id	sid	tid	token	lemma	pos
ejpam-5586	1	1	european	european	PROPN
ejpam-5586	1	2	journal	journal	PROPN
ejpam-5586	1	3	of	of	ADP
ejpam-5586	1	4	pure	pure	ADJ
ejpam-5586	1	5	and	and	CCONJ
ejpam-5586	1	6	applied	applied	ADJ
ejpam-5586	1	7	mathematics	mathematic	NOUN
ejpam-5586	1	8	2025	2025	NUM
ejpam-5586	1	9	,	,	PUNCT
ejpam-5586	1	10	vol	vol	NOUN
ejpam-5586	1	11	.	.	PROPN
ejpam-5586	1	12	18	18	NUM
ejpam-5586	1	13	,	,	PUNCT
ejpam-5586	1	14	issue	issue	NOUN
ejpam-5586	1	15	1	1	NUM
ejpam-5586	1	16	,	,	PUNCT
ejpam-5586	1	17	article	article	NOUN
ejpam-5586	1	18	number	number	NOUN
ejpam-5586	1	19	5586	5586	NUM
ejpam-5586	1	20	issn	issn	PROPN
ejpam-5586	1	21	1307	1307	NUM
ejpam-5586	1	22	-	-	SYM
ejpam-5586	1	23	5543	5543	NUM
ejpam-5586	1	24	–	–	PUNCT
ejpam-5586	1	25	ejpam.com	ejpam.com	X
ejpam-5586	1	26	published	publish	VERB
ejpam-5586	1	27	by	by	ADP
ejpam-5586	1	28	new	new	PROPN
ejpam-5586	1	29	york	york	PROPN
ejpam-5586	1	30	business	business	PROPN
ejpam-5586	1	31	global	global	ADJ
ejpam-5586	1	32	new	new	ADJ
ejpam-5586	1	33	improvements	improvement	NOUN
ejpam-5586	1	34	to	to	PART
ejpam-5586	1	35	heron	heron	VERB
ejpam-5586	1	36	and	and	CCONJ
ejpam-5586	1	37	heinz	heinz	PROPN
ejpam-5586	1	38	inequality	inequality	NOUN
ejpam-5586	1	39	using	use	VERB
ejpam-5586	1	40	matrix	matrix	NOUN
ejpam-5586	1	41	techniques	technique	NOUN
ejpam-5586	1	42	m.h.m	m.h.m	PROPN
ejpam-5586	1	43	rashid1,∗	rashid1,∗	NOUN
ejpam-5586	1	44	,	,	PUNCT
ejpam-5586	1	45	wael	wael	PROPN
ejpam-5586	1	46	mahmoud	mahmoud	PROPN
ejpam-5586	1	47	mohammad	mohammad	PROPN
ejpam-5586	1	48	salameh2	salameh2	PROPN
ejpam-5586	1	49	1	1	NUM
ejpam-5586	1	50	department	department	NOUN
ejpam-5586	1	51	of	of	ADP
ejpam-5586	1	52	mathematics	mathematic	NOUN
ejpam-5586	1	53	,	,	PUNCT
ejpam-5586	1	54	faculty	faculty	NOUN
ejpam-5586	1	55	of	of	ADP
ejpam-5586	1	56	science	science	NOUN
ejpam-5586	1	57	p.o.box(7	p.o.box(7	NOUN
ejpam-5586	1	58	)	)	PUNCT
ejpam-5586	1	59	,	,	PUNCT
ejpam-5586	1	60	mutah	mutah	PROPN
ejpam-5586	1	61	university	university	PROPN
ejpam-5586	1	62	,	,	PUNCT
ejpam-5586	1	63	al	al	PROPN
ejpam-5586	1	64	-	-	PUNCT
ejpam-5586	1	65	karak	karak	PROPN
ejpam-5586	1	66	,	,	PUNCT
ejpam-5586	1	67	jordan	jordan	PROPN
ejpam-5586	1	68	2	2	NUM
ejpam-5586	1	69	faculty	faculty	NOUN
ejpam-5586	1	70	of	of	ADP
ejpam-5586	1	71	information	information	NOUN
ejpam-5586	1	72	technology	technology	NOUN
ejpam-5586	1	73	,	,	PUNCT
ejpam-5586	1	74	abu	abu	PROPN
ejpam-5586	1	75	dhabi	dhabi	PROPN
ejpam-5586	1	76	university	university	PROPN
ejpam-5586	1	77	,	,	PUNCT
ejpam-5586	1	78	abu	abu	PROPN
ejpam-5586	1	79	dhabi	dhabi	PROPN
ejpam-5586	1	80	59911	59911	NUM
ejpam-5586	1	81	,	,	PUNCT
ejpam-5586	1	82	united	united	PROPN
ejpam-5586	1	83	arab	arab	PROPN
ejpam-5586	1	84	emirates	emirates	PROPN
ejpam-5586	1	85	abstract	abstract	PROPN
ejpam-5586	1	86	.	.	PUNCT
ejpam-5586	2	1	this	this	DET
ejpam-5586	2	2	paper	paper	NOUN
ejpam-5586	2	3	presents	present	VERB
ejpam-5586	2	4	a	a	DET
ejpam-5586	2	5	comprehensive	comprehensive	ADJ
ejpam-5586	2	6	study	study	NOUN
ejpam-5586	2	7	on	on	ADP
ejpam-5586	2	8	matrix	matrix	NOUN
ejpam-5586	2	9	means	mean	VERB
ejpam-5586	2	10	interpolation	interpolation	NOUN
ejpam-5586	2	11	and	and	CCONJ
ejpam-5586	2	12	comparison	comparison	NOUN
ejpam-5586	2	13	,	,	PUNCT
ejpam-5586	2	14	extending	extend	VERB
ejpam-5586	2	15	the	the	DET
ejpam-5586	2	16	parameter	parameter	NOUN
ejpam-5586	2	17	ϑ	ϑ	PROPN
ejpam-5586	2	18	from	from	ADP
ejpam-5586	2	19	the	the	DET
ejpam-5586	2	20	traditional	traditional	ADJ
ejpam-5586	2	21	closed	closed	ADJ
ejpam-5586	2	22	interval	interval	NOUN
ejpam-5586	2	23	[	[	X
ejpam-5586	2	24	0	0	NUM
ejpam-5586	2	25	,	,	PUNCT
ejpam-5586	2	26	1	1	NUM
ejpam-5586	2	27	]	]	PUNCT
ejpam-5586	2	28	to	to	PART
ejpam-5586	2	29	encompass	encompass	VERB
ejpam-5586	2	30	the	the	DET
ejpam-5586	2	31	entire	entire	ADJ
ejpam-5586	2	32	positive	positive	ADJ
ejpam-5586	2	33	real	real	ADJ
ejpam-5586	2	34	line	line	NOUN
ejpam-5586	2	35	,	,	PUNCT
ejpam-5586	2	36	denoted	denote	VERB
ejpam-5586	2	37	as	as	ADP
ejpam-5586	2	38	r+	r+	X
ejpam-5586	2	39	.	.	PUNCT
ejpam-5586	3	1	the	the	DET
ejpam-5586	3	2	research	research	NOUN
ejpam-5586	3	3	delves	delve	VERB
ejpam-5586	3	4	into	into	ADP
ejpam-5586	3	5	further	further	ADJ
ejpam-5586	3	6	results	result	NOUN
ejpam-5586	3	7	involving	involve	VERB
ejpam-5586	3	8	heinz	heinz	ADJ
ejpam-5586	3	9	means	mean	NOUN
ejpam-5586	3	10	,	,	PUNCT
ejpam-5586	3	11	proposing	propose	VERB
ejpam-5586	3	12	novel	novel	ADJ
ejpam-5586	3	13	scalar	scalar	ADJ
ejpam-5586	3	14	adaptations	adaptation	NOUN
ejpam-5586	3	15	of	of	ADP
ejpam-5586	3	16	heinz	heinz	ADJ
ejpam-5586	3	17	inequalities	inequality	NOUN
ejpam-5586	3	18	that	that	PRON
ejpam-5586	3	19	integrate	integrate	VERB
ejpam-5586	3	20	kantorovich	kantorovich	PROPN
ejpam-5586	3	21	’s	’s	PART
ejpam-5586	3	22	constant	constant	ADJ
ejpam-5586	3	23	.	.	PUNCT
ejpam-5586	4	1	additionally	additionally	ADV
ejpam-5586	4	2	,	,	PUNCT
ejpam-5586	4	3	the	the	DET
ejpam-5586	4	4	operator	operator	NOUN
ejpam-5586	4	5	version	version	NOUN
ejpam-5586	4	6	of	of	ADP
ejpam-5586	4	7	these	these	DET
ejpam-5586	4	8	inequalities	inequality	NOUN
ejpam-5586	4	9	is	be	AUX
ejpam-5586	4	10	strengthened	strengthen	VERB
ejpam-5586	4	11	.	.	PUNCT
ejpam-5586	5	1	a	a	DET
ejpam-5586	5	2	key	key	ADJ
ejpam-5586	5	3	contribution	contribution	NOUN
ejpam-5586	5	4	of	of	ADP
ejpam-5586	5	5	this	this	DET
ejpam-5586	5	6	work	work	NOUN
ejpam-5586	5	7	is	be	AUX
ejpam-5586	5	8	the	the	DET
ejpam-5586	5	9	development	development	NOUN
ejpam-5586	5	10	of	of	ADP
ejpam-5586	5	11	refined	refined	ADJ
ejpam-5586	5	12	young	young	PROPN
ejpam-5586	5	13	’s	’s	PART
ejpam-5586	5	14	type	type	NOUN
ejpam-5586	5	15	inequalities	inequality	NOUN
ejpam-5586	5	16	tailored	tailor	VERB
ejpam-5586	5	17	for	for	ADP
ejpam-5586	5	18	the	the	DET
ejpam-5586	5	19	traces	trace	NOUN
ejpam-5586	5	20	,	,	PUNCT
ejpam-5586	5	21	determinants	determinant	NOUN
ejpam-5586	5	22	,	,	PUNCT
ejpam-5586	5	23	and	and	CCONJ
ejpam-5586	5	24	norms	norm	NOUN
ejpam-5586	5	25	of	of	ADP
ejpam-5586	5	26	positive	positive	ADJ
ejpam-5586	5	27	semi	semi	ADJ
ejpam-5586	5	28	-	-	ADJ
ejpam-5586	5	29	definite	definite	ADJ
ejpam-5586	5	30	matrices	matrix	NOUN
ejpam-5586	5	31	.	.	PUNCT
ejpam-5586	6	1	these	these	DET
ejpam-5586	6	2	refinements	refinement	NOUN
ejpam-5586	6	3	offer	offer	VERB
ejpam-5586	6	4	deeper	deep	ADJ
ejpam-5586	6	5	insights	insight	NOUN
ejpam-5586	6	6	into	into	ADP
ejpam-5586	6	7	matrix	matrix	NOUN
ejpam-5586	6	8	analysis	analysis	NOUN
ejpam-5586	6	9	,	,	PUNCT
ejpam-5586	6	10	especially	especially	ADV
ejpam-5586	6	11	in	in	ADP
ejpam-5586	6	12	the	the	DET
ejpam-5586	6	13	context	context	NOUN
ejpam-5586	6	14	of	of	ADP
ejpam-5586	6	15	operator	operator	NOUN
ejpam-5586	6	16	theory	theory	NOUN
ejpam-5586	6	17	and	and	CCONJ
ejpam-5586	6	18	inequality	inequality	NOUN
ejpam-5586	6	19	theory	theory	NOUN
ejpam-5586	6	20	.	.	PUNCT
ejpam-5586	7	1	through	through	ADP
ejpam-5586	7	2	these	these	DET
ejpam-5586	7	3	advancements	advancement	NOUN
ejpam-5586	7	4	,	,	PUNCT
ejpam-5586	7	5	the	the	DET
ejpam-5586	7	6	paper	paper	NOUN
ejpam-5586	7	7	enhances	enhance	VERB
ejpam-5586	7	8	the	the	DET
ejpam-5586	7	9	mathematical	mathematical	ADJ
ejpam-5586	7	10	framework	framework	NOUN
ejpam-5586	7	11	for	for	ADP
ejpam-5586	7	12	studying	study	VERB
ejpam-5586	7	13	matrix	matrix	NOUN
ejpam-5586	7	14	means	mean	NOUN
ejpam-5586	7	15	and	and	CCONJ
ejpam-5586	7	16	their	their	PRON
ejpam-5586	7	17	associated	associated	ADJ
ejpam-5586	7	18	inequalities	inequality	NOUN
ejpam-5586	7	19	,	,	PUNCT
ejpam-5586	7	20	providing	provide	VERB
ejpam-5586	7	21	useful	useful	ADJ
ejpam-5586	7	22	tools	tool	NOUN
ejpam-5586	7	23	for	for	ADP
ejpam-5586	7	24	both	both	CCONJ
ejpam-5586	7	25	theoretical	theoretical	ADJ
ejpam-5586	7	26	exploration	exploration	NOUN
ejpam-5586	7	27	and	and	CCONJ
ejpam-5586	7	28	practical	practical	ADJ
ejpam-5586	7	29	applications	application	NOUN
ejpam-5586	7	30	in	in	ADP
ejpam-5586	7	31	linear	linear	ADJ
ejpam-5586	7	32	algebra	algebra	NOUN
ejpam-5586	7	33	and	and	CCONJ
ejpam-5586	7	34	related	related	ADJ
ejpam-5586	7	35	fields	field	NOUN
ejpam-5586	7	36	.	.	PUNCT
ejpam-5586	8	1	2020	2020	NUM
ejpam-5586	8	2	mathematics	mathematic	NOUN
ejpam-5586	8	3	subject	subject	NOUN
ejpam-5586	8	4	classifications	classification	NOUN
ejpam-5586	8	5	:	:	PUNCT
ejpam-5586	8	6	26d07	26d07	NUM
ejpam-5586	8	7	,	,	PUNCT
ejpam-5586	8	8	26d15	26d15	NUM
ejpam-5586	8	9	,	,	PUNCT
ejpam-5586	8	10	15a18	15a18	NUM
ejpam-5586	8	11	,	,	PUNCT
ejpam-5586	8	12	47a63	47a63	NUM
ejpam-5586	8	13	key	key	ADJ
ejpam-5586	8	14	words	word	NOUN
ejpam-5586	8	15	and	and	CCONJ
ejpam-5586	8	16	phrases	phrase	NOUN
ejpam-5586	8	17	:	:	PUNCT
ejpam-5586	8	18	heinz	heinz	ADJ
ejpam-5586	8	19	mean	mean	NOUN
ejpam-5586	8	20	inequalities	inequality	NOUN
ejpam-5586	8	21	,	,	PUNCT
ejpam-5586	8	22	positive	positive	ADJ
ejpam-5586	8	23	semi	semi	ADJ
ejpam-5586	8	24	-	-	ADJ
ejpam-5586	8	25	definite	definite	ADJ
ejpam-5586	8	26	matrices	matrix	NOUN
ejpam-5586	8	27	,	,	PUNCT
ejpam-5586	8	28	hilbertschmidt	hilbertschmidt	PROPN
ejpam-5586	8	29	norm	norm	NOUN
ejpam-5586	8	30	,	,	PUNCT
ejpam-5586	8	31	young	young	ADJ
ejpam-5586	8	32	inequality	inequality	NOUN
ejpam-5586	8	33	1	1	NUM
ejpam-5586	8	34	.	.	PUNCT
ejpam-5586	9	1	introduction	introduction	NOUN
ejpam-5586	9	2	consider	consider	VERB
ejpam-5586	9	3	the	the	DET
ejpam-5586	9	4	algebra	algebra	NOUN
ejpam-5586	9	5	of	of	ADP
ejpam-5586	9	6	complex	complex	ADJ
ejpam-5586	9	7	matrices	matrix	NOUN
ejpam-5586	9	8	of	of	ADP
ejpam-5586	9	9	size	size	NOUN
ejpam-5586	9	10	n×	n×	PROPN
ejpam-5586	9	11	n	n	CCONJ
ejpam-5586	9	12	,	,	PUNCT
ejpam-5586	9	13	denoted	denote	VERB
ejpam-5586	9	14	as	as	ADP
ejpam-5586	9	15	mn(c	mn(c	NOUN
ejpam-5586	9	16	)	)	PUNCT
ejpam-5586	9	17	.	.	PUNCT
ejpam-5586	10	1	a	a	DET
ejpam-5586	10	2	matrix	matrix	NOUN
ejpam-5586	10	3	t	t	NOUN
ejpam-5586	10	4	in	in	ADP
ejpam-5586	10	5	mn(c	mn(c	NOUN
ejpam-5586	10	6	)	)	PUNCT
ejpam-5586	10	7	is	be	AUX
ejpam-5586	10	8	considered	consider	VERB
ejpam-5586	10	9	positive	positive	ADJ
ejpam-5586	10	10	semi	semi	ADJ
ejpam-5586	10	11	-	-	ADJ
ejpam-5586	10	12	definite	definite	ADJ
ejpam-5586	10	13	,	,	PUNCT
ejpam-5586	10	14	written	write	VERB
ejpam-5586	10	15	as	as	ADP
ejpam-5586	10	16	t	t	PROPN
ejpam-5586	10	17	≥	≥	PROPN
ejpam-5586	10	18	0	0	NUM
ejpam-5586	10	19	,	,	PUNCT
ejpam-5586	10	20	if	if	SCONJ
ejpam-5586	10	21	it	it	PRON
ejpam-5586	10	22	is	be	AUX
ejpam-5586	10	23	hermitian	hermitian	ADJ
ejpam-5586	10	24	and	and	CCONJ
ejpam-5586	10	25	satisfies	satisfie	NOUN
ejpam-5586	10	26	⟨tx	⟨tx	ADP
ejpam-5586	10	27	,	,	PUNCT
ejpam-5586	10	28	x⟩	x⟩	PUNCT
ejpam-5586	10	29	≥	≥	X
ejpam-5586	10	30	0	0	NUM
ejpam-5586	10	31	for	for	ADP
ejpam-5586	10	32	all	all	DET
ejpam-5586	10	33	vectors	vector	NOUN
ejpam-5586	10	34	x	x	PUNCT
ejpam-5586	10	35	in	in	ADP
ejpam-5586	10	36	cn	cn	PROPN
ejpam-5586	10	37	.	.	PUNCT
ejpam-5586	11	1	if	if	SCONJ
ejpam-5586	11	2	,	,	PUNCT
ejpam-5586	11	3	for	for	ADP
ejpam-5586	11	4	a	a	DET
ejpam-5586	11	5	hermitian	hermitian	ADJ
ejpam-5586	11	6	matrix	matrix	NOUN
ejpam-5586	11	7	t	t	NOUN
ejpam-5586	11	8	in	in	ADP
ejpam-5586	11	9	mn(c	mn(c	PROPN
ejpam-5586	11	10	)	)	PUNCT
ejpam-5586	11	11	,	,	PUNCT
ejpam-5586	11	12	⟨tx	⟨tx	PROPN
ejpam-5586	11	13	,	,	PUNCT
ejpam-5586	11	14	x⟩	x⟩	PUNCT
ejpam-5586	11	15	>	>	X
ejpam-5586	11	16	0	0	NUM
ejpam-5586	11	17	holds	hold	VERB
ejpam-5586	11	18	for	for	ADP
ejpam-5586	11	19	all	all	DET
ejpam-5586	11	20	nonzero	nonzero	PROPN
ejpam-5586	11	21	vectors	vector	NOUN
ejpam-5586	11	22	x	x	PUNCT
ejpam-5586	11	23	in	in	ADP
ejpam-5586	11	24	cn	cn	PROPN
ejpam-5586	11	25	,	,	PUNCT
ejpam-5586	11	26	it	it	PRON
ejpam-5586	11	27	is	be	AUX
ejpam-5586	11	28	termed	term	VERB
ejpam-5586	11	29	a	a	DET
ejpam-5586	11	30	positive	positive	ADJ
ejpam-5586	11	31	definite	definite	ADJ
ejpam-5586	11	32	matrix	matrix	NOUN
ejpam-5586	11	33	,	,	PUNCT
ejpam-5586	11	34	denoted	denote	VERB
ejpam-5586	11	35	as	as	ADP
ejpam-5586	11	36	t	t	PROPN
ejpam-5586	11	37	>	>	X
ejpam-5586	11	38	0	0	PROPN
ejpam-5586	11	39	.	.	PUNCT
ejpam-5586	12	1	the	the	DET
ejpam-5586	12	2	set	set	NOUN
ejpam-5586	12	3	of	of	ADP
ejpam-5586	12	4	all	all	DET
ejpam-5586	12	5	positive	positive	ADJ
ejpam-5586	12	6	matrices	matrix	NOUN
ejpam-5586	12	7	is	be	AUX
ejpam-5586	12	8	denoted	denote	VERB
ejpam-5586	12	9	as	as	ADP
ejpam-5586	12	10	m+	m+	NUM
ejpam-5586	12	11	n	n	PROPN
ejpam-5586	12	12	(	(	PUNCT
ejpam-5586	12	13	c	c	NOUN
ejpam-5586	12	14	)	)	PUNCT
ejpam-5586	12	15	,	,	PUNCT
ejpam-5586	12	16	and	and	CCONJ
ejpam-5586	12	17	the	the	DET
ejpam-5586	12	18	subset	subset	NOUN
ejpam-5586	12	19	of	of	ADP
ejpam-5586	12	20	definite	definite	ADJ
ejpam-5586	12	21	matrices	matrix	NOUN
ejpam-5586	12	22	within	within	ADP
ejpam-5586	12	23	m+	m+	NUM
ejpam-5586	12	24	n	n	PROPN
ejpam-5586	12	25	(	(	PUNCT
ejpam-5586	12	26	c	c	X
ejpam-5586	12	27	)	)	PUNCT
ejpam-5586	12	28	is	be	AUX
ejpam-5586	12	29	represented	represent	VERB
ejpam-5586	12	30	as	as	ADP
ejpam-5586	12	31	m++	m++	NOUN
ejpam-5586	12	32	n	n	CCONJ
ejpam-5586	12	33	(	(	PUNCT
ejpam-5586	12	34	c	c	NOUN
ejpam-5586	12	35	)	)	PUNCT
ejpam-5586	12	36	.	.	PUNCT
ejpam-5586	13	1	the	the	DET
ejpam-5586	13	2	schur	schur	PROPN
ejpam-5586	13	3	product	product	NOUN
ejpam-5586	13	4	of	of	ADP
ejpam-5586	13	5	two	two	NUM
ejpam-5586	13	6	matrices	matrix	NOUN
ejpam-5586	13	7	t	t	NOUN
ejpam-5586	13	8	=	=	PUNCT
ejpam-5586	14	1	[	[	X
ejpam-5586	14	2	tij	tij	X
ejpam-5586	14	3	]	]	X
ejpam-5586	14	4	i	i	PRON
ejpam-5586	14	5	,	,	PUNCT
ejpam-5586	14	6	j	j	PROPN
ejpam-5586	14	7	and	and	CCONJ
ejpam-5586	14	8	s	s	PROPN
ejpam-5586	14	9	=	=	PUNCT
ejpam-5586	15	1	[	[	X
ejpam-5586	15	2	sij	sij	X
ejpam-5586	15	3	]	]	X
ejpam-5586	15	4	i	i	PRON
ejpam-5586	15	5	,	,	PUNCT
ejpam-5586	15	6	j	j	PROPN
ejpam-5586	15	7	in	in	ADP
ejpam-5586	15	8	mn(c	mn(c	NOUN
ejpam-5586	15	9	)	)	PUNCT
ejpam-5586	15	10	is	be	AUX
ejpam-5586	15	11	defined	define	VERB
ejpam-5586	15	12	as	as	ADP
ejpam-5586	15	13	the	the	DET
ejpam-5586	15	14	matrix	matrix	NOUN
ejpam-5586	15	15	t	t	PROPN
ejpam-5586	15	16	◦	◦	NOUN
ejpam-5586	15	17	s	s	NUM
ejpam-5586	15	18	with	with	ADP
ejpam-5586	15	19	entries	entry	NOUN
ejpam-5586	15	20	∗corresponding	∗corresponde	VERB
ejpam-5586	15	21	author	author	NOUN
ejpam-5586	15	22	.	.	PUNCT
ejpam-5586	16	1	doi	doi	NOUN
ejpam-5586	16	2	:	:	PUNCT
ejpam-5586	16	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5586	https://doi.org/10.29020/nybg.ejpam.v18i1.5586	ADJ
ejpam-5586	16	4	email	email	NOUN
ejpam-5586	16	5	addresses	address	NOUN
ejpam-5586	16	6	:	:	PUNCT
ejpam-5586	16	7	malik	malik	PROPN
ejpam-5586	16	8	okasha@yahoo.com	okasha@yahoo.com	X
ejpam-5586	16	9	(	(	PUNCT
ejpam-5586	16	10	m.h.m	m.h.m	PROPN
ejpam-5586	16	11	rashid	rashid	PROPN
ejpam-5586	16	12	)	)	PUNCT
ejpam-5586	16	13	,	,	PUNCT
ejpam-5586	16	14	wael.salameh1@adu.ac.ae	wael.salameh1@adu.ac.ae	CCONJ
ejpam-5586	16	15	(	(	PUNCT
ejpam-5586	16	16	w.m.m	w.m.m	NOUN
ejpam-5586	16	17	.	.	PUNCT
ejpam-5586	16	18	salameh	salameh	PROPN
ejpam-5586	16	19	)	)	PUNCT
ejpam-5586	16	20	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5586	16	21	1	1	NUM
ejpam-5586	16	22	copyright	copyright	NOUN
ejpam-5586	16	23	:	:	PUNCT
ejpam-5586	17	1	©	©	PROPN
ejpam-5586	17	2	2025	2025	NUM
ejpam-5586	17	3	the	the	DET
ejpam-5586	17	4	author(s	author(s	NOUN
ejpam-5586	17	5	)	)	PUNCT
ejpam-5586	17	6	.	.	PUNCT
ejpam-5586	18	1	(	(	PUNCT
ejpam-5586	18	2	cc	cc	NOUN
ejpam-5586	18	3	by	by	ADP
ejpam-5586	18	4	-	-	PUNCT
ejpam-5586	18	5	nc	nc	PROPN
ejpam-5586	18	6	4.0	4.0	NUM
ejpam-5586	18	7	)	)	PUNCT
ejpam-5586	18	8	m.h.m	m.h.m	NOUN
ejpam-5586	18	9	rashid	rashid	PROPN
ejpam-5586	18	10	,	,	PUNCT
ejpam-5586	18	11	w.m.m	w.m.m	NOUN
ejpam-5586	18	12	.	.	PUNCT
ejpam-5586	19	1	salameh	salameh	PROPN
ejpam-5586	19	2	/	/	SYM
ejpam-5586	19	3	eur	eur	PROPN
ejpam-5586	19	4	.	.	PUNCT
ejpam-5586	20	1	j.	j.	PROPN
ejpam-5586	20	2	pure	pure	PROPN
ejpam-5586	20	3	appl	appl	PROPN
ejpam-5586	20	4	.	.	PROPN
ejpam-5586	20	5	math	math	PROPN
ejpam-5586	20	6	,	,	PUNCT
ejpam-5586	20	7	18	18	NUM
ejpam-5586	20	8	(	(	PUNCT
ejpam-5586	20	9	1	1	NUM
ejpam-5586	20	10	)	)	PUNCT
ejpam-5586	20	11	(	(	PUNCT
ejpam-5586	20	12	2025	2025	NUM
ejpam-5586	20	13	)	)	PUNCT
ejpam-5586	20	14	,	,	PUNCT
ejpam-5586	20	15	5586	5586	NUM
ejpam-5586	20	16	2	2	NUM
ejpam-5586	20	17	of	of	ADP
ejpam-5586	20	18	21	21	NUM
ejpam-5586	20	19	tijsij	tijsij	NOUN
ejpam-5586	20	20	.	.	PUNCT
ejpam-5586	21	1	a	a	DET
ejpam-5586	21	2	norm	norm	NOUN
ejpam-5586	21	3	|||.|||	|||.|||	NOUN
ejpam-5586	21	4	on	on	ADP
ejpam-5586	21	5	the	the	DET
ejpam-5586	21	6	set	set	NOUN
ejpam-5586	21	7	of	of	ADP
ejpam-5586	21	8	complex	complex	ADJ
ejpam-5586	21	9	matrices	matrix	NOUN
ejpam-5586	21	10	of	of	ADP
ejpam-5586	21	11	size	size	NOUN
ejpam-5586	21	12	n	n	CCONJ
ejpam-5586	21	13	×	×	NOUN
ejpam-5586	21	14	n	n	CCONJ
ejpam-5586	21	15	,	,	PUNCT
ejpam-5586	21	16	denoted	denote	VERB
ejpam-5586	21	17	as	as	ADP
ejpam-5586	21	18	mn(c	mn(c	NOUN
ejpam-5586	21	19	)	)	PUNCT
ejpam-5586	21	20	,	,	PUNCT
ejpam-5586	21	21	is	be	AUX
ejpam-5586	21	22	termed	term	VERB
ejpam-5586	21	23	unitarily	unitarily	ADV
ejpam-5586	21	24	invariant	invariant	ADJ
ejpam-5586	21	25	if	if	SCONJ
ejpam-5586	21	26	|||uav	|||uav	NOUN
ejpam-5586	21	27	|||	|||	NOUN
ejpam-5586	21	28	=	=	SYM
ejpam-5586	21	29	|||t	|||t	ADJ
ejpam-5586	21	30	|||	|||	NOUN
ejpam-5586	21	31	for	for	ADP
ejpam-5586	21	32	any	any	DET
ejpam-5586	21	33	matrix	matrix	NOUN
ejpam-5586	21	34	t	t	X
ejpam-5586	21	35	inmn(c	inmn(c	PROPN
ejpam-5586	21	36	)	)	PUNCT
ejpam-5586	21	37	and	and	CCONJ
ejpam-5586	21	38	for	for	ADP
ejpam-5586	21	39	all	all	DET
ejpam-5586	21	40	unitary	unitary	ADJ
ejpam-5586	21	41	matrices	matrix	NOUN
ejpam-5586	21	42	u	u	NOUN
ejpam-5586	21	43	and	and	CCONJ
ejpam-5586	21	44	v	v	NOUN
ejpam-5586	21	45	in	in	ADP
ejpam-5586	21	46	mn(c	mn(c	NOUN
ejpam-5586	21	47	)	)	PUNCT
ejpam-5586	21	48	.	.	PUNCT
ejpam-5586	22	1	for	for	ADP
ejpam-5586	22	2	a	a	DET
ejpam-5586	22	3	matrix	matrix	NOUN
ejpam-5586	22	4	t	t	NOUN
ejpam-5586	22	5	=	=	PUNCT
ejpam-5586	23	1	[	[	X
ejpam-5586	23	2	tij	tij	X
ejpam-5586	23	3	]	]	PUNCT
ejpam-5586	23	4	∈mn(c	∈mn(c	NOUN
ejpam-5586	23	5	)	)	PUNCT
ejpam-5586	23	6	,	,	PUNCT
ejpam-5586	23	7	the	the	DET
ejpam-5586	23	8	hilbert	hilbert	NOUN
ejpam-5586	23	9	-	-	PUNCT
ejpam-5586	23	10	schmidt	schmidt	ADJ
ejpam-5586	23	11	norm	norm	NOUN
ejpam-5586	23	12	(	(	PUNCT
ejpam-5586	23	13	also	also	ADV
ejpam-5586	23	14	known	know	VERB
ejpam-5586	23	15	as	as	ADP
ejpam-5586	23	16	the	the	DET
ejpam-5586	23	17	frobenius	frobenius	NOUN
ejpam-5586	23	18	norm	norm	NOUN
ejpam-5586	23	19	)	)	PUNCT
ejpam-5586	23	20	and	and	CCONJ
ejpam-5586	23	21	the	the	DET
ejpam-5586	23	22	trace	trace	NOUN
ejpam-5586	23	23	norm	norm	NOUN
ejpam-5586	23	24	of	of	ADP
ejpam-5586	23	25	t	t	PROPN
ejpam-5586	23	26	are	be	AUX
ejpam-5586	23	27	defined	define	VERB
ejpam-5586	23	28	as	as	SCONJ
ejpam-5586	23	29	follows	follow	VERB
ejpam-5586	23	30	∥t∥2	∥t∥2	X
ejpam-5586	23	31	=	=	SYM
ejpam-5586	23	32			PROPN
ejpam-5586	23	33	n∑	n∑	PROPN
ejpam-5586	23	34	j=1	j=1	PROPN
ejpam-5586	23	35	s2j	s2j	NOUN
ejpam-5586	23	36	(	(	PUNCT
ejpam-5586	23	37	t	t	PROPN
ejpam-5586	23	38	)	)	PUNCT
ejpam-5586	24	1			PROPN
ejpam-5586	24	2	1	1	NUM
ejpam-5586	24	3	2	2	NUM
ejpam-5586	24	4	,	,	PUNCT
ejpam-5586	24	5	∥t∥1	∥t∥1	X
ejpam-5586	24	6	=	=	SYM
ejpam-5586	24	7	tr(|t	tr(|t	NOUN
ejpam-5586	24	8	|	|	NOUN
ejpam-5586	24	9	)	)	PUNCT
ejpam-5586	25	1	=	=	PUNCT
ejpam-5586	25	2	n∑	n∑	PROPN
ejpam-5586	25	3	j=1	j=1	NOUN
ejpam-5586	25	4	sj(t	sj(t	PRON
ejpam-5586	25	5	)	)	PUNCT
ejpam-5586	25	6	(	(	PUNCT
ejpam-5586	25	7	1	1	X
ejpam-5586	25	8	)	)	PUNCT
ejpam-5586	25	9	here	here	ADV
ejpam-5586	25	10	,	,	PUNCT
ejpam-5586	25	11	s1(t	s1(t	X
ejpam-5586	25	12	)	)	PUNCT
ejpam-5586	25	13	≥	≥	NOUN
ejpam-5586	25	14	s2(t	s2(t	NUM
ejpam-5586	25	15	)	)	PUNCT
ejpam-5586	25	16	≥	≥	NOUN
ejpam-5586	25	17	·	·	PUNCT
ejpam-5586	25	18	·	·	PUNCT
ejpam-5586	25	19	·	·	PUNCT
ejpam-5586	25	20	≥	≥	X
ejpam-5586	25	21	sn(t	sn(t	NUM
ejpam-5586	25	22	)	)	PUNCT
ejpam-5586	25	23	≥	≥	X
ejpam-5586	25	24	0	0	NUM
ejpam-5586	25	25	represent	represent	VERB
ejpam-5586	25	26	the	the	DET
ejpam-5586	25	27	singular	singular	ADJ
ejpam-5586	25	28	values	value	NOUN
ejpam-5586	25	29	of	of	ADP
ejpam-5586	25	30	t	t	PROPN
ejpam-5586	25	31	,	,	PUNCT
ejpam-5586	25	32	which	which	PRON
ejpam-5586	25	33	are	be	AUX
ejpam-5586	25	34	the	the	DET
ejpam-5586	25	35	eigenvalues	eigenvalue	NOUN
ejpam-5586	25	36	of	of	ADP
ejpam-5586	25	37	the	the	DET
ejpam-5586	25	38	positive	positive	ADJ
ejpam-5586	25	39	matrix	matrix	NOUN
ejpam-5586	25	40	|t	|t	VERB
ejpam-5586	26	1	|	|	ADV
ejpam-5586	26	2	=	=	SYM
ejpam-5586	26	3	√	√	PROPN
ejpam-5586	26	4	t	t	PROPN
ejpam-5586	26	5	∗t	∗t	PROPN
ejpam-5586	26	6	arranged	arrange	VERB
ejpam-5586	26	7	in	in	ADP
ejpam-5586	26	8	decreasing	decrease	VERB
ejpam-5586	26	9	order	order	NOUN
ejpam-5586	26	10	and	and	CCONJ
ejpam-5586	26	11	repeated	repeat	VERB
ejpam-5586	26	12	according	accord	VERB
ejpam-5586	26	13	to	to	ADP
ejpam-5586	26	14	multiplicity	multiplicity	NOUN
ejpam-5586	26	15	.	.	PUNCT
ejpam-5586	27	1	the	the	DET
ejpam-5586	27	2	symbol	symbol	NOUN
ejpam-5586	27	3	tr	tr	VERB
ejpam-5586	27	4	(	(	PUNCT
ejpam-5586	27	5	.	.	PUNCT
ejpam-5586	27	6	)	)	PUNCT
ejpam-5586	27	7	denotes	denote	VERB
ejpam-5586	27	8	the	the	DET
ejpam-5586	27	9	usual	usual	ADJ
ejpam-5586	27	10	trace	trace	NOUN
ejpam-5586	27	11	operation	operation	NOUN
ejpam-5586	27	12	.	.	PUNCT
ejpam-5586	28	1	it	it	PRON
ejpam-5586	28	2	’s	’	VERB
ejpam-5586	28	3	important	important	ADJ
ejpam-5586	28	4	to	to	PART
ejpam-5586	28	5	note	note	VERB
ejpam-5586	28	6	that	that	SCONJ
ejpam-5586	28	7	the	the	DET
ejpam-5586	28	8	mathematical	mathematical	ADJ
ejpam-5586	28	9	norms	norm	VERB
ejpam-5586	28	10	∥·∥2	∥·∥2	NOUN
ejpam-5586	28	11	and	and	CCONJ
ejpam-5586	28	12	∥·∥1	∥·∥1	NOUN
ejpam-5586	28	13	are	be	AUX
ejpam-5586	28	14	widely	widely	ADV
ejpam-5586	28	15	recognized	recognize	VERB
ejpam-5586	28	16	for	for	ADP
ejpam-5586	28	17	being	be	AUX
ejpam-5586	28	18	unitarily	unitarily	ADV
ejpam-5586	28	19	invariant	invariant	ADJ
ejpam-5586	28	20	.	.	PUNCT
ejpam-5586	29	1	the	the	DET
ejpam-5586	29	2	classic	classic	ADJ
ejpam-5586	29	3	young	young	PROPN
ejpam-5586	29	4	’s	’s	PART
ejpam-5586	29	5	inequality	inequality	NOUN
ejpam-5586	29	6	for	for	ADP
ejpam-5586	29	7	non	non	ADJ
ejpam-5586	29	8	-	-	ADJ
ejpam-5586	29	9	negative	negative	ADJ
ejpam-5586	29	10	real	real	ADJ
ejpam-5586	29	11	numbers	number	NOUN
ejpam-5586	29	12	states	state	VERB
ejpam-5586	29	13	that	that	SCONJ
ejpam-5586	29	14	if	if	SCONJ
ejpam-5586	29	15	ρ	ρ	PROPN
ejpam-5586	29	16	,	,	PUNCT
ejpam-5586	29	17	σ	σ	PROPN
ejpam-5586	29	18	≥	≥	NOUN
ejpam-5586	29	19	0	0	NUM
ejpam-5586	29	20	and	and	CCONJ
ejpam-5586	29	21	0	0	NUM
ejpam-5586	29	22	≤	≤	NUM
ejpam-5586	29	23	κ	κ	X
ejpam-5586	29	24	≤	≤	NUM
ejpam-5586	29	25	1	1	NUM
ejpam-5586	29	26	,	,	PUNCT
ejpam-5586	29	27	then	then	ADV
ejpam-5586	29	28	ρκσ1−κ	ρκσ1−κ	PRON
ejpam-5586	29	29	≤	≤	ADJ
ejpam-5586	29	30	κρ+	κρ+	NOUN
ejpam-5586	29	31	(	(	PUNCT
ejpam-5586	29	32	1−	1−	NUM
ejpam-5586	29	33	κ)σ	κ)σ	X
ejpam-5586	29	34	(	(	PUNCT
ejpam-5586	29	35	2	2	X
ejpam-5586	29	36	)	)	PUNCT
ejpam-5586	29	37	equality	equality	NOUN
ejpam-5586	29	38	occurs	occur	VERB
ejpam-5586	29	39	if	if	SCONJ
ejpam-5586	29	40	and	and	CCONJ
ejpam-5586	30	1	only	only	ADV
ejpam-5586	30	2	if	if	SCONJ
ejpam-5586	30	3	ρ	ρ	PROPN
ejpam-5586	30	4	=	=	SYM
ejpam-5586	30	5	σ	σ	PROPN
ejpam-5586	30	6	.	.	PUNCT
ejpam-5586	31	1	when	when	SCONJ
ejpam-5586	31	2	κ	κ	PROPN
ejpam-5586	31	3	is	be	AUX
ejpam-5586	31	4	1	1	NUM
ejpam-5586	31	5	2	2	NUM
ejpam-5586	31	6	,	,	PUNCT
ejpam-5586	31	7	substituting	substitute	VERB
ejpam-5586	31	8	into	into	ADP
ejpam-5586	31	9	the	the	DET
ejpam-5586	31	10	inequality	inequality	NOUN
ejpam-5586	31	11	yields	yield	VERB
ejpam-5586	31	12	the	the	DET
ejpam-5586	31	13	arithmetic	arithmetic	ADJ
ejpam-5586	31	14	-	-	PUNCT
ejpam-5586	31	15	geometric	geometric	ADJ
ejpam-5586	31	16	mean	mean	NOUN
ejpam-5586	31	17	inequality	inequality	NOUN
ejpam-5586	31	18	√	√	ADP
ejpam-5586	31	19	ρσ	ρσ	PRON
ejpam-5586	31	20	≤	≤	NUM
ejpam-5586	31	21	ρ+	ρ+	NUM
ejpam-5586	31	22	σ	σ	X
ejpam-5586	31	23	2	2	NUM
ejpam-5586	31	24	.	.	PUNCT
ejpam-5586	32	1	(	(	PUNCT
ejpam-5586	32	2	3	3	X
ejpam-5586	32	3	)	)	PUNCT
ejpam-5586	32	4	manasarah	manasarah	PROPN
ejpam-5586	32	5	and	and	CCONJ
ejpam-5586	32	6	kittaneh	kittaneh	PROPN
ejpam-5586	32	7	,	,	PUNCT
ejpam-5586	32	8	as	as	SCONJ
ejpam-5586	32	9	presented	present	VERB
ejpam-5586	32	10	in	in	ADP
ejpam-5586	32	11	[	[	X
ejpam-5586	32	12	10	10	NUM
ejpam-5586	32	13	]	]	PUNCT
ejpam-5586	32	14	,	,	PUNCT
ejpam-5586	32	15	improved	improved	ADJ
ejpam-5586	32	16	young	young	ADJ
ejpam-5586	32	17	’s	’s	PART
ejpam-5586	32	18	inequality	inequality	NOUN
ejpam-5586	32	19	with	with	ADP
ejpam-5586	32	20	the	the	DET
ejpam-5586	32	21	following	follow	VERB
ejpam-5586	32	22	refinement	refinement	NOUN
ejpam-5586	32	23	(	(	PUNCT
ejpam-5586	32	24	ρκσ1−κ	ρκσ1−κ	PROPN
ejpam-5586	32	25	)	)	PUNCT
ejpam-5586	32	26	m	m	VERB
ejpam-5586	33	1	+	+	NUM
ejpam-5586	33	2	rm0	rm0	NOUN
ejpam-5586	33	3	(	(	PUNCT
ejpam-5586	33	4	ρ	ρ	PROPN
ejpam-5586	33	5	m	m	NOUN
ejpam-5586	33	6	2	2	NUM
ejpam-5586	33	7	−	−	PROPN
ejpam-5586	33	8	σ	σ	NUM
ejpam-5586	33	9	m	m	VERB
ejpam-5586	33	10	2	2	NUM
ejpam-5586	33	11	)	)	SYM
ejpam-5586	33	12	2	2	NUM
ejpam-5586	33	13	≤	≤	NOUN
ejpam-5586	33	14	(	(	PUNCT
ejpam-5586	33	15	κρr	κρr	NOUN
ejpam-5586	33	16	+	+	CCONJ
ejpam-5586	33	17	(	(	PUNCT
ejpam-5586	33	18	1−	1−	NUM
ejpam-5586	33	19	κ)σr	κ)σr	PROPN
ejpam-5586	33	20	)	)	PUNCT
ejpam-5586	33	21	m	m	VERB
ejpam-5586	33	22	r	r	NOUN
ejpam-5586	33	23	,	,	PUNCT
ejpam-5586	33	24	r	r	NOUN
ejpam-5586	33	25	≥	≥	NUM
ejpam-5586	33	26	1	1	NUM
ejpam-5586	33	27	(	(	PUNCT
ejpam-5586	33	28	4	4	NUM
ejpam-5586	33	29	)	)	PUNCT
ejpam-5586	33	30	where	where	SCONJ
ejpam-5586	33	31	m	m	VERB
ejpam-5586	33	32	∈	∈	PROPN
ejpam-5586	33	33	n	n	NOUN
ejpam-5586	33	34	and	and	CCONJ
ejpam-5586	33	35	r0	r0	NOUN
ejpam-5586	33	36	=	=	SYM
ejpam-5586	33	37	min{κ	min{κ	PROPN
ejpam-5586	33	38	,	,	PUNCT
ejpam-5586	33	39	1−	1−	NUM
ejpam-5586	33	40	κ	κ	NOUN
ejpam-5586	33	41	}	}	PUNCT
ejpam-5586	33	42	.	.	PUNCT
ejpam-5586	34	1	the	the	DET
ejpam-5586	34	2	kantorovich	kantorovich	PROPN
ejpam-5586	34	3	constant	constant	ADJ
ejpam-5586	34	4	,	,	PUNCT
ejpam-5586	34	5	denoted	denote	VERB
ejpam-5586	34	6	as	as	ADP
ejpam-5586	34	7	k(t	k(t	PROPN
ejpam-5586	34	8	,	,	PUNCT
ejpam-5586	34	9	2	2	NUM
ejpam-5586	34	10	)	)	PUNCT
ejpam-5586	34	11	,	,	PUNCT
ejpam-5586	34	12	is	be	AUX
ejpam-5586	34	13	defined	define	VERB
ejpam-5586	34	14	as	as	ADP
ejpam-5586	34	15	(	(	PUNCT
ejpam-5586	34	16	t+1)2	t+1)2	PROPN
ejpam-5586	34	17	4	4	NUM
ejpam-5586	34	18	t	t	NOUN
ejpam-5586	34	19	.	.	PUNCT
ejpam-5586	35	1	it	it	PRON
ejpam-5586	35	2	possesses	possess	VERB
ejpam-5586	35	3	several	several	ADJ
ejpam-5586	35	4	key	key	ADJ
ejpam-5586	35	5	properties	property	NOUN
ejpam-5586	35	6	:	:	PUNCT
ejpam-5586	35	7	k(1	k(1	NOUN
ejpam-5586	35	8	,	,	PUNCT
ejpam-5586	35	9	2	2	NUM
ejpam-5586	35	10	)	)	PUNCT
ejpam-5586	35	11	=	=	SYM
ejpam-5586	35	12	1	1	NUM
ejpam-5586	35	13	,	,	PUNCT
ejpam-5586	35	14	k(t	k(t	PROPN
ejpam-5586	35	15	,	,	PUNCT
ejpam-5586	35	16	2	2	NUM
ejpam-5586	35	17	)	)	PUNCT
ejpam-5586	36	1	=	=	SYM
ejpam-5586	36	2	k	k	PROPN
ejpam-5586	36	3	(	(	PUNCT
ejpam-5586	36	4	1	1	NUM
ejpam-5586	36	5	t	t	NOUN
ejpam-5586	36	6	,	,	PUNCT
ejpam-5586	36	7	2	2	NUM
ejpam-5586	36	8	)	)	PUNCT
ejpam-5586	36	9	≥	≥	NOUN
ejpam-5586	36	10	1	1	NUM
ejpam-5586	36	11	(	(	PUNCT
ejpam-5586	36	12	t	t	X
ejpam-5586	36	13	>	>	X
ejpam-5586	36	14	0	0	NUM
ejpam-5586	36	15	)	)	PUNCT
ejpam-5586	36	16	and	and	CCONJ
ejpam-5586	36	17	k(t	k(t	PROPN
ejpam-5586	36	18	,	,	PUNCT
ejpam-5586	36	19	2	2	NUM
ejpam-5586	36	20	)	)	PUNCT
ejpam-5586	36	21	is	be	AUX
ejpam-5586	36	22	monotone	monotone	ADJ
ejpam-5586	36	23	increasing	increase	VERB
ejpam-5586	36	24	on	on	ADP
ejpam-5586	36	25	[	[	X
ejpam-5586	36	26	1,∞	1,∞	NUM
ejpam-5586	36	27	)	)	PUNCT
ejpam-5586	36	28	,	,	PUNCT
ejpam-5586	36	29	and	and	CCONJ
ejpam-5586	36	30	monotone	monotone	NOUN
ejpam-5586	36	31	decreasing	decrease	VERB
ejpam-5586	36	32	on	on	ADP
ejpam-5586	36	33	(	(	PUNCT
ejpam-5586	36	34	0	0	NUM
ejpam-5586	36	35	,	,	PUNCT
ejpam-5586	36	36	1	1	NUM
ejpam-5586	36	37	]	]	PUNCT
ejpam-5586	36	38	.	.	PUNCT
ejpam-5586	37	1	for	for	ADP
ejpam-5586	37	2	more	more	ADV
ejpam-5586	37	3	detailed	detailed	ADJ
ejpam-5586	37	4	information	information	NOUN
ejpam-5586	37	5	about	about	ADP
ejpam-5586	37	6	the	the	DET
ejpam-5586	37	7	kantorovich	kantorovich	PROPN
ejpam-5586	37	8	constant	constant	ADJ
ejpam-5586	37	9	,	,	PUNCT
ejpam-5586	37	10	interested	interested	ADJ
ejpam-5586	37	11	readers	reader	NOUN
ejpam-5586	37	12	can	can	AUX
ejpam-5586	37	13	refer	refer	VERB
ejpam-5586	37	14	to	to	ADP
ejpam-5586	37	15	[	[	X
ejpam-5586	37	16	11	11	NUM
ejpam-5586	37	17	,	,	PUNCT
ejpam-5586	37	18	15	15	NUM
ejpam-5586	37	19	,	,	PUNCT
ejpam-5586	37	20	17	17	NUM
ejpam-5586	37	21	,	,	PUNCT
ejpam-5586	37	22	22	22	NUM
ejpam-5586	37	23	]	]	PUNCT
ejpam-5586	37	24	..	..	PUNCT
ejpam-5586	38	1	the	the	DET
ejpam-5586	38	2	following	follow	VERB
ejpam-5586	38	3	multiplicative	multiplicative	ADJ
ejpam-5586	38	4	refinement	refinement	NOUN
ejpam-5586	38	5	and	and	CCONJ
ejpam-5586	38	6	reversal	reversal	NOUN
ejpam-5586	38	7	of	of	ADP
ejpam-5586	38	8	young	young	PROPN
ejpam-5586	38	9	’s	’s	PART
ejpam-5586	38	10	inequality	inequality	NOUN
ejpam-5586	38	11	,	,	PUNCT
ejpam-5586	38	12	expressed	express	VERB
ejpam-5586	38	13	in	in	ADP
ejpam-5586	38	14	terms	term	NOUN
ejpam-5586	38	15	of	of	ADP
ejpam-5586	38	16	kantorovich	kantorovich	PROPN
ejpam-5586	38	17	’s	’s	PART
ejpam-5586	38	18	constant	constant	ADJ
ejpam-5586	38	19	,	,	PUNCT
ejpam-5586	38	20	can	can	AUX
ejpam-5586	38	21	be	be	AUX
ejpam-5586	38	22	stated	state	VERB
ejpam-5586	38	23	as	as	SCONJ
ejpam-5586	38	24	follows	follow	VERB
ejpam-5586	38	25	k(h	k(h	PROPN
ejpam-5586	38	26	,	,	PUNCT
ejpam-5586	38	27	2)rρ♯κσ	2)rρ♯κσ	NUM
ejpam-5586	38	28	≤	≤	NUM
ejpam-5586	38	29	ρ∇κσ	ρ∇κσ	NUM
ejpam-5586	38	30	≤	≤	NUM
ejpam-5586	38	31	k(h	k(h	PROPN
ejpam-5586	38	32	,	,	PUNCT
ejpam-5586	38	33	2)rρ♯κσ	2)rρ♯κσ	NUM
ejpam-5586	38	34	,	,	PUNCT
ejpam-5586	38	35	(	(	PUNCT
ejpam-5586	38	36	5	5	NUM
ejpam-5586	38	37	)	)	PUNCT
ejpam-5586	38	38	where	where	SCONJ
ejpam-5586	38	39	ρ	ρ	PROPN
ejpam-5586	38	40	and	and	CCONJ
ejpam-5586	38	41	σ	σ	PROPN
ejpam-5586	38	42	are	be	AUX
ejpam-5586	38	43	both	both	ADV
ejpam-5586	38	44	greater	great	ADJ
ejpam-5586	38	45	than	than	ADP
ejpam-5586	38	46	0	0	NUM
ejpam-5586	38	47	,	,	PUNCT
ejpam-5586	38	48	κ	κ	PROPN
ejpam-5586	38	49	belongs	belong	VERB
ejpam-5586	38	50	to	to	ADP
ejpam-5586	38	51	the	the	DET
ejpam-5586	38	52	interval	interval	NOUN
ejpam-5586	38	53	[	[	X
ejpam-5586	38	54	0	0	NUM
ejpam-5586	38	55	,	,	PUNCT
ejpam-5586	38	56	1	1	NUM
ejpam-5586	38	57	]	]	PUNCT
ejpam-5586	38	58	,	,	PUNCT
ejpam-5586	38	59	r	r	NOUN
ejpam-5586	38	60	is	be	AUX
ejpam-5586	38	61	the	the	DET
ejpam-5586	38	62	minimum	minimum	NOUN
ejpam-5586	38	63	of	of	ADP
ejpam-5586	38	64	κ	κ	NOUN
ejpam-5586	38	65	and	and	CCONJ
ejpam-5586	38	66	1−	1−	NUM
ejpam-5586	38	67	κ	κ	NOUN
ejpam-5586	38	68	,	,	PUNCT
ejpam-5586	38	69	r	r	NOUN
ejpam-5586	38	70	is	be	AUX
ejpam-5586	38	71	the	the	DET
ejpam-5586	38	72	maximum	maximum	NOUN
ejpam-5586	38	73	of	of	ADP
ejpam-5586	38	74	κ	κ	PROPN
ejpam-5586	38	75	and	and	CCONJ
ejpam-5586	38	76	1−	1−	NUM
ejpam-5586	38	77	κ	κ	NOUN
ejpam-5586	38	78	,	,	PUNCT
ejpam-5586	38	79	and	and	CCONJ
ejpam-5586	38	80	h	h	NOUN
ejpam-5586	38	81	is	be	AUX
ejpam-5586	38	82	defined	define	VERB
ejpam-5586	38	83	as	as	ADP
ejpam-5586	38	84	σ	σ	PROPN
ejpam-5586	38	85	ρ	ρ	PROPN
ejpam-5586	38	86	.	.	PUNCT
ejpam-5586	39	1	the	the	DET
ejpam-5586	39	2	second	second	ADJ
ejpam-5586	39	3	inequality	inequality	NOUN
ejpam-5586	39	4	in	in	ADP
ejpam-5586	39	5	(	(	PUNCT
ejpam-5586	39	6	5	5	NUM
ejpam-5586	39	7	)	)	PUNCT
ejpam-5586	39	8	is	be	AUX
ejpam-5586	39	9	credited	credit	VERB
ejpam-5586	39	10	to	to	ADP
ejpam-5586	39	11	liao	liao	PROPN
ejpam-5586	39	12	et	et	PROPN
ejpam-5586	39	13	al	al	PROPN
ejpam-5586	39	14	.	.	PUNCT
ejpam-5586	40	1	[	[	X
ejpam-5586	40	2	12	12	NUM
ejpam-5586	40	3	]	]	PUNCT
ejpam-5586	40	4	,	,	PUNCT
ejpam-5586	40	5	while	while	SCONJ
ejpam-5586	40	6	the	the	DET
ejpam-5586	40	7	first	first	ADJ
ejpam-5586	40	8	one	one	NOUN
ejpam-5586	40	9	is	be	AUX
ejpam-5586	40	10	attributed	attribute	VERB
ejpam-5586	40	11	to	to	ADP
ejpam-5586	40	12	zou	zou	PROPN
ejpam-5586	40	13	et	et	PROPN
ejpam-5586	40	14	al	al	PROPN
ejpam-5586	40	15	.	.	PUNCT
ejpam-5586	41	1	[	[	X
ejpam-5586	41	2	11	11	NUM
ejpam-5586	41	3	]	]	PUNCT
ejpam-5586	41	4	.	.	PUNCT
ejpam-5586	42	1	in	in	ADP
ejpam-5586	42	2	[	[	X
ejpam-5586	42	3	19	19	NUM
ejpam-5586	42	4	]	]	PUNCT
ejpam-5586	42	5	,	,	PUNCT
ejpam-5586	42	6	the	the	DET
ejpam-5586	42	7	authors	author	NOUN
ejpam-5586	42	8	obtained	obtain	VERB
ejpam-5586	42	9	another	another	DET
ejpam-5586	42	10	improvement	improvement	NOUN
ejpam-5586	42	11	of	of	ADP
ejpam-5586	42	12	the	the	DET
ejpam-5586	42	13	young	young	ADJ
ejpam-5586	42	14	inequality	inequality	NOUN
ejpam-5586	42	15	and	and	CCONJ
ejpam-5586	42	16	its	its	PRON
ejpam-5586	42	17	reverse	reverse	NOUN
ejpam-5586	42	18	as	as	SCONJ
ejpam-5586	42	19	follows	follow	VERB
ejpam-5586	42	20	:	:	PUNCT
ejpam-5586	42	21	r	r	X
ejpam-5586	42	22	(	(	PUNCT
ejpam-5586	42	23	√	√	PUNCT
ejpam-5586	42	24	ρ−	ρ−	NOUN
ejpam-5586	42	25	√	√	VERB
ejpam-5586	43	1	σ)2	σ)2	NOUN
ejpam-5586	44	1	+	+	PROPN
ejpam-5586	44	2	k	k	PROPN
ejpam-5586	44	3	(	(	PUNCT
ejpam-5586	44	4	√	√	NUM
ejpam-5586	44	5	h	h	NOUN
ejpam-5586	44	6	,	,	PUNCT
ejpam-5586	44	7	2)r	2)r	NUM
ejpam-5586	44	8	′	′	NUM
ejpam-5586	44	9	ρ♯κσ	ρ♯κσ	PROPN
ejpam-5586	44	10	≤	≤	PROPN
ejpam-5586	44	11	ρ∇κσ	ρ∇κσ	X
ejpam-5586	44	12	,	,	PUNCT
ejpam-5586	44	13	(	(	PUNCT
ejpam-5586	44	14	6	6	NUM
ejpam-5586	44	15	)	)	PUNCT
ejpam-5586	44	16	m.h.m	m.h.m	NOUN
ejpam-5586	44	17	rashid	rashid	PROPN
ejpam-5586	44	18	,	,	PUNCT
ejpam-5586	44	19	w.m.m	w.m.m	NOUN
ejpam-5586	44	20	.	.	PUNCT
ejpam-5586	45	1	salameh	salameh	PROPN
ejpam-5586	45	2	/	/	SYM
ejpam-5586	45	3	eur	eur	PROPN
ejpam-5586	45	4	.	.	PUNCT
ejpam-5586	46	1	j.	j.	PROPN
ejpam-5586	46	2	pure	pure	PROPN
ejpam-5586	46	3	appl	appl	PROPN
ejpam-5586	46	4	.	.	PROPN
ejpam-5586	46	5	math	math	PROPN
ejpam-5586	46	6	,	,	PUNCT
ejpam-5586	46	7	18	18	NUM
ejpam-5586	46	8	(	(	PUNCT
ejpam-5586	46	9	1	1	NUM
ejpam-5586	46	10	)	)	PUNCT
ejpam-5586	46	11	(	(	PUNCT
ejpam-5586	46	12	2025	2025	NUM
ejpam-5586	46	13	)	)	PUNCT
ejpam-5586	46	14	,	,	PUNCT
ejpam-5586	46	15	5586	5586	NUM
ejpam-5586	46	16	3	3	NUM
ejpam-5586	46	17	of	of	ADP
ejpam-5586	46	18	21	21	NUM
ejpam-5586	46	19	and	and	CCONJ
ejpam-5586	47	1	ρ∇κσ	ρ∇κσ	SYM
ejpam-5586	47	2	≤	≤	NUM
ejpam-5586	48	1	k	k	X
ejpam-5586	48	2	(	(	PUNCT
ejpam-5586	48	3	√	√	PROPN
ejpam-5586	48	4	h	h	NOUN
ejpam-5586	48	5	,	,	PUNCT
ejpam-5586	48	6	2)−r′ρ♯κσ	2)−r′ρ♯κσ	NUM
ejpam-5586	49	1	+	+	NOUN
ejpam-5586	49	2	r	r	NOUN
ejpam-5586	49	3	(	(	PUNCT
ejpam-5586	49	4	√	√	PUNCT
ejpam-5586	49	5	ρ−	ρ−	NOUN
ejpam-5586	49	6	√	√	VERB
ejpam-5586	49	7	σ)2	σ)2	NOUN
ejpam-5586	49	8	(	(	PUNCT
ejpam-5586	49	9	7	7	NUM
ejpam-5586	49	10	)	)	PUNCT
ejpam-5586	49	11	where	where	SCONJ
ejpam-5586	49	12	h	h	NOUN
ejpam-5586	49	13	=	=	SYM
ejpam-5586	49	14	σ	σ	PROPN
ejpam-5586	49	15	ρ	ρ	PROPN
ejpam-5586	49	16	,	,	PUNCT
ejpam-5586	49	17	r	r	NOUN
ejpam-5586	49	18	=	=	SYM
ejpam-5586	49	19	min{κ	min{κ	PROPN
ejpam-5586	49	20	,	,	PUNCT
ejpam-5586	49	21	1	1	NUM
ejpam-5586	49	22	−	−	NOUN
ejpam-5586	49	23	κ	κ	NOUN
ejpam-5586	49	24	}	}	PUNCT
ejpam-5586	49	25	,	,	PUNCT
ejpam-5586	49	26	r	r	NOUN
ejpam-5586	49	27	=	=	SYM
ejpam-5586	49	28	max{κ	max{κ	NOUN
ejpam-5586	49	29	,	,	PUNCT
ejpam-5586	49	30	1	1	NUM
ejpam-5586	49	31	−	−	NOUN
ejpam-5586	49	32	κ	κ	NOUN
ejpam-5586	49	33	}	}	PUNCT
ejpam-5586	49	34	and	and	CCONJ
ejpam-5586	49	35	r′	r′	PROPN
ejpam-5586	49	36	=	=	SYM
ejpam-5586	49	37	min{2r	min{2r	PROPN
ejpam-5586	49	38	,	,	PUNCT
ejpam-5586	49	39	1	1	NUM
ejpam-5586	49	40	−	−	NOUN
ejpam-5586	49	41	2r	2r	NUM
ejpam-5586	49	42	}	}	PUNCT
ejpam-5586	49	43	.	.	PUNCT
ejpam-5586	50	1	in	in	ADP
ejpam-5586	50	2	addition	addition	NOUN
ejpam-5586	50	3	,	,	PUNCT
ejpam-5586	50	4	another	another	DET
ejpam-5586	50	5	kind	kind	NOUN
ejpam-5586	50	6	of	of	ADP
ejpam-5586	50	7	the	the	DET
ejpam-5586	50	8	reversal	reversal	NOUN
ejpam-5586	50	9	of	of	ADP
ejpam-5586	50	10	young	young	ADJ
ejpam-5586	50	11	inequality	inequality	NOUN
ejpam-5586	50	12	utilizing	utilize	VERB
ejpam-5586	50	13	kantorovich	kantorovich	PROPN
ejpam-5586	50	14	’s	’s	PART
ejpam-5586	50	15	constant	constant	ADJ
ejpam-5586	50	16	is	be	AUX
ejpam-5586	50	17	described	describe	VERB
ejpam-5586	50	18	in	in	ADP
ejpam-5586	50	19	[	[	X
ejpam-5586	50	20	12	12	NUM
ejpam-5586	50	21	]	]	PUNCT
ejpam-5586	50	22	with	with	ADP
ejpam-5586	50	23	the	the	DET
ejpam-5586	50	24	same	same	ADJ
ejpam-5586	50	25	notation	notation	NOUN
ejpam-5586	50	26	as	as	ADP
ejpam-5586	50	27	above	above	ADV
ejpam-5586	50	28	.	.	PUNCT
ejpam-5586	51	1	ρ∇κσ	ρ∇κσ	X
ejpam-5586	51	2	−r	−r	PROPN
ejpam-5586	51	3	(	(	PUNCT
ejpam-5586	51	4	√	√	PROPN
ejpam-5586	51	5	ρ−	ρ−	NOUN
ejpam-5586	51	6	√	√	NUM
ejpam-5586	51	7	σ)2	σ)2	NOUN
ejpam-5586	51	8	≤	≤	ADJ
ejpam-5586	52	1	k	k	PROPN
ejpam-5586	52	2	(	(	PUNCT
ejpam-5586	52	3	√	√	PROPN
ejpam-5586	52	4	h	h	NOUN
ejpam-5586	52	5	,	,	PUNCT
ejpam-5586	52	6	2)r	2)r	NUM
ejpam-5586	52	7	′	′	NUM
ejpam-5586	52	8	ρ♯κσ	ρ♯κσ	PROPN
ejpam-5586	52	9	,	,	PUNCT
ejpam-5586	52	10	(	(	PUNCT
ejpam-5586	52	11	8)	8)	NUM
ejpam-5586	52	12	where	where	SCONJ
ejpam-5586	52	13	r′	r′	PROPN
ejpam-5586	52	14	=	=	SYM
ejpam-5586	52	15	max{2r	max{2r	PROPN
ejpam-5586	52	16	,	,	PUNCT
ejpam-5586	52	17	1−	1−	NUM
ejpam-5586	52	18	2r	2r	NUM
ejpam-5586	52	19	}	}	PUNCT
ejpam-5586	52	20	.	.	PUNCT
ejpam-5586	53	1	for	for	ADP
ejpam-5586	53	2	κ	κ	PROPN
ejpam-5586	53	3	in	in	ADP
ejpam-5586	53	4	the	the	DET
ejpam-5586	53	5	range	range	NOUN
ejpam-5586	53	6	of	of	ADP
ejpam-5586	53	7	[	[	X
ejpam-5586	53	8	0	0	NUM
ejpam-5586	53	9	,	,	PUNCT
ejpam-5586	53	10	1	1	NUM
ejpam-5586	53	11	]	]	PUNCT
ejpam-5586	53	12	and	and	CCONJ
ejpam-5586	53	13	two	two	NUM
ejpam-5586	53	14	non	non	ADJ
ejpam-5586	53	15	-	-	ADJ
ejpam-5586	53	16	negative	negative	ADJ
ejpam-5586	53	17	real	real	ADJ
ejpam-5586	53	18	numbers	number	NOUN
ejpam-5586	53	19	ρ	ρ	PROPN
ejpam-5586	53	20	and	and	CCONJ
ejpam-5586	53	21	σ	σ	PROPN
ejpam-5586	53	22	,	,	PUNCT
ejpam-5586	53	23	the	the	DET
ejpam-5586	53	24	heinz	heinz	ADJ
ejpam-5586	53	25	mean	mean	NOUN
ejpam-5586	53	26	serves	serve	VERB
ejpam-5586	53	27	as	as	ADP
ejpam-5586	53	28	an	an	DET
ejpam-5586	53	29	interpolation	interpolation	NOUN
ejpam-5586	53	30	between	between	ADP
ejpam-5586	53	31	the	the	DET
ejpam-5586	53	32	κ	κ	NOUN
ejpam-5586	53	33	-	-	ADJ
ejpam-5586	53	34	arithmetic	arithmetic	ADJ
ejpam-5586	53	35	mean	mean	NOUN
ejpam-5586	53	36	and	and	CCONJ
ejpam-5586	53	37	the	the	DET
ejpam-5586	53	38	κ	κ	NOUN
ejpam-5586	53	39	-	-	PUNCT
ejpam-5586	53	40	geometric	geometric	ADJ
ejpam-5586	53	41	mean	mean	NOUN
ejpam-5586	53	42	.	.	PUNCT
ejpam-5586	54	1	these	these	PRON
ejpam-5586	54	2	are	be	AUX
ejpam-5586	54	3	defined	define	VERB
ejpam-5586	54	4	by	by	ADP
ejpam-5586	54	5	the	the	DET
ejpam-5586	54	6	expression	expression	NOUN
ejpam-5586	54	7	hκ(ρ	hκ(ρ	ADP
ejpam-5586	54	8	,	,	PUNCT
ejpam-5586	54	9	σ	σ	NOUN
ejpam-5586	54	10	)	)	PUNCT
ejpam-5586	54	11	=	=	NOUN
ejpam-5586	54	12	ρ♯κσ	ρ♯κσ	NOUN
ejpam-5586	54	13	+	+	CCONJ
ejpam-5586	54	14	ρ♯1−κσ	ρ♯1−κσ	NUM
ejpam-5586	54	15	2	2	NUM
ejpam-5586	54	16	,	,	PUNCT
ejpam-5586	54	17	(	(	PUNCT
ejpam-5586	54	18	9	9	X
ejpam-5586	54	19	)	)	PUNCT
ejpam-5586	55	1	where	where	SCONJ
ejpam-5586	55	2	ρ♯κσ	ρ♯κσ	PROPN
ejpam-5586	55	3	=	=	PROPN
ejpam-5586	55	4	ρκσ1−κ	ρκσ1−κ	PROPN
ejpam-5586	55	5	represents	represent	VERB
ejpam-5586	55	6	the	the	DET
ejpam-5586	55	7	κ	κ	NOUN
ejpam-5586	55	8	-	-	PUNCT
ejpam-5586	55	9	geometric	geometric	ADJ
ejpam-5586	55	10	mean	mean	NOUN
ejpam-5586	55	11	.	.	PUNCT
ejpam-5586	56	1	the	the	DET
ejpam-5586	56	2	heinz	heinz	ADJ
ejpam-5586	56	3	mean	mean	NOUN
ejpam-5586	56	4	possesses	possess	VERB
ejpam-5586	56	5	certain	certain	ADJ
ejpam-5586	56	6	properties	property	NOUN
ejpam-5586	56	7	,	,	PUNCT
ejpam-5586	56	8	including	include	VERB
ejpam-5586	56	9	convexity	convexity	NOUN
ejpam-5586	56	10	concerning	concern	VERB
ejpam-5586	56	11	κ	κ	NOUN
ejpam-5586	56	12	within	within	ADP
ejpam-5586	56	13	the	the	DET
ejpam-5586	56	14	interval	interval	NOUN
ejpam-5586	56	15	[	[	X
ejpam-5586	56	16	0	0	NUM
ejpam-5586	56	17	,	,	PUNCT
ejpam-5586	56	18	1	1	NUM
ejpam-5586	56	19	]	]	PUNCT
ejpam-5586	56	20	.	.	PUNCT
ejpam-5586	57	1	its	its	PRON
ejpam-5586	57	2	minimum	minimum	NOUN
ejpam-5586	57	3	occurs	occur	VERB
ejpam-5586	57	4	at	at	ADP
ejpam-5586	57	5	κ	κ	NOUN
ejpam-5586	57	6	=	=	SYM
ejpam-5586	57	7	1	1	NUM
ejpam-5586	57	8	2	2	NUM
ejpam-5586	57	9	,	,	PUNCT
ejpam-5586	57	10	and	and	CCONJ
ejpam-5586	57	11	its	its	PRON
ejpam-5586	57	12	maximum	maximum	ADJ
ejpam-5586	57	13	values	value	NOUN
ejpam-5586	57	14	are	be	AUX
ejpam-5586	57	15	found	find	VERB
ejpam-5586	57	16	at	at	ADP
ejpam-5586	57	17	κ	κ	X
ejpam-5586	57	18	=	=	SYM
ejpam-5586	57	19	0	0	PROPN
ejpam-5586	57	20	and	and	CCONJ
ejpam-5586	57	21	κ	κ	X
ejpam-5586	58	1	=	=	NOUN
ejpam-5586	58	2	1	1	X
ejpam-5586	58	3	.	.	PUNCT
ejpam-5586	58	4	additionally	additionally	ADV
ejpam-5586	58	5	,	,	PUNCT
ejpam-5586	58	6	the	the	DET
ejpam-5586	58	7	following	follow	VERB
ejpam-5586	58	8	inequalities	inequality	NOUN
ejpam-5586	58	9	are	be	AUX
ejpam-5586	58	10	true	true	ADJ
ejpam-5586	58	11	√	√	ADP
ejpam-5586	58	12	ρσ	ρσ	ADP
ejpam-5586	58	13	≤	≤	NOUN
ejpam-5586	58	14	hκ(ρ	hκ(ρ	NUM
ejpam-5586	58	15	,	,	PUNCT
ejpam-5586	58	16	σ	σ	PROPN
ejpam-5586	58	17	)	)	PUNCT
ejpam-5586	58	18	≤	≤	NOUN
ejpam-5586	58	19	ρ+	ρ+	NUM
ejpam-5586	58	20	σ	σ	X
ejpam-5586	58	21	2	2	NUM
ejpam-5586	58	22	.	.	PUNCT
ejpam-5586	59	1	(	(	PUNCT
ejpam-5586	59	2	10	10	NUM
ejpam-5586	59	3	)	)	PUNCT
ejpam-5586	59	4	it	it	PRON
ejpam-5586	59	5	is	be	AUX
ejpam-5586	59	6	worth	worth	ADJ
ejpam-5586	59	7	noting	note	VERB
ejpam-5586	59	8	that	that	SCONJ
ejpam-5586	59	9	the	the	DET
ejpam-5586	59	10	function	function	NOUN
ejpam-5586	59	11	hκ(ρ	hκ(ρ	PROPN
ejpam-5586	59	12	,	,	PUNCT
ejpam-5586	59	13	σ	σ	PROPN
ejpam-5586	59	14	)	)	PUNCT
ejpam-5586	59	15	exhibits	exhibit	VERB
ejpam-5586	59	16	symmetry	symmetry	NOUN
ejpam-5586	59	17	with	with	ADP
ejpam-5586	59	18	respect	respect	NOUN
ejpam-5586	59	19	to	to	ADP
ejpam-5586	59	20	the	the	DET
ejpam-5586	59	21	point	point	NOUN
ejpam-5586	59	22	κ	κ	X
ejpam-5586	59	23	=	=	NOUN
ejpam-5586	59	24	1	1	NUM
ejpam-5586	59	25	2	2	NUM
ejpam-5586	59	26	,	,	PUNCT
ejpam-5586	59	27	meaning	mean	VERB
ejpam-5586	59	28	that	that	SCONJ
ejpam-5586	59	29	hκ(ρ	hκ(ρ	PROPN
ejpam-5586	59	30	,	,	PUNCT
ejpam-5586	59	31	σ	σ	PROPN
ejpam-5586	59	32	)	)	PUNCT
ejpam-5586	59	33	=	=	SYM
ejpam-5586	60	1	h1−κ(ρ	h1−κ(ρ	PROPN
ejpam-5586	60	2	,	,	PUNCT
ejpam-5586	60	3	σ	σ	PROPN
ejpam-5586	60	4	)	)	PUNCT
ejpam-5586	60	5	.	.	PUNCT
ejpam-5586	61	1	the	the	DET
ejpam-5586	61	2	heron	heron	NOUN
ejpam-5586	61	3	mean	mean	VERB
ejpam-5586	61	4	is	be	AUX
ejpam-5586	61	5	defined	define	VERB
ejpam-5586	61	6	by	by	ADP
ejpam-5586	61	7	the	the	DET
ejpam-5586	61	8	expression	expression	NOUN
ejpam-5586	61	9	fϑ(ρ	fϑ(ρ	PROPN
ejpam-5586	61	10	,	,	PUNCT
ejpam-5586	61	11	σ	σ	NOUN
ejpam-5586	61	12	)	)	PUNCT
ejpam-5586	61	13	=	=	PUNCT
ejpam-5586	62	1	(	(	PUNCT
ejpam-5586	62	2	1−	1−	NUM
ejpam-5586	62	3	ϑ	ϑ	NOUN
ejpam-5586	62	4	)	)	PUNCT
ejpam-5586	62	5	√	√	NOUN
ejpam-5586	62	6	ρσ	ρσ	ADP
ejpam-5586	62	7	+	+	CCONJ
ejpam-5586	62	8	ϑ	ϑ	X
ejpam-5586	62	9	(	(	PUNCT
ejpam-5586	62	10	ρ+	ρ+	NUM
ejpam-5586	62	11	σ	σ	NOUN
ejpam-5586	62	12	2	2	NUM
ejpam-5586	62	13	)	)	PUNCT
ejpam-5586	62	14	,	,	PUNCT
ejpam-5586	62	15	ϑ	ϑ	X
ejpam-5586	62	16	∈	∈	X
ejpam-5586	63	1	[	[	X
ejpam-5586	63	2	0	0	NUM
ejpam-5586	63	3	,	,	PUNCT
ejpam-5586	63	4	1	1	NUM
ejpam-5586	63	5	]	]	PUNCT
ejpam-5586	63	6	and	and	CCONJ
ejpam-5586	63	7	ρ	ρ	PROPN
ejpam-5586	63	8	,	,	PUNCT
ejpam-5586	63	9	σ	σ	PROPN
ejpam-5586	63	10	∈	∈	PROPN
ejpam-5586	63	11	r+	r+	X
ejpam-5586	63	12	.	.	PUNCT
ejpam-5586	64	1	(	(	PUNCT
ejpam-5586	64	2	11	11	NUM
ejpam-5586	64	3	)	)	PUNCT
ejpam-5586	64	4	where	where	SCONJ
ejpam-5586	64	5	ϑ	ϑ	NOUN
ejpam-5586	64	6	takes	take	VERB
ejpam-5586	64	7	values	value	NOUN
ejpam-5586	64	8	in	in	ADP
ejpam-5586	64	9	the	the	DET
ejpam-5586	64	10	interval	interval	NOUN
ejpam-5586	64	11	[	[	X
ejpam-5586	64	12	0	0	NUM
ejpam-5586	64	13	,	,	PUNCT
ejpam-5586	64	14	1	1	NUM
ejpam-5586	64	15	]	]	PUNCT
ejpam-5586	64	16	,	,	PUNCT
ejpam-5586	64	17	and	and	CCONJ
ejpam-5586	64	18	ρ	ρ	PROPN
ejpam-5586	64	19	and	and	CCONJ
ejpam-5586	64	20	σ	σ	PROPN
ejpam-5586	64	21	are	be	AUX
ejpam-5586	64	22	positive	positive	ADJ
ejpam-5586	64	23	real	real	ADJ
ejpam-5586	64	24	numbers	number	NOUN
ejpam-5586	64	25	.	.	PUNCT
ejpam-5586	65	1	evidently	evidently	ADV
ejpam-5586	65	2	,	,	PUNCT
ejpam-5586	65	3	the	the	DET
ejpam-5586	65	4	heron	heron	NOUN
ejpam-5586	65	5	mean	mean	VERB
ejpam-5586	65	6	serves	serve	VERB
ejpam-5586	65	7	as	as	ADP
ejpam-5586	65	8	a	a	DET
ejpam-5586	65	9	linear	linear	ADJ
ejpam-5586	65	10	interpolation	interpolation	NOUN
ejpam-5586	65	11	between	between	ADP
ejpam-5586	65	12	the	the	DET
ejpam-5586	65	13	arithmetic	arithmetic	ADJ
ejpam-5586	65	14	and	and	CCONJ
ejpam-5586	65	15	geometric	geometric	ADJ
ejpam-5586	65	16	means	mean	NOUN
ejpam-5586	65	17	.	.	PUNCT
ejpam-5586	66	1	it	it	PRON
ejpam-5586	66	2	adheres	adhere	VERB
ejpam-5586	66	3	to	to	ADP
ejpam-5586	66	4	the	the	DET
ejpam-5586	66	5	inequality	inequality	NOUN
ejpam-5586	66	6	fϑ	fϑ	ADV
ejpam-5586	66	7	≤	≤	PROPN
ejpam-5586	66	8	fϱ	fϱ	ADV
ejpam-5586	66	9	whenever	whenever	SCONJ
ejpam-5586	66	10	ϑ	ϑ	X
ejpam-5586	66	11	≤	≤	X
ejpam-5586	66	12	ϱ	ϱ	VERB
ejpam-5586	66	13	,	,	PUNCT
ejpam-5586	66	14	with	with	ADP
ejpam-5586	66	15	both	both	CCONJ
ejpam-5586	66	16	ϑ	ϑ	X
ejpam-5586	66	17	and	and	CCONJ
ejpam-5586	66	18	ϱ	ϱ	ADP
ejpam-5586	66	19	belonging	belong	VERB
ejpam-5586	66	20	to	to	ADP
ejpam-5586	66	21	the	the	DET
ejpam-5586	66	22	positive	positive	ADJ
ejpam-5586	66	23	real	real	ADJ
ejpam-5586	66	24	numbers	number	NOUN
ejpam-5586	66	25	.	.	PUNCT
ejpam-5586	67	1	in	in	ADP
ejpam-5586	67	2	a	a	DET
ejpam-5586	67	3	study	study	NOUN
ejpam-5586	67	4	by	by	ADP
ejpam-5586	67	5	bhatia	bhatia	PROPN
ejpam-5586	67	6	published	publish	VERB
ejpam-5586	67	7	in	in	ADP
ejpam-5586	67	8	[	[	X
ejpam-5586	67	9	2	2	NUM
ejpam-5586	67	10	]	]	PUNCT
ejpam-5586	67	11	,	,	PUNCT
ejpam-5586	67	12	it	it	PRON
ejpam-5586	67	13	was	be	AUX
ejpam-5586	67	14	demonstrated	demonstrate	VERB
ejpam-5586	67	15	that	that	SCONJ
ejpam-5586	67	16	for	for	ADP
ejpam-5586	67	17	ϑ(κ	ϑ(κ	NOUN
ejpam-5586	67	18	)	)	PUNCT
ejpam-5586	68	1	=	=	PRON
ejpam-5586	68	2	(	(	PUNCT
ejpam-5586	68	3	2κ	2κ	NOUN
ejpam-5586	68	4	−	−	PROPN
ejpam-5586	68	5	1)2	1)2	NUM
ejpam-5586	68	6	and	and	CCONJ
ejpam-5586	68	7	κ	κ	X
ejpam-5586	68	8	within	within	ADP
ejpam-5586	68	9	the	the	DET
ejpam-5586	68	10	range	range	NOUN
ejpam-5586	68	11	of	of	ADP
ejpam-5586	68	12	[	[	X
ejpam-5586	68	13	0	0	NUM
ejpam-5586	68	14	,	,	PUNCT
ejpam-5586	68	15	1	1	NUM
ejpam-5586	68	16	]	]	PUNCT
ejpam-5586	68	17	,	,	PUNCT
ejpam-5586	68	18	the	the	DET
ejpam-5586	68	19	following	follow	VERB
ejpam-5586	68	20	relation	relation	NOUN
ejpam-5586	68	21	holds	hold	VERB
ejpam-5586	68	22	hκ(ρ	hκ(ρ	PROPN
ejpam-5586	68	23	,	,	PUNCT
ejpam-5586	68	24	σ	σ	PROPN
ejpam-5586	68	25	)	)	PUNCT
ejpam-5586	68	26	≤	≤	PUNCT
ejpam-5586	68	27	fϑ(κ)(ρ	fϑ(κ)(ρ	PROPN
ejpam-5586	68	28	,	,	PUNCT
ejpam-5586	68	29	σ	σ	PROPN
ejpam-5586	68	30	)	)	PUNCT
ejpam-5586	68	31	.	.	PUNCT
ejpam-5586	69	1	(	(	PUNCT
ejpam-5586	69	2	12	12	X
ejpam-5586	69	3	)	)	PUNCT
ejpam-5586	69	4	our	our	PRON
ejpam-5586	69	5	paper	paper	NOUN
ejpam-5586	69	6	is	be	AUX
ejpam-5586	69	7	structured	structure	VERB
ejpam-5586	69	8	as	as	SCONJ
ejpam-5586	69	9	follows	follow	VERB
ejpam-5586	69	10	:	:	PUNCT
ejpam-5586	69	11	in	in	ADP
ejpam-5586	69	12	the	the	DET
ejpam-5586	69	13	upcoming	upcoming	ADJ
ejpam-5586	69	14	section	section	NOUN
ejpam-5586	69	15	,	,	PUNCT
ejpam-5586	69	16	we	we	PRON
ejpam-5586	69	17	will	will	AUX
ejpam-5586	69	18	conduct	conduct	VERB
ejpam-5586	69	19	an	an	DET
ejpam-5586	69	20	indepth	indepth	ADJ
ejpam-5586	69	21	investigation	investigation	NOUN
ejpam-5586	69	22	into	into	ADP
ejpam-5586	69	23	matrix	matrix	NOUN
ejpam-5586	69	24	interpolation	interpolation	NOUN
ejpam-5586	69	25	and	and	CCONJ
ejpam-5586	69	26	mean	mean	ADJ
ejpam-5586	69	27	comparisons	comparison	NOUN
ejpam-5586	69	28	.	.	PUNCT
ejpam-5586	70	1	this	this	DET
ejpam-5586	70	2	analysis	analysis	NOUN
ejpam-5586	70	3	extends	extend	VERB
ejpam-5586	70	4	the	the	DET
ejpam-5586	70	5	scope	scope	NOUN
ejpam-5586	70	6	of	of	ADP
ejpam-5586	70	7	ϑ	ϑ	PROPN
ejpam-5586	70	8	beyond	beyond	ADP
ejpam-5586	70	9	the	the	DET
ejpam-5586	70	10	closed	closed	ADJ
ejpam-5586	70	11	interval	interval	NOUN
ejpam-5586	70	12	[	[	X
ejpam-5586	70	13	0	0	NUM
ejpam-5586	70	14	,	,	PUNCT
ejpam-5586	70	15	1	1	NUM
ejpam-5586	70	16	]	]	PUNCT
ejpam-5586	70	17	to	to	PART
ejpam-5586	70	18	include	include	VERB
ejpam-5586	70	19	all	all	DET
ejpam-5586	70	20	positive	positive	ADJ
ejpam-5586	70	21	real	real	ADJ
ejpam-5586	70	22	numbers	number	NOUN
ejpam-5586	70	23	,	,	PUNCT
ejpam-5586	70	24	represented	represent	VERB
ejpam-5586	70	25	as	as	ADP
ejpam-5586	70	26	r+	r+	X
ejpam-5586	70	27	.	.	PUNCT
ejpam-5586	71	1	additionally	additionally	ADV
ejpam-5586	71	2	,	,	PUNCT
ejpam-5586	71	3	we	we	PRON
ejpam-5586	71	4	will	will	AUX
ejpam-5586	71	5	explore	explore	VERB
ejpam-5586	71	6	additional	additional	ADJ
ejpam-5586	71	7	findings	finding	NOUN
ejpam-5586	71	8	pertaining	pertain	VERB
ejpam-5586	71	9	to	to	ADP
ejpam-5586	71	10	heinz	heinz	PROPN
ejpam-5586	71	11	means	mean	NOUN
ejpam-5586	71	12	.	.	PUNCT
ejpam-5586	72	1	section	section	NOUN
ejpam-5586	72	2	three	three	NUM
ejpam-5586	72	3	is	be	AUX
ejpam-5586	72	4	dedicated	dedicate	VERB
ejpam-5586	72	5	to	to	ADP
ejpam-5586	72	6	exploring	explore	VERB
ejpam-5586	72	7	refinements	refinement	NOUN
ejpam-5586	72	8	in	in	ADP
ejpam-5586	72	9	heinz	heinz	ADJ
ejpam-5586	72	10	inequality	inequality	NOUN
ejpam-5586	72	11	,	,	PUNCT
ejpam-5586	72	12	incorporating	incorporate	VERB
ejpam-5586	72	13	the	the	DET
ejpam-5586	72	14	kantorovich	kantorovich	PROPN
ejpam-5586	72	15	constant	constant	PROPN
ejpam-5586	72	16	.	.	PUNCT
ejpam-5586	73	1	section	section	NOUN
ejpam-5586	73	2	4	4	NUM
ejpam-5586	73	3	focuses	focus	VERB
ejpam-5586	73	4	on	on	ADP
ejpam-5586	73	5	examining	examine	VERB
ejpam-5586	73	6	enhanced	enhanced	ADJ
ejpam-5586	73	7	variations	variation	NOUN
ejpam-5586	73	8	of	of	ADP
ejpam-5586	73	9	heinz	heinz	ADJ
ejpam-5586	73	10	-	-	PUNCT
ejpam-5586	73	11	type	type	NOUN
ejpam-5586	73	12	operator	operator	NOUN
ejpam-5586	73	13	inequalities	inequality	NOUN
ejpam-5586	73	14	and	and	CCONJ
ejpam-5586	73	15	their	their	PRON
ejpam-5586	73	16	corresponding	corresponding	ADJ
ejpam-5586	73	17	reversals	reversal	NOUN
ejpam-5586	73	18	.	.	PUNCT
ejpam-5586	74	1	finally	finally	ADV
ejpam-5586	74	2	,	,	PUNCT
ejpam-5586	74	3	in	in	ADP
ejpam-5586	74	4	section	section	NOUN
ejpam-5586	74	5	5	5	NUM
ejpam-5586	74	6	,	,	PUNCT
ejpam-5586	74	7	we	we	PRON
ejpam-5586	74	8	present	present	VERB
ejpam-5586	74	9	refined	refined	ADJ
ejpam-5586	74	10	inequalities	inequality	NOUN
ejpam-5586	74	11	of	of	ADP
ejpam-5586	74	12	young	young	PROPN
ejpam-5586	74	13	’s	’s	PART
ejpam-5586	74	14	type	type	NOUN
ejpam-5586	74	15	,	,	PUNCT
ejpam-5586	74	16	specifically	specifically	ADV
ejpam-5586	74	17	designed	design	VERB
ejpam-5586	74	18	for	for	ADP
ejpam-5586	74	19	traces	trace	NOUN
ejpam-5586	74	20	,	,	PUNCT
ejpam-5586	74	21	determinants	determinant	NOUN
ejpam-5586	74	22	,	,	PUNCT
ejpam-5586	74	23	and	and	CCONJ
ejpam-5586	74	24	norms	norm	NOUN
ejpam-5586	74	25	of	of	ADP
ejpam-5586	74	26	positive	positive	ADJ
ejpam-5586	74	27	semi	semi	ADJ
ejpam-5586	74	28	-	-	ADJ
ejpam-5586	74	29	definite	definite	ADJ
ejpam-5586	74	30	matrices	matrix	NOUN
ejpam-5586	74	31	.	.	PUNCT
ejpam-5586	75	1	m.h.m	m.h.m	PROPN
ejpam-5586	75	2	rashid	rashid	PROPN
ejpam-5586	75	3	,	,	PUNCT
ejpam-5586	75	4	w.m.m	w.m.m	NOUN
ejpam-5586	75	5	.	.	PUNCT
ejpam-5586	76	1	salameh	salameh	PROPN
ejpam-5586	76	2	/	/	SYM
ejpam-5586	76	3	eur	eur	PROPN
ejpam-5586	76	4	.	.	PUNCT
ejpam-5586	77	1	j.	j.	PROPN
ejpam-5586	77	2	pure	pure	PROPN
ejpam-5586	77	3	appl	appl	PROPN
ejpam-5586	77	4	.	.	PROPN
ejpam-5586	77	5	math	math	PROPN
ejpam-5586	77	6	,	,	PUNCT
ejpam-5586	77	7	18	18	NUM
ejpam-5586	77	8	(	(	PUNCT
ejpam-5586	77	9	1	1	NUM
ejpam-5586	77	10	)	)	PUNCT
ejpam-5586	77	11	(	(	PUNCT
ejpam-5586	77	12	2025	2025	NUM
ejpam-5586	77	13	)	)	PUNCT
ejpam-5586	77	14	,	,	PUNCT
ejpam-5586	77	15	5586	5586	NUM
ejpam-5586	77	16	4	4	NUM
ejpam-5586	77	17	of	of	ADP
ejpam-5586	77	18	21	21	NUM
ejpam-5586	77	19	2	2	NUM
ejpam-5586	77	20	.	.	PUNCT
ejpam-5586	77	21	full	full	ADJ
ejpam-5586	77	22	interpolation	interpolation	NOUN
ejpam-5586	77	23	of	of	ADP
ejpam-5586	77	24	matrix	matrix	NOUN
ejpam-5586	77	25	variants	variant	NOUN
ejpam-5586	77	26	of	of	ADP
ejpam-5586	77	27	heron	heron	NOUN
ejpam-5586	77	28	and	and	CCONJ
ejpam-5586	77	29	heinz	heinz	ADJ
ejpam-5586	77	30	means	mean	NOUN
ejpam-5586	77	31	in	in	ADP
ejpam-5586	77	32	the	the	DET
ejpam-5586	77	33	paper	paper	NOUN
ejpam-5586	77	34	referenced	reference	VERB
ejpam-5586	77	35	as	as	ADP
ejpam-5586	77	36	[	[	X
ejpam-5586	77	37	2	2	NUM
ejpam-5586	77	38	]	]	PUNCT
ejpam-5586	77	39	,	,	PUNCT
ejpam-5586	77	40	r.	r.	PROPN
ejpam-5586	77	41	bhatia	bhatia	PROPN
ejpam-5586	77	42	established	establish	VERB
ejpam-5586	77	43	a	a	DET
ejpam-5586	77	44	noteworthy	noteworthy	ADJ
ejpam-5586	77	45	result	result	NOUN
ejpam-5586	77	46	.	.	PUNCT
ejpam-5586	78	1	in	in	ADP
ejpam-5586	78	2	particular	particular	ADJ
ejpam-5586	78	3	,	,	PUNCT
ejpam-5586	78	4	it	it	PRON
ejpam-5586	78	5	was	be	AUX
ejpam-5586	78	6	shown	show	VERB
ejpam-5586	78	7	that	that	SCONJ
ejpam-5586	78	8	for	for	ADP
ejpam-5586	78	9	values	value	NOUN
ejpam-5586	78	10	of	of	ADP
ejpam-5586	78	11	ϑ	ϑ	PROPN
ejpam-5586	78	12	in	in	ADP
ejpam-5586	78	13	the	the	DET
ejpam-5586	78	14	interval	interval	NOUN
ejpam-5586	78	15	[	[	X
ejpam-5586	78	16	0	0	NUM
ejpam-5586	78	17	,	,	PUNCT
ejpam-5586	78	18	1/2	1/2	NUM
ejpam-5586	78	19	]	]	PUNCT
ejpam-5586	78	20	,	,	PUNCT
ejpam-5586	78	21	the	the	DET
ejpam-5586	78	22	function	function	NOUN
ejpam-5586	78	23	ψ(ϑ	ψ(ϑ	PROPN
ejpam-5586	78	24	)	)	PUNCT
ejpam-5586	78	25	adheres	adhere	VERB
ejpam-5586	78	26	to	to	ADP
ejpam-5586	78	27	the	the	DET
ejpam-5586	78	28	inequality	inequality	NOUN
ejpam-5586	78	29	ψ(ϑ	ψ(ϑ	PROPN
ejpam-5586	78	30	)	)	PUNCT
ejpam-5586	78	31	≤	≤	NUM
ejpam-5586	78	32	ψ(1/2	ψ(1/2	PROPN
ejpam-5586	78	33	)	)	PUNCT
ejpam-5586	78	34	.	.	PUNCT
ejpam-5586	79	1	here	here	ADV
ejpam-5586	79	2	,	,	PUNCT
ejpam-5586	79	3	ψ(ϑ	ψ(ϑ	PROPN
ejpam-5586	79	4	)	)	PUNCT
ejpam-5586	79	5	denotes	denote	VERB
ejpam-5586	79	6	one	one	NUM
ejpam-5586	79	7	of	of	ADP
ejpam-5586	79	8	the	the	DET
ejpam-5586	79	9	potential	potential	ADJ
ejpam-5586	79	10	matrix	matrix	NOUN
ejpam-5586	79	11	formulations	formulation	NOUN
ejpam-5586	79	12	of	of	ADP
ejpam-5586	79	13	equation	equation	NOUN
ejpam-5586	79	14	(	(	PUNCT
ejpam-5586	79	15	11	11	NUM
ejpam-5586	79	16	)	)	PUNCT
ejpam-5586	79	17	,	,	PUNCT
ejpam-5586	79	18	and	and	CCONJ
ejpam-5586	79	19	its	its	PRON
ejpam-5586	79	20	definition	definition	NOUN
ejpam-5586	79	21	is	be	AUX
ejpam-5586	79	22	as	as	SCONJ
ejpam-5586	79	23	follows	follow	VERB
ejpam-5586	79	24	ψ(ϑ	ψ(ϑ	NOUN
ejpam-5586	79	25	)	)	PUNCT
ejpam-5586	79	26	=	=	PUNCT
ejpam-5586	79	27	∣∣∣∣∣∣∣∣∣∣∣∣(1−	∣∣∣∣∣∣∣∣∣∣∣∣(1−	X
ejpam-5586	79	28	ϑ)t	ϑ)t	X
ejpam-5586	79	29	1/2xs1/2	1/2xs1/2	PROPN
ejpam-5586	79	30	+	+	CCONJ
ejpam-5586	79	31	ϑ	ϑ	X
ejpam-5586	79	32	(	(	PUNCT
ejpam-5586	79	33	tx	tx	PROPN
ejpam-5586	79	34	+	+	PROPN
ejpam-5586	79	35	xs	xs	PROPN
ejpam-5586	79	36	2	2	NUM
ejpam-5586	79	37	)	)	PUNCT
ejpam-5586	79	38	∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5586	79	39	,	,	PUNCT
ejpam-5586	79	40	(	(	PUNCT
ejpam-5586	79	41	13	13	NUM
ejpam-5586	79	42	)	)	PUNCT
ejpam-5586	79	43	this	this	DET
ejpam-5586	79	44	definition	definition	NOUN
ejpam-5586	79	45	involves	involve	VERB
ejpam-5586	79	46	matrices	matrix	NOUN
ejpam-5586	79	47	t	t	PROPN
ejpam-5586	79	48	,	,	PUNCT
ejpam-5586	79	49	s	s	X
ejpam-5586	79	50	,	,	PUNCT
ejpam-5586	79	51	and	and	CCONJ
ejpam-5586	79	52	x	x	NOUN
ejpam-5586	79	53	,	,	PUNCT
ejpam-5586	79	54	subject	subject	ADJ
ejpam-5586	79	55	to	to	ADP
ejpam-5586	79	56	the	the	DET
ejpam-5586	79	57	conditions	condition	NOUN
ejpam-5586	79	58	that	that	PRON
ejpam-5586	79	59	t	t	PROPN
ejpam-5586	79	60	and	and	CCONJ
ejpam-5586	79	61	s	s	VERB
ejpam-5586	79	62	belong	belong	VERB
ejpam-5586	79	63	to	to	ADP
ejpam-5586	79	64	the	the	DET
ejpam-5586	79	65	set	set	NOUN
ejpam-5586	79	66	of	of	ADP
ejpam-5586	79	67	positive	positive	ADJ
ejpam-5586	79	68	definite	definite	ADJ
ejpam-5586	79	69	matrices	matrix	NOUN
ejpam-5586	79	70	in	in	ADP
ejpam-5586	79	71	c	c	NOUN
ejpam-5586	79	72	,	,	PUNCT
ejpam-5586	79	73	denoted	denote	VERB
ejpam-5586	79	74	as	as	ADP
ejpam-5586	79	75	m++	m++	NOUN
ejpam-5586	79	76	n	n	CCONJ
ejpam-5586	79	77	(	(	PUNCT
ejpam-5586	79	78	c	c	NOUN
ejpam-5586	79	79	)	)	PUNCT
ejpam-5586	79	80	,	,	PUNCT
ejpam-5586	79	81	and	and	CCONJ
ejpam-5586	79	82	x	x	X
ejpam-5586	79	83	is	be	AUX
ejpam-5586	79	84	a	a	DET
ejpam-5586	79	85	member	member	NOUN
ejpam-5586	79	86	of	of	ADP
ejpam-5586	79	87	the	the	DET
ejpam-5586	79	88	set	set	NOUN
ejpam-5586	79	89	of	of	ADP
ejpam-5586	79	90	n×	n×	PROPN
ejpam-5586	79	91	n	n	NOUN
ejpam-5586	79	92	matrices	matrix	NOUN
ejpam-5586	79	93	over	over	ADP
ejpam-5586	79	94	c	c	NOUN
ejpam-5586	79	95	,	,	PUNCT
ejpam-5586	79	96	denoted	denote	VERB
ejpam-5586	79	97	as	as	ADP
ejpam-5586	79	98	mn(c	mn(c	NOUN
ejpam-5586	79	99	)	)	PUNCT
ejpam-5586	79	100	.	.	PUNCT
ejpam-5586	80	1	for	for	ADP
ejpam-5586	80	2	further	further	ADJ
ejpam-5586	80	3	insights	insight	NOUN
ejpam-5586	80	4	into	into	ADP
ejpam-5586	80	5	the	the	DET
ejpam-5586	80	6	matrix	matrix	NOUN
ejpam-5586	80	7	formulations	formulation	NOUN
ejpam-5586	80	8	of	of	ADP
ejpam-5586	80	9	equation	equation	NOUN
ejpam-5586	80	10	(	(	PUNCT
ejpam-5586	80	11	9	9	NUM
ejpam-5586	80	12	)	)	PUNCT
ejpam-5586	80	13	and	and	CCONJ
ejpam-5586	80	14	equation	equation	NOUN
ejpam-5586	80	15	(	(	PUNCT
ejpam-5586	80	16	12	12	NUM
ejpam-5586	80	17	)	)	PUNCT
ejpam-5586	80	18	,	,	PUNCT
ejpam-5586	80	19	as	as	ADV
ejpam-5586	80	20	well	well	ADV
ejpam-5586	80	21	as	as	ADP
ejpam-5586	80	22	additional	additional	ADJ
ejpam-5586	80	23	details	detail	NOUN
ejpam-5586	80	24	,	,	PUNCT
ejpam-5586	80	25	interested	interested	ADJ
ejpam-5586	80	26	readers	reader	NOUN
ejpam-5586	80	27	are	be	AUX
ejpam-5586	80	28	encouraged	encourage	VERB
ejpam-5586	80	29	to	to	PART
ejpam-5586	80	30	refer	refer	VERB
ejpam-5586	80	31	to	to	ADP
ejpam-5586	80	32	the	the	DET
ejpam-5586	80	33	following	following	ADJ
ejpam-5586	80	34	references	reference	NOUN
ejpam-5586	80	35	:	:	PUNCT
ejpam-5586	81	1	[	[	X
ejpam-5586	81	2	2	2	NUM
ejpam-5586	81	3	]	]	PUNCT
ejpam-5586	81	4	,	,	PUNCT
ejpam-5586	81	5	[	[	X
ejpam-5586	81	6	5	5	NUM
ejpam-5586	81	7	]	]	PUNCT
ejpam-5586	81	8	,	,	PUNCT
ejpam-5586	81	9	[	[	X
ejpam-5586	81	10	6	6	NUM
ejpam-5586	81	11	]	]	PUNCT
ejpam-5586	81	12	,	,	PUNCT
ejpam-5586	81	13	[	[	X
ejpam-5586	81	14	4	4	NUM
ejpam-5586	81	15	]	]	PUNCT
ejpam-5586	81	16	,	,	PUNCT
ejpam-5586	81	17	and	and	CCONJ
ejpam-5586	81	18	[	[	X
ejpam-5586	81	19	8	8	NUM
ejpam-5586	81	20	]	]	PUNCT
ejpam-5586	81	21	.	.	PUNCT
ejpam-5586	82	1	within	within	ADP
ejpam-5586	82	2	the	the	DET
ejpam-5586	82	3	context	context	NOUN
ejpam-5586	82	4	of	of	ADP
ejpam-5586	82	5	this	this	DET
ejpam-5586	82	6	article	article	NOUN
ejpam-5586	82	7	,	,	PUNCT
ejpam-5586	82	8	the	the	DET
ejpam-5586	82	9	author	author	NOUN
ejpam-5586	82	10	endeavors	endeavor	VERB
ejpam-5586	82	11	to	to	PART
ejpam-5586	82	12	demonstrate	demonstrate	VERB
ejpam-5586	82	13	that	that	SCONJ
ejpam-5586	82	14	for	for	ADP
ejpam-5586	82	15	ϑ	ϑ	PRON
ejpam-5586	82	16	values	value	NOUN
ejpam-5586	82	17	within	within	ADP
ejpam-5586	82	18	the	the	DET
ejpam-5586	82	19	interval	interval	NOUN
ejpam-5586	82	20	[	[	X
ejpam-5586	82	21	0	0	NUM
ejpam-5586	82	22	,	,	PUNCT
ejpam-5586	82	23	1/2	1/2	NUM
ejpam-5586	82	24	]	]	PUNCT
ejpam-5586	82	25	,	,	PUNCT
ejpam-5586	82	26	the	the	DET
ejpam-5586	82	27	function	function	NOUN
ejpam-5586	82	28	ψ(ϑ	ψ(ϑ	PROPN
ejpam-5586	82	29	,	,	PUNCT
ejpam-5586	82	30	κ	κ	NOUN
ejpam-5586	82	31	)	)	PUNCT
ejpam-5586	82	32	adheres	adhere	VERB
ejpam-5586	82	33	to	to	ADP
ejpam-5586	82	34	the	the	DET
ejpam-5586	82	35	inequality	inequality	NOUN
ejpam-5586	82	36	ψ(ϑ	ψ(ϑ	PROPN
ejpam-5586	82	37	,	,	PUNCT
ejpam-5586	82	38	κ	κ	NOUN
ejpam-5586	82	39	)	)	PUNCT
ejpam-5586	82	40	≤	≤	NOUN
ejpam-5586	82	41	ψ(1/2	ψ(1/2	PROPN
ejpam-5586	82	42	,	,	PUNCT
ejpam-5586	82	43	κ	κ	NOUN
ejpam-5586	82	44	)	)	PUNCT
ejpam-5586	82	45	.	.	PUNCT
ejpam-5586	83	1	additionally	additionally	ADV
ejpam-5586	83	2	,	,	PUNCT
ejpam-5586	83	3	it	it	PRON
ejpam-5586	83	4	is	be	AUX
ejpam-5586	83	5	asserted	assert	VERB
ejpam-5586	83	6	that	that	SCONJ
ejpam-5586	83	7	ψ(ϑ	ψ(ϑ	PROPN
ejpam-5586	83	8	,	,	PUNCT
ejpam-5586	83	9	κ	κ	NOUN
ejpam-5586	83	10	)	)	PUNCT
ejpam-5586	83	11	displays	display	VERB
ejpam-5586	83	12	an	an	DET
ejpam-5586	83	13	increasing	increase	VERB
ejpam-5586	83	14	trend	trend	NOUN
ejpam-5586	83	15	as	as	ADP
ejpam-5586	83	16	ϑ	ϑ	X
ejpam-5586	83	17	varies	varie	NOUN
ejpam-5586	83	18	within	within	ADP
ejpam-5586	83	19	the	the	DET
ejpam-5586	83	20	range	range	NOUN
ejpam-5586	83	21	[	[	X
ejpam-5586	83	22	1/2,∞	1/2,∞	NUM
ejpam-5586	83	23	)	)	PUNCT
ejpam-5586	83	24	.	.	PUNCT
ejpam-5586	84	1	this	this	DET
ejpam-5586	84	2	result	result	NOUN
ejpam-5586	84	3	serves	serve	VERB
ejpam-5586	84	4	as	as	ADP
ejpam-5586	84	5	a	a	DET
ejpam-5586	84	6	generalization	generalization	NOUN
ejpam-5586	84	7	of	of	ADP
ejpam-5586	84	8	the	the	DET
ejpam-5586	84	9	previously	previously	ADV
ejpam-5586	84	10	established	establish	VERB
ejpam-5586	84	11	monotonic	monotonic	ADJ
ejpam-5586	84	12	property	property	NOUN
ejpam-5586	84	13	associated	associate	VERB
ejpam-5586	84	14	with	with	ADP
ejpam-5586	84	15	the	the	DET
ejpam-5586	84	16	matrix	matrix	NOUN
ejpam-5586	84	17	version	version	NOUN
ejpam-5586	84	18	of	of	ADP
ejpam-5586	84	19	equation	equation	NOUN
ejpam-5586	84	20	(	(	PUNCT
ejpam-5586	84	21	11	11	NUM
ejpam-5586	84	22	)	)	PUNCT
ejpam-5586	84	23	.	.	PUNCT
ejpam-5586	85	1	this	this	DET
ejpam-5586	85	2	generalization	generalization	NOUN
ejpam-5586	85	3	mirrors	mirror	VERB
ejpam-5586	85	4	the	the	DET
ejpam-5586	85	5	behavior	behavior	NOUN
ejpam-5586	85	6	of	of	ADP
ejpam-5586	85	7	fϑ(ρ	fϑ(ρ	PROPN
ejpam-5586	85	8	,	,	PUNCT
ejpam-5586	85	9	σ	σ	PROPN
ejpam-5586	85	10	)	)	PUNCT
ejpam-5586	85	11	for	for	ADP
ejpam-5586	85	12	positive	positive	ADJ
ejpam-5586	85	13	real	real	ADJ
ejpam-5586	85	14	numbers	number	NOUN
ejpam-5586	85	15	a	a	PRON
ejpam-5586	85	16	and	and	CCONJ
ejpam-5586	85	17	b	b	NOUN
ejpam-5586	85	18	when	when	SCONJ
ejpam-5586	85	19	ϑ	ϑ	PROPN
ejpam-5586	85	20	belongs	belong	VERB
ejpam-5586	85	21	to	to	ADP
ejpam-5586	85	22	the	the	DET
ejpam-5586	85	23	set	set	NOUN
ejpam-5586	85	24	of	of	ADP
ejpam-5586	85	25	positive	positive	ADJ
ejpam-5586	85	26	real	real	ADJ
ejpam-5586	85	27	numbers	number	NOUN
ejpam-5586	85	28	,	,	PUNCT
ejpam-5586	85	29	r+	r+	X
ejpam-5586	85	30	.	.	PUNCT
ejpam-5586	86	1	as	as	ADP
ejpam-5586	86	2	a	a	DET
ejpam-5586	86	3	consequential	consequential	ADJ
ejpam-5586	86	4	outcome	outcome	NOUN
ejpam-5586	86	5	of	of	ADP
ejpam-5586	86	6	these	these	DET
ejpam-5586	86	7	findings	finding	NOUN
ejpam-5586	86	8	,	,	PUNCT
ejpam-5586	86	9	the	the	DET
ejpam-5586	86	10	author	author	NOUN
ejpam-5586	86	11	will	will	AUX
ejpam-5586	86	12	introduce	introduce	VERB
ejpam-5586	86	13	a	a	DET
ejpam-5586	86	14	potential	potential	ADJ
ejpam-5586	86	15	generalized	generalized	ADJ
ejpam-5586	86	16	matrix	matrix	NOUN
ejpam-5586	86	17	equivalent	equivalent	NOUN
ejpam-5586	86	18	of	of	ADP
ejpam-5586	86	19	equation	equation	NOUN
ejpam-5586	86	20	(	(	PUNCT
ejpam-5586	86	21	12	12	NUM
ejpam-5586	86	22	)	)	PUNCT
ejpam-5586	86	23	,	,	PUNCT
ejpam-5586	86	24	which	which	PRON
ejpam-5586	86	25	can	can	AUX
ejpam-5586	86	26	be	be	AUX
ejpam-5586	86	27	expressed	express	VERB
ejpam-5586	86	28	as	as	SCONJ
ejpam-5586	86	29	follows	follow	VERB
ejpam-5586	86	30	1	1	NUM
ejpam-5586	86	31	2	2	NUM
ejpam-5586	86	32	∣∣∣∣∣∣tµxs1−µ	∣∣∣∣∣∣tµxs1−µ	PROPN
ejpam-5586	86	33	+	+	CCONJ
ejpam-5586	86	34	t	t	PROPN
ejpam-5586	86	35	1−µxsµ	1−µxsµ	NUM
ejpam-5586	86	36	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-5586	86	37	≤	≤	NOUN
ejpam-5586	86	38	∣∣∣∣∣∣∣∣∣∣∣∣(1−	∣∣∣∣∣∣∣∣∣∣∣∣(1−	X
ejpam-5586	86	39	ϑ)t	ϑ)t	X
ejpam-5586	86	40	κxs1−κ	κxs1−κ	NOUN
ejpam-5586	86	41	+	+	CCONJ
ejpam-5586	86	42	ϑ	ϑ	X
ejpam-5586	86	43	(	(	PUNCT
ejpam-5586	86	44	tx	tx	PROPN
ejpam-5586	86	45	+	+	PROPN
ejpam-5586	86	46	xs	xs	PROPN
ejpam-5586	86	47	2	2	NUM
ejpam-5586	86	48	)	)	PUNCT
ejpam-5586	86	49	∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5586	86	50	(	(	PUNCT
ejpam-5586	86	51	14	14	NUM
ejpam-5586	86	52	)	)	PUNCT
ejpam-5586	86	53	this	this	DET
ejpam-5586	86	54	inequality	inequality	NOUN
ejpam-5586	86	55	is	be	AUX
ejpam-5586	86	56	valid	valid	ADJ
ejpam-5586	86	57	for	for	ADP
ejpam-5586	86	58	particular	particular	ADJ
ejpam-5586	86	59	values	value	NOUN
ejpam-5586	86	60	of	of	ADP
ejpam-5586	86	61	µ	µ	PRON
ejpam-5586	86	62	∈	∈	NOUN
ejpam-5586	87	1	[	[	X
ejpam-5586	87	2	1/4	1/4	NUM
ejpam-5586	87	3	,	,	PUNCT
ejpam-5586	87	4	3/4	3/4	NUM
ejpam-5586	87	5	]	]	PUNCT
ejpam-5586	87	6	,	,	PUNCT
ejpam-5586	87	7	κ	κ	PROPN
ejpam-5586	87	8	∈	∈	PROPN
ejpam-5586	88	1	[	[	X
ejpam-5586	88	2	0	0	NUM
ejpam-5586	88	3	,	,	PUNCT
ejpam-5586	88	4	1	1	NUM
ejpam-5586	88	5	]	]	PUNCT
ejpam-5586	88	6	,	,	PUNCT
ejpam-5586	88	7	and	and	CCONJ
ejpam-5586	88	8	ϑ	ϑ	X
ejpam-5586	88	9	∈	∈	X
ejpam-5586	89	1	[	[	X
ejpam-5586	89	2	1/2,∞	1/2,∞	NUM
ejpam-5586	89	3	)	)	PUNCT
ejpam-5586	89	4	.	.	PUNCT
ejpam-5586	90	1	in	in	ADP
ejpam-5586	90	2	this	this	DET
ejpam-5586	90	3	section	section	NOUN
ejpam-5586	90	4	,	,	PUNCT
ejpam-5586	90	5	we	we	PRON
ejpam-5586	90	6	will	will	AUX
ejpam-5586	90	7	undertake	undertake	VERB
ejpam-5586	90	8	a	a	DET
ejpam-5586	90	9	thorough	thorough	ADJ
ejpam-5586	90	10	investigation	investigation	NOUN
ejpam-5586	90	11	of	of	ADP
ejpam-5586	90	12	matrix	matrix	NOUN
ejpam-5586	90	13	interpolation	interpolation	NOUN
ejpam-5586	90	14	and	and	CCONJ
ejpam-5586	90	15	mean	mean	ADJ
ejpam-5586	90	16	comparisons	comparison	NOUN
ejpam-5586	90	17	.	.	PUNCT
ejpam-5586	91	1	this	this	DET
ejpam-5586	91	2	scrutiny	scrutiny	NOUN
ejpam-5586	91	3	broadens	broaden	VERB
ejpam-5586	91	4	the	the	DET
ejpam-5586	91	5	range	range	NOUN
ejpam-5586	91	6	of	of	ADP
ejpam-5586	91	7	ϑ	ϑ	PRON
ejpam-5586	91	8	from	from	ADP
ejpam-5586	91	9	the	the	DET
ejpam-5586	91	10	closed	closed	ADJ
ejpam-5586	91	11	interval	interval	NOUN
ejpam-5586	91	12	[	[	X
ejpam-5586	91	13	0	0	NUM
ejpam-5586	91	14	,	,	PUNCT
ejpam-5586	91	15	1	1	NUM
ejpam-5586	91	16	]	]	PUNCT
ejpam-5586	91	17	to	to	PART
ejpam-5586	91	18	encompass	encompass	VERB
ejpam-5586	91	19	the	the	DET
ejpam-5586	91	20	entirety	entirety	NOUN
ejpam-5586	91	21	of	of	ADP
ejpam-5586	91	22	positive	positive	ADJ
ejpam-5586	91	23	real	real	ADJ
ejpam-5586	91	24	numbers	number	NOUN
ejpam-5586	91	25	,	,	PUNCT
ejpam-5586	91	26	denoted	denote	VERB
ejpam-5586	91	27	as	as	ADP
ejpam-5586	91	28	r+	r+	X
ejpam-5586	91	29	.	.	PUNCT
ejpam-5586	92	1	furthermore	furthermore	ADV
ejpam-5586	92	2	,	,	PUNCT
ejpam-5586	92	3	we	we	PRON
ejpam-5586	92	4	will	will	AUX
ejpam-5586	92	5	delve	delve	VERB
ejpam-5586	92	6	into	into	ADP
ejpam-5586	92	7	additional	additional	ADJ
ejpam-5586	92	8	findings	finding	NOUN
ejpam-5586	92	9	associated	associate	VERB
ejpam-5586	92	10	with	with	ADP
ejpam-5586	92	11	heinz	heinz	PROPN
ejpam-5586	92	12	means	mean	NOUN
ejpam-5586	92	13	.	.	PUNCT
ejpam-5586	93	1	theorem	theorem	NOUN
ejpam-5586	93	2	1	1	NUM
ejpam-5586	93	3	.	.	PUNCT
ejpam-5586	94	1	[	[	X
ejpam-5586	94	2	6	6	NUM
ejpam-5586	94	3	]	]	PUNCT
ejpam-5586	94	4	let	let	VERB
ejpam-5586	94	5	t	t	PROPN
ejpam-5586	94	6	,	,	PUNCT
ejpam-5586	94	7	s	s	PART
ejpam-5586	94	8	∈mn(c	∈mn(c	NOUN
ejpam-5586	94	9	)	)	PUNCT
ejpam-5586	94	10	such	such	ADJ
ejpam-5586	94	11	that	that	SCONJ
ejpam-5586	94	12	t	t	PROPN
ejpam-5586	94	13	is	be	AUX
ejpam-5586	94	14	a	a	DET
ejpam-5586	94	15	positive	positive	ADJ
ejpam-5586	94	16	semi	semi	ADJ
ejpam-5586	94	17	-	-	ADJ
ejpam-5586	94	18	definite	definite	ADJ
ejpam-5586	94	19	.	.	PUNCT
ejpam-5586	95	1	then	then	ADV
ejpam-5586	95	2	|||t	|||t	VERB
ejpam-5586	95	3	◦	◦	NOUN
ejpam-5586	95	4	s|||	s|||	VERB
ejpam-5586	95	5	≤	≤	ADJ
ejpam-5586	95	6	max	max	PROPN
ejpam-5586	95	7	1≤i≤n	1≤i≤n	NUM
ejpam-5586	95	8	tii|||s|||	tii|||s|||	PROPN
ejpam-5586	95	9	,	,	PUNCT
ejpam-5586	95	10	where	where	SCONJ
ejpam-5586	95	11	tii	tii	PROPN
ejpam-5586	95	12	for	for	ADP
ejpam-5586	95	13	i	i	PROPN
ejpam-5586	95	14	=	=	NOUN
ejpam-5586	95	15	1	1	NUM
ejpam-5586	95	16	,	,	PUNCT
ejpam-5586	95	17	2	2	NUM
ejpam-5586	95	18	,	,	PUNCT
ejpam-5586	95	19	·	·	PUNCT
ejpam-5586	95	20	·	·	PUNCT
ejpam-5586	95	21	·	·	PUNCT
ejpam-5586	95	22	,	,	PUNCT
ejpam-5586	95	23	n	n	PRON
ejpam-5586	95	24	are	be	AUX
ejpam-5586	95	25	the	the	DET
ejpam-5586	95	26	diagonal	diagonal	ADJ
ejpam-5586	95	27	entries	entry	NOUN
ejpam-5586	95	28	of	of	ADP
ejpam-5586	95	29	matrix	matrix	NOUN
ejpam-5586	95	30	t	t	NOUN
ejpam-5586	95	31	.	.	PUNCT
ejpam-5586	96	1	lemma	lemma	PROPN
ejpam-5586	96	2	1	1	NUM
ejpam-5586	96	3	.	.	PUNCT
ejpam-5586	97	1	[	[	X
ejpam-5586	97	2	21	21	NUM
ejpam-5586	97	3	]	]	X
ejpam-5586	97	4	let	let	VERB
ejpam-5586	97	5	κ1	κ1	NOUN
ejpam-5586	97	6	,	,	PUNCT
ejpam-5586	97	7	κ2	κ2	NOUN
ejpam-5586	97	8	,	,	PUNCT
ejpam-5586	97	9	·	·	PUNCT
ejpam-5586	97	10	·	·	PUNCT
ejpam-5586	97	11	·	·	PUNCT
ejpam-5586	97	12	,	,	PUNCT
ejpam-5586	97	13	κn	κn	NOUN
ejpam-5586	97	14	be	be	AUX
ejpam-5586	97	15	positive	positive	ADJ
ejpam-5586	97	16	numbers	number	NOUN
ejpam-5586	97	17	,	,	PUNCT
ejpam-5586	97	18	r	r	NOUN
ejpam-5586	97	19	∈	∈	PROPN
ejpam-5586	98	1	[	[	X
ejpam-5586	98	2	−1	−1	NOUN
ejpam-5586	98	3	,	,	PUNCT
ejpam-5586	98	4	1	1	NUM
ejpam-5586	98	5	]	]	PUNCT
ejpam-5586	98	6	,	,	PUNCT
ejpam-5586	98	7	and	and	CCONJ
ejpam-5586	98	8	t	t	PROPN
ejpam-5586	98	9	∈	∈	PROPN
ejpam-5586	98	10	(	(	PUNCT
ejpam-5586	98	11	−2	−2	NOUN
ejpam-5586	98	12	,	,	PUNCT
ejpam-5586	98	13	2	2	NUM
ejpam-5586	98	14	]	]	PUNCT
ejpam-5586	98	15	.	.	PUNCT
ejpam-5586	99	1	then	then	ADV
ejpam-5586	99	2	the	the	DET
ejpam-5586	99	3	n×	n×	PROPN
ejpam-5586	99	4	n	n	NOUN
ejpam-5586	99	5	matrix	matrix	NOUN
ejpam-5586	99	6	matrix	matrix	NOUN
ejpam-5586	99	7	γ	γ	X
ejpam-5586	99	8	=	=	SYM
ejpam-5586	99	9	(	(	PUNCT
ejpam-5586	99	10	κri	κri	PROPN
ejpam-5586	99	11	+	+	NUM
ejpam-5586	99	12	κrj	κrj	NOUN
ejpam-5586	99	13	κ2i	κ2i	PROPN
ejpam-5586	99	14	+	+	CCONJ
ejpam-5586	99	15	tκiκj	tκiκj	PROPN
ejpam-5586	99	16	+	+	CCONJ
ejpam-5586	99	17	κ2j	κ2j	PROPN
ejpam-5586	99	18	)	)	PUNCT
ejpam-5586	99	19	is	be	AUX
ejpam-5586	99	20	positive	positive	ADJ
ejpam-5586	99	21	semi	semi	ADJ
ejpam-5586	99	22	-	-	ADJ
ejpam-5586	99	23	definite	definite	ADJ
ejpam-5586	99	24	.	.	PUNCT
ejpam-5586	100	1	m.h.m	m.h.m	PROPN
ejpam-5586	100	2	rashid	rashid	PROPN
ejpam-5586	100	3	,	,	PUNCT
ejpam-5586	100	4	w.m.m	w.m.m	NOUN
ejpam-5586	100	5	.	.	PUNCT
ejpam-5586	101	1	salameh	salameh	PROPN
ejpam-5586	101	2	/	/	SYM
ejpam-5586	101	3	eur	eur	PROPN
ejpam-5586	101	4	.	.	PUNCT
ejpam-5586	102	1	j.	j.	PROPN
ejpam-5586	102	2	pure	pure	PROPN
ejpam-5586	102	3	appl	appl	PROPN
ejpam-5586	102	4	.	.	PROPN
ejpam-5586	102	5	math	math	PROPN
ejpam-5586	102	6	,	,	PUNCT
ejpam-5586	102	7	18	18	NUM
ejpam-5586	102	8	(	(	PUNCT
ejpam-5586	102	9	1	1	NUM
ejpam-5586	102	10	)	)	PUNCT
ejpam-5586	102	11	(	(	PUNCT
ejpam-5586	102	12	2025	2025	NUM
ejpam-5586	102	13	)	)	PUNCT
ejpam-5586	102	14	,	,	PUNCT
ejpam-5586	102	15	5586	5586	NUM
ejpam-5586	102	16	5	5	NUM
ejpam-5586	102	17	of	of	ADP
ejpam-5586	102	18	21	21	NUM
ejpam-5586	102	19	theorem	theorem	NOUN
ejpam-5586	102	20	2	2	NUM
ejpam-5586	102	21	.	.	PUNCT
ejpam-5586	103	1	let	let	VERB
ejpam-5586	103	2	t	t	PROPN
ejpam-5586	103	3	,	,	PUNCT
ejpam-5586	103	4	s	s	PROPN
ejpam-5586	103	5	,	,	PUNCT
ejpam-5586	103	6	x	x	SYM
ejpam-5586	103	7	∈mn(c	∈mn(c	NOUN
ejpam-5586	103	8	)	)	PUNCT
ejpam-5586	103	9	such	such	ADJ
ejpam-5586	103	10	that	that	SCONJ
ejpam-5586	103	11	t	t	PROPN
ejpam-5586	103	12	and	and	CCONJ
ejpam-5586	103	13	s	s	VERB
ejpam-5586	103	14	are	be	AUX
ejpam-5586	103	15	positive	positive	ADJ
ejpam-5586	103	16	semi	semi	ADJ
ejpam-5586	103	17	-	-	ADJ
ejpam-5586	103	18	definite	definite	ADJ
ejpam-5586	103	19	,	,	PUNCT
ejpam-5586	103	20	κ	κ	PROPN
ejpam-5586	103	21	∈	∈	PROPN
ejpam-5586	104	1	[	[	X
ejpam-5586	104	2	0	0	NUM
ejpam-5586	104	3	,	,	PUNCT
ejpam-5586	104	4	1	1	NUM
ejpam-5586	104	5	]	]	PUNCT
ejpam-5586	104	6	and	and	CCONJ
ejpam-5586	104	7	|||.|||	|||.|||	VERB
ejpam-5586	104	8	any	any	DET
ejpam-5586	104	9	unitarily	unitarily	ADV
ejpam-5586	104	10	invariant	invariant	ADJ
ejpam-5586	104	11	norm	norm	NOUN
ejpam-5586	104	12	,	,	PUNCT
ejpam-5586	104	13	the	the	DET
ejpam-5586	104	14	function	function	NOUN
ejpam-5586	104	15	ψ(ϑ	ψ(ϑ	PROPN
ejpam-5586	104	16	,	,	PUNCT
ejpam-5586	104	17	κ	κ	NOUN
ejpam-5586	104	18	)	)	PUNCT
ejpam-5586	104	19	=	=	SYM
ejpam-5586	104	20	∣∣∣∣∣∣∣∣∣∣∣∣(1−	∣∣∣∣∣∣∣∣∣∣∣∣(1−	X
ejpam-5586	104	21	ϑ)t	ϑ)t	X
ejpam-5586	104	22	κxs1−κ	κxs1−κ	NOUN
ejpam-5586	104	23	+	+	CCONJ
ejpam-5586	104	24	ϑ	ϑ	X
ejpam-5586	104	25	(	(	PUNCT
ejpam-5586	104	26	tx	tx	PROPN
ejpam-5586	104	27	+	+	PROPN
ejpam-5586	104	28	xs	xs	PROPN
ejpam-5586	104	29	2	2	NUM
ejpam-5586	104	30	)	)	PUNCT
ejpam-5586	104	31	∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5586	104	32	is	be	AUX
ejpam-5586	104	33	increasing	increase	VERB
ejpam-5586	104	34	for	for	ADP
ejpam-5586	104	35	1	1	NUM
ejpam-5586	104	36	2	2	NUM
ejpam-5586	104	37	≤	≤	NOUN
ejpam-5586	104	38	ϑ	ϑ	X
ejpam-5586	104	39	<	<	X
ejpam-5586	104	40	∞	∞	PROPN
ejpam-5586	104	41	and	and	CCONJ
ejpam-5586	104	42	ψ(ϑ	ψ(ϑ	PROPN
ejpam-5586	104	43	,	,	PUNCT
ejpam-5586	104	44	κ	κ	NOUN
ejpam-5586	104	45	)	)	PUNCT
ejpam-5586	104	46	≤	≤	NUM
ejpam-5586	104	47	ψ	ψ	X
ejpam-5586	104	48	(	(	PUNCT
ejpam-5586	104	49	1	1	NUM
ejpam-5586	104	50	2	2	NUM
ejpam-5586	104	51	,	,	PUNCT
ejpam-5586	104	52	κ	κ	NOUN
ejpam-5586	104	53	)	)	PUNCT
ejpam-5586	104	54	for	for	ADP
ejpam-5586	104	55	all	all	PRON
ejpam-5586	104	56	ϑ	ϑ	PRON
ejpam-5586	104	57	∈	∈	X
ejpam-5586	104	58	[	[	PUNCT
ejpam-5586	104	59	0	0	NUM
ejpam-5586	104	60	,	,	PUNCT
ejpam-5586	104	61	12	12	NUM
ejpam-5586	104	62	]	]	PUNCT
ejpam-5586	104	63	.	.	PUNCT
ejpam-5586	105	1	proof	proof	NOUN
ejpam-5586	105	2	.	.	PUNCT
ejpam-5586	106	1	we	we	PRON
ejpam-5586	106	2	first	first	ADV
ejpam-5586	106	3	prove	prove	VERB
ejpam-5586	106	4	the	the	DET
ejpam-5586	106	5	result	result	NOUN
ejpam-5586	106	6	for	for	ADP
ejpam-5586	106	7	ϑ	ϑ	NOUN
ejpam-5586	106	8	>	>	X
ejpam-5586	106	9	0	0	NUM
ejpam-5586	106	10	and	and	CCONJ
ejpam-5586	106	11	t	t	PROPN
ejpam-5586	106	12	=	=	SYM
ejpam-5586	106	13	s	s	PROPN
ejpam-5586	106	14	,	,	PUNCT
ejpam-5586	106	15	that	that	SCONJ
ejpam-5586	106	16	is,∣∣∣∣∣∣∣∣∣∣∣∣(1−	is,∣∣∣∣∣∣∣∣∣∣∣∣(1−	ADJ
ejpam-5586	106	17	ϑ)t	ϑ)t	ADJ
ejpam-5586	106	18	κxs1−κ	κxs1−κ	NOUN
ejpam-5586	106	19	+	+	CCONJ
ejpam-5586	106	20	ϑ	ϑ	X
ejpam-5586	106	21	(	(	PUNCT
ejpam-5586	106	22	tx	tx	PROPN
ejpam-5586	106	23	+	+	PROPN
ejpam-5586	106	24	xs	xs	PROPN
ejpam-5586	106	25	2	2	NUM
ejpam-5586	106	26	)	)	PUNCT
ejpam-5586	106	27	∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣	NOUN
ejpam-5586	106	28	=	=	PUNCT
ejpam-5586	106	29	ϑ	ϑ	X
ejpam-5586	106	30	2	2	NUM
ejpam-5586	106	31	z(ϑ	z(ϑ	PROPN
ejpam-5586	106	32	)	)	PUNCT
ejpam-5586	106	33	,	,	PUNCT
ejpam-5586	106	34	where	where	SCONJ
ejpam-5586	106	35	z(ϑ	z(ϑ	NOUN
ejpam-5586	106	36	)	)	PUNCT
ejpam-5586	106	37	=	=	PUNCT
ejpam-5586	106	38	∣∣∣∣∣∣q(ϑ)t	∣∣∣∣∣∣q(ϑ)t	X
ejpam-5586	106	39	κxt	κxt	VERB
ejpam-5586	106	40	1−κ	1−κ	PROPN
ejpam-5586	106	41	+	+	NUM
ejpam-5586	106	42	tx	tx	PROPN
ejpam-5586	106	43	+	+	PROPN
ejpam-5586	106	44	xt	xt	X
ejpam-5586	106	45	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-5586	106	46	and	and	CCONJ
ejpam-5586	106	47	q(ϑ	q(ϑ	PROPN
ejpam-5586	106	48	)	)	PUNCT
ejpam-5586	106	49	=	=	SYM
ejpam-5586	106	50	2	2	NUM
ejpam-5586	106	51	(	(	PUNCT
ejpam-5586	106	52	1	1	NUM
ejpam-5586	106	53	ϑ	ϑ	NOUN
ejpam-5586	106	54	−	−	PROPN
ejpam-5586	106	55	1	1	NUM
ejpam-5586	106	56	)	)	PUNCT
ejpam-5586	106	57	.	.	PUNCT
ejpam-5586	107	1	we	we	PRON
ejpam-5586	107	2	may	may	AUX
ejpam-5586	107	3	assume	assume	VERB
ejpam-5586	107	4	without	without	ADP
ejpam-5586	107	5	loss	loss	NOUN
ejpam-5586	107	6	of	of	ADP
ejpam-5586	107	7	generality	generality	NOUN
ejpam-5586	107	8	,	,	PUNCT
ejpam-5586	107	9	t	t	NOUN
ejpam-5586	107	10	=	=	SYM
ejpam-5586	107	11	diag	diag	PROPN
ejpam-5586	107	12	(	(	PUNCT
ejpam-5586	107	13	η1	η1	NOUN
ejpam-5586	107	14	,	,	PUNCT
ejpam-5586	107	15	·	·	PUNCT
ejpam-5586	107	16	·	·	PUNCT
ejpam-5586	107	17	·	·	PUNCT
ejpam-5586	107	18	,	,	PUNCT
ejpam-5586	107	19	ηn	ηn	INTJ
ejpam-5586	107	20	)	)	PUNCT
ejpam-5586	107	21	,	,	PUNCT
ejpam-5586	107	22	ηj	ηj	ADP
ejpam-5586	107	23	>	>	X
ejpam-5586	107	24	0	0	X
ejpam-5586	107	25	.	.	PUNCT
ejpam-5586	108	1	then	then	ADV
ejpam-5586	108	2	q(ϑ)t	q(ϑ)t	PROPN
ejpam-5586	108	3	κxt	κxt	VERB
ejpam-5586	108	4	1−κ	1−κ	PROPN
ejpam-5586	109	1	+	+	NUM
ejpam-5586	109	2	tx	tx	PROPN
ejpam-5586	109	3	+	+	PROPN
ejpam-5586	109	4	xt	xt	X
ejpam-5586	109	5	=	=	SYM
ejpam-5586	109	6	(	(	PUNCT
ejpam-5586	109	7	(	(	PUNCT
ejpam-5586	109	8	q(ϑ)ηκi	q(ϑ)ηκi	PROPN
ejpam-5586	109	9	η	η	PROPN
ejpam-5586	109	10	1−κ	1−κ	PROPN
ejpam-5586	109	11	j	j	PROPN
ejpam-5586	110	1	+	+	CCONJ
ejpam-5586	110	2	ηi	ηi	X
ejpam-5586	110	3	+	+	CCONJ
ejpam-5586	110	4	ηj	ηj	NOUN
ejpam-5586	110	5	)	)	PUNCT
ejpam-5586	110	6	xij	xij	PROPN
ejpam-5586	110	7	)	)	PUNCT
ejpam-5586	111	1	i	i	PRON
ejpam-5586	111	2	,	,	PUNCT
ejpam-5586	111	3	j	j	PROPN
ejpam-5586	111	4	=	=	PRON
ejpam-5586	111	5	(	(	PUNCT
ejpam-5586	111	6	q(ϑ)ηκi	q(ϑ)ηκi	PROPN
ejpam-5586	111	7	η	η	PROPN
ejpam-5586	111	8	1−κ	1−κ	PROPN
ejpam-5586	111	9	j	j	PROPN
ejpam-5586	112	1	+	+	CCONJ
ejpam-5586	112	2	ηi	ηi	X
ejpam-5586	112	3	+	+	CCONJ
ejpam-5586	112	4	ηj	ηj	ADP
ejpam-5586	112	5	q(ϱ)ηκi	q(ϱ)ηκi	PROPN
ejpam-5586	112	6	η	η	PROPN
ejpam-5586	112	7	1−κ	1−κ	PROPN
ejpam-5586	112	8	j	j	PROPN
ejpam-5586	113	1	+	+	CCONJ
ejpam-5586	113	2	ηi	ηi	X
ejpam-5586	113	3	+	+	CCONJ
ejpam-5586	113	4	ηj	ηj	NOUN
ejpam-5586	113	5	)	)	PUNCT
ejpam-5586	114	1	i	i	PRON
ejpam-5586	114	2	,	,	PUNCT
ejpam-5586	114	3	j	j	PROPN
ejpam-5586	114	4	◦	◦	NOUN
ejpam-5586	114	5	(	(	PUNCT
ejpam-5586	114	6	q(ϱ)t	q(ϱ)t	INTJ
ejpam-5586	114	7	κxt	κxt	VERB
ejpam-5586	114	8	1−κ	1−κ	PROPN
ejpam-5586	115	1	+	+	NUM
ejpam-5586	115	2	tx	tx	PROPN
ejpam-5586	115	3	+	+	PROPN
ejpam-5586	115	4	xt	xt	X
ejpam-5586	115	5	)	)	PUNCT
ejpam-5586	116	1	=	=	PUNCT
ejpam-5586	116	2	e	e	X
ejpam-5586	116	3	◦	◦	NOUN
ejpam-5586	116	4	(	(	PUNCT
ejpam-5586	116	5	q(ϱ)t	q(ϱ)t	PRON
ejpam-5586	116	6	κxt	κxt	VERB
ejpam-5586	116	7	1−κ	1−κ	PROPN
ejpam-5586	116	8	+	+	NUM
ejpam-5586	116	9	tx	tx	PROPN
ejpam-5586	116	10	+	+	PROPN
ejpam-5586	116	11	xt	xt	X
ejpam-5586	116	12	)	)	PUNCT
ejpam-5586	116	13	,	,	PUNCT
ejpam-5586	116	14	where	where	SCONJ
ejpam-5586	116	15	e	e	NOUN
ejpam-5586	116	16	=	=	PRON
ejpam-5586	116	17	(	(	PUNCT
ejpam-5586	116	18	q(ϑ)ηκi	q(ϑ)ηκi	PROPN
ejpam-5586	116	19	η	η	PROPN
ejpam-5586	116	20	1−κ	1−κ	PROPN
ejpam-5586	116	21	j	j	PROPN
ejpam-5586	117	1	+	+	ADJ
ejpam-5586	117	2	ηi+ηj	ηi+ηj	VERB
ejpam-5586	117	3	q(ϱ)ηκi	q(ϱ)ηκi	PROPN
ejpam-5586	117	4	η	η	PROPN
ejpam-5586	117	5	1−κ	1−κ	PROPN
ejpam-5586	117	6	j	j	PROPN
ejpam-5586	117	7	+	+	NOUN
ejpam-5586	117	8	ηi+ηj	ηi+ηj	X
ejpam-5586	117	9	)	)	PUNCT
ejpam-5586	117	10	i	i	PRON
ejpam-5586	117	11	,	,	PUNCT
ejpam-5586	117	12	j	j	PROPN
ejpam-5586	117	13	.	.	PUNCT
ejpam-5586	118	1	now	now	ADV
ejpam-5586	118	2	the	the	DET
ejpam-5586	118	3	matrix	matrix	NOUN
ejpam-5586	118	4	e	e	NOUN
ejpam-5586	118	5	can	can	AUX
ejpam-5586	118	6	be	be	AUX
ejpam-5586	118	7	written	write	VERB
ejpam-5586	118	8	as	as	ADP
ejpam-5586	118	9	(	(	PUNCT
ejpam-5586	118	10	1	1	NUM
ejpam-5586	118	11	+	+	CCONJ
ejpam-5586	118	12	(	(	PUNCT
ejpam-5586	118	13	q(ϑ)−q(ϱ))ηκi	q(ϑ)−q(ϱ))ηκi	PROPN
ejpam-5586	118	14	η	η	PROPN
ejpam-5586	118	15	1−κ	1−κ	PROPN
ejpam-5586	118	16	j	j	PROPN
ejpam-5586	118	17	q(ϱ)ηκi	q(ϱ)ηκi	PROPN
ejpam-5586	118	18	η	η	PROPN
ejpam-5586	118	19	1−κ	1−κ	PROPN
ejpam-5586	118	20	j	j	PROPN
ejpam-5586	119	1	+	+	CCONJ
ejpam-5586	119	2	ηi	ηi	X
ejpam-5586	119	3	+	+	CCONJ
ejpam-5586	119	4	ηj	ηj	NOUN
ejpam-5586	119	5	)	)	PUNCT
ejpam-5586	119	6	=	=	SYM
ejpam-5586	119	7	(	(	PUNCT
ejpam-5586	119	8	1)i	1)i	NUM
ejpam-5586	119	9	,	,	PUNCT
ejpam-5586	119	10	j	j	PROPN
ejpam-5586	119	11	+	+	CCONJ
ejpam-5586	119	12	(	(	PUNCT
ejpam-5586	119	13	ηκi	ηκi	PROPN
ejpam-5586	119	14	(	(	PUNCT
ejpam-5586	119	15	q(ϑ)−q(ϱ	q(ϑ)−q(ϱ	NOUN
ejpam-5586	119	16	)	)	PUNCT
ejpam-5586	119	17	q(ϱ)ηκi	q(ϱ)ηκi	PROPN
ejpam-5586	119	18	η	η	PROPN
ejpam-5586	119	19	1−κ	1−κ	PROPN
ejpam-5586	119	20	j	j	PROPN
ejpam-5586	120	1	+	+	CCONJ
ejpam-5586	120	2	ηi	ηi	X
ejpam-5586	120	3	+	+	CCONJ
ejpam-5586	120	4	ηj	ηj	NOUN
ejpam-5586	120	5	)	)	PUNCT
ejpam-5586	120	6	η1−κ	η1−κ	PROPN
ejpam-5586	120	7	j	j	PROPN
ejpam-5586	120	8	)	)	PUNCT
ejpam-5586	120	9	which	which	PRON
ejpam-5586	120	10	will	will	AUX
ejpam-5586	120	11	be	be	AUX
ejpam-5586	120	12	positive	positive	ADJ
ejpam-5586	120	13	semidefinite	semidefinite	NOUN
ejpam-5586	120	14	if	if	SCONJ
ejpam-5586	120	15	the	the	DET
ejpam-5586	120	16	matrix	matrix	NOUN
ejpam-5586	120	17	,	,	PUNCT
ejpam-5586	120	18	g	g	NOUN
ejpam-5586	120	19	=	=	PUNCT
ejpam-5586	120	20	(	(	PUNCT
ejpam-5586	120	21	q(ϑ)−q(ϱ	q(ϑ)−q(ϱ	NOUN
ejpam-5586	120	22	)	)	PUNCT
ejpam-5586	120	23	q(ϱ)ηκi	q(ϱ)ηκi	PROPN
ejpam-5586	120	24	η	η	PROPN
ejpam-5586	120	25	1−κ	1−κ	PROPN
ejpam-5586	120	26	j	j	PROPN
ejpam-5586	121	1	+	+	CCONJ
ejpam-5586	121	2	ηi	ηi	X
ejpam-5586	121	3	+	+	CCONJ
ejpam-5586	121	4	ηj	ηj	NOUN
ejpam-5586	121	5	)	)	PUNCT
ejpam-5586	122	1	i	i	PRON
ejpam-5586	122	2	,	,	PUNCT
ejpam-5586	122	3	j	j	PROPN
ejpam-5586	122	4	is	be	AUX
ejpam-5586	122	5	positive	positive	ADJ
ejpam-5586	122	6	semidefinite	semidefinite	NOUN
ejpam-5586	122	7	.	.	PUNCT
ejpam-5586	123	1	according	accord	VERB
ejpam-5586	123	2	to	to	ADP
ejpam-5586	123	3	lemma	lemma	PROPN
ejpam-5586	123	4	1	1	NUM
ejpam-5586	123	5	,	,	PUNCT
ejpam-5586	123	6	the	the	DET
ejpam-5586	123	7	latter	latter	ADJ
ejpam-5586	123	8	matrix	matrix	NOUN
ejpam-5586	123	9	is	be	AUX
ejpam-5586	123	10	positive	positive	ADJ
ejpam-5586	123	11	semidefinite	semidefinite	NOUN
ejpam-5586	123	12	if	if	SCONJ
ejpam-5586	123	13	and	and	CCONJ
ejpam-5586	123	14	only	only	ADV
ejpam-5586	123	15	if	if	SCONJ
ejpam-5586	123	16	q(ϑ	q(ϑ	NOUN
ejpam-5586	123	17	)	)	PUNCT
ejpam-5586	123	18	≥	≥	PROPN
ejpam-5586	123	19	q(ϱ	q(ϱ	PROPN
ejpam-5586	123	20	)	)	PUNCT
ejpam-5586	123	21	and	and	CCONJ
ejpam-5586	123	22	q(ϱ	q(ϱ	PROPN
ejpam-5586	123	23	)	)	PUNCT
ejpam-5586	123	24	∈	∈	PROPN
ejpam-5586	124	1	[	[	X
ejpam-5586	124	2	−2	−2	X
ejpam-5586	124	3	,	,	PUNCT
ejpam-5586	124	4	2	2	NUM
ejpam-5586	124	5	]	]	PUNCT
ejpam-5586	124	6	.	.	PUNCT
ejpam-5586	125	1	since	since	SCONJ
ejpam-5586	125	2	q(ϑ	q(ϑ	PROPN
ejpam-5586	125	3	)	)	PUNCT
ejpam-5586	125	4	=	=	SYM
ejpam-5586	125	5	2	2	NUM
ejpam-5586	125	6	(	(	PUNCT
ejpam-5586	125	7	1	1	NUM
ejpam-5586	125	8	ϑ	ϑ	NOUN
ejpam-5586	125	9	−	−	PROPN
ejpam-5586	125	10	1	1	NUM
ejpam-5586	125	11	)	)	PUNCT
ejpam-5586	125	12	is	be	AUX
ejpam-5586	125	13	a	a	DET
ejpam-5586	125	14	continuous	continuous	ADJ
ejpam-5586	125	15	and	and	CCONJ
ejpam-5586	125	16	decreasing	decrease	VERB
ejpam-5586	125	17	function	function	NOUN
ejpam-5586	125	18	on	on	ADP
ejpam-5586	125	19	the	the	DET
ejpam-5586	125	20	positive	positive	ADJ
ejpam-5586	125	21	half	half	ADJ
ejpam-5586	125	22	-	-	PUNCT
ejpam-5586	125	23	line	line	NOUN
ejpam-5586	125	24	,	,	PUNCT
ejpam-5586	125	25	ranging	range	VERB
ejpam-5586	125	26	from	from	ADP
ejpam-5586	125	27	[	[	X
ejpam-5586	125	28	12	12	NUM
ejpam-5586	125	29	,	,	PUNCT
ejpam-5586	125	30	∞	∞	PROPN
ejpam-5586	125	31	)	)	PUNCT
ejpam-5586	125	32	into	into	ADP
ejpam-5586	125	33	[	[	X
ejpam-5586	125	34	−2	−2	X
ejpam-5586	125	35	,	,	PUNCT
ejpam-5586	125	36	2	2	NUM
ejpam-5586	125	37	]	]	PUNCT
ejpam-5586	125	38	,	,	PUNCT
ejpam-5586	125	39	it	it	PRON
ejpam-5586	125	40	follows	follow	VERB
ejpam-5586	125	41	that	that	SCONJ
ejpam-5586	125	42	q(ϑ	q(ϑ	PROPN
ejpam-5586	125	43	)	)	PUNCT
ejpam-5586	125	44	≥	≥	PROPN
ejpam-5586	125	45	q(ϱ	q(ϱ	PROPN
ejpam-5586	125	46	)	)	PUNCT
ejpam-5586	125	47	for	for	SCONJ
ejpam-5586	125	48	all	all	PRON
ejpam-5586	125	49	ϱ	ϱ	ADP
ejpam-5586	125	50	≥	≥	NOUN
ejpam-5586	125	51	ϑ.	ϑ.	VERB
ejpam-5586	125	52	consequently	consequently	ADV
ejpam-5586	125	53	,	,	PUNCT
ejpam-5586	125	54	using	use	VERB
ejpam-5586	125	55	theorem	theorem	NOUN
ejpam-5586	125	56	1	1	NUM
ejpam-5586	125	57	,	,	PUNCT
ejpam-5586	125	58	we	we	PRON
ejpam-5586	125	59	can	can	AUX
ejpam-5586	125	60	deduce	deduce	VERB
ejpam-5586	125	61	that	that	DET
ejpam-5586	125	62	z(ϑ	z(ϑ	NOUN
ejpam-5586	125	63	)	)	PUNCT
ejpam-5586	125	64	≤	≤	NOUN
ejpam-5586	125	65	(	(	PUNCT
ejpam-5586	125	66	q(ϑ)+2	q(ϑ)+2	NOUN
ejpam-5586	125	67	q(ϱ)+2	q(ϱ)+2	NOUN
ejpam-5586	125	68	)	)	PUNCT
ejpam-5586	125	69	t	t	PROPN
ejpam-5586	125	70	(	(	PUNCT
ejpam-5586	125	71	ϱ	ϱ	PROPN
ejpam-5586	125	72	)	)	PUNCT
ejpam-5586	125	73	.	.	PUNCT
ejpam-5586	126	1	thus	thus	ADV
ejpam-5586	126	2	,	,	PUNCT
ejpam-5586	126	3	the	the	DET
ejpam-5586	126	4	result	result	NOUN
ejpam-5586	126	5	holds	hold	VERB
ejpam-5586	126	6	for	for	ADP
ejpam-5586	126	7	t	t	NOUN
ejpam-5586	126	8	=	=	SYM
ejpam-5586	126	9	s	s	PROPN
ejpam-5586	126	10	and	and	CCONJ
ejpam-5586	126	11	ϑ	ϑ	X
ejpam-5586	126	12	≥	≥	NUM
ejpam-5586	126	13	1	1	NUM
ejpam-5586	126	14	2	2	NUM
ejpam-5586	126	15	.	.	PUNCT
ejpam-5586	127	1	for	for	ADP
ejpam-5586	127	2	ϑ	ϑ	PROPN
ejpam-5586	127	3	∈	∈	PROPN
ejpam-5586	127	4	(	(	PUNCT
ejpam-5586	127	5	0	0	NUM
ejpam-5586	127	6	,	,	PUNCT
ejpam-5586	127	7	1/2	1/2	NUM
ejpam-5586	127	8	]	]	PUNCT
ejpam-5586	127	9	,	,	PUNCT
ejpam-5586	127	10	we	we	PRON
ejpam-5586	127	11	have	have	VERB
ejpam-5586	127	12	2	2	NUM
ejpam-5586	127	13	≤	≤	NUM
ejpam-5586	127	14	q(ϑ	q(ϑ	NOUN
ejpam-5586	127	15	)	)	PUNCT
ejpam-5586	127	16	<	<	X
ejpam-5586	127	17	∞	∞	PROPN
ejpam-5586	127	18	,	,	PUNCT
ejpam-5586	127	19	and	and	CCONJ
ejpam-5586	127	20	q(ϑ	q(ϑ	PROPN
ejpam-5586	127	21	)	)	PUNCT
ejpam-5586	127	22	>	>	X
ejpam-5586	128	1	q	q	X
ejpam-5586	128	2	(	(	PUNCT
ejpam-5586	128	3	1	1	NUM
ejpam-5586	128	4	2	2	NUM
ejpam-5586	128	5	)	)	PUNCT
ejpam-5586	128	6	=	=	SYM
ejpam-5586	128	7	2	2	X
ejpam-5586	128	8	.	.	X
ejpam-5586	128	9	therefore	therefore	ADV
ejpam-5586	128	10	,	,	PUNCT
ejpam-5586	128	11	the	the	DET
ejpam-5586	128	12	matrix	matrix	NOUN
ejpam-5586	128	13	e	e	NOUN
ejpam-5586	128	14	with	with	ADP
ejpam-5586	128	15	ϱ	ϱ	NOUN
ejpam-5586	128	16	=	=	SYM
ejpam-5586	128	17	1	1	NUM
ejpam-5586	128	18	2	2	NUM
ejpam-5586	128	19	is	be	AUX
ejpam-5586	128	20	positive	positive	ADJ
ejpam-5586	128	21	semidefinite	semidefinite	NOUN
ejpam-5586	128	22	,	,	PUNCT
ejpam-5586	128	23	as	as	ADP
ejpam-5586	128	24	per	per	ADP
ejpam-5586	128	25	lemma	lemma	PROPN
ejpam-5586	128	26	1	1	NUM
ejpam-5586	128	27	.	.	PUNCT
ejpam-5586	129	1	the	the	DET
ejpam-5586	129	2	case	case	NOUN
ejpam-5586	129	3	ϑ	ϑ	X
ejpam-5586	129	4	=	=	SYM
ejpam-5586	129	5	0	0	NUM
ejpam-5586	129	6	is	be	AUX
ejpam-5586	129	7	straightforward	straightforward	ADJ
ejpam-5586	129	8	since	since	SCONJ
ejpam-5586	129	9	,	,	PUNCT
ejpam-5586	129	10	by	by	ADP
ejpam-5586	129	11	lemma	lemma	PROPN
ejpam-5586	129	12	1	1	NUM
ejpam-5586	129	13	,	,	PUNCT
ejpam-5586	129	14	the	the	DET
ejpam-5586	129	15	matrix	matrix	NOUN
ejpam-5586	129	16	(	(	PUNCT
ejpam-5586	129	17	ηκi	ηκi	PROPN
ejpam-5586	129	18	η	η	PROPN
ejpam-5586	129	19	1−κ	1−κ	PROPN
ejpam-5586	129	20	j	j	PROPN
ejpam-5586	129	21	ηκi	ηκi	PROPN
ejpam-5586	129	22	η	η	PROPN
ejpam-5586	129	23	1−κ	1−κ	PROPN
ejpam-5586	129	24	j	j	PROPN
ejpam-5586	130	1	+	+	CCONJ
ejpam-5586	130	2	ηi	ηi	X
ejpam-5586	130	3	+	+	CCONJ
ejpam-5586	130	4	ηj	ηj	NOUN
ejpam-5586	130	5	)	)	PUNCT
ejpam-5586	131	1	i	i	PRON
ejpam-5586	131	2	,	,	PUNCT
ejpam-5586	131	3	j	j	PROPN
ejpam-5586	131	4	=	=	PRON
ejpam-5586	131	5	(	(	PUNCT
ejpam-5586	131	6	ηκi	ηκi	PROPN
ejpam-5586	131	7	(	(	PUNCT
ejpam-5586	131	8	1	1	NUM
ejpam-5586	131	9	ηκi	ηκi	PROPN
ejpam-5586	131	10	η	η	PROPN
ejpam-5586	131	11	1−κ	1−κ	PROPN
ejpam-5586	131	12	j	j	PROPN
ejpam-5586	132	1	+	+	CCONJ
ejpam-5586	132	2	ηi	ηi	X
ejpam-5586	132	3	+	+	CCONJ
ejpam-5586	132	4	ηj	ηj	NOUN
ejpam-5586	132	5	)	)	PUNCT
ejpam-5586	132	6	η1−κ	η1−κ	PROPN
ejpam-5586	132	7	j	j	PROPN
ejpam-5586	132	8	)	)	PUNCT
ejpam-5586	133	1	i	i	PRON
ejpam-5586	133	2	,	,	PUNCT
ejpam-5586	133	3	j	j	PROPN
ejpam-5586	133	4	m.h.m	m.h.m	PROPN
ejpam-5586	133	5	rashid	rashid	PROPN
ejpam-5586	133	6	,	,	PUNCT
ejpam-5586	133	7	w.m.m	w.m.m	NOUN
ejpam-5586	133	8	.	.	PUNCT
ejpam-5586	134	1	salameh	salameh	PROPN
ejpam-5586	134	2	/	/	SYM
ejpam-5586	134	3	eur	eur	PROPN
ejpam-5586	134	4	.	.	PUNCT
ejpam-5586	135	1	j.	j.	PROPN
ejpam-5586	135	2	pure	pure	PROPN
ejpam-5586	135	3	appl	appl	PROPN
ejpam-5586	135	4	.	.	PROPN
ejpam-5586	135	5	math	math	PROPN
ejpam-5586	135	6	,	,	PUNCT
ejpam-5586	135	7	18	18	NUM
ejpam-5586	135	8	(	(	PUNCT
ejpam-5586	135	9	1	1	NUM
ejpam-5586	135	10	)	)	PUNCT
ejpam-5586	135	11	(	(	PUNCT
ejpam-5586	135	12	2025	2025	NUM
ejpam-5586	135	13	)	)	PUNCT
ejpam-5586	135	14	,	,	PUNCT
ejpam-5586	135	15	5586	5586	NUM
ejpam-5586	135	16	6	6	NUM
ejpam-5586	135	17	of	of	ADP
ejpam-5586	135	18	21	21	NUM
ejpam-5586	135	19	is	be	AUX
ejpam-5586	135	20	positive	positive	ADJ
ejpam-5586	135	21	semidefinite	semidefinite	NOUN
ejpam-5586	135	22	.	.	PUNCT
ejpam-5586	136	1	thus	thus	ADV
ejpam-5586	136	2	,	,	PUNCT
ejpam-5586	136	3	we	we	PRON
ejpam-5586	136	4	have	have	AUX
ejpam-5586	136	5	established	establish	VERB
ejpam-5586	136	6	the	the	DET
ejpam-5586	136	7	desired	desire	VERB
ejpam-5586	136	8	result	result	NOUN
ejpam-5586	136	9	for	for	ADP
ejpam-5586	136	10	this	this	DET
ejpam-5586	136	11	case	case	NOUN
ejpam-5586	136	12	,	,	PUNCT
ejpam-5586	136	13	i.e.	i.e.	X
ejpam-5586	136	14	,	,	PUNCT
ejpam-5586	136	15	ϑz(ϑ	ϑz(ϑ	NOUN
ejpam-5586	136	16	)	)	PUNCT
ejpam-5586	136	17	≤	≤	NUM
ejpam-5586	136	18	1	1	NUM
ejpam-5586	136	19	2z	2z	NUM
ejpam-5586	136	20	(	(	PUNCT
ejpam-5586	136	21	1	1	NUM
ejpam-5586	136	22	2	2	NUM
ejpam-5586	136	23	)	)	PUNCT
ejpam-5586	136	24	.	.	PUNCT
ejpam-5586	137	1	in	in	ADP
ejpam-5586	137	2	other	other	ADJ
ejpam-5586	137	3	words	word	NOUN
ejpam-5586	137	4	,	,	PUNCT
ejpam-5586	137	5	ψ(ϑ	ψ(ϑ	PROPN
ejpam-5586	137	6	,	,	PUNCT
ejpam-5586	137	7	κ	κ	NOUN
ejpam-5586	137	8	)	)	PUNCT
ejpam-5586	137	9	≤	≤	NUM
ejpam-5586	137	10	ψ	ψ	X
ejpam-5586	137	11	(	(	PUNCT
ejpam-5586	137	12	1	1	NUM
ejpam-5586	137	13	2	2	NUM
ejpam-5586	137	14	,	,	PUNCT
ejpam-5586	137	15	κ	κ	NOUN
ejpam-5586	137	16	)	)	PUNCT
ejpam-5586	137	17	for	for	ADP
ejpam-5586	137	18	all	all	DET
ejpam-5586	137	19	ϑ	ϑ	PRON
ejpam-5586	137	20	∈	∈	NOUN
ejpam-5586	137	21	[	[	X
ejpam-5586	137	22	0	0	NUM
ejpam-5586	137	23	,	,	PUNCT
ejpam-5586	137	24	1/2	1/2	NUM
ejpam-5586	137	25	]	]	PUNCT
ejpam-5586	137	26	.	.	PUNCT
ejpam-5586	138	1	the	the	DET
ejpam-5586	138	2	general	general	ADJ
ejpam-5586	138	3	case	case	NOUN
ejpam-5586	138	4	can	can	AUX
ejpam-5586	138	5	be	be	AUX
ejpam-5586	138	6	derived	derive	VERB
ejpam-5586	138	7	by	by	ADP
ejpam-5586	138	8	substituting	substitute	VERB
ejpam-5586	138	9	t	t	NOUN
ejpam-5586	138	10	with	with	ADP
ejpam-5586	138	11	(	(	PUNCT
ejpam-5586	138	12	t	t	NOUN
ejpam-5586	138	13	0	0	NUM
ejpam-5586	138	14	0	0	NUM
ejpam-5586	138	15	s	s	PART
ejpam-5586	138	16	)	)	PUNCT
ejpam-5586	138	17	and	and	CCONJ
ejpam-5586	138	18	x	x	PUNCT
ejpam-5586	138	19	by	by	ADP
ejpam-5586	138	20	(	(	PUNCT
ejpam-5586	138	21	x	x	SYM
ejpam-5586	138	22	0	0	NUM
ejpam-5586	138	23	0	0	NUM
ejpam-5586	138	24	0	0	NUM
ejpam-5586	138	25	)	)	PUNCT
ejpam-5586	138	26	.	.	PUNCT
ejpam-5586	139	1	remark	remark	NOUN
ejpam-5586	139	2	1	1	NUM
ejpam-5586	139	3	.	.	PUNCT
ejpam-5586	140	1	by	by	ADP
ejpam-5586	140	2	setting	set	VERB
ejpam-5586	140	3	κ	κ	PRON
ejpam-5586	140	4	to	to	PART
ejpam-5586	140	5	be	be	AUX
ejpam-5586	140	6	equal	equal	ADJ
ejpam-5586	140	7	to	to	ADP
ejpam-5586	140	8	half	half	NOUN
ejpam-5586	140	9	(	(	PUNCT
ejpam-5586	140	10	i.e.	i.e.	X
ejpam-5586	140	11	,	,	PUNCT
ejpam-5586	140	12	κ	κ	X
ejpam-5586	140	13	=	=	SYM
ejpam-5586	140	14	1	1	NUM
ejpam-5586	140	15	2	2	NUM
ejpam-5586	140	16	)	)	PUNCT
ejpam-5586	140	17	in	in	ADP
ejpam-5586	140	18	theorem	theorem	NOUN
ejpam-5586	140	19	2	2	NUM
ejpam-5586	140	20	,	,	PUNCT
ejpam-5586	140	21	we	we	PRON
ejpam-5586	140	22	can	can	AUX
ejpam-5586	140	23	deduce	deduce	VERB
ejpam-5586	140	24	that	that	SCONJ
ejpam-5586	140	25	we	we	PRON
ejpam-5586	140	26	arrive	arrive	VERB
ejpam-5586	140	27	at	at	ADP
ejpam-5586	140	28	theorem	theorem	ADJ
ejpam-5586	140	29	2.3	2.3	NUM
ejpam-5586	140	30	as	as	SCONJ
ejpam-5586	140	31	presented	present	VERB
ejpam-5586	140	32	in	in	ADP
ejpam-5586	140	33	[	[	X
ejpam-5586	140	34	8	8	NUM
ejpam-5586	140	35	]	]	PUNCT
ejpam-5586	140	36	.	.	PUNCT
ejpam-5586	141	1	consequently	consequently	ADV
ejpam-5586	141	2	,	,	PUNCT
ejpam-5586	141	3	our	our	PRON
ejpam-5586	141	4	findings	finding	NOUN
ejpam-5586	141	5	represent	represent	VERB
ejpam-5586	141	6	an	an	DET
ejpam-5586	141	7	enhancement	enhancement	NOUN
ejpam-5586	141	8	of	of	ADP
ejpam-5586	141	9	the	the	DET
ejpam-5586	141	10	results	result	NOUN
ejpam-5586	141	11	established	establish	VERB
ejpam-5586	141	12	in	in	ADP
ejpam-5586	141	13	that	that	DET
ejpam-5586	141	14	theorem	theorem	VERB
ejpam-5586	141	15	.	.	PUNCT
ejpam-5586	142	1	as	as	ADP
ejpam-5586	142	2	a	a	DET
ejpam-5586	142	3	consequence	consequence	NOUN
ejpam-5586	142	4	of	of	ADP
ejpam-5586	142	5	theorem	theorem	NOUN
ejpam-5586	142	6	2	2	NUM
ejpam-5586	142	7	,	,	PUNCT
ejpam-5586	142	8	we	we	PRON
ejpam-5586	142	9	have	have	VERB
ejpam-5586	142	10	corollary	corollary	ADJ
ejpam-5586	142	11	1	1	NUM
ejpam-5586	142	12	.	.	PUNCT
ejpam-5586	143	1	let	let	VERB
ejpam-5586	143	2	t	t	PROPN
ejpam-5586	143	3	,	,	PUNCT
ejpam-5586	143	4	s	s	X
ejpam-5586	143	5	,	,	PUNCT
ejpam-5586	143	6	x	x	SYM
ejpam-5586	143	7	∈	∈	NOUN
ejpam-5586	143	8	mn(c	mn(c	X
ejpam-5586	143	9	)	)	PUNCT
ejpam-5586	143	10	with	with	ADP
ejpam-5586	143	11	t	t	PROPN
ejpam-5586	143	12	,	,	PUNCT
ejpam-5586	143	13	s	s	VERB
ejpam-5586	143	14	positive	positive	ADJ
ejpam-5586	143	15	definite	definite	NOUN
ejpam-5586	143	16	.	.	PUNCT
ejpam-5586	144	1	then	then	ADV
ejpam-5586	144	2	for	for	ADP
ejpam-5586	144	3	any	any	DET
ejpam-5586	144	4	unitarily	unitarily	ADJ
ejpam-5586	144	5	invariant	invariant	ADJ
ejpam-5586	144	6	norm	norm	NOUN
ejpam-5586	144	7	|||·|||	|||·|||	NOUN
ejpam-5586	144	8	and	and	CCONJ
ejpam-5586	144	9	a	a	DET
ejpam-5586	144	10	matrix	matrix	NOUN
ejpam-5586	144	11	monotone	monotone	NOUN
ejpam-5586	144	12	increasing	increase	VERB
ejpam-5586	144	13	function	function	NOUN
ejpam-5586	144	14	ψ	ψ	NOUN
ejpam-5586	144	15	:	:	PUNCT
ejpam-5586	144	16	(	(	PUNCT
ejpam-5586	144	17	0,∞	0,∞	NOUN
ejpam-5586	144	18	)	)	PUNCT
ejpam-5586	144	19	−→	−→	NOUN
ejpam-5586	144	20	(	(	PUNCT
ejpam-5586	144	21	0,∞	0,∞	NOUN
ejpam-5586	144	22	)	)	PUNCT
ejpam-5586	144	23	with	with	ADP
ejpam-5586	144	24	ψ∗(x	ψ∗(x	PROPN
ejpam-5586	144	25	)	)	PUNCT
ejpam-5586	144	26	=	=	SYM
ejpam-5586	144	27	x(ψ(x))−1	x(ψ(x))−1	PROPN
ejpam-5586	144	28	,	,	PUNCT
ejpam-5586	144	29	1	1	NUM
ejpam-5586	144	30	2	2	NUM
ejpam-5586	144	31	∣∣∣∣∣∣∣∣∣t	∣∣∣∣∣∣∣∣∣t	NOUN
ejpam-5586	144	32	µ	µ	VERB
ejpam-5586	144	33	2	2	NUM
ejpam-5586	144	34	(	(	PUNCT
ejpam-5586	144	35	ψ(tµ)xψ∗(sµ	ψ(tµ)xψ∗(sµ	NOUN
ejpam-5586	144	36	)	)	PUNCT
ejpam-5586	144	37	+	+	NUM
ejpam-5586	144	38	ψ∗(tµ)xψ(sµ))s	ψ∗(tµ)xψ(sµ))s	X
ejpam-5586	144	39	µ	µ	PRON
ejpam-5586	144	40	2	2	NUM
ejpam-5586	144	41	∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣	SYM
ejpam-5586	144	42	≤	≤	NOUN
ejpam-5586	144	43	∣∣∣∣∣∣∣∣∣∣∣∣(1−	∣∣∣∣∣∣∣∣∣∣∣∣(1−	X
ejpam-5586	144	44	ϑ)t	ϑ)t	X
ejpam-5586	144	45	κxs1−κ	κxs1−κ	NOUN
ejpam-5586	144	46	+	+	CCONJ
ejpam-5586	144	47	ϑ	ϑ	X
ejpam-5586	144	48	(	(	PUNCT
ejpam-5586	144	49	tx	tx	PROPN
ejpam-5586	144	50	+	+	PROPN
ejpam-5586	144	51	xs	xs	PROPN
ejpam-5586	144	52	2	2	NUM
ejpam-5586	144	53	)	)	PUNCT
ejpam-5586	144	54	∣∣∣∣∣∣∣∣∣∣∣∣.	∣∣∣∣∣∣∣∣∣∣∣∣.	NOUN
ejpam-5586	144	55	corollary	corollary	NOUN
ejpam-5586	144	56	2	2	NUM
ejpam-5586	144	57	.	.	PUNCT
ejpam-5586	145	1	let	let	VERB
ejpam-5586	145	2	t	t	PROPN
ejpam-5586	145	3	,	,	PUNCT
ejpam-5586	145	4	s	s	X
ejpam-5586	145	5	,	,	PUNCT
ejpam-5586	145	6	x	x	SYM
ejpam-5586	145	7	∈	∈	NOUN
ejpam-5586	145	8	mn(c	mn(c	X
ejpam-5586	145	9	)	)	PUNCT
ejpam-5586	145	10	with	with	ADP
ejpam-5586	145	11	t	t	PROPN
ejpam-5586	145	12	,	,	PUNCT
ejpam-5586	145	13	s	s	VERB
ejpam-5586	145	14	positive	positive	ADJ
ejpam-5586	145	15	definite	definite	NOUN
ejpam-5586	145	16	.	.	PUNCT
ejpam-5586	146	1	then	then	ADV
ejpam-5586	146	2	for	for	ADP
ejpam-5586	146	3	any	any	DET
ejpam-5586	146	4	unitarily	unitarily	ADJ
ejpam-5586	146	5	invariant	invariant	ADJ
ejpam-5586	146	6	norm	norm	NOUN
ejpam-5586	146	7	|||·|||	|||·|||	NOUN
ejpam-5586	146	8	,	,	PUNCT
ejpam-5586	146	9	1	1	NUM
ejpam-5586	146	10	4	4	NUM
ejpam-5586	146	11	≤	≤	NOUN
ejpam-5586	146	12	µ	µ	PRON
ejpam-5586	146	13	≤	≤	NOUN
ejpam-5586	146	14	3	3	NUM
ejpam-5586	146	15	4	4	NUM
ejpam-5586	146	16	,	,	PUNCT
ejpam-5586	146	17	κ	κ	PROPN
ejpam-5586	146	18	∈	∈	PROPN
ejpam-5586	147	1	[	[	X
ejpam-5586	147	2	0	0	NUM
ejpam-5586	147	3	,	,	PUNCT
ejpam-5586	147	4	1	1	NUM
ejpam-5586	147	5	]	]	PUNCT
ejpam-5586	147	6	and	and	CCONJ
ejpam-5586	147	7	ϑ	ϑ	X
ejpam-5586	147	8	∈	∈	X
ejpam-5586	147	9	[	[	X
ejpam-5586	147	10	1/2,∞	1/2,∞	NUM
ejpam-5586	147	11	)	)	PUNCT
ejpam-5586	147	12	,	,	PUNCT
ejpam-5586	147	13	1	1	NUM
ejpam-5586	147	14	2	2	NUM
ejpam-5586	147	15	∣∣∣∣∣∣tµxs1−µ	∣∣∣∣∣∣tµxs1−µ	PROPN
ejpam-5586	147	16	+	+	CCONJ
ejpam-5586	147	17	t	t	PROPN
ejpam-5586	147	18	1−µxsµ	1−µxsµ	NUM
ejpam-5586	147	19	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-5586	147	20	≤	≤	NOUN
ejpam-5586	147	21	∣∣∣∣∣∣∣∣∣∣∣∣(1−	∣∣∣∣∣∣∣∣∣∣∣∣(1−	X
ejpam-5586	147	22	ϑ)t	ϑ)t	X
ejpam-5586	147	23	κxs1−κ	κxs1−κ	NOUN
ejpam-5586	147	24	+	+	CCONJ
ejpam-5586	147	25	ϑ	ϑ	X
ejpam-5586	147	26	(	(	PUNCT
ejpam-5586	147	27	tx	tx	PROPN
ejpam-5586	147	28	+	+	PROPN
ejpam-5586	147	29	xs	xs	PROPN
ejpam-5586	147	30	2	2	NUM
ejpam-5586	147	31	)	)	PUNCT
ejpam-5586	147	32	∣∣∣∣∣∣∣∣∣∣∣∣.	∣∣∣∣∣∣∣∣∣∣∣∣.	NUM
ejpam-5586	147	33	proof	proof	NOUN
ejpam-5586	147	34	.	.	PUNCT
ejpam-5586	148	1	letting	let	VERB
ejpam-5586	148	2	ψ(x	ψ(x	NOUN
ejpam-5586	148	3	)	)	PUNCT
ejpam-5586	149	1	=	=	PUNCT
ejpam-5586	150	1	√	√	NUM
ejpam-5586	150	2	x	x	PUNCT
ejpam-5586	150	3	in	in	ADP
ejpam-5586	150	4	corollary	corollary	ADJ
ejpam-5586	150	5	1	1	NUM
ejpam-5586	150	6	,	,	PUNCT
ejpam-5586	150	7	we	we	PRON
ejpam-5586	150	8	derived	derive	VERB
ejpam-5586	150	9	the	the	DET
ejpam-5586	150	10	result	result	NOUN
ejpam-5586	150	11	.	.	PUNCT
ejpam-5586	151	1	the	the	DET
ejpam-5586	151	2	following	following	ADJ
ejpam-5586	151	3	result	result	NOUN
ejpam-5586	151	4	is	be	AUX
ejpam-5586	151	5	a	a	DET
ejpam-5586	151	6	consequence	consequence	NOUN
ejpam-5586	151	7	of	of	ADP
ejpam-5586	151	8	theorem	theorem	ADJ
ejpam-5586	151	9	2	2	NUM
ejpam-5586	151	10	.	.	PUNCT
ejpam-5586	151	11	corollary	corollary	ADJ
ejpam-5586	151	12	3	3	X
ejpam-5586	151	13	.	.	PUNCT
ejpam-5586	152	1	let	let	VERB
ejpam-5586	152	2	t	t	PROPN
ejpam-5586	152	3	,	,	PUNCT
ejpam-5586	152	4	s	s	X
ejpam-5586	152	5	,	,	PUNCT
ejpam-5586	152	6	x	x	SYM
ejpam-5586	152	7	∈	∈	NOUN
ejpam-5586	152	8	mn(c	mn(c	X
ejpam-5586	152	9	)	)	PUNCT
ejpam-5586	152	10	with	with	ADP
ejpam-5586	152	11	t	t	PROPN
ejpam-5586	152	12	,	,	PUNCT
ejpam-5586	152	13	s	s	VERB
ejpam-5586	152	14	positive	positive	ADJ
ejpam-5586	152	15	definite	definite	ADJ
ejpam-5586	152	16	,	,	PUNCT
ejpam-5586	152	17	η	η	NOUN
ejpam-5586	152	18	=	=	SYM
ejpam-5586	152	19	min{sp(t	min{sp(t	PROPN
ejpam-5586	152	20	)	)	PUNCT
ejpam-5586	152	21	,	,	PUNCT
ejpam-5586	152	22	sp(s	sp(s	NUM
ejpam-5586	152	23	)	)	PUNCT
ejpam-5586	152	24	}	}	PUNCT
ejpam-5586	152	25	,	,	PUNCT
ejpam-5586	152	26	µ	µ	X
ejpam-5586	152	27	∈	∈	NOUN
ejpam-5586	153	1	[	[	X
ejpam-5586	153	2	1/4	1/4	NUM
ejpam-5586	153	3	,	,	PUNCT
ejpam-5586	153	4	3/4	3/4	NUM
ejpam-5586	153	5	]	]	PUNCT
ejpam-5586	153	6	and	and	CCONJ
ejpam-5586	153	7	κ	κ	ADP
ejpam-5586	153	8	∈	∈	PROPN
ejpam-5586	154	1	[	[	X
ejpam-5586	154	2	0	0	NUM
ejpam-5586	154	3	,	,	PUNCT
ejpam-5586	154	4	1	1	NUM
ejpam-5586	154	5	]	]	PUNCT
ejpam-5586	154	6	.	.	PUNCT
ejpam-5586	155	1	then	then	ADV
ejpam-5586	155	2	for	for	ADP
ejpam-5586	155	3	any	any	DET
ejpam-5586	155	4	unitarily	unitarily	ADJ
ejpam-5586	155	5	invariant	invariant	ADJ
ejpam-5586	155	6	norm	norm	NOUN
ejpam-5586	155	7	|||·|||	|||·|||	NOUN
ejpam-5586	155	8	and	and	CCONJ
ejpam-5586	155	9	a	a	DET
ejpam-5586	155	10	matrix	matrix	NOUN
ejpam-5586	155	11	monotone	monotone	NOUN
ejpam-5586	155	12	increasing	increase	VERB
ejpam-5586	155	13	function	function	NOUN
ejpam-5586	155	14	ψ	ψ	NOUN
ejpam-5586	155	15	:	:	PUNCT
ejpam-5586	155	16	(	(	PUNCT
ejpam-5586	155	17	0,∞	0,∞	NOUN
ejpam-5586	155	18	)	)	PUNCT
ejpam-5586	155	19	−→	−→	NOUN
ejpam-5586	155	20	(	(	PUNCT
ejpam-5586	155	21	0,∞	0,∞	PROPN
ejpam-5586	155	22	)	)	PUNCT
ejpam-5586	155	23	η	η	PROPN
ejpam-5586	155	24	2f(η	2f(η	NUM
ejpam-5586	155	25	)	)	PUNCT
ejpam-5586	155	26	∣∣∣∣∣∣∣∣∣t	∣∣∣∣∣∣∣∣∣t	VERB
ejpam-5586	155	27	µ	µ	ADJ
ejpam-5586	155	28	2	2	NUM
ejpam-5586	155	29	(	(	PUNCT
ejpam-5586	155	30	ψ(tµ)x	ψ(tµ)x	PROPN
ejpam-5586	156	1	+	+	PROPN
ejpam-5586	156	2	xψ(sµ))s	xψ(sµ))s	X
ejpam-5586	156	3	µ	µ	X
ejpam-5586	156	4	2	2	NUM
ejpam-5586	156	5	∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣	SYM
ejpam-5586	156	6	≤	≤	NOUN
ejpam-5586	156	7	∣∣∣∣∣∣∣∣∣∣∣∣(1−	∣∣∣∣∣∣∣∣∣∣∣∣(1−	X
ejpam-5586	156	8	ϑ)t	ϑ)t	X
ejpam-5586	156	9	κxs1−κ	κxs1−κ	NOUN
ejpam-5586	156	10	+	+	CCONJ
ejpam-5586	156	11	ϑ	ϑ	X
ejpam-5586	156	12	(	(	PUNCT
ejpam-5586	156	13	tx	tx	PROPN
ejpam-5586	156	14	+	+	PROPN
ejpam-5586	156	15	xs	xs	PROPN
ejpam-5586	156	16	2	2	NUM
ejpam-5586	156	17	)	)	PUNCT
ejpam-5586	156	18	∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5586	156	19	holds	hold	VERB
ejpam-5586	156	20	for	for	ADP
ejpam-5586	156	21	every	every	DET
ejpam-5586	156	22	ϑ	ϑ	X
ejpam-5586	156	23	∈	∈	NOUN
ejpam-5586	157	1	[	[	X
ejpam-5586	157	2	1/2,∞	1/2,∞	NUM
ejpam-5586	157	3	)	)	PUNCT
ejpam-5586	157	4	.	.	PUNCT
ejpam-5586	158	1	choosing	choose	VERB
ejpam-5586	158	2	ψ(x	ψ(x	NOUN
ejpam-5586	158	3	)	)	PUNCT
ejpam-5586	159	1	=	=	SYM
ejpam-5586	159	2	log(1	log(1	NOUN
ejpam-5586	159	3	+	+	CCONJ
ejpam-5586	159	4	x	x	X
ejpam-5586	159	5	)	)	PUNCT
ejpam-5586	159	6	in	in	ADP
ejpam-5586	159	7	corollary	corollary	ADJ
ejpam-5586	159	8	3	3	NUM
ejpam-5586	159	9	,	,	PUNCT
ejpam-5586	159	10	we	we	PRON
ejpam-5586	159	11	have	have	VERB
ejpam-5586	159	12	corollary	corollary	ADJ
ejpam-5586	159	13	4	4	NUM
ejpam-5586	159	14	.	.	PUNCT
ejpam-5586	160	1	let	let	VERB
ejpam-5586	160	2	t	t	PROPN
ejpam-5586	160	3	,	,	PUNCT
ejpam-5586	160	4	s	s	X
ejpam-5586	160	5	,	,	PUNCT
ejpam-5586	160	6	x	x	SYM
ejpam-5586	160	7	∈	∈	NOUN
ejpam-5586	160	8	mn(c	mn(c	X
ejpam-5586	160	9	)	)	PUNCT
ejpam-5586	160	10	with	with	ADP
ejpam-5586	160	11	t	t	PROPN
ejpam-5586	160	12	,	,	PUNCT
ejpam-5586	160	13	s	s	VERB
ejpam-5586	160	14	positive	positive	ADJ
ejpam-5586	160	15	definite	definite	ADJ
ejpam-5586	160	16	,	,	PUNCT
ejpam-5586	160	17	η	η	NOUN
ejpam-5586	160	18	=	=	SYM
ejpam-5586	160	19	min{sp(t	min{sp(t	PROPN
ejpam-5586	160	20	)	)	PUNCT
ejpam-5586	160	21	,	,	PUNCT
ejpam-5586	160	22	sp(s	sp(s	NUM
ejpam-5586	160	23	)	)	PUNCT
ejpam-5586	160	24	}	}	PUNCT
ejpam-5586	160	25	,	,	PUNCT
ejpam-5586	160	26	µ	µ	X
ejpam-5586	160	27	∈	∈	NOUN
ejpam-5586	161	1	[	[	X
ejpam-5586	161	2	1/4	1/4	NUM
ejpam-5586	161	3	,	,	PUNCT
ejpam-5586	161	4	3/4	3/4	NUM
ejpam-5586	161	5	]	]	PUNCT
ejpam-5586	161	6	and	and	CCONJ
ejpam-5586	161	7	κ	κ	ADP
ejpam-5586	161	8	∈	∈	PROPN
ejpam-5586	162	1	[	[	X
ejpam-5586	162	2	0	0	NUM
ejpam-5586	162	3	,	,	PUNCT
ejpam-5586	162	4	1	1	NUM
ejpam-5586	162	5	]	]	PUNCT
ejpam-5586	162	6	.	.	PUNCT
ejpam-5586	163	1	then	then	ADV
ejpam-5586	163	2	for	for	SCONJ
ejpam-5586	163	3	any	any	DET
ejpam-5586	163	4	unitarily	unitarily	ADJ
ejpam-5586	163	5	invariant	invariant	ADJ
ejpam-5586	163	6	norm	norm	NOUN
ejpam-5586	163	7	|||·|||	|||·|||	X
ejpam-5586	163	8	η	η	X
ejpam-5586	163	9	2	2	NUM
ejpam-5586	163	10	log(1	log(1	NOUN
ejpam-5586	163	11	+	+	CCONJ
ejpam-5586	163	12	η	η	NOUN
ejpam-5586	163	13	)	)	PUNCT
ejpam-5586	163	14	∣∣∣∣∣∣∣∣∣t	∣∣∣∣∣∣∣∣∣t	VERB
ejpam-5586	163	15	µ	µ	ADJ
ejpam-5586	163	16	2	2	NUM
ejpam-5586	163	17	(	(	PUNCT
ejpam-5586	163	18	log(1	log(1	NOUN
ejpam-5586	164	1	+	+	CCONJ
ejpam-5586	165	1	tµ)x	tµ)x	PRON
ejpam-5586	165	2	+	+	NOUN
ejpam-5586	165	3	x	x	NOUN
ejpam-5586	165	4	log(1	log(1	NOUN
ejpam-5586	165	5	+	+	CCONJ
ejpam-5586	166	1	sµ))s	sµ))	NOUN
ejpam-5586	166	2	µ	µ	PRON
ejpam-5586	166	3	2	2	NUM
ejpam-5586	166	4	∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣	SYM
ejpam-5586	166	5	≤	≤	NOUN
ejpam-5586	166	6	∣∣∣∣∣∣∣∣∣∣∣∣(1−	∣∣∣∣∣∣∣∣∣∣∣∣(1−	X
ejpam-5586	166	7	ϑ)t	ϑ)t	X
ejpam-5586	166	8	κxs1−κ	κxs1−κ	NOUN
ejpam-5586	166	9	+	+	CCONJ
ejpam-5586	166	10	ϑ	ϑ	X
ejpam-5586	166	11	(	(	PUNCT
ejpam-5586	166	12	tx	tx	PROPN
ejpam-5586	166	13	+	+	PROPN
ejpam-5586	166	14	xs	xs	PROPN
ejpam-5586	166	15	2	2	NUM
ejpam-5586	166	16	)	)	PUNCT
ejpam-5586	166	17	∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5586	166	18	holds	hold	VERB
ejpam-5586	166	19	for	for	ADP
ejpam-5586	166	20	every	every	DET
ejpam-5586	166	21	ϑ	ϑ	X
ejpam-5586	166	22	∈	∈	NOUN
ejpam-5586	167	1	[	[	X
ejpam-5586	167	2	1/2,∞	1/2,∞	NUM
ejpam-5586	167	3	)	)	PUNCT
ejpam-5586	167	4	.	.	PUNCT
ejpam-5586	168	1	m.h.m	m.h.m	PROPN
ejpam-5586	168	2	rashid	rashid	PROPN
ejpam-5586	168	3	,	,	PUNCT
ejpam-5586	168	4	w.m.m	w.m.m	NOUN
ejpam-5586	168	5	.	.	PUNCT
ejpam-5586	169	1	salameh	salameh	PROPN
ejpam-5586	169	2	/	/	SYM
ejpam-5586	169	3	eur	eur	PROPN
ejpam-5586	169	4	.	.	PUNCT
ejpam-5586	170	1	j.	j.	PROPN
ejpam-5586	170	2	pure	pure	PROPN
ejpam-5586	170	3	appl	appl	PROPN
ejpam-5586	170	4	.	.	PROPN
ejpam-5586	170	5	math	math	PROPN
ejpam-5586	170	6	,	,	PUNCT
ejpam-5586	170	7	18	18	NUM
ejpam-5586	170	8	(	(	PUNCT
ejpam-5586	170	9	1	1	NUM
ejpam-5586	170	10	)	)	PUNCT
ejpam-5586	170	11	(	(	PUNCT
ejpam-5586	170	12	2025	2025	NUM
ejpam-5586	170	13	)	)	PUNCT
ejpam-5586	170	14	,	,	PUNCT
ejpam-5586	170	15	5586	5586	NUM
ejpam-5586	170	16	7	7	NUM
ejpam-5586	170	17	of	of	ADP
ejpam-5586	170	18	21	21	NUM
ejpam-5586	170	19	theorem	theorem	NOUN
ejpam-5586	170	20	3	3	NUM
ejpam-5586	170	21	.	.	X
ejpam-5586	170	22	consider	consider	VERB
ejpam-5586	170	23	t	t	PROPN
ejpam-5586	170	24	,	,	PUNCT
ejpam-5586	170	25	s	s	X
ejpam-5586	170	26	,	,	PUNCT
ejpam-5586	170	27	x	x	SYM
ejpam-5586	170	28	∈	∈	NOUN
ejpam-5586	170	29	mn(c	mn(c	X
ejpam-5586	170	30	)	)	PUNCT
ejpam-5586	170	31	with	with	ADP
ejpam-5586	170	32	t	t	PROPN
ejpam-5586	170	33	and	and	CCONJ
ejpam-5586	170	34	s	s	AUX
ejpam-5586	170	35	being	be	AUX
ejpam-5586	170	36	positive	positive	ADJ
ejpam-5586	170	37	definite	definite	ADJ
ejpam-5586	170	38	,	,	PUNCT
ejpam-5586	170	39	κ	κ	PROPN
ejpam-5586	170	40	∈	∈	PROPN
ejpam-5586	171	1	[	[	X
ejpam-5586	171	2	0	0	NUM
ejpam-5586	171	3	,	,	PUNCT
ejpam-5586	171	4	1	1	NUM
ejpam-5586	171	5	]	]	PUNCT
ejpam-5586	171	6	,	,	PUNCT
ejpam-5586	171	7	and	and	CCONJ
ejpam-5586	171	8	|||.|||	|||.|||	VERB
ejpam-5586	171	9	denoting	denote	VERB
ejpam-5586	171	10	any	any	DET
ejpam-5586	171	11	unitarily	unitarily	ADV
ejpam-5586	171	12	invariant	invariant	ADJ
ejpam-5586	171	13	norm	norm	NOUN
ejpam-5586	171	14	.	.	PUNCT
ejpam-5586	172	1	the	the	DET
ejpam-5586	172	2	function	function	NOUN
ejpam-5586	172	3	can	can	AUX
ejpam-5586	172	4	be	be	AUX
ejpam-5586	172	5	expressed	express	VERB
ejpam-5586	172	6	as	as	ADP
ejpam-5586	172	7	:	:	PUNCT
ejpam-5586	172	8	ϕ(ϑ	ϕ(ϑ	PROPN
ejpam-5586	172	9	,	,	PUNCT
ejpam-5586	172	10	κ	κ	NOUN
ejpam-5586	172	11	)	)	PUNCT
ejpam-5586	172	12	=	=	SYM
ejpam-5586	172	13	∣∣∣∣∣∣∣∣∣∣∣∣(1−	∣∣∣∣∣∣∣∣∣∣∣∣(1−	X
ejpam-5586	172	14	ϑ	ϑ	X
ejpam-5586	172	15	2	2	NUM
ejpam-5586	172	16	)	)	PUNCT
ejpam-5586	172	17	(	(	PUNCT
ejpam-5586	172	18	t	t	PROPN
ejpam-5586	172	19	κxs1−κ	κxs1−κ	PROPN
ejpam-5586	172	20	+	+	PROPN
ejpam-5586	172	21	t	t	PROPN
ejpam-5586	172	22	1−κxsκ	1−κxsκ	NOUN
ejpam-5586	172	23	)	)	PUNCT
ejpam-5586	173	1	+	+	CCONJ
ejpam-5586	173	2	ϑ	ϑ	X
ejpam-5586	173	3	(	(	PUNCT
ejpam-5586	173	4	tx	tx	PROPN
ejpam-5586	173	5	+	+	PROPN
ejpam-5586	173	6	xs	xs	PROPN
ejpam-5586	173	7	2	2	NUM
ejpam-5586	173	8	)	)	PUNCT
ejpam-5586	173	9	∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5586	173	10	is	be	AUX
ejpam-5586	173	11	increasing	increase	VERB
ejpam-5586	173	12	for	for	ADP
ejpam-5586	173	13	1	1	NUM
ejpam-5586	173	14	2	2	NUM
ejpam-5586	173	15	≤	≤	NOUN
ejpam-5586	173	16	ϑ	ϑ	X
ejpam-5586	173	17	<	<	X
ejpam-5586	173	18	∞	∞	NUM
ejpam-5586	173	19	and	and	CCONJ
ejpam-5586	173	20	ϕ(ϑ	ϕ(ϑ	PROPN
ejpam-5586	173	21	,	,	PUNCT
ejpam-5586	173	22	κ	κ	NOUN
ejpam-5586	173	23	)	)	PUNCT
ejpam-5586	173	24	≤	≤	NOUN
ejpam-5586	173	25	ϕ	ϕ	X
ejpam-5586	173	26	(	(	PUNCT
ejpam-5586	173	27	1	1	NUM
ejpam-5586	173	28	2	2	NUM
ejpam-5586	173	29	,	,	PUNCT
ejpam-5586	173	30	κ	κ	NOUN
ejpam-5586	173	31	)	)	PUNCT
ejpam-5586	173	32	for	for	ADP
ejpam-5586	173	33	all	all	PRON
ejpam-5586	173	34	ϑ	ϑ	PRON
ejpam-5586	173	35	∈	∈	X
ejpam-5586	173	36	[	[	PUNCT
ejpam-5586	173	37	0	0	NUM
ejpam-5586	173	38	,	,	PUNCT
ejpam-5586	173	39	12	12	NUM
ejpam-5586	173	40	]	]	PUNCT
ejpam-5586	173	41	.	.	PUNCT
ejpam-5586	174	1	proof	proof	NOUN
ejpam-5586	174	2	.	.	PUNCT
ejpam-5586	175	1	once	once	ADV
ejpam-5586	175	2	again	again	ADV
ejpam-5586	175	3	following	follow	VERB
ejpam-5586	175	4	the	the	DET
ejpam-5586	175	5	same	same	ADJ
ejpam-5586	175	6	lines	line	NOUN
ejpam-5586	175	7	of	of	ADP
ejpam-5586	175	8	the	the	DET
ejpam-5586	175	9	proof	proof	NOUN
ejpam-5586	175	10	of	of	ADP
ejpam-5586	175	11	theorem	theorem	NOUN
ejpam-5586	175	12	(	(	PUNCT
ejpam-5586	175	13	2	2	NUM
ejpam-5586	175	14	)	)	PUNCT
ejpam-5586	175	15	,	,	PUNCT
ejpam-5586	175	16	we	we	PRON
ejpam-5586	175	17	shall	shall	AUX
ejpam-5586	175	18	prove	prove	VERB
ejpam-5586	175	19	the	the	DET
ejpam-5586	175	20	result	result	NOUN
ejpam-5586	175	21	for	for	ADP
ejpam-5586	175	22	ϑ	ϑ	X
ejpam-5586	175	23	>	>	X
ejpam-5586	175	24	0	0	PROPN
ejpam-5586	175	25	,	,	PUNCT
ejpam-5586	175	26	t	t	PROPN
ejpam-5586	175	27	=	=	SYM
ejpam-5586	175	28	s	s	PROPN
ejpam-5586	175	29	and	and	CCONJ
ejpam-5586	175	30	t	t	NOUN
ejpam-5586	175	31	=	=	PUNCT
ejpam-5586	175	32	diag(η1	diag(η1	NOUN
ejpam-5586	175	33	,	,	PUNCT
ejpam-5586	175	34	·	·	PUNCT
ejpam-5586	175	35	·	·	PUNCT
ejpam-5586	175	36	·	·	PUNCT
ejpam-5586	175	37	,	,	PUNCT
ejpam-5586	175	38	ηn	ηn	ADJ
ejpam-5586	175	39	)	)	PUNCT
ejpam-5586	175	40	.	.	PUNCT
ejpam-5586	176	1	suppose	suppose	VERB
ejpam-5586	176	2	ϕ(ϑ	ϕ(ϑ	NOUN
ejpam-5586	176	3	,	,	PUNCT
ejpam-5586	176	4	κ	κ	NOUN
ejpam-5586	176	5	)	)	PUNCT
ejpam-5586	176	6	=	=	SYM
ejpam-5586	176	7	∣∣∣∣∣∣∣∣∣∣∣∣(1−	∣∣∣∣∣∣∣∣∣∣∣∣(1−	X
ejpam-5586	176	8	ϑ	ϑ	X
ejpam-5586	176	9	2	2	NUM
ejpam-5586	176	10	)	)	PUNCT
ejpam-5586	176	11	(	(	PUNCT
ejpam-5586	176	12	t	t	PROPN
ejpam-5586	176	13	κxt	κxt	PROPN
ejpam-5586	176	14	1−κ	1−κ	PROPN
ejpam-5586	176	15	+	+	NUM
ejpam-5586	176	16	t	t	PROPN
ejpam-5586	176	17	1−κxt	1−κxt	NUM
ejpam-5586	176	18	κ	κ	NOUN
ejpam-5586	176	19	)	)	PUNCT
ejpam-5586	177	1	+	+	CCONJ
ejpam-5586	177	2	ϑ	ϑ	X
ejpam-5586	177	3	(	(	PUNCT
ejpam-5586	177	4	tx	tx	PROPN
ejpam-5586	177	5	+	+	PROPN
ejpam-5586	177	6	xt	xt	PROPN
ejpam-5586	177	7	2	2	NUM
ejpam-5586	177	8	)	)	PUNCT
ejpam-5586	177	9	∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣	NOUN
ejpam-5586	177	10	=	=	PUNCT
ejpam-5586	177	11	ϑ	ϑ	X
ejpam-5586	177	12	2	2	NUM
ejpam-5586	177	13	z(ϑ	z(ϑ	PROPN
ejpam-5586	177	14	,	,	PUNCT
ejpam-5586	177	15	κ	κ	NOUN
ejpam-5586	177	16	)	)	PUNCT
ejpam-5586	177	17	,	,	PUNCT
ejpam-5586	177	18	where	where	SCONJ
ejpam-5586	177	19	z(ϑ	z(ϑ	PROPN
ejpam-5586	177	20	,	,	PUNCT
ejpam-5586	177	21	κ	κ	NOUN
ejpam-5586	177	22	)	)	PUNCT
ejpam-5586	177	23	=	=	SYM
ejpam-5586	177	24	∣∣∣∣∣∣w1(ϑ	∣∣∣∣∣∣w1(ϑ	PROPN
ejpam-5586	177	25	)	)	PUNCT
ejpam-5586	177	26	(	(	PUNCT
ejpam-5586	177	27	t	t	PROPN
ejpam-5586	177	28	κxt	κxt	PROPN
ejpam-5586	177	29	1−κ	1−κ	PROPN
ejpam-5586	178	1	+	+	NUM
ejpam-5586	178	2	t	t	PROPN
ejpam-5586	178	3	1−κxt	1−κxt	NUM
ejpam-5586	178	4	κ	κ	NOUN
ejpam-5586	178	5	)	)	PUNCT
ejpam-5586	179	1	+	+	CCONJ
ejpam-5586	179	2	(	(	PUNCT
ejpam-5586	179	3	tx	tx	VERB
ejpam-5586	179	4	+	+	PROPN
ejpam-5586	179	5	xt	xt	X
ejpam-5586	179	6	)	)	PUNCT
ejpam-5586	179	7	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-5586	179	8	and	and	CCONJ
ejpam-5586	179	9	w1(ϑ	w1(ϑ	PROPN
ejpam-5586	179	10	)	)	PUNCT
ejpam-5586	179	11	=	=	SYM
ejpam-5586	179	12	2	2	NUM
ejpam-5586	179	13	ϑ	ϑ	NOUN
ejpam-5586	179	14	−	−	PROPN
ejpam-5586	179	15	1	1	NUM
ejpam-5586	179	16	.	.	PUNCT
ejpam-5586	180	1	w1(ϑ	w1(ϑ	X
ejpam-5586	180	2	)	)	PUNCT
ejpam-5586	180	3	(	(	PUNCT
ejpam-5586	180	4	t	t	PROPN
ejpam-5586	180	5	κxt	κxt	PROPN
ejpam-5586	180	6	1−κ	1−κ	PROPN
ejpam-5586	181	1	+	+	NUM
ejpam-5586	181	2	t	t	PROPN
ejpam-5586	181	3	1−κxt	1−κxt	NUM
ejpam-5586	181	4	κ	κ	NOUN
ejpam-5586	181	5	)	)	PUNCT
ejpam-5586	182	1	+	+	CCONJ
ejpam-5586	182	2	(	(	PUNCT
ejpam-5586	182	3	tx	tx	VERB
ejpam-5586	182	4	+	+	PROPN
ejpam-5586	182	5	xt	xt	X
ejpam-5586	182	6	)	)	PUNCT
ejpam-5586	183	1	=	=	PUNCT
ejpam-5586	184	1	[	[	X
ejpam-5586	184	2	(	(	PUNCT
ejpam-5586	184	3	w1(ϑ	w1(ϑ	PROPN
ejpam-5586	184	4	)	)	PUNCT
ejpam-5586	184	5	(	(	PUNCT
ejpam-5586	184	6	ηµi	ηµi	NOUN
ejpam-5586	184	7	η	η	PROPN
ejpam-5586	184	8	1−µ	1−µ	PROPN
ejpam-5586	184	9	j	j	PROPN
ejpam-5586	184	10	+	+	CCONJ
ejpam-5586	184	11	η1−µ	η1−µ	PROPN
ejpam-5586	184	12	i	i	PRON
ejpam-5586	184	13	ηµj	ηµj	VERB
ejpam-5586	184	14	)	)	PUNCT
ejpam-5586	185	1	+	+	CCONJ
ejpam-5586	185	2	ηi	ηi	X
ejpam-5586	185	3	+	+	CCONJ
ejpam-5586	185	4	ηj	ηj	NOUN
ejpam-5586	185	5	)	)	PUNCT
ejpam-5586	185	6	xij	xij	PROPN
ejpam-5586	185	7	]	]	PUNCT
ejpam-5586	186	1	i	i	PRON
ejpam-5586	186	2	,	,	PUNCT
ejpam-5586	186	3	j	j	PROPN
ejpam-5586	186	4	=	=	SYM
ejpam-5586	186	5	y	y	PROPN
ejpam-5586	186	6	◦	◦	NOUN
ejpam-5586	186	7	(	(	PUNCT
ejpam-5586	186	8	w1(ϱ	w1(ϱ	PROPN
ejpam-5586	186	9	)	)	PUNCT
ejpam-5586	186	10	(	(	PUNCT
ejpam-5586	186	11	t	t	PROPN
ejpam-5586	186	12	κxt	κxt	PROPN
ejpam-5586	186	13	1−κ	1−κ	PROPN
ejpam-5586	187	1	+	+	NUM
ejpam-5586	187	2	t	t	PROPN
ejpam-5586	187	3	1−κxt	1−κxt	NUM
ejpam-5586	187	4	κ	κ	NOUN
ejpam-5586	187	5	)	)	PUNCT
ejpam-5586	188	1	+	+	CCONJ
ejpam-5586	188	2	tx	tx	PROPN
ejpam-5586	188	3	+	+	PROPN
ejpam-5586	188	4	xs	xs	PROPN
ejpam-5586	188	5	)	)	PUNCT
ejpam-5586	188	6	.	.	PUNCT
ejpam-5586	189	1	now	now	ADV
ejpam-5586	189	2	the	the	DET
ejpam-5586	189	3	matrix	matrix	NOUN
ejpam-5586	189	4	y	y	PROPN
ejpam-5586	189	5	can	can	AUX
ejpam-5586	189	6	be	be	AUX
ejpam-5586	189	7	written	write	VERB
ejpam-5586	189	8	asw1(ϑ	asw1(ϑ	PROPN
ejpam-5586	189	9	)	)	PUNCT
ejpam-5586	189	10	(	(	PUNCT
ejpam-5586	189	11	ηµi	ηµi	NOUN
ejpam-5586	189	12	η	η	PROPN
ejpam-5586	189	13	1−µ	1−µ	PROPN
ejpam-5586	189	14	j	j	PROPN
ejpam-5586	190	1	+	+	CCONJ
ejpam-5586	190	2	η1−µ	η1−µ	PROPN
ejpam-5586	190	3	i	i	PRON
ejpam-5586	190	4	ηµj	ηµj	VERB
ejpam-5586	190	5	)	)	PUNCT
ejpam-5586	191	1	+	+	CCONJ
ejpam-5586	191	2	ηi	ηi	X
ejpam-5586	191	3	+	+	CCONJ
ejpam-5586	191	4	ηj	ηj	ADP
ejpam-5586	191	5	w1(ϱ	w1(ϱ	PROPN
ejpam-5586	191	6	)	)	PUNCT
ejpam-5586	191	7	(	(	PUNCT
ejpam-5586	191	8	ηµi	ηµi	NOUN
ejpam-5586	191	9	η	η	PROPN
ejpam-5586	191	10	1−µ	1−µ	PROPN
ejpam-5586	191	11	j	j	PROPN
ejpam-5586	192	1	+	+	CCONJ
ejpam-5586	192	2	η1−µ	η1−µ	PROPN
ejpam-5586	192	3	i	i	PRON
ejpam-5586	192	4	ηµj	ηµj	VERB
ejpam-5586	192	5	)	)	PUNCT
ejpam-5586	193	1	+	+	CCONJ
ejpam-5586	193	2	ηi	ηi	X
ejpam-5586	193	3	+	+	CCONJ
ejpam-5586	193	4	ηj	ηj	ADP
ejpam-5586	193	5			PROPN
ejpam-5586	193	6	i	i	PRON
ejpam-5586	193	7	,	,	PUNCT
ejpam-5586	193	8	j	j	PROPN
ejpam-5586	193	9	=	=	PRON
ejpam-5586	193	10	(	(	PUNCT
ejpam-5586	193	11	1	1	NUM
ejpam-5586	193	12	+	+	CCONJ
ejpam-5586	193	13	(	(	PUNCT
ejpam-5586	193	14	w1(ϑ)−w1(ϱ))η	w1(ϑ)−w1(ϱ))η	NOUN
ejpam-5586	193	15	κ	κ	PROPN
ejpam-5586	193	16	i	i	PROPN
ejpam-5586	193	17	η	η	PROPN
ejpam-5586	193	18	κ	κ	PROPN
ejpam-5586	193	19	j	j	PROPN
ejpam-5586	193	20	(	(	PUNCT
ejpam-5586	193	21	w1(ϱ)−	w1(ϱ)−	PROPN
ejpam-5586	193	22	1)ηκi	1)ηκi	NUM
ejpam-5586	193	23	η	η	PROPN
ejpam-5586	193	24	κ	κ	PROPN
ejpam-5586	193	25	j	j	PROPN
ejpam-5586	193	26	+	+	CCONJ
ejpam-5586	193	27	η1−κ	η1−κ	PROPN
ejpam-5586	193	28	i	i	PROPN
ejpam-5586	193	29	+	+	PROPN
ejpam-5586	193	30	η1−κ	η1−κ	PROPN
ejpam-5586	193	31	j	j	PROPN
ejpam-5586	193	32	)	)	PUNCT
ejpam-5586	194	1	i	i	PRON
ejpam-5586	194	2	,	,	PUNCT
ejpam-5586	194	3	j	j	PROPN
ejpam-5586	194	4	=	=	PUNCT
ejpam-5586	194	5	(	(	PUNCT
ejpam-5586	194	6	1)i	1)i	NUM
ejpam-5586	194	7	,	,	PUNCT
ejpam-5586	194	8	j	j	PROPN
ejpam-5586	194	9	+	+	CCONJ
ejpam-5586	194	10	(	(	PUNCT
ejpam-5586	194	11	ηκi	ηκi	PROPN
ejpam-5586	194	12	(	(	PUNCT
ejpam-5586	194	13	w1(ϑ)−w1(ϱ	w1(ϑ)−w1(ϱ	NUM
ejpam-5586	194	14	)	)	PUNCT
ejpam-5586	194	15	(	(	PUNCT
ejpam-5586	194	16	w1(ϱ)−	w1(ϱ)−	PROPN
ejpam-5586	194	17	1)ηκi	1)ηκi	NUM
ejpam-5586	194	18	η	η	PROPN
ejpam-5586	194	19	κ	κ	PROPN
ejpam-5586	194	20	j	j	PROPN
ejpam-5586	194	21	+	+	CCONJ
ejpam-5586	194	22	η1−κ	η1−κ	PROPN
ejpam-5586	194	23	i	i	PROPN
ejpam-5586	194	24	+	+	PROPN
ejpam-5586	194	25	η1−κ	η1−κ	PROPN
ejpam-5586	194	26	j	j	PROPN
ejpam-5586	194	27	)	)	PUNCT
ejpam-5586	194	28	ηµj	ηµj	PROPN
ejpam-5586	194	29	)	)	PUNCT
ejpam-5586	195	1	i	i	PRON
ejpam-5586	195	2	,	,	PUNCT
ejpam-5586	195	3	j	j	PROPN
ejpam-5586	195	4	once	once	ADV
ejpam-5586	195	5	again	again	ADV
ejpam-5586	195	6	,	,	PUNCT
ejpam-5586	195	7	considering	consider	VERB
ejpam-5586	195	8	lemma	lemma	PROPN
ejpam-5586	195	9	(	(	PUNCT
ejpam-5586	195	10	1	1	NUM
ejpam-5586	195	11	)	)	PUNCT
ejpam-5586	195	12	,	,	PUNCT
ejpam-5586	195	13	we	we	PRON
ejpam-5586	195	14	observe	observe	VERB
ejpam-5586	195	15	that	that	SCONJ
ejpam-5586	195	16	the	the	DET
ejpam-5586	195	17	latter	latter	ADJ
ejpam-5586	195	18	matrix	matrix	NOUN
ejpam-5586	195	19	is	be	AUX
ejpam-5586	195	20	positive	positive	ADJ
ejpam-5586	195	21	semidefinite	semidefinite	NOUN
ejpam-5586	195	22	if	if	SCONJ
ejpam-5586	195	23	and	and	CCONJ
ejpam-5586	195	24	only	only	ADV
ejpam-5586	195	25	if	if	SCONJ
ejpam-5586	195	26	w1(ϑ	w1(ϑ	NOUN
ejpam-5586	195	27	)	)	PUNCT
ejpam-5586	195	28	>	>	X
ejpam-5586	195	29	w1(ϱ	w1(ϱ	PROPN
ejpam-5586	195	30	)	)	PUNCT
ejpam-5586	195	31	and	and	CCONJ
ejpam-5586	195	32	2	2	NUM
ejpam-5586	195	33	>	>	SYM
ejpam-5586	195	34	w1(ϱ)−	w1(ϱ)−	SYM
ejpam-5586	195	35	1	1	X
ejpam-5586	195	36	>	>	SYM
ejpam-5586	195	37	−2	−2	NOUN
ejpam-5586	195	38	.	.	PUNCT
ejpam-5586	196	1	since	since	SCONJ
ejpam-5586	196	2	w	w	PROPN
ejpam-5586	196	3	(	(	PUNCT
ejpam-5586	196	4	ϑ	ϑ	NOUN
ejpam-5586	196	5	)	)	PUNCT
ejpam-5586	196	6	=	=	SYM
ejpam-5586	196	7	w1(ϑ)−	w1(ϑ)−	PROPN
ejpam-5586	196	8	1	1	NUM
ejpam-5586	196	9	=	=	SYM
ejpam-5586	196	10	(	(	PUNCT
ejpam-5586	196	11	2ϑ−1	2ϑ−1	NOUN
ejpam-5586	196	12	−	−	NOUN
ejpam-5586	196	13	2	2	NUM
ejpam-5586	196	14	)	)	PUNCT
ejpam-5586	196	15	,	,	PUNCT
ejpam-5586	196	16	it	it	PRON
ejpam-5586	196	17	is	be	AUX
ejpam-5586	196	18	a	a	DET
ejpam-5586	196	19	continuously	continuously	ADV
ejpam-5586	196	20	decreasing	decrease	VERB
ejpam-5586	196	21	function	function	NOUN
ejpam-5586	196	22	in	in	ADP
ejpam-5586	196	23	the	the	DET
ejpam-5586	196	24	positive	positive	ADJ
ejpam-5586	196	25	half	half	ADJ
ejpam-5586	196	26	-	-	PUNCT
ejpam-5586	196	27	line	line	NOUN
ejpam-5586	196	28	and	and	CCONJ
ejpam-5586	196	29	maps	map	NOUN
ejpam-5586	196	30	to	to	ADP
ejpam-5586	196	31	the	the	DET
ejpam-5586	196	32	interval	interval	NOUN
ejpam-5586	196	33	(	(	PUNCT
ejpam-5586	196	34	2	2	NUM
ejpam-5586	196	35	,	,	PUNCT
ejpam-5586	196	36	2	2	NUM
ejpam-5586	196	37	]	]	PUNCT
ejpam-5586	196	38	for	for	ADP
ejpam-5586	196	39	ϑ	ϑ	PRON
ejpam-5586	196	40	in	in	ADP
ejpam-5586	196	41	the	the	DET
ejpam-5586	196	42	range	range	NOUN
ejpam-5586	196	43	[	[	X
ejpam-5586	196	44	1/2,∞	1/2,∞	NUM
ejpam-5586	196	45	)	)	PUNCT
ejpam-5586	196	46	.	.	PUNCT
ejpam-5586	197	1	therefore	therefore	ADV
ejpam-5586	197	2	,	,	PUNCT
ejpam-5586	197	3	as	as	SCONJ
ejpam-5586	197	4	demonstrated	demonstrate	VERB
ejpam-5586	197	5	in	in	ADP
ejpam-5586	197	6	theorem	theorem	NOUN
ejpam-5586	197	7	(	(	PUNCT
ejpam-5586	197	8	2	2	NUM
ejpam-5586	197	9	)	)	PUNCT
ejpam-5586	197	10	,	,	PUNCT
ejpam-5586	197	11	we	we	PRON
ejpam-5586	197	12	can	can	AUX
ejpam-5586	197	13	deduce	deduce	VERB
ejpam-5586	197	14	that	that	PRON
ejpam-5586	197	15	w	w	NOUN
ejpam-5586	197	16	(	(	PUNCT
ejpam-5586	197	17	ϑ	ϑ	NOUN
ejpam-5586	197	18	)	)	PUNCT
ejpam-5586	197	19	>	>	X
ejpam-5586	198	1	w	w	PROPN
ejpam-5586	198	2	(	(	PUNCT
ejpam-5586	198	3	ϱ	ϱ	PROPN
ejpam-5586	198	4	)	)	PUNCT
ejpam-5586	198	5	and	and	CCONJ
ejpam-5586	198	6	consequently	consequently	ADV
ejpam-5586	198	7	,	,	PUNCT
ejpam-5586	198	8	w1(ϑ	w1(ϑ	PROPN
ejpam-5586	198	9	)	)	PUNCT
ejpam-5586	198	10	>	>	X
ejpam-5586	198	11	w1(ϱ	w1(ϱ	PROPN
ejpam-5586	198	12	)	)	PUNCT
ejpam-5586	198	13	for	for	ADP
ejpam-5586	198	14	all	all	PRON
ejpam-5586	198	15	ϑ	ϑ	PRON
ejpam-5586	198	16	≤	≤	X
ejpam-5586	198	17	ϱ.	ϱ.	NOUN
ejpam-5586	198	18	applying	apply	VERB
ejpam-5586	198	19	theorem	theorem	NOUN
ejpam-5586	198	20	(	(	PUNCT
ejpam-5586	198	21	1	1	NUM
ejpam-5586	198	22	)	)	PUNCT
ejpam-5586	198	23	,	,	PUNCT
ejpam-5586	198	24	we	we	PRON
ejpam-5586	198	25	establish	establish	VERB
ejpam-5586	198	26	that	that	SCONJ
ejpam-5586	198	27	t	t	PROPN
ejpam-5586	198	28	(	(	PUNCT
ejpam-5586	198	29	ϑ	ϑ	X
ejpam-5586	198	30	,	,	PUNCT
ejpam-5586	198	31	κ	κ	NOUN
ejpam-5586	198	32	)	)	PUNCT
ejpam-5586	198	33	≤	≤	NOUN
ejpam-5586	198	34	w1(ϑ)+1	w1(ϑ)+1	VERB
ejpam-5586	198	35	w1(ϱ)+1	w1(ϱ)+1	PROPN
ejpam-5586	198	36	t	t	PROPN
ejpam-5586	198	37	(	(	PUNCT
ejpam-5586	198	38	ϱ	ϱ	PROPN
ejpam-5586	198	39	,	,	PUNCT
ejpam-5586	198	40	κ	κ	NOUN
ejpam-5586	198	41	)	)	PUNCT
ejpam-5586	198	42	.	.	PUNCT
ejpam-5586	199	1	this	this	DET
ejpam-5586	199	2	verifies	verifie	NOUN
ejpam-5586	199	3	the	the	DET
ejpam-5586	199	4	result	result	NOUN
ejpam-5586	199	5	for	for	ADP
ejpam-5586	199	6	the	the	DET
ejpam-5586	199	7	case	case	NOUN
ejpam-5586	199	8	when	when	SCONJ
ejpam-5586	199	9	t	t	PROPN
ejpam-5586	199	10	=	=	SYM
ejpam-5586	199	11	s	s	PROPN
ejpam-5586	199	12	and	and	CCONJ
ejpam-5586	199	13	ϑ	ϑ	X
ejpam-5586	199	14	∈	∈	X
ejpam-5586	200	1	[	[	X
ejpam-5586	200	2	1/2,∞	1/2,∞	NUM
ejpam-5586	200	3	)	)	PUNCT
ejpam-5586	200	4	.	.	PUNCT
ejpam-5586	201	1	for	for	ADP
ejpam-5586	201	2	ϑ	ϑ	PROPN
ejpam-5586	201	3	∈	∈	PROPN
ejpam-5586	201	4	(	(	PUNCT
ejpam-5586	201	5	0	0	NUM
ejpam-5586	201	6	,	,	PUNCT
ejpam-5586	201	7	1/2	1/2	NUM
ejpam-5586	201	8	]	]	PUNCT
ejpam-5586	201	9	,	,	PUNCT
ejpam-5586	201	10	we	we	PRON
ejpam-5586	201	11	can	can	AUX
ejpam-5586	201	12	observe	observe	VERB
ejpam-5586	201	13	that	that	SCONJ
ejpam-5586	201	14	3	3	NUM
ejpam-5586	201	15	=	=	SYM
ejpam-5586	201	16	w1(1/2	w1(1/2	NOUN
ejpam-5586	201	17	)	)	PUNCT
ejpam-5586	201	18	≤	≤	NOUN
ejpam-5586	201	19	w1(ϑ	w1(ϑ	X
ejpam-5586	201	20	)	)	PUNCT
ejpam-5586	201	21	<	<	X
ejpam-5586	201	22	∞	∞	PROPN
ejpam-5586	201	23	,	,	PUNCT
ejpam-5586	201	24	and	and	CCONJ
ejpam-5586	201	25	according	accord	VERB
ejpam-5586	201	26	to	to	ADP
ejpam-5586	201	27	lemma	lemma	PROPN
ejpam-5586	201	28	(	(	PUNCT
ejpam-5586	201	29	1	1	NUM
ejpam-5586	201	30	)	)	PUNCT
ejpam-5586	201	31	,	,	PUNCT
ejpam-5586	201	32	the	the	DET
ejpam-5586	201	33	matrix	matrix	NOUN
ejpam-5586	201	34	y	y	PROPN
ejpam-5586	201	35	with	with	ADP
ejpam-5586	201	36	ϱ	ϱ	NOUN
ejpam-5586	201	37	=	=	SYM
ejpam-5586	201	38	1/2	1/2	NUM
ejpam-5586	201	39	is	be	AUX
ejpam-5586	201	40	positive	positive	ADJ
ejpam-5586	201	41	semidefinite	semidefinite	NOUN
ejpam-5586	201	42	.	.	PUNCT
ejpam-5586	202	1	similarly	similarly	ADV
ejpam-5586	202	2	,	,	PUNCT
ejpam-5586	202	3	the	the	DET
ejpam-5586	202	4	case	case	NOUN
ejpam-5586	202	5	ϑ	ϑ	X
ejpam-5586	202	6	=	=	SYM
ejpam-5586	202	7	0	0	NUM
ejpam-5586	202	8	can	can	AUX
ejpam-5586	202	9	be	be	AUX
ejpam-5586	202	10	established	establish	VERB
ejpam-5586	202	11	through	through	ADP
ejpam-5586	202	12	the	the	DET
ejpam-5586	202	13	positive	positive	ADJ
ejpam-5586	202	14	semidefiniteness	semidefiniteness	NOUN
ejpam-5586	202	15	of	of	ADP
ejpam-5586	202	16	the	the	DET
ejpam-5586	202	17	matrix	matrix	NOUN
ejpam-5586	202	18	(	(	PUNCT
ejpam-5586	202	19	ηκi	ηκi	PROPN
ejpam-5586	202	20	(	(	PUNCT
ejpam-5586	202	21	w1(ϑ)−w1(ϱ	w1(ϑ)−w1(ϱ	NUM
ejpam-5586	202	22	)	)	PUNCT
ejpam-5586	202	23	(	(	PUNCT
ejpam-5586	202	24	w1(ϱ)−1)ηκi	w1(ϱ)−1)ηκi	PROPN
ejpam-5586	202	25	η	η	PROPN
ejpam-5586	202	26	κ	κ	PROPN
ejpam-5586	202	27	j	j	PROPN
ejpam-5586	202	28	+	+	PROPN
ejpam-5586	202	29	η1−κ	η1−κ	PROPN
ejpam-5586	202	30	i	i	PROPN
ejpam-5586	202	31	+	+	PROPN
ejpam-5586	202	32	η1−κ	η1−κ	PROPN
ejpam-5586	202	33	j	j	PROPN
ejpam-5586	202	34	)	)	PUNCT
ejpam-5586	202	35	ηµj	ηµj	PROPN
ejpam-5586	202	36	)	)	PUNCT
ejpam-5586	203	1	i	i	PRON
ejpam-5586	203	2	,	,	PUNCT
ejpam-5586	203	3	j	j	PROPN
ejpam-5586	203	4	,	,	PUNCT
ejpam-5586	203	5	which	which	PRON
ejpam-5586	203	6	is	be	AUX
ejpam-5586	203	7	confirmed	confirm	VERB
ejpam-5586	203	8	by	by	ADP
ejpam-5586	203	9	utilizing	utilize	VERB
ejpam-5586	203	10	lemma	lemma	PROPN
ejpam-5586	203	11	(	(	PUNCT
ejpam-5586	203	12	1	1	NUM
ejpam-5586	203	13	)	)	PUNCT
ejpam-5586	203	14	.	.	PUNCT
ejpam-5586	204	1	this	this	PRON
ejpam-5586	204	2	leads	lead	VERB
ejpam-5586	204	3	us	we	PRON
ejpam-5586	204	4	to	to	ADP
ejpam-5586	204	5	the	the	DET
ejpam-5586	204	6	desired	desire	VERB
ejpam-5586	204	7	result	result	NOUN
ejpam-5586	204	8	for	for	ADP
ejpam-5586	204	9	this	this	DET
ejpam-5586	204	10	case	case	NOUN
ejpam-5586	204	11	,	,	PUNCT
ejpam-5586	204	12	i.e.	i.e.	X
ejpam-5586	204	13	,	,	PUNCT
ejpam-5586	204	14	ϑz(ϑ	ϑz(ϑ	NOUN
ejpam-5586	204	15	,	,	PUNCT
ejpam-5586	204	16	κ	κ	NOUN
ejpam-5586	204	17	)	)	PUNCT
ejpam-5586	204	18	≤	≤	NOUN
ejpam-5586	204	19	1	1	NUM
ejpam-5586	204	20	2z	2z	NUM
ejpam-5586	204	21	(	(	PUNCT
ejpam-5586	204	22	1	1	NUM
ejpam-5586	204	23	2	2	NUM
ejpam-5586	204	24	,	,	PUNCT
ejpam-5586	204	25	κ	κ	NOUN
ejpam-5586	204	26	)	)	PUNCT
ejpam-5586	204	27	.	.	PUNCT
ejpam-5586	205	1	in	in	ADP
ejpam-5586	205	2	other	other	ADJ
ejpam-5586	205	3	words	word	NOUN
ejpam-5586	205	4	,	,	PUNCT
ejpam-5586	205	5	ϕ(ϑ	ϕ(ϑ	PROPN
ejpam-5586	205	6	,	,	PUNCT
ejpam-5586	205	7	κ	κ	NOUN
ejpam-5586	205	8	)	)	PUNCT
ejpam-5586	205	9	≤	≤	NOUN
ejpam-5586	205	10	ϕ(1/2	ϕ(1/2	PROPN
ejpam-5586	205	11	,	,	PUNCT
ejpam-5586	205	12	κ	κ	NOUN
ejpam-5586	205	13	)	)	PUNCT
ejpam-5586	205	14	holds	hold	VERB
ejpam-5586	205	15	for	for	ADP
ejpam-5586	205	16	all	all	DET
ejpam-5586	205	17	ϑ	ϑ	PRON
ejpam-5586	205	18	∈	∈	NOUN
ejpam-5586	206	1	[	[	X
ejpam-5586	206	2	0	0	NUM
ejpam-5586	206	3	,	,	PUNCT
ejpam-5586	206	4	1/2	1/2	NUM
ejpam-5586	206	5	]	]	PUNCT
ejpam-5586	206	6	.	.	PUNCT
ejpam-5586	207	1	the	the	DET
ejpam-5586	207	2	general	general	ADJ
ejpam-5586	207	3	case	case	NOUN
ejpam-5586	207	4	can	can	AUX
ejpam-5586	207	5	be	be	AUX
ejpam-5586	207	6	obtained	obtain	VERB
ejpam-5586	207	7	by	by	ADP
ejpam-5586	207	8	substituting	substitute	VERB
ejpam-5586	207	9	t	t	NOUN
ejpam-5586	207	10	with	with	ADP
ejpam-5586	207	11	(	(	PUNCT
ejpam-5586	207	12	t	t	NOUN
ejpam-5586	207	13	0	0	NUM
ejpam-5586	207	14	0	0	NUM
ejpam-5586	207	15	s	s	PART
ejpam-5586	207	16	)	)	PUNCT
ejpam-5586	207	17	and	and	CCONJ
ejpam-5586	207	18	x	x	PUNCT
ejpam-5586	207	19	by	by	ADP
ejpam-5586	207	20	(	(	PUNCT
ejpam-5586	207	21	x	x	SYM
ejpam-5586	207	22	0	0	NUM
ejpam-5586	207	23	0	0	NUM
ejpam-5586	207	24	0	0	NUM
ejpam-5586	207	25	)	)	PUNCT
ejpam-5586	207	26	.	.	PUNCT
ejpam-5586	208	1	m.h.m	m.h.m	PROPN
ejpam-5586	208	2	rashid	rashid	PROPN
ejpam-5586	208	3	,	,	PUNCT
ejpam-5586	208	4	w.m.m	w.m.m	NOUN
ejpam-5586	208	5	.	.	PUNCT
ejpam-5586	209	1	salameh	salameh	PROPN
ejpam-5586	209	2	/	/	SYM
ejpam-5586	209	3	eur	eur	PROPN
ejpam-5586	209	4	.	.	PUNCT
ejpam-5586	210	1	j.	j.	PROPN
ejpam-5586	210	2	pure	pure	PROPN
ejpam-5586	210	3	appl	appl	PROPN
ejpam-5586	210	4	.	.	PROPN
ejpam-5586	210	5	math	math	PROPN
ejpam-5586	210	6	,	,	PUNCT
ejpam-5586	210	7	18	18	NUM
ejpam-5586	210	8	(	(	PUNCT
ejpam-5586	210	9	1	1	NUM
ejpam-5586	210	10	)	)	PUNCT
ejpam-5586	210	11	(	(	PUNCT
ejpam-5586	210	12	2025	2025	NUM
ejpam-5586	210	13	)	)	PUNCT
ejpam-5586	210	14	,	,	PUNCT
ejpam-5586	210	15	5586	5586	NUM
ejpam-5586	210	16	8	8	NUM
ejpam-5586	210	17	of	of	ADP
ejpam-5586	210	18	21	21	NUM
ejpam-5586	210	19	the	the	DET
ejpam-5586	210	20	following	follow	VERB
ejpam-5586	210	21	outcome	outcome	NOUN
ejpam-5586	210	22	is	be	AUX
ejpam-5586	210	23	an	an	DET
ejpam-5586	210	24	implication	implication	NOUN
ejpam-5586	210	25	of	of	ADP
ejpam-5586	210	26	theorems	theorem	NOUN
ejpam-5586	210	27	2	2	NUM
ejpam-5586	210	28	,	,	PUNCT
ejpam-5586	210	29	3	3	NUM
ejpam-5586	210	30	,	,	PUNCT
ejpam-5586	210	31	and	and	CCONJ
ejpam-5586	210	32	corollary	corollary	ADJ
ejpam-5586	210	33	2	2	NUM
ejpam-5586	210	34	,	,	PUNCT
ejpam-5586	210	35	resulting	result	VERB
ejpam-5586	210	36	in	in	ADP
ejpam-5586	210	37	:	:	PUNCT
ejpam-5586	210	38	corollary	corollary	ADJ
ejpam-5586	210	39	5	5	NUM
ejpam-5586	210	40	.	.	PUNCT
ejpam-5586	211	1	let	let	VERB
ejpam-5586	211	2	t	t	PROPN
ejpam-5586	211	3	,	,	PUNCT
ejpam-5586	211	4	s	s	X
ejpam-5586	211	5	,	,	PUNCT
ejpam-5586	211	6	x	x	SYM
ejpam-5586	211	7	∈	∈	NOUN
ejpam-5586	211	8	mn(c	mn(c	X
ejpam-5586	211	9	)	)	PUNCT
ejpam-5586	211	10	with	with	ADP
ejpam-5586	211	11	t	t	PROPN
ejpam-5586	211	12	,	,	PUNCT
ejpam-5586	211	13	s	s	VERB
ejpam-5586	211	14	positive	positive	ADJ
ejpam-5586	211	15	definite	definite	ADJ
ejpam-5586	211	16	,	,	PUNCT
ejpam-5586	211	17	κ	κ	PROPN
ejpam-5586	211	18	∈	∈	PROPN
ejpam-5586	212	1	[	[	X
ejpam-5586	212	2	0	0	NUM
ejpam-5586	212	3	,	,	PUNCT
ejpam-5586	212	4	1	1	NUM
ejpam-5586	212	5	]	]	PUNCT
ejpam-5586	212	6	and	and	CCONJ
ejpam-5586	212	7	ψ(ϑ	ψ(ϑ	PROPN
ejpam-5586	212	8	,	,	PUNCT
ejpam-5586	212	9	κ	κ	PROPN
ejpam-5586	212	10	)	)	PUNCT
ejpam-5586	212	11	and	and	CCONJ
ejpam-5586	212	12	ϕ(ϑ	ϕ(ϑ	PROPN
ejpam-5586	212	13	,	,	PUNCT
ejpam-5586	212	14	κ	κ	NOUN
ejpam-5586	212	15	)	)	PUNCT
ejpam-5586	212	16	are	be	AUX
ejpam-5586	212	17	same	same	ADJ
ejpam-5586	212	18	as	as	SCONJ
ejpam-5586	212	19	taken	take	VERB
ejpam-5586	212	20	in	in	ADP
ejpam-5586	212	21	theorem	theorem	NOUN
ejpam-5586	212	22	(	(	PUNCT
ejpam-5586	212	23	2	2	NUM
ejpam-5586	212	24	)	)	PUNCT
ejpam-5586	212	25	and	and	CCONJ
ejpam-5586	212	26	(	(	PUNCT
ejpam-5586	212	27	3	3	X
ejpam-5586	212	28	)	)	PUNCT
ejpam-5586	212	29	respectively	respectively	ADV
ejpam-5586	212	30	.	.	PUNCT
ejpam-5586	213	1	then	then	ADV
ejpam-5586	213	2	ψ(0	ψ(0	PROPN
ejpam-5586	213	3	,	,	PUNCT
ejpam-5586	213	4	κ	κ	NOUN
ejpam-5586	213	5	)	)	PUNCT
ejpam-5586	213	6	≤	≤	NUM
ejpam-5586	213	7	1	1	NUM
ejpam-5586	213	8	2	2	NUM
ejpam-5586	213	9	ϕ(0	ϕ(0	PROPN
ejpam-5586	213	10	,	,	PUNCT
ejpam-5586	213	11	κ	κ	NOUN
ejpam-5586	213	12	)	)	PUNCT
ejpam-5586	213	13	≤	≤	NOUN
ejpam-5586	213	14	ψ(ϑ	ψ(ϑ	PROPN
ejpam-5586	213	15	,	,	PUNCT
ejpam-5586	213	16	κ	κ	NOUN
ejpam-5586	213	17	)	)	PUNCT
ejpam-5586	213	18	(	(	PUNCT
ejpam-5586	213	19	15	15	NUM
ejpam-5586	213	20	)	)	PUNCT
ejpam-5586	213	21	for	for	ADP
ejpam-5586	213	22	ϑ	ϑ	PROPN
ejpam-5586	213	23	∈	∈	PROPN
ejpam-5586	213	24	[	[	X
ejpam-5586	213	25	1/2,∞	1/2,∞	NUM
ejpam-5586	213	26	)	)	PUNCT
ejpam-5586	213	27	,	,	PUNCT
ejpam-5586	213	28	or	or	CCONJ
ejpam-5586	213	29	equivalently	equivalently	ADV
ejpam-5586	213	30	,	,	PUNCT
ejpam-5586	213	31	for	for	ADP
ejpam-5586	213	32	any	any	DET
ejpam-5586	213	33	unitarily	unitarily	ADJ
ejpam-5586	213	34	invariant	invariant	ADJ
ejpam-5586	213	35	norm	norm	NOUN
ejpam-5586	213	36	|||·|||	|||·|||	NOUN
ejpam-5586	213	37	and	and	CCONJ
ejpam-5586	213	38	2	2	NUM
ejpam-5586	213	39	<	<	X
ejpam-5586	213	40	t	t	X
ejpam-5586	213	41	≤	≤	NOUN
ejpam-5586	213	42	2,∣∣∣∣∣∣t	2,∣∣∣∣∣∣t	NUM
ejpam-5586	213	43	κxs1−κ	κxs1−κ	PROPN
ejpam-5586	213	44	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-5586	213	45	≤	≤	NUM
ejpam-5586	213	46	1	1	NUM
ejpam-5586	213	47	2	2	NUM
ejpam-5586	213	48	∣∣∣∣∣∣t	∣∣∣∣∣∣t	NOUN
ejpam-5586	213	49	κxs1−κ	κxs1−κ	VERB
ejpam-5586	213	50	+	+	PROPN
ejpam-5586	213	51	t	t	NOUN
ejpam-5586	213	52	1−κxsκ	1−κxsκ	NOUN
ejpam-5586	213	53	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-5586	213	54	≤	≤	ADV
ejpam-5586	213	55	1	1	NUM
ejpam-5586	213	56	t+	t+	NUM
ejpam-5586	213	57	2	2	NUM
ejpam-5586	213	58	∣∣∣∣∣∣tx	∣∣∣∣∣∣tx	VERB
ejpam-5586	213	59	+	+	PROPN
ejpam-5586	213	60	xs	xs	PROPN
ejpam-5586	213	61	+	+	CCONJ
ejpam-5586	213	62	tt	tt	PROPN
ejpam-5586	213	63	κxs1−κ	κxs1−κ	VERB
ejpam-5586	213	64	∣∣∣∣∣∣.	∣∣∣∣∣∣.	PROPN
ejpam-5586	213	65	remark	remark	NOUN
ejpam-5586	213	66	2	2	NUM
ejpam-5586	213	67	.	.	PUNCT
ejpam-5586	214	1	(	(	PUNCT
ejpam-5586	214	2	i	i	NOUN
ejpam-5586	214	3	)	)	PUNCT
ejpam-5586	214	4	it	it	PRON
ejpam-5586	214	5	’s	’	VERB
ejpam-5586	214	6	worth	worth	ADJ
ejpam-5586	214	7	noting	note	VERB
ejpam-5586	214	8	that	that	SCONJ
ejpam-5586	214	9	the	the	DET
ejpam-5586	214	10	corollary	corollary	NOUN
ejpam-5586	214	11	mentioned	mention	VERB
ejpam-5586	214	12	earlier	early	ADV
ejpam-5586	214	13	(	(	PUNCT
ejpam-5586	214	14	1	1	X
ejpam-5586	214	15	)	)	PUNCT
ejpam-5586	214	16	represents	represent	VERB
ejpam-5586	214	17	one	one	NUM
ejpam-5586	214	18	of	of	ADP
ejpam-5586	214	19	the	the	DET
ejpam-5586	214	20	potential	potential	ADJ
ejpam-5586	214	21	enhancements	enhancement	NOUN
ejpam-5586	214	22	to	to	ADP
ejpam-5586	214	23	an	an	DET
ejpam-5586	214	24	inequality	inequality	NOUN
ejpam-5586	214	25	introduced	introduce	VERB
ejpam-5586	214	26	by	by	ADP
ejpam-5586	214	27	kaur	kaur	PROPN
ejpam-5586	214	28	and	and	CCONJ
ejpam-5586	214	29	singh	singh	PROPN
ejpam-5586	214	30	in	in	ADP
ejpam-5586	214	31	their	their	PRON
ejpam-5586	214	32	work	work	NOUN
ejpam-5586	214	33	(	(	PUNCT
ejpam-5586	214	34	see	see	VERB
ejpam-5586	214	35	[	[	X
ejpam-5586	214	36	8	8	NUM
ejpam-5586	214	37	,	,	PUNCT
ejpam-5586	214	38	corollary	corollary	ADJ
ejpam-5586	214	39	2.4	2.4	NUM
ejpam-5586	214	40	]	]	PUNCT
ejpam-5586	214	41	)	)	PUNCT
ejpam-5586	214	42	.	.	PUNCT
ejpam-5586	215	1	(	(	PUNCT
ejpam-5586	215	2	ii	ii	NOUN
ejpam-5586	215	3	)	)	PUNCT
ejpam-5586	215	4	take	take	VERB
ejpam-5586	215	5	note	note	NOUN
ejpam-5586	215	6	that	that	SCONJ
ejpam-5586	215	7	when	when	SCONJ
ejpam-5586	215	8	we	we	PRON
ejpam-5586	215	9	set	set	VERB
ejpam-5586	215	10	κ	κ	PRON
ejpam-5586	215	11	to	to	ADP
ejpam-5586	215	12	the	the	DET
ejpam-5586	215	13	value	value	NOUN
ejpam-5586	215	14	of	of	ADP
ejpam-5586	215	15	one	one	NUM
ejpam-5586	215	16	-	-	PUNCT
ejpam-5586	215	17	third	third	NOUN
ejpam-5586	215	18	(	(	PUNCT
ejpam-5586	215	19	i.e.	i.e.	X
ejpam-5586	215	20	,	,	PUNCT
ejpam-5586	215	21	κ	κ	X
ejpam-5586	215	22	=	=	SYM
ejpam-5586	215	23	1	1	NUM
ejpam-5586	215	24	3	3	NUM
ejpam-5586	215	25	)	)	PUNCT
ejpam-5586	215	26	,	,	PUNCT
ejpam-5586	215	27	it	it	PRON
ejpam-5586	215	28	is	be	AUX
ejpam-5586	215	29	evident	evident	ADJ
ejpam-5586	215	30	that	that	SCONJ
ejpam-5586	215	31	we	we	PRON
ejpam-5586	215	32	arrive	arrive	VERB
ejpam-5586	215	33	at	at	ADP
ejpam-5586	215	34	the	the	DET
ejpam-5586	215	35	outcome	outcome	NOUN
ejpam-5586	215	36	outlined	outline	VERB
ejpam-5586	215	37	in	in	ADP
ejpam-5586	215	38	theorem	theorem	NOUN
ejpam-5586	215	39	2.10	2.10	NUM
ejpam-5586	215	40	in	in	ADP
ejpam-5586	215	41	[	[	X
ejpam-5586	215	42	8	8	NUM
ejpam-5586	215	43	]	]	PUNCT
ejpam-5586	215	44	.	.	PUNCT
ejpam-5586	216	1	this	this	PRON
ejpam-5586	216	2	implies	imply	VERB
ejpam-5586	216	3	that	that	SCONJ
ejpam-5586	216	4	our	our	PRON
ejpam-5586	216	5	finding	finding	NOUN
ejpam-5586	216	6	constitutes	constitute	VERB
ejpam-5586	216	7	a	a	DET
ejpam-5586	216	8	broader	broad	ADJ
ejpam-5586	216	9	and	and	CCONJ
ejpam-5586	216	10	more	more	ADV
ejpam-5586	216	11	generalized	generalized	ADJ
ejpam-5586	216	12	version	version	NOUN
ejpam-5586	216	13	of	of	ADP
ejpam-5586	216	14	their	their	PRON
ejpam-5586	216	15	result	result	NOUN
ejpam-5586	216	16	.	.	PUNCT
ejpam-5586	217	1	3	3	X
ejpam-5586	217	2	.	.	X
ejpam-5586	217	3	sharpening	sharpening	NOUN
ejpam-5586	217	4	of	of	ADP
ejpam-5586	217	5	the	the	DET
ejpam-5586	217	6	heinz	heinz	ADJ
ejpam-5586	217	7	inequalities	inequality	NOUN
ejpam-5586	217	8	and	and	CCONJ
ejpam-5586	217	9	its	its	PRON
ejpam-5586	217	10	reverses	reverse	NOUN
ejpam-5586	217	11	with	with	ADP
ejpam-5586	217	12	the	the	DET
ejpam-5586	217	13	kantorovich	kantorovich	PROPN
ejpam-5586	217	14	constant	constant	ADJ
ejpam-5586	217	15	in	in	ADP
ejpam-5586	217	16	this	this	DET
ejpam-5586	217	17	section	section	NOUN
ejpam-5586	217	18	,	,	PUNCT
ejpam-5586	217	19	we	we	PRON
ejpam-5586	217	20	make	make	VERB
ejpam-5586	217	21	a	a	DET
ejpam-5586	217	22	refinement	refinement	NOUN
ejpam-5586	217	23	of	of	ADP
ejpam-5586	217	24	heinz	heinz	ADJ
ejpam-5586	217	25	inequality	inequality	NOUN
ejpam-5586	217	26	with	with	ADP
ejpam-5586	217	27	the	the	DET
ejpam-5586	217	28	kantorovich	kantorovich	PROPN
ejpam-5586	217	29	constant	constant	PROPN
ejpam-5586	217	30	.	.	PUNCT
ejpam-5586	218	1	lemma	lemma	PROPN
ejpam-5586	218	2	2	2	X
ejpam-5586	218	3	.	.	PUNCT
ejpam-5586	219	1	let	let	VERB
ejpam-5586	219	2	ρ	ρ	NOUN
ejpam-5586	219	3	,	,	PUNCT
ejpam-5586	219	4	σ	σ	PROPN
ejpam-5586	219	5	>	>	X
ejpam-5586	219	6	0	0	NUM
ejpam-5586	219	7	and	and	CCONJ
ejpam-5586	219	8	0	0	NUM
ejpam-5586	219	9	≤	≤	NUM
ejpam-5586	219	10	ν	ν	ADP
ejpam-5586	219	11	<	<	X
ejpam-5586	219	12	κ	κ	X
ejpam-5586	219	13	≤	≤	NOUN
ejpam-5586	219	14	1	1	NUM
ejpam-5586	219	15	.	.	PUNCT
ejpam-5586	220	1	then	then	ADV
ejpam-5586	220	2	r	r	X
ejpam-5586	220	3	(	(	PUNCT
ejpam-5586	220	4	√	√	PROPN
ejpam-5586	220	5	ρ♯κσ	ρ♯κσ	NOUN
ejpam-5586	220	6	−	−	NOUN
ejpam-5586	220	7	√	√	PROPN
ejpam-5586	220	8	σ)2	σ)2	PROPN
ejpam-5586	221	1	+	+	PROPN
ejpam-5586	221	2	k	k	PROPN
ejpam-5586	221	3	(	(	PUNCT
ejpam-5586	221	4	√	√	NUM
ejpam-5586	221	5	h	h	NOUN
ejpam-5586	221	6	,	,	PUNCT
ejpam-5586	221	7	2)r	2)r	NUM
ejpam-5586	221	8	′	′	NUM
ejpam-5586	221	9	ρ♯νσ	ρ♯νσ	PROPN
ejpam-5586	221	10	≤	≤	X
ejpam-5586	221	11	νρ+	νρ+	NOUN
ejpam-5586	221	12	(	(	PUNCT
ejpam-5586	221	13	1−	1−	NUM
ejpam-5586	221	14	ν)σ	ν)σ	NOUN
ejpam-5586	221	15	−	−	PROPN
ejpam-5586	221	16	(	(	PUNCT
ejpam-5586	221	17	ν	ν	NOUN
ejpam-5586	221	18	κ	κ	NOUN
ejpam-5586	221	19	)	)	PUNCT
ejpam-5586	221	20	(	(	PUNCT
ejpam-5586	221	21	ρ∇κσ	ρ∇κσ	X
ejpam-5586	221	22	−	−	PROPN
ejpam-5586	221	23	ρ♯κσ	ρ♯κσ	PROPN
ejpam-5586	221	24	)	)	PUNCT
ejpam-5586	221	25	,	,	PUNCT
ejpam-5586	221	26	(	(	PUNCT
ejpam-5586	221	27	16	16	NUM
ejpam-5586	221	28	)	)	PUNCT
ejpam-5586	221	29	where	where	SCONJ
ejpam-5586	221	30	r	r	NOUN
ejpam-5586	221	31	=	=	SYM
ejpam-5586	221	32	min	min	PROPN
ejpam-5586	221	33	{	{	PUNCT
ejpam-5586	221	34	ν	ν	X
ejpam-5586	221	35	κ	κ	NOUN
ejpam-5586	221	36	,	,	PUNCT
ejpam-5586	221	37	1−	1−	NUM
ejpam-5586	221	38	ν	ν	NOUN
ejpam-5586	221	39	κ	κ	NOUN
ejpam-5586	221	40	}	}	PUNCT
ejpam-5586	221	41	,	,	PUNCT
ejpam-5586	221	42	h	h	NOUN
ejpam-5586	221	43	=	=	SYM
ejpam-5586	221	44	ρ	ρ	PROPN
ejpam-5586	221	45	σ	σ	PROPN
ejpam-5586	221	46	and	and	CCONJ
ejpam-5586	221	47	r′	r′	PROPN
ejpam-5586	221	48	=	=	SYM
ejpam-5586	221	49	min{2r	min{2r	PROPN
ejpam-5586	221	50	,	,	PUNCT
ejpam-5586	221	51	1−	1−	NUM
ejpam-5586	221	52	2r	2r	NUM
ejpam-5586	221	53	}	}	PUNCT
ejpam-5586	221	54	.	.	PUNCT
ejpam-5586	222	1	proof	proof	NOUN
ejpam-5586	222	2	.	.	PUNCT
ejpam-5586	223	1	an	an	DET
ejpam-5586	223	2	simple	simple	ADJ
ejpam-5586	223	3	argument	argument	NOUN
ejpam-5586	223	4	shows	show	VERB
ejpam-5586	223	5	that	that	PRON
ejpam-5586	223	6	νρ+	νρ+	NOUN
ejpam-5586	223	7	(	(	PUNCT
ejpam-5586	223	8	1−	1−	NUM
ejpam-5586	223	9	ν)σ	ν)σ	NOUN
ejpam-5586	223	10	−	−	PROPN
ejpam-5586	223	11	ν	ν	X
ejpam-5586	223	12	κ	κ	X
ejpam-5586	223	13	(	(	PUNCT
ejpam-5586	223	14	ρ∇κσ	ρ∇κσ	X
ejpam-5586	223	15	−	−	PROPN
ejpam-5586	223	16	ρ♯κσ	ρ♯κσ	NOUN
ejpam-5586	223	17	)	)	PUNCT
ejpam-5586	223	18	=	=	PUNCT
ejpam-5586	224	1	νρ+	νρ+	ADJ
ejpam-5586	224	2	(	(	PUNCT
ejpam-5586	224	3	1−	1−	NUM
ejpam-5586	224	4	ν)σ	ν)σ	NOUN
ejpam-5586	224	5	−	−	PROPN
ejpam-5586	224	6	ν	ν	NOUN
ejpam-5586	224	7	κ	κ	X
ejpam-5586	224	8	(	(	PUNCT
ejpam-5586	224	9	κρ+	κρ+	NOUN
ejpam-5586	224	10	(	(	PUNCT
ejpam-5586	224	11	1−	1−	NUM
ejpam-5586	224	12	κ)σ	κ)σ	PUNCT
ejpam-5586	224	13	−	−	PROPN
ejpam-5586	224	14	ρκσ1−κ	ρκσ1−κ	PROPN
ejpam-5586	224	15	)	)	PUNCT
ejpam-5586	224	16	=	=	PUNCT
ejpam-5586	225	1	ν	ν	X
ejpam-5586	225	2	κ	κ	X
ejpam-5586	225	3	ρκσ1−κ	ρκσ1−κ	PROPN
ejpam-5586	225	4	+	+	CCONJ
ejpam-5586	225	5	(	(	PUNCT
ejpam-5586	225	6	1−	1−	NUM
ejpam-5586	225	7	ν	ν	NOUN
ejpam-5586	225	8	κ	κ	PROPN
ejpam-5586	225	9	)	)	PUNCT
ejpam-5586	225	10	σ	σ	PROPN
ejpam-5586	225	11	=	=	SYM
ejpam-5586	225	12	(	(	PUNCT
ejpam-5586	225	13	ρ♯κσ)∇	ρ♯κσ)∇	PROPN
ejpam-5586	225	14	ν	ν	PROPN
ejpam-5586	225	15	κ	κ	PROPN
ejpam-5586	225	16	σ	σ	PROPN
ejpam-5586	225	17	.	.	PUNCT
ejpam-5586	226	1	(	(	PUNCT
ejpam-5586	226	2	17	17	NUM
ejpam-5586	226	3	)	)	PUNCT
ejpam-5586	226	4	by	by	ADP
ejpam-5586	226	5	applying	apply	VERB
ejpam-5586	226	6	the	the	DET
ejpam-5586	226	7	inequality	inequality	NOUN
ejpam-5586	226	8	(	(	PUNCT
ejpam-5586	226	9	6	6	NUM
ejpam-5586	226	10	)	)	PUNCT
ejpam-5586	226	11	for	for	ADP
ejpam-5586	226	12	the	the	DET
ejpam-5586	226	13	relation	relation	NOUN
ejpam-5586	226	14	(	(	PUNCT
ejpam-5586	226	15	17	17	NUM
ejpam-5586	226	16	)	)	PUNCT
ejpam-5586	226	17	,	,	PUNCT
ejpam-5586	226	18	it	it	PRON
ejpam-5586	226	19	follows	follow	VERB
ejpam-5586	226	20	that	that	SCONJ
ejpam-5586	227	1	r	r	NOUN
ejpam-5586	227	2	(	(	PUNCT
ejpam-5586	227	3	√	√	PROPN
ejpam-5586	227	4	ρ♯κσ	ρ♯κσ	NOUN
ejpam-5586	227	5	−	−	NOUN
ejpam-5586	227	6	√	√	PROPN
ejpam-5586	227	7	σ)2	σ)2	PROPN
ejpam-5586	228	1	+	+	PROPN
ejpam-5586	228	2	k	k	PROPN
ejpam-5586	228	3	(	(	PUNCT
ejpam-5586	228	4	√	√	NUM
ejpam-5586	228	5	h	h	NOUN
ejpam-5586	228	6	,	,	PUNCT
ejpam-5586	228	7	2)r	2)r	NUM
ejpam-5586	228	8	′	′	NUM
ejpam-5586	228	9	ρ♯νσ	ρ♯νσ	NOUN
ejpam-5586	228	10	≤	≤	NOUN
ejpam-5586	228	11	(	(	PUNCT
ejpam-5586	228	12	ρ♯κσ)∇	ρ♯κσ)∇	PROPN
ejpam-5586	228	13	ν	ν	PROPN
ejpam-5586	228	14	κ	κ	PROPN
ejpam-5586	228	15	σ	σ	PROPN
ejpam-5586	228	16	.	.	PUNCT
ejpam-5586	229	1	hence	hence	ADV
ejpam-5586	229	2	,	,	PUNCT
ejpam-5586	229	3	the	the	DET
ejpam-5586	229	4	inequality	inequality	NOUN
ejpam-5586	229	5	(	(	PUNCT
ejpam-5586	229	6	16	16	NUM
ejpam-5586	229	7	)	)	PUNCT
ejpam-5586	229	8	follows	follow	VERB
ejpam-5586	229	9	.	.	PUNCT
ejpam-5586	230	1	m.h.m	m.h.m	PROPN
ejpam-5586	230	2	rashid	rashid	PROPN
ejpam-5586	230	3	,	,	PUNCT
ejpam-5586	230	4	w.m.m	w.m.m	NOUN
ejpam-5586	230	5	.	.	PUNCT
ejpam-5586	231	1	salameh	salameh	PROPN
ejpam-5586	231	2	/	/	SYM
ejpam-5586	231	3	eur	eur	PROPN
ejpam-5586	231	4	.	.	PUNCT
ejpam-5586	232	1	j.	j.	PROPN
ejpam-5586	232	2	pure	pure	PROPN
ejpam-5586	232	3	appl	appl	PROPN
ejpam-5586	232	4	.	.	PROPN
ejpam-5586	232	5	math	math	PROPN
ejpam-5586	232	6	,	,	PUNCT
ejpam-5586	232	7	18	18	NUM
ejpam-5586	232	8	(	(	PUNCT
ejpam-5586	232	9	1	1	NUM
ejpam-5586	232	10	)	)	PUNCT
ejpam-5586	232	11	(	(	PUNCT
ejpam-5586	232	12	2025	2025	NUM
ejpam-5586	232	13	)	)	PUNCT
ejpam-5586	232	14	,	,	PUNCT
ejpam-5586	232	15	5586	5586	NUM
ejpam-5586	232	16	9	9	NUM
ejpam-5586	232	17	of	of	ADP
ejpam-5586	232	18	21	21	NUM
ejpam-5586	232	19	lemma	lemma	PROPN
ejpam-5586	232	20	3	3	X
ejpam-5586	232	21	.	.	PUNCT
ejpam-5586	233	1	let	let	VERB
ejpam-5586	233	2	ρ	ρ	NOUN
ejpam-5586	233	3	,	,	PUNCT
ejpam-5586	233	4	σ	σ	PROPN
ejpam-5586	233	5	>	>	X
ejpam-5586	233	6	0	0	NUM
ejpam-5586	233	7	and	and	CCONJ
ejpam-5586	233	8	0	0	NUM
ejpam-5586	233	9	≤	≤	NUM
ejpam-5586	233	10	ν	ν	ADP
ejpam-5586	233	11	<	<	X
ejpam-5586	233	12	κ	κ	X
ejpam-5586	233	13	≤	≤	NOUN
ejpam-5586	233	14	1	1	NUM
ejpam-5586	233	15	.	.	PUNCT
ejpam-5586	234	1	then	then	ADV
ejpam-5586	234	2	νρ+	νρ+	X
ejpam-5586	234	3	(	(	PUNCT
ejpam-5586	234	4	1−	1−	NUM
ejpam-5586	234	5	ν)σ	ν)σ	NOUN
ejpam-5586	234	6	−	−	PROPN
ejpam-5586	234	7	(	(	PUNCT
ejpam-5586	234	8	ν	ν	NOUN
ejpam-5586	234	9	κ	κ	NOUN
ejpam-5586	234	10	)	)	PUNCT
ejpam-5586	234	11	(	(	PUNCT
ejpam-5586	234	12	ρ∇κσ	ρ∇κσ	SYM
ejpam-5586	234	13	−	−	PROPN
ejpam-5586	234	14	ρ♯κσ	ρ♯κσ	PROPN
ejpam-5586	234	15	)	)	PUNCT
ejpam-5586	234	16	≤	≤	PUNCT
ejpam-5586	235	1	k	k	PROPN
ejpam-5586	235	2	(	(	PUNCT
ejpam-5586	235	3	√	√	PROPN
ejpam-5586	235	4	h	h	NOUN
ejpam-5586	235	5	,	,	PUNCT
ejpam-5586	235	6	2)−r′ρ♯νσ	2)−r′ρ♯νσ	PROPN
ejpam-5586	236	1	+	+	NOUN
ejpam-5586	236	2	r	r	NOUN
ejpam-5586	236	3	(	(	PUNCT
ejpam-5586	236	4	√	√	PROPN
ejpam-5586	236	5	ρ♯κσ	ρ♯κσ	NOUN
ejpam-5586	236	6	−	−	NOUN
ejpam-5586	236	7	√	√	PROPN
ejpam-5586	236	8	σ)2	σ)2	NOUN
ejpam-5586	236	9	(	(	PUNCT
ejpam-5586	236	10	18	18	NUM
ejpam-5586	236	11	)	)	PUNCT
ejpam-5586	236	12	where	where	SCONJ
ejpam-5586	236	13	r	r	NOUN
ejpam-5586	236	14	=	=	SYM
ejpam-5586	236	15	max	max	PROPN
ejpam-5586	236	16	{	{	PUNCT
ejpam-5586	236	17	ν	ν	X
ejpam-5586	236	18	κ	κ	NOUN
ejpam-5586	236	19	,	,	PUNCT
ejpam-5586	236	20	1−	1−	NUM
ejpam-5586	236	21	ν	ν	NOUN
ejpam-5586	236	22	κ	κ	NOUN
ejpam-5586	236	23	}	}	PUNCT
ejpam-5586	236	24	,	,	PUNCT
ejpam-5586	236	25	h	h	NOUN
ejpam-5586	236	26	=	=	SYM
ejpam-5586	236	27	ρ	ρ	PROPN
ejpam-5586	236	28	σ	σ	PROPN
ejpam-5586	236	29	and	and	CCONJ
ejpam-5586	236	30	r′	r′	PROPN
ejpam-5586	236	31	=	=	SYM
ejpam-5586	236	32	min{2r	min{2r	PROPN
ejpam-5586	236	33	,	,	PUNCT
ejpam-5586	236	34	1−	1−	NUM
ejpam-5586	236	35	2r	2r	NUM
ejpam-5586	236	36	}	}	PUNCT
ejpam-5586	236	37	.	.	PUNCT
ejpam-5586	237	1	proof	proof	NOUN
ejpam-5586	237	2	.	.	PUNCT
ejpam-5586	238	1	by	by	ADP
ejpam-5586	238	2	applying	apply	VERB
ejpam-5586	238	3	the	the	DET
ejpam-5586	238	4	inequality	inequality	NOUN
ejpam-5586	238	5	(	(	PUNCT
ejpam-5586	238	6	7	7	NUM
ejpam-5586	238	7	)	)	PUNCT
ejpam-5586	238	8	for	for	ADP
ejpam-5586	238	9	the	the	DET
ejpam-5586	238	10	relation	relation	NOUN
ejpam-5586	238	11	(	(	PUNCT
ejpam-5586	238	12	17	17	NUM
ejpam-5586	238	13	)	)	PUNCT
ejpam-5586	238	14	,	,	PUNCT
ejpam-5586	238	15	it	it	PRON
ejpam-5586	238	16	follows	follow	VERB
ejpam-5586	238	17	that	that	DET
ejpam-5586	238	18	νρ+	νρ+	NOUN
ejpam-5586	238	19	(	(	PUNCT
ejpam-5586	238	20	1−	1−	NUM
ejpam-5586	238	21	ν)σ	ν)σ	NOUN
ejpam-5586	238	22	−	−	PROPN
ejpam-5586	238	23	(	(	PUNCT
ejpam-5586	238	24	ν	ν	NOUN
ejpam-5586	238	25	κ	κ	NOUN
ejpam-5586	238	26	)	)	PUNCT
ejpam-5586	238	27	(	(	PUNCT
ejpam-5586	238	28	ρ∇κσ	ρ∇κσ	SYM
ejpam-5586	238	29	−	−	PROPN
ejpam-5586	238	30	ρ♯κσ	ρ♯κσ	PROPN
ejpam-5586	238	31	)	)	PUNCT
ejpam-5586	238	32	≤	≤	PUNCT
ejpam-5586	239	1	k	k	PROPN
ejpam-5586	239	2	(	(	PUNCT
ejpam-5586	239	3	√	√	PROPN
ejpam-5586	239	4	h	h	NOUN
ejpam-5586	239	5	,	,	PUNCT
ejpam-5586	239	6	2)−r′ρ♯νσ	2)−r′ρ♯νσ	PROPN
ejpam-5586	240	1	+	+	NOUN
ejpam-5586	240	2	r	r	NOUN
ejpam-5586	240	3	(	(	PUNCT
ejpam-5586	240	4	√	√	PROPN
ejpam-5586	240	5	ρ♯κσ	ρ♯κσ	PROPN
ejpam-5586	240	6	−	−	PROPN
ejpam-5586	240	7	√	√	PROPN
ejpam-5586	240	8	σ)2	σ)2	PROPN
ejpam-5586	240	9	.	.	PUNCT
ejpam-5586	241	1	so	so	ADV
ejpam-5586	241	2	,	,	PUNCT
ejpam-5586	241	3	we	we	PRON
ejpam-5586	241	4	get	get	VERB
ejpam-5586	241	5	the	the	DET
ejpam-5586	241	6	inequality	inequality	NOUN
ejpam-5586	241	7	(	(	PUNCT
ejpam-5586	241	8	18	18	NUM
ejpam-5586	241	9	)	)	PUNCT
ejpam-5586	241	10	.	.	PUNCT
ejpam-5586	242	1	for	for	ADP
ejpam-5586	242	2	two	two	NUM
ejpam-5586	242	3	non	non	ADJ
ejpam-5586	242	4	-	-	ADJ
ejpam-5586	242	5	negative	negative	ADJ
ejpam-5586	242	6	real	real	ADJ
ejpam-5586	242	7	numbers	number	NOUN
ejpam-5586	242	8	ρ	ρ	PROPN
ejpam-5586	242	9	and	and	CCONJ
ejpam-5586	242	10	σ	σ	PROPN
ejpam-5586	242	11	,	,	PUNCT
ejpam-5586	242	12	we	we	PRON
ejpam-5586	242	13	define	define	VERB
ejpam-5586	242	14	the	the	DET
ejpam-5586	242	15	heinz	heinz	ADJ
ejpam-5586	242	16	mean	mean	NOUN
ejpam-5586	242	17	in	in	ADP
ejpam-5586	242	18	the	the	DET
ejpam-5586	242	19	parameter	parameter	NOUN
ejpam-5586	242	20	µ	µ	NOUN
ejpam-5586	242	21	,	,	PUNCT
ejpam-5586	242	22	0	0	NUM
ejpam-5586	242	23	≤	≤	NUM
ejpam-5586	243	1	µ	µ	X
ejpam-5586	243	2	≤	≤	NUM
ejpam-5586	243	3	1	1	NUM
ejpam-5586	243	4	,	,	PUNCT
ejpam-5586	243	5	as	as	ADP
ejpam-5586	243	6	hµ	hµ	NOUN
ejpam-5586	243	7	=	=	SYM
ejpam-5586	243	8	ρµσ1−µ	ρµσ1−µ	PROPN
ejpam-5586	243	9	+	+	NUM
ejpam-5586	243	10	ρ1−µσµ	ρ1−µσµ	X
ejpam-5586	243	11	2	2	NUM
ejpam-5586	243	12	.	.	PUNCT
ejpam-5586	244	1	(	(	PUNCT
ejpam-5586	244	2	19	19	NUM
ejpam-5586	244	3	)	)	PUNCT
ejpam-5586	244	4	note	note	NOUN
ejpam-5586	244	5	that	that	SCONJ
ejpam-5586	244	6	h0(ρ	h0(ρ	PROPN
ejpam-5586	244	7	,	,	PUNCT
ejpam-5586	244	8	σ	σ	PROPN
ejpam-5586	244	9	)	)	PUNCT
ejpam-5586	244	10	=	=	SYM
ejpam-5586	244	11	h1(ρ	h1(ρ	PROPN
ejpam-5586	244	12	,	,	PUNCT
ejpam-5586	244	13	σ	σ	NOUN
ejpam-5586	244	14	)	)	PUNCT
ejpam-5586	244	15	=	=	NOUN
ejpam-5586	245	1	ρ+σ	ρ+σ	NUM
ejpam-5586	245	2	2	2	NUM
ejpam-5586	245	3	and	and	CCONJ
ejpam-5586	245	4	h	h	NOUN
ejpam-5586	245	5	1	1	NUM
ejpam-5586	245	6	2	2	NUM
ejpam-5586	245	7	(	(	PUNCT
ejpam-5586	245	8	ρ	ρ	PROPN
ejpam-5586	245	9	,	,	PUNCT
ejpam-5586	245	10	σ	σ	NOUN
ejpam-5586	245	11	)	)	PUNCT
ejpam-5586	245	12	=	=	PUNCT
ejpam-5586	246	1	√	√	NUM
ejpam-5586	246	2	ρσ	ρσ	NOUN
ejpam-5586	246	3	.	.	PUNCT
ejpam-5586	247	1	it	it	PRON
ejpam-5586	247	2	is	be	AUX
ejpam-5586	247	3	easy	easy	ADJ
ejpam-5586	247	4	to	to	PART
ejpam-5586	247	5	see	see	VERB
ejpam-5586	247	6	that	that	PRON
ejpam-5586	247	7	as	as	ADP
ejpam-5586	247	8	a	a	DET
ejpam-5586	247	9	function	function	NOUN
ejpam-5586	247	10	of	of	ADP
ejpam-5586	247	11	µ	µ	NOUN
ejpam-5586	247	12	,	,	PUNCT
ejpam-5586	247	13	hµ(ρ	hµ(ρ	NOUN
ejpam-5586	247	14	,	,	PUNCT
ejpam-5586	247	15	σ	σ	PROPN
ejpam-5586	247	16	)	)	PUNCT
ejpam-5586	247	17	is	be	AUX
ejpam-5586	247	18	convex	convex	PROPN
ejpam-5586	247	19	,	,	PUNCT
ejpam-5586	247	20	attains	attain	VERB
ejpam-5586	247	21	its	its	PRON
ejpam-5586	247	22	minimum	minimum	NOUN
ejpam-5586	247	23	at	at	ADP
ejpam-5586	247	24	µ	µ	NOUN
ejpam-5586	247	25	=	=	SYM
ejpam-5586	247	26	1	1	NUM
ejpam-5586	247	27	2	2	NUM
ejpam-5586	247	28	,	,	PUNCT
ejpam-5586	247	29	and	and	CCONJ
ejpam-5586	247	30	attains	attain	VERB
ejpam-5586	247	31	its	its	PRON
ejpam-5586	247	32	maximum	maximum	NOUN
ejpam-5586	247	33	at	at	ADP
ejpam-5586	247	34	µ	µ	NOUN
ejpam-5586	247	35	=	=	SYM
ejpam-5586	247	36	0	0	NUM
ejpam-5586	247	37	and	and	CCONJ
ejpam-5586	247	38	µ	µ	X
ejpam-5586	248	1	=	=	SYM
ejpam-5586	248	2	1	1	X
ejpam-5586	248	3	.	.	PUNCT
ejpam-5586	249	1	moreover	moreover	ADV
ejpam-5586	249	2	,	,	PUNCT
ejpam-5586	249	3	hµ(ρ	hµ(ρ	PROPN
ejpam-5586	249	4	,	,	PUNCT
ejpam-5586	249	5	σ	σ	PROPN
ejpam-5586	249	6	)	)	PUNCT
ejpam-5586	249	7	=	=	SYM
ejpam-5586	249	8	h1−µ(ρ	h1−µ(ρ	NOUN
ejpam-5586	249	9	,	,	PUNCT
ejpam-5586	249	10	σ	σ	PROPN
ejpam-5586	249	11	)	)	PUNCT
ejpam-5586	249	12	for	for	ADP
ejpam-5586	249	13	0	0	NUM
ejpam-5586	249	14	≤	≤	NUM
ejpam-5586	249	15	µ	µ	X
ejpam-5586	249	16	≤	≤	NUM
ejpam-5586	249	17	1	1	NUM
ejpam-5586	249	18	.	.	PUNCT
ejpam-5586	250	1	thus	thus	ADV
ejpam-5586	250	2	,	,	PUNCT
ejpam-5586	250	3	the	the	DET
ejpam-5586	250	4	heinz	heinz	ADJ
ejpam-5586	250	5	mean	mean	NOUN
ejpam-5586	250	6	interpolates	interpolate	VERB
ejpam-5586	250	7	between	between	ADP
ejpam-5586	250	8	the	the	DET
ejpam-5586	250	9	geometric	geometric	ADJ
ejpam-5586	250	10	mean	mean	NOUN
ejpam-5586	250	11	and	and	CCONJ
ejpam-5586	250	12	the	the	DET
ejpam-5586	250	13	arithmetic	arithmetic	ADJ
ejpam-5586	250	14	mean	mean	NOUN
ejpam-5586	250	15	:	:	PUNCT
ejpam-5586	250	16	√	√	X
ejpam-5586	250	17	ρσ	ρσ	ADP
ejpam-5586	250	18	≤	≤	NUM
ejpam-5586	250	19	hµ(ρ	hµ(ρ	PROPN
ejpam-5586	250	20	,	,	PUNCT
ejpam-5586	250	21	σ	σ	PROPN
ejpam-5586	250	22	)	)	PUNCT
ejpam-5586	250	23	≤	≤	NOUN
ejpam-5586	250	24	ρ+	ρ+	NUM
ejpam-5586	250	25	σ	σ	X
ejpam-5586	250	26	2	2	NUM
ejpam-5586	250	27	for	for	ADP
ejpam-5586	250	28	0	0	NUM
ejpam-5586	250	29	≤	≤	NOUN
ejpam-5586	250	30	µ	µ	X
ejpam-5586	250	31	≤	≤	NUM
ejpam-5586	250	32	1	1	NUM
ejpam-5586	250	33	.	.	PUNCT
ejpam-5586	251	1	(	(	PUNCT
ejpam-5586	251	2	20	20	NUM
ejpam-5586	251	3	)	)	PUNCT
ejpam-5586	251	4	theorem	theorem	NOUN
ejpam-5586	251	5	4	4	NUM
ejpam-5586	251	6	.	.	PUNCT
ejpam-5586	252	1	let	let	VERB
ejpam-5586	252	2	ρ	ρ	NOUN
ejpam-5586	252	3	,	,	PUNCT
ejpam-5586	252	4	σ	σ	PROPN
ejpam-5586	252	5	>	>	X
ejpam-5586	252	6	0	0	NUM
ejpam-5586	252	7	and	and	CCONJ
ejpam-5586	252	8	0	0	NUM
ejpam-5586	252	9	≤	≤	NUM
ejpam-5586	252	10	ν	ν	ADP
ejpam-5586	252	11	<	<	X
ejpam-5586	252	12	κ	κ	X
ejpam-5586	252	13	≤	≤	NOUN
ejpam-5586	252	14	1	1	NUM
ejpam-5586	252	15	.	.	PUNCT
ejpam-5586	253	1	then	then	ADV
ejpam-5586	253	2	r	r	X
ejpam-5586	253	3	[	[	PUNCT
ejpam-5586	253	4	hκ(ρ	hκ(ρ	PROPN
ejpam-5586	253	5	,	,	PUNCT
ejpam-5586	253	6	σ	σ	PROPN
ejpam-5586	253	7	)	)	PUNCT
ejpam-5586	253	8	+	+	PROPN
ejpam-5586	253	9	h0(ρ	h0(ρ	PROPN
ejpam-5586	253	10	,	,	PUNCT
ejpam-5586	253	11	σ)−hκ	σ)−hκ	PROPN
ejpam-5586	253	12	2	2	NUM
ejpam-5586	253	13	(	(	PUNCT
ejpam-5586	253	14	ρ	ρ	PROPN
ejpam-5586	253	15	,	,	PUNCT
ejpam-5586	253	16	σ	σ	PROPN
ejpam-5586	253	17	)	)	PUNCT
ejpam-5586	253	18	]	]	PUNCT
ejpam-5586	254	1	+	+	PUNCT
ejpam-5586	254	2	k	k	X
ejpam-5586	254	3	[	[	X
ejpam-5586	254	4	√	√	NUM
ejpam-5586	254	5	h	h	NOUN
ejpam-5586	254	6	,	,	PUNCT
ejpam-5586	254	7	2	2	NUM
ejpam-5586	254	8	]	]	SYM
ejpam-5586	254	9	r′	r′	NUM
ejpam-5586	254	10	hν(ρ	hν(ρ	NOUN
ejpam-5586	254	11	,	,	PUNCT
ejpam-5586	254	12	σ	σ	NOUN
ejpam-5586	254	13	)	)	PUNCT
ejpam-5586	254	14	≤	≤	PUNCT
ejpam-5586	254	15	h0(ρ	h0(ρ	PROPN
ejpam-5586	254	16	,	,	PUNCT
ejpam-5586	254	17	σ)−	σ)−	PROPN
ejpam-5586	254	18	(	(	PUNCT
ejpam-5586	254	19	ν	ν	PROPN
ejpam-5586	254	20	κ	κ	PROPN
ejpam-5586	254	21	)	)	PUNCT
ejpam-5586	255	1	[	[	X
ejpam-5586	255	2	h0(ρ	h0(ρ	PROPN
ejpam-5586	255	3	,	,	PUNCT
ejpam-5586	255	4	σ)−hκ(ρ	σ)−hκ(ρ	PROPN
ejpam-5586	255	5	,	,	PUNCT
ejpam-5586	255	6	σ	σ	PROPN
ejpam-5586	255	7	)	)	PUNCT
ejpam-5586	255	8	]	]	PUNCT
ejpam-5586	255	9	,	,	PUNCT
ejpam-5586	255	10	(	(	PUNCT
ejpam-5586	255	11	21	21	NUM
ejpam-5586	255	12	)	)	PUNCT
ejpam-5586	255	13	where	where	SCONJ
ejpam-5586	255	14	r	r	NOUN
ejpam-5586	255	15	=	=	SYM
ejpam-5586	255	16	min	min	PROPN
ejpam-5586	255	17	{	{	PUNCT
ejpam-5586	255	18	ν	ν	X
ejpam-5586	255	19	κ	κ	NOUN
ejpam-5586	255	20	,	,	PUNCT
ejpam-5586	255	21	1−	1−	NUM
ejpam-5586	255	22	ν	ν	NOUN
ejpam-5586	255	23	κ	κ	NOUN
ejpam-5586	255	24	}	}	PUNCT
ejpam-5586	255	25	,	,	PUNCT
ejpam-5586	255	26	h	h	NOUN
ejpam-5586	255	27	=	=	SYM
ejpam-5586	255	28	ρ	ρ	PROPN
ejpam-5586	255	29	σ	σ	PROPN
ejpam-5586	255	30	and	and	CCONJ
ejpam-5586	255	31	r′	r′	PROPN
ejpam-5586	255	32	=	=	SYM
ejpam-5586	255	33	min{2r	min{2r	PROPN
ejpam-5586	255	34	,	,	PUNCT
ejpam-5586	255	35	1−	1−	NUM
ejpam-5586	255	36	2r	2r	NUM
ejpam-5586	255	37	}	}	PUNCT
ejpam-5586	255	38	.	.	PUNCT
ejpam-5586	256	1	proof	proof	NOUN
ejpam-5586	256	2	.	.	PUNCT
ejpam-5586	257	1	interchanging	interchange	VERB
ejpam-5586	257	2	ρ	ρ	PROPN
ejpam-5586	257	3	with	with	ADP
ejpam-5586	257	4	σ	σ	PROPN
ejpam-5586	257	5	and	and	CCONJ
ejpam-5586	257	6	σ	σ	PROPN
ejpam-5586	257	7	with	with	ADP
ejpam-5586	257	8	ρ	ρ	PROPN
ejpam-5586	257	9	in	in	ADP
ejpam-5586	257	10	inequality	inequality	NOUN
ejpam-5586	257	11	(	(	PUNCT
ejpam-5586	257	12	16	16	NUM
ejpam-5586	257	13	)	)	PUNCT
ejpam-5586	257	14	,	,	PUNCT
ejpam-5586	257	15	we	we	PRON
ejpam-5586	257	16	get	get	VERB
ejpam-5586	257	17	r	r	NOUN
ejpam-5586	257	18	(	(	PUNCT
ejpam-5586	257	19	√	√	NUM
ejpam-5586	257	20	σ♯κρ−	σ♯κρ−	VERB
ejpam-5586	257	21	√	√	VERB
ejpam-5586	257	22	ρ)2	ρ)2	NOUN
ejpam-5586	258	1	+	+	PROPN
ejpam-5586	258	2	k	k	PROPN
ejpam-5586	258	3	(	(	PUNCT
ejpam-5586	258	4	√	√	NUM
ejpam-5586	258	5	h	h	NOUN
ejpam-5586	258	6	,	,	PUNCT
ejpam-5586	258	7	2)r	2)r	NUM
ejpam-5586	258	8	′	′	NUM
ejpam-5586	258	9	σ♯νρ	σ♯νρ	PROPN
ejpam-5586	258	10	≤	≤	NUM
ejpam-5586	258	11	νσ	νσ	VERB
ejpam-5586	258	12	+	+	CCONJ
ejpam-5586	258	13	(	(	PUNCT
ejpam-5586	258	14	1−	1−	NUM
ejpam-5586	258	15	ν)ρ−	ν)ρ−	NOUN
ejpam-5586	258	16	(	(	PUNCT
ejpam-5586	258	17	ν	ν	NOUN
ejpam-5586	258	18	κ	κ	PROPN
ejpam-5586	258	19	)	)	PUNCT
ejpam-5586	258	20	(	(	PUNCT
ejpam-5586	258	21	σ∇κρ−	σ∇κρ−	PROPN
ejpam-5586	258	22	σ♯κρ	σ♯κρ	NOUN
ejpam-5586	258	23	)	)	PUNCT
ejpam-5586	258	24	.	.	PUNCT
ejpam-5586	259	1	(	(	PUNCT
ejpam-5586	259	2	22	22	X
ejpam-5586	259	3	)	)	PUNCT
ejpam-5586	259	4	adding	add	VERB
ejpam-5586	259	5	(	(	PUNCT
ejpam-5586	259	6	16	16	NUM
ejpam-5586	259	7	)	)	PUNCT
ejpam-5586	259	8	and	and	CCONJ
ejpam-5586	259	9	(	(	PUNCT
ejpam-5586	259	10	22	22	NUM
ejpam-5586	259	11	)	)	PUNCT
ejpam-5586	259	12	,	,	PUNCT
ejpam-5586	259	13	we	we	PRON
ejpam-5586	259	14	have	have	VERB
ejpam-5586	259	15	r	r	NOUN
ejpam-5586	259	16	[	[	PUNCT
ejpam-5586	259	17	(	(	PUNCT
ejpam-5586	259	18	√	√	NUM
ejpam-5586	259	19	ρ♯κσ	ρ♯κσ	NOUN
ejpam-5586	259	20	−	−	NOUN
ejpam-5586	259	21	√	√	PROPN
ejpam-5586	259	22	σ)2	σ)2	NOUN
ejpam-5586	259	23	+	+	CCONJ
ejpam-5586	259	24	(	(	PUNCT
ejpam-5586	259	25	√	√	NUM
ejpam-5586	259	26	σ♯κρ−	σ♯κρ−	VERB
ejpam-5586	259	27	√	√	VERB
ejpam-5586	259	28	ρ)2	ρ)2	NOUN
ejpam-5586	259	29	]	]	PUNCT
ejpam-5586	260	1	+	+	PUNCT
ejpam-5586	260	2	k	k	X
ejpam-5586	260	3	[	[	X
ejpam-5586	260	4	√	√	NUM
ejpam-5586	260	5	h	h	NOUN
ejpam-5586	260	6	,	,	PUNCT
ejpam-5586	260	7	2	2	NUM
ejpam-5586	260	8	]	]	SYM
ejpam-5586	260	9	r′	r′	X
ejpam-5586	260	10	(	(	PUNCT
ejpam-5586	260	11	2hν(ρ	2hν(ρ	NUM
ejpam-5586	260	12	,	,	PUNCT
ejpam-5586	260	13	σ	σ	PROPN
ejpam-5586	260	14	)	)	PUNCT
ejpam-5586	260	15	)	)	PUNCT
ejpam-5586	260	16	≤	≤	NUM
ejpam-5586	260	17	2h0(ρ	2h0(ρ	PROPN
ejpam-5586	260	18	,	,	PUNCT
ejpam-5586	260	19	σ)−	σ)−	PROPN
ejpam-5586	260	20	(	(	PUNCT
ejpam-5586	260	21	ν	ν	PROPN
ejpam-5586	260	22	κ	κ	PROPN
ejpam-5586	260	23	)	)	PUNCT
ejpam-5586	261	1	[	[	X
ejpam-5586	261	2	2h0(ρ	2h0(ρ	PROPN
ejpam-5586	261	3	,	,	PUNCT
ejpam-5586	261	4	σ)−	σ)−	PROPN
ejpam-5586	261	5	2hκ(ρ	2hκ(ρ	NUM
ejpam-5586	261	6	,	,	PUNCT
ejpam-5586	261	7	σ	σ	PROPN
ejpam-5586	261	8	)	)	PUNCT
ejpam-5586	261	9	]	]	PUNCT
ejpam-5586	261	10	and	and	CCONJ
ejpam-5586	261	11	so	so	ADV
ejpam-5586	261	12	r	r	NOUN
ejpam-5586	261	13	[	[	PUNCT
ejpam-5586	261	14	hκ(ρ	hκ(ρ	PROPN
ejpam-5586	261	15	,	,	PUNCT
ejpam-5586	261	16	σ	σ	PROPN
ejpam-5586	261	17	)	)	PUNCT
ejpam-5586	261	18	+	+	PROPN
ejpam-5586	261	19	h0(ρ	h0(ρ	PROPN
ejpam-5586	261	20	,	,	PUNCT
ejpam-5586	261	21	σ)−hκ	σ)−hκ	PROPN
ejpam-5586	261	22	2	2	NUM
ejpam-5586	261	23	(	(	PUNCT
ejpam-5586	261	24	ρ	ρ	PROPN
ejpam-5586	261	25	,	,	PUNCT
ejpam-5586	261	26	σ	σ	PROPN
ejpam-5586	261	27	)	)	PUNCT
ejpam-5586	261	28	]	]	PUNCT
ejpam-5586	262	1	+	+	PUNCT
ejpam-5586	262	2	k	k	X
ejpam-5586	262	3	[	[	X
ejpam-5586	262	4	√	√	NUM
ejpam-5586	262	5	h	h	NOUN
ejpam-5586	262	6	,	,	PUNCT
ejpam-5586	262	7	2	2	NUM
ejpam-5586	262	8	]	]	SYM
ejpam-5586	262	9	r′	r′	NUM
ejpam-5586	262	10	hν(ρ	hν(ρ	NOUN
ejpam-5586	262	11	,	,	PUNCT
ejpam-5586	262	12	σ	σ	NOUN
ejpam-5586	262	13	)	)	PUNCT
ejpam-5586	262	14	≤	≤	PUNCT
ejpam-5586	262	15	h0(ρ	h0(ρ	PROPN
ejpam-5586	262	16	,	,	PUNCT
ejpam-5586	262	17	σ)−	σ)−	PROPN
ejpam-5586	262	18	(	(	PUNCT
ejpam-5586	262	19	ν	ν	PROPN
ejpam-5586	262	20	κ	κ	PROPN
ejpam-5586	262	21	)	)	PUNCT
ejpam-5586	263	1	[	[	X
ejpam-5586	263	2	h0(ρ	h0(ρ	PROPN
ejpam-5586	263	3	,	,	PUNCT
ejpam-5586	263	4	σ)−hκ(ρ	σ)−hκ(ρ	PROPN
ejpam-5586	263	5	,	,	PUNCT
ejpam-5586	263	6	σ	σ	PROPN
ejpam-5586	263	7	)	)	PUNCT
ejpam-5586	263	8	]	]	PUNCT
ejpam-5586	263	9	.	.	PUNCT
ejpam-5586	264	1	in	in	ADP
ejpam-5586	264	2	similar	similar	ADJ
ejpam-5586	264	3	of	of	ADP
ejpam-5586	264	4	proof	proof	NOUN
ejpam-5586	264	5	of	of	ADP
ejpam-5586	264	6	theorem	theorem	ADJ
ejpam-5586	264	7	4	4	NUM
ejpam-5586	264	8	,	,	PUNCT
ejpam-5586	264	9	we	we	PRON
ejpam-5586	264	10	can	can	AUX
ejpam-5586	264	11	prove	prove	VERB
ejpam-5586	264	12	the	the	DET
ejpam-5586	264	13	following	follow	VERB
ejpam-5586	264	14	result	result	NOUN
ejpam-5586	264	15	.	.	PUNCT
ejpam-5586	265	1	m.h.m	m.h.m	PROPN
ejpam-5586	265	2	rashid	rashid	PROPN
ejpam-5586	265	3	,	,	PUNCT
ejpam-5586	265	4	w.m.m	w.m.m	NOUN
ejpam-5586	265	5	.	.	PUNCT
ejpam-5586	266	1	salameh	salameh	PROPN
ejpam-5586	266	2	/	/	SYM
ejpam-5586	266	3	eur	eur	PROPN
ejpam-5586	266	4	.	.	PUNCT
ejpam-5586	267	1	j.	j.	PROPN
ejpam-5586	267	2	pure	pure	PROPN
ejpam-5586	267	3	appl	appl	PROPN
ejpam-5586	267	4	.	.	PROPN
ejpam-5586	267	5	math	math	PROPN
ejpam-5586	267	6	,	,	PUNCT
ejpam-5586	267	7	18	18	NUM
ejpam-5586	267	8	(	(	PUNCT
ejpam-5586	267	9	1	1	NUM
ejpam-5586	267	10	)	)	PUNCT
ejpam-5586	267	11	(	(	PUNCT
ejpam-5586	267	12	2025	2025	NUM
ejpam-5586	267	13	)	)	PUNCT
ejpam-5586	267	14	,	,	PUNCT
ejpam-5586	267	15	5586	5586	NUM
ejpam-5586	267	16	10	10	NUM
ejpam-5586	267	17	of	of	ADP
ejpam-5586	267	18	21	21	NUM
ejpam-5586	267	19	theorem	theorem	NOUN
ejpam-5586	267	20	5	5	NUM
ejpam-5586	267	21	.	.	PUNCT
ejpam-5586	268	1	let	let	VERB
ejpam-5586	268	2	ρ	ρ	NOUN
ejpam-5586	268	3	,	,	PUNCT
ejpam-5586	268	4	σ	σ	PROPN
ejpam-5586	268	5	>	>	X
ejpam-5586	268	6	0	0	NUM
ejpam-5586	268	7	and	and	CCONJ
ejpam-5586	268	8	0	0	NUM
ejpam-5586	268	9	≤	≤	NUM
ejpam-5586	268	10	ν	ν	ADP
ejpam-5586	268	11	<	<	X
ejpam-5586	268	12	κ	κ	X
ejpam-5586	268	13	≤	≤	NOUN
ejpam-5586	268	14	1	1	NUM
ejpam-5586	268	15	.	.	PUNCT
ejpam-5586	269	1	then	then	ADV
ejpam-5586	269	2	h0(ρ	h0(ρ	PROPN
ejpam-5586	269	3	,	,	PUNCT
ejpam-5586	269	4	σ)−	σ)−	PROPN
ejpam-5586	269	5	(	(	PUNCT
ejpam-5586	269	6	ν	ν	PROPN
ejpam-5586	269	7	κ	κ	PROPN
ejpam-5586	269	8	)	)	PUNCT
ejpam-5586	270	1	[	[	X
ejpam-5586	270	2	h0(ρ	h0(ρ	PROPN
ejpam-5586	270	3	,	,	PUNCT
ejpam-5586	270	4	σ)−hκ(ρ	σ)−hκ(ρ	PROPN
ejpam-5586	270	5	,	,	PUNCT
ejpam-5586	270	6	σ	σ	PROPN
ejpam-5586	270	7	)	)	PUNCT
ejpam-5586	270	8	]	]	PUNCT
ejpam-5586	271	1	≤	≤	NUM
ejpam-5586	271	2	k	k	X
ejpam-5586	272	1	[	[	X
ejpam-5586	272	2	√	√	NUM
ejpam-5586	272	3	h	h	NOUN
ejpam-5586	272	4	,	,	PUNCT
ejpam-5586	272	5	2	2	NUM
ejpam-5586	272	6	]	]	SYM
ejpam-5586	272	7	−r′	−r′	PROPN
ejpam-5586	272	8	hν(ρ	hν(ρ	PROPN
ejpam-5586	272	9	,	,	PUNCT
ejpam-5586	272	10	σ	σ	X
ejpam-5586	272	11	)	)	PUNCT
ejpam-5586	273	1	+	+	NOUN
ejpam-5586	273	2	r	r	NOUN
ejpam-5586	273	3	[	[	PUNCT
ejpam-5586	273	4	hκ(ρ	hκ(ρ	NUM
ejpam-5586	273	5	,	,	PUNCT
ejpam-5586	273	6	σ	σ	PROPN
ejpam-5586	273	7	)	)	PUNCT
ejpam-5586	273	8	+	+	PROPN
ejpam-5586	273	9	h0(ρ	h0(ρ	PROPN
ejpam-5586	273	10	,	,	PUNCT
ejpam-5586	273	11	σ)−hκ	σ)−hκ	PROPN
ejpam-5586	273	12	2	2	NUM
ejpam-5586	273	13	(	(	PUNCT
ejpam-5586	273	14	ρ	ρ	PROPN
ejpam-5586	273	15	,	,	PUNCT
ejpam-5586	273	16	σ	σ	PROPN
ejpam-5586	273	17	)	)	PUNCT
ejpam-5586	273	18	]	]	PUNCT
ejpam-5586	273	19	,	,	PUNCT
ejpam-5586	273	20	(	(	PUNCT
ejpam-5586	273	21	23	23	NUM
ejpam-5586	273	22	)	)	PUNCT
ejpam-5586	273	23	where	where	SCONJ
ejpam-5586	273	24	r	r	NOUN
ejpam-5586	273	25	=	=	SYM
ejpam-5586	273	26	min	min	PROPN
ejpam-5586	273	27	{	{	PUNCT
ejpam-5586	273	28	ν	ν	X
ejpam-5586	273	29	κ	κ	NOUN
ejpam-5586	273	30	,	,	PUNCT
ejpam-5586	273	31	1−	1−	NUM
ejpam-5586	273	32	ν	ν	NOUN
ejpam-5586	273	33	κ	κ	NOUN
ejpam-5586	273	34	}	}	PUNCT
ejpam-5586	273	35	,	,	PUNCT
ejpam-5586	273	36	h	h	NOUN
ejpam-5586	273	37	=	=	SYM
ejpam-5586	273	38	ρ	ρ	PROPN
ejpam-5586	273	39	σ	σ	PROPN
ejpam-5586	273	40	and	and	CCONJ
ejpam-5586	273	41	r′	r′	PROPN
ejpam-5586	273	42	=	=	SYM
ejpam-5586	273	43	min{2r	min{2r	PROPN
ejpam-5586	273	44	,	,	PUNCT
ejpam-5586	273	45	1−	1−	NUM
ejpam-5586	273	46	2r	2r	NUM
ejpam-5586	273	47	}	}	PUNCT
ejpam-5586	273	48	.	.	PUNCT
ejpam-5586	274	1	4	4	X
ejpam-5586	274	2	.	.	X
ejpam-5586	274	3	new	new	ADJ
ejpam-5586	274	4	operator	operator	NOUN
ejpam-5586	274	5	versions	version	NOUN
ejpam-5586	274	6	of	of	ADP
ejpam-5586	274	7	heinz	heinz	ADJ
ejpam-5586	274	8	-	-	PUNCT
ejpam-5586	274	9	type	type	NOUN
ejpam-5586	274	10	inequalities	inequality	NOUN
ejpam-5586	274	11	let	let	VERB
ejpam-5586	274	12	h	h	NOUN
ejpam-5586	274	13	represent	represent	VERB
ejpam-5586	274	14	a	a	DET
ejpam-5586	274	15	complex	complex	ADJ
ejpam-5586	274	16	hilbert	hilbert	NOUN
ejpam-5586	274	17	space	space	NOUN
ejpam-5586	274	18	,	,	PUNCT
ejpam-5586	274	19	and	and	CCONJ
ejpam-5586	274	20	b(h	b(h	PROPN
ejpam-5586	274	21	)	)	PUNCT
ejpam-5586	274	22	denote	denote	VERB
ejpam-5586	274	23	the	the	DET
ejpam-5586	274	24	c∗-algebra	c∗-algebra	NOUN
ejpam-5586	274	25	comprising	comprise	VERB
ejpam-5586	274	26	all	all	DET
ejpam-5586	274	27	bounded	bounded	ADJ
ejpam-5586	274	28	linear	linear	PROPN
ejpam-5586	274	29	operators	operator	NOUN
ejpam-5586	274	30	on	on	ADP
ejpam-5586	274	31	h.	h.	PROPN
ejpam-5586	274	32	an	an	DET
ejpam-5586	274	33	operator	operator	NOUN
ejpam-5586	274	34	t	t	PROPN
ejpam-5586	274	35	∈	∈	PROPN
ejpam-5586	274	36	b(h	b(h	PROPN
ejpam-5586	274	37	)	)	PUNCT
ejpam-5586	274	38	is	be	AUX
ejpam-5586	274	39	considered	consider	VERB
ejpam-5586	274	40	positive	positive	ADJ
ejpam-5586	274	41	if	if	SCONJ
ejpam-5586	274	42	⟨tx	⟨tx	PROPN
ejpam-5586	274	43	,	,	PUNCT
ejpam-5586	274	44	x⟩	x⟩	PUNCT
ejpam-5586	274	45	≥	≥	X
ejpam-5586	274	46	0	0	NUM
ejpam-5586	274	47	holds	hold	VERB
ejpam-5586	274	48	true	true	ADJ
ejpam-5586	274	49	for	for	ADP
ejpam-5586	274	50	every	every	DET
ejpam-5586	274	51	x	x	PROPN
ejpam-5586	274	52	∈	∈	PROPN
ejpam-5586	274	53	h.	h.	NOUN
ejpam-5586	274	54	we	we	PRON
ejpam-5586	274	55	express	express	VERB
ejpam-5586	274	56	this	this	PRON
ejpam-5586	274	57	as	as	ADP
ejpam-5586	274	58	t	t	PROPN
ejpam-5586	274	59	≥	≥	NOUN
ejpam-5586	274	60	0	0	NUM
ejpam-5586	274	61	.	.	PUNCT
ejpam-5586	275	1	now	now	ADV
ejpam-5586	275	2	,	,	PUNCT
ejpam-5586	275	3	let	let	VERB
ejpam-5586	275	4	t	t	NOUN
ejpam-5586	275	5	and	and	CCONJ
ejpam-5586	275	6	s	s	AUX
ejpam-5586	275	7	be	be	AUX
ejpam-5586	275	8	two	two	NUM
ejpam-5586	275	9	positive	positive	ADJ
ejpam-5586	275	10	operators	operator	NOUN
ejpam-5586	275	11	in	in	ADP
ejpam-5586	275	12	b(h	b(h	PROPN
ejpam-5586	275	13	)	)	PUNCT
ejpam-5586	275	14	,	,	PUNCT
ejpam-5586	275	15	and	and	CCONJ
ejpam-5586	275	16	κ	κ	X
ejpam-5586	275	17	take	take	VERB
ejpam-5586	275	18	on	on	ADP
ejpam-5586	275	19	values	value	NOUN
ejpam-5586	275	20	in	in	ADP
ejpam-5586	275	21	the	the	DET
ejpam-5586	275	22	interval	interval	NOUN
ejpam-5586	275	23	[	[	X
ejpam-5586	275	24	0	0	NUM
ejpam-5586	275	25	,	,	PUNCT
ejpam-5586	275	26	1	1	NUM
ejpam-5586	275	27	]	]	PUNCT
ejpam-5586	275	28	.	.	PUNCT
ejpam-5586	276	1	the	the	DET
ejpam-5586	276	2	κ	κ	NOUN
ejpam-5586	276	3	-	-	PUNCT
ejpam-5586	276	4	weighted	weight	VERB
ejpam-5586	276	5	arithmetic	arithmetic	ADJ
ejpam-5586	276	6	mean	mean	NOUN
ejpam-5586	276	7	of	of	ADP
ejpam-5586	276	8	t	t	PROPN
ejpam-5586	276	9	and	and	CCONJ
ejpam-5586	276	10	s	s	PROPN
ejpam-5586	276	11	,	,	PUNCT
ejpam-5586	276	12	denoted	denote	VERB
ejpam-5586	276	13	as	as	ADP
ejpam-5586	276	14	t∇κs	t∇κs	NOUN
ejpam-5586	276	15	,	,	PUNCT
ejpam-5586	276	16	is	be	AUX
ejpam-5586	276	17	defined	define	VERB
ejpam-5586	276	18	as	as	ADP
ejpam-5586	276	19	:	:	PUNCT
ejpam-5586	276	20	t∇κs	t∇κs	X
ejpam-5586	276	21	=	=	SYM
ejpam-5586	276	22	(	(	PUNCT
ejpam-5586	276	23	1−	1−	NUM
ejpam-5586	276	24	κ)t	κ)t	ADJ
ejpam-5586	276	25	+	+	CCONJ
ejpam-5586	276	26	κs	κs	NOUN
ejpam-5586	276	27	.	.	PUNCT
ejpam-5586	277	1	when	when	SCONJ
ejpam-5586	277	2	t	t	PROPN
ejpam-5586	277	3	is	be	AUX
ejpam-5586	277	4	invertible	invertible	ADJ
ejpam-5586	277	5	,	,	PUNCT
ejpam-5586	277	6	the	the	DET
ejpam-5586	277	7	κ	κ	NOUN
ejpam-5586	277	8	-	-	ADJ
ejpam-5586	277	9	geometric	geometric	ADJ
ejpam-5586	277	10	mean	mean	NOUN
ejpam-5586	277	11	of	of	ADP
ejpam-5586	277	12	t	t	PROPN
ejpam-5586	277	13	and	and	CCONJ
ejpam-5586	277	14	s	s	PROPN
ejpam-5586	277	15	,	,	PUNCT
ejpam-5586	277	16	represented	represent	VERB
ejpam-5586	277	17	as	as	ADP
ejpam-5586	277	18	t♯κs	t♯κs	ADJ
ejpam-5586	277	19	,	,	PUNCT
ejpam-5586	277	20	is	be	AUX
ejpam-5586	277	21	defined	define	VERB
ejpam-5586	277	22	as	as	ADP
ejpam-5586	277	23	:	:	PUNCT
ejpam-5586	277	24	t♯κs	t♯κs	PROPN
ejpam-5586	277	25	=	=	SYM
ejpam-5586	277	26	t	t	PROPN
ejpam-5586	277	27	1	1	NUM
ejpam-5586	277	28	2	2	NUM
ejpam-5586	277	29	(	(	PUNCT
ejpam-5586	277	30	t−	t−	PROPN
ejpam-5586	277	31	1	1	NUM
ejpam-5586	277	32	2st−	2st−	NUM
ejpam-5586	277	33	1	1	NUM
ejpam-5586	277	34	2	2	NUM
ejpam-5586	277	35	)	)	PUNCT
ejpam-5586	277	36	κ	κ	PROPN
ejpam-5586	277	37	t	t	PROPN
ejpam-5586	277	38	1	1	NUM
ejpam-5586	277	39	2	2	NUM
ejpam-5586	277	40	.	.	PUNCT
ejpam-5586	278	1	in	in	ADP
ejpam-5586	278	2	the	the	DET
ejpam-5586	278	3	case	case	NOUN
ejpam-5586	278	4	where	where	SCONJ
ejpam-5586	278	5	κ	κ	NOUN
ejpam-5586	278	6	=	=	NOUN
ejpam-5586	278	7	1	1	NUM
ejpam-5586	278	8	2	2	NUM
ejpam-5586	278	9	,	,	PUNCT
ejpam-5586	278	10	we	we	PRON
ejpam-5586	278	11	can	can	AUX
ejpam-5586	278	12	simplify	simplify	VERB
ejpam-5586	278	13	the	the	DET
ejpam-5586	278	14	notation	notation	NOUN
ejpam-5586	278	15	to	to	ADP
ejpam-5586	278	16	t∇s	t∇s	NUM
ejpam-5586	278	17	and	and	CCONJ
ejpam-5586	278	18	t♯s	t♯s	NUM
ejpam-5586	278	19	to	to	PART
ejpam-5586	278	20	refer	refer	VERB
ejpam-5586	278	21	to	to	ADP
ejpam-5586	278	22	the	the	DET
ejpam-5586	278	23	κ	κ	NOUN
ejpam-5586	278	24	-	-	PUNCT
ejpam-5586	278	25	weighted	weight	VERB
ejpam-5586	278	26	arithmetic	arithmetic	ADJ
ejpam-5586	278	27	mean	mean	NOUN
ejpam-5586	278	28	and	and	CCONJ
ejpam-5586	278	29	the	the	DET
ejpam-5586	278	30	κ	κ	NOUN
ejpam-5586	278	31	-	-	PUNCT
ejpam-5586	278	32	geometric	geometric	ADJ
ejpam-5586	278	33	mean	mean	NOUN
ejpam-5586	278	34	,	,	PUNCT
ejpam-5586	278	35	respectively	respectively	ADV
ejpam-5586	278	36	.	.	PUNCT
ejpam-5586	279	1	it	it	PRON
ejpam-5586	279	2	is	be	AUX
ejpam-5586	279	3	well	well	ADV
ejpam-5586	279	4	-	-	PUNCT
ejpam-5586	279	5	known	know	VERB
ejpam-5586	279	6	that	that	SCONJ
ejpam-5586	279	7	for	for	ADP
ejpam-5586	279	8	positive	positive	ADJ
ejpam-5586	279	9	invertible	invertible	ADJ
ejpam-5586	279	10	operators	operator	NOUN
ejpam-5586	279	11	t	t	PROPN
ejpam-5586	279	12	and	and	CCONJ
ejpam-5586	279	13	s	s	PROPN
ejpam-5586	279	14	,	,	PUNCT
ejpam-5586	279	15	the	the	DET
ejpam-5586	279	16	following	follow	VERB
ejpam-5586	279	17	inequality	inequality	NOUN
ejpam-5586	279	18	holds	hold	VERB
ejpam-5586	279	19	:	:	PUNCT
ejpam-5586	279	20	t♯κs	t♯κs	ADJ
ejpam-5586	279	21	≤	≤	NOUN
ejpam-5586	279	22	t∇κs	t∇κs	VERB
ejpam-5586	279	23	,	,	PUNCT
ejpam-5586	279	24	κ	κ	PROPN
ejpam-5586	279	25	∈	∈	PROPN
ejpam-5586	280	1	[	[	X
ejpam-5586	280	2	0	0	NUM
ejpam-5586	280	3	,	,	PUNCT
ejpam-5586	280	4	1	1	NUM
ejpam-5586	280	5	]	]	PUNCT
ejpam-5586	280	6	.	.	PUNCT
ejpam-5586	281	1	additionally	additionally	ADV
ejpam-5586	281	2	,	,	PUNCT
ejpam-5586	281	3	we	we	PRON
ejpam-5586	281	4	define	define	VERB
ejpam-5586	281	5	the	the	DET
ejpam-5586	281	6	operator	operator	NOUN
ejpam-5586	281	7	version	version	NOUN
ejpam-5586	281	8	of	of	ADP
ejpam-5586	281	9	the	the	DET
ejpam-5586	281	10	heinz	heinz	ADJ
ejpam-5586	281	11	mean	mean	NOUN
ejpam-5586	281	12	as	as	ADP
ejpam-5586	281	13	hκ(t	hκ(t	X
ejpam-5586	281	14	,	,	PUNCT
ejpam-5586	281	15	s	s	PART
ejpam-5586	281	16	):	):	PUNCT
ejpam-5586	281	17	hκ(t	hκ(t	X
ejpam-5586	281	18	,	,	PUNCT
ejpam-5586	281	19	s	s	X
ejpam-5586	281	20	)	)	PUNCT
ejpam-5586	281	21	=	=	SYM
ejpam-5586	282	1	t♯κs	t♯κs	NOUN
ejpam-5586	283	1	+	+	CCONJ
ejpam-5586	283	2	t♯1−κs	t♯1−κs	NOUN
ejpam-5586	283	3	2	2	NUM
ejpam-5586	283	4	for	for	ADP
ejpam-5586	283	5	the	the	DET
ejpam-5586	283	6	case	case	NOUN
ejpam-5586	283	7	where	where	SCONJ
ejpam-5586	283	8	t	t	NOUN
ejpam-5586	283	9	and	and	CCONJ
ejpam-5586	283	10	s	s	VERB
ejpam-5586	283	11	are	be	AUX
ejpam-5586	283	12	positive	positive	ADJ
ejpam-5586	283	13	invertible	invertible	ADJ
ejpam-5586	283	14	operators	operator	NOUN
ejpam-5586	283	15	and	and	CCONJ
ejpam-5586	283	16	κ	κ	PRON
ejpam-5586	283	17	∈	∈	PROPN
ejpam-5586	284	1	[	[	X
ejpam-5586	284	2	0	0	NUM
ejpam-5586	284	3	,	,	PUNCT
ejpam-5586	284	4	1	1	NUM
ejpam-5586	284	5	]	]	PUNCT
ejpam-5586	284	6	.	.	PUNCT
ejpam-5586	285	1	in	in	ADP
ejpam-5586	285	2	this	this	DET
ejpam-5586	285	3	section	section	NOUN
ejpam-5586	285	4	,	,	PUNCT
ejpam-5586	285	5	we	we	PRON
ejpam-5586	285	6	will	will	AUX
ejpam-5586	285	7	present	present	VERB
ejpam-5586	285	8	improved	improved	ADJ
ejpam-5586	285	9	variants	variant	NOUN
ejpam-5586	285	10	of	of	ADP
ejpam-5586	285	11	heinz	heinz	ADJ
ejpam-5586	285	12	-	-	PUNCT
ejpam-5586	285	13	type	type	NOUN
ejpam-5586	285	14	operator	operator	NOUN
ejpam-5586	285	15	inequalities	inequality	NOUN
ejpam-5586	285	16	and	and	CCONJ
ejpam-5586	285	17	their	their	PRON
ejpam-5586	285	18	converses	converse	NOUN
ejpam-5586	285	19	,	,	PUNCT
ejpam-5586	285	20	exploiting	exploit	VERB
ejpam-5586	285	21	the	the	DET
ejpam-5586	285	22	monotonicity	monotonicity	NOUN
ejpam-5586	285	23	of	of	ADP
ejpam-5586	285	24	operator	operator	NOUN
ejpam-5586	285	25	functions	function	NOUN
ejpam-5586	285	26	as	as	ADP
ejpam-5586	285	27	the	the	DET
ejpam-5586	285	28	foundational	foundational	ADJ
ejpam-5586	285	29	concept	concept	NOUN
ejpam-5586	285	30	for	for	ADP
ejpam-5586	285	31	the	the	DET
ejpam-5586	285	32	ensuing	ensue	VERB
ejpam-5586	285	33	discussion	discussion	NOUN
ejpam-5586	285	34	.	.	PUNCT
ejpam-5586	286	1	lemma	lemma	PROPN
ejpam-5586	286	2	4	4	NUM
ejpam-5586	286	3	.	.	PUNCT
ejpam-5586	287	1	[	[	X
ejpam-5586	287	2	7	7	X
ejpam-5586	287	3	]	]	PUNCT
ejpam-5586	287	4	suppose	suppose	VERB
ejpam-5586	287	5	t	t	PROPN
ejpam-5586	287	6	∈	∈	PROPN
ejpam-5586	287	7	b(h	b(h	PROPN
ejpam-5586	287	8	)	)	PUNCT
ejpam-5586	287	9	is	be	AUX
ejpam-5586	287	10	self	self	NOUN
ejpam-5586	287	11	-	-	PUNCT
ejpam-5586	287	12	adjoint	adjoint	NOUN
ejpam-5586	287	13	.	.	PUNCT
ejpam-5586	288	1	if	if	SCONJ
ejpam-5586	288	2	f	f	PROPN
ejpam-5586	288	3	and	and	CCONJ
ejpam-5586	288	4	g	g	PROPN
ejpam-5586	288	5	are	be	AUX
ejpam-5586	288	6	continuous	continuous	ADJ
ejpam-5586	288	7	functions	function	NOUN
ejpam-5586	288	8	such	such	ADJ
ejpam-5586	288	9	that	that	SCONJ
ejpam-5586	288	10	f(t	f(t	NOUN
ejpam-5586	288	11	)	)	PUNCT
ejpam-5586	288	12	≥	≥	NOUN
ejpam-5586	288	13	g(t	g(t	PROPN
ejpam-5586	288	14	)	)	PUNCT
ejpam-5586	288	15	for	for	ADP
ejpam-5586	288	16	t	t	PROPN
ejpam-5586	288	17	∈	∈	PROPN
ejpam-5586	288	18	sp(t	sp(t	PUNCT
ejpam-5586	288	19	)	)	PUNCT
ejpam-5586	288	20	(	(	PUNCT
ejpam-5586	288	21	where	where	SCONJ
ejpam-5586	288	22	sp(t	sp(t	PUNCT
ejpam-5586	288	23	)	)	PUNCT
ejpam-5586	288	24	represents	represent	VERB
ejpam-5586	288	25	the	the	DET
ejpam-5586	288	26	spectrum	spectrum	NOUN
ejpam-5586	288	27	of	of	ADP
ejpam-5586	288	28	the	the	DET
ejpam-5586	288	29	operator	operator	NOUN
ejpam-5586	288	30	t	t	PROPN
ejpam-5586	288	31	)	)	PUNCT
ejpam-5586	288	32	,	,	PUNCT
ejpam-5586	288	33	then	then	ADV
ejpam-5586	288	34	it	it	PRON
ejpam-5586	288	35	follows	follow	VERB
ejpam-5586	288	36	that	that	SCONJ
ejpam-5586	288	37	f(t	f(t	PROPN
ejpam-5586	288	38	)	)	PUNCT
ejpam-5586	288	39	≥	≥	PROPN
ejpam-5586	288	40	g(t	g(t	PROPN
ejpam-5586	288	41	)	)	PUNCT
ejpam-5586	288	42	.	.	PUNCT
ejpam-5586	289	1	next	next	ADV
ejpam-5586	289	2	,	,	PUNCT
ejpam-5586	289	3	we	we	PRON
ejpam-5586	289	4	present	present	VERB
ejpam-5586	289	5	our	our	PRON
ejpam-5586	289	6	main	main	ADJ
ejpam-5586	289	7	results	result	NOUN
ejpam-5586	289	8	on	on	ADP
ejpam-5586	289	9	the	the	DET
ejpam-5586	289	10	basis	basis	NOUN
ejpam-5586	289	11	of	of	ADP
ejpam-5586	289	12	inequality	inequality	NOUN
ejpam-5586	289	13	(	(	PUNCT
ejpam-5586	289	14	21	21	NUM
ejpam-5586	289	15	)	)	PUNCT
ejpam-5586	289	16	.	.	PUNCT
ejpam-5586	290	1	by	by	ADP
ejpam-5586	290	2	lemma	lemma	PROPN
ejpam-5586	290	3	4	4	NUM
ejpam-5586	290	4	,	,	PUNCT
ejpam-5586	290	5	we	we	PRON
ejpam-5586	290	6	have	have	VERB
ejpam-5586	290	7	the	the	DET
ejpam-5586	290	8	following	following	NOUN
ejpam-5586	290	9	.	.	PUNCT
ejpam-5586	291	1	m.h.m	m.h.m	PROPN
ejpam-5586	291	2	rashid	rashid	PROPN
ejpam-5586	291	3	,	,	PUNCT
ejpam-5586	291	4	w.m.m	w.m.m	NOUN
ejpam-5586	291	5	.	.	PUNCT
ejpam-5586	292	1	salameh	salameh	PROPN
ejpam-5586	292	2	/	/	SYM
ejpam-5586	292	3	eur	eur	PROPN
ejpam-5586	292	4	.	.	PUNCT
ejpam-5586	293	1	j.	j.	PROPN
ejpam-5586	293	2	pure	pure	PROPN
ejpam-5586	293	3	appl	appl	PROPN
ejpam-5586	293	4	.	.	PROPN
ejpam-5586	293	5	math	math	PROPN
ejpam-5586	293	6	,	,	PUNCT
ejpam-5586	293	7	18	18	NUM
ejpam-5586	293	8	(	(	PUNCT
ejpam-5586	293	9	1	1	NUM
ejpam-5586	293	10	)	)	PUNCT
ejpam-5586	293	11	(	(	PUNCT
ejpam-5586	293	12	2025	2025	NUM
ejpam-5586	293	13	)	)	PUNCT
ejpam-5586	293	14	,	,	PUNCT
ejpam-5586	293	15	5586	5586	NUM
ejpam-5586	293	16	11	11	NUM
ejpam-5586	293	17	of	of	ADP
ejpam-5586	293	18	21	21	NUM
ejpam-5586	293	19	theorem	theorem	NOUN
ejpam-5586	293	20	6	6	NUM
ejpam-5586	293	21	.	.	PUNCT
ejpam-5586	294	1	let	let	AUX
ejpam-5586	294	2	t	t	PROPN
ejpam-5586	294	3	,	,	PUNCT
ejpam-5586	294	4	s	s	PART
ejpam-5586	294	5	∈	∈	PROPN
ejpam-5586	294	6	b(h	b(h	PROPN
ejpam-5586	294	7	)	)	PUNCT
ejpam-5586	294	8	be	be	VERB
ejpam-5586	294	9	positive	positive	ADJ
ejpam-5586	294	10	invertible	invertible	ADJ
ejpam-5586	294	11	operators	operator	NOUN
ejpam-5586	294	12	,	,	PUNCT
ejpam-5586	294	13	i	i	PRON
ejpam-5586	294	14	is	be	AUX
ejpam-5586	294	15	the	the	DET
ejpam-5586	294	16	identity	identity	NOUN
ejpam-5586	294	17	operator	operator	NOUN
ejpam-5586	294	18	and	and	CCONJ
ejpam-5586	294	19	0	0	NUM
ejpam-5586	294	20	≤	≤	NUM
ejpam-5586	294	21	ν	ν	ADP
ejpam-5586	294	22	<	<	X
ejpam-5586	294	23	κ	κ	X
ejpam-5586	294	24	≤	≤	NOUN
ejpam-5586	294	25	1	1	NUM
ejpam-5586	294	26	.	.	PUNCT
ejpam-5586	295	1	if	if	SCONJ
ejpam-5586	295	2	all	all	DET
ejpam-5586	295	3	positive	positive	ADJ
ejpam-5586	295	4	numbers	number	NOUN
ejpam-5586	295	5	m	m	ADP
ejpam-5586	295	6	,	,	PUNCT
ejpam-5586	295	7	m′	m′	ADJ
ejpam-5586	295	8	andm	andm	X
ejpam-5586	295	9	,	,	PUNCT
ejpam-5586	295	10	m	m	VERB
ejpam-5586	295	11	′	′	NUM
ejpam-5586	295	12	satisfy	satisfy	NOUN
ejpam-5586	295	13	either	either	ADV
ejpam-5586	295	14	of	of	ADP
ejpam-5586	295	15	the	the	DET
ejpam-5586	295	16	conditions	condition	NOUN
ejpam-5586	295	17	0	0	PUNCT
ejpam-5586	295	18	<	<	X
ejpam-5586	295	19	mi	mi	PROPN
ejpam-5586	295	20	≤	≤	PROPN
ejpam-5586	295	21	t	t	PROPN
ejpam-5586	295	22	≤	≤	NUM
ejpam-5586	295	23	m′i	m′i	NOUN
ejpam-5586	295	24	<	<	X
ejpam-5586	295	25	m	m	VERB
ejpam-5586	295	26	′i	′i	NOUN
ejpam-5586	295	27	≤	≤	NUM
ejpam-5586	295	28	s	s	PART
ejpam-5586	295	29	≤mi	≤mi	NOUN
ejpam-5586	295	30	or	or	CCONJ
ejpam-5586	295	31	0	0	NUM
ejpam-5586	295	32	<	<	X
ejpam-5586	295	33	mi	mi	PROPN
ejpam-5586	296	1	≤	≤	PROPN
ejpam-5586	296	2	s	s	PART
ejpam-5586	296	3	≤	≤	NUM
ejpam-5586	296	4	m′i	m′i	NOUN
ejpam-5586	296	5	≤	≤	NUM
ejpam-5586	296	6	t	t	PROPN
ejpam-5586	296	7	≤mi	≤mi	PROPN
ejpam-5586	296	8	,	,	PUNCT
ejpam-5586	296	9	then	then	ADV
ejpam-5586	296	10	:	:	PUNCT
ejpam-5586	296	11	r	r	NOUN
ejpam-5586	296	12	[	[	PUNCT
ejpam-5586	296	13	hκ(t	hκ(t	X
ejpam-5586	296	14	,	,	PUNCT
ejpam-5586	296	15	s	s	X
ejpam-5586	296	16	)	)	PUNCT
ejpam-5586	297	1	+	+	NOUN
ejpam-5586	297	2	h0(t	h0(t	PROPN
ejpam-5586	297	3	,	,	PUNCT
ejpam-5586	297	4	s)−hκ	s)−hκ	PROPN
ejpam-5586	297	5	2	2	NUM
ejpam-5586	297	6	(	(	PUNCT
ejpam-5586	297	7	t	t	PROPN
ejpam-5586	297	8	,	,	PUNCT
ejpam-5586	297	9	s	s	PROPN
ejpam-5586	297	10	)	)	PUNCT
ejpam-5586	297	11	]	]	PUNCT
ejpam-5586	298	1	+	+	PUNCT
ejpam-5586	298	2	k	k	X
ejpam-5586	299	1	[	[	X
ejpam-5586	299	2	√	√	NUM
ejpam-5586	299	3	h	h	NOUN
ejpam-5586	299	4	,	,	PUNCT
ejpam-5586	299	5	2	2	NUM
ejpam-5586	299	6	]	]	SYM
ejpam-5586	299	7	r′	r′	NOUN
ejpam-5586	299	8	hν(t	hν(t	NOUN
ejpam-5586	299	9	,	,	PUNCT
ejpam-5586	299	10	s	s	X
ejpam-5586	299	11	)	)	PUNCT
ejpam-5586	299	12	≤	≤	NOUN
ejpam-5586	299	13	h0(t	h0(t	PROPN
ejpam-5586	299	14	,	,	PUNCT
ejpam-5586	299	15	s)−	s)−	PROPN
ejpam-5586	299	16	(	(	PUNCT
ejpam-5586	299	17	ν	ν	X
ejpam-5586	299	18	κ	κ	NOUN
ejpam-5586	299	19	)	)	PUNCT
ejpam-5586	300	1	[	[	X
ejpam-5586	300	2	h0(t	h0(t	X
ejpam-5586	300	3	,	,	PUNCT
ejpam-5586	300	4	s)−hκ(t	s)−hκ(t	PROPN
ejpam-5586	300	5	,	,	PUNCT
ejpam-5586	300	6	s	s	PART
ejpam-5586	300	7	)	)	PUNCT
ejpam-5586	300	8	]	]	PUNCT
ejpam-5586	300	9	,	,	PUNCT
ejpam-5586	300	10	(	(	PUNCT
ejpam-5586	300	11	24	24	NUM
ejpam-5586	300	12	)	)	PUNCT
ejpam-5586	301	1	where	where	SCONJ
ejpam-5586	301	2	r	r	NOUN
ejpam-5586	301	3	=	=	SYM
ejpam-5586	301	4	min	min	PROPN
ejpam-5586	301	5	{	{	PUNCT
ejpam-5586	301	6	ν	ν	X
ejpam-5586	301	7	κ	κ	NOUN
ejpam-5586	301	8	,	,	PUNCT
ejpam-5586	301	9	1−	1−	NUM
ejpam-5586	301	10	ν	ν	NOUN
ejpam-5586	301	11	κ	κ	NOUN
ejpam-5586	301	12	}	}	PUNCT
ejpam-5586	301	13	,	,	PUNCT
ejpam-5586	301	14	h	h	NOUN
ejpam-5586	302	1	=	=	NOUN
ejpam-5586	302	2	m	m	VERB
ejpam-5586	302	3	m	m	VERB
ejpam-5586	302	4	and	and	CCONJ
ejpam-5586	302	5	r′	r′	PROPN
ejpam-5586	302	6	=	=	SYM
ejpam-5586	302	7	min{2r	min{2r	PROPN
ejpam-5586	302	8	,	,	PUNCT
ejpam-5586	302	9	1−	1−	NUM
ejpam-5586	302	10	2r	2r	NUM
ejpam-5586	302	11	}	}	PUNCT
ejpam-5586	302	12	.	.	PUNCT
ejpam-5586	303	1	proof	proof	NOUN
ejpam-5586	303	2	.	.	PUNCT
ejpam-5586	304	1	assuming	assume	VERB
ejpam-5586	304	2	that	that	SCONJ
ejpam-5586	304	3	0	0	NUM
ejpam-5586	304	4	≤	≤	NUM
ejpam-5586	304	5	ν	ν	ADP
ejpam-5586	304	6	<	<	X
ejpam-5586	304	7	κ	κ	X
ejpam-5586	304	8	≤	≤	NUM
ejpam-5586	304	9	1	1	NUM
ejpam-5586	304	10	,	,	PUNCT
ejpam-5586	304	11	according	accord	VERB
ejpam-5586	304	12	to	to	ADP
ejpam-5586	304	13	inequality	inequality	NOUN
ejpam-5586	304	14	(	(	PUNCT
ejpam-5586	304	15	21	21	NUM
ejpam-5586	304	16	)	)	PUNCT
ejpam-5586	304	17	,	,	PUNCT
ejpam-5586	304	18	for	for	ADP
ejpam-5586	304	19	any	any	DET
ejpam-5586	304	20	positive	positive	ADJ
ejpam-5586	304	21	value	value	NOUN
ejpam-5586	304	22	of	of	ADP
ejpam-5586	304	23	x	x	PRON
ejpam-5586	304	24	,	,	PUNCT
ejpam-5586	304	25	we	we	PRON
ejpam-5586	304	26	can	can	AUX
ejpam-5586	304	27	conclude	conclude	VERB
ejpam-5586	304	28	:	:	PUNCT
ejpam-5586	305	1	r	r	X
ejpam-5586	305	2	[	[	PUNCT
ejpam-5586	305	3	hκ(1	hκ(1	PROPN
ejpam-5586	305	4	,	,	PUNCT
ejpam-5586	305	5	x	x	X
ejpam-5586	305	6	)	)	PUNCT
ejpam-5586	306	1	+	+	SYM
ejpam-5586	306	2	h0(1	h0(1	PROPN
ejpam-5586	306	3	,	,	PUNCT
ejpam-5586	306	4	x)−hκ	x)−hκ	PROPN
ejpam-5586	306	5	2	2	NUM
ejpam-5586	306	6	(	(	PUNCT
ejpam-5586	306	7	1	1	NUM
ejpam-5586	306	8	,	,	PUNCT
ejpam-5586	306	9	x	x	NOUN
ejpam-5586	306	10	)	)	PUNCT
ejpam-5586	306	11	]	]	PUNCT
ejpam-5586	307	1	+	+	PUNCT
ejpam-5586	307	2	k	k	X
ejpam-5586	307	3	[	[	X
ejpam-5586	307	4	√	√	NUM
ejpam-5586	307	5	h	h	NOUN
ejpam-5586	307	6	,	,	PUNCT
ejpam-5586	307	7	2	2	NUM
ejpam-5586	307	8	]	]	SYM
ejpam-5586	307	9	r′	r′	X
ejpam-5586	307	10	hν(1	hν(1	PROPN
ejpam-5586	307	11	,	,	PUNCT
ejpam-5586	307	12	x	x	NOUN
ejpam-5586	307	13	)	)	PUNCT
ejpam-5586	307	14	≤	≤	PUNCT
ejpam-5586	307	15	h0(1	h0(1	PROPN
ejpam-5586	307	16	,	,	PUNCT
ejpam-5586	307	17	x)−	x)−	PROPN
ejpam-5586	307	18	(	(	PUNCT
ejpam-5586	307	19	ν	ν	NOUN
ejpam-5586	307	20	κ	κ	NOUN
ejpam-5586	307	21	)	)	PUNCT
ejpam-5586	308	1	[	[	X
ejpam-5586	308	2	h0(1	h0(1	PROPN
ejpam-5586	308	3	,	,	PUNCT
ejpam-5586	308	4	x)−hκ(1	x)−hκ(1	PROPN
ejpam-5586	308	5	,	,	PUNCT
ejpam-5586	308	6	x	x	NOUN
ejpam-5586	308	7	)	)	PUNCT
ejpam-5586	308	8	]	]	PUNCT
ejpam-5586	308	9	,	,	PUNCT
ejpam-5586	308	10	regarding	regard	VERB
ejpam-5586	308	11	the	the	DET
ejpam-5586	308	12	operator	operator	NOUN
ejpam-5586	308	13	x	x	PUNCT
ejpam-5586	308	14	=	=	SYM
ejpam-5586	308	15	t−1/2st−1/2	t−1/2st−1/2	PROPN
ejpam-5586	308	16	,	,	PUNCT
ejpam-5586	308	17	within	within	ADP
ejpam-5586	308	18	the	the	DET
ejpam-5586	308	19	framework	framework	NOUN
ejpam-5586	308	20	of	of	ADP
ejpam-5586	308	21	the	the	DET
ejpam-5586	308	22	first	first	ADJ
ejpam-5586	308	23	condition	condition	NOUN
ejpam-5586	308	24	,	,	PUNCT
ejpam-5586	308	25	we	we	PRON
ejpam-5586	308	26	establish	establish	VERB
ejpam-5586	308	27	the	the	DET
ejpam-5586	308	28	following	following	ADJ
ejpam-5586	308	29	range	range	NOUN
ejpam-5586	308	30	:	:	PUNCT
ejpam-5586	308	31	i	i	PRON
ejpam-5586	308	32	≤	≤	PUNCT
ejpam-5586	308	33	hi	hi	INTJ
ejpam-5586	309	1	=	=	VERB
ejpam-5586	309	2	m	m	VERB
ejpam-5586	309	3	m	m	VERB
ejpam-5586	309	4	i	i	PRON
ejpam-5586	309	5	≤	≤	NUM
ejpam-5586	309	6	x	x	PUNCT
ejpam-5586	309	7	≤	≤	NUM
ejpam-5586	309	8	h′i	h′i	PROPN
ejpam-5586	310	1	=	=	PUNCT
ejpam-5586	310	2	m	m	VERB
ejpam-5586	310	3	′	′	NUM
ejpam-5586	310	4	m′	m′	PROPN
ejpam-5586	310	5	i.	i.	NOUN
ejpam-5586	310	6	consequently	consequently	ADV
ejpam-5586	310	7	,	,	PUNCT
ejpam-5586	310	8	we	we	PRON
ejpam-5586	310	9	infer	infer	VERB
ejpam-5586	310	10	that	that	SCONJ
ejpam-5586	310	11	σ(x	σ(x	NOUN
ejpam-5586	310	12	)	)	PUNCT
ejpam-5586	310	13	⊆	⊆	NUM
ejpam-5586	310	14	[	[	X
ejpam-5586	310	15	h	h	NOUN
ejpam-5586	310	16	,	,	PUNCT
ejpam-5586	310	17	h′	h′	PROPN
ejpam-5586	310	18	]	]	PUNCT
ejpam-5586	310	19	⊆	⊆	NUM
ejpam-5586	310	20	(	(	PUNCT
ejpam-5586	310	21	1,∞	1,∞	NUM
ejpam-5586	310	22	)	)	PUNCT
ejpam-5586	310	23	.	.	PUNCT
ejpam-5586	311	1	applying	apply	VERB
ejpam-5586	311	2	lemma	lemma	PROPN
ejpam-5586	311	3	4	4	NUM
ejpam-5586	311	4	,	,	PUNCT
ejpam-5586	311	5	we	we	PRON
ejpam-5586	311	6	obtain	obtain	VERB
ejpam-5586	311	7	:	:	PUNCT
ejpam-5586	311	8	r	r	NOUN
ejpam-5586	311	9	[	[	PUNCT
ejpam-5586	311	10	hκ(i	hκ(i	NOUN
ejpam-5586	311	11	,	,	PUNCT
ejpam-5586	311	12	x	x	X
ejpam-5586	311	13	)	)	PUNCT
ejpam-5586	312	1	+	+	ADJ
ejpam-5586	312	2	h0(i	h0(i	ADJ
ejpam-5586	312	3	,	,	PUNCT
ejpam-5586	312	4	x)−hκ	x)−hκ	PROPN
ejpam-5586	312	5	2	2	NUM
ejpam-5586	312	6	(	(	PUNCT
ejpam-5586	312	7	i	i	NOUN
ejpam-5586	312	8	,	,	PUNCT
ejpam-5586	312	9	x	x	X
ejpam-5586	312	10	)	)	PUNCT
ejpam-5586	312	11	]	]	PUNCT
ejpam-5586	313	1	+	+	CCONJ
ejpam-5586	313	2	min	min	PROPN
ejpam-5586	313	3	h≤x≤h′	h≤x≤h′	PROPN
ejpam-5586	313	4	k	k	PROPN
ejpam-5586	314	1	[	[	X
ejpam-5586	314	2	√	√	NUM
ejpam-5586	314	3	x	x	SYM
ejpam-5586	314	4	,	,	PUNCT
ejpam-5586	314	5	2	2	NUM
ejpam-5586	314	6	]	]	SYM
ejpam-5586	314	7	r′	r′	NOUN
ejpam-5586	314	8	hν(i	hν(i	NOUN
ejpam-5586	314	9	,	,	PUNCT
ejpam-5586	314	10	x	x	NOUN
ejpam-5586	314	11	)	)	PUNCT
ejpam-5586	314	12	≤	≤	NOUN
ejpam-5586	315	1	h0(i	h0(i	PROPN
ejpam-5586	315	2	,	,	PUNCT
ejpam-5586	315	3	x)−	x)−	PROPN
ejpam-5586	315	4	(	(	PUNCT
ejpam-5586	315	5	ν	ν	NOUN
ejpam-5586	315	6	κ	κ	NOUN
ejpam-5586	315	7	)	)	PUNCT
ejpam-5586	316	1	[	[	X
ejpam-5586	316	2	h0(i	h0(i	X
ejpam-5586	316	3	,	,	PUNCT
ejpam-5586	316	4	x)−hκ(i	x)−hκ(i	PROPN
ejpam-5586	316	5	,	,	PUNCT
ejpam-5586	316	6	x	x	NOUN
ejpam-5586	316	7	)	)	PUNCT
ejpam-5586	316	8	]	]	PUNCT
ejpam-5586	316	9	,	,	PUNCT
ejpam-5586	316	10	as	as	SCONJ
ejpam-5586	316	11	the	the	DET
ejpam-5586	316	12	kantorovich	kantorovich	PROPN
ejpam-5586	316	13	constant	constant	PROPN
ejpam-5586	316	14	k(t	k(t	PROPN
ejpam-5586	316	15	,	,	PUNCT
ejpam-5586	316	16	2	2	X
ejpam-5586	316	17	)	)	PUNCT
ejpam-5586	316	18	=	=	SYM
ejpam-5586	317	1	(	(	PUNCT
ejpam-5586	317	2	1+t)2	1+t)2	NOUN
ejpam-5586	317	3	4	4	NUM
ejpam-5586	317	4	t	t	NOUN
ejpam-5586	317	5	exhibits	exhibit	VERB
ejpam-5586	317	6	monotonicity	monotonicity	NOUN
ejpam-5586	317	7	within	within	ADP
ejpam-5586	317	8	the	the	DET
ejpam-5586	317	9	interval	interval	NOUN
ejpam-5586	317	10	(	(	PUNCT
ejpam-5586	317	11	0,∞	0,∞	NUM
ejpam-5586	317	12	)	)	PUNCT
ejpam-5586	317	13	,	,	PUNCT
ejpam-5586	317	14	it	it	PRON
ejpam-5586	317	15	follows	follow	VERB
ejpam-5586	317	16	that	that	PRON
ejpam-5586	317	17	:	:	PUNCT
ejpam-5586	317	18	r	r	X
ejpam-5586	317	19	[	[	PUNCT
ejpam-5586	317	20	hκ(i	hκ(i	NOUN
ejpam-5586	317	21	,	,	PUNCT
ejpam-5586	317	22	t	t	NOUN
ejpam-5586	317	23	−1/2st−1/2	−1/2st−1/2	NOUN
ejpam-5586	317	24	)	)	PUNCT
ejpam-5586	318	1	+	+	PUNCT
ejpam-5586	318	2	h0(i	h0(i	ADJ
ejpam-5586	318	3	,	,	PUNCT
ejpam-5586	318	4	t	t	PROPN
ejpam-5586	318	5	−1/2st−1/2)−hκ	−1/2st−1/2)−hκ	NUM
ejpam-5586	318	6	2	2	NUM
ejpam-5586	318	7	(	(	PUNCT
ejpam-5586	318	8	i	i	PROPN
ejpam-5586	318	9	,	,	PUNCT
ejpam-5586	318	10	t−1/2st−1/2	t−1/2st−1/2	PROPN
ejpam-5586	318	11	)	)	PUNCT
ejpam-5586	318	12	]	]	PUNCT
ejpam-5586	319	1	+	+	CCONJ
ejpam-5586	319	2	min	min	PROPN
ejpam-5586	319	3	h≤x≤h′	h≤x≤h′	PROPN
ejpam-5586	319	4	k	k	PROPN
ejpam-5586	320	1	[	[	X
ejpam-5586	320	2	√	√	NUM
ejpam-5586	320	3	x	x	SYM
ejpam-5586	320	4	,	,	PUNCT
ejpam-5586	320	5	2	2	NUM
ejpam-5586	320	6	]	]	SYM
ejpam-5586	320	7	r′	r′	NOUN
ejpam-5586	320	8	hν(i	hν(i	NOUN
ejpam-5586	320	9	,	,	PUNCT
ejpam-5586	320	10	t	t	NOUN
ejpam-5586	320	11	−1/2st−1/2	−1/2st−1/2	NOUN
ejpam-5586	320	12	)	)	PUNCT
ejpam-5586	320	13	≤	≤	NOUN
ejpam-5586	321	1	h0(i	h0(i	PROPN
ejpam-5586	321	2	,	,	PUNCT
ejpam-5586	321	3	t	t	PROPN
ejpam-5586	321	4	−1/2st−1/2	−1/2st−1/2	NOUN
ejpam-5586	321	5	)	)	PUNCT
ejpam-5586	322	1	−	−	PROPN
ejpam-5586	322	2	(	(	PUNCT
ejpam-5586	322	3	ν	ν	NOUN
ejpam-5586	322	4	κ	κ	NOUN
ejpam-5586	322	5	)	)	PUNCT
ejpam-5586	322	6	[	[	PUNCT
ejpam-5586	322	7	h0(i	h0(i	PROPN
ejpam-5586	322	8	,	,	PUNCT
ejpam-5586	322	9	t	t	PROPN
ejpam-5586	322	10	−1/2st−1/2)−hκ(i	−1/2st−1/2)−hκ(i	PROPN
ejpam-5586	322	11	,	,	PUNCT
ejpam-5586	322	12	t	t	NOUN
ejpam-5586	322	13	−1/2st−1/2	−1/2st−1/2	NOUN
ejpam-5586	322	14	)	)	PUNCT
ejpam-5586	322	15	]	]	PUNCT
ejpam-5586	322	16	,	,	PUNCT
ejpam-5586	322	17	(	(	PUNCT
ejpam-5586	322	18	25	25	NUM
ejpam-5586	322	19	)	)	PUNCT
ejpam-5586	322	20	likewise	likewise	ADV
ejpam-5586	322	21	,	,	PUNCT
ejpam-5586	322	22	within	within	ADP
ejpam-5586	322	23	the	the	DET
ejpam-5586	322	24	context	context	NOUN
ejpam-5586	322	25	of	of	ADP
ejpam-5586	322	26	the	the	DET
ejpam-5586	322	27	second	second	ADJ
ejpam-5586	322	28	condition	condition	NOUN
ejpam-5586	322	29	,	,	PUNCT
ejpam-5586	322	30	we	we	PRON
ejpam-5586	322	31	observe	observe	VERB
ejpam-5586	322	32	that	that	SCONJ
ejpam-5586	322	33	i	i	PRON
ejpam-5586	322	34	≤	≤	NOUN
ejpam-5586	322	35	1	1	NUM
ejpam-5586	323	1	hi	hi	INTJ
ejpam-5586	323	2	=	=	NOUN
ejpam-5586	323	3	m	m	VERB
ejpam-5586	323	4	m	m	VERB
ejpam-5586	323	5	h	h	NOUN
ejpam-5586	323	6	≤	≤	NUM
ejpam-5586	323	7	x	x	SYM
ejpam-5586	323	8	≤	≤	NUM
ejpam-5586	323	9	1	1	NUM
ejpam-5586	323	10	h′	h′	NOUN
ejpam-5586	323	11	i	i	NOUN
ejpam-5586	323	12	=	=	PUNCT
ejpam-5586	323	13	m′	m′	VERB
ejpam-5586	323	14	m	m	VERB
ejpam-5586	323	15	′	′	NOUN
ejpam-5586	323	16	i.	i.	NOUN
ejpam-5586	323	17	utilizing	utilize	VERB
ejpam-5586	323	18	lemma	lemma	PROPN
ejpam-5586	323	19	4	4	NUM
ejpam-5586	323	20	,	,	PUNCT
ejpam-5586	323	21	we	we	PRON
ejpam-5586	323	22	obtain	obtain	VERB
ejpam-5586	323	23	the	the	DET
ejpam-5586	323	24	following	following	NOUN
ejpam-5586	323	25	:	:	PUNCT
ejpam-5586	324	1	r	r	NOUN
ejpam-5586	324	2	[	[	PUNCT
ejpam-5586	324	3	hκ(i	hκ(i	NOUN
ejpam-5586	324	4	,	,	PUNCT
ejpam-5586	324	5	x	x	X
ejpam-5586	324	6	)	)	PUNCT
ejpam-5586	325	1	+	+	ADJ
ejpam-5586	325	2	h0(i	h0(i	ADJ
ejpam-5586	325	3	,	,	PUNCT
ejpam-5586	325	4	x)−hκ	x)−hκ	PROPN
ejpam-5586	325	5	2	2	NUM
ejpam-5586	325	6	(	(	PUNCT
ejpam-5586	325	7	i	i	NOUN
ejpam-5586	325	8	,	,	PUNCT
ejpam-5586	325	9	x	x	NOUN
ejpam-5586	325	10	)	)	PUNCT
ejpam-5586	325	11	]	]	PUNCT
ejpam-5586	326	1	+	+	PUNCT
ejpam-5586	326	2	min	min	NOUN
ejpam-5586	326	3	1	1	NUM
ejpam-5586	326	4	h′≤x≤	h′≤x≤	NUM
ejpam-5586	326	5	1	1	NUM
ejpam-5586	326	6	h	h	NOUN
ejpam-5586	326	7	k	k	NOUN
ejpam-5586	326	8	[	[	PUNCT
ejpam-5586	326	9	√	√	NUM
ejpam-5586	326	10	x	x	SYM
ejpam-5586	326	11	,	,	PUNCT
ejpam-5586	326	12	2	2	NUM
ejpam-5586	326	13	]	]	PUNCT
ejpam-5586	326	14	r′	r′	NUM
ejpam-5586	326	15	hν(i	hν(i	NOUN
ejpam-5586	326	16	,	,	PUNCT
ejpam-5586	326	17	x	x	NOUN
ejpam-5586	326	18	)	)	PUNCT
ejpam-5586	326	19	≤	≤	NOUN
ejpam-5586	327	1	h0(i	h0(i	PROPN
ejpam-5586	327	2	,	,	PUNCT
ejpam-5586	327	3	x)−	x)−	PROPN
ejpam-5586	327	4	(	(	PUNCT
ejpam-5586	327	5	ν	ν	NOUN
ejpam-5586	327	6	κ	κ	NOUN
ejpam-5586	327	7	)	)	PUNCT
ejpam-5586	328	1	[	[	X
ejpam-5586	328	2	h0(i	h0(i	X
ejpam-5586	328	3	,	,	PUNCT
ejpam-5586	328	4	x)−hκ(i	x)−hκ(i	PROPN
ejpam-5586	328	5	,	,	PUNCT
ejpam-5586	328	6	x	x	NOUN
ejpam-5586	328	7	)	)	PUNCT
ejpam-5586	328	8	]	]	PUNCT
ejpam-5586	328	9	,	,	PUNCT
ejpam-5586	328	10	since	since	SCONJ
ejpam-5586	328	11	the	the	DET
ejpam-5586	328	12	kantorovich	kantorovich	PROPN
ejpam-5586	328	13	constant	constant	PROPN
ejpam-5586	328	14	k(t	k(t	PROPN
ejpam-5586	328	15	,	,	PUNCT
ejpam-5586	328	16	2	2	X
ejpam-5586	328	17	)	)	PUNCT
ejpam-5586	328	18	=	=	SYM
ejpam-5586	328	19	(	(	PUNCT
ejpam-5586	328	20	1+t)2	1+t)2	NOUN
ejpam-5586	328	21	4	4	NUM
ejpam-5586	328	22	t	t	NOUN
ejpam-5586	328	23	is	be	AUX
ejpam-5586	328	24	an	an	DET
ejpam-5586	328	25	increasing	increase	VERB
ejpam-5586	328	26	function	function	NOUN
ejpam-5586	328	27	on	on	ADP
ejpam-5586	328	28	(	(	PUNCT
ejpam-5586	328	29	0,∞	0,∞	NOUN
ejpam-5586	328	30	)	)	PUNCT
ejpam-5586	328	31	,	,	PUNCT
ejpam-5586	328	32	then	then	ADV
ejpam-5586	328	33	r	r	X
ejpam-5586	328	34	[	[	PUNCT
ejpam-5586	328	35	hκ(i	hκ(i	NOUN
ejpam-5586	328	36	,	,	PUNCT
ejpam-5586	328	37	t	t	NOUN
ejpam-5586	328	38	−1/2st−1/2	−1/2st−1/2	NOUN
ejpam-5586	328	39	)	)	PUNCT
ejpam-5586	329	1	+	+	PUNCT
ejpam-5586	329	2	h0(i	h0(i	ADJ
ejpam-5586	329	3	,	,	PUNCT
ejpam-5586	329	4	t	t	PROPN
ejpam-5586	329	5	−1/2st−1/2)−hκ	−1/2st−1/2)−hκ	NUM
ejpam-5586	329	6	2	2	NUM
ejpam-5586	329	7	(	(	PUNCT
ejpam-5586	329	8	i	i	PROPN
ejpam-5586	329	9	,	,	PUNCT
ejpam-5586	329	10	t−1/2st−1/2	t−1/2st−1/2	PROPN
ejpam-5586	329	11	)	)	PUNCT
ejpam-5586	329	12	]	]	PUNCT
ejpam-5586	330	1	+	+	CCONJ
ejpam-5586	330	2	min	min	NOUN
ejpam-5586	330	3	1	1	NUM
ejpam-5586	330	4	h′≤x≤	h′≤x≤	NUM
ejpam-5586	330	5	1	1	NUM
ejpam-5586	330	6	h	h	NOUN
ejpam-5586	330	7	k	k	PROPN
ejpam-5586	331	1	[	[	X
ejpam-5586	331	2	√	√	NUM
ejpam-5586	331	3	x	x	SYM
ejpam-5586	331	4	,	,	PUNCT
ejpam-5586	331	5	2	2	NUM
ejpam-5586	331	6	]	]	SYM
ejpam-5586	331	7	r′	r′	NOUN
ejpam-5586	331	8	hν(i	hν(i	NOUN
ejpam-5586	331	9	,	,	PUNCT
ejpam-5586	331	10	t	t	NOUN
ejpam-5586	331	11	−1/2st−1/2	−1/2st−1/2	NOUN
ejpam-5586	331	12	)	)	PUNCT
ejpam-5586	331	13	≤	≤	NOUN
ejpam-5586	332	1	h0(i	h0(i	PROPN
ejpam-5586	332	2	,	,	PUNCT
ejpam-5586	332	3	t	t	PROPN
ejpam-5586	332	4	−1/2st−1/2	−1/2st−1/2	NOUN
ejpam-5586	332	5	)	)	PUNCT
ejpam-5586	332	6	m.h.m	m.h.m	PROPN
ejpam-5586	332	7	rashid	rashid	PROPN
ejpam-5586	332	8	,	,	PUNCT
ejpam-5586	332	9	w.m.m	w.m.m	NOUN
ejpam-5586	332	10	.	.	PUNCT
ejpam-5586	333	1	salameh	salameh	PROPN
ejpam-5586	333	2	/	/	SYM
ejpam-5586	333	3	eur	eur	PROPN
ejpam-5586	333	4	.	.	PUNCT
ejpam-5586	334	1	j.	j.	PROPN
ejpam-5586	334	2	pure	pure	PROPN
ejpam-5586	334	3	appl	appl	PROPN
ejpam-5586	334	4	.	.	PROPN
ejpam-5586	334	5	math	math	PROPN
ejpam-5586	334	6	,	,	PUNCT
ejpam-5586	334	7	18	18	NUM
ejpam-5586	334	8	(	(	PUNCT
ejpam-5586	334	9	1	1	NUM
ejpam-5586	334	10	)	)	PUNCT
ejpam-5586	334	11	(	(	PUNCT
ejpam-5586	334	12	2025	2025	NUM
ejpam-5586	334	13	)	)	PUNCT
ejpam-5586	334	14	,	,	PUNCT
ejpam-5586	334	15	5586	5586	NUM
ejpam-5586	334	16	12	12	NUM
ejpam-5586	334	17	of	of	ADP
ejpam-5586	334	18	21	21	NUM
ejpam-5586	334	19	−	−	NOUN
ejpam-5586	334	20	(	(	PUNCT
ejpam-5586	334	21	ν	ν	NOUN
ejpam-5586	334	22	κ	κ	NOUN
ejpam-5586	334	23	)	)	PUNCT
ejpam-5586	334	24	[	[	PUNCT
ejpam-5586	334	25	h0(i	h0(i	PROPN
ejpam-5586	334	26	,	,	PUNCT
ejpam-5586	334	27	t	t	PROPN
ejpam-5586	334	28	−1/2st−1/2)−hκ(i	−1/2st−1/2)−hκ(i	PROPN
ejpam-5586	334	29	,	,	PUNCT
ejpam-5586	334	30	t	t	NOUN
ejpam-5586	334	31	−1/2st−1/2	−1/2st−1/2	NOUN
ejpam-5586	334	32	)	)	PUNCT
ejpam-5586	334	33	]	]	PUNCT
ejpam-5586	334	34	,	,	PUNCT
ejpam-5586	334	35	by	by	ADP
ejpam-5586	334	36	multiplying	multiply	VERB
ejpam-5586	334	37	both	both	DET
ejpam-5586	334	38	inequalities	inequality	NOUN
ejpam-5586	334	39	(	(	PUNCT
ejpam-5586	334	40	25	25	NUM
ejpam-5586	334	41	)	)	PUNCT
ejpam-5586	334	42	and	and	CCONJ
ejpam-5586	334	43	(	(	PUNCT
ejpam-5586	334	44	26	26	NUM
ejpam-5586	334	45	)	)	PUNCT
ejpam-5586	334	46	on	on	ADP
ejpam-5586	334	47	both	both	CCONJ
ejpam-5586	334	48	the	the	DET
ejpam-5586	334	49	left	left	ADJ
ejpam-5586	334	50	-	-	PUNCT
ejpam-5586	334	51	hand	hand	NOUN
ejpam-5586	334	52	and	and	CCONJ
ejpam-5586	334	53	right	right	ADJ
ejpam-5586	334	54	-	-	PUNCT
ejpam-5586	334	55	hand	hand	NOUN
ejpam-5586	334	56	sides	side	NOUN
ejpam-5586	334	57	by	by	ADP
ejpam-5586	334	58	the	the	DET
ejpam-5586	334	59	operator	operator	NOUN
ejpam-5586	334	60	t	t	PROPN
ejpam-5586	334	61	1/2	1/2	NUM
ejpam-5586	334	62	,	,	PUNCT
ejpam-5586	334	63	we	we	PRON
ejpam-5586	334	64	can	can	AUX
ejpam-5586	334	65	infer	infer	VERB
ejpam-5586	334	66	the	the	DET
ejpam-5586	334	67	desired	desire	VERB
ejpam-5586	334	68	inequality	inequality	NOUN
ejpam-5586	334	69	(	(	PUNCT
ejpam-5586	334	70	24	24	NUM
ejpam-5586	334	71	)	)	PUNCT
ejpam-5586	334	72	.	.	PUNCT
ejpam-5586	335	1	theorem	theorem	ADJ
ejpam-5586	335	2	7	7	NUM
ejpam-5586	335	3	.	.	PUNCT
ejpam-5586	335	4	consider	consider	VERB
ejpam-5586	335	5	positive	positive	ADJ
ejpam-5586	335	6	invertible	invertible	ADJ
ejpam-5586	335	7	operators	operator	NOUN
ejpam-5586	335	8	t	t	PROPN
ejpam-5586	335	9	and	and	CCONJ
ejpam-5586	335	10	s	s	X
ejpam-5586	335	11	in	in	ADP
ejpam-5586	335	12	a	a	DET
ejpam-5586	335	13	hilbert	hilbert	NOUN
ejpam-5586	335	14	space	space	NOUN
ejpam-5586	335	15	h	h	NOUN
ejpam-5586	335	16	,	,	PUNCT
ejpam-5586	335	17	where	where	SCONJ
ejpam-5586	335	18	i	i	PRON
ejpam-5586	335	19	represents	represent	VERB
ejpam-5586	335	20	the	the	DET
ejpam-5586	335	21	identity	identity	NOUN
ejpam-5586	335	22	operator	operator	NOUN
ejpam-5586	335	23	.	.	PUNCT
ejpam-5586	336	1	additionally	additionally	ADV
ejpam-5586	336	2	,	,	PUNCT
ejpam-5586	336	3	let	let	VERB
ejpam-5586	336	4	κ	κ	PART
ejpam-5586	336	5	be	be	AUX
ejpam-5586	336	6	a	a	DET
ejpam-5586	336	7	non	non	ADJ
ejpam-5586	336	8	-	-	ADJ
ejpam-5586	336	9	negative	negative	ADJ
ejpam-5586	336	10	number	number	NOUN
ejpam-5586	337	1	such	such	ADJ
ejpam-5586	337	2	that	that	SCONJ
ejpam-5586	337	3	0	0	NUM
ejpam-5586	337	4	≤	≤	NUM
ejpam-5586	337	5	ν	ν	ADP
ejpam-5586	337	6	<	<	X
ejpam-5586	337	7	κ	κ	X
ejpam-5586	337	8	≤	≤	NOUN
ejpam-5586	337	9	1	1	NUM
ejpam-5586	337	10	.	.	PUNCT
ejpam-5586	338	1	assuming	assume	VERB
ejpam-5586	338	2	that	that	SCONJ
ejpam-5586	338	3	there	there	PRON
ejpam-5586	338	4	exist	exist	VERB
ejpam-5586	338	5	positive	positive	ADJ
ejpam-5586	338	6	real	real	ADJ
ejpam-5586	338	7	numbers	number	NOUN
ejpam-5586	338	8	m	m	PROPN
ejpam-5586	338	9	,	,	PUNCT
ejpam-5586	338	10	m′,m	m′,m	PROPN
ejpam-5586	338	11	,	,	PUNCT
ejpam-5586	338	12	m	m	VERB
ejpam-5586	338	13	′	′	NOUN
ejpam-5586	338	14	that	that	PRON
ejpam-5586	338	15	satisfy	satisfy	VERB
ejpam-5586	338	16	either	either	ADV
ejpam-5586	338	17	of	of	ADP
ejpam-5586	338	18	the	the	DET
ejpam-5586	338	19	following	follow	VERB
ejpam-5586	338	20	conditions	condition	NOUN
ejpam-5586	338	21	:	:	PUNCT
ejpam-5586	338	22	(	(	PUNCT
ejpam-5586	338	23	a	a	X
ejpam-5586	338	24	)	)	PUNCT
ejpam-5586	338	25	0	0	PUNCT
ejpam-5586	338	26	<	<	X
ejpam-5586	338	27	mi	mi	PROPN
ejpam-5586	338	28	≤	≤	PROPN
ejpam-5586	338	29	t	t	PROPN
ejpam-5586	338	30	≤	≤	NUM
ejpam-5586	338	31	m′i	m′i	NOUN
ejpam-5586	338	32	<	<	X
ejpam-5586	338	33	m	m	VERB
ejpam-5586	338	34	′i	′i	NOUN
ejpam-5586	338	35	≤	≤	NUM
ejpam-5586	338	36	s	s	PART
ejpam-5586	338	37	≤mi	≤mi	NOUN
ejpam-5586	338	38	(	(	PUNCT
ejpam-5586	338	39	b	b	NOUN
ejpam-5586	338	40	)	)	PUNCT
ejpam-5586	338	41	0	0	PUNCT
ejpam-5586	338	42	<	<	X
ejpam-5586	338	43	mi	mi	PROPN
ejpam-5586	338	44	≤	≤	PROPN
ejpam-5586	338	45	s	s	PART
ejpam-5586	338	46	≤	≤	NUM
ejpam-5586	338	47	m′i	m′i	NOUN
ejpam-5586	338	48	≤	≤	NUM
ejpam-5586	338	49	t	t	PROPN
ejpam-5586	338	50	≤mi	≤mi	PROPN
ejpam-5586	338	51	then	then	ADV
ejpam-5586	338	52	,	,	PUNCT
ejpam-5586	338	53	the	the	DET
ejpam-5586	338	54	following	follow	VERB
ejpam-5586	338	55	conclusions	conclusion	NOUN
ejpam-5586	338	56	hold	hold	VERB
ejpam-5586	338	57	:	:	PUNCT
ejpam-5586	338	58	h0(t	h0(t	PROPN
ejpam-5586	338	59	,	,	PUNCT
ejpam-5586	338	60	s)−	s)−	PROPN
ejpam-5586	338	61	(	(	PUNCT
ejpam-5586	338	62	ν	ν	X
ejpam-5586	338	63	κ	κ	NOUN
ejpam-5586	338	64	)	)	PUNCT
ejpam-5586	339	1	[	[	X
ejpam-5586	339	2	h0(t	h0(t	X
ejpam-5586	339	3	,	,	PUNCT
ejpam-5586	339	4	s)−hκ(t	s)−hκ(t	PROPN
ejpam-5586	339	5	,	,	PUNCT
ejpam-5586	339	6	s	s	PART
ejpam-5586	339	7	)	)	PUNCT
ejpam-5586	339	8	]	]	PUNCT
ejpam-5586	339	9	≤	≤	NUM
ejpam-5586	339	10	k	k	PROPN
ejpam-5586	340	1	[	[	X
ejpam-5586	340	2	√	√	NUM
ejpam-5586	340	3	h	h	NOUN
ejpam-5586	340	4	,	,	PUNCT
ejpam-5586	340	5	2	2	NUM
ejpam-5586	340	6	]	]	SYM
ejpam-5586	340	7	−r′	−r′	PROPN
ejpam-5586	340	8	hν(t	hν(t	PROPN
ejpam-5586	340	9	,	,	PUNCT
ejpam-5586	340	10	s	s	X
ejpam-5586	340	11	)	)	PUNCT
ejpam-5586	341	1	+	+	NOUN
ejpam-5586	341	2	r	r	NOUN
ejpam-5586	341	3	[	[	PUNCT
ejpam-5586	341	4	hκ(t	hκ(t	X
ejpam-5586	341	5	,	,	PUNCT
ejpam-5586	341	6	s	s	X
ejpam-5586	341	7	)	)	PUNCT
ejpam-5586	341	8	+	+	NOUN
ejpam-5586	341	9	h0(t	h0(t	PROPN
ejpam-5586	341	10	,	,	PUNCT
ejpam-5586	341	11	s)−hκ	s)−hκ	PROPN
ejpam-5586	341	12	2	2	NUM
ejpam-5586	341	13	(	(	PUNCT
ejpam-5586	341	14	t	t	PROPN
ejpam-5586	341	15	,	,	PUNCT
ejpam-5586	341	16	s	s	PROPN
ejpam-5586	341	17	)	)	PUNCT
ejpam-5586	341	18	]	]	PUNCT
ejpam-5586	341	19	,	,	PUNCT
ejpam-5586	341	20	(	(	PUNCT
ejpam-5586	341	21	26	26	NUM
ejpam-5586	341	22	)	)	PUNCT
ejpam-5586	342	1	where	where	SCONJ
ejpam-5586	342	2	r	r	NOUN
ejpam-5586	342	3	=	=	SYM
ejpam-5586	342	4	min	min	PROPN
ejpam-5586	342	5	{	{	PUNCT
ejpam-5586	342	6	ν	ν	X
ejpam-5586	342	7	κ	κ	NOUN
ejpam-5586	342	8	,	,	PUNCT
ejpam-5586	342	9	1−	1−	NUM
ejpam-5586	342	10	ν	ν	NOUN
ejpam-5586	342	11	κ	κ	NOUN
ejpam-5586	342	12	}	}	PUNCT
ejpam-5586	342	13	,	,	PUNCT
ejpam-5586	342	14	h	h	NOUN
ejpam-5586	342	15	=	=	NOUN
ejpam-5586	342	16	m	m	VERB
ejpam-5586	342	17	m	m	VERB
ejpam-5586	342	18	and	and	CCONJ
ejpam-5586	342	19	r′	r′	PROPN
ejpam-5586	342	20	=	=	SYM
ejpam-5586	342	21	min{2r	min{2r	PROPN
ejpam-5586	342	22	,	,	PUNCT
ejpam-5586	342	23	1−	1−	NUM
ejpam-5586	342	24	2r	2r	NUM
ejpam-5586	342	25	}	}	PUNCT
ejpam-5586	342	26	.	.	PUNCT
ejpam-5586	343	1	proof	proof	NOUN
ejpam-5586	343	2	.	.	PUNCT
ejpam-5586	344	1	the	the	DET
ejpam-5586	344	2	proof	proof	NOUN
ejpam-5586	344	3	process	process	NOUN
ejpam-5586	344	4	is	be	AUX
ejpam-5586	344	5	similar	similar	ADJ
ejpam-5586	344	6	to	to	ADP
ejpam-5586	344	7	that	that	PRON
ejpam-5586	344	8	of	of	ADP
ejpam-5586	344	9	theorem	theorem	ADJ
ejpam-5586	344	10	6	6	NUM
ejpam-5586	344	11	,	,	PUNCT
ejpam-5586	344	12	and	and	CCONJ
ejpam-5586	344	13	thus	thus	ADV
ejpam-5586	344	14	,	,	PUNCT
ejpam-5586	344	15	we	we	PRON
ejpam-5586	344	16	will	will	AUX
ejpam-5586	344	17	not	not	PART
ejpam-5586	344	18	provide	provide	VERB
ejpam-5586	344	19	it	it	PRON
ejpam-5586	344	20	here	here	ADV
ejpam-5586	344	21	.	.	PUNCT
ejpam-5586	345	1	remark	remark	VERB
ejpam-5586	345	2	3	3	NUM
ejpam-5586	345	3	.	.	PUNCT
ejpam-5586	346	1	the	the	DET
ejpam-5586	346	2	nature	nature	NOUN
ejpam-5586	346	3	of	of	ADP
ejpam-5586	346	4	the	the	DET
ejpam-5586	346	5	kantorovich	kantorovich	PROPN
ejpam-5586	346	6	constant	constant	PROPN
ejpam-5586	346	7	’s	’s	PART
ejpam-5586	346	8	characteristics	characteristic	NOUN
ejpam-5586	346	9	makes	make	VERB
ejpam-5586	346	10	it	it	PRON
ejpam-5586	346	11	clear	clear	ADJ
ejpam-5586	346	12	that	that	SCONJ
ejpam-5586	346	13	the	the	DET
ejpam-5586	346	14	inequalities	inequality	NOUN
ejpam-5586	346	15	outlined	outline	VERB
ejpam-5586	346	16	in	in	ADP
ejpam-5586	346	17	theorems	theorem	NOUN
ejpam-5586	346	18	6	6	NUM
ejpam-5586	346	19	and	and	CCONJ
ejpam-5586	346	20	7	7	NUM
ejpam-5586	346	21	signify	signify	VERB
ejpam-5586	346	22	improved	improved	ADJ
ejpam-5586	346	23	results	result	NOUN
ejpam-5586	346	24	compared	compare	VERB
ejpam-5586	346	25	to	to	ADP
ejpam-5586	346	26	those	those	PRON
ejpam-5586	346	27	detailed	detail	VERB
ejpam-5586	346	28	in	in	ADP
ejpam-5586	346	29	[	[	X
ejpam-5586	346	30	13	13	NUM
ejpam-5586	346	31	]	]	PUNCT
ejpam-5586	346	32	,	,	PUNCT
ejpam-5586	346	33	[	[	X
ejpam-5586	346	34	14	14	NUM
ejpam-5586	346	35	]	]	PUNCT
ejpam-5586	346	36	,	,	PUNCT
ejpam-5586	346	37	[	[	X
ejpam-5586	346	38	18	18	NUM
ejpam-5586	346	39	]	]	PUNCT
ejpam-5586	346	40	,	,	PUNCT
ejpam-5586	346	41	[	[	X
ejpam-5586	346	42	20	20	NUM
ejpam-5586	346	43	]	]	PUNCT
ejpam-5586	346	44	,	,	PUNCT
ejpam-5586	346	45	and	and	CCONJ
ejpam-5586	346	46	[	[	X
ejpam-5586	346	47	23	23	NUM
ejpam-5586	346	48	]	]	PUNCT
ejpam-5586	346	49	.	.	PUNCT
ejpam-5586	347	1	5	5	X
ejpam-5586	347	2	.	.	X
ejpam-5586	347	3	utilizations	utilization	NOUN
ejpam-5586	347	4	of	of	ADP
ejpam-5586	347	5	the	the	DET
ejpam-5586	347	6	improved	improved	ADJ
ejpam-5586	347	7	young	young	ADJ
ejpam-5586	347	8	-	-	PUNCT
ejpam-5586	347	9	type	type	NOUN
ejpam-5586	347	10	inequalities	inequality	NOUN
ejpam-5586	347	11	for	for	ADP
ejpam-5586	347	12	traces	trace	NOUN
ejpam-5586	347	13	,	,	PUNCT
ejpam-5586	347	14	determinants	determinant	NOUN
ejpam-5586	347	15	,	,	PUNCT
ejpam-5586	347	16	and	and	CCONJ
ejpam-5586	347	17	norms	norm	NOUN
ejpam-5586	347	18	of	of	ADP
ejpam-5586	347	19	positive	positive	ADJ
ejpam-5586	347	20	definite	definite	ADJ
ejpam-5586	347	21	matrices	matrix	NOUN
ejpam-5586	347	22	in	in	ADP
ejpam-5586	347	23	this	this	DET
ejpam-5586	347	24	section	section	NOUN
ejpam-5586	347	25	,	,	PUNCT
ejpam-5586	347	26	we	we	PRON
ejpam-5586	347	27	introduce	introduce	VERB
ejpam-5586	347	28	a	a	DET
ejpam-5586	347	29	collection	collection	NOUN
ejpam-5586	347	30	of	of	ADP
ejpam-5586	347	31	improved	improved	ADJ
ejpam-5586	347	32	young	young	ADJ
ejpam-5586	347	33	-	-	PUNCT
ejpam-5586	347	34	type	type	NOUN
ejpam-5586	347	35	inequalities	inequality	NOUN
ejpam-5586	347	36	designed	design	VERB
ejpam-5586	347	37	specifically	specifically	ADV
ejpam-5586	347	38	for	for	ADP
ejpam-5586	347	39	traces	trace	NOUN
ejpam-5586	347	40	,	,	PUNCT
ejpam-5586	347	41	determinants	determinant	NOUN
ejpam-5586	347	42	,	,	PUNCT
ejpam-5586	347	43	and	and	CCONJ
ejpam-5586	347	44	norms	norm	NOUN
ejpam-5586	347	45	of	of	ADP
ejpam-5586	347	46	positive	positive	ADJ
ejpam-5586	347	47	semi	semi	ADJ
ejpam-5586	347	48	-	-	ADJ
ejpam-5586	347	49	definite	definite	ADJ
ejpam-5586	347	50	matrices	matrix	NOUN
ejpam-5586	347	51	.	.	PUNCT
ejpam-5586	348	1	a	a	DET
ejpam-5586	348	2	matrix	matrix	NOUN
ejpam-5586	348	3	version	version	NOUN
ejpam-5586	348	4	proved	prove	VERB
ejpam-5586	348	5	in	in	ADP
ejpam-5586	348	6	[	[	X
ejpam-5586	348	7	1	1	NUM
ejpam-5586	348	8	]	]	PUNCT
ejpam-5586	348	9	says	say	VERB
ejpam-5586	348	10	that	that	SCONJ
ejpam-5586	348	11	if	if	SCONJ
ejpam-5586	348	12	t	t	PROPN
ejpam-5586	348	13	,	,	PUNCT
ejpam-5586	348	14	s	s	PART
ejpam-5586	348	15	∈	∈	NOUN
ejpam-5586	348	16	mn(c	mn(c	X
ejpam-5586	348	17	)	)	PUNCT
ejpam-5586	348	18	are	be	AUX
ejpam-5586	348	19	positive	positive	ADJ
ejpam-5586	348	20	semi	semi	ADJ
ejpam-5586	348	21	-	-	ADJ
ejpam-5586	348	22	definite	definite	ADJ
ejpam-5586	348	23	,	,	PUNCT
ejpam-5586	348	24	then	then	ADV
ejpam-5586	348	25	sj(ts	sj(ts	PROPN
ejpam-5586	348	26	)	)	PUNCT
ejpam-5586	348	27	≤	≤	PUNCT
ejpam-5586	349	1	sj	sj	INTJ
ejpam-5586	349	2	(	(	PUNCT
ejpam-5586	349	3	1	1	NUM
ejpam-5586	349	4	p	p	NOUN
ejpam-5586	349	5	t	t	X
ejpam-5586	350	1	p	p	NOUN
ejpam-5586	351	1	+	+	CCONJ
ejpam-5586	351	2	1	1	NUM
ejpam-5586	351	3	q	q	NOUN
ejpam-5586	351	4	sq	sq	PROPN
ejpam-5586	351	5	)	)	PUNCT
ejpam-5586	351	6	(	(	PUNCT
ejpam-5586	351	7	27	27	NUM
ejpam-5586	351	8	)	)	PUNCT
ejpam-5586	351	9	for	for	ADP
ejpam-5586	351	10	j	j	PROPN
ejpam-5586	351	11	=	=	SYM
ejpam-5586	351	12	1	1	NUM
ejpam-5586	351	13	,	,	PUNCT
ejpam-5586	351	14	·	·	PUNCT
ejpam-5586	351	15	·	·	PUNCT
ejpam-5586	351	16	·	·	PUNCT
ejpam-5586	351	17	,	,	PUNCT
ejpam-5586	351	18	n	n	CCONJ
ejpam-5586	351	19	lemma	lemma	PROPN
ejpam-5586	351	20	5	5	X
ejpam-5586	351	21	.	.	PUNCT
ejpam-5586	352	1	let	let	VERB
ejpam-5586	352	2	ρ	ρ	NOUN
ejpam-5586	352	3	,	,	PUNCT
ejpam-5586	352	4	σ	σ	PROPN
ejpam-5586	352	5	>	>	X
ejpam-5586	352	6	0	0	NUM
ejpam-5586	352	7	,	,	PUNCT
ejpam-5586	352	8	p	p	X
ejpam-5586	352	9	,	,	PUNCT
ejpam-5586	352	10	q	q	X
ejpam-5586	352	11	>	>	X
ejpam-5586	352	12	1	1	NUM
ejpam-5586	352	13	such	such	ADJ
ejpam-5586	352	14	that	that	SCONJ
ejpam-5586	352	15	1	1	NUM
ejpam-5586	352	16	p	p	NOUN
ejpam-5586	353	1	+	+	NOUN
ejpam-5586	353	2	1	1	NUM
ejpam-5586	353	3	q	q	NOUN
ejpam-5586	353	4	=	=	ADJ
ejpam-5586	353	5	1	1	X
ejpam-5586	353	6	.	.	PUNCT
ejpam-5586	353	7	then	then	ADV
ejpam-5586	353	8	for	for	ADP
ejpam-5586	353	9	m	m	PROPN
ejpam-5586	353	10	∈	∈	PROPN
ejpam-5586	353	11	n	n	CCONJ
ejpam-5586	353	12	,	,	PUNCT
ejpam-5586	353	13	we	we	PRON
ejpam-5586	353	14	have	have	VERB
ejpam-5586	353	15	(	(	PUNCT
ejpam-5586	353	16	ρ	ρ	PROPN
ejpam-5586	353	17	1	1	NUM
ejpam-5586	353	18	pσ	pσ	PROPN
ejpam-5586	353	19	1	1	NUM
ejpam-5586	353	20	q	q	NOUN
ejpam-5586	353	21	)	)	PUNCT
ejpam-5586	353	22	m	m	VERB
ejpam-5586	353	23	+	+	NUM
ejpam-5586	353	24	rm0	rm0	NOUN
ejpam-5586	353	25	(	(	PUNCT
ejpam-5586	353	26	ρ	ρ	PROPN
ejpam-5586	353	27	m	m	NOUN
ejpam-5586	353	28	2	2	NUM
ejpam-5586	353	29	−	−	PROPN
ejpam-5586	353	30	σ	σ	NUM
ejpam-5586	353	31	m	m	VERB
ejpam-5586	353	32	2	2	NUM
ejpam-5586	353	33	)	)	SYM
ejpam-5586	353	34	2	2	NUM
ejpam-5586	353	35	≤	≤	NOUN
ejpam-5586	353	36	(	(	PUNCT
ejpam-5586	353	37	ρr	ρr	PROPN
ejpam-5586	353	38	p	p	X
ejpam-5586	354	1	+	+	PROPN
ejpam-5586	354	2	σr	σr	PROPN
ejpam-5586	354	3	q	q	PROPN
ejpam-5586	354	4	)	)	PUNCT
ejpam-5586	354	5	m	m	VERB
ejpam-5586	354	6	r	r	NOUN
ejpam-5586	354	7	,	,	PUNCT
ejpam-5586	354	8	r	r	NOUN
ejpam-5586	354	9	≥	≥	NUM
ejpam-5586	354	10	1	1	NUM
ejpam-5586	354	11	(	(	PUNCT
ejpam-5586	354	12	28	28	NUM
ejpam-5586	354	13	)	)	PUNCT
ejpam-5586	354	14	where	where	SCONJ
ejpam-5586	354	15	r0	r0	NOUN
ejpam-5586	354	16	=	=	PROPN
ejpam-5586	354	17	min{1	min{1	PROPN
ejpam-5586	354	18	p	p	NOUN
ejpam-5586	354	19	,	,	PUNCT
ejpam-5586	354	20	1	1	NUM
ejpam-5586	354	21	q	q	NOUN
ejpam-5586	354	22	}	}	PUNCT
ejpam-5586	354	23	.	.	PUNCT
ejpam-5586	355	1	m.h.m	m.h.m	PROPN
ejpam-5586	355	2	rashid	rashid	PROPN
ejpam-5586	355	3	,	,	PUNCT
ejpam-5586	355	4	w.m.m	w.m.m	NOUN
ejpam-5586	355	5	.	.	PUNCT
ejpam-5586	356	1	salameh	salameh	PROPN
ejpam-5586	356	2	/	/	SYM
ejpam-5586	356	3	eur	eur	PROPN
ejpam-5586	356	4	.	.	PUNCT
ejpam-5586	357	1	j.	j.	PROPN
ejpam-5586	357	2	pure	pure	PROPN
ejpam-5586	357	3	appl	appl	PROPN
ejpam-5586	357	4	.	.	PROPN
ejpam-5586	357	5	math	math	PROPN
ejpam-5586	357	6	,	,	PUNCT
ejpam-5586	357	7	18	18	NUM
ejpam-5586	357	8	(	(	PUNCT
ejpam-5586	357	9	1	1	NUM
ejpam-5586	357	10	)	)	PUNCT
ejpam-5586	357	11	(	(	PUNCT
ejpam-5586	357	12	2025	2025	NUM
ejpam-5586	357	13	)	)	PUNCT
ejpam-5586	357	14	,	,	PUNCT
ejpam-5586	357	15	5586	5586	NUM
ejpam-5586	357	16	13	13	NUM
ejpam-5586	357	17	of	of	ADP
ejpam-5586	357	18	21	21	NUM
ejpam-5586	357	19	lemma	lemma	PROPN
ejpam-5586	357	20	6	6	NUM
ejpam-5586	357	21	.	.	PUNCT
ejpam-5586	358	1	let	let	VERB
ejpam-5586	358	2	ti	ti	NOUN
ejpam-5586	358	3	∈mn(c	∈mn(c	VERB
ejpam-5586	358	4	)	)	PUNCT
ejpam-5586	359	1	(	(	PUNCT
ejpam-5586	359	2	i	i	NOUN
ejpam-5586	359	3	=	=	NOUN
ejpam-5586	359	4	1	1	NUM
ejpam-5586	359	5	,	,	PUNCT
ejpam-5586	359	6	·	·	PUNCT
ejpam-5586	359	7	·	·	PUNCT
ejpam-5586	359	8	·	·	PUNCT
ejpam-5586	359	9	,	,	PUNCT
ejpam-5586	359	10	n	n	CCONJ
ejpam-5586	359	11	)	)	PUNCT
ejpam-5586	359	12	,	,	PUNCT
ejpam-5586	359	13	.	.	PUNCT
ejpam-5586	360	1	then	then	ADV
ejpam-5586	360	2	n∑	n∑	PROPN
ejpam-5586	360	3	j=1	j=1	NOUN
ejpam-5586	360	4	sj(t1	sj(t1	X
ejpam-5586	360	5	·	·	PUNCT
ejpam-5586	360	6	·	·	PUNCT
ejpam-5586	360	7	·	·	PUNCT
ejpam-5586	360	8	tn	tn	PROPN
ejpam-5586	360	9	)	)	PUNCT
ejpam-5586	360	10	≤	≤	NOUN
ejpam-5586	361	1	n∑	n∑	PROPN
ejpam-5586	361	2	j=1	j=1	PROPN
ejpam-5586	361	3	sj(t1	sj(t1	NOUN
ejpam-5586	361	4	)	)	PUNCT
ejpam-5586	361	5	·	·	PUNCT
ejpam-5586	362	1	·	·	PUNCT
ejpam-5586	362	2	·	·	PUNCT
ejpam-5586	362	3	sj(tk	sj(tk	NOUN
ejpam-5586	362	4	)	)	PUNCT
ejpam-5586	362	5	.	.	PUNCT
ejpam-5586	363	1	theorem	theorem	VERB
ejpam-5586	363	2	8	8	NUM
ejpam-5586	363	3	.	.	PUNCT
ejpam-5586	364	1	let	let	VERB
ejpam-5586	364	2	t	t	PROPN
ejpam-5586	364	3	,	,	PUNCT
ejpam-5586	364	4	s	s	PART
ejpam-5586	364	5	∈	∈	PROPN
ejpam-5586	364	6	b(h	b(h	PROPN
ejpam-5586	364	7	)	)	PUNCT
ejpam-5586	364	8	be	be	AUX
ejpam-5586	364	9	positive	positive	ADJ
ejpam-5586	364	10	definite	definite	ADJ
ejpam-5586	364	11	,	,	PUNCT
ejpam-5586	364	12	p	p	X
ejpam-5586	364	13	,	,	PUNCT
ejpam-5586	364	14	q	q	X
ejpam-5586	364	15	>	>	X
ejpam-5586	364	16	1	1	NUM
ejpam-5586	365	1	such	such	ADJ
ejpam-5586	365	2	that	that	SCONJ
ejpam-5586	365	3	1	1	NUM
ejpam-5586	365	4	p+	p+	NOUN
ejpam-5586	365	5	1	1	NUM
ejpam-5586	365	6	q	q	NOUN
ejpam-5586	365	7	=	=	SYM
ejpam-5586	365	8	1	1	NUM
ejpam-5586	365	9	and	and	CCONJ
ejpam-5586	365	10	m	m	PROPN
ejpam-5586	365	11	∈	∈	PROPN
ejpam-5586	365	12	n.	n.	NOUN
ejpam-5586	365	13	then	then	ADV
ejpam-5586	365	14	(	(	PUNCT
ejpam-5586	365	15	tr(t	tr(t	PUNCT
ejpam-5586	365	16	r	r	X
ejpam-5586	365	17	)	)	PUNCT
ejpam-5586	365	18	p	p	NOUN
ejpam-5586	366	1	+	+	NUM
ejpam-5586	366	2	tr(sr	tr(sr	ADJ
ejpam-5586	366	3	)	)	PUNCT
ejpam-5586	366	4	q	q	NOUN
ejpam-5586	366	5	)	)	PUNCT
ejpam-5586	366	6	m	m	VERB
ejpam-5586	366	7	r	r	NOUN
ejpam-5586	366	8	≥	≥	NOUN
ejpam-5586	366	9	(	(	PUNCT
ejpam-5586	366	10	tr	tr	VERB
ejpam-5586	366	11	∣∣∣t	∣∣∣t	NOUN
ejpam-5586	366	12	1	1	NUM
ejpam-5586	366	13	ps	ps	NOUN
ejpam-5586	366	14	1	1	NUM
ejpam-5586	366	15	q	q	NOUN
ejpam-5586	366	16	∣∣∣)m	∣∣∣)m	NOUN
ejpam-5586	366	17	+	+	CCONJ
ejpam-5586	366	18	rm0	rm0	NOUN
ejpam-5586	366	19	(	(	PUNCT
ejpam-5586	366	20	(	(	PUNCT
ejpam-5586	366	21	tr(t	tr(t	NOUN
ejpam-5586	366	22	)	)	PUNCT
ejpam-5586	366	23	)	)	PUNCT
ejpam-5586	367	1	m	m	VERB
ejpam-5586	367	2	2	2	NUM
ejpam-5586	367	3	−	−	NOUN
ejpam-5586	367	4	(	(	PUNCT
ejpam-5586	367	5	tr(s	tr(s	NOUN
ejpam-5586	367	6	)	)	PUNCT
ejpam-5586	367	7	)	)	PUNCT
ejpam-5586	368	1	m	m	VERB
ejpam-5586	368	2	2	2	NUM
ejpam-5586	368	3	)	)	PUNCT
ejpam-5586	368	4	2	2	NUM
ejpam-5586	368	5	,	,	PUNCT
ejpam-5586	368	6	(	(	PUNCT
ejpam-5586	368	7	29	29	NUM
ejpam-5586	368	8	)	)	PUNCT
ejpam-5586	368	9	where	where	SCONJ
ejpam-5586	368	10	r0	r0	NOUN
ejpam-5586	368	11	=	=	PROPN
ejpam-5586	368	12	min{1	min{1	PROPN
ejpam-5586	368	13	p	p	NOUN
ejpam-5586	368	14	,	,	PUNCT
ejpam-5586	368	15	1	1	NUM
ejpam-5586	368	16	q	q	NOUN
ejpam-5586	368	17	}	}	PUNCT
ejpam-5586	368	18	.	.	PUNCT
ejpam-5586	369	1	proof	proof	NOUN
ejpam-5586	369	2	.	.	PUNCT
ejpam-5586	370	1	by	by	ADP
ejpam-5586	370	2	inequality	inequality	NOUN
ejpam-5586	370	3	(	(	PUNCT
ejpam-5586	370	4	29	29	NUM
ejpam-5586	370	5	)	)	PUNCT
ejpam-5586	370	6	,	,	PUNCT
ejpam-5586	370	7	we	we	PRON
ejpam-5586	370	8	have	have	VERB
ejpam-5586	370	9	s	s	VERB
ejpam-5586	370	10	m	m	PROPN
ejpam-5586	370	11	r	r	NOUN
ejpam-5586	370	12	j	j	PROPN
ejpam-5586	370	13	(	(	PUNCT
ejpam-5586	370	14	t	t	NOUN
ejpam-5586	370	15	r	r	NOUN
ejpam-5586	370	16	p	p	PROPN
ejpam-5586	371	1	+	+	NUM
ejpam-5586	371	2	sr	sr	PROPN
ejpam-5586	371	3	q	q	PROPN
ejpam-5586	371	4	)	)	PUNCT
ejpam-5586	372	1	=	=	SYM
ejpam-5586	372	2	sm	sm	X
ejpam-5586	372	3	r	r	PROPN
ejpam-5586	372	4	j	j	PROPN
ejpam-5586	372	5	(	(	PUNCT
ejpam-5586	372	6	t	t	NOUN
ejpam-5586	372	7	r	r	NOUN
ejpam-5586	372	8	)	)	PUNCT
ejpam-5586	372	9	p	p	NOUN
ejpam-5586	373	1	+	+	NUM
ejpam-5586	373	2	s	s	NOUN
ejpam-5586	373	3	m	m	VERB
ejpam-5586	373	4	r	r	NOUN
ejpam-5586	373	5	j	j	PROPN
ejpam-5586	373	6	(	(	PUNCT
ejpam-5586	373	7	sr	sr	PROPN
ejpam-5586	373	8	)	)	PUNCT
ejpam-5586	373	9	q	q	PROPN
ejpam-5586	374	1			PROPN
ejpam-5586	374	2	≥	≥	X
ejpam-5586	374	3	smj	smj	X
ejpam-5586	374	4	(	(	PUNCT
ejpam-5586	374	5	t	t	PROPN
ejpam-5586	374	6	1	1	NUM
ejpam-5586	374	7	p	p	NOUN
ejpam-5586	374	8	)	)	PUNCT
ejpam-5586	374	9	smj	smj	PROPN
ejpam-5586	374	10	(	(	PUNCT
ejpam-5586	374	11	s	s	PROPN
ejpam-5586	374	12	1	1	NUM
ejpam-5586	374	13	q	q	NOUN
ejpam-5586	374	14	)	)	PUNCT
ejpam-5586	375	1	+	+	CCONJ
ejpam-5586	375	2	rm0	rm0	NOUN
ejpam-5586	375	3	(	(	PUNCT
ejpam-5586	375	4	s	s	NOUN
ejpam-5586	375	5	m	m	PROPN
ejpam-5586	375	6	2	2	NUM
ejpam-5586	375	7	j	j	PROPN
ejpam-5586	375	8	(	(	PUNCT
ejpam-5586	375	9	t	t	PROPN
ejpam-5586	375	10	)	)	PUNCT
ejpam-5586	375	11	−	−	PROPN
ejpam-5586	376	1	s	s	NOUN
ejpam-5586	376	2	m	m	VERB
ejpam-5586	376	3	2	2	NUM
ejpam-5586	376	4	j	j	PROPN
ejpam-5586	376	5	(	(	PUNCT
ejpam-5586	376	6	s	s	NOUN
ejpam-5586	376	7	)	)	PUNCT
ejpam-5586	376	8	)	)	PUNCT
ejpam-5586	376	9	2	2	X
ejpam-5586	376	10	=	=	SYM
ejpam-5586	376	11	smj	smj	X
ejpam-5586	376	12	(	(	PUNCT
ejpam-5586	376	13	t	t	PROPN
ejpam-5586	376	14	1	1	NUM
ejpam-5586	376	15	p	p	NOUN
ejpam-5586	376	16	)	)	PUNCT
ejpam-5586	376	17	smj	smj	PROPN
ejpam-5586	376	18	(	(	PUNCT
ejpam-5586	376	19	s	s	PROPN
ejpam-5586	376	20	1	1	NUM
ejpam-5586	376	21	q	q	NOUN
ejpam-5586	376	22	)	)	PUNCT
ejpam-5586	377	1	+	+	CCONJ
ejpam-5586	377	2	rm0	rm0	NOUN
ejpam-5586	377	3	(	(	PUNCT
ejpam-5586	377	4	smj	smj	X
ejpam-5586	377	5	(	(	PUNCT
ejpam-5586	377	6	t	t	PROPN
ejpam-5586	377	7	)	)	PUNCT
ejpam-5586	378	1	+	+	CCONJ
ejpam-5586	378	2	smj	smj	X
ejpam-5586	378	3	(	(	PUNCT
ejpam-5586	378	4	s)−	s)−	PROPN
ejpam-5586	378	5	2s	2s	NUM
ejpam-5586	378	6	m	m	VERB
ejpam-5586	378	7	2	2	NUM
ejpam-5586	378	8	j	j	PROPN
ejpam-5586	378	9	(	(	PUNCT
ejpam-5586	378	10	t	t	PROPN
ejpam-5586	378	11	)	)	PUNCT
ejpam-5586	378	12	s	s	PART
ejpam-5586	378	13	m	m	VERB
ejpam-5586	378	14	2	2	NUM
ejpam-5586	378	15	j	j	PROPN
ejpam-5586	378	16	(	(	PUNCT
ejpam-5586	378	17	s	s	NOUN
ejpam-5586	378	18	)	)	PUNCT
ejpam-5586	378	19	)	)	PUNCT
ejpam-5586	378	20	for	for	ADP
ejpam-5586	378	21	j	j	PROPN
ejpam-5586	378	22	=	=	SYM
ejpam-5586	378	23	1	1	NUM
ejpam-5586	378	24	,	,	PUNCT
ejpam-5586	378	25	·	·	PUNCT
ejpam-5586	378	26	·	·	PUNCT
ejpam-5586	378	27	·	·	PUNCT
ejpam-5586	378	28	,	,	PUNCT
ejpam-5586	378	29	n.	n.	PROPN
ejpam-5586	378	30	thus	thus	ADV
ejpam-5586	378	31	,	,	PUNCT
ejpam-5586	378	32	by	by	ADP
ejpam-5586	378	33	lemma	lemma	PROPN
ejpam-5586	378	34	6	6	NUM
ejpam-5586	378	35	and	and	CCONJ
ejpam-5586	378	36	the	the	DET
ejpam-5586	378	37	cauchy	cauchy	PROPN
ejpam-5586	378	38	-	-	PUNCT
ejpam-5586	378	39	schwarz	schwarz	PROPN
ejpam-5586	378	40	inequality	inequality	NOUN
ejpam-5586	378	41	,	,	PUNCT
ejpam-5586	378	42	we	we	PRON
ejpam-5586	378	43	have	have	AUX
ejpam-5586	378	44	tr	tr	VERB
ejpam-5586	378	45	m	m	NOUN
ejpam-5586	378	46	r	r	NOUN
ejpam-5586	378	47	(	(	PUNCT
ejpam-5586	378	48	t	t	NOUN
ejpam-5586	378	49	r	r	NOUN
ejpam-5586	378	50	p	p	PROPN
ejpam-5586	379	1	+	+	NUM
ejpam-5586	379	2	sr	sr	PROPN
ejpam-5586	379	3	q	q	PROPN
ejpam-5586	379	4	)	)	PUNCT
ejpam-5586	380	1	=	=	PUNCT
ejpam-5586	381	1	n∑	n∑	NOUN
ejpam-5586	381	2	j=1	j=1	PROPN
ejpam-5586	381	3	s	s	VERB
ejpam-5586	381	4	m	m	VERB
ejpam-5586	381	5	r	r	NOUN
ejpam-5586	381	6	j	j	PROPN
ejpam-5586	381	7	(	(	PUNCT
ejpam-5586	381	8	t	t	NOUN
ejpam-5586	381	9	r	r	NOUN
ejpam-5586	381	10	p	p	PROPN
ejpam-5586	382	1	+	+	NUM
ejpam-5586	382	2	sr	sr	PROPN
ejpam-5586	382	3	q	q	PROPN
ejpam-5586	382	4	)	)	PUNCT
ejpam-5586	382	5	≥	≥	PROPN
ejpam-5586	382	6	n∑	n∑	NOUN
ejpam-5586	382	7	j=1	j=1	PROPN
ejpam-5586	382	8	smj	smj	PROPN
ejpam-5586	382	9	(	(	PUNCT
ejpam-5586	382	10	t	t	PROPN
ejpam-5586	382	11	1	1	NUM
ejpam-5586	382	12	p	p	NOUN
ejpam-5586	382	13	)	)	PUNCT
ejpam-5586	382	14	smj	smj	PROPN
ejpam-5586	382	15	(	(	PUNCT
ejpam-5586	382	16	s	s	PROPN
ejpam-5586	382	17	1	1	NUM
ejpam-5586	382	18	q	q	NOUN
ejpam-5586	382	19	)	)	PUNCT
ejpam-5586	382	20	+	+	CCONJ
ejpam-5586	382	21	rm0	rm0	PROPN
ejpam-5586	382	22			PROPN
ejpam-5586	382	23	n∑	n∑	PROPN
ejpam-5586	382	24	j=1	j=1	PROPN
ejpam-5586	382	25	smj	smj	PROPN
ejpam-5586	382	26	(	(	PUNCT
ejpam-5586	382	27	t	t	PROPN
ejpam-5586	382	28	)	)	PUNCT
ejpam-5586	383	1	+	+	CCONJ
ejpam-5586	383	2	n∑	n∑	PROPN
ejpam-5586	383	3	j=1	j=1	NOUN
ejpam-5586	383	4	smj	smj	PROPN
ejpam-5586	383	5	(	(	PUNCT
ejpam-5586	383	6	s)−	s)−	PROPN
ejpam-5586	383	7	2	2	NUM
ejpam-5586	383	8	n∑	n∑	NOUN
ejpam-5586	383	9	j=1	j=1	PROPN
ejpam-5586	383	10	s	s	VERB
ejpam-5586	383	11	m	m	VERB
ejpam-5586	383	12	2	2	NUM
ejpam-5586	383	13	j	j	PROPN
ejpam-5586	383	14	(	(	PUNCT
ejpam-5586	383	15	t	t	PROPN
ejpam-5586	383	16	)	)	PUNCT
ejpam-5586	383	17	s	s	PART
ejpam-5586	383	18	m	m	VERB
ejpam-5586	383	19	2	2	NUM
ejpam-5586	383	20	j	j	PROPN
ejpam-5586	383	21	(	(	PUNCT
ejpam-5586	383	22	s	s	NOUN
ejpam-5586	383	23	)	)	PUNCT
ejpam-5586	383	24			PROPN
ejpam-5586	383	25	hence	hence	ADV
ejpam-5586	383	26	tr	tr	NOUN
ejpam-5586	383	27	m	m	PROPN
ejpam-5586	383	28	r	r	NOUN
ejpam-5586	383	29	(	(	PUNCT
ejpam-5586	383	30	t	t	NOUN
ejpam-5586	383	31	r	r	NOUN
ejpam-5586	383	32	p	p	PROPN
ejpam-5586	383	33	+	+	NUM
ejpam-5586	383	34	sr	sr	PROPN
ejpam-5586	383	35	q	q	PROPN
ejpam-5586	383	36	)	)	PUNCT
ejpam-5586	383	37	≥	≥	PROPN
ejpam-5586	383	38	n∑	n∑	NOUN
ejpam-5586	383	39	j=1	j=1	PROPN
ejpam-5586	383	40	smj	smj	PROPN
ejpam-5586	383	41	(	(	PUNCT
ejpam-5586	383	42	t	t	PROPN
ejpam-5586	383	43	1	1	NUM
ejpam-5586	383	44	ps	ps	PROPN
ejpam-5586	383	45	1	1	NUM
ejpam-5586	383	46	q	q	NOUN
ejpam-5586	383	47	)	)	PUNCT
ejpam-5586	384	1	+	+	CCONJ
ejpam-5586	384	2	rm0	rm0	PROPN
ejpam-5586	384	3			PROPN
ejpam-5586	384	4	n∑	n∑	PROPN
ejpam-5586	384	5	j=1	j=1	PROPN
ejpam-5586	384	6	smj	smj	PROPN
ejpam-5586	384	7	(	(	PUNCT
ejpam-5586	384	8	t	t	PROPN
ejpam-5586	384	9	)	)	PUNCT
ejpam-5586	385	1	+	+	CCONJ
ejpam-5586	385	2	n∑	n∑	PROPN
ejpam-5586	385	3	j=1	j=1	NOUN
ejpam-5586	385	4	smj	smj	PROPN
ejpam-5586	385	5	(	(	PUNCT
ejpam-5586	385	6	s)−	s)−	PROPN
ejpam-5586	385	7	2	2	NUM
ejpam-5586	385	8	n∑	n∑	NOUN
ejpam-5586	385	9	j=1	j=1	PROPN
ejpam-5586	385	10	s	s	VERB
ejpam-5586	385	11	m	m	VERB
ejpam-5586	385	12	2	2	NUM
ejpam-5586	385	13	j	j	PROPN
ejpam-5586	385	14	(	(	PUNCT
ejpam-5586	385	15	t	t	PROPN
ejpam-5586	385	16	)	)	PUNCT
ejpam-5586	385	17	s	s	PART
ejpam-5586	385	18	m	m	VERB
ejpam-5586	385	19	2	2	NUM
ejpam-5586	385	20	j	j	PROPN
ejpam-5586	385	21	(	(	PUNCT
ejpam-5586	385	22	s	s	NOUN
ejpam-5586	385	23	)	)	PUNCT
ejpam-5586	385	24			PROPN
ejpam-5586	385	25	≥	≥	NOUN
ejpam-5586	385	26	(	(	PUNCT
ejpam-5586	385	27	tr	tr	VERB
ejpam-5586	385	28	∣∣∣(t	∣∣∣(t	PROPN
ejpam-5586	385	29	1	1	NUM
ejpam-5586	385	30	ps	ps	NOUN
ejpam-5586	385	31	1	1	NUM
ejpam-5586	385	32	q	q	NOUN
ejpam-5586	385	33	)	)	PUNCT
ejpam-5586	385	34	∣∣∣)m	∣∣∣)m	NOUN
ejpam-5586	385	35	+	+	CCONJ
ejpam-5586	385	36	rm0	rm0	NOUN
ejpam-5586	385	37	[	[	X
ejpam-5586	385	38	(	(	PUNCT
ejpam-5586	385	39	tr(t	tr(t	NOUN
ejpam-5586	385	40	)	)	PUNCT
ejpam-5586	385	41	)	)	PUNCT
ejpam-5586	386	1	m	m	VERB
ejpam-5586	386	2	+	+	X
ejpam-5586	386	3	(	(	PUNCT
ejpam-5586	386	4	tr(s))m	tr(s))m	X
ejpam-5586	386	5	m.h.m	m.h.m	PROPN
ejpam-5586	386	6	rashid	rashid	PROPN
ejpam-5586	386	7	,	,	PUNCT
ejpam-5586	386	8	w.m.m	w.m.m	NOUN
ejpam-5586	386	9	.	.	PUNCT
ejpam-5586	387	1	salameh	salameh	PROPN
ejpam-5586	387	2	/	/	SYM
ejpam-5586	387	3	eur	eur	PROPN
ejpam-5586	387	4	.	.	PUNCT
ejpam-5586	388	1	j.	j.	PROPN
ejpam-5586	388	2	pure	pure	PROPN
ejpam-5586	388	3	appl	appl	PROPN
ejpam-5586	388	4	.	.	PROPN
ejpam-5586	388	5	math	math	PROPN
ejpam-5586	388	6	,	,	PUNCT
ejpam-5586	388	7	18	18	NUM
ejpam-5586	388	8	(	(	PUNCT
ejpam-5586	388	9	1	1	NUM
ejpam-5586	388	10	)	)	PUNCT
ejpam-5586	388	11	(	(	PUNCT
ejpam-5586	388	12	2025	2025	NUM
ejpam-5586	388	13	)	)	PUNCT
ejpam-5586	388	14	,	,	PUNCT
ejpam-5586	388	15	5586	5586	NUM
ejpam-5586	388	16	14	14	NUM
ejpam-5586	388	17	of	of	ADP
ejpam-5586	388	18	21	21	NUM
ejpam-5586	388	19	−	−	NOUN
ejpam-5586	388	20	2	2	NUM
ejpam-5586	388	21			PROPN
ejpam-5586	388	22	n∑	n∑	PROPN
ejpam-5586	388	23	j=1	j=1	NOUN
ejpam-5586	388	24	sj(t	sj(t	PRON
ejpam-5586	388	25	)	)	PUNCT
ejpam-5586	388	26	m	m	NOUN
ejpam-5586	388	27	2	2	NUM
ejpam-5586	389	1			PROPN
ejpam-5586	389	2	n∑	n∑	PROPN
ejpam-5586	389	3	j=1	j=1	PROPN
ejpam-5586	389	4	sj(s	sj(s	X
ejpam-5586	389	5	)	)	PUNCT
ejpam-5586	389	6	m	m	NOUN
ejpam-5586	389	7	2	2	NUM
ejpam-5586	389	8			NUM
ejpam-5586	389	9	=	=	PUNCT
ejpam-5586	389	10	(	(	PUNCT
ejpam-5586	389	11	tr	tr	VERB
ejpam-5586	389	12	∣∣∣(t	∣∣∣(t	PROPN
ejpam-5586	389	13	1	1	NUM
ejpam-5586	389	14	ps	ps	NOUN
ejpam-5586	389	15	1	1	NUM
ejpam-5586	389	16	q	q	NOUN
ejpam-5586	389	17	)	)	PUNCT
ejpam-5586	389	18	∣∣∣)m	∣∣∣)m	NOUN
ejpam-5586	390	1	+	+	PUNCT
ejpam-5586	390	2	rm0	rm0	NOUN
ejpam-5586	390	3	(	(	PUNCT
ejpam-5586	390	4	(	(	PUNCT
ejpam-5586	390	5	tr(t	tr(t	NOUN
ejpam-5586	390	6	)	)	PUNCT
ejpam-5586	390	7	)	)	PUNCT
ejpam-5586	390	8	m	m	VERB
ejpam-5586	390	9	2	2	NUM
ejpam-5586	390	10	−	−	NOUN
ejpam-5586	390	11	(	(	PUNCT
ejpam-5586	390	12	tr(s	tr(s	NOUN
ejpam-5586	390	13	)	)	PUNCT
ejpam-5586	390	14	)	)	PUNCT
ejpam-5586	391	1	m	m	VERB
ejpam-5586	391	2	2	2	NUM
ejpam-5586	391	3	)	)	SYM
ejpam-5586	391	4	2	2	NUM
ejpam-5586	391	5	remark	remark	NOUN
ejpam-5586	391	6	4	4	NUM
ejpam-5586	391	7	.	.	PUNCT
ejpam-5586	391	8	ando	ando	PROPN
ejpam-5586	391	9	’s	’s	PART
ejpam-5586	391	10	singular	singular	PROPN
ejpam-5586	391	11	value	value	NOUN
ejpam-5586	391	12	inequality	inequality	NOUN
ejpam-5586	391	13	(	(	PUNCT
ejpam-5586	391	14	27	27	NUM
ejpam-5586	391	15	)	)	PUNCT
ejpam-5586	391	16	entails	entail	VERB
ejpam-5586	391	17	the	the	DET
ejpam-5586	391	18	norm	norm	NOUN
ejpam-5586	391	19	inequality∣∣∣∣∣∣t	inequality∣∣∣∣∣∣t	NOUN
ejpam-5586	391	20	κs1−κ	κs1−κ	VERB
ejpam-5586	391	21	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-5586	391	22	≤	≤	NUM
ejpam-5586	391	23	|||κt	|||κt	NOUN
ejpam-5586	391	24	+	+	CCONJ
ejpam-5586	391	25	(	(	PUNCT
ejpam-5586	391	26	1−	1−	NUM
ejpam-5586	391	27	κ)s|||	κ)s|||	NOUN
ejpam-5586	391	28	.	.	PUNCT
ejpam-5586	392	1	(	(	PUNCT
ejpam-5586	392	2	30	30	NUM
ejpam-5586	392	3	)	)	PUNCT
ejpam-5586	392	4	so	so	ADV
ejpam-5586	392	5	,	,	PUNCT
ejpam-5586	392	6	our	our	PRON
ejpam-5586	392	7	theorem	theorem	ADJ
ejpam-5586	392	8	8	8	NUM
ejpam-5586	392	9	improves	improve	VERB
ejpam-5586	392	10	this	this	DET
ejpam-5586	392	11	inequality	inequality	NOUN
ejpam-5586	392	12	for	for	ADP
ejpam-5586	392	13	the	the	DET
ejpam-5586	392	14	trace	trace	NOUN
ejpam-5586	393	1	norm:∥∥∥t	norm:∥∥∥t	ADJ
ejpam-5586	393	2	1	1	NUM
ejpam-5586	393	3	ps	ps	PROPN
ejpam-5586	393	4	1	1	NUM
ejpam-5586	393	5	q	q	NOUN
ejpam-5586	393	6	∥∥∥m	∥∥∥m	ADV
ejpam-5586	393	7	1	1	NUM
ejpam-5586	394	1	+	+	NUM
ejpam-5586	394	2	rm0	rm0	NOUN
ejpam-5586	394	3	(	(	PUNCT
ejpam-5586	394	4	∥t∥	∥t∥	ADP
ejpam-5586	394	5	m	m	PROPN
ejpam-5586	394	6	2	2	NUM
ejpam-5586	394	7	1	1	NUM
ejpam-5586	394	8	−	−	NOUN
ejpam-5586	394	9	∥s∥	∥s∥	ADJ
ejpam-5586	394	10	m	m	VERB
ejpam-5586	394	11	2	2	NUM
ejpam-5586	394	12	1	1	NUM
ejpam-5586	394	13	)	)	SYM
ejpam-5586	394	14	2	2	NUM
ejpam-5586	394	15	≤	≤	NOUN
ejpam-5586	394	16	∥∥∥∥1pt	∥∥∥∥1pt	VERB
ejpam-5586	394	17	r	r	NOUN
ejpam-5586	394	18	+	+	NOUN
ejpam-5586	394	19	1	1	NUM
ejpam-5586	394	20	q	q	NOUN
ejpam-5586	394	21	sr	sr	PROPN
ejpam-5586	394	22	∥∥∥∥m	∥∥∥∥m	NOUN
ejpam-5586	394	23	r	r	NOUN
ejpam-5586	394	24	1	1	NUM
ejpam-5586	394	25	(	(	PUNCT
ejpam-5586	394	26	31	31	NUM
ejpam-5586	394	27	)	)	PUNCT
ejpam-5586	394	28	theorem	theorem	NOUN
ejpam-5586	394	29	9	9	NUM
ejpam-5586	394	30	.	.	PUNCT
ejpam-5586	395	1	let	let	VERB
ejpam-5586	395	2	t	t	PROPN
ejpam-5586	395	3	,	,	PUNCT
ejpam-5586	395	4	s	s	PART
ejpam-5586	395	5	∈	∈	PROPN
ejpam-5586	395	6	b(h	b(h	PROPN
ejpam-5586	395	7	)	)	PUNCT
ejpam-5586	395	8	be	be	AUX
ejpam-5586	395	9	positive	positive	ADJ
ejpam-5586	395	10	definite	definite	ADJ
ejpam-5586	395	11	,	,	PUNCT
ejpam-5586	395	12	p	p	X
ejpam-5586	395	13	,	,	PUNCT
ejpam-5586	395	14	q	q	X
ejpam-5586	395	15	>	>	X
ejpam-5586	395	16	1	1	NUM
ejpam-5586	395	17	such	such	ADJ
ejpam-5586	395	18	that	that	SCONJ
ejpam-5586	395	19	1	1	NUM
ejpam-5586	395	20	p+	p+	NOUN
ejpam-5586	395	21	1	1	NUM
ejpam-5586	395	22	q	q	NOUN
ejpam-5586	395	23	=	=	SYM
ejpam-5586	395	24	1	1	NUM
ejpam-5586	395	25	and	and	CCONJ
ejpam-5586	395	26	m	m	PROPN
ejpam-5586	395	27	∈	∈	PROPN
ejpam-5586	395	28	n.	n.	NOUN
ejpam-5586	395	29	then	then	ADV
ejpam-5586	395	30	for	for	ADP
ejpam-5586	395	31	all	all	DET
ejpam-5586	395	32	r	r	NOUN
ejpam-5586	395	33	≥	≥	NUM
ejpam-5586	395	34	1	1	NUM
ejpam-5586	395	35	det	det	X
ejpam-5586	395	36	(	(	PUNCT
ejpam-5586	396	1	t	t	NOUN
ejpam-5586	396	2	r	r	NOUN
ejpam-5586	396	3	p	p	PROPN
ejpam-5586	397	1	+	+	NUM
ejpam-5586	397	2	sr	sr	PROPN
ejpam-5586	397	3	q	q	PROPN
ejpam-5586	397	4	)	)	PUNCT
ejpam-5586	397	5	m	m	VERB
ejpam-5586	397	6	r	r	NOUN
ejpam-5586	397	7	≥	≥	NOUN
ejpam-5586	397	8	det	det	NOUN
ejpam-5586	397	9	(	(	PUNCT
ejpam-5586	397	10	t	t	PROPN
ejpam-5586	397	11	1	1	NUM
ejpam-5586	397	12	ps	ps	PROPN
ejpam-5586	397	13	1	1	NUM
ejpam-5586	397	14	q	q	NOUN
ejpam-5586	397	15	)	)	PUNCT
ejpam-5586	397	16	m	m	VERB
ejpam-5586	397	17	+	+	CCONJ
ejpam-5586	397	18	rmn	rmn	PROPN
ejpam-5586	397	19	0	0	PROPN
ejpam-5586	397	20	det	det	PROPN
ejpam-5586	397	21	(	(	PUNCT
ejpam-5586	397	22	tm	tm	PROPN
ejpam-5586	397	23	+	+	PROPN
ejpam-5586	397	24	sm	sm	PROPN
ejpam-5586	397	25	−	−	PROPN
ejpam-5586	398	1	2s	2s	NUM
ejpam-5586	398	2	m	m	VERB
ejpam-5586	398	3	2	2	NUM
ejpam-5586	398	4	(	(	PUNCT
ejpam-5586	398	5	s−	s−	PROPN
ejpam-5586	398	6	1	1	NUM
ejpam-5586	398	7	2ts−	2ts−	NUM
ejpam-5586	398	8	1	1	NUM
ejpam-5586	398	9	2	2	NUM
ejpam-5586	398	10	)	)	PUNCT
ejpam-5586	398	11	m	m	PROPN
ejpam-5586	398	12	s	s	NOUN
ejpam-5586	398	13	m	m	ADJ
ejpam-5586	398	14	2	2	NUM
ejpam-5586	398	15	)	)	PUNCT
ejpam-5586	398	16	2	2	NUM
ejpam-5586	398	17	,	,	PUNCT
ejpam-5586	398	18	(	(	PUNCT
ejpam-5586	398	19	32	32	NUM
ejpam-5586	398	20	)	)	PUNCT
ejpam-5586	398	21	where	where	SCONJ
ejpam-5586	398	22	r0	r0	NOUN
ejpam-5586	398	23	=	=	PROPN
ejpam-5586	398	24	min{1	min{1	PROPN
ejpam-5586	398	25	p	p	NOUN
ejpam-5586	398	26	,	,	PUNCT
ejpam-5586	398	27	1	1	NUM
ejpam-5586	398	28	q	q	NOUN
ejpam-5586	398	29	}	}	PUNCT
ejpam-5586	398	30	.	.	PUNCT
ejpam-5586	399	1	proof	proof	NOUN
ejpam-5586	399	2	.	.	PUNCT
ejpam-5586	400	1	by	by	ADP
ejpam-5586	400	2	inequality	inequality	NOUN
ejpam-5586	400	3	(	(	PUNCT
ejpam-5586	400	4	28	28	NUM
ejpam-5586	400	5	)	)	PUNCT
ejpam-5586	400	6	,	,	PUNCT
ejpam-5586	400	7	we	we	PRON
ejpam-5586	400	8	have	have	VERB
ejpam-5586	400	9	s	s	VERB
ejpam-5586	400	10	m	m	PROPN
ejpam-5586	400	11	r	r	NOUN
ejpam-5586	400	12	j	j	PROPN
ejpam-5586	401	1	(	(	PUNCT
ejpam-5586	401	2	1	1	NUM
ejpam-5586	401	3	p	p	NOUN
ejpam-5586	401	4	(	(	PUNCT
ejpam-5586	401	5	s−	s−	PROPN
ejpam-5586	401	6	r	r	NOUN
ejpam-5586	401	7	2	2	NUM
ejpam-5586	401	8	t	t	NOUN
ejpam-5586	401	9	rs−	rs−	PUNCT
ejpam-5586	401	10	r	r	NOUN
ejpam-5586	401	11	2	2	NUM
ejpam-5586	401	12	)	)	PUNCT
ejpam-5586	401	13	+	+	CCONJ
ejpam-5586	401	14	1	1	NUM
ejpam-5586	401	15	q	q	NOUN
ejpam-5586	401	16	i	i	PROPN
ejpam-5586	401	17	)	)	PUNCT
ejpam-5586	401	18	≥	≥	PROPN
ejpam-5586	401	19	s	s	NOUN
ejpam-5586	401	20	m	m	PROPN
ejpam-5586	401	21	p	p	ADJ
ejpam-5586	401	22	j	j	PROPN
ejpam-5586	401	23	(	(	PUNCT
ejpam-5586	401	24	s−	s−	PROPN
ejpam-5586	401	25	1	1	NUM
ejpam-5586	401	26	2ts−	2ts−	NUM
ejpam-5586	401	27	1	1	NUM
ejpam-5586	401	28	2	2	NUM
ejpam-5586	401	29	)	)	PUNCT
ejpam-5586	402	1	+	+	CCONJ
ejpam-5586	402	2	rm0	rm0	NOUN
ejpam-5586	402	3	(	(	PUNCT
ejpam-5586	402	4	s	s	NOUN
ejpam-5586	402	5	m	m	PROPN
ejpam-5586	402	6	2	2	NUM
ejpam-5586	402	7	j	j	NOUN
ejpam-5586	402	8	(	(	PUNCT
ejpam-5586	402	9	s−	s−	PROPN
ejpam-5586	402	10	1	1	NUM
ejpam-5586	402	11	2ts−	2ts−	NUM
ejpam-5586	402	12	1	1	NUM
ejpam-5586	402	13	2	2	NUM
ejpam-5586	402	14	)	)	PUNCT
ejpam-5586	402	15	−	−	NOUN
ejpam-5586	402	16	1	1	NUM
ejpam-5586	402	17	)	)	PUNCT
ejpam-5586	402	18	2	2	NUM
ejpam-5586	402	19	for	for	ADP
ejpam-5586	402	20	all	all	DET
ejpam-5586	402	21	j	j	NOUN
ejpam-5586	402	22	=	=	SYM
ejpam-5586	402	23	1	1	NUM
ejpam-5586	402	24	,	,	PUNCT
ejpam-5586	402	25	·	·	PUNCT
ejpam-5586	402	26	·	·	PUNCT
ejpam-5586	402	27	·	·	PUNCT
ejpam-5586	402	28	,	,	PUNCT
ejpam-5586	402	29	n.	n.	PROPN
ejpam-5586	402	30	det	det	PROPN
ejpam-5586	402	31	(	(	PUNCT
ejpam-5586	402	32	1	1	NUM
ejpam-5586	402	33	p	p	NOUN
ejpam-5586	402	34	s−	s−	PROPN
ejpam-5586	402	35	r	r	NOUN
ejpam-5586	402	36	2ts−	2ts−	NUM
ejpam-5586	402	37	r	r	NOUN
ejpam-5586	402	38	2	2	NUM
ejpam-5586	402	39	+	+	CCONJ
ejpam-5586	402	40	1	1	NUM
ejpam-5586	402	41	q	q	NOUN
ejpam-5586	402	42	)	)	PUNCT
ejpam-5586	402	43	m	m	NOUN
ejpam-5586	402	44	r	r	NOUN
ejpam-5586	402	45	=	=	SYM
ejpam-5586	402	46	n∏	n∏	PROPN
ejpam-5586	402	47	j=1	j=1	NOUN
ejpam-5586	402	48	(	(	PUNCT
ejpam-5586	402	49	1	1	NUM
ejpam-5586	402	50	p	p	NOUN
ejpam-5586	402	51	s	s	NOUN
ejpam-5586	402	52	m	m	NOUN
ejpam-5586	402	53	r	r	NOUN
ejpam-5586	402	54	j	j	NOUN
ejpam-5586	402	55	(	(	PUNCT
ejpam-5586	402	56	s−	s−	PROPN
ejpam-5586	402	57	r	r	NOUN
ejpam-5586	402	58	2	2	NUM
ejpam-5586	402	59	t	t	NOUN
ejpam-5586	402	60	rs−	rs−	PUNCT
ejpam-5586	402	61	r	r	NOUN
ejpam-5586	402	62	2	2	NUM
ejpam-5586	402	63	+	+	SYM
ejpam-5586	402	64	1	1	NUM
ejpam-5586	402	65	q	q	NOUN
ejpam-5586	402	66	)	)	PUNCT
ejpam-5586	402	67	)	)	PUNCT
ejpam-5586	402	68	≥	≥	PROPN
ejpam-5586	403	1	n∏	n∏	NOUN
ejpam-5586	403	2	j=1	j=1	NOUN
ejpam-5586	403	3	[	[	PUNCT
ejpam-5586	403	4	s	s	VERB
ejpam-5586	403	5	m	m	PROPN
ejpam-5586	403	6	p	p	ADJ
ejpam-5586	403	7	j	j	PROPN
ejpam-5586	403	8	(	(	PUNCT
ejpam-5586	403	9	s−	s−	PROPN
ejpam-5586	403	10	1	1	NUM
ejpam-5586	403	11	2ts−	2ts−	NUM
ejpam-5586	403	12	1	1	NUM
ejpam-5586	403	13	2	2	NUM
ejpam-5586	403	14	)	)	PUNCT
ejpam-5586	404	1	+	+	CCONJ
ejpam-5586	404	2	rm0	rm0	NOUN
ejpam-5586	404	3	(	(	PUNCT
ejpam-5586	404	4	s	s	NOUN
ejpam-5586	404	5	m	m	PROPN
ejpam-5586	404	6	2	2	NUM
ejpam-5586	404	7	j	j	NOUN
ejpam-5586	404	8	(	(	PUNCT
ejpam-5586	404	9	s−	s−	PROPN
ejpam-5586	404	10	1	1	NUM
ejpam-5586	404	11	2ts−	2ts−	NUM
ejpam-5586	404	12	1	1	NUM
ejpam-5586	404	13	2	2	NUM
ejpam-5586	404	14	)	)	PUNCT
ejpam-5586	404	15	−	−	NOUN
ejpam-5586	404	16	1	1	NUM
ejpam-5586	404	17	)	)	PUNCT
ejpam-5586	404	18	2	2	NUM
ejpam-5586	404	19	]	]	PUNCT
ejpam-5586	404	20	≥	≥	NOUN
ejpam-5586	404	21	n∏	n∏	NOUN
ejpam-5586	404	22	j=1	j=1	NOUN
ejpam-5586	404	23	[	[	PUNCT
ejpam-5586	404	24	s	s	VERB
ejpam-5586	404	25	1	1	NUM
ejpam-5586	404	26	p	p	NOUN
ejpam-5586	404	27	j	j	PROPN
ejpam-5586	404	28	(	(	PUNCT
ejpam-5586	404	29	s−	s−	PROPN
ejpam-5586	404	30	1	1	NUM
ejpam-5586	404	31	2ts−	2ts−	NUM
ejpam-5586	404	32	1	1	NUM
ejpam-5586	404	33	2	2	NUM
ejpam-5586	404	34	)	)	PUNCT
ejpam-5586	404	35	m	m	VERB
ejpam-5586	404	36	]	]	PUNCT
ejpam-5586	405	1	+	+	CCONJ
ejpam-5586	405	2	rmn	rmn	PROPN
ejpam-5586	405	3	0	0	PROPN
ejpam-5586	405	4	n∏	n∏	PROPN
ejpam-5586	405	5	j=1	j=1	NOUN
ejpam-5586	405	6	[	[	PUNCT
ejpam-5586	405	7	s	s	NOUN
ejpam-5586	405	8	m	m	VERB
ejpam-5586	405	9	2	2	NUM
ejpam-5586	405	10	j	j	NOUN
ejpam-5586	405	11	(	(	PUNCT
ejpam-5586	405	12	s−	s−	PROPN
ejpam-5586	405	13	1	1	NUM
ejpam-5586	405	14	2ts−	2ts−	NUM
ejpam-5586	405	15	1	1	NUM
ejpam-5586	405	16	2	2	NUM
ejpam-5586	405	17	)	)	PUNCT
ejpam-5586	405	18	−	−	NOUN
ejpam-5586	405	19	1	1	NUM
ejpam-5586	405	20	]	]	SYM
ejpam-5586	405	21	2	2	NUM
ejpam-5586	405	22	=	=	SYM
ejpam-5586	405	23	det	det	X
ejpam-5586	405	24	(	(	PUNCT
ejpam-5586	405	25	s−	s−	PROPN
ejpam-5586	405	26	1	1	NUM
ejpam-5586	405	27	2ts−	2ts−	NUM
ejpam-5586	405	28	1	1	NUM
ejpam-5586	405	29	2	2	NUM
ejpam-5586	405	30	)	)	PUNCT
ejpam-5586	405	31	m	m	VERB
ejpam-5586	405	32	p	p	NOUN
ejpam-5586	405	33	+	+	CCONJ
ejpam-5586	405	34	rmn	rmn	NOUN
ejpam-5586	405	35	0	0	PUNCT
ejpam-5586	406	1	[	[	X
ejpam-5586	406	2	(	(	PUNCT
ejpam-5586	406	3	s−	s−	PROPN
ejpam-5586	406	4	1	1	NUM
ejpam-5586	406	5	2ts−	2ts−	NUM
ejpam-5586	406	6	1	1	NUM
ejpam-5586	406	7	2	2	NUM
ejpam-5586	406	8	)	)	PUNCT
ejpam-5586	406	9	m	m	VERB
ejpam-5586	406	10	2	2	NUM
ejpam-5586	406	11	−	−	NOUN
ejpam-5586	406	12	i	i	PRON
ejpam-5586	406	13	]	]	X
ejpam-5586	406	14	2	2	X
ejpam-5586	406	15	.	.	PUNCT
ejpam-5586	407	1	m.h.m	m.h.m	PROPN
ejpam-5586	407	2	rashid	rashid	PROPN
ejpam-5586	407	3	,	,	PUNCT
ejpam-5586	407	4	w.m.m	w.m.m	NOUN
ejpam-5586	407	5	.	.	PUNCT
ejpam-5586	408	1	salameh	salameh	PROPN
ejpam-5586	408	2	/	/	SYM
ejpam-5586	408	3	eur	eur	PROPN
ejpam-5586	408	4	.	.	PUNCT
ejpam-5586	409	1	j.	j.	PROPN
ejpam-5586	409	2	pure	pure	PROPN
ejpam-5586	409	3	appl	appl	PROPN
ejpam-5586	409	4	.	.	PROPN
ejpam-5586	409	5	math	math	PROPN
ejpam-5586	409	6	,	,	PUNCT
ejpam-5586	409	7	18	18	NUM
ejpam-5586	409	8	(	(	PUNCT
ejpam-5586	409	9	1	1	NUM
ejpam-5586	409	10	)	)	PUNCT
ejpam-5586	409	11	(	(	PUNCT
ejpam-5586	409	12	2025	2025	NUM
ejpam-5586	409	13	)	)	PUNCT
ejpam-5586	409	14	,	,	PUNCT
ejpam-5586	409	15	5586	5586	NUM
ejpam-5586	409	16	15	15	NUM
ejpam-5586	409	17	of	of	ADP
ejpam-5586	409	18	21	21	NUM
ejpam-5586	409	19	consequently	consequently	ADV
ejpam-5586	409	20	det	det	PROPN
ejpam-5586	409	21	(	(	PUNCT
ejpam-5586	409	22	t	t	NOUN
ejpam-5586	409	23	r	r	NOUN
ejpam-5586	409	24	p	p	PROPN
ejpam-5586	409	25	+	+	NUM
ejpam-5586	409	26	sr	sr	PROPN
ejpam-5586	409	27	q	q	PROPN
ejpam-5586	409	28	)	)	PUNCT
ejpam-5586	409	29	m	m	VERB
ejpam-5586	409	30	r	r	NOUN
ejpam-5586	409	31	≥	≥	NOUN
ejpam-5586	409	32	det	det	NOUN
ejpam-5586	409	33	(	(	PUNCT
ejpam-5586	409	34	t	t	PROPN
ejpam-5586	409	35	1	1	NUM
ejpam-5586	409	36	ps	ps	PROPN
ejpam-5586	409	37	1	1	NUM
ejpam-5586	409	38	q	q	NOUN
ejpam-5586	409	39	)	)	PUNCT
ejpam-5586	409	40	m	m	VERB
ejpam-5586	409	41	+	+	CCONJ
ejpam-5586	409	42	rmn	rmn	PROPN
ejpam-5586	409	43	0	0	PROPN
ejpam-5586	409	44	det	det	PROPN
ejpam-5586	409	45	(	(	PUNCT
ejpam-5586	409	46	tm	tm	PROPN
ejpam-5586	409	47	+	+	PROPN
ejpam-5586	410	1	sm	sm	PROPN
ejpam-5586	411	1	−	−	PROPN
ejpam-5586	411	2	2s	2s	NUM
ejpam-5586	411	3	m	m	VERB
ejpam-5586	411	4	2	2	NUM
ejpam-5586	411	5	(	(	PUNCT
ejpam-5586	411	6	s−	s−	PROPN
ejpam-5586	411	7	1	1	NUM
ejpam-5586	411	8	2ts−	2ts−	NUM
ejpam-5586	411	9	1	1	NUM
ejpam-5586	411	10	2	2	NUM
ejpam-5586	411	11	)	)	PUNCT
ejpam-5586	411	12	m	m	PROPN
ejpam-5586	411	13	s	s	NOUN
ejpam-5586	411	14	m	m	ADJ
ejpam-5586	411	15	2	2	NUM
ejpam-5586	411	16	)	)	PUNCT
ejpam-5586	411	17	2	2	NUM
ejpam-5586	411	18	.	.	PUNCT
ejpam-5586	412	1	theorem	theorem	NOUN
ejpam-5586	412	2	10	10	NUM
ejpam-5586	412	3	.	.	PUNCT
ejpam-5586	413	1	let	let	VERB
ejpam-5586	413	2	t	t	PROPN
ejpam-5586	413	3	,	,	PUNCT
ejpam-5586	413	4	s	s	X
ejpam-5586	413	5	,	,	PUNCT
ejpam-5586	413	6	x	x	SYM
ejpam-5586	413	7	∈	∈	NOUN
ejpam-5586	413	8	mn(c	mn(c	X
ejpam-5586	413	9	)	)	PUNCT
ejpam-5586	413	10	such	such	ADJ
ejpam-5586	413	11	that	that	SCONJ
ejpam-5586	413	12	t	t	PROPN
ejpam-5586	413	13	and	and	CCONJ
ejpam-5586	413	14	s	s	VERB
ejpam-5586	413	15	are	be	AUX
ejpam-5586	413	16	positive	positive	ADJ
ejpam-5586	413	17	semi	semi	ADJ
ejpam-5586	413	18	-	-	ADJ
ejpam-5586	413	19	definite	definite	ADJ
ejpam-5586	413	20	and	and	CCONJ
ejpam-5586	413	21	p	p	X
ejpam-5586	413	22	,	,	PUNCT
ejpam-5586	413	23	q	q	X
ejpam-5586	413	24	>	>	X
ejpam-5586	413	25	1	1	NUM
ejpam-5586	413	26	with	with	ADP
ejpam-5586	413	27	1	1	NUM
ejpam-5586	413	28	p	p	NOUN
ejpam-5586	414	1	+	+	NOUN
ejpam-5586	414	2	1	1	NUM
ejpam-5586	414	3	q	q	NOUN
ejpam-5586	414	4	=	=	SYM
ejpam-5586	414	5	1	1	NUM
ejpam-5586	414	6	and	and	CCONJ
ejpam-5586	414	7	m	m	PROPN
ejpam-5586	414	8	∈	∈	PROPN
ejpam-5586	414	9	n.	n.	NOUN
ejpam-5586	414	10	then	then	ADV
ejpam-5586	414	11	for	for	ADP
ejpam-5586	414	12	all	all	DET
ejpam-5586	414	13	r	r	NOUN
ejpam-5586	414	14	≥	≥	NOUN
ejpam-5586	414	15	1	1	NUM
ejpam-5586	414	16	,	,	PUNCT
ejpam-5586	414	17	we	we	PRON
ejpam-5586	414	18	have	have	AUX
ejpam-5586	414	19	∣∣∣∣∣∣∣∣∣t	∣∣∣∣∣∣∣∣∣t	NOUN
ejpam-5586	414	20	1	1	NUM
ejpam-5586	414	21	pxs	pxs	NOUN
ejpam-5586	414	22	1	1	NUM
ejpam-5586	414	23	q	q	NOUN
ejpam-5586	414	24	∣∣∣∣∣∣∣∣∣m	∣∣∣∣∣∣∣∣∣m	NOUN
ejpam-5586	414	25	+	+	CCONJ
ejpam-5586	414	26	rm0	rm0	NOUN
ejpam-5586	414	27	(	(	PUNCT
ejpam-5586	414	28	|||tx|||	|||tx|||	X
ejpam-5586	414	29	m	m	VERB
ejpam-5586	414	30	2	2	NUM
ejpam-5586	414	31	−	−	NOUN
ejpam-5586	414	32	|||sx|||	|||sx|||	NOUN
ejpam-5586	414	33	m	m	PROPN
ejpam-5586	414	34	2	2	NUM
ejpam-5586	414	35	)	)	SYM
ejpam-5586	414	36	2	2	NUM
ejpam-5586	414	37	≤	≤	NOUN
ejpam-5586	414	38	(	(	PUNCT
ejpam-5586	414	39	1	1	NUM
ejpam-5586	414	40	p	p	NOUN
ejpam-5586	414	41	|||tx|||r	|||tx|||r	ADP
ejpam-5586	414	42	+	+	CCONJ
ejpam-5586	414	43	1	1	NUM
ejpam-5586	414	44	q	q	NOUN
ejpam-5586	414	45	|||xb|||r	|||xb|||r	PROPN
ejpam-5586	414	46	)	)	PUNCT
ejpam-5586	414	47	m	m	PROPN
ejpam-5586	414	48	r	r	NOUN
ejpam-5586	414	49	,	,	PUNCT
ejpam-5586	414	50	(	(	PUNCT
ejpam-5586	414	51	33	33	NUM
ejpam-5586	414	52	)	)	PUNCT
ejpam-5586	414	53	where	where	SCONJ
ejpam-5586	414	54	r0	r0	NOUN
ejpam-5586	414	55	=	=	PROPN
ejpam-5586	414	56	min{1	min{1	PROPN
ejpam-5586	414	57	p	p	NOUN
ejpam-5586	414	58	,	,	PUNCT
ejpam-5586	414	59	1	1	NUM
ejpam-5586	414	60	q	q	NOUN
ejpam-5586	414	61	}	}	PUNCT
ejpam-5586	414	62	.	.	PUNCT
ejpam-5586	415	1	to	to	PART
ejpam-5586	415	2	prove	prove	VERB
ejpam-5586	415	3	theorem	theorem	VERB
ejpam-5586	415	4	10	10	NUM
ejpam-5586	415	5	,	,	PUNCT
ejpam-5586	415	6	we	we	PRON
ejpam-5586	415	7	need	need	VERB
ejpam-5586	415	8	the	the	DET
ejpam-5586	415	9	following	follow	VERB
ejpam-5586	415	10	lemma	lemma	PROPN
ejpam-5586	415	11	which	which	PRON
ejpam-5586	415	12	is	be	AUX
ejpam-5586	415	13	known	know	VERB
ejpam-5586	415	14	as	as	ADP
ejpam-5586	415	15	the	the	DET
ejpam-5586	415	16	heinz	heinz	PROPN
ejpam-5586	415	17	-	-	PUNCT
ejpam-5586	415	18	kato	kato	PROPN
ejpam-5586	415	19	type	type	NOUN
ejpam-5586	415	20	for	for	ADP
ejpam-5586	415	21	unitarily	unitarily	ADJ
ejpam-5586	415	22	invariant	invariant	ADJ
ejpam-5586	415	23	norm	norm	NOUN
ejpam-5586	415	24	.	.	PUNCT
ejpam-5586	416	1	lemma	lemma	PROPN
ejpam-5586	416	2	7	7	NUM
ejpam-5586	416	3	(	(	PUNCT
ejpam-5586	416	4	[	[	X
ejpam-5586	416	5	9	9	NUM
ejpam-5586	416	6	]	]	PUNCT
ejpam-5586	416	7	)	)	PUNCT
ejpam-5586	416	8	.	.	PUNCT
ejpam-5586	417	1	let	let	VERB
ejpam-5586	417	2	t	t	NOUN
ejpam-5586	417	3	,	,	PUNCT
ejpam-5586	417	4	s	s	PART
ejpam-5586	417	5	∈	∈	NOUN
ejpam-5586	417	6	mn(c	mn(c	X
ejpam-5586	417	7	)	)	PUNCT
ejpam-5586	417	8	be	be	AUX
ejpam-5586	417	9	positive	positive	ADJ
ejpam-5586	417	10	definite	definite	ADJ
ejpam-5586	417	11	matrices	matrix	NOUN
ejpam-5586	417	12	and	and	CCONJ
ejpam-5586	417	13	0	0	NUM
ejpam-5586	417	14	≤	≤	NOUN
ejpam-5586	418	1	ϑ	ϑ	PRON
ejpam-5586	418	2	≤	≤	ADJ
ejpam-5586	418	3	1	1	NUM
ejpam-5586	418	4	.	.	PUNCT
ejpam-5586	419	1	then	then	ADV
ejpam-5586	419	2	we	we	PRON
ejpam-5586	419	3	have	have	AUX
ejpam-5586	419	4	∣∣∣∣∣∣∣∣∣t	∣∣∣∣∣∣∣∣∣t	NOUN
ejpam-5586	419	5	ϑxs1−ϑ	ϑxs1−ϑ	X
ejpam-5586	419	6	∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5586	419	7	≤	≤	NUM
ejpam-5586	419	8	|||tx|||ϑ|||xb|||1−ϑ.	|||tx|||ϑ|||xb|||1−ϑ.	NUM
ejpam-5586	419	9	(	(	PUNCT
ejpam-5586	419	10	34	34	NUM
ejpam-5586	419	11	)	)	PUNCT
ejpam-5586	419	12	in	in	ADP
ejpam-5586	419	13	particular	particular	ADJ
ejpam-5586	419	14	tr	tr	PUNCT
ejpam-5586	419	15	∣∣∣t	∣∣∣t	NOUN
ejpam-5586	419	16	ϑxs1−ϑ	ϑxs1−ϑ	SYM
ejpam-5586	419	17	∣∣∣	∣∣∣	NOUN
ejpam-5586	419	18	≤	≤	NUM
ejpam-5586	419	19	(	(	PUNCT
ejpam-5586	419	20	tr(t	tr(t	NOUN
ejpam-5586	419	21	)	)	PUNCT
ejpam-5586	419	22	)	)	PUNCT
ejpam-5586	419	23	ϑ	ϑ	X
ejpam-5586	419	24	(	(	PUNCT
ejpam-5586	419	25	tr(s))1−ϑ	tr(s))1−ϑ	PROPN
ejpam-5586	419	26	.	.	PUNCT
ejpam-5586	420	1	(	(	PUNCT
ejpam-5586	420	2	35	35	NUM
ejpam-5586	420	3	)	)	PUNCT
ejpam-5586	420	4	proof	proof	NOUN
ejpam-5586	420	5	.	.	PUNCT
ejpam-5586	421	1	[	[	X
ejpam-5586	421	2	proof	proof	NOUN
ejpam-5586	421	3	of	of	ADP
ejpam-5586	421	4	theorem	theorem	NOUN
ejpam-5586	421	5	10	10	NUM
ejpam-5586	421	6	]	]	PUNCT
ejpam-5586	421	7	we	we	PRON
ejpam-5586	421	8	have∣∣∣∣∣∣∣∣∣t	have∣∣∣∣∣∣∣∣∣t	VERB
ejpam-5586	421	9	1	1	NUM
ejpam-5586	421	10	pxs	pxs	NOUN
ejpam-5586	421	11	1	1	NUM
ejpam-5586	421	12	q	q	NOUN
ejpam-5586	421	13	∣∣∣∣∣∣∣∣∣m	∣∣∣∣∣∣∣∣∣m	NOUN
ejpam-5586	421	14	+	+	CCONJ
ejpam-5586	421	15	rm0	rm0	NOUN
ejpam-5586	421	16	(	(	PUNCT
ejpam-5586	421	17	|||tx|||	|||tx|||	X
ejpam-5586	421	18	m	m	VERB
ejpam-5586	421	19	2	2	NUM
ejpam-5586	421	20	−	−	NOUN
ejpam-5586	421	21	|||sx|||	|||sx|||	NOUN
ejpam-5586	421	22	m	m	PROPN
ejpam-5586	421	23	2	2	NUM
ejpam-5586	421	24	)	)	SYM
ejpam-5586	421	25	2	2	NUM
ejpam-5586	421	26	≤	≤	NOUN
ejpam-5586	421	27	[	[	PUNCT
ejpam-5586	421	28	|||tx|||	|||tx|||	CCONJ
ejpam-5586	421	29	1	1	NUM
ejpam-5586	421	30	p	p	NOUN
ejpam-5586	421	31	|||xb|||	|||xb|||	NUM
ejpam-5586	421	32	1	1	NUM
ejpam-5586	421	33	q	q	NOUN
ejpam-5586	421	34	]	]	X
ejpam-5586	421	35	m	m	VERB
ejpam-5586	421	36	+	+	ADJ
ejpam-5586	421	37	rm0	rm0	NOUN
ejpam-5586	421	38	(	(	PUNCT
ejpam-5586	421	39	|||tx|||	|||tx|||	X
ejpam-5586	421	40	m	m	VERB
ejpam-5586	421	41	2	2	NUM
ejpam-5586	421	42	−	−	NOUN
ejpam-5586	421	43	|||sx|||	|||sx|||	NOUN
ejpam-5586	421	44	m	m	PROPN
ejpam-5586	421	45	2	2	NUM
ejpam-5586	421	46	)	)	PUNCT
ejpam-5586	421	47	2	2	NUM
ejpam-5586	421	48	(	(	PUNCT
ejpam-5586	421	49	by	by	ADP
ejpam-5586	421	50	lemma	lemma	PROPN
ejpam-5586	421	51	7	7	NUM
ejpam-5586	421	52	)	)	PUNCT
ejpam-5586	421	53	≤	≤	NOUN
ejpam-5586	421	54	(	(	PUNCT
ejpam-5586	421	55	1	1	NUM
ejpam-5586	421	56	p	p	NOUN
ejpam-5586	421	57	|||tx|||r	|||tx|||r	ADP
ejpam-5586	421	58	+	+	CCONJ
ejpam-5586	421	59	1	1	NUM
ejpam-5586	421	60	q	q	NOUN
ejpam-5586	421	61	|||xb|||r	|||xb|||r	PROPN
ejpam-5586	421	62	)	)	PUNCT
ejpam-5586	421	63	m	m	PROPN
ejpam-5586	421	64	r	r	NOUN
ejpam-5586	421	65	(	(	PUNCT
ejpam-5586	421	66	by	by	ADP
ejpam-5586	421	67	inequality	inequality	NOUN
ejpam-5586	421	68	28	28	NUM
ejpam-5586	421	69	)	)	PUNCT
ejpam-5586	421	70	.	.	PUNCT
ejpam-5586	422	1	lemma	lemma	PROPN
ejpam-5586	422	2	8	8	NUM
ejpam-5586	422	3	(	(	PUNCT
ejpam-5586	422	4	[	[	X
ejpam-5586	422	5	3	3	NUM
ejpam-5586	422	6	]	]	NUM
ejpam-5586	422	7	)	)	PUNCT
ejpam-5586	422	8	.	.	PUNCT
ejpam-5586	423	1	let	let	VERB
ejpam-5586	423	2	ω1	ω1	PROPN
ejpam-5586	423	3	,	,	PUNCT
ejpam-5586	423	4	·	·	PUNCT
ejpam-5586	423	5	·	·	PUNCT
ejpam-5586	423	6	·	·	PUNCT
ejpam-5586	423	7	,	,	PUNCT
ejpam-5586	423	8	ωn	ωn	PRON
ejpam-5586	423	9	be	be	AUX
ejpam-5586	423	10	non	non	ADJ
ejpam-5586	423	11	-	-	ADJ
ejpam-5586	423	12	negative	negative	ADJ
ejpam-5586	423	13	real	real	ADJ
ejpam-5586	423	14	numbers	number	NOUN
ejpam-5586	423	15	and	and	CCONJ
ejpam-5586	423	16	ϑ1	ϑ1	NOUN
ejpam-5586	423	17	,	,	PUNCT
ejpam-5586	423	18	·	·	PUNCT
ejpam-5586	423	19	·	·	PUNCT
ejpam-5586	423	20	·	·	PUNCT
ejpam-5586	423	21	,	,	PUNCT
ejpam-5586	423	22	ϑn	ϑn	ADP
ejpam-5586	423	23	be	be	AUX
ejpam-5586	423	24	positive	positive	ADJ
ejpam-5586	423	25	real	real	ADJ
ejpam-5586	423	26	numbers	number	NOUN
ejpam-5586	423	27	with	with	ADP
ejpam-5586	423	28	∑n	∑n	PROPN
ejpam-5586	423	29	i=1	i=1	PROPN
ejpam-5586	423	30	ϑi	ϑi	PROPN
ejpam-5586	423	31	=	=	ADJ
ejpam-5586	423	32	1	1	X
ejpam-5586	423	33	.	.	PUNCT
ejpam-5586	424	1	then	then	ADV
ejpam-5586	424	2	we	we	PRON
ejpam-5586	424	3	have	have	VERB
ejpam-5586	424	4	n∏	n∏	PROPN
ejpam-5586	424	5	k=1	k=1	PROPN
ejpam-5586	424	6	ωϑk	ωϑk	NOUN
ejpam-5586	425	1	k	k	NOUN
ejpam-5586	426	1	+	+	CCONJ
ejpam-5586	426	2	r	r	X
ejpam-5586	426	3			PROPN
ejpam-5586	426	4	n∑	n∑	NOUN
ejpam-5586	426	5	k=1	k=1	NOUN
ejpam-5586	426	6	ωk	ωk	ADP
ejpam-5586	426	7	−	−	PROPN
ejpam-5586	426	8	n	n	CCONJ
ejpam-5586	426	9	n	n	PRON
ejpam-5586	426	10	√√√√	√√√√	NOUN
ejpam-5586	426	11	n∏	n∏	PROPN
ejpam-5586	426	12	k=1	k=1	PROPN
ejpam-5586	426	13	ωk	ωk	ADP
ejpam-5586	426	14			PROPN
ejpam-5586	426	15	≤	≤	PROPN
ejpam-5586	426	16	n∑	n∑	NOUN
ejpam-5586	427	1	i=1	i=1	PROPN
ejpam-5586	427	2	ϑkωk	ϑkωk	NOUN
ejpam-5586	427	3	,	,	PUNCT
ejpam-5586	427	4	(	(	PUNCT
ejpam-5586	427	5	36	36	NUM
ejpam-5586	427	6	)	)	PUNCT
ejpam-5586	427	7	where	where	SCONJ
ejpam-5586	427	8	r	r	NOUN
ejpam-5586	427	9	=	=	SYM
ejpam-5586	427	10	min	min	PROPN
ejpam-5586	427	11	{	{	PUNCT
ejpam-5586	427	12	ϑk	ϑk	NOUN
ejpam-5586	427	13	:	:	PUNCT
ejpam-5586	427	14	k	k	X
ejpam-5586	427	15	=	=	SYM
ejpam-5586	427	16	1	1	NUM
ejpam-5586	427	17	,	,	PUNCT
ejpam-5586	427	18	·	·	PUNCT
ejpam-5586	427	19	·	·	PUNCT
ejpam-5586	427	20	·	·	PUNCT
ejpam-5586	427	21	,	,	PUNCT
ejpam-5586	427	22	n	n	CCONJ
ejpam-5586	427	23	}	}	PUNCT
ejpam-5586	427	24	.	.	PUNCT
ejpam-5586	428	1	m.h.m	m.h.m	PROPN
ejpam-5586	428	2	rashid	rashid	PROPN
ejpam-5586	428	3	,	,	PUNCT
ejpam-5586	428	4	w.m.m	w.m.m	NOUN
ejpam-5586	428	5	.	.	PUNCT
ejpam-5586	429	1	salameh	salameh	PROPN
ejpam-5586	429	2	/	/	SYM
ejpam-5586	429	3	eur	eur	PROPN
ejpam-5586	429	4	.	.	PUNCT
ejpam-5586	430	1	j.	j.	PROPN
ejpam-5586	430	2	pure	pure	PROPN
ejpam-5586	430	3	appl	appl	PROPN
ejpam-5586	430	4	.	.	PROPN
ejpam-5586	430	5	math	math	PROPN
ejpam-5586	430	6	,	,	PUNCT
ejpam-5586	430	7	18	18	NUM
ejpam-5586	430	8	(	(	PUNCT
ejpam-5586	430	9	1	1	NUM
ejpam-5586	430	10	)	)	PUNCT
ejpam-5586	430	11	(	(	PUNCT
ejpam-5586	430	12	2025	2025	NUM
ejpam-5586	430	13	)	)	PUNCT
ejpam-5586	430	14	,	,	PUNCT
ejpam-5586	430	15	5586	5586	NUM
ejpam-5586	430	16	16	16	NUM
ejpam-5586	430	17	of	of	ADP
ejpam-5586	430	18	21	21	NUM
ejpam-5586	430	19	theorem	theorem	VERB
ejpam-5586	430	20	11	11	NUM
ejpam-5586	430	21	.	.	PUNCT
ejpam-5586	431	1	let	let	VERB
ejpam-5586	431	2	ti	ti	PROPN
ejpam-5586	431	3	∈	∈	PROPN
ejpam-5586	431	4	mn(c	mn(c	X
ejpam-5586	431	5	)	)	PUNCT
ejpam-5586	432	1	(	(	PUNCT
ejpam-5586	432	2	i	i	NOUN
ejpam-5586	432	3	=	=	NOUN
ejpam-5586	432	4	1	1	NUM
ejpam-5586	432	5	,	,	PUNCT
ejpam-5586	432	6	·	·	PUNCT
ejpam-5586	432	7	·	·	PUNCT
ejpam-5586	432	8	·	·	PUNCT
ejpam-5586	432	9	,	,	PUNCT
ejpam-5586	432	10	n	n	CCONJ
ejpam-5586	432	11	)	)	PUNCT
ejpam-5586	432	12	be	be	AUX
ejpam-5586	432	13	positive	positive	ADJ
ejpam-5586	432	14	semi	semi	ADJ
ejpam-5586	432	15	-	-	ADJ
ejpam-5586	432	16	definite	definite	ADJ
ejpam-5586	432	17	.	.	PUNCT
ejpam-5586	433	1	if	if	SCONJ
ejpam-5586	433	2	0	0	NUM
ejpam-5586	433	3	≤	≤	NUM
ejpam-5586	433	4	ϑi	ϑi	NOUN
ejpam-5586	433	5	≤	≤	NUM
ejpam-5586	433	6	1	1	NUM
ejpam-5586	433	7	(	(	PUNCT
ejpam-5586	433	8	i	i	NOUN
ejpam-5586	433	9	=	=	NOUN
ejpam-5586	433	10	1	1	NUM
ejpam-5586	433	11	,	,	PUNCT
ejpam-5586	433	12	·	·	PUNCT
ejpam-5586	433	13	·	·	PUNCT
ejpam-5586	433	14	·	·	PUNCT
ejpam-5586	433	15	,	,	PUNCT
ejpam-5586	433	16	n	n	CCONJ
ejpam-5586	433	17	)	)	PUNCT
ejpam-5586	433	18	with	with	ADP
ejpam-5586	433	19	∑n	∑n	PROPN
ejpam-5586	433	20	i=1	i=1	PROPN
ejpam-5586	433	21	ϑi	ϑi	PROPN
ejpam-5586	433	22	=	=	SYM
ejpam-5586	433	23	1	1	NUM
ejpam-5586	433	24	,	,	PUNCT
ejpam-5586	433	25	then	then	ADV
ejpam-5586	433	26	n∑	n∑	INTJ
ejpam-5586	433	27	k=1	k=1	X
ejpam-5586	433	28	tr(ϑktk	tr(ϑktk	PROPN
ejpam-5586	433	29	)	)	PUNCT
ejpam-5586	433	30	≥	≥	NOUN
ejpam-5586	433	31	tr	tr	VERB
ejpam-5586	433	32	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5586	433	33	n∏	n∏	PROPN
ejpam-5586	434	1	k=1	k=1	PROPN
ejpam-5586	434	2	t	t	PROPN
ejpam-5586	435	1	ϑk	ϑk	PROPN
ejpam-5586	436	1	k	k	PROPN
ejpam-5586	436	2	∣∣∣∣∣+	∣∣∣∣∣+	PROPN
ejpam-5586	436	3	r	r	PROPN
ejpam-5586	436	4			PROPN
ejpam-5586	436	5	n∑	n∑	NOUN
ejpam-5586	436	6	k=1	k=1	PUNCT
ejpam-5586	437	1	tr(tk)−	tr(tk)−	PROPN
ejpam-5586	437	2	n	n	CCONJ
ejpam-5586	437	3	n	n	PRON
ejpam-5586	437	4	√√√√	√√√√	PRON
ejpam-5586	437	5	n∏	n∏	PROPN
ejpam-5586	437	6	k=1	k=1	NOUN
ejpam-5586	437	7	tr(tk	tr(tk	PROPN
ejpam-5586	437	8	)	)	PUNCT
ejpam-5586	438	1			PROPN
ejpam-5586	438	2	,	,	PUNCT
ejpam-5586	438	3	(	(	PUNCT
ejpam-5586	438	4	37	37	NUM
ejpam-5586	438	5	)	)	PUNCT
ejpam-5586	438	6	where	where	SCONJ
ejpam-5586	438	7	r	r	NOUN
ejpam-5586	438	8	=	=	SYM
ejpam-5586	438	9	min	min	PROPN
ejpam-5586	438	10	{	{	PUNCT
ejpam-5586	438	11	ϑk	ϑk	NOUN
ejpam-5586	438	12	:	:	PUNCT
ejpam-5586	438	13	k	k	X
ejpam-5586	438	14	=	=	SYM
ejpam-5586	438	15	1	1	NUM
ejpam-5586	438	16	,	,	PUNCT
ejpam-5586	438	17	·	·	PUNCT
ejpam-5586	438	18	·	·	PUNCT
ejpam-5586	438	19	·	·	PUNCT
ejpam-5586	438	20	,	,	PUNCT
ejpam-5586	438	21	n	n	CCONJ
ejpam-5586	438	22	}	}	PUNCT
ejpam-5586	438	23	.	.	PUNCT
ejpam-5586	439	1	proof	proof	NOUN
ejpam-5586	439	2	.	.	PUNCT
ejpam-5586	440	1	by	by	ADP
ejpam-5586	440	2	inequality	inequality	NOUN
ejpam-5586	440	3	(	(	PUNCT
ejpam-5586	440	4	36	36	NUM
ejpam-5586	440	5	)	)	PUNCT
ejpam-5586	440	6	,	,	PUNCT
ejpam-5586	440	7	we	we	PRON
ejpam-5586	440	8	have	have	VERB
ejpam-5586	440	9	n∑	n∑	NOUN
ejpam-5586	440	10	k=1	k=1	VERB
ejpam-5586	440	11	ϑksj(tk	ϑksj(tk	PROPN
ejpam-5586	440	12	)	)	PUNCT
ejpam-5586	440	13	≥	≥	NOUN
ejpam-5586	440	14	n∏	n∏	PROPN
ejpam-5586	441	1	k=1	k=1	PROPN
ejpam-5586	441	2	sj(tk	sj(tk	PROPN
ejpam-5586	441	3	)	)	PUNCT
ejpam-5586	442	1	ϑk	ϑk	PROPN
ejpam-5586	443	1	+	+	CCONJ
ejpam-5586	443	2	r	r	PROPN
ejpam-5586	443	3			PROPN
ejpam-5586	443	4	n∑	n∑	NOUN
ejpam-5586	443	5	k=1	k=1	PUNCT
ejpam-5586	443	6	sj(tk)−	sj(tk)−	PROPN
ejpam-5586	443	7	n	n	CCONJ
ejpam-5586	443	8	n	n	PRON
ejpam-5586	443	9	√√√√	√√√√	PRON
ejpam-5586	443	10	n∏	n∏	PROPN
ejpam-5586	443	11	k=1	k=1	PROPN
ejpam-5586	443	12	sj(tk	sj(tk	PROPN
ejpam-5586	443	13	)	)	PUNCT
ejpam-5586	444	1			PROPN
ejpam-5586	444	2	for	for	ADP
ejpam-5586	444	3	j	j	PROPN
ejpam-5586	444	4	=	=	SYM
ejpam-5586	444	5	1	1	NUM
ejpam-5586	444	6	,	,	PUNCT
ejpam-5586	444	7	·	·	PUNCT
ejpam-5586	444	8	·	·	PUNCT
ejpam-5586	444	9	·	·	PUNCT
ejpam-5586	444	10	,	,	PUNCT
ejpam-5586	444	11	n.	n.	PROPN
ejpam-5586	444	12	thus	thus	ADV
ejpam-5586	444	13	,	,	PUNCT
ejpam-5586	444	14	by	by	ADP
ejpam-5586	444	15	lemma	lemma	PROPN
ejpam-5586	444	16	6	6	NUM
ejpam-5586	444	17	and	and	CCONJ
ejpam-5586	444	18	the	the	DET
ejpam-5586	444	19	generalized	generalized	ADJ
ejpam-5586	444	20	cauchy	cauchy	PROPN
ejpam-5586	444	21	-	-	PUNCT
ejpam-5586	444	22	schwarz	schwarz	PROPN
ejpam-5586	444	23	inequality	inequality	NOUN
ejpam-5586	444	24	,	,	PUNCT
ejpam-5586	444	25	we	we	PRON
ejpam-5586	444	26	have	have	VERB
ejpam-5586	444	27	tr	tr	VERB
ejpam-5586	444	28	(	(	PUNCT
ejpam-5586	444	29	n∑	n∑	NOUN
ejpam-5586	444	30	k=1	k=1	PROPN
ejpam-5586	444	31	ϑktk	ϑktk	PROPN
ejpam-5586	444	32	)	)	PUNCT
ejpam-5586	445	1	=	=	PUNCT
ejpam-5586	445	2	n∑	n∑	NOUN
ejpam-5586	445	3	k=1	k=1	X
ejpam-5586	445	4	ϑktr(tk	ϑktr(tk	NOUN
ejpam-5586	445	5	)	)	PUNCT
ejpam-5586	445	6	=	=	PUNCT
ejpam-5586	446	1	n∑	n∑	NOUN
ejpam-5586	446	2	k=1	k=1	PUNCT
ejpam-5586	447	1	ϑk	ϑk	PROPN
ejpam-5586	447	2	n∑	n∑	PROPN
ejpam-5586	447	3	j=1	j=1	PROPN
ejpam-5586	447	4	sj(tk	sj(tk	PROPN
ejpam-5586	447	5	)	)	PUNCT
ejpam-5586	448	1	=	=	PUNCT
ejpam-5586	449	1	n∑	n∑	NOUN
ejpam-5586	449	2	j=1	j=1	PROPN
ejpam-5586	450	1	n∑	n∑	NOUN
ejpam-5586	450	2	k=1	k=1	PROPN
ejpam-5586	450	3	ϑksj(tk	ϑksj(tk	PROPN
ejpam-5586	450	4	)	)	PUNCT
ejpam-5586	450	5	≥	≥	NOUN
ejpam-5586	450	6	n∑	n∑	PUNCT
ejpam-5586	451	1	j=1	j=1	PROPN
ejpam-5586	451	2	sj(t	sj(t	PRON
ejpam-5586	451	3	ϑ1	ϑ1	NOUN
ejpam-5586	451	4	1	1	NUM
ejpam-5586	451	5	)	)	PUNCT
ejpam-5586	451	6	·	·	PUNCT
ejpam-5586	451	7	·	·	PUNCT
ejpam-5586	451	8	·	·	PUNCT
ejpam-5586	451	9	sj(t	sj(t	PUNCT
ejpam-5586	451	10	ϑn	ϑn	PROPN
ejpam-5586	451	11	k	k	PROPN
ejpam-5586	451	12	)	)	PUNCT
ejpam-5586	452	1	+	+	PUNCT
ejpam-5586	452	2	r	r	X
ejpam-5586	452	3			PROPN
ejpam-5586	452	4	n∑	n∑	NOUN
ejpam-5586	452	5	j=1	j=1	PROPN
ejpam-5586	453	1	n∑	n∑	PROPN
ejpam-5586	453	2	k=1	k=1	PUNCT
ejpam-5586	454	1	sj(tk)−	sj(tk)−	PROPN
ejpam-5586	454	2	n	n	NUM
ejpam-5586	454	3	n∑	n∑	NOUN
ejpam-5586	454	4	j=1	j=1	NOUN
ejpam-5586	454	5	n	n	CCONJ
ejpam-5586	454	6	√√√√	√√√√	PRON
ejpam-5586	454	7	n∏	n∏	PROPN
ejpam-5586	454	8	k=1	k=1	PROPN
ejpam-5586	454	9	sj(tn	sj(tn	PROPN
ejpam-5586	454	10	)	)	PUNCT
ejpam-5586	454	11			PROPN
ejpam-5586	454	12	≥	≥	NOUN
ejpam-5586	454	13	n∑	n∑	NOUN
ejpam-5586	455	1	j=1	j=1	PROPN
ejpam-5586	455	2	sj(t	sj(t	PRON
ejpam-5586	455	3	ϑ1	ϑ1	NOUN
ejpam-5586	455	4	1	1	NUM
ejpam-5586	455	5	·	·	PUNCT
ejpam-5586	455	6	·	·	PUNCT
ejpam-5586	455	7	·	·	PUNCT
ejpam-5586	455	8	t	t	PROPN
ejpam-5586	455	9	ϑn	ϑn	NOUN
ejpam-5586	455	10	n	n	PROPN
ejpam-5586	455	11	)	)	PUNCT
ejpam-5586	456	1	+	+	CCONJ
ejpam-5586	456	2	r	r	X
ejpam-5586	456	3			PROPN
ejpam-5586	456	4	n∑	n∑	NOUN
ejpam-5586	456	5	j=1	j=1	PROPN
ejpam-5586	457	1	n∑	n∑	PROPN
ejpam-5586	457	2	k=1	k=1	PUNCT
ejpam-5586	458	1	sj(tk)−	sj(tk)−	PROPN
ejpam-5586	458	2	n	n	CCONJ
ejpam-5586	458	3	n	n	PRON
ejpam-5586	458	4	√√√√	√√√√	NOUN
ejpam-5586	458	5	n∏	n∏	PROPN
ejpam-5586	458	6	k=1	k=1	PROPN
ejpam-5586	458	7	n∑	n∑	PROPN
ejpam-5586	459	1	j=1	j=1	PROPN
ejpam-5586	459	2	sj(tk	sj(tk	PROPN
ejpam-5586	459	3	)	)	PUNCT
ejpam-5586	460	1			PROPN
ejpam-5586	460	2	≥	≥	NUM
ejpam-5586	461	1	tr	tr	VERB
ejpam-5586	461	2	∣∣∣t	∣∣∣t	VERB
ejpam-5586	461	3	ϑ1	ϑ1	NOUN
ejpam-5586	461	4	1	1	NUM
ejpam-5586	461	5	·	·	PUNCT
ejpam-5586	461	6	·	·	PUNCT
ejpam-5586	461	7	·	·	PUNCT
ejpam-5586	461	8	t	t	PROPN
ejpam-5586	461	9	ϑn	ϑn	NOUN
ejpam-5586	461	10	n	n	PROPN
ejpam-5586	461	11	∣∣∣+	∣∣∣+	PROPN
ejpam-5586	461	12	r	r	NOUN
ejpam-5586	461	13			PROPN
ejpam-5586	461	14	n∑	n∑	NOUN
ejpam-5586	461	15	k=1	k=1	PUNCT
ejpam-5586	461	16	tr(tk)−	tr(tk)−	PROPN
ejpam-5586	461	17	n	n	CCONJ
ejpam-5586	461	18	n	n	PRON
ejpam-5586	461	19	√√√√	√√√√	PRON
ejpam-5586	461	20	n∏	n∏	PROPN
ejpam-5586	461	21	k=1	k=1	NOUN
ejpam-5586	461	22	tr(tk	tr(tk	PROPN
ejpam-5586	461	23	)	)	PUNCT
ejpam-5586	462	1			PROPN
ejpam-5586	462	2	where	where	SCONJ
ejpam-5586	462	3	r	r	NOUN
ejpam-5586	462	4	=	=	SYM
ejpam-5586	462	5	min	min	PROPN
ejpam-5586	462	6	{	{	PUNCT
ejpam-5586	462	7	ϑk	ϑk	NOUN
ejpam-5586	462	8	:	:	PUNCT
ejpam-5586	462	9	k	k	X
ejpam-5586	462	10	=	=	SYM
ejpam-5586	462	11	1	1	NUM
ejpam-5586	462	12	,	,	PUNCT
ejpam-5586	462	13	·	·	PUNCT
ejpam-5586	462	14	·	·	PUNCT
ejpam-5586	462	15	·	·	PUNCT
ejpam-5586	462	16	,	,	PUNCT
ejpam-5586	462	17	n	n	CCONJ
ejpam-5586	462	18	}	}	PUNCT
ejpam-5586	462	19	.	.	PUNCT
ejpam-5586	463	1	our	our	PRON
ejpam-5586	463	2	theorem	theorem	ADJ
ejpam-5586	463	3	11	11	NUM
ejpam-5586	463	4	entils	entil	VERB
ejpam-5586	463	5	the	the	DET
ejpam-5586	463	6	following	follow	VERB
ejpam-5586	463	7	trace	trace	NOUN
ejpam-5586	464	1	norm∥∥∥∥∥	norm∥∥∥∥∥	PROPN
ejpam-5586	464	2	n∑	n∑	PROPN
ejpam-5586	465	1	k=1	k=1	PROPN
ejpam-5586	465	2	ϑktk	ϑktk	VERB
ejpam-5586	465	3	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-5586	465	4	1	1	NUM
ejpam-5586	465	5	≥	≥	NOUN
ejpam-5586	465	6	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-5586	466	1	n∏	n∏	NOUN
ejpam-5586	467	1	k=1	k=1	PROPN
ejpam-5586	467	2	t	t	PROPN
ejpam-5586	467	3	ϑk	ϑk	PROPN
ejpam-5586	468	1	k	k	PROPN
ejpam-5586	468	2	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-5586	468	3	1	1	NUM
ejpam-5586	468	4	+	+	NUM
ejpam-5586	468	5	r	r	NOUN
ejpam-5586	468	6	∥∥∥∥∥	∥∥∥∥∥	NOUN
ejpam-5586	468	7	n∑	n∑	INTJ
ejpam-5586	469	1	k=1	k=1	PROPN
ejpam-5586	470	1	tk	tk	PROPN
ejpam-5586	470	2	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-5586	470	3	1	1	NUM
ejpam-5586	470	4	−	−	PROPN
ejpam-5586	470	5	n	n	CCONJ
ejpam-5586	470	6	n	n	PRON
ejpam-5586	470	7	√√√√	√√√√	PRON
ejpam-5586	470	8	n∏	n∏	PROPN
ejpam-5586	471	1	k=1	k=1	NOUN
ejpam-5586	471	2	∥tk∥1	∥tk∥1	VERB
ejpam-5586	472	1			PROPN
ejpam-5586	472	2	,	,	PUNCT
ejpam-5586	472	3	(	(	PUNCT
ejpam-5586	472	4	38	38	NUM
ejpam-5586	472	5	)	)	PUNCT
ejpam-5586	472	6	where	where	SCONJ
ejpam-5586	472	7	r	r	NOUN
ejpam-5586	472	8	=	=	SYM
ejpam-5586	472	9	min	min	PROPN
ejpam-5586	472	10	{	{	PUNCT
ejpam-5586	472	11	ϑk	ϑk	NOUN
ejpam-5586	472	12	:	:	PUNCT
ejpam-5586	472	13	k	k	X
ejpam-5586	472	14	=	=	SYM
ejpam-5586	472	15	1	1	NUM
ejpam-5586	472	16	,	,	PUNCT
ejpam-5586	472	17	·	·	PUNCT
ejpam-5586	472	18	·	·	PUNCT
ejpam-5586	472	19	·	·	PUNCT
ejpam-5586	472	20	,	,	PUNCT
ejpam-5586	472	21	n	n	CCONJ
ejpam-5586	472	22	}	}	PUNCT
ejpam-5586	472	23	.	.	PUNCT
ejpam-5586	473	1	m.h.m	m.h.m	PROPN
ejpam-5586	473	2	rashid	rashid	PROPN
ejpam-5586	473	3	,	,	PUNCT
ejpam-5586	473	4	w.m.m	w.m.m	NOUN
ejpam-5586	473	5	.	.	PUNCT
ejpam-5586	474	1	salameh	salameh	PROPN
ejpam-5586	474	2	/	/	SYM
ejpam-5586	474	3	eur	eur	PROPN
ejpam-5586	474	4	.	.	PUNCT
ejpam-5586	475	1	j.	j.	PROPN
ejpam-5586	475	2	pure	pure	PROPN
ejpam-5586	475	3	appl	appl	PROPN
ejpam-5586	475	4	.	.	PROPN
ejpam-5586	475	5	math	math	PROPN
ejpam-5586	475	6	,	,	PUNCT
ejpam-5586	475	7	18	18	NUM
ejpam-5586	475	8	(	(	PUNCT
ejpam-5586	475	9	1	1	NUM
ejpam-5586	475	10	)	)	PUNCT
ejpam-5586	475	11	(	(	PUNCT
ejpam-5586	475	12	2025	2025	NUM
ejpam-5586	475	13	)	)	PUNCT
ejpam-5586	475	14	,	,	PUNCT
ejpam-5586	475	15	5586	5586	NUM
ejpam-5586	475	16	17	17	NUM
ejpam-5586	475	17	of	of	ADP
ejpam-5586	475	18	21	21	NUM
ejpam-5586	475	19	theorem	theorem	NOUN
ejpam-5586	475	20	12	12	NUM
ejpam-5586	475	21	.	.	PUNCT
ejpam-5586	476	1	let	let	VERB
ejpam-5586	476	2	ti	ti	PROPN
ejpam-5586	476	3	∈	∈	PROPN
ejpam-5586	476	4	mn(c	mn(c	X
ejpam-5586	476	5	)	)	PUNCT
ejpam-5586	477	1	(	(	PUNCT
ejpam-5586	477	2	i	i	NOUN
ejpam-5586	477	3	=	=	NOUN
ejpam-5586	477	4	1	1	NUM
ejpam-5586	477	5	,	,	PUNCT
ejpam-5586	477	6	·	·	PUNCT
ejpam-5586	477	7	·	·	PUNCT
ejpam-5586	477	8	·	·	PUNCT
ejpam-5586	477	9	,	,	PUNCT
ejpam-5586	477	10	n	n	CCONJ
ejpam-5586	477	11	)	)	PUNCT
ejpam-5586	477	12	be	be	AUX
ejpam-5586	477	13	positive	positive	ADJ
ejpam-5586	477	14	definite	definite	ADJ
ejpam-5586	477	15	.	.	PUNCT
ejpam-5586	478	1	if	if	SCONJ
ejpam-5586	478	2	0	0	NUM
ejpam-5586	478	3	≤	≤	NUM
ejpam-5586	478	4	ϑi	ϑi	NOUN
ejpam-5586	478	5	≤	≤	NUM
ejpam-5586	478	6	1	1	NUM
ejpam-5586	478	7	(	(	PUNCT
ejpam-5586	478	8	i	i	NOUN
ejpam-5586	478	9	=	=	NOUN
ejpam-5586	478	10	1	1	NUM
ejpam-5586	478	11	,	,	PUNCT
ejpam-5586	478	12	·	·	PUNCT
ejpam-5586	478	13	·	·	PUNCT
ejpam-5586	478	14	·	·	PUNCT
ejpam-5586	478	15	,	,	PUNCT
ejpam-5586	478	16	n	n	CCONJ
ejpam-5586	478	17	)	)	PUNCT
ejpam-5586	478	18	with	with	ADP
ejpam-5586	478	19	∑n	∑n	PROPN
ejpam-5586	478	20	i=1	i=1	PROPN
ejpam-5586	478	21	ϑi	ϑi	PROPN
ejpam-5586	478	22	=	=	SYM
ejpam-5586	478	23	1	1	NUM
ejpam-5586	478	24	,	,	PUNCT
ejpam-5586	478	25	then	then	ADV
ejpam-5586	478	26	det	det	PROPN
ejpam-5586	478	27	(	(	PUNCT
ejpam-5586	478	28	n∑	n∑	NOUN
ejpam-5586	478	29	k=1	k=1	PROPN
ejpam-5586	478	30	ϑktk	ϑktk	PROPN
ejpam-5586	478	31	)	)	PUNCT
ejpam-5586	478	32	≥	≥	PROPN
ejpam-5586	478	33	n∏	n∏	PROPN
ejpam-5586	478	34	k=1	k=1	PROPN
ejpam-5586	478	35	det	det	PROPN
ejpam-5586	478	36	(	(	PUNCT
ejpam-5586	478	37	t	t	PROPN
ejpam-5586	478	38	ϑk	ϑk	PROPN
ejpam-5586	478	39	k	k	PROPN
ejpam-5586	478	40	)	)	PUNCT
ejpam-5586	479	1	+	+	NUM
ejpam-5586	479	2	r	r	NOUN
ejpam-5586	479	3	det	det	NOUN
ejpam-5586	479	4	(	(	PUNCT
ejpam-5586	479	5	n∑	n∑	NOUN
ejpam-5586	479	6	k=1	k=1	PROPN
ejpam-5586	479	7	tk	tk	PROPN
ejpam-5586	479	8	)	)	PUNCT
ejpam-5586	479	9	−	−	PROPN
ejpam-5586	479	10	n	n	CCONJ
ejpam-5586	479	11	n	n	PRON
ejpam-5586	479	12	√√√√	√√√√	PRON
ejpam-5586	479	13	n∏	n∏	PROPN
ejpam-5586	479	14	k=1	k=1	PROPN
ejpam-5586	479	15	det(tk	det(tk	NOUN
ejpam-5586	479	16	)	)	PUNCT
ejpam-5586	480	1			PROPN
ejpam-5586	480	2	,	,	PUNCT
ejpam-5586	480	3	(	(	PUNCT
ejpam-5586	480	4	39	39	NUM
ejpam-5586	480	5	)	)	PUNCT
ejpam-5586	480	6	where	where	SCONJ
ejpam-5586	480	7	r	r	NOUN
ejpam-5586	480	8	=	=	SYM
ejpam-5586	480	9	min	min	PROPN
ejpam-5586	480	10	{	{	PUNCT
ejpam-5586	480	11	ϑk	ϑk	NOUN
ejpam-5586	480	12	:	:	PUNCT
ejpam-5586	480	13	k	k	X
ejpam-5586	480	14	=	=	SYM
ejpam-5586	480	15	1	1	NUM
ejpam-5586	480	16	,	,	PUNCT
ejpam-5586	480	17	·	·	PUNCT
ejpam-5586	480	18	·	·	PUNCT
ejpam-5586	480	19	·	·	PUNCT
ejpam-5586	480	20	,	,	PUNCT
ejpam-5586	480	21	n	n	CCONJ
ejpam-5586	480	22	}	}	PUNCT
ejpam-5586	480	23	.	.	PUNCT
ejpam-5586	481	1	to	to	PART
ejpam-5586	481	2	prove	prove	VERB
ejpam-5586	481	3	theorem	theorem	ADJ
ejpam-5586	481	4	12	12	NUM
ejpam-5586	481	5	,	,	PUNCT
ejpam-5586	481	6	we	we	PRON
ejpam-5586	481	7	need	need	VERB
ejpam-5586	481	8	the	the	DET
ejpam-5586	481	9	following	follow	VERB
ejpam-5586	481	10	lemma	lemma	PROPN
ejpam-5586	481	11	.	.	PUNCT
ejpam-5586	482	1	lemma	lemma	PROPN
ejpam-5586	482	2	9	9	NUM
ejpam-5586	482	3	(	(	PUNCT
ejpam-5586	482	4	[	[	X
ejpam-5586	482	5	5	5	NUM
ejpam-5586	482	6	]	]	PUNCT
ejpam-5586	482	7	)	)	PUNCT
ejpam-5586	482	8	.	.	PUNCT
ejpam-5586	483	1	let	let	AUX
ejpam-5586	483	2	t	t	PROPN
ejpam-5586	483	3	,	,	PUNCT
ejpam-5586	483	4	s	s	PART
ejpam-5586	483	5	∈mn(c	∈mn(c	NOUN
ejpam-5586	483	6	)	)	PUNCT
ejpam-5586	483	7	be	be	AUX
ejpam-5586	483	8	positive	positive	ADJ
ejpam-5586	483	9	definite	definite	ADJ
ejpam-5586	483	10	.	.	PUNCT
ejpam-5586	484	1	then	then	ADV
ejpam-5586	484	2	we	we	PRON
ejpam-5586	484	3	have	have	VERB
ejpam-5586	484	4	det(t	det(t	NOUN
ejpam-5586	484	5	+	+	SYM
ejpam-5586	484	6	s	s	X
ejpam-5586	484	7	)	)	PUNCT
ejpam-5586	484	8	1	1	NUM
ejpam-5586	484	9	n	n	NUM
ejpam-5586	484	10	≥	≥	NOUN
ejpam-5586	484	11	det(t	det(t	NOUN
ejpam-5586	484	12	)	)	PUNCT
ejpam-5586	484	13	1	1	NUM
ejpam-5586	484	14	n	n	NOUN
ejpam-5586	484	15	+	+	NUM
ejpam-5586	484	16	det(s	det(s	X
ejpam-5586	484	17	)	)	PUNCT
ejpam-5586	484	18	1	1	NUM
ejpam-5586	484	19	n	n	NOUN
ejpam-5586	484	20	.	.	PUNCT
ejpam-5586	485	1	(	(	PUNCT
ejpam-5586	485	2	40	40	NUM
ejpam-5586	485	3	)	)	PUNCT
ejpam-5586	485	4	proof	proof	NOUN
ejpam-5586	485	5	.	.	PUNCT
ejpam-5586	486	1	[	[	X
ejpam-5586	486	2	proof	proof	NOUN
ejpam-5586	486	3	of	of	ADP
ejpam-5586	486	4	theorem	theorem	NOUN
ejpam-5586	486	5	12	12	NUM
ejpam-5586	486	6	]	]	PUNCT
ejpam-5586	486	7	we	we	PRON
ejpam-5586	486	8	have	have	VERB
ejpam-5586	486	9	det	det	NOUN
ejpam-5586	486	10	(	(	PUNCT
ejpam-5586	486	11	n∑	n∑	NOUN
ejpam-5586	486	12	k=1	k=1	PROPN
ejpam-5586	486	13	ϑktk	ϑktk	INTJ
ejpam-5586	486	14	)	)	PUNCT
ejpam-5586	486	15	=	=	SYM
ejpam-5586	486	16	det	det	PROPN
ejpam-5586	486	17	(	(	PUNCT
ejpam-5586	486	18	n∑	n∑	NOUN
ejpam-5586	486	19	k=1	k=1	PROPN
ejpam-5586	486	20	ϑktk	ϑktk	PROPN
ejpam-5586	486	21	)	)	PUNCT
ejpam-5586	486	22	1	1	NUM
ejpam-5586	486	23	n	n	PRON
ejpam-5586	486	24	n	n	NOUN
ejpam-5586	486	25	≥	≥	NOUN
ejpam-5586	486	26	[	[	PUNCT
ejpam-5586	486	27	n∑	n∑	NOUN
ejpam-5586	486	28	k=1	k=1	PROPN
ejpam-5586	486	29	det	det	PROPN
ejpam-5586	486	30	(	(	PUNCT
ejpam-5586	486	31	ϑktk	ϑktk	PROPN
ejpam-5586	486	32	)	)	PUNCT
ejpam-5586	486	33	1	1	NUM
ejpam-5586	486	34	n	n	NOUN
ejpam-5586	486	35	]	]	SYM
ejpam-5586	486	36	n	n	CCONJ
ejpam-5586	486	37	(	(	PUNCT
ejpam-5586	486	38	by	by	ADP
ejpam-5586	486	39	lemma	lemma	PROPN
ejpam-5586	486	40	9	9	NUM
ejpam-5586	486	41	)	)	PUNCT
ejpam-5586	486	42	≥	≥	NOUN
ejpam-5586	487	1	[	[	PUNCT
ejpam-5586	487	2	n∑	n∑	NOUN
ejpam-5586	487	3	k=1	k=1	PROPN
ejpam-5586	487	4	ϑk	ϑk	PROPN
ejpam-5586	487	5	det	det	PROPN
ejpam-5586	487	6	(	(	PUNCT
ejpam-5586	487	7	tk	tk	PROPN
ejpam-5586	487	8	)	)	PUNCT
ejpam-5586	487	9	1	1	NUM
ejpam-5586	487	10	n	n	NOUN
ejpam-5586	487	11	]	]	X
ejpam-5586	487	12	n	n	PRON
ejpam-5586	487	13	≥	≥	NOUN
ejpam-5586	487	14	[	[	PUNCT
ejpam-5586	487	15	n∏	n∏	NOUN
ejpam-5586	487	16	k=1	k=1	PROPN
ejpam-5586	487	17	(	(	PUNCT
ejpam-5586	487	18	(	(	PUNCT
ejpam-5586	487	19	tk	tk	PROPN
ejpam-5586	487	20	)	)	PUNCT
ejpam-5586	487	21	1	1	NUM
ejpam-5586	487	22	n	n	NOUN
ejpam-5586	487	23	)	)	PUNCT
ejpam-5586	487	24	ϑk	ϑk	NOUN
ejpam-5586	487	25	]	]	SYM
ejpam-5586	487	26	n	n	X
ejpam-5586	487	27	+	+	NUM
ejpam-5586	487	28	rn	rn	X
ejpam-5586	487	29			PROPN
ejpam-5586	487	30	n∑	n∑	PROPN
ejpam-5586	487	31	k=1	k=1	PROPN
ejpam-5586	487	32	det	det	PROPN
ejpam-5586	487	33	(	(	PUNCT
ejpam-5586	487	34	tk	tk	PROPN
ejpam-5586	487	35	)	)	PUNCT
ejpam-5586	487	36	1	1	NUM
ejpam-5586	487	37	n	n	NUM
ejpam-5586	487	38	−	−	PROPN
ejpam-5586	487	39	n	n	CCONJ
ejpam-5586	487	40	n	n	PRON
ejpam-5586	487	41	√√√√det	√√√√det	NOUN
ejpam-5586	487	42	n∏	n∏	PROPN
ejpam-5586	488	1	k=1	k=1	PROPN
ejpam-5586	489	1	tk	tk	PROPN
ejpam-5586	490	1			PROPN
ejpam-5586	490	2	=	=	SYM
ejpam-5586	490	3	n∏	n∏	PROPN
ejpam-5586	490	4	k=1	k=1	PROPN
ejpam-5586	490	5	det	det	PROPN
ejpam-5586	490	6	(	(	PUNCT
ejpam-5586	490	7	t	t	PROPN
ejpam-5586	490	8	ϑk	ϑk	PROPN
ejpam-5586	490	9	k	k	PROPN
ejpam-5586	490	10	)	)	PUNCT
ejpam-5586	491	1	+	+	CCONJ
ejpam-5586	491	2	rn	rn	X
ejpam-5586	491	3			PROPN
ejpam-5586	491	4	n∑	n∑	PROPN
ejpam-5586	491	5	k=1	k=1	PROPN
ejpam-5586	491	6	det	det	PROPN
ejpam-5586	491	7	(	(	PUNCT
ejpam-5586	491	8	tk	tk	PROPN
ejpam-5586	491	9	)	)	PUNCT
ejpam-5586	491	10	1	1	NUM
ejpam-5586	491	11	n	n	NUM
ejpam-5586	491	12	−	−	PROPN
ejpam-5586	491	13	n	n	CCONJ
ejpam-5586	491	14	n	n	PRON
ejpam-5586	491	15	√√√√det	√√√√det	NOUN
ejpam-5586	491	16	n∏	n∏	PROPN
ejpam-5586	491	17	k=1	k=1	PROPN
ejpam-5586	491	18	tk	tk	PROPN
ejpam-5586	492	1			PROPN
ejpam-5586	492	2	lemma	lemma	PROPN
ejpam-5586	492	3	10	10	NUM
ejpam-5586	492	4	(	(	PUNCT
ejpam-5586	492	5	[	[	X
ejpam-5586	492	6	16	16	NUM
ejpam-5586	492	7	]	]	PUNCT
ejpam-5586	492	8	)	)	PUNCT
ejpam-5586	492	9	.	.	PUNCT
ejpam-5586	493	1	let	let	VERB
ejpam-5586	493	2	γ1	γ1	NOUN
ejpam-5586	493	3	,	,	PUNCT
ejpam-5586	493	4	γ2	γ2	PROPN
ejpam-5586	493	5	,	,	PUNCT
ejpam-5586	493	6	·	·	PUNCT
ejpam-5586	493	7	·	·	PUNCT
ejpam-5586	493	8	·	·	PUNCT
ejpam-5586	493	9	,	,	PUNCT
ejpam-5586	493	10	γn	γn	NOUN
ejpam-5586	493	11	be	be	AUX
ejpam-5586	493	12	a	a	DET
ejpam-5586	493	13	set	set	NOUN
ejpam-5586	493	14	of	of	ADP
ejpam-5586	493	15	non	non	ADJ
ejpam-5586	493	16	-	-	ADJ
ejpam-5586	493	17	negative	negative	ADJ
ejpam-5586	493	18	real	real	ADJ
ejpam-5586	493	19	numbers	number	NOUN
ejpam-5586	493	20	constrained	constrain	VERB
ejpam-5586	493	21	by	by	ADP
ejpam-5586	493	22	j∑	j∑	PROPN
ejpam-5586	493	23	k=1	k=1	PROPN
ejpam-5586	493	24	γk	γk	PROPN
ejpam-5586	494	1	=	=	SYM
ejpam-5586	494	2	γj	γj	PROPN
ejpam-5586	494	3	.	.	PUNCT
ejpam-5586	495	1	if	if	SCONJ
ejpam-5586	495	2	ω1	ω1	PROPN
ejpam-5586	495	3	,	,	PUNCT
ejpam-5586	495	4	ω2	ω2	ADJ
ejpam-5586	495	5	,	,	PUNCT
ejpam-5586	495	6	·	·	PUNCT
ejpam-5586	495	7	·	·	PUNCT
ejpam-5586	495	8	·	·	PUNCT
ejpam-5586	495	9	,	,	PUNCT
ejpam-5586	495	10	ωn	ωn	PRON
ejpam-5586	495	11	are	be	AUX
ejpam-5586	495	12	positive	positive	ADJ
ejpam-5586	495	13	real	real	ADJ
ejpam-5586	495	14	numbers	number	NOUN
ejpam-5586	495	15	,	,	PUNCT
ejpam-5586	495	16	then	then	ADV
ejpam-5586	495	17	1	1	NUM
ejpam-5586	495	18	γn	γn	NOUN
ejpam-5586	495	19	n∑	n∑	PROPN
ejpam-5586	495	20	k=1	k=1	PROPN
ejpam-5586	496	1	γkωk	γkωk	NOUN
ejpam-5586	496	2	+	+	CCONJ
ejpam-5586	496	3	√√√√1	√√√√1	NOUN
ejpam-5586	496	4	+	+	CCONJ
ejpam-5586	496	5	(	(	PUNCT
ejpam-5586	496	6	1	1	NUM
ejpam-5586	496	7	γn	γn	NOUN
ejpam-5586	496	8	n∑	n∑	PROPN
ejpam-5586	496	9	k=1	k=1	PROPN
ejpam-5586	496	10	γkωk	γkωk	NOUN
ejpam-5586	496	11	)	)	PUNCT
ejpam-5586	496	12	2	2	NUM
ejpam-5586	496	13	≥	≥	NOUN
ejpam-5586	496	14	[	[	PUNCT
ejpam-5586	496	15	n∏	n∏	NOUN
ejpam-5586	496	16	k=1	k=1	PROPN
ejpam-5586	497	1	(	(	PUNCT
ejpam-5586	497	2	ωk	ωk	ADP
ejpam-5586	497	3	+	+	CCONJ
ejpam-5586	497	4	√	√	NUM
ejpam-5586	497	5	1	1	NUM
ejpam-5586	497	6	+	+	CCONJ
ejpam-5586	497	7	ω2	ω2	ADJ
ejpam-5586	497	8	k	k	PROPN
ejpam-5586	497	9	)	)	PUNCT
ejpam-5586	497	10	γk	γk	NOUN
ejpam-5586	497	11	]	]	PUNCT
ejpam-5586	497	12	1	1	NUM
ejpam-5586	497	13	γn	γn	NOUN
ejpam-5586	497	14	(	(	PUNCT
ejpam-5586	497	15	41	41	NUM
ejpam-5586	497	16	)	)	PUNCT
ejpam-5586	497	17	holds	hold	VERB
ejpam-5586	497	18	.	.	PUNCT
ejpam-5586	498	1	m.h.m	m.h.m	PROPN
ejpam-5586	498	2	rashid	rashid	PROPN
ejpam-5586	498	3	,	,	PUNCT
ejpam-5586	498	4	w.m.m	w.m.m	NOUN
ejpam-5586	498	5	.	.	PUNCT
ejpam-5586	499	1	salameh	salameh	PROPN
ejpam-5586	499	2	/	/	SYM
ejpam-5586	499	3	eur	eur	PROPN
ejpam-5586	499	4	.	.	PUNCT
ejpam-5586	500	1	j.	j.	PROPN
ejpam-5586	500	2	pure	pure	PROPN
ejpam-5586	500	3	appl	appl	PROPN
ejpam-5586	500	4	.	.	PROPN
ejpam-5586	500	5	math	math	PROPN
ejpam-5586	500	6	,	,	PUNCT
ejpam-5586	500	7	18	18	NUM
ejpam-5586	500	8	(	(	PUNCT
ejpam-5586	500	9	1	1	NUM
ejpam-5586	500	10	)	)	PUNCT
ejpam-5586	500	11	(	(	PUNCT
ejpam-5586	500	12	2025	2025	NUM
ejpam-5586	500	13	)	)	PUNCT
ejpam-5586	500	14	,	,	PUNCT
ejpam-5586	500	15	5586	5586	NUM
ejpam-5586	500	16	18	18	NUM
ejpam-5586	500	17	of	of	ADP
ejpam-5586	500	18	21	21	NUM
ejpam-5586	500	19	theorem	theorem	NOUN
ejpam-5586	500	20	13	13	NUM
ejpam-5586	500	21	.	.	PUNCT
ejpam-5586	501	1	let	let	AUX
ejpam-5586	501	2	t1	t1	VERB
ejpam-5586	501	3	,	,	PUNCT
ejpam-5586	501	4	·	·	PUNCT
ejpam-5586	501	5	·	·	PUNCT
ejpam-5586	501	6	·	·	PUNCT
ejpam-5586	501	7	,	,	PUNCT
ejpam-5586	501	8	tk	tk	PROPN
ejpam-5586	501	9	∈mn(c	∈mn(c	PROPN
ejpam-5586	501	10	)	)	PUNCT
ejpam-5586	501	11	be	be	AUX
ejpam-5586	501	12	positive	positive	ADJ
ejpam-5586	501	13	define	define	NOUN
ejpam-5586	501	14	and	and	CCONJ
ejpam-5586	501	15	let	let	VERB
ejpam-5586	501	16	γ1	γ1	NOUN
ejpam-5586	501	17	,	,	PUNCT
ejpam-5586	501	18	γ2	γ2	PROPN
ejpam-5586	501	19	,	,	PUNCT
ejpam-5586	501	20	·	·	PUNCT
ejpam-5586	501	21	·	·	PUNCT
ejpam-5586	501	22	·	·	PUNCT
ejpam-5586	501	23	,	,	PUNCT
ejpam-5586	501	24	γn	γn	NOUN
ejpam-5586	501	25	be	be	AUX
ejpam-5586	501	26	a	a	DET
ejpam-5586	501	27	set	set	NOUN
ejpam-5586	501	28	of	of	ADP
ejpam-5586	501	29	non	non	ADJ
ejpam-5586	501	30	-	-	ADJ
ejpam-5586	501	31	negative	negative	ADJ
ejpam-5586	501	32	real	real	ADJ
ejpam-5586	501	33	numbers	number	NOUN
ejpam-5586	501	34	such	such	ADJ
ejpam-5586	501	35	that	that	SCONJ
ejpam-5586	501	36	n∑	n∑	NOUN
ejpam-5586	501	37	k=1	k=1	NOUN
ejpam-5586	501	38	γk	γk	PROPN
ejpam-5586	501	39	=	=	SYM
ejpam-5586	501	40	γn	γn	PROPN
ejpam-5586	501	41	.	.	PUNCT
ejpam-5586	502	1	then	then	ADV
ejpam-5586	502	2	1	1	NUM
ejpam-5586	502	3	γn	γn	NOUN
ejpam-5586	502	4	n∑	n∑	INTJ
ejpam-5586	503	1	k=1	k=1	X
ejpam-5586	503	2	tr(tk	tr(tk	PROPN
ejpam-5586	503	3	)	)	PUNCT
ejpam-5586	504	1	+	+	NUM
ejpam-5586	504	2	√√√√1	√√√√1	NOUN
ejpam-5586	504	3	+	+	CCONJ
ejpam-5586	504	4	(	(	PUNCT
ejpam-5586	504	5	1	1	NUM
ejpam-5586	504	6	γn	γn	ADP
ejpam-5586	504	7	n∑	n∑	INTJ
ejpam-5586	504	8	k=1	k=1	X
ejpam-5586	504	9	tr(tk	tr(tk	PROPN
ejpam-5586	504	10	)	)	PUNCT
ejpam-5586	504	11	)	)	PUNCT
ejpam-5586	504	12	2	2	NUM
ejpam-5586	504	13	≥	≥	NOUN
ejpam-5586	504	14	n∏	n∏	SYM
ejpam-5586	504	15	k=1	k=1	PROPN
ejpam-5586	504	16	[	[	PUNCT
ejpam-5586	504	17	tr(tk	tr(tk	NOUN
ejpam-5586	504	18	)	)	PUNCT
ejpam-5586	505	1	+	+	CCONJ
ejpam-5586	505	2	√	√	NUM
ejpam-5586	505	3	1	1	NUM
ejpam-5586	505	4	+	+	CCONJ
ejpam-5586	505	5	tr(t	tr(t	NUM
ejpam-5586	505	6	2	2	NUM
ejpam-5586	505	7	k	k	NOUN
ejpam-5586	505	8	)	)	PUNCT
ejpam-5586	505	9	]	]	PUNCT
ejpam-5586	506	1	1	1	NUM
ejpam-5586	506	2	γn	γn	NOUN
ejpam-5586	506	3	.	.	PUNCT
ejpam-5586	507	1	(	(	PUNCT
ejpam-5586	507	2	42	42	X
ejpam-5586	507	3	)	)	PUNCT
ejpam-5586	507	4	proof	proof	NOUN
ejpam-5586	507	5	.	.	PUNCT
ejpam-5586	508	1	by	by	ADP
ejpam-5586	508	2	inequality	inequality	NOUN
ejpam-5586	508	3	(	(	PUNCT
ejpam-5586	508	4	41	41	NUM
ejpam-5586	508	5	)	)	PUNCT
ejpam-5586	508	6	,	,	PUNCT
ejpam-5586	508	7	we	we	PRON
ejpam-5586	508	8	have	have	VERB
ejpam-5586	508	9	1	1	NUM
ejpam-5586	508	10	γn	γn	NOUN
ejpam-5586	508	11	n∑	n∑	PROPN
ejpam-5586	508	12	k=1	k=1	PROPN
ejpam-5586	508	13	γksj(tk)+	γksj(tk)+	PROPN
ejpam-5586	508	14	√√√√1	√√√√1	NOUN
ejpam-5586	508	15	+	+	CCONJ
ejpam-5586	509	1	(	(	PUNCT
ejpam-5586	509	2	1	1	NUM
ejpam-5586	509	3	γn	γn	NOUN
ejpam-5586	509	4	n∑	n∑	NOUN
ejpam-5586	509	5	k=1	k=1	PUNCT
ejpam-5586	509	6	γksj(tk	γksj(tk	PROPN
ejpam-5586	509	7	)	)	PUNCT
ejpam-5586	509	8	)	)	PUNCT
ejpam-5586	509	9	2	2	NUM
ejpam-5586	509	10	≥	≥	NOUN
ejpam-5586	509	11	[	[	PUNCT
ejpam-5586	509	12	n∏	n∏	NOUN
ejpam-5586	509	13	k=1	k=1	PROPN
ejpam-5586	509	14	(	(	PUNCT
ejpam-5586	509	15	sj(tk	sj(tk	PROPN
ejpam-5586	509	16	)	)	PUNCT
ejpam-5586	510	1	+	+	CCONJ
ejpam-5586	510	2	√	√	NUM
ejpam-5586	510	3	1	1	NUM
ejpam-5586	510	4	+	+	NUM
ejpam-5586	510	5	s2j	s2j	PROPN
ejpam-5586	510	6	(	(	PUNCT
ejpam-5586	510	7	tk	tk	PROPN
ejpam-5586	510	8	)	)	PUNCT
ejpam-5586	510	9	)	)	PUNCT
ejpam-5586	510	10	γk	γk	X
ejpam-5586	510	11	]	]	PUNCT
ejpam-5586	510	12	1	1	NUM
ejpam-5586	510	13	γn	γn	NOUN
ejpam-5586	510	14	(	(	PUNCT
ejpam-5586	510	15	43	43	NUM
ejpam-5586	510	16	)	)	PUNCT
ejpam-5586	510	17	for	for	ADP
ejpam-5586	510	18	all	all	PRON
ejpam-5586	510	19	j	j	NOUN
ejpam-5586	510	20	=	=	SYM
ejpam-5586	510	21	1	1	NUM
ejpam-5586	510	22	,	,	PUNCT
ejpam-5586	510	23	·	·	PUNCT
ejpam-5586	510	24	·	·	PUNCT
ejpam-5586	510	25	·	·	PUNCT
ejpam-5586	510	26	,	,	PUNCT
ejpam-5586	510	27	n.	n.	PROPN
ejpam-5586	510	28	hence	hence	ADV
ejpam-5586	510	29	we	we	PRON
ejpam-5586	510	30	have	have	VERB
ejpam-5586	510	31	1	1	NUM
ejpam-5586	510	32	γn	γn	NOUN
ejpam-5586	511	1	n∑	n∑	NOUN
ejpam-5586	511	2	k=1	k=1	PROPN
ejpam-5586	512	1	γk	γk	PROPN
ejpam-5586	512	2	n∑	n∑	PROPN
ejpam-5586	512	3	j=1	j=1	PROPN
ejpam-5586	512	4	sj(tk	sj(tk	PROPN
ejpam-5586	512	5	)	)	PUNCT
ejpam-5586	513	1	+	+	CCONJ
ejpam-5586	513	2	√√√√√1	√√√√√1	NOUN
ejpam-5586	513	3	+	+	CCONJ
ejpam-5586	513	4			PROPN
ejpam-5586	513	5	1	1	NUM
ejpam-5586	513	6	γn	γn	NOUN
ejpam-5586	513	7	n∑	n∑	NOUN
ejpam-5586	513	8	k=1	k=1	PROPN
ejpam-5586	513	9	γk	γk	PROPN
ejpam-5586	513	10	n∑	n∑	PROPN
ejpam-5586	513	11	j=1	j=1	PROPN
ejpam-5586	513	12	sj(tk	sj(tk	PROPN
ejpam-5586	513	13	)	)	PUNCT
ejpam-5586	514	1	2	2	PROPN
ejpam-5586	514	2	≥	≥	PRON
ejpam-5586	514	3			PROPN
ejpam-5586	514	4	n∏	n∏	PROPN
ejpam-5586	514	5	k=1	k=1	PUNCT
ejpam-5586	515	1			PROPN
ejpam-5586	515	2	n∑	n∑	PROPN
ejpam-5586	515	3	j=1	j=1	PROPN
ejpam-5586	515	4	sj(tk	sj(tk	PROPN
ejpam-5586	515	5	)	)	PUNCT
ejpam-5586	516	1	+	+	NUM
ejpam-5586	516	2	√√√√1	√√√√1	NOUN
ejpam-5586	516	3	+	+	CCONJ
ejpam-5586	516	4	n∑	n∑	PROPN
ejpam-5586	516	5	j=1	j=1	NOUN
ejpam-5586	516	6	s2j	s2j	PROPN
ejpam-5586	516	7	(	(	PUNCT
ejpam-5586	516	8	tk	tk	PROPN
ejpam-5586	516	9	)	)	PUNCT
ejpam-5586	516	10	γk	γk	PUNCT
ejpam-5586	516	11			NOUN
ejpam-5586	516	12	1	1	NUM
ejpam-5586	516	13	γn	γn	ADV
ejpam-5586	516	14	consequently	consequently	ADV
ejpam-5586	516	15	,	,	PUNCT
ejpam-5586	516	16	tr	tr	VERB
ejpam-5586	516	17	(	(	PUNCT
ejpam-5586	516	18	1	1	NUM
ejpam-5586	516	19	γn	γn	ADP
ejpam-5586	516	20	n∑	n∑	NOUN
ejpam-5586	516	21	k=1	k=1	PROPN
ejpam-5586	516	22	γktk	γktk	PROPN
ejpam-5586	516	23	)	)	PUNCT
ejpam-5586	517	1	+	+	NUM
ejpam-5586	517	2	√√√√1	√√√√1	NOUN
ejpam-5586	517	3	+	+	CCONJ
ejpam-5586	517	4	(	(	PUNCT
ejpam-5586	517	5	1	1	NUM
ejpam-5586	517	6	γn	γn	NOUN
ejpam-5586	517	7	n∑	n∑	NOUN
ejpam-5586	517	8	k=1	k=1	PUNCT
ejpam-5586	517	9	γktr(tk	γktr(tk	PROPN
ejpam-5586	517	10	)	)	PUNCT
ejpam-5586	517	11	)	)	PUNCT
ejpam-5586	517	12	2	2	NUM
ejpam-5586	517	13	=	=	SYM
ejpam-5586	517	14	1	1	NUM
ejpam-5586	517	15	γn	γn	NOUN
ejpam-5586	517	16	n∑	n∑	NOUN
ejpam-5586	517	17	k=1	k=1	PUNCT
ejpam-5586	517	18	γktr(tk	γktr(tk	PROPN
ejpam-5586	517	19	)	)	PUNCT
ejpam-5586	517	20	+	+	NUM
ejpam-5586	517	21	√√√√1	√√√√1	NOUN
ejpam-5586	517	22	+	+	CCONJ
ejpam-5586	517	23	(	(	PUNCT
ejpam-5586	517	24	1	1	NUM
ejpam-5586	517	25	γn	γn	NOUN
ejpam-5586	517	26	n∑	n∑	NOUN
ejpam-5586	517	27	k=1	k=1	PUNCT
ejpam-5586	517	28	γktr(tk	γktr(tk	PROPN
ejpam-5586	517	29	)	)	PUNCT
ejpam-5586	517	30	)	)	PUNCT
ejpam-5586	517	31	2	2	NUM
ejpam-5586	517	32	≥	≥	NOUN
ejpam-5586	517	33			PROPN
ejpam-5586	517	34	n∏	n∏	PROPN
ejpam-5586	517	35	k=1	k=1	PROPN
ejpam-5586	517	36	tr(tk	tr(tk	NOUN
ejpam-5586	517	37	)	)	PUNCT
ejpam-5586	517	38	+	+	NUM
ejpam-5586	517	39	√√√√1	√√√√1	NOUN
ejpam-5586	517	40	+	+	CCONJ
ejpam-5586	517	41	n∑	n∑	ADJ
ejpam-5586	517	42	j=1	j=1	NOUN
ejpam-5586	517	43	tr(t	tr(t	PUNCT
ejpam-5586	517	44	2	2	NUM
ejpam-5586	517	45	k	k	X
ejpam-5586	517	46	)	)	PUNCT
ejpam-5586	517	47	γk	γk	PUNCT
ejpam-5586	517	48			NOUN
ejpam-5586	517	49	1	1	NUM
ejpam-5586	517	50	γn	γn	NUM
ejpam-5586	517	51	6	6	NUM
ejpam-5586	517	52	.	.	PUNCT
ejpam-5586	517	53	conclusion	conclusion	NOUN
ejpam-5586	517	54	and	and	CCONJ
ejpam-5586	517	55	future	future	ADJ
ejpam-5586	517	56	work	work	NOUN
ejpam-5586	517	57	in	in	ADP
ejpam-5586	517	58	conclusion	conclusion	NOUN
ejpam-5586	517	59	,	,	PUNCT
ejpam-5586	517	60	this	this	DET
ejpam-5586	517	61	paper	paper	NOUN
ejpam-5586	517	62	has	have	AUX
ejpam-5586	517	63	embarked	embark	VERB
ejpam-5586	517	64	on	on	ADP
ejpam-5586	517	65	an	an	DET
ejpam-5586	517	66	extensive	extensive	ADJ
ejpam-5586	517	67	investigation	investigation	NOUN
ejpam-5586	517	68	into	into	ADP
ejpam-5586	517	69	the	the	DET
ejpam-5586	517	70	domain	domain	NOUN
ejpam-5586	517	71	of	of	ADP
ejpam-5586	517	72	matrix	matrix	NOUN
ejpam-5586	517	73	means	mean	VERB
ejpam-5586	517	74	interpolation	interpolation	NOUN
ejpam-5586	517	75	and	and	CCONJ
ejpam-5586	517	76	comparison	comparison	NOUN
ejpam-5586	517	77	.	.	PUNCT
ejpam-5586	518	1	a	a	DET
ejpam-5586	518	2	key	key	ADJ
ejpam-5586	518	3	aspect	aspect	NOUN
ejpam-5586	518	4	of	of	ADP
ejpam-5586	518	5	this	this	DET
ejpam-5586	518	6	research	research	NOUN
ejpam-5586	518	7	has	have	AUX
ejpam-5586	518	8	been	be	AUX
ejpam-5586	518	9	the	the	DET
ejpam-5586	518	10	expansion	expansion	NOUN
ejpam-5586	518	11	of	of	ADP
ejpam-5586	518	12	the	the	DET
ejpam-5586	518	13	parameter	parameter	NOUN
ejpam-5586	518	14	ϑ	ϑ	PROPN
ejpam-5586	518	15	from	from	ADP
ejpam-5586	518	16	the	the	DET
ejpam-5586	518	17	closed	closed	ADJ
ejpam-5586	518	18	interval	interval	NOUN
ejpam-5586	518	19	[	[	X
ejpam-5586	518	20	0	0	NUM
ejpam-5586	518	21	,	,	PUNCT
ejpam-5586	518	22	1	1	NUM
ejpam-5586	518	23	]	]	PUNCT
ejpam-5586	518	24	to	to	PART
ejpam-5586	518	25	encompass	encompass	VERB
ejpam-5586	518	26	the	the	DET
ejpam-5586	518	27	entire	entire	ADJ
ejpam-5586	518	28	positive	positive	ADJ
ejpam-5586	518	29	real	real	ADJ
ejpam-5586	518	30	line	line	NOUN
ejpam-5586	518	31	,	,	PUNCT
ejpam-5586	518	32	represented	represent	VERB
ejpam-5586	518	33	as	as	ADP
ejpam-5586	518	34	r+	r+	X
ejpam-5586	518	35	.	.	PUNCT
ejpam-5586	519	1	this	this	DET
ejpam-5586	519	2	extension	extension	NOUN
ejpam-5586	519	3	has	have	AUX
ejpam-5586	519	4	allowed	allow	VERB
ejpam-5586	519	5	us	we	PRON
ejpam-5586	519	6	to	to	PART
ejpam-5586	519	7	explore	explore	VERB
ejpam-5586	519	8	a	a	DET
ejpam-5586	519	9	broader	broad	ADJ
ejpam-5586	519	10	spectrum	spectrum	NOUN
ejpam-5586	519	11	of	of	ADP
ejpam-5586	519	12	mathematical	mathematical	ADJ
ejpam-5586	519	13	relationships	relationship	NOUN
ejpam-5586	519	14	and	and	CCONJ
ejpam-5586	519	15	properties	property	NOUN
ejpam-5586	519	16	within	within	ADP
ejpam-5586	519	17	this	this	DET
ejpam-5586	519	18	framework	framework	NOUN
ejpam-5586	519	19	.	.	PUNCT
ejpam-5586	520	1	m.h.m	m.h.m	PROPN
ejpam-5586	520	2	rashid	rashid	PROPN
ejpam-5586	520	3	,	,	PUNCT
ejpam-5586	520	4	w.m.m	w.m.m	NOUN
ejpam-5586	520	5	.	.	PUNCT
ejpam-5586	521	1	salameh	salameh	PROPN
ejpam-5586	521	2	/	/	SYM
ejpam-5586	521	3	eur	eur	PROPN
ejpam-5586	521	4	.	.	PUNCT
ejpam-5586	522	1	j.	j.	PROPN
ejpam-5586	522	2	pure	pure	PROPN
ejpam-5586	522	3	appl	appl	PROPN
ejpam-5586	522	4	.	.	PROPN
ejpam-5586	522	5	math	math	PROPN
ejpam-5586	522	6	,	,	PUNCT
ejpam-5586	522	7	18	18	NUM
ejpam-5586	522	8	(	(	PUNCT
ejpam-5586	522	9	1	1	NUM
ejpam-5586	522	10	)	)	PUNCT
ejpam-5586	522	11	(	(	PUNCT
ejpam-5586	522	12	2025	2025	NUM
ejpam-5586	522	13	)	)	PUNCT
ejpam-5586	522	14	,	,	PUNCT
ejpam-5586	522	15	5586	5586	NUM
ejpam-5586	522	16	19	19	NUM
ejpam-5586	522	17	of	of	ADP
ejpam-5586	522	18	21	21	NUM
ejpam-5586	522	19	furthermore	furthermore	ADV
ejpam-5586	522	20	,	,	PUNCT
ejpam-5586	522	21	our	our	PRON
ejpam-5586	522	22	exploration	exploration	NOUN
ejpam-5586	522	23	has	have	AUX
ejpam-5586	522	24	led	lead	VERB
ejpam-5586	522	25	to	to	ADP
ejpam-5586	522	26	the	the	DET
ejpam-5586	522	27	development	development	NOUN
ejpam-5586	522	28	of	of	ADP
ejpam-5586	522	29	various	various	ADJ
ejpam-5586	522	30	novel	novel	NOUN
ejpam-5586	522	31	results	result	NOUN
ejpam-5586	522	32	related	relate	VERB
ejpam-5586	522	33	to	to	ADP
ejpam-5586	522	34	heinz	heinz	ADJ
ejpam-5586	522	35	means	mean	NOUN
ejpam-5586	522	36	.	.	PUNCT
ejpam-5586	523	1	we	we	PRON
ejpam-5586	523	2	have	have	AUX
ejpam-5586	523	3	introduced	introduce	VERB
ejpam-5586	523	4	scalar	scalar	ADJ
ejpam-5586	523	5	variants	variant	NOUN
ejpam-5586	523	6	of	of	ADP
ejpam-5586	523	7	heinz	heinz	ADJ
ejpam-5586	523	8	inequalities	inequality	NOUN
ejpam-5586	523	9	,	,	PUNCT
ejpam-5586	523	10	leveraging	leverage	VERB
ejpam-5586	523	11	kantorovich	kantorovich	PROPN
ejpam-5586	523	12	’s	’s	NOUN
ejpam-5586	523	13	constant	constant	ADJ
ejpam-5586	523	14	,	,	PUNCT
ejpam-5586	523	15	and	and	CCONJ
ejpam-5586	523	16	have	have	AUX
ejpam-5586	523	17	extended	extend	VERB
ejpam-5586	523	18	these	these	DET
ejpam-5586	523	19	inequalities	inequality	NOUN
ejpam-5586	523	20	to	to	ADP
ejpam-5586	523	21	the	the	DET
ejpam-5586	523	22	operator	operator	NOUN
ejpam-5586	523	23	realm	realm	NOUN
ejpam-5586	523	24	.	.	PUNCT
ejpam-5586	524	1	this	this	DET
ejpam-5586	524	2	expansion	expansion	NOUN
ejpam-5586	524	3	not	not	PART
ejpam-5586	524	4	only	only	ADV
ejpam-5586	524	5	deepens	deepen	VERB
ejpam-5586	524	6	our	our	PRON
ejpam-5586	524	7	understanding	understanding	NOUN
ejpam-5586	524	8	of	of	ADP
ejpam-5586	524	9	heinz	heinz	ADJ
ejpam-5586	524	10	means	mean	NOUN
ejpam-5586	524	11	but	but	CCONJ
ejpam-5586	524	12	also	also	ADV
ejpam-5586	524	13	opens	open	VERB
ejpam-5586	524	14	up	up	ADP
ejpam-5586	524	15	new	new	ADJ
ejpam-5586	524	16	avenues	avenue	NOUN
ejpam-5586	524	17	for	for	ADP
ejpam-5586	524	18	applications	application	NOUN
ejpam-5586	524	19	in	in	ADP
ejpam-5586	524	20	diverse	diverse	ADJ
ejpam-5586	524	21	mathematical	mathematical	ADJ
ejpam-5586	524	22	contexts	contexts	NOUN
ejpam-5586	524	23	.	.	PUNCT
ejpam-5586	525	1	lastly	lastly	ADV
ejpam-5586	525	2	,	,	PUNCT
ejpam-5586	525	3	we	we	PRON
ejpam-5586	525	4	have	have	AUX
ejpam-5586	525	5	presented	present	VERB
ejpam-5586	525	6	refined	refined	ADJ
ejpam-5586	525	7	young	young	PROPN
ejpam-5586	525	8	’s	’s	PART
ejpam-5586	525	9	type	type	NOUN
ejpam-5586	525	10	inequalities	inequality	NOUN
ejpam-5586	525	11	specifically	specifically	ADV
ejpam-5586	525	12	tailored	tailor	VERB
ejpam-5586	525	13	for	for	ADP
ejpam-5586	525	14	traces	trace	NOUN
ejpam-5586	525	15	,	,	PUNCT
ejpam-5586	525	16	determinants	determinant	NOUN
ejpam-5586	525	17	,	,	PUNCT
ejpam-5586	525	18	and	and	CCONJ
ejpam-5586	525	19	norms	norm	NOUN
ejpam-5586	525	20	of	of	ADP
ejpam-5586	525	21	positive	positive	ADJ
ejpam-5586	525	22	semi	semi	ADJ
ejpam-5586	525	23	-	-	ADJ
ejpam-5586	525	24	definite	definite	ADJ
ejpam-5586	525	25	matrices	matrix	NOUN
ejpam-5586	525	26	.	.	PUNCT
ejpam-5586	526	1	these	these	DET
ejpam-5586	526	2	refined	refined	ADJ
ejpam-5586	526	3	inequalities	inequality	NOUN
ejpam-5586	526	4	are	be	AUX
ejpam-5586	526	5	expected	expect	VERB
ejpam-5586	526	6	to	to	PART
ejpam-5586	526	7	find	find	VERB
ejpam-5586	526	8	utility	utility	NOUN
ejpam-5586	526	9	in	in	ADP
ejpam-5586	526	10	various	various	ADJ
ejpam-5586	526	11	matrix	matrix	NOUN
ejpam-5586	526	12	analysis	analysis	NOUN
ejpam-5586	526	13	and	and	CCONJ
ejpam-5586	526	14	linear	linear	NOUN
ejpam-5586	526	15	algebra	algebra	NOUN
ejpam-5586	526	16	problems	problem	NOUN
ejpam-5586	526	17	,	,	PUNCT
ejpam-5586	526	18	enhancing	enhance	VERB
ejpam-5586	526	19	our	our	PRON
ejpam-5586	526	20	ability	ability	NOUN
ejpam-5586	526	21	to	to	PART
ejpam-5586	526	22	derive	derive	VERB
ejpam-5586	526	23	meaningful	meaningful	ADJ
ejpam-5586	526	24	conclusions	conclusion	NOUN
ejpam-5586	526	25	and	and	CCONJ
ejpam-5586	526	26	insights	insight	NOUN
ejpam-5586	526	27	from	from	ADP
ejpam-5586	526	28	the	the	DET
ejpam-5586	526	29	study	study	NOUN
ejpam-5586	526	30	of	of	ADP
ejpam-5586	526	31	positive	positive	ADJ
ejpam-5586	526	32	semi	semi	ADJ
ejpam-5586	526	33	-	-	ADJ
ejpam-5586	526	34	definite	definite	ADJ
ejpam-5586	526	35	matrices	matrix	NOUN
ejpam-5586	526	36	.	.	PUNCT
ejpam-5586	527	1	as	as	ADP
ejpam-5586	527	2	for	for	ADP
ejpam-5586	527	3	future	future	ADJ
ejpam-5586	527	4	work	work	NOUN
ejpam-5586	527	5	,	,	PUNCT
ejpam-5586	527	6	there	there	PRON
ejpam-5586	527	7	are	be	VERB
ejpam-5586	527	8	several	several	ADJ
ejpam-5586	527	9	intriguing	intriguing	ADJ
ejpam-5586	527	10	directions	direction	NOUN
ejpam-5586	527	11	to	to	PART
ejpam-5586	527	12	consider	consider	VERB
ejpam-5586	527	13	.	.	PUNCT
ejpam-5586	528	1	firstly	firstly	ADV
ejpam-5586	528	2	,	,	PUNCT
ejpam-5586	528	3	it	it	PRON
ejpam-5586	528	4	may	may	AUX
ejpam-5586	528	5	be	be	AUX
ejpam-5586	528	6	valuable	valuable	ADJ
ejpam-5586	528	7	to	to	PART
ejpam-5586	528	8	explore	explore	VERB
ejpam-5586	528	9	further	further	ADJ
ejpam-5586	528	10	extensions	extension	NOUN
ejpam-5586	528	11	of	of	ADP
ejpam-5586	528	12	the	the	DET
ejpam-5586	528	13	parameter	parameter	NOUN
ejpam-5586	528	14	space	space	NOUN
ejpam-5586	528	15	beyond	beyond	ADP
ejpam-5586	528	16	r+	r+	NOUN
ejpam-5586	528	17	and	and	CCONJ
ejpam-5586	528	18	investigate	investigate	VERB
ejpam-5586	528	19	the	the	DET
ejpam-5586	528	20	implications	implication	NOUN
ejpam-5586	528	21	of	of	ADP
ejpam-5586	528	22	such	such	ADJ
ejpam-5586	528	23	extensions	extension	NOUN
ejpam-5586	528	24	on	on	ADP
ejpam-5586	528	25	matrix	matrix	NOUN
ejpam-5586	528	26	means	mean	NOUN
ejpam-5586	528	27	and	and	CCONJ
ejpam-5586	528	28	related	related	ADJ
ejpam-5586	528	29	inequalities	inequality	NOUN
ejpam-5586	528	30	.	.	PUNCT
ejpam-5586	529	1	additionally	additionally	ADV
ejpam-5586	529	2	,	,	PUNCT
ejpam-5586	529	3	the	the	DET
ejpam-5586	529	4	applicability	applicability	NOUN
ejpam-5586	529	5	of	of	ADP
ejpam-5586	529	6	the	the	DET
ejpam-5586	529	7	developed	develop	VERB
ejpam-5586	529	8	results	result	NOUN
ejpam-5586	529	9	in	in	ADP
ejpam-5586	529	10	practical	practical	ADJ
ejpam-5586	529	11	fields	field	NOUN
ejpam-5586	529	12	such	such	ADJ
ejpam-5586	529	13	as	as	ADP
ejpam-5586	529	14	physics	physics	NOUN
ejpam-5586	529	15	,	,	PUNCT
ejpam-5586	529	16	engineering	engineering	NOUN
ejpam-5586	529	17	,	,	PUNCT
ejpam-5586	529	18	and	and	CCONJ
ejpam-5586	529	19	data	datum	NOUN
ejpam-5586	529	20	science	science	NOUN
ejpam-5586	529	21	warrants	warrant	NOUN
ejpam-5586	529	22	investigation	investigation	NOUN
ejpam-5586	529	23	.	.	PUNCT
ejpam-5586	530	1	finally	finally	ADV
ejpam-5586	530	2	,	,	PUNCT
ejpam-5586	530	3	refining	refine	VERB
ejpam-5586	530	4	and	and	CCONJ
ejpam-5586	530	5	expanding	expand	VERB
ejpam-5586	530	6	upon	upon	SCONJ
ejpam-5586	530	7	the	the	DET
ejpam-5586	530	8	presented	present	VERB
ejpam-5586	530	9	inequalities	inequality	NOUN
ejpam-5586	530	10	could	could	AUX
ejpam-5586	530	11	lead	lead	VERB
ejpam-5586	530	12	to	to	ADP
ejpam-5586	530	13	even	even	ADV
ejpam-5586	530	14	more	more	ADV
ejpam-5586	530	15	powerful	powerful	ADJ
ejpam-5586	530	16	tools	tool	NOUN
ejpam-5586	530	17	for	for	ADP
ejpam-5586	530	18	matrix	matrix	NOUN
ejpam-5586	530	19	analysis	analysis	NOUN
ejpam-5586	530	20	and	and	CCONJ
ejpam-5586	530	21	optimization	optimization	NOUN
ejpam-5586	530	22	,	,	PUNCT
ejpam-5586	530	23	offering	offer	VERB
ejpam-5586	530	24	new	new	ADJ
ejpam-5586	530	25	insights	insight	NOUN
ejpam-5586	530	26	and	and	CCONJ
ejpam-5586	530	27	solutions	solution	NOUN
ejpam-5586	530	28	to	to	ADP
ejpam-5586	530	29	complex	complex	ADJ
ejpam-5586	530	30	problems	problem	NOUN
ejpam-5586	530	31	in	in	ADP
ejpam-5586	530	32	mathematics	mathematic	NOUN
ejpam-5586	530	33	and	and	CCONJ
ejpam-5586	530	34	its	its	PRON
ejpam-5586	530	35	applications	application	NOUN
ejpam-5586	530	36	.	.	PUNCT
ejpam-5586	531	1	declaration	declaration	NOUN
ejpam-5586	531	2	•	•	NUM
ejpam-5586	531	3	author	author	NOUN
ejpam-5586	531	4	contributions	contribution	NOUN
ejpam-5586	531	5	:	:	PUNCT
ejpam-5586	531	6	the	the	DET
ejpam-5586	531	7	author	author	NOUN
ejpam-5586	531	8	have	have	AUX
ejpam-5586	531	9	read	read	VERB
ejpam-5586	531	10	and	and	CCONJ
ejpam-5586	531	11	agreed	agree	VERB
ejpam-5586	531	12	to	to	ADP
ejpam-5586	531	13	the	the	DET
ejpam-5586	531	14	published	publish	VERB
ejpam-5586	531	15	version	version	NOUN
ejpam-5586	531	16	of	of	ADP
ejpam-5586	531	17	the	the	DET
ejpam-5586	531	18	manuscript	manuscript	NOUN
ejpam-5586	531	19	.	.	PUNCT
ejpam-5586	532	1	•	•	NUM
ejpam-5586	532	2	funding	funding	NOUN
ejpam-5586	532	3	:	:	PUNCT
ejpam-5586	532	4	no	no	DET
ejpam-5586	532	5	funding	funding	NOUN
ejpam-5586	532	6	is	be	AUX
ejpam-5586	532	7	applicable	applicable	ADJ
ejpam-5586	532	8	•	•	ADP
ejpam-5586	532	9	conflicts	conflict	NOUN
ejpam-5586	532	10	of	of	ADP
ejpam-5586	532	11	interest	interest	NOUN
ejpam-5586	532	12	:	:	PUNCT
ejpam-5586	532	13	the	the	DET
ejpam-5586	532	14	authors	author	NOUN
ejpam-5586	532	15	declare	declare	VERB
ejpam-5586	532	16	no	no	DET
ejpam-5586	532	17	conflict	conflict	NOUN
ejpam-5586	532	18	of	of	ADP
ejpam-5586	532	19	interest	interest	NOUN
ejpam-5586	532	20	.	.	PUNCT
ejpam-5586	533	1	acknowledgements	acknowledgement	NOUN
ejpam-5586	533	2	the	the	DET
ejpam-5586	533	3	authors	author	NOUN
ejpam-5586	533	4	sincerely	sincerely	ADV
ejpam-5586	533	5	thank	thank	VERB
ejpam-5586	533	6	the	the	DET
ejpam-5586	533	7	reviewers	reviewer	NOUN
ejpam-5586	533	8	for	for	ADP
ejpam-5586	533	9	their	their	PRON
ejpam-5586	533	10	insightful	insightful	ADJ
ejpam-5586	533	11	feedback	feedback	NOUN
ejpam-5586	533	12	,	,	PUNCT
ejpam-5586	533	13	valuable	valuable	ADJ
ejpam-5586	533	14	suggestions	suggestion	NOUN
ejpam-5586	533	15	,	,	PUNCT
ejpam-5586	533	16	and	and	CCONJ
ejpam-5586	533	17	expertise	expertise	NOUN
ejpam-5586	533	18	,	,	PUNCT
ejpam-5586	533	19	which	which	PRON
ejpam-5586	533	20	have	have	AUX
ejpam-5586	533	21	greatly	greatly	ADV
ejpam-5586	533	22	contributed	contribute	VERB
ejpam-5586	533	23	to	to	ADP
ejpam-5586	533	24	improving	improve	VERB
ejpam-5586	533	25	the	the	DET
ejpam-5586	533	26	clarity	clarity	NOUN
ejpam-5586	533	27	,	,	PUNCT
ejpam-5586	533	28	quality	quality	NOUN
ejpam-5586	533	29	,	,	PUNCT
ejpam-5586	533	30	and	and	CCONJ
ejpam-5586	533	31	overall	overall	ADJ
ejpam-5586	533	32	impact	impact	NOUN
ejpam-5586	533	33	of	of	ADP
ejpam-5586	533	34	this	this	DET
ejpam-5586	533	35	study	study	NOUN
ejpam-5586	533	36	.	.	PUNCT
ejpam-5586	534	1	references	reference	NOUN
ejpam-5586	534	2	[	[	X
ejpam-5586	534	3	1	1	NUM
ejpam-5586	534	4	]	]	PUNCT
ejpam-5586	534	5	tsuyoshi	tsuyoshi	PROPN
ejpam-5586	534	6	andô.	andô.	PROPN
ejpam-5586	534	7	matrix	matrix	VERB
ejpam-5586	534	8	young	young	ADJ
ejpam-5586	534	9	inequalities	inequality	NOUN
ejpam-5586	534	10	.	.	PUNCT
ejpam-5586	535	1	operator	operator	NOUN
ejpam-5586	535	2	theory	theory	NOUN
ejpam-5586	535	3	,	,	PUNCT
ejpam-5586	535	4	75:33–38	75:33–38	NUM
ejpam-5586	535	5	,	,	PUNCT
ejpam-5586	535	6	1995	1995	NUM
ejpam-5586	535	7	.	.	PUNCT
ejpam-5586	536	1	[	[	X
ejpam-5586	536	2	2	2	NUM
ejpam-5586	536	3	]	]	X
ejpam-5586	536	4	rajendra	rajendra	PROPN
ejpam-5586	536	5	bhatia	bhatia	PROPN
ejpam-5586	536	6	.	.	PUNCT
ejpam-5586	537	1	interpolating	interpolate	VERB
ejpam-5586	537	2	the	the	DET
ejpam-5586	537	3	arithmetic	arithmetic	ADJ
ejpam-5586	537	4	–	–	PUNCT
ejpam-5586	537	5	geometric	geometric	ADJ
ejpam-5586	537	6	mean	mean	NOUN
ejpam-5586	537	7	inequality	inequality	NOUN
ejpam-5586	537	8	and	and	CCONJ
ejpam-5586	537	9	its	its	PRON
ejpam-5586	537	10	operator	operator	NOUN
ejpam-5586	537	11	version	version	NOUN
ejpam-5586	537	12	.	.	PUNCT
ejpam-5586	538	1	linear	linear	ADJ
ejpam-5586	538	2	algebra	algebra	NOUN
ejpam-5586	538	3	and	and	CCONJ
ejpam-5586	538	4	its	its	PRON
ejpam-5586	538	5	applications	application	NOUN
ejpam-5586	538	6	,	,	PUNCT
ejpam-5586	538	7	413(2):355–363	413(2):355–363	NUM
ejpam-5586	538	8	,	,	PUNCT
ejpam-5586	538	9	2006	2006	NUM
ejpam-5586	538	10	.	.	PUNCT
ejpam-5586	539	1	special	special	ADJ
ejpam-5586	539	2	issue	issue	NOUN
ejpam-5586	539	3	on	on	ADP
ejpam-5586	539	4	the	the	DET
ejpam-5586	539	5	11th	11th	ADJ
ejpam-5586	539	6	conference	conference	NOUN
ejpam-5586	539	7	of	of	ADP
ejpam-5586	539	8	the	the	DET
ejpam-5586	539	9	international	international	ADJ
ejpam-5586	539	10	linear	linear	PROPN
ejpam-5586	539	11	algebra	algebra	PROPN
ejpam-5586	539	12	society	society	NOUN
ejpam-5586	539	13	,	,	PUNCT
ejpam-5586	539	14	coimbra	coimbra	PROPN
ejpam-5586	539	15	,	,	PUNCT
ejpam-5586	539	16	2004	2004	NUM
ejpam-5586	539	17	.	.	PUNCT
ejpam-5586	540	1	[	[	X
ejpam-5586	540	2	3	3	NUM
ejpam-5586	540	3	]	]	X
ejpam-5586	540	4	shigeru	shigeru	NOUN
ejpam-5586	540	5	furuichi	furuichi	PROPN
ejpam-5586	540	6	.	.	PUNCT
ejpam-5586	541	1	on	on	ADP
ejpam-5586	541	2	refined	refined	ADJ
ejpam-5586	541	3	young	young	ADJ
ejpam-5586	541	4	inequalities	inequality	NOUN
ejpam-5586	541	5	and	and	CCONJ
ejpam-5586	541	6	reverse	reverse	ADJ
ejpam-5586	541	7	inequalities	inequality	NOUN
ejpam-5586	541	8	.	.	PUNCT
ejpam-5586	542	1	journal	journal	PROPN
ejpam-5586	542	2	of	of	ADP
ejpam-5586	542	3	mathematical	mathematical	ADJ
ejpam-5586	542	4	inequalities	inequality	NOUN
ejpam-5586	542	5	,	,	PUNCT
ejpam-5586	542	6	5	5	NUM
ejpam-5586	542	7	,	,	PUNCT
ejpam-5586	542	8	01	01	NUM
ejpam-5586	542	9	2010	2010	NUM
ejpam-5586	542	10	.	.	PUNCT
ejpam-5586	543	1	m.h.m	m.h.m	PROPN
ejpam-5586	543	2	rashid	rashid	PROPN
ejpam-5586	543	3	,	,	PUNCT
ejpam-5586	543	4	w.m.m	w.m.m	NOUN
ejpam-5586	543	5	.	.	PUNCT
ejpam-5586	544	1	salameh	salameh	PROPN
ejpam-5586	544	2	/	/	SYM
ejpam-5586	544	3	eur	eur	PROPN
ejpam-5586	544	4	.	.	PUNCT
ejpam-5586	545	1	j.	j.	PROPN
ejpam-5586	545	2	pure	pure	PROPN
ejpam-5586	545	3	appl	appl	PROPN
ejpam-5586	545	4	.	.	PROPN
ejpam-5586	545	5	math	math	PROPN
ejpam-5586	545	6	,	,	PUNCT
ejpam-5586	545	7	18	18	NUM
ejpam-5586	545	8	(	(	PUNCT
ejpam-5586	545	9	1	1	NUM
ejpam-5586	545	10	)	)	PUNCT
ejpam-5586	545	11	(	(	PUNCT
ejpam-5586	545	12	2025	2025	NUM
ejpam-5586	545	13	)	)	PUNCT
ejpam-5586	545	14	,	,	PUNCT
ejpam-5586	545	15	5586	5586	NUM
ejpam-5586	545	16	20	20	NUM
ejpam-5586	545	17	of	of	ADP
ejpam-5586	545	18	21	21	NUM
ejpam-5586	545	19	[	[	SYM
ejpam-5586	545	20	4	4	NUM
ejpam-5586	545	21	]	]	PUNCT
ejpam-5586	545	22	fumio	fumio	ADJ
ejpam-5586	545	23	hiai	hiai	NOUN
ejpam-5586	545	24	and	and	CCONJ
ejpam-5586	545	25	hideki	hideki	PROPN
ejpam-5586	545	26	kosaki	kosaki	PROPN
ejpam-5586	545	27	.	.	PUNCT
ejpam-5586	546	1	means	mean	VERB
ejpam-5586	546	2	for	for	ADP
ejpam-5586	546	3	matrices	matrix	NOUN
ejpam-5586	546	4	and	and	CCONJ
ejpam-5586	546	5	comparison	comparison	NOUN
ejpam-5586	546	6	of	of	ADP
ejpam-5586	546	7	their	their	PRON
ejpam-5586	546	8	norms	norm	NOUN
ejpam-5586	546	9	.	.	PUNCT
ejpam-5586	547	1	indiana	indiana	PROPN
ejpam-5586	547	2	university	university	PROPN
ejpam-5586	547	3	mathematics	mathematics	PROPN
ejpam-5586	547	4	journal	journal	NOUN
ejpam-5586	547	5	,	,	PUNCT
ejpam-5586	547	6	48:899–936	48:899–936	PROPN
ejpam-5586	547	7	,	,	PUNCT
ejpam-5586	547	8	1999	1999	NUM
ejpam-5586	547	9	.	.	PUNCT
ejpam-5586	548	1	[	[	X
ejpam-5586	548	2	5	5	NUM
ejpam-5586	548	3	]	]	X
ejpam-5586	548	4	r.a	r.a	PROPN
ejpam-5586	548	5	.	.	PROPN
ejpam-5586	548	6	horn	horn	PROPN
ejpam-5586	548	7	and	and	CCONJ
ejpam-5586	548	8	c.r	c.r	PROPN
ejpam-5586	548	9	johnson	johnson	PROPN
ejpam-5586	548	10	.	.	PROPN
ejpam-5586	548	11	matrix	matrix	NOUN
ejpam-5586	548	12	analysis	analysis	NOUN
ejpam-5586	548	13	.	.	PUNCT
ejpam-5586	549	1	cambridge	cambridge	PROPN
ejpam-5586	549	2	univ	univ	PROPN
ejpam-5586	549	3	.	.	PUNCT
ejpam-5586	550	1	press	press	PROPN
ejpam-5586	550	2	,	,	PUNCT
ejpam-5586	550	3	new	new	PROPN
ejpam-5586	550	4	york	york	PROPN
ejpam-5586	550	5	,	,	PUNCT
ejpam-5586	550	6	1985	1985	NUM
ejpam-5586	550	7	.	.	PUNCT
ejpam-5586	551	1	[	[	X
ejpam-5586	551	2	6	6	NUM
ejpam-5586	551	3	]	]	X
ejpam-5586	551	4	r.a	r.a	PROPN
ejpam-5586	551	5	.	.	PROPN
ejpam-5586	551	6	horn	horn	PROPN
ejpam-5586	551	7	and	and	CCONJ
ejpam-5586	551	8	c.r	c.r	PROPN
ejpam-5586	551	9	johnson	johnson	PROPN
ejpam-5586	551	10	.	.	PUNCT
ejpam-5586	552	1	topics	topic	NOUN
ejpam-5586	552	2	in	in	ADP
ejpam-5586	552	3	matrix	matrix	NOUN
ejpam-5586	552	4	analysis	analysis	NOUN
ejpam-5586	552	5	.	.	PUNCT
ejpam-5586	553	1	cambridge	cambridge	PROPN
ejpam-5586	553	2	univ	univ	PROPN
ejpam-5586	553	3	.	.	PUNCT
ejpam-5586	554	1	press	press	PROPN
ejpam-5586	554	2	,	,	PUNCT
ejpam-5586	554	3	new	new	PROPN
ejpam-5586	554	4	york	york	PROPN
ejpam-5586	554	5	,	,	PUNCT
ejpam-5586	554	6	1990	1990	NUM
ejpam-5586	554	7	.	.	PUNCT
ejpam-5586	555	1	[	[	X
ejpam-5586	555	2	7	7	X
ejpam-5586	555	3	]	]	PUNCT
ejpam-5586	555	4	j.	j.	PROPN
ejpam-5586	555	5	míscísc	míscísc	PROPN
ejpam-5586	555	6	hot	hot	ADJ
ejpam-5586	555	7	j.pemcarísc	j.pemcarísc	PROPN
ejpam-5586	555	8	,	,	PUNCT
ejpam-5586	555	9	t.	t.	PROPN
ejpam-5586	555	10	furuta	furuta	PROPN
ejpam-5586	555	11	and	and	CCONJ
ejpam-5586	555	12	y.	y.	PROPN
ejpam-5586	555	13	seo	seo	PROPN
ejpam-5586	555	14	.	.	PUNCT
ejpam-5586	556	1	mondpencariéc	mondpencariéc	NOUN
ejpam-5586	556	2	method	method	VERB
ejpam-5586	556	3	in	in	ADP
ejpam-5586	556	4	operator	operator	NOUN
ejpam-5586	556	5	inequalities	inequality	NOUN
ejpam-5586	556	6	,	,	PUNCT
ejpam-5586	556	7	inequalities	inequality	NOUN
ejpam-5586	556	8	for	for	ADP
ejpam-5586	556	9	bounded	bounded	ADJ
ejpam-5586	556	10	selfadjoint	selfadjoint	NOUN
ejpam-5586	556	11	operators	operator	NOUN
ejpam-5586	556	12	on	on	ADP
ejpam-5586	556	13	a	a	DET
ejpam-5586	556	14	hilbert	hilbert	NOUN
ejpam-5586	556	15	space	space	NOUN
ejpam-5586	556	16	.	.	PUNCT
ejpam-5586	557	1	2005	2005	NUM
ejpam-5586	557	2	.	.	PUNCT
ejpam-5586	558	1	[	[	X
ejpam-5586	558	2	8	8	NUM
ejpam-5586	558	3	]	]	PUNCT
ejpam-5586	558	4	rupinderjit	rupinderjit	NOUN
ejpam-5586	558	5	kaur	kaur	PROPN
ejpam-5586	558	6	and	and	CCONJ
ejpam-5586	558	7	mandeep	mandeep	PROPN
ejpam-5586	558	8	singh	singh	PROPN
ejpam-5586	558	9	.	.	PUNCT
ejpam-5586	559	1	complete	complete	ADJ
ejpam-5586	559	2	interpolation	interpolation	NOUN
ejpam-5586	559	3	of	of	ADP
ejpam-5586	559	4	matrix	matrix	NOUN
ejpam-5586	559	5	versions	version	NOUN
ejpam-5586	559	6	of	of	ADP
ejpam-5586	559	7	heron	heron	NOUN
ejpam-5586	559	8	and	and	CCONJ
ejpam-5586	559	9	heinz	heinz	ADJ
ejpam-5586	559	10	means	mean	NOUN
ejpam-5586	559	11	.	.	PUNCT
ejpam-5586	560	1	mathematical	mathematical	ADJ
ejpam-5586	560	2	inequalities	inequality	NOUN
ejpam-5586	560	3	and	and	CCONJ
ejpam-5586	560	4	applications	application	NOUN
ejpam-5586	560	5	,	,	PUNCT
ejpam-5586	560	6	16	16	NUM
ejpam-5586	560	7	,	,	PUNCT
ejpam-5586	560	8	12	12	NUM
ejpam-5586	560	9	2011	2011	NUM
ejpam-5586	560	10	.	.	PUNCT
ejpam-5586	561	1	[	[	X
ejpam-5586	561	2	9	9	X
ejpam-5586	561	3	]	]	X
ejpam-5586	561	4	fuad	fuad	PROPN
ejpam-5586	561	5	kittaneh	kittaneh	PROPN
ejpam-5586	561	6	.	.	PUNCT
ejpam-5586	562	1	norm	norm	NOUN
ejpam-5586	562	2	inequalities	inequality	NOUN
ejpam-5586	562	3	for	for	ADP
ejpam-5586	562	4	fractional	fractional	ADJ
ejpam-5586	562	5	powers	power	NOUN
ejpam-5586	562	6	of	of	ADP
ejpam-5586	562	7	positive	positive	ADJ
ejpam-5586	562	8	operators	operator	NOUN
ejpam-5586	562	9	.	.	PUNCT
ejpam-5586	563	1	letters	letter	NOUN
ejpam-5586	563	2	in	in	ADP
ejpam-5586	563	3	mathematical	mathematical	ADJ
ejpam-5586	563	4	physics	physics	NOUN
ejpam-5586	563	5	,	,	PUNCT
ejpam-5586	563	6	27:279–285	27:279–285	PROPN
ejpam-5586	563	7	,	,	PUNCT
ejpam-5586	563	8	1993	1993	NUM
ejpam-5586	563	9	.	.	PUNCT
ejpam-5586	564	1	[	[	X
ejpam-5586	564	2	10	10	NUM
ejpam-5586	564	3	]	]	X
ejpam-5586	564	4	fuad	fuad	PROPN
ejpam-5586	564	5	kittaneh	kittaneh	PROPN
ejpam-5586	564	6	and	and	CCONJ
ejpam-5586	564	7	yousef	yousef	PROPN
ejpam-5586	564	8	manasrah	manasrah	PROPN
ejpam-5586	564	9	.	.	PUNCT
ejpam-5586	565	1	improved	improve	VERB
ejpam-5586	565	2	young	young	ADJ
ejpam-5586	565	3	and	and	CCONJ
ejpam-5586	565	4	heinz	heinz	ADJ
ejpam-5586	565	5	inequalities	inequality	NOUN
ejpam-5586	565	6	for	for	ADP
ejpam-5586	565	7	matrices	matrix	NOUN
ejpam-5586	565	8	.	.	PUNCT
ejpam-5586	566	1	journal	journal	PROPN
ejpam-5586	566	2	of	of	ADP
ejpam-5586	566	3	mathematical	mathematical	ADJ
ejpam-5586	566	4	analysis	analysis	NOUN
ejpam-5586	566	5	and	and	CCONJ
ejpam-5586	566	6	applications	application	NOUN
ejpam-5586	566	7	,	,	PUNCT
ejpam-5586	566	8	361(1):262–269	361(1):262–269	ADP
ejpam-5586	566	9	,	,	PUNCT
ejpam-5586	566	10	2010	2010	NUM
ejpam-5586	566	11	.	.	PUNCT
ejpam-5586	567	1	[	[	X
ejpam-5586	567	2	11	11	NUM
ejpam-5586	567	3	]	]	PUNCT
ejpam-5586	567	4	hong	hong	PROPN
ejpam-5586	567	5	liang	liang	PROPN
ejpam-5586	567	6	zuo	zuo	PROPN
ejpam-5586	567	7	,	,	PUNCT
ejpam-5586	567	8	guanghua	guanghua	PROPN
ejpam-5586	567	9	shi	shi	PROPN
ejpam-5586	567	10	,	,	PUNCT
ejpam-5586	567	11	and	and	CCONJ
ejpam-5586	567	12	masatoshi	masatoshi	PROPN
ejpam-5586	567	13	fujii	fujii	PROPN
ejpam-5586	567	14	.	.	PUNCT
ejpam-5586	568	1	refined	refined	ADJ
ejpam-5586	568	2	young	young	ADJ
ejpam-5586	568	3	inequality	inequality	NOUN
ejpam-5586	568	4	with	with	ADP
ejpam-5586	568	5	kantorovich	kantorovich	PROPN
ejpam-5586	568	6	constant	constant	PROPN
ejpam-5586	568	7	.	.	PUNCT
ejpam-5586	569	1	journal	journal	PROPN
ejpam-5586	569	2	of	of	ADP
ejpam-5586	569	3	mathematical	mathematical	ADJ
ejpam-5586	569	4	inequalities	inequality	NOUN
ejpam-5586	569	5	,	,	PUNCT
ejpam-5586	569	6	pages	page	NOUN
ejpam-5586	569	7	551–556	551–556	NUM
ejpam-5586	569	8	,	,	PUNCT
ejpam-5586	569	9	2011	2011	NUM
ejpam-5586	569	10	.	.	PUNCT
ejpam-5586	570	1	[	[	X
ejpam-5586	570	2	12	12	NUM
ejpam-5586	570	3	]	]	SYM
ejpam-5586	570	4	wenshi	wenshi	PROPN
ejpam-5586	570	5	liao	liao	PROPN
ejpam-5586	570	6	,	,	PUNCT
ejpam-5586	570	7	junliang	junliang	PROPN
ejpam-5586	570	8	wu	wu	PROPN
ejpam-5586	570	9	,	,	PUNCT
ejpam-5586	570	10	and	and	CCONJ
ejpam-5586	570	11	jianguo	jianguo	PROPN
ejpam-5586	570	12	zhao	zhao	PROPN
ejpam-5586	570	13	.	.	PUNCT
ejpam-5586	571	1	new	new	ADJ
ejpam-5586	571	2	versions	version	NOUN
ejpam-5586	571	3	of	of	ADP
ejpam-5586	571	4	reverse	reverse	ADJ
ejpam-5586	571	5	young	young	ADJ
ejpam-5586	571	6	and	and	CCONJ
ejpam-5586	571	7	heinz	heinz	ADJ
ejpam-5586	571	8	mean	mean	NOUN
ejpam-5586	571	9	inequalities	inequality	NOUN
ejpam-5586	571	10	with	with	ADP
ejpam-5586	571	11	the	the	DET
ejpam-5586	571	12	kantorovich	kantorovich	PROPN
ejpam-5586	571	13	constant	constant	PROPN
ejpam-5586	571	14	.	.	PUNCT
ejpam-5586	572	1	taiwanese	taiwanese	ADJ
ejpam-5586	572	2	journal	journal	NOUN
ejpam-5586	572	3	of	of	ADP
ejpam-5586	572	4	mathematics	mathematic	NOUN
ejpam-5586	572	5	,	,	PUNCT
ejpam-5586	572	6	19(2):467	19(2):467	NUM
ejpam-5586	572	7	–	–	PUNCT
ejpam-5586	572	8	479	479	NUM
ejpam-5586	572	9	,	,	PUNCT
ejpam-5586	572	10	2015	2015	NUM
ejpam-5586	572	11	.	.	PUNCT
ejpam-5586	573	1	[	[	X
ejpam-5586	573	2	13	13	NUM
ejpam-5586	573	3	]	]	X
ejpam-5586	573	4	m.h.m.rashid	m.h.m.rashid	PROPN
ejpam-5586	573	5	.	.	PUNCT
ejpam-5586	573	6	young	young	ADJ
ejpam-5586	573	7	type	type	NOUN
ejpam-5586	573	8	inequalities	inequality	NOUN
ejpam-5586	573	9	and	and	CCONJ
ejpam-5586	573	10	reverses	reverse	VERB
ejpam-5586	573	11	for	for	ADP
ejpam-5586	573	12	matrices	matrix	NOUN
ejpam-5586	573	13	.	.	PUNCT
ejpam-5586	574	1	matematicki	matematicki	NOUN
ejpam-5586	574	2	vesnik	vesnik	NOUN
ejpam-5586	574	3	,	,	PUNCT
ejpam-5586	574	4	74(3):163–173	74(3):163–173	PROPN
ejpam-5586	574	5	,	,	PUNCT
ejpam-5586	574	6	2022	2022	NUM
ejpam-5586	574	7	.	.	PUNCT
ejpam-5586	575	1	[	[	X
ejpam-5586	575	2	14	14	NUM
ejpam-5586	575	3	]	]	X
ejpam-5586	575	4	m.h.m.rashid	m.h.m.rashid	PROPN
ejpam-5586	575	5	and	and	CCONJ
ejpam-5586	575	6	n.	n.	PROPN
ejpam-5586	575	7	snaid	snaid	PROPN
ejpam-5586	575	8	.	.	PUNCT
ejpam-5586	576	1	a	a	DET
ejpam-5586	576	2	new	new	ADJ
ejpam-5586	576	3	generalization	generalization	NOUN
ejpam-5586	576	4	of	of	ADP
ejpam-5586	576	5	young	young	ADJ
ejpam-5586	576	6	type	type	NOUN
ejpam-5586	576	7	inequality	inequality	NOUN
ejpam-5586	576	8	and	and	CCONJ
ejpam-5586	576	9	applications	application	NOUN
ejpam-5586	576	10	.	.	PUNCT
ejpam-5586	577	1	hacettepe	hacettepe	PROPN
ejpam-5586	577	2	journal	journal	PROPN
ejpam-5586	577	3	of	of	ADP
ejpam-5586	577	4	mathematics	mathematics	PROPN
ejpam-5586	577	5	&	&	CCONJ
ejpam-5586	577	6	statistics	statistics	PROPN
ejpam-5586	577	7	,	,	PUNCT
ejpam-5586	577	8	51(5):1371–1378	51(5):1371–1378	NUM
ejpam-5586	577	9	,	,	PUNCT
ejpam-5586	577	10	2022	2022	NUM
ejpam-5586	577	11	.	.	PUNCT
ejpam-5586	578	1	[	[	X
ejpam-5586	578	2	15	15	NUM
ejpam-5586	578	3	]	]	X
ejpam-5586	578	4	leila	leila	PROPN
ejpam-5586	578	5	nasiri	nasiri	ADV
ejpam-5586	578	6	and	and	CCONJ
ejpam-5586	578	7	mahmood	mahmood	PROPN
ejpam-5586	578	8	shakoori	shakoori	PROPN
ejpam-5586	578	9	.	.	PUNCT
ejpam-5586	579	1	a	a	DET
ejpam-5586	579	2	note	note	NOUN
ejpam-5586	579	3	on	on	ADP
ejpam-5586	579	4	improved	improved	ADJ
ejpam-5586	579	5	young	young	ADJ
ejpam-5586	579	6	type	type	NOUN
ejpam-5586	579	7	inequalities	inequality	NOUN
ejpam-5586	579	8	with	with	ADP
ejpam-5586	579	9	kantorovich	kantorovich	PROPN
ejpam-5586	579	10	constant	constant	PROPN
ejpam-5586	579	11	.	.	PUNCT
ejpam-5586	580	1	journal	journal	PROPN
ejpam-5586	580	2	of	of	ADP
ejpam-5586	580	3	mathematics	mathematic	NOUN
ejpam-5586	580	4	and	and	CCONJ
ejpam-5586	580	5	statistics	statistic	NOUN
ejpam-5586	580	6	,	,	PUNCT
ejpam-5586	580	7	12:201–205	12:201–205	NUM
ejpam-5586	580	8	,	,	PUNCT
ejpam-5586	580	9	03	03	NUM
ejpam-5586	580	10	2016	2016	NUM
ejpam-5586	580	11	.	.	PUNCT
ejpam-5586	581	1	[	[	X
ejpam-5586	581	2	16	16	NUM
ejpam-5586	581	3	]	]	X
ejpam-5586	581	4	zlatko	zlatko	PROPN
ejpam-5586	581	5	pavić.	pavić.	PROPN
ejpam-5586	581	6	certain	certain	ADJ
ejpam-5586	581	7	inequalities	inequality	NOUN
ejpam-5586	581	8	for	for	ADP
ejpam-5586	581	9	convex	convex	NOUN
ejpam-5586	581	10	functions	function	NOUN
ejpam-5586	581	11	.	.	PUNCT
ejpam-5586	582	1	journal	journal	NOUN
ejpam-5586	582	2	of	of	ADP
ejpam-5586	582	3	mathematical	mathematical	ADJ
ejpam-5586	582	4	inequalities	inequality	NOUN
ejpam-5586	582	5	,	,	PUNCT
ejpam-5586	582	6	pages	page	NOUN
ejpam-5586	582	7	1349–1364	1349–1364	NUM
ejpam-5586	582	8	,	,	PUNCT
ejpam-5586	582	9	01	01	NUM
ejpam-5586	582	10	2015	2015	NUM
ejpam-5586	582	11	.	.	PUNCT
ejpam-5586	583	1	[	[	X
ejpam-5586	583	2	17	17	NUM
ejpam-5586	583	3	]	]	X
ejpam-5586	583	4	mohammad	mohammad	PROPN
ejpam-5586	583	5	h.	h.	PROPN
ejpam-5586	583	6	m.	m.	PROPN
ejpam-5586	583	7	rashid	rashid	PROPN
ejpam-5586	583	8	and	and	CCONJ
ejpam-5586	583	9	feras	feras	PROPN
ejpam-5586	583	10	bani	bani	PROPN
ejpam-5586	583	11	-	-	PUNCT
ejpam-5586	583	12	ahmad	ahmad	PROPN
ejpam-5586	583	13	.	.	PUNCT
ejpam-5586	584	1	new	new	ADJ
ejpam-5586	584	2	versions	version	NOUN
ejpam-5586	584	3	of	of	ADP
ejpam-5586	584	4	refinements	refinement	NOUN
ejpam-5586	584	5	and	and	CCONJ
ejpam-5586	584	6	reverses	reverse	NOUN
ejpam-5586	584	7	of	of	ADP
ejpam-5586	584	8	young	young	ADJ
ejpam-5586	584	9	-	-	PUNCT
ejpam-5586	584	10	type	type	NOUN
ejpam-5586	584	11	inequalities	inequality	NOUN
ejpam-5586	584	12	with	with	ADP
ejpam-5586	584	13	the	the	DET
ejpam-5586	584	14	kantorovich	kantorovich	PROPN
ejpam-5586	584	15	constant	constant	PROPN
ejpam-5586	584	16	.	.	PUNCT
ejpam-5586	585	1	special	special	ADJ
ejpam-5586	585	2	matrices	matrix	NOUN
ejpam-5586	585	3	,	,	PUNCT
ejpam-5586	585	4	11(1):20220180	11(1):20220180	NUM
ejpam-5586	585	5	,	,	PUNCT
ejpam-5586	585	6	2023	2023	NUM
ejpam-5586	585	7	.	.	PUNCT
ejpam-5586	586	1	[	[	X
ejpam-5586	586	2	18	18	NUM
ejpam-5586	586	3	]	]	PUNCT
ejpam-5586	586	4	a.	a.	NOUN
ejpam-5586	586	5	salemi	salemi	NOUN
ejpam-5586	586	6	and	and	CCONJ
ejpam-5586	586	7	a.	a.	PROPN
ejpam-5586	586	8	sheikh	sheikh	PROPN
ejpam-5586	586	9	hosseini	hosseini	PROPN
ejpam-5586	586	10	.	.	PUNCT
ejpam-5586	587	1	on	on	ADP
ejpam-5586	587	2	reversing	reverse	VERB
ejpam-5586	587	3	of	of	ADP
ejpam-5586	587	4	the	the	DET
ejpam-5586	587	5	modified	modify	VERB
ejpam-5586	587	6	young	young	ADJ
ejpam-5586	587	7	inequality	inequality	NOUN
ejpam-5586	587	8	.	.	PUNCT
ejpam-5586	588	1	annals	annal	NOUN
ejpam-5586	588	2	of	of	ADP
ejpam-5586	588	3	functional	functional	ADJ
ejpam-5586	588	4	analysis	analysis	NOUN
ejpam-5586	588	5	,	,	PUNCT
ejpam-5586	588	6	5(1):70	5(1):70	NUM
ejpam-5586	588	7	–	–	PUNCT
ejpam-5586	588	8	76	76	NUM
ejpam-5586	588	9	,	,	PUNCT
ejpam-5586	588	10	2014	2014	NUM
ejpam-5586	588	11	.	.	PUNCT
ejpam-5586	589	1	[	[	X
ejpam-5586	589	2	19	19	NUM
ejpam-5586	589	3	]	]	X
ejpam-5586	589	4	j.	j.	PROPN
ejpam-5586	589	5	wu	wu	PROPN
ejpam-5586	589	6	and	and	CCONJ
ejpam-5586	589	7	j.	j.	PROPN
ejpam-5586	589	8	zhao	zhao	PROPN
ejpam-5586	589	9	.	.	PUNCT
ejpam-5586	590	1	operator	operator	NOUN
ejpam-5586	590	2	inequalities	inequality	NOUN
ejpam-5586	590	3	and	and	CCONJ
ejpam-5586	590	4	reverse	reverse	ADJ
ejpam-5586	590	5	inequalities	inequality	NOUN
ejpam-5586	590	6	related	relate	VERB
ejpam-5586	590	7	to	to	ADP
ejpam-5586	590	8	the	the	DET
ejpam-5586	590	9	kittaneh	kittaneh	PROPN
ejpam-5586	590	10	–	–	PUNCT
ejpam-5586	590	11	manasrah	manasrah	PROPN
ejpam-5586	590	12	inequalities	inequality	NOUN
ejpam-5586	590	13	.	.	PUNCT
ejpam-5586	591	1	linear	linear	PROPN
ejpam-5586	591	2	and	and	CCONJ
ejpam-5586	591	3	multilinear	multilinear	PROPN
ejpam-5586	591	4	algebra	algebra	NOUN
ejpam-5586	591	5	,	,	PUNCT
ejpam-5586	591	6	62(7):884–894	62(7):884–894	NUM
ejpam-5586	591	7	,	,	PUNCT
ejpam-5586	591	8	2014	2014	NUM
ejpam-5586	591	9	.	.	PUNCT
ejpam-5586	592	1	[	[	X
ejpam-5586	592	2	20	20	NUM
ejpam-5586	592	3	]	]	SYM
ejpam-5586	592	4	changsen	changsen	PROPN
ejpam-5586	592	5	yang	yang	PROPN
ejpam-5586	592	6	and	and	CCONJ
ejpam-5586	592	7	yu	yu	PROPN
ejpam-5586	592	8	li	li	PROPN
ejpam-5586	592	9	.	.	PROPN
ejpam-5586	592	10	refinements	refinement	NOUN
ejpam-5586	592	11	and	and	CCONJ
ejpam-5586	592	12	reverses	reverse	NOUN
ejpam-5586	592	13	of	of	ADP
ejpam-5586	592	14	young	young	ADJ
ejpam-5586	592	15	type	type	NOUN
ejpam-5586	592	16	inequalities	inequality	NOUN
ejpam-5586	592	17	.	.	PUNCT
ejpam-5586	593	1	journal	journal	PROPN
ejpam-5586	593	2	of	of	ADP
ejpam-5586	593	3	mathematical	mathematical	ADJ
ejpam-5586	593	4	inequalities	inequality	NOUN
ejpam-5586	593	5	,	,	PUNCT
ejpam-5586	593	6	pages	page	NOUN
ejpam-5586	593	7	401–419	401–419	NUM
ejpam-5586	593	8	,	,	PUNCT
ejpam-5586	593	9	01	01	NUM
ejpam-5586	593	10	2020	2020	NUM
ejpam-5586	593	11	.	.	PUNCT
ejpam-5586	594	1	[	[	X
ejpam-5586	594	2	21	21	NUM
ejpam-5586	594	3	]	]	PUNCT
ejpam-5586	594	4	x.	x.	NOUN
ejpam-5586	594	5	zhan	zhan	PROPN
ejpam-5586	594	6	.	.	PUNCT
ejpam-5586	594	7	matrix	matrix	NOUN
ejpam-5586	594	8	inequalities	inequality	NOUN
ejpam-5586	594	9	,	,	PUNCT
ejpam-5586	594	10	lecture	lecture	NOUN
ejpam-5586	594	11	notes	note	NOUN
ejpam-5586	594	12	in	in	ADP
ejpam-5586	594	13	mathematics	mathematics	PROPN
ejpam-5586	594	14	1790	1790	NUM
ejpam-5586	594	15	.	.	PUNCT
ejpam-5586	595	1	springer	springer	NOUN
ejpam-5586	595	2	,	,	PUNCT
ejpam-5586	595	3	new	new	PROPN
ejpam-5586	595	4	york	york	PROPN
ejpam-5586	595	5	,	,	PUNCT
ejpam-5586	595	6	2002	2002	NUM
ejpam-5586	595	7	.	.	PUNCT
ejpam-5586	596	1	[	[	X
ejpam-5586	596	2	22	22	NUM
ejpam-5586	596	3	]	]	X
ejpam-5586	596	4	jie	jie	PROPN
ejpam-5586	596	5	zhang	zhang	PROPN
ejpam-5586	596	6	and	and	CCONJ
ejpam-5586	596	7	junliang	junliang	PROPN
ejpam-5586	596	8	wu	wu	PROPN
ejpam-5586	596	9	.	.	PUNCT
ejpam-5586	597	1	new	new	ADJ
ejpam-5586	597	2	progress	progress	NOUN
ejpam-5586	597	3	on	on	ADP
ejpam-5586	597	4	the	the	DET
ejpam-5586	597	5	operator	operator	NOUN
ejpam-5586	597	6	inequalities	inequality	NOUN
ejpam-5586	597	7	involving	involve	VERB
ejpam-5586	597	8	improved	improved	ADJ
ejpam-5586	597	9	young	young	ADJ
ejpam-5586	597	10	’s	’s	PART
ejpam-5586	597	11	and	and	CCONJ
ejpam-5586	597	12	its	its	PRON
ejpam-5586	597	13	reverse	reverse	ADJ
ejpam-5586	597	14	inequalities	inequality	NOUN
ejpam-5586	597	15	relating	relate	VERB
ejpam-5586	597	16	to	to	ADP
ejpam-5586	597	17	the	the	DET
ejpam-5586	597	18	kantorovich	kantorovich	PROPN
ejpam-5586	597	19	constant	constant	PROPN
ejpam-5586	597	20	.	.	PUNCT
ejpam-5586	598	1	journal	journal	PROPN
ejpam-5586	598	2	of	of	ADP
ejpam-5586	598	3	inequalities	inequality	NOUN
ejpam-5586	598	4	and	and	CCONJ
ejpam-5586	598	5	applications	application	NOUN
ejpam-5586	598	6	,	,	PUNCT
ejpam-5586	598	7	2017	2017	NUM
ejpam-5586	598	8	,	,	PUNCT
ejpam-5586	598	9	04	04	NUM
ejpam-5586	598	10	2017	2017	NUM
ejpam-5586	598	11	.	.	PUNCT
ejpam-5586	599	1	[	[	X
ejpam-5586	599	2	23	23	NUM
ejpam-5586	599	3	]	]	PUNCT
ejpam-5586	599	4	jianguo	jianguo	PROPN
ejpam-5586	599	5	zhao	zhao	PROPN
ejpam-5586	599	6	and	and	CCONJ
ejpam-5586	599	7	junliang	junliang	PROPN
ejpam-5586	599	8	wu	wu	PROPN
ejpam-5586	599	9	.	.	PUNCT
ejpam-5586	600	1	operator	operator	NOUN
ejpam-5586	600	2	inequalities	inequality	NOUN
ejpam-5586	600	3	involving	involve	VERB
ejpam-5586	600	4	improved	improve	VERB
ejpam-5586	600	5	young	young	ADJ
ejpam-5586	600	6	m.h.m	m.h.m	NOUN
ejpam-5586	600	7	rashid	rashid	NOUN
ejpam-5586	600	8	,	,	PUNCT
ejpam-5586	600	9	w.m.m	w.m.m	NOUN
ejpam-5586	600	10	.	.	PUNCT
ejpam-5586	601	1	salameh	salameh	PROPN
ejpam-5586	601	2	/	/	SYM
ejpam-5586	601	3	eur	eur	PROPN
ejpam-5586	601	4	.	.	PUNCT
ejpam-5586	602	1	j.	j.	PROPN
ejpam-5586	602	2	pure	pure	PROPN
ejpam-5586	602	3	appl	appl	PROPN
ejpam-5586	602	4	.	.	PROPN
ejpam-5586	602	5	math	math	PROPN
ejpam-5586	602	6	,	,	PUNCT
ejpam-5586	602	7	18	18	NUM
ejpam-5586	602	8	(	(	PUNCT
ejpam-5586	602	9	1	1	NUM
ejpam-5586	602	10	)	)	PUNCT
ejpam-5586	602	11	(	(	PUNCT
ejpam-5586	602	12	2025	2025	NUM
ejpam-5586	602	13	)	)	PUNCT
ejpam-5586	602	14	,	,	PUNCT
ejpam-5586	602	15	5586	5586	NUM
ejpam-5586	602	16	21	21	NUM
ejpam-5586	602	17	of	of	ADP
ejpam-5586	602	18	21	21	NUM
ejpam-5586	602	19	and	and	CCONJ
ejpam-5586	602	20	its	its	PRON
ejpam-5586	602	21	reverse	reverse	ADJ
ejpam-5586	602	22	inequalities	inequality	NOUN
ejpam-5586	602	23	.	.	PUNCT
ejpam-5586	603	1	journal	journal	PROPN
ejpam-5586	603	2	of	of	ADP
ejpam-5586	603	3	mathematical	mathematical	ADJ
ejpam-5586	603	4	analysis	analysis	NOUN
ejpam-5586	603	5	and	and	CCONJ
ejpam-5586	603	6	applications	application	NOUN
ejpam-5586	603	7	,	,	PUNCT
ejpam-5586	603	8	421(2):1779–1789	421(2):1779–1789	NOUN
ejpam-5586	603	9	,	,	PUNCT
ejpam-5586	603	10	2015	2015	NUM
ejpam-5586	603	11	.	.	PUNCT