id	sid	tid	token	lemma	pos
ejpam-5790	1	1	european	european	PROPN
ejpam-5790	1	2	journal	journal	PROPN
ejpam-5790	1	3	of	of	ADP
ejpam-5790	1	4	pure	pure	ADJ
ejpam-5790	1	5	and	and	CCONJ
ejpam-5790	1	6	applied	applied	ADJ
ejpam-5790	1	7	mathematics	mathematic	NOUN
ejpam-5790	1	8	2025	2025	NUM
ejpam-5790	1	9	,	,	PUNCT
ejpam-5790	1	10	vol	vol	NOUN
ejpam-5790	1	11	.	.	PROPN
ejpam-5790	1	12	18	18	NUM
ejpam-5790	1	13	,	,	PUNCT
ejpam-5790	1	14	issue	issue	NOUN
ejpam-5790	1	15	1	1	NUM
ejpam-5790	1	16	,	,	PUNCT
ejpam-5790	1	17	article	article	NOUN
ejpam-5790	1	18	number	number	NOUN
ejpam-5790	1	19	5790	5790	NUM
ejpam-5790	1	20	issn	issn	VERB
ejpam-5790	1	21	1307	1307	NUM
ejpam-5790	1	22	-	-	SYM
ejpam-5790	1	23	5543	5543	NUM
ejpam-5790	1	24	–	–	PUNCT
ejpam-5790	1	25	ejpam.com	ejpam.com	X
ejpam-5790	1	26	published	publish	VERB
ejpam-5790	1	27	by	by	ADP
ejpam-5790	1	28	new	new	PROPN
ejpam-5790	1	29	york	york	PROPN
ejpam-5790	1	30	business	business	PROPN
ejpam-5790	1	31	global	global	PROPN
ejpam-5790	1	32	gradient	gradient	ADJ
ejpam-5790	1	33	descent	descent	NOUN
ejpam-5790	1	34	and	and	CCONJ
ejpam-5790	1	35	twice	twice	ADV
ejpam-5790	1	36	differentiable	differentiable	ADJ
ejpam-5790	1	37	simpson	simpson	NOUN
ejpam-5790	1	38	-	-	PUNCT
ejpam-5790	1	39	type	type	NOUN
ejpam-5790	1	40	inequalities	inequality	NOUN
ejpam-5790	1	41	via	via	ADP
ejpam-5790	1	42	k	k	PROPN
ejpam-5790	1	43	-	-	PUNCT
ejpam-5790	1	44	riemann	riemann	PROPN
ejpam-5790	1	45	-	-	PUNCT
ejpam-5790	1	46	liouville	liouville	VERB
ejpam-5790	1	47	fractional	fractional	ADJ
ejpam-5790	1	48	operators	operator	NOUN
ejpam-5790	1	49	in	in	ADP
ejpam-5790	1	50	function	function	NOUN
ejpam-5790	1	51	spaces	space	NOUN
ejpam-5790	1	52	waqar	waqar	VERB
ejpam-5790	1	53	afzal1	afzal1	PROPN
ejpam-5790	1	54	,	,	PUNCT
ejpam-5790	1	55	mujahid	mujahid	PROPN
ejpam-5790	1	56	abbas2,3	abbas2,3	PROPN
ejpam-5790	1	57	,	,	PUNCT
ejpam-5790	1	58	jorge	jorge	PROPN
ejpam-5790	1	59	e.	e.	PROPN
ejpam-5790	1	60	maćıas	maćıas	PROPN
ejpam-5790	1	61	-	-	PUNCT
ejpam-5790	1	62	dı́az4,5,∗	dı́az4,5,∗	PROPN
ejpam-5790	1	63	,	,	PUNCT
ejpam-5790	1	64	mutum	mutum	PROPN
ejpam-5790	1	65	zico	zico	PROPN
ejpam-5790	1	66	meetei6	meetei6	PROPN
ejpam-5790	1	67	,	,	PUNCT
ejpam-5790	1	68	mehreen	mehreen	NOUN
ejpam-5790	1	69	s.	s.	PROPN
ejpam-5790	1	70	khan7	khan7	PROPN
ejpam-5790	1	71	,	,	PUNCT
ejpam-5790	1	72	armando	armando	PROPN
ejpam-5790	1	73	gallegos8	gallegos8	PROPN
ejpam-5790	1	74	1	1	NUM
ejpam-5790	1	75	abdus	abdus	NOUN
ejpam-5790	1	76	salam	salam	PROPN
ejpam-5790	1	77	school	school	PROPN
ejpam-5790	1	78	of	of	ADP
ejpam-5790	1	79	mathematical	mathematical	ADJ
ejpam-5790	1	80	sciences	science	NOUN
ejpam-5790	1	81	,	,	PUNCT
ejpam-5790	1	82	government	government	NOUN
ejpam-5790	1	83	college	college	NOUN
ejpam-5790	1	84	university	university	NOUN
ejpam-5790	1	85	,	,	PUNCT
ejpam-5790	1	86	68	68	NUM
ejpam-5790	1	87	-	-	SYM
ejpam-5790	1	88	b	b	NOUN
ejpam-5790	1	89	,	,	PUNCT
ejpam-5790	1	90	new	new	ADJ
ejpam-5790	1	91	muslim	muslim	ADJ
ejpam-5790	1	92	town	town	NOUN
ejpam-5790	1	93	,	,	PUNCT
ejpam-5790	1	94	lahore	lahore	PROPN
ejpam-5790	1	95	54600	54600	NUM
ejpam-5790	1	96	,	,	PUNCT
ejpam-5790	1	97	pakistan	pakistan	PROPN
ejpam-5790	1	98	2	2	NUM
ejpam-5790	1	99	department	department	NOUN
ejpam-5790	1	100	of	of	ADP
ejpam-5790	1	101	mechanical	mechanical	ADJ
ejpam-5790	1	102	engineering	engineering	NOUN
ejpam-5790	1	103	sciences	science	NOUN
ejpam-5790	1	104	,	,	PUNCT
ejpam-5790	1	105	faculty	faculty	NOUN
ejpam-5790	1	106	of	of	ADP
ejpam-5790	1	107	engineering	engineering	NOUN
ejpam-5790	1	108	and	and	CCONJ
ejpam-5790	1	109	the	the	DET
ejpam-5790	1	110	built	build	VERB
ejpam-5790	1	111	environment	environment	NOUN
ejpam-5790	1	112	,	,	PUNCT
ejpam-5790	1	113	doornfontein	doornfontein	ADJ
ejpam-5790	1	114	campus	campus	NOUN
ejpam-5790	1	115	,	,	PUNCT
ejpam-5790	1	116	university	university	PROPN
ejpam-5790	1	117	of	of	ADP
ejpam-5790	1	118	johannesburg	johannesburg	PROPN
ejpam-5790	1	119	,	,	PUNCT
ejpam-5790	1	120	south	south	PROPN
ejpam-5790	1	121	africa	africa	PROPN
ejpam-5790	1	122	3	3	NUM
ejpam-5790	1	123	department	department	PROPN
ejpam-5790	1	124	of	of	ADP
ejpam-5790	1	125	medical	medical	ADJ
ejpam-5790	1	126	research	research	NOUN
ejpam-5790	1	127	,	,	PUNCT
ejpam-5790	1	128	china	china	PROPN
ejpam-5790	1	129	medical	medical	PROPN
ejpam-5790	1	130	university	university	PROPN
ejpam-5790	1	131	,	,	PUNCT
ejpam-5790	1	132	taichung	taichung	PROPN
ejpam-5790	1	133	406040	406040	NUM
ejpam-5790	1	134	,	,	PUNCT
ejpam-5790	1	135	taiwan	taiwan	PROPN
ejpam-5790	1	136	4	4	NUM
ejpam-5790	1	137	department	department	NOUN
ejpam-5790	1	138	of	of	ADP
ejpam-5790	1	139	mathematics	mathematic	NOUN
ejpam-5790	1	140	and	and	CCONJ
ejpam-5790	1	141	didactics	didactics	NOUN
ejpam-5790	1	142	of	of	ADP
ejpam-5790	1	143	mathematics	mathematic	NOUN
ejpam-5790	1	144	,	,	PUNCT
ejpam-5790	1	145	tallinn	tallinn	PROPN
ejpam-5790	1	146	university	university	PROPN
ejpam-5790	1	147	,	,	PUNCT
ejpam-5790	1	148	tallinn	tallinn	PROPN
ejpam-5790	1	149	10120	10120	NUM
ejpam-5790	1	150	,	,	PUNCT
ejpam-5790	1	151	estonia	estonia	PROPN
ejpam-5790	1	152	5	5	NUM
ejpam-5790	1	153	department	department	NOUN
ejpam-5790	1	154	of	of	ADP
ejpam-5790	1	155	mathematics	mathematics	PROPN
ejpam-5790	1	156	and	and	CCONJ
ejpam-5790	1	157	physics	physics	PROPN
ejpam-5790	1	158	,	,	PUNCT
ejpam-5790	1	159	autonomous	autonomous	ADJ
ejpam-5790	1	160	university	university	NOUN
ejpam-5790	1	161	of	of	ADP
ejpam-5790	1	162	aguascalientes	aguascaliente	NOUN
ejpam-5790	1	163	,	,	PUNCT
ejpam-5790	1	164	aguascalientes	aguascaliente	NOUN
ejpam-5790	1	165	20100	20100	NUM
ejpam-5790	1	166	,	,	PUNCT
ejpam-5790	1	167	mexico	mexico	PROPN
ejpam-5790	1	168	6	6	NUM
ejpam-5790	1	169	department	department	NOUN
ejpam-5790	1	170	of	of	ADP
ejpam-5790	1	171	mathematics	mathematic	NOUN
ejpam-5790	1	172	,	,	PUNCT
ejpam-5790	1	173	college	college	NOUN
ejpam-5790	1	174	of	of	ADP
ejpam-5790	1	175	science	science	PROPN
ejpam-5790	1	176	,	,	PUNCT
ejpam-5790	1	177	jazan	jazan	PROPN
ejpam-5790	1	178	university	university	PROPN
ejpam-5790	1	179	,	,	PUNCT
ejpam-5790	1	180	p.o	p.o	PROPN
ejpam-5790	1	181	.	.	PROPN
ejpam-5790	1	182	box	box	PROPN
ejpam-5790	1	183	114	114	NUM
ejpam-5790	1	184	,	,	PUNCT
ejpam-5790	1	185	jazan	jazan	NOUN
ejpam-5790	1	186	45142	45142	NUM
ejpam-5790	1	187	,	,	PUNCT
ejpam-5790	1	188	saudi	saudi	PROPN
ejpam-5790	1	189	arabia	arabia	PROPN
ejpam-5790	1	190	7	7	NUM
ejpam-5790	1	191	department	department	NOUN
ejpam-5790	1	192	of	of	ADP
ejpam-5790	1	193	mathematics	mathematic	NOUN
ejpam-5790	1	194	,	,	PUNCT
ejpam-5790	1	195	faculty	faculty	NOUN
ejpam-5790	1	196	of	of	ADP
ejpam-5790	1	197	science	science	NOUN
ejpam-5790	1	198	,	,	PUNCT
ejpam-5790	1	199	jazan	jazan	PROPN
ejpam-5790	1	200	university	university	PROPN
ejpam-5790	1	201	,	,	PUNCT
ejpam-5790	1	202	jazan	jazan	NOUN
ejpam-5790	1	203	45142	45142	NUM
ejpam-5790	1	204	,	,	PUNCT
ejpam-5790	1	205	saudi	saudi	PROPN
ejpam-5790	1	206	arabia	arabia	PROPN
ejpam-5790	1	207	8	8	NUM
ejpam-5790	1	208	university	university	NOUN
ejpam-5790	1	209	center	center	NOUN
ejpam-5790	1	210	of	of	ADP
ejpam-5790	1	211	los	los	PROPN
ejpam-5790	1	212	lagos	lagos	PROPN
ejpam-5790	1	213	,	,	PUNCT
ejpam-5790	1	214	university	university	PROPN
ejpam-5790	1	215	of	of	ADP
ejpam-5790	1	216	guadalajara	guadalajara	PROPN
ejpam-5790	1	217	,	,	PUNCT
ejpam-5790	1	218	jalisco	jalisco	PROPN
ejpam-5790	1	219	47460	47460	NUM
ejpam-5790	1	220	,	,	PUNCT
ejpam-5790	1	221	mexico	mexico	PROPN
ejpam-5790	1	222	abstract	abstract	NOUN
ejpam-5790	1	223	.	.	PUNCT
ejpam-5790	2	1	this	this	DET
ejpam-5790	2	2	paper	paper	NOUN
ejpam-5790	2	3	investigates	investigate	VERB
ejpam-5790	2	4	novel	novel	ADJ
ejpam-5790	2	5	properties	property	NOUN
ejpam-5790	2	6	of	of	ADP
ejpam-5790	2	7	hilbert	hilbert	PROPN
ejpam-5790	2	8	spaces	space	NOUN
ejpam-5790	2	9	through	through	ADP
ejpam-5790	2	10	tensor	tensor	NOUN
ejpam-5790	2	11	operations	operation	NOUN
ejpam-5790	2	12	and	and	CCONJ
ejpam-5790	2	13	establishes	establish	VERB
ejpam-5790	2	14	new	new	ADJ
ejpam-5790	2	15	bounds	bound	NOUN
ejpam-5790	2	16	for	for	ADP
ejpam-5790	2	17	simpson	simpson	NOUN
ejpam-5790	2	18	-	-	PUNCT
ejpam-5790	2	19	type	type	NOUN
ejpam-5790	2	20	inequalities	inequality	NOUN
ejpam-5790	2	21	using	use	VERB
ejpam-5790	2	22	fractional	fractional	ADJ
ejpam-5790	2	23	integral	integral	ADJ
ejpam-5790	2	24	operators	operator	NOUN
ejpam-5790	2	25	.	.	PUNCT
ejpam-5790	3	1	the	the	DET
ejpam-5790	3	2	results	result	NOUN
ejpam-5790	3	3	contribute	contribute	VERB
ejpam-5790	3	4	to	to	ADP
ejpam-5790	3	5	advancing	advance	VERB
ejpam-5790	3	6	the	the	DET
ejpam-5790	3	7	theoretical	theoretical	ADJ
ejpam-5790	3	8	understanding	understanding	NOUN
ejpam-5790	3	9	of	of	ADP
ejpam-5790	3	10	these	these	DET
ejpam-5790	3	11	mathematical	mathematical	ADJ
ejpam-5790	3	12	structures	structure	NOUN
ejpam-5790	3	13	and	and	CCONJ
ejpam-5790	3	14	their	their	PRON
ejpam-5790	3	15	applications	application	NOUN
ejpam-5790	3	16	in	in	ADP
ejpam-5790	3	17	functional	functional	ADJ
ejpam-5790	3	18	analysis	analysis	NOUN
ejpam-5790	3	19	and	and	CCONJ
ejpam-5790	3	20	related	related	ADJ
ejpam-5790	3	21	fields	field	NOUN
ejpam-5790	3	22	.	.	PUNCT
ejpam-5790	4	1	2020	2020	NUM
ejpam-5790	4	2	mathematics	mathematic	NOUN
ejpam-5790	4	3	subject	subject	NOUN
ejpam-5790	4	4	classifications	classification	NOUN
ejpam-5790	4	5	:	:	PUNCT
ejpam-5790	4	6	11b73	11b73	NUM
ejpam-5790	4	7	,	,	PUNCT
ejpam-5790	4	8	11b83	11b83	NUM
ejpam-5790	4	9	key	key	ADJ
ejpam-5790	4	10	words	word	NOUN
ejpam-5790	4	11	and	and	CCONJ
ejpam-5790	4	12	phrases	phrase	NOUN
ejpam-5790	4	13	:	:	PUNCT
ejpam-5790	4	14	simpson	simpson	PROPN
ejpam-5790	4	15	,	,	PUNCT
ejpam-5790	4	16	hilbert	hilbert	PROPN
ejpam-5790	4	17	spaces	space	NOUN
ejpam-5790	4	18	,	,	PUNCT
ejpam-5790	4	19	generalized	generalize	VERB
ejpam-5790	4	20	convex	convex	ADJ
ejpam-5790	4	21	mappings	mapping	NOUN
ejpam-5790	4	22	1	1	NUM
ejpam-5790	4	23	.	.	PUNCT
ejpam-5790	4	24	introduction	introduction	NOUN
ejpam-5790	4	25	the	the	DET
ejpam-5790	4	26	concept	concept	NOUN
ejpam-5790	4	27	of	of	ADP
ejpam-5790	4	28	convexity	convexity	NOUN
ejpam-5790	4	29	is	be	AUX
ejpam-5790	4	30	integral	integral	ADJ
ejpam-5790	4	31	to	to	ADP
ejpam-5790	4	32	numerous	numerous	ADJ
ejpam-5790	4	33	disciplines	discipline	NOUN
ejpam-5790	4	34	within	within	ADP
ejpam-5790	4	35	mathematics	mathematic	NOUN
ejpam-5790	4	36	and	and	CCONJ
ejpam-5790	4	37	applied	applied	ADJ
ejpam-5790	4	38	sciences	science	NOUN
ejpam-5790	4	39	,	,	PUNCT
ejpam-5790	4	40	including	include	VERB
ejpam-5790	4	41	optimization	optimization	NOUN
ejpam-5790	4	42	,	,	PUNCT
ejpam-5790	4	43	machine	machine	NOUN
ejpam-5790	4	44	learning	learning	NOUN
ejpam-5790	4	45	,	,	PUNCT
ejpam-5790	4	46	and	and	CCONJ
ejpam-5790	4	47	energy	energy	NOUN
ejpam-5790	4	48	systems	system	NOUN
ejpam-5790	4	49	.	.	PUNCT
ejpam-5790	5	1	recent	recent	ADJ
ejpam-5790	5	2	advancements	advancement	NOUN
ejpam-5790	5	3	have	have	AUX
ejpam-5790	5	4	highlighted	highlight	VERB
ejpam-5790	5	5	the	the	DET
ejpam-5790	5	6	utility	utility	NOUN
ejpam-5790	5	7	of	of	ADP
ejpam-5790	5	8	convex	convex	NOUN
ejpam-5790	5	9	functions	function	NOUN
ejpam-5790	5	10	in	in	ADP
ejpam-5790	5	11	addressing	address	VERB
ejpam-5790	5	12	complex	complex	ADJ
ejpam-5790	5	13	realworld	realworld	PROPN
ejpam-5790	5	14	problems	problem	NOUN
ejpam-5790	5	15	.	.	PUNCT
ejpam-5790	6	1	for	for	ADP
ejpam-5790	6	2	instance	instance	NOUN
ejpam-5790	6	3	,	,	PUNCT
ejpam-5790	6	4	machine	machine	NOUN
ejpam-5790	6	5	learning	learn	VERB
ejpam-5790	6	6	techniques	technique	NOUN
ejpam-5790	6	7	leverage	leverage	NOUN
ejpam-5790	6	8	convexity	convexity	NOUN
ejpam-5790	6	9	for	for	ADP
ejpam-5790	6	10	improving	improve	VERB
ejpam-5790	6	11	market	market	NOUN
ejpam-5790	6	12	surveillance	surveillance	NOUN
ejpam-5790	6	13	and	and	CCONJ
ejpam-5790	6	14	customer	customer	NOUN
ejpam-5790	6	15	relationship	relationship	NOUN
ejpam-5790	6	16	management	management	NOUN
ejpam-5790	6	17	systems	system	NOUN
ejpam-5790	6	18	to	to	PART
ejpam-5790	6	19	estimate	estimate	VERB
ejpam-5790	6	20	∗corresponding	∗corresponde	VERB
ejpam-5790	6	21	author	author	NOUN
ejpam-5790	6	22	.	.	PUNCT
ejpam-5790	7	1	doi	doi	NOUN
ejpam-5790	7	2	:	:	PUNCT
ejpam-5790	7	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5790	https://doi.org/10.29020/nybg.ejpam.v18i1.5790	VERB
ejpam-5790	7	4	email	email	NOUN
ejpam-5790	7	5	address	address	NOUN
ejpam-5790	7	6	:	:	PUNCT
ejpam-5790	7	7	jemacias@correo.uaa.mx	jemacias@correo.uaa.mx	PROPN
ejpam-5790	7	8	(	(	PUNCT
ejpam-5790	7	9	j.	j.	PROPN
ejpam-5790	7	10	e.	e.	PROPN
ejpam-5790	7	11	maćıas	maćıas	PROPN
ejpam-5790	7	12	-	-	PUNCT
ejpam-5790	7	13	dı́az	dı́az	NOUN
ejpam-5790	7	14	)	)	PUNCT
ejpam-5790	7	15	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5790	8	1	1	1	NUM
ejpam-5790	8	2	copyright	copyright	NOUN
ejpam-5790	8	3	:	:	PUNCT
ejpam-5790	8	4	©	©	PROPN
ejpam-5790	8	5	2025	2025	NUM
ejpam-5790	8	6	the	the	DET
ejpam-5790	8	7	author(s	author(s	NOUN
ejpam-5790	8	8	)	)	PUNCT
ejpam-5790	8	9	.	.	PUNCT
ejpam-5790	9	1	(	(	PUNCT
ejpam-5790	9	2	cc	cc	NOUN
ejpam-5790	9	3	by	by	ADP
ejpam-5790	9	4	-	-	PUNCT
ejpam-5790	9	5	nc	nc	PROPN
ejpam-5790	9	6	4.0	4.0	NUM
ejpam-5790	9	7	)	)	PUNCT
ejpam-5790	9	8	w.	w.	PROPN
ejpam-5790	9	9	afzal	afzal	PROPN
ejpam-5790	9	10	et	et	PROPN
ejpam-5790	9	11	al	al	PROPN
ejpam-5790	9	12	.	.	PUNCT
ejpam-5790	9	13	/	/	SYM
ejpam-5790	9	14	eur	eur	PROPN
ejpam-5790	9	15	.	.	PUNCT
ejpam-5790	10	1	j.	j.	PROPN
ejpam-5790	10	2	pure	pure	PROPN
ejpam-5790	10	3	appl	appl	PROPN
ejpam-5790	10	4	.	.	PROPN
ejpam-5790	10	5	math	math	PROPN
ejpam-5790	10	6	,	,	PUNCT
ejpam-5790	10	7	18	18	NUM
ejpam-5790	10	8	(	(	PUNCT
ejpam-5790	10	9	1	1	NUM
ejpam-5790	10	10	)	)	PUNCT
ejpam-5790	10	11	(	(	PUNCT
ejpam-5790	10	12	2025	2025	NUM
ejpam-5790	10	13	)	)	PUNCT
ejpam-5790	10	14	,	,	PUNCT
ejpam-5790	10	15	5790	5790	NUM
ejpam-5790	10	16	2	2	NUM
ejpam-5790	10	17	of	of	ADP
ejpam-5790	10	18	30	30	NUM
ejpam-5790	10	19	error	error	NOUN
ejpam-5790	10	20	terms	term	NOUN
ejpam-5790	10	21	using	use	VERB
ejpam-5790	10	22	inequalities	inequality	NOUN
ejpam-5790	10	23	[	[	X
ejpam-5790	10	24	9	9	NUM
ejpam-5790	10	25	]	]	PUNCT
ejpam-5790	10	26	.	.	PUNCT
ejpam-5790	11	1	convexity	convexity	NOUN
ejpam-5790	11	2	principles	principle	NOUN
ejpam-5790	11	3	are	be	AUX
ejpam-5790	11	4	also	also	ADV
ejpam-5790	11	5	applied	apply	VERB
ejpam-5790	11	6	to	to	ADP
ejpam-5790	11	7	transportation	transportation	NOUN
ejpam-5790	11	8	systems	system	NOUN
ejpam-5790	11	9	,	,	PUNCT
ejpam-5790	11	10	such	such	ADJ
ejpam-5790	11	11	as	as	ADP
ejpam-5790	11	12	in	in	ADP
ejpam-5790	11	13	fatigue	fatigue	NOUN
ejpam-5790	11	14	detection	detection	NOUN
ejpam-5790	11	15	for	for	ADP
ejpam-5790	11	16	drivers	driver	NOUN
ejpam-5790	11	17	using	use	VERB
ejpam-5790	11	18	adaptive	adaptive	ADJ
ejpam-5790	11	19	fuzzy	fuzzy	ADJ
ejpam-5790	11	20	classifiers	classifier	NOUN
ejpam-5790	11	21	[	[	X
ejpam-5790	11	22	44	44	NUM
ejpam-5790	11	23	]	]	PUNCT
ejpam-5790	11	24	.	.	PUNCT
ejpam-5790	12	1	in	in	ADP
ejpam-5790	12	2	industrial	industrial	ADJ
ejpam-5790	12	3	optimization	optimization	NOUN
ejpam-5790	12	4	,	,	PUNCT
ejpam-5790	12	5	convexity	convexity	NOUN
ejpam-5790	12	6	plays	play	VERB
ejpam-5790	12	7	a	a	DET
ejpam-5790	12	8	critical	critical	ADJ
ejpam-5790	12	9	role	role	NOUN
ejpam-5790	12	10	in	in	ADP
ejpam-5790	12	11	designing	design	VERB
ejpam-5790	12	12	squeeze	squeeze	NOUN
ejpam-5790	12	13	casting	cast	VERB
ejpam-5790	12	14	parameters	parameter	NOUN
ejpam-5790	12	15	with	with	ADP
ejpam-5790	12	16	neural	neural	ADJ
ejpam-5790	12	17	networks	network	NOUN
ejpam-5790	12	18	[	[	X
ejpam-5790	12	19	43	43	NUM
ejpam-5790	12	20	]	]	PUNCT
ejpam-5790	12	21	.	.	PUNCT
ejpam-5790	13	1	moreover	moreover	ADV
ejpam-5790	13	2	,	,	PUNCT
ejpam-5790	13	3	it	it	PRON
ejpam-5790	13	4	contributes	contribute	VERB
ejpam-5790	13	5	to	to	ADP
ejpam-5790	13	6	the	the	DET
ejpam-5790	13	7	efficient	efficient	ADJ
ejpam-5790	13	8	design	design	NOUN
ejpam-5790	13	9	of	of	ADP
ejpam-5790	13	10	perovskite	perovskite	ADJ
ejpam-5790	13	11	solar	solar	ADJ
ejpam-5790	13	12	cells	cell	NOUN
ejpam-5790	13	13	by	by	ADP
ejpam-5790	13	14	enabling	enable	VERB
ejpam-5790	13	15	specific	specific	ADJ
ejpam-5790	13	16	material	material	NOUN
ejpam-5790	13	17	configurations	configuration	NOUN
ejpam-5790	13	18	[	[	X
ejpam-5790	13	19	42	42	NUM
ejpam-5790	13	20	]	]	PUNCT
ejpam-5790	13	21	.	.	PUNCT
ejpam-5790	14	1	in	in	ADP
ejpam-5790	14	2	the	the	DET
ejpam-5790	14	3	field	field	NOUN
ejpam-5790	14	4	of	of	ADP
ejpam-5790	14	5	control	control	NOUN
ejpam-5790	14	6	systems	system	NOUN
ejpam-5790	14	7	,	,	PUNCT
ejpam-5790	14	8	convex	convex	NOUN
ejpam-5790	14	9	optimization	optimization	NOUN
ejpam-5790	14	10	is	be	AUX
ejpam-5790	14	11	employed	employ	VERB
ejpam-5790	14	12	to	to	PART
ejpam-5790	14	13	achieve	achieve	VERB
ejpam-5790	14	14	robust	robust	ADJ
ejpam-5790	14	15	stability	stability	NOUN
ejpam-5790	14	16	designs	design	NOUN
ejpam-5790	14	17	for	for	ADP
ejpam-5790	14	18	inverters	inverter	NOUN
ejpam-5790	14	19	[	[	X
ejpam-5790	14	20	51	51	NUM
ejpam-5790	14	21	]	]	PUNCT
ejpam-5790	14	22	.	.	PUNCT
ejpam-5790	15	1	for	for	ADP
ejpam-5790	15	2	autonomous	autonomous	ADJ
ejpam-5790	15	3	systems	system	NOUN
ejpam-5790	15	4	,	,	PUNCT
ejpam-5790	15	5	convexity	convexity	NOUN
ejpam-5790	15	6	-	-	PUNCT
ejpam-5790	15	7	based	base	VERB
ejpam-5790	15	8	methods	method	NOUN
ejpam-5790	15	9	improve	improve	VERB
ejpam-5790	15	10	docking	dock	VERB
ejpam-5790	15	11	control	control	NOUN
ejpam-5790	15	12	for	for	ADP
ejpam-5790	15	13	underwater	underwater	ADJ
ejpam-5790	15	14	vehicles	vehicle	NOUN
ejpam-5790	15	15	through	through	ADP
ejpam-5790	15	16	adaptive	adaptive	ADJ
ejpam-5790	15	17	reinforcement	reinforcement	NOUN
ejpam-5790	15	18	learning	learning	NOUN
ejpam-5790	16	1	[	[	X
ejpam-5790	16	2	64	64	NUM
ejpam-5790	16	3	]	]	PUNCT
ejpam-5790	16	4	.	.	PUNCT
ejpam-5790	17	1	lastly	lastly	ADV
ejpam-5790	17	2	,	,	PUNCT
ejpam-5790	17	3	convex	convex	NOUN
ejpam-5790	17	4	functions	function	NOUN
ejpam-5790	17	5	have	have	AUX
ejpam-5790	17	6	enabled	enable	VERB
ejpam-5790	17	7	advancements	advancement	NOUN
ejpam-5790	17	8	in	in	ADP
ejpam-5790	17	9	biotechnology	biotechnology	NOUN
ejpam-5790	17	10	,	,	PUNCT
ejpam-5790	17	11	such	such	ADJ
ejpam-5790	17	12	as	as	ADP
ejpam-5790	17	13	efficient	efficient	ADJ
ejpam-5790	17	14	co	co	NOUN
ejpam-5790	17	15	-	-	NOUN
ejpam-5790	17	16	production	production	NOUN
ejpam-5790	17	17	of	of	ADP
ejpam-5790	17	18	hydrogen	hydrogen	NOUN
ejpam-5790	17	19	and	and	CCONJ
ejpam-5790	17	20	methane	methane	NOUN
ejpam-5790	17	21	through	through	ADP
ejpam-5790	17	22	microbial	microbial	ADJ
ejpam-5790	17	23	regulation	regulation	NOUN
ejpam-5790	17	24	[	[	X
ejpam-5790	17	25	63	63	NUM
ejpam-5790	17	26	]	]	PUNCT
ejpam-5790	17	27	.	.	PUNCT
ejpam-5790	18	1	these	these	DET
ejpam-5790	18	2	applications	application	NOUN
ejpam-5790	18	3	demonstrate	demonstrate	VERB
ejpam-5790	18	4	the	the	DET
ejpam-5790	18	5	extensive	extensive	ADJ
ejpam-5790	18	6	and	and	CCONJ
ejpam-5790	18	7	varied	varied	ADJ
ejpam-5790	18	8	impact	impact	NOUN
ejpam-5790	18	9	of	of	ADP
ejpam-5790	18	10	convexity	convexity	NOUN
ejpam-5790	18	11	across	across	ADP
ejpam-5790	18	12	multiple	multiple	ADJ
ejpam-5790	18	13	domains	domain	NOUN
ejpam-5790	18	14	[	[	X
ejpam-5790	18	15	33	33	NUM
ejpam-5790	18	16	,	,	PUNCT
ejpam-5790	18	17	60	60	NUM
ejpam-5790	18	18	,	,	PUNCT
ejpam-5790	18	19	65	65	NUM
ejpam-5790	18	20	]	]	PUNCT
ejpam-5790	18	21	.	.	PUNCT
ejpam-5790	19	1	recent	recent	ADJ
ejpam-5790	19	2	years	year	NOUN
ejpam-5790	19	3	have	have	AUX
ejpam-5790	19	4	witnessed	witness	VERB
ejpam-5790	19	5	remarkable	remarkable	ADJ
ejpam-5790	19	6	progress	progress	NOUN
ejpam-5790	19	7	in	in	ADP
ejpam-5790	19	8	fractional	fractional	ADJ
ejpam-5790	19	9	calculus	calculus	NOUN
ejpam-5790	19	10	,	,	PUNCT
ejpam-5790	19	11	influencing	influence	VERB
ejpam-5790	19	12	diverse	diverse	ADJ
ejpam-5790	19	13	domains	domain	NOUN
ejpam-5790	19	14	of	of	ADP
ejpam-5790	19	15	mathematics	mathematic	NOUN
ejpam-5790	19	16	and	and	CCONJ
ejpam-5790	19	17	applied	apply	VERB
ejpam-5790	19	18	sciences	science	NOUN
ejpam-5790	19	19	[	[	X
ejpam-5790	19	20	26	26	NUM
ejpam-5790	19	21	,	,	PUNCT
ejpam-5790	19	22	29	29	NUM
ejpam-5790	19	23	,	,	PUNCT
ejpam-5790	19	24	35	35	NUM
ejpam-5790	19	25	,	,	PUNCT
ejpam-5790	19	26	52	52	NUM
ejpam-5790	19	27	]	]	PUNCT
ejpam-5790	19	28	.	.	PUNCT
ejpam-5790	20	1	the	the	DET
ejpam-5790	20	2	development	development	NOUN
ejpam-5790	20	3	of	of	ADP
ejpam-5790	20	4	novel	novel	ADJ
ejpam-5790	20	5	definitions	definition	NOUN
ejpam-5790	20	6	for	for	ADP
ejpam-5790	20	7	fractional	fractional	ADJ
ejpam-5790	20	8	integrals	integral	NOUN
ejpam-5790	20	9	and	and	CCONJ
ejpam-5790	20	10	derivatives	derivative	NOUN
ejpam-5790	20	11	,	,	PUNCT
ejpam-5790	20	12	extending	extend	VERB
ejpam-5790	20	13	classical	classical	ADJ
ejpam-5790	20	14	approaches	approach	NOUN
ejpam-5790	20	15	,	,	PUNCT
ejpam-5790	20	16	has	have	AUX
ejpam-5790	20	17	attracted	attract	VERB
ejpam-5790	20	18	significant	significant	ADJ
ejpam-5790	20	19	research	research	NOUN
ejpam-5790	20	20	interest	interest	NOUN
ejpam-5790	20	21	.	.	PUNCT
ejpam-5790	21	1	these	these	DET
ejpam-5790	21	2	new	new	ADJ
ejpam-5790	21	3	definitions	definition	NOUN
ejpam-5790	21	4	have	have	AUX
ejpam-5790	21	5	become	become	VERB
ejpam-5790	21	6	a	a	DET
ejpam-5790	21	7	central	central	ADJ
ejpam-5790	21	8	focus	focus	NOUN
ejpam-5790	21	9	in	in	ADP
ejpam-5790	21	10	mathematical	mathematical	ADJ
ejpam-5790	21	11	analysis	analysis	NOUN
ejpam-5790	21	12	,	,	PUNCT
ejpam-5790	21	13	paving	pave	VERB
ejpam-5790	21	14	the	the	DET
ejpam-5790	21	15	way	way	NOUN
ejpam-5790	21	16	for	for	ADP
ejpam-5790	21	17	innovative	innovative	ADJ
ejpam-5790	21	18	methodologies	methodology	NOUN
ejpam-5790	21	19	.	.	PUNCT
ejpam-5790	22	1	the	the	DET
ejpam-5790	22	2	adaptability	adaptability	NOUN
ejpam-5790	22	3	of	of	ADP
ejpam-5790	22	4	fractional	fractional	ADJ
ejpam-5790	22	5	calculus	calculus	NOUN
ejpam-5790	22	6	[	[	X
ejpam-5790	22	7	23	23	NUM
ejpam-5790	22	8	,	,	PUNCT
ejpam-5790	22	9	24	24	NUM
ejpam-5790	22	10	,	,	PUNCT
ejpam-5790	22	11	61	61	NUM
ejpam-5790	22	12	]	]	PUNCT
ejpam-5790	22	13	has	have	AUX
ejpam-5790	22	14	enabled	enable	VERB
ejpam-5790	22	15	researchers	researcher	NOUN
ejpam-5790	22	16	to	to	PART
ejpam-5790	22	17	establish	establish	VERB
ejpam-5790	22	18	convex	convex	ADJ
ejpam-5790	22	19	integral	integral	ADJ
ejpam-5790	22	20	inequalities	inequality	NOUN
ejpam-5790	22	21	,	,	PUNCT
ejpam-5790	22	22	which	which	PRON
ejpam-5790	22	23	play	play	VERB
ejpam-5790	22	24	a	a	DET
ejpam-5790	22	25	crucial	crucial	ADJ
ejpam-5790	22	26	role	role	NOUN
ejpam-5790	22	27	in	in	ADP
ejpam-5790	22	28	approximation	approximation	NOUN
ejpam-5790	22	29	theory	theory	NOUN
ejpam-5790	22	30	.	.	PUNCT
ejpam-5790	23	1	inequalities	inequality	NOUN
ejpam-5790	23	2	such	such	ADJ
ejpam-5790	23	3	as	as	ADP
ejpam-5790	23	4	jensen	jensen	PROPN
ejpam-5790	23	5	’s	’s	PART
ejpam-5790	23	6	[	[	X
ejpam-5790	23	7	49	49	NUM
ejpam-5790	23	8	]	]	PUNCT
ejpam-5790	23	9	,	,	PUNCT
ejpam-5790	23	10	simpson	simpson	PROPN
ejpam-5790	23	11	’s	’s	PART
ejpam-5790	24	1	[	[	X
ejpam-5790	24	2	37	37	NUM
ejpam-5790	24	3	]	]	PUNCT
ejpam-5790	24	4	,	,	PUNCT
ejpam-5790	24	5	ostrowski	ostrowski	PROPN
ejpam-5790	24	6	’s	’s	PART
ejpam-5790	24	7	[	[	X
ejpam-5790	24	8	8	8	NUM
ejpam-5790	24	9	]	]	PUNCT
ejpam-5790	24	10	,	,	PUNCT
ejpam-5790	24	11	hermite	hermite	ADJ
ejpam-5790	24	12	–	–	PUNCT
ejpam-5790	24	13	hadamard	hadamard	NOUN
ejpam-5790	24	14	’s	’s	PART
ejpam-5790	25	1	[	[	X
ejpam-5790	25	2	48	48	NUM
ejpam-5790	25	3	]	]	PUNCT
ejpam-5790	25	4	,	,	PUNCT
ejpam-5790	25	5	and	and	CCONJ
ejpam-5790	25	6	trapezoidal	trapezoidal	ADJ
ejpam-5790	25	7	[	[	X
ejpam-5790	25	8	1	1	NUM
ejpam-5790	25	9	]	]	X
ejpam-5790	25	10	inequalities	inequality	NOUN
ejpam-5790	25	11	are	be	AUX
ejpam-5790	25	12	frequently	frequently	ADV
ejpam-5790	25	13	employed	employ	VERB
ejpam-5790	25	14	to	to	PART
ejpam-5790	25	15	derive	derive	VERB
ejpam-5790	25	16	error	error	NOUN
ejpam-5790	25	17	bounds	bound	NOUN
ejpam-5790	25	18	for	for	ADP
ejpam-5790	25	19	numerical	numerical	ADJ
ejpam-5790	25	20	integration	integration	NOUN
ejpam-5790	25	21	methods	method	NOUN
ejpam-5790	25	22	.	.	PUNCT
ejpam-5790	26	1	to	to	PART
ejpam-5790	26	2	construct	construct	VERB
ejpam-5790	26	3	such	such	ADJ
ejpam-5790	26	4	inequalities	inequality	NOUN
ejpam-5790	26	5	,	,	PUNCT
ejpam-5790	26	6	researchers	researcher	NOUN
ejpam-5790	26	7	utilize	utilize	VERB
ejpam-5790	26	8	different	different	ADJ
ejpam-5790	26	9	ways	way	NOUN
ejpam-5790	26	10	,	,	PUNCT
ejpam-5790	26	11	including	include	VERB
ejpam-5790	26	12	maps	map	NOUN
ejpam-5790	26	13	,	,	PUNCT
ejpam-5790	26	14	operators	operator	NOUN
ejpam-5790	26	15	,	,	PUNCT
ejpam-5790	26	16	relations	relation	NOUN
ejpam-5790	26	17	,	,	PUNCT
ejpam-5790	26	18	and	and	CCONJ
ejpam-5790	26	19	other	other	ADJ
ejpam-5790	26	20	analytical	analytical	ADJ
ejpam-5790	26	21	techniques	technique	NOUN
ejpam-5790	26	22	,	,	PUNCT
ejpam-5790	26	23	demonstrating	demonstrate	VERB
ejpam-5790	26	24	the	the	DET
ejpam-5790	26	25	profound	profound	ADJ
ejpam-5790	26	26	impact	impact	NOUN
ejpam-5790	26	27	of	of	ADP
ejpam-5790	26	28	fractional	fractional	ADJ
ejpam-5790	26	29	calculus	calculus	NOUN
ejpam-5790	26	30	in	in	ADP
ejpam-5790	26	31	modern	modern	ADJ
ejpam-5790	26	32	mathematical	mathematical	ADJ
ejpam-5790	26	33	analysis	analysis	NOUN
ejpam-5790	26	34	.	.	PUNCT
ejpam-5790	27	1	for	for	ADP
ejpam-5790	27	2	instance	instance	NOUN
ejpam-5790	27	3	,	,	PUNCT
ejpam-5790	27	4	in	in	ADP
ejpam-5790	27	5	[	[	PUNCT
ejpam-5790	27	6	5	5	NUM
ejpam-5790	27	7	]	]	PUNCT
ejpam-5790	27	8	,	,	PUNCT
ejpam-5790	27	9	the	the	DET
ejpam-5790	27	10	creators	creator	NOUN
ejpam-5790	27	11	used	use	VERB
ejpam-5790	27	12	symmetric	symmetric	ADJ
ejpam-5790	27	13	curved	curve	VERB
ejpam-5790	27	14	composed	compose	VERB
ejpam-5790	27	15	capabilities	capability	NOUN
ejpam-5790	27	16	to	to	PART
ejpam-5790	27	17	foster	foster	VERB
ejpam-5790	27	18	hermite	hermite	PROPN
ejpam-5790	27	19	-	-	PUNCT
ejpam-5790	27	20	hadamard	hadamard	ADJ
ejpam-5790	27	21	imbalances	imbalance	NOUN
ejpam-5790	27	22	.	.	PUNCT
ejpam-5790	28	1	in	in	ADP
ejpam-5790	28	2	[	[	X
ejpam-5790	28	3	55	55	NUM
ejpam-5790	28	4	]	]	PUNCT
ejpam-5790	28	5	,	,	PUNCT
ejpam-5790	28	6	partial	partial	ADJ
ejpam-5790	28	7	riemann	riemann	PROPN
ejpam-5790	28	8	-	-	PUNCT
ejpam-5790	28	9	liouville	liouville	NOUN
ejpam-5790	28	10	integrals	integral	NOUN
ejpam-5790	28	11	were	be	AUX
ejpam-5790	28	12	utilized	utilize	VERB
ejpam-5790	28	13	to	to	PART
ejpam-5790	28	14	determine	determine	VERB
ejpam-5790	28	15	newton	newton	PROPN
ejpam-5790	28	16	-	-	PUNCT
ejpam-5790	28	17	type	type	NOUN
ejpam-5790	28	18	disparities	disparity	NOUN
ejpam-5790	28	19	for	for	ADP
ejpam-5790	28	20	summed	sum	VERB
ejpam-5790	28	21	up	up	ADP
ejpam-5790	28	22	arched	arched	ADJ
ejpam-5790	28	23	capabilities	capability	NOUN
ejpam-5790	28	24	.	.	PUNCT
ejpam-5790	29	1	the	the	DET
ejpam-5790	29	2	work	work	NOUN
ejpam-5790	29	3	in	in	ADP
ejpam-5790	29	4	[	[	X
ejpam-5790	29	5	53	53	NUM
ejpam-5790	29	6	]	]	PUNCT
ejpam-5790	29	7	introduced	introduce	VERB
ejpam-5790	29	8	simpson	simpson	PROPN
ejpam-5790	29	9	-	-	PUNCT
ejpam-5790	29	10	type	type	NOUN
ejpam-5790	29	11	results	result	NOUN
ejpam-5790	29	12	utilizing	utilize	VERB
ejpam-5790	29	13	different	different	ADJ
ejpam-5790	29	14	classes	class	NOUN
ejpam-5790	29	15	of	of	ADP
ejpam-5790	29	16	convexities	convexity	NOUN
ejpam-5790	29	17	,	,	PUNCT
ejpam-5790	29	18	while	while	SCONJ
ejpam-5790	29	19	[	[	X
ejpam-5790	29	20	66	66	NUM
ejpam-5790	29	21	]	]	PUNCT
ejpam-5790	29	22	presented	present	VERB
ejpam-5790	29	23	bullen	bullen	PROPN
ejpam-5790	29	24	-	-	PUNCT
ejpam-5790	29	25	type	type	NOUN
ejpam-5790	29	26	results	result	NOUN
ejpam-5790	29	27	utilizing	utilize	VERB
ejpam-5790	29	28	various	various	ADJ
ejpam-5790	29	29	novel	novel	ADJ
ejpam-5790	29	30	convex	convex	NOUN
ejpam-5790	29	31	mappings	mapping	NOUN
ejpam-5790	29	32	.	.	PUNCT
ejpam-5790	30	1	the	the	DET
ejpam-5790	30	2	authors	author	NOUN
ejpam-5790	30	3	of	of	ADP
ejpam-5790	30	4	[	[	X
ejpam-5790	30	5	19	19	NUM
ejpam-5790	30	6	]	]	PUNCT
ejpam-5790	30	7	upgraded	upgrade	VERB
ejpam-5790	30	8	young	young	ADJ
ejpam-5790	30	9	’s	’s	PART
ejpam-5790	30	10	disparity	disparity	NOUN
ejpam-5790	30	11	by	by	ADP
ejpam-5790	30	12	giving	give	VERB
ejpam-5790	30	13	interesting	interesting	ADJ
ejpam-5790	30	14	limits	limit	NOUN
ejpam-5790	30	15	and	and	CCONJ
ejpam-5790	30	16	applications	application	NOUN
ejpam-5790	30	17	,	,	PUNCT
ejpam-5790	30	18	while	while	SCONJ
ejpam-5790	30	19	[	[	X
ejpam-5790	30	20	30	30	NUM
ejpam-5790	30	21	]	]	PUNCT
ejpam-5790	30	22	broadened	broaden	VERB
ejpam-5790	30	23	hölder	hölder	PROPN
ejpam-5790	30	24	’s	’s	PART
ejpam-5790	30	25	type	type	NOUN
ejpam-5790	30	26	result	result	NOUN
ejpam-5790	30	27	by	by	ADP
ejpam-5790	30	28	addressing	address	VERB
ejpam-5790	30	29	defer	defer	NOUN
ejpam-5790	30	30	differential	differential	NOUN
ejpam-5790	30	31	conditions	condition	NOUN
ejpam-5790	30	32	through	through	ADP
ejpam-5790	30	33	mean	mean	NOUN
ejpam-5790	30	34	congruity	congruity	NOUN
ejpam-5790	30	35	and	and	CCONJ
ejpam-5790	30	36	demonstrating	demonstrate	VERB
ejpam-5790	30	37	their	their	PRON
ejpam-5790	30	38	uniqueness	uniqueness	NOUN
ejpam-5790	30	39	.	.	PUNCT
ejpam-5790	31	1	moreover	moreover	ADV
ejpam-5790	31	2	,	,	PUNCT
ejpam-5790	31	3	in	in	ADP
ejpam-5790	31	4	[	[	PUNCT
ejpam-5790	31	5	16	16	NUM
ejpam-5790	31	6	]	]	PUNCT
ejpam-5790	31	7	,	,	PUNCT
ejpam-5790	31	8	ostrowski	ostrowski	ADJ
ejpam-5790	31	9	-	-	PUNCT
ejpam-5790	31	10	type	type	NOUN
ejpam-5790	31	11	imbalances	imbalance	NOUN
ejpam-5790	31	12	were	be	AUX
ejpam-5790	31	13	created	create	VERB
ejpam-5790	31	14	utilizing	utilize	VERB
ejpam-5790	31	15	differentiable	differentiable	ADJ
ejpam-5790	31	16	s	s	ADJ
ejpam-5790	31	17	-	-	ADJ
ejpam-5790	31	18	arched	arched	ADJ
ejpam-5790	31	19	mappings	mapping	NOUN
ejpam-5790	31	20	,	,	PUNCT
ejpam-5790	31	21	and	and	CCONJ
ejpam-5790	31	22	[	[	X
ejpam-5790	31	23	54	54	NUM
ejpam-5790	31	24	]	]	PUNCT
ejpam-5790	31	25	presented	present	VERB
ejpam-5790	31	26	trapezoidal	trapezoidal	ADJ
ejpam-5790	31	27	-	-	PUNCT
ejpam-5790	31	28	type	type	NOUN
ejpam-5790	31	29	disparities	disparity	NOUN
ejpam-5790	31	30	utilizing	utilize	VERB
ejpam-5790	31	31	quantum	quantum	NOUN
ejpam-5790	31	32	integrals	integral	NOUN
ejpam-5790	31	33	.	.	PUNCT
ejpam-5790	32	1	simpson	simpson	PROPN
ejpam-5790	32	2	’s	’s	PART
ejpam-5790	32	3	disparity	disparity	NOUN
ejpam-5790	32	4	is	be	AUX
ejpam-5790	32	5	pivotal	pivotal	ADJ
ejpam-5790	32	6	as	as	SCONJ
ejpam-5790	32	7	it	it	PRON
ejpam-5790	32	8	not	not	PART
ejpam-5790	32	9	just	just	ADV
ejpam-5790	32	10	lays	lay	VERB
ejpam-5790	32	11	out	out	ADP
ejpam-5790	32	12	a	a	DET
ejpam-5790	32	13	hypothetical	hypothetical	ADJ
ejpam-5790	32	14	reason	reason	NOUN
ejpam-5790	32	15	for	for	ADP
ejpam-5790	32	16	surveying	survey	VERB
ejpam-5790	32	17	the	the	DET
ejpam-5790	32	18	accuracy	accuracy	NOUN
ejpam-5790	32	19	of	of	ADP
ejpam-5790	32	20	mathematical	mathematical	ADJ
ejpam-5790	32	21	combination	combination	NOUN
ejpam-5790	32	22	procedures	procedure	NOUN
ejpam-5790	32	23	yet	yet	ADV
ejpam-5790	32	24	in	in	ADP
ejpam-5790	32	25	addition	addition	NOUN
ejpam-5790	32	26	helps	help	VERB
ejpam-5790	32	27	scientists	scientist	NOUN
ejpam-5790	32	28	in	in	ADP
ejpam-5790	32	29	choosing	choose	VERB
ejpam-5790	32	30	ideal	ideal	ADJ
ejpam-5790	32	31	techniques	technique	NOUN
ejpam-5790	32	32	in	in	ADP
ejpam-5790	32	33	view	view	NOUN
ejpam-5790	32	34	of	of	ADP
ejpam-5790	32	35	the	the	DET
ejpam-5790	32	36	particular	particular	ADJ
ejpam-5790	32	37	properties	property	NOUN
ejpam-5790	32	38	of	of	ADP
ejpam-5790	32	39	the	the	DET
ejpam-5790	32	40	capabilities	capability	NOUN
ejpam-5790	32	41	being	be	AUX
ejpam-5790	32	42	scrutinized	scrutinize	VERB
ejpam-5790	32	43	,	,	PUNCT
ejpam-5790	32	44	especially	especially	ADV
ejpam-5790	32	45	in	in	ADP
ejpam-5790	32	46	the	the	DET
ejpam-5790	32	47	domains	domain	NOUN
ejpam-5790	32	48	of	of	ADP
ejpam-5790	32	49	quadrature	quadrature	NOUN
ejpam-5790	32	50	mistake	mistake	NOUN
ejpam-5790	32	51	assessment	assessment	NOUN
ejpam-5790	32	52	and	and	CCONJ
ejpam-5790	32	53	complex	complex	ADJ
ejpam-5790	32	54	distinct	distinct	ADJ
ejpam-5790	32	55	integrals	integral	NOUN
ejpam-5790	32	56	.	.	PUNCT
ejpam-5790	33	1	beginning	begin	VERB
ejpam-5790	33	2	from	from	ADP
ejpam-5790	33	3	crafted	craft	VERB
ejpam-5790	33	4	by	by	ADP
ejpam-5790	33	5	eighteenth	eighteenth	ADJ
ejpam-5790	33	6	century	century	NOUN
ejpam-5790	33	7	mathematician	mathematician	NOUN
ejpam-5790	33	8	thomas	thomas	PROPN
ejpam-5790	33	9	simpson	simpson	PROPN
ejpam-5790	33	10	,	,	PUNCT
ejpam-5790	33	11	simpson	simpson	PROPN
ejpam-5790	33	12	’s	’s	PROPN
ejpam-5790	33	13	standard	standard	PROPN
ejpam-5790	33	14	supports	support	VERB
ejpam-5790	33	15	this	this	DET
ejpam-5790	33	16	disparity	disparity	NOUN
ejpam-5790	33	17	.	.	PUNCT
ejpam-5790	34	1	the	the	DET
ejpam-5790	34	2	standard	standard	PROPN
ejpam-5790	34	3	approximates	approximate	VERB
ejpam-5790	34	4	a	a	DET
ejpam-5790	34	5	capability	capability	NOUN
ejpam-5790	34	6	utilizing	utilize	VERB
ejpam-5790	34	7	a	a	DET
ejpam-5790	34	8	quadratic	quadratic	ADJ
ejpam-5790	34	9	polynomial	polynomial	NOUN
ejpam-5790	34	10	,	,	PUNCT
ejpam-5790	34	11	giving	give	VERB
ejpam-5790	34	12	a	a	DET
ejpam-5790	34	13	viable	viable	ADJ
ejpam-5790	34	14	means	mean	NOUN
ejpam-5790	34	15	to	to	PART
ejpam-5790	34	16	gauge	gauge	VERB
ejpam-5790	34	17	its	its	PRON
ejpam-5790	34	18	vital	vital	NOUN
ejpam-5790	34	19	.	.	PUNCT
ejpam-5790	35	1	in	in	ADP
ejpam-5790	35	2	particular	particular	ADJ
ejpam-5790	35	3	,	,	PUNCT
ejpam-5790	35	4	for	for	ADP
ejpam-5790	35	5	a	a	DET
ejpam-5790	35	6	capability	capability	NOUN
ejpam-5790	35	7	ℑ	ℑ	NOUN
ejpam-5790	35	8	that	that	PRON
ejpam-5790	35	9	is	be	AUX
ejpam-5790	35	10	ceaseless	ceaseless	ADJ
ejpam-5790	35	11	more	more	ADJ
ejpam-5790	35	12	than	than	ADP
ejpam-5790	35	13	the	the	DET
ejpam-5790	35	14	span	span	NOUN
ejpam-5790	35	15	[	[	X
ejpam-5790	35	16	ν1	ν1	NOUN
ejpam-5790	35	17	,	,	PUNCT
ejpam-5790	35	18	ν2	ν2	NOUN
ejpam-5790	35	19	]	]	PUNCT
ejpam-5790	35	20	,	,	PUNCT
ejpam-5790	35	21	simpson	simpson	PROPN
ejpam-5790	35	22	’s	’s	PART
ejpam-5790	35	23	3	3	NUM
ejpam-5790	35	24	8	8	NUM
ejpam-5790	35	25	rule	rule	NOUN
ejpam-5790	35	26	approximates	approximate	VERB
ejpam-5790	35	27	the	the	DET
ejpam-5790	35	28	basic	basic	ADJ
ejpam-5790	35	29	as	as	ADP
ejpam-5790	35	30	observes	observe	NOUN
ejpam-5790	35	31	:	:	PUNCT
ejpam-5790	35	32	w.	w.	PROPN
ejpam-5790	35	33	afzal	afzal	PROPN
ejpam-5790	35	34	et	et	PROPN
ejpam-5790	35	35	al	al	PROPN
ejpam-5790	35	36	.	.	PUNCT
ejpam-5790	35	37	/	/	SYM
ejpam-5790	35	38	eur	eur	PROPN
ejpam-5790	35	39	.	.	PUNCT
ejpam-5790	36	1	j.	j.	PROPN
ejpam-5790	36	2	pure	pure	PROPN
ejpam-5790	36	3	appl	appl	PROPN
ejpam-5790	36	4	.	.	PROPN
ejpam-5790	36	5	math	math	PROPN
ejpam-5790	36	6	,	,	PUNCT
ejpam-5790	36	7	18	18	NUM
ejpam-5790	36	8	(	(	PUNCT
ejpam-5790	36	9	1	1	NUM
ejpam-5790	36	10	)	)	PUNCT
ejpam-5790	36	11	(	(	PUNCT
ejpam-5790	36	12	2025	2025	NUM
ejpam-5790	36	13	)	)	PUNCT
ejpam-5790	36	14	,	,	PUNCT
ejpam-5790	36	15	5790	5790	NUM
ejpam-5790	36	16	3	3	NUM
ejpam-5790	36	17	of	of	ADP
ejpam-5790	36	18	30	30	NUM
ejpam-5790	36	19	∫	∫	NOUN
ejpam-5790	36	20	ν2	ν2	PROPN
ejpam-5790	36	21	ν1	ν1	NOUN
ejpam-5790	36	22	ℑ(w)dw	ℑ(w)dw	PROPN
ejpam-5790	36	23	≈	≈	PROPN
ejpam-5790	36	24	ν2	ν2	NOUN
ejpam-5790	36	25	−	−	PROPN
ejpam-5790	36	26	ν1	ν1	NOUN
ejpam-5790	36	27	8	8	NUM
ejpam-5790	36	28	[	[	PUNCT
ejpam-5790	36	29	ℑ(ν1	ℑ(ν1	NOUN
ejpam-5790	36	30	)	)	PUNCT
ejpam-5790	36	31	+	+	NUM
ejpam-5790	36	32	3ℑ	3ℑ	NOUN
ejpam-5790	36	33	(	(	PUNCT
ejpam-5790	36	34	2ν1	2ν1	NUM
ejpam-5790	36	35	+	+	CCONJ
ejpam-5790	36	36	ν2	ν2	NOUN
ejpam-5790	36	37	3	3	NUM
ejpam-5790	36	38	)	)	PUNCT
ejpam-5790	37	1	+	+	CCONJ
ejpam-5790	37	2	3ℑ	3ℑ	NOUN
ejpam-5790	37	3	(	(	PUNCT
ejpam-5790	37	4	ν1	ν1	NOUN
ejpam-5790	37	5	+	+	CCONJ
ejpam-5790	37	6	2ν2	2ν2	NUM
ejpam-5790	37	7	3	3	NUM
ejpam-5790	37	8	)	)	PUNCT
ejpam-5790	37	9	+	+	CCONJ
ejpam-5790	37	10	ℑ(ν2	ℑ(ν2	PROPN
ejpam-5790	37	11	)	)	PUNCT
ejpam-5790	37	12	]	]	PUNCT
ejpam-5790	37	13	.	.	PUNCT
ejpam-5790	38	1	the	the	DET
ejpam-5790	38	2	most	most	ADV
ejpam-5790	38	3	frequently	frequently	ADV
ejpam-5790	38	4	utilized	utilize	VERB
ejpam-5790	38	5	simpson	simpson	NOUN
ejpam-5790	38	6	-	-	PUNCT
ejpam-5790	38	7	type	type	NOUN
ejpam-5790	38	8	disparity	disparity	NOUN
ejpam-5790	38	9	has	have	VERB
ejpam-5790	38	10	the	the	DET
ejpam-5790	38	11	accompanying	accompanying	ADJ
ejpam-5790	38	12	definition	definition	NOUN
ejpam-5790	38	13	.	.	PUNCT
ejpam-5790	39	1	theorem	theorem	NOUN
ejpam-5790	39	2	1	1	NUM
ejpam-5790	39	3	(	(	PUNCT
ejpam-5790	39	4	see	see	VERB
ejpam-5790	39	5	[	[	X
ejpam-5790	39	6	36	36	NUM
ejpam-5790	39	7	]	]	NUM
ejpam-5790	39	8	)	)	PUNCT
ejpam-5790	39	9	.	.	PUNCT
ejpam-5790	40	1	assume	assume	VERB
ejpam-5790	40	2	ℑ	ℑ	NOUN
ejpam-5790	40	3	:	:	PUNCT
ejpam-5790	41	1	[	[	X
ejpam-5790	41	2	ν1	ν1	NOUN
ejpam-5790	41	3	,	,	PUNCT
ejpam-5790	41	4	ν2	ν2	NOUN
ejpam-5790	41	5	]	]	PUNCT
ejpam-5790	41	6	→	→	SYM
ejpam-5790	41	7	r	r	NOUN
ejpam-5790	41	8	be	be	AUX
ejpam-5790	41	9	a	a	DET
ejpam-5790	41	10	real	real	ADV
ejpam-5790	41	11	-	-	PUNCT
ejpam-5790	41	12	valued	value	VERB
ejpam-5790	41	13	convex	convex	NOUN
ejpam-5790	41	14	map	map	NOUN
ejpam-5790	41	15	,	,	PUNCT
ejpam-5790	41	16	and	and	CCONJ
ejpam-5790	41	17	suppose	suppose	VERB
ejpam-5790	41	18	that	that	SCONJ
ejpam-5790	41	19	∥∥ℑ(4	∥∥ℑ(4	PROPN
ejpam-5790	41	20	)	)	PUNCT
ejpam-5790	41	21	∥∥	∥∥	X
ejpam-5790	41	22	∞	∞	NUM
ejpam-5790	41	23	=	=	SYM
ejpam-5790	41	24	supw∈(ν1,ν2	supw∈(ν1,ν2	PROPN
ejpam-5790	41	25	)	)	PUNCT
ejpam-5790	41	26	∣∣ℑ(4)(w	∣∣ℑ(4)(w	PROPN
ejpam-5790	41	27	)	)	PUNCT
ejpam-5790	41	28	∣∣	∣∣	X
ejpam-5790	41	29	<	<	X
ejpam-5790	41	30	∞.	∞.	PROPN
ejpam-5790	41	31	then	then	ADV
ejpam-5790	41	32	,	,	PUNCT
ejpam-5790	41	33	we	we	PRON
ejpam-5790	41	34	have∣∣∣16	have∣∣∣16	VERB
ejpam-5790	42	1	[	[	X
ejpam-5790	42	2	ℑ(ν1	ℑ(ν1	NOUN
ejpam-5790	42	3	)	)	PUNCT
ejpam-5790	42	4	+	+	NUM
ejpam-5790	42	5	4ℑ	4ℑ	NOUN
ejpam-5790	42	6	(	(	PUNCT
ejpam-5790	42	7	ν1+ν2	ν1+ν2	NOUN
ejpam-5790	42	8	2	2	NUM
ejpam-5790	42	9	)	)	PUNCT
ejpam-5790	42	10	+	+	CCONJ
ejpam-5790	42	11	ℑ(ν2	ℑ(ν2	PROPN
ejpam-5790	42	12	)	)	PUNCT
ejpam-5790	42	13	]	]	PUNCT
ejpam-5790	43	1	−	−	PROPN
ejpam-5790	43	2	1	1	NUM
ejpam-5790	43	3	ν2−ν1	ν2−ν1	NUM
ejpam-5790	43	4	∫	∫	PROPN
ejpam-5790	43	5	ν2	ν2	PROPN
ejpam-5790	43	6	ν1	ν1	PROPN
ejpam-5790	43	7	ℑ(w)dw	ℑ(w)dw	ADJ
ejpam-5790	43	8	∣∣∣	∣∣∣	NOUN
ejpam-5790	43	9	≤	≤	NUM
ejpam-5790	43	10	1	1	NUM
ejpam-5790	43	11	2880	2880	NUM
ejpam-5790	43	12	∥∥ℑ(4	∥∥ℑ(4	PROPN
ejpam-5790	43	13	)	)	PUNCT
ejpam-5790	43	14	∥∥	∥∥	X
ejpam-5790	43	15	∞	∞	NUM
ejpam-5790	43	16	(	(	PUNCT
ejpam-5790	43	17	ν2	ν2	NOUN
ejpam-5790	43	18	−	−	PROPN
ejpam-5790	43	19	ν1	ν1	NOUN
ejpam-5790	43	20	)	)	PUNCT
ejpam-5790	43	21	4	4	NUM
ejpam-5790	43	22	.	.	PUNCT
ejpam-5790	43	23	scholars	scholar	NOUN
ejpam-5790	43	24	have	have	AUX
ejpam-5790	43	25	utilized	utilize	VERB
ejpam-5790	43	26	various	various	ADJ
ejpam-5790	43	27	approaches	approach	NOUN
ejpam-5790	43	28	to	to	PART
ejpam-5790	43	29	investigate	investigate	VERB
ejpam-5790	43	30	simpson	simpson	PROPN
ejpam-5790	43	31	’s	’s	PART
ejpam-5790	43	32	inequality	inequality	NOUN
ejpam-5790	43	33	.	.	PUNCT
ejpam-5790	44	1	for	for	ADP
ejpam-5790	44	2	example	example	NOUN
ejpam-5790	44	3	,	,	PUNCT
ejpam-5790	44	4	the	the	DET
ejpam-5790	44	5	authors	author	NOUN
ejpam-5790	44	6	of	of	ADP
ejpam-5790	44	7	[	[	X
ejpam-5790	44	8	12	12	NUM
ejpam-5790	44	9	]	]	PUNCT
ejpam-5790	44	10	established	establish	VERB
ejpam-5790	44	11	several	several	ADJ
ejpam-5790	44	12	novel	novel	ADJ
ejpam-5790	44	13	inequalities	inequality	NOUN
ejpam-5790	44	14	using	use	VERB
ejpam-5790	44	15	bi	bi	ADJ
ejpam-5790	44	16	-	-	ADJ
ejpam-5790	44	17	dimensional	dimensional	ADJ
ejpam-5790	44	18	convex	convex	NOUN
ejpam-5790	44	19	functions	function	NOUN
ejpam-5790	44	20	using	use	VERB
ejpam-5790	44	21	quantum	quantum	ADJ
ejpam-5790	44	22	integral	integral	ADJ
ejpam-5790	44	23	operators	operator	NOUN
ejpam-5790	44	24	.	.	PUNCT
ejpam-5790	45	1	in	in	ADP
ejpam-5790	45	2	[	[	X
ejpam-5790	45	3	21	21	NUM
ejpam-5790	45	4	]	]	PUNCT
ejpam-5790	45	5	,	,	PUNCT
ejpam-5790	45	6	researchers	researcher	NOUN
ejpam-5790	45	7	employed	employ	VERB
ejpam-5790	45	8	various	various	ADJ
ejpam-5790	45	9	non	non	ADJ
ejpam-5790	45	10	-	-	ADJ
ejpam-5790	45	11	integer	integer	ADJ
ejpam-5790	45	12	integral	integral	ADJ
ejpam-5790	45	13	operators	operator	NOUN
ejpam-5790	45	14	to	to	PART
ejpam-5790	45	15	,	,	PUNCT
ejpam-5790	45	16	uncovering	uncover	VERB
ejpam-5790	45	17	numerous	numerous	ADJ
ejpam-5790	45	18	enhanced	enhanced	ADJ
ejpam-5790	45	19	bounds	bound	NOUN
ejpam-5790	45	20	.	.	PUNCT
ejpam-5790	46	1	the	the	DET
ejpam-5790	46	2	work	work	NOUN
ejpam-5790	46	3	in	in	ADP
ejpam-5790	46	4	[	[	X
ejpam-5790	46	5	15	15	NUM
ejpam-5790	46	6	]	]	X
ejpam-5790	46	7	focused	focus	VERB
ejpam-5790	46	8	on	on	ADP
ejpam-5790	46	9	refinements	refinement	NOUN
ejpam-5790	46	10	and	and	CCONJ
ejpam-5790	46	11	reversals	reversal	NOUN
ejpam-5790	46	12	of	of	ADP
ejpam-5790	46	13	simpson	simpson	PROPN
ejpam-5790	46	14	’s	’s	PART
ejpam-5790	46	15	inequality	inequality	NOUN
ejpam-5790	46	16	by	by	ADP
ejpam-5790	46	17	utilizing	utilize	VERB
ejpam-5790	46	18	preinvex	preinvex	ADJ
ejpam-5790	46	19	mappings	mapping	NOUN
ejpam-5790	46	20	and	and	CCONJ
ejpam-5790	46	21	quantum	quantum	NOUN
ejpam-5790	46	22	calculus	calculus	NOUN
ejpam-5790	46	23	.	.	PUNCT
ejpam-5790	47	1	similarly	similarly	ADV
ejpam-5790	47	2	,	,	PUNCT
ejpam-5790	47	3	the	the	DET
ejpam-5790	47	4	authors	author	NOUN
ejpam-5790	47	5	of	of	ADP
ejpam-5790	47	6	[	[	X
ejpam-5790	47	7	11	11	NUM
ejpam-5790	47	8	]	]	PUNCT
ejpam-5790	47	9	explored	explore	VERB
ejpam-5790	47	10	the	the	DET
ejpam-5790	47	11	concept	concept	NOUN
ejpam-5790	47	12	of	of	ADP
ejpam-5790	47	13	tempered	temper	VERB
ejpam-5790	47	14	fractional	fractional	ADJ
ejpam-5790	47	15	integral	integral	ADJ
ejpam-5790	47	16	operators	operator	NOUN
ejpam-5790	47	17	,	,	PUNCT
ejpam-5790	47	18	while	while	SCONJ
ejpam-5790	47	19	[	[	X
ejpam-5790	47	20	45	45	NUM
ejpam-5790	47	21	]	]	PUNCT
ejpam-5790	47	22	employed	employ	VERB
ejpam-5790	47	23	multiplicative	multiplicative	ADJ
ejpam-5790	47	24	calculus	calculus	NOUN
ejpam-5790	47	25	to	to	PART
ejpam-5790	47	26	derive	derive	VERB
ejpam-5790	47	27	a	a	DET
ejpam-5790	47	28	range	range	NOUN
ejpam-5790	47	29	of	of	ADP
ejpam-5790	47	30	bounds	bound	NOUN
ejpam-5790	47	31	and	and	CCONJ
ejpam-5790	47	32	reversals	reversal	NOUN
ejpam-5790	47	33	for	for	ADP
ejpam-5790	47	34	such	such	ADJ
ejpam-5790	47	35	inequalities	inequality	NOUN
ejpam-5790	47	36	.	.	PUNCT
ejpam-5790	48	1	for	for	ADP
ejpam-5790	48	2	further	further	ADJ
ejpam-5790	48	3	insights	insight	NOUN
ejpam-5790	48	4	into	into	ADP
ejpam-5790	48	5	these	these	DET
ejpam-5790	48	6	related	relate	VERB
ejpam-5790	48	7	developments	development	NOUN
ejpam-5790	48	8	,	,	PUNCT
ejpam-5790	48	9	readers	reader	NOUN
ejpam-5790	48	10	are	be	AUX
ejpam-5790	48	11	encouraged	encourage	VERB
ejpam-5790	48	12	to	to	PART
ejpam-5790	48	13	consult	consult	VERB
ejpam-5790	48	14	[	[	X
ejpam-5790	48	15	6	6	NUM
ejpam-5790	48	16	,	,	PUNCT
ejpam-5790	48	17	10	10	NUM
ejpam-5790	48	18	,	,	PUNCT
ejpam-5790	48	19	18	18	NUM
ejpam-5790	48	20	,	,	PUNCT
ejpam-5790	48	21	20	20	NUM
ejpam-5790	48	22	,	,	PUNCT
ejpam-5790	48	23	38	38	NUM
ejpam-5790	48	24	,	,	PUNCT
ejpam-5790	48	25	39	39	NUM
ejpam-5790	48	26	,	,	PUNCT
ejpam-5790	48	27	47	47	NUM
ejpam-5790	48	28	]	]	PUNCT
ejpam-5790	48	29	and	and	CCONJ
ejpam-5790	48	30	the	the	DET
ejpam-5790	48	31	associated	associated	ADJ
ejpam-5790	48	32	references	reference	NOUN
ejpam-5790	48	33	.	.	PUNCT
ejpam-5790	49	1	self	self	NOUN
ejpam-5790	49	2	-	-	PUNCT
ejpam-5790	49	3	adjoint	adjoint	NOUN
ejpam-5790	49	4	operators	operator	NOUN
ejpam-5790	49	5	,	,	PUNCT
ejpam-5790	49	6	a	a	DET
ejpam-5790	49	7	crucial	crucial	ADJ
ejpam-5790	49	8	concept	concept	NOUN
ejpam-5790	49	9	in	in	ADP
ejpam-5790	49	10	mathematics	mathematic	NOUN
ejpam-5790	49	11	and	and	CCONJ
ejpam-5790	49	12	physics	physic	NOUN
ejpam-5790	49	13	,	,	PUNCT
ejpam-5790	49	14	enable	enable	VERB
ejpam-5790	49	15	the	the	DET
ejpam-5790	49	16	extension	extension	NOUN
ejpam-5790	49	17	of	of	ADP
ejpam-5790	49	18	classical	classical	ADJ
ejpam-5790	49	19	numerical	numerical	ADJ
ejpam-5790	49	20	inequalities	inequality	NOUN
ejpam-5790	49	21	to	to	PART
ejpam-5790	49	22	linear	linear	VERB
ejpam-5790	49	23	operators	operator	NOUN
ejpam-5790	49	24	on	on	ADP
ejpam-5790	49	25	hilbert	hilbert	PROPN
ejpam-5790	49	26	spaces	space	NOUN
ejpam-5790	49	27	.	.	PUNCT
ejpam-5790	50	1	these	these	DET
ejpam-5790	50	2	operators	operator	NOUN
ejpam-5790	50	3	,	,	PUNCT
ejpam-5790	50	4	generalizing	generalize	VERB
ejpam-5790	50	5	hermitian	hermitian	ADJ
ejpam-5790	50	6	matrices	matrix	NOUN
ejpam-5790	50	7	,	,	PUNCT
ejpam-5790	50	8	are	be	AUX
ejpam-5790	50	9	characterized	characterize	VERB
ejpam-5790	50	10	by	by	ADP
ejpam-5790	50	11	their	their	PRON
ejpam-5790	50	12	symmetry	symmetry	NOUN
ejpam-5790	50	13	,	,	PUNCT
ejpam-5790	50	14	ensuring	ensure	VERB
ejpam-5790	50	15	real	real	ADJ
ejpam-5790	50	16	eigenvalues	eigenvalue	NOUN
ejpam-5790	50	17	and	and	CCONJ
ejpam-5790	50	18	orthogonal	orthogonal	ADJ
ejpam-5790	50	19	eigenvectors	eigenvector	NOUN
ejpam-5790	50	20	.	.	PUNCT
ejpam-5790	51	1	the	the	DET
ejpam-5790	51	2	study	study	NOUN
ejpam-5790	51	3	of	of	ADP
ejpam-5790	51	4	such	such	ADJ
ejpam-5790	51	5	inequalities	inequality	NOUN
ejpam-5790	51	6	has	have	VERB
ejpam-5790	51	7	significant	significant	ADJ
ejpam-5790	51	8	applications	application	NOUN
ejpam-5790	51	9	in	in	ADP
ejpam-5790	51	10	areas	area	NOUN
ejpam-5790	51	11	such	such	ADJ
ejpam-5790	51	12	as	as	ADP
ejpam-5790	51	13	functional	functional	ADJ
ejpam-5790	51	14	analysis	analysis	NOUN
ejpam-5790	51	15	,	,	PUNCT
ejpam-5790	51	16	quantum	quantum	NOUN
ejpam-5790	51	17	mechanics	mechanic	NOUN
ejpam-5790	51	18	,	,	PUNCT
ejpam-5790	51	19	operator	operator	NOUN
ejpam-5790	51	20	theory	theory	NOUN
ejpam-5790	51	21	,	,	PUNCT
ejpam-5790	51	22	and	and	CCONJ
ejpam-5790	51	23	optimization	optimization	NOUN
ejpam-5790	51	24	.	.	PUNCT
ejpam-5790	52	1	recently	recently	ADV
ejpam-5790	52	2	,	,	PUNCT
ejpam-5790	52	3	researchers	researcher	NOUN
ejpam-5790	52	4	have	have	AUX
ejpam-5790	52	5	focused	focus	VERB
ejpam-5790	52	6	on	on	ADP
ejpam-5790	52	7	adapting	adapt	VERB
ejpam-5790	52	8	classical	classical	ADJ
ejpam-5790	52	9	inequalities	inequality	NOUN
ejpam-5790	52	10	like	like	ADP
ejpam-5790	52	11	hermite	hermite	X
ejpam-5790	52	12	–	–	PUNCT
ejpam-5790	52	13	hadamard	hadamard	NOUN
ejpam-5790	52	14	,	,	PUNCT
ejpam-5790	52	15	jensen	jensen	PROPN
ejpam-5790	52	16	,	,	PUNCT
ejpam-5790	52	17	and	and	CCONJ
ejpam-5790	52	18	hölder	hölder	NOUN
ejpam-5790	52	19	inequalities	inequality	NOUN
ejpam-5790	52	20	to	to	ADP
ejpam-5790	52	21	the	the	DET
ejpam-5790	52	22	operator	operator	NOUN
ejpam-5790	52	23	framework	framework	NOUN
ejpam-5790	52	24	,	,	PUNCT
ejpam-5790	52	25	deepening	deepen	VERB
ejpam-5790	52	26	their	their	PRON
ejpam-5790	52	27	applicability	applicability	NOUN
ejpam-5790	52	28	in	in	ADP
ejpam-5790	52	29	quantum	quantum	ADJ
ejpam-5790	52	30	physics	physics	NOUN
ejpam-5790	52	31	,	,	PUNCT
ejpam-5790	52	32	matrix	matrix	NOUN
ejpam-5790	52	33	theory	theory	NOUN
ejpam-5790	52	34	,	,	PUNCT
ejpam-5790	52	35	and	and	CCONJ
ejpam-5790	52	36	variational	variational	ADJ
ejpam-5790	52	37	methods	method	NOUN
ejpam-5790	52	38	within	within	ADP
ejpam-5790	52	39	hilbert	hilbert	NOUN
ejpam-5790	52	40	space	space	NOUN
ejpam-5790	52	41	settings	setting	NOUN
ejpam-5790	52	42	.	.	PUNCT
ejpam-5790	53	1	for	for	ADP
ejpam-5790	53	2	instance	instance	NOUN
ejpam-5790	53	3	,	,	PUNCT
ejpam-5790	53	4	in	in	ADP
ejpam-5790	53	5	[	[	X
ejpam-5790	53	6	46	46	NUM
ejpam-5790	53	7	]	]	PUNCT
ejpam-5790	53	8	,	,	PUNCT
ejpam-5790	53	9	operators	operator	NOUN
ejpam-5790	53	10	within	within	ADP
ejpam-5790	53	11	hilbert	hilbert	NOUN
ejpam-5790	53	12	spaces	space	NOUN
ejpam-5790	53	13	were	be	AUX
ejpam-5790	53	14	utilized	utilize	VERB
ejpam-5790	53	15	to	to	PART
ejpam-5790	53	16	derive	derive	VERB
ejpam-5790	53	17	numerical	numerical	ADJ
ejpam-5790	53	18	-	-	PUNCT
ejpam-5790	53	19	type	type	NOUN
ejpam-5790	53	20	inequalities	inequality	NOUN
ejpam-5790	53	21	,	,	PUNCT
ejpam-5790	53	22	highlighting	highlight	VERB
ejpam-5790	53	23	their	their	PRON
ejpam-5790	53	24	significance	significance	NOUN
ejpam-5790	53	25	in	in	ADP
ejpam-5790	53	26	functional	functional	ADJ
ejpam-5790	53	27	analysis	analysis	NOUN
ejpam-5790	53	28	and	and	CCONJ
ejpam-5790	53	29	optimization	optimization	NOUN
ejpam-5790	53	30	.	.	PUNCT
ejpam-5790	54	1	similarly	similarly	ADV
ejpam-5790	54	2	,	,	PUNCT
ejpam-5790	54	3	[	[	X
ejpam-5790	54	4	31	31	NUM
ejpam-5790	54	5	]	]	PUNCT
ejpam-5790	54	6	introduced	introduce	VERB
ejpam-5790	54	7	various	various	ADJ
ejpam-5790	54	8	means	mean	NOUN
ejpam-5790	54	9	inequalities	inequality	NOUN
ejpam-5790	54	10	for	for	ADP
ejpam-5790	54	11	bounded	bounded	ADJ
ejpam-5790	54	12	operators	operator	NOUN
ejpam-5790	54	13	,	,	PUNCT
ejpam-5790	54	14	further	far	ADV
ejpam-5790	54	15	enriching	enrich	VERB
ejpam-5790	54	16	the	the	DET
ejpam-5790	54	17	theoretical	theoretical	ADJ
ejpam-5790	54	18	framework	framework	NOUN
ejpam-5790	54	19	of	of	ADP
ejpam-5790	54	20	operator	operator	NOUN
ejpam-5790	54	21	inequalities	inequality	NOUN
ejpam-5790	54	22	in	in	ADP
ejpam-5790	54	23	hilbert	hilbert	PROPN
ejpam-5790	54	24	spaces	space	NOUN
ejpam-5790	54	25	.	.	PUNCT
ejpam-5790	55	1	in	in	ADP
ejpam-5790	55	2	[	[	X
ejpam-5790	55	3	27	27	NUM
ejpam-5790	55	4	]	]	PUNCT
ejpam-5790	55	5	,	,	PUNCT
ejpam-5790	55	6	hölder	hölder	NOUN
ejpam-5790	55	7	form	form	NOUN
ejpam-5790	55	8	inequalities	inequality	NOUN
ejpam-5790	55	9	involving	involve	VERB
ejpam-5790	55	10	power	power	NOUN
ejpam-5790	55	11	series	series	NOUN
ejpam-5790	55	12	were	be	AUX
ejpam-5790	55	13	proposed	propose	VERB
ejpam-5790	55	14	,	,	PUNCT
ejpam-5790	55	15	revealing	reveal	VERB
ejpam-5790	55	16	intriguing	intriguing	ADJ
ejpam-5790	55	17	applications	application	NOUN
ejpam-5790	55	18	within	within	ADP
ejpam-5790	55	19	hilbert	hilbert	NOUN
ejpam-5790	55	20	space	space	NOUN
ejpam-5790	55	21	settings	setting	NOUN
ejpam-5790	55	22	.	.	PUNCT
ejpam-5790	56	1	additionally	additionally	ADV
ejpam-5790	56	2	,	,	PUNCT
ejpam-5790	56	3	[	[	X
ejpam-5790	56	4	59	59	NUM
ejpam-5790	56	5	]	]	PUNCT
ejpam-5790	56	6	investigated	investigate	VERB
ejpam-5790	56	7	variational	variational	ADJ
ejpam-5790	56	8	problems	problem	NOUN
ejpam-5790	56	9	linked	link	VERB
ejpam-5790	56	10	to	to	ADP
ejpam-5790	56	11	inequalities	inequality	NOUN
ejpam-5790	56	12	and	and	CCONJ
ejpam-5790	56	13	graph	graph	NOUN
ejpam-5790	56	14	structures	structure	NOUN
ejpam-5790	56	15	in	in	ADP
ejpam-5790	56	16	hilbert	hilbert	NOUN
ejpam-5790	56	17	spaces	space	NOUN
ejpam-5790	56	18	,	,	PUNCT
ejpam-5790	56	19	showcasing	showcase	VERB
ejpam-5790	56	20	their	their	PRON
ejpam-5790	56	21	utility	utility	NOUN
ejpam-5790	56	22	in	in	ADP
ejpam-5790	56	23	diverse	diverse	ADJ
ejpam-5790	56	24	mathematical	mathematical	ADJ
ejpam-5790	56	25	and	and	CCONJ
ejpam-5790	56	26	physical	physical	ADJ
ejpam-5790	56	27	contexts	contexts	NOUN
ejpam-5790	56	28	.	.	PUNCT
ejpam-5790	57	1	for	for	ADP
ejpam-5790	57	2	additional	additional	ADJ
ejpam-5790	57	3	insights	insight	NOUN
ejpam-5790	57	4	and	and	CCONJ
ejpam-5790	57	5	related	related	ADJ
ejpam-5790	57	6	results	result	NOUN
ejpam-5790	57	7	,	,	PUNCT
ejpam-5790	57	8	readers	reader	NOUN
ejpam-5790	57	9	are	be	AUX
ejpam-5790	57	10	referred	refer	VERB
ejpam-5790	57	11	to	to	ADP
ejpam-5790	57	12	the	the	DET
ejpam-5790	57	13	references	reference	NOUN
ejpam-5790	57	14	in	in	ADP
ejpam-5790	57	15	[	[	X
ejpam-5790	57	16	4	4	NUM
ejpam-5790	57	17	,	,	PUNCT
ejpam-5790	57	18	7	7	NUM
ejpam-5790	57	19	,	,	PUNCT
ejpam-5790	57	20	14	14	NUM
ejpam-5790	57	21	,	,	PUNCT
ejpam-5790	57	22	17	17	NUM
ejpam-5790	57	23	,	,	PUNCT
ejpam-5790	57	24	34	34	NUM
ejpam-5790	57	25	,	,	PUNCT
ejpam-5790	57	26	40	40	NUM
ejpam-5790	57	27	,	,	PUNCT
ejpam-5790	57	28	62	62	NUM
ejpam-5790	57	29	,	,	PUNCT
ejpam-5790	57	30	67	67	NUM
ejpam-5790	57	31	]	]	PUNCT
ejpam-5790	57	32	.	.	PUNCT
ejpam-5790	58	1	dragomir	dragomir	PROPN
ejpam-5790	58	2	[	[	X
ejpam-5790	58	3	28	28	NUM
ejpam-5790	58	4	]	]	X
ejpam-5790	58	5	introduces	introduce	VERB
ejpam-5790	58	6	various	various	ADJ
ejpam-5790	58	7	innovative	innovative	ADJ
ejpam-5790	58	8	modifications	modification	NOUN
ejpam-5790	58	9	and	and	CCONJ
ejpam-5790	58	10	refinements	refinement	NOUN
ejpam-5790	58	11	of	of	ADP
ejpam-5790	58	12	the	the	DET
ejpam-5790	58	13	following	follow	VERB
ejpam-5790	58	14	double	double	ADJ
ejpam-5790	58	15	inequality	inequality	NOUN
ejpam-5790	58	16	within	within	ADP
ejpam-5790	58	17	the	the	DET
ejpam-5790	58	18	tensorial	tensorial	ADJ
ejpam-5790	58	19	framework	framework	NOUN
ejpam-5790	58	20	.	.	PUNCT
ejpam-5790	59	1	theorem	theorem	NOUN
ejpam-5790	59	2	2	2	NUM
ejpam-5790	59	3	(	(	PUNCT
ejpam-5790	59	4	see	see	VERB
ejpam-5790	59	5	[	[	X
ejpam-5790	59	6	28	28	NUM
ejpam-5790	59	7	]	]	NUM
ejpam-5790	59	8	)	)	PUNCT
ejpam-5790	59	9	.	.	PUNCT
ejpam-5790	60	1	let	let	VERB
ejpam-5790	60	2	d	d	PRON
ejpam-5790	60	3	be	be	AUX
ejpam-5790	60	4	a	a	DET
ejpam-5790	60	5	complete	complete	ADJ
ejpam-5790	60	6	inner	inner	ADJ
ejpam-5790	60	7	product	product	NOUN
ejpam-5790	60	8	space	space	NOUN
ejpam-5790	60	9	.	.	PUNCT
ejpam-5790	61	1	suppose	suppose	VERB
ejpam-5790	61	2	the	the	DET
ejpam-5790	61	3	operators	operator	NOUN
ejpam-5790	61	4	(	(	PUNCT
ejpam-5790	61	5	adjoint	adjoint	PROPN
ejpam-5790	61	6	)	)	PUNCT
ejpam-5790	61	7	u	u	NOUN
ejpam-5790	61	8	and	and	CCONJ
ejpam-5790	61	9	d	d	NOUN
ejpam-5790	61	10	satisfy	satisfy	VERB
ejpam-5790	61	11	the	the	DET
ejpam-5790	61	12	condition	condition	NOUN
ejpam-5790	61	13	0	0	PUNCT
ejpam-5790	61	14	<	<	X
ejpam-5790	61	15	s1	s1	PROPN
ejpam-5790	61	16	≤	≤	NUM
ejpam-5790	61	17	u	u	PROPN
ejpam-5790	61	18	,	,	PUNCT
ejpam-5790	61	19	d	d	PROPN
ejpam-5790	61	20	≤	≤	NUM
ejpam-5790	61	21	s2	s2	PROPN
ejpam-5790	61	22	,	,	PUNCT
ejpam-5790	61	23	where	where	SCONJ
ejpam-5790	61	24	s1	s1	NOUN
ejpam-5790	61	25	and	and	CCONJ
ejpam-5790	61	26	s2	s2	NOUN
ejpam-5790	61	27	are	be	AUX
ejpam-5790	61	28	positive	positive	ADJ
ejpam-5790	61	29	w.	w.	PROPN
ejpam-5790	61	30	afzal	afzal	PROPN
ejpam-5790	61	31	et	et	PROPN
ejpam-5790	61	32	al	al	PROPN
ejpam-5790	61	33	.	.	PUNCT
ejpam-5790	61	34	/	/	SYM
ejpam-5790	61	35	eur	eur	PROPN
ejpam-5790	61	36	.	.	PUNCT
ejpam-5790	62	1	j.	j.	PROPN
ejpam-5790	62	2	pure	pure	PROPN
ejpam-5790	62	3	appl	appl	PROPN
ejpam-5790	62	4	.	.	PROPN
ejpam-5790	62	5	math	math	PROPN
ejpam-5790	62	6	,	,	PUNCT
ejpam-5790	62	7	18	18	NUM
ejpam-5790	62	8	(	(	PUNCT
ejpam-5790	62	9	1	1	NUM
ejpam-5790	62	10	)	)	PUNCT
ejpam-5790	62	11	(	(	PUNCT
ejpam-5790	62	12	2025	2025	NUM
ejpam-5790	62	13	)	)	PUNCT
ejpam-5790	62	14	,	,	PUNCT
ejpam-5790	62	15	5790	5790	NUM
ejpam-5790	62	16	4	4	NUM
ejpam-5790	62	17	of	of	ADP
ejpam-5790	62	18	30	30	NUM
ejpam-5790	62	19	constants	constant	NOUN
ejpam-5790	62	20	.	.	PUNCT
ejpam-5790	63	1	then	then	ADV
ejpam-5790	63	2	0	0	NUM
ejpam-5790	63	3	≤	≤	NOUN
ejpam-5790	63	4	s1	s1	PROPN
ejpam-5790	63	5	s2	s2	NOUN
ejpam-5790	63	6	2	2	NUM
ejpam-5790	63	7	w(1−w	w(1−w	NOUN
ejpam-5790	63	8	)	)	PUNCT
ejpam-5790	63	9	(	(	PUNCT
ejpam-5790	63	10	u2	u2	PROPN
ejpam-5790	63	11	⊗	⊗	PROPN
ejpam-5790	63	12	1	1	NUM
ejpam-5790	64	1	+	+	NUM
ejpam-5790	64	2	1⊗d2	1⊗d2	NUM
ejpam-5790	64	3	2	2	NUM
ejpam-5790	64	4	−	−	PROPN
ejpam-5790	64	5	u	u	NOUN
ejpam-5790	64	6	⊗d	⊗d	NOUN
ejpam-5790	64	7	)	)	PUNCT
ejpam-5790	64	8	≤	≤	PROPN
ejpam-5790	64	9	(	(	PUNCT
ejpam-5790	64	10	1−w)u	1−w)u	NUM
ejpam-5790	64	11	⊗	⊗	NOUN
ejpam-5790	64	12	1	1	NUM
ejpam-5790	65	1	+	+	NOUN
ejpam-5790	65	2	w1⊗d	w1⊗d	NOUN
ejpam-5790	65	3	−	−	VERB
ejpam-5790	65	4	u1−w	u1−w	PROPN
ejpam-5790	65	5	⊗dw	⊗dw	NOUN
ejpam-5790	65	6	≤	≤	PUNCT
ejpam-5790	65	7	s2	s2	NOUN
ejpam-5790	65	8	s2	s2	NOUN
ejpam-5790	65	9	1	1	NUM
ejpam-5790	65	10	w(1−w	w(1−w	NOUN
ejpam-5790	65	11	)	)	PUNCT
ejpam-5790	65	12	(	(	PUNCT
ejpam-5790	65	13	u2	u2	PROPN
ejpam-5790	65	14	⊗	⊗	PROPN
ejpam-5790	65	15	1	1	NUM
ejpam-5790	65	16	+	+	NUM
ejpam-5790	65	17	1⊗d2	1⊗d2	NUM
ejpam-5790	65	18	2	2	NUM
ejpam-5790	65	19	−	−	PROPN
ejpam-5790	65	20	u	u	PROPN
ejpam-5790	65	21	⊗d	⊗d	NOUN
ejpam-5790	65	22	)	)	PUNCT
ejpam-5790	65	23	.	.	PUNCT
ejpam-5790	66	1	theorem	theorem	ADJ
ejpam-5790	66	2	3	3	NUM
ejpam-5790	66	3	(	(	PUNCT
ejpam-5790	66	4	see	see	VERB
ejpam-5790	66	5	[	[	X
ejpam-5790	66	6	2	2	NUM
ejpam-5790	66	7	]	]	PUNCT
ejpam-5790	66	8	)	)	PUNCT
ejpam-5790	66	9	.	.	PUNCT
ejpam-5790	67	1	assume	assume	VERB
ejpam-5790	67	2	that	that	SCONJ
ejpam-5790	67	3	u	u	PROPN
ejpam-5790	67	4	and	and	CCONJ
ejpam-5790	67	5	d	d	PROPN
ejpam-5790	67	6	are	be	AUX
ejpam-5790	67	7	operators	operator	NOUN
ejpam-5790	67	8	operators	operator	NOUN
ejpam-5790	67	9	(	(	PUNCT
ejpam-5790	67	10	adjoint	adjoint	PROPN
ejpam-5790	67	11	)	)	PUNCT
ejpam-5790	67	12	with	with	ADP
ejpam-5790	67	13	corresponding	correspond	VERB
ejpam-5790	67	14	spectra	spectra	ADJ
ejpam-5790	67	15	sp(u),sp(d	sp(u),sp(d	NOUN
ejpam-5790	67	16	)	)	PUNCT
ejpam-5790	67	17	⊂	⊂	PROPN
ejpam-5790	68	1	∆.	∆.	NOUN
ejpam-5790	68	2	let	let	VERB
ejpam-5790	68	3	ℑ	ℑ	PRON
ejpam-5790	68	4	is	be	AUX
ejpam-5790	68	5	a	a	DET
ejpam-5790	68	6	continous	continous	ADJ
ejpam-5790	68	7	function	function	NOUN
ejpam-5790	68	8	on	on	ADP
ejpam-5790	68	9	∆	∆	PROPN
ejpam-5790	68	10	,	,	PUNCT
ejpam-5790	68	11	then	then	ADV
ejpam-5790	68	12	we	we	PRON
ejpam-5790	68	13	have	have	VERB
ejpam-5790	68	14	2min{κ	2min{κ	NUM
ejpam-5790	68	15	,	,	PUNCT
ejpam-5790	68	16	1−	1−	NUM
ejpam-5790	68	17	κ	κ	NOUN
ejpam-5790	68	18	}	}	PUNCT
ejpam-5790	68	19	[	[	PUNCT
ejpam-5790	68	20	ℑ(u)⊗	ℑ(u)⊗	NUM
ejpam-5790	68	21	1	1	NUM
ejpam-5790	68	22	+	+	SYM
ejpam-5790	68	23	1⊗ℑ(d	1⊗ℑ(d	NUM
ejpam-5790	68	24	)	)	PUNCT
ejpam-5790	68	25	2	2	NUM
ejpam-5790	68	26	−ℑ	−ℑ	NOUN
ejpam-5790	68	27	(	(	PUNCT
ejpam-5790	68	28	2u	2u	PROPN
ejpam-5790	68	29	⊗	⊗	PROPN
ejpam-5790	68	30	1⊗d	1⊗d	NUM
ejpam-5790	69	1	⊗	⊗	NUM
ejpam-5790	69	2	1	1	NUM
ejpam-5790	69	3	u	u	NOUN
ejpam-5790	69	4	⊗	⊗	NOUN
ejpam-5790	69	5	1	1	NUM
ejpam-5790	69	6	+	+	NUM
ejpam-5790	69	7	1⊗d	1⊗d	NUM
ejpam-5790	69	8	)	)	PUNCT
ejpam-5790	69	9	]	]	PUNCT
ejpam-5790	69	10	≤	≤	NUM
ejpam-5790	69	11	κℑ(u)⊗	κℑ(u)⊗	NOUN
ejpam-5790	69	12	1	1	NUM
ejpam-5790	69	13	+	+	CCONJ
ejpam-5790	69	14	(	(	PUNCT
ejpam-5790	69	15	1−	1−	NUM
ejpam-5790	69	16	κ)1⊗ℑ(d)−ℑ(κu	κ)1⊗ℑ(d)−ℑ(κu	NOUN
ejpam-5790	69	17	⊗	⊗	PROPN
ejpam-5790	69	18	1	1	NUM
ejpam-5790	69	19	+	+	CCONJ
ejpam-5790	69	20	(	(	PUNCT
ejpam-5790	69	21	1−	1−	NUM
ejpam-5790	69	22	κ)1⊗d	κ)1⊗d	PROPN
ejpam-5790	69	23	)	)	PUNCT
ejpam-5790	69	24	≤	≤	NUM
ejpam-5790	69	25	2min{κ	2min{κ	NUM
ejpam-5790	69	26	,	,	PUNCT
ejpam-5790	69	27	1−	1−	NUM
ejpam-5790	69	28	κ	κ	NOUN
ejpam-5790	69	29	}	}	PUNCT
ejpam-5790	69	30	[	[	PUNCT
ejpam-5790	69	31	ℑ(u)⊗	ℑ(u)⊗	NUM
ejpam-5790	69	32	1	1	NUM
ejpam-5790	69	33	+	+	SYM
ejpam-5790	69	34	1⊗ℑ(d	1⊗ℑ(d	NUM
ejpam-5790	69	35	)	)	PUNCT
ejpam-5790	69	36	2	2	NUM
ejpam-5790	69	37	−ℑ	−ℑ	NOUN
ejpam-5790	69	38	(	(	PUNCT
ejpam-5790	69	39	2u	2u	PROPN
ejpam-5790	69	40	⊗	⊗	PROPN
ejpam-5790	69	41	1⊗d	1⊗d	NUM
ejpam-5790	69	42	⊗	⊗	NUM
ejpam-5790	69	43	1	1	NUM
ejpam-5790	69	44	u	u	NOUN
ejpam-5790	69	45	⊗	⊗	NOUN
ejpam-5790	69	46	1	1	NUM
ejpam-5790	69	47	+	+	NUM
ejpam-5790	69	48	1⊗d	1⊗d	NUM
ejpam-5790	69	49	)	)	PUNCT
ejpam-5790	69	50	]	]	PUNCT
ejpam-5790	69	51	.	.	PUNCT
ejpam-5790	70	1	the	the	DET
ejpam-5790	70	2	author	author	NOUN
ejpam-5790	70	3	of	of	ADP
ejpam-5790	70	4	[	[	X
ejpam-5790	70	5	56	56	NUM
ejpam-5790	70	6	]	]	PUNCT
ejpam-5790	70	7	used	use	VERB
ejpam-5790	70	8	standard	standard	ADJ
ejpam-5790	70	9	operators	operator	NOUN
ejpam-5790	70	10	and	and	CCONJ
ejpam-5790	70	11	differentiable	differentiable	ADJ
ejpam-5790	70	12	mappings	mapping	NOUN
ejpam-5790	70	13	to	to	PART
ejpam-5790	70	14	generate	generate	VERB
ejpam-5790	70	15	the	the	DET
ejpam-5790	70	16	following	follow	VERB
ejpam-5790	70	17	type	type	NOUN
ejpam-5790	70	18	of	of	ADP
ejpam-5790	70	19	double	double	ADJ
ejpam-5790	70	20	inequalities	inequality	NOUN
ejpam-5790	70	21	.	.	PUNCT
ejpam-5790	71	1	theorem	theorem	NOUN
ejpam-5790	71	2	4	4	NUM
ejpam-5790	71	3	(	(	PUNCT
ejpam-5790	71	4	see	see	VERB
ejpam-5790	71	5	[	[	X
ejpam-5790	71	6	2	2	NUM
ejpam-5790	71	7	,	,	PUNCT
ejpam-5790	71	8	56	56	NUM
ejpam-5790	71	9	]	]	NUM
ejpam-5790	71	10	)	)	PUNCT
ejpam-5790	71	11	.	.	PUNCT
ejpam-5790	72	1	assume	assume	VERB
ejpam-5790	72	2	that	that	SCONJ
ejpam-5790	72	3	u	u	PROPN
ejpam-5790	72	4	and	and	CCONJ
ejpam-5790	72	5	d	d	PROPN
ejpam-5790	72	6	are	be	AUX
ejpam-5790	72	7	selfadjoint	selfadjoint	VERB
ejpam-5790	72	8	operators	operator	NOUN
ejpam-5790	72	9	with	with	ADP
ejpam-5790	72	10	associated	associated	ADJ
ejpam-5790	72	11	sepctrums	sepctrum	NOUN
ejpam-5790	72	12	sp(u),sp(d	sp(u),sp(d	NOUN
ejpam-5790	72	13	)	)	PUNCT
ejpam-5790	72	14	⊂	⊂	PROPN
ejpam-5790	73	1	∆.	∆.	NOUN
ejpam-5790	73	2	let	let	VERB
ejpam-5790	73	3	ℑ	ℑ	PRON
ejpam-5790	73	4	is	be	AUX
ejpam-5790	73	5	a	a	DET
ejpam-5790	73	6	continous	continous	ADJ
ejpam-5790	73	7	function	function	NOUN
ejpam-5790	73	8	on	on	ADP
ejpam-5790	73	9	∆	∆	PROPN
ejpam-5790	73	10	,	,	PUNCT
ejpam-5790	73	11	then	then	ADV
ejpam-5790	73	12	we	we	PRON
ejpam-5790	73	13	have∫	have∫	VERB
ejpam-5790	73	14	1	1	NUM
ejpam-5790	73	15	0	0	NUM
ejpam-5790	73	16	ℑ((1−w)u	ℑ((1−w)u	NOUN
ejpam-5790	73	17	⊗	⊗	PROPN
ejpam-5790	73	18	1	1	NUM
ejpam-5790	74	1	+	+	NOUN
ejpam-5790	74	2	w1⊗d)dw	w1⊗d)dw	NOUN
ejpam-5790	74	3	−ℑ	−ℑ	VERB
ejpam-5790	74	4	(	(	PUNCT
ejpam-5790	74	5	u	u	NOUN
ejpam-5790	74	6	⊗	⊗	PROPN
ejpam-5790	74	7	1	1	NUM
ejpam-5790	74	8	+	+	NUM
ejpam-5790	74	9	1⊗d	1⊗d	NUM
ejpam-5790	74	10	2	2	NUM
ejpam-5790	74	11	)	)	PUNCT
ejpam-5790	74	12	=	=	SYM
ejpam-5790	75	1	(	(	PUNCT
ejpam-5790	75	2	1⊗d	1⊗d	NUM
ejpam-5790	75	3	−	−	PROPN
ejpam-5790	75	4	u	u	NOUN
ejpam-5790	75	5	⊗	⊗	PROPN
ejpam-5790	75	6	1)2	1)2	NUM
ejpam-5790	75	7	16	16	NUM
ejpam-5790	76	1	[	[	X
ejpam-5790	76	2	∫	∫	PROPN
ejpam-5790	76	3	1	1	NUM
ejpam-5790	76	4	0	0	NUM
ejpam-5790	76	5	w2ℑ′′	w2ℑ′′	INTJ
ejpam-5790	76	6	(	(	PUNCT
ejpam-5790	76	7	(	(	PUNCT
ejpam-5790	76	8	1−w)u	1−w)u	NUM
ejpam-5790	76	9	⊗	⊗	NOUN
ejpam-5790	76	10	1	1	NUM
ejpam-5790	76	11	+	+	NOUN
ejpam-5790	76	12	w1⊗d	w1⊗d	NOUN
ejpam-5790	76	13	)	)	PUNCT
ejpam-5790	76	14	dw	dw	PROPN
ejpam-5790	77	1	+	+	CCONJ
ejpam-5790	77	2	∫	∫	PROPN
ejpam-5790	77	3	1	1	NUM
ejpam-5790	77	4	0	0	NUM
ejpam-5790	78	1	(	(	PUNCT
ejpam-5790	78	2	w	w	NOUN
ejpam-5790	78	3	−	−	PROPN
ejpam-5790	78	4	1)2ℑ′′	1)2ℑ′′	X
ejpam-5790	78	5	(	(	PUNCT
ejpam-5790	78	6	(	(	PUNCT
ejpam-5790	78	7	1−w	1−w	NUM
ejpam-5790	78	8	2	2	NUM
ejpam-5790	78	9	)	)	PUNCT
ejpam-5790	78	10	u	u	NOUN
ejpam-5790	78	11	⊗	⊗	PROPN
ejpam-5790	78	12	1	1	NUM
ejpam-5790	78	13	+	+	CCONJ
ejpam-5790	78	14	(	(	PUNCT
ejpam-5790	78	15	1	1	NUM
ejpam-5790	78	16	+	+	NOUN
ejpam-5790	78	17	w	w	NOUN
ejpam-5790	78	18	2	2	NUM
ejpam-5790	78	19	)	)	PUNCT
ejpam-5790	78	20	1⊗d	1⊗d	PROPN
ejpam-5790	78	21	)	)	PUNCT
ejpam-5790	78	22	dw	dw	NOUN
ejpam-5790	78	23	]	]	PUNCT
ejpam-5790	78	24	.	.	PUNCT
ejpam-5790	79	1	the	the	DET
ejpam-5790	79	2	following	follow	VERB
ejpam-5790	79	3	double	double	ADJ
ejpam-5790	79	4	inequality	inequality	NOUN
ejpam-5790	79	5	was	be	AUX
ejpam-5790	79	6	derived	derive	VERB
ejpam-5790	79	7	by	by	ADP
ejpam-5790	79	8	the	the	DET
ejpam-5790	79	9	authors	author	NOUN
ejpam-5790	79	10	using	use	VERB
ejpam-5790	79	11	positive	positive	ADJ
ejpam-5790	79	12	semidefinite	semidefinite	NOUN
ejpam-5790	79	13	operators	operator	NOUN
ejpam-5790	79	14	on	on	ADP
ejpam-5790	79	15	a	a	DET
ejpam-5790	79	16	hilbert	hilbert	NOUN
ejpam-5790	79	17	space	space	NOUN
ejpam-5790	79	18	.	.	PUNCT
ejpam-5790	80	1	theorem	theorem	NOUN
ejpam-5790	80	2	5	5	NUM
ejpam-5790	80	3	(	(	PUNCT
ejpam-5790	80	4	see	see	VERB
ejpam-5790	80	5	[	[	X
ejpam-5790	80	6	25	25	NUM
ejpam-5790	80	7	]	]	PUNCT
ejpam-5790	80	8	)	)	PUNCT
ejpam-5790	80	9	.	.	PUNCT
ejpam-5790	81	1	let	let	VERB
ejpam-5790	81	2	u	u	PRON
ejpam-5790	81	3	and	and	CCONJ
ejpam-5790	81	4	d	d	NOUN
ejpam-5790	81	5	be	be	AUX
ejpam-5790	81	6	positive	positive	ADJ
ejpam-5790	81	7	and	and	CCONJ
ejpam-5790	81	8	semidefinite	semidefinite	PROPN
ejpam-5790	81	9	operators	operator	NOUN
ejpam-5790	81	10	,	,	PUNCT
ejpam-5790	81	11	with	with	ADP
ejpam-5790	81	12	associated	associated	ADJ
ejpam-5790	81	13	spectrums	spectrum	NOUN
ejpam-5790	81	14	sp(u),sp(d	sp(u),sp(d	NOUN
ejpam-5790	81	15	)	)	PUNCT
ejpam-5790	81	16	⊂	⊂	PROPN
ejpam-5790	82	1	∆.	∆.	X
ejpam-5790	82	2	then	then	ADV
ejpam-5790	82	3	(	(	PUNCT
ejpam-5790	82	4	u#d)⊗	u#d)⊗	PROPN
ejpam-5790	82	5	(	(	PUNCT
ejpam-5790	82	6	u#d	u#d	PROPN
ejpam-5790	82	7	)	)	PUNCT
ejpam-5790	82	8	⩽	⩽	NOUN
ejpam-5790	82	9	1	1	NUM
ejpam-5790	82	10	2	2	NUM
ejpam-5790	82	11	{	{	PUNCT
ejpam-5790	82	12	(	(	PUNCT
ejpam-5790	82	13	uσd)⊗	uσd)⊗	PROPN
ejpam-5790	82	14	(	(	PUNCT
ejpam-5790	82	15	uσ⊥d	uσ⊥d	ADV
ejpam-5790	82	16	)	)	PUNCT
ejpam-5790	83	1	+	+	CCONJ
ejpam-5790	83	2	(	(	PUNCT
ejpam-5790	83	3	uσ⊥d	uσ⊥d	ADJ
ejpam-5790	83	4	)	)	PUNCT
ejpam-5790	84	1	⊗	⊗	PROPN
ejpam-5790	84	2	(	(	PUNCT
ejpam-5790	84	3	uσd	uσd	PROPN
ejpam-5790	84	4	)	)	PUNCT
ejpam-5790	84	5	}	}	PUNCT
ejpam-5790	84	6	⩽	⩽	NOUN
ejpam-5790	84	7	1	1	NUM
ejpam-5790	84	8	2	2	NUM
ejpam-5790	84	9	{	{	PUNCT
ejpam-5790	84	10	(	(	PUNCT
ejpam-5790	84	11	u	u	NOUN
ejpam-5790	84	12	⊗	⊗	PROPN
ejpam-5790	84	13	d	d	PROPN
ejpam-5790	84	14	)	)	PUNCT
ejpam-5790	85	1	+	+	CCONJ
ejpam-5790	85	2	(	(	PUNCT
ejpam-5790	85	3	d	d	PROPN
ejpam-5790	85	4	⊗	⊗	PROPN
ejpam-5790	85	5	u	u	NOUN
ejpam-5790	85	6	)	)	PUNCT
ejpam-5790	85	7	}	}	PUNCT
ejpam-5790	85	8	.	.	PUNCT
ejpam-5790	86	1	significance	significance	NOUN
ejpam-5790	86	2	of	of	ADP
ejpam-5790	86	3	the	the	DET
ejpam-5790	86	4	study	study	NOUN
ejpam-5790	86	5	tensor	tensor	NOUN
ejpam-5790	86	6	inequalities	inequality	NOUN
ejpam-5790	86	7	extend	extend	VERB
ejpam-5790	86	8	the	the	DET
ejpam-5790	86	9	concepts	concept	NOUN
ejpam-5790	86	10	of	of	ADP
ejpam-5790	86	11	scalar	scalar	ADJ
ejpam-5790	86	12	and	and	CCONJ
ejpam-5790	86	13	matrix	matrix	NOUN
ejpam-5790	86	14	inequalities	inequality	NOUN
ejpam-5790	86	15	to	to	ADP
ejpam-5790	86	16	higherdimensional	higherdimensional	ADJ
ejpam-5790	86	17	spaces	space	NOUN
ejpam-5790	86	18	,	,	PUNCT
ejpam-5790	86	19	offering	offer	VERB
ejpam-5790	86	20	a	a	DET
ejpam-5790	86	21	framework	framework	NOUN
ejpam-5790	86	22	to	to	PART
ejpam-5790	86	23	handle	handle	VERB
ejpam-5790	86	24	multi	multi	ADJ
ejpam-5790	86	25	-	-	ADJ
ejpam-5790	86	26	dimensional	dimensional	ADJ
ejpam-5790	86	27	data	datum	NOUN
ejpam-5790	86	28	.	.	PUNCT
ejpam-5790	87	1	his	his	PRON
ejpam-5790	87	2	generalization	generalization	NOUN
ejpam-5790	87	3	allows	allow	VERB
ejpam-5790	87	4	researchers	researcher	NOUN
ejpam-5790	87	5	to	to	PART
ejpam-5790	87	6	study	study	VERB
ejpam-5790	87	7	and	and	CCONJ
ejpam-5790	87	8	model	model	NOUN
ejpam-5790	87	9	problems	problem	NOUN
ejpam-5790	87	10	in	in	ADP
ejpam-5790	87	11	more	more	ADJ
ejpam-5790	87	12	complex	complex	ADJ
ejpam-5790	87	13	settings	setting	NOUN
ejpam-5790	87	14	where	where	SCONJ
ejpam-5790	87	15	scalar	scalar	ADJ
ejpam-5790	87	16	w.	w.	PROPN
ejpam-5790	87	17	afzal	afzal	PROPN
ejpam-5790	87	18	et	et	PROPN
ejpam-5790	87	19	al	al	PROPN
ejpam-5790	87	20	.	.	PUNCT
ejpam-5790	87	21	/	/	SYM
ejpam-5790	87	22	eur	eur	PROPN
ejpam-5790	87	23	.	.	PUNCT
ejpam-5790	88	1	j.	j.	PROPN
ejpam-5790	88	2	pure	pure	PROPN
ejpam-5790	88	3	appl	appl	PROPN
ejpam-5790	88	4	.	.	PROPN
ejpam-5790	88	5	math	math	PROPN
ejpam-5790	88	6	,	,	PUNCT
ejpam-5790	88	7	18	18	NUM
ejpam-5790	88	8	(	(	PUNCT
ejpam-5790	88	9	1	1	NUM
ejpam-5790	88	10	)	)	PUNCT
ejpam-5790	88	11	(	(	PUNCT
ejpam-5790	88	12	2025	2025	NUM
ejpam-5790	88	13	)	)	PUNCT
ejpam-5790	88	14	,	,	PUNCT
ejpam-5790	88	15	5790	5790	NUM
ejpam-5790	88	16	5	5	NUM
ejpam-5790	88	17	of	of	ADP
ejpam-5790	88	18	30	30	NUM
ejpam-5790	88	19	or	or	CCONJ
ejpam-5790	88	20	matrix	matrix	NOUN
ejpam-5790	88	21	representations	representation	NOUN
ejpam-5790	88	22	are	be	AUX
ejpam-5790	88	23	insufficient	insufficient	ADJ
ejpam-5790	88	24	.	.	PUNCT
ejpam-5790	89	1	they	they	PRON
ejpam-5790	89	2	often	often	ADV
ejpam-5790	89	3	play	play	VERB
ejpam-5790	89	4	a	a	DET
ejpam-5790	89	5	role	role	NOUN
ejpam-5790	89	6	in	in	ADP
ejpam-5790	89	7	estimating	estimate	VERB
ejpam-5790	89	8	operator	operator	NOUN
ejpam-5790	89	9	norms	norm	NOUN
ejpam-5790	89	10	and	and	CCONJ
ejpam-5790	89	11	proving	prove	VERB
ejpam-5790	89	12	convergence	convergence	NOUN
ejpam-5790	89	13	results	result	NOUN
ejpam-5790	89	14	in	in	ADP
ejpam-5790	89	15	functional	functional	ADJ
ejpam-5790	89	16	spaces	space	NOUN
ejpam-5790	89	17	.	.	PUNCT
ejpam-5790	90	1	in	in	ADP
ejpam-5790	90	2	optimization	optimization	NOUN
ejpam-5790	90	3	,	,	PUNCT
ejpam-5790	90	4	tensor	tensor	NOUN
ejpam-5790	90	5	inequalities	inequality	NOUN
ejpam-5790	90	6	provide	provide	VERB
ejpam-5790	90	7	constraints	constraint	NOUN
ejpam-5790	90	8	and	and	CCONJ
ejpam-5790	90	9	bounds	bound	NOUN
ejpam-5790	90	10	that	that	PRON
ejpam-5790	90	11	facilitate	facilitate	VERB
ejpam-5790	90	12	the	the	DET
ejpam-5790	90	13	solution	solution	NOUN
ejpam-5790	90	14	of	of	ADP
ejpam-5790	90	15	multi	multi	ADJ
ejpam-5790	90	16	-	-	ADJ
ejpam-5790	90	17	dimensional	dimensional	ADJ
ejpam-5790	90	18	problems	problem	NOUN
ejpam-5790	90	19	,	,	PUNCT
ejpam-5790	90	20	including	include	VERB
ejpam-5790	90	21	those	those	PRON
ejpam-5790	90	22	involving	involve	VERB
ejpam-5790	90	23	tensor	tensor	NOUN
ejpam-5790	90	24	decompositions	decomposition	NOUN
ejpam-5790	90	25	or	or	CCONJ
ejpam-5790	90	26	eigenvalue	eigenvalue	NOUN
ejpam-5790	90	27	problems	problem	NOUN
ejpam-5790	90	28	.	.	PUNCT
ejpam-5790	91	1	tensor	tensor	NOUN
ejpam-5790	91	2	inequalities	inequality	NOUN
ejpam-5790	91	3	provide	provide	VERB
ejpam-5790	91	4	bounds	bound	NOUN
ejpam-5790	91	5	for	for	ADP
ejpam-5790	91	6	quantum	quantum	ADJ
ejpam-5790	91	7	information	information	NOUN
ejpam-5790	91	8	measures	measure	NOUN
ejpam-5790	91	9	,	,	PUNCT
ejpam-5790	91	10	such	such	ADJ
ejpam-5790	91	11	as	as	ADP
ejpam-5790	91	12	entanglement	entanglement	NOUN
ejpam-5790	91	13	entropy	entropy	NOUN
ejpam-5790	91	14	and	and	CCONJ
ejpam-5790	91	15	mutual	mutual	ADJ
ejpam-5790	91	16	information	information	NOUN
ejpam-5790	91	17	.	.	PUNCT
ejpam-5790	92	1	tensor	tensor	NOUN
ejpam-5790	92	2	inequalities	inequality	NOUN
ejpam-5790	92	3	are	be	AUX
ejpam-5790	92	4	vital	vital	ADJ
ejpam-5790	92	5	in	in	ADP
ejpam-5790	92	6	understanding	understand	VERB
ejpam-5790	92	7	geometric	geometric	ADJ
ejpam-5790	92	8	structures	structure	NOUN
ejpam-5790	92	9	like	like	ADP
ejpam-5790	92	10	curvature	curvature	NOUN
ejpam-5790	92	11	in	in	ADP
ejpam-5790	92	12	riemannian	riemannian	ADJ
ejpam-5790	92	13	geometry	geometry	NOUN
ejpam-5790	92	14	,	,	PUNCT
ejpam-5790	92	15	where	where	SCONJ
ejpam-5790	92	16	tensors	tensor	NOUN
ejpam-5790	92	17	such	such	ADJ
ejpam-5790	92	18	as	as	ADP
ejpam-5790	92	19	the	the	DET
ejpam-5790	92	20	riemann	riemann	PROPN
ejpam-5790	92	21	curvature	curvature	PROPN
ejpam-5790	92	22	tensor	tensor	NOUN
ejpam-5790	92	23	play	play	VERB
ejpam-5790	92	24	a	a	DET
ejpam-5790	92	25	central	central	ADJ
ejpam-5790	92	26	role	role	NOUN
ejpam-5790	92	27	.	.	PUNCT
ejpam-5790	93	1	our	our	PRON
ejpam-5790	93	2	motivation	motivation	NOUN
ejpam-5790	93	3	to	to	PART
ejpam-5790	93	4	develop	develop	VERB
ejpam-5790	93	5	an	an	DET
ejpam-5790	93	6	advanced	advanced	ADJ
ejpam-5790	93	7	and	and	CCONJ
ejpam-5790	93	8	novel	novel	ADJ
ejpam-5790	93	9	version	version	NOUN
ejpam-5790	93	10	of	of	ADP
ejpam-5790	93	11	various	various	ADJ
ejpam-5790	93	12	inequalities	inequality	NOUN
ejpam-5790	93	13	in	in	ADP
ejpam-5790	93	14	tensor	tensor	NOUN
ejpam-5790	93	15	hilbert	hilbert	NOUN
ejpam-5790	93	16	spaces	space	NOUN
ejpam-5790	93	17	is	be	AUX
ejpam-5790	93	18	largely	largely	ADV
ejpam-5790	93	19	inspired	inspire	VERB
ejpam-5790	93	20	by	by	ADP
ejpam-5790	93	21	the	the	DET
ejpam-5790	93	22	works	work	NOUN
ejpam-5790	93	23	of	of	ADP
ejpam-5790	93	24	[	[	X
ejpam-5790	93	25	2	2	NUM
ejpam-5790	93	26	,	,	PUNCT
ejpam-5790	93	27	22	22	NUM
ejpam-5790	93	28	,	,	PUNCT
ejpam-5790	93	29	57	57	NUM
ejpam-5790	93	30	,	,	PUNCT
ejpam-5790	93	31	68	68	NUM
ejpam-5790	93	32	]	]	PUNCT
ejpam-5790	93	33	.	.	PUNCT
ejpam-5790	94	1	by	by	ADP
ejpam-5790	94	2	incorporating	incorporate	VERB
ejpam-5790	94	3	innovative	innovative	ADJ
ejpam-5790	94	4	techniques	technique	NOUN
ejpam-5790	94	5	and	and	CCONJ
ejpam-5790	94	6	perspectives	perspective	NOUN
ejpam-5790	94	7	that	that	PRON
ejpam-5790	94	8	have	have	AUX
ejpam-5790	94	9	been	be	AUX
ejpam-5790	94	10	explored	explore	VERB
ejpam-5790	94	11	in	in	ADP
ejpam-5790	94	12	only	only	ADV
ejpam-5790	94	13	a	a	DET
ejpam-5790	94	14	limited	limited	ADJ
ejpam-5790	94	15	number	number	NOUN
ejpam-5790	94	16	of	of	ADP
ejpam-5790	94	17	studies	study	NOUN
ejpam-5790	94	18	,	,	PUNCT
ejpam-5790	94	19	this	this	DET
ejpam-5790	94	20	work	work	NOUN
ejpam-5790	94	21	aims	aim	VERB
ejpam-5790	94	22	to	to	PART
ejpam-5790	94	23	significantly	significantly	ADV
ejpam-5790	94	24	expand	expand	VERB
ejpam-5790	94	25	and	and	CCONJ
ejpam-5790	94	26	enhance	enhance	VERB
ejpam-5790	94	27	the	the	DET
ejpam-5790	94	28	existing	exist	VERB
ejpam-5790	94	29	theory	theory	NOUN
ejpam-5790	94	30	of	of	ADP
ejpam-5790	94	31	inequalities	inequality	NOUN
ejpam-5790	94	32	.	.	PUNCT
ejpam-5790	95	1	the	the	DET
ejpam-5790	95	2	paper	paper	NOUN
ejpam-5790	95	3	is	be	AUX
ejpam-5790	95	4	organized	organize	VERB
ejpam-5790	95	5	into	into	ADP
ejpam-5790	95	6	five	five	NUM
ejpam-5790	95	7	sections	section	NOUN
ejpam-5790	95	8	.	.	PUNCT
ejpam-5790	96	1	section	section	NOUN
ejpam-5790	96	2	2	2	NUM
ejpam-5790	96	3	presents	present	VERB
ejpam-5790	96	4	a	a	DET
ejpam-5790	96	5	summary	summary	NOUN
ejpam-5790	96	6	of	of	ADP
ejpam-5790	96	7	fundamental	fundamental	ADJ
ejpam-5790	96	8	concepts	concept	NOUN
ejpam-5790	96	9	associated	associate	VERB
ejpam-5790	96	10	with	with	ADP
ejpam-5790	96	11	hilbert	hilbert	NOUN
ejpam-5790	96	12	spaces	space	NOUN
ejpam-5790	96	13	and	and	CCONJ
ejpam-5790	96	14	their	their	PRON
ejpam-5790	96	15	basic	basic	ADJ
ejpam-5790	96	16	operations	operation	NOUN
ejpam-5790	96	17	.	.	PUNCT
ejpam-5790	97	1	in	in	ADP
ejpam-5790	97	2	section	section	NOUN
ejpam-5790	97	3	3	3	NUM
ejpam-5790	97	4	,	,	PUNCT
ejpam-5790	97	5	we	we	PRON
ejpam-5790	97	6	derive	derive	VERB
ejpam-5790	97	7	various	various	ADJ
ejpam-5790	97	8	new	new	ADJ
ejpam-5790	97	9	bounds	bound	NOUN
ejpam-5790	97	10	for	for	ADP
ejpam-5790	97	11	numerical	numerical	ADJ
ejpam-5790	97	12	integral	integral	ADJ
ejpam-5790	97	13	inequalities	inequality	NOUN
ejpam-5790	97	14	.	.	PUNCT
ejpam-5790	98	1	section	section	NOUN
ejpam-5790	98	2	4	4	NUM
ejpam-5790	98	3	explores	explore	VERB
ejpam-5790	98	4	non	non	ADJ
ejpam-5790	98	5	-	-	ADJ
ejpam-5790	98	6	trivial	trivial	ADJ
ejpam-5790	98	7	examples	example	NOUN
ejpam-5790	98	8	and	and	CCONJ
ejpam-5790	98	9	general	general	ADJ
ejpam-5790	98	10	observations	observation	NOUN
ejpam-5790	98	11	.	.	PUNCT
ejpam-5790	99	1	finally	finally	ADV
ejpam-5790	99	2	,	,	PUNCT
ejpam-5790	99	3	section	section	NOUN
ejpam-5790	99	4	5	5	NUM
ejpam-5790	99	5	discusses	discuss	VERB
ejpam-5790	99	6	the	the	DET
ejpam-5790	99	7	main	main	ADJ
ejpam-5790	99	8	findings	finding	NOUN
ejpam-5790	99	9	and	and	CCONJ
ejpam-5790	99	10	potential	potential	ADJ
ejpam-5790	99	11	directions	direction	NOUN
ejpam-5790	99	12	for	for	ADP
ejpam-5790	99	13	future	future	ADJ
ejpam-5790	99	14	research	research	NOUN
ejpam-5790	99	15	related	relate	VERB
ejpam-5790	99	16	to	to	ADP
ejpam-5790	99	17	these	these	DET
ejpam-5790	99	18	results	result	NOUN
ejpam-5790	99	19	.	.	PUNCT
ejpam-5790	100	1	2	2	X
ejpam-5790	100	2	.	.	X
ejpam-5790	100	3	preliminaries	preliminary	NOUN
ejpam-5790	100	4	in	in	ADP
ejpam-5790	100	5	this	this	DET
ejpam-5790	100	6	section	section	NOUN
ejpam-5790	100	7	,	,	PUNCT
ejpam-5790	100	8	we	we	PRON
ejpam-5790	100	9	revisit	revisit	VERB
ejpam-5790	100	10	fundamental	fundamental	ADJ
ejpam-5790	100	11	concepts	concept	NOUN
ejpam-5790	100	12	related	relate	VERB
ejpam-5790	100	13	to	to	ADP
ejpam-5790	100	14	hilbert	hilbert	NOUN
ejpam-5790	100	15	spaces	space	NOUN
ejpam-5790	100	16	and	and	CCONJ
ejpam-5790	100	17	extended	extend	VERB
ejpam-5790	100	18	convex	convex	NOUN
ejpam-5790	100	19	mappings	mapping	NOUN
ejpam-5790	100	20	.	.	PUNCT
ejpam-5790	101	1	for	for	ADP
ejpam-5790	101	2	further	further	ADJ
ejpam-5790	101	3	details	detail	NOUN
ejpam-5790	101	4	and	and	CCONJ
ejpam-5790	101	5	additional	additional	ADJ
ejpam-5790	101	6	insights	insight	NOUN
ejpam-5790	101	7	,	,	PUNCT
ejpam-5790	101	8	readers	reader	NOUN
ejpam-5790	101	9	are	be	AUX
ejpam-5790	101	10	encouraged	encourage	VERB
ejpam-5790	101	11	to	to	PART
ejpam-5790	101	12	consult	consult	VERB
ejpam-5790	101	13	[	[	X
ejpam-5790	101	14	14	14	NUM
ejpam-5790	101	15	]	]	PUNCT
ejpam-5790	101	16	.	.	PUNCT
ejpam-5790	102	1	definition	definition	NOUN
ejpam-5790	102	2	1	1	NUM
ejpam-5790	102	3	(	(	PUNCT
ejpam-5790	102	4	see	see	VERB
ejpam-5790	102	5	[	[	X
ejpam-5790	102	6	41	41	NUM
ejpam-5790	102	7	]	]	NUM
ejpam-5790	102	8	)	)	PUNCT
ejpam-5790	102	9	.	.	PUNCT
ejpam-5790	103	1	a	a	DET
ejpam-5790	103	2	pre	pre	ADJ
ejpam-5790	103	3	-	-	ADJ
ejpam-5790	103	4	hilbert	hilbert	ADJ
ejpam-5790	103	5	space	space	NOUN
ejpam-5790	103	6	on	on	ADP
ejpam-5790	103	7	r	r	NOUN
ejpam-5790	103	8	is	be	AUX
ejpam-5790	103	9	defined	define	VERB
ejpam-5790	103	10	as	as	ADP
ejpam-5790	103	11	(	(	PUNCT
ejpam-5790	103	12	·	·	PUNCT
ejpam-5790	103	13	,	,	PUNCT
ejpam-5790	103	14	·	·	PUNCT
ejpam-5790	103	15	)	)	PUNCT
ejpam-5790	103	16	:	:	PUNCT
ejpam-5790	104	1	r×	r×	NOUN
ejpam-5790	104	2	r	r	NOUN
ejpam-5790	104	3	→	→	SYM
ejpam-5790	104	4	c	c	NOUN
ejpam-5790	104	5	,	,	PUNCT
ejpam-5790	104	6	for	for	ADP
ejpam-5790	104	7	all	all	DET
ejpam-5790	104	8	w1,w2,w3	w1,w2,w3	NOUN
ejpam-5790	104	9	∈	∈	NOUN
ejpam-5790	104	10	r	r	NOUN
ejpam-5790	104	11	and	and	CCONJ
ejpam-5790	104	12	λ	λ	X
ejpam-5790	104	13	∈	∈	PROPN
ejpam-5790	104	14	c	c	X
ejpam-5790	104	15	,	,	PUNCT
ejpam-5790	104	16	we	we	PRON
ejpam-5790	104	17	have	have	VERB
ejpam-5790	104	18	⟨w1	⟨w1	PROPN
ejpam-5790	104	19	+	+	PROPN
ejpam-5790	104	20	w2,w3⟩	w2,w3⟩	PROPN
ejpam-5790	104	21	=	=	SYM
ejpam-5790	104	22	⟨w1,w3⟩+	⟨w1,w3⟩+	PROPN
ejpam-5790	104	23	⟨w2	⟨w2	PROPN
ejpam-5790	104	24	+	+	NOUN
ejpam-5790	104	25	w3⟩	w3⟩	X
ejpam-5790	104	26	⟨λw1,w2⟩	⟨λw1,w2⟩	NOUN
ejpam-5790	105	1	=	=	SYM
ejpam-5790	105	2	λ⟨w1,w2⟩	λ⟨w1,w2⟩	NUM
ejpam-5790	105	3	⟨w1,w2⟩	⟨w1,w2⟩	NOUN
ejpam-5790	105	4	=	=	PUNCT
ejpam-5790	106	1	⟨w2,w1⟩	⟨w2,w1⟩	PROPN
ejpam-5790	106	2	⟨w1,w1⟩	⟨w1,w1⟩	PROPN
ejpam-5790	106	3	≥	≥	NOUN
ejpam-5790	106	4	0	0	NUM
ejpam-5790	106	5	,	,	PUNCT
ejpam-5790	106	6	⟨w1,w1⟩	⟨w1,w1⟩	PUNCT
ejpam-5790	107	1	=	=	SYM
ejpam-5790	107	2	0	0	NUM
ejpam-5790	108	1	⇐	⇐	ADJ
ejpam-5790	108	2	⇒	⇒	NOUN
ejpam-5790	108	3	w1	w1	NOUN
ejpam-5790	108	4	=	=	SYM
ejpam-5790	108	5	0	0	X
ejpam-5790	108	6	.	.	PUNCT
ejpam-5790	109	1	definition	definition	NOUN
ejpam-5790	109	2	2	2	NUM
ejpam-5790	109	3	(	(	PUNCT
ejpam-5790	109	4	see	see	VERB
ejpam-5790	109	5	[	[	X
ejpam-5790	109	6	41	41	NUM
ejpam-5790	109	7	]	]	PUNCT
ejpam-5790	109	8	)	)	PUNCT
ejpam-5790	109	9	.	.	PUNCT
ejpam-5790	110	1	assume	assume	VERB
ejpam-5790	110	2	ℑ	ℑ	NOUN
ejpam-5790	110	3	:	:	PUNCT
ejpam-5790	110	4	u	u	NOUN
ejpam-5790	110	5	×d	×d	NOUN
ejpam-5790	110	6	→	→	PUNCT
ejpam-5790	110	7	r	r	NOUN
ejpam-5790	110	8	be	be	AUX
ejpam-5790	110	9	a	a	DET
ejpam-5790	110	10	function	function	NOUN
ejpam-5790	110	11	.	.	PUNCT
ejpam-5790	111	1	the	the	DET
ejpam-5790	111	2	corresponding	correspond	VERB
ejpam-5790	111	3	product	product	NOUN
ejpam-5790	111	4	of	of	ADP
ejpam-5790	111	5	u	u	NOUN
ejpam-5790	111	6	with	with	ADP
ejpam-5790	111	7	d	d	PROPN
ejpam-5790	111	8	on	on	ADP
ejpam-5790	111	9	hilbert	hilbert	NOUN
ejpam-5790	111	10	space	space	NOUN
ejpam-5790	111	11	r	r	NOUN
ejpam-5790	111	12	is	be	AUX
ejpam-5790	111	13	denoted	denote	VERB
ejpam-5790	111	14	as	as	ADP
ejpam-5790	111	15	•	•	NUM
ejpam-5790	111	16	the	the	DET
ejpam-5790	111	17	space	space	NOUN
ejpam-5790	111	18	r	r	NOUN
ejpam-5790	111	19	be	be	AUX
ejpam-5790	111	20	a	a	DET
ejpam-5790	111	21	collections	collection	NOUN
ejpam-5790	111	22	of	of	ADP
ejpam-5790	111	23	all	all	DET
ejpam-5790	111	24	vectors	vector	NOUN
ejpam-5790	111	25	ℑ(ν1	ℑ(ν1	NOUN
ejpam-5790	111	26	,	,	PUNCT
ejpam-5790	111	27	ν2)(ν1	ν2)(ν1	NOUN
ejpam-5790	111	28	∈	∈	PROPN
ejpam-5790	111	29	u	u	NOUN
ejpam-5790	111	30	,	,	PUNCT
ejpam-5790	111	31	ν2	ν2	PROPN
ejpam-5790	111	32	∈	∈	PROPN
ejpam-5790	111	33	d	d	NOUN
ejpam-5790	111	34	)	)	PUNCT
ejpam-5790	111	35	such	such	ADJ
ejpam-5790	111	36	that	that	SCONJ
ejpam-5790	111	37	r	r	NOUN
ejpam-5790	111	38	is	be	AUX
ejpam-5790	111	39	generated	generate	VERB
ejpam-5790	111	40	;	;	PUNCT
ejpam-5790	112	1	•	•	X
ejpam-5790	112	2	(	(	PUNCT
ejpam-5790	112	3	ℑ	ℑ	PROPN
ejpam-5790	112	4	(	(	PUNCT
ejpam-5790	112	5	ν1	ν1	NOUN
ejpam-5790	112	6	,	,	PUNCT
ejpam-5790	112	7	ν2	ν2	NOUN
ejpam-5790	112	8	)	)	PUNCT
ejpam-5790	112	9	|	|	ADV
ejpam-5790	112	10	ℑ	ℑ	PROPN
ejpam-5790	112	11	(	(	PUNCT
ejpam-5790	112	12	ν3	ν3	NOUN
ejpam-5790	112	13	,	,	PUNCT
ejpam-5790	112	14	ν4	ν4	PROPN
ejpam-5790	112	15	)	)	PUNCT
ejpam-5790	112	16	)	)	PUNCT
ejpam-5790	113	1	=	=	PRON
ejpam-5790	113	2	(	(	PUNCT
ejpam-5790	113	3	ν1	ν1	NOUN
ejpam-5790	113	4	|	|	ADV
ejpam-5790	113	5	ν2	ν2	NOUN
ejpam-5790	113	6	)	)	PUNCT
ejpam-5790	113	7	(	(	PUNCT
ejpam-5790	113	8	ν3	ν3	NOUN
ejpam-5790	113	9	|	|	ADV
ejpam-5790	113	10	ν4	ν4	PROPN
ejpam-5790	113	11	)	)	PUNCT
ejpam-5790	113	12	for	for	ADP
ejpam-5790	113	13	ν1	ν1	NOUN
ejpam-5790	113	14	,	,	PUNCT
ejpam-5790	113	15	ν2	ν2	NOUN
ejpam-5790	113	16	∈	∈	PROPN
ejpam-5790	113	17	u	u	NOUN
ejpam-5790	113	18	,	,	PUNCT
ejpam-5790	113	19	ν3	ν3	NOUN
ejpam-5790	113	20	,	,	PUNCT
ejpam-5790	113	21	ν4	ν4	PROPN
ejpam-5790	113	22	∈	∈	PROPN
ejpam-5790	113	23	d.	d.	PROPN
ejpam-5790	113	24	if	if	SCONJ
ejpam-5790	113	25	(	(	PUNCT
ejpam-5790	113	26	k,ℑ	k,ℑ	PROPN
ejpam-5790	113	27	)	)	PUNCT
ejpam-5790	113	28	is	be	AUX
ejpam-5790	113	29	taken	take	VERB
ejpam-5790	113	30	to	to	PART
ejpam-5790	113	31	be	be	AUX
ejpam-5790	113	32	product	product	NOUN
ejpam-5790	113	33	of	of	ADP
ejpam-5790	113	34	u	u	NOUN
ejpam-5790	113	35	and	and	CCONJ
ejpam-5790	113	36	d	d	NOUN
ejpam-5790	113	37	,	,	PUNCT
ejpam-5790	113	38	it	it	PRON
ejpam-5790	113	39	is	be	AUX
ejpam-5790	113	40	write	write	ADJ
ejpam-5790	113	41	ν1	ν1	NOUN
ejpam-5790	113	42	⊗	⊗	PROPN
ejpam-5790	113	43	ν2	ν2	PROPN
ejpam-5790	113	44	inplace	inplace	NOUN
ejpam-5790	113	45	of	of	ADP
ejpam-5790	113	46	ℑ(ν1	ℑ(ν1	PROPN
ejpam-5790	113	47	,	,	PUNCT
ejpam-5790	113	48	ν2	ν2	NOUN
ejpam-5790	113	49	)	)	PUNCT
ejpam-5790	113	50	.	.	PUNCT
ejpam-5790	114	1	a	a	DET
ejpam-5790	114	2	product	product	NOUN
ejpam-5790	114	3	w.	w.	PROPN
ejpam-5790	114	4	afzal	afzal	PROPN
ejpam-5790	114	5	et	et	PROPN
ejpam-5790	114	6	al	al	PROPN
ejpam-5790	114	7	.	.	PUNCT
ejpam-5790	114	8	/	/	SYM
ejpam-5790	114	9	eur	eur	PROPN
ejpam-5790	114	10	.	.	PUNCT
ejpam-5790	115	1	j.	j.	PROPN
ejpam-5790	115	2	pure	pure	PROPN
ejpam-5790	115	3	appl	appl	PROPN
ejpam-5790	115	4	.	.	PROPN
ejpam-5790	115	5	math	math	PROPN
ejpam-5790	115	6	,	,	PUNCT
ejpam-5790	115	7	18	18	NUM
ejpam-5790	115	8	(	(	PUNCT
ejpam-5790	115	9	1	1	NUM
ejpam-5790	115	10	)	)	PUNCT
ejpam-5790	115	11	(	(	PUNCT
ejpam-5790	115	12	2025	2025	NUM
ejpam-5790	115	13	)	)	PUNCT
ejpam-5790	115	14	,	,	PUNCT
ejpam-5790	115	15	5790	5790	NUM
ejpam-5790	115	16	6	6	NUM
ejpam-5790	115	17	of	of	ADP
ejpam-5790	115	18	30	30	NUM
ejpam-5790	115	19	u	u	NOUN
ejpam-5790	115	20	⊗	⊗	PROPN
ejpam-5790	115	21	d	d	PROPN
ejpam-5790	115	22	and	and	CCONJ
ejpam-5790	115	23	a	a	DET
ejpam-5790	115	24	mapping	mapping	NOUN
ejpam-5790	115	25	(	(	PUNCT
ejpam-5790	115	26	ν1	ν1	NOUN
ejpam-5790	115	27	,	,	PUNCT
ejpam-5790	115	28	ν2	ν2	NOUN
ejpam-5790	115	29	)	)	PUNCT
ejpam-5790	115	30	7→	7→	NUM
ejpam-5790	115	31	ν1	ν1	NOUN
ejpam-5790	115	32	⊗	⊗	ADJ
ejpam-5790	115	33	ν2	ν2	NOUN
ejpam-5790	115	34	of	of	ADP
ejpam-5790	115	35	u	u	NOUN
ejpam-5790	115	36	×	×	PROPN
ejpam-5790	115	37	d	d	PROPN
ejpam-5790	115	38	into	into	ADP
ejpam-5790	115	39	u	u	PROPN
ejpam-5790	115	40	⊗	⊗	PROPN
ejpam-5790	115	41	d	d	PROPN
ejpam-5790	115	42	,	,	PUNCT
ejpam-5790	115	43	holds	hold	VERB
ejpam-5790	115	44	(	(	PUNCT
ejpam-5790	115	45	ν1	ν1	NOUN
ejpam-5790	115	46	+	+	CCONJ
ejpam-5790	115	47	ν2)⊗	ν2)⊗	ADP
ejpam-5790	115	48	ν2	ν2	NOUN
ejpam-5790	115	49	=	=	SYM
ejpam-5790	115	50	ν1	ν1	NOUN
ejpam-5790	115	51	⊗	⊗	NOUN
ejpam-5790	115	52	ν2	ν2	PROPN
ejpam-5790	115	53	+	+	CCONJ
ejpam-5790	115	54	ν2	ν2	ADJ
ejpam-5790	115	55	⊗	⊗	NUM
ejpam-5790	115	56	ν2	ν2	NOUN
ejpam-5790	115	57	(	(	PUNCT
ejpam-5790	115	58	λν1)⊗	λν1)⊗	PROPN
ejpam-5790	115	59	ν2	ν2	NOUN
ejpam-5790	115	60	=	=	SYM
ejpam-5790	115	61	λ(ν1	λ(ν1	NOUN
ejpam-5790	115	62	⊗	⊗	PROPN
ejpam-5790	115	63	ν2	ν2	PROPN
ejpam-5790	115	64	)	)	PUNCT
ejpam-5790	115	65	ν1	ν1	NOUN
ejpam-5790	115	66	⊗	⊗	NOUN
ejpam-5790	115	67	(	(	PUNCT
ejpam-5790	115	68	ν3	ν3	NOUN
ejpam-5790	115	69	+	+	CCONJ
ejpam-5790	115	70	ν4	ν4	PROPN
ejpam-5790	115	71	)	)	PUNCT
ejpam-5790	116	1	=	=	PROPN
ejpam-5790	116	2	ν1	ν1	NOUN
ejpam-5790	116	3	⊗	⊗	PROPN
ejpam-5790	116	4	ν3	ν3	PROPN
ejpam-5790	116	5	+	+	CCONJ
ejpam-5790	116	6	ν1	ν1	NOUN
ejpam-5790	116	7	⊗	⊗	PROPN
ejpam-5790	116	8	ν3	ν3	PROPN
ejpam-5790	116	9	ν1	ν1	NOUN
ejpam-5790	116	10	⊗	⊗	PROPN
ejpam-5790	116	11	(	(	PUNCT
ejpam-5790	116	12	λν2	λν2	PROPN
ejpam-5790	116	13	)	)	PUNCT
ejpam-5790	116	14	=	=	PUNCT
ejpam-5790	116	15	λ(ν1	λ(ν1	NOUN
ejpam-5790	116	16	⊗	⊗	NUM
ejpam-5790	116	17	ν2	ν2	PROPN
ejpam-5790	116	18	)	)	PUNCT
ejpam-5790	116	19	,	,	PUNCT
ejpam-5790	116	20	where	where	SCONJ
ejpam-5790	116	21	λ	λ	PROPN
ejpam-5790	116	22	∈	∈	PROPN
ejpam-5790	116	23	r.	r.	PROPN
ejpam-5790	116	24	assume	assume	VERB
ejpam-5790	116	25	ℑ	ℑ	PROPN
ejpam-5790	116	26	:	:	PUNCT
ejpam-5790	116	27	∆1	∆1	PROPN
ejpam-5790	116	28	×	×	NOUN
ejpam-5790	116	29	.	.	PUNCT
ejpam-5790	116	30	.	.	PUNCT
ejpam-5790	116	31	.	.	PUNCT
ejpam-5790	117	1	×	×	NOUN
ejpam-5790	117	2	∆p	∆p	PROPN
ejpam-5790	117	3	→	→	PUNCT
ejpam-5790	117	4	r	r	NOUN
ejpam-5790	117	5	be	be	AUX
ejpam-5790	117	6	mapping	mapping	NOUN
ejpam-5790	117	7	defined	define	VERB
ejpam-5790	117	8	over	over	ADP
ejpam-5790	117	9	intervals	interval	NOUN
ejpam-5790	117	10	.	.	PUNCT
ejpam-5790	118	1	assume	assume	VERB
ejpam-5790	118	2	that	that	SCONJ
ejpam-5790	118	3	p	p	PROPN
ejpam-5790	118	4	=	=	X
ejpam-5790	118	5	(	(	PUNCT
ejpam-5790	118	6	p1	p1	PROPN
ejpam-5790	118	7	,	,	PUNCT
ejpam-5790	118	8	.	.	PUNCT
ejpam-5790	118	9	.	.	PUNCT
ejpam-5790	119	1	.	.	PUNCT
ejpam-5790	120	1	,	,	PUNCT
ejpam-5790	120	2	pp	pp	CCONJ
ejpam-5790	120	3	)	)	PUNCT
ejpam-5790	120	4	be	be	AUX
ejpam-5790	120	5	a	a	DET
ejpam-5790	120	6	collections	collection	NOUN
ejpam-5790	120	7	of	of	ADP
ejpam-5790	120	8	operators	operator	NOUN
ejpam-5790	120	9	with	with	ADP
ejpam-5790	120	10	e1	e1	NOUN
ejpam-5790	120	11	,	,	PUNCT
ejpam-5790	120	12	.	.	PUNCT
ejpam-5790	120	13	.	.	PUNCT
ejpam-5790	121	1	.	.	PUNCT
ejpam-5790	122	1	,	,	PUNCT
ejpam-5790	122	2	ep	ep	PROPN
ejpam-5790	122	3	are	be	AUX
ejpam-5790	122	4	associated	associate	VERB
ejpam-5790	122	5	hilbert	hilbert	NOUN
ejpam-5790	122	6	spaces	space	NOUN
ejpam-5790	122	7	.	.	PUNCT
ejpam-5790	123	1	then	then	ADV
ejpam-5790	123	2	pi	pi	NOUN
ejpam-5790	124	1	=	=	SYM
ejpam-5790	124	2	∫	∫	PROPN
ejpam-5790	124	3	∆i	∆i	PROPN
ejpam-5790	124	4	widei	widei	PROPN
ejpam-5790	124	5	(	(	PUNCT
ejpam-5790	124	6	wi	wi	PROPN
ejpam-5790	124	7	)	)	PUNCT
ejpam-5790	124	8	is	be	AUX
ejpam-5790	124	9	the	the	DET
ejpam-5790	124	10	spectra	spectra	NOUN
ejpam-5790	124	11	of	of	ADP
ejpam-5790	124	12	possible	possible	ADJ
ejpam-5790	124	13	operators	operator	NOUN
ejpam-5790	124	14	for	for	ADP
ejpam-5790	124	15	i	i	PROPN
ejpam-5790	124	16	=	=	NOUN
ejpam-5790	124	17	1	1	NUM
ejpam-5790	124	18	,	,	PUNCT
ejpam-5790	124	19	.	.	PUNCT
ejpam-5790	124	20	.	.	PUNCT
ejpam-5790	125	1	.	.	PUNCT
ejpam-5790	126	1	,	,	PUNCT
ejpam-5790	126	2	p	p	X
ejpam-5790	126	3	;	;	PUNCT
ejpam-5790	126	4	following	follow	VERB
ejpam-5790	126	5	[	[	X
ejpam-5790	126	6	25	25	NUM
ejpam-5790	126	7	]	]	PUNCT
ejpam-5790	126	8	,	,	PUNCT
ejpam-5790	126	9	we	we	PRON
ejpam-5790	126	10	define	define	VERB
ejpam-5790	126	11	pi	pi	NOUN
ejpam-5790	126	12	as	as	SCONJ
ejpam-5790	126	13	follows	follow	VERB
ejpam-5790	126	14	:	:	PUNCT
ejpam-5790	126	15	ℑ	ℑ	PROPN
ejpam-5790	126	16	(	(	PUNCT
ejpam-5790	126	17	p1	p1	PROPN
ejpam-5790	126	18	,	,	PUNCT
ejpam-5790	126	19	.	.	PUNCT
ejpam-5790	126	20	.	.	PUNCT
ejpam-5790	127	1	.	.	PUNCT
ejpam-5790	128	1	,	,	PUNCT
ejpam-5790	128	2	pp	pp	ADV
ejpam-5790	128	3	)	)	PUNCT
ejpam-5790	128	4	:	:	PUNCT
ejpam-5790	129	1	=	=	SYM
ejpam-5790	129	2	∫	∫	PROPN
ejpam-5790	129	3	∆1	∆1	PROPN
ejpam-5790	129	4	.	.	PUNCT
ejpam-5790	129	5	.	.	PUNCT
ejpam-5790	129	6	.	.	PUNCT
ejpam-5790	130	1	∫	∫	PROPN
ejpam-5790	130	2	∆p	∆p	PROPN
ejpam-5790	130	3	ℑ	ℑ	PROPN
ejpam-5790	130	4	(	(	PUNCT
ejpam-5790	130	5	w1	w1	NOUN
ejpam-5790	130	6	,	,	PUNCT
ejpam-5790	130	7	.	.	PUNCT
ejpam-5790	130	8	.	.	PUNCT
ejpam-5790	130	9	.	.	PUNCT
ejpam-5790	131	1	,	,	PUNCT
ejpam-5790	131	2	wp	wp	PROPN
ejpam-5790	131	3	)	)	PUNCT
ejpam-5790	131	4	de1	de1	PROPN
ejpam-5790	131	5	(	(	PUNCT
ejpam-5790	131	6	w1)⊗	w1)⊗	NOUN
ejpam-5790	131	7	.	.	PUNCT
ejpam-5790	131	8	.	.	PUNCT
ejpam-5790	132	1	.⊗	.⊗	PROPN
ejpam-5790	132	2	dep	dep	PROPN
ejpam-5790	132	3	(	(	PUNCT
ejpam-5790	132	4	wp	wp	PROPN
ejpam-5790	132	5	)	)	PUNCT
ejpam-5790	132	6	.	.	PUNCT
ejpam-5790	133	1	integrating	integrate	VERB
ejpam-5790	133	2	processes	process	NOUN
ejpam-5790	133	3	into	into	ADP
ejpam-5790	133	4	finite	finite	ADJ
ejpam-5790	133	5	summations	summation	NOUN
ejpam-5790	133	6	can	can	AUX
ejpam-5790	133	7	significantly	significantly	ADV
ejpam-5790	133	8	reduce	reduce	VERB
ejpam-5790	133	9	the	the	DET
ejpam-5790	133	10	complexity	complexity	NOUN
ejpam-5790	133	11	of	of	ADP
ejpam-5790	133	12	many	many	ADJ
ejpam-5790	133	13	complex	complex	ADJ
ejpam-5790	133	14	processes	process	NOUN
ejpam-5790	133	15	when	when	SCONJ
ejpam-5790	133	16	the	the	DET
ejpam-5790	133	17	dimensions	dimension	NOUN
ejpam-5790	133	18	of	of	ADP
ejpam-5790	133	19	hilbert	hilbert	PROPN
ejpam-5790	133	20	spaces	space	NOUN
ejpam-5790	133	21	are	be	AUX
ejpam-5790	133	22	finite	finite	ADJ
ejpam-5790	133	23	.	.	PUNCT
ejpam-5790	134	1	in	in	ADP
ejpam-5790	134	2	[	[	X
ejpam-5790	134	3	68	68	NUM
ejpam-5790	134	4	]	]	PUNCT
ejpam-5790	134	5	,	,	PUNCT
ejpam-5790	134	6	the	the	DET
ejpam-5790	134	7	author	author	NOUN
ejpam-5790	134	8	elaborates	elaborate	VERB
ejpam-5790	134	9	on	on	ADP
ejpam-5790	134	10	the	the	DET
ejpam-5790	134	11	construction	construction	NOUN
ejpam-5790	134	12	[	[	X
ejpam-5790	134	13	25	25	NUM
ejpam-5790	134	14	]	]	PUNCT
ejpam-5790	134	15	and	and	CCONJ
ejpam-5790	134	16	defines	define	VERB
ejpam-5790	134	17	it	it	PRON
ejpam-5790	134	18	as	as	SCONJ
ejpam-5790	134	19	follows	follow	VERB
ejpam-5790	134	20	:	:	PUNCT
ejpam-5790	134	21	ℑ	ℑ	PROPN
ejpam-5790	134	22	(	(	PUNCT
ejpam-5790	134	23	p1	p1	PROPN
ejpam-5790	134	24	,	,	PUNCT
ejpam-5790	134	25	.	.	PUNCT
ejpam-5790	134	26	.	.	PUNCT
ejpam-5790	134	27	.	.	PUNCT
ejpam-5790	135	1	,	,	PUNCT
ejpam-5790	135	2	pp	pp	ADV
ejpam-5790	135	3	)	)	PUNCT
ejpam-5790	135	4	=	=	SYM
ejpam-5790	135	5	ℑ1	ℑ1	PROPN
ejpam-5790	135	6	(	(	PUNCT
ejpam-5790	135	7	p1)⊗	p1)⊗	NOUN
ejpam-5790	135	8	.	.	PUNCT
ejpam-5790	135	9	.	.	PUNCT
ejpam-5790	136	1	.⊗ℑp	.⊗ℑp	PUNCT
ejpam-5790	137	1	(	(	PUNCT
ejpam-5790	137	2	pp	pp	ADP
ejpam-5790	137	3	)	)	PUNCT
ejpam-5790	137	4	,	,	PUNCT
ejpam-5790	137	5	where	where	SCONJ
ejpam-5790	137	6	ℑ	ℑ	PROPN
ejpam-5790	137	7	is	be	AUX
ejpam-5790	137	8	a	a	DET
ejpam-5790	137	9	product	product	NOUN
ejpam-5790	137	10	of	of	ADP
ejpam-5790	137	11	one	one	NUM
ejpam-5790	137	12	variable	variable	ADJ
ejpam-5790	137	13	mapping	mapping	NOUN
ejpam-5790	137	14	and	and	CCONJ
ejpam-5790	137	15	can	can	AUX
ejpam-5790	137	16	be	be	AUX
ejpam-5790	137	17	split	split	VERB
ejpam-5790	137	18	.	.	PUNCT
ejpam-5790	138	1	ℑ	ℑ	PROPN
ejpam-5790	138	2	(	(	PUNCT
ejpam-5790	138	3	a1	a1	PROPN
ejpam-5790	138	4	,	,	PUNCT
ejpam-5790	138	5	.	.	PUNCT
ejpam-5790	138	6	.	.	PUNCT
ejpam-5790	138	7	.	.	PUNCT
ejpam-5790	139	1	,	,	PUNCT
ejpam-5790	139	2	ap	ap	PROPN
ejpam-5790	139	3	)	)	PUNCT
ejpam-5790	140	1	=	=	SYM
ejpam-5790	140	2	ℑ1	ℑ1	NOUN
ejpam-5790	140	3	(	(	PUNCT
ejpam-5790	140	4	a1	a1	PROPN
ejpam-5790	140	5	)	)	PUNCT
ejpam-5790	140	6	.	.	PUNCT
ejpam-5790	140	7	.	.	PUNCT
ejpam-5790	141	1	.ℑp	.ℑp	PROPN
ejpam-5790	142	1	(	(	PUNCT
ejpam-5790	142	2	ap	ap	PROPN
ejpam-5790	142	3	)	)	PUNCT
ejpam-5790	142	4	.	.	PUNCT
ejpam-5790	143	1	if	if	SCONJ
ejpam-5790	143	2	ℑ	ℑ	PROPN
ejpam-5790	143	3	is	be	AUX
ejpam-5790	143	4	sub(super)-multiplicative	sub(super)-multiplicative	ADJ
ejpam-5790	143	5	across	across	ADP
ejpam-5790	143	6	the	the	DET
ejpam-5790	143	7	interval	interval	NOUN
ejpam-5790	143	8	∆	∆	PROPN
ejpam-5790	143	9	,	,	PUNCT
ejpam-5790	143	10	then	then	ADV
ejpam-5790	143	11	ℑ(ν1ν2	ℑ(ν1ν2	NOUN
ejpam-5790	143	12	)	)	PUNCT
ejpam-5790	143	13	≥	≥	PROPN
ejpam-5790	143	14	(	(	PUNCT
ejpam-5790	143	15	≤)ℑ(ν1)ℑ(ν2	≤)ℑ(ν1)ℑ(ν2	PROPN
ejpam-5790	143	16	)	)	PUNCT
ejpam-5790	143	17	for	for	ADP
ejpam-5790	143	18	all	all	PRON
ejpam-5790	143	19	ν1ν2	ν1ν2	ADP
ejpam-5790	143	20	∈	∈	PROPN
ejpam-5790	143	21	[	[	X
ejpam-5790	143	22	0,∞	0,∞	NOUN
ejpam-5790	143	23	)	)	PUNCT
ejpam-5790	143	24	.	.	PUNCT
ejpam-5790	144	1	if	if	SCONJ
ejpam-5790	144	2	ℑ	ℑ	PROPN
ejpam-5790	144	3	is	be	AUX
ejpam-5790	144	4	continuous	continuous	ADJ
ejpam-5790	144	5	on	on	ADP
ejpam-5790	144	6	the	the	DET
ejpam-5790	144	7	interval	interval	NOUN
ejpam-5790	144	8	[	[	X
ejpam-5790	144	9	0,∞	0,∞	NOUN
ejpam-5790	144	10	)	)	PUNCT
ejpam-5790	144	11	,	,	PUNCT
ejpam-5790	144	12	then	then	ADV
ejpam-5790	144	13	ℑ(u	ℑ(u	VERB
ejpam-5790	144	14	⊗	⊗	PROPN
ejpam-5790	144	15	d	d	PROPN
ejpam-5790	144	16	)	)	PUNCT
ejpam-5790	144	17	≥	≥	NOUN
ejpam-5790	144	18	(	(	PUNCT
ejpam-5790	144	19	≤)ℑ(u)⊗ℑ(d	≤)ℑ(u)⊗ℑ(d	PROPN
ejpam-5790	144	20	)	)	PUNCT
ejpam-5790	144	21	for	for	ADP
ejpam-5790	144	22	all	all	DET
ejpam-5790	144	23	u	u	NOUN
ejpam-5790	144	24	,	,	PUNCT
ejpam-5790	144	25	d	d	PROPN
ejpam-5790	144	26	≥	≥	NOUN
ejpam-5790	144	27	0	0	NUM
ejpam-5790	144	28	.	.	PUNCT
ejpam-5790	145	1	this	this	PRON
ejpam-5790	145	2	leads	lead	VERB
ejpam-5790	145	3	to	to	ADP
ejpam-5790	145	4	the	the	DET
ejpam-5790	145	5	conclusion	conclusion	NOUN
ejpam-5790	145	6	that	that	SCONJ
ejpam-5790	145	7	,	,	PUNCT
ejpam-5790	145	8	if	if	SCONJ
ejpam-5790	145	9	u	u	PRON
ejpam-5790	145	10	=	=	SYM
ejpam-5790	145	11	∫	∫	PROPN
ejpam-5790	145	12	[	[	X
ejpam-5790	145	13	0,∞	0,∞	NUM
ejpam-5790	145	14	)	)	PUNCT
ejpam-5790	145	15	ν1de(ν1	ν1de(ν1	PROPN
ejpam-5790	145	16	)	)	PUNCT
ejpam-5790	145	17	and	and	CCONJ
ejpam-5790	145	18	d	d	NOUN
ejpam-5790	145	19	=	=	SYM
ejpam-5790	145	20	∫	∫	PROPN
ejpam-5790	146	1	[	[	X
ejpam-5790	146	2	0,∞	0,∞	X
ejpam-5790	146	3	)	)	PUNCT
ejpam-5790	146	4	ν2df(ν2	ν2df(ν2	NUM
ejpam-5790	146	5	)	)	PUNCT
ejpam-5790	146	6	are	be	AUX
ejpam-5790	146	7	the	the	DET
ejpam-5790	146	8	assocaited	assocaite	VERB
ejpam-5790	146	9	spectrums	spectrum	NOUN
ejpam-5790	146	10	.	.	PUNCT
ejpam-5790	147	1	ℑ(u	ℑ(u	PUNCT
ejpam-5790	148	1	⊗	⊗	PROPN
ejpam-5790	148	2	d	d	NOUN
ejpam-5790	148	3	)	)	PUNCT
ejpam-5790	148	4	=	=	SYM
ejpam-5790	149	1	∫	∫	PROPN
ejpam-5790	150	1	[	[	X
ejpam-5790	150	2	0,∞	0,∞	NUM
ejpam-5790	150	3	)	)	PUNCT
ejpam-5790	150	4	∫	∫	PROPN
ejpam-5790	151	1	[	[	X
ejpam-5790	151	2	0,∞	0,∞	NOUN
ejpam-5790	151	3	)	)	PUNCT
ejpam-5790	151	4	ℑ(ν1ν2)de(ν1)⊗	ℑ(ν1ν2)de(ν1)⊗	PROPN
ejpam-5790	151	5	df(ν2	df(ν2	PROPN
ejpam-5790	151	6	)	)	PUNCT
ejpam-5790	151	7	.	.	PUNCT
ejpam-5790	152	1	the	the	DET
ejpam-5790	152	2	geometric	geometric	ADJ
ejpam-5790	152	3	property	property	NOUN
ejpam-5790	152	4	of	of	ADP
ejpam-5790	152	5	linear	linear	PROPN
ejpam-5790	152	6	bounded	bound	VERB
ejpam-5790	152	7	operator	operator	NOUN
ejpam-5790	152	8	u	u	NOUN
ejpam-5790	152	9	,	,	PUNCT
ejpam-5790	152	10	d	d	PROPN
ejpam-5790	152	11	>	>	X
ejpam-5790	152	12	0	0	NUM
ejpam-5790	152	13	is	be	AUX
ejpam-5790	152	14	defined	define	VERB
ejpam-5790	152	15	as	as	SCONJ
ejpam-5790	152	16	follows	follow	VERB
ejpam-5790	152	17	.	.	PUNCT
ejpam-5790	153	1	w.	w.	PROPN
ejpam-5790	153	2	afzal	afzal	PROPN
ejpam-5790	153	3	et	et	PROPN
ejpam-5790	153	4	al	al	PROPN
ejpam-5790	153	5	.	.	PUNCT
ejpam-5790	153	6	/	/	SYM
ejpam-5790	153	7	eur	eur	PROPN
ejpam-5790	153	8	.	.	PUNCT
ejpam-5790	154	1	j.	j.	PROPN
ejpam-5790	154	2	pure	pure	PROPN
ejpam-5790	154	3	appl	appl	PROPN
ejpam-5790	154	4	.	.	PROPN
ejpam-5790	154	5	math	math	PROPN
ejpam-5790	154	6	,	,	PUNCT
ejpam-5790	154	7	18	18	NUM
ejpam-5790	154	8	(	(	PUNCT
ejpam-5790	154	9	1	1	NUM
ejpam-5790	154	10	)	)	PUNCT
ejpam-5790	154	11	(	(	PUNCT
ejpam-5790	154	12	2025	2025	NUM
ejpam-5790	154	13	)	)	PUNCT
ejpam-5790	154	14	,	,	PUNCT
ejpam-5790	154	15	5790	5790	NUM
ejpam-5790	154	16	7	7	NUM
ejpam-5790	154	17	of	of	ADP
ejpam-5790	154	18	30	30	NUM
ejpam-5790	154	19	u#pd	u#pd	NOUN
ejpam-5790	154	20	:	:	PUNCT
ejpam-5790	154	21	=	=	SYM
ejpam-5790	154	22	u1/2	u1/2	PROPN
ejpam-5790	154	23	(	(	PUNCT
ejpam-5790	154	24	u−1/2du−1/2	u−1/2du−1/2	NOUN
ejpam-5790	154	25	)	)	PUNCT
ejpam-5790	154	26	p	p	NOUN
ejpam-5790	154	27	u1/2	u1/2	PROPN
ejpam-5790	154	28	,	,	PUNCT
ejpam-5790	155	1	where	where	SCONJ
ejpam-5790	155	2	p	p	PRON
ejpam-5790	155	3	∈	∈	PROPN
ejpam-5790	156	1	[	[	X
ejpam-5790	156	2	0	0	NUM
ejpam-5790	156	3	,	,	PUNCT
ejpam-5790	156	4	1	1	NUM
ejpam-5790	156	5	]	]	PUNCT
ejpam-5790	156	6	and	and	CCONJ
ejpam-5790	156	7	u#d	u#d	ADJ
ejpam-5790	156	8	:	:	PUNCT
ejpam-5790	156	9	=	=	SYM
ejpam-5790	156	10	u1/2	u1/2	PROPN
ejpam-5790	156	11	(	(	PUNCT
ejpam-5790	156	12	u−1/2du−1/2	u−1/2du−1/2	NOUN
ejpam-5790	156	13	)	)	PUNCT
ejpam-5790	156	14	1/2	1/2	NUM
ejpam-5790	156	15	u1/2	u1/2	NOUN
ejpam-5790	156	16	.	.	PUNCT
ejpam-5790	157	1	by	by	ADP
ejpam-5790	157	2	the	the	DET
ejpam-5790	157	3	definitions	definition	NOUN
ejpam-5790	157	4	of	of	ADP
ejpam-5790	157	5	#	#	NOUN
ejpam-5790	157	6	and	and	CCONJ
ejpam-5790	157	7	⊗	⊗	NOUN
ejpam-5790	157	8	we	we	PRON
ejpam-5790	157	9	have	have	VERB
ejpam-5790	157	10	u#d	u#d	PROPN
ejpam-5790	157	11	=	=	PRON
ejpam-5790	158	1	d#u	d#u	PROPN
ejpam-5790	158	2	and	and	CCONJ
ejpam-5790	158	3	(	(	PUNCT
ejpam-5790	158	4	u#d)⊗	u#d)⊗	NOUN
ejpam-5790	158	5	(	(	PUNCT
ejpam-5790	158	6	d#u	d#u	NOUN
ejpam-5790	158	7	)	)	PUNCT
ejpam-5790	158	8	=	=	SYM
ejpam-5790	158	9	(	(	PUNCT
ejpam-5790	158	10	u	u	NOUN
ejpam-5790	158	11	⊗	⊗	PROPN
ejpam-5790	158	12	d)#(d	d)#(d	PROPN
ejpam-5790	158	13	⊗	⊗	PROPN
ejpam-5790	158	14	u	u	NOUN
ejpam-5790	158	15	)	)	PUNCT
ejpam-5790	158	16	.	.	PUNCT
ejpam-5790	159	1	consider	consider	VERB
ejpam-5790	159	2	the	the	DET
ejpam-5790	159	3	eventually	eventually	ADV
ejpam-5790	159	4	similar	similar	ADJ
ejpam-5790	159	5	to	to	ADP
ejpam-5790	159	6	the	the	DET
ejpam-5790	159	7	tensorial	tensorial	ADJ
ejpam-5790	159	8	product	product	NOUN
ejpam-5790	159	9	:	:	PUNCT
ejpam-5790	159	10	(	(	PUNCT
ejpam-5790	159	11	uβ)⊗	uβ)⊗	X
ejpam-5790	159	12	(	(	PUNCT
ejpam-5790	159	13	ds	ds	ADJ
ejpam-5790	159	14	)	)	PUNCT
ejpam-5790	159	15	=	=	PUNCT
ejpam-5790	159	16	(	(	PUNCT
ejpam-5790	159	17	u	u	NOUN
ejpam-5790	159	18	⊗	⊗	PROPN
ejpam-5790	159	19	d)(u	d)(u	PROPN
ejpam-5790	159	20	⊗	⊗	PROPN
ejpam-5790	159	21	s	s	PROPN
ejpam-5790	159	22	)	)	PUNCT
ejpam-5790	159	23	,	,	PUNCT
ejpam-5790	159	24	that	that	PRON
ejpam-5790	159	25	holds	hold	VERB
ejpam-5790	159	26	∀u	∀u	NOUN
ejpam-5790	159	27	,	,	PUNCT
ejpam-5790	159	28	d	d	PROPN
ejpam-5790	159	29	,	,	PUNCT
ejpam-5790	159	30	β	β	X
ejpam-5790	159	31	,	,	PUNCT
ejpam-5790	159	32	s	s	PROPN
ejpam-5790	159	33	∈	∈	PROPN
ejpam-5790	159	34	b(ν2	b(ν2	NOUN
ejpam-5790	159	35	)	)	PUNCT
ejpam-5790	159	36	.	.	PUNCT
ejpam-5790	160	1	if	if	SCONJ
ejpam-5790	160	2	we	we	PRON
ejpam-5790	160	3	take	take	VERB
ejpam-5790	160	4	β	β	NOUN
ejpam-5790	160	5	=	=	SYM
ejpam-5790	160	6	u	u	NOUN
ejpam-5790	160	7	and	and	CCONJ
ejpam-5790	160	8	s	s	NOUN
ejpam-5790	160	9	=	=	SYM
ejpam-5790	160	10	d	d	PROPN
ejpam-5790	160	11	,	,	PUNCT
ejpam-5790	160	12	then	then	ADV
ejpam-5790	160	13	we	we	PRON
ejpam-5790	160	14	get	get	VERB
ejpam-5790	160	15	u2	u2	NOUN
ejpam-5790	160	16	⊗d2	⊗d2	PROPN
ejpam-5790	160	17	=	=	PUNCT
ejpam-5790	160	18	(	(	PUNCT
ejpam-5790	160	19	u	u	NOUN
ejpam-5790	160	20	⊗	⊗	PROPN
ejpam-5790	160	21	d)2	d)2	PROPN
ejpam-5790	160	22	.	.	PUNCT
ejpam-5790	161	1	through	through	ADP
ejpam-5790	161	2	induction	induction	NOUN
ejpam-5790	161	3	,	,	PUNCT
ejpam-5790	161	4	we	we	PRON
ejpam-5790	161	5	have	have	VERB
ejpam-5790	161	6	up	up	ADP
ejpam-5790	161	7	⊗dp	⊗dp	ADV
ejpam-5790	162	1	=	=	SYM
ejpam-5790	162	2	(	(	PUNCT
ejpam-5790	162	3	u	u	NOUN
ejpam-5790	162	4	⊗	⊗	PROPN
ejpam-5790	162	5	d)p	d)p	NOUN
ejpam-5790	162	6	for	for	ADP
ejpam-5790	162	7	natural	natural	ADJ
ejpam-5790	162	8	number	number	NOUN
ejpam-5790	162	9	σ	σ	PROPN
ejpam-5790	162	10	≥	≥	PROPN
ejpam-5790	162	11	0	0	NUM
ejpam-5790	162	12	.	.	PUNCT
ejpam-5790	163	1	specifically	specifically	ADV
ejpam-5790	163	2	uκ	uκ	INTJ
ejpam-5790	163	3	⊗	⊗	PROPN
ejpam-5790	163	4	1	1	NUM
ejpam-5790	164	1	=	=	SYM
ejpam-5790	164	2	(	(	PUNCT
ejpam-5790	164	3	u	u	NOUN
ejpam-5790	164	4	⊗	⊗	PROPN
ejpam-5790	164	5	1)κ	1)κ	NUM
ejpam-5790	164	6	and	and	CCONJ
ejpam-5790	164	7	1⊗dκ	1⊗dκ	NUM
ejpam-5790	164	8	=	=	SYM
ejpam-5790	164	9	(	(	PUNCT
ejpam-5790	164	10	1⊗d)κ	1⊗d)κ	NUM
ejpam-5790	164	11	for	for	ADP
ejpam-5790	164	12	all	all	DET
ejpam-5790	164	13	κ	κ	PRON
ejpam-5790	164	14	≥	≥	NOUN
ejpam-5790	164	15	0	0	NUM
ejpam-5790	164	16	.	.	PUNCT
ejpam-5790	165	1	additionally	additionally	ADV
ejpam-5790	165	2	,	,	PUNCT
ejpam-5790	165	3	we	we	PRON
ejpam-5790	165	4	note	note	VERB
ejpam-5790	165	5	that	that	SCONJ
ejpam-5790	165	6	the	the	DET
ejpam-5790	165	7	1⊗d	1⊗d	PROPN
ejpam-5790	165	8	and	and	CCONJ
ejpam-5790	165	9	u	u	NOUN
ejpam-5790	165	10	⊗	⊗	PROPN
ejpam-5790	165	11	1	1	NUM
ejpam-5790	165	12	are	be	AUX
ejpam-5790	165	13	commutative	commutative	ADJ
ejpam-5790	165	14	with	with	ADP
ejpam-5790	165	15	each	each	DET
ejpam-5790	165	16	other	other	ADJ
ejpam-5790	165	17	(	(	PUNCT
ejpam-5790	165	18	u	u	NOUN
ejpam-5790	165	19	⊗	⊗	PROPN
ejpam-5790	165	20	1)(1⊗d	1)(1⊗d	NUM
ejpam-5790	165	21	)	)	PUNCT
ejpam-5790	165	22	=	=	PUNCT
ejpam-5790	166	1	(	(	PUNCT
ejpam-5790	166	2	1⊗d)(u	1⊗d)(u	NUM
ejpam-5790	166	3	⊗	⊗	PROPN
ejpam-5790	166	4	1	1	NUM
ejpam-5790	166	5	)	)	PUNCT
ejpam-5790	166	6	=	=	SYM
ejpam-5790	166	7	u	u	PROPN
ejpam-5790	166	8	⊗	⊗	PROPN
ejpam-5790	166	9	d.	d.	PROPN
ejpam-5790	166	10	moreover	moreover	ADV
ejpam-5790	166	11	,	,	PUNCT
ejpam-5790	166	12	for	for	ADP
ejpam-5790	166	13	any	any	DET
ejpam-5790	166	14	two	two	NUM
ejpam-5790	166	15	natural	natural	ADJ
ejpam-5790	166	16	numbers	number	NOUN
ejpam-5790	166	17	κ1	κ1	NOUN
ejpam-5790	166	18	,	,	PUNCT
ejpam-5790	166	19	κ2	κ2	PROPN
ejpam-5790	166	20	(	(	PUNCT
ejpam-5790	166	21	u	u	NOUN
ejpam-5790	166	22	⊗	⊗	PROPN
ejpam-5790	166	23	1)κ1(1⊗d)κ2	1)κ1(1⊗d)κ2	PROPN
ejpam-5790	166	24	=	=	SYM
ejpam-5790	166	25	(	(	PUNCT
ejpam-5790	166	26	1⊗d)κ1(u	1⊗d)κ1(u	NUM
ejpam-5790	166	27	⊗	⊗	PROPN
ejpam-5790	166	28	1)κ2	1)κ2	PROPN
ejpam-5790	166	29	=	=	PUNCT
ejpam-5790	167	1	uκ2	uκ2	INTJ
ejpam-5790	167	2	⊗dκ1	⊗dκ1	PROPN
ejpam-5790	167	3	.	.	PUNCT
ejpam-5790	168	1	definition	definition	NOUN
ejpam-5790	168	2	3	3	NUM
ejpam-5790	168	3	(	(	PUNCT
ejpam-5790	168	4	see	see	VERB
ejpam-5790	168	5	[	[	X
ejpam-5790	168	6	3	3	NUM
ejpam-5790	168	7	]	]	NUM
ejpam-5790	168	8	)	)	PUNCT
ejpam-5790	168	9	.	.	PUNCT
ejpam-5790	169	1	a	a	DET
ejpam-5790	169	2	function	function	NOUN
ejpam-5790	169	3	ℑ	ℑ	NOUN
ejpam-5790	169	4	:	:	PUNCT
ejpam-5790	169	5	∆	∆	PROPN
ejpam-5790	169	6	→	→	PUNCT
ejpam-5790	169	7	r	r	NOUN
ejpam-5790	169	8	is	be	AUX
ejpam-5790	169	9	known	know	VERB
ejpam-5790	169	10	as	as	ADP
ejpam-5790	169	11	convex	convex	NOUN
ejpam-5790	169	12	over	over	ADP
ejpam-5790	169	13	∆	∆	PROPN
ejpam-5790	169	14	,	,	PUNCT
ejpam-5790	169	15	if	if	SCONJ
ejpam-5790	169	16	ℑ(wν1	ℑ(wν1	ADP
ejpam-5790	169	17	+	+	X
ejpam-5790	169	18	(	(	PUNCT
ejpam-5790	169	19	1−w)ν2	1−w)ν2	NUM
ejpam-5790	169	20	)	)	PUNCT
ejpam-5790	169	21	≤	≤	NOUN
ejpam-5790	169	22	(	(	PUNCT
ejpam-5790	169	23	≥)wℑ(ν1	≥)wℑ(ν1	NUM
ejpam-5790	169	24	)	)	PUNCT
ejpam-5790	169	25	+	+	CCONJ
ejpam-5790	169	26	(	(	PUNCT
ejpam-5790	169	27	1−w)ℑ(ν2	1−w)ℑ(ν2	NUM
ejpam-5790	169	28	)	)	PUNCT
ejpam-5790	169	29	valid	valid	NOUN
ejpam-5790	169	30	for	for	ADP
ejpam-5790	169	31	all	all	DET
ejpam-5790	169	32	ν1	ν1	NOUN
ejpam-5790	169	33	,	,	PUNCT
ejpam-5790	169	34	ν2	ν2	NOUN
ejpam-5790	169	35	∈	∈	NOUN
ejpam-5790	169	36	∆	∆	PROPN
ejpam-5790	169	37	and	and	CCONJ
ejpam-5790	169	38	w	w	PROPN
ejpam-5790	169	39	∈	∈	PROPN
ejpam-5790	170	1	[	[	X
ejpam-5790	170	2	0	0	NUM
ejpam-5790	170	3	,	,	PUNCT
ejpam-5790	170	4	1	1	NUM
ejpam-5790	170	5	]	]	PUNCT
ejpam-5790	170	6	.	.	PUNCT
ejpam-5790	171	1	definition	definition	NOUN
ejpam-5790	171	2	4	4	NUM
ejpam-5790	171	3	(	(	PUNCT
ejpam-5790	171	4	see	see	VERB
ejpam-5790	171	5	[	[	X
ejpam-5790	171	6	3	3	NUM
ejpam-5790	171	7	]	]	NUM
ejpam-5790	171	8	)	)	PUNCT
ejpam-5790	171	9	.	.	PUNCT
ejpam-5790	172	1	a	a	DET
ejpam-5790	172	2	mapping	mapping	NOUN
ejpam-5790	172	3	ℑ	ℑ	NOUN
ejpam-5790	172	4	:	:	PUNCT
ejpam-5790	172	5	∆	∆	PROPN
ejpam-5790	172	6	→	→	PUNCT
ejpam-5790	172	7	r	r	NOUN
ejpam-5790	172	8	is	be	AUX
ejpam-5790	172	9	known	know	VERB
ejpam-5790	172	10	as	as	ADP
ejpam-5790	172	11	convex	convex	NOUN
ejpam-5790	172	12	in	in	ADP
ejpam-5790	172	13	quasi	quasi	ADJ
ejpam-5790	172	14	sense	sense	NOUN
ejpam-5790	172	15	,	,	PUNCT
ejpam-5790	172	16	if	if	SCONJ
ejpam-5790	172	17	ℑ((1−w)ν1	ℑ((1−w)ν1	PROPN
ejpam-5790	172	18	+	+	NOUN
ejpam-5790	172	19	wν2	wν2	NOUN
ejpam-5790	172	20	)	)	PUNCT
ejpam-5790	172	21	≤	≤	NUM
ejpam-5790	172	22	max{ℑ(ν2),ℑ(ν1	max{ℑ(ν2),ℑ(ν1	NOUN
ejpam-5790	172	23	)	)	PUNCT
ejpam-5790	172	24	}	}	PUNCT
ejpam-5790	172	25	=	=	SYM
ejpam-5790	172	26	1	1	NUM
ejpam-5790	172	27	2	2	NUM
ejpam-5790	172	28	(	(	PUNCT
ejpam-5790	172	29	ℑ(ν2	ℑ(ν2	PROPN
ejpam-5790	172	30	)	)	PUNCT
ejpam-5790	172	31	+	+	CCONJ
ejpam-5790	172	32	ℑ(ν1	ℑ(ν1	NOUN
ejpam-5790	172	33	)	)	PUNCT
ejpam-5790	172	34	+	+	NUM
ejpam-5790	172	35	|ℑ(ν2)−d(ν1)|	|ℑ(ν2)−d(ν1)|	PROPN
ejpam-5790	172	36	)	)	PUNCT
ejpam-5790	172	37	for	for	ADP
ejpam-5790	172	38	all	all	DET
ejpam-5790	172	39	ν1	ν1	NOUN
ejpam-5790	172	40	,	,	PUNCT
ejpam-5790	172	41	ν2	ν2	NOUN
ejpam-5790	172	42	∈	∈	NOUN
ejpam-5790	172	43	∆	∆	PROPN
ejpam-5790	172	44	and	and	CCONJ
ejpam-5790	172	45	w	w	PROPN
ejpam-5790	172	46	∈	∈	PROPN
ejpam-5790	173	1	[	[	X
ejpam-5790	173	2	0	0	NUM
ejpam-5790	173	3	,	,	PUNCT
ejpam-5790	173	4	1	1	NUM
ejpam-5790	173	5	]	]	PUNCT
ejpam-5790	173	6	.	.	PUNCT
ejpam-5790	174	1	w.	w.	PROPN
ejpam-5790	174	2	afzal	afzal	PROPN
ejpam-5790	174	3	et	et	PROPN
ejpam-5790	174	4	al	al	PROPN
ejpam-5790	174	5	.	.	PUNCT
ejpam-5790	174	6	/	/	SYM
ejpam-5790	174	7	eur	eur	PROPN
ejpam-5790	174	8	.	.	PUNCT
ejpam-5790	175	1	j.	j.	PROPN
ejpam-5790	175	2	pure	pure	PROPN
ejpam-5790	175	3	appl	appl	PROPN
ejpam-5790	175	4	.	.	PROPN
ejpam-5790	175	5	math	math	PROPN
ejpam-5790	175	6	,	,	PUNCT
ejpam-5790	175	7	18	18	NUM
ejpam-5790	175	8	(	(	PUNCT
ejpam-5790	175	9	1	1	NUM
ejpam-5790	175	10	)	)	PUNCT
ejpam-5790	175	11	(	(	PUNCT
ejpam-5790	175	12	2025	2025	NUM
ejpam-5790	175	13	)	)	PUNCT
ejpam-5790	175	14	,	,	PUNCT
ejpam-5790	175	15	5790	5790	NUM
ejpam-5790	175	16	8	8	NUM
ejpam-5790	175	17	of	of	ADP
ejpam-5790	175	18	30	30	NUM
ejpam-5790	175	19	some	some	DET
ejpam-5790	175	20	needed	need	VERB
ejpam-5790	175	21	technical	technical	ADJ
ejpam-5790	175	22	lemmas	lemmas	PROPN
ejpam-5790	175	23	lemma	lemma	PROPN
ejpam-5790	175	24	1	1	X
ejpam-5790	175	25	.	.	PUNCT
ejpam-5790	176	1	let	let	VERB
ejpam-5790	176	2	u	u	PRON
ejpam-5790	176	3	and	and	CCONJ
ejpam-5790	176	4	d	d	NOUN
ejpam-5790	176	5	be	be	AUX
ejpam-5790	176	6	self	self	NOUN
ejpam-5790	176	7	-	-	PUNCT
ejpam-5790	176	8	adjoint	adjoint	NOUN
ejpam-5790	176	9	operators	operator	NOUN
ejpam-5790	176	10	such	such	ADJ
ejpam-5790	176	11	that	that	SCONJ
ejpam-5790	176	12	the	the	DET
ejpam-5790	176	13	spectra	spectra	NOUN
ejpam-5790	176	14	of	of	ADP
ejpam-5790	176	15	u	u	PROPN
ejpam-5790	176	16	and	and	CCONJ
ejpam-5790	176	17	d	d	PROPN
ejpam-5790	176	18	are	be	AUX
ejpam-5790	176	19	contained	contain	VERB
ejpam-5790	176	20	within	within	ADP
ejpam-5790	176	21	the	the	DET
ejpam-5790	176	22	set	set	NOUN
ejpam-5790	176	23	∆	∆	PROPN
ejpam-5790	176	24	(	(	PUNCT
ejpam-5790	176	25	i.e.	i.e.	X
ejpam-5790	176	26	,	,	PUNCT
ejpam-5790	176	27	sp(u	sp(u	NOUN
ejpam-5790	176	28	)	)	PUNCT
ejpam-5790	176	29	⊂	⊂	PROPN
ejpam-5790	176	30	∆	∆	PROPN
ejpam-5790	176	31	and	and	CCONJ
ejpam-5790	176	32	sp(d	sp(d	PUNCT
ejpam-5790	176	33	)	)	PUNCT
ejpam-5790	177	1	⊂	⊂	PRON
ejpam-5790	177	2	∆	∆	X
ejpam-5790	177	3	)	)	PUNCT
ejpam-5790	177	4	.	.	PUNCT
ejpam-5790	178	1	if	if	SCONJ
ejpam-5790	178	2	ℑ	ℑ	PROPN
ejpam-5790	178	3	is	be	AUX
ejpam-5790	178	4	a	a	DET
ejpam-5790	178	5	convex	convex	ADJ
ejpam-5790	178	6	and	and	CCONJ
ejpam-5790	178	7	differentiable	differentiable	ADJ
ejpam-5790	178	8	function	function	NOUN
ejpam-5790	178	9	defined	define	VERB
ejpam-5790	178	10	on	on	ADP
ejpam-5790	178	11	∆	∆	PROPN
ejpam-5790	178	12	,	,	PUNCT
ejpam-5790	178	13	the	the	DET
ejpam-5790	178	14	following	follow	VERB
ejpam-5790	178	15	inequality	inequality	NOUN
ejpam-5790	178	16	holds	hold	VERB
ejpam-5790	178	17	:	:	PUNCT
ejpam-5790	178	18	(	(	PUNCT
ejpam-5790	178	19	ℑ′(u)⊗	ℑ′(u)⊗	INTJ
ejpam-5790	178	20	1	1	NUM
ejpam-5790	178	21	)	)	PUNCT
ejpam-5790	178	22	(	(	PUNCT
ejpam-5790	178	23	u	u	NOUN
ejpam-5790	178	24	⊗	⊗	PROPN
ejpam-5790	178	25	1−	1−	NUM
ejpam-5790	178	26	1⊗d	1⊗d	NUM
ejpam-5790	178	27	)	)	PUNCT
ejpam-5790	178	28	≤	≤	NUM
ejpam-5790	179	1	ℑ(u)⊗	ℑ(u)⊗	PROPN
ejpam-5790	179	2	1−	1−	NUM
ejpam-5790	179	3	1⊗ℑ(d	1⊗ℑ(d	NUM
ejpam-5790	179	4	)	)	PUNCT
ejpam-5790	179	5	≤	≤	NOUN
ejpam-5790	179	6	(	(	PUNCT
ejpam-5790	179	7	u	u	NOUN
ejpam-5790	179	8	⊗	⊗	PROPN
ejpam-5790	179	9	1−	1−	NUM
ejpam-5790	179	10	1⊗d	1⊗d	NUM
ejpam-5790	179	11	)	)	PUNCT
ejpam-5790	179	12	(	(	PUNCT
ejpam-5790	179	13	1⊗ℑ′(d	1⊗ℑ′(d	NUM
ejpam-5790	179	14	)	)	PUNCT
ejpam-5790	179	15	)	)	PUNCT
ejpam-5790	179	16	.	.	PUNCT
ejpam-5790	180	1	(	(	PUNCT
ejpam-5790	180	2	2.1	2.1	NUM
ejpam-5790	180	3	)	)	PUNCT
ejpam-5790	180	4	proof	proof	NOUN
ejpam-5790	180	5	.	.	PUNCT
ejpam-5790	181	1	taking	take	VERB
ejpam-5790	181	2	into	into	ADP
ejpam-5790	181	3	account	account	NOUN
ejpam-5790	181	4	th	th	X
ejpam-5790	181	5	following	follow	VERB
ejpam-5790	181	6	double	double	ADJ
ejpam-5790	181	7	inequality	inequality	NOUN
ejpam-5790	181	8	for	for	ADP
ejpam-5790	181	9	ℑ	ℑ	NOUN
ejpam-5790	181	10	on	on	ADP
ejpam-5790	181	11	∆	∆	PROPN
ejpam-5790	181	12	,	,	PUNCT
ejpam-5790	181	13	we	we	PRON
ejpam-5790	181	14	derive	derive	VERB
ejpam-5790	181	15	ℑ′(κ)(κ−	ℑ′(κ)(κ−	NOUN
ejpam-5790	181	16	γ	γ	PROPN
ejpam-5790	181	17	)	)	PUNCT
ejpam-5790	181	18	≤	≤	NOUN
ejpam-5790	181	19	ℑ(κ)−ℑ(γ	ℑ(κ)−ℑ(γ	NOUN
ejpam-5790	181	20	)	)	PUNCT
ejpam-5790	181	21	≤	≤	NUM
ejpam-5790	181	22	ℑ′(γ)(κ−	ℑ′(γ)(κ−	NUM
ejpam-5790	181	23	γ	γ	NOUN
ejpam-5790	181	24	)	)	PUNCT
ejpam-5790	181	25	for	for	ADP
ejpam-5790	181	26	all	all	DET
ejpam-5790	181	27	κ	κ	NOUN
ejpam-5790	181	28	,	,	PUNCT
ejpam-5790	182	1	γ	γ	X
ejpam-5790	182	2	∈	∈	PROPN
ejpam-5790	182	3	∆.	∆.	X
ejpam-5790	182	4	since	since	SCONJ
ejpam-5790	182	5	u	u	NOUN
ejpam-5790	182	6	=	=	PROPN
ejpam-5790	182	7	∫	∫	PROPN
ejpam-5790	182	8	∆	∆	PROPN
ejpam-5790	182	9	κde(κ	κde(κ	X
ejpam-5790	182	10	)	)	PUNCT
ejpam-5790	182	11	and	and	CCONJ
ejpam-5790	182	12	d	d	NOUN
ejpam-5790	182	13	=	=	SYM
ejpam-5790	182	14	∫	∫	PROPN
ejpam-5790	182	15	∆	∆	PROPN
ejpam-5790	182	16	γdf(γ	γdf(γ	PART
ejpam-5790	182	17	)	)	PUNCT
ejpam-5790	182	18	.	.	PUNCT
ejpam-5790	183	1	this	this	PRON
ejpam-5790	183	2	imply	imply	VERB
ejpam-5790	183	3	that∫	that∫	NOUN
ejpam-5790	183	4	∆	∆	PROPN
ejpam-5790	183	5	∫	∫	PROPN
ejpam-5790	183	6	∆	∆	PROPN
ejpam-5790	183	7	ℑ′(κ)(κ−	ℑ′(κ)(κ−	NOUN
ejpam-5790	183	8	γ)deκ	γ)deκ	PROPN
ejpam-5790	183	9	⊗	⊗	PROPN
ejpam-5790	183	10	deγ	deγ	X
ejpam-5790	183	11	≤	≤	NUM
ejpam-5790	183	12	∫	∫	PROPN
ejpam-5790	183	13	∆	∆	PROPN
ejpam-5790	184	1	∫	∫	PROPN
ejpam-5790	184	2	∆	∆	PROPN
ejpam-5790	184	3	(	(	PUNCT
ejpam-5790	184	4	ℑ(κ)−ℑ(γ))deκ	ℑ(κ)−ℑ(γ))deκ	NOUN
ejpam-5790	184	5	⊗	⊗	NOUN
ejpam-5790	184	6	deγ	deγ	VERB
ejpam-5790	184	7	≤	≤	NUM
ejpam-5790	184	8	∫	∫	PROPN
ejpam-5790	184	9	∆	∆	PROPN
ejpam-5790	184	10	∫	∫	PROPN
ejpam-5790	184	11	∆	∆	PROPN
ejpam-5790	184	12	ℑ′(γ)(κ−	ℑ′(γ)(κ−	NOUN
ejpam-5790	184	13	γ)deκ	γ)deκ	PROPN
ejpam-5790	184	14	⊗	⊗	PROPN
ejpam-5790	184	15	deγ	deγ	NOUN
ejpam-5790	184	16	.	.	PUNCT
ejpam-5790	185	1	(	(	PUNCT
ejpam-5790	185	2	2.2	2.2	NUM
ejpam-5790	185	3	)	)	PUNCT
ejpam-5790	185	4	observe	observe	VERB
ejpam-5790	185	5	that	that	SCONJ
ejpam-5790	185	6	∫	∫	PROPN
ejpam-5790	185	7	∆	∆	PROPN
ejpam-5790	185	8	∫	∫	PROPN
ejpam-5790	185	9	∆	∆	PROPN
ejpam-5790	185	10	ℑ′(κ)(κ−	ℑ′(κ)(κ−	NOUN
ejpam-5790	185	11	γ)deκ	γ)deκ	PROPN
ejpam-5790	185	12	⊗	⊗	PROPN
ejpam-5790	185	13	deγ	deγ	NOUN
ejpam-5790	186	1	=	=	SYM
ejpam-5790	186	2	∫	∫	PROPN
ejpam-5790	186	3	∆	∆	PROPN
ejpam-5790	187	1	∫	∫	PROPN
ejpam-5790	187	2	∆	∆	PROPN
ejpam-5790	187	3	(	(	PUNCT
ejpam-5790	187	4	ℑ′(κ)κ−ℑ′(κ)γ	ℑ′(κ)κ−ℑ′(κ)γ	PROPN
ejpam-5790	187	5	)	)	PUNCT
ejpam-5790	187	6	deκ	deκ	NOUN
ejpam-5790	187	7	⊗	⊗	PROPN
ejpam-5790	187	8	deγ	deγ	NOUN
ejpam-5790	187	9	=	=	SYM
ejpam-5790	187	10	∫	∫	PROPN
ejpam-5790	187	11	∆	∆	PROPN
ejpam-5790	187	12	∫	∫	PROPN
ejpam-5790	187	13	∆	∆	PROPN
ejpam-5790	187	14	ℑ′(κ)tdeκ	ℑ′(κ)tdeκ	PROPN
ejpam-5790	187	15	⊗	⊗	PROPN
ejpam-5790	187	16	deγ	deγ	VERB
ejpam-5790	187	17	−	−	PROPN
ejpam-5790	187	18	∫	∫	PROPN
ejpam-5790	187	19	∆	∆	PROPN
ejpam-5790	187	20	∫	∫	PROPN
ejpam-5790	187	21	∆	∆	PROPN
ejpam-5790	187	22	ℑ′(κ)γdeκ	ℑ′(κ)γdeκ	PROPN
ejpam-5790	187	23	⊗	⊗	PROPN
ejpam-5790	187	24	deγ	deγ	NOUN
ejpam-5790	187	25	=	=	PUNCT
ejpam-5790	187	26	(	(	PUNCT
ejpam-5790	187	27	ℑ′(u)u	ℑ′(u)u	NUM
ejpam-5790	187	28	)	)	PUNCT
ejpam-5790	188	1	⊗	⊗	PROPN
ejpam-5790	188	2	1−ℑ′(u)⊗d∫	1−ℑ′(u)⊗d∫	NUM
ejpam-5790	188	3	∆	∆	ADJ
ejpam-5790	188	4	∫	∫	NOUN
ejpam-5790	188	5	∆	∆	PROPN
ejpam-5790	188	6	(	(	PUNCT
ejpam-5790	188	7	ℑ(κ)−ℑ(γ))deκ	ℑ(κ)−ℑ(γ))deκ	NOUN
ejpam-5790	188	8	⊗	⊗	NOUN
ejpam-5790	188	9	deγ	deγ	NOUN
ejpam-5790	189	1	=	=	SYM
ejpam-5790	189	2	ℑ(u)⊗	ℑ(u)⊗	NUM
ejpam-5790	189	3	1−	1−	NUM
ejpam-5790	189	4	1⊗ℑ(d	1⊗ℑ(d	NUM
ejpam-5790	189	5	)	)	PUNCT
ejpam-5790	189	6	(	(	PUNCT
ejpam-5790	189	7	2.3	2.3	NUM
ejpam-5790	189	8	)	)	PUNCT
ejpam-5790	189	9	and	and	CCONJ
ejpam-5790	189	10	∫	∫	PROPN
ejpam-5790	189	11	∆	∆	PROPN
ejpam-5790	189	12	∫	∫	PROPN
ejpam-5790	189	13	∆	∆	PROPN
ejpam-5790	189	14	ℑ′(γ)(κ−	ℑ′(γ)(κ−	NOUN
ejpam-5790	189	15	γ)deκ	γ)deκ	PROPN
ejpam-5790	189	16	⊗	⊗	PROPN
ejpam-5790	189	17	deγ	deγ	NOUN
ejpam-5790	189	18	=	=	SYM
ejpam-5790	189	19	∫	∫	PROPN
ejpam-5790	189	20	∆	∆	PROPN
ejpam-5790	189	21	∫	∫	PROPN
ejpam-5790	189	22	∆	∆	PROPN
ejpam-5790	189	23	(	(	PUNCT
ejpam-5790	189	24	κℑ′(γ)−ℑ′(γ)γ	κℑ′(γ)−ℑ′(γ)γ	PROPN
ejpam-5790	189	25	)	)	PUNCT
ejpam-5790	189	26	deκ	deκ	PROPN
ejpam-5790	189	27	⊗	⊗	PROPN
ejpam-5790	189	28	deγ	deγ	NOUN
ejpam-5790	190	1	=	=	SYM
ejpam-5790	190	2	∫	∫	PROPN
ejpam-5790	190	3	∆	∆	PROPN
ejpam-5790	191	1	∫	∫	PROPN
ejpam-5790	191	2	∆	∆	PROPN
ejpam-5790	191	3	κℑ′(γ)deκ	κℑ′(γ)deκ	PROPN
ejpam-5790	192	1	⊗	⊗	PROPN
ejpam-5790	192	2	deγ	deγ	X
ejpam-5790	192	3	−	−	PROPN
ejpam-5790	192	4	∫	∫	PROPN
ejpam-5790	192	5	∆	∆	PROPN
ejpam-5790	192	6	∫	∫	PROPN
ejpam-5790	192	7	∆	∆	PROPN
ejpam-5790	192	8	ℑ′(γ)γdeκ	ℑ′(γ)γdeκ	PROPN
ejpam-5790	193	1	⊗	⊗	PROPN
ejpam-5790	193	2	deγ	deγ	NOUN
ejpam-5790	193	3	=	=	PUNCT
ejpam-5790	193	4	u	u	X
ejpam-5790	193	5	⊗	⊗	PROPN
ejpam-5790	193	6	ℑ′(d)−	ℑ′(d)−	PROPN
ejpam-5790	193	7	1⊗	1⊗	NUM
ejpam-5790	193	8	(	(	PUNCT
ejpam-5790	193	9	ℑ′(d)d	ℑ′(d)d	NUM
ejpam-5790	193	10	)	)	PUNCT
ejpam-5790	193	11	w.	w.	PROPN
ejpam-5790	193	12	afzal	afzal	PROPN
ejpam-5790	193	13	et	et	PROPN
ejpam-5790	193	14	al	al	PROPN
ejpam-5790	193	15	.	.	PUNCT
ejpam-5790	193	16	/	/	SYM
ejpam-5790	193	17	eur	eur	PROPN
ejpam-5790	193	18	.	.	PUNCT
ejpam-5790	194	1	j.	j.	PROPN
ejpam-5790	194	2	pure	pure	PROPN
ejpam-5790	194	3	appl	appl	PROPN
ejpam-5790	194	4	.	.	PROPN
ejpam-5790	194	5	math	math	PROPN
ejpam-5790	194	6	,	,	PUNCT
ejpam-5790	194	7	18	18	NUM
ejpam-5790	194	8	(	(	PUNCT
ejpam-5790	194	9	1	1	NUM
ejpam-5790	194	10	)	)	PUNCT
ejpam-5790	194	11	(	(	PUNCT
ejpam-5790	194	12	2025	2025	NUM
ejpam-5790	194	13	)	)	PUNCT
ejpam-5790	194	14	,	,	PUNCT
ejpam-5790	194	15	5790	5790	NUM
ejpam-5790	194	16	9	9	NUM
ejpam-5790	194	17	of	of	ADP
ejpam-5790	194	18	30	30	NUM
ejpam-5790	194	19	and	and	CCONJ
ejpam-5790	194	20	by	by	ADP
ejpam-5790	194	21	(	(	PUNCT
ejpam-5790	194	22	2.3	2.3	NUM
ejpam-5790	194	23	)	)	PUNCT
ejpam-5790	194	24	we	we	PRON
ejpam-5790	194	25	derive	derive	VERB
ejpam-5790	194	26	the	the	DET
ejpam-5790	194	27	inequality	inequality	NOUN
ejpam-5790	194	28	of	of	ADP
ejpam-5790	194	29	interest	interest	NOUN
ejpam-5790	194	30	lemma	lemma	PROPN
ejpam-5790	194	31	2	2	X
ejpam-5790	194	32	.	.	PUNCT
ejpam-5790	195	1	let	let	VERB
ejpam-5790	195	2	u	u	PRON
ejpam-5790	195	3	and	and	CCONJ
ejpam-5790	195	4	d	d	AUX
ejpam-5790	195	5	be	be	AUX
ejpam-5790	195	6	adjoint	adjoint	NOUN
ejpam-5790	195	7	operators	operator	NOUN
ejpam-5790	195	8	,	,	PUNCT
ejpam-5790	195	9	with	with	SCONJ
ejpam-5790	195	10	their	their	PRON
ejpam-5790	195	11	spectra	spectra	NOUN
ejpam-5790	195	12	denoted	denote	VERB
ejpam-5790	195	13	by	by	ADP
ejpam-5790	195	14	σ1	σ1	PROPN
ejpam-5790	195	15	and	and	CCONJ
ejpam-5790	195	16	σ2	σ2	NOUN
ejpam-5790	195	17	,	,	PUNCT
ejpam-5790	195	18	respectively	respectively	ADV
ejpam-5790	195	19	.	.	PUNCT
ejpam-5790	196	1	suppose	suppose	VERB
ejpam-5790	196	2	the	the	DET
ejpam-5790	196	3	functions	function	NOUN
ejpam-5790	196	4	ℑ	ℑ	PROPN
ejpam-5790	196	5	and	and	CCONJ
ejpam-5790	196	6	ϑ	ϑ	X
ejpam-5790	196	7	are	be	AUX
ejpam-5790	196	8	defined	define	VERB
ejpam-5790	196	9	on	on	ADP
ejpam-5790	196	10	σ1	σ1	PROPN
ejpam-5790	196	11	,	,	PUNCT
ejpam-5790	196	12	while	while	SCONJ
ejpam-5790	196	13	d	d	PROPN
ejpam-5790	196	14	and	and	CCONJ
ejpam-5790	196	15	q	q	PROPN
ejpam-5790	196	16	are	be	AUX
ejpam-5790	196	17	defined	define	VERB
ejpam-5790	196	18	on	on	ADP
ejpam-5790	196	19	σ2	σ2	NOUN
ejpam-5790	196	20	,	,	PUNCT
ejpam-5790	196	21	and	and	CCONJ
ejpam-5790	196	22	let	let	VERB
ejpam-5790	196	23	φ	φ	PROPN
ejpam-5790	196	24	be	be	AUX
ejpam-5790	196	25	convex	convex	NOUN
ejpam-5790	196	26	on	on	ADP
ejpam-5790	196	27	σ	σ	PROPN
ejpam-5790	196	28	.	.	PUNCT
ejpam-5790	197	1	then	then	ADV
ejpam-5790	197	2	,	,	PUNCT
ejpam-5790	197	3	the	the	DET
ejpam-5790	197	4	set	set	NOUN
ejpam-5790	197	5	ϑ(σ1)+ℑ(σ2	ϑ(σ1)+ℑ(σ2	NUM
ejpam-5790	197	6	)	)	PUNCT
ejpam-5790	197	7	satisfies	satisfy	VERB
ejpam-5790	197	8	the	the	DET
ejpam-5790	197	9	following	follow	VERB
ejpam-5790	197	10	equality	equality	NOUN
ejpam-5790	197	11	:	:	PUNCT
ejpam-5790	197	12	(	(	PUNCT
ejpam-5790	197	13	ℑ(u)⊗	ℑ(u)⊗	NOUN
ejpam-5790	197	14	1	1	NUM
ejpam-5790	197	15	+	+	NUM
ejpam-5790	197	16	1⊗d(d))φ(ϑ(u)⊗	1⊗d(d))φ(ϑ(u)⊗	NUM
ejpam-5790	197	17	1	1	NUM
ejpam-5790	197	18	+	+	NUM
ejpam-5790	197	19	1⊗ℑ(d	1⊗ℑ(d	NUM
ejpam-5790	197	20	)	)	PUNCT
ejpam-5790	197	21	)	)	PUNCT
ejpam-5790	198	1	=	=	SYM
ejpam-5790	199	1	∫	∫	PROPN
ejpam-5790	200	1	σ1	σ1	PROPN
ejpam-5790	200	2	∫	∫	PROPN
ejpam-5790	200	3	σ2	σ2	PROPN
ejpam-5790	200	4	(	(	PUNCT
ejpam-5790	200	5	ℑ(ν2	ℑ(ν2	PROPN
ejpam-5790	200	6	)	)	PUNCT
ejpam-5790	200	7	+	+	NOUN
ejpam-5790	200	8	d(ν1))φ(ϑ(ν2	d(ν1))φ(ϑ(ν2	PROPN
ejpam-5790	200	9	)	)	PUNCT
ejpam-5790	201	1	+	+	PROPN
ejpam-5790	201	2	q(ν1))deν2	q(ν1))deν2	PROPN
ejpam-5790	201	3	⊗	⊗	PROPN
ejpam-5790	201	4	dfν1	dfν1	PROPN
ejpam-5790	201	5	,	,	PUNCT
ejpam-5790	201	6	(	(	PUNCT
ejpam-5790	201	7	2.4	2.4	NUM
ejpam-5790	201	8	)	)	PUNCT
ejpam-5790	201	9	where	where	SCONJ
ejpam-5790	201	10	u	u	NOUN
ejpam-5790	201	11	and	and	CCONJ
ejpam-5790	201	12	d	d	PROPN
ejpam-5790	201	13	have	have	VERB
ejpam-5790	201	14	the	the	DET
ejpam-5790	201	15	spectral	spectral	ADJ
ejpam-5790	201	16	resolutions	resolution	NOUN
ejpam-5790	201	17	u	u	NOUN
ejpam-5790	201	18	=	=	PROPN
ejpam-5790	201	19	∫	∫	PROPN
ejpam-5790	201	20	σ1	σ1	PROPN
ejpam-5790	201	21	ν2de(ν2	ν2de(ν2	PROPN
ejpam-5790	201	22	)	)	PUNCT
ejpam-5790	201	23	and	and	CCONJ
ejpam-5790	201	24	d	d	NOUN
ejpam-5790	201	25	=	=	SYM
ejpam-5790	201	26	∫	∫	PROPN
ejpam-5790	201	27	σ2	σ2	PROPN
ejpam-5790	201	28	ν1df(ν1	ν1df(ν1	PROPN
ejpam-5790	201	29	)	)	PUNCT
ejpam-5790	201	30	.	.	PUNCT
ejpam-5790	202	1	proof	proof	NOUN
ejpam-5790	202	2	.	.	PUNCT
ejpam-5790	203	1	according	accord	VERB
ejpam-5790	203	2	to	to	ADP
ejpam-5790	203	3	stone	stone	NOUN
ejpam-5790	203	4	-	-	PUNCT
ejpam-5790	203	5	weierstrass	weierstrass	NOUN
ejpam-5790	203	6	,	,	PUNCT
ejpam-5790	203	7	any	any	DET
ejpam-5790	203	8	continuous	continuous	ADJ
ejpam-5790	203	9	function	function	NOUN
ejpam-5790	203	10	can	can	AUX
ejpam-5790	203	11	be	be	AUX
ejpam-5790	203	12	represented	represent	VERB
ejpam-5790	203	13	in	in	ADP
ejpam-5790	203	14	terms	term	NOUN
ejpam-5790	203	15	of	of	ADP
ejpam-5790	203	16	polynomial	polynomial	ADJ
ejpam-5790	203	17	sequence	sequence	NOUN
ejpam-5790	203	18	,	,	PUNCT
ejpam-5790	203	19	hence	hence	ADV
ejpam-5790	203	20	simply	simply	ADV
ejpam-5790	203	21	checking	check	VERB
ejpam-5790	203	22	its	its	PRON
ejpam-5790	203	23	equivalence	equivalence	NOUN
ejpam-5790	203	24	is	be	AUX
ejpam-5790	203	25	adequate	adequate	ADJ
ejpam-5790	203	26	.	.	PUNCT
ejpam-5790	204	1	let	let	VERB
ejpam-5790	204	2	d(µ	d(µ	PROPN
ejpam-5790	204	3	)	)	PUNCT
ejpam-5790	205	1	=	=	PRON
ejpam-5790	205	2	{	{	PUNCT
ejpam-5790	205	3	1	1	NUM
ejpam-5790	205	4	2µ	2µ	NUM
ejpam-5790	205	5	2σ1	2σ1	NUM
ejpam-5790	205	6	,	,	PUNCT
ejpam-5790	205	7	−σ	−σ	NOUN
ejpam-5790	205	8	≤	≤	PROPN
ejpam-5790	205	9	µ	µ	PROPN
ejpam-5790	205	10	≤	≤	PROPN
ejpam-5790	205	11	σ	σ	PROPN
ejpam-5790	205	12	σ	σ	PROPN
ejpam-5790	205	13	(	(	PUNCT
ejpam-5790	205	14	|µ|σ1	|µ|σ1	NOUN
ejpam-5790	205	15	−	−	PROPN
ejpam-5790	205	16	σ	σ	PROPN
ejpam-5790	205	17	2	2	NUM
ejpam-5790	205	18	)	)	PUNCT
ejpam-5790	205	19	,	,	PUNCT
ejpam-5790	205	20	σ	σ	X
ejpam-5790	205	21	>	>	X
ejpam-5790	205	22	µ	µ	X
ejpam-5790	205	23	>	>	X
ejpam-5790	205	24	−σ	−σ	NOUN
ejpam-5790	205	25	.	.	PUNCT
ejpam-5790	206	1	if	if	SCONJ
ejpam-5790	206	2	σ1	σ1	PROPN
ejpam-5790	206	3	and	and	CCONJ
ejpam-5790	206	4	σ2	σ2	PROPN
ejpam-5790	206	5	are	be	AUX
ejpam-5790	206	6	integers	integer	NOUN
ejpam-5790	206	7	,	,	PUNCT
ejpam-5790	206	8	and	and	CCONJ
ejpam-5790	206	9	|µ|	|µ|	PROPN
ejpam-5790	206	10	≤	≤	PROPN
ejpam-5790	206	11	σ	σ	PROPN
ejpam-5790	206	12	,	,	PUNCT
ejpam-5790	206	13	then	then	ADV
ejpam-5790	206	14	the	the	DET
ejpam-5790	206	15	following	follow	VERB
ejpam-5790	206	16	holds	hold	VERB
ejpam-5790	206	17	:	:	PUNCT
ejpam-5790	206	18	ℑ	ℑ	NOUN
ejpam-5790	206	19	:	:	PUNCT
ejpam-5790	207	1	=	=	SYM
ejpam-5790	207	2	∫	∫	PROPN
ejpam-5790	207	3	σ1	σ1	PROPN
ejpam-5790	207	4	∫	∫	PROPN
ejpam-5790	207	5	σ2	σ2	PROPN
ejpam-5790	207	6	(	(	PUNCT
ejpam-5790	207	7	ℑ(ν2	ℑ(ν2	PROPN
ejpam-5790	207	8	)	)	PUNCT
ejpam-5790	207	9	+	+	NOUN
ejpam-5790	207	10	d(ν1	d(ν1	NOUN
ejpam-5790	207	11	)	)	PUNCT
ejpam-5790	207	12	)	)	PUNCT
ejpam-5790	207	13	1	1	NUM
ejpam-5790	207	14	2	2	NUM
ejpam-5790	207	15	(	(	PUNCT
ejpam-5790	207	16	ϑ(ν2	ϑ(ν2	NUM
ejpam-5790	207	17	)	)	PUNCT
ejpam-5790	207	18	+	+	ADJ
ejpam-5790	207	19	q(ν1	q(ν1	NOUN
ejpam-5790	207	20	)	)	PUNCT
ejpam-5790	207	21	)	)	PUNCT
ejpam-5790	208	1	2σ1deν2	2σ1deν2	NUM
ejpam-5790	208	2	⊗	⊗	PROPN
ejpam-5790	208	3	dfν1	dfν1	PROPN
ejpam-5790	208	4	=	=	SYM
ejpam-5790	209	1	∫	∫	PROPN
ejpam-5790	209	2	σ1	σ1	PROPN
ejpam-5790	209	3	∫	∫	PROPN
ejpam-5790	209	4	σ2	σ2	PROPN
ejpam-5790	209	5	(	(	PUNCT
ejpam-5790	209	6	ℑ(ν2	ℑ(ν2	PROPN
ejpam-5790	209	7	)	)	PUNCT
ejpam-5790	209	8	+	+	NOUN
ejpam-5790	209	9	d(ν1	d(ν1	NOUN
ejpam-5790	209	10	)	)	PUNCT
ejpam-5790	209	11	)	)	PUNCT
ejpam-5790	210	1	σ2∑	σ2∑	PROPN
ejpam-5790	210	2	σ1=0	σ1=0	PROPN
ejpam-5790	210	3	cσ1	cσ1	NOUN
ejpam-5790	210	4	σ2	σ2	NOUN
ejpam-5790	210	5	1	1	NUM
ejpam-5790	210	6	2	2	NUM
ejpam-5790	210	7	[	[	X
ejpam-5790	210	8	ϑ(ν2	ϑ(ν2	ADV
ejpam-5790	210	9	)	)	PUNCT
ejpam-5790	210	10	]	]	PUNCT
ejpam-5790	211	1	2σ1	2σ1	NUM
ejpam-5790	211	2	[	[	PUNCT
ejpam-5790	211	3	q(ν1	q(ν1	NOUN
ejpam-5790	211	4	)	)	PUNCT
ejpam-5790	211	5	]	]	PUNCT
ejpam-5790	211	6	2σ2−2σ1deν2	2σ2−2σ1deν2	NUM
ejpam-5790	211	7	⊗	⊗	PROPN
ejpam-5790	211	8	dfν1	dfν1	PROPN
ejpam-5790	211	9	=	=	PUNCT
ejpam-5790	212	1	σ2∑	σ2∑	PROPN
ejpam-5790	212	2	σ1=0	σ1=0	PROPN
ejpam-5790	212	3	cσ1	cσ1	NOUN
ejpam-5790	212	4	σ2	σ2	PROPN
ejpam-5790	212	5	∫	∫	PROPN
ejpam-5790	212	6	σ1	σ1	PROPN
ejpam-5790	212	7	∫	∫	PROPN
ejpam-5790	212	8	σ2	σ2	PROPN
ejpam-5790	212	9	(	(	PUNCT
ejpam-5790	212	10	ℑ(ν2	ℑ(ν2	PROPN
ejpam-5790	212	11	)	)	PUNCT
ejpam-5790	212	12	+	+	NOUN
ejpam-5790	212	13	d(ν1	d(ν1	NOUN
ejpam-5790	212	14	)	)	PUNCT
ejpam-5790	212	15	)	)	PUNCT
ejpam-5790	212	16	1	1	NUM
ejpam-5790	212	17	2	2	NUM
ejpam-5790	212	18	[	[	X
ejpam-5790	212	19	ϑ(ν2	ϑ(ν2	ADV
ejpam-5790	212	20	)	)	PUNCT
ejpam-5790	212	21	]	]	PUNCT
ejpam-5790	213	1	2σ1	2σ1	NUM
ejpam-5790	213	2	[	[	PUNCT
ejpam-5790	213	3	q(ν1	q(ν1	NOUN
ejpam-5790	213	4	)	)	PUNCT
ejpam-5790	213	5	]	]	PUNCT
ejpam-5790	213	6	2σ2−2σ1deν2	2σ2−2σ1deν2	NUM
ejpam-5790	213	7	⊗	⊗	PROPN
ejpam-5790	213	8	dfν1	dfν1	PROPN
ejpam-5790	213	9	=	=	PUNCT
ejpam-5790	214	1	σ2∑	σ2∑	PROPN
ejpam-5790	214	2	σ1=0	σ1=0	PROPN
ejpam-5790	214	3	cσ1	cσ1	NOUN
ejpam-5790	214	4	σ2	σ2	PROPN
ejpam-5790	214	5	[	[	X
ejpam-5790	214	6	∫	∫	PROPN
ejpam-5790	214	7	σ1	σ1	PROPN
ejpam-5790	214	8	∫	∫	PROPN
ejpam-5790	214	9	σ2	σ2	PROPN
ejpam-5790	214	10	ℑ(ν2	ℑ(ν2	PROPN
ejpam-5790	214	11	)	)	PUNCT
ejpam-5790	214	12	1	1	NUM
ejpam-5790	214	13	2	2	NUM
ejpam-5790	214	14	[	[	X
ejpam-5790	214	15	ϑ(ν2	ϑ(ν2	ADV
ejpam-5790	214	16	)	)	PUNCT
ejpam-5790	214	17	]	]	PUNCT
ejpam-5790	215	1	2σ1	2σ1	NUM
ejpam-5790	215	2	[	[	PUNCT
ejpam-5790	215	3	q(ν1	q(ν1	NOUN
ejpam-5790	215	4	)	)	PUNCT
ejpam-5790	215	5	]	]	PUNCT
ejpam-5790	216	1	2σ2−2σ1deν2	2σ2−2σ1deν2	NUM
ejpam-5790	216	2	⊗	⊗	PROPN
ejpam-5790	216	3	dfν1	dfν1	PROPN
ejpam-5790	216	4	+	+	CCONJ
ejpam-5790	216	5	∫	∫	PROPN
ejpam-5790	216	6	σ1	σ1	PROPN
ejpam-5790	216	7	∫	∫	PROPN
ejpam-5790	216	8	σ2	σ2	PROPN
ejpam-5790	216	9	d(ν1	d(ν1	NOUN
ejpam-5790	216	10	)	)	PUNCT
ejpam-5790	216	11	1	1	NUM
ejpam-5790	216	12	2	2	NUM
ejpam-5790	216	13	[	[	X
ejpam-5790	216	14	ϑ(ν2	ϑ(ν2	ADV
ejpam-5790	216	15	)	)	PUNCT
ejpam-5790	216	16	]	]	PUNCT
ejpam-5790	217	1	2σ1	2σ1	NUM
ejpam-5790	217	2	[	[	PUNCT
ejpam-5790	217	3	q(ν1	q(ν1	NOUN
ejpam-5790	217	4	)	)	PUNCT
ejpam-5790	217	5	]	]	PUNCT
ejpam-5790	217	6	2σ2−2σ1deν2	2σ2−2σ1deν2	NUM
ejpam-5790	217	7	⊗	⊗	PROPN
ejpam-5790	217	8	dfν1	dfν1	PROPN
ejpam-5790	217	9	]	]	PUNCT
ejpam-5790	217	10	.	.	PUNCT
ejpam-5790	218	1	observe	observe	VERB
ejpam-5790	218	2	that∫	that∫	PROPN
ejpam-5790	218	3	σ1	σ1	PROPN
ejpam-5790	218	4	∫	∫	PROPN
ejpam-5790	218	5	σ2	σ2	PROPN
ejpam-5790	218	6	ℑ(ν2	ℑ(ν2	PROPN
ejpam-5790	218	7	)	)	PUNCT
ejpam-5790	218	8	1	1	NUM
ejpam-5790	218	9	2	2	NUM
ejpam-5790	218	10	[	[	X
ejpam-5790	218	11	ϑ(ν2	ϑ(ν2	ADV
ejpam-5790	218	12	)	)	PUNCT
ejpam-5790	218	13	]	]	PUNCT
ejpam-5790	219	1	2σ1	2σ1	NUM
ejpam-5790	219	2	[	[	PUNCT
ejpam-5790	219	3	q(ν1	q(ν1	NOUN
ejpam-5790	219	4	)	)	PUNCT
ejpam-5790	219	5	]	]	PUNCT
ejpam-5790	220	1	2σ2−2σ1deν2	2σ2−2σ1deν2	NUM
ejpam-5790	220	2	⊗	⊗	PROPN
ejpam-5790	220	3	dfν1	dfν1	PROPN
ejpam-5790	220	4	=	=	PUNCT
ejpam-5790	220	5	ℑ(u)1	ℑ(u)1	PROPN
ejpam-5790	220	6	2	2	NUM
ejpam-5790	221	1	[	[	X
ejpam-5790	221	2	ϑ(u)]2σ1	ϑ(u)]2σ1	X
ejpam-5790	221	3	⊗	⊗	X
ejpam-5790	222	1	[	[	X
ejpam-5790	222	2	ℑ(d)]2σ2−2σ1	ℑ(d)]2σ2−2σ1	PROPN
ejpam-5790	222	3	=	=	SYM
ejpam-5790	222	4	(	(	PUNCT
ejpam-5790	222	5	ℑ(u)⊗	ℑ(u)⊗	PROPN
ejpam-5790	222	6	1	1	NUM
ejpam-5790	222	7	)	)	PUNCT
ejpam-5790	222	8	(	(	PUNCT
ejpam-5790	223	1	[	[	X
ejpam-5790	223	2	ϑ(u)]2σ2	ϑ(u)]2σ2	X
ejpam-5790	223	3	⊗	⊗	NOUN
ejpam-5790	223	4	[	[	X
ejpam-5790	223	5	ℑ(d)]2σ2−2σ1	ℑ(d)]2σ2−2σ1	PROPN
ejpam-5790	223	6	)	)	PUNCT
ejpam-5790	223	7	=	=	PUNCT
ejpam-5790	223	8	(	(	PUNCT
ejpam-5790	223	9	ℑ(u)⊗	ℑ(u)⊗	PROPN
ejpam-5790	223	10	1	1	NUM
ejpam-5790	223	11	)	)	PUNCT
ejpam-5790	223	12	1	1	NUM
ejpam-5790	223	13	2	2	NUM
ejpam-5790	223	14	(	(	PUNCT
ejpam-5790	223	15	[	[	X
ejpam-5790	223	16	ϑ(u)]2σ2	ϑ(u)]2σ2	X
ejpam-5790	223	17	⊗	⊗	PROPN
ejpam-5790	223	18	1	1	NUM
ejpam-5790	223	19	)	)	PUNCT
ejpam-5790	223	20	(	(	PUNCT
ejpam-5790	223	21	1⊗	1⊗	NUM
ejpam-5790	223	22	[	[	X
ejpam-5790	223	23	ℑ(d)]2σ2−2σ1	ℑ(d)]2σ2−2σ1	PROPN
ejpam-5790	223	24	)	)	PUNCT
ejpam-5790	223	25	=	=	PUNCT
ejpam-5790	223	26	(	(	PUNCT
ejpam-5790	223	27	ℑ(u)⊗	ℑ(u)⊗	PROPN
ejpam-5790	223	28	1	1	NUM
ejpam-5790	223	29	)	)	PUNCT
ejpam-5790	223	30	1	1	NUM
ejpam-5790	223	31	2	2	NUM
ejpam-5790	223	32	(	(	PUNCT
ejpam-5790	223	33	ϑ(u)⊗	ϑ(u)⊗	NOUN
ejpam-5790	223	34	1)2σ1(1⊗ℑ(d))2σ2−2σ1	1)2σ1(1⊗ℑ(d))2σ2−2σ1	PROPN
ejpam-5790	223	35	w.	w.	PROPN
ejpam-5790	223	36	afzal	afzal	PROPN
ejpam-5790	223	37	et	et	PROPN
ejpam-5790	223	38	al	al	PROPN
ejpam-5790	223	39	.	.	PUNCT
ejpam-5790	223	40	/	/	SYM
ejpam-5790	223	41	eur	eur	PROPN
ejpam-5790	223	42	.	.	PUNCT
ejpam-5790	224	1	j.	j.	PROPN
ejpam-5790	224	2	pure	pure	PROPN
ejpam-5790	224	3	appl	appl	PROPN
ejpam-5790	224	4	.	.	PROPN
ejpam-5790	224	5	math	math	PROPN
ejpam-5790	224	6	,	,	PUNCT
ejpam-5790	224	7	18	18	NUM
ejpam-5790	224	8	(	(	PUNCT
ejpam-5790	224	9	1	1	NUM
ejpam-5790	224	10	)	)	PUNCT
ejpam-5790	224	11	(	(	PUNCT
ejpam-5790	224	12	2025	2025	NUM
ejpam-5790	224	13	)	)	PUNCT
ejpam-5790	224	14	,	,	PUNCT
ejpam-5790	224	15	5790	5790	NUM
ejpam-5790	224	16	10	10	NUM
ejpam-5790	224	17	of	of	ADP
ejpam-5790	224	18	30	30	NUM
ejpam-5790	224	19	and	and	CCONJ
ejpam-5790	224	20	∫	∫	PROPN
ejpam-5790	224	21	σ1	σ1	PROPN
ejpam-5790	224	22	∫	∫	PROPN
ejpam-5790	225	1	σ2	σ2	PROPN
ejpam-5790	225	2	1	1	NUM
ejpam-5790	225	3	2	2	NUM
ejpam-5790	225	4	[	[	X
ejpam-5790	225	5	ϑ(ν2	ϑ(ν2	ADJ
ejpam-5790	225	6	)	)	PUNCT
ejpam-5790	225	7	]	]	PUNCT
ejpam-5790	225	8	2σ1d(ν1)[q(ν1	2σ1d(ν1)[q(ν1	NOUN
ejpam-5790	225	9	)	)	PUNCT
ejpam-5790	225	10	]	]	PUNCT
ejpam-5790	226	1	2σ2−2σ1deν2	2σ2−2σ1deν2	NUM
ejpam-5790	226	2	⊗	⊗	PROPN
ejpam-5790	226	3	dfν1	dfν1	PROPN
ejpam-5790	226	4	=	=	SYM
ejpam-5790	226	5	1	1	NUM
ejpam-5790	226	6	2	2	NUM
ejpam-5790	226	7	[	[	X
ejpam-5790	226	8	ϑ(u)]2σ1	ϑ(u)]2σ1	X
ejpam-5790	226	9	⊗	⊗	PROPN
ejpam-5790	226	10	(	(	PUNCT
ejpam-5790	226	11	d(d)[ℑ(d)]2σ2−2σ1	d(d)[ℑ(d)]2σ2−2σ1	PROPN
ejpam-5790	226	12	)	)	PUNCT
ejpam-5790	226	13	=	=	PUNCT
ejpam-5790	226	14	(	(	PUNCT
ejpam-5790	226	15	1⊗d(d	1⊗d(d	NUM
ejpam-5790	226	16	)	)	PUNCT
ejpam-5790	226	17	)	)	PUNCT
ejpam-5790	226	18	1	1	NUM
ejpam-5790	226	19	2	2	NUM
ejpam-5790	226	20	(	(	PUNCT
ejpam-5790	226	21	[	[	X
ejpam-5790	226	22	ϑ(u)]2σ2	ϑ(u)]2σ2	X
ejpam-5790	226	23	⊗	⊗	NOUN
ejpam-5790	226	24	[	[	X
ejpam-5790	226	25	ℑ(d)]2σ2−2σ1	ℑ(d)]2σ2−2σ1	PROPN
ejpam-5790	226	26	)	)	PUNCT
ejpam-5790	226	27	=	=	PUNCT
ejpam-5790	226	28	(	(	PUNCT
ejpam-5790	226	29	1⊗d(d	1⊗d(d	NUM
ejpam-5790	226	30	)	)	PUNCT
ejpam-5790	226	31	)	)	PUNCT
ejpam-5790	226	32	1	1	NUM
ejpam-5790	226	33	2	2	NUM
ejpam-5790	226	34	(	(	PUNCT
ejpam-5790	226	35	[	[	X
ejpam-5790	226	36	ϑ(u)]2σ2	ϑ(u)]2σ2	X
ejpam-5790	226	37	⊗	⊗	PROPN
ejpam-5790	226	38	1	1	NUM
ejpam-5790	226	39	)	)	PUNCT
ejpam-5790	226	40	(	(	PUNCT
ejpam-5790	226	41	1⊗	1⊗	NUM
ejpam-5790	226	42	[	[	X
ejpam-5790	226	43	ℑ(d)]2σ2−2σ1	ℑ(d)]2σ2−2σ1	PROPN
ejpam-5790	226	44	)	)	PUNCT
ejpam-5790	226	45	=	=	PUNCT
ejpam-5790	226	46	(	(	PUNCT
ejpam-5790	226	47	1⊗d(d	1⊗d(d	NUM
ejpam-5790	226	48	)	)	PUNCT
ejpam-5790	226	49	)	)	PUNCT
ejpam-5790	226	50	1	1	NUM
ejpam-5790	226	51	2	2	NUM
ejpam-5790	226	52	(	(	PUNCT
ejpam-5790	226	53	ϑ(u)⊗	ϑ(u)⊗	NOUN
ejpam-5790	226	54	1)2σ1(1⊗ℑ(d))2σ2−2σ1	1)2σ1(1⊗ℑ(d))2σ2−2σ1	NUM
ejpam-5790	226	55	where	where	SCONJ
ejpam-5790	226	56	1	1	NUM
ejpam-5790	226	57	2(ϑ(u)⊗	2(ϑ(u)⊗	NUM
ejpam-5790	226	58	1	1	NUM
ejpam-5790	226	59	)	)	PUNCT
ejpam-5790	226	60	and	and	CCONJ
ejpam-5790	226	61	1	1	NUM
ejpam-5790	226	62	2(1⊗ℑ(d	2(1⊗ℑ(d	NUM
ejpam-5790	226	63	)	)	PUNCT
ejpam-5790	226	64	)	)	PUNCT
ejpam-5790	226	65	are	be	AUX
ejpam-5790	226	66	commutative	commutative	ADJ
ejpam-5790	226	67	,	,	PUNCT
ejpam-5790	226	68	so	so	SCONJ
ejpam-5790	226	69	we	we	PRON
ejpam-5790	226	70	have	have	VERB
ejpam-5790	226	71	ℑ	ℑ	NOUN
ejpam-5790	226	72	=	=	PUNCT
ejpam-5790	226	73	(	(	PUNCT
ejpam-5790	226	74	ℑ(u)⊗	ℑ(u)⊗	PROPN
ejpam-5790	226	75	1	1	NUM
ejpam-5790	226	76	+	+	SYM
ejpam-5790	226	77	1⊗d(d	1⊗d(d	NUM
ejpam-5790	226	78	)	)	PUNCT
ejpam-5790	226	79	)	)	PUNCT
ejpam-5790	227	1	σ2∑	σ2∑	PROPN
ejpam-5790	227	2	σ1=0	σ1=0	PROPN
ejpam-5790	227	3	cσ1	cσ1	NOUN
ejpam-5790	227	4	σ2	σ2	NOUN
ejpam-5790	227	5	1	1	NUM
ejpam-5790	227	6	2	2	NUM
ejpam-5790	227	7	(	(	PUNCT
ejpam-5790	227	8	ϑ(u)⊗	ϑ(u)⊗	NOUN
ejpam-5790	227	9	1)2σ1(1⊗ℑ(d))2σ2−2σ1	1)2σ1(1⊗ℑ(d))2σ2−2σ1	NUM
ejpam-5790	227	10	=	=	SYM
ejpam-5790	227	11	(	(	PUNCT
ejpam-5790	227	12	ℑ(u)⊗	ℑ(u)⊗	PROPN
ejpam-5790	227	13	1	1	NUM
ejpam-5790	227	14	+	+	SYM
ejpam-5790	227	15	1⊗d(d	1⊗d(d	NUM
ejpam-5790	227	16	)	)	PUNCT
ejpam-5790	227	17	)	)	PUNCT
ejpam-5790	227	18	1	1	NUM
ejpam-5790	227	19	2	2	NUM
ejpam-5790	227	20	(	(	PUNCT
ejpam-5790	227	21	ϑ(u)⊗	ϑ(u)⊗	NOUN
ejpam-5790	227	22	1	1	NUM
ejpam-5790	227	23	+	+	SYM
ejpam-5790	227	24	1⊗ℑ(d))2σ2	1⊗ℑ(d))2σ2	NUM
ejpam-5790	227	25	.	.	PUNCT
ejpam-5790	228	1	taking	take	VERB
ejpam-5790	228	2	into	into	ADP
ejpam-5790	228	3	account	account	NOUN
ejpam-5790	228	4	:	:	PUNCT
ejpam-5790	228	5	if	if	SCONJ
ejpam-5790	228	6	|µ|	|µ|	PROPN
ejpam-5790	228	7	>	>	X
ejpam-5790	228	8	σ	σ	PROPN
ejpam-5790	228	9	,	,	PUNCT
ejpam-5790	228	10	then	then	ADV
ejpam-5790	228	11	ℑ	ℑ	PROPN
ejpam-5790	228	12	:	:	PUNCT
ejpam-5790	228	13	=	=	SYM
ejpam-5790	228	14	∫	∫	PROPN
ejpam-5790	228	15	σ1	σ1	PROPN
ejpam-5790	228	16	∫	∫	PROPN
ejpam-5790	228	17	σ2	σ2	PROPN
ejpam-5790	228	18	(	(	PUNCT
ejpam-5790	228	19	ℑ(ν2	ℑ(ν2	PROPN
ejpam-5790	228	20	)	)	PUNCT
ejpam-5790	228	21	+	+	NOUN
ejpam-5790	228	22	d(ν1))σ	d(ν1))σ	PROPN
ejpam-5790	228	23	(	(	PUNCT
ejpam-5790	228	24	|(ϑ(ν2	|(ϑ(ν2	NOUN
ejpam-5790	228	25	)	)	PUNCT
ejpam-5790	229	1	+	+	ADV
ejpam-5790	229	2	q(ν1))|σ1	q(ν1))|σ1	ADV
ejpam-5790	229	3	−	−	PROPN
ejpam-5790	229	4	σ	σ	PROPN
ejpam-5790	229	5	2	2	NUM
ejpam-5790	229	6	)	)	PUNCT
ejpam-5790	229	7	deν2	deν2	PROPN
ejpam-5790	229	8	⊗	⊗	PROPN
ejpam-5790	229	9	dfν1	dfν1	PROPN
ejpam-5790	230	1	=	=	SYM
ejpam-5790	230	2	∫	∫	PROPN
ejpam-5790	230	3	σ1	σ1	PROPN
ejpam-5790	230	4	∫	∫	PROPN
ejpam-5790	230	5	σ2	σ2	PROPN
ejpam-5790	230	6	(	(	PUNCT
ejpam-5790	230	7	ℑ(ν2	ℑ(ν2	PROPN
ejpam-5790	230	8	)	)	PUNCT
ejpam-5790	230	9	+	+	NOUN
ejpam-5790	230	10	d(ν1	d(ν1	NOUN
ejpam-5790	230	11	)	)	PUNCT
ejpam-5790	230	12	)	)	PUNCT
ejpam-5790	231	1	σ2∑	σ2∑	PROPN
ejpam-5790	231	2	σ1=0	σ1=0	PROPN
ejpam-5790	231	3	cσ1	cσ1	NOUN
ejpam-5790	231	4	σ2	σ2	PROPN
ejpam-5790	231	5	σ	σ	PROPN
ejpam-5790	231	6	(	(	PUNCT
ejpam-5790	231	7	|(ϑ(ν2))|σ1	|(ϑ(ν2))|σ1	PROPN
ejpam-5790	231	8	−	−	PROPN
ejpam-5790	231	9	σ	σ	PROPN
ejpam-5790	231	10	2	2	PROPN
ejpam-5790	231	11	)	)	PUNCT
ejpam-5790	231	12	σ	σ	NOUN
ejpam-5790	231	13	(	(	PUNCT
ejpam-5790	231	14	|(q(ν1))|σ2−σ1	|(q(ν1))|σ2−σ1	VERB
ejpam-5790	231	15	−	−	PROPN
ejpam-5790	231	16	σ	σ	NOUN
ejpam-5790	231	17	2	2	PROPN
ejpam-5790	231	18	)	)	PUNCT
ejpam-5790	231	19	deν2	deν2	PROPN
ejpam-5790	231	20	⊗	⊗	PROPN
ejpam-5790	231	21	dfν1	dfν1	PROPN
ejpam-5790	231	22	=	=	PUNCT
ejpam-5790	232	1	σ2∑	σ2∑	PROPN
ejpam-5790	232	2	σ1=0	σ1=0	PROPN
ejpam-5790	232	3	cσ1	cσ1	NOUN
ejpam-5790	232	4	σ2	σ2	PROPN
ejpam-5790	232	5	∫	∫	PROPN
ejpam-5790	232	6	σ1	σ1	PROPN
ejpam-5790	232	7	∫	∫	PROPN
ejpam-5790	232	8	σ2	σ2	PROPN
ejpam-5790	232	9	(	(	PUNCT
ejpam-5790	232	10	ℑ(ν2	ℑ(ν2	PROPN
ejpam-5790	232	11	)	)	PUNCT
ejpam-5790	232	12	+	+	NOUN
ejpam-5790	232	13	d(ν1))σ	d(ν1))σ	NOUN
ejpam-5790	232	14	(	(	PUNCT
ejpam-5790	232	15	|(ϑ(ν2))|σ1	|(ϑ(ν2))|σ1	PROPN
ejpam-5790	232	16	−	−	PROPN
ejpam-5790	232	17	σ	σ	PROPN
ejpam-5790	232	18	2	2	PROPN
ejpam-5790	232	19	)	)	PUNCT
ejpam-5790	232	20	σ	σ	NOUN
ejpam-5790	232	21	(	(	PUNCT
ejpam-5790	232	22	|(q(ν1))|σ2−σ1	|(q(ν1))|σ2−σ1	VERB
ejpam-5790	232	23	−	−	PROPN
ejpam-5790	232	24	σ	σ	NOUN
ejpam-5790	232	25	2	2	PROPN
ejpam-5790	232	26	)	)	PUNCT
ejpam-5790	232	27	deν2	deν2	PROPN
ejpam-5790	232	28	⊗	⊗	PROPN
ejpam-5790	232	29	dfν1	dfν1	PROPN
ejpam-5790	232	30	=	=	PUNCT
ejpam-5790	233	1	σ2∑	σ2∑	PROPN
ejpam-5790	233	2	σ1=0	σ1=0	PROPN
ejpam-5790	233	3	cσ1	cσ1	NOUN
ejpam-5790	233	4	σ2	σ2	PROPN
ejpam-5790	233	5	[	[	X
ejpam-5790	233	6	∫	∫	PROPN
ejpam-5790	233	7	σ1	σ1	PROPN
ejpam-5790	233	8	∫	∫	PROPN
ejpam-5790	233	9	σ2	σ2	PROPN
ejpam-5790	233	10	ℑ(ν2)σ	ℑ(ν2)σ	PROPN
ejpam-5790	233	11	(	(	PUNCT
ejpam-5790	233	12	|(ϑ(ν2))|σ1	|(ϑ(ν2))|σ1	PROPN
ejpam-5790	233	13	−	−	PROPN
ejpam-5790	233	14	σ	σ	PROPN
ejpam-5790	233	15	2	2	PROPN
ejpam-5790	233	16	)	)	PUNCT
ejpam-5790	233	17	σ	σ	NOUN
ejpam-5790	233	18	(	(	PUNCT
ejpam-5790	233	19	|(q(ν1))|σ2−σ1	|(q(ν1))|σ2−σ1	VERB
ejpam-5790	233	20	−	−	PROPN
ejpam-5790	234	1	σ	σ	NOUN
ejpam-5790	234	2	2	2	PROPN
ejpam-5790	234	3	)	)	PUNCT
ejpam-5790	234	4	deν2	deν2	PROPN
ejpam-5790	234	5	⊗	⊗	PROPN
ejpam-5790	234	6	dfν1	dfν1	PROPN
ejpam-5790	235	1	+	+	CCONJ
ejpam-5790	235	2	∫	∫	PROPN
ejpam-5790	235	3	σ1	σ1	PROPN
ejpam-5790	235	4	∫	∫	PROPN
ejpam-5790	235	5	σ2	σ2	PROPN
ejpam-5790	235	6	d(ν1)σ	d(ν1)σ	PROPN
ejpam-5790	235	7	(	(	PUNCT
ejpam-5790	235	8	|(ϑ(ν2))|σ1	|(ϑ(ν2))|σ1	PROPN
ejpam-5790	235	9	−	−	PROPN
ejpam-5790	235	10	σ	σ	PROPN
ejpam-5790	235	11	2	2	PROPN
ejpam-5790	235	12	)	)	PUNCT
ejpam-5790	235	13	σ	σ	NOUN
ejpam-5790	235	14	(	(	PUNCT
ejpam-5790	235	15	|(q(ν1))|σ2−σ1	|(q(ν1))|σ2−σ1	VERB
ejpam-5790	235	16	−	−	PROPN
ejpam-5790	235	17	σ	σ	NOUN
ejpam-5790	235	18	2	2	PROPN
ejpam-5790	235	19	)	)	PUNCT
ejpam-5790	235	20	deν2	deν2	PROPN
ejpam-5790	235	21	⊗	⊗	PROPN
ejpam-5790	235	22	dfν1	dfν1	PROPN
ejpam-5790	235	23	]	]	PUNCT
ejpam-5790	235	24	.	.	PUNCT
ejpam-5790	236	1	observe	observe	VERB
ejpam-5790	236	2	that∫	that∫	PROPN
ejpam-5790	236	3	σ1	σ1	PROPN
ejpam-5790	236	4	∫	∫	PROPN
ejpam-5790	236	5	σ2	σ2	PROPN
ejpam-5790	236	6	ℑ(ν2)σ	ℑ(ν2)σ	PROPN
ejpam-5790	236	7	(	(	PUNCT
ejpam-5790	236	8	|(ϑ(ν2))|σ1	|(ϑ(ν2))|σ1	PROPN
ejpam-5790	236	9	−	−	PROPN
ejpam-5790	236	10	σ	σ	PROPN
ejpam-5790	236	11	2	2	PROPN
ejpam-5790	236	12	)	)	PUNCT
ejpam-5790	236	13	σ	σ	NOUN
ejpam-5790	236	14	(	(	PUNCT
ejpam-5790	236	15	|(q(ν1))|σ2−σ1	|(q(ν1))|σ2−σ1	VERB
ejpam-5790	236	16	−	−	PROPN
ejpam-5790	236	17	σ	σ	NOUN
ejpam-5790	236	18	2	2	PROPN
ejpam-5790	236	19	)	)	PUNCT
ejpam-5790	236	20	deν2	deν2	PROPN
ejpam-5790	236	21	⊗	⊗	PROPN
ejpam-5790	236	22	dfν1	dfν1	PROPN
ejpam-5790	237	1	=	=	PUNCT
ejpam-5790	237	2	ℑ(u)σ	ℑ(u)σ	NOUN
ejpam-5790	237	3	(	(	PUNCT
ejpam-5790	237	4	|(ϑ(u))|σ1	|(ϑ(u))|σ1	X
ejpam-5790	237	5	−	−	PROPN
ejpam-5790	237	6	σ	σ	PROPN
ejpam-5790	237	7	2	2	PROPN
ejpam-5790	237	8	)	)	PUNCT
ejpam-5790	237	9	⊗	⊗	PROPN
ejpam-5790	237	10	σ	σ	PROPN
ejpam-5790	237	11	(	(	PUNCT
ejpam-5790	237	12	|(ℑ(d))|σ2−σ1	|(ℑ(d))|σ2−σ1	PROPN
ejpam-5790	237	13	−	−	PROPN
ejpam-5790	237	14	σ	σ	NOUN
ejpam-5790	237	15	2	2	NUM
ejpam-5790	237	16	)	)	PUNCT
ejpam-5790	237	17	=	=	PUNCT
ejpam-5790	237	18	(	(	PUNCT
ejpam-5790	237	19	ℑ(u)⊗	ℑ(u)⊗	PROPN
ejpam-5790	237	20	1	1	NUM
ejpam-5790	237	21	)	)	PUNCT
ejpam-5790	237	22	[	[	PUNCT
ejpam-5790	237	23	σ	σ	X
ejpam-5790	237	24	(	(	PUNCT
ejpam-5790	237	25	|(ϑ(u))|σ1	|(ϑ(u))|σ1	NOUN
ejpam-5790	237	26	−	−	PROPN
ejpam-5790	237	27	σ	σ	PROPN
ejpam-5790	237	28	2	2	PROPN
ejpam-5790	237	29	)	)	PUNCT
ejpam-5790	237	30	⊗	⊗	PROPN
ejpam-5790	237	31	σ	σ	PROPN
ejpam-5790	237	32	(	(	PUNCT
ejpam-5790	237	33	|(ℑ(d))|σ2−σ1	|(ℑ(d))|σ2−σ1	PROPN
ejpam-5790	237	34	−	−	PROPN
ejpam-5790	237	35	σ	σ	NOUN
ejpam-5790	237	36	2	2	NUM
ejpam-5790	237	37	)	)	PUNCT
ejpam-5790	237	38	]	]	PUNCT
ejpam-5790	237	39	=	=	PUNCT
ejpam-5790	237	40	(	(	PUNCT
ejpam-5790	237	41	ℑ(u)⊗	ℑ(u)⊗	PROPN
ejpam-5790	237	42	1	1	NUM
ejpam-5790	237	43	)	)	PUNCT
ejpam-5790	238	1	[	[	PUNCT
ejpam-5790	238	2	σ	σ	X
ejpam-5790	238	3	(	(	PUNCT
ejpam-5790	238	4	|(ϑ(u))|σ1	|(ϑ(u))|σ1	PROPN
ejpam-5790	238	5	⊗	⊗	PROPN
ejpam-5790	238	6	1−	1−	NUM
ejpam-5790	238	7	σ	σ	PROPN
ejpam-5790	238	8	2	2	PROPN
ejpam-5790	238	9	)	)	PUNCT
ejpam-5790	238	10	⊗	⊗	PROPN
ejpam-5790	238	11	σ	σ	PROPN
ejpam-5790	238	12	(	(	PUNCT
ejpam-5790	238	13	1⊗	1⊗	NUM
ejpam-5790	238	14	|(ℑ(d))|σ2−σ1	|(ℑ(d))|σ2−σ1	NOUN
ejpam-5790	238	15	−	−	PROPN
ejpam-5790	238	16	σ	σ	NOUN
ejpam-5790	238	17	2	2	NUM
ejpam-5790	238	18	)	)	PUNCT
ejpam-5790	238	19	]	]	PUNCT
ejpam-5790	239	1	=	=	PUNCT
ejpam-5790	239	2	(	(	PUNCT
ejpam-5790	239	3	ℑ(u)⊗	ℑ(u)⊗	PROPN
ejpam-5790	239	4	1	1	NUM
ejpam-5790	239	5	)	)	PUNCT
ejpam-5790	239	6	[	[	PUNCT
ejpam-5790	239	7	σ	σ	X
ejpam-5790	239	8	(	(	PUNCT
ejpam-5790	239	9	(	(	PUNCT
ejpam-5790	239	10	|(ϑ(u))|	|(ϑ(u))|	X
ejpam-5790	239	11	⊗	⊗	PROPN
ejpam-5790	239	12	1)σ1	1)σ1	NUM
ejpam-5790	239	13	−	−	PROPN
ejpam-5790	239	14	σ	σ	PROPN
ejpam-5790	239	15	2	2	PROPN
ejpam-5790	239	16	)	)	PUNCT
ejpam-5790	239	17	⊗	⊗	PROPN
ejpam-5790	239	18	σ	σ	PROPN
ejpam-5790	239	19	(	(	PUNCT
ejpam-5790	239	20	(	(	PUNCT
ejpam-5790	239	21	1⊗	1⊗	NUM
ejpam-5790	239	22	|(ℑ(d))|)σ2−σ1	|(ℑ(d))|)σ2−σ1	NOUN
ejpam-5790	239	23	−	−	PROPN
ejpam-5790	239	24	σ	σ	PROPN
ejpam-5790	239	25	2	2	NUM
ejpam-5790	239	26	)	)	PUNCT
ejpam-5790	239	27	]	]	PUNCT
ejpam-5790	239	28	w.	w.	PROPN
ejpam-5790	239	29	afzal	afzal	PROPN
ejpam-5790	239	30	et	et	PROPN
ejpam-5790	239	31	al	al	PROPN
ejpam-5790	239	32	.	.	PUNCT
ejpam-5790	239	33	/	/	SYM
ejpam-5790	239	34	eur	eur	PROPN
ejpam-5790	239	35	.	.	PUNCT
ejpam-5790	240	1	j.	j.	PROPN
ejpam-5790	240	2	pure	pure	PROPN
ejpam-5790	240	3	appl	appl	PROPN
ejpam-5790	240	4	.	.	PROPN
ejpam-5790	240	5	math	math	PROPN
ejpam-5790	240	6	,	,	PUNCT
ejpam-5790	240	7	18	18	NUM
ejpam-5790	240	8	(	(	PUNCT
ejpam-5790	240	9	1	1	NUM
ejpam-5790	240	10	)	)	PUNCT
ejpam-5790	240	11	(	(	PUNCT
ejpam-5790	240	12	2025	2025	NUM
ejpam-5790	240	13	)	)	PUNCT
ejpam-5790	240	14	,	,	PUNCT
ejpam-5790	240	15	5790	5790	NUM
ejpam-5790	240	16	11	11	NUM
ejpam-5790	240	17	of	of	ADP
ejpam-5790	240	18	30	30	NUM
ejpam-5790	240	19	and	and	CCONJ
ejpam-5790	240	20	∫	∫	PROPN
ejpam-5790	240	21	σ1	σ1	PROPN
ejpam-5790	240	22	∫	∫	PROPN
ejpam-5790	240	23	σ2	σ2	PROPN
ejpam-5790	240	24	d(ν1)σ	d(ν1)σ	PROPN
ejpam-5790	240	25	(	(	PUNCT
ejpam-5790	240	26	|(ϑ(ν2))|σ1	|(ϑ(ν2))|σ1	PROPN
ejpam-5790	240	27	−	−	PROPN
ejpam-5790	240	28	σ	σ	PROPN
ejpam-5790	240	29	2	2	PROPN
ejpam-5790	240	30	)	)	PUNCT
ejpam-5790	240	31	σ	σ	NOUN
ejpam-5790	240	32	(	(	PUNCT
ejpam-5790	240	33	|(q(ν1))|σ2−σ1	|(q(ν1))|σ2−σ1	VERB
ejpam-5790	240	34	−	−	PROPN
ejpam-5790	240	35	σ	σ	NOUN
ejpam-5790	240	36	2	2	PROPN
ejpam-5790	240	37	)	)	PUNCT
ejpam-5790	241	1	deν2	deν2	PROPN
ejpam-5790	241	2	⊗	⊗	PROPN
ejpam-5790	241	3	dfν1	dfν1	PROPN
ejpam-5790	241	4	=	=	SYM
ejpam-5790	241	5	d(ν1)σ	d(ν1)σ	PROPN
ejpam-5790	241	6	(	(	PUNCT
ejpam-5790	241	7	|(ϑ(u))|σ1	|(ϑ(u))|σ1	X
ejpam-5790	241	8	−	−	PROPN
ejpam-5790	241	9	σ	σ	PROPN
ejpam-5790	241	10	2	2	PROPN
ejpam-5790	241	11	)	)	PUNCT
ejpam-5790	241	12	⊗	⊗	PROPN
ejpam-5790	241	13	σ	σ	PROPN
ejpam-5790	241	14	(	(	PUNCT
ejpam-5790	241	15	|(ℑ(d))|σ2−σ1	|(ℑ(d))|σ2−σ1	PROPN
ejpam-5790	241	16	−	−	PROPN
ejpam-5790	241	17	σ	σ	NOUN
ejpam-5790	241	18	2	2	NUM
ejpam-5790	241	19	)	)	PUNCT
ejpam-5790	241	20	=	=	PUNCT
ejpam-5790	241	21	(	(	PUNCT
ejpam-5790	241	22	1⊗d(ν1	1⊗d(ν1	NUM
ejpam-5790	241	23	)	)	PUNCT
ejpam-5790	241	24	)	)	PUNCT
ejpam-5790	242	1	[	[	PUNCT
ejpam-5790	242	2	σ	σ	X
ejpam-5790	242	3	(	(	PUNCT
ejpam-5790	242	4	|(ϑ(u))|σ1	|(ϑ(u))|σ1	NOUN
ejpam-5790	242	5	−	−	PROPN
ejpam-5790	242	6	σ	σ	PROPN
ejpam-5790	242	7	2	2	PROPN
ejpam-5790	242	8	)	)	PUNCT
ejpam-5790	242	9	⊗	⊗	PROPN
ejpam-5790	242	10	σ	σ	PROPN
ejpam-5790	242	11	(	(	PUNCT
ejpam-5790	242	12	|(ℑ(d))|σ2−σ1	|(ℑ(d))|σ2−σ1	PROPN
ejpam-5790	242	13	−	−	PROPN
ejpam-5790	242	14	σ	σ	NOUN
ejpam-5790	242	15	2	2	NUM
ejpam-5790	242	16	)	)	PUNCT
ejpam-5790	242	17	]	]	PUNCT
ejpam-5790	243	1	=	=	PUNCT
ejpam-5790	243	2	(	(	PUNCT
ejpam-5790	243	3	1⊗d(ν1	1⊗d(ν1	NUM
ejpam-5790	243	4	)	)	PUNCT
ejpam-5790	243	5	)	)	PUNCT
ejpam-5790	244	1	[	[	PUNCT
ejpam-5790	244	2	σ	σ	X
ejpam-5790	244	3	(	(	PUNCT
ejpam-5790	244	4	|(ϑ(u))|σ1	|(ϑ(u))|σ1	PROPN
ejpam-5790	244	5	⊗	⊗	PROPN
ejpam-5790	244	6	1−	1−	NUM
ejpam-5790	244	7	σ	σ	PROPN
ejpam-5790	244	8	2	2	PROPN
ejpam-5790	244	9	)	)	PUNCT
ejpam-5790	244	10	⊗	⊗	PROPN
ejpam-5790	244	11	σ	σ	PROPN
ejpam-5790	244	12	(	(	PUNCT
ejpam-5790	244	13	1⊗	1⊗	NUM
ejpam-5790	244	14	|(ℑ(d))|σ2−σ1	|(ℑ(d))|σ2−σ1	NOUN
ejpam-5790	244	15	−	−	PROPN
ejpam-5790	244	16	σ	σ	NOUN
ejpam-5790	244	17	2	2	NUM
ejpam-5790	244	18	)	)	PUNCT
ejpam-5790	244	19	]	]	PUNCT
ejpam-5790	245	1	=	=	PUNCT
ejpam-5790	245	2	(	(	PUNCT
ejpam-5790	245	3	1⊗d(ν1	1⊗d(ν1	NUM
ejpam-5790	245	4	)	)	PUNCT
ejpam-5790	245	5	)	)	PUNCT
ejpam-5790	246	1	[	[	PUNCT
ejpam-5790	246	2	σ	σ	X
ejpam-5790	246	3	(	(	PUNCT
ejpam-5790	246	4	(	(	PUNCT
ejpam-5790	246	5	|(ϑ(u))|	|(ϑ(u))|	X
ejpam-5790	246	6	⊗	⊗	PROPN
ejpam-5790	246	7	1)σ1	1)σ1	NUM
ejpam-5790	246	8	−	−	PROPN
ejpam-5790	246	9	σ	σ	PROPN
ejpam-5790	246	10	2	2	PROPN
ejpam-5790	246	11	)	)	PUNCT
ejpam-5790	246	12	⊗	⊗	PROPN
ejpam-5790	246	13	σ	σ	PROPN
ejpam-5790	246	14	(	(	PUNCT
ejpam-5790	246	15	(	(	PUNCT
ejpam-5790	246	16	1⊗	1⊗	NUM
ejpam-5790	246	17	|(ℑ(d))|)σ2−σ1	|(ℑ(d))|)σ2−σ1	NOUN
ejpam-5790	246	18	−	−	PROPN
ejpam-5790	246	19	σ	σ	PROPN
ejpam-5790	246	20	2	2	NUM
ejpam-5790	246	21	)	)	PUNCT
ejpam-5790	246	22	]	]	PUNCT
ejpam-5790	246	23	where	where	SCONJ
ejpam-5790	246	24	σ	σ	PROPN
ejpam-5790	246	25	(	(	PUNCT
ejpam-5790	246	26	|(ϑ(u))|	|(ϑ(u))|	PROPN
ejpam-5790	246	27	⊗	⊗	PROPN
ejpam-5790	246	28	1)−	1)−	PROPN
ejpam-5790	246	29	σ	σ	PROPN
ejpam-5790	246	30	2	2	NUM
ejpam-5790	246	31	)	)	PUNCT
ejpam-5790	246	32	and	and	CCONJ
ejpam-5790	246	33	σ	σ	NUM
ejpam-5790	246	34	(	(	PUNCT
ejpam-5790	246	35	1⊗	1⊗	NUM
ejpam-5790	246	36	|(ℑ(d))|)−	|(ℑ(d))|)−	PROPN
ejpam-5790	246	37	σ	σ	PROPN
ejpam-5790	246	38	2	2	NUM
ejpam-5790	246	39	)	)	PUNCT
ejpam-5790	246	40	are	be	AUX
ejpam-5790	246	41	commute	commute	NOUN
ejpam-5790	246	42	with	with	ADP
ejpam-5790	246	43	each	each	DET
ejpam-5790	246	44	other	other	ADJ
ejpam-5790	246	45	.	.	PUNCT
ejpam-5790	247	1	therefore	therefore	ADV
ejpam-5790	247	2	ℑ	ℑ	PROPN
ejpam-5790	247	3	=	=	SYM
ejpam-5790	247	4	(	(	PUNCT
ejpam-5790	247	5	ℑ(u)⊗	ℑ(u)⊗	PROPN
ejpam-5790	247	6	1	1	NUM
ejpam-5790	247	7	+	+	SYM
ejpam-5790	247	8	1⊗d(d	1⊗d(d	NUM
ejpam-5790	247	9	)	)	PUNCT
ejpam-5790	247	10	)	)	PUNCT
ejpam-5790	248	1	σ2∑	σ2∑	PROPN
ejpam-5790	248	2	σ1=0	σ1=0	PROPN
ejpam-5790	248	3	cσ1	cσ1	NOUN
ejpam-5790	248	4	σ2	σ2	PROPN
ejpam-5790	248	5	σ	σ	PROPN
ejpam-5790	248	6	(	(	PUNCT
ejpam-5790	248	7	(	(	PUNCT
ejpam-5790	248	8	|(ϑ(u))|	|(ϑ(u))|	X
ejpam-5790	248	9	⊗	⊗	PROPN
ejpam-5790	248	10	1)σ1	1)σ1	NUM
ejpam-5790	248	11	−	−	PROPN
ejpam-5790	248	12	σ	σ	PROPN
ejpam-5790	248	13	2	2	NUM
ejpam-5790	248	14	)	)	PUNCT
ejpam-5790	248	15	σ	σ	NOUN
ejpam-5790	248	16	(	(	PUNCT
ejpam-5790	248	17	(	(	PUNCT
ejpam-5790	248	18	1⊗	1⊗	NUM
ejpam-5790	248	19	|(ℑ(d))|)σ2−σ1	|(ℑ(d))|)σ2−σ1	NOUN
ejpam-5790	248	20	−	−	PROPN
ejpam-5790	248	21	σ	σ	PROPN
ejpam-5790	248	22	2	2	NUM
ejpam-5790	248	23	)	)	PUNCT
ejpam-5790	248	24	=	=	PUNCT
ejpam-5790	248	25	(	(	PUNCT
ejpam-5790	248	26	ℑ(u)⊗	ℑ(u)⊗	NOUN
ejpam-5790	248	27	1	1	NUM
ejpam-5790	248	28	+	+	SYM
ejpam-5790	248	29	1⊗d(d	1⊗d(d	NUM
ejpam-5790	248	30	)	)	PUNCT
ejpam-5790	248	31	)	)	PUNCT
ejpam-5790	249	1	[	[	PUNCT
ejpam-5790	249	2	σ	σ	X
ejpam-5790	249	3	(	(	PUNCT
ejpam-5790	249	4	(	(	PUNCT
ejpam-5790	249	5	|(ϑ(u))|	|(ϑ(u))|	X
ejpam-5790	249	6	⊗	⊗	PROPN
ejpam-5790	249	7	1)−	1)−	PROPN
ejpam-5790	249	8	σ	σ	PROPN
ejpam-5790	249	9	2	2	NUM
ejpam-5790	249	10	)	)	PUNCT
ejpam-5790	249	11	+	+	CCONJ
ejpam-5790	249	12	σ	σ	NOUN
ejpam-5790	249	13	(	(	PUNCT
ejpam-5790	249	14	(	(	PUNCT
ejpam-5790	249	15	1⊗	1⊗	NUM
ejpam-5790	249	16	|(ℑ(d))|)−	|(ℑ(d))|)−	PROPN
ejpam-5790	249	17	σ	σ	PROPN
ejpam-5790	249	18	2	2	NUM
ejpam-5790	249	19	)	)	PUNCT
ejpam-5790	249	20	]	]	PUNCT
ejpam-5790	249	21	σ2	σ2	PROPN
ejpam-5790	249	22	lemma	lemma	PROPN
ejpam-5790	249	23	3	3	X
ejpam-5790	249	24	.	.	PUNCT
ejpam-5790	249	25	let	let	VERB
ejpam-5790	249	26	u	u	PRON
ejpam-5790	249	27	and	and	CCONJ
ejpam-5790	249	28	d	d	AUX
ejpam-5790	249	29	be	be	AUX
ejpam-5790	249	30	adjoint	adjoint	NOUN
ejpam-5790	249	31	operators	operator	NOUN
ejpam-5790	249	32	,	,	PUNCT
ejpam-5790	249	33	with	with	ADP
ejpam-5790	249	34	their	their	PRON
ejpam-5790	249	35	spectra	spectra	NOUN
ejpam-5790	249	36	lying	lie	VERB
ejpam-5790	249	37	within	within	ADP
ejpam-5790	249	38	the	the	DET
ejpam-5790	249	39	sets	set	NOUN
ejpam-5790	249	40	∆1	∆1	PUNCT
ejpam-5790	249	41	and	and	CCONJ
ejpam-5790	249	42	∆2	∆2	PROPN
ejpam-5790	249	43	,	,	PUNCT
ejpam-5790	249	44	respectively	respectively	ADV
ejpam-5790	249	45	.	.	PUNCT
ejpam-5790	250	1	assume	assume	VERB
ejpam-5790	250	2	that	that	SCONJ
ejpam-5790	250	3	the	the	DET
ejpam-5790	250	4	functions	function	NOUN
ejpam-5790	250	5	ℑ	ℑ	PROPN
ejpam-5790	250	6	and	and	CCONJ
ejpam-5790	250	7	ϑ	ϑ	X
ejpam-5790	250	8	are	be	AUX
ejpam-5790	250	9	continuous	continuous	ADJ
ejpam-5790	250	10	on	on	ADP
ejpam-5790	250	11	∆1	∆1	NOUN
ejpam-5790	250	12	,	,	PUNCT
ejpam-5790	250	13	while	while	SCONJ
ejpam-5790	250	14	d	d	PROPN
ejpam-5790	250	15	and	and	CCONJ
ejpam-5790	250	16	ℑ	ℑ	PROPN
ejpam-5790	250	17	are	be	AUX
ejpam-5790	250	18	continuous	continuous	ADJ
ejpam-5790	250	19	on	on	ADP
ejpam-5790	250	20	∆2	∆2	PROPN
ejpam-5790	250	21	,	,	PUNCT
ejpam-5790	250	22	and	and	CCONJ
ejpam-5790	250	23	φ	φ	PROPN
ejpam-5790	250	24	is	be	AUX
ejpam-5790	250	25	convex	convex	ADJ
ejpam-5790	250	26	on	on	ADP
ejpam-5790	250	27	∆.	∆.	NOUN
ejpam-5790	250	28	then	then	ADV
ejpam-5790	250	29	,	,	PUNCT
ejpam-5790	250	30	the	the	DET
ejpam-5790	250	31	product	product	NOUN
ejpam-5790	250	32	of	of	ADP
ejpam-5790	250	33	the	the	DET
ejpam-5790	250	34	intervals	interval	NOUN
ejpam-5790	250	35	ϑ(∆1	ϑ(∆1	NOUN
ejpam-5790	250	36	)	)	PUNCT
ejpam-5790	250	37	+	+	NUM
ejpam-5790	250	38	ℑ(∆2	ℑ(∆2	NOUN
ejpam-5790	250	39	)	)	PUNCT
ejpam-5790	250	40	satisfies	satisfy	VERB
ejpam-5790	250	41	the	the	DET
ejpam-5790	250	42	following	follow	VERB
ejpam-5790	250	43	equality	equality	NOUN
ejpam-5790	250	44	:	:	PUNCT
ejpam-5790	250	45	φ(ℑ(u)⊗d(d))χ(ϑ(u)⊗ℑ(d	φ(ℑ(u)⊗d(d))χ(ϑ(u)⊗ℑ(d	PROPN
ejpam-5790	250	46	)	)	PUNCT
ejpam-5790	250	47	)	)	PUNCT
ejpam-5790	251	1	=	=	SYM
ejpam-5790	251	2	∫	∫	PROPN
ejpam-5790	252	1	∆1	∆1	PROPN
ejpam-5790	253	1	∫	∫	PROPN
ejpam-5790	254	1	∆2	∆2	PROPN
ejpam-5790	255	1	φ(ℑ(ν2)d(ν1))χ(ϑ(ν2)ℑ(ν1))deν1	φ(ℑ(ν2)d(ν1))χ(ϑ(ν2)ℑ(ν1))deν1	PROPN
ejpam-5790	255	2	⊗	⊗	PROPN
ejpam-5790	255	3	dfν2	dfν2	PROPN
ejpam-5790	255	4	(	(	PUNCT
ejpam-5790	255	5	2.5	2.5	NUM
ejpam-5790	255	6	)	)	PUNCT
ejpam-5790	255	7	where	where	SCONJ
ejpam-5790	255	8	u	u	NOUN
ejpam-5790	255	9	and	and	CCONJ
ejpam-5790	255	10	d	d	PROPN
ejpam-5790	255	11	have	have	VERB
ejpam-5790	255	12	the	the	DET
ejpam-5790	255	13	spectral	spectral	ADJ
ejpam-5790	255	14	resolutions	resolution	NOUN
ejpam-5790	255	15	u	u	NOUN
ejpam-5790	255	16	=	=	PROPN
ejpam-5790	255	17	∫	∫	PROPN
ejpam-5790	255	18	∆1	∆1	PROPN
ejpam-5790	255	19	ν2de(ν2	ν2de(ν2	PROPN
ejpam-5790	255	20	)	)	PUNCT
ejpam-5790	255	21	and	and	CCONJ
ejpam-5790	255	22	d	d	NOUN
ejpam-5790	255	23	=	=	SYM
ejpam-5790	255	24	∫	∫	PROPN
ejpam-5790	255	25	∆2	∆2	PROPN
ejpam-5790	255	26	ν1df(ν1	ν1df(ν1	PROPN
ejpam-5790	255	27	)	)	PUNCT
ejpam-5790	255	28	.	.	PUNCT
ejpam-5790	256	1	proof	proof	NOUN
ejpam-5790	256	2	.	.	PUNCT
ejpam-5790	257	1	according	accord	VERB
ejpam-5790	257	2	to	to	ADP
ejpam-5790	257	3	weierstrass	weierstrass	NOUN
ejpam-5790	257	4	,	,	PUNCT
ejpam-5790	257	5	any	any	DET
ejpam-5790	257	6	real	real	ADV
ejpam-5790	257	7	-	-	PUNCT
ejpam-5790	257	8	valued	value	VERB
ejpam-5790	257	9	differentiable	differentiable	ADJ
ejpam-5790	257	10	mapping	mapping	NOUN
ejpam-5790	257	11	can	can	AUX
ejpam-5790	257	12	be	be	AUX
ejpam-5790	257	13	represented	represent	VERB
ejpam-5790	257	14	in	in	ADP
ejpam-5790	257	15	terms	term	NOUN
ejpam-5790	257	16	of	of	ADP
ejpam-5790	257	17	polynomial	polynomial	ADJ
ejpam-5790	257	18	sequence	sequence	NOUN
ejpam-5790	257	19	,	,	PUNCT
ejpam-5790	257	20	hence	hence	ADV
ejpam-5790	257	21	simply	simply	ADV
ejpam-5790	257	22	checking	check	VERB
ejpam-5790	257	23	its	its	PRON
ejpam-5790	257	24	equivalence	equivalence	NOUN
ejpam-5790	257	25	is	be	AUX
ejpam-5790	257	26	adequate	adequate	ADJ
ejpam-5790	257	27	.	.	PUNCT
ejpam-5790	258	1	let	let	VERB
ejpam-5790	258	2	two	two	NUM
ejpam-5790	258	3	non	non	ADJ
ejpam-5790	258	4	-	-	ADJ
ejpam-5790	258	5	negative	negative	ADJ
ejpam-5790	258	6	mappings	mapping	NOUN
ejpam-5790	258	7	φ(µ	φ(µ	NOUN
ejpam-5790	258	8	)	)	PUNCT
ejpam-5790	259	1	=	=	SYM
ejpam-5790	259	2	eµσ1	eµσ1	NOUN
ejpam-5790	259	3	,	,	PUNCT
ejpam-5790	259	4	χ(µ	χ(µ	PROPN
ejpam-5790	259	5	)	)	PUNCT
ejpam-5790	259	6	=	=	PUNCT
ejpam-5790	259	7	eµσ2	eµσ2	PROPN
ejpam-5790	259	8	with	with	ADP
ejpam-5790	259	9	σ1	σ1	PROPN
ejpam-5790	259	10	and	and	CCONJ
ejpam-5790	259	11	σ2	σ2	NOUN
ejpam-5790	259	12	for	for	ADP
ejpam-5790	259	13	each	each	DET
ejpam-5790	259	14	natural	natural	ADJ
ejpam-5790	259	15	numbers	number	NOUN
ejpam-5790	259	16	,	,	PUNCT
ejpam-5790	259	17	one	one	NUM
ejpam-5790	259	18	has	have	AUX
ejpam-5790	259	19	∫	∫	PROPN
ejpam-5790	259	20	∆1	∆1	PROPN
ejpam-5790	259	21	∫	∫	PROPN
ejpam-5790	259	22	∆2	∆2	PROPN
ejpam-5790	259	23	(	(	PUNCT
ejpam-5790	259	24	eν1eν2)σ2(eν1eν2)σ1deν1	eν1eν2)σ2(eν1eν2)σ1deν1	PROPN
ejpam-5790	259	25	⊗	⊗	PROPN
ejpam-5790	259	26	dfν2	dfν2	PROPN
ejpam-5790	259	27	=	=	SYM
ejpam-5790	259	28	∫	∫	PROPN
ejpam-5790	260	1	∆1	∆1	PROPN
ejpam-5790	260	2	∫	∫	PROPN
ejpam-5790	260	3	∆2	∆2	PROPN
ejpam-5790	261	1	[	[	X
ejpam-5790	261	2	eν1	eν1	X
ejpam-5790	261	3	]	]	X
ejpam-5790	261	4	σ2	σ2	NOUN
ejpam-5790	262	1	[	[	X
ejpam-5790	262	2	eν2	eν2	X
ejpam-5790	262	3	]	]	X
ejpam-5790	262	4	σ2	σ2	NOUN
ejpam-5790	263	1	[	[	X
ejpam-5790	263	2	eν1	eν1	X
ejpam-5790	263	3	]	]	X
ejpam-5790	263	4	σ1	σ1	NOUN
ejpam-5790	264	1	[	[	X
ejpam-5790	264	2	eν2	eν2	X
ejpam-5790	264	3	]	]	X
ejpam-5790	264	4	σ1deν1	σ1deν1	NOUN
ejpam-5790	264	5	⊗	⊗	NOUN
ejpam-5790	264	6	dfν2	dfν2	NOUN
ejpam-5790	264	7	=	=	SYM
ejpam-5790	264	8	∫	∫	PROPN
ejpam-5790	264	9	∆1	∆1	PROPN
ejpam-5790	264	10	∫	∫	PROPN
ejpam-5790	264	11	∆2	∆2	PROPN
ejpam-5790	265	1	[	[	X
ejpam-5790	265	2	eν1	eν1	X
ejpam-5790	265	3	]	]	X
ejpam-5790	265	4	σ2	σ2	NOUN
ejpam-5790	265	5	[	[	X
ejpam-5790	265	6	eν1	eν1	X
ejpam-5790	265	7	]	]	X
ejpam-5790	265	8	σ1	σ1	NOUN
ejpam-5790	266	1	[	[	X
ejpam-5790	266	2	eν2	eν2	X
ejpam-5790	266	3	]	]	X
ejpam-5790	266	4	σ2	σ2	NOUN
ejpam-5790	266	5	[	[	X
ejpam-5790	266	6	eν2	eν2	X
ejpam-5790	266	7	]	]	X
ejpam-5790	266	8	σ1deν1	σ1deν1	NOUN
ejpam-5790	266	9	⊗	⊗	NOUN
ejpam-5790	266	10	dfν2	dfν2	NOUN
ejpam-5790	266	11	=	=	PUNCT
ejpam-5790	267	1	(	(	PUNCT
ejpam-5790	267	2	[	[	X
ejpam-5790	267	3	eu	eu	X
ejpam-5790	267	4	]	]	X
ejpam-5790	267	5	σ2	σ2	PROPN
ejpam-5790	267	6	[	[	X
ejpam-5790	267	7	eu	eu	X
ejpam-5790	267	8	]	]	X
ejpam-5790	267	9	σ1	σ1	X
ejpam-5790	267	10	)	)	PUNCT
ejpam-5790	268	1	⊗	⊗	PROPN
ejpam-5790	268	2	(	(	PUNCT
ejpam-5790	268	3	[	[	X
ejpam-5790	268	4	ed]σ2	ed]σ2	NOUN
ejpam-5790	268	5	[	[	X
ejpam-5790	268	6	ed]σ1	ed]σ1	NOUN
ejpam-5790	268	7	)	)	PUNCT
ejpam-5790	269	1	=	=	PUNCT
ejpam-5790	270	1	(	(	PUNCT
ejpam-5790	270	2	[	[	X
ejpam-5790	270	3	eu	eu	X
ejpam-5790	270	4	]	]	PUNCT
ejpam-5790	270	5	σ2	σ2	PROPN
ejpam-5790	270	6	⊗	⊗	PROPN
ejpam-5790	270	7	[	[	X
ejpam-5790	270	8	ed]σ2	ed]σ2	NOUN
ejpam-5790	270	9	)	)	PUNCT
ejpam-5790	270	10	(	(	PUNCT
ejpam-5790	271	1	[	[	X
ejpam-5790	271	2	eu	eu	X
ejpam-5790	271	3	]	]	X
ejpam-5790	271	4	σ1	σ1	PROPN
ejpam-5790	271	5	⊗	⊗	PROPN
ejpam-5790	271	6	[	[	X
ejpam-5790	271	7	ed]σ1	ed]σ1	NOUN
ejpam-5790	271	8	)	)	PUNCT
ejpam-5790	271	9	=	=	PUNCT
ejpam-5790	272	1	(	(	PUNCT
ejpam-5790	272	2	eu	eu	PROPN
ejpam-5790	272	3	⊗	⊗	PROPN
ejpam-5790	272	4	ed)σ2(eu	ed)σ2(eu	PROPN
ejpam-5790	272	5	⊗	⊗	PROPN
ejpam-5790	272	6	ed)σ1	ed)σ1	PROPN
ejpam-5790	272	7	and	and	CCONJ
ejpam-5790	272	8	the	the	DET
ejpam-5790	272	9	equality	equality	NOUN
ejpam-5790	272	10	(	(	PUNCT
ejpam-5790	272	11	2.5	2.5	NUM
ejpam-5790	272	12	)	)	PUNCT
ejpam-5790	272	13	is	be	AUX
ejpam-5790	272	14	proven	prove	VERB
ejpam-5790	272	15	.	.	PUNCT
ejpam-5790	273	1	w.	w.	PROPN
ejpam-5790	273	2	afzal	afzal	PROPN
ejpam-5790	273	3	et	et	PROPN
ejpam-5790	273	4	al	al	PROPN
ejpam-5790	273	5	.	.	PUNCT
ejpam-5790	273	6	/	/	SYM
ejpam-5790	273	7	eur	eur	PROPN
ejpam-5790	273	8	.	.	PUNCT
ejpam-5790	274	1	j.	j.	PROPN
ejpam-5790	274	2	pure	pure	PROPN
ejpam-5790	274	3	appl	appl	PROPN
ejpam-5790	274	4	.	.	PROPN
ejpam-5790	274	5	math	math	PROPN
ejpam-5790	274	6	,	,	PUNCT
ejpam-5790	274	7	18	18	NUM
ejpam-5790	274	8	(	(	PUNCT
ejpam-5790	274	9	1	1	NUM
ejpam-5790	274	10	)	)	PUNCT
ejpam-5790	274	11	(	(	PUNCT
ejpam-5790	274	12	2025	2025	NUM
ejpam-5790	274	13	)	)	PUNCT
ejpam-5790	274	14	,	,	PUNCT
ejpam-5790	274	15	5790	5790	NUM
ejpam-5790	274	16	12	12	NUM
ejpam-5790	274	17	of	of	ADP
ejpam-5790	274	18	30	30	NUM
ejpam-5790	274	19	3	3	NUM
ejpam-5790	274	20	.	.	PUNCT
ejpam-5790	275	1	the	the	DET
ejpam-5790	275	2	main	main	ADJ
ejpam-5790	275	3	results	result	NOUN
ejpam-5790	275	4	first	first	ADV
ejpam-5790	275	5	,	,	PUNCT
ejpam-5790	275	6	we	we	PRON
ejpam-5790	275	7	recall	recall	VERB
ejpam-5790	275	8	the	the	DET
ejpam-5790	275	9	following	follow	VERB
ejpam-5790	275	10	fractional	fractional	ADJ
ejpam-5790	275	11	operators	operator	NOUN
ejpam-5790	275	12	that	that	PRON
ejpam-5790	275	13	play	play	VERB
ejpam-5790	275	14	a	a	DET
ejpam-5790	275	15	key	key	ADJ
ejpam-5790	275	16	role	role	NOUN
ejpam-5790	275	17	in	in	ADP
ejpam-5790	275	18	our	our	PRON
ejpam-5790	275	19	main	main	ADJ
ejpam-5790	275	20	findings	finding	NOUN
ejpam-5790	275	21	:	:	PUNCT
ejpam-5790	275	22	definition	definition	NOUN
ejpam-5790	275	23	5	5	NUM
ejpam-5790	275	24	(	(	PUNCT
ejpam-5790	275	25	see	see	VERB
ejpam-5790	275	26	[	[	X
ejpam-5790	275	27	22	22	NUM
ejpam-5790	275	28	]	]	PUNCT
ejpam-5790	275	29	)	)	PUNCT
ejpam-5790	275	30	.	.	PUNCT
ejpam-5790	276	1	let	let	VERB
ejpam-5790	276	2	ℑ	ℑ	PROPN
ejpam-5790	276	3	:	:	PUNCT
ejpam-5790	277	1	[	[	X
ejpam-5790	277	2	ν1	ν1	NOUN
ejpam-5790	277	3	,	,	PUNCT
ejpam-5790	277	4	ν2	ν2	NOUN
ejpam-5790	277	5	]	]	PUNCT
ejpam-5790	277	6	→	→	SYM
ejpam-5790	277	7	r	r	NOUN
ejpam-5790	277	8	be	be	AUX
ejpam-5790	277	9	a	a	DET
ejpam-5790	277	10	continuous	continuous	ADJ
ejpam-5790	277	11	mapping	mapping	NOUN
ejpam-5790	277	12	on	on	ADP
ejpam-5790	277	13	[	[	X
ejpam-5790	277	14	ν1	ν1	NOUN
ejpam-5790	277	15	,	,	PUNCT
ejpam-5790	277	16	ν2	ν2	NOUN
ejpam-5790	277	17	]	]	PUNCT
ejpam-5790	277	18	.	.	PUNCT
ejpam-5790	278	1	for	for	ADP
ejpam-5790	278	2	s	s	PROPN
ejpam-5790	278	3	>	>	X
ejpam-5790	278	4	0	0	NUM
ejpam-5790	279	1	the	the	DET
ejpam-5790	279	2	associated	associate	VERB
ejpam-5790	279	3	integrals	integral	NOUN
ejpam-5790	279	4	are	be	AUX
ejpam-5790	279	5	defined	define	VERB
ejpam-5790	279	6	as	as	ADP
ejpam-5790	279	7	:	:	PUNCT
ejpam-5790	279	8	jsν1+,kℑ(℘	jsν1+,kℑ(℘	NUM
ejpam-5790	279	9	)	)	PUNCT
ejpam-5790	279	10	=	=	SYM
ejpam-5790	279	11	1	1	NUM
ejpam-5790	279	12	γ(s	γ(s	PROPN
ejpam-5790	279	13	)	)	PUNCT
ejpam-5790	279	14	∫	∫	PROPN
ejpam-5790	279	15	℘	℘	PROPN
ejpam-5790	279	16	ν1	ν1	NOUN
ejpam-5790	279	17	(	(	PUNCT
ejpam-5790	279	18	℘−	℘−	NOUN
ejpam-5790	279	19	ε	ε	PROPN
ejpam-5790	279	20	)	)	PUNCT
ejpam-5790	279	21	s−k	s−k	NOUN
ejpam-5790	279	22	k	k	PROPN
ejpam-5790	279	23	ℑ(ε)dε	ℑ(ε)dε	NOUN
ejpam-5790	279	24	for	for	ADP
ejpam-5790	279	25	ν1	ν1	NOUN
ejpam-5790	279	26	<	<	X
ejpam-5790	279	27	℘	℘	PROPN
ejpam-5790	279	28	⩽	⩽	ADJ
ejpam-5790	279	29	ν2	ν2	NOUN
ejpam-5790	279	30	and	and	CCONJ
ejpam-5790	279	31	jsν2−,kℑ(℘	jsν2−,kℑ(℘	NOUN
ejpam-5790	279	32	)	)	PUNCT
ejpam-5790	279	33	=	=	SYM
ejpam-5790	279	34	1	1	NUM
ejpam-5790	279	35	γ(s	γ(s	PROPN
ejpam-5790	279	36	)	)	PUNCT
ejpam-5790	279	37	∫	∫	PROPN
ejpam-5790	279	38	ν2	ν2	PROPN
ejpam-5790	279	39	℘	℘	PROPN
ejpam-5790	279	40	(	(	PUNCT
ejpam-5790	279	41	ε−	ε−	NOUN
ejpam-5790	279	42	℘	℘	NUM
ejpam-5790	279	43	)	)	PUNCT
ejpam-5790	279	44	s−k	s−k	NOUN
ejpam-5790	279	45	k	k	ADJ
ejpam-5790	279	46	ℑ(ε)dε	ℑ(ε)dε	NOUN
ejpam-5790	279	47	for	for	ADP
ejpam-5790	279	48	ν1	ν1	NOUN
ejpam-5790	279	49	⩽	⩽	PROPN
ejpam-5790	279	50	℘	℘	PROPN
ejpam-5790	279	51	<	<	X
ejpam-5790	279	52	ν2	ν2	NOUN
ejpam-5790	279	53	,	,	PUNCT
ejpam-5790	279	54	where	where	SCONJ
ejpam-5790	279	55	γ	γ	PROPN
ejpam-5790	279	56	is	be	AUX
ejpam-5790	279	57	the	the	DET
ejpam-5790	279	58	gamma	gamma	PROPN
ejpam-5790	279	59	function	function	NOUN
ejpam-5790	279	60	.	.	PUNCT
ejpam-5790	280	1	we	we	PRON
ejpam-5790	280	2	now	now	ADV
ejpam-5790	280	3	have	have	AUX
ejpam-5790	280	4	defined	define	VERB
ejpam-5790	280	5	thek	thek	PROPN
ejpam-5790	280	6	-	-	PUNCT
ejpam-5790	280	7	riemann	riemann	NOUN
ejpam-5790	280	8	-	-	PUNCT
ejpam-5790	280	9	liouville	liouville	VERB
ejpam-5790	280	10	fractional	fractional	ADJ
ejpam-5790	280	11	integral	integral	ADJ
ejpam-5790	280	12	operators	operator	NOUN
ejpam-5790	280	13	and	and	CCONJ
ejpam-5790	280	14	their	their	PRON
ejpam-5790	280	15	corresponding	corresponding	ADJ
ejpam-5790	280	16	generic	generic	ADJ
ejpam-5790	280	17	identities	identity	NOUN
ejpam-5790	280	18	.	.	PUNCT
ejpam-5790	281	1	definition	definition	NOUN
ejpam-5790	281	2	6	6	NUM
ejpam-5790	281	3	(	(	PUNCT
ejpam-5790	281	4	see	see	VERB
ejpam-5790	281	5	[	[	X
ejpam-5790	281	6	22	22	NUM
ejpam-5790	281	7	]	]	PUNCT
ejpam-5790	281	8	)	)	PUNCT
ejpam-5790	281	9	.	.	PUNCT
ejpam-5790	282	1	let	let	VERB
ejpam-5790	282	2	ℑ	ℑ	PROPN
ejpam-5790	282	3	:	:	PUNCT
ejpam-5790	283	1	[	[	X
ejpam-5790	283	2	ν1	ν1	NOUN
ejpam-5790	283	3	,	,	PUNCT
ejpam-5790	283	4	ν2	ν2	NOUN
ejpam-5790	283	5	]	]	PUNCT
ejpam-5790	283	6	→	→	SYM
ejpam-5790	283	7	r	r	NOUN
ejpam-5790	283	8	be	be	AUX
ejpam-5790	283	9	a	a	DET
ejpam-5790	283	10	real	real	ADV
ejpam-5790	283	11	-	-	PUNCT
ejpam-5790	283	12	valued	value	VERB
ejpam-5790	283	13	mapping	mapping	NOUN
ejpam-5790	283	14	on	on	ADP
ejpam-5790	283	15	[	[	X
ejpam-5790	283	16	ν1	ν1	NOUN
ejpam-5790	283	17	,	,	PUNCT
ejpam-5790	283	18	ν2	ν2	NOUN
ejpam-5790	283	19	]	]	PUNCT
ejpam-5790	283	20	.	.	PUNCT
ejpam-5790	284	1	for	for	ADP
ejpam-5790	284	2	k	k	PROPN
ejpam-5790	284	3	,	,	PUNCT
ejpam-5790	284	4	s	s	PART
ejpam-5790	284	5	>	>	X
ejpam-5790	284	6	0	0	NUM
ejpam-5790	285	1	the	the	DET
ejpam-5790	285	2	associated	associated	ADJ
ejpam-5790	285	3	k	k	PROPN
ejpam-5790	285	4	-	-	PUNCT
ejpam-5790	285	5	riemann	riemann	ADJ
ejpam-5790	285	6	-	-	PUNCT
ejpam-5790	285	7	liouville	liouville	NOUN
ejpam-5790	285	8	integrals	integral	NOUN
ejpam-5790	285	9	are	be	AUX
ejpam-5790	285	10	represented	represent	VERB
ejpam-5790	285	11	as	as	ADP
ejpam-5790	285	12	:	:	PUNCT
ejpam-5790	285	13	jsν1+,kℑ(℘	jsν1+,kℑ(℘	NUM
ejpam-5790	285	14	)	)	PUNCT
ejpam-5790	285	15	=	=	NOUN
ejpam-5790	285	16	1	1	NUM
ejpam-5790	285	17	kγk(s	kγk(s	PROPN
ejpam-5790	285	18	)	)	PUNCT
ejpam-5790	285	19	∫	∫	PROPN
ejpam-5790	285	20	℘	℘	PROPN
ejpam-5790	285	21	ν1	ν1	NOUN
ejpam-5790	285	22	(	(	PUNCT
ejpam-5790	285	23	℘−	℘−	NOUN
ejpam-5790	285	24	ε	ε	PROPN
ejpam-5790	285	25	)	)	PUNCT
ejpam-5790	285	26	s−k	s−k	NOUN
ejpam-5790	285	27	k	k	PROPN
ejpam-5790	285	28	ℑ(ε)dε	ℑ(ε)dε	NOUN
ejpam-5790	285	29	for	for	ADP
ejpam-5790	285	30	ν1	ν1	NOUN
ejpam-5790	285	31	<	<	X
ejpam-5790	285	32	℘	℘	PROPN
ejpam-5790	285	33	⩽	⩽	ADJ
ejpam-5790	285	34	ν2	ν2	NOUN
ejpam-5790	285	35	and	and	CCONJ
ejpam-5790	285	36	jsν2−,kℑ(℘	jsν2−,kℑ(℘	NOUN
ejpam-5790	285	37	)	)	PUNCT
ejpam-5790	285	38	=	=	SYM
ejpam-5790	285	39	1	1	NUM
ejpam-5790	285	40	kγk(s	kγk(s	PROPN
ejpam-5790	285	41	)	)	PUNCT
ejpam-5790	285	42	∫	∫	PROPN
ejpam-5790	285	43	ν2	ν2	PROPN
ejpam-5790	285	44	℘	℘	PROPN
ejpam-5790	285	45	(	(	PUNCT
ejpam-5790	285	46	ε−	ε−	NOUN
ejpam-5790	285	47	℘	℘	NUM
ejpam-5790	285	48	)	)	PUNCT
ejpam-5790	285	49	s−k	s−k	NOUN
ejpam-5790	285	50	k	k	ADJ
ejpam-5790	285	51	ℑ(ε)dε	ℑ(ε)dε	NOUN
ejpam-5790	285	52	for	for	ADP
ejpam-5790	285	53	ν1	ν1	NOUN
ejpam-5790	285	54	⩽	⩽	PROPN
ejpam-5790	285	55	℘	℘	PROPN
ejpam-5790	285	56	<	<	X
ejpam-5790	285	57	ν2	ν2	NOUN
ejpam-5790	285	58	,	,	PUNCT
ejpam-5790	285	59	where	where	SCONJ
ejpam-5790	285	60	γk	γk	PROPN
ejpam-5790	285	61	is	be	AUX
ejpam-5790	285	62	the	the	DET
ejpam-5790	285	63	k	k	PROPN
ejpam-5790	285	64	-	-	PUNCT
ejpam-5790	285	65	gamma	gamma	NOUN
ejpam-5790	285	66	function	function	NOUN
ejpam-5790	285	67	.	.	PUNCT
ejpam-5790	286	1	lemma	lemma	PROPN
ejpam-5790	286	2	4	4	X
ejpam-5790	286	3	.	.	PUNCT
ejpam-5790	287	1	let	let	VERB
ejpam-5790	287	2	ℑ	ℑ	PROPN
ejpam-5790	287	3	:	:	PUNCT
ejpam-5790	288	1	[	[	X
ejpam-5790	288	2	ν1	ν1	NOUN
ejpam-5790	288	3	,	,	PUNCT
ejpam-5790	288	4	ν2	ν2	NOUN
ejpam-5790	288	5	]	]	PUNCT
ejpam-5790	288	6	→	→	SYM
ejpam-5790	288	7	r	r	NOUN
ejpam-5790	288	8	be	be	AUX
ejpam-5790	288	9	a	a	DET
ejpam-5790	288	10	real	real	ADV
ejpam-5790	288	11	-	-	PUNCT
ejpam-5790	288	12	valued	value	VERB
ejpam-5790	288	13	mapping	mapping	NOUN
ejpam-5790	288	14	on	on	ADP
ejpam-5790	288	15	[	[	X
ejpam-5790	288	16	ν1	ν1	NOUN
ejpam-5790	288	17	,	,	PUNCT
ejpam-5790	288	18	ν2	ν2	NOUN
ejpam-5790	288	19	]	]	PUNCT
ejpam-5790	288	20	.	.	PUNCT
ejpam-5790	289	1	for	for	ADP
ejpam-5790	289	2	any	any	DET
ejpam-5790	289	3	℘	℘	PROPN
ejpam-5790	289	4	∈	∈	PROPN
ejpam-5790	289	5	(	(	PUNCT
ejpam-5790	289	6	ν1	ν1	NOUN
ejpam-5790	289	7	,	,	PUNCT
ejpam-5790	289	8	ν2	ν2	NOUN
ejpam-5790	289	9	)	)	PUNCT
ejpam-5790	289	10	we	we	PRON
ejpam-5790	289	11	have	have	VERB
ejpam-5790	289	12	j	j	PROPN
ejpam-5790	289	13	s	s	PART
ejpam-5790	289	14	ν1+,kℑ(℘	ν1+,kℑ(℘	PROPN
ejpam-5790	289	15	)	)	PUNCT
ejpam-5790	289	16	+	+	CCONJ
ejpam-5790	289	17	jsν2−,kℑ(℘	jsν2−,kℑ(℘	X
ejpam-5790	289	18	)	)	PUNCT
ejpam-5790	289	19	=	=	SYM
ejpam-5790	290	1	1	1	NUM
ejpam-5790	290	2	kγk(s	kγk(s	PROPN
ejpam-5790	290	3	+	+	CCONJ
ejpam-5790	290	4	k	k	NOUN
ejpam-5790	290	5	)	)	PUNCT
ejpam-5790	290	6	[	[	PUNCT
ejpam-5790	290	7	(	(	PUNCT
ejpam-5790	290	8	℘−	℘−	NOUN
ejpam-5790	290	9	ν1	ν1	NOUN
ejpam-5790	290	10	)	)	PUNCT
ejpam-5790	290	11	s	s	PART
ejpam-5790	290	12	k	k	PROPN
ejpam-5790	290	13	ℑ(ν1	ℑ(ν1	PROPN
ejpam-5790	290	14	)	)	PUNCT
ejpam-5790	290	15	+	+	CCONJ
ejpam-5790	290	16	(	(	PUNCT
ejpam-5790	290	17	ν2	ν2	NOUN
ejpam-5790	290	18	−	−	PROPN
ejpam-5790	290	19	℘	℘	NUM
ejpam-5790	290	20	)	)	PUNCT
ejpam-5790	290	21	s	s	PART
ejpam-5790	290	22	k	k	PROPN
ejpam-5790	290	23	ℑ(ν2	ℑ(ν2	PROPN
ejpam-5790	290	24	)	)	PUNCT
ejpam-5790	290	25	]	]	PUNCT
ejpam-5790	291	1	+	+	CCONJ
ejpam-5790	291	2	1	1	NUM
ejpam-5790	291	3	kγk(s	kγk(s	PROPN
ejpam-5790	291	4	+	+	CCONJ
ejpam-5790	291	5	k	k	NOUN
ejpam-5790	291	6	)	)	PUNCT
ejpam-5790	292	1	[	[	X
ejpam-5790	292	2	∫	∫	NOUN
ejpam-5790	292	3	℘	℘	PROPN
ejpam-5790	292	4	ν1	ν1	NOUN
ejpam-5790	292	5	(	(	PUNCT
ejpam-5790	292	6	℘−	℘−	NOUN
ejpam-5790	292	7	ε	ε	PROPN
ejpam-5790	292	8	)	)	PUNCT
ejpam-5790	292	9	s	s	PART
ejpam-5790	292	10	k	k	NOUN
ejpam-5790	292	11	ℑ′(ε)dε−	ℑ′(ε)dε−	NOUN
ejpam-5790	292	12	∫	∫	NOUN
ejpam-5790	292	13	ν2	ν2	NOUN
ejpam-5790	292	14	℘	℘	PROPN
ejpam-5790	292	15	(	(	PUNCT
ejpam-5790	292	16	ε−	ε−	NOUN
ejpam-5790	292	17	℘	℘	NUM
ejpam-5790	292	18	)	)	PUNCT
ejpam-5790	292	19	s	s	PART
ejpam-5790	293	1	k	k	X
ejpam-5790	293	2	ℑ′(ε)dε	ℑ′(ε)dε	PRON
ejpam-5790	293	3	]	]	PUNCT
ejpam-5790	293	4	.	.	PUNCT
ejpam-5790	294	1	(	(	PUNCT
ejpam-5790	294	2	3.1	3.1	NUM
ejpam-5790	294	3	)	)	PUNCT
ejpam-5790	294	4	proof	proof	NOUN
ejpam-5790	294	5	.	.	PUNCT
ejpam-5790	295	1	let	let	VERB
ejpam-5790	295	2	ℑ	ℑ	PROPN
ejpam-5790	295	3	:	:	PUNCT
ejpam-5790	296	1	[	[	X
ejpam-5790	296	2	ν1	ν1	NOUN
ejpam-5790	296	3	,	,	PUNCT
ejpam-5790	296	4	ν2	ν2	NOUN
ejpam-5790	296	5	]	]	PUNCT
ejpam-5790	296	6	→	→	SYM
ejpam-5790	296	7	r	r	NOUN
ejpam-5790	296	8	be	be	AUX
ejpam-5790	296	9	a	a	DET
ejpam-5790	296	10	continuous	continuous	ADJ
ejpam-5790	296	11	function	function	NOUN
ejpam-5790	296	12	.	.	PUNCT
ejpam-5790	297	1	in	in	ADP
ejpam-5790	297	2	this	this	DET
ejpam-5790	297	3	case	case	NOUN
ejpam-5790	297	4	,	,	PUNCT
ejpam-5790	297	5	the	the	DET
ejpam-5790	297	6	symmetry	symmetry	NOUN
ejpam-5790	297	7	of	of	ADP
ejpam-5790	297	8	the	the	DET
ejpam-5790	297	9	integrals	integral	NOUN
ejpam-5790	297	10	is	be	AUX
ejpam-5790	297	11	given	give	VERB
ejpam-5790	297	12	by:∫	by:∫	ADP
ejpam-5790	297	13	℘	℘	NUM
ejpam-5790	297	14	ν1	ν1	NOUN
ejpam-5790	297	15	(	(	PUNCT
ejpam-5790	297	16	℘−	℘−	NOUN
ejpam-5790	297	17	ε	ε	PROPN
ejpam-5790	297	18	)	)	PUNCT
ejpam-5790	297	19	s	s	PART
ejpam-5790	297	20	k	k	X
ejpam-5790	297	21	ℑ′(ε)dε	ℑ′(ε)dε	PROPN
ejpam-5790	297	22	and	and	CCONJ
ejpam-5790	297	23	∫	∫	PROPN
ejpam-5790	297	24	ν2	ν2	PROPN
ejpam-5790	297	25	℘	℘	PROPN
ejpam-5790	297	26	(	(	PUNCT
ejpam-5790	297	27	ε−	ε−	NOUN
ejpam-5790	297	28	℘	℘	NUM
ejpam-5790	297	29	)	)	PUNCT
ejpam-5790	297	30	s	s	PART
ejpam-5790	297	31	k	k	X
ejpam-5790	297	32	ℑ′(ε)dε	ℑ′(ε)dε	PROPN
ejpam-5790	297	33	,	,	PUNCT
ejpam-5790	297	34	w.	w.	PROPN
ejpam-5790	297	35	afzal	afzal	PROPN
ejpam-5790	297	36	et	et	PROPN
ejpam-5790	297	37	al	al	PROPN
ejpam-5790	297	38	.	.	PUNCT
ejpam-5790	297	39	/	/	SYM
ejpam-5790	297	40	eur	eur	PROPN
ejpam-5790	297	41	.	.	PUNCT
ejpam-5790	298	1	j.	j.	PROPN
ejpam-5790	298	2	pure	pure	PROPN
ejpam-5790	298	3	appl	appl	PROPN
ejpam-5790	298	4	.	.	PROPN
ejpam-5790	298	5	math	math	PROPN
ejpam-5790	298	6	,	,	PUNCT
ejpam-5790	298	7	18	18	NUM
ejpam-5790	298	8	(	(	PUNCT
ejpam-5790	298	9	1	1	NUM
ejpam-5790	298	10	)	)	PUNCT
ejpam-5790	298	11	(	(	PUNCT
ejpam-5790	298	12	2025	2025	NUM
ejpam-5790	298	13	)	)	PUNCT
ejpam-5790	298	14	,	,	PUNCT
ejpam-5790	298	15	5790	5790	NUM
ejpam-5790	298	16	13	13	NUM
ejpam-5790	298	17	of	of	ADP
ejpam-5790	298	18	30	30	NUM
ejpam-5790	298	19	applying	apply	VERB
ejpam-5790	298	20	integration	integration	NOUN
ejpam-5790	298	21	this	this	PRON
ejpam-5790	298	22	follows	follow	VERB
ejpam-5790	298	23	1	1	NUM
ejpam-5790	298	24	kγk(s	kγk(s	PROPN
ejpam-5790	298	25	+	+	CCONJ
ejpam-5790	298	26	k	k	NOUN
ejpam-5790	298	27	)	)	PUNCT
ejpam-5790	298	28	∫	∫	PROPN
ejpam-5790	298	29	℘	℘	PROPN
ejpam-5790	298	30	ν1	ν1	NOUN
ejpam-5790	298	31	(	(	PUNCT
ejpam-5790	298	32	℘−	℘−	NOUN
ejpam-5790	298	33	ε	ε	PROPN
ejpam-5790	298	34	)	)	PUNCT
ejpam-5790	298	35	s	s	PART
ejpam-5790	298	36	k	k	X
ejpam-5790	298	37	ℑ′(ε)dε	ℑ′(ε)dε	PRON
ejpam-5790	298	38	=	=	SYM
ejpam-5790	298	39	1	1	NUM
ejpam-5790	298	40	γ(s	γ(s	PROPN
ejpam-5790	298	41	)	)	PUNCT
ejpam-5790	298	42	∫	∫	PROPN
ejpam-5790	298	43	℘	℘	PROPN
ejpam-5790	298	44	ν1	ν1	NOUN
ejpam-5790	298	45	(	(	PUNCT
ejpam-5790	298	46	℘−	℘−	NOUN
ejpam-5790	298	47	ε	ε	PROPN
ejpam-5790	298	48	)	)	PUNCT
ejpam-5790	298	49	s−k	s−k	NOUN
ejpam-5790	299	1	k	k	NOUN
ejpam-5790	299	2	ℑ(ε)dε−	ℑ(ε)dε−	SYM
ejpam-5790	299	3	1	1	NUM
ejpam-5790	299	4	kγk(s	kγk(s	PROPN
ejpam-5790	300	1	+	+	CCONJ
ejpam-5790	301	1	k	k	NOUN
ejpam-5790	301	2	)	)	PUNCT
ejpam-5790	301	3	(	(	PUNCT
ejpam-5790	301	4	℘−	℘−	NOUN
ejpam-5790	301	5	ν1	ν1	PROPN
ejpam-5790	301	6	)	)	PUNCT
ejpam-5790	301	7	s	s	PART
ejpam-5790	301	8	k	k	PROPN
ejpam-5790	301	9	ℑ(ν1	ℑ(ν1	PROPN
ejpam-5790	301	10	)	)	PUNCT
ejpam-5790	301	11	=	=	PUNCT
ejpam-5790	302	1	jsν1+,kℑ(℘)−	jsν1+,kℑ(℘)−	ADJ
ejpam-5790	302	2	1	1	NUM
ejpam-5790	302	3	kγk(s	kγk(s	PROPN
ejpam-5790	302	4	+	+	CCONJ
ejpam-5790	302	5	k	k	NOUN
ejpam-5790	302	6	)	)	PUNCT
ejpam-5790	302	7	(	(	PUNCT
ejpam-5790	302	8	℘−	℘−	NOUN
ejpam-5790	302	9	ν1	ν1	PROPN
ejpam-5790	302	10	)	)	PUNCT
ejpam-5790	302	11	s	s	PART
ejpam-5790	302	12	k	k	PROPN
ejpam-5790	302	13	ℑ(ν1	ℑ(ν1	PROPN
ejpam-5790	302	14	)	)	PUNCT
ejpam-5790	302	15	(	(	PUNCT
ejpam-5790	302	16	3.2	3.2	NUM
ejpam-5790	302	17	)	)	PUNCT
ejpam-5790	302	18	for	for	ADP
ejpam-5790	302	19	ν1	ν1	NOUN
ejpam-5790	302	20	<	<	X
ejpam-5790	302	21	℘	℘	PROPN
ejpam-5790	302	22	⩽	⩽	ADJ
ejpam-5790	302	23	ν2	ν2	NOUN
ejpam-5790	302	24	and	and	CCONJ
ejpam-5790	302	25	1	1	NUM
ejpam-5790	302	26	kγk(s	kγk(s	PROPN
ejpam-5790	302	27	+	+	CCONJ
ejpam-5790	302	28	k	k	NOUN
ejpam-5790	302	29	)	)	PUNCT
ejpam-5790	302	30	∫	∫	PROPN
ejpam-5790	302	31	ν2	ν2	PROPN
ejpam-5790	302	32	℘	℘	PROPN
ejpam-5790	302	33	(	(	PUNCT
ejpam-5790	302	34	ε−	ε−	NOUN
ejpam-5790	302	35	℘	℘	NUM
ejpam-5790	302	36	)	)	PUNCT
ejpam-5790	302	37	s	s	PART
ejpam-5790	302	38	k	k	X
ejpam-5790	303	1	ℑ′(ε)dε	ℑ′(ε)dε	PRON
ejpam-5790	303	2	=	=	SYM
ejpam-5790	303	3	1	1	NUM
ejpam-5790	303	4	kγk(s	kγk(s	PROPN
ejpam-5790	303	5	+	+	CCONJ
ejpam-5790	303	6	k	k	NOUN
ejpam-5790	303	7	)	)	PUNCT
ejpam-5790	303	8	(	(	PUNCT
ejpam-5790	303	9	ν2	ν2	NOUN
ejpam-5790	303	10	−	−	PROPN
ejpam-5790	303	11	℘	℘	NUM
ejpam-5790	303	12	)	)	PUNCT
ejpam-5790	303	13	s	s	PART
ejpam-5790	303	14	k	k	NOUN
ejpam-5790	303	15	ℑ(ν2)−	ℑ(ν2)−	ADJ
ejpam-5790	303	16	1	1	NUM
ejpam-5790	303	17	γ(s	γ(	NOUN
ejpam-5790	303	18	)	)	PUNCT
ejpam-5790	303	19	∫	∫	PROPN
ejpam-5790	303	20	ν2	ν2	PROPN
ejpam-5790	303	21	℘	℘	PROPN
ejpam-5790	303	22	(	(	PUNCT
ejpam-5790	303	23	ε−	ε−	NOUN
ejpam-5790	303	24	℘	℘	NUM
ejpam-5790	303	25	)	)	PUNCT
ejpam-5790	303	26	s−k	s−k	NOUN
ejpam-5790	303	27	k	k	NOUN
ejpam-5790	303	28	ℑ(ε)dε	ℑ(ε)dε	NOUN
ejpam-5790	303	29	=	=	SYM
ejpam-5790	303	30	1	1	NUM
ejpam-5790	303	31	kγk(s	kγk(s	PROPN
ejpam-5790	303	32	+	+	CCONJ
ejpam-5790	303	33	k	k	NOUN
ejpam-5790	303	34	)	)	PUNCT
ejpam-5790	303	35	(	(	PUNCT
ejpam-5790	303	36	ν2	ν2	NOUN
ejpam-5790	303	37	−	−	PROPN
ejpam-5790	303	38	℘	℘	NUM
ejpam-5790	303	39	)	)	PUNCT
ejpam-5790	303	40	s	s	PART
ejpam-5790	303	41	k	k	NOUN
ejpam-5790	303	42	ℑ(ν2)−	ℑ(ν2)−	X
ejpam-5790	303	43	jsν2−,kℑ(℘	jsν2−,kℑ(℘	NOUN
ejpam-5790	303	44	)	)	PUNCT
ejpam-5790	303	45	(	(	PUNCT
ejpam-5790	303	46	3.3	3.3	NUM
ejpam-5790	303	47	)	)	PUNCT
ejpam-5790	303	48	for	for	ADP
ejpam-5790	303	49	ν1	ν1	NOUN
ejpam-5790	303	50	⩽	⩽	PROPN
ejpam-5790	303	51	℘	℘	PROPN
ejpam-5790	303	52	<	<	X
ejpam-5790	303	53	ν2	ν2	NOUN
ejpam-5790	303	54	.	.	PUNCT
ejpam-5790	304	1	from	from	ADP
ejpam-5790	304	2	(	(	PUNCT
ejpam-5790	304	3	3.2	3.2	NUM
ejpam-5790	304	4	)	)	PUNCT
ejpam-5790	304	5	,	,	PUNCT
ejpam-5790	304	6	one	one	PRON
ejpam-5790	304	7	has	have	VERB
ejpam-5790	304	8	jsν1+,kℑ(℘	jsν1+,kℑ(℘	NUM
ejpam-5790	304	9	)	)	PUNCT
ejpam-5790	305	1	=	=	SYM
ejpam-5790	305	2	1	1	NUM
ejpam-5790	305	3	kγk(s	kγk(s	PROPN
ejpam-5790	305	4	+	+	CCONJ
ejpam-5790	305	5	k	k	NOUN
ejpam-5790	305	6	)	)	PUNCT
ejpam-5790	305	7	(	(	PUNCT
ejpam-5790	305	8	℘−	℘−	NOUN
ejpam-5790	305	9	ν1	ν1	PROPN
ejpam-5790	305	10	)	)	PUNCT
ejpam-5790	305	11	s	s	PART
ejpam-5790	305	12	k	k	PROPN
ejpam-5790	305	13	ℑ(ν1	ℑ(ν1	PROPN
ejpam-5790	305	14	)	)	PUNCT
ejpam-5790	305	15	+	+	NOUN
ejpam-5790	306	1	1	1	NUM
ejpam-5790	306	2	kγk(s	kγk(s	PROPN
ejpam-5790	306	3	+	+	CCONJ
ejpam-5790	306	4	k	k	NOUN
ejpam-5790	306	5	)	)	PUNCT
ejpam-5790	306	6	∫	∫	PROPN
ejpam-5790	306	7	℘	℘	PROPN
ejpam-5790	306	8	ν1	ν1	NOUN
ejpam-5790	306	9	(	(	PUNCT
ejpam-5790	306	10	℘−	℘−	NOUN
ejpam-5790	306	11	ε	ε	PROPN
ejpam-5790	306	12	)	)	PUNCT
ejpam-5790	306	13	s	s	PART
ejpam-5790	306	14	k	k	X
ejpam-5790	306	15	ℑ′(ε)dε	ℑ′(ε)dε	NOUN
ejpam-5790	306	16	for	for	ADP
ejpam-5790	306	17	ν1	ν1	NOUN
ejpam-5790	306	18	<	<	X
ejpam-5790	306	19	℘	℘	PROPN
ejpam-5790	306	20	⩽	⩽	ADJ
ejpam-5790	306	21	ν2	ν2	NOUN
ejpam-5790	306	22	and	and	CCONJ
ejpam-5790	306	23	from	from	ADP
ejpam-5790	306	24	(	(	PUNCT
ejpam-5790	306	25	3.3	3.3	NUM
ejpam-5790	306	26	)	)	PUNCT
ejpam-5790	306	27	,	,	PUNCT
ejpam-5790	306	28	one	one	PRON
ejpam-5790	306	29	has	have	AUX
ejpam-5790	306	30	jsν2−,kℑ(℘	jsν2−,kℑ(℘	VERB
ejpam-5790	306	31	)	)	PUNCT
ejpam-5790	306	32	=	=	SYM
ejpam-5790	306	33	1	1	NUM
ejpam-5790	306	34	kγk(s	kγk(s	PROPN
ejpam-5790	306	35	+	+	CCONJ
ejpam-5790	306	36	k	k	NOUN
ejpam-5790	306	37	)	)	PUNCT
ejpam-5790	306	38	(	(	PUNCT
ejpam-5790	306	39	ν2	ν2	NOUN
ejpam-5790	306	40	−	−	PROPN
ejpam-5790	306	41	℘	℘	NUM
ejpam-5790	306	42	)	)	PUNCT
ejpam-5790	306	43	s	s	PART
ejpam-5790	306	44	k	k	NOUN
ejpam-5790	306	45	ℑ(ν2)−	ℑ(ν2)−	ADJ
ejpam-5790	306	46	1	1	NUM
ejpam-5790	306	47	kγk(s	kγk(s	PROPN
ejpam-5790	306	48	+	+	CCONJ
ejpam-5790	306	49	k	k	NOUN
ejpam-5790	306	50	)	)	PUNCT
ejpam-5790	306	51	∫	∫	PROPN
ejpam-5790	306	52	ν2	ν2	PROPN
ejpam-5790	306	53	℘	℘	PROPN
ejpam-5790	306	54	(	(	PUNCT
ejpam-5790	306	55	ε−	ε−	NOUN
ejpam-5790	306	56	℘	℘	NUM
ejpam-5790	306	57	)	)	PUNCT
ejpam-5790	306	58	s	s	PART
ejpam-5790	306	59	k	k	X
ejpam-5790	306	60	ℑ′(ε)dε	ℑ′(ε)dε	PROPN
ejpam-5790	306	61	.	.	PUNCT
ejpam-5790	307	1	now	now	ADV
ejpam-5790	307	2	,	,	PUNCT
ejpam-5790	307	3	for	for	ADP
ejpam-5790	307	4	any	any	DET
ejpam-5790	307	5	℘	℘	PROPN
ejpam-5790	307	6	∈	∈	PROPN
ejpam-5790	307	7	(	(	PUNCT
ejpam-5790	307	8	ν1	ν1	NOUN
ejpam-5790	307	9	,	,	PUNCT
ejpam-5790	307	10	ν2	ν2	NOUN
ejpam-5790	307	11	)	)	PUNCT
ejpam-5790	307	12	we	we	PRON
ejpam-5790	307	13	have	have	VERB
ejpam-5790	307	14	j	j	PROPN
ejpam-5790	307	15	s	s	PROPN
ejpam-5790	307	16	℘−,kℑ(ν1	℘−,kℑ(ν1	PROPN
ejpam-5790	307	17	)	)	PUNCT
ejpam-5790	307	18	+	+	NUM
ejpam-5790	307	19	js℘+,kℑ(ν2	js℘+,kℑ(ν2	X
ejpam-5790	307	20	)	)	PUNCT
ejpam-5790	308	1	=	=	SYM
ejpam-5790	308	2	1	1	NUM
ejpam-5790	308	3	kγk(s	kγk(s	PROPN
ejpam-5790	308	4	+	+	CCONJ
ejpam-5790	308	5	k	k	NOUN
ejpam-5790	308	6	)	)	PUNCT
ejpam-5790	308	7	[	[	PUNCT
ejpam-5790	308	8	(	(	PUNCT
ejpam-5790	308	9	℘−	℘−	NOUN
ejpam-5790	308	10	ν1	ν1	NOUN
ejpam-5790	308	11	)	)	PUNCT
ejpam-5790	308	12	s	s	PART
ejpam-5790	309	1	k	k	X
ejpam-5790	310	1	+	+	CCONJ
ejpam-5790	310	2	(	(	PUNCT
ejpam-5790	310	3	ν2	ν2	NOUN
ejpam-5790	310	4	−	−	PROPN
ejpam-5790	310	5	℘	℘	NUM
ejpam-5790	310	6	)	)	PUNCT
ejpam-5790	310	7	s	s	PART
ejpam-5790	310	8	k	k	X
ejpam-5790	310	9	]	]	X
ejpam-5790	310	10	ℑ(℘	ℑ(℘	NOUN
ejpam-5790	310	11	)	)	PUNCT
ejpam-5790	310	12	+	+	CCONJ
ejpam-5790	310	13	1	1	NUM
ejpam-5790	310	14	kγk(s	kγk(s	PROPN
ejpam-5790	310	15	+	+	CCONJ
ejpam-5790	310	16	k	k	NOUN
ejpam-5790	310	17	)	)	PUNCT
ejpam-5790	311	1	[	[	X
ejpam-5790	311	2	∫	∫	X
ejpam-5790	311	3	ν2	ν2	NOUN
ejpam-5790	311	4	℘	℘	PROPN
ejpam-5790	311	5	(	(	PUNCT
ejpam-5790	311	6	ν2	ν2	NOUN
ejpam-5790	311	7	−	−	PROPN
ejpam-5790	311	8	ε	ε	PROPN
ejpam-5790	311	9	)	)	PUNCT
ejpam-5790	311	10	s	s	AUX
ejpam-5790	311	11	k	k	NOUN
ejpam-5790	311	12	ℑ′(ε)dε−	ℑ′(ε)dε−	NOUN
ejpam-5790	311	13	∫	∫	NOUN
ejpam-5790	311	14	℘	℘	PROPN
ejpam-5790	311	15	ν1	ν1	NOUN
ejpam-5790	311	16	(	(	PUNCT
ejpam-5790	311	17	ε−	ε−	PROPN
ejpam-5790	311	18	ν1	ν1	NOUN
ejpam-5790	311	19	)	)	PUNCT
ejpam-5790	311	20	s	s	PART
ejpam-5790	312	1	k	k	X
ejpam-5790	312	2	ℑ′(ε)dε	ℑ′(ε)dε	PRON
ejpam-5790	312	3	]	]	PUNCT
ejpam-5790	312	4	.	.	PUNCT
ejpam-5790	313	1	proof	proof	NOUN
ejpam-5790	313	2	.	.	PUNCT
ejpam-5790	314	1	since	since	SCONJ
ejpam-5790	314	2	we	we	PRON
ejpam-5790	314	3	have	have	VERB
ejpam-5790	314	4	js℘+,kℑ(ν2	js℘+,kℑ(ν2	PROPN
ejpam-5790	314	5	)	)	PUNCT
ejpam-5790	315	1	=	=	SYM
ejpam-5790	315	2	1	1	NUM
ejpam-5790	315	3	kγ(s	kγ(s	ADV
ejpam-5790	315	4	)	)	PUNCT
ejpam-5790	315	5	∫	∫	PROPN
ejpam-5790	315	6	ν2	ν2	PROPN
ejpam-5790	315	7	℘	℘	PROPN
ejpam-5790	315	8	(	(	PUNCT
ejpam-5790	315	9	ν2	ν2	NOUN
ejpam-5790	315	10	−	−	PROPN
ejpam-5790	315	11	ε	ε	PROPN
ejpam-5790	315	12	)	)	PUNCT
ejpam-5790	315	13	s−k	s−k	NOUN
ejpam-5790	315	14	k	k	ADJ
ejpam-5790	315	15	ℑ(ε)dε	ℑ(ε)dε	NOUN
ejpam-5790	315	16	for	for	ADP
ejpam-5790	315	17	ν1	ν1	NOUN
ejpam-5790	315	18	⩽	⩽	PROPN
ejpam-5790	315	19	℘	℘	PROPN
ejpam-5790	315	20	<	<	X
ejpam-5790	315	21	ν2	ν2	NOUN
ejpam-5790	315	22	and	and	CCONJ
ejpam-5790	315	23	js℘−,kℑ(ν1	js℘−,kℑ(ν1	NOUN
ejpam-5790	315	24	)	)	PUNCT
ejpam-5790	315	25	=	=	SYM
ejpam-5790	315	26	1	1	NUM
ejpam-5790	315	27	γ(s	γ(s	PROPN
ejpam-5790	315	28	)	)	PUNCT
ejpam-5790	315	29	∫	∫	PROPN
ejpam-5790	315	30	℘	℘	PROPN
ejpam-5790	315	31	ν1	ν1	NOUN
ejpam-5790	315	32	(	(	PUNCT
ejpam-5790	315	33	ε−	ε−	PROPN
ejpam-5790	315	34	ν1	ν1	NOUN
ejpam-5790	315	35	)	)	PUNCT
ejpam-5790	315	36	s−k	s−k	NOUN
ejpam-5790	315	37	k	k	PROPN
ejpam-5790	315	38	ℑ(ε)dε	ℑ(ε)dε	PROPN
ejpam-5790	315	39	w.	w.	PROPN
ejpam-5790	315	40	afzal	afzal	PROPN
ejpam-5790	315	41	et	et	PROPN
ejpam-5790	315	42	al	al	PROPN
ejpam-5790	315	43	.	.	PUNCT
ejpam-5790	315	44	/	/	SYM
ejpam-5790	315	45	eur	eur	PROPN
ejpam-5790	315	46	.	.	PUNCT
ejpam-5790	316	1	j.	j.	PROPN
ejpam-5790	316	2	pure	pure	PROPN
ejpam-5790	316	3	appl	appl	PROPN
ejpam-5790	316	4	.	.	PROPN
ejpam-5790	316	5	math	math	PROPN
ejpam-5790	316	6	,	,	PUNCT
ejpam-5790	316	7	18	18	NUM
ejpam-5790	316	8	(	(	PUNCT
ejpam-5790	316	9	1	1	NUM
ejpam-5790	316	10	)	)	PUNCT
ejpam-5790	316	11	(	(	PUNCT
ejpam-5790	316	12	2025	2025	NUM
ejpam-5790	316	13	)	)	PUNCT
ejpam-5790	316	14	,	,	PUNCT
ejpam-5790	316	15	5790	5790	NUM
ejpam-5790	316	16	14	14	NUM
ejpam-5790	316	17	of	of	ADP
ejpam-5790	316	18	30	30	NUM
ejpam-5790	316	19	for	for	ADP
ejpam-5790	316	20	ν1	ν1	NOUN
ejpam-5790	316	21	<	<	X
ejpam-5790	316	22	℘	℘	PROPN
ejpam-5790	316	23	⩽	⩽	ADJ
ejpam-5790	316	24	ν2	ν2	NOUN
ejpam-5790	316	25	.	.	PUNCT
ejpam-5790	317	1	since	since	SCONJ
ejpam-5790	317	2	ℑ	ℑ	PROPN
ejpam-5790	317	3	:	:	PUNCT
ejpam-5790	317	4	[	[	X
ejpam-5790	317	5	ν1	ν1	NOUN
ejpam-5790	317	6	,	,	PUNCT
ejpam-5790	317	7	ν2	ν2	NOUN
ejpam-5790	317	8	]	]	PUNCT
ejpam-5790	317	9	→	→	SYM
ejpam-5790	317	10	r	r	NOUN
ejpam-5790	317	11	be	be	AUX
ejpam-5790	317	12	an	an	DET
ejpam-5790	317	13	continuous	continuous	ADJ
ejpam-5790	317	14	function	function	NOUN
ejpam-5790	317	15	[	[	X
ejpam-5790	317	16	ν1	ν1	NOUN
ejpam-5790	317	17	,	,	PUNCT
ejpam-5790	317	18	ν2	ν2	NOUN
ejpam-5790	317	19	]	]	PUNCT
ejpam-5790	317	20	,	,	PUNCT
ejpam-5790	317	21	then	then	ADV
ejpam-5790	317	22	the	the	DET
ejpam-5790	317	23	integrals∫	integrals∫	ADJ
ejpam-5790	317	24	℘	℘	PROPN
ejpam-5790	317	25	ν1	ν1	NOUN
ejpam-5790	317	26	(	(	PUNCT
ejpam-5790	317	27	ε−	ε−	PROPN
ejpam-5790	317	28	ν1	ν1	NOUN
ejpam-5790	317	29	)	)	PUNCT
ejpam-5790	317	30	sℑ′(ε)dε	sℑ′(ε)dε	NOUN
ejpam-5790	317	31	and	and	CCONJ
ejpam-5790	317	32	∫	∫	PROPN
ejpam-5790	317	33	ν2	ν2	PROPN
ejpam-5790	317	34	℘	℘	PROPN
ejpam-5790	317	35	(	(	PUNCT
ejpam-5790	317	36	ν2	ν2	NOUN
ejpam-5790	317	37	−	−	PROPN
ejpam-5790	317	38	ε)sℑ′(ε)dε	ε)sℑ′(ε)dε	NOUN
ejpam-5790	317	39	,	,	PUNCT
ejpam-5790	317	40	holds	hold	NOUN
ejpam-5790	317	41	,	,	PUNCT
ejpam-5790	317	42	and	and	CCONJ
ejpam-5790	317	43	by	by	ADP
ejpam-5790	317	44	performing	perform	VERB
ejpam-5790	317	45	the	the	DET
ejpam-5790	317	46	integration	integration	NOUN
ejpam-5790	317	47	,	,	PUNCT
ejpam-5790	317	48	we	we	PRON
ejpam-5790	317	49	obtain	obtain	VERB
ejpam-5790	317	50	:	:	PUNCT
ejpam-5790	317	51	1	1	NUM
ejpam-5790	317	52	kγk(s	kγk(s	PROPN
ejpam-5790	317	53	+	+	CCONJ
ejpam-5790	317	54	k	k	NOUN
ejpam-5790	317	55	)	)	PUNCT
ejpam-5790	317	56	∫	∫	PROPN
ejpam-5790	317	57	℘	℘	PROPN
ejpam-5790	317	58	ν1	ν1	NOUN
ejpam-5790	317	59	(	(	PUNCT
ejpam-5790	317	60	ε−	ε−	PROPN
ejpam-5790	317	61	ν1	ν1	NOUN
ejpam-5790	317	62	)	)	PUNCT
ejpam-5790	317	63	sℑ′(ε)dε	sℑ′(ε)dε	NOUN
ejpam-5790	317	64	=	=	SYM
ejpam-5790	317	65	1	1	NUM
ejpam-5790	317	66	kγk(s	kγk(s	PROPN
ejpam-5790	317	67	+	+	CCONJ
ejpam-5790	317	68	k	k	NOUN
ejpam-5790	317	69	)	)	PUNCT
ejpam-5790	317	70	(	(	PUNCT
ejpam-5790	317	71	℘−	℘−	NOUN
ejpam-5790	317	72	ν1	ν1	PROPN
ejpam-5790	317	73	)	)	PUNCT
ejpam-5790	317	74	s	s	PART
ejpam-5790	317	75	k	k	NOUN
ejpam-5790	317	76	ℑ(℘)−	ℑ(℘)−	ADJ
ejpam-5790	317	77	1	1	NUM
ejpam-5790	317	78	kγ(s	kγ(s	ADV
ejpam-5790	317	79	)	)	PUNCT
ejpam-5790	317	80	∫	∫	PROPN
ejpam-5790	317	81	℘	℘	PROPN
ejpam-5790	317	82	ν1	ν1	NOUN
ejpam-5790	317	83	(	(	PUNCT
ejpam-5790	317	84	ε−	ε−	PROPN
ejpam-5790	317	85	ν1	ν1	NOUN
ejpam-5790	317	86	)	)	PUNCT
ejpam-5790	317	87	s−k	s−k	NOUN
ejpam-5790	317	88	k	k	NOUN
ejpam-5790	317	89	ℑ(ε)dε	ℑ(ε)dε	NOUN
ejpam-5790	317	90	=	=	SYM
ejpam-5790	317	91	1	1	NUM
ejpam-5790	317	92	kγk(s	kγk(s	PROPN
ejpam-5790	317	93	+	+	CCONJ
ejpam-5790	317	94	k	k	NOUN
ejpam-5790	317	95	)	)	PUNCT
ejpam-5790	317	96	(	(	PUNCT
ejpam-5790	317	97	℘−	℘−	NOUN
ejpam-5790	317	98	ν1	ν1	PROPN
ejpam-5790	317	99	)	)	PUNCT
ejpam-5790	317	100	s	s	PART
ejpam-5790	317	101	k	k	X
ejpam-5790	317	102	ℑ(℘)−	ℑ(℘)−	ADJ
ejpam-5790	317	103	js℘−,kℑ(ν1	js℘−,kℑ(ν1	NOUN
ejpam-5790	317	104	)	)	PUNCT
ejpam-5790	317	105	(	(	PUNCT
ejpam-5790	317	106	3.4	3.4	NUM
ejpam-5790	317	107	)	)	PUNCT
ejpam-5790	317	108	for	for	ADP
ejpam-5790	317	109	ν1	ν1	NOUN
ejpam-5790	317	110	<	<	X
ejpam-5790	317	111	℘	℘	PROPN
ejpam-5790	317	112	⩽	⩽	ADJ
ejpam-5790	317	113	ν2	ν2	NOUN
ejpam-5790	317	114	and	and	CCONJ
ejpam-5790	317	115	1	1	NUM
ejpam-5790	317	116	kγk(s	kγk(s	PROPN
ejpam-5790	317	117	+	+	CCONJ
ejpam-5790	317	118	k	k	NOUN
ejpam-5790	317	119	)	)	PUNCT
ejpam-5790	317	120	∫	∫	PROPN
ejpam-5790	317	121	ν2	ν2	PROPN
ejpam-5790	317	122	℘	℘	PROPN
ejpam-5790	317	123	(	(	PUNCT
ejpam-5790	317	124	ν2	ν2	NOUN
ejpam-5790	317	125	−	−	PROPN
ejpam-5790	317	126	ε	ε	PROPN
ejpam-5790	317	127	)	)	PUNCT
ejpam-5790	317	128	s	s	PART
ejpam-5790	318	1	k	k	X
ejpam-5790	318	2	ℑ′(ε)dε	ℑ′(ε)dε	PRON
ejpam-5790	318	3	=	=	SYM
ejpam-5790	318	4	1	1	NUM
ejpam-5790	318	5	kγ(s	kγ(s	ADV
ejpam-5790	318	6	)	)	PUNCT
ejpam-5790	318	7	∫	∫	PROPN
ejpam-5790	318	8	ν2	ν2	PROPN
ejpam-5790	318	9	℘	℘	PROPN
ejpam-5790	318	10	(	(	PUNCT
ejpam-5790	318	11	ν2	ν2	NOUN
ejpam-5790	318	12	−	−	PROPN
ejpam-5790	318	13	ε	ε	PROPN
ejpam-5790	318	14	)	)	PUNCT
ejpam-5790	318	15	s−k	s−k	NOUN
ejpam-5790	318	16	k	k	NOUN
ejpam-5790	318	17	ℑ(ε)dε−	ℑ(ε)dε−	SYM
ejpam-5790	318	18	1	1	NUM
ejpam-5790	318	19	kγk(s	kγk(s	PROPN
ejpam-5790	318	20	+	+	CCONJ
ejpam-5790	318	21	k	k	NOUN
ejpam-5790	318	22	)	)	PUNCT
ejpam-5790	318	23	(	(	PUNCT
ejpam-5790	318	24	ν2	ν2	NOUN
ejpam-5790	318	25	−	−	PROPN
ejpam-5790	318	26	℘	℘	NUM
ejpam-5790	318	27	)	)	PUNCT
ejpam-5790	318	28	s	s	PART
ejpam-5790	318	29	k	k	NOUN
ejpam-5790	318	30	ℑ(℘	ℑ(℘	PROPN
ejpam-5790	318	31	)	)	PUNCT
ejpam-5790	318	32	=	=	PRON
ejpam-5790	318	33	js℘+,kℑ(ν2)−	js℘+,kℑ(ν2)−	VERB
ejpam-5790	318	34	1	1	NUM
ejpam-5790	318	35	kγk(s	kγk(s	PROPN
ejpam-5790	318	36	+	+	CCONJ
ejpam-5790	318	37	k	k	NOUN
ejpam-5790	318	38	)	)	PUNCT
ejpam-5790	318	39	(	(	PUNCT
ejpam-5790	318	40	ν2	ν2	NOUN
ejpam-5790	318	41	−	−	PROPN
ejpam-5790	318	42	℘	℘	NUM
ejpam-5790	318	43	)	)	PUNCT
ejpam-5790	318	44	s	s	PART
ejpam-5790	318	45	k	k	NOUN
ejpam-5790	318	46	ℑ(℘	ℑ(℘	PROPN
ejpam-5790	318	47	)	)	PUNCT
ejpam-5790	318	48	(	(	PUNCT
ejpam-5790	318	49	3.5	3.5	NUM
ejpam-5790	318	50	)	)	PUNCT
ejpam-5790	318	51	for	for	ADP
ejpam-5790	318	52	ν1	ν1	NOUN
ejpam-5790	318	53	⩽	⩽	PROPN
ejpam-5790	318	54	℘	℘	PROPN
ejpam-5790	318	55	<	<	X
ejpam-5790	318	56	ν2	ν2	NOUN
ejpam-5790	318	57	.	.	PUNCT
ejpam-5790	319	1	from	from	ADP
ejpam-5790	319	2	(	(	PUNCT
ejpam-5790	319	3	3.4	3.4	NUM
ejpam-5790	319	4	)	)	PUNCT
ejpam-5790	319	5	we	we	PRON
ejpam-5790	319	6	have	have	VERB
ejpam-5790	319	7	js℘−,kℑ(ν1	js℘−,kℑ(ν1	NOUN
ejpam-5790	319	8	)	)	PUNCT
ejpam-5790	319	9	=	=	SYM
ejpam-5790	320	1	1	1	NUM
ejpam-5790	320	2	kγk(s	kγk(s	PROPN
ejpam-5790	320	3	+	+	CCONJ
ejpam-5790	320	4	k	k	NOUN
ejpam-5790	320	5	)	)	PUNCT
ejpam-5790	320	6	(	(	PUNCT
ejpam-5790	320	7	℘−	℘−	NOUN
ejpam-5790	320	8	ν1	ν1	PROPN
ejpam-5790	320	9	)	)	PUNCT
ejpam-5790	320	10	s	s	PART
ejpam-5790	320	11	k	k	NOUN
ejpam-5790	320	12	ℑ(℘)−	ℑ(℘)−	ADJ
ejpam-5790	320	13	1	1	NUM
ejpam-5790	320	14	kγk(s	kγk(s	PROPN
ejpam-5790	320	15	+	+	CCONJ
ejpam-5790	320	16	k	k	NOUN
ejpam-5790	320	17	)	)	PUNCT
ejpam-5790	320	18	∫	∫	PROPN
ejpam-5790	320	19	℘	℘	PROPN
ejpam-5790	320	20	ν1	ν1	NOUN
ejpam-5790	320	21	(	(	PUNCT
ejpam-5790	320	22	ε−	ε−	PROPN
ejpam-5790	320	23	ν1	ν1	NOUN
ejpam-5790	320	24	)	)	PUNCT
ejpam-5790	320	25	s	s	PART
ejpam-5790	320	26	k	k	X
ejpam-5790	320	27	ℑ′(ε)dε	ℑ′(ε)dε	NOUN
ejpam-5790	320	28	for	for	ADP
ejpam-5790	320	29	ν1	ν1	NOUN
ejpam-5790	320	30	<	<	X
ejpam-5790	320	31	℘	℘	PROPN
ejpam-5790	320	32	⩽	⩽	ADJ
ejpam-5790	320	33	ν2	ν2	NOUN
ejpam-5790	320	34	and	and	CCONJ
ejpam-5790	320	35	from	from	ADP
ejpam-5790	320	36	(	(	PUNCT
ejpam-5790	320	37	3.5	3.5	NUM
ejpam-5790	320	38	)	)	PUNCT
ejpam-5790	320	39	js℘+,kℑ(ν2	js℘+,kℑ(ν2	PROPN
ejpam-5790	320	40	)	)	PUNCT
ejpam-5790	320	41	=	=	SYM
ejpam-5790	321	1	1	1	NUM
ejpam-5790	321	2	kγk(s	kγk(s	PROPN
ejpam-5790	321	3	+	+	CCONJ
ejpam-5790	321	4	k	k	NOUN
ejpam-5790	321	5	)	)	PUNCT
ejpam-5790	321	6	(	(	PUNCT
ejpam-5790	321	7	ν2	ν2	NOUN
ejpam-5790	321	8	−	−	PROPN
ejpam-5790	321	9	℘	℘	NUM
ejpam-5790	321	10	)	)	PUNCT
ejpam-5790	321	11	s	s	PART
ejpam-5790	321	12	k	k	NOUN
ejpam-5790	321	13	ℑ(℘	ℑ(℘	PROPN
ejpam-5790	321	14	)	)	PUNCT
ejpam-5790	321	15	+	+	CCONJ
ejpam-5790	321	16	1	1	NUM
ejpam-5790	321	17	kγk(s	kγk(s	PROPN
ejpam-5790	321	18	+	+	CCONJ
ejpam-5790	321	19	k	k	NOUN
ejpam-5790	321	20	)	)	PUNCT
ejpam-5790	321	21	∫	∫	PROPN
ejpam-5790	321	22	ν2	ν2	PROPN
ejpam-5790	321	23	℘	℘	PROPN
ejpam-5790	321	24	(	(	PUNCT
ejpam-5790	321	25	ν2	ν2	NOUN
ejpam-5790	321	26	−	−	PROPN
ejpam-5790	321	27	ε	ε	PROPN
ejpam-5790	321	28	)	)	PUNCT
ejpam-5790	321	29	s	s	PART
ejpam-5790	321	30	k	k	X
ejpam-5790	321	31	ℑ′(ε)dε	ℑ′(ε)dε	PROPN
ejpam-5790	321	32	.	.	PROPN
ejpam-5790	321	33	3.1	3.1	NUM
ejpam-5790	321	34	.	.	PUNCT
ejpam-5790	322	1	some	some	DET
ejpam-5790	322	2	new	new	ADJ
ejpam-5790	322	3	fractional	fractional	ADJ
ejpam-5790	322	4	identities	identity	NOUN
ejpam-5790	322	5	we	we	PRON
ejpam-5790	322	6	draw	draw	VERB
ejpam-5790	322	7	inspiration	inspiration	NOUN
ejpam-5790	322	8	from	from	ADP
ejpam-5790	322	9	section	section	NOUN
ejpam-5790	322	10	2.1	2.1	NUM
ejpam-5790	322	11	in	in	ADP
ejpam-5790	322	12	this	this	DET
ejpam-5790	322	13	section	section	NOUN
ejpam-5790	322	14	,	,	PUNCT
ejpam-5790	322	15	which	which	PRON
ejpam-5790	322	16	enables	enable	VERB
ejpam-5790	322	17	us	we	PRON
ejpam-5790	322	18	to	to	PART
ejpam-5790	322	19	construct	construct	VERB
ejpam-5790	322	20	fractional	fractional	ADJ
ejpam-5790	322	21	identities	identity	NOUN
ejpam-5790	322	22	at	at	ADP
ejpam-5790	322	23	the	the	DET
ejpam-5790	322	24	interval	interval	NOUN
ejpam-5790	322	25	’s	’s	PART
ejpam-5790	322	26	midpoint	midpoint	NOUN
ejpam-5790	322	27	,	,	PUNCT
ejpam-5790	322	28	which	which	PRON
ejpam-5790	322	29	we	we	PRON
ejpam-5790	322	30	utilize	utilize	VERB
ejpam-5790	322	31	in	in	ADP
ejpam-5790	322	32	important	important	ADJ
ejpam-5790	322	33	findings	finding	NOUN
ejpam-5790	322	34	.	.	PUNCT
ejpam-5790	323	1	lemma	lemma	PROPN
ejpam-5790	323	2	5	5	X
ejpam-5790	323	3	.	.	PUNCT
ejpam-5790	324	1	let	let	VERB
ejpam-5790	324	2	ℑ	ℑ	PROPN
ejpam-5790	324	3	:	:	PUNCT
ejpam-5790	325	1	[	[	X
ejpam-5790	325	2	ν1	ν1	NOUN
ejpam-5790	325	3	,	,	PUNCT
ejpam-5790	325	4	ν2	ν2	NOUN
ejpam-5790	325	5	]	]	PUNCT
ejpam-5790	325	6	→	→	SYM
ejpam-5790	325	7	r	r	NOUN
ejpam-5790	325	8	be	be	AUX
ejpam-5790	325	9	a	a	DET
ejpam-5790	325	10	real	real	ADV
ejpam-5790	325	11	-	-	PUNCT
ejpam-5790	325	12	valued	value	VERB
ejpam-5790	325	13	mapping	mapping	NOUN
ejpam-5790	325	14	on	on	ADP
ejpam-5790	325	15	[	[	X
ejpam-5790	325	16	ν1	ν1	NOUN
ejpam-5790	325	17	,	,	PUNCT
ejpam-5790	325	18	ν2	ν2	NOUN
ejpam-5790	325	19	]	]	PUNCT
ejpam-5790	325	20	.	.	PUNCT
ejpam-5790	326	1	we	we	PRON
ejpam-5790	326	2	have	have	VERB
ejpam-5790	326	3	the	the	DET
ejpam-5790	326	4	following	follow	VERB
ejpam-5790	326	5	double	double	ADJ
ejpam-5790	326	6	equality	equality	NOUN
ejpam-5790	326	7	j	j	PROPN
ejpam-5790	326	8	s	s	PROPN
ejpam-5790	326	9	ν1+,kℑ	ν1+,kℑ	X
ejpam-5790	326	10	(	(	PUNCT
ejpam-5790	326	11	ν1	ν1	NOUN
ejpam-5790	326	12	+	+	CCONJ
ejpam-5790	326	13	ν2	ν2	NOUN
ejpam-5790	326	14	2	2	NUM
ejpam-5790	326	15	)	)	PUNCT
ejpam-5790	327	1	+	+	CCONJ
ejpam-5790	328	1	jsν2−,kℑ	jsν2−,kℑ	PROPN
ejpam-5790	328	2	(	(	PUNCT
ejpam-5790	328	3	ν1	ν1	NOUN
ejpam-5790	328	4	+	+	CCONJ
ejpam-5790	328	5	ν2	ν2	NOUN
ejpam-5790	328	6	2	2	NUM
ejpam-5790	328	7	)	)	PUNCT
ejpam-5790	328	8	=	=	SYM
ejpam-5790	328	9	1	1	NUM
ejpam-5790	328	10	2	2	NUM
ejpam-5790	328	11	s−k	s−k	NOUN
ejpam-5790	328	12	k	k	PROPN
ejpam-5790	328	13	kγk(s	kγk(s	PROPN
ejpam-5790	329	1	+	+	CCONJ
ejpam-5790	329	2	k	k	NOUN
ejpam-5790	329	3	)	)	PUNCT
ejpam-5790	329	4	q(ν1	q(ν1	NOUN
ejpam-5790	329	5	)	)	PUNCT
ejpam-5790	330	1	+	+	SYM
ejpam-5790	330	2	ℑ(ν2	ℑ(ν2	NOUN
ejpam-5790	330	3	)	)	PUNCT
ejpam-5790	330	4	2	2	NUM
ejpam-5790	331	1	+	+	SYM
ejpam-5790	331	2	1	1	NUM
ejpam-5790	331	3	kγk(s	kγk(s	PROPN
ejpam-5790	331	4	+	+	CCONJ
ejpam-5790	331	5	k	k	NOUN
ejpam-5790	331	6	)	)	PUNCT
ejpam-5790	332	1	[	[	X
ejpam-5790	332	2	∫	∫	X
ejpam-5790	332	3	ν1+ν2	ν1+ν2	PROPN
ejpam-5790	332	4	2	2	NUM
ejpam-5790	332	5	ν1	ν1	NOUN
ejpam-5790	332	6	(	(	PUNCT
ejpam-5790	332	7	ν1	ν1	NOUN
ejpam-5790	332	8	+	+	CCONJ
ejpam-5790	332	9	ν2	ν2	PROPN
ejpam-5790	332	10	2	2	NUM
ejpam-5790	332	11	−	−	NOUN
ejpam-5790	332	12	ε	ε	PROPN
ejpam-5790	332	13	)	)	PUNCT
ejpam-5790	332	14	s	s	AUX
ejpam-5790	332	15	k	k	NOUN
ejpam-5790	332	16	ℑ′(ε)dε−	ℑ′(ε)dε−	NOUN
ejpam-5790	332	17	∫	∫	NOUN
ejpam-5790	332	18	ν2	ν2	NOUN
ejpam-5790	332	19	ν1+ν2	ν1+ν2	NOUN
ejpam-5790	332	20	2	2	NUM
ejpam-5790	332	21	(	(	PUNCT
ejpam-5790	332	22	ε−	ε−	NUM
ejpam-5790	332	23	ν1	ν1	NOUN
ejpam-5790	332	24	+	+	CCONJ
ejpam-5790	332	25	ν2	ν2	NOUN
ejpam-5790	332	26	2	2	NUM
ejpam-5790	332	27	)	)	PUNCT
ejpam-5790	332	28	s	s	PART
ejpam-5790	333	1	k	k	X
ejpam-5790	333	2	ℑ′(ε)dε	ℑ′(ε)dε	X
ejpam-5790	333	3	]	]	PUNCT
ejpam-5790	333	4	w.	w.	PROPN
ejpam-5790	333	5	afzal	afzal	PROPN
ejpam-5790	333	6	et	et	PROPN
ejpam-5790	333	7	al	al	PROPN
ejpam-5790	333	8	.	.	PUNCT
ejpam-5790	333	9	/	/	SYM
ejpam-5790	333	10	eur	eur	PROPN
ejpam-5790	333	11	.	.	PUNCT
ejpam-5790	334	1	j.	j.	PROPN
ejpam-5790	334	2	pure	pure	PROPN
ejpam-5790	334	3	appl	appl	PROPN
ejpam-5790	334	4	.	.	PROPN
ejpam-5790	334	5	math	math	PROPN
ejpam-5790	334	6	,	,	PUNCT
ejpam-5790	334	7	18	18	NUM
ejpam-5790	334	8	(	(	PUNCT
ejpam-5790	334	9	1	1	NUM
ejpam-5790	334	10	)	)	PUNCT
ejpam-5790	334	11	(	(	PUNCT
ejpam-5790	334	12	2025	2025	NUM
ejpam-5790	334	13	)	)	PUNCT
ejpam-5790	334	14	,	,	PUNCT
ejpam-5790	334	15	5790	5790	NUM
ejpam-5790	334	16	15	15	NUM
ejpam-5790	334	17	of	of	ADP
ejpam-5790	334	18	30	30	NUM
ejpam-5790	334	19	and	and	CCONJ
ejpam-5790	334	20	j	j	PROPN
ejpam-5790	334	21	s	s	PROPN
ejpam-5790	334	22	ν1+ν2	ν1+ν2	PROPN
ejpam-5790	334	23	2	2	NUM
ejpam-5790	334	24	−,k	−,k	NOUN
ejpam-5790	334	25	ℑ(ν1	ℑ(ν1	NOUN
ejpam-5790	334	26	)	)	PUNCT
ejpam-5790	334	27	+	+	NUM
ejpam-5790	334	28	jsν1+ν2	jsν1+ν2	NOUN
ejpam-5790	334	29	2	2	NUM
ejpam-5790	335	1	+	+	PROPN
ejpam-5790	335	2	,	,	PUNCT
ejpam-5790	335	3	k	k	PROPN
ejpam-5790	335	4	ℑ(ν2	ℑ(ν2	PROPN
ejpam-5790	335	5	)	)	PUNCT
ejpam-5790	335	6	=	=	SYM
ejpam-5790	335	7	1	1	NUM
ejpam-5790	335	8	2	2	NUM
ejpam-5790	335	9	s−k	s−k	NOUN
ejpam-5790	335	10	k	k	PROPN
ejpam-5790	335	11	kγk(s	kγk(s	PROPN
ejpam-5790	335	12	+	+	CCONJ
ejpam-5790	335	13	k	k	ADJ
ejpam-5790	335	14	)	)	PUNCT
ejpam-5790	335	15	ℑ	ℑ	PROPN
ejpam-5790	335	16	(	(	PUNCT
ejpam-5790	335	17	ν1	ν1	NOUN
ejpam-5790	335	18	+	+	CCONJ
ejpam-5790	335	19	ν2	ν2	PROPN
ejpam-5790	335	20	2	2	NUM
ejpam-5790	335	21	)	)	PUNCT
ejpam-5790	335	22	(	(	PUNCT
ejpam-5790	335	23	ν2	ν2	NOUN
ejpam-5790	335	24	−	−	PROPN
ejpam-5790	335	25	ν1	ν1	NOUN
ejpam-5790	335	26	)	)	PUNCT
ejpam-5790	335	27	s	s	PART
ejpam-5790	335	28	k	k	X
ejpam-5790	336	1	+	+	CCONJ
ejpam-5790	336	2	1	1	NUM
ejpam-5790	336	3	kγk(s	kγk(s	PROPN
ejpam-5790	336	4	+	+	CCONJ
ejpam-5790	336	5	k	k	NOUN
ejpam-5790	336	6	)	)	PUNCT
ejpam-5790	337	1	[	[	X
ejpam-5790	337	2	∫	∫	X
ejpam-5790	337	3	ν2	ν2	NOUN
ejpam-5790	337	4	ν1+ν2	ν1+ν2	PROPN
ejpam-5790	337	5	2	2	NUM
ejpam-5790	337	6	(	(	PUNCT
ejpam-5790	337	7	ε−	ε−	NOUN
ejpam-5790	337	8	ν2	ν2	NOUN
ejpam-5790	337	9	)	)	PUNCT
ejpam-5790	337	10	s	s	PART
ejpam-5790	337	11	k	k	NOUN
ejpam-5790	337	12	ℑ′(ε)dε−	ℑ′(ε)dε−	PROPN
ejpam-5790	337	13	∫	∫	NOUN
ejpam-5790	337	14	ν1+ν2	ν1+ν2	PROPN
ejpam-5790	337	15	2	2	NUM
ejpam-5790	337	16	ν1	ν1	NOUN
ejpam-5790	337	17	(	(	PUNCT
ejpam-5790	337	18	ε−	ε−	PROPN
ejpam-5790	337	19	ν1	ν1	NOUN
ejpam-5790	337	20	)	)	PUNCT
ejpam-5790	337	21	s	s	PART
ejpam-5790	338	1	k	k	X
ejpam-5790	338	2	ℑ′(ε)dε	ℑ′(ε)dε	X
ejpam-5790	338	3	]	]	PUNCT
ejpam-5790	338	4	,	,	PUNCT
ejpam-5790	338	5	(	(	PUNCT
ejpam-5790	338	6	3.6	3.6	NUM
ejpam-5790	338	7	)	)	PUNCT
ejpam-5790	338	8	for	for	ADP
ejpam-5790	338	9	ν1	ν1	NOUN
ejpam-5790	338	10	⩽	⩽	NOUN
ejpam-5790	338	11	ν1+ν2	ν1+ν2	PROPN
ejpam-5790	338	12	2	2	NUM
ejpam-5790	338	13	<	<	NOUN
ejpam-5790	338	14	ν2	ν2	NOUN
ejpam-5790	338	15	.	.	PUNCT
ejpam-5790	339	1	from	from	ADP
ejpam-5790	339	2	(	(	PUNCT
ejpam-5790	339	3	3.6	3.6	NUM
ejpam-5790	339	4	)	)	PUNCT
ejpam-5790	339	5	we	we	PRON
ejpam-5790	339	6	have	have	VERB
ejpam-5790	339	7	j	j	PROPN
ejpam-5790	339	8	s	s	PROPN
ejpam-5790	339	9	ν1+ν2	ν1+ν2	PROPN
ejpam-5790	339	10	2	2	NUM
ejpam-5790	339	11	−,k	−,k	NOUN
ejpam-5790	339	12	ℑ(ν1	ℑ(ν1	NOUN
ejpam-5790	339	13	)	)	PUNCT
ejpam-5790	339	14	=	=	SYM
ejpam-5790	339	15	1	1	NUM
ejpam-5790	339	16	2	2	NUM
ejpam-5790	339	17	s−k	s−k	NOUN
ejpam-5790	339	18	k	k	PROPN
ejpam-5790	339	19	kγk(s	kγk(s	PROPN
ejpam-5790	339	20	+	+	CCONJ
ejpam-5790	339	21	k	k	ADJ
ejpam-5790	339	22	)	)	PUNCT
ejpam-5790	339	23	ℑ	ℑ	PROPN
ejpam-5790	339	24	(	(	PUNCT
ejpam-5790	339	25	ν1	ν1	NOUN
ejpam-5790	339	26	+	+	CCONJ
ejpam-5790	339	27	ν2	ν2	PROPN
ejpam-5790	339	28	2	2	NUM
ejpam-5790	339	29	)	)	PUNCT
ejpam-5790	339	30	(	(	PUNCT
ejpam-5790	339	31	ν2	ν2	NOUN
ejpam-5790	339	32	−	−	PROPN
ejpam-5790	339	33	ν1	ν1	NOUN
ejpam-5790	339	34	)	)	PUNCT
ejpam-5790	339	35	s	s	PART
ejpam-5790	340	1	k	k	NOUN
ejpam-5790	340	2	−	−	PROPN
ejpam-5790	340	3	1	1	NUM
ejpam-5790	340	4	kγk(s	kγk(s	PROPN
ejpam-5790	340	5	+	+	CCONJ
ejpam-5790	340	6	k	k	NOUN
ejpam-5790	340	7	)	)	PUNCT
ejpam-5790	341	1	[	[	X
ejpam-5790	341	2	∫	∫	X
ejpam-5790	341	3	ν1+ν2	ν1+ν2	PROPN
ejpam-5790	341	4	2	2	NUM
ejpam-5790	341	5	ν1	ν1	NOUN
ejpam-5790	341	6	(	(	PUNCT
ejpam-5790	341	7	ε−	ε−	PROPN
ejpam-5790	341	8	ν1	ν1	NOUN
ejpam-5790	341	9	)	)	PUNCT
ejpam-5790	341	10	s	s	PART
ejpam-5790	342	1	k	k	X
ejpam-5790	343	1	ℑ′(ε)dε	ℑ′(ε)dε	PRON
ejpam-5790	343	2	]	]	PUNCT
ejpam-5790	343	3	=	=	SYM
ejpam-5790	343	4	1	1	NUM
ejpam-5790	343	5	2	2	NUM
ejpam-5790	343	6	s−k	s−k	NOUN
ejpam-5790	343	7	k	k	PROPN
ejpam-5790	343	8	kγk(s	kγk(s	PROPN
ejpam-5790	343	9	+	+	CCONJ
ejpam-5790	343	10	k	k	ADJ
ejpam-5790	343	11	)	)	PUNCT
ejpam-5790	343	12	ℑ	ℑ	PROPN
ejpam-5790	343	13	(	(	PUNCT
ejpam-5790	343	14	ν1	ν1	NOUN
ejpam-5790	343	15	+	+	CCONJ
ejpam-5790	343	16	ν2	ν2	PROPN
ejpam-5790	343	17	2	2	NUM
ejpam-5790	343	18	)	)	PUNCT
ejpam-5790	343	19	(	(	PUNCT
ejpam-5790	343	20	ν2	ν2	NOUN
ejpam-5790	343	21	−	−	PROPN
ejpam-5790	343	22	ν1	ν1	NOUN
ejpam-5790	343	23	)	)	PUNCT
ejpam-5790	343	24	s	s	PART
ejpam-5790	344	1	k	k	NOUN
ejpam-5790	344	2	−	−	PROPN
ejpam-5790	345	1	w	w	PROPN
ejpam-5790	345	2	s	s	PROPN
ejpam-5790	345	3	k	k	X
ejpam-5790	345	4	(	(	PUNCT
ejpam-5790	345	5	ν2	ν2	NOUN
ejpam-5790	345	6	−	−	PROPN
ejpam-5790	345	7	ν1	ν1	NOUN
ejpam-5790	345	8	)	)	PUNCT
ejpam-5790	345	9	s+k	s+k	PUNCT
ejpam-5790	346	1	k	k	PROPN
ejpam-5790	346	2	2	2	X
ejpam-5790	346	3	s+k	s+k	NOUN
ejpam-5790	346	4	k	k	PROPN
ejpam-5790	346	5	kγk(s	kγk(s	PROPN
ejpam-5790	347	1	+	+	CCONJ
ejpam-5790	348	1	k	k	NOUN
ejpam-5790	348	2	)	)	PUNCT
ejpam-5790	349	1	[	[	X
ejpam-5790	349	2	∫	∫	X
ejpam-5790	349	3	1	1	NUM
ejpam-5790	349	4	0	0	NUM
ejpam-5790	349	5	ℑ′	ℑ′	X
ejpam-5790	349	6	(	(	PUNCT
ejpam-5790	349	7	(	(	PUNCT
ejpam-5790	349	8	1−w)ν1	1−w)ν1	NUM
ejpam-5790	349	9	+	+	CCONJ
ejpam-5790	349	10	(	(	PUNCT
ejpam-5790	349	11	ν1	ν1	NOUN
ejpam-5790	349	12	+	+	CCONJ
ejpam-5790	349	13	ν2	ν2	PROPN
ejpam-5790	349	14	2	2	NUM
ejpam-5790	349	15	)	)	PUNCT
ejpam-5790	349	16	w	w	NOUN
ejpam-5790	349	17	)	)	PUNCT
ejpam-5790	349	18	dw	dw	NOUN
ejpam-5790	349	19	]	]	PUNCT
ejpam-5790	349	20	,	,	PUNCT
ejpam-5790	349	21	(	(	PUNCT
ejpam-5790	349	22	3.7	3.7	NUM
ejpam-5790	349	23	)	)	PUNCT
ejpam-5790	349	24	for	for	ADP
ejpam-5790	349	25	ν1	ν1	NOUN
ejpam-5790	349	26	<	<	X
ejpam-5790	349	27	ν1+ν2	ν1+ν2	PROPN
ejpam-5790	349	28	2	2	NUM
ejpam-5790	349	29	⩽	⩽	ADJ
ejpam-5790	349	30	ν2	ν2	NOUN
ejpam-5790	349	31	and	and	CCONJ
ejpam-5790	349	32	from	from	ADP
ejpam-5790	349	33	(	(	PUNCT
ejpam-5790	349	34	3.6	3.6	NUM
ejpam-5790	349	35	)	)	PUNCT
ejpam-5790	349	36	we	we	PRON
ejpam-5790	349	37	have	have	VERB
ejpam-5790	349	38	j	j	PROPN
ejpam-5790	349	39	s	s	PROPN
ejpam-5790	349	40	ν1+ν2	ν1+ν2	PROPN
ejpam-5790	349	41	2	2	NUM
ejpam-5790	349	42	+	+	NOUN
ejpam-5790	349	43	,	,	PUNCT
ejpam-5790	349	44	k	k	PROPN
ejpam-5790	349	45	ℑ(ν2	ℑ(ν2	PROPN
ejpam-5790	349	46	)	)	PUNCT
ejpam-5790	349	47	=	=	SYM
ejpam-5790	349	48	1	1	NUM
ejpam-5790	349	49	2	2	NUM
ejpam-5790	349	50	s−k	s−k	NOUN
ejpam-5790	349	51	k	k	PROPN
ejpam-5790	349	52	kγk(s	kγk(s	PROPN
ejpam-5790	349	53	+	+	CCONJ
ejpam-5790	349	54	k	k	ADJ
ejpam-5790	349	55	)	)	PUNCT
ejpam-5790	349	56	ℑ	ℑ	PROPN
ejpam-5790	349	57	(	(	PUNCT
ejpam-5790	349	58	ν1	ν1	NOUN
ejpam-5790	349	59	+	+	CCONJ
ejpam-5790	349	60	ν2	ν2	PROPN
ejpam-5790	349	61	2	2	NUM
ejpam-5790	349	62	)	)	PUNCT
ejpam-5790	349	63	(	(	PUNCT
ejpam-5790	349	64	ν2	ν2	NOUN
ejpam-5790	349	65	−	−	PROPN
ejpam-5790	349	66	ν1	ν1	NOUN
ejpam-5790	349	67	)	)	PUNCT
ejpam-5790	349	68	s	s	PART
ejpam-5790	350	1	k	k	X
ejpam-5790	350	2	+	+	CCONJ
ejpam-5790	350	3	1	1	NUM
ejpam-5790	350	4	kγk(s	kγk(s	PROPN
ejpam-5790	350	5	+	+	CCONJ
ejpam-5790	350	6	k	k	NOUN
ejpam-5790	350	7	)	)	PUNCT
ejpam-5790	351	1	[	[	X
ejpam-5790	351	2	∫	∫	X
ejpam-5790	351	3	ν2	ν2	NOUN
ejpam-5790	351	4	ν1+ν2	ν1+ν2	PROPN
ejpam-5790	351	5	2	2	NUM
ejpam-5790	351	6	(	(	PUNCT
ejpam-5790	351	7	ν2	ν2	NOUN
ejpam-5790	351	8	−	−	PROPN
ejpam-5790	351	9	ε)sℑ′(ε)dε	ε)sℑ′(ε)dε	NOUN
ejpam-5790	351	10	]	]	PUNCT
ejpam-5790	352	1	=	=	SYM
ejpam-5790	352	2	1	1	NUM
ejpam-5790	352	3	2	2	NUM
ejpam-5790	352	4	s−k	s−k	NOUN
ejpam-5790	352	5	k	k	PROPN
ejpam-5790	352	6	kγk(s	kγk(s	PROPN
ejpam-5790	353	1	+	+	CCONJ
ejpam-5790	353	2	k	k	ADJ
ejpam-5790	353	3	)	)	PUNCT
ejpam-5790	353	4	ℑ	ℑ	PROPN
ejpam-5790	353	5	(	(	PUNCT
ejpam-5790	353	6	ν1	ν1	NOUN
ejpam-5790	353	7	+	+	CCONJ
ejpam-5790	353	8	ν2	ν2	PROPN
ejpam-5790	353	9	2	2	NUM
ejpam-5790	353	10	)	)	PUNCT
ejpam-5790	353	11	(	(	PUNCT
ejpam-5790	353	12	ν2	ν2	NOUN
ejpam-5790	353	13	−	−	PROPN
ejpam-5790	353	14	ν1	ν1	NOUN
ejpam-5790	353	15	)	)	PUNCT
ejpam-5790	353	16	s	s	PART
ejpam-5790	353	17	k	k	X
ejpam-5790	353	18	−	−	PROPN
ejpam-5790	353	19	(	(	PUNCT
ejpam-5790	353	20	1−w	1−w	NUM
ejpam-5790	353	21	)	)	PUNCT
ejpam-5790	354	1	s	s	PART
ejpam-5790	355	1	k	k	X
ejpam-5790	355	2	(	(	PUNCT
ejpam-5790	355	3	ν2	ν2	NOUN
ejpam-5790	355	4	−	−	PROPN
ejpam-5790	355	5	ν1	ν1	NOUN
ejpam-5790	355	6	)	)	PUNCT
ejpam-5790	355	7	s+k	s+k	PUNCT
ejpam-5790	356	1	k	k	PROPN
ejpam-5790	356	2	2	2	X
ejpam-5790	356	3	s+k	s+k	NOUN
ejpam-5790	356	4	k	k	PROPN
ejpam-5790	356	5	kγk(s	kγk(s	PROPN
ejpam-5790	357	1	+	+	CCONJ
ejpam-5790	358	1	k	k	NOUN
ejpam-5790	358	2	)	)	PUNCT
ejpam-5790	359	1	[	[	X
ejpam-5790	359	2	∫	∫	X
ejpam-5790	359	3	1	1	NUM
ejpam-5790	359	4	0	0	NUM
ejpam-5790	359	5	ℑ′	ℑ′	X
ejpam-5790	359	6	(	(	PUNCT
ejpam-5790	359	7	(	(	PUNCT
ejpam-5790	359	8	1−w	1−w	NUM
ejpam-5790	359	9	)	)	PUNCT
ejpam-5790	359	10	(	(	PUNCT
ejpam-5790	359	11	ν1	ν1	NOUN
ejpam-5790	359	12	+	+	CCONJ
ejpam-5790	359	13	ν2	ν2	PROPN
ejpam-5790	359	14	2	2	NUM
ejpam-5790	359	15	)	)	PUNCT
ejpam-5790	360	1	+	+	CCONJ
ejpam-5790	360	2	ν2w	ν2w	PROPN
ejpam-5790	360	3	)	)	PUNCT
ejpam-5790	360	4	dw	dw	PROPN
ejpam-5790	360	5	]	]	PUNCT
ejpam-5790	360	6	.	.	PUNCT
ejpam-5790	361	1	(	(	PUNCT
ejpam-5790	361	2	3.8	3.8	NUM
ejpam-5790	361	3	)	)	PUNCT
ejpam-5790	361	4	lemma	lemma	PROPN
ejpam-5790	361	5	6	6	NUM
ejpam-5790	361	6	.	.	PUNCT
ejpam-5790	362	1	assume	assume	VERB
ejpam-5790	362	2	ℑ	ℑ	PROPN
ejpam-5790	362	3	is	be	AUX
ejpam-5790	362	4	a	a	DET
ejpam-5790	362	5	convex	convex	NOUN
ejpam-5790	362	6	mapping	mapping	NOUN
ejpam-5790	362	7	on	on	ADP
ejpam-5790	362	8	∆	∆	PROPN
ejpam-5790	362	9	,	,	PUNCT
ejpam-5790	362	10	and	and	CCONJ
ejpam-5790	362	11	u	u	NOUN
ejpam-5790	362	12	,	,	PUNCT
ejpam-5790	362	13	d	d	X
ejpam-5790	362	14	are	be	AUX
ejpam-5790	362	15	adjoint	adjoint	NOUN
ejpam-5790	362	16	operators	operator	NOUN
ejpam-5790	362	17	whose	whose	DET
ejpam-5790	362	18	spectra	spectra	ADJ
ejpam-5790	362	19	sp(u),sp(d	sp(u),sp(d	NOUN
ejpam-5790	362	20	)	)	PUNCT
ejpam-5790	363	1	⊂	⊂	PROPN
ejpam-5790	364	1	∆	∆	PROPN
ejpam-5790	364	2	,	,	PUNCT
ejpam-5790	364	3	then	then	ADV
ejpam-5790	364	4	[	[	PUNCT
ejpam-5790	364	5	1	1	NUM
ejpam-5790	364	6	6	6	NUM
ejpam-5790	364	7	(	(	PUNCT
ejpam-5790	364	8	ℑ(u)⊗	ℑ(u)⊗	PROPN
ejpam-5790	364	9	1	1	NUM
ejpam-5790	364	10	)	)	PUNCT
ejpam-5790	364	11	+	+	CCONJ
ejpam-5790	364	12	2	2	NUM
ejpam-5790	364	13	3	3	NUM
ejpam-5790	364	14	ℑ	ℑ	NOUN
ejpam-5790	364	15	(	(	PUNCT
ejpam-5790	364	16	u	u	NOUN
ejpam-5790	364	17	⊗	⊗	PROPN
ejpam-5790	364	18	1	1	NUM
ejpam-5790	364	19	+	+	NUM
ejpam-5790	364	20	1⊗d	1⊗d	NUM
ejpam-5790	364	21	2	2	NUM
ejpam-5790	364	22	)	)	PUNCT
ejpam-5790	364	23	+	+	CCONJ
ejpam-5790	364	24	1	1	NUM
ejpam-5790	364	25	6	6	NUM
ejpam-5790	364	26	(	(	PUNCT
ejpam-5790	364	27	1⊗ℑ(d	1⊗ℑ(d	NUM
ejpam-5790	364	28	)	)	PUNCT
ejpam-5790	364	29	)	)	PUNCT
ejpam-5790	364	30	]	]	PUNCT
ejpam-5790	365	1	−	−	PROPN
ejpam-5790	365	2	[	[	PUNCT
ejpam-5790	365	3	ℑ	ℑ	PROPN
ejpam-5790	365	4	(	(	PUNCT
ejpam-5790	365	5	u	u	NOUN
ejpam-5790	365	6	⊗	⊗	PROPN
ejpam-5790	365	7	1	1	NUM
ejpam-5790	365	8	+	+	NUM
ejpam-5790	365	9	1⊗d	1⊗d	NUM
ejpam-5790	365	10	2	2	NUM
ejpam-5790	365	11	)	)	PUNCT
ejpam-5790	365	12	−	−	PROPN
ejpam-5790	366	1	w	w	PROPN
ejpam-5790	366	2	s	s	PROPN
ejpam-5790	366	3	k	k	X
ejpam-5790	366	4	(	(	PUNCT
ejpam-5790	366	5	ν2	ν2	NOUN
ejpam-5790	366	6	−	−	PROPN
ejpam-5790	366	7	ν1	ν1	NOUN
ejpam-5790	366	8	)	)	PUNCT
ejpam-5790	366	9	4	4	NUM
ejpam-5790	367	1	[	[	X
ejpam-5790	367	2	∫	∫	PROPN
ejpam-5790	367	3	1	1	NUM
ejpam-5790	367	4	0	0	NUM
ejpam-5790	367	5	ℑ′	ℑ′	X
ejpam-5790	367	6	(	(	PUNCT
ejpam-5790	367	7	(	(	PUNCT
ejpam-5790	367	8	1−w)u	1−w)u	NUM
ejpam-5790	367	9	⊗	⊗	NOUN
ejpam-5790	367	10	1	1	NUM
ejpam-5790	367	11	+	+	CCONJ
ejpam-5790	367	12	(	(	PUNCT
ejpam-5790	367	13	w1⊗d	w1⊗d	NOUN
ejpam-5790	367	14	2	2	NUM
ejpam-5790	367	15	)	)	PUNCT
ejpam-5790	367	16	)	)	PUNCT
ejpam-5790	367	17	dw	dw	NOUN
ejpam-5790	367	18	]	]	PUNCT
ejpam-5790	368	1	+	+	CCONJ
ejpam-5790	368	2	ℑ	ℑ	PROPN
ejpam-5790	368	3	(	(	PUNCT
ejpam-5790	368	4	u	u	NOUN
ejpam-5790	368	5	⊗	⊗	PROPN
ejpam-5790	368	6	1	1	NUM
ejpam-5790	368	7	+	+	NUM
ejpam-5790	368	8	1⊗d	1⊗d	NUM
ejpam-5790	368	9	2	2	NUM
ejpam-5790	368	10	)	)	PUNCT
ejpam-5790	368	11	−	−	PROPN
ejpam-5790	368	12	(	(	PUNCT
ejpam-5790	368	13	1−w	1−w	NUM
ejpam-5790	368	14	)	)	PUNCT
ejpam-5790	368	15	s	s	PART
ejpam-5790	368	16	k	k	X
ejpam-5790	368	17	(	(	PUNCT
ejpam-5790	368	18	ν2	ν2	NOUN
ejpam-5790	368	19	−	−	PROPN
ejpam-5790	368	20	ν1	ν1	NOUN
ejpam-5790	368	21	)	)	PUNCT
ejpam-5790	368	22	4	4	NUM
ejpam-5790	369	1	[	[	X
ejpam-5790	369	2	∫	∫	PROPN
ejpam-5790	369	3	1	1	NUM
ejpam-5790	369	4	0	0	NUM
ejpam-5790	369	5	ℑ′	ℑ′	X
ejpam-5790	369	6	(	(	PUNCT
ejpam-5790	369	7	(	(	PUNCT
ejpam-5790	369	8	1−w	1−w	NUM
ejpam-5790	369	9	2	2	NUM
ejpam-5790	369	10	)	)	PUNCT
ejpam-5790	369	11	u	u	NOUN
ejpam-5790	369	12	⊗	⊗	PROPN
ejpam-5790	369	13	1	1	NUM
ejpam-5790	369	14	+	+	CCONJ
ejpam-5790	369	15	(	(	PUNCT
ejpam-5790	369	16	1	1	NUM
ejpam-5790	369	17	+	+	NOUN
ejpam-5790	369	18	w	w	NOUN
ejpam-5790	369	19	2	2	NUM
ejpam-5790	369	20	)	)	PUNCT
ejpam-5790	369	21	1⊗d	1⊗d	PROPN
ejpam-5790	369	22	)	)	PUNCT
ejpam-5790	369	23	dw	dw	PROPN
ejpam-5790	369	24	]	]	PUNCT
ejpam-5790	369	25	w.	w.	PROPN
ejpam-5790	369	26	afzal	afzal	PROPN
ejpam-5790	369	27	et	et	PROPN
ejpam-5790	369	28	al	al	PROPN
ejpam-5790	369	29	.	.	PUNCT
ejpam-5790	369	30	/	/	SYM
ejpam-5790	369	31	eur	eur	PROPN
ejpam-5790	369	32	.	.	PUNCT
ejpam-5790	370	1	j.	j.	PROPN
ejpam-5790	370	2	pure	pure	PROPN
ejpam-5790	370	3	appl	appl	PROPN
ejpam-5790	370	4	.	.	PROPN
ejpam-5790	370	5	math	math	PROPN
ejpam-5790	370	6	,	,	PUNCT
ejpam-5790	370	7	18	18	NUM
ejpam-5790	370	8	(	(	PUNCT
ejpam-5790	370	9	1	1	NUM
ejpam-5790	370	10	)	)	PUNCT
ejpam-5790	370	11	(	(	PUNCT
ejpam-5790	370	12	2025	2025	NUM
ejpam-5790	370	13	)	)	PUNCT
ejpam-5790	370	14	,	,	PUNCT
ejpam-5790	370	15	5790	5790	NUM
ejpam-5790	370	16	16	16	NUM
ejpam-5790	370	17	of	of	ADP
ejpam-5790	370	18	30	30	NUM
ejpam-5790	370	19	=	=	SYM
ejpam-5790	370	20	(	(	PUNCT
ejpam-5790	370	21	1⊗d	1⊗d	NUM
ejpam-5790	370	22	−	−	PROPN
ejpam-5790	370	23	u	u	NOUN
ejpam-5790	370	24	⊗	⊗	PROPN
ejpam-5790	370	25	1)2	1)2	NUM
ejpam-5790	370	26	6	6	NUM
ejpam-5790	371	1	[	[	X
ejpam-5790	371	2	∫	∫	PROPN
ejpam-5790	371	3	1	1	NUM
ejpam-5790	371	4	2	2	NUM
ejpam-5790	371	5	0	0	NUM
ejpam-5790	371	6	(	(	PUNCT
ejpam-5790	371	7	w	w	NOUN
ejpam-5790	371	8	−	−	PROPN
ejpam-5790	371	9	3k.2	3k.2	NUM
ejpam-5790	371	10	s	s	X
ejpam-5790	371	11	k	k	PROPN
ejpam-5790	371	12	w	w	PROPN
ejpam-5790	371	13	s+k	s+k	PROPN
ejpam-5790	371	14	k	k	PROPN
ejpam-5790	371	15	s	s	X
ejpam-5790	372	1	+	+	CCONJ
ejpam-5790	372	2	k	k	NOUN
ejpam-5790	372	3	)	)	PUNCT
ejpam-5790	372	4	[	[	PUNCT
ejpam-5790	372	5	ℑ′′	ℑ′′	ADV
ejpam-5790	372	6	(	(	PUNCT
ejpam-5790	372	7	u	u	NOUN
ejpam-5790	372	8	⊗	⊗	NOUN
ejpam-5790	372	9	1w	1w	VERB
ejpam-5790	372	10	+	+	CCONJ
ejpam-5790	372	11	1⊗	1⊗	NUM
ejpam-5790	372	12	u	u	NOUN
ejpam-5790	372	13	(	(	PUNCT
ejpam-5790	372	14	1−w	1−w	NUM
ejpam-5790	372	15	)	)	PUNCT
ejpam-5790	372	16	)	)	PUNCT
ejpam-5790	373	1	dw	dw	NOUN
ejpam-5790	373	2	]	]	PUNCT
ejpam-5790	374	1	+	+	CCONJ
ejpam-5790	374	2	∫	∫	PROPN
ejpam-5790	374	3	1	1	NUM
ejpam-5790	374	4	1	1	NUM
ejpam-5790	374	5	2	2	NUM
ejpam-5790	374	6	(	(	PUNCT
ejpam-5790	374	7	(	(	PUNCT
ejpam-5790	374	8	1−w)−	1−w)−	NUM
ejpam-5790	374	9	3k.2	3k.2	NUM
ejpam-5790	374	10	s	s	X
ejpam-5790	374	11	k	k	X
ejpam-5790	374	12	(	(	PUNCT
ejpam-5790	374	13	1−w	1−w	NUM
ejpam-5790	374	14	)	)	PUNCT
ejpam-5790	374	15	s+k	s+k	NOUN
ejpam-5790	375	1	k	k	PROPN
ejpam-5790	375	2	s	s	X
ejpam-5790	376	1	+	+	X
ejpam-5790	376	2	k	k	X
ejpam-5790	376	3	)	)	PUNCT
ejpam-5790	376	4	ℑ′′	ℑ′′	ADV
ejpam-5790	376	5	(	(	PUNCT
ejpam-5790	376	6	u	u	PROPN
ejpam-5790	376	7	⊗	⊗	NOUN
ejpam-5790	376	8	1w	1w	VERB
ejpam-5790	376	9	+	+	CCONJ
ejpam-5790	376	10	1⊗	1⊗	NUM
ejpam-5790	376	11	u	u	NOUN
ejpam-5790	376	12	(	(	PUNCT
ejpam-5790	376	13	1−w	1−w	NUM
ejpam-5790	376	14	)	)	PUNCT
ejpam-5790	376	15	)	)	PUNCT
ejpam-5790	377	1	dw	dw	NOUN
ejpam-5790	377	2	]	]	PUNCT
ejpam-5790	377	3	.	.	PUNCT
ejpam-5790	378	1	(	(	PUNCT
ejpam-5790	378	2	3.9	3.9	NUM
ejpam-5790	378	3	)	)	PUNCT
ejpam-5790	378	4	proof	proof	NOUN
ejpam-5790	378	5	.	.	PUNCT
ejpam-5790	379	1	considering	consider	VERB
ejpam-5790	379	2	the	the	DET
ejpam-5790	379	3	following	follow	VERB
ejpam-5790	379	4	result	result	NOUN
ejpam-5790	379	5	[	[	X
ejpam-5790	379	6	13	13	NUM
ejpam-5790	379	7	]	]	PUNCT
ejpam-5790	379	8	.	.	PUNCT
ejpam-5790	380	1	let	let	VERB
ejpam-5790	380	2	mapping	mapping	NOUN
ejpam-5790	380	3	ℑ	ℑ	PROPN
ejpam-5790	380	4	:	:	PUNCT
ejpam-5790	381	1	[	[	X
ejpam-5790	381	2	ν1	ν1	NOUN
ejpam-5790	381	3	,	,	PUNCT
ejpam-5790	381	4	ν2	ν2	NOUN
ejpam-5790	381	5	]	]	PUNCT
ejpam-5790	381	6	→	→	SYM
ejpam-5790	381	7	r	r	NOUN
ejpam-5790	381	8	be	be	AUX
ejpam-5790	381	9	defined	define	VERB
ejpam-5790	381	10	over	over	ADP
ejpam-5790	381	11	interval	interval	NOUN
ejpam-5790	381	12	(	(	PUNCT
ejpam-5790	381	13	ν1	ν1	NOUN
ejpam-5790	381	14	,	,	PUNCT
ejpam-5790	381	15	ν2	ν2	NOUN
ejpam-5790	381	16	)	)	PUNCT
ejpam-5790	381	17	such	such	ADJ
ejpam-5790	381	18	that	that	SCONJ
ejpam-5790	381	19	ℑ′′	ℑ′′	PROPN
ejpam-5790	381	20	∈	∈	PROPN
ejpam-5790	381	21	l([ν1	l([ν1	PROPN
ejpam-5790	381	22	,	,	PUNCT
ejpam-5790	381	23	ν2	ν2	NOUN
ejpam-5790	381	24	]	]	PUNCT
ejpam-5790	381	25	)	)	PUNCT
ejpam-5790	381	26	.	.	PUNCT
ejpam-5790	382	1	then	then	ADV
ejpam-5790	382	2	,	,	PUNCT
ejpam-5790	382	3	we	we	PRON
ejpam-5790	382	4	have	have	VERB
ejpam-5790	382	5	1	1	NUM
ejpam-5790	382	6	6	6	NUM
ejpam-5790	382	7	[	[	PUNCT
ejpam-5790	382	8	ℑ(ν1	ℑ(ν1	NOUN
ejpam-5790	382	9	)	)	PUNCT
ejpam-5790	382	10	+	+	NUM
ejpam-5790	382	11	4ℑ	4ℑ	NOUN
ejpam-5790	382	12	(	(	PUNCT
ejpam-5790	382	13	ν1	ν1	NOUN
ejpam-5790	382	14	+	+	CCONJ
ejpam-5790	382	15	ν2	ν2	NOUN
ejpam-5790	382	16	2	2	NUM
ejpam-5790	382	17	)	)	PUNCT
ejpam-5790	382	18	+	+	CCONJ
ejpam-5790	382	19	ℑ(ν2	ℑ(ν2	PROPN
ejpam-5790	382	20	)	)	PUNCT
ejpam-5790	382	21	]	]	PUNCT
ejpam-5790	383	1	−	−	PROPN
ejpam-5790	383	2	2	2	NUM
ejpam-5790	383	3	s−k	s−k	NOUN
ejpam-5790	383	4	k	k	NOUN
ejpam-5790	383	5	γ(s	γ(s	PROPN
ejpam-5790	383	6	+	+	CCONJ
ejpam-5790	383	7	k	k	X
ejpam-5790	383	8	)	)	PUNCT
ejpam-5790	383	9	(	(	PUNCT
ejpam-5790	383	10	ν2	ν2	NOUN
ejpam-5790	383	11	−	−	PROPN
ejpam-5790	383	12	ν1	ν1	NOUN
ejpam-5790	383	13	)	)	PUNCT
ejpam-5790	383	14	s	s	PART
ejpam-5790	383	15	k	k	X
ejpam-5790	383	16	[	[	PUNCT
ejpam-5790	383	17	jsν1+ν2	jsν1+ν2	NOUN
ejpam-5790	383	18	2	2	NUM
ejpam-5790	383	19	−,k	−,k	NOUN
ejpam-5790	383	20	ℑ(ν1	ℑ(ν1	PROPN
ejpam-5790	383	21	)	)	PUNCT
ejpam-5790	383	22	+	+	NUM
ejpam-5790	383	23	jsν1+ν2	jsν1+ν2	NOUN
ejpam-5790	383	24	2	2	NUM
ejpam-5790	383	25	+	+	PROPN
ejpam-5790	383	26	,	,	PUNCT
ejpam-5790	383	27	k	k	PROPN
ejpam-5790	383	28	ℑ(ν2	ℑ(ν2	PROPN
ejpam-5790	383	29	)	)	PUNCT
ejpam-5790	383	30	]	]	PUNCT
ejpam-5790	384	1	=	=	PUNCT
ejpam-5790	384	2	(	(	PUNCT
ejpam-5790	384	3	ν2	ν2	NOUN
ejpam-5790	384	4	−	−	PROPN
ejpam-5790	384	5	ν1	ν1	NOUN
ejpam-5790	384	6	)	)	PUNCT
ejpam-5790	384	7	2	2	NUM
ejpam-5790	384	8	6	6	NUM
ejpam-5790	385	1	[	[	X
ejpam-5790	385	2	∫	∫	PROPN
ejpam-5790	385	3	1	1	NUM
ejpam-5790	385	4	2	2	NUM
ejpam-5790	385	5	0	0	NUM
ejpam-5790	385	6	(	(	PUNCT
ejpam-5790	385	7	w	w	NOUN
ejpam-5790	385	8	−	−	PROPN
ejpam-5790	385	9	3k.2	3k.2	NUM
ejpam-5790	385	10	s	s	X
ejpam-5790	385	11	k	k	PROPN
ejpam-5790	385	12	w	w	PROPN
ejpam-5790	385	13	s+k	s+k	PROPN
ejpam-5790	385	14	k	k	PROPN
ejpam-5790	385	15	s	s	X
ejpam-5790	386	1	+	+	CCONJ
ejpam-5790	386	2	k	k	NOUN
ejpam-5790	386	3	)	)	PUNCT
ejpam-5790	386	4	[	[	PUNCT
ejpam-5790	386	5	ℑ′′	ℑ′′	ADV
ejpam-5790	386	6	(	(	PUNCT
ejpam-5790	386	7	ν2w	ν2w	PROPN
ejpam-5790	386	8	+	+	CCONJ
ejpam-5790	386	9	(	(	PUNCT
ejpam-5790	386	10	1−w	1−w	NUM
ejpam-5790	386	11	)	)	PUNCT
ejpam-5790	386	12	ν2	ν2	NOUN
ejpam-5790	386	13	)	)	PUNCT
ejpam-5790	386	14	]	]	PUNCT
ejpam-5790	387	1	dw	dw	PROPN
ejpam-5790	388	1	+	+	CCONJ
ejpam-5790	388	2	∫	∫	PROPN
ejpam-5790	388	3	1	1	NUM
ejpam-5790	388	4	1	1	NUM
ejpam-5790	388	5	2	2	NUM
ejpam-5790	388	6	(	(	PUNCT
ejpam-5790	388	7	(	(	PUNCT
ejpam-5790	388	8	1−w)−	1−w)−	NUM
ejpam-5790	388	9	3k.2	3k.2	NUM
ejpam-5790	388	10	s	s	X
ejpam-5790	388	11	k	k	X
ejpam-5790	388	12	(	(	PUNCT
ejpam-5790	388	13	1−w	1−w	NUM
ejpam-5790	388	14	)	)	PUNCT
ejpam-5790	388	15	s+k	s+k	NOUN
ejpam-5790	389	1	k	k	PROPN
ejpam-5790	389	2	s	s	X
ejpam-5790	390	1	+	+	CCONJ
ejpam-5790	390	2	k	k	NOUN
ejpam-5790	390	3	)	)	PUNCT
ejpam-5790	390	4	[	[	PUNCT
ejpam-5790	390	5	ℑ′′	ℑ′′	ADV
ejpam-5790	390	6	(	(	PUNCT
ejpam-5790	390	7	ν2w	ν2w	PROPN
ejpam-5790	390	8	+	+	CCONJ
ejpam-5790	390	9	(	(	PUNCT
ejpam-5790	390	10	1−w	1−w	NUM
ejpam-5790	390	11	)	)	PUNCT
ejpam-5790	390	12	ν2	ν2	NOUN
ejpam-5790	390	13	)	)	PUNCT
ejpam-5790	390	14	]	]	PUNCT
ejpam-5790	391	1	dw	dw	X
ejpam-5790	391	2	]	]	PUNCT
ejpam-5790	391	3	.	.	PUNCT
ejpam-5790	392	1	(	(	PUNCT
ejpam-5790	392	2	3.10	3.10	NUM
ejpam-5790	392	3	)	)	PUNCT
ejpam-5790	392	4	by	by	ADP
ejpam-5790	392	5	applying	apply	VERB
ejpam-5790	392	6	substitution	substitution	NOUN
ejpam-5790	392	7	from	from	ADP
ejpam-5790	392	8	equations	equation	NOUN
ejpam-5790	392	9	(	(	PUNCT
ejpam-5790	392	10	3.7	3.7	NUM
ejpam-5790	392	11	)	)	PUNCT
ejpam-5790	392	12	and	and	CCONJ
ejpam-5790	392	13	(	(	PUNCT
ejpam-5790	392	14	3.8	3.8	NUM
ejpam-5790	392	15	)	)	PUNCT
ejpam-5790	392	16	,	,	PUNCT
ejpam-5790	392	17	we	we	PRON
ejpam-5790	392	18	obtain	obtain	VERB
ejpam-5790	392	19	:	:	PUNCT
ejpam-5790	392	20	1	1	NUM
ejpam-5790	392	21	6	6	NUM
ejpam-5790	392	22	[	[	PUNCT
ejpam-5790	392	23	ℑ(ν1	ℑ(ν1	NOUN
ejpam-5790	392	24	)	)	PUNCT
ejpam-5790	392	25	+	+	NUM
ejpam-5790	393	1	4ℑ	4ℑ	NOUN
ejpam-5790	393	2	(	(	PUNCT
ejpam-5790	393	3	ν1	ν1	NOUN
ejpam-5790	393	4	+	+	CCONJ
ejpam-5790	393	5	ν2	ν2	NOUN
ejpam-5790	393	6	2	2	NUM
ejpam-5790	393	7	)	)	PUNCT
ejpam-5790	393	8	+	+	CCONJ
ejpam-5790	393	9	ℑ(ν2	ℑ(ν2	PROPN
ejpam-5790	393	10	)	)	PUNCT
ejpam-5790	393	11	]	]	PUNCT
ejpam-5790	394	1	−	−	PROPN
ejpam-5790	394	2	2	2	NUM
ejpam-5790	394	3	s−k	s−k	NOUN
ejpam-5790	394	4	k	k	PROPN
ejpam-5790	394	5	kγk(s	kγk(s	PROPN
ejpam-5790	394	6	+	+	CCONJ
ejpam-5790	394	7	k	k	NOUN
ejpam-5790	394	8	)	)	PUNCT
ejpam-5790	394	9	(	(	PUNCT
ejpam-5790	394	10	ν2	ν2	NOUN
ejpam-5790	394	11	−	−	PROPN
ejpam-5790	394	12	ν1	ν1	NOUN
ejpam-5790	394	13	)	)	PUNCT
ejpam-5790	394	14	s	s	PART
ejpam-5790	395	1	k	k	X
ejpam-5790	395	2	[	[	PUNCT
ejpam-5790	395	3	ℑ	ℑ	PROPN
ejpam-5790	395	4	(	(	PUNCT
ejpam-5790	395	5	ν1+ν2	ν1+ν2	PROPN
ejpam-5790	395	6	2	2	NUM
ejpam-5790	395	7	)	)	PUNCT
ejpam-5790	395	8	(	(	PUNCT
ejpam-5790	395	9	ν2	ν2	NOUN
ejpam-5790	395	10	−	−	PROPN
ejpam-5790	395	11	ν1	ν1	NOUN
ejpam-5790	395	12	)	)	PUNCT
ejpam-5790	395	13	s	s	PART
ejpam-5790	395	14	k	k	NOUN
ejpam-5790	395	15	2	2	NUM
ejpam-5790	395	16	s−k	s−k	NOUN
ejpam-5790	395	17	k	k	PROPN
ejpam-5790	395	18	kγk(s	kγk(s	PROPN
ejpam-5790	396	1	+	+	CCONJ
ejpam-5790	396	2	k	k	NOUN
ejpam-5790	396	3	)	)	PUNCT
ejpam-5790	397	1	−	−	PROPN
ejpam-5790	398	1	w	w	PROPN
ejpam-5790	398	2	s	s	PROPN
ejpam-5790	398	3	k	k	X
ejpam-5790	398	4	(	(	PUNCT
ejpam-5790	398	5	ν2	ν2	NOUN
ejpam-5790	398	6	−	−	PROPN
ejpam-5790	398	7	ν1	ν1	NOUN
ejpam-5790	398	8	)	)	PUNCT
ejpam-5790	398	9	s+k	s+k	PUNCT
ejpam-5790	399	1	k	k	PROPN
ejpam-5790	399	2	2	2	X
ejpam-5790	399	3	s+k	s+k	NOUN
ejpam-5790	399	4	k	k	PROPN
ejpam-5790	399	5	kγk(s	kγk(s	PROPN
ejpam-5790	400	1	+	+	CCONJ
ejpam-5790	401	1	k	k	NOUN
ejpam-5790	401	2	)	)	PUNCT
ejpam-5790	402	1	[	[	X
ejpam-5790	402	2	∫	∫	X
ejpam-5790	402	3	1	1	NUM
ejpam-5790	402	4	0	0	NUM
ejpam-5790	402	5	ℑ′	ℑ′	X
ejpam-5790	402	6	(	(	PUNCT
ejpam-5790	402	7	(	(	PUNCT
ejpam-5790	402	8	1−w)ν1	1−w)ν1	NUM
ejpam-5790	402	9	+	+	CCONJ
ejpam-5790	402	10	(	(	PUNCT
ejpam-5790	402	11	ν1	ν1	NOUN
ejpam-5790	402	12	+	+	CCONJ
ejpam-5790	402	13	ν2	ν2	PROPN
ejpam-5790	402	14	2	2	NUM
ejpam-5790	402	15	)	)	PUNCT
ejpam-5790	402	16	w	w	NOUN
ejpam-5790	402	17	)	)	PUNCT
ejpam-5790	402	18	dw	dw	NOUN
ejpam-5790	402	19	]	]	PUNCT
ejpam-5790	403	1	+	+	CCONJ
ejpam-5790	403	2	ℑ	ℑ	PROPN
ejpam-5790	403	3	(	(	PUNCT
ejpam-5790	403	4	ν1+ν2	ν1+ν2	NOUN
ejpam-5790	403	5	2	2	NUM
ejpam-5790	403	6	)	)	PUNCT
ejpam-5790	403	7	(	(	PUNCT
ejpam-5790	403	8	ν2	ν2	NOUN
ejpam-5790	403	9	−	−	PROPN
ejpam-5790	403	10	ν1	ν1	NOUN
ejpam-5790	403	11	)	)	PUNCT
ejpam-5790	403	12	s	s	PART
ejpam-5790	403	13	k	k	NOUN
ejpam-5790	403	14	2	2	NUM
ejpam-5790	403	15	s−k	s−k	NOUN
ejpam-5790	403	16	k	k	PROPN
ejpam-5790	403	17	kγk(s	kγk(s	PROPN
ejpam-5790	403	18	+	+	CCONJ
ejpam-5790	403	19	k	k	NOUN
ejpam-5790	403	20	)	)	PUNCT
ejpam-5790	403	21	−	−	PROPN
ejpam-5790	403	22	(	(	PUNCT
ejpam-5790	403	23	1−w	1−w	NUM
ejpam-5790	403	24	)	)	PUNCT
ejpam-5790	403	25	s	s	PART
ejpam-5790	403	26	k	k	X
ejpam-5790	403	27	(	(	PUNCT
ejpam-5790	403	28	ν2	ν2	NOUN
ejpam-5790	403	29	−	−	PROPN
ejpam-5790	403	30	ν1	ν1	NOUN
ejpam-5790	403	31	)	)	PUNCT
ejpam-5790	403	32	s+k	s+k	PUNCT
ejpam-5790	404	1	k	k	PROPN
ejpam-5790	404	2	2	2	X
ejpam-5790	404	3	s+k	s+k	NOUN
ejpam-5790	404	4	k	k	PROPN
ejpam-5790	404	5	kγk(s	kγk(s	PROPN
ejpam-5790	405	1	+	+	CCONJ
ejpam-5790	406	1	k	k	NOUN
ejpam-5790	406	2	)	)	PUNCT
ejpam-5790	407	1	[	[	X
ejpam-5790	407	2	∫	∫	X
ejpam-5790	407	3	1	1	NUM
ejpam-5790	407	4	0	0	NUM
ejpam-5790	407	5	ℑ′	ℑ′	X
ejpam-5790	407	6	(	(	PUNCT
ejpam-5790	407	7	(	(	PUNCT
ejpam-5790	407	8	1−w	1−w	NUM
ejpam-5790	407	9	)	)	PUNCT
ejpam-5790	407	10	(	(	PUNCT
ejpam-5790	407	11	ν1	ν1	NOUN
ejpam-5790	407	12	+	+	CCONJ
ejpam-5790	407	13	ν2	ν2	PROPN
ejpam-5790	407	14	2	2	NUM
ejpam-5790	407	15	)	)	PUNCT
ejpam-5790	408	1	+	+	CCONJ
ejpam-5790	408	2	ν2w	ν2w	PROPN
ejpam-5790	408	3	)	)	PUNCT
ejpam-5790	408	4	dw	dw	NOUN
ejpam-5790	408	5	]	]	X
ejpam-5790	408	6	]	]	X
ejpam-5790	409	1	=	=	SYM
ejpam-5790	409	2	(	(	PUNCT
ejpam-5790	409	3	ν2	ν2	NOUN
ejpam-5790	409	4	−	−	PROPN
ejpam-5790	409	5	ν1	ν1	NOUN
ejpam-5790	409	6	)	)	PUNCT
ejpam-5790	409	7	2	2	NUM
ejpam-5790	409	8	6	6	NUM
ejpam-5790	410	1	[	[	X
ejpam-5790	410	2	∫	∫	PROPN
ejpam-5790	410	3	1	1	NUM
ejpam-5790	410	4	2	2	NUM
ejpam-5790	410	5	0	0	NUM
ejpam-5790	410	6	(	(	PUNCT
ejpam-5790	410	7	w	w	NOUN
ejpam-5790	410	8	−	−	X
ejpam-5790	410	9	3k	3k	X
ejpam-5790	410	10	·	·	PUNCT
ejpam-5790	410	11	2	2	NUM
ejpam-5790	410	12	s	s	X
ejpam-5790	411	1	k	k	PROPN
ejpam-5790	411	2	w	w	PROPN
ejpam-5790	411	3	s+k	s+k	PROPN
ejpam-5790	411	4	k	k	PROPN
ejpam-5790	411	5	s	s	X
ejpam-5790	412	1	+	+	CCONJ
ejpam-5790	412	2	k	k	NOUN
ejpam-5790	412	3	)	)	PUNCT
ejpam-5790	412	4	[	[	PUNCT
ejpam-5790	412	5	ℑ′′	ℑ′′	ADV
ejpam-5790	412	6	(	(	PUNCT
ejpam-5790	412	7	ν2w	ν2w	PROPN
ejpam-5790	412	8	+	+	CCONJ
ejpam-5790	412	9	(	(	PUNCT
ejpam-5790	412	10	1−w)ν2	1−w)ν2	NUM
ejpam-5790	412	11	)	)	PUNCT
ejpam-5790	412	12	]	]	PUNCT
ejpam-5790	412	13	dw	dw	PROPN
ejpam-5790	413	1	+	+	CCONJ
ejpam-5790	413	2	∫	∫	PROPN
ejpam-5790	413	3	1	1	NUM
ejpam-5790	413	4	1	1	NUM
ejpam-5790	413	5	2	2	NUM
ejpam-5790	413	6	(	(	PUNCT
ejpam-5790	413	7	(	(	PUNCT
ejpam-5790	413	8	1−w)−	1−w)−	NUM
ejpam-5790	413	9	3k	3k	X
ejpam-5790	413	10	·	·	PUNCT
ejpam-5790	413	11	2	2	NUM
ejpam-5790	413	12	s	s	PART
ejpam-5790	413	13	k	k	X
ejpam-5790	413	14	(	(	PUNCT
ejpam-5790	413	15	1−w	1−w	NUM
ejpam-5790	413	16	)	)	PUNCT
ejpam-5790	413	17	s+k	s+k	NOUN
ejpam-5790	414	1	k	k	PROPN
ejpam-5790	414	2	s	s	X
ejpam-5790	415	1	+	+	CCONJ
ejpam-5790	415	2	k	k	NOUN
ejpam-5790	415	3	)	)	PUNCT
ejpam-5790	415	4	[	[	PUNCT
ejpam-5790	415	5	ℑ′′	ℑ′′	ADV
ejpam-5790	415	6	(	(	PUNCT
ejpam-5790	415	7	ν2w	ν2w	PROPN
ejpam-5790	415	8	+	+	CCONJ
ejpam-5790	415	9	(	(	PUNCT
ejpam-5790	415	10	1−w)ν2	1−w)ν2	NUM
ejpam-5790	415	11	)	)	PUNCT
ejpam-5790	415	12	]	]	PUNCT
ejpam-5790	415	13	dw	dw	X
ejpam-5790	415	14	]	]	PUNCT
ejpam-5790	415	15	.	.	PUNCT
ejpam-5790	416	1	(	(	PUNCT
ejpam-5790	416	2	3.11	3.11	NUM
ejpam-5790	416	3	)	)	PUNCT
ejpam-5790	416	4	by	by	ADP
ejpam-5790	416	5	making	make	VERB
ejpam-5790	416	6	several	several	ADJ
ejpam-5790	416	7	simplifications	simplification	NOUN
ejpam-5790	416	8	,	,	PUNCT
ejpam-5790	416	9	we	we	PRON
ejpam-5790	416	10	may	may	AUX
ejpam-5790	416	11	have	have	VERB
ejpam-5790	416	12	1	1	NUM
ejpam-5790	416	13	6	6	NUM
ejpam-5790	416	14	[	[	PUNCT
ejpam-5790	416	15	ℑ(ν1	ℑ(ν1	NOUN
ejpam-5790	416	16	)	)	PUNCT
ejpam-5790	416	17	+	+	NUM
ejpam-5790	416	18	4ℑ	4ℑ	NOUN
ejpam-5790	416	19	(	(	PUNCT
ejpam-5790	416	20	ν1	ν1	NOUN
ejpam-5790	416	21	+	+	CCONJ
ejpam-5790	416	22	ν2	ν2	NOUN
ejpam-5790	416	23	2	2	NUM
ejpam-5790	416	24	)	)	PUNCT
ejpam-5790	416	25	+	+	CCONJ
ejpam-5790	416	26	ℑ(ν2	ℑ(ν2	PROPN
ejpam-5790	416	27	)	)	PUNCT
ejpam-5790	416	28	]	]	PUNCT
ejpam-5790	417	1	−	−	PROPN
ejpam-5790	417	2	[	[	PUNCT
ejpam-5790	417	3	ℑ	ℑ	PROPN
ejpam-5790	417	4	(	(	PUNCT
ejpam-5790	417	5	ν1	ν1	NOUN
ejpam-5790	417	6	+	+	CCONJ
ejpam-5790	417	7	ν2	ν2	PROPN
ejpam-5790	417	8	2	2	NUM
ejpam-5790	417	9	)	)	PUNCT
ejpam-5790	417	10	−	−	PROPN
ejpam-5790	418	1	w	w	PROPN
ejpam-5790	418	2	s	s	PROPN
ejpam-5790	418	3	k	k	X
ejpam-5790	418	4	(	(	PUNCT
ejpam-5790	418	5	ν2	ν2	NOUN
ejpam-5790	418	6	−	−	PROPN
ejpam-5790	418	7	ν1	ν1	NOUN
ejpam-5790	418	8	)	)	PUNCT
ejpam-5790	418	9	4	4	NUM
ejpam-5790	419	1	[	[	X
ejpam-5790	419	2	∫	∫	PROPN
ejpam-5790	419	3	1	1	NUM
ejpam-5790	419	4	0	0	NUM
ejpam-5790	419	5	ℑ′	ℑ′	X
ejpam-5790	419	6	(	(	PUNCT
ejpam-5790	419	7	(	(	PUNCT
ejpam-5790	419	8	1−w	1−w	NUM
ejpam-5790	419	9	)	)	PUNCT
ejpam-5790	419	10	ν1	ν1	NOUN
ejpam-5790	419	11	+	+	CCONJ
ejpam-5790	419	12	(	(	PUNCT
ejpam-5790	419	13	ν2	ν2	PROPN
ejpam-5790	419	14	2	2	NUM
ejpam-5790	419	15	)	)	PUNCT
ejpam-5790	419	16	w	w	NOUN
ejpam-5790	419	17	)	)	PUNCT
ejpam-5790	419	18	dw	dw	PROPN
ejpam-5790	419	19	]	]	PUNCT
ejpam-5790	419	20	w.	w.	PROPN
ejpam-5790	419	21	afzal	afzal	PROPN
ejpam-5790	419	22	et	et	PROPN
ejpam-5790	419	23	al	al	PROPN
ejpam-5790	419	24	.	.	PUNCT
ejpam-5790	419	25	/	/	SYM
ejpam-5790	419	26	eur	eur	PROPN
ejpam-5790	419	27	.	.	PUNCT
ejpam-5790	420	1	j.	j.	PROPN
ejpam-5790	420	2	pure	pure	PROPN
ejpam-5790	420	3	appl	appl	PROPN
ejpam-5790	420	4	.	.	PROPN
ejpam-5790	420	5	math	math	PROPN
ejpam-5790	420	6	,	,	PUNCT
ejpam-5790	420	7	18	18	NUM
ejpam-5790	420	8	(	(	PUNCT
ejpam-5790	420	9	1	1	NUM
ejpam-5790	420	10	)	)	PUNCT
ejpam-5790	420	11	(	(	PUNCT
ejpam-5790	420	12	2025	2025	NUM
ejpam-5790	420	13	)	)	PUNCT
ejpam-5790	420	14	,	,	PUNCT
ejpam-5790	420	15	5790	5790	NUM
ejpam-5790	420	16	17	17	NUM
ejpam-5790	420	17	of	of	ADP
ejpam-5790	420	18	30	30	NUM
ejpam-5790	420	19	+	+	NOUN
ejpam-5790	420	20	ℑ	ℑ	PROPN
ejpam-5790	420	21	(	(	PUNCT
ejpam-5790	420	22	ν1	ν1	NOUN
ejpam-5790	420	23	+	+	CCONJ
ejpam-5790	420	24	ν2	ν2	PROPN
ejpam-5790	420	25	2	2	NUM
ejpam-5790	420	26	)	)	PUNCT
ejpam-5790	420	27	−	−	PROPN
ejpam-5790	420	28	(	(	PUNCT
ejpam-5790	420	29	1−w	1−w	NUM
ejpam-5790	420	30	)	)	PUNCT
ejpam-5790	420	31	s	s	PART
ejpam-5790	421	1	k	k	X
ejpam-5790	421	2	(	(	PUNCT
ejpam-5790	421	3	ν2	ν2	NOUN
ejpam-5790	421	4	−	−	PROPN
ejpam-5790	421	5	ν1	ν1	NOUN
ejpam-5790	421	6	)	)	PUNCT
ejpam-5790	421	7	4	4	NUM
ejpam-5790	422	1	[	[	X
ejpam-5790	422	2	∫	∫	PROPN
ejpam-5790	422	3	1	1	NUM
ejpam-5790	422	4	0	0	NUM
ejpam-5790	422	5	ℑ′	ℑ′	X
ejpam-5790	422	6	(	(	PUNCT
ejpam-5790	422	7	(	(	PUNCT
ejpam-5790	422	8	1−w	1−w	NUM
ejpam-5790	422	9	2	2	NUM
ejpam-5790	422	10	)	)	PUNCT
ejpam-5790	422	11	ν1	ν1	NOUN
ejpam-5790	422	12	+	+	CCONJ
ejpam-5790	422	13	(	(	PUNCT
ejpam-5790	422	14	(	(	PUNCT
ejpam-5790	422	15	1	1	NUM
ejpam-5790	422	16	+	+	NOUN
ejpam-5790	422	17	w	w	NOUN
ejpam-5790	422	18	2	2	NUM
ejpam-5790	422	19	)	)	PUNCT
ejpam-5790	422	20	ν2	ν2	NOUN
ejpam-5790	422	21	)	)	PUNCT
ejpam-5790	422	22	dw	dw	NOUN
ejpam-5790	422	23	]	]	X
ejpam-5790	422	24	]	]	X
ejpam-5790	422	25	=	=	SYM
ejpam-5790	422	26	(	(	PUNCT
ejpam-5790	422	27	ν2	ν2	NOUN
ejpam-5790	422	28	−	−	PROPN
ejpam-5790	422	29	ν1	ν1	NOUN
ejpam-5790	422	30	)	)	PUNCT
ejpam-5790	422	31	2	2	NUM
ejpam-5790	422	32	6	6	NUM
ejpam-5790	423	1	[	[	X
ejpam-5790	423	2	∫	∫	PROPN
ejpam-5790	423	3	1	1	NUM
ejpam-5790	423	4	2	2	NUM
ejpam-5790	423	5	0	0	NUM
ejpam-5790	423	6	(	(	PUNCT
ejpam-5790	423	7	w	w	NOUN
ejpam-5790	423	8	−	−	PROPN
ejpam-5790	423	9	3k.2	3k.2	NUM
ejpam-5790	423	10	s	s	X
ejpam-5790	423	11	k	k	PROPN
ejpam-5790	423	12	w	w	PROPN
ejpam-5790	423	13	s+k	s+k	PROPN
ejpam-5790	424	1	k	k	PROPN
ejpam-5790	424	2	s	s	X
ejpam-5790	424	3	+	+	CCONJ
ejpam-5790	424	4	k	k	NOUN
ejpam-5790	424	5	)	)	PUNCT
ejpam-5790	424	6	[	[	PUNCT
ejpam-5790	424	7	ℑ′′	ℑ′′	ADV
ejpam-5790	424	8	(	(	PUNCT
ejpam-5790	424	9	ν2w	ν2w	PROPN
ejpam-5790	424	10	+	+	CCONJ
ejpam-5790	424	11	(	(	PUNCT
ejpam-5790	424	12	1−w	1−w	NUM
ejpam-5790	424	13	)	)	PUNCT
ejpam-5790	424	14	ν2	ν2	NOUN
ejpam-5790	424	15	)	)	PUNCT
ejpam-5790	424	16	]	]	PUNCT
ejpam-5790	425	1	dw	dw	PROPN
ejpam-5790	426	1	+	+	CCONJ
ejpam-5790	426	2	∫	∫	PROPN
ejpam-5790	426	3	1	1	NUM
ejpam-5790	426	4	1	1	NUM
ejpam-5790	426	5	2	2	NUM
ejpam-5790	426	6	(	(	PUNCT
ejpam-5790	426	7	(	(	PUNCT
ejpam-5790	426	8	1−w)−	1−w)−	NUM
ejpam-5790	426	9	3k.2	3k.2	NUM
ejpam-5790	426	10	s	s	X
ejpam-5790	426	11	k	k	X
ejpam-5790	426	12	(	(	PUNCT
ejpam-5790	426	13	1−w	1−w	NUM
ejpam-5790	426	14	)	)	PUNCT
ejpam-5790	426	15	s+k	s+k	NOUN
ejpam-5790	427	1	k	k	PROPN
ejpam-5790	427	2	s	s	X
ejpam-5790	428	1	+	+	CCONJ
ejpam-5790	428	2	k	k	NOUN
ejpam-5790	428	3	)	)	PUNCT
ejpam-5790	428	4	[	[	PUNCT
ejpam-5790	428	5	ℑ′′	ℑ′′	ADV
ejpam-5790	428	6	(	(	PUNCT
ejpam-5790	428	7	ν2w	ν2w	PROPN
ejpam-5790	428	8	+	+	CCONJ
ejpam-5790	428	9	(	(	PUNCT
ejpam-5790	428	10	1−w	1−w	NUM
ejpam-5790	428	11	)	)	PUNCT
ejpam-5790	428	12	ν2	ν2	NOUN
ejpam-5790	428	13	)	)	PUNCT
ejpam-5790	428	14	]	]	PUNCT
ejpam-5790	429	1	dw	dw	X
ejpam-5790	429	2	]	]	PUNCT
ejpam-5790	429	3	.	.	PUNCT
ejpam-5790	430	1	(	(	PUNCT
ejpam-5790	430	2	3.12	3.12	NUM
ejpam-5790	430	3	)	)	PUNCT
ejpam-5790	430	4	assume	assume	VERB
ejpam-5790	430	5	that	that	SCONJ
ejpam-5790	430	6	the	the	DET
ejpam-5790	430	7	spectral	spectral	ADJ
ejpam-5790	430	8	resolutions	resolution	NOUN
ejpam-5790	430	9	of	of	ADP
ejpam-5790	430	10	u	u	NOUN
ejpam-5790	430	11	and	and	CCONJ
ejpam-5790	430	12	d	d	ADP
ejpam-5790	430	13	u	u	NOUN
ejpam-5790	430	14	=	=	PROPN
ejpam-5790	430	15	∫	∫	PROPN
ejpam-5790	430	16	∆	∆	PROPN
ejpam-5790	430	17	ν2de(ν2	ν2de(ν2	PROPN
ejpam-5790	430	18	)	)	PUNCT
ejpam-5790	430	19	and	and	CCONJ
ejpam-5790	430	20	d	d	NOUN
ejpam-5790	430	21	=	=	SYM
ejpam-5790	430	22	∫	∫	PROPN
ejpam-5790	430	23	∆	∆	PROPN
ejpam-5790	430	24	ν1df(ν1).∫	ν1df(ν1).∫	ADJ
ejpam-5790	430	25	∆	∆	X
ejpam-5790	430	26	∫	∫	PROPN
ejpam-5790	430	27	∆	∆	PROPN
ejpam-5790	430	28	over	over	ADP
ejpam-5790	430	29	deν1	deν1	PROPN
ejpam-5790	430	30	⊗	⊗	PROPN
ejpam-5790	430	31	dfν2	dfν2	PROPN
ejpam-5790	430	32	in	in	ADP
ejpam-5790	430	33	(	(	PUNCT
ejpam-5790	430	34	3.12	3.12	NUM
ejpam-5790	430	35	)	)	PUNCT
ejpam-5790	430	36	,	,	PUNCT
ejpam-5790	430	37	then	then	ADV
ejpam-5790	430	38	we	we	PRON
ejpam-5790	430	39	get∫	get∫	ADJ
ejpam-5790	430	40	∆	∆	PROPN
ejpam-5790	430	41	∫	∫	PROPN
ejpam-5790	430	42	∆	∆	PROPN
ejpam-5790	430	43	1	1	NUM
ejpam-5790	430	44	6	6	NUM
ejpam-5790	430	45	[	[	PUNCT
ejpam-5790	430	46	ℑ(ν1	ℑ(ν1	NOUN
ejpam-5790	430	47	)	)	PUNCT
ejpam-5790	430	48	+	+	NUM
ejpam-5790	430	49	4ℑ	4ℑ	NOUN
ejpam-5790	430	50	(	(	PUNCT
ejpam-5790	430	51	ν1	ν1	NOUN
ejpam-5790	430	52	+	+	CCONJ
ejpam-5790	430	53	ν2	ν2	NOUN
ejpam-5790	430	54	2	2	NUM
ejpam-5790	430	55	)	)	PUNCT
ejpam-5790	430	56	+	+	CCONJ
ejpam-5790	430	57	ℑ(ν2	ℑ(ν2	PROPN
ejpam-5790	430	58	)	)	PUNCT
ejpam-5790	430	59	]	]	PUNCT
ejpam-5790	431	1	deν1	deν1	PROPN
ejpam-5790	431	2	⊗	⊗	PROPN
ejpam-5790	431	3	dfν2	dfν2	PROPN
ejpam-5790	431	4	−	−	PROPN
ejpam-5790	432	1	[	[	X
ejpam-5790	432	2	∫	∫	X
ejpam-5790	432	3	∆	∆	PROPN
ejpam-5790	432	4	∫	∫	PROPN
ejpam-5790	432	5	∆	∆	PROPN
ejpam-5790	432	6	(	(	PUNCT
ejpam-5790	432	7	ℑ	ℑ	PROPN
ejpam-5790	432	8	(	(	PUNCT
ejpam-5790	432	9	ν1	ν1	NOUN
ejpam-5790	432	10	+	+	CCONJ
ejpam-5790	432	11	ν2	ν2	PROPN
ejpam-5790	432	12	2	2	NUM
ejpam-5790	432	13	)	)	PUNCT
ejpam-5790	432	14	−	−	PROPN
ejpam-5790	433	1	w	w	PROPN
ejpam-5790	433	2	s	s	PROPN
ejpam-5790	433	3	k	k	X
ejpam-5790	433	4	(	(	PUNCT
ejpam-5790	433	5	ν2	ν2	NOUN
ejpam-5790	433	6	−	−	PROPN
ejpam-5790	433	7	ν1	ν1	NOUN
ejpam-5790	433	8	)	)	PUNCT
ejpam-5790	433	9	4	4	NUM
ejpam-5790	434	1	[	[	X
ejpam-5790	434	2	∫	∫	PROPN
ejpam-5790	434	3	1	1	NUM
ejpam-5790	434	4	0	0	NUM
ejpam-5790	434	5	ℑ′	ℑ′	X
ejpam-5790	434	6	(	(	PUNCT
ejpam-5790	434	7	(	(	PUNCT
ejpam-5790	434	8	1−w	1−w	NUM
ejpam-5790	434	9	)	)	PUNCT
ejpam-5790	434	10	ν1	ν1	NOUN
ejpam-5790	434	11	+	+	CCONJ
ejpam-5790	434	12	(	(	PUNCT
ejpam-5790	434	13	ν2	ν2	PROPN
ejpam-5790	434	14	2	2	NUM
ejpam-5790	434	15	)	)	PUNCT
ejpam-5790	434	16	w	w	NOUN
ejpam-5790	434	17	)	)	PUNCT
ejpam-5790	434	18	dw	dw	NOUN
ejpam-5790	434	19	)	)	PUNCT
ejpam-5790	434	20	]	]	PUNCT
ejpam-5790	435	1	deν1	deν1	PROPN
ejpam-5790	435	2	⊗	⊗	PROPN
ejpam-5790	435	3	dfν2	dfν2	PROPN
ejpam-5790	435	4	+	+	CCONJ
ejpam-5790	435	5	∫	∫	PROPN
ejpam-5790	435	6	∆	∆	PROPN
ejpam-5790	435	7	∫	∫	PROPN
ejpam-5790	435	8	∆	∆	PROPN
ejpam-5790	435	9	(	(	PUNCT
ejpam-5790	435	10	ℑ	ℑ	PROPN
ejpam-5790	435	11	(	(	PUNCT
ejpam-5790	435	12	ν1	ν1	NOUN
ejpam-5790	435	13	+	+	CCONJ
ejpam-5790	435	14	ν2	ν2	PROPN
ejpam-5790	435	15	2	2	NUM
ejpam-5790	435	16	)	)	PUNCT
ejpam-5790	435	17	−	−	PROPN
ejpam-5790	435	18	(	(	PUNCT
ejpam-5790	435	19	1−w	1−w	NUM
ejpam-5790	435	20	)	)	PUNCT
ejpam-5790	435	21	s	s	PART
ejpam-5790	435	22	k	k	X
ejpam-5790	435	23	(	(	PUNCT
ejpam-5790	435	24	ν2	ν2	NOUN
ejpam-5790	435	25	−	−	PROPN
ejpam-5790	435	26	ν1	ν1	NOUN
ejpam-5790	435	27	)	)	PUNCT
ejpam-5790	435	28	4	4	NUM
ejpam-5790	435	29	×	×	NOUN
ejpam-5790	436	1	[	[	X
ejpam-5790	436	2	∫	∫	PROPN
ejpam-5790	436	3	1	1	NUM
ejpam-5790	436	4	0	0	NUM
ejpam-5790	436	5	ℑ′	ℑ′	X
ejpam-5790	436	6	(	(	PUNCT
ejpam-5790	436	7	(	(	PUNCT
ejpam-5790	436	8	1−w	1−w	NUM
ejpam-5790	436	9	2	2	NUM
ejpam-5790	436	10	)	)	PUNCT
ejpam-5790	436	11	ν1	ν1	NOUN
ejpam-5790	436	12	+	+	CCONJ
ejpam-5790	436	13	(	(	PUNCT
ejpam-5790	436	14	(	(	PUNCT
ejpam-5790	436	15	1	1	NUM
ejpam-5790	436	16	+	+	NOUN
ejpam-5790	436	17	w	w	NOUN
ejpam-5790	436	18	2	2	NUM
ejpam-5790	436	19	)	)	PUNCT
ejpam-5790	436	20	ν2	ν2	NOUN
ejpam-5790	436	21	)	)	PUNCT
ejpam-5790	436	22	dw	dw	NOUN
ejpam-5790	436	23	]	]	PUNCT
ejpam-5790	437	1	deν1	deν1	PROPN
ejpam-5790	437	2	⊗	⊗	PROPN
ejpam-5790	437	3	dfν2	dfν2	PROPN
ejpam-5790	437	4	]	]	PUNCT
ejpam-5790	437	5	=	=	PUNCT
ejpam-5790	437	6	(	(	PUNCT
ejpam-5790	437	7	ν2	ν2	NOUN
ejpam-5790	437	8	−	−	PROPN
ejpam-5790	437	9	ν1	ν1	NOUN
ejpam-5790	437	10	)	)	PUNCT
ejpam-5790	437	11	2	2	NUM
ejpam-5790	437	12	6	6	NUM
ejpam-5790	437	13	∫	∫	NOUN
ejpam-5790	437	14	∆	∆	PROPN
ejpam-5790	437	15	∫	∫	PROPN
ejpam-5790	437	16	∆	∆	PROPN
ejpam-5790	438	1	[	[	X
ejpam-5790	438	2	∫	∫	X
ejpam-5790	438	3	1	1	NUM
ejpam-5790	438	4	2	2	NUM
ejpam-5790	438	5	0	0	NUM
ejpam-5790	438	6	(	(	PUNCT
ejpam-5790	438	7	w	w	NOUN
ejpam-5790	438	8	−	−	PROPN
ejpam-5790	438	9	3k.2	3k.2	NUM
ejpam-5790	438	10	s	s	X
ejpam-5790	438	11	k	k	PROPN
ejpam-5790	438	12	w	w	PROPN
ejpam-5790	438	13	s+k	s+k	PROPN
ejpam-5790	438	14	k	k	PROPN
ejpam-5790	438	15	s	s	X
ejpam-5790	439	1	+	+	CCONJ
ejpam-5790	439	2	k	k	NOUN
ejpam-5790	439	3	)	)	PUNCT
ejpam-5790	439	4	[	[	PUNCT
ejpam-5790	439	5	ℑ′′	ℑ′′	ADV
ejpam-5790	439	6	(	(	PUNCT
ejpam-5790	439	7	ν2w	ν2w	PROPN
ejpam-5790	439	8	+	+	CCONJ
ejpam-5790	439	9	(	(	PUNCT
ejpam-5790	439	10	1−w	1−w	NUM
ejpam-5790	439	11	)	)	PUNCT
ejpam-5790	439	12	ν2	ν2	NOUN
ejpam-5790	439	13	)	)	PUNCT
ejpam-5790	439	14	]	]	PUNCT
ejpam-5790	440	1	dw	dw	PROPN
ejpam-5790	441	1	+	+	CCONJ
ejpam-5790	441	2	∫	∫	PROPN
ejpam-5790	441	3	1	1	NUM
ejpam-5790	441	4	1	1	NUM
ejpam-5790	441	5	2	2	NUM
ejpam-5790	441	6	(	(	PUNCT
ejpam-5790	441	7	(	(	PUNCT
ejpam-5790	441	8	1−w)−	1−w)−	NUM
ejpam-5790	441	9	3k.2	3k.2	NUM
ejpam-5790	441	10	s	s	X
ejpam-5790	441	11	k	k	X
ejpam-5790	441	12	(	(	PUNCT
ejpam-5790	441	13	1−w	1−w	NUM
ejpam-5790	441	14	)	)	PUNCT
ejpam-5790	441	15	s+k	s+k	NOUN
ejpam-5790	442	1	k	k	PROPN
ejpam-5790	442	2	s	s	X
ejpam-5790	443	1	+	+	CCONJ
ejpam-5790	443	2	k	k	NOUN
ejpam-5790	443	3	)	)	PUNCT
ejpam-5790	443	4	[	[	PUNCT
ejpam-5790	443	5	ℑ′′	ℑ′′	ADV
ejpam-5790	443	6	(	(	PUNCT
ejpam-5790	443	7	ν2w	ν2w	PROPN
ejpam-5790	443	8	+	+	CCONJ
ejpam-5790	443	9	(	(	PUNCT
ejpam-5790	443	10	1−w	1−w	NUM
ejpam-5790	443	11	)	)	PUNCT
ejpam-5790	443	12	ν2	ν2	NOUN
ejpam-5790	443	13	)	)	PUNCT
ejpam-5790	443	14	]	]	PUNCT
ejpam-5790	444	1	dw	dw	X
ejpam-5790	444	2	]	]	PUNCT
ejpam-5790	444	3	deν1	deν1	PROPN
ejpam-5790	444	4	⊗	⊗	PROPN
ejpam-5790	444	5	dfν2	dfν2	PROPN
ejpam-5790	444	6	.	.	PUNCT
ejpam-5790	445	1	(	(	PUNCT
ejpam-5790	445	2	3.13	3.13	NUM
ejpam-5790	445	3	)	)	PUNCT
ejpam-5790	445	4	taking	take	VERB
ejpam-5790	445	5	into	into	ADP
ejpam-5790	445	6	account	account	NOUN
ejpam-5790	445	7	lemma	lemma	PROPN
ejpam-5790	445	8	2	2	NUM
ejpam-5790	445	9	and	and	CCONJ
ejpam-5790	445	10	fubini	fubini	NOUN
ejpam-5790	445	11	’s	’s	PART
ejpam-5790	445	12	theorem	theorem	NOUN
ejpam-5790	445	13	,	,	PUNCT
ejpam-5790	445	14	we	we	PRON
ejpam-5790	445	15	obtain	obtain	VERB
ejpam-5790	445	16	:	:	PUNCT
ejpam-5790	445	17	∫	∫	PROPN
ejpam-5790	445	18	∆	∆	PROPN
ejpam-5790	445	19	∫	∫	PROPN
ejpam-5790	445	20	∆	∆	PROPN
ejpam-5790	445	21	ℑ(ν2)deν1	ℑ(ν2)deν1	NOUN
ejpam-5790	445	22	⊗	⊗	PROPN
ejpam-5790	445	23	dfν2	dfν2	PROPN
ejpam-5790	445	24	=	=	PUNCT
ejpam-5790	445	25	(	(	PUNCT
ejpam-5790	445	26	ℑ(u)⊗	ℑ(u)⊗	NUM
ejpam-5790	445	27	1),∫	1),∫	NUM
ejpam-5790	445	28	∆	∆	PROPN
ejpam-5790	445	29	∫	∫	PROPN
ejpam-5790	445	30	∆	∆	PROPN
ejpam-5790	445	31	ℑ	ℑ	PROPN
ejpam-5790	445	32	(	(	PUNCT
ejpam-5790	445	33	ν1	ν1	NOUN
ejpam-5790	445	34	+	+	CCONJ
ejpam-5790	445	35	ν2	ν2	NOUN
ejpam-5790	445	36	2	2	NUM
ejpam-5790	445	37	)	)	PUNCT
ejpam-5790	445	38	deν1	deν1	PROPN
ejpam-5790	445	39	⊗	⊗	PROPN
ejpam-5790	445	40	dfν2	dfν2	PROPN
ejpam-5790	445	41	=	=	SYM
ejpam-5790	445	42	ℑ	ℑ	PROPN
ejpam-5790	445	43	(	(	PUNCT
ejpam-5790	445	44	u	u	NOUN
ejpam-5790	445	45	⊗	⊗	PROPN
ejpam-5790	445	46	1	1	NUM
ejpam-5790	446	1	+	+	NUM
ejpam-5790	446	2	1⊗d	1⊗d	NUM
ejpam-5790	446	3	2	2	NUM
ejpam-5790	446	4	)	)	PUNCT
ejpam-5790	446	5	,	,	PUNCT
ejpam-5790	446	6	∫	∫	PROPN
ejpam-5790	446	7	∆	∆	PROPN
ejpam-5790	446	8	∫	∫	PROPN
ejpam-5790	446	9	∆	∆	PROPN
ejpam-5790	446	10	ℑ(ν1)deν1	ℑ(ν1)deν1	NOUN
ejpam-5790	446	11	⊗	⊗	PROPN
ejpam-5790	446	12	dfν2	dfν2	PROPN
ejpam-5790	446	13	=	=	PUNCT
ejpam-5790	446	14	(	(	PUNCT
ejpam-5790	446	15	1⊗ℑ(d)),∫	1⊗ℑ(d)),∫	NUM
ejpam-5790	446	16	∆	∆	PROPN
ejpam-5790	446	17	∫	∫	PROPN
ejpam-5790	446	18	∆	∆	PROPN
ejpam-5790	446	19	∫	∫	PROPN
ejpam-5790	446	20	1	1	NUM
ejpam-5790	446	21	0	0	NUM
ejpam-5790	446	22	ℑ′	ℑ′	X
ejpam-5790	446	23	(	(	PUNCT
ejpam-5790	446	24	(	(	PUNCT
ejpam-5790	446	25	1−w	1−w	NUM
ejpam-5790	446	26	)	)	PUNCT
ejpam-5790	446	27	ν1	ν1	NOUN
ejpam-5790	446	28	+	+	CCONJ
ejpam-5790	446	29	(	(	PUNCT
ejpam-5790	446	30	ν2	ν2	PROPN
ejpam-5790	446	31	2	2	NUM
ejpam-5790	446	32	)	)	PUNCT
ejpam-5790	446	33	w	w	NOUN
ejpam-5790	446	34	)	)	PUNCT
ejpam-5790	446	35	dwdeν1	dwdeν1	NOUN
ejpam-5790	446	36	⊗	⊗	PROPN
ejpam-5790	447	1	dfν2	dfν2	PROPN
ejpam-5790	447	2	w.	w.	PROPN
ejpam-5790	447	3	afzal	afzal	PROPN
ejpam-5790	447	4	et	et	PROPN
ejpam-5790	447	5	al	al	PROPN
ejpam-5790	447	6	.	.	PUNCT
ejpam-5790	447	7	/	/	SYM
ejpam-5790	447	8	eur	eur	PROPN
ejpam-5790	447	9	.	.	PUNCT
ejpam-5790	448	1	j.	j.	PROPN
ejpam-5790	448	2	pure	pure	PROPN
ejpam-5790	448	3	appl	appl	PROPN
ejpam-5790	448	4	.	.	PROPN
ejpam-5790	448	5	math	math	PROPN
ejpam-5790	448	6	,	,	PUNCT
ejpam-5790	448	7	18	18	NUM
ejpam-5790	448	8	(	(	PUNCT
ejpam-5790	448	9	1	1	NUM
ejpam-5790	448	10	)	)	PUNCT
ejpam-5790	448	11	(	(	PUNCT
ejpam-5790	448	12	2025	2025	NUM
ejpam-5790	448	13	)	)	PUNCT
ejpam-5790	448	14	,	,	PUNCT
ejpam-5790	448	15	5790	5790	NUM
ejpam-5790	448	16	18	18	NUM
ejpam-5790	448	17	of	of	ADP
ejpam-5790	448	18	30	30	NUM
ejpam-5790	448	19	=	=	SYM
ejpam-5790	448	20	∫	∫	PROPN
ejpam-5790	448	21	1	1	NUM
ejpam-5790	448	22	0	0	NUM
ejpam-5790	448	23	∫	∫	PROPN
ejpam-5790	448	24	∆	∆	PROPN
ejpam-5790	448	25	∫	∫	PROPN
ejpam-5790	448	26	∆	∆	PROPN
ejpam-5790	449	1	ℑ′	ℑ′	X
ejpam-5790	449	2	(	(	PUNCT
ejpam-5790	449	3	(	(	PUNCT
ejpam-5790	449	4	1−w	1−w	NUM
ejpam-5790	449	5	)	)	PUNCT
ejpam-5790	449	6	ν1	ν1	NOUN
ejpam-5790	449	7	+	+	CCONJ
ejpam-5790	449	8	(	(	PUNCT
ejpam-5790	449	9	ν2	ν2	PROPN
ejpam-5790	449	10	2	2	NUM
ejpam-5790	449	11	)	)	PUNCT
ejpam-5790	449	12	w	w	NOUN
ejpam-5790	449	13	)	)	PUNCT
ejpam-5790	449	14	deν1	deν1	PROPN
ejpam-5790	449	15	⊗	⊗	PROPN
ejpam-5790	449	16	dfν2dw	dfν2dw	PROPN
ejpam-5790	449	17	=	=	SYM
ejpam-5790	449	18	∫	∫	PROPN
ejpam-5790	449	19	1	1	NUM
ejpam-5790	449	20	0	0	NUM
ejpam-5790	449	21	ℑ′	ℑ′	X
ejpam-5790	449	22	(	(	PUNCT
ejpam-5790	449	23	(	(	PUNCT
ejpam-5790	449	24	1−w)u	1−w)u	NUM
ejpam-5790	449	25	⊗	⊗	NOUN
ejpam-5790	449	26	1	1	NUM
ejpam-5790	449	27	+	+	CCONJ
ejpam-5790	449	28	(	(	PUNCT
ejpam-5790	449	29	w1⊗d	w1⊗d	NOUN
ejpam-5790	449	30	2	2	NUM
ejpam-5790	449	31	)	)	PUNCT
ejpam-5790	449	32	)	)	PUNCT
ejpam-5790	449	33	dw,∫	dw,∫	X
ejpam-5790	450	1	∆	∆	X
ejpam-5790	450	2	∫	∫	PROPN
ejpam-5790	450	3	∆	∆	PROPN
ejpam-5790	451	1	∫	∫	PROPN
ejpam-5790	452	1	1	1	NUM
ejpam-5790	452	2	0	0	NUM
ejpam-5790	452	3	ℑ′	ℑ′	X
ejpam-5790	452	4	(	(	PUNCT
ejpam-5790	452	5	(	(	PUNCT
ejpam-5790	452	6	1−w	1−w	NUM
ejpam-5790	452	7	2	2	NUM
ejpam-5790	452	8	)	)	PUNCT
ejpam-5790	452	9	ν1	ν1	NOUN
ejpam-5790	452	10	+	+	CCONJ
ejpam-5790	452	11	(	(	PUNCT
ejpam-5790	452	12	1	1	NUM
ejpam-5790	452	13	+	+	NOUN
ejpam-5790	452	14	w	w	NOUN
ejpam-5790	452	15	2	2	NUM
ejpam-5790	452	16	)	)	PUNCT
ejpam-5790	452	17	ν2	ν2	NOUN
ejpam-5790	452	18	)	)	PUNCT
ejpam-5790	452	19	dwdeν1	dwdeν1	NOUN
ejpam-5790	452	20	⊗	⊗	PROPN
ejpam-5790	453	1	dfν2	dfν2	PROPN
ejpam-5790	453	2	=	=	SYM
ejpam-5790	454	1	∫	∫	PROPN
ejpam-5790	454	2	1	1	NUM
ejpam-5790	454	3	0	0	NUM
ejpam-5790	454	4	∫	∫	PROPN
ejpam-5790	454	5	∆	∆	PROPN
ejpam-5790	455	1	∫	∫	PROPN
ejpam-5790	455	2	∆	∆	PROPN
ejpam-5790	455	3	ℑ′	ℑ′	X
ejpam-5790	455	4	(	(	PUNCT
ejpam-5790	455	5	(	(	PUNCT
ejpam-5790	455	6	1−w	1−w	NUM
ejpam-5790	455	7	2	2	NUM
ejpam-5790	455	8	)	)	PUNCT
ejpam-5790	455	9	ν1	ν1	NOUN
ejpam-5790	455	10	+	+	CCONJ
ejpam-5790	455	11	(	(	PUNCT
ejpam-5790	455	12	1	1	NUM
ejpam-5790	455	13	+	+	NOUN
ejpam-5790	455	14	w	w	NOUN
ejpam-5790	455	15	2	2	NUM
ejpam-5790	455	16	)	)	PUNCT
ejpam-5790	455	17	ν2	ν2	NOUN
ejpam-5790	455	18	)	)	PUNCT
ejpam-5790	455	19	deν1	deν1	PROPN
ejpam-5790	455	20	⊗	⊗	PROPN
ejpam-5790	455	21	dfν2dw	dfν2dw	PROPN
ejpam-5790	455	22	=	=	SYM
ejpam-5790	456	1	∫	∫	PROPN
ejpam-5790	456	2	1	1	NUM
ejpam-5790	456	3	0	0	NUM
ejpam-5790	456	4	∫	∫	PROPN
ejpam-5790	456	5	∆	∆	PROPN
ejpam-5790	457	1	∫	∫	PROPN
ejpam-5790	457	2	∆	∆	PROPN
ejpam-5790	457	3	ℑ′	ℑ′	X
ejpam-5790	457	4	(	(	PUNCT
ejpam-5790	457	5	(	(	PUNCT
ejpam-5790	457	6	1−w	1−w	NUM
ejpam-5790	457	7	2	2	NUM
ejpam-5790	457	8	)	)	PUNCT
ejpam-5790	457	9	u	u	NOUN
ejpam-5790	457	10	⊗	⊗	PROPN
ejpam-5790	457	11	1	1	NUM
ejpam-5790	457	12	+	+	CCONJ
ejpam-5790	457	13	(	(	PUNCT
ejpam-5790	457	14	1	1	NUM
ejpam-5790	457	15	+	+	NOUN
ejpam-5790	457	16	w	w	NOUN
ejpam-5790	457	17	2	2	NUM
ejpam-5790	457	18	)	)	PUNCT
ejpam-5790	457	19	1⊗d	1⊗d	PROPN
ejpam-5790	457	20	)	)	PUNCT
ejpam-5790	457	21	dw	dw	NOUN
ejpam-5790	457	22	,	,	PUNCT
ejpam-5790	457	23	ℑ′′	ℑ′′	ADV
ejpam-5790	457	24	(	(	PUNCT
ejpam-5790	457	25	ν1w	ν1w	NOUN
ejpam-5790	457	26	+	+	NUM
ejpam-5790	457	27	ν1	ν1	NOUN
ejpam-5790	457	28	(	(	PUNCT
ejpam-5790	457	29	1−w	1−w	NUM
ejpam-5790	457	30	)	)	PUNCT
ejpam-5790	457	31	)	)	PUNCT
ejpam-5790	458	1	dwdeν1	dwdeν1	NOUN
ejpam-5790	458	2	⊗	⊗	PROPN
ejpam-5790	458	3	dfν2	dfν2	PROPN
ejpam-5790	458	4	=	=	SYM
ejpam-5790	458	5	ℑ′′	ℑ′′	ADV
ejpam-5790	458	6	(	(	PUNCT
ejpam-5790	458	7	u	u	NOUN
ejpam-5790	458	8	⊗	⊗	NOUN
ejpam-5790	458	9	1w	1w	VERB
ejpam-5790	458	10	+	+	CCONJ
ejpam-5790	458	11	1⊗	1⊗	NUM
ejpam-5790	458	12	u	u	NOUN
ejpam-5790	458	13	(	(	PUNCT
ejpam-5790	458	14	1−w	1−w	NUM
ejpam-5790	458	15	)	)	PUNCT
ejpam-5790	458	16	)	)	PUNCT
ejpam-5790	459	1	dw	dw	PROPN
ejpam-5790	459	2	.	.	PROPN
ejpam-5790	460	1	(	(	PUNCT
ejpam-5790	460	2	3.14	3.14	NUM
ejpam-5790	460	3	)	)	PUNCT
ejpam-5790	460	4	a	a	DET
ejpam-5790	460	5	same	same	ADJ
ejpam-5790	460	6	technique	technique	NOUN
ejpam-5790	460	7	has	have	AUX
ejpam-5790	460	8	been	be	AUX
ejpam-5790	460	9	taking	take	VERB
ejpam-5790	460	10	into	into	ADP
ejpam-5790	460	11	consideration	consideration	NOUN
ejpam-5790	460	12	we	we	PRON
ejpam-5790	460	13	have∫	have∫	VERB
ejpam-5790	460	14	∆	∆	PUNCT
ejpam-5790	461	1	∫	∫	PROPN
ejpam-5790	461	2	∆	∆	PROPN
ejpam-5790	461	3	(	(	PUNCT
ejpam-5790	461	4	ν2	ν2	NOUN
ejpam-5790	461	5	−	−	PROPN
ejpam-5790	461	6	ν1	ν1	NOUN
ejpam-5790	461	7	)	)	PUNCT
ejpam-5790	461	8	2	2	NUM
ejpam-5790	461	9	6	6	NUM
ejpam-5790	461	10	[	[	X
ejpam-5790	461	11	∫	∫	PROPN
ejpam-5790	461	12	1	1	NUM
ejpam-5790	461	13	2	2	NUM
ejpam-5790	461	14	0	0	NUM
ejpam-5790	461	15	(	(	PUNCT
ejpam-5790	461	16	w	w	NOUN
ejpam-5790	461	17	−	−	PROPN
ejpam-5790	461	18	3k.2	3k.2	NUM
ejpam-5790	461	19	s	s	X
ejpam-5790	461	20	k	k	PROPN
ejpam-5790	461	21	w	w	PROPN
ejpam-5790	461	22	s+k	s+k	PROPN
ejpam-5790	461	23	k	k	PROPN
ejpam-5790	461	24	s	s	X
ejpam-5790	462	1	+	+	CCONJ
ejpam-5790	462	2	k	k	NOUN
ejpam-5790	462	3	)	)	PUNCT
ejpam-5790	462	4	[	[	PUNCT
ejpam-5790	462	5	ℑ′′	ℑ′′	ADV
ejpam-5790	462	6	(	(	PUNCT
ejpam-5790	462	7	ν2w	ν2w	PROPN
ejpam-5790	462	8	+	+	CCONJ
ejpam-5790	462	9	(	(	PUNCT
ejpam-5790	462	10	1−w	1−w	NUM
ejpam-5790	462	11	)	)	PUNCT
ejpam-5790	462	12	ν2	ν2	NOUN
ejpam-5790	462	13	)	)	PUNCT
ejpam-5790	462	14	]	]	PUNCT
ejpam-5790	463	1	dw	dw	PROPN
ejpam-5790	464	1	+	+	CCONJ
ejpam-5790	464	2	∫	∫	PROPN
ejpam-5790	464	3	1	1	NUM
ejpam-5790	464	4	1	1	NUM
ejpam-5790	464	5	2	2	NUM
ejpam-5790	464	6	(	(	PUNCT
ejpam-5790	464	7	(	(	PUNCT
ejpam-5790	464	8	1−w)−	1−w)−	NUM
ejpam-5790	464	9	3k.2	3k.2	NUM
ejpam-5790	464	10	s	s	X
ejpam-5790	464	11	k	k	X
ejpam-5790	464	12	(	(	PUNCT
ejpam-5790	464	13	1−w	1−w	NUM
ejpam-5790	464	14	)	)	PUNCT
ejpam-5790	464	15	s+k	s+k	NOUN
ejpam-5790	465	1	k	k	PROPN
ejpam-5790	465	2	s	s	X
ejpam-5790	466	1	+	+	CCONJ
ejpam-5790	466	2	k	k	NOUN
ejpam-5790	466	3	)	)	PUNCT
ejpam-5790	466	4	[	[	PUNCT
ejpam-5790	466	5	ℑ′′	ℑ′′	ADV
ejpam-5790	466	6	(	(	PUNCT
ejpam-5790	466	7	ν2w	ν2w	PROPN
ejpam-5790	466	8	+	+	CCONJ
ejpam-5790	466	9	(	(	PUNCT
ejpam-5790	466	10	1−w	1−w	NUM
ejpam-5790	466	11	)	)	PUNCT
ejpam-5790	466	12	ν2	ν2	NOUN
ejpam-5790	466	13	)	)	PUNCT
ejpam-5790	466	14	]	]	PUNCT
ejpam-5790	467	1	dw	dw	X
ejpam-5790	467	2	]	]	PUNCT
ejpam-5790	468	1	deν1	deν1	PROPN
ejpam-5790	468	2	⊗	⊗	PROPN
ejpam-5790	468	3	dfν2	dfν2	PROPN
ejpam-5790	468	4	=	=	SYM
ejpam-5790	468	5	(	(	PUNCT
ejpam-5790	468	6	1⊗d	1⊗d	NUM
ejpam-5790	468	7	−	−	PROPN
ejpam-5790	468	8	u	u	NOUN
ejpam-5790	468	9	⊗	⊗	PROPN
ejpam-5790	468	10	1)2	1)2	NUM
ejpam-5790	468	11	6	6	NUM
ejpam-5790	468	12	[	[	X
ejpam-5790	468	13	∫	∫	PROPN
ejpam-5790	468	14	1	1	NUM
ejpam-5790	468	15	2	2	NUM
ejpam-5790	468	16	0	0	NUM
ejpam-5790	468	17	(	(	PUNCT
ejpam-5790	468	18	w	w	NOUN
ejpam-5790	468	19	−	−	PROPN
ejpam-5790	468	20	3k.2	3k.2	NUM
ejpam-5790	468	21	s	s	X
ejpam-5790	468	22	k	k	PROPN
ejpam-5790	468	23	w	w	PROPN
ejpam-5790	468	24	s+k	s+k	PROPN
ejpam-5790	469	1	k	k	PROPN
ejpam-5790	469	2	s	s	X
ejpam-5790	469	3	+	+	CCONJ
ejpam-5790	469	4	k	k	NOUN
ejpam-5790	469	5	)	)	PUNCT
ejpam-5790	469	6	[	[	PUNCT
ejpam-5790	469	7	ℑ′′	ℑ′′	ADV
ejpam-5790	469	8	(	(	PUNCT
ejpam-5790	469	9	u	u	NOUN
ejpam-5790	469	10	⊗	⊗	NOUN
ejpam-5790	469	11	1w	1w	VERB
ejpam-5790	469	12	+	+	CCONJ
ejpam-5790	469	13	1⊗	1⊗	NUM
ejpam-5790	469	14	u	u	NOUN
ejpam-5790	469	15	(	(	PUNCT
ejpam-5790	469	16	1−w	1−w	NUM
ejpam-5790	469	17	)	)	PUNCT
ejpam-5790	469	18	)	)	PUNCT
ejpam-5790	470	1	dw	dw	NOUN
ejpam-5790	470	2	]	]	PUNCT
ejpam-5790	471	1	+	+	CCONJ
ejpam-5790	471	2	∫	∫	PROPN
ejpam-5790	471	3	1	1	NUM
ejpam-5790	471	4	1	1	NUM
ejpam-5790	471	5	2	2	NUM
ejpam-5790	471	6	(	(	PUNCT
ejpam-5790	471	7	(	(	PUNCT
ejpam-5790	471	8	1−w)−	1−w)−	NUM
ejpam-5790	471	9	3k.2	3k.2	NUM
ejpam-5790	471	10	s	s	X
ejpam-5790	471	11	k	k	X
ejpam-5790	471	12	(	(	PUNCT
ejpam-5790	471	13	1−w	1−w	NUM
ejpam-5790	471	14	)	)	PUNCT
ejpam-5790	471	15	s+k	s+k	NOUN
ejpam-5790	472	1	k	k	PROPN
ejpam-5790	472	2	s	s	X
ejpam-5790	473	1	+	+	X
ejpam-5790	473	2	k	k	X
ejpam-5790	473	3	)	)	PUNCT
ejpam-5790	473	4	ℑ′′	ℑ′′	ADV
ejpam-5790	473	5	(	(	PUNCT
ejpam-5790	473	6	u	u	PROPN
ejpam-5790	473	7	⊗	⊗	NOUN
ejpam-5790	473	8	1w	1w	VERB
ejpam-5790	473	9	+	+	CCONJ
ejpam-5790	473	10	1⊗	1⊗	NUM
ejpam-5790	473	11	u	u	NOUN
ejpam-5790	473	12	(	(	PUNCT
ejpam-5790	473	13	1−w	1−w	NUM
ejpam-5790	473	14	)	)	PUNCT
ejpam-5790	473	15	)	)	PUNCT
ejpam-5790	474	1	dw	dw	NOUN
ejpam-5790	474	2	]	]	PUNCT
ejpam-5790	474	3	.	.	PUNCT
ejpam-5790	475	1	(	(	PUNCT
ejpam-5790	475	2	3.15	3.15	NUM
ejpam-5790	475	3	)	)	PUNCT
ejpam-5790	475	4	the	the	DET
ejpam-5790	475	5	desired	desire	VERB
ejpam-5790	475	6	result	result	NOUN
ejpam-5790	475	7	is	be	AUX
ejpam-5790	475	8	obtained	obtain	VERB
ejpam-5790	475	9	by	by	ADP
ejpam-5790	475	10	incorporating	incorporate	VERB
ejpam-5790	475	11	(	(	PUNCT
ejpam-5790	475	12	3.14	3.14	NUM
ejpam-5790	475	13	)	)	PUNCT
ejpam-5790	475	14	and	and	CCONJ
ejpam-5790	475	15	(	(	PUNCT
ejpam-5790	475	16	3.15	3.15	NUM
ejpam-5790	475	17	)	)	PUNCT
ejpam-5790	475	18	into	into	ADP
ejpam-5790	475	19	(	(	PUNCT
ejpam-5790	475	20	3.13	3.13	NUM
ejpam-5790	475	21	)	)	PUNCT
ejpam-5790	475	22	.	.	PUNCT
ejpam-5790	476	1	remark	remark	PROPN
ejpam-5790	476	2	1	1	NUM
ejpam-5790	476	3	.	.	NOUN
ejpam-5790	476	4	•	•	NOUN
ejpam-5790	477	1	choosing	choose	VERB
ejpam-5790	477	2	s	s	NOUN
ejpam-5790	477	3	and	and	CCONJ
ejpam-5790	477	4	k	k	NOUN
ejpam-5790	477	5	=	=	SYM
ejpam-5790	477	6	1	1	NUM
ejpam-5790	477	7	in	in	ADP
ejpam-5790	477	8	lemma	lemma	PROPN
ejpam-5790	477	9	6	6	NUM
ejpam-5790	477	10	leads	lead	VERB
ejpam-5790	477	11	to	to	ADP
ejpam-5790	477	12	a	a	DET
ejpam-5790	477	13	refinement	refinement	NOUN
ejpam-5790	477	14	of	of	ADP
ejpam-5790	477	15	lemma	lemma	PROPN
ejpam-5790	477	16	2.1	2.1	NUM
ejpam-5790	477	17	,	,	PUNCT
ejpam-5790	477	18	in	in	ADP
ejpam-5790	477	19	[	[	X
ejpam-5790	477	20	57	57	NUM
ejpam-5790	477	21	]	]	PUNCT
ejpam-5790	477	22	.	.	PUNCT
ejpam-5790	478	1	•	•	NUM
ejpam-5790	478	2	by	by	ADP
ejpam-5790	478	3	choosing	choose	VERB
ejpam-5790	478	4	s	s	NOUN
ejpam-5790	478	5	and	and	CCONJ
ejpam-5790	478	6	k	k	NOUN
ejpam-5790	478	7	=	=	SYM
ejpam-5790	478	8	1	1	NUM
ejpam-5790	478	9	in	in	ADP
ejpam-5790	478	10	lemma	lemma	PROPN
ejpam-5790	478	11	6	6	NUM
ejpam-5790	478	12	,	,	PUNCT
ejpam-5790	478	13	we	we	PRON
ejpam-5790	478	14	obtain	obtain	VERB
ejpam-5790	478	15	a	a	DET
ejpam-5790	478	16	refined	refined	ADJ
ejpam-5790	478	17	version	version	NOUN
ejpam-5790	478	18	of	of	ADP
ejpam-5790	478	19	lemma	lemma	PROPN
ejpam-5790	478	20	2.3	2.3	NUM
ejpam-5790	478	21	,	,	PUNCT
ejpam-5790	478	22	in	in	ADP
ejpam-5790	478	23	[	[	X
ejpam-5790	478	24	2	2	NUM
ejpam-5790	478	25	]	]	PUNCT
ejpam-5790	478	26	.	.	PUNCT
ejpam-5790	479	1	•	•	NUM
ejpam-5790	479	2	by	by	ADP
ejpam-5790	479	3	setting	set	VERB
ejpam-5790	479	4	s	s	NOUN
ejpam-5790	479	5	and	and	CCONJ
ejpam-5790	479	6	k	k	NOUN
ejpam-5790	479	7	=	=	SYM
ejpam-5790	479	8	1	1	NUM
ejpam-5790	479	9	in	in	ADP
ejpam-5790	479	10	lemma	lemma	PROPN
ejpam-5790	479	11	6	6	NUM
ejpam-5790	479	12	,	,	PUNCT
ejpam-5790	479	13	we	we	PRON
ejpam-5790	479	14	enhance	enhance	VERB
ejpam-5790	479	15	lemma	lemma	PROPN
ejpam-5790	479	16	3	3	NUM
ejpam-5790	479	17	,	,	PUNCT
ejpam-5790	479	18	in	in	ADP
ejpam-5790	479	19	[	[	X
ejpam-5790	479	20	58	58	NUM
ejpam-5790	479	21	]	]	PUNCT
ejpam-5790	479	22	.	.	PUNCT
ejpam-5790	480	1	theorem	theorem	ADJ
ejpam-5790	480	2	6	6	NUM
ejpam-5790	480	3	.	.	PUNCT
ejpam-5790	481	1	assume	assume	VERB
ejpam-5790	481	2	ℑ	ℑ	PROPN
ejpam-5790	481	3	is	be	AUX
ejpam-5790	481	4	a	a	DET
ejpam-5790	481	5	convex	convex	NOUN
ejpam-5790	481	6	mapping	mapping	NOUN
ejpam-5790	481	7	on	on	ADP
ejpam-5790	481	8	∆	∆	PROPN
ejpam-5790	481	9	,	,	PUNCT
ejpam-5790	481	10	and	and	CCONJ
ejpam-5790	481	11	u	u	NOUN
ejpam-5790	481	12	,	,	PUNCT
ejpam-5790	481	13	d	d	X
ejpam-5790	481	14	are	be	AUX
ejpam-5790	481	15	adjoint	adjoint	NOUN
ejpam-5790	481	16	operators	operator	NOUN
ejpam-5790	481	17	whose	whose	DET
ejpam-5790	481	18	spectra	spectra	ADJ
ejpam-5790	481	19	sp(u),sp(d	sp(u),sp(d	NOUN
ejpam-5790	481	20	)	)	PUNCT
ejpam-5790	482	1	⊂	⊂	PROPN
ejpam-5790	482	2	∆	∆	PROPN
ejpam-5790	482	3	,	,	PUNCT
ejpam-5790	482	4	then	then	ADV
ejpam-5790	482	5	∥∥∥∥∥	∥∥∥∥∥	X
ejpam-5790	482	6	[	[	PUNCT
ejpam-5790	482	7	1	1	NUM
ejpam-5790	482	8	6	6	NUM
ejpam-5790	482	9	(	(	PUNCT
ejpam-5790	482	10	ℑ(u)⊗	ℑ(u)⊗	PROPN
ejpam-5790	482	11	1	1	NUM
ejpam-5790	482	12	)	)	PUNCT
ejpam-5790	482	13	+	+	CCONJ
ejpam-5790	482	14	2	2	NUM
ejpam-5790	482	15	3	3	NUM
ejpam-5790	482	16	ℑ	ℑ	NOUN
ejpam-5790	482	17	(	(	PUNCT
ejpam-5790	482	18	u	u	NOUN
ejpam-5790	482	19	⊗	⊗	PROPN
ejpam-5790	482	20	1	1	NUM
ejpam-5790	482	21	+	+	NUM
ejpam-5790	482	22	1⊗d	1⊗d	NUM
ejpam-5790	482	23	2	2	NUM
ejpam-5790	482	24	)	)	PUNCT
ejpam-5790	482	25	+	+	CCONJ
ejpam-5790	482	26	1	1	NUM
ejpam-5790	482	27	6	6	NUM
ejpam-5790	482	28	(	(	PUNCT
ejpam-5790	482	29	1⊗ℑ(d	1⊗ℑ(d	NUM
ejpam-5790	482	30	)	)	PUNCT
ejpam-5790	482	31	)	)	PUNCT
ejpam-5790	482	32	]	]	PUNCT
ejpam-5790	483	1	w.	w.	PROPN
ejpam-5790	483	2	afzal	afzal	PROPN
ejpam-5790	483	3	et	et	PROPN
ejpam-5790	483	4	al	al	PROPN
ejpam-5790	483	5	.	.	PUNCT
ejpam-5790	483	6	/	/	SYM
ejpam-5790	483	7	eur	eur	PROPN
ejpam-5790	483	8	.	.	PUNCT
ejpam-5790	484	1	j.	j.	PROPN
ejpam-5790	484	2	pure	pure	PROPN
ejpam-5790	484	3	appl	appl	PROPN
ejpam-5790	484	4	.	.	PROPN
ejpam-5790	484	5	math	math	PROPN
ejpam-5790	484	6	,	,	PUNCT
ejpam-5790	484	7	18	18	NUM
ejpam-5790	484	8	(	(	PUNCT
ejpam-5790	484	9	1	1	NUM
ejpam-5790	484	10	)	)	PUNCT
ejpam-5790	484	11	(	(	PUNCT
ejpam-5790	484	12	2025	2025	NUM
ejpam-5790	484	13	)	)	PUNCT
ejpam-5790	484	14	,	,	PUNCT
ejpam-5790	484	15	5790	5790	NUM
ejpam-5790	484	16	19	19	NUM
ejpam-5790	484	17	of	of	ADP
ejpam-5790	484	18	30	30	NUM
ejpam-5790	484	19	−	−	NOUN
ejpam-5790	484	20	[	[	PUNCT
ejpam-5790	484	21	ℑ	ℑ	PROPN
ejpam-5790	484	22	(	(	PUNCT
ejpam-5790	484	23	u	u	NOUN
ejpam-5790	484	24	⊗	⊗	PROPN
ejpam-5790	484	25	1	1	NUM
ejpam-5790	484	26	+	+	NUM
ejpam-5790	484	27	1⊗d	1⊗d	NUM
ejpam-5790	484	28	2	2	NUM
ejpam-5790	484	29	)	)	PUNCT
ejpam-5790	484	30	−	−	PROPN
ejpam-5790	485	1	w	w	PROPN
ejpam-5790	485	2	s	s	PROPN
ejpam-5790	485	3	k	k	X
ejpam-5790	485	4	(	(	PUNCT
ejpam-5790	485	5	ν2	ν2	NOUN
ejpam-5790	485	6	−	−	PROPN
ejpam-5790	485	7	ν1	ν1	NOUN
ejpam-5790	485	8	)	)	PUNCT
ejpam-5790	485	9	4	4	NUM
ejpam-5790	486	1	[	[	X
ejpam-5790	486	2	∫	∫	PROPN
ejpam-5790	486	3	1	1	NUM
ejpam-5790	486	4	0	0	NUM
ejpam-5790	486	5	ℑ′	ℑ′	X
ejpam-5790	486	6	(	(	PUNCT
ejpam-5790	486	7	(	(	PUNCT
ejpam-5790	486	8	1−w)u	1−w)u	NUM
ejpam-5790	486	9	⊗	⊗	NOUN
ejpam-5790	486	10	1	1	NUM
ejpam-5790	486	11	+	+	CCONJ
ejpam-5790	486	12	(	(	PUNCT
ejpam-5790	486	13	w1⊗d	w1⊗d	NOUN
ejpam-5790	486	14	2	2	NUM
ejpam-5790	486	15	)	)	PUNCT
ejpam-5790	486	16	)	)	PUNCT
ejpam-5790	486	17	dw	dw	NOUN
ejpam-5790	486	18	]	]	PUNCT
ejpam-5790	487	1	+	+	CCONJ
ejpam-5790	487	2	ℑ	ℑ	PROPN
ejpam-5790	487	3	(	(	PUNCT
ejpam-5790	487	4	u	u	NOUN
ejpam-5790	487	5	⊗	⊗	PROPN
ejpam-5790	487	6	1	1	NUM
ejpam-5790	487	7	+	+	NUM
ejpam-5790	487	8	1⊗d	1⊗d	NUM
ejpam-5790	487	9	2	2	NUM
ejpam-5790	487	10	)	)	PUNCT
ejpam-5790	487	11	−	−	PROPN
ejpam-5790	487	12	(	(	PUNCT
ejpam-5790	487	13	1−w	1−w	NUM
ejpam-5790	487	14	)	)	PUNCT
ejpam-5790	487	15	s	s	PART
ejpam-5790	487	16	k	k	X
ejpam-5790	487	17	(	(	PUNCT
ejpam-5790	487	18	ν2	ν2	NOUN
ejpam-5790	487	19	−	−	PROPN
ejpam-5790	487	20	ν1	ν1	NOUN
ejpam-5790	487	21	)	)	PUNCT
ejpam-5790	487	22	4	4	NUM
ejpam-5790	488	1	[	[	X
ejpam-5790	488	2	∫	∫	PROPN
ejpam-5790	488	3	1	1	NUM
ejpam-5790	488	4	0	0	NUM
ejpam-5790	488	5	ℑ′	ℑ′	X
ejpam-5790	488	6	(	(	PUNCT
ejpam-5790	488	7	(	(	PUNCT
ejpam-5790	488	8	1−w	1−w	NUM
ejpam-5790	488	9	2	2	NUM
ejpam-5790	488	10	)	)	PUNCT
ejpam-5790	488	11	u	u	NOUN
ejpam-5790	488	12	⊗	⊗	PROPN
ejpam-5790	488	13	1	1	NUM
ejpam-5790	488	14	+	+	CCONJ
ejpam-5790	488	15	(	(	PUNCT
ejpam-5790	488	16	1	1	NUM
ejpam-5790	488	17	+	+	NOUN
ejpam-5790	488	18	w	w	NOUN
ejpam-5790	488	19	2	2	NUM
ejpam-5790	488	20	)	)	PUNCT
ejpam-5790	488	21	1⊗d	1⊗d	PROPN
ejpam-5790	488	22	)	)	PUNCT
ejpam-5790	488	23	dw	dw	NOUN
ejpam-5790	488	24	]	]	PUNCT
ejpam-5790	488	25	∥∥∥∥∥	∥∥∥∥∥	PUNCT
ejpam-5790	488	26	≤	≤	ADV
ejpam-5790	488	27	∥(1⊗d	∥(1⊗d	NOUN
ejpam-5790	488	28	−	−	PROPN
ejpam-5790	488	29	u	u	NOUN
ejpam-5790	488	30	⊗	⊗	NOUN
ejpam-5790	488	31	1)2∥	1)2∥	NUM
ejpam-5790	488	32	6	6	NUM
ejpam-5790	488	33	[	[	X
ejpam-5790	488	34	(	(	PUNCT
ejpam-5790	488	35	s(s	s(s	PROPN
ejpam-5790	488	36	+	+	CCONJ
ejpam-5790	488	37	k	k	X
ejpam-5790	488	38	)	)	PUNCT
ejpam-5790	488	39	a+2k	a+2k	PROPN
ejpam-5790	488	40	s	s	PART
ejpam-5790	488	41	+	+	NUM
ejpam-5790	488	42	3	3	NUM
ejpam-5790	488	43	s+2k	s+2k	PROPN
ejpam-5790	488	44	a	a	PRON
ejpam-5790	488	45	k	k	NOUN
ejpam-5790	488	46	2s+2k	2s+2k	NUM
ejpam-5790	488	47	s	s	PART
ejpam-5790	488	48	4	4	NUM
ejpam-5790	488	49	·	·	SYM
ejpam-5790	488	50	3	3	NUM
ejpam-5790	488	51	2k	2k	PROPN
ejpam-5790	488	52	s	s	PART
ejpam-5790	488	53	k	k	PROPN
ejpam-5790	488	54	2k	2k	PROPN
ejpam-5790	488	55	s	s	X
ejpam-5790	488	56	(	(	PUNCT
ejpam-5790	488	57	s	s	PART
ejpam-5790	488	58	+	+	CCONJ
ejpam-5790	488	59	k)(s	k)(s	NOUN
ejpam-5790	488	60	+	+	CCONJ
ejpam-5790	488	61	2k	2k	NUM
ejpam-5790	488	62	)	)	PUNCT
ejpam-5790	488	63	−	−	PROPN
ejpam-5790	488	64	1	1	NUM
ejpam-5790	488	65	8	8	NUM
ejpam-5790	488	66	)	)	PUNCT
ejpam-5790	488	67	∥∥∥	∥∥∥	PROPN
ejpam-5790	488	68	∣∣ℑ′′	∣∣ℑ′′	PROPN
ejpam-5790	488	69	(	(	PUNCT
ejpam-5790	488	70	u	u	NOUN
ejpam-5790	488	71	)	)	PUNCT
ejpam-5790	488	72	∣∣+	∣∣+	PROPN
ejpam-5790	488	73	∣∣ℑ′′	∣∣ℑ′′	PROPN
ejpam-5790	488	74	(	(	PUNCT
ejpam-5790	488	75	d	d	PROPN
ejpam-5790	488	76	)	)	PUNCT
ejpam-5790	488	77	∣∣	∣∣	X
ejpam-5790	488	78	∥∥∥	∥∥∥	PROPN
ejpam-5790	488	79	]	]	PUNCT
ejpam-5790	488	80	.	.	PUNCT
ejpam-5790	489	1	proof	proof	NOUN
ejpam-5790	489	2	.	.	PUNCT
ejpam-5790	490	1	as	as	ADP
ejpam-5790	490	2	|ℑ′′|	|ℑ′′|	PROPN
ejpam-5790	490	3	is	be	AUX
ejpam-5790	490	4	convex	convex	ADJ
ejpam-5790	490	5	over	over	ADP
ejpam-5790	490	6	∆	∆	PROPN
ejpam-5790	490	7	,	,	PUNCT
ejpam-5790	490	8	one	one	NUM
ejpam-5790	490	9	has	have	VERB
ejpam-5790	490	10	∣∣ℑ′′	∣∣ℑ′′	PROPN
ejpam-5790	490	11	(	(	PUNCT
ejpam-5790	490	12	ν1w	ν1w	NOUN
ejpam-5790	490	13	+	+	NUM
ejpam-5790	490	14	ν1	ν1	NOUN
ejpam-5790	490	15	(	(	PUNCT
ejpam-5790	490	16	1−w	1−w	NUM
ejpam-5790	490	17	)	)	PUNCT
ejpam-5790	490	18	)	)	PUNCT
ejpam-5790	491	1	∣∣	∣∣	NUM
ejpam-5790	491	2	≤	≤	NUM
ejpam-5790	491	3	w	w	ADP
ejpam-5790	491	4	∣∣ℑ′′	∣∣ℑ′′	PROPN
ejpam-5790	491	5	(	(	PUNCT
ejpam-5790	491	6	ν1	ν1	PROPN
ejpam-5790	491	7	)	)	PUNCT
ejpam-5790	491	8	∣∣+	∣∣+	PUNCT
ejpam-5790	491	9	(	(	PUNCT
ejpam-5790	491	10	1−w	1−w	NUM
ejpam-5790	491	11	)	)	PUNCT
ejpam-5790	491	12	∣∣ℑ′′(ν1	∣∣ℑ′′(ν1	NOUN
ejpam-5790	491	13	)	)	PUNCT
ejpam-5790	491	14	∣∣	∣∣	NUM
ejpam-5790	491	15	similarly	similarly	ADV
ejpam-5790	491	16	,	,	PUNCT
ejpam-5790	491	17	we	we	PRON
ejpam-5790	491	18	get∣∣ℑ′′	get∣∣ℑ′′	VERB
ejpam-5790	491	19	(	(	PUNCT
ejpam-5790	491	20	ν2w	ν2w	PROPN
ejpam-5790	491	21	+	+	CCONJ
ejpam-5790	491	22	ν2	ν2	PROPN
ejpam-5790	491	23	(	(	PUNCT
ejpam-5790	491	24	1−w	1−w	NUM
ejpam-5790	491	25	)	)	PUNCT
ejpam-5790	491	26	)	)	PUNCT
ejpam-5790	492	1	∣∣	∣∣	NUM
ejpam-5790	492	2	≤	≤	NUM
ejpam-5790	492	3	w	w	ADP
ejpam-5790	492	4	∣∣ℑ′′	∣∣ℑ′′	PROPN
ejpam-5790	492	5	(	(	PUNCT
ejpam-5790	492	6	ν2	ν2	PROPN
ejpam-5790	492	7	)	)	PUNCT
ejpam-5790	492	8	∣∣+	∣∣+	X
ejpam-5790	492	9	(	(	PUNCT
ejpam-5790	492	10	(	(	PUNCT
ejpam-5790	492	11	1−w	1−w	NUM
ejpam-5790	492	12	)	)	PUNCT
ejpam-5790	492	13	)	)	PUNCT
ejpam-5790	493	1	∣∣ℑ′′(ν2	∣∣ℑ′′(ν2	NUM
ejpam-5790	493	2	)	)	PUNCT
ejpam-5790	494	1	∣∣	∣∣	X
ejpam-5790	494	2	for	for	ADP
ejpam-5790	494	3	all	all	PRON
ejpam-5790	494	4	for	for	ADP
ejpam-5790	494	5	τ	τ	PROPN
ejpam-5790	494	6	∈	∈	PROPN
ejpam-5790	495	1	[	[	X
ejpam-5790	495	2	0	0	NUM
ejpam-5790	495	3	,	,	PUNCT
ejpam-5790	495	4	1	1	NUM
ejpam-5790	495	5	]	]	PUNCT
ejpam-5790	495	6	and	and	CCONJ
ejpam-5790	495	7	ν1	ν1	NOUN
ejpam-5790	495	8	,	,	PUNCT
ejpam-5790	495	9	ν2	ν2	NOUN
ejpam-5790	495	10	∈	∈	PROPN
ejpam-5790	495	11	∆.	∆.	NOUN
ejpam-5790	495	12	taking	take	VERB
ejpam-5790	495	13	∫	∫	PROPN
ejpam-5790	495	14	∆	∆	PROPN
ejpam-5790	495	15	∫	∫	PROPN
ejpam-5790	495	16	∆	∆	PROPN
ejpam-5790	495	17	over	over	ADP
ejpam-5790	495	18	deν1	deν1	PROPN
ejpam-5790	495	19	⊗	⊗	PROPN
ejpam-5790	495	20	dfν2	dfν2	PROPN
ejpam-5790	495	21	,	,	PUNCT
ejpam-5790	495	22	then	then	ADV
ejpam-5790	495	23	we	we	PRON
ejpam-5790	495	24	get∣∣ℑ′′	get∣∣ℑ′′	PROPN
ejpam-5790	495	25	(	(	PUNCT
ejpam-5790	495	26	1⊗	1⊗	NUM
ejpam-5790	495	27	uw	uw	PROPN
ejpam-5790	495	28	+	+	PROPN
ejpam-5790	495	29	1⊗	1⊗	NUM
ejpam-5790	495	30	u	u	NOUN
ejpam-5790	495	31	(	(	PUNCT
ejpam-5790	495	32	1−w	1−w	NUM
ejpam-5790	495	33	)	)	PUNCT
ejpam-5790	495	34	)	)	PUNCT
ejpam-5790	496	1	∣∣	∣∣	X
ejpam-5790	497	1	=	=	SYM
ejpam-5790	497	2	∫	∫	PROPN
ejpam-5790	497	3	∆	∆	PROPN
ejpam-5790	498	1	∫	∫	PROPN
ejpam-5790	498	2	∆	∆	PROPN
ejpam-5790	499	1	∣∣ℑ′′	∣∣ℑ′′	PROPN
ejpam-5790	499	2	(	(	PUNCT
ejpam-5790	499	3	ν1w	ν1w	NOUN
ejpam-5790	499	4	+	+	NUM
ejpam-5790	499	5	ν1	ν1	NOUN
ejpam-5790	499	6	(	(	PUNCT
ejpam-5790	499	7	1−w	1−w	NUM
ejpam-5790	499	8	)	)	PUNCT
ejpam-5790	499	9	)	)	PUNCT
ejpam-5790	500	1	∣∣	∣∣	PROPN
ejpam-5790	500	2	deν1	deν1	PROPN
ejpam-5790	500	3	⊗	⊗	PROPN
ejpam-5790	500	4	dfν2	dfν2	PROPN
ejpam-5790	500	5	≤	≤	NUM
ejpam-5790	500	6	∫	∫	PROPN
ejpam-5790	500	7	∆	∆	PROPN
ejpam-5790	501	1	∫	∫	PROPN
ejpam-5790	501	2	∆	∆	PROPN
ejpam-5790	501	3	w	w	PROPN
ejpam-5790	501	4	∣∣ℑ′′	∣∣ℑ′′	PROPN
ejpam-5790	501	5	(	(	PUNCT
ejpam-5790	501	6	ν1	ν1	PROPN
ejpam-5790	501	7	)	)	PUNCT
ejpam-5790	501	8	∣∣+	∣∣+	PUNCT
ejpam-5790	501	9	(	(	PUNCT
ejpam-5790	501	10	1−w	1−w	NUM
ejpam-5790	501	11	)	)	PUNCT
ejpam-5790	501	12	∣∣ℑ′′(ν1	∣∣ℑ′′(ν1	NOUN
ejpam-5790	501	13	)	)	PUNCT
ejpam-5790	501	14	∣∣	∣∣	PROPN
ejpam-5790	501	15	deν1	deν1	PROPN
ejpam-5790	501	16	⊗	⊗	PROPN
ejpam-5790	501	17	dfν2	dfν2	PROPN
ejpam-5790	501	18	≤	≤	NUM
ejpam-5790	501	19	w1⊗	w1⊗	NOUN
ejpam-5790	501	20	∣∣ℑ′′	∣∣ℑ′′	PROPN
ejpam-5790	501	21	(	(	PUNCT
ejpam-5790	501	22	u	u	NOUN
ejpam-5790	501	23	)	)	PUNCT
ejpam-5790	501	24	∣∣+	∣∣+	X
ejpam-5790	501	25	(	(	PUNCT
ejpam-5790	501	26	1−w	1−w	NUM
ejpam-5790	501	27	)	)	PUNCT
ejpam-5790	501	28	∣∣ℑ′′(u	∣∣ℑ′′(u	PROPN
ejpam-5790	501	29	)	)	PUNCT
ejpam-5790	501	30	∣∣⊗	∣∣⊗	PROPN
ejpam-5790	502	1	1	1	X
ejpam-5790	502	2	.	.	PUNCT
ejpam-5790	503	1	(	(	PUNCT
ejpam-5790	503	2	3.16	3.16	NUM
ejpam-5790	503	3	)	)	PUNCT
ejpam-5790	503	4	if	if	SCONJ
ejpam-5790	503	5	we	we	PRON
ejpam-5790	503	6	apply	apply	VERB
ejpam-5790	503	7	norm	norm	NOUN
ejpam-5790	503	8	in	in	ADP
ejpam-5790	503	9	(	(	PUNCT
ejpam-5790	503	10	3.16	3.16	NUM
ejpam-5790	503	11	)	)	PUNCT
ejpam-5790	503	12	,	,	PUNCT
ejpam-5790	503	13	then	then	ADV
ejpam-5790	503	14	we	we	PRON
ejpam-5790	503	15	have	have	VERB
ejpam-5790	503	16	∥∥ℑ′′	∥∥ℑ′′	NOUN
ejpam-5790	503	17	(	(	PUNCT
ejpam-5790	503	18	1⊗	1⊗	NUM
ejpam-5790	503	19	uw	uw	PROPN
ejpam-5790	503	20	+	+	PROPN
ejpam-5790	503	21	1⊗	1⊗	NUM
ejpam-5790	503	22	u	u	NOUN
ejpam-5790	503	23	(	(	PUNCT
ejpam-5790	503	24	1−w	1−w	NUM
ejpam-5790	503	25	)	)	PUNCT
ejpam-5790	503	26	)	)	PUNCT
ejpam-5790	504	1	∥∥	∥∥	PROPN
ejpam-5790	504	2	≤	≤	NUM
ejpam-5790	504	3	∥∥w1⊗	∥∥w1⊗	NOUN
ejpam-5790	504	4	∣∣ℑ′′	∣∣ℑ′′	PROPN
ejpam-5790	504	5	(	(	PUNCT
ejpam-5790	504	6	u	u	NOUN
ejpam-5790	504	7	)	)	PUNCT
ejpam-5790	504	8	∣∣+	∣∣+	X
ejpam-5790	504	9	(	(	PUNCT
ejpam-5790	504	10	1−w	1−w	NUM
ejpam-5790	504	11	)	)	PUNCT
ejpam-5790	504	12	∣∣ℑ′′(u	∣∣ℑ′′(u	PROPN
ejpam-5790	504	13	)	)	PUNCT
ejpam-5790	504	14	∣∣⊗	∣∣⊗	PROPN
ejpam-5790	504	15	1	1	NUM
ejpam-5790	504	16	∥∥	∥∥	PUNCT
ejpam-5790	504	17	≤	≤	PROPN
ejpam-5790	504	18	w	w	PROPN
ejpam-5790	504	19	∥∥ℑ′′(u	∥∥ℑ′′(u	PROPN
ejpam-5790	504	20	)	)	PUNCT
ejpam-5790	504	21	∥∥+	∥∥+	PUNCT
ejpam-5790	505	1	(	(	PUNCT
ejpam-5790	505	2	1−w	1−w	NUM
ejpam-5790	505	3	)	)	PUNCT
ejpam-5790	505	4	∥∥ℑ′′(u	∥∥ℑ′′(u	NOUN
ejpam-5790	505	5	)	)	PUNCT
ejpam-5790	505	6	∥∥	∥∥	X
ejpam-5790	505	7	.	.	PUNCT
ejpam-5790	506	1	similarly	similarly	ADV
ejpam-5790	506	2	,	,	PUNCT
ejpam-5790	506	3	we	we	PRON
ejpam-5790	506	4	get∥∥ℑ′′	get∥∥ℑ′′	VERB
ejpam-5790	506	5	(	(	PUNCT
ejpam-5790	506	6	1⊗dw	1⊗dw	NUM
ejpam-5790	506	7	+	+	NUM
ejpam-5790	506	8	1⊗d	1⊗d	NUM
ejpam-5790	506	9	(	(	PUNCT
ejpam-5790	506	10	1−w	1−w	NUM
ejpam-5790	506	11	)	)	PUNCT
ejpam-5790	506	12	)	)	PUNCT
ejpam-5790	507	1	∥∥	∥∥	PROPN
ejpam-5790	507	2	≤	≤	NUM
ejpam-5790	507	3	∥∥w1⊗	∥∥w1⊗	NOUN
ejpam-5790	507	4	∣∣ℑ′′	∣∣ℑ′′	PROPN
ejpam-5790	507	5	(	(	PUNCT
ejpam-5790	507	6	d	d	PROPN
ejpam-5790	507	7	)	)	PUNCT
ejpam-5790	507	8	∣∣+	∣∣+	X
ejpam-5790	507	9	(	(	PUNCT
ejpam-5790	507	10	(	(	PUNCT
ejpam-5790	507	11	1−w	1−w	NUM
ejpam-5790	507	12	)	)	PUNCT
ejpam-5790	507	13	)	)	PUNCT
ejpam-5790	508	1	∣∣ℑ′′(d	∣∣ℑ′′(d	NOUN
ejpam-5790	508	2	)	)	PUNCT
ejpam-5790	508	3	∣∣⊗	∣∣⊗	NOUN
ejpam-5790	508	4	1	1	NUM
ejpam-5790	508	5	∥∥	∥∥	PUNCT
ejpam-5790	508	6	≤	≤	PROPN
ejpam-5790	508	7	w	w	PROPN
ejpam-5790	508	8	∥∥ℑ′′(d	∥∥ℑ′′(d	NOUN
ejpam-5790	508	9	)	)	PUNCT
ejpam-5790	508	10	∥∥+	∥∥+	PROPN
ejpam-5790	509	1	(	(	PUNCT
ejpam-5790	509	2	(	(	PUNCT
ejpam-5790	509	3	1−w	1−w	NUM
ejpam-5790	509	4	)	)	PUNCT
ejpam-5790	509	5	)	)	PUNCT
ejpam-5790	509	6	∥∥ℑ′′(d	∥∥ℑ′′(d	X
ejpam-5790	509	7	)	)	PUNCT
ejpam-5790	509	8	∥∥	∥∥	X
ejpam-5790	509	9	.	.	PUNCT
ejpam-5790	510	1	using	use	VERB
ejpam-5790	510	2	the	the	DET
ejpam-5790	510	3	norm	norm	NOUN
ejpam-5790	510	4	in	in	ADP
ejpam-5790	510	5	(	(	PUNCT
ejpam-5790	510	6	3.12	3.12	NUM
ejpam-5790	510	7	)	)	PUNCT
ejpam-5790	510	8	and	and	CCONJ
ejpam-5790	510	9	considering	consider	VERB
ejpam-5790	510	10	triangle	triangle	NOUN
ejpam-5790	510	11	inequality	inequality	NOUN
ejpam-5790	510	12	,	,	PUNCT
ejpam-5790	510	13	we	we	PRON
ejpam-5790	510	14	have	have	VERB
ejpam-5790	510	15	∥∥∥∥[16(ℑ(u)⊗	∥∥∥∥[16(ℑ(u)⊗	NOUN
ejpam-5790	510	16	1	1	NUM
ejpam-5790	510	17	)	)	PUNCT
ejpam-5790	510	18	+	+	CCONJ
ejpam-5790	510	19	2	2	NUM
ejpam-5790	510	20	3	3	NUM
ejpam-5790	510	21	ℑ	ℑ	NOUN
ejpam-5790	510	22	(	(	PUNCT
ejpam-5790	510	23	u	u	NOUN
ejpam-5790	510	24	⊗	⊗	PROPN
ejpam-5790	510	25	1	1	NUM
ejpam-5790	510	26	+	+	NUM
ejpam-5790	510	27	1⊗d	1⊗d	NUM
ejpam-5790	510	28	2	2	NUM
ejpam-5790	510	29	)	)	PUNCT
ejpam-5790	510	30	+	+	CCONJ
ejpam-5790	510	31	1	1	NUM
ejpam-5790	510	32	6	6	NUM
ejpam-5790	510	33	(	(	PUNCT
ejpam-5790	510	34	1⊗ℑ(d	1⊗ℑ(d	NUM
ejpam-5790	510	35	)	)	PUNCT
ejpam-5790	510	36	)	)	PUNCT
ejpam-5790	510	37	]	]	PUNCT
ejpam-5790	511	1	−	−	PROPN
ejpam-5790	511	2	[	[	PUNCT
ejpam-5790	511	3	ℑ	ℑ	PROPN
ejpam-5790	511	4	(	(	PUNCT
ejpam-5790	511	5	u	u	NOUN
ejpam-5790	511	6	⊗	⊗	PROPN
ejpam-5790	511	7	1	1	NUM
ejpam-5790	511	8	+	+	NUM
ejpam-5790	511	9	1⊗d	1⊗d	NUM
ejpam-5790	511	10	2	2	NUM
ejpam-5790	511	11	)	)	PUNCT
ejpam-5790	511	12	−	−	PROPN
ejpam-5790	512	1	w	w	PROPN
ejpam-5790	512	2	s	s	PROPN
ejpam-5790	512	3	k	k	X
ejpam-5790	512	4	(	(	PUNCT
ejpam-5790	512	5	ν2	ν2	NOUN
ejpam-5790	512	6	−	−	PROPN
ejpam-5790	512	7	ν1	ν1	NOUN
ejpam-5790	512	8	)	)	PUNCT
ejpam-5790	512	9	4	4	NUM
ejpam-5790	513	1	[	[	X
ejpam-5790	513	2	∫	∫	PROPN
ejpam-5790	513	3	1	1	NUM
ejpam-5790	513	4	0	0	NUM
ejpam-5790	513	5	ℑ′	ℑ′	X
ejpam-5790	513	6	(	(	PUNCT
ejpam-5790	513	7	(	(	PUNCT
ejpam-5790	513	8	1−w)u	1−w)u	NUM
ejpam-5790	513	9	⊗	⊗	NOUN
ejpam-5790	513	10	1	1	NUM
ejpam-5790	513	11	+	+	CCONJ
ejpam-5790	513	12	(	(	PUNCT
ejpam-5790	513	13	w1⊗d	w1⊗d	NOUN
ejpam-5790	513	14	2	2	NUM
ejpam-5790	513	15	)	)	PUNCT
ejpam-5790	513	16	)	)	PUNCT
ejpam-5790	513	17	dw	dw	PROPN
ejpam-5790	513	18	]	]	PUNCT
ejpam-5790	513	19	w.	w.	PROPN
ejpam-5790	513	20	afzal	afzal	PROPN
ejpam-5790	513	21	et	et	PROPN
ejpam-5790	513	22	al	al	PROPN
ejpam-5790	513	23	.	.	PUNCT
ejpam-5790	513	24	/	/	SYM
ejpam-5790	513	25	eur	eur	PROPN
ejpam-5790	513	26	.	.	PUNCT
ejpam-5790	514	1	j.	j.	PROPN
ejpam-5790	514	2	pure	pure	PROPN
ejpam-5790	514	3	appl	appl	PROPN
ejpam-5790	514	4	.	.	PROPN
ejpam-5790	514	5	math	math	PROPN
ejpam-5790	514	6	,	,	PUNCT
ejpam-5790	514	7	18	18	NUM
ejpam-5790	514	8	(	(	PUNCT
ejpam-5790	514	9	1	1	NUM
ejpam-5790	514	10	)	)	PUNCT
ejpam-5790	514	11	(	(	PUNCT
ejpam-5790	514	12	2025	2025	NUM
ejpam-5790	514	13	)	)	PUNCT
ejpam-5790	514	14	,	,	PUNCT
ejpam-5790	514	15	5790	5790	NUM
ejpam-5790	514	16	20	20	NUM
ejpam-5790	514	17	of	of	ADP
ejpam-5790	514	18	30	30	NUM
ejpam-5790	514	19	+	+	CCONJ
ejpam-5790	514	20	ℑ	ℑ	PROPN
ejpam-5790	514	21	(	(	PUNCT
ejpam-5790	514	22	u	u	NOUN
ejpam-5790	514	23	⊗	⊗	PROPN
ejpam-5790	514	24	1	1	NUM
ejpam-5790	515	1	+	+	NUM
ejpam-5790	515	2	1⊗d	1⊗d	NUM
ejpam-5790	515	3	2	2	NUM
ejpam-5790	515	4	)	)	PUNCT
ejpam-5790	515	5	−	−	PROPN
ejpam-5790	515	6	(	(	PUNCT
ejpam-5790	515	7	1−w	1−w	NUM
ejpam-5790	515	8	)	)	PUNCT
ejpam-5790	515	9	s	s	PART
ejpam-5790	515	10	k	k	X
ejpam-5790	515	11	(	(	PUNCT
ejpam-5790	515	12	ν2	ν2	NOUN
ejpam-5790	515	13	−	−	PROPN
ejpam-5790	515	14	ν1	ν1	NOUN
ejpam-5790	515	15	)	)	PUNCT
ejpam-5790	515	16	4	4	NUM
ejpam-5790	516	1	[	[	X
ejpam-5790	516	2	∫	∫	PROPN
ejpam-5790	516	3	1	1	NUM
ejpam-5790	516	4	0	0	NUM
ejpam-5790	516	5	ℑ′	ℑ′	X
ejpam-5790	516	6	(	(	PUNCT
ejpam-5790	516	7	(	(	PUNCT
ejpam-5790	516	8	1−w	1−w	NUM
ejpam-5790	516	9	2	2	NUM
ejpam-5790	516	10	)	)	PUNCT
ejpam-5790	516	11	u	u	NOUN
ejpam-5790	516	12	⊗	⊗	PROPN
ejpam-5790	516	13	1	1	NUM
ejpam-5790	516	14	+	+	CCONJ
ejpam-5790	516	15	(	(	PUNCT
ejpam-5790	516	16	1	1	NUM
ejpam-5790	516	17	+	+	NOUN
ejpam-5790	516	18	w	w	NOUN
ejpam-5790	516	19	2	2	NUM
ejpam-5790	516	20	)	)	PUNCT
ejpam-5790	516	21	1⊗d	1⊗d	PROPN
ejpam-5790	516	22	)	)	PUNCT
ejpam-5790	516	23	dw	dw	NOUN
ejpam-5790	516	24	]	]	PUNCT
ejpam-5790	516	25	∥∥∥∥∥	∥∥∥∥∥	PUNCT
ejpam-5790	516	26	≤	≤	ADV
ejpam-5790	516	27	∥(1⊗d	∥(1⊗d	NOUN
ejpam-5790	516	28	−	−	PROPN
ejpam-5790	516	29	u	u	NOUN
ejpam-5790	516	30	⊗	⊗	PROPN
ejpam-5790	516	31	1)2∥	1)2∥	NUM
ejpam-5790	516	32	6	6	NUM
ejpam-5790	516	33	(	(	PUNCT
ejpam-5790	516	34	∥∥∥∥∥	∥∥∥∥∥	NUM
ejpam-5790	516	35	∫	∫	PROPN
ejpam-5790	516	36	1	1	NUM
ejpam-5790	516	37	2	2	NUM
ejpam-5790	516	38	0	0	NUM
ejpam-5790	516	39	(	(	PUNCT
ejpam-5790	516	40	w	w	NOUN
ejpam-5790	516	41	−	−	PROPN
ejpam-5790	516	42	3k.2	3k.2	NUM
ejpam-5790	516	43	s	s	X
ejpam-5790	516	44	k	k	PROPN
ejpam-5790	516	45	w	w	PROPN
ejpam-5790	516	46	s+k	s+k	PROPN
ejpam-5790	516	47	k	k	PROPN
ejpam-5790	516	48	s	s	X
ejpam-5790	517	1	+	+	CCONJ
ejpam-5790	517	2	k	k	NOUN
ejpam-5790	517	3	)	)	PUNCT
ejpam-5790	517	4	[	[	PUNCT
ejpam-5790	517	5	ℑ′′	ℑ′′	ADV
ejpam-5790	517	6	(	(	PUNCT
ejpam-5790	517	7	u	u	NOUN
ejpam-5790	517	8	⊗	⊗	NOUN
ejpam-5790	517	9	1w	1w	VERB
ejpam-5790	517	10	+	+	CCONJ
ejpam-5790	517	11	1⊗	1⊗	NUM
ejpam-5790	517	12	u	u	NOUN
ejpam-5790	517	13	(	(	PUNCT
ejpam-5790	517	14	1−w	1−w	NUM
ejpam-5790	517	15	)	)	PUNCT
ejpam-5790	517	16	)	)	PUNCT
ejpam-5790	518	1	dw	dw	NOUN
ejpam-5790	518	2	]	]	PUNCT
ejpam-5790	519	1	+	+	CCONJ
ejpam-5790	519	2	∫	∫	PROPN
ejpam-5790	519	3	1	1	NUM
ejpam-5790	519	4	1	1	NUM
ejpam-5790	519	5	2	2	NUM
ejpam-5790	519	6	(	(	PUNCT
ejpam-5790	519	7	(	(	PUNCT
ejpam-5790	519	8	1−w)−	1−w)−	NUM
ejpam-5790	519	9	3k.2	3k.2	NUM
ejpam-5790	519	10	s	s	X
ejpam-5790	519	11	k	k	X
ejpam-5790	519	12	(	(	PUNCT
ejpam-5790	519	13	1−w	1−w	NUM
ejpam-5790	519	14	)	)	PUNCT
ejpam-5790	519	15	s+k	s+k	NOUN
ejpam-5790	520	1	k	k	PROPN
ejpam-5790	520	2	s	s	X
ejpam-5790	521	1	+	+	X
ejpam-5790	521	2	k	k	X
ejpam-5790	521	3	)	)	PUNCT
ejpam-5790	521	4	ℑ′′	ℑ′′	ADV
ejpam-5790	521	5	(	(	PUNCT
ejpam-5790	521	6	u	u	PROPN
ejpam-5790	521	7	⊗	⊗	NOUN
ejpam-5790	521	8	1w	1w	VERB
ejpam-5790	521	9	+	+	CCONJ
ejpam-5790	521	10	1⊗	1⊗	NUM
ejpam-5790	521	11	u	u	NOUN
ejpam-5790	521	12	(	(	PUNCT
ejpam-5790	521	13	1−w	1−w	NUM
ejpam-5790	521	14	)	)	PUNCT
ejpam-5790	521	15	)	)	PUNCT
ejpam-5790	521	16	∥∥∥∥∥	∥∥∥∥∥	NUM
ejpam-5790	521	17	)	)	PUNCT
ejpam-5790	522	1	≤	≤	PUNCT
ejpam-5790	523	1	∥(1⊗d	∥(1⊗d	NOUN
ejpam-5790	523	2	−	−	PROPN
ejpam-5790	523	3	u	u	NOUN
ejpam-5790	523	4	⊗	⊗	PROPN
ejpam-5790	523	5	1)2∥	1)2∥	NUM
ejpam-5790	523	6	6	6	NUM
ejpam-5790	523	7	(	(	PUNCT
ejpam-5790	523	8	∥∥∥∥∥	∥∥∥∥∥	NUM
ejpam-5790	523	9	∫	∫	PROPN
ejpam-5790	523	10	1	1	NUM
ejpam-5790	523	11	2	2	NUM
ejpam-5790	523	12	0	0	NUM
ejpam-5790	523	13	(	(	PUNCT
ejpam-5790	523	14	w	w	NOUN
ejpam-5790	523	15	−	−	PROPN
ejpam-5790	523	16	3k.2	3k.2	NUM
ejpam-5790	523	17	s	s	X
ejpam-5790	523	18	k	k	PROPN
ejpam-5790	523	19	w	w	PROPN
ejpam-5790	523	20	s+k	s+k	PROPN
ejpam-5790	523	21	k	k	PROPN
ejpam-5790	523	22	s	s	X
ejpam-5790	524	1	+	+	CCONJ
ejpam-5790	524	2	k	k	NOUN
ejpam-5790	524	3	)	)	PUNCT
ejpam-5790	524	4	[	[	PUNCT
ejpam-5790	524	5	w1⊗	w1⊗	NOUN
ejpam-5790	524	6	∣∣ℑ′′	∣∣ℑ′′	PROPN
ejpam-5790	524	7	(	(	PUNCT
ejpam-5790	524	8	u	u	NOUN
ejpam-5790	524	9	)	)	PUNCT
ejpam-5790	524	10	∣∣+	∣∣+	X
ejpam-5790	524	11	(	(	PUNCT
ejpam-5790	524	12	1−w	1−w	NUM
ejpam-5790	524	13	)	)	PUNCT
ejpam-5790	524	14	∣∣ℑ′′(u	∣∣ℑ′′(u	PROPN
ejpam-5790	524	15	)	)	PUNCT
ejpam-5790	524	16	∣∣⊗	∣∣⊗	PROPN
ejpam-5790	525	1	1	1	NUM
ejpam-5790	525	2	]	]	PUNCT
ejpam-5790	525	3	dw	dw	X
ejpam-5790	525	4	+	+	CCONJ
ejpam-5790	525	5	∫	∫	PROPN
ejpam-5790	525	6	1	1	NUM
ejpam-5790	525	7	1	1	NUM
ejpam-5790	525	8	2	2	NUM
ejpam-5790	525	9	(	(	PUNCT
ejpam-5790	525	10	(	(	PUNCT
ejpam-5790	525	11	1−w)−	1−w)−	NUM
ejpam-5790	525	12	3k.2	3k.2	NUM
ejpam-5790	525	13	s	s	X
ejpam-5790	525	14	k	k	X
ejpam-5790	525	15	(	(	PUNCT
ejpam-5790	525	16	1−w	1−w	NUM
ejpam-5790	525	17	)	)	PUNCT
ejpam-5790	525	18	s+k	s+k	NOUN
ejpam-5790	526	1	k	k	PROPN
ejpam-5790	526	2	s	s	X
ejpam-5790	526	3	+	+	CCONJ
ejpam-5790	526	4	k	k	ADJ
ejpam-5790	526	5	)	)	PUNCT
ejpam-5790	526	6	w1⊗	w1⊗	NOUN
ejpam-5790	526	7	∣∣ℑ′′	∣∣ℑ′′	PROPN
ejpam-5790	526	8	(	(	PUNCT
ejpam-5790	526	9	d	d	PROPN
ejpam-5790	526	10	)	)	PUNCT
ejpam-5790	526	11	∣∣+	∣∣+	X
ejpam-5790	526	12	(	(	PUNCT
ejpam-5790	526	13	1−w	1−w	NUM
ejpam-5790	526	14	)	)	PUNCT
ejpam-5790	526	15	∣∣ℑ′′(d	∣∣ℑ′′(d	NOUN
ejpam-5790	526	16	)	)	PUNCT
ejpam-5790	526	17	∣∣⊗	∣∣⊗	NOUN
ejpam-5790	526	18	1	1	NUM
ejpam-5790	526	19	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-5790	526	20	)	)	PUNCT
ejpam-5790	526	21	≤	≤	NUM
ejpam-5790	527	1	∥(1⊗d	∥(1⊗d	NOUN
ejpam-5790	527	2	−	−	PROPN
ejpam-5790	527	3	u	u	NOUN
ejpam-5790	527	4	⊗	⊗	PROPN
ejpam-5790	527	5	1)2∥	1)2∥	NUM
ejpam-5790	527	6	6	6	NUM
ejpam-5790	527	7	(	(	PUNCT
ejpam-5790	527	8	∥∥∥∥∥	∥∥∥∥∥	NUM
ejpam-5790	527	9	∫	∫	PROPN
ejpam-5790	527	10	1	1	NUM
ejpam-5790	527	11	2	2	NUM
ejpam-5790	527	12	0	0	NUM
ejpam-5790	527	13	(	(	PUNCT
ejpam-5790	527	14	w2	w2	NOUN
ejpam-5790	527	15	−	−	PROPN
ejpam-5790	527	16	3.2sws+2	3.2sws+2	PROPN
ejpam-5790	527	17	s	s	PART
ejpam-5790	527	18	+	+	NOUN
ejpam-5790	527	19	1	1	NUM
ejpam-5790	527	20	)	)	PUNCT
ejpam-5790	527	21	⊗	⊗	PROPN
ejpam-5790	527	22	∣∣ℑ′′	∣∣ℑ′′	PROPN
ejpam-5790	527	23	(	(	PUNCT
ejpam-5790	527	24	u	u	NOUN
ejpam-5790	527	25	)	)	PUNCT
ejpam-5790	527	26	∣∣	∣∣	X
ejpam-5790	528	1	+	+	CCONJ
ejpam-5790	528	2	∫	∫	PROPN
ejpam-5790	528	3	1	1	NUM
ejpam-5790	528	4	1	1	NUM
ejpam-5790	528	5	2	2	NUM
ejpam-5790	528	6	(	(	PUNCT
ejpam-5790	528	7	(	(	PUNCT
ejpam-5790	528	8	w	w	NOUN
ejpam-5790	528	9	−w2)−	−w2)−	PROPN
ejpam-5790	528	10	3.2sw(1−w)s+1	3.2sw(1−w)s+1	NUM
ejpam-5790	528	11	s	s	NOUN
ejpam-5790	528	12	+	+	NOUN
ejpam-5790	528	13	1	1	NUM
ejpam-5790	528	14	)	)	PUNCT
ejpam-5790	529	1	⊗	⊗	PROPN
ejpam-5790	529	2	∣∣ℑ′′	∣∣ℑ′′	PROPN
ejpam-5790	529	3	(	(	PUNCT
ejpam-5790	529	4	d	d	PROPN
ejpam-5790	529	5	)	)	PUNCT
ejpam-5790	529	6	∣∣	∣∣	X
ejpam-5790	529	7	∥∥∥∥∥	∥∥∥∥∥	X
ejpam-5790	529	8	)	)	PUNCT
ejpam-5790	529	9	dw	dw	PROPN
ejpam-5790	529	10	≤	≤	ADJ
ejpam-5790	529	11	∥(1⊗d	∥(1⊗d	NOUN
ejpam-5790	529	12	−	−	PROPN
ejpam-5790	529	13	u	u	NOUN
ejpam-5790	529	14	⊗	⊗	NOUN
ejpam-5790	529	15	1)2∥	1)2∥	NUM
ejpam-5790	529	16	6	6	NUM
ejpam-5790	530	1	[	[	X
ejpam-5790	530	2	(	(	PUNCT
ejpam-5790	530	3	k	k	X
ejpam-5790	530	4	4	4	NUM
ejpam-5790	530	5	(	(	PUNCT
ejpam-5790	530	6	s	s	PART
ejpam-5790	530	7	+	+	CCONJ
ejpam-5790	530	8	2	2	NUM
ejpam-5790	530	9	k	k	NOUN
ejpam-5790	530	10	)	)	PUNCT
ejpam-5790	530	11	(	(	PUNCT
ejpam-5790	530	12	s	s	VERB
ejpam-5790	530	13	k	k	X
ejpam-5790	530	14	(	(	PUNCT
ejpam-5790	530	15	s	s	PROPN
ejpam-5790	530	16	+	+	CCONJ
ejpam-5790	530	17	k	k	PROPN
ejpam-5790	530	18	3	3	NUM
ejpam-5790	530	19	k	k	NOUN
ejpam-5790	530	20	)	)	PUNCT
ejpam-5790	530	21	2	2	NUM
ejpam-5790	530	22	k	k	NOUN
ejpam-5790	530	23	s	s	X
ejpam-5790	530	24	+	+	PROPN
ejpam-5790	530	25	3	3	NUM
ejpam-5790	530	26	k	k	NOUN
ejpam-5790	530	27	s	s	X
ejpam-5790	530	28	+	+	CCONJ
ejpam-5790	530	29	k	k	NOUN
ejpam-5790	530	30	)	)	PUNCT
ejpam-5790	530	31	−	−	PROPN
ejpam-5790	530	32	1	1	NUM
ejpam-5790	530	33	8	8	NUM
ejpam-5790	530	34	)	)	PUNCT
ejpam-5790	530	35	∥∥∥	∥∥∥	PROPN
ejpam-5790	530	36	∣∣ℑ′′	∣∣ℑ′′	PROPN
ejpam-5790	530	37	(	(	PUNCT
ejpam-5790	530	38	u	u	NOUN
ejpam-5790	530	39	)	)	PUNCT
ejpam-5790	530	40	∣∣+	∣∣+	PROPN
ejpam-5790	530	41	∣∣ℑ′′	∣∣ℑ′′	PROPN
ejpam-5790	530	42	(	(	PUNCT
ejpam-5790	530	43	d	d	PROPN
ejpam-5790	530	44	)	)	PUNCT
ejpam-5790	530	45	∣∣	∣∣	X
ejpam-5790	530	46	∥∥∥	∥∥∥	NOUN
ejpam-5790	530	47	]	]	PUNCT
ejpam-5790	530	48	=	=	PUNCT
ejpam-5790	531	1	∥(1⊗d	∥(1⊗d	NOUN
ejpam-5790	531	2	−	−	PROPN
ejpam-5790	531	3	u	u	NOUN
ejpam-5790	531	4	⊗	⊗	NOUN
ejpam-5790	531	5	1)2∥	1)2∥	NUM
ejpam-5790	531	6	6	6	NUM
ejpam-5790	531	7	[	[	X
ejpam-5790	531	8	(	(	PUNCT
ejpam-5790	531	9	s(s	s(s	PROPN
ejpam-5790	531	10	+	+	CCONJ
ejpam-5790	531	11	k	k	X
ejpam-5790	531	12	)	)	PUNCT
ejpam-5790	531	13	a+2k	a+2k	PROPN
ejpam-5790	531	14	s	s	PART
ejpam-5790	531	15	+	+	NUM
ejpam-5790	531	16	3	3	NUM
ejpam-5790	531	17	s+2k	s+2k	PROPN
ejpam-5790	531	18	a	a	PRON
ejpam-5790	531	19	k	k	NOUN
ejpam-5790	531	20	2s+2k	2s+2k	NUM
ejpam-5790	531	21	s	s	PART
ejpam-5790	531	22	4	4	NUM
ejpam-5790	531	23	·	·	SYM
ejpam-5790	531	24	3	3	NUM
ejpam-5790	531	25	2k	2k	PROPN
ejpam-5790	531	26	s	s	PART
ejpam-5790	531	27	k	k	PROPN
ejpam-5790	531	28	2k	2k	PROPN
ejpam-5790	531	29	s	s	X
ejpam-5790	531	30	(	(	PUNCT
ejpam-5790	531	31	s	s	PART
ejpam-5790	531	32	+	+	CCONJ
ejpam-5790	531	33	k)(s	k)(s	NOUN
ejpam-5790	531	34	+	+	CCONJ
ejpam-5790	531	35	2k	2k	NUM
ejpam-5790	531	36	)	)	PUNCT
ejpam-5790	531	37	−	−	PROPN
ejpam-5790	531	38	1	1	NUM
ejpam-5790	531	39	8	8	NUM
ejpam-5790	531	40	)	)	PUNCT
ejpam-5790	531	41	∥∥∥	∥∥∥	PROPN
ejpam-5790	531	42	∣∣ℑ′′	∣∣ℑ′′	PROPN
ejpam-5790	531	43	(	(	PUNCT
ejpam-5790	531	44	u	u	NOUN
ejpam-5790	531	45	)	)	PUNCT
ejpam-5790	531	46	∣∣+	∣∣+	PROPN
ejpam-5790	532	1	∣∣ℑ′′	∣∣ℑ′′	PROPN
ejpam-5790	532	2	(	(	PUNCT
ejpam-5790	532	3	d	d	PROPN
ejpam-5790	532	4	)	)	PUNCT
ejpam-5790	532	5	∣∣	∣∣	X
ejpam-5790	532	6	∥∥∥	∥∥∥	PROPN
ejpam-5790	532	7	]	]	PUNCT
ejpam-5790	532	8	.	.	PUNCT
ejpam-5790	533	1	(	(	PUNCT
ejpam-5790	533	2	3.17	3.17	NUM
ejpam-5790	533	3	)	)	PUNCT
ejpam-5790	533	4	remark	remark	NOUN
ejpam-5790	533	5	2	2	NUM
ejpam-5790	533	6	.	.	NOUN
ejpam-5790	533	7	•	•	NOUN
ejpam-5790	533	8	setting	set	VERB
ejpam-5790	533	9	s	s	X
ejpam-5790	533	10	and	and	CCONJ
ejpam-5790	533	11	k	k	NOUN
ejpam-5790	533	12	=	=	SYM
ejpam-5790	533	13	1	1	NUM
ejpam-5790	533	14	,	,	PUNCT
ejpam-5790	533	15	and	and	CCONJ
ejpam-5790	533	16	the	the	DET
ejpam-5790	533	17	tensor	tensor	NOUN
ejpam-5790	533	18	operations	operation	NOUN
ejpam-5790	533	19	are	be	AUX
ejpam-5790	533	20	vanished	vanish	VERB
ejpam-5790	533	21	in	in	ADP
ejpam-5790	533	22	theorem	theorem	ADJ
ejpam-5790	533	23	6	6	NUM
ejpam-5790	533	24	,	,	PUNCT
ejpam-5790	533	25	then	then	ADV
ejpam-5790	533	26	theorem	theorem	VERB
ejpam-5790	533	27	6	6	NUM
ejpam-5790	533	28	reduces	reduce	VERB
ejpam-5790	533	29	to	to	PART
ejpam-5790	533	30	theorem	theorem	VERB
ejpam-5790	533	31	2.2	2.2	NUM
ejpam-5790	533	32	in	in	ADP
ejpam-5790	533	33	[	[	X
ejpam-5790	533	34	50	50	NUM
ejpam-5790	533	35	]	]	PUNCT
ejpam-5790	533	36	.	.	PUNCT
ejpam-5790	534	1	•	•	INTJ
ejpam-5790	534	2	if	if	SCONJ
ejpam-5790	534	3	the	the	DET
ejpam-5790	534	4	norm	norm	NOUN
ejpam-5790	534	5	structure	structure	NOUN
ejpam-5790	534	6	and	and	CCONJ
ejpam-5790	534	7	tensor	tensor	NOUN
ejpam-5790	534	8	operations	operation	NOUN
ejpam-5790	534	9	are	be	AUX
ejpam-5790	534	10	vanished	vanish	VERB
ejpam-5790	534	11	in	in	ADP
ejpam-5790	534	12	theorem	theorem	ADJ
ejpam-5790	534	13	6	6	NUM
ejpam-5790	534	14	,	,	PUNCT
ejpam-5790	534	15	then	then	ADV
ejpam-5790	534	16	theorem	theorem	VERB
ejpam-5790	534	17	6	6	NUM
ejpam-5790	534	18	simplifies	simplifie	NOUN
ejpam-5790	534	19	to	to	PART
ejpam-5790	534	20	corollary	corollary	VERB
ejpam-5790	534	21	2	2	NUM
ejpam-5790	534	22	in	in	ADP
ejpam-5790	534	23	[	[	X
ejpam-5790	534	24	13	13	NUM
ejpam-5790	534	25	]	]	PUNCT
ejpam-5790	534	26	.	.	PUNCT
ejpam-5790	535	1	•	•	INTJ
ejpam-5790	535	2	if	if	SCONJ
ejpam-5790	535	3	the	the	DET
ejpam-5790	535	4	tensor	tensor	NOUN
ejpam-5790	535	5	operations	operation	NOUN
ejpam-5790	535	6	are	be	AUX
ejpam-5790	535	7	vanished	vanish	VERB
ejpam-5790	535	8	in	in	ADP
ejpam-5790	535	9	theorem	theorem	ADJ
ejpam-5790	535	10	6	6	NUM
ejpam-5790	535	11	,	,	PUNCT
ejpam-5790	535	12	then	then	ADV
ejpam-5790	535	13	theorem	theorem	VERB
ejpam-5790	535	14	6	6	NUM
ejpam-5790	535	15	simplifies	simplifie	NOUN
ejpam-5790	535	16	to	to	PART
ejpam-5790	535	17	theorem	theorem	VERB
ejpam-5790	535	18	2.3	2.3	NUM
ejpam-5790	535	19	in	in	ADP
ejpam-5790	535	20	[	[	X
ejpam-5790	535	21	32	32	NUM
ejpam-5790	535	22	]	]	PUNCT
ejpam-5790	535	23	.	.	PUNCT
ejpam-5790	536	1	•	•	NUM
ejpam-5790	536	2	setting	set	VERB
ejpam-5790	536	3	s	s	NOUN
ejpam-5790	536	4	,	,	PUNCT
ejpam-5790	536	5	k	k	PROPN
ejpam-5790	536	6	=	=	SYM
ejpam-5790	536	7	1	1	NUM
ejpam-5790	536	8	in	in	ADP
ejpam-5790	536	9	theorem	theorem	NOUN
ejpam-5790	536	10	6	6	NUM
ejpam-5790	536	11	,	,	PUNCT
ejpam-5790	536	12	it	it	PRON
ejpam-5790	536	13	strained	strain	VERB
ejpam-5790	536	14	theorem	theorem	VERB
ejpam-5790	536	15	2.3	2.3	NUM
ejpam-5790	536	16	in	in	ADP
ejpam-5790	536	17	[	[	X
ejpam-5790	536	18	57	57	NUM
ejpam-5790	536	19	]	]	PUNCT
ejpam-5790	536	20	.	.	PUNCT
ejpam-5790	537	1	•	•	NUM
ejpam-5790	537	2	setting	set	VERB
ejpam-5790	537	3	s	s	NOUN
ejpam-5790	537	4	,	,	PUNCT
ejpam-5790	537	5	k	k	PROPN
ejpam-5790	537	6	=	=	SYM
ejpam-5790	537	7	1	1	NUM
ejpam-5790	537	8	in	in	ADP
ejpam-5790	537	9	theorem	theorem	NOUN
ejpam-5790	537	10	6	6	NUM
ejpam-5790	537	11	,	,	PUNCT
ejpam-5790	537	12	it	it	PRON
ejpam-5790	537	13	strained	strain	VERB
ejpam-5790	537	14	theorem	theorem	VERB
ejpam-5790	537	15	2.3	2.3	NUM
ejpam-5790	537	16	in	in	ADP
ejpam-5790	537	17	[	[	X
ejpam-5790	537	18	2	2	NUM
ejpam-5790	537	19	]	]	PUNCT
ejpam-5790	537	20	.	.	PUNCT
ejpam-5790	538	1	•	•	INTJ
ejpam-5790	538	2	if	if	SCONJ
ejpam-5790	538	3	we	we	PRON
ejpam-5790	538	4	choose	choose	VERB
ejpam-5790	538	5	s	s	NOUN
ejpam-5790	538	6	,	,	PUNCT
ejpam-5790	538	7	k	k	PROPN
ejpam-5790	538	8	=	=	SYM
ejpam-5790	538	9	1	1	NUM
ejpam-5790	538	10	in	in	ADP
ejpam-5790	538	11	theorem	theorem	NOUN
ejpam-5790	538	12	6	6	NUM
ejpam-5790	538	13	,	,	PUNCT
ejpam-5790	538	14	it	it	PRON
ejpam-5790	538	15	strained	strain	VERB
ejpam-5790	538	16	theorem	theorem	VERB
ejpam-5790	538	17	9	9	NUM
ejpam-5790	538	18	in	in	ADP
ejpam-5790	538	19	[	[	X
ejpam-5790	538	20	58	58	NUM
ejpam-5790	538	21	]	]	PUNCT
ejpam-5790	538	22	.	.	PUNCT
ejpam-5790	539	1	theorem	theorem	ADJ
ejpam-5790	539	2	7	7	NUM
ejpam-5790	539	3	.	.	PUNCT
ejpam-5790	540	1	let	let	VERB
ejpam-5790	540	2	u	u	PRON
ejpam-5790	540	3	and	and	CCONJ
ejpam-5790	540	4	d	d	NOUN
ejpam-5790	540	5	be	be	AUX
ejpam-5790	540	6	adjoint	adjoint	NOUN
ejpam-5790	540	7	operators	operator	NOUN
ejpam-5790	540	8	whose	whose	DET
ejpam-5790	540	9	spectra	spectra	NOUN
ejpam-5790	540	10	lies	lie	VERB
ejpam-5790	540	11	in	in	ADP
ejpam-5790	540	12	∆1	∆1	PROPN
ejpam-5790	540	13	and	and	CCONJ
ejpam-5790	540	14	∆2	∆2	PROPN
ejpam-5790	540	15	respectively	respectively	ADV
ejpam-5790	540	16	.	.	PUNCT
ejpam-5790	541	1	let	let	VERB
ejpam-5790	541	2	ℑ	ℑ	PRON
ejpam-5790	541	3	be	be	AUX
ejpam-5790	541	4	a	a	DET
ejpam-5790	541	5	continuous	continuous	ADJ
ejpam-5790	541	6	over	over	ADP
ejpam-5790	541	7	∆	∆	PROPN
ejpam-5790	541	8	with	with	ADP
ejpam-5790	541	9	∥ℑ′′∥∆,∞	∥ℑ′′∥∆,∞	ADV
ejpam-5790	541	10	:	:	PUNCT
ejpam-5790	541	11	=	=	SYM
ejpam-5790	541	12	sups∈∆	sups∈∆	NOUN
ejpam-5790	541	13	|ℑ′′(s)|	|ℑ′′(s)|	PROPN
ejpam-5790	541	14	<	<	X
ejpam-5790	541	15	∞	∞	PROPN
ejpam-5790	541	16	,	,	PUNCT
ejpam-5790	541	17	then	then	ADV
ejpam-5790	541	18	we	we	PRON
ejpam-5790	541	19	w.	w.	PROPN
ejpam-5790	541	20	afzal	afzal	PROPN
ejpam-5790	541	21	et	et	PROPN
ejpam-5790	541	22	al	al	PROPN
ejpam-5790	541	23	.	.	PUNCT
ejpam-5790	541	24	/	/	SYM
ejpam-5790	541	25	eur	eur	PROPN
ejpam-5790	541	26	.	.	PUNCT
ejpam-5790	542	1	j.	j.	PROPN
ejpam-5790	542	2	pure	pure	PROPN
ejpam-5790	542	3	appl	appl	PROPN
ejpam-5790	542	4	.	.	PROPN
ejpam-5790	542	5	math	math	PROPN
ejpam-5790	542	6	,	,	PUNCT
ejpam-5790	542	7	18	18	NUM
ejpam-5790	542	8	(	(	PUNCT
ejpam-5790	542	9	1	1	NUM
ejpam-5790	542	10	)	)	PUNCT
ejpam-5790	542	11	(	(	PUNCT
ejpam-5790	542	12	2025	2025	NUM
ejpam-5790	542	13	)	)	PUNCT
ejpam-5790	542	14	,	,	PUNCT
ejpam-5790	542	15	5790	5790	NUM
ejpam-5790	542	16	21	21	NUM
ejpam-5790	542	17	of	of	ADP
ejpam-5790	542	18	30	30	NUM
ejpam-5790	542	19	have∥∥∥∥∥	have∥∥∥∥∥	PROPN
ejpam-5790	542	20	[	[	PUNCT
ejpam-5790	542	21	1	1	NUM
ejpam-5790	542	22	6	6	NUM
ejpam-5790	542	23	(	(	PUNCT
ejpam-5790	542	24	ℑ(u)⊗	ℑ(u)⊗	PROPN
ejpam-5790	542	25	1	1	NUM
ejpam-5790	542	26	)	)	PUNCT
ejpam-5790	542	27	+	+	CCONJ
ejpam-5790	542	28	2	2	NUM
ejpam-5790	542	29	3	3	NUM
ejpam-5790	542	30	ℑ	ℑ	NOUN
ejpam-5790	542	31	(	(	PUNCT
ejpam-5790	542	32	u	u	NOUN
ejpam-5790	542	33	⊗	⊗	PROPN
ejpam-5790	542	34	1	1	NUM
ejpam-5790	542	35	+	+	NUM
ejpam-5790	542	36	1⊗d	1⊗d	NUM
ejpam-5790	542	37	2	2	NUM
ejpam-5790	542	38	)	)	PUNCT
ejpam-5790	542	39	+	+	CCONJ
ejpam-5790	543	1	1	1	NUM
ejpam-5790	543	2	6	6	NUM
ejpam-5790	543	3	(	(	PUNCT
ejpam-5790	543	4	1⊗ℑ(d	1⊗ℑ(d	NUM
ejpam-5790	543	5	)	)	PUNCT
ejpam-5790	543	6	)	)	PUNCT
ejpam-5790	543	7	]	]	PUNCT
ejpam-5790	543	8	−	−	PROPN
ejpam-5790	543	9	[	[	PUNCT
ejpam-5790	543	10	ℑ	ℑ	PROPN
ejpam-5790	543	11	(	(	PUNCT
ejpam-5790	543	12	u	u	NOUN
ejpam-5790	543	13	⊗	⊗	PROPN
ejpam-5790	543	14	1	1	NUM
ejpam-5790	543	15	+	+	NUM
ejpam-5790	543	16	1⊗d	1⊗d	NUM
ejpam-5790	543	17	2	2	NUM
ejpam-5790	543	18	)	)	PUNCT
ejpam-5790	543	19	−	−	PROPN
ejpam-5790	544	1	w	w	PROPN
ejpam-5790	544	2	s	s	PROPN
ejpam-5790	544	3	k	k	X
ejpam-5790	544	4	(	(	PUNCT
ejpam-5790	544	5	ν2	ν2	NOUN
ejpam-5790	544	6	−	−	PROPN
ejpam-5790	544	7	ν1	ν1	NOUN
ejpam-5790	544	8	)	)	PUNCT
ejpam-5790	544	9	4	4	NUM
ejpam-5790	545	1	[	[	X
ejpam-5790	545	2	∫	∫	PROPN
ejpam-5790	545	3	1	1	NUM
ejpam-5790	545	4	0	0	NUM
ejpam-5790	545	5	ℑ′	ℑ′	X
ejpam-5790	545	6	(	(	PUNCT
ejpam-5790	545	7	(	(	PUNCT
ejpam-5790	545	8	1−w)u	1−w)u	NUM
ejpam-5790	545	9	⊗	⊗	NOUN
ejpam-5790	545	10	1	1	NUM
ejpam-5790	545	11	+	+	CCONJ
ejpam-5790	545	12	(	(	PUNCT
ejpam-5790	545	13	w1⊗d	w1⊗d	NOUN
ejpam-5790	545	14	2	2	NUM
ejpam-5790	545	15	)	)	PUNCT
ejpam-5790	545	16	)	)	PUNCT
ejpam-5790	545	17	dw	dw	NOUN
ejpam-5790	545	18	]	]	PUNCT
ejpam-5790	546	1	+	+	CCONJ
ejpam-5790	546	2	ℑ	ℑ	PROPN
ejpam-5790	546	3	(	(	PUNCT
ejpam-5790	546	4	u	u	NOUN
ejpam-5790	546	5	⊗	⊗	PROPN
ejpam-5790	546	6	1	1	NUM
ejpam-5790	546	7	+	+	NUM
ejpam-5790	546	8	1⊗d	1⊗d	NUM
ejpam-5790	546	9	2	2	NUM
ejpam-5790	546	10	)	)	PUNCT
ejpam-5790	546	11	−	−	PROPN
ejpam-5790	546	12	(	(	PUNCT
ejpam-5790	546	13	1−w	1−w	NUM
ejpam-5790	546	14	)	)	PUNCT
ejpam-5790	546	15	s	s	PART
ejpam-5790	546	16	k	k	X
ejpam-5790	546	17	(	(	PUNCT
ejpam-5790	546	18	ν2	ν2	NOUN
ejpam-5790	546	19	−	−	PROPN
ejpam-5790	546	20	ν1	ν1	NOUN
ejpam-5790	546	21	)	)	PUNCT
ejpam-5790	546	22	4	4	NUM
ejpam-5790	547	1	[	[	X
ejpam-5790	547	2	∫	∫	PROPN
ejpam-5790	547	3	1	1	NUM
ejpam-5790	547	4	0	0	NUM
ejpam-5790	547	5	ℑ′	ℑ′	X
ejpam-5790	547	6	(	(	PUNCT
ejpam-5790	547	7	(	(	PUNCT
ejpam-5790	547	8	1−w	1−w	NUM
ejpam-5790	547	9	2	2	NUM
ejpam-5790	547	10	)	)	PUNCT
ejpam-5790	547	11	u	u	NOUN
ejpam-5790	547	12	⊗	⊗	PROPN
ejpam-5790	547	13	1	1	NUM
ejpam-5790	547	14	+	+	CCONJ
ejpam-5790	547	15	(	(	PUNCT
ejpam-5790	547	16	1	1	NUM
ejpam-5790	547	17	+	+	NOUN
ejpam-5790	547	18	w	w	NOUN
ejpam-5790	547	19	2	2	NUM
ejpam-5790	547	20	)	)	PUNCT
ejpam-5790	547	21	1⊗d	1⊗d	PROPN
ejpam-5790	547	22	)	)	PUNCT
ejpam-5790	547	23	dw	dw	NOUN
ejpam-5790	547	24	]	]	PUNCT
ejpam-5790	547	25	∥∥∥∥∥	∥∥∥∥∥	PUNCT
ejpam-5790	547	26	≤	≤	ADV
ejpam-5790	547	27	∥(1⊗d	∥(1⊗d	NOUN
ejpam-5790	547	28	−	−	PROPN
ejpam-5790	547	29	u	u	NOUN
ejpam-5790	547	30	⊗	⊗	NOUN
ejpam-5790	547	31	1)2∥	1)2∥	NUM
ejpam-5790	547	32	6	6	NUM
ejpam-5790	548	1	[	[	X
ejpam-5790	548	2	(	(	PUNCT
ejpam-5790	548	3	w2	w2	NOUN
ejpam-5790	548	4	2	2	NUM
ejpam-5790	548	5	+	+	SYM
ejpam-5790	548	6	6	6	NUM
ejpam-5790	548	7	ln−	ln−	NOUN
ejpam-5790	548	8	s	s	PART
ejpam-5790	548	9	k	k	X
ejpam-5790	548	10	−1	−1	NOUN
ejpam-5790	548	11	(	(	PUNCT
ejpam-5790	548	12	2	2	X
ejpam-5790	548	13	)	)	PUNCT
ejpam-5790	548	14	kγk	kγk	NOUN
ejpam-5790	548	15	(	(	PUNCT
ejpam-5790	548	16	s	s	VERB
ejpam-5790	548	17	+	+	X
ejpam-5790	548	18	k	k	X
ejpam-5790	548	19	,	,	PUNCT
ejpam-5790	548	20	ln	ln	X
ejpam-5790	548	21	(	(	PUNCT
ejpam-5790	548	22	2	2	NUM
ejpam-5790	548	23	)	)	PUNCT
ejpam-5790	548	24	(	(	PUNCT
ejpam-5790	548	25	1−w	1−w	NUM
ejpam-5790	548	26	)	)	PUNCT
ejpam-5790	548	27	)	)	PUNCT
ejpam-5790	549	1	s	s	VERB
ejpam-5790	550	1	+	+	CCONJ
ejpam-5790	550	2	k	k	X
ejpam-5790	550	3	+	+	PROPN
ejpam-5790	550	4	w2	w2	NOUN
ejpam-5790	550	5	2	2	NUM
ejpam-5790	550	6	+	+	PROPN
ejpam-5790	550	7	w	w	PROPN
ejpam-5790	550	8	+	+	NUM
ejpam-5790	550	9	6	6	NUM
ejpam-5790	550	10	ln−s−1	ln−s−1	NOUN
ejpam-5790	550	11	(	(	PUNCT
ejpam-5790	550	12	2	2	X
ejpam-5790	550	13	)	)	PUNCT
ejpam-5790	550	14	kγk	kγk	NOUN
ejpam-5790	550	15	(	(	PUNCT
ejpam-5790	550	16	s	s	VERB
ejpam-5790	550	17	+	+	X
ejpam-5790	550	18	k	k	X
ejpam-5790	550	19	,	,	PUNCT
ejpam-5790	550	20	ln	ln	X
ejpam-5790	550	21	(	(	PUNCT
ejpam-5790	550	22	2	2	NUM
ejpam-5790	550	23	)	)	PUNCT
ejpam-5790	550	24	(	(	PUNCT
ejpam-5790	550	25	1−w	1−w	NUM
ejpam-5790	550	26	)	)	PUNCT
ejpam-5790	550	27	)	)	PUNCT
ejpam-5790	551	1	s	s	VERB
ejpam-5790	552	1	+	+	CCONJ
ejpam-5790	552	2	k	k	NOUN
ejpam-5790	552	3	)	)	PUNCT
ejpam-5790	552	4	∥∥ℑ′∥∥	∥∥ℑ′∥∥	NOUN
ejpam-5790	552	5	∆,+∞	∆,+∞	PROPN
ejpam-5790	552	6	)	)	PUNCT
ejpam-5790	552	7	]	]	PUNCT
ejpam-5790	552	8	.	.	PUNCT
ejpam-5790	553	1	proof	proof	NOUN
ejpam-5790	553	2	.	.	PUNCT
ejpam-5790	554	1	taking	take	VERB
ejpam-5790	554	2	into	into	ADP
ejpam-5790	554	3	account	account	NOUN
ejpam-5790	554	4	lemma	lemma	PROPN
ejpam-5790	554	5	6	6	NUM
ejpam-5790	554	6	and	and	CCONJ
ejpam-5790	554	7	applying	apply	VERB
ejpam-5790	554	8	the	the	DET
ejpam-5790	554	9	triangle	triangle	NOUN
ejpam-5790	554	10	result	result	NOUN
ejpam-5790	554	11	,	,	PUNCT
ejpam-5790	554	12	we	we	PRON
ejpam-5790	554	13	have∥∥∥∥[16(ℑ(u)⊗	have∥∥∥∥[16(ℑ(u)⊗	VERB
ejpam-5790	554	14	1	1	NUM
ejpam-5790	554	15	)	)	PUNCT
ejpam-5790	554	16	+	+	CCONJ
ejpam-5790	554	17	2	2	NUM
ejpam-5790	554	18	3	3	NUM
ejpam-5790	554	19	ℑ	ℑ	NOUN
ejpam-5790	554	20	(	(	PUNCT
ejpam-5790	554	21	u	u	NOUN
ejpam-5790	554	22	⊗	⊗	PROPN
ejpam-5790	554	23	1	1	NUM
ejpam-5790	554	24	+	+	NUM
ejpam-5790	554	25	1⊗d	1⊗d	NUM
ejpam-5790	554	26	2	2	NUM
ejpam-5790	554	27	)	)	PUNCT
ejpam-5790	554	28	+	+	CCONJ
ejpam-5790	554	29	1	1	NUM
ejpam-5790	554	30	6	6	NUM
ejpam-5790	554	31	(	(	PUNCT
ejpam-5790	554	32	1⊗ℑ(d	1⊗ℑ(d	NUM
ejpam-5790	554	33	)	)	PUNCT
ejpam-5790	554	34	)	)	PUNCT
ejpam-5790	554	35	]	]	PUNCT
ejpam-5790	555	1	−	−	PROPN
ejpam-5790	555	2	[	[	PUNCT
ejpam-5790	555	3	ℑ	ℑ	PROPN
ejpam-5790	555	4	(	(	PUNCT
ejpam-5790	555	5	u	u	NOUN
ejpam-5790	555	6	⊗	⊗	PROPN
ejpam-5790	555	7	1	1	NUM
ejpam-5790	555	8	+	+	NUM
ejpam-5790	555	9	1⊗d	1⊗d	NUM
ejpam-5790	555	10	2	2	NUM
ejpam-5790	555	11	)	)	PUNCT
ejpam-5790	555	12	−	−	PROPN
ejpam-5790	556	1	w	w	PROPN
ejpam-5790	556	2	s	s	PROPN
ejpam-5790	556	3	k	k	X
ejpam-5790	556	4	(	(	PUNCT
ejpam-5790	556	5	ν2	ν2	NOUN
ejpam-5790	556	6	−	−	PROPN
ejpam-5790	556	7	ν1	ν1	NOUN
ejpam-5790	556	8	)	)	PUNCT
ejpam-5790	556	9	4	4	NUM
ejpam-5790	557	1	[	[	X
ejpam-5790	557	2	∫	∫	PROPN
ejpam-5790	557	3	1	1	NUM
ejpam-5790	557	4	0	0	NUM
ejpam-5790	557	5	ℑ′	ℑ′	X
ejpam-5790	557	6	(	(	PUNCT
ejpam-5790	557	7	(	(	PUNCT
ejpam-5790	557	8	1−w)u	1−w)u	NUM
ejpam-5790	557	9	⊗	⊗	NOUN
ejpam-5790	557	10	1	1	NUM
ejpam-5790	557	11	+	+	CCONJ
ejpam-5790	557	12	(	(	PUNCT
ejpam-5790	557	13	w1⊗d	w1⊗d	NOUN
ejpam-5790	557	14	2	2	NUM
ejpam-5790	557	15	)	)	PUNCT
ejpam-5790	557	16	)	)	PUNCT
ejpam-5790	557	17	dw	dw	NOUN
ejpam-5790	557	18	]	]	PUNCT
ejpam-5790	558	1	+	+	CCONJ
ejpam-5790	558	2	ℑ	ℑ	PROPN
ejpam-5790	558	3	(	(	PUNCT
ejpam-5790	558	4	u	u	NOUN
ejpam-5790	558	5	⊗	⊗	PROPN
ejpam-5790	558	6	1	1	NUM
ejpam-5790	558	7	+	+	NUM
ejpam-5790	558	8	1⊗d	1⊗d	NUM
ejpam-5790	558	9	2	2	NUM
ejpam-5790	558	10	)	)	PUNCT
ejpam-5790	558	11	−	−	PROPN
ejpam-5790	558	12	(	(	PUNCT
ejpam-5790	558	13	1−w	1−w	NUM
ejpam-5790	558	14	)	)	PUNCT
ejpam-5790	558	15	s	s	PART
ejpam-5790	558	16	k	k	X
ejpam-5790	558	17	(	(	PUNCT
ejpam-5790	558	18	ν2	ν2	NOUN
ejpam-5790	558	19	−	−	PROPN
ejpam-5790	558	20	ν1	ν1	NOUN
ejpam-5790	558	21	)	)	PUNCT
ejpam-5790	558	22	4	4	NUM
ejpam-5790	559	1	[	[	X
ejpam-5790	559	2	∫	∫	PROPN
ejpam-5790	559	3	1	1	NUM
ejpam-5790	559	4	0	0	NUM
ejpam-5790	559	5	ℑ′	ℑ′	X
ejpam-5790	559	6	(	(	PUNCT
ejpam-5790	559	7	(	(	PUNCT
ejpam-5790	559	8	1−w	1−w	NUM
ejpam-5790	559	9	2	2	NUM
ejpam-5790	559	10	)	)	PUNCT
ejpam-5790	559	11	u	u	NOUN
ejpam-5790	559	12	⊗	⊗	PROPN
ejpam-5790	559	13	1	1	NUM
ejpam-5790	559	14	+	+	CCONJ
ejpam-5790	559	15	(	(	PUNCT
ejpam-5790	559	16	1	1	NUM
ejpam-5790	559	17	+	+	NOUN
ejpam-5790	559	18	w	w	NOUN
ejpam-5790	559	19	2	2	NUM
ejpam-5790	559	20	)	)	PUNCT
ejpam-5790	559	21	1⊗d	1⊗d	PROPN
ejpam-5790	559	22	)	)	PUNCT
ejpam-5790	559	23	dw	dw	NOUN
ejpam-5790	559	24	]	]	PUNCT
ejpam-5790	559	25	∥∥∥∥∥	∥∥∥∥∥	PUNCT
ejpam-5790	559	26	≤	≤	ADV
ejpam-5790	559	27	∥(1⊗d	∥(1⊗d	NOUN
ejpam-5790	559	28	−	−	PROPN
ejpam-5790	559	29	u	u	NOUN
ejpam-5790	559	30	⊗	⊗	PROPN
ejpam-5790	559	31	1)2∥	1)2∥	NUM
ejpam-5790	559	32	6	6	NUM
ejpam-5790	559	33	∥∥∥∥∥	∥∥∥∥∥	SYM
ejpam-5790	559	34	∫	∫	PROPN
ejpam-5790	559	35	1	1	NUM
ejpam-5790	559	36	2	2	NUM
ejpam-5790	559	37	0	0	NUM
ejpam-5790	560	1	(	(	PUNCT
ejpam-5790	560	2	w	w	NOUN
ejpam-5790	560	3	−	−	PROPN
ejpam-5790	560	4	3k.2	3k.2	NUM
ejpam-5790	560	5	s	s	X
ejpam-5790	560	6	k	k	PROPN
ejpam-5790	560	7	w	w	PROPN
ejpam-5790	560	8	s+k	s+k	PROPN
ejpam-5790	560	9	k	k	PROPN
ejpam-5790	560	10	s	s	X
ejpam-5790	560	11	+	+	CCONJ
ejpam-5790	560	12	k	k	NOUN
ejpam-5790	560	13	)	)	PUNCT
ejpam-5790	560	14	[	[	PUNCT
ejpam-5790	560	15	ℑ′′	ℑ′′	ADV
ejpam-5790	560	16	(	(	PUNCT
ejpam-5790	560	17	u	u	NOUN
ejpam-5790	560	18	⊗	⊗	NOUN
ejpam-5790	560	19	1w	1w	VERB
ejpam-5790	560	20	+	+	CCONJ
ejpam-5790	560	21	1⊗	1⊗	NUM
ejpam-5790	560	22	u	u	NOUN
ejpam-5790	560	23	(	(	PUNCT
ejpam-5790	560	24	1−w	1−w	NUM
ejpam-5790	560	25	)	)	PUNCT
ejpam-5790	560	26	)	)	PUNCT
ejpam-5790	561	1	dw	dw	NOUN
ejpam-5790	561	2	]	]	PUNCT
ejpam-5790	562	1	+	+	CCONJ
ejpam-5790	562	2	∫	∫	PROPN
ejpam-5790	562	3	1	1	NUM
ejpam-5790	562	4	1	1	NUM
ejpam-5790	562	5	2	2	NUM
ejpam-5790	562	6	(	(	PUNCT
ejpam-5790	562	7	(	(	PUNCT
ejpam-5790	562	8	1−w)−	1−w)−	NUM
ejpam-5790	562	9	3k.2	3k.2	NUM
ejpam-5790	562	10	s	s	X
ejpam-5790	562	11	k	k	X
ejpam-5790	562	12	(	(	PUNCT
ejpam-5790	562	13	1−w	1−w	NUM
ejpam-5790	562	14	)	)	PUNCT
ejpam-5790	562	15	s+k	s+k	NOUN
ejpam-5790	563	1	k	k	PROPN
ejpam-5790	563	2	s	s	X
ejpam-5790	564	1	+	+	X
ejpam-5790	564	2	k	k	X
ejpam-5790	564	3	)	)	PUNCT
ejpam-5790	564	4	ℑ′′	ℑ′′	ADV
ejpam-5790	564	5	(	(	PUNCT
ejpam-5790	564	6	u	u	PROPN
ejpam-5790	564	7	⊗	⊗	NOUN
ejpam-5790	564	8	1w	1w	VERB
ejpam-5790	564	9	+	+	CCONJ
ejpam-5790	564	10	1⊗	1⊗	NUM
ejpam-5790	564	11	u	u	NOUN
ejpam-5790	564	12	(	(	PUNCT
ejpam-5790	564	13	1−w	1−w	NUM
ejpam-5790	564	14	)	)	PUNCT
ejpam-5790	564	15	)	)	PUNCT
ejpam-5790	565	1	∥∥∥∥∥	∥∥∥∥∥	PUNCT
ejpam-5790	565	2	≤	≤	ADJ
ejpam-5790	565	3	∥(1⊗d	∥(1⊗d	NOUN
ejpam-5790	565	4	−	−	PROPN
ejpam-5790	565	5	u	u	NOUN
ejpam-5790	565	6	⊗	⊗	PROPN
ejpam-5790	565	7	1)2∥	1)2∥	NUM
ejpam-5790	565	8	6	6	NUM
ejpam-5790	565	9	(	(	PUNCT
ejpam-5790	565	10	∥∥∥∥∥	∥∥∥∥∥	NUM
ejpam-5790	565	11	∫	∫	PROPN
ejpam-5790	565	12	1	1	NUM
ejpam-5790	565	13	2	2	NUM
ejpam-5790	565	14	0	0	NUM
ejpam-5790	565	15	(	(	PUNCT
ejpam-5790	565	16	w	w	NOUN
ejpam-5790	565	17	−	−	PROPN
ejpam-5790	565	18	3k.2	3k.2	NUM
ejpam-5790	565	19	s	s	X
ejpam-5790	565	20	k	k	PROPN
ejpam-5790	565	21	w	w	PROPN
ejpam-5790	565	22	s+k	s+k	PROPN
ejpam-5790	566	1	k	k	PROPN
ejpam-5790	566	2	s	s	X
ejpam-5790	566	3	+	+	CCONJ
ejpam-5790	566	4	k	k	NOUN
ejpam-5790	566	5	)	)	PUNCT
ejpam-5790	566	6	[	[	PUNCT
ejpam-5790	566	7	ℑ′′	ℑ′′	ADV
ejpam-5790	566	8	(	(	PUNCT
ejpam-5790	566	9	u	u	NOUN
ejpam-5790	566	10	⊗	⊗	NOUN
ejpam-5790	566	11	1w	1w	VERB
ejpam-5790	566	12	+	+	CCONJ
ejpam-5790	566	13	1⊗	1⊗	NUM
ejpam-5790	566	14	u	u	NOUN
ejpam-5790	566	15	(	(	PUNCT
ejpam-5790	566	16	1−w	1−w	NUM
ejpam-5790	566	17	)	)	PUNCT
ejpam-5790	566	18	)	)	PUNCT
ejpam-5790	567	1	dw	dw	NOUN
ejpam-5790	567	2	]	]	PUNCT
ejpam-5790	568	1	+	+	CCONJ
ejpam-5790	568	2	∫	∫	PROPN
ejpam-5790	568	3	1	1	NUM
ejpam-5790	568	4	1	1	NUM
ejpam-5790	568	5	2	2	NUM
ejpam-5790	568	6	(	(	PUNCT
ejpam-5790	568	7	(	(	PUNCT
ejpam-5790	568	8	1−w)−	1−w)−	NUM
ejpam-5790	568	9	3k.2	3k.2	NUM
ejpam-5790	568	10	s	s	X
ejpam-5790	568	11	k	k	X
ejpam-5790	568	12	(	(	PUNCT
ejpam-5790	568	13	1−w	1−w	NUM
ejpam-5790	568	14	)	)	PUNCT
ejpam-5790	568	15	s+k	s+k	NOUN
ejpam-5790	569	1	k	k	PROPN
ejpam-5790	569	2	s	s	X
ejpam-5790	570	1	+	+	X
ejpam-5790	570	2	k	k	X
ejpam-5790	570	3	)	)	PUNCT
ejpam-5790	570	4	ℑ′′	ℑ′′	ADV
ejpam-5790	570	5	(	(	PUNCT
ejpam-5790	570	6	u	u	PROPN
ejpam-5790	570	7	⊗	⊗	NOUN
ejpam-5790	570	8	1w	1w	VERB
ejpam-5790	570	9	+	+	CCONJ
ejpam-5790	570	10	1⊗	1⊗	NUM
ejpam-5790	570	11	u	u	NOUN
ejpam-5790	570	12	(	(	PUNCT
ejpam-5790	570	13	1−w	1−w	NUM
ejpam-5790	570	14	)	)	PUNCT
ejpam-5790	570	15	)	)	PUNCT
ejpam-5790	570	16	∥∥∥∥∥	∥∥∥∥∥	NUM
ejpam-5790	570	17	)	)	PUNCT
ejpam-5790	570	18	.	.	PUNCT
ejpam-5790	571	1	(	(	PUNCT
ejpam-5790	571	2	3.18	3.18	NUM
ejpam-5790	571	3	)	)	PUNCT
ejpam-5790	571	4	observe	observe	VERB
ejpam-5790	571	5	that	that	SCONJ
ejpam-5790	571	6	,	,	PUNCT
ejpam-5790	571	7	by	by	ADP
ejpam-5790	571	8	lemma	lemma	PROPN
ejpam-5790	571	9	2	2	NUM
ejpam-5790	571	10	∣∣∣∣(ℑ′′	∣∣∣∣(ℑ′′	PROPN
ejpam-5790	571	11	(	(	PUNCT
ejpam-5790	571	12	u1⊗w	u1⊗w	ADJ
ejpam-5790	571	13	+	+	CCONJ
ejpam-5790	571	14	1⊗	1⊗	NUM
ejpam-5790	571	15	u	u	NOUN
ejpam-5790	571	16	(	(	PUNCT
ejpam-5790	571	17	1−w	1−w	NUM
ejpam-5790	571	18	)	)	PUNCT
ejpam-5790	571	19	)	)	PUNCT
ejpam-5790	571	20	∣∣	∣∣	X
ejpam-5790	572	1	=	=	SYM
ejpam-5790	572	2	∫	∫	PROPN
ejpam-5790	572	3	∆	∆	PROPN
ejpam-5790	572	4	∫	∫	PROPN
ejpam-5790	572	5	∆	∆	PROPN
ejpam-5790	572	6	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5790	572	7	(	(	PUNCT
ejpam-5790	572	8	ℑ′′	ℑ′′	ADV
ejpam-5790	572	9	(	(	PUNCT
ejpam-5790	572	10	ν1w	ν1w	NOUN
ejpam-5790	572	11	+	+	NUM
ejpam-5790	572	12	ν1	ν1	NOUN
ejpam-5790	572	13	(	(	PUNCT
ejpam-5790	572	14	1−w	1−w	NUM
ejpam-5790	572	15	)	)	PUNCT
ejpam-5790	572	16	)	)	PUNCT
ejpam-5790	573	1	∣∣∣∣deν1	∣∣∣∣deν1	PROPN
ejpam-5790	573	2	⊗	⊗	PROPN
ejpam-5790	573	3	dfν2	dfν2	PROPN
ejpam-5790	573	4	.	.	PUNCT
ejpam-5790	574	1	since	since	SCONJ
ejpam-5790	574	2	∣∣∣(ℑ′′	∣∣∣(ℑ′′	X
ejpam-5790	574	3	(	(	PUNCT
ejpam-5790	574	4	ν1w	ν1w	NOUN
ejpam-5790	574	5	+	+	NUM
ejpam-5790	574	6	ν1	ν1	NOUN
ejpam-5790	574	7	(	(	PUNCT
ejpam-5790	574	8	1−w	1−w	NUM
ejpam-5790	574	9	)	)	PUNCT
ejpam-5790	574	10	)	)	PUNCT
ejpam-5790	574	11	∣∣	∣∣	NUM
ejpam-5790	574	12	⩽	⩽	SCONJ
ejpam-5790	574	13	∥∥ℑ′∥∥	∥∥ℑ′∥∥	PROPN
ejpam-5790	575	1	∆,+∞	∆,+∞	PROPN
ejpam-5790	575	2	w.	w.	PROPN
ejpam-5790	575	3	afzal	afzal	PROPN
ejpam-5790	575	4	et	et	PROPN
ejpam-5790	575	5	al	al	PROPN
ejpam-5790	575	6	.	.	PUNCT
ejpam-5790	575	7	/	/	SYM
ejpam-5790	575	8	eur	eur	PROPN
ejpam-5790	575	9	.	.	PUNCT
ejpam-5790	576	1	j.	j.	PROPN
ejpam-5790	576	2	pure	pure	PROPN
ejpam-5790	576	3	appl	appl	PROPN
ejpam-5790	576	4	.	.	PROPN
ejpam-5790	576	5	math	math	PROPN
ejpam-5790	576	6	,	,	PUNCT
ejpam-5790	576	7	18	18	NUM
ejpam-5790	576	8	(	(	PUNCT
ejpam-5790	576	9	1	1	NUM
ejpam-5790	576	10	)	)	PUNCT
ejpam-5790	576	11	(	(	PUNCT
ejpam-5790	576	12	2025	2025	NUM
ejpam-5790	576	13	)	)	PUNCT
ejpam-5790	576	14	,	,	PUNCT
ejpam-5790	576	15	5790	5790	NUM
ejpam-5790	576	16	22	22	NUM
ejpam-5790	576	17	of	of	ADP
ejpam-5790	576	18	30	30	NUM
ejpam-5790	576	19	for	for	ADP
ejpam-5790	576	20	all	all	DET
ejpam-5790	576	21	ν1	ν1	NOUN
ejpam-5790	576	22	,	,	PUNCT
ejpam-5790	576	23	ν2	ν2	NOUN
ejpam-5790	576	24	∈	∈	PROPN
ejpam-5790	577	1	∆.	∆.	NOUN
ejpam-5790	577	2	taking	take	VERB
ejpam-5790	577	3	∫	∫	PROPN
ejpam-5790	577	4	∆	∆	PROPN
ejpam-5790	577	5	∫	∫	PROPN
ejpam-5790	577	6	∆	∆	PROPN
ejpam-5790	577	7	over	over	ADP
ejpam-5790	577	8	deν1	deν1	PROPN
ejpam-5790	577	9	⊗	⊗	PROPN
ejpam-5790	577	10	dfν2	dfν2	PROPN
ejpam-5790	577	11	,	,	PUNCT
ejpam-5790	577	12	then	then	ADV
ejpam-5790	577	13	we	we	PRON
ejpam-5790	577	14	get	get	VERB
ejpam-5790	577	15	∣∣ℑ′′	∣∣ℑ′′	PROPN
ejpam-5790	577	16	(	(	PUNCT
ejpam-5790	577	17	1⊗	1⊗	NUM
ejpam-5790	577	18	uw	uw	PROPN
ejpam-5790	577	19	+	+	PROPN
ejpam-5790	577	20	1⊗	1⊗	NUM
ejpam-5790	577	21	u	u	NOUN
ejpam-5790	577	22	(	(	PUNCT
ejpam-5790	577	23	1−w	1−w	NUM
ejpam-5790	577	24	)	)	PUNCT
ejpam-5790	577	25	)	)	PUNCT
ejpam-5790	578	1	∣∣	∣∣	X
ejpam-5790	579	1	=	=	SYM
ejpam-5790	579	2	∫	∫	PROPN
ejpam-5790	579	3	∆	∆	PROPN
ejpam-5790	580	1	∫	∫	PROPN
ejpam-5790	580	2	∆	∆	PROPN
ejpam-5790	581	1	∣∣ℑ′′	∣∣ℑ′′	PROPN
ejpam-5790	581	2	(	(	PUNCT
ejpam-5790	581	3	ν1w	ν1w	NOUN
ejpam-5790	581	4	+	+	NUM
ejpam-5790	581	5	ν1	ν1	NOUN
ejpam-5790	581	6	(	(	PUNCT
ejpam-5790	581	7	1−w	1−w	NUM
ejpam-5790	581	8	)	)	PUNCT
ejpam-5790	581	9	)	)	PUNCT
ejpam-5790	582	1	∣∣	∣∣	PROPN
ejpam-5790	582	2	deν1	deν1	PROPN
ejpam-5790	582	3	⊗	⊗	PROPN
ejpam-5790	582	4	dfν2	dfν2	PROPN
ejpam-5790	582	5	⩽	⩽	PROPN
ejpam-5790	582	6	∥∥ℑ′∥∥	∥∥ℑ′∥∥	PROPN
ejpam-5790	582	7	∆,+∞	∆,+∞	ADJ
ejpam-5790	582	8	∫	∫	PROPN
ejpam-5790	582	9	∆	∆	PROPN
ejpam-5790	583	1	∫	∫	PROPN
ejpam-5790	583	2	∆	∆	PROPN
ejpam-5790	583	3	deν1	deν1	PROPN
ejpam-5790	583	4	⊗	⊗	PROPN
ejpam-5790	583	5	dfν2	dfν2	PROPN
ejpam-5790	583	6	=	=	PUNCT
ejpam-5790	583	7	∥∥ℑ′∥∥	∥∥ℑ′∥∥	PROPN
ejpam-5790	583	8	∆,+∞	∆,+∞	PROPN
ejpam-5790	583	9	.	.	PUNCT
ejpam-5790	584	1	(	(	PUNCT
ejpam-5790	584	2	3.19	3.19	NUM
ejpam-5790	584	3	)	)	PUNCT
ejpam-5790	584	4	similarly	similarly	ADV
ejpam-5790	584	5	,	,	PUNCT
ejpam-5790	584	6	we	we	PRON
ejpam-5790	584	7	get∣∣ℑ′′	get∣∣ℑ′′	PROPN
ejpam-5790	584	8	(	(	PUNCT
ejpam-5790	584	9	1⊗dw	1⊗dw	NUM
ejpam-5790	584	10	+	+	NUM
ejpam-5790	584	11	1⊗d	1⊗d	NUM
ejpam-5790	584	12	(	(	PUNCT
ejpam-5790	584	13	1−w	1−w	NUM
ejpam-5790	584	14	)	)	PUNCT
ejpam-5790	584	15	)	)	PUNCT
ejpam-5790	584	16	∣∣	∣∣	X
ejpam-5790	585	1	=	=	SYM
ejpam-5790	585	2	∫	∫	PROPN
ejpam-5790	585	3	∆	∆	PROPN
ejpam-5790	586	1	∫	∫	PROPN
ejpam-5790	586	2	∆	∆	PROPN
ejpam-5790	587	1	∣∣ℑ′′	∣∣ℑ′′	PROPN
ejpam-5790	587	2	(	(	PUNCT
ejpam-5790	587	3	ν2w	ν2w	PROPN
ejpam-5790	587	4	+	+	CCONJ
ejpam-5790	587	5	ν2	ν2	PROPN
ejpam-5790	587	6	(	(	PUNCT
ejpam-5790	587	7	1−w	1−w	NUM
ejpam-5790	587	8	)	)	PUNCT
ejpam-5790	587	9	)	)	PUNCT
ejpam-5790	588	1	∣∣	∣∣	PROPN
ejpam-5790	588	2	deν1	deν1	PROPN
ejpam-5790	588	3	⊗	⊗	PROPN
ejpam-5790	588	4	dfν2	dfν2	PROPN
ejpam-5790	588	5	⩽	⩽	PROPN
ejpam-5790	588	6	∥∥ℑ′∥∥	∥∥ℑ′∥∥	PROPN
ejpam-5790	588	7	∆,+∞	∆,+∞	ADJ
ejpam-5790	588	8	∫	∫	PROPN
ejpam-5790	588	9	∆	∆	PROPN
ejpam-5790	589	1	∫	∫	PROPN
ejpam-5790	589	2	∆	∆	PROPN
ejpam-5790	589	3	deν1	deν1	PROPN
ejpam-5790	589	4	⊗	⊗	PROPN
ejpam-5790	589	5	dfν2	dfν2	PROPN
ejpam-5790	589	6	=	=	PUNCT
ejpam-5790	589	7	∥∥ℑ′∥∥	∥∥ℑ′∥∥	PROPN
ejpam-5790	589	8	∆,+∞	∆,+∞	PROPN
ejpam-5790	589	9	.	.	PUNCT
ejpam-5790	590	1	(	(	PUNCT
ejpam-5790	590	2	3.20	3.20	NUM
ejpam-5790	590	3	)	)	PUNCT
ejpam-5790	590	4	taking	take	VERB
ejpam-5790	590	5	into	into	ADP
ejpam-5790	590	6	account	account	NOUN
ejpam-5790	590	7	equation	equation	NOUN
ejpam-5790	590	8	(	(	PUNCT
ejpam-5790	590	9	3.18	3.18	NUM
ejpam-5790	590	10	)	)	PUNCT
ejpam-5790	590	11	,	,	PUNCT
ejpam-5790	590	12	this	this	PRON
ejpam-5790	590	13	follows	follow	VERB
ejpam-5790	590	14	∥(1⊗d	∥(1⊗d	NOUN
ejpam-5790	590	15	−	−	PROPN
ejpam-5790	590	16	u	u	NOUN
ejpam-5790	590	17	⊗	⊗	PROPN
ejpam-5790	590	18	1)2∥	1)2∥	NUM
ejpam-5790	590	19	6	6	NUM
ejpam-5790	590	20	(	(	PUNCT
ejpam-5790	590	21	∥∥∥∥∥	∥∥∥∥∥	NUM
ejpam-5790	590	22	∫	∫	PROPN
ejpam-5790	590	23	1	1	NUM
ejpam-5790	590	24	2	2	NUM
ejpam-5790	590	25	0	0	NUM
ejpam-5790	590	26	(	(	PUNCT
ejpam-5790	590	27	w	w	NOUN
ejpam-5790	590	28	−	−	PROPN
ejpam-5790	590	29	3k.2	3k.2	NUM
ejpam-5790	590	30	s	s	X
ejpam-5790	590	31	k	k	PROPN
ejpam-5790	590	32	w	w	PROPN
ejpam-5790	590	33	s+k	s+k	PROPN
ejpam-5790	591	1	k	k	PROPN
ejpam-5790	591	2	s	s	X
ejpam-5790	591	3	+	+	CCONJ
ejpam-5790	591	4	k	k	NOUN
ejpam-5790	591	5	)	)	PUNCT
ejpam-5790	591	6	[	[	PUNCT
ejpam-5790	591	7	ℑ′′	ℑ′′	ADV
ejpam-5790	591	8	(	(	PUNCT
ejpam-5790	591	9	u	u	NOUN
ejpam-5790	591	10	⊗	⊗	NOUN
ejpam-5790	591	11	1w	1w	VERB
ejpam-5790	591	12	+	+	CCONJ
ejpam-5790	591	13	1⊗	1⊗	NUM
ejpam-5790	591	14	u	u	NOUN
ejpam-5790	591	15	(	(	PUNCT
ejpam-5790	591	16	1−w	1−w	NUM
ejpam-5790	591	17	)	)	PUNCT
ejpam-5790	591	18	)	)	PUNCT
ejpam-5790	592	1	dw	dw	NOUN
ejpam-5790	592	2	]	]	PUNCT
ejpam-5790	593	1	+	+	CCONJ
ejpam-5790	593	2	∫	∫	PROPN
ejpam-5790	593	3	1	1	NUM
ejpam-5790	593	4	1	1	NUM
ejpam-5790	593	5	2	2	NUM
ejpam-5790	593	6	(	(	PUNCT
ejpam-5790	593	7	(	(	PUNCT
ejpam-5790	593	8	1−w)−	1−w)−	NUM
ejpam-5790	593	9	3k.2	3k.2	NUM
ejpam-5790	593	10	s	s	X
ejpam-5790	593	11	k	k	X
ejpam-5790	593	12	(	(	PUNCT
ejpam-5790	593	13	1−w	1−w	NUM
ejpam-5790	593	14	)	)	PUNCT
ejpam-5790	593	15	s+k	s+k	NOUN
ejpam-5790	594	1	k	k	PROPN
ejpam-5790	594	2	s	s	X
ejpam-5790	595	1	+	+	X
ejpam-5790	595	2	k	k	X
ejpam-5790	595	3	)	)	PUNCT
ejpam-5790	595	4	ℑ′′	ℑ′′	ADV
ejpam-5790	595	5	(	(	PUNCT
ejpam-5790	595	6	u	u	PROPN
ejpam-5790	595	7	⊗	⊗	NOUN
ejpam-5790	595	8	1w	1w	VERB
ejpam-5790	595	9	+	+	CCONJ
ejpam-5790	595	10	1⊗	1⊗	NUM
ejpam-5790	595	11	u	u	NOUN
ejpam-5790	595	12	(	(	PUNCT
ejpam-5790	595	13	1−w	1−w	NUM
ejpam-5790	595	14	)	)	PUNCT
ejpam-5790	595	15	)	)	PUNCT
ejpam-5790	595	16	∥∥∥∥∥	∥∥∥∥∥	NUM
ejpam-5790	595	17	)	)	PUNCT
ejpam-5790	596	1	≤	≤	PUNCT
ejpam-5790	597	1	∥(1⊗d	∥(1⊗d	NOUN
ejpam-5790	597	2	−	−	PROPN
ejpam-5790	597	3	u	u	NOUN
ejpam-5790	597	4	⊗	⊗	PROPN
ejpam-5790	597	5	1)2∥	1)2∥	NUM
ejpam-5790	597	6	6	6	NUM
ejpam-5790	597	7	(	(	PUNCT
ejpam-5790	597	8	∥∥∥∥∥	∥∥∥∥∥	NUM
ejpam-5790	597	9	∫	∫	PROPN
ejpam-5790	597	10	1	1	NUM
ejpam-5790	597	11	2	2	NUM
ejpam-5790	597	12	0	0	NUM
ejpam-5790	597	13	(	(	PUNCT
ejpam-5790	597	14	w	w	NOUN
ejpam-5790	597	15	−	−	PROPN
ejpam-5790	597	16	3k.2	3k.2	NUM
ejpam-5790	597	17	s	s	X
ejpam-5790	597	18	k	k	PROPN
ejpam-5790	597	19	w	w	PROPN
ejpam-5790	597	20	s+k	s+k	PROPN
ejpam-5790	597	21	k	k	PROPN
ejpam-5790	597	22	s	s	X
ejpam-5790	598	1	+	+	CCONJ
ejpam-5790	598	2	k	k	X
ejpam-5790	598	3	)	)	PUNCT
ejpam-5790	598	4	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-5790	599	1	∥∥∥∥∥ℑ′′′	∥∥∥∥∥ℑ′′′	NOUN
ejpam-5790	599	2	(	(	PUNCT
ejpam-5790	599	3	1⊗	1⊗	NUM
ejpam-5790	599	4	uw	uw	PROPN
ejpam-5790	599	5	+	+	PROPN
ejpam-5790	599	6	1⊗	1⊗	NUM
ejpam-5790	599	7	u	u	NOUN
ejpam-5790	599	8	(	(	PUNCT
ejpam-5790	599	9	1−w	1−w	NUM
ejpam-5790	599	10	)	)	PUNCT
ejpam-5790	599	11	)	)	PUNCT
ejpam-5790	599	12	∥∥∥∥∥	∥∥∥∥∥	PUNCT
ejpam-5790	600	1	+	+	CCONJ
ejpam-5790	600	2	∥∥∥∥∥	∥∥∥∥∥	X
ejpam-5790	600	3	∫	∫	NOUN
ejpam-5790	600	4	1	1	NUM
ejpam-5790	600	5	1	1	NUM
ejpam-5790	600	6	2	2	NUM
ejpam-5790	600	7	(	(	PUNCT
ejpam-5790	600	8	(	(	PUNCT
ejpam-5790	600	9	1−w)−	1−w)−	NUM
ejpam-5790	600	10	3k.2	3k.2	NUM
ejpam-5790	600	11	s	s	X
ejpam-5790	600	12	k	k	X
ejpam-5790	600	13	(	(	PUNCT
ejpam-5790	600	14	1−w	1−w	NUM
ejpam-5790	600	15	)	)	PUNCT
ejpam-5790	600	16	s+k	s+k	NOUN
ejpam-5790	601	1	k	k	PROPN
ejpam-5790	601	2	s	s	X
ejpam-5790	601	3	+	+	CCONJ
ejpam-5790	601	4	k	k	PROPN
ejpam-5790	601	5	)	)	PUNCT
ejpam-5790	601	6	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-5790	601	7	∥∥∥∥∥ℑ′′	∥∥∥∥∥ℑ′′	PROPN
ejpam-5790	601	8	(	(	PUNCT
ejpam-5790	601	9	1⊗	1⊗	NUM
ejpam-5790	601	10	uw	uw	PROPN
ejpam-5790	601	11	+	+	PROPN
ejpam-5790	601	12	1⊗	1⊗	NUM
ejpam-5790	601	13	u	u	NOUN
ejpam-5790	601	14	(	(	PUNCT
ejpam-5790	601	15	1−w	1−w	NUM
ejpam-5790	601	16	)	)	PUNCT
ejpam-5790	601	17	)	)	PUNCT
ejpam-5790	601	18	dw	dw	PROPN
ejpam-5790	601	19	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-5790	601	20	)	)	PUNCT
ejpam-5790	601	21	≤	≤	NUM
ejpam-5790	602	1	∥(1⊗d	∥(1⊗d	NOUN
ejpam-5790	602	2	−	−	PROPN
ejpam-5790	602	3	u	u	NOUN
ejpam-5790	602	4	⊗	⊗	PROPN
ejpam-5790	602	5	1)2∥	1)2∥	NUM
ejpam-5790	602	6	6	6	NUM
ejpam-5790	602	7	(	(	PUNCT
ejpam-5790	602	8	∥∥∥∥∥w2	∥∥∥∥∥w2	PROPN
ejpam-5790	602	9	2	2	NUM
ejpam-5790	602	10	−	−	PROPN
ejpam-5790	602	11	6	6	NUM
ejpam-5790	602	12	ln−	ln−	PROPN
ejpam-5790	602	13	s	s	PART
ejpam-5790	602	14	k	k	X
ejpam-5790	602	15	−1	−1	NOUN
ejpam-5790	602	16	(	(	PUNCT
ejpam-5790	602	17	2	2	X
ejpam-5790	602	18	)	)	PUNCT
ejpam-5790	602	19	kγk	kγk	NOUN
ejpam-5790	602	20	(	(	PUNCT
ejpam-5790	602	21	s	s	VERB
ejpam-5790	602	22	+	+	X
ejpam-5790	602	23	k	k	X
ejpam-5790	602	24	,	,	PUNCT
ejpam-5790	602	25	ln	ln	X
ejpam-5790	602	26	(	(	PUNCT
ejpam-5790	602	27	2	2	NUM
ejpam-5790	602	28	)	)	PUNCT
ejpam-5790	602	29	(	(	PUNCT
ejpam-5790	602	30	1−w	1−w	NUM
ejpam-5790	602	31	)	)	PUNCT
ejpam-5790	602	32	)	)	PUNCT
ejpam-5790	602	33	s	s	VERB
ejpam-5790	603	1	+	+	CCONJ
ejpam-5790	603	2	k	k	X
ejpam-5790	603	3	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-5790	603	4	∥∥∥∥∥ℑ′′′	∥∥∥∥∥ℑ′′′	PROPN
ejpam-5790	603	5	(	(	PUNCT
ejpam-5790	603	6	1⊗	1⊗	NUM
ejpam-5790	603	7	uw	uw	PROPN
ejpam-5790	603	8	+	+	PROPN
ejpam-5790	603	9	1⊗	1⊗	NUM
ejpam-5790	603	10	u	u	NOUN
ejpam-5790	603	11	(	(	PUNCT
ejpam-5790	603	12	1−w	1−w	NUM
ejpam-5790	603	13	)	)	PUNCT
ejpam-5790	603	14	)	)	PUNCT
ejpam-5790	603	15	∥∥∥∥∥	∥∥∥∥∥	PUNCT
ejpam-5790	604	1	+	+	CCONJ
ejpam-5790	604	2	∥∥∥∥∥−	∥∥∥∥∥−	PROPN
ejpam-5790	604	3	w2	w2	NOUN
ejpam-5790	604	4	2	2	NUM
ejpam-5790	604	5	+	+	PROPN
ejpam-5790	604	6	w	w	PROPN
ejpam-5790	604	7	−	−	NUM
ejpam-5790	604	8	6	6	NUM
ejpam-5790	604	9	ln−	ln−	PROPN
ejpam-5790	604	10	s	s	PART
ejpam-5790	604	11	k	k	X
ejpam-5790	604	12	−1	−1	NOUN
ejpam-5790	604	13	(	(	PUNCT
ejpam-5790	604	14	2	2	X
ejpam-5790	604	15	)	)	PUNCT
ejpam-5790	604	16	kγk	kγk	NOUN
ejpam-5790	604	17	(	(	PUNCT
ejpam-5790	604	18	s	s	VERB
ejpam-5790	604	19	+	+	X
ejpam-5790	604	20	k	k	X
ejpam-5790	604	21	,	,	PUNCT
ejpam-5790	604	22	ln	ln	X
ejpam-5790	604	23	(	(	PUNCT
ejpam-5790	604	24	2	2	NUM
ejpam-5790	604	25	)	)	PUNCT
ejpam-5790	604	26	(	(	PUNCT
ejpam-5790	604	27	1−w	1−w	NUM
ejpam-5790	604	28	)	)	PUNCT
ejpam-5790	604	29	)	)	PUNCT
ejpam-5790	605	1	s	s	VERB
ejpam-5790	606	1	+	+	CCONJ
ejpam-5790	606	2	k	k	X
ejpam-5790	606	3	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-5790	606	4	∥∥∥∥∥ℑ′′	∥∥∥∥∥ℑ′′	PROPN
ejpam-5790	606	5	(	(	PUNCT
ejpam-5790	606	6	1⊗	1⊗	NUM
ejpam-5790	606	7	uw	uw	PROPN
ejpam-5790	606	8	+	+	PROPN
ejpam-5790	606	9	1⊗	1⊗	NUM
ejpam-5790	606	10	u	u	NOUN
ejpam-5790	606	11	(	(	PUNCT
ejpam-5790	606	12	1−w	1−w	NUM
ejpam-5790	606	13	)	)	PUNCT
ejpam-5790	606	14	)	)	PUNCT
ejpam-5790	606	15	dw	dw	PROPN
ejpam-5790	606	16	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-5790	606	17	)	)	PUNCT
ejpam-5790	606	18	≤	≤	NUM
ejpam-5790	607	1	∥(1⊗d	∥(1⊗d	NOUN
ejpam-5790	607	2	−	−	PROPN
ejpam-5790	607	3	u	u	NOUN
ejpam-5790	607	4	⊗	⊗	PROPN
ejpam-5790	607	5	1)2∥	1)2∥	NUM
ejpam-5790	607	6	6	6	NUM
ejpam-5790	607	7	(	(	PUNCT
ejpam-5790	607	8	∥∥∥∥∥w2	∥∥∥∥∥w2	PROPN
ejpam-5790	607	9	2	2	NUM
ejpam-5790	607	10	+	+	NUM
ejpam-5790	607	11	6	6	NUM
ejpam-5790	607	12	ln−	ln−	NOUN
ejpam-5790	607	13	s	s	PART
ejpam-5790	607	14	k	k	X
ejpam-5790	607	15	−1	−1	NOUN
ejpam-5790	607	16	(	(	PUNCT
ejpam-5790	607	17	2	2	X
ejpam-5790	607	18	)	)	PUNCT
ejpam-5790	607	19	kγk	kγk	NOUN
ejpam-5790	607	20	(	(	PUNCT
ejpam-5790	607	21	s	s	VERB
ejpam-5790	607	22	+	+	X
ejpam-5790	607	23	k	k	X
ejpam-5790	607	24	,	,	PUNCT
ejpam-5790	607	25	ln	ln	X
ejpam-5790	607	26	(	(	PUNCT
ejpam-5790	607	27	2	2	NUM
ejpam-5790	607	28	)	)	PUNCT
ejpam-5790	607	29	(	(	PUNCT
ejpam-5790	607	30	1−w	1−w	NUM
ejpam-5790	607	31	)	)	PUNCT
ejpam-5790	607	32	)	)	PUNCT
ejpam-5790	608	1	s	s	VERB
ejpam-5790	609	1	+	+	CCONJ
ejpam-5790	609	2	k	k	PROPN
ejpam-5790	609	3	∥∥∥∥∥∥∥ℑ′∥∥	∥∥∥∥∥∥∥ℑ′∥∥	PROPN
ejpam-5790	609	4	∆,+∞	∆,+∞	PROPN
ejpam-5790	609	5	+	+	CCONJ
ejpam-5790	609	6	∥∥∥∥∥w2	∥∥∥∥∥w2	PROPN
ejpam-5790	609	7	2	2	NUM
ejpam-5790	609	8	+	+	NOUN
ejpam-5790	609	9	w	w	PROPN
ejpam-5790	609	10	+	+	NUM
ejpam-5790	609	11	6	6	NUM
ejpam-5790	609	12	ln−s−1	ln−s−1	NOUN
ejpam-5790	609	13	(	(	PUNCT
ejpam-5790	609	14	2	2	X
ejpam-5790	609	15	)	)	PUNCT
ejpam-5790	609	16	kγk	kγk	NOUN
ejpam-5790	609	17	(	(	PUNCT
ejpam-5790	609	18	s	s	VERB
ejpam-5790	609	19	+	+	ADJ
ejpam-5790	609	20	1	1	NUM
ejpam-5790	609	21	,	,	PUNCT
ejpam-5790	609	22	ln	ln	X
ejpam-5790	609	23	(	(	PUNCT
ejpam-5790	609	24	2	2	NUM
ejpam-5790	609	25	)	)	PUNCT
ejpam-5790	609	26	(	(	PUNCT
ejpam-5790	609	27	1−w	1−w	NUM
ejpam-5790	609	28	)	)	PUNCT
ejpam-5790	609	29	)	)	PUNCT
ejpam-5790	610	1	s	s	VERB
ejpam-5790	611	1	+	+	ADJ
ejpam-5790	611	2	1	1	NUM
ejpam-5790	611	3	∥∥∥∥∥∥∥ℑ′∥∥	∥∥∥∥∥∥∥ℑ′∥∥	PROPN
ejpam-5790	611	4	∆,+∞	∆,+∞	PROPN
ejpam-5790	611	5	)	)	PUNCT
ejpam-5790	611	6	≤	≤	PUNCT
ejpam-5790	612	1	∥(1⊗d	∥(1⊗d	NOUN
ejpam-5790	612	2	−	−	PROPN
ejpam-5790	612	3	u	u	NOUN
ejpam-5790	612	4	⊗	⊗	NOUN
ejpam-5790	612	5	1)2∥	1)2∥	NUM
ejpam-5790	612	6	6	6	NUM
ejpam-5790	613	1	[	[	X
ejpam-5790	613	2	(	(	PUNCT
ejpam-5790	613	3	w2	w2	NOUN
ejpam-5790	613	4	2	2	NUM
ejpam-5790	613	5	+	+	SYM
ejpam-5790	613	6	6	6	NUM
ejpam-5790	613	7	ln−	ln−	NOUN
ejpam-5790	613	8	s	s	PART
ejpam-5790	613	9	k	k	X
ejpam-5790	613	10	−1	−1	NOUN
ejpam-5790	613	11	(	(	PUNCT
ejpam-5790	613	12	2	2	X
ejpam-5790	613	13	)	)	PUNCT
ejpam-5790	613	14	kγk	kγk	NOUN
ejpam-5790	613	15	(	(	PUNCT
ejpam-5790	613	16	s	s	VERB
ejpam-5790	613	17	+	+	ADJ
ejpam-5790	613	18	1	1	NUM
ejpam-5790	613	19	,	,	PUNCT
ejpam-5790	613	20	ln	ln	X
ejpam-5790	613	21	(	(	PUNCT
ejpam-5790	613	22	2	2	NUM
ejpam-5790	613	23	)	)	PUNCT
ejpam-5790	613	24	(	(	PUNCT
ejpam-5790	613	25	1−w	1−w	NUM
ejpam-5790	613	26	)	)	PUNCT
ejpam-5790	613	27	)	)	PUNCT
ejpam-5790	613	28	s	s	VERB
ejpam-5790	614	1	+	+	ADJ
ejpam-5790	614	2	1	1	NUM
ejpam-5790	614	3	+	+	NOUN
ejpam-5790	614	4	w2	w2	NOUN
ejpam-5790	614	5	2	2	NUM
ejpam-5790	614	6	+	+	PROPN
ejpam-5790	614	7	w	w	PROPN
ejpam-5790	614	8	+	+	NUM
ejpam-5790	614	9	6	6	NUM
ejpam-5790	614	10	ln−s−1	ln−s−1	NOUN
ejpam-5790	614	11	(	(	PUNCT
ejpam-5790	614	12	2	2	X
ejpam-5790	614	13	)	)	PUNCT
ejpam-5790	614	14	kγk	kγk	NOUN
ejpam-5790	614	15	(	(	PUNCT
ejpam-5790	614	16	s	s	VERB
ejpam-5790	614	17	+	+	X
ejpam-5790	614	18	k	k	X
ejpam-5790	614	19	,	,	PUNCT
ejpam-5790	614	20	ln	ln	X
ejpam-5790	614	21	(	(	PUNCT
ejpam-5790	614	22	2	2	NUM
ejpam-5790	614	23	)	)	PUNCT
ejpam-5790	614	24	(	(	PUNCT
ejpam-5790	614	25	1−w	1−w	NUM
ejpam-5790	614	26	)	)	PUNCT
ejpam-5790	614	27	)	)	PUNCT
ejpam-5790	615	1	s	s	VERB
ejpam-5790	616	1	+	+	CCONJ
ejpam-5790	616	2	k	k	NOUN
ejpam-5790	616	3	)	)	PUNCT
ejpam-5790	616	4	∥∥ℑ′∥∥	∥∥ℑ′∥∥	NOUN
ejpam-5790	616	5	∆,+∞	∆,+∞	PROPN
ejpam-5790	616	6	)	)	PUNCT
ejpam-5790	616	7	]	]	PUNCT
ejpam-5790	616	8	.	.	PUNCT
ejpam-5790	617	1	(	(	PUNCT
ejpam-5790	617	2	3.21	3.21	NUM
ejpam-5790	617	3	)	)	PUNCT
ejpam-5790	617	4	w.	w.	PROPN
ejpam-5790	617	5	afzal	afzal	PROPN
ejpam-5790	617	6	et	et	PROPN
ejpam-5790	617	7	al	al	PROPN
ejpam-5790	617	8	.	.	PUNCT
ejpam-5790	617	9	/	/	SYM
ejpam-5790	617	10	eur	eur	PROPN
ejpam-5790	617	11	.	.	PUNCT
ejpam-5790	618	1	j.	j.	PROPN
ejpam-5790	618	2	pure	pure	PROPN
ejpam-5790	618	3	appl	appl	PROPN
ejpam-5790	618	4	.	.	PROPN
ejpam-5790	618	5	math	math	PROPN
ejpam-5790	618	6	,	,	PUNCT
ejpam-5790	618	7	18	18	NUM
ejpam-5790	618	8	(	(	PUNCT
ejpam-5790	618	9	1	1	NUM
ejpam-5790	618	10	)	)	PUNCT
ejpam-5790	618	11	(	(	PUNCT
ejpam-5790	618	12	2025	2025	NUM
ejpam-5790	618	13	)	)	PUNCT
ejpam-5790	618	14	,	,	PUNCT
ejpam-5790	618	15	5790	5790	NUM
ejpam-5790	618	16	23	23	NUM
ejpam-5790	618	17	of	of	ADP
ejpam-5790	618	18	30	30	NUM
ejpam-5790	618	19	using	use	VERB
ejpam-5790	618	20	equation	equation	NOUN
ejpam-5790	618	21	(	(	PUNCT
ejpam-5790	618	22	3.21	3.21	NUM
ejpam-5790	618	23	)	)	PUNCT
ejpam-5790	618	24	in	in	ADP
ejpam-5790	618	25	(	(	PUNCT
ejpam-5790	618	26	3.18	3.18	NUM
ejpam-5790	618	27	)	)	PUNCT
ejpam-5790	618	28	,	,	PUNCT
ejpam-5790	618	29	we	we	PRON
ejpam-5790	618	30	get	get	VERB
ejpam-5790	618	31	required	require	VERB
ejpam-5790	618	32	result	result	NOUN
ejpam-5790	618	33	.	.	PUNCT
ejpam-5790	619	1	theorem	theorem	ADJ
ejpam-5790	619	2	8	8	NUM
ejpam-5790	619	3	.	.	PUNCT
ejpam-5790	620	1	let	let	VERB
ejpam-5790	620	2	ℑ	ℑ	PRON
ejpam-5790	620	3	be	be	AUX
ejpam-5790	620	4	a	a	DET
ejpam-5790	620	5	twice	twice	ADV
ejpam-5790	620	6	differentiable	differentiable	ADJ
ejpam-5790	620	7	as	as	ADV
ejpam-5790	620	8	well	well	ADV
ejpam-5790	620	9	as	as	ADP
ejpam-5790	620	10	quasi	quasi	X
ejpam-5790	620	11	convex	convex	NOUN
ejpam-5790	620	12	|ℑ′′|	|ℑ′′|	X
ejpam-5790	620	13	on	on	ADP
ejpam-5790	620	14	∆	∆	PROPN
ejpam-5790	620	15	,	,	PUNCT
ejpam-5790	620	16	then	then	ADV
ejpam-5790	620	17	the	the	DET
ejpam-5790	620	18	following	follow	VERB
ejpam-5790	620	19	inequality	inequality	NOUN
ejpam-5790	620	20	holds	hold	VERB
ejpam-5790	620	21	true:∥∥∥∥∥	true:∥∥∥∥∥	NOUN
ejpam-5790	620	22	[	[	PUNCT
ejpam-5790	620	23	1	1	NUM
ejpam-5790	620	24	6	6	NUM
ejpam-5790	620	25	(	(	PUNCT
ejpam-5790	620	26	ℑ(u)⊗	ℑ(u)⊗	PROPN
ejpam-5790	620	27	1	1	NUM
ejpam-5790	620	28	)	)	PUNCT
ejpam-5790	620	29	+	+	CCONJ
ejpam-5790	620	30	2	2	NUM
ejpam-5790	620	31	3	3	NUM
ejpam-5790	620	32	ℑ	ℑ	NOUN
ejpam-5790	620	33	(	(	PUNCT
ejpam-5790	620	34	u	u	NOUN
ejpam-5790	620	35	⊗	⊗	PROPN
ejpam-5790	620	36	1	1	NUM
ejpam-5790	620	37	+	+	NUM
ejpam-5790	620	38	1⊗d	1⊗d	NUM
ejpam-5790	620	39	2	2	NUM
ejpam-5790	620	40	)	)	PUNCT
ejpam-5790	620	41	+	+	CCONJ
ejpam-5790	620	42	1	1	NUM
ejpam-5790	620	43	6	6	NUM
ejpam-5790	620	44	(	(	PUNCT
ejpam-5790	620	45	1⊗ℑ(d	1⊗ℑ(d	NUM
ejpam-5790	620	46	)	)	PUNCT
ejpam-5790	620	47	)	)	PUNCT
ejpam-5790	620	48	]	]	PUNCT
ejpam-5790	621	1	−	−	PROPN
ejpam-5790	621	2	[	[	PUNCT
ejpam-5790	621	3	ℑ	ℑ	PROPN
ejpam-5790	621	4	(	(	PUNCT
ejpam-5790	621	5	u	u	NOUN
ejpam-5790	621	6	⊗	⊗	PROPN
ejpam-5790	621	7	1	1	NUM
ejpam-5790	621	8	+	+	NUM
ejpam-5790	621	9	1⊗d	1⊗d	NUM
ejpam-5790	621	10	2	2	NUM
ejpam-5790	621	11	)	)	PUNCT
ejpam-5790	621	12	−	−	PROPN
ejpam-5790	622	1	w	w	PROPN
ejpam-5790	622	2	s	s	PROPN
ejpam-5790	622	3	k	k	X
ejpam-5790	622	4	(	(	PUNCT
ejpam-5790	622	5	ν2	ν2	NOUN
ejpam-5790	622	6	−	−	PROPN
ejpam-5790	622	7	ν1	ν1	NOUN
ejpam-5790	622	8	)	)	PUNCT
ejpam-5790	622	9	4	4	NUM
ejpam-5790	623	1	[	[	X
ejpam-5790	623	2	∫	∫	PROPN
ejpam-5790	623	3	1	1	NUM
ejpam-5790	623	4	0	0	NUM
ejpam-5790	623	5	ℑ′	ℑ′	X
ejpam-5790	623	6	(	(	PUNCT
ejpam-5790	623	7	(	(	PUNCT
ejpam-5790	623	8	1−w)u	1−w)u	NUM
ejpam-5790	623	9	⊗	⊗	NOUN
ejpam-5790	623	10	1	1	NUM
ejpam-5790	623	11	+	+	CCONJ
ejpam-5790	623	12	(	(	PUNCT
ejpam-5790	623	13	w1⊗d	w1⊗d	NOUN
ejpam-5790	623	14	2	2	NUM
ejpam-5790	623	15	)	)	PUNCT
ejpam-5790	623	16	)	)	PUNCT
ejpam-5790	623	17	dw	dw	NOUN
ejpam-5790	623	18	]	]	PUNCT
ejpam-5790	624	1	+	+	CCONJ
ejpam-5790	624	2	ℑ	ℑ	PROPN
ejpam-5790	624	3	(	(	PUNCT
ejpam-5790	624	4	u	u	NOUN
ejpam-5790	624	5	⊗	⊗	PROPN
ejpam-5790	624	6	1	1	NUM
ejpam-5790	624	7	+	+	NUM
ejpam-5790	624	8	1⊗d	1⊗d	NUM
ejpam-5790	624	9	2	2	NUM
ejpam-5790	624	10	)	)	PUNCT
ejpam-5790	624	11	−	−	PROPN
ejpam-5790	624	12	(	(	PUNCT
ejpam-5790	624	13	1−w	1−w	NUM
ejpam-5790	624	14	)	)	PUNCT
ejpam-5790	624	15	s	s	PART
ejpam-5790	624	16	k	k	X
ejpam-5790	624	17	(	(	PUNCT
ejpam-5790	624	18	ν2	ν2	NOUN
ejpam-5790	624	19	−	−	PROPN
ejpam-5790	624	20	ν1	ν1	NOUN
ejpam-5790	624	21	)	)	PUNCT
ejpam-5790	624	22	4	4	NUM
ejpam-5790	625	1	[	[	X
ejpam-5790	625	2	∫	∫	PROPN
ejpam-5790	625	3	1	1	NUM
ejpam-5790	625	4	0	0	NUM
ejpam-5790	625	5	ℑ′	ℑ′	X
ejpam-5790	625	6	(	(	PUNCT
ejpam-5790	625	7	(	(	PUNCT
ejpam-5790	625	8	1−w	1−w	NUM
ejpam-5790	625	9	2	2	NUM
ejpam-5790	625	10	)	)	PUNCT
ejpam-5790	625	11	u	u	NOUN
ejpam-5790	625	12	⊗	⊗	PROPN
ejpam-5790	625	13	1	1	NUM
ejpam-5790	625	14	+	+	CCONJ
ejpam-5790	625	15	(	(	PUNCT
ejpam-5790	625	16	1	1	NUM
ejpam-5790	625	17	+	+	NOUN
ejpam-5790	625	18	w	w	NOUN
ejpam-5790	625	19	2	2	NUM
ejpam-5790	625	20	)	)	PUNCT
ejpam-5790	625	21	1⊗d	1⊗d	PROPN
ejpam-5790	625	22	)	)	PUNCT
ejpam-5790	625	23	dw	dw	NOUN
ejpam-5790	625	24	]	]	PUNCT
ejpam-5790	625	25	∥∥∥∥∥	∥∥∥∥∥	PUNCT
ejpam-5790	625	26	≤	≤	ADV
ejpam-5790	625	27	∥(1⊗d	∥(1⊗d	NOUN
ejpam-5790	625	28	−	−	PROPN
ejpam-5790	625	29	u	u	NOUN
ejpam-5790	625	30	⊗	⊗	PROPN
ejpam-5790	625	31	1)2∥	1)2∥	NUM
ejpam-5790	625	32	6	6	NUM
ejpam-5790	625	33	(	(	PUNCT
ejpam-5790	625	34	k	k	X
ejpam-5790	625	35	(	(	PUNCT
ejpam-5790	625	36	4s	4s	NUM
ejpam-5790	625	37	+	+	NUM
ejpam-5790	625	38	8	8	NUM
ejpam-5790	625	39	k	k	NOUN
ejpam-5790	625	40	)	)	PUNCT
ejpam-5790	625	41	(	(	PUNCT
ejpam-5790	625	42	s	s	AUX
ejpam-5790	625	43	k	k	X
ejpam-5790	625	44	(	(	PUNCT
ejpam-5790	625	45	s	s	PROPN
ejpam-5790	625	46	+	+	CCONJ
ejpam-5790	625	47	k	k	PROPN
ejpam-5790	625	48	3	3	NUM
ejpam-5790	625	49	k	k	NOUN
ejpam-5790	625	50	)	)	PUNCT
ejpam-5790	625	51	2	2	NUM
ejpam-5790	626	1	k	k	NOUN
ejpam-5790	626	2	s	s	X
ejpam-5790	627	1	+	+	PROPN
ejpam-5790	627	2	3	3	NUM
ejpam-5790	627	3	k	k	NOUN
ejpam-5790	627	4	s	s	X
ejpam-5790	627	5	+	+	CCONJ
ejpam-5790	627	6	k	k	NOUN
ejpam-5790	627	7	)	)	PUNCT
ejpam-5790	628	1	−	−	PROPN
ejpam-5790	628	2	1	1	NUM
ejpam-5790	628	3	8	8	NUM
ejpam-5790	628	4	)	)	PUNCT
ejpam-5790	628	5	×	×	NOUN
ejpam-5790	628	6	∥∥∥∥12	∥∥∥∥12	NOUN
ejpam-5790	628	7	(	(	PUNCT
ejpam-5790	628	8	∣∣ℑ′′(u	∣∣ℑ′′(u	PROPN
ejpam-5790	628	9	)	)	PUNCT
ejpam-5790	628	10	∣∣⊗	∣∣⊗	NOUN
ejpam-5790	629	1	1	1	NUM
ejpam-5790	629	2	+	+	SYM
ejpam-5790	629	3	1⊗	1⊗	NUM
ejpam-5790	629	4	∣∣ℑ′′(d	∣∣ℑ′′(d	NOUN
ejpam-5790	629	5	)	)	PUNCT
ejpam-5790	629	6	∣∣+	∣∣+	NOUN
ejpam-5790	630	1	||ℑ′′(u)|	||ℑ′′(u)|	PROPN
ejpam-5790	630	2	⊗	⊗	PROPN
ejpam-5790	630	3	1−	1−	NUM
ejpam-5790	631	1	1⊗	1⊗	NUM
ejpam-5790	631	2	|ℑ′′(d)||	|ℑ′′(d)||	NUM
ejpam-5790	631	3	)	)	PUNCT
ejpam-5790	631	4	∥∥∥∥	∥∥∥∥	NUM
ejpam-5790	631	5	.	.	PUNCT
ejpam-5790	632	1	proof	proof	NOUN
ejpam-5790	632	2	.	.	PUNCT
ejpam-5790	633	1	as	as	ADP
ejpam-5790	633	2	|ℑ′′|	|ℑ′′|	PROPN
ejpam-5790	633	3	is	be	AUX
ejpam-5790	633	4	convex	convex	ADJ
ejpam-5790	633	5	in	in	ADP
ejpam-5790	633	6	a	a	DET
ejpam-5790	633	7	quasi	quasi	ADJ
ejpam-5790	633	8	sense	sense	NOUN
ejpam-5790	633	9	over	over	ADP
ejpam-5790	633	10	∆	∆	PROPN
ejpam-5790	633	11	,	,	PUNCT
ejpam-5790	633	12	then	then	ADV
ejpam-5790	633	13	one	one	NUM
ejpam-5790	633	14	has∣∣(ℑ′′	has∣∣(ℑ′′	NOUN
ejpam-5790	633	15	(	(	PUNCT
ejpam-5790	633	16	ν1w	ν1w	NOUN
ejpam-5790	633	17	+	+	NUM
ejpam-5790	633	18	ν1	ν1	NOUN
ejpam-5790	633	19	(	(	PUNCT
ejpam-5790	633	20	1−w))−ℑ′′	1−w))−ℑ′′	NUM
ejpam-5790	633	21	(	(	PUNCT
ejpam-5790	633	22	ν2w	ν2w	PROPN
ejpam-5790	633	23	+	+	CCONJ
ejpam-5790	633	24	ν2	ν2	PROPN
ejpam-5790	633	25	(	(	PUNCT
ejpam-5790	633	26	1−w	1−w	NUM
ejpam-5790	633	27	)	)	PUNCT
ejpam-5790	633	28	)	)	PUNCT
ejpam-5790	633	29	)	)	PUNCT
ejpam-5790	634	1	∣∣	∣∣	PROPN
ejpam-5790	634	2	≤	≤	ADV
ejpam-5790	634	3	∣∣(ℑ′′	∣∣(ℑ′′	PROPN
ejpam-5790	634	4	(	(	PUNCT
ejpam-5790	634	5	ν1w	ν1w	NOUN
ejpam-5790	634	6	+	+	NUM
ejpam-5790	634	7	ν1	ν1	NOUN
ejpam-5790	634	8	(	(	PUNCT
ejpam-5790	634	9	1−w	1−w	NUM
ejpam-5790	634	10	)	)	PUNCT
ejpam-5790	634	11	)	)	PUNCT
ejpam-5790	635	1	+	+	CCONJ
ejpam-5790	635	2	ℑ′′	ℑ′′	ADV
ejpam-5790	635	3	(	(	PUNCT
ejpam-5790	635	4	ν2w	ν2w	PROPN
ejpam-5790	635	5	+	+	CCONJ
ejpam-5790	635	6	ν2	ν2	PROPN
ejpam-5790	635	7	(	(	PUNCT
ejpam-5790	635	8	1−w	1−w	NUM
ejpam-5790	635	9	)	)	PUNCT
ejpam-5790	635	10	)	)	PUNCT
ejpam-5790	635	11	)	)	PUNCT
ejpam-5790	635	12	∣∣	∣∣	X
ejpam-5790	635	13	≤	≤	NUM
ejpam-5790	635	14	1	1	NUM
ejpam-5790	635	15	2	2	NUM
ejpam-5790	635	16	(	(	PUNCT
ejpam-5790	635	17	∣∣ℑ′′(ν2	∣∣ℑ′′(ν2	PROPN
ejpam-5790	635	18	)	)	PUNCT
ejpam-5790	635	19	∣∣+	∣∣+	NOUN
ejpam-5790	635	20	∣∣ℑ′′(ν1	∣∣ℑ′′(ν1	PROPN
ejpam-5790	635	21	)	)	PUNCT
ejpam-5790	635	22	∣∣+	∣∣+	NOUN
ejpam-5790	635	23	||ℑ′′(ν2)|	||ℑ′′(ν2)|	PROPN
ejpam-5790	635	24	−	−	PROPN
ejpam-5790	635	25	|ℑ′′(ν1)||	|ℑ′′(ν1)||	PROPN
ejpam-5790	635	26	)	)	PUNCT
ejpam-5790	635	27	∀	∀	PUNCT
ejpam-5790	636	1	τ	τ	X
ejpam-5790	636	2	∈	∈	PROPN
ejpam-5790	637	1	[	[	X
ejpam-5790	637	2	0	0	NUM
ejpam-5790	637	3	,	,	PUNCT
ejpam-5790	637	4	1	1	NUM
ejpam-5790	637	5	]	]	PUNCT
ejpam-5790	637	6	and	and	CCONJ
ejpam-5790	637	7	ν1	ν1	NOUN
ejpam-5790	637	8	,	,	PUNCT
ejpam-5790	637	9	ν2	ν2	NOUN
ejpam-5790	637	10	∈	∈	PROPN
ejpam-5790	638	1	∆.	∆.	NOUN
ejpam-5790	638	2	taking	take	VERB
ejpam-5790	638	3	∫	∫	PROPN
ejpam-5790	638	4	∆	∆	PROPN
ejpam-5790	638	5	∫	∫	PROPN
ejpam-5790	638	6	∆	∆	PROPN
ejpam-5790	638	7	over	over	ADP
ejpam-5790	638	8	deν1	deν1	PROPN
ejpam-5790	638	9	⊗	⊗	PROPN
ejpam-5790	638	10	dfν2	dfν2	PROPN
ejpam-5790	638	11	yields	yield	VERB
ejpam-5790	638	12	:	:	PUNCT
ejpam-5790	638	13	∣∣(ℑ′′	∣∣(ℑ′′	PROPN
ejpam-5790	638	14	(	(	PUNCT
ejpam-5790	638	15	1⊗	1⊗	NUM
ejpam-5790	638	16	uw	uw	PROPN
ejpam-5790	638	17	+	+	PROPN
ejpam-5790	638	18	1⊗	1⊗	NUM
ejpam-5790	638	19	u	u	NOUN
ejpam-5790	638	20	(	(	PUNCT
ejpam-5790	638	21	1−w))−ℑ′′	1−w))−ℑ′′	NUM
ejpam-5790	638	22	(	(	PUNCT
ejpam-5790	638	23	1⊗dw	1⊗dw	NUM
ejpam-5790	638	24	+	+	NUM
ejpam-5790	638	25	1⊗d	1⊗d	NUM
ejpam-5790	638	26	(	(	PUNCT
ejpam-5790	638	27	1−w	1−w	NUM
ejpam-5790	638	28	)	)	PUNCT
ejpam-5790	638	29	)	)	PUNCT
ejpam-5790	638	30	)	)	PUNCT
ejpam-5790	639	1	∣∣	∣∣	X
ejpam-5790	639	2	=	=	SYM
ejpam-5790	639	3	∫	∫	PROPN
ejpam-5790	639	4	∆	∆	PROPN
ejpam-5790	639	5	∫	∫	PROPN
ejpam-5790	639	6	∆	∆	PROPN
ejpam-5790	639	7	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5790	639	8	(	(	PUNCT
ejpam-5790	639	9	ℑ′′	ℑ′′	ADV
ejpam-5790	639	10	(	(	PUNCT
ejpam-5790	639	11	ν1w	ν1w	NOUN
ejpam-5790	639	12	+	+	NUM
ejpam-5790	639	13	ν1	ν1	NOUN
ejpam-5790	639	14	(	(	PUNCT
ejpam-5790	639	15	1−w))−ℑ′′	1−w))−ℑ′′	NUM
ejpam-5790	639	16	(	(	PUNCT
ejpam-5790	639	17	ν2w	ν2w	PROPN
ejpam-5790	639	18	+	+	CCONJ
ejpam-5790	639	19	ν2	ν2	PROPN
ejpam-5790	639	20	(	(	PUNCT
ejpam-5790	639	21	1−w	1−w	NUM
ejpam-5790	639	22	)	)	PUNCT
ejpam-5790	639	23	)	)	PUNCT
ejpam-5790	639	24	)	)	PUNCT
ejpam-5790	640	1	∣∣∣∣deν1	∣∣∣∣deν1	PROPN
ejpam-5790	640	2	⊗	⊗	PROPN
ejpam-5790	640	3	dfν2	dfν2	PROPN
ejpam-5790	640	4	≤	≤	NUM
ejpam-5790	640	5	1	1	NUM
ejpam-5790	640	6	2	2	NUM
ejpam-5790	640	7	∫	∫	NOUN
ejpam-5790	640	8	∆	∆	PROPN
ejpam-5790	640	9	∫	∫	PROPN
ejpam-5790	640	10	∆	∆	PROPN
ejpam-5790	640	11	(	(	PUNCT
ejpam-5790	640	12	∣∣ℑ′′(ν2	∣∣ℑ′′(ν2	PROPN
ejpam-5790	640	13	)	)	PUNCT
ejpam-5790	640	14	∣∣+	∣∣+	NOUN
ejpam-5790	640	15	∣∣ℑ′′(ν1	∣∣ℑ′′(ν1	PROPN
ejpam-5790	640	16	)	)	PUNCT
ejpam-5790	640	17	∣∣+	∣∣+	NOUN
ejpam-5790	641	1	||ℑ′′(ν2)|	||ℑ′′(ν2)|	PROPN
ejpam-5790	641	2	−	−	PROPN
ejpam-5790	641	3	|ℑ′′(ν1)||	|ℑ′′(ν1)||	PROPN
ejpam-5790	641	4	)	)	PUNCT
ejpam-5790	642	1	deν1	deν1	PROPN
ejpam-5790	642	2	⊗	⊗	PROPN
ejpam-5790	642	3	dfν2	dfν2	PROPN
ejpam-5790	642	4	=	=	NOUN
ejpam-5790	642	5	1	1	NUM
ejpam-5790	642	6	2	2	NUM
ejpam-5790	642	7	(	(	PUNCT
ejpam-5790	642	8	∣∣ℑ′′(u	∣∣ℑ′′(u	PROPN
ejpam-5790	642	9	)	)	PUNCT
ejpam-5790	642	10	∣∣⊗	∣∣⊗	NOUN
ejpam-5790	642	11	1	1	NUM
ejpam-5790	643	1	+	+	SYM
ejpam-5790	643	2	1⊗	1⊗	NUM
ejpam-5790	643	3	∣∣ℑ′′(d	∣∣ℑ′′(d	NOUN
ejpam-5790	643	4	)	)	PUNCT
ejpam-5790	643	5	∣∣+	∣∣+	NOUN
ejpam-5790	644	1	||ℑ′′(u)|	||ℑ′′(u)|	PROPN
ejpam-5790	644	2	⊗	⊗	PROPN
ejpam-5790	644	3	1−	1−	NUM
ejpam-5790	645	1	1⊗	1⊗	NUM
ejpam-5790	645	2	|ℑ′′(d)||	|ℑ′′(d)||	NUM
ejpam-5790	645	3	)	)	PUNCT
ejpam-5790	645	4	.	.	PUNCT
ejpam-5790	646	1	applying	apply	VERB
ejpam-5790	646	2	the	the	DET
ejpam-5790	646	3	norm	norm	NOUN
ejpam-5790	646	4	this	this	PRON
ejpam-5790	646	5	follows	follow	VERB
ejpam-5790	646	6	as	as	ADP
ejpam-5790	646	7	∥∥(ℑ′′	∥∥(ℑ′′	NOUN
ejpam-5790	646	8	(	(	PUNCT
ejpam-5790	646	9	1⊗	1⊗	NUM
ejpam-5790	646	10	uw	uw	PROPN
ejpam-5790	646	11	+	+	PROPN
ejpam-5790	646	12	1⊗	1⊗	NUM
ejpam-5790	646	13	u	u	NOUN
ejpam-5790	646	14	(	(	PUNCT
ejpam-5790	646	15	1−w))−ℑ′′	1−w))−ℑ′′	NUM
ejpam-5790	646	16	(	(	PUNCT
ejpam-5790	646	17	1⊗dw	1⊗dw	NUM
ejpam-5790	646	18	+	+	NUM
ejpam-5790	646	19	1⊗d	1⊗d	NUM
ejpam-5790	646	20	(	(	PUNCT
ejpam-5790	646	21	1−w	1−w	NUM
ejpam-5790	646	22	)	)	PUNCT
ejpam-5790	646	23	)	)	PUNCT
ejpam-5790	646	24	)	)	PUNCT
ejpam-5790	646	25	∥∥	∥∥	PROPN
ejpam-5790	646	26	≤	≤	ADJ
ejpam-5790	646	27	∥∥∥∥12	∥∥∥∥12	NOUN
ejpam-5790	646	28	(	(	PUNCT
ejpam-5790	646	29	∣∣ℑ′′(u	∣∣ℑ′′(u	PROPN
ejpam-5790	646	30	)	)	PUNCT
ejpam-5790	646	31	∣∣⊗	∣∣⊗	NOUN
ejpam-5790	646	32	1	1	NUM
ejpam-5790	646	33	+	+	SYM
ejpam-5790	646	34	1⊗	1⊗	NUM
ejpam-5790	646	35	∣∣ℑ′′(d	∣∣ℑ′′(d	NOUN
ejpam-5790	646	36	)	)	PUNCT
ejpam-5790	646	37	∣∣+	∣∣+	NOUN
ejpam-5790	647	1	||ℑ′′(u)|	||ℑ′′(u)|	PROPN
ejpam-5790	647	2	⊗	⊗	PROPN
ejpam-5790	647	3	1−	1−	NUM
ejpam-5790	648	1	1⊗	1⊗	NUM
ejpam-5790	648	2	|ℑ′′(d)||	|ℑ′′(d)||	NUM
ejpam-5790	648	3	)	)	PUNCT
ejpam-5790	649	1	∥∥∥∥	∥∥∥∥	PROPN
ejpam-5790	650	1	w.	w.	PROPN
ejpam-5790	650	2	afzal	afzal	PROPN
ejpam-5790	650	3	et	et	PROPN
ejpam-5790	650	4	al	al	PROPN
ejpam-5790	650	5	.	.	PUNCT
ejpam-5790	650	6	/	/	SYM
ejpam-5790	650	7	eur	eur	PROPN
ejpam-5790	650	8	.	.	PUNCT
ejpam-5790	651	1	j.	j.	PROPN
ejpam-5790	651	2	pure	pure	PROPN
ejpam-5790	651	3	appl	appl	PROPN
ejpam-5790	651	4	.	.	PROPN
ejpam-5790	651	5	math	math	PROPN
ejpam-5790	651	6	,	,	PUNCT
ejpam-5790	651	7	18	18	NUM
ejpam-5790	651	8	(	(	PUNCT
ejpam-5790	651	9	1	1	NUM
ejpam-5790	651	10	)	)	PUNCT
ejpam-5790	651	11	(	(	PUNCT
ejpam-5790	651	12	2025	2025	NUM
ejpam-5790	651	13	)	)	PUNCT
ejpam-5790	651	14	,	,	PUNCT
ejpam-5790	651	15	5790	5790	NUM
ejpam-5790	651	16	24	24	NUM
ejpam-5790	651	17	of	of	ADP
ejpam-5790	651	18	30	30	NUM
ejpam-5790	651	19	⩽	⩽	NOUN
ejpam-5790	651	20	1	1	NUM
ejpam-5790	651	21	2	2	NUM
ejpam-5790	651	22	(	(	PUNCT
ejpam-5790	651	23	∥∥∣∣ℑ′′(u	∥∥∣∣ℑ′′(u	NOUN
ejpam-5790	651	24	)	)	PUNCT
ejpam-5790	651	25	∣∣⊗	∣∣⊗	PROPN
ejpam-5790	652	1	1	1	NUM
ejpam-5790	652	2	+	+	SYM
ejpam-5790	652	3	1⊗	1⊗	NUM
ejpam-5790	652	4	∣∣ℑ′′(d	∣∣ℑ′′(d	PROPN
ejpam-5790	652	5	)	)	PUNCT
ejpam-5790	652	6	∣∣∥∥+	∣∣∥∥+	NUM
ejpam-5790	652	7	∥∥∣∣ℑ′′(u	∥∥∣∣ℑ′′(u	NOUN
ejpam-5790	652	8	)	)	PUNCT
ejpam-5790	652	9	∣∣⊗	∣∣⊗	PROPN
ejpam-5790	652	10	1−	1−	NUM
ejpam-5790	652	11	1⊗	1⊗	NUM
ejpam-5790	652	12	∣∣ℑ′′(d	∣∣ℑ′′(d	PROPN
ejpam-5790	652	13	)	)	PUNCT
ejpam-5790	652	14	∣∣∥∥	∣∣∥∥	PROPN
ejpam-5790	652	15	)	)	PUNCT
ejpam-5790	652	16	.	.	PUNCT
ejpam-5790	653	1	involving	involve	VERB
ejpam-5790	653	2	the	the	DET
ejpam-5790	653	3	norm	norm	NOUN
ejpam-5790	653	4	in	in	ADP
ejpam-5790	653	5	(	(	PUNCT
ejpam-5790	653	6	3.12	3.12	NUM
ejpam-5790	653	7	)	)	PUNCT
ejpam-5790	653	8	and	and	CCONJ
ejpam-5790	653	9	,	,	PUNCT
ejpam-5790	653	10	we	we	PRON
ejpam-5790	653	11	have	have	VERB
ejpam-5790	653	12	∥∥∥∥[16(ℑ(u)⊗	∥∥∥∥[16(ℑ(u)⊗	NOUN
ejpam-5790	653	13	1	1	NUM
ejpam-5790	653	14	)	)	PUNCT
ejpam-5790	653	15	+	+	CCONJ
ejpam-5790	653	16	2	2	NUM
ejpam-5790	653	17	3	3	NUM
ejpam-5790	653	18	ℑ	ℑ	NOUN
ejpam-5790	653	19	(	(	PUNCT
ejpam-5790	653	20	u	u	NOUN
ejpam-5790	653	21	⊗	⊗	PROPN
ejpam-5790	653	22	1	1	NUM
ejpam-5790	653	23	+	+	NUM
ejpam-5790	653	24	1⊗d	1⊗d	NUM
ejpam-5790	653	25	2	2	NUM
ejpam-5790	653	26	)	)	PUNCT
ejpam-5790	653	27	+	+	CCONJ
ejpam-5790	653	28	1	1	NUM
ejpam-5790	653	29	6	6	NUM
ejpam-5790	653	30	(	(	PUNCT
ejpam-5790	653	31	1⊗ℑ(d	1⊗ℑ(d	NUM
ejpam-5790	653	32	)	)	PUNCT
ejpam-5790	653	33	)	)	PUNCT
ejpam-5790	653	34	]	]	PUNCT
ejpam-5790	654	1	−	−	PROPN
ejpam-5790	654	2	[	[	PUNCT
ejpam-5790	654	3	ℑ	ℑ	PROPN
ejpam-5790	654	4	(	(	PUNCT
ejpam-5790	654	5	u	u	NOUN
ejpam-5790	654	6	⊗	⊗	PROPN
ejpam-5790	654	7	1	1	NUM
ejpam-5790	654	8	+	+	NUM
ejpam-5790	654	9	1⊗d	1⊗d	NUM
ejpam-5790	654	10	2	2	NUM
ejpam-5790	654	11	)	)	PUNCT
ejpam-5790	654	12	−	−	PROPN
ejpam-5790	655	1	w	w	PROPN
ejpam-5790	655	2	s	s	PROPN
ejpam-5790	655	3	k	k	X
ejpam-5790	655	4	(	(	PUNCT
ejpam-5790	655	5	ν2	ν2	NOUN
ejpam-5790	655	6	−	−	PROPN
ejpam-5790	655	7	ν1	ν1	NOUN
ejpam-5790	655	8	)	)	PUNCT
ejpam-5790	655	9	4	4	NUM
ejpam-5790	656	1	[	[	X
ejpam-5790	656	2	∫	∫	PROPN
ejpam-5790	656	3	1	1	NUM
ejpam-5790	656	4	0	0	NUM
ejpam-5790	656	5	ℑ′	ℑ′	X
ejpam-5790	656	6	(	(	PUNCT
ejpam-5790	656	7	(	(	PUNCT
ejpam-5790	656	8	1−w)u	1−w)u	NUM
ejpam-5790	656	9	⊗	⊗	NOUN
ejpam-5790	656	10	1	1	NUM
ejpam-5790	656	11	+	+	CCONJ
ejpam-5790	656	12	(	(	PUNCT
ejpam-5790	656	13	w1⊗d	w1⊗d	NOUN
ejpam-5790	656	14	2	2	NUM
ejpam-5790	656	15	)	)	PUNCT
ejpam-5790	656	16	)	)	PUNCT
ejpam-5790	656	17	dw	dw	NOUN
ejpam-5790	656	18	]	]	PUNCT
ejpam-5790	657	1	+	+	CCONJ
ejpam-5790	657	2	ℑ	ℑ	PROPN
ejpam-5790	657	3	(	(	PUNCT
ejpam-5790	657	4	u	u	NOUN
ejpam-5790	657	5	⊗	⊗	PROPN
ejpam-5790	657	6	1	1	NUM
ejpam-5790	657	7	+	+	NUM
ejpam-5790	657	8	1⊗d	1⊗d	NUM
ejpam-5790	657	9	2	2	NUM
ejpam-5790	657	10	)	)	PUNCT
ejpam-5790	657	11	−	−	PROPN
ejpam-5790	657	12	(	(	PUNCT
ejpam-5790	657	13	1−w	1−w	NUM
ejpam-5790	657	14	)	)	PUNCT
ejpam-5790	657	15	s	s	PART
ejpam-5790	657	16	k	k	X
ejpam-5790	657	17	(	(	PUNCT
ejpam-5790	657	18	ν2	ν2	NOUN
ejpam-5790	657	19	−	−	PROPN
ejpam-5790	657	20	ν1	ν1	NOUN
ejpam-5790	657	21	)	)	PUNCT
ejpam-5790	657	22	4	4	NUM
ejpam-5790	658	1	[	[	X
ejpam-5790	658	2	∫	∫	PROPN
ejpam-5790	658	3	1	1	NUM
ejpam-5790	658	4	0	0	NUM
ejpam-5790	658	5	ℑ′	ℑ′	X
ejpam-5790	658	6	(	(	PUNCT
ejpam-5790	658	7	(	(	PUNCT
ejpam-5790	658	8	1−w	1−w	NUM
ejpam-5790	658	9	2	2	NUM
ejpam-5790	658	10	)	)	PUNCT
ejpam-5790	658	11	u	u	NOUN
ejpam-5790	658	12	⊗	⊗	PROPN
ejpam-5790	658	13	1	1	NUM
ejpam-5790	658	14	+	+	CCONJ
ejpam-5790	658	15	(	(	PUNCT
ejpam-5790	658	16	1	1	NUM
ejpam-5790	658	17	+	+	NOUN
ejpam-5790	658	18	w	w	NOUN
ejpam-5790	658	19	2	2	NUM
ejpam-5790	658	20	)	)	PUNCT
ejpam-5790	658	21	1⊗d	1⊗d	PROPN
ejpam-5790	658	22	)	)	PUNCT
ejpam-5790	658	23	dw	dw	NOUN
ejpam-5790	658	24	]	]	PUNCT
ejpam-5790	658	25	∥∥∥∥∥	∥∥∥∥∥	PUNCT
ejpam-5790	658	26	≤	≤	ADV
ejpam-5790	658	27	∥(1⊗d	∥(1⊗d	NOUN
ejpam-5790	658	28	−	−	PROPN
ejpam-5790	658	29	u	u	NOUN
ejpam-5790	658	30	⊗	⊗	PROPN
ejpam-5790	658	31	1)2∥	1)2∥	NUM
ejpam-5790	658	32	6	6	NUM
ejpam-5790	658	33	(	(	PUNCT
ejpam-5790	658	34	∥∥∥∥∥	∥∥∥∥∥	NUM
ejpam-5790	658	35	∫	∫	PROPN
ejpam-5790	658	36	1	1	NUM
ejpam-5790	658	37	2	2	NUM
ejpam-5790	658	38	0	0	NUM
ejpam-5790	658	39	(	(	PUNCT
ejpam-5790	658	40	w	w	NOUN
ejpam-5790	658	41	−	−	PROPN
ejpam-5790	658	42	3k.2	3k.2	NUM
ejpam-5790	658	43	s	s	X
ejpam-5790	658	44	k	k	PROPN
ejpam-5790	658	45	w	w	PROPN
ejpam-5790	658	46	s+k	s+k	PROPN
ejpam-5790	658	47	k	k	PROPN
ejpam-5790	658	48	s	s	X
ejpam-5790	659	1	+	+	CCONJ
ejpam-5790	659	2	k	k	NOUN
ejpam-5790	659	3	)	)	PUNCT
ejpam-5790	659	4	[	[	PUNCT
ejpam-5790	659	5	ℑ′′	ℑ′′	ADV
ejpam-5790	659	6	(	(	PUNCT
ejpam-5790	659	7	u	u	NOUN
ejpam-5790	659	8	⊗	⊗	NOUN
ejpam-5790	659	9	1w	1w	VERB
ejpam-5790	659	10	+	+	CCONJ
ejpam-5790	659	11	1⊗	1⊗	NUM
ejpam-5790	659	12	u	u	NOUN
ejpam-5790	659	13	(	(	PUNCT
ejpam-5790	659	14	1−w	1−w	NUM
ejpam-5790	659	15	)	)	PUNCT
ejpam-5790	659	16	)	)	PUNCT
ejpam-5790	660	1	dw	dw	NOUN
ejpam-5790	660	2	]	]	PUNCT
ejpam-5790	661	1	+	+	CCONJ
ejpam-5790	661	2	∫	∫	PROPN
ejpam-5790	661	3	1	1	NUM
ejpam-5790	661	4	1	1	NUM
ejpam-5790	661	5	2	2	NUM
ejpam-5790	661	6	(	(	PUNCT
ejpam-5790	661	7	(	(	PUNCT
ejpam-5790	661	8	1−w)−	1−w)−	NUM
ejpam-5790	661	9	3k.2	3k.2	NUM
ejpam-5790	661	10	s	s	X
ejpam-5790	661	11	k	k	X
ejpam-5790	661	12	(	(	PUNCT
ejpam-5790	661	13	1−w	1−w	NUM
ejpam-5790	661	14	)	)	PUNCT
ejpam-5790	661	15	s+k	s+k	NOUN
ejpam-5790	662	1	k	k	PROPN
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ejpam-5790	663	1	+	+	X
ejpam-5790	663	2	k	k	X
ejpam-5790	663	3	)	)	PUNCT
ejpam-5790	663	4	ℑ′′	ℑ′′	ADV
ejpam-5790	663	5	(	(	PUNCT
ejpam-5790	663	6	u	u	PROPN
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ejpam-5790	663	8	1w	1w	VERB
ejpam-5790	663	9	+	+	CCONJ
ejpam-5790	663	10	1⊗	1⊗	NUM
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ejpam-5790	663	13	1−w	1−w	NUM
ejpam-5790	663	14	)	)	PUNCT
ejpam-5790	663	15	)	)	PUNCT
ejpam-5790	663	16	∥∥∥∥∥	∥∥∥∥∥	NUM
ejpam-5790	663	17	)	)	PUNCT
ejpam-5790	664	1	≤	≤	PUNCT
ejpam-5790	665	1	∥(1⊗d	∥(1⊗d	NOUN
ejpam-5790	665	2	−	−	PROPN
ejpam-5790	665	3	u	u	NOUN
ejpam-5790	665	4	⊗	⊗	NOUN
ejpam-5790	665	5	1)2∥	1)2∥	NUM
ejpam-5790	665	6	6	6	NUM
ejpam-5790	665	7	×	×	NOUN
ejpam-5790	665	8	(	(	PUNCT
ejpam-5790	665	9	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-5790	665	10	∫	∫	PROPN
ejpam-5790	665	11	1	1	NUM
ejpam-5790	665	12	2	2	NUM
ejpam-5790	665	13	0	0	NUM
ejpam-5790	665	14	(	(	PUNCT
ejpam-5790	665	15	w	w	NOUN
ejpam-5790	665	16	−	−	PROPN
ejpam-5790	665	17	3k.2	3k.2	NUM
ejpam-5790	665	18	s	s	X
ejpam-5790	665	19	k	k	PROPN
ejpam-5790	665	20	w	w	PROPN
ejpam-5790	665	21	s+k	s+k	PROPN
ejpam-5790	665	22	k	k	PROPN
ejpam-5790	665	23	s	s	X
ejpam-5790	665	24	+	+	CCONJ
ejpam-5790	665	25	k	k	X
ejpam-5790	665	26	)	)	PUNCT
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ejpam-5790	665	28	1	1	NUM
ejpam-5790	665	29	2	2	NUM
ejpam-5790	665	30	(	(	PUNCT
ejpam-5790	665	31	∣∣ℑ′′(u	∣∣ℑ′′(u	PROPN
ejpam-5790	665	32	)	)	PUNCT
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ejpam-5790	666	1	1	1	NUM
ejpam-5790	666	2	+	+	SYM
ejpam-5790	666	3	1⊗	1⊗	NUM
ejpam-5790	666	4	∣∣ℑ′′(d	∣∣ℑ′′(d	NOUN
ejpam-5790	666	5	)	)	PUNCT
ejpam-5790	666	6	∣∣+	∣∣+	NOUN
ejpam-5790	667	1	||ℑ′′(u)|	||ℑ′′(u)|	PROPN
ejpam-5790	667	2	⊗	⊗	PROPN
ejpam-5790	667	3	1−	1−	NUM
ejpam-5790	668	1	1⊗	1⊗	NUM
ejpam-5790	668	2	|ℑ′′(d)||	|ℑ′′(d)||	NUM
ejpam-5790	668	3	)	)	PUNCT
ejpam-5790	669	1	+	+	CCONJ
ejpam-5790	669	2	∫	∫	PROPN
ejpam-5790	669	3	1	1	NUM
ejpam-5790	669	4	1	1	NUM
ejpam-5790	669	5	2	2	NUM
ejpam-5790	669	6	(	(	PUNCT
ejpam-5790	669	7	(	(	PUNCT
ejpam-5790	669	8	1−w)−	1−w)−	NUM
ejpam-5790	669	9	3k.2	3k.2	NUM
ejpam-5790	669	10	s	s	X
ejpam-5790	669	11	k	k	X
ejpam-5790	669	12	(	(	PUNCT
ejpam-5790	669	13	1−w	1−w	NUM
ejpam-5790	669	14	)	)	PUNCT
ejpam-5790	669	15	s+k	s+k	NOUN
ejpam-5790	670	1	k	k	PROPN
ejpam-5790	670	2	s	s	X
ejpam-5790	670	3	+	+	CCONJ
ejpam-5790	670	4	k	k	X
ejpam-5790	670	5	)	)	PUNCT
ejpam-5790	670	6	dw	dw	PROPN
ejpam-5790	670	7	×	×	NOUN
ejpam-5790	670	8	1	1	NUM
ejpam-5790	670	9	2	2	NUM
ejpam-5790	670	10	(	(	PUNCT
ejpam-5790	670	11	∣∣ℑ′′(u	∣∣ℑ′′(u	PROPN
ejpam-5790	670	12	)	)	PUNCT
ejpam-5790	670	13	∣∣⊗	∣∣⊗	NOUN
ejpam-5790	671	1	1	1	NUM
ejpam-5790	671	2	+	+	SYM
ejpam-5790	671	3	1⊗	1⊗	NUM
ejpam-5790	671	4	∣∣ℑ′′(d	∣∣ℑ′′(d	NOUN
ejpam-5790	671	5	)	)	PUNCT
ejpam-5790	671	6	∣∣+	∣∣+	NOUN
ejpam-5790	672	1	||ℑ′′(u)|	||ℑ′′(u)|	PROPN
ejpam-5790	672	2	⊗	⊗	PROPN
ejpam-5790	672	3	1−	1−	NUM
ejpam-5790	673	1	1⊗	1⊗	NUM
ejpam-5790	673	2	|ℑ′′(d)||	|ℑ′′(d)||	NUM
ejpam-5790	673	3	)	)	PUNCT
ejpam-5790	673	4	∥∥∥∥∥	∥∥∥∥∥	NUM
ejpam-5790	673	5	)	)	PUNCT
ejpam-5790	674	1	≤	≤	PUNCT
ejpam-5790	675	1	∥(1⊗d	∥(1⊗d	NOUN
ejpam-5790	675	2	−	−	PROPN
ejpam-5790	675	3	u	u	NOUN
ejpam-5790	675	4	⊗	⊗	PROPN
ejpam-5790	675	5	1)∥	1)∥	NUM
ejpam-5790	675	6	6	6	NUM
ejpam-5790	675	7	∥∥∥∥∥	∥∥∥∥∥	NUM
ejpam-5790	675	8	(	(	PUNCT
ejpam-5790	675	9	1	1	NUM
ejpam-5790	675	10	(	(	PUNCT
ejpam-5790	675	11	4s	4s	NUM
ejpam-5790	675	12	+	+	NOUN
ejpam-5790	675	13	4	4	NUM
ejpam-5790	675	14	)	)	PUNCT
ejpam-5790	675	15	(	(	PUNCT
ejpam-5790	675	16	s	s	X
ejpam-5790	675	17	(	(	PUNCT
ejpam-5790	675	18	s	s	VERB
ejpam-5790	675	19	+	+	CCONJ
ejpam-5790	675	20	4	4	NUM
ejpam-5790	675	21	2	2	NUM
ejpam-5790	675	22	)	)	PUNCT
ejpam-5790	675	23	3	3	NUM
ejpam-5790	675	24	2s	2s	NOUN
ejpam-5790	676	1	+	+	NOUN
ejpam-5790	676	2	3	3	NUM
ejpam-5790	676	3	2s	2s	NUM
ejpam-5790	676	4	+	+	NOUN
ejpam-5790	676	5	2	2	NUM
ejpam-5790	676	6	)	)	PUNCT
ejpam-5790	676	7	−	−	NOUN
ejpam-5790	676	8	1	1	NUM
ejpam-5790	676	9	8	8	NUM
ejpam-5790	676	10	)	)	PUNCT
ejpam-5790	676	11	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-5790	677	1	×	×	NOUN
ejpam-5790	677	2	∥∥∥∥12	∥∥∥∥12	NOUN
ejpam-5790	677	3	(	(	PUNCT
ejpam-5790	677	4	∣∣ℑ′′(u	∣∣ℑ′′(u	PROPN
ejpam-5790	677	5	)	)	PUNCT
ejpam-5790	677	6	∣∣⊗	∣∣⊗	NOUN
ejpam-5790	677	7	1	1	NUM
ejpam-5790	677	8	+	+	SYM
ejpam-5790	677	9	1⊗	1⊗	NUM
ejpam-5790	677	10	∣∣ℑ′′(d	∣∣ℑ′′(d	NOUN
ejpam-5790	677	11	)	)	PUNCT
ejpam-5790	677	12	∣∣+	∣∣+	NOUN
ejpam-5790	678	1	||ℑ′′(u)|	||ℑ′′(u)|	PROPN
ejpam-5790	678	2	⊗	⊗	PROPN
ejpam-5790	678	3	1−	1−	NUM
ejpam-5790	679	1	1⊗	1⊗	NUM
ejpam-5790	679	2	|ℑ′′(d)||	|ℑ′′(d)||	NUM
ejpam-5790	679	3	)	)	PUNCT
ejpam-5790	679	4	∥∥∥∥	∥∥∥∥	PUNCT
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ejpam-5790	680	9	(	(	PUNCT
ejpam-5790	680	10	k	k	X
ejpam-5790	680	11	(	(	PUNCT
ejpam-5790	680	12	4s	4s	NUM
ejpam-5790	680	13	+	+	NUM
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ejpam-5790	680	15	k	k	NOUN
ejpam-5790	680	16	)	)	PUNCT
ejpam-5790	680	17	(	(	PUNCT
ejpam-5790	680	18	s	s	AUX
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ejpam-5790	680	20	(	(	PUNCT
ejpam-5790	680	21	s	s	PROPN
ejpam-5790	680	22	+	+	CCONJ
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ejpam-5790	680	24	3	3	NUM
ejpam-5790	680	25	k	k	NOUN
ejpam-5790	680	26	)	)	PUNCT
ejpam-5790	680	27	2	2	NUM
ejpam-5790	681	1	k	k	NOUN
ejpam-5790	681	2	s	s	X
ejpam-5790	682	1	+	+	PROPN
ejpam-5790	682	2	3	3	NUM
ejpam-5790	682	3	k	k	NOUN
ejpam-5790	682	4	s	s	X
ejpam-5790	682	5	+	+	X
ejpam-5790	682	6	k	k	X
ejpam-5790	682	7	)	)	PUNCT
ejpam-5790	683	1	+	+	CCONJ
ejpam-5790	683	2	1	1	NUM
ejpam-5790	683	3	8	8	NUM
ejpam-5790	683	4	)	)	PUNCT
ejpam-5790	683	5	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-5790	683	6	×	×	PROPN
ejpam-5790	683	7	∥∥(∣∣ℑ′′(u	∥∥(∣∣ℑ′′(u	NOUN
ejpam-5790	683	8	)	)	PUNCT
ejpam-5790	683	9	∣∣⊗	∣∣⊗	NOUN
ejpam-5790	684	1	1	1	NUM
ejpam-5790	684	2	+	+	SYM
ejpam-5790	684	3	1⊗	1⊗	NUM
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ejpam-5790	684	5	)	)	PUNCT
ejpam-5790	684	6	∣∣+	∣∣+	NOUN
ejpam-5790	685	1	||ℑ′′(u)|	||ℑ′′(u)|	PROPN
ejpam-5790	685	2	⊗	⊗	NUM
ejpam-5790	685	3	1	1	NUM
ejpam-5790	686	1	+	+	SYM
ejpam-5790	686	2	1⊗	1⊗	NUM
ejpam-5790	686	3	|ℑ′′(d)||	|ℑ′′(d)||	NUM
ejpam-5790	686	4	)	)	PUNCT
ejpam-5790	686	5	∥∥	∥∥	X
ejpam-5790	687	1	=	=	SYM
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ejpam-5790	687	3	−	−	PROPN
ejpam-5790	687	4	u	u	NOUN
ejpam-5790	687	5	⊗	⊗	NOUN
ejpam-5790	687	6	1)2∥	1)2∥	NUM
ejpam-5790	687	7	12	12	NUM
ejpam-5790	687	8	(	(	PUNCT
ejpam-5790	687	9	s(s	s(s	PROPN
ejpam-5790	687	10	+	+	CCONJ
ejpam-5790	687	11	k	k	X
ejpam-5790	687	12	)	)	PUNCT
ejpam-5790	687	13	a+2k	a+2k	PROPN
ejpam-5790	687	14	s	s	PART
ejpam-5790	687	15	+	+	NUM
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ejpam-5790	687	17	s+2k	s+2k	PROPN
ejpam-5790	687	18	a	a	PRON
ejpam-5790	687	19	k	k	NOUN
ejpam-5790	687	20	2s+2k	2s+2k	NUM
ejpam-5790	687	21	s	s	PART
ejpam-5790	687	22	4	4	NUM
ejpam-5790	687	23	·	·	SYM
ejpam-5790	687	24	3	3	NUM
ejpam-5790	687	25	2k	2k	PROPN
ejpam-5790	687	26	s	s	PART
ejpam-5790	687	27	k	k	PROPN
ejpam-5790	687	28	2k	2k	PROPN
ejpam-5790	687	29	s	s	X
ejpam-5790	687	30	(	(	PUNCT
ejpam-5790	687	31	s	s	PART
ejpam-5790	687	32	+	+	CCONJ
ejpam-5790	687	33	k)(s	k)(s	NOUN
ejpam-5790	687	34	+	+	CCONJ
ejpam-5790	687	35	2k	2k	NUM
ejpam-5790	687	36	)	)	PUNCT
ejpam-5790	688	1	+	+	CCONJ
ejpam-5790	688	2	1	1	NUM
ejpam-5790	688	3	8	8	NUM
ejpam-5790	688	4	)	)	PUNCT
ejpam-5790	688	5	×	×	NOUN
ejpam-5790	688	6	∥∥(∣∣ℑ′′(u	∥∥(∣∣ℑ′′(u	NOUN
ejpam-5790	688	7	)	)	PUNCT
ejpam-5790	688	8	∣∣⊗	∣∣⊗	NOUN
ejpam-5790	689	1	1	1	NUM
ejpam-5790	689	2	+	+	SYM
ejpam-5790	689	3	1⊗	1⊗	NUM
ejpam-5790	689	4	∣∣ℑ′′(d	∣∣ℑ′′(d	NOUN
ejpam-5790	689	5	)	)	PUNCT
ejpam-5790	689	6	∣∣+	∣∣+	NOUN
ejpam-5790	690	1	||ℑ′′(u)|	||ℑ′′(u)|	PROPN
ejpam-5790	690	2	⊗	⊗	NUM
ejpam-5790	690	3	1	1	NUM
ejpam-5790	691	1	+	+	SYM
ejpam-5790	691	2	1⊗	1⊗	NUM
ejpam-5790	691	3	|ℑ′′(d)||	|ℑ′′(d)||	NUM
ejpam-5790	691	4	)	)	PUNCT
ejpam-5790	691	5	∥∥	∥∥	X
ejpam-5790	691	6	.	.	PUNCT
ejpam-5790	692	1	(	(	PUNCT
ejpam-5790	692	2	3.22	3.22	NUM
ejpam-5790	692	3	)	)	PUNCT
ejpam-5790	692	4	remark	remark	NOUN
ejpam-5790	692	5	3	3	NUM
ejpam-5790	692	6	.	.	NOUN
ejpam-5790	692	7	•	•	NOUN
ejpam-5790	692	8	setting	set	VERB
ejpam-5790	692	9	s	s	PART
ejpam-5790	692	10	=	=	SYM
ejpam-5790	692	11	1	1	NUM
ejpam-5790	692	12	in	in	ADP
ejpam-5790	692	13	theorem	theorem	NOUN
ejpam-5790	692	14	8	8	NUM
ejpam-5790	692	15	,	,	PUNCT
ejpam-5790	692	16	then	then	ADV
ejpam-5790	692	17	it	it	PRON
ejpam-5790	692	18	strained	strain	VERB
ejpam-5790	692	19	theorem	theorem	VERB
ejpam-5790	692	20	2.4	2.4	NUM
ejpam-5790	692	21	in	in	ADP
ejpam-5790	692	22	[	[	X
ejpam-5790	692	23	57	57	NUM
ejpam-5790	692	24	]	]	PUNCT
ejpam-5790	692	25	.	.	PUNCT
ejpam-5790	693	1	w.	w.	PROPN
ejpam-5790	693	2	afzal	afzal	PROPN
ejpam-5790	693	3	et	et	PROPN
ejpam-5790	693	4	al	al	PROPN
ejpam-5790	693	5	.	.	PUNCT
ejpam-5790	693	6	/	/	SYM
ejpam-5790	693	7	eur	eur	PROPN
ejpam-5790	693	8	.	.	PUNCT
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ejpam-5790	694	4	.	.	PROPN
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ejpam-5790	694	6	,	,	PUNCT
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ejpam-5790	694	8	(	(	PUNCT
ejpam-5790	694	9	1	1	NUM
ejpam-5790	694	10	)	)	PUNCT
ejpam-5790	694	11	(	(	PUNCT
ejpam-5790	694	12	2025	2025	NUM
ejpam-5790	694	13	)	)	PUNCT
ejpam-5790	694	14	,	,	PUNCT
ejpam-5790	694	15	5790	5790	NUM
ejpam-5790	694	16	25	25	NUM
ejpam-5790	694	17	of	of	ADP
ejpam-5790	694	18	30	30	NUM
ejpam-5790	694	19	•	•	NOUN
ejpam-5790	694	20	setting	set	VERB
ejpam-5790	694	21	s	s	PART
ejpam-5790	694	22	=	=	SYM
ejpam-5790	694	23	1	1	NUM
ejpam-5790	694	24	in	in	ADP
ejpam-5790	694	25	theorem	theorem	NOUN
ejpam-5790	694	26	8	8	NUM
ejpam-5790	694	27	,	,	PUNCT
ejpam-5790	694	28	then	then	ADV
ejpam-5790	694	29	it	it	PRON
ejpam-5790	694	30	strained	strain	VERB
ejpam-5790	694	31	theorem	theorem	VERB
ejpam-5790	694	32	2.4	2.4	NUM
ejpam-5790	694	33	in	in	ADP
ejpam-5790	694	34	[	[	X
ejpam-5790	694	35	2	2	NUM
ejpam-5790	694	36	]	]	PUNCT
ejpam-5790	694	37	.	.	PUNCT
ejpam-5790	695	1	•	•	NUM
ejpam-5790	696	1	setting	set	VERB
ejpam-5790	696	2	s	s	PART
ejpam-5790	696	3	=	=	SYM
ejpam-5790	696	4	1	1	NUM
ejpam-5790	696	5	in	in	ADP
ejpam-5790	696	6	theorem	theorem	NOUN
ejpam-5790	696	7	8	8	NUM
ejpam-5790	696	8	,	,	PUNCT
ejpam-5790	696	9	then	then	ADV
ejpam-5790	696	10	it	it	PRON
ejpam-5790	696	11	strained	strain	VERB
ejpam-5790	696	12	theorem	theorem	VERB
ejpam-5790	696	13	10	10	NUM
ejpam-5790	696	14	in	in	ADP
ejpam-5790	696	15	[	[	X
ejpam-5790	696	16	58	58	NUM
ejpam-5790	696	17	]	]	PUNCT
ejpam-5790	696	18	.	.	PUNCT
ejpam-5790	697	1	4	4	X
ejpam-5790	697	2	.	.	X
ejpam-5790	697	3	examples	example	NOUN
ejpam-5790	697	4	and	and	CCONJ
ejpam-5790	697	5	consequences	consequence	NOUN
ejpam-5790	697	6	for	for	ADP
ejpam-5790	697	7	an	an	DET
ejpam-5790	697	8	exponential	exponential	ADJ
ejpam-5790	697	9	function	function	NOUN
ejpam-5790	697	10	,	,	PUNCT
ejpam-5790	697	11	if	if	SCONJ
ejpam-5790	697	12	self	self	NOUN
ejpam-5790	697	13	-	-	PUNCT
ejpam-5790	697	14	adjoint	adjoint	NOUN
ejpam-5790	697	15	operators	operator	NOUN
ejpam-5790	697	16	u	u	PROPN
ejpam-5790	697	17	and	and	CCONJ
ejpam-5790	697	18	d	d	PROPN
ejpam-5790	697	19	are	be	AUX
ejpam-5790	697	20	commute	commute	NOUN
ejpam-5790	697	21	,	,	PUNCT
ejpam-5790	697	22	then	then	ADV
ejpam-5790	697	23	we	we	PRON
ejpam-5790	697	24	have	have	AUX
ejpam-5790	697	25	eued	eue	VERB
ejpam-5790	697	26	=	=	SYM
ejpam-5790	697	27	edeu	edeu	NOUN
ejpam-5790	697	28	=	=	SYM
ejpam-5790	697	29	e(u+d	e(u+d	PROPN
ejpam-5790	697	30	)	)	PUNCT
ejpam-5790	697	31	.	.	PUNCT
ejpam-5790	698	1	further	far	ADV
ejpam-5790	698	2	,	,	PUNCT
ejpam-5790	698	3	if	if	SCONJ
ejpam-5790	698	4	u	u	NOUN
ejpam-5790	698	5	is	be	AUX
ejpam-5790	698	6	invertible	invertible	ADJ
ejpam-5790	698	7	and	and	CCONJ
ejpam-5790	698	8	ν1	ν1	NOUN
ejpam-5790	698	9	,	,	PUNCT
ejpam-5790	698	10	ν2	ν2	NOUN
ejpam-5790	698	11	∈	∈	NOUN
ejpam-5790	698	12	r	r	NOUN
ejpam-5790	698	13	with	with	ADP
ejpam-5790	698	14	ν1	ν1	NOUN
ejpam-5790	698	15	<	<	X
ejpam-5790	698	16	ν2	ν2	NOUN
ejpam-5790	698	17	,	,	PUNCT
ejpam-5790	698	18	then∫	then∫	NOUN
ejpam-5790	698	19	ν2	ν2	ADJ
ejpam-5790	698	20	ν1	ν1	NOUN
ejpam-5790	698	21	ewudw	ewudw	NOUN
ejpam-5790	698	22	=	=	PUNCT
ejpam-5790	699	1	[	[	PUNCT
ejpam-5790	699	2	eν2u	eν2u	ADJ
ejpam-5790	699	3	−	−	PROPN
ejpam-5790	699	4	eν1u	eν1u	NOUN
ejpam-5790	699	5	]	]	PUNCT
ejpam-5790	699	6	u	u	NOUN
ejpam-5790	699	7	.	.	PUNCT
ejpam-5790	700	1	further	far	ADV
ejpam-5790	700	2	if	if	SCONJ
ejpam-5790	700	3	d	d	PROPN
ejpam-5790	700	4	−	−	X
ejpam-5790	700	5	u	u	NOUN
ejpam-5790	700	6	is	be	AUX
ejpam-5790	700	7	invertible	invertible	ADJ
ejpam-5790	700	8	,	,	PUNCT
ejpam-5790	700	9	then	then	ADV
ejpam-5790	700	10	we	we	PRON
ejpam-5790	700	11	have∫	have∫	VERB
ejpam-5790	700	12	1	1	NUM
ejpam-5790	700	13	0	0	NUM
ejpam-5790	700	14	e((1−ν2)u+sd)ds	e((1−ν2)u+sd)ds	PROPN
ejpam-5790	700	15	=	=	SYM
ejpam-5790	701	1	∫	∫	PROPN
ejpam-5790	701	2	1	1	NUM
ejpam-5790	701	3	0	0	X
ejpam-5790	701	4	e(s(d−u))euds	e(s(d−u))euds	ADJ
ejpam-5790	701	5	=	=	SYM
ejpam-5790	701	6	(	(	PUNCT
ejpam-5790	701	7	∫	∫	PROPN
ejpam-5790	701	8	1	1	NUM
ejpam-5790	701	9	0	0	NUM
ejpam-5790	701	10	e(s(d−u))ds	e(s(d−u))ds	NOUN
ejpam-5790	701	11	)	)	PUNCT
ejpam-5790	701	12	eu	eu	PROPN
ejpam-5790	702	1	=	=	PUNCT
ejpam-5790	702	2	[	[	X
ejpam-5790	702	3	e(d−u	e(d−u	NOUN
ejpam-5790	702	4	)	)	PUNCT
ejpam-5790	702	5	−	−	ADP
ejpam-5790	702	6	i]eu	i]eu	NOUN
ejpam-5790	703	1	d	d	NOUN
ejpam-5790	703	2	−	−	NOUN
ejpam-5790	703	3	u	u	NOUN
ejpam-5790	703	4	=	=	PUNCT
ejpam-5790	704	1	[	[	X
ejpam-5790	704	2	ed	ed	NOUN
ejpam-5790	704	3	−	−	PROPN
ejpam-5790	704	4	eu	eu	PROPN
ejpam-5790	704	5	]	]	PUNCT
ejpam-5790	705	1	d	d	X
ejpam-5790	705	2	−	−	PROPN
ejpam-5790	705	3	u	u	PROPN
ejpam-5790	705	4	.	.	PUNCT
ejpam-5790	706	1	corollary	corollary	ADJ
ejpam-5790	706	2	4.1	4.1	NUM
ejpam-5790	706	3	.	.	PUNCT
ejpam-5790	707	1	assume	assume	VERB
ejpam-5790	707	2	the	the	DET
ejpam-5790	707	3	identical	identical	ADJ
ejpam-5790	707	4	hypothesis	hypothesis	NOUN
ejpam-5790	707	5	of	of	ADP
ejpam-5790	707	6	theorem	theorem	NOUN
ejpam-5790	707	7	7	7	NUM
ejpam-5790	707	8	with	with	ADP
ejpam-5790	707	9	ℑ(µ	ℑ(µ	NOUN
ejpam-5790	707	10	)	)	PUNCT
ejpam-5790	708	1	=	=	VERB
ejpam-5790	708	2	lnµ	lnµ	NOUN
ejpam-5790	708	3	over	over	ADP
ejpam-5790	708	4	∆	∆	PROPN
ejpam-5790	708	5	,	,	PUNCT
ejpam-5790	708	6	and	and	CCONJ
ejpam-5790	708	7	s	s	VERB
ejpam-5790	708	8	=	=	SYM
ejpam-5790	708	9	1	1	NUM
ejpam-5790	708	10	5	5	NUM
ejpam-5790	708	11	,	,	PUNCT
ejpam-5790	708	12	k	k	PROPN
ejpam-5790	708	13	=	=	SYM
ejpam-5790	708	14	1	1	NUM
ejpam-5790	708	15	2	2	NUM
ejpam-5790	708	16	,	,	PUNCT
ejpam-5790	708	17	then	then	ADV
ejpam-5790	708	18	∥∥∥∥∥	∥∥∥∥∥	X
ejpam-5790	708	19	[	[	PUNCT
ejpam-5790	708	20	1	1	NUM
ejpam-5790	708	21	6	6	NUM
ejpam-5790	708	22	(	(	PUNCT
ejpam-5790	708	23	lnµ(u)⊗	lnµ(u)⊗	X
ejpam-5790	708	24	1	1	NUM
ejpam-5790	708	25	)	)	PUNCT
ejpam-5790	708	26	+	+	CCONJ
ejpam-5790	708	27	2	2	NUM
ejpam-5790	708	28	3	3	NUM
ejpam-5790	708	29	lnµ	lnµ	NOUN
ejpam-5790	708	30	(	(	PUNCT
ejpam-5790	708	31	u	u	NOUN
ejpam-5790	708	32	⊗	⊗	PROPN
ejpam-5790	708	33	1	1	NUM
ejpam-5790	708	34	+	+	NUM
ejpam-5790	708	35	1⊗d	1⊗d	NUM
ejpam-5790	708	36	2	2	NUM
ejpam-5790	708	37	)	)	PUNCT
ejpam-5790	708	38	+	+	CCONJ
ejpam-5790	708	39	1	1	NUM
ejpam-5790	708	40	6	6	NUM
ejpam-5790	708	41	(	(	PUNCT
ejpam-5790	708	42	1⊗	1⊗	NUM
ejpam-5790	708	43	lnµ(d	lnµ(d	PROPN
ejpam-5790	708	44	)	)	PUNCT
ejpam-5790	708	45	)	)	PUNCT
ejpam-5790	708	46	]	]	PUNCT
ejpam-5790	709	1	−	−	PROPN
ejpam-5790	709	2	[	[	PUNCT
ejpam-5790	709	3	lnµ	lnµ	NOUN
ejpam-5790	709	4	(	(	PUNCT
ejpam-5790	709	5	u	u	NOUN
ejpam-5790	709	6	⊗	⊗	PROPN
ejpam-5790	709	7	1	1	NUM
ejpam-5790	709	8	+	+	NUM
ejpam-5790	709	9	1⊗d	1⊗d	NUM
ejpam-5790	709	10	2	2	NUM
ejpam-5790	709	11	)	)	PUNCT
ejpam-5790	710	1	−	−	PROPN
ejpam-5790	710	2	w	w	NOUN
ejpam-5790	710	3	2	2	NUM
ejpam-5790	710	4	5	5	NUM
ejpam-5790	710	5	(	(	PUNCT
ejpam-5790	710	6	ν2	ν2	NOUN
ejpam-5790	710	7	−	−	PROPN
ejpam-5790	710	8	ν1	ν1	NOUN
ejpam-5790	710	9	)	)	PUNCT
ejpam-5790	710	10	4	4	NUM
ejpam-5790	711	1	[	[	X
ejpam-5790	711	2	∫	∫	PROPN
ejpam-5790	711	3	1	1	NUM
ejpam-5790	711	4	0	0	NUM
ejpam-5790	711	5	lnµ′	lnµ′	NOUN
ejpam-5790	711	6	(	(	PUNCT
ejpam-5790	711	7	(	(	PUNCT
ejpam-5790	711	8	1−w)u	1−w)u	NUM
ejpam-5790	711	9	⊗	⊗	NOUN
ejpam-5790	711	10	1	1	NUM
ejpam-5790	712	1	+	+	CCONJ
ejpam-5790	712	2	(	(	PUNCT
ejpam-5790	712	3	w1⊗d	w1⊗d	NOUN
ejpam-5790	712	4	2	2	NUM
ejpam-5790	712	5	)	)	PUNCT
ejpam-5790	712	6	)	)	PUNCT
ejpam-5790	712	7	dw	dw	NOUN
ejpam-5790	712	8	]	]	PUNCT
ejpam-5790	713	1	+	+	CCONJ
ejpam-5790	713	2	lnµ	lnµ	NOUN
ejpam-5790	713	3	(	(	PUNCT
ejpam-5790	713	4	u	u	NOUN
ejpam-5790	713	5	⊗	⊗	PROPN
ejpam-5790	713	6	1	1	NUM
ejpam-5790	713	7	+	+	NUM
ejpam-5790	713	8	1⊗d	1⊗d	NUM
ejpam-5790	713	9	2	2	NUM
ejpam-5790	713	10	)	)	PUNCT
ejpam-5790	713	11	−	−	PROPN
ejpam-5790	713	12	(	(	PUNCT
ejpam-5790	713	13	1−w	1−w	NUM
ejpam-5790	713	14	)	)	PUNCT
ejpam-5790	713	15	2	2	NUM
ejpam-5790	713	16	3	3	NUM
ejpam-5790	713	17	(	(	PUNCT
ejpam-5790	713	18	ν2	ν2	NOUN
ejpam-5790	713	19	−	−	PROPN
ejpam-5790	713	20	ν1	ν1	NOUN
ejpam-5790	713	21	)	)	PUNCT
ejpam-5790	713	22	4	4	NUM
ejpam-5790	714	1	[	[	X
ejpam-5790	714	2	∫	∫	PROPN
ejpam-5790	714	3	1	1	NUM
ejpam-5790	714	4	0	0	NUM
ejpam-5790	714	5	lnµ′	lnµ′	NOUN
ejpam-5790	714	6	(	(	PUNCT
ejpam-5790	714	7	(	(	PUNCT
ejpam-5790	714	8	1−w	1−w	NUM
ejpam-5790	714	9	2	2	NUM
ejpam-5790	714	10	)	)	PUNCT
ejpam-5790	714	11	u	u	NOUN
ejpam-5790	714	12	⊗	⊗	PROPN
ejpam-5790	714	13	1	1	NUM
ejpam-5790	714	14	+	+	CCONJ
ejpam-5790	714	15	(	(	PUNCT
ejpam-5790	714	16	1	1	NUM
ejpam-5790	714	17	+	+	NOUN
ejpam-5790	714	18	w	w	NOUN
ejpam-5790	714	19	2	2	NUM
ejpam-5790	714	20	)	)	PUNCT
ejpam-5790	714	21	1⊗d	1⊗d	PROPN
ejpam-5790	714	22	)	)	PUNCT
ejpam-5790	714	23	dw	dw	NOUN
ejpam-5790	714	24	]	]	PUNCT
ejpam-5790	714	25	∥∥∥∥∥	∥∥∥∥∥	PUNCT
ejpam-5790	714	26	≤	≤	ADV
ejpam-5790	714	27	∥(1⊗d	∥(1⊗d	NOUN
ejpam-5790	714	28	−	−	PROPN
ejpam-5790	714	29	u	u	NOUN
ejpam-5790	714	30	⊗	⊗	PROPN
ejpam-5790	714	31	1)2∥	1)2∥	NUM
ejpam-5790	714	32	6	6	NUM
ejpam-5790	714	33	[	[	PUNCT
ejpam-5790	714	34	1	1	NUM
ejpam-5790	714	35	5	5	NUM
ejpam-5790	714	36	(	(	PUNCT
ejpam-5790	714	37	1	1	NUM
ejpam-5790	714	38	5	5	NUM
ejpam-5790	714	39	+	+	CCONJ
ejpam-5790	714	40	2	2	NUM
ejpam-5790	714	41	)	)	PUNCT
ejpam-5790	714	42	(	(	PUNCT
ejpam-5790	714	43	1	1	NUM
ejpam-5790	714	44	5	5	NUM
ejpam-5790	714	45	(	(	PUNCT
ejpam-5790	714	46	1	1	NUM
ejpam-5790	714	47	3	3	NUM
ejpam-5790	714	48	+	+	CCONJ
ejpam-5790	714	49	1	1	NUM
ejpam-5790	714	50	3	3	NUM
ejpam-5790	714	51	)	)	PUNCT
ejpam-5790	714	52	2	2	NUM
ejpam-5790	714	53	2	2	NUM
ejpam-5790	714	54	5	5	NUM
ejpam-5790	714	55	+	+	CCONJ
ejpam-5790	714	56	3	3	NUM
ejpam-5790	714	57	1	1	NUM
ejpam-5790	714	58	5	5	NUM
ejpam-5790	714	59	+	+	CCONJ
ejpam-5790	714	60	1	1	NUM
ejpam-5790	714	61	)	)	PUNCT
ejpam-5790	714	62	−	−	PROPN
ejpam-5790	714	63	1	1	NUM
ejpam-5790	714	64	8	8	NUM
ejpam-5790	714	65	)	)	PUNCT
ejpam-5790	714	66	∥∥∥	∥∥∥	PROPN
ejpam-5790	714	67	∣∣lnµ′′	∣∣lnµ′′	NOUN
ejpam-5790	714	68	(	(	PUNCT
ejpam-5790	714	69	u	u	NOUN
ejpam-5790	714	70	)	)	PUNCT
ejpam-5790	714	71	∣∣+	∣∣+	PROPN
ejpam-5790	714	72	∣∣lnµ′′	∣∣lnµ′′	PROPN
ejpam-5790	714	73	(	(	PUNCT
ejpam-5790	714	74	d	d	X
ejpam-5790	714	75	)	)	PUNCT
ejpam-5790	714	76	∣∣	∣∣	X
ejpam-5790	714	77	∥∥∥.	∥∥∥.	ADP
ejpam-5790	714	78	5	5	NUM
ejpam-5790	714	79	.	.	X
ejpam-5790	714	80	conclusion	conclusion	NOUN
ejpam-5790	714	81	and	and	CCONJ
ejpam-5790	714	82	future	future	ADJ
ejpam-5790	714	83	remarks	remark	NOUN
ejpam-5790	714	84	tensor	tensor	NOUN
ejpam-5790	714	85	hilbert	hilbert	NOUN
ejpam-5790	714	86	spaces	space	NOUN
ejpam-5790	714	87	allow	allow	VERB
ejpam-5790	714	88	for	for	ADP
ejpam-5790	714	89	the	the	DET
ejpam-5790	714	90	extension	extension	NOUN
ejpam-5790	714	91	and	and	CCONJ
ejpam-5790	714	92	decomposition	decomposition	NOUN
ejpam-5790	714	93	of	of	ADP
ejpam-5790	714	94	operators	operator	NOUN
ejpam-5790	714	95	in	in	ADP
ejpam-5790	714	96	higher	high	ADJ
ejpam-5790	714	97	dimensions	dimension	NOUN
ejpam-5790	714	98	,	,	PUNCT
ejpam-5790	714	99	useful	useful	ADJ
ejpam-5790	714	100	in	in	ADP
ejpam-5790	714	101	spectral	spectral	ADJ
ejpam-5790	714	102	theory	theory	NOUN
ejpam-5790	714	103	.	.	PUNCT
ejpam-5790	715	1	through	through	ADP
ejpam-5790	715	2	the	the	DET
ejpam-5790	715	3	use	use	NOUN
ejpam-5790	715	4	of	of	ADP
ejpam-5790	715	5	tensor	tensor	NOUN
ejpam-5790	715	6	operations	operation	NOUN
ejpam-5790	715	7	for	for	ADP
ejpam-5790	715	8	continuous	continuous	ADJ
ejpam-5790	715	9	differentiable	differentiable	ADJ
ejpam-5790	715	10	mappings	mapping	NOUN
ejpam-5790	715	11	,	,	PUNCT
ejpam-5790	715	12	we	we	PRON
ejpam-5790	715	13	introduced	introduce	VERB
ejpam-5790	715	14	gradient	gradient	ADJ
ejpam-5790	715	15	type	type	NOUN
ejpam-5790	715	16	result	result	NOUN
ejpam-5790	715	17	in	in	ADP
ejpam-5790	715	18	the	the	DET
ejpam-5790	715	19	setup	setup	NOUN
ejpam-5790	715	20	of	of	ADP
ejpam-5790	715	21	function	function	NOUN
ejpam-5790	715	22	spaces	space	NOUN
ejpam-5790	715	23	,	,	PUNCT
ejpam-5790	715	24	offering	offer	VERB
ejpam-5790	715	25	improvements	improvement	NOUN
ejpam-5790	715	26	and	and	CCONJ
ejpam-5790	715	27	extensions	extension	NOUN
ejpam-5790	715	28	of	of	ADP
ejpam-5790	715	29	earlier	early	ADJ
ejpam-5790	715	30	findings	finding	NOUN
ejpam-5790	715	31	that	that	PRON
ejpam-5790	715	32	take	take	VERB
ejpam-5790	715	33	fractional	fractional	ADJ
ejpam-5790	715	34	operators	operator	NOUN
ejpam-5790	715	35	into	into	ADP
ejpam-5790	715	36	w.	w.	PROPN
ejpam-5790	715	37	afzal	afzal	PROPN
ejpam-5790	715	38	et	et	PROPN
ejpam-5790	715	39	al	al	PROPN
ejpam-5790	715	40	.	.	PUNCT
ejpam-5790	715	41	/	/	SYM
ejpam-5790	715	42	eur	eur	PROPN
ejpam-5790	715	43	.	.	PUNCT
ejpam-5790	716	1	j.	j.	PROPN
ejpam-5790	716	2	pure	pure	PROPN
ejpam-5790	716	3	appl	appl	PROPN
ejpam-5790	716	4	.	.	PROPN
ejpam-5790	716	5	math	math	PROPN
ejpam-5790	716	6	,	,	PUNCT
ejpam-5790	716	7	18	18	NUM
ejpam-5790	716	8	(	(	PUNCT
ejpam-5790	716	9	1	1	NUM
ejpam-5790	716	10	)	)	PUNCT
ejpam-5790	716	11	(	(	PUNCT
ejpam-5790	716	12	2025	2025	NUM
ejpam-5790	716	13	)	)	PUNCT
ejpam-5790	716	14	,	,	PUNCT
ejpam-5790	716	15	5790	5790	NUM
ejpam-5790	716	16	26	26	NUM
ejpam-5790	716	17	of	of	ADP
ejpam-5790	716	18	30	30	NUM
ejpam-5790	716	19	account	account	NOUN
ejpam-5790	716	20	.	.	PUNCT
ejpam-5790	717	1	we	we	PRON
ejpam-5790	717	2	also	also	ADV
ejpam-5790	717	3	point	point	VERB
ejpam-5790	717	4	out	out	ADP
ejpam-5790	717	5	important	important	ADJ
ejpam-5790	717	6	implications	implication	NOUN
ejpam-5790	717	7	and	and	CCONJ
ejpam-5790	717	8	comments	comment	NOUN
ejpam-5790	717	9	that	that	PRON
ejpam-5790	717	10	relate	relate	VERB
ejpam-5790	717	11	our	our	PRON
ejpam-5790	717	12	results	result	NOUN
ejpam-5790	717	13	to	to	ADP
ejpam-5790	717	14	previous	previous	ADJ
ejpam-5790	717	15	research	research	NOUN
ejpam-5790	717	16	.	.	PUNCT
ejpam-5790	718	1	in	in	ADP
ejpam-5790	718	2	addition	addition	NOUN
ejpam-5790	718	3	to	to	ADP
ejpam-5790	718	4	promoting	promote	VERB
ejpam-5790	718	5	further	further	ADJ
ejpam-5790	718	6	study	study	NOUN
ejpam-5790	718	7	of	of	ADP
ejpam-5790	718	8	simpson	simpson	PROPN
ejpam-5790	718	9	-	-	PUNCT
ejpam-5790	718	10	type	type	NOUN
ejpam-5790	718	11	inequalities	inequality	NOUN
ejpam-5790	718	12	and	and	CCONJ
ejpam-5790	718	13	other	other	ADJ
ejpam-5790	718	14	quantum	quantum	NOUN
ejpam-5790	718	15	,	,	PUNCT
ejpam-5790	718	16	fractional	fractional	ADJ
ejpam-5790	718	17	,	,	PUNCT
ejpam-5790	718	18	and	and	CCONJ
ejpam-5790	718	19	stochastic	stochastic	ADJ
ejpam-5790	718	20	integrals	integral	NOUN
ejpam-5790	718	21	,	,	PUNCT
ejpam-5790	718	22	this	this	DET
ejpam-5790	718	23	publication	publication	NOUN
ejpam-5790	718	24	advances	advance	VERB
ejpam-5790	718	25	mathematical	mathematical	ADJ
ejpam-5790	718	26	inequality	inequality	NOUN
ejpam-5790	718	27	theory	theory	NOUN
ejpam-5790	718	28	in	in	ADP
ejpam-5790	718	29	tensor	tensor	NOUN
ejpam-5790	718	30	hilbert	hilbert	NOUN
ejpam-5790	718	31	spaces	space	NOUN
ejpam-5790	718	32	,	,	PUNCT
ejpam-5790	718	33	an	an	DET
ejpam-5790	718	34	area	area	NOUN
ejpam-5790	718	35	that	that	PRON
ejpam-5790	718	36	has	have	AUX
ejpam-5790	718	37	received	receive	VERB
ejpam-5790	718	38	little	little	ADJ
ejpam-5790	718	39	attention	attention	NOUN
ejpam-5790	718	40	.	.	PUNCT
ejpam-5790	719	1	operators	operator	NOUN
ejpam-5790	719	2	.	.	PUNCT
ejpam-5790	720	1	acknowledgements	acknowledgement	VERB
ejpam-5790	720	2	the	the	DET
ejpam-5790	720	3	authors	author	NOUN
ejpam-5790	720	4	acknowledge	acknowledge	VERB
ejpam-5790	720	5	the	the	DET
ejpam-5790	720	6	financial	financial	ADJ
ejpam-5790	720	7	support	support	NOUN
ejpam-5790	720	8	from	from	ADP
ejpam-5790	720	9	the	the	DET
ejpam-5790	720	10	program	program	NOUN
ejpam-5790	720	11	prosni	prosni	NOUN
ejpam-5790	720	12	of	of	ADP
ejpam-5790	720	13	the	the	DET
ejpam-5790	720	14	university	university	PROPN
ejpam-5790	720	15	of	of	ADP
ejpam-5790	720	16	guadalajara	guadalajara	PROPN
ejpam-5790	720	17	,	,	PUNCT
ejpam-5790	720	18	mexico	mexico	PROPN
ejpam-5790	720	19	.	.	PUNCT
ejpam-5790	721	1	references	reference	NOUN
ejpam-5790	721	2	[	[	X
ejpam-5790	721	3	1	1	NUM
ejpam-5790	721	4	]	]	PUNCT
ejpam-5790	721	5	m.	m.	NOUN
ejpam-5790	721	6	abbas	abbas	PROPN
ejpam-5790	721	7	,	,	PUNCT
ejpam-5790	721	8	w.	w.	PROPN
ejpam-5790	721	9	afzal	afzal	PROPN
ejpam-5790	721	10	,	,	PUNCT
ejpam-5790	721	11	t.	t.	NOUN
ejpam-5790	721	12	botmart	botmart	NOUN
ejpam-5790	721	13	,	,	PUNCT
ejpam-5790	721	14	and	and	CCONJ
ejpam-5790	721	15	a.	a.	NOUN
ejpam-5790	721	16	m.	m.	PROPN
ejpam-5790	721	17	galal	galal	PROPN
ejpam-5790	721	18	.	.	PUNCT
ejpam-5790	722	1	jensen	jensen	PROPN
ejpam-5790	722	2	,	,	PUNCT
ejpam-5790	722	3	ostrowski	ostrowski	NOUN
ejpam-5790	722	4	and	and	CCONJ
ejpam-5790	722	5	hermitehadamard	hermitehadamard	ADJ
ejpam-5790	722	6	type	type	NOUN
ejpam-5790	722	7	inequalities	inequality	NOUN
ejpam-5790	722	8	for	for	ADP
ejpam-5790	722	9	h	h	NOUN
ejpam-5790	722	10	-	-	PUNCT
ejpam-5790	722	11	convex	convex	ADJ
ejpam-5790	722	12	stochastic	stochastic	NOUN
ejpam-5790	722	13	processes	process	NOUN
ejpam-5790	722	14	by	by	ADP
ejpam-5790	722	15	means	mean	NOUN
ejpam-5790	722	16	of	of	ADP
ejpam-5790	722	17	centerradius	centerradius	ADJ
ejpam-5790	722	18	order	order	NOUN
ejpam-5790	722	19	relation	relation	NOUN
ejpam-5790	722	20	.	.	PUNCT
ejpam-5790	723	1	2023	2023	NUM
ejpam-5790	723	2	.	.	PUNCT
ejpam-5790	724	1	[	[	X
ejpam-5790	724	2	2	2	NUM
ejpam-5790	724	3	]	]	PUNCT
ejpam-5790	724	4	w.	w.	PROPN
ejpam-5790	724	5	afzal	afzal	PROPN
ejpam-5790	724	6	,	,	PUNCT
ejpam-5790	724	7	m.	m.	NOUN
ejpam-5790	724	8	abbas	abbas	PROPN
ejpam-5790	724	9	,	,	PUNCT
ejpam-5790	724	10	and	and	CCONJ
ejpam-5790	724	11	o.	o.	PROPN
ejpam-5790	724	12	m.	m.	NOUN
ejpam-5790	724	13	alsalami	alsalami	NOUN
ejpam-5790	724	14	.	.	PUNCT
ejpam-5790	725	1	bounds	bound	NOUN
ejpam-5790	725	2	of	of	ADP
ejpam-5790	725	3	different	different	ADJ
ejpam-5790	725	4	integral	integral	ADJ
ejpam-5790	725	5	operators	operator	NOUN
ejpam-5790	725	6	in	in	ADP
ejpam-5790	725	7	tensorial	tensorial	ADJ
ejpam-5790	725	8	hilbert	hilbert	NOUN
ejpam-5790	725	9	and	and	CCONJ
ejpam-5790	725	10	variable	variable	ADJ
ejpam-5790	725	11	exponent	exponent	NOUN
ejpam-5790	725	12	function	function	NOUN
ejpam-5790	725	13	spaces	space	VERB
ejpam-5790	725	14	.	.	PUNCT
ejpam-5790	726	1	mathematics	mathematic	NOUN
ejpam-5790	726	2	,	,	PUNCT
ejpam-5790	726	3	12(16):1–33	12(16):1–33	NUM
ejpam-5790	726	4	,	,	PUNCT
ejpam-5790	726	5	2024	2024	NUM
ejpam-5790	726	6	.	.	PUNCT
ejpam-5790	727	1	[	[	X
ejpam-5790	727	2	3	3	X
ejpam-5790	727	3	]	]	X
ejpam-5790	727	4	w.	w.	PROPN
ejpam-5790	727	5	afzal	afzal	PROPN
ejpam-5790	727	6	,	,	PUNCT
ejpam-5790	727	7	m.	m.	NOUN
ejpam-5790	727	8	abbas	abbas	PROPN
ejpam-5790	727	9	,	,	PUNCT
ejpam-5790	727	10	d.	d.	PROPN
ejpam-5790	727	11	breaz	breaz	PROPN
ejpam-5790	727	12	,	,	PUNCT
ejpam-5790	727	13	and	and	CCONJ
ejpam-5790	727	14	l.	l.	PROPN
ejpam-5790	727	15	i.	i.	PROPN
ejpam-5790	727	16	cot̂ırlă.	cot̂ırlă.	PROPN
ejpam-5790	727	17	fractional	fractional	ADJ
ejpam-5790	727	18	hermite	hermite	ADJ
ejpam-5790	727	19	–	–	PUNCT
ejpam-5790	727	20	hadamard	hadamard	NOUN
ejpam-5790	727	21	,	,	PUNCT
ejpam-5790	727	22	newton	newton	PROPN
ejpam-5790	727	23	–	–	PUNCT
ejpam-5790	727	24	milne	milne	PROPN
ejpam-5790	727	25	,	,	PUNCT
ejpam-5790	727	26	and	and	CCONJ
ejpam-5790	727	27	convexity	convexity	NOUN
ejpam-5790	727	28	involving	involve	VERB
ejpam-5790	727	29	arithmetic	arithmetic	ADJ
ejpam-5790	727	30	–	–	PUNCT
ejpam-5790	727	31	geometric	geometric	ADJ
ejpam-5790	727	32	mean	mean	ADJ
ejpam-5790	727	33	-	-	PUNCT
ejpam-5790	727	34	type	type	NOUN
ejpam-5790	727	35	inequalities	inequality	NOUN
ejpam-5790	727	36	in	in	ADP
ejpam-5790	727	37	hilbert	hilbert	PROPN
ejpam-5790	727	38	and	and	CCONJ
ejpam-5790	727	39	mixed	mixed	ADJ
ejpam-5790	727	40	-	-	PUNCT
ejpam-5790	727	41	norm	norm	NOUN
ejpam-5790	727	42	morrey	morrey	NOUN
ejpam-5790	727	43	spaces	space	VERB
ejpam-5790	727	44	with	with	ADP
ejpam-5790	727	45	variable	variable	ADJ
ejpam-5790	727	46	exponents	exponent	NOUN
ejpam-5790	727	47	.	.	PUNCT
ejpam-5790	728	1	fractal	fractal	PROPN
ejpam-5790	728	2	&	&	CCONJ
ejpam-5790	728	3	fractional	fractional	ADJ
ejpam-5790	728	4	,	,	PUNCT
ejpam-5790	728	5	8(9	8(9	NUM
ejpam-5790	728	6	)	)	PUNCT
ejpam-5790	728	7	,	,	PUNCT
ejpam-5790	728	8	2024	2024	NUM
ejpam-5790	728	9	.	.	PUNCT
ejpam-5790	729	1	[	[	X
ejpam-5790	729	2	4	4	X
ejpam-5790	729	3	]	]	PUNCT
ejpam-5790	729	4	w.	w.	PROPN
ejpam-5790	729	5	afzal	afzal	PROPN
ejpam-5790	729	6	,	,	PUNCT
ejpam-5790	729	7	m.	m.	NOUN
ejpam-5790	729	8	abbas	abbas	PROPN
ejpam-5790	729	9	,	,	PUNCT
ejpam-5790	729	10	j.	j.	PROPN
ejpam-5790	729	11	e.	e.	PROPN
ejpam-5790	729	12	maćıas	maćıas	PROPN
ejpam-5790	729	13	-	-	PUNCT
ejpam-5790	729	14	dı́az	dı́az	NOUN
ejpam-5790	729	15	,	,	PUNCT
ejpam-5790	729	16	and	and	CCONJ
ejpam-5790	729	17	s.	s.	PROPN
ejpam-5790	729	18	treanţă.	treanţă.	VERB
ejpam-5790	729	19	some	some	DET
ejpam-5790	729	20	h	h	NOUN
ejpam-5790	729	21	-	-	PUNCT
ejpam-5790	729	22	godunova	godunova	ADJ
ejpam-5790	729	23	–	–	PUNCT
ejpam-5790	729	24	levin	levin	PROPN
ejpam-5790	729	25	function	function	PROPN
ejpam-5790	729	26	inequalities	inequality	NOUN
ejpam-5790	729	27	using	use	VERB
ejpam-5790	729	28	center	center	NOUN
ejpam-5790	729	29	radius	radius	NOUN
ejpam-5790	729	30	(	(	PUNCT
ejpam-5790	729	31	cr	cr	NOUN
ejpam-5790	729	32	)	)	PUNCT
ejpam-5790	729	33	order	order	NOUN
ejpam-5790	729	34	relation	relation	NOUN
ejpam-5790	729	35	.	.	PUNCT
ejpam-5790	730	1	fractal	fractal	PROPN
ejpam-5790	730	2	and	and	CCONJ
ejpam-5790	730	3	fractional	fractional	ADJ
ejpam-5790	730	4	,	,	PUNCT
ejpam-5790	730	5	6(9):518	6(9):518	NUM
ejpam-5790	730	6	,	,	PUNCT
ejpam-5790	730	7	2022	2022	NUM
ejpam-5790	730	8	.	.	PUNCT
ejpam-5790	731	1	[	[	X
ejpam-5790	731	2	5	5	X
ejpam-5790	731	3	]	]	PUNCT
ejpam-5790	731	4	w.	w.	PROPN
ejpam-5790	731	5	afzal	afzal	PROPN
ejpam-5790	731	6	,	,	PUNCT
ejpam-5790	731	7	d.	d.	PROPN
ejpam-5790	731	8	breaz	breaz	PROPN
ejpam-5790	731	9	,	,	PUNCT
ejpam-5790	731	10	m.	m.	NOUN
ejpam-5790	731	11	abbas	abbas	PROPN
ejpam-5790	731	12	,	,	PUNCT
ejpam-5790	731	13	l.	l.	PROPN
ejpam-5790	731	14	i.	i.	PROPN
ejpam-5790	731	15	cot̂ırlă	cot̂ırlă	PROPN
ejpam-5790	731	16	,	,	PUNCT
ejpam-5790	731	17	z.	z.	PROPN
ejpam-5790	731	18	a.	a.	PROPN
ejpam-5790	731	19	khan	khan	PROPN
ejpam-5790	731	20	,	,	PUNCT
ejpam-5790	731	21	and	and	CCONJ
ejpam-5790	731	22	e.	e.	PROPN
ejpam-5790	731	23	rapeanu	rapeanu	PROPN
ejpam-5790	731	24	.	.	PUNCT
ejpam-5790	732	1	hyers	hyer	NOUN
ejpam-5790	732	2	–	–	PUNCT
ejpam-5790	732	3	ulam	ulam	PROPN
ejpam-5790	732	4	stability	stability	NOUN
ejpam-5790	732	5	of	of	ADP
ejpam-5790	732	6	2d	2d	NOUN
ejpam-5790	732	7	-	-	PUNCT
ejpam-5790	732	8	convex	convex	NOUN
ejpam-5790	732	9	mappings	mapping	NOUN
ejpam-5790	732	10	and	and	CCONJ
ejpam-5790	732	11	some	some	DET
ejpam-5790	732	12	related	relate	VERB
ejpam-5790	732	13	new	new	ADJ
ejpam-5790	732	14	hermite	hermite	ADJ
ejpam-5790	732	15	–	–	PUNCT
ejpam-5790	732	16	hadamard	hadamard	NOUN
ejpam-5790	732	17	,	,	PUNCT
ejpam-5790	732	18	pachpatte	pachpatte	NOUN
ejpam-5790	732	19	,	,	PUNCT
ejpam-5790	732	20	and	and	CCONJ
ejpam-5790	732	21	fejér	fejér	NOUN
ejpam-5790	732	22	type	type	VERB
ejpam-5790	732	23	integral	integral	ADJ
ejpam-5790	732	24	inequalities	inequality	NOUN
ejpam-5790	732	25	using	use	VERB
ejpam-5790	732	26	novel	novel	ADJ
ejpam-5790	732	27	fractional	fractional	ADJ
ejpam-5790	732	28	integral	integral	ADJ
ejpam-5790	732	29	operators	operator	NOUN
ejpam-5790	732	30	via	via	ADP
ejpam-5790	732	31	totally	totally	ADV
ejpam-5790	732	32	interval	interval	NOUN
ejpam-5790	732	33	-	-	PUNCT
ejpam-5790	732	34	order	order	NOUN
ejpam-5790	732	35	relations	relation	NOUN
ejpam-5790	732	36	with	with	ADP
ejpam-5790	732	37	open	open	ADJ
ejpam-5790	732	38	problem	problem	NOUN
ejpam-5790	732	39	.	.	PUNCT
ejpam-5790	733	1	mathematics	mathematic	NOUN
ejpam-5790	733	2	,	,	PUNCT
ejpam-5790	733	3	12(8):1238	12(8):1238	NUM
ejpam-5790	733	4	,	,	PUNCT
ejpam-5790	733	5	2024	2024	NUM
ejpam-5790	733	6	.	.	PUNCT
ejpam-5790	734	1	[	[	X
ejpam-5790	734	2	6	6	NUM
ejpam-5790	734	3	]	]	PUNCT
ejpam-5790	734	4	w.	w.	PROPN
ejpam-5790	734	5	afzal	afzal	PROPN
ejpam-5790	734	6	,	,	PUNCT
ejpam-5790	734	7	s.	s.	PROPN
ejpam-5790	734	8	m.	m.	PROPN
ejpam-5790	734	9	eldin	eldin	PROPN
ejpam-5790	734	10	,	,	PUNCT
ejpam-5790	734	11	w.	w.	PROPN
ejpam-5790	734	12	nazeer	nazeer	PROPN
ejpam-5790	734	13	,	,	PUNCT
ejpam-5790	734	14	and	and	CCONJ
ejpam-5790	734	15	a.	a.	NOUN
ejpam-5790	734	16	m.	m.	NOUN
ejpam-5790	734	17	galal	galal	PROPN
ejpam-5790	734	18	.	.	PUNCT
ejpam-5790	735	1	some	some	DET
ejpam-5790	735	2	integral	integral	ADJ
ejpam-5790	735	3	inequalities	inequality	NOUN
ejpam-5790	735	4	for	for	ADP
ejpam-5790	735	5	harmonical	harmonical	ADJ
ejpam-5790	735	6	cr	cr	PROPN
ejpam-5790	735	7	-	-	PUNCT
ejpam-5790	735	8	h	h	NOUN
ejpam-5790	735	9	-	-	PUNCT
ejpam-5790	735	10	godunova	godunova	ADJ
ejpam-5790	735	11	–	–	PUNCT
ejpam-5790	735	12	levin	levin	PROPN
ejpam-5790	735	13	stochastic	stochastic	NOUN
ejpam-5790	735	14	processes	process	NOUN
ejpam-5790	735	15	.	.	PUNCT
ejpam-5790	736	1	aims	aim	VERB
ejpam-5790	736	2	mathematics	mathematic	NOUN
ejpam-5790	736	3	,	,	PUNCT
ejpam-5790	736	4	8:13473	8:13473	NUM
ejpam-5790	736	5	–	–	PUNCT
ejpam-5790	736	6	13491	13491	NUM
ejpam-5790	736	7	,	,	PUNCT
ejpam-5790	736	8	2023	2023	NUM
ejpam-5790	736	9	.	.	PUNCT
ejpam-5790	737	1	[	[	X
ejpam-5790	737	2	7	7	X
ejpam-5790	737	3	]	]	X
ejpam-5790	737	4	w.	w.	PROPN
ejpam-5790	737	5	afzal	afzal	PROPN
ejpam-5790	737	6	,	,	PUNCT
ejpam-5790	737	7	w.	w.	PROPN
ejpam-5790	737	8	nazeer	nazeer	PROPN
ejpam-5790	737	9	,	,	PUNCT
ejpam-5790	737	10	t.	t.	NOUN
ejpam-5790	737	11	botmart	botmart	NOUN
ejpam-5790	737	12	,	,	PUNCT
ejpam-5790	737	13	and	and	CCONJ
ejpam-5790	737	14	s.	s.	PROPN
ejpam-5790	737	15	treanta	treanta	PROPN
ejpam-5790	737	16	.	.	PUNCT
ejpam-5790	738	1	some	some	DET
ejpam-5790	738	2	properties	property	NOUN
ejpam-5790	738	3	and	and	CCONJ
ejpam-5790	738	4	inequalities	inequality	NOUN
ejpam-5790	738	5	for	for	ADP
ejpam-5790	738	6	generalized	generalized	ADJ
ejpam-5790	738	7	class	class	NOUN
ejpam-5790	738	8	of	of	ADP
ejpam-5790	738	9	harmonical	harmonical	ADJ
ejpam-5790	738	10	godunova	godunova	PROPN
ejpam-5790	738	11	-	-	PUNCT
ejpam-5790	738	12	levin	levin	PROPN
ejpam-5790	738	13	function	function	PROPN
ejpam-5790	738	14	via	via	ADP
ejpam-5790	738	15	center	center	ADJ
ejpam-5790	738	16	radius	radius	NOUN
ejpam-5790	738	17	order	order	NOUN
ejpam-5790	738	18	relation	relation	NOUN
ejpam-5790	738	19	.	.	PUNCT
ejpam-5790	739	1	aims	aim	VERB
ejpam-5790	739	2	mathematics	mathematic	NOUN
ejpam-5790	739	3	,	,	PUNCT
ejpam-5790	739	4	8(1):1696–1712	8(1):1696–1712	NOUN
ejpam-5790	739	5	,	,	PUNCT
ejpam-5790	739	6	2023	2023	NUM
ejpam-5790	739	7	.	.	PUNCT
ejpam-5790	740	1	[	[	X
ejpam-5790	740	2	8	8	NUM
ejpam-5790	740	3	]	]	X
ejpam-5790	740	4	w.	w.	PROPN
ejpam-5790	740	5	afzal	afzal	PROPN
ejpam-5790	740	6	,	,	PUNCT
ejpam-5790	740	7	e.	e.	PROPN
ejpam-5790	740	8	y.	y.	PROPN
ejpam-5790	740	9	prosviryakov	prosviryakov	PROPN
ejpam-5790	740	10	,	,	PUNCT
ejpam-5790	740	11	s.	s.	PROPN
ejpam-5790	740	12	m.	m.	PROPN
ejpam-5790	740	13	el	el	PROPN
ejpam-5790	740	14	-	-	PUNCT
ejpam-5790	740	15	deeb	deeb	PROPN
ejpam-5790	740	16	,	,	PUNCT
ejpam-5790	740	17	and	and	CCONJ
ejpam-5790	740	18	y.	y.	PROPN
ejpam-5790	740	19	almalki	almalki	ADV
ejpam-5790	740	20	.	.	PUNCT
ejpam-5790	741	1	some	some	DET
ejpam-5790	741	2	new	new	ADJ
ejpam-5790	741	3	estimates	estimate	NOUN
ejpam-5790	741	4	of	of	ADP
ejpam-5790	741	5	hermite	hermite	ADJ
ejpam-5790	741	6	–	–	PUNCT
ejpam-5790	741	7	hadamard	hadamard	ADJ
ejpam-5790	741	8	,	,	PUNCT
ejpam-5790	741	9	ostrowski	ostrowski	NOUN
ejpam-5790	741	10	and	and	CCONJ
ejpam-5790	741	11	jensen	jensen	PROPN
ejpam-5790	741	12	-	-	PUNCT
ejpam-5790	741	13	type	type	NOUN
ejpam-5790	741	14	inclusions	inclusion	NOUN
ejpam-5790	741	15	for	for	ADP
ejpam-5790	741	16	h	h	NOUN
ejpam-5790	741	17	-	-	PUNCT
ejpam-5790	741	18	convex	convex	ADJ
ejpam-5790	741	19	stochastic	stochastic	ADJ
ejpam-5790	741	20	process	process	NOUN
ejpam-5790	741	21	via	via	ADP
ejpam-5790	741	22	interval	interval	NOUN
ejpam-5790	741	23	-	-	PUNCT
ejpam-5790	741	24	valued	value	VERB
ejpam-5790	741	25	functions	function	NOUN
ejpam-5790	741	26	.	.	PUNCT
ejpam-5790	742	1	symmetry	symmetry	NOUN
ejpam-5790	742	2	,	,	PUNCT
ejpam-5790	742	3	15(4):831	15(4):831	PROPN
ejpam-5790	742	4	,	,	PUNCT
ejpam-5790	742	5	2023	2023	NUM
ejpam-5790	742	6	.	.	PUNCT
ejpam-5790	743	1	[	[	X
ejpam-5790	743	2	9	9	NUM
ejpam-5790	743	3	]	]	PUNCT
ejpam-5790	743	4	a.	a.	NOUN
ejpam-5790	743	5	a.	a.	PROPN
ejpam-5790	743	6	h.	h.	PROPN
ejpam-5790	743	7	ahmadini	ahmadini	PROPN
ejpam-5790	743	8	,	,	PUNCT
ejpam-5790	743	9	w.	w.	PROPN
ejpam-5790	743	10	afzal	afzal	PROPN
ejpam-5790	743	11	,	,	PUNCT
ejpam-5790	743	12	m.	m.	NOUN
ejpam-5790	743	13	abbas	abbas	PROPN
ejpam-5790	743	14	,	,	PUNCT
ejpam-5790	743	15	and	and	CCONJ
ejpam-5790	743	16	e.	e.	PROPN
ejpam-5790	743	17	s.	s.	PROPN
ejpam-5790	743	18	aly	aly	PROPN
ejpam-5790	743	19	.	.	PROPN
ejpam-5790	744	1	weighted	weight	VERB
ejpam-5790	744	2	fejér	fejér	NOUN
ejpam-5790	744	3	,	,	PUNCT
ejpam-5790	744	4	hermite	hermite	ADJ
ejpam-5790	744	5	–	–	PUNCT
ejpam-5790	744	6	hadamard	hadamard	ADJ
ejpam-5790	744	7	,	,	PUNCT
ejpam-5790	744	8	and	and	CCONJ
ejpam-5790	744	9	trapezium	trapezium	NOUN
ejpam-5790	744	10	-	-	PUNCT
ejpam-5790	744	11	type	type	NOUN
ejpam-5790	744	12	inequalities	inequality	NOUN
ejpam-5790	744	13	for	for	ADP
ejpam-5790	744	14	(	(	PUNCT
ejpam-5790	744	15	h1	h1	PROPN
ejpam-5790	744	16	,	,	PUNCT
ejpam-5790	744	17	h2)–godunova	h2)–godunova	PROPN
ejpam-5790	744	18	–	–	PUNCT
ejpam-5790	744	19	levin	levin	PROPN
ejpam-5790	744	20	preinvex	preinvex	PROPN
ejpam-5790	744	21	function	function	NOUN
ejpam-5790	744	22	with	with	ADP
ejpam-5790	744	23	applications	application	NOUN
ejpam-5790	744	24	and	and	CCONJ
ejpam-5790	744	25	two	two	NUM
ejpam-5790	744	26	open	open	ADJ
ejpam-5790	744	27	problems	problem	NOUN
ejpam-5790	744	28	.	.	PUNCT
ejpam-5790	745	1	mathematics	mathematic	NOUN
ejpam-5790	745	2	,	,	PUNCT
ejpam-5790	745	3	12:382	12:382	NUM
ejpam-5790	745	4	,	,	PUNCT
ejpam-5790	745	5	2024	2024	NUM
ejpam-5790	745	6	.	.	PUNCT
ejpam-5790	746	1	w.	w.	PROPN
ejpam-5790	746	2	afzal	afzal	PROPN
ejpam-5790	746	3	et	et	PROPN
ejpam-5790	746	4	al	al	PROPN
ejpam-5790	746	5	.	.	PUNCT
ejpam-5790	746	6	/	/	SYM
ejpam-5790	746	7	eur	eur	PROPN
ejpam-5790	746	8	.	.	PUNCT
ejpam-5790	747	1	j.	j.	PROPN
ejpam-5790	747	2	pure	pure	PROPN
ejpam-5790	747	3	appl	appl	PROPN
ejpam-5790	747	4	.	.	PROPN
ejpam-5790	747	5	math	math	PROPN
ejpam-5790	747	6	,	,	PUNCT
ejpam-5790	747	7	18	18	NUM
ejpam-5790	747	8	(	(	PUNCT
ejpam-5790	747	9	1	1	NUM
ejpam-5790	747	10	)	)	PUNCT
ejpam-5790	747	11	(	(	PUNCT
ejpam-5790	747	12	2025	2025	NUM
ejpam-5790	747	13	)	)	PUNCT
ejpam-5790	747	14	,	,	PUNCT
ejpam-5790	747	15	5790	5790	NUM
ejpam-5790	747	16	27	27	NUM
ejpam-5790	747	17	of	of	ADP
ejpam-5790	747	18	30	30	NUM
ejpam-5790	748	1	[	[	SYM
ejpam-5790	748	2	10	10	NUM
ejpam-5790	748	3	]	]	PUNCT
ejpam-5790	748	4	a.	a.	NOUN
ejpam-5790	748	5	al	al	PROPN
ejpam-5790	748	6	e’damat	e’damat	PROPN
ejpam-5790	748	7	,	,	PUNCT
ejpam-5790	748	8	a.	a.	PROPN
ejpam-5790	748	9	verma	verma	PROPN
ejpam-5790	748	10	,	,	PUNCT
ejpam-5790	748	11	j.	j.	PROPN
ejpam-5790	748	12	younis	younis	PROPN
ejpam-5790	748	13	,	,	PUNCT
ejpam-5790	748	14	and	and	CCONJ
ejpam-5790	748	15	h.	h.	PROPN
ejpam-5790	748	16	aydi	aydi	VERB
ejpam-5790	748	17	.	.	PUNCT
ejpam-5790	749	1	some	some	DET
ejpam-5790	749	2	properties	property	NOUN
ejpam-5790	749	3	of	of	ADP
ejpam-5790	749	4	incomplete	incomplete	ADJ
ejpam-5790	749	5	first	first	ADJ
ejpam-5790	749	6	appell	appell	ADJ
ejpam-5790	749	7	hypergeometric	hypergeometric	ADJ
ejpam-5790	749	8	matrix	matrix	NOUN
ejpam-5790	749	9	functions	function	NOUN
ejpam-5790	749	10	.	.	PUNCT
ejpam-5790	750	1	applied	apply	VERB
ejpam-5790	750	2	mathematics	mathematic	NOUN
ejpam-5790	750	3	,	,	PUNCT
ejpam-5790	750	4	17(3):429–435	17(3):429–435	NUM
ejpam-5790	750	5	,	,	PUNCT
ejpam-5790	750	6	2023	2023	NUM
ejpam-5790	750	7	.	.	PUNCT
ejpam-5790	751	1	[	[	X
ejpam-5790	751	2	11	11	NUM
ejpam-5790	751	3	]	]	PUNCT
ejpam-5790	751	4	m.	m.	NOUN
ejpam-5790	751	5	a.	a.	PROPN
ejpam-5790	751	6	ali	ali	PROPN
ejpam-5790	751	7	,	,	PUNCT
ejpam-5790	751	8	m.	m.	NOUN
ejpam-5790	751	9	abbas	abbas	PROPN
ejpam-5790	751	10	,	,	PUNCT
ejpam-5790	751	11	h.	h.	PROPN
ejpam-5790	751	12	budak	budak	PROPN
ejpam-5790	751	13	,	,	PUNCT
ejpam-5790	751	14	p.	p.	PROPN
ejpam-5790	751	15	agarwal	agarwal	PROPN
ejpam-5790	751	16	,	,	PUNCT
ejpam-5790	751	17	g.	g.	PROPN
ejpam-5790	751	18	murtaza	murtaza	PROPN
ejpam-5790	751	19	,	,	PUNCT
ejpam-5790	751	20	and	and	CCONJ
ejpam-5790	751	21	y.-m	y.-m	NOUN
ejpam-5790	751	22	.	.	PUNCT
ejpam-5790	752	1	chu	chu	PROPN
ejpam-5790	752	2	.	.	PUNCT
ejpam-5790	753	1	new	new	ADJ
ejpam-5790	753	2	quantum	quantum	ADJ
ejpam-5790	753	3	boundaries	boundary	NOUN
ejpam-5790	753	4	for	for	ADP
ejpam-5790	753	5	quantum	quantum	PROPN
ejpam-5790	753	6	simpson	simpson	PROPN
ejpam-5790	753	7	’s	’s	PART
ejpam-5790	753	8	and	and	CCONJ
ejpam-5790	753	9	quantum	quantum	PROPN
ejpam-5790	753	10	newton	newton	PROPN
ejpam-5790	753	11	’s	’s	PART
ejpam-5790	753	12	type	type	NOUN
ejpam-5790	753	13	inequalities	inequality	NOUN
ejpam-5790	753	14	for	for	ADP
ejpam-5790	753	15	preinvex	preinvex	NOUN
ejpam-5790	753	16	functions	function	NOUN
ejpam-5790	753	17	.	.	PUNCT
ejpam-5790	754	1	advances	advance	NOUN
ejpam-5790	754	2	in	in	ADP
ejpam-5790	754	3	differential	differential	ADJ
ejpam-5790	754	4	equations	equation	NOUN
ejpam-5790	754	5	,	,	PUNCT
ejpam-5790	754	6	2021:64	2021:64	NUM
ejpam-5790	754	7	,	,	PUNCT
ejpam-5790	754	8	2021	2021	NUM
ejpam-5790	754	9	.	.	PUNCT
ejpam-5790	755	1	[	[	X
ejpam-5790	755	2	12	12	NUM
ejpam-5790	755	3	]	]	PUNCT
ejpam-5790	755	4	m.	m.	NOUN
ejpam-5790	755	5	a.	a.	PROPN
ejpam-5790	755	6	ali	ali	PROPN
ejpam-5790	755	7	,	,	PUNCT
ejpam-5790	755	8	h.	h.	PROPN
ejpam-5790	755	9	budak	budak	PROPN
ejpam-5790	755	10	,	,	PUNCT
ejpam-5790	755	11	z.	z.	PROPN
ejpam-5790	755	12	zhang	zhang	PROPN
ejpam-5790	755	13	,	,	PUNCT
ejpam-5790	755	14	and	and	CCONJ
ejpam-5790	755	15	h.	h.	PROPN
ejpam-5790	755	16	yildirim	yildirim	PROPN
ejpam-5790	755	17	.	.	PUNCT
ejpam-5790	756	1	some	some	DET
ejpam-5790	756	2	new	new	PROPN
ejpam-5790	756	3	simpson	simpson	PROPN
ejpam-5790	756	4	’s	’s	PART
ejpam-5790	756	5	type	type	NOUN
ejpam-5790	756	6	inequalities	inequality	NOUN
ejpam-5790	756	7	for	for	ADP
ejpam-5790	756	8	coordinated	coordinated	ADJ
ejpam-5790	756	9	convex	convex	NOUN
ejpam-5790	756	10	functions	function	NOUN
ejpam-5790	756	11	in	in	ADP
ejpam-5790	756	12	quantum	quantum	NOUN
ejpam-5790	756	13	calculus	calculus	NOUN
ejpam-5790	756	14	.	.	PUNCT
ejpam-5790	757	1	mathematical	mathematical	ADJ
ejpam-5790	757	2	methods	method	NOUN
ejpam-5790	757	3	in	in	ADP
ejpam-5790	757	4	applied	applied	ADJ
ejpam-5790	757	5	sciences	science	NOUN
ejpam-5790	757	6	,	,	PUNCT
ejpam-5790	757	7	44:4515–4540	44:4515–4540	NUM
ejpam-5790	757	8	,	,	PUNCT
ejpam-5790	757	9	2021	2021	NUM
ejpam-5790	757	10	.	.	PUNCT
ejpam-5790	758	1	[	[	X
ejpam-5790	758	2	13	13	NUM
ejpam-5790	758	3	]	]	X
ejpam-5790	758	4	m.a	m.a	PROPN
ejpam-5790	758	5	.	.	PROPN
ejpam-5790	758	6	ali	ali	PROPN
ejpam-5790	758	7	,	,	PUNCT
ejpam-5790	758	8	h.	h.	PROPN
ejpam-5790	758	9	kara	kara	PROPN
ejpam-5790	758	10	,	,	PUNCT
ejpam-5790	758	11	j.	j.	PROPN
ejpam-5790	758	12	tariboon	tariboon	PROPN
ejpam-5790	758	13	,	,	PUNCT
ejpam-5790	758	14	s.	s.	PROPN
ejpam-5790	758	15	asawasamrit	asawasamrit	PROPN
ejpam-5790	758	16	,	,	PUNCT
ejpam-5790	758	17	h.	h.	PROPN
ejpam-5790	758	18	budak	budak	PROPN
ejpam-5790	758	19	,	,	PUNCT
ejpam-5790	758	20	and	and	CCONJ
ejpam-5790	758	21	f.	f.	PROPN
ejpam-5790	758	22	hezenci	hezenci	PROPN
ejpam-5790	758	23	.	.	PUNCT
ejpam-5790	759	1	some	some	DET
ejpam-5790	759	2	new	new	ADJ
ejpam-5790	759	3	simpson’s	simpson’s	ADJ
ejpam-5790	759	4	-	-	PUNCT
ejpam-5790	759	5	formula	formula	NOUN
ejpam-5790	759	6	-	-	PUNCT
ejpam-5790	759	7	type	type	NOUN
ejpam-5790	759	8	inequalities	inequality	NOUN
ejpam-5790	759	9	for	for	ADP
ejpam-5790	759	10	twice	twice	ADV
ejpam-5790	759	11	-	-	PUNCT
ejpam-5790	759	12	differentiable	differentiable	ADJ
ejpam-5790	759	13	convex	convex	NOUN
ejpam-5790	759	14	functions	function	NOUN
ejpam-5790	759	15	via	via	ADP
ejpam-5790	759	16	generalized	generalized	ADJ
ejpam-5790	759	17	fractional	fractional	ADJ
ejpam-5790	759	18	operators	operator	NOUN
ejpam-5790	759	19	.	.	PUNCT
ejpam-5790	760	1	symmetry	symmetry	NOUN
ejpam-5790	760	2	,	,	PUNCT
ejpam-5790	760	3	13:2249	13:2249	NUM
ejpam-5790	760	4	,	,	PUNCT
ejpam-5790	760	5	2021	2021	NUM
ejpam-5790	760	6	.	.	PUNCT
ejpam-5790	761	1	[	[	X
ejpam-5790	761	2	14	14	NUM
ejpam-5790	761	3	]	]	X
ejpam-5790	761	4	y.	y.	NOUN
ejpam-5790	761	5	almalki	almalki	PROPN
ejpam-5790	761	6	and	and	CCONJ
ejpam-5790	761	7	w.	w.	PROPN
ejpam-5790	761	8	afzal	afzal	PROPN
ejpam-5790	761	9	.	.	PUNCT
ejpam-5790	762	1	some	some	DET
ejpam-5790	762	2	new	new	ADJ
ejpam-5790	762	3	estimates	estimate	NOUN
ejpam-5790	762	4	of	of	ADP
ejpam-5790	762	5	hermite	hermite	ADJ
ejpam-5790	762	6	–	–	PUNCT
ejpam-5790	762	7	hadamard	hadamard	ADJ
ejpam-5790	762	8	inequalities	inequality	NOUN
ejpam-5790	762	9	for	for	ADP
ejpam-5790	762	10	harmonical	harmonical	ADJ
ejpam-5790	762	11	cr	cr	PROPN
ejpam-5790	762	12	-	-	PUNCT
ejpam-5790	762	13	h	h	NOUN
ejpam-5790	762	14	-	-	PUNCT
ejpam-5790	762	15	convex	convex	NOUN
ejpam-5790	762	16	functions	function	NOUN
ejpam-5790	762	17	via	via	ADP
ejpam-5790	762	18	generalized	generalized	ADJ
ejpam-5790	762	19	fractional	fractional	ADJ
ejpam-5790	762	20	integral	integral	ADJ
ejpam-5790	762	21	operator	operator	NOUN
ejpam-5790	762	22	on	on	ADP
ejpam-5790	762	23	set	set	NOUN
ejpam-5790	762	24	-	-	PUNCT
ejpam-5790	762	25	valued	value	VERB
ejpam-5790	762	26	mappings	mapping	NOUN
ejpam-5790	762	27	.	.	PUNCT
ejpam-5790	763	1	mathematics	mathematic	NOUN
ejpam-5790	763	2	,	,	PUNCT
ejpam-5790	763	3	11(19):4041	11(19):4041	NUM
ejpam-5790	763	4	,	,	PUNCT
ejpam-5790	763	5	2023	2023	NUM
ejpam-5790	763	6	.	.	PUNCT
ejpam-5790	764	1	[	[	X
ejpam-5790	764	2	15	15	NUM
ejpam-5790	764	3	]	]	X
ejpam-5790	764	4	a.	a.	NOUN
ejpam-5790	764	5	a.	a.	PROPN
ejpam-5790	764	6	almoneef	almoneef	PROPN
ejpam-5790	764	7	,	,	PUNCT
ejpam-5790	764	8	a.-a	a.-a	PROPN
ejpam-5790	764	9	.	.	PUNCT
ejpam-5790	765	1	hyder	hyder	PROPN
ejpam-5790	765	2	,	,	PUNCT
ejpam-5790	765	3	f.	f.	PROPN
ejpam-5790	765	4	hezenci	hezenci	PROPN
ejpam-5790	765	5	,	,	PUNCT
ejpam-5790	765	6	and	and	CCONJ
ejpam-5790	765	7	h.	h.	PROPN
ejpam-5790	765	8	budak	budak	PROPN
ejpam-5790	765	9	.	.	PUNCT
ejpam-5790	766	1	simpson	simpson	PROPN
ejpam-5790	766	2	-	-	PUNCT
ejpam-5790	766	3	type	type	NOUN
ejpam-5790	766	4	inequalities	inequality	NOUN
ejpam-5790	766	5	by	by	ADP
ejpam-5790	766	6	means	mean	NOUN
ejpam-5790	766	7	of	of	ADP
ejpam-5790	766	8	tempered	temper	VERB
ejpam-5790	766	9	fractional	fractional	ADJ
ejpam-5790	766	10	integrals	integral	NOUN
ejpam-5790	766	11	.	.	PUNCT
ejpam-5790	767	1	aims	aim	VERB
ejpam-5790	767	2	mathematics	mathematic	NOUN
ejpam-5790	767	3	,	,	PUNCT
ejpam-5790	767	4	8:29411–29423	8:29411–29423	NUM
ejpam-5790	767	5	,	,	PUNCT
ejpam-5790	767	6	2023	2023	NUM
ejpam-5790	767	7	.	.	PUNCT
ejpam-5790	768	1	[	[	X
ejpam-5790	768	2	16	16	NUM
ejpam-5790	768	3	]	]	PUNCT
ejpam-5790	768	4	m.	m.	NOUN
ejpam-5790	768	5	alomari	alomari	PROPN
ejpam-5790	768	6	,	,	PUNCT
ejpam-5790	768	7	m.	m.	NOUN
ejpam-5790	768	8	darus	darus	NOUN
ejpam-5790	768	9	,	,	PUNCT
ejpam-5790	768	10	s.	s.	PROPN
ejpam-5790	768	11	s.	s.	PROPN
ejpam-5790	768	12	dragomir	dragomir	PROPN
ejpam-5790	768	13	,	,	PUNCT
ejpam-5790	768	14	and	and	CCONJ
ejpam-5790	768	15	p.	p.	PROPN
ejpam-5790	768	16	cerone	cerone	PROPN
ejpam-5790	768	17	.	.	PUNCT
ejpam-5790	769	1	ostrowski	ostrowski	ADJ
ejpam-5790	769	2	type	type	NOUN
ejpam-5790	769	3	inequalities	inequality	NOUN
ejpam-5790	769	4	for	for	ADP
ejpam-5790	769	5	functions	function	NOUN
ejpam-5790	769	6	whose	whose	DET
ejpam-5790	769	7	derivatives	derivative	NOUN
ejpam-5790	769	8	are	be	AUX
ejpam-5790	769	9	s	s	NOUN
ejpam-5790	769	10	-	-	NOUN
ejpam-5790	769	11	convex	convex	ADJ
ejpam-5790	769	12	in	in	ADP
ejpam-5790	769	13	the	the	DET
ejpam-5790	769	14	second	second	ADJ
ejpam-5790	769	15	sense	sense	NOUN
ejpam-5790	769	16	.	.	PUNCT
ejpam-5790	770	1	applied	apply	VERB
ejpam-5790	770	2	mathematics	mathematics	NOUN
ejpam-5790	770	3	letters	letter	NOUN
ejpam-5790	770	4	,	,	PUNCT
ejpam-5790	770	5	23:1071–1076	23:1071–1076	NUM
ejpam-5790	770	6	,	,	PUNCT
ejpam-5790	770	7	2010	2010	NUM
ejpam-5790	770	8	.	.	PUNCT
ejpam-5790	771	1	[	[	X
ejpam-5790	771	2	17	17	NUM
ejpam-5790	771	3	]	]	PUNCT
ejpam-5790	771	4	h.	h.	PROPN
ejpam-5790	771	5	araki	araki	PROPN
ejpam-5790	771	6	and	and	CCONJ
ejpam-5790	771	7	f.	f.	PROPN
ejpam-5790	771	8	hansen	hansen	PROPN
ejpam-5790	771	9	.	.	PUNCT
ejpam-5790	772	1	jensen	jensen	PROPN
ejpam-5790	772	2	’s	’s	PART
ejpam-5790	772	3	operator	operator	NOUN
ejpam-5790	772	4	inequality	inequality	NOUN
ejpam-5790	772	5	for	for	ADP
ejpam-5790	772	6	functions	function	NOUN
ejpam-5790	772	7	of	of	ADP
ejpam-5790	772	8	several	several	ADJ
ejpam-5790	772	9	variables	variable	NOUN
ejpam-5790	772	10	.	.	PUNCT
ejpam-5790	773	1	proc	proc	NOUN
ejpam-5790	773	2	.	.	PUNCT
ejpam-5790	774	1	amer	amer	PROPN
ejpam-5790	774	2	.	.	PUNCT
ejpam-5790	774	3	math	math	PROPN
ejpam-5790	774	4	.	.	PUNCT
ejpam-5790	775	1	soc	soc	PROPN
ejpam-5790	775	2	.	.	PUNCT
ejpam-5790	775	3	,	,	PUNCT
ejpam-5790	775	4	7:2075–2084	7:2075–2084	NUM
ejpam-5790	775	5	,	,	PUNCT
ejpam-5790	775	6	2000	2000	NUM
ejpam-5790	775	7	.	.	PUNCT
ejpam-5790	776	1	[	[	X
ejpam-5790	776	2	18	18	NUM
ejpam-5790	776	3	]	]	PUNCT
ejpam-5790	776	4	m.	m.	NOUN
ejpam-5790	776	5	g.	g.	PROPN
ejpam-5790	776	6	bin	bin	PROPN
ejpam-5790	776	7	-	-	PROPN
ejpam-5790	776	8	saad	saad	PROPN
ejpam-5790	776	9	,	,	PUNCT
ejpam-5790	776	10	a.	a.	PROPN
ejpam-5790	776	11	m.	m.	PROPN
ejpam-5790	776	12	al	al	PROPN
ejpam-5790	776	13	-	-	PUNCT
ejpam-5790	776	14	hashami	hashami	NOUN
ejpam-5790	776	15	,	,	PUNCT
ejpam-5790	776	16	and	and	CCONJ
ejpam-5790	776	17	j.	j.	PROPN
ejpam-5790	776	18	a.	a.	PROPN
ejpam-5790	776	19	younis	younis	PROPN
ejpam-5790	776	20	.	.	PUNCT
ejpam-5790	777	1	some	some	DET
ejpam-5790	777	2	fractional	fractional	ADJ
ejpam-5790	777	3	calculus	calculus	NOUN
ejpam-5790	777	4	properties	property	NOUN
ejpam-5790	777	5	of	of	ADP
ejpam-5790	777	6	the	the	DET
ejpam-5790	777	7	bivariate	bivariate	ADJ
ejpam-5790	777	8	mittag	mittag	ADJ
ejpam-5790	777	9	-	-	PUNCT
ejpam-5790	777	10	leffler	leffler	NOUN
ejpam-5790	777	11	function	function	NOUN
ejpam-5790	777	12	.	.	PUNCT
ejpam-5790	778	1	journal	journal	NOUN
ejpam-5790	778	2	of	of	ADP
ejpam-5790	778	3	fractional	fractional	ADJ
ejpam-5790	778	4	calculus	calculus	NOUN
ejpam-5790	778	5	and	and	CCONJ
ejpam-5790	778	6	applications	application	NOUN
ejpam-5790	778	7	,	,	PUNCT
ejpam-5790	778	8	14(1):214–227	14(1):214–227	NUM
ejpam-5790	778	9	,	,	PUNCT
ejpam-5790	778	10	2023	2023	NUM
ejpam-5790	778	11	.	.	PUNCT
ejpam-5790	779	1	[	[	X
ejpam-5790	779	2	19	19	NUM
ejpam-5790	779	3	]	]	PUNCT
ejpam-5790	779	4	r.	r.	PROPN
ejpam-5790	779	5	p.	p.	PROPN
ejpam-5790	779	6	boas	boas	PROPN
ejpam-5790	779	7	and	and	CCONJ
ejpam-5790	779	8	m.	m.	PROPN
ejpam-5790	779	9	b.	b.	PROPN
ejpam-5790	779	10	marcus	marcus	PROPN
ejpam-5790	779	11	.	.	PUNCT
ejpam-5790	780	1	generalizations	generalization	NOUN
ejpam-5790	780	2	of	of	ADP
ejpam-5790	780	3	young	young	PROPN
ejpam-5790	780	4	’s	’s	PART
ejpam-5790	780	5	inequality	inequality	NOUN
ejpam-5790	780	6	.	.	PUNCT
ejpam-5790	781	1	journal	journal	PROPN
ejpam-5790	781	2	of	of	ADP
ejpam-5790	781	3	mathematical	mathematical	ADJ
ejpam-5790	781	4	analysis	analysis	NOUN
ejpam-5790	781	5	and	and	CCONJ
ejpam-5790	781	6	applications	application	NOUN
ejpam-5790	781	7	,	,	PUNCT
ejpam-5790	781	8	46:36–40	46:36–40	NUM
ejpam-5790	781	9	,	,	PUNCT
ejpam-5790	781	10	1974	1974	NUM
ejpam-5790	781	11	.	.	PUNCT
ejpam-5790	782	1	[	[	X
ejpam-5790	782	2	20	20	NUM
ejpam-5790	782	3	]	]	PUNCT
ejpam-5790	782	4	a.	a.	NOUN
ejpam-5790	782	5	bouchenak	bouchenak	NOUN
ejpam-5790	782	6	,	,	PUNCT
ejpam-5790	782	7	m.	m.	NOUN
ejpam-5790	782	8	al	al	PROPN
ejpam-5790	782	9	horani	horani	PROPN
ejpam-5790	782	10	,	,	PUNCT
ejpam-5790	782	11	j.	j.	PROPN
ejpam-5790	782	12	younis	younis	PROPN
ejpam-5790	782	13	,	,	PUNCT
ejpam-5790	782	14	r.	r.	PROPN
ejpam-5790	782	15	khalil	khalil	PROPN
ejpam-5790	782	16	,	,	PUNCT
ejpam-5790	782	17	and	and	CCONJ
ejpam-5790	782	18	m.	m.	NOUN
ejpam-5790	782	19	a.	a.	PROPN
ejpam-5790	782	20	abd	abd	PROPN
ejpam-5790	782	21	el	el	PROPN
ejpam-5790	782	22	salam	salam	PROPN
ejpam-5790	782	23	.	.	PUNCT
ejpam-5790	783	1	fractional	fractional	ADJ
ejpam-5790	783	2	laplace	laplace	NOUN
ejpam-5790	783	3	transform	transform	NOUN
ejpam-5790	783	4	for	for	ADP
ejpam-5790	783	5	matrix	matrix	NOUN
ejpam-5790	783	6	valued	value	VERB
ejpam-5790	783	7	functions	function	NOUN
ejpam-5790	783	8	with	with	ADP
ejpam-5790	783	9	applications	application	NOUN
ejpam-5790	783	10	.	.	PUNCT
ejpam-5790	784	1	arab	arab	PROPN
ejpam-5790	784	2	journal	journal	PROPN
ejpam-5790	784	3	of	of	ADP
ejpam-5790	784	4	basic	basic	ADJ
ejpam-5790	784	5	and	and	CCONJ
ejpam-5790	784	6	applied	applied	ADJ
ejpam-5790	784	7	sciences	science	NOUN
ejpam-5790	784	8	,	,	PUNCT
ejpam-5790	784	9	29(1):330–336	29(1):330–336	NOUN
ejpam-5790	784	10	,	,	PUNCT
ejpam-5790	784	11	2022	2022	NUM
ejpam-5790	784	12	.	.	PUNCT
ejpam-5790	785	1	[	[	X
ejpam-5790	785	2	21	21	NUM
ejpam-5790	785	3	]	]	X
ejpam-5790	785	4	h.	h.	PROPN
ejpam-5790	785	5	budak	budak	PROPN
ejpam-5790	785	6	,	,	PUNCT
ejpam-5790	785	7	f.	f.	PROPN
ejpam-5790	785	8	hezenci	hezenci	PROPN
ejpam-5790	785	9	,	,	PUNCT
ejpam-5790	785	10	h.	h.	PROPN
ejpam-5790	785	11	kara	kara	PROPN
ejpam-5790	785	12	,	,	PUNCT
ejpam-5790	785	13	and	and	CCONJ
ejpam-5790	785	14	m.	m.	PROPN
ejpam-5790	785	15	z.	z.	PROPN
ejpam-5790	785	16	sarikaya	sarikaya	PROPN
ejpam-5790	785	17	.	.	PUNCT
ejpam-5790	785	18	bounds	bound	VERB
ejpam-5790	785	19	for	for	ADP
ejpam-5790	785	20	the	the	DET
ejpam-5790	785	21	error	error	NOUN
ejpam-5790	785	22	in	in	ADP
ejpam-5790	785	23	approximating	approximate	VERB
ejpam-5790	785	24	a	a	DET
ejpam-5790	785	25	fractional	fractional	ADJ
ejpam-5790	785	26	integral	integral	ADJ
ejpam-5790	785	27	by	by	ADP
ejpam-5790	785	28	simpson	simpson	PROPN
ejpam-5790	785	29	’s	’s	PART
ejpam-5790	785	30	rule	rule	NOUN
ejpam-5790	785	31	.	.	PUNCT
ejpam-5790	786	1	mathematics	mathematic	NOUN
ejpam-5790	786	2	,	,	PUNCT
ejpam-5790	786	3	11:2282	11:2282	NUM
ejpam-5790	786	4	,	,	PUNCT
ejpam-5790	786	5	2023	2023	NUM
ejpam-5790	786	6	.	.	PUNCT
ejpam-5790	787	1	[	[	X
ejpam-5790	787	2	22	22	NUM
ejpam-5790	787	3	]	]	X
ejpam-5790	787	4	h.	h.	PROPN
ejpam-5790	787	5	budak	budak	PROPN
ejpam-5790	787	6	,	,	PUNCT
ejpam-5790	787	7	h.	h.	PROPN
ejpam-5790	787	8	kara	kara	PROPN
ejpam-5790	787	9	,	,	PUNCT
ejpam-5790	787	10	and	and	CCONJ
ejpam-5790	787	11	f.	f.	PROPN
ejpam-5790	787	12	hezenci	hezenci	PROPN
ejpam-5790	787	13	.	.	PUNCT
ejpam-5790	788	1	fractional	fractional	ADJ
ejpam-5790	788	2	simpson	simpson	PROPN
ejpam-5790	788	3	-	-	PUNCT
ejpam-5790	788	4	type	type	NOUN
ejpam-5790	788	5	inequalities	inequality	NOUN
ejpam-5790	788	6	for	for	ADP
ejpam-5790	788	7	twice	twice	ADJ
ejpam-5790	788	8	differentiable	differentiable	ADJ
ejpam-5790	788	9	functions	function	NOUN
ejpam-5790	788	10	.	.	PUNCT
ejpam-5790	789	1	scma	scma	PROPN
ejpam-5790	789	2	,	,	PUNCT
ejpam-5790	789	3	2023	2023	NUM
ejpam-5790	789	4	.	.	PUNCT
ejpam-5790	790	1	[	[	X
ejpam-5790	790	2	23	23	NUM
ejpam-5790	790	3	]	]	PUNCT
ejpam-5790	790	4	z.	z.	PROPN
ejpam-5790	790	5	chen	chen	PROPN
ejpam-5790	790	6	,	,	PUNCT
ejpam-5790	790	7	b.	b.	PROPN
ejpam-5790	790	8	li	li	PROPN
ejpam-5790	790	9	,	,	PUNCT
ejpam-5790	790	10	and	and	CCONJ
ejpam-5790	790	11	b.	b.	PROPN
ejpam-5790	790	12	wang	wang	PROPN
ejpam-5790	790	13	.	.	PUNCT
ejpam-5790	791	1	robust	robust	ADJ
ejpam-5790	791	2	stability	stability	NOUN
ejpam-5790	791	3	design	design	NOUN
ejpam-5790	791	4	for	for	ADP
ejpam-5790	791	5	inverters	inverter	NOUN
ejpam-5790	791	6	using	use	VERB
ejpam-5790	791	7	phase	phase	NOUN
ejpam-5790	791	8	lag	lag	NOUN
ejpam-5790	791	9	in	in	ADP
ejpam-5790	791	10	proportional	proportional	ADJ
ejpam-5790	791	11	-	-	PUNCT
ejpam-5790	791	12	resonant	resonant	NOUN
ejpam-5790	791	13	controllers	controller	NOUN
ejpam-5790	791	14	.	.	PUNCT
ejpam-5790	792	1	ieee	ieee	NOUN
ejpam-5790	792	2	transactions	transaction	NOUN
ejpam-5790	792	3	on	on	ADP
ejpam-5790	792	4	industrial	industrial	ADJ
ejpam-5790	792	5	electronics	electronic	NOUN
ejpam-5790	792	6	,	,	PUNCT
ejpam-5790	792	7	2024	2024	NUM
ejpam-5790	792	8	.	.	PUNCT
ejpam-5790	793	1	[	[	X
ejpam-5790	793	2	24	24	NUM
ejpam-5790	793	3	]	]	X
ejpam-5790	793	4	s.	s.	PROPN
ejpam-5790	793	5	chu	chu	PROPN
ejpam-5790	793	6	,	,	PUNCT
ejpam-5790	793	7	m.	m.	PROPN
ejpam-5790	793	8	lin	lin	PROPN
ejpam-5790	793	9	,	,	PUNCT
ejpam-5790	793	10	d.	d.	PROPN
ejpam-5790	793	11	li	li	PROPN
ejpam-5790	793	12	,	,	PUNCT
ejpam-5790	793	13	r.	r.	PROPN
ejpam-5790	793	14	lin	lin	PROPN
ejpam-5790	793	15	,	,	PUNCT
ejpam-5790	793	16	and	and	CCONJ
ejpam-5790	793	17	s.	s.	PROPN
ejpam-5790	793	18	xiao	xiao	PROPN
ejpam-5790	793	19	.	.	PROPN
ejpam-5790	794	1	adaptive	adaptive	PROPN
ejpam-5790	794	2	reward	reward	NOUN
ejpam-5790	794	3	shaping	shape	VERB
ejpam-5790	794	4	based	base	VERB
ejpam-5790	794	5	reinforcement	reinforcement	NOUN
ejpam-5790	794	6	learning	learning	NOUN
ejpam-5790	794	7	for	for	ADP
ejpam-5790	794	8	docking	dock	VERB
ejpam-5790	794	9	control	control	NOUN
ejpam-5790	794	10	of	of	ADP
ejpam-5790	794	11	autonomous	autonomous	ADJ
ejpam-5790	794	12	underwater	underwater	ADJ
ejpam-5790	794	13	vehicles	vehicle	NOUN
ejpam-5790	794	14	.	.	PUNCT
ejpam-5790	795	1	ocean	ocean	NOUN
ejpam-5790	795	2	engineering	engineering	NOUN
ejpam-5790	795	3	,	,	PUNCT
ejpam-5790	795	4	318:120139	318:120139	NUM
ejpam-5790	795	5	,	,	PUNCT
ejpam-5790	795	6	2025	2025	NUM
ejpam-5790	795	7	.	.	PUNCT
ejpam-5790	796	1	[	[	X
ejpam-5790	796	2	25	25	NUM
ejpam-5790	796	3	]	]	X
ejpam-5790	796	4	s.	s.	PROPN
ejpam-5790	796	5	chu	chu	PROPN
ejpam-5790	796	6	,	,	PUNCT
ejpam-5790	796	7	z.	z.	PROPN
ejpam-5790	796	8	xie	xie	PROPN
ejpam-5790	796	9	,	,	PUNCT
ejpam-5790	796	10	p.	p.	PROPN
ejpam-5790	796	11	k.	k.	PROPN
ejpam-5790	796	12	wong	wong	PROPN
ejpam-5790	796	13	,	,	PUNCT
ejpam-5790	796	14	p.	p.	PROPN
ejpam-5790	796	15	li	li	PROPN
ejpam-5790	796	16	,	,	PUNCT
ejpam-5790	796	17	w.	w.	PROPN
ejpam-5790	796	18	li	li	PROPN
ejpam-5790	796	19	,	,	PUNCT
ejpam-5790	796	20	and	and	CCONJ
ejpam-5790	796	21	j.	j.	PROPN
ejpam-5790	796	22	zhao	zhao	PROPN
ejpam-5790	796	23	.	.	PUNCT
ejpam-5790	797	1	observer	observer	NOUN
ejpam-5790	797	2	-	-	PUNCT
ejpam-5790	797	3	based	base	VERB
ejpam-5790	797	4	gain	gain	NOUN
ejpam-5790	797	5	scheduling	scheduling	NOUN
ejpam-5790	797	6	path	path	NOUN
ejpam-5790	797	7	following	follow	VERB
ejpam-5790	797	8	control	control	NOUN
ejpam-5790	797	9	for	for	ADP
ejpam-5790	797	10	autonomous	autonomous	ADJ
ejpam-5790	797	11	electric	electric	ADJ
ejpam-5790	797	12	vehicles	vehicle	NOUN
ejpam-5790	797	13	subject	subject	ADJ
ejpam-5790	797	14	to	to	ADP
ejpam-5790	797	15	time	time	NOUN
ejpam-5790	797	16	delay	delay	NOUN
ejpam-5790	797	17	.	.	PUNCT
ejpam-5790	798	1	vehicle	vehicle	NOUN
ejpam-5790	798	2	system	system	NOUN
ejpam-5790	798	3	dynamics	dynamic	NOUN
ejpam-5790	798	4	,	,	PUNCT
ejpam-5790	798	5	60(5):1602–1626	60(5):1602–1626	NUM
ejpam-5790	798	6	,	,	PUNCT
ejpam-5790	798	7	2022	2022	NUM
ejpam-5790	798	8	.	.	PUNCT
ejpam-5790	799	1	[	[	X
ejpam-5790	799	2	26	26	NUM
ejpam-5790	799	3	]	]	PUNCT
ejpam-5790	799	4	j.	j.	PROPN
ejpam-5790	799	5	deng	deng	PROPN
ejpam-5790	799	6	,	,	PUNCT
ejpam-5790	799	7	g.	g.	PROPN
ejpam-5790	799	8	liu	liu	PROPN
ejpam-5790	799	9	,	,	PUNCT
ejpam-5790	799	10	l.	l.	PROPN
ejpam-5790	799	11	wang	wang	PROPN
ejpam-5790	799	12	,	,	PUNCT
ejpam-5790	799	13	g.	g.	PROPN
ejpam-5790	799	14	liu	liu	PROPN
ejpam-5790	799	15	,	,	PUNCT
ejpam-5790	799	16	and	and	CCONJ
ejpam-5790	799	17	x.	x.	PROPN
ejpam-5790	799	18	wu	wu	PROPN
ejpam-5790	799	19	.	.	PUNCT
ejpam-5790	800	1	intelligent	intelligent	ADJ
ejpam-5790	800	2	optimization	optimization	NOUN
ejpam-5790	800	3	design	design	NOUN
ejpam-5790	800	4	of	of	ADP
ejpam-5790	800	5	squeeze	squeeze	NOUN
ejpam-5790	800	6	casting	casting	NOUN
ejpam-5790	800	7	process	process	NOUN
ejpam-5790	800	8	parameters	parameter	NOUN
ejpam-5790	800	9	based	base	VERB
ejpam-5790	800	10	on	on	ADP
ejpam-5790	800	11	neural	neural	ADJ
ejpam-5790	800	12	network	network	NOUN
ejpam-5790	800	13	and	and	CCONJ
ejpam-5790	800	14	improved	improve	VERB
ejpam-5790	800	15	sparrow	sparrow	PROPN
ejpam-5790	800	16	w.	w.	PROPN
ejpam-5790	800	17	afzal	afzal	PROPN
ejpam-5790	800	18	et	et	PROPN
ejpam-5790	800	19	al	al	PROPN
ejpam-5790	800	20	.	.	PUNCT
ejpam-5790	800	21	/	/	SYM
ejpam-5790	800	22	eur	eur	PROPN
ejpam-5790	800	23	.	.	PUNCT
ejpam-5790	801	1	j.	j.	PROPN
ejpam-5790	801	2	pure	pure	PROPN
ejpam-5790	801	3	appl	appl	PROPN
ejpam-5790	801	4	.	.	PROPN
ejpam-5790	801	5	math	math	PROPN
ejpam-5790	801	6	,	,	PUNCT
ejpam-5790	801	7	18	18	NUM
ejpam-5790	801	8	(	(	PUNCT
ejpam-5790	801	9	1	1	NUM
ejpam-5790	801	10	)	)	PUNCT
ejpam-5790	801	11	(	(	PUNCT
ejpam-5790	801	12	2025	2025	NUM
ejpam-5790	801	13	)	)	PUNCT
ejpam-5790	801	14	,	,	PUNCT
ejpam-5790	801	15	5790	5790	NUM
ejpam-5790	801	16	28	28	NUM
ejpam-5790	801	17	of	of	ADP
ejpam-5790	801	18	30	30	NUM
ejpam-5790	801	19	search	search	NOUN
ejpam-5790	801	20	algorithm	algorithm	NOUN
ejpam-5790	801	21	.	.	PUNCT
ejpam-5790	802	1	journal	journal	PROPN
ejpam-5790	802	2	of	of	ADP
ejpam-5790	802	3	industrial	industrial	ADJ
ejpam-5790	802	4	information	information	NOUN
ejpam-5790	802	5	integration	integration	NOUN
ejpam-5790	802	6	,	,	PUNCT
ejpam-5790	802	7	39:100600	39:100600	NUM
ejpam-5790	802	8	,	,	PUNCT
ejpam-5790	802	9	2024	2024	NUM
ejpam-5790	802	10	.	.	PUNCT
ejpam-5790	803	1	[	[	X
ejpam-5790	803	2	27	27	NUM
ejpam-5790	803	3	]	]	PUNCT
ejpam-5790	803	4	j.	j.	PROPN
ejpam-5790	803	5	f.	f.	PROPN
ejpam-5790	803	6	dong	dong	PROPN
ejpam-5790	803	7	,	,	PUNCT
ejpam-5790	803	8	y.	y.	PROPN
ejpam-5790	803	9	c.	c.	PROPN
ejpam-5790	803	10	liu	liu	PROPN
ejpam-5790	803	11	,	,	PUNCT
ejpam-5790	803	12	y.	y.	PROPN
ejpam-5790	803	13	xu	xu	PROPN
ejpam-5790	803	14	,	,	PUNCT
ejpam-5790	803	15	s.	s.	PROPN
ejpam-5790	803	16	c.	c.	PROPN
ejpam-5790	803	17	yuan	yuan	PROPN
ejpam-5790	803	18	,	,	PUNCT
ejpam-5790	803	19	q.	q.	PROPN
ejpam-5790	803	20	y.	y.	PROPN
ejpam-5790	803	21	wang	wang	PROPN
ejpam-5790	803	22	,	,	PUNCT
ejpam-5790	803	23	z.	z.	PROPN
ejpam-5790	803	24	w.	w.	PROPN
ejpam-5790	803	25	guan	guan	PROPN
ejpam-5790	803	26	,	,	PUNCT
ejpam-5790	803	27	and	and	CCONJ
ejpam-5790	803	28	h.	h.	PROPN
ejpam-5790	803	29	k.	k.	PROPN
ejpam-5790	803	30	chai	chai	PROPN
ejpam-5790	803	31	.	.	PUNCT
ejpam-5790	804	1	investigating	investigate	VERB
ejpam-5790	804	2	the	the	DET
ejpam-5790	804	3	structural	structural	ADJ
ejpam-5790	804	4	behavior	behavior	NOUN
ejpam-5790	804	5	of	of	ADP
ejpam-5790	804	6	double	double	ADJ
ejpam-5790	804	7	-	-	PUNCT
ejpam-5790	804	8	skin	skin	NOUN
ejpam-5790	804	9	steel	steel	NOUN
ejpam-5790	804	10	tubes	tube	NOUN
ejpam-5790	804	11	filled	fill	VERB
ejpam-5790	804	12	with	with	ADP
ejpam-5790	804	13	basalt	basalt	NOUN
ejpam-5790	804	14	fibre	fibre	NOUN
ejpam-5790	804	15	reinforced	reinforce	VERB
ejpam-5790	804	16	recycled	recycle	VERB
ejpam-5790	804	17	aggregate	aggregate	ADJ
ejpam-5790	804	18	concrete	concrete	NOUN
ejpam-5790	804	19	under	under	ADP
ejpam-5790	804	20	high	high	ADJ
ejpam-5790	804	21	temperature	temperature	NOUN
ejpam-5790	804	22	.	.	PUNCT
ejpam-5790	805	1	journal	journal	NOUN
ejpam-5790	805	2	of	of	ADP
ejpam-5790	805	3	building	build	VERB
ejpam-5790	805	4	engineering	engineering	NOUN
ejpam-5790	805	5	,	,	PUNCT
ejpam-5790	805	6	page	page	NOUN
ejpam-5790	805	7	111782	111782	NUM
ejpam-5790	805	8	,	,	PUNCT
ejpam-5790	805	9	2025	2025	NUM
ejpam-5790	805	10	.	.	PUNCT
ejpam-5790	806	1	[	[	X
ejpam-5790	806	2	28	28	NUM
ejpam-5790	806	3	]	]	X
ejpam-5790	806	4	s.	s.	PROPN
ejpam-5790	806	5	dragomir	dragomir	PROPN
ejpam-5790	806	6	.	.	PUNCT
ejpam-5790	807	1	refinements	refinement	NOUN
ejpam-5790	807	2	and	and	CCONJ
ejpam-5790	807	3	reverses	reverse	NOUN
ejpam-5790	807	4	of	of	ADP
ejpam-5790	807	5	tensorial	tensorial	ADJ
ejpam-5790	807	6	and	and	CCONJ
ejpam-5790	807	7	hadamard	hadamard	ADJ
ejpam-5790	807	8	product	product	NOUN
ejpam-5790	807	9	inequalities	inequality	NOUN
ejpam-5790	807	10	for	for	ADP
ejpam-5790	807	11	selfadjoint	selfadjoint	NOUN
ejpam-5790	807	12	operators	operator	NOUN
ejpam-5790	807	13	in	in	ADP
ejpam-5790	807	14	hilbert	hilbert	PROPN
ejpam-5790	807	15	spaces	space	NOUN
ejpam-5790	807	16	related	relate	VERB
ejpam-5790	807	17	to	to	ADP
ejpam-5790	807	18	young	young	PROPN
ejpam-5790	807	19	’s	’s	PART
ejpam-5790	807	20	result	result	NOUN
ejpam-5790	807	21	.	.	PUNCT
ejpam-5790	808	1	communications	communication	NOUN
ejpam-5790	808	2	in	in	ADP
ejpam-5790	808	3	advanced	advanced	ADJ
ejpam-5790	808	4	mathematical	mathematical	ADJ
ejpam-5790	808	5	sciences	science	NOUN
ejpam-5790	808	6	,	,	PUNCT
ejpam-5790	808	7	7:56–70	7:56–70	NUM
ejpam-5790	808	8	,	,	PUNCT
ejpam-5790	808	9	2024	2024	NUM
ejpam-5790	808	10	.	.	PUNCT
ejpam-5790	809	1	[	[	X
ejpam-5790	809	2	29	29	NUM
ejpam-5790	809	3	]	]	X
ejpam-5790	809	4	d.	d.	PROPN
ejpam-5790	809	5	gao	gao	PROPN
ejpam-5790	809	6	,	,	PUNCT
ejpam-5790	809	7	s.	s.	PROPN
ejpam-5790	809	8	liu	liu	PROPN
ejpam-5790	809	9	,	,	PUNCT
ejpam-5790	809	10	y.	y.	PROPN
ejpam-5790	809	11	gao	gao	PROPN
ejpam-5790	809	12	,	,	PUNCT
ejpam-5790	809	13	p.	p.	PROPN
ejpam-5790	809	14	li	li	PROPN
ejpam-5790	809	15	,	,	PUNCT
ejpam-5790	809	16	h.	h.	PROPN
ejpam-5790	809	17	zhang	zhang	PROPN
ejpam-5790	809	18	,	,	PUNCT
ejpam-5790	809	19	m.	m.	PROPN
ejpam-5790	809	20	wang	wang	PROPN
ejpam-5790	809	21	,	,	PUNCT
ejpam-5790	809	22	and	and	CCONJ
ejpam-5790	809	23	y.	y.	PROPN
ejpam-5790	809	24	zhang	zhang	PROPN
ejpam-5790	809	25	.	.	PUNCT
ejpam-5790	810	1	a	a	DET
ejpam-5790	810	2	comprehensive	comprehensive	ADJ
ejpam-5790	810	3	adaptive	adaptive	ADJ
ejpam-5790	810	4	interpretable	interpretable	ADJ
ejpam-5790	810	5	takagi	takagi	PROPN
ejpam-5790	810	6	-	-	PUNCT
ejpam-5790	810	7	sugeuo	sugeuo	PROPN
ejpam-5790	810	8	-	-	PUNCT
ejpam-5790	810	9	kang	kang	PROPN
ejpam-5790	810	10	fuzzy	fuzzy	ADJ
ejpam-5790	810	11	classifier	classifier	NOUN
ejpam-5790	810	12	for	for	ADP
ejpam-5790	810	13	fatigue	fatigue	NOUN
ejpam-5790	810	14	driving	drive	VERB
ejpam-5790	810	15	detection	detection	NOUN
ejpam-5790	810	16	.	.	PUNCT
ejpam-5790	811	1	ieee	ieee	NOUN
ejpam-5790	811	2	transactions	transaction	NOUN
ejpam-5790	811	3	on	on	ADP
ejpam-5790	811	4	fuzzy	fuzzy	ADJ
ejpam-5790	811	5	systems	system	NOUN
ejpam-5790	811	6	,	,	PUNCT
ejpam-5790	811	7	2024	2024	NUM
ejpam-5790	811	8	.	.	PUNCT
ejpam-5790	812	1	[	[	X
ejpam-5790	812	2	30	30	NUM
ejpam-5790	812	3	]	]	PUNCT
ejpam-5790	812	4	s.	s.	PROPN
ejpam-5790	812	5	q.	q.	PROPN
ejpam-5790	812	6	hasan	hasan	PROPN
ejpam-5790	812	7	.	.	PUNCT
ejpam-5790	812	8	holder	holder	PROPN
ejpam-5790	812	9	’s	’s	PART
ejpam-5790	812	10	inequality	inequality	NOUN
ejpam-5790	812	11	mean	mean	VERB
ejpam-5790	812	12	continuity	continuity	NOUN
ejpam-5790	812	13	for	for	ADP
ejpam-5790	812	14	existence	existence	NOUN
ejpam-5790	812	15	and	and	CCONJ
ejpam-5790	812	16	uniqueness	uniqueness	ADJ
ejpam-5790	812	17	solution	solution	NOUN
ejpam-5790	812	18	of	of	ADP
ejpam-5790	812	19	fractional	fractional	ADJ
ejpam-5790	812	20	multi	multi	ADJ
ejpam-5790	812	21	-	-	ADJ
ejpam-5790	812	22	integrodifferential	integrodifferential	ADJ
ejpam-5790	812	23	delay	delay	NOUN
ejpam-5790	812	24	system	system	NOUN
ejpam-5790	812	25	.	.	PUNCT
ejpam-5790	813	1	journal	journal	NOUN
ejpam-5790	813	2	of	of	ADP
ejpam-5790	813	3	mathematics	mathematic	NOUN
ejpam-5790	813	4	,	,	PUNCT
ejpam-5790	813	5	2020:1–16	2020:1–16	NOUN
ejpam-5790	813	6	,	,	PUNCT
ejpam-5790	813	7	2020	2020	NUM
ejpam-5790	813	8	.	.	PUNCT
ejpam-5790	814	1	[	[	X
ejpam-5790	814	2	31	31	NUM
ejpam-5790	814	3	]	]	X
ejpam-5790	814	4	y.	y.	PROPN
ejpam-5790	814	5	hu	hu	PROPN
ejpam-5790	814	6	and	and	CCONJ
ejpam-5790	814	7	y.	y.	PROPN
ejpam-5790	814	8	sugiyama	sugiyama	PROPN
ejpam-5790	814	9	.	.	PUNCT
ejpam-5790	815	1	well	well	ADJ
ejpam-5790	815	2	-	-	PUNCT
ejpam-5790	815	3	posedness	posedness	NOUN
ejpam-5790	815	4	of	of	ADP
ejpam-5790	815	5	the	the	DET
ejpam-5790	815	6	initial	initial	ADJ
ejpam-5790	815	7	-	-	PUNCT
ejpam-5790	815	8	boundary	boundary	NOUN
ejpam-5790	815	9	value	value	NOUN
ejpam-5790	815	10	problem	problem	NOUN
ejpam-5790	815	11	for	for	ADP
ejpam-5790	815	12	1d	1d	NUM
ejpam-5790	815	13	degenerate	degenerate	ADJ
ejpam-5790	815	14	quasilinear	quasilinear	NOUN
ejpam-5790	815	15	wave	wave	NOUN
ejpam-5790	815	16	equations	equation	NOUN
ejpam-5790	815	17	.	.	PUNCT
ejpam-5790	816	1	advances	advance	NOUN
ejpam-5790	816	2	in	in	ADP
ejpam-5790	816	3	differential	differential	ADJ
ejpam-5790	816	4	equations	equation	NOUN
ejpam-5790	816	5	,	,	PUNCT
ejpam-5790	816	6	30(3/4):177–206	30(3/4):177–206	NUM
ejpam-5790	816	7	,	,	PUNCT
ejpam-5790	816	8	2025	2025	NUM
ejpam-5790	816	9	.	.	PUNCT
ejpam-5790	817	1	[	[	X
ejpam-5790	817	2	32	32	NUM
ejpam-5790	817	3	]	]	PUNCT
ejpam-5790	817	4	s.	s.	PROPN
ejpam-5790	817	5	iftikhar	iftikhar	PROPN
ejpam-5790	817	6	,	,	PUNCT
ejpam-5790	817	7	m.u	m.u	PROPN
ejpam-5790	817	8	.	.	PROPN
ejpam-5790	817	9	awan	awan	PROPN
ejpam-5790	817	10	,	,	PUNCT
ejpam-5790	817	11	and	and	CCONJ
ejpam-5790	817	12	h.	h.	PROPN
ejpam-5790	817	13	budak	budak	PROPN
ejpam-5790	817	14	.	.	PUNCT
ejpam-5790	817	15	exploring	explore	VERB
ejpam-5790	817	16	quantum	quantum	PROPN
ejpam-5790	817	17	simpson	simpson	ADJ
ejpam-5790	817	18	-	-	PUNCT
ejpam-5790	817	19	type	type	NOUN
ejpam-5790	817	20	inequalities	inequality	NOUN
ejpam-5790	817	21	for	for	ADP
ejpam-5790	817	22	convex	convex	NOUN
ejpam-5790	817	23	functions	function	NOUN
ejpam-5790	817	24	:	:	PUNCT
ejpam-5790	817	25	a	a	DET
ejpam-5790	817	26	novel	novel	ADJ
ejpam-5790	817	27	investigation	investigation	NOUN
ejpam-5790	817	28	.	.	PUNCT
ejpam-5790	818	1	symmetry	symmetry	NOUN
ejpam-5790	818	2	,	,	PUNCT
ejpam-5790	818	3	15:1312	15:1312	NUM
ejpam-5790	818	4	,	,	PUNCT
ejpam-5790	818	5	2023	2023	NUM
ejpam-5790	818	6	.	.	PUNCT
ejpam-5790	819	1	[	[	X
ejpam-5790	819	2	33	33	NUM
ejpam-5790	819	3	]	]	PUNCT
ejpam-5790	819	4	x.	x.	NOUN
ejpam-5790	819	5	ji	ji	PROPN
ejpam-5790	819	6	,	,	PUNCT
ejpam-5790	819	7	p.	p.	PROPN
ejpam-5790	819	8	jiang	jiang	PROPN
ejpam-5790	819	9	,	,	PUNCT
ejpam-5790	819	10	y.	y.	PROPN
ejpam-5790	819	11	jiang	jiang	PROPN
ejpam-5790	819	12	,	,	PUNCT
ejpam-5790	819	13	h.	h.	PROPN
ejpam-5790	819	14	chen	chen	PROPN
ejpam-5790	819	15	,	,	PUNCT
ejpam-5790	819	16	w.	w.	PROPN
ejpam-5790	819	17	wang	wang	PROPN
ejpam-5790	819	18	,	,	PUNCT
ejpam-5790	819	19	w.	w.	PROPN
ejpam-5790	819	20	zhong	zhong	PROPN
ejpam-5790	819	21	,	,	PUNCT
ejpam-5790	819	22	and	and	CCONJ
ejpam-5790	819	23	d.	d.	PROPN
ejpam-5790	819	24	zang	zang	PROPN
ejpam-5790	819	25	.	.	PUNCT
ejpam-5790	820	1	toward	toward	ADP
ejpam-5790	820	2	enhanced	enhanced	ADJ
ejpam-5790	820	3	aerosol	aerosol	NOUN
ejpam-5790	820	4	particle	particle	NOUN
ejpam-5790	820	5	adsorption	adsorption	NOUN
ejpam-5790	820	6	in	in	ADP
ejpam-5790	820	7	never	never	ADV
ejpam-5790	820	8	-	-	PUNCT
ejpam-5790	820	9	bursting	burst	VERB
ejpam-5790	820	10	bubble	bubble	NOUN
ejpam-5790	820	11	via	via	ADP
ejpam-5790	820	12	acoustic	acoustic	ADJ
ejpam-5790	820	13	levitation	levitation	PROPN
ejpam-5790	820	14	and	and	CCONJ
ejpam-5790	820	15	controlled	control	VERB
ejpam-5790	820	16	liquid	liquid	ADJ
ejpam-5790	820	17	compensation	compensation	NOUN
ejpam-5790	820	18	.	.	PUNCT
ejpam-5790	821	1	advanced	advanced	ADJ
ejpam-5790	821	2	science	science	NOUN
ejpam-5790	821	3	,	,	PUNCT
ejpam-5790	821	4	10(19):2300049	10(19):2300049	NUM
ejpam-5790	821	5	,	,	PUNCT
ejpam-5790	821	6	2023	2023	NUM
ejpam-5790	821	7	.	.	PUNCT
ejpam-5790	822	1	[	[	X
ejpam-5790	822	2	34	34	NUM
ejpam-5790	822	3	]	]	PUNCT
ejpam-5790	822	4	x.	x.	NOUN
ejpam-5790	822	5	ji	ji	PROPN
ejpam-5790	822	6	,	,	PUNCT
ejpam-5790	822	7	p.	p.	PROPN
ejpam-5790	822	8	jiang	jiang	PROPN
ejpam-5790	822	9	,	,	PUNCT
ejpam-5790	822	10	y.	y.	PROPN
ejpam-5790	822	11	jiang	jiang	PROPN
ejpam-5790	822	12	,	,	PUNCT
ejpam-5790	822	13	h.	h.	PROPN
ejpam-5790	822	14	chen	chen	PROPN
ejpam-5790	822	15	,	,	PUNCT
ejpam-5790	822	16	w.	w.	PROPN
ejpam-5790	822	17	wang	wang	PROPN
ejpam-5790	822	18	,	,	PUNCT
ejpam-5790	822	19	w.	w.	PROPN
ejpam-5790	822	20	zhong	zhong	PROPN
ejpam-5790	822	21	,	,	PUNCT
ejpam-5790	822	22	and	and	CCONJ
ejpam-5790	822	23	d.	d.	PROPN
ejpam-5790	822	24	zang	zang	PROPN
ejpam-5790	822	25	.	.	PUNCT
ejpam-5790	823	1	toward	toward	ADP
ejpam-5790	823	2	enhanced	enhanced	ADJ
ejpam-5790	823	3	aerosol	aerosol	NOUN
ejpam-5790	823	4	particle	particle	NOUN
ejpam-5790	823	5	adsorption	adsorption	NOUN
ejpam-5790	823	6	in	in	ADP
ejpam-5790	823	7	never	never	ADV
ejpam-5790	823	8	-	-	PUNCT
ejpam-5790	823	9	bursting	burst	VERB
ejpam-5790	823	10	bubble	bubble	NOUN
ejpam-5790	823	11	via	via	ADP
ejpam-5790	823	12	acoustic	acoustic	ADJ
ejpam-5790	823	13	levitation	levitation	PROPN
ejpam-5790	823	14	and	and	CCONJ
ejpam-5790	823	15	controlled	control	VERB
ejpam-5790	823	16	liquid	liquid	ADJ
ejpam-5790	823	17	compensation	compensation	NOUN
ejpam-5790	823	18	.	.	PUNCT
ejpam-5790	824	1	advanced	advanced	ADJ
ejpam-5790	824	2	science	science	NOUN
ejpam-5790	824	3	,	,	PUNCT
ejpam-5790	824	4	10(19):2300049	10(19):2300049	NUM
ejpam-5790	824	5	,	,	PUNCT
ejpam-5790	824	6	2023	2023	NUM
ejpam-5790	824	7	.	.	PUNCT
ejpam-5790	825	1	[	[	X
ejpam-5790	825	2	35	35	NUM
ejpam-5790	825	3	]	]	X
ejpam-5790	825	4	s.	s.	PROPN
ejpam-5790	825	5	jia	jia	PROPN
ejpam-5790	825	6	,	,	PUNCT
ejpam-5790	825	7	y.	y.	PROPN
ejpam-5790	825	8	li	li	PROPN
ejpam-5790	825	9	,	,	PUNCT
ejpam-5790	825	10	c.	c.	PROPN
ejpam-5790	825	11	gao	gao	PROPN
ejpam-5790	825	12	,	,	PUNCT
ejpam-5790	825	13	g.	g.	PROPN
ejpam-5790	825	14	liu	liu	PROPN
ejpam-5790	825	15	,	,	PUNCT
ejpam-5790	825	16	y.	y.	PROPN
ejpam-5790	825	17	ren	ren	PROPN
ejpam-5790	825	18	,	,	PUNCT
ejpam-5790	825	19	c.	c.	PROPN
ejpam-5790	825	20	he	he	PRON
ejpam-5790	825	21	,	,	PUNCT
ejpam-5790	825	22	and	and	CCONJ
ejpam-5790	825	23	x.	x.	PROPN
ejpam-5790	825	24	t.	t.	PROPN
ejpam-5790	825	25	an	an	PROPN
ejpam-5790	825	26	.	.	PUNCT
ejpam-5790	825	27	realization	realization	NOUN
ejpam-5790	825	28	of	of	ADP
ejpam-5790	825	29	p	p	NOUN
ejpam-5790	825	30	-	-	PUNCT
ejpam-5790	825	31	type	type	NOUN
ejpam-5790	825	32	ma	ma	NOUN
ejpam-5790	825	33	-	-	PUNCT
ejpam-5790	825	34	based	base	VERB
ejpam-5790	825	35	perovskite	perovskite	ADJ
ejpam-5790	825	36	solar	solar	ADJ
ejpam-5790	825	37	cells	cell	NOUN
ejpam-5790	825	38	based	base	VERB
ejpam-5790	825	39	on	on	ADP
ejpam-5790	825	40	exposure	exposure	NOUN
ejpam-5790	825	41	of	of	ADP
ejpam-5790	825	42	the	the	DET
ejpam-5790	825	43	(	(	PUNCT
ejpam-5790	825	44	002	002	NUM
ejpam-5790	825	45	)	)	PUNCT
ejpam-5790	825	46	facet	facet	PROPN
ejpam-5790	825	47	.	.	PUNCT
ejpam-5790	826	1	applied	apply	VERB
ejpam-5790	826	2	physics	physics	NOUN
ejpam-5790	826	3	letters	letter	NOUN
ejpam-5790	826	4	,	,	PUNCT
ejpam-5790	826	5	126(2	126(2	NUM
ejpam-5790	826	6	)	)	PUNCT
ejpam-5790	826	7	,	,	PUNCT
ejpam-5790	826	8	2025	2025	NUM
ejpam-5790	826	9	.	.	PUNCT
ejpam-5790	827	1	[	[	X
ejpam-5790	827	2	36	36	NUM
ejpam-5790	827	3	]	]	X
ejpam-5790	827	4	h.	h.	PROPN
ejpam-5790	827	5	kara	kara	PROPN
ejpam-5790	827	6	,	,	PUNCT
ejpam-5790	827	7	h.	h.	PROPN
ejpam-5790	827	8	budak	budak	PROPN
ejpam-5790	827	9	,	,	PUNCT
ejpam-5790	827	10	m.	m.	PROPN
ejpam-5790	827	11	a.	a.	PROPN
ejpam-5790	827	12	ali	ali	PROPN
ejpam-5790	827	13	,	,	PUNCT
ejpam-5790	827	14	and	and	CCONJ
ejpam-5790	827	15	f.	f.	PROPN
ejpam-5790	827	16	hezenci	hezenci	PROPN
ejpam-5790	827	17	.	.	PUNCT
ejpam-5790	828	1	on	on	ADP
ejpam-5790	828	2	inequalities	inequality	NOUN
ejpam-5790	828	3	of	of	ADP
ejpam-5790	828	4	simpson	simpson	PROPN
ejpam-5790	828	5	’s	’s	PART
ejpam-5790	828	6	type	type	NOUN
ejpam-5790	828	7	for	for	ADP
ejpam-5790	828	8	convex	convex	NOUN
ejpam-5790	828	9	functions	function	NOUN
ejpam-5790	828	10	via	via	ADP
ejpam-5790	828	11	generalized	generalized	ADJ
ejpam-5790	828	12	fractional	fractional	ADJ
ejpam-5790	828	13	integrals	integral	NOUN
ejpam-5790	828	14	.	.	PUNCT
ejpam-5790	829	1	communications	communication	NOUN
ejpam-5790	829	2	faculty	faculty	NOUN
ejpam-5790	829	3	of	of	ADP
ejpam-5790	829	4	sciences	sciences	PROPN
ejpam-5790	829	5	university	university	PROPN
ejpam-5790	829	6	of	of	ADP
ejpam-5790	829	7	ankara	ankara	PROPN
ejpam-5790	829	8	series	series	PROPN
ejpam-5790	829	9	a1	a1	PROPN
ejpam-5790	829	10	mathematics	mathematic	NOUN
ejpam-5790	829	11	and	and	CCONJ
ejpam-5790	829	12	statistics	statistic	NOUN
ejpam-5790	829	13	,	,	PUNCT
ejpam-5790	829	14	71:806–825	71:806–825	NUM
ejpam-5790	829	15	,	,	PUNCT
ejpam-5790	829	16	2022	2022	NUM
ejpam-5790	829	17	.	.	PUNCT
ejpam-5790	830	1	[	[	X
ejpam-5790	830	2	37	37	NUM
ejpam-5790	830	3	]	]	PUNCT
ejpam-5790	830	4	z.	z.	PROPN
ejpam-5790	830	5	a.	a.	PROPN
ejpam-5790	830	6	khan	khan	PROPN
ejpam-5790	830	7	,	,	PUNCT
ejpam-5790	830	8	w.	w.	PROPN
ejpam-5790	830	9	afzal	afzal	PROPN
ejpam-5790	830	10	,	,	PUNCT
ejpam-5790	830	11	m.	m.	NOUN
ejpam-5790	830	12	abbas	abbas	PROPN
ejpam-5790	830	13	,	,	PUNCT
ejpam-5790	830	14	j.	j.	PROPN
ejpam-5790	830	15	ro	ro	PROPN
ejpam-5790	830	16	,	,	PUNCT
ejpam-5790	830	17	and	and	CCONJ
ejpam-5790	830	18	n.	n.	PROPN
ejpam-5790	830	19	m.	m.	PROPN
ejpam-5790	830	20	aloraini	aloraini	PROPN
ejpam-5790	830	21	.	.	PUNCT
ejpam-5790	831	1	a	a	DET
ejpam-5790	831	2	novel	novel	ADJ
ejpam-5790	831	3	fractional	fractional	ADJ
ejpam-5790	831	4	approach	approach	NOUN
ejpam-5790	831	5	to	to	ADP
ejpam-5790	831	6	finding	find	VERB
ejpam-5790	831	7	the	the	DET
ejpam-5790	831	8	upper	upper	ADJ
ejpam-5790	831	9	bounds	bound	NOUN
ejpam-5790	831	10	of	of	ADP
ejpam-5790	831	11	simpson	simpson	PROPN
ejpam-5790	831	12	and	and	CCONJ
ejpam-5790	831	13	hermite	hermite	PROPN
ejpam-5790	831	14	-	-	PUNCT
ejpam-5790	831	15	hadamard	hadamard	ADJ
ejpam-5790	831	16	-	-	PUNCT
ejpam-5790	831	17	type	type	NOUN
ejpam-5790	831	18	inequalities	inequality	NOUN
ejpam-5790	831	19	in	in	ADP
ejpam-5790	831	20	tensorial	tensorial	ADJ
ejpam-5790	831	21	hilbert	hilbert	NOUN
ejpam-5790	831	22	spaces	space	NOUN
ejpam-5790	831	23	by	by	ADP
ejpam-5790	831	24	using	use	VERB
ejpam-5790	831	25	differentiable	differentiable	ADJ
ejpam-5790	831	26	convex	convex	NOUN
ejpam-5790	831	27	mappings	mapping	NOUN
ejpam-5790	831	28	.	.	PUNCT
ejpam-5790	832	1	aims	aim	VERB
ejpam-5790	832	2	mathematics	mathematic	NOUN
ejpam-5790	832	3	,	,	PUNCT
ejpam-5790	832	4	9(12):35151–35180	9(12):35151–35180	NUM
ejpam-5790	832	5	,	,	PUNCT
ejpam-5790	832	6	2024	2024	NUM
ejpam-5790	832	7	.	.	PUNCT
ejpam-5790	833	1	[	[	X
ejpam-5790	833	2	38	38	NUM
ejpam-5790	833	3	]	]	PUNCT
ejpam-5790	833	4	z.	z.	PROPN
ejpam-5790	833	5	a.	a.	PROPN
ejpam-5790	833	6	khan	khan	PROPN
ejpam-5790	833	7	,	,	PUNCT
ejpam-5790	833	8	w.	w.	PROPN
ejpam-5790	833	9	afzal	afzal	PROPN
ejpam-5790	833	10	,	,	PUNCT
ejpam-5790	833	11	m.	m.	NOUN
ejpam-5790	833	12	abbas	abbas	PROPN
ejpam-5790	833	13	,	,	PUNCT
ejpam-5790	833	14	j.	j.	PROPN
ejpam-5790	833	15	s.	s.	PROPN
ejpam-5790	833	16	ro	ro	PROPN
ejpam-5790	833	17	,	,	PUNCT
ejpam-5790	833	18	and	and	CCONJ
ejpam-5790	833	19	a.	a.	NOUN
ejpam-5790	833	20	a.	a.	NOUN
ejpam-5790	833	21	zaagan	zaagan	PROPN
ejpam-5790	833	22	.	.	PUNCT
ejpam-5790	834	1	some	some	DET
ejpam-5790	834	2	well	well	ADV
ejpam-5790	834	3	-	-	PUNCT
ejpam-5790	834	4	known	know	VERB
ejpam-5790	834	5	inequalities	inequality	NOUN
ejpam-5790	834	6	on	on	ADP
ejpam-5790	834	7	two	two	NUM
ejpam-5790	834	8	-	-	PUNCT
ejpam-5790	834	9	dimensional	dimensional	ADJ
ejpam-5790	834	10	convex	convex	NOUN
ejpam-5790	834	11	mappings	mapping	NOUN
ejpam-5790	834	12	by	by	ADP
ejpam-5790	834	13	means	mean	NOUN
ejpam-5790	834	14	of	of	ADP
ejpam-5790	834	15	pseudo	pseudo	NOUN
ejpam-5790	834	16	lr	lr	NOUN
ejpam-5790	834	17	interval	interval	NOUN
ejpam-5790	834	18	order	order	NOUN
ejpam-5790	834	19	relations	relation	NOUN
ejpam-5790	834	20	via	via	ADP
ejpam-5790	834	21	fractional	fractional	ADJ
ejpam-5790	834	22	integral	integral	ADJ
ejpam-5790	834	23	operators	operator	NOUN
ejpam-5790	834	24	having	have	VERB
ejpam-5790	834	25	non	non	ADJ
ejpam-5790	834	26	-	-	ADJ
ejpam-5790	834	27	singular	singular	ADJ
ejpam-5790	834	28	kernel	kernel	NOUN
ejpam-5790	834	29	.	.	PUNCT
ejpam-5790	835	1	aims	aim	VERB
ejpam-5790	835	2	mathematics	mathematic	NOUN
ejpam-5790	835	3	,	,	PUNCT
ejpam-5790	835	4	9(6):16061–16092	9(6):16061–16092	PROPN
ejpam-5790	835	5	,	,	PUNCT
ejpam-5790	835	6	2024	2024	NUM
ejpam-5790	835	7	.	.	PUNCT
ejpam-5790	836	1	[	[	X
ejpam-5790	836	2	39	39	NUM
ejpam-5790	836	3	]	]	PUNCT
ejpam-5790	836	4	z.	z.	PROPN
ejpam-5790	836	5	a.	a.	PROPN
ejpam-5790	836	6	khan	khan	PROPN
ejpam-5790	836	7	,	,	PUNCT
ejpam-5790	836	8	w.	w.	PROPN
ejpam-5790	836	9	afzal	afzal	PROPN
ejpam-5790	836	10	,	,	PUNCT
ejpam-5790	836	11	w.	w.	PROPN
ejpam-5790	836	12	nazeer	nazeer	PROPN
ejpam-5790	836	13	,	,	PUNCT
ejpam-5790	836	14	and	and	CCONJ
ejpam-5790	836	15	j.	j.	PROPN
ejpam-5790	836	16	k.	k.	PROPN
ejpam-5790	836	17	asamoah	asamoah	PROPN
ejpam-5790	836	18	.	.	PUNCT
ejpam-5790	837	1	some	some	DET
ejpam-5790	837	2	new	new	ADJ
ejpam-5790	837	3	variants	variant	NOUN
ejpam-5790	837	4	of	of	ADP
ejpam-5790	837	5	hermite	hermite	ADJ
ejpam-5790	837	6	–	–	PUNCT
ejpam-5790	837	7	hadamard	hadamard	ADJ
ejpam-5790	837	8	and	and	CCONJ
ejpam-5790	837	9	fejér	fejér	NOUN
ejpam-5790	837	10	-	-	PUNCT
ejpam-5790	837	11	type	type	NOUN
ejpam-5790	837	12	inequalities	inequality	NOUN
ejpam-5790	837	13	for	for	ADP
ejpam-5790	837	14	godunova	godunova	PROPN
ejpam-5790	837	15	–	–	PUNCT
ejpam-5790	837	16	levin	levin	PROPN
ejpam-5790	837	17	preinvex	preinvex	PROPN
ejpam-5790	837	18	class	class	NOUN
ejpam-5790	837	19	of	of	ADP
ejpam-5790	837	20	interval	interval	NOUN
ejpam-5790	837	21	-	-	PUNCT
ejpam-5790	837	22	valued	value	VERB
ejpam-5790	837	23	functions	function	NOUN
ejpam-5790	837	24	.	.	PUNCT
ejpam-5790	838	1	journal	journal	NOUN
ejpam-5790	838	2	of	of	ADP
ejpam-5790	838	3	mathematics	mathematic	NOUN
ejpam-5790	838	4	,	,	PUNCT
ejpam-5790	838	5	2024(1):8814585	2024(1):8814585	NUM
ejpam-5790	838	6	,	,	PUNCT
ejpam-5790	838	7	2024	2024	NUM
ejpam-5790	838	8	.	.	PUNCT
ejpam-5790	839	1	w.	w.	PROPN
ejpam-5790	839	2	afzal	afzal	PROPN
ejpam-5790	839	3	et	et	PROPN
ejpam-5790	839	4	al	al	PROPN
ejpam-5790	839	5	.	.	PUNCT
ejpam-5790	839	6	/	/	SYM
ejpam-5790	839	7	eur	eur	PROPN
ejpam-5790	839	8	.	.	PUNCT
ejpam-5790	840	1	j.	j.	PROPN
ejpam-5790	840	2	pure	pure	PROPN
ejpam-5790	840	3	appl	appl	PROPN
ejpam-5790	840	4	.	.	PROPN
ejpam-5790	840	5	math	math	PROPN
ejpam-5790	840	6	,	,	PUNCT
ejpam-5790	840	7	18	18	NUM
ejpam-5790	840	8	(	(	PUNCT
ejpam-5790	840	9	1	1	NUM
ejpam-5790	840	10	)	)	PUNCT
ejpam-5790	840	11	(	(	PUNCT
ejpam-5790	840	12	2025	2025	NUM
ejpam-5790	840	13	)	)	PUNCT
ejpam-5790	840	14	,	,	PUNCT
ejpam-5790	840	15	5790	5790	NUM
ejpam-5790	840	16	29	29	NUM
ejpam-5790	840	17	of	of	ADP
ejpam-5790	840	18	30	30	NUM
ejpam-5790	840	19	[	[	SYM
ejpam-5790	840	20	40	40	NUM
ejpam-5790	840	21	]	]	PUNCT
ejpam-5790	840	22	j.	j.	PROPN
ejpam-5790	840	23	li	li	PROPN
ejpam-5790	840	24	,	,	PUNCT
ejpam-5790	840	25	d.	d.	PROPN
ejpam-5790	840	26	han	han	PROPN
ejpam-5790	840	27	,	,	PUNCT
ejpam-5790	840	28	t.	t.	PROPN
ejpam-5790	840	29	h.	h.	PROPN
ejpam-5790	840	30	weng	weng	PROPN
ejpam-5790	840	31	,	,	PUNCT
ejpam-5790	840	32	h.	h.	PROPN
ejpam-5790	840	33	wu	wu	PROPN
ejpam-5790	840	34	,	,	PUNCT
ejpam-5790	840	35	k.	k.	PROPN
ejpam-5790	840	36	c.	c.	PROPN
ejpam-5790	840	37	li	li	PROPN
ejpam-5790	840	38	,	,	PUNCT
ejpam-5790	840	39	and	and	CCONJ
ejpam-5790	840	40	a.	a.	NOUN
ejpam-5790	840	41	castiglione	castiglione	NOUN
ejpam-5790	840	42	.	.	PUNCT
ejpam-5790	841	1	a	a	DET
ejpam-5790	841	2	secure	secure	ADJ
ejpam-5790	841	3	data	data	NOUN
ejpam-5790	841	4	storage	storage	NOUN
ejpam-5790	841	5	and	and	CCONJ
ejpam-5790	841	6	sharing	share	VERB
ejpam-5790	841	7	scheme	scheme	NOUN
ejpam-5790	841	8	for	for	ADP
ejpam-5790	841	9	port	port	NOUN
ejpam-5790	841	10	supply	supply	NOUN
ejpam-5790	841	11	chain	chain	NOUN
ejpam-5790	841	12	based	base	VERB
ejpam-5790	841	13	on	on	ADP
ejpam-5790	841	14	blockchain	blockchain	PROPN
ejpam-5790	841	15	and	and	CCONJ
ejpam-5790	841	16	dynamic	dynamic	ADJ
ejpam-5790	841	17	searchable	searchable	ADJ
ejpam-5790	841	18	encryption	encryption	NOUN
ejpam-5790	841	19	.	.	PUNCT
ejpam-5790	842	1	computer	computer	NOUN
ejpam-5790	842	2	standards	standard	NOUN
ejpam-5790	842	3	interfaces	interface	NOUN
ejpam-5790	842	4	,	,	PUNCT
ejpam-5790	842	5	91:103887	91:103887	NUM
ejpam-5790	842	6	,	,	PUNCT
ejpam-5790	842	7	2025	2025	NUM
ejpam-5790	842	8	.	.	PUNCT
ejpam-5790	843	1	[	[	X
ejpam-5790	843	2	41	41	NUM
ejpam-5790	843	3	]	]	X
ejpam-5790	843	4	w.	w.	PROPN
ejpam-5790	843	5	li	li	PROPN
ejpam-5790	843	6	,	,	PUNCT
ejpam-5790	843	7	z.	z.	PROPN
ejpam-5790	843	8	xie	xie	PROPN
ejpam-5790	843	9	,	,	PUNCT
ejpam-5790	843	10	j.	j.	PROPN
ejpam-5790	843	11	zhao	zhao	PROPN
ejpam-5790	843	12	,	,	PUNCT
ejpam-5790	843	13	p.	p.	PROPN
ejpam-5790	843	14	k.	k.	PROPN
ejpam-5790	843	15	wong	wong	PROPN
ejpam-5790	843	16	,	,	PUNCT
ejpam-5790	843	17	and	and	CCONJ
ejpam-5790	843	18	p.	p.	PROPN
ejpam-5790	843	19	li	li	PROPN
ejpam-5790	843	20	.	.	PROPN
ejpam-5790	843	21	fuzzy	fuzzy	ADJ
ejpam-5790	843	22	finite	finite	ADJ
ejpam-5790	843	23	-	-	ADJ
ejpam-5790	843	24	frequency	frequency	ADJ
ejpam-5790	843	25	output	output	NOUN
ejpam-5790	843	26	feedback	feedback	NOUN
ejpam-5790	843	27	control	control	NOUN
ejpam-5790	843	28	for	for	ADP
ejpam-5790	843	29	nonlinear	nonlinear	ADJ
ejpam-5790	843	30	active	active	ADJ
ejpam-5790	843	31	suspension	suspension	NOUN
ejpam-5790	843	32	systems	system	NOUN
ejpam-5790	843	33	with	with	ADP
ejpam-5790	843	34	time	time	NOUN
ejpam-5790	843	35	delay	delay	NOUN
ejpam-5790	843	36	and	and	CCONJ
ejpam-5790	843	37	output	output	NOUN
ejpam-5790	843	38	constraints	constraint	NOUN
ejpam-5790	843	39	.	.	PUNCT
ejpam-5790	844	1	mechanical	mechanical	ADJ
ejpam-5790	844	2	systems	system	NOUN
ejpam-5790	844	3	and	and	CCONJ
ejpam-5790	844	4	signal	signal	PROPN
ejpam-5790	844	5	processing	processing	NOUN
ejpam-5790	844	6	,	,	PUNCT
ejpam-5790	844	7	132:315–334	132:315–334	NUM
ejpam-5790	844	8	,	,	PUNCT
ejpam-5790	844	9	2019	2019	NUM
ejpam-5790	844	10	.	.	PUNCT
ejpam-5790	845	1	[	[	X
ejpam-5790	845	2	42	42	NUM
ejpam-5790	845	3	]	]	PUNCT
ejpam-5790	845	4	j.	j.	PROPN
ejpam-5790	845	5	liang	liang	PROPN
ejpam-5790	845	6	,	,	PUNCT
ejpam-5790	845	7	w.	w.	PROPN
ejpam-5790	845	8	xu	xu	PROPN
ejpam-5790	845	9	,	,	PUNCT
ejpam-5790	845	10	t.	t.	PROPN
ejpam-5790	845	11	wang	wang	PROPN
ejpam-5790	845	12	,	,	PUNCT
ejpam-5790	845	13	q.	q.	PROPN
ejpam-5790	845	14	yang	yang	PROPN
ejpam-5790	845	15	,	,	PUNCT
ejpam-5790	845	16	and	and	CCONJ
ejpam-5790	845	17	s.	s.	PROPN
ejpam-5790	845	18	zhang	zhang	PROPN
ejpam-5790	845	19	.	.	PUNCT
ejpam-5790	846	1	implementing	implement	VERB
ejpam-5790	846	2	nat	nat	NOUN
ejpam-5790	846	3	holpunching	holpunche	VERB
ejpam-5790	846	4	with	with	ADP
ejpam-5790	846	5	quic	quic	NOUN
ejpam-5790	846	6	.	.	PUNCT
ejpam-5790	847	1	in	in	ADP
ejpam-5790	847	2	2024	2024	NUM
ejpam-5790	847	3	ieee	ieee	NOUN
ejpam-5790	847	4	100th	100th	ADJ
ejpam-5790	847	5	vehicular	vehicular	ADJ
ejpam-5790	847	6	technology	technology	NOUN
ejpam-5790	847	7	conference	conference	NOUN
ejpam-5790	847	8	(	(	PUNCT
ejpam-5790	847	9	vtc2024	vtc2024	NOUN
ejpam-5790	847	10	-	-	PUNCT
ejpam-5790	847	11	fall	fall	NOUN
ejpam-5790	847	12	)	)	PUNCT
ejpam-5790	847	13	,	,	PUNCT
ejpam-5790	847	14	pages	page	NOUN
ejpam-5790	847	15	1–7	1–7	NUM
ejpam-5790	847	16	.	.	PUNCT
ejpam-5790	847	17	ieee	ieee	PROPN
ejpam-5790	847	18	,	,	PUNCT
ejpam-5790	847	19	october	october	PROPN
ejpam-5790	847	20	2024	2024	NUM
ejpam-5790	847	21	.	.	PUNCT
ejpam-5790	848	1	[	[	X
ejpam-5790	848	2	43	43	NUM
ejpam-5790	848	3	]	]	X
ejpam-5790	848	4	f.	f.	PROPN
ejpam-5790	848	5	meng	meng	PROPN
ejpam-5790	848	6	,	,	PUNCT
ejpam-5790	848	7	a.	a.	NOUN
ejpam-5790	848	8	pang	pang	PROPN
ejpam-5790	848	9	,	,	PUNCT
ejpam-5790	848	10	x.	x.	NOUN
ejpam-5790	848	11	dong	dong	PROPN
ejpam-5790	848	12	,	,	PUNCT
ejpam-5790	848	13	c.	c.	PROPN
ejpam-5790	848	14	han	han	PROPN
ejpam-5790	848	15	,	,	PUNCT
ejpam-5790	848	16	and	and	CCONJ
ejpam-5790	848	17	x.	x.	PROPN
ejpam-5790	848	18	sha	sha	PROPN
ejpam-5790	848	19	.	.	PUNCT
ejpam-5790	849	1	h	h	PROPN
ejpam-5790	849	2	optimal	optimal	ADJ
ejpam-5790	849	3	performance	performance	NOUN
ejpam-5790	849	4	design	design	NOUN
ejpam-5790	849	5	of	of	ADP
ejpam-5790	849	6	an	an	DET
ejpam-5790	849	7	unstable	unstable	ADJ
ejpam-5790	849	8	plant	plant	NOUN
ejpam-5790	849	9	under	under	ADP
ejpam-5790	849	10	bode	bode	VERB
ejpam-5790	849	11	integral	integral	ADJ
ejpam-5790	849	12	constraint	constraint	NOUN
ejpam-5790	849	13	.	.	PUNCT
ejpam-5790	850	1	complexity	complexity	NOUN
ejpam-5790	850	2	,	,	PUNCT
ejpam-5790	850	3	2018:4942906	2018:4942906	NUM
ejpam-5790	850	4	,	,	PUNCT
ejpam-5790	850	5	2018	2018	NUM
ejpam-5790	850	6	.	.	PUNCT
ejpam-5790	851	1	[	[	X
ejpam-5790	851	2	44	44	NUM
ejpam-5790	851	3	]	]	PUNCT
ejpam-5790	851	4	s.	s.	PROPN
ejpam-5790	851	5	meng	meng	PROPN
ejpam-5790	851	6	,	,	PUNCT
ejpam-5790	851	7	f.	f.	PROPN
ejpam-5790	851	8	meng	meng	PROPN
ejpam-5790	851	9	,	,	PUNCT
ejpam-5790	851	10	f.	f.	PROPN
ejpam-5790	851	11	zhang	zhang	PROPN
ejpam-5790	851	12	,	,	PUNCT
ejpam-5790	851	13	q.	q.	PROPN
ejpam-5790	851	14	li	li	PROPN
ejpam-5790	851	15	,	,	PUNCT
ejpam-5790	851	16	y.	y.	PROPN
ejpam-5790	851	17	zhang	zhang	PROPN
ejpam-5790	851	18	,	,	PUNCT
ejpam-5790	851	19	and	and	CCONJ
ejpam-5790	851	20	a.	a.	PROPN
ejpam-5790	851	21	zemouche	zemouche	PROPN
ejpam-5790	851	22	.	.	PUNCT
ejpam-5790	851	23	observer	observer	PROPN
ejpam-5790	851	24	design	design	NOUN
ejpam-5790	851	25	method	method	NOUN
ejpam-5790	851	26	for	for	ADP
ejpam-5790	851	27	nonlinear	nonlinear	ADJ
ejpam-5790	851	28	generalized	generalized	ADJ
ejpam-5790	851	29	systems	system	NOUN
ejpam-5790	851	30	with	with	ADP
ejpam-5790	851	31	nonlinear	nonlinear	ADJ
ejpam-5790	851	32	algebraic	algebraic	ADJ
ejpam-5790	851	33	constraints	constraint	NOUN
ejpam-5790	851	34	with	with	ADP
ejpam-5790	851	35	applications	application	NOUN
ejpam-5790	851	36	.	.	PUNCT
ejpam-5790	852	1	automatica	automatica	PROPN
ejpam-5790	852	2	,	,	PUNCT
ejpam-5790	852	3	162:111512	162:111512	NUM
ejpam-5790	852	4	,	,	PUNCT
ejpam-5790	852	5	2024	2024	NUM
ejpam-5790	852	6	.	.	PUNCT
ejpam-5790	853	1	[	[	X
ejpam-5790	853	2	45	45	NUM
ejpam-5790	853	3	]	]	PUNCT
ejpam-5790	853	4	a.	a.	NOUN
ejpam-5790	853	5	moumen	moumen	PROPN
ejpam-5790	853	6	,	,	PUNCT
ejpam-5790	853	7	h.	h.	PROPN
ejpam-5790	853	8	boulares	boulares	PROPN
ejpam-5790	853	9	,	,	PUNCT
ejpam-5790	853	10	b.	b.	PROPN
ejpam-5790	853	11	meftah	meftah	PROPN
ejpam-5790	853	12	,	,	PUNCT
ejpam-5790	853	13	r.	r.	PROPN
ejpam-5790	853	14	shafqat	shafqat	PROPN
ejpam-5790	853	15	,	,	PUNCT
ejpam-5790	853	16	t.	t.	NOUN
ejpam-5790	853	17	alraqad	alraqad	PROPN
ejpam-5790	853	18	,	,	PUNCT
ejpam-5790	853	19	e.	e.	PROPN
ejpam-5790	853	20	e.	e.	PROPN
ejpam-5790	853	21	ali	ali	PROPN
ejpam-5790	853	22	,	,	PUNCT
ejpam-5790	853	23	and	and	CCONJ
ejpam-5790	853	24	z.	z.	PROPN
ejpam-5790	853	25	khaled	khaled	PROPN
ejpam-5790	853	26	.	.	PUNCT
ejpam-5790	854	1	multiplicatively	multiplicatively	PROPN
ejpam-5790	854	2	simpson	simpson	PROPN
ejpam-5790	854	3	type	type	PROPN
ejpam-5790	854	4	inequalities	inequality	NOUN
ejpam-5790	854	5	via	via	ADP
ejpam-5790	854	6	fractional	fractional	ADJ
ejpam-5790	854	7	integral	integral	ADJ
ejpam-5790	854	8	.	.	PUNCT
ejpam-5790	854	9	symmetry	symmetry	NOUN
ejpam-5790	854	10	,	,	PUNCT
ejpam-5790	854	11	15:460	15:460	NUM
ejpam-5790	854	12	,	,	PUNCT
ejpam-5790	854	13	2023	2023	NUM
ejpam-5790	854	14	.	.	PUNCT
ejpam-5790	855	1	[	[	X
ejpam-5790	855	2	46	46	NUM
ejpam-5790	855	3	]	]	X
ejpam-5790	855	4	m.	m.	NOUN
ejpam-5790	855	5	h.	h.	PROPN
ejpam-5790	855	6	m.	m.	PROPN
ejpam-5790	855	7	rashid	rashid	PROPN
ejpam-5790	855	8	and	and	CCONJ
ejpam-5790	855	9	f.	f.	PROPN
ejpam-5790	855	10	bani	bani	PROPN
ejpam-5790	855	11	-	-	PUNCT
ejpam-5790	855	12	ahmad	ahmad	PROPN
ejpam-5790	855	13	.	.	PUNCT
ejpam-5790	856	1	an	an	DET
ejpam-5790	856	2	estimate	estimate	NOUN
ejpam-5790	856	3	for	for	ADP
ejpam-5790	856	4	the	the	DET
ejpam-5790	856	5	numerical	numerical	ADJ
ejpam-5790	856	6	radius	radius	NOUN
ejpam-5790	856	7	of	of	ADP
ejpam-5790	856	8	the	the	DET
ejpam-5790	856	9	hilbert	hilbert	PROPN
ejpam-5790	856	10	space	space	NOUN
ejpam-5790	856	11	operators	operator	NOUN
ejpam-5790	856	12	and	and	CCONJ
ejpam-5790	856	13	a	a	DET
ejpam-5790	856	14	numerical	numerical	ADJ
ejpam-5790	856	15	radius	radius	NOUN
ejpam-5790	856	16	inequality	inequality	NOUN
ejpam-5790	856	17	.	.	PUNCT
ejpam-5790	857	1	aims	aim	VERB
ejpam-5790	857	2	mathematics	mathematic	NOUN
ejpam-5790	857	3	,	,	PUNCT
ejpam-5790	857	4	8:26384–26405	8:26384–26405	NUM
ejpam-5790	857	5	,	,	PUNCT
ejpam-5790	857	6	2023	2023	NUM
ejpam-5790	857	7	.	.	PUNCT
ejpam-5790	858	1	[	[	X
ejpam-5790	858	2	47	47	NUM
ejpam-5790	858	3	]	]	PUNCT
ejpam-5790	858	4	t.	t.	PROPN
ejpam-5790	858	5	saeed	saeed	PROPN
ejpam-5790	858	6	,	,	PUNCT
ejpam-5790	858	7	w.	w.	PROPN
ejpam-5790	858	8	afzal	afzal	PROPN
ejpam-5790	858	9	,	,	PUNCT
ejpam-5790	858	10	m.	m.	NOUN
ejpam-5790	858	11	abbas	abbas	PROPN
ejpam-5790	858	12	,	,	PUNCT
ejpam-5790	858	13	s.	s.	PROPN
ejpam-5790	858	14	treanţă	treanţă	PROPN
ejpam-5790	858	15	,	,	PUNCT
ejpam-5790	858	16	and	and	CCONJ
ejpam-5790	858	17	m.	m.	PROPN
ejpam-5790	858	18	de	de	PROPN
ejpam-5790	858	19	la	la	PROPN
ejpam-5790	858	20	sen	sen	PROPN
ejpam-5790	858	21	.	.	PROPN
ejpam-5790	859	1	some	some	DET
ejpam-5790	859	2	new	new	ADJ
ejpam-5790	859	3	generalizations	generalization	NOUN
ejpam-5790	859	4	of	of	ADP
ejpam-5790	859	5	integral	integral	ADJ
ejpam-5790	859	6	inequalities	inequality	NOUN
ejpam-5790	859	7	for	for	ADP
ejpam-5790	859	8	harmonical	harmonical	ADJ
ejpam-5790	859	9	cr-(h	cr-(h	X
ejpam-5790	859	10	,	,	PUNCT
ejpam-5790	859	11	h)-godunova	h)-godunova	X
ejpam-5790	859	12	–	–	PUNCT
ejpam-5790	859	13	levin	levin	NOUN
ejpam-5790	859	14	functions	function	NOUN
ejpam-5790	859	15	and	and	CCONJ
ejpam-5790	859	16	applications	application	NOUN
ejpam-5790	859	17	.	.	PUNCT
ejpam-5790	860	1	mathematics	mathematic	NOUN
ejpam-5790	860	2	,	,	PUNCT
ejpam-5790	860	3	10(23):4540	10(23):4540	NUM
ejpam-5790	860	4	,	,	PUNCT
ejpam-5790	860	5	2022	2022	NUM
ejpam-5790	860	6	.	.	PUNCT
ejpam-5790	861	1	[	[	X
ejpam-5790	861	2	48	48	NUM
ejpam-5790	861	3	]	]	PUNCT
ejpam-5790	861	4	t.	t.	PROPN
ejpam-5790	861	5	saeed	saeed	PROPN
ejpam-5790	861	6	,	,	PUNCT
ejpam-5790	861	7	w.	w.	PROPN
ejpam-5790	861	8	afzal	afzal	PROPN
ejpam-5790	861	9	,	,	PUNCT
ejpam-5790	861	10	k.	k.	PROPN
ejpam-5790	861	11	shabbir	shabbir	PROPN
ejpam-5790	861	12	,	,	PUNCT
ejpam-5790	861	13	s.	s.	PROPN
ejpam-5790	861	14	treanţă	treanţă	PROPN
ejpam-5790	861	15	,	,	PUNCT
ejpam-5790	861	16	and	and	CCONJ
ejpam-5790	861	17	m.	m.	PROPN
ejpam-5790	861	18	de	de	PROPN
ejpam-5790	861	19	la	la	PROPN
ejpam-5790	861	20	sen	sen	PROPN
ejpam-5790	861	21	.	.	PROPN
ejpam-5790	862	1	some	some	DET
ejpam-5790	862	2	novel	novel	ADJ
ejpam-5790	862	3	estimates	estimate	NOUN
ejpam-5790	862	4	of	of	ADP
ejpam-5790	862	5	hermite	hermite	ADJ
ejpam-5790	862	6	–	–	PUNCT
ejpam-5790	862	7	hadamard	hadamard	ADJ
ejpam-5790	862	8	and	and	CCONJ
ejpam-5790	862	9	jensen	jensen	PROPN
ejpam-5790	862	10	type	type	NOUN
ejpam-5790	862	11	inequalities	inequality	NOUN
ejpam-5790	862	12	for	for	ADP
ejpam-5790	862	13	(	(	PUNCT
ejpam-5790	862	14	h	h	NOUN
ejpam-5790	862	15	,	,	PUNCT
ejpam-5790	862	16	h)-convex	h)-convex	NOUN
ejpam-5790	862	17	functions	function	NOUN
ejpam-5790	862	18	pertaining	pertain	VERB
ejpam-5790	862	19	to	to	ADP
ejpam-5790	862	20	total	total	ADJ
ejpam-5790	862	21	order	order	NOUN
ejpam-5790	862	22	relation	relation	NOUN
ejpam-5790	862	23	.	.	PUNCT
ejpam-5790	863	1	mathematics	mathematic	NOUN
ejpam-5790	863	2	,	,	PUNCT
ejpam-5790	863	3	10(24):4777	10(24):4777	NUM
ejpam-5790	863	4	,	,	PUNCT
ejpam-5790	863	5	2022	2022	NUM
ejpam-5790	863	6	.	.	PUNCT
ejpam-5790	864	1	[	[	X
ejpam-5790	864	2	49	49	NUM
ejpam-5790	864	3	]	]	PUNCT
ejpam-5790	864	4	s.	s.	PROPN
ejpam-5790	864	5	k.	k.	PROPN
ejpam-5790	864	6	sahoo	sahoo	PROPN
ejpam-5790	864	7	,	,	PUNCT
ejpam-5790	864	8	p.	p.	PROPN
ejpam-5790	864	9	o.	o.	PROPN
ejpam-5790	864	10	mohammed	mohammed	PROPN
ejpam-5790	864	11	,	,	PUNCT
ejpam-5790	864	12	d.	d.	PROPN
ejpam-5790	864	13	o.	o.	PROPN
ejpam-5790	864	14	regan	regan	PROPN
ejpam-5790	864	15	,	,	PUNCT
ejpam-5790	864	16	m.	m.	NOUN
ejpam-5790	864	17	tariq	tariq	PROPN
ejpam-5790	864	18	,	,	PUNCT
ejpam-5790	864	19	and	and	CCONJ
ejpam-5790	864	20	k.	k.	X
ejpam-5790	864	21	nonlaopon	nonlaopon	PROPN
ejpam-5790	864	22	.	.	PUNCT
ejpam-5790	865	1	new	new	ADJ
ejpam-5790	865	2	hermite	hermite	ADJ
ejpam-5790	865	3	–	–	PUNCT
ejpam-5790	865	4	hadamard	hadamard	ADJ
ejpam-5790	865	5	type	type	NOUN
ejpam-5790	865	6	inequalities	inequality	NOUN
ejpam-5790	865	7	in	in	ADP
ejpam-5790	865	8	connection	connection	NOUN
ejpam-5790	865	9	with	with	ADP
ejpam-5790	865	10	interval	interval	NOUN
ejpam-5790	865	11	-	-	PUNCT
ejpam-5790	865	12	valued	value	VERB
ejpam-5790	865	13	generalized	generalize	VERB
ejpam-5790	865	14	harmonically	harmonically	ADV
ejpam-5790	865	15	(	(	PUNCT
ejpam-5790	865	16	h1	h1	PROPN
ejpam-5790	865	17	,	,	PUNCT
ejpam-5790	865	18	h2)-godunova	h2)-godunova	PROPN
ejpam-5790	865	19	–	–	PUNCT
ejpam-5790	865	20	levin	levin	NOUN
ejpam-5790	865	21	functions	function	NOUN
ejpam-5790	865	22	.	.	PUNCT
ejpam-5790	866	1	symmetry	symmetry	NOUN
ejpam-5790	866	2	,	,	PUNCT
ejpam-5790	866	3	14(10):1964	14(10):1964	NUM
ejpam-5790	866	4	,	,	PUNCT
ejpam-5790	866	5	2022	2022	NUM
ejpam-5790	866	6	.	.	PUNCT
ejpam-5790	867	1	[	[	X
ejpam-5790	867	2	50	50	NUM
ejpam-5790	867	3	]	]	X
ejpam-5790	867	4	m.z	m.z	PROPN
ejpam-5790	867	5	.	.	PROPN
ejpam-5790	867	6	sarikaya	sarikaya	PROPN
ejpam-5790	867	7	,	,	PUNCT
ejpam-5790	867	8	erhan	erhan	ADP
ejpam-5790	867	9	set	set	VERB
ejpam-5790	867	10	,	,	PUNCT
ejpam-5790	867	11	and	and	CCONJ
ejpam-5790	867	12	m.e	m.e	PROPN
ejpam-5790	867	13	.	.	PROPN
ejpam-5790	867	14	ozdemir	ozdemir	PROPN
ejpam-5790	867	15	.	.	PUNCT
ejpam-5790	868	1	on	on	ADP
ejpam-5790	868	2	new	new	ADJ
ejpam-5790	868	3	inequalities	inequality	NOUN
ejpam-5790	868	4	of	of	ADP
ejpam-5790	868	5	simpson	simpson	PROPN
ejpam-5790	868	6	’s	’s	PART
ejpam-5790	868	7	type	type	NOUN
ejpam-5790	868	8	for	for	ADP
ejpam-5790	868	9	functions	function	NOUN
ejpam-5790	868	10	whose	whose	DET
ejpam-5790	868	11	second	second	ADJ
ejpam-5790	868	12	derivatives	derivative	NOUN
ejpam-5790	868	13	absolute	absolute	ADJ
ejpam-5790	868	14	values	value	NOUN
ejpam-5790	868	15	are	be	AUX
ejpam-5790	868	16	convex	convex	PROPN
ejpam-5790	868	17	.	.	PUNCT
ejpam-5790	869	1	journal	journal	PROPN
ejpam-5790	869	2	of	of	ADP
ejpam-5790	869	3	applied	apply	VERB
ejpam-5790	869	4	mathematics	mathematic	NOUN
ejpam-5790	869	5	,	,	PUNCT
ejpam-5790	869	6	statistics	statistic	NOUN
ejpam-5790	869	7	and	and	CCONJ
ejpam-5790	869	8	informatics	informatic	NOUN
ejpam-5790	869	9	,	,	PUNCT
ejpam-5790	869	10	9:37–45	9:37–45	NUM
ejpam-5790	869	11	,	,	PUNCT
ejpam-5790	869	12	2013	2013	NUM
ejpam-5790	869	13	.	.	PUNCT
ejpam-5790	870	1	[	[	X
ejpam-5790	870	2	51	51	NUM
ejpam-5790	870	3	]	]	PUNCT
ejpam-5790	870	4	x.	x.	PROPN
ejpam-5790	870	5	shi	shi	PROPN
ejpam-5790	870	6	,	,	PUNCT
ejpam-5790	870	7	u.	u.	PROPN
ejpam-5790	870	8	ishtiaq	ishtiaq	PROPN
ejpam-5790	870	9	,	,	PUNCT
ejpam-5790	870	10	m.	m.	PROPN
ejpam-5790	870	11	din	din	PROPN
ejpam-5790	870	12	,	,	PUNCT
ejpam-5790	870	13	and	and	CCONJ
ejpam-5790	870	14	m.	m.	PROPN
ejpam-5790	870	15	akram	akram	PROPN
ejpam-5790	870	16	.	.	PUNCT
ejpam-5790	871	1	fractals	fractal	NOUN
ejpam-5790	871	2	of	of	ADP
ejpam-5790	871	3	interpolative	interpolative	ADJ
ejpam-5790	871	4	kannan	kannan	PROPN
ejpam-5790	871	5	mappings	mapping	NOUN
ejpam-5790	871	6	.	.	PUNCT
ejpam-5790	872	1	fractal	fractal	PROPN
ejpam-5790	872	2	and	and	CCONJ
ejpam-5790	872	3	fractional	fractional	ADJ
ejpam-5790	872	4	,	,	PUNCT
ejpam-5790	872	5	8(8):493	8(8):493	NUM
ejpam-5790	872	6	,	,	PUNCT
ejpam-5790	872	7	2024	2024	NUM
ejpam-5790	872	8	.	.	PUNCT
ejpam-5790	873	1	[	[	X
ejpam-5790	873	2	52	52	NUM
ejpam-5790	873	3	]	]	PUNCT
ejpam-5790	873	4	x.	x.	PROPN
ejpam-5790	873	5	shi	shi	PROPN
ejpam-5790	873	6	,	,	PUNCT
ejpam-5790	873	7	y.	y.	PROPN
ejpam-5790	873	8	zhang	zhang	PROPN
ejpam-5790	873	9	,	,	PUNCT
ejpam-5790	873	10	m.	m.	PROPN
ejpam-5790	873	11	yu	yu	PROPN
ejpam-5790	873	12	,	,	PUNCT
ejpam-5790	873	13	and	and	CCONJ
ejpam-5790	873	14	l.	l.	PROPN
ejpam-5790	873	15	zhang	zhang	PROPN
ejpam-5790	873	16	.	.	PUNCT
ejpam-5790	874	1	revolutionizing	revolutionize	VERB
ejpam-5790	874	2	market	market	NOUN
ejpam-5790	874	3	surveillance	surveillance	NOUN
ejpam-5790	874	4	:	:	PUNCT
ejpam-5790	874	5	customer	customer	NOUN
ejpam-5790	874	6	relationship	relationship	NOUN
ejpam-5790	874	7	management	management	NOUN
ejpam-5790	874	8	with	with	ADP
ejpam-5790	874	9	machine	machine	NOUN
ejpam-5790	874	10	learning	learning	NOUN
ejpam-5790	874	11	.	.	PUNCT
ejpam-5790	875	1	peerj	peerj	PROPN
ejpam-5790	875	2	computer	computer	NOUN
ejpam-5790	875	3	science	science	NOUN
ejpam-5790	875	4	,	,	PUNCT
ejpam-5790	875	5	10	10	NUM
ejpam-5790	875	6	:	:	PUNCT
ejpam-5790	875	7	e2583	e2583	ADJ
ejpam-5790	875	8	,	,	PUNCT
ejpam-5790	875	9	2024	2024	NUM
ejpam-5790	875	10	.	.	PUNCT
ejpam-5790	876	1	[	[	X
ejpam-5790	876	2	53	53	NUM
ejpam-5790	876	3	]	]	X
ejpam-5790	876	4	y.	y.	PROPN
ejpam-5790	876	5	shi	shi	PROPN
ejpam-5790	876	6	and	and	CCONJ
ejpam-5790	876	7	z.	z.	PROPN
ejpam-5790	876	8	liu	liu	PROPN
ejpam-5790	876	9	.	.	PUNCT
ejpam-5790	877	1	some	some	DET
ejpam-5790	877	2	sharp	sharp	PROPN
ejpam-5790	877	3	simpson	simpson	PROPN
ejpam-5790	877	4	type	type	NOUN
ejpam-5790	877	5	inequalities	inequality	NOUN
ejpam-5790	877	6	and	and	CCONJ
ejpam-5790	877	7	applications	application	NOUN
ejpam-5790	877	8	.	.	PUNCT
ejpam-5790	878	1	applied	apply	VERB
ejpam-5790	878	2	mathematics	mathematic	NOUN
ejpam-5790	878	3	e	e	NOUN
ejpam-5790	879	1	-	-	NOUN
ejpam-5790	879	2	notes	note	NOUN
ejpam-5790	879	3	,	,	PUNCT
ejpam-5790	879	4	9:205–215	9:205–215	NOUN
ejpam-5790	879	5	,	,	PUNCT
ejpam-5790	879	6	2009	2009	NUM
ejpam-5790	879	7	.	.	PUNCT
ejpam-5790	880	1	[	[	X
ejpam-5790	880	2	54	54	NUM
ejpam-5790	880	3	]	]	PUNCT
ejpam-5790	880	4	s.	s.	PROPN
ejpam-5790	880	5	sitho	sitho	PROPN
ejpam-5790	880	6	,	,	PUNCT
ejpam-5790	880	7	m.	m.	NOUN
ejpam-5790	880	8	a.	a.	PROPN
ejpam-5790	880	9	ali	ali	PROPN
ejpam-5790	880	10	,	,	PUNCT
ejpam-5790	880	11	h.	h.	PROPN
ejpam-5790	880	12	budak	budak	PROPN
ejpam-5790	880	13	,	,	PUNCT
ejpam-5790	880	14	s.	s.	PROPN
ejpam-5790	880	15	k.	k.	PROPN
ejpam-5790	880	16	ntouyas	ntouyas	PROPN
ejpam-5790	880	17	,	,	PUNCT
ejpam-5790	880	18	and	and	CCONJ
ejpam-5790	880	19	j.	j.	PROPN
ejpam-5790	880	20	tariboon	tariboon	PROPN
ejpam-5790	880	21	.	.	PUNCT
ejpam-5790	881	1	trapezoid	trapezoid	NOUN
ejpam-5790	881	2	and	and	CCONJ
ejpam-5790	881	3	midpoint	midpoint	NOUN
ejpam-5790	881	4	type	type	NOUN
ejpam-5790	881	5	inequalities	inequality	NOUN
ejpam-5790	881	6	for	for	ADP
ejpam-5790	881	7	preinvex	preinvex	NOUN
ejpam-5790	881	8	functions	function	NOUN
ejpam-5790	881	9	via	via	ADP
ejpam-5790	881	10	quantum	quantum	NOUN
ejpam-5790	881	11	calculus	calculus	NOUN
ejpam-5790	881	12	.	.	PUNCT
ejpam-5790	882	1	mathematics	mathematic	NOUN
ejpam-5790	882	2	,	,	PUNCT
ejpam-5790	882	3	9:1666	9:1666	NUM
ejpam-5790	882	4	,	,	PUNCT
ejpam-5790	882	5	2021	2021	NUM
ejpam-5790	882	6	.	.	PUNCT
ejpam-5790	883	1	[	[	X
ejpam-5790	883	2	55	55	NUM
ejpam-5790	883	3	]	]	PUNCT
ejpam-5790	883	4	t.	t.	NOUN
ejpam-5790	883	5	sitthiwirattham	sitthiwirattham	PROPN
ejpam-5790	883	6	,	,	PUNCT
ejpam-5790	883	7	k.	k.	PROPN
ejpam-5790	883	8	nonlaopon	nonlaopon	PROPN
ejpam-5790	883	9	,	,	PUNCT
ejpam-5790	883	10	m.	m.	NOUN
ejpam-5790	883	11	a.	a.	PROPN
ejpam-5790	883	12	ali	ali	PROPN
ejpam-5790	883	13	,	,	PUNCT
ejpam-5790	883	14	and	and	CCONJ
ejpam-5790	883	15	h.	h.	PROPN
ejpam-5790	883	16	budak	budak	PROPN
ejpam-5790	883	17	.	.	PUNCT
ejpam-5790	884	1	riemann	riemann	PROPN
ejpam-5790	884	2	–	–	PUNCT
ejpam-5790	884	3	liouville	liouville	VERB
ejpam-5790	884	4	w.	w.	PROPN
ejpam-5790	884	5	afzal	afzal	PROPN
ejpam-5790	884	6	et	et	PROPN
ejpam-5790	884	7	al	al	PROPN
ejpam-5790	884	8	.	.	PUNCT
ejpam-5790	884	9	/	/	SYM
ejpam-5790	884	10	eur	eur	PROPN
ejpam-5790	884	11	.	.	PUNCT
ejpam-5790	885	1	j.	j.	PROPN
ejpam-5790	885	2	pure	pure	PROPN
ejpam-5790	885	3	appl	appl	PROPN
ejpam-5790	885	4	.	.	PROPN
ejpam-5790	885	5	math	math	PROPN
ejpam-5790	885	6	,	,	PUNCT
ejpam-5790	885	7	18	18	NUM
ejpam-5790	885	8	(	(	PUNCT
ejpam-5790	885	9	1	1	NUM
ejpam-5790	885	10	)	)	PUNCT
ejpam-5790	885	11	(	(	PUNCT
ejpam-5790	885	12	2025	2025	NUM
ejpam-5790	885	13	)	)	PUNCT
ejpam-5790	885	14	,	,	PUNCT
ejpam-5790	885	15	5790	5790	NUM
ejpam-5790	885	16	30	30	NUM
ejpam-5790	885	17	of	of	ADP
ejpam-5790	885	18	30	30	NUM
ejpam-5790	885	19	fractional	fractional	PROPN
ejpam-5790	885	20	newton	newton	PROPN
ejpam-5790	885	21	’s	’s	PART
ejpam-5790	885	22	type	type	NOUN
ejpam-5790	885	23	inequalities	inequality	NOUN
ejpam-5790	885	24	for	for	ADP
ejpam-5790	885	25	differentiable	differentiable	ADJ
ejpam-5790	885	26	convex	convex	NOUN
ejpam-5790	885	27	functions	function	NOUN
ejpam-5790	885	28	.	.	PUNCT
ejpam-5790	886	1	fractal	fractal	ADJ
ejpam-5790	886	2	and	and	CCONJ
ejpam-5790	886	3	fractional	fractional	ADJ
ejpam-5790	886	4	,	,	PUNCT
ejpam-5790	886	5	6:175	6:175	NUM
ejpam-5790	886	6	,	,	PUNCT
ejpam-5790	886	7	2022	2022	NUM
ejpam-5790	886	8	.	.	PUNCT
ejpam-5790	887	1	[	[	X
ejpam-5790	887	2	56	56	NUM
ejpam-5790	887	3	]	]	PUNCT
ejpam-5790	887	4	v.	v.	CCONJ
ejpam-5790	887	5	stojiljkovic	stojiljkovic	VERB
ejpam-5790	887	6	.	.	PUNCT
ejpam-5790	888	1	twice	twice	DET
ejpam-5790	888	2	differentiable	differentiable	ADJ
ejpam-5790	888	3	ostrowski	ostrowski	ADJ
ejpam-5790	888	4	type	type	NOUN
ejpam-5790	888	5	tensorial	tensorial	ADJ
ejpam-5790	888	6	norm	norm	NOUN
ejpam-5790	888	7	inequality	inequality	NOUN
ejpam-5790	888	8	for	for	ADP
ejpam-5790	888	9	continuous	continuous	ADJ
ejpam-5790	888	10	functions	function	NOUN
ejpam-5790	888	11	of	of	ADP
ejpam-5790	888	12	selfadjoint	selfadjoint	NOUN
ejpam-5790	888	13	operators	operator	NOUN
ejpam-5790	888	14	in	in	ADP
ejpam-5790	888	15	hilbert	hilbert	PROPN
ejpam-5790	888	16	spaces	space	NOUN
ejpam-5790	888	17	.	.	PUNCT
ejpam-5790	889	1	eur	eur	PROPN
ejpam-5790	889	2	.	.	PUNCT
ejpam-5790	890	1	j.	j.	PROPN
ejpam-5790	890	2	pure	pure	PROPN
ejpam-5790	890	3	appl	appl	PROPN
ejpam-5790	890	4	.	.	PUNCT
ejpam-5790	890	5	math	math	PROPN
ejpam-5790	890	6	.	.	PUNCT
ejpam-5790	890	7	,	,	PUNCT
ejpam-5790	890	8	16:1421–1433	16:1421–1433	NUM
ejpam-5790	890	9	,	,	PUNCT
ejpam-5790	890	10	2023	2023	NUM
ejpam-5790	890	11	.	.	PUNCT
ejpam-5790	891	1	[	[	X
ejpam-5790	891	2	57	57	NUM
ejpam-5790	891	3	]	]	PUNCT
ejpam-5790	891	4	v.	v.	CCONJ
ejpam-5790	891	5	stojiljkovic	stojiljkovic	VERB
ejpam-5790	891	6	.	.	PUNCT
ejpam-5790	892	1	generalized	generalize	VERB
ejpam-5790	892	2	tensorial	tensorial	ADJ
ejpam-5790	892	3	simpson	simpson	PROPN
ejpam-5790	892	4	type	type	PROPN
ejpam-5790	892	5	inequalities	inequality	NOUN
ejpam-5790	892	6	for	for	ADP
ejpam-5790	892	7	convex	convex	NOUN
ejpam-5790	892	8	functions	function	NOUN
ejpam-5790	892	9	of	of	ADP
ejpam-5790	892	10	selfadjoint	selfadjoint	NOUN
ejpam-5790	892	11	operators	operator	NOUN
ejpam-5790	892	12	in	in	ADP
ejpam-5790	892	13	hilbert	hilbert	NOUN
ejpam-5790	892	14	space	space	NOUN
ejpam-5790	892	15	.	.	PUNCT
ejpam-5790	893	1	maltepe	maltepe	ADJ
ejpam-5790	893	2	journal	journal	NOUN
ejpam-5790	893	3	of	of	ADP
ejpam-5790	893	4	mathematics	mathematic	NOUN
ejpam-5790	893	5	,	,	PUNCT
ejpam-5790	893	6	6:78–89	6:78–89	NUM
ejpam-5790	893	7	,	,	PUNCT
ejpam-5790	893	8	2024	2024	NUM
ejpam-5790	893	9	.	.	PUNCT
ejpam-5790	894	1	[	[	X
ejpam-5790	894	2	58	58	X
ejpam-5790	894	3	]	]	PUNCT
ejpam-5790	894	4	v.	v.	CCONJ
ejpam-5790	894	5	stojiljković	stojiljković	NOUN
ejpam-5790	894	6	and	and	CCONJ
ejpam-5790	894	7	s.s	s.s	PROPN
ejpam-5790	894	8	.	.	PROPN
ejpam-5790	894	9	dragomir	dragomir	PROPN
ejpam-5790	894	10	.	.	PROPN
ejpam-5790	894	11	tensorial	tensorial	PROPN
ejpam-5790	894	12	simpson	simpson	PROPN
ejpam-5790	894	13	1/8	1/8	NUM
ejpam-5790	894	14	type	type	NOUN
ejpam-5790	894	15	inequalities	inequality	NOUN
ejpam-5790	894	16	for	for	ADP
ejpam-5790	894	17	convex	convex	NOUN
ejpam-5790	894	18	functions	function	NOUN
ejpam-5790	894	19	of	of	ADP
ejpam-5790	894	20	selfadjoint	selfadjoint	NOUN
ejpam-5790	894	21	operators	operator	NOUN
ejpam-5790	894	22	in	in	ADP
ejpam-5790	894	23	hilbert	hilbert	PROPN
ejpam-5790	894	24	space	space	NOUN
ejpam-5790	894	25	.	.	PUNCT
ejpam-5790	895	1	eur	eur	PROPN
ejpam-5790	895	2	.	.	PUNCT
ejpam-5790	896	1	j.	j.	PROPN
ejpam-5790	896	2	math	math	PROPN
ejpam-5790	896	3	.	.	PUNCT
ejpam-5790	897	1	anal	anal	PROPN
ejpam-5790	897	2	.	.	PUNCT
ejpam-5790	897	3	,	,	PUNCT
ejpam-5790	897	4	4:17	4:17	NUM
ejpam-5790	897	5	,	,	PUNCT
ejpam-5790	897	6	2024	2024	NUM
ejpam-5790	897	7	.	.	PUNCT
ejpam-5790	898	1	[	[	X
ejpam-5790	898	2	59	59	NUM
ejpam-5790	898	3	]	]	PUNCT
ejpam-5790	898	4	l.	l.	PROPN
ejpam-5790	898	5	wang	wang	PROPN
ejpam-5790	898	6	,	,	PUNCT
ejpam-5790	898	7	g.	g.	PROPN
ejpam-5790	898	8	liu	liu	PROPN
ejpam-5790	898	9	,	,	PUNCT
ejpam-5790	898	10	g.	g.	PROPN
ejpam-5790	898	11	wang	wang	PROPN
ejpam-5790	898	12	,	,	PUNCT
ejpam-5790	898	13	and	and	CCONJ
ejpam-5790	898	14	k.	k.	PROPN
ejpam-5790	898	15	zhang	zhang	PROPN
ejpam-5790	898	16	.	.	PUNCT
ejpam-5790	899	1	m	m	PROPN
ejpam-5790	899	2	-	-	PUNCT
ejpam-5790	899	3	pinn	pinn	PROPN
ejpam-5790	899	4	:	:	PUNCT
ejpam-5790	899	5	a	a	DET
ejpam-5790	899	6	mesh	mesh	NOUN
ejpam-5790	899	7	-	-	PUNCT
ejpam-5790	899	8	based	base	VERB
ejpam-5790	899	9	physics	physics	NOUN
ejpam-5790	899	10	-	-	PUNCT
ejpam-5790	899	11	informed	inform	VERB
ejpam-5790	899	12	neural	neural	ADJ
ejpam-5790	899	13	network	network	NOUN
ejpam-5790	899	14	for	for	ADP
ejpam-5790	899	15	linear	linear	ADJ
ejpam-5790	899	16	elastic	elastic	ADJ
ejpam-5790	899	17	problems	problem	NOUN
ejpam-5790	899	18	in	in	ADP
ejpam-5790	899	19	solid	solid	ADJ
ejpam-5790	899	20	mechanics	mechanic	NOUN
ejpam-5790	899	21	.	.	PUNCT
ejpam-5790	900	1	international	international	ADJ
ejpam-5790	900	2	journal	journal	PROPN
ejpam-5790	900	3	for	for	ADP
ejpam-5790	900	4	numerical	numerical	ADJ
ejpam-5790	900	5	methods	method	NOUN
ejpam-5790	900	6	in	in	ADP
ejpam-5790	900	7	engineering	engineering	NOUN
ejpam-5790	900	8	,	,	PUNCT
ejpam-5790	900	9	125(9):e7444	125(9):e7444	NUM
ejpam-5790	900	10	,	,	PUNCT
ejpam-5790	900	11	2024	2024	NUM
ejpam-5790	900	12	.	.	PUNCT
ejpam-5790	901	1	[	[	X
ejpam-5790	901	2	60	60	NUM
ejpam-5790	901	3	]	]	PUNCT
ejpam-5790	901	4	z.	z.	PROPN
ejpam-5790	901	5	wang	wang	PROPN
ejpam-5790	901	6	,	,	PUNCT
ejpam-5790	901	7	z.	z.	PROPN
ejpam-5790	901	8	liao	liao	PROPN
ejpam-5790	901	9	,	,	PUNCT
ejpam-5790	901	10	b.	b.	PROPN
ejpam-5790	901	11	zhou	zhou	PROPN
ejpam-5790	901	12	,	,	PUNCT
ejpam-5790	901	13	g.	g.	PROPN
ejpam-5790	901	14	yu	yu	PROPN
ejpam-5790	901	15	,	,	PUNCT
ejpam-5790	901	16	and	and	CCONJ
ejpam-5790	901	17	w.	w.	PROPN
ejpam-5790	901	18	luo	luo	PROPN
ejpam-5790	901	19	.	.	PUNCT
ejpam-5790	901	20	swinurnet	swinurnet	PROPN
ejpam-5790	901	21	:	:	PUNCT
ejpam-5790	901	22	hybrid	hybrid	ADJ
ejpam-5790	901	23	transformer	transformer	NOUN
ejpam-5790	901	24	-	-	PUNCT
ejpam-5790	901	25	cnn	cnn	NOUN
ejpam-5790	901	26	architecture	architecture	NOUN
ejpam-5790	901	27	for	for	ADP
ejpam-5790	901	28	real	real	ADJ
ejpam-5790	901	29	-	-	PUNCT
ejpam-5790	901	30	time	time	NOUN
ejpam-5790	901	31	unstructured	unstructured	ADJ
ejpam-5790	901	32	road	road	NOUN
ejpam-5790	901	33	segmentation	segmentation	NOUN
ejpam-5790	901	34	.	.	PUNCT
ejpam-5790	902	1	ieee	ieee	NOUN
ejpam-5790	902	2	transactions	transaction	NOUN
ejpam-5790	902	3	on	on	ADP
ejpam-5790	902	4	instrumentation	instrumentation	NOUN
ejpam-5790	902	5	and	and	CCONJ
ejpam-5790	902	6	measurement	measurement	NOUN
ejpam-5790	902	7	,	,	PUNCT
ejpam-5790	902	8	2024	2024	NUM
ejpam-5790	902	9	.	.	PUNCT
ejpam-5790	903	1	[	[	X
ejpam-5790	903	2	61	61	NUM
ejpam-5790	903	3	]	]	PUNCT
ejpam-5790	903	4	h.	h.	PROPN
ejpam-5790	903	5	wu	wu	PROPN
ejpam-5790	903	6	,	,	PUNCT
ejpam-5790	903	7	h.	h.	PROPN
ejpam-5790	903	8	zhang	zhang	PROPN
ejpam-5790	903	9	,	,	PUNCT
ejpam-5790	903	10	r.	r.	PROPN
ejpam-5790	903	11	yan	yan	PROPN
ejpam-5790	903	12	,	,	PUNCT
ejpam-5790	903	13	s.	s.	PROPN
ejpam-5790	903	14	li	li	PROPN
ejpam-5790	903	15	,	,	PUNCT
ejpam-5790	903	16	x.	x.	PROPN
ejpam-5790	903	17	guo	guo	PROPN
ejpam-5790	903	18	,	,	PUNCT
ejpam-5790	903	19	l.	l.	PROPN
ejpam-5790	903	20	qiu	qiu	PROPN
ejpam-5790	903	21	,	,	PUNCT
ejpam-5790	903	22	and	and	CCONJ
ejpam-5790	903	23	y.	y.	PROPN
ejpam-5790	903	24	yao	yao	PROPN
ejpam-5790	903	25	.	.	PUNCT
ejpam-5790	904	1	limosilactobacillus	limosilactobacillus	PROPN
ejpam-5790	904	2	regulating	regulate	VERB
ejpam-5790	904	3	microbial	microbial	ADJ
ejpam-5790	904	4	communities	community	NOUN
ejpam-5790	904	5	to	to	PART
ejpam-5790	904	6	overcome	overcome	VERB
ejpam-5790	904	7	the	the	DET
ejpam-5790	904	8	hydrolysis	hydrolysis	NOUN
ejpam-5790	904	9	bottleneck	bottleneck	NOUN
ejpam-5790	904	10	with	with	ADP
ejpam-5790	904	11	efficient	efficient	ADJ
ejpam-5790	904	12	one	one	NUM
ejpam-5790	904	13	-	-	PUNCT
ejpam-5790	904	14	step	step	NOUN
ejpam-5790	904	15	co	co	NOUN
ejpam-5790	904	16	-	-	NOUN
ejpam-5790	904	17	production	production	NOUN
ejpam-5790	904	18	of	of	ADP
ejpam-5790	904	19	h2	h2	PROPN
ejpam-5790	904	20	and	and	CCONJ
ejpam-5790	904	21	ch4	ch4	PROPN
ejpam-5790	904	22	.	.	PUNCT
ejpam-5790	905	1	advanced	advanced	ADJ
ejpam-5790	905	2	science	science	NOUN
ejpam-5790	905	3	,	,	PUNCT
ejpam-5790	905	4	11(43):2406119	11(43):2406119	NUM
ejpam-5790	905	5	,	,	PUNCT
ejpam-5790	905	6	2024	2024	NUM
ejpam-5790	905	7	.	.	PUNCT
ejpam-5790	906	1	[	[	X
ejpam-5790	906	2	62	62	NUM
ejpam-5790	906	3	]	]	X
ejpam-5790	906	4	y.	y.	PROPN
ejpam-5790	906	5	wu	wu	PROPN
ejpam-5790	906	6	and	and	CCONJ
ejpam-5790	906	7	t.	t.	PROPN
ejpam-5790	906	8	shen	shen	PROPN
ejpam-5790	906	9	.	.	PUNCT
ejpam-5790	907	1	a	a	DET
ejpam-5790	907	2	finite	finite	ADJ
ejpam-5790	907	3	convergence	convergence	NOUN
ejpam-5790	907	4	criterion	criterion	NOUN
ejpam-5790	907	5	for	for	ADP
ejpam-5790	907	6	the	the	DET
ejpam-5790	907	7	discounted	discount	VERB
ejpam-5790	907	8	optimal	optimal	ADJ
ejpam-5790	907	9	control	control	NOUN
ejpam-5790	907	10	of	of	ADP
ejpam-5790	907	11	stochastic	stochastic	ADJ
ejpam-5790	907	12	logical	logical	ADJ
ejpam-5790	907	13	networks	network	NOUN
ejpam-5790	907	14	.	.	PUNCT
ejpam-5790	908	1	ieee	ieee	NOUN
ejpam-5790	908	2	transactions	transaction	NOUN
ejpam-5790	908	3	on	on	ADP
ejpam-5790	908	4	automatic	automatic	ADJ
ejpam-5790	908	5	control	control	NOUN
ejpam-5790	908	6	,	,	PUNCT
ejpam-5790	908	7	63(1):262	63(1):262	NOUN
ejpam-5790	908	8	–	–	PUNCT
ejpam-5790	908	9	268	268	NUM
ejpam-5790	908	10	,	,	PUNCT
ejpam-5790	908	11	2017	2017	NUM
ejpam-5790	908	12	.	.	PUNCT
ejpam-5790	909	1	[	[	X
ejpam-5790	909	2	63	63	NUM
ejpam-5790	909	3	]	]	PUNCT
ejpam-5790	909	4	c.	c.	PROPN
ejpam-5790	909	5	yan	yan	PROPN
ejpam-5790	909	6	,	,	PUNCT
ejpam-5790	909	7	m.	m.	NOUN
ejpam-5790	909	8	feng	feng	PROPN
ejpam-5790	909	9	,	,	PUNCT
ejpam-5790	909	10	z.	z.	PROPN
ejpam-5790	909	11	wu	wu	PROPN
ejpam-5790	909	12	,	,	PUNCT
ejpam-5790	909	13	y.	y.	PROPN
ejpam-5790	909	14	guo	guo	PROPN
ejpam-5790	909	15	,	,	PUNCT
ejpam-5790	909	16	w.	w.	PROPN
ejpam-5790	909	17	dong	dong	PROPN
ejpam-5790	909	18	,	,	PUNCT
ejpam-5790	909	19	y.	y.	PROPN
ejpam-5790	909	20	wang	wang	PROPN
ejpam-5790	909	21	,	,	PUNCT
ejpam-5790	909	22	and	and	CCONJ
ejpam-5790	909	23	a.	a.	PROPN
ejpam-5790	909	24	mian	mian	PROPN
ejpam-5790	909	25	.	.	PUNCT
ejpam-5790	910	1	discriminative	discriminative	NOUN
ejpam-5790	910	2	correspondence	correspondence	NOUN
ejpam-5790	910	3	estimation	estimation	NOUN
ejpam-5790	910	4	for	for	ADP
ejpam-5790	910	5	unsupervised	unsupervised	ADJ
ejpam-5790	910	6	rgb	rgb	PROPN
ejpam-5790	910	7	-	-	PROPN
ejpam-5790	910	8	d	d	PROPN
ejpam-5790	910	9	point	point	NOUN
ejpam-5790	910	10	cloud	cloud	NOUN
ejpam-5790	910	11	registration	registration	NOUN
ejpam-5790	910	12	.	.	PUNCT
ejpam-5790	911	1	ieee	ieee	NOUN
ejpam-5790	911	2	transactions	transaction	NOUN
ejpam-5790	911	3	on	on	ADP
ejpam-5790	911	4	circuits	circuit	NOUN
ejpam-5790	911	5	and	and	CCONJ
ejpam-5790	911	6	systems	system	NOUN
ejpam-5790	911	7	for	for	ADP
ejpam-5790	911	8	video	video	NOUN
ejpam-5790	911	9	technology	technology	NOUN
ejpam-5790	911	10	,	,	PUNCT
ejpam-5790	911	11	2024	2024	NUM
ejpam-5790	911	12	.	.	PUNCT
ejpam-5790	912	1	[	[	X
ejpam-5790	912	2	64	64	NUM
ejpam-5790	912	3	]	]	PUNCT
ejpam-5790	912	4	h.	h.	PROPN
ejpam-5790	912	5	zhang	zhang	PROPN
ejpam-5790	912	6	,	,	PUNCT
ejpam-5790	912	7	y.	y.	PROPN
ejpam-5790	912	8	chang	chang	PROPN
ejpam-5790	912	9	,	,	PUNCT
ejpam-5790	912	10	y.	y.	PROPN
ejpam-5790	912	11	xu	xu	PROPN
ejpam-5790	912	12	,	,	PUNCT
ejpam-5790	912	13	c.	c.	PROPN
ejpam-5790	912	14	liu	liu	PROPN
ejpam-5790	912	15	,	,	PUNCT
ejpam-5790	912	16	x.	x.	PROPN
ejpam-5790	912	17	xiao	xiao	PROPN
ejpam-5790	912	18	,	,	PUNCT
ejpam-5790	912	19	j.	j.	PROPN
ejpam-5790	912	20	li	li	PROPN
ejpam-5790	912	21	,	,	PUNCT
ejpam-5790	912	22	and	and	CCONJ
ejpam-5790	912	23	h.	h.	PROPN
ejpam-5790	912	24	guo	guo	PROPN
ejpam-5790	912	25	.	.	PUNCT
ejpam-5790	912	26	design	design	NOUN
ejpam-5790	912	27	and	and	CCONJ
ejpam-5790	912	28	fabrication	fabrication	NOUN
ejpam-5790	912	29	of	of	ADP
ejpam-5790	912	30	a	a	DET
ejpam-5790	912	31	chalcogenide	chalcogenide	ADJ
ejpam-5790	912	32	hollow	hollow	ADJ
ejpam-5790	912	33	-	-	PUNCT
ejpam-5790	912	34	core	core	NOUN
ejpam-5790	912	35	anti	anti	ADJ
ejpam-5790	912	36	-	-	ADJ
ejpam-5790	912	37	resonant	resonant	ADJ
ejpam-5790	912	38	fiber	fiber	NOUN
ejpam-5790	912	39	for	for	ADP
ejpam-5790	912	40	mid	mid	ADJ
ejpam-5790	912	41	-	-	ADJ
ejpam-5790	912	42	infrared	infrared	ADJ
ejpam-5790	912	43	applications	application	NOUN
ejpam-5790	912	44	.	.	PUNCT
ejpam-5790	913	1	optics	optic	NOUN
ejpam-5790	913	2	express	express	VERB
ejpam-5790	913	3	,	,	PUNCT
ejpam-5790	913	4	31(5):7659–7670	31(5):7659–7670	NUM
ejpam-5790	913	5	,	,	PUNCT
ejpam-5790	913	6	2023	2023	NUM
ejpam-5790	913	7	.	.	PUNCT
ejpam-5790	914	1	[	[	X
ejpam-5790	914	2	65	65	NUM
ejpam-5790	914	3	]	]	X
ejpam-5790	914	4	h.	h.	PROPN
ejpam-5790	914	5	h.	h.	PROPN
ejpam-5790	914	6	zhang	zhang	PROPN
ejpam-5790	914	7	,	,	PUNCT
ejpam-5790	914	8	j.	j.	PROPN
ejpam-5790	914	9	b.	b.	PROPN
ejpam-5790	914	10	chao	chao	PROPN
ejpam-5790	914	11	,	,	PUNCT
ejpam-5790	914	12	y.	y.	PROPN
ejpam-5790	914	13	w.	w.	PROPN
ejpam-5790	914	14	wang	wang	PROPN
ejpam-5790	914	15	,	,	PUNCT
ejpam-5790	914	16	y.	y.	PROPN
ejpam-5790	914	17	liu	liu	PROPN
ejpam-5790	914	18	,	,	PUNCT
ejpam-5790	914	19	h.	h.	PROPN
ejpam-5790	914	20	m.	m.	PROPN
ejpam-5790	914	21	yao	yao	PROPN
ejpam-5790	914	22	,	,	PUNCT
ejpam-5790	914	23	z.	z.	PROPN
ejpam-5790	914	24	p.	p.	PROPN
ejpam-5790	914	25	zhao	zhao	PROPN
ejpam-5790	914	26	,	,	PUNCT
ejpam-5790	914	27	and	and	CCONJ
ejpam-5790	914	28	k.	k.	PROPN
ejpam-5790	914	29	niu	niu	PROPN
ejpam-5790	914	30	.	.	PUNCT
ejpam-5790	915	1	5	5	NUM
ejpam-5790	915	2	g	g	NOUN
ejpam-5790	915	3	base	base	NOUN
ejpam-5790	915	4	station	station	NOUN
ejpam-5790	915	5	antenna	antenna	NOUN
ejpam-5790	915	6	array	array	NOUN
ejpam-5790	915	7	with	with	ADP
ejpam-5790	915	8	heatsink	heatsink	NOUN
ejpam-5790	915	9	radome	radome	NOUN
ejpam-5790	915	10	.	.	PUNCT
ejpam-5790	916	1	ieee	ieee	NOUN
ejpam-5790	916	2	transactions	transaction	NOUN
ejpam-5790	916	3	on	on	ADP
ejpam-5790	916	4	antennas	antenna	NOUN
ejpam-5790	916	5	and	and	CCONJ
ejpam-5790	916	6	propagation	propagation	NOUN
ejpam-5790	916	7	,	,	PUNCT
ejpam-5790	916	8	2024	2024	NUM
ejpam-5790	916	9	.	.	PUNCT
ejpam-5790	917	1	[	[	X
ejpam-5790	917	2	66	66	NUM
ejpam-5790	917	3	]	]	PUNCT
ejpam-5790	917	4	x.	x.	PROPN
ejpam-5790	917	5	zhang	zhang	PROPN
ejpam-5790	917	6	,	,	PUNCT
ejpam-5790	917	7	k.	k.	PROPN
ejpam-5790	917	8	shabbir	shabbir	PROPN
ejpam-5790	917	9	,	,	PUNCT
ejpam-5790	917	10	w.	w.	PROPN
ejpam-5790	917	11	afzal	afzal	PROPN
ejpam-5790	917	12	,	,	PUNCT
ejpam-5790	917	13	h.	h.	PROPN
ejpam-5790	917	14	xiao	xiao	PROPN
ejpam-5790	917	15	,	,	PUNCT
ejpam-5790	917	16	and	and	CCONJ
ejpam-5790	917	17	d.	d.	PROPN
ejpam-5790	917	18	lin	lin	PROPN
ejpam-5790	917	19	.	.	PUNCT
ejpam-5790	918	1	hermite	hermite	PROPN
ejpam-5790	918	2	–	–	PUNCT
ejpam-5790	918	3	hadamard	hadamard	PROPN
ejpam-5790	918	4	and	and	CCONJ
ejpam-5790	918	5	jensen	jensen	PROPN
ejpam-5790	918	6	-	-	PUNCT
ejpam-5790	918	7	type	type	NOUN
ejpam-5790	918	8	inequalities	inequality	NOUN
ejpam-5790	918	9	via	via	ADP
ejpam-5790	918	10	riemann	riemann	PROPN
ejpam-5790	918	11	integral	integral	ADJ
ejpam-5790	918	12	operator	operator	NOUN
ejpam-5790	918	13	for	for	ADP
ejpam-5790	918	14	a	a	DET
ejpam-5790	918	15	generalized	generalized	ADJ
ejpam-5790	918	16	class	class	NOUN
ejpam-5790	918	17	of	of	ADP
ejpam-5790	918	18	godunova	godunova	PROPN
ejpam-5790	918	19	–	–	PUNCT
ejpam-5790	918	20	levin	levin	PROPN
ejpam-5790	918	21	functions	function	NOUN
ejpam-5790	918	22	.	.	PUNCT
ejpam-5790	919	1	journal	journal	NOUN
ejpam-5790	919	2	of	of	ADP
ejpam-5790	919	3	mathematics	mathematic	NOUN
ejpam-5790	919	4	,	,	PUNCT
ejpam-5790	919	5	2022(1):3830324	2022(1):3830324	NUM
ejpam-5790	919	6	,	,	PUNCT
ejpam-5790	919	7	2022	2022	NUM
ejpam-5790	919	8	.	.	PUNCT
ejpam-5790	920	1	[	[	X
ejpam-5790	920	2	67	67	NUM
ejpam-5790	920	3	]	]	PUNCT
ejpam-5790	920	4	x.	x.	PROPN
ejpam-5790	920	5	zhang	zhang	PROPN
ejpam-5790	920	6	,	,	PUNCT
ejpam-5790	920	7	m.	m.	PROPN
ejpam-5790	920	8	usman	usman	PROPN
ejpam-5790	920	9	,	,	PUNCT
ejpam-5790	920	10	a.	a.	PROPN
ejpam-5790	920	11	u.	u.	PROPN
ejpam-5790	920	12	r.	r.	PROPN
ejpam-5790	920	13	irshad	irshad	PROPN
ejpam-5790	920	14	,	,	PUNCT
ejpam-5790	920	15	m.	m.	NOUN
ejpam-5790	920	16	rashid	rashid	PROPN
ejpam-5790	920	17	,	,	PUNCT
ejpam-5790	920	18	and	and	CCONJ
ejpam-5790	920	19	a.	a.	PROPN
ejpam-5790	920	20	khattak	khattak	PROPN
ejpam-5790	920	21	.	.	PUNCT
ejpam-5790	921	1	investigating	investigate	VERB
ejpam-5790	921	2	spatial	spatial	ADJ
ejpam-5790	921	3	effects	effect	NOUN
ejpam-5790	921	4	through	through	ADP
ejpam-5790	921	5	machine	machine	NOUN
ejpam-5790	921	6	learning	learning	NOUN
ejpam-5790	921	7	and	and	CCONJ
ejpam-5790	921	8	leveraging	leverage	VERB
ejpam-5790	921	9	explainable	explainable	ADJ
ejpam-5790	921	10	ai	ai	NOUN
ejpam-5790	921	11	for	for	ADP
ejpam-5790	921	12	child	child	NOUN
ejpam-5790	921	13	malnutrition	malnutrition	NOUN
ejpam-5790	921	14	in	in	ADP
ejpam-5790	921	15	pakistan	pakistan	PROPN
ejpam-5790	921	16	.	.	PUNCT
ejpam-5790	922	1	isprs	isprs	PROPN
ejpam-5790	922	2	international	international	PROPN
ejpam-5790	922	3	journal	journal	PROPN
ejpam-5790	922	4	of	of	ADP
ejpam-5790	922	5	geo	geo	PROPN
ejpam-5790	922	6	-	-	PUNCT
ejpam-5790	922	7	information	information	NOUN
ejpam-5790	922	8	,	,	PUNCT
ejpam-5790	922	9	13(9):330	13(9):330	NUM
ejpam-5790	922	10	,	,	PUNCT
ejpam-5790	922	11	2024	2024	NUM
ejpam-5790	922	12	.	.	PUNCT
ejpam-5790	923	1	[	[	X
ejpam-5790	923	2	68	68	NUM
ejpam-5790	923	3	]	]	PUNCT
ejpam-5790	923	4	j.	j.	PROPN
ejpam-5790	923	5	zhao	zhao	PROPN
ejpam-5790	923	6	,	,	PUNCT
ejpam-5790	923	7	x.	x.	PROPN
ejpam-5790	923	8	wang	wang	PROPN
ejpam-5790	923	9	,	,	PUNCT
ejpam-5790	923	10	p.	p.	PROPN
ejpam-5790	923	11	k.	k.	PROPN
ejpam-5790	923	12	wong	wong	PROPN
ejpam-5790	923	13	,	,	PUNCT
ejpam-5790	923	14	z.	z.	PROPN
ejpam-5790	923	15	xie	xie	PROPN
ejpam-5790	923	16	,	,	PUNCT
ejpam-5790	923	17	j.	j.	PROPN
ejpam-5790	923	18	jia	jia	PROPN
ejpam-5790	923	19	,	,	PUNCT
ejpam-5790	923	20	and	and	CCONJ
ejpam-5790	923	21	w.	w.	PROPN
ejpam-5790	923	22	li	li	PROPN
ejpam-5790	923	23	.	.	PUNCT
ejpam-5790	923	24	multi	multi	ADJ
ejpam-5790	923	25	-	-	ADJ
ejpam-5790	923	26	objective	objective	ADJ
ejpam-5790	923	27	frequency	frequency	NOUN
ejpam-5790	923	28	domain	domain	NOUN
ejpam-5790	923	29	-	-	PUNCT
ejpam-5790	923	30	constrained	constrain	VERB
ejpam-5790	923	31	static	static	ADJ
ejpam-5790	923	32	output	output	NOUN
ejpam-5790	923	33	feedback	feedback	NOUN
ejpam-5790	923	34	control	control	NOUN
ejpam-5790	923	35	for	for	ADP
ejpam-5790	923	36	delayed	delay	VERB
ejpam-5790	923	37	active	active	ADJ
ejpam-5790	923	38	suspension	suspension	NOUN
ejpam-5790	923	39	systems	system	NOUN
ejpam-5790	923	40	with	with	ADP
ejpam-5790	923	41	wheelbase	wheelbase	ADJ
ejpam-5790	923	42	preview	preview	NOUN
ejpam-5790	923	43	information	information	NOUN
ejpam-5790	923	44	.	.	PUNCT
ejpam-5790	924	1	nonlinear	nonlinear	ADJ
ejpam-5790	924	2	dynamics	dynamic	NOUN
ejpam-5790	924	3	,	,	PUNCT
ejpam-5790	924	4	103(2):1757–1774	103(2):1757–1774	NUM
ejpam-5790	924	5	,	,	PUNCT
ejpam-5790	924	6	2021	2021	NUM
ejpam-5790	924	7	.	.	PUNCT