejpam-5594	654	12	}	}	PUNCT
ejpam-5594	654	13	]	]	PUNCT
ejpam-5594	655	1	−	−	PROPN
ejpam-5594	655	2	1	1	NUM
ejpam-5594	655	3	(	(	PUNCT
ejpam-5594	655	4	ε2	ε2	ADJ
ejpam-5594	655	5	−	−	PROPN
ejpam-5594	655	6	ε1)b(ς	ε1)b(ς	PROPN
ejpam-5594	655	7	)	)	PUNCT
ejpam-5594	655	8	[	[	PUNCT
ejpam-5594	655	9	φ(ε1	φ(ε1	NOUN
ejpam-5594	655	10	)	)	PUNCT
ejpam-5594	655	11	+	+	SYM
ejpam-5594	655	12	φ(ε2	φ(ε2	NUM
ejpam-5594	655	13	)	)	PUNCT
ejpam-5594	655	14	]	]	PUNCT
ejpam-5594	656	1	−	−	PROPN
ejpam-5594	656	2	(	(	PUNCT
ejpam-5594	656	3	ε2	ε2	ADJ
ejpam-5594	656	4	−	−	PROPN
ejpam-5594	656	5	ε1	ε1	PROPN
ejpam-5594	656	6	)	)	PUNCT
ejpam-5594	656	7	ς−1	ς−1	PROPN
ejpam-5594	656	8	2ς−1b(ς)γ(ς	2ς−1b(ς)γ(ς	NUM
ejpam-5594	656	9	)	)	PUNCT
ejpam-5594	656	10	φ	φ	PROPN
ejpam-5594	656	11	(	(	PUNCT
ejpam-5594	656	12	ε2	ε2	PROPN
ejpam-5594	656	13	+	+	CCONJ
ejpam-5594	656	14	ε1	ε1	PROPN
ejpam-5594	656	15	2	2	NUM
ejpam-5594	656	16	)	)	PUNCT
ejpam-5594	656	17	⪯cr	⪯cr	NUM
ejpam-5594	656	18	(	(	PUNCT
ejpam-5594	656	19	ε2	ε2	ADJ
ejpam-5594	656	20	−	−	PROPN
ejpam-5594	656	21	ε1	ε1	PROPN
ejpam-5594	656	22	)	)	PUNCT
ejpam-5594	657	1	ς−1	ς−1	PROPN
ejpam-5594	657	2	2(ς	2(ς	NUM
ejpam-5594	657	3	+	+	CCONJ
ejpam-5594	657	4	1)b(ς)γ(ς	1)b(ς)γ(ς	NUM
ejpam-5594	657	5	)	)	PUNCT
ejpam-5594	657	6	[	[	PUNCT
ejpam-5594	657	7	2	2	NUM
ejpam-5594	657	8	p	p	NOUN
ejpam-5594	657	9	∫	∫	PROPN
ejpam-5594	657	10	1	1	NUM
ejpam-5594	657	11	0	0	NUM
ejpam-5594	657	12	|wς(	|wς(	NUM
ejpam-5594	657	13	♭	♭	SYM
ejpam-5594	657	14	)|pd	)|pd	PUNCT
ejpam-5594	657	15	♭	♭	PROPN
ejpam-5594	658	1	+	+	NUM
ejpam-5594	658	2	1	1	NUM
ejpam-5594	658	3	q	q	NOUN
ejpam-5594	658	4	(	(	PUNCT
ejpam-5594	658	5	∫	∫	PROPN
ejpam-5594	658	6	1	1	NUM
ejpam-5594	658	7	0	0	NUM
ejpam-5594	658	8	|φ′′(	|φ′′(	NOUN
ejpam-5594	658	9	♭	♭	PRON
ejpam-5594	658	10	ε1	ε1	VERB
ejpam-5594	658	11	+	+	CCONJ
ejpam-5594	658	12	(	(	PUNCT
ejpam-5594	658	13	1−	1−	NUM
ejpam-5594	658	14	♭	♭	INTJ
ejpam-5594	658	15	)	)	PUNCT
ejpam-5594	658	16	ε2)|qd	ε2)|qd	NOUN
ejpam-5594	658	17	♭	♭	PROPN
ejpam-5594	658	18	+	+	NUM
ejpam-5594	658	19	∫	∫	PROPN
ejpam-5594	658	20	1	1	NUM
ejpam-5594	658	21	0	0	NUM
ejpam-5594	658	22	|φ′′(	|φ′′(	NOUN
ejpam-5594	658	23	♭	♭	NOUN
ejpam-5594	658	24	ε2	ε2	NOUN
ejpam-5594	658	25	+	+	CCONJ
ejpam-5594	658	26	(	(	PUNCT
ejpam-5594	658	27	1−	1−	NUM
ejpam-5594	658	28	♭	♭	INTJ
ejpam-5594	658	29	)	)	PUNCT
ejpam-5594	658	30	ε1)|qd	ε1)|qd	PROPN
ejpam-5594	658	31	♭	♭	PROPN
ejpam-5594	658	32	)	)	PUNCT
ejpam-5594	658	33	]	]	PUNCT
ejpam-5594	658	34	.	.	PUNCT
ejpam-5594	659	1	as	as	SCONJ
ejpam-5594	659	2	|φ′′|q	|φ′′|q	PROPN
ejpam-5594	659	3	is	be	AUX
ejpam-5594	659	4	cr	cr	PROPN
ejpam-5594	659	5	-	-	PUNCT
ejpam-5594	659	6	h	h	NOUN
ejpam-5594	659	7	-	-	PUNCT
ejpam-5594	659	8	godunova	godunova	NOUN
ejpam-5594	659	9	-	-	PUNCT
ejpam-5594	659	10	levin	levin	PROPN
ejpam-5594	659	11	,	,	PUNCT
ejpam-5594	659	12	one	one	PRON
ejpam-5594	659	13	has	have	VERB
ejpam-5594	659	14	1	1	NUM
ejpam-5594	659	15	ε2	ε2	ADJ
ejpam-5594	659	16	−	−	PROPN
ejpam-5594	660	1	ε1	ε1	PROPN
ejpam-5594	660	2	[	[	PUNCT
ejpam-5594	660	3	abiςε2+ε1	abiςε2+ε1	PROPN
ejpam-5594	660	4	2	2	NUM
ejpam-5594	660	5	{	{	PUNCT
ejpam-5594	660	6	φ(ε1)}+	φ(ε1)}+	PROPN
ejpam-5594	660	7	ab	ab	PROPN
ejpam-5594	660	8	ε2+ε1	ε2+ε1	PROPN
ejpam-5594	660	9	2	2	NUM
ejpam-5594	660	10	iςε2{φ(ε2	iςε2{φ(ε2	NOUN
ejpam-5594	660	11	)	)	PUNCT
ejpam-5594	660	12	}	}	PUNCT
ejpam-5594	660	13	]	]	PUNCT
ejpam-5594	661	1	−	−	PROPN
ejpam-5594	661	2	1	1	NUM
ejpam-5594	661	3	(	(	PUNCT
ejpam-5594	661	4	ε2	ε2	ADJ
ejpam-5594	661	5	−	−	PROPN
ejpam-5594	661	6	ε1)b(ς	ε1)b(ς	PROPN
ejpam-5594	661	7	)	)	PUNCT
ejpam-5594	661	8	[	[	PUNCT
ejpam-5594	661	9	φ(ε1	φ(ε1	NOUN
ejpam-5594	661	10	)	)	PUNCT
ejpam-5594	661	11	+	+	SYM
ejpam-5594	661	12	φ(ε2	φ(ε2	NUM
ejpam-5594	661	13	)	)	PUNCT
ejpam-5594	661	14	]	]	PUNCT
ejpam-5594	662	1	−	−	PROPN
ejpam-5594	662	2	(	(	PUNCT
ejpam-5594	662	3	ε2	ε2	ADJ
ejpam-5594	662	4	−	−	PROPN
ejpam-5594	662	5	ε1	ε1	PROPN
ejpam-5594	662	6	)	)	PUNCT
ejpam-5594	662	7	ς−1	ς−1	PROPN
ejpam-5594	662	8	2ς−1b(ς)γ(ς	2ς−1b(ς)γ(ς	NUM
ejpam-5594	662	9	)	)	PUNCT
ejpam-5594	662	10	φ	φ	PROPN
ejpam-5594	662	11	(	(	PUNCT
ejpam-5594	662	12	ε2	ε2	PROPN
ejpam-5594	662	13	+	+	CCONJ
ejpam-5594	662	14	ε1	ε1	PROPN
ejpam-5594	662	15	2	2	NUM
ejpam-5594	662	16	)	)	PUNCT
ejpam-5594	662	17	⪯cr	⪯cr	NUM
ejpam-5594	662	18	(	(	PUNCT
ejpam-5594	662	19	ε2	ε2	ADJ
ejpam-5594	662	20	−	−	PROPN
ejpam-5594	662	21	ε1	ε1	PROPN
ejpam-5594	662	22	)	)	PUNCT
ejpam-5594	663	1	ς−1	ς−1	PROPN
ejpam-5594	663	2	2(ς	2(ς	NUM
ejpam-5594	663	3	+	+	CCONJ
ejpam-5594	663	4	1)b(ς)γ(ς	1)b(ς)γ(ς	NUM
ejpam-5594	663	5	)	)	PUNCT
ejpam-5594	663	6	{	{	PUNCT
ejpam-5594	663	7	2	2	NUM
ejpam-5594	663	8	p	p	NOUN
ejpam-5594	663	9	∫	∫	PROPN
ejpam-5594	663	10	1	1	NUM
ejpam-5594	663	11	0	0	NUM
ejpam-5594	663	12	|wς(	|wς(	NUM
ejpam-5594	663	13	♭	♭	SYM
ejpam-5594	663	14	)|pd	)|pd	PUNCT
ejpam-5594	663	15	♭	♭	PROPN
ejpam-5594	664	1	+	+	NUM
ejpam-5594	664	2	1	1	NUM
ejpam-5594	664	3	q	q	NOUN
ejpam-5594	665	1	[	[	X
ejpam-5594	665	2	∫	∫	PROPN
ejpam-5594	665	3	1	1	NUM
ejpam-5594	665	4	0	0	NUM
ejpam-5594	665	5	|φ′′(ε1)|qd	|φ′′(ε1)|qd	NUM
ejpam-5594	665	6	♭	♭	PROPN
ejpam-5594	665	7	h	h	PROPN
ejpam-5594	665	8	(	(	PUNCT
ejpam-5594	665	9	♭	♭	PROPN
ejpam-5594	665	10	)	)	PUNCT
ejpam-5594	665	11	+	+	CCONJ
ejpam-5594	665	12	∫	∫	PROPN
ejpam-5594	665	13	1	1	NUM
ejpam-5594	665	14	0	0	NUM
ejpam-5594	665	15	|φ′′(ε2)|qd	|φ′′(ε2)|qd	NUM
ejpam-5594	665	16	♭	♭	PROPN
ejpam-5594	665	17	h(1−	h(1−	PROPN
ejpam-5594	665	18	♭	♭	PROPN
ejpam-5594	665	19	)	)	PUNCT
ejpam-5594	666	1	+	+	CCONJ
ejpam-5594	666	2	∫	∫	PROPN
ejpam-5594	666	3	1	1	NUM
ejpam-5594	666	4	0	0	NUM
ejpam-5594	666	5	|φ′′(ε2)|qd	|φ′′(ε2)|qd	NUM
ejpam-5594	666	6	♭	♭	PROPN
ejpam-5594	666	7	h	h	PROPN
ejpam-5594	666	8	(	(	PUNCT
ejpam-5594	666	9	♭	♭	INTJ
ejpam-5594	666	10	)	)	PUNCT
ejpam-5594	667	1	+	+	CCONJ
ejpam-5594	667	2	∫	∫	PROPN
ejpam-5594	667	3	1	1	NUM
ejpam-5594	667	4	0	0	NUM
ejpam-5594	667	5	|φ′′(ε1)|qd	|φ′′(ε1)|qd	NUM
ejpam-5594	667	6	♭	♭	PROPN
ejpam-5594	667	7	h(1−	h(1−	PROPN
ejpam-5594	667	8	♭	♭	PROPN
ejpam-5594	667	9	)	)	PUNCT
ejpam-5594	667	10	]	]	PUNCT
ejpam-5594	667	11	}	}	PUNCT
ejpam-5594	667	12	=	=	SYM
ejpam-5594	667	13	(	(	PUNCT
ejpam-5594	667	14	ε2	ε2	PROPN
ejpam-5594	667	15	−	−	PROPN
ejpam-5594	667	16	ε1	ε1	PROPN
ejpam-5594	667	17	)	)	PUNCT
ejpam-5594	668	1	ς−1	ς−1	PROPN
ejpam-5594	668	2	2(ς	2(ς	NUM
ejpam-5594	668	3	+	+	CCONJ
ejpam-5594	668	4	1)b(ς)γ(ς	1)b(ς)γ(ς	NUM
ejpam-5594	668	5	)	)	PUNCT
ejpam-5594	668	6	{	{	PUNCT
ejpam-5594	668	7	(	(	PUNCT
ejpam-5594	668	8	1	1	NUM
ejpam-5594	668	9	2	2	NUM
ejpam-5594	668	10	)	)	PUNCT
ejpam-5594	668	11	ςp+p−1	ςp+p−1	NOUN
ejpam-5594	668	12	(	(	PUNCT
ejpam-5594	668	13	ςp+	ςp+	NOUN
ejpam-5594	668	14	p+	p+	NOUN
ejpam-5594	668	15	1)p	1)p	NUM
ejpam-5594	668	16	+	+	NOUN
ejpam-5594	668	17	1	1	NUM
ejpam-5594	668	18	q	q	NOUN
ejpam-5594	668	19	[	[	PUNCT
ejpam-5594	668	20	|φ′′(ε1)|q+|φ′′(ε2)|q	|φ′′(ε1)|q+|φ′′(ε2)|q	NOUN
ejpam-5594	668	21	]	]	PUNCT
ejpam-5594	668	22	j.	j.	PROPN
ejpam-5594	668	23	e.	e.	PROPN
ejpam-5594	668	24	maćıas	maćıas	PROPN
ejpam-5594	668	25	-	-	PUNCT
ejpam-5594	668	26	dı́az	dı́az	NOUN
ejpam-5594	668	27	et	et	NOUN
ejpam-5594	668	28	al	al	PROPN
ejpam-5594	668	29	.	.	PUNCT
ejpam-5594	668	30	/	/	SYM
ejpam-5594	668	31	eur	eur	PROPN
ejpam-5594	668	32	.	.	PUNCT
ejpam-5594	669	1	j.	j.	PROPN
ejpam-5594	669	2	pure	pure	PROPN
ejpam-5594	669	3	appl	appl	PROPN
ejpam-5594	669	4	.	.	PROPN
ejpam-5594	669	5	math	math	PROPN
ejpam-5594	669	6	,	,	PUNCT
ejpam-5594	669	7	17	17	NUM
ejpam-5594	669	8	(	(	PUNCT
ejpam-5594	669	9	4	4	NUM
ejpam-5594	669	10	)	)	PUNCT
ejpam-5594	669	11	(	(	PUNCT
ejpam-5594	669	12	2024	2024	NUM
ejpam-5594	669	13	)	)	PUNCT
ejpam-5594	669	14	,	,	PUNCT
ejpam-5594	669	15	4014	4014	NUM
ejpam-5594	669	16	-	-	SYM
ejpam-5594	669	17	4049	4049	NUM
ejpam-5594	669	18	4039	4039	NUM
ejpam-5594	669	19	×	×	NOUN
ejpam-5594	669	20	∫	∫	PROPN
ejpam-5594	669	21	1	1	NUM
ejpam-5594	669	22	0	0	NUM
ejpam-5594	669	23	(	(	PUNCT
ejpam-5594	669	24	1	1	NUM
ejpam-5594	669	25	h	h	NOUN
ejpam-5594	669	26	(	(	PUNCT
ejpam-5594	669	27	♭	♭	PROPN
ejpam-5594	669	28	)	)	PUNCT
ejpam-5594	670	1	+	+	CCONJ
ejpam-5594	670	2	1	1	NUM
ejpam-5594	670	3	h(1−	h(1−	NOUN
ejpam-5594	670	4	♭	♭	PROPN
ejpam-5594	670	5	)	)	PUNCT
ejpam-5594	670	6	)	)	PUNCT
ejpam-5594	671	1	d	d	X
ejpam-5594	671	2	♭	♭	PROPN
ejpam-5594	671	3	}	}	PUNCT
ejpam-5594	671	4	.	.	PUNCT
ejpam-5594	672	1	the	the	DET
ejpam-5594	672	2	proof	proof	NOUN
ejpam-5594	672	3	is	be	AUX
ejpam-5594	672	4	completed	complete	VERB
ejpam-5594	672	5	.	.	PUNCT
ejpam-5594	673	1	remark	remark	PROPN
ejpam-5594	673	2	8	8	NUM
ejpam-5594	673	3	.	.	PUNCT
ejpam-5594	674	1	(	(	PUNCT
ejpam-5594	674	2	i	i	NOUN
ejpam-5594	674	3	)	)	PUNCT
ejpam-5594	674	4	if	if	SCONJ
ejpam-5594	674	5	h	h	X
ejpam-5594	674	6	(	(	PUNCT
ejpam-5594	674	7	♭	♭	INTJ
ejpam-5594	674	8	)	)	PUNCT
ejpam-5594	675	1	=	=	SYM
ejpam-5594	675	2	1	1	NUM
ejpam-5594	675	3	♭	♭	NOUN
ejpam-5594	675	4	s	s	PART
ejpam-5594	675	5	,	,	PUNCT
ejpam-5594	675	6	then	then	ADV
ejpam-5594	675	7	theorem	theorem	VERB
ejpam-5594	675	8	16	16	NUM
ejpam-5594	675	9	yields	yield	NOUN
ejpam-5594	675	10	an	an	DET
ejpam-5594	675	11	outcome	outcome	NOUN
ejpam-5594	675	12	for	for	ADP
ejpam-5594	675	13	the	the	DET
ejpam-5594	675	14	cr	cr	PROPN
ejpam-5594	675	15	-	-	PUNCT
ejpam-5594	675	16	s	s	NOUN
ejpam-5594	675	17	-	-	PUNCT
ejpam-5594	675	18	convex	convex	ADJ
ejpam-5594	675	19	function	function	NOUN
ejpam-5594	675	20	for	for	ADP
ejpam-5594	675	21	ab	ab	PROPN
ejpam-5594	675	22	integral	integral	ADJ
ejpam-5594	675	23	operators	operator	NOUN
ejpam-5594	675	24	:	:	PUNCT
ejpam-5594	675	25	1	1	NUM
ejpam-5594	675	26	ε2	ε2	ADJ
ejpam-5594	675	27	−	−	PROPN
ejpam-5594	675	28	ε1	ε1	PROPN
ejpam-5594	675	29	[	[	PUNCT
ejpam-5594	675	30	abiςε2+ε1	abiςε2+ε1	PROPN
ejpam-5594	675	31	2	2	NUM
ejpam-5594	675	32	{	{	PUNCT
ejpam-5594	675	33	φ(ε1)}+	φ(ε1)}+	PROPN
ejpam-5594	675	34	ab	ab	PROPN
ejpam-5594	675	35	ε2+ε1	ε2+ε1	PROPN
ejpam-5594	675	36	2	2	NUM
ejpam-5594	675	37	iςε2{φ(ε2	iςε2{φ(ε2	NOUN
ejpam-5594	675	38	)	)	PUNCT
ejpam-5594	675	39	}	}	PUNCT
ejpam-5594	675	40	]	]	PUNCT
ejpam-5594	676	1	−	−	PROPN
ejpam-5594	676	2	1	1	NUM
ejpam-5594	676	3	(	(	PUNCT
ejpam-5594	676	4	ε2	ε2	ADJ
ejpam-5594	676	5	−	−	PROPN
ejpam-5594	676	6	ε1)b(ς	ε1)b(ς	PROPN
ejpam-5594	676	7	)	)	PUNCT
ejpam-5594	676	8	[	[	PUNCT
ejpam-5594	676	9	φ(ε1	φ(ε1	NOUN
ejpam-5594	676	10	)	)	PUNCT
ejpam-5594	676	11	+	+	SYM
ejpam-5594	676	12	φ(ε2	φ(ε2	NUM
ejpam-5594	676	13	)	)	PUNCT
ejpam-5594	676	14	]	]	PUNCT
ejpam-5594	677	1	−	−	PROPN
ejpam-5594	677	2	(	(	PUNCT
ejpam-5594	677	3	ε2	ε2	ADJ
ejpam-5594	677	4	−	−	PROPN
ejpam-5594	677	5	ε1	ε1	PROPN
ejpam-5594	677	6	)	)	PUNCT
ejpam-5594	677	7	ς−1	ς−1	PROPN
ejpam-5594	677	8	2ς−1b(ς)γ(ς	2ς−1b(ς)γ(ς	NUM
ejpam-5594	677	9	)	)	PUNCT
ejpam-5594	677	10	φ	φ	PROPN
ejpam-5594	677	11	(	(	PUNCT
ejpam-5594	677	12	ε2	ε2	PROPN
ejpam-5594	677	13	+	+	CCONJ
ejpam-5594	677	14	ε1	ε1	PROPN
ejpam-5594	677	15	2	2	NUM
ejpam-5594	677	16	)	)	PUNCT
ejpam-5594	677	17	⪯cr	⪯cr	NUM
ejpam-5594	677	18	(	(	PUNCT
ejpam-5594	677	19	ε2	ε2	ADJ
ejpam-5594	677	20	−	−	PROPN
ejpam-5594	677	21	ε1	ε1	PROPN
ejpam-5594	677	22	)	)	PUNCT
ejpam-5594	678	1	ς−1	ς−1	PROPN
ejpam-5594	678	2	(	(	PUNCT
ejpam-5594	678	3	ς	ς	PROPN
ejpam-5594	678	4	+	+	NOUN
ejpam-5594	678	5	1)b(ς)γ(ς	1)b(ς)γ(ς	NUM
ejpam-5594	678	6	)	)	PUNCT
ejpam-5594	678	7	{	{	PUNCT
ejpam-5594	678	8	(	(	PUNCT
ejpam-5594	678	9	1	1	NUM
ejpam-5594	678	10	2	2	NUM
ejpam-5594	678	11	)	)	PUNCT
ejpam-5594	678	12	ςp+p	ςp+p	PROPN
ejpam-5594	678	13	(	(	PUNCT
ejpam-5594	678	14	ςp+	ςp+	PROPN
ejpam-5594	678	15	p+	p+	NOUN
ejpam-5594	678	16	1)p	1)p	NUM
ejpam-5594	678	17	+	+	CCONJ
ejpam-5594	678	18	1	1	NUM
ejpam-5594	678	19	q(s+1	q(s+1	NUM
ejpam-5594	678	20	)	)	PUNCT
ejpam-5594	678	21	[	[	PUNCT
ejpam-5594	678	22	|φ′′(ε1)|q+|φ′′(ε2)|q	|φ′′(ε1)|q+|φ′′(ε2)|q	NOUN
ejpam-5594	678	23	]	]	PUNCT
ejpam-5594	678	24	}	}	PUNCT
ejpam-5594	678	25	.	.	PUNCT
ejpam-5594	679	1	(	(	PUNCT
ejpam-5594	679	2	ii	ii	NOUN
ejpam-5594	679	3	)	)	PUNCT
ejpam-5594	679	4	if	if	SCONJ
ejpam-5594	679	5	h	h	PROPN
ejpam-5594	679	6	(	(	PUNCT
ejpam-5594	679	7	♭	♭	INTJ
ejpam-5594	679	8	)	)	PUNCT
ejpam-5594	679	9	=	=	SYM
ejpam-5594	679	10	1	1	NUM
ejpam-5594	679	11	,	,	PUNCT
ejpam-5594	679	12	then	then	ADV
ejpam-5594	679	13	theorem	theorem	VERB
ejpam-5594	679	14	16	16	NUM
ejpam-5594	679	15	yields	yield	NOUN
ejpam-5594	679	16	an	an	DET
ejpam-5594	679	17	outcome	outcome	NOUN
ejpam-5594	679	18	for	for	ADP
ejpam-5594	679	19	the	the	DET
ejpam-5594	679	20	cr	cr	PROPN
ejpam-5594	679	21	-	-	PUNCT
ejpam-5594	679	22	p	p	NOUN
ejpam-5594	679	23	-	-	PUNCT
ejpam-5594	679	24	convex	convex	NOUN
ejpam-5594	679	25	function	function	NOUN
ejpam-5594	679	26	for	for	ADP
ejpam-5594	679	27	ab	ab	PROPN
ejpam-5594	679	28	integral	integral	ADJ
ejpam-5594	679	29	operators	operator	NOUN
ejpam-5594	679	30	:	:	PUNCT
ejpam-5594	679	31	1	1	NUM
ejpam-5594	679	32	ε2	ε2	ADJ
ejpam-5594	679	33	−	−	PROPN
ejpam-5594	679	34	ε1	ε1	PROPN
ejpam-5594	679	35	[	[	PUNCT
ejpam-5594	679	36	abiςε2+ε1	abiςε2+ε1	PROPN
ejpam-5594	679	37	2	2	NUM
ejpam-5594	679	38	{	{	PUNCT
ejpam-5594	679	39	φ(ε1)}+	φ(ε1)}+	PROPN
ejpam-5594	679	40	ab	ab	PROPN
ejpam-5594	679	41	ε2+ε1	ε2+ε1	PROPN
ejpam-5594	679	42	2	2	NUM
ejpam-5594	679	43	iςε2{φ(ε2	iςε2{φ(ε2	NOUN
ejpam-5594	679	44	)	)	PUNCT
ejpam-5594	679	45	}	}	PUNCT
ejpam-5594	679	46	]	]	PUNCT
ejpam-5594	680	1	−	−	PROPN
ejpam-5594	680	2	1	1	NUM
ejpam-5594	680	3	(	(	PUNCT
ejpam-5594	680	4	ε2	ε2	ADJ
ejpam-5594	680	5	−	−	PROPN
ejpam-5594	680	6	ε1)b(ς	ε1)b(ς	PROPN
ejpam-5594	680	7	)	)	PUNCT
ejpam-5594	680	8	[	[	PUNCT
ejpam-5594	680	9	φ(ε1	φ(ε1	NOUN
ejpam-5594	680	10	)	)	PUNCT
ejpam-5594	680	11	+	+	SYM
ejpam-5594	680	12	φ(ε2	φ(ε2	NUM
ejpam-5594	680	13	)	)	PUNCT
ejpam-5594	680	14	]	]	PUNCT
ejpam-5594	681	1	−	−	PROPN
ejpam-5594	681	2	(	(	PUNCT
ejpam-5594	681	3	ε2	ε2	ADJ
ejpam-5594	681	4	−	−	PROPN
ejpam-5594	681	5	ε1	ε1	PROPN
ejpam-5594	681	6	)	)	PUNCT
ejpam-5594	681	7	ς−1	ς−1	PROPN
ejpam-5594	681	8	2ς−1b(ς)γ(ς	2ς−1b(ς)γ(ς	NUM
ejpam-5594	681	9	)	)	PUNCT
ejpam-5594	681	10	φ	φ	PROPN
ejpam-5594	681	11	(	(	PUNCT
ejpam-5594	681	12	ε2	ε2	PROPN
ejpam-5594	681	13	+	+	CCONJ
ejpam-5594	681	14	ε1	ε1	PROPN
ejpam-5594	681	15	2	2	NUM
ejpam-5594	681	16	)	)	PUNCT
ejpam-5594	681	17	⪯cr	⪯cr	NUM
ejpam-5594	681	18	(	(	PUNCT
ejpam-5594	681	19	ε2	ε2	ADJ
ejpam-5594	681	20	−	−	PROPN
ejpam-5594	681	21	ε1	ε1	PROPN
ejpam-5594	681	22	)	)	PUNCT
ejpam-5594	682	1	ς−1	ς−1	PROPN
ejpam-5594	682	2	(	(	PUNCT
ejpam-5594	682	3	ς	ς	PROPN
ejpam-5594	682	4	+	+	NOUN
ejpam-5594	682	5	1)b(ς)γ(ς	1)b(ς)γ(ς	NUM
ejpam-5594	682	6	)	)	PUNCT
ejpam-5594	682	7	{	{	PUNCT
ejpam-5594	682	8	(	(	PUNCT
ejpam-5594	682	9	1	1	NUM
ejpam-5594	682	10	2	2	NUM
ejpam-5594	682	11	)	)	PUNCT
ejpam-5594	682	12	ςp+p	ςp+p	PROPN
ejpam-5594	682	13	(	(	PUNCT
ejpam-5594	682	14	ςp+	ςp+	PROPN
ejpam-5594	682	15	p+	p+	NOUN
ejpam-5594	683	1	1)p	1)p	NUM
ejpam-5594	683	2	+	+	NOUN
ejpam-5594	683	3	1	1	NUM
ejpam-5594	683	4	q	q	NOUN
ejpam-5594	683	5	[	[	PUNCT
ejpam-5594	683	6	|φ′′(ε1)|q+|φ′′(ε2)|q	|φ′′(ε1)|q+|φ′′(ε2)|q	NOUN
ejpam-5594	683	7	]	]	PUNCT
ejpam-5594	683	8	}	}	PUNCT
ejpam-5594	683	9	.	.	PUNCT
ejpam-5594	684	1	theorem	theorem	ADJ
ejpam-5594	684	2	17	17	NUM
ejpam-5594	684	3	.	.	PUNCT
ejpam-5594	685	1	let	let	VERB
ejpam-5594	685	2	h	h	NOUN
ejpam-5594	685	3	:	:	PUNCT
ejpam-5594	685	4	(	(	PUNCT
ejpam-5594	685	5	0	0	NUM
ejpam-5594	685	6	,	,	PUNCT
ejpam-5594	685	7	1	1	NUM
ejpam-5594	685	8	)	)	PUNCT
ejpam-5594	685	9	→	→	NOUN
ejpam-5594	685	10	r+	r+	NOUN
ejpam-5594	685	11	and	and	CCONJ
ejpam-5594	685	12	h	h	NOUN
ejpam-5594	685	13	̸=	̸=	PROPN
ejpam-5594	685	14	0	0	NUM
ejpam-5594	685	15	.	.	PUNCT
ejpam-5594	686	1	let	let	VERB
ejpam-5594	686	2	φ	φ	NOUN
ejpam-5594	686	3	:	:	PUNCT
ejpam-5594	687	1	[	[	X
ejpam-5594	687	2	ε1	ε1	NOUN
ejpam-5594	687	3	,	,	PUNCT
ejpam-5594	687	4	ε2	ε2	PROPN
ejpam-5594	687	5	]	]	PUNCT
ejpam-5594	687	6	→	→	SYM
ejpam-5594	687	7	r+	r+	NOUN
ejpam-5594	687	8	i	i	PRON
ejpam-5594	687	9	is	be	AUX
ejpam-5594	687	10	cr	cr	PROPN
ejpam-5594	687	11	-	-	PUNCT
ejpam-5594	687	12	h	h	NOUN
ejpam-5594	687	13	-	-	PUNCT
ejpam-5594	687	14	godunovalevin	godunovalevin	ADJ
ejpam-5594	687	15	mapping	mapping	NOUN
ejpam-5594	687	16	,	,	PUNCT
ejpam-5594	687	17	ε1	ε1	PROPN
ejpam-5594	687	18	,	,	PUNCT
ejpam-5594	687	19	ε2	ε2	PROPN
ejpam-5594	687	20	∈	∈	PROPN
ejpam-5594	687	21	r+	r+	NOUN
ejpam-5594	687	22	,	,	PUNCT
ejpam-5594	687	23	ε1	ε1	VERB
ejpam-5594	687	24	<	<	X
ejpam-5594	687	25	ε2	ε2	ADJ
ejpam-5594	687	26	and	and	CCONJ
ejpam-5594	687	27	[	[	X
ejpam-5594	688	1	h(	h(	PROPN
ejpam-5594	688	2	♭	♭	SYM
ejpam-5594	688	3	)]q	)]q	PUNCT
ejpam-5594	688	4	∈	∈	PROPN
ejpam-5594	688	5	l1[0	l1[0	PROPN
ejpam-5594	688	6	,	,	PUNCT
ejpam-5594	688	7	1],φ	1],φ	NUM
ejpam-5594	688	8	∈	∈	PROPN
ejpam-5594	688	9	l1[ε1	l1[ε1	PROPN
ejpam-5594	688	10	,	,	PUNCT
ejpam-5594	688	11	ε2	ε2	PROPN
ejpam-5594	688	12	]	]	PUNCT
ejpam-5594	688	13	.	.	PUNCT
ejpam-5594	689	1	if	if	SCONJ
ejpam-5594	689	2	|φ′|	|φ′|	PROPN
ejpam-5594	689	3	is	be	AUX
ejpam-5594	689	4	an	an	DET
ejpam-5594	689	5	cr	cr	NOUN
ejpam-5594	689	6	-	-	PUNCT
ejpam-5594	689	7	h	h	NOUN
ejpam-5594	689	8	-	-	PUNCT
ejpam-5594	689	9	godunova	godunova	ADJ
ejpam-5594	689	10	-	-	PUNCT
ejpam-5594	689	11	levin	levin	PROPN
ejpam-5594	689	12	mapping	mapping	NOUN
ejpam-5594	689	13	on	on	ADP
ejpam-5594	689	14	[	[	X
ejpam-5594	689	15	ε1	ε1	NOUN
ejpam-5594	689	16	,	,	PUNCT
ejpam-5594	689	17	ε2	ε2	PROPN
ejpam-5594	689	18	]	]	PUNCT
ejpam-5594	689	19	,	,	PUNCT
ejpam-5594	689	20	then	then	ADV
ejpam-5594	689	21	the	the	DET
ejpam-5594	689	22	following	follow	VERB
ejpam-5594	689	23	relation	relation	NOUN
ejpam-5594	689	24	|bk(φ	|bk(φ	PROPN
ejpam-5594	689	25	,	,	PUNCT
ejpam-5594	689	26	ε1	ε1	PROPN
ejpam-5594	689	27	,	,	PUNCT
ejpam-5594	689	28	ε2)|	ε2)|	PROPN
ejpam-5594	689	29	=	=	SYM
ejpam-5594	689	30	k−1∑	k−1∑	PROPN
ejpam-5594	689	31	ȷ=0	ȷ=0	PROPN
ejpam-5594	689	32	ε2	ε2	ADJ
ejpam-5594	689	33	−	−	PROPN
ejpam-5594	689	34	ε1	ε1	PROPN
ejpam-5594	689	35	2k2	2k2	NUM
ejpam-5594	690	1	[	[	X
ejpam-5594	690	2	(	(	PUNCT
ejpam-5594	690	3	1	1	NUM
ejpam-5594	690	4	2	2	NUM
ejpam-5594	690	5	)	)	PUNCT
ejpam-5594	691	1	q−1	q−1	PROPN
ejpam-5594	691	2	q	q	PROPN
ejpam-5594	692	1	(	(	PUNCT
ejpam-5594	692	2	∫	∫	PROPN
ejpam-5594	692	3	1	1	NUM
ejpam-5594	692	4	0	0	NUM
ejpam-5594	692	5	|1−	|1−	NOUN
ejpam-5594	692	6	2	2	NUM
ejpam-5594	692	7	♭	♭	INTJ
ejpam-5594	692	8	|	|	ADJ
ejpam-5594	692	9	h	h	NOUN
ejpam-5594	692	10	(	(	PUNCT
ejpam-5594	692	11	♭	♭	INTJ
ejpam-5594	692	12	)	)	PUNCT
ejpam-5594	693	1	∣∣∣∣φ′	∣∣∣∣φ′	INTJ
ejpam-5594	693	2	(	(	PUNCT
ejpam-5594	693	3	(	(	PUNCT
ejpam-5594	693	4	k−ȷ)ε1	k−ȷ)ε1	X
ejpam-5594	693	5	+	+	NUM
ejpam-5594	693	6	ȷε2	ȷε2	NOUN
ejpam-5594	693	7	k	k	PROPN
ejpam-5594	693	8	)	)	PUNCT
ejpam-5594	693	9	∣∣∣∣q	∣∣∣∣q	PUNCT
ejpam-5594	694	1	d	d	PUNCT
ejpam-5594	694	2	♭	♭	PROPN
ejpam-5594	694	3	+	+	NUM
ejpam-5594	694	4	∫	∫	PROPN
ejpam-5594	694	5	1	1	NUM
ejpam-5594	694	6	0	0	NUM
ejpam-5594	694	7	|1−	|1−	NOUN
ejpam-5594	694	8	2	2	NUM
ejpam-5594	694	9	♭	♭	NOUN
ejpam-5594	694	10	|	|	NOUN
ejpam-5594	694	11	h(1−	h(1−	NOUN
ejpam-5594	694	12	♭	♭	INTJ
ejpam-5594	694	13	)	)	PUNCT
ejpam-5594	695	1	∣∣∣∣φ′	∣∣∣∣φ′	INTJ
ejpam-5594	695	2	(	(	PUNCT
ejpam-5594	695	3	(	(	PUNCT
ejpam-5594	695	4	k−ȷ−	k−ȷ−	PROPN
ejpam-5594	695	5	1)ε1	1)ε1	NUM
ejpam-5594	695	6	+	+	CCONJ
ejpam-5594	695	7	(	(	PUNCT
ejpam-5594	695	8	ȷ+	ȷ+	ADV
ejpam-5594	695	9	1)ε2	1)ε2	NUM
ejpam-5594	695	10	k	k	NOUN
ejpam-5594	695	11	)	)	PUNCT
ejpam-5594	695	12	∣∣∣∣q	∣∣∣∣q	PROPN
ejpam-5594	696	1	d	d	X
ejpam-5594	696	2	♭	♭	PROPN
ejpam-5594	696	3	)	)	PUNCT
ejpam-5594	696	4	1	1	NUM
ejpam-5594	696	5	q	q	NOUN
ejpam-5594	696	6	]	]	PUNCT
ejpam-5594	696	7	holds	hold	NOUN
ejpam-5594	696	8	,	,	PUNCT
ejpam-5594	696	9	where	where	SCONJ
ejpam-5594	696	10	1	1	NUM
ejpam-5594	696	11	<	<	X
ejpam-5594	696	12	p	p	NOUN
ejpam-5594	696	13	and	and	CCONJ
ejpam-5594	696	14	1	1	NUM
ejpam-5594	696	15	p	p	NOUN
ejpam-5594	697	1	+	+	NOUN
ejpam-5594	697	2	1	1	NUM
ejpam-5594	697	3	q	q	NOUN
ejpam-5594	697	4	=	=	NOUN
ejpam-5594	697	5	1	1	X
ejpam-5594	697	6	.	.	PUNCT
ejpam-5594	697	7	proof	proof	NOUN
ejpam-5594	697	8	.	.	PUNCT
ejpam-5594	698	1	let	let	VERB
ejpam-5594	698	2	q	q	PRON
ejpam-5594	698	3	≥	≥	NUM
ejpam-5594	698	4	1	1	NUM
ejpam-5594	698	5	and	and	CCONJ
ejpam-5594	698	6	using	use	VERB
ejpam-5594	698	7	identity	identity	NOUN
ejpam-5594	698	8	from	from	ADP
ejpam-5594	698	9	lemma	lemma	PROPN
ejpam-5594	698	10	2.1	2.1	NUM
ejpam-5594	698	11	and	and	CCONJ
ejpam-5594	698	12	taking	take	VERB
ejpam-5594	698	13	into	into	ADP
ejpam-5594	698	14	account	account	NOUN
ejpam-5594	698	15	powerj	powerj	NOUN
ejpam-5594	698	16	.	.	PUNCT
ejpam-5594	699	1	e.	e.	PROPN
ejpam-5594	699	2	maćıas	maćıas	PROPN
ejpam-5594	699	3	-	-	PUNCT
ejpam-5594	699	4	dı́az	dı́az	NOUN
ejpam-5594	699	5	et	et	NOUN
ejpam-5594	699	6	al	al	PROPN
ejpam-5594	699	7	.	.	PUNCT
ejpam-5594	699	8	/	/	SYM
ejpam-5594	699	9	eur	eur	PROPN
ejpam-5594	699	10	.	.	PUNCT
ejpam-5594	700	1	j.	j.	PROPN
ejpam-5594	700	2	pure	pure	PROPN
ejpam-5594	700	3	appl	appl	PROPN
ejpam-5594	700	4	.	.	PROPN
ejpam-5594	700	5	math	math	PROPN
ejpam-5594	700	6	,	,	PUNCT
ejpam-5594	700	7	17	17	NUM
ejpam-5594	700	8	(	(	PUNCT
ejpam-5594	700	9	4	4	NUM
ejpam-5594	700	10	)	)	PUNCT
ejpam-5594	700	11	(	(	PUNCT
ejpam-5594	700	12	2024	2024	NUM
ejpam-5594	700	13	)	)	PUNCT
ejpam-5594	700	14	,	,	PUNCT
ejpam-5594	700	15	4014	4014	NUM
ejpam-5594	700	16	-	-	SYM
ejpam-5594	700	17	4049	4049	NUM
ejpam-5594	700	18	4040	4040	NUM
ejpam-5594	700	19	mean	mean	NOUN
ejpam-5594	700	20	inequality	inequality	NOUN
ejpam-5594	700	21	,	,	PUNCT
ejpam-5594	700	22	then	then	ADV
ejpam-5594	700	23	we	we	PRON
ejpam-5594	700	24	have	have	VERB
ejpam-5594	700	25	|bk(φ	|bk(φ	NUM
ejpam-5594	700	26	,	,	PUNCT
ejpam-5594	700	27	ε1	ε1	PROPN
ejpam-5594	700	28	,	,	PUNCT
ejpam-5594	700	29	ε2)|	ε2)|	PROPN
ejpam-5594	700	30	⪯cr	⪯cr	NUM
ejpam-5594	700	31	k−1∑	k−1∑	PROPN
ejpam-5594	700	32	ȷ=0	ȷ=0	PROPN
ejpam-5594	701	1	ε2	ε2	ADJ
ejpam-5594	701	2	−	−	PROPN
ejpam-5594	701	3	ε1	ε1	PROPN
ejpam-5594	701	4	2k2	2k2	NUM
ejpam-5594	701	5	(	(	PUNCT
ejpam-5594	701	6	∫	∫	PROPN
ejpam-5594	701	7	1	1	NUM
ejpam-5594	701	8	0	0	NUM
ejpam-5594	701	9	∣∣∣∣(1−	∣∣∣∣(1−	NOUN
ejpam-5594	701	10	2	2	NUM
ejpam-5594	701	11	♭	♭	PROPN
ejpam-5594	701	12	)φ′	)φ′	PROPN
ejpam-5594	701	13	(	(	PUNCT
ejpam-5594	701	14	♭	♭	X
ejpam-5594	701	15	(	(	PUNCT
ejpam-5594	701	16	k−ȷ)ε1	k−ȷ)ε1	PROPN
ejpam-5594	701	17	+	+	NUM
ejpam-5594	701	18	ȷε2	ȷε2	NOUN
ejpam-5594	701	19	k	k	PROPN
ejpam-5594	702	1	+	+	CCONJ
ejpam-5594	703	1	(	(	PUNCT
ejpam-5594	703	2	1−	1−	NUM
ejpam-5594	703	3	♭	♭	INTJ
ejpam-5594	703	4	)	)	PUNCT
ejpam-5594	703	5	(	(	PUNCT
ejpam-5594	703	6	k−ȷ−	k−ȷ−	PROPN
ejpam-5594	703	7	1)ε1	1)ε1	NUM
ejpam-5594	703	8	+	+	CCONJ
ejpam-5594	703	9	(	(	PUNCT
ejpam-5594	703	10	ȷ+	ȷ+	ADV
ejpam-5594	703	11	1)ε2	1)ε2	NUM
ejpam-5594	703	12	k	k	NOUN
ejpam-5594	703	13	)	)	PUNCT
ejpam-5594	703	14	∣∣∣∣d	∣∣∣∣d	PROPN
ejpam-5594	703	15	♭	♭	PROPN
ejpam-5594	703	16	)	)	PUNCT
ejpam-5594	703	17	⪯cr	⪯cr	NOUN
ejpam-5594	703	18	k−1∑	k−1∑	PROPN
ejpam-5594	703	19	ȷ=0	ȷ=0	PROPN
ejpam-5594	703	20	ε2	ε2	ADJ
ejpam-5594	703	21	−	−	PROPN
ejpam-5594	703	22	ε1	ε1	PROPN
ejpam-5594	703	23	2k2	2k2	NUM
ejpam-5594	703	24	(	(	PUNCT
ejpam-5594	703	25	∫	∫	PROPN
ejpam-5594	703	26	1	1	NUM
ejpam-5594	703	27	0	0	NUM
ejpam-5594	703	28	|1−	|1−	NOUN
ejpam-5594	703	29	2	2	NUM
ejpam-5594	703	30	♭	♭	PROPN
ejpam-5594	703	31	|d	|d	NOUN
ejpam-5594	703	32	♭	♭	PROPN
ejpam-5594	703	33	)	)	PUNCT
ejpam-5594	703	34	1−	1−	PROPN
ejpam-5594	703	35	1	1	NUM
ejpam-5594	703	36	q	q	NOUN
ejpam-5594	703	37	×	×	NOUN
ejpam-5594	703	38	(	(	PUNCT
ejpam-5594	703	39	∫	∫	PROPN
ejpam-5594	703	40	1	1	NUM
ejpam-5594	703	41	0	0	NUM
ejpam-5594	703	42	|1−	|1−	NOUN
ejpam-5594	703	43	2	2	NUM
ejpam-5594	703	44	♭	♭	INTJ
ejpam-5594	703	45	|	|	ADV
ejpam-5594	703	46	∣∣∣∣φ′	∣∣∣∣φ′	PROPN
ejpam-5594	703	47	(	(	PUNCT
ejpam-5594	703	48	♭	♭	INTJ
ejpam-5594	703	49	(	(	PUNCT
ejpam-5594	703	50	k−ȷ)ε1	k−ȷ)ε1	PROPN
ejpam-5594	703	51	+	+	NUM
ejpam-5594	703	52	ȷε2	ȷε2	NOUN
ejpam-5594	703	53	k	k	PROPN
ejpam-5594	703	54	+	+	CCONJ
ejpam-5594	703	55	(	(	PUNCT
ejpam-5594	703	56	1−	1−	NUM
ejpam-5594	703	57	♭	♭	INTJ
ejpam-5594	703	58	)	)	PUNCT
ejpam-5594	703	59	(	(	PUNCT
ejpam-5594	703	60	k−ȷ−	k−ȷ−	PROPN
ejpam-5594	703	61	1)ε1	1)ε1	NUM
ejpam-5594	703	62	+	+	CCONJ
ejpam-5594	703	63	(	(	PUNCT
ejpam-5594	703	64	ȷ+	ȷ+	ADV
ejpam-5594	703	65	1)ε2	1)ε2	NUM
ejpam-5594	703	66	k	k	NOUN
ejpam-5594	703	67	)	)	PUNCT
ejpam-5594	703	68	∣∣∣∣q	∣∣∣∣q	PROPN
ejpam-5594	704	1	d	d	X
ejpam-5594	704	2	♭	♭	PROPN
ejpam-5594	704	3	)	)	PUNCT
ejpam-5594	704	4	1	1	NUM
ejpam-5594	704	5	q	q	NOUN
ejpam-5594	704	6	.	.	PUNCT
ejpam-5594	705	1	as	as	SCONJ
ejpam-5594	705	2	|φ′|q	|φ′|q	PUNCT
ejpam-5594	705	3	is	be	AUX
ejpam-5594	705	4	cr	cr	PROPN
ejpam-5594	705	5	-	-	PUNCT
ejpam-5594	705	6	h	h	NOUN
ejpam-5594	705	7	-	-	PUNCT
ejpam-5594	705	8	godunova	godunova	ADJ
ejpam-5594	705	9	-	-	PUNCT
ejpam-5594	705	10	levin	levin	PROPN
ejpam-5594	705	11	function	function	PROPN
ejpam-5594	705	12	,	,	PUNCT
ejpam-5594	705	13	we	we	PRON
ejpam-5594	705	14	have	have	VERB
ejpam-5594	705	15	|bk(φ	|bk(φ	NUM
ejpam-5594	705	16	,	,	PUNCT
ejpam-5594	705	17	ε1	ε1	PROPN
ejpam-5594	705	18	,	,	PUNCT
ejpam-5594	705	19	ε2)|	ε2)|	PROPN
ejpam-5594	705	20	⪯cr	⪯cr	NUM
ejpam-5594	705	21	k−1∑	k−1∑	PROPN
ejpam-5594	705	22	ȷ=0	ȷ=0	PROPN
ejpam-5594	706	1	ε2	ε2	ADJ
ejpam-5594	706	2	−	−	PROPN
ejpam-5594	706	3	ε1	ε1	PROPN
ejpam-5594	706	4	2k2	2k2	NUM
ejpam-5594	707	1	[	[	X
ejpam-5594	707	2	∫	∫	PROPN
ejpam-5594	707	3	1	1	NUM
ejpam-5594	707	4	0	0	NUM
ejpam-5594	707	5	|1−	|1−	NOUN
ejpam-5594	707	6	2	2	NUM
ejpam-5594	707	7	♭	♭	PROPN
ejpam-5594	707	8	|d	|d	NOUN
ejpam-5594	707	9	♭	♭	X
ejpam-5594	707	10	]	]	SYM
ejpam-5594	707	11	1−	1−	NUM
ejpam-5594	707	12	1	1	NUM
ejpam-5594	707	13	q	q	NOUN
ejpam-5594	708	1	[	[	X
ejpam-5594	708	2	∫	∫	PROPN
ejpam-5594	708	3	1	1	NUM
ejpam-5594	708	4	0	0	NUM
ejpam-5594	708	5	|1−	|1−	NOUN
ejpam-5594	708	6	2	2	NUM
ejpam-5594	708	7	♭	♭	NOUN
ejpam-5594	708	8	|	|	NOUN
ejpam-5594	708	9	(	(	PUNCT
ejpam-5594	708	10	1	1	NUM
ejpam-5594	708	11	h	h	NOUN
ejpam-5594	708	12	(	(	PUNCT
ejpam-5594	708	13	♭	♭	INTJ
ejpam-5594	708	14	)	)	PUNCT
ejpam-5594	708	15	∣∣∣∣φ′	∣∣∣∣φ′	INTJ
ejpam-5594	708	16	(	(	PUNCT
ejpam-5594	708	17	(	(	PUNCT
ejpam-5594	708	18	k−ȷ)ε1	k−ȷ)ε1	X
ejpam-5594	708	19	+	+	NUM
ejpam-5594	708	20	ȷε2	ȷε2	NOUN
ejpam-5594	708	21	k	k	PROPN
ejpam-5594	708	22	)	)	PUNCT
ejpam-5594	708	23	∣∣∣∣q	∣∣∣∣q	PROPN
ejpam-5594	709	1	+	+	PUNCT
ejpam-5594	709	2	1	1	NUM
ejpam-5594	709	3	h(1−	h(1−	NOUN
ejpam-5594	709	4	♭	♭	PROPN
ejpam-5594	709	5	)	)	PUNCT
ejpam-5594	709	6	·	·	PUNCT
ejpam-5594	710	1	∣∣∣∣φ′	∣∣∣∣φ′	INTJ
ejpam-5594	710	2	(	(	PUNCT
ejpam-5594	710	3	(	(	PUNCT
ejpam-5594	710	4	k−ȷ−	k−ȷ−	PROPN
ejpam-5594	710	5	1)ε1	1)ε1	NUM
ejpam-5594	710	6	+	+	CCONJ
ejpam-5594	710	7	(	(	PUNCT
ejpam-5594	710	8	ȷ+	ȷ+	ADV
ejpam-5594	710	9	1)ε2	1)ε2	NUM
ejpam-5594	710	10	k	k	NOUN
ejpam-5594	710	11	)	)	PUNCT
ejpam-5594	710	12	∣∣∣∣q)d	∣∣∣∣q)d	X
ejpam-5594	710	13	♭	♭	PROPN
ejpam-5594	710	14	]	]	PUNCT
ejpam-5594	710	15	1	1	NUM
ejpam-5594	710	16	q	q	NOUN
ejpam-5594	710	17	=	=	SYM
ejpam-5594	710	18	k−1∑	k−1∑	X
ejpam-5594	710	19	ȷ=0	ȷ=0	PROPN
ejpam-5594	710	20	ε2	ε2	ADJ
ejpam-5594	710	21	−	−	PROPN
ejpam-5594	710	22	ε1	ε1	PROPN
ejpam-5594	710	23	2k2	2k2	NUM
ejpam-5594	710	24	(	(	PUNCT
ejpam-5594	710	25	∫	∫	PROPN
ejpam-5594	710	26	1	1	NUM
ejpam-5594	710	27	0	0	NUM
ejpam-5594	710	28	|1−	|1−	NOUN
ejpam-5594	710	29	2	2	NUM
ejpam-5594	710	30	♭	♭	PROPN
ejpam-5594	710	31	|d	|d	NOUN
ejpam-5594	710	32	♭	♭	PROPN
ejpam-5594	710	33	)	)	PUNCT
ejpam-5594	710	34	1−	1−	PROPN
ejpam-5594	710	35	1	1	NUM
ejpam-5594	710	36	q	q	NOUN
ejpam-5594	710	37	(	(	PUNCT
ejpam-5594	710	38	∫	∫	PROPN
ejpam-5594	710	39	1	1	NUM
ejpam-5594	710	40	0	0	NUM
ejpam-5594	710	41	|1−	|1−	NOUN
ejpam-5594	710	42	2	2	NUM
ejpam-5594	710	43	♭	♭	INTJ
ejpam-5594	710	44	|	|	ADJ
ejpam-5594	710	45	h	h	NOUN
ejpam-5594	710	46	(	(	PUNCT
ejpam-5594	710	47	♭	♭	INTJ
ejpam-5594	710	48	)	)	PUNCT
ejpam-5594	710	49	∣∣∣∣φ′	∣∣∣∣φ′	INTJ
ejpam-5594	710	50	(	(	PUNCT
ejpam-5594	710	51	(	(	PUNCT
ejpam-5594	710	52	k−ȷ)ε1	k−ȷ)ε1	X
ejpam-5594	710	53	+	+	NUM
ejpam-5594	710	54	ȷε2	ȷε2	NOUN
ejpam-5594	710	55	k	k	PROPN
ejpam-5594	710	56	)	)	PUNCT
ejpam-5594	710	57	∣∣∣∣q	∣∣∣∣q	PUNCT
ejpam-5594	711	1	d	d	PUNCT
ejpam-5594	711	2	♭	♭	PROPN
ejpam-5594	711	3	+	+	NUM
ejpam-5594	711	4	∫	∫	PROPN
ejpam-5594	711	5	1	1	NUM
ejpam-5594	711	6	0	0	NUM
ejpam-5594	711	7	|1−	|1−	NOUN
ejpam-5594	711	8	2	2	NUM
ejpam-5594	711	9	♭	♭	NOUN
ejpam-5594	711	10	|	|	NOUN
ejpam-5594	711	11	h(1−	h(1−	NOUN
ejpam-5594	711	12	♭	♭	INTJ
ejpam-5594	711	13	)	)	PUNCT
ejpam-5594	712	1	∣∣∣∣φ′	∣∣∣∣φ′	INTJ
ejpam-5594	712	2	(	(	PUNCT
ejpam-5594	712	3	(	(	PUNCT
ejpam-5594	712	4	k−ȷ−	k−ȷ−	PROPN
ejpam-5594	712	5	1)ε1	1)ε1	NUM
ejpam-5594	712	6	+	+	CCONJ
ejpam-5594	712	7	(	(	PUNCT
ejpam-5594	712	8	ȷ+	ȷ+	ADV
ejpam-5594	712	9	1)ε2	1)ε2	NUM
ejpam-5594	712	10	k	k	NOUN
ejpam-5594	712	11	)	)	PUNCT
ejpam-5594	712	12	∣∣∣∣q	∣∣∣∣q	PROPN
ejpam-5594	713	1	d	d	X
ejpam-5594	713	2	♭	♭	PROPN
ejpam-5594	713	3	)	)	PUNCT
ejpam-5594	713	4	1	1	NUM
ejpam-5594	713	5	q	q	NOUN
ejpam-5594	713	6	=	=	SYM
ejpam-5594	713	7	k−1∑	k−1∑	X
ejpam-5594	713	8	ȷ=0	ȷ=0	PROPN
ejpam-5594	713	9	ε2	ε2	ADJ
ejpam-5594	713	10	−	−	PROPN
ejpam-5594	713	11	ε1	ε1	PROPN
ejpam-5594	713	12	2k2	2k2	NUM
ejpam-5594	714	1	[	[	X
ejpam-5594	714	2	(	(	PUNCT
ejpam-5594	714	3	1	1	NUM
ejpam-5594	714	4	2	2	NUM
ejpam-5594	714	5	)	)	PUNCT
ejpam-5594	715	1	q−1	q−1	PROPN
ejpam-5594	715	2	q	q	PROPN
ejpam-5594	716	1	(	(	PUNCT
ejpam-5594	716	2	∫	∫	PROPN
ejpam-5594	716	3	1	1	NUM
ejpam-5594	716	4	0	0	NUM
ejpam-5594	716	5	|1−	|1−	NOUN
ejpam-5594	716	6	2	2	NUM
ejpam-5594	716	7	♭	♭	INTJ
ejpam-5594	716	8	|	|	ADJ
ejpam-5594	716	9	h	h	NOUN
ejpam-5594	716	10	(	(	PUNCT
ejpam-5594	716	11	♭	♭	PROPN
ejpam-5594	716	12	)	)	PUNCT
ejpam-5594	716	13	·	·	PUNCT
ejpam-5594	717	1	∣∣∣∣φ′	∣∣∣∣φ′	INTJ
ejpam-5594	717	2	(	(	PUNCT
ejpam-5594	717	3	(	(	PUNCT
ejpam-5594	717	4	k−ȷ)ε1	k−ȷ)ε1	X
ejpam-5594	717	5	+	+	NUM
ejpam-5594	717	6	ȷε2	ȷε2	NOUN
ejpam-5594	717	7	k	k	PROPN
ejpam-5594	717	8	)	)	PUNCT
ejpam-5594	717	9	∣∣∣∣q	∣∣∣∣q	PUNCT
ejpam-5594	718	1	d	d	PUNCT
ejpam-5594	718	2	♭	♭	PROPN
ejpam-5594	718	3	+	+	NUM
ejpam-5594	718	4	∫	∫	PROPN
ejpam-5594	718	5	1	1	NUM
ejpam-5594	718	6	0	0	NUM
ejpam-5594	718	7	|1−	|1−	NOUN
ejpam-5594	718	8	2	2	NUM
ejpam-5594	718	9	♭	♭	NOUN
ejpam-5594	718	10	|	|	NOUN
ejpam-5594	718	11	h(1−	h(1−	NOUN
ejpam-5594	718	12	♭	♭	INTJ
ejpam-5594	718	13	)	)	PUNCT
ejpam-5594	719	1	∣∣∣∣φ′	∣∣∣∣φ′	INTJ
ejpam-5594	719	2	(	(	PUNCT
ejpam-5594	719	3	(	(	PUNCT
ejpam-5594	719	4	k−ȷ−	k−ȷ−	PROPN
ejpam-5594	719	5	1)ε1	1)ε1	NUM
ejpam-5594	719	6	+	+	CCONJ
ejpam-5594	719	7	(	(	PUNCT
ejpam-5594	719	8	ȷ+	ȷ+	ADV
ejpam-5594	719	9	1)ε2	1)ε2	NUM
ejpam-5594	719	10	k	k	NOUN
ejpam-5594	719	11	)	)	PUNCT
ejpam-5594	719	12	∣∣∣∣q	∣∣∣∣q	PROPN
ejpam-5594	720	1	d	d	X
ejpam-5594	720	2	♭	♭	PROPN
ejpam-5594	720	3	)	)	PUNCT
ejpam-5594	720	4	1	1	NUM
ejpam-5594	720	5	q	q	NOUN
ejpam-5594	720	6	]	]	PUNCT
ejpam-5594	720	7	.	.	PUNCT
ejpam-5594	721	1	corollary	corollary	ADJ
ejpam-5594	721	2	1	1	NUM
ejpam-5594	721	3	.	.	PUNCT
ejpam-5594	722	1	setting	set	VERB
ejpam-5594	722	2	h	h	NOUN
ejpam-5594	722	3	(	(	PUNCT
ejpam-5594	722	4	♭	♭	INTJ
ejpam-5594	722	5	)	)	PUNCT
ejpam-5594	723	1	=	=	SYM
ejpam-5594	723	2	1	1	NUM
ejpam-5594	723	3	♭	♭	PROPN
ejpam-5594	723	4	and	and	CCONJ
ejpam-5594	723	5	φ	φ	NUM
ejpam-5594	723	6	=	=	SYM
ejpam-5594	723	7	φ	φ	PROPN
ejpam-5594	723	8	in	in	ADP
ejpam-5594	723	9	theorem	theorem	PROPN
ejpam-5594	723	10	17	17	NUM
ejpam-5594	723	11	,	,	PUNCT
ejpam-5594	723	12	we	we	PRON
ejpam-5594	723	13	get	get	VERB
ejpam-5594	723	14	|bk(φ	|bk(φ	PRON
ejpam-5594	723	15	,	,	PUNCT
ejpam-5594	723	16	ε1	ε1	PROPN
ejpam-5594	723	17	,	,	PUNCT
ejpam-5594	723	18	ε2)|	ε2)|	PROPN
ejpam-5594	723	19	=	=	SYM
ejpam-5594	723	20	k−1∑	k−1∑	PROPN
ejpam-5594	723	21	ȷ=0	ȷ=0	PROPN
ejpam-5594	723	22	ε2	ε2	ADJ
ejpam-5594	723	23	−	−	PROPN
ejpam-5594	723	24	ε1	ε1	PROPN
ejpam-5594	723	25	k2(2	k2(2	PROPN
ejpam-5594	723	26	)	)	PUNCT
ejpam-5594	723	27	2	2	NUM
ejpam-5594	724	1	+	+	SYM
ejpam-5594	724	2	1	1	NUM
ejpam-5594	724	3	q	q	NOUN
ejpam-5594	724	4	(	(	PUNCT
ejpam-5594	724	5	∣∣∣∣φ′	∣∣∣∣φ′	PROPN
ejpam-5594	724	6	(	(	PUNCT
ejpam-5594	724	7	(	(	PUNCT
ejpam-5594	724	8	k−ȷ)ε1	k−ȷ)ε1	X
ejpam-5594	724	9	+	+	NUM
ejpam-5594	724	10	ȷε2	ȷε2	NOUN
ejpam-5594	724	11	z	z	NOUN
ejpam-5594	724	12	)	)	PUNCT
ejpam-5594	724	13	∣∣∣∣q	∣∣∣∣q	X
ejpam-5594	725	1	+	+	CCONJ
ejpam-5594	725	2	∣∣∣∣φ′	∣∣∣∣φ′	PROPN
ejpam-5594	725	3	(	(	PUNCT
ejpam-5594	725	4	(	(	PUNCT
ejpam-5594	725	5	k−ȷ−	k−ȷ−	PROPN
ejpam-5594	725	6	1)ε1	1)ε1	NUM
ejpam-5594	725	7	+	+	CCONJ
ejpam-5594	725	8	(	(	PUNCT
ejpam-5594	725	9	ȷ+	ȷ+	ADV
ejpam-5594	725	10	1)ε2	1)ε2	NUM
ejpam-5594	725	11	k	k	NOUN
ejpam-5594	725	12	)	)	PUNCT
ejpam-5594	725	13	∣∣∣∣q	∣∣∣∣q	PROPN
ejpam-5594	725	14	)	)	PUNCT
ejpam-5594	725	15	1	1	NUM
ejpam-5594	725	16	q	q	NOUN
ejpam-5594	725	17	which	which	PRON
ejpam-5594	725	18	has	have	AUX
ejpam-5594	725	19	been	be	AUX
ejpam-5594	725	20	obtained	obtain	VERB
ejpam-5594	725	21	by	by	ADP
ejpam-5594	725	22	authors	author	NOUN
ejpam-5594	725	23	in	in	ADP
ejpam-5594	725	24	[	[	X
ejpam-5594	725	25	29	29	NUM
ejpam-5594	725	26	]	]	PUNCT
ejpam-5594	725	27	.	.	PUNCT
ejpam-5594	726	1	j.	j.	PROPN
ejpam-5594	726	2	e.	e.	PROPN
ejpam-5594	726	3	maćıas	maćıas	PROPN
ejpam-5594	726	4	-	-	PUNCT
ejpam-5594	726	5	dı́az	dı́az	NOUN
ejpam-5594	726	6	et	et	NOUN
ejpam-5594	726	7	al	al	PROPN
ejpam-5594	726	8	.	.	PUNCT
ejpam-5594	726	9	/	/	SYM
ejpam-5594	726	10	eur	eur	PROPN
ejpam-5594	726	11	.	.	PUNCT
ejpam-5594	727	1	j.	j.	PROPN
ejpam-5594	727	2	pure	pure	PROPN
ejpam-5594	727	3	appl	appl	PROPN
ejpam-5594	727	4	.	.	PROPN
ejpam-5594	727	5	math	math	PROPN
ejpam-5594	727	6	,	,	PUNCT
ejpam-5594	727	7	17	17	NUM
ejpam-5594	727	8	(	(	PUNCT
ejpam-5594	727	9	4	4	NUM
ejpam-5594	727	10	)	)	PUNCT
ejpam-5594	727	11	(	(	PUNCT
ejpam-5594	727	12	2024	2024	NUM
ejpam-5594	727	13	)	)	PUNCT
ejpam-5594	727	14	,	,	PUNCT
ejpam-5594	727	15	4014	4014	NUM
ejpam-5594	727	16	-	-	SYM
ejpam-5594	727	17	4049	4049	NUM
ejpam-5594	727	18	4041	4041	NUM
ejpam-5594	727	19	corollary	corollary	NOUN
ejpam-5594	727	20	2	2	NUM
ejpam-5594	727	21	.	.	PUNCT
ejpam-5594	727	22	setting	set	VERB
ejpam-5594	727	23	h	h	NOUN
ejpam-5594	727	24	(	(	PUNCT
ejpam-5594	727	25	♭	♭	INTJ
ejpam-5594	727	26	)	)	PUNCT
ejpam-5594	728	1	=	=	SYM
ejpam-5594	728	2	1	1	NUM
ejpam-5594	728	3	♭	♭	PROPN
ejpam-5594	728	4	s	s	NOUN
ejpam-5594	728	5	and	and	CCONJ
ejpam-5594	728	6	φ	φ	PROPN
ejpam-5594	728	7	=	=	SYM
ejpam-5594	728	8	φ	φ	PROPN
ejpam-5594	728	9	in	in	ADP
ejpam-5594	728	10	theorem	theorem	PROPN
ejpam-5594	728	11	17	17	NUM
ejpam-5594	728	12	,	,	PUNCT
ejpam-5594	728	13	we	we	PRON
ejpam-5594	728	14	get	get	VERB
ejpam-5594	728	15	|bk(φ	|bk(φ	PRON
ejpam-5594	728	16	,	,	PUNCT
ejpam-5594	728	17	ε1	ε1	PROPN
ejpam-5594	728	18	,	,	PUNCT
ejpam-5594	728	19	ε2)|	ε2)|	PROPN
ejpam-5594	728	20	⪯cr	⪯cr	NUM
ejpam-5594	728	21	k−1∑	k−1∑	PROPN
ejpam-5594	728	22	ε=0	ε=0	PROPN
ejpam-5594	728	23	ε2	ε2	PROPN
ejpam-5594	728	24	−	−	PROPN
ejpam-5594	728	25	ε1	ε1	PROPN
ejpam-5594	728	26	k22	k22	NOUN
ejpam-5594	728	27	2−	2−	NUM
ejpam-5594	728	28	1	1	NUM
ejpam-5594	728	29	q	q	NOUN
ejpam-5594	728	30	(	(	PUNCT
ejpam-5594	728	31	1	1	NUM
ejpam-5594	728	32	2s(s+	2s(s+	NUM
ejpam-5594	728	33	1)(s+	1)(s+	NUM
ejpam-5594	728	34	2	2	NUM
ejpam-5594	728	35	)	)	PUNCT
ejpam-5594	729	1	+	+	PRON
ejpam-5594	729	2	s	s	X
ejpam-5594	729	3	(	(	PUNCT
ejpam-5594	729	4	s+	s+	NUM
ejpam-5594	729	5	1)(s+	1)(s+	NUM
ejpam-5594	729	6	2	2	NUM
ejpam-5594	729	7	)	)	PUNCT
ejpam-5594	729	8	)	)	PUNCT
ejpam-5594	730	1	1	1	NUM
ejpam-5594	730	2	q	q	NOUN
ejpam-5594	730	3	×	×	NOUN
ejpam-5594	731	1	[	[	X
ejpam-5594	731	2	∣∣∣∣φ′	∣∣∣∣φ′	INTJ
ejpam-5594	731	3	(	(	PUNCT
ejpam-5594	731	4	(	(	PUNCT
ejpam-5594	731	5	k−ε)ε1	k−ε)ε1	PROPN
ejpam-5594	731	6	+	+	ADP
ejpam-5594	731	7	εr	εr	ADJ
ejpam-5594	731	8	k	k	NOUN
ejpam-5594	731	9	)	)	PUNCT
ejpam-5594	731	10	∣∣∣∣q	∣∣∣∣q	PROPN
ejpam-5594	732	1	+	+	CCONJ
ejpam-5594	732	2	∣∣∣∣φ′	∣∣∣∣φ′	PROPN
ejpam-5594	732	3	(	(	PUNCT
ejpam-5594	732	4	(	(	PUNCT
ejpam-5594	732	5	k−ε−	k−ε−	PROPN
ejpam-5594	732	6	1)ε1	1)ε1	NUM
ejpam-5594	732	7	+	+	CCONJ
ejpam-5594	732	8	(	(	PUNCT
ejpam-5594	732	9	ε+	ε+	X
ejpam-5594	732	10	1)ε2	1)ε2	NUM
ejpam-5594	732	11	k	k	NOUN
ejpam-5594	732	12	)	)	PUNCT
ejpam-5594	732	13	∣∣∣∣q	∣∣∣∣q	PROPN
ejpam-5594	732	14	]	]	X
ejpam-5594	732	15	1	1	NUM
ejpam-5594	732	16	q	q	NOUN
ejpam-5594	732	17	,	,	PUNCT
ejpam-5594	732	18	which	which	PRON
ejpam-5594	732	19	has	have	AUX
ejpam-5594	732	20	been	be	AUX
ejpam-5594	732	21	proved	prove	VERB
ejpam-5594	732	22	by	by	ADP
ejpam-5594	732	23	authors	author	NOUN
ejpam-5594	732	24	in	in	ADP
ejpam-5594	732	25	[	[	X
ejpam-5594	732	26	57	57	NUM
ejpam-5594	732	27	]	]	PUNCT
ejpam-5594	732	28	.	.	PUNCT
ejpam-5594	733	1	theorem	theorem	PROPN
ejpam-5594	733	2	18	18	NUM
ejpam-5594	733	3	.	.	PUNCT
ejpam-5594	734	1	let	let	VERB
ejpam-5594	734	2	h	h	NOUN
ejpam-5594	734	3	:	:	PUNCT
ejpam-5594	734	4	(	(	PUNCT
ejpam-5594	734	5	0	0	NUM
ejpam-5594	734	6	,	,	PUNCT
ejpam-5594	734	7	1	1	NUM
ejpam-5594	734	8	)	)	PUNCT
ejpam-5594	734	9	→	→	NOUN
ejpam-5594	734	10	r+	r+	NOUN
ejpam-5594	734	11	and	and	CCONJ
ejpam-5594	734	12	h	h	NOUN
ejpam-5594	734	13	̸=	̸=	PROPN
ejpam-5594	734	14	0	0	NUM
ejpam-5594	734	15	.	.	PUNCT
ejpam-5594	735	1	let	let	VERB
ejpam-5594	735	2	φ	φ	NOUN
ejpam-5594	735	3	:	:	PUNCT
ejpam-5594	736	1	[	[	X
ejpam-5594	736	2	ε1	ε1	NOUN
ejpam-5594	736	3	,	,	PUNCT
ejpam-5594	736	4	ε2	ε2	PROPN
ejpam-5594	736	5	]	]	PUNCT
ejpam-5594	736	6	→	→	SYM
ejpam-5594	736	7	r+	r+	NOUN
ejpam-5594	736	8	i	i	PRON
ejpam-5594	736	9	is	be	AUX
ejpam-5594	736	10	cr	cr	PROPN
ejpam-5594	736	11	-	-	PUNCT
ejpam-5594	736	12	h	h	NOUN
ejpam-5594	736	13	-	-	PUNCT
ejpam-5594	736	14	godunovalevin	godunovalevin	ADJ
ejpam-5594	736	15	mapping	mapping	NOUN
ejpam-5594	736	16	,	,	PUNCT
ejpam-5594	736	17	ε1	ε1	PROPN
ejpam-5594	736	18	,	,	PUNCT
ejpam-5594	736	19	ε2	ε2	PROPN
ejpam-5594	736	20	∈	∈	PROPN
ejpam-5594	736	21	r+	r+	NOUN
ejpam-5594	736	22	,	,	PUNCT
ejpam-5594	736	23	ε1	ε1	VERB
ejpam-5594	736	24	<	<	X
ejpam-5594	736	25	ε2	ε2	ADJ
ejpam-5594	736	26	and	and	CCONJ
ejpam-5594	736	27	[	[	X
ejpam-5594	737	1	h(	h(	PROPN
ejpam-5594	737	2	♭	♭	SYM
ejpam-5594	737	3	)]q	)]q	PUNCT
ejpam-5594	737	4	∈	∈	PROPN
ejpam-5594	737	5	l1[0	l1[0	PROPN
ejpam-5594	737	6	,	,	PUNCT
ejpam-5594	737	7	1],φ	1],φ	NUM
ejpam-5594	737	8	∈	∈	PROPN
ejpam-5594	737	9	l1[ε1	l1[ε1	PROPN
ejpam-5594	737	10	,	,	PUNCT
ejpam-5594	737	11	ε2	ε2	PROPN
ejpam-5594	737	12	]	]	PUNCT
ejpam-5594	737	13	.	.	PUNCT
ejpam-5594	738	1	if	if	SCONJ
ejpam-5594	738	2	|φ′|	|φ′|	PROPN
ejpam-5594	738	3	is	be	AUX
ejpam-5594	738	4	also	also	ADV
ejpam-5594	738	5	cr	cr	NOUN
ejpam-5594	738	6	-	-	PUNCT
ejpam-5594	738	7	h	h	NOUN
ejpam-5594	738	8	-	-	PUNCT
ejpam-5594	738	9	godunova	godunova	ADJ
ejpam-5594	738	10	-	-	PUNCT
ejpam-5594	738	11	levin	levin	PROPN
ejpam-5594	738	12	mapping	mapping	NOUN
ejpam-5594	738	13	on	on	ADP
ejpam-5594	738	14	[	[	X
ejpam-5594	738	15	ε1	ε1	NOUN
ejpam-5594	738	16	,	,	PUNCT
ejpam-5594	738	17	ε2	ε2	PROPN
ejpam-5594	738	18	]	]	PUNCT
ejpam-5594	738	19	,	,	PUNCT
ejpam-5594	738	20	then	then	ADV
ejpam-5594	738	21	the	the	DET
ejpam-5594	738	22	following	follow	VERB
ejpam-5594	738	23	relation	relation	NOUN
ejpam-5594	738	24	|bk(φ	|bk(φ	PROPN
ejpam-5594	738	25	,	,	PUNCT
ejpam-5594	738	26	ε1	ε1	PROPN
ejpam-5594	738	27	,	,	PUNCT
ejpam-5594	738	28	ε2)|	ε2)|	PROPN
ejpam-5594	738	29	⪯cr	⪯cr	NUM
ejpam-5594	738	30	k−1∑	k−1∑	PROPN
ejpam-5594	738	31	ȷ=0	ȷ=0	PROPN
ejpam-5594	738	32	ε2	ε2	ADJ
ejpam-5594	738	33	−	−	PROPN
ejpam-5594	738	34	ε1	ε1	PROPN
ejpam-5594	738	35	2k2	2k2	NUM
ejpam-5594	739	1	[	[	X
ejpam-5594	739	2	(	(	PUNCT
ejpam-5594	739	3	1	1	NUM
ejpam-5594	739	4	1	1	NUM
ejpam-5594	739	5	+	+	CCONJ
ejpam-5594	739	6	p	p	NOUN
ejpam-5594	739	7	)	)	PUNCT
ejpam-5594	739	8	1	1	NUM
ejpam-5594	739	9	p	p	NOUN
ejpam-5594	739	10	×	×	NOUN
ejpam-5594	739	11	(	(	PUNCT
ejpam-5594	739	12	∫	∫	PROPN
ejpam-5594	739	13	1	1	NUM
ejpam-5594	739	14	0	0	NUM
ejpam-5594	739	15	(	(	PUNCT
ejpam-5594	739	16	1	1	NUM
ejpam-5594	739	17	h	h	NOUN
ejpam-5594	739	18	(	(	PUNCT
ejpam-5594	739	19	♭	♭	INTJ
ejpam-5594	739	20	)	)	PUNCT
ejpam-5594	739	21	∣∣∣∣φ′	∣∣∣∣φ′	INTJ
ejpam-5594	739	22	(	(	PUNCT
ejpam-5594	739	23	(	(	PUNCT
ejpam-5594	739	24	k−ȷ)ε1	k−ȷ)ε1	X
ejpam-5594	739	25	+	+	NUM
ejpam-5594	739	26	ȷε2	ȷε2	NOUN
ejpam-5594	739	27	k	k	PROPN
ejpam-5594	739	28	)	)	PUNCT
ejpam-5594	739	29	∣∣∣∣q	∣∣∣∣q	PROPN
ejpam-5594	740	1	+	+	PUNCT
ejpam-5594	740	2	1	1	NUM
ejpam-5594	740	3	h(1−	h(1−	NOUN
ejpam-5594	740	4	♭	♭	INTJ
ejpam-5594	740	5	)	)	PUNCT
ejpam-5594	741	1	∣∣∣∣φ′	∣∣∣∣φ′	INTJ
ejpam-5594	741	2	(	(	PUNCT
ejpam-5594	741	3	(	(	PUNCT
ejpam-5594	741	4	k−ȷ−	k−ȷ−	PROPN
ejpam-5594	741	5	1)ε1	1)ε1	NUM
ejpam-5594	741	6	+	+	CCONJ
ejpam-5594	741	7	(	(	PUNCT
ejpam-5594	741	8	ȷ+	ȷ+	ADV
ejpam-5594	741	9	1)ε2	1)ε2	NUM
ejpam-5594	741	10	k	k	NOUN
ejpam-5594	741	11	)	)	PUNCT
ejpam-5594	741	12	∣∣∣∣q)d	∣∣∣∣q)d	PROPN
ejpam-5594	741	13	♭	♭	PROPN
ejpam-5594	741	14	)	)	PUNCT
ejpam-5594	741	15	1	1	NUM
ejpam-5594	741	16	q	q	NOUN
ejpam-5594	741	17	]	]	PUNCT
ejpam-5594	741	18	holds	hold	NOUN
ejpam-5594	741	19	,	,	PUNCT
ejpam-5594	741	20	where	where	SCONJ
ejpam-5594	741	21	1	1	X
ejpam-5594	741	22	q	q	NOUN
ejpam-5594	741	23	+	+	NUM
ejpam-5594	741	24	1	1	NUM
ejpam-5594	741	25	p	p	NOUN
ejpam-5594	741	26	=	=	NOUN
ejpam-5594	741	27	1	1	X
ejpam-5594	741	28	.	.	PUNCT
ejpam-5594	742	1	proof	proof	NOUN
ejpam-5594	742	2	.	.	PUNCT
ejpam-5594	743	1	assume	assume	VERB
ejpam-5594	743	2	that	that	SCONJ
ejpam-5594	743	3	1	1	X
ejpam-5594	743	4	<	<	X
ejpam-5594	743	5	p.	p.	NOUN
ejpam-5594	743	6	taking	taking	NOUN
ejpam-5594	743	7	into	into	ADP
ejpam-5594	743	8	account	account	NOUN
ejpam-5594	743	9	lemma	lemma	PROPN
ejpam-5594	743	10	2.1	2.1	NUM
ejpam-5594	743	11	and	and	CCONJ
ejpam-5594	743	12	the	the	DET
ejpam-5594	743	13	hölder	hölder	NOUN
ejpam-5594	743	14	inequality	inequality	NOUN
ejpam-5594	743	15	,	,	PUNCT
ejpam-5594	743	16	one	one	PRON
ejpam-5594	743	17	has	have	VERB
ejpam-5594	743	18	|bk(φ	|bk(φ	NUM
ejpam-5594	743	19	,	,	PUNCT
ejpam-5594	743	20	ε1	ε1	PROPN
ejpam-5594	743	21	,	,	PUNCT
ejpam-5594	743	22	ε2)|	ε2)|	PROPN
ejpam-5594	743	23	⪯cr	⪯cr	NUM
ejpam-5594	743	24	k−1∑	k−1∑	PROPN
ejpam-5594	743	25	ȷ=0	ȷ=0	PROPN
ejpam-5594	743	26	ε2	ε2	ADJ
ejpam-5594	743	27	−	−	PROPN
ejpam-5594	743	28	ε1	ε1	PROPN
ejpam-5594	743	29	2k2	2k2	NUM
ejpam-5594	744	1	[	[	X
ejpam-5594	744	2	(	(	PUNCT
ejpam-5594	744	3	∫	∫	PROPN
ejpam-5594	744	4	1	1	NUM
ejpam-5594	744	5	0	0	NUM
ejpam-5594	744	6	∣∣∣∣(1−	∣∣∣∣(1−	NOUN
ejpam-5594	744	7	2	2	NUM
ejpam-5594	744	8	♭	♭	PROPN
ejpam-5594	744	9	)φ′	)φ′	PROPN
ejpam-5594	744	10	(	(	PUNCT
ejpam-5594	744	11	♭	♭	X
ejpam-5594	744	12	(	(	PUNCT
ejpam-5594	744	13	k−ȷ)ε1	k−ȷ)ε1	PROPN
ejpam-5594	744	14	+	+	NUM
ejpam-5594	744	15	ȷε2	ȷε2	NOUN
ejpam-5594	744	16	k	k	PROPN
ejpam-5594	744	17	+	+	CCONJ
ejpam-5594	744	18	(	(	PUNCT
ejpam-5594	744	19	1−	1−	NUM
ejpam-5594	744	20	♭	♭	INTJ
ejpam-5594	744	21	)	)	PUNCT
ejpam-5594	744	22	(	(	PUNCT
ejpam-5594	744	23	k−ȷ−	k−ȷ−	PROPN
ejpam-5594	744	24	1)ε1	1)ε1	NUM
ejpam-5594	744	25	+	+	CCONJ
ejpam-5594	744	26	(	(	PUNCT
ejpam-5594	744	27	ȷ+	ȷ+	ADV
ejpam-5594	744	28	1)ε2	1)ε2	NUM
ejpam-5594	744	29	k	k	NOUN
ejpam-5594	744	30	)	)	PUNCT
ejpam-5594	744	31	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5594	744	32	d	d	NOUN
ejpam-5594	744	33	♭	♭	PROPN
ejpam-5594	744	34	)	)	PUNCT
ejpam-5594	744	35	]	]	PUNCT
ejpam-5594	744	36	⪯cr	⪯cr	CCONJ
ejpam-5594	744	37	k−1∑	k−1∑	PROPN
ejpam-5594	744	38	ȷ=0	ȷ=0	PROPN
ejpam-5594	744	39	ε2	ε2	ADJ
ejpam-5594	744	40	−	−	PROPN
ejpam-5594	744	41	ε1	ε1	PROPN
ejpam-5594	744	42	2k2	2k2	NUM
ejpam-5594	745	1	[	[	X
ejpam-5594	745	2	(	(	PUNCT
ejpam-5594	745	3	∫	∫	PROPN
ejpam-5594	745	4	1	1	NUM
ejpam-5594	745	5	0	0	NUM
ejpam-5594	745	6	|1−	|1−	NOUN
ejpam-5594	745	7	2	2	NUM
ejpam-5594	745	8	♭	♭	SYM
ejpam-5594	745	9	|pd	|pd	X
ejpam-5594	745	10	♭	♭	NOUN
ejpam-5594	745	11	)	)	PUNCT
ejpam-5594	745	12	1	1	NUM
ejpam-5594	745	13	p	p	NOUN
ejpam-5594	745	14	×	×	NOUN
ejpam-5594	745	15	(	(	PUNCT
ejpam-5594	745	16	∫	∫	PROPN
ejpam-5594	745	17	1	1	NUM
ejpam-5594	745	18	0	0	NUM
ejpam-5594	746	1	∣∣∣∣φ′	∣∣∣∣φ′	PROPN
ejpam-5594	746	2	(	(	PUNCT
ejpam-5594	746	3	♭	♭	INTJ
ejpam-5594	746	4	(	(	PUNCT
ejpam-5594	746	5	k−ȷ)ε1	k−ȷ)ε1	PROPN
ejpam-5594	746	6	+	+	ADP
ejpam-5594	746	7	ȷb	ȷb	PROPN
ejpam-5594	746	8	k	k	NOUN
ejpam-5594	746	9	+	+	CCONJ
ejpam-5594	746	10	(	(	PUNCT
ejpam-5594	746	11	1−	1−	NUM
ejpam-5594	746	12	♭	♭	INTJ
ejpam-5594	746	13	)	)	PUNCT
ejpam-5594	746	14	(	(	PUNCT
ejpam-5594	746	15	k−ȷ−	k−ȷ−	PROPN
ejpam-5594	746	16	1)ε1	1)ε1	NUM
ejpam-5594	746	17	+	+	CCONJ
ejpam-5594	746	18	(	(	PUNCT
ejpam-5594	746	19	ȷ+	ȷ+	ADV
ejpam-5594	746	20	1)b	1)b	X
ejpam-5594	746	21	k	k	X
ejpam-5594	746	22	)	)	PUNCT
ejpam-5594	746	23	∣∣∣∣q	∣∣∣∣q	PROPN
ejpam-5594	747	1	d	d	X
ejpam-5594	747	2	♭	♭	PROPN
ejpam-5594	747	3	)	)	PUNCT
ejpam-5594	747	4	1	1	NUM
ejpam-5594	747	5	q	q	NOUN
ejpam-5594	747	6	]	]	PUNCT
ejpam-5594	747	7	.	.	PUNCT
ejpam-5594	748	1	as	as	SCONJ
ejpam-5594	748	2	|φ′|q	|φ′|q	PUNCT
ejpam-5594	748	3	is	be	AUX
ejpam-5594	748	4	cr	cr	PROPN
ejpam-5594	748	5	-	-	PUNCT
ejpam-5594	748	6	h	h	NOUN
ejpam-5594	748	7	-	-	PUNCT
ejpam-5594	748	8	godunova	godunova	ADJ
ejpam-5594	748	9	-	-	PUNCT
ejpam-5594	748	10	levin	levin	PROPN
ejpam-5594	748	11	mapping	mapping	PROPN
ejpam-5594	748	12	,	,	PUNCT
ejpam-5594	748	13	one	one	NUM
ejpam-5594	748	14	has∫	has∫	NOUN
ejpam-5594	748	15	1	1	NUM
ejpam-5594	748	16	0	0	NUM
ejpam-5594	749	1	∣∣∣∣φ′	∣∣∣∣φ′	PROPN
ejpam-5594	749	2	(	(	PUNCT
ejpam-5594	749	3	♭	♭	INTJ
ejpam-5594	749	4	(	(	PUNCT
ejpam-5594	749	5	k−ȷ)ε1	k−ȷ)ε1	PROPN
ejpam-5594	749	6	+	+	NUM
ejpam-5594	749	7	ȷε2	ȷε2	NOUN
ejpam-5594	749	8	k	k	PROPN
ejpam-5594	749	9	+	+	CCONJ
ejpam-5594	749	10	(	(	PUNCT
ejpam-5594	749	11	1−	1−	NUM
ejpam-5594	749	12	♭	♭	INTJ
ejpam-5594	749	13	)	)	PUNCT
ejpam-5594	749	14	(	(	PUNCT
ejpam-5594	749	15	k−ȷ−	k−ȷ−	PROPN
ejpam-5594	749	16	1)ε1	1)ε1	NUM
ejpam-5594	749	17	+	+	CCONJ
ejpam-5594	749	18	(	(	PUNCT
ejpam-5594	749	19	ȷ+	ȷ+	ADV
ejpam-5594	749	20	1)ε2	1)ε2	NUM
ejpam-5594	749	21	k	k	NOUN
ejpam-5594	749	22	)	)	PUNCT
ejpam-5594	749	23	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5594	749	24	d	d	PROPN
ejpam-5594	749	25	♭	♭	PROPN
ejpam-5594	749	26	⪯cr	⪯cr	NUM
ejpam-5594	749	27	∫	∫	PROPN
ejpam-5594	749	28	1	1	NUM
ejpam-5594	749	29	0	0	NUM
ejpam-5594	749	30	(	(	PUNCT
ejpam-5594	749	31	1	1	NUM
ejpam-5594	749	32	h	h	NOUN
ejpam-5594	749	33	(	(	PUNCT
ejpam-5594	749	34	♭	♭	INTJ
ejpam-5594	749	35	)	)	PUNCT
ejpam-5594	750	1	∣∣∣∣φ′	∣∣∣∣φ′	INTJ
ejpam-5594	750	2	(	(	PUNCT
ejpam-5594	750	3	(	(	PUNCT
ejpam-5594	750	4	k−ȷ)ε1	k−ȷ)ε1	X
ejpam-5594	750	5	+	+	NUM
ejpam-5594	750	6	ȷε2	ȷε2	NOUN
ejpam-5594	750	7	k	k	PROPN
ejpam-5594	750	8	)	)	PUNCT
ejpam-5594	750	9	∣∣∣∣q	∣∣∣∣q	PROPN
ejpam-5594	751	1	+	+	PUNCT
ejpam-5594	751	2	1	1	NUM
ejpam-5594	751	3	h(1−	h(1−	NOUN
ejpam-5594	751	4	♭	♭	INTJ
ejpam-5594	751	5	)	)	PUNCT
ejpam-5594	752	1	∣∣∣∣φ′	∣∣∣∣φ′	INTJ
ejpam-5594	752	2	(	(	PUNCT
ejpam-5594	752	3	(	(	PUNCT
ejpam-5594	752	4	k−ȷ−	k−ȷ−	PROPN
ejpam-5594	752	5	1)ε1	1)ε1	NUM
ejpam-5594	752	6	+	+	CCONJ
ejpam-5594	752	7	(	(	PUNCT
ejpam-5594	752	8	ȷ+	ȷ+	ADV
ejpam-5594	752	9	1)ε2	1)ε2	NUM
ejpam-5594	752	10	k	k	NOUN
ejpam-5594	752	11	)	)	PUNCT
ejpam-5594	752	12	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5594	752	13	)	)	PUNCT
ejpam-5594	753	1	d	d	NOUN
ejpam-5594	753	2	♭	♭	INTJ
ejpam-5594	753	3	.	.	PUNCT
ejpam-5594	754	1	therefore	therefore	ADV
ejpam-5594	754	2	,	,	PUNCT
ejpam-5594	754	3	we	we	PRON
ejpam-5594	754	4	deduce	deduce	VERB
ejpam-5594	754	5	j.	j.	PROPN
ejpam-5594	754	6	e.	e.	PROPN
ejpam-5594	754	7	maćıas	maćıas	PROPN
ejpam-5594	754	8	-	-	PUNCT
ejpam-5594	754	9	dı́az	dı́az	NOUN
ejpam-5594	754	10	et	et	NOUN
ejpam-5594	754	11	al	al	PROPN
ejpam-5594	754	12	.	.	PUNCT
ejpam-5594	754	13	/	/	SYM
ejpam-5594	754	14	eur	eur	PROPN
ejpam-5594	754	15	.	.	PUNCT
ejpam-5594	755	1	j.	j.	PROPN
ejpam-5594	755	2	pure	pure	PROPN
ejpam-5594	755	3	appl	appl	PROPN
ejpam-5594	755	4	.	.	PROPN
ejpam-5594	755	5	math	math	PROPN
ejpam-5594	755	6	,	,	PUNCT
ejpam-5594	755	7	17	17	NUM
ejpam-5594	755	8	(	(	PUNCT
ejpam-5594	755	9	4	4	NUM
ejpam-5594	755	10	)	)	PUNCT
ejpam-5594	755	11	(	(	PUNCT
ejpam-5594	755	12	2024	2024	NUM
ejpam-5594	755	13	)	)	PUNCT
ejpam-5594	755	14	,	,	PUNCT
ejpam-5594	755	15	4014	4014	NUM
ejpam-5594	755	16	-	-	SYM
ejpam-5594	755	17	4049	4049	NUM
ejpam-5594	755	18	4042	4042	NUM
ejpam-5594	755	19	|bk(φ	|bk(φ	PROPN
ejpam-5594	755	20	,	,	PUNCT
ejpam-5594	755	21	ε1	ε1	PROPN
ejpam-5594	755	22	,	,	PUNCT
ejpam-5594	755	23	ε2)|	ε2)|	PROPN
ejpam-5594	755	24	⪯cr	⪯cr	NUM
ejpam-5594	755	25	k−1∑	k−1∑	PROPN
ejpam-5594	755	26	ȷ=0	ȷ=0	PROPN
ejpam-5594	755	27	ε2	ε2	ADJ
ejpam-5594	755	28	−	−	PROPN
ejpam-5594	755	29	ε1	ε1	PROPN
ejpam-5594	755	30	2k2	2k2	NUM
ejpam-5594	756	1	[	[	X
ejpam-5594	756	2	(	(	PUNCT
ejpam-5594	756	3	∫	∫	PROPN
ejpam-5594	756	4	1	1	NUM
ejpam-5594	756	5	0	0	NUM
ejpam-5594	756	6	|1−	|1−	NOUN
ejpam-5594	756	7	2	2	NUM
ejpam-5594	756	8	♭	♭	SYM
ejpam-5594	756	9	|pd	|pd	X
ejpam-5594	756	10	♭	♭	NOUN
ejpam-5594	756	11	)	)	PUNCT
ejpam-5594	756	12	1	1	NUM
ejpam-5594	756	13	p	p	NOUN
ejpam-5594	756	14	×	×	NOUN
ejpam-5594	756	15	(	(	PUNCT
ejpam-5594	756	16	∫	∫	PROPN
ejpam-5594	756	17	1	1	NUM
ejpam-5594	756	18	0	0	NUM
ejpam-5594	756	19	(	(	PUNCT
ejpam-5594	756	20	1	1	NUM
ejpam-5594	756	21	h	h	NOUN
ejpam-5594	756	22	(	(	PUNCT
ejpam-5594	756	23	♭	♭	INTJ
ejpam-5594	756	24	)	)	PUNCT
ejpam-5594	756	25	∣∣∣∣φ′	∣∣∣∣φ′	INTJ
ejpam-5594	756	26	(	(	PUNCT
ejpam-5594	756	27	(	(	PUNCT
ejpam-5594	756	28	k−ȷ)ε1	k−ȷ)ε1	X
ejpam-5594	756	29	+	+	NUM
ejpam-5594	756	30	ȷε2	ȷε2	NOUN
ejpam-5594	756	31	k	k	PROPN
ejpam-5594	756	32	)	)	PUNCT
ejpam-5594	756	33	∣∣∣∣q	∣∣∣∣q	PROPN
ejpam-5594	757	1	+	+	PUNCT
ejpam-5594	757	2	1	1	NUM
ejpam-5594	757	3	h(1−	h(1−	NOUN
ejpam-5594	757	4	♭	♭	INTJ
ejpam-5594	757	5	)	)	PUNCT
ejpam-5594	758	1	∣∣∣∣φ′	∣∣∣∣φ′	INTJ
ejpam-5594	758	2	(	(	PUNCT
ejpam-5594	758	3	(	(	PUNCT
ejpam-5594	758	4	k−ȷ−	k−ȷ−	PROPN
ejpam-5594	758	5	1)ε1	1)ε1	NUM
ejpam-5594	758	6	+	+	CCONJ
ejpam-5594	758	7	(	(	PUNCT
ejpam-5594	758	8	ȷ+	ȷ+	ADV
ejpam-5594	758	9	1)ε2	1)ε2	NUM
ejpam-5594	758	10	k	k	NOUN
ejpam-5594	758	11	)	)	PUNCT
ejpam-5594	758	12	∣∣∣∣q	∣∣∣∣q	PROPN
ejpam-5594	758	13	)	)	PUNCT
ejpam-5594	759	1	d	d	X
ejpam-5594	759	2	♭	♭	PROPN
ejpam-5594	759	3	)	)	PUNCT
ejpam-5594	759	4	1	1	NUM
ejpam-5594	759	5	q	q	NOUN
ejpam-5594	759	6	]	]	PUNCT
ejpam-5594	759	7	⪯cr	⪯cr	NUM
ejpam-5594	759	8	k−1∑	k−1∑	PROPN
ejpam-5594	759	9	ȷ=0	ȷ=0	PROPN
ejpam-5594	759	10	ε2	ε2	ADJ
ejpam-5594	759	11	−	−	PROPN
ejpam-5594	759	12	ε1	ε1	PROPN
ejpam-5594	759	13	2k2	2k2	NUM
ejpam-5594	760	1	[	[	X
ejpam-5594	760	2	(	(	PUNCT
ejpam-5594	760	3	1	1	NUM
ejpam-5594	760	4	1	1	NUM
ejpam-5594	760	5	+	+	CCONJ
ejpam-5594	760	6	p	p	NOUN
ejpam-5594	760	7	)	)	PUNCT
ejpam-5594	760	8	1	1	NUM
ejpam-5594	760	9	p	p	NOUN
ejpam-5594	760	10	×	×	NOUN
ejpam-5594	760	11	(	(	PUNCT
ejpam-5594	760	12	∫	∫	PROPN
ejpam-5594	760	13	1	1	NUM
ejpam-5594	760	14	0	0	NUM
ejpam-5594	760	15	(	(	PUNCT
ejpam-5594	760	16	1	1	NUM
ejpam-5594	760	17	h	h	NOUN
ejpam-5594	760	18	(	(	PUNCT
ejpam-5594	760	19	♭	♭	INTJ
ejpam-5594	760	20	)	)	PUNCT
ejpam-5594	760	21	∣∣∣∣φ′	∣∣∣∣φ′	INTJ
ejpam-5594	760	22	(	(	PUNCT
ejpam-5594	760	23	(	(	PUNCT
ejpam-5594	760	24	k−ȷ)ε1	k−ȷ)ε1	X
ejpam-5594	760	25	+	+	NUM
ejpam-5594	760	26	ȷε2	ȷε2	NOUN
ejpam-5594	760	27	k	k	PROPN
ejpam-5594	760	28	)	)	PUNCT
ejpam-5594	760	29	∣∣∣∣q	∣∣∣∣q	PROPN
ejpam-5594	761	1	+	+	PUNCT
ejpam-5594	761	2	1	1	NUM
ejpam-5594	761	3	h(1−	h(1−	NOUN
ejpam-5594	761	4	♭	♭	INTJ
ejpam-5594	761	5	)	)	PUNCT
ejpam-5594	762	1	∣∣∣∣φ′	∣∣∣∣φ′	INTJ
ejpam-5594	762	2	(	(	PUNCT
ejpam-5594	762	3	(	(	PUNCT
ejpam-5594	762	4	k−ȷ−	k−ȷ−	PROPN
ejpam-5594	762	5	1)ε1	1)ε1	NUM
ejpam-5594	762	6	+	+	CCONJ
ejpam-5594	762	7	(	(	PUNCT
ejpam-5594	762	8	ȷ+	ȷ+	ADV
ejpam-5594	762	9	1)ε2	1)ε2	NUM
ejpam-5594	762	10	k	k	NOUN
ejpam-5594	762	11	)	)	PUNCT
ejpam-5594	762	12	∣∣∣∣q	∣∣∣∣q	PROPN
ejpam-5594	762	13	)	)	PUNCT
ejpam-5594	763	1	d	d	X
ejpam-5594	763	2	♭	♭	PROPN
ejpam-5594	763	3	)	)	PUNCT
ejpam-5594	763	4	1	1	NUM
ejpam-5594	763	5	q	q	NOUN
ejpam-5594	763	6	]	]	PUNCT
ejpam-5594	763	7	.	.	PUNCT
ejpam-5594	764	1	remark	remark	PROPN
ejpam-5594	764	2	9	9	NUM
ejpam-5594	764	3	.	.	PUNCT
ejpam-5594	765	1	setting	set	VERB
ejpam-5594	765	2	h	h	NOUN
ejpam-5594	765	3	(	(	PUNCT
ejpam-5594	765	4	♭	♭	INTJ
ejpam-5594	765	5	)	)	PUNCT
ejpam-5594	765	6	=	=	SYM
ejpam-5594	765	7	♭	♭	PROPN
ejpam-5594	765	8	−s	−s	PROPN
ejpam-5594	765	9	and	and	CCONJ
ejpam-5594	765	10	φ	φ	NOUN
ejpam-5594	765	11	=	=	SYM
ejpam-5594	765	12	φ	φ	PROPN
ejpam-5594	765	13	in	in	ADP
ejpam-5594	765	14	theorem	theorem	PROPN
ejpam-5594	765	15	18	18	NUM
ejpam-5594	765	16	,	,	PUNCT
ejpam-5594	765	17	then	then	ADV
ejpam-5594	765	18	we	we	PRON
ejpam-5594	765	19	get	get	AUX
ejpam-5594	765	20	theorem	theorem	VERB
ejpam-5594	765	21	6	6	NUM
ejpam-5594	765	22	in	in	ADP
ejpam-5594	765	23	[	[	X
ejpam-5594	765	24	57	57	NUM
ejpam-5594	765	25	]	]	PUNCT
ejpam-5594	765	26	.	.	PUNCT
ejpam-5594	766	1	4	4	X
ejpam-5594	766	2	.	.	X
ejpam-5594	766	3	applications	application	NOUN
ejpam-5594	766	4	to	to	ADP
ejpam-5594	766	5	special	special	ADJ
ejpam-5594	766	6	means	mean	VERB
ejpam-5594	766	7	the	the	DET
ejpam-5594	766	8	following	follow	VERB
ejpam-5594	766	9	section	section	NOUN
ejpam-5594	766	10	relates	relate	VERB
ejpam-5594	766	11	some	some	PRON
ejpam-5594	766	12	of	of	ADP
ejpam-5594	766	13	our	our	PRON
ejpam-5594	766	14	main	main	ADJ
ejpam-5594	766	15	results	result	NOUN
ejpam-5594	766	16	with	with	ADP
ejpam-5594	766	17	special	special	ADJ
ejpam-5594	766	18	means	mean	NOUN
ejpam-5594	766	19	,	,	PUNCT
ejpam-5594	766	20	and	and	CCONJ
ejpam-5594	766	21	illustrates	illustrate	VERB
ejpam-5594	766	22	some	some	PRON
ejpam-5594	766	23	of	of	ADP
ejpam-5594	766	24	their	their	PRON
ejpam-5594	766	25	applications	application	NOUN
ejpam-5594	766	26	.	.	PUNCT
ejpam-5594	767	1	let	let	VERB
ejpam-5594	767	2	ε1	ε1	VERB
ejpam-5594	767	3	,	,	PUNCT
ejpam-5594	767	4	ε2	ε2	PROPN
ejpam-5594	767	5	∈	∈	PROPN
ejpam-5594	767	6	r	r	NOUN
ejpam-5594	767	7	,	,	PUNCT
ejpam-5594	767	8	(	(	PUNCT
ejpam-5594	767	9	i	i	NOUN
ejpam-5594	767	10	)	)	PUNCT
ejpam-5594	768	1	the	the	DET
ejpam-5594	768	2	arithmetic	arithmetic	ADJ
ejpam-5594	768	3	mean	mean	NOUN
ejpam-5594	768	4	:	:	PUNCT
ejpam-5594	768	5	a	a	DET
ejpam-5594	768	6	=	=	PUNCT
ejpam-5594	768	7	a(ε1	a(ε1	NOUN
ejpam-5594	768	8	,	,	PUNCT
ejpam-5594	768	9	ε2	ε2	PROPN
ejpam-5594	768	10	)	)	PUNCT
ejpam-5594	768	11	:	:	PUNCT
ejpam-5594	768	12	=	=	SYM
ejpam-5594	768	13	ε1	ε1	PROPN
ejpam-5594	768	14	+	+	CCONJ
ejpam-5594	768	15	ε2	ε2	ADJ
ejpam-5594	768	16	2	2	NUM
ejpam-5594	768	17	,	,	PUNCT
ejpam-5594	768	18	ε1	ε1	PROPN
ejpam-5594	768	19	,	,	PUNCT
ejpam-5594	768	20	ε2	ε2	ADJ
ejpam-5594	768	21	≥	≥	NOUN
ejpam-5594	768	22	0	0	NUM
ejpam-5594	768	23	.	.	PUNCT
ejpam-5594	769	1	(	(	PUNCT
ejpam-5594	769	2	ii	ii	NOUN
ejpam-5594	769	3	)	)	PUNCT
ejpam-5594	769	4	the	the	DET
ejpam-5594	769	5	harmonic	harmonic	ADJ
ejpam-5594	769	6	mean	mean	NOUN
ejpam-5594	769	7	:	:	PUNCT
ejpam-5594	769	8	h	h	NOUN
ejpam-5594	769	9	=	=	PUNCT
ejpam-5594	769	10	h(ε1	h(ε1	PROPN
ejpam-5594	769	11	,	,	PUNCT
ejpam-5594	769	12	ε2	ε2	PROPN
ejpam-5594	769	13	)	)	PUNCT
ejpam-5594	769	14	:	:	PUNCT
ejpam-5594	770	1	=	=	SYM
ejpam-5594	770	2	2ε1ε2	2ε1ε2	NUM
ejpam-5594	770	3	ε1	ε1	PROPN
ejpam-5594	770	4	+	+	CCONJ
ejpam-5594	770	5	ε2	ε2	ADV
ejpam-5594	770	6	,	,	PUNCT
ejpam-5594	770	7	ε1	ε1	PROPN
ejpam-5594	770	8	,	,	PUNCT
ejpam-5594	770	9	ε2	ε2	ADJ
ejpam-5594	770	10	>	>	X
ejpam-5594	770	11	0	0	X
ejpam-5594	770	12	.	.	PUNCT
ejpam-5594	770	13	(	(	PUNCT
ejpam-5594	770	14	iii	iii	X
ejpam-5594	770	15	)	)	PUNCT
ejpam-5594	770	16	the	the	DET
ejpam-5594	770	17	logarithmic	logarithmic	ADJ
ejpam-5594	770	18	mean	mean	NOUN
ejpam-5594	770	19	:	:	PUNCT
ejpam-5594	770	20	l	l	NOUN
ejpam-5594	770	21	=	=	SYM
ejpam-5594	770	22	l(ε1	l(ε1	PROPN
ejpam-5594	770	23	,	,	PUNCT
ejpam-5594	770	24	ε2	ε2	ADJ
ejpam-5594	770	25	)	)	PUNCT
ejpam-5594	770	26	:	:	PUNCT
ejpam-5594	770	27	=	=	PRON
ejpam-5594	770	28	{	{	PUNCT
ejpam-5594	770	29	ε1	ε1	PROPN
ejpam-5594	770	30	,	,	PUNCT
ejpam-5594	770	31	if	if	SCONJ
ejpam-5594	770	32	ε1	ε1	PROPN
ejpam-5594	770	33	=	=	SYM
ejpam-5594	770	34	ε2	ε2	PROPN
ejpam-5594	770	35	ε2−ε1	ε2−ε1	PROPN
ejpam-5594	770	36	ln	ln	PROPN
ejpam-5594	770	37	ε2−ln	ε2−ln	PROPN
ejpam-5594	770	38	ε1	ε1	PROPN
ejpam-5594	770	39	,	,	PUNCT
ejpam-5594	770	40	if	if	SCONJ
ejpam-5594	770	41	ε1	ε1	VERB
ejpam-5594	770	42	̸=	̸=	PROPN
ejpam-5594	770	43	ε2	ε2	NOUN
ejpam-5594	770	44	,	,	PUNCT
ejpam-5594	770	45	ε1	ε1	PROPN
ejpam-5594	770	46	,	,	PUNCT
ejpam-5594	770	47	ε2	ε2	ADJ
ejpam-5594	770	48	>	>	X
ejpam-5594	770	49	0	0	X
ejpam-5594	770	50	.	.	PUNCT
ejpam-5594	770	51	(	(	PUNCT
ejpam-5594	770	52	iv	iv	X
ejpam-5594	770	53	)	)	PUNCT
ejpam-5594	770	54	the	the	DET
ejpam-5594	770	55	p	p	NOUN
ejpam-5594	770	56	-	-	PUNCT
ejpam-5594	770	57	logarithmic	logarithmic	ADJ
ejpam-5594	770	58	mean	mean	NOUN
ejpam-5594	770	59	:	:	PUNCT
ejpam-5594	770	60	lp	lp	PROPN
ejpam-5594	770	61	=	=	SYM
ejpam-5594	770	62	lp(ε1	lp(ε1	X
ejpam-5594	770	63	,	,	PUNCT
ejpam-5594	770	64	ε2	ε2	NOUN
ejpam-5594	770	65	)	)	PUNCT
ejpam-5594	770	66	:	:	PUNCT
ejpam-5594	770	67	=	=	X
ejpam-5594	770	68			PUNCT
ejpam-5594	770	69	ε1	ε1	PROPN
ejpam-5594	770	70	,	,	PUNCT
ejpam-5594	770	71	if	if	SCONJ
ejpam-5594	770	72	ε1	ε1	PROPN
ejpam-5594	770	73	=	=	SYM
ejpam-5594	770	74	ε2	ε2	PROPN
ejpam-5594	770	75	[	[	PUNCT
ejpam-5594	770	76	rp+1−ε1p+1	rp+1−ε1p+1	NOUN
ejpam-5594	770	77	(	(	PUNCT
ejpam-5594	770	78	p+1)(ε2−ε1	p+1)(ε2−ε1	NOUN
ejpam-5594	770	79	)	)	PUNCT
ejpam-5594	770	80	]	]	PUNCT
ejpam-5594	770	81	1	1	NUM
ejpam-5594	770	82	p	p	NOUN
ejpam-5594	770	83	,	,	PUNCT
ejpam-5594	770	84	if	if	SCONJ
ejpam-5594	770	85	ε1	ε1	VERB
ejpam-5594	770	86	̸=	̸=	PROPN
ejpam-5594	770	87	ε2	ε2	NOUN
ejpam-5594	770	88	,	,	PUNCT
ejpam-5594	770	89	p	p	PROPN
ejpam-5594	770	90	∈	∈	PROPN
ejpam-5594	770	91	r\{−1	r\{−1	NOUN
ejpam-5594	770	92	,	,	PUNCT
ejpam-5594	770	93	0	0	NUM
ejpam-5594	770	94	}	}	PUNCT
ejpam-5594	770	95	,	,	PUNCT
ejpam-5594	770	96	ε1	ε1	PROPN
ejpam-5594	770	97	,	,	PUNCT
ejpam-5594	770	98	ε2	ε2	ADJ
ejpam-5594	770	99	>	>	X
ejpam-5594	770	100	0	0	X
ejpam-5594	770	101	.	.	PUNCT
ejpam-5594	771	1	let	let	AUX
ejpam-5594	771	2	ε1	ε1	VERB
ejpam-5594	771	3	,	,	PUNCT
ejpam-5594	771	4	ε2	ε2	PROPN
ejpam-5594	771	5	∈	∈	PROPN
ejpam-5594	771	6	r	r	NOUN
ejpam-5594	771	7	,	,	PUNCT
ejpam-5594	771	8	0	0	NUM
ejpam-5594	771	9	<	<	X
ejpam-5594	771	10	ε1	ε1	VERB
ejpam-5594	771	11	<	<	X
ejpam-5594	771	12	ε2	ε2	PROPN
ejpam-5594	771	13	,	,	PUNCT
ejpam-5594	771	14	and	and	CCONJ
ejpam-5594	771	15	m	m	PROPN
ejpam-5594	771	16	∈	∈	PROPN
ejpam-5594	771	17	n	n	CCONJ
ejpam-5594	771	18	,	,	PUNCT
ejpam-5594	771	19	m	m	VERB
ejpam-5594	771	20	≥	≥	NOUN
ejpam-5594	771	21	2	2	NUM
ejpam-5594	771	22	.	.	PUNCT
ejpam-5594	772	1	then	then	ADV
ejpam-5594	772	2	,	,	PUNCT
ejpam-5594	772	3	the	the	DET
ejpam-5594	772	4	following	follow	VERB
ejpam-5594	772	5	j.	j.	PROPN
ejpam-5594	772	6	e.	e.	PROPN
ejpam-5594	772	7	maćıas	maćıas	PROPN
ejpam-5594	772	8	-	-	PUNCT
ejpam-5594	772	9	dı́az	dı́az	NOUN
ejpam-5594	772	10	et	et	NOUN
ejpam-5594	772	11	al	al	PROPN
ejpam-5594	772	12	.	.	PUNCT
ejpam-5594	772	13	/	/	SYM
ejpam-5594	772	14	eur	eur	PROPN
ejpam-5594	772	15	.	.	PUNCT
ejpam-5594	773	1	j.	j.	PROPN
ejpam-5594	773	2	pure	pure	PROPN
ejpam-5594	773	3	appl	appl	PROPN
ejpam-5594	773	4	.	.	PROPN
ejpam-5594	773	5	math	math	PROPN
ejpam-5594	773	6	,	,	PUNCT
ejpam-5594	773	7	17	17	NUM
ejpam-5594	773	8	(	(	PUNCT
ejpam-5594	773	9	4	4	NUM
ejpam-5594	773	10	)	)	PUNCT
ejpam-5594	773	11	(	(	PUNCT
ejpam-5594	773	12	2024	2024	NUM
ejpam-5594	773	13	)	)	PUNCT
ejpam-5594	773	14	,	,	PUNCT
ejpam-5594	773	15	4014	4014	NUM
ejpam-5594	773	16	-	-	SYM
ejpam-5594	773	17	4049	4049	NUM
ejpam-5594	773	18	4043∣∣∣∣∣∣	4043∣∣∣∣∣∣	NOUN
ejpam-5594	773	19	k−1∑	k−1∑	PROPN
ejpam-5594	773	20	ȷ=0	ȷ=0	PROPN
ejpam-5594	773	21	1	1	NUM
ejpam-5594	773	22	kȷ	kȷ	PROPN
ejpam-5594	773	23	a	a	X
ejpam-5594	773	24	(	(	PUNCT
ejpam-5594	773	25	(	(	PUNCT
ejpam-5594	773	26	(	(	PUNCT
ejpam-5594	773	27	k−ȷ)ε1	k−ȷ)ε1	X
ejpam-5594	773	28	+	+	NUM
ejpam-5594	773	29	ȷε2	ȷε2	NOUN
ejpam-5594	773	30	k	k	PROPN
ejpam-5594	773	31	)	)	PUNCT
ejpam-5594	773	32	m	m	VERB
ejpam-5594	773	33	,	,	PUNCT
ejpam-5594	773	34	(	(	PUNCT
ejpam-5594	773	35	(	(	PUNCT
ejpam-5594	773	36	k−ȷ−	k−ȷ−	PROPN
ejpam-5594	773	37	1)ε1	1)ε1	NUM
ejpam-5594	773	38	+	+	CCONJ
ejpam-5594	773	39	(	(	PUNCT
ejpam-5594	773	40	ȷ+	ȷ+	ADV
ejpam-5594	773	41	1)ε2	1)ε2	NUM
ejpam-5594	773	42	k	k	NOUN
ejpam-5594	773	43	)	)	PUNCT
ejpam-5594	773	44	m	m	PROPN
ejpam-5594	773	45	)	)	PUNCT
ejpam-5594	773	46	−	−	PROPN
ejpam-5594	774	1	lm	lm	X
ejpam-5594	775	1	m(ε1	m(ε1	NOUN
ejpam-5594	775	2	,	,	PUNCT
ejpam-5594	775	3	ε2	ε2	ADJ
ejpam-5594	775	4	)	)	PUNCT
ejpam-5594	775	5	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-5594	775	6	⪯cr	⪯cr	NUM
ejpam-5594	775	7	k−1∑	k−1∑	PROPN
ejpam-5594	775	8	ȷ=0	ȷ=0	PROPN
ejpam-5594	775	9	(	(	PUNCT
ejpam-5594	775	10	ε2	ε2	ADJ
ejpam-5594	775	11	−	−	NOUN
ejpam-5594	775	12	ε1)m	ε1)m	ADJ
ejpam-5594	775	13	2	2	NUM
ejpam-5594	775	14	2−	2−	NUM
ejpam-5594	775	15	1	1	NUM
ejpam-5594	775	16	q	q	PROPN
ejpam-5594	775	17	k2	k2	PROPN
ejpam-5594	776	1	[	[	X
ejpam-5594	776	2	(	(	PUNCT
ejpam-5594	776	3	∫	∫	PROPN
ejpam-5594	776	4	1	1	NUM
ejpam-5594	776	5	0	0	NUM
ejpam-5594	776	6	|1−	|1−	NOUN
ejpam-5594	776	7	2	2	NUM
ejpam-5594	776	8	♭	♭	INTJ
ejpam-5594	776	9	|	|	ADJ
ejpam-5594	776	10	h	h	NOUN
ejpam-5594	776	11	(	(	PUNCT
ejpam-5594	776	12	♭	♭	INTJ
ejpam-5594	776	13	)	)	PUNCT
ejpam-5594	777	1	d	d	NOUN
ejpam-5594	777	2	♭	♭	PROPN
ejpam-5594	777	3	)	)	PUNCT
ejpam-5594	777	4	(	(	PUNCT
ejpam-5594	777	5	(	(	PUNCT
ejpam-5594	777	6	k−ȷ)ε1	k−ȷ)ε1	X
ejpam-5594	777	7	+	+	NUM
ejpam-5594	777	8	ȷε2	ȷε2	NOUN
ejpam-5594	777	9	k	k	PROPN
ejpam-5594	777	10	)	)	PUNCT
ejpam-5594	777	11	(	(	PUNCT
ejpam-5594	777	12	m−1)q	m−1)q	NOUN
ejpam-5594	777	13	+	+	CCONJ
ejpam-5594	777	14	(	(	PUNCT
ejpam-5594	777	15	∫	∫	PROPN
ejpam-5594	777	16	1	1	NUM
ejpam-5594	777	17	0	0	NUM
ejpam-5594	777	18	|1−	|1−	NOUN
ejpam-5594	777	19	2	2	NUM
ejpam-5594	777	20	♭	♭	NOUN
ejpam-5594	777	21	|	|	NOUN
ejpam-5594	777	22	h(1−	h(1−	NOUN
ejpam-5594	777	23	♭	♭	INTJ
ejpam-5594	777	24	)	)	PUNCT
ejpam-5594	778	1	d	d	NOUN
ejpam-5594	778	2	♭	♭	PROPN
ejpam-5594	778	3	)	)	PUNCT
ejpam-5594	778	4	(	(	PUNCT
ejpam-5594	778	5	(	(	PUNCT
ejpam-5594	778	6	k−ȷ−	k−ȷ−	PROPN
ejpam-5594	778	7	1)ε1	1)ε1	NUM
ejpam-5594	778	8	+	+	CCONJ
ejpam-5594	778	9	(	(	PUNCT
ejpam-5594	778	10	ȷ+	ȷ+	ADV
ejpam-5594	778	11	1)ε2	1)ε2	NUM
ejpam-5594	778	12	k	k	NOUN
ejpam-5594	778	13	)	)	PUNCT
ejpam-5594	778	14	(	(	PUNCT
ejpam-5594	778	15	m−1)q	m−1)q	NOUN
ejpam-5594	778	16	)	)	PUNCT
ejpam-5594	778	17	]	]	PUNCT
ejpam-5594	778	18	1	1	NUM
ejpam-5594	778	19	q	q	NOUN
ejpam-5594	778	20	holds	hold	VERB
ejpam-5594	778	21	,	,	PUNCT
ejpam-5594	778	22	for	for	ADP
ejpam-5594	778	23	all	all	DET
ejpam-5594	778	24	1	1	NUM
ejpam-5594	778	25	⪯cr	⪯cr	NUM
ejpam-5594	778	26	q.	q.	NOUN
ejpam-5594	778	27	proof	proof	NOUN
ejpam-5594	778	28	.	.	PUNCT
ejpam-5594	779	1	this	this	DET
ejpam-5594	779	2	proof	proof	NOUN
ejpam-5594	779	3	is	be	AUX
ejpam-5594	779	4	proven	prove	VERB
ejpam-5594	779	5	using	use	VERB
ejpam-5594	779	6	theorem	theorem	NOUN
ejpam-5594	779	7	17	17	NUM
ejpam-5594	779	8	with	with	ADP
ejpam-5594	779	9	the	the	DET
ejpam-5594	779	10	following	follow	VERB
ejpam-5594	779	11	settings	setting	NOUN
ejpam-5594	779	12	φ	φ	PROPN
ejpam-5594	779	13	(	(	PUNCT
ejpam-5594	779	14	♭	♭	INTJ
ejpam-5594	779	15	)	)	PUNCT
ejpam-5594	779	16	=	=	SYM
ejpam-5594	780	1	♭	♭	PROPN
ejpam-5594	780	2	m	m	PROPN
ejpam-5594	780	3	,	,	PUNCT
ejpam-5594	780	4	♭	♭	PROPN
ejpam-5594	780	5	∈	∈	PROPN
ejpam-5594	781	1	[	[	X
ejpam-5594	781	2	ε1	ε1	NOUN
ejpam-5594	781	3	,	,	PUNCT
ejpam-5594	781	4	ε2	ε2	PROPN
ejpam-5594	781	5	]	]	PUNCT
ejpam-5594	781	6	,	,	PUNCT
ejpam-5594	781	7	m	m	PROPN
ejpam-5594	781	8	∈	∈	PROPN
ejpam-5594	781	9	n	n	CCONJ
ejpam-5594	781	10	,	,	PUNCT
ejpam-5594	781	11	m	m	VERB
ejpam-5594	781	12	≥	≥	NOUN
ejpam-5594	781	13	2	2	X
ejpam-5594	781	14	.	.	PUNCT
ejpam-5594	782	1	let	let	VERB
ejpam-5594	782	2	ε1	ε1	VERB
ejpam-5594	782	3	,	,	PUNCT
ejpam-5594	782	4	ε2	ε2	PROPN
ejpam-5594	782	5	∈	∈	PROPN
ejpam-5594	782	6	r	r	NOUN
ejpam-5594	782	7	,	,	PUNCT
ejpam-5594	782	8	0	0	NUM
ejpam-5594	782	9	<	<	X
ejpam-5594	782	10	ε1	ε1	VERB
ejpam-5594	782	11	<	<	X
ejpam-5594	782	12	ε2	ε2	PROPN
ejpam-5594	782	13	,	,	PUNCT
ejpam-5594	782	14	and	and	CCONJ
ejpam-5594	782	15	m	m	PROPN
ejpam-5594	782	16	∈	∈	PROPN
ejpam-5594	782	17	n	n	CCONJ
ejpam-5594	782	18	,	,	PUNCT
ejpam-5594	782	19	m	m	VERB
ejpam-5594	782	20	≥	≥	NOUN
ejpam-5594	782	21	2	2	NUM
ejpam-5594	782	22	.	.	PUNCT
ejpam-5594	783	1	then	then	ADV
ejpam-5594	783	2	,	,	PUNCT
ejpam-5594	783	3	the	the	DET
ejpam-5594	783	4	following∣∣∣∣∣∣	following∣∣∣∣∣∣	ADJ
ejpam-5594	783	5	k−1∑	k−1∑	X
ejpam-5594	783	6	ȷ=0	ȷ=0	PROPN
ejpam-5594	783	7	1	1	NUM
ejpam-5594	783	8	k	k	NOUN
ejpam-5594	783	9	a	a	X
ejpam-5594	783	10	(	(	PUNCT
ejpam-5594	783	11	(	(	PUNCT
ejpam-5594	783	12	(	(	PUNCT
ejpam-5594	783	13	k−ȷ)ε1	k−ȷ)ε1	X
ejpam-5594	783	14	+	+	NUM
ejpam-5594	783	15	ȷε2	ȷε2	NOUN
ejpam-5594	783	16	k	k	PROPN
ejpam-5594	783	17	)	)	PUNCT
ejpam-5594	783	18	m	m	VERB
ejpam-5594	783	19	,	,	PUNCT
ejpam-5594	783	20	(	(	PUNCT
ejpam-5594	783	21	(	(	PUNCT
ejpam-5594	783	22	k−ȷ−	k−ȷ−	PROPN
ejpam-5594	783	23	1)ε1	1)ε1	NUM
ejpam-5594	783	24	+	+	CCONJ
ejpam-5594	783	25	(	(	PUNCT
ejpam-5594	783	26	ȷ+	ȷ+	ADV
ejpam-5594	783	27	1)ε2	1)ε2	NUM
ejpam-5594	783	28	k	k	NOUN
ejpam-5594	783	29	)	)	PUNCT
ejpam-5594	783	30	m	m	PROPN
ejpam-5594	783	31	)	)	PUNCT
ejpam-5594	784	1	−	−	PROPN
ejpam-5594	784	2	lm	lm	X
ejpam-5594	785	1	m(ε1	m(ε1	NOUN
ejpam-5594	785	2	,	,	PUNCT
ejpam-5594	785	3	ε2	ε2	ADJ
ejpam-5594	785	4	)	)	PUNCT
ejpam-5594	785	5	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-5594	785	6	⪯cr	⪯cr	NUM
ejpam-5594	785	7	k−1∑	k−1∑	PROPN
ejpam-5594	785	8	ȷ=0	ȷ=0	PROPN
ejpam-5594	785	9	(	(	PUNCT
ejpam-5594	785	10	ε2	ε2	ADJ
ejpam-5594	785	11	−	−	NOUN
ejpam-5594	785	12	ε1)m	ε1)m	ADJ
ejpam-5594	785	13	2	2	NUM
ejpam-5594	785	14	2−	2−	NUM
ejpam-5594	785	15	1	1	NUM
ejpam-5594	785	16	q	q	PROPN
ejpam-5594	785	17	k2	k2	X
ejpam-5594	785	18	(	(	PUNCT
ejpam-5594	785	19	1	1	NUM
ejpam-5594	785	20	p+	p+	NOUN
ejpam-5594	785	21	1	1	NUM
ejpam-5594	785	22	)	)	PUNCT
ejpam-5594	785	23	1	1	NUM
ejpam-5594	786	1	p	p	NOUN
ejpam-5594	786	2	×	×	NOUN
ejpam-5594	787	1	[	[	X
ejpam-5594	787	2	(	(	PUNCT
ejpam-5594	787	3	∫	∫	PROPN
ejpam-5594	787	4	1	1	NUM
ejpam-5594	787	5	0	0	NUM
ejpam-5594	787	6	d	d	X
ejpam-5594	787	7	♭	♭	INTJ
ejpam-5594	787	8	h	h	PROPN
ejpam-5594	787	9	(	(	PUNCT
ejpam-5594	787	10	♭	♭	PROPN
ejpam-5594	787	11	)	)	PUNCT
ejpam-5594	787	12	)	)	PUNCT
ejpam-5594	787	13	(	(	PUNCT
ejpam-5594	787	14	(	(	PUNCT
ejpam-5594	787	15	k−ȷ)ε1	k−ȷ)ε1	X
ejpam-5594	787	16	+	+	NUM
ejpam-5594	787	17	ȷε2	ȷε2	NOUN
ejpam-5594	787	18	k	k	PROPN
ejpam-5594	787	19	)	)	PUNCT
ejpam-5594	787	20	(	(	PUNCT
ejpam-5594	787	21	m−1)q	m−1)q	NOUN
ejpam-5594	787	22	+	+	CCONJ
ejpam-5594	787	23	(	(	PUNCT
ejpam-5594	787	24	∫	∫	PROPN
ejpam-5594	787	25	1	1	NUM
ejpam-5594	787	26	0	0	NUM
ejpam-5594	787	27	d	d	X
ejpam-5594	787	28	♭	♭	PROPN
ejpam-5594	787	29	h(1−	h(1−	PROPN
ejpam-5594	787	30	♭	♭	PROPN
ejpam-5594	787	31	)	)	PUNCT
ejpam-5594	787	32	)	)	PUNCT
ejpam-5594	787	33	(	(	PUNCT
ejpam-5594	787	34	(	(	PUNCT
ejpam-5594	787	35	k−ȷ−	k−ȷ−	PROPN
ejpam-5594	787	36	1)ε1	1)ε1	NUM
ejpam-5594	787	37	+	+	CCONJ
ejpam-5594	787	38	(	(	PUNCT
ejpam-5594	787	39	ȷ+	ȷ+	ADV
ejpam-5594	787	40	1)ε2	1)ε2	NUM
ejpam-5594	787	41	k	k	NOUN
ejpam-5594	787	42	)	)	PUNCT
ejpam-5594	787	43	(	(	PUNCT
ejpam-5594	787	44	m−1)q	m−1)q	NOUN
ejpam-5594	787	45	)	)	PUNCT
ejpam-5594	787	46	]	]	PUNCT
ejpam-5594	787	47	1	1	NUM
ejpam-5594	787	48	q	q	NOUN
ejpam-5594	787	49	holds	hold	VERB
ejpam-5594	787	50	,	,	PUNCT
ejpam-5594	787	51	for	for	ADP
ejpam-5594	787	52	all	all	DET
ejpam-5594	787	53	1	1	NUM
ejpam-5594	787	54	⪯cr	⪯cr	NUM
ejpam-5594	787	55	q.	q.	NOUN
ejpam-5594	787	56	proof	proof	NOUN
ejpam-5594	787	57	.	.	PUNCT
ejpam-5594	788	1	this	this	DET
ejpam-5594	788	2	proof	proof	NOUN
ejpam-5594	788	3	is	be	AUX
ejpam-5594	788	4	proven	prove	VERB
ejpam-5594	788	5	using	use	VERB
ejpam-5594	788	6	theorem	theorem	NOUN
ejpam-5594	788	7	18	18	NUM
ejpam-5594	788	8	with	with	ADP
ejpam-5594	788	9	the	the	DET
ejpam-5594	788	10	following	follow	VERB
ejpam-5594	788	11	settings	setting	NOUN
ejpam-5594	788	12	φ	φ	PROPN
ejpam-5594	788	13	(	(	PUNCT
ejpam-5594	788	14	♭	♭	INTJ
ejpam-5594	788	15	)	)	PUNCT
ejpam-5594	788	16	=	=	SYM
ejpam-5594	789	1	♭	♭	PROPN
ejpam-5594	789	2	m	m	PROPN
ejpam-5594	789	3	,	,	PUNCT
ejpam-5594	789	4	♭	♭	PROPN
ejpam-5594	789	5	∈	∈	PROPN
ejpam-5594	790	1	[	[	X
ejpam-5594	790	2	ε1	ε1	NOUN
ejpam-5594	790	3	,	,	PUNCT
ejpam-5594	790	4	ε2	ε2	PROPN
ejpam-5594	790	5	]	]	PUNCT
ejpam-5594	790	6	,	,	PUNCT
ejpam-5594	790	7	m	m	PROPN
ejpam-5594	790	8	∈	∈	PROPN
ejpam-5594	790	9	n	n	CCONJ
ejpam-5594	790	10	,	,	PUNCT
ejpam-5594	790	11	m	m	VERB
ejpam-5594	790	12	≥	≥	NOUN
ejpam-5594	790	13	2	2	NUM
ejpam-5594	790	14	.	.	NOUN
ejpam-5594	790	15	5	5	NUM
ejpam-5594	790	16	.	.	X
ejpam-5594	790	17	conclusion	conclusion	VERB
ejpam-5594	790	18	the	the	DET
ejpam-5594	790	19	primary	primary	ADJ
ejpam-5594	790	20	contribution	contribution	NOUN
ejpam-5594	790	21	in	in	ADP
ejpam-5594	790	22	this	this	DET
ejpam-5594	790	23	paper	paper	NOUN
ejpam-5594	790	24	to	to	PART
ejpam-5594	790	25	present	present	VERB
ejpam-5594	790	26	the	the	DET
ejpam-5594	790	27	different	different	ADJ
ejpam-5594	790	28	variants	variant	NOUN
ejpam-5594	790	29	of	of	ADP
ejpam-5594	790	30	double	double	ADJ
ejpam-5594	790	31	inequalities	inequality	NOUN
ejpam-5594	790	32	by	by	ADP
ejpam-5594	790	33	using	use	VERB
ejpam-5594	790	34	fractional	fractional	ADJ
ejpam-5594	790	35	integral	integral	ADJ
ejpam-5594	790	36	operators	operator	NOUN
ejpam-5594	790	37	involving	involve	VERB
ejpam-5594	790	38	special	special	ADJ
ejpam-5594	790	39	functions	function	NOUN
ejpam-5594	790	40	.	.	PUNCT
ejpam-5594	791	1	recently	recently	ADV
ejpam-5594	791	2	,	,	PUNCT
ejpam-5594	791	3	authors	author	NOUN
ejpam-5594	791	4	in	in	ADP
ejpam-5594	791	5	[	[	X
ejpam-5594	791	6	4	4	NUM
ejpam-5594	791	7	,	,	PUNCT
ejpam-5594	791	8	11	11	NUM
ejpam-5594	791	9	,	,	PUNCT
ejpam-5594	791	10	13	13	NUM
ejpam-5594	791	11	]	]	PUNCT
ejpam-5594	791	12	developed	develop	VERB
ejpam-5594	791	13	several	several	ADJ
ejpam-5594	791	14	relevant	relevant	ADJ
ejpam-5594	791	15	results	result	NOUN
ejpam-5594	791	16	by	by	ADP
ejpam-5594	791	17	using	use	VERB
ejpam-5594	791	18	classical	classical	ADJ
ejpam-5594	791	19	integral	integral	ADJ
ejpam-5594	791	20	operators	operator	NOUN
ejpam-5594	791	21	and	and	CCONJ
ejpam-5594	791	22	partial	partial	ADJ
ejpam-5594	791	23	standard	standard	ADJ
ejpam-5594	791	24	order	order	NOUN
ejpam-5594	791	25	relation	relation	NOUN
ejpam-5594	791	26	.	.	PUNCT
ejpam-5594	792	1	additionally	additionally	ADV
ejpam-5594	792	2	,	,	PUNCT
ejpam-5594	792	3	we	we	PRON
ejpam-5594	792	4	use	use	VERB
ejpam-5594	792	5	a	a	DET
ejpam-5594	792	6	number	number	NOUN
ejpam-5594	792	7	of	of	ADP
ejpam-5594	792	8	other	other	ADJ
ejpam-5594	792	9	wellknown	wellknown	ADJ
ejpam-5594	792	10	inequalities	inequality	NOUN
ejpam-5594	792	11	,	,	PUNCT
ejpam-5594	792	12	including	include	VERB
ejpam-5594	792	13	holder	holder	NOUN
ejpam-5594	792	14	’s	’s	PART
ejpam-5594	792	15	,	,	PUNCT
ejpam-5594	792	16	young	young	ADJ
ejpam-5594	792	17	’s	’s	ADV
ejpam-5594	792	18	,	,	PUNCT
ejpam-5594	792	19	and	and	CCONJ
ejpam-5594	792	20	minkowski	minkowski	PROPN
ejpam-5594	792	21	’s	’s	NOUN
ejpam-5594	792	22	,	,	PUNCT
ejpam-5594	792	23	to	to	PART
ejpam-5594	792	24	extend	extend	VERB
ejpam-5594	792	25	these	these	DET
ejpam-5594	792	26	upper	upper	ADJ
ejpam-5594	792	27	bounds	bound	NOUN
ejpam-5594	792	28	for	for	ADP
ejpam-5594	792	29	hermite	hermite	ADJ
ejpam-5594	792	30	-	-	PUNCT
ejpam-5594	792	31	hadamard	hadamard	ADJ
ejpam-5594	792	32	inequality	inequality	NOUN
ejpam-5594	792	33	.	.	PUNCT
ejpam-5594	793	1	furthermore	furthermore	ADV
ejpam-5594	793	2	,	,	PUNCT
ejpam-5594	793	3	these	these	DET
ejpam-5594	793	4	types	type	NOUN
ejpam-5594	793	5	of	of	ADP
ejpam-5594	793	6	results	result	NOUN
ejpam-5594	793	7	involving	involve	VERB
ejpam-5594	793	8	godunova	godunova	PROPN
ejpam-5594	793	9	-	-	PUNCT
ejpam-5594	793	10	levin	levin	NOUN
ejpam-5594	793	11	mappings	mapping	NOUN
ejpam-5594	793	12	and	and	CCONJ
ejpam-5594	793	13	fractional	fractional	ADJ
ejpam-5594	793	14	operators	operator	NOUN
ejpam-5594	793	15	are	be	AUX
ejpam-5594	793	16	not	not	PART
ejpam-5594	793	17	initiated	initiate	VERB
ejpam-5594	793	18	,	,	PUNCT
ejpam-5594	793	19	and	and	CCONJ
ejpam-5594	793	20	we	we	PRON
ejpam-5594	793	21	believe	believe	VERB
ejpam-5594	793	22	that	that	SCONJ
ejpam-5594	793	23	our	our	PRON
ejpam-5594	793	24	study	study	NOUN
ejpam-5594	793	25	opens	open	VERB
ejpam-5594	793	26	up	up	ADP
ejpam-5594	793	27	a	a	DET
ejpam-5594	793	28	whole	whole	ADJ
ejpam-5594	793	29	new	new	ADJ
ejpam-5594	793	30	path	path	NOUN
ejpam-5594	793	31	for	for	ADP
ejpam-5594	793	32	other	other	ADJ
ejpam-5594	793	33	relevant	relevant	ADJ
ejpam-5594	793	34	classes	class	NOUN
ejpam-5594	793	35	of	of	ADP
ejpam-5594	793	36	godunova	godunova	PROPN
ejpam-5594	793	37	-	-	PUNCT
ejpam-5594	793	38	levin	levin	PROPN
ejpam-5594	793	39	functions	function	NOUN
ejpam-5594	793	40	,	,	PUNCT
ejpam-5594	793	41	including	include	VERB
ejpam-5594	793	42	s	s	NOUN
ejpam-5594	793	43	-	-	PUNCT
ejpam-5594	793	44	godunova	godunova	ADJ
ejpam-5594	793	45	-	-	PUNCT
ejpam-5594	793	46	levin	levin	PROPN
ejpam-5594	793	47	,	,	PUNCT
ejpam-5594	793	48	tgs	tgs	PROPN
ejpam-5594	793	49	-	-	PUNCT
ejpam-5594	793	50	godunova	godunova	PROPN
ejpam-5594	793	51	-	-	PUNCT
ejpam-5594	793	52	levin	levin	PROPN
ejpam-5594	793	53	,	,	PUNCT
ejpam-5594	793	54	harmonic	harmonic	NOUN
ejpam-5594	793	55	,	,	PUNCT
ejpam-5594	793	56	and	and	CCONJ
ejpam-5594	793	57	various	various	ADJ
ejpam-5594	793	58	others	other	NOUN
ejpam-5594	793	59	.	.	PUNCT
ejpam-5594	794	1	in	in	ADP
ejpam-5594	794	2	the	the	DET
ejpam-5594	794	3	future	future	NOUN
ejpam-5594	794	4	,	,	PUNCT
ejpam-5594	794	5	we	we	PRON
ejpam-5594	794	6	suggest	suggest	VERB
ejpam-5594	794	7	that	that	SCONJ
ejpam-5594	794	8	readers	reader	NOUN
ejpam-5594	794	9	extend	extend	VERB
ejpam-5594	794	10	these	these	DET
ejpam-5594	794	11	inequalities	inequality	NOUN
ejpam-5594	794	12	to	to	PART
ejpam-5594	794	13	probabilistic	probabilistic	VERB
ejpam-5594	794	14	and	and	CCONJ
ejpam-5594	794	15	fractional	fractional	ADJ
ejpam-5594	794	16	stochastic	stochastic	ADJ
ejpam-5594	794	17	settings	setting	NOUN
ejpam-5594	794	18	,	,	PUNCT
ejpam-5594	794	19	where	where	SCONJ
ejpam-5594	794	20	randomness	randomness	NOUN
ejpam-5594	794	21	is	be	AUX
ejpam-5594	794	22	incorporated	incorporate	VERB
ejpam-5594	794	23	into	into	ADP
ejpam-5594	794	24	the	the	DET
ejpam-5594	794	25	functions	function	NOUN
ejpam-5594	794	26	themselves	themselves	PRON
ejpam-5594	794	27	or	or	CCONJ
ejpam-5594	794	28	into	into	ADP
ejpam-5594	794	29	the	the	DET
ejpam-5594	794	30	bounds	bound	NOUN
ejpam-5594	794	31	,	,	PUNCT
ejpam-5594	794	32	so	so	SCONJ
ejpam-5594	794	33	they	they	PRON
ejpam-5594	794	34	can	can	AUX
ejpam-5594	794	35	use	use	VERB
ejpam-5594	794	36	them	they	PRON
ejpam-5594	794	37	more	more	ADV
ejpam-5594	794	38	effectively	effectively	ADV
ejpam-5594	794	39	in	in	ADP
ejpam-5594	794	40	risk	risk	NOUN
ejpam-5594	794	41	analysis	analysis	NOUN
ejpam-5594	794	42	,	,	PUNCT
ejpam-5594	794	43	finance	finance	NOUN
ejpam-5594	794	44	,	,	PUNCT
ejpam-5594	794	45	or	or	CCONJ
ejpam-5594	794	46	uncertainty	uncertainty	NOUN
ejpam-5594	794	47	quantification	quantification	NOUN
ejpam-5594	794	48	.	.	PUNCT
ejpam-5594	795	1	furthermore	furthermore	ADV
ejpam-5594	795	2	,	,	PUNCT
ejpam-5594	795	3	generalizing	generalize	VERB
ejpam-5594	795	4	hermite	hermite	ADJ
ejpam-5594	795	5	-	-	PUNCT
ejpam-5594	795	6	hadamard	hadamard	ADJ
ejpam-5594	795	7	inequalities	inequality	NOUN
ejpam-5594	795	8	references	reference	NOUN
ejpam-5594	795	9	4044	4044	NUM
ejpam-5594	795	10	to	to	ADP
ejpam-5594	795	11	multiple	multiple	ADJ
ejpam-5594	795	12	variables	variable	NOUN
ejpam-5594	795	13	,	,	PUNCT
ejpam-5594	795	14	especially	especially	ADV
ejpam-5594	795	15	in	in	ADP
ejpam-5594	795	16	convexity	convexity	NOUN
ejpam-5594	795	17	spaces	space	NOUN
ejpam-5594	795	18	like	like	ADP
ejpam-5594	795	19	convex	convex	NOUN
ejpam-5594	795	20	domains	domain	NOUN
ejpam-5594	795	21	in	in	ADP
ejpam-5594	795	22	rn	rn	PROPN
ejpam-5594	795	23	,	,	PUNCT
ejpam-5594	795	24	may	may	AUX
ejpam-5594	795	25	yield	yield	VERB
ejpam-5594	795	26	inequalities	inequality	NOUN
ejpam-5594	795	27	useful	useful	ADJ
ejpam-5594	795	28	in	in	ADP
ejpam-5594	795	29	multivariate	multivariate	NOUN
ejpam-5594	795	30	optimization	optimization	NOUN
ejpam-5594	795	31	,	,	PUNCT
ejpam-5594	795	32	machine	machine	NOUN
ejpam-5594	795	33	learning	learning	NOUN
ejpam-5594	795	34	,	,	PUNCT
ejpam-5594	795	35	and	and	CCONJ
ejpam-5594	795	36	control	control	NOUN
ejpam-5594	795	37	theory	theory	NOUN
ejpam-5594	795	38	.	.	PUNCT
ejpam-5594	796	1	acknowledgements	acknowledgement	NOUN
ejpam-5594	796	2	the	the	DET
ejpam-5594	796	3	authors	author	NOUN
ejpam-5594	796	4	acknowledge	acknowledge	VERB
ejpam-5594	796	5	the	the	DET
ejpam-5594	796	6	financial	financial	ADJ
ejpam-5594	796	7	support	support	NOUN
ejpam-5594	796	8	from	from	ADP
ejpam-5594	796	9	the	the	DET
ejpam-5594	796	10	program	program	NOUN
ejpam-5594	796	11	prosni	prosni	NOUN
ejpam-5594	796	12	of	of	ADP
ejpam-5594	796	13	the	the	DET
ejpam-5594	796	14	university	university	PROPN
ejpam-5594	796	15	of	of	ADP
ejpam-5594	796	16	guadalajara	guadalajara	PROPN
ejpam-5594	796	17	,	,	PUNCT
ejpam-5594	796	18	mexico	mexico	PROPN
ejpam-5594	796	19	.	.	PUNCT
ejpam-5594	797	1	references	reference	NOUN
ejpam-5594	797	2	[	[	X
ejpam-5594	797	3	1	1	NUM
ejpam-5594	797	4	]	]	X
ejpam-5594	797	5	thabet	thabet	ADJ
ejpam-5594	797	6	abdeljawad	abdeljawad	NOUN
ejpam-5594	797	7	.	.	PUNCT
ejpam-5594	798	1	on	on	ADP
ejpam-5594	798	2	conformable	conformable	ADJ
ejpam-5594	798	3	fractional	fractional	ADJ
ejpam-5594	798	4	calculus	calculus	NOUN
ejpam-5594	798	5	.	.	PUNCT
ejpam-5594	799	1	journal	journal	PROPN
ejpam-5594	799	2	of	of	ADP
ejpam-5594	799	3	computational	computational	ADJ
ejpam-5594	799	4	and	and	CCONJ
ejpam-5594	799	5	applied	applied	ADJ
ejpam-5594	799	6	mathematics	mathematic	NOUN
ejpam-5594	799	7	,	,	PUNCT
ejpam-5594	799	8	279:57–66	279:57–66	NUM
ejpam-5594	799	9	,	,	PUNCT
ejpam-5594	799	10	2015	2015	NUM
ejpam-5594	799	11	.	.	PUNCT
ejpam-5594	800	1	[	[	X
ejpam-5594	800	2	2	2	NUM
ejpam-5594	800	3	]	]	X
ejpam-5594	800	4	waqar	waqar	PROPN
ejpam-5594	800	5	afzal	afzal	PROPN
ejpam-5594	800	6	,	,	PUNCT
ejpam-5594	800	7	mujahid	mujahid	NOUN
ejpam-5594	800	8	abbas	abbas	PROPN
ejpam-5594	800	9	,	,	PUNCT
ejpam-5594	800	10	and	and	CCONJ
ejpam-5594	800	11	omar	omar	PROPN
ejpam-5594	800	12	mutab	mutab	PROPN
ejpam-5594	800	13	alsalami	alsalami	NOUN
ejpam-5594	800	14	.	.	PUNCT
ejpam-5594	801	1	bounds	bound	NOUN
ejpam-5594	801	2	of	of	ADP
ejpam-5594	801	3	different	different	ADJ
ejpam-5594	801	4	integral	integral	ADJ
ejpam-5594	801	5	operators	operator	NOUN
ejpam-5594	801	6	in	in	ADP
ejpam-5594	801	7	tensorial	tensorial	ADJ
ejpam-5594	801	8	hilbert	hilbert	NOUN
ejpam-5594	801	9	and	and	CCONJ
ejpam-5594	801	10	variable	variable	ADJ
ejpam-5594	801	11	exponent	exponent	NOUN
ejpam-5594	801	12	function	function	NOUN
ejpam-5594	801	13	spaces	space	VERB
ejpam-5594	801	14	.	.	PUNCT
ejpam-5594	802	1	mathematics	mathematic	NOUN
ejpam-5594	802	2	,	,	PUNCT
ejpam-5594	802	3	12(16):1–33	12(16):1–33	NUM
ejpam-5594	802	4	,	,	PUNCT
ejpam-5594	802	5	2024	2024	NUM
ejpam-5594	802	6	.	.	PUNCT
ejpam-5594	803	1	[	[	X
ejpam-5594	803	2	3	3	NUM
ejpam-5594	803	3	]	]	X
ejpam-5594	803	4	waqar	waqar	PROPN
ejpam-5594	803	5	afzal	afzal	PROPN
ejpam-5594	803	6	,	,	PUNCT
ejpam-5594	803	7	mujahid	mujahid	PROPN
ejpam-5594	803	8	abbas	abbas	PROPN
ejpam-5594	803	9	,	,	PUNCT
ejpam-5594	803	10	waleed	waleed	PROPN
ejpam-5594	803	11	hamali	hamali	PROPN
ejpam-5594	803	12	,	,	PUNCT
ejpam-5594	803	13	ali	ali	PROPN
ejpam-5594	803	14	m	m	PROPN
ejpam-5594	803	15	mahnashi	mahnashi	PROPN
ejpam-5594	803	16	,	,	PUNCT
ejpam-5594	803	17	and	and	CCONJ
ejpam-5594	803	18	m	m	PROPN
ejpam-5594	803	19	de	de	X
ejpam-5594	803	20	la	la	PROPN
ejpam-5594	803	21	sen	sen	PROPN
ejpam-5594	803	22	.	.	PROPN
ejpam-5594	803	23	hermite	hermite	PROPN
ejpam-5594	803	24	–	–	PUNCT
ejpam-5594	803	25	hadamard	hadamard	ADJ
ejpam-5594	803	26	-	-	PUNCT
ejpam-5594	803	27	type	type	NOUN
ejpam-5594	803	28	inequalities	inequality	NOUN
ejpam-5594	803	29	via	via	ADP
ejpam-5594	803	30	caputo	caputo	PROPN
ejpam-5594	803	31	–	–	PUNCT
ejpam-5594	803	32	fabrizio	fabrizio	PROPN
ejpam-5594	803	33	fractional	fractional	NOUN
ejpam-5594	803	34	integral	integral	ADJ
ejpam-5594	803	35	for	for	ADP
ejpam-5594	803	36	hgodunova	hgodunova	PROPN
ejpam-5594	803	37	–	–	PUNCT
ejpam-5594	803	38	levin	levin	PROPN
ejpam-5594	803	39	and	and	CCONJ
ejpam-5594	803	40	(	(	PUNCT
ejpam-5594	803	41	h	h	NOUN
ejpam-5594	803	42	1	1	NUM
ejpam-5594	803	43	,	,	PUNCT
ejpam-5594	803	44	h	h	NOUN
ejpam-5594	803	45	2)-convex	2)-convex	NUM
ejpam-5594	803	46	functions	function	NOUN
ejpam-5594	803	47	.	.	PUNCT
ejpam-5594	804	1	fractal	fractal	ADJ
ejpam-5594	804	2	and	and	CCONJ
ejpam-5594	804	3	fractional	fractional	ADJ
ejpam-5594	804	4	,	,	PUNCT
ejpam-5594	804	5	7(9):687	7(9):687	NUM
ejpam-5594	804	6	,	,	PUNCT
ejpam-5594	804	7	2023	2023	NUM
ejpam-5594	804	8	.	.	PUNCT
ejpam-5594	805	1	[	[	X
ejpam-5594	805	2	4	4	NUM
ejpam-5594	805	3	]	]	X
ejpam-5594	805	4	waqar	waqar	PROPN
ejpam-5594	805	5	afzal	afzal	PROPN
ejpam-5594	805	6	,	,	PUNCT
ejpam-5594	805	7	mujahid	mujahid	PROPN
ejpam-5594	805	8	abbas	abbas	PROPN
ejpam-5594	805	9	,	,	PUNCT
ejpam-5594	805	10	jorge	jorge	PROPN
ejpam-5594	805	11	e	e	PROPN
ejpam-5594	805	12	maćıas	maćıas	PROPN
ejpam-5594	805	13	-	-	PUNCT
ejpam-5594	805	14	dı́az	dı́az	NOUN
ejpam-5594	805	15	,	,	PUNCT
ejpam-5594	805	16	and	and	CCONJ
ejpam-5594	805	17	savin	savin	NOUN
ejpam-5594	805	18	treanţă.	treanţă.	NOUN
ejpam-5594	805	19	some	some	DET
ejpam-5594	805	20	hgodunova	hgodunova	NOUN
ejpam-5594	805	21	–	–	PUNCT
ejpam-5594	805	22	levin	levin	PROPN
ejpam-5594	805	23	function	function	PROPN
ejpam-5594	805	24	inequalities	inequality	NOUN
ejpam-5594	805	25	using	use	VERB
ejpam-5594	805	26	center	center	NOUN
ejpam-5594	805	27	radius	radius	NOUN
ejpam-5594	805	28	(	(	PUNCT
ejpam-5594	805	29	cr	cr	NOUN
ejpam-5594	805	30	)	)	PUNCT
ejpam-5594	805	31	order	order	NOUN
ejpam-5594	805	32	relation	relation	NOUN
ejpam-5594	805	33	.	.	PUNCT
ejpam-5594	806	1	fractal	fractal	PROPN
ejpam-5594	806	2	and	and	CCONJ
ejpam-5594	806	3	fractional	fractional	ADJ
ejpam-5594	806	4	,	,	PUNCT
ejpam-5594	806	5	6(9):518	6(9):518	NUM
ejpam-5594	806	6	,	,	PUNCT
ejpam-5594	806	7	2022	2022	NUM
ejpam-5594	806	8	.	.	PUNCT
ejpam-5594	807	1	[	[	X
ejpam-5594	807	2	5	5	NUM
ejpam-5594	807	3	]	]	X
ejpam-5594	807	4	waqar	waqar	PROPN
ejpam-5594	807	5	afzal	afzal	PROPN
ejpam-5594	807	6	,	,	PUNCT
ejpam-5594	807	7	najla	najla	PROPN
ejpam-5594	807	8	m	m	PROPN
ejpam-5594	807	9	aloraini	aloraini	PROPN
ejpam-5594	807	10	,	,	PUNCT
ejpam-5594	807	11	mujahid	mujahid	NOUN
ejpam-5594	807	12	abbas	abbas	PROPN
ejpam-5594	807	13	,	,	PUNCT
ejpam-5594	807	14	jong	jong	PROPN
ejpam-5594	807	15	-	-	PUNCT
ejpam-5594	807	16	suk	suk	PROPN
ejpam-5594	807	17	ro	ro	NOUN
ejpam-5594	807	18	,	,	PUNCT
ejpam-5594	807	19	and	and	CCONJ
ejpam-5594	807	20	abdullah	abdullah	VERB
ejpam-5594	807	21	a	a	DET
ejpam-5594	807	22	zaagan	zaagan	NOUN
ejpam-5594	807	23	.	.	PUNCT
ejpam-5594	808	1	hermite	hermite	PROPN
ejpam-5594	808	2	-	-	PUNCT
ejpam-5594	808	3	hadamard	hadamard	PROPN
ejpam-5594	808	4	,	,	PUNCT
ejpam-5594	808	5	fejér	fejér	NOUN
ejpam-5594	808	6	and	and	CCONJ
ejpam-5594	808	7	trapezoid	trapezoid	ADJ
ejpam-5594	808	8	type	type	NOUN
ejpam-5594	808	9	inequalities	inequality	NOUN
ejpam-5594	808	10	using	use	VERB
ejpam-5594	808	11	godunova	godunova	PROPN
ejpam-5594	808	12	-	-	PUNCT
ejpam-5594	808	13	levin	levin	PROPN
ejpam-5594	808	14	preinvex	preinvex	PROPN
ejpam-5594	808	15	functions	function	NOUN
ejpam-5594	808	16	via	via	ADP
ejpam-5594	808	17	bhunia	bhunia	NOUN
ejpam-5594	808	18	’s	’s	PART
ejpam-5594	808	19	order	order	NOUN
ejpam-5594	808	20	and	and	CCONJ
ejpam-5594	808	21	with	with	ADP
ejpam-5594	808	22	applications	application	NOUN
ejpam-5594	808	23	to	to	ADP
ejpam-5594	808	24	quadrature	quadrature	NOUN
ejpam-5594	808	25	formula	formula	NOUN
ejpam-5594	808	26	and	and	CCONJ
ejpam-5594	808	27	random	random	ADJ
ejpam-5594	808	28	variable	variable	NOUN
ejpam-5594	808	29	.	.	PUNCT
ejpam-5594	809	1	mathematical	mathematical	ADJ
ejpam-5594	809	2	biosciences	bioscience	NOUN
ejpam-5594	809	3	and	and	CCONJ
ejpam-5594	809	4	engineering	engineering	NOUN
ejpam-5594	809	5	:	:	PUNCT
ejpam-5594	809	6	mbe	mbe	PROPN
ejpam-5594	809	7	,	,	PUNCT
ejpam-5594	809	8	21(2):3422–3447	21(2):3422–3447	NUM
ejpam-5594	809	9	,	,	PUNCT
ejpam-5594	809	10	2024	2024	NUM
ejpam-5594	809	11	.	.	PUNCT
ejpam-5594	810	1	[	[	X
ejpam-5594	810	2	6	6	NUM
ejpam-5594	810	3	]	]	X
ejpam-5594	810	4	waqar	waqar	PROPN
ejpam-5594	810	5	afzal	afzal	PROPN
ejpam-5594	810	6	,	,	PUNCT
ejpam-5594	810	7	thongchai	thongchai	PROPN
ejpam-5594	810	8	botmart	botmart	PROPN
ejpam-5594	810	9	,	,	PUNCT
ejpam-5594	810	10	w	w	PROPN
ejpam-5594	810	11	afzal	afzal	PROPN
ejpam-5594	810	12	,	,	PUNCT
ejpam-5594	810	13	and	and	CCONJ
ejpam-5594	810	14	t	t	PROPN
ejpam-5594	810	15	botmart	botmart	NOUN
ejpam-5594	810	16	.	.	PUNCT
ejpam-5594	811	1	some	some	DET
ejpam-5594	811	2	novel	novel	ADJ
ejpam-5594	811	3	estimates	estimate	NOUN
ejpam-5594	811	4	of	of	ADP
ejpam-5594	811	5	jensen	jensen	PROPN
ejpam-5594	811	6	and	and	CCONJ
ejpam-5594	811	7	hermite	hermite	PROPN
ejpam-5594	811	8	-	-	PUNCT
ejpam-5594	811	9	hadamard	hadamard	ADJ
ejpam-5594	811	10	inequalities	inequality	NOUN
ejpam-5594	811	11	for	for	ADP
ejpam-5594	811	12	h	h	NOUN
ejpam-5594	811	13	-	-	PUNCT
ejpam-5594	811	14	godunova	godunova	ADJ
ejpam-5594	811	15	–	–	PUNCT
ejpam-5594	811	16	levin	levin	PROPN
ejpam-5594	811	17	stochastic	stochastic	NOUN
ejpam-5594	811	18	processes	process	NOUN
ejpam-5594	811	19	.	.	PUNCT
ejpam-5594	812	1	aims	aim	VERB
ejpam-5594	812	2	math	math	NOUN
ejpam-5594	812	3	,	,	PUNCT
ejpam-5594	812	4	8:7277–7291	8:7277–7291	NUM
ejpam-5594	812	5	,	,	PUNCT
ejpam-5594	812	6	2023	2023	NUM
ejpam-5594	812	7	.	.	PUNCT
ejpam-5594	813	1	[	[	X
ejpam-5594	813	2	7	7	NUM
ejpam-5594	813	3	]	]	X
ejpam-5594	813	4	waqar	waqar	PROPN
ejpam-5594	813	5	afzal	afzal	PROPN
ejpam-5594	813	6	,	,	PUNCT
ejpam-5594	813	7	daniel	daniel	PROPN
ejpam-5594	813	8	breaz	breaz	PROPN
ejpam-5594	813	9	,	,	PUNCT
ejpam-5594	813	10	mujahid	mujahid	PROPN
ejpam-5594	813	11	abbas	abbas	PROPN
ejpam-5594	813	12	,	,	PUNCT
ejpam-5594	813	13	luminiţa	luminiţa	PROPN
ejpam-5594	813	14	-	-	PUNCT
ejpam-5594	813	15	ioana	ioana	PROPN
ejpam-5594	813	16	cot̂ırlă	cot̂ırlă	PROPN
ejpam-5594	813	17	,	,	PUNCT
ejpam-5594	813	18	zareen	zareen	X
ejpam-5594	813	19	a	a	DET
ejpam-5594	813	20	khan	khan	PROPN
ejpam-5594	813	21	,	,	PUNCT
ejpam-5594	813	22	and	and	CCONJ
ejpam-5594	813	23	eleonora	eleonora	PROPN
ejpam-5594	813	24	rapeanu	rapeanu	PROPN
ejpam-5594	813	25	.	.	PUNCT
ejpam-5594	814	1	hyers	hyer	NOUN
ejpam-5594	814	2	–	–	PUNCT
ejpam-5594	814	3	ulam	ulam	X
ejpam-5594	814	4	stability	stability	NOUN
ejpam-5594	814	5	of	of	ADP
ejpam-5594	814	6	2	2	NUM
ejpam-5594	814	7	d	d	ADJ
ejpam-5594	814	8	-	-	ADJ
ejpam-5594	814	9	convex	convex	ADJ
ejpam-5594	814	10	mappings	mapping	NOUN
ejpam-5594	814	11	and	and	CCONJ
ejpam-5594	814	12	some	some	DET
ejpam-5594	814	13	related	relate	VERB
ejpam-5594	814	14	new	new	ADJ
ejpam-5594	814	15	hermite	hermite	ADJ
ejpam-5594	814	16	–	–	PUNCT
ejpam-5594	814	17	hadamard	hadamard	NOUN
ejpam-5594	814	18	,	,	PUNCT
ejpam-5594	814	19	pachpatte	pachpatte	NOUN
ejpam-5594	814	20	,	,	PUNCT
ejpam-5594	814	21	and	and	CCONJ
ejpam-5594	814	22	fejér	fejér	NOUN
ejpam-5594	814	23	type	type	VERB
ejpam-5594	814	24	integral	integral	ADJ
ejpam-5594	814	25	inequalities	inequality	NOUN
ejpam-5594	814	26	using	use	VERB
ejpam-5594	814	27	novel	novel	ADJ
ejpam-5594	814	28	fractional	fractional	ADJ
ejpam-5594	814	29	integral	integral	ADJ
ejpam-5594	814	30	operators	operator	NOUN
ejpam-5594	814	31	via	via	ADP
ejpam-5594	814	32	totally	totally	ADV
ejpam-5594	814	33	interval	interval	NOUN
ejpam-5594	814	34	-	-	PUNCT
ejpam-5594	814	35	order	order	NOUN
ejpam-5594	814	36	relations	relation	NOUN
ejpam-5594	814	37	with	with	ADP
ejpam-5594	814	38	open	open	ADJ
ejpam-5594	814	39	problem	problem	NOUN
ejpam-5594	814	40	.	.	PUNCT
ejpam-5594	815	1	mathematics	mathematic	NOUN
ejpam-5594	815	2	,	,	PUNCT
ejpam-5594	815	3	12(8):1238	12(8):1238	NUM
ejpam-5594	815	4	,	,	PUNCT
ejpam-5594	815	5	2024	2024	NUM
ejpam-5594	815	6	.	.	PUNCT
ejpam-5594	816	1	[	[	X
ejpam-5594	816	2	8	8	NUM
ejpam-5594	816	3	]	]	X
ejpam-5594	816	4	waqar	waqar	PROPN
ejpam-5594	816	5	afzal	afzal	PROPN
ejpam-5594	816	6	,	,	PUNCT
ejpam-5594	816	7	khurram	khurram	PROPN
ejpam-5594	816	8	shabbir	shabbir	PROPN
ejpam-5594	816	9	,	,	PUNCT
ejpam-5594	816	10	mubashar	mubashar	NOUN
ejpam-5594	816	11	arshad	arshad	VERB
ejpam-5594	816	12	,	,	PUNCT
ejpam-5594	816	13	joshua	joshua	PROPN
ejpam-5594	816	14	kiddy	kiddy	PROPN
ejpam-5594	816	15	k	k	PROPN
ejpam-5594	816	16	asamoah	asamoah	PROPN
ejpam-5594	816	17	,	,	PUNCT
ejpam-5594	816	18	and	and	CCONJ
ejpam-5594	816	19	ahmed	ahmed	PROPN
ejpam-5594	816	20	m	m	PROPN
ejpam-5594	816	21	galal	galal	PROPN
ejpam-5594	816	22	.	.	PUNCT
ejpam-5594	817	1	some	some	DET
ejpam-5594	817	2	novel	novel	ADJ
ejpam-5594	817	3	estimates	estimate	NOUN
ejpam-5594	817	4	of	of	ADP
ejpam-5594	817	5	integral	integral	ADJ
ejpam-5594	817	6	inequalities	inequality	NOUN
ejpam-5594	817	7	for	for	ADP
ejpam-5594	817	8	a	a	DET
ejpam-5594	817	9	generalized	generalized	ADJ
ejpam-5594	817	10	class	class	NOUN
ejpam-5594	817	11	of	of	ADP
ejpam-5594	817	12	harmonical	harmonical	ADJ
ejpam-5594	817	13	convex	convex	NOUN
ejpam-5594	817	14	mappings	mapping	NOUN
ejpam-5594	817	15	by	by	ADP
ejpam-5594	817	16	means	mean	NOUN
ejpam-5594	817	17	of	of	ADP
ejpam-5594	817	18	center	center	ADJ
ejpam-5594	817	19	-	-	PUNCT
ejpam-5594	817	20	radius	radius	NOUN
ejpam-5594	817	21	order	order	NOUN
ejpam-5594	817	22	relation	relation	NOUN
ejpam-5594	817	23	.	.	PUNCT
ejpam-5594	818	1	journal	journal	PROPN
ejpam-5594	818	2	of	of	ADP
ejpam-5594	818	3	mathematics	mathematic	NOUN
ejpam-5594	818	4	,	,	PUNCT
ejpam-5594	818	5	2023(1):8865992	2023(1):8865992	NUM
ejpam-5594	818	6	,	,	PUNCT
ejpam-5594	818	7	2023	2023	NUM
ejpam-5594	818	8	.	.	PUNCT
ejpam-5594	819	1	references	reference	NOUN
ejpam-5594	819	2	4045	4045	NUM
ejpam-5594	820	1	[	[	X
ejpam-5594	820	2	9	9	NUM
ejpam-5594	820	3	]	]	X
ejpam-5594	820	4	waqar	waqar	PROPN
ejpam-5594	820	5	afzal	afzal	PROPN
ejpam-5594	820	6	,	,	PUNCT
ejpam-5594	820	7	khurram	khurram	PROPN
ejpam-5594	820	8	shabbir	shabbir	PROPN
ejpam-5594	820	9	,	,	PUNCT
ejpam-5594	820	10	and	and	CCONJ
ejpam-5594	820	11	thongchai	thongchai	ADJ
ejpam-5594	820	12	botmart	botmart	PROPN
ejpam-5594	820	13	.	.	PUNCT
ejpam-5594	821	1	generalized	generalize	VERB
ejpam-5594	821	2	version	version	NOUN
ejpam-5594	821	3	of	of	ADP
ejpam-5594	821	4	jensen	jensen	PROPN
ejpam-5594	821	5	and	and	CCONJ
ejpam-5594	821	6	hermite	hermite	PROPN
ejpam-5594	821	7	-	-	PUNCT
ejpam-5594	821	8	hadamard	hadamard	ADJ
ejpam-5594	821	9	inequalities	inequality	NOUN
ejpam-5594	821	10	for	for	ADP
ejpam-5594	821	11	interval	interval	NOUN
ejpam-5594	821	12	-	-	PUNCT
ejpam-5594	821	13	valued	value	VERB
ejpam-5594	821	14	(	(	PUNCT
ejpam-5594	821	15	h1	h1	PROPN
ejpam-5594	821	16	,	,	PUNCT
ejpam-5594	821	17	h2)-godunova	h2)-godunova	PROPN
ejpam-5594	821	18	-	-	PUNCT
ejpam-5594	821	19	levin	levin	PROPN
ejpam-5594	821	20	functions	function	NOUN
ejpam-5594	821	21	.	.	PUNCT
ejpam-5594	822	1	aims	aim	VERB
ejpam-5594	822	2	math	math	NOUN
ejpam-5594	822	3	,	,	PUNCT
ejpam-5594	822	4	7:19372–19387	7:19372–19387	NUM
ejpam-5594	822	5	,	,	PUNCT
ejpam-5594	822	6	2022	2022	NUM
ejpam-5594	822	7	.	.	PUNCT
ejpam-5594	823	1	[	[	X
ejpam-5594	823	2	10	10	NUM
ejpam-5594	823	3	]	]	X
ejpam-5594	823	4	abdullah	abdullah	PROPN
ejpam-5594	823	5	ali	ali	PROPN
ejpam-5594	823	6	h	h	PROPN
ejpam-5594	823	7	ahmadini	ahmadini	PROPN
ejpam-5594	823	8	,	,	PUNCT
ejpam-5594	823	9	waqar	waqar	PROPN
ejpam-5594	823	10	afzal	afzal	PROPN
ejpam-5594	823	11	,	,	PUNCT
ejpam-5594	823	12	mujahid	mujahid	NOUN
ejpam-5594	823	13	abbas	abbas	NOUN
ejpam-5594	823	14	,	,	PUNCT
ejpam-5594	823	15	and	and	CCONJ
ejpam-5594	823	16	elkhateeb	elkhateeb	PROPN
ejpam-5594	823	17	s	s	PROPN
ejpam-5594	823	18	aly	aly	PROPN
ejpam-5594	823	19	.	.	PROPN
ejpam-5594	823	20	weighted	weight	VERB
ejpam-5594	823	21	fejér	fejér	NOUN
ejpam-5594	823	22	,	,	PUNCT
ejpam-5594	823	23	hermite	hermite	ADJ
ejpam-5594	823	24	–	–	PUNCT
ejpam-5594	823	25	hadamard	hadamard	ADJ
ejpam-5594	823	26	,	,	PUNCT
ejpam-5594	823	27	and	and	CCONJ
ejpam-5594	823	28	trapezium	trapezium	NOUN
ejpam-5594	823	29	-	-	PUNCT
ejpam-5594	823	30	type	type	NOUN
ejpam-5594	823	31	inequalities	inequality	NOUN
ejpam-5594	823	32	for	for	ADP
ejpam-5594	823	33	(	(	PUNCT
ejpam-5594	823	34	h	h	NOUN
ejpam-5594	823	35	1	1	NUM
ejpam-5594	823	36	,	,	PUNCT
ejpam-5594	823	37	h	h	NOUN
ejpam-5594	823	38	2	2	NUM
ejpam-5594	823	39	)	)	PUNCT
ejpam-5594	823	40	–	–	PUNCT
ejpam-5594	823	41	godunova	godunova	PROPN
ejpam-5594	823	42	–	–	PUNCT
ejpam-5594	823	43	levin	levin	PROPN
ejpam-5594	823	44	preinvex	preinvex	PROPN
ejpam-5594	823	45	function	function	NOUN
ejpam-5594	823	46	with	with	ADP
ejpam-5594	823	47	applications	application	NOUN
ejpam-5594	823	48	and	and	CCONJ
ejpam-5594	823	49	two	two	NUM
ejpam-5594	823	50	open	open	ADJ
ejpam-5594	823	51	problems	problem	NOUN
ejpam-5594	823	52	.	.	PUNCT
ejpam-5594	824	1	mathematics	mathematic	NOUN
ejpam-5594	824	2	,	,	PUNCT
ejpam-5594	824	3	12(3):382	12(3):382	NUM
ejpam-5594	824	4	,	,	PUNCT
ejpam-5594	824	5	2024	2024	NUM
ejpam-5594	824	6	.	.	PUNCT
ejpam-5594	825	1	[	[	X
ejpam-5594	825	2	11	11	NUM
ejpam-5594	825	3	]	]	X
ejpam-5594	825	4	sabila	sabila	PROPN
ejpam-5594	825	5	ali	ali	PROPN
ejpam-5594	825	6	,	,	PUNCT
ejpam-5594	825	7	rana	rana	PROPN
ejpam-5594	825	8	safdar	safdar	PROPN
ejpam-5594	825	9	ali	ali	PROPN
ejpam-5594	825	10	,	,	PUNCT
ejpam-5594	825	11	miguel	miguel	PROPN
ejpam-5594	825	12	vivas	vivas	PROPN
ejpam-5594	825	13	-	-	PROPN
ejpam-5594	825	14	cortez	cortez	PROPN
ejpam-5594	825	15	,	,	PUNCT
ejpam-5594	825	16	shahid	shahid	PROPN
ejpam-5594	825	17	mubeen	mubeen	PROPN
ejpam-5594	825	18	,	,	PUNCT
ejpam-5594	825	19	gauhar	gauhar	PROPN
ejpam-5594	825	20	rahman	rahman	PROPN
ejpam-5594	825	21	,	,	PUNCT
ejpam-5594	825	22	and	and	CCONJ
ejpam-5594	825	23	kottakkaran	kottakkaran	VERB
ejpam-5594	825	24	sooppy	sooppy	ADJ
ejpam-5594	825	25	nisar	nisar	PROPN
ejpam-5594	825	26	.	.	PUNCT
ejpam-5594	826	1	some	some	DET
ejpam-5594	826	2	fractional	fractional	ADJ
ejpam-5594	826	3	integral	integral	ADJ
ejpam-5594	826	4	inequalities	inequality	NOUN
ejpam-5594	826	5	via	via	ADP
ejpam-5594	826	6	h	h	PROPN
ejpam-5594	826	7	-	-	PUNCT
ejpam-5594	826	8	godunova	godunova	ADJ
ejpam-5594	826	9	–	–	PUNCT
ejpam-5594	826	10	levin	levin	PROPN
ejpam-5594	826	11	preinvex	preinvex	PROPN
ejpam-5594	826	12	function	function	PROPN
ejpam-5594	826	13	.	.	PUNCT
ejpam-5594	827	1	aims	aim	VERB
ejpam-5594	827	2	math	math	NOUN
ejpam-5594	827	3	,	,	PUNCT
ejpam-5594	827	4	7:13832–13844	7:13832–13844	NUM
ejpam-5594	827	5	,	,	PUNCT
ejpam-5594	827	6	2022	2022	NUM
ejpam-5594	827	7	.	.	PUNCT
ejpam-5594	828	1	[	[	X
ejpam-5594	828	2	12	12	NUM
ejpam-5594	828	3	]	]	X
ejpam-5594	828	4	yahya	yahya	PROPN
ejpam-5594	828	5	almalki	almalki	ADV
ejpam-5594	828	6	and	and	CCONJ
ejpam-5594	828	7	waqar	waqar	PROPN
ejpam-5594	828	8	afzal	afzal	PROPN
ejpam-5594	828	9	.	.	PUNCT
ejpam-5594	829	1	some	some	DET
ejpam-5594	829	2	new	new	ADJ
ejpam-5594	829	3	estimates	estimate	NOUN
ejpam-5594	829	4	of	of	ADP
ejpam-5594	829	5	hermite	hermite	ADJ
ejpam-5594	829	6	–	–	PUNCT
ejpam-5594	829	7	hadamard	hadamard	ADJ
ejpam-5594	829	8	inequalities	inequality	NOUN
ejpam-5594	829	9	for	for	ADP
ejpam-5594	829	10	harmonical	harmonical	ADJ
ejpam-5594	829	11	cr	cr	PROPN
ejpam-5594	829	12	-	-	PUNCT
ejpam-5594	829	13	h	h	NOUN
ejpam-5594	829	14	-	-	PUNCT
ejpam-5594	829	15	convex	convex	NOUN
ejpam-5594	829	16	functions	function	NOUN
ejpam-5594	829	17	via	via	ADP
ejpam-5594	829	18	generalized	generalized	ADJ
ejpam-5594	829	19	fractional	fractional	ADJ
ejpam-5594	829	20	integral	integral	ADJ
ejpam-5594	829	21	operator	operator	NOUN
ejpam-5594	829	22	on	on	ADP
ejpam-5594	829	23	set	set	NOUN
ejpam-5594	829	24	-	-	PUNCT
ejpam-5594	829	25	valued	value	VERB
ejpam-5594	829	26	mappings	mapping	NOUN
ejpam-5594	829	27	.	.	PUNCT
ejpam-5594	830	1	mathematics	mathematic	NOUN
ejpam-5594	830	2	,	,	PUNCT
ejpam-5594	830	3	11(19):4041	11(19):4041	NUM
ejpam-5594	830	4	,	,	PUNCT
ejpam-5594	830	5	2023	2023	NUM
ejpam-5594	830	6	.	.	PUNCT
ejpam-5594	831	1	[	[	X
ejpam-5594	831	2	13	13	NUM
ejpam-5594	831	3	]	]	PUNCT
ejpam-5594	831	4	ohud	ohud	PROPN
ejpam-5594	831	5	almutairi	almutairi	PROPN
ejpam-5594	831	6	and	and	CCONJ
ejpam-5594	831	7	adem	adem	PROPN
ejpam-5594	831	8	kılıçman	kılıçman	PROPN
ejpam-5594	831	9	.	.	PUNCT
ejpam-5594	832	1	some	some	DET
ejpam-5594	832	2	integral	integral	ADJ
ejpam-5594	832	3	inequalities	inequality	NOUN
ejpam-5594	832	4	for	for	ADP
ejpam-5594	832	5	h	h	NOUN
ejpam-5594	832	6	-	-	PUNCT
ejpam-5594	832	7	godunova	godunova	ADJ
ejpam-5594	832	8	-	-	PUNCT
ejpam-5594	832	9	levin	levin	PROPN
ejpam-5594	832	10	preinvexity	preinvexity	PROPN
ejpam-5594	832	11	.	.	PUNCT
ejpam-5594	833	1	symmetry	symmetry	PROPN
ejpam-5594	833	2	,	,	PUNCT
ejpam-5594	833	3	11(12):1500	11(12):1500	NUM
ejpam-5594	833	4	,	,	PUNCT
ejpam-5594	833	5	2019	2019	NUM
ejpam-5594	833	6	.	.	PUNCT
ejpam-5594	834	1	[	[	X
ejpam-5594	834	2	14	14	NUM
ejpam-5594	834	3	]	]	X
ejpam-5594	834	4	xiaohua	xiaohua	PROPN
ejpam-5594	834	5	bao	bao	PROPN
ejpam-5594	834	6	,	,	PUNCT
ejpam-5594	834	7	haicen	haicen	PROPN
ejpam-5594	834	8	yuan	yuan	PROPN
ejpam-5594	834	9	,	,	PUNCT
ejpam-5594	834	10	jun	jun	PROPN
ejpam-5594	834	11	shen	shen	PROPN
ejpam-5594	834	12	,	,	PUNCT
ejpam-5594	834	13	chunxun	chunxun	PROPN
ejpam-5594	834	14	liu	liu	PROPN
ejpam-5594	834	15	,	,	PUNCT
ejpam-5594	834	16	xiangsheng	xiangsheng	PROPN
ejpam-5594	834	17	chen	chen	PROPN
ejpam-5594	834	18	,	,	PUNCT
ejpam-5594	834	19	and	and	CCONJ
ejpam-5594	834	20	hongzhi	hongzhi	PROPN
ejpam-5594	834	21	cui	cui	PROPN
ejpam-5594	834	22	.	.	PUNCT
ejpam-5594	835	1	numerical	numerical	ADJ
ejpam-5594	835	2	analysis	analysis	NOUN
ejpam-5594	835	3	of	of	ADP
ejpam-5594	835	4	seismic	seismic	ADJ
ejpam-5594	835	5	response	response	NOUN
ejpam-5594	835	6	of	of	ADP
ejpam-5594	835	7	a	a	DET
ejpam-5594	835	8	circular	circular	ADJ
ejpam-5594	835	9	tunnel	tunnel	NOUN
ejpam-5594	835	10	-	-	PUNCT
ejpam-5594	835	11	rectangular	rectangular	ADJ
ejpam-5594	835	12	underpass	underpass	NOUN
ejpam-5594	835	13	system	system	NOUN
ejpam-5594	835	14	in	in	ADP
ejpam-5594	835	15	liquefiable	liquefiable	ADJ
ejpam-5594	835	16	soil	soil	NOUN
ejpam-5594	835	17	.	.	PUNCT
ejpam-5594	836	1	computers	computer	NOUN
ejpam-5594	836	2	and	and	CCONJ
ejpam-5594	836	3	geotechnics	geotechnic	NOUN
ejpam-5594	836	4	,	,	PUNCT
ejpam-5594	836	5	174:106642	174:106642	NUM
ejpam-5594	836	6	,	,	PUNCT
ejpam-5594	836	7	2024	2024	NUM
ejpam-5594	836	8	.	.	PUNCT
ejpam-5594	837	1	[	[	X
ejpam-5594	837	2	15	15	NUM
ejpam-5594	837	3	]	]	X
ejpam-5594	837	4	bandar	bandar	PROPN
ejpam-5594	837	5	bin	bin	PROPN
ejpam-5594	837	6	-	-	PUNCT
ejpam-5594	837	7	mohsin	mohsin	PROPN
ejpam-5594	837	8	,	,	PUNCT
ejpam-5594	837	9	muhammad	muhammad	PROPN
ejpam-5594	837	10	zakria	zakria	PROPN
ejpam-5594	837	11	javed	javed	PROPN
ejpam-5594	837	12	,	,	PUNCT
ejpam-5594	837	13	muhammad	muhammad	PROPN
ejpam-5594	837	14	uzair	uzair	PROPN
ejpam-5594	837	15	awan	awan	PROPN
ejpam-5594	837	16	,	,	PUNCT
ejpam-5594	837	17	and	and	CCONJ
ejpam-5594	837	18	artion	artion	NOUN
ejpam-5594	837	19	kashuri	kashuri	PROPN
ejpam-5594	837	20	.	.	PUNCT
ejpam-5594	838	1	on	on	ADP
ejpam-5594	838	2	some	some	DET
ejpam-5594	838	3	new	new	ADJ
ejpam-5594	838	4	ab	ab	ADJ
ejpam-5594	838	5	-	-	PUNCT
ejpam-5594	838	6	fractional	fractional	ADJ
ejpam-5594	838	7	inclusion	inclusion	NOUN
ejpam-5594	838	8	relations	relation	NOUN
ejpam-5594	838	9	.	.	PUNCT
ejpam-5594	839	1	fractal	fractal	PROPN
ejpam-5594	839	2	and	and	CCONJ
ejpam-5594	839	3	fractional	fractional	ADJ
ejpam-5594	839	4	,	,	PUNCT
ejpam-5594	839	5	7(10):725	7(10):725	PROPN
ejpam-5594	839	6	,	,	PUNCT
ejpam-5594	839	7	2023	2023	NUM
ejpam-5594	839	8	.	.	PUNCT
ejpam-5594	840	1	[	[	X
ejpam-5594	840	2	16	16	NUM
ejpam-5594	840	3	]	]	X
ejpam-5594	840	4	rp	rp	NOUN
ejpam-5594	840	5	boas	boas	X
ejpam-5594	840	6	jr	jr	PROPN
ejpam-5594	840	7	and	and	CCONJ
ejpam-5594	840	8	mb	mb	PROPN
ejpam-5594	840	9	marcus	marcus	PROPN
ejpam-5594	840	10	.	.	PUNCT
ejpam-5594	841	1	generalizations	generalization	NOUN
ejpam-5594	841	2	of	of	ADP
ejpam-5594	841	3	young	young	PROPN
ejpam-5594	841	4	’s	’s	PART
ejpam-5594	841	5	inequality	inequality	NOUN
ejpam-5594	841	6	.	.	PUNCT
ejpam-5594	842	1	j.	j.	PROPN
ejpam-5594	842	2	math	math	PROPN
ejpam-5594	842	3	.	.	PUNCT
ejpam-5594	843	1	anal	anal	PROPN
ejpam-5594	843	2	.	.	PUNCT
ejpam-5594	843	3	appl	appl	PROPN
ejpam-5594	843	4	,	,	PUNCT
ejpam-5594	843	5	46:36–40	46:36–40	NUM
ejpam-5594	843	6	,	,	PUNCT
ejpam-5594	843	7	1974	1974	NUM
ejpam-5594	843	8	.	.	PUNCT
ejpam-5594	844	1	[	[	X
ejpam-5594	844	2	17	17	NUM
ejpam-5594	844	3	]	]	X
ejpam-5594	844	4	jonathan	jonathan	PROPN
ejpam-5594	844	5	m	m	PROPN
ejpam-5594	844	6	borwein	borwein	PROPN
ejpam-5594	844	7	,	,	PUNCT
ejpam-5594	844	8	jp	jp	NOUN
ejpam-5594	844	9	penot	penot	PROPN
ejpam-5594	844	10	,	,	PUNCT
ejpam-5594	844	11	and	and	CCONJ
ejpam-5594	844	12	m	m	PROPN
ejpam-5594	844	13	thera	thera	NOUN
ejpam-5594	844	14	.	.	PUNCT
ejpam-5594	845	1	conjugate	conjugate	ADJ
ejpam-5594	845	2	convex	convex	NOUN
ejpam-5594	845	3	operators	operator	NOUN
ejpam-5594	845	4	.	.	PUNCT
ejpam-5594	846	1	journal	journal	PROPN
ejpam-5594	846	2	of	of	ADP
ejpam-5594	846	3	mathematical	mathematical	ADJ
ejpam-5594	846	4	analysis	analysis	NOUN
ejpam-5594	846	5	and	and	CCONJ
ejpam-5594	846	6	applications	application	NOUN
ejpam-5594	846	7	,	,	PUNCT
ejpam-5594	846	8	102(2):399–414	102(2):399–414	NUM
ejpam-5594	846	9	,	,	PUNCT
ejpam-5594	846	10	1984	1984	NUM
ejpam-5594	846	11	.	.	PUNCT
ejpam-5594	847	1	[	[	X
ejpam-5594	847	2	18	18	NUM
ejpam-5594	847	3	]	]	PUNCT
ejpam-5594	847	4	sever	sever	PROPN
ejpam-5594	847	5	silvestru	silvestru	PROPN
ejpam-5594	847	6	dragomir	dragomir	PROPN
ejpam-5594	847	7	.	.	PUNCT
ejpam-5594	848	1	hermite	hermite	PROPN
ejpam-5594	848	2	–	–	PUNCT
ejpam-5594	848	3	hadamard	hadamard	NOUN
ejpam-5594	848	4	’s	’s	PART
ejpam-5594	848	5	type	type	NOUN
ejpam-5594	848	6	inequalities	inequality	NOUN
ejpam-5594	848	7	for	for	ADP
ejpam-5594	848	8	operator	operator	NOUN
ejpam-5594	848	9	convex	convex	NOUN
ejpam-5594	848	10	functions	function	NOUN
ejpam-5594	848	11	.	.	PUNCT
ejpam-5594	849	1	applied	apply	VERB
ejpam-5594	849	2	mathematics	mathematic	NOUN
ejpam-5594	849	3	and	and	CCONJ
ejpam-5594	849	4	computation	computation	NOUN
ejpam-5594	849	5	,	,	PUNCT
ejpam-5594	849	6	218(3):766–772	218(3):766–772	NUM
ejpam-5594	849	7	,	,	PUNCT
ejpam-5594	849	8	2011	2011	NUM
ejpam-5594	849	9	.	.	PUNCT
ejpam-5594	850	1	[	[	X
ejpam-5594	850	2	19	19	NUM
ejpam-5594	850	3	]	]	X
ejpam-5594	850	4	asfand	asfand	PROPN
ejpam-5594	850	5	fahad	fahad	PROPN
ejpam-5594	850	6	,	,	PUNCT
ejpam-5594	850	7	youhua	youhua	PROPN
ejpam-5594	850	8	qian	qian	PROPN
ejpam-5594	850	9	,	,	PUNCT
ejpam-5594	850	10	zammad	zammad	PROPN
ejpam-5594	850	11	ali	ali	PROPN
ejpam-5594	850	12	,	,	PUNCT
ejpam-5594	850	13	and	and	CCONJ
ejpam-5594	850	14	awais	awais	PROPN
ejpam-5594	850	15	younus	younus	PROPN
ejpam-5594	850	16	.	.	PUNCT
ejpam-5594	851	1	on	on	ADP
ejpam-5594	851	2	generalization	generalization	NOUN
ejpam-5594	851	3	of	of	ADP
ejpam-5594	851	4	hermite	hermite	PROPN
ejpam-5594	851	5	-	-	PUNCT
ejpam-5594	851	6	hadamard	hadamard	ADJ
ejpam-5594	851	7	-	-	PUNCT
ejpam-5594	851	8	mercer	mercer	NOUN
ejpam-5594	851	9	inequalities	inequality	NOUN
ejpam-5594	851	10	for	for	ADP
ejpam-5594	851	11	interval	interval	NOUN
ejpam-5594	851	12	-	-	PUNCT
ejpam-5594	851	13	valued	value	VERB
ejpam-5594	851	14	functions	function	NOUN
ejpam-5594	851	15	with	with	ADP
ejpam-5594	851	16	generalized	generalized	ADJ
ejpam-5594	851	17	geometric	geometric	ADJ
ejpam-5594	851	18	-	-	PUNCT
ejpam-5594	851	19	arithmetic	arithmetic	ADJ
ejpam-5594	851	20	convexity	convexity	NOUN
ejpam-5594	851	21	.	.	PUNCT
ejpam-5594	852	1	international	international	ADJ
ejpam-5594	852	2	journal	journal	NOUN
ejpam-5594	852	3	of	of	ADP
ejpam-5594	852	4	geometric	geometric	ADJ
ejpam-5594	852	5	methods	method	NOUN
ejpam-5594	852	6	in	in	ADP
ejpam-5594	852	7	modern	modern	ADJ
ejpam-5594	852	8	physics	physic	NOUN
ejpam-5594	852	9	,	,	PUNCT
ejpam-5594	852	10	2024	2024	NUM
ejpam-5594	852	11	.	.	PUNCT
ejpam-5594	853	1	[	[	X
ejpam-5594	853	2	20	20	NUM
ejpam-5594	853	3	]	]	X
ejpam-5594	853	4	asfand	asfand	PROPN
ejpam-5594	853	5	fahad	fahad	PROPN
ejpam-5594	853	6	,	,	PUNCT
ejpam-5594	853	7	yuanheng	yuanheng	PROPN
ejpam-5594	853	8	wang	wang	PROPN
ejpam-5594	853	9	,	,	PUNCT
ejpam-5594	853	10	zammad	zammad	PROPN
ejpam-5594	853	11	ali	ali	PROPN
ejpam-5594	853	12	,	,	PUNCT
ejpam-5594	853	13	riaz	riaz	PROPN
ejpam-5594	853	14	hussain	hussain	PROPN
ejpam-5594	853	15	,	,	PUNCT
ejpam-5594	853	16	and	and	CCONJ
ejpam-5594	853	17	shigeru	shigeru	PROPN
ejpam-5594	853	18	furuichi	furuichi	PROPN
ejpam-5594	853	19	.	.	PUNCT
ejpam-5594	854	1	exploring	explore	VERB
ejpam-5594	854	2	properties	property	NOUN
ejpam-5594	854	3	and	and	CCONJ
ejpam-5594	854	4	inequalities	inequality	NOUN
ejpam-5594	854	5	for	for	ADP
ejpam-5594	854	6	geometrically	geometrically	ADV
ejpam-5594	854	7	arithmetically	arithmetically	ADV
ejpam-5594	854	8	-	-	PUNCT
ejpam-5594	854	9	cr	cr	NOUN
ejpam-5594	854	10	-	-	PUNCT
ejpam-5594	854	11	convex	convex	NOUN
ejpam-5594	854	12	functions	function	NOUN
ejpam-5594	854	13	with	with	ADP
ejpam-5594	854	14	cr	cr	NOUN
ejpam-5594	854	15	-	-	PUNCT
ejpam-5594	854	16	order	order	NOUN
ejpam-5594	854	17	relative	relative	ADJ
ejpam-5594	854	18	entropy	entropy	NOUN
ejpam-5594	854	19	.	.	PUNCT
ejpam-5594	855	1	information	information	NOUN
ejpam-5594	855	2	sciences	sciences	PROPN
ejpam-5594	855	3	,	,	PUNCT
ejpam-5594	855	4	662:120219	662:120219	NUM
ejpam-5594	855	5	,	,	PUNCT
ejpam-5594	855	6	2024	2024	NUM
ejpam-5594	855	7	.	.	PUNCT
ejpam-5594	856	1	references	reference	NOUN
ejpam-5594	856	2	4046	4046	NUM
ejpam-5594	856	3	[	[	X
ejpam-5594	856	4	21	21	NUM
ejpam-5594	856	5	]	]	X
ejpam-5594	856	6	arran	arran	PROPN
ejpam-5594	856	7	fernandez	fernandez	PROPN
ejpam-5594	856	8	and	and	CCONJ
ejpam-5594	856	9	pshtiwan	pshtiwan	PROPN
ejpam-5594	856	10	mohammed	mohammed	PROPN
ejpam-5594	856	11	.	.	PUNCT
ejpam-5594	857	1	hermite	hermite	PROPN
ejpam-5594	857	2	-	-	PUNCT
ejpam-5594	857	3	hadamard	hadamard	ADJ
ejpam-5594	857	4	inequalities	inequality	NOUN
ejpam-5594	857	5	in	in	ADP
ejpam-5594	857	6	fractional	fractional	ADJ
ejpam-5594	857	7	calculus	calculus	NOUN
ejpam-5594	857	8	defined	define	VERB
ejpam-5594	857	9	using	use	VERB
ejpam-5594	857	10	mittag	mittag	ADJ
ejpam-5594	857	11	-	-	PUNCT
ejpam-5594	857	12	leffler	leffler	NOUN
ejpam-5594	857	13	kernels	kernel	NOUN
ejpam-5594	857	14	.	.	PUNCT
ejpam-5594	858	1	mathematical	mathematical	ADJ
ejpam-5594	858	2	methods	method	NOUN
ejpam-5594	858	3	in	in	ADP
ejpam-5594	858	4	the	the	DET
ejpam-5594	858	5	applied	apply	VERB
ejpam-5594	858	6	sciences	science	NOUN
ejpam-5594	858	7	,	,	PUNCT
ejpam-5594	858	8	44(10):8414–8431	44(10):8414–8431	NUM
ejpam-5594	858	9	,	,	PUNCT
ejpam-5594	858	10	2021	2021	NUM
ejpam-5594	858	11	.	.	PUNCT
ejpam-5594	859	1	[	[	X
ejpam-5594	859	2	22	22	NUM
ejpam-5594	859	3	]	]	X
ejpam-5594	859	4	guanghe	guanghe	PROPN
ejpam-5594	859	5	han	han	PROPN
ejpam-5594	859	6	,	,	PUNCT
ejpam-5594	859	7	jiahui	jiahui	PROPN
ejpam-5594	859	8	xu	xu	PROPN
ejpam-5594	859	9	,	,	PUNCT
ejpam-5594	859	10	xin	xin	PROPN
ejpam-5594	859	11	zhang	zhang	PROPN
ejpam-5594	859	12	,	,	PUNCT
ejpam-5594	859	13	and	and	CCONJ
ejpam-5594	859	14	xin	xin	PROPN
ejpam-5594	859	15	pan	pan	PROPN
ejpam-5594	859	16	.	.	PROPN
ejpam-5594	859	17	efficiency	efficiency	NOUN
ejpam-5594	859	18	and	and	CCONJ
ejpam-5594	859	19	driving	drive	VERB
ejpam-5594	859	20	factors	factor	NOUN
ejpam-5594	859	21	of	of	ADP
ejpam-5594	859	22	agricultural	agricultural	ADJ
ejpam-5594	859	23	carbon	carbon	NOUN
ejpam-5594	859	24	emissions	emission	NOUN
ejpam-5594	859	25	:	:	PUNCT
ejpam-5594	859	26	a	a	DET
ejpam-5594	859	27	study	study	NOUN
ejpam-5594	859	28	in	in	ADP
ejpam-5594	859	29	chinese	chinese	ADJ
ejpam-5594	859	30	state	state	NOUN
ejpam-5594	859	31	farms	farm	NOUN
ejpam-5594	859	32	.	.	PUNCT
ejpam-5594	860	1	agriculture	agriculture	NOUN
ejpam-5594	860	2	,	,	PUNCT
ejpam-5594	860	3	14(9):1454	14(9):1454	NUM
ejpam-5594	860	4	,	,	PUNCT
ejpam-5594	860	5	2024	2024	NUM
ejpam-5594	860	6	.	.	PUNCT
ejpam-5594	861	1	[	[	X
ejpam-5594	861	2	23	23	NUM
ejpam-5594	861	3	]	]	X
ejpam-5594	861	4	bao	bao	AUX
ejpam-5594	861	5	qing	qe	VERB
ejpam-5594	861	6	hu	hu	PROPN
ejpam-5594	861	7	and	and	CCONJ
ejpam-5594	861	8	song	song	PROPN
ejpam-5594	861	9	wang	wang	PROPN
ejpam-5594	861	10	.	.	PUNCT
ejpam-5594	862	1	a	a	DET
ejpam-5594	862	2	novel	novel	ADJ
ejpam-5594	862	3	approach	approach	NOUN
ejpam-5594	862	4	in	in	ADP
ejpam-5594	862	5	uncertain	uncertain	ADJ
ejpam-5594	862	6	programming	programming	NOUN
ejpam-5594	862	7	part	part	NOUN
ejpam-5594	862	8	i	i	NOUN
ejpam-5594	862	9	:	:	PUNCT
ejpam-5594	862	10	new	new	ADJ
ejpam-5594	862	11	arithmetic	arithmetic	ADJ
ejpam-5594	862	12	and	and	CCONJ
ejpam-5594	862	13	order	order	NOUN
ejpam-5594	862	14	relation	relation	NOUN
ejpam-5594	862	15	for	for	ADP
ejpam-5594	862	16	interval	interval	NOUN
ejpam-5594	862	17	numbers	number	NOUN
ejpam-5594	862	18	.	.	PUNCT
ejpam-5594	863	1	journal	journal	NOUN
ejpam-5594	863	2	of	of	ADP
ejpam-5594	863	3	industrial	industrial	ADJ
ejpam-5594	863	4	and	and	CCONJ
ejpam-5594	863	5	management	management	NOUN
ejpam-5594	863	6	optimization	optimization	NOUN
ejpam-5594	863	7	,	,	PUNCT
ejpam-5594	863	8	2(4):351–371	2(4):351–371	NUM
ejpam-5594	863	9	,	,	PUNCT
ejpam-5594	863	10	2006	2006	NUM
ejpam-5594	863	11	.	.	PUNCT
ejpam-5594	864	1	[	[	X
ejpam-5594	864	2	24	24	NUM
ejpam-5594	864	3	]	]	PUNCT
ejpam-5594	864	4	yu	yu	PROPN
ejpam-5594	864	5	hu	hu	PROPN
ejpam-5594	864	6	,	,	PUNCT
ejpam-5594	864	7	xu	xu	PROPN
ejpam-5594	864	8	chao	chao	PROPN
ejpam-5594	864	9	zhang	zhang	PROPN
ejpam-5594	864	10	,	,	PUNCT
ejpam-5594	864	11	guo	guo	PROPN
ejpam-5594	864	12	qiang	qiang	PROPN
ejpam-5594	864	13	wang	wang	PROPN
ejpam-5594	864	14	,	,	PUNCT
ejpam-5594	864	15	xue	xue	PROPN
ejpam-5594	864	16	peng	peng	PROPN
ejpam-5594	864	17	zhang	zhang	PROPN
ejpam-5594	864	18	,	,	PUNCT
ejpam-5594	864	19	and	and	CCONJ
ejpam-5594	864	20	han	han	PROPN
ejpam-5594	864	21	zhen	zhen	PROPN
ejpam-5594	864	22	li	li	PROPN
ejpam-5594	864	23	.	.	PUNCT
ejpam-5594	864	24	hovering	hover	VERB
ejpam-5594	864	25	efficiency	efficiency	NOUN
ejpam-5594	864	26	optimization	optimization	NOUN
ejpam-5594	864	27	of	of	ADP
ejpam-5594	864	28	ducted	ducte	VERB
ejpam-5594	864	29	propeller	propeller	NOUN
ejpam-5594	864	30	with	with	ADP
ejpam-5594	864	31	large	large	ADJ
ejpam-5594	864	32	blade	blade	NOUN
ejpam-5594	864	33	tip	tip	NOUN
ejpam-5594	864	34	clearance	clearance	NOUN
ejpam-5594	864	35	based	base	VERB
ejpam-5594	864	36	on	on	ADP
ejpam-5594	864	37	grooved	groove	VERB
ejpam-5594	864	38	duct	duct	NOUN
ejpam-5594	864	39	configuration	configuration	NOUN
ejpam-5594	864	40	.	.	PUNCT
ejpam-5594	865	1	aerospace	aerospace	NOUN
ejpam-5594	865	2	science	science	NOUN
ejpam-5594	865	3	and	and	CCONJ
ejpam-5594	865	4	technology	technology	NOUN
ejpam-5594	865	5	,	,	PUNCT
ejpam-5594	865	6	150:109226	150:109226	NUM
ejpam-5594	865	7	,	,	PUNCT
ejpam-5594	865	8	2024	2024	NUM
ejpam-5594	865	9	.	.	PUNCT
ejpam-5594	866	1	[	[	X
ejpam-5594	866	2	25	25	NUM
ejpam-5594	866	3	]	]	PUNCT
ejpam-5594	866	4	yu	yu	PROPN
ejpam-5594	866	5	hu	hu	PROPN
ejpam-5594	866	6	,	,	PUNCT
ejpam-5594	866	7	xu	xu	PROPN
ejpam-5594	866	8	chao	chao	PROPN
ejpam-5594	866	9	zhang	zhang	PROPN
ejpam-5594	866	10	,	,	PUNCT
ejpam-5594	866	11	guo	guo	PROPN
ejpam-5594	866	12	qiang	qiang	PROPN
ejpam-5594	866	13	wang	wang	PROPN
ejpam-5594	866	14	,	,	PUNCT
ejpam-5594	866	15	xue	xue	PROPN
ejpam-5594	866	16	peng	peng	PROPN
ejpam-5594	866	17	zhang	zhang	PROPN
ejpam-5594	866	18	,	,	PUNCT
ejpam-5594	866	19	and	and	CCONJ
ejpam-5594	866	20	han	han	PROPN
ejpam-5594	866	21	zhen	zhen	PROPN
ejpam-5594	866	22	li	li	PROPN
ejpam-5594	866	23	.	.	PUNCT
ejpam-5594	867	1	hovering	hover	VERB
ejpam-5594	867	2	efficiency	efficiency	NOUN
ejpam-5594	867	3	optimization	optimization	NOUN
ejpam-5594	867	4	of	of	ADP
ejpam-5594	867	5	ducted	ducte	VERB
ejpam-5594	867	6	propeller	propeller	NOUN
ejpam-5594	867	7	with	with	ADP
ejpam-5594	867	8	large	large	ADJ
ejpam-5594	867	9	blade	blade	NOUN
ejpam-5594	867	10	tip	tip	NOUN
ejpam-5594	867	11	clearance	clearance	NOUN
ejpam-5594	867	12	based	base	VERB
ejpam-5594	867	13	on	on	ADP
ejpam-5594	867	14	grooved	groove	VERB
ejpam-5594	867	15	duct	duct	NOUN
ejpam-5594	867	16	configuration	configuration	NOUN
ejpam-5594	867	17	.	.	PUNCT
ejpam-5594	868	1	aerospace	aerospace	NOUN
ejpam-5594	868	2	science	science	NOUN
ejpam-5594	868	3	and	and	CCONJ
ejpam-5594	868	4	technology	technology	NOUN
ejpam-5594	868	5	,	,	PUNCT
ejpam-5594	868	6	150:109226	150:109226	NUM
ejpam-5594	868	7	,	,	PUNCT
ejpam-5594	868	8	2024	2024	NUM
ejpam-5594	868	9	.	.	PUNCT
ejpam-5594	869	1	[	[	X
ejpam-5594	869	2	26	26	NUM
ejpam-5594	869	3	]	]	X
ejpam-5594	869	4	ben	ben	PROPN
ejpam-5594	869	5	huang	huang	PROPN
ejpam-5594	869	6	,	,	PUNCT
ejpam-5594	869	7	fei	fei	PROPN
ejpam-5594	869	8	kang	kang	PROPN
ejpam-5594	869	9	,	,	PUNCT
ejpam-5594	869	10	xinyu	xinyu	PROPN
ejpam-5594	869	11	li	li	PROPN
ejpam-5594	869	12	,	,	PUNCT
ejpam-5594	869	13	and	and	CCONJ
ejpam-5594	869	14	sisi	sisi	PROPN
ejpam-5594	869	15	zhu	zhu	PROPN
ejpam-5594	869	16	.	.	PUNCT
ejpam-5594	870	1	underwater	underwater	ADJ
ejpam-5594	870	2	dam	dam	NOUN
ejpam-5594	870	3	crack	crack	VERB
ejpam-5594	870	4	image	image	NOUN
ejpam-5594	870	5	generation	generation	NOUN
ejpam-5594	870	6	based	base	VERB
ejpam-5594	870	7	on	on	ADP
ejpam-5594	870	8	unsupervised	unsupervised	ADJ
ejpam-5594	870	9	image	image	NOUN
ejpam-5594	870	10	-	-	PUNCT
ejpam-5594	870	11	to	to	ADP
ejpam-5594	870	12	-	-	PUNCT
ejpam-5594	870	13	image	image	NOUN
ejpam-5594	870	14	translation	translation	NOUN
ejpam-5594	870	15	.	.	PUNCT
ejpam-5594	871	1	automation	automation	NOUN
ejpam-5594	871	2	in	in	ADP
ejpam-5594	871	3	construction	construction	NOUN
ejpam-5594	871	4	,	,	PUNCT
ejpam-5594	871	5	163:105430	163:105430	NUM
ejpam-5594	871	6	,	,	PUNCT
ejpam-5594	871	7	2024	2024	NUM
ejpam-5594	871	8	.	.	PUNCT
ejpam-5594	872	1	[	[	X
ejpam-5594	872	2	27	27	NUM
ejpam-5594	872	3	]	]	X
ejpam-5594	872	4	zhenhua	zhenhua	PROPN
ejpam-5594	872	5	huang	huang	PROPN
ejpam-5594	872	6	,	,	PUNCT
ejpam-5594	872	7	kunhao	kunhao	PROPN
ejpam-5594	872	8	li	li	PROPN
ejpam-5594	872	9	,	,	PUNCT
ejpam-5594	872	10	yihang	yihang	PROPN
ejpam-5594	872	11	jiang	jiang	PROPN
ejpam-5594	872	12	,	,	PUNCT
ejpam-5594	872	13	zhaohong	zhaohong	PROPN
ejpam-5594	872	14	jia	jia	PROPN
ejpam-5594	872	15	,	,	PUNCT
ejpam-5594	872	16	linyuan	linyuan	PROPN
ejpam-5594	872	17	lv	lv	PROPN
ejpam-5594	872	18	,	,	PUNCT
ejpam-5594	872	19	and	and	CCONJ
ejpam-5594	872	20	yunjie	yunjie	PROPN
ejpam-5594	872	21	ma	ma	PROPN
ejpam-5594	872	22	.	.	PROPN
ejpam-5594	873	1	graph	graph	NOUN
ejpam-5594	873	2	relearn	relearn	NOUN
ejpam-5594	873	3	network	network	NOUN
ejpam-5594	873	4	:	:	PUNCT
ejpam-5594	873	5	reducing	reduce	VERB
ejpam-5594	873	6	performance	performance	NOUN
ejpam-5594	873	7	variance	variance	NOUN
ejpam-5594	873	8	and	and	CCONJ
ejpam-5594	873	9	improving	improve	VERB
ejpam-5594	873	10	prediction	prediction	NOUN
ejpam-5594	873	11	accuracy	accuracy	NOUN
ejpam-5594	873	12	of	of	ADP
ejpam-5594	873	13	graph	graph	NOUN
ejpam-5594	873	14	neural	neural	ADJ
ejpam-5594	873	15	networks	network	NOUN
ejpam-5594	873	16	.	.	PUNCT
ejpam-5594	874	1	knowledge	knowledge	NOUN
ejpam-5594	874	2	-	-	PUNCT
ejpam-5594	874	3	based	base	VERB
ejpam-5594	874	4	systems	system	NOUN
ejpam-5594	874	5	,	,	PUNCT
ejpam-5594	874	6	301:112311	301:112311	NUM
ejpam-5594	874	7	,	,	PUNCT
ejpam-5594	874	8	2024	2024	NUM
ejpam-5594	874	9	.	.	PUNCT
ejpam-5594	875	1	[	[	X
ejpam-5594	875	2	28	28	NUM
ejpam-5594	875	3	]	]	X
ejpam-5594	875	4	abd	abd	PROPN
ejpam-5594	875	5	-	-	PUNCT
ejpam-5594	875	6	allah	allah	PROPN
ejpam-5594	875	7	hyder	hyder	PROPN
ejpam-5594	875	8	,	,	PUNCT
ejpam-5594	875	9	hüseyin	hüseyin	PROPN
ejpam-5594	875	10	budak	budak	PROPN
ejpam-5594	875	11	,	,	PUNCT
ejpam-5594	875	12	and	and	CCONJ
ejpam-5594	875	13	areej	areej	VERB
ejpam-5594	875	14	a	a	DET
ejpam-5594	875	15	almoneef	almoneef	NOUN
ejpam-5594	875	16	.	.	PUNCT
ejpam-5594	876	1	further	further	ADJ
ejpam-5594	876	2	midpoint	midpoint	NOUN
ejpam-5594	876	3	inequalities	inequality	NOUN
ejpam-5594	876	4	via	via	ADP
ejpam-5594	876	5	generalized	generalize	VERB
ejpam-5594	876	6	fractional	fractional	ADJ
ejpam-5594	876	7	operators	operator	NOUN
ejpam-5594	876	8	in	in	ADP
ejpam-5594	876	9	riemann	riemann	PROPN
ejpam-5594	876	10	–	–	PUNCT
ejpam-5594	876	11	liouville	liouville	VERB
ejpam-5594	876	12	sense	sense	NOUN
ejpam-5594	876	13	.	.	PUNCT
ejpam-5594	877	1	fractal	fractal	ADJ
ejpam-5594	877	2	and	and	CCONJ
ejpam-5594	877	3	fractional	fractional	ADJ
ejpam-5594	877	4	,	,	PUNCT
ejpam-5594	877	5	6(9):496	6(9):496	NUM
ejpam-5594	877	6	,	,	PUNCT
ejpam-5594	877	7	2022	2022	NUM
ejpam-5594	877	8	.	.	PUNCT
ejpam-5594	878	1	[	[	X
ejpam-5594	878	2	29	29	NUM
ejpam-5594	878	3	]	]	X
ejpam-5594	878	4	i	i	PRON
ejpam-5594	878	5	iscan	iscan	VERB
ejpam-5594	878	6	,	,	PUNCT
ejpam-5594	878	7	teki̇n	teki̇n	PROPN
ejpam-5594	878	8	toplu	toplu	NOUN
ejpam-5594	878	9	,	,	PUNCT
ejpam-5594	878	10	and	and	CCONJ
ejpam-5594	878	11	fati̇h	fati̇h	PROPN
ejpam-5594	878	12	yetgin	yetgin	NOUN
ejpam-5594	878	13	.	.	PUNCT
ejpam-5594	879	1	some	some	DET
ejpam-5594	879	2	new	new	ADJ
ejpam-5594	879	3	inequalities	inequality	NOUN
ejpam-5594	879	4	on	on	ADP
ejpam-5594	879	5	generalization	generalization	NOUN
ejpam-5594	879	6	of	of	ADP
ejpam-5594	879	7	hermite	hermite	PROPN
ejpam-5594	879	8	–	–	PUNCT
ejpam-5594	879	9	hadamard	hadamard	ADJ
ejpam-5594	879	10	and	and	CCONJ
ejpam-5594	879	11	bullen	bullen	PROPN
ejpam-5594	879	12	type	type	NOUN
ejpam-5594	879	13	inequalities	inequality	NOUN
ejpam-5594	879	14	,	,	PUNCT
ejpam-5594	879	15	applications	application	NOUN
ejpam-5594	879	16	to	to	ADP
ejpam-5594	879	17	trapezoidal	trapezoidal	ADJ
ejpam-5594	879	18	and	and	CCONJ
ejpam-5594	879	19	midpoint	midpoint	NOUN
ejpam-5594	879	20	formula	formula	NOUN
ejpam-5594	879	21	.	.	PUNCT
ejpam-5594	880	1	j.	j.	PROPN
ejpam-5594	880	2	math	math	PROPN
ejpam-5594	880	3	,	,	PUNCT
ejpam-5594	880	4	45(4):647–657	45(4):647–657	PROPN
ejpam-5594	880	5	,	,	PUNCT
ejpam-5594	880	6	2021	2021	NUM
ejpam-5594	880	7	.	.	PUNCT
ejpam-5594	881	1	[	[	X
ejpam-5594	881	2	30	30	NUM
ejpam-5594	881	3	]	]	X
ejpam-5594	881	4	fahd	fahd	PROPN
ejpam-5594	881	5	jarad	jarad	PROPN
ejpam-5594	881	6	,	,	PUNCT
ejpam-5594	881	7	thabet	thabet	ADJ
ejpam-5594	881	8	abdeljawad	abdeljawad	NOUN
ejpam-5594	881	9	,	,	PUNCT
ejpam-5594	881	10	and	and	CCONJ
ejpam-5594	881	11	dumitru	dumitru	PROPN
ejpam-5594	881	12	baleanu	baleanu	NOUN
ejpam-5594	881	13	.	.	PUNCT
ejpam-5594	882	1	caputo	caputo	NOUN
ejpam-5594	882	2	-	-	PUNCT
ejpam-5594	882	3	type	type	NOUN
ejpam-5594	882	4	modification	modification	NOUN
ejpam-5594	882	5	of	of	ADP
ejpam-5594	882	6	the	the	DET
ejpam-5594	882	7	hadamard	hadamard	ADJ
ejpam-5594	882	8	fractional	fractional	ADJ
ejpam-5594	882	9	derivatives	derivative	NOUN
ejpam-5594	882	10	.	.	PUNCT
ejpam-5594	883	1	advances	advance	NOUN
ejpam-5594	883	2	in	in	ADP
ejpam-5594	883	3	difference	difference	NOUN
ejpam-5594	883	4	equations	equation	NOUN
ejpam-5594	883	5	,	,	PUNCT
ejpam-5594	883	6	2012:1–8	2012:1–8	NUM
ejpam-5594	883	7	,	,	PUNCT
ejpam-5594	883	8	2012	2012	NUM
ejpam-5594	883	9	.	.	PUNCT
ejpam-5594	884	1	[	[	X
ejpam-5594	884	2	31	31	NUM
ejpam-5594	884	3	]	]	X
ejpam-5594	884	4	hasan	hasan	PROPN
ejpam-5594	884	5	kara	kara	PROPN
ejpam-5594	884	6	,	,	PUNCT
ejpam-5594	884	7	hüseyin	hüseyin	PROPN
ejpam-5594	884	8	budak	budak	PROPN
ejpam-5594	884	9	,	,	PUNCT
ejpam-5594	884	10	muhammad	muhammad	PROPN
ejpam-5594	884	11	aamir	aamir	PROPN
ejpam-5594	884	12	ali	ali	PROPN
ejpam-5594	884	13	,	,	PUNCT
ejpam-5594	884	14	mehmet	mehmet	PROPN
ejpam-5594	884	15	zeki	zeki	PROPN
ejpam-5594	884	16	sarikaya	sarikaya	PROPN
ejpam-5594	884	17	,	,	PUNCT
ejpam-5594	884	18	and	and	CCONJ
ejpam-5594	884	19	yuming	yuming	PROPN
ejpam-5594	884	20	chu	chu	PROPN
ejpam-5594	884	21	.	.	PROPN
ejpam-5594	884	22	weighted	weight	VERB
ejpam-5594	884	23	hermite	hermite	ADJ
ejpam-5594	884	24	–	–	PUNCT
ejpam-5594	884	25	hadamard	hadamard	ADJ
ejpam-5594	884	26	type	type	NOUN
ejpam-5594	884	27	inclusions	inclusion	NOUN
ejpam-5594	884	28	for	for	ADP
ejpam-5594	884	29	products	product	NOUN
ejpam-5594	884	30	of	of	ADP
ejpam-5594	884	31	co	co	VERB
ejpam-5594	884	32	-	-	ADJ
ejpam-5594	884	33	ordinated	ordinated	ADJ
ejpam-5594	884	34	convex	convex	NOUN
ejpam-5594	884	35	interval	interval	NOUN
ejpam-5594	884	36	-	-	PUNCT
ejpam-5594	884	37	valued	value	VERB
ejpam-5594	884	38	functions	function	NOUN
ejpam-5594	884	39	.	.	PUNCT
ejpam-5594	885	1	advances	advance	NOUN
ejpam-5594	885	2	in	in	ADP
ejpam-5594	885	3	difference	difference	NOUN
ejpam-5594	885	4	equations	equation	NOUN
ejpam-5594	885	5	,	,	PUNCT
ejpam-5594	885	6	2021:1–16	2021:1–16	NOUN
ejpam-5594	885	7	,	,	PUNCT
ejpam-5594	885	8	2021	2021	NUM
ejpam-5594	885	9	.	.	PUNCT
ejpam-5594	886	1	[	[	X
ejpam-5594	886	2	32	32	NUM
ejpam-5594	886	3	]	]	PUNCT
ejpam-5594	886	4	havva	havva	NOUN
ejpam-5594	886	5	kavurmacı	kavurmacı	PROPN
ejpam-5594	886	6	önalan	önalan	PROPN
ejpam-5594	886	7	,	,	PUNCT
ejpam-5594	886	8	ahmet	ahmet	PROPN
ejpam-5594	886	9	ocak	ocak	PROPN
ejpam-5594	886	10	akdemir	akdemir	NOUN
ejpam-5594	886	11	,	,	PUNCT
ejpam-5594	886	12	merve	merve	NOUN
ejpam-5594	886	13	avcı	avcı	PROPN
ejpam-5594	886	14	ardıç	ardıç	PROPN
ejpam-5594	886	15	,	,	PUNCT
ejpam-5594	886	16	and	and	CCONJ
ejpam-5594	886	17	dumitru	dumitru	PROPN
ejpam-5594	886	18	baleanu	baleanu	NOUN
ejpam-5594	886	19	.	.	PUNCT
ejpam-5594	887	1	on	on	ADP
ejpam-5594	887	2	new	new	ADJ
ejpam-5594	887	3	general	general	ADJ
ejpam-5594	887	4	versions	version	NOUN
ejpam-5594	887	5	of	of	ADP
ejpam-5594	887	6	hermite	hermite	ADJ
ejpam-5594	887	7	–	–	PUNCT
ejpam-5594	887	8	hadamard	hadamard	ADJ
ejpam-5594	887	9	type	type	NOUN
ejpam-5594	887	10	integral	integral	ADJ
ejpam-5594	887	11	inequalities	inequality	NOUN
ejpam-5594	887	12	via	via	ADP
ejpam-5594	887	13	fractional	fractional	ADJ
ejpam-5594	887	14	integral	integral	ADJ
ejpam-5594	887	15	operators	operator	NOUN
ejpam-5594	887	16	with	with	ADP
ejpam-5594	887	17	mittag	mittag	ADJ
ejpam-5594	887	18	-	-	PUNCT
ejpam-5594	887	19	leffler	leffler	NOUN
ejpam-5594	887	20	kernel	kernel	NOUN
ejpam-5594	887	21	.	.	PUNCT
ejpam-5594	887	22	journal	journal	PROPN
ejpam-5594	887	23	of	of	ADP
ejpam-5594	887	24	inequalities	inequality	NOUN
ejpam-5594	887	25	and	and	CCONJ
ejpam-5594	887	26	applications	application	NOUN
ejpam-5594	887	27	,	,	PUNCT
ejpam-5594	887	28	2021:1–16	2021:1–16	NOUN
ejpam-5594	887	29	,	,	PUNCT
ejpam-5594	887	30	2021	2021	NUM
ejpam-5594	887	31	.	.	PUNCT
ejpam-5594	888	1	references	reference	NOUN
ejpam-5594	888	2	4047	4047	NUM
ejpam-5594	888	3	[	[	X
ejpam-5594	888	4	33	33	NUM
ejpam-5594	888	5	]	]	X
ejpam-5594	888	6	dawood	dawood	PROPN
ejpam-5594	888	7	khan	khan	PROPN
ejpam-5594	888	8	and	and	CCONJ
ejpam-5594	888	9	saad	saad	PROPN
ejpam-5594	888	10	ihsan	ihsan	PROPN
ejpam-5594	888	11	butt	butt	PROPN
ejpam-5594	888	12	.	.	PUNCT
ejpam-5594	889	1	superquadraticity	superquadraticity	NOUN
ejpam-5594	889	2	and	and	CCONJ
ejpam-5594	889	3	its	its	PRON
ejpam-5594	889	4	fractional	fractional	ADJ
ejpam-5594	889	5	perspective	perspective	NOUN
ejpam-5594	889	6	via	via	ADP
ejpam-5594	889	7	center	center	ADJ
ejpam-5594	889	8	-	-	PUNCT
ejpam-5594	889	9	radius	radius	NOUN
ejpam-5594	889	10	cr	cr	NOUN
ejpam-5594	889	11	-	-	PUNCT
ejpam-5594	889	12	order	order	NOUN
ejpam-5594	889	13	relation	relation	NOUN
ejpam-5594	889	14	.	.	PUNCT
ejpam-5594	890	1	chaos	chaos	NOUN
ejpam-5594	890	2	,	,	PUNCT
ejpam-5594	890	3	solitons	soliton	NOUN
ejpam-5594	890	4	&	&	CCONJ
ejpam-5594	890	5	fractals	fractal	NOUN
ejpam-5594	890	6	,	,	PUNCT
ejpam-5594	890	7	182:114821	182:114821	NUM
ejpam-5594	890	8	,	,	PUNCT
ejpam-5594	890	9	2024	2024	NUM
ejpam-5594	890	10	.	.	PUNCT
ejpam-5594	891	1	[	[	X
ejpam-5594	891	2	34	34	NUM
ejpam-5594	891	3	]	]	X
ejpam-5594	891	4	muhammad	muhammad	PROPN
ejpam-5594	891	5	bilal	bilal	PROPN
ejpam-5594	891	6	khan	khan	PROPN
ejpam-5594	891	7	,	,	PUNCT
ejpam-5594	891	8	jorge	jorge	PROPN
ejpam-5594	891	9	e	e	PROPN
ejpam-5594	891	10	maćıas	maćıas	PROPN
ejpam-5594	891	11	-	-	PUNCT
ejpam-5594	891	12	dı́az	dı́az	NOUN
ejpam-5594	891	13	,	,	PUNCT
ejpam-5594	891	14	savin	savin	NOUN
ejpam-5594	891	15	treant	treant	NOUN
ejpam-5594	891	16	,	,	PUNCT
ejpam-5594	891	17	ǎ	ǎ	PROPN
ejpam-5594	891	18	,	,	PUNCT
ejpam-5594	891	19	and	and	CCONJ
ejpam-5594	891	20	mohamed	mohamed	PROPN
ejpam-5594	891	21	s	s	PROPN
ejpam-5594	891	22	soliman	soliman	NOUN
ejpam-5594	891	23	.	.	PUNCT
ejpam-5594	892	1	some	some	DET
ejpam-5594	892	2	fejér	fejér	ADJ
ejpam-5594	892	3	-	-	PUNCT
ejpam-5594	892	4	type	type	NOUN
ejpam-5594	892	5	inequalities	inequality	NOUN
ejpam-5594	892	6	for	for	ADP
ejpam-5594	892	7	generalized	generalized	ADJ
ejpam-5594	892	8	interval	interval	NOUN
ejpam-5594	892	9	-	-	PUNCT
ejpam-5594	892	10	valued	value	VERB
ejpam-5594	892	11	convex	convex	NOUN
ejpam-5594	892	12	functions	function	NOUN
ejpam-5594	892	13	.	.	PUNCT
ejpam-5594	893	1	mathematics	mathematic	NOUN
ejpam-5594	893	2	,	,	PUNCT
ejpam-5594	893	3	10(20):3851	10(20):3851	NUM
ejpam-5594	893	4	,	,	PUNCT
ejpam-5594	893	5	2022	2022	NUM
ejpam-5594	893	6	.	.	PUNCT
ejpam-5594	894	1	[	[	X
ejpam-5594	894	2	35	35	NUM
ejpam-5594	894	3	]	]	X
ejpam-5594	894	4	ruonan	ruonan	NOUN
ejpam-5594	894	5	liu	liu	PROPN
ejpam-5594	894	6	and	and	CCONJ
ejpam-5594	894	7	run	run	VERB
ejpam-5594	894	8	xu	xu	INTJ
ejpam-5594	894	9	.	.	PUNCT
ejpam-5594	895	1	hermite	hermite	PROPN
ejpam-5594	895	2	-	-	PUNCT
ejpam-5594	895	3	hadamard	hadamard	ADJ
ejpam-5594	895	4	type	type	NOUN
ejpam-5594	895	5	inequalities	inequality	NOUN
ejpam-5594	895	6	for	for	ADP
ejpam-5594	895	7	harmonical	harmonical	ADJ
ejpam-5594	895	8	(	(	PUNCT
ejpam-5594	895	9	h1	h1	PROPN
ejpam-5594	895	10	,	,	PUNCT
ejpam-5594	895	11	h2)-convex	h2)-convex	NOUN
ejpam-5594	895	12	interval	interval	NOUN
ejpam-5594	895	13	-	-	PUNCT
ejpam-5594	895	14	valued	value	VERB
ejpam-5594	895	15	functions	function	NOUN
ejpam-5594	895	16	.	.	PUNCT
ejpam-5594	896	1	mathematical	mathematical	ADJ
ejpam-5594	896	2	foundations	foundation	NOUN
ejpam-5594	896	3	of	of	ADP
ejpam-5594	896	4	computing	computing	NOUN
ejpam-5594	896	5	,	,	PUNCT
ejpam-5594	896	6	4(2	4(2	NUM
ejpam-5594	896	7	)	)	PUNCT
ejpam-5594	896	8	,	,	PUNCT
ejpam-5594	896	9	2021	2021	NUM
ejpam-5594	896	10	.	.	PUNCT
ejpam-5594	897	1	[	[	X
ejpam-5594	897	2	36	36	NUM
ejpam-5594	897	3	]	]	X
ejpam-5594	897	4	wei	wei	PROPN
ejpam-5594	897	5	liu	liu	PROPN
ejpam-5594	897	6	,	,	PUNCT
ejpam-5594	897	7	fangfang	fangfang	PROPN
ejpam-5594	897	8	shi	shi	PROPN
ejpam-5594	897	9	,	,	PUNCT
ejpam-5594	897	10	guoju	guoju	PROPN
ejpam-5594	897	11	ye	ye	PROPN
ejpam-5594	897	12	,	,	PUNCT
ejpam-5594	897	13	and	and	CCONJ
ejpam-5594	897	14	dafang	dafang	PROPN
ejpam-5594	897	15	zhao	zhao	PROPN
ejpam-5594	897	16	.	.	PUNCT
ejpam-5594	898	1	the	the	DET
ejpam-5594	898	2	properties	property	NOUN
ejpam-5594	898	3	of	of	ADP
ejpam-5594	898	4	harmonically	harmonically	ADV
ejpam-5594	898	5	cr	cr	ADP
ejpam-5594	898	6	-	-	PUNCT
ejpam-5594	898	7	h	h	NOUN
ejpam-5594	898	8	-	-	PUNCT
ejpam-5594	898	9	convex	convex	NOUN
ejpam-5594	898	10	function	function	NOUN
ejpam-5594	898	11	and	and	CCONJ
ejpam-5594	898	12	its	its	PRON
ejpam-5594	898	13	applications	application	NOUN
ejpam-5594	898	14	.	.	PUNCT
ejpam-5594	899	1	mathematics	mathematic	NOUN
ejpam-5594	899	2	,	,	PUNCT
ejpam-5594	899	3	10(12):2089	10(12):2089	NUM
ejpam-5594	899	4	,	,	PUNCT
ejpam-5594	899	5	2022	2022	NUM
ejpam-5594	899	6	.	.	PUNCT
ejpam-5594	900	1	[	[	X
ejpam-5594	900	2	37	37	NUM
ejpam-5594	900	3	]	]	X
ejpam-5594	900	4	wei	wei	PROPN
ejpam-5594	900	5	liu	liu	PROPN
ejpam-5594	900	6	,	,	PUNCT
ejpam-5594	900	7	fangfang	fangfang	PROPN
ejpam-5594	900	8	shi	shi	PROPN
ejpam-5594	900	9	,	,	PUNCT
ejpam-5594	900	10	guoju	guoju	PROPN
ejpam-5594	900	11	ye	ye	PROPN
ejpam-5594	900	12	,	,	PUNCT
ejpam-5594	900	13	and	and	CCONJ
ejpam-5594	900	14	dafang	dafang	PROPN
ejpam-5594	900	15	zhao	zhao	PROPN
ejpam-5594	900	16	.	.	PUNCT
ejpam-5594	901	1	some	some	DET
ejpam-5594	901	2	inequalities	inequality	NOUN
ejpam-5594	901	3	for	for	ADP
ejpam-5594	901	4	cr	cr	NOUN
ejpam-5594	901	5	-	-	PUNCT
ejpam-5594	901	6	log	log	NOUN
ejpam-5594	901	7	-	-	PUNCT
ejpam-5594	901	8	hconvex	hconvex	NOUN
ejpam-5594	901	9	functions	function	NOUN
ejpam-5594	901	10	.	.	PUNCT
ejpam-5594	902	1	journal	journal	PROPN
ejpam-5594	902	2	of	of	ADP
ejpam-5594	902	3	inequalities	inequality	NOUN
ejpam-5594	902	4	and	and	CCONJ
ejpam-5594	902	5	applications	application	NOUN
ejpam-5594	902	6	,	,	PUNCT
ejpam-5594	902	7	2022(1):160	2022(1):160	NUM
ejpam-5594	902	8	,	,	PUNCT
ejpam-5594	902	9	2022	2022	NUM
ejpam-5594	902	10	.	.	PUNCT
ejpam-5594	903	1	[	[	X
ejpam-5594	903	2	38	38	NUM
ejpam-5594	903	3	]	]	PUNCT
ejpam-5594	903	4	yucui	yucui	PROPN
ejpam-5594	903	5	lu	lu	PROPN
ejpam-5594	903	6	,	,	PUNCT
ejpam-5594	903	7	linyin	linyin	PROPN
ejpam-5594	903	8	qin	qin	PROPN
ejpam-5594	903	9	,	,	PUNCT
ejpam-5594	903	10	yuanhui	yuanhui	PROPN
ejpam-5594	903	11	mao	mao	PROPN
ejpam-5594	903	12	,	,	PUNCT
ejpam-5594	903	13	xianmei	xianmei	PROPN
ejpam-5594	903	14	lnong	lnong	PROPN
ejpam-5594	903	15	,	,	PUNCT
ejpam-5594	903	16	qianni	qianni	PROPN
ejpam-5594	903	17	wei	wei	PROPN
ejpam-5594	903	18	,	,	PUNCT
ejpam-5594	903	19	junwen	junwen	PROPN
ejpam-5594	903	20	su	su	PROPN
ejpam-5594	903	21	,	,	PUNCT
ejpam-5594	903	22	shuwen	shuwen	PROPN
ejpam-5594	903	23	chen	chen	PROPN
ejpam-5594	903	24	,	,	PUNCT
ejpam-5594	903	25	zhongshi	zhongshi	PROPN
ejpam-5594	903	26	wei	wei	PROPN
ejpam-5594	903	27	,	,	PUNCT
ejpam-5594	903	28	lijing	lije	VERB
ejpam-5594	903	29	wang	wang	PROPN
ejpam-5594	903	30	,	,	PUNCT
ejpam-5594	903	31	xiayun	xiayun	PROPN
ejpam-5594	903	32	liao	liao	PROPN
ejpam-5594	903	33	,	,	PUNCT
ejpam-5594	903	34	et	et	PROPN
ejpam-5594	903	35	al	al	PROPN
ejpam-5594	903	36	.	.	PUNCT
ejpam-5594	903	37	antibacterial	antibacterial	ADJ
ejpam-5594	903	38	activity	activity	NOUN
ejpam-5594	903	39	of	of	ADP
ejpam-5594	903	40	a	a	DET
ejpam-5594	903	41	polysaccharide	polysaccharide	NOUN
ejpam-5594	903	42	isolated	isolate	VERB
ejpam-5594	903	43	from	from	ADP
ejpam-5594	903	44	litchi	litchi	PROPN
ejpam-5594	903	45	(	(	PUNCT
ejpam-5594	903	46	litchi	litchi	PROPN
ejpam-5594	903	47	chinensis	chinensis	PROPN
ejpam-5594	903	48	sonn	sonn	PROPN
ejpam-5594	903	49	.	.	PUNCT
ejpam-5594	903	50	)	)	PUNCT
ejpam-5594	904	1	pericarp	pericarp	ADJ
ejpam-5594	904	2	against	against	ADP
ejpam-5594	904	3	staphylococcus	staphylococcus	NOUN
ejpam-5594	904	4	aureus	aureus	NOUN
ejpam-5594	904	5	and	and	CCONJ
ejpam-5594	904	6	the	the	DET
ejpam-5594	904	7	mechanism	mechanism	NOUN
ejpam-5594	904	8	investigation	investigation	NOUN
ejpam-5594	904	9	.	.	PUNCT
ejpam-5594	905	1	international	international	ADJ
ejpam-5594	905	2	journal	journal	NOUN
ejpam-5594	905	3	of	of	ADP
ejpam-5594	905	4	biological	biological	ADJ
ejpam-5594	905	5	macromolecules	macromolecule	NOUN
ejpam-5594	905	6	,	,	PUNCT
ejpam-5594	905	7	279:134788	279:134788	NUM
ejpam-5594	905	8	,	,	PUNCT
ejpam-5594	905	9	2024	2024	NUM
ejpam-5594	905	10	.	.	PUNCT
ejpam-5594	906	1	[	[	X
ejpam-5594	906	2	39	39	NUM
ejpam-5594	906	3	]	]	PUNCT
ejpam-5594	906	4	jorge	jorge	NOUN
ejpam-5594	906	5	e	e	PROPN
ejpam-5594	906	6	maćıas	maćıas	PROPN
ejpam-5594	906	7	-	-	PUNCT
ejpam-5594	906	8	dı́az	dı́az	NOUN
ejpam-5594	906	9	,	,	PUNCT
ejpam-5594	906	10	muhammad	muhammad	PROPN
ejpam-5594	906	11	bilal	bilal	PROPN
ejpam-5594	906	12	khan	khan	PROPN
ejpam-5594	906	13	,	,	PUNCT
ejpam-5594	906	14	muhammad	muhammad	PROPN
ejpam-5594	906	15	aslam	aslam	PROPN
ejpam-5594	906	16	noor	noor	PROPN
ejpam-5594	906	17	,	,	PUNCT
ejpam-5594	906	18	a	a	DET
ejpam-5594	906	19	mousa	mousa	PROPN
ejpam-5594	906	20	abd	abd	PROPN
ejpam-5594	906	21	allah	allah	PROPN
ejpam-5594	906	22	,	,	PUNCT
ejpam-5594	906	23	and	and	CCONJ
ejpam-5594	906	24	safar	safar	PROPN
ejpam-5594	906	25	m	m	PROPN
ejpam-5594	906	26	alghamdi	alghamdi	NOUN
ejpam-5594	906	27	.	.	PUNCT
ejpam-5594	907	1	hermite	hermite	PROPN
ejpam-5594	907	2	-	-	PUNCT
ejpam-5594	907	3	hadamard	hadamard	ADJ
ejpam-5594	907	4	inequalities	inequality	NOUN
ejpam-5594	907	5	for	for	ADP
ejpam-5594	907	6	generalized	generalized	ADJ
ejpam-5594	907	7	convex	convex	NOUN
ejpam-5594	907	8	functions	function	NOUN
ejpam-5594	907	9	in	in	ADP
ejpam-5594	907	10	interval	interval	NOUN
ejpam-5594	907	11	-	-	PUNCT
ejpam-5594	907	12	valued	value	VERB
ejpam-5594	907	13	calculus	calculus	NOUN
ejpam-5594	907	14	.	.	PUNCT
ejpam-5594	908	1	aims	aim	VERB
ejpam-5594	908	2	math	math	NOUN
ejpam-5594	908	3	,	,	PUNCT
ejpam-5594	908	4	7(3):4266–4292	7(3):4266–4292	NUM
ejpam-5594	908	5	,	,	PUNCT
ejpam-5594	908	6	2022	2022	NUM
ejpam-5594	908	7	.	.	PUNCT
ejpam-5594	909	1	[	[	X
ejpam-5594	909	2	40	40	NUM
ejpam-5594	909	3	]	]	PUNCT
ejpam-5594	909	4	sikander	sikander	PROPN
ejpam-5594	909	5	mehmood	mehmood	PROPN
ejpam-5594	909	6	,	,	PUNCT
ejpam-5594	909	7	pshtiwan	pshtiwan	PROPN
ejpam-5594	909	8	othman	othman	PROPN
ejpam-5594	909	9	mohammed	mohammed	PROPN
ejpam-5594	909	10	,	,	PUNCT
ejpam-5594	909	11	artion	artion	NOUN
ejpam-5594	909	12	kashuri	kashuri	PROPN
ejpam-5594	909	13	,	,	PUNCT
ejpam-5594	909	14	nejmeddine	nejmeddine	PROPN
ejpam-5594	909	15	chorfi	chorfi	PROPN
ejpam-5594	909	16	,	,	PUNCT
ejpam-5594	909	17	sarkhel	sarkhel	PROPN
ejpam-5594	909	18	akbar	akbar	PROPN
ejpam-5594	909	19	mahmood	mahmood	PROPN
ejpam-5594	909	20	,	,	PUNCT
ejpam-5594	909	21	and	and	CCONJ
ejpam-5594	909	22	majeed	majeed	VERB
ejpam-5594	909	23	a	a	DET
ejpam-5594	909	24	yousif	yousif	PROPN
ejpam-5594	909	25	.	.	PUNCT
ejpam-5594	910	1	some	some	DET
ejpam-5594	910	2	new	new	ADJ
ejpam-5594	910	3	fractional	fractional	ADJ
ejpam-5594	910	4	inequalities	inequality	NOUN
ejpam-5594	910	5	defined	define	VERB
ejpam-5594	910	6	using	use	VERB
ejpam-5594	910	7	cr	cr	NOUN
ejpam-5594	910	8	-	-	PUNCT
ejpam-5594	910	9	log	log	NOUN
ejpam-5594	910	10	-	-	PUNCT
ejpam-5594	910	11	h	h	NOUN
ejpam-5594	910	12	-	-	PUNCT
ejpam-5594	910	13	convex	convex	NOUN
ejpam-5594	910	14	functions	function	NOUN
ejpam-5594	910	15	and	and	CCONJ
ejpam-5594	910	16	applications	application	NOUN
ejpam-5594	910	17	.	.	PUNCT
ejpam-5594	911	1	symmetry	symmetry	NOUN
ejpam-5594	911	2	,	,	PUNCT
ejpam-5594	911	3	16(4):407	16(4):407	NUM
ejpam-5594	911	4	,	,	PUNCT
ejpam-5594	911	5	2024	2024	NUM
ejpam-5594	911	6	.	.	PUNCT
ejpam-5594	912	1	[	[	X
ejpam-5594	912	2	41	41	NUM
ejpam-5594	912	3	]	]	X
ejpam-5594	912	4	bandar	bandar	PROPN
ejpam-5594	912	5	bin	bin	PROPN
ejpam-5594	912	6	mohsin	mohsin	PROPN
ejpam-5594	912	7	,	,	PUNCT
ejpam-5594	912	8	muhammad	muhammad	PROPN
ejpam-5594	912	9	uzair	uzair	PROPN
ejpam-5594	912	10	awan	awan	PROPN
ejpam-5594	912	11	,	,	PUNCT
ejpam-5594	912	12	muhammad	muhammad	PROPN
ejpam-5594	912	13	zakria	zakria	PROPN
ejpam-5594	912	14	javed	javed	PROPN
ejpam-5594	912	15	,	,	PUNCT
ejpam-5594	912	16	hüseyin	hüseyin	PROPN
ejpam-5594	912	17	budak	budak	PROPN
ejpam-5594	912	18	,	,	PUNCT
ejpam-5594	912	19	awais	awais	PROPN
ejpam-5594	912	20	gul	gul	PROPN
ejpam-5594	912	21	khan	khan	PROPN
ejpam-5594	912	22	,	,	PUNCT
ejpam-5594	912	23	and	and	CCONJ
ejpam-5594	912	24	muhammad	muhammad	PROPN
ejpam-5594	912	25	aslam	aslam	PROPN
ejpam-5594	912	26	noor	noor	PROPN
ejpam-5594	912	27	.	.	PUNCT
ejpam-5594	913	1	inclusions	inclusion	NOUN
ejpam-5594	913	2	involving	involve	VERB
ejpam-5594	913	3	intervalvalued	intervalvalue	VERB
ejpam-5594	913	4	harmonically	harmonically	ADV
ejpam-5594	913	5	co	co	VERB
ejpam-5594	913	6	-	-	ADJ
ejpam-5594	913	7	ordinated	ordinated	ADJ
ejpam-5594	913	8	convex	convex	NOUN
ejpam-5594	913	9	functions	function	NOUN
ejpam-5594	913	10	and	and	CCONJ
ejpam-5594	913	11	raina	raina	PROPN
ejpam-5594	913	12	’s	’s	PART
ejpam-5594	913	13	fractional	fractional	ADJ
ejpam-5594	913	14	double	double	ADJ
ejpam-5594	913	15	integrals	integral	NOUN
ejpam-5594	913	16	.	.	PUNCT
ejpam-5594	914	1	journal	journal	NOUN
ejpam-5594	914	2	of	of	ADP
ejpam-5594	914	3	mathematics	mathematic	NOUN
ejpam-5594	914	4	,	,	PUNCT
ejpam-5594	914	5	2022(1):5815993	2022(1):5815993	NOUN
ejpam-5594	914	6	,	,	PUNCT
ejpam-5594	914	7	2022	2022	NUM
ejpam-5594	914	8	.	.	PUNCT
ejpam-5594	915	1	[	[	X
ejpam-5594	915	2	42	42	NUM
ejpam-5594	915	3	]	]	X
ejpam-5594	915	4	s	s	PART
ejpam-5594	915	5	mubeen	mubeen	NOUN
ejpam-5594	915	6	and	and	CCONJ
ejpam-5594	915	7	gm	gm	PROPN
ejpam-5594	915	8	habibullah	habibullah	PROPN
ejpam-5594	915	9	.	.	PUNCT
ejpam-5594	916	1	k	k	ADJ
ejpam-5594	916	2	-	-	PUNCT
ejpam-5594	916	3	fractional	fractional	ADJ
ejpam-5594	916	4	integrals	integral	NOUN
ejpam-5594	916	5	and	and	CCONJ
ejpam-5594	916	6	application	application	NOUN
ejpam-5594	916	7	.	.	PUNCT
ejpam-5594	917	1	int	int	NOUN
ejpam-5594	917	2	.	.	PUNCT
ejpam-5594	918	1	j.	j.	PROPN
ejpam-5594	918	2	contemp	contemp	PROPN
ejpam-5594	918	3	.	.	PUNCT
ejpam-5594	919	1	math	math	NOUN
ejpam-5594	919	2	.	.	PUNCT
ejpam-5594	920	1	sci	sci	PROPN
ejpam-5594	920	2	,	,	PUNCT
ejpam-5594	920	3	7(2):89–94	7(2):89–94	NUM
ejpam-5594	920	4	,	,	PUNCT
ejpam-5594	920	5	2012	2012	NUM
ejpam-5594	920	6	.	.	PUNCT
ejpam-5594	921	1	[	[	X
ejpam-5594	921	2	43	43	NUM
ejpam-5594	921	3	]	]	X
ejpam-5594	921	4	uma	uma	PROPN
ejpam-5594	921	5	devi	devi	PROPN
ejpam-5594	921	6	patel	patel	PROPN
ejpam-5594	921	7	and	and	CCONJ
ejpam-5594	921	8	stojan	stojan	ADP
ejpam-5594	921	9	radenović.	radenović.	PRON
ejpam-5594	921	10	an	an	DET
ejpam-5594	921	11	application	application	NOUN
ejpam-5594	921	12	to	to	ADP
ejpam-5594	921	13	nonlinear	nonlinear	ADJ
ejpam-5594	921	14	fractional	fractional	ADJ
ejpam-5594	921	15	differential	differential	ADJ
ejpam-5594	921	16	equation	equation	NOUN
ejpam-5594	921	17	via	via	ADP
ejpam-5594	921	18	α	α	NOUN
ejpam-5594	921	19	-	-	PUNCT
ejpam-5594	921	20	γ	γ	ADJ
ejpam-5594	921	21	f	f	NOUN
ejpam-5594	921	22	-	-	PUNCT
ejpam-5594	921	23	fuzzy	fuzzy	ADJ
ejpam-5594	921	24	contractive	contractive	ADJ
ejpam-5594	921	25	mappings	mapping	NOUN
ejpam-5594	921	26	in	in	ADP
ejpam-5594	921	27	a	a	DET
ejpam-5594	921	28	fuzzy	fuzzy	ADJ
ejpam-5594	921	29	metric	metric	ADJ
ejpam-5594	921	30	space	space	NOUN
ejpam-5594	921	31	.	.	PUNCT
ejpam-5594	922	1	mathematics	mathematic	NOUN
ejpam-5594	922	2	,	,	PUNCT
ejpam-5594	922	3	10(16):2831	10(16):2831	NUM
ejpam-5594	922	4	,	,	PUNCT
ejpam-5594	922	5	2022	2022	NUM
ejpam-5594	922	6	.	.	PUNCT
ejpam-5594	923	1	[	[	X
ejpam-5594	923	2	44	44	NUM
ejpam-5594	923	3	]	]	PUNCT
ejpam-5594	923	4	soubhagya	soubhagya	PROPN
ejpam-5594	923	5	kumar	kumar	PROPN
ejpam-5594	923	6	sahoo	sahoo	PROPN
ejpam-5594	923	7	,	,	PUNCT
ejpam-5594	923	8	eman	eman	PROPN
ejpam-5594	923	9	al	al	PROPN
ejpam-5594	923	10	-	-	PUNCT
ejpam-5594	923	11	sarairah	sarairah	PROPN
ejpam-5594	923	12	,	,	PUNCT
ejpam-5594	923	13	pshtiwan	pshtiwan	PROPN
ejpam-5594	923	14	othman	othman	PROPN
ejpam-5594	923	15	mohammed	mohammed	PROPN
ejpam-5594	923	16	,	,	PUNCT
ejpam-5594	923	17	muhammad	muhammad	PROPN
ejpam-5594	923	18	tariq	tariq	PROPN
ejpam-5594	923	19	,	,	PUNCT
ejpam-5594	923	20	and	and	CCONJ
ejpam-5594	923	21	kamsing	kamse	VERB
ejpam-5594	923	22	nonlaopon	nonlaopon	ADV
ejpam-5594	923	23	.	.	PUNCT
ejpam-5594	924	1	modified	modify	VERB
ejpam-5594	924	2	inequalities	inequality	NOUN
ejpam-5594	924	3	on	on	ADP
ejpam-5594	924	4	center	center	ADJ
ejpam-5594	924	5	-	-	PUNCT
ejpam-5594	924	6	radius	radius	NOUN
ejpam-5594	924	7	order	order	NOUN
ejpam-5594	924	8	interval	interval	NOUN
ejpam-5594	924	9	-	-	PUNCT
ejpam-5594	924	10	valued	value	VERB
ejpam-5594	924	11	functions	function	NOUN
ejpam-5594	924	12	pertaining	pertain	VERB
ejpam-5594	924	13	to	to	ADP
ejpam-5594	924	14	riemann	riemann	PROPN
ejpam-5594	924	15	–	–	PUNCT
ejpam-5594	924	16	liouville	liouville	VERB
ejpam-5594	924	17	fractional	fractional	ADJ
ejpam-5594	924	18	integrals	integral	NOUN
ejpam-5594	924	19	.	.	PUNCT
ejpam-5594	925	1	axioms	axiom	NOUN
ejpam-5594	925	2	,	,	PUNCT
ejpam-5594	925	3	11(12):732	11(12):732	NUM
ejpam-5594	925	4	,	,	PUNCT
ejpam-5594	925	5	2022	2022	NUM
ejpam-5594	925	6	.	.	PUNCT
ejpam-5594	926	1	references	reference	NOUN
ejpam-5594	926	2	4048	4048	NUM
ejpam-5594	926	3	[	[	X
ejpam-5594	926	4	45	45	NUM
ejpam-5594	926	5	]	]	PUNCT
ejpam-5594	926	6	soubhagya	soubhagya	PROPN
ejpam-5594	926	7	kumar	kumar	PROPN
ejpam-5594	926	8	sahoo	sahoo	PROPN
ejpam-5594	926	9	,	,	PUNCT
ejpam-5594	926	10	hleil	hleil	VERB
ejpam-5594	926	11	alrweili	alrweili	NOUN
ejpam-5594	926	12	,	,	PUNCT
ejpam-5594	926	13	savin	savin	NOUN
ejpam-5594	926	14	treanţă	treanţă	PROPN
ejpam-5594	926	15	,	,	PUNCT
ejpam-5594	926	16	and	and	CCONJ
ejpam-5594	926	17	zareen	zareen	VERB
ejpam-5594	926	18	a	a	DET
ejpam-5594	926	19	khan	khan	PROPN
ejpam-5594	926	20	.	.	PUNCT
ejpam-5594	927	1	new	new	ADJ
ejpam-5594	927	2	fractional	fractional	ADJ
ejpam-5594	927	3	integral	integral	ADJ
ejpam-5594	927	4	inequalities	inequality	NOUN
ejpam-5594	927	5	pertaining	pertain	VERB
ejpam-5594	927	6	to	to	ADP
ejpam-5594	927	7	center	center	NOUN
ejpam-5594	927	8	-	-	PUNCT
ejpam-5594	927	9	radius	radius	NOUN
ejpam-5594	927	10	(	(	PUNCT
ejpam-5594	927	11	cr)-ordered	cr)-ordere	VERB
ejpam-5594	927	12	convex	convex	NOUN
ejpam-5594	927	13	functions	function	NOUN
ejpam-5594	927	14	.	.	PUNCT
ejpam-5594	928	1	fractal	fractal	ADJ
ejpam-5594	928	2	and	and	CCONJ
ejpam-5594	928	3	fractional	fractional	ADJ
ejpam-5594	928	4	,	,	PUNCT
ejpam-5594	928	5	7(1):81	7(1):81	NUM
ejpam-5594	928	6	,	,	PUNCT
ejpam-5594	928	7	2023	2023	NUM
ejpam-5594	928	8	.	.	PUNCT
ejpam-5594	929	1	[	[	X
ejpam-5594	929	2	46	46	NUM
ejpam-5594	929	3	]	]	X
ejpam-5594	929	4	soubhagya	soubhagya	PROPN
ejpam-5594	929	5	kumar	kumar	PROPN
ejpam-5594	929	6	sahoo	sahoo	PROPN
ejpam-5594	929	7	,	,	PUNCT
ejpam-5594	929	8	muhammad	muhammad	PROPN
ejpam-5594	929	9	amer	amer	PROPN
ejpam-5594	929	10	latif	latif	PROPN
ejpam-5594	929	11	,	,	PUNCT
ejpam-5594	929	12	omar	omar	PROPN
ejpam-5594	929	13	mutab	mutab	PROPN
ejpam-5594	929	14	alsalami	alsalami	NOUN
ejpam-5594	929	15	,	,	PUNCT
ejpam-5594	929	16	savin	savin	PROPN
ejpam-5594	929	17	treanţă	treanţă	PROPN
ejpam-5594	929	18	,	,	PUNCT
ejpam-5594	929	19	weerawat	weerawat	VERB
ejpam-5594	929	20	sudsutad	sudsutad	NOUN
ejpam-5594	929	21	,	,	PUNCT
ejpam-5594	929	22	and	and	CCONJ
ejpam-5594	929	23	jutarat	jutarat	PROPN
ejpam-5594	929	24	kongson	kongson	PROPN
ejpam-5594	929	25	.	.	PUNCT
ejpam-5594	930	1	hermite	hermite	ADJ
ejpam-5594	930	2	–	–	PUNCT
ejpam-5594	930	3	hadamard	hadamard	NOUN
ejpam-5594	930	4	,	,	PUNCT
ejpam-5594	930	5	fejér	fejér	NOUN
ejpam-5594	930	6	and	and	CCONJ
ejpam-5594	930	7	pachpatte	pachpatte	NOUN
ejpam-5594	930	8	-	-	PUNCT
ejpam-5594	930	9	type	type	NOUN
ejpam-5594	930	10	integral	integral	ADJ
ejpam-5594	930	11	inequalities	inequality	NOUN
ejpam-5594	930	12	for	for	ADP
ejpam-5594	930	13	center	center	ADJ
ejpam-5594	930	14	-	-	PUNCT
ejpam-5594	930	15	radius	radius	NOUN
ejpam-5594	930	16	order	order	NOUN
ejpam-5594	930	17	interval	interval	NOUN
ejpam-5594	930	18	-	-	PUNCT
ejpam-5594	930	19	valued	value	VERB
ejpam-5594	930	20	preinvex	preinvex	NOUN
ejpam-5594	930	21	functions	function	NOUN
ejpam-5594	930	22	.	.	PUNCT
ejpam-5594	931	1	fractal	fractal	ADJ
ejpam-5594	931	2	and	and	CCONJ
ejpam-5594	931	3	fractional	fractional	ADJ
ejpam-5594	931	4	,	,	PUNCT
ejpam-5594	931	5	6(9):506	6(9):506	NUM
ejpam-5594	931	6	,	,	PUNCT
ejpam-5594	931	7	2022	2022	NUM
ejpam-5594	931	8	.	.	PUNCT
ejpam-5594	932	1	[	[	X
ejpam-5594	932	2	47	47	NUM
ejpam-5594	932	3	]	]	X
ejpam-5594	932	4	ahsan	ahsan	PROPN
ejpam-5594	932	5	fareed	fareed	PROPN
ejpam-5594	932	6	shah	shah	PROPN
ejpam-5594	932	7	,	,	PUNCT
ejpam-5594	932	8	serap	serap	NOUN
ejpam-5594	932	9	özcan	özcan	PROPN
ejpam-5594	932	10	,	,	PUNCT
ejpam-5594	932	11	miguel	miguel	PROPN
ejpam-5594	932	12	vivas	vivas	PROPN
ejpam-5594	932	13	-	-	PROPN
ejpam-5594	932	14	cortez	cortez	PROPN
ejpam-5594	932	15	,	,	PUNCT
ejpam-5594	932	16	muhammad	muhammad	PROPN
ejpam-5594	932	17	shoaib	shoaib	PROPN
ejpam-5594	932	18	saleem	saleem	PROPN
ejpam-5594	932	19	,	,	PUNCT
ejpam-5594	932	20	and	and	CCONJ
ejpam-5594	932	21	artion	artion	PROPN
ejpam-5594	932	22	kashuri	kashuri	PROPN
ejpam-5594	932	23	.	.	PUNCT
ejpam-5594	932	24	fractional	fractional	ADJ
ejpam-5594	932	25	hermite	hermite	PROPN
ejpam-5594	932	26	–	–	PUNCT
ejpam-5594	932	27	hadamard	hadamard	NOUN
ejpam-5594	932	28	–	–	PUNCT
ejpam-5594	932	29	mercer	mercer	NOUN
ejpam-5594	932	30	-	-	PUNCT
ejpam-5594	932	31	type	type	NOUN
ejpam-5594	932	32	inequalities	inequality	NOUN
ejpam-5594	932	33	for	for	ADP
ejpam-5594	932	34	interval	interval	NOUN
ejpam-5594	932	35	-	-	PUNCT
ejpam-5594	932	36	valued	value	VERB
ejpam-5594	932	37	convex	convex	NOUN
ejpam-5594	932	38	stochastic	stochastic	NOUN
ejpam-5594	932	39	processes	process	NOUN
ejpam-5594	932	40	with	with	ADP
ejpam-5594	932	41	center	center	ADJ
ejpam-5594	932	42	-	-	PUNCT
ejpam-5594	932	43	radius	radius	NOUN
ejpam-5594	932	44	order	order	NOUN
ejpam-5594	932	45	and	and	CCONJ
ejpam-5594	932	46	their	their	PRON
ejpam-5594	932	47	related	related	ADJ
ejpam-5594	932	48	applications	application	NOUN
ejpam-5594	932	49	in	in	ADP
ejpam-5594	932	50	entropy	entropy	NOUN
ejpam-5594	932	51	and	and	CCONJ
ejpam-5594	932	52	information	information	NOUN
ejpam-5594	932	53	theory	theory	NOUN
ejpam-5594	932	54	.	.	PUNCT
ejpam-5594	933	1	fractal	fractal	PROPN
ejpam-5594	933	2	and	and	CCONJ
ejpam-5594	933	3	fractional	fractional	ADJ
ejpam-5594	933	4	,	,	PUNCT
ejpam-5594	933	5	8(7):408	8(7):408	NUM
ejpam-5594	933	6	,	,	PUNCT
ejpam-5594	933	7	2024	2024	NUM
ejpam-5594	933	8	.	.	PUNCT
ejpam-5594	934	1	[	[	X
ejpam-5594	934	2	48	48	NUM
ejpam-5594	934	3	]	]	PUNCT
ejpam-5594	934	4	nidhi	nidhi	PROPN
ejpam-5594	934	5	sharma	sharma	PROPN
ejpam-5594	934	6	,	,	PUNCT
ejpam-5594	934	7	sanjeev	sanjeev	PROPN
ejpam-5594	934	8	kumar	kumar	PROPN
ejpam-5594	934	9	singh	singh	PROPN
ejpam-5594	934	10	,	,	PUNCT
ejpam-5594	934	11	shashi	shashi	PROPN
ejpam-5594	934	12	kant	kant	PROPN
ejpam-5594	934	13	mishra	mishra	PROPN
ejpam-5594	934	14	,	,	PUNCT
ejpam-5594	934	15	and	and	CCONJ
ejpam-5594	934	16	abdelouahed	abdelouahe	VERB
ejpam-5594	934	17	hamdi	hamdi	PROPN
ejpam-5594	934	18	.	.	PUNCT
ejpam-5594	935	1	hermite	hermite	PROPN
ejpam-5594	935	2	–	–	PUNCT
ejpam-5594	935	3	hadamard	hadamard	ADJ
ejpam-5594	935	4	-	-	PUNCT
ejpam-5594	935	5	type	type	NOUN
ejpam-5594	935	6	inequalities	inequality	NOUN
ejpam-5594	935	7	for	for	ADP
ejpam-5594	935	8	interval	interval	NOUN
ejpam-5594	935	9	-	-	PUNCT
ejpam-5594	935	10	valued	value	VERB
ejpam-5594	935	11	preinvex	preinvex	NOUN
ejpam-5594	935	12	functions	function	NOUN
ejpam-5594	935	13	via	via	ADP
ejpam-5594	935	14	riemann	riemann	PROPN
ejpam-5594	935	15	–	–	PUNCT
ejpam-5594	935	16	liouville	liouville	VERB
ejpam-5594	935	17	fractional	fractional	ADJ
ejpam-5594	935	18	integrals	integral	NOUN
ejpam-5594	935	19	.	.	PUNCT
ejpam-5594	936	1	journal	journal	PROPN
ejpam-5594	936	2	of	of	ADP
ejpam-5594	936	3	inequalities	inequality	NOUN
ejpam-5594	936	4	and	and	CCONJ
ejpam-5594	936	5	applications	application	NOUN
ejpam-5594	936	6	,	,	PUNCT
ejpam-5594	936	7	2021:1–15	2021:1–15	NUM
ejpam-5594	936	8	,	,	PUNCT
ejpam-5594	936	9	2021	2021	NUM
ejpam-5594	936	10	.	.	PUNCT
ejpam-5594	937	1	[	[	X
ejpam-5594	937	2	49	49	NUM
ejpam-5594	937	3	]	]	X
ejpam-5594	937	4	fangfang	fangfang	PROPN
ejpam-5594	937	5	shi	shi	PROPN
ejpam-5594	937	6	,	,	PUNCT
ejpam-5594	937	7	guoju	guoju	PROPN
ejpam-5594	937	8	ye	ye	PROPN
ejpam-5594	937	9	,	,	PUNCT
ejpam-5594	937	10	dafang	dafang	PROPN
ejpam-5594	937	11	zhao	zhao	PROPN
ejpam-5594	937	12	,	,	PUNCT
ejpam-5594	937	13	and	and	CCONJ
ejpam-5594	937	14	wei	wei	PROPN
ejpam-5594	937	15	liu	liu	PROPN
ejpam-5594	937	16	.	.	PUNCT
ejpam-5594	938	1	some	some	DET
ejpam-5594	938	2	integral	integral	ADJ
ejpam-5594	938	3	inequalities	inequality	NOUN
ejpam-5594	938	4	for	for	ADP
ejpam-5594	938	5	coordinated	coordinated	ADJ
ejpam-5594	938	6	log	log	NOUN
ejpam-5594	938	7	-	-	PUNCT
ejpam-5594	938	8	h	h	NOUN
ejpam-5594	938	9	-	-	PUNCT
ejpam-5594	938	10	convex	convex	NOUN
ejpam-5594	938	11	interval	interval	NOUN
ejpam-5594	938	12	-	-	PUNCT
ejpam-5594	938	13	valued	value	VERB
ejpam-5594	938	14	functions	function	NOUN
ejpam-5594	938	15	.	.	PUNCT
ejpam-5594	939	1	aims	aim	VERB
ejpam-5594	939	2	mathematics	mathematic	NOUN
ejpam-5594	939	3	,	,	PUNCT
ejpam-5594	939	4	7(1):156	7(1):156	NUM
ejpam-5594	939	5	–	–	PUNCT
ejpam-5594	939	6	170	170	NUM
ejpam-5594	939	7	,	,	PUNCT
ejpam-5594	939	8	2022	2022	NUM
ejpam-5594	939	9	.	.	PUNCT
ejpam-5594	940	1	[	[	X
ejpam-5594	940	2	50	50	NUM
ejpam-5594	940	3	]	]	X
ejpam-5594	940	4	hari	hari	PROPN
ejpam-5594	940	5	mohan	mohan	PROPN
ejpam-5594	940	6	srivastava	srivastava	PROPN
ejpam-5594	940	7	,	,	PUNCT
ejpam-5594	940	8	soubhagya	soubhagya	PROPN
ejpam-5594	940	9	kumar	kumar	PROPN
ejpam-5594	940	10	sahoo	sahoo	PROPN
ejpam-5594	940	11	,	,	PUNCT
ejpam-5594	940	12	pshtiwan	pshtiwan	PROPN
ejpam-5594	940	13	othman	othman	PROPN
ejpam-5594	940	14	mohammed	mohammed	PROPN
ejpam-5594	940	15	,	,	PUNCT
ejpam-5594	940	16	dumitru	dumitru	PROPN
ejpam-5594	940	17	baleanu	baleanu	NOUN
ejpam-5594	940	18	,	,	PUNCT
ejpam-5594	940	19	and	and	CCONJ
ejpam-5594	940	20	bibhakar	bibhakar	PROPN
ejpam-5594	940	21	kodamasingh	kodamasingh	PROPN
ejpam-5594	940	22	.	.	PUNCT
ejpam-5594	941	1	hermite	hermite	PROPN
ejpam-5594	941	2	–	–	PUNCT
ejpam-5594	941	3	hadamard	hadamard	ADJ
ejpam-5594	941	4	type	type	NOUN
ejpam-5594	941	5	inequalities	inequality	NOUN
ejpam-5594	941	6	for	for	ADP
ejpam-5594	941	7	interval	interval	NOUN
ejpam-5594	941	8	-	-	PUNCT
ejpam-5594	941	9	valued	value	VERB
ejpam-5594	941	10	preinvex	preinvex	NOUN
ejpam-5594	941	11	functions	function	NOUN
ejpam-5594	941	12	via	via	ADP
ejpam-5594	941	13	fractional	fractional	ADJ
ejpam-5594	941	14	integral	integral	ADJ
ejpam-5594	941	15	operators	operator	NOUN
ejpam-5594	941	16	.	.	PUNCT
ejpam-5594	942	1	international	international	ADJ
ejpam-5594	942	2	journal	journal	NOUN
ejpam-5594	942	3	of	of	ADP
ejpam-5594	942	4	computational	computational	ADJ
ejpam-5594	942	5	intelligence	intelligence	NOUN
ejpam-5594	942	6	systems	system	NOUN
ejpam-5594	942	7	,	,	PUNCT
ejpam-5594	942	8	15(1):8	15(1):8	NUM
ejpam-5594	942	9	,	,	PUNCT
ejpam-5594	942	10	2022	2022	NUM
ejpam-5594	942	11	.	.	PUNCT
ejpam-5594	943	1	[	[	X
ejpam-5594	943	2	51	51	NUM
ejpam-5594	943	3	]	]	X
ejpam-5594	943	4	hari	hari	PROPN
ejpam-5594	943	5	mohan	mohan	PROPN
ejpam-5594	943	6	srivastava	srivastava	PROPN
ejpam-5594	943	7	,	,	PUNCT
ejpam-5594	943	8	soubhagya	soubhagya	PROPN
ejpam-5594	943	9	kumar	kumar	PROPN
ejpam-5594	943	10	sahoo	sahoo	PROPN
ejpam-5594	943	11	,	,	PUNCT
ejpam-5594	943	12	pshtiwan	pshtiwan	PROPN
ejpam-5594	943	13	othman	othman	PROPN
ejpam-5594	943	14	mohammed	mohammed	PROPN
ejpam-5594	943	15	,	,	PUNCT
ejpam-5594	943	16	artion	artion	NOUN
ejpam-5594	943	17	kashuri	kashuri	PROPN
ejpam-5594	943	18	,	,	PUNCT
ejpam-5594	943	19	and	and	CCONJ
ejpam-5594	943	20	nejmeddine	nejmeddine	PROPN
ejpam-5594	943	21	chorfi	chorfi	PROPN
ejpam-5594	943	22	.	.	PUNCT
ejpam-5594	943	23	results	result	NOUN
ejpam-5594	943	24	on	on	ADP
ejpam-5594	943	25	minkowski	minkowski	ADJ
ejpam-5594	943	26	-	-	PUNCT
ejpam-5594	943	27	type	type	NOUN
ejpam-5594	943	28	inequalities	inequality	NOUN
ejpam-5594	943	29	for	for	ADP
ejpam-5594	943	30	weighted	weight	VERB
ejpam-5594	943	31	fractional	fractional	ADJ
ejpam-5594	943	32	integral	integral	ADJ
ejpam-5594	943	33	operators	operator	NOUN
ejpam-5594	943	34	.	.	PUNCT
ejpam-5594	944	1	symmetry	symmetry	NOUN
ejpam-5594	944	2	,	,	PUNCT
ejpam-5594	944	3	15(8):1522	15(8):1522	NUM
ejpam-5594	944	4	,	,	PUNCT
ejpam-5594	944	5	2023	2023	NUM
ejpam-5594	944	6	.	.	PUNCT
ejpam-5594	945	1	[	[	X
ejpam-5594	945	2	52	52	NUM
ejpam-5594	945	3	]	]	PUNCT
ejpam-5594	945	4	vuk	vuk	PROPN
ejpam-5594	945	5	stojiljković	stojiljković	PROPN
ejpam-5594	945	6	,	,	PUNCT
ejpam-5594	945	7	nikola	nikola	PROPN
ejpam-5594	945	8	mirkov	mirkov	PROPN
ejpam-5594	945	9	,	,	PUNCT
ejpam-5594	945	10	and	and	CCONJ
ejpam-5594	945	11	stojan	stojan	ADP
ejpam-5594	945	12	radenović.	radenović.	PROPN
ejpam-5594	945	13	variations	variation	NOUN
ejpam-5594	945	14	in	in	ADP
ejpam-5594	945	15	the	the	DET
ejpam-5594	945	16	tensorial	tensorial	ADJ
ejpam-5594	945	17	trapezoid	trapezoid	ADJ
ejpam-5594	945	18	type	type	NOUN
ejpam-5594	945	19	inequalities	inequality	NOUN
ejpam-5594	945	20	for	for	ADP
ejpam-5594	945	21	convex	convex	NOUN
ejpam-5594	945	22	functions	function	NOUN
ejpam-5594	945	23	of	of	ADP
ejpam-5594	945	24	self	self	NOUN
ejpam-5594	945	25	-	-	PUNCT
ejpam-5594	945	26	adjoint	adjoint	NOUN
ejpam-5594	945	27	operators	operator	NOUN
ejpam-5594	945	28	in	in	ADP
ejpam-5594	945	29	hilbert	hilbert	PROPN
ejpam-5594	945	30	spaces	space	NOUN
ejpam-5594	945	31	.	.	PUNCT
ejpam-5594	946	1	symmetry	symmetry	NOUN
ejpam-5594	946	2	,	,	PUNCT
ejpam-5594	946	3	16(1):121	16(1):121	NUM
ejpam-5594	946	4	,	,	PUNCT
ejpam-5594	946	5	2024	2024	NUM
ejpam-5594	946	6	.	.	PUNCT
ejpam-5594	947	1	[	[	X
ejpam-5594	947	2	53	53	NUM
ejpam-5594	947	3	]	]	PUNCT
ejpam-5594	947	4	avanidhar	avanidhar	PROPN
ejpam-5594	947	5	subrahmanyam	subrahmanyam	PROPN
ejpam-5594	947	6	,	,	PUNCT
ejpam-5594	947	7	ke	ke	PROPN
ejpam-5594	947	8	tang	tang	PROPN
ejpam-5594	947	9	,	,	PUNCT
ejpam-5594	947	10	jingyuan	jingyuan	PROPN
ejpam-5594	947	11	wang	wang	PROPN
ejpam-5594	947	12	,	,	PUNCT
ejpam-5594	947	13	and	and	CCONJ
ejpam-5594	947	14	xuewei	xuewei	PROPN
ejpam-5594	947	15	yang	yang	PROPN
ejpam-5594	947	16	.	.	PUNCT
ejpam-5594	947	17	leverage	leverage	NOUN
ejpam-5594	947	18	is	be	AUX
ejpam-5594	947	19	a	a	DET
ejpam-5594	947	20	double	double	ADJ
ejpam-5594	947	21	-	-	PUNCT
ejpam-5594	947	22	edged	edge	VERB
ejpam-5594	947	23	sword	sword	NOUN
ejpam-5594	947	24	.	.	PUNCT
ejpam-5594	948	1	the	the	DET
ejpam-5594	948	2	journal	journal	PROPN
ejpam-5594	948	3	of	of	ADP
ejpam-5594	948	4	finance	finance	NOUN
ejpam-5594	948	5	,	,	PUNCT
ejpam-5594	948	6	79(2):1579–1634	79(2):1579–1634	PROPN
ejpam-5594	948	7	,	,	PUNCT
ejpam-5594	948	8	2024	2024	NUM
ejpam-5594	948	9	.	.	PUNCT
ejpam-5594	949	1	[	[	X
ejpam-5594	949	2	54	54	NUM
ejpam-5594	949	3	]	]	PUNCT
ejpam-5594	949	4	chunzheng	chunzheng	PROPN
ejpam-5594	949	5	wang	wang	PROPN
ejpam-5594	949	6	,	,	PUNCT
ejpam-5594	949	7	lei	lei	PROPN
ejpam-5594	949	8	yang	yang	PROPN
ejpam-5594	949	9	,	,	PUNCT
ejpam-5594	949	10	minghua	minghua	PROPN
ejpam-5594	949	11	hu	hu	PROPN
ejpam-5594	949	12	,	,	PUNCT
ejpam-5594	949	13	yanjun	yanjun	PROPN
ejpam-5594	949	14	wang	wang	PROPN
ejpam-5594	949	15	,	,	PUNCT
ejpam-5594	949	16	and	and	CCONJ
ejpam-5594	949	17	zheng	zheng	PROPN
ejpam-5594	949	18	zhao	zhao	PROPN
ejpam-5594	949	19	.	.	PUNCT
ejpam-5594	950	1	ondemand	ondemand	PROPN
ejpam-5594	950	2	airport	airport	NOUN
ejpam-5594	950	3	slot	slot	NOUN
ejpam-5594	950	4	management	management	NOUN
ejpam-5594	950	5	:	:	PUNCT
ejpam-5594	950	6	tree	tree	NOUN
ejpam-5594	950	7	-	-	PUNCT
ejpam-5594	950	8	structured	structure	VERB
ejpam-5594	950	9	capacity	capacity	NOUN
ejpam-5594	950	10	profile	profile	NOUN
ejpam-5594	950	11	and	and	CCONJ
ejpam-5594	950	12	coadapted	coadapte	VERB
ejpam-5594	950	13	fire	fire	NOUN
ejpam-5594	950	14	-	-	PUNCT
ejpam-5594	950	15	break	break	NOUN
ejpam-5594	950	16	setting	setting	NOUN
ejpam-5594	950	17	and	and	CCONJ
ejpam-5594	950	18	slot	slot	NOUN
ejpam-5594	950	19	allocation	allocation	NOUN
ejpam-5594	950	20	.	.	PUNCT
ejpam-5594	951	1	transportmetrica	transportmetrica	PROPN
ejpam-5594	951	2	a	a	DET
ejpam-5594	951	3	:	:	PUNCT
ejpam-5594	951	4	transport	transport	NOUN
ejpam-5594	951	5	science	science	NOUN
ejpam-5594	951	6	,	,	PUNCT
ejpam-5594	951	7	pages	page	NOUN
ejpam-5594	951	8	1–35	1–35	PROPN
ejpam-5594	951	9	,	,	PUNCT
ejpam-5594	951	10	2024	2024	NUM
ejpam-5594	951	11	.	.	PUNCT
ejpam-5594	952	1	[	[	X
ejpam-5594	952	2	55	55	NUM
ejpam-5594	952	3	]	]	X
ejpam-5594	952	4	li	li	PROPN
ejpam-5594	952	5	xinde	xinde	PROPN
ejpam-5594	952	6	,	,	PUNCT
ejpam-5594	952	7	fir	fir	NOUN
ejpam-5594	952	8	dunkin	dunkin	NOUN
ejpam-5594	952	9	,	,	PUNCT
ejpam-5594	952	10	and	and	CCONJ
ejpam-5594	952	11	jean	jean	PROPN
ejpam-5594	952	12	dezert	dezert	PROPN
ejpam-5594	952	13	.	.	PUNCT
ejpam-5594	953	1	multi	multi	ADJ
ejpam-5594	953	2	-	-	ADJ
ejpam-5594	953	3	source	source	ADJ
ejpam-5594	953	4	information	information	NOUN
ejpam-5594	953	5	fusion	fusion	NOUN
ejpam-5594	953	6	:	:	PUNCT
ejpam-5594	953	7	progress	progress	NOUN
ejpam-5594	953	8	and	and	CCONJ
ejpam-5594	953	9	future	future	NOUN
ejpam-5594	953	10	.	.	PUNCT
ejpam-5594	954	1	chinese	chinese	ADJ
ejpam-5594	954	2	journal	journal	PROPN
ejpam-5594	954	3	of	of	ADP
ejpam-5594	954	4	aeronautics	aeronautic	NOUN
ejpam-5594	954	5	,	,	PUNCT
ejpam-5594	954	6	2023	2023	NUM
ejpam-5594	954	7	.	.	PUNCT
ejpam-5594	955	1	references	reference	NOUN
ejpam-5594	955	2	4049	4049	NUM
ejpam-5594	956	1	[	[	X
ejpam-5594	956	2	56	56	NUM
ejpam-5594	956	3	]	]	X
ejpam-5594	956	4	heng	heng	PROPN
ejpam-5594	956	5	yao	yao	PROPN
ejpam-5594	956	6	,	,	PUNCT
ejpam-5594	956	7	diego	diego	NOUN
ejpam-5594	956	8	pugliese	pugliese	PROPN
ejpam-5594	956	9	,	,	PUNCT
ejpam-5594	956	10	matthieu	matthieu	PROPN
ejpam-5594	956	11	lancry	lancry	PROPN
ejpam-5594	956	12	,	,	PUNCT
ejpam-5594	956	13	and	and	CCONJ
ejpam-5594	956	14	ye	ye	PROPN
ejpam-5594	956	15	dai	dai	PROPN
ejpam-5594	956	16	.	.	PROPN
ejpam-5594	956	17	ultrafast	ultrafast	PROPN
ejpam-5594	956	18	laser	laser	NOUN
ejpam-5594	956	19	direct	direct	ADJ
ejpam-5594	956	20	writing	writing	NOUN
ejpam-5594	956	21	nanogratings	nanograting	NOUN
ejpam-5594	956	22	and	and	CCONJ
ejpam-5594	956	23	their	their	PRON
ejpam-5594	956	24	engineering	engineering	NOUN
ejpam-5594	956	25	in	in	ADP
ejpam-5594	956	26	transparent	transparent	ADJ
ejpam-5594	956	27	materials	material	NOUN
ejpam-5594	956	28	.	.	PUNCT
ejpam-5594	957	1	laser	laser	PROPN
ejpam-5594	957	2	&	&	CCONJ
ejpam-5594	957	3	photonics	photonic	NOUN
ejpam-5594	957	4	reviews	review	NOUN
ejpam-5594	957	5	,	,	PUNCT
ejpam-5594	957	6	page	page	NOUN
ejpam-5594	957	7	2300891	2300891	NUM
ejpam-5594	957	8	.	.	PUNCT
ejpam-5594	958	1	[	[	X
ejpam-5594	958	2	57	57	NUM
ejpam-5594	958	3	]	]	X
ejpam-5594	958	4	çetin	çetin	PROPN
ejpam-5594	958	5	yildiz	yildiz	PROPN
ejpam-5594	958	6	,	,	PUNCT
ejpam-5594	958	7	büşra	büşra	PROPN
ejpam-5594	958	8	yergöz	yergöz	PROPN
ejpam-5594	958	9	,	,	PUNCT
ejpam-5594	958	10	and	and	CCONJ
ejpam-5594	958	11	abdulvahit	abdulvahit	VERB
ejpam-5594	958	12	yergöz	yergöz	PROPN
ejpam-5594	958	13	.	.	PUNCT
ejpam-5594	959	1	on	on	ADP
ejpam-5594	959	2	new	new	ADJ
ejpam-5594	959	3	general	general	ADJ
ejpam-5594	959	4	inequalities	inequality	NOUN
ejpam-5594	959	5	for	for	ADP
ejpam-5594	959	6	s	s	NOUN
ejpam-5594	959	7	-	-	PUNCT
ejpam-5594	959	8	convex	convex	NOUN
ejpam-5594	959	9	functions	function	NOUN
ejpam-5594	959	10	and	and	CCONJ
ejpam-5594	959	11	their	their	PRON
ejpam-5594	959	12	applications	application	NOUN
ejpam-5594	959	13	.	.	PUNCT
ejpam-5594	960	1	journal	journal	PROPN
ejpam-5594	960	2	of	of	ADP
ejpam-5594	960	3	inequalities	inequality	NOUN
ejpam-5594	960	4	and	and	CCONJ
ejpam-5594	960	5	applications	application	NOUN
ejpam-5594	960	6	,	,	PUNCT
ejpam-5594	960	7	2023(1):11	2023(1):11	NUM
ejpam-5594	960	8	,	,	PUNCT
ejpam-5594	960	9	2023	2023	NUM
ejpam-5594	960	10	.	.	PUNCT
ejpam-5594	961	1	[	[	X
ejpam-5594	961	2	58	58	NUM
ejpam-5594	961	3	]	]	X
ejpam-5594	961	4	hui	hui	PROPN
ejpam-5594	961	5	zhang	zhang	PROPN
ejpam-5594	961	6	,	,	PUNCT
ejpam-5594	961	7	dai	dai	PROPN
ejpam-5594	961	8	songjie	songjie	PROPN
ejpam-5594	961	9	,	,	PUNCT
ejpam-5594	961	10	liu	liu	PROPN
ejpam-5594	961	11	yang	yang	PROPN
ejpam-5594	961	12	,	,	PUNCT
ejpam-5594	961	13	zhu	zhu	PROPN
ejpam-5594	961	14	yijun	yijun	PROPN
ejpam-5594	961	15	,	,	PUNCT
ejpam-5594	961	16	xu	xu	PROPN
ejpam-5594	961	17	yangdong	yangdong	PROPN
ejpam-5594	961	18	,	,	PUNCT
ejpam-5594	961	19	baotong	baotong	PROPN
ejpam-5594	961	20	li	li	PROPN
ejpam-5594	961	21	,	,	PUNCT
ejpam-5594	961	22	and	and	CCONJ
ejpam-5594	961	23	dong	dong	PROPN
ejpam-5594	961	24	guangneng	guangneng	PROPN
ejpam-5594	961	25	.	.	PUNCT
ejpam-5594	962	1	fishbone	fishbone	NOUN
ejpam-5594	962	2	-	-	PUNCT
ejpam-5594	962	3	like	like	ADJ
ejpam-5594	962	4	micro	micro	ADJ
ejpam-5594	962	5	-	-	ADJ
ejpam-5594	962	6	textured	textured	ADJ
ejpam-5594	962	7	surface	surface	NOUN
ejpam-5594	962	8	for	for	ADP
ejpam-5594	962	9	unidirectional	unidirectional	ADJ
ejpam-5594	962	10	spreading	spreading	NOUN
ejpam-5594	962	11	of	of	ADP
ejpam-5594	962	12	droplets	droplet	NOUN
ejpam-5594	962	13	and	and	CCONJ
ejpam-5594	962	14	lubricity	lubricity	NOUN
ejpam-5594	962	15	improvement	improvement	NOUN
ejpam-5594	962	16	.	.	PUNCT
ejpam-5594	963	1	tribology	tribology	PROPN
ejpam-5594	963	2	international	international	PROPN
ejpam-5594	963	3	,	,	PUNCT
ejpam-5594	963	4	198:109932	198:109932	NUM
ejpam-5594	963	5	,	,	PUNCT
ejpam-5594	963	6	2024	2024	NUM
ejpam-5594	963	7	.	.	PUNCT
ejpam-5594	964	1	[	[	X
ejpam-5594	964	2	59	59	NUM
ejpam-5594	964	3	]	]	PUNCT
ejpam-5594	964	4	hui	hui	PROPN
ejpam-5594	964	5	zhang	zhang	PROPN
ejpam-5594	964	6	,	,	PUNCT
ejpam-5594	964	7	pu	pu	PROPN
ejpam-5594	964	8	wang	wang	PROPN
ejpam-5594	964	9	,	,	PUNCT
ejpam-5594	964	10	yang	yang	PROPN
ejpam-5594	964	11	liu	liu	PROPN
ejpam-5594	964	12	,	,	PUNCT
ejpam-5594	964	13	songjie	songjie	PROPN
ejpam-5594	964	14	dai	dai	PROPN
ejpam-5594	964	15	,	,	PUNCT
ejpam-5594	964	16	yijun	yijun	PROPN
ejpam-5594	964	17	zhu	zhu	PROPN
ejpam-5594	964	18	,	,	PUNCT
ejpam-5594	964	19	baotong	baotong	PROPN
ejpam-5594	964	20	li	li	PROPN
ejpam-5594	964	21	,	,	PUNCT
ejpam-5594	964	22	and	and	CCONJ
ejpam-5594	964	23	guangneng	guangneng	PROPN
ejpam-5594	964	24	dong	dong	PROPN
ejpam-5594	964	25	.	.	PUNCT
ejpam-5594	964	26	stretch	stretch	PROPN
ejpam-5594	964	27	-	-	PUNCT
ejpam-5594	964	28	controlled	control	VERB
ejpam-5594	964	29	branch	branch	NOUN
ejpam-5594	964	30	shape	shape	NOUN
ejpam-5594	964	31	microstructures	microstructure	NOUN
ejpam-5594	964	32	for	for	ADP
ejpam-5594	964	33	switchable	switchable	ADJ
ejpam-5594	964	34	unidirectional	unidirectional	ADJ
ejpam-5594	964	35	self	self	NOUN
ejpam-5594	964	36	-	-	PUNCT
ejpam-5594	964	37	driven	drive	VERB
ejpam-5594	964	38	spreading	spreading	NOUN
ejpam-5594	964	39	of	of	ADP
ejpam-5594	964	40	oil	oil	NOUN
ejpam-5594	964	41	droplets	droplet	NOUN
ejpam-5594	964	42	.	.	PUNCT
ejpam-5594	965	1	acs	acs	PROPN
ejpam-5594	965	2	applied	apply	VERB
ejpam-5594	965	3	materials	material	NOUN
ejpam-5594	965	4	&	&	CCONJ
ejpam-5594	965	5	interfaces	interface	NOUN
ejpam-5594	965	6	,	,	PUNCT
ejpam-5594	965	7	16(31):41694–41703	16(31):41694–41703	NUM
ejpam-5594	965	8	,	,	PUNCT
ejpam-5594	965	9	2024	2024	NUM
ejpam-5594	965	10	.	.	PUNCT
ejpam-5594	966	1	[	[	X
ejpam-5594	966	2	60	60	NUM
ejpam-5594	966	3	]	]	PUNCT
ejpam-5594	966	4	xiaoju	xiaoju	PROPN
ejpam-5594	966	5	zhang	zhang	PROPN
ejpam-5594	966	6	,	,	PUNCT
ejpam-5594	966	7	khurram	khurram	PROPN
ejpam-5594	966	8	shabbir	shabbir	PROPN
ejpam-5594	966	9	,	,	PUNCT
ejpam-5594	966	10	waqar	waqar	PROPN
ejpam-5594	966	11	afzal	afzal	PROPN
ejpam-5594	966	12	,	,	PUNCT
ejpam-5594	966	13	he	he	PRON
ejpam-5594	966	14	xiao	xiao	PROPN
ejpam-5594	966	15	,	,	PUNCT
ejpam-5594	966	16	and	and	CCONJ
ejpam-5594	966	17	dong	dong	PROPN
ejpam-5594	966	18	lin	lin	PROPN
ejpam-5594	966	19	.	.	PUNCT
ejpam-5594	967	1	hermite	hermite	PROPN
ejpam-5594	967	2	–	–	PUNCT
ejpam-5594	967	3	hadamard	hadamard	NOUN
ejpam-5594	967	4	and	and	CCONJ
ejpam-5594	967	5	jensen	jensen	PROPN
ejpam-5594	967	6	-	-	PUNCT
ejpam-5594	967	7	type	type	NOUN
ejpam-5594	967	8	inequalities	inequality	NOUN
ejpam-5594	967	9	via	via	ADP
ejpam-5594	967	10	riemann	riemann	PROPN
ejpam-5594	967	11	integral	integral	ADJ
ejpam-5594	967	12	operator	operator	NOUN
ejpam-5594	967	13	for	for	ADP
ejpam-5594	967	14	a	a	DET
ejpam-5594	967	15	generalized	generalized	ADJ
ejpam-5594	967	16	class	class	NOUN
ejpam-5594	967	17	of	of	ADP
ejpam-5594	967	18	godunova	godunova	PROPN
ejpam-5594	967	19	–	–	PUNCT
ejpam-5594	967	20	levin	levin	PROPN
ejpam-5594	967	21	functions	function	NOUN
ejpam-5594	967	22	.	.	PUNCT
ejpam-5594	968	1	journal	journal	NOUN
ejpam-5594	968	2	of	of	ADP
ejpam-5594	968	3	mathematics	mathematic	NOUN
ejpam-5594	968	4	,	,	PUNCT
ejpam-5594	968	5	2022(1):3830324	2022(1):3830324	NUM
ejpam-5594	968	6	,	,	PUNCT
ejpam-5594	968	7	2022	2022	NUM
ejpam-5594	968	8	.	.	PUNCT
ejpam-5594	969	1	[	[	X
ejpam-5594	969	2	61	61	NUM
ejpam-5594	969	3	]	]	SYM
ejpam-5594	969	4	zhentong	zhentong	PROPN
ejpam-5594	969	5	zhang	zhang	PROPN
ejpam-5594	969	6	,	,	PUNCT
ejpam-5594	969	7	xinde	xinde	PROPN
ejpam-5594	969	8	li	li	PROPN
ejpam-5594	969	9	,	,	PUNCT
ejpam-5594	969	10	heqing	heqe	VERB
ejpam-5594	969	11	li	li	PROPN
ejpam-5594	969	12	,	,	PUNCT
ejpam-5594	969	13	fir	fir	NOUN
ejpam-5594	969	14	dunkin	dunkin	NOUN
ejpam-5594	969	15	,	,	PUNCT
ejpam-5594	969	16	bing	bing	VERB
ejpam-5594	969	17	li	li	PROPN
ejpam-5594	969	18	,	,	PUNCT
ejpam-5594	969	19	and	and	CCONJ
ejpam-5594	969	20	zhijun	zhijun	PROPN
ejpam-5594	969	21	li	li	PROPN
ejpam-5594	969	22	.	.	PROPN
ejpam-5594	969	23	dualbranch	dualbranch	PROPN
ejpam-5594	969	24	sparse	sparse	VERB
ejpam-5594	969	25	self	self	NOUN
ejpam-5594	969	26	-	-	PUNCT
ejpam-5594	969	27	learning	learning	NOUN
ejpam-5594	969	28	with	with	ADP
ejpam-5594	969	29	instance	instance	NOUN
ejpam-5594	969	30	binding	bind	VERB
ejpam-5594	969	31	augmentation	augmentation	NOUN
ejpam-5594	969	32	for	for	ADP
ejpam-5594	969	33	adversarial	adversarial	ADJ
ejpam-5594	969	34	detection	detection	NOUN
ejpam-5594	969	35	in	in	ADP
ejpam-5594	969	36	remote	remote	ADJ
ejpam-5594	969	37	sensing	sensing	NOUN
ejpam-5594	969	38	images	image	NOUN
ejpam-5594	969	39	.	.	PUNCT
ejpam-5594	970	1	ieee	ieee	NOUN
ejpam-5594	970	2	transactions	transaction	NOUN
ejpam-5594	970	3	on	on	ADP
ejpam-5594	970	4	geoscience	geoscience	NOUN
ejpam-5594	970	5	and	and	CCONJ
ejpam-5594	970	6	remote	remote	ADJ
ejpam-5594	970	7	sensing	sensing	NOUN
ejpam-5594	970	8	,	,	PUNCT
ejpam-5594	970	9	2024	2024	NUM
ejpam-5594	970	10	.	.	PUNCT
ejpam-5594	971	1	[	[	X
ejpam-5594	971	2	62	62	NUM
ejpam-5594	971	3	]	]	X
ejpam-5594	971	4	zhiyue	zhiyue	PROPN
ejpam-5594	971	5	zhang	zhang	PROPN
ejpam-5594	971	6	,	,	PUNCT
ejpam-5594	971	7	muhammad	muhammad	PROPN
ejpam-5594	971	8	aamir	aamir	PROPN
ejpam-5594	971	9	ali	ali	PROPN
ejpam-5594	971	10	,	,	PUNCT
ejpam-5594	971	11	hüseyin	hüseyin	PROPN
ejpam-5594	971	12	budak	budak	PROPN
ejpam-5594	971	13	,	,	PUNCT
ejpam-5594	971	14	and	and	CCONJ
ejpam-5594	971	15	mehmet	mehmet	PROPN
ejpam-5594	971	16	zeki	zeki	PROPN
ejpam-5594	971	17	sarıkaya	sarıkaya	PROPN
ejpam-5594	971	18	.	.	PUNCT
ejpam-5594	972	1	on	on	ADP
ejpam-5594	972	2	hermite	hermite	PROPN
ejpam-5594	972	3	-	-	PUNCT
ejpam-5594	972	4	hadamard	hadamard	ADJ
ejpam-5594	972	5	type	type	NOUN
ejpam-5594	972	6	inequalities	inequality	NOUN
ejpam-5594	972	7	for	for	ADP
ejpam-5594	972	8	interval	interval	NOUN
ejpam-5594	972	9	-	-	PUNCT
ejpam-5594	972	10	valued	value	VERB
ejpam-5594	972	11	multiplicative	multiplicative	ADJ
ejpam-5594	972	12	integrals	integral	NOUN
ejpam-5594	972	13	.	.	PUNCT
ejpam-5594	973	1	communications	communication	NOUN
ejpam-5594	973	2	faculty	faculty	NOUN
ejpam-5594	973	3	of	of	ADP
ejpam-5594	973	4	sciences	sciences	PROPN
ejpam-5594	973	5	university	university	PROPN
ejpam-5594	973	6	of	of	ADP
ejpam-5594	973	7	ankara	ankara	PROPN
ejpam-5594	973	8	series	series	PROPN
ejpam-5594	973	9	a1	a1	PROPN
ejpam-5594	973	10	mathematics	mathematic	NOUN
ejpam-5594	973	11	and	and	CCONJ
ejpam-5594	973	12	statistics	statistic	NOUN
ejpam-5594	973	13	,	,	PUNCT
ejpam-5594	973	14	69(2):1428–1448	69(2):1428–1448	NUM
ejpam-5594	973	15	,	,	PUNCT
ejpam-5594	973	16	2020	2020	NUM
ejpam-5594	973	17	.	.	PUNCT
ejpam-5594	974	1	[	[	X
ejpam-5594	974	2	63	63	NUM
ejpam-5594	974	3	]	]	PUNCT
ejpam-5594	974	4	dafang	dafang	PROPN
ejpam-5594	974	5	zhao	zhao	PROPN
ejpam-5594	974	6	,	,	PUNCT
ejpam-5594	974	7	guohui	guohui	PROPN
ejpam-5594	974	8	zhao	zhao	PROPN
ejpam-5594	974	9	,	,	PUNCT
ejpam-5594	974	10	guoju	guoju	PROPN
ejpam-5594	974	11	ye	ye	PROPN
ejpam-5594	974	12	,	,	PUNCT
ejpam-5594	974	13	wei	wei	PROPN
ejpam-5594	974	14	liu	liu	PROPN
ejpam-5594	974	15	,	,	PUNCT
ejpam-5594	974	16	and	and	CCONJ
ejpam-5594	974	17	silvestru	silvestru	PROPN
ejpam-5594	974	18	sever	sever	VERB
ejpam-5594	974	19	dragomir	dragomir	ADJ
ejpam-5594	974	20	.	.	PUNCT
ejpam-5594	975	1	on	on	ADP
ejpam-5594	975	2	hermite	hermite	ADJ
ejpam-5594	975	3	–	–	PUNCT
ejpam-5594	975	4	hadamard	hadamard	ADJ
ejpam-5594	975	5	-	-	PUNCT
ejpam-5594	975	6	type	type	NOUN
ejpam-5594	975	7	inequalities	inequality	NOUN
ejpam-5594	975	8	for	for	ADP
ejpam-5594	975	9	coordinated	coordinated	ADJ
ejpam-5594	975	10	h	h	ADJ
ejpam-5594	975	11	-	-	PUNCT
ejpam-5594	975	12	convex	convex	NOUN
ejpam-5594	975	13	interval	interval	NOUN
ejpam-5594	975	14	-	-	PUNCT
ejpam-5594	975	15	valued	value	VERB
ejpam-5594	975	16	functions	function	NOUN
ejpam-5594	975	17	.	.	PUNCT
ejpam-5594	976	1	mathematics	mathematic	NOUN
ejpam-5594	976	2	,	,	PUNCT
ejpam-5594	976	3	9(19):2352	9(19):2352	NOUN
ejpam-5594	976	4	,	,	PUNCT
ejpam-5594	976	5	2021	2021	NUM
ejpam-5594	976	6	.	.	PUNCT
ejpam-5594	977	1	[	[	X
ejpam-5594	977	2	64	64	NUM
ejpam-5594	977	3	]	]	PUNCT
ejpam-5594	977	4	daqiong	daqiong	PROPN
ejpam-5594	977	5	zhou	zhou	PROPN
ejpam-5594	977	6	,	,	PUNCT
ejpam-5594	977	7	zaiyun	zaiyun	PROPN
ejpam-5594	977	8	peng	peng	PROPN
ejpam-5594	977	9	,	,	PUNCT
ejpam-5594	977	10	zhi	zhi	PROPN
ejpam-5594	977	11	lin	lin	PROPN
ejpam-5594	977	12	,	,	PUNCT
ejpam-5594	977	13	and	and	CCONJ
ejpam-5594	977	14	jingjing	jingjing	PROPN
ejpam-5594	977	15	wang	wang	PROPN
ejpam-5594	977	16	.	.	PUNCT
ejpam-5594	978	1	continuity	continuity	NOUN
ejpam-5594	978	2	of	of	ADP
ejpam-5594	978	3	the	the	DET
ejpam-5594	978	4	solution	solution	NOUN
ejpam-5594	978	5	set	set	VERB
ejpam-5594	978	6	mappings	mapping	NOUN
ejpam-5594	978	7	to	to	PART
ejpam-5594	978	8	parametric	parametric	VERB
ejpam-5594	978	9	unified	unified	ADJ
ejpam-5594	978	10	weak	weak	ADJ
ejpam-5594	978	11	vector	vector	NOUN
ejpam-5594	978	12	equilibrium	equilibrium	NOUN
ejpam-5594	978	13	problems	problem	NOUN
ejpam-5594	978	14	via	via	ADP
ejpam-5594	978	15	free	free	ADJ
ejpam-5594	978	16	-	-	PUNCT
ejpam-5594	978	17	disposal	disposal	NOUN
ejpam-5594	978	18	sets	set	NOUN
ejpam-5594	978	19	.	.	PUNCT
ejpam-5594	979	1	rairo	rairo	NOUN
ejpam-5594	979	2	-	-	PUNCT
ejpam-5594	979	3	operations	operation	NOUN
ejpam-5594	979	4	research	research	NOUN
ejpam-5594	979	5	,	,	PUNCT
ejpam-5594	979	6	2024	2024	NUM
ejpam-5594	979	7	.	.	PUNCT