id	sid	tid	token	lemma	pos
ejpam-5757	1	1	european	european	PROPN
ejpam-5757	1	2	journal	journal	PROPN
ejpam-5757	1	3	of	of	ADP
ejpam-5757	1	4	pure	pure	ADJ
ejpam-5757	1	5	and	and	CCONJ
ejpam-5757	1	6	applied	applied	ADJ
ejpam-5757	1	7	mathematics	mathematic	NOUN
ejpam-5757	1	8	2025	2025	NUM
ejpam-5757	1	9	,	,	PUNCT
ejpam-5757	1	10	vol	vol	NOUN
ejpam-5757	1	11	.	.	PROPN
ejpam-5757	1	12	18	18	NUM
ejpam-5757	1	13	,	,	PUNCT
ejpam-5757	1	14	issue	issue	NOUN
ejpam-5757	1	15	1	1	NUM
ejpam-5757	1	16	,	,	PUNCT
ejpam-5757	1	17	article	article	NOUN
ejpam-5757	1	18	number	number	NOUN
ejpam-5757	1	19	5757	5757	NUM
ejpam-5757	1	20	issn	issn	VERB
ejpam-5757	1	21	1307	1307	NUM
ejpam-5757	1	22	-	-	SYM
ejpam-5757	1	23	5543	5543	NUM
ejpam-5757	1	24	–	–	PUNCT
ejpam-5757	1	25	ejpam.com	ejpam.com	X
ejpam-5757	1	26	published	publish	VERB
ejpam-5757	1	27	by	by	ADP
ejpam-5757	1	28	new	new	PROPN
ejpam-5757	1	29	york	york	PROPN
ejpam-5757	1	30	business	business	PROPN
ejpam-5757	1	31	global	global	ADJ
ejpam-5757	1	32	hyperstability	hyperstability	NOUN
ejpam-5757	1	33	of	of	ADP
ejpam-5757	1	34	functional	functional	ADJ
ejpam-5757	1	35	equation	equation	NOUN
ejpam-5757	1	36	deriving	derive	VERB
ejpam-5757	1	37	from	from	ADP
ejpam-5757	1	38	quintic	quintic	ADJ
ejpam-5757	1	39	mapping	mapping	NOUN
ejpam-5757	1	40	in	in	ADP
ejpam-5757	1	41	banach	banach	NOUN
ejpam-5757	1	42	spaces	space	NOUN
ejpam-5757	1	43	by	by	ADP
ejpam-5757	1	44	fixed	fix	VERB
ejpam-5757	1	45	point	point	NOUN
ejpam-5757	1	46	method	method	NOUN
ejpam-5757	1	47	subramani	subramani	ADJ
ejpam-5757	1	48	karthikeyan1	karthikeyan1	PROPN
ejpam-5757	1	49	,	,	PUNCT
ejpam-5757	1	50	siriluk	siriluk	PROPN
ejpam-5757	1	51	donganont2,∗	donganont2,∗	PROPN
ejpam-5757	1	52	,	,	PUNCT
ejpam-5757	1	53	choonkil	choonkil	PROPN
ejpam-5757	1	54	park3	park3	PROPN
ejpam-5757	1	55	,	,	PUNCT
ejpam-5757	1	56	kandhasamy	kandhasamy	ADJ
ejpam-5757	1	57	tamilvanan1	tamilvanan1	NOUN
ejpam-5757	1	58	,	,	PUNCT
ejpam-5757	1	59	yongqiao	yongqiao	NOUN
ejpam-5757	1	60	wang4	wang4	PROPN
ejpam-5757	1	61	1	1	NUM
ejpam-5757	1	62	department	department	NOUN
ejpam-5757	1	63	of	of	ADP
ejpam-5757	1	64	mathematics	mathematic	NOUN
ejpam-5757	1	65	,	,	PUNCT
ejpam-5757	1	66	faculty	faculty	NOUN
ejpam-5757	1	67	of	of	ADP
ejpam-5757	1	68	science	science	PROPN
ejpam-5757	1	69	&	&	CCONJ
ejpam-5757	1	70	humanities	humanities	PROPN
ejpam-5757	1	71	,	,	PUNCT
ejpam-5757	1	72	r.m.k	r.m.k	NOUN
ejpam-5757	1	73	.	.	PUNCT
ejpam-5757	2	1	engineering	engineering	PROPN
ejpam-5757	2	2	college	college	PROPN
ejpam-5757	2	3	,	,	PUNCT
ejpam-5757	2	4	kavaraipettai	kavaraipettai	PROPN
ejpam-5757	2	5	,	,	PUNCT
ejpam-5757	2	6	tiruvallur	tiruvallur	VERB
ejpam-5757	2	7	601	601	NUM
ejpam-5757	2	8	206	206	NUM
ejpam-5757	2	9	,	,	PUNCT
ejpam-5757	2	10	tamil	tamil	PROPN
ejpam-5757	2	11	nadu	nadu	PROPN
ejpam-5757	2	12	,	,	PUNCT
ejpam-5757	2	13	india	india	PROPN
ejpam-5757	2	14	2	2	NUM
ejpam-5757	2	15	school	school	NOUN
ejpam-5757	2	16	of	of	ADP
ejpam-5757	2	17	science	science	NOUN
ejpam-5757	2	18	,	,	PUNCT
ejpam-5757	2	19	university	university	NOUN
ejpam-5757	2	20	of	of	ADP
ejpam-5757	2	21	phayao	phayao	NOUN
ejpam-5757	2	22	,	,	PUNCT
ejpam-5757	2	23	phayao	phayao	NOUN
ejpam-5757	2	24	56000	56000	NUM
ejpam-5757	2	25	,	,	PUNCT
ejpam-5757	2	26	thailand	thailand	PROPN
ejpam-5757	2	27	3	3	NUM
ejpam-5757	2	28	department	department	NOUN
ejpam-5757	2	29	of	of	ADP
ejpam-5757	2	30	mathematics	mathematic	NOUN
ejpam-5757	2	31	,	,	PUNCT
ejpam-5757	2	32	research	research	NOUN
ejpam-5757	2	33	institute	institute	NOUN
ejpam-5757	2	34	for	for	ADP
ejpam-5757	2	35	convergence	convergence	NOUN
ejpam-5757	2	36	of	of	ADP
ejpam-5757	2	37	basic	basic	ADJ
ejpam-5757	2	38	science	science	NOUN
ejpam-5757	2	39	,	,	PUNCT
ejpam-5757	2	40	hanyang	hanyang	NOUN
ejpam-5757	2	41	university	university	PROPN
ejpam-5757	2	42	,	,	PUNCT
ejpam-5757	2	43	seoul	seoul	PROPN
ejpam-5757	2	44	04763	04763	NUM
ejpam-5757	2	45	,	,	PUNCT
ejpam-5757	2	46	korea	korea	PROPN
ejpam-5757	2	47	4	4	NUM
ejpam-5757	2	48	school	school	NOUN
ejpam-5757	2	49	of	of	ADP
ejpam-5757	2	50	science	science	NOUN
ejpam-5757	2	51	,	,	PUNCT
ejpam-5757	2	52	dalian	dalian	PROPN
ejpam-5757	2	53	maritime	maritime	PROPN
ejpam-5757	2	54	university	university	PROPN
ejpam-5757	2	55	,	,	PUNCT
ejpam-5757	2	56	dalian	dalian	PROPN
ejpam-5757	2	57	116026	116026	NUM
ejpam-5757	2	58	,	,	PUNCT
ejpam-5757	3	1	p.	p.	PROPN
ejpam-5757	3	2	r.	r.	PROPN
ejpam-5757	3	3	china	china	PROPN
ejpam-5757	3	4	abstract	abstract	PROPN
ejpam-5757	3	5	.	.	PUNCT
ejpam-5757	4	1	in	in	ADP
ejpam-5757	4	2	this	this	DET
ejpam-5757	4	3	work	work	NOUN
ejpam-5757	4	4	,	,	PUNCT
ejpam-5757	4	5	we	we	PRON
ejpam-5757	4	6	examine	examine	VERB
ejpam-5757	4	7	the	the	DET
ejpam-5757	4	8	hyperstability	hyperstability	NOUN
ejpam-5757	4	9	of	of	ADP
ejpam-5757	4	10	the	the	DET
ejpam-5757	4	11	quintic	quintic	ADJ
ejpam-5757	4	12	functional	functional	ADJ
ejpam-5757	4	13	equation	equation	NOUN
ejpam-5757	4	14	ϕ(u	ϕ(u	NOUN
ejpam-5757	5	1	+	+	CCONJ
ejpam-5757	6	1	3v)−	3v)−	NUM
ejpam-5757	6	2	5ϕ(u+	5ϕ(u+	NUM
ejpam-5757	6	3	2v)−	2v)−	NUM
ejpam-5757	6	4	ϕ(u−	ϕ(u−	NUM
ejpam-5757	6	5	2v	2v	NUM
ejpam-5757	6	6	)	)	PUNCT
ejpam-5757	7	1	+	+	CCONJ
ejpam-5757	7	2	10ϕ(u+	10ϕ(u+	NUM
ejpam-5757	7	3	v	v	NOUN
ejpam-5757	7	4	)	)	PUNCT
ejpam-5757	8	1	+	+	CCONJ
ejpam-5757	8	2	5ϕ(u−	5ϕ(u−	NUM
ejpam-5757	8	3	v)−	v)−	PROPN
ejpam-5757	8	4	10ϕ(u)−	10ϕ(u)−	NUM
ejpam-5757	8	5	120ϕ(v	120ϕ(v	NOUN
ejpam-5757	8	6	)	)	PUNCT
ejpam-5757	8	7	=	=	SYM
ejpam-5757	8	8	0	0	NUM
ejpam-5757	8	9	,	,	PUNCT
ejpam-5757	8	10	in	in	ADP
ejpam-5757	8	11	banach	banach	NOUN
ejpam-5757	8	12	spaces	space	NOUN
ejpam-5757	8	13	by	by	ADP
ejpam-5757	8	14	means	mean	NOUN
ejpam-5757	8	15	of	of	ADP
ejpam-5757	8	16	brzdȩk	brzdȩk	NOUN
ejpam-5757	8	17	’s	’s	PART
ejpam-5757	8	18	fixed	fix	VERB
ejpam-5757	8	19	point	point	NOUN
ejpam-5757	8	20	theorem	theorem	VERB
ejpam-5757	8	21	.	.	PROPN
ejpam-5757	8	22	2020	2020	NUM
ejpam-5757	8	23	mathematics	mathematics	PROPN
ejpam-5757	8	24	subject	subject	NOUN
ejpam-5757	8	25	classifications	classification	NOUN
ejpam-5757	8	26	:	:	PUNCT
ejpam-5757	8	27	39b52	39b52	NUM
ejpam-5757	8	28	,	,	PUNCT
ejpam-5757	8	29	39b72	39b72	NUM
ejpam-5757	8	30	,	,	PUNCT
ejpam-5757	8	31	39b82	39b82	NUM
ejpam-5757	8	32	,	,	PUNCT
ejpam-5757	8	33	47h10	47h10	PRON
ejpam-5757	8	34	key	key	ADJ
ejpam-5757	8	35	words	word	NOUN
ejpam-5757	8	36	and	and	CCONJ
ejpam-5757	8	37	phrases	phrase	NOUN
ejpam-5757	8	38	:	:	PUNCT
ejpam-5757	8	39	quintic	quintic	ADJ
ejpam-5757	8	40	functional	functional	ADJ
ejpam-5757	8	41	equation	equation	NOUN
ejpam-5757	8	42	,	,	PUNCT
ejpam-5757	8	43	hyperstability	hyperstability	NOUN
ejpam-5757	8	44	,	,	PUNCT
ejpam-5757	8	45	fixed	fix	VERB
ejpam-5757	8	46	point	point	NOUN
ejpam-5757	8	47	,	,	PUNCT
ejpam-5757	8	48	stability	stability	NOUN
ejpam-5757	8	49	1	1	NUM
ejpam-5757	8	50	.	.	PUNCT
ejpam-5757	9	1	introduction	introduction	NOUN
ejpam-5757	9	2	and	and	CCONJ
ejpam-5757	9	3	preliminaries	preliminary	NOUN
ejpam-5757	9	4	one	one	NUM
ejpam-5757	9	5	of	of	ADP
ejpam-5757	9	6	the	the	DET
ejpam-5757	9	7	most	most	ADV
ejpam-5757	9	8	important	important	ADJ
ejpam-5757	9	9	areas	area	NOUN
ejpam-5757	9	10	of	of	ADP
ejpam-5757	9	11	mathematical	mathematical	ADJ
ejpam-5757	9	12	research	research	NOUN
ejpam-5757	9	13	,	,	PUNCT
ejpam-5757	9	14	which	which	PRON
ejpam-5757	9	15	has	have	VERB
ejpam-5757	9	16	its	its	PRON
ejpam-5757	9	17	origins	origin	NOUN
ejpam-5757	9	18	in	in	ADP
ejpam-5757	9	19	problems	problem	NOUN
ejpam-5757	9	20	relating	relate	VERB
ejpam-5757	9	21	to	to	ADP
ejpam-5757	9	22	applied	apply	VERB
ejpam-5757	9	23	mathematics	mathematic	NOUN
ejpam-5757	9	24	,	,	PUNCT
ejpam-5757	9	25	is	be	AUX
ejpam-5757	9	26	the	the	DET
ejpam-5757	9	27	investigation	investigation	NOUN
ejpam-5757	9	28	of	of	ADP
ejpam-5757	9	29	stability	stability	NOUN
ejpam-5757	9	30	issues	issue	NOUN
ejpam-5757	9	31	for	for	ADP
ejpam-5757	9	32	functional	functional	ADJ
ejpam-5757	9	33	equations	equation	NOUN
ejpam-5757	9	34	.	.	PUNCT
ejpam-5757	10	1	ulam	ulam	PROPN
ejpam-5757	11	1	[	[	X
ejpam-5757	11	2	28	28	NUM
ejpam-5757	11	3	]	]	PUNCT
ejpam-5757	11	4	stated	state	VERB
ejpam-5757	11	5	the	the	DET
ejpam-5757	11	6	following	following	NOUN
ejpam-5757	11	7	as	as	ADP
ejpam-5757	11	8	the	the	DET
ejpam-5757	11	9	first	first	ADJ
ejpam-5757	11	10	query	query	NOUN
ejpam-5757	11	11	pertaining	pertain	VERB
ejpam-5757	11	12	to	to	ADP
ejpam-5757	11	13	the	the	DET
ejpam-5757	11	14	stability	stability	NOUN
ejpam-5757	11	15	of	of	ADP
ejpam-5757	11	16	homomorphisms	homomorphism	NOUN
ejpam-5757	11	17	.	.	PUNCT
ejpam-5757	12	1	let	let	VERB
ejpam-5757	12	2	u	u	PRON
ejpam-5757	12	3	be	be	AUX
ejpam-5757	12	4	a	a	DET
ejpam-5757	12	5	group	group	NOUN
ejpam-5757	12	6	and	and	CCONJ
ejpam-5757	12	7	v	v	AUX
ejpam-5757	12	8	be	be	AUX
ejpam-5757	12	9	a	a	DET
ejpam-5757	12	10	metric	metric	ADJ
ejpam-5757	12	11	group	group	NOUN
ejpam-5757	12	12	with	with	ADP
ejpam-5757	12	13	a	a	DET
ejpam-5757	12	14	metric	metric	ADJ
ejpam-5757	12	15	d	d	NOUN
ejpam-5757	12	16	(	(	PUNCT
ejpam-5757	12	17	·	·	PUNCT
ejpam-5757	12	18	,	,	PUNCT
ejpam-5757	12	19	·	·	PUNCT
ejpam-5757	12	20	)	)	PUNCT
ejpam-5757	12	21	.	.	PUNCT
ejpam-5757	13	1	given	give	VERB
ejpam-5757	13	2	ϵ	ϵ	ADP
ejpam-5757	13	3	>	>	X
ejpam-5757	13	4	0	0	NUM
ejpam-5757	13	5	,	,	PUNCT
ejpam-5757	13	6	is	be	AUX
ejpam-5757	13	7	there	there	PRON
ejpam-5757	13	8	a	a	DET
ejpam-5757	13	9	δ	δ	NOUN
ejpam-5757	13	10	>	>	X
ejpam-5757	13	11	0	0	NUM
ejpam-5757	14	1	such	such	ADJ
ejpam-5757	14	2	that	that	SCONJ
ejpam-5757	14	3	if	if	SCONJ
ejpam-5757	14	4	a	a	DET
ejpam-5757	14	5	function	function	NOUN
ejpam-5757	14	6	ϕ	ϕ	NOUN
ejpam-5757	14	7	:	:	PUNCT
ejpam-5757	14	8	u	u	X
ejpam-5757	14	9	→	→	SYM
ejpam-5757	14	10	v	v	NUM
ejpam-5757	14	11	fulfills	fulfills	PROPN
ejpam-5757	14	12	d(ϕ(uv	d(ϕ(uv	NOUN
ejpam-5757	14	13	)	)	PUNCT
ejpam-5757	14	14	,	,	PUNCT
ejpam-5757	14	15	ϕ(u)ϕ(v	ϕ(u)ϕ(v	NOUN
ejpam-5757	14	16	)	)	PUNCT
ejpam-5757	14	17	)	)	PUNCT
ejpam-5757	15	1	<	<	X
ejpam-5757	15	2	δ	δ	PROPN
ejpam-5757	15	3	,	,	PUNCT
ejpam-5757	15	4	for	for	ADP
ejpam-5757	15	5	all	all	DET
ejpam-5757	15	6	u	u	NOUN
ejpam-5757	15	7	,	,	PUNCT
ejpam-5757	15	8	v	v	PROPN
ejpam-5757	15	9	∈	∈	PROPN
ejpam-5757	15	10	u	u	NOUN
ejpam-5757	15	11	,	,	PUNCT
ejpam-5757	15	12	then	then	ADV
ejpam-5757	15	13	there	there	PRON
ejpam-5757	15	14	is	be	VERB
ejpam-5757	15	15	a	a	DET
ejpam-5757	15	16	homomorphism	homomorphism	NOUN
ejpam-5757	15	17	φ	φ	X
ejpam-5757	15	18	:	:	PUNCT
ejpam-5757	15	19	u	u	NOUN
ejpam-5757	15	20	→	→	SYM
ejpam-5757	15	21	v	v	NOUN
ejpam-5757	15	22	with	with	ADP
ejpam-5757	15	23	d	d	PROPN
ejpam-5757	15	24	(	(	PUNCT
ejpam-5757	15	25	ϕ(u),φ(u	ϕ(u),φ(u	PROPN
ejpam-5757	15	26	)	)	PUNCT
ejpam-5757	15	27	)	)	PUNCT
ejpam-5757	15	28	<	<	X
ejpam-5757	15	29	ϵ	ϵ	X
ejpam-5757	15	30	,	,	PUNCT
ejpam-5757	15	31	∗corresponding	∗corresponde	VERB
ejpam-5757	15	32	author	author	NOUN
ejpam-5757	15	33	.	.	PUNCT
ejpam-5757	16	1	doi	doi	PROPN
ejpam-5757	16	2	:	:	PUNCT
ejpam-5757	16	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5757	https://doi.org/10.29020/nybg.ejpam.v18i1.5757	VERB
ejpam-5757	16	4	email	email	NOUN
ejpam-5757	16	5	addresses	address	NOUN
ejpam-5757	16	6	:	:	PUNCT
ejpam-5757	16	7	karthik.sma204@yahoo.com	karthik.sma204@yahoo.com	PROPN
ejpam-5757	16	8	(	(	PUNCT
ejpam-5757	16	9	s.	s.	PROPN
ejpam-5757	16	10	karthikeyan	karthikeyan	PROPN
ejpam-5757	16	11	)	)	PUNCT
ejpam-5757	16	12	,	,	PUNCT
ejpam-5757	16	13	siriluk.pa@up.ac.th	siriluk.pa@up.ac.th	PROPN
ejpam-5757	16	14	(	(	PUNCT
ejpam-5757	16	15	s.	s.	PROPN
ejpam-5757	16	16	donganont	donganont	PROPN
ejpam-5757	16	17	)	)	PUNCT
ejpam-5757	16	18	,	,	PUNCT
ejpam-5757	16	19	baak@hanyang.ac.kr	baak@hanyang.ac.kr	PROPN
ejpam-5757	16	20	(	(	PUNCT
ejpam-5757	16	21	c.	c.	PROPN
ejpam-5757	16	22	park	park	PROPN
ejpam-5757	16	23	)	)	PUNCT
ejpam-5757	16	24	,	,	PUNCT
ejpam-5757	16	25	tamiltamilk7@gmail.com	tamiltamilk7@gmail.com	X
ejpam-5757	16	26	(	(	PUNCT
ejpam-5757	16	27	k.	k.	PROPN
ejpam-5757	16	28	tamilvanan	tamilvanan	PROPN
ejpam-5757	16	29	)	)	PUNCT
ejpam-5757	16	30	,	,	PUNCT
ejpam-5757	16	31	wangyq@dimu.edu.cn	wangyq@dimu.edu.cn	NOUN
ejpam-5757	16	32	(	(	PUNCT
ejpam-5757	16	33	y.	y.	PROPN
ejpam-5757	16	34	wang	wang	PROPN
ejpam-5757	16	35	)	)	PUNCT
ejpam-5757	16	36	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5757	17	1	1	1	NUM
ejpam-5757	17	2	copyright	copyright	NOUN
ejpam-5757	17	3	:	:	PUNCT
ejpam-5757	17	4	©	©	PROPN
ejpam-5757	17	5	2025	2025	NUM
ejpam-5757	17	6	the	the	DET
ejpam-5757	17	7	author(s	author(s	NOUN
ejpam-5757	17	8	)	)	PUNCT
ejpam-5757	17	9	.	.	PUNCT
ejpam-5757	18	1	(	(	PUNCT
ejpam-5757	18	2	cc	cc	NOUN
ejpam-5757	18	3	by	by	ADP
ejpam-5757	18	4	-	-	PUNCT
ejpam-5757	18	5	nc	nc	PROPN
ejpam-5757	18	6	4.0	4.0	NUM
ejpam-5757	18	7	)	)	PUNCT
ejpam-5757	18	8	s.	s.	PROPN
ejpam-5757	18	9	karthikeyan	karthikeyan	PROPN
ejpam-5757	18	10	et	et	PROPN
ejpam-5757	18	11	al	al	PROPN
ejpam-5757	18	12	.	.	PUNCT
ejpam-5757	18	13	/	/	SYM
ejpam-5757	18	14	eur	eur	PROPN
ejpam-5757	18	15	.	.	PUNCT
ejpam-5757	19	1	j.	j.	PROPN
ejpam-5757	19	2	pure	pure	PROPN
ejpam-5757	19	3	appl	appl	PROPN
ejpam-5757	19	4	.	.	PROPN
ejpam-5757	19	5	math	math	PROPN
ejpam-5757	19	6	,	,	PUNCT
ejpam-5757	19	7	18	18	NUM
ejpam-5757	19	8	(	(	PUNCT
ejpam-5757	19	9	1	1	NUM
ejpam-5757	19	10	)	)	PUNCT
ejpam-5757	19	11	(	(	PUNCT
ejpam-5757	19	12	2025	2025	NUM
ejpam-5757	19	13	)	)	PUNCT
ejpam-5757	19	14	,	,	PUNCT
ejpam-5757	19	15	5757	5757	NUM
ejpam-5757	19	16	2	2	NUM
ejpam-5757	19	17	of	of	ADP
ejpam-5757	19	18	18	18	NUM
ejpam-5757	19	19	for	for	ADP
ejpam-5757	19	20	all	all	DET
ejpam-5757	19	21	u	u	PROPN
ejpam-5757	19	22	∈	∈	PROPN
ejpam-5757	19	23	u	u	NOUN
ejpam-5757	19	24	?	?	PUNCT
ejpam-5757	20	1	hyers	hyer	NOUN
ejpam-5757	20	2	provided	provide	VERB
ejpam-5757	20	3	the	the	DET
ejpam-5757	20	4	first	first	ADJ
ejpam-5757	20	5	partial	partial	ADJ
ejpam-5757	20	6	answer	answer	NOUN
ejpam-5757	20	7	to	to	ADP
ejpam-5757	20	8	ulam	ulam	PROPN
ejpam-5757	20	9	’s	’s	PART
ejpam-5757	20	10	concern	concern	NOUN
ejpam-5757	20	11	regarding	regard	VERB
ejpam-5757	20	12	the	the	DET
ejpam-5757	20	13	cauchy	cauchy	ADJ
ejpam-5757	20	14	equation	equation	NOUN
ejpam-5757	20	15	in	in	ADP
ejpam-5757	20	16	banach	banach	NOUN
ejpam-5757	20	17	spaces	space	NOUN
ejpam-5757	20	18	in	in	ADP
ejpam-5757	20	19	[	[	X
ejpam-5757	20	20	19	19	NUM
ejpam-5757	20	21	]	]	PUNCT
ejpam-5757	20	22	.	.	PUNCT
ejpam-5757	21	1	later	later	ADV
ejpam-5757	21	2	,	,	PUNCT
ejpam-5757	21	3	aoki	aoki	PROPN
ejpam-5757	21	4	was	be	AUX
ejpam-5757	21	5	the	the	DET
ejpam-5757	21	6	first	first	ADJ
ejpam-5757	21	7	to	to	PART
ejpam-5757	21	8	generalize	generalize	VERB
ejpam-5757	21	9	hyers	hyer	NOUN
ejpam-5757	21	10	’	’	PART
ejpam-5757	21	11	findings	finding	NOUN
ejpam-5757	21	12	and	and	CCONJ
ejpam-5757	21	13	not	not	PART
ejpam-5757	21	14	until	until	ADP
ejpam-5757	21	15	much	much	ADV
ejpam-5757	21	16	later	later	ADV
ejpam-5757	21	17	by	by	ADP
ejpam-5757	21	18	rassias	rassias	PROPN
ejpam-5757	21	19	[	[	X
ejpam-5757	21	20	24	24	NUM
ejpam-5757	21	21	]	]	PUNCT
ejpam-5757	21	22	and	and	CCONJ
ejpam-5757	21	23	găvruţa	găvruţa	X
ejpam-5757	21	24	[	[	X
ejpam-5757	21	25	18	18	NUM
ejpam-5757	21	26	]	]	PUNCT
ejpam-5757	21	27	.	.	PUNCT
ejpam-5757	22	1	since	since	SCONJ
ejpam-5757	22	2	then	then	ADV
ejpam-5757	22	3	,	,	PUNCT
ejpam-5757	22	4	several	several	ADJ
ejpam-5757	22	5	functional	functional	ADJ
ejpam-5757	22	6	equations	equation	NOUN
ejpam-5757	22	7	’	'	PUNCT
ejpam-5757	22	8	stability	stability	NOUN
ejpam-5757	22	9	issues	issue	NOUN
ejpam-5757	22	10	have	have	AUX
ejpam-5757	22	11	been	be	AUX
ejpam-5757	22	12	thoroughly	thoroughly	ADV
ejpam-5757	22	13	researched	research	VERB
ejpam-5757	22	14	(	(	PUNCT
ejpam-5757	22	15	see	see	VERB
ejpam-5757	22	16	[	[	X
ejpam-5757	22	17	7	7	NUM
ejpam-5757	22	18	,	,	PUNCT
ejpam-5757	22	19	8	8	NUM
ejpam-5757	22	20	,	,	PUNCT
ejpam-5757	22	21	20	20	NUM
ejpam-5757	22	22	,	,	PUNCT
ejpam-5757	22	23	25	25	NUM
ejpam-5757	22	24	]	]	PUNCT
ejpam-5757	22	25	)	)	PUNCT
ejpam-5757	22	26	.	.	PUNCT
ejpam-5757	23	1	if	if	SCONJ
ejpam-5757	23	2	any	any	DET
ejpam-5757	23	3	function	function	NOUN
ejpam-5757	23	4	f	f	PROPN
ejpam-5757	23	5	approximates	approximate	VERB
ejpam-5757	23	6	(	(	PUNCT
ejpam-5757	23	7	in	in	ADP
ejpam-5757	23	8	some	some	DET
ejpam-5757	23	9	sense	sense	NOUN
ejpam-5757	23	10	)	)	PUNCT
ejpam-5757	23	11	the	the	DET
ejpam-5757	23	12	solution	solution	NOUN
ejpam-5757	23	13	to	to	ADP
ejpam-5757	23	14	the	the	DET
ejpam-5757	23	15	functional	functional	ADJ
ejpam-5757	23	16	equation	equation	NOUN
ejpam-5757	23	17	,	,	PUNCT
ejpam-5757	23	18	then	then	ADV
ejpam-5757	23	19	the	the	DET
ejpam-5757	23	20	functional	functional	ADJ
ejpam-5757	23	21	equation	equation	NOUN
ejpam-5757	23	22	is	be	AUX
ejpam-5757	23	23	said	say	VERB
ejpam-5757	23	24	to	to	PART
ejpam-5757	23	25	be	be	AUX
ejpam-5757	23	26	hyperstable	hyperstable	ADJ
ejpam-5757	23	27	.	.	PUNCT
ejpam-5757	24	1	it	it	PRON
ejpam-5757	24	2	appears	appear	VERB
ejpam-5757	24	3	that	that	SCONJ
ejpam-5757	24	4	the	the	DET
ejpam-5757	24	5	first	first	ADJ
ejpam-5757	24	6	hyperstability	hyperstability	NOUN
ejpam-5757	24	7	finding	finding	NOUN
ejpam-5757	24	8	,	,	PUNCT
ejpam-5757	24	9	which	which	PRON
ejpam-5757	24	10	dealt	deal	VERB
ejpam-5757	24	11	with	with	ADP
ejpam-5757	24	12	ring	ring	NOUN
ejpam-5757	24	13	homomorphisms	homomorphism	NOUN
ejpam-5757	24	14	,	,	PUNCT
ejpam-5757	24	15	was	be	AUX
ejpam-5757	24	16	published	publish	VERB
ejpam-5757	24	17	in	in	ADP
ejpam-5757	24	18	[	[	X
ejpam-5757	24	19	6	6	NUM
ejpam-5757	24	20	]	]	PUNCT
ejpam-5757	24	21	.	.	PUNCT
ejpam-5757	25	1	hyperstability	hyperstability	NOUN
ejpam-5757	25	2	,	,	PUNCT
ejpam-5757	25	3	however	however	ADV
ejpam-5757	25	4	,	,	PUNCT
ejpam-5757	25	5	is	be	AUX
ejpam-5757	25	6	mentioned	mention	VERB
ejpam-5757	25	7	for	for	ADP
ejpam-5757	25	8	the	the	DET
ejpam-5757	25	9	first	first	ADJ
ejpam-5757	25	10	time	time	NOUN
ejpam-5757	25	11	in	in	ADP
ejpam-5757	25	12	[	[	X
ejpam-5757	25	13	21	21	NUM
ejpam-5757	25	14	]	]	PUNCT
ejpam-5757	25	15	.	.	PUNCT
ejpam-5757	26	1	brzdȩk	brzdȩk	PROPN
ejpam-5757	26	2	investigated	investigate	VERB
ejpam-5757	26	3	the	the	DET
ejpam-5757	26	4	hyperstability	hyperstability	NOUN
ejpam-5757	26	5	results	result	NOUN
ejpam-5757	26	6	for	for	ADP
ejpam-5757	26	7	the	the	DET
ejpam-5757	26	8	cauchy	cauchy	ADJ
ejpam-5757	26	9	equation	equation	NOUN
ejpam-5757	26	10	(	(	PUNCT
ejpam-5757	26	11	see	see	VERB
ejpam-5757	26	12	[	[	X
ejpam-5757	26	13	9–11	9–11	X
ejpam-5757	26	14	]	]	X
ejpam-5757	26	15	)	)	PUNCT
ejpam-5757	26	16	.	.	PUNCT
ejpam-5757	27	1	the	the	DET
ejpam-5757	27	2	hyperstability	hyperstability	NOUN
ejpam-5757	27	3	of	of	ADP
ejpam-5757	27	4	the	the	DET
ejpam-5757	27	5	parametric	parametric	ADJ
ejpam-5757	27	6	basic	basic	ADJ
ejpam-5757	27	7	equation	equation	NOUN
ejpam-5757	27	8	of	of	ADP
ejpam-5757	27	9	information	information	NOUN
ejpam-5757	27	10	was	be	AUX
ejpam-5757	27	11	addressed	address	VERB
ejpam-5757	27	12	by	by	ADP
ejpam-5757	27	13	gselmann	gselmann	NOUN
ejpam-5757	27	14	in	in	ADP
ejpam-5757	27	15	[	[	X
ejpam-5757	27	16	17	17	NUM
ejpam-5757	27	17	]	]	SYM
ejpam-5757	27	18	.	.	PUNCT
ejpam-5757	28	1	bahyrycz	bahyrycz	PROPN
ejpam-5757	28	2	and	and	CCONJ
ejpam-5757	28	3	piszczek	piszczek	NOUN
ejpam-5757	28	4	reported	report	VERB
ejpam-5757	28	5	the	the	DET
ejpam-5757	28	6	jensen	jensen	PROPN
ejpam-5757	28	7	functional	functional	ADJ
ejpam-5757	28	8	equation	equation	NOUN
ejpam-5757	28	9	’s	’s	PART
ejpam-5757	28	10	hyperstability	hyperstability	NOUN
ejpam-5757	28	11	in	in	ADP
ejpam-5757	28	12	[	[	X
ejpam-5757	28	13	4	4	NUM
ejpam-5757	28	14	]	]	PUNCT
ejpam-5757	28	15	.	.	PUNCT
ejpam-5757	29	1	for	for	ADP
ejpam-5757	29	2	a	a	DET
ejpam-5757	29	3	certain	certain	ADJ
ejpam-5757	29	4	class	class	NOUN
ejpam-5757	29	5	of	of	ADP
ejpam-5757	29	6	complete	complete	ADJ
ejpam-5757	29	7	metric	metric	ADJ
ejpam-5757	29	8	spaces	space	NOUN
ejpam-5757	29	9	,	,	PUNCT
ejpam-5757	29	10	brzdȩk	brzdȩk	NOUN
ejpam-5757	29	11	and	and	CCONJ
ejpam-5757	29	12	ciepliński	ciepliński	ADJ
ejpam-5757	29	13	[	[	X
ejpam-5757	29	14	13	13	NUM
ejpam-5757	29	15	]	]	PUNCT
ejpam-5757	29	16	demonstrated	demonstrate	VERB
ejpam-5757	29	17	a	a	DET
ejpam-5757	29	18	simple	simple	ADJ
ejpam-5757	29	19	fixed	fix	VERB
ejpam-5757	29	20	point	point	NOUN
ejpam-5757	29	21	theorem	theorem	ADJ
ejpam-5757	29	22	,	,	PUNCT
ejpam-5757	29	23	namely	namely	ADV
ejpam-5757	29	24	,	,	PUNCT
ejpam-5757	29	25	complete	complete	ADJ
ejpam-5757	29	26	non	non	ADJ
ejpam-5757	29	27	-	-	ADJ
ejpam-5757	29	28	archimedean	archimedean	ADJ
ejpam-5757	29	29	metric	metric	ADJ
ejpam-5757	29	30	spaces	space	NOUN
ejpam-5757	29	31	,	,	PUNCT
ejpam-5757	29	32	p	p	ADJ
ejpam-5757	29	33	-	-	PUNCT
ejpam-5757	29	34	adic	adic	ADJ
ejpam-5757	29	35	strings	string	NOUN
ejpam-5757	29	36	,	,	PUNCT
ejpam-5757	29	37	and	and	CCONJ
ejpam-5757	29	38	superstrings	superstring	NOUN
ejpam-5757	29	39	that	that	PRON
ejpam-5757	29	40	are	be	AUX
ejpam-5757	29	41	related	relate	VERB
ejpam-5757	29	42	to	to	ADP
ejpam-5757	29	43	several	several	ADJ
ejpam-5757	29	44	quantum	quantum	ADJ
ejpam-5757	29	45	physics	physics	NOUN
ejpam-5757	29	46	-	-	PUNCT
ejpam-5757	29	47	related	relate	VERB
ejpam-5757	29	48	phenomena	phenomenon	NOUN
ejpam-5757	29	49	.	.	PUNCT
ejpam-5757	30	1	they	they	PRON
ejpam-5757	30	2	also	also	ADV
ejpam-5757	30	3	demonstrated	demonstrate	VERB
ejpam-5757	30	4	that	that	SCONJ
ejpam-5757	30	5	how	how	SCONJ
ejpam-5757	30	6	effective	effective	ADJ
ejpam-5757	30	7	and	and	CCONJ
ejpam-5757	30	8	practical	practical	ADJ
ejpam-5757	30	9	this	this	DET
ejpam-5757	30	10	theorem	theorem	NOUN
ejpam-5757	30	11	is	be	AUX
ejpam-5757	30	12	for	for	ADP
ejpam-5757	30	13	demonstrating	demonstrate	VERB
ejpam-5757	30	14	the	the	DET
ejpam-5757	30	15	hyers	hyers	PROPN
ejpam-5757	30	16	-	-	PUNCT
ejpam-5757	30	17	ulam	ulam	ADJ
ejpam-5757	30	18	stability	stability	NOUN
ejpam-5757	30	19	of	of	ADP
ejpam-5757	30	20	a	a	DET
ejpam-5757	30	21	huge	huge	ADJ
ejpam-5757	30	22	class	class	NOUN
ejpam-5757	30	23	of	of	ADP
ejpam-5757	30	24	functional	functional	ADJ
ejpam-5757	30	25	equations	equation	NOUN
ejpam-5757	30	26	in	in	ADP
ejpam-5757	30	27	a	a	DET
ejpam-5757	30	28	single	single	ADJ
ejpam-5757	30	29	variable	variable	NOUN
ejpam-5757	30	30	.	.	PUNCT
ejpam-5757	31	1	the	the	DET
ejpam-5757	31	2	fixed	fix	VERB
ejpam-5757	31	3	point	point	NOUN
ejpam-5757	31	4	theorem	theorem	VERB
ejpam-5757	31	5	[	[	X
ejpam-5757	31	6	12	12	NUM
ejpam-5757	31	7	,	,	PUNCT
ejpam-5757	31	8	theorem	theorem	VERB
ejpam-5757	31	9	1	1	NUM
ejpam-5757	31	10	]	]	PUNCT
ejpam-5757	31	11	was	be	AUX
ejpam-5757	31	12	restated	restate	VERB
ejpam-5757	31	13	in	in	ADP
ejpam-5757	31	14	2	2	NUM
ejpam-5757	31	15	-	-	PUNCT
ejpam-5757	31	16	banach	banach	NOUN
ejpam-5757	31	17	spaces	space	NOUN
ejpam-5757	31	18	by	by	ADP
ejpam-5757	31	19	el	el	PROPN
ejpam-5757	31	20	-	-	PROPN
ejpam-5757	31	21	fassi	fassi	PROPN
ejpam-5757	32	1	[	[	X
ejpam-5757	32	2	15	15	NUM
ejpam-5757	32	3	]	]	PUNCT
ejpam-5757	32	4	in	in	ADP
ejpam-5757	32	5	2017	2017	NUM
ejpam-5757	32	6	,	,	PUNCT
ejpam-5757	32	7	and	and	CCONJ
ejpam-5757	32	8	a	a	DET
ejpam-5757	32	9	radical	radical	ADJ
ejpam-5757	32	10	quartic	quartic	ADJ
ejpam-5757	32	11	functional	functional	ADJ
ejpam-5757	32	12	equation	equation	NOUN
ejpam-5757	32	13	was	be	AUX
ejpam-5757	32	14	introduced	introduce	VERB
ejpam-5757	32	15	and	and	CCONJ
ejpam-5757	32	16	examined	examine	VERB
ejpam-5757	32	17	its	its	PRON
ejpam-5757	32	18	ulam	ulam	PROPN
ejpam-5757	32	19	stability	stability	NOUN
ejpam-5757	32	20	in	in	ADP
ejpam-5757	32	21	2	2	NUM
ejpam-5757	32	22	-	-	PUNCT
ejpam-5757	32	23	banach	banach	NOUN
ejpam-5757	32	24	spaces	space	NOUN
ejpam-5757	32	25	by	by	ADP
ejpam-5757	32	26	fixed	fix	VERB
ejpam-5757	32	27	-	-	PUNCT
ejpam-5757	32	28	point	point	NOUN
ejpam-5757	32	29	approache	approache	NOUN
ejpam-5757	32	30	.	.	PUNCT
ejpam-5757	33	1	in	in	ADP
ejpam-5757	33	2	[	[	X
ejpam-5757	33	3	5	5	NUM
ejpam-5757	33	4	]	]	PUNCT
ejpam-5757	33	5	,	,	PUNCT
ejpam-5757	33	6	bounader	bounader	NOUN
ejpam-5757	33	7	examined	examine	VERB
ejpam-5757	33	8	the	the	DET
ejpam-5757	33	9	hyperstability	hyperstability	NOUN
ejpam-5757	33	10	of	of	ADP
ejpam-5757	33	11	the	the	DET
ejpam-5757	33	12	quartic	quartic	ADJ
ejpam-5757	33	13	functional	functional	ADJ
ejpam-5757	33	14	equation	equation	NOUN
ejpam-5757	33	15	in	in	ADP
ejpam-5757	33	16	banach	banach	NOUN
ejpam-5757	33	17	spaces	space	NOUN
ejpam-5757	33	18	.	.	PUNCT
ejpam-5757	34	1	in	in	ADP
ejpam-5757	34	2	[	[	X
ejpam-5757	34	3	2	2	NUM
ejpam-5757	34	4	]	]	PUNCT
ejpam-5757	34	5	,	,	PUNCT
ejpam-5757	34	6	aribou	aribou	PROPN
ejpam-5757	34	7	et	et	PROPN
ejpam-5757	34	8	al	al	PROPN
ejpam-5757	34	9	.	.	PROPN
ejpam-5757	34	10	presented	present	VERB
ejpam-5757	34	11	the	the	DET
ejpam-5757	34	12	hyperstability	hyperstability	NOUN
ejpam-5757	34	13	results	result	NOUN
ejpam-5757	34	14	of	of	ADP
ejpam-5757	34	15	a	a	DET
ejpam-5757	34	16	cubicquartic	cubicquartic	ADJ
ejpam-5757	34	17	functional	functional	ADJ
ejpam-5757	34	18	equation	equation	NOUN
ejpam-5757	34	19	in	in	ADP
ejpam-5757	34	20	ultrametric	ultrametric	ADJ
ejpam-5757	34	21	banach	banach	NOUN
ejpam-5757	34	22	spaces	space	VERB
ejpam-5757	34	23	.	.	PUNCT
ejpam-5757	35	1	and	and	CCONJ
ejpam-5757	35	2	also	also	ADV
ejpam-5757	35	3	,	,	PUNCT
ejpam-5757	35	4	in	in	ADP
ejpam-5757	35	5	2020	2020	NUM
ejpam-5757	35	6	,	,	PUNCT
ejpam-5757	35	7	sayar	sayar	NOUN
ejpam-5757	35	8	and	and	CCONJ
ejpam-5757	35	9	bergam	bergam	NOUN
ejpam-5757	36	1	[	[	X
ejpam-5757	36	2	27	27	NUM
ejpam-5757	36	3	]	]	PUNCT
ejpam-5757	36	4	,	,	PUNCT
ejpam-5757	36	5	examined	examine	VERB
ejpam-5757	36	6	stability	stability	NOUN
ejpam-5757	36	7	and	and	CCONJ
ejpam-5757	36	8	hyperstability	hyperstability	NOUN
ejpam-5757	36	9	for	for	ADP
ejpam-5757	36	10	the	the	DET
ejpam-5757	36	11	quadratic	quadratic	ADJ
ejpam-5757	36	12	functional	functional	ADJ
ejpam-5757	36	13	equation	equation	NOUN
ejpam-5757	36	14	in	in	ADP
ejpam-5757	36	15	2	2	NUM
ejpam-5757	36	16	-	-	PUNCT
ejpam-5757	36	17	banach	banach	NOUN
ejpam-5757	36	18	space	space	NOUN
ejpam-5757	36	19	by	by	ADP
ejpam-5757	36	20	brzdȩk	brzdȩk	NOUN
ejpam-5757	36	21	fixed	fix	VERB
ejpam-5757	36	22	-	-	PUNCT
ejpam-5757	36	23	point	point	NOUN
ejpam-5757	36	24	theorem	theorem	VERB
ejpam-5757	36	25	.	.	PROPN
ejpam-5757	36	26	motivated	motivate	VERB
ejpam-5757	36	27	by	by	ADP
ejpam-5757	36	28	the	the	DET
ejpam-5757	36	29	above	above	ADJ
ejpam-5757	36	30	results	result	NOUN
ejpam-5757	36	31	on	on	ADP
ejpam-5757	36	32	the	the	DET
ejpam-5757	36	33	hyperstability	hyperstability	NOUN
ejpam-5757	36	34	of	of	ADP
ejpam-5757	36	35	additive	additive	ADJ
ejpam-5757	36	36	functional	functional	ADJ
ejpam-5757	36	37	equations	equation	NOUN
ejpam-5757	36	38	,	,	PUNCT
ejpam-5757	36	39	quadratic	quadratic	ADJ
ejpam-5757	36	40	functional	functional	ADJ
ejpam-5757	36	41	equations	equation	NOUN
ejpam-5757	36	42	,	,	PUNCT
ejpam-5757	36	43	cubic	cubic	ADJ
ejpam-5757	36	44	functional	functional	ADJ
ejpam-5757	36	45	equations	equation	NOUN
ejpam-5757	36	46	and	and	CCONJ
ejpam-5757	36	47	quartic	quartic	ADJ
ejpam-5757	36	48	functional	functional	ADJ
ejpam-5757	36	49	equations	equation	NOUN
ejpam-5757	36	50	,	,	PUNCT
ejpam-5757	36	51	in	in	ADP
ejpam-5757	36	52	the	the	DET
ejpam-5757	36	53	current	current	ADJ
ejpam-5757	36	54	work	work	NOUN
ejpam-5757	36	55	,	,	PUNCT
ejpam-5757	36	56	we	we	PRON
ejpam-5757	36	57	try	try	VERB
ejpam-5757	36	58	to	to	PART
ejpam-5757	36	59	examine	examine	VERB
ejpam-5757	36	60	the	the	DET
ejpam-5757	36	61	hyperstability	hyperstability	NOUN
ejpam-5757	36	62	of	of	ADP
ejpam-5757	36	63	the	the	DET
ejpam-5757	36	64	following	follow	VERB
ejpam-5757	36	65	quintic	quintic	ADJ
ejpam-5757	36	66	functional	functional	ADJ
ejpam-5757	36	67	equation	equation	NOUN
ejpam-5757	36	68	ϕ(u+	ϕ(u+	PROPN
ejpam-5757	37	1	3v)−	3v)−	NUM
ejpam-5757	37	2	5ϕ(u+	5ϕ(u+	NUM
ejpam-5757	37	3	2v)−	2v)−	NUM
ejpam-5757	37	4	ϕ(u−	ϕ(u−	NUM
ejpam-5757	37	5	2v	2v	NUM
ejpam-5757	37	6	)	)	PUNCT
ejpam-5757	38	1	+	+	CCONJ
ejpam-5757	38	2	10ϕ(u+	10ϕ(u+	NUM
ejpam-5757	38	3	v	v	NOUN
ejpam-5757	38	4	)	)	PUNCT
ejpam-5757	39	1	+	+	CCONJ
ejpam-5757	39	2	5ϕ(u−	5ϕ(u−	NUM
ejpam-5757	39	3	v)−	v)−	PROPN
ejpam-5757	39	4	10ϕ(u)−	10ϕ(u)−	NUM
ejpam-5757	39	5	120ϕ(v	120ϕ(v	NOUN
ejpam-5757	39	6	)	)	PUNCT
ejpam-5757	39	7	=	=	SYM
ejpam-5757	39	8	0	0	NUM
ejpam-5757	39	9	,	,	PUNCT
ejpam-5757	39	10	in	in	ADP
ejpam-5757	39	11	banach	banach	NOUN
ejpam-5757	39	12	spaces	space	NOUN
ejpam-5757	39	13	by	by	ADP
ejpam-5757	39	14	means	mean	NOUN
ejpam-5757	39	15	of	of	ADP
ejpam-5757	39	16	brzdȩk	brzdȩk	NOUN
ejpam-5757	39	17	’s	’s	PART
ejpam-5757	39	18	fixed	fix	VERB
ejpam-5757	39	19	point	point	NOUN
ejpam-5757	39	20	approach	approach	NOUN
ejpam-5757	39	21	.	.	PUNCT
ejpam-5757	40	1	a	a	DET
ejpam-5757	40	2	concept	concept	NOUN
ejpam-5757	40	3	employed	employ	VERB
ejpam-5757	40	4	by	by	ADP
ejpam-5757	40	5	brzdȩk	brzdȩk	PROPN
ejpam-5757	40	6	in	in	ADP
ejpam-5757	40	7	[	[	X
ejpam-5757	40	8	9–11	9–11	NOUN
ejpam-5757	40	9	]	]	PUNCT
ejpam-5757	40	10	and	and	CCONJ
ejpam-5757	40	11	later	later	ADV
ejpam-5757	40	12	by	by	ADP
ejpam-5757	40	13	piszczek	piszczek	NOUN
ejpam-5757	40	14	[	[	X
ejpam-5757	40	15	23	23	NUM
ejpam-5757	40	16	]	]	PUNCT
ejpam-5757	40	17	served	serve	VERB
ejpam-5757	40	18	as	as	ADP
ejpam-5757	40	19	the	the	DET
ejpam-5757	40	20	inspiration	inspiration	NOUN
ejpam-5757	40	21	for	for	ADP
ejpam-5757	40	22	the	the	DET
ejpam-5757	40	23	manner	manner	NOUN
ejpam-5757	40	24	of	of	ADP
ejpam-5757	40	25	the	the	DET
ejpam-5757	40	26	primary	primary	ADJ
ejpam-5757	40	27	results	result	NOUN
ejpam-5757	40	28	’	'	PUNCT
ejpam-5757	40	29	confirmation	confirmation	NOUN
ejpam-5757	40	30	.	.	PUNCT
ejpam-5757	41	1	its	its	PRON
ejpam-5757	41	2	foundation	foundation	NOUN
ejpam-5757	41	3	is	be	AUX
ejpam-5757	41	4	a	a	DET
ejpam-5757	41	5	fixedpoint	fixedpoint	NOUN
ejpam-5757	41	6	theorem	theorem	NOUN
ejpam-5757	41	7	for	for	ADP
ejpam-5757	41	8	functional	functional	ADJ
ejpam-5757	41	9	spaces	space	NOUN
ejpam-5757	41	10	discovered	discover	VERB
ejpam-5757	41	11	by	by	ADP
ejpam-5757	41	12	brzdȩk	brzdȩk	PROPN
ejpam-5757	41	13	(	(	PUNCT
ejpam-5757	41	14	see	see	VERB
ejpam-5757	41	15	[	[	X
ejpam-5757	41	16	12	12	NUM
ejpam-5757	41	17	]	]	PUNCT
ejpam-5757	41	18	,	,	PUNCT
ejpam-5757	41	19	theorem	theorem	VERB
ejpam-5757	41	20	1	1	NUM
ejpam-5757	41	21	]	]	PUNCT
ejpam-5757	41	22	)	)	PUNCT
ejpam-5757	41	23	.	.	PUNCT
ejpam-5757	42	1	most	most	ADV
ejpam-5757	42	2	frequently	frequently	ADV
ejpam-5757	42	3	,	,	PUNCT
ejpam-5757	42	4	the	the	DET
ejpam-5757	42	5	superstability	superstability	NOUN
ejpam-5757	42	6	and	and	CCONJ
ejpam-5757	42	7	hyperstability	hyperstability	NOUN
ejpam-5757	42	8	,	,	PUNCT
ejpam-5757	42	9	which	which	PRON
ejpam-5757	42	10	also	also	ADV
ejpam-5757	42	11	accepts	accept	VERB
ejpam-5757	42	12	bounded	bounded	ADJ
ejpam-5757	42	13	functions	function	NOUN
ejpam-5757	42	14	-	-	PUNCT
ejpam-5757	42	15	are	be	AUX
ejpam-5757	42	16	concerned	concern	VERB
ejpam-5757	42	17	.	.	PUNCT
ejpam-5757	43	1	numerous	numerous	ADJ
ejpam-5757	43	2	articles	article	NOUN
ejpam-5757	43	3	have	have	AUX
ejpam-5757	43	4	been	be	AUX
ejpam-5757	43	5	written	write	VERB
ejpam-5757	43	6	on	on	ADP
ejpam-5757	43	7	this	this	DET
ejpam-5757	43	8	topic	topic	NOUN
ejpam-5757	43	9	and	and	CCONJ
ejpam-5757	43	10	we	we	PRON
ejpam-5757	43	11	refer	refer	VERB
ejpam-5757	43	12	to	to	ADP
ejpam-5757	43	13	[	[	X
ejpam-5757	43	14	1	1	NUM
ejpam-5757	43	15	,	,	PUNCT
ejpam-5757	43	16	3	3	NUM
ejpam-5757	43	17	,	,	PUNCT
ejpam-5757	43	18	4	4	NUM
ejpam-5757	43	19	,	,	PUNCT
ejpam-5757	43	20	14	14	NUM
ejpam-5757	43	21	,	,	PUNCT
ejpam-5757	43	22	16	16	NUM
ejpam-5757	43	23	,	,	PUNCT
ejpam-5757	43	24	17	17	NUM
ejpam-5757	43	25	,	,	PUNCT
ejpam-5757	43	26	21	21	NUM
ejpam-5757	43	27	,	,	PUNCT
ejpam-5757	43	28	22	22	NUM
ejpam-5757	43	29	,	,	PUNCT
ejpam-5757	43	30	26	26	NUM
ejpam-5757	43	31	,	,	PUNCT
ejpam-5757	43	32	29	29	NUM
ejpam-5757	43	33	]	]	PUNCT
ejpam-5757	43	34	.	.	PUNCT
ejpam-5757	44	1	throughout	throughout	ADP
ejpam-5757	44	2	the	the	DET
ejpam-5757	44	3	paper	paper	NOUN
ejpam-5757	44	4	,	,	PUNCT
ejpam-5757	44	5	n	n	PRON
ejpam-5757	44	6	denote	denote	VERB
ejpam-5757	44	7	the	the	DET
ejpam-5757	44	8	set	set	NOUN
ejpam-5757	44	9	of	of	ADP
ejpam-5757	44	10	all	all	DET
ejpam-5757	44	11	natural	natural	ADJ
ejpam-5757	44	12	numbers	number	NOUN
ejpam-5757	44	13	,	,	PUNCT
ejpam-5757	44	14	n0	n0	X
ejpam-5757	44	15	=	=	SYM
ejpam-5757	44	16	n	n	PRON
ejpam-5757	44	17	∪	∪	X
ejpam-5757	44	18	{	{	PUNCT
ejpam-5757	44	19	0	0	NUM
ejpam-5757	44	20	}	}	PUNCT
ejpam-5757	44	21	,	,	PUNCT
ejpam-5757	44	22	r	r	NOUN
ejpam-5757	44	23	denote	denote	VERB
ejpam-5757	44	24	the	the	DET
ejpam-5757	44	25	set	set	NOUN
ejpam-5757	44	26	of	of	ADP
ejpam-5757	44	27	all	all	DET
ejpam-5757	44	28	real	real	ADJ
ejpam-5757	44	29	numbers	number	NOUN
ejpam-5757	44	30	,	,	PUNCT
ejpam-5757	44	31	nm	nm	NOUN
ejpam-5757	44	32	denote	denote	VERB
ejpam-5757	44	33	the	the	DET
ejpam-5757	44	34	set	set	NOUN
ejpam-5757	44	35	of	of	ADP
ejpam-5757	44	36	all	all	DET
ejpam-5757	44	37	natural	natural	ADJ
ejpam-5757	44	38	numbers	number	NOUN
ejpam-5757	44	39	greater	great	ADJ
ejpam-5757	44	40	than	than	ADP
ejpam-5757	44	41	or	or	CCONJ
ejpam-5757	44	42	equal	equal	ADJ
ejpam-5757	44	43	to	to	ADP
ejpam-5757	44	44	m	m	PRON
ejpam-5757	44	45	,	,	PUNCT
ejpam-5757	44	46	for	for	ADP
ejpam-5757	44	47	every	every	DET
ejpam-5757	44	48	m	m	NOUN
ejpam-5757	44	49	∈	∈	NOUN
ejpam-5757	44	50	n	n	NOUN
ejpam-5757	44	51	and	and	CCONJ
ejpam-5757	44	52	r+	r+	NOUN
ejpam-5757	44	53	denote	denote	VERB
ejpam-5757	44	54	the	the	DET
ejpam-5757	44	55	set	set	NOUN
ejpam-5757	44	56	of	of	ADP
ejpam-5757	44	57	all	all	DET
ejpam-5757	44	58	positive	positive	ADJ
ejpam-5757	44	59	real	real	ADJ
ejpam-5757	44	60	numbers	number	NOUN
ejpam-5757	44	61	.	.	PUNCT
ejpam-5757	45	1	we	we	PRON
ejpam-5757	45	2	use	use	VERB
ejpam-5757	45	3	the	the	DET
ejpam-5757	45	4	notation	notation	NOUN
ejpam-5757	45	5	u0	u0	NOUN
ejpam-5757	45	6	for	for	ADP
ejpam-5757	45	7	the	the	DET
ejpam-5757	45	8	set	set	NOUN
ejpam-5757	45	9	u\{0	u\{0	NOUN
ejpam-5757	45	10	}	}	PUNCT
ejpam-5757	45	11	.	.	PUNCT
ejpam-5757	46	1	s.	s.	PROPN
ejpam-5757	46	2	karthikeyan	karthikeyan	PROPN
ejpam-5757	46	3	et	et	PROPN
ejpam-5757	46	4	al	al	PROPN
ejpam-5757	46	5	.	.	PUNCT
ejpam-5757	46	6	/	/	SYM
ejpam-5757	46	7	eur	eur	PROPN
ejpam-5757	46	8	.	.	PUNCT
ejpam-5757	47	1	j.	j.	PROPN
ejpam-5757	47	2	pure	pure	PROPN
ejpam-5757	47	3	appl	appl	PROPN
ejpam-5757	47	4	.	.	PROPN
ejpam-5757	47	5	math	math	PROPN
ejpam-5757	47	6	,	,	PUNCT
ejpam-5757	47	7	18	18	NUM
ejpam-5757	47	8	(	(	PUNCT
ejpam-5757	47	9	1	1	NUM
ejpam-5757	47	10	)	)	PUNCT
ejpam-5757	47	11	(	(	PUNCT
ejpam-5757	47	12	2025	2025	NUM
ejpam-5757	47	13	)	)	PUNCT
ejpam-5757	47	14	,	,	PUNCT
ejpam-5757	47	15	5757	5757	NUM
ejpam-5757	47	16	3	3	NUM
ejpam-5757	47	17	of	of	ADP
ejpam-5757	47	18	18	18	NUM
ejpam-5757	47	19	theorem	theorem	NOUN
ejpam-5757	47	20	1	1	NUM
ejpam-5757	47	21	.	.	PUNCT
ejpam-5757	48	1	[	[	X
ejpam-5757	48	2	13	13	NUM
ejpam-5757	48	3	]	]	PUNCT
ejpam-5757	48	4	let	let	VERB
ejpam-5757	48	5	u	u	PRON
ejpam-5757	48	6	be	be	AUX
ejpam-5757	48	7	a	a	DET
ejpam-5757	48	8	non	non	ADJ
ejpam-5757	48	9	-	-	ADJ
ejpam-5757	48	10	empty	empty	ADJ
ejpam-5757	48	11	set	set	NOUN
ejpam-5757	48	12	,	,	PUNCT
ejpam-5757	48	13	(	(	PUNCT
ejpam-5757	48	14	v	v	NOUN
ejpam-5757	48	15	,	,	PUNCT
ejpam-5757	48	16	d	d	NOUN
ejpam-5757	48	17	)	)	PUNCT
ejpam-5757	48	18	be	be	AUX
ejpam-5757	48	19	a	a	DET
ejpam-5757	48	20	complete	complete	ADJ
ejpam-5757	48	21	metric	metric	ADJ
ejpam-5757	48	22	space	space	NOUN
ejpam-5757	48	23	,	,	PUNCT
ejpam-5757	48	24	and	and	CCONJ
ejpam-5757	48	25	υ	υ	NOUN
ejpam-5757	48	26	:	:	PUNCT
ejpam-5757	48	27	vu	vu	PROPN
ejpam-5757	48	28	→	→	SYM
ejpam-5757	48	29	vu	vu	X
ejpam-5757	48	30	fulfill	fulfill	VERB
ejpam-5757	48	31	the	the	DET
ejpam-5757	48	32	hypothesis	hypothesis	NOUN
ejpam-5757	49	1	lim	lim	PROPN
ejpam-5757	49	2	m→+∞	m→+∞	PROPN
ejpam-5757	49	3	υδm	υδm	PROPN
ejpam-5757	49	4	=	=	PUNCT
ejpam-5757	49	5	0	0	PROPN
ejpam-5757	49	6	,	,	PUNCT
ejpam-5757	49	7	for	for	ADP
ejpam-5757	49	8	{	{	PUNCT
ejpam-5757	49	9	δm}m∈n	δm}m∈n	X
ejpam-5757	49	10	in	in	ADP
ejpam-5757	49	11	vu	vu	X
ejpam-5757	49	12	with	with	ADP
ejpam-5757	49	13	lim	lim	PROPN
ejpam-5757	49	14	m→+∞	m→+∞	PROPN
ejpam-5757	49	15	δm	δm	PROPN
ejpam-5757	49	16	=	=	NOUN
ejpam-5757	49	17	0	0	PROPN
ejpam-5757	49	18	.	.	PUNCT
ejpam-5757	49	19	suppose	suppose	VERB
ejpam-5757	49	20	that	that	SCONJ
ejpam-5757	49	21	an	an	DET
ejpam-5757	49	22	operator	operator	NOUN
ejpam-5757	49	23	φ	φ	NOUN
ejpam-5757	49	24	:	:	PUNCT
ejpam-5757	49	25	vu	vu	PROPN
ejpam-5757	49	26	→	→	SYM
ejpam-5757	49	27	vu	vu	X
ejpam-5757	49	28	fulfills	fulfills	PROPN
ejpam-5757	49	29	d	d	X
ejpam-5757	49	30	(	(	PUNCT
ejpam-5757	49	31	φψ(u),φς(u	φψ(u),φς(u	NOUN
ejpam-5757	49	32	)	)	PUNCT
ejpam-5757	49	33	)	)	PUNCT
ejpam-5757	49	34	≤	≤	NUM
ejpam-5757	49	35	υ(∆(ψ	υ(∆(ψ	ADJ
ejpam-5757	49	36	,	,	PUNCT
ejpam-5757	49	37	ς	ς	NOUN
ejpam-5757	49	38	)	)	PUNCT
ejpam-5757	49	39	)	)	PUNCT
ejpam-5757	49	40	)	)	PUNCT
ejpam-5757	49	41	,	,	PUNCT
ejpam-5757	49	42	ψ	ψ	X
ejpam-5757	49	43	,	,	PUNCT
ejpam-5757	49	44	ς	ς	PROPN
ejpam-5757	49	45	∈	∈	PROPN
ejpam-5757	49	46	vu	vu	NOUN
ejpam-5757	49	47	,	,	PUNCT
ejpam-5757	49	48	for	for	ADP
ejpam-5757	49	49	all	all	PRON
ejpam-5757	49	50	u	u	PRON
ejpam-5757	49	51	∈	∈	PROPN
ejpam-5757	49	52	u	u	NOUN
ejpam-5757	49	53	,	,	PUNCT
ejpam-5757	49	54	where	where	SCONJ
ejpam-5757	49	55	a	a	DET
ejpam-5757	49	56	mapping	mapping	NOUN
ejpam-5757	49	57	∆	∆	PROPN
ejpam-5757	49	58	:	:	PUNCT
ejpam-5757	49	59	vu	vu	X
ejpam-5757	49	60	×	×	PROPN
ejpam-5757	49	61	vu	vu	PROPN
ejpam-5757	49	62	→	→	X
ejpam-5757	49	63	ru	ru	PROPN
ejpam-5757	49	64	+	+	CCONJ
ejpam-5757	49	65	is	be	AUX
ejpam-5757	49	66	defined	define	VERB
ejpam-5757	49	67	by	by	ADP
ejpam-5757	49	68	∆(ψ	∆(ψ	PROPN
ejpam-5757	49	69	,	,	PUNCT
ejpam-5757	49	70	ς	ς	NOUN
ejpam-5757	49	71	)	)	PUNCT
ejpam-5757	49	72	(	(	PUNCT
ejpam-5757	49	73	u	u	NOUN
ejpam-5757	49	74	)	)	PUNCT
ejpam-5757	49	75	:	:	PUNCT
ejpam-5757	49	76	=	=	PUNCT
ejpam-5757	49	77	d(ψ(u	d(ψ(u	PROPN
ejpam-5757	49	78	)	)	PUNCT
ejpam-5757	49	79	,	,	PUNCT
ejpam-5757	49	80	ς(u	ς(u	PROPN
ejpam-5757	49	81	)	)	PUNCT
ejpam-5757	49	82	)	)	PUNCT
ejpam-5757	49	83	,	,	PUNCT
ejpam-5757	49	84	ψ	ψ	X
ejpam-5757	49	85	,	,	PUNCT
ejpam-5757	49	86	ς	ς	PROPN
ejpam-5757	49	87	∈	∈	PROPN
ejpam-5757	49	88	vu	vu	NOUN
ejpam-5757	49	89	,	,	PUNCT
ejpam-5757	49	90	u	u	PROPN
ejpam-5757	49	91	∈	∈	PROPN
ejpam-5757	49	92	u	u	NOUN
ejpam-5757	49	93	.	.	PUNCT
ejpam-5757	50	1	if	if	SCONJ
ejpam-5757	50	2	there	there	PRON
ejpam-5757	50	3	is	be	VERB
ejpam-5757	50	4	a	a	DET
ejpam-5757	50	5	mapping	mapping	NOUN
ejpam-5757	50	6	ϑ	ϑ	X
ejpam-5757	50	7	:	:	PUNCT
ejpam-5757	50	8	u	u	X
ejpam-5757	50	9	→	→	SYM
ejpam-5757	50	10	r+	r+	NOUN
ejpam-5757	50	11	and	and	CCONJ
ejpam-5757	50	12	ζ	ζ	NOUN
ejpam-5757	50	13	:	:	PUNCT
ejpam-5757	50	14	u	u	NOUN
ejpam-5757	50	15	→	→	SYM
ejpam-5757	50	16	v	v	NUM
ejpam-5757	50	17	fulfilling	fulfil	VERB
ejpam-5757	50	18	d	d	X
ejpam-5757	50	19	(	(	PUNCT
ejpam-5757	50	20	φψ(u),φς(u	φψ(u),φς(u	NOUN
ejpam-5757	50	21	)	)	PUNCT
ejpam-5757	50	22	)	)	PUNCT
ejpam-5757	50	23	≤	≤	PROPN
ejpam-5757	50	24	ψ(u	ψ(u	PROPN
ejpam-5757	50	25	)	)	PUNCT
ejpam-5757	50	26	and	and	CCONJ
ejpam-5757	50	27	ϑ∗(u	ϑ∗(u	NUM
ejpam-5757	50	28	)	)	PUNCT
ejpam-5757	50	29	:	:	PUNCT
ejpam-5757	50	30	=	=	PUNCT
ejpam-5757	50	31	∑	∑	PUNCT
ejpam-5757	50	32	m∈n0	m∈n0	PROPN
ejpam-5757	50	33	(	(	PUNCT
ejpam-5757	50	34	υmϑ	υmϑ	PROPN
ejpam-5757	50	35	)	)	PUNCT
ejpam-5757	50	36	(	(	PUNCT
ejpam-5757	50	37	u	u	NOUN
ejpam-5757	50	38	)	)	PUNCT
ejpam-5757	50	39	<	<	X
ejpam-5757	50	40	∞	∞	NUM
ejpam-5757	50	41	for	for	ADP
ejpam-5757	50	42	all	all	DET
ejpam-5757	50	43	u	u	PROPN
ejpam-5757	50	44	∈	∈	PROPN
ejpam-5757	50	45	u	u	NOUN
ejpam-5757	50	46	,	,	PUNCT
ejpam-5757	50	47	then	then	ADV
ejpam-5757	50	48	the	the	DET
ejpam-5757	50	49	limit	limit	NOUN
ejpam-5757	50	50	lim	lim	PROPN
ejpam-5757	50	51	m→+∞	m→+∞	PROPN
ejpam-5757	50	52	(	(	PUNCT
ejpam-5757	50	53	φmζ	φmζ	PROPN
ejpam-5757	50	54	)	)	PUNCT
ejpam-5757	50	55	(	(	PUNCT
ejpam-5757	50	56	u	u	NOUN
ejpam-5757	50	57	)	)	PUNCT
ejpam-5757	50	58	exists	exist	VERB
ejpam-5757	50	59	for	for	ADP
ejpam-5757	50	60	each	each	DET
ejpam-5757	50	61	u	u	PROPN
ejpam-5757	50	62	∈	∈	PROPN
ejpam-5757	50	63	u	u	NOUN
ejpam-5757	50	64	.	.	PUNCT
ejpam-5757	51	1	furthermore	furthermore	ADV
ejpam-5757	51	2	,	,	PUNCT
ejpam-5757	51	3	the	the	DET
ejpam-5757	51	4	mapping	mapping	NOUN
ejpam-5757	51	5	χ	χ	ADP
ejpam-5757	51	6	∈	∈	PROPN
ejpam-5757	51	7	vu	vu	NOUN
ejpam-5757	51	8	,	,	PUNCT
ejpam-5757	51	9	defined	define	VERB
ejpam-5757	51	10	by	by	ADP
ejpam-5757	51	11	χ(u	χ(u	NOUN
ejpam-5757	51	12	)	)	PUNCT
ejpam-5757	51	13	:	:	PUNCT
ejpam-5757	51	14	=	=	SYM
ejpam-5757	51	15	lim	lim	PROPN
ejpam-5757	51	16	m→+∞	m→+∞	PROPN
ejpam-5757	51	17	(	(	PUNCT
ejpam-5757	51	18	φmζ	φmζ	PROPN
ejpam-5757	51	19	)	)	PUNCT
ejpam-5757	51	20	(	(	PUNCT
ejpam-5757	51	21	u	u	NOUN
ejpam-5757	51	22	)	)	PUNCT
ejpam-5757	51	23	is	be	AUX
ejpam-5757	51	24	a	a	DET
ejpam-5757	51	25	fixed	fix	VERB
ejpam-5757	51	26	point	point	NOUN
ejpam-5757	51	27	of	of	ADP
ejpam-5757	51	28	φ	φ	PROPN
ejpam-5757	51	29	with	with	ADP
ejpam-5757	51	30	d	d	PROPN
ejpam-5757	51	31	(	(	PUNCT
ejpam-5757	51	32	ζ(u	ζ(u	ADJ
ejpam-5757	51	33	)	)	PUNCT
ejpam-5757	51	34	,	,	PUNCT
ejpam-5757	51	35	χ(u	χ(u	NOUN
ejpam-5757	51	36	)	)	PUNCT
ejpam-5757	51	37	)	)	PUNCT
ejpam-5757	51	38	≤	≤	NUM
ejpam-5757	51	39	ϑ∗(u	ϑ∗(u	PROPN
ejpam-5757	51	40	)	)	PUNCT
ejpam-5757	51	41	for	for	ADP
ejpam-5757	51	42	all	all	PRON
ejpam-5757	51	43	u	u	PRON
ejpam-5757	51	44	∈	∈	PROPN
ejpam-5757	51	45	u	u	NOUN
ejpam-5757	51	46	.	.	PUNCT
ejpam-5757	52	1	the	the	DET
ejpam-5757	52	2	upcoming	upcoming	ADJ
ejpam-5757	52	3	fixed	fix	VERB
ejpam-5757	52	4	point	point	NOUN
ejpam-5757	52	5	theorem	theorem	VERB
ejpam-5757	52	6	,	,	PUNCT
ejpam-5757	52	7	which	which	PRON
ejpam-5757	52	8	corresponds	correspond	VERB
ejpam-5757	52	9	to	to	ADP
ejpam-5757	52	10	theorem	theorem	NOUN
ejpam-5757	52	11	1	1	NUM
ejpam-5757	52	12	in	in	ADP
ejpam-5757	52	13	complete	complete	ADJ
ejpam-5757	52	14	normed	normed	ADJ
ejpam-5757	52	15	space	space	NOUN
ejpam-5757	52	16	,	,	PUNCT
ejpam-5757	52	17	is	be	AUX
ejpam-5757	52	18	then	then	ADV
ejpam-5757	52	19	discussed	discuss	VERB
ejpam-5757	52	20	.	.	PUNCT
ejpam-5757	53	1	this	this	DET
ejpam-5757	53	2	outcome	outcome	NOUN
ejpam-5757	53	3	is	be	AUX
ejpam-5757	53	4	an	an	DET
ejpam-5757	53	5	important	important	ADJ
ejpam-5757	53	6	factor	factor	NOUN
ejpam-5757	53	7	in	in	ADP
ejpam-5757	53	8	the	the	DET
ejpam-5757	53	9	formulation	formulation	NOUN
ejpam-5757	53	10	of	of	ADP
ejpam-5757	53	11	stability	stability	NOUN
ejpam-5757	53	12	findings	finding	NOUN
ejpam-5757	53	13	.	.	PUNCT
ejpam-5757	54	1	theorem	theorem	NOUN
ejpam-5757	54	2	2	2	NUM
ejpam-5757	54	3	.	.	PUNCT
ejpam-5757	55	1	let	let	VERB
ejpam-5757	55	2	u	u	PRON
ejpam-5757	55	3	be	be	AUX
ejpam-5757	55	4	a	a	DET
ejpam-5757	55	5	nonempty	nonempty	ADJ
ejpam-5757	55	6	set	set	VERB
ejpam-5757	55	7	,	,	PUNCT
ejpam-5757	55	8	(	(	PUNCT
ejpam-5757	55	9	v	v	NOUN
ejpam-5757	55	10	,	,	PUNCT
ejpam-5757	55	11	∥	∥	X
ejpam-5757	55	12	·	·	PUNCT
ejpam-5757	55	13	∥	∥	X
ejpam-5757	55	14	)	)	PUNCT
ejpam-5757	55	15	be	be	AUX
ejpam-5757	55	16	a	a	DET
ejpam-5757	55	17	banach	banach	NOUN
ejpam-5757	55	18	space	space	NOUN
ejpam-5757	55	19	and	and	CCONJ
ejpam-5757	55	20	let	let	VERB
ejpam-5757	55	21	ϕ1	ϕ1	NOUN
ejpam-5757	55	22	,	,	PUNCT
ejpam-5757	55	23	ϕ2	ϕ2	ADV
ejpam-5757	55	24	,	,	PUNCT
ejpam-5757	55	25	·	·	PUNCT
ejpam-5757	55	26	·	·	PUNCT
ejpam-5757	55	27	·	·	PUNCT
ejpam-5757	55	28	,	,	PUNCT
ejpam-5757	55	29	ϕl	ϕl	INTJ
ejpam-5757	55	30	:	:	PUNCT
ejpam-5757	55	31	u	u	PROPN
ejpam-5757	55	32	→	→	SYM
ejpam-5757	55	33	u	u	NOUN
ejpam-5757	55	34	be	be	AUX
ejpam-5757	55	35	mappings	mapping	NOUN
ejpam-5757	55	36	and	and	CCONJ
ejpam-5757	55	37	l1	l1	PROPN
ejpam-5757	55	38	,	,	PUNCT
ejpam-5757	55	39	·	·	PUNCT
ejpam-5757	55	40	·	·	PUNCT
ejpam-5757	55	41	·	·	PUNCT
ejpam-5757	55	42	,	,	PUNCT
ejpam-5757	55	43	ll	ll	AUX
ejpam-5757	55	44	:	:	PUNCT
ejpam-5757	55	45	x	x	X
ejpam-5757	55	46	→	→	SYM
ejpam-5757	55	47	r+be	r+be	NOUN
ejpam-5757	55	48	functions	function	NOUN
ejpam-5757	55	49	.	.	PUNCT
ejpam-5757	56	1	suppose	suppose	VERB
ejpam-5757	56	2	that	that	SCONJ
ejpam-5757	56	3	φ	φ	PROPN
ejpam-5757	56	4	:	:	PUNCT
ejpam-5757	56	5	vu	vu	PROPN
ejpam-5757	56	6	→	→	SYM
ejpam-5757	56	7	vu	vu	X
ejpam-5757	56	8	and	and	CCONJ
ejpam-5757	56	9	two	two	NUM
ejpam-5757	56	10	operators	operator	NOUN
ejpam-5757	56	11	υ	υ	NOUN
ejpam-5757	56	12	:	:	PUNCT
ejpam-5757	56	13	ru×u	ru×u	PROPN
ejpam-5757	56	14	+	+	CCONJ
ejpam-5757	56	15	→	→	PUNCT
ejpam-5757	56	16	ru×u	ru×u	NOUN
ejpam-5757	56	17	+	+	NOUN
ejpam-5757	56	18	fulfill	fulfill	VERB
ejpam-5757	56	19	the	the	DET
ejpam-5757	56	20	conditions	condition	NOUN
ejpam-5757	56	21	:	:	PUNCT
ejpam-5757	56	22	∥φψ(u)−	∥φψ(u)−	NOUN
ejpam-5757	56	23	φς(u)∥	φς(u)∥	VERB
ejpam-5757	56	24	≤	≤	NUM
ejpam-5757	56	25	l∑	l∑	PUNCT
ejpam-5757	56	26	i=1	i=1	PROPN
ejpam-5757	56	27	li(u	li(u	NOUN
ejpam-5757	56	28	)	)	PUNCT
ejpam-5757	57	1	∥ψ	∥ψ	NOUN
ejpam-5757	57	2	(	(	PUNCT
ejpam-5757	57	3	ϕi(u))−	ϕi(u))−	NOUN
ejpam-5757	57	4	ς	ς	PROPN
ejpam-5757	57	5	(	(	PUNCT
ejpam-5757	57	6	ϕi(u))∥	ϕi(u))∥	PROPN
ejpam-5757	57	7	s.	s.	PROPN
ejpam-5757	57	8	karthikeyan	karthikeyan	PROPN
ejpam-5757	57	9	et	et	PROPN
ejpam-5757	57	10	al	al	PROPN
ejpam-5757	57	11	.	.	PUNCT
ejpam-5757	57	12	/	/	SYM
ejpam-5757	57	13	eur	eur	PROPN
ejpam-5757	57	14	.	.	PUNCT
ejpam-5757	58	1	j.	j.	PROPN
ejpam-5757	58	2	pure	pure	PROPN
ejpam-5757	58	3	appl	appl	PROPN
ejpam-5757	58	4	.	.	PROPN
ejpam-5757	58	5	math	math	PROPN
ejpam-5757	58	6	,	,	PUNCT
ejpam-5757	58	7	18	18	NUM
ejpam-5757	58	8	(	(	PUNCT
ejpam-5757	58	9	1	1	NUM
ejpam-5757	58	10	)	)	PUNCT
ejpam-5757	58	11	(	(	PUNCT
ejpam-5757	58	12	2025	2025	NUM
ejpam-5757	58	13	)	)	PUNCT
ejpam-5757	58	14	,	,	PUNCT
ejpam-5757	58	15	5757	5757	NUM
ejpam-5757	58	16	4	4	NUM
ejpam-5757	58	17	of	of	ADP
ejpam-5757	58	18	18	18	NUM
ejpam-5757	58	19	for	for	ADP
ejpam-5757	58	20	all	all	DET
ejpam-5757	58	21	ψ	ψ	NOUN
ejpam-5757	58	22	,	,	PUNCT
ejpam-5757	58	23	ς	ς	PROPN
ejpam-5757	58	24	∈	∈	PROPN
ejpam-5757	58	25	vu	vu	NOUN
ejpam-5757	58	26	,	,	PUNCT
ejpam-5757	58	27	u	u	PROPN
ejpam-5757	58	28	∈	∈	PROPN
ejpam-5757	58	29	u	u	NOUN
ejpam-5757	58	30	and	and	CCONJ
ejpam-5757	58	31	υδ(u	υδ(u	NOUN
ejpam-5757	58	32	)	)	PUNCT
ejpam-5757	58	33	:	:	PUNCT
ejpam-5757	59	1	=	=	NOUN
ejpam-5757	59	2	l∑	l∑	X
ejpam-5757	59	3	i=1	i=1	PROPN
ejpam-5757	59	4	li(u)δ	li(u)δ	PROPN
ejpam-5757	59	5	(	(	PUNCT
ejpam-5757	59	6	ϕi(u	ϕi(u	NOUN
ejpam-5757	59	7	)	)	PUNCT
ejpam-5757	59	8	)	)	PUNCT
ejpam-5757	59	9	,	,	PUNCT
ejpam-5757	59	10	δ	δ	PROPN
ejpam-5757	59	11	∈	∈	PROPN
ejpam-5757	59	12	ru×u	ru×u	PROPN
ejpam-5757	59	13	+	+	CCONJ
ejpam-5757	59	14	,	,	PUNCT
ejpam-5757	59	15	u	u	PROPN
ejpam-5757	59	16	∈	∈	PROPN
ejpam-5757	59	17	u	u	NOUN
ejpam-5757	59	18	.	.	PUNCT
ejpam-5757	60	1	if	if	SCONJ
ejpam-5757	60	2	there	there	PRON
ejpam-5757	60	3	exist	exist	VERB
ejpam-5757	60	4	mappings	mapping	NOUN
ejpam-5757	60	5	ϑ	ϑ	X
ejpam-5757	60	6	:	:	PUNCT
ejpam-5757	60	7	u	u	NOUN
ejpam-5757	60	8	×	×	PROPN
ejpam-5757	60	9	u	u	INTJ
ejpam-5757	60	10	→	→	X
ejpam-5757	60	11	r+	r+	NOUN
ejpam-5757	60	12	and	and	CCONJ
ejpam-5757	60	13	ζ	ζ	NOUN
ejpam-5757	60	14	:	:	PUNCT
ejpam-5757	60	15	u	u	NOUN
ejpam-5757	60	16	→	→	SYM
ejpam-5757	60	17	v	v	ADJ
ejpam-5757	60	18	satisfying	satisfy	VERB
ejpam-5757	60	19	∥φζ(u)−	∥φζ(u)−	NOUN
ejpam-5757	60	20	ζ(u)∥	ζ(u)∥	VERB
ejpam-5757	60	21	≤	≤	NUM
ejpam-5757	60	22	ϑ(u	ϑ(u	VERB
ejpam-5757	60	23	)	)	PUNCT
ejpam-5757	60	24	and	and	CCONJ
ejpam-5757	60	25	ϑ∗(u	ϑ∗(u	NUM
ejpam-5757	60	26	)	)	PUNCT
ejpam-5757	60	27	:	:	PUNCT
ejpam-5757	61	1	=	=	SYM
ejpam-5757	61	2	∞∑	∞∑	NUM
ejpam-5757	61	3	m=0	m=0	PROPN
ejpam-5757	61	4	(	(	PUNCT
ejpam-5757	61	5	υmϑ	υmϑ	PROPN
ejpam-5757	61	6	)	)	PUNCT
ejpam-5757	61	7	(	(	PUNCT
ejpam-5757	61	8	u	u	NOUN
ejpam-5757	61	9	)	)	PUNCT
ejpam-5757	61	10	<	<	X
ejpam-5757	61	11	∞	∞	NUM
ejpam-5757	61	12	for	for	ADP
ejpam-5757	61	13	all	all	DET
ejpam-5757	61	14	u	u	PROPN
ejpam-5757	61	15	∈	∈	PROPN
ejpam-5757	61	16	u	u	NOUN
ejpam-5757	61	17	,	,	PUNCT
ejpam-5757	61	18	then	then	ADV
ejpam-5757	61	19	the	the	DET
ejpam-5757	61	20	limit	limit	NOUN
ejpam-5757	61	21	lim	lim	PROPN
ejpam-5757	61	22	m→+∞	m→+∞	PROPN
ejpam-5757	61	23	(	(	PUNCT
ejpam-5757	61	24	φmζ	φmζ	PROPN
ejpam-5757	61	25	)	)	PUNCT
ejpam-5757	61	26	(	(	PUNCT
ejpam-5757	61	27	u	u	NOUN
ejpam-5757	61	28	)	)	PUNCT
ejpam-5757	61	29	(	(	PUNCT
ejpam-5757	61	30	1	1	X
ejpam-5757	61	31	)	)	PUNCT
ejpam-5757	61	32	exists	exist	VERB
ejpam-5757	61	33	for	for	ADP
ejpam-5757	61	34	every	every	DET
ejpam-5757	61	35	u	u	PROPN
ejpam-5757	61	36	∈	∈	PROPN
ejpam-5757	61	37	u	u	NOUN
ejpam-5757	61	38	.	.	PUNCT
ejpam-5757	62	1	furthermore	furthermore	ADV
ejpam-5757	62	2	,	,	PUNCT
ejpam-5757	62	3	the	the	DET
ejpam-5757	62	4	mapping	mapping	NOUN
ejpam-5757	62	5	χ	χ	X
ejpam-5757	62	6	:	:	PUNCT
ejpam-5757	62	7	u	u	X
ejpam-5757	62	8	→	→	SYM
ejpam-5757	62	9	v	v	NUM
ejpam-5757	62	10	defined	define	VERB
ejpam-5757	62	11	by	by	ADP
ejpam-5757	62	12	χ	χ	X
ejpam-5757	62	13	:	:	PUNCT
ejpam-5757	62	14	=	=	SYM
ejpam-5757	62	15	lim	lim	PROPN
ejpam-5757	62	16	m→+∞	m→+∞	PROPN
ejpam-5757	62	17	(	(	PUNCT
ejpam-5757	62	18	φmζ	φmζ	PROPN
ejpam-5757	62	19	)	)	PUNCT
ejpam-5757	62	20	(	(	PUNCT
ejpam-5757	62	21	u	u	NOUN
ejpam-5757	62	22	)	)	PUNCT
ejpam-5757	62	23	is	be	AUX
ejpam-5757	62	24	a	a	DET
ejpam-5757	62	25	fixed	fix	VERB
ejpam-5757	62	26	point	point	NOUN
ejpam-5757	62	27	of	of	ADP
ejpam-5757	62	28	φ	φ	PROPN
ejpam-5757	62	29	with	with	ADP
ejpam-5757	62	30	∥ζ(u)−	∥ζ(u)−	NOUN
ejpam-5757	62	31	χ(u)∥	χ(u)∥	VERB
ejpam-5757	62	32	≤	≤	NUM
ejpam-5757	62	33	ϑ∗(u	ϑ∗(u	PROPN
ejpam-5757	62	34	)	)	PUNCT
ejpam-5757	62	35	for	for	ADP
ejpam-5757	62	36	all	all	PRON
ejpam-5757	62	37	u	u	PRON
ejpam-5757	62	38	∈	∈	PROPN
ejpam-5757	62	39	u	u	NOUN
ejpam-5757	62	40	.	.	PUNCT
ejpam-5757	63	1	for	for	ADP
ejpam-5757	63	2	our	our	PRON
ejpam-5757	63	3	notational	notational	ADJ
ejpam-5757	63	4	handiness	handiness	NOUN
ejpam-5757	63	5	,	,	PUNCT
ejpam-5757	63	6	we	we	PRON
ejpam-5757	63	7	use	use	VERB
ejpam-5757	63	8	the	the	DET
ejpam-5757	63	9	abbreviation	abbreviation	NOUN
ejpam-5757	63	10	dϕ(u	dϕ(u	NOUN
ejpam-5757	63	11	,	,	PUNCT
ejpam-5757	63	12	v	v	NOUN
ejpam-5757	63	13	)	)	PUNCT
ejpam-5757	63	14	=	=	PUNCT
ejpam-5757	64	1	ϕ(u+	ϕ(u+	PROPN
ejpam-5757	65	1	3v)−	3v)−	NUM
ejpam-5757	65	2	5ϕ(2v	5ϕ(2v	NUM
ejpam-5757	65	3	+	+	CCONJ
ejpam-5757	65	4	u)−	u)−	PROPN
ejpam-5757	65	5	ϕ(u−	ϕ(u−	NUM
ejpam-5757	65	6	2v	2v	NUM
ejpam-5757	65	7	)	)	PUNCT
ejpam-5757	66	1	+	+	CCONJ
ejpam-5757	66	2	10ϕ(v	10ϕ(v	NUM
ejpam-5757	66	3	+	+	CCONJ
ejpam-5757	66	4	u	u	NOUN
ejpam-5757	66	5	)	)	PUNCT
ejpam-5757	66	6	+5ϕ(u−	+5ϕ(u−	PROPN
ejpam-5757	66	7	v)−	v)−	PROPN
ejpam-5757	66	8	10ϕ(u)−	10ϕ(u)−	NUM
ejpam-5757	66	9	120ϕ(v	120ϕ(v	NOUN
ejpam-5757	66	10	)	)	PUNCT
ejpam-5757	66	11	.	.	PUNCT
ejpam-5757	67	1	(	(	PUNCT
ejpam-5757	67	2	2	2	NUM
ejpam-5757	67	3	)	)	SYM
ejpam-5757	67	4	2	2	NUM
ejpam-5757	67	5	.	.	X
ejpam-5757	67	6	main	main	ADJ
ejpam-5757	67	7	results	result	NOUN
ejpam-5757	67	8	in	in	ADP
ejpam-5757	67	9	this	this	DET
ejpam-5757	67	10	section	section	NOUN
ejpam-5757	67	11	,	,	PUNCT
ejpam-5757	67	12	we	we	PRON
ejpam-5757	67	13	demonstrate	demonstrate	VERB
ejpam-5757	67	14	various	various	ADJ
ejpam-5757	67	15	hyperstability	hyperstability	NOUN
ejpam-5757	67	16	and	and	CCONJ
ejpam-5757	67	17	stability	stability	NOUN
ejpam-5757	67	18	of	of	ADP
ejpam-5757	67	19	(	(	PUNCT
ejpam-5757	67	20	2	2	NUM
ejpam-5757	67	21	)	)	PUNCT
ejpam-5757	67	22	in	in	ADP
ejpam-5757	67	23	banach	banach	NOUN
ejpam-5757	67	24	spaces	space	NOUN
ejpam-5757	67	25	utilizing	utilize	VERB
ejpam-5757	67	26	theorem	theorem	NOUN
ejpam-5757	67	27	2	2	NUM
ejpam-5757	67	28	.	.	PUNCT
ejpam-5757	67	29	suppose	suppose	VERB
ejpam-5757	67	30	that	that	SCONJ
ejpam-5757	67	31	u	u	PROPN
ejpam-5757	67	32	is	be	AUX
ejpam-5757	67	33	a	a	DET
ejpam-5757	67	34	normed	normed	ADJ
ejpam-5757	67	35	space	space	NOUN
ejpam-5757	67	36	along	along	ADP
ejpam-5757	67	37	with	with	ADP
ejpam-5757	67	38	u0	u0	ADJ
ejpam-5757	67	39	=	=	SYM
ejpam-5757	67	40	u\{0	u\{0	PROPN
ejpam-5757	67	41	}	}	PUNCT
ejpam-5757	67	42	and	and	CCONJ
ejpam-5757	67	43	(	(	PUNCT
ejpam-5757	67	44	v	v	NOUN
ejpam-5757	67	45	,	,	PUNCT
ejpam-5757	67	46	∥	∥	X
ejpam-5757	67	47	·	·	PUNCT
ejpam-5757	67	48	∥	∥	X
ejpam-5757	67	49	)	)	PUNCT
ejpam-5757	67	50	is	be	AUX
ejpam-5757	67	51	a	a	DET
ejpam-5757	67	52	banach	banach	NOUN
ejpam-5757	67	53	space	space	NOUN
ejpam-5757	67	54	.	.	PUNCT
ejpam-5757	68	1	theorem	theorem	NOUN
ejpam-5757	68	2	3	3	X
ejpam-5757	68	3	.	.	PUNCT
ejpam-5757	69	1	let	let	VERB
ejpam-5757	69	2	τ1	τ1	NOUN
ejpam-5757	69	3	,	,	PUNCT
ejpam-5757	69	4	τ2	τ2	NOUN
ejpam-5757	69	5	:	:	PUNCT
ejpam-5757	69	6	u0	u0	ADJ
ejpam-5757	69	7	×	×	PROPN
ejpam-5757	69	8	u0	u0	NOUN
ejpam-5757	69	9	→	→	PUNCT
ejpam-5757	69	10	r+	r+	NOUN
ejpam-5757	69	11	be	be	AUX
ejpam-5757	69	12	two	two	NUM
ejpam-5757	69	13	functions	function	NOUN
ejpam-5757	69	14	such	such	ADJ
ejpam-5757	69	15	that	that	PRON
ejpam-5757	69	16	w	w	NOUN
ejpam-5757	69	17	:	:	PUNCT
ejpam-5757	69	18	=	=	X
ejpam-5757	69	19	{	{	PUNCT
ejpam-5757	69	20	m	m	VERB
ejpam-5757	69	21	∈	∈	NOUN
ejpam-5757	69	22	n	n	NOUN
ejpam-5757	69	23	:	:	PUNCT
ejpam-5757	69	24	αm	αm	NOUN
ejpam-5757	69	25	<	<	X
ejpam-5757	69	26	1	1	NUM
ejpam-5757	69	27	}	}	PUNCT
ejpam-5757	69	28	=	=	NOUN
ejpam-5757	69	29	∅	∅	NOUN
ejpam-5757	69	30	,	,	PUNCT
ejpam-5757	69	31	where	where	SCONJ
ejpam-5757	69	32	αm	αm	ADV
ejpam-5757	69	33	:	:	PUNCT
ejpam-5757	69	34	=	=	NOUN
ejpam-5757	70	1	1	1	NUM
ejpam-5757	70	2	120	120	NUM
ejpam-5757	70	3	η1(m+	η1(m+	PROPN
ejpam-5757	70	4	3)η2(m+	3)η2(m+	NUM
ejpam-5757	70	5	3	3	NUM
ejpam-5757	70	6	)	)	PUNCT
ejpam-5757	70	7	+	+	CCONJ
ejpam-5757	70	8	1	1	NUM
ejpam-5757	70	9	120	120	NUM
ejpam-5757	70	10	η1(m−	η1(m−	NOUN
ejpam-5757	70	11	2)η2(m−	2)η2(m−	NUM
ejpam-5757	70	12	2	2	NUM
ejpam-5757	70	13	)	)	PUNCT
ejpam-5757	70	14	+	+	CCONJ
ejpam-5757	70	15	1	1	NUM
ejpam-5757	70	16	24	24	NUM
ejpam-5757	70	17	η1(m+	η1(m+	PROPN
ejpam-5757	70	18	2)η2(m+	2)η2(m+	NUM
ejpam-5757	70	19	2	2	NUM
ejpam-5757	70	20	)	)	PUNCT
ejpam-5757	70	21	+	+	CCONJ
ejpam-5757	70	22	1	1	NUM
ejpam-5757	70	23	12	12	NUM
ejpam-5757	70	24	η1(m+	η1(m+	PROPN
ejpam-5757	70	25	1)η2(m+	1)η2(m+	NUM
ejpam-5757	70	26	1	1	NUM
ejpam-5757	70	27	)	)	PUNCT
ejpam-5757	70	28	+	+	CCONJ
ejpam-5757	70	29	1	1	NUM
ejpam-5757	70	30	12	12	NUM
ejpam-5757	70	31	η1(m)η2(m	η1(m)η2(m	ADP
ejpam-5757	70	32	)	)	PUNCT
ejpam-5757	70	33	+	+	CCONJ
ejpam-5757	70	34	1	1	NUM
ejpam-5757	70	35	24	24	NUM
ejpam-5757	70	36	η1(m−	η1(m−	NOUN
ejpam-5757	70	37	1)η2(m−	1)η2(m−	DET
ejpam-5757	70	38	1	1	X
ejpam-5757	70	39	)	)	PUNCT
ejpam-5757	70	40	s.	s.	PROPN
ejpam-5757	70	41	karthikeyan	karthikeyan	PROPN
ejpam-5757	70	42	et	et	PROPN
ejpam-5757	70	43	al	al	PROPN
ejpam-5757	70	44	.	.	PUNCT
ejpam-5757	70	45	/	/	SYM
ejpam-5757	70	46	eur	eur	PROPN
ejpam-5757	70	47	.	.	PUNCT
ejpam-5757	71	1	j.	j.	PROPN
ejpam-5757	71	2	pure	pure	PROPN
ejpam-5757	71	3	appl	appl	PROPN
ejpam-5757	71	4	.	.	PROPN
ejpam-5757	71	5	math	math	PROPN
ejpam-5757	71	6	,	,	PUNCT
ejpam-5757	71	7	18	18	NUM
ejpam-5757	71	8	(	(	PUNCT
ejpam-5757	71	9	1	1	NUM
ejpam-5757	71	10	)	)	PUNCT
ejpam-5757	71	11	(	(	PUNCT
ejpam-5757	71	12	2025	2025	NUM
ejpam-5757	71	13	)	)	PUNCT
ejpam-5757	71	14	,	,	PUNCT
ejpam-5757	71	15	5757	5757	NUM
ejpam-5757	71	16	5	5	NUM
ejpam-5757	71	17	of	of	ADP
ejpam-5757	71	18	18	18	NUM
ejpam-5757	71	19	and	and	CCONJ
ejpam-5757	71	20	ηi(m	ηi(m	NUM
ejpam-5757	71	21	)	)	PUNCT
ejpam-5757	71	22	:	:	PUNCT
ejpam-5757	71	23	=	=	SYM
ejpam-5757	71	24	inf	inf	NOUN
ejpam-5757	71	25	{	{	PUNCT
ejpam-5757	71	26	l	l	NOUN
ejpam-5757	71	27	∈	∈	PROPN
ejpam-5757	71	28	r+	r+	NOUN
ejpam-5757	71	29	:	:	PUNCT
ejpam-5757	71	30	τi(mu	τi(mu	NOUN
ejpam-5757	71	31	)	)	PUNCT
ejpam-5757	71	32	≤	≤	NUM
ejpam-5757	72	1	lτi(u	lτi(u	NUM
ejpam-5757	72	2	)	)	PUNCT
ejpam-5757	72	3	,	,	PUNCT
ejpam-5757	72	4	u	u	PROPN
ejpam-5757	72	5	∈	∈	PROPN
ejpam-5757	72	6	u0	u0	PROPN
ejpam-5757	72	7	}	}	PUNCT
ejpam-5757	72	8	for	for	ADP
ejpam-5757	72	9	all	all	DET
ejpam-5757	72	10	m	m	NOUN
ejpam-5757	72	11	∈	∈	NOUN
ejpam-5757	72	12	n	n	CCONJ
ejpam-5757	72	13	,	,	PUNCT
ejpam-5757	72	14	where	where	SCONJ
ejpam-5757	72	15	i	i	PRON
ejpam-5757	72	16	=	=	NOUN
ejpam-5757	72	17	1	1	NUM
ejpam-5757	72	18	,	,	PUNCT
ejpam-5757	72	19	2	2	NUM
ejpam-5757	72	20	.	.	X
ejpam-5757	72	21	assume	assume	VERB
ejpam-5757	72	22	that	that	SCONJ
ejpam-5757	72	23	ϕ	ϕ	X
ejpam-5757	72	24	:	:	PUNCT
ejpam-5757	72	25	u	u	PROPN
ejpam-5757	72	26	→	→	SYM
ejpam-5757	72	27	v	v	PROPN
ejpam-5757	72	28	fulfills	fulfills	PROPN
ejpam-5757	72	29	∥dϕ(u	∥dϕ(u	PROPN
ejpam-5757	72	30	,	,	PUNCT
ejpam-5757	72	31	v)∥	v)∥	PUNCT
ejpam-5757	72	32	≤	≤	NUM
ejpam-5757	72	33	τ1(u)τ2(v	τ1(u)τ2(v	NUM
ejpam-5757	72	34	)	)	PUNCT
ejpam-5757	72	35	,	,	PUNCT
ejpam-5757	72	36	u	u	NOUN
ejpam-5757	72	37	,	,	PUNCT
ejpam-5757	72	38	v	v	PROPN
ejpam-5757	72	39	∈	∈	PROPN
ejpam-5757	72	40	u0	u0	NOUN
ejpam-5757	72	41	(	(	PUNCT
ejpam-5757	72	42	3	3	NUM
ejpam-5757	72	43	)	)	PUNCT
ejpam-5757	72	44	such	such	ADJ
ejpam-5757	72	45	that	that	SCONJ
ejpam-5757	72	46	3v+	3v+	NUM
ejpam-5757	72	47	u	u	NOUN
ejpam-5757	72	48	̸=	̸=	PROPN
ejpam-5757	72	49	0	0	NUM
ejpam-5757	72	50	,	,	PUNCT
ejpam-5757	72	51	2v+	2v+	NUM
ejpam-5757	72	52	u	u	NOUN
ejpam-5757	72	53	̸=	̸=	PROPN
ejpam-5757	72	54	0	0	NUM
ejpam-5757	72	55	,	,	PUNCT
ejpam-5757	72	56	u−	u−	PROPN
ejpam-5757	72	57	2v	2v	PROPN
ejpam-5757	72	58	̸=	̸=	PROPN
ejpam-5757	72	59	0	0	NUM
ejpam-5757	72	60	,	,	PUNCT
ejpam-5757	72	61	u−	u−	PROPN
ejpam-5757	72	62	v	v	ADP
ejpam-5757	72	63	̸=	̸=	PROPN
ejpam-5757	72	64	0	0	NUM
ejpam-5757	73	1	and	and	CCONJ
ejpam-5757	73	2	v+	v+	ADP
ejpam-5757	73	3	u	u	NOUN
ejpam-5757	73	4	̸=	̸=	PROPN
ejpam-5757	73	5	0	0	NUM
ejpam-5757	73	6	.	.	PUNCT
ejpam-5757	74	1	then	then	ADV
ejpam-5757	74	2	there	there	PRON
ejpam-5757	74	3	is	be	VERB
ejpam-5757	74	4	only	only	ADV
ejpam-5757	74	5	one	one	NUM
ejpam-5757	74	6	quintic	quintic	ADJ
ejpam-5757	74	7	mapping	mapping	NOUN
ejpam-5757	74	8	h	h	NOUN
ejpam-5757	74	9	:	:	PUNCT
ejpam-5757	74	10	u	u	X
ejpam-5757	74	11	→	→	SYM
ejpam-5757	74	12	v	v	ADJ
ejpam-5757	74	13	fulfilling	fulfil	VERB
ejpam-5757	74	14	∥ϕ(u)−h(u)∥	∥ϕ(u)−h(u)∥	NOUN
ejpam-5757	74	15	≤	≤	NUM
ejpam-5757	74	16	η0τ1(u)τ2(u	η0τ1(u)τ2(u	NOUN
ejpam-5757	74	17	)	)	PUNCT
ejpam-5757	74	18	for	for	ADP
ejpam-5757	74	19	all	all	DET
ejpam-5757	74	20	u	u	PROPN
ejpam-5757	74	21	∈	∈	PROPN
ejpam-5757	74	22	u0	u0	NOUN
ejpam-5757	74	23	,	,	PUNCT
ejpam-5757	74	24	where	where	SCONJ
ejpam-5757	74	25	η0	η0	ADJ
ejpam-5757	74	26	:	:	PUNCT
ejpam-5757	74	27	=	=	SYM
ejpam-5757	74	28	inf	inf	ADJ
ejpam-5757	74	29	m∈w	m∈w	NOUN
ejpam-5757	74	30	{	{	PUNCT
ejpam-5757	74	31	η1(m	η1(m	PROPN
ejpam-5757	74	32	)	)	PUNCT
ejpam-5757	74	33	120(1−	120(1−	NUM
ejpam-5757	74	34	αm	αm	NOUN
ejpam-5757	74	35	)	)	PUNCT
ejpam-5757	74	36	}	}	PUNCT
ejpam-5757	74	37	.	.	PUNCT
ejpam-5757	75	1	proof	proof	NOUN
ejpam-5757	75	2	.	.	PUNCT
ejpam-5757	76	1	replacing	replace	VERB
ejpam-5757	76	2	(	(	PUNCT
ejpam-5757	76	3	u	u	NOUN
ejpam-5757	76	4	,	,	PUNCT
ejpam-5757	76	5	v	v	NOUN
ejpam-5757	76	6	)	)	PUNCT
ejpam-5757	76	7	by	by	ADP
ejpam-5757	76	8	(	(	PUNCT
ejpam-5757	76	9	nu	nu	PROPN
ejpam-5757	76	10	,	,	PUNCT
ejpam-5757	76	11	u	u	NOUN
ejpam-5757	76	12	)	)	PUNCT
ejpam-5757	76	13	in	in	ADP
ejpam-5757	76	14	(	(	PUNCT
ejpam-5757	76	15	3	3	NUM
ejpam-5757	76	16	)	)	PUNCT
ejpam-5757	76	17	,	,	PUNCT
ejpam-5757	76	18	we	we	PRON
ejpam-5757	76	19	obtain∥∥∥∥	obtain∥∥∥∥	NOUN
ejpam-5757	76	20	1	1	NUM
ejpam-5757	76	21	120	120	NUM
ejpam-5757	77	1	ϕ((3	ϕ((3	NOUN
ejpam-5757	77	2	+	+	PUNCT
ejpam-5757	77	3	n)u)−	n)u)−	NUM
ejpam-5757	77	4	1	1	NUM
ejpam-5757	77	5	24	24	NUM
ejpam-5757	77	6	ϕ((2	ϕ((2	PROPN
ejpam-5757	77	7	+	+	CCONJ
ejpam-5757	77	8	n)u)−	n)u)−	NUM
ejpam-5757	77	9	1	1	NUM
ejpam-5757	77	10	120	120	NUM
ejpam-5757	77	11	ϕ((n−	ϕ((n−	PROPN
ejpam-5757	77	12	2)u	2)u	NUM
ejpam-5757	77	13	)	)	PUNCT
ejpam-5757	78	1	+	+	CCONJ
ejpam-5757	78	2	1	1	NUM
ejpam-5757	78	3	12	12	NUM
ejpam-5757	78	4	ϕ((1	ϕ((1	NOUN
ejpam-5757	78	5	+	+	CCONJ
ejpam-5757	78	6	n)u	n)u	ADJ
ejpam-5757	78	7	)	)	PUNCT
ejpam-5757	79	1	+	+	CCONJ
ejpam-5757	79	2	1	1	NUM
ejpam-5757	79	3	24	24	NUM
ejpam-5757	79	4	ϕ((n−	ϕ((n−	PROPN
ejpam-5757	79	5	1)u)−	1)u)−	NUM
ejpam-5757	79	6	1	1	NUM
ejpam-5757	79	7	12	12	NUM
ejpam-5757	79	8	ϕ(nu)−	ϕ(nu)−	NOUN
ejpam-5757	79	9	ϕ(u	ϕ(u	PROPN
ejpam-5757	79	10	)	)	PUNCT
ejpam-5757	79	11	∥∥∥∥	∥∥∥∥	PUNCT
ejpam-5757	80	1	≤	≤	NUM
ejpam-5757	80	2	1	1	NUM
ejpam-5757	80	3	120	120	NUM
ejpam-5757	80	4	τ1(nu)τ2(u	τ1(nu)τ2(u	NUM
ejpam-5757	80	5	)	)	PUNCT
ejpam-5757	80	6	(	(	PUNCT
ejpam-5757	80	7	4	4	X
ejpam-5757	80	8	)	)	PUNCT
ejpam-5757	80	9	for	for	ADP
ejpam-5757	80	10	all	all	DET
ejpam-5757	80	11	u	u	PROPN
ejpam-5757	80	12	∈	∈	PROPN
ejpam-5757	80	13	u0	u0	NOUN
ejpam-5757	80	14	and	and	CCONJ
ejpam-5757	80	15	all	all	DET
ejpam-5757	80	16	n	n	PRON
ejpam-5757	80	17	∈	∈	NOUN
ejpam-5757	80	18	n.	n.	NOUN
ejpam-5757	80	19	for	for	ADP
ejpam-5757	80	20	any	any	DET
ejpam-5757	80	21	n	n	PRON
ejpam-5757	80	22	∈	∈	PROPN
ejpam-5757	80	23	n	n	CCONJ
ejpam-5757	80	24	,	,	PUNCT
ejpam-5757	80	25	we	we	PRON
ejpam-5757	80	26	define	define	VERB
ejpam-5757	80	27	the	the	DET
ejpam-5757	80	28	operator	operator	NOUN
ejpam-5757	80	29	φn	φn	ADP
ejpam-5757	80	30	:	:	PUNCT
ejpam-5757	80	31	vu0	vu0	PROPN
ejpam-5757	80	32	→	→	SYM
ejpam-5757	80	33	vu0	vu0	NUM
ejpam-5757	80	34	by	by	ADP
ejpam-5757	80	35	φnψ(u	φnψ(u	PROPN
ejpam-5757	80	36	)	)	PUNCT
ejpam-5757	80	37	:	:	PUNCT
ejpam-5757	81	1	=	=	SYM
ejpam-5757	81	2	1	1	NUM
ejpam-5757	81	3	120	120	NUM
ejpam-5757	81	4	ψ((3	ψ((3	VERB
ejpam-5757	81	5	+	+	CCONJ
ejpam-5757	81	6	n)u)−	n)u)−	NUM
ejpam-5757	81	7	1	1	NUM
ejpam-5757	81	8	24	24	NUM
ejpam-5757	81	9	ψ((2	ψ((2	PROPN
ejpam-5757	81	10	+	+	NUM
ejpam-5757	81	11	n)u)−	n)u)−	NUM
ejpam-5757	81	12	1	1	NUM
ejpam-5757	81	13	120	120	NUM
ejpam-5757	81	14	ψ((n−	ψ((n−	PROPN
ejpam-5757	81	15	2)u	2)u	NUM
ejpam-5757	81	16	)	)	PUNCT
ejpam-5757	81	17	+	+	CCONJ
ejpam-5757	81	18	1	1	NUM
ejpam-5757	81	19	12	12	NUM
ejpam-5757	81	20	ψ((1	ψ((1	PROPN
ejpam-5757	81	21	+	+	CCONJ
ejpam-5757	81	22	n)u	n)u	ADJ
ejpam-5757	81	23	)	)	PUNCT
ejpam-5757	81	24	+	+	CCONJ
ejpam-5757	81	25	1	1	NUM
ejpam-5757	81	26	24	24	NUM
ejpam-5757	81	27	ψ((n−	ψ((n−	PROPN
ejpam-5757	81	28	1)u)−	1)u)−	NUM
ejpam-5757	81	29	1	1	NUM
ejpam-5757	81	30	12	12	NUM
ejpam-5757	81	31	ψ(nu	ψ(nu	NOUN
ejpam-5757	81	32	)	)	PUNCT
ejpam-5757	81	33	(	(	PUNCT
ejpam-5757	81	34	5	5	NUM
ejpam-5757	81	35	)	)	PUNCT
ejpam-5757	81	36	for	for	ADP
ejpam-5757	81	37	all	all	DET
ejpam-5757	81	38	ψ	ψ	PRON
ejpam-5757	81	39	∈	∈	PRON
ejpam-5757	81	40	vu0	vu0	PROPN
ejpam-5757	81	41	and	and	CCONJ
ejpam-5757	81	42	all	all	PRON
ejpam-5757	81	43	u	u	NOUN
ejpam-5757	81	44	∈	∈	PROPN
ejpam-5757	81	45	u0	u0	NOUN
ejpam-5757	81	46	.	.	PUNCT
ejpam-5757	82	1	moreover	moreover	ADV
ejpam-5757	82	2	,	,	PUNCT
ejpam-5757	82	3	putting	put	VERB
ejpam-5757	82	4	ϑn(u	ϑn(u	NOUN
ejpam-5757	82	5	)	)	PUNCT
ejpam-5757	82	6	:	:	PUNCT
ejpam-5757	83	1	=	=	SYM
ejpam-5757	83	2	1	1	NUM
ejpam-5757	83	3	120	120	NUM
ejpam-5757	83	4	τ1(nu)τ2(u	τ1(nu)τ2(u	NUM
ejpam-5757	83	5	)	)	PUNCT
ejpam-5757	83	6	(	(	PUNCT
ejpam-5757	83	7	6	6	NUM
ejpam-5757	83	8	)	)	PUNCT
ejpam-5757	83	9	for	for	ADP
ejpam-5757	83	10	all	all	DET
ejpam-5757	83	11	u	u	PROPN
ejpam-5757	83	12	∈	∈	PROPN
ejpam-5757	83	13	u0	u0	NOUN
ejpam-5757	83	14	,	,	PUNCT
ejpam-5757	83	15	and	and	CCONJ
ejpam-5757	83	16	observe	observe	VERB
ejpam-5757	83	17	that	that	PRON
ejpam-5757	83	18	ϑn(u	ϑn(u	NOUN
ejpam-5757	83	19	)	)	PUNCT
ejpam-5757	83	20	=	=	SYM
ejpam-5757	83	21	1	1	NUM
ejpam-5757	83	22	120	120	NUM
ejpam-5757	83	23	τ1(nu)τ2(u	τ1(nu)τ2(u	NOUN
ejpam-5757	83	24	)	)	PUNCT
ejpam-5757	83	25	≤	≤	NUM
ejpam-5757	83	26	1	1	NUM
ejpam-5757	83	27	120	120	NUM
ejpam-5757	83	28	η1(n)τ1(u)τ2(u	η1(n)τ1(u)τ2(u	PROPN
ejpam-5757	83	29	)	)	PUNCT
ejpam-5757	83	30	(	(	PUNCT
ejpam-5757	83	31	7	7	X
ejpam-5757	83	32	)	)	PUNCT
ejpam-5757	83	33	for	for	ADP
ejpam-5757	83	34	all	all	DET
ejpam-5757	83	35	u	u	PROPN
ejpam-5757	83	36	∈	∈	PROPN
ejpam-5757	83	37	u0	u0	NOUN
ejpam-5757	83	38	and	and	CCONJ
ejpam-5757	83	39	all	all	DET
ejpam-5757	83	40	n	n	PRON
ejpam-5757	83	41	∈	∈	PROPN
ejpam-5757	83	42	n.	n.	NOUN
ejpam-5757	83	43	using	use	VERB
ejpam-5757	83	44	the	the	DET
ejpam-5757	83	45	conditions	condition	NOUN
ejpam-5757	83	46	(	(	PUNCT
ejpam-5757	83	47	5	5	NUM
ejpam-5757	83	48	)	)	PUNCT
ejpam-5757	83	49	and	and	CCONJ
ejpam-5757	83	50	(	(	PUNCT
ejpam-5757	83	51	7	7	X
ejpam-5757	83	52	)	)	PUNCT
ejpam-5757	83	53	in	in	ADP
ejpam-5757	83	54	(	(	PUNCT
ejpam-5757	83	55	4	4	NUM
ejpam-5757	83	56	)	)	PUNCT
ejpam-5757	83	57	,	,	PUNCT
ejpam-5757	83	58	we	we	PRON
ejpam-5757	83	59	get	get	VERB
ejpam-5757	83	60	∥ϕ(u)−	∥ϕ(u)−	NUM
ejpam-5757	83	61	φnϕ(u)∥	φnϕ(u)∥	PROPN
ejpam-5757	83	62	≤	≤	NOUN
ejpam-5757	83	63	ϑn(u	ϑn(u	NOUN
ejpam-5757	83	64	)	)	PUNCT
ejpam-5757	83	65	for	for	ADP
ejpam-5757	83	66	all	all	DET
ejpam-5757	83	67	u	u	PROPN
ejpam-5757	83	68	∈	∈	PROPN
ejpam-5757	83	69	u0	u0	NOUN
ejpam-5757	83	70	.	.	PUNCT
ejpam-5757	84	1	moreover	moreover	ADV
ejpam-5757	84	2	,	,	PUNCT
ejpam-5757	84	3	for	for	ADP
ejpam-5757	84	4	any	any	DET
ejpam-5757	84	5	u	u	PROPN
ejpam-5757	84	6	∈	∈	PROPN
ejpam-5757	84	7	u0	u0	NOUN
ejpam-5757	84	8	and	and	CCONJ
ejpam-5757	84	9	every	every	DET
ejpam-5757	84	10	ψ	ψ	NOUN
ejpam-5757	84	11	,	,	PUNCT
ejpam-5757	84	12	ς	ς	PROPN
ejpam-5757	84	13	∈	∈	PROPN
ejpam-5757	84	14	vu0	vu0	PROPN
ejpam-5757	84	15	,	,	PUNCT
ejpam-5757	84	16	we	we	PRON
ejpam-5757	84	17	obtain	obtain	VERB
ejpam-5757	84	18	∥φnψ(u)−	∥φnψ(u)−	ADJ
ejpam-5757	84	19	φnς(u)∥	φnς(u)∥	PROPN
ejpam-5757	84	20	=	=	SYM
ejpam-5757	84	21	∥∥∥∥	∥∥∥∥	NUM
ejpam-5757	84	22	1	1	NUM
ejpam-5757	84	23	120	120	NUM
ejpam-5757	84	24	ψ((3	ψ((3	VERB
ejpam-5757	84	25	+	+	CCONJ
ejpam-5757	84	26	n)u)−	n)u)−	NUM
ejpam-5757	84	27	1	1	NUM
ejpam-5757	84	28	24	24	NUM
ejpam-5757	84	29	ψ((2	ψ((2	PROPN
ejpam-5757	84	30	+	+	NUM
ejpam-5757	84	31	n)u)−	n)u)−	NUM
ejpam-5757	84	32	1	1	NUM
ejpam-5757	84	33	120	120	NUM
ejpam-5757	84	34	ψ((n−	ψ((n−	PROPN
ejpam-5757	84	35	2)u	2)u	NUM
ejpam-5757	84	36	)	)	PUNCT
ejpam-5757	84	37	s.	s.	PROPN
ejpam-5757	84	38	karthikeyan	karthikeyan	PROPN
ejpam-5757	84	39	et	et	PROPN
ejpam-5757	84	40	al	al	PROPN
ejpam-5757	84	41	.	.	PUNCT
ejpam-5757	84	42	/	/	SYM
ejpam-5757	84	43	eur	eur	PROPN
ejpam-5757	84	44	.	.	PUNCT
ejpam-5757	85	1	j.	j.	PROPN
ejpam-5757	85	2	pure	pure	PROPN
ejpam-5757	85	3	appl	appl	PROPN
ejpam-5757	85	4	.	.	PROPN
ejpam-5757	85	5	math	math	PROPN
ejpam-5757	85	6	,	,	PUNCT
ejpam-5757	85	7	18	18	NUM
ejpam-5757	85	8	(	(	PUNCT
ejpam-5757	85	9	1	1	NUM
ejpam-5757	85	10	)	)	PUNCT
ejpam-5757	85	11	(	(	PUNCT
ejpam-5757	85	12	2025	2025	NUM
ejpam-5757	85	13	)	)	PUNCT
ejpam-5757	85	14	,	,	PUNCT
ejpam-5757	85	15	5757	5757	NUM
ejpam-5757	85	16	6	6	NUM
ejpam-5757	85	17	of	of	ADP
ejpam-5757	85	18	18	18	NUM
ejpam-5757	85	19	+	+	SYM
ejpam-5757	85	20	1	1	NUM
ejpam-5757	85	21	12	12	NUM
ejpam-5757	85	22	ψ((1	ψ((1	PROPN
ejpam-5757	85	23	+	+	CCONJ
ejpam-5757	85	24	n)u	n)u	ADJ
ejpam-5757	85	25	)	)	PUNCT
ejpam-5757	86	1	+	+	CCONJ
ejpam-5757	86	2	1	1	NUM
ejpam-5757	86	3	24	24	NUM
ejpam-5757	86	4	ψ((n−	ψ((n−	PROPN
ejpam-5757	86	5	1)u)−	1)u)−	NUM
ejpam-5757	86	6	1	1	NUM
ejpam-5757	86	7	12	12	NUM
ejpam-5757	86	8	ψ(nu	ψ(nu	NOUN
ejpam-5757	86	9	)	)	PUNCT
ejpam-5757	86	10	−	−	PROPN
ejpam-5757	86	11	1	1	NUM
ejpam-5757	86	12	120	120	NUM
ejpam-5757	86	13	ς((3	ς((3	NOUN
ejpam-5757	86	14	+	+	CCONJ
ejpam-5757	86	15	n)u	n)u	ADJ
ejpam-5757	86	16	)	)	PUNCT
ejpam-5757	86	17	+	+	CCONJ
ejpam-5757	86	18	1	1	NUM
ejpam-5757	86	19	24	24	NUM
ejpam-5757	86	20	ς((2	ς((2	PROPN
ejpam-5757	86	21	+	+	CCONJ
ejpam-5757	86	22	n)u	n)u	ADJ
ejpam-5757	86	23	)	)	PUNCT
ejpam-5757	86	24	+	+	CCONJ
ejpam-5757	86	25	1	1	NUM
ejpam-5757	86	26	120	120	NUM
ejpam-5757	86	27	ς((n−	ς((n−	PROPN
ejpam-5757	86	28	2)u	2)u	NUM
ejpam-5757	86	29	)	)	PUNCT
ejpam-5757	86	30	−	−	NOUN
ejpam-5757	86	31	1	1	NUM
ejpam-5757	86	32	12	12	NUM
ejpam-5757	87	1	ς((1	ς((1	NOUN
ejpam-5757	87	2	+	+	CCONJ
ejpam-5757	87	3	n)u)−	n)u)−	NUM
ejpam-5757	87	4	1	1	NUM
ejpam-5757	87	5	24	24	NUM
ejpam-5757	87	6	ς((n−	ς((n−	PROPN
ejpam-5757	87	7	1)u	1)u	NUM
ejpam-5757	87	8	)	)	PUNCT
ejpam-5757	87	9	+	+	CCONJ
ejpam-5757	87	10	1	1	NUM
ejpam-5757	87	11	12	12	NUM
ejpam-5757	87	12	ς(nu	ς(nu	NOUN
ejpam-5757	87	13	)	)	PUNCT
ejpam-5757	87	14	∥∥∥∥	∥∥∥∥	PUNCT
ejpam-5757	88	1	≤	≤	NUM
ejpam-5757	88	2	1	1	NUM
ejpam-5757	88	3	120	120	NUM
ejpam-5757	88	4	∥∥∥∥(ψ	∥∥∥∥(ψ	NOUN
ejpam-5757	88	5	−	−	NOUN
ejpam-5757	89	1	ς)((3	ς)((3	NOUN
ejpam-5757	89	2	+	+	CCONJ
ejpam-5757	89	3	n)u	n)u	ADJ
ejpam-5757	89	4	)	)	PUNCT
ejpam-5757	89	5	∥∥∥∥+	∥∥∥∥+	NOUN
ejpam-5757	89	6	1	1	NUM
ejpam-5757	89	7	24	24	NUM
ejpam-5757	89	8	∥∥∥∥(ψ	∥∥∥∥(ψ	NOUN
ejpam-5757	89	9	−	−	PROPN
ejpam-5757	89	10	ς)((2	ς)((2	NOUN
ejpam-5757	89	11	+	+	CCONJ
ejpam-5757	89	12	n)u	n)u	ADJ
ejpam-5757	89	13	)	)	PUNCT
ejpam-5757	89	14	∥∥∥∥	∥∥∥∥	PUNCT
ejpam-5757	90	1	+	+	CCONJ
ejpam-5757	91	1	1	1	NUM
ejpam-5757	91	2	120	120	NUM
ejpam-5757	91	3	∥∥∥∥(ψ	∥∥∥∥(ψ	NOUN
ejpam-5757	91	4	−	−	ADP
ejpam-5757	91	5	ς)((n−	ς)((n−	PROPN
ejpam-5757	91	6	2)u	2)u	NUM
ejpam-5757	91	7	)	)	PUNCT
ejpam-5757	91	8	∥∥∥∥+	∥∥∥∥+	NOUN
ejpam-5757	91	9	1	1	NUM
ejpam-5757	91	10	12	12	NUM
ejpam-5757	91	11	∥∥∥∥(ψ	∥∥∥∥(ψ	NOUN
ejpam-5757	91	12	−	−	NOUN
ejpam-5757	91	13	ς)((1	ς)((1	PROPN
ejpam-5757	91	14	+	+	CCONJ
ejpam-5757	91	15	n)u	n)u	ADJ
ejpam-5757	91	16	)	)	PUNCT
ejpam-5757	91	17	∥∥∥∥	∥∥∥∥	PUNCT
ejpam-5757	92	1	+	+	CCONJ
ejpam-5757	92	2	1	1	NUM
ejpam-5757	92	3	24	24	NUM
ejpam-5757	92	4	∥∥∥∥(ψ	∥∥∥∥(ψ	NOUN
ejpam-5757	92	5	−	−	ADP
ejpam-5757	92	6	ς)((n−	ς)((n−	PROPN
ejpam-5757	92	7	1)u	1)u	NUM
ejpam-5757	92	8	)	)	PUNCT
ejpam-5757	92	9	∥∥∥∥+	∥∥∥∥+	NOUN
ejpam-5757	92	10	1	1	NUM
ejpam-5757	92	11	12	12	NUM
ejpam-5757	92	12	∥∥∥∥(ψ	∥∥∥∥(ψ	NOUN
ejpam-5757	92	13	−	−	NOUN
ejpam-5757	92	14	ς)(nu	ς)(nu	NUM
ejpam-5757	92	15	)	)	PUNCT
ejpam-5757	92	16	∥∥∥∥.	∥∥∥∥.	NOUN
ejpam-5757	92	17	this	this	PRON
ejpam-5757	92	18	brings	bring	VERB
ejpam-5757	92	19	us	we	PRON
ejpam-5757	92	20	to	to	PART
ejpam-5757	92	21	define	define	VERB
ejpam-5757	92	22	the	the	DET
ejpam-5757	92	23	operator	operator	NOUN
ejpam-5757	92	24	υn	υn	NOUN
ejpam-5757	92	25	:	:	PUNCT
ejpam-5757	92	26	ru0×u0	ru0×u0	PROPN
ejpam-5757	92	27	+	+	PROPN
ejpam-5757	92	28	→	→	SYM
ejpam-5757	92	29	ru0×u0	ru0×u0	PROPN
ejpam-5757	92	30	+	+	CCONJ
ejpam-5757	92	31	by	by	ADP
ejpam-5757	92	32	υnδ(u	υnδ(u	NUM
ejpam-5757	92	33	)	)	PUNCT
ejpam-5757	92	34	:	:	PUNCT
ejpam-5757	93	1	=	=	NOUN
ejpam-5757	93	2	1	1	NUM
ejpam-5757	93	3	120	120	NUM
ejpam-5757	93	4	δ((3	δ((3	ADJ
ejpam-5757	93	5	+	+	NOUN
ejpam-5757	93	6	n)u	n)u	ADJ
ejpam-5757	93	7	)	)	PUNCT
ejpam-5757	93	8	+	+	CCONJ
ejpam-5757	93	9	1	1	NUM
ejpam-5757	93	10	24	24	NUM
ejpam-5757	93	11	δ((2	δ((2	PROPN
ejpam-5757	93	12	+	+	ADJ
ejpam-5757	93	13	n)u	n)u	ADJ
ejpam-5757	93	14	)	)	PUNCT
ejpam-5757	93	15	+	+	CCONJ
ejpam-5757	93	16	1	1	NUM
ejpam-5757	93	17	120	120	NUM
ejpam-5757	93	18	δ((n−	δ((n−	PROPN
ejpam-5757	93	19	2)u	2)u	NUM
ejpam-5757	93	20	)	)	PUNCT
ejpam-5757	94	1	+	+	CCONJ
ejpam-5757	94	2	1	1	NUM
ejpam-5757	94	3	12	12	NUM
ejpam-5757	94	4	δ((1	δ((1	PROPN
ejpam-5757	94	5	+	+	CCONJ
ejpam-5757	94	6	n)u	n)u	ADJ
ejpam-5757	94	7	)	)	PUNCT
ejpam-5757	95	1	+	+	CCONJ
ejpam-5757	95	2	1	1	NUM
ejpam-5757	95	3	24	24	NUM
ejpam-5757	95	4	δ((n−	δ((n−	PROPN
ejpam-5757	95	5	1)u	1)u	NUM
ejpam-5757	95	6	)	)	PUNCT
ejpam-5757	95	7	+	+	CCONJ
ejpam-5757	95	8	1	1	NUM
ejpam-5757	95	9	12	12	NUM
ejpam-5757	95	10	δ(nu	δ(nu	NOUN
ejpam-5757	95	11	)	)	PUNCT
ejpam-5757	95	12	for	for	ADP
ejpam-5757	95	13	all	all	DET
ejpam-5757	95	14	u	u	PROPN
ejpam-5757	95	15	∈	∈	PROPN
ejpam-5757	95	16	u0	u0	NOUN
ejpam-5757	95	17	and	and	CCONJ
ejpam-5757	95	18	all	all	DET
ejpam-5757	95	19	δ	δ	PROPN
ejpam-5757	95	20	∈	∈	PROPN
ejpam-5757	95	21	ru0×u0	ru0×u0	PROPN
ejpam-5757	95	22	+	+	PUNCT
ejpam-5757	95	23	.	.	PUNCT
ejpam-5757	96	1	for	for	ADP
ejpam-5757	96	2	every	every	DET
ejpam-5757	96	3	n	n	PRON
ejpam-5757	96	4	∈	∈	PROPN
ejpam-5757	96	5	n	n	CCONJ
ejpam-5757	96	6	,	,	PUNCT
ejpam-5757	96	7	the	the	DET
ejpam-5757	96	8	operator	operator	NOUN
ejpam-5757	96	9	previously	previously	ADV
ejpam-5757	96	10	defined	define	VERB
ejpam-5757	96	11	has	have	VERB
ejpam-5757	96	12	the	the	DET
ejpam-5757	96	13	form	form	NOUN
ejpam-5757	96	14	specified	specify	VERB
ejpam-5757	96	15	in	in	ADP
ejpam-5757	96	16	(	(	PUNCT
ejpam-5757	96	17	1	1	NUM
ejpam-5757	96	18	)	)	PUNCT
ejpam-5757	96	19	with	with	ADP
ejpam-5757	96	20	ϕ1(u	ϕ1(u	NOUN
ejpam-5757	96	21	)	)	PUNCT
ejpam-5757	96	22	=	=	PUNCT
ejpam-5757	96	23	(	(	PUNCT
ejpam-5757	96	24	3	3	NUM
ejpam-5757	96	25	+	+	CCONJ
ejpam-5757	96	26	n)u	n)u	ADJ
ejpam-5757	96	27	,	,	PUNCT
ejpam-5757	96	28	l1(u	l1(u	X
ejpam-5757	96	29	)	)	PUNCT
ejpam-5757	96	30	=	=	SYM
ejpam-5757	96	31	1	1	NUM
ejpam-5757	96	32	120	120	NUM
ejpam-5757	96	33	;	;	PUNCT
ejpam-5757	96	34	ϕ2(u	ϕ2(u	X
ejpam-5757	96	35	)	)	PUNCT
ejpam-5757	96	36	=	=	SYM
ejpam-5757	97	1	(	(	PUNCT
ejpam-5757	97	2	2	2	NUM
ejpam-5757	97	3	+	+	CCONJ
ejpam-5757	97	4	n)u	n)u	ADJ
ejpam-5757	97	5	,	,	PUNCT
ejpam-5757	97	6	l2(u	l2(u	PROPN
ejpam-5757	97	7	)	)	PUNCT
ejpam-5757	97	8	=	=	SYM
ejpam-5757	97	9	1	1	NUM
ejpam-5757	97	10	24	24	NUM
ejpam-5757	97	11	;	;	PUNCT
ejpam-5757	97	12	ϕ3(u	ϕ3(u	NUM
ejpam-5757	97	13	)	)	PUNCT
ejpam-5757	97	14	=	=	SYM
ejpam-5757	97	15	(	(	PUNCT
ejpam-5757	97	16	n−2)u	n−2)u	X
ejpam-5757	97	17	,	,	PUNCT
ejpam-5757	97	18	l3(u	l3(u	NOUN
ejpam-5757	97	19	)	)	PUNCT
ejpam-5757	97	20	=	=	SYM
ejpam-5757	97	21	1	1	NUM
ejpam-5757	97	22	120	120	NUM
ejpam-5757	97	23	;	;	PUNCT
ejpam-5757	97	24	ϕ4(u	ϕ4(u	X
ejpam-5757	97	25	)	)	PUNCT
ejpam-5757	97	26	=	=	SYM
ejpam-5757	97	27	(	(	PUNCT
ejpam-5757	97	28	1+n)u	1+n)u	NUM
ejpam-5757	97	29	,	,	PUNCT
ejpam-5757	97	30	l4(u	l4(u	PROPN
ejpam-5757	97	31	)	)	PUNCT
ejpam-5757	97	32	=	=	SYM
ejpam-5757	97	33	1	1	NUM
ejpam-5757	97	34	12	12	NUM
ejpam-5757	97	35	;	;	PUNCT
ejpam-5757	97	36	ϕ5(u	ϕ5(u	X
ejpam-5757	97	37	)	)	PUNCT
ejpam-5757	97	38	=	=	SYM
ejpam-5757	97	39	(	(	PUNCT
ejpam-5757	97	40	n−1)u	n−1)u	PROPN
ejpam-5757	97	41	,	,	PUNCT
ejpam-5757	97	42	l5(u	l5(u	PROPN
ejpam-5757	97	43	)	)	PUNCT
ejpam-5757	97	44	=	=	SYM
ejpam-5757	97	45	1	1	NUM
ejpam-5757	97	46	24	24	NUM
ejpam-5757	97	47	;	;	PUNCT
ejpam-5757	97	48	ϕ6(u	ϕ6(u	X
ejpam-5757	97	49	)	)	PUNCT
ejpam-5757	97	50	=	=	SYM
ejpam-5757	97	51	nu	nu	PROPN
ejpam-5757	97	52	,	,	PUNCT
ejpam-5757	97	53	l6(u	l6(u	PROPN
ejpam-5757	97	54	)	)	PUNCT
ejpam-5757	97	55	=	=	SYM
ejpam-5757	97	56	1	1	NUM
ejpam-5757	97	57	12	12	NUM
ejpam-5757	97	58	for	for	ADP
ejpam-5757	97	59	all	all	DET
ejpam-5757	97	60	u	u	PROPN
ejpam-5757	97	61	∈	∈	PROPN
ejpam-5757	97	62	u0	u0	NOUN
ejpam-5757	97	63	.	.	PUNCT
ejpam-5757	98	1	by	by	ADP
ejpam-5757	98	2	induction	induction	NOUN
ejpam-5757	98	3	,	,	PUNCT
ejpam-5757	98	4	we	we	PRON
ejpam-5757	98	5	will	will	AUX
ejpam-5757	98	6	prove	prove	VERB
ejpam-5757	98	7	that	that	SCONJ
ejpam-5757	98	8	for	for	ADP
ejpam-5757	98	9	all	all	DET
ejpam-5757	98	10	u	u	PROPN
ejpam-5757	98	11	∈	∈	PROPN
ejpam-5757	98	12	u0	u0	NOUN
ejpam-5757	98	13	,	,	PUNCT
ejpam-5757	98	14	m	m	PROPN
ejpam-5757	98	15	∈	∈	PROPN
ejpam-5757	98	16	n0	n0	NUM
ejpam-5757	98	17	,	,	PUNCT
ejpam-5757	98	18	and	and	CCONJ
ejpam-5757	98	19	n	n	NUM
ejpam-5757	98	20	∈w	∈w	NOUN
ejpam-5757	98	21	,	,	PUNCT
ejpam-5757	98	22	we	we	PRON
ejpam-5757	98	23	have	have	VERB
ejpam-5757	98	24	(	(	PUNCT
ejpam-5757	98	25	υm	υm	NOUN
ejpam-5757	98	26	n	n	PRON
ejpam-5757	98	27	ϑn	ϑn	NOUN
ejpam-5757	98	28	)	)	PUNCT
ejpam-5757	98	29	(	(	PUNCT
ejpam-5757	98	30	u	u	NOUN
ejpam-5757	98	31	)	)	PUNCT
ejpam-5757	98	32	≤	≤	NUM
ejpam-5757	99	1	1	1	NUM
ejpam-5757	99	2	120	120	NUM
ejpam-5757	99	3	η1(n)α	η1(n)α	NUM
ejpam-5757	99	4	m	m	VERB
ejpam-5757	99	5	n	n	PRON
ejpam-5757	99	6	τ1(u)τ2(u	τ1(u)τ2(u	NOUN
ejpam-5757	99	7	)	)	PUNCT
ejpam-5757	99	8	.	.	PUNCT
ejpam-5757	100	1	(	(	PUNCT
ejpam-5757	100	2	8)	8)	NUM
ejpam-5757	100	3	we	we	PRON
ejpam-5757	100	4	may	may	AUX
ejpam-5757	100	5	deduce	deduce	VERB
ejpam-5757	100	6	the	the	DET
ejpam-5757	100	7	inequality	inequality	NOUN
ejpam-5757	100	8	(	(	PUNCT
ejpam-5757	100	9	8)	8)	NUM
ejpam-5757	100	10	holds	hold	VERB
ejpam-5757	100	11	for	for	ADP
ejpam-5757	100	12	m	m	NOUN
ejpam-5757	100	13	=	=	NOUN
ejpam-5757	100	14	0	0	NUM
ejpam-5757	100	15	from	from	ADP
ejpam-5757	100	16	(	(	PUNCT
ejpam-5757	100	17	6	6	NUM
ejpam-5757	100	18	)	)	PUNCT
ejpam-5757	100	19	and	and	CCONJ
ejpam-5757	100	20	(	(	PUNCT
ejpam-5757	100	21	7	7	NUM
ejpam-5757	100	22	)	)	PUNCT
ejpam-5757	100	23	.	.	PUNCT
ejpam-5757	101	1	following	follow	VERB
ejpam-5757	101	2	that	that	PRON
ejpam-5757	101	3	,	,	PUNCT
ejpam-5757	101	4	we	we	PRON
ejpam-5757	101	5	suppose	suppose	VERB
ejpam-5757	101	6	that	that	SCONJ
ejpam-5757	101	7	(	(	PUNCT
ejpam-5757	101	8	8)	8)	NUM
ejpam-5757	101	9	is	be	AUX
ejpam-5757	101	10	true	true	ADJ
ejpam-5757	101	11	for	for	ADP
ejpam-5757	101	12	m	m	PROPN
ejpam-5757	101	13	=	=	SYM
ejpam-5757	101	14	k	k	NOUN
ejpam-5757	101	15	,	,	PUNCT
ejpam-5757	101	16	where	where	SCONJ
ejpam-5757	101	17	k	k	PROPN
ejpam-5757	101	18	∈	∈	PROPN
ejpam-5757	101	19	n.	n.	NOUN
ejpam-5757	101	20	then	then	ADV
ejpam-5757	101	21	(	(	PUNCT
ejpam-5757	101	22	υk+1	υk+1	NOUN
ejpam-5757	101	23	n	n	PRON
ejpam-5757	101	24	ϑn	ϑn	NOUN
ejpam-5757	101	25	)	)	PUNCT
ejpam-5757	101	26	(	(	PUNCT
ejpam-5757	101	27	u	u	NOUN
ejpam-5757	101	28	)	)	PUNCT
ejpam-5757	101	29	=	=	PUNCT
ejpam-5757	101	30	υn	υn	NOUN
ejpam-5757	101	31	(	(	PUNCT
ejpam-5757	101	32	(	(	PUNCT
ejpam-5757	101	33	υk	υk	VERB
ejpam-5757	101	34	nϑn	nϑn	NOUN
ejpam-5757	101	35	)	)	PUNCT
ejpam-5757	101	36	(	(	PUNCT
ejpam-5757	101	37	u	u	NOUN
ejpam-5757	101	38	)	)	PUNCT
ejpam-5757	101	39	)	)	PUNCT
ejpam-5757	102	1	=	=	PUNCT
ejpam-5757	103	1	1	1	NUM
ejpam-5757	103	2	120	120	NUM
ejpam-5757	103	3	(	(	PUNCT
ejpam-5757	103	4	υn	υn	NOUN
ejpam-5757	103	5	nϑn	nϑn	PROPN
ejpam-5757	103	6	)	)	PUNCT
ejpam-5757	103	7	(	(	PUNCT
ejpam-5757	103	8	(	(	PUNCT
ejpam-5757	103	9	3	3	NUM
ejpam-5757	103	10	+	+	NUM
ejpam-5757	103	11	n)x	n)x	ADV
ejpam-5757	103	12	)	)	PUNCT
ejpam-5757	103	13	+	+	CCONJ
ejpam-5757	103	14	1	1	NUM
ejpam-5757	103	15	24	24	NUM
ejpam-5757	103	16	(	(	PUNCT
ejpam-5757	103	17	υn	υn	NOUN
ejpam-5757	103	18	nϑn	nϑn	PROPN
ejpam-5757	103	19	)	)	PUNCT
ejpam-5757	103	20	(	(	PUNCT
ejpam-5757	103	21	(	(	PUNCT
ejpam-5757	103	22	2	2	NUM
ejpam-5757	103	23	+	+	NOUN
ejpam-5757	103	24	n)u	n)u	ADJ
ejpam-5757	103	25	)	)	PUNCT
ejpam-5757	103	26	+	+	CCONJ
ejpam-5757	103	27	1	1	NUM
ejpam-5757	103	28	120	120	NUM
ejpam-5757	103	29	(	(	PUNCT
ejpam-5757	103	30	υn	υn	NOUN
ejpam-5757	103	31	nϑn	nϑn	PROPN
ejpam-5757	103	32	)	)	PUNCT
ejpam-5757	103	33	(	(	PUNCT
ejpam-5757	103	34	(	(	PUNCT
ejpam-5757	103	35	n−	n−	NOUN
ejpam-5757	103	36	2)u	2)u	NUM
ejpam-5757	103	37	)	)	PUNCT
ejpam-5757	103	38	+	+	CCONJ
ejpam-5757	103	39	1	1	NUM
ejpam-5757	103	40	12	12	NUM
ejpam-5757	103	41	(	(	PUNCT
ejpam-5757	103	42	υn	υn	NOUN
ejpam-5757	103	43	nϑn	nϑn	PROPN
ejpam-5757	103	44	)	)	PUNCT
ejpam-5757	103	45	(	(	PUNCT
ejpam-5757	103	46	(	(	PUNCT
ejpam-5757	103	47	1	1	NUM
ejpam-5757	103	48	+	+	CCONJ
ejpam-5757	103	49	n)u	n)u	ADJ
ejpam-5757	103	50	)	)	PUNCT
ejpam-5757	103	51	+	+	CCONJ
ejpam-5757	103	52	1	1	NUM
ejpam-5757	103	53	24	24	NUM
ejpam-5757	103	54	(	(	PUNCT
ejpam-5757	103	55	υn	υn	NOUN
ejpam-5757	103	56	nϑn	nϑn	PROPN
ejpam-5757	103	57	)	)	PUNCT
ejpam-5757	103	58	(	(	PUNCT
ejpam-5757	103	59	(	(	PUNCT
ejpam-5757	103	60	n−	n−	NOUN
ejpam-5757	103	61	1)u	1)u	NOUN
ejpam-5757	103	62	)	)	PUNCT
ejpam-5757	103	63	+	+	CCONJ
ejpam-5757	103	64	1	1	NUM
ejpam-5757	103	65	12	12	NUM
ejpam-5757	103	66	(	(	PUNCT
ejpam-5757	103	67	υn	υn	NOUN
ejpam-5757	103	68	nϑn	nϑn	PROPN
ejpam-5757	103	69	)	)	PUNCT
ejpam-5757	103	70	(	(	PUNCT
ejpam-5757	103	71	nu	nu	NOUN
ejpam-5757	103	72	)	)	PUNCT
ejpam-5757	103	73	≤	≤	NOUN
ejpam-5757	103	74	1	1	NUM
ejpam-5757	103	75	120	120	NUM
ejpam-5757	103	76	(	(	PUNCT
ejpam-5757	103	77	1	1	NUM
ejpam-5757	103	78	120	120	NUM
ejpam-5757	103	79	η1(n)α	η1(n)α	ADV
ejpam-5757	104	1	k	k	X
ejpam-5757	104	2	nτ1((3	nτ1((3	X
ejpam-5757	104	3	+	+	CCONJ
ejpam-5757	104	4	n)u)τ2((3	n)u)τ2((3	ADJ
ejpam-5757	104	5	+	+	CCONJ
ejpam-5757	104	6	n)u	n)u	ADJ
ejpam-5757	104	7	)	)	PUNCT
ejpam-5757	104	8	)	)	PUNCT
ejpam-5757	105	1	+	+	CCONJ
ejpam-5757	105	2	1	1	NUM
ejpam-5757	105	3	24	24	NUM
ejpam-5757	105	4	(	(	PUNCT
ejpam-5757	105	5	1	1	NUM
ejpam-5757	105	6	120	120	NUM
ejpam-5757	105	7	η1(n)α	η1(n)α	ADV
ejpam-5757	106	1	k	k	PROPN
ejpam-5757	106	2	nτ1((2	nτ1((2	PROPN
ejpam-5757	107	1	+	+	CCONJ
ejpam-5757	107	2	n)u)τ2((2	n)u)τ2((2	X
ejpam-5757	107	3	+	+	CCONJ
ejpam-5757	107	4	n)u	n)u	ADJ
ejpam-5757	107	5	)	)	PUNCT
ejpam-5757	107	6	)	)	PUNCT
ejpam-5757	108	1	+	+	CCONJ
ejpam-5757	108	2	1	1	NUM
ejpam-5757	108	3	120	120	NUM
ejpam-5757	108	4	(	(	PUNCT
ejpam-5757	108	5	1	1	NUM
ejpam-5757	108	6	120	120	NUM
ejpam-5757	108	7	η1(n)α	η1(n)α	ADV
ejpam-5757	108	8	k	k	X
ejpam-5757	109	1	nτ1((n−	nτ1((n−	PROPN
ejpam-5757	109	2	2)u)τ2((n−	2)u)τ2((n−	NUM
ejpam-5757	109	3	2)u	2)u	NUM
ejpam-5757	109	4	)	)	PUNCT
ejpam-5757	109	5	)	)	PUNCT
ejpam-5757	110	1	s.	s.	PROPN
ejpam-5757	110	2	karthikeyan	karthikeyan	PROPN
ejpam-5757	110	3	et	et	PROPN
ejpam-5757	110	4	al	al	PROPN
ejpam-5757	110	5	.	.	PUNCT
ejpam-5757	110	6	/	/	SYM
ejpam-5757	110	7	eur	eur	PROPN
ejpam-5757	110	8	.	.	PUNCT
ejpam-5757	111	1	j.	j.	PROPN
ejpam-5757	111	2	pure	pure	PROPN
ejpam-5757	111	3	appl	appl	PROPN
ejpam-5757	111	4	.	.	PROPN
ejpam-5757	111	5	math	math	PROPN
ejpam-5757	111	6	,	,	PUNCT
ejpam-5757	111	7	18	18	NUM
ejpam-5757	111	8	(	(	PUNCT
ejpam-5757	111	9	1	1	NUM
ejpam-5757	111	10	)	)	PUNCT
ejpam-5757	111	11	(	(	PUNCT
ejpam-5757	111	12	2025	2025	NUM
ejpam-5757	111	13	)	)	PUNCT
ejpam-5757	111	14	,	,	PUNCT
ejpam-5757	111	15	5757	5757	NUM
ejpam-5757	111	16	7	7	NUM
ejpam-5757	111	17	of	of	ADP
ejpam-5757	111	18	18	18	NUM
ejpam-5757	111	19	+	+	CCONJ
ejpam-5757	111	20	1	1	NUM
ejpam-5757	111	21	12	12	NUM
ejpam-5757	111	22	(	(	PUNCT
ejpam-5757	111	23	1	1	NUM
ejpam-5757	111	24	120	120	NUM
ejpam-5757	111	25	η1(n)α	η1(n)α	PROPN
ejpam-5757	111	26	k	k	PROPN
ejpam-5757	111	27	nτ1((1	nτ1((1	PROPN
ejpam-5757	112	1	+	+	CCONJ
ejpam-5757	112	2	n)u)τ2((1	n)u)τ2((1	ADJ
ejpam-5757	112	3	+	+	CCONJ
ejpam-5757	112	4	n)u	n)u	ADJ
ejpam-5757	112	5	)	)	PUNCT
ejpam-5757	112	6	)	)	PUNCT
ejpam-5757	113	1	+	+	CCONJ
ejpam-5757	113	2	1	1	NUM
ejpam-5757	113	3	24	24	NUM
ejpam-5757	113	4	(	(	PUNCT
ejpam-5757	113	5	1	1	NUM
ejpam-5757	113	6	120	120	NUM
ejpam-5757	113	7	η1(n)α	η1(n)α	ADV
ejpam-5757	113	8	k	k	X
ejpam-5757	114	1	nτ1((n−	nτ1((n−	PROPN
ejpam-5757	114	2	1)u)τ2((n−	1)u)τ2((n−	PROPN
ejpam-5757	114	3	1)u	1)u	NUM
ejpam-5757	114	4	)	)	PUNCT
ejpam-5757	114	5	)	)	PUNCT
ejpam-5757	115	1	+	+	CCONJ
ejpam-5757	116	1	1	1	NUM
ejpam-5757	116	2	12	12	NUM
ejpam-5757	116	3	(	(	PUNCT
ejpam-5757	116	4	1	1	NUM
ejpam-5757	116	5	120	120	NUM
ejpam-5757	116	6	η1(n)α	η1(n)α	NUM
ejpam-5757	116	7	k	k	PROPN
ejpam-5757	116	8	nτ1(nu)τ2(nu	nτ1(nu)τ2(nu	PROPN
ejpam-5757	116	9	)	)	PUNCT
ejpam-5757	116	10	)	)	PUNCT
ejpam-5757	116	11	≤	≤	NUM
ejpam-5757	116	12	1	1	NUM
ejpam-5757	116	13	120	120	NUM
ejpam-5757	116	14	η1(n)α	η1(n)α	ADV
ejpam-5757	116	15	k+1	k+1	NOUN
ejpam-5757	116	16	n	n	NUM
ejpam-5757	116	17	τ1(u)τ2(u	τ1(u)τ2(u	PUNCT
ejpam-5757	116	18	)	)	PUNCT
ejpam-5757	116	19	for	for	ADP
ejpam-5757	116	20	all	all	DET
ejpam-5757	116	21	u	u	PROPN
ejpam-5757	116	22	∈	∈	PROPN
ejpam-5757	116	23	u0	u0	NOUN
ejpam-5757	116	24	and	and	CCONJ
ejpam-5757	116	25	all	all	PRON
ejpam-5757	116	26	n	n	PRON
ejpam-5757	116	27	∈	∈	PROPN
ejpam-5757	116	28	w	w	NOUN
ejpam-5757	116	29	.	.	PUNCT
ejpam-5757	117	1	thus	thus	ADV
ejpam-5757	117	2	,	,	PUNCT
ejpam-5757	117	3	for	for	ADP
ejpam-5757	117	4	m	m	PROPN
ejpam-5757	117	5	=	=	SYM
ejpam-5757	117	6	k	k	PROPN
ejpam-5757	118	1	+	+	NOUN
ejpam-5757	118	2	1	1	NUM
ejpam-5757	118	3	,	,	PUNCT
ejpam-5757	118	4	the	the	DET
ejpam-5757	118	5	inequality	inequality	NOUN
ejpam-5757	118	6	(	(	PUNCT
ejpam-5757	118	7	8)	8)	NUM
ejpam-5757	118	8	holds	hold	VERB
ejpam-5757	118	9	.	.	PUNCT
ejpam-5757	119	1	since	since	SCONJ
ejpam-5757	119	2	the	the	DET
ejpam-5757	119	3	inequality	inequality	NOUN
ejpam-5757	119	4	(	(	PUNCT
ejpam-5757	119	5	8)	8)	NUM
ejpam-5757	119	6	holds	hold	VERB
ejpam-5757	119	7	for	for	ADP
ejpam-5757	119	8	all	all	DET
ejpam-5757	119	9	m	m	PROPN
ejpam-5757	119	10	∈	∈	PROPN
ejpam-5757	119	11	n0	n0	NUM
ejpam-5757	119	12	,	,	PUNCT
ejpam-5757	119	13	we	we	PRON
ejpam-5757	119	14	may	may	AUX
ejpam-5757	119	15	obtain	obtain	VERB
ejpam-5757	119	16	this	this	DET
ejpam-5757	119	17	conclusion	conclusion	NOUN
ejpam-5757	119	18	.	.	PUNCT
ejpam-5757	120	1	thus	thus	ADV
ejpam-5757	120	2	we	we	PRON
ejpam-5757	120	3	obtain	obtain	VERB
ejpam-5757	120	4	ϑ∗n(u	ϑ∗n(u	PRON
ejpam-5757	120	5	)	)	PUNCT
ejpam-5757	120	6	=	=	PUNCT
ejpam-5757	121	1	∞∑	∞∑	NUM
ejpam-5757	121	2	m=0	m=0	PROPN
ejpam-5757	121	3	(	(	PUNCT
ejpam-5757	121	4	υm	υm	NOUN
ejpam-5757	121	5	n	n	PRON
ejpam-5757	121	6	ϑn	ϑn	NOUN
ejpam-5757	121	7	)	)	PUNCT
ejpam-5757	121	8	(	(	PUNCT
ejpam-5757	121	9	u	u	NOUN
ejpam-5757	121	10	)	)	PUNCT
ejpam-5757	121	11	≤	≤	NOUN
ejpam-5757	121	12	∑	∑	PUNCT
ejpam-5757	121	13	0≤n≤∞	0≤n≤∞	NUM
ejpam-5757	121	14	1	1	NUM
ejpam-5757	121	15	120	120	NUM
ejpam-5757	121	16	η1(n)α	η1(n)α	NUM
ejpam-5757	121	17	m	m	VERB
ejpam-5757	121	18	n	n	NUM
ejpam-5757	121	19	τ1(u)τ2(u	τ1(u)τ2(u	NOUN
ejpam-5757	121	20	)	)	PUNCT
ejpam-5757	121	21	≤	≤	NOUN
ejpam-5757	121	22	η1(n	η1(n	NOUN
ejpam-5757	121	23	)	)	PUNCT
ejpam-5757	121	24	120(1−	120(1−	NUM
ejpam-5757	121	25	αn	αn	NOUN
ejpam-5757	121	26	)	)	PUNCT
ejpam-5757	121	27	τ1(u)τ2(u	τ1(u)τ2(u	PUNCT
ejpam-5757	121	28	)	)	PUNCT
ejpam-5757	122	1	<	<	X
ejpam-5757	122	2	∞	∞	NUM
ejpam-5757	122	3	for	for	ADP
ejpam-5757	122	4	all	all	DET
ejpam-5757	122	5	u	u	PROPN
ejpam-5757	122	6	∈	∈	PROPN
ejpam-5757	122	7	u0	u0	NOUN
ejpam-5757	122	8	and	and	CCONJ
ejpam-5757	122	9	n	n	PRON
ejpam-5757	122	10	∈w	∈w	NOUN
ejpam-5757	122	11	.	.	PUNCT
ejpam-5757	123	1	therefore	therefore	ADV
ejpam-5757	123	2	,	,	PUNCT
ejpam-5757	123	3	according	accord	VERB
ejpam-5757	123	4	to	to	ADP
ejpam-5757	123	5	theorem	theorem	NOUN
ejpam-5757	123	6	2	2	NUM
ejpam-5757	123	7	,	,	PUNCT
ejpam-5757	123	8	we	we	PRON
ejpam-5757	123	9	obtain	obtain	VERB
ejpam-5757	123	10	the	the	DET
ejpam-5757	123	11	limit	limit	NOUN
ejpam-5757	123	12	mapping	mapping	NOUN
ejpam-5757	123	13	hn(u	hn(u	NOUN
ejpam-5757	123	14	)	)	PUNCT
ejpam-5757	123	15	:	:	PUNCT
ejpam-5757	123	16	=	=	SYM
ejpam-5757	123	17	lim	lim	PROPN
ejpam-5757	123	18	m→+∞	m→+∞	PROPN
ejpam-5757	123	19	(	(	PUNCT
ejpam-5757	123	20	φm	φm	PROPN
ejpam-5757	123	21	n	n	DET
ejpam-5757	123	22	ϕ	ϕ	NOUN
ejpam-5757	123	23	)	)	PUNCT
ejpam-5757	123	24	(	(	PUNCT
ejpam-5757	123	25	u	u	NOUN
ejpam-5757	123	26	)	)	PUNCT
ejpam-5757	123	27	exists	exist	VERB
ejpam-5757	123	28	for	for	ADP
ejpam-5757	123	29	each	each	DET
ejpam-5757	123	30	u	u	PROPN
ejpam-5757	123	31	∈	∈	PROPN
ejpam-5757	123	32	u0	u0	NOUN
ejpam-5757	123	33	and	and	CCONJ
ejpam-5757	123	34	n	n	PRON
ejpam-5757	123	35	∈w	∈w	NOUN
ejpam-5757	123	36	,	,	PUNCT
ejpam-5757	123	37	and	and	CCONJ
ejpam-5757	123	38	∥ϕ(u)−hn(u)∥	∥ϕ(u)−hn(u)∥	VERB
ejpam-5757	123	39	≤	≤	NUM
ejpam-5757	123	40	η1(n)τ1(u)τ2(u	η1(n)τ1(u)τ2(u	PROPN
ejpam-5757	123	41	)	)	PUNCT
ejpam-5757	123	42	120(1−	120(1−	NUM
ejpam-5757	123	43	αn	αn	NOUN
ejpam-5757	123	44	)	)	PUNCT
ejpam-5757	123	45	(	(	PUNCT
ejpam-5757	123	46	9	9	NUM
ejpam-5757	123	47	)	)	PUNCT
ejpam-5757	123	48	for	for	ADP
ejpam-5757	123	49	all	all	DET
ejpam-5757	123	50	u	u	PROPN
ejpam-5757	123	51	∈	∈	PROPN
ejpam-5757	123	52	u0	u0	NOUN
ejpam-5757	123	53	and	and	CCONJ
ejpam-5757	123	54	n	n	PRON
ejpam-5757	123	55	∈w	∈w	NOUN
ejpam-5757	123	56	.	.	PUNCT
ejpam-5757	124	1	now	now	ADV
ejpam-5757	124	2	,	,	PUNCT
ejpam-5757	124	3	we	we	PRON
ejpam-5757	124	4	will	will	AUX
ejpam-5757	124	5	prove	prove	VERB
ejpam-5757	124	6	that	that	SCONJ
ejpam-5757	124	7	hn	hn	PROPN
ejpam-5757	124	8	fulfills	fulfill	VERB
ejpam-5757	124	9	(	(	PUNCT
ejpam-5757	124	10	2	2	NUM
ejpam-5757	124	11	)	)	PUNCT
ejpam-5757	124	12	.	.	PUNCT
ejpam-5757	125	1	it	it	PRON
ejpam-5757	125	2	is	be	AUX
ejpam-5757	125	3	enough	enough	ADJ
ejpam-5757	125	4	to	to	PART
ejpam-5757	125	5	prove	prove	VERB
ejpam-5757	125	6	the	the	DET
ejpam-5757	125	7	following	follow	VERB
ejpam-5757	125	8	inequality	inequality	NOUN
ejpam-5757	125	9	∥d(φm	∥d(φm	PROPN
ejpam-5757	125	10	n	n	CCONJ
ejpam-5757	125	11	ϕ)(u	ϕ)(u	ADJ
ejpam-5757	125	12	,	,	PUNCT
ejpam-5757	125	13	v)∥	v)∥	PUNCT
ejpam-5757	125	14	≤	≤	NUM
ejpam-5757	125	15	αm	αm	NOUN
ejpam-5757	125	16	n	n	PRON
ejpam-5757	125	17	τ1(u)τ2(v	τ1(u)τ2(v	NOUN
ejpam-5757	125	18	)	)	PUNCT
ejpam-5757	125	19	,	,	PUNCT
ejpam-5757	125	20	(	(	PUNCT
ejpam-5757	125	21	10	10	NUM
ejpam-5757	125	22	)	)	PUNCT
ejpam-5757	125	23	for	for	ADP
ejpam-5757	125	24	all	all	DET
ejpam-5757	125	25	u	u	NOUN
ejpam-5757	125	26	,	,	PUNCT
ejpam-5757	125	27	v	v	PROPN
ejpam-5757	125	28	∈	∈	PROPN
ejpam-5757	125	29	u0	u0	NOUN
ejpam-5757	125	30	and	and	CCONJ
ejpam-5757	125	31	n	n	CCONJ
ejpam-5757	125	32	∈	∈	PROPN
ejpam-5757	125	33	w	w	PROPN
ejpam-5757	125	34	.	.	PUNCT
ejpam-5757	126	1	consider	consider	VERB
ejpam-5757	126	2	k	k	PROPN
ejpam-5757	126	3	∈	∈	PROPN
ejpam-5757	126	4	n	n	ADV
ejpam-5757	126	5	and	and	CCONJ
ejpam-5757	126	6	suppose	suppose	VERB
ejpam-5757	126	7	that	that	SCONJ
ejpam-5757	126	8	(	(	PUNCT
ejpam-5757	126	9	10	10	NUM
ejpam-5757	126	10	)	)	PUNCT
ejpam-5757	126	11	holds	hold	VERB
ejpam-5757	126	12	for	for	ADP
ejpam-5757	126	13	m	m	PROPN
ejpam-5757	126	14	=	=	PROPN
ejpam-5757	126	15	k.	k.	PROPN
ejpam-5757	126	16	then	then	ADV
ejpam-5757	126	17	,	,	PUNCT
ejpam-5757	126	18	for	for	ADP
ejpam-5757	126	19	each	each	DET
ejpam-5757	126	20	u	u	NOUN
ejpam-5757	126	21	,	,	PUNCT
ejpam-5757	126	22	v	v	PROPN
ejpam-5757	126	23	∈	∈	PROPN
ejpam-5757	126	24	u0	u0	NOUN
ejpam-5757	126	25	and	and	CCONJ
ejpam-5757	126	26	n	n	PRON
ejpam-5757	126	27	∈w	∈w	NOUN
ejpam-5757	126	28	,	,	PUNCT
ejpam-5757	126	29	we	we	PRON
ejpam-5757	126	30	get	get	VERB
ejpam-5757	126	31	∥∥∥d(φk+1	∥∥∥d(φk+1	PUNCT
ejpam-5757	126	32	n	n	PRON
ejpam-5757	126	33	ϕ)(u	ϕ)(u	ADJ
ejpam-5757	126	34	,	,	PUNCT
ejpam-5757	126	35	v	v	NOUN
ejpam-5757	126	36	)	)	PUNCT
ejpam-5757	126	37	∥∥∥	∥∥∥	PROPN
ejpam-5757	126	38	≤	≤	NUM
ejpam-5757	126	39	1	1	NUM
ejpam-5757	126	40	120	120	NUM
ejpam-5757	126	41	αk	αk	NOUN
ejpam-5757	126	42	nτ1((3	nτ1((3	ADJ
ejpam-5757	126	43	+	+	NOUN
ejpam-5757	126	44	n)u)τ2((3	n)u)τ2((3	ADJ
ejpam-5757	126	45	+	+	X
ejpam-5757	126	46	n)v	n)v	NOUN
ejpam-5757	126	47	)	)	PUNCT
ejpam-5757	127	1	+	+	CCONJ
ejpam-5757	127	2	1	1	NUM
ejpam-5757	127	3	24	24	NUM
ejpam-5757	127	4	αk	αk	NOUN
ejpam-5757	127	5	nτ1((2	nτ1((2	NOUN
ejpam-5757	127	6	+	+	CCONJ
ejpam-5757	127	7	n)u)τ2((2	n)u)τ2((2	X
ejpam-5757	127	8	+	+	SYM
ejpam-5757	127	9	n)v	n)v	NOUN
ejpam-5757	127	10	)	)	PUNCT
ejpam-5757	128	1	+	+	CCONJ
ejpam-5757	128	2	1	1	NUM
ejpam-5757	128	3	120	120	NUM
ejpam-5757	128	4	αk	αk	NOUN
ejpam-5757	128	5	nτ1((n−	nτ1((n−	PROPN
ejpam-5757	128	6	2)u)τ2((n−	2)u)τ2((n−	NUM
ejpam-5757	128	7	2)v	2)v	NUM
ejpam-5757	128	8	)	)	PUNCT
ejpam-5757	128	9	+	+	CCONJ
ejpam-5757	128	10	1	1	NUM
ejpam-5757	128	11	12	12	NUM
ejpam-5757	128	12	αk	αk	NOUN
ejpam-5757	128	13	nτ1((1	nτ1((1	PROPN
ejpam-5757	128	14	+	+	CCONJ
ejpam-5757	128	15	n)u)τ2((1	n)u)τ2((1	ADJ
ejpam-5757	128	16	+	+	NUM
ejpam-5757	128	17	n)v	n)v	NOUN
ejpam-5757	128	18	)	)	PUNCT
ejpam-5757	129	1	+	+	CCONJ
ejpam-5757	129	2	1	1	NUM
ejpam-5757	129	3	24	24	NUM
ejpam-5757	129	4	αk	αk	NOUN
ejpam-5757	129	5	nτ1((n−	nτ1((n−	PROPN
ejpam-5757	129	6	1)u)τ2((n−	1)u)τ2((n−	PROPN
ejpam-5757	129	7	1)v	1)v	NUM
ejpam-5757	129	8	)	)	PUNCT
ejpam-5757	130	1	+	+	CCONJ
ejpam-5757	130	2	1	1	NUM
ejpam-5757	130	3	12	12	NUM
ejpam-5757	130	4	αk	αk	NOUN
ejpam-5757	130	5	nτ1((n)u)τ2((n)v	nτ1((n)u)τ2((n)v	PROPN
ejpam-5757	130	6	)	)	PUNCT
ejpam-5757	130	7	≤	≤	NUM
ejpam-5757	130	8	αk+1	αk+1	NUM
ejpam-5757	130	9	n	n	PRON
ejpam-5757	130	10	τ1(u)τ2(v	τ1(u)τ2(v	NUM
ejpam-5757	130	11	)	)	PUNCT
ejpam-5757	130	12	.	.	PUNCT
ejpam-5757	131	1	s.	s.	PROPN
ejpam-5757	131	2	karthikeyan	karthikeyan	PROPN
ejpam-5757	131	3	et	et	PROPN
ejpam-5757	131	4	al	al	PROPN
ejpam-5757	131	5	.	.	PUNCT
ejpam-5757	131	6	/	/	SYM
ejpam-5757	131	7	eur	eur	PROPN
ejpam-5757	131	8	.	.	PUNCT
ejpam-5757	132	1	j.	j.	PROPN
ejpam-5757	132	2	pure	pure	PROPN
ejpam-5757	132	3	appl	appl	PROPN
ejpam-5757	132	4	.	.	PROPN
ejpam-5757	132	5	math	math	PROPN
ejpam-5757	132	6	,	,	PUNCT
ejpam-5757	132	7	18	18	NUM
ejpam-5757	132	8	(	(	PUNCT
ejpam-5757	132	9	1	1	NUM
ejpam-5757	132	10	)	)	PUNCT
ejpam-5757	132	11	(	(	PUNCT
ejpam-5757	132	12	2025	2025	NUM
ejpam-5757	132	13	)	)	PUNCT
ejpam-5757	132	14	,	,	PUNCT
ejpam-5757	132	15	5757	5757	NUM
ejpam-5757	132	16	8	8	NUM
ejpam-5757	132	17	of	of	ADP
ejpam-5757	132	18	18	18	NUM
ejpam-5757	132	19	by	by	ADP
ejpam-5757	132	20	induction	induction	NOUN
ejpam-5757	132	21	,	,	PUNCT
ejpam-5757	132	22	we	we	PRON
ejpam-5757	132	23	need	need	VERB
ejpam-5757	132	24	to	to	PART
ejpam-5757	132	25	prove	prove	VERB
ejpam-5757	132	26	that	that	SCONJ
ejpam-5757	132	27	(	(	PUNCT
ejpam-5757	132	28	10	10	NUM
ejpam-5757	132	29	)	)	PUNCT
ejpam-5757	132	30	holds	hold	VERB
ejpam-5757	132	31	for	for	ADP
ejpam-5757	132	32	all	all	DET
ejpam-5757	132	33	u	u	NOUN
ejpam-5757	132	34	,	,	PUNCT
ejpam-5757	132	35	v	v	NOUN
ejpam-5757	132	36	∈	∈	PROPN
ejpam-5757	132	37	u0	u0	NOUN
ejpam-5757	132	38	,	,	PUNCT
ejpam-5757	132	39	m	m	PROPN
ejpam-5757	132	40	∈	∈	PROPN
ejpam-5757	132	41	n0	n0	NUM
ejpam-5757	132	42	,	,	PUNCT
ejpam-5757	132	43	and	and	CCONJ
ejpam-5757	132	44	n	n	PRON
ejpam-5757	132	45	∈	∈	PROPN
ejpam-5757	132	46	w	w	NOUN
ejpam-5757	132	47	.	.	PUNCT
ejpam-5757	133	1	taking	take	VERB
ejpam-5757	133	2	the	the	DET
ejpam-5757	133	3	limit	limit	NOUN
ejpam-5757	133	4	m→	m→	NOUN
ejpam-5757	133	5	∞	∞	NUM
ejpam-5757	133	6	in	in	ADP
ejpam-5757	133	7	(	(	PUNCT
ejpam-5757	133	8	10	10	NUM
ejpam-5757	133	9	)	)	PUNCT
ejpam-5757	133	10	,	,	PUNCT
ejpam-5757	133	11	we	we	PRON
ejpam-5757	133	12	get	get	VERB
ejpam-5757	133	13	hn(u+	hn(u+	NOUN
ejpam-5757	133	14	3v)−	3v)−	NUM
ejpam-5757	133	15	5hn(u+	5hn(u+	NUM
ejpam-5757	133	16	2v)−hn(u−	2v)−hn(u−	NUM
ejpam-5757	133	17	2v	2v	NUM
ejpam-5757	133	18	)	)	PUNCT
ejpam-5757	134	1	+	+	CCONJ
ejpam-5757	134	2	10hn(u+	10hn(u+	NUM
ejpam-5757	134	3	v	v	NOUN
ejpam-5757	134	4	)	)	PUNCT
ejpam-5757	135	1	+5hn(u−	+5hn(u−	PROPN
ejpam-5757	135	2	v)−	v)−	PROPN
ejpam-5757	135	3	10hn(u)−	10hn(u)−	NUM
ejpam-5757	135	4	120hn(v	120hn(v	NUM
ejpam-5757	135	5	)	)	PUNCT
ejpam-5757	135	6	=	=	SYM
ejpam-5757	135	7	0	0	NUM
ejpam-5757	135	8	for	for	ADP
ejpam-5757	135	9	all	all	DET
ejpam-5757	135	10	u	u	NOUN
ejpam-5757	135	11	,	,	PUNCT
ejpam-5757	135	12	v	v	PROPN
ejpam-5757	135	13	∈	∈	PROPN
ejpam-5757	135	14	u0	u0	NOUN
ejpam-5757	135	15	such	such	ADJ
ejpam-5757	135	16	that	that	DET
ejpam-5757	135	17	3v+u	3v+u	NUM
ejpam-5757	135	18	̸=	̸=	PROPN
ejpam-5757	135	19	0	0	NUM
ejpam-5757	135	20	,	,	PUNCT
ejpam-5757	135	21	2v+u	2v+u	NUM
ejpam-5757	135	22	̸=	̸=	PROPN
ejpam-5757	135	23	0	0	NUM
ejpam-5757	135	24	,	,	PUNCT
ejpam-5757	135	25	u−2v	u−2v	ADP
ejpam-5757	135	26	̸=	̸=	PROPN
ejpam-5757	135	27	0	0	NUM
ejpam-5757	135	28	,	,	PUNCT
ejpam-5757	135	29	u−v	u−v	X
ejpam-5757	135	30	̸=	̸=	PROPN
ejpam-5757	135	31	0	0	NUM
ejpam-5757	135	32	,	,	PUNCT
ejpam-5757	135	33	v+u	v+u	CCONJ
ejpam-5757	135	34	̸=	̸=	PROPN
ejpam-5757	135	35	0	0	NUM
ejpam-5757	135	36	,	,	PUNCT
ejpam-5757	135	37	m	m	PROPN
ejpam-5757	135	38	∈	∈	NOUN
ejpam-5757	135	39	n0	n0	NUM
ejpam-5757	135	40	,	,	PUNCT
ejpam-5757	135	41	and	and	CCONJ
ejpam-5757	135	42	n	n	PRON
ejpam-5757	135	43	∈w	∈w	NOUN
ejpam-5757	135	44	.	.	PUNCT
ejpam-5757	136	1	this	this	PRON
ejpam-5757	136	2	implies	imply	VERB
ejpam-5757	136	3	that	that	SCONJ
ejpam-5757	136	4	we	we	PRON
ejpam-5757	136	5	can	can	AUX
ejpam-5757	136	6	be	be	AUX
ejpam-5757	136	7	defined	define	VERB
ejpam-5757	136	8	h	h	NOUN
ejpam-5757	136	9	:	:	PUNCT
ejpam-5757	136	10	u	u	X
ejpam-5757	136	11	→	→	SYM
ejpam-5757	136	12	v	v	NUM
ejpam-5757	136	13	which	which	PRON
ejpam-5757	136	14	fulfills	fulfill	VERB
ejpam-5757	136	15	h(u	h(u	PROPN
ejpam-5757	136	16	)	)	PUNCT
ejpam-5757	136	17	:	:	PUNCT
ejpam-5757	137	1	=	=	SYM
ejpam-5757	137	2	1	1	NUM
ejpam-5757	137	3	120	120	NUM
ejpam-5757	137	4	h((n+	h((n+	NOUN
ejpam-5757	137	5	3)u)−	3)u)−	NUM
ejpam-5757	137	6	1	1	NUM
ejpam-5757	137	7	120	120	NUM
ejpam-5757	137	8	h((n−	h((n−	PROPN
ejpam-5757	137	9	2)u)−	2)u)−	NUM
ejpam-5757	137	10	1	1	NUM
ejpam-5757	137	11	24	24	NUM
ejpam-5757	137	12	h((n+	h((n+	NOUN
ejpam-5757	137	13	2)u	2)u	NOUN
ejpam-5757	137	14	)	)	PUNCT
ejpam-5757	137	15	+	+	CCONJ
ejpam-5757	137	16	1	1	NUM
ejpam-5757	137	17	12	12	NUM
ejpam-5757	137	18	h((n+	h((n+	NOUN
ejpam-5757	137	19	1)u)−	1)u)−	NUM
ejpam-5757	137	20	1	1	NUM
ejpam-5757	137	21	12	12	NUM
ejpam-5757	137	22	h(nu	h(nu	NOUN
ejpam-5757	137	23	)	)	PUNCT
ejpam-5757	137	24	+	+	CCONJ
ejpam-5757	137	25	1	1	NUM
ejpam-5757	137	26	24	24	NUM
ejpam-5757	137	27	h((n−	h((n−	PROPN
ejpam-5757	137	28	1)u	1)u	NUM
ejpam-5757	137	29	)	)	PUNCT
ejpam-5757	137	30	,	,	PUNCT
ejpam-5757	137	31	(	(	PUNCT
ejpam-5757	137	32	11	11	NUM
ejpam-5757	137	33	)	)	PUNCT
ejpam-5757	137	34	for	for	ADP
ejpam-5757	137	35	all	all	DET
ejpam-5757	137	36	u	u	PROPN
ejpam-5757	137	37	∈	∈	PROPN
ejpam-5757	137	38	u0	u0	NOUN
ejpam-5757	137	39	and	and	CCONJ
ejpam-5757	137	40	all	all	DET
ejpam-5757	137	41	n	n	PRON
ejpam-5757	137	42	∈w	∈w	NOUN
ejpam-5757	137	43	.	.	PUNCT
ejpam-5757	138	1	next	next	ADV
ejpam-5757	138	2	,	,	PUNCT
ejpam-5757	138	3	we	we	PRON
ejpam-5757	138	4	need	need	VERB
ejpam-5757	138	5	to	to	PART
ejpam-5757	138	6	show	show	VERB
ejpam-5757	138	7	that	that	SCONJ
ejpam-5757	138	8	each	each	DET
ejpam-5757	138	9	quintic	quintic	ADJ
ejpam-5757	138	10	mapping	mapping	NOUN
ejpam-5757	138	11	h	h	NOUN
ejpam-5757	138	12	:	:	PUNCT
ejpam-5757	138	13	u	u	X
ejpam-5757	138	14	→	→	SYM
ejpam-5757	138	15	v	v	NUM
ejpam-5757	138	16	fulfills	fulfill	VERB
ejpam-5757	138	17	the	the	DET
ejpam-5757	138	18	inequality	inequality	NOUN
ejpam-5757	138	19	∥ϕ(u)−h(u)∥	∥ϕ(u)−h(u)∥	NOUN
ejpam-5757	138	20	≤	≤	NUM
ejpam-5757	138	21	lτ1(u)τ2(u	lτ1(u)τ2(u	NOUN
ejpam-5757	138	22	)	)	PUNCT
ejpam-5757	138	23	(	(	PUNCT
ejpam-5757	138	24	12	12	NUM
ejpam-5757	138	25	)	)	PUNCT
ejpam-5757	138	26	for	for	ADP
ejpam-5757	138	27	all	all	DET
ejpam-5757	138	28	u	u	PROPN
ejpam-5757	138	29	∈	∈	PROPN
ejpam-5757	138	30	u0	u0	NOUN
ejpam-5757	138	31	,	,	PUNCT
ejpam-5757	138	32	with	with	ADP
ejpam-5757	138	33	0	0	NUM
ejpam-5757	138	34	<	<	X
ejpam-5757	138	35	l	l	NOUN
ejpam-5757	138	36	,	,	PUNCT
ejpam-5757	138	37	is	be	AUX
ejpam-5757	138	38	equal	equal	ADJ
ejpam-5757	138	39	to	to	ADP
ejpam-5757	138	40	hn	hn	PROPN
ejpam-5757	138	41	for	for	ADP
ejpam-5757	138	42	every	every	DET
ejpam-5757	138	43	n	n	NOUN
ejpam-5757	138	44	∈	∈	PROPN
ejpam-5757	138	45	w	w	NOUN
ejpam-5757	138	46	.	.	PUNCT
ejpam-5757	139	1	as	as	ADP
ejpam-5757	139	2	a	a	DET
ejpam-5757	139	3	result	result	NOUN
ejpam-5757	139	4	,	,	PUNCT
ejpam-5757	139	5	we	we	PRON
ejpam-5757	139	6	set	set	VERB
ejpam-5757	139	7	n0	n0	PROPN
ejpam-5757	139	8	∈	∈	PROPN
ejpam-5757	139	9	w	w	PROPN
ejpam-5757	139	10	and	and	CCONJ
ejpam-5757	139	11	h	h	NOUN
ejpam-5757	139	12	:	:	PUNCT
ejpam-5757	139	13	u	u	X
ejpam-5757	139	14	→	→	SYM
ejpam-5757	139	15	v	v	NUM
ejpam-5757	139	16	fulfilling	fulfil	VERB
ejpam-5757	139	17	(	(	PUNCT
ejpam-5757	139	18	12	12	NUM
ejpam-5757	139	19	)	)	PUNCT
ejpam-5757	139	20	.	.	PUNCT
ejpam-5757	140	1	from	from	ADP
ejpam-5757	140	2	(	(	PUNCT
ejpam-5757	140	3	9	9	NUM
ejpam-5757	140	4	)	)	PUNCT
ejpam-5757	140	5	,	,	PUNCT
ejpam-5757	140	6	for	for	ADP
ejpam-5757	140	7	every	every	DET
ejpam-5757	140	8	u	u	PROPN
ejpam-5757	140	9	∈	∈	PROPN
ejpam-5757	140	10	u0	u0	NOUN
ejpam-5757	140	11	,	,	PUNCT
ejpam-5757	140	12	we	we	PRON
ejpam-5757	140	13	have	have	VERB
ejpam-5757	140	14	∥h(u)−hn0(u)∥	∥h(u)−hn0(u)∥	NOUN
ejpam-5757	140	15	≤	≤	ADJ
ejpam-5757	140	16	∥h(u)−	∥h(u)−	NOUN
ejpam-5757	140	17	ϕ(u)∥+	ϕ(u)∥+	ADV
ejpam-5757	141	1	∥ϕ(u)−hn0(u)∥	∥ϕ(u)−hn0(u)∥	NUM
ejpam-5757	141	2	≤	≤	NUM
ejpam-5757	141	3	lτ1(u)τ2(u	lτ1(u)τ2(u	NOUN
ejpam-5757	141	4	)	)	PUNCT
ejpam-5757	142	1	+	+	CCONJ
ejpam-5757	142	2	ϑ∗n0	ϑ∗n0	NOUN
ejpam-5757	142	3	(	(	PUNCT
ejpam-5757	142	4	u	u	NOUN
ejpam-5757	142	5	)	)	PUNCT
ejpam-5757	142	6	≤	≤	NOUN
ejpam-5757	142	7	l0τ1(u)τ2(u	l0τ1(u)τ2(u	ADP
ejpam-5757	142	8	)	)	PUNCT
ejpam-5757	143	1	∞∑	∞∑	NUM
ejpam-5757	143	2	m=0	m=0	PROPN
ejpam-5757	143	3	αm	αm	PROPN
ejpam-5757	143	4	n0	n0	PROPN
ejpam-5757	143	5	,	,	PUNCT
ejpam-5757	143	6	(	(	PUNCT
ejpam-5757	143	7	13	13	NUM
ejpam-5757	143	8	)	)	PUNCT
ejpam-5757	143	9	where	where	SCONJ
ejpam-5757	143	10	l0	l0	NOUN
ejpam-5757	143	11	:	:	PUNCT
ejpam-5757	143	12	=	=	SYM
ejpam-5757	143	13	(	(	PUNCT
ejpam-5757	143	14	1−αn0)l+	1−αn0)l+	NUM
ejpam-5757	143	15	1	1	NUM
ejpam-5757	143	16	120η1(n0	120η1(n0	NUM
ejpam-5757	143	17	)	)	PUNCT
ejpam-5757	143	18	>	>	X
ejpam-5757	143	19	0	0	PUNCT
ejpam-5757	144	1	and	and	CCONJ
ejpam-5757	144	2	we	we	PRON
ejpam-5757	144	3	exclude	exclude	VERB
ejpam-5757	144	4	the	the	DET
ejpam-5757	144	5	case	case	NOUN
ejpam-5757	144	6	that	that	SCONJ
ejpam-5757	144	7	τ1(u	τ1(u	X
ejpam-5757	144	8	)	)	PUNCT
ejpam-5757	144	9	≡	≡	PROPN
ejpam-5757	144	10	0	0	NUM
ejpam-5757	144	11	or	or	CCONJ
ejpam-5757	144	12	τ2(u	τ2(u	NUM
ejpam-5757	144	13	)	)	PUNCT
ejpam-5757	144	14	≡	≡	PROPN
ejpam-5757	144	15	0	0	NUM
ejpam-5757	144	16	which	which	PRON
ejpam-5757	144	17	is	be	AUX
ejpam-5757	144	18	trivial	trivial	ADJ
ejpam-5757	144	19	.	.	PUNCT
ejpam-5757	145	1	from	from	ADP
ejpam-5757	145	2	the	the	DET
ejpam-5757	145	3	observation	observation	NOUN
ejpam-5757	145	4	,	,	PUNCT
ejpam-5757	145	5	the	the	DET
ejpam-5757	145	6	functions	function	NOUN
ejpam-5757	145	7	h	h	NOUN
ejpam-5757	145	8	and	and	CCONJ
ejpam-5757	145	9	hn0	hn0	NOUN
ejpam-5757	145	10	are	be	AUX
ejpam-5757	145	11	the	the	DET
ejpam-5757	145	12	solutions	solution	NOUN
ejpam-5757	145	13	to	to	ADP
ejpam-5757	145	14	the	the	DET
ejpam-5757	145	15	functional	functional	ADJ
ejpam-5757	145	16	equation	equation	NOUN
ejpam-5757	145	17	(	(	PUNCT
ejpam-5757	145	18	11	11	NUM
ejpam-5757	145	19	)	)	PUNCT
ejpam-5757	145	20	for	for	ADP
ejpam-5757	145	21	every	every	DET
ejpam-5757	145	22	n	n	NOUN
ejpam-5757	145	23	∈w	∈w	NOUN
ejpam-5757	145	24	.	.	PUNCT
ejpam-5757	146	1	next	next	ADV
ejpam-5757	146	2	,	,	PUNCT
ejpam-5757	146	3	we	we	PRON
ejpam-5757	146	4	prove	prove	VERB
ejpam-5757	146	5	that	that	SCONJ
ejpam-5757	146	6	,	,	PUNCT
ejpam-5757	146	7	for	for	ADP
ejpam-5757	146	8	every	every	DET
ejpam-5757	146	9	j	j	PROPN
ejpam-5757	146	10	∈	∈	PROPN
ejpam-5757	146	11	n0	n0	PROPN
ejpam-5757	146	12	,	,	PUNCT
ejpam-5757	146	13	we	we	PRON
ejpam-5757	146	14	obtain	obtain	VERB
ejpam-5757	146	15	∥h(u)−hn0(u)∥	∥h(u)−hn0(u)∥	PROPN
ejpam-5757	146	16	≤	≤	X
ejpam-5757	146	17	l0τ1(u)τ2(u	l0τ1(u)τ2(u	ADJ
ejpam-5757	146	18	)	)	PUNCT
ejpam-5757	147	1	∞∑	∞∑	NUM
ejpam-5757	147	2	m	m	NOUN
ejpam-5757	147	3	=	=	ADJ
ejpam-5757	147	4	j	j	PROPN
ejpam-5757	147	5	α∞	α∞	NUM
ejpam-5757	147	6	n0	n0	X
ejpam-5757	147	7	(	(	PUNCT
ejpam-5757	147	8	14	14	NUM
ejpam-5757	147	9	)	)	PUNCT
ejpam-5757	147	10	for	for	ADP
ejpam-5757	147	11	all	all	DET
ejpam-5757	147	12	u	u	PROPN
ejpam-5757	147	13	∈	∈	PROPN
ejpam-5757	147	14	u0	u0	NOUN
ejpam-5757	147	15	.	.	PUNCT
ejpam-5757	148	1	the	the	DET
ejpam-5757	148	2	inequality	inequality	NOUN
ejpam-5757	148	3	(	(	PUNCT
ejpam-5757	148	4	13	13	NUM
ejpam-5757	148	5	)	)	PUNCT
ejpam-5757	148	6	is	be	AUX
ejpam-5757	148	7	valid	valid	ADJ
ejpam-5757	148	8	for	for	ADP
ejpam-5757	148	9	the	the	DET
ejpam-5757	148	10	case	case	NOUN
ejpam-5757	148	11	j	j	PROPN
ejpam-5757	148	12	=	=	SYM
ejpam-5757	148	13	0	0	PROPN
ejpam-5757	148	14	.	.	PUNCT
ejpam-5757	149	1	the	the	DET
ejpam-5757	149	2	next	next	ADJ
ejpam-5757	149	3	step	step	NOUN
ejpam-5757	149	4	is	be	AUX
ejpam-5757	149	5	to	to	PART
ejpam-5757	149	6	correct	correct	VERB
ejpam-5757	149	7	k	k	PROPN
ejpam-5757	149	8	∈	∈	PROPN
ejpam-5757	149	9	n	n	ADV
ejpam-5757	149	10	and	and	CCONJ
ejpam-5757	149	11	suppose	suppose	VERB
ejpam-5757	149	12	that	that	SCONJ
ejpam-5757	149	13	(	(	PUNCT
ejpam-5757	149	14	14	14	NUM
ejpam-5757	149	15	)	)	PUNCT
ejpam-5757	149	16	is	be	AUX
ejpam-5757	149	17	true	true	ADJ
ejpam-5757	149	18	for	for	ADP
ejpam-5757	149	19	j	j	PROPN
ejpam-5757	149	20	=	=	PROPN
ejpam-5757	149	21	k.	k.	PROPN
ejpam-5757	149	22	in	in	ADP
ejpam-5757	149	23	the	the	DET
ejpam-5757	149	24	sense	sense	NOUN
ejpam-5757	149	25	of	of	ADP
ejpam-5757	149	26	(	(	PUNCT
ejpam-5757	149	27	13	13	NUM
ejpam-5757	149	28	)	)	PUNCT
ejpam-5757	149	29	,	,	PUNCT
ejpam-5757	149	30	for	for	ADP
ejpam-5757	149	31	every	every	DET
ejpam-5757	149	32	u	u	PROPN
ejpam-5757	149	33	∈	∈	PROPN
ejpam-5757	149	34	u0	u0	NOUN
ejpam-5757	149	35	,	,	PUNCT
ejpam-5757	149	36	we	we	PRON
ejpam-5757	149	37	obtain	obtain	VERB
ejpam-5757	149	38	∥h(u)−hn0(u)∥	∥h(u)−hn0(u)∥	PROPN
ejpam-5757	149	39	≤	≤	PROPN
ejpam-5757	149	40	1	1	NUM
ejpam-5757	149	41	120	120	NUM
ejpam-5757	149	42	l0τ1((3	l0τ1((3	NUM
ejpam-5757	149	43	+	+	CCONJ
ejpam-5757	149	44	n0)u)τ2((3	n0)u)τ2((3	PROPN
ejpam-5757	149	45	+	+	CCONJ
ejpam-5757	149	46	n0)u	n0)u	NOUN
ejpam-5757	149	47	)	)	PUNCT
ejpam-5757	149	48	)	)	PUNCT
ejpam-5757	150	1	∞∑	∞∑	NUM
ejpam-5757	150	2	m	m	NOUN
ejpam-5757	150	3	=	=	PROPN
ejpam-5757	150	4	k	k	PROPN
ejpam-5757	150	5	αm	αm	PROPN
ejpam-5757	150	6	n0	n0	PROPN
ejpam-5757	150	7	+	+	CCONJ
ejpam-5757	150	8	1	1	NUM
ejpam-5757	150	9	24	24	NUM
ejpam-5757	150	10	l0τ1((2	l0τ1((2	NUM
ejpam-5757	150	11	+	+	CCONJ
ejpam-5757	150	12	n0)u)τ2((2	n0)u)τ2((2	NOUN
ejpam-5757	150	13	+	+	CCONJ
ejpam-5757	150	14	n0)u	n0)u	PROPN
ejpam-5757	150	15	)	)	PUNCT
ejpam-5757	150	16	)	)	PUNCT
ejpam-5757	151	1	∞∑	∞∑	NUM
ejpam-5757	151	2	m	m	NOUN
ejpam-5757	151	3	=	=	PROPN
ejpam-5757	151	4	k	k	PROPN
ejpam-5757	151	5	αm	αm	PROPN
ejpam-5757	151	6	n0	n0	PROPN
ejpam-5757	151	7	s.	s.	PROPN
ejpam-5757	151	8	karthikeyan	karthikeyan	PROPN
ejpam-5757	151	9	et	et	PROPN
ejpam-5757	151	10	al	al	PROPN
ejpam-5757	151	11	.	.	PUNCT
ejpam-5757	151	12	/	/	SYM
ejpam-5757	151	13	eur	eur	PROPN
ejpam-5757	151	14	.	.	PUNCT
ejpam-5757	152	1	j.	j.	PROPN
ejpam-5757	152	2	pure	pure	PROPN
ejpam-5757	152	3	appl	appl	PROPN
ejpam-5757	152	4	.	.	PROPN
ejpam-5757	152	5	math	math	PROPN
ejpam-5757	152	6	,	,	PUNCT
ejpam-5757	152	7	18	18	NUM
ejpam-5757	152	8	(	(	PUNCT
ejpam-5757	152	9	1	1	NUM
ejpam-5757	152	10	)	)	PUNCT
ejpam-5757	152	11	(	(	PUNCT
ejpam-5757	152	12	2025	2025	NUM
ejpam-5757	152	13	)	)	PUNCT
ejpam-5757	152	14	,	,	PUNCT
ejpam-5757	152	15	5757	5757	NUM
ejpam-5757	152	16	9	9	NUM
ejpam-5757	152	17	of	of	ADP
ejpam-5757	152	18	18	18	NUM
ejpam-5757	152	19	+	+	SYM
ejpam-5757	152	20	1	1	NUM
ejpam-5757	152	21	120	120	NUM
ejpam-5757	152	22	l0τ1((−2	l0τ1((−2	NOUN
ejpam-5757	152	23	+	+	CCONJ
ejpam-5757	152	24	n0)u)τ2((−2	n0)u)τ2((−2	PROPN
ejpam-5757	152	25	+	+	CCONJ
ejpam-5757	152	26	n0)u	n0)u	PROPN
ejpam-5757	152	27	)	)	PUNCT
ejpam-5757	152	28	)	)	PUNCT
ejpam-5757	153	1	∞∑	∞∑	NUM
ejpam-5757	153	2	m	m	NOUN
ejpam-5757	153	3	=	=	PROPN
ejpam-5757	153	4	k	k	PROPN
ejpam-5757	153	5	αm	αm	PROPN
ejpam-5757	153	6	n0	n0	PROPN
ejpam-5757	153	7	+	+	CCONJ
ejpam-5757	153	8	1	1	NUM
ejpam-5757	153	9	12	12	NUM
ejpam-5757	153	10	l0τ1((1	l0τ1((1	NUM
ejpam-5757	153	11	+	+	CCONJ
ejpam-5757	153	12	n0)u)τ2((1	n0)u)τ2((1	PROPN
ejpam-5757	153	13	+	+	CCONJ
ejpam-5757	153	14	n0)u	n0)u	PROPN
ejpam-5757	153	15	)	)	PUNCT
ejpam-5757	153	16	)	)	PUNCT
ejpam-5757	154	1	∞∑	∞∑	NUM
ejpam-5757	154	2	m	m	NOUN
ejpam-5757	154	3	=	=	PROPN
ejpam-5757	154	4	k	k	PROPN
ejpam-5757	154	5	αm	αm	PROPN
ejpam-5757	154	6	n0	n0	PROPN
ejpam-5757	154	7	+	+	CCONJ
ejpam-5757	154	8	1	1	NUM
ejpam-5757	154	9	24	24	NUM
ejpam-5757	154	10	l0τ1((−1	l0τ1((−1	PROPN
ejpam-5757	154	11	+	+	CCONJ
ejpam-5757	154	12	n0)u)τ2((−1	n0)u)τ2((−1	PROPN
ejpam-5757	154	13	+	+	CCONJ
ejpam-5757	154	14	n0)u	n0)u	PROPN
ejpam-5757	154	15	)	)	PUNCT
ejpam-5757	154	16	)	)	PUNCT
ejpam-5757	155	1	∞∑	∞∑	NUM
ejpam-5757	155	2	m	m	NOUN
ejpam-5757	155	3	=	=	PROPN
ejpam-5757	155	4	k	k	PROPN
ejpam-5757	155	5	αm	αm	PROPN
ejpam-5757	155	6	n0	n0	PROPN
ejpam-5757	155	7	+	+	CCONJ
ejpam-5757	155	8	1	1	NUM
ejpam-5757	155	9	12	12	NUM
ejpam-5757	155	10	l0τ1((n0)u)τ2((n0)u	l0τ1((n0)u)τ2((n0)u	PROPN
ejpam-5757	155	11	)	)	PUNCT
ejpam-5757	155	12	)	)	PUNCT
ejpam-5757	156	1	∞∑	∞∑	NUM
ejpam-5757	156	2	m	m	NOUN
ejpam-5757	156	3	=	=	PROPN
ejpam-5757	156	4	k	k	PROPN
ejpam-5757	156	5	αm	αm	PROPN
ejpam-5757	156	6	n0	n0	PROPN
ejpam-5757	156	7	≤	≤	PROPN
ejpam-5757	156	8	l0αn0τ1(u)τ2(u	l0αn0τ1(u)τ2(u	PROPN
ejpam-5757	156	9	)	)	PUNCT
ejpam-5757	156	10	∞∑	∞∑	NUM
ejpam-5757	156	11	m	m	NOUN
ejpam-5757	156	12	=	=	PROPN
ejpam-5757	156	13	k	k	PROPN
ejpam-5757	156	14	αm	αm	PROPN
ejpam-5757	156	15	n0	n0	PROPN
ejpam-5757	156	16	≤	≤	PROPN
ejpam-5757	156	17	l0τ1(u)τ2(u	l0τ1(u)τ2(u	ADJ
ejpam-5757	156	18	)	)	PUNCT
ejpam-5757	157	1	∞∑	∞∑	NUM
ejpam-5757	157	2	m	m	NOUN
ejpam-5757	157	3	=	=	ADJ
ejpam-5757	157	4	k+1	k+1	X
ejpam-5757	157	5	αm	αm	PROPN
ejpam-5757	157	6	n0	n0	PROPN
ejpam-5757	157	7	.	.	PUNCT
ejpam-5757	158	1	thus	thus	ADV
ejpam-5757	158	2	the	the	DET
ejpam-5757	158	3	condition	condition	NOUN
ejpam-5757	158	4	(	(	PUNCT
ejpam-5757	158	5	14	14	NUM
ejpam-5757	158	6	)	)	PUNCT
ejpam-5757	158	7	is	be	AUX
ejpam-5757	158	8	valid	valid	ADJ
ejpam-5757	158	9	for	for	ADP
ejpam-5757	158	10	j	j	PROPN
ejpam-5757	158	11	=	=	SYM
ejpam-5757	158	12	1	1	PROPN
ejpam-5757	158	13	+	+	NUM
ejpam-5757	158	14	k.	k.	NOUN
ejpam-5757	158	15	as	as	ADP
ejpam-5757	158	16	a	a	DET
ejpam-5757	158	17	result	result	NOUN
ejpam-5757	158	18	,	,	PUNCT
ejpam-5757	158	19	we	we	PRON
ejpam-5757	158	20	may	may	AUX
ejpam-5757	158	21	say	say	VERB
ejpam-5757	158	22	that	that	SCONJ
ejpam-5757	158	23	the	the	DET
ejpam-5757	158	24	inequality	inequality	NOUN
ejpam-5757	158	25	(	(	PUNCT
ejpam-5757	158	26	14	14	NUM
ejpam-5757	158	27	)	)	PUNCT
ejpam-5757	158	28	is	be	AUX
ejpam-5757	158	29	true	true	ADJ
ejpam-5757	158	30	for	for	ADP
ejpam-5757	158	31	all	all	DET
ejpam-5757	158	32	j	j	PROPN
ejpam-5757	158	33	∈	∈	PROPN
ejpam-5757	158	34	n0	n0	PROPN
ejpam-5757	158	35	.	.	PUNCT
ejpam-5757	159	1	taking	take	VERB
ejpam-5757	159	2	the	the	DET
ejpam-5757	159	3	limit	limit	NOUN
ejpam-5757	159	4	j	j	PROPN
ejpam-5757	159	5	→	→	SYM
ejpam-5757	159	6	∞	∞	PROPN
ejpam-5757	159	7	in	in	ADP
ejpam-5757	159	8	inequality	inequality	NOUN
ejpam-5757	159	9	(	(	PUNCT
ejpam-5757	159	10	14	14	NUM
ejpam-5757	159	11	)	)	PUNCT
ejpam-5757	159	12	,	,	PUNCT
ejpam-5757	159	13	we	we	PRON
ejpam-5757	159	14	obtain	obtain	VERB
ejpam-5757	159	15	h	h	NOUN
ejpam-5757	159	16	=	=	SYM
ejpam-5757	159	17	hn0	hn0	PROPN
ejpam-5757	159	18	.	.	PUNCT
ejpam-5757	160	1	(	(	PUNCT
ejpam-5757	160	2	15	15	NUM
ejpam-5757	160	3	)	)	PUNCT
ejpam-5757	160	4	also	also	ADV
ejpam-5757	160	5	,	,	PUNCT
ejpam-5757	160	6	in	in	ADP
ejpam-5757	160	7	view	view	NOUN
ejpam-5757	160	8	of	of	ADP
ejpam-5757	160	9	(	(	PUNCT
ejpam-5757	160	10	9	9	NUM
ejpam-5757	160	11	)	)	PUNCT
ejpam-5757	160	12	,	,	PUNCT
ejpam-5757	160	13	we	we	PRON
ejpam-5757	160	14	have	have	VERB
ejpam-5757	160	15	∥ϕ(u)−hn0(u)∥	∥ϕ(u)−hn0(u)∥	NUM
ejpam-5757	160	16	≤	≤	NUM
ejpam-5757	160	17	η1(n)τ1(u)τ2(u	η1(n)τ1(u)τ2(u	PROPN
ejpam-5757	160	18	)	)	PUNCT
ejpam-5757	160	19	120(1−	120(1−	NUM
ejpam-5757	160	20	αn	αn	NOUN
ejpam-5757	160	21	)	)	PUNCT
ejpam-5757	160	22	,	,	PUNCT
ejpam-5757	160	23	for	for	ADP
ejpam-5757	160	24	all	all	DET
ejpam-5757	160	25	u	u	PROPN
ejpam-5757	160	26	∈	∈	PROPN
ejpam-5757	160	27	u0	u0	NOUN
ejpam-5757	160	28	and	and	CCONJ
ejpam-5757	161	1	all	all	DET
ejpam-5757	161	2	n	n	PRON
ejpam-5757	161	3	∈w	∈w	NOUN
ejpam-5757	161	4	.	.	PUNCT
ejpam-5757	162	1	this	this	PRON
ejpam-5757	162	2	implies	imply	VERB
ejpam-5757	162	3	the	the	DET
ejpam-5757	162	4	condition	condition	NOUN
ejpam-5757	162	5	(	(	PUNCT
ejpam-5757	162	6	3	3	NUM
ejpam-5757	162	7	)	)	PUNCT
ejpam-5757	162	8	with	with	ADP
ejpam-5757	162	9	h	h	NOUN
ejpam-5757	162	10	=	=	SYM
ejpam-5757	162	11	hn0	hn0	PROPN
ejpam-5757	162	12	and	and	CCONJ
ejpam-5757	162	13	(	(	PUNCT
ejpam-5757	162	14	15	15	NUM
ejpam-5757	162	15	)	)	PUNCT
ejpam-5757	162	16	shows	show	VERB
ejpam-5757	162	17	the	the	DET
ejpam-5757	162	18	uniqueness	uniqueness	NOUN
ejpam-5757	162	19	of	of	ADP
ejpam-5757	162	20	h.	h.	PROPN
ejpam-5757	162	21	theorem	theorem	PROPN
ejpam-5757	162	22	4	4	X
ejpam-5757	162	23	.	.	PUNCT
ejpam-5757	163	1	let	let	VERB
ejpam-5757	163	2	τ	τ	PROPN
ejpam-5757	163	3	:	:	PUNCT
ejpam-5757	163	4	u0	u0	ADJ
ejpam-5757	163	5	×	×	PROPN
ejpam-5757	163	6	u0	u0	NOUN
ejpam-5757	163	7	→	→	PUNCT
ejpam-5757	163	8	r+	r+	PRON
ejpam-5757	163	9	be	be	AUX
ejpam-5757	163	10	a	a	DET
ejpam-5757	163	11	function	function	NOUN
ejpam-5757	163	12	such	such	ADJ
ejpam-5757	163	13	that	that	PRON
ejpam-5757	163	14	w	w	NOUN
ejpam-5757	163	15	:	:	PUNCT
ejpam-5757	163	16	=	=	X
ejpam-5757	163	17	{	{	PUNCT
ejpam-5757	163	18	m	m	VERB
ejpam-5757	163	19	∈	∈	NOUN
ejpam-5757	164	1	n	n	NOUN
ejpam-5757	164	2	:	:	PUNCT
ejpam-5757	164	3	αm	αm	NOUN
ejpam-5757	164	4	<	<	X
ejpam-5757	164	5	1	1	NUM
ejpam-5757	164	6	}	}	PUNCT
ejpam-5757	164	7	=	=	NOUN
ejpam-5757	164	8	∅	∅	NOUN
ejpam-5757	164	9	,	,	PUNCT
ejpam-5757	164	10	where	where	SCONJ
ejpam-5757	164	11	αm	αm	ADV
ejpam-5757	164	12	:	:	PUNCT
ejpam-5757	164	13	=	=	SYM
ejpam-5757	164	14	1	1	NUM
ejpam-5757	164	15	120	120	NUM
ejpam-5757	164	16	η(3	η(3	PROPN
ejpam-5757	164	17	+	+	NOUN
ejpam-5757	164	18	m	m	NOUN
ejpam-5757	164	19	)	)	PUNCT
ejpam-5757	165	1	+	+	CCONJ
ejpam-5757	165	2	1	1	NUM
ejpam-5757	165	3	24	24	NUM
ejpam-5757	165	4	η(2	η(2	PROPN
ejpam-5757	165	5	+	+	NOUN
ejpam-5757	165	6	m	m	NOUN
ejpam-5757	165	7	)	)	PUNCT
ejpam-5757	166	1	+	+	CCONJ
ejpam-5757	166	2	1	1	NUM
ejpam-5757	166	3	120	120	NUM
ejpam-5757	166	4	η(−2	η(−2	NOUN
ejpam-5757	166	5	+	+	NOUN
ejpam-5757	166	6	m	m	NOUN
ejpam-5757	166	7	)	)	PUNCT
ejpam-5757	167	1	+	+	CCONJ
ejpam-5757	167	2	1	1	NUM
ejpam-5757	167	3	12	12	NUM
ejpam-5757	167	4	η(1	η(1	PROPN
ejpam-5757	167	5	+	+	PROPN
ejpam-5757	167	6	m	m	NOUN
ejpam-5757	167	7	)	)	PUNCT
ejpam-5757	168	1	+	+	CCONJ
ejpam-5757	168	2	1	1	NUM
ejpam-5757	168	3	24	24	NUM
ejpam-5757	168	4	η(−1	η(−1	NOUN
ejpam-5757	168	5	+	+	NOUN
ejpam-5757	168	6	m	m	NOUN
ejpam-5757	168	7	)	)	PUNCT
ejpam-5757	169	1	+	+	CCONJ
ejpam-5757	169	2	1	1	NUM
ejpam-5757	169	3	12	12	NUM
ejpam-5757	169	4	η(m	η(m	NOUN
ejpam-5757	169	5	)	)	PUNCT
ejpam-5757	169	6	and	and	CCONJ
ejpam-5757	169	7	η(m	η(m	PROPN
ejpam-5757	169	8	)	)	PUNCT
ejpam-5757	169	9	:	:	PUNCT
ejpam-5757	169	10	=	=	SYM
ejpam-5757	169	11	inf	inf	NOUN
ejpam-5757	169	12	{	{	PUNCT
ejpam-5757	169	13	l	l	NOUN
ejpam-5757	169	14	∈	∈	PROPN
ejpam-5757	169	15	r+	r+	NOUN
ejpam-5757	169	16	:	:	PUNCT
ejpam-5757	169	17	τ(mu	τ(mu	NUM
ejpam-5757	169	18	)	)	PUNCT
ejpam-5757	169	19	≤	≤	NOUN
ejpam-5757	169	20	lτ(u	lτ(u	NUM
ejpam-5757	169	21	)	)	PUNCT
ejpam-5757	169	22	,	,	PUNCT
ejpam-5757	169	23	u	u	PROPN
ejpam-5757	169	24	∈	∈	PROPN
ejpam-5757	169	25	u0	u0	PROPN
ejpam-5757	169	26	}	}	PUNCT
ejpam-5757	169	27	,	,	PUNCT
ejpam-5757	169	28	(	(	PUNCT
ejpam-5757	169	29	16	16	NUM
ejpam-5757	169	30	)	)	PUNCT
ejpam-5757	169	31	for	for	ADP
ejpam-5757	169	32	every	every	DET
ejpam-5757	169	33	m	m	PROPN
ejpam-5757	169	34	∈	∈	PROPN
ejpam-5757	169	35	n.	n.	NOUN
ejpam-5757	169	36	assume	assume	VERB
ejpam-5757	169	37	that	that	SCONJ
ejpam-5757	169	38	ϕ	ϕ	X
ejpam-5757	169	39	:	:	PUNCT
ejpam-5757	169	40	u	u	PROPN
ejpam-5757	169	41	→	→	SYM
ejpam-5757	169	42	v	v	PROPN
ejpam-5757	169	43	fulfills	fulfills	PROPN
ejpam-5757	169	44	∥dϕ(u	∥dϕ(u	PROPN
ejpam-5757	169	45	,	,	PUNCT
ejpam-5757	169	46	v)∥	v)∥	PUNCT
ejpam-5757	169	47	≤	≤	X
ejpam-5757	169	48	τ(u	τ(u	ADV
ejpam-5757	169	49	)	)	PUNCT
ejpam-5757	170	1	+	+	CCONJ
ejpam-5757	170	2	τ(v	τ(v	NOUN
ejpam-5757	170	3	)	)	PUNCT
ejpam-5757	170	4	(	(	PUNCT
ejpam-5757	170	5	17	17	NUM
ejpam-5757	170	6	)	)	PUNCT
ejpam-5757	170	7	s.	s.	PROPN
ejpam-5757	170	8	karthikeyan	karthikeyan	PROPN
ejpam-5757	170	9	et	et	PROPN
ejpam-5757	170	10	al	al	PROPN
ejpam-5757	170	11	.	.	PUNCT
ejpam-5757	170	12	/	/	SYM
ejpam-5757	170	13	eur	eur	PROPN
ejpam-5757	170	14	.	.	PUNCT
ejpam-5757	171	1	j.	j.	PROPN
ejpam-5757	171	2	pure	pure	PROPN
ejpam-5757	171	3	appl	appl	PROPN
ejpam-5757	171	4	.	.	PROPN
ejpam-5757	171	5	math	math	PROPN
ejpam-5757	171	6	,	,	PUNCT
ejpam-5757	171	7	18	18	NUM
ejpam-5757	171	8	(	(	PUNCT
ejpam-5757	171	9	1	1	NUM
ejpam-5757	171	10	)	)	PUNCT
ejpam-5757	171	11	(	(	PUNCT
ejpam-5757	171	12	2025	2025	NUM
ejpam-5757	171	13	)	)	PUNCT
ejpam-5757	171	14	,	,	PUNCT
ejpam-5757	171	15	5757	5757	NUM
ejpam-5757	171	16	10	10	NUM
ejpam-5757	171	17	of	of	ADP
ejpam-5757	171	18	18	18	NUM
ejpam-5757	171	19	for	for	ADP
ejpam-5757	171	20	all	all	DET
ejpam-5757	171	21	u	u	NOUN
ejpam-5757	171	22	,	,	PUNCT
ejpam-5757	171	23	v	v	NOUN
ejpam-5757	171	24	∈	∈	PROPN
ejpam-5757	171	25	u0	u0	NOUN
ejpam-5757	171	26	,	,	PUNCT
ejpam-5757	171	27	such	such	ADJ
ejpam-5757	171	28	that	that	SCONJ
ejpam-5757	171	29	3v	3v	NUM
ejpam-5757	171	30	+	+	CCONJ
ejpam-5757	171	31	u	u	NOUN
ejpam-5757	171	32	̸=	̸=	PROPN
ejpam-5757	171	33	0	0	NUM
ejpam-5757	171	34	,	,	PUNCT
ejpam-5757	171	35	2v	2v	PROPN
ejpam-5757	171	36	+	+	CCONJ
ejpam-5757	171	37	u	u	NOUN
ejpam-5757	171	38	̸=	̸=	PROPN
ejpam-5757	171	39	0	0	NUM
ejpam-5757	171	40	,	,	PUNCT
ejpam-5757	171	41	u−	u−	PROPN
ejpam-5757	171	42	2v	2v	PROPN
ejpam-5757	171	43	̸=	̸=	PROPN
ejpam-5757	171	44	0	0	NUM
ejpam-5757	171	45	,	,	PUNCT
ejpam-5757	171	46	u−	u−	PROPN
ejpam-5757	171	47	v	v	ADP
ejpam-5757	171	48	̸=	̸=	PROPN
ejpam-5757	171	49	0	0	NUM
ejpam-5757	171	50	and	and	CCONJ
ejpam-5757	171	51	v	v	ADP
ejpam-5757	171	52	+	+	CCONJ
ejpam-5757	171	53	u	u	NOUN
ejpam-5757	171	54	̸=	̸=	PROPN
ejpam-5757	171	55	0	0	NUM
ejpam-5757	171	56	.	.	PUNCT
ejpam-5757	172	1	then	then	ADV
ejpam-5757	172	2	there	there	PRON
ejpam-5757	172	3	is	be	VERB
ejpam-5757	172	4	only	only	ADV
ejpam-5757	172	5	one	one	NUM
ejpam-5757	172	6	quintic	quintic	ADJ
ejpam-5757	172	7	mapping	mapping	NOUN
ejpam-5757	172	8	h	h	NOUN
ejpam-5757	172	9	:	:	PUNCT
ejpam-5757	172	10	u	u	X
ejpam-5757	172	11	→	→	SYM
ejpam-5757	172	12	v	v	NOUN
ejpam-5757	172	13	satisfying	satisfy	VERB
ejpam-5757	172	14	∥h(u)−	∥h(u)−	NOUN
ejpam-5757	172	15	ϕ(u)∥	ϕ(u)∥	ADJ
ejpam-5757	172	16	≤	≤	PROPN
ejpam-5757	172	17	η0τ(u	η0τ(u	PROPN
ejpam-5757	172	18	)	)	PUNCT
ejpam-5757	172	19	,	,	PUNCT
ejpam-5757	172	20	(	(	PUNCT
ejpam-5757	172	21	18	18	NUM
ejpam-5757	172	22	)	)	PUNCT
ejpam-5757	172	23	for	for	ADP
ejpam-5757	172	24	all	all	DET
ejpam-5757	172	25	u	u	PROPN
ejpam-5757	172	26	∈	∈	PROPN
ejpam-5757	172	27	u0	u0	NOUN
ejpam-5757	172	28	,	,	PUNCT
ejpam-5757	172	29	where	where	SCONJ
ejpam-5757	172	30	η0	η0	ADJ
ejpam-5757	172	31	:	:	PUNCT
ejpam-5757	172	32	=	=	SYM
ejpam-5757	172	33	inf	inf	ADJ
ejpam-5757	172	34	m∈w	m∈w	NOUN
ejpam-5757	172	35	{	{	PUNCT
ejpam-5757	172	36	1	1	NUM
ejpam-5757	172	37	+	+	CCONJ
ejpam-5757	172	38	η(m	η(m	NOUN
ejpam-5757	172	39	)	)	PUNCT
ejpam-5757	172	40	120(1−	120(1−	NUM
ejpam-5757	172	41	αm	αm	NOUN
ejpam-5757	172	42	)	)	PUNCT
ejpam-5757	172	43	}	}	PUNCT
ejpam-5757	172	44	.	.	PUNCT
ejpam-5757	173	1	proof	proof	NOUN
ejpam-5757	173	2	.	.	PUNCT
ejpam-5757	174	1	replacing	replace	VERB
ejpam-5757	174	2	(	(	PUNCT
ejpam-5757	174	3	u	u	NOUN
ejpam-5757	174	4	,	,	PUNCT
ejpam-5757	174	5	v	v	NOUN
ejpam-5757	174	6	)	)	PUNCT
ejpam-5757	174	7	by	by	ADP
ejpam-5757	174	8	(	(	PUNCT
ejpam-5757	174	9	nu	nu	PROPN
ejpam-5757	174	10	,	,	PUNCT
ejpam-5757	174	11	u	u	NOUN
ejpam-5757	174	12	)	)	PUNCT
ejpam-5757	174	13	in	in	ADP
ejpam-5757	174	14	(	(	PUNCT
ejpam-5757	174	15	17	17	NUM
ejpam-5757	174	16	)	)	PUNCT
ejpam-5757	174	17	,	,	PUNCT
ejpam-5757	174	18	we	we	PRON
ejpam-5757	174	19	have∥∥∥∥	have∥∥∥∥	VERB
ejpam-5757	174	20	1	1	NUM
ejpam-5757	174	21	120	120	NUM
ejpam-5757	175	1	ϕ((3	ϕ((3	NOUN
ejpam-5757	176	1	+	+	PUNCT
ejpam-5757	176	2	n)u)−	n)u)−	NUM
ejpam-5757	176	3	1	1	NUM
ejpam-5757	176	4	24	24	NUM
ejpam-5757	176	5	ϕ((2	ϕ((2	PROPN
ejpam-5757	176	6	+	+	CCONJ
ejpam-5757	176	7	n)u)−	n)u)−	NUM
ejpam-5757	176	8	1	1	NUM
ejpam-5757	176	9	120	120	NUM
ejpam-5757	176	10	ϕ((−2	ϕ((−2	PUNCT
ejpam-5757	176	11	+	+	CCONJ
ejpam-5757	176	12	n)u	n)u	ADJ
ejpam-5757	176	13	)	)	PUNCT
ejpam-5757	176	14	+	+	CCONJ
ejpam-5757	176	15	1	1	NUM
ejpam-5757	176	16	12	12	NUM
ejpam-5757	176	17	ϕ((1	ϕ((1	NOUN
ejpam-5757	176	18	+	+	CCONJ
ejpam-5757	176	19	n)u	n)u	ADJ
ejpam-5757	176	20	)	)	PUNCT
ejpam-5757	176	21	+	+	CCONJ
ejpam-5757	176	22	1	1	NUM
ejpam-5757	176	23	24	24	NUM
ejpam-5757	176	24	ϕ((−1	ϕ((−1	NUM
ejpam-5757	177	1	+	+	CCONJ
ejpam-5757	177	2	n)u)−	n)u)−	PUNCT
ejpam-5757	177	3	1	1	NUM
ejpam-5757	177	4	12	12	NUM
ejpam-5757	177	5	ϕ(nu)−	ϕ(nu)−	NOUN
ejpam-5757	177	6	ϕ(u	ϕ(u	PROPN
ejpam-5757	177	7	)	)	PUNCT
ejpam-5757	177	8	∥∥∥∥	∥∥∥∥	PUNCT
ejpam-5757	178	1	≤	≤	NUM
ejpam-5757	178	2	1	1	NUM
ejpam-5757	178	3	120	120	NUM
ejpam-5757	178	4	(	(	PUNCT
ejpam-5757	178	5	τ1(nu	τ1(nu	NUM
ejpam-5757	178	6	)	)	PUNCT
ejpam-5757	178	7	+	+	CCONJ
ejpam-5757	178	8	τ2(u	τ2(u	NUM
ejpam-5757	178	9	)	)	PUNCT
ejpam-5757	178	10	)	)	PUNCT
ejpam-5757	178	11	(	(	PUNCT
ejpam-5757	178	12	19	19	NUM
ejpam-5757	178	13	)	)	PUNCT
ejpam-5757	178	14	for	for	ADP
ejpam-5757	178	15	all	all	DET
ejpam-5757	178	16	u	u	PROPN
ejpam-5757	178	17	∈	∈	PROPN
ejpam-5757	178	18	u0	u0	NOUN
ejpam-5757	178	19	and	and	CCONJ
ejpam-5757	178	20	all	all	DET
ejpam-5757	178	21	n	n	PRON
ejpam-5757	178	22	∈	∈	NOUN
ejpam-5757	178	23	n.	n.	NOUN
ejpam-5757	178	24	for	for	ADP
ejpam-5757	178	25	any	any	DET
ejpam-5757	178	26	n	n	PRON
ejpam-5757	178	27	∈	∈	PROPN
ejpam-5757	178	28	n	n	CCONJ
ejpam-5757	178	29	,	,	PUNCT
ejpam-5757	178	30	we	we	PRON
ejpam-5757	178	31	define	define	VERB
ejpam-5757	178	32	the	the	DET
ejpam-5757	178	33	operator	operator	NOUN
ejpam-5757	178	34	φn	φn	ADP
ejpam-5757	178	35	:	:	PUNCT
ejpam-5757	178	36	vu0	vu0	PROPN
ejpam-5757	178	37	→	→	SYM
ejpam-5757	178	38	vu0	vu0	NUM
ejpam-5757	178	39	by	by	ADP
ejpam-5757	178	40	φnψ(u	φnψ(u	PROPN
ejpam-5757	178	41	)	)	PUNCT
ejpam-5757	178	42	:	:	PUNCT
ejpam-5757	178	43	=	=	SYM
ejpam-5757	178	44	1	1	NUM
ejpam-5757	178	45	120	120	NUM
ejpam-5757	178	46	ψ((n+	ψ((n+	NUM
ejpam-5757	178	47	3)u)−	3)u)−	NUM
ejpam-5757	178	48	1	1	NUM
ejpam-5757	178	49	24	24	NUM
ejpam-5757	178	50	ψ((n+	ψ((n+	NUM
ejpam-5757	178	51	2)u)−	2)u)−	NUM
ejpam-5757	178	52	1	1	NUM
ejpam-5757	178	53	120	120	NUM
ejpam-5757	178	54	ψ((n−	ψ((n−	PROPN
ejpam-5757	178	55	2)u	2)u	NUM
ejpam-5757	178	56	)	)	PUNCT
ejpam-5757	178	57	+	+	CCONJ
ejpam-5757	178	58	1	1	NUM
ejpam-5757	178	59	12	12	NUM
ejpam-5757	178	60	ψ((n+	ψ((n+	NOUN
ejpam-5757	178	61	1)u	1)u	NUM
ejpam-5757	178	62	)	)	PUNCT
ejpam-5757	178	63	+	+	CCONJ
ejpam-5757	178	64	1	1	NUM
ejpam-5757	178	65	24	24	NUM
ejpam-5757	178	66	ψ((n−	ψ((n−	PROPN
ejpam-5757	178	67	1)u)−	1)u)−	NUM
ejpam-5757	178	68	1	1	NUM
ejpam-5757	178	69	12	12	NUM
ejpam-5757	178	70	ψ(nu	ψ(nu	NOUN
ejpam-5757	178	71	)	)	PUNCT
ejpam-5757	178	72	for	for	ADP
ejpam-5757	178	73	all	all	DET
ejpam-5757	178	74	ψ	ψ	PRON
ejpam-5757	178	75	∈	∈	PRON
ejpam-5757	178	76	vu0	vu0	PROPN
ejpam-5757	178	77	and	and	CCONJ
ejpam-5757	178	78	all	all	PRON
ejpam-5757	178	79	u	u	NOUN
ejpam-5757	178	80	∈	∈	PROPN
ejpam-5757	178	81	u0	u0	NOUN
ejpam-5757	178	82	.	.	PUNCT
ejpam-5757	179	1	moreover	moreover	ADV
ejpam-5757	179	2	,	,	PUNCT
ejpam-5757	179	3	put	put	VERB
ejpam-5757	179	4	ϑn(u	ϑn(u	NOUN
ejpam-5757	179	5	)	)	PUNCT
ejpam-5757	179	6	:	:	PUNCT
ejpam-5757	180	1	=	=	SYM
ejpam-5757	180	2	1	1	NUM
ejpam-5757	180	3	120	120	NUM
ejpam-5757	180	4	(	(	PUNCT
ejpam-5757	180	5	τ(nu	τ(nu	NOUN
ejpam-5757	180	6	)	)	PUNCT
ejpam-5757	180	7	+	+	CCONJ
ejpam-5757	180	8	τ(u	τ(u	PROPN
ejpam-5757	180	9	)	)	PUNCT
ejpam-5757	180	10	)	)	PUNCT
ejpam-5757	180	11	,	,	PUNCT
ejpam-5757	180	12	(	(	PUNCT
ejpam-5757	180	13	20	20	NUM
ejpam-5757	180	14	)	)	PUNCT
ejpam-5757	180	15	for	for	ADP
ejpam-5757	180	16	all	all	DET
ejpam-5757	180	17	u	u	PROPN
ejpam-5757	180	18	∈	∈	PROPN
ejpam-5757	180	19	u0	u0	NOUN
ejpam-5757	180	20	,	,	PUNCT
ejpam-5757	180	21	and	and	CCONJ
ejpam-5757	180	22	observe	observe	VERB
ejpam-5757	180	23	that	that	PRON
ejpam-5757	180	24	ϑn(u	ϑn(u	NOUN
ejpam-5757	180	25	)	)	PUNCT
ejpam-5757	180	26	=	=	SYM
ejpam-5757	180	27	1	1	NUM
ejpam-5757	180	28	120	120	NUM
ejpam-5757	180	29	(	(	PUNCT
ejpam-5757	180	30	τ(nu	τ(nu	NOUN
ejpam-5757	180	31	)	)	PUNCT
ejpam-5757	180	32	+	+	CCONJ
ejpam-5757	180	33	τ(u	τ(u	PROPN
ejpam-5757	180	34	)	)	PUNCT
ejpam-5757	180	35	)	)	PUNCT
ejpam-5757	180	36	≤	≤	NUM
ejpam-5757	180	37	1	1	NUM
ejpam-5757	180	38	120	120	NUM
ejpam-5757	180	39	(	(	PUNCT
ejpam-5757	180	40	η(n	η(n	VERB
ejpam-5757	180	41	)	)	PUNCT
ejpam-5757	180	42	+	+	CCONJ
ejpam-5757	180	43	1	1	NUM
ejpam-5757	180	44	)	)	PUNCT
ejpam-5757	180	45	τ(u	τ(u	NUM
ejpam-5757	180	46	)	)	PUNCT
ejpam-5757	180	47	(	(	PUNCT
ejpam-5757	180	48	21	21	NUM
ejpam-5757	180	49	)	)	PUNCT
ejpam-5757	180	50	for	for	ADP
ejpam-5757	180	51	all	all	DET
ejpam-5757	180	52	u	u	PROPN
ejpam-5757	180	53	∈	∈	PROPN
ejpam-5757	180	54	u0	u0	NOUN
ejpam-5757	180	55	and	and	CCONJ
ejpam-5757	180	56	all	all	DET
ejpam-5757	180	57	n	n	PRON
ejpam-5757	180	58	∈	∈	PROPN
ejpam-5757	180	59	n.	n.	NOUN
ejpam-5757	180	60	the	the	DET
ejpam-5757	180	61	inequality	inequality	NOUN
ejpam-5757	180	62	(	(	PUNCT
ejpam-5757	180	63	19	19	NUM
ejpam-5757	180	64	)	)	PUNCT
ejpam-5757	180	65	,	,	PUNCT
ejpam-5757	180	66	then	then	ADV
ejpam-5757	180	67	has	have	VERB
ejpam-5757	180	68	the	the	DET
ejpam-5757	180	69	following	follow	VERB
ejpam-5757	180	70	form	form	NOUN
ejpam-5757	180	71	∥ϕ(u)−	∥ϕ(u)−	NUM
ejpam-5757	180	72	φnϕ(u)∥	φnϕ(u)∥	PROPN
ejpam-5757	180	73	≤	≤	NOUN
ejpam-5757	180	74	ϑn(u	ϑn(u	NOUN
ejpam-5757	180	75	)	)	PUNCT
ejpam-5757	180	76	for	for	ADP
ejpam-5757	180	77	all	all	DET
ejpam-5757	180	78	u	u	PROPN
ejpam-5757	180	79	∈	∈	PROPN
ejpam-5757	180	80	u0	u0	NOUN
ejpam-5757	180	81	.	.	PUNCT
ejpam-5757	181	1	moreover	moreover	ADV
ejpam-5757	181	2	,	,	PUNCT
ejpam-5757	181	3	for	for	ADP
ejpam-5757	181	4	any	any	DET
ejpam-5757	181	5	u	u	PROPN
ejpam-5757	181	6	∈	∈	PROPN
ejpam-5757	181	7	u0	u0	NOUN
ejpam-5757	181	8	and	and	CCONJ
ejpam-5757	181	9	every	every	DET
ejpam-5757	181	10	ψ	ψ	NOUN
ejpam-5757	181	11	,	,	PUNCT
ejpam-5757	181	12	ς	ς	PROPN
ejpam-5757	181	13	∈	∈	PROPN
ejpam-5757	181	14	vu0	vu0	PROPN
ejpam-5757	181	15	,	,	PUNCT
ejpam-5757	181	16	we	we	PRON
ejpam-5757	181	17	obtain	obtain	VERB
ejpam-5757	181	18	∥φnψ(u)−	∥φnψ(u)−	NOUN
ejpam-5757	181	19	φnς(u)∥	φnς(u)∥	ADJ
ejpam-5757	181	20	≤	≤	NUM
ejpam-5757	181	21	1	1	NUM
ejpam-5757	181	22	120	120	NUM
ejpam-5757	181	23	∥∥∥∥(ψ	∥∥∥∥(ψ	NOUN
ejpam-5757	181	24	−	−	PROPN
ejpam-5757	181	25	ς)((n+	ς)((n+	ADJ
ejpam-5757	181	26	3)u	3)u	NUM
ejpam-5757	181	27	)	)	PUNCT
ejpam-5757	181	28	∥∥∥∥+	∥∥∥∥+	NOUN
ejpam-5757	181	29	1	1	NUM
ejpam-5757	181	30	24	24	NUM
ejpam-5757	181	31	∥∥∥∥(ψ	∥∥∥∥(ψ	NOUN
ejpam-5757	181	32	−	−	PROPN
ejpam-5757	181	33	ς)((n+	ς)((n+	ADJ
ejpam-5757	181	34	2)u	2)u	NOUN
ejpam-5757	181	35	)	)	PUNCT
ejpam-5757	181	36	∥∥∥∥	∥∥∥∥	PUNCT
ejpam-5757	182	1	+	+	CCONJ
ejpam-5757	183	1	1	1	NUM
ejpam-5757	183	2	120	120	NUM
ejpam-5757	183	3	∥∥∥∥(ψ	∥∥∥∥(ψ	NOUN
ejpam-5757	183	4	−	−	ADP
ejpam-5757	183	5	ς)((n−	ς)((n−	PROPN
ejpam-5757	183	6	2)u	2)u	NUM
ejpam-5757	183	7	)	)	PUNCT
ejpam-5757	183	8	∥∥∥∥+	∥∥∥∥+	NOUN
ejpam-5757	183	9	1	1	NUM
ejpam-5757	183	10	12	12	NUM
ejpam-5757	183	11	∥∥∥∥(ψ	∥∥∥∥(ψ	NOUN
ejpam-5757	183	12	−	−	PROPN
ejpam-5757	183	13	ς)((n+	ς)((n+	PROPN
ejpam-5757	183	14	1)u	1)u	NOUN
ejpam-5757	183	15	)	)	PUNCT
ejpam-5757	183	16	∥∥∥∥	∥∥∥∥	PUNCT
ejpam-5757	184	1	+	+	CCONJ
ejpam-5757	184	2	1	1	NUM
ejpam-5757	184	3	24	24	NUM
ejpam-5757	184	4	∥∥∥∥(ψ	∥∥∥∥(ψ	NOUN
ejpam-5757	184	5	−	−	ADP
ejpam-5757	184	6	ς)((n−	ς)((n−	PROPN
ejpam-5757	184	7	1)u	1)u	NUM
ejpam-5757	184	8	)	)	PUNCT
ejpam-5757	184	9	∥∥∥∥+	∥∥∥∥+	NOUN
ejpam-5757	184	10	1	1	NUM
ejpam-5757	184	11	12	12	NUM
ejpam-5757	184	12	∥∥∥∥(ψ	∥∥∥∥(ψ	NOUN
ejpam-5757	184	13	−	−	NOUN
ejpam-5757	184	14	ς)(nu	ς)(nu	NUM
ejpam-5757	184	15	)	)	PUNCT
ejpam-5757	184	16	∥∥∥∥.	∥∥∥∥.	NOUN
ejpam-5757	184	17	this	this	PRON
ejpam-5757	184	18	brings	bring	VERB
ejpam-5757	184	19	us	we	PRON
ejpam-5757	184	20	to	to	PART
ejpam-5757	184	21	define	define	VERB
ejpam-5757	184	22	the	the	DET
ejpam-5757	184	23	operator	operator	NOUN
ejpam-5757	184	24	υn	υn	NOUN
ejpam-5757	184	25	:	:	PUNCT
ejpam-5757	184	26	ru0×u0	ru0×u0	PROPN
ejpam-5757	184	27	+	+	PROPN
ejpam-5757	184	28	→	→	SYM
ejpam-5757	184	29	ru0×u0	ru0×u0	PROPN
ejpam-5757	184	30	+	+	CCONJ
ejpam-5757	184	31	by	by	ADP
ejpam-5757	184	32	υnδ(u	υnδ(u	NUM
ejpam-5757	184	33	)	)	PUNCT
ejpam-5757	184	34	:	:	PUNCT
ejpam-5757	185	1	=	=	SYM
ejpam-5757	185	2	1	1	NUM
ejpam-5757	185	3	120	120	NUM
ejpam-5757	185	4	δ((n+	δ((n+	NOUN
ejpam-5757	185	5	3)u	3)u	NUM
ejpam-5757	185	6	)	)	PUNCT
ejpam-5757	186	1	+	+	CCONJ
ejpam-5757	186	2	1	1	NUM
ejpam-5757	186	3	24	24	NUM
ejpam-5757	186	4	δ((n+	δ((n+	NOUN
ejpam-5757	186	5	2)u	2)u	NUM
ejpam-5757	186	6	)	)	PUNCT
ejpam-5757	187	1	+	+	CCONJ
ejpam-5757	187	2	1	1	NUM
ejpam-5757	187	3	120	120	NUM
ejpam-5757	187	4	δ((n−	δ((n−	PROPN
ejpam-5757	187	5	2)u	2)u	NUM
ejpam-5757	187	6	)	)	PUNCT
ejpam-5757	188	1	s.	s.	PROPN
ejpam-5757	188	2	karthikeyan	karthikeyan	PROPN
ejpam-5757	188	3	et	et	PROPN
ejpam-5757	188	4	al	al	PROPN
ejpam-5757	188	5	.	.	PUNCT
ejpam-5757	188	6	/	/	SYM
ejpam-5757	188	7	eur	eur	PROPN
ejpam-5757	188	8	.	.	PUNCT
ejpam-5757	189	1	j.	j.	PROPN
ejpam-5757	189	2	pure	pure	PROPN
ejpam-5757	189	3	appl	appl	PROPN
ejpam-5757	189	4	.	.	PROPN
ejpam-5757	189	5	math	math	PROPN
ejpam-5757	189	6	,	,	PUNCT
ejpam-5757	189	7	18	18	NUM
ejpam-5757	189	8	(	(	PUNCT
ejpam-5757	189	9	1	1	NUM
ejpam-5757	189	10	)	)	PUNCT
ejpam-5757	189	11	(	(	PUNCT
ejpam-5757	189	12	2025	2025	NUM
ejpam-5757	189	13	)	)	PUNCT
ejpam-5757	189	14	,	,	PUNCT
ejpam-5757	189	15	5757	5757	NUM
ejpam-5757	189	16	11	11	NUM
ejpam-5757	189	17	of	of	ADP
ejpam-5757	189	18	18	18	NUM
ejpam-5757	189	19	+	+	SYM
ejpam-5757	189	20	1	1	NUM
ejpam-5757	189	21	12	12	NUM
ejpam-5757	189	22	δ((n+	δ((n+	NOUN
ejpam-5757	189	23	1)u	1)u	NUM
ejpam-5757	189	24	)	)	PUNCT
ejpam-5757	190	1	+	+	CCONJ
ejpam-5757	190	2	1	1	NUM
ejpam-5757	190	3	24	24	NUM
ejpam-5757	190	4	δ((n−	δ((n−	PROPN
ejpam-5757	190	5	1)u	1)u	NUM
ejpam-5757	190	6	)	)	PUNCT
ejpam-5757	190	7	+	+	CCONJ
ejpam-5757	190	8	1	1	NUM
ejpam-5757	190	9	12	12	NUM
ejpam-5757	190	10	δ(nu	δ(nu	NOUN
ejpam-5757	190	11	)	)	PUNCT
ejpam-5757	190	12	for	for	ADP
ejpam-5757	190	13	all	all	DET
ejpam-5757	190	14	u	u	PROPN
ejpam-5757	190	15	∈	∈	PROPN
ejpam-5757	190	16	u0	u0	NOUN
ejpam-5757	190	17	and	and	CCONJ
ejpam-5757	190	18	all	all	DET
ejpam-5757	190	19	δ	δ	PROPN
ejpam-5757	190	20	∈	∈	PROPN
ejpam-5757	190	21	ru0×u0	ru0×u0	PROPN
ejpam-5757	190	22	+	+	PUNCT
ejpam-5757	190	23	.	.	PUNCT
ejpam-5757	191	1	for	for	ADP
ejpam-5757	191	2	every	every	DET
ejpam-5757	191	3	n	n	PRON
ejpam-5757	191	4	∈	∈	PROPN
ejpam-5757	191	5	n	n	CCONJ
ejpam-5757	191	6	,	,	PUNCT
ejpam-5757	191	7	the	the	DET
ejpam-5757	191	8	form	form	NOUN
ejpam-5757	191	9	of	of	ADP
ejpam-5757	191	10	the	the	DET
ejpam-5757	191	11	operator	operator	NOUN
ejpam-5757	191	12	previously	previously	ADV
ejpam-5757	191	13	specified	specify	VERB
ejpam-5757	191	14	is	be	AUX
ejpam-5757	191	15	given	give	VERB
ejpam-5757	191	16	in	in	ADP
ejpam-5757	191	17	(	(	PUNCT
ejpam-5757	191	18	1	1	NUM
ejpam-5757	191	19	)	)	PUNCT
ejpam-5757	191	20	with	with	ADP
ejpam-5757	191	21	ϕ1(u	ϕ1(u	NOUN
ejpam-5757	191	22	)	)	PUNCT
ejpam-5757	191	23	=	=	SYM
ejpam-5757	191	24	(	(	PUNCT
ejpam-5757	191	25	n+	n+	X
ejpam-5757	191	26	3)u	3)u	NUM
ejpam-5757	191	27	,	,	PUNCT
ejpam-5757	191	28	l1(u	l1(u	X
ejpam-5757	191	29	)	)	PUNCT
ejpam-5757	191	30	=	=	SYM
ejpam-5757	192	1	1	1	NUM
ejpam-5757	192	2	120	120	NUM
ejpam-5757	192	3	,	,	PUNCT
ejpam-5757	192	4	ϕ2(u	ϕ2(u	X
ejpam-5757	192	5	)	)	PUNCT
ejpam-5757	192	6	=	=	SYM
ejpam-5757	192	7	(	(	PUNCT
ejpam-5757	192	8	n+	n+	NUM
ejpam-5757	192	9	2)u	2)u	NOUN
ejpam-5757	192	10	,	,	PUNCT
ejpam-5757	192	11	l2(u	l2(u	PROPN
ejpam-5757	192	12	)	)	PUNCT
ejpam-5757	192	13	=	=	SYM
ejpam-5757	192	14	1	1	NUM
ejpam-5757	192	15	24	24	NUM
ejpam-5757	192	16	,	,	PUNCT
ejpam-5757	192	17	ϕ3(u	ϕ3(u	NUM
ejpam-5757	192	18	)	)	PUNCT
ejpam-5757	192	19	=	=	SYM
ejpam-5757	192	20	(	(	PUNCT
ejpam-5757	192	21	n−	n−	NOUN
ejpam-5757	192	22	2)u	2)u	NOUN
ejpam-5757	192	23	,	,	PUNCT
ejpam-5757	192	24	l3(u	l3(u	NOUN
ejpam-5757	192	25	)	)	PUNCT
ejpam-5757	192	26	=	=	SYM
ejpam-5757	192	27	1	1	NUM
ejpam-5757	192	28	120	120	NUM
ejpam-5757	192	29	,	,	PUNCT
ejpam-5757	192	30	ϕ4(u	ϕ4(u	PROPN
ejpam-5757	192	31	)	)	PUNCT
ejpam-5757	192	32	=	=	PUNCT
ejpam-5757	193	1	(	(	PUNCT
ejpam-5757	193	2	n+	n+	NUM
ejpam-5757	193	3	1)u	1)u	NUM
ejpam-5757	193	4	,	,	PUNCT
ejpam-5757	193	5	l4(u	l4(u	PROPN
ejpam-5757	193	6	)	)	PUNCT
ejpam-5757	193	7	=	=	SYM
ejpam-5757	193	8	1	1	NUM
ejpam-5757	193	9	12	12	NUM
ejpam-5757	193	10	,	,	PUNCT
ejpam-5757	193	11	ϕ5(u	ϕ5(u	PROPN
ejpam-5757	193	12	)	)	PUNCT
ejpam-5757	193	13	=	=	SYM
ejpam-5757	194	1	(	(	PUNCT
ejpam-5757	194	2	n−	n−	NOUN
ejpam-5757	194	3	1)u	1)u	NUM
ejpam-5757	194	4	,	,	PUNCT
ejpam-5757	194	5	l5(u	l5(u	PROPN
ejpam-5757	194	6	)	)	PUNCT
ejpam-5757	194	7	=	=	SYM
ejpam-5757	194	8	1	1	NUM
ejpam-5757	194	9	24	24	NUM
ejpam-5757	194	10	,	,	PUNCT
ejpam-5757	194	11	ϕ6(u	ϕ6(u	PROPN
ejpam-5757	194	12	)	)	PUNCT
ejpam-5757	194	13	=	=	SYM
ejpam-5757	194	14	nu	nu	PROPN
ejpam-5757	194	15	,	,	PUNCT
ejpam-5757	194	16	l6(u	l6(u	PROPN
ejpam-5757	194	17	)	)	PUNCT
ejpam-5757	194	18	=	=	SYM
ejpam-5757	194	19	1	1	NUM
ejpam-5757	194	20	12	12	NUM
ejpam-5757	194	21	for	for	ADP
ejpam-5757	194	22	all	all	DET
ejpam-5757	194	23	u	u	PROPN
ejpam-5757	194	24	∈	∈	PROPN
ejpam-5757	194	25	u0	u0	NOUN
ejpam-5757	194	26	.	.	PUNCT
ejpam-5757	195	1	by	by	ADP
ejpam-5757	195	2	induction	induction	NOUN
ejpam-5757	195	3	,	,	PUNCT
ejpam-5757	195	4	we	we	PRON
ejpam-5757	195	5	will	will	AUX
ejpam-5757	195	6	verify	verify	VERB
ejpam-5757	195	7	that	that	SCONJ
ejpam-5757	195	8	for	for	ADP
ejpam-5757	195	9	every	every	DET
ejpam-5757	195	10	u	u	PROPN
ejpam-5757	195	11	∈	∈	PROPN
ejpam-5757	195	12	u0	u0	NOUN
ejpam-5757	195	13	,	,	PUNCT
ejpam-5757	195	14	m	m	PROPN
ejpam-5757	195	15	∈	∈	PROPN
ejpam-5757	195	16	n0	n0	NUM
ejpam-5757	195	17	,	,	PUNCT
ejpam-5757	195	18	and	and	CCONJ
ejpam-5757	195	19	n	n	NUM
ejpam-5757	195	20	∈w	∈w	NOUN
ejpam-5757	195	21	,	,	PUNCT
ejpam-5757	195	22	we	we	PRON
ejpam-5757	195	23	have	have	VERB
ejpam-5757	195	24	(	(	PUNCT
ejpam-5757	195	25	υm	υm	NOUN
ejpam-5757	195	26	n	n	PRON
ejpam-5757	195	27	ϑn	ϑn	NOUN
ejpam-5757	195	28	)	)	PUNCT
ejpam-5757	195	29	(	(	PUNCT
ejpam-5757	195	30	u	u	NOUN
ejpam-5757	195	31	)	)	PUNCT
ejpam-5757	195	32	≤	≤	NUM
ejpam-5757	195	33	1	1	NUM
ejpam-5757	195	34	120	120	NUM
ejpam-5757	195	35	(	(	PUNCT
ejpam-5757	195	36	η(n	η(n	VERB
ejpam-5757	195	37	)	)	PUNCT
ejpam-5757	195	38	+	+	CCONJ
ejpam-5757	195	39	1)αm	1)αm	NUM
ejpam-5757	195	40	n	n	CCONJ
ejpam-5757	195	41	τ(u	τ(u	PROPN
ejpam-5757	195	42	)	)	PUNCT
ejpam-5757	195	43	.	.	PUNCT
ejpam-5757	196	1	(	(	PUNCT
ejpam-5757	196	2	22	22	NUM
ejpam-5757	196	3	)	)	PUNCT
ejpam-5757	196	4	the	the	DET
ejpam-5757	196	5	condition	condition	NOUN
ejpam-5757	196	6	(	(	PUNCT
ejpam-5757	196	7	22	22	NUM
ejpam-5757	196	8	)	)	PUNCT
ejpam-5757	196	9	for	for	ADP
ejpam-5757	196	10	m	m	PROPN
ejpam-5757	196	11	=	=	SYM
ejpam-5757	196	12	0	0	NUM
ejpam-5757	196	13	is	be	AUX
ejpam-5757	196	14	derived	derive	VERB
ejpam-5757	196	15	from	from	ADP
ejpam-5757	196	16	(	(	PUNCT
ejpam-5757	196	17	20	20	NUM
ejpam-5757	196	18	)	)	PUNCT
ejpam-5757	196	19	and	and	CCONJ
ejpam-5757	196	20	(	(	PUNCT
ejpam-5757	196	21	21	21	NUM
ejpam-5757	196	22	)	)	PUNCT
ejpam-5757	196	23	.	.	PUNCT
ejpam-5757	197	1	suppose	suppose	VERB
ejpam-5757	197	2	that	that	SCONJ
ejpam-5757	197	3	(	(	PUNCT
ejpam-5757	197	4	22	22	NUM
ejpam-5757	197	5	)	)	PUNCT
ejpam-5757	197	6	holds	hold	VERB
ejpam-5757	197	7	for	for	ADP
ejpam-5757	197	8	m	m	PROPN
ejpam-5757	197	9	=	=	PROPN
ejpam-5757	197	10	k.	k.	PROPN
ejpam-5757	197	11	then	then	ADV
ejpam-5757	197	12	(	(	PUNCT
ejpam-5757	197	13	υk+1	υk+1	NOUN
ejpam-5757	197	14	n	n	PRON
ejpam-5757	197	15	ϑn	ϑn	NOUN
ejpam-5757	197	16	)	)	PUNCT
ejpam-5757	197	17	(	(	PUNCT
ejpam-5757	197	18	u	u	NOUN
ejpam-5757	197	19	)	)	PUNCT
ejpam-5757	197	20	=	=	PUNCT
ejpam-5757	197	21	υn	υn	NOUN
ejpam-5757	197	22	(	(	PUNCT
ejpam-5757	197	23	(	(	PUNCT
ejpam-5757	197	24	υk	υk	VERB
ejpam-5757	197	25	nϑn	nϑn	NOUN
ejpam-5757	197	26	)	)	PUNCT
ejpam-5757	197	27	(	(	PUNCT
ejpam-5757	197	28	u	u	NOUN
ejpam-5757	197	29	)	)	PUNCT
ejpam-5757	197	30	)	)	PUNCT
ejpam-5757	198	1	=	=	PUNCT
ejpam-5757	199	1	1	1	NUM
ejpam-5757	199	2	120	120	NUM
ejpam-5757	199	3	(	(	PUNCT
ejpam-5757	199	4	υn	υn	NOUN
ejpam-5757	199	5	nϑn	nϑn	PROPN
ejpam-5757	199	6	)	)	PUNCT
ejpam-5757	199	7	(	(	PUNCT
ejpam-5757	199	8	(	(	PUNCT
ejpam-5757	199	9	n+	n+	X
ejpam-5757	199	10	3)x	3)x	NUM
ejpam-5757	199	11	)	)	PUNCT
ejpam-5757	199	12	+	+	CCONJ
ejpam-5757	199	13	1	1	NUM
ejpam-5757	199	14	24	24	NUM
ejpam-5757	199	15	(	(	PUNCT
ejpam-5757	199	16	υn	υn	NOUN
ejpam-5757	199	17	nϑn	nϑn	PROPN
ejpam-5757	199	18	)	)	PUNCT
ejpam-5757	199	19	(	(	PUNCT
ejpam-5757	199	20	(	(	PUNCT
ejpam-5757	199	21	n+	n+	NOUN
ejpam-5757	199	22	2)u	2)u	NUM
ejpam-5757	199	23	)	)	PUNCT
ejpam-5757	199	24	+	+	CCONJ
ejpam-5757	199	25	1	1	NUM
ejpam-5757	199	26	120	120	NUM
ejpam-5757	199	27	(	(	PUNCT
ejpam-5757	199	28	υn	υn	NOUN
ejpam-5757	199	29	nϑn	nϑn	PROPN
ejpam-5757	199	30	)	)	PUNCT
ejpam-5757	199	31	(	(	PUNCT
ejpam-5757	199	32	(	(	PUNCT
ejpam-5757	199	33	n−	n−	NOUN
ejpam-5757	199	34	2)u	2)u	NUM
ejpam-5757	199	35	)	)	PUNCT
ejpam-5757	200	1	+	+	CCONJ
ejpam-5757	200	2	1	1	NUM
ejpam-5757	200	3	12	12	NUM
ejpam-5757	200	4	(	(	PUNCT
ejpam-5757	200	5	υn	υn	NOUN
ejpam-5757	200	6	nϑn	nϑn	PROPN
ejpam-5757	200	7	)	)	PUNCT
ejpam-5757	200	8	(	(	PUNCT
ejpam-5757	200	9	(	(	PUNCT
ejpam-5757	200	10	n+	n+	NOUN
ejpam-5757	200	11	1)u	1)u	NUM
ejpam-5757	200	12	)	)	PUNCT
ejpam-5757	200	13	+	+	CCONJ
ejpam-5757	200	14	1	1	NUM
ejpam-5757	200	15	24	24	NUM
ejpam-5757	200	16	(	(	PUNCT
ejpam-5757	200	17	υn	υn	NOUN
ejpam-5757	200	18	nϑn	nϑn	PROPN
ejpam-5757	200	19	)	)	PUNCT
ejpam-5757	200	20	(	(	PUNCT
ejpam-5757	200	21	(	(	PUNCT
ejpam-5757	200	22	n−	n−	NOUN
ejpam-5757	200	23	1)u	1)u	NOUN
ejpam-5757	200	24	)	)	PUNCT
ejpam-5757	200	25	+	+	CCONJ
ejpam-5757	200	26	1	1	NUM
ejpam-5757	200	27	12	12	NUM
ejpam-5757	200	28	(	(	PUNCT
ejpam-5757	200	29	υn	υn	NOUN
ejpam-5757	200	30	nϑn	nϑn	PROPN
ejpam-5757	200	31	)	)	PUNCT
ejpam-5757	200	32	(	(	PUNCT
ejpam-5757	200	33	nu	nu	NOUN
ejpam-5757	200	34	)	)	PUNCT
ejpam-5757	200	35	≤	≤	NOUN
ejpam-5757	200	36	1	1	NUM
ejpam-5757	200	37	120	120	NUM
ejpam-5757	200	38	(	(	PUNCT
ejpam-5757	200	39	η(n	η(n	VERB
ejpam-5757	200	40	)	)	PUNCT
ejpam-5757	200	41	+	+	CCONJ
ejpam-5757	200	42	1)αk+1	1)αk+1	NUM
ejpam-5757	200	43	n	n	CCONJ
ejpam-5757	200	44	τ(u	τ(u	PROPN
ejpam-5757	200	45	)	)	PUNCT
ejpam-5757	200	46	,	,	PUNCT
ejpam-5757	200	47	for	for	ADP
ejpam-5757	200	48	all	all	DET
ejpam-5757	200	49	u	u	PROPN
ejpam-5757	200	50	∈	∈	PROPN
ejpam-5757	200	51	u0	u0	NOUN
ejpam-5757	200	52	and	and	CCONJ
ejpam-5757	200	53	every	every	PRON
ejpam-5757	200	54	n	n	NOUN
ejpam-5757	200	55	∈w	∈w	NOUN
ejpam-5757	200	56	.	.	PUNCT
ejpam-5757	201	1	therefore	therefore	ADV
ejpam-5757	201	2	,	,	PUNCT
ejpam-5757	201	3	for	for	ADP
ejpam-5757	201	4	m	m	PROPN
ejpam-5757	201	5	=	=	SYM
ejpam-5757	201	6	k+1	k+1	PROPN
ejpam-5757	201	7	,	,	PUNCT
ejpam-5757	201	8	the	the	DET
ejpam-5757	201	9	inequality	inequality	NOUN
ejpam-5757	201	10	(	(	PUNCT
ejpam-5757	201	11	22	22	NUM
ejpam-5757	201	12	)	)	PUNCT
ejpam-5757	201	13	holds	hold	VERB
ejpam-5757	201	14	.	.	PUNCT
ejpam-5757	202	1	as	as	ADP
ejpam-5757	202	2	a	a	DET
ejpam-5757	202	3	result	result	NOUN
ejpam-5757	202	4	,	,	PUNCT
ejpam-5757	202	5	we	we	PRON
ejpam-5757	202	6	may	may	AUX
ejpam-5757	202	7	say	say	VERB
ejpam-5757	202	8	that	that	SCONJ
ejpam-5757	202	9	the	the	DET
ejpam-5757	202	10	inequality	inequality	NOUN
ejpam-5757	202	11	(	(	PUNCT
ejpam-5757	202	12	22	22	NUM
ejpam-5757	202	13	)	)	PUNCT
ejpam-5757	202	14	holds	hold	VERB
ejpam-5757	202	15	for	for	ADP
ejpam-5757	202	16	all	all	DET
ejpam-5757	202	17	m	m	PROPN
ejpam-5757	202	18	∈	∈	PROPN
ejpam-5757	202	19	n0	n0	PROPN
ejpam-5757	202	20	.	.	PUNCT
ejpam-5757	203	1	thus	thus	ADV
ejpam-5757	203	2	we	we	PRON
ejpam-5757	203	3	have	have	VERB
ejpam-5757	203	4	ϑ∗n(u	ϑ∗n(u	NOUN
ejpam-5757	203	5	)	)	PUNCT
ejpam-5757	203	6	=	=	PUNCT
ejpam-5757	204	1	∞∑	∞∑	NUM
ejpam-5757	204	2	m=0	m=0	PROPN
ejpam-5757	204	3	(	(	PUNCT
ejpam-5757	204	4	υm	υm	NOUN
ejpam-5757	204	5	n	n	PRON
ejpam-5757	204	6	ϑn	ϑn	NOUN
ejpam-5757	204	7	)	)	PUNCT
ejpam-5757	204	8	(	(	PUNCT
ejpam-5757	204	9	u	u	NOUN
ejpam-5757	204	10	)	)	PUNCT
ejpam-5757	204	11	≤	≤	NOUN
ejpam-5757	204	12	∞∑	∞∑	PRON
ejpam-5757	204	13	n=0	n=0	NUM
ejpam-5757	204	14	1	1	NUM
ejpam-5757	204	15	120	120	NUM
ejpam-5757	204	16	(	(	PUNCT
ejpam-5757	204	17	η(n	η(n	VERB
ejpam-5757	204	18	)	)	PUNCT
ejpam-5757	204	19	+	+	CCONJ
ejpam-5757	204	20	1)αm	1)αm	NUM
ejpam-5757	204	21	n	n	CCONJ
ejpam-5757	204	22	τ(u	τ(u	PROPN
ejpam-5757	204	23	)	)	PUNCT
ejpam-5757	204	24	≤	≤	NOUN
ejpam-5757	204	25	(	(	PUNCT
ejpam-5757	204	26	η(n	η(n	NOUN
ejpam-5757	204	27	)	)	PUNCT
ejpam-5757	204	28	+	+	CCONJ
ejpam-5757	204	29	1	1	X
ejpam-5757	204	30	)	)	PUNCT
ejpam-5757	204	31	120(1−	120(1−	NUM
ejpam-5757	204	32	αn	αn	NOUN
ejpam-5757	204	33	)	)	PUNCT
ejpam-5757	204	34	τ(u	τ(u	PUNCT
ejpam-5757	204	35	)	)	PUNCT
ejpam-5757	205	1	<	<	X
ejpam-5757	205	2	∞	∞	PROPN
ejpam-5757	205	3	s.	s.	PROPN
ejpam-5757	205	4	karthikeyan	karthikeyan	PROPN
ejpam-5757	205	5	et	et	PROPN
ejpam-5757	205	6	al	al	PROPN
ejpam-5757	205	7	.	.	PUNCT
ejpam-5757	205	8	/	/	SYM
ejpam-5757	205	9	eur	eur	PROPN
ejpam-5757	205	10	.	.	PUNCT
ejpam-5757	206	1	j.	j.	PROPN
ejpam-5757	206	2	pure	pure	PROPN
ejpam-5757	206	3	appl	appl	PROPN
ejpam-5757	206	4	.	.	PROPN
ejpam-5757	206	5	math	math	PROPN
ejpam-5757	206	6	,	,	PUNCT
ejpam-5757	206	7	18	18	NUM
ejpam-5757	206	8	(	(	PUNCT
ejpam-5757	206	9	1	1	NUM
ejpam-5757	206	10	)	)	PUNCT
ejpam-5757	206	11	(	(	PUNCT
ejpam-5757	206	12	2025	2025	NUM
ejpam-5757	206	13	)	)	PUNCT
ejpam-5757	206	14	,	,	PUNCT
ejpam-5757	206	15	5757	5757	NUM
ejpam-5757	206	16	12	12	NUM
ejpam-5757	206	17	of	of	ADP
ejpam-5757	206	18	18	18	NUM
ejpam-5757	206	19	for	for	ADP
ejpam-5757	206	20	all	all	DET
ejpam-5757	206	21	u	u	PROPN
ejpam-5757	206	22	∈	∈	PROPN
ejpam-5757	206	23	u0	u0	NOUN
ejpam-5757	206	24	and	and	CCONJ
ejpam-5757	206	25	n	n	PRON
ejpam-5757	206	26	∈w	∈w	NOUN
ejpam-5757	206	27	.	.	PUNCT
ejpam-5757	207	1	therefore	therefore	ADV
ejpam-5757	207	2	,	,	PUNCT
ejpam-5757	207	3	according	accord	VERB
ejpam-5757	207	4	to	to	ADP
ejpam-5757	207	5	theorem	theorem	NOUN
ejpam-5757	207	6	2	2	NUM
ejpam-5757	207	7	,	,	PUNCT
ejpam-5757	207	8	we	we	PRON
ejpam-5757	207	9	obtain	obtain	VERB
ejpam-5757	207	10	the	the	DET
ejpam-5757	207	11	limit	limit	NOUN
ejpam-5757	207	12	function	function	NOUN
ejpam-5757	207	13	hn(u	hn(u	NOUN
ejpam-5757	207	14	)	)	PUNCT
ejpam-5757	207	15	:	:	PUNCT
ejpam-5757	207	16	=	=	SYM
ejpam-5757	207	17	lim	lim	PROPN
ejpam-5757	207	18	m→+∞	m→+∞	PROPN
ejpam-5757	207	19	(	(	PUNCT
ejpam-5757	207	20	φm	φm	PROPN
ejpam-5757	207	21	n	n	DET
ejpam-5757	207	22	ϕ	ϕ	NOUN
ejpam-5757	207	23	)	)	PUNCT
ejpam-5757	207	24	(	(	PUNCT
ejpam-5757	207	25	u	u	NOUN
ejpam-5757	207	26	)	)	PUNCT
ejpam-5757	207	27	exists	exist	VERB
ejpam-5757	207	28	for	for	ADP
ejpam-5757	207	29	every	every	DET
ejpam-5757	207	30	u	u	PROPN
ejpam-5757	207	31	∈	∈	PROPN
ejpam-5757	207	32	u0	u0	NOUN
ejpam-5757	207	33	and	and	CCONJ
ejpam-5757	207	34	every	every	PRON
ejpam-5757	207	35	n	n	NOUN
ejpam-5757	207	36	∈w	∈w	NOUN
ejpam-5757	207	37	,	,	PUNCT
ejpam-5757	207	38	and	and	CCONJ
ejpam-5757	207	39	∥ϕ(u)−hn(u)∥	∥ϕ(u)−hn(u)∥	VERB
ejpam-5757	207	40	≤	≤	NUM
ejpam-5757	207	41	(	(	PUNCT
ejpam-5757	207	42	η(n	η(n	NOUN
ejpam-5757	207	43	)	)	PUNCT
ejpam-5757	207	44	+	+	NOUN
ejpam-5757	207	45	1)τ(u	1)τ(u	NUM
ejpam-5757	207	46	)	)	PUNCT
ejpam-5757	207	47	120(1−	120(1−	NUM
ejpam-5757	207	48	αn	αn	NOUN
ejpam-5757	207	49	)	)	PUNCT
ejpam-5757	207	50	(	(	PUNCT
ejpam-5757	207	51	23	23	NUM
ejpam-5757	207	52	)	)	PUNCT
ejpam-5757	207	53	for	for	ADP
ejpam-5757	207	54	all	all	DET
ejpam-5757	207	55	u	u	PROPN
ejpam-5757	207	56	∈	∈	PROPN
ejpam-5757	207	57	u0	u0	NOUN
ejpam-5757	207	58	and	and	CCONJ
ejpam-5757	207	59	n	n	PRON
ejpam-5757	207	60	∈w	∈w	NOUN
ejpam-5757	207	61	.	.	PUNCT
ejpam-5757	208	1	now	now	ADV
ejpam-5757	208	2	,	,	PUNCT
ejpam-5757	208	3	we	we	PRON
ejpam-5757	208	4	want	want	VERB
ejpam-5757	208	5	to	to	PART
ejpam-5757	208	6	prove	prove	VERB
ejpam-5757	208	7	that	that	SCONJ
ejpam-5757	208	8	hn	hn	PROPN
ejpam-5757	208	9	fulfills	fulfill	VERB
ejpam-5757	208	10	(	(	PUNCT
ejpam-5757	208	11	2	2	NUM
ejpam-5757	208	12	)	)	PUNCT
ejpam-5757	208	13	,	,	PUNCT
ejpam-5757	208	14	it	it	PRON
ejpam-5757	208	15	is	be	AUX
ejpam-5757	208	16	enough	enough	ADJ
ejpam-5757	208	17	to	to	PART
ejpam-5757	208	18	show	show	VERB
ejpam-5757	208	19	the	the	DET
ejpam-5757	208	20	following	follow	VERB
ejpam-5757	208	21	inequality	inequality	NOUN
ejpam-5757	208	22	∥d(φm	∥d(φm	PROPN
ejpam-5757	208	23	n	n	CCONJ
ejpam-5757	208	24	ϕ)(u	ϕ)(u	ADJ
ejpam-5757	208	25	,	,	PUNCT
ejpam-5757	208	26	v)∥	v)∥	PUNCT
ejpam-5757	208	27	≤	≤	NUM
ejpam-5757	209	1	αm	αm	NOUN
ejpam-5757	209	2	n	n	PROPN
ejpam-5757	209	3	(	(	PUNCT
ejpam-5757	209	4	τ(u	τ(u	PROPN
ejpam-5757	209	5	)	)	PUNCT
ejpam-5757	209	6	+	+	CCONJ
ejpam-5757	209	7	τ(v	τ(v	NOUN
ejpam-5757	209	8	)	)	PUNCT
ejpam-5757	209	9	)	)	PUNCT
ejpam-5757	210	1	(	(	PUNCT
ejpam-5757	210	2	24	24	NUM
ejpam-5757	210	3	)	)	PUNCT
ejpam-5757	210	4	for	for	ADP
ejpam-5757	210	5	all	all	DET
ejpam-5757	210	6	u	u	NOUN
ejpam-5757	210	7	,	,	PUNCT
ejpam-5757	210	8	v	v	NOUN
ejpam-5757	210	9	∈	∈	PROPN
ejpam-5757	210	10	u0	u0	NOUN
ejpam-5757	210	11	,	,	PUNCT
ejpam-5757	210	12	m	m	PROPN
ejpam-5757	210	13	∈	∈	PROPN
ejpam-5757	210	14	n0	n0	NUM
ejpam-5757	210	15	,	,	PUNCT
ejpam-5757	210	16	and	and	CCONJ
ejpam-5757	210	17	n	n	PRON
ejpam-5757	210	18	∈	∈	PROPN
ejpam-5757	210	19	w	w	NOUN
ejpam-5757	210	20	.	.	PUNCT
ejpam-5757	211	1	since	since	SCONJ
ejpam-5757	211	2	the	the	DET
ejpam-5757	211	3	condition	condition	NOUN
ejpam-5757	211	4	(	(	PUNCT
ejpam-5757	211	5	17	17	NUM
ejpam-5757	211	6	)	)	PUNCT
ejpam-5757	211	7	is	be	AUX
ejpam-5757	211	8	all	all	PRON
ejpam-5757	211	9	that	that	PRON
ejpam-5757	211	10	is	be	AUX
ejpam-5757	211	11	required	require	VERB
ejpam-5757	211	12	in	in	ADP
ejpam-5757	211	13	the	the	DET
ejpam-5757	211	14	situation	situation	NOUN
ejpam-5757	211	15	m	m	NOUN
ejpam-5757	211	16	=	=	SYM
ejpam-5757	211	17	0	0	NUM
ejpam-5757	211	18	,	,	PUNCT
ejpam-5757	211	19	assume	assume	VERB
ejpam-5757	211	20	that	that	SCONJ
ejpam-5757	211	21	k	k	PROPN
ejpam-5757	211	22	∈	∈	PROPN
ejpam-5757	211	23	n	n	ADV
ejpam-5757	211	24	and	and	CCONJ
ejpam-5757	211	25	suppose	suppose	VERB
ejpam-5757	211	26	that	that	SCONJ
ejpam-5757	211	27	(	(	PUNCT
ejpam-5757	211	28	24	24	NUM
ejpam-5757	211	29	)	)	PUNCT
ejpam-5757	211	30	holds	hold	VERB
ejpam-5757	211	31	for	for	ADP
ejpam-5757	211	32	every	every	DET
ejpam-5757	211	33	m	m	NOUN
ejpam-5757	211	34	=	=	SYM
ejpam-5757	211	35	k	k	PROPN
ejpam-5757	211	36	and	and	CCONJ
ejpam-5757	211	37	u	u	PROPN
ejpam-5757	211	38	,	,	PUNCT
ejpam-5757	211	39	v	v	PROPN
ejpam-5757	211	40	∈	∈	PROPN
ejpam-5757	211	41	u0	u0	NOUN
ejpam-5757	211	42	and	and	CCONJ
ejpam-5757	211	43	n	n	PRON
ejpam-5757	211	44	∈w	∈w	NOUN
ejpam-5757	211	45	.	.	PUNCT
ejpam-5757	212	1	then	then	ADV
ejpam-5757	212	2	,	,	PUNCT
ejpam-5757	212	3	for	for	ADP
ejpam-5757	212	4	each	each	DET
ejpam-5757	212	5	u	u	NOUN
ejpam-5757	212	6	,	,	PUNCT
ejpam-5757	212	7	v	v	PROPN
ejpam-5757	212	8	∈	∈	PROPN
ejpam-5757	212	9	u0	u0	NOUN
ejpam-5757	212	10	and	and	CCONJ
ejpam-5757	212	11	n	n	PRON
ejpam-5757	212	12	∈w	∈w	NOUN
ejpam-5757	212	13	,	,	PUNCT
ejpam-5757	212	14	we	we	PRON
ejpam-5757	212	15	have∥∥∥d(φk+1	have∥∥∥d(φk+1	VERB
ejpam-5757	212	16	n	n	CCONJ
ejpam-5757	212	17	ϕ)(u	ϕ)(u	ADJ
ejpam-5757	212	18	,	,	PUNCT
ejpam-5757	212	19	v	v	NOUN
ejpam-5757	212	20	)	)	PUNCT
ejpam-5757	212	21	∥∥∥	∥∥∥	PROPN
ejpam-5757	212	22	≤	≤	NUM
ejpam-5757	212	23	αk+1	αk+1	NUM
ejpam-5757	212	24	n	n	CCONJ
ejpam-5757	212	25	(	(	PUNCT
ejpam-5757	212	26	τ(u	τ(u	PROPN
ejpam-5757	212	27	)	)	PUNCT
ejpam-5757	212	28	+	+	CCONJ
ejpam-5757	212	29	τ2(v	τ2(v	NOUN
ejpam-5757	212	30	)	)	PUNCT
ejpam-5757	212	31	)	)	PUNCT
ejpam-5757	212	32	.	.	PUNCT
ejpam-5757	213	1	by	by	ADP
ejpam-5757	213	2	induction	induction	NOUN
ejpam-5757	213	3	,	,	PUNCT
ejpam-5757	213	4	we	we	PRON
ejpam-5757	213	5	need	need	VERB
ejpam-5757	213	6	to	to	PART
ejpam-5757	213	7	prove	prove	VERB
ejpam-5757	213	8	that	that	SCONJ
ejpam-5757	213	9	(	(	PUNCT
ejpam-5757	213	10	24	24	NUM
ejpam-5757	213	11	)	)	PUNCT
ejpam-5757	213	12	holds	hold	VERB
ejpam-5757	213	13	for	for	ADP
ejpam-5757	213	14	every	every	DET
ejpam-5757	213	15	u	u	NOUN
ejpam-5757	213	16	,	,	PUNCT
ejpam-5757	213	17	v	v	PROPN
ejpam-5757	213	18	∈	∈	PROPN
ejpam-5757	213	19	u0	u0	NOUN
ejpam-5757	213	20	,	,	PUNCT
ejpam-5757	213	21	m	m	PROPN
ejpam-5757	213	22	∈	∈	PROPN
ejpam-5757	213	23	n0	n0	NUM
ejpam-5757	213	24	,	,	PUNCT
ejpam-5757	213	25	and	and	CCONJ
ejpam-5757	213	26	n	n	PRON
ejpam-5757	213	27	∈	∈	PROPN
ejpam-5757	213	28	w	w	NOUN
ejpam-5757	213	29	.	.	PUNCT
ejpam-5757	214	1	taking	take	VERB
ejpam-5757	214	2	the	the	DET
ejpam-5757	214	3	limit	limit	NOUN
ejpam-5757	214	4	m→	m→	NOUN
ejpam-5757	214	5	∞	∞	NUM
ejpam-5757	214	6	in	in	ADP
ejpam-5757	214	7	(	(	PUNCT
ejpam-5757	214	8	24	24	NUM
ejpam-5757	214	9	)	)	PUNCT
ejpam-5757	214	10	,	,	PUNCT
ejpam-5757	214	11	we	we	PRON
ejpam-5757	214	12	obtain	obtain	VERB
ejpam-5757	214	13	dhn(u	dhn(u	PROPN
ejpam-5757	214	14	,	,	PUNCT
ejpam-5757	214	15	v	v	NOUN
ejpam-5757	214	16	)	)	PUNCT
ejpam-5757	214	17	=	=	SYM
ejpam-5757	214	18	0	0	NUM
ejpam-5757	215	1	for	for	ADP
ejpam-5757	215	2	all	all	DET
ejpam-5757	215	3	u	u	NOUN
ejpam-5757	215	4	,	,	PUNCT
ejpam-5757	215	5	v	v	NOUN
ejpam-5757	215	6	∈	∈	PROPN
ejpam-5757	215	7	u0	u0	NOUN
ejpam-5757	215	8	,	,	PUNCT
ejpam-5757	215	9	m	m	PROPN
ejpam-5757	215	10	∈	∈	PROPN
ejpam-5757	215	11	n0	n0	NUM
ejpam-5757	215	12	,	,	PUNCT
ejpam-5757	215	13	and	and	CCONJ
ejpam-5757	215	14	n	n	PRON
ejpam-5757	215	15	∈w	∈w	NOUN
ejpam-5757	215	16	.	.	PUNCT
ejpam-5757	216	1	this	this	PRON
ejpam-5757	216	2	implies	imply	VERB
ejpam-5757	216	3	that	that	SCONJ
ejpam-5757	216	4	the	the	DET
ejpam-5757	216	5	mapping	mapping	NOUN
ejpam-5757	216	6	h	h	NOUN
ejpam-5757	216	7	:	:	PUNCT
ejpam-5757	216	8	u	u	X
ejpam-5757	216	9	→	→	SYM
ejpam-5757	216	10	v	v	NUM
ejpam-5757	216	11	satisfies	satisfie	NOUN
ejpam-5757	216	12	h(u	h(u	PROPN
ejpam-5757	216	13	)	)	PUNCT
ejpam-5757	216	14	:	:	PUNCT
ejpam-5757	217	1	=	=	SYM
ejpam-5757	217	2	1	1	NUM
ejpam-5757	217	3	120	120	NUM
ejpam-5757	217	4	h((n+	h((n+	NOUN
ejpam-5757	217	5	3)u)−	3)u)−	NUM
ejpam-5757	217	6	1	1	NUM
ejpam-5757	217	7	24	24	NUM
ejpam-5757	217	8	h((n+	h((n+	NOUN
ejpam-5757	217	9	2)u)−	2)u)−	NUM
ejpam-5757	217	10	1	1	NUM
ejpam-5757	217	11	120	120	NUM
ejpam-5757	217	12	h((n−	h((n−	PROPN
ejpam-5757	217	13	2)u	2)u	NUM
ejpam-5757	217	14	)	)	PUNCT
ejpam-5757	217	15	+	+	CCONJ
ejpam-5757	217	16	1	1	NUM
ejpam-5757	217	17	12	12	NUM
ejpam-5757	217	18	h((n+	h((n+	NOUN
ejpam-5757	217	19	1)u	1)u	NUM
ejpam-5757	217	20	)	)	PUNCT
ejpam-5757	217	21	+	+	CCONJ
ejpam-5757	217	22	1	1	NUM
ejpam-5757	217	23	24	24	NUM
ejpam-5757	217	24	h((n−	h((n−	PROPN
ejpam-5757	217	25	1)u)−	1)u)−	NUM
ejpam-5757	217	26	1	1	NUM
ejpam-5757	217	27	12	12	NUM
ejpam-5757	217	28	h(nu	h(nu	NOUN
ejpam-5757	217	29	)	)	PUNCT
ejpam-5757	217	30	(	(	PUNCT
ejpam-5757	217	31	25	25	NUM
ejpam-5757	217	32	)	)	PUNCT
ejpam-5757	217	33	for	for	ADP
ejpam-5757	217	34	all	all	DET
ejpam-5757	217	35	u	u	PROPN
ejpam-5757	217	36	∈	∈	PROPN
ejpam-5757	217	37	u0	u0	NOUN
ejpam-5757	217	38	and	and	CCONJ
ejpam-5757	217	39	all	all	DET
ejpam-5757	217	40	n	n	PRON
ejpam-5757	217	41	∈w	∈w	NOUN
ejpam-5757	217	42	.	.	PUNCT
ejpam-5757	218	1	next	next	ADV
ejpam-5757	218	2	,	,	PUNCT
ejpam-5757	218	3	we	we	PRON
ejpam-5757	218	4	need	need	VERB
ejpam-5757	218	5	to	to	PART
ejpam-5757	218	6	show	show	VERB
ejpam-5757	218	7	that	that	SCONJ
ejpam-5757	218	8	each	each	DET
ejpam-5757	218	9	quintic	quintic	ADJ
ejpam-5757	218	10	mapping	mapping	NOUN
ejpam-5757	218	11	h	h	NOUN
ejpam-5757	218	12	:	:	PUNCT
ejpam-5757	218	13	u	u	X
ejpam-5757	218	14	→	→	SYM
ejpam-5757	218	15	v	v	NUM
ejpam-5757	218	16	fulfills	fulfill	VERB
ejpam-5757	218	17	the	the	DET
ejpam-5757	218	18	inequality	inequality	NOUN
ejpam-5757	218	19	∥ϕ(u)−h(u)∥	∥ϕ(u)−h(u)∥	INTJ
ejpam-5757	218	20	≤	≤	NOUN
ejpam-5757	218	21	lτ(u	lτ(u	NUM
ejpam-5757	218	22	)	)	PUNCT
ejpam-5757	218	23	(	(	PUNCT
ejpam-5757	218	24	26	26	NUM
ejpam-5757	218	25	)	)	PUNCT
ejpam-5757	218	26	for	for	ADP
ejpam-5757	218	27	all	all	DET
ejpam-5757	218	28	u	u	PROPN
ejpam-5757	218	29	∈	∈	PROPN
ejpam-5757	218	30	u0	u0	NOUN
ejpam-5757	218	31	,	,	PUNCT
ejpam-5757	218	32	with	with	ADP
ejpam-5757	218	33	some	some	PRON
ejpam-5757	218	34	0	0	NUM
ejpam-5757	218	35	<	<	X
ejpam-5757	218	36	l	l	NOUN
ejpam-5757	218	37	,	,	PUNCT
ejpam-5757	218	38	is	be	AUX
ejpam-5757	218	39	equal	equal	ADJ
ejpam-5757	218	40	to	to	ADP
ejpam-5757	218	41	hn	hn	PROPN
ejpam-5757	218	42	for	for	ADP
ejpam-5757	218	43	every	every	DET
ejpam-5757	218	44	n	n	NOUN
ejpam-5757	218	45	∈	∈	PROPN
ejpam-5757	218	46	w	w	NOUN
ejpam-5757	218	47	.	.	PUNCT
ejpam-5757	219	1	as	as	ADP
ejpam-5757	219	2	a	a	DET
ejpam-5757	219	3	result	result	NOUN
ejpam-5757	219	4	,	,	PUNCT
ejpam-5757	219	5	we	we	PRON
ejpam-5757	219	6	fix	fix	VERB
ejpam-5757	219	7	n0	n0	ADJ
ejpam-5757	219	8	∈w	∈w	NOUN
ejpam-5757	219	9	and	and	CCONJ
ejpam-5757	219	10	h	h	NOUN
ejpam-5757	219	11	:	:	PUNCT
ejpam-5757	219	12	u	u	X
ejpam-5757	219	13	→	→	SYM
ejpam-5757	219	14	v	v	NUM
ejpam-5757	219	15	fulfills	fulfill	NOUN
ejpam-5757	219	16	(	(	PUNCT
ejpam-5757	219	17	26	26	NUM
ejpam-5757	219	18	)	)	PUNCT
ejpam-5757	219	19	.	.	PUNCT
ejpam-5757	220	1	from	from	ADP
ejpam-5757	220	2	(	(	PUNCT
ejpam-5757	220	3	16	16	NUM
ejpam-5757	220	4	)	)	PUNCT
ejpam-5757	220	5	,	,	PUNCT
ejpam-5757	220	6	for	for	ADP
ejpam-5757	220	7	every	every	DET
ejpam-5757	220	8	u	u	PROPN
ejpam-5757	220	9	∈	∈	PROPN
ejpam-5757	220	10	u0	u0	NOUN
ejpam-5757	220	11	,	,	PUNCT
ejpam-5757	220	12	we	we	PRON
ejpam-5757	220	13	get	get	VERB
ejpam-5757	220	14	∥h(u)−hn0(u)∥	∥h(u)−hn0(u)∥	PROPN
ejpam-5757	220	15	≤	≤	ADJ
ejpam-5757	220	16	∥h(u)−	∥h(u)−	NOUN
ejpam-5757	220	17	ϕ(u)∥+	ϕ(u)∥+	ADV
ejpam-5757	220	18	∥ϕ(u)−hn0(u)∥	∥ϕ(u)−hn0(u)∥	NUM
ejpam-5757	220	19	≤	≤	NOUN
ejpam-5757	220	20	lτ(u	lτ(u	NUM
ejpam-5757	220	21	)	)	PUNCT
ejpam-5757	221	1	+	+	CCONJ
ejpam-5757	221	2	ϑ∗n0	ϑ∗n0	NOUN
ejpam-5757	221	3	(	(	PUNCT
ejpam-5757	221	4	u	u	NOUN
ejpam-5757	221	5	)	)	PUNCT
ejpam-5757	221	6	≤	≤	NOUN
ejpam-5757	221	7	l0τ(u	l0τ(u	NOUN
ejpam-5757	221	8	)	)	PUNCT
ejpam-5757	221	9	∞∑	∞∑	PROPN
ejpam-5757	221	10	m=0	m=0	PROPN
ejpam-5757	221	11	αm	αm	PROPN
ejpam-5757	221	12	n0	n0	PROPN
ejpam-5757	221	13	,	,	PUNCT
ejpam-5757	221	14	(	(	PUNCT
ejpam-5757	221	15	27	27	NUM
ejpam-5757	221	16	)	)	PUNCT
ejpam-5757	221	17	s.	s.	PROPN
ejpam-5757	221	18	karthikeyan	karthikeyan	PROPN
ejpam-5757	221	19	et	et	PROPN
ejpam-5757	221	20	al	al	PROPN
ejpam-5757	221	21	.	.	PUNCT
ejpam-5757	221	22	/	/	SYM
ejpam-5757	221	23	eur	eur	PROPN
ejpam-5757	221	24	.	.	PUNCT
ejpam-5757	222	1	j.	j.	PROPN
ejpam-5757	222	2	pure	pure	PROPN
ejpam-5757	222	3	appl	appl	PROPN
ejpam-5757	222	4	.	.	PROPN
ejpam-5757	222	5	math	math	PROPN
ejpam-5757	222	6	,	,	PUNCT
ejpam-5757	222	7	18	18	NUM
ejpam-5757	222	8	(	(	PUNCT
ejpam-5757	222	9	1	1	NUM
ejpam-5757	222	10	)	)	PUNCT
ejpam-5757	222	11	(	(	PUNCT
ejpam-5757	222	12	2025	2025	NUM
ejpam-5757	222	13	)	)	PUNCT
ejpam-5757	222	14	,	,	PUNCT
ejpam-5757	222	15	5757	5757	NUM
ejpam-5757	222	16	13	13	NUM
ejpam-5757	222	17	of	of	ADP
ejpam-5757	222	18	18	18	NUM
ejpam-5757	222	19	where	where	SCONJ
ejpam-5757	222	20	l0	l0	NOUN
ejpam-5757	222	21	:	:	PUNCT
ejpam-5757	222	22	=	=	SYM
ejpam-5757	222	23	(	(	PUNCT
ejpam-5757	222	24	1	1	NUM
ejpam-5757	222	25	−	−	PROPN
ejpam-5757	222	26	αn0)l	αn0)l	NOUN
ejpam-5757	222	27	+	+	CCONJ
ejpam-5757	222	28	1	1	NUM
ejpam-5757	222	29	120η(n0	120η(n0	NOUN
ejpam-5757	222	30	)	)	PUNCT
ejpam-5757	222	31	>	>	X
ejpam-5757	222	32	0	0	PUNCT
ejpam-5757	223	1	and	and	CCONJ
ejpam-5757	223	2	we	we	PRON
ejpam-5757	223	3	exclude	exclude	VERB
ejpam-5757	223	4	the	the	DET
ejpam-5757	223	5	case	case	NOUN
ejpam-5757	223	6	that	that	SCONJ
ejpam-5757	223	7	τ(u	τ(u	PROPN
ejpam-5757	223	8	)	)	PUNCT
ejpam-5757	223	9	≡	≡	PROPN
ejpam-5757	223	10	0	0	NUM
ejpam-5757	223	11	which	which	PRON
ejpam-5757	223	12	is	be	AUX
ejpam-5757	223	13	trivial	trivial	ADJ
ejpam-5757	223	14	.	.	PUNCT
ejpam-5757	224	1	from	from	ADP
ejpam-5757	224	2	the	the	DET
ejpam-5757	224	3	observation	observation	NOUN
ejpam-5757	224	4	,	,	PUNCT
ejpam-5757	224	5	the	the	DET
ejpam-5757	224	6	functions	function	NOUN
ejpam-5757	224	7	h	h	NOUN
ejpam-5757	224	8	and	and	CCONJ
ejpam-5757	224	9	hn0	hn0	NOUN
ejpam-5757	224	10	are	be	AUX
ejpam-5757	224	11	the	the	DET
ejpam-5757	224	12	solutions	solution	NOUN
ejpam-5757	224	13	to	to	ADP
ejpam-5757	224	14	the	the	DET
ejpam-5757	224	15	equations	equation	NOUN
ejpam-5757	224	16	(	(	PUNCT
ejpam-5757	224	17	25	25	NUM
ejpam-5757	224	18	)	)	PUNCT
ejpam-5757	224	19	for	for	ADP
ejpam-5757	224	20	every	every	DET
ejpam-5757	224	21	n	n	NOUN
ejpam-5757	224	22	∈w	∈w	NOUN
ejpam-5757	224	23	.	.	PUNCT
ejpam-5757	225	1	next	next	ADV
ejpam-5757	225	2	,	,	PUNCT
ejpam-5757	225	3	we	we	PRON
ejpam-5757	225	4	prove	prove	VERB
ejpam-5757	225	5	that	that	SCONJ
ejpam-5757	225	6	,	,	PUNCT
ejpam-5757	225	7	for	for	ADP
ejpam-5757	225	8	every	every	DET
ejpam-5757	225	9	j	j	PROPN
ejpam-5757	225	10	∈	∈	PROPN
ejpam-5757	225	11	n0	n0	PROPN
ejpam-5757	225	12	,	,	PUNCT
ejpam-5757	225	13	we	we	PRON
ejpam-5757	225	14	obtain	obtain	VERB
ejpam-5757	225	15	∥h(u)−hn0(u)∥	∥h(u)−hn0(u)∥	PROPN
ejpam-5757	225	16	≤	≤	PROPN
ejpam-5757	225	17	l0τ(u	l0τ(u	NOUN
ejpam-5757	225	18	)	)	PUNCT
ejpam-5757	226	1	∞∑	∞∑	NUM
ejpam-5757	226	2	m	m	NOUN
ejpam-5757	226	3	=	=	ADJ
ejpam-5757	226	4	j	j	PROPN
ejpam-5757	226	5	α∞	α∞	NUM
ejpam-5757	226	6	n0	n0	X
ejpam-5757	226	7	,	,	PUNCT
ejpam-5757	226	8	(	(	PUNCT
ejpam-5757	226	9	28	28	NUM
ejpam-5757	226	10	)	)	PUNCT
ejpam-5757	226	11	for	for	ADP
ejpam-5757	226	12	all	all	DET
ejpam-5757	226	13	u	u	PROPN
ejpam-5757	226	14	∈	∈	PROPN
ejpam-5757	226	15	u0	u0	NOUN
ejpam-5757	226	16	.	.	PUNCT
ejpam-5757	227	1	the	the	DET
ejpam-5757	227	2	inequality	inequality	NOUN
ejpam-5757	227	3	(	(	PUNCT
ejpam-5757	227	4	27	27	NUM
ejpam-5757	227	5	)	)	PUNCT
ejpam-5757	227	6	is	be	AUX
ejpam-5757	227	7	valid	valid	ADJ
ejpam-5757	227	8	for	for	ADP
ejpam-5757	227	9	the	the	DET
ejpam-5757	227	10	case	case	NOUN
ejpam-5757	227	11	j	j	PROPN
ejpam-5757	228	1	=	=	SYM
ejpam-5757	228	2	0	0	PROPN
ejpam-5757	228	3	.	.	PUNCT
ejpam-5757	229	1	next	next	ADV
ejpam-5757	229	2	,	,	PUNCT
ejpam-5757	229	3	we	we	PRON
ejpam-5757	229	4	set	set	VERB
ejpam-5757	229	5	k	k	PROPN
ejpam-5757	229	6	∈	∈	PROPN
ejpam-5757	229	7	n	n	PROPN
ejpam-5757	229	8	and	and	CCONJ
ejpam-5757	229	9	assume	assume	VERB
ejpam-5757	229	10	(	(	PUNCT
ejpam-5757	229	11	28	28	NUM
ejpam-5757	229	12	)	)	PUNCT
ejpam-5757	229	13	is	be	AUX
ejpam-5757	229	14	true	true	ADJ
ejpam-5757	229	15	for	for	ADP
ejpam-5757	229	16	j	j	PROPN
ejpam-5757	229	17	=	=	PROPN
ejpam-5757	229	18	k.	k.	PROPN
ejpam-5757	230	1	in	in	ADP
ejpam-5757	230	2	view	view	NOUN
ejpam-5757	230	3	of	of	ADP
ejpam-5757	230	4	(	(	PUNCT
ejpam-5757	230	5	27	27	NUM
ejpam-5757	230	6	)	)	PUNCT
ejpam-5757	230	7	,	,	PUNCT
ejpam-5757	230	8	for	for	ADP
ejpam-5757	230	9	every	every	DET
ejpam-5757	230	10	u	u	PROPN
ejpam-5757	230	11	∈	∈	PROPN
ejpam-5757	230	12	u0	u0	NOUN
ejpam-5757	230	13	,	,	PUNCT
ejpam-5757	230	14	we	we	PRON
ejpam-5757	230	15	have	have	VERB
ejpam-5757	230	16	∥h(u)−hn0(u)∥	∥h(u)−hn0(u)∥	NOUN
ejpam-5757	230	17	≤	≤	NUM
ejpam-5757	230	18	1	1	NUM
ejpam-5757	230	19	120	120	NUM
ejpam-5757	230	20	l0τ((n0	l0τ((n0	NOUN
ejpam-5757	230	21	+	+	CCONJ
ejpam-5757	230	22	3)u	3)u	NUM
ejpam-5757	230	23	)	)	PUNCT
ejpam-5757	230	24	∞∑	∞∑	NUM
ejpam-5757	230	25	m	m	NOUN
ejpam-5757	230	26	=	=	PROPN
ejpam-5757	230	27	k	k	PROPN
ejpam-5757	230	28	αm	αm	PROPN
ejpam-5757	230	29	n0	n0	PROPN
ejpam-5757	230	30	+	+	CCONJ
ejpam-5757	230	31	1	1	NUM
ejpam-5757	230	32	24	24	NUM
ejpam-5757	230	33	l0τ((n0	l0τ((n0	NOUN
ejpam-5757	230	34	+	+	CCONJ
ejpam-5757	230	35	2)u	2)u	NOUN
ejpam-5757	230	36	)	)	PUNCT
ejpam-5757	230	37	∞∑	∞∑	NUM
ejpam-5757	230	38	m	m	NOUN
ejpam-5757	230	39	=	=	PROPN
ejpam-5757	230	40	k	k	PROPN
ejpam-5757	230	41	αm	αm	PROPN
ejpam-5757	230	42	n0	n0	PROPN
ejpam-5757	231	1	+	+	CCONJ
ejpam-5757	231	2	1	1	NUM
ejpam-5757	231	3	120	120	NUM
ejpam-5757	231	4	l0τ((n0	l0τ((n0	NOUN
ejpam-5757	231	5	−	−	NOUN
ejpam-5757	231	6	2)u	2)u	NOUN
ejpam-5757	231	7	)	)	PUNCT
ejpam-5757	231	8	∞∑	∞∑	NUM
ejpam-5757	231	9	m	m	NOUN
ejpam-5757	231	10	=	=	PROPN
ejpam-5757	231	11	k	k	PROPN
ejpam-5757	231	12	αm	αm	PROPN
ejpam-5757	231	13	n0	n0	PROPN
ejpam-5757	231	14	+	+	CCONJ
ejpam-5757	231	15	1	1	NUM
ejpam-5757	231	16	12	12	NUM
ejpam-5757	231	17	l0τ((n0	l0τ((n0	NOUN
ejpam-5757	231	18	+	+	CCONJ
ejpam-5757	231	19	1)u	1)u	NOUN
ejpam-5757	231	20	)	)	PUNCT
ejpam-5757	231	21	∞∑	∞∑	NUM
ejpam-5757	231	22	m	m	NOUN
ejpam-5757	231	23	=	=	PROPN
ejpam-5757	231	24	k	k	PROPN
ejpam-5757	231	25	αm	αm	PROPN
ejpam-5757	231	26	n0	n0	PROPN
ejpam-5757	232	1	+	+	CCONJ
ejpam-5757	232	2	1	1	NUM
ejpam-5757	232	3	24	24	NUM
ejpam-5757	232	4	l0τ((n0	l0τ((n0	PROPN
ejpam-5757	232	5	−	−	PROPN
ejpam-5757	232	6	1)u	1)u	NOUN
ejpam-5757	232	7	)	)	PUNCT
ejpam-5757	232	8	∞∑	∞∑	NUM
ejpam-5757	232	9	m	m	NOUN
ejpam-5757	232	10	=	=	PROPN
ejpam-5757	232	11	k	k	PROPN
ejpam-5757	232	12	αm	αm	PROPN
ejpam-5757	232	13	n0	n0	PROPN
ejpam-5757	233	1	+	+	CCONJ
ejpam-5757	233	2	1	1	NUM
ejpam-5757	233	3	12	12	NUM
ejpam-5757	233	4	l0τ((n0)u	l0τ((n0)u	NOUN
ejpam-5757	233	5	)	)	PUNCT
ejpam-5757	233	6	∞∑	∞∑	NUM
ejpam-5757	233	7	m	m	NOUN
ejpam-5757	233	8	=	=	PROPN
ejpam-5757	233	9	k	k	PROPN
ejpam-5757	233	10	αm	αm	PROPN
ejpam-5757	233	11	n0	n0	PROPN
ejpam-5757	233	12	≤	≤	PROPN
ejpam-5757	233	13	l0αn0τ(u)(u	l0αn0τ(u)(u	NOUN
ejpam-5757	233	14	)	)	PUNCT
ejpam-5757	233	15	∞∑	∞∑	NUM
ejpam-5757	233	16	m	m	NOUN
ejpam-5757	233	17	=	=	PROPN
ejpam-5757	233	18	k	k	PROPN
ejpam-5757	233	19	αm	αm	PROPN
ejpam-5757	233	20	n0	n0	PROPN
ejpam-5757	233	21	.	.	PUNCT
ejpam-5757	234	1	thus	thus	ADV
ejpam-5757	234	2	∥h(u)−hn0(u)∥	∥h(u)−hn0(u)∥	PROPN
ejpam-5757	234	3	≤	≤	PROPN
ejpam-5757	234	4	l0τ(u	l0τ(u	NOUN
ejpam-5757	234	5	)	)	PUNCT
ejpam-5757	235	1	∞∑	∞∑	NUM
ejpam-5757	235	2	m	m	NOUN
ejpam-5757	235	3	=	=	ADJ
ejpam-5757	235	4	k+1	k+1	X
ejpam-5757	235	5	αm	αm	PROPN
ejpam-5757	235	6	n0	n0	PROPN
ejpam-5757	235	7	.	.	PUNCT
ejpam-5757	236	1	so	so	ADV
ejpam-5757	236	2	the	the	DET
ejpam-5757	236	3	condition	condition	NOUN
ejpam-5757	236	4	(	(	PUNCT
ejpam-5757	236	5	28	28	NUM
ejpam-5757	236	6	)	)	PUNCT
ejpam-5757	236	7	is	be	AUX
ejpam-5757	236	8	valid	valid	ADJ
ejpam-5757	236	9	for	for	ADP
ejpam-5757	236	10	j	j	PROPN
ejpam-5757	236	11	=	=	SYM
ejpam-5757	236	12	k	k	PROPN
ejpam-5757	237	1	+	+	NOUN
ejpam-5757	237	2	1	1	X
ejpam-5757	237	3	.	.	X
ejpam-5757	237	4	hence	hence	ADV
ejpam-5757	237	5	we	we	PRON
ejpam-5757	237	6	may	may	AUX
ejpam-5757	237	7	infer	infer	VERB
ejpam-5757	237	8	that	that	SCONJ
ejpam-5757	237	9	for	for	ADP
ejpam-5757	237	10	any	any	DET
ejpam-5757	237	11	j	j	PROPN
ejpam-5757	237	12	∈	∈	PROPN
ejpam-5757	237	13	n0	n0	PROPN
ejpam-5757	237	14	,	,	PUNCT
ejpam-5757	237	15	the	the	DET
ejpam-5757	237	16	inequality	inequality	NOUN
ejpam-5757	237	17	(	(	PUNCT
ejpam-5757	237	18	28	28	NUM
ejpam-5757	237	19	)	)	PUNCT
ejpam-5757	237	20	holds	hold	VERB
ejpam-5757	237	21	.	.	PUNCT
ejpam-5757	238	1	taking	take	VERB
ejpam-5757	238	2	the	the	DET
ejpam-5757	238	3	limit	limit	NOUN
ejpam-5757	238	4	j	j	PROPN
ejpam-5757	238	5	→	→	SYM
ejpam-5757	238	6	∞	∞	PROPN
ejpam-5757	238	7	in	in	ADP
ejpam-5757	238	8	(	(	PUNCT
ejpam-5757	238	9	28	28	NUM
ejpam-5757	238	10	)	)	PUNCT
ejpam-5757	238	11	,	,	PUNCT
ejpam-5757	238	12	we	we	PRON
ejpam-5757	238	13	obtain	obtain	VERB
ejpam-5757	238	14	h	h	NOUN
ejpam-5757	238	15	=	=	SYM
ejpam-5757	238	16	hn0	hn0	PROPN
ejpam-5757	238	17	.	.	PUNCT
ejpam-5757	239	1	(	(	PUNCT
ejpam-5757	239	2	29	29	NUM
ejpam-5757	239	3	)	)	PUNCT
ejpam-5757	239	4	also	also	ADV
ejpam-5757	239	5	,	,	PUNCT
ejpam-5757	239	6	in	in	ADP
ejpam-5757	239	7	view	view	NOUN
ejpam-5757	239	8	of	of	ADP
ejpam-5757	239	9	(	(	PUNCT
ejpam-5757	239	10	23	23	NUM
ejpam-5757	239	11	)	)	PUNCT
ejpam-5757	239	12	,	,	PUNCT
ejpam-5757	239	13	we	we	PRON
ejpam-5757	239	14	have	have	VERB
ejpam-5757	239	15	∥ϕ(u)−hn0(u)∥	∥ϕ(u)−hn0(u)∥	NUM
ejpam-5757	239	16	≤	≤	PROPN
ejpam-5757	239	17	(	(	PUNCT
ejpam-5757	239	18	η(n	η(n	NOUN
ejpam-5757	239	19	)	)	PUNCT
ejpam-5757	239	20	+	+	NOUN
ejpam-5757	240	1	1)τ(u	1)τ(u	NUM
ejpam-5757	240	2	)	)	PUNCT
ejpam-5757	240	3	120(1−	120(1−	NUM
ejpam-5757	240	4	αn	αn	NOUN
ejpam-5757	240	5	)	)	PUNCT
ejpam-5757	240	6	for	for	ADP
ejpam-5757	240	7	all	all	DET
ejpam-5757	240	8	u	u	PROPN
ejpam-5757	240	9	∈	∈	PROPN
ejpam-5757	240	10	u0	u0	NOUN
ejpam-5757	240	11	and	and	CCONJ
ejpam-5757	240	12	all	all	PRON
ejpam-5757	240	13	n	n	DET
ejpam-5757	240	14	∈	∈	PROPN
ejpam-5757	240	15	w	w	NOUN
ejpam-5757	240	16	.	.	PUNCT
ejpam-5757	241	1	this	this	PRON
ejpam-5757	241	2	implies	imply	VERB
ejpam-5757	241	3	the	the	DET
ejpam-5757	241	4	condition	condition	NOUN
ejpam-5757	241	5	(	(	PUNCT
ejpam-5757	241	6	18	18	NUM
ejpam-5757	241	7	)	)	PUNCT
ejpam-5757	241	8	with	with	ADP
ejpam-5757	241	9	h	h	NOUN
ejpam-5757	241	10	=	=	SYM
ejpam-5757	241	11	hn0	hn0	PROPN
ejpam-5757	241	12	and	and	CCONJ
ejpam-5757	241	13	(	(	PUNCT
ejpam-5757	241	14	29	29	NUM
ejpam-5757	241	15	)	)	PUNCT
ejpam-5757	241	16	confirms	confirm	VERB
ejpam-5757	241	17	the	the	DET
ejpam-5757	241	18	uniqueness	uniqueness	NOUN
ejpam-5757	241	19	of	of	ADP
ejpam-5757	241	20	h.	h.	PROPN
ejpam-5757	241	21	3	3	NUM
ejpam-5757	241	22	.	.	X
ejpam-5757	241	23	hyperstability	hyperstability	VERB
ejpam-5757	241	24	the	the	DET
ejpam-5757	241	25	φ	φ	NOUN
ejpam-5757	241	26	-	-	NOUN
ejpam-5757	241	27	hyperstability	hyperstability	NOUN
ejpam-5757	241	28	of	of	ADP
ejpam-5757	241	29	(	(	PUNCT
ejpam-5757	241	30	2	2	NUM
ejpam-5757	241	31	)	)	PUNCT
ejpam-5757	241	32	in	in	ADP
ejpam-5757	241	33	banach	banach	NOUN
ejpam-5757	241	34	spaces	space	NOUN
ejpam-5757	241	35	is	be	AUX
ejpam-5757	241	36	the	the	DET
ejpam-5757	241	37	subject	subject	NOUN
ejpam-5757	241	38	of	of	ADP
ejpam-5757	241	39	the	the	DET
ejpam-5757	241	40	following	follow	VERB
ejpam-5757	241	41	theorem	theorem	NOUN
ejpam-5757	241	42	.	.	PUNCT
ejpam-5757	242	1	in	in	ADP
ejpam-5757	242	2	particular	particular	ADJ
ejpam-5757	242	3	,	,	PUNCT
ejpam-5757	242	4	we	we	PRON
ejpam-5757	242	5	take	take	VERB
ejpam-5757	242	6	into	into	ADP
ejpam-5757	242	7	account	account	NOUN
ejpam-5757	242	8	functions	function	NOUN
ejpam-5757	242	9	ϕ	ϕ	NOUN
ejpam-5757	242	10	:	:	PUNCT
ejpam-5757	242	11	u	u	X
ejpam-5757	242	12	→	→	SYM
ejpam-5757	242	13	v	v	NUM
ejpam-5757	242	14	fulfilling	fulfil	VERB
ejpam-5757	242	15	(	(	PUNCT
ejpam-5757	242	16	2	2	NUM
ejpam-5757	242	17	)	)	PUNCT
ejpam-5757	242	18	,	,	PUNCT
ejpam-5757	242	19	i.e.	i.e.	X
ejpam-5757	242	20	,	,	PUNCT
ejpam-5757	242	21	∥dϕ(u	∥dϕ(u	PROPN
ejpam-5757	242	22	,	,	PUNCT
ejpam-5757	242	23	v)∥	v)∥	NUM
ejpam-5757	242	24	≤	≤	NUM
ejpam-5757	242	25	φ(u	φ(u	NOUN
ejpam-5757	242	26	,	,	PUNCT
ejpam-5757	242	27	v	v	NOUN
ejpam-5757	242	28	)	)	PUNCT
ejpam-5757	242	29	s.	s.	PROPN
ejpam-5757	242	30	karthikeyan	karthikeyan	PROPN
ejpam-5757	242	31	et	et	PROPN
ejpam-5757	242	32	al	al	PROPN
ejpam-5757	242	33	.	.	PUNCT
ejpam-5757	242	34	/	/	SYM
ejpam-5757	242	35	eur	eur	PROPN
ejpam-5757	242	36	.	.	PUNCT
ejpam-5757	243	1	j.	j.	PROPN
ejpam-5757	243	2	pure	pure	PROPN
ejpam-5757	243	3	appl	appl	PROPN
ejpam-5757	243	4	.	.	PROPN
ejpam-5757	243	5	math	math	PROPN
ejpam-5757	243	6	,	,	PUNCT
ejpam-5757	243	7	18	18	NUM
ejpam-5757	243	8	(	(	PUNCT
ejpam-5757	243	9	1	1	NUM
ejpam-5757	243	10	)	)	PUNCT
ejpam-5757	243	11	(	(	PUNCT
ejpam-5757	243	12	2025	2025	NUM
ejpam-5757	243	13	)	)	PUNCT
ejpam-5757	243	14	,	,	PUNCT
ejpam-5757	243	15	5757	5757	NUM
ejpam-5757	243	16	14	14	NUM
ejpam-5757	243	17	of	of	ADP
ejpam-5757	243	18	18	18	NUM
ejpam-5757	243	19	for	for	ADP
ejpam-5757	243	20	all	all	DET
ejpam-5757	243	21	u	u	NOUN
ejpam-5757	243	22	,	,	PUNCT
ejpam-5757	243	23	v	v	PROPN
ejpam-5757	243	24	∈	∈	PROPN
ejpam-5757	243	25	u0	u0	NOUN
ejpam-5757	243	26	such	such	ADJ
ejpam-5757	243	27	that	that	SCONJ
ejpam-5757	243	28	u+	u+	NOUN
ejpam-5757	243	29	3v	3v	NUM
ejpam-5757	243	30	̸=	̸=	PROPN
ejpam-5757	243	31	0	0	NUM
ejpam-5757	243	32	,	,	PUNCT
ejpam-5757	243	33	u+	u+	NUM
ejpam-5757	243	34	2v	2v	PROPN
ejpam-5757	243	35	̸=	̸=	PROPN
ejpam-5757	243	36	0	0	NUM
ejpam-5757	243	37	,	,	PUNCT
ejpam-5757	243	38	u−	u−	PROPN
ejpam-5757	243	39	2v	2v	PROPN
ejpam-5757	243	40	̸=	̸=	PROPN
ejpam-5757	243	41	0	0	NUM
ejpam-5757	243	42	,	,	PUNCT
ejpam-5757	243	43	u−	u−	PROPN
ejpam-5757	243	44	v	v	ADP
ejpam-5757	243	45	̸=	̸=	PROPN
ejpam-5757	243	46	0	0	NUM
ejpam-5757	243	47	,	,	PUNCT
ejpam-5757	243	48	u+	u+	NOUN
ejpam-5757	243	49	v	v	ADP
ejpam-5757	243	50	̸=	̸=	PROPN
ejpam-5757	243	51	0	0	NUM
ejpam-5757	243	52	with	with	ADP
ejpam-5757	243	53	a	a	DET
ejpam-5757	243	54	given	give	VERB
ejpam-5757	243	55	mapping	mapping	NOUN
ejpam-5757	243	56	φ	φ	NOUN
ejpam-5757	243	57	:	:	PUNCT
ejpam-5757	243	58	u0	u0	ADJ
ejpam-5757	243	59	×	×	PROPN
ejpam-5757	243	60	u0	u0	NOUN
ejpam-5757	243	61	→	→	NOUN
ejpam-5757	243	62	r+	r+	X
ejpam-5757	243	63	.	.	PUNCT
ejpam-5757	244	1	next	next	ADV
ejpam-5757	244	2	,	,	PUNCT
ejpam-5757	244	3	we	we	PRON
ejpam-5757	244	4	find	find	VERB
ejpam-5757	244	5	a	a	DET
ejpam-5757	244	6	unique	unique	ADJ
ejpam-5757	244	7	quintic	quintic	ADJ
ejpam-5757	244	8	mapping	mapping	NOUN
ejpam-5757	244	9	h	h	NOUN
ejpam-5757	244	10	:	:	PUNCT
ejpam-5757	244	11	u	u	X
ejpam-5757	244	12	→	→	SYM
ejpam-5757	244	13	v	v	X
ejpam-5757	244	14	which	which	PRON
ejpam-5757	244	15	is	be	AUX
ejpam-5757	244	16	near	near	ADJ
ejpam-5757	244	17	to	to	ADP
ejpam-5757	244	18	ϕ.	ϕ.	PROPN
ejpam-5757	244	19	after	after	ADP
ejpam-5757	244	20	that	that	PRON
ejpam-5757	244	21	,	,	PUNCT
ejpam-5757	244	22	assuming	assume	VERB
ejpam-5757	244	23	some	some	DET
ejpam-5757	244	24	further	further	ADJ
ejpam-5757	244	25	φ	φ	PROPN
ejpam-5757	244	26	assumptions	assumption	NOUN
ejpam-5757	244	27	,	,	PUNCT
ejpam-5757	244	28	we	we	PRON
ejpam-5757	244	29	demonstrate	demonstrate	VERB
ejpam-5757	244	30	that	that	SCONJ
ejpam-5757	244	31	the	the	DET
ejpam-5757	244	32	conditional	conditional	ADJ
ejpam-5757	244	33	functional	functional	ADJ
ejpam-5757	244	34	equation	equation	NOUN
ejpam-5757	244	35	(	(	PUNCT
ejpam-5757	244	36	2	2	X
ejpam-5757	244	37	)	)	PUNCT
ejpam-5757	244	38	belongs	belong	VERB
ejpam-5757	244	39	to	to	ADP
ejpam-5757	244	40	the	the	DET
ejpam-5757	244	41	family	family	NOUN
ejpam-5757	244	42	of	of	ADP
ejpam-5757	244	43	functions	function	NOUN
ejpam-5757	244	44	ϕ	ϕ	NOUN
ejpam-5757	244	45	:	:	PUNCT
ejpam-5757	244	46	u	u	X
ejpam-5757	244	47	→	→	SYM
ejpam-5757	244	48	v	v	NOUN
ejpam-5757	244	49	and	and	CCONJ
ejpam-5757	244	50	is	be	AUX
ejpam-5757	244	51	φ	φ	VERB
ejpam-5757	244	52	-	-	ADJ
ejpam-5757	244	53	hyperstable	hyperstable	ADJ
ejpam-5757	244	54	.	.	PUNCT
ejpam-5757	245	1	theorem	theorem	NOUN
ejpam-5757	245	2	5	5	NUM
ejpam-5757	245	3	.	.	PUNCT
ejpam-5757	246	1	let	let	VERB
ejpam-5757	246	2	τ1	τ1	NOUN
ejpam-5757	246	3	,	,	PUNCT
ejpam-5757	246	4	τ2	τ2	PROPN
ejpam-5757	246	5	,	,	PUNCT
ejpam-5757	246	6	αm	αm	NOUN
ejpam-5757	246	7	and	and	CCONJ
ejpam-5757	246	8	w	w	NOUN
ejpam-5757	246	9	be	be	AUX
ejpam-5757	246	10	as	as	ADP
ejpam-5757	246	11	in	in	ADP
ejpam-5757	246	12	theorem	theorem	NOUN
ejpam-5757	246	13	3	3	X
ejpam-5757	247	1	.	.	X
ejpam-5757	247	2	assume	assume	VERB
ejpam-5757	247	3	that	that	X
ejpam-5757	247	4	limm→+∞	limm→+∞	X
ejpam-5757	247	5	η1(m	η1(m	PROPN
ejpam-5757	247	6	)	)	PUNCT
ejpam-5757	247	7	=	=	SYM
ejpam-5757	248	1	0	0	NUM
ejpam-5757	248	2	,	,	PUNCT
ejpam-5757	248	3	limm→+∞	limm→+∞	VERB
ejpam-5757	248	4	η1(m)η2(m	η1(m)η2(m	ADP
ejpam-5757	248	5	)	)	PUNCT
ejpam-5757	248	6	=	=	SYM
ejpam-5757	248	7	0	0	NUM
ejpam-5757	248	8	,	,	PUNCT
ejpam-5757	248	9	limm→+∞	limm→+∞	VERB
ejpam-5757	248	10	η1(m−	η1(m−	PROPN
ejpam-5757	249	1	2)η2(m−	2)η2(m−	NUM
ejpam-5757	249	2	2	2	NUM
ejpam-5757	249	3	)	)	PUNCT
ejpam-5757	249	4	=	=	SYM
ejpam-5757	250	1	0	0	X
ejpam-5757	250	2	.	.	PUNCT
ejpam-5757	251	1	then	then	ADV
ejpam-5757	251	2	every	every	DET
ejpam-5757	251	3	mapping	mapping	NOUN
ejpam-5757	251	4	ϕ	ϕ	NOUN
ejpam-5757	251	5	:	:	PUNCT
ejpam-5757	251	6	u	u	X
ejpam-5757	251	7	→	→	SYM
ejpam-5757	251	8	v	v	NUM
ejpam-5757	251	9	fulfilling	fulfil	VERB
ejpam-5757	251	10	(	(	PUNCT
ejpam-5757	251	11	3	3	NUM
ejpam-5757	251	12	)	)	PUNCT
ejpam-5757	251	13	is	be	AUX
ejpam-5757	251	14	a	a	DET
ejpam-5757	251	15	solution	solution	NOUN
ejpam-5757	251	16	of	of	ADP
ejpam-5757	251	17	(	(	PUNCT
ejpam-5757	251	18	2	2	NUM
ejpam-5757	251	19	)	)	PUNCT
ejpam-5757	251	20	on	on	ADP
ejpam-5757	251	21	u0	u0	ADJ
ejpam-5757	251	22	.	.	PUNCT
ejpam-5757	252	1	proof	proof	NOUN
ejpam-5757	252	2	.	.	PUNCT
ejpam-5757	253	1	suppose	suppose	VERB
ejpam-5757	253	2	that	that	SCONJ
ejpam-5757	253	3	ϕ	ϕ	NOUN
ejpam-5757	253	4	:	:	PUNCT
ejpam-5757	253	5	u	u	PROPN
ejpam-5757	253	6	→	→	SYM
ejpam-5757	253	7	v	v	NUM
ejpam-5757	253	8	fulfills	fulfill	NOUN
ejpam-5757	253	9	(	(	PUNCT
ejpam-5757	253	10	3	3	NUM
ejpam-5757	253	11	)	)	PUNCT
ejpam-5757	253	12	.	.	PUNCT
ejpam-5757	254	1	by	by	ADP
ejpam-5757	254	2	theorem	theorem	NOUN
ejpam-5757	254	3	3	3	NUM
ejpam-5757	254	4	,	,	PUNCT
ejpam-5757	254	5	there	there	PRON
ejpam-5757	254	6	is	be	VERB
ejpam-5757	254	7	a	a	DET
ejpam-5757	254	8	mapping	mapping	NOUN
ejpam-5757	254	9	h	h	NOUN
ejpam-5757	254	10	:	:	PUNCT
ejpam-5757	254	11	u	u	X
ejpam-5757	254	12	→	→	SYM
ejpam-5757	254	13	v	v	NUM
ejpam-5757	254	14	fulfilling	fulfil	VERB
ejpam-5757	254	15	(	(	PUNCT
ejpam-5757	254	16	2	2	NUM
ejpam-5757	254	17	)	)	PUNCT
ejpam-5757	254	18	and	and	CCONJ
ejpam-5757	254	19	∥ϕ(u)−h(u)∥	∥ϕ(u)−h(u)∥	NOUN
ejpam-5757	254	20	≤	≤	NUM
ejpam-5757	254	21	η0τ1(u)τ2(u	η0τ1(u)τ2(u	NOUN
ejpam-5757	254	22	)	)	PUNCT
ejpam-5757	254	23	for	for	ADP
ejpam-5757	254	24	all	all	DET
ejpam-5757	254	25	u	u	PROPN
ejpam-5757	254	26	∈	∈	PROPN
ejpam-5757	254	27	u0	u0	NOUN
ejpam-5757	254	28	,	,	PUNCT
ejpam-5757	254	29	where	where	SCONJ
ejpam-5757	254	30	η0	η0	ADJ
ejpam-5757	254	31	:	:	PUNCT
ejpam-5757	254	32	=	=	SYM
ejpam-5757	254	33	inf	inf	ADJ
ejpam-5757	254	34	m∈w	m∈w	NOUN
ejpam-5757	254	35	{	{	PUNCT
ejpam-5757	254	36	η1(m	η1(m	PROPN
ejpam-5757	254	37	)	)	PUNCT
ejpam-5757	254	38	120(1−	120(1−	NUM
ejpam-5757	254	39	αm	αm	NOUN
ejpam-5757	254	40	)	)	PUNCT
ejpam-5757	254	41	}	}	PUNCT
ejpam-5757	254	42	.	.	PUNCT
ejpam-5757	255	1	so	so	ADV
ejpam-5757	255	2	,	,	PUNCT
ejpam-5757	255	3	in	in	ADP
ejpam-5757	255	4	view	view	NOUN
ejpam-5757	255	5	of	of	ADP
ejpam-5757	255	6	(	(	PUNCT
ejpam-5757	255	7	5	5	NUM
ejpam-5757	255	8	)	)	PUNCT
ejpam-5757	255	9	,	,	PUNCT
ejpam-5757	255	10	η0	η0	NOUN
ejpam-5757	255	11	=	=	SYM
ejpam-5757	255	12	0	0	NUM
ejpam-5757	255	13	.	.	PUNCT
ejpam-5757	256	1	this	this	PRON
ejpam-5757	256	2	means	mean	VERB
ejpam-5757	256	3	that	that	SCONJ
ejpam-5757	256	4	ϕ(u	ϕ(u	NOUN
ejpam-5757	256	5	)	)	PUNCT
ejpam-5757	257	1	=	=	SYM
ejpam-5757	257	2	h(u	h(u	PROPN
ejpam-5757	257	3	)	)	PUNCT
ejpam-5757	257	4	for	for	ADP
ejpam-5757	257	5	all	all	DET
ejpam-5757	257	6	u	u	PROPN
ejpam-5757	257	7	∈	∈	PROPN
ejpam-5757	257	8	u0	u0	NOUN
ejpam-5757	257	9	.	.	PUNCT
ejpam-5757	258	1	so	so	ADV
ejpam-5757	258	2	dϕ(u	dϕ(u	NUM
ejpam-5757	258	3	,	,	PUNCT
ejpam-5757	258	4	v	v	NOUN
ejpam-5757	258	5	)	)	PUNCT
ejpam-5757	258	6	=	=	SYM
ejpam-5757	258	7	0	0	NUM
ejpam-5757	259	1	for	for	ADP
ejpam-5757	259	2	all	all	DET
ejpam-5757	259	3	u	u	NOUN
ejpam-5757	259	4	,	,	PUNCT
ejpam-5757	259	5	v	v	PROPN
ejpam-5757	259	6	∈	∈	PROPN
ejpam-5757	259	7	u0	u0	NOUN
ejpam-5757	259	8	such	such	ADJ
ejpam-5757	259	9	that	that	SCONJ
ejpam-5757	259	10	u+	u+	NOUN
ejpam-5757	259	11	3v	3v	NUM
ejpam-5757	259	12	̸=	̸=	PROPN
ejpam-5757	259	13	0	0	NUM
ejpam-5757	259	14	,	,	PUNCT
ejpam-5757	259	15	u+	u+	NUM
ejpam-5757	259	16	2v	2v	PROPN
ejpam-5757	259	17	̸=	̸=	PROPN
ejpam-5757	259	18	0	0	NUM
ejpam-5757	259	19	,	,	PUNCT
ejpam-5757	259	20	u−	u−	PROPN
ejpam-5757	259	21	2v	2v	PROPN
ejpam-5757	259	22	̸=	̸=	PROPN
ejpam-5757	259	23	0	0	NUM
ejpam-5757	259	24	,	,	PUNCT
ejpam-5757	259	25	u−	u−	PROPN
ejpam-5757	259	26	v	v	ADP
ejpam-5757	259	27	̸=	̸=	PROPN
ejpam-5757	259	28	0	0	NUM
ejpam-5757	259	29	,	,	PUNCT
ejpam-5757	259	30	u+	u+	NOUN
ejpam-5757	259	31	v	v	ADP
ejpam-5757	259	32	̸=	̸=	PROPN
ejpam-5757	259	33	0	0	NUM
ejpam-5757	259	34	which	which	PRON
ejpam-5757	259	35	gives	give	VERB
ejpam-5757	259	36	that	that	PRON
ejpam-5757	259	37	ϕ	ϕ	PROPN
ejpam-5757	259	38	fulfills	fulfills	PROPN
ejpam-5757	259	39	(	(	PUNCT
ejpam-5757	259	40	2	2	NUM
ejpam-5757	259	41	)	)	PUNCT
ejpam-5757	259	42	on	on	ADP
ejpam-5757	259	43	u0	u0	ADJ
ejpam-5757	259	44	.	.	PUNCT
ejpam-5757	260	1	corollary	corollary	ADJ
ejpam-5757	260	2	1	1	NUM
ejpam-5757	260	3	.	.	PUNCT
ejpam-5757	261	1	let	let	VERB
ejpam-5757	261	2	ϵ	ϵ	PRON
ejpam-5757	261	3	≥	≥	NOUN
ejpam-5757	261	4	0	0	NUM
ejpam-5757	261	5	,	,	PUNCT
ejpam-5757	261	6	c1	c1	NOUN
ejpam-5757	261	7	,	,	PUNCT
ejpam-5757	261	8	c2	c2	PROPN
ejpam-5757	261	9	∈	∈	PROPN
ejpam-5757	261	10	r	r	NOUN
ejpam-5757	261	11	with	with	ADP
ejpam-5757	261	12	c1	c1	PROPN
ejpam-5757	261	13	+	+	CCONJ
ejpam-5757	261	14	c2	c2	PROPN
ejpam-5757	261	15	<	<	X
ejpam-5757	261	16	0	0	X
ejpam-5757	261	17	.	.	PUNCT
ejpam-5757	261	18	assume	assume	VERB
ejpam-5757	261	19	that	that	SCONJ
ejpam-5757	261	20	a	a	DET
ejpam-5757	261	21	mapping	mapping	NOUN
ejpam-5757	261	22	ϕ	ϕ	NOUN
ejpam-5757	261	23	:	:	PUNCT
ejpam-5757	261	24	u	u	X
ejpam-5757	261	25	→	→	SYM
ejpam-5757	261	26	v	v	NUM
ejpam-5757	261	27	fulfills	fulfill	VERB
ejpam-5757	261	28	ϕ(0	ϕ(0	PRON
ejpam-5757	261	29	)	)	PUNCT
ejpam-5757	261	30	=	=	SYM
ejpam-5757	261	31	0	0	NUM
ejpam-5757	261	32	and	and	CCONJ
ejpam-5757	261	33	∥dϕ(u	∥dϕ(u	PROPN
ejpam-5757	261	34	,	,	PUNCT
ejpam-5757	261	35	v)∥	v)∥	PUNCT
ejpam-5757	261	36	≤	≤	NUM
ejpam-5757	261	37	ϵ∥u∥c1∥v∥c2	ϵ∥u∥c1∥v∥c2	X
ejpam-5757	261	38	(	(	PUNCT
ejpam-5757	261	39	30	30	NUM
ejpam-5757	261	40	)	)	PUNCT
ejpam-5757	261	41	for	for	ADP
ejpam-5757	261	42	all	all	DET
ejpam-5757	261	43	u	u	NOUN
ejpam-5757	261	44	,	,	PUNCT
ejpam-5757	261	45	v	v	PROPN
ejpam-5757	261	46	∈	∈	NOUN
ejpam-5757	261	47	u0	u0	NOUN
ejpam-5757	261	48	such	such	ADJ
ejpam-5757	261	49	that	that	SCONJ
ejpam-5757	261	50	u+3v	u+3v	PROPN
ejpam-5757	261	51	̸=	̸=	PROPN
ejpam-5757	261	52	0	0	NUM
ejpam-5757	261	53	,	,	PUNCT
ejpam-5757	261	54	u+2v	u+2v	PROPN
ejpam-5757	261	55	̸=	̸=	PROPN
ejpam-5757	261	56	0	0	NUM
ejpam-5757	261	57	,	,	PUNCT
ejpam-5757	261	58	u−	u−	PROPN
ejpam-5757	261	59	2v	2v	PROPN
ejpam-5757	261	60	̸=	̸=	PROPN
ejpam-5757	261	61	0	0	NUM
ejpam-5757	261	62	,	,	PUNCT
ejpam-5757	261	63	u−	u−	PROPN
ejpam-5757	261	64	v	v	ADP
ejpam-5757	261	65	̸=	̸=	PROPN
ejpam-5757	261	66	0	0	NUM
ejpam-5757	261	67	,	,	PUNCT
ejpam-5757	261	68	u+	u+	NOUN
ejpam-5757	261	69	v	v	ADP
ejpam-5757	261	70	̸=	̸=	PROPN
ejpam-5757	261	71	0	0	NUM
ejpam-5757	261	72	.	.	PUNCT
ejpam-5757	262	1	then	then	ADV
ejpam-5757	262	2	ϕ	ϕ	PROPN
ejpam-5757	262	3	is	be	AUX
ejpam-5757	262	4	quintic	quintic	ADJ
ejpam-5757	262	5	on	on	ADP
ejpam-5757	262	6	u0	u0	ADJ
ejpam-5757	262	7	.	.	PUNCT
ejpam-5757	263	1	proof	proof	NOUN
ejpam-5757	263	2	.	.	PUNCT
ejpam-5757	264	1	theorem	theorem	NOUN
ejpam-5757	264	2	3	3	NUM
ejpam-5757	264	3	is	be	AUX
ejpam-5757	264	4	supported	support	VERB
ejpam-5757	264	5	by	by	ADP
ejpam-5757	264	6	the	the	DET
ejpam-5757	264	7	proof	proof	NOUN
ejpam-5757	264	8	,	,	PUNCT
ejpam-5757	264	9	which	which	PRON
ejpam-5757	264	10	defines	define	VERB
ejpam-5757	264	11	τ1	τ1	NOUN
ejpam-5757	264	12	,	,	PUNCT
ejpam-5757	264	13	τ2	τ2	NOUN
ejpam-5757	264	14	:	:	PUNCT
ejpam-5757	264	15	u0	u0	ADJ
ejpam-5757	264	16	×	×	PROPN
ejpam-5757	264	17	u0	u0	NOUN
ejpam-5757	264	18	→	→	NOUN
ejpam-5757	264	19	r+	r+	NOUN
ejpam-5757	264	20	by	by	ADP
ejpam-5757	264	21	τ1(u	τ1(u	PUNCT
ejpam-5757	264	22	)	)	PUNCT
ejpam-5757	264	23	=	=	NUM
ejpam-5757	264	24	ϵ1∥u∥c1	ϵ1∥u∥c1	NOUN
ejpam-5757	264	25	,	,	PUNCT
ejpam-5757	264	26	τ2(v	τ2(v	X
ejpam-5757	264	27	)	)	PUNCT
ejpam-5757	265	1	=	=	SYM
ejpam-5757	265	2	ϵ2∥v∥c2	ϵ2∥v∥c2	NOUN
ejpam-5757	265	3	and	and	CCONJ
ejpam-5757	265	4	τ1(0	τ1(0	PROPN
ejpam-5757	265	5	)	)	PUNCT
ejpam-5757	265	6	=	=	SYM
ejpam-5757	265	7	τ2(0	τ2(0	PROPN
ejpam-5757	265	8	)	)	PUNCT
ejpam-5757	265	9	=	=	SYM
ejpam-5757	265	10	0	0	NUM
ejpam-5757	265	11	with	with	ADP
ejpam-5757	265	12	ϵ1	ϵ1	ADJ
ejpam-5757	265	13	,	,	PUNCT
ejpam-5757	265	14	ϵ2	ϵ2	PROPN
ejpam-5757	265	15	∈	∈	PROPN
ejpam-5757	265	16	r+	r+	NOUN
ejpam-5757	265	17	and	and	CCONJ
ejpam-5757	265	18	c1	c1	NOUN
ejpam-5757	265	19	,	,	PUNCT
ejpam-5757	265	20	c2	c2	PROPN
ejpam-5757	265	21	∈	∈	PROPN
ejpam-5757	265	22	r	r	NOUN
ejpam-5757	265	23	such	such	ADJ
ejpam-5757	265	24	that	that	SCONJ
ejpam-5757	265	25	ϵ1ϵ2	ϵ1ϵ2	PROPN
ejpam-5757	265	26	=	=	SYM
ejpam-5757	265	27	ϵ	ϵ	PROPN
ejpam-5757	265	28	and	and	CCONJ
ejpam-5757	265	29	c1	c1	PROPN
ejpam-5757	265	30	+	+	CCONJ
ejpam-5757	265	31	c2	c2	PROPN
ejpam-5757	265	32	<	<	X
ejpam-5757	265	33	0	0	NUM
ejpam-5757	265	34	.	.	PUNCT
ejpam-5757	266	1	for	for	ADP
ejpam-5757	266	2	each	each	DET
ejpam-5757	266	3	m	m	PROPN
ejpam-5757	266	4	∈	∈	PROPN
ejpam-5757	266	5	n	n	CCONJ
ejpam-5757	266	6	,	,	PUNCT
ejpam-5757	266	7	we	we	PRON
ejpam-5757	266	8	obtain	obtain	VERB
ejpam-5757	266	9	η1(m	η1(m	PROPN
ejpam-5757	266	10	)	)	PUNCT
ejpam-5757	266	11	=	=	SYM
ejpam-5757	266	12	inf{l	inf{l	PROPN
ejpam-5757	266	13	∈	∈	PROPN
ejpam-5757	266	14	r+	r+	NOUN
ejpam-5757	266	15	:	:	PUNCT
ejpam-5757	266	16	τ1(mx	τ1(mx	NUM
ejpam-5757	266	17	)	)	PUNCT
ejpam-5757	266	18	≤	≤	NUM
ejpam-5757	266	19	τ1(u	τ1(u	PUNCT
ejpam-5757	266	20	)	)	PUNCT
ejpam-5757	266	21	,	,	PUNCT
ejpam-5757	266	22	u	u	PROPN
ejpam-5757	266	23	∈	∈	PROPN
ejpam-5757	266	24	u0	u0	NOUN
ejpam-5757	266	25	}	}	PUNCT
ejpam-5757	266	26	=	=	SYM
ejpam-5757	266	27	inf{l	inf{l	PROPN
ejpam-5757	266	28	∈	∈	PROPN
ejpam-5757	266	29	r+	r+	NOUN
ejpam-5757	266	30	:	:	PUNCT
ejpam-5757	266	31	ϵ1∥mu∥c1	ϵ1∥mu∥c1	VERB
ejpam-5757	266	32	≤	≤	ADV
ejpam-5757	266	33	lϵ1∥u∥c1	lϵ1∥u∥c1	PUNCT
ejpam-5757	266	34	,	,	PUNCT
ejpam-5757	266	35	u	u	PROPN
ejpam-5757	266	36	∈	∈	PROPN
ejpam-5757	266	37	u0	u0	PROPN
ejpam-5757	266	38	}	}	PUNCT
ejpam-5757	266	39	s.	s.	PROPN
ejpam-5757	266	40	karthikeyan	karthikeyan	PROPN
ejpam-5757	266	41	et	et	PROPN
ejpam-5757	266	42	al	al	PROPN
ejpam-5757	266	43	.	.	PUNCT
ejpam-5757	266	44	/	/	SYM
ejpam-5757	266	45	eur	eur	PROPN
ejpam-5757	266	46	.	.	PUNCT
ejpam-5757	267	1	j.	j.	PROPN
ejpam-5757	267	2	pure	pure	PROPN
ejpam-5757	267	3	appl	appl	PROPN
ejpam-5757	267	4	.	.	PROPN
ejpam-5757	267	5	math	math	PROPN
ejpam-5757	267	6	,	,	PUNCT
ejpam-5757	267	7	18	18	NUM
ejpam-5757	267	8	(	(	PUNCT
ejpam-5757	267	9	1	1	NUM
ejpam-5757	267	10	)	)	PUNCT
ejpam-5757	267	11	(	(	PUNCT
ejpam-5757	267	12	2025	2025	NUM
ejpam-5757	267	13	)	)	PUNCT
ejpam-5757	267	14	,	,	PUNCT
ejpam-5757	267	15	5757	5757	NUM
ejpam-5757	267	16	15	15	NUM
ejpam-5757	267	17	of	of	ADP
ejpam-5757	267	18	18	18	NUM
ejpam-5757	267	19	=	=	SYM
ejpam-5757	267	20	mc1	mc1	PROPN
ejpam-5757	267	21	.	.	PUNCT
ejpam-5757	268	1	similarly	similarly	ADV
ejpam-5757	268	2	,	,	PUNCT
ejpam-5757	268	3	we	we	PRON
ejpam-5757	268	4	obtain	obtain	VERB
ejpam-5757	268	5	η2(m	η2(m	PRON
ejpam-5757	268	6	)	)	PUNCT
ejpam-5757	268	7	=	=	SYM
ejpam-5757	268	8	mc2	mc2	NOUN
ejpam-5757	268	9	for	for	ADP
ejpam-5757	268	10	all	all	DET
ejpam-5757	268	11	m	m	PROPN
ejpam-5757	268	12	∈	∈	PROPN
ejpam-5757	268	13	n.	n.	NOUN
ejpam-5757	268	14	now	now	ADV
ejpam-5757	268	15	,	,	PUNCT
ejpam-5757	268	16	we	we	PRON
ejpam-5757	268	17	can	can	AUX
ejpam-5757	268	18	find	find	VERB
ejpam-5757	268	19	m0	m0	NOUN
ejpam-5757	268	20	∈	∈	PROPN
ejpam-5757	268	21	n	n	PRON
ejpam-5757	268	22	such	such	ADJ
ejpam-5757	268	23	that	that	DET
ejpam-5757	268	24	αm	αm	NOUN
ejpam-5757	268	25	=	=	SYM
ejpam-5757	268	26	1	1	NUM
ejpam-5757	268	27	120	120	NUM
ejpam-5757	268	28	(	(	PUNCT
ejpam-5757	268	29	m+	m+	NOUN
ejpam-5757	268	30	3)c1+c2	3)c1+c2	NUM
ejpam-5757	268	31	+	+	CCONJ
ejpam-5757	268	32	1	1	NUM
ejpam-5757	268	33	24	24	NUM
ejpam-5757	268	34	(	(	PUNCT
ejpam-5757	268	35	m+	m+	NOUN
ejpam-5757	268	36	2)c1+c2	2)c1+c2	NUM
ejpam-5757	269	1	+	+	CCONJ
ejpam-5757	269	2	1	1	NUM
ejpam-5757	269	3	120	120	NUM
ejpam-5757	269	4	(	(	PUNCT
ejpam-5757	269	5	m−	m−	PROPN
ejpam-5757	269	6	2)c1+c2	2)c1+c2	PROPN
ejpam-5757	269	7	+	+	CCONJ
ejpam-5757	269	8	1	1	NUM
ejpam-5757	269	9	12	12	NUM
ejpam-5757	269	10	(	(	PUNCT
ejpam-5757	269	11	m+	m+	NOUN
ejpam-5757	269	12	1)c1+c2	1)c1+c2	NUM
ejpam-5757	269	13	+	+	CCONJ
ejpam-5757	269	14	1	1	NUM
ejpam-5757	269	15	24	24	NUM
ejpam-5757	269	16	(	(	PUNCT
ejpam-5757	269	17	m−	m−	PROPN
ejpam-5757	269	18	1)c1+c2	1)c1+c2	NUM
ejpam-5757	269	19	+	+	CCONJ
ejpam-5757	269	20	1	1	NUM
ejpam-5757	269	21	12	12	NUM
ejpam-5757	269	22	(	(	PUNCT
ejpam-5757	269	23	m)c1+c2	m)c1+c2	X
ejpam-5757	269	24	<	<	X
ejpam-5757	269	25	1	1	NUM
ejpam-5757	269	26	for	for	ADP
ejpam-5757	269	27	all	all	DET
ejpam-5757	269	28	m	m	PROPN
ejpam-5757	269	29	≥	≥	NOUN
ejpam-5757	269	30	m0	m0	NOUN
ejpam-5757	269	31	.	.	PUNCT
ejpam-5757	270	1	according	accord	VERB
ejpam-5757	270	2	to	to	ADP
ejpam-5757	270	3	theorem	theorem	NOUN
ejpam-5757	270	4	3	3	NUM
ejpam-5757	270	5	,	,	PUNCT
ejpam-5757	270	6	there	there	PRON
ejpam-5757	270	7	is	be	VERB
ejpam-5757	270	8	only	only	ADV
ejpam-5757	270	9	one	one	NUM
ejpam-5757	270	10	quintic	quintic	ADJ
ejpam-5757	270	11	mapping	mapping	NOUN
ejpam-5757	270	12	h	h	NOUN
ejpam-5757	270	13	:	:	PUNCT
ejpam-5757	270	14	u	u	X
ejpam-5757	270	15	→	→	SYM
ejpam-5757	270	16	v	v	ADJ
ejpam-5757	270	17	satisfying	satisfy	VERB
ejpam-5757	270	18	∥ϕ(u)−h(u)∥	∥ϕ(u)−h(u)∥	NOUN
ejpam-5757	270	19	≤	≤	NUM
ejpam-5757	270	20	ϵη0τ1(u)τ2(u	ϵη0τ1(u)τ2(u	NUM
ejpam-5757	270	21	)	)	PUNCT
ejpam-5757	270	22	for	for	ADP
ejpam-5757	270	23	all	all	DET
ejpam-5757	270	24	m	m	PROPN
ejpam-5757	270	25	∈	∈	ADJ
ejpam-5757	270	26	u0	u0	NOUN
ejpam-5757	270	27	.	.	PUNCT
ejpam-5757	271	1	since	since	SCONJ
ejpam-5757	271	2	c1	c1	PROPN
ejpam-5757	271	3	+	+	CCONJ
ejpam-5757	271	4	c2	c2	PROPN
ejpam-5757	271	5	<	<	X
ejpam-5757	271	6	0	0	PROPN
ejpam-5757	271	7	,	,	PUNCT
ejpam-5757	271	8	one	one	NUM
ejpam-5757	271	9	of	of	ADP
ejpam-5757	271	10	c1	c1	PROPN
ejpam-5757	271	11	and	and	CCONJ
ejpam-5757	271	12	c2	c2	PROPN
ejpam-5757	271	13	must	must	AUX
ejpam-5757	271	14	be	be	AUX
ejpam-5757	271	15	negative	negative	ADJ
ejpam-5757	271	16	.	.	PUNCT
ejpam-5757	272	1	assume	assume	VERB
ejpam-5757	272	2	that	that	SCONJ
ejpam-5757	272	3	c2	c2	PROPN
ejpam-5757	272	4	<	<	X
ejpam-5757	272	5	0	0	PROPN
ejpam-5757	272	6	.	.	PUNCT
ejpam-5757	273	1	then	then	ADV
ejpam-5757	273	2			PRON
ejpam-5757	273	3	limm→+∞	limm→+∞	VERB
ejpam-5757	273	4	η1(m	η1(m	PROPN
ejpam-5757	273	5	)	)	PUNCT
ejpam-5757	273	6	=	=	SYM
ejpam-5757	273	7	limm→+∞mc1	limm→+∞mc1	NOUN
ejpam-5757	273	8	=	=	SYM
ejpam-5757	273	9	0	0	NUM
ejpam-5757	273	10	,	,	PUNCT
ejpam-5757	273	11	limm→+∞	limm→+∞	VERB
ejpam-5757	273	12	η1(m)η2(m	η1(m)η2(m	ADP
ejpam-5757	273	13	)	)	PUNCT
ejpam-5757	273	14	=	=	VERB
ejpam-5757	274	1	limm→+∞mc1+c2	limm→+∞mc1+c2	NOUN
ejpam-5757	274	2	=	=	SYM
ejpam-5757	274	3	0	0	NUM
ejpam-5757	274	4	,	,	PUNCT
ejpam-5757	274	5	limm→+∞	limm→+∞	VERB
ejpam-5757	274	6	η1(m−	η1(m−	PROPN
ejpam-5757	274	7	2)η2(m−	2)η2(m−	NUM
ejpam-5757	274	8	2	2	NUM
ejpam-5757	274	9	)	)	PUNCT
ejpam-5757	274	10	=	=	NOUN
ejpam-5757	275	1	limm→+∞(m−	limm→+∞(m−	PROPN
ejpam-5757	275	2	2)c1+c2	2)c1+c2	NUM
ejpam-5757	275	3	=	=	SYM
ejpam-5757	275	4	0	0	X
ejpam-5757	275	5	.	.	PUNCT
ejpam-5757	276	1	the	the	DET
ejpam-5757	276	2	expected	expect	VERB
ejpam-5757	276	3	outcomes	outcome	NOUN
ejpam-5757	276	4	are	be	AUX
ejpam-5757	276	5	thus	thus	ADV
ejpam-5757	276	6	obtained	obtain	VERB
ejpam-5757	276	7	by	by	ADP
ejpam-5757	276	8	theorem	theorem	NOUN
ejpam-5757	276	9	5	5	NUM
ejpam-5757	276	10	.	.	NOUN
ejpam-5757	276	11	example	example	NOUN
ejpam-5757	277	1	1	1	NUM
ejpam-5757	277	2	.	.	PUNCT
ejpam-5757	278	1	let	let	VERB
ejpam-5757	278	2	u	u	PRON
ejpam-5757	278	3	be	be	AUX
ejpam-5757	278	4	a	a	DET
ejpam-5757	278	5	normed	normed	ADJ
ejpam-5757	278	6	space	space	NOUN
ejpam-5757	278	7	and	and	CCONJ
ejpam-5757	278	8	v	v	AUX
ejpam-5757	278	9	be	be	AUX
ejpam-5757	278	10	a	a	DET
ejpam-5757	278	11	banach	banach	NOUN
ejpam-5757	278	12	space	space	NOUN
ejpam-5757	278	13	.	.	PUNCT
ejpam-5757	279	1	let	let	VERB
ejpam-5757	279	2	ϕ	ϕ	NOUN
ejpam-5757	279	3	:	:	PUNCT
ejpam-5757	279	4	u	u	NOUN
ejpam-5757	279	5	→	→	SYM
ejpam-5757	279	6	v	v	NUM
ejpam-5757	279	7	be	be	AUX
ejpam-5757	279	8	a	a	DET
ejpam-5757	279	9	mapping	mapping	NOUN
ejpam-5757	279	10	such	such	ADJ
ejpam-5757	279	11	that	that	DET
ejpam-5757	279	12	dϕ(u0	dϕ(u0	PROPN
ejpam-5757	279	13	,	,	PUNCT
ejpam-5757	279	14	v0	v0	PROPN
ejpam-5757	279	15	)	)	PUNCT
ejpam-5757	279	16	̸=	̸=	PROPN
ejpam-5757	279	17	0	0	NUM
ejpam-5757	279	18	for	for	ADP
ejpam-5757	279	19	some	some	DET
ejpam-5757	279	20	u0	u0	ADJ
ejpam-5757	279	21	,	,	PUNCT
ejpam-5757	279	22	v0	v0	PROPN
ejpam-5757	279	23	∈	∈	PROPN
ejpam-5757	279	24	u	u	NOUN
ejpam-5757	279	25	and	and	CCONJ
ejpam-5757	279	26	∥dϕ(u	∥dϕ(u	PROPN
ejpam-5757	279	27	,	,	PUNCT
ejpam-5757	279	28	v)∥	v)∥	NUM
ejpam-5757	279	29	≤	≤	NUM
ejpam-5757	279	30	c∥u∥c1∥v∥c2	c∥u∥c1∥v∥c2	NOUN
ejpam-5757	279	31	for	for	ADP
ejpam-5757	279	32	all	all	DET
ejpam-5757	279	33	u	u	NOUN
ejpam-5757	279	34	,	,	PUNCT
ejpam-5757	279	35	v	v	PROPN
ejpam-5757	279	36	∈	∈	PROPN
ejpam-5757	279	37	u0	u0	NOUN
ejpam-5757	279	38	such	such	ADJ
ejpam-5757	279	39	that	that	SCONJ
ejpam-5757	279	40	u	u	NOUN
ejpam-5757	279	41	+	+	X
ejpam-5757	279	42	3v	3v	NUM
ejpam-5757	279	43	̸=	̸=	PROPN
ejpam-5757	279	44	0	0	NUM
ejpam-5757	279	45	,	,	PUNCT
ejpam-5757	279	46	u	u	PROPN
ejpam-5757	279	47	+	+	PROPN
ejpam-5757	279	48	2v	2v	PROPN
ejpam-5757	279	49	̸=	̸=	PROPN
ejpam-5757	279	50	0	0	NUM
ejpam-5757	279	51	,	,	PUNCT
ejpam-5757	279	52	u	u	NOUN
ejpam-5757	279	53	−	−	PROPN
ejpam-5757	279	54	2v	2v	PROPN
ejpam-5757	279	55	̸=	̸=	PROPN
ejpam-5757	279	56	0	0	NUM
ejpam-5757	279	57	,	,	PUNCT
ejpam-5757	279	58	u	u	NOUN
ejpam-5757	279	59	−	−	PROPN
ejpam-5757	279	60	v	v	ADP
ejpam-5757	279	61	̸=	̸=	PROPN
ejpam-5757	279	62	0	0	NUM
ejpam-5757	279	63	,	,	PUNCT
ejpam-5757	279	64	u	u	NOUN
ejpam-5757	279	65	+	+	NOUN
ejpam-5757	279	66	v	v	ADP
ejpam-5757	279	67	̸=	̸=	PROPN
ejpam-5757	279	68	0	0	NUM
ejpam-5757	279	69	,	,	PUNCT
ejpam-5757	279	70	where	where	SCONJ
ejpam-5757	279	71	ϵ	ϵ	X
ejpam-5757	279	72	>	>	X
ejpam-5757	279	73	0	0	PUNCT
ejpam-5757	279	74	and	and	CCONJ
ejpam-5757	279	75	c1	c1	PROPN
ejpam-5757	279	76	,	,	PUNCT
ejpam-5757	279	77	c2	c2	PROPN
ejpam-5757	279	78	∈	∈	PROPN
ejpam-5757	279	79	r.	r.	PROPN
ejpam-5757	279	80	assume	assume	VERB
ejpam-5757	279	81	that	that	SCONJ
ejpam-5757	279	82	the	the	DET
ejpam-5757	279	83	numbers	number	NOUN
ejpam-5757	279	84	c1	c1	PROPN
ejpam-5757	279	85	,	,	PUNCT
ejpam-5757	279	86	c2	c2	PROPN
ejpam-5757	279	87	satisfy	satisfy	PROPN
ejpam-5757	279	88	c1	c1	PROPN
ejpam-5757	279	89	+	+	CCONJ
ejpam-5757	279	90	c2	c2	PROPN
ejpam-5757	279	91	<	<	X
ejpam-5757	279	92	0	0	PROPN
ejpam-5757	279	93	.	.	PUNCT
ejpam-5757	280	1	then	then	ADV
ejpam-5757	280	2	the	the	DET
ejpam-5757	280	3	functional	functional	ADJ
ejpam-5757	280	4	equation	equation	NOUN
ejpam-5757	280	5	ϕ(u+	ϕ(u+	PROPN
ejpam-5757	281	1	3v)−	3v)−	NUM
ejpam-5757	281	2	5ϕ(u+	5ϕ(u+	NUM
ejpam-5757	281	3	2v)−	2v)−	NUM
ejpam-5757	281	4	ϕ(u−	ϕ(u−	NUM
ejpam-5757	281	5	2v	2v	NUM
ejpam-5757	281	6	)	)	PUNCT
ejpam-5757	282	1	+	+	CCONJ
ejpam-5757	282	2	10ϕ(u+	10ϕ(u+	NUM
ejpam-5757	282	3	v	v	NOUN
ejpam-5757	282	4	)	)	PUNCT
ejpam-5757	283	1	+	+	CCONJ
ejpam-5757	283	2	5ϕ(u−	5ϕ(u−	NUM
ejpam-5757	283	3	v)−	v)−	PROPN
ejpam-5757	283	4	10ϕ(u)−	10ϕ(u)−	NUM
ejpam-5757	283	5	120ϕ(v	120ϕ(v	NOUN
ejpam-5757	283	6	)	)	PUNCT
ejpam-5757	283	7	=	=	SYM
ejpam-5757	283	8	0	0	NUM
ejpam-5757	283	9	,	,	PUNCT
ejpam-5757	283	10	∀u	∀u	NOUN
ejpam-5757	283	11	,	,	PUNCT
ejpam-5757	283	12	v	v	X
ejpam-5757	283	13	∈	∈	PROPN
ejpam-5757	283	14	u0	u0	NOUN
ejpam-5757	283	15	,	,	PUNCT
ejpam-5757	283	16	(	(	PUNCT
ejpam-5757	283	17	31	31	NUM
ejpam-5757	283	18	)	)	PUNCT
ejpam-5757	283	19	has	have	VERB
ejpam-5757	283	20	no	no	DET
ejpam-5757	283	21	solution	solution	NOUN
ejpam-5757	283	22	in	in	ADP
ejpam-5757	283	23	the	the	DET
ejpam-5757	283	24	class	class	NOUN
ejpam-5757	283	25	of	of	ADP
ejpam-5757	283	26	functions	function	NOUN
ejpam-5757	283	27	ϕ	ϕ	NOUN
ejpam-5757	283	28	:	:	PUNCT
ejpam-5757	283	29	u	u	X
ejpam-5757	283	30	→	→	X
ejpam-5757	283	31	v.	v.	ADP
ejpam-5757	283	32	proof	proof	NOUN
ejpam-5757	283	33	.	.	PUNCT
ejpam-5757	284	1	suppose	suppose	VERB
ejpam-5757	284	2	that	that	SCONJ
ejpam-5757	284	3	ϕ	ϕ	NOUN
ejpam-5757	284	4	:	:	PUNCT
ejpam-5757	284	5	u	u	NOUN
ejpam-5757	284	6	→	→	SYM
ejpam-5757	284	7	v	v	PROPN
ejpam-5757	284	8	is	be	AUX
ejpam-5757	284	9	a	a	DET
ejpam-5757	284	10	solution	solution	NOUN
ejpam-5757	284	11	of	of	ADP
ejpam-5757	284	12	(	(	PUNCT
ejpam-5757	284	13	31	31	NUM
ejpam-5757	284	14	)	)	PUNCT
ejpam-5757	284	15	.	.	PUNCT
ejpam-5757	285	1	then	then	ADV
ejpam-5757	285	2	(	(	PUNCT
ejpam-5757	285	3	30	30	NUM
ejpam-5757	285	4	)	)	PUNCT
ejpam-5757	285	5	holds	hold	NOUN
ejpam-5757	285	6	,	,	PUNCT
ejpam-5757	285	7	and	and	CCONJ
ejpam-5757	285	8	consequently	consequently	ADV
ejpam-5757	285	9	,	,	PUNCT
ejpam-5757	285	10	according	accord	VERB
ejpam-5757	285	11	to	to	ADP
ejpam-5757	285	12	corollary	corollary	ADJ
ejpam-5757	285	13	1	1	NUM
ejpam-5757	285	14	,	,	PUNCT
ejpam-5757	285	15	ϕ	ϕ	NOUN
ejpam-5757	285	16	is	be	AUX
ejpam-5757	285	17	a	a	DET
ejpam-5757	285	18	quintic	quintic	ADJ
ejpam-5757	285	19	mapping	mapping	NOUN
ejpam-5757	285	20	on	on	ADP
ejpam-5757	285	21	u0	u0	PROPN
ejpam-5757	285	22	,	,	PUNCT
ejpam-5757	285	23	which	which	PRON
ejpam-5757	285	24	means	mean	VERB
ejpam-5757	285	25	that	that	SCONJ
ejpam-5757	285	26	dϕ(u0	dϕ(u0	PROPN
ejpam-5757	285	27	,	,	PUNCT
ejpam-5757	285	28	v0	v0	PROPN
ejpam-5757	285	29	)	)	PUNCT
ejpam-5757	285	30	=	=	SYM
ejpam-5757	286	1	0	0	X
ejpam-5757	286	2	.	.	PUNCT
ejpam-5757	287	1	this	this	PRON
ejpam-5757	287	2	is	be	AUX
ejpam-5757	287	3	a	a	DET
ejpam-5757	287	4	contradiction	contradiction	NOUN
ejpam-5757	287	5	.	.	PUNCT
ejpam-5757	288	1	corollary	corollary	ADJ
ejpam-5757	288	2	2	2	NUM
ejpam-5757	288	3	.	.	PUNCT
ejpam-5757	289	1	let	let	VERB
ejpam-5757	289	2	ϵ	ϵ	PRON
ejpam-5757	289	3	≥	≥	NOUN
ejpam-5757	289	4	0	0	NUM
ejpam-5757	289	5	,	,	PUNCT
ejpam-5757	289	6	c	c	PROPN
ejpam-5757	289	7	∈	∈	PROPN
ejpam-5757	289	8	r	r	NOUN
ejpam-5757	289	9	with	with	ADP
ejpam-5757	289	10	c	c	PROPN
ejpam-5757	289	11	<	<	X
ejpam-5757	289	12	0	0	NUM
ejpam-5757	289	13	.	.	PUNCT
ejpam-5757	290	1	if	if	SCONJ
ejpam-5757	290	2	a	a	DET
ejpam-5757	290	3	mapping	mapping	NOUN
ejpam-5757	290	4	ϕ	ϕ	NOUN
ejpam-5757	290	5	:	:	PUNCT
ejpam-5757	290	6	u	u	X
ejpam-5757	290	7	→	→	SYM
ejpam-5757	290	8	v	v	NUM
ejpam-5757	290	9	fulfills	fulfill	VERB
ejpam-5757	290	10	ϕ(0	ϕ(0	PRON
ejpam-5757	290	11	)	)	PUNCT
ejpam-5757	290	12	=	=	SYM
ejpam-5757	290	13	0	0	NUM
ejpam-5757	290	14	and	and	CCONJ
ejpam-5757	290	15	∥dϕ(u	∥dϕ(u	PROPN
ejpam-5757	290	16	,	,	PUNCT
ejpam-5757	290	17	v)∥	v)∥	NUM
ejpam-5757	290	18	≤	≤	PUNCT
ejpam-5757	290	19	ϵ	ϵ	X
ejpam-5757	290	20	(	(	PUNCT
ejpam-5757	290	21	∥u∥c	∥u∥c	NOUN
ejpam-5757	290	22	+	+	CCONJ
ejpam-5757	290	23	∥v∥c	∥v∥c	ADJ
ejpam-5757	290	24	)	)	PUNCT
ejpam-5757	290	25	(	(	PUNCT
ejpam-5757	290	26	32	32	NUM
ejpam-5757	290	27	)	)	PUNCT
ejpam-5757	290	28	for	for	ADP
ejpam-5757	290	29	all	all	DET
ejpam-5757	290	30	u	u	NOUN
ejpam-5757	290	31	,	,	PUNCT
ejpam-5757	290	32	v	v	PROPN
ejpam-5757	290	33	∈	∈	NOUN
ejpam-5757	290	34	u0	u0	NOUN
ejpam-5757	290	35	such	such	ADJ
ejpam-5757	290	36	that	that	SCONJ
ejpam-5757	290	37	u+3v	u+3v	PROPN
ejpam-5757	290	38	̸=	̸=	PROPN
ejpam-5757	290	39	0	0	NUM
ejpam-5757	290	40	,	,	PUNCT
ejpam-5757	290	41	u+2v	u+2v	PROPN
ejpam-5757	290	42	̸=	̸=	PROPN
ejpam-5757	290	43	0	0	NUM
ejpam-5757	290	44	,	,	PUNCT
ejpam-5757	290	45	u−	u−	PROPN
ejpam-5757	290	46	2v	2v	PROPN
ejpam-5757	290	47	̸=	̸=	PROPN
ejpam-5757	290	48	0	0	NUM
ejpam-5757	290	49	,	,	PUNCT
ejpam-5757	290	50	u−	u−	PROPN
ejpam-5757	290	51	v	v	ADP
ejpam-5757	290	52	̸=	̸=	PROPN
ejpam-5757	290	53	0	0	NUM
ejpam-5757	290	54	,	,	PUNCT
ejpam-5757	290	55	u+	u+	NOUN
ejpam-5757	290	56	v	v	ADP
ejpam-5757	290	57	̸=	̸=	PROPN
ejpam-5757	290	58	0	0	NUM
ejpam-5757	290	59	.	.	PUNCT
ejpam-5757	291	1	then	then	ADV
ejpam-5757	291	2	ϕ	ϕ	PROPN
ejpam-5757	291	3	is	be	AUX
ejpam-5757	291	4	quintic	quintic	ADJ
ejpam-5757	291	5	on	on	ADP
ejpam-5757	291	6	u0	u0	PROPN
ejpam-5757	291	7	.	.	PUNCT
ejpam-5757	292	1	s.	s.	PROPN
ejpam-5757	292	2	karthikeyan	karthikeyan	PROPN
ejpam-5757	292	3	et	et	PROPN
ejpam-5757	292	4	al	al	PROPN
ejpam-5757	292	5	.	.	PUNCT
ejpam-5757	292	6	/	/	SYM
ejpam-5757	292	7	eur	eur	PROPN
ejpam-5757	292	8	.	.	PUNCT
ejpam-5757	293	1	j.	j.	PROPN
ejpam-5757	293	2	pure	pure	PROPN
ejpam-5757	293	3	appl	appl	PROPN
ejpam-5757	293	4	.	.	PROPN
ejpam-5757	293	5	math	math	PROPN
ejpam-5757	293	6	,	,	PUNCT
ejpam-5757	293	7	18	18	NUM
ejpam-5757	293	8	(	(	PUNCT
ejpam-5757	293	9	1	1	NUM
ejpam-5757	293	10	)	)	PUNCT
ejpam-5757	293	11	(	(	PUNCT
ejpam-5757	293	12	2025	2025	NUM
ejpam-5757	293	13	)	)	PUNCT
ejpam-5757	293	14	,	,	PUNCT
ejpam-5757	293	15	5757	5757	NUM
ejpam-5757	293	16	16	16	NUM
ejpam-5757	293	17	of	of	ADP
ejpam-5757	293	18	18	18	NUM
ejpam-5757	293	19	example	example	NOUN
ejpam-5757	293	20	2	2	NUM
ejpam-5757	293	21	.	.	PUNCT
ejpam-5757	294	1	let	let	VERB
ejpam-5757	294	2	u0	u0	ADJ
ejpam-5757	294	3	be	be	AUX
ejpam-5757	294	4	a	a	DET
ejpam-5757	294	5	normed	normed	ADJ
ejpam-5757	294	6	space	space	NOUN
ejpam-5757	294	7	and	and	CCONJ
ejpam-5757	294	8	v	v	AUX
ejpam-5757	294	9	be	be	AUX
ejpam-5757	294	10	a	a	DET
ejpam-5757	294	11	banach	banach	NOUN
ejpam-5757	294	12	space	space	NOUN
ejpam-5757	294	13	.	.	PUNCT
ejpam-5757	295	1	let	let	VERB
ejpam-5757	295	2	ϕ	ϕ	NOUN
ejpam-5757	295	3	:	:	PUNCT
ejpam-5757	295	4	u0	u0	ADJ
ejpam-5757	295	5	→	→	SYM
ejpam-5757	295	6	v	v	NUM
ejpam-5757	295	7	be	be	AUX
ejpam-5757	295	8	a	a	DET
ejpam-5757	295	9	mapping	mapping	NOUN
ejpam-5757	295	10	such	such	ADJ
ejpam-5757	295	11	that	that	DET
ejpam-5757	295	12	dϕ(u0	dϕ(u0	PROPN
ejpam-5757	295	13	,	,	PUNCT
ejpam-5757	295	14	v0	v0	PROPN
ejpam-5757	295	15	)	)	PUNCT
ejpam-5757	295	16	̸=	̸=	PROPN
ejpam-5757	295	17	0	0	NUM
ejpam-5757	295	18	for	for	ADP
ejpam-5757	295	19	some	some	DET
ejpam-5757	295	20	u0	u0	ADJ
ejpam-5757	295	21	,	,	PUNCT
ejpam-5757	295	22	v0	v0	PROPN
ejpam-5757	295	23	∈	∈	PROPN
ejpam-5757	295	24	u0	u0	NOUN
ejpam-5757	295	25	and	and	CCONJ
ejpam-5757	295	26	∥dϕ(u	∥dϕ(u	PROPN
ejpam-5757	295	27	,	,	PUNCT
ejpam-5757	295	28	v)∥	v)∥	PUNCT
ejpam-5757	295	29	≤	≤	NUM
ejpam-5757	295	30	c∥u∥c∥v∥c	c∥u∥c∥v∥c	NOUN
ejpam-5757	295	31	for	for	ADP
ejpam-5757	295	32	all	all	DET
ejpam-5757	295	33	u	u	NOUN
ejpam-5757	295	34	,	,	PUNCT
ejpam-5757	295	35	v	v	PROPN
ejpam-5757	295	36	∈	∈	NOUN
ejpam-5757	295	37	u0	u0	NOUN
ejpam-5757	295	38	such	such	ADJ
ejpam-5757	295	39	that	that	SCONJ
ejpam-5757	295	40	u+3v	u+3v	PROPN
ejpam-5757	295	41	̸=	̸=	PROPN
ejpam-5757	295	42	0	0	NUM
ejpam-5757	295	43	,	,	PUNCT
ejpam-5757	295	44	u+2v	u+2v	PROPN
ejpam-5757	295	45	̸=	̸=	PROPN
ejpam-5757	295	46	0	0	NUM
ejpam-5757	295	47	,	,	PUNCT
ejpam-5757	295	48	u−	u−	PROPN
ejpam-5757	295	49	2v	2v	PROPN
ejpam-5757	295	50	̸=	̸=	PROPN
ejpam-5757	295	51	0	0	NUM
ejpam-5757	295	52	,	,	PUNCT
ejpam-5757	295	53	u−	u−	PROPN
ejpam-5757	295	54	v	v	ADP
ejpam-5757	295	55	̸=	̸=	PROPN
ejpam-5757	295	56	0	0	NUM
ejpam-5757	295	57	,	,	PUNCT
ejpam-5757	295	58	u+	u+	NOUN
ejpam-5757	295	59	v	v	ADP
ejpam-5757	295	60	̸=	̸=	PROPN
ejpam-5757	295	61	0	0	NUM
ejpam-5757	295	62	,	,	PUNCT
ejpam-5757	295	63	where	where	SCONJ
ejpam-5757	295	64	ϵ	ϵ	X
ejpam-5757	295	65	>	>	X
ejpam-5757	295	66	0	0	PUNCT
ejpam-5757	295	67	and	and	CCONJ
ejpam-5757	295	68	c	c	PROPN
ejpam-5757	295	69	∈	∈	PROPN
ejpam-5757	295	70	r.	r.	PROPN
ejpam-5757	295	71	assume	assume	VERB
ejpam-5757	295	72	that	that	SCONJ
ejpam-5757	295	73	the	the	DET
ejpam-5757	295	74	number	number	NOUN
ejpam-5757	295	75	c	c	NOUN
ejpam-5757	295	76	satisfies	satisfy	VERB
ejpam-5757	295	77	c	c	X
ejpam-5757	295	78	<	<	X
ejpam-5757	295	79	0	0	NUM
ejpam-5757	295	80	.	.	PUNCT
ejpam-5757	296	1	then	then	ADV
ejpam-5757	296	2	the	the	DET
ejpam-5757	296	3	functional	functional	ADJ
ejpam-5757	296	4	equation	equation	NOUN
ejpam-5757	296	5	ϕ(u+	ϕ(u+	PROPN
ejpam-5757	297	1	3v)−	3v)−	NUM
ejpam-5757	297	2	5ϕ(u+	5ϕ(u+	NUM
ejpam-5757	297	3	2v)−	2v)−	NUM
ejpam-5757	297	4	ϕ(u−	ϕ(u−	NUM
ejpam-5757	297	5	2v	2v	NUM
ejpam-5757	297	6	)	)	PUNCT
ejpam-5757	298	1	+	+	CCONJ
ejpam-5757	298	2	10ϕ(u+	10ϕ(u+	NUM
ejpam-5757	298	3	v	v	NOUN
ejpam-5757	298	4	)	)	PUNCT
ejpam-5757	299	1	+	+	CCONJ
ejpam-5757	299	2	5ϕ(u−	5ϕ(u−	NUM
ejpam-5757	299	3	v)−	v)−	PROPN
ejpam-5757	299	4	10ϕ(u)−	10ϕ(u)−	NUM
ejpam-5757	299	5	120ϕ(v	120ϕ(v	NOUN
ejpam-5757	299	6	)	)	PUNCT
ejpam-5757	299	7	=	=	SYM
ejpam-5757	299	8	0	0	NUM
ejpam-5757	299	9	,	,	PUNCT
ejpam-5757	299	10	∀u	∀u	NOUN
ejpam-5757	299	11	,	,	PUNCT
ejpam-5757	299	12	v	v	X
ejpam-5757	299	13	∈	∈	PROPN
ejpam-5757	299	14	u0	u0	NOUN
ejpam-5757	299	15	,	,	PUNCT
ejpam-5757	299	16	(	(	PUNCT
ejpam-5757	299	17	33	33	NUM
ejpam-5757	299	18	)	)	PUNCT
ejpam-5757	299	19	has	have	VERB
ejpam-5757	299	20	no	no	DET
ejpam-5757	299	21	solution	solution	NOUN
ejpam-5757	299	22	in	in	ADP
ejpam-5757	299	23	the	the	DET
ejpam-5757	299	24	class	class	NOUN
ejpam-5757	299	25	of	of	ADP
ejpam-5757	299	26	functions	function	NOUN
ejpam-5757	299	27	ϕ	ϕ	NOUN
ejpam-5757	299	28	:	:	PUNCT
ejpam-5757	299	29	u	u	X
ejpam-5757	299	30	→	→	X
ejpam-5757	299	31	v.	v.	ADP
ejpam-5757	299	32	proof	proof	NOUN
ejpam-5757	299	33	.	.	PUNCT
ejpam-5757	300	1	suppose	suppose	VERB
ejpam-5757	300	2	that	that	SCONJ
ejpam-5757	300	3	ϕ	ϕ	NOUN
ejpam-5757	300	4	:	:	PUNCT
ejpam-5757	300	5	u	u	NOUN
ejpam-5757	300	6	→	→	SYM
ejpam-5757	300	7	v	v	PROPN
ejpam-5757	300	8	is	be	AUX
ejpam-5757	300	9	a	a	DET
ejpam-5757	300	10	solution	solution	NOUN
ejpam-5757	300	11	of	of	ADP
ejpam-5757	300	12	(	(	PUNCT
ejpam-5757	300	13	33	33	NUM
ejpam-5757	300	14	)	)	PUNCT
ejpam-5757	300	15	.	.	PUNCT
ejpam-5757	301	1	then	then	ADV
ejpam-5757	301	2	(	(	PUNCT
ejpam-5757	301	3	32	32	NUM
ejpam-5757	301	4	)	)	PUNCT
ejpam-5757	301	5	holds	hold	NOUN
ejpam-5757	301	6	,	,	PUNCT
ejpam-5757	301	7	and	and	CCONJ
ejpam-5757	301	8	consequently	consequently	ADV
ejpam-5757	301	9	,	,	PUNCT
ejpam-5757	301	10	according	accord	VERB
ejpam-5757	301	11	to	to	ADP
ejpam-5757	301	12	corollary	corollary	ADJ
ejpam-5757	301	13	2	2	NUM
ejpam-5757	301	14	,	,	PUNCT
ejpam-5757	301	15	ϕ	ϕ	NOUN
ejpam-5757	301	16	is	be	AUX
ejpam-5757	301	17	a	a	DET
ejpam-5757	301	18	quintic	quintic	ADJ
ejpam-5757	301	19	mapping	mapping	NOUN
ejpam-5757	301	20	on	on	ADP
ejpam-5757	301	21	u0	u0	PROPN
ejpam-5757	301	22	,	,	PUNCT
ejpam-5757	301	23	which	which	PRON
ejpam-5757	301	24	means	mean	VERB
ejpam-5757	301	25	that	that	SCONJ
ejpam-5757	301	26	dϕ(u0	dϕ(u0	PROPN
ejpam-5757	301	27	,	,	PUNCT
ejpam-5757	301	28	v0	v0	PROPN
ejpam-5757	301	29	)	)	PUNCT
ejpam-5757	301	30	=	=	SYM
ejpam-5757	302	1	0	0	X
ejpam-5757	302	2	.	.	PUNCT
ejpam-5757	303	1	this	this	PRON
ejpam-5757	303	2	is	be	AUX
ejpam-5757	303	3	a	a	DET
ejpam-5757	303	4	contradiction	contradiction	NOUN
ejpam-5757	303	5	.	.	PUNCT
ejpam-5757	304	1	the	the	DET
ejpam-5757	304	2	findings	finding	NOUN
ejpam-5757	304	3	of	of	ADP
ejpam-5757	304	4	hyperstability	hyperstability	NOUN
ejpam-5757	304	5	for	for	ADP
ejpam-5757	304	6	inhomogeneous	inhomogeneous	ADJ
ejpam-5757	304	7	quintic	quintic	ADJ
ejpam-5757	304	8	functional	functional	ADJ
ejpam-5757	304	9	equations	equation	NOUN
ejpam-5757	304	10	are	be	AUX
ejpam-5757	304	11	demonstrated	demonstrate	VERB
ejpam-5757	304	12	by	by	ADP
ejpam-5757	304	13	the	the	DET
ejpam-5757	304	14	following	follow	VERB
ejpam-5757	304	15	corollary	corollary	NOUN
ejpam-5757	304	16	.	.	PUNCT
ejpam-5757	305	1	corollary	corollary	ADJ
ejpam-5757	305	2	3	3	NUM
ejpam-5757	305	3	.	.	PUNCT
ejpam-5757	306	1	let	let	AUX
ejpam-5757	306	2	ϵ	ϵ	X
ejpam-5757	306	3	,	,	PUNCT
ejpam-5757	306	4	c1	c1	PROPN
ejpam-5757	306	5	,	,	PUNCT
ejpam-5757	306	6	c2	c2	PROPN
ejpam-5757	306	7	∈	∈	PROPN
ejpam-5757	306	8	r	r	NOUN
ejpam-5757	306	9	with	with	ADP
ejpam-5757	306	10	ϵ	ϵ	PRON
ejpam-5757	306	11	≥	≥	NOUN
ejpam-5757	306	12	0	0	NUM
ejpam-5757	306	13	and	and	CCONJ
ejpam-5757	306	14	c1	c1	PROPN
ejpam-5757	306	15	+	+	CCONJ
ejpam-5757	306	16	c2	c2	PROPN
ejpam-5757	306	17	<	<	X
ejpam-5757	306	18	0	0	X
ejpam-5757	306	19	.	.	PUNCT
ejpam-5757	306	20	assume	assume	VERB
ejpam-5757	306	21	that	that	SCONJ
ejpam-5757	306	22	mappings	mapping	VERB
ejpam-5757	306	23	g	g	NOUN
ejpam-5757	306	24	:	:	PUNCT
ejpam-5757	306	25	u2	u2	PROPN
ejpam-5757	306	26	→	→	SYM
ejpam-5757	306	27	v	v	PROPN
ejpam-5757	306	28	and	and	CCONJ
ejpam-5757	306	29	ϕ	ϕ	NOUN
ejpam-5757	306	30	:	:	PUNCT
ejpam-5757	306	31	u	u	NOUN
ejpam-5757	306	32	→	→	SYM
ejpam-5757	306	33	v	v	NUM
ejpam-5757	306	34	fulfill	fulfill	NOUN
ejpam-5757	306	35	ϕ(0	ϕ(0	NOUN
ejpam-5757	306	36	)	)	PUNCT
ejpam-5757	307	1	=	=	SYM
ejpam-5757	307	2	0	0	NUM
ejpam-5757	307	3	and	and	CCONJ
ejpam-5757	307	4	∥dϕ(u	∥dϕ(u	NOUN
ejpam-5757	307	5	,	,	PUNCT
ejpam-5757	307	6	v)−g(u	v)−g(u	X
ejpam-5757	307	7	,	,	PUNCT
ejpam-5757	307	8	v)∥	v)∥	PUNCT
ejpam-5757	307	9	≤	≤	NUM
ejpam-5757	307	10	ϵ∥u∥c1∥v∥c2	ϵ∥u∥c1∥v∥c2	NOUN
ejpam-5757	307	11	(	(	PUNCT
ejpam-5757	307	12	34	34	NUM
ejpam-5757	307	13	)	)	PUNCT
ejpam-5757	307	14	for	for	ADP
ejpam-5757	307	15	all	all	DET
ejpam-5757	307	16	u	u	NOUN
ejpam-5757	307	17	,	,	PUNCT
ejpam-5757	307	18	v	v	PROPN
ejpam-5757	307	19	∈	∈	PROPN
ejpam-5757	307	20	u0	u0	NOUN
ejpam-5757	307	21	such	such	ADJ
ejpam-5757	307	22	that	that	SCONJ
ejpam-5757	307	23	u	u	NOUN
ejpam-5757	307	24	+	+	X
ejpam-5757	307	25	3v	3v	NUM
ejpam-5757	307	26	̸=	̸=	PROPN
ejpam-5757	307	27	0	0	NUM
ejpam-5757	307	28	,	,	PUNCT
ejpam-5757	307	29	u	u	PROPN
ejpam-5757	307	30	+	+	PROPN
ejpam-5757	307	31	2v	2v	PROPN
ejpam-5757	307	32	̸=	̸=	PROPN
ejpam-5757	307	33	0	0	NUM
ejpam-5757	307	34	,	,	PUNCT
ejpam-5757	307	35	u	u	NOUN
ejpam-5757	307	36	−	−	PROPN
ejpam-5757	307	37	2v	2v	PROPN
ejpam-5757	307	38	̸=	̸=	PROPN
ejpam-5757	307	39	0	0	NUM
ejpam-5757	307	40	,	,	PUNCT
ejpam-5757	307	41	u	u	NOUN
ejpam-5757	307	42	−	−	PROPN
ejpam-5757	307	43	v	v	ADP
ejpam-5757	307	44	̸=	̸=	PROPN
ejpam-5757	307	45	0	0	NUM
ejpam-5757	307	46	,	,	PUNCT
ejpam-5757	307	47	u	u	NOUN
ejpam-5757	307	48	+	+	NOUN
ejpam-5757	307	49	v	v	ADP
ejpam-5757	307	50	̸=	̸=	PROPN
ejpam-5757	307	51	0	0	NUM
ejpam-5757	307	52	.	.	PUNCT
ejpam-5757	308	1	if	if	SCONJ
ejpam-5757	308	2	the	the	DET
ejpam-5757	308	3	functional	functional	ADJ
ejpam-5757	308	4	equation	equation	NOUN
ejpam-5757	308	5	dϕ(u	dϕ(u	NOUN
ejpam-5757	308	6	,	,	PUNCT
ejpam-5757	308	7	v	v	NOUN
ejpam-5757	308	8	)	)	PUNCT
ejpam-5757	308	9	=	=	SYM
ejpam-5757	308	10	g(u	g(u	PROPN
ejpam-5757	308	11	,	,	PUNCT
ejpam-5757	308	12	v	v	NOUN
ejpam-5757	308	13	)	)	PUNCT
ejpam-5757	308	14	for	for	ADP
ejpam-5757	308	15	all	all	DET
ejpam-5757	308	16	u	u	NOUN
ejpam-5757	308	17	,	,	PUNCT
ejpam-5757	308	18	v	v	PROPN
ejpam-5757	308	19	∈	∈	PROPN
ejpam-5757	308	20	u0	u0	NOUN
ejpam-5757	308	21	,	,	PUNCT
ejpam-5757	308	22	has	have	VERB
ejpam-5757	308	23	a	a	DET
ejpam-5757	308	24	solution	solution	NOUN
ejpam-5757	308	25	ϕ0	ϕ0	NOUN
ejpam-5757	308	26	:	:	PUNCT
ejpam-5757	308	27	u	u	NOUN
ejpam-5757	308	28	→	→	SYM
ejpam-5757	308	29	v	v	NOUN
ejpam-5757	308	30	on	on	ADP
ejpam-5757	308	31	u0	u0	ADJ
ejpam-5757	308	32	,	,	PUNCT
ejpam-5757	308	33	then	then	ADV
ejpam-5757	308	34	ϕ	ϕ	NOUN
ejpam-5757	308	35	satisfies	satisfie	NOUN
ejpam-5757	308	36	(	(	PUNCT
ejpam-5757	308	37	34	34	NUM
ejpam-5757	308	38	)	)	PUNCT
ejpam-5757	308	39	on	on	ADP
ejpam-5757	308	40	u0	u0	ADJ
ejpam-5757	308	41	.	.	PUNCT
ejpam-5757	309	1	proof	proof	NOUN
ejpam-5757	309	2	.	.	PUNCT
ejpam-5757	310	1	from	from	ADP
ejpam-5757	310	2	(	(	PUNCT
ejpam-5757	310	3	34	34	NUM
ejpam-5757	310	4	)	)	PUNCT
ejpam-5757	310	5	,	,	PUNCT
ejpam-5757	310	6	we	we	PRON
ejpam-5757	310	7	obtain	obtain	VERB
ejpam-5757	310	8	the	the	DET
ejpam-5757	310	9	mapping	mapping	NOUN
ejpam-5757	310	10	f	f	NOUN
ejpam-5757	310	11	:	:	PUNCT
ejpam-5757	310	12	u	u	X
ejpam-5757	310	13	→	→	SYM
ejpam-5757	310	14	v	v	NUM
ejpam-5757	310	15	defined	define	VERB
ejpam-5757	310	16	by	by	ADP
ejpam-5757	310	17	f	f	PROPN
ejpam-5757	310	18	:	:	PUNCT
ejpam-5757	310	19	=	=	SYM
ejpam-5757	310	20	ϕ	ϕ	PROPN
ejpam-5757	310	21	−	−	PROPN
ejpam-5757	310	22	ϕ0	ϕ0	NOUN
ejpam-5757	310	23	fulfills	fulfill	NOUN
ejpam-5757	310	24	(	(	PUNCT
ejpam-5757	310	25	32	32	NUM
ejpam-5757	310	26	)	)	PUNCT
ejpam-5757	310	27	.	.	PUNCT
ejpam-5757	311	1	the	the	DET
ejpam-5757	311	2	equation	equation	NOUN
ejpam-5757	311	3	(	(	PUNCT
ejpam-5757	311	4	2	2	NUM
ejpam-5757	311	5	)	)	PUNCT
ejpam-5757	311	6	on	on	ADP
ejpam-5757	311	7	u0	u0	ADJ
ejpam-5757	311	8	is	be	AUX
ejpam-5757	311	9	therefore	therefore	ADV
ejpam-5757	311	10	implied	imply	VERB
ejpam-5757	311	11	by	by	ADP
ejpam-5757	311	12	corollary	corollary	ADJ
ejpam-5757	311	13	1	1	NUM
ejpam-5757	311	14	,	,	PUNCT
ejpam-5757	311	15	which	which	PRON
ejpam-5757	311	16	states	state	VERB
ejpam-5757	311	17	that	that	SCONJ
ejpam-5757	311	18	f	f	PROPN
ejpam-5757	311	19	is	be	AUX
ejpam-5757	311	20	a	a	DET
ejpam-5757	311	21	solution	solution	NOUN
ejpam-5757	311	22	.	.	PUNCT
ejpam-5757	312	1	thus	thus	ADV
ejpam-5757	312	2	dϕ(u	dϕ(u	NUM
ejpam-5757	312	3	,	,	PUNCT
ejpam-5757	312	4	v)−g(u	v)−g(u	X
ejpam-5757	312	5	,	,	PUNCT
ejpam-5757	312	6	v	v	NOUN
ejpam-5757	312	7	)	)	PUNCT
ejpam-5757	312	8	=	=	PUNCT
ejpam-5757	312	9	d(f	d(f	NOUN
ejpam-5757	312	10	+	+	CCONJ
ejpam-5757	312	11	ϕ0)(u	ϕ0)(u	ADJ
ejpam-5757	312	12	,	,	PUNCT
ejpam-5757	312	13	v)−g(u	v)−g(u	X
ejpam-5757	312	14	,	,	PUNCT
ejpam-5757	312	15	v	v	NOUN
ejpam-5757	312	16	)	)	PUNCT
ejpam-5757	312	17	=	=	SYM
ejpam-5757	312	18	0	0	NUM
ejpam-5757	312	19	for	for	ADP
ejpam-5757	312	20	all	all	DET
ejpam-5757	312	21	u	u	NOUN
ejpam-5757	312	22	,	,	PUNCT
ejpam-5757	312	23	v	v	PROPN
ejpam-5757	312	24	∈	∈	PROPN
ejpam-5757	312	25	u0	u0	NOUN
ejpam-5757	312	26	such	such	ADJ
ejpam-5757	312	27	that	that	SCONJ
ejpam-5757	312	28	u+	u+	NOUN
ejpam-5757	312	29	3v	3v	NUM
ejpam-5757	312	30	̸=	̸=	PROPN
ejpam-5757	312	31	0	0	NUM
ejpam-5757	312	32	,	,	PUNCT
ejpam-5757	312	33	u+	u+	NUM
ejpam-5757	312	34	2v	2v	PROPN
ejpam-5757	312	35	̸=	̸=	PROPN
ejpam-5757	312	36	0	0	NUM
ejpam-5757	312	37	,	,	PUNCT
ejpam-5757	312	38	u−	u−	PROPN
ejpam-5757	312	39	2v	2v	PROPN
ejpam-5757	312	40	̸=	̸=	PROPN
ejpam-5757	312	41	0	0	NUM
ejpam-5757	312	42	,	,	PUNCT
ejpam-5757	312	43	u−	u−	PROPN
ejpam-5757	312	44	v	v	ADP
ejpam-5757	312	45	̸=	̸=	PROPN
ejpam-5757	312	46	0	0	NUM
ejpam-5757	312	47	,	,	PUNCT
ejpam-5757	312	48	u+	u+	NOUN
ejpam-5757	312	49	v	v	ADP
ejpam-5757	312	50	̸=	̸=	PROPN
ejpam-5757	312	51	0	0	NUM
ejpam-5757	312	52	,	,	PUNCT
ejpam-5757	312	53	which	which	PRON
ejpam-5757	312	54	means	mean	VERB
ejpam-5757	312	55	that	that	SCONJ
ejpam-5757	312	56	ϕ	ϕ	NOUN
ejpam-5757	312	57	is	be	AUX
ejpam-5757	312	58	a	a	DET
ejpam-5757	312	59	solution	solution	NOUN
ejpam-5757	312	60	to	to	ADP
ejpam-5757	312	61	(	(	PUNCT
ejpam-5757	312	62	3	3	X
ejpam-5757	312	63	)	)	PUNCT
ejpam-5757	312	64	on	on	ADP
ejpam-5757	312	65	u0	u0	ADJ
ejpam-5757	312	66	.	.	PUNCT
ejpam-5757	312	67	4	4	X
ejpam-5757	312	68	.	.	X
ejpam-5757	312	69	conclusion	conclusion	NOUN
ejpam-5757	312	70	we	we	PRON
ejpam-5757	312	71	proved	prove	VERB
ejpam-5757	312	72	the	the	DET
ejpam-5757	312	73	hyperstability	hyperstability	NOUN
ejpam-5757	312	74	of	of	ADP
ejpam-5757	312	75	the	the	DET
ejpam-5757	312	76	quintic	quintic	ADJ
ejpam-5757	312	77	functional	functional	ADJ
ejpam-5757	312	78	equation	equation	NOUN
ejpam-5757	312	79	ϕ(u	ϕ(u	PROPN
ejpam-5757	312	80	+	+	CCONJ
ejpam-5757	312	81	3v	3v	NUM
ejpam-5757	312	82	)	)	PUNCT
ejpam-5757	312	83	−	−	PROPN
ejpam-5757	312	84	5ϕ(u	5ϕ(u	PROPN
ejpam-5757	312	85	+	+	NUM
ejpam-5757	312	86	2v	2v	NUM
ejpam-5757	312	87	)	)	PUNCT
ejpam-5757	313	1	−	−	PROPN
ejpam-5757	313	2	ϕ(u	ϕ(u	PROPN
ejpam-5757	313	3	−	−	PROPN
ejpam-5757	313	4	2v	2v	NUM
ejpam-5757	313	5	)	)	PUNCT
ejpam-5757	314	1	+	+	CCONJ
ejpam-5757	314	2	10ϕ(u	10ϕ(u	NUM
ejpam-5757	314	3	+	+	CCONJ
ejpam-5757	314	4	v	v	NOUN
ejpam-5757	314	5	)	)	PUNCT
ejpam-5757	315	1	+	+	CCONJ
ejpam-5757	315	2	5ϕ(u	5ϕ(u	ADJ
ejpam-5757	315	3	−	−	PROPN
ejpam-5757	315	4	v	v	NOUN
ejpam-5757	315	5	)	)	PUNCT
ejpam-5757	315	6	−	−	PROPN
ejpam-5757	315	7	10ϕ(u	10ϕ(u	NUM
ejpam-5757	315	8	)	)	PUNCT
ejpam-5757	316	1	−	−	PROPN
ejpam-5757	316	2	120ϕ(v	120ϕ(v	NOUN
ejpam-5757	316	3	)	)	PUNCT
ejpam-5757	316	4	=	=	SYM
ejpam-5757	316	5	0	0	NUM
ejpam-5757	316	6	,	,	PUNCT
ejpam-5757	316	7	in	in	ADP
ejpam-5757	316	8	banach	banach	NOUN
ejpam-5757	316	9	spaces	space	NOUN
ejpam-5757	316	10	by	by	ADP
ejpam-5757	316	11	means	mean	NOUN
ejpam-5757	316	12	of	of	ADP
ejpam-5757	316	13	brzdȩk	brzdȩk	NOUN
ejpam-5757	316	14	’s	’s	PART
ejpam-5757	316	15	fixed	fix	VERB
ejpam-5757	316	16	point	point	NOUN
ejpam-5757	316	17	theorem	theorem	VERB
ejpam-5757	316	18	.	.	PUNCT
ejpam-5757	317	1	s.	s.	PROPN
ejpam-5757	317	2	karthikeyan	karthikeyan	PROPN
ejpam-5757	317	3	et	et	PROPN
ejpam-5757	317	4	al	al	PROPN
ejpam-5757	317	5	.	.	PUNCT
ejpam-5757	317	6	/	/	SYM
ejpam-5757	317	7	eur	eur	PROPN
ejpam-5757	317	8	.	.	PUNCT
ejpam-5757	318	1	j.	j.	PROPN
ejpam-5757	318	2	pure	pure	PROPN
ejpam-5757	318	3	appl	appl	PROPN
ejpam-5757	318	4	.	.	PROPN
ejpam-5757	318	5	math	math	PROPN
ejpam-5757	318	6	,	,	PUNCT
ejpam-5757	318	7	18	18	NUM
ejpam-5757	318	8	(	(	PUNCT
ejpam-5757	318	9	1	1	NUM
ejpam-5757	318	10	)	)	PUNCT
ejpam-5757	318	11	(	(	PUNCT
ejpam-5757	318	12	2025	2025	NUM
ejpam-5757	318	13	)	)	PUNCT
ejpam-5757	318	14	,	,	PUNCT
ejpam-5757	318	15	5757	5757	NUM
ejpam-5757	318	16	17	17	NUM
ejpam-5757	318	17	of	of	ADP
ejpam-5757	318	18	18	18	NUM
ejpam-5757	318	19	acknowledgements	acknowledgement	NOUN
ejpam-5757	318	20	the	the	DET
ejpam-5757	318	21	authors	author	NOUN
ejpam-5757	318	22	are	be	AUX
ejpam-5757	318	23	thankful	thankful	ADJ
ejpam-5757	318	24	to	to	ADP
ejpam-5757	318	25	the	the	DET
ejpam-5757	318	26	editors	editor	NOUN
ejpam-5757	318	27	and	and	CCONJ
ejpam-5757	318	28	the	the	DET
ejpam-5757	318	29	anonymous	anonymous	ADJ
ejpam-5757	318	30	reviewers	reviewer	NOUN
ejpam-5757	318	31	for	for	ADP
ejpam-5757	318	32	many	many	ADJ
ejpam-5757	318	33	valuable	valuable	ADJ
ejpam-5757	318	34	suggestions	suggestion	NOUN
ejpam-5757	318	35	to	to	PART
ejpam-5757	318	36	improve	improve	VERB
ejpam-5757	318	37	this	this	DET
ejpam-5757	318	38	paper	paper	NOUN
ejpam-5757	318	39	.	.	PUNCT
ejpam-5757	319	1	fundings	funding	NOUN
ejpam-5757	319	2	s.	s.	PROPN
ejpam-5757	319	3	donganont	donganont	PROPN
ejpam-5757	319	4	was	be	AUX
ejpam-5757	319	5	supported	support	VERB
ejpam-5757	319	6	by	by	ADP
ejpam-5757	319	7	the	the	DET
ejpam-5757	319	8	university	university	NOUN
ejpam-5757	319	9	of	of	ADP
ejpam-5757	319	10	phayao	phayao	PROPN
ejpam-5757	319	11	and	and	CCONJ
ejpam-5757	319	12	thailand	thailand	PROPN
ejpam-5757	319	13	science	science	PROPN
ejpam-5757	319	14	research	research	PROPN
ejpam-5757	319	15	and	and	CCONJ
ejpam-5757	319	16	innovation	innovation	NOUN
ejpam-5757	319	17	fund	fund	NOUN
ejpam-5757	319	18	(	(	PUNCT
ejpam-5757	319	19	fundamental	fundamental	ADJ
ejpam-5757	319	20	fund	fund	NOUN
ejpam-5757	319	21	2025	2025	NUM
ejpam-5757	319	22	,	,	PUNCT
ejpam-5757	319	23	grant	grant	VERB
ejpam-5757	319	24	no	no	NOUN
ejpam-5757	319	25	.	.	PUNCT
ejpam-5757	320	1	5020/2567	5020/2567	NUM
ejpam-5757	320	2	)	)	PUNCT
ejpam-5757	320	3	.	.	PUNCT
ejpam-5757	321	1	declarations	declaration	NOUN
ejpam-5757	321	2	availablity	availablity	NOUN
ejpam-5757	321	3	of	of	ADP
ejpam-5757	321	4	data	datum	NOUN
ejpam-5757	321	5	and	and	CCONJ
ejpam-5757	321	6	materials	material	NOUN
ejpam-5757	321	7	not	not	PART
ejpam-5757	321	8	applicable	applicable	ADJ
ejpam-5757	321	9	.	.	PUNCT
ejpam-5757	322	1	human	human	ADJ
ejpam-5757	322	2	and	and	CCONJ
ejpam-5757	322	3	animal	animal	NOUN
ejpam-5757	322	4	rights	right	NOUN
ejpam-5757	322	5	we	we	PRON
ejpam-5757	322	6	would	would	AUX
ejpam-5757	322	7	like	like	VERB
ejpam-5757	322	8	to	to	PART
ejpam-5757	322	9	mention	mention	VERB
ejpam-5757	322	10	that	that	SCONJ
ejpam-5757	322	11	this	this	DET
ejpam-5757	322	12	article	article	NOUN
ejpam-5757	322	13	does	do	AUX
ejpam-5757	322	14	not	not	PART
ejpam-5757	322	15	contain	contain	VERB
ejpam-5757	322	16	any	any	DET
ejpam-5757	322	17	studies	study	NOUN
ejpam-5757	322	18	with	with	ADP
ejpam-5757	322	19	animals	animal	NOUN
ejpam-5757	322	20	and	and	CCONJ
ejpam-5757	322	21	does	do	AUX
ejpam-5757	322	22	not	not	PART
ejpam-5757	322	23	involve	involve	VERB
ejpam-5757	322	24	any	any	DET
ejpam-5757	322	25	studies	study	NOUN
ejpam-5757	322	26	over	over	ADP
ejpam-5757	322	27	human	human	ADJ
ejpam-5757	322	28	being	being	NOUN
ejpam-5757	322	29	.	.	PUNCT
ejpam-5757	323	1	conflict	conflict	NOUN
ejpam-5757	323	2	of	of	ADP
ejpam-5757	323	3	interest	interest	NOUN
ejpam-5757	323	4	the	the	DET
ejpam-5757	323	5	authors	author	NOUN
ejpam-5757	323	6	declare	declare	VERB
ejpam-5757	323	7	that	that	SCONJ
ejpam-5757	323	8	they	they	PRON
ejpam-5757	323	9	have	have	VERB
ejpam-5757	323	10	no	no	DET
ejpam-5757	323	11	competing	compete	VERB
ejpam-5757	323	12	interests	interest	NOUN
ejpam-5757	323	13	.	.	PUNCT
ejpam-5757	324	1	references	reference	NOUN
ejpam-5757	324	2	[	[	X
ejpam-5757	324	3	1	1	NUM
ejpam-5757	324	4	]	]	PUNCT
ejpam-5757	324	5	l	l	NOUN
ejpam-5757	324	6	aiemsomboon	aiemsomboon	NOUN
ejpam-5757	324	7	and	and	CCONJ
ejpam-5757	324	8	w	w	PROPN
ejpam-5757	324	9	sintunavarat	sintunavarat	NOUN
ejpam-5757	324	10	.	.	PUNCT
ejpam-5757	325	1	on	on	ADP
ejpam-5757	325	2	new	new	ADJ
ejpam-5757	325	3	approximations	approximation	NOUN
ejpam-5757	325	4	for	for	ADP
ejpam-5757	325	5	generalized	generalized	ADJ
ejpam-5757	325	6	cauchy	cauchy	ADJ
ejpam-5757	325	7	functional	functional	ADJ
ejpam-5757	325	8	equations	equation	NOUN
ejpam-5757	325	9	using	use	VERB
ejpam-5757	325	10	brzdȩk	brzdȩk	PROPN
ejpam-5757	325	11	and	and	CCONJ
ejpam-5757	325	12	ciepliński	ciepliński	PROPN
ejpam-5757	325	13	’s	’s	PART
ejpam-5757	325	14	fixed	fix	VERB
ejpam-5757	325	15	point	point	NOUN
ejpam-5757	325	16	theorems	theorem	NOUN
ejpam-5757	325	17	in	in	ADP
ejpam-5757	325	18	2	2	NUM
ejpam-5757	325	19	-	-	PUNCT
ejpam-5757	325	20	banach	banach	NOUN
ejpam-5757	325	21	spaces	space	NOUN
ejpam-5757	325	22	.	.	PUNCT
ejpam-5757	326	1	acta	acta	PROPN
ejpam-5757	326	2	.	.	PUNCT
ejpam-5757	327	1	math	math	NOUN
ejpam-5757	327	2	.	.	PUNCT
ejpam-5757	328	1	sci	sci	PROPN
ejpam-5757	328	2	.	.	PROPN
ejpam-5757	328	3	,	,	PUNCT
ejpam-5757	328	4	40(3):824–834	40(3):824–834	NOUN
ejpam-5757	328	5	,	,	PUNCT
ejpam-5757	328	6	2020	2020	NUM
ejpam-5757	328	7	.	.	PUNCT
ejpam-5757	329	1	[	[	X
ejpam-5757	329	2	2	2	NUM
ejpam-5757	329	3	]	]	PUNCT
ejpam-5757	329	4	y	y	PROPN
ejpam-5757	329	5	aribou	aribou	PROPN
ejpam-5757	329	6	,	,	PUNCT
ejpam-5757	329	7	h	h	NOUN
ejpam-5757	329	8	dimou	dimou	ADJ
ejpam-5757	329	9	,	,	PUNCT
ejpam-5757	329	10	and	and	CCONJ
ejpam-5757	329	11	s	s	VERB
ejpam-5757	329	12	kabbaj	kabbaj	PROPN
ejpam-5757	329	13	.	.	PROPN
ejpam-5757	329	14	hyperstability	hyperstability	NOUN
ejpam-5757	329	15	of	of	ADP
ejpam-5757	329	16	a	a	DET
ejpam-5757	329	17	mixed	mixed	ADJ
ejpam-5757	329	18	type	type	NOUN
ejpam-5757	329	19	cubic	cubic	ADJ
ejpam-5757	329	20	-	-	PUNCT
ejpam-5757	329	21	quartic	quartic	ADJ
ejpam-5757	329	22	functional	functional	ADJ
ejpam-5757	329	23	equation	equation	NOUN
ejpam-5757	329	24	in	in	ADP
ejpam-5757	329	25	ultrametric	ultrametric	ADJ
ejpam-5757	329	26	spaces	space	NOUN
ejpam-5757	329	27	.	.	PUNCT
ejpam-5757	330	1	j.	j.	PROPN
ejpam-5757	330	2	class	class	PROPN
ejpam-5757	330	3	.	.	PUNCT
ejpam-5757	331	1	anal	anal	PROPN
ejpam-5757	331	2	.	.	PUNCT
ejpam-5757	331	3	,	,	PUNCT
ejpam-5757	331	4	14(2):105–120	14(2):105–120	NUM
ejpam-5757	331	5	,	,	PUNCT
ejpam-5757	331	6	2019	2019	NUM
ejpam-5757	331	7	.	.	PUNCT
ejpam-5757	332	1	[	[	X
ejpam-5757	332	2	3	3	X
ejpam-5757	332	3	]	]	X
ejpam-5757	332	4	y	y	PROPN
ejpam-5757	332	5	aribou	aribou	PROPN
ejpam-5757	332	6	,	,	PUNCT
ejpam-5757	332	7	h	h	NOUN
ejpam-5757	332	8	dimou	dimou	ADJ
ejpam-5757	332	9	,	,	PUNCT
ejpam-5757	332	10	and	and	CCONJ
ejpam-5757	332	11	m	m	PROPN
ejpam-5757	332	12	rossafi	rossafi	NOUN
ejpam-5757	332	13	.	.	PUNCT
ejpam-5757	333	1	hyperstability	hyperstability	NOUN
ejpam-5757	333	2	of	of	ADP
ejpam-5757	333	3	cubic	cubic	ADJ
ejpam-5757	333	4	functional	functional	ADJ
ejpam-5757	333	5	equation	equation	NOUN
ejpam-5757	333	6	in	in	ADP
ejpam-5757	333	7	banach	banach	NOUN
ejpam-5757	333	8	space	space	NOUN
ejpam-5757	333	9	.	.	PUNCT
ejpam-5757	334	1	ann	ann	PROPN
ejpam-5757	334	2	.	.	PROPN
ejpam-5757	334	3	univ	univ	PROPN
ejpam-5757	334	4	.	.	PROPN
ejpam-5757	334	5	ferrara	ferrara	PROPN
ejpam-5757	334	6	sez	sez	PROPN
ejpam-5757	334	7	.	.	PUNCT
ejpam-5757	335	1	vii	vii	PROPN
ejpam-5757	335	2	sci	sci	PROPN
ejpam-5757	335	3	.	.	PROPN
ejpam-5757	335	4	mat	mat	PROPN
ejpam-5757	335	5	.	.	PROPN
ejpam-5757	335	6	,	,	PUNCT
ejpam-5757	335	7	69(2):317–328	69(2):317–328	PROPN
ejpam-5757	335	8	,	,	PUNCT
ejpam-5757	335	9	2023	2023	NUM
ejpam-5757	335	10	.	.	PUNCT
ejpam-5757	336	1	[	[	X
ejpam-5757	336	2	4	4	X
ejpam-5757	336	3	]	]	X
ejpam-5757	336	4	a	a	DET
ejpam-5757	336	5	bahyrycz	bahyrycz	NOUN
ejpam-5757	336	6	and	and	CCONJ
ejpam-5757	336	7	m	m	NOUN
ejpam-5757	336	8	piszczek	piszczek	NOUN
ejpam-5757	336	9	.	.	PUNCT
ejpam-5757	337	1	hyperstability	hyperstability	NOUN
ejpam-5757	337	2	of	of	ADP
ejpam-5757	337	3	the	the	DET
ejpam-5757	337	4	jensen	jensen	PROPN
ejpam-5757	337	5	functional	functional	ADJ
ejpam-5757	337	6	equation	equation	NOUN
ejpam-5757	337	7	.	.	PUNCT
ejpam-5757	338	1	acta	acta	PROPN
ejpam-5757	338	2	math	math	PROPN
ejpam-5757	338	3	.	.	PUNCT
ejpam-5757	339	1	hungar	hungar	PROPN
ejpam-5757	339	2	.	.	PUNCT
ejpam-5757	339	3	,	,	PUNCT
ejpam-5757	339	4	142:353–365	142:353–365	NUM
ejpam-5757	339	5	,	,	PUNCT
ejpam-5757	339	6	2014	2014	NUM
ejpam-5757	339	7	.	.	PUNCT
ejpam-5757	340	1	[	[	X
ejpam-5757	340	2	5	5	NUM
ejpam-5757	340	3	]	]	PUNCT
ejpam-5757	340	4	n	n	PRON
ejpam-5757	340	5	bounader	bounader	NOUN
ejpam-5757	340	6	.	.	PUNCT
ejpam-5757	341	1	on	on	ADP
ejpam-5757	341	2	the	the	DET
ejpam-5757	341	3	hyperstability	hyperstability	NOUN
ejpam-5757	341	4	of	of	ADP
ejpam-5757	341	5	a	a	DET
ejpam-5757	341	6	quartic	quartic	ADJ
ejpam-5757	341	7	functional	functional	ADJ
ejpam-5757	341	8	equation	equation	NOUN
ejpam-5757	341	9	in	in	ADP
ejpam-5757	341	10	banach	banach	NOUN
ejpam-5757	341	11	spaces	space	NOUN
ejpam-5757	341	12	.	.	PUNCT
ejpam-5757	342	1	proyecciones	proyeccione	NOUN
ejpam-5757	342	2	,	,	PUNCT
ejpam-5757	342	3	36(1):29–44	36(1):29–44	NUM
ejpam-5757	342	4	,	,	PUNCT
ejpam-5757	342	5	2017	2017	NUM
ejpam-5757	342	6	.	.	PUNCT
ejpam-5757	343	1	[	[	X
ejpam-5757	343	2	6	6	NUM
ejpam-5757	343	3	]	]	PUNCT
ejpam-5757	343	4	d	d	X
ejpam-5757	343	5	g	g	PROPN
ejpam-5757	343	6	bourgin	bourgin	NOUN
ejpam-5757	343	7	.	.	PUNCT
ejpam-5757	344	1	approximately	approximately	ADV
ejpam-5757	344	2	isometric	isometric	ADJ
ejpam-5757	344	3	and	and	CCONJ
ejpam-5757	344	4	multiplicative	multiplicative	ADJ
ejpam-5757	344	5	transformations	transformation	NOUN
ejpam-5757	344	6	on	on	ADP
ejpam-5757	344	7	continuous	continuous	ADJ
ejpam-5757	344	8	function	function	NOUN
ejpam-5757	344	9	rings	ring	NOUN
ejpam-5757	344	10	.	.	PUNCT
ejpam-5757	345	1	duke	duke	PROPN
ejpam-5757	345	2	math	math	PROPN
ejpam-5757	345	3	.	.	PUNCT
ejpam-5757	346	1	j.	j.	PROPN
ejpam-5757	346	2	,	,	PUNCT
ejpam-5757	346	3	16:383–397	16:383–397	NUM
ejpam-5757	346	4	,	,	PUNCT
ejpam-5757	346	5	2019	2019	NUM
ejpam-5757	346	6	.	.	PUNCT
ejpam-5757	347	1	[	[	X
ejpam-5757	347	2	7	7	NUM
ejpam-5757	347	3	]	]	X
ejpam-5757	347	4	s	s	PART
ejpam-5757	347	5	bowmiya	bowmiya	NOUN
ejpam-5757	347	6	,	,	PUNCT
ejpam-5757	347	7	g	g	PROPN
ejpam-5757	347	8	balasubramanian	balasubramanian	PROPN
ejpam-5757	347	9	,	,	PUNCT
ejpam-5757	347	10	v	v	ADJ
ejpam-5757	347	11	govindan	govindan	PROPN
ejpam-5757	347	12	,	,	PUNCT
ejpam-5757	347	13	m	m	VERB
ejpam-5757	347	14	donganont	donganont	NOUN
ejpam-5757	347	15	,	,	PUNCT
ejpam-5757	347	16	and	and	CCONJ
ejpam-5757	347	17	h	h	NOUN
ejpam-5757	347	18	byeon	byeon	NOUN
ejpam-5757	347	19	.	.	PUNCT
ejpam-5757	348	1	generalized	generalize	VERB
ejpam-5757	348	2	linear	linear	PROPN
ejpam-5757	348	3	differential	differential	NOUN
ejpam-5757	348	4	equation	equation	NOUN
ejpam-5757	348	5	using	use	VERB
ejpam-5757	348	6	hyers	hyers	PROPN
ejpam-5757	348	7	-	-	PUNCT
ejpam-5757	348	8	ulam	ulam	PROPN
ejpam-5757	348	9	stability	stability	PROPN
ejpam-5757	348	10	approach	approach	NOUN
ejpam-5757	348	11	.	.	PUNCT
ejpam-5757	349	1	eur	eur	PROPN
ejpam-5757	349	2	.	.	PUNCT
ejpam-5757	350	1	j.	j.	PROPN
ejpam-5757	350	2	pure	pure	PROPN
ejpam-5757	350	3	appl	appl	PROPN
ejpam-5757	350	4	.	.	PUNCT
ejpam-5757	350	5	math	math	PROPN
ejpam-5757	350	6	.	.	PUNCT
ejpam-5757	350	7	,	,	PUNCT
ejpam-5757	350	8	17(4):3415–3435	17(4):3415–3435	NUM
ejpam-5757	350	9	,	,	PUNCT
ejpam-5757	350	10	2024	2024	NUM
ejpam-5757	350	11	.	.	PUNCT
ejpam-5757	351	1	[	[	X
ejpam-5757	351	2	8	8	NUM
ejpam-5757	351	3	]	]	SYM
ejpam-5757	351	4	s	s	PART
ejpam-5757	351	5	bowmiya	bowmiya	NOUN
ejpam-5757	351	6	,	,	PUNCT
ejpam-5757	351	7	g	g	PROPN
ejpam-5757	351	8	balasubramanian	balasubramanian	PROPN
ejpam-5757	351	9	,	,	PUNCT
ejpam-5757	351	10	v	v	ADJ
ejpam-5757	351	11	govindan	govindan	PROPN
ejpam-5757	351	12	,	,	PUNCT
ejpam-5757	351	13	m	m	VERB
ejpam-5757	351	14	donganont	donganont	NOUN
ejpam-5757	351	15	,	,	PUNCT
ejpam-5757	351	16	and	and	CCONJ
ejpam-5757	351	17	h	h	NOUN
ejpam-5757	351	18	byeon	byeon	NOUN
ejpam-5757	351	19	.	.	PUNCT
ejpam-5757	352	1	hyersulam	hyersulam	PROPN
ejpam-5757	352	2	stability	stability	NOUN
ejpam-5757	352	3	of	of	ADP
ejpam-5757	352	4	fifth	fifth	ADJ
ejpam-5757	352	5	order	order	NOUN
ejpam-5757	352	6	linear	linear	PROPN
ejpam-5757	352	7	differential	differential	NOUN
ejpam-5757	352	8	equations	equation	NOUN
ejpam-5757	352	9	.	.	PUNCT
ejpam-5757	353	1	eur	eur	PROPN
ejpam-5757	353	2	.	.	PUNCT
ejpam-5757	354	1	j.	j.	PROPN
ejpam-5757	354	2	pure	pure	PROPN
ejpam-5757	354	3	appl	appl	PROPN
ejpam-5757	354	4	.	.	PUNCT
ejpam-5757	354	5	math	math	PROPN
ejpam-5757	354	6	.	.	PUNCT
ejpam-5757	354	7	,	,	PUNCT
ejpam-5757	354	8	17(4):3585–3609	17(4):3585–3609	NUM
ejpam-5757	354	9	,	,	PUNCT
ejpam-5757	354	10	2024	2024	NUM
ejpam-5757	354	11	.	.	PUNCT
ejpam-5757	355	1	[	[	X
ejpam-5757	355	2	9	9	NUM
ejpam-5757	355	3	]	]	X
ejpam-5757	355	4	j	j	PROPN
ejpam-5757	355	5	brzdȩk	brzdȩk	PROPN
ejpam-5757	355	6	.	.	PUNCT
ejpam-5757	355	7	hyperstability	hyperstability	NOUN
ejpam-5757	355	8	of	of	ADP
ejpam-5757	355	9	the	the	DET
ejpam-5757	355	10	cauchy	cauchy	ADJ
ejpam-5757	355	11	equation	equation	NOUN
ejpam-5757	355	12	on	on	ADP
ejpam-5757	355	13	restricted	restricted	ADJ
ejpam-5757	355	14	domains	domain	NOUN
ejpam-5757	355	15	.	.	PUNCT
ejpam-5757	356	1	acta	acta	PROPN
ejpam-5757	356	2	math	math	PROPN
ejpam-5757	356	3	.	.	PUNCT
ejpam-5757	357	1	hungar	hungar	PROPN
ejpam-5757	357	2	.	.	PUNCT
ejpam-5757	357	3	,	,	PUNCT
ejpam-5757	357	4	14:58–67	14:58–67	NUM
ejpam-5757	357	5	,	,	PUNCT
ejpam-5757	357	6	2013	2013	NUM
ejpam-5757	357	7	.	.	PUNCT
ejpam-5757	358	1	s.	s.	PROPN
ejpam-5757	358	2	karthikeyan	karthikeyan	PROPN
ejpam-5757	358	3	et	et	PROPN
ejpam-5757	358	4	al	al	PROPN
ejpam-5757	358	5	.	.	PUNCT
ejpam-5757	358	6	/	/	SYM
ejpam-5757	358	7	eur	eur	PROPN
ejpam-5757	358	8	.	.	PUNCT
ejpam-5757	359	1	j.	j.	PROPN
ejpam-5757	359	2	pure	pure	PROPN
ejpam-5757	359	3	appl	appl	PROPN
ejpam-5757	359	4	.	.	PROPN
ejpam-5757	359	5	math	math	PROPN
ejpam-5757	359	6	,	,	PUNCT
ejpam-5757	359	7	18	18	NUM
ejpam-5757	359	8	(	(	PUNCT
ejpam-5757	359	9	1	1	NUM
ejpam-5757	359	10	)	)	PUNCT
ejpam-5757	359	11	(	(	PUNCT
ejpam-5757	359	12	2025	2025	NUM
ejpam-5757	359	13	)	)	PUNCT
ejpam-5757	359	14	,	,	PUNCT
ejpam-5757	359	15	5757	5757	NUM
ejpam-5757	359	16	18	18	NUM
ejpam-5757	359	17	of	of	ADP
ejpam-5757	359	18	18	18	NUM
ejpam-5757	359	19	[	[	SYM
ejpam-5757	359	20	10	10	NUM
ejpam-5757	359	21	]	]	X
ejpam-5757	359	22	j	j	PROPN
ejpam-5757	359	23	brzdȩk	brzdȩk	PROPN
ejpam-5757	359	24	.	.	PUNCT
ejpam-5757	360	1	remarks	remark	NOUN
ejpam-5757	360	2	on	on	ADP
ejpam-5757	360	3	hyperstability	hyperstability	NOUN
ejpam-5757	360	4	of	of	ADP
ejpam-5757	360	5	the	the	DET
ejpam-5757	360	6	cauchy	cauchy	ADJ
ejpam-5757	360	7	functional	functional	ADJ
ejpam-5757	360	8	equation	equation	NOUN
ejpam-5757	360	9	.	.	PUNCT
ejpam-5757	361	1	aequationes	aequatione	NOUN
ejpam-5757	361	2	math	math	PROPN
ejpam-5757	361	3	.	.	PUNCT
ejpam-5757	361	4	,	,	PUNCT
ejpam-5757	362	1	86:255–267	86:255–267	PROPN
ejpam-5757	362	2	,	,	PUNCT
ejpam-5757	362	3	2013	2013	NUM
ejpam-5757	362	4	.	.	PUNCT
ejpam-5757	363	1	[	[	X
ejpam-5757	363	2	11	11	NUM
ejpam-5757	363	3	]	]	X
ejpam-5757	363	4	j	j	PROPN
ejpam-5757	363	5	brzdȩk	brzdȩk	PROPN
ejpam-5757	363	6	.	.	PUNCT
ejpam-5757	364	1	a	a	DET
ejpam-5757	364	2	hyperstability	hyperstability	NOUN
ejpam-5757	364	3	result	result	NOUN
ejpam-5757	364	4	for	for	ADP
ejpam-5757	364	5	the	the	DET
ejpam-5757	364	6	cauchy	cauchy	ADJ
ejpam-5757	364	7	equation	equation	NOUN
ejpam-5757	364	8	.	.	PUNCT
ejpam-5757	365	1	bull	bull	NOUN
ejpam-5757	365	2	.	.	PUNCT
ejpam-5757	366	1	aust	aust	PROPN
ejpam-5757	366	2	.	.	PUNCT
ejpam-5757	366	3	math	math	PROPN
ejpam-5757	366	4	.	.	PUNCT
ejpam-5757	367	1	soc	soc	PROPN
ejpam-5757	367	2	.	.	PUNCT
ejpam-5757	367	3	,	,	PUNCT
ejpam-5757	367	4	89(1):33–40	89(1):33–40	NUM
ejpam-5757	367	5	,	,	PUNCT
ejpam-5757	367	6	2014	2014	NUM
ejpam-5757	367	7	.	.	PUNCT
ejpam-5757	368	1	[	[	X
ejpam-5757	368	2	12	12	NUM
ejpam-5757	368	3	]	]	X
ejpam-5757	368	4	j	j	PROPN
ejpam-5757	368	5	brzdȩk	brzdȩk	PROPN
ejpam-5757	368	6	,	,	PUNCT
ejpam-5757	368	7	j	j	PROPN
ejpam-5757	368	8	chudziak	chudziak	PROPN
ejpam-5757	368	9	,	,	PUNCT
ejpam-5757	368	10	and	and	CCONJ
ejpam-5757	368	11	z	z	NOUN
ejpam-5757	368	12	páles	pále	NOUN
ejpam-5757	368	13	.	.	PUNCT
ejpam-5757	369	1	a	a	DET
ejpam-5757	369	2	fixed	fix	VERB
ejpam-5757	369	3	point	point	NOUN
ejpam-5757	369	4	approach	approach	NOUN
ejpam-5757	369	5	to	to	ADP
ejpam-5757	369	6	stability	stability	NOUN
ejpam-5757	369	7	of	of	ADP
ejpam-5757	369	8	functional	functional	ADJ
ejpam-5757	369	9	equations	equation	NOUN
ejpam-5757	369	10	.	.	PUNCT
ejpam-5757	370	1	nonlinear	nonlinear	ADJ
ejpam-5757	370	2	anal	anal	PROPN
ejpam-5757	370	3	.	.	PUNCT
ejpam-5757	370	4	,	,	PUNCT
ejpam-5757	370	5	74:6728–6732	74:6728–6732	NUM
ejpam-5757	370	6	,	,	PUNCT
ejpam-5757	370	7	2011	2011	NUM
ejpam-5757	370	8	.	.	PUNCT
ejpam-5757	371	1	[	[	X
ejpam-5757	371	2	13	13	NUM
ejpam-5757	371	3	]	]	SYM
ejpam-5757	371	4	j	j	PROPN
ejpam-5757	371	5	brzdȩk	brzdȩk	PROPN
ejpam-5757	371	6	and	and	CCONJ
ejpam-5757	371	7	k	k	PROPN
ejpam-5757	371	8	ciepliński	ciepliński	PROPN
ejpam-5757	371	9	.	.	PUNCT
ejpam-5757	372	1	a	a	DET
ejpam-5757	372	2	fixed	fix	VERB
ejpam-5757	372	3	point	point	NOUN
ejpam-5757	372	4	approach	approach	NOUN
ejpam-5757	372	5	to	to	ADP
ejpam-5757	372	6	the	the	DET
ejpam-5757	372	7	stability	stability	NOUN
ejpam-5757	372	8	of	of	ADP
ejpam-5757	372	9	functional	functional	ADJ
ejpam-5757	372	10	equations	equation	NOUN
ejpam-5757	372	11	in	in	ADP
ejpam-5757	372	12	non	non	ADJ
ejpam-5757	372	13	-	-	ADJ
ejpam-5757	372	14	archimedean	archimedean	ADJ
ejpam-5757	372	15	metric	metric	ADJ
ejpam-5757	372	16	spaces	space	NOUN
ejpam-5757	372	17	.	.	PUNCT
ejpam-5757	373	1	nonlinear	nonlinear	ADJ
ejpam-5757	373	2	anal	anal	PROPN
ejpam-5757	373	3	.	.	PUNCT
ejpam-5757	373	4	,	,	PUNCT
ejpam-5757	373	5	74:6861–6867	74:6861–6867	NUM
ejpam-5757	373	6	,	,	PUNCT
ejpam-5757	373	7	2011	2011	NUM
ejpam-5757	373	8	.	.	PUNCT
ejpam-5757	374	1	[	[	X
ejpam-5757	374	2	14	14	NUM
ejpam-5757	374	3	]	]	X
ejpam-5757	374	4	j	j	PROPN
ejpam-5757	374	5	brzdȩk	brzdȩk	PROPN
ejpam-5757	374	6	and	and	CCONJ
ejpam-5757	374	7	k	k	PROPN
ejpam-5757	374	8	ciepliński	ciepliński	PROPN
ejpam-5757	374	9	.	.	PUNCT
ejpam-5757	374	10	hyperstability	hyperstability	NOUN
ejpam-5757	374	11	and	and	CCONJ
ejpam-5757	374	12	superstability	superstability	NOUN
ejpam-5757	374	13	.	.	PUNCT
ejpam-5757	375	1	abstr	abstr	PROPN
ejpam-5757	375	2	.	.	PUNCT
ejpam-5757	375	3	appl	appl	PROPN
ejpam-5757	375	4	.	.	PUNCT
ejpam-5757	376	1	anal	anal	PROPN
ejpam-5757	376	2	.	.	PUNCT
ejpam-5757	376	3	,	,	PUNCT
ejpam-5757	376	4	2017(401756):1–7	2017(401756):1–7	PROPN
ejpam-5757	376	5	,	,	PUNCT
ejpam-5757	376	6	2017	2017	NUM
ejpam-5757	376	7	.	.	PUNCT
ejpam-5757	377	1	[	[	X
ejpam-5757	377	2	15	15	NUM
ejpam-5757	377	3	]	]	X
ejpam-5757	377	4	i	i	PROPN
ejpam-5757	377	5	el	el	PROPN
ejpam-5757	377	6	-	-	PUNCT
ejpam-5757	377	7	fassii	fassii	NOUN
ejpam-5757	377	8	.	.	PUNCT
ejpam-5757	378	1	approximate	approximate	ADJ
ejpam-5757	378	2	solution	solution	NOUN
ejpam-5757	378	3	of	of	ADP
ejpam-5757	378	4	radical	radical	ADJ
ejpam-5757	378	5	quartic	quartic	ADJ
ejpam-5757	378	6	functional	functional	ADJ
ejpam-5757	378	7	equation	equation	NOUN
ejpam-5757	378	8	related	relate	VERB
ejpam-5757	378	9	to	to	AUX
ejpam-5757	378	10	additive	additive	VERB
ejpam-5757	378	11	mapping	mapping	NOUN
ejpam-5757	378	12	in	in	ADP
ejpam-5757	378	13	2	2	NUM
ejpam-5757	378	14	-	-	PUNCT
ejpam-5757	378	15	banach	banach	NOUN
ejpam-5757	378	16	spaces	space	NOUN
ejpam-5757	378	17	.	.	PUNCT
ejpam-5757	379	1	j.	j.	PROPN
ejpam-5757	379	2	math	math	PROPN
ejpam-5757	379	3	.	.	PUNCT
ejpam-5757	380	1	anal	anal	PROPN
ejpam-5757	380	2	.	.	PUNCT
ejpam-5757	381	1	appl	appl	PROPN
ejpam-5757	381	2	.	.	PROPN
ejpam-5757	381	3	,	,	PUNCT
ejpam-5757	381	4	455:2001–2013	455:2001–2013	PROPN
ejpam-5757	381	5	,	,	PUNCT
ejpam-5757	381	6	2017	2017	NUM
ejpam-5757	381	7	.	.	PUNCT
ejpam-5757	382	1	[	[	X
ejpam-5757	382	2	16	16	NUM
ejpam-5757	382	3	]	]	X
ejpam-5757	382	4	i	i	PROPN
ejpam-5757	382	5	el	el	PROPN
ejpam-5757	382	6	-	-	PUNCT
ejpam-5757	382	7	fassii	fassii	NOUN
ejpam-5757	382	8	.	.	PUNCT
ejpam-5757	383	1	hyperstability	hyperstability	NOUN
ejpam-5757	383	2	of	of	ADP
ejpam-5757	383	3	the	the	DET
ejpam-5757	383	4	generalized	generalized	ADJ
ejpam-5757	383	5	multi	multi	ADJ
ejpam-5757	383	6	-	-	ADJ
ejpam-5757	383	7	drygas	drygas	ADJ
ejpam-5757	383	8	equation	equation	NOUN
ejpam-5757	383	9	in	in	ADP
ejpam-5757	383	10	complete	complete	ADJ
ejpam-5757	383	11	bmetric	bmetric	ADJ
ejpam-5757	383	12	abelian	abelian	ADJ
ejpam-5757	383	13	groups	group	NOUN
ejpam-5757	383	14	.	.	PUNCT
ejpam-5757	384	1	bull	bull	NOUN
ejpam-5757	384	2	.	.	PUNCT
ejpam-5757	385	1	sci	sci	PROPN
ejpam-5757	385	2	.	.	PUNCT
ejpam-5757	385	3	math	math	PROPN
ejpam-5757	385	4	.	.	PUNCT
ejpam-5757	385	5	,	,	PUNCT
ejpam-5757	385	6	197(103532):1–30	197(103532):1–30	NUM
ejpam-5757	385	7	,	,	PUNCT
ejpam-5757	385	8	2024	2024	NUM
ejpam-5757	385	9	.	.	PUNCT
ejpam-5757	386	1	[	[	X
ejpam-5757	386	2	17	17	NUM
ejpam-5757	386	3	]	]	X
ejpam-5757	386	4	e	e	NOUN
ejpam-5757	386	5	gselmann	gselmann	NOUN
ejpam-5757	386	6	.	.	PUNCT
ejpam-5757	387	1	hyperstability	hyperstability	NOUN
ejpam-5757	387	2	of	of	ADP
ejpam-5757	387	3	a	a	DET
ejpam-5757	387	4	functional	functional	ADJ
ejpam-5757	387	5	equation	equation	NOUN
ejpam-5757	387	6	.	.	PUNCT
ejpam-5757	388	1	acta	acta	PROPN
ejpam-5757	388	2	math	math	PROPN
ejpam-5757	388	3	.	.	PUNCT
ejpam-5757	389	1	hungar	hungar	PROPN
ejpam-5757	389	2	.	.	PUNCT
ejpam-5757	390	1	,	,	PUNCT
ejpam-5757	390	2	124:179	124:179	PROPN
ejpam-5757	390	3	–	–	PUNCT
ejpam-5757	390	4	188	188	NUM
ejpam-5757	390	5	,	,	PUNCT
ejpam-5757	390	6	2009	2009	NUM
ejpam-5757	390	7	.	.	PUNCT
ejpam-5757	391	1	[	[	X
ejpam-5757	391	2	18	18	NUM
ejpam-5757	391	3	]	]	X
ejpam-5757	391	4	p	p	X
ejpam-5757	391	5	gǎvruţa	gǎvruţa	NOUN
ejpam-5757	391	6	.	.	PUNCT
ejpam-5757	391	7	approximate	approximate	ADJ
ejpam-5757	391	8	solution	solution	NOUN
ejpam-5757	391	9	of	of	ADP
ejpam-5757	391	10	radical	radical	ADJ
ejpam-5757	391	11	quartic	quartic	ADJ
ejpam-5757	391	12	functional	functional	ADJ
ejpam-5757	391	13	equation	equation	NOUN
ejpam-5757	391	14	related	relate	VERB
ejpam-5757	391	15	to	to	AUX
ejpam-5757	391	16	additive	additive	VERB
ejpam-5757	391	17	mapping	mapping	NOUN
ejpam-5757	391	18	in	in	ADP
ejpam-5757	391	19	2	2	NUM
ejpam-5757	391	20	-	-	PUNCT
ejpam-5757	391	21	banach	banach	NOUN
ejpam-5757	391	22	spaces	space	NOUN
ejpam-5757	391	23	.	.	PUNCT
ejpam-5757	392	1	j.	j.	PROPN
ejpam-5757	392	2	math	math	PROPN
ejpam-5757	392	3	.	.	PUNCT
ejpam-5757	393	1	anal	anal	PROPN
ejpam-5757	393	2	.	.	PUNCT
ejpam-5757	394	1	appl	appl	PROPN
ejpam-5757	394	2	.	.	PROPN
ejpam-5757	394	3	,	,	PUNCT
ejpam-5757	394	4	184:431–436	184:431–436	NUM
ejpam-5757	394	5	,	,	PUNCT
ejpam-5757	394	6	1994	1994	NUM
ejpam-5757	394	7	.	.	PUNCT
ejpam-5757	395	1	[	[	X
ejpam-5757	395	2	19	19	NUM
ejpam-5757	395	3	]	]	X
ejpam-5757	395	4	d	d	PROPN
ejpam-5757	395	5	h	h	PROPN
ejpam-5757	395	6	hyers	hyer	NOUN
ejpam-5757	395	7	.	.	PUNCT
ejpam-5757	396	1	on	on	ADP
ejpam-5757	396	2	the	the	DET
ejpam-5757	396	3	stability	stability	NOUN
ejpam-5757	396	4	of	of	ADP
ejpam-5757	396	5	the	the	DET
ejpam-5757	396	6	linear	linear	ADJ
ejpam-5757	396	7	functional	functional	ADJ
ejpam-5757	396	8	equation	equation	NOUN
ejpam-5757	396	9	.	.	PUNCT
ejpam-5757	397	1	proc	proc	PROPN
ejpam-5757	397	2	.	.	PUNCT
ejpam-5757	398	1	natl	natl	PROPN
ejpam-5757	398	2	.	.	PUNCT
ejpam-5757	399	1	acad	acad	PROPN
ejpam-5757	399	2	.	.	PUNCT
ejpam-5757	400	1	sci	sci	PROPN
ejpam-5757	400	2	.	.	PUNCT
ejpam-5757	400	3	u.s.a	u.s.a	PROPN
ejpam-5757	400	4	.	.	PROPN
ejpam-5757	400	5	,	,	PUNCT
ejpam-5757	400	6	27:222–224	27:222–224	NUM
ejpam-5757	400	7	,	,	PUNCT
ejpam-5757	400	8	1941	1941	NUM
ejpam-5757	400	9	.	.	PUNCT
ejpam-5757	401	1	[	[	X
ejpam-5757	401	2	20	20	NUM
ejpam-5757	401	3	]	]	SYM
ejpam-5757	401	4	b	b	X
ejpam-5757	401	5	v	v	NUM
ejpam-5757	401	6	senthil	senthil	PROPN
ejpam-5757	401	7	kumar	kumar	PROPN
ejpam-5757	401	8	,	,	PUNCT
ejpam-5757	401	9	h	h	PROPN
ejpam-5757	401	10	dutta	dutta	PROPN
ejpam-5757	401	11	,	,	PUNCT
ejpam-5757	401	12	and	and	CCONJ
ejpam-5757	401	13	s	s	NOUN
ejpam-5757	401	14	sabarinathan	sabarinathan	NOUN
ejpam-5757	401	15	.	.	PUNCT
ejpam-5757	402	1	modular	modular	ADJ
ejpam-5757	402	2	stabilities	stability	NOUN
ejpam-5757	402	3	of	of	ADP
ejpam-5757	402	4	a	a	DET
ejpam-5757	402	5	reciprocal	reciprocal	ADJ
ejpam-5757	402	6	second	second	ADJ
ejpam-5757	402	7	power	power	NOUN
ejpam-5757	402	8	functional	functional	ADJ
ejpam-5757	402	9	equation	equation	NOUN
ejpam-5757	402	10	.	.	PUNCT
ejpam-5757	403	1	eur	eur	PROPN
ejpam-5757	403	2	.	.	PUNCT
ejpam-5757	404	1	j.	j.	PROPN
ejpam-5757	404	2	pure	pure	PROPN
ejpam-5757	404	3	appl	appl	PROPN
ejpam-5757	404	4	.	.	PUNCT
ejpam-5757	404	5	math	math	PROPN
ejpam-5757	404	6	.	.	PUNCT
ejpam-5757	404	7	,	,	PUNCT
ejpam-5757	405	1	13(5):1162–1175	13(5):1162–1175	NUM
ejpam-5757	405	2	,	,	PUNCT
ejpam-5757	405	3	2020	2020	NUM
ejpam-5757	405	4	.	.	PUNCT
ejpam-5757	406	1	[	[	X
ejpam-5757	406	2	21	21	NUM
ejpam-5757	406	3	]	]	X
ejpam-5757	406	4	g	g	PROPN
ejpam-5757	406	5	maksa	maksa	ADJ
ejpam-5757	406	6	and	and	CCONJ
ejpam-5757	406	7	z	z	NOUN
ejpam-5757	406	8	páles	pále	NOUN
ejpam-5757	406	9	.	.	PUNCT
ejpam-5757	407	1	hyperstability	hyperstability	NOUN
ejpam-5757	407	2	of	of	ADP
ejpam-5757	407	3	a	a	DET
ejpam-5757	407	4	class	class	NOUN
ejpam-5757	407	5	of	of	ADP
ejpam-5757	407	6	linear	linear	ADJ
ejpam-5757	407	7	functional	functional	ADJ
ejpam-5757	407	8	equations	equation	NOUN
ejpam-5757	407	9	.	.	PUNCT
ejpam-5757	408	1	acta	acta	PROPN
ejpam-5757	408	2	math	math	PROPN
ejpam-5757	408	3	.	.	PUNCT
ejpam-5757	409	1	acad	acad	PROPN
ejpam-5757	409	2	.	.	PUNCT
ejpam-5757	410	1	paedagog	paedagog	PROPN
ejpam-5757	410	2	.	.	PUNCT
ejpam-5757	411	1	nyházi	nyházi	AUX
ejpam-5757	411	2	.	.	PUNCT
ejpam-5757	412	1	(	(	PUNCT
ejpam-5757	412	2	n.s	n.s	PROPN
ejpam-5757	412	3	.	.	PROPN
ejpam-5757	412	4	)	)	PUNCT
ejpam-5757	412	5	,	,	PUNCT
ejpam-5757	412	6	17(2):107–224	17(2):107–224	NUM
ejpam-5757	412	7	,	,	PUNCT
ejpam-5757	412	8	2001	2001	NUM
ejpam-5757	412	9	.	.	PUNCT
ejpam-5757	413	1	[	[	X
ejpam-5757	413	2	22	22	NUM
ejpam-5757	413	3	]	]	PUNCT
ejpam-5757	413	4	a	a	DET
ejpam-5757	413	5	najati	najati	NOUN
ejpam-5757	413	6	and	and	CCONJ
ejpam-5757	413	7	c	c	NOUN
ejpam-5757	413	8	park	park	NOUN
ejpam-5757	413	9	.	.	PUNCT
ejpam-5757	414	1	on	on	ADP
ejpam-5757	414	2	ulam	ulam	PROPN
ejpam-5757	414	3	stability	stability	NOUN
ejpam-5757	414	4	and	and	CCONJ
ejpam-5757	414	5	hyperstability	hyperstability	NOUN
ejpam-5757	414	6	of	of	ADP
ejpam-5757	414	7	a	a	DET
ejpam-5757	414	8	functional	functional	ADJ
ejpam-5757	414	9	equation	equation	NOUN
ejpam-5757	414	10	in	in	ADP
ejpam-5757	414	11	m	m	NOUN
ejpam-5757	414	12	-	-	ADJ
ejpam-5757	414	13	banach	banach	NOUN
ejpam-5757	414	14	spaces	space	NOUN
ejpam-5757	414	15	.	.	PUNCT
ejpam-5757	415	1	palest	pale	ADJ
ejpam-5757	415	2	.	.	PUNCT
ejpam-5757	416	1	j.	j.	PROPN
ejpam-5757	416	2	math	math	PROPN
ejpam-5757	416	3	.	.	PUNCT
ejpam-5757	416	4	,	,	PUNCT
ejpam-5757	416	5	13(3):738–745	13(3):738–745	NUM
ejpam-5757	416	6	,	,	PUNCT
ejpam-5757	416	7	2024	2024	NUM
ejpam-5757	416	8	.	.	PUNCT
ejpam-5757	417	1	[	[	X
ejpam-5757	417	2	23	23	NUM
ejpam-5757	417	3	]	]	X
ejpam-5757	417	4	m	m	VERB
ejpam-5757	417	5	piszczek	piszczek	NOUN
ejpam-5757	417	6	.	.	PUNCT
ejpam-5757	418	1	remark	remark	NOUN
ejpam-5757	418	2	on	on	ADP
ejpam-5757	418	3	hyperstability	hyperstability	NOUN
ejpam-5757	418	4	of	of	ADP
ejpam-5757	418	5	the	the	DET
ejpam-5757	418	6	general	general	ADJ
ejpam-5757	418	7	linear	linear	PROPN
ejpam-5757	418	8	equation	equation	NOUN
ejpam-5757	418	9	.	.	PUNCT
ejpam-5757	419	1	aequationes	aequatione	NOUN
ejpam-5757	419	2	math	math	PROPN
ejpam-5757	419	3	.	.	PUNCT
ejpam-5757	419	4	,	,	PUNCT
ejpam-5757	420	1	88:163–168	88:163–168	NOUN
ejpam-5757	420	2	,	,	PUNCT
ejpam-5757	420	3	2014	2014	NUM
ejpam-5757	420	4	.	.	PUNCT
ejpam-5757	421	1	[	[	X
ejpam-5757	421	2	24	24	NUM
ejpam-5757	421	3	]	]	X
ejpam-5757	421	4	t	t	PROPN
ejpam-5757	421	5	m	m	NOUN
ejpam-5757	421	6	rassias	rassias	PROPN
ejpam-5757	421	7	.	.	PUNCT
ejpam-5757	422	1	on	on	ADP
ejpam-5757	422	2	the	the	DET
ejpam-5757	422	3	stability	stability	NOUN
ejpam-5757	422	4	of	of	ADP
ejpam-5757	422	5	the	the	DET
ejpam-5757	422	6	linear	linear	ADJ
ejpam-5757	422	7	mapping	mapping	NOUN
ejpam-5757	422	8	in	in	ADP
ejpam-5757	422	9	banach	banach	NOUN
ejpam-5757	422	10	spaces	space	NOUN
ejpam-5757	422	11	.	.	PUNCT
ejpam-5757	423	1	proc	proc	NOUN
ejpam-5757	423	2	.	.	PUNCT
ejpam-5757	424	1	amer	amer	PROPN
ejpam-5757	424	2	.	.	PUNCT
ejpam-5757	424	3	math	math	PROPN
ejpam-5757	424	4	.	.	PUNCT
ejpam-5757	425	1	soc	soc	PROPN
ejpam-5757	425	2	.	.	PUNCT
ejpam-5757	425	3	,	,	PUNCT
ejpam-5757	425	4	72:297–300	72:297–300	PROPN
ejpam-5757	425	5	,	,	PUNCT
ejpam-5757	425	6	1978	1978	NUM
ejpam-5757	425	7	.	.	PUNCT
ejpam-5757	426	1	[	[	X
ejpam-5757	426	2	25	25	NUM
ejpam-5757	426	3	]	]	X
ejpam-5757	426	4	k	k	PROPN
ejpam-5757	426	5	ravi	ravi	PROPN
ejpam-5757	426	6	and	and	CCONJ
ejpam-5757	426	7	b	b	PROPN
ejpam-5757	426	8	v	v	PROPN
ejpam-5757	426	9	senthil	senthil	PROPN
ejpam-5757	426	10	kumar	kumar	PROPN
ejpam-5757	426	11	.	.	PROPN
ejpam-5757	427	1	generalized	generalized	PROPN
ejpam-5757	427	2	hyers	hyers	PROPN
ejpam-5757	427	3	-	-	PUNCT
ejpam-5757	427	4	ulam	ulam	ADJ
ejpam-5757	427	5	-	-	PUNCT
ejpam-5757	427	6	rassias	rassias	PROPN
ejpam-5757	427	7	stability	stability	NOUN
ejpam-5757	427	8	of	of	ADP
ejpam-5757	427	9	a	a	DET
ejpam-5757	427	10	system	system	NOUN
ejpam-5757	427	11	of	of	ADP
ejpam-5757	427	12	bi	bi	ADJ
ejpam-5757	427	13	-	-	ADJ
ejpam-5757	427	14	reciprocal	reciprocal	ADJ
ejpam-5757	427	15	functional	functional	ADJ
ejpam-5757	427	16	equations	equation	NOUN
ejpam-5757	427	17	.	.	PUNCT
ejpam-5757	428	1	eur	eur	PROPN
ejpam-5757	428	2	.	.	PUNCT
ejpam-5757	429	1	j.	j.	PROPN
ejpam-5757	429	2	pure	pure	PROPN
ejpam-5757	429	3	appl	appl	PROPN
ejpam-5757	429	4	.	.	PUNCT
ejpam-5757	429	5	math	math	PROPN
ejpam-5757	429	6	.	.	PUNCT
ejpam-5757	429	7	,	,	PUNCT
ejpam-5757	429	8	8(2):283–293	8(2):283–293	NUM
ejpam-5757	429	9	,	,	PUNCT
ejpam-5757	429	10	2015	2015	NUM
ejpam-5757	429	11	.	.	PUNCT
ejpam-5757	430	1	[	[	X
ejpam-5757	430	2	26	26	NUM
ejpam-5757	430	3	]	]	X
ejpam-5757	430	4	s	s	VERB
ejpam-5757	430	5	salimi	salimi	NOUN
ejpam-5757	430	6	and	and	CCONJ
ejpam-5757	430	7	a	a	DET
ejpam-5757	430	8	bodaghi	bodaghi	NOUN
ejpam-5757	430	9	.	.	PUNCT
ejpam-5757	431	1	approximate	approximate	ADJ
ejpam-5757	431	2	solutions	solution	NOUN
ejpam-5757	431	3	of	of	ADP
ejpam-5757	431	4	a	a	DET
ejpam-5757	431	5	quadratic	quadratic	ADJ
ejpam-5757	431	6	functional	functional	ADJ
ejpam-5757	431	7	equation	equation	NOUN
ejpam-5757	431	8	in	in	ADP
ejpam-5757	431	9	2	2	NUM
ejpam-5757	431	10	-	-	PUNCT
ejpam-5757	431	11	banach	banach	NOUN
ejpam-5757	431	12	spaces	space	NOUN
ejpam-5757	431	13	using	use	VERB
ejpam-5757	431	14	fixed	fix	VERB
ejpam-5757	431	15	point	point	NOUN
ejpam-5757	431	16	theorem	theorem	VERB
ejpam-5757	431	17	.	.	PUNCT
ejpam-5757	432	1	j.	j.	PROPN
ejpam-5757	432	2	fixed	fix	VERB
ejpam-5757	432	3	point	point	PROPN
ejpam-5757	432	4	theory	theory	NOUN
ejpam-5757	432	5	appl	appl	PROPN
ejpam-5757	432	6	.	.	PROPN
ejpam-5757	432	7	,	,	PUNCT
ejpam-5757	432	8	22(9):1–15	22(9):1–15	NUM
ejpam-5757	432	9	,	,	PUNCT
ejpam-5757	432	10	2020	2020	NUM
ejpam-5757	432	11	.	.	PUNCT
ejpam-5757	433	1	[	[	X
ejpam-5757	433	2	27	27	NUM
ejpam-5757	433	3	]	]	X
ejpam-5757	433	4	k	k	PROPN
ejpam-5757	433	5	y	y	PROPN
ejpam-5757	433	6	n	n	PRON
ejpam-5757	433	7	sayar	sayar	NOUN
ejpam-5757	433	8	and	and	CCONJ
ejpam-5757	433	9	a	a	DET
ejpam-5757	433	10	bergam	bergam	NOUN
ejpam-5757	433	11	.	.	PUNCT
ejpam-5757	434	1	approximate	approximate	ADJ
ejpam-5757	434	2	solutions	solution	NOUN
ejpam-5757	434	3	of	of	ADP
ejpam-5757	434	4	a	a	DET
ejpam-5757	434	5	quadratic	quadratic	ADJ
ejpam-5757	434	6	functional	functional	ADJ
ejpam-5757	434	7	equation	equation	NOUN
ejpam-5757	434	8	in	in	ADP
ejpam-5757	434	9	2	2	NUM
ejpam-5757	434	10	-	-	PUNCT
ejpam-5757	434	11	banach	banach	NOUN
ejpam-5757	434	12	spaces	space	NOUN
ejpam-5757	434	13	using	use	VERB
ejpam-5757	434	14	fixed	fix	VERB
ejpam-5757	434	15	point	point	NOUN
ejpam-5757	434	16	theorem	theorem	VERB
ejpam-5757	434	17	.	.	PUNCT
ejpam-5757	435	1	j.	j.	PROPN
ejpam-5757	435	2	fixed	fix	VERB
ejpam-5757	435	3	point	point	PROPN
ejpam-5757	435	4	theory	theory	NOUN
ejpam-5757	435	5	appl	appl	PROPN
ejpam-5757	435	6	.	.	PROPN
ejpam-5757	435	7	,	,	PUNCT
ejpam-5757	435	8	22(3):1	22(3):1	PROPN
ejpam-5757	435	9	–	–	PUNCT
ejpam-5757	435	10	16	16	NUM
ejpam-5757	435	11	,	,	PUNCT
ejpam-5757	435	12	2020	2020	NUM
ejpam-5757	435	13	.	.	PUNCT
ejpam-5757	436	1	[	[	X
ejpam-5757	436	2	28	28	NUM
ejpam-5757	436	3	]	]	X
ejpam-5757	436	4	s	s	PART
ejpam-5757	436	5	m	m	NOUN
ejpam-5757	436	6	ulam	ulam	PROPN
ejpam-5757	436	7	.	.	PUNCT
ejpam-5757	437	1	problems	problem	NOUN
ejpam-5757	437	2	in	in	ADP
ejpam-5757	437	3	modern	modern	ADJ
ejpam-5757	437	4	mathematics	mathematic	NOUN
ejpam-5757	437	5	.	.	PUNCT
ejpam-5757	438	1	john	john	PROPN
ejpam-5757	438	2	wiley	wiley	PROPN
ejpam-5757	438	3	&	&	CCONJ
ejpam-5757	438	4	sons	sons	PROPN
ejpam-5757	438	5	,	,	PUNCT
ejpam-5757	438	6	inc	inc	PROPN
ejpam-5757	438	7	.	.	PROPN
ejpam-5757	438	8	,	,	PUNCT
ejpam-5757	438	9	new	new	PROPN
ejpam-5757	438	10	york	york	PROPN
ejpam-5757	438	11	,	,	PUNCT
ejpam-5757	438	12	1964	1964	NUM
ejpam-5757	438	13	.	.	PUNCT
ejpam-5757	439	1	[	[	X
ejpam-5757	439	2	29	29	NUM
ejpam-5757	439	3	]	]	X
ejpam-5757	439	4	k	k	PROPN
ejpam-5757	439	5	yadav	yadav	PROPN
ejpam-5757	439	6	and	and	CCONJ
ejpam-5757	439	7	d	d	PROPN
ejpam-5757	439	8	kumar	kumar	PROPN
ejpam-5757	439	9	.	.	PUNCT
ejpam-5757	440	1	some	some	DET
ejpam-5757	440	2	hyperstability	hyperstability	NOUN
ejpam-5757	440	3	results	result	VERB
ejpam-5757	440	4	for	for	ADP
ejpam-5757	440	5	quadratic	quadratic	ADJ
ejpam-5757	440	6	type	type	NOUN
ejpam-5757	440	7	functional	functional	ADJ
ejpam-5757	440	8	equations	equation	NOUN
ejpam-5757	440	9	.	.	PUNCT
ejpam-5757	441	1	appl	appl	PROPN
ejpam-5757	441	2	.	.	PROPN
ejpam-5757	441	3	math	math	NOUN
ejpam-5757	441	4	.	.	PUNCT
ejpam-5757	442	1	e	e	X
ejpam-5757	442	2	-	-	NOUN
ejpam-5757	442	3	notes	note	NOUN
ejpam-5757	442	4	,	,	PUNCT
ejpam-5757	442	5	24:212–227	24:212–227	NUM
ejpam-5757	442	6	,	,	PUNCT
ejpam-5757	442	7	2024	2024	NUM
ejpam-5757	442	8	.	.	PUNCT