id	sid	tid	token	lemma	pos
ejpam-5897	1	1	european	european	PROPN
ejpam-5897	1	2	journal	journal	PROPN
ejpam-5897	1	3	of	of	ADP
ejpam-5897	1	4	pure	pure	ADJ
ejpam-5897	1	5	and	and	CCONJ
ejpam-5897	1	6	applied	applied	ADJ
ejpam-5897	1	7	mathematics	mathematic	NOUN
ejpam-5897	1	8	2025	2025	NUM
ejpam-5897	1	9	,	,	PUNCT
ejpam-5897	1	10	vol	vol	NOUN
ejpam-5897	1	11	.	.	PROPN
ejpam-5897	1	12	18	18	NUM
ejpam-5897	1	13	,	,	PUNCT
ejpam-5897	1	14	issue	issue	NOUN
ejpam-5897	1	15	2	2	NUM
ejpam-5897	1	16	,	,	PUNCT
ejpam-5897	1	17	article	article	NOUN
ejpam-5897	1	18	number	number	NOUN
ejpam-5897	1	19	5897	5897	NUM
ejpam-5897	1	20	issn	issn	PROPN
ejpam-5897	1	21	1307	1307	NUM
ejpam-5897	1	22	-	-	SYM
ejpam-5897	1	23	5543	5543	NUM
ejpam-5897	1	24	–	–	PUNCT
ejpam-5897	1	25	ejpam.com	ejpam.com	X
ejpam-5897	1	26	published	publish	VERB
ejpam-5897	1	27	by	by	ADP
ejpam-5897	1	28	new	new	PROPN
ejpam-5897	1	29	york	york	PROPN
ejpam-5897	1	30	business	business	PROPN
ejpam-5897	1	31	global	global	ADJ
ejpam-5897	1	32	stability	stability	NOUN
ejpam-5897	1	33	of	of	ADP
ejpam-5897	1	34	hyper	hyper	ADJ
ejpam-5897	1	35	3	3	NUM
ejpam-5897	1	36	-	-	PUNCT
ejpam-5897	1	37	homomorphisms	homomorphism	NOUN
ejpam-5897	1	38	and	and	CCONJ
ejpam-5897	1	39	hyper	hyper	ADJ
ejpam-5897	1	40	3	3	NUM
ejpam-5897	1	41	-	-	PUNCT
ejpam-5897	1	42	derivations	derivation	NOUN
ejpam-5897	1	43	in	in	ADP
ejpam-5897	1	44	ternary	ternary	ADJ
ejpam-5897	1	45	algebras	algebras	PROPN
ejpam-5897	1	46	eunhwa	eunhwa	PROPN
ejpam-5897	1	47	shim1	shim1	PROPN
ejpam-5897	1	48	,	,	PUNCT
ejpam-5897	1	49	siriluk	siriluk	PROPN
ejpam-5897	1	50	donganont2,∗	donganont2,∗	PROPN
ejpam-5897	1	51	,	,	PUNCT
ejpam-5897	1	52	choonkil	choonkil	ADJ
ejpam-5897	1	53	park3	park3	PROPN
ejpam-5897	1	54	1	1	NUM
ejpam-5897	1	55	department	department	NOUN
ejpam-5897	1	56	of	of	ADP
ejpam-5897	1	57	mathematics	mathematics	PROPN
ejpam-5897	1	58	,	,	PUNCT
ejpam-5897	1	59	hanyang	hanyang	PROPN
ejpam-5897	1	60	university	university	PROPN
ejpam-5897	1	61	,	,	PUNCT
ejpam-5897	1	62	seoul	seoul	PROPN
ejpam-5897	1	63	04763	04763	NUM
ejpam-5897	1	64	,	,	PUNCT
ejpam-5897	1	65	korea	korea	PROPN
ejpam-5897	1	66	2	2	NUM
ejpam-5897	1	67	school	school	NOUN
ejpam-5897	1	68	of	of	ADP
ejpam-5897	1	69	science	science	NOUN
ejpam-5897	1	70	,	,	PUNCT
ejpam-5897	1	71	university	university	NOUN
ejpam-5897	1	72	of	of	ADP
ejpam-5897	1	73	phayao	phayao	NOUN
ejpam-5897	1	74	,	,	PUNCT
ejpam-5897	1	75	phayao	phayao	NOUN
ejpam-5897	1	76	56000	56000	NUM
ejpam-5897	1	77	,	,	PUNCT
ejpam-5897	1	78	thailand	thailand	PROPN
ejpam-5897	1	79	3	3	NUM
ejpam-5897	1	80	department	department	NOUN
ejpam-5897	1	81	of	of	ADP
ejpam-5897	1	82	mathematics	mathematic	NOUN
ejpam-5897	1	83	,	,	PUNCT
ejpam-5897	1	84	research	research	NOUN
ejpam-5897	1	85	institute	institute	NOUN
ejpam-5897	1	86	for	for	ADP
ejpam-5897	1	87	convergence	convergence	NOUN
ejpam-5897	1	88	of	of	ADP
ejpam-5897	1	89	basic	basic	ADJ
ejpam-5897	1	90	science	science	NOUN
ejpam-5897	1	91	,	,	PUNCT
ejpam-5897	1	92	hanyang	hanyang	NOUN
ejpam-5897	1	93	university	university	PROPN
ejpam-5897	1	94	,	,	PUNCT
ejpam-5897	1	95	seoul	seoul	PROPN
ejpam-5897	1	96	04763	04763	NUM
ejpam-5897	1	97	,	,	PUNCT
ejpam-5897	1	98	korea	korea	PROPN
ejpam-5897	1	99	abstract	abstract	NOUN
ejpam-5897	1	100	.	.	PUNCT
ejpam-5897	2	1	in	in	ADP
ejpam-5897	2	2	this	this	DET
ejpam-5897	2	3	paper	paper	NOUN
ejpam-5897	2	4	,	,	PUNCT
ejpam-5897	2	5	we	we	PRON
ejpam-5897	2	6	introduce	introduce	VERB
ejpam-5897	2	7	hyper	hyper	ADJ
ejpam-5897	2	8	3	3	NUM
ejpam-5897	2	9	-	-	PUNCT
ejpam-5897	2	10	homomorphisms	homomorphism	NOUN
ejpam-5897	2	11	and	and	CCONJ
ejpam-5897	2	12	hyper	hyper	ADJ
ejpam-5897	2	13	3	3	NUM
ejpam-5897	2	14	-	-	PUNCT
ejpam-5897	2	15	derivations	derivation	NOUN
ejpam-5897	2	16	in	in	ADP
ejpam-5897	2	17	complex	complex	ADJ
ejpam-5897	2	18	ternary	ternary	ADJ
ejpam-5897	2	19	algebras	algebra	NOUN
ejpam-5897	2	20	and	and	CCONJ
ejpam-5897	2	21	we	we	PRON
ejpam-5897	2	22	prove	prove	VERB
ejpam-5897	2	23	the	the	DET
ejpam-5897	2	24	hyers	hyers	PROPN
ejpam-5897	2	25	-	-	PUNCT
ejpam-5897	2	26	ulam	ulam	ADJ
ejpam-5897	2	27	stability	stability	NOUN
ejpam-5897	2	28	of	of	ADP
ejpam-5897	2	29	hyper	hyper	ADJ
ejpam-5897	2	30	3	3	NUM
ejpam-5897	2	31	-	-	PUNCT
ejpam-5897	2	32	homomorphisms	homomorphism	NOUN
ejpam-5897	2	33	and	and	CCONJ
ejpam-5897	2	34	hyper	hyper	ADJ
ejpam-5897	2	35	3	3	NUM
ejpam-5897	2	36	-	-	PUNCT
ejpam-5897	2	37	derivations	derivation	NOUN
ejpam-5897	2	38	in	in	ADP
ejpam-5897	2	39	complex	complex	ADJ
ejpam-5897	2	40	ternary	ternary	ADJ
ejpam-5897	2	41	algebras	algebra	NOUN
ejpam-5897	2	42	for	for	ADP
ejpam-5897	2	43	the	the	DET
ejpam-5897	2	44	following	follow	VERB
ejpam-5897	2	45	3	3	NUM
ejpam-5897	2	46	-	-	PUNCT
ejpam-5897	2	47	additive	additive	ADJ
ejpam-5897	2	48	functional	functional	ADJ
ejpam-5897	2	49	equation	equation	NOUN
ejpam-5897	2	50	f(x1	f(x1	ADJ
ejpam-5897	3	1	+	+	X
ejpam-5897	3	2	x2	x2	ADJ
ejpam-5897	3	3	,	,	PUNCT
ejpam-5897	3	4	y1	y1	NOUN
ejpam-5897	3	5	+	+	CCONJ
ejpam-5897	3	6	y2	y2	ADJ
ejpam-5897	3	7	,	,	PUNCT
ejpam-5897	3	8	z1	z1	PROPN
ejpam-5897	3	9	+	+	CCONJ
ejpam-5897	3	10	z2	z2	NUM
ejpam-5897	3	11	)	)	PUNCT
ejpam-5897	3	12	=	=	SYM
ejpam-5897	4	1	2∑	2∑	NUM
ejpam-5897	4	2	i	i	NOUN
ejpam-5897	4	3	,	,	PUNCT
ejpam-5897	4	4	j	j	PROPN
ejpam-5897	4	5	,	,	PUNCT
ejpam-5897	4	6	k=1	k=1	PROPN
ejpam-5897	4	7	f(xi	f(xi	PROPN
ejpam-5897	4	8	,	,	PUNCT
ejpam-5897	4	9	yj	yj	PROPN
ejpam-5897	4	10	,	,	PUNCT
ejpam-5897	4	11	zk	zk	PROPN
ejpam-5897	4	12	)	)	PUNCT
ejpam-5897	4	13	.	.	PUNCT
ejpam-5897	5	1	(	(	PUNCT
ejpam-5897	5	2	1	1	X
ejpam-5897	5	3	)	)	PUNCT
ejpam-5897	5	4	further	far	ADV
ejpam-5897	5	5	,	,	PUNCT
ejpam-5897	5	6	we	we	PRON
ejpam-5897	5	7	investigate	investigate	VERB
ejpam-5897	5	8	isomorphisms	isomorphism	NOUN
ejpam-5897	5	9	between	between	ADP
ejpam-5897	5	10	complex	complex	ADJ
ejpam-5897	5	11	ternary	ternary	ADJ
ejpam-5897	5	12	algebras	algebra	NOUN
ejpam-5897	5	13	,	,	PUNCT
ejpam-5897	5	14	associated	associate	VERB
ejpam-5897	5	15	with	with	ADP
ejpam-5897	5	16	the	the	DET
ejpam-5897	5	17	3additive	3additive	NUM
ejpam-5897	5	18	functional	functional	ADJ
ejpam-5897	5	19	equation	equation	NOUN
ejpam-5897	5	20	.	.	PUNCT
ejpam-5897	6	1	2020	2020	NUM
ejpam-5897	6	2	mathematics	mathematic	NOUN
ejpam-5897	6	3	subject	subject	NOUN
ejpam-5897	6	4	classifications	classification	NOUN
ejpam-5897	6	5	:	:	PUNCT
ejpam-5897	6	6	11e20	11e20	NUM
ejpam-5897	6	7	,	,	PUNCT
ejpam-5897	6	8	39b52	39b52	NUM
ejpam-5897	6	9	,	,	PUNCT
ejpam-5897	6	10	39b82	39b82	NUM
ejpam-5897	6	11	key	key	ADJ
ejpam-5897	6	12	words	word	NOUN
ejpam-5897	6	13	and	and	CCONJ
ejpam-5897	6	14	phrases	phrase	NOUN
ejpam-5897	6	15	:	:	PUNCT
ejpam-5897	6	16	hyers	hyers	PROPN
ejpam-5897	6	17	-	-	PUNCT
ejpam-5897	6	18	ulam	ulam	PROPN
ejpam-5897	6	19	stability	stability	NOUN
ejpam-5897	6	20	,	,	PUNCT
ejpam-5897	6	21	3	3	NUM
ejpam-5897	6	22	-	-	PUNCT
ejpam-5897	6	23	additive	additive	ADJ
ejpam-5897	6	24	functional	functional	ADJ
ejpam-5897	6	25	equation	equation	NOUN
ejpam-5897	6	26	,	,	PUNCT
ejpam-5897	6	27	ternary	ternary	ADJ
ejpam-5897	6	28	algebra	algebra	NOUN
ejpam-5897	6	29	,	,	PUNCT
ejpam-5897	6	30	hyper	hyper	ADJ
ejpam-5897	6	31	3	3	NUM
ejpam-5897	6	32	-	-	PUNCT
ejpam-5897	6	33	homomorphism	homomorphism	NOUN
ejpam-5897	6	34	,	,	PUNCT
ejpam-5897	6	35	hyper	hyper	ADJ
ejpam-5897	6	36	3	3	NUM
ejpam-5897	6	37	-	-	PUNCT
ejpam-5897	6	38	derivation	derivation	NOUN
ejpam-5897	6	39	1	1	NUM
ejpam-5897	6	40	.	.	PUNCT
ejpam-5897	6	41	introduction	introduction	NOUN
ejpam-5897	6	42	and	and	CCONJ
ejpam-5897	6	43	preliminaries	preliminary	NOUN
ejpam-5897	6	44	the	the	DET
ejpam-5897	6	45	first	first	ADJ
ejpam-5897	6	46	stability	stability	NOUN
ejpam-5897	6	47	proplem	proplem	NOUN
ejpam-5897	6	48	was	be	AUX
ejpam-5897	6	49	raised	raise	VERB
ejpam-5897	6	50	by	by	ADP
ejpam-5897	6	51	ulam	ulam	PROPN
ejpam-5897	6	52	[	[	X
ejpam-5897	6	53	1	1	NUM
ejpam-5897	6	54	]	]	PUNCT
ejpam-5897	6	55	during	during	ADP
ejpam-5897	6	56	his	his	PRON
ejpam-5897	6	57	talk	talk	NOUN
ejpam-5897	6	58	at	at	ADP
ejpam-5897	6	59	university	university	PROPN
ejpam-5897	6	60	of	of	ADP
ejpam-5897	6	61	wisconsin	wisconsin	PROPN
ejpam-5897	6	62	in	in	ADP
ejpam-5897	6	63	1940	1940	NUM
ejpam-5897	6	64	.	.	PUNCT
ejpam-5897	7	1	in	in	ADP
ejpam-5897	7	2	1941	1941	NUM
ejpam-5897	7	3	,	,	PUNCT
ejpam-5897	7	4	hyers	hyer	NOUN
ejpam-5897	7	5	[	[	X
ejpam-5897	7	6	2	2	X
ejpam-5897	7	7	]	]	PUNCT
ejpam-5897	7	8	gave	give	VERB
ejpam-5897	7	9	a	a	DET
ejpam-5897	7	10	first	first	ADJ
ejpam-5897	7	11	affirmative	affirmative	ADJ
ejpam-5897	7	12	answer	answer	NOUN
ejpam-5897	7	13	to	to	ADP
ejpam-5897	7	14	the	the	DET
ejpam-5897	7	15	question	question	NOUN
ejpam-5897	7	16	of	of	ADP
ejpam-5897	7	17	ulam	ulam	NOUN
ejpam-5897	7	18	for	for	ADP
ejpam-5897	7	19	banach	banach	NOUN
ejpam-5897	7	20	spaces	space	NOUN
ejpam-5897	7	21	.	.	PUNCT
ejpam-5897	8	1	let	let	VERB
ejpam-5897	8	2	f	f	NOUN
ejpam-5897	8	3	:	:	PUNCT
ejpam-5897	8	4	e	e	X
ejpam-5897	8	5	→	→	SYM
ejpam-5897	8	6	e′	e′	X
ejpam-5897	8	7	be	be	AUX
ejpam-5897	8	8	a	a	DET
ejpam-5897	8	9	mapping	mapping	NOUN
ejpam-5897	8	10	between	between	ADP
ejpam-5897	8	11	banach	banach	NOUN
ejpam-5897	8	12	spaces	space	NOUN
ejpam-5897	8	13	such	such	ADJ
ejpam-5897	8	14	that	that	DET
ejpam-5897	8	15	∥f(x+	∥f(x+	VERB
ejpam-5897	8	16	y)−	y)−	PROPN
ejpam-5897	8	17	f(x)−	f(x)−	PROPN
ejpam-5897	8	18	f(y)∥	f(y)∥	NOUN
ejpam-5897	8	19	≤	≤	ADJ
ejpam-5897	8	20	δ	δ	PROPN
ejpam-5897	8	21	for	for	ADP
ejpam-5897	8	22	all	all	DET
ejpam-5897	8	23	x	x	NOUN
ejpam-5897	8	24	,	,	PUNCT
ejpam-5897	8	25	y	y	PROPN
ejpam-5897	8	26	∈	∈	PROPN
ejpam-5897	8	27	e	e	PROPN
ejpam-5897	8	28	and	and	CCONJ
ejpam-5897	8	29	for	for	ADP
ejpam-5897	8	30	some	some	DET
ejpam-5897	8	31	δ	δ	PROPN
ejpam-5897	8	32	>	>	X
ejpam-5897	8	33	0	0	PROPN
ejpam-5897	8	34	.	.	PUNCT
ejpam-5897	9	1	then	then	ADV
ejpam-5897	9	2	,	,	PUNCT
ejpam-5897	9	3	there	there	PRON
ejpam-5897	9	4	exists	exist	VERB
ejpam-5897	9	5	a	a	DET
ejpam-5897	9	6	unique	unique	ADJ
ejpam-5897	9	7	additive	additive	ADJ
ejpam-5897	9	8	mapping	mapping	NOUN
ejpam-5897	9	9	l	l	NOUN
ejpam-5897	9	10	:	:	PUNCT
ejpam-5897	10	1	e	e	X
ejpam-5897	10	2	→	→	SYM
ejpam-5897	10	3	e′	e′	X
ejpam-5897	10	4	such	such	ADJ
ejpam-5897	10	5	that	that	AUX
ejpam-5897	10	6	∥f(x)−	∥f(x)−	PROPN
ejpam-5897	10	7	l(x)∥	l(x)∥	PROPN
ejpam-5897	10	8	≤	≤	PROPN
ejpam-5897	10	9	δ	δ	PROPN
ejpam-5897	10	10	∗corresponding	∗corresponde	VERB
ejpam-5897	10	11	author	author	NOUN
ejpam-5897	10	12	.	.	PUNCT
ejpam-5897	11	1	doi	doi	NOUN
ejpam-5897	11	2	:	:	PUNCT
ejpam-5897	11	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5897	https://doi.org/10.29020/nybg.ejpam.v18i2.5897	PROPN
ejpam-5897	11	4	email	email	NOUN
ejpam-5897	11	5	addresses	address	NOUN
ejpam-5897	11	6	:	:	PUNCT
ejpam-5897	11	7	stareun97@hanyang.ac.kr	stareun97@hanyang.ac.kr	X
ejpam-5897	11	8	(	(	PUNCT
ejpam-5897	11	9	e.	e.	PROPN
ejpam-5897	11	10	shim	shim	PROPN
ejpam-5897	11	11	)	)	PUNCT
ejpam-5897	11	12	,	,	PUNCT
ejpam-5897	11	13	siriluk.pa@up.ac.th	siriluk.pa@up.ac.th	PROPN
ejpam-5897	11	14	(	(	PUNCT
ejpam-5897	11	15	s.	s.	PROPN
ejpam-5897	11	16	donganont	donganont	PROPN
ejpam-5897	11	17	)	)	PUNCT
ejpam-5897	11	18	,	,	PUNCT
ejpam-5897	11	19	baak@hanyang.ac.kr	baak@hanyang.ac.kr	PROPN
ejpam-5897	11	20	(	(	PUNCT
ejpam-5897	11	21	c.	c.	PROPN
ejpam-5897	11	22	park	park	PROPN
ejpam-5897	11	23	)	)	PUNCT
ejpam-5897	11	24	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5897	12	1	1	1	NUM
ejpam-5897	12	2	copyright	copyright	NOUN
ejpam-5897	12	3	:	:	PUNCT
ejpam-5897	12	4	©	©	PROPN
ejpam-5897	12	5	2025	2025	NUM
ejpam-5897	12	6	the	the	DET
ejpam-5897	12	7	author(s	author(s	NOUN
ejpam-5897	12	8	)	)	PUNCT
ejpam-5897	12	9	.	.	PUNCT
ejpam-5897	13	1	(	(	PUNCT
ejpam-5897	13	2	cc	cc	NOUN
ejpam-5897	13	3	by	by	ADP
ejpam-5897	13	4	-	-	PUNCT
ejpam-5897	13	5	nc	nc	PROPN
ejpam-5897	13	6	4.0	4.0	NUM
ejpam-5897	13	7	)	)	PUNCT
ejpam-5897	13	8	e.	e.	PROPN
ejpam-5897	13	9	shim	shim	PROPN
ejpam-5897	13	10	,	,	PUNCT
ejpam-5897	13	11	s.	s.	PROPN
ejpam-5897	13	12	donganont	donganont	PROPN
ejpam-5897	13	13	,	,	PUNCT
ejpam-5897	13	14	c.	c.	PROPN
ejpam-5897	13	15	park	park	PROPN
ejpam-5897	13	16	/	/	SYM
ejpam-5897	13	17	eur	eur	PROPN
ejpam-5897	13	18	.	.	PUNCT
ejpam-5897	14	1	j.	j.	PROPN
ejpam-5897	14	2	pure	pure	PROPN
ejpam-5897	14	3	appl	appl	PROPN
ejpam-5897	14	4	.	.	PROPN
ejpam-5897	14	5	math	math	PROPN
ejpam-5897	14	6	,	,	PUNCT
ejpam-5897	14	7	18	18	NUM
ejpam-5897	14	8	(	(	PUNCT
ejpam-5897	14	9	2	2	NUM
ejpam-5897	14	10	)	)	PUNCT
ejpam-5897	14	11	(	(	PUNCT
ejpam-5897	14	12	2025	2025	NUM
ejpam-5897	14	13	)	)	PUNCT
ejpam-5897	14	14	,	,	PUNCT
ejpam-5897	14	15	5897	5897	NUM
ejpam-5897	14	16	2	2	NUM
ejpam-5897	14	17	of	of	ADP
ejpam-5897	14	18	14	14	NUM
ejpam-5897	14	19	for	for	ADP
ejpam-5897	14	20	all	all	DET
ejpam-5897	14	21	x	x	SYM
ejpam-5897	14	22	∈	∈	PROPN
ejpam-5897	14	23	e.	e.	PROPN
ejpam-5897	14	24	this	this	DET
ejpam-5897	14	25	stability	stability	NOUN
ejpam-5897	14	26	phenomenon	phenomenon	NOUN
ejpam-5897	14	27	is	be	AUX
ejpam-5897	14	28	called	call	VERB
ejpam-5897	14	29	the	the	DET
ejpam-5897	14	30	hyers	hyers	PROPN
ejpam-5897	14	31	-	-	PUNCT
ejpam-5897	14	32	ulam	ulam	ADJ
ejpam-5897	14	33	stability	stability	NOUN
ejpam-5897	14	34	of	of	ADP
ejpam-5897	14	35	the	the	DET
ejpam-5897	14	36	additive	additive	ADJ
ejpam-5897	14	37	functional	functional	ADJ
ejpam-5897	14	38	equation	equation	NOUN
ejpam-5897	14	39	g(x+	g(x+	NOUN
ejpam-5897	14	40	y	y	X
ejpam-5897	14	41	)	)	PUNCT
ejpam-5897	14	42	=	=	PUNCT
ejpam-5897	14	43	g(x)+	g(x)+	NOUN
ejpam-5897	14	44	g(y	g(y	NOUN
ejpam-5897	14	45	)	)	PUNCT
ejpam-5897	14	46	.	.	PUNCT
ejpam-5897	15	1	in	in	ADP
ejpam-5897	15	2	1978	1978	NUM
ejpam-5897	15	3	,	,	PUNCT
ejpam-5897	15	4	rassias	rassia	VERB
ejpam-5897	15	5	[	[	X
ejpam-5897	15	6	3	3	NUM
ejpam-5897	15	7	]	]	PUNCT
ejpam-5897	15	8	generalized	generalize	VERB
ejpam-5897	15	9	the	the	DET
ejpam-5897	15	10	theorem	theorem	NOUN
ejpam-5897	15	11	of	of	ADP
ejpam-5897	15	12	hyers	hyer	NOUN
ejpam-5897	15	13	by	by	ADP
ejpam-5897	15	14	considering	consider	VERB
ejpam-5897	15	15	the	the	DET
ejpam-5897	15	16	stability	stability	NOUN
ejpam-5897	15	17	problem	problem	NOUN
ejpam-5897	15	18	with	with	ADP
ejpam-5897	15	19	unbounded	unbounded	ADJ
ejpam-5897	15	20	cauchy	cauchy	NOUN
ejpam-5897	15	21	differences	difference	NOUN
ejpam-5897	15	22	.	.	PUNCT
ejpam-5897	16	1	moreover	moreover	ADV
ejpam-5897	16	2	if	if	SCONJ
ejpam-5897	16	3	f(µx	f(µx	PROPN
ejpam-5897	16	4	)	)	PUNCT
ejpam-5897	16	5	is	be	AUX
ejpam-5897	16	6	continuous	continuous	ADJ
ejpam-5897	16	7	in	in	ADP
ejpam-5897	16	8	µ	µ	PRON
ejpam-5897	16	9	∈	∈	NOUN
ejpam-5897	16	10	r	r	NOUN
ejpam-5897	16	11	for	for	ADP
ejpam-5897	16	12	each	each	DET
ejpam-5897	16	13	fixed	fix	VERB
ejpam-5897	16	14	x	x	SYM
ejpam-5897	16	15	∈	∈	PROPN
ejpam-5897	16	16	e	e	NOUN
ejpam-5897	16	17	,	,	PUNCT
ejpam-5897	16	18	then	then	ADV
ejpam-5897	16	19	l	l	PROPN
ejpam-5897	16	20	is	be	AUX
ejpam-5897	16	21	r	r	NOUN
ejpam-5897	16	22	-	-	PUNCT
ejpam-5897	16	23	linear	linear	NOUN
ejpam-5897	16	24	.	.	PUNCT
ejpam-5897	17	1	găvruta	găvruta	PROPN
ejpam-5897	18	1	[	[	X
ejpam-5897	18	2	4	4	NUM
ejpam-5897	18	3	]	]	PUNCT
ejpam-5897	18	4	obtained	obtain	VERB
ejpam-5897	18	5	a	a	DET
ejpam-5897	18	6	generalized	generalized	ADJ
ejpam-5897	18	7	result	result	NOUN
ejpam-5897	18	8	of	of	ADP
ejpam-5897	18	9	the	the	DET
ejpam-5897	18	10	rassias	rassias	PROPN
ejpam-5897	18	11	theorem	theorem	VERB
ejpam-5897	18	12	which	which	PRON
ejpam-5897	18	13	allows	allow	VERB
ejpam-5897	18	14	the	the	DET
ejpam-5897	18	15	cauchy	cauchy	ADJ
ejpam-5897	18	16	difference	difference	NOUN
ejpam-5897	18	17	to	to	PART
ejpam-5897	18	18	be	be	AUX
ejpam-5897	18	19	controlled	control	VERB
ejpam-5897	18	20	by	by	ADP
ejpam-5897	18	21	a	a	DET
ejpam-5897	18	22	general	general	ADJ
ejpam-5897	18	23	unbounded	unbounded	ADJ
ejpam-5897	18	24	function	function	NOUN
ejpam-5897	18	25	.	.	PUNCT
ejpam-5897	19	1	the	the	DET
ejpam-5897	19	2	stability	stability	NOUN
ejpam-5897	19	3	problems	problem	NOUN
ejpam-5897	19	4	of	of	ADP
ejpam-5897	19	5	various	various	ADJ
ejpam-5897	19	6	functional	functional	ADJ
ejpam-5897	19	7	equations	equation	NOUN
ejpam-5897	19	8	and	and	CCONJ
ejpam-5897	19	9	functional	functional	ADJ
ejpam-5897	19	10	inequalities	inequality	NOUN
ejpam-5897	19	11	have	have	AUX
ejpam-5897	19	12	been	be	AUX
ejpam-5897	19	13	extensively	extensively	ADV
ejpam-5897	19	14	investigated	investigate	VERB
ejpam-5897	19	15	by	by	ADP
ejpam-5897	19	16	a	a	DET
ejpam-5897	19	17	number	number	NOUN
ejpam-5897	19	18	of	of	ADP
ejpam-5897	19	19	authors	author	NOUN
ejpam-5897	19	20	(	(	PUNCT
ejpam-5897	19	21	see	see	VERB
ejpam-5897	19	22	[	[	X
ejpam-5897	19	23	5–14	5–14	PROPN
ejpam-5897	19	24	]	]	X
ejpam-5897	19	25	)	)	PUNCT
ejpam-5897	19	26	.	.	PUNCT
ejpam-5897	20	1	ternary	ternary	ADJ
ejpam-5897	20	2	structures	structure	NOUN
ejpam-5897	20	3	and	and	CCONJ
ejpam-5897	20	4	their	their	PRON
ejpam-5897	20	5	generalization	generalization	NOUN
ejpam-5897	20	6	,	,	PUNCT
ejpam-5897	20	7	the	the	DET
ejpam-5897	20	8	so	so	ADV
ejpam-5897	20	9	-	-	PUNCT
ejpam-5897	20	10	called	call	VERB
ejpam-5897	20	11	n	n	CCONJ
ejpam-5897	20	12	-	-	PUNCT
ejpam-5897	20	13	ary	ary	PROPN
ejpam-5897	20	14	structures	structure	NOUN
ejpam-5897	20	15	,	,	PUNCT
ejpam-5897	20	16	raise	raise	VERB
ejpam-5897	20	17	certain	certain	ADJ
ejpam-5897	20	18	hopes	hope	NOUN
ejpam-5897	20	19	in	in	ADP
ejpam-5897	20	20	view	view	NOUN
ejpam-5897	20	21	of	of	ADP
ejpam-5897	20	22	their	their	PRON
ejpam-5897	20	23	applications	application	NOUN
ejpam-5897	20	24	in	in	ADP
ejpam-5897	20	25	physics	physics	NOUN
ejpam-5897	20	26	(	(	PUNCT
ejpam-5897	20	27	see	see	VERB
ejpam-5897	20	28	[	[	X
ejpam-5897	20	29	15–17	15–17	NUM
ejpam-5897	20	30	]	]	PUNCT
ejpam-5897	20	31	)	)	PUNCT
ejpam-5897	20	32	.	.	PUNCT
ejpam-5897	21	1	a	a	DET
ejpam-5897	21	2	general	general	ADJ
ejpam-5897	21	3	ternary	ternary	ADJ
ejpam-5897	21	4	algebra	algebra	NOUN
ejpam-5897	21	5	is	be	AUX
ejpam-5897	21	6	defined	define	VERB
ejpam-5897	21	7	as	as	ADP
ejpam-5897	21	8	internal	internal	ADJ
ejpam-5897	21	9	ternary	ternary	ADJ
ejpam-5897	21	10	multiplication	multiplication	NOUN
ejpam-5897	21	11	in	in	ADP
ejpam-5897	21	12	a	a	DET
ejpam-5897	21	13	vector	vector	NOUN
ejpam-5897	21	14	space	space	NOUN
ejpam-5897	21	15	.	.	PUNCT
ejpam-5897	22	1	let	let	VERB
ejpam-5897	22	2	a	a	PRON
ejpam-5897	22	3	be	be	AUX
ejpam-5897	22	4	a	a	DET
ejpam-5897	22	5	linear	linear	ADJ
ejpam-5897	22	6	space	space	NOUN
ejpam-5897	22	7	over	over	ADP
ejpam-5897	22	8	a	a	DET
ejpam-5897	22	9	complex	complex	ADJ
ejpam-5897	22	10	number	number	NOUN
ejpam-5897	22	11	field	field	NOUN
ejpam-5897	22	12	equipped	equip	VERB
ejpam-5897	22	13	with	with	ADP
ejpam-5897	22	14	a	a	DET
ejpam-5897	22	15	mapping	mapping	NOUN
ejpam-5897	22	16	[	[	X
ejpam-5897	22	17	·	·	PUNCT
ejpam-5897	22	18	,	,	PUNCT
ejpam-5897	22	19	·	·	PUNCT
ejpam-5897	22	20	,	,	PUNCT
ejpam-5897	22	21	·	·	PUNCT
ejpam-5897	22	22	]	]	X
ejpam-5897	22	23	:	:	PUNCT
ejpam-5897	22	24	a3	a3	NOUN
ejpam-5897	22	25	=	=	PUNCT
ejpam-5897	22	26	a	a	DET
ejpam-5897	22	27	×	×	NOUN
ejpam-5897	22	28	a	a	DET
ejpam-5897	22	29	×	×	NOUN
ejpam-5897	22	30	a	a	DET
ejpam-5897	22	31	→	→	PUNCT
ejpam-5897	22	32	a	a	DET
ejpam-5897	22	33	with	with	ADP
ejpam-5897	22	34	(	(	PUNCT
ejpam-5897	22	35	x	x	NOUN
ejpam-5897	22	36	,	,	PUNCT
ejpam-5897	22	37	y	y	PROPN
ejpam-5897	22	38	,	,	PUNCT
ejpam-5897	22	39	z	z	NOUN
ejpam-5897	22	40	)	)	PUNCT
ejpam-5897	22	41	7→	7→	NUM
ejpam-5897	23	1	[	[	X
ejpam-5897	23	2	x	x	X
ejpam-5897	23	3	,	,	PUNCT
ejpam-5897	23	4	y	y	PROPN
ejpam-5897	23	5	,	,	PUNCT
ejpam-5897	23	6	z	z	NOUN
ejpam-5897	23	7	]	]	X
ejpam-5897	23	8	,	,	PUNCT
ejpam-5897	23	9	which	which	PRON
ejpam-5897	23	10	is	be	AUX
ejpam-5897	23	11	c	c	NOUN
ejpam-5897	23	12	-	-	PUNCT
ejpam-5897	23	13	inear	inear	NOUN
ejpam-5897	23	14	in	in	ADP
ejpam-5897	23	15	each	each	DET
ejpam-5897	23	16	outer	outer	ADJ
ejpam-5897	23	17	variable	variable	NOUN
ejpam-5897	23	18	and	and	CCONJ
ejpam-5897	23	19	conjugate	conjugate	ADJ
ejpam-5897	23	20	c	c	NOUN
ejpam-5897	23	21	-	-	PUNCT
ejpam-5897	23	22	linear	linear	NOUN
ejpam-5897	23	23	in	in	ADP
ejpam-5897	23	24	the	the	DET
ejpam-5897	23	25	middle	middle	ADJ
ejpam-5897	23	26	variable	variable	NOUN
ejpam-5897	23	27	,	,	PUNCT
ejpam-5897	23	28	and	and	CCONJ
ejpam-5897	23	29	satisfies	satisfy	VERB
ejpam-5897	23	30	the	the	DET
ejpam-5897	23	31	following	following	ADJ
ejpam-5897	23	32	associative	associative	ADJ
ejpam-5897	23	33	identity	identity	NOUN
ejpam-5897	23	34	condition	condition	NOUN
ejpam-5897	24	1	[	[	X
ejpam-5897	24	2	[	[	X
ejpam-5897	24	3	x	x	X
ejpam-5897	24	4	,	,	PUNCT
ejpam-5897	24	5	y	y	PROPN
ejpam-5897	24	6	,	,	PUNCT
ejpam-5897	24	7	z	z	NOUN
ejpam-5897	24	8	]	]	X
ejpam-5897	24	9	,	,	PUNCT
ejpam-5897	24	10	u	u	NOUN
ejpam-5897	24	11	,	,	PUNCT
ejpam-5897	24	12	v	v	NOUN
ejpam-5897	24	13	]	]	PUNCT
ejpam-5897	24	14	=	=	PUNCT
ejpam-5897	25	1	[	[	X
ejpam-5897	25	2	x	x	X
ejpam-5897	25	3	,	,	PUNCT
ejpam-5897	25	4	[	[	X
ejpam-5897	25	5	y	y	X
ejpam-5897	25	6	,	,	PUNCT
ejpam-5897	25	7	z	z	PROPN
ejpam-5897	25	8	,	,	PUNCT
ejpam-5897	25	9	u	u	NOUN
ejpam-5897	25	10	]	]	X
ejpam-5897	25	11	,	,	PUNCT
ejpam-5897	25	12	v	v	ADP
ejpam-5897	25	13	]	]	X
ejpam-5897	25	14	=	=	PUNCT
ejpam-5897	26	1	[	[	X
ejpam-5897	26	2	x	x	X
ejpam-5897	26	3	,	,	PUNCT
ejpam-5897	26	4	y	y	PROPN
ejpam-5897	26	5	,	,	PUNCT
ejpam-5897	26	6	[	[	X
ejpam-5897	26	7	z	z	NOUN
ejpam-5897	26	8	,	,	PUNCT
ejpam-5897	26	9	u	u	NOUN
ejpam-5897	26	10	,	,	PUNCT
ejpam-5897	26	11	v	v	ADP
ejpam-5897	26	12	]	]	X
ejpam-5897	26	13	]	]	PUNCT
ejpam-5897	26	14	for	for	ADP
ejpam-5897	26	15	all	all	DET
ejpam-5897	26	16	x	x	PROPN
ejpam-5897	26	17	,	,	PUNCT
ejpam-5897	26	18	y	y	PROPN
ejpam-5897	26	19	,	,	PUNCT
ejpam-5897	26	20	z	z	PROPN
ejpam-5897	26	21	,	,	PUNCT
ejpam-5897	26	22	u	u	NOUN
ejpam-5897	26	23	,	,	PUNCT
ejpam-5897	26	24	v	v	PROPN
ejpam-5897	26	25	∈	∈	NOUN
ejpam-5897	26	26	a.	a.	NOUN
ejpam-5897	26	27	then	then	ADV
ejpam-5897	26	28	the	the	DET
ejpam-5897	26	29	pair	pair	NOUN
ejpam-5897	26	30	(	(	PUNCT
ejpam-5897	26	31	a	a	X
ejpam-5897	26	32	,	,	PUNCT
ejpam-5897	26	33	[	[	X
ejpam-5897	26	34	·	·	PUNCT
ejpam-5897	26	35	,	,	PUNCT
ejpam-5897	26	36	·	·	PUNCT
ejpam-5897	26	37	,	,	PUNCT
ejpam-5897	26	38	·	·	PUNCT
ejpam-5897	26	39	]	]	PUNCT
ejpam-5897	26	40	)	)	PUNCT
ejpam-5897	26	41	is	be	AUX
ejpam-5897	26	42	called	call	VERB
ejpam-5897	26	43	a	a	DET
ejpam-5897	26	44	complex	complex	ADJ
ejpam-5897	26	45	ternary	ternary	ADJ
ejpam-5897	26	46	algebra	algebra	NOUN
ejpam-5897	26	47	.	.	PUNCT
ejpam-5897	27	1	assume	assume	VERB
ejpam-5897	27	2	that	that	SCONJ
ejpam-5897	27	3	a	a	PRON
ejpam-5897	27	4	is	be	AUX
ejpam-5897	27	5	a	a	DET
ejpam-5897	27	6	complex	complex	ADJ
ejpam-5897	27	7	ternary	ternary	ADJ
ejpam-5897	27	8	algebra	algebra	NOUN
ejpam-5897	27	9	.	.	PUNCT
ejpam-5897	28	1	then	then	ADV
ejpam-5897	28	2	we	we	PRON
ejpam-5897	28	3	say	say	VERB
ejpam-5897	28	4	that	that	SCONJ
ejpam-5897	28	5	a	a	PRON
ejpam-5897	28	6	has	have	VERB
ejpam-5897	28	7	a	a	DET
ejpam-5897	28	8	unit	unit	NOUN
ejpam-5897	28	9	if	if	SCONJ
ejpam-5897	28	10	there	there	PRON
ejpam-5897	28	11	exist	exist	VERB
ejpam-5897	28	12	an	an	DET
ejpam-5897	28	13	element	element	NOUN
ejpam-5897	28	14	e	e	NOUN
ejpam-5897	28	15	∈	∈	PROPN
ejpam-5897	28	16	a	a	DET
ejpam-5897	28	17	such	such	ADJ
ejpam-5897	28	18	that	that	SCONJ
ejpam-5897	29	1	[	[	X
ejpam-5897	29	2	e	e	X
ejpam-5897	29	3	,	,	PUNCT
ejpam-5897	29	4	e	e	NOUN
ejpam-5897	29	5	,	,	PUNCT
ejpam-5897	29	6	a	a	X
ejpam-5897	29	7	]	]	X
ejpam-5897	29	8	=	=	PUNCT
ejpam-5897	30	1	[	[	X
ejpam-5897	30	2	e	e	NOUN
ejpam-5897	30	3	,	,	PUNCT
ejpam-5897	30	4	a	a	PRON
ejpam-5897	30	5	,	,	PUNCT
ejpam-5897	30	6	e	e	X
ejpam-5897	30	7	]	]	PUNCT
ejpam-5897	30	8	=	=	PUNCT
ejpam-5897	31	1	[	[	X
ejpam-5897	31	2	a	a	X
ejpam-5897	31	3	,	,	PUNCT
ejpam-5897	31	4	e	e	NOUN
ejpam-5897	31	5	,	,	PUNCT
ejpam-5897	31	6	e	e	X
ejpam-5897	31	7	]	]	X
ejpam-5897	31	8	=	=	PUNCT
ejpam-5897	31	9	a	a	PRON
ejpam-5897	31	10	for	for	ADP
ejpam-5897	31	11	all	all	DET
ejpam-5897	31	12	a	a	DET
ejpam-5897	31	13	∈	∈	PROPN
ejpam-5897	31	14	a.	a.	NOUN
ejpam-5897	31	15	park	park	NOUN
ejpam-5897	31	16	[	[	X
ejpam-5897	31	17	18	18	NUM
ejpam-5897	31	18	]	]	PUNCT
ejpam-5897	31	19	and	and	CCONJ
ejpam-5897	31	20	moslehian	moslehian	NOUN
ejpam-5897	31	21	[	[	X
ejpam-5897	31	22	19	19	NUM
ejpam-5897	31	23	]	]	PUNCT
ejpam-5897	31	24	contributed	contribute	VERB
ejpam-5897	31	25	works	work	NOUN
ejpam-5897	31	26	on	on	ADP
ejpam-5897	31	27	the	the	DET
ejpam-5897	31	28	stability	stability	NOUN
ejpam-5897	31	29	problem	problem	NOUN
ejpam-5897	31	30	of	of	ADP
ejpam-5897	31	31	ternary	ternary	ADJ
ejpam-5897	31	32	homomorphisms	homomorphism	NOUN
ejpam-5897	31	33	and	and	CCONJ
ejpam-5897	31	34	ternary	ternary	ADJ
ejpam-5897	31	35	derivations	derivation	NOUN
ejpam-5897	31	36	and	and	CCONJ
ejpam-5897	31	37	bavand	bavand	ADJ
ejpam-5897	31	38	savadkouhi	savadkouhi	NOUN
ejpam-5897	32	1	[	[	X
ejpam-5897	32	2	20	20	NUM
ejpam-5897	32	3	]	]	PUNCT
ejpam-5897	32	4	investigated	investigate	VERB
ejpam-5897	32	5	the	the	DET
ejpam-5897	32	6	stability	stability	NOUN
ejpam-5897	32	7	problem	problem	NOUN
ejpam-5897	32	8	of	of	ADP
ejpam-5897	32	9	ternary	ternary	ADJ
ejpam-5897	32	10	jordan	jordan	PROPN
ejpam-5897	32	11	homomorphisms	homomorphisms	PROPN
ejpam-5897	32	12	and	and	CCONJ
ejpam-5897	32	13	ternary	ternary	ADJ
ejpam-5897	32	14	jordan	jordan	PROPN
ejpam-5897	32	15	derivations	derivations	PROPN
ejpam-5897	32	16	.	.	PUNCT
ejpam-5897	33	1	the	the	DET
ejpam-5897	33	2	stability	stability	NOUN
ejpam-5897	33	3	probelms	probelm	NOUN
ejpam-5897	33	4	of	of	ADP
ejpam-5897	33	5	several	several	ADJ
ejpam-5897	33	6	functional	functional	ADJ
ejpam-5897	33	7	equations	equation	NOUN
ejpam-5897	33	8	have	have	AUX
ejpam-5897	33	9	been	be	AUX
ejpam-5897	33	10	extensively	extensively	ADV
ejpam-5897	33	11	investigated	investigate	VERB
ejpam-5897	33	12	by	by	ADP
ejpam-5897	33	13	a	a	DET
ejpam-5897	33	14	number	number	NOUN
ejpam-5897	33	15	of	of	ADP
ejpam-5897	33	16	authors	author	NOUN
ejpam-5897	33	17	and	and	CCONJ
ejpam-5897	33	18	there	there	PRON
ejpam-5897	33	19	are	be	VERB
ejpam-5897	33	20	many	many	ADJ
ejpam-5897	33	21	interesting	interesting	ADJ
ejpam-5897	33	22	results	result	NOUN
ejpam-5897	33	23	,	,	PUNCT
ejpam-5897	33	24	containing	contain	VERB
ejpam-5897	33	25	ternary	ternary	ADJ
ejpam-5897	33	26	homomorphisms	homomorphism	NOUN
ejpam-5897	33	27	and	and	CCONJ
ejpam-5897	33	28	ternary	ternary	ADJ
ejpam-5897	33	29	derivations	derivation	NOUN
ejpam-5897	33	30	,	,	PUNCT
ejpam-5897	33	31	concerning	concern	VERB
ejpam-5897	33	32	this	this	DET
ejpam-5897	33	33	problem	problem	NOUN
ejpam-5897	33	34	(	(	PUNCT
ejpam-5897	33	35	see	see	VERB
ejpam-5897	33	36	[	[	X
ejpam-5897	33	37	21–26	21–26	NOUN
ejpam-5897	33	38	]	]	PUNCT
ejpam-5897	33	39	)	)	PUNCT
ejpam-5897	33	40	.	.	PUNCT
ejpam-5897	34	1	let	let	VERB
ejpam-5897	34	2	a	a	PRON
ejpam-5897	34	3	and	and	CCONJ
ejpam-5897	34	4	a′	a′	NOUN
ejpam-5897	34	5	be	be	AUX
ejpam-5897	34	6	complex	complex	ADJ
ejpam-5897	34	7	ternary	ternary	ADJ
ejpam-5897	34	8	algebras	algebra	NOUN
ejpam-5897	34	9	.	.	PUNCT
ejpam-5897	35	1	a	a	DET
ejpam-5897	35	2	c	c	NOUN
ejpam-5897	35	3	-	-	PUNCT
ejpam-5897	35	4	linear	linear	ADJ
ejpam-5897	35	5	mapping	mapping	NOUN
ejpam-5897	35	6	h	h	NOUN
ejpam-5897	35	7	:	:	PUNCT
ejpam-5897	35	8	a	a	DET
ejpam-5897	35	9	→	→	PUNCT
ejpam-5897	35	10	a′	a′	PROPN
ejpam-5897	35	11	is	be	AUX
ejpam-5897	35	12	called	call	VERB
ejpam-5897	35	13	a	a	DET
ejpam-5897	35	14	ternary	ternary	ADJ
ejpam-5897	35	15	algebra	algebra	NOUN
ejpam-5897	35	16	homomorphism	homomorphism	NOUN
ejpam-5897	35	17	if	if	SCONJ
ejpam-5897	35	18	h([x	h([x	PROPN
ejpam-5897	35	19	,	,	PUNCT
ejpam-5897	35	20	y	y	PROPN
ejpam-5897	35	21	,	,	PUNCT
ejpam-5897	35	22	z	z	NOUN
ejpam-5897	35	23	]	]	X
ejpam-5897	35	24	)	)	PUNCT
ejpam-5897	36	1	=	=	PUNCT
ejpam-5897	37	1	[	[	X
ejpam-5897	37	2	h(x	h(x	PROPN
ejpam-5897	37	3	)	)	PUNCT
ejpam-5897	37	4	,	,	PUNCT
ejpam-5897	37	5	h(y	h(y	ADV
ejpam-5897	37	6	)	)	PUNCT
ejpam-5897	37	7	,	,	PUNCT
ejpam-5897	37	8	h(z	h(z	NOUN
ejpam-5897	37	9	)	)	PUNCT
ejpam-5897	37	10	]	]	PUNCT
ejpam-5897	37	11	for	for	ADP
ejpam-5897	37	12	all	all	PRON
ejpam-5897	37	13	x	x	PROPN
ejpam-5897	37	14	,	,	PUNCT
ejpam-5897	37	15	y	y	PROPN
ejpam-5897	37	16	,	,	PUNCT
ejpam-5897	37	17	z	z	PROPN
ejpam-5897	37	18	∈	∈	PROPN
ejpam-5897	37	19	a.	a.	NOUN
ejpam-5897	37	20	if	if	SCONJ
ejpam-5897	37	21	,	,	PUNCT
ejpam-5897	37	22	in	in	ADP
ejpam-5897	37	23	addition	addition	NOUN
ejpam-5897	37	24	,	,	PUNCT
ejpam-5897	37	25	the	the	DET
ejpam-5897	37	26	c	c	NOUN
ejpam-5897	37	27	-	-	PUNCT
ejpam-5897	37	28	linear	linear	NOUN
ejpam-5897	37	29	mapping	mapping	NOUN
ejpam-5897	37	30	h	h	NOUN
ejpam-5897	37	31	is	be	AUX
ejpam-5897	37	32	bijective	bijective	ADJ
ejpam-5897	37	33	,	,	PUNCT
ejpam-5897	37	34	then	then	ADV
ejpam-5897	37	35	the	the	DET
ejpam-5897	37	36	c	c	NOUN
ejpam-5897	37	37	-	-	PUNCT
ejpam-5897	37	38	linear	linear	ADJ
ejpam-5897	37	39	mapping	mapping	NOUN
ejpam-5897	37	40	h	h	NOUN
ejpam-5897	37	41	:	:	PUNCT
ejpam-5897	37	42	a	a	DET
ejpam-5897	37	43	→	→	PUNCT
ejpam-5897	37	44	a′	a′	PROPN
ejpam-5897	37	45	is	be	AUX
ejpam-5897	37	46	called	call	VERB
ejpam-5897	37	47	a	a	DET
ejpam-5897	37	48	ternary	ternary	ADJ
ejpam-5897	37	49	algebra	algebra	NOUN
ejpam-5897	37	50	isomorphism	isomorphism	NOUN
ejpam-5897	37	51	.	.	PUNCT
ejpam-5897	38	1	a	a	DET
ejpam-5897	38	2	c	c	NOUN
ejpam-5897	38	3	-	-	PUNCT
ejpam-5897	38	4	linear	linear	ADJ
ejpam-5897	38	5	mapping	mapping	NOUN
ejpam-5897	38	6	δ	δ	NOUN
ejpam-5897	38	7	:	:	PUNCT
ejpam-5897	38	8	a	a	PRON
ejpam-5897	38	9	→	→	X
ejpam-5897	38	10	a	a	PRON
ejpam-5897	38	11	is	be	AUX
ejpam-5897	38	12	called	call	VERB
ejpam-5897	38	13	a	a	DET
ejpam-5897	38	14	ternary	ternary	ADJ
ejpam-5897	38	15	algebra	algebra	NOUN
ejpam-5897	38	16	derivation	derivation	NOUN
ejpam-5897	38	17	if	if	SCONJ
ejpam-5897	38	18	δ([x	δ([x	PROPN
ejpam-5897	38	19	,	,	PUNCT
ejpam-5897	38	20	y	y	PROPN
ejpam-5897	38	21	,	,	PUNCT
ejpam-5897	38	22	z	z	NOUN
ejpam-5897	38	23	]	]	X
ejpam-5897	38	24	)	)	PUNCT
ejpam-5897	39	1	=	=	PUNCT
ejpam-5897	40	1	[	[	X
ejpam-5897	40	2	δ(x	δ(x	NOUN
ejpam-5897	40	3	)	)	PUNCT
ejpam-5897	40	4	,	,	PUNCT
ejpam-5897	40	5	y	y	PROPN
ejpam-5897	40	6	,	,	PUNCT
ejpam-5897	40	7	z	z	X
ejpam-5897	40	8	]	]	X
ejpam-5897	41	1	+	+	CCONJ
ejpam-5897	42	1	[	[	X
ejpam-5897	42	2	x	x	X
ejpam-5897	42	3	,	,	PUNCT
ejpam-5897	42	4	δ(y	δ(y	ADV
ejpam-5897	42	5	)	)	PUNCT
ejpam-5897	42	6	,	,	PUNCT
ejpam-5897	42	7	z	z	X
ejpam-5897	42	8	]	]	X
ejpam-5897	43	1	+	+	CCONJ
ejpam-5897	43	2	[	[	X
ejpam-5897	43	3	x	x	X
ejpam-5897	43	4	,	,	PUNCT
ejpam-5897	43	5	y	y	PROPN
ejpam-5897	43	6	,	,	PUNCT
ejpam-5897	43	7	δ(z	δ(z	PROPN
ejpam-5897	43	8	)	)	PUNCT
ejpam-5897	43	9	]	]	PUNCT
ejpam-5897	43	10	for	for	ADP
ejpam-5897	43	11	all	all	DET
ejpam-5897	43	12	x	x	PROPN
ejpam-5897	43	13	,	,	PUNCT
ejpam-5897	43	14	y	y	PROPN
ejpam-5897	43	15	,	,	PUNCT
ejpam-5897	43	16	z	z	PROPN
ejpam-5897	43	17	∈	∈	PROPN
ejpam-5897	43	18	a	a	DET
ejpam-5897	43	19	(	(	PUNCT
ejpam-5897	43	20	see	see	VERB
ejpam-5897	43	21	[	[	X
ejpam-5897	43	22	27–30	27–30	NUM
ejpam-5897	43	23	]	]	PUNCT
ejpam-5897	43	24	)	)	PUNCT
ejpam-5897	43	25	.	.	PUNCT
ejpam-5897	44	1	let	let	VERB
ejpam-5897	44	2	x	x	PRON
ejpam-5897	44	3	be	be	AUX
ejpam-5897	44	4	a	a	DET
ejpam-5897	44	5	complex	complex	ADJ
ejpam-5897	44	6	ternary	ternary	ADJ
ejpam-5897	44	7	algebra	algebra	NOUN
ejpam-5897	44	8	.	.	PUNCT
ejpam-5897	45	1	a	a	DET
ejpam-5897	45	2	mapping	mapping	NOUN
ejpam-5897	45	3	f	f	NOUN
ejpam-5897	45	4	:	:	PUNCT
ejpam-5897	45	5	x3	x3	VERB
ejpam-5897	45	6	→	→	SYM
ejpam-5897	45	7	x	x	X
ejpam-5897	45	8	is	be	AUX
ejpam-5897	45	9	3	3	NUM
ejpam-5897	45	10	-	-	PUNCT
ejpam-5897	45	11	additive	additive	ADJ
ejpam-5897	45	12	if	if	SCONJ
ejpam-5897	45	13	f(x1	f(x1	ADJ
ejpam-5897	45	14	+	+	X
ejpam-5897	45	15	x2	x2	ADJ
ejpam-5897	45	16	,	,	PUNCT
ejpam-5897	45	17	y1	y1	NOUN
ejpam-5897	45	18	+	+	CCONJ
ejpam-5897	45	19	y2	y2	ADJ
ejpam-5897	45	20	,	,	PUNCT
ejpam-5897	45	21	z1	z1	PROPN
ejpam-5897	45	22	+	+	CCONJ
ejpam-5897	45	23	z2	z2	NUM
ejpam-5897	45	24	)	)	PUNCT
ejpam-5897	45	25	=	=	SYM
ejpam-5897	46	1	2∑	2∑	NUM
ejpam-5897	46	2	i	i	NOUN
ejpam-5897	46	3	,	,	PUNCT
ejpam-5897	46	4	j	j	PROPN
ejpam-5897	46	5	,	,	PUNCT
ejpam-5897	46	6	k=1	k=1	PROPN
ejpam-5897	46	7	f(xi	f(xi	PROPN
ejpam-5897	46	8	,	,	PUNCT
ejpam-5897	46	9	yj	yj	PROPN
ejpam-5897	46	10	,	,	PUNCT
ejpam-5897	46	11	zk	zk	PROPN
ejpam-5897	46	12	)	)	PUNCT
ejpam-5897	46	13	for	for	ADP
ejpam-5897	46	14	all	all	PRON
ejpam-5897	46	15	x1	x1	PROPN
ejpam-5897	46	16	,	,	PUNCT
ejpam-5897	46	17	y1	y1	NOUN
ejpam-5897	46	18	,	,	PUNCT
ejpam-5897	46	19	z1	z1	NOUN
ejpam-5897	46	20	,	,	PUNCT
ejpam-5897	46	21	x2	x2	PROPN
ejpam-5897	46	22	,	,	PUNCT
ejpam-5897	46	23	y2	y2	PROPN
ejpam-5897	46	24	,	,	PUNCT
ejpam-5897	46	25	z2	z2	PROPN
ejpam-5897	46	26	∈	∈	PROPN
ejpam-5897	46	27	x.	x.	NOUN
ejpam-5897	46	28	a	a	DET
ejpam-5897	46	29	mapping	mapping	NOUN
ejpam-5897	46	30	f	f	NOUN
ejpam-5897	46	31	:	:	PUNCT
ejpam-5897	47	1	x3	x3	VERB
ejpam-5897	47	2	→	→	SYM
ejpam-5897	47	3	x	x	X
ejpam-5897	47	4	is	be	AUX
ejpam-5897	47	5	called	call	VERB
ejpam-5897	47	6	3	3	NUM
ejpam-5897	47	7	-	-	PUNCT
ejpam-5897	47	8	linear	linear	NOUN
ejpam-5897	47	9	if	if	SCONJ
ejpam-5897	47	10	f	f	PROPN
ejpam-5897	47	11	is	be	AUX
ejpam-5897	47	12	3	3	NUM
ejpam-5897	47	13	-	-	PUNCT
ejpam-5897	47	14	additive	additive	ADJ
ejpam-5897	47	15	and	and	CCONJ
ejpam-5897	47	16	c	c	NOUN
ejpam-5897	47	17	-	-	PUNCT
ejpam-5897	47	18	linear	linear	NOUN
ejpam-5897	47	19	for	for	ADP
ejpam-5897	47	20	each	each	DET
ejpam-5897	47	21	variable	variable	NOUN
ejpam-5897	47	22	.	.	PUNCT
ejpam-5897	48	1	throughout	throughout	ADP
ejpam-5897	48	2	the	the	DET
ejpam-5897	48	3	paper	paper	NOUN
ejpam-5897	48	4	,	,	PUNCT
ejpam-5897	48	5	assume	assume	VERB
ejpam-5897	48	6	that	that	SCONJ
ejpam-5897	48	7	x	x	PRON
ejpam-5897	48	8	is	be	AUX
ejpam-5897	48	9	a	a	DET
ejpam-5897	48	10	complex	complex	ADJ
ejpam-5897	48	11	ternary	ternary	ADJ
ejpam-5897	48	12	algebra	algebra	NOUN
ejpam-5897	48	13	,	,	PUNCT
ejpam-5897	48	14	y	y	PROPN
ejpam-5897	48	15	is	be	AUX
ejpam-5897	48	16	a	a	DET
ejpam-5897	48	17	complex	complex	ADJ
ejpam-5897	48	18	ternary	ternary	ADJ
ejpam-5897	48	19	banach	banach	NOUN
ejpam-5897	48	20	algebra	algebra	NOUN
ejpam-5897	48	21	and	and	CCONJ
ejpam-5897	48	22	t	t	PROPN
ejpam-5897	48	23	is	be	AUX
ejpam-5897	48	24	a	a	DET
ejpam-5897	48	25	fixed	fix	VERB
ejpam-5897	48	26	nonzero	nonzero	NOUN
ejpam-5897	48	27	real	real	ADJ
ejpam-5897	48	28	number	number	NOUN
ejpam-5897	48	29	with	with	ADP
ejpam-5897	48	30	|t|	|t|	NOUN
ejpam-5897	48	31	<	<	X
ejpam-5897	48	32	1	1	NUM
ejpam-5897	48	33	.	.	PUNCT
ejpam-5897	48	34	e.	e.	PROPN
ejpam-5897	48	35	shim	shim	PROPN
ejpam-5897	48	36	,	,	PUNCT
ejpam-5897	48	37	s.	s.	PROPN
ejpam-5897	48	38	donganont	donganont	PROPN
ejpam-5897	48	39	,	,	PUNCT
ejpam-5897	48	40	c.	c.	PROPN
ejpam-5897	48	41	park	park	PROPN
ejpam-5897	48	42	/	/	SYM
ejpam-5897	48	43	eur	eur	PROPN
ejpam-5897	48	44	.	.	PUNCT
ejpam-5897	49	1	j.	j.	PROPN
ejpam-5897	49	2	pure	pure	PROPN
ejpam-5897	49	3	appl	appl	PROPN
ejpam-5897	49	4	.	.	PROPN
ejpam-5897	49	5	math	math	PROPN
ejpam-5897	49	6	,	,	PUNCT
ejpam-5897	49	7	18	18	NUM
ejpam-5897	49	8	(	(	PUNCT
ejpam-5897	49	9	2	2	NUM
ejpam-5897	49	10	)	)	PUNCT
ejpam-5897	49	11	(	(	PUNCT
ejpam-5897	49	12	2025	2025	NUM
ejpam-5897	49	13	)	)	PUNCT
ejpam-5897	49	14	,	,	PUNCT
ejpam-5897	49	15	5897	5897	NUM
ejpam-5897	49	16	3	3	NUM
ejpam-5897	49	17	of	of	ADP
ejpam-5897	49	18	14	14	NUM
ejpam-5897	49	19	2	2	NUM
ejpam-5897	49	20	.	.	PUNCT
ejpam-5897	50	1	stability	stability	NOUN
ejpam-5897	50	2	of	of	ADP
ejpam-5897	50	3	hyper	hyper	ADJ
ejpam-5897	50	4	3	3	NUM
ejpam-5897	50	5	-	-	PUNCT
ejpam-5897	50	6	homomorphisms	homomorphism	NOUN
ejpam-5897	50	7	in	in	ADP
ejpam-5897	50	8	ternary	ternary	ADJ
ejpam-5897	50	9	algebras	algebra	NOUN
ejpam-5897	50	10	in	in	ADP
ejpam-5897	50	11	this	this	DET
ejpam-5897	50	12	section	section	NOUN
ejpam-5897	50	13	,	,	PUNCT
ejpam-5897	50	14	we	we	PRON
ejpam-5897	50	15	prove	prove	VERB
ejpam-5897	50	16	the	the	DET
ejpam-5897	50	17	hyers	hyers	PROPN
ejpam-5897	50	18	-	-	PUNCT
ejpam-5897	50	19	ulam	ulam	ADJ
ejpam-5897	50	20	stability	stability	NOUN
ejpam-5897	50	21	of	of	ADP
ejpam-5897	50	22	hyper	hyper	ADJ
ejpam-5897	50	23	3	3	NUM
ejpam-5897	50	24	-	-	PUNCT
ejpam-5897	50	25	homomorphisms	homomorphism	NOUN
ejpam-5897	50	26	in	in	ADP
ejpam-5897	50	27	complex	complex	ADJ
ejpam-5897	50	28	ternary	ternary	ADJ
ejpam-5897	50	29	algebras	algebra	NOUN
ejpam-5897	50	30	and	and	CCONJ
ejpam-5897	50	31	we	we	PRON
ejpam-5897	50	32	investigate	investigate	VERB
ejpam-5897	50	33	ternary	ternary	ADJ
ejpam-5897	50	34	algebra	algebra	NOUN
ejpam-5897	50	35	isomorphisms	isomorphism	NOUN
ejpam-5897	50	36	between	between	ADP
ejpam-5897	50	37	complex	complex	ADJ
ejpam-5897	50	38	ternary	ternary	ADJ
ejpam-5897	50	39	algebras	algebra	NOUN
ejpam-5897	50	40	,	,	PUNCT
ejpam-5897	50	41	associated	associate	VERB
ejpam-5897	50	42	with	with	ADP
ejpam-5897	50	43	the	the	DET
ejpam-5897	50	44	3	3	NUM
ejpam-5897	50	45	-	-	PUNCT
ejpam-5897	50	46	additive	additive	ADJ
ejpam-5897	50	47	functional	functional	ADJ
ejpam-5897	50	48	equation	equation	NOUN
ejpam-5897	50	49	(	(	PUNCT
ejpam-5897	50	50	1	1	NUM
ejpam-5897	50	51	)	)	PUNCT
ejpam-5897	50	52	.	.	PUNCT
ejpam-5897	51	1	definition	definition	NOUN
ejpam-5897	51	2	1	1	NUM
ejpam-5897	51	3	.	.	PUNCT
ejpam-5897	52	1	let	let	VERB
ejpam-5897	52	2	x	x	PRON
ejpam-5897	52	3	and	and	CCONJ
ejpam-5897	52	4	y	y	PROPN
ejpam-5897	52	5	be	be	AUX
ejpam-5897	52	6	complex	complex	ADJ
ejpam-5897	52	7	ternary	ternary	ADJ
ejpam-5897	52	8	algebras	algebra	NOUN
ejpam-5897	52	9	.	.	PUNCT
ejpam-5897	53	1	a	a	DET
ejpam-5897	53	2	3	3	NUM
ejpam-5897	53	3	-	-	PUNCT
ejpam-5897	53	4	linear	linear	NOUN
ejpam-5897	53	5	mapping	mapping	NOUN
ejpam-5897	53	6	h	h	NOUN
ejpam-5897	53	7	:	:	PUNCT
ejpam-5897	53	8	x3	x3	ADJ
ejpam-5897	53	9	→	→	SYM
ejpam-5897	53	10	y	y	PROPN
ejpam-5897	53	11	is	be	AUX
ejpam-5897	53	12	called	call	VERB
ejpam-5897	53	13	a	a	DET
ejpam-5897	53	14	hyper	hyper	ADJ
ejpam-5897	53	15	3	3	NUM
ejpam-5897	53	16	-	-	PUNCT
ejpam-5897	53	17	additivec	additivec	NOUN
ejpam-5897	53	18	mapping	mapping	NOUN
ejpam-5897	53	19	if	if	SCONJ
ejpam-5897	53	20	h	h	NOUN
ejpam-5897	53	21	satisfies	satisfy	VERB
ejpam-5897	53	22	8h(x1	8h(x1	NUM
ejpam-5897	53	23	,	,	PUNCT
ejpam-5897	53	24	y1	y1	NOUN
ejpam-5897	53	25	,	,	PUNCT
ejpam-5897	53	26	z1	z1	NOUN
ejpam-5897	53	27	)	)	PUNCT
ejpam-5897	53	28	=	=	SYM
ejpam-5897	54	1	2∑	2∑	NUM
ejpam-5897	54	2	i	i	NOUN
ejpam-5897	54	3	,	,	PUNCT
ejpam-5897	54	4	j	j	PROPN
ejpam-5897	54	5	,	,	PUNCT
ejpam-5897	54	6	k=1	k=1	PROPN
ejpam-5897	54	7	h(xi	h(xi	PROPN
ejpam-5897	54	8	+	+	CCONJ
ejpam-5897	54	9	(	(	PUNCT
ejpam-5897	54	10	−1)ix2	−1)ix2	PROPN
ejpam-5897	54	11	,	,	PUNCT
ejpam-5897	54	12	yj	yj	PROPN
ejpam-5897	54	13	+	+	X
ejpam-5897	54	14	(	(	PUNCT
ejpam-5897	54	15	−1)jy2	−1)jy2	PROPN
ejpam-5897	54	16	,	,	PUNCT
ejpam-5897	54	17	z1	z1	PROPN
ejpam-5897	54	18	+	+	CCONJ
ejpam-5897	54	19	(	(	PUNCT
ejpam-5897	54	20	−1)kz2	−1)kz2	PROPN
ejpam-5897	54	21	)	)	PUNCT
ejpam-5897	54	22	(	(	PUNCT
ejpam-5897	54	23	2	2	X
ejpam-5897	54	24	)	)	PUNCT
ejpam-5897	54	25	for	for	ADP
ejpam-5897	54	26	all	all	PRON
ejpam-5897	54	27	x1	x1	PROPN
ejpam-5897	54	28	,	,	PUNCT
ejpam-5897	54	29	y1	y1	NOUN
ejpam-5897	54	30	,	,	PUNCT
ejpam-5897	54	31	z1	z1	NOUN
ejpam-5897	54	32	,	,	PUNCT
ejpam-5897	54	33	x2	x2	PROPN
ejpam-5897	54	34	,	,	PUNCT
ejpam-5897	54	35	y2	y2	PROPN
ejpam-5897	54	36	,	,	PUNCT
ejpam-5897	54	37	z2	z2	PROPN
ejpam-5897	54	38	∈	∈	PROPN
ejpam-5897	54	39	x.	x.	NOUN
ejpam-5897	54	40	definition	definition	NOUN
ejpam-5897	54	41	2	2	NUM
ejpam-5897	54	42	.	.	PUNCT
ejpam-5897	55	1	let	let	VERB
ejpam-5897	55	2	x	x	PRON
ejpam-5897	55	3	and	and	CCONJ
ejpam-5897	55	4	y	y	PROPN
ejpam-5897	55	5	be	be	AUX
ejpam-5897	55	6	complex	complex	ADJ
ejpam-5897	55	7	ternary	ternary	ADJ
ejpam-5897	55	8	algebras	algebra	NOUN
ejpam-5897	55	9	.	.	PUNCT
ejpam-5897	56	1	a	a	DET
ejpam-5897	56	2	3	3	NUM
ejpam-5897	56	3	-	-	PUNCT
ejpam-5897	56	4	linear	linear	NOUN
ejpam-5897	56	5	mapping	mapping	NOUN
ejpam-5897	56	6	h	h	NOUN
ejpam-5897	56	7	:	:	PUNCT
ejpam-5897	56	8	x3	x3	ADJ
ejpam-5897	56	9	→	→	SYM
ejpam-5897	56	10	y	y	PROPN
ejpam-5897	56	11	is	be	AUX
ejpam-5897	56	12	called	call	VERB
ejpam-5897	56	13	a	a	DET
ejpam-5897	56	14	hyper	hyper	ADJ
ejpam-5897	56	15	3	3	NUM
ejpam-5897	56	16	-	-	NUM
ejpam-5897	56	17	homomorphism	homomorphism	NOUN
ejpam-5897	56	18	if	if	SCONJ
ejpam-5897	56	19	h	h	NOUN
ejpam-5897	56	20	satisfies	satisfie	NOUN
ejpam-5897	56	21	h([x1	h([x1	NOUN
ejpam-5897	56	22	,	,	PUNCT
ejpam-5897	56	23	y1	y1	NOUN
ejpam-5897	56	24	,	,	PUNCT
ejpam-5897	56	25	z1	z1	NOUN
ejpam-5897	56	26	]	]	PUNCT
ejpam-5897	56	27	,	,	PUNCT
ejpam-5897	57	1	[	[	X
ejpam-5897	57	2	x2	x2	X
ejpam-5897	57	3	,	,	PUNCT
ejpam-5897	57	4	y2	y2	PROPN
ejpam-5897	57	5	,	,	PUNCT
ejpam-5897	57	6	z2	z2	PROPN
ejpam-5897	57	7	]	]	PUNCT
ejpam-5897	57	8	,	,	PUNCT
ejpam-5897	57	9	[	[	X
ejpam-5897	57	10	x3	x3	ADJ
ejpam-5897	57	11	,	,	PUNCT
ejpam-5897	57	12	y3	y3	NOUN
ejpam-5897	57	13	,	,	PUNCT
ejpam-5897	57	14	z3	z3	PROPN
ejpam-5897	57	15	]	]	PUNCT
ejpam-5897	57	16	)	)	PUNCT
ejpam-5897	57	17	=	=	PUNCT
ejpam-5897	58	1	[	[	X
ejpam-5897	58	2	h(x1	h(x1	X
ejpam-5897	58	3	,	,	PUNCT
ejpam-5897	58	4	x2	x2	PROPN
ejpam-5897	58	5	,	,	PUNCT
ejpam-5897	58	6	x3	x3	ADJ
ejpam-5897	58	7	)	)	PUNCT
ejpam-5897	58	8	,	,	PUNCT
ejpam-5897	58	9	h(y1	h(y1	NOUN
ejpam-5897	58	10	,	,	PUNCT
ejpam-5897	58	11	y2	y2	PROPN
ejpam-5897	58	12	,	,	PUNCT
ejpam-5897	58	13	y3	y3	PROPN
ejpam-5897	58	14	)	)	PUNCT
ejpam-5897	58	15	,	,	PUNCT
ejpam-5897	58	16	h(z1	h(z1	NOUN
ejpam-5897	58	17	,	,	PUNCT
ejpam-5897	58	18	z2	z2	PROPN
ejpam-5897	58	19	,	,	PUNCT
ejpam-5897	58	20	z3	z3	PROPN
ejpam-5897	58	21	)	)	PUNCT
ejpam-5897	58	22	]	]	PUNCT
ejpam-5897	58	23	for	for	ADP
ejpam-5897	58	24	all	all	DET
ejpam-5897	58	25	x1	x1	PROPN
ejpam-5897	58	26	,	,	PUNCT
ejpam-5897	58	27	x2	x2	PROPN
ejpam-5897	58	28	,	,	PUNCT
ejpam-5897	58	29	x3	x3	ADJ
ejpam-5897	58	30	,	,	PUNCT
ejpam-5897	58	31	y1	y1	NOUN
ejpam-5897	58	32	,	,	PUNCT
ejpam-5897	58	33	y2	y2	PROPN
ejpam-5897	58	34	,	,	PUNCT
ejpam-5897	58	35	y3	y3	PROPN
ejpam-5897	58	36	,	,	PUNCT
ejpam-5897	58	37	z1	z1	PROPN
ejpam-5897	58	38	,	,	PUNCT
ejpam-5897	58	39	z2	z2	PROPN
ejpam-5897	58	40	,	,	PUNCT
ejpam-5897	58	41	z3	z3	PROPN
ejpam-5897	58	42	∈	∈	PROPN
ejpam-5897	58	43	x.	x.	NOUN
ejpam-5897	58	44	lemma	lemma	PROPN
ejpam-5897	59	1	1	1	X
ejpam-5897	59	2	.	.	PUNCT
ejpam-5897	60	1	let	let	VERB
ejpam-5897	60	2	x	x	PRON
ejpam-5897	60	3	and	and	CCONJ
ejpam-5897	60	4	y	y	PROPN
ejpam-5897	60	5	be	be	AUX
ejpam-5897	60	6	complex	complex	ADJ
ejpam-5897	60	7	ternary	ternary	ADJ
ejpam-5897	60	8	algebras	algebra	NOUN
ejpam-5897	60	9	.	.	PUNCT
ejpam-5897	61	1	let	let	VERB
ejpam-5897	61	2	h	h	NOUN
ejpam-5897	61	3	:	:	PUNCT
ejpam-5897	61	4	x3	x3	VERB
ejpam-5897	61	5	→	→	SYM
ejpam-5897	61	6	y	y	PROPN
ejpam-5897	61	7	be	be	AUX
ejpam-5897	61	8	a	a	DET
ejpam-5897	61	9	hyper	hyper	ADJ
ejpam-5897	61	10	3	3	NUM
ejpam-5897	61	11	-	-	PUNCT
ejpam-5897	61	12	additive	additive	ADJ
ejpam-5897	61	13	mapping	mapping	NOUN
ejpam-5897	61	14	and	and	CCONJ
ejpam-5897	61	15	satisfy	satisfy	NOUN
ejpam-5897	61	16	h(2x	h(2x	VERB
ejpam-5897	61	17	,	,	PUNCT
ejpam-5897	61	18	2y	2y	NUM
ejpam-5897	61	19	,	,	PUNCT
ejpam-5897	61	20	2z	2z	NUM
ejpam-5897	61	21	)	)	PUNCT
ejpam-5897	61	22	=	=	SYM
ejpam-5897	61	23	8h(x	8h(x	NUM
ejpam-5897	61	24	,	,	PUNCT
ejpam-5897	61	25	y	y	PROPN
ejpam-5897	61	26	,	,	PUNCT
ejpam-5897	61	27	z	z	NOUN
ejpam-5897	61	28	)	)	PUNCT
ejpam-5897	61	29	for	for	ADP
ejpam-5897	61	30	all	all	DET
ejpam-5897	61	31	x	x	NOUN
ejpam-5897	61	32	,	,	PUNCT
ejpam-5897	61	33	y	y	PROPN
ejpam-5897	61	34	,	,	PUNCT
ejpam-5897	61	35	z	z	PROPN
ejpam-5897	61	36	∈	∈	NOUN
ejpam-5897	61	37	x3	x3	PROPN
ejpam-5897	61	38	,	,	PUNCT
ejpam-5897	61	39	then	then	ADV
ejpam-5897	61	40	h	h	PROPN
ejpam-5897	61	41	is	be	AUX
ejpam-5897	61	42	3	3	NUM
ejpam-5897	61	43	-	-	PUNCT
ejpam-5897	61	44	additive	additive	NOUN
ejpam-5897	61	45	.	.	PUNCT
ejpam-5897	62	1	proof	proof	NOUN
ejpam-5897	62	2	.	.	PUNCT
ejpam-5897	63	1	for	for	ADP
ejpam-5897	63	2	x1	x1	PROPN
ejpam-5897	63	3	,	,	PUNCT
ejpam-5897	63	4	x2	x2	PROPN
ejpam-5897	63	5	,	,	PUNCT
ejpam-5897	63	6	y1	y1	NOUN
ejpam-5897	63	7	,	,	PUNCT
ejpam-5897	63	8	y2	y2	PROPN
ejpam-5897	63	9	,	,	PUNCT
ejpam-5897	63	10	z1	z1	VERB
ejpam-5897	63	11	,	,	PUNCT
ejpam-5897	63	12	z2	z2	PROPN
ejpam-5897	63	13	∈	∈	PROPN
ejpam-5897	63	14	x	x	NOUN
ejpam-5897	63	15	,	,	PUNCT
ejpam-5897	63	16	we	we	PRON
ejpam-5897	63	17	define	define	VERB
ejpam-5897	63	18	p1	p1	NOUN
ejpam-5897	63	19	:	:	PUNCT
ejpam-5897	64	1	=	=	SYM
ejpam-5897	64	2	x1	x1	PROPN
ejpam-5897	65	1	+	+	CCONJ
ejpam-5897	65	2	x2	x2	PROPN
ejpam-5897	65	3	2	2	NUM
ejpam-5897	65	4	,	,	PUNCT
ejpam-5897	65	5	p2	p2	PUNCT
ejpam-5897	65	6	:	:	PUNCT
ejpam-5897	65	7	=	=	SYM
ejpam-5897	66	1	x1	x1	NUM
ejpam-5897	66	2	−	−	PUNCT
ejpam-5897	67	1	x2	x2	NOUN
ejpam-5897	67	2	2	2	NUM
ejpam-5897	67	3	,	,	PUNCT
ejpam-5897	67	4	q1	q1	NOUN
ejpam-5897	67	5	:	:	PUNCT
ejpam-5897	67	6	=	=	SYM
ejpam-5897	67	7	y1	y1	INTJ
ejpam-5897	67	8	+	+	CCONJ
ejpam-5897	67	9	y2	y2	PROPN
ejpam-5897	67	10	2	2	NUM
ejpam-5897	67	11	,	,	PUNCT
ejpam-5897	67	12	q2	q2	NOUN
ejpam-5897	67	13	:	:	PUNCT
ejpam-5897	67	14	=	=	SYM
ejpam-5897	67	15	y1	y1	INTJ
ejpam-5897	67	16	−	−	PROPN
ejpam-5897	68	1	y2	y2	NOUN
ejpam-5897	68	2	2	2	NUM
ejpam-5897	68	3	,	,	PUNCT
ejpam-5897	68	4	r1	r1	NOUN
ejpam-5897	68	5	:	:	PUNCT
ejpam-5897	68	6	=	=	SYM
ejpam-5897	68	7	z1	z1	VERB
ejpam-5897	68	8	+	+	CCONJ
ejpam-5897	68	9	z2	z2	PROPN
ejpam-5897	68	10	2	2	NUM
ejpam-5897	68	11	and	and	CCONJ
ejpam-5897	68	12	r2	r2	PROPN
ejpam-5897	68	13	:	:	PUNCT
ejpam-5897	69	1	=	=	SYM
ejpam-5897	69	2	z1	z1	PROPN
ejpam-5897	69	3	−	−	PROPN
ejpam-5897	69	4	z2	z2	PROPN
ejpam-5897	69	5	2	2	NUM
ejpam-5897	69	6	.	.	PUNCT
ejpam-5897	70	1	it	it	PRON
ejpam-5897	70	2	follows	follow	VERB
ejpam-5897	70	3	from	from	ADP
ejpam-5897	70	4	(	(	PUNCT
ejpam-5897	70	5	2	2	NUM
ejpam-5897	70	6	)	)	PUNCT
ejpam-5897	70	7	that	that	DET
ejpam-5897	70	8	h(x1	h(x1	NOUN
ejpam-5897	70	9	+	+	CCONJ
ejpam-5897	70	10	x2	x2	PROPN
ejpam-5897	70	11	,	,	PUNCT
ejpam-5897	70	12	y1	y1	NOUN
ejpam-5897	70	13	+	+	CCONJ
ejpam-5897	70	14	y2	y2	ADJ
ejpam-5897	70	15	,	,	PUNCT
ejpam-5897	70	16	z1	z1	PROPN
ejpam-5897	70	17	+	+	CCONJ
ejpam-5897	70	18	z2	z2	NUM
ejpam-5897	70	19	)	)	PUNCT
ejpam-5897	70	20	=	=	SYM
ejpam-5897	70	21	h(2p1	h(2p1	NUM
ejpam-5897	70	22	,	,	PUNCT
ejpam-5897	70	23	2q1	2q1	NUM
ejpam-5897	70	24	,	,	PUNCT
ejpam-5897	70	25	2r1	2r1	NUM
ejpam-5897	70	26	)	)	PUNCT
ejpam-5897	70	27	=	=	SYM
ejpam-5897	70	28	8h(p1	8h(p1	NUM
ejpam-5897	70	29	,	,	PUNCT
ejpam-5897	70	30	q1	q1	PROPN
ejpam-5897	70	31	,	,	PUNCT
ejpam-5897	70	32	r1	r1	PROPN
ejpam-5897	70	33	)	)	PUNCT
ejpam-5897	70	34	=	=	PUNCT
ejpam-5897	71	1	2∑	2∑	NUM
ejpam-5897	71	2	i	i	NOUN
ejpam-5897	71	3	,	,	PUNCT
ejpam-5897	71	4	j	j	PROPN
ejpam-5897	71	5	,	,	PUNCT
ejpam-5897	71	6	k=1	k=1	PROPN
ejpam-5897	71	7	h(p1	h(p1	NOUN
ejpam-5897	71	8	+	+	CCONJ
ejpam-5897	71	9	(	(	PUNCT
ejpam-5897	71	10	−1)ip2	−1)ip2	PROPN
ejpam-5897	71	11	,	,	PUNCT
ejpam-5897	71	12	q1	q1	PROPN
ejpam-5897	71	13	+	+	CCONJ
ejpam-5897	71	14	(	(	PUNCT
ejpam-5897	71	15	−1)jq2	−1)jq2	PROPN
ejpam-5897	71	16	,	,	PUNCT
ejpam-5897	71	17	r1	r1	PROPN
ejpam-5897	71	18	+	+	CCONJ
ejpam-5897	71	19	(	(	PUNCT
ejpam-5897	71	20	−1)kr2	−1)kr2	PROPN
ejpam-5897	71	21	)	)	PUNCT
ejpam-5897	71	22	=	=	SYM
ejpam-5897	72	1	2∑	2∑	NUM
ejpam-5897	72	2	i	i	PRON
ejpam-5897	72	3	,	,	PUNCT
ejpam-5897	72	4	j	j	PROPN
ejpam-5897	72	5	,	,	PUNCT
ejpam-5897	72	6	k=1	k=1	PROPN
ejpam-5897	72	7	h(xi	h(xi	PROPN
ejpam-5897	72	8	,	,	PUNCT
ejpam-5897	72	9	yj	yj	PROPN
ejpam-5897	72	10	,	,	PUNCT
ejpam-5897	72	11	zk	zk	PROPN
ejpam-5897	72	12	)	)	PUNCT
ejpam-5897	72	13	.	.	PUNCT
ejpam-5897	73	1	this	this	PRON
ejpam-5897	73	2	completes	complete	VERB
ejpam-5897	73	3	the	the	DET
ejpam-5897	73	4	proof	proof	NOUN
ejpam-5897	73	5	.	.	PUNCT
ejpam-5897	74	1	lemma	lemma	PROPN
ejpam-5897	74	2	2	2	NUM
ejpam-5897	74	3	.	.	PUNCT
ejpam-5897	75	1	[	[	X
ejpam-5897	75	2	31	31	NUM
ejpam-5897	75	3	]	]	PUNCT
ejpam-5897	75	4	let	let	VERB
ejpam-5897	75	5	x	x	PRON
ejpam-5897	75	6	and	and	CCONJ
ejpam-5897	75	7	y	y	PROPN
ejpam-5897	75	8	be	be	AUX
ejpam-5897	75	9	complex	complex	ADJ
ejpam-5897	75	10	vector	vector	NOUN
ejpam-5897	75	11	spaces	space	NOUN
ejpam-5897	75	12	and	and	CCONJ
ejpam-5897	75	13	f	f	NOUN
ejpam-5897	75	14	:	:	PUNCT
ejpam-5897	75	15	x3	x3	ADJ
ejpam-5897	75	16	→	→	SYM
ejpam-5897	75	17	y	y	PROPN
ejpam-5897	75	18	be	be	AUX
ejpam-5897	75	19	a	a	DET
ejpam-5897	75	20	3	3	NUM
ejpam-5897	75	21	-	-	PUNCT
ejpam-5897	75	22	additive	additive	ADJ
ejpam-5897	75	23	mapping	mapping	NOUN
ejpam-5897	76	1	such	such	ADJ
ejpam-5897	76	2	that	that	SCONJ
ejpam-5897	76	3	f(λx	f(λx	NOUN
ejpam-5897	76	4	,	,	PUNCT
ejpam-5897	76	5	µy	µy	X
ejpam-5897	76	6	,	,	PUNCT
ejpam-5897	76	7	νz	νz	NOUN
ejpam-5897	76	8	)	)	PUNCT
ejpam-5897	76	9	=	=	SYM
ejpam-5897	76	10	λµνf(x	λµνf(x	PROPN
ejpam-5897	76	11	,	,	PUNCT
ejpam-5897	76	12	y	y	PROPN
ejpam-5897	76	13	,	,	PUNCT
ejpam-5897	76	14	z	z	NOUN
ejpam-5897	76	15	)	)	PUNCT
ejpam-5897	76	16	for	for	ADP
ejpam-5897	76	17	all	all	DET
ejpam-5897	76	18	λ	λ	PROPN
ejpam-5897	76	19	,	,	PUNCT
ejpam-5897	76	20	µ	µ	NOUN
ejpam-5897	76	21	,	,	PUNCT
ejpam-5897	76	22	ν	ν	PROPN
ejpam-5897	76	23	∈	∈	PROPN
ejpam-5897	76	24	t1	t1	NOUN
ejpam-5897	76	25	:	:	PUNCT
ejpam-5897	76	26	=	=	X
ejpam-5897	76	27	{	{	PUNCT
ejpam-5897	76	28	κ	κ	NOUN
ejpam-5897	76	29	∈	∈	PROPN
ejpam-5897	76	30	r	r	NOUN
ejpam-5897	76	31	|	|	NOUN
ejpam-5897	76	32	|κ|	|κ|	ADV
ejpam-5897	76	33	=	=	SYM
ejpam-5897	76	34	1	1	NUM
ejpam-5897	76	35	}	}	PUNCT
ejpam-5897	76	36	and	and	CCONJ
ejpam-5897	76	37	x	x	ADJ
ejpam-5897	76	38	,	,	PUNCT
ejpam-5897	76	39	y	y	PROPN
ejpam-5897	76	40	,	,	PUNCT
ejpam-5897	76	41	z	z	PROPN
ejpam-5897	76	42	∈	∈	PROPN
ejpam-5897	76	43	x.	x.	NOUN
ejpam-5897	77	1	then	then	ADV
ejpam-5897	77	2	f	f	PROPN
ejpam-5897	77	3	is	be	AUX
ejpam-5897	77	4	3	3	NUM
ejpam-5897	77	5	-	-	PUNCT
ejpam-5897	77	6	linear	linear	NOUN
ejpam-5897	77	7	.	.	PUNCT
ejpam-5897	78	1	e.	e.	PROPN
ejpam-5897	78	2	shim	shim	PROPN
ejpam-5897	78	3	,	,	PUNCT
ejpam-5897	78	4	s.	s.	PROPN
ejpam-5897	78	5	donganont	donganont	PROPN
ejpam-5897	78	6	,	,	PUNCT
ejpam-5897	78	7	c.	c.	PROPN
ejpam-5897	78	8	park	park	PROPN
ejpam-5897	78	9	/	/	SYM
ejpam-5897	78	10	eur	eur	PROPN
ejpam-5897	78	11	.	.	PUNCT
ejpam-5897	79	1	j.	j.	PROPN
ejpam-5897	79	2	pure	pure	PROPN
ejpam-5897	79	3	appl	appl	PROPN
ejpam-5897	79	4	.	.	PROPN
ejpam-5897	79	5	math	math	PROPN
ejpam-5897	79	6	,	,	PUNCT
ejpam-5897	79	7	18	18	NUM
ejpam-5897	79	8	(	(	PUNCT
ejpam-5897	79	9	2	2	NUM
ejpam-5897	79	10	)	)	PUNCT
ejpam-5897	79	11	(	(	PUNCT
ejpam-5897	79	12	2025	2025	NUM
ejpam-5897	79	13	)	)	PUNCT
ejpam-5897	79	14	,	,	PUNCT
ejpam-5897	79	15	5897	5897	NUM
ejpam-5897	79	16	4	4	NUM
ejpam-5897	79	17	of	of	ADP
ejpam-5897	79	18	14	14	NUM
ejpam-5897	79	19	theorem	theorem	NOUN
ejpam-5897	79	20	1	1	NUM
ejpam-5897	79	21	.	.	PUNCT
ejpam-5897	80	1	let	let	VERB
ejpam-5897	80	2	x	x	PRON
ejpam-5897	80	3	and	and	CCONJ
ejpam-5897	80	4	y	y	PROPN
ejpam-5897	80	5	be	be	AUX
ejpam-5897	80	6	complex	complex	ADJ
ejpam-5897	80	7	ternary	ternary	ADJ
ejpam-5897	80	8	algebras	algebra	NOUN
ejpam-5897	80	9	and	and	CCONJ
ejpam-5897	80	10	t	t	PROPN
ejpam-5897	80	11	be	be	AUX
ejpam-5897	80	12	a	a	DET
ejpam-5897	80	13	real	real	ADJ
ejpam-5897	80	14	number	number	NOUN
ejpam-5897	80	15	satisfying	satisfying	NOUN
ejpam-5897	81	1	|t|	|t|	NOUN
ejpam-5897	81	2	<	<	X
ejpam-5897	81	3	1	1	X
ejpam-5897	81	4	.	.	PUNCT
ejpam-5897	81	5	assume	assume	VERB
ejpam-5897	81	6	that	that	SCONJ
ejpam-5897	81	7	a	a	DET
ejpam-5897	81	8	mapping	mapping	NOUN
ejpam-5897	81	9	h	h	NOUN
ejpam-5897	81	10	:	:	PUNCT
ejpam-5897	81	11	x3	x3	ADJ
ejpam-5897	81	12	→	→	SYM
ejpam-5897	81	13	y	y	PROPN
ejpam-5897	81	14	satisfies	satisfy	VERB
ejpam-5897	81	15	h(0	h(0	PROPN
ejpam-5897	81	16	,	,	PUNCT
ejpam-5897	81	17	a	a	DET
ejpam-5897	81	18	,	,	PUNCT
ejpam-5897	81	19	b	b	NOUN
ejpam-5897	81	20	)	)	PUNCT
ejpam-5897	81	21	=	=	SYM
ejpam-5897	81	22	h(a	h(a	PROPN
ejpam-5897	81	23	,	,	PUNCT
ejpam-5897	81	24	0	0	NUM
ejpam-5897	81	25	,	,	PUNCT
ejpam-5897	81	26	b	b	NOUN
ejpam-5897	81	27	)	)	PUNCT
ejpam-5897	81	28	=	=	SYM
ejpam-5897	81	29	h(a	h(a	PROPN
ejpam-5897	81	30	,	,	PUNCT
ejpam-5897	81	31	b	b	NOUN
ejpam-5897	81	32	,	,	PUNCT
ejpam-5897	81	33	0	0	NUM
ejpam-5897	81	34	)	)	PUNCT
ejpam-5897	81	35	=	=	SYM
ejpam-5897	81	36	0	0	NUM
ejpam-5897	81	37	and	and	CCONJ
ejpam-5897	81	38	∥∥∥∥∥∥8h(x1	∥∥∥∥∥∥8h(x1	PROPN
ejpam-5897	81	39	,	,	PUNCT
ejpam-5897	81	40	y1	y1	PROPN
ejpam-5897	81	41	,	,	PUNCT
ejpam-5897	81	42	z1)−	z1)−	PROPN
ejpam-5897	81	43	2∑	2∑	NUM
ejpam-5897	81	44	i	i	NOUN
ejpam-5897	81	45	,	,	PUNCT
ejpam-5897	81	46	j	j	PROPN
ejpam-5897	81	47	,	,	PUNCT
ejpam-5897	81	48	k=1	k=1	PROPN
ejpam-5897	81	49	h(x1	h(x1	PROPN
ejpam-5897	81	50	+	+	CCONJ
ejpam-5897	81	51	(	(	PUNCT
ejpam-5897	81	52	−1)ix2	−1)ix2	ADJ
ejpam-5897	81	53	,	,	PUNCT
ejpam-5897	81	54	y1	y1	NOUN
ejpam-5897	81	55	+	+	X
ejpam-5897	81	56	(	(	PUNCT
ejpam-5897	81	57	−1)jy2	−1)jy2	PROPN
ejpam-5897	81	58	,	,	PUNCT
ejpam-5897	81	59	z1	z1	PROPN
ejpam-5897	81	60	+	+	CCONJ
ejpam-5897	81	61	(	(	PUNCT
ejpam-5897	81	62	−1)kz2	−1)kz2	PROPN
ejpam-5897	81	63	)	)	PUNCT
ejpam-5897	81	64	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-5897	82	1	(	(	PUNCT
ejpam-5897	82	2	3	3	X
ejpam-5897	82	3	)	)	PUNCT
ejpam-5897	82	4	≤	≤	NOUN
ejpam-5897	82	5	∥∥∥∥∥∥t	∥∥∥∥∥∥t	PUNCT
ejpam-5897	83	1	8	8	PROPN
ejpam-5897	83	2	2∑	2∑	NUM
ejpam-5897	84	1	i	i	PROPN
ejpam-5897	84	2	,	,	PUNCT
ejpam-5897	84	3	j	j	PROPN
ejpam-5897	84	4	,	,	PUNCT
ejpam-5897	84	5	k=1	k=1	PROPN
ejpam-5897	84	6	h	h	NOUN
ejpam-5897	84	7	(	(	PUNCT
ejpam-5897	84	8	x1	x1	PROPN
ejpam-5897	84	9	+	+	CCONJ
ejpam-5897	84	10	(	(	PUNCT
ejpam-5897	84	11	−1)ix2	−1)ix2	ADJ
ejpam-5897	84	12	2	2	NUM
ejpam-5897	84	13	,	,	PUNCT
ejpam-5897	84	14	y1	y1	NOUN
ejpam-5897	84	15	+	+	X
ejpam-5897	84	16	(	(	PUNCT
ejpam-5897	84	17	−1)jy2	−1)jy2	PROPN
ejpam-5897	84	18	2	2	NUM
ejpam-5897	84	19	,	,	PUNCT
ejpam-5897	84	20	z1	z1	PROPN
ejpam-5897	84	21	+	+	CCONJ
ejpam-5897	84	22	(	(	PUNCT
ejpam-5897	84	23	−1)kz2	−1)kz2	NOUN
ejpam-5897	84	24	2	2	NUM
ejpam-5897	84	25	)	)	PUNCT
ejpam-5897	84	26	−	−	NOUN
ejpam-5897	84	27	8h(x1	8h(x1	NUM
ejpam-5897	84	28	,	,	PUNCT
ejpam-5897	84	29	y1	y1	NOUN
ejpam-5897	84	30	,	,	PUNCT
ejpam-5897	84	31	z1	z1	PROPN
ejpam-5897	84	32	)	)	PUNCT
ejpam-5897	84	33	∥∥∥∥∥∥	∥∥∥∥∥∥	NOUN
ejpam-5897	85	1	for	for	ADP
ejpam-5897	85	2	all	all	DET
ejpam-5897	85	3	a	a	DET
ejpam-5897	85	4	,	,	PUNCT
ejpam-5897	85	5	b	b	X
ejpam-5897	85	6	∈	∈	PROPN
ejpam-5897	85	7	x	x	X
ejpam-5897	85	8	and	and	CCONJ
ejpam-5897	85	9	all	all	PRON
ejpam-5897	85	10	(	(	PUNCT
ejpam-5897	85	11	x1	x1	PROPN
ejpam-5897	85	12	,	,	PUNCT
ejpam-5897	85	13	y1	y1	PROPN
ejpam-5897	85	14	,	,	PUNCT
ejpam-5897	85	15	z1	z1	NOUN
ejpam-5897	85	16	)	)	PUNCT
ejpam-5897	85	17	,	,	PUNCT
ejpam-5897	85	18	(	(	PUNCT
ejpam-5897	85	19	x2	x2	PROPN
ejpam-5897	85	20	,	,	PUNCT
ejpam-5897	85	21	y2	y2	PROPN
ejpam-5897	85	22	,	,	PUNCT
ejpam-5897	85	23	z2	z2	PROPN
ejpam-5897	85	24	)	)	PUNCT
ejpam-5897	85	25	∈	∈	PROPN
ejpam-5897	85	26	x3	x3	PROPN
ejpam-5897	85	27	.	.	PUNCT
ejpam-5897	86	1	then	then	ADV
ejpam-5897	86	2	h	h	PROPN
ejpam-5897	86	3	is	be	AUX
ejpam-5897	86	4	hyper	hyper	ADJ
ejpam-5897	86	5	3	3	NUM
ejpam-5897	86	6	-	-	PUNCT
ejpam-5897	86	7	additive	additive	NOUN
ejpam-5897	86	8	.	.	PUNCT
ejpam-5897	87	1	proof	proof	NOUN
ejpam-5897	87	2	.	.	PUNCT
ejpam-5897	88	1	letting	let	VERB
ejpam-5897	88	2	x1	x1	NOUN
ejpam-5897	89	1	=	=	SYM
ejpam-5897	89	2	x2	x2	INTJ
ejpam-5897	89	3	:	:	PUNCT
ejpam-5897	89	4	=	=	SYM
ejpam-5897	89	5	x	x	X
ejpam-5897	89	6	,	,	PUNCT
ejpam-5897	89	7	y1	y1	INTJ
ejpam-5897	89	8	=	=	PUNCT
ejpam-5897	89	9	y2	y2	INTJ
ejpam-5897	89	10	:	:	PUNCT
ejpam-5897	89	11	=	=	SYM
ejpam-5897	89	12	y	y	PROPN
ejpam-5897	89	13	and	and	CCONJ
ejpam-5897	89	14	z1	z1	PROPN
ejpam-5897	89	15	=	=	SYM
ejpam-5897	89	16	z2	z2	PROPN
ejpam-5897	89	17	:	:	PUNCT
ejpam-5897	89	18	=	=	SYM
ejpam-5897	89	19	z	z	X
ejpam-5897	89	20	in	in	ADP
ejpam-5897	89	21	(	(	PUNCT
ejpam-5897	89	22	3	3	NUM
ejpam-5897	89	23	)	)	PUNCT
ejpam-5897	89	24	,	,	PUNCT
ejpam-5897	89	25	we	we	PRON
ejpam-5897	89	26	get	get	AUX
ejpam-5897	89	27	∥h(2x	∥h(2x	VERB
ejpam-5897	89	28	,	,	PUNCT
ejpam-5897	89	29	2y	2y	NUM
ejpam-5897	89	30	,	,	PUNCT
ejpam-5897	89	31	2z)−	2z)−	NUM
ejpam-5897	89	32	8h(x	8h(x	NUM
ejpam-5897	89	33	,	,	PUNCT
ejpam-5897	89	34	y	y	PROPN
ejpam-5897	89	35	,	,	PUNCT
ejpam-5897	89	36	z)∥	z)∥	NUM
ejpam-5897	89	37	≤	≤	NOUN
ejpam-5897	89	38	0	0	NUM
ejpam-5897	89	39	for	for	ADP
ejpam-5897	89	40	all	all	DET
ejpam-5897	89	41	x	x	NOUN
ejpam-5897	89	42	,	,	PUNCT
ejpam-5897	89	43	y	y	PROPN
ejpam-5897	89	44	,	,	PUNCT
ejpam-5897	89	45	z	z	PROPN
ejpam-5897	89	46	∈	∈	PROPN
ejpam-5897	89	47	x.	x.	NOUN
ejpam-5897	90	1	so	so	ADV
ejpam-5897	90	2	h(2x	h(2x	VERB
ejpam-5897	90	3	,	,	PUNCT
ejpam-5897	90	4	2y	2y	NUM
ejpam-5897	90	5	,	,	PUNCT
ejpam-5897	90	6	2z	2z	NUM
ejpam-5897	90	7	)	)	PUNCT
ejpam-5897	91	1	=	=	SYM
ejpam-5897	91	2	8h(x	8h(x	NUM
ejpam-5897	91	3	,	,	PUNCT
ejpam-5897	91	4	y	y	PROPN
ejpam-5897	91	5	,	,	PUNCT
ejpam-5897	91	6	z	z	NOUN
ejpam-5897	91	7	)	)	PUNCT
ejpam-5897	91	8	for	for	ADP
ejpam-5897	91	9	all	all	DET
ejpam-5897	91	10	x	x	NOUN
ejpam-5897	91	11	,	,	PUNCT
ejpam-5897	91	12	y	y	PROPN
ejpam-5897	91	13	,	,	PUNCT
ejpam-5897	91	14	z	z	NOUN
ejpam-5897	91	15	∈	∈	PROPN
ejpam-5897	91	16	x.	x.	NOUN
ejpam-5897	92	1	it	it	PRON
ejpam-5897	92	2	follows	follow	VERB
ejpam-5897	92	3	from	from	ADP
ejpam-5897	92	4	(	(	PUNCT
ejpam-5897	92	5	3	3	NUM
ejpam-5897	92	6	)	)	PUNCT
ejpam-5897	92	7	that∥∥∥∥∥∥8h(x1	that∥∥∥∥∥∥8h(x1	NOUN
ejpam-5897	92	8	,	,	PUNCT
ejpam-5897	92	9	y1	y1	NOUN
ejpam-5897	92	10	,	,	PUNCT
ejpam-5897	92	11	z1)−	z1)−	PROPN
ejpam-5897	92	12	2∑	2∑	NUM
ejpam-5897	92	13	i	i	NOUN
ejpam-5897	92	14	,	,	PUNCT
ejpam-5897	92	15	j	j	PROPN
ejpam-5897	92	16	,	,	PUNCT
ejpam-5897	92	17	k=1	k=1	PROPN
ejpam-5897	92	18	h(x1	h(x1	PROPN
ejpam-5897	92	19	+	+	CCONJ
ejpam-5897	92	20	(	(	PUNCT
ejpam-5897	92	21	−1)ix2	−1)ix2	ADJ
ejpam-5897	92	22	,	,	PUNCT
ejpam-5897	92	23	y1	y1	NOUN
ejpam-5897	92	24	+	+	X
ejpam-5897	92	25	(	(	PUNCT
ejpam-5897	92	26	−1)jy2	−1)jy2	PROPN
ejpam-5897	92	27	,	,	PUNCT
ejpam-5897	92	28	z1	z1	PROPN
ejpam-5897	92	29	+	+	CCONJ
ejpam-5897	92	30	(	(	PUNCT
ejpam-5897	92	31	−1)kz2	−1)kz2	PROPN
ejpam-5897	92	32	)	)	PUNCT
ejpam-5897	92	33	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-5897	93	1	≤	≤	NUM
ejpam-5897	93	2	∥∥∥∥∥∥t	∥∥∥∥∥∥t	PUNCT
ejpam-5897	94	1	8h(x1	8h(x1	ADJ
ejpam-5897	94	2	,	,	PUNCT
ejpam-5897	94	3	y1	y1	NOUN
ejpam-5897	94	4	,	,	PUNCT
ejpam-5897	94	5	z1)−	z1)−	PROPN
ejpam-5897	94	6	2∑	2∑	NUM
ejpam-5897	95	1	i	i	NOUN
ejpam-5897	95	2	,	,	PUNCT
ejpam-5897	95	3	j	j	PROPN
ejpam-5897	95	4	,	,	PUNCT
ejpam-5897	95	5	k=1	k=1	PROPN
ejpam-5897	95	6	h(x1	h(x1	PROPN
ejpam-5897	95	7	+	+	CCONJ
ejpam-5897	95	8	(	(	PUNCT
ejpam-5897	95	9	−1)ix2	−1)ix2	ADJ
ejpam-5897	95	10	,	,	PUNCT
ejpam-5897	95	11	y1	y1	NOUN
ejpam-5897	95	12	+	+	X
ejpam-5897	95	13	(	(	PUNCT
ejpam-5897	95	14	−1)jy2	−1)jy2	PROPN
ejpam-5897	95	15	,	,	PUNCT
ejpam-5897	95	16	z1	z1	PROPN
ejpam-5897	95	17	+	+	CCONJ
ejpam-5897	95	18	(	(	PUNCT
ejpam-5897	95	19	−1)kz2	−1)kz2	PROPN
ejpam-5897	95	20	)	)	PUNCT
ejpam-5897	95	21	∥∥∥∥∥∥	∥∥∥∥∥∥	VERB
ejpam-5897	96	1	for	for	ADP
ejpam-5897	96	2	all	all	DET
ejpam-5897	96	3	(	(	PUNCT
ejpam-5897	96	4	x1	x1	PROPN
ejpam-5897	96	5	,	,	PUNCT
ejpam-5897	96	6	y1	y1	PROPN
ejpam-5897	96	7	,	,	PUNCT
ejpam-5897	96	8	z1	z1	NOUN
ejpam-5897	96	9	)	)	PUNCT
ejpam-5897	96	10	,	,	PUNCT
ejpam-5897	96	11	(	(	PUNCT
ejpam-5897	96	12	x2	x2	PROPN
ejpam-5897	96	13	,	,	PUNCT
ejpam-5897	96	14	y2	y2	PROPN
ejpam-5897	96	15	,	,	PUNCT
ejpam-5897	96	16	z2	z2	PROPN
ejpam-5897	96	17	)	)	PUNCT
ejpam-5897	96	18	∈	∈	PROPN
ejpam-5897	96	19	x3	x3	PROPN
ejpam-5897	96	20	.	.	PUNCT
ejpam-5897	97	1	thus	thus	ADV
ejpam-5897	97	2	8h(x1	8h(x1	NUM
ejpam-5897	97	3	,	,	PUNCT
ejpam-5897	97	4	y1	y1	NOUN
ejpam-5897	97	5	,	,	PUNCT
ejpam-5897	97	6	z1	z1	NOUN
ejpam-5897	97	7	)	)	PUNCT
ejpam-5897	97	8	=	=	SYM
ejpam-5897	98	1	2∑	2∑	NUM
ejpam-5897	98	2	i	i	NOUN
ejpam-5897	98	3	,	,	PUNCT
ejpam-5897	98	4	j	j	PROPN
ejpam-5897	98	5	,	,	PUNCT
ejpam-5897	98	6	k=1	k=1	PROPN
ejpam-5897	98	7	h(x1	h(x1	PROPN
ejpam-5897	98	8	+	+	CCONJ
ejpam-5897	98	9	(	(	PUNCT
ejpam-5897	98	10	−1)ix2	−1)ix2	ADJ
ejpam-5897	98	11	,	,	PUNCT
ejpam-5897	98	12	y1	y1	NOUN
ejpam-5897	98	13	+	+	X
ejpam-5897	98	14	(	(	PUNCT
ejpam-5897	98	15	−1)jy2	−1)jy2	PROPN
ejpam-5897	98	16	,	,	PUNCT
ejpam-5897	98	17	z1	z1	PROPN
ejpam-5897	98	18	+	+	CCONJ
ejpam-5897	98	19	(	(	PUNCT
ejpam-5897	98	20	−1)kz2	−1)kz2	PROPN
ejpam-5897	98	21	)	)	PUNCT
ejpam-5897	98	22	for	for	ADP
ejpam-5897	98	23	all	all	DET
ejpam-5897	98	24	(	(	PUNCT
ejpam-5897	98	25	x1	x1	PROPN
ejpam-5897	98	26	,	,	PUNCT
ejpam-5897	98	27	y1	y1	PROPN
ejpam-5897	98	28	,	,	PUNCT
ejpam-5897	98	29	z1	z1	NOUN
ejpam-5897	98	30	)	)	PUNCT
ejpam-5897	98	31	,	,	PUNCT
ejpam-5897	98	32	(	(	PUNCT
ejpam-5897	98	33	x2	x2	PROPN
ejpam-5897	98	34	,	,	PUNCT
ejpam-5897	98	35	y2	y2	PROPN
ejpam-5897	98	36	,	,	PUNCT
ejpam-5897	98	37	z2	z2	PROPN
ejpam-5897	98	38	)	)	PUNCT
ejpam-5897	98	39	∈	∈	PROPN
ejpam-5897	98	40	x3	x3	PROPN
ejpam-5897	98	41	,	,	PUNCT
ejpam-5897	98	42	since	since	SCONJ
ejpam-5897	98	43	|t|	|t|	VERB
ejpam-5897	98	44	<	<	X
ejpam-5897	98	45	1	1	NUM
ejpam-5897	98	46	.	.	PUNCT
ejpam-5897	99	1	thus	thus	ADV
ejpam-5897	99	2	,	,	PUNCT
ejpam-5897	99	3	the	the	DET
ejpam-5897	99	4	mapping	mapping	NOUN
ejpam-5897	99	5	h	h	NOUN
ejpam-5897	99	6	is	be	AUX
ejpam-5897	99	7	hyper	hyper	ADJ
ejpam-5897	99	8	3	3	NUM
ejpam-5897	99	9	-	-	PUNCT
ejpam-5897	99	10	additive	additive	NOUN
ejpam-5897	99	11	.	.	PUNCT
ejpam-5897	100	1	theorem	theorem	NOUN
ejpam-5897	100	2	2	2	NUM
ejpam-5897	100	3	.	.	PUNCT
ejpam-5897	101	1	let	let	VERB
ejpam-5897	101	2	x	x	PRON
ejpam-5897	101	3	be	be	AUX
ejpam-5897	101	4	a	a	DET
ejpam-5897	101	5	complex	complex	ADJ
ejpam-5897	101	6	ternary	ternary	ADJ
ejpam-5897	101	7	algebra	algebra	NOUN
ejpam-5897	101	8	,	,	PUNCT
ejpam-5897	101	9	y	y	PROPN
ejpam-5897	101	10	be	be	VERB
ejpam-5897	101	11	a	a	DET
ejpam-5897	101	12	complex	complex	ADJ
ejpam-5897	101	13	ternary	ternary	ADJ
ejpam-5897	101	14	banach	banach	NOUN
ejpam-5897	101	15	algebra	algebra	NOUN
ejpam-5897	101	16	and	and	CCONJ
ejpam-5897	101	17	t	t	PROPN
ejpam-5897	101	18	be	be	AUX
ejpam-5897	102	1	a	a	DET
ejpam-5897	102	2	real	real	ADJ
ejpam-5897	102	3	number	number	NOUN
ejpam-5897	102	4	satisfying	satisfying	NOUN
ejpam-5897	102	5	|t|	|t|	NOUN
ejpam-5897	102	6	<	<	X
ejpam-5897	102	7	1	1	X
ejpam-5897	102	8	.	.	PUNCT
ejpam-5897	103	1	let	let	VERB
ejpam-5897	103	2	φ	φ	NOUN
ejpam-5897	103	3	:	:	PUNCT
ejpam-5897	103	4	x6	x6	PROPN
ejpam-5897	103	5	→	→	SYM
ejpam-5897	104	1	[	[	X
ejpam-5897	104	2	0,∞	0,∞	NUM
ejpam-5897	104	3	)	)	PUNCT
ejpam-5897	104	4	and	and	CCONJ
ejpam-5897	104	5	ψ	ψ	X
ejpam-5897	104	6	:	:	PUNCT
ejpam-5897	104	7	x9	x9	NOUN
ejpam-5897	104	8	→	→	PUNCT
ejpam-5897	105	1	[	[	X
ejpam-5897	105	2	0,∞	0,∞	X
ejpam-5897	105	3	)	)	PUNCT
ejpam-5897	105	4	be	be	AUX
ejpam-5897	105	5	functions	function	NOUN
ejpam-5897	105	6	such	such	ADJ
ejpam-5897	105	7	that	that	SCONJ
ejpam-5897	105	8	+	+	ADJ
ejpam-5897	105	9	∞∑	∞∑	NUM
ejpam-5897	105	10	j=1	j=1	ADJ
ejpam-5897	105	11	8jφ	8jφ	NOUN
ejpam-5897	105	12	(	(	PUNCT
ejpam-5897	105	13	x	x	SYM
ejpam-5897	105	14	2j	2j	NOUN
ejpam-5897	105	15	,	,	PUNCT
ejpam-5897	105	16	y	y	PROPN
ejpam-5897	105	17	2j	2j	NUM
ejpam-5897	105	18	,	,	PUNCT
ejpam-5897	105	19	z	z	NOUN
ejpam-5897	105	20	2j	2j	NOUN
ejpam-5897	105	21	,	,	PUNCT
ejpam-5897	105	22	x	x	X
ejpam-5897	105	23	2j	2j	NOUN
ejpam-5897	105	24	,	,	PUNCT
ejpam-5897	105	25	y	y	PROPN
ejpam-5897	105	26	2j	2j	NUM
ejpam-5897	105	27	,	,	PUNCT
ejpam-5897	105	28	z	z	NOUN
ejpam-5897	105	29	2j	2j	X
ejpam-5897	105	30	)	)	PUNCT
ejpam-5897	106	1	<	<	X
ejpam-5897	106	2	∞	∞	NUM
ejpam-5897	106	3	and	and	CCONJ
ejpam-5897	106	4	+	+	ADJ
ejpam-5897	106	5	∞∑	∞∑	ADJ
ejpam-5897	106	6	j=1	j=1	ADJ
ejpam-5897	106	7	83jψ	83jψ	NOUN
ejpam-5897	106	8	(	(	PUNCT
ejpam-5897	106	9	x	x	SYM
ejpam-5897	106	10	2j	2j	NOUN
ejpam-5897	106	11	,	,	PUNCT
ejpam-5897	106	12	x	x	X
ejpam-5897	106	13	2j	2j	NOUN
ejpam-5897	106	14	,	,	PUNCT
ejpam-5897	106	15	x	x	X
ejpam-5897	106	16	2j	2j	NOUN
ejpam-5897	106	17	,	,	PUNCT
ejpam-5897	106	18	y	y	PROPN
ejpam-5897	106	19	2j	2j	NOUN
ejpam-5897	106	20	,	,	PUNCT
ejpam-5897	106	21	y	y	PROPN
ejpam-5897	106	22	2j	2j	NOUN
ejpam-5897	106	23	,	,	PUNCT
ejpam-5897	106	24	y	y	PROPN
ejpam-5897	106	25	2j	2j	NUM
ejpam-5897	106	26	,	,	PUNCT
ejpam-5897	106	27	z	z	NOUN
ejpam-5897	106	28	2j	2j	NOUN
ejpam-5897	106	29	,	,	PUNCT
ejpam-5897	106	30	z	z	NOUN
ejpam-5897	106	31	2j	2j	NOUN
ejpam-5897	106	32	,	,	PUNCT
ejpam-5897	106	33	z	z	NOUN
ejpam-5897	106	34	2j	2j	NOUN
ejpam-5897	106	35	)	)	PUNCT
ejpam-5897	106	36	<	<	X
ejpam-5897	106	37	∞	∞	PROPN
ejpam-5897	106	38	e.	e.	PROPN
ejpam-5897	106	39	shim	shim	PROPN
ejpam-5897	106	40	,	,	PUNCT
ejpam-5897	106	41	s.	s.	PROPN
ejpam-5897	106	42	donganont	donganont	PROPN
ejpam-5897	106	43	,	,	PUNCT
ejpam-5897	106	44	c.	c.	PROPN
ejpam-5897	106	45	park	park	PROPN
ejpam-5897	106	46	/	/	SYM
ejpam-5897	106	47	eur	eur	PROPN
ejpam-5897	106	48	.	.	PUNCT
ejpam-5897	107	1	j.	j.	PROPN
ejpam-5897	107	2	pure	pure	PROPN
ejpam-5897	107	3	appl	appl	PROPN
ejpam-5897	107	4	.	.	PROPN
ejpam-5897	107	5	math	math	PROPN
ejpam-5897	107	6	,	,	PUNCT
ejpam-5897	107	7	18	18	NUM
ejpam-5897	107	8	(	(	PUNCT
ejpam-5897	107	9	2	2	NUM
ejpam-5897	107	10	)	)	PUNCT
ejpam-5897	107	11	(	(	PUNCT
ejpam-5897	107	12	2025	2025	NUM
ejpam-5897	107	13	)	)	PUNCT
ejpam-5897	107	14	,	,	PUNCT
ejpam-5897	107	15	5897	5897	NUM
ejpam-5897	107	16	5	5	NUM
ejpam-5897	107	17	of	of	ADP
ejpam-5897	107	18	14	14	NUM
ejpam-5897	107	19	for	for	ADP
ejpam-5897	107	20	all	all	DET
ejpam-5897	107	21	x	x	NOUN
ejpam-5897	107	22	,	,	PUNCT
ejpam-5897	107	23	y	y	PROPN
ejpam-5897	107	24	,	,	PUNCT
ejpam-5897	107	25	z	z	PROPN
ejpam-5897	107	26	∈	∈	PROPN
ejpam-5897	107	27	x.	x.	NOUN
ejpam-5897	107	28	assume	assume	VERB
ejpam-5897	107	29	that	that	SCONJ
ejpam-5897	107	30	a	a	DET
ejpam-5897	107	31	mapping	mapping	NOUN
ejpam-5897	107	32	h	h	NOUN
ejpam-5897	107	33	:	:	PUNCT
ejpam-5897	107	34	x3	x3	ADJ
ejpam-5897	107	35	→	→	SYM
ejpam-5897	107	36	y	y	PROPN
ejpam-5897	107	37	satisfies	satisfy	VERB
ejpam-5897	107	38	h(0	h(0	PROPN
ejpam-5897	107	39	,	,	PUNCT
ejpam-5897	107	40	a	a	DET
ejpam-5897	107	41	,	,	PUNCT
ejpam-5897	107	42	b	b	NOUN
ejpam-5897	107	43	)	)	PUNCT
ejpam-5897	107	44	=	=	SYM
ejpam-5897	107	45	h(a	h(a	PROPN
ejpam-5897	107	46	,	,	PUNCT
ejpam-5897	107	47	0	0	NUM
ejpam-5897	107	48	,	,	PUNCT
ejpam-5897	107	49	b	b	NOUN
ejpam-5897	107	50	)	)	PUNCT
ejpam-5897	107	51	=	=	SYM
ejpam-5897	107	52	h(a	h(a	PROPN
ejpam-5897	107	53	,	,	PUNCT
ejpam-5897	107	54	b	b	NOUN
ejpam-5897	107	55	,	,	PUNCT
ejpam-5897	107	56	0	0	NUM
ejpam-5897	107	57	)	)	PUNCT
ejpam-5897	107	58	=	=	SYM
ejpam-5897	107	59	0	0	NUM
ejpam-5897	107	60	and	and	CCONJ
ejpam-5897	107	61	∥∥∥∥∥∥8µh(x1	∥∥∥∥∥∥8µh(x1	PROPN
ejpam-5897	107	62	,	,	PUNCT
ejpam-5897	107	63	y1	y1	NOUN
ejpam-5897	107	64	,	,	PUNCT
ejpam-5897	107	65	z1)−	z1)−	PROPN
ejpam-5897	107	66	2∑	2∑	NUM
ejpam-5897	107	67	i	i	NOUN
ejpam-5897	107	68	,	,	PUNCT
ejpam-5897	107	69	j	j	PROPN
ejpam-5897	107	70	,	,	PUNCT
ejpam-5897	107	71	k=1	k=1	PROPN
ejpam-5897	107	72	h(µ(x1	h(µ(x1	PROPN
ejpam-5897	107	73	+	+	CCONJ
ejpam-5897	107	74	(	(	PUNCT
ejpam-5897	107	75	−1)ix2	−1)ix2	ADJ
ejpam-5897	107	76	)	)	PUNCT
ejpam-5897	107	77	,	,	PUNCT
ejpam-5897	107	78	µ(y1	µ(y1	VERB
ejpam-5897	107	79	+	+	CCONJ
ejpam-5897	107	80	(	(	PUNCT
ejpam-5897	107	81	−1)jy2	−1)jy2	PROPN
ejpam-5897	107	82	)	)	PUNCT
ejpam-5897	107	83	,	,	PUNCT
ejpam-5897	107	84	µ(z1	µ(z1	NOUN
ejpam-5897	107	85	+	+	CCONJ
ejpam-5897	107	86	(	(	PUNCT
ejpam-5897	107	87	−1)kz2	−1)kz2	PROPN
ejpam-5897	107	88	)	)	PUNCT
ejpam-5897	107	89	)	)	PUNCT
ejpam-5897	107	90	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-5897	108	1	(	(	PUNCT
ejpam-5897	108	2	4	4	X
ejpam-5897	108	3	)	)	PUNCT
ejpam-5897	108	4	≤	≤	NOUN
ejpam-5897	108	5	∥∥∥∥∥∥t	∥∥∥∥∥∥t	PUNCT
ejpam-5897	109	1	8µh(x1	8µh(x1	PROPN
ejpam-5897	109	2	,	,	PUNCT
ejpam-5897	109	3	y1	y1	NOUN
ejpam-5897	109	4	,	,	PUNCT
ejpam-5897	109	5	z1)−	z1)−	PROPN
ejpam-5897	109	6	2∑	2∑	NUM
ejpam-5897	110	1	i	i	NOUN
ejpam-5897	110	2	,	,	PUNCT
ejpam-5897	110	3	j	j	PROPN
ejpam-5897	110	4	,	,	PUNCT
ejpam-5897	110	5	k=1	k=1	PROPN
ejpam-5897	110	6	h	h	PROPN
ejpam-5897	110	7	(	(	PUNCT
ejpam-5897	110	8	µ	µ	PROPN
ejpam-5897	110	9	x1	x1	NOUN
ejpam-5897	110	10	+	+	CCONJ
ejpam-5897	110	11	(	(	PUNCT
ejpam-5897	110	12	−1)ix2	−1)ix2	ADJ
ejpam-5897	110	13	2	2	NUM
ejpam-5897	110	14	,	,	PUNCT
ejpam-5897	110	15	µ	µ	X
ejpam-5897	110	16	y1	y1	NOUN
ejpam-5897	110	17	+	+	X
ejpam-5897	110	18	(	(	PUNCT
ejpam-5897	110	19	−1)jy2	−1)jy2	PROPN
ejpam-5897	110	20	2	2	NUM
ejpam-5897	110	21	,	,	PUNCT
ejpam-5897	110	22	µ	µ	NOUN
ejpam-5897	110	23	z1	z1	NOUN
ejpam-5897	110	24	+	+	CCONJ
ejpam-5897	110	25	(	(	PUNCT
ejpam-5897	110	26	−1)kz2	−1)kz2	PRON
ejpam-5897	110	27	2	2	NUM
ejpam-5897	110	28	)	)	PUNCT
ejpam-5897	110	29	∥∥∥∥∥∥	∥∥∥∥∥∥	PUNCT
ejpam-5897	111	1	+	+	NOUN
ejpam-5897	111	2	φ(x1	φ(x1	ADJ
ejpam-5897	111	3	,	,	PUNCT
ejpam-5897	111	4	y1	y1	NOUN
ejpam-5897	111	5	,	,	PUNCT
ejpam-5897	111	6	z1	z1	NOUN
ejpam-5897	111	7	,	,	PUNCT
ejpam-5897	111	8	x2	x2	PROPN
ejpam-5897	111	9	,	,	PUNCT
ejpam-5897	111	10	y2	y2	PROPN
ejpam-5897	111	11	,	,	PUNCT
ejpam-5897	111	12	z2	z2	PROPN
ejpam-5897	111	13	)	)	PUNCT
ejpam-5897	111	14	for	for	ADP
ejpam-5897	111	15	all	all	DET
ejpam-5897	111	16	a	a	PRON
ejpam-5897	111	17	,	,	PUNCT
ejpam-5897	111	18	b	b	X
ejpam-5897	111	19	∈	∈	PROPN
ejpam-5897	111	20	x	x	X
ejpam-5897	111	21	and	and	CCONJ
ejpam-5897	111	22	all	all	PRON
ejpam-5897	111	23	(	(	PUNCT
ejpam-5897	111	24	x1	x1	PROPN
ejpam-5897	111	25	,	,	PUNCT
ejpam-5897	111	26	y1	y1	PROPN
ejpam-5897	111	27	,	,	PUNCT
ejpam-5897	111	28	z1	z1	NOUN
ejpam-5897	111	29	)	)	PUNCT
ejpam-5897	111	30	,	,	PUNCT
ejpam-5897	111	31	(	(	PUNCT
ejpam-5897	111	32	x2	x2	PROPN
ejpam-5897	111	33	,	,	PUNCT
ejpam-5897	111	34	y2	y2	PROPN
ejpam-5897	111	35	,	,	PUNCT
ejpam-5897	111	36	z2	z2	PROPN
ejpam-5897	111	37	)	)	PUNCT
ejpam-5897	111	38	∈	∈	PROPN
ejpam-5897	111	39	x3	x3	NOUN
ejpam-5897	111	40	and	and	CCONJ
ejpam-5897	111	41	all	all	DET
ejpam-5897	111	42	µ	µ	PRON
ejpam-5897	111	43	∈	∈	NOUN
ejpam-5897	111	44	t1	t1	NOUN
ejpam-5897	111	45	.	.	PUNCT
ejpam-5897	112	1	let	let	VERB
ejpam-5897	112	2	h	h	NOUN
ejpam-5897	112	3	:	:	PUNCT
ejpam-5897	112	4	x3	x3	VERB
ejpam-5897	112	5	→	→	SYM
ejpam-5897	112	6	x	x	PART
ejpam-5897	112	7	satisfy	satisfy	VERB
ejpam-5897	112	8	∥h([x1	∥h([x1	PRON
ejpam-5897	112	9	,	,	PUNCT
ejpam-5897	112	10	y1	y1	NOUN
ejpam-5897	112	11	,	,	PUNCT
ejpam-5897	112	12	z1	z1	NOUN
ejpam-5897	112	13	]	]	PUNCT
ejpam-5897	112	14	,	,	PUNCT
ejpam-5897	113	1	[	[	X
ejpam-5897	113	2	x2	x2	X
ejpam-5897	113	3	,	,	PUNCT
ejpam-5897	113	4	y2	y2	PROPN
ejpam-5897	113	5	,	,	PUNCT
ejpam-5897	113	6	z2	z2	PROPN
ejpam-5897	113	7	]	]	PUNCT
ejpam-5897	113	8	,	,	PUNCT
ejpam-5897	113	9	[	[	X
ejpam-5897	113	10	x3	x3	ADJ
ejpam-5897	113	11	,	,	PUNCT
ejpam-5897	113	12	y3	y3	NOUN
ejpam-5897	113	13	,	,	PUNCT
ejpam-5897	113	14	z3])−	z3])−	X
ejpam-5897	114	1	[	[	X
ejpam-5897	114	2	h(x1	h(x1	X
ejpam-5897	114	3	,	,	PUNCT
ejpam-5897	114	4	x2	x2	PROPN
ejpam-5897	114	5	,	,	PUNCT
ejpam-5897	114	6	x3	x3	ADJ
ejpam-5897	114	7	)	)	PUNCT
ejpam-5897	114	8	,	,	PUNCT
ejpam-5897	114	9	h(y1	h(y1	NOUN
ejpam-5897	114	10	,	,	PUNCT
ejpam-5897	114	11	y2	y2	PROPN
ejpam-5897	114	12	,	,	PUNCT
ejpam-5897	114	13	y3	y3	PROPN
ejpam-5897	114	14	)	)	PUNCT
ejpam-5897	114	15	,	,	PUNCT
ejpam-5897	114	16	h(z1	h(z1	NOUN
ejpam-5897	114	17	,	,	PUNCT
ejpam-5897	114	18	z2	z2	PROPN
ejpam-5897	114	19	,	,	PUNCT
ejpam-5897	114	20	x3)]∥	x3)]∥	NOUN
ejpam-5897	114	21	(	(	PUNCT
ejpam-5897	114	22	5	5	NUM
ejpam-5897	114	23	)	)	PUNCT
ejpam-5897	114	24	≤	≤	NOUN
ejpam-5897	114	25	ψ(x1	ψ(x1	NOUN
ejpam-5897	114	26	,	,	PUNCT
ejpam-5897	114	27	x2	x2	PROPN
ejpam-5897	114	28	,	,	PUNCT
ejpam-5897	114	29	x3	x3	ADJ
ejpam-5897	114	30	,	,	PUNCT
ejpam-5897	114	31	y1	y1	NOUN
ejpam-5897	114	32	,	,	PUNCT
ejpam-5897	114	33	y2	y2	PROPN
ejpam-5897	114	34	,	,	PUNCT
ejpam-5897	114	35	y3	y3	PROPN
ejpam-5897	114	36	,	,	PUNCT
ejpam-5897	114	37	z1	z1	PROPN
ejpam-5897	114	38	,	,	PUNCT
ejpam-5897	114	39	z2	z2	PROPN
ejpam-5897	114	40	,	,	PUNCT
ejpam-5897	114	41	z3	z3	PROPN
ejpam-5897	114	42	)	)	PUNCT
ejpam-5897	114	43	for	for	ADP
ejpam-5897	114	44	all	all	PRON
ejpam-5897	114	45	x1	x1	PROPN
ejpam-5897	114	46	,	,	PUNCT
ejpam-5897	114	47	x2	x2	PROPN
ejpam-5897	114	48	,	,	PUNCT
ejpam-5897	114	49	x3	x3	ADJ
ejpam-5897	114	50	,	,	PUNCT
ejpam-5897	114	51	y1	y1	NOUN
ejpam-5897	114	52	,	,	PUNCT
ejpam-5897	114	53	y2	y2	PROPN
ejpam-5897	114	54	,	,	PUNCT
ejpam-5897	114	55	y3	y3	PROPN
ejpam-5897	114	56	,	,	PUNCT
ejpam-5897	114	57	z1	z1	PROPN
ejpam-5897	114	58	,	,	PUNCT
ejpam-5897	114	59	z2	z2	PROPN
ejpam-5897	114	60	,	,	PUNCT
ejpam-5897	114	61	z3	z3	PROPN
ejpam-5897	114	62	∈	∈	PROPN
ejpam-5897	114	63	x.	x.	NOUN
ejpam-5897	114	64	then	then	ADV
ejpam-5897	114	65	there	there	PRON
ejpam-5897	114	66	exists	exist	VERB
ejpam-5897	114	67	a	a	DET
ejpam-5897	114	68	unique	unique	ADJ
ejpam-5897	114	69	hyper	hyper	ADJ
ejpam-5897	114	70	3	3	NUM
ejpam-5897	114	71	-	-	NUM
ejpam-5897	114	72	homomorphism	homomorphism	NOUN
ejpam-5897	114	73	h	h	NOUN
ejpam-5897	114	74	:	:	PUNCT
ejpam-5897	114	75	x3	x3	VERB
ejpam-5897	114	76	→	→	SYM
ejpam-5897	114	77	y	y	PROPN
ejpam-5897	114	78	such	such	ADJ
ejpam-5897	114	79	that	that	SCONJ
ejpam-5897	114	80	∥h(x	∥h(x	PROPN
ejpam-5897	114	81	,	,	PUNCT
ejpam-5897	114	82	y	y	PROPN
ejpam-5897	114	83	,	,	PUNCT
ejpam-5897	114	84	z)−h(x	z)−h(x	NUM
ejpam-5897	114	85	,	,	PUNCT
ejpam-5897	114	86	y	y	PROPN
ejpam-5897	114	87	,	,	PUNCT
ejpam-5897	114	88	z)∥	z)∥	NUM
ejpam-5897	114	89	≤	≤	NOUN
ejpam-5897	115	1	+	+	ADP
ejpam-5897	115	2	∞∑	∞∑	NUM
ejpam-5897	115	3	j=0	j=0	ADJ
ejpam-5897	115	4	8jφ	8jφ	NOUN
ejpam-5897	115	5	(	(	PUNCT
ejpam-5897	115	6	x	x	SYM
ejpam-5897	115	7	2j+1	2j+1	NOUN
ejpam-5897	115	8	,	,	PUNCT
ejpam-5897	115	9	y	y	PROPN
ejpam-5897	115	10	2j+1	2j+1	PROPN
ejpam-5897	115	11	,	,	PUNCT
ejpam-5897	115	12	z	z	NOUN
ejpam-5897	115	13	2j+1	2j+1	NOUN
ejpam-5897	115	14	,	,	PUNCT
ejpam-5897	115	15	x	x	SYM
ejpam-5897	115	16	2j+1	2j+1	NOUN
ejpam-5897	115	17	,	,	PUNCT
ejpam-5897	115	18	y	y	PROPN
ejpam-5897	115	19	2j+1	2j+1	PROPN
ejpam-5897	115	20	,	,	PUNCT
ejpam-5897	115	21	z	z	NOUN
ejpam-5897	115	22	2j+1	2j+1	NOUN
ejpam-5897	115	23	)	)	PUNCT
ejpam-5897	115	24	(	(	PUNCT
ejpam-5897	115	25	6	6	NUM
ejpam-5897	115	26	)	)	PUNCT
ejpam-5897	115	27	for	for	ADP
ejpam-5897	115	28	all	all	DET
ejpam-5897	115	29	x	x	NOUN
ejpam-5897	115	30	,	,	PUNCT
ejpam-5897	115	31	y	y	PROPN
ejpam-5897	115	32	,	,	PUNCT
ejpam-5897	115	33	z	z	NOUN
ejpam-5897	115	34	∈	∈	NOUN
ejpam-5897	115	35	x.	x.	NOUN
ejpam-5897	115	36	proof	proof	NOUN
ejpam-5897	115	37	.	.	PUNCT
ejpam-5897	116	1	letting	let	VERB
ejpam-5897	116	2	µ	µ	X
ejpam-5897	116	3	=	=	SYM
ejpam-5897	116	4	1	1	NUM
ejpam-5897	116	5	,	,	PUNCT
ejpam-5897	116	6	x1	x1	PROPN
ejpam-5897	117	1	=	=	SYM
ejpam-5897	117	2	x2	x2	INTJ
ejpam-5897	117	3	:	:	PUNCT
ejpam-5897	117	4	=	=	SYM
ejpam-5897	117	5	x	x	X
ejpam-5897	117	6	,	,	PUNCT
ejpam-5897	117	7	y1	y1	INTJ
ejpam-5897	117	8	=	=	PUNCT
ejpam-5897	117	9	y2	y2	INTJ
ejpam-5897	117	10	:	:	PUNCT
ejpam-5897	117	11	=	=	SYM
ejpam-5897	117	12	y	y	PROPN
ejpam-5897	117	13	and	and	CCONJ
ejpam-5897	117	14	z1	z1	PROPN
ejpam-5897	117	15	=	=	SYM
ejpam-5897	117	16	z2	z2	PROPN
ejpam-5897	117	17	:	:	PUNCT
ejpam-5897	117	18	=	=	SYM
ejpam-5897	117	19	z	z	X
ejpam-5897	117	20	in	in	ADP
ejpam-5897	117	21	(	(	PUNCT
ejpam-5897	117	22	4	4	NUM
ejpam-5897	117	23	)	)	PUNCT
ejpam-5897	117	24	,	,	PUNCT
ejpam-5897	117	25	we	we	PRON
ejpam-5897	117	26	get	get	AUX
ejpam-5897	117	27	∥h(2x	∥h(2x	VERB
ejpam-5897	117	28	,	,	PUNCT
ejpam-5897	117	29	2y	2y	NUM
ejpam-5897	117	30	,	,	PUNCT
ejpam-5897	117	31	2z)−	2z)−	NUM
ejpam-5897	117	32	8h(x	8h(x	NUM
ejpam-5897	117	33	,	,	PUNCT
ejpam-5897	117	34	y	y	PROPN
ejpam-5897	117	35	,	,	PUNCT
ejpam-5897	117	36	z)∥	z)∥	NUM
ejpam-5897	117	37	≤	≤	NUM
ejpam-5897	117	38	φ(x	φ(x	NOUN
ejpam-5897	117	39	,	,	PUNCT
ejpam-5897	117	40	y	y	PROPN
ejpam-5897	117	41	,	,	PUNCT
ejpam-5897	117	42	z	z	PROPN
ejpam-5897	117	43	,	,	PUNCT
ejpam-5897	117	44	x	x	PROPN
ejpam-5897	117	45	,	,	PUNCT
ejpam-5897	117	46	y	y	PROPN
ejpam-5897	117	47	,	,	PUNCT
ejpam-5897	117	48	z	z	NOUN
ejpam-5897	117	49	)	)	PUNCT
ejpam-5897	117	50	and	and	CCONJ
ejpam-5897	117	51	so	so	ADV
ejpam-5897	117	52	∥∥∥h(x	∥∥∥h(x	PROPN
ejpam-5897	117	53	,	,	PUNCT
ejpam-5897	117	54	y	y	PROPN
ejpam-5897	117	55	,	,	PUNCT
ejpam-5897	117	56	z)−	z)−	PROPN
ejpam-5897	117	57	8h	8h	NUM
ejpam-5897	117	58	(	(	PUNCT
ejpam-5897	117	59	x	x	SYM
ejpam-5897	117	60	2	2	NUM
ejpam-5897	117	61	,	,	PUNCT
ejpam-5897	117	62	y	y	PROPN
ejpam-5897	117	63	2	2	NUM
ejpam-5897	117	64	,	,	PUNCT
ejpam-5897	117	65	z	z	NOUN
ejpam-5897	117	66	2	2	NUM
ejpam-5897	117	67	)	)	PUNCT
ejpam-5897	117	68	∥∥∥	∥∥∥	PROPN
ejpam-5897	118	1	≤	≤	NUM
ejpam-5897	118	2	φ	φ	PROPN
ejpam-5897	118	3	(	(	PUNCT
ejpam-5897	118	4	x	x	PROPN
ejpam-5897	118	5	2	2	NUM
ejpam-5897	118	6	,	,	PUNCT
ejpam-5897	118	7	y	y	PROPN
ejpam-5897	118	8	2	2	NUM
ejpam-5897	118	9	,	,	PUNCT
ejpam-5897	118	10	z	z	NOUN
ejpam-5897	118	11	2	2	NUM
ejpam-5897	118	12	,	,	PUNCT
ejpam-5897	118	13	x	x	PROPN
ejpam-5897	118	14	2	2	NUM
ejpam-5897	118	15	,	,	PUNCT
ejpam-5897	118	16	y	y	PROPN
ejpam-5897	118	17	2	2	NUM
ejpam-5897	118	18	,	,	PUNCT
ejpam-5897	118	19	z	z	NOUN
ejpam-5897	118	20	2	2	NUM
ejpam-5897	118	21	)	)	PUNCT
ejpam-5897	118	22	for	for	ADP
ejpam-5897	118	23	all	all	DET
ejpam-5897	118	24	x	x	NOUN
ejpam-5897	118	25	,	,	PUNCT
ejpam-5897	118	26	y	y	PROPN
ejpam-5897	118	27	,	,	PUNCT
ejpam-5897	118	28	z	z	PROPN
ejpam-5897	118	29	∈	∈	NOUN
ejpam-5897	118	30	x.	x.	PUNCT
ejpam-5897	119	1	hence∥∥∥8lh	hence∥∥∥8lh	PROPN
ejpam-5897	119	2	(	(	PUNCT
ejpam-5897	119	3	x	x	NOUN
ejpam-5897	119	4	2l	2l	NUM
ejpam-5897	119	5	,	,	PUNCT
ejpam-5897	119	6	y	y	PROPN
ejpam-5897	119	7	2l	2l	NUM
ejpam-5897	119	8	,	,	PUNCT
ejpam-5897	119	9	z	z	NOUN
ejpam-5897	119	10	2l	2l	NUM
ejpam-5897	119	11	)	)	PUNCT
ejpam-5897	119	12	−	−	PROPN
ejpam-5897	119	13	8l+kh	8l+kh	NUM
ejpam-5897	119	14	(	(	PUNCT
ejpam-5897	119	15	x	x	NOUN
ejpam-5897	119	16	2l+k	2l+k	NUM
ejpam-5897	119	17	,	,	PUNCT
ejpam-5897	119	18	y	y	PROPN
ejpam-5897	119	19	2l+k	2l+k	NUM
ejpam-5897	119	20	,	,	PUNCT
ejpam-5897	119	21	z	z	NOUN
ejpam-5897	119	22	2l+k	2l+k	NUM
ejpam-5897	119	23	)	)	PUNCT
ejpam-5897	119	24	∥∥∥	∥∥∥	PROPN
ejpam-5897	119	25	(	(	PUNCT
ejpam-5897	119	26	7	7	NUM
ejpam-5897	119	27	)	)	PUNCT
ejpam-5897	119	28	≤	≤	NOUN
ejpam-5897	119	29	k−1∑	k−1∑	AUX
ejpam-5897	119	30	j=0	j=0	PROPN
ejpam-5897	119	31	∥∥∥8l+jh	∥∥∥8l+jh	NOUN
ejpam-5897	120	1	(	(	PUNCT
ejpam-5897	120	2	x	x	PROPN
ejpam-5897	120	3	2l+j	2l+j	NUM
ejpam-5897	120	4	,	,	PUNCT
ejpam-5897	120	5	y	y	PROPN
ejpam-5897	120	6	2l+j	2l+j	NUM
ejpam-5897	120	7	,	,	PUNCT
ejpam-5897	120	8	z	z	NOUN
ejpam-5897	120	9	2l+j	2l+j	NUM
ejpam-5897	120	10	)	)	PUNCT
ejpam-5897	121	1	−	−	PROPN
ejpam-5897	122	1	8l+(j+1)h	8l+(j+1)h	NOUN
ejpam-5897	122	2	(	(	PUNCT
ejpam-5897	122	3	x	x	PROPN
ejpam-5897	122	4	2l+j+1	2l+j+1	NUM
ejpam-5897	122	5	,	,	PUNCT
ejpam-5897	122	6	y	y	PROPN
ejpam-5897	122	7	2l+j+1	2l+j+1	NUM
ejpam-5897	122	8	,	,	PUNCT
ejpam-5897	122	9	z	z	NOUN
ejpam-5897	122	10	2l+j+1	2l+j+1	NUM
ejpam-5897	122	11	)	)	PUNCT
ejpam-5897	122	12	∥∥∥	∥∥∥	PROPN
ejpam-5897	122	13	=	=	SYM
ejpam-5897	122	14	k−1∑	k−1∑	PROPN
ejpam-5897	122	15	j=0	j=0	PROPN
ejpam-5897	122	16	8l+j	8l+j	NUM
ejpam-5897	122	17	∥∥∥h	∥∥∥h	ADJ
ejpam-5897	122	18	(	(	PUNCT
ejpam-5897	122	19	x	x	PROPN
ejpam-5897	122	20	2l+j	2l+j	NUM
ejpam-5897	122	21	,	,	PUNCT
ejpam-5897	122	22	y	y	PROPN
ejpam-5897	122	23	2l+j	2l+j	NUM
ejpam-5897	122	24	,	,	PUNCT
ejpam-5897	122	25	z	z	NOUN
ejpam-5897	122	26	2l+j	2l+j	NUM
ejpam-5897	122	27	)	)	PUNCT
ejpam-5897	123	1	−	−	PROPN
ejpam-5897	123	2	8h	8h	NUM
ejpam-5897	123	3	(	(	PUNCT
ejpam-5897	123	4	x	x	SYM
ejpam-5897	123	5	2l+j+1	2l+j+1	NUM
ejpam-5897	123	6	,	,	PUNCT
ejpam-5897	123	7	y	y	PROPN
ejpam-5897	123	8	2l+j+1	2l+j+1	NUM
ejpam-5897	123	9	,	,	PUNCT
ejpam-5897	123	10	z	z	NOUN
ejpam-5897	123	11	2l+j+1	2l+j+1	NUM
ejpam-5897	123	12	)	)	PUNCT
ejpam-5897	123	13	∥∥∥	∥∥∥	PROPN
ejpam-5897	123	14	e.	e.	PROPN
ejpam-5897	123	15	shim	shim	PROPN
ejpam-5897	123	16	,	,	PUNCT
ejpam-5897	123	17	s.	s.	PROPN
ejpam-5897	123	18	donganont	donganont	PROPN
ejpam-5897	123	19	,	,	PUNCT
ejpam-5897	123	20	c.	c.	PROPN
ejpam-5897	123	21	park	park	PROPN
ejpam-5897	123	22	/	/	SYM
ejpam-5897	123	23	eur	eur	PROPN
ejpam-5897	123	24	.	.	PUNCT
ejpam-5897	124	1	j.	j.	PROPN
ejpam-5897	124	2	pure	pure	PROPN
ejpam-5897	124	3	appl	appl	PROPN
ejpam-5897	124	4	.	.	PROPN
ejpam-5897	124	5	math	math	PROPN
ejpam-5897	124	6	,	,	PUNCT
ejpam-5897	124	7	18	18	NUM
ejpam-5897	124	8	(	(	PUNCT
ejpam-5897	124	9	2	2	NUM
ejpam-5897	124	10	)	)	PUNCT
ejpam-5897	124	11	(	(	PUNCT
ejpam-5897	124	12	2025	2025	NUM
ejpam-5897	124	13	)	)	PUNCT
ejpam-5897	124	14	,	,	PUNCT
ejpam-5897	124	15	5897	5897	NUM
ejpam-5897	124	16	6	6	NUM
ejpam-5897	124	17	of	of	ADP
ejpam-5897	124	18	14	14	NUM
ejpam-5897	124	19	≤	≤	NUM
ejpam-5897	124	20	k−1∑	k−1∑	AUX
ejpam-5897	124	21	j=0	j=0	PROPN
ejpam-5897	124	22	8l+jφ	8l+jφ	NUM
ejpam-5897	124	23	(	(	PUNCT
ejpam-5897	124	24	x	x	PROPN
ejpam-5897	124	25	2l+j+1	2l+j+1	NUM
ejpam-5897	124	26	,	,	PUNCT
ejpam-5897	124	27	y	y	PROPN
ejpam-5897	124	28	2l+j+1	2l+j+1	NUM
ejpam-5897	124	29	,	,	PUNCT
ejpam-5897	124	30	z	z	NOUN
ejpam-5897	124	31	2l+j+1	2l+j+1	NUM
ejpam-5897	124	32	,	,	PUNCT
ejpam-5897	124	33	x	x	PROPN
ejpam-5897	124	34	2l+j+1	2l+j+1	NUM
ejpam-5897	124	35	,	,	PUNCT
ejpam-5897	124	36	y	y	PROPN
ejpam-5897	124	37	2l+j+1	2l+j+1	NUM
ejpam-5897	124	38	,	,	PUNCT
ejpam-5897	124	39	z	z	NOUN
ejpam-5897	124	40	2l+j+1	2l+j+1	NUM
ejpam-5897	124	41	)	)	PUNCT
ejpam-5897	124	42	for	for	ADP
ejpam-5897	124	43	all	all	DET
ejpam-5897	124	44	nonnegative	nonnegative	ADJ
ejpam-5897	124	45	integers	integer	NOUN
ejpam-5897	124	46	l	l	NOUN
ejpam-5897	124	47	,	,	PUNCT
ejpam-5897	124	48	k	k	PROPN
ejpam-5897	124	49	and	and	CCONJ
ejpam-5897	124	50	all	all	DET
ejpam-5897	124	51	x	x	NOUN
ejpam-5897	124	52	,	,	PUNCT
ejpam-5897	124	53	y	y	PROPN
ejpam-5897	124	54	,	,	PUNCT
ejpam-5897	124	55	z	z	NOUN
ejpam-5897	124	56	∈	∈	PROPN
ejpam-5897	124	57	x.	x.	NOUN
ejpam-5897	125	1	it	it	PRON
ejpam-5897	125	2	follows	follow	VERB
ejpam-5897	125	3	that	that	SCONJ
ejpam-5897	125	4	{	{	PUNCT
ejpam-5897	125	5	8jh	8jh	ADJ
ejpam-5897	125	6	(	(	PUNCT
ejpam-5897	125	7	x	x	SYM
ejpam-5897	125	8	2j	2j	NOUN
ejpam-5897	125	9	,	,	PUNCT
ejpam-5897	125	10	y	y	PROPN
ejpam-5897	125	11	2j	2j	NUM
ejpam-5897	125	12	,	,	PUNCT
ejpam-5897	125	13	z	z	NOUN
ejpam-5897	125	14	2j	2j	NOUN
ejpam-5897	125	15	)	)	PUNCT
ejpam-5897	125	16	}	}	PUNCT
ejpam-5897	125	17	is	be	AUX
ejpam-5897	125	18	a	a	DET
ejpam-5897	125	19	cauchy	cauchy	ADJ
ejpam-5897	125	20	sequence	sequence	NOUN
ejpam-5897	125	21	for	for	ADP
ejpam-5897	125	22	each	each	DET
ejpam-5897	125	23	(	(	PUNCT
ejpam-5897	125	24	x	x	PROPN
ejpam-5897	125	25	,	,	PUNCT
ejpam-5897	125	26	y	y	PROPN
ejpam-5897	125	27	,	,	PUNCT
ejpam-5897	125	28	z	z	NOUN
ejpam-5897	125	29	)	)	PUNCT
ejpam-5897	125	30	∈	∈	PROPN
ejpam-5897	125	31	x3	x3	PROPN
ejpam-5897	125	32	.	.	PUNCT
ejpam-5897	126	1	since	since	SCONJ
ejpam-5897	126	2	y	y	PROPN
ejpam-5897	126	3	is	be	AUX
ejpam-5897	126	4	complete	complete	ADJ
ejpam-5897	126	5	,	,	PUNCT
ejpam-5897	126	6	{	{	PUNCT
ejpam-5897	126	7	8jh	8jh	NOUN
ejpam-5897	126	8	(	(	PUNCT
ejpam-5897	126	9	x	x	SYM
ejpam-5897	126	10	2j	2j	NOUN
ejpam-5897	126	11	,	,	PUNCT
ejpam-5897	126	12	y	y	PROPN
ejpam-5897	126	13	2j	2j	NUM
ejpam-5897	126	14	,	,	PUNCT
ejpam-5897	126	15	z	z	NOUN
ejpam-5897	126	16	2j	2j	NOUN
ejpam-5897	126	17	)	)	PUNCT
ejpam-5897	126	18	}	}	PUNCT
ejpam-5897	126	19	converges	converge	VERB
ejpam-5897	126	20	.	.	PUNCT
ejpam-5897	127	1	thus	thus	ADV
ejpam-5897	127	2	one	one	PRON
ejpam-5897	127	3	can	can	AUX
ejpam-5897	127	4	define	define	VERB
ejpam-5897	127	5	the	the	DET
ejpam-5897	127	6	mapping	mapping	NOUN
ejpam-5897	127	7	h	h	NOUN
ejpam-5897	127	8	:	:	PUNCT
ejpam-5897	127	9	x3	x3	ADJ
ejpam-5897	127	10	→	→	SYM
ejpam-5897	127	11	y	y	PROPN
ejpam-5897	127	12	by	by	ADP
ejpam-5897	127	13	h(x	h(x	PROPN
ejpam-5897	127	14	,	,	PUNCT
ejpam-5897	127	15	y	y	PROPN
ejpam-5897	127	16	,	,	PUNCT
ejpam-5897	127	17	z	z	NOUN
ejpam-5897	127	18	)	)	PUNCT
ejpam-5897	127	19	:	:	PUNCT
ejpam-5897	127	20	=	=	SYM
ejpam-5897	127	21	lim	lim	PROPN
ejpam-5897	127	22	n→+∞	n→+∞	PROPN
ejpam-5897	127	23	8nh	8nh	NOUN
ejpam-5897	127	24	(	(	PUNCT
ejpam-5897	127	25	x	x	PROPN
ejpam-5897	127	26	2n	2n	NUM
ejpam-5897	127	27	,	,	PUNCT
ejpam-5897	127	28	y	y	PROPN
ejpam-5897	127	29	2n	2n	NUM
ejpam-5897	127	30	,	,	PUNCT
ejpam-5897	127	31	z	z	NOUN
ejpam-5897	127	32	2n	2n	NUM
ejpam-5897	127	33	)	)	PUNCT
ejpam-5897	127	34	for	for	ADP
ejpam-5897	127	35	all	all	DET
ejpam-5897	127	36	(	(	PUNCT
ejpam-5897	127	37	x	x	NOUN
ejpam-5897	127	38	,	,	PUNCT
ejpam-5897	127	39	y	y	PROPN
ejpam-5897	127	40	,	,	PUNCT
ejpam-5897	127	41	z	z	NOUN
ejpam-5897	127	42	)	)	PUNCT
ejpam-5897	127	43	∈	∈	PROPN
ejpam-5897	127	44	x3	x3	PROPN
ejpam-5897	127	45	.	.	PUNCT
ejpam-5897	128	1	moreover	moreover	ADV
ejpam-5897	128	2	,	,	PUNCT
ejpam-5897	128	3	letting	let	VERB
ejpam-5897	128	4	l	l	NOUN
ejpam-5897	128	5	=	=	SYM
ejpam-5897	128	6	0	0	PUNCT
ejpam-5897	128	7	and	and	CCONJ
ejpam-5897	128	8	passing	pass	VERB
ejpam-5897	128	9	the	the	DET
ejpam-5897	128	10	limit	limit	NOUN
ejpam-5897	128	11	k	k	PROPN
ejpam-5897	128	12	→	→	SYM
ejpam-5897	128	13	∞	∞	PROPN
ejpam-5897	128	14	in	in	ADP
ejpam-5897	128	15	(	(	PUNCT
ejpam-5897	128	16	7	7	NUM
ejpam-5897	128	17	)	)	PUNCT
ejpam-5897	128	18	,	,	PUNCT
ejpam-5897	128	19	we	we	PRON
ejpam-5897	128	20	get	get	VERB
ejpam-5897	128	21	(	(	PUNCT
ejpam-5897	128	22	6	6	NUM
ejpam-5897	128	23	)	)	PUNCT
ejpam-5897	128	24	.	.	PUNCT
ejpam-5897	129	1	it	it	PRON
ejpam-5897	129	2	follows	follow	VERB
ejpam-5897	129	3	from	from	ADP
ejpam-5897	129	4	(	(	PUNCT
ejpam-5897	129	5	4	4	NUM
ejpam-5897	129	6	)	)	PUNCT
ejpam-5897	129	7	that∥∥∥∥∥∥8µh(x1	that∥∥∥∥∥∥8µh(x1	NOUN
ejpam-5897	129	8	,	,	PUNCT
ejpam-5897	129	9	y1	y1	NOUN
ejpam-5897	129	10	,	,	PUNCT
ejpam-5897	129	11	z1)−	z1)−	PROPN
ejpam-5897	129	12	2∑	2∑	NUM
ejpam-5897	129	13	i	i	NOUN
ejpam-5897	129	14	,	,	PUNCT
ejpam-5897	129	15	j	j	PROPN
ejpam-5897	129	16	,	,	PUNCT
ejpam-5897	129	17	k=1	k=1	PROPN
ejpam-5897	129	18	h(µ(x1	h(µ(x1	PROPN
ejpam-5897	129	19	+	+	CCONJ
ejpam-5897	129	20	(	(	PUNCT
ejpam-5897	129	21	−1)ix2	−1)ix2	ADJ
ejpam-5897	129	22	)	)	PUNCT
ejpam-5897	129	23	,	,	PUNCT
ejpam-5897	129	24	µ(y1	µ(y1	VERB
ejpam-5897	129	25	+	+	CCONJ
ejpam-5897	129	26	(	(	PUNCT
ejpam-5897	129	27	−1)jy2	−1)jy2	PROPN
ejpam-5897	129	28	)	)	PUNCT
ejpam-5897	129	29	,	,	PUNCT
ejpam-5897	129	30	µ(z1	µ(z1	NOUN
ejpam-5897	129	31	+	+	CCONJ
ejpam-5897	129	32	(	(	PUNCT
ejpam-5897	129	33	−1)kz2	−1)kz2	PROPN
ejpam-5897	129	34	)	)	PUNCT
ejpam-5897	129	35	)	)	PUNCT
ejpam-5897	129	36	∥∥∥∥∥∥	∥∥∥∥∥∥	PUNCT
ejpam-5897	130	1	=	=	NOUN
ejpam-5897	130	2	lim	lim	PROPN
ejpam-5897	130	3	n→+∞	n→+∞	VERB
ejpam-5897	130	4	8n	8n	NOUN
ejpam-5897	130	5	∥∥∥8µh(x1	∥∥∥8µh(x1	PROPN
ejpam-5897	130	6	2n	2n	NUM
ejpam-5897	130	7	,	,	PUNCT
ejpam-5897	130	8	y1	y1	NOUN
ejpam-5897	130	9	2n	2n	NUM
ejpam-5897	130	10	,	,	PUNCT
ejpam-5897	130	11	z1	z1	NOUN
ejpam-5897	130	12	2n	2n	NUM
ejpam-5897	130	13	)	)	PUNCT
ejpam-5897	130	14	−	−	PROPN
ejpam-5897	131	1	2∑	2∑	NUM
ejpam-5897	131	2	i	i	PROPN
ejpam-5897	131	3	,	,	PUNCT
ejpam-5897	131	4	j	j	PROPN
ejpam-5897	131	5	,	,	PUNCT
ejpam-5897	131	6	k=1	k=1	PROPN
ejpam-5897	131	7	h	h	PROPN
ejpam-5897	131	8	(	(	PUNCT
ejpam-5897	131	9	µ	µ	PROPN
ejpam-5897	131	10	x1	x1	NOUN
ejpam-5897	131	11	+	+	CCONJ
ejpam-5897	131	12	(	(	PUNCT
ejpam-5897	131	13	−1)ix2	−1)ix2	ADJ
ejpam-5897	131	14	2n	2n	NUM
ejpam-5897	131	15	,	,	PUNCT
ejpam-5897	131	16	µ	µ	X
ejpam-5897	131	17	y1	y1	NOUN
ejpam-5897	131	18	+	+	X
ejpam-5897	131	19	(	(	PUNCT
ejpam-5897	131	20	−1)jy2	−1)jy2	PROPN
ejpam-5897	131	21	2n	2n	NUM
ejpam-5897	131	22	,	,	PUNCT
ejpam-5897	131	23	µ	µ	X
ejpam-5897	131	24	z1	z1	NOUN
ejpam-5897	131	25	+	+	CCONJ
ejpam-5897	131	26	(	(	PUNCT
ejpam-5897	131	27	−1)kz2	−1)kz2	PROPN
ejpam-5897	131	28	2n	2n	NUM
ejpam-5897	131	29	)	)	PUNCT
ejpam-5897	131	30	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-5897	132	1	≤	≤	PROPN
ejpam-5897	132	2	lim	lim	PROPN
ejpam-5897	132	3	n→+∞	n→+∞	VERB
ejpam-5897	132	4	8n	8n	NOUN
ejpam-5897	132	5	∥∥∥t(8µh(x1	∥∥∥t(8µh(x1	ADJ
ejpam-5897	132	6	2n	2n	NUM
ejpam-5897	132	7	,	,	PUNCT
ejpam-5897	132	8	y1	y1	NOUN
ejpam-5897	132	9	2n	2n	NUM
ejpam-5897	132	10	,	,	PUNCT
ejpam-5897	132	11	z1	z1	NOUN
ejpam-5897	132	12	2n	2n	NUM
ejpam-5897	132	13	)	)	PUNCT
ejpam-5897	132	14	−	−	PROPN
ejpam-5897	133	1	2∑	2∑	NUM
ejpam-5897	133	2	i	i	PROPN
ejpam-5897	133	3	,	,	PUNCT
ejpam-5897	133	4	j	j	PROPN
ejpam-5897	133	5	,	,	PUNCT
ejpam-5897	133	6	k=1	k=1	PROPN
ejpam-5897	133	7	h	h	PROPN
ejpam-5897	133	8	(	(	PUNCT
ejpam-5897	133	9	µ	µ	PROPN
ejpam-5897	133	10	x1	x1	NOUN
ejpam-5897	133	11	+	+	CCONJ
ejpam-5897	133	12	(	(	PUNCT
ejpam-5897	133	13	−1)ix2	−1)ix2	ADJ
ejpam-5897	133	14	2n	2n	NUM
ejpam-5897	133	15	,	,	PUNCT
ejpam-5897	133	16	µ	µ	X
ejpam-5897	133	17	y1	y1	NOUN
ejpam-5897	133	18	+	+	X
ejpam-5897	133	19	(	(	PUNCT
ejpam-5897	133	20	−1)jy2	−1)jy2	PROPN
ejpam-5897	133	21	2n	2n	NUM
ejpam-5897	133	22	,	,	PUNCT
ejpam-5897	133	23	µ	µ	X
ejpam-5897	133	24	z1	z1	NOUN
ejpam-5897	133	25	+	+	CCONJ
ejpam-5897	133	26	(	(	PUNCT
ejpam-5897	133	27	−1)kz2	−1)kz2	NOUN
ejpam-5897	133	28	2n	2n	NUM
ejpam-5897	133	29	)	)	PUNCT
ejpam-5897	133	30	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-5897	134	1	+	+	CCONJ
ejpam-5897	134	2	lim	lim	PROPN
ejpam-5897	134	3	n→+∞	n→+∞	PROPN
ejpam-5897	134	4	8nφ	8nφ	NOUN
ejpam-5897	134	5	(	(	PUNCT
ejpam-5897	134	6	x1	x1	PROPN
ejpam-5897	134	7	2n	2n	NUM
ejpam-5897	134	8	,	,	PUNCT
ejpam-5897	134	9	y1	y1	NOUN
ejpam-5897	134	10	2n	2n	NUM
ejpam-5897	134	11	,	,	PUNCT
ejpam-5897	134	12	z1	z1	NUM
ejpam-5897	134	13	2n	2n	NUM
ejpam-5897	134	14	,	,	PUNCT
ejpam-5897	134	15	x2	x2	PROPN
ejpam-5897	134	16	2n	2n	NUM
ejpam-5897	134	17	,	,	PUNCT
ejpam-5897	134	18	y2	y2	PROPN
ejpam-5897	134	19	2n	2n	NUM
ejpam-5897	134	20	,	,	PUNCT
ejpam-5897	134	21	z2	z2	PROPN
ejpam-5897	134	22	2n	2n	NUM
ejpam-5897	134	23	)	)	PUNCT
ejpam-5897	135	1	=	=	SYM
ejpam-5897	135	2	∥t	∥t	PROPN
ejpam-5897	135	3	(	(	PUNCT
ejpam-5897	135	4	8µh(x1	8µh(x1	NUM
ejpam-5897	135	5	,	,	PUNCT
ejpam-5897	135	6	y1	y1	NOUN
ejpam-5897	135	7	,	,	PUNCT
ejpam-5897	135	8	z1	z1	NOUN
ejpam-5897	135	9	)	)	PUNCT
ejpam-5897	135	10	−	−	PROPN
ejpam-5897	135	11	2∑	2∑	NUM
ejpam-5897	136	1	i	i	PROPN
ejpam-5897	136	2	,	,	PUNCT
ejpam-5897	136	3	j	j	PROPN
ejpam-5897	136	4	,	,	PUNCT
ejpam-5897	136	5	k=1	k=1	PROPN
ejpam-5897	136	6	h(µ(x1	h(µ(x1	PROPN
ejpam-5897	136	7	+	+	CCONJ
ejpam-5897	136	8	(	(	PUNCT
ejpam-5897	136	9	−1)ix2	−1)ix2	ADJ
ejpam-5897	136	10	)	)	PUNCT
ejpam-5897	136	11	,	,	PUNCT
ejpam-5897	136	12	µ(y1	µ(y1	VERB
ejpam-5897	136	13	+	+	CCONJ
ejpam-5897	136	14	(	(	PUNCT
ejpam-5897	136	15	−1)jy2	−1)jy2	PROPN
ejpam-5897	136	16	)	)	PUNCT
ejpam-5897	136	17	,	,	PUNCT
ejpam-5897	136	18	µ(z1	µ(z1	NOUN
ejpam-5897	136	19	+	+	CCONJ
ejpam-5897	136	20	(	(	PUNCT
ejpam-5897	136	21	−1)kz2	−1)kz2	PROPN
ejpam-5897	136	22	)	)	PUNCT
ejpam-5897	136	23	)	)	PUNCT
ejpam-5897	137	1	∥∥∥∥∥∥	∥∥∥∥∥∥	VERB
ejpam-5897	137	2	for	for	ADP
ejpam-5897	137	3	all	all	DET
ejpam-5897	137	4	(	(	PUNCT
ejpam-5897	137	5	x1	x1	PROPN
ejpam-5897	137	6	,	,	PUNCT
ejpam-5897	137	7	y1	y1	PROPN
ejpam-5897	137	8	,	,	PUNCT
ejpam-5897	137	9	z1	z1	NOUN
ejpam-5897	137	10	)	)	PUNCT
ejpam-5897	137	11	,	,	PUNCT
ejpam-5897	137	12	(	(	PUNCT
ejpam-5897	137	13	x2	x2	PROPN
ejpam-5897	137	14	,	,	PUNCT
ejpam-5897	137	15	y2	y2	PROPN
ejpam-5897	137	16	,	,	PUNCT
ejpam-5897	137	17	z2	z2	PROPN
ejpam-5897	137	18	)	)	PUNCT
ejpam-5897	137	19	∈	∈	PROPN
ejpam-5897	137	20	x3	x3	NOUN
ejpam-5897	137	21	and	and	CCONJ
ejpam-5897	137	22	µ	µ	PRON
ejpam-5897	137	23	∈	∈	PROPN
ejpam-5897	137	24	t1	t1	NOUN
ejpam-5897	137	25	.	.	PUNCT
ejpam-5897	138	1	thus∥∥∥∥∥∥8µh(x1	thus∥∥∥∥∥∥8µh(x1	ADJ
ejpam-5897	138	2	,	,	PUNCT
ejpam-5897	138	3	y1	y1	NOUN
ejpam-5897	138	4	,	,	PUNCT
ejpam-5897	138	5	z1)−	z1)−	PROPN
ejpam-5897	138	6	2∑	2∑	NUM
ejpam-5897	139	1	i	i	NOUN
ejpam-5897	139	2	,	,	PUNCT
ejpam-5897	139	3	j	j	PROPN
ejpam-5897	139	4	,	,	PUNCT
ejpam-5897	139	5	k=1	k=1	PROPN
ejpam-5897	139	6	h(µ(x1	h(µ(x1	PROPN
ejpam-5897	139	7	+	+	CCONJ
ejpam-5897	139	8	(	(	PUNCT
ejpam-5897	139	9	−1)ix2	−1)ix2	ADJ
ejpam-5897	139	10	)	)	PUNCT
ejpam-5897	139	11	,	,	PUNCT
ejpam-5897	139	12	µ(y1	µ(y1	VERB
ejpam-5897	139	13	+	+	CCONJ
ejpam-5897	139	14	(	(	PUNCT
ejpam-5897	139	15	−1)jy2	−1)jy2	PROPN
ejpam-5897	139	16	)	)	PUNCT
ejpam-5897	139	17	,	,	PUNCT
ejpam-5897	139	18	µ(z1	µ(z1	NOUN
ejpam-5897	139	19	+	+	CCONJ
ejpam-5897	139	20	(	(	PUNCT
ejpam-5897	139	21	−1)kz2	−1)kz2	PROPN
ejpam-5897	139	22	)	)	PUNCT
ejpam-5897	139	23	)	)	PUNCT
ejpam-5897	139	24	∥∥∥∥∥∥	∥∥∥∥∥∥	X
ejpam-5897	140	1	≤	≤	NUM
ejpam-5897	140	2	∥t	∥t	PROPN
ejpam-5897	140	3	(	(	PUNCT
ejpam-5897	140	4	8µh(x1	8µh(x1	NUM
ejpam-5897	140	5	,	,	PUNCT
ejpam-5897	140	6	y1	y1	NOUN
ejpam-5897	140	7	,	,	PUNCT
ejpam-5897	140	8	z1	z1	PROPN
ejpam-5897	140	9	)	)	PUNCT
ejpam-5897	140	10	(	(	PUNCT
ejpam-5897	140	11	8)	8)	NUM
ejpam-5897	140	12	−	−	PROPN
ejpam-5897	140	13	2∑	2∑	NUM
ejpam-5897	141	1	i	i	PROPN
ejpam-5897	141	2	,	,	PUNCT
ejpam-5897	141	3	j	j	PROPN
ejpam-5897	141	4	,	,	PUNCT
ejpam-5897	141	5	k=1	k=1	PROPN
ejpam-5897	141	6	h(µ(x1	h(µ(x1	PROPN
ejpam-5897	141	7	+	+	CCONJ
ejpam-5897	141	8	(	(	PUNCT
ejpam-5897	141	9	−1)ix2	−1)ix2	ADJ
ejpam-5897	141	10	)	)	PUNCT
ejpam-5897	141	11	,	,	PUNCT
ejpam-5897	141	12	µ(y1	µ(y1	VERB
ejpam-5897	141	13	+	+	CCONJ
ejpam-5897	141	14	(	(	PUNCT
ejpam-5897	141	15	−1)jy2	−1)jy2	PROPN
ejpam-5897	141	16	)	)	PUNCT
ejpam-5897	141	17	,	,	PUNCT
ejpam-5897	141	18	µ(z1	µ(z1	NOUN
ejpam-5897	141	19	+	+	CCONJ
ejpam-5897	141	20	(	(	PUNCT
ejpam-5897	141	21	−1)kz2	−1)kz2	PROPN
ejpam-5897	141	22	)	)	PUNCT
ejpam-5897	141	23	)	)	PUNCT
ejpam-5897	142	1	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-5897	143	1	e.	e.	PROPN
ejpam-5897	143	2	shim	shim	PROPN
ejpam-5897	143	3	,	,	PUNCT
ejpam-5897	143	4	s.	s.	PROPN
ejpam-5897	143	5	donganont	donganont	PROPN
ejpam-5897	143	6	,	,	PUNCT
ejpam-5897	143	7	c.	c.	PROPN
ejpam-5897	143	8	park	park	PROPN
ejpam-5897	143	9	/	/	SYM
ejpam-5897	143	10	eur	eur	PROPN
ejpam-5897	143	11	.	.	PUNCT
ejpam-5897	144	1	j.	j.	PROPN
ejpam-5897	144	2	pure	pure	PROPN
ejpam-5897	144	3	appl	appl	PROPN
ejpam-5897	144	4	.	.	PROPN
ejpam-5897	144	5	math	math	PROPN
ejpam-5897	144	6	,	,	PUNCT
ejpam-5897	144	7	18	18	NUM
ejpam-5897	144	8	(	(	PUNCT
ejpam-5897	144	9	2	2	NUM
ejpam-5897	144	10	)	)	PUNCT
ejpam-5897	144	11	(	(	PUNCT
ejpam-5897	144	12	2025	2025	NUM
ejpam-5897	144	13	)	)	PUNCT
ejpam-5897	144	14	,	,	PUNCT
ejpam-5897	144	15	5897	5897	NUM
ejpam-5897	144	16	7	7	NUM
ejpam-5897	144	17	of	of	ADP
ejpam-5897	144	18	14	14	NUM
ejpam-5897	144	19	for	for	ADP
ejpam-5897	144	20	all	all	DET
ejpam-5897	144	21	(	(	PUNCT
ejpam-5897	144	22	x1	x1	PROPN
ejpam-5897	144	23	,	,	PUNCT
ejpam-5897	144	24	y1	y1	PROPN
ejpam-5897	144	25	,	,	PUNCT
ejpam-5897	144	26	z1	z1	NOUN
ejpam-5897	144	27	)	)	PUNCT
ejpam-5897	144	28	,	,	PUNCT
ejpam-5897	144	29	(	(	PUNCT
ejpam-5897	144	30	x2	x2	PROPN
ejpam-5897	144	31	,	,	PUNCT
ejpam-5897	144	32	y2	y2	PROPN
ejpam-5897	144	33	,	,	PUNCT
ejpam-5897	144	34	z2	z2	PROPN
ejpam-5897	144	35	)	)	PUNCT
ejpam-5897	144	36	∈	∈	PROPN
ejpam-5897	144	37	x3	x3	NOUN
ejpam-5897	144	38	and	and	CCONJ
ejpam-5897	144	39	µ	µ	PRON
ejpam-5897	144	40	∈	∈	NOUN
ejpam-5897	144	41	t1	t1	NOUN
ejpam-5897	144	42	.	.	PUNCT
ejpam-5897	145	1	let	let	VERB
ejpam-5897	145	2	µ	µ	X
ejpam-5897	145	3	=	=	SYM
ejpam-5897	145	4	1	1	NUM
ejpam-5897	145	5	in	in	ADP
ejpam-5897	145	6	(	(	PUNCT
ejpam-5897	145	7	8)	8)	NUM
ejpam-5897	145	8	.	.	PUNCT
ejpam-5897	145	9	by	by	ADP
ejpam-5897	145	10	theorem	theorem	NOUN
ejpam-5897	145	11	1	1	NUM
ejpam-5897	145	12	,	,	PUNCT
ejpam-5897	145	13	the	the	DET
ejpam-5897	145	14	mapping	mapping	NOUN
ejpam-5897	145	15	h	h	NOUN
ejpam-5897	145	16	:	:	PUNCT
ejpam-5897	145	17	x3	x3	ADJ
ejpam-5897	145	18	→	→	SYM
ejpam-5897	145	19	x	x	X
ejpam-5897	145	20	is	be	AUX
ejpam-5897	145	21	3	3	NUM
ejpam-5897	145	22	-	-	PUNCT
ejpam-5897	145	23	additive	additive	NOUN
ejpam-5897	145	24	.	.	PUNCT
ejpam-5897	146	1	it	it	PRON
ejpam-5897	146	2	follows	follow	VERB
ejpam-5897	146	3	from	from	ADP
ejpam-5897	146	4	(	(	PUNCT
ejpam-5897	146	5	8)	8)	NUM
ejpam-5897	146	6	and	and	CCONJ
ejpam-5897	146	7	the	the	DET
ejpam-5897	146	8	3	3	NUM
ejpam-5897	146	9	-	-	PUNCT
ejpam-5897	146	10	additivity	additivity	NOUN
ejpam-5897	146	11	of	of	ADP
ejpam-5897	146	12	h	h	NOUN
ejpam-5897	146	13	that∥∥∥∥∥∥8µh(x1	that∥∥∥∥∥∥8µh(x1	NOUN
ejpam-5897	146	14	,	,	PUNCT
ejpam-5897	146	15	y1	y1	NOUN
ejpam-5897	146	16	,	,	PUNCT
ejpam-5897	146	17	z1)−	z1)−	PROPN
ejpam-5897	146	18	2∑	2∑	NUM
ejpam-5897	146	19	i	i	NOUN
ejpam-5897	146	20	,	,	PUNCT
ejpam-5897	146	21	j	j	PROPN
ejpam-5897	146	22	,	,	PUNCT
ejpam-5897	146	23	k=1	k=1	PROPN
ejpam-5897	146	24	h(µ(x1	h(µ(x1	PROPN
ejpam-5897	146	25	+	+	CCONJ
ejpam-5897	146	26	(	(	PUNCT
ejpam-5897	146	27	−1)ix2	−1)ix2	ADJ
ejpam-5897	146	28	)	)	PUNCT
ejpam-5897	146	29	,	,	PUNCT
ejpam-5897	146	30	µ(y1	µ(y1	VERB
ejpam-5897	146	31	+	+	CCONJ
ejpam-5897	146	32	(	(	PUNCT
ejpam-5897	146	33	−1)jy2	−1)jy2	PROPN
ejpam-5897	146	34	)	)	PUNCT
ejpam-5897	146	35	,	,	PUNCT
ejpam-5897	146	36	µ(z1	µ(z1	NOUN
ejpam-5897	146	37	+	+	CCONJ
ejpam-5897	146	38	(	(	PUNCT
ejpam-5897	146	39	−1)kz2	−1)kz2	PROPN
ejpam-5897	146	40	)	)	PUNCT
ejpam-5897	146	41	)	)	PUNCT
ejpam-5897	146	42	∥∥∥∥∥∥	∥∥∥∥∥∥	X
ejpam-5897	147	1	≤	≤	NUM
ejpam-5897	147	2	∥t	∥t	PROPN
ejpam-5897	147	3	(	(	PUNCT
ejpam-5897	147	4	8µh(x1	8µh(x1	NUM
ejpam-5897	147	5	,	,	PUNCT
ejpam-5897	147	6	y1	y1	NOUN
ejpam-5897	147	7	,	,	PUNCT
ejpam-5897	147	8	z1	z1	NOUN
ejpam-5897	147	9	)	)	PUNCT
ejpam-5897	147	10	−	−	PROPN
ejpam-5897	147	11	2∑	2∑	NUM
ejpam-5897	148	1	i	i	PROPN
ejpam-5897	148	2	,	,	PUNCT
ejpam-5897	148	3	j	j	PROPN
ejpam-5897	148	4	,	,	PUNCT
ejpam-5897	148	5	k=1	k=1	PROPN
ejpam-5897	148	6	h(µ(x1	h(µ(x1	PROPN
ejpam-5897	148	7	+	+	CCONJ
ejpam-5897	148	8	(	(	PUNCT
ejpam-5897	148	9	−1)ix2	−1)ix2	ADJ
ejpam-5897	148	10	)	)	PUNCT
ejpam-5897	148	11	,	,	PUNCT
ejpam-5897	148	12	µ(y1	µ(y1	VERB
ejpam-5897	148	13	+	+	CCONJ
ejpam-5897	148	14	(	(	PUNCT
ejpam-5897	148	15	−1)jy2	−1)jy2	PROPN
ejpam-5897	148	16	)	)	PUNCT
ejpam-5897	148	17	,	,	PUNCT
ejpam-5897	148	18	µ(z1	µ(z1	NOUN
ejpam-5897	148	19	+	+	CCONJ
ejpam-5897	148	20	(	(	PUNCT
ejpam-5897	148	21	−1)kz2	−1)kz2	PROPN
ejpam-5897	148	22	)	)	PUNCT
ejpam-5897	148	23	)	)	PUNCT
ejpam-5897	149	1	∥∥∥∥∥∥	∥∥∥∥∥∥	VERB
ejpam-5897	149	2	for	for	ADP
ejpam-5897	149	3	all	all	DET
ejpam-5897	149	4	(	(	PUNCT
ejpam-5897	149	5	x1	x1	PROPN
ejpam-5897	149	6	,	,	PUNCT
ejpam-5897	149	7	y1	y1	PROPN
ejpam-5897	149	8	,	,	PUNCT
ejpam-5897	149	9	z1	z1	NOUN
ejpam-5897	149	10	)	)	PUNCT
ejpam-5897	149	11	,	,	PUNCT
ejpam-5897	149	12	(	(	PUNCT
ejpam-5897	149	13	x2	x2	PROPN
ejpam-5897	149	14	,	,	PUNCT
ejpam-5897	149	15	y2	y2	PROPN
ejpam-5897	149	16	,	,	PUNCT
ejpam-5897	149	17	z2	z2	PROPN
ejpam-5897	149	18	)	)	PUNCT
ejpam-5897	149	19	∈	∈	PROPN
ejpam-5897	149	20	x3	x3	NOUN
ejpam-5897	149	21	and	and	CCONJ
ejpam-5897	149	22	µ	µ	PRON
ejpam-5897	149	23	∈	∈	NOUN
ejpam-5897	149	24	t1	t1	NOUN
ejpam-5897	149	25	.	.	PUNCT
ejpam-5897	150	1	since	since	SCONJ
ejpam-5897	150	2	|t|	|t|	VERB
ejpam-5897	150	3	<	<	X
ejpam-5897	150	4	1	1	NUM
ejpam-5897	150	5	,	,	PUNCT
ejpam-5897	150	6	8µh(x1	8µh(x1	NUM
ejpam-5897	150	7	,	,	PUNCT
ejpam-5897	150	8	y1	y1	NOUN
ejpam-5897	150	9	,	,	PUNCT
ejpam-5897	150	10	z1	z1	NOUN
ejpam-5897	150	11	)	)	PUNCT
ejpam-5897	151	1	=	=	SYM
ejpam-5897	152	1	2∑	2∑	NUM
ejpam-5897	152	2	i	i	NOUN
ejpam-5897	152	3	,	,	PUNCT
ejpam-5897	152	4	j	j	PROPN
ejpam-5897	152	5	,	,	PUNCT
ejpam-5897	152	6	k=1	k=1	PROPN
ejpam-5897	152	7	h(µ(x1	h(µ(x1	PROPN
ejpam-5897	152	8	+	+	CCONJ
ejpam-5897	152	9	(	(	PUNCT
ejpam-5897	152	10	−1)ix2	−1)ix2	ADJ
ejpam-5897	152	11	)	)	PUNCT
ejpam-5897	152	12	,	,	PUNCT
ejpam-5897	152	13	µ(y1	µ(y1	VERB
ejpam-5897	152	14	+	+	CCONJ
ejpam-5897	152	15	(	(	PUNCT
ejpam-5897	152	16	−1)jy2	−1)jy2	PROPN
ejpam-5897	152	17	)	)	PUNCT
ejpam-5897	152	18	,	,	PUNCT
ejpam-5897	152	19	µ(z1	µ(z1	NOUN
ejpam-5897	152	20	+	+	CCONJ
ejpam-5897	152	21	(	(	PUNCT
ejpam-5897	152	22	−1)kz2	−1)kz2	PROPN
ejpam-5897	152	23	)	)	PUNCT
ejpam-5897	152	24	)	)	PUNCT
ejpam-5897	152	25	,	,	PUNCT
ejpam-5897	152	26	and	and	CCONJ
ejpam-5897	152	27	h(µ(x1	h(µ(x1	PROPN
ejpam-5897	152	28	,	,	PUNCT
ejpam-5897	152	29	y1	y1	NOUN
ejpam-5897	152	30	,	,	PUNCT
ejpam-5897	152	31	z1	z1	NOUN
ejpam-5897	152	32	)	)	PUNCT
ejpam-5897	152	33	)	)	PUNCT
ejpam-5897	153	1	=	=	SYM
ejpam-5897	153	2	µh(x1	µh(x1	NOUN
ejpam-5897	153	3	,	,	PUNCT
ejpam-5897	153	4	y1	y1	NOUN
ejpam-5897	153	5	,	,	PUNCT
ejpam-5897	153	6	z1	z1	NOUN
ejpam-5897	153	7	)	)	PUNCT
ejpam-5897	153	8	for	for	ADP
ejpam-5897	153	9	all	all	DET
ejpam-5897	153	10	(	(	PUNCT
ejpam-5897	153	11	x1	x1	PROPN
ejpam-5897	153	12	,	,	PUNCT
ejpam-5897	153	13	y1	y1	PROPN
ejpam-5897	153	14	,	,	PUNCT
ejpam-5897	153	15	z1	z1	ADJ
ejpam-5897	153	16	)	)	PUNCT
ejpam-5897	153	17	∈	∈	NOUN
ejpam-5897	153	18	x3	x3	NOUN
ejpam-5897	153	19	and	and	CCONJ
ejpam-5897	153	20	µ	µ	PRON
ejpam-5897	153	21	∈	∈	NOUN
ejpam-5897	153	22	t1	t1	NOUN
ejpam-5897	153	23	.	.	PUNCT
ejpam-5897	154	1	by	by	ADP
ejpam-5897	154	2	lemma	lemma	PROPN
ejpam-5897	154	3	2	2	NUM
ejpam-5897	154	4	,	,	PUNCT
ejpam-5897	154	5	the	the	DET
ejpam-5897	154	6	mapping	mapping	NOUN
ejpam-5897	154	7	h	h	NOUN
ejpam-5897	154	8	:	:	PUNCT
ejpam-5897	154	9	x3	x3	ADJ
ejpam-5897	154	10	→	→	SYM
ejpam-5897	154	11	x	x	X
ejpam-5897	154	12	is	be	AUX
ejpam-5897	154	13	3	3	NUM
ejpam-5897	154	14	-	-	PUNCT
ejpam-5897	154	15	linear	linear	NOUN
ejpam-5897	154	16	.	.	PUNCT
ejpam-5897	155	1	it	it	PRON
ejpam-5897	155	2	follows	follow	VERB
ejpam-5897	155	3	from	from	ADP
ejpam-5897	155	4	(	(	PUNCT
ejpam-5897	155	5	5	5	NUM
ejpam-5897	155	6	)	)	PUNCT
ejpam-5897	155	7	and	and	CCONJ
ejpam-5897	155	8	the	the	DET
ejpam-5897	155	9	3	3	NUM
ejpam-5897	155	10	-	-	PUNCT
ejpam-5897	155	11	additivity	additivity	NOUN
ejpam-5897	155	12	of	of	ADP
ejpam-5897	155	13	h	h	NOUN
ejpam-5897	155	14	that	that	PRON
ejpam-5897	155	15	∥h([x1	∥h([x1	VERB
ejpam-5897	155	16	,	,	PUNCT
ejpam-5897	155	17	y1	y1	NOUN
ejpam-5897	155	18	,	,	PUNCT
ejpam-5897	155	19	z1	z1	NOUN
ejpam-5897	155	20	]	]	PUNCT
ejpam-5897	155	21	,	,	PUNCT
ejpam-5897	155	22	[	[	X
ejpam-5897	155	23	x2	x2	X
ejpam-5897	155	24	,	,	PUNCT
ejpam-5897	155	25	y2	y2	PROPN
ejpam-5897	155	26	,	,	PUNCT
ejpam-5897	155	27	z2	z2	PROPN
ejpam-5897	155	28	]	]	PUNCT
ejpam-5897	155	29	,	,	PUNCT
ejpam-5897	155	30	[	[	X
ejpam-5897	155	31	x3	x3	ADJ
ejpam-5897	155	32	,	,	PUNCT
ejpam-5897	155	33	y3	y3	NOUN
ejpam-5897	155	34	,	,	PUNCT
ejpam-5897	155	35	z3])−	z3])−	X
ejpam-5897	156	1	[	[	X
ejpam-5897	156	2	h(x1	h(x1	X
ejpam-5897	156	3	,	,	PUNCT
ejpam-5897	156	4	x2	x2	PROPN
ejpam-5897	156	5	,	,	PUNCT
ejpam-5897	156	6	x3	x3	ADJ
ejpam-5897	156	7	)	)	PUNCT
ejpam-5897	156	8	,	,	PUNCT
ejpam-5897	156	9	h(y1	h(y1	NOUN
ejpam-5897	156	10	,	,	PUNCT
ejpam-5897	156	11	y2	y2	PROPN
ejpam-5897	156	12	,	,	PUNCT
ejpam-5897	156	13	y3	y3	PROPN
ejpam-5897	156	14	)	)	PUNCT
ejpam-5897	156	15	,	,	PUNCT
ejpam-5897	156	16	h(z1	h(z1	NOUN
ejpam-5897	156	17	,	,	PUNCT
ejpam-5897	156	18	z2	z2	PROPN
ejpam-5897	156	19	,	,	PUNCT
ejpam-5897	156	20	z3)]∥	z3)]∥	X
ejpam-5897	156	21	=	=	SYM
ejpam-5897	156	22	lim	lim	PROPN
ejpam-5897	156	23	n→+∞	n→+∞	PROPN
ejpam-5897	156	24	83n	83n	NUM
ejpam-5897	156	25	∥∥∥h	∥∥∥h	PROPN
ejpam-5897	156	26	(	(	PUNCT
ejpam-5897	156	27	[	[	X
ejpam-5897	156	28	x1	x1	PROPN
ejpam-5897	156	29	,	,	PUNCT
ejpam-5897	156	30	y1	y1	PROPN
ejpam-5897	156	31	,	,	PUNCT
ejpam-5897	156	32	z1	z1	NOUN
ejpam-5897	156	33	]	]	PUNCT
ejpam-5897	156	34	8n	8n	NOUN
ejpam-5897	156	35	,	,	PUNCT
ejpam-5897	156	36	[	[	X
ejpam-5897	156	37	x2	x2	X
ejpam-5897	156	38	,	,	PUNCT
ejpam-5897	156	39	y2	y2	PROPN
ejpam-5897	156	40	,	,	PUNCT
ejpam-5897	156	41	z2	z2	PROPN
ejpam-5897	156	42	]	]	X
ejpam-5897	156	43	8n	8n	NOUN
ejpam-5897	156	44	,	,	PUNCT
ejpam-5897	156	45	[	[	X
ejpam-5897	156	46	x3	x3	ADJ
ejpam-5897	156	47	,	,	PUNCT
ejpam-5897	156	48	y3	y3	NOUN
ejpam-5897	156	49	,	,	PUNCT
ejpam-5897	156	50	z3	z3	PROPN
ejpam-5897	156	51	]	]	PUNCT
ejpam-5897	156	52	8n	8n	NOUN
ejpam-5897	156	53	)	)	PUNCT
ejpam-5897	156	54	−	−	PROPN
ejpam-5897	157	1	[	[	PUNCT
ejpam-5897	157	2	h	h	NOUN
ejpam-5897	157	3	(	(	PUNCT
ejpam-5897	157	4	x1	x1	PROPN
ejpam-5897	157	5	2n	2n	NUM
ejpam-5897	157	6	,	,	PUNCT
ejpam-5897	157	7	x2	x2	PROPN
ejpam-5897	157	8	2n	2n	NUM
ejpam-5897	157	9	,	,	PUNCT
ejpam-5897	157	10	x3	x3	PROPN
ejpam-5897	157	11	2n	2n	NUM
ejpam-5897	157	12	)	)	PUNCT
ejpam-5897	157	13	,	,	PUNCT
ejpam-5897	157	14	h	h	NOUN
ejpam-5897	157	15	(	(	PUNCT
ejpam-5897	157	16	y1	y1	INTJ
ejpam-5897	157	17	2n	2n	NUM
ejpam-5897	157	18	,	,	PUNCT
ejpam-5897	157	19	y2	y2	PROPN
ejpam-5897	157	20	2n	2n	NUM
ejpam-5897	157	21	,	,	PUNCT
ejpam-5897	157	22	y3	y3	PROPN
ejpam-5897	157	23	2n	2n	NUM
ejpam-5897	157	24	)	)	PUNCT
ejpam-5897	157	25	,	,	PUNCT
ejpam-5897	157	26	h	h	NOUN
ejpam-5897	157	27	(	(	PUNCT
ejpam-5897	157	28	z1	z1	PROPN
ejpam-5897	157	29	2n	2n	NUM
ejpam-5897	157	30	,	,	PUNCT
ejpam-5897	157	31	z2	z2	PROPN
ejpam-5897	157	32	2n	2n	NUM
ejpam-5897	157	33	,	,	PUNCT
ejpam-5897	157	34	z3	z3	PROPN
ejpam-5897	157	35	2n	2n	NUM
ejpam-5897	157	36	)	)	PUNCT
ejpam-5897	157	37	]	]	PUNCT
ejpam-5897	157	38	∥∥∥	∥∥∥	PROPN
ejpam-5897	157	39	≤	≤	PROPN
ejpam-5897	157	40	lim	lim	PROPN
ejpam-5897	157	41	n→+∞	n→+∞	VERB
ejpam-5897	157	42	83nψ	83nψ	PROPN
ejpam-5897	157	43	(	(	PUNCT
ejpam-5897	157	44	x1	x1	PROPN
ejpam-5897	157	45	2n	2n	NUM
ejpam-5897	157	46	,	,	PUNCT
ejpam-5897	157	47	x2	x2	PROPN
ejpam-5897	157	48	2n	2n	NUM
ejpam-5897	157	49	,	,	PUNCT
ejpam-5897	157	50	x3	x3	PROPN
ejpam-5897	157	51	2n	2n	NUM
ejpam-5897	157	52	,	,	PUNCT
ejpam-5897	157	53	y1	y1	NOUN
ejpam-5897	157	54	2n	2n	NUM
ejpam-5897	157	55	,	,	PUNCT
ejpam-5897	157	56	y2	y2	PROPN
ejpam-5897	157	57	2n	2n	NUM
ejpam-5897	157	58	,	,	PUNCT
ejpam-5897	157	59	y3	y3	PROPN
ejpam-5897	157	60	2n	2n	NUM
ejpam-5897	157	61	,	,	PUNCT
ejpam-5897	157	62	z1	z1	PROPN
ejpam-5897	157	63	2n	2n	NUM
ejpam-5897	157	64	,	,	PUNCT
ejpam-5897	157	65	z2	z2	PROPN
ejpam-5897	157	66	2n	2n	NUM
ejpam-5897	157	67	,	,	PUNCT
ejpam-5897	157	68	z3	z3	PROPN
ejpam-5897	157	69	2n	2n	NUM
ejpam-5897	157	70	)	)	PUNCT
ejpam-5897	158	1	=	=	SYM
ejpam-5897	158	2	0	0	X
ejpam-5897	158	3	.	.	PUNCT
ejpam-5897	159	1	so	so	ADV
ejpam-5897	159	2	h([x1	h([x1	NOUN
ejpam-5897	159	3	,	,	PUNCT
ejpam-5897	159	4	y1	y1	NOUN
ejpam-5897	159	5	,	,	PUNCT
ejpam-5897	159	6	z1	z1	NOUN
ejpam-5897	159	7	]	]	PUNCT
ejpam-5897	159	8	,	,	PUNCT
ejpam-5897	160	1	[	[	X
ejpam-5897	160	2	x2	x2	X
ejpam-5897	160	3	,	,	PUNCT
ejpam-5897	160	4	y2	y2	PROPN
ejpam-5897	160	5	,	,	PUNCT
ejpam-5897	160	6	z2	z2	PROPN
ejpam-5897	160	7	]	]	PUNCT
ejpam-5897	160	8	,	,	PUNCT
ejpam-5897	160	9	[	[	X
ejpam-5897	160	10	x3	x3	ADJ
ejpam-5897	160	11	,	,	PUNCT
ejpam-5897	160	12	y3	y3	NOUN
ejpam-5897	160	13	,	,	PUNCT
ejpam-5897	160	14	z3	z3	PROPN
ejpam-5897	160	15	]	]	PUNCT
ejpam-5897	160	16	)	)	PUNCT
ejpam-5897	160	17	=	=	PUNCT
ejpam-5897	161	1	[	[	X
ejpam-5897	161	2	h(x1	h(x1	X
ejpam-5897	161	3	,	,	PUNCT
ejpam-5897	161	4	x2	x2	PROPN
ejpam-5897	161	5	,	,	PUNCT
ejpam-5897	161	6	x3	x3	ADJ
ejpam-5897	161	7	)	)	PUNCT
ejpam-5897	161	8	,	,	PUNCT
ejpam-5897	161	9	h(y1	h(y1	NOUN
ejpam-5897	161	10	,	,	PUNCT
ejpam-5897	161	11	y2	y2	PROPN
ejpam-5897	161	12	,	,	PUNCT
ejpam-5897	161	13	y3	y3	PROPN
ejpam-5897	161	14	)	)	PUNCT
ejpam-5897	161	15	,	,	PUNCT
ejpam-5897	161	16	h(z1	h(z1	NOUN
ejpam-5897	161	17	,	,	PUNCT
ejpam-5897	161	18	z2	z2	PROPN
ejpam-5897	161	19	,	,	PUNCT
ejpam-5897	161	20	z3	z3	PROPN
ejpam-5897	161	21	)	)	PUNCT
ejpam-5897	161	22	]	]	PUNCT
ejpam-5897	161	23	for	for	ADP
ejpam-5897	161	24	all	all	DET
ejpam-5897	161	25	x1	x1	PROPN
ejpam-5897	161	26	,	,	PUNCT
ejpam-5897	161	27	x2	x2	PROPN
ejpam-5897	161	28	,	,	PUNCT
ejpam-5897	161	29	x3	x3	ADJ
ejpam-5897	161	30	,	,	PUNCT
ejpam-5897	161	31	y1	y1	NOUN
ejpam-5897	161	32	,	,	PUNCT
ejpam-5897	161	33	y2	y2	PROPN
ejpam-5897	161	34	,	,	PUNCT
ejpam-5897	161	35	y3	y3	PROPN
ejpam-5897	161	36	,	,	PUNCT
ejpam-5897	161	37	z1	z1	PROPN
ejpam-5897	161	38	,	,	PUNCT
ejpam-5897	161	39	z2	z2	PROPN
ejpam-5897	161	40	,	,	PUNCT
ejpam-5897	161	41	z3	z3	PROPN
ejpam-5897	161	42	∈	∈	PROPN
ejpam-5897	161	43	x.	x.	NOUN
ejpam-5897	161	44	therefore	therefore	ADV
ejpam-5897	161	45	,	,	PUNCT
ejpam-5897	161	46	the	the	DET
ejpam-5897	161	47	mapping	mapping	NOUN
ejpam-5897	161	48	h	h	NOUN
ejpam-5897	161	49	is	be	AUX
ejpam-5897	161	50	a	a	DET
ejpam-5897	161	51	unique	unique	ADJ
ejpam-5897	161	52	hyper	hyper	ADJ
ejpam-5897	161	53	3	3	NUM
ejpam-5897	161	54	-	-	PUNCT
ejpam-5897	161	55	homomor	homomor	NOUN
ejpam-5897	161	56	-	-	PUNCT
ejpam-5897	161	57	phism	phism	NOUN
ejpam-5897	161	58	satisfying	satisfying	NOUN
ejpam-5897	161	59	(	(	PUNCT
ejpam-5897	161	60	6	6	NUM
ejpam-5897	161	61	)	)	PUNCT
ejpam-5897	161	62	.	.	PUNCT
ejpam-5897	162	1	theorem	theorem	NOUN
ejpam-5897	162	2	3	3	X
ejpam-5897	162	3	.	.	PUNCT
ejpam-5897	163	1	let	let	VERB
ejpam-5897	163	2	x	x	PRON
ejpam-5897	163	3	be	be	AUX
ejpam-5897	163	4	a	a	DET
ejpam-5897	163	5	complex	complex	ADJ
ejpam-5897	163	6	ternary	ternary	ADJ
ejpam-5897	163	7	algebra	algebra	NOUN
ejpam-5897	163	8	,	,	PUNCT
ejpam-5897	163	9	y	y	PROPN
ejpam-5897	163	10	be	be	VERB
ejpam-5897	163	11	a	a	DET
ejpam-5897	163	12	complex	complex	ADJ
ejpam-5897	163	13	ternary	ternary	ADJ
ejpam-5897	163	14	banach	banach	NOUN
ejpam-5897	163	15	algebra	algebra	NOUN
ejpam-5897	163	16	and	and	CCONJ
ejpam-5897	163	17	t	t	PROPN
ejpam-5897	163	18	be	be	AUX
ejpam-5897	164	1	a	a	DET
ejpam-5897	164	2	real	real	ADJ
ejpam-5897	164	3	number	number	NOUN
ejpam-5897	164	4	satisfying	satisfying	NOUN
ejpam-5897	164	5	|t|	|t|	NOUN
ejpam-5897	164	6	<	<	X
ejpam-5897	164	7	1	1	X
ejpam-5897	164	8	.	.	PUNCT
ejpam-5897	165	1	let	let	VERB
ejpam-5897	165	2	h	h	NOUN
ejpam-5897	165	3	:	:	PUNCT
ejpam-5897	165	4	x3	x3	VERB
ejpam-5897	165	5	→	→	SYM
ejpam-5897	165	6	y	y	PROPN
ejpam-5897	165	7	be	be	AUX
ejpam-5897	165	8	a	a	DET
ejpam-5897	165	9	bijective	bijective	ADJ
ejpam-5897	165	10	mapping	mapping	NOUN
ejpam-5897	165	11	satisfying	satisfy	VERB
ejpam-5897	165	12	(	(	PUNCT
ejpam-5897	165	13	4	4	NUM
ejpam-5897	165	14	)	)	PUNCT
ejpam-5897	165	15	such	such	ADJ
ejpam-5897	165	16	that	that	SCONJ
ejpam-5897	165	17	h([x1	h([x1	NOUN
ejpam-5897	165	18	,	,	PUNCT
ejpam-5897	165	19	y1	y1	PROPN
ejpam-5897	165	20	,	,	PUNCT
ejpam-5897	165	21	z1	z1	NOUN
ejpam-5897	165	22	]	]	PUNCT
ejpam-5897	165	23	,	,	PUNCT
ejpam-5897	166	1	[	[	X
ejpam-5897	166	2	x2	x2	X
ejpam-5897	166	3	,	,	PUNCT
ejpam-5897	166	4	y2	y2	PROPN
ejpam-5897	166	5	,	,	PUNCT
ejpam-5897	166	6	z2	z2	PROPN
ejpam-5897	166	7	]	]	PUNCT
ejpam-5897	166	8	,	,	PUNCT
ejpam-5897	166	9	[	[	X
ejpam-5897	166	10	x3	x3	ADJ
ejpam-5897	166	11	,	,	PUNCT
ejpam-5897	166	12	y3	y3	NOUN
ejpam-5897	166	13	,	,	PUNCT
ejpam-5897	166	14	z3	z3	PROPN
ejpam-5897	166	15	]	]	PUNCT
ejpam-5897	166	16	)	)	PUNCT
ejpam-5897	166	17	=	=	PUNCT
ejpam-5897	167	1	[	[	X
ejpam-5897	167	2	h(x1	h(x1	X
ejpam-5897	167	3	,	,	PUNCT
ejpam-5897	167	4	x2	x2	PROPN
ejpam-5897	167	5	,	,	PUNCT
ejpam-5897	167	6	x3	x3	ADJ
ejpam-5897	167	7	)	)	PUNCT
ejpam-5897	167	8	,	,	PUNCT
ejpam-5897	167	9	h(y1	h(y1	NOUN
ejpam-5897	167	10	,	,	PUNCT
ejpam-5897	167	11	y2	y2	PROPN
ejpam-5897	167	12	,	,	PUNCT
ejpam-5897	167	13	y3	y3	PROPN
ejpam-5897	167	14	)	)	PUNCT
ejpam-5897	167	15	,	,	PUNCT
ejpam-5897	167	16	h(z1	h(z1	NOUN
ejpam-5897	167	17	,	,	PUNCT
ejpam-5897	167	18	z2	z2	PROPN
ejpam-5897	167	19	,	,	PUNCT
ejpam-5897	167	20	z3	z3	PROPN
ejpam-5897	167	21	)	)	PUNCT
ejpam-5897	167	22	]	]	PUNCT
ejpam-5897	167	23	(	(	PUNCT
ejpam-5897	167	24	9	9	X
ejpam-5897	167	25	)	)	PUNCT
ejpam-5897	167	26	for	for	ADP
ejpam-5897	167	27	all	all	PRON
ejpam-5897	167	28	x1	x1	PROPN
ejpam-5897	167	29	,	,	PUNCT
ejpam-5897	167	30	x2	x2	PROPN
ejpam-5897	167	31	,	,	PUNCT
ejpam-5897	167	32	x3	x3	ADJ
ejpam-5897	167	33	,	,	PUNCT
ejpam-5897	167	34	y1	y1	NOUN
ejpam-5897	167	35	,	,	PUNCT
ejpam-5897	167	36	y2	y2	PROPN
ejpam-5897	167	37	,	,	PUNCT
ejpam-5897	167	38	y3	y3	PROPN
ejpam-5897	167	39	,	,	PUNCT
ejpam-5897	167	40	z1	z1	PROPN
ejpam-5897	167	41	,	,	PUNCT
ejpam-5897	167	42	z2	z2	PROPN
ejpam-5897	167	43	,	,	PUNCT
ejpam-5897	167	44	z3	z3	PROPN
ejpam-5897	167	45	∈	∈	PROPN
ejpam-5897	167	46	x.	x.	NOUN
ejpam-5897	168	1	if	if	SCONJ
ejpam-5897	168	2	h(αx0	h(αx0	NOUN
ejpam-5897	168	3	,	,	PUNCT
ejpam-5897	168	4	βy0	βy0	PROPN
ejpam-5897	168	5	,	,	PUNCT
ejpam-5897	168	6	γz0	γz0	ADV
ejpam-5897	168	7	)	)	PUNCT
ejpam-5897	168	8	is	be	AUX
ejpam-5897	168	9	continuous	continuous	ADJ
ejpam-5897	168	10	in	in	ADP
ejpam-5897	168	11	α	α	PROPN
ejpam-5897	168	12	,	,	PUNCT
ejpam-5897	168	13	β	β	X
ejpam-5897	168	14	,	,	PUNCT
ejpam-5897	168	15	γ	γ	PROPN
ejpam-5897	168	16	∈	∈	NOUN
ejpam-5897	168	17	r	r	NOUN
ejpam-5897	168	18	for	for	ADP
ejpam-5897	168	19	each	each	DET
ejpam-5897	168	20	fixed	fix	VERB
ejpam-5897	168	21	(	(	PUNCT
ejpam-5897	168	22	x0	x0	PROPN
ejpam-5897	168	23	,	,	PUNCT
ejpam-5897	168	24	y0	y0	PROPN
ejpam-5897	168	25	,	,	PUNCT
ejpam-5897	168	26	z0	z0	PROPN
ejpam-5897	168	27	)	)	PUNCT
ejpam-5897	168	28	∈	∈	PROPN
ejpam-5897	168	29	x3	x3	NOUN
ejpam-5897	168	30	and	and	CCONJ
ejpam-5897	168	31	limn→+∞	limn→+∞	PROPN
ejpam-5897	168	32	8nh	8nh	NOUN
ejpam-5897	168	33	(	(	PUNCT
ejpam-5897	168	34	e	e	NOUN
ejpam-5897	168	35	2n	2n	NUM
ejpam-5897	168	36	,	,	PUNCT
ejpam-5897	168	37	e	e	X
ejpam-5897	168	38	2n	2n	NUM
ejpam-5897	168	39	,	,	PUNCT
ejpam-5897	168	40	e	e	X
ejpam-5897	168	41	2n	2n	NUM
ejpam-5897	168	42	)	)	PUNCT
ejpam-5897	169	1	=	=	SYM
ejpam-5897	169	2	e′	e′	PROPN
ejpam-5897	169	3	,	,	PUNCT
ejpam-5897	169	4	then	then	ADV
ejpam-5897	169	5	the	the	DET
ejpam-5897	169	6	mapping	mapping	NOUN
ejpam-5897	169	7	h	h	NOUN
ejpam-5897	169	8	:	:	PUNCT
ejpam-5897	169	9	x3	x3	ADJ
ejpam-5897	169	10	→	→	SYM
ejpam-5897	169	11	y	y	PROPN
ejpam-5897	169	12	is	be	AUX
ejpam-5897	169	13	a	a	DET
ejpam-5897	169	14	hyper	hyper	ADJ
ejpam-5897	169	15	3	3	NUM
ejpam-5897	169	16	-	-	PUNCT
ejpam-5897	169	17	isomorphism	isomorphism	NOUN
ejpam-5897	169	18	.	.	PUNCT
ejpam-5897	170	1	e.	e.	PROPN
ejpam-5897	170	2	shim	shim	PROPN
ejpam-5897	170	3	,	,	PUNCT
ejpam-5897	170	4	s.	s.	PROPN
ejpam-5897	170	5	donganont	donganont	PROPN
ejpam-5897	170	6	,	,	PUNCT
ejpam-5897	170	7	c.	c.	PROPN
ejpam-5897	170	8	park	park	PROPN
ejpam-5897	170	9	/	/	SYM
ejpam-5897	170	10	eur	eur	PROPN
ejpam-5897	170	11	.	.	PUNCT
ejpam-5897	171	1	j.	j.	PROPN
ejpam-5897	171	2	pure	pure	PROPN
ejpam-5897	171	3	appl	appl	PROPN
ejpam-5897	171	4	.	.	PROPN
ejpam-5897	171	5	math	math	PROPN
ejpam-5897	171	6	,	,	PUNCT
ejpam-5897	171	7	18	18	NUM
ejpam-5897	171	8	(	(	PUNCT
ejpam-5897	171	9	2	2	NUM
ejpam-5897	171	10	)	)	PUNCT
ejpam-5897	171	11	(	(	PUNCT
ejpam-5897	171	12	2025	2025	NUM
ejpam-5897	171	13	)	)	PUNCT
ejpam-5897	171	14	,	,	PUNCT
ejpam-5897	171	15	5897	5897	NUM
ejpam-5897	171	16	8	8	NUM
ejpam-5897	171	17	of	of	ADP
ejpam-5897	171	18	14	14	NUM
ejpam-5897	171	19	proof	proof	NOUN
ejpam-5897	171	20	.	.	PUNCT
ejpam-5897	172	1	since	since	SCONJ
ejpam-5897	172	2	h	h	NOUN
ejpam-5897	172	3	satisfies	satisfie	NOUN
ejpam-5897	172	4	(	(	PUNCT
ejpam-5897	172	5	9	9	NUM
ejpam-5897	172	6	)	)	PUNCT
ejpam-5897	172	7	,	,	PUNCT
ejpam-5897	172	8	the	the	DET
ejpam-5897	172	9	mapping	mapping	NOUN
ejpam-5897	172	10	h	h	NOUN
ejpam-5897	172	11	:	:	PUNCT
ejpam-5897	172	12	x3	x3	ADJ
ejpam-5897	172	13	→	→	SYM
ejpam-5897	172	14	y	y	PROPN
ejpam-5897	172	15	satisfies	satisfie	NOUN
ejpam-5897	172	16	(	(	PUNCT
ejpam-5897	172	17	4	4	NUM
ejpam-5897	172	18	)	)	PUNCT
ejpam-5897	172	19	by	by	ADP
ejpam-5897	172	20	theorem	theorem	NOUN
ejpam-5897	172	21	1	1	NUM
ejpam-5897	172	22	,	,	PUNCT
ejpam-5897	172	23	there	there	PRON
ejpam-5897	172	24	exists	exist	VERB
ejpam-5897	172	25	a	a	DET
ejpam-5897	172	26	hyper	hyper	ADJ
ejpam-5897	172	27	3	3	NUM
ejpam-5897	172	28	-	-	NUM
ejpam-5897	172	29	homomorphism	homomorphism	NOUN
ejpam-5897	172	30	h	h	NOUN
ejpam-5897	172	31	:	:	PUNCT
ejpam-5897	172	32	x3	x3	VERB
ejpam-5897	172	33	→	→	SYM
ejpam-5897	172	34	y	y	PROPN
ejpam-5897	172	35	satisfying	satisfying	NOUN
ejpam-5897	172	36	(	(	PUNCT
ejpam-5897	172	37	6	6	NUM
ejpam-5897	172	38	)	)	PUNCT
ejpam-5897	172	39	.	.	PUNCT
ejpam-5897	173	1	the	the	DET
ejpam-5897	173	2	mapping	mapping	NOUN
ejpam-5897	173	3	h	h	NOUN
ejpam-5897	173	4	:	:	PUNCT
ejpam-5897	173	5	x3	x3	ADJ
ejpam-5897	173	6	→	→	SYM
ejpam-5897	173	7	y	y	PROPN
ejpam-5897	173	8	is	be	AUX
ejpam-5897	173	9	defined	define	VERB
ejpam-5897	173	10	by	by	ADP
ejpam-5897	173	11	h(x	h(x	PROPN
ejpam-5897	173	12	,	,	PUNCT
ejpam-5897	173	13	y	y	PROPN
ejpam-5897	173	14	,	,	PUNCT
ejpam-5897	173	15	z	z	NOUN
ejpam-5897	173	16	)	)	PUNCT
ejpam-5897	173	17	:	:	PUNCT
ejpam-5897	173	18	=	=	SYM
ejpam-5897	173	19	lim	lim	PROPN
ejpam-5897	173	20	n→+∞	n→+∞	PROPN
ejpam-5897	173	21	8nh	8nh	NOUN
ejpam-5897	173	22	(	(	PUNCT
ejpam-5897	173	23	x	x	PROPN
ejpam-5897	173	24	2n	2n	NUM
ejpam-5897	173	25	,	,	PUNCT
ejpam-5897	173	26	y	y	PROPN
ejpam-5897	173	27	2n	2n	NUM
ejpam-5897	173	28	,	,	PUNCT
ejpam-5897	173	29	z	z	NOUN
ejpam-5897	173	30	2n	2n	NUM
ejpam-5897	173	31	)	)	PUNCT
ejpam-5897	173	32	for	for	ADP
ejpam-5897	173	33	all	all	DET
ejpam-5897	173	34	x	x	PROPN
ejpam-5897	173	35	,	,	PUNCT
ejpam-5897	173	36	y	y	PROPN
ejpam-5897	173	37	,	,	PUNCT
ejpam-5897	173	38	z	z	NOUN
ejpam-5897	173	39	∈	∈	PROPN
ejpam-5897	173	40	x.	x.	NOUN
ejpam-5897	174	1	it	it	PRON
ejpam-5897	174	2	follows	follow	VERB
ejpam-5897	174	3	from	from	ADP
ejpam-5897	174	4	(	(	PUNCT
ejpam-5897	174	5	9	9	NUM
ejpam-5897	174	6	)	)	PUNCT
ejpam-5897	174	7	that	that	SCONJ
ejpam-5897	174	8	∥[h(x1	∥[h(x1	ADJ
ejpam-5897	174	9	,	,	PUNCT
ejpam-5897	174	10	x2	x2	PROPN
ejpam-5897	174	11	,	,	PUNCT
ejpam-5897	174	12	x3	x3	ADJ
ejpam-5897	174	13	)	)	PUNCT
ejpam-5897	174	14	,	,	PUNCT
ejpam-5897	174	15	h(y1	h(y1	NOUN
ejpam-5897	174	16	,	,	PUNCT
ejpam-5897	174	17	y2	y2	PROPN
ejpam-5897	174	18	,	,	PUNCT
ejpam-5897	174	19	y3	y3	PROPN
ejpam-5897	174	20	)	)	PUNCT
ejpam-5897	174	21	,	,	PUNCT
ejpam-5897	174	22	h(z1	h(z1	NOUN
ejpam-5897	174	23	,	,	PUNCT
ejpam-5897	174	24	z2	z2	PROPN
ejpam-5897	174	25	,	,	PUNCT
ejpam-5897	174	26	z3)]−	z3)]−	PROPN
ejpam-5897	174	27	[	[	X
ejpam-5897	174	28	h(x1	h(x1	X
ejpam-5897	174	29	,	,	PUNCT
ejpam-5897	174	30	x2	x2	PROPN
ejpam-5897	174	31	,	,	PUNCT
ejpam-5897	174	32	x3	x3	ADJ
ejpam-5897	174	33	)	)	PUNCT
ejpam-5897	174	34	,	,	PUNCT
ejpam-5897	174	35	h(y1	h(y1	NOUN
ejpam-5897	174	36	,	,	PUNCT
ejpam-5897	174	37	y2	y2	PROPN
ejpam-5897	174	38	,	,	PUNCT
ejpam-5897	174	39	y3	y3	PROPN
ejpam-5897	174	40	)	)	PUNCT
ejpam-5897	174	41	,	,	PUNCT
ejpam-5897	174	42	h(z1	h(z1	NOUN
ejpam-5897	174	43	,	,	PUNCT
ejpam-5897	174	44	z2	z2	PROPN
ejpam-5897	174	45	,	,	PUNCT
ejpam-5897	174	46	z3)]∥	z3)]∥	X
ejpam-5897	174	47	=	=	SYM
ejpam-5897	174	48	∥h([x1	∥h([x1	PROPN
ejpam-5897	174	49	,	,	PUNCT
ejpam-5897	174	50	y1	y1	NOUN
ejpam-5897	174	51	,	,	PUNCT
ejpam-5897	174	52	z1	z1	NOUN
ejpam-5897	174	53	]	]	PUNCT
ejpam-5897	174	54	,	,	PUNCT
ejpam-5897	175	1	[	[	X
ejpam-5897	175	2	x2	x2	X
ejpam-5897	175	3	,	,	PUNCT
ejpam-5897	175	4	y2	y2	PROPN
ejpam-5897	175	5	,	,	PUNCT
ejpam-5897	175	6	z2	z2	PROPN
ejpam-5897	175	7	]	]	PUNCT
ejpam-5897	175	8	,	,	PUNCT
ejpam-5897	175	9	[	[	X
ejpam-5897	175	10	x3	x3	ADJ
ejpam-5897	175	11	,	,	PUNCT
ejpam-5897	175	12	y3	y3	NOUN
ejpam-5897	175	13	,	,	PUNCT
ejpam-5897	175	14	z3])−	z3])−	X
ejpam-5897	176	1	[	[	X
ejpam-5897	176	2	h(x1	h(x1	X
ejpam-5897	176	3	,	,	PUNCT
ejpam-5897	176	4	x2	x2	PROPN
ejpam-5897	176	5	,	,	PUNCT
ejpam-5897	176	6	x3	x3	ADJ
ejpam-5897	176	7	)	)	PUNCT
ejpam-5897	176	8	,	,	PUNCT
ejpam-5897	176	9	h(y1	h(y1	NOUN
ejpam-5897	176	10	,	,	PUNCT
ejpam-5897	176	11	y2	y2	PROPN
ejpam-5897	176	12	,	,	PUNCT
ejpam-5897	176	13	y3	y3	PROPN
ejpam-5897	176	14	)	)	PUNCT
ejpam-5897	176	15	,	,	PUNCT
ejpam-5897	176	16	h(z1	h(z1	NOUN
ejpam-5897	176	17	,	,	PUNCT
ejpam-5897	176	18	z2	z2	PROPN
ejpam-5897	176	19	,	,	PUNCT
ejpam-5897	176	20	z3)]∥	z3)]∥	X
ejpam-5897	176	21	=	=	SYM
ejpam-5897	176	22	lim	lim	PROPN
ejpam-5897	176	23	n→+∞	n→+∞	VERB
ejpam-5897	176	24	82n	82n	NOUN
ejpam-5897	176	25	∥∥∥h([x1	∥∥∥h([x1	PUNCT
ejpam-5897	176	26	2n	2n	NUM
ejpam-5897	176	27	,	,	PUNCT
ejpam-5897	176	28	y1	y1	NOUN
ejpam-5897	176	29	2n	2n	NUM
ejpam-5897	176	30	,	,	PUNCT
ejpam-5897	176	31	z1	z1	PROPN
ejpam-5897	176	32	]	]	PUNCT
ejpam-5897	176	33	,	,	PUNCT
ejpam-5897	177	1	[	[	X
ejpam-5897	177	2	x2	x2	X
ejpam-5897	177	3	2n	2n	NUM
ejpam-5897	177	4	,	,	PUNCT
ejpam-5897	177	5	y2	y2	PROPN
ejpam-5897	177	6	2n	2n	NUM
ejpam-5897	177	7	,	,	PUNCT
ejpam-5897	177	8	z2	z2	PROPN
ejpam-5897	177	9	]	]	PUNCT
ejpam-5897	177	10	,	,	PUNCT
ejpam-5897	178	1	[	[	X
ejpam-5897	178	2	x3	x3	X
ejpam-5897	178	3	2n	2n	NUM
ejpam-5897	178	4	,	,	PUNCT
ejpam-5897	178	5	y3	y3	PROPN
ejpam-5897	178	6	2n	2n	NUM
ejpam-5897	178	7	,	,	PUNCT
ejpam-5897	178	8	z3	z3	PROPN
ejpam-5897	178	9	]	]	X
ejpam-5897	178	10	)	)	PUNCT
ejpam-5897	179	1	−	−	PROPN
ejpam-5897	180	1	[	[	PUNCT
ejpam-5897	180	2	h	h	NOUN
ejpam-5897	180	3	(	(	PUNCT
ejpam-5897	180	4	x1	x1	PROPN
ejpam-5897	180	5	2n	2n	NUM
ejpam-5897	180	6	,	,	PUNCT
ejpam-5897	180	7	x2	x2	PROPN
ejpam-5897	180	8	2n	2n	NUM
ejpam-5897	180	9	,	,	PUNCT
ejpam-5897	180	10	x3	x3	PROPN
ejpam-5897	180	11	2n	2n	NUM
ejpam-5897	180	12	)	)	PUNCT
ejpam-5897	180	13	,	,	PUNCT
ejpam-5897	180	14	h	h	NOUN
ejpam-5897	180	15	(	(	PUNCT
ejpam-5897	180	16	y1	y1	INTJ
ejpam-5897	180	17	2n	2n	NUM
ejpam-5897	180	18	,	,	PUNCT
ejpam-5897	180	19	y2	y2	PROPN
ejpam-5897	180	20	2n	2n	NUM
ejpam-5897	180	21	,	,	PUNCT
ejpam-5897	180	22	y3	y3	PROPN
ejpam-5897	180	23	2n	2n	NUM
ejpam-5897	180	24	)	)	PUNCT
ejpam-5897	180	25	,	,	PUNCT
ejpam-5897	180	26	h(z1	h(z1	NOUN
ejpam-5897	180	27	,	,	PUNCT
ejpam-5897	180	28	z2	z2	PROPN
ejpam-5897	180	29	,	,	PUNCT
ejpam-5897	180	30	z3	z3	PROPN
ejpam-5897	180	31	)	)	PUNCT
ejpam-5897	180	32	]	]	PUNCT
ejpam-5897	181	1	∥∥∥	∥∥∥	PROPN
ejpam-5897	181	2	≤	≤	PROPN
ejpam-5897	181	3	lim	lim	PROPN
ejpam-5897	181	4	n→+∞	n→+∞	VERB
ejpam-5897	181	5	82nψ	82nψ	ADJ
ejpam-5897	181	6	(	(	PUNCT
ejpam-5897	181	7	x1	x1	PROPN
ejpam-5897	181	8	2n	2n	NUM
ejpam-5897	181	9	,	,	PUNCT
ejpam-5897	181	10	x2	x2	PROPN
ejpam-5897	181	11	2n	2n	NUM
ejpam-5897	181	12	,	,	PUNCT
ejpam-5897	181	13	x3	x3	PROPN
ejpam-5897	181	14	2n	2n	NUM
ejpam-5897	181	15	,	,	PUNCT
ejpam-5897	181	16	y1	y1	NOUN
ejpam-5897	181	17	2n	2n	NUM
ejpam-5897	181	18	,	,	PUNCT
ejpam-5897	181	19	y2	y2	PROPN
ejpam-5897	181	20	2n	2n	NUM
ejpam-5897	181	21	,	,	PUNCT
ejpam-5897	181	22	y3	y3	PROPN
ejpam-5897	181	23	2n	2n	NUM
ejpam-5897	181	24	,	,	PUNCT
ejpam-5897	181	25	z1	z1	PROPN
ejpam-5897	181	26	,	,	PUNCT
ejpam-5897	181	27	z2	z2	PROPN
ejpam-5897	181	28	,	,	PUNCT
ejpam-5897	181	29	z3	z3	PROPN
ejpam-5897	181	30	)	)	PUNCT
ejpam-5897	182	1	=	=	SYM
ejpam-5897	182	2	0	0	NUM
ejpam-5897	183	1	for	for	ADP
ejpam-5897	183	2	all	all	DET
ejpam-5897	183	3	x1	x1	PROPN
ejpam-5897	183	4	,	,	PUNCT
ejpam-5897	183	5	x2	x2	PROPN
ejpam-5897	183	6	,	,	PUNCT
ejpam-5897	183	7	x3	x3	ADJ
ejpam-5897	183	8	,	,	PUNCT
ejpam-5897	183	9	y1	y1	NOUN
ejpam-5897	183	10	,	,	PUNCT
ejpam-5897	183	11	y2	y2	PROPN
ejpam-5897	183	12	,	,	PUNCT
ejpam-5897	183	13	y3	y3	PROPN
ejpam-5897	183	14	,	,	PUNCT
ejpam-5897	183	15	z1	z1	PROPN
ejpam-5897	183	16	,	,	PUNCT
ejpam-5897	183	17	z2	z2	PROPN
ejpam-5897	183	18	,	,	PUNCT
ejpam-5897	183	19	z3	z3	PROPN
ejpam-5897	183	20	∈	∈	PROPN
ejpam-5897	183	21	x.	x.	NOUN
ejpam-5897	184	1	so	so	CCONJ
ejpam-5897	185	1	[	[	X
ejpam-5897	185	2	h(x1	h(x1	X
ejpam-5897	185	3	,	,	PUNCT
ejpam-5897	185	4	x2	x2	PROPN
ejpam-5897	185	5	,	,	PUNCT
ejpam-5897	185	6	x3	x3	ADJ
ejpam-5897	185	7	)	)	PUNCT
ejpam-5897	185	8	,	,	PUNCT
ejpam-5897	185	9	h(y1	h(y1	NOUN
ejpam-5897	185	10	,	,	PUNCT
ejpam-5897	185	11	y2	y2	PROPN
ejpam-5897	185	12	,	,	PUNCT
ejpam-5897	185	13	y3	y3	PROPN
ejpam-5897	185	14	)	)	PUNCT
ejpam-5897	185	15	,	,	PUNCT
ejpam-5897	185	16	h(z1	h(z1	NOUN
ejpam-5897	185	17	,	,	PUNCT
ejpam-5897	185	18	z2	z2	PROPN
ejpam-5897	185	19	,	,	PUNCT
ejpam-5897	185	20	z3	z3	PROPN
ejpam-5897	185	21	)	)	PUNCT
ejpam-5897	185	22	]	]	PUNCT
ejpam-5897	186	1	=	=	PUNCT
ejpam-5897	187	1	[	[	X
ejpam-5897	187	2	h(x1	h(x1	X
ejpam-5897	187	3	,	,	PUNCT
ejpam-5897	187	4	x2	x2	PROPN
ejpam-5897	187	5	,	,	PUNCT
ejpam-5897	187	6	x3	x3	ADJ
ejpam-5897	187	7	)	)	PUNCT
ejpam-5897	187	8	,	,	PUNCT
ejpam-5897	187	9	h(y1	h(y1	NOUN
ejpam-5897	187	10	,	,	PUNCT
ejpam-5897	187	11	y2	y2	PROPN
ejpam-5897	187	12	,	,	PUNCT
ejpam-5897	187	13	y3	y3	PROPN
ejpam-5897	187	14	)	)	PUNCT
ejpam-5897	187	15	,	,	PUNCT
ejpam-5897	187	16	h(z1	h(z1	NOUN
ejpam-5897	187	17	,	,	PUNCT
ejpam-5897	187	18	z2	z2	PROPN
ejpam-5897	187	19	,	,	PUNCT
ejpam-5897	187	20	z3	z3	PROPN
ejpam-5897	187	21	)	)	PUNCT
ejpam-5897	187	22	]	]	PUNCT
ejpam-5897	187	23	for	for	ADP
ejpam-5897	187	24	all	all	DET
ejpam-5897	187	25	x1	x1	PROPN
ejpam-5897	187	26	,	,	PUNCT
ejpam-5897	187	27	x2	x2	PROPN
ejpam-5897	187	28	,	,	PUNCT
ejpam-5897	187	29	x3	x3	ADJ
ejpam-5897	187	30	,	,	PUNCT
ejpam-5897	187	31	y1	y1	NOUN
ejpam-5897	187	32	,	,	PUNCT
ejpam-5897	187	33	y2	y2	PROPN
ejpam-5897	187	34	,	,	PUNCT
ejpam-5897	187	35	y3	y3	PROPN
ejpam-5897	187	36	,	,	PUNCT
ejpam-5897	187	37	z1	z1	PROPN
ejpam-5897	187	38	,	,	PUNCT
ejpam-5897	187	39	z2	z2	PROPN
ejpam-5897	187	40	,	,	PUNCT
ejpam-5897	187	41	z3	z3	PROPN
ejpam-5897	187	42	∈	∈	PROPN
ejpam-5897	187	43	x.	x.	NOUN
ejpam-5897	187	44	letting	let	VERB
ejpam-5897	187	45	x1	x1	PROPN
ejpam-5897	187	46	=	=	PUNCT
ejpam-5897	187	47	y1	y1	NOUN
ejpam-5897	187	48	=	=	SYM
ejpam-5897	187	49	x2	x2	NOUN
ejpam-5897	187	50	=	=	PUNCT
ejpam-5897	187	51	y2	y2	NOUN
ejpam-5897	187	52	=	=	SYM
ejpam-5897	188	1	x3	x3	ADJ
ejpam-5897	188	2	=	=	SYM
ejpam-5897	188	3	y3	y3	NOUN
ejpam-5897	188	4	=	=	SYM
ejpam-5897	188	5	e	e	NOUN
ejpam-5897	188	6	in	in	ADP
ejpam-5897	188	7	the	the	DET
ejpam-5897	188	8	last	last	ADJ
ejpam-5897	188	9	equality	equality	NOUN
ejpam-5897	188	10	,	,	PUNCT
ejpam-5897	188	11	we	we	PRON
ejpam-5897	188	12	get	get	VERB
ejpam-5897	188	13	h(z1	h(z1	NOUN
ejpam-5897	188	14	,	,	PUNCT
ejpam-5897	188	15	z2	z2	PROPN
ejpam-5897	188	16	,	,	PUNCT
ejpam-5897	188	17	z3	z3	PROPN
ejpam-5897	188	18	)	)	PUNCT
ejpam-5897	188	19	=	=	SYM
ejpam-5897	188	20	h(z1	h(z1	NOUN
ejpam-5897	188	21	,	,	PUNCT
ejpam-5897	188	22	z2	z2	PROPN
ejpam-5897	188	23	,	,	PUNCT
ejpam-5897	188	24	z3	z3	PROPN
ejpam-5897	188	25	)	)	PUNCT
ejpam-5897	188	26	for	for	ADP
ejpam-5897	188	27	all	all	DET
ejpam-5897	188	28	z1	z1	ADJ
ejpam-5897	188	29	,	,	PUNCT
ejpam-5897	188	30	z2	z2	PROPN
ejpam-5897	188	31	,	,	PUNCT
ejpam-5897	188	32	z3	z3	PROPN
ejpam-5897	188	33	∈	∈	PROPN
ejpam-5897	188	34	x.	x.	NOUN
ejpam-5897	188	35	therefore	therefore	ADV
ejpam-5897	188	36	,	,	PUNCT
ejpam-5897	188	37	the	the	DET
ejpam-5897	188	38	bijective	bijective	ADJ
ejpam-5897	188	39	mapping	mapping	NOUN
ejpam-5897	188	40	h	h	NOUN
ejpam-5897	188	41	:	:	PUNCT
ejpam-5897	188	42	x3	x3	ADJ
ejpam-5897	188	43	→	→	SYM
ejpam-5897	188	44	y	y	PROPN
ejpam-5897	188	45	is	be	AUX
ejpam-5897	188	46	a	a	DET
ejpam-5897	188	47	hyper	hyper	ADJ
ejpam-5897	188	48	3	3	NUM
ejpam-5897	188	49	-	-	PUNCT
ejpam-5897	188	50	isomorphism	isomorphism	NOUN
ejpam-5897	188	51	.	.	PUNCT
ejpam-5897	189	1	3	3	X
ejpam-5897	189	2	.	.	X
ejpam-5897	189	3	stability	stability	NOUN
ejpam-5897	189	4	of	of	ADP
ejpam-5897	189	5	hyper	hyper	ADJ
ejpam-5897	189	6	3	3	NUM
ejpam-5897	189	7	-	-	PUNCT
ejpam-5897	189	8	derivations	derivation	NOUN
ejpam-5897	189	9	in	in	ADP
ejpam-5897	189	10	ternary	ternary	ADJ
ejpam-5897	189	11	algebras	algebra	NOUN
ejpam-5897	189	12	in	in	ADP
ejpam-5897	189	13	this	this	DET
ejpam-5897	189	14	section	section	NOUN
ejpam-5897	189	15	,	,	PUNCT
ejpam-5897	189	16	we	we	PRON
ejpam-5897	189	17	prove	prove	VERB
ejpam-5897	189	18	the	the	DET
ejpam-5897	189	19	hyers	hyers	PROPN
ejpam-5897	189	20	-	-	PUNCT
ejpam-5897	189	21	ulam	ulam	ADJ
ejpam-5897	189	22	stability	stability	NOUN
ejpam-5897	189	23	of	of	ADP
ejpam-5897	189	24	hyper	hyper	ADJ
ejpam-5897	189	25	3	3	NUM
ejpam-5897	189	26	-	-	PUNCT
ejpam-5897	189	27	derivations	derivation	NOUN
ejpam-5897	189	28	in	in	ADP
ejpam-5897	189	29	complex	complex	ADJ
ejpam-5897	189	30	ternary	ternary	ADJ
ejpam-5897	189	31	algebras	algebra	NOUN
ejpam-5897	189	32	.	.	PUNCT
ejpam-5897	190	1	definition	definition	NOUN
ejpam-5897	190	2	3	3	X
ejpam-5897	190	3	.	.	PUNCT
ejpam-5897	191	1	let	let	VERB
ejpam-5897	191	2	x	x	PRON
ejpam-5897	191	3	be	be	AUX
ejpam-5897	191	4	a	a	DET
ejpam-5897	191	5	ternary	ternary	ADJ
ejpam-5897	191	6	algebra	algebra	NOUN
ejpam-5897	191	7	.	.	PUNCT
ejpam-5897	192	1	a	a	DET
ejpam-5897	192	2	3	3	NUM
ejpam-5897	192	3	-	-	PUNCT
ejpam-5897	192	4	linear	linear	NOUN
ejpam-5897	192	5	mapping	mapping	NOUN
ejpam-5897	192	6	f	f	NOUN
ejpam-5897	192	7	:	:	PUNCT
ejpam-5897	192	8	x3	x3	VERB
ejpam-5897	192	9	→	→	SYM
ejpam-5897	192	10	x	x	X
ejpam-5897	192	11	is	be	AUX
ejpam-5897	192	12	called	call	VERB
ejpam-5897	192	13	a	a	DET
ejpam-5897	192	14	hyper	hyper	ADJ
ejpam-5897	192	15	3	3	NUM
ejpam-5897	192	16	-	-	PUNCT
ejpam-5897	192	17	derivation	derivation	NOUN
ejpam-5897	192	18	if	if	SCONJ
ejpam-5897	192	19	f	f	PROPN
ejpam-5897	192	20	satisfies	satisfy	VERB
ejpam-5897	192	21	f([x1	f([x1	ADV
ejpam-5897	192	22	,	,	PUNCT
ejpam-5897	192	23	y1	y1	NOUN
ejpam-5897	192	24	,	,	PUNCT
ejpam-5897	192	25	z1	z1	NOUN
ejpam-5897	192	26	]	]	PUNCT
ejpam-5897	192	27	,	,	PUNCT
ejpam-5897	192	28	[	[	X
ejpam-5897	192	29	x2	x2	X
ejpam-5897	192	30	,	,	PUNCT
ejpam-5897	192	31	y2	y2	PROPN
ejpam-5897	192	32	,	,	PUNCT
ejpam-5897	192	33	z2	z2	PROPN
ejpam-5897	192	34	]	]	PUNCT
ejpam-5897	192	35	,	,	PUNCT
ejpam-5897	192	36	[	[	X
ejpam-5897	192	37	x3	x3	ADJ
ejpam-5897	192	38	,	,	PUNCT
ejpam-5897	192	39	y3	y3	NOUN
ejpam-5897	192	40	,	,	PUNCT
ejpam-5897	192	41	z3	z3	PROPN
ejpam-5897	192	42	]	]	PUNCT
ejpam-5897	192	43	)	)	PUNCT
ejpam-5897	192	44	=	=	PUNCT
ejpam-5897	193	1	[	[	X
ejpam-5897	193	2	f(x1	f(x1	ADJ
ejpam-5897	193	3	,	,	PUNCT
ejpam-5897	193	4	x2	x2	PROPN
ejpam-5897	193	5	,	,	PUNCT
ejpam-5897	193	6	x3	x3	ADJ
ejpam-5897	193	7	)	)	PUNCT
ejpam-5897	193	8	,	,	PUNCT
ejpam-5897	194	1	[	[	X
ejpam-5897	194	2	y1	y1	X
ejpam-5897	194	3	,	,	PUNCT
ejpam-5897	194	4	y2	y2	PROPN
ejpam-5897	194	5	,	,	PUNCT
ejpam-5897	194	6	y3	y3	PROPN
ejpam-5897	194	7	]	]	PUNCT
ejpam-5897	194	8	,	,	PUNCT
ejpam-5897	194	9	[	[	X
ejpam-5897	194	10	z1	z1	ADJ
ejpam-5897	194	11	,	,	PUNCT
ejpam-5897	194	12	z2	z2	PROPN
ejpam-5897	194	13	,	,	PUNCT
ejpam-5897	194	14	z3	z3	PROPN
ejpam-5897	194	15	]	]	X
ejpam-5897	194	16	]	]	PUNCT
ejpam-5897	195	1	+	+	CCONJ
ejpam-5897	196	1	[	[	X
ejpam-5897	196	2	[	[	X
ejpam-5897	196	3	x1	x1	ADJ
ejpam-5897	196	4	,	,	PUNCT
ejpam-5897	196	5	x2	x2	PROPN
ejpam-5897	196	6	,	,	PUNCT
ejpam-5897	196	7	x3	x3	ADJ
ejpam-5897	196	8	]	]	PUNCT
ejpam-5897	196	9	,	,	PUNCT
ejpam-5897	196	10	f(y1	f(y1	NOUN
ejpam-5897	196	11	,	,	PUNCT
ejpam-5897	196	12	y2	y2	PROPN
ejpam-5897	196	13	,	,	PUNCT
ejpam-5897	196	14	y3	y3	PROPN
ejpam-5897	196	15	)	)	PUNCT
ejpam-5897	196	16	,	,	PUNCT
ejpam-5897	196	17	[	[	X
ejpam-5897	196	18	z1	z1	ADJ
ejpam-5897	196	19	,	,	PUNCT
ejpam-5897	196	20	z2	z2	PROPN
ejpam-5897	196	21	,	,	PUNCT
ejpam-5897	196	22	z3	z3	PROPN
ejpam-5897	196	23	]	]	X
ejpam-5897	196	24	]	]	PUNCT
ejpam-5897	197	1	+	+	CCONJ
ejpam-5897	198	1	[	[	X
ejpam-5897	198	2	[	[	X
ejpam-5897	198	3	x1	x1	ADJ
ejpam-5897	198	4	,	,	PUNCT
ejpam-5897	198	5	x2	x2	PROPN
ejpam-5897	198	6	,	,	PUNCT
ejpam-5897	198	7	x3	x3	ADJ
ejpam-5897	198	8	]	]	PUNCT
ejpam-5897	198	9	,	,	PUNCT
ejpam-5897	199	1	[	[	X
ejpam-5897	199	2	y1	y1	X
ejpam-5897	199	3	,	,	PUNCT
ejpam-5897	199	4	y2	y2	PROPN
ejpam-5897	199	5	,	,	PUNCT
ejpam-5897	199	6	y3	y3	PROPN
ejpam-5897	199	7	]	]	PUNCT
ejpam-5897	199	8	,	,	PUNCT
ejpam-5897	199	9	f(z1	f(z1	ADJ
ejpam-5897	199	10	,	,	PUNCT
ejpam-5897	199	11	z2	z2	PROPN
ejpam-5897	199	12	,	,	PUNCT
ejpam-5897	199	13	z3	z3	PROPN
ejpam-5897	199	14	)	)	PUNCT
ejpam-5897	199	15	]	]	PUNCT
ejpam-5897	199	16	for	for	ADP
ejpam-5897	199	17	all	all	PRON
ejpam-5897	199	18	x1	x1	PROPN
ejpam-5897	199	19	,	,	PUNCT
ejpam-5897	199	20	x2	x2	PROPN
ejpam-5897	199	21	,	,	PUNCT
ejpam-5897	199	22	x3	x3	ADJ
ejpam-5897	199	23	,	,	PUNCT
ejpam-5897	199	24	y1	y1	NOUN
ejpam-5897	199	25	,	,	PUNCT
ejpam-5897	199	26	y2	y2	PROPN
ejpam-5897	199	27	,	,	PUNCT
ejpam-5897	199	28	y3	y3	PROPN
ejpam-5897	199	29	,	,	PUNCT
ejpam-5897	199	30	z1	z1	PROPN
ejpam-5897	199	31	,	,	PUNCT
ejpam-5897	199	32	z2	z2	PROPN
ejpam-5897	199	33	,	,	PUNCT
ejpam-5897	199	34	z3	z3	PROPN
ejpam-5897	199	35	∈	∈	PROPN
ejpam-5897	199	36	x.	x.	NOUN
ejpam-5897	199	37	theorem	theorem	VERB
ejpam-5897	199	38	4	4	NUM
ejpam-5897	199	39	.	.	PUNCT
ejpam-5897	200	1	let	let	VERB
ejpam-5897	200	2	x	x	PRON
ejpam-5897	200	3	be	be	AUX
ejpam-5897	200	4	a	a	DET
ejpam-5897	200	5	ternary	ternary	ADJ
ejpam-5897	200	6	algebra	algebra	NOUN
ejpam-5897	200	7	and	and	CCONJ
ejpam-5897	200	8	t	t	PROPN
ejpam-5897	200	9	be	be	AUX
ejpam-5897	200	10	a	a	DET
ejpam-5897	200	11	real	real	ADJ
ejpam-5897	200	12	number	number	NOUN
ejpam-5897	200	13	satisfying	satisfying	NOUN
ejpam-5897	200	14	|t|	|t|	NOUN
ejpam-5897	200	15	<	<	X
ejpam-5897	200	16	1	1	NUM
ejpam-5897	200	17	.	.	PUNCT
ejpam-5897	201	1	if	if	SCONJ
ejpam-5897	201	2	a	a	DET
ejpam-5897	201	3	mapping	mapping	NOUN
ejpam-5897	201	4	f	f	NOUN
ejpam-5897	201	5	:	:	PUNCT
ejpam-5897	202	1	x3	x3	ADJ
ejpam-5897	202	2	→	→	SYM
ejpam-5897	202	3	x	x	SYM
ejpam-5897	202	4	satisfies∥∥∥∥∥∥f(x1	satisfies∥∥∥∥∥∥f(x1	NOUN
ejpam-5897	202	5	+	+	CCONJ
ejpam-5897	202	6	x2	x2	ADJ
ejpam-5897	202	7	,	,	PUNCT
ejpam-5897	202	8	y1	y1	NOUN
ejpam-5897	202	9	+	+	CCONJ
ejpam-5897	202	10	y2	y2	NOUN
ejpam-5897	202	11	,	,	PUNCT
ejpam-5897	202	12	z1	z1	PROPN
ejpam-5897	202	13	+	+	CCONJ
ejpam-5897	202	14	z2)−	z2)−	PROPN
ejpam-5897	202	15	2∑	2∑	NUM
ejpam-5897	202	16	i	i	PROPN
ejpam-5897	202	17	,	,	PUNCT
ejpam-5897	202	18	j	j	PROPN
ejpam-5897	202	19	,	,	PUNCT
ejpam-5897	202	20	k=1	k=1	PROPN
ejpam-5897	202	21	f(xi	f(xi	PROPN
ejpam-5897	202	22	,	,	PUNCT
ejpam-5897	202	23	yj	yj	PROPN
ejpam-5897	202	24	,	,	PUNCT
ejpam-5897	202	25	zk	zk	PROPN
ejpam-5897	202	26	)	)	PUNCT
ejpam-5897	202	27	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-5897	203	1	(	(	PUNCT
ejpam-5897	203	2	10	10	NUM
ejpam-5897	203	3	)	)	PUNCT
ejpam-5897	203	4	e.	e.	PROPN
ejpam-5897	203	5	shim	shim	PROPN
ejpam-5897	203	6	,	,	PUNCT
ejpam-5897	203	7	s.	s.	PROPN
ejpam-5897	203	8	donganont	donganont	PROPN
ejpam-5897	203	9	,	,	PUNCT
ejpam-5897	203	10	c.	c.	PROPN
ejpam-5897	203	11	park	park	PROPN
ejpam-5897	203	12	/	/	SYM
ejpam-5897	203	13	eur	eur	PROPN
ejpam-5897	203	14	.	.	PUNCT
ejpam-5897	204	1	j.	j.	PROPN
ejpam-5897	204	2	pure	pure	PROPN
ejpam-5897	204	3	appl	appl	PROPN
ejpam-5897	204	4	.	.	PROPN
ejpam-5897	204	5	math	math	PROPN
ejpam-5897	204	6	,	,	PUNCT
ejpam-5897	204	7	18	18	NUM
ejpam-5897	204	8	(	(	PUNCT
ejpam-5897	204	9	2	2	NUM
ejpam-5897	204	10	)	)	PUNCT
ejpam-5897	204	11	(	(	PUNCT
ejpam-5897	204	12	2025	2025	NUM
ejpam-5897	204	13	)	)	PUNCT
ejpam-5897	204	14	,	,	PUNCT
ejpam-5897	204	15	5897	5897	NUM
ejpam-5897	204	16	9	9	NUM
ejpam-5897	204	17	of	of	ADP
ejpam-5897	204	18	14	14	NUM
ejpam-5897	204	19	≤	≤	NOUN
ejpam-5897	204	20	∥∥∥∥∥∥t	∥∥∥∥∥∥t	PUNCT
ejpam-5897	204	21	8f	8f	NOUN
ejpam-5897	204	22	(	(	PUNCT
ejpam-5897	204	23	x1	x1	PROPN
ejpam-5897	205	1	+	+	CCONJ
ejpam-5897	205	2	x2	x2	PROPN
ejpam-5897	205	3	2	2	NUM
ejpam-5897	205	4	,	,	PUNCT
ejpam-5897	205	5	y1	y1	NOUN
ejpam-5897	205	6	+	+	CCONJ
ejpam-5897	205	7	y2	y2	PROPN
ejpam-5897	205	8	2	2	NUM
ejpam-5897	205	9	,	,	PUNCT
ejpam-5897	205	10	z1	z1	PROPN
ejpam-5897	205	11	+	+	CCONJ
ejpam-5897	205	12	z2	z2	PROPN
ejpam-5897	205	13	2	2	NUM
ejpam-5897	205	14	)	)	PUNCT
ejpam-5897	205	15	−	−	PROPN
ejpam-5897	206	1	2∑	2∑	NUM
ejpam-5897	206	2	i	i	PROPN
ejpam-5897	206	3	,	,	PUNCT
ejpam-5897	206	4	j	j	PROPN
ejpam-5897	206	5	,	,	PUNCT
ejpam-5897	206	6	k=1	k=1	PROPN
ejpam-5897	206	7	f(xi	f(xi	PROPN
ejpam-5897	206	8	,	,	PUNCT
ejpam-5897	206	9	yj	yj	PROPN
ejpam-5897	206	10	,	,	PUNCT
ejpam-5897	206	11	zk	zk	PROPN
ejpam-5897	206	12	)	)	PUNCT
ejpam-5897	206	13	∥∥∥∥∥∥	∥∥∥∥∥∥	VERB
ejpam-5897	207	1	for	for	ADP
ejpam-5897	207	2	all	all	DET
ejpam-5897	207	3	(	(	PUNCT
ejpam-5897	207	4	x1	x1	PROPN
ejpam-5897	207	5	,	,	PUNCT
ejpam-5897	207	6	y1	y1	PROPN
ejpam-5897	207	7	,	,	PUNCT
ejpam-5897	207	8	z1	z1	NOUN
ejpam-5897	207	9	)	)	PUNCT
ejpam-5897	207	10	,	,	PUNCT
ejpam-5897	207	11	(	(	PUNCT
ejpam-5897	207	12	x2	x2	PROPN
ejpam-5897	207	13	,	,	PUNCT
ejpam-5897	207	14	y2	y2	PROPN
ejpam-5897	207	15	,	,	PUNCT
ejpam-5897	207	16	z2	z2	PROPN
ejpam-5897	207	17	)	)	PUNCT
ejpam-5897	207	18	∈	∈	PROPN
ejpam-5897	207	19	x3	x3	PROPN
ejpam-5897	207	20	.	.	PUNCT
ejpam-5897	208	1	then	then	ADV
ejpam-5897	208	2	f	f	PROPN
ejpam-5897	208	3	is	be	AUX
ejpam-5897	208	4	3	3	NUM
ejpam-5897	208	5	-	-	PUNCT
ejpam-5897	208	6	additive	additive	NOUN
ejpam-5897	208	7	.	.	PUNCT
ejpam-5897	209	1	proof	proof	NOUN
ejpam-5897	209	2	.	.	PUNCT
ejpam-5897	210	1	letting	let	VERB
ejpam-5897	210	2	x1	x1	NOUN
ejpam-5897	211	1	=	=	SYM
ejpam-5897	211	2	x2	x2	INTJ
ejpam-5897	211	3	:	:	PUNCT
ejpam-5897	211	4	=	=	SYM
ejpam-5897	211	5	x	x	X
ejpam-5897	211	6	,	,	PUNCT
ejpam-5897	211	7	y1	y1	INTJ
ejpam-5897	211	8	=	=	PUNCT
ejpam-5897	211	9	y2	y2	INTJ
ejpam-5897	211	10	:	:	PUNCT
ejpam-5897	211	11	=	=	SYM
ejpam-5897	211	12	y	y	PROPN
ejpam-5897	211	13	and	and	CCONJ
ejpam-5897	211	14	z1	z1	PROPN
ejpam-5897	211	15	=	=	SYM
ejpam-5897	211	16	z2	z2	PROPN
ejpam-5897	211	17	:	:	PUNCT
ejpam-5897	211	18	=	=	SYM
ejpam-5897	211	19	z	z	X
ejpam-5897	211	20	in	in	ADP
ejpam-5897	211	21	(	(	PUNCT
ejpam-5897	211	22	10	10	NUM
ejpam-5897	211	23	)	)	PUNCT
ejpam-5897	211	24	,	,	PUNCT
ejpam-5897	211	25	we	we	PRON
ejpam-5897	211	26	get	get	AUX
ejpam-5897	211	27	∥f(2x	∥f(2x	VERB
ejpam-5897	211	28	,	,	PUNCT
ejpam-5897	211	29	2y	2y	NUM
ejpam-5897	211	30	,	,	PUNCT
ejpam-5897	211	31	2z)−	2z)−	NUM
ejpam-5897	211	32	8f(x	8f(x	PROPN
ejpam-5897	211	33	,	,	PUNCT
ejpam-5897	211	34	y	y	PROPN
ejpam-5897	211	35	,	,	PUNCT
ejpam-5897	211	36	z)∥	z)∥	NUM
ejpam-5897	211	37	≤	≤	NOUN
ejpam-5897	211	38	0	0	NUM
ejpam-5897	211	39	for	for	ADP
ejpam-5897	211	40	all	all	DET
ejpam-5897	211	41	x	x	NOUN
ejpam-5897	211	42	,	,	PUNCT
ejpam-5897	211	43	y	y	PROPN
ejpam-5897	211	44	,	,	PUNCT
ejpam-5897	211	45	z	z	PROPN
ejpam-5897	211	46	∈	∈	PROPN
ejpam-5897	211	47	x.	x.	NOUN
ejpam-5897	212	1	so	so	ADV
ejpam-5897	212	2	f(2x	f(2x	PROPN
ejpam-5897	212	3	,	,	PUNCT
ejpam-5897	212	4	2y	2y	NUM
ejpam-5897	212	5	,	,	PUNCT
ejpam-5897	212	6	2z	2z	NUM
ejpam-5897	212	7	)	)	PUNCT
ejpam-5897	212	8	=	=	SYM
ejpam-5897	212	9	8f(x	8f(x	PROPN
ejpam-5897	212	10	,	,	PUNCT
ejpam-5897	212	11	y	y	PROPN
ejpam-5897	212	12	,	,	PUNCT
ejpam-5897	212	13	z	z	NOUN
ejpam-5897	212	14	)	)	PUNCT
ejpam-5897	212	15	for	for	ADP
ejpam-5897	212	16	all	all	DET
ejpam-5897	212	17	x	x	NOUN
ejpam-5897	212	18	,	,	PUNCT
ejpam-5897	212	19	y	y	PROPN
ejpam-5897	212	20	,	,	PUNCT
ejpam-5897	212	21	z	z	NOUN
ejpam-5897	212	22	∈	∈	PROPN
ejpam-5897	212	23	x.	x.	NOUN
ejpam-5897	213	1	it	it	PRON
ejpam-5897	213	2	follows	follow	VERB
ejpam-5897	213	3	from	from	ADP
ejpam-5897	213	4	(	(	PUNCT
ejpam-5897	213	5	10	10	NUM
ejpam-5897	213	6	)	)	PUNCT
ejpam-5897	214	1	that	that	PRON
ejpam-5897	214	2	∥∥∥∥∥∥f(x1	∥∥∥∥∥∥f(x1	PRON
ejpam-5897	214	3	+	+	X
ejpam-5897	214	4	x2	x2	ADJ
ejpam-5897	214	5	,	,	PUNCT
ejpam-5897	214	6	y1	y1	NOUN
ejpam-5897	214	7	+	+	CCONJ
ejpam-5897	214	8	y2	y2	NOUN
ejpam-5897	214	9	,	,	PUNCT
ejpam-5897	214	10	z1	z1	PROPN
ejpam-5897	214	11	+	+	CCONJ
ejpam-5897	214	12	z2)−	z2)−	PROPN
ejpam-5897	214	13	2∑	2∑	NUM
ejpam-5897	214	14	i	i	PROPN
ejpam-5897	214	15	,	,	PUNCT
ejpam-5897	214	16	j	j	PROPN
ejpam-5897	214	17	,	,	PUNCT
ejpam-5897	214	18	k=1	k=1	PROPN
ejpam-5897	214	19	f(xi	f(xi	PROPN
ejpam-5897	214	20	,	,	PUNCT
ejpam-5897	214	21	yj	yj	PROPN
ejpam-5897	214	22	,	,	PUNCT
ejpam-5897	214	23	zk	zk	PROPN
ejpam-5897	214	24	)	)	PUNCT
ejpam-5897	214	25	∥∥∥∥∥∥	∥∥∥∥∥∥	PUNCT
ejpam-5897	214	26	≤	≤	NUM
ejpam-5897	214	27	∥∥∥∥∥∥t	∥∥∥∥∥∥t	PUNCT
ejpam-5897	215	1	f(x1	f(x1	PROPN
ejpam-5897	215	2	+	+	CCONJ
ejpam-5897	215	3	x2	x2	PROPN
ejpam-5897	215	4	,	,	PUNCT
ejpam-5897	215	5	y1	y1	NOUN
ejpam-5897	215	6	+	+	CCONJ
ejpam-5897	215	7	y2	y2	NOUN
ejpam-5897	215	8	,	,	PUNCT
ejpam-5897	215	9	z1	z1	PROPN
ejpam-5897	215	10	+	+	CCONJ
ejpam-5897	215	11	z2)−	z2)−	PROPN
ejpam-5897	215	12	2∑	2∑	NUM
ejpam-5897	216	1	i	i	PROPN
ejpam-5897	216	2	,	,	PUNCT
ejpam-5897	216	3	j	j	PROPN
ejpam-5897	216	4	,	,	PUNCT
ejpam-5897	216	5	k=1	k=1	PROPN
ejpam-5897	216	6	f(xi	f(xi	PROPN
ejpam-5897	216	7	,	,	PUNCT
ejpam-5897	216	8	yj	yj	PROPN
ejpam-5897	216	9	,	,	PUNCT
ejpam-5897	216	10	zk	zk	PROPN
ejpam-5897	216	11	)	)	PUNCT
ejpam-5897	216	12	∥∥∥∥∥∥	∥∥∥∥∥∥	VERB
ejpam-5897	217	1	for	for	ADP
ejpam-5897	217	2	all	all	DET
ejpam-5897	217	3	(	(	PUNCT
ejpam-5897	217	4	x1	x1	PROPN
ejpam-5897	217	5	,	,	PUNCT
ejpam-5897	217	6	y1	y1	PROPN
ejpam-5897	217	7	,	,	PUNCT
ejpam-5897	217	8	z1	z1	NOUN
ejpam-5897	217	9	)	)	PUNCT
ejpam-5897	217	10	,	,	PUNCT
ejpam-5897	217	11	(	(	PUNCT
ejpam-5897	217	12	x2	x2	PROPN
ejpam-5897	217	13	,	,	PUNCT
ejpam-5897	217	14	y2	y2	PROPN
ejpam-5897	217	15	,	,	PUNCT
ejpam-5897	217	16	z2	z2	PROPN
ejpam-5897	217	17	)	)	PUNCT
ejpam-5897	217	18	∈	∈	PROPN
ejpam-5897	217	19	x3	x3	PROPN
ejpam-5897	217	20	.	.	PUNCT
ejpam-5897	218	1	thus	thus	ADV
ejpam-5897	218	2	f(x1	f(x1	ADJ
ejpam-5897	218	3	+	+	CCONJ
ejpam-5897	218	4	x2	x2	ADJ
ejpam-5897	218	5	,	,	PUNCT
ejpam-5897	218	6	y1	y1	NOUN
ejpam-5897	218	7	+	+	CCONJ
ejpam-5897	218	8	y2	y2	ADJ
ejpam-5897	218	9	,	,	PUNCT
ejpam-5897	218	10	z1	z1	PROPN
ejpam-5897	218	11	+	+	CCONJ
ejpam-5897	218	12	z2	z2	NUM
ejpam-5897	218	13	)	)	PUNCT
ejpam-5897	218	14	=	=	SYM
ejpam-5897	219	1	2∑	2∑	NUM
ejpam-5897	219	2	i	i	NOUN
ejpam-5897	219	3	,	,	PUNCT
ejpam-5897	219	4	j	j	PROPN
ejpam-5897	219	5	,	,	PUNCT
ejpam-5897	219	6	k=1	k=1	PROPN
ejpam-5897	219	7	f(xi	f(xi	PROPN
ejpam-5897	219	8	,	,	PUNCT
ejpam-5897	219	9	yj	yj	PROPN
ejpam-5897	219	10	,	,	PUNCT
ejpam-5897	219	11	zk	zk	PROPN
ejpam-5897	219	12	)	)	PUNCT
ejpam-5897	219	13	for	for	ADP
ejpam-5897	219	14	all	all	DET
ejpam-5897	219	15	(	(	PUNCT
ejpam-5897	219	16	x1	x1	PROPN
ejpam-5897	219	17	,	,	PUNCT
ejpam-5897	219	18	y1	y1	PROPN
ejpam-5897	219	19	,	,	PUNCT
ejpam-5897	219	20	z1	z1	NOUN
ejpam-5897	219	21	)	)	PUNCT
ejpam-5897	219	22	,	,	PUNCT
ejpam-5897	219	23	(	(	PUNCT
ejpam-5897	219	24	x2	x2	PROPN
ejpam-5897	219	25	,	,	PUNCT
ejpam-5897	219	26	y2	y2	PROPN
ejpam-5897	219	27	,	,	PUNCT
ejpam-5897	219	28	z2	z2	PROPN
ejpam-5897	219	29	)	)	PUNCT
ejpam-5897	219	30	∈	∈	PROPN
ejpam-5897	219	31	x3	x3	PROPN
ejpam-5897	219	32	,	,	PUNCT
ejpam-5897	219	33	since	since	SCONJ
ejpam-5897	219	34	|t|	|t|	VERB
ejpam-5897	219	35	<	<	X
ejpam-5897	219	36	1	1	NUM
ejpam-5897	219	37	.	.	PUNCT
ejpam-5897	220	1	thus	thus	ADV
ejpam-5897	220	2	the	the	DET
ejpam-5897	220	3	mapping	mapping	NOUN
ejpam-5897	220	4	f	f	PROPN
ejpam-5897	220	5	is	be	AUX
ejpam-5897	220	6	3	3	NUM
ejpam-5897	220	7	-	-	PUNCT
ejpam-5897	220	8	additive	additive	NOUN
ejpam-5897	220	9	.	.	PUNCT
ejpam-5897	221	1	theorem	theorem	NOUN
ejpam-5897	221	2	5	5	NUM
ejpam-5897	221	3	.	.	PUNCT
ejpam-5897	222	1	let	let	VERB
ejpam-5897	222	2	x	x	PRON
ejpam-5897	222	3	be	be	AUX
ejpam-5897	222	4	a	a	DET
ejpam-5897	222	5	ternary	ternary	ADJ
ejpam-5897	222	6	banach	banach	NOUN
ejpam-5897	222	7	algebra	algebra	NOUN
ejpam-5897	222	8	and	and	CCONJ
ejpam-5897	222	9	t	t	PROPN
ejpam-5897	222	10	be	be	AUX
ejpam-5897	222	11	a	a	DET
ejpam-5897	222	12	real	real	ADJ
ejpam-5897	222	13	number	number	NOUN
ejpam-5897	222	14	satisfying	satisfying	NOUN
ejpam-5897	222	15	|t|	|t|	NOUN
ejpam-5897	222	16	<	<	X
ejpam-5897	222	17	1	1	X
ejpam-5897	222	18	.	.	PUNCT
ejpam-5897	223	1	let	let	VERB
ejpam-5897	223	2	φ	φ	NOUN
ejpam-5897	223	3	:	:	PUNCT
ejpam-5897	223	4	x6	x6	PROPN
ejpam-5897	223	5	→	→	SYM
ejpam-5897	224	1	[	[	X
ejpam-5897	224	2	0,∞	0,∞	NUM
ejpam-5897	224	3	)	)	PUNCT
ejpam-5897	224	4	and	and	CCONJ
ejpam-5897	224	5	ψ	ψ	X
ejpam-5897	224	6	:	:	PUNCT
ejpam-5897	224	7	x9	x9	NOUN
ejpam-5897	224	8	→	→	PUNCT
ejpam-5897	225	1	[	[	X
ejpam-5897	225	2	0,∞	0,∞	X
ejpam-5897	225	3	)	)	PUNCT
ejpam-5897	225	4	be	be	AUX
ejpam-5897	225	5	functions	function	NOUN
ejpam-5897	225	6	such	such	ADJ
ejpam-5897	225	7	that	that	SCONJ
ejpam-5897	225	8	+	+	ADJ
ejpam-5897	225	9	∞∑	∞∑	NUM
ejpam-5897	225	10	j=1	j=1	ADJ
ejpam-5897	225	11	8jφ	8jφ	NOUN
ejpam-5897	225	12	(	(	PUNCT
ejpam-5897	225	13	x	x	SYM
ejpam-5897	225	14	2j	2j	NOUN
ejpam-5897	225	15	,	,	PUNCT
ejpam-5897	225	16	y	y	PROPN
ejpam-5897	225	17	2j	2j	NUM
ejpam-5897	225	18	,	,	PUNCT
ejpam-5897	225	19	z	z	NOUN
ejpam-5897	225	20	2j	2j	NOUN
ejpam-5897	225	21	,	,	PUNCT
ejpam-5897	225	22	x	x	X
ejpam-5897	225	23	2j	2j	NOUN
ejpam-5897	225	24	,	,	PUNCT
ejpam-5897	225	25	y	y	PROPN
ejpam-5897	225	26	2j	2j	NUM
ejpam-5897	225	27	,	,	PUNCT
ejpam-5897	225	28	z	z	NOUN
ejpam-5897	225	29	2j	2j	X
ejpam-5897	225	30	)	)	PUNCT
ejpam-5897	226	1	<	<	X
ejpam-5897	226	2	∞	∞	NUM
ejpam-5897	226	3	and	and	CCONJ
ejpam-5897	226	4	+	+	ADJ
ejpam-5897	226	5	∞∑	∞∑	ADJ
ejpam-5897	226	6	j=1	j=1	ADJ
ejpam-5897	226	7	83jψ	83jψ	NOUN
ejpam-5897	226	8	(	(	PUNCT
ejpam-5897	226	9	x	x	SYM
ejpam-5897	226	10	2j	2j	NOUN
ejpam-5897	226	11	,	,	PUNCT
ejpam-5897	226	12	x	x	X
ejpam-5897	226	13	2j	2j	NOUN
ejpam-5897	226	14	,	,	PUNCT
ejpam-5897	226	15	x	x	X
ejpam-5897	226	16	2j	2j	NOUN
ejpam-5897	226	17	,	,	PUNCT
ejpam-5897	226	18	y	y	PROPN
ejpam-5897	226	19	2j	2j	NOUN
ejpam-5897	226	20	,	,	PUNCT
ejpam-5897	226	21	y	y	PROPN
ejpam-5897	226	22	2j	2j	NOUN
ejpam-5897	226	23	,	,	PUNCT
ejpam-5897	226	24	y	y	PROPN
ejpam-5897	226	25	2j	2j	NUM
ejpam-5897	226	26	,	,	PUNCT
ejpam-5897	226	27	z	z	NOUN
ejpam-5897	226	28	2j	2j	NOUN
ejpam-5897	226	29	,	,	PUNCT
ejpam-5897	226	30	z	z	NOUN
ejpam-5897	226	31	2j	2j	NOUN
ejpam-5897	226	32	,	,	PUNCT
ejpam-5897	226	33	z	z	NOUN
ejpam-5897	226	34	2j	2j	NOUN
ejpam-5897	226	35	)	)	PUNCT
ejpam-5897	227	1	<	<	X
ejpam-5897	227	2	∞	∞	NUM
ejpam-5897	227	3	for	for	ADP
ejpam-5897	227	4	all	all	DET
ejpam-5897	227	5	x	x	NOUN
ejpam-5897	227	6	,	,	PUNCT
ejpam-5897	227	7	y	y	PROPN
ejpam-5897	227	8	,	,	PUNCT
ejpam-5897	227	9	z	z	PROPN
ejpam-5897	227	10	∈	∈	PROPN
ejpam-5897	227	11	x.	x.	NOUN
ejpam-5897	227	12	let	let	VERB
ejpam-5897	227	13	f	f	NOUN
ejpam-5897	227	14	:	:	PUNCT
ejpam-5897	227	15	x3	x3	VERB
ejpam-5897	227	16	→	→	SYM
ejpam-5897	227	17	x	x	PART
ejpam-5897	227	18	be	be	AUX
ejpam-5897	227	19	a	a	DET
ejpam-5897	227	20	mapping	mapping	NOUN
ejpam-5897	227	21	satisfying∥∥∥∥∥∥f(µ(x1	satisfying∥∥∥∥∥∥f(µ(x1	NOUN
ejpam-5897	228	1	+	+	CCONJ
ejpam-5897	228	2	x2	x2	PROPN
ejpam-5897	228	3	,	,	PUNCT
ejpam-5897	228	4	y1	y1	NOUN
ejpam-5897	228	5	+	+	CCONJ
ejpam-5897	228	6	y2	y2	NOUN
ejpam-5897	228	7	,	,	PUNCT
ejpam-5897	228	8	z1	z1	PROPN
ejpam-5897	228	9	+	+	CCONJ
ejpam-5897	228	10	z2))−	z2))−	PROPN
ejpam-5897	228	11	µ	µ	PRON
ejpam-5897	228	12	2∑	2∑	NUM
ejpam-5897	228	13	i	i	PROPN
ejpam-5897	228	14	,	,	PUNCT
ejpam-5897	228	15	j	j	PROPN
ejpam-5897	228	16	,	,	PUNCT
ejpam-5897	228	17	k=1	k=1	PROPN
ejpam-5897	228	18	f(xi	f(xi	PROPN
ejpam-5897	228	19	,	,	PUNCT
ejpam-5897	228	20	yj	yj	PROPN
ejpam-5897	228	21	,	,	PUNCT
ejpam-5897	228	22	zk	zk	PROPN
ejpam-5897	228	23	)	)	PUNCT
ejpam-5897	228	24	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-5897	229	1	(	(	PUNCT
ejpam-5897	229	2	11	11	NUM
ejpam-5897	229	3	)	)	PUNCT
ejpam-5897	229	4	≤	≤	NOUN
ejpam-5897	229	5	∥∥∥∥∥∥t	∥∥∥∥∥∥t	PUNCT
ejpam-5897	229	6	8f	8f	PROPN
ejpam-5897	229	7	(	(	PUNCT
ejpam-5897	229	8	µ	µ	X
ejpam-5897	229	9	(	(	PUNCT
ejpam-5897	229	10	x1	x1	PROPN
ejpam-5897	230	1	+	+	CCONJ
ejpam-5897	230	2	x2	x2	PROPN
ejpam-5897	230	3	2	2	NUM
ejpam-5897	230	4	,	,	PUNCT
ejpam-5897	230	5	y1	y1	NOUN
ejpam-5897	230	6	+	+	CCONJ
ejpam-5897	230	7	y2	y2	PROPN
ejpam-5897	230	8	2	2	NUM
ejpam-5897	230	9	,	,	PUNCT
ejpam-5897	230	10	z1	z1	PROPN
ejpam-5897	230	11	+	+	CCONJ
ejpam-5897	230	12	z2	z2	PROPN
ejpam-5897	230	13	2	2	NUM
ejpam-5897	230	14	)	)	PUNCT
ejpam-5897	230	15	)	)	PUNCT
ejpam-5897	231	1	−	−	PROPN
ejpam-5897	231	2	µ	µ	NUM
ejpam-5897	231	3	2∑	2∑	NUM
ejpam-5897	232	1	i	i	PROPN
ejpam-5897	232	2	,	,	PUNCT
ejpam-5897	232	3	j	j	PROPN
ejpam-5897	232	4	,	,	PUNCT
ejpam-5897	232	5	k=1	k=1	PROPN
ejpam-5897	232	6	f(xi	f(xi	PROPN
ejpam-5897	232	7	,	,	PUNCT
ejpam-5897	232	8	yj	yj	PROPN
ejpam-5897	232	9	,	,	PUNCT
ejpam-5897	232	10	zk	zk	PROPN
ejpam-5897	232	11	)	)	PUNCT
ejpam-5897	232	12	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-5897	233	1	e.	e.	PROPN
ejpam-5897	233	2	shim	shim	PROPN
ejpam-5897	233	3	,	,	PUNCT
ejpam-5897	233	4	s.	s.	PROPN
ejpam-5897	233	5	donganont	donganont	PROPN
ejpam-5897	233	6	,	,	PUNCT
ejpam-5897	233	7	c.	c.	PROPN
ejpam-5897	233	8	park	park	PROPN
ejpam-5897	233	9	/	/	SYM
ejpam-5897	233	10	eur	eur	PROPN
ejpam-5897	233	11	.	.	PUNCT
ejpam-5897	234	1	j.	j.	PROPN
ejpam-5897	234	2	pure	pure	PROPN
ejpam-5897	234	3	appl	appl	PROPN
ejpam-5897	234	4	.	.	PROPN
ejpam-5897	234	5	math	math	PROPN
ejpam-5897	234	6	,	,	PUNCT
ejpam-5897	234	7	18	18	NUM
ejpam-5897	234	8	(	(	PUNCT
ejpam-5897	234	9	2	2	NUM
ejpam-5897	234	10	)	)	PUNCT
ejpam-5897	234	11	(	(	PUNCT
ejpam-5897	234	12	2025	2025	NUM
ejpam-5897	234	13	)	)	PUNCT
ejpam-5897	234	14	,	,	PUNCT
ejpam-5897	234	15	5897	5897	NUM
ejpam-5897	234	16	10	10	NUM
ejpam-5897	234	17	of	of	ADP
ejpam-5897	234	18	14	14	NUM
ejpam-5897	235	1	+	+	NOUN
ejpam-5897	235	2	φ(x1	φ(x1	ADJ
ejpam-5897	235	3	,	,	PUNCT
ejpam-5897	235	4	y1	y1	NOUN
ejpam-5897	235	5	,	,	PUNCT
ejpam-5897	235	6	z1	z1	NOUN
ejpam-5897	235	7	,	,	PUNCT
ejpam-5897	235	8	x2	x2	PROPN
ejpam-5897	235	9	,	,	PUNCT
ejpam-5897	235	10	y2	y2	PROPN
ejpam-5897	235	11	,	,	PUNCT
ejpam-5897	235	12	z2	z2	PROPN
ejpam-5897	235	13	)	)	PUNCT
ejpam-5897	235	14	for	for	ADP
ejpam-5897	235	15	all	all	DET
ejpam-5897	235	16	(	(	PUNCT
ejpam-5897	235	17	x1	x1	PROPN
ejpam-5897	235	18	,	,	PUNCT
ejpam-5897	235	19	y1	y1	PROPN
ejpam-5897	235	20	,	,	PUNCT
ejpam-5897	235	21	z1	z1	NOUN
ejpam-5897	235	22	)	)	PUNCT
ejpam-5897	235	23	,	,	PUNCT
ejpam-5897	235	24	(	(	PUNCT
ejpam-5897	235	25	x2	x2	PROPN
ejpam-5897	235	26	,	,	PUNCT
ejpam-5897	235	27	y2	y2	PROPN
ejpam-5897	235	28	,	,	PUNCT
ejpam-5897	235	29	z2	z2	PROPN
ejpam-5897	235	30	)	)	PUNCT
ejpam-5897	235	31	∈	∈	PROPN
ejpam-5897	235	32	x3	x3	NOUN
ejpam-5897	235	33	and	and	CCONJ
ejpam-5897	235	34	µ	µ	PRON
ejpam-5897	235	35	∈	∈	NOUN
ejpam-5897	235	36	t1	t1	NOUN
ejpam-5897	235	37	,	,	PUNCT
ejpam-5897	235	38	and	and	CCONJ
ejpam-5897	235	39	∥f([x1	∥f([x1	NUM
ejpam-5897	235	40	,	,	PUNCT
ejpam-5897	235	41	y1	y1	X
ejpam-5897	235	42	,	,	PUNCT
ejpam-5897	235	43	z1	z1	NOUN
ejpam-5897	235	44	]	]	PUNCT
ejpam-5897	235	45	,	,	PUNCT
ejpam-5897	235	46	[	[	X
ejpam-5897	235	47	x2	x2	X
ejpam-5897	235	48	,	,	PUNCT
ejpam-5897	235	49	y2	y2	PROPN
ejpam-5897	235	50	,	,	PUNCT
ejpam-5897	235	51	z2	z2	PROPN
ejpam-5897	235	52	]	]	PUNCT
ejpam-5897	235	53	,	,	PUNCT
ejpam-5897	235	54	[	[	X
ejpam-5897	235	55	x3	x3	ADJ
ejpam-5897	235	56	,	,	PUNCT
ejpam-5897	235	57	y3	y3	NOUN
ejpam-5897	235	58	,	,	PUNCT
ejpam-5897	235	59	z3])−	z3])−	X
ejpam-5897	236	1	[	[	X
ejpam-5897	236	2	f(x1	f(x1	ADJ
ejpam-5897	236	3	,	,	PUNCT
ejpam-5897	236	4	x2	x2	PROPN
ejpam-5897	236	5	,	,	PUNCT
ejpam-5897	236	6	x3	x3	ADJ
ejpam-5897	236	7	)	)	PUNCT
ejpam-5897	236	8	,	,	PUNCT
ejpam-5897	237	1	[	[	X
ejpam-5897	237	2	y1	y1	X
ejpam-5897	237	3	,	,	PUNCT
ejpam-5897	237	4	y2	y2	PROPN
ejpam-5897	237	5	,	,	PUNCT
ejpam-5897	237	6	y3	y3	PROPN
ejpam-5897	237	7	]	]	PUNCT
ejpam-5897	237	8	,	,	PUNCT
ejpam-5897	237	9	[	[	X
ejpam-5897	237	10	z1	z1	ADJ
ejpam-5897	237	11	,	,	PUNCT
ejpam-5897	237	12	z2	z2	PROPN
ejpam-5897	237	13	,	,	PUNCT
ejpam-5897	237	14	z3	z3	PROPN
ejpam-5897	237	15	]	]	X
ejpam-5897	237	16	]	]	X
ejpam-5897	237	17	(	(	PUNCT
ejpam-5897	237	18	12	12	NUM
ejpam-5897	237	19	)	)	PUNCT
ejpam-5897	237	20	−[[x1	−[[x1	NOUN
ejpam-5897	237	21	,	,	PUNCT
ejpam-5897	237	22	x2	x2	PROPN
ejpam-5897	237	23	,	,	PUNCT
ejpam-5897	237	24	x3	x3	ADJ
ejpam-5897	237	25	]	]	PUNCT
ejpam-5897	237	26	,	,	PUNCT
ejpam-5897	237	27	f(y1	f(y1	NOUN
ejpam-5897	237	28	,	,	PUNCT
ejpam-5897	237	29	y2	y2	PROPN
ejpam-5897	237	30	,	,	PUNCT
ejpam-5897	237	31	y3	y3	PROPN
ejpam-5897	237	32	)	)	PUNCT
ejpam-5897	237	33	,	,	PUNCT
ejpam-5897	237	34	[	[	X
ejpam-5897	237	35	z1	z1	ADJ
ejpam-5897	237	36	,	,	PUNCT
ejpam-5897	237	37	z2	z2	PROPN
ejpam-5897	237	38	,	,	PUNCT
ejpam-5897	237	39	z3]]−	z3]]−	PROPN
ejpam-5897	238	1	[	[	X
ejpam-5897	238	2	[	[	X
ejpam-5897	238	3	x1	x1	PROPN
ejpam-5897	238	4	,	,	PUNCT
ejpam-5897	238	5	x2	x2	PROPN
ejpam-5897	238	6	,	,	PUNCT
ejpam-5897	238	7	x3	x3	ADJ
ejpam-5897	238	8	]	]	PUNCT
ejpam-5897	238	9	,	,	PUNCT
ejpam-5897	239	1	[	[	X
ejpam-5897	239	2	y1	y1	X
ejpam-5897	239	3	,	,	PUNCT
ejpam-5897	239	4	y2	y2	PROPN
ejpam-5897	239	5	,	,	PUNCT
ejpam-5897	239	6	y3	y3	PROPN
ejpam-5897	239	7	]	]	PUNCT
ejpam-5897	239	8	,	,	PUNCT
ejpam-5897	239	9	f(z1	f(z1	ADJ
ejpam-5897	239	10	,	,	PUNCT
ejpam-5897	239	11	z2	z2	PROPN
ejpam-5897	239	12	,	,	PUNCT
ejpam-5897	239	13	z3)]∥	z3)]∥	NOUN
ejpam-5897	239	14	≤	≤	PROPN
ejpam-5897	239	15	ψ(x1	ψ(x1	NOUN
ejpam-5897	239	16	,	,	PUNCT
ejpam-5897	239	17	x2	x2	PROPN
ejpam-5897	239	18	,	,	PUNCT
ejpam-5897	239	19	x3	x3	ADJ
ejpam-5897	239	20	,	,	PUNCT
ejpam-5897	239	21	y1	y1	NOUN
ejpam-5897	239	22	,	,	PUNCT
ejpam-5897	239	23	y2	y2	PROPN
ejpam-5897	239	24	,	,	PUNCT
ejpam-5897	239	25	y3	y3	PROPN
ejpam-5897	239	26	,	,	PUNCT
ejpam-5897	239	27	z1	z1	PROPN
ejpam-5897	239	28	,	,	PUNCT
ejpam-5897	239	29	z2	z2	PROPN
ejpam-5897	239	30	,	,	PUNCT
ejpam-5897	239	31	z3	z3	PROPN
ejpam-5897	239	32	)	)	PUNCT
ejpam-5897	239	33	for	for	ADP
ejpam-5897	239	34	all	all	PRON
ejpam-5897	239	35	x1	x1	PROPN
ejpam-5897	239	36	,	,	PUNCT
ejpam-5897	239	37	x2	x2	PROPN
ejpam-5897	239	38	,	,	PUNCT
ejpam-5897	239	39	x3	x3	ADJ
ejpam-5897	239	40	,	,	PUNCT
ejpam-5897	239	41	y1	y1	NOUN
ejpam-5897	239	42	,	,	PUNCT
ejpam-5897	239	43	y2	y2	PROPN
ejpam-5897	239	44	,	,	PUNCT
ejpam-5897	239	45	y3	y3	PROPN
ejpam-5897	239	46	,	,	PUNCT
ejpam-5897	239	47	z1	z1	PROPN
ejpam-5897	239	48	,	,	PUNCT
ejpam-5897	239	49	z2	z2	PROPN
ejpam-5897	239	50	,	,	PUNCT
ejpam-5897	239	51	z3	z3	PROPN
ejpam-5897	239	52	∈	∈	PROPN
ejpam-5897	239	53	x.	x.	NOUN
ejpam-5897	239	54	then	then	ADV
ejpam-5897	239	55	there	there	PRON
ejpam-5897	239	56	exists	exist	VERB
ejpam-5897	239	57	a	a	DET
ejpam-5897	239	58	unique	unique	ADJ
ejpam-5897	239	59	hyper	hyper	ADJ
ejpam-5897	239	60	3	3	NUM
ejpam-5897	239	61	-	-	PUNCT
ejpam-5897	239	62	derivation	derivation	NOUN
ejpam-5897	239	63	d	d	NOUN
ejpam-5897	239	64	:	:	PUNCT
ejpam-5897	239	65	x3	x3	ADJ
ejpam-5897	239	66	→	→	SYM
ejpam-5897	239	67	x	x	X
ejpam-5897	239	68	such	such	ADJ
ejpam-5897	239	69	that	that	SCONJ
ejpam-5897	239	70	∥f(x	∥f(x	PROPN
ejpam-5897	239	71	,	,	PUNCT
ejpam-5897	239	72	y	y	PROPN
ejpam-5897	239	73	,	,	PUNCT
ejpam-5897	239	74	z)−d(x	z)−d(x	NUM
ejpam-5897	239	75	,	,	PUNCT
ejpam-5897	239	76	y	y	PROPN
ejpam-5897	239	77	,	,	PUNCT
ejpam-5897	239	78	z)∥	z)∥	NUM
ejpam-5897	239	79	≤	≤	NOUN
ejpam-5897	240	1	+	+	ADP
ejpam-5897	240	2	∞∑	∞∑	NUM
ejpam-5897	240	3	j=0	j=0	ADJ
ejpam-5897	240	4	8jφ	8jφ	NOUN
ejpam-5897	240	5	(	(	PUNCT
ejpam-5897	240	6	x	x	SYM
ejpam-5897	240	7	2j+1	2j+1	NOUN
ejpam-5897	240	8	,	,	PUNCT
ejpam-5897	240	9	y	y	PROPN
ejpam-5897	240	10	2j+1	2j+1	PROPN
ejpam-5897	240	11	,	,	PUNCT
ejpam-5897	240	12	z	z	NOUN
ejpam-5897	240	13	2j+1	2j+1	NOUN
ejpam-5897	240	14	,	,	PUNCT
ejpam-5897	240	15	x	x	SYM
ejpam-5897	240	16	2j+1	2j+1	NOUN
ejpam-5897	240	17	,	,	PUNCT
ejpam-5897	240	18	y	y	PROPN
ejpam-5897	240	19	2j+1	2j+1	PROPN
ejpam-5897	240	20	,	,	PUNCT
ejpam-5897	240	21	z	z	NOUN
ejpam-5897	240	22	2j+1	2j+1	NOUN
ejpam-5897	240	23	)	)	PUNCT
ejpam-5897	240	24	(	(	PUNCT
ejpam-5897	240	25	13	13	NUM
ejpam-5897	240	26	)	)	PUNCT
ejpam-5897	240	27	for	for	ADP
ejpam-5897	240	28	all	all	DET
ejpam-5897	240	29	x	x	NOUN
ejpam-5897	240	30	,	,	PUNCT
ejpam-5897	240	31	y	y	PROPN
ejpam-5897	240	32	,	,	PUNCT
ejpam-5897	240	33	z	z	NOUN
ejpam-5897	240	34	∈	∈	NOUN
ejpam-5897	240	35	x.	x.	NOUN
ejpam-5897	240	36	proof	proof	NOUN
ejpam-5897	240	37	.	.	PUNCT
ejpam-5897	241	1	letting	let	VERB
ejpam-5897	241	2	µ	µ	X
ejpam-5897	241	3	=	=	SYM
ejpam-5897	241	4	1	1	NUM
ejpam-5897	241	5	,	,	PUNCT
ejpam-5897	241	6	x1	x1	PROPN
ejpam-5897	242	1	=	=	SYM
ejpam-5897	242	2	x2	x2	INTJ
ejpam-5897	242	3	:	:	PUNCT
ejpam-5897	242	4	=	=	SYM
ejpam-5897	242	5	x	x	X
ejpam-5897	242	6	,	,	PUNCT
ejpam-5897	242	7	y1	y1	INTJ
ejpam-5897	242	8	=	=	PUNCT
ejpam-5897	242	9	y2	y2	INTJ
ejpam-5897	242	10	:	:	PUNCT
ejpam-5897	242	11	=	=	SYM
ejpam-5897	242	12	y	y	PROPN
ejpam-5897	242	13	and	and	CCONJ
ejpam-5897	242	14	z1	z1	PROPN
ejpam-5897	242	15	=	=	SYM
ejpam-5897	242	16	z2	z2	PROPN
ejpam-5897	242	17	:	:	PUNCT
ejpam-5897	242	18	=	=	SYM
ejpam-5897	242	19	z	z	X
ejpam-5897	242	20	in	in	ADP
ejpam-5897	242	21	(	(	PUNCT
ejpam-5897	242	22	11	11	NUM
ejpam-5897	242	23	)	)	PUNCT
ejpam-5897	242	24	,	,	PUNCT
ejpam-5897	242	25	we	we	PRON
ejpam-5897	242	26	get	get	AUX
ejpam-5897	242	27	∥f(2x	∥f(2x	VERB
ejpam-5897	242	28	,	,	PUNCT
ejpam-5897	242	29	2y	2y	NUM
ejpam-5897	242	30	,	,	PUNCT
ejpam-5897	242	31	2z)−	2z)−	NUM
ejpam-5897	242	32	8f(x	8f(x	PROPN
ejpam-5897	242	33	,	,	PUNCT
ejpam-5897	242	34	y	y	PROPN
ejpam-5897	242	35	,	,	PUNCT
ejpam-5897	242	36	z)∥	z)∥	NUM
ejpam-5897	242	37	≤	≤	NUM
ejpam-5897	242	38	φ(x	φ(x	NOUN
ejpam-5897	242	39	,	,	PUNCT
ejpam-5897	242	40	y	y	PROPN
ejpam-5897	242	41	,	,	PUNCT
ejpam-5897	242	42	z	z	PROPN
ejpam-5897	242	43	,	,	PUNCT
ejpam-5897	242	44	x	x	PROPN
ejpam-5897	242	45	,	,	PUNCT
ejpam-5897	242	46	y	y	PROPN
ejpam-5897	242	47	,	,	PUNCT
ejpam-5897	242	48	z	z	NOUN
ejpam-5897	242	49	)	)	PUNCT
ejpam-5897	242	50	for	for	ADP
ejpam-5897	242	51	all	all	DET
ejpam-5897	242	52	x	x	NOUN
ejpam-5897	242	53	,	,	PUNCT
ejpam-5897	242	54	y	y	PROPN
ejpam-5897	242	55	,	,	PUNCT
ejpam-5897	242	56	z	z	NOUN
ejpam-5897	242	57	∈	∈	PROPN
ejpam-5897	242	58	x.	x.	NOUN
ejpam-5897	242	59	by	by	ADP
ejpam-5897	242	60	induction	induction	NOUN
ejpam-5897	242	61	,	,	PUNCT
ejpam-5897	242	62	we	we	PRON
ejpam-5897	242	63	have∥∥∥f(x	have∥∥∥f(x	PROPN
ejpam-5897	242	64	,	,	PUNCT
ejpam-5897	242	65	y	y	PROPN
ejpam-5897	242	66	,	,	PUNCT
ejpam-5897	242	67	z)−	z)−	PROPN
ejpam-5897	242	68	8nf	8nf	NOUN
ejpam-5897	242	69	(	(	PUNCT
ejpam-5897	242	70	x	x	PROPN
ejpam-5897	242	71	2n	2n	NUM
ejpam-5897	242	72	,	,	PUNCT
ejpam-5897	242	73	y	y	PROPN
ejpam-5897	242	74	2n	2n	NUM
ejpam-5897	242	75	,	,	PUNCT
ejpam-5897	242	76	z	z	NOUN
ejpam-5897	242	77	2n	2n	NUM
ejpam-5897	242	78	)	)	PUNCT
ejpam-5897	242	79	∥∥∥	∥∥∥	PROPN
ejpam-5897	242	80	≤	≤	PROPN
ejpam-5897	242	81	n−1∑	n−1∑	NUM
ejpam-5897	242	82	j=0	j=0	ADJ
ejpam-5897	242	83	8jφ	8jφ	NOUN
ejpam-5897	242	84	(	(	PUNCT
ejpam-5897	242	85	x	x	SYM
ejpam-5897	242	86	2j	2j	NOUN
ejpam-5897	242	87	,	,	PUNCT
ejpam-5897	242	88	y	y	PROPN
ejpam-5897	242	89	2j	2j	NUM
ejpam-5897	242	90	,	,	PUNCT
ejpam-5897	242	91	z	z	NOUN
ejpam-5897	242	92	2j	2j	NOUN
ejpam-5897	242	93	,	,	PUNCT
ejpam-5897	242	94	x	x	X
ejpam-5897	242	95	2j	2j	NOUN
ejpam-5897	242	96	,	,	PUNCT
ejpam-5897	242	97	y	y	PROPN
ejpam-5897	242	98	2j	2j	NUM
ejpam-5897	242	99	,	,	PUNCT
ejpam-5897	242	100	z	z	NOUN
ejpam-5897	242	101	2j	2j	NOUN
ejpam-5897	242	102	)	)	PUNCT
ejpam-5897	242	103	for	for	ADP
ejpam-5897	242	104	all	all	DET
ejpam-5897	242	105	x	x	NOUN
ejpam-5897	242	106	,	,	PUNCT
ejpam-5897	242	107	y	y	PROPN
ejpam-5897	243	1	,	,	PUNCT
ejpam-5897	243	2	z	z	NOUN
ejpam-5897	243	3	∈	∈	PROPN
ejpam-5897	243	4	x.	x.	NOUN
ejpam-5897	243	5	hence∥∥∥8lf	hence∥∥∥8lf	PROPN
ejpam-5897	243	6	(	(	PUNCT
ejpam-5897	243	7	x	x	SYM
ejpam-5897	243	8	2l	2l	NUM
ejpam-5897	243	9	,	,	PUNCT
ejpam-5897	243	10	y	y	PROPN
ejpam-5897	243	11	2l	2l	NUM
ejpam-5897	243	12	,	,	PUNCT
ejpam-5897	243	13	z	z	NOUN
ejpam-5897	243	14	2l	2l	NUM
ejpam-5897	243	15	)	)	PUNCT
ejpam-5897	244	1	−	−	PROPN
ejpam-5897	244	2	8kf	8kf	ADJ
ejpam-5897	244	3	(	(	PUNCT
ejpam-5897	244	4	x	x	SYM
ejpam-5897	244	5	2k	2k	NUM
ejpam-5897	244	6	,	,	PUNCT
ejpam-5897	244	7	y	y	PROPN
ejpam-5897	244	8	2k	2k	NUM
ejpam-5897	244	9	,	,	PUNCT
ejpam-5897	244	10	z	z	NOUN
ejpam-5897	244	11	2k	2k	NUM
ejpam-5897	244	12	)	)	PUNCT
ejpam-5897	244	13	∥∥∥	∥∥∥	PROPN
ejpam-5897	244	14	(	(	PUNCT
ejpam-5897	244	15	14	14	NUM
ejpam-5897	244	16	)	)	PUNCT
ejpam-5897	244	17	≤	≤	NOUN
ejpam-5897	244	18	k−1∑	k−1∑	PROPN
ejpam-5897	244	19	j	j	PROPN
ejpam-5897	244	20	=	=	PROPN
ejpam-5897	244	21	l	l	NOUN
ejpam-5897	244	22	∥∥∥8jf	∥∥∥8jf	NOUN
ejpam-5897	244	23	(	(	PUNCT
ejpam-5897	244	24	x	x	X
ejpam-5897	244	25	2j	2j	NOUN
ejpam-5897	244	26	,	,	PUNCT
ejpam-5897	244	27	y	y	PROPN
ejpam-5897	244	28	2j	2j	NUM
ejpam-5897	244	29	,	,	PUNCT
ejpam-5897	244	30	z	z	NOUN
ejpam-5897	244	31	2j	2j	NOUN
ejpam-5897	244	32	)	)	PUNCT
ejpam-5897	245	1	−	−	PROPN
ejpam-5897	245	2	8j+1f	8j+1f	NUM
ejpam-5897	245	3	(	(	PUNCT
ejpam-5897	245	4	x	x	SYM
ejpam-5897	245	5	2j+1	2j+1	NOUN
ejpam-5897	245	6	,	,	PUNCT
ejpam-5897	245	7	y	y	PROPN
ejpam-5897	245	8	2j+1	2j+1	PROPN
ejpam-5897	245	9	,	,	PUNCT
ejpam-5897	245	10	z	z	NOUN
ejpam-5897	245	11	2j+1	2j+1	NOUN
ejpam-5897	245	12	)	)	PUNCT
ejpam-5897	245	13	∥∥∥	∥∥∥	PROPN
ejpam-5897	245	14	≤	≤	PROPN
ejpam-5897	245	15	k−1∑	k−1∑	PROPN
ejpam-5897	245	16	j	j	PROPN
ejpam-5897	245	17	=	=	PROPN
ejpam-5897	245	18	l	l	NOUN
ejpam-5897	245	19	8jφ	8jφ	NOUN
ejpam-5897	245	20	(	(	PUNCT
ejpam-5897	245	21	x	x	SYM
ejpam-5897	245	22	2j+1	2j+1	NOUN
ejpam-5897	245	23	,	,	PUNCT
ejpam-5897	245	24	y	y	PROPN
ejpam-5897	245	25	2j+1	2j+1	PROPN
ejpam-5897	245	26	,	,	PUNCT
ejpam-5897	245	27	z	z	NOUN
ejpam-5897	245	28	2j+1	2j+1	NOUN
ejpam-5897	245	29	,	,	PUNCT
ejpam-5897	245	30	x	x	SYM
ejpam-5897	245	31	2j+1	2j+1	NOUN
ejpam-5897	245	32	,	,	PUNCT
ejpam-5897	245	33	y	y	PROPN
ejpam-5897	245	34	2j+1	2j+1	PROPN
ejpam-5897	245	35	,	,	PUNCT
ejpam-5897	245	36	z	z	NOUN
ejpam-5897	245	37	2j+1	2j+1	NOUN
ejpam-5897	245	38	)	)	PUNCT
ejpam-5897	245	39	for	for	ADP
ejpam-5897	245	40	all	all	DET
ejpam-5897	245	41	nonnegative	nonnegative	ADJ
ejpam-5897	245	42	integers	integer	NOUN
ejpam-5897	245	43	l	l	NOUN
ejpam-5897	245	44	,	,	PUNCT
ejpam-5897	245	45	k(k	k(k	X
ejpam-5897	245	46	>	>	X
ejpam-5897	245	47	l	l	NOUN
ejpam-5897	245	48	)	)	PUNCT
ejpam-5897	245	49	and	and	CCONJ
ejpam-5897	245	50	all	all	DET
ejpam-5897	245	51	x	x	NOUN
ejpam-5897	245	52	,	,	PUNCT
ejpam-5897	245	53	y	y	PROPN
ejpam-5897	245	54	,	,	PUNCT
ejpam-5897	245	55	z	z	NOUN
ejpam-5897	245	56	∈	∈	PROPN
ejpam-5897	245	57	x.	x.	NOUN
ejpam-5897	246	1	it	it	PRON
ejpam-5897	246	2	follows	follow	VERB
ejpam-5897	246	3	that	that	SCONJ
ejpam-5897	246	4	the	the	DET
ejpam-5897	246	5	sequence	sequence	NOUN
ejpam-5897	246	6	{	{	PUNCT
ejpam-5897	246	7	8kf	8kf	ADJ
ejpam-5897	246	8	(	(	PUNCT
ejpam-5897	246	9	x	x	SYM
ejpam-5897	246	10	2k	2k	NUM
ejpam-5897	246	11	,	,	PUNCT
ejpam-5897	246	12	y	y	PROPN
ejpam-5897	246	13	2k	2k	NUM
ejpam-5897	246	14	,	,	PUNCT
ejpam-5897	246	15	z	z	NOUN
ejpam-5897	246	16	2k	2k	NUM
ejpam-5897	246	17	)	)	PUNCT
ejpam-5897	246	18	}	}	PUNCT
ejpam-5897	246	19	is	be	AUX
ejpam-5897	246	20	a	a	DET
ejpam-5897	246	21	cauchy	cauchy	ADJ
ejpam-5897	246	22	sequence	sequence	NOUN
ejpam-5897	246	23	for	for	ADP
ejpam-5897	246	24	each	each	DET
ejpam-5897	246	25	(	(	PUNCT
ejpam-5897	246	26	x	x	PROPN
ejpam-5897	246	27	,	,	PUNCT
ejpam-5897	246	28	y	y	PROPN
ejpam-5897	246	29	,	,	PUNCT
ejpam-5897	246	30	z	z	NOUN
ejpam-5897	246	31	)	)	PUNCT
ejpam-5897	246	32	∈	∈	PROPN
ejpam-5897	246	33	x3	x3	PROPN
ejpam-5897	246	34	.	.	PUNCT
ejpam-5897	247	1	since	since	SCONJ
ejpam-5897	247	2	x	x	PRON
ejpam-5897	247	3	is	be	AUX
ejpam-5897	247	4	complete	complete	ADJ
ejpam-5897	247	5	,	,	PUNCT
ejpam-5897	247	6	the	the	DET
ejpam-5897	247	7	sequence	sequence	NOUN
ejpam-5897	247	8	{	{	PUNCT
ejpam-5897	247	9	8kf	8kf	ADJ
ejpam-5897	247	10	(	(	PUNCT
ejpam-5897	247	11	x	x	SYM
ejpam-5897	247	12	2k	2k	NUM
ejpam-5897	247	13	,	,	PUNCT
ejpam-5897	247	14	y	y	PROPN
ejpam-5897	247	15	2k	2k	NUM
ejpam-5897	247	16	,	,	PUNCT
ejpam-5897	247	17	z	z	NOUN
ejpam-5897	247	18	2k	2k	NUM
ejpam-5897	247	19	)	)	PUNCT
ejpam-5897	247	20	}	}	PUNCT
ejpam-5897	247	21	converges	converge	VERB
ejpam-5897	247	22	.	.	PUNCT
ejpam-5897	248	1	thus	thus	ADV
ejpam-5897	248	2	one	one	PRON
ejpam-5897	248	3	can	can	AUX
ejpam-5897	248	4	define	define	VERB
ejpam-5897	248	5	the	the	DET
ejpam-5897	248	6	mapping	mapping	NOUN
ejpam-5897	248	7	d	d	NOUN
ejpam-5897	248	8	:	:	PUNCT
ejpam-5897	248	9	x3	x3	ADJ
ejpam-5897	248	10	→	→	SYM
ejpam-5897	248	11	x	x	X
ejpam-5897	248	12	by	by	ADP
ejpam-5897	248	13	d(x	d(x	PROPN
ejpam-5897	248	14	,	,	PUNCT
ejpam-5897	248	15	y	y	PROPN
ejpam-5897	248	16	,	,	PUNCT
ejpam-5897	248	17	z	z	NOUN
ejpam-5897	248	18	)	)	PUNCT
ejpam-5897	248	19	:	:	PUNCT
ejpam-5897	248	20	=	=	SYM
ejpam-5897	248	21	lim	lim	PROPN
ejpam-5897	248	22	n→+∞	n→+∞	PROPN
ejpam-5897	248	23	8nf	8nf	NOUN
ejpam-5897	248	24	(	(	PUNCT
ejpam-5897	248	25	x	x	PROPN
ejpam-5897	248	26	2n	2n	NUM
ejpam-5897	248	27	,	,	PUNCT
ejpam-5897	248	28	y	y	PROPN
ejpam-5897	248	29	2n	2n	NUM
ejpam-5897	248	30	,	,	PUNCT
ejpam-5897	248	31	z	z	NOUN
ejpam-5897	248	32	2n	2n	NUM
ejpam-5897	248	33	)	)	PUNCT
ejpam-5897	248	34	for	for	ADP
ejpam-5897	248	35	all	all	DET
ejpam-5897	248	36	(	(	PUNCT
ejpam-5897	248	37	x	x	NOUN
ejpam-5897	248	38	,	,	PUNCT
ejpam-5897	248	39	y	y	PROPN
ejpam-5897	248	40	,	,	PUNCT
ejpam-5897	248	41	z	z	NOUN
ejpam-5897	248	42	)	)	PUNCT
ejpam-5897	248	43	∈	∈	PROPN
ejpam-5897	248	44	x3	x3	PROPN
ejpam-5897	248	45	.	.	PUNCT
ejpam-5897	249	1	moreover	moreover	ADV
ejpam-5897	249	2	,	,	PUNCT
ejpam-5897	249	3	letting	let	VERB
ejpam-5897	249	4	l	l	NOUN
ejpam-5897	249	5	=	=	SYM
ejpam-5897	249	6	0	0	PUNCT
ejpam-5897	249	7	and	and	CCONJ
ejpam-5897	249	8	passing	pass	VERB
ejpam-5897	249	9	the	the	DET
ejpam-5897	249	10	limit	limit	NOUN
ejpam-5897	249	11	k	k	PROPN
ejpam-5897	249	12	→	→	SYM
ejpam-5897	249	13	∞	∞	PROPN
ejpam-5897	249	14	in	in	ADP
ejpam-5897	249	15	(	(	PUNCT
ejpam-5897	249	16	14	14	NUM
ejpam-5897	249	17	)	)	PUNCT
ejpam-5897	249	18	,	,	PUNCT
ejpam-5897	249	19	we	we	PRON
ejpam-5897	249	20	get	get	VERB
ejpam-5897	249	21	(	(	PUNCT
ejpam-5897	249	22	13	13	NUM
ejpam-5897	249	23	)	)	PUNCT
ejpam-5897	249	24	.	.	PUNCT
ejpam-5897	250	1	it	it	PRON
ejpam-5897	250	2	follows	follow	VERB
ejpam-5897	250	3	from	from	ADP
ejpam-5897	250	4	(	(	PUNCT
ejpam-5897	250	5	11	11	NUM
ejpam-5897	250	6	)	)	PUNCT
ejpam-5897	250	7	that	that	SCONJ
ejpam-5897	250	8	∥d(µ(x1	∥d(µ(x1	X
ejpam-5897	250	9	+	+	CCONJ
ejpam-5897	250	10	x2	x2	ADJ
ejpam-5897	250	11	,	,	PUNCT
ejpam-5897	250	12	y1	y1	NOUN
ejpam-5897	250	13	+	+	CCONJ
ejpam-5897	250	14	y2	y2	NOUN
ejpam-5897	250	15	,	,	PUNCT
ejpam-5897	250	16	z1	z1	PROPN
ejpam-5897	250	17	+	+	CCONJ
ejpam-5897	250	18	z2))−	z2))−	PROPN
ejpam-5897	250	19	µ	µ	PRON
ejpam-5897	250	20	2∑	2∑	NUM
ejpam-5897	250	21	i	i	PROPN
ejpam-5897	250	22	,	,	PUNCT
ejpam-5897	250	23	j	j	PROPN
ejpam-5897	250	24	,	,	PUNCT
ejpam-5897	250	25	k=1	k=1	PROPN
ejpam-5897	250	26	d(xi	d(xi	PROPN
ejpam-5897	250	27	,	,	PUNCT
ejpam-5897	250	28	yj	yj	PROPN
ejpam-5897	250	29	,	,	PUNCT
ejpam-5897	250	30	zk)∥	zk)∥	PROPN
ejpam-5897	250	31	e.	e.	PROPN
ejpam-5897	250	32	shim	shim	PROPN
ejpam-5897	250	33	,	,	PUNCT
ejpam-5897	250	34	s.	s.	PROPN
ejpam-5897	250	35	donganont	donganont	PROPN
ejpam-5897	250	36	,	,	PUNCT
ejpam-5897	250	37	c.	c.	PROPN
ejpam-5897	250	38	park	park	PROPN
ejpam-5897	250	39	/	/	SYM
ejpam-5897	250	40	eur	eur	PROPN
ejpam-5897	250	41	.	.	PUNCT
ejpam-5897	251	1	j.	j.	PROPN
ejpam-5897	251	2	pure	pure	PROPN
ejpam-5897	251	3	appl	appl	PROPN
ejpam-5897	251	4	.	.	PROPN
ejpam-5897	251	5	math	math	PROPN
ejpam-5897	251	6	,	,	PUNCT
ejpam-5897	251	7	18	18	NUM
ejpam-5897	251	8	(	(	PUNCT
ejpam-5897	251	9	2	2	NUM
ejpam-5897	251	10	)	)	PUNCT
ejpam-5897	251	11	(	(	PUNCT
ejpam-5897	251	12	2025	2025	NUM
ejpam-5897	251	13	)	)	PUNCT
ejpam-5897	251	14	,	,	PUNCT
ejpam-5897	251	15	5897	5897	NUM
ejpam-5897	251	16	11	11	NUM
ejpam-5897	251	17	of	of	ADP
ejpam-5897	251	18	14	14	NUM
ejpam-5897	251	19	=	=	SYM
ejpam-5897	251	20	lim	lim	PROPN
ejpam-5897	251	21	n→+∞	n→+∞	VERB
ejpam-5897	251	22	8n	8n	NOUN
ejpam-5897	251	23	∥∥∥∥∥∥f	∥∥∥∥∥∥f	ADP
ejpam-5897	251	24	µ(x1	µ(x1	PROPN
ejpam-5897	251	25	+	+	CCONJ
ejpam-5897	251	26	x2	x2	PROPN
ejpam-5897	251	27	2n	2n	NUM
ejpam-5897	251	28	,	,	PUNCT
ejpam-5897	251	29	y1	y1	INTJ
ejpam-5897	251	30	+	+	CCONJ
ejpam-5897	251	31	y2	y2	PROPN
ejpam-5897	251	32	2n	2n	NUM
ejpam-5897	251	33	,	,	PUNCT
ejpam-5897	251	34	z1	z1	PROPN
ejpam-5897	251	35	+	+	CCONJ
ejpam-5897	251	36	z2	z2	PROPN
ejpam-5897	251	37	2n	2n	NUM
ejpam-5897	251	38	)	)	PUNCT
ejpam-5897	252	1	−	−	PROPN
ejpam-5897	252	2	µ	µ	NUM
ejpam-5897	252	3	2∑	2∑	NUM
ejpam-5897	253	1	i	i	PROPN
ejpam-5897	253	2	,	,	PUNCT
ejpam-5897	253	3	j	j	PROPN
ejpam-5897	253	4	,	,	PUNCT
ejpam-5897	253	5	k=1	k=1	PROPN
ejpam-5897	253	6	f	f	X
ejpam-5897	253	7	(	(	PUNCT
ejpam-5897	253	8	xi	xi	ADP
ejpam-5897	253	9	2n	2n	NUM
ejpam-5897	253	10	,	,	PUNCT
ejpam-5897	253	11	yj	yj	PROPN
ejpam-5897	253	12	2n	2n	NUM
ejpam-5897	253	13	,	,	PUNCT
ejpam-5897	253	14	zk	zk	PROPN
ejpam-5897	253	15	2n	2n	NUM
ejpam-5897	253	16	)	)	PUNCT
ejpam-5897	254	1	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-5897	254	2	≤	≤	PROPN
ejpam-5897	254	3	lim	lim	PROPN
ejpam-5897	254	4	n→+∞	n→+∞	VERB
ejpam-5897	254	5	8n	8n	NOUN
ejpam-5897	254	6	∥∥∥∥∥∥t	∥∥∥∥∥∥t	X
ejpam-5897	254	7	8f	8f	PROPN
ejpam-5897	254	8	(	(	PUNCT
ejpam-5897	254	9	µ	µ	X
ejpam-5897	254	10	(	(	PUNCT
ejpam-5897	254	11	x1	x1	PROPN
ejpam-5897	254	12	+	+	PROPN
ejpam-5897	254	13	x2	x2	PROPN
ejpam-5897	254	14	2n+1	2n+1	PROPN
ejpam-5897	254	15	,	,	PUNCT
ejpam-5897	254	16	y1	y1	PROPN
ejpam-5897	254	17	+	+	CCONJ
ejpam-5897	254	18	y2	y2	PROPN
ejpam-5897	254	19	2n+1	2n+1	NOUN
ejpam-5897	254	20	,	,	PUNCT
ejpam-5897	254	21	z1	z1	PROPN
ejpam-5897	254	22	+	+	CCONJ
ejpam-5897	254	23	z2	z2	PROPN
ejpam-5897	254	24	2n+1	2n+1	PROPN
ejpam-5897	254	25	)	)	PUNCT
ejpam-5897	254	26	)	)	PUNCT
ejpam-5897	255	1	−	−	PROPN
ejpam-5897	255	2	µ	µ	NUM
ejpam-5897	255	3	2∑	2∑	NUM
ejpam-5897	256	1	i	i	PROPN
ejpam-5897	256	2	,	,	PUNCT
ejpam-5897	256	3	j	j	PROPN
ejpam-5897	256	4	,	,	PUNCT
ejpam-5897	256	5	k=1	k=1	PROPN
ejpam-5897	256	6	f	f	X
ejpam-5897	256	7	(	(	PUNCT
ejpam-5897	256	8	xi	xi	ADP
ejpam-5897	256	9	2n	2n	NUM
ejpam-5897	256	10	,	,	PUNCT
ejpam-5897	256	11	yj	yj	PROPN
ejpam-5897	256	12	2n	2n	NUM
ejpam-5897	256	13	,	,	PUNCT
ejpam-5897	256	14	zk	zk	PROPN
ejpam-5897	256	15	2n	2n	NUM
ejpam-5897	256	16	)	)	PUNCT
ejpam-5897	256	17	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-5897	257	1	+	+	CCONJ
ejpam-5897	257	2	lim	lim	PROPN
ejpam-5897	257	3	n→+∞	n→+∞	PROPN
ejpam-5897	257	4	8nφ	8nφ	NOUN
ejpam-5897	257	5	(	(	PUNCT
ejpam-5897	257	6	x1	x1	PROPN
ejpam-5897	257	7	2n	2n	NUM
ejpam-5897	257	8	,	,	PUNCT
ejpam-5897	257	9	y1	y1	NOUN
ejpam-5897	257	10	2n	2n	NUM
ejpam-5897	257	11	,	,	PUNCT
ejpam-5897	257	12	z1	z1	NUM
ejpam-5897	257	13	2n	2n	NUM
ejpam-5897	257	14	,	,	PUNCT
ejpam-5897	257	15	x2	x2	PROPN
ejpam-5897	257	16	2n	2n	NUM
ejpam-5897	257	17	,	,	PUNCT
ejpam-5897	257	18	y2	y2	PROPN
ejpam-5897	257	19	2n	2n	NUM
ejpam-5897	257	20	,	,	PUNCT
ejpam-5897	257	21	z2	z2	PROPN
ejpam-5897	257	22	2n	2n	NUM
ejpam-5897	257	23	)	)	PUNCT
ejpam-5897	258	1	=	=	PUNCT
ejpam-5897	258	2	∥∥∥∥∥∥t	∥∥∥∥∥∥t	PROPN
ejpam-5897	258	3	8d	8d	NOUN
ejpam-5897	258	4	(	(	PUNCT
ejpam-5897	258	5	µ	µ	X
ejpam-5897	258	6	(	(	PUNCT
ejpam-5897	258	7	x1	x1	PROPN
ejpam-5897	259	1	+	+	CCONJ
ejpam-5897	259	2	x2	x2	PROPN
ejpam-5897	259	3	2	2	NUM
ejpam-5897	259	4	,	,	PUNCT
ejpam-5897	259	5	y1	y1	NOUN
ejpam-5897	259	6	+	+	CCONJ
ejpam-5897	259	7	y2	y2	PROPN
ejpam-5897	259	8	2	2	NUM
ejpam-5897	259	9	,	,	PUNCT
ejpam-5897	259	10	z1	z1	PROPN
ejpam-5897	259	11	+	+	CCONJ
ejpam-5897	259	12	z2	z2	PROPN
ejpam-5897	259	13	2	2	NUM
ejpam-5897	259	14	)	)	PUNCT
ejpam-5897	259	15	)	)	PUNCT
ejpam-5897	260	1	−	−	PROPN
ejpam-5897	260	2	µ	µ	NUM
ejpam-5897	260	3	2∑	2∑	NUM
ejpam-5897	261	1	i	i	PROPN
ejpam-5897	261	2	,	,	PUNCT
ejpam-5897	261	3	j	j	PROPN
ejpam-5897	261	4	,	,	PUNCT
ejpam-5897	261	5	k=1	k=1	PROPN
ejpam-5897	261	6	d(xi	d(xi	PROPN
ejpam-5897	261	7	,	,	PUNCT
ejpam-5897	261	8	yj	yj	PROPN
ejpam-5897	261	9	,	,	PUNCT
ejpam-5897	261	10	zk	zk	PROPN
ejpam-5897	261	11	)	)	PUNCT
ejpam-5897	261	12	∥∥∥∥∥∥	∥∥∥∥∥∥	VERB
ejpam-5897	262	1	for	for	ADP
ejpam-5897	262	2	all	all	DET
ejpam-5897	262	3	(	(	PUNCT
ejpam-5897	262	4	x1	x1	PROPN
ejpam-5897	262	5	,	,	PUNCT
ejpam-5897	262	6	y1	y1	PROPN
ejpam-5897	262	7	,	,	PUNCT
ejpam-5897	262	8	z1	z1	NOUN
ejpam-5897	262	9	)	)	PUNCT
ejpam-5897	262	10	,	,	PUNCT
ejpam-5897	262	11	(	(	PUNCT
ejpam-5897	262	12	x2	x2	PROPN
ejpam-5897	262	13	,	,	PUNCT
ejpam-5897	262	14	y2	y2	PROPN
ejpam-5897	262	15	,	,	PUNCT
ejpam-5897	262	16	z2	z2	PROPN
ejpam-5897	262	17	)	)	PUNCT
ejpam-5897	262	18	∈	∈	PROPN
ejpam-5897	262	19	x3	x3	NOUN
ejpam-5897	262	20	and	and	CCONJ
ejpam-5897	262	21	µ	µ	PRON
ejpam-5897	262	22	∈	∈	NOUN
ejpam-5897	262	23	t1	t1	NOUN
ejpam-5897	262	24	.	.	PUNCT
ejpam-5897	263	1	thus	thus	ADV
ejpam-5897	263	2	∥d(µ(x1	∥d(µ(x1	X
ejpam-5897	263	3	+	+	CCONJ
ejpam-5897	263	4	x2	x2	ADJ
ejpam-5897	263	5	,	,	PUNCT
ejpam-5897	263	6	y1	y1	NOUN
ejpam-5897	263	7	+	+	CCONJ
ejpam-5897	263	8	y2	y2	NOUN
ejpam-5897	263	9	,	,	PUNCT
ejpam-5897	263	10	z1	z1	PROPN
ejpam-5897	263	11	+	+	CCONJ
ejpam-5897	263	12	z2))−	z2))−	PROPN
ejpam-5897	263	13	µ	µ	PRON
ejpam-5897	263	14	2∑	2∑	NUM
ejpam-5897	263	15	i	i	PROPN
ejpam-5897	263	16	,	,	PUNCT
ejpam-5897	263	17	j	j	PROPN
ejpam-5897	263	18	,	,	PUNCT
ejpam-5897	263	19	k=1	k=1	PROPN
ejpam-5897	263	20	d(xi	d(xi	PROPN
ejpam-5897	263	21	,	,	PUNCT
ejpam-5897	263	22	yj	yj	PROPN
ejpam-5897	263	23	,	,	PUNCT
ejpam-5897	263	24	zk)∥	zk)∥	PROPN
ejpam-5897	263	25	(	(	PUNCT
ejpam-5897	263	26	15	15	NUM
ejpam-5897	263	27	)	)	PUNCT
ejpam-5897	263	28	≤	≤	NOUN
ejpam-5897	264	1	∥∥∥∥∥∥t	∥∥∥∥∥∥t	PROPN
ejpam-5897	264	2	8d	8d	PROPN
ejpam-5897	264	3	(	(	PUNCT
ejpam-5897	264	4	µ	µ	X
ejpam-5897	264	5	(	(	PUNCT
ejpam-5897	264	6	x1	x1	PROPN
ejpam-5897	265	1	+	+	CCONJ
ejpam-5897	265	2	x2	x2	PROPN
ejpam-5897	265	3	2	2	NUM
ejpam-5897	265	4	,	,	PUNCT
ejpam-5897	265	5	y1	y1	NOUN
ejpam-5897	265	6	+	+	CCONJ
ejpam-5897	265	7	y2	y2	PROPN
ejpam-5897	265	8	2	2	NUM
ejpam-5897	265	9	,	,	PUNCT
ejpam-5897	265	10	z1	z1	PROPN
ejpam-5897	265	11	+	+	CCONJ
ejpam-5897	265	12	z2	z2	PROPN
ejpam-5897	265	13	2	2	NUM
ejpam-5897	265	14	)	)	PUNCT
ejpam-5897	265	15	)	)	PUNCT
ejpam-5897	266	1	−	−	PROPN
ejpam-5897	266	2	µ	µ	NUM
ejpam-5897	266	3	2∑	2∑	NUM
ejpam-5897	267	1	i	i	PROPN
ejpam-5897	267	2	,	,	PUNCT
ejpam-5897	267	3	j	j	PROPN
ejpam-5897	267	4	,	,	PUNCT
ejpam-5897	267	5	k=1	k=1	PROPN
ejpam-5897	267	6	d(xi	d(xi	PROPN
ejpam-5897	267	7	,	,	PUNCT
ejpam-5897	267	8	yj	yj	PROPN
ejpam-5897	267	9	,	,	PUNCT
ejpam-5897	267	10	zk	zk	PROPN
ejpam-5897	267	11	)	)	PUNCT
ejpam-5897	267	12	∥∥∥∥∥∥	∥∥∥∥∥∥	VERB
ejpam-5897	268	1	for	for	ADP
ejpam-5897	268	2	all	all	DET
ejpam-5897	268	3	(	(	PUNCT
ejpam-5897	268	4	x1	x1	PROPN
ejpam-5897	268	5	,	,	PUNCT
ejpam-5897	268	6	y1	y1	PROPN
ejpam-5897	268	7	,	,	PUNCT
ejpam-5897	268	8	z1	z1	NOUN
ejpam-5897	268	9	)	)	PUNCT
ejpam-5897	268	10	,	,	PUNCT
ejpam-5897	268	11	(	(	PUNCT
ejpam-5897	268	12	x2	x2	PROPN
ejpam-5897	268	13	,	,	PUNCT
ejpam-5897	268	14	y2	y2	PROPN
ejpam-5897	268	15	,	,	PUNCT
ejpam-5897	268	16	z2	z2	PROPN
ejpam-5897	268	17	)	)	PUNCT
ejpam-5897	268	18	∈	∈	PROPN
ejpam-5897	268	19	x3	x3	NOUN
ejpam-5897	268	20	and	and	CCONJ
ejpam-5897	268	21	µ	µ	PRON
ejpam-5897	268	22	∈	∈	NOUN
ejpam-5897	268	23	t1	t1	NOUN
ejpam-5897	268	24	.	.	PUNCT
ejpam-5897	269	1	let	let	VERB
ejpam-5897	269	2	µ	µ	X
ejpam-5897	269	3	=	=	SYM
ejpam-5897	269	4	1	1	NUM
ejpam-5897	269	5	in	in	ADP
ejpam-5897	269	6	(	(	PUNCT
ejpam-5897	269	7	15	15	NUM
ejpam-5897	269	8	)	)	PUNCT
ejpam-5897	269	9	.	.	PUNCT
ejpam-5897	270	1	by	by	ADP
ejpam-5897	270	2	theorem	theorem	NOUN
ejpam-5897	270	3	4	4	NUM
ejpam-5897	270	4	,	,	PUNCT
ejpam-5897	270	5	the	the	DET
ejpam-5897	270	6	mapping	mapping	NOUN
ejpam-5897	270	7	d	d	NOUN
ejpam-5897	270	8	:	:	PUNCT
ejpam-5897	270	9	x3	x3	ADJ
ejpam-5897	270	10	→	→	SYM
ejpam-5897	270	11	x	x	X
ejpam-5897	270	12	is	be	AUX
ejpam-5897	270	13	3	3	NUM
ejpam-5897	270	14	-	-	PUNCT
ejpam-5897	270	15	additive	additive	NOUN
ejpam-5897	270	16	.	.	PUNCT
ejpam-5897	271	1	it	it	PRON
ejpam-5897	271	2	follows	follow	VERB
ejpam-5897	271	3	from	from	ADP
ejpam-5897	271	4	(	(	PUNCT
ejpam-5897	271	5	15	15	NUM
ejpam-5897	271	6	)	)	PUNCT
ejpam-5897	271	7	and	and	CCONJ
ejpam-5897	271	8	the	the	DET
ejpam-5897	271	9	3	3	NUM
ejpam-5897	271	10	-	-	PUNCT
ejpam-5897	271	11	additivity	additivity	NOUN
ejpam-5897	271	12	of	of	ADP
ejpam-5897	271	13	d	d	PROPN
ejpam-5897	271	14	that	that	PRON
ejpam-5897	271	15	∥d(µ(x1	∥d(µ(x1	NUM
ejpam-5897	271	16	+	+	CCONJ
ejpam-5897	271	17	x2	x2	ADJ
ejpam-5897	271	18	,	,	PUNCT
ejpam-5897	271	19	y1	y1	NOUN
ejpam-5897	271	20	+	+	CCONJ
ejpam-5897	271	21	y2	y2	NOUN
ejpam-5897	271	22	,	,	PUNCT
ejpam-5897	271	23	z1	z1	PROPN
ejpam-5897	271	24	+	+	CCONJ
ejpam-5897	271	25	z2))−	z2))−	PROPN
ejpam-5897	271	26	µ	µ	PRON
ejpam-5897	271	27	2∑	2∑	NUM
ejpam-5897	271	28	i	i	PROPN
ejpam-5897	271	29	,	,	PUNCT
ejpam-5897	271	30	j	j	PROPN
ejpam-5897	271	31	,	,	PUNCT
ejpam-5897	271	32	k=1	k=1	PROPN
ejpam-5897	271	33	d(xi	d(xi	PROPN
ejpam-5897	271	34	,	,	PUNCT
ejpam-5897	271	35	yj	yj	PROPN
ejpam-5897	271	36	,	,	PUNCT
ejpam-5897	271	37	zk)∥	zk)∥	NUM
ejpam-5897	271	38	≤	≤	NUM
ejpam-5897	271	39	∥∥∥∥∥∥t	∥∥∥∥∥∥t	PUNCT
ejpam-5897	272	1	d(µ(x1	d(µ(x1	NOUN
ejpam-5897	272	2	+	+	CCONJ
ejpam-5897	272	3	x2	x2	ADJ
ejpam-5897	272	4	,	,	PUNCT
ejpam-5897	272	5	y1	y1	NOUN
ejpam-5897	272	6	+	+	CCONJ
ejpam-5897	272	7	y2	y2	NOUN
ejpam-5897	272	8	,	,	PUNCT
ejpam-5897	272	9	z1	z1	PROPN
ejpam-5897	272	10	+	+	CCONJ
ejpam-5897	272	11	z2))−	z2))−	PROPN
ejpam-5897	272	12	µ	µ	PRON
ejpam-5897	272	13	2∑	2∑	NUM
ejpam-5897	273	1	i	i	PROPN
ejpam-5897	273	2	,	,	PUNCT
ejpam-5897	273	3	j	j	PROPN
ejpam-5897	273	4	,	,	PUNCT
ejpam-5897	273	5	k=1	k=1	PROPN
ejpam-5897	273	6	d(xi	d(xi	PROPN
ejpam-5897	273	7	,	,	PUNCT
ejpam-5897	273	8	yj	yj	PROPN
ejpam-5897	273	9	,	,	PUNCT
ejpam-5897	273	10	zk	zk	PROPN
ejpam-5897	273	11	)	)	PUNCT
ejpam-5897	273	12	∥∥∥∥∥∥	∥∥∥∥∥∥	VERB
ejpam-5897	274	1	for	for	ADP
ejpam-5897	274	2	all	all	DET
ejpam-5897	274	3	(	(	PUNCT
ejpam-5897	274	4	x1	x1	PROPN
ejpam-5897	274	5	,	,	PUNCT
ejpam-5897	274	6	y1	y1	PROPN
ejpam-5897	274	7	,	,	PUNCT
ejpam-5897	274	8	z1	z1	NOUN
ejpam-5897	274	9	)	)	PUNCT
ejpam-5897	274	10	,	,	PUNCT
ejpam-5897	274	11	(	(	PUNCT
ejpam-5897	274	12	x2	x2	PROPN
ejpam-5897	274	13	,	,	PUNCT
ejpam-5897	274	14	y2	y2	PROPN
ejpam-5897	274	15	,	,	PUNCT
ejpam-5897	274	16	z2	z2	PROPN
ejpam-5897	274	17	)	)	PUNCT
ejpam-5897	274	18	∈	∈	PROPN
ejpam-5897	274	19	x3	x3	NOUN
ejpam-5897	274	20	and	and	CCONJ
ejpam-5897	274	21	µ	µ	PRON
ejpam-5897	274	22	∈	∈	NOUN
ejpam-5897	274	23	t1	t1	NOUN
ejpam-5897	274	24	.	.	PUNCT
ejpam-5897	275	1	since	since	SCONJ
ejpam-5897	275	2	|t|	|t|	VERB
ejpam-5897	275	3	<	<	X
ejpam-5897	275	4	1	1	NUM
ejpam-5897	275	5	,	,	PUNCT
ejpam-5897	275	6	d(µ(x1	d(µ(x1	NOUN
ejpam-5897	275	7	+	+	CCONJ
ejpam-5897	275	8	x2	x2	ADJ
ejpam-5897	275	9	,	,	PUNCT
ejpam-5897	275	10	y1	y1	NOUN
ejpam-5897	275	11	+	+	CCONJ
ejpam-5897	275	12	y2	y2	ADJ
ejpam-5897	275	13	,	,	PUNCT
ejpam-5897	275	14	z1	z1	PROPN
ejpam-5897	275	15	+	+	CCONJ
ejpam-5897	275	16	z2	z2	NOUN
ejpam-5897	275	17	)	)	PUNCT
ejpam-5897	275	18	)	)	PUNCT
ejpam-5897	276	1	=	=	SYM
ejpam-5897	277	1	µ	µ	NUM
ejpam-5897	277	2	2∑	2∑	NUM
ejpam-5897	277	3	i	i	PROPN
ejpam-5897	277	4	,	,	PUNCT
ejpam-5897	277	5	j	j	PROPN
ejpam-5897	277	6	,	,	PUNCT
ejpam-5897	277	7	k=1	k=1	PROPN
ejpam-5897	277	8	d(xi	d(xi	PROPN
ejpam-5897	277	9	,	,	PUNCT
ejpam-5897	277	10	yj	yj	PROPN
ejpam-5897	277	11	,	,	PUNCT
ejpam-5897	277	12	zk	zk	PROPN
ejpam-5897	277	13	)	)	PUNCT
ejpam-5897	277	14	and	and	CCONJ
ejpam-5897	277	15	d(µ(x1	d(µ(x1	PROPN
ejpam-5897	277	16	,	,	PUNCT
ejpam-5897	277	17	y1	y1	NOUN
ejpam-5897	277	18	,	,	PUNCT
ejpam-5897	277	19	z1	z1	NOUN
ejpam-5897	277	20	)	)	PUNCT
ejpam-5897	277	21	)	)	PUNCT
ejpam-5897	278	1	=	=	SYM
ejpam-5897	278	2	µd(x1	µd(x1	NOUN
ejpam-5897	278	3	,	,	PUNCT
ejpam-5897	278	4	y1	y1	NOUN
ejpam-5897	278	5	,	,	PUNCT
ejpam-5897	278	6	z1	z1	NOUN
ejpam-5897	278	7	)	)	PUNCT
ejpam-5897	278	8	for	for	ADP
ejpam-5897	278	9	all	all	DET
ejpam-5897	278	10	(	(	PUNCT
ejpam-5897	278	11	x1	x1	PROPN
ejpam-5897	278	12	,	,	PUNCT
ejpam-5897	278	13	y1	y1	PROPN
ejpam-5897	278	14	,	,	PUNCT
ejpam-5897	278	15	z1	z1	ADJ
ejpam-5897	278	16	)	)	PUNCT
ejpam-5897	278	17	∈	∈	NOUN
ejpam-5897	278	18	x3	x3	NOUN
ejpam-5897	278	19	and	and	CCONJ
ejpam-5897	278	20	µ	µ	PRON
ejpam-5897	278	21	∈	∈	NOUN
ejpam-5897	278	22	t1	t1	NOUN
ejpam-5897	278	23	.	.	PUNCT
ejpam-5897	279	1	by	by	ADP
ejpam-5897	279	2	lemma	lemma	PROPN
ejpam-5897	279	3	2	2	NUM
ejpam-5897	279	4	,	,	PUNCT
ejpam-5897	279	5	the	the	DET
ejpam-5897	279	6	mapping	mapping	NOUN
ejpam-5897	279	7	d	d	NOUN
ejpam-5897	279	8	:	:	PUNCT
ejpam-5897	279	9	x3	x3	ADJ
ejpam-5897	279	10	→	→	SYM
ejpam-5897	279	11	x	x	X
ejpam-5897	279	12	is	be	AUX
ejpam-5897	279	13	3	3	NUM
ejpam-5897	279	14	-	-	PUNCT
ejpam-5897	279	15	linear	linear	NOUN
ejpam-5897	279	16	.	.	PUNCT
ejpam-5897	280	1	it	it	PRON
ejpam-5897	280	2	follows	follow	VERB
ejpam-5897	280	3	from	from	ADP
ejpam-5897	280	4	(	(	PUNCT
ejpam-5897	280	5	12	12	NUM
ejpam-5897	280	6	)	)	PUNCT
ejpam-5897	280	7	and	and	CCONJ
ejpam-5897	280	8	the	the	DET
ejpam-5897	280	9	3	3	NUM
ejpam-5897	280	10	-	-	PUNCT
ejpam-5897	280	11	additivity	additivity	NOUN
ejpam-5897	280	12	of	of	ADP
ejpam-5897	280	13	d	d	PROPN
ejpam-5897	280	14	that	that	SCONJ
ejpam-5897	280	15	∥d([x1	∥d([x1	PROPN
ejpam-5897	280	16	,	,	PUNCT
ejpam-5897	280	17	y1	y1	PROPN
ejpam-5897	280	18	,	,	PUNCT
ejpam-5897	280	19	z1	z1	NOUN
ejpam-5897	280	20	]	]	PUNCT
ejpam-5897	280	21	,	,	PUNCT
ejpam-5897	280	22	[	[	X
ejpam-5897	280	23	x2	x2	X
ejpam-5897	280	24	,	,	PUNCT
ejpam-5897	280	25	y2	y2	PROPN
ejpam-5897	280	26	,	,	PUNCT
ejpam-5897	280	27	z2	z2	PROPN
ejpam-5897	280	28	]	]	PUNCT
ejpam-5897	280	29	,	,	PUNCT
ejpam-5897	280	30	[	[	X
ejpam-5897	280	31	x3	x3	ADJ
ejpam-5897	280	32	,	,	PUNCT
ejpam-5897	280	33	y3	y3	NOUN
ejpam-5897	280	34	,	,	PUNCT
ejpam-5897	280	35	z3])−	z3])−	X
ejpam-5897	281	1	[	[	X
ejpam-5897	281	2	d(x1	d(x1	NOUN
ejpam-5897	281	3	,	,	PUNCT
ejpam-5897	281	4	x2	x2	PROPN
ejpam-5897	281	5	,	,	PUNCT
ejpam-5897	281	6	x3	x3	ADJ
ejpam-5897	281	7	)	)	PUNCT
ejpam-5897	281	8	,	,	PUNCT
ejpam-5897	281	9	[	[	X
ejpam-5897	281	10	y1	y1	X
ejpam-5897	281	11	,	,	PUNCT
ejpam-5897	281	12	y2	y2	PROPN
ejpam-5897	281	13	,	,	PUNCT
ejpam-5897	281	14	y3	y3	PROPN
ejpam-5897	281	15	]	]	PUNCT
ejpam-5897	281	16	,	,	PUNCT
ejpam-5897	281	17	[	[	X
ejpam-5897	281	18	z1	z1	ADJ
ejpam-5897	281	19	,	,	PUNCT
ejpam-5897	281	20	z2	z2	PROPN
ejpam-5897	281	21	,	,	PUNCT
ejpam-5897	281	22	z3	z3	PROPN
ejpam-5897	281	23	]	]	X
ejpam-5897	281	24	]	]	X
ejpam-5897	281	25	−[[x1	−[[x1	NUM
ejpam-5897	281	26	,	,	PUNCT
ejpam-5897	281	27	x2	x2	PROPN
ejpam-5897	281	28	,	,	PUNCT
ejpam-5897	281	29	x3	x3	PROPN
ejpam-5897	281	30	]	]	PUNCT
ejpam-5897	281	31	,	,	PUNCT
ejpam-5897	281	32	d(y1	d(y1	NOUN
ejpam-5897	281	33	,	,	PUNCT
ejpam-5897	281	34	y2	y2	PROPN
ejpam-5897	281	35	,	,	PUNCT
ejpam-5897	281	36	y3	y3	PROPN
ejpam-5897	281	37	)	)	PUNCT
ejpam-5897	281	38	,	,	PUNCT
ejpam-5897	281	39	[	[	X
ejpam-5897	281	40	z1	z1	ADJ
ejpam-5897	281	41	,	,	PUNCT
ejpam-5897	281	42	z2	z2	PROPN
ejpam-5897	281	43	,	,	PUNCT
ejpam-5897	281	44	z3]]−	z3]]−	PROPN
ejpam-5897	282	1	[	[	X
ejpam-5897	282	2	[	[	X
ejpam-5897	282	3	x1	x1	PROPN
ejpam-5897	282	4	,	,	PUNCT
ejpam-5897	282	5	x2	x2	PROPN
ejpam-5897	282	6	,	,	PUNCT
ejpam-5897	282	7	x3	x3	ADJ
ejpam-5897	282	8	]	]	PUNCT
ejpam-5897	282	9	,	,	PUNCT
ejpam-5897	282	10	[	[	X
ejpam-5897	282	11	y1	y1	X
ejpam-5897	282	12	,	,	PUNCT
ejpam-5897	282	13	y2	y2	PROPN
ejpam-5897	282	14	,	,	PUNCT
ejpam-5897	282	15	y3	y3	PROPN
ejpam-5897	282	16	]	]	PUNCT
ejpam-5897	282	17	,	,	PUNCT
ejpam-5897	282	18	d(z1	d(z1	NOUN
ejpam-5897	282	19	,	,	PUNCT
ejpam-5897	282	20	z2	z2	PROPN
ejpam-5897	282	21	,	,	PUNCT
ejpam-5897	282	22	z3)]∥	z3)]∥	X
ejpam-5897	282	23	=	=	SYM
ejpam-5897	282	24	lim	lim	PROPN
ejpam-5897	282	25	n→+∞	n→+∞	VERB
ejpam-5897	282	26	83n	83n	NOUN
ejpam-5897	282	27	∥∥∥f	∥∥∥f	NOUN
ejpam-5897	282	28	(	(	PUNCT
ejpam-5897	282	29	[	[	X
ejpam-5897	282	30	x1	x1	PROPN
ejpam-5897	282	31	,	,	PUNCT
ejpam-5897	282	32	y1	y1	PROPN
ejpam-5897	282	33	,	,	PUNCT
ejpam-5897	282	34	z1	z1	NOUN
ejpam-5897	282	35	]	]	PUNCT
ejpam-5897	282	36	8n	8n	NOUN
ejpam-5897	282	37	,	,	PUNCT
ejpam-5897	282	38	[	[	X
ejpam-5897	282	39	x2	x2	X
ejpam-5897	282	40	,	,	PUNCT
ejpam-5897	282	41	y2	y2	PROPN
ejpam-5897	282	42	,	,	PUNCT
ejpam-5897	282	43	z2	z2	PROPN
ejpam-5897	282	44	]	]	X
ejpam-5897	282	45	8n	8n	NOUN
ejpam-5897	282	46	,	,	PUNCT
ejpam-5897	282	47	[	[	X
ejpam-5897	282	48	x3	x3	ADJ
ejpam-5897	282	49	,	,	PUNCT
ejpam-5897	282	50	y3	y3	NOUN
ejpam-5897	282	51	,	,	PUNCT
ejpam-5897	282	52	z3	z3	PROPN
ejpam-5897	282	53	]	]	PUNCT
ejpam-5897	282	54	8n	8n	NOUN
ejpam-5897	282	55	)	)	PUNCT
ejpam-5897	282	56	−	−	PROPN
ejpam-5897	283	1	[	[	PUNCT
ejpam-5897	283	2	f	f	X
ejpam-5897	283	3	(	(	PUNCT
ejpam-5897	283	4	x1	x1	PROPN
ejpam-5897	283	5	2n	2n	NUM
ejpam-5897	283	6	,	,	PUNCT
ejpam-5897	283	7	x2	x2	PROPN
ejpam-5897	283	8	2n	2n	NUM
ejpam-5897	283	9	,	,	PUNCT
ejpam-5897	283	10	x3	x3	PROPN
ejpam-5897	283	11	2n	2n	NUM
ejpam-5897	283	12	)	)	PUNCT
ejpam-5897	283	13	,	,	PUNCT
ejpam-5897	284	1	[	[	X
ejpam-5897	284	2	y1	y1	X
ejpam-5897	284	3	,	,	PUNCT
ejpam-5897	284	4	y2	y2	PROPN
ejpam-5897	284	5	,	,	PUNCT
ejpam-5897	284	6	y3	y3	NOUN
ejpam-5897	284	7	]	]	PUNCT
ejpam-5897	284	8	8n	8n	NOUN
ejpam-5897	284	9	,	,	PUNCT
ejpam-5897	284	10	[	[	X
ejpam-5897	284	11	z1	z1	ADJ
ejpam-5897	284	12	,	,	PUNCT
ejpam-5897	284	13	z2	z2	PROPN
ejpam-5897	284	14	,	,	PUNCT
ejpam-5897	284	15	z3	z3	NOUN
ejpam-5897	284	16	]	]	PUNCT
ejpam-5897	284	17	8n	8n	NOUN
ejpam-5897	284	18	]	]	PUNCT
ejpam-5897	284	19	e.	e.	PROPN
ejpam-5897	284	20	shim	shim	PROPN
ejpam-5897	284	21	,	,	PUNCT
ejpam-5897	284	22	s.	s.	PROPN
ejpam-5897	284	23	donganont	donganont	PROPN
ejpam-5897	284	24	,	,	PUNCT
ejpam-5897	284	25	c.	c.	PROPN
ejpam-5897	284	26	park	park	PROPN
ejpam-5897	284	27	/	/	SYM
ejpam-5897	284	28	eur	eur	PROPN
ejpam-5897	284	29	.	.	PUNCT
ejpam-5897	285	1	j.	j.	PROPN
ejpam-5897	285	2	pure	pure	PROPN
ejpam-5897	285	3	appl	appl	PROPN
ejpam-5897	285	4	.	.	PROPN
ejpam-5897	285	5	math	math	PROPN
ejpam-5897	285	6	,	,	PUNCT
ejpam-5897	285	7	18	18	NUM
ejpam-5897	285	8	(	(	PUNCT
ejpam-5897	285	9	2	2	NUM
ejpam-5897	285	10	)	)	PUNCT
ejpam-5897	285	11	(	(	PUNCT
ejpam-5897	285	12	2025	2025	NUM
ejpam-5897	285	13	)	)	PUNCT
ejpam-5897	285	14	,	,	PUNCT
ejpam-5897	285	15	5897	5897	NUM
ejpam-5897	285	16	12	12	NUM
ejpam-5897	285	17	of	of	ADP
ejpam-5897	285	18	14	14	NUM
ejpam-5897	285	19	−	−	NOUN
ejpam-5897	286	1	[	[	PUNCT
ejpam-5897	286	2	[	[	X
ejpam-5897	286	3	x1	x1	PROPN
ejpam-5897	286	4	,	,	PUNCT
ejpam-5897	286	5	x2	x2	PROPN
ejpam-5897	286	6	,	,	PUNCT
ejpam-5897	286	7	x3	x3	ADJ
ejpam-5897	286	8	]	]	PUNCT
ejpam-5897	286	9	8n	8n	NOUN
ejpam-5897	286	10	,	,	PUNCT
ejpam-5897	286	11	f	f	PROPN
ejpam-5897	286	12	(	(	PUNCT
ejpam-5897	286	13	y1	y1	INTJ
ejpam-5897	286	14	2n	2n	NUM
ejpam-5897	286	15	,	,	PUNCT
ejpam-5897	286	16	y2	y2	PROPN
ejpam-5897	286	17	2n	2n	NUM
ejpam-5897	286	18	,	,	PUNCT
ejpam-5897	286	19	y3	y3	PROPN
ejpam-5897	286	20	2n	2n	NUM
ejpam-5897	286	21	)	)	PUNCT
ejpam-5897	286	22	,	,	PUNCT
ejpam-5897	287	1	[	[	X
ejpam-5897	287	2	z1	z1	ADJ
ejpam-5897	287	3	,	,	PUNCT
ejpam-5897	287	4	z2	z2	PROPN
ejpam-5897	287	5	,	,	PUNCT
ejpam-5897	287	6	z3	z3	NOUN
ejpam-5897	287	7	]	]	PUNCT
ejpam-5897	287	8	8n	8n	NOUN
ejpam-5897	287	9	]	]	PUNCT
ejpam-5897	287	10	−	−	PROPN
ejpam-5897	287	11	[	[	PUNCT
ejpam-5897	287	12	[	[	X
ejpam-5897	287	13	x1	x1	PROPN
ejpam-5897	287	14	,	,	PUNCT
ejpam-5897	287	15	x2	x2	PROPN
ejpam-5897	287	16	,	,	PUNCT
ejpam-5897	287	17	x3	x3	ADJ
ejpam-5897	287	18	]	]	PUNCT
ejpam-5897	287	19	8n	8n	NOUN
ejpam-5897	287	20	,	,	PUNCT
ejpam-5897	288	1	[	[	X
ejpam-5897	288	2	y1	y1	X
ejpam-5897	288	3	,	,	PUNCT
ejpam-5897	288	4	y2	y2	PROPN
ejpam-5897	288	5	,	,	PUNCT
ejpam-5897	288	6	y3	y3	NOUN
ejpam-5897	288	7	]	]	PUNCT
ejpam-5897	288	8	8n	8n	NOUN
ejpam-5897	288	9	,	,	PUNCT
ejpam-5897	288	10	f	f	PROPN
ejpam-5897	288	11	(	(	PUNCT
ejpam-5897	288	12	z1	z1	PROPN
ejpam-5897	288	13	2n	2n	NUM
ejpam-5897	288	14	,	,	PUNCT
ejpam-5897	288	15	z2	z2	PROPN
ejpam-5897	288	16	2n	2n	NUM
ejpam-5897	288	17	,	,	PUNCT
ejpam-5897	288	18	z3	z3	PROPN
ejpam-5897	288	19	2n	2n	NUM
ejpam-5897	288	20	)	)	PUNCT
ejpam-5897	288	21	]	]	PUNCT
ejpam-5897	288	22	∥∥∥	∥∥∥	PROPN
ejpam-5897	288	23	≤	≤	PROPN
ejpam-5897	288	24	lim	lim	PROPN
ejpam-5897	288	25	n→+∞	n→+∞	VERB
ejpam-5897	288	26	83nψ	83nψ	PROPN
ejpam-5897	288	27	(	(	PUNCT
ejpam-5897	288	28	x1	x1	PROPN
ejpam-5897	288	29	2n	2n	NUM
ejpam-5897	288	30	,	,	PUNCT
ejpam-5897	288	31	x2	x2	PROPN
ejpam-5897	288	32	2n	2n	NUM
ejpam-5897	288	33	,	,	PUNCT
ejpam-5897	288	34	x3	x3	PROPN
ejpam-5897	288	35	2n	2n	NUM
ejpam-5897	288	36	,	,	PUNCT
ejpam-5897	288	37	y1	y1	NOUN
ejpam-5897	288	38	2n	2n	NUM
ejpam-5897	288	39	,	,	PUNCT
ejpam-5897	288	40	y2	y2	PROPN
ejpam-5897	288	41	2n	2n	NUM
ejpam-5897	288	42	,	,	PUNCT
ejpam-5897	288	43	y3	y3	PROPN
ejpam-5897	288	44	2n	2n	NUM
ejpam-5897	288	45	,	,	PUNCT
ejpam-5897	288	46	z1	z1	PROPN
ejpam-5897	288	47	2n	2n	NUM
ejpam-5897	288	48	,	,	PUNCT
ejpam-5897	288	49	z2	z2	PROPN
ejpam-5897	288	50	2n	2n	NUM
ejpam-5897	288	51	,	,	PUNCT
ejpam-5897	288	52	z3	z3	PROPN
ejpam-5897	288	53	2n	2n	NUM
ejpam-5897	288	54	)	)	PUNCT
ejpam-5897	289	1	=	=	SYM
ejpam-5897	289	2	0	0	NUM
ejpam-5897	289	3	for	for	ADP
ejpam-5897	289	4	all	all	DET
ejpam-5897	289	5	x1	x1	PROPN
ejpam-5897	289	6	,	,	PUNCT
ejpam-5897	289	7	x2	x2	PROPN
ejpam-5897	289	8	,	,	PUNCT
ejpam-5897	289	9	x3	x3	ADJ
ejpam-5897	289	10	,	,	PUNCT
ejpam-5897	289	11	y1	y1	NOUN
ejpam-5897	289	12	,	,	PUNCT
ejpam-5897	289	13	y2	y2	PROPN
ejpam-5897	289	14	,	,	PUNCT
ejpam-5897	289	15	y3	y3	PROPN
ejpam-5897	289	16	,	,	PUNCT
ejpam-5897	289	17	z1	z1	PROPN
ejpam-5897	289	18	,	,	PUNCT
ejpam-5897	289	19	z2	z2	PROPN
ejpam-5897	289	20	,	,	PUNCT
ejpam-5897	289	21	z3	z3	PROPN
ejpam-5897	289	22	∈	∈	PROPN
ejpam-5897	289	23	x.	x.	NOUN
ejpam-5897	290	1	so	so	SCONJ
ejpam-5897	290	2	d([x1	d([x1	NOUN
ejpam-5897	290	3	,	,	PUNCT
ejpam-5897	290	4	y1	y1	NOUN
ejpam-5897	290	5	,	,	PUNCT
ejpam-5897	290	6	z1	z1	NOUN
ejpam-5897	290	7	]	]	PUNCT
ejpam-5897	290	8	,	,	PUNCT
ejpam-5897	290	9	[	[	X
ejpam-5897	290	10	x2	x2	X
ejpam-5897	290	11	,	,	PUNCT
ejpam-5897	290	12	y2	y2	PROPN
ejpam-5897	290	13	,	,	PUNCT
ejpam-5897	290	14	z2	z2	PROPN
ejpam-5897	290	15	]	]	PUNCT
ejpam-5897	290	16	,	,	PUNCT
ejpam-5897	290	17	[	[	X
ejpam-5897	290	18	x3	x3	ADJ
ejpam-5897	290	19	,	,	PUNCT
ejpam-5897	290	20	y3	y3	NOUN
ejpam-5897	290	21	,	,	PUNCT
ejpam-5897	290	22	z3	z3	PROPN
ejpam-5897	290	23	]	]	PUNCT
ejpam-5897	290	24	)	)	PUNCT
ejpam-5897	290	25	=	=	PUNCT
ejpam-5897	291	1	[	[	X
ejpam-5897	291	2	d(x1	d(x1	NOUN
ejpam-5897	291	3	,	,	PUNCT
ejpam-5897	291	4	x2	x2	PROPN
ejpam-5897	291	5	,	,	PUNCT
ejpam-5897	291	6	x3	x3	ADJ
ejpam-5897	291	7	)	)	PUNCT
ejpam-5897	291	8	,	,	PUNCT
ejpam-5897	291	9	[	[	X
ejpam-5897	291	10	y1	y1	X
ejpam-5897	291	11	,	,	PUNCT
ejpam-5897	291	12	y2	y2	PROPN
ejpam-5897	291	13	,	,	PUNCT
ejpam-5897	291	14	y3	y3	PROPN
ejpam-5897	291	15	]	]	PUNCT
ejpam-5897	291	16	,	,	PUNCT
ejpam-5897	291	17	[	[	X
ejpam-5897	291	18	z1	z1	ADJ
ejpam-5897	291	19	,	,	PUNCT
ejpam-5897	291	20	z2	z2	PROPN
ejpam-5897	291	21	,	,	PUNCT
ejpam-5897	291	22	z3	z3	PROPN
ejpam-5897	291	23	]	]	X
ejpam-5897	291	24	]	]	X
ejpam-5897	291	25	−[[x1	−[[x1	NUM
ejpam-5897	291	26	,	,	PUNCT
ejpam-5897	291	27	x2	x2	PROPN
ejpam-5897	291	28	,	,	PUNCT
ejpam-5897	291	29	x3	x3	PROPN
ejpam-5897	291	30	]	]	PUNCT
ejpam-5897	291	31	,	,	PUNCT
ejpam-5897	291	32	d(y1	d(y1	NOUN
ejpam-5897	291	33	,	,	PUNCT
ejpam-5897	291	34	y2	y2	PROPN
ejpam-5897	291	35	,	,	PUNCT
ejpam-5897	291	36	y3	y3	PROPN
ejpam-5897	291	37	)	)	PUNCT
ejpam-5897	291	38	,	,	PUNCT
ejpam-5897	291	39	[	[	X
ejpam-5897	291	40	z1	z1	ADJ
ejpam-5897	291	41	,	,	PUNCT
ejpam-5897	291	42	z2	z2	PROPN
ejpam-5897	291	43	,	,	PUNCT
ejpam-5897	291	44	z3]]−	z3]]−	PROPN
ejpam-5897	292	1	[	[	X
ejpam-5897	292	2	[	[	X
ejpam-5897	292	3	x1	x1	PROPN
ejpam-5897	292	4	,	,	PUNCT
ejpam-5897	292	5	x2	x2	PROPN
ejpam-5897	292	6	,	,	PUNCT
ejpam-5897	292	7	x3	x3	ADJ
ejpam-5897	292	8	]	]	PUNCT
ejpam-5897	292	9	,	,	PUNCT
ejpam-5897	293	1	[	[	X
ejpam-5897	293	2	y1	y1	X
ejpam-5897	293	3	,	,	PUNCT
ejpam-5897	293	4	y2	y2	PROPN
ejpam-5897	293	5	,	,	PUNCT
ejpam-5897	293	6	y3	y3	PROPN
ejpam-5897	293	7	]	]	PUNCT
ejpam-5897	293	8	,	,	PUNCT
ejpam-5897	293	9	d(z1	d(z1	NOUN
ejpam-5897	293	10	,	,	PUNCT
ejpam-5897	293	11	z2	z2	PROPN
ejpam-5897	293	12	,	,	PUNCT
ejpam-5897	293	13	z3	z3	PROPN
ejpam-5897	293	14	)	)	PUNCT
ejpam-5897	293	15	]	]	PUNCT
ejpam-5897	293	16	for	for	ADP
ejpam-5897	293	17	all	all	PRON
ejpam-5897	293	18	x1	x1	PROPN
ejpam-5897	293	19	,	,	PUNCT
ejpam-5897	293	20	x2	x2	PROPN
ejpam-5897	293	21	,	,	PUNCT
ejpam-5897	293	22	x3	x3	ADJ
ejpam-5897	293	23	,	,	PUNCT
ejpam-5897	293	24	y1	y1	NOUN
ejpam-5897	293	25	,	,	PUNCT
ejpam-5897	293	26	y2	y2	PROPN
ejpam-5897	293	27	,	,	PUNCT
ejpam-5897	293	28	y3	y3	PROPN
ejpam-5897	293	29	,	,	PUNCT
ejpam-5897	293	30	z1	z1	PROPN
ejpam-5897	293	31	,	,	PUNCT
ejpam-5897	293	32	z2	z2	PROPN
ejpam-5897	293	33	,	,	PUNCT
ejpam-5897	293	34	z3	z3	PROPN
ejpam-5897	293	35	∈	∈	PROPN
ejpam-5897	293	36	x.	x.	NOUN
ejpam-5897	293	37	therefore	therefore	ADV
ejpam-5897	293	38	,	,	PUNCT
ejpam-5897	293	39	the	the	DET
ejpam-5897	293	40	mapping	mapping	NOUN
ejpam-5897	293	41	h	h	NOUN
ejpam-5897	293	42	is	be	AUX
ejpam-5897	293	43	a	a	DET
ejpam-5897	293	44	unique	unique	ADJ
ejpam-5897	293	45	hyper	hyper	ADJ
ejpam-5897	293	46	3	3	NUM
ejpam-5897	293	47	-	-	PUNCT
ejpam-5897	293	48	derivation	derivation	NOUN
ejpam-5897	293	49	satisfying	satisfying	NOUN
ejpam-5897	293	50	(	(	PUNCT
ejpam-5897	293	51	13	13	NUM
ejpam-5897	293	52	)	)	PUNCT
ejpam-5897	293	53	.	.	PUNCT
ejpam-5897	294	1	4	4	X
ejpam-5897	294	2	.	.	X
ejpam-5897	294	3	conclusion	conclusion	NOUN
ejpam-5897	294	4	and	and	CCONJ
ejpam-5897	294	5	future	future	ADJ
ejpam-5897	294	6	work	work	NOUN
ejpam-5897	294	7	in	in	ADP
ejpam-5897	294	8	this	this	DET
ejpam-5897	294	9	paper	paper	NOUN
ejpam-5897	294	10	,	,	PUNCT
ejpam-5897	294	11	we	we	PRON
ejpam-5897	294	12	introduced	introduce	VERB
ejpam-5897	294	13	hyper	hyper	ADJ
ejpam-5897	294	14	3	3	NUM
ejpam-5897	294	15	-	-	PUNCT
ejpam-5897	294	16	homomorphisms	homomorphism	NOUN
ejpam-5897	294	17	and	and	CCONJ
ejpam-5897	294	18	hyper	hyper	ADJ
ejpam-5897	294	19	3	3	NUM
ejpam-5897	294	20	-	-	PUNCT
ejpam-5897	294	21	derivations	derivation	NOUN
ejpam-5897	294	22	in	in	ADP
ejpam-5897	294	23	ternary	ternary	ADJ
ejpam-5897	294	24	algebras	algebra	NOUN
ejpam-5897	294	25	and	and	CCONJ
ejpam-5897	294	26	we	we	PRON
ejpam-5897	294	27	proved	prove	VERB
ejpam-5897	294	28	the	the	DET
ejpam-5897	294	29	hyers	hyers	PROPN
ejpam-5897	294	30	-	-	PUNCT
ejpam-5897	294	31	ulam	ulam	ADJ
ejpam-5897	294	32	stability	stability	NOUN
ejpam-5897	294	33	of	of	ADP
ejpam-5897	294	34	hyper	hyper	ADJ
ejpam-5897	294	35	3	3	NUM
ejpam-5897	294	36	-	-	PUNCT
ejpam-5897	294	37	homomorphisms	homomorphism	NOUN
ejpam-5897	294	38	and	and	CCONJ
ejpam-5897	294	39	hyper	hyper	ADJ
ejpam-5897	294	40	3	3	NUM
ejpam-5897	294	41	-	-	PUNCT
ejpam-5897	294	42	derivations	derivation	NOUN
ejpam-5897	294	43	in	in	ADP
ejpam-5897	294	44	ternary	ternary	ADJ
ejpam-5897	294	45	banach	banach	NOUN
ejpam-5897	294	46	algebras	algebra	NOUN
ejpam-5897	294	47	,	,	PUNCT
ejpam-5897	294	48	associated	associate	VERB
ejpam-5897	294	49	with	with	ADP
ejpam-5897	294	50	the	the	DET
ejpam-5897	294	51	3	3	NUM
ejpam-5897	294	52	-	-	PUNCT
ejpam-5897	294	53	additive	additive	ADJ
ejpam-5897	294	54	functional	functional	ADJ
ejpam-5897	294	55	equation	equation	NOUN
ejpam-5897	294	56	(	(	PUNCT
ejpam-5897	294	57	1	1	NUM
ejpam-5897	294	58	)	)	PUNCT
ejpam-5897	294	59	.	.	PUNCT
ejpam-5897	295	1	we	we	PRON
ejpam-5897	295	2	will	will	AUX
ejpam-5897	295	3	provide	provide	VERB
ejpam-5897	295	4	suitable	suitable	ADJ
ejpam-5897	295	5	examples	example	NOUN
ejpam-5897	295	6	and	and	CCONJ
ejpam-5897	295	7	useful	useful	ADJ
ejpam-5897	295	8	applications	application	NOUN
ejpam-5897	295	9	in	in	ADP
ejpam-5897	295	10	next	next	ADJ
ejpam-5897	295	11	work	work	NOUN
ejpam-5897	295	12	.	.	PUNCT
ejpam-5897	296	1	acknowledgements	acknowledgement	NOUN
ejpam-5897	296	2	the	the	DET
ejpam-5897	296	3	authors	author	NOUN
ejpam-5897	296	4	are	be	AUX
ejpam-5897	296	5	thankful	thankful	ADJ
ejpam-5897	296	6	to	to	ADP
ejpam-5897	296	7	the	the	DET
ejpam-5897	296	8	editors	editor	NOUN
ejpam-5897	296	9	and	and	CCONJ
ejpam-5897	296	10	the	the	DET
ejpam-5897	296	11	anonymous	anonymous	ADJ
ejpam-5897	296	12	reviewers	reviewer	NOUN
ejpam-5897	296	13	for	for	ADP
ejpam-5897	296	14	many	many	ADJ
ejpam-5897	296	15	valuable	valuable	ADJ
ejpam-5897	296	16	suggestions	suggestion	NOUN
ejpam-5897	296	17	to	to	PART
ejpam-5897	296	18	improve	improve	VERB
ejpam-5897	296	19	this	this	DET
ejpam-5897	296	20	paper	paper	NOUN
ejpam-5897	296	21	.	.	PUNCT
ejpam-5897	297	1	declarations	declaration	NOUN
ejpam-5897	297	2	availablity	availablity	NOUN
ejpam-5897	297	3	of	of	ADP
ejpam-5897	297	4	data	datum	NOUN
ejpam-5897	297	5	and	and	CCONJ
ejpam-5897	297	6	materials	material	NOUN
ejpam-5897	297	7	not	not	PART
ejpam-5897	297	8	applicable	applicable	ADJ
ejpam-5897	297	9	.	.	PUNCT
ejpam-5897	298	1	human	human	ADJ
ejpam-5897	298	2	and	and	CCONJ
ejpam-5897	298	3	animal	animal	NOUN
ejpam-5897	298	4	rights	right	NOUN
ejpam-5897	298	5	we	we	PRON
ejpam-5897	298	6	would	would	AUX
ejpam-5897	298	7	like	like	VERB
ejpam-5897	298	8	to	to	PART
ejpam-5897	298	9	mention	mention	VERB
ejpam-5897	298	10	that	that	SCONJ
ejpam-5897	298	11	this	this	DET
ejpam-5897	298	12	article	article	NOUN
ejpam-5897	298	13	does	do	AUX
ejpam-5897	298	14	not	not	PART
ejpam-5897	298	15	contain	contain	VERB
ejpam-5897	298	16	any	any	DET
ejpam-5897	298	17	studies	study	NOUN
ejpam-5897	298	18	with	with	ADP
ejpam-5897	298	19	animals	animal	NOUN
ejpam-5897	298	20	and	and	CCONJ
ejpam-5897	298	21	does	do	AUX
ejpam-5897	298	22	not	not	PART
ejpam-5897	298	23	involve	involve	VERB
ejpam-5897	298	24	any	any	DET
ejpam-5897	298	25	studies	study	NOUN
ejpam-5897	298	26	over	over	ADP
ejpam-5897	298	27	human	human	ADJ
ejpam-5897	298	28	being	being	NOUN
ejpam-5897	298	29	.	.	PUNCT
ejpam-5897	299	1	conflict	conflict	NOUN
ejpam-5897	299	2	of	of	ADP
ejpam-5897	299	3	interest	interest	NOUN
ejpam-5897	299	4	the	the	DET
ejpam-5897	299	5	authors	author	NOUN
ejpam-5897	299	6	declare	declare	VERB
ejpam-5897	299	7	that	that	SCONJ
ejpam-5897	299	8	they	they	PRON
ejpam-5897	299	9	have	have	VERB
ejpam-5897	299	10	no	no	DET
ejpam-5897	299	11	competing	compete	VERB
ejpam-5897	299	12	interests	interest	NOUN
ejpam-5897	299	13	.	.	PUNCT
ejpam-5897	300	1	fundings	funding	NOUN
ejpam-5897	300	2	s.	s.	PROPN
ejpam-5897	300	3	donganont	donganont	PROPN
ejpam-5897	300	4	was	be	AUX
ejpam-5897	300	5	supported	support	VERB
ejpam-5897	300	6	by	by	ADP
ejpam-5897	300	7	the	the	DET
ejpam-5897	300	8	university	university	NOUN
ejpam-5897	300	9	of	of	ADP
ejpam-5897	300	10	phayao	phayao	PROPN
ejpam-5897	300	11	and	and	CCONJ
ejpam-5897	300	12	thailand	thailand	PROPN
ejpam-5897	300	13	science	science	PROPN
ejpam-5897	300	14	research	research	PROPN
ejpam-5897	300	15	and	and	CCONJ
ejpam-5897	300	16	innovation	innovation	NOUN
ejpam-5897	300	17	fund	fund	NOUN
ejpam-5897	300	18	(	(	PUNCT
ejpam-5897	300	19	fundamental	fundamental	ADJ
ejpam-5897	300	20	fund	fund	NOUN
ejpam-5897	300	21	2025	2025	NUM
ejpam-5897	300	22	,	,	PUNCT
ejpam-5897	300	23	grant	grant	VERB
ejpam-5897	300	24	no	no	NOUN
ejpam-5897	300	25	.	.	PUNCT
ejpam-5897	301	1	5020/2567	5020/2567	NUM
ejpam-5897	301	2	)	)	PUNCT
ejpam-5897	301	3	.	.	PUNCT
ejpam-5897	302	1	e.	e.	PROPN
ejpam-5897	302	2	shim	shim	PROPN
ejpam-5897	302	3	,	,	PUNCT
ejpam-5897	302	4	s.	s.	PROPN
ejpam-5897	302	5	donganont	donganont	PROPN
ejpam-5897	302	6	,	,	PUNCT
ejpam-5897	302	7	c.	c.	PROPN
ejpam-5897	302	8	park	park	PROPN
ejpam-5897	302	9	/	/	SYM
ejpam-5897	302	10	eur	eur	PROPN
ejpam-5897	302	11	.	.	PUNCT
ejpam-5897	303	1	j.	j.	PROPN
ejpam-5897	303	2	pure	pure	PROPN
ejpam-5897	303	3	appl	appl	PROPN
ejpam-5897	303	4	.	.	PROPN
ejpam-5897	303	5	math	math	PROPN
ejpam-5897	303	6	,	,	PUNCT
ejpam-5897	303	7	18	18	NUM
ejpam-5897	303	8	(	(	PUNCT
ejpam-5897	303	9	2	2	NUM
ejpam-5897	303	10	)	)	PUNCT
ejpam-5897	303	11	(	(	PUNCT
ejpam-5897	303	12	2025	2025	NUM
ejpam-5897	303	13	)	)	PUNCT
ejpam-5897	303	14	,	,	PUNCT
ejpam-5897	303	15	5897	5897	NUM
ejpam-5897	303	16	13	13	NUM
ejpam-5897	303	17	of	of	ADP
ejpam-5897	303	18	14	14	NUM
ejpam-5897	303	19	references	reference	NOUN
ejpam-5897	303	20	[	[	X
ejpam-5897	303	21	1	1	NUM
ejpam-5897	303	22	]	]	X
ejpam-5897	303	23	s	s	NOUN
ejpam-5897	303	24	m	m	NOUN
ejpam-5897	303	25	ulam	ulam	PROPN
ejpam-5897	303	26	.	.	PUNCT
ejpam-5897	304	1	problems	problem	NOUN
ejpam-5897	304	2	in	in	ADP
ejpam-5897	304	3	modern	modern	ADJ
ejpam-5897	304	4	mathematics	mathematic	NOUN
ejpam-5897	304	5	.	.	PUNCT
ejpam-5897	305	1	john	john	PROPN
ejpam-5897	305	2	wiley	wiley	PROPN
ejpam-5897	305	3	&	&	CCONJ
ejpam-5897	305	4	sons	sons	PROPN
ejpam-5897	305	5	,	,	PUNCT
ejpam-5897	305	6	inc	inc	PROPN
ejpam-5897	305	7	.	.	PROPN
ejpam-5897	305	8	,	,	PUNCT
ejpam-5897	305	9	new	new	PROPN
ejpam-5897	305	10	york	york	PROPN
ejpam-5897	305	11	,	,	PUNCT
ejpam-5897	305	12	1964	1964	NUM
ejpam-5897	305	13	.	.	PUNCT
ejpam-5897	306	1	[	[	X
ejpam-5897	306	2	2	2	NUM
ejpam-5897	306	3	]	]	PUNCT
ejpam-5897	306	4	d	d	PROPN
ejpam-5897	306	5	h	h	PROPN
ejpam-5897	306	6	hyers	hyer	NOUN
ejpam-5897	306	7	.	.	PUNCT
ejpam-5897	307	1	on	on	ADP
ejpam-5897	307	2	the	the	DET
ejpam-5897	307	3	stability	stability	NOUN
ejpam-5897	307	4	of	of	ADP
ejpam-5897	307	5	the	the	DET
ejpam-5897	307	6	linear	linear	ADJ
ejpam-5897	307	7	functional	functional	ADJ
ejpam-5897	307	8	equation	equation	NOUN
ejpam-5897	307	9	.	.	PUNCT
ejpam-5897	308	1	proc	proc	PROPN
ejpam-5897	308	2	.	.	PUNCT
ejpam-5897	309	1	natl	natl	PROPN
ejpam-5897	309	2	.	.	PUNCT
ejpam-5897	310	1	acad	acad	PROPN
ejpam-5897	310	2	.	.	PUNCT
ejpam-5897	311	1	sci	sci	PROPN
ejpam-5897	311	2	.	.	PUNCT
ejpam-5897	311	3	u.s.a	u.s.a	PROPN
ejpam-5897	311	4	.	.	PROPN
ejpam-5897	311	5	,	,	PUNCT
ejpam-5897	311	6	27:222–224	27:222–224	NUM
ejpam-5897	311	7	,	,	PUNCT
ejpam-5897	311	8	1941	1941	NUM
ejpam-5897	311	9	.	.	PUNCT
ejpam-5897	312	1	[	[	X
ejpam-5897	312	2	3	3	X
ejpam-5897	312	3	]	]	X
ejpam-5897	312	4	t	t	PROPN
ejpam-5897	312	5	m	m	NOUN
ejpam-5897	312	6	rassias	rassias	PROPN
ejpam-5897	312	7	.	.	PUNCT
ejpam-5897	313	1	on	on	ADP
ejpam-5897	313	2	the	the	DET
ejpam-5897	313	3	stability	stability	NOUN
ejpam-5897	313	4	of	of	ADP
ejpam-5897	313	5	the	the	DET
ejpam-5897	313	6	linear	linear	ADJ
ejpam-5897	313	7	mapping	mapping	NOUN
ejpam-5897	313	8	in	in	ADP
ejpam-5897	313	9	banach	banach	NOUN
ejpam-5897	313	10	spaces	space	NOUN
ejpam-5897	313	11	.	.	PUNCT
ejpam-5897	314	1	proc	proc	NOUN
ejpam-5897	314	2	.	.	PUNCT
ejpam-5897	315	1	amer	amer	PROPN
ejpam-5897	315	2	.	.	PUNCT
ejpam-5897	315	3	math	math	PROPN
ejpam-5897	315	4	.	.	PUNCT
ejpam-5897	316	1	soc	soc	PROPN
ejpam-5897	316	2	.	.	PUNCT
ejpam-5897	316	3	,	,	PUNCT
ejpam-5897	316	4	72:297–300	72:297–300	PROPN
ejpam-5897	316	5	,	,	PUNCT
ejpam-5897	316	6	1978	1978	NUM
ejpam-5897	316	7	.	.	PUNCT
ejpam-5897	317	1	[	[	X
ejpam-5897	317	2	4	4	X
ejpam-5897	317	3	]	]	X
ejpam-5897	317	4	p	p	DET
ejpam-5897	317	5	gavruţa	gavruţa	NOUN
ejpam-5897	317	6	.	.	PUNCT
ejpam-5897	317	7	approximate	approximate	ADJ
ejpam-5897	317	8	solution	solution	NOUN
ejpam-5897	317	9	of	of	ADP
ejpam-5897	317	10	radical	radical	ADJ
ejpam-5897	317	11	quartic	quartic	ADJ
ejpam-5897	317	12	functional	functional	ADJ
ejpam-5897	317	13	equation	equation	NOUN
ejpam-5897	317	14	related	relate	VERB
ejpam-5897	317	15	to	to	AUX
ejpam-5897	317	16	additive	additive	VERB
ejpam-5897	317	17	mapping	mapping	NOUN
ejpam-5897	317	18	in	in	ADP
ejpam-5897	317	19	2	2	NUM
ejpam-5897	317	20	-	-	PUNCT
ejpam-5897	317	21	banach	banach	NOUN
ejpam-5897	317	22	spaces	space	NOUN
ejpam-5897	317	23	.	.	PUNCT
ejpam-5897	318	1	j.	j.	PROPN
ejpam-5897	318	2	math	math	PROPN
ejpam-5897	318	3	.	.	PUNCT
ejpam-5897	319	1	anal	anal	PROPN
ejpam-5897	319	2	.	.	PUNCT
ejpam-5897	320	1	appl	appl	PROPN
ejpam-5897	320	2	.	.	PROPN
ejpam-5897	320	3	,	,	PUNCT
ejpam-5897	320	4	184:431–436	184:431–436	NUM
ejpam-5897	320	5	,	,	PUNCT
ejpam-5897	320	6	1994	1994	NUM
ejpam-5897	320	7	.	.	PUNCT
ejpam-5897	321	1	[	[	X
ejpam-5897	321	2	5	5	NUM
ejpam-5897	321	3	]	]	PUNCT
ejpam-5897	321	4	a	a	DET
ejpam-5897	321	5	baza	baza	NOUN
ejpam-5897	321	6	and	and	CCONJ
ejpam-5897	321	7	m	m	PROPN
ejpam-5897	321	8	rossafi	rossafi	NOUN
ejpam-5897	321	9	.	.	PUNCT
ejpam-5897	322	1	generalized	generalize	VERB
ejpam-5897	322	2	hyers	hyers	PROPN
ejpam-5897	322	3	-	-	PUNCT
ejpam-5897	322	4	ulam	ulam	PROPN
ejpam-5897	322	5	stability	stability	NOUN
ejpam-5897	322	6	of	of	ADP
ejpam-5897	322	7	quadratic	quadratic	ADJ
ejpam-5897	322	8	functional	functional	ADJ
ejpam-5897	322	9	inequality	inequality	NOUN
ejpam-5897	322	10	in	in	ADP
ejpam-5897	322	11	modular	modular	ADJ
ejpam-5897	322	12	spaces	space	NOUN
ejpam-5897	322	13	and	and	CCONJ
ejpam-5897	322	14	β	β	NOUN
ejpam-5897	322	15	-	-	ADJ
ejpam-5897	322	16	homogeneous	homogeneous	ADJ
ejpam-5897	322	17	banach	banach	NOUN
ejpam-5897	322	18	spaces	space	VERB
ejpam-5897	322	19	.	.	PUNCT
ejpam-5897	323	1	nonlinear	nonlinear	ADJ
ejpam-5897	323	2	funct	funct	NOUN
ejpam-5897	323	3	.	.	PUNCT
ejpam-5897	324	1	anal	anal	PROPN
ejpam-5897	324	2	.	.	PUNCT
ejpam-5897	324	3	appl	appl	PROPN
ejpam-5897	324	4	.	.	PROPN
ejpam-5897	325	1	,	,	PUNCT
ejpam-5897	325	2	29(1):295–306	29(1):295–306	NUM
ejpam-5897	325	3	,	,	PUNCT
ejpam-5897	325	4	2024	2024	NUM
ejpam-5897	325	5	.	.	PUNCT
ejpam-5897	326	1	[	[	X
ejpam-5897	326	2	6	6	NUM
ejpam-5897	326	3	]	]	PUNCT
ejpam-5897	326	4	s	s	PART
ejpam-5897	326	5	bowmiya	bowmiya	NOUN
ejpam-5897	326	6	,	,	PUNCT
ejpam-5897	326	7	g	g	PROPN
ejpam-5897	326	8	balasubramanian	balasubramanian	PROPN
ejpam-5897	326	9	,	,	PUNCT
ejpam-5897	326	10	v	v	ADJ
ejpam-5897	326	11	govindan	govindan	PROPN
ejpam-5897	326	12	,	,	PUNCT
ejpam-5897	326	13	m	m	VERB
ejpam-5897	326	14	donganont	donganont	NOUN
ejpam-5897	326	15	,	,	PUNCT
ejpam-5897	326	16	and	and	CCONJ
ejpam-5897	326	17	h	h	NOUN
ejpam-5897	326	18	byeon	byeon	NOUN
ejpam-5897	326	19	.	.	PUNCT
ejpam-5897	327	1	generalized	generalize	VERB
ejpam-5897	327	2	linear	linear	PROPN
ejpam-5897	327	3	differential	differential	NOUN
ejpam-5897	327	4	equation	equation	NOUN
ejpam-5897	327	5	using	use	VERB
ejpam-5897	327	6	hyers	hyers	PROPN
ejpam-5897	327	7	-	-	PUNCT
ejpam-5897	327	8	ulam	ulam	PROPN
ejpam-5897	327	9	stability	stability	PROPN
ejpam-5897	327	10	approach	approach	NOUN
ejpam-5897	327	11	.	.	PUNCT
ejpam-5897	328	1	eur	eur	PROPN
ejpam-5897	328	2	.	.	PUNCT
ejpam-5897	329	1	j.	j.	PROPN
ejpam-5897	329	2	pure	pure	PROPN
ejpam-5897	329	3	appl	appl	PROPN
ejpam-5897	329	4	.	.	PUNCT
ejpam-5897	329	5	math	math	PROPN
ejpam-5897	329	6	.	.	PUNCT
ejpam-5897	329	7	,	,	PUNCT
ejpam-5897	329	8	17(4):3415–3435	17(4):3415–3435	NUM
ejpam-5897	329	9	,	,	PUNCT
ejpam-5897	329	10	2024	2024	NUM
ejpam-5897	329	11	.	.	PUNCT
ejpam-5897	330	1	[	[	X
ejpam-5897	330	2	7	7	NUM
ejpam-5897	330	3	]	]	X
ejpam-5897	330	4	s	s	PART
ejpam-5897	330	5	bowmiya	bowmiya	NOUN
ejpam-5897	330	6	,	,	PUNCT
ejpam-5897	330	7	g	g	PROPN
ejpam-5897	330	8	balasubramanian	balasubramanian	PROPN
ejpam-5897	330	9	,	,	PUNCT
ejpam-5897	330	10	v	v	ADJ
ejpam-5897	330	11	govindan	govindan	PROPN
ejpam-5897	330	12	,	,	PUNCT
ejpam-5897	330	13	m	m	VERB
ejpam-5897	330	14	donganont	donganont	NOUN
ejpam-5897	330	15	,	,	PUNCT
ejpam-5897	330	16	and	and	CCONJ
ejpam-5897	330	17	h	h	NOUN
ejpam-5897	330	18	byeon	byeon	NOUN
ejpam-5897	330	19	.	.	PUNCT
ejpam-5897	331	1	hyersulam	hyersulam	PROPN
ejpam-5897	331	2	stability	stability	NOUN
ejpam-5897	331	3	of	of	ADP
ejpam-5897	331	4	fifth	fifth	ADJ
ejpam-5897	331	5	order	order	NOUN
ejpam-5897	331	6	linear	linear	PROPN
ejpam-5897	331	7	differential	differential	NOUN
ejpam-5897	331	8	equations	equation	NOUN
ejpam-5897	331	9	.	.	PUNCT
ejpam-5897	332	1	eur	eur	PROPN
ejpam-5897	332	2	.	.	PUNCT
ejpam-5897	333	1	j.	j.	PROPN
ejpam-5897	333	2	pure	pure	PROPN
ejpam-5897	333	3	appl	appl	PROPN
ejpam-5897	333	4	.	.	PUNCT
ejpam-5897	333	5	math	math	PROPN
ejpam-5897	333	6	.	.	PUNCT
ejpam-5897	333	7	,	,	PUNCT
ejpam-5897	333	8	17(4):3585–3609	17(4):3585–3609	NUM
ejpam-5897	333	9	,	,	PUNCT
ejpam-5897	333	10	2024	2024	NUM
ejpam-5897	333	11	.	.	PUNCT
ejpam-5897	334	1	[	[	X
ejpam-5897	334	2	8	8	NUM
ejpam-5897	334	3	]	]	X
ejpam-5897	334	4	i	i	PRON
ejpam-5897	334	5	s	s	VERB
ejpam-5897	334	6	chang	chang	PROPN
ejpam-5897	334	7	and	and	CCONJ
ejpam-5897	334	8	h	h	NOUN
ejpam-5897	334	9	m	m	PROPN
ejpam-5897	334	10	kim	kim	PROPN
ejpam-5897	334	11	.	.	PUNCT
ejpam-5897	335	1	almost	almost	ADV
ejpam-5897	335	2	quadratic	quadratic	ADJ
ejpam-5897	335	3	lie	lie	NOUN
ejpam-5897	335	4	∗-derivations	∗-derivation	NOUN
ejpam-5897	335	5	on	on	ADP
ejpam-5897	335	6	convex	convex	ADJ
ejpam-5897	335	7	modular	modular	ADJ
ejpam-5897	335	8	∗-algebras	∗-algebra	NOUN
ejpam-5897	335	9	.	.	PUNCT
ejpam-5897	336	1	nonlinear	nonlinear	ADJ
ejpam-5897	336	2	funct	funct	NOUN
ejpam-5897	336	3	.	.	PUNCT
ejpam-5897	337	1	anal	anal	PROPN
ejpam-5897	337	2	.	.	PUNCT
ejpam-5897	337	3	appl	appl	PROPN
ejpam-5897	337	4	.	.	PROPN
ejpam-5897	337	5	,	,	PUNCT
ejpam-5897	337	6	28(4):887–902	28(4):887–902	PROPN
ejpam-5897	337	7	,	,	PUNCT
ejpam-5897	337	8	2023	2023	NUM
ejpam-5897	337	9	.	.	PUNCT
ejpam-5897	338	1	[	[	X
ejpam-5897	338	2	9	9	NUM
ejpam-5897	338	3	]	]	SYM
ejpam-5897	338	4	m	m	PROPN
ejpam-5897	338	5	e	e	NOUN
ejpam-5897	338	6	gordji	gordji	NOUN
ejpam-5897	338	7	,	,	PUNCT
ejpam-5897	338	8	m	m	PROPN
ejpam-5897	338	9	b	b	NOUN
ejpam-5897	338	10	ghaemi	ghaemi	NOUN
ejpam-5897	338	11	,	,	PUNCT
ejpam-5897	338	12	and	and	CCONJ
ejpam-5897	338	13	b	b	X
ejpam-5897	338	14	alizadeh	alizadeh	NOUN
ejpam-5897	338	15	.	.	PUNCT
ejpam-5897	339	1	a	a	DET
ejpam-5897	339	2	fixed	fix	VERB
ejpam-5897	339	3	point	point	NOUN
ejpam-5897	339	4	method	method	NOUN
ejpam-5897	339	5	for	for	ADP
ejpam-5897	339	6	perturbation	perturbation	NOUN
ejpam-5897	339	7	of	of	ADP
ejpam-5897	339	8	higher	high	ADJ
ejpam-5897	339	9	ring	ring	NOUN
ejpam-5897	339	10	derivations	derivation	NOUN
ejpam-5897	339	11	in	in	ADP
ejpam-5897	339	12	non	non	ADJ
ejpam-5897	339	13	-	-	ADJ
ejpam-5897	339	14	archimedean	archimedean	ADJ
ejpam-5897	339	15	banach	banach	NOUN
ejpam-5897	339	16	algebras	algebra	VERB
ejpam-5897	339	17	.	.	PUNCT
ejpam-5897	340	1	int	int	NOUN
ejpam-5897	340	2	.	.	PUNCT
ejpam-5897	341	1	j.	j.	PROPN
ejpam-5897	341	2	geom	geom	PROPN
ejpam-5897	341	3	.	.	PUNCT
ejpam-5897	342	1	methods	methods	PROPN
ejpam-5897	342	2	mod	mod	PROPN
ejpam-5897	342	3	.	.	PUNCT
ejpam-5897	343	1	phys	phys	PROPN
ejpam-5897	343	2	.	.	PUNCT
ejpam-5897	343	3	,	,	PUNCT
ejpam-5897	343	4	8(7):1611–1625	8(7):1611–1625	NUM
ejpam-5897	343	5	,	,	PUNCT
ejpam-5897	343	6	2011	2011	NUM
ejpam-5897	343	7	.	.	PUNCT
ejpam-5897	344	1	[	[	X
ejpam-5897	344	2	10	10	NUM
ejpam-5897	344	3	]	]	X
ejpam-5897	344	4	m	m	PROPN
ejpam-5897	344	5	e	e	NOUN
ejpam-5897	344	6	gordji	gordji	NOUN
ejpam-5897	344	7	and	and	CCONJ
ejpam-5897	344	8	n	n	DET
ejpam-5897	344	9	ghobadipour	ghobadipour	NOUN
ejpam-5897	344	10	.	.	PUNCT
ejpam-5897	345	1	stability	stability	NOUN
ejpam-5897	345	2	of	of	ADP
ejpam-5897	345	3	(	(	PUNCT
ejpam-5897	345	4	α	α	PROPN
ejpam-5897	345	5	,	,	PUNCT
ejpam-5897	345	6	β	β	X
ejpam-5897	345	7	,	,	PUNCT
ejpam-5897	345	8	γ)-derivations	γ)-derivation	NOUN
ejpam-5897	345	9	on	on	ADP
ejpam-5897	345	10	lie	lie	NOUN
ejpam-5897	345	11	c∗-algebras	c∗-algebras	PROPN
ejpam-5897	345	12	.	.	PROPN
ejpam-5897	345	13	int	int	PROPN
ejpam-5897	345	14	.	.	PUNCT
ejpam-5897	346	1	j.	j.	PROPN
ejpam-5897	346	2	geom	geom	PROPN
ejpam-5897	346	3	.	.	PUNCT
ejpam-5897	347	1	methods	methods	PROPN
ejpam-5897	347	2	mod	mod	PROPN
ejpam-5897	347	3	.	.	PUNCT
ejpam-5897	348	1	phys	phy	NOUN
ejpam-5897	348	2	.	.	PUNCT
ejpam-5897	348	3	,	,	PUNCT
ejpam-5897	348	4	7(7):1093–1102	7(7):1093–1102	NOUN
ejpam-5897	348	5	,	,	PUNCT
ejpam-5897	348	6	2011	2011	NUM
ejpam-5897	348	7	.	.	PUNCT
ejpam-5897	349	1	[	[	X
ejpam-5897	349	2	11	11	NUM
ejpam-5897	349	3	]	]	SYM
ejpam-5897	349	4	s	s	PART
ejpam-5897	349	5	m	m	NOUN
ejpam-5897	349	6	jung	jung	NOUN
ejpam-5897	349	7	,	,	PUNCT
ejpam-5897	349	8	d	d	NOUN
ejpam-5897	349	9	popa	popa	NOUN
ejpam-5897	349	10	,	,	PUNCT
ejpam-5897	349	11	and	and	CCONJ
ejpam-5897	349	12	m	m	PROPN
ejpam-5897	349	13	t	t	NOUN
ejpam-5897	349	14	rassias	rassias	PROPN
ejpam-5897	349	15	.	.	PUNCT
ejpam-5897	350	1	on	on	ADP
ejpam-5897	350	2	the	the	DET
ejpam-5897	350	3	stability	stability	NOUN
ejpam-5897	350	4	of	of	ADP
ejpam-5897	350	5	the	the	DET
ejpam-5897	350	6	linear	linear	ADJ
ejpam-5897	350	7	functional	functional	ADJ
ejpam-5897	350	8	equation	equation	NOUN
ejpam-5897	350	9	in	in	ADP
ejpam-5897	350	10	a	a	DET
ejpam-5897	350	11	single	single	ADJ
ejpam-5897	350	12	variable	variable	NOUN
ejpam-5897	350	13	on	on	ADP
ejpam-5897	350	14	complete	complete	ADJ
ejpam-5897	350	15	metric	metric	ADJ
ejpam-5897	350	16	spaces	space	NOUN
ejpam-5897	350	17	.	.	PUNCT
ejpam-5897	351	1	j.	j.	PROPN
ejpam-5897	351	2	global	global	PROPN
ejpam-5897	351	3	optim	optim	PROPN
ejpam-5897	351	4	.	.	PROPN
ejpam-5897	351	5	,	,	PUNCT
ejpam-5897	352	1	59:13–16	59:13–16	NUM
ejpam-5897	352	2	,	,	PUNCT
ejpam-5897	352	3	2014	2014	NUM
ejpam-5897	352	4	.	.	PUNCT
ejpam-5897	353	1	[	[	X
ejpam-5897	353	2	12	12	NUM
ejpam-5897	353	3	]	]	X
ejpam-5897	353	4	b	b	X
ejpam-5897	353	5	v	v	ADP
ejpam-5897	353	6	s	s	X
ejpam-5897	353	7	kumar	kumar	PROPN
ejpam-5897	353	8	,	,	PUNCT
ejpam-5897	353	9	h	h	PROPN
ejpam-5897	353	10	dutta	dutta	PROPN
ejpam-5897	353	11	,	,	PUNCT
ejpam-5897	353	12	and	and	CCONJ
ejpam-5897	353	13	s	s	NOUN
ejpam-5897	353	14	sabarinathan	sabarinathan	NOUN
ejpam-5897	353	15	.	.	PUNCT
ejpam-5897	354	1	modular	modular	ADJ
ejpam-5897	354	2	stabilities	stability	NOUN
ejpam-5897	354	3	of	of	ADP
ejpam-5897	354	4	a	a	DET
ejpam-5897	354	5	reciprocal	reciprocal	ADJ
ejpam-5897	354	6	second	second	ADJ
ejpam-5897	354	7	power	power	NOUN
ejpam-5897	354	8	functional	functional	ADJ
ejpam-5897	354	9	equation	equation	NOUN
ejpam-5897	354	10	.	.	PUNCT
ejpam-5897	355	1	eur	eur	PROPN
ejpam-5897	355	2	.	.	PUNCT
ejpam-5897	356	1	j.	j.	PROPN
ejpam-5897	356	2	pure	pure	PROPN
ejpam-5897	356	3	appl	appl	PROPN
ejpam-5897	356	4	.	.	PUNCT
ejpam-5897	356	5	math	math	PROPN
ejpam-5897	356	6	.	.	PUNCT
ejpam-5897	356	7	,	,	PUNCT
ejpam-5897	357	1	13(5):1162–1175	13(5):1162–1175	NUM
ejpam-5897	357	2	,	,	PUNCT
ejpam-5897	357	3	2020	2020	NUM
ejpam-5897	357	4	.	.	PUNCT
ejpam-5897	358	1	[	[	X
ejpam-5897	358	2	13	13	NUM
ejpam-5897	358	3	]	]	X
ejpam-5897	358	4	y	y	PROPN
ejpam-5897	358	5	h	h	PROPN
ejpam-5897	358	6	lee	lee	PROPN
ejpam-5897	358	7	,	,	PUNCT
ejpam-5897	358	8	s	s	PART
ejpam-5897	358	9	m	m	PROPN
ejpam-5897	358	10	jung	jung	NOUN
ejpam-5897	358	11	,	,	PUNCT
ejpam-5897	358	12	and	and	CCONJ
ejpam-5897	358	13	m	m	PROPN
ejpam-5897	358	14	t	t	NOUN
ejpam-5897	358	15	rassias	rassias	PROPN
ejpam-5897	358	16	.	.	PUNCT
ejpam-5897	359	1	uniqueness	uniqueness	NOUN
ejpam-5897	359	2	theorems	theorem	NOUN
ejpam-5897	359	3	on	on	ADP
ejpam-5897	359	4	functional	functional	ADJ
ejpam-5897	359	5	inequalities	inequality	NOUN
ejpam-5897	359	6	concerning	concern	VERB
ejpam-5897	359	7	cubic	cubic	ADJ
ejpam-5897	359	8	-	-	PUNCT
ejpam-5897	359	9	quadratic	quadratic	ADJ
ejpam-5897	359	10	-	-	PUNCT
ejpam-5897	359	11	additive	additive	NOUN
ejpam-5897	359	12	equation	equation	NOUN
ejpam-5897	359	13	.	.	PUNCT
ejpam-5897	360	1	j.	j.	PROPN
ejpam-5897	360	2	math	math	PROPN
ejpam-5897	360	3	.	.	PUNCT
ejpam-5897	361	1	inequal	inequal	ADJ
ejpam-5897	361	2	.	.	PUNCT
ejpam-5897	361	3	,	,	PUNCT
ejpam-5897	361	4	12(1):43–61	12(1):43–61	NUM
ejpam-5897	361	5	,	,	PUNCT
ejpam-5897	361	6	2018	2018	NUM
ejpam-5897	361	7	.	.	PUNCT
ejpam-5897	362	1	[	[	X
ejpam-5897	362	2	14	14	NUM
ejpam-5897	362	3	]	]	X
ejpam-5897	362	4	d	d	X
ejpam-5897	362	5	miheţ	miheţ	PROPN
ejpam-5897	362	6	and	and	CCONJ
ejpam-5897	362	7	v	v	ADP
ejpam-5897	362	8	radu	radu	PROPN
ejpam-5897	362	9	.	.	PUNCT
ejpam-5897	363	1	on	on	ADP
ejpam-5897	363	2	the	the	DET
ejpam-5897	363	3	stability	stability	NOUN
ejpam-5897	363	4	of	of	ADP
ejpam-5897	363	5	the	the	DET
ejpam-5897	363	6	additive	additive	ADJ
ejpam-5897	363	7	cauchy	cauchy	ADJ
ejpam-5897	363	8	functional	functional	ADJ
ejpam-5897	363	9	equation	equation	NOUN
ejpam-5897	363	10	in	in	ADP
ejpam-5897	363	11	random	random	ADJ
ejpam-5897	363	12	normed	normed	ADJ
ejpam-5897	363	13	spaces	space	NOUN
ejpam-5897	363	14	.	.	PUNCT
ejpam-5897	364	1	j.	j.	PROPN
ejpam-5897	364	2	math	math	PROPN
ejpam-5897	364	3	.	.	PUNCT
ejpam-5897	365	1	anal	anal	PROPN
ejpam-5897	365	2	.	.	PUNCT
ejpam-5897	365	3	appl	appl	PROPN
ejpam-5897	365	4	.	.	PROPN
ejpam-5897	365	5	,	,	PUNCT
ejpam-5897	365	6	343:567–572	343:567–572	NUM
ejpam-5897	365	7	,	,	PUNCT
ejpam-5897	365	8	2008	2008	NUM
ejpam-5897	365	9	.	.	PUNCT
ejpam-5897	366	1	[	[	X
ejpam-5897	366	2	15	15	NUM
ejpam-5897	366	3	]	]	X
ejpam-5897	366	4	g	g	PROPN
ejpam-5897	366	5	l	l	PROPN
ejpam-5897	366	6	sewell	sewell	NOUN
ejpam-5897	366	7	.	.	PUNCT
ejpam-5897	367	1	quantum	quantum	ADJ
ejpam-5897	367	2	mechanics	mechanic	NOUN
ejpam-5897	367	3	and	and	CCONJ
ejpam-5897	367	4	its	its	PRON
ejpam-5897	367	5	emergent	emergent	ADJ
ejpam-5897	367	6	macrophysics	macrophysic	NOUN
ejpam-5897	367	7	.	.	PUNCT
ejpam-5897	368	1	princeton	princeton	PROPN
ejpam-5897	368	2	university	university	PROPN
ejpam-5897	368	3	press	press	PROPN
ejpam-5897	368	4	,	,	PUNCT
ejpam-5897	368	5	princeton	princeton	PROPN
ejpam-5897	368	6	,	,	PUNCT
ejpam-5897	368	7	2002	2002	NUM
ejpam-5897	368	8	.	.	PUNCT
ejpam-5897	369	1	[	[	X
ejpam-5897	369	2	16	16	NUM
ejpam-5897	369	3	]	]	PUNCT
ejpam-5897	369	4	l	l	NOUN
ejpam-5897	369	5	vainerman	vainerman	NOUN
ejpam-5897	369	6	and	and	CCONJ
ejpam-5897	369	7	r	r	PROPN
ejpam-5897	369	8	kerner	kerner	PROPN
ejpam-5897	369	9	.	.	PUNCT
ejpam-5897	370	1	on	on	ADP
ejpam-5897	370	2	special	special	ADJ
ejpam-5897	370	3	classes	class	NOUN
ejpam-5897	370	4	of	of	ADP
ejpam-5897	370	5	n	n	CCONJ
ejpam-5897	370	6	-	-	PUNCT
ejpam-5897	370	7	algebras	algebras	PROPN
ejpam-5897	370	8	.	.	PUNCT
ejpam-5897	371	1	j.	j.	PROPN
ejpam-5897	371	2	math	math	PROPN
ejpam-5897	371	3	.	.	PUNCT
ejpam-5897	372	1	phys	phy	NOUN
ejpam-5897	372	2	.	.	PUNCT
ejpam-5897	372	3	,	,	PUNCT
ejpam-5897	372	4	37(5):2553–2565	37(5):2553–2565	NUM
ejpam-5897	372	5	,	,	PUNCT
ejpam-5897	372	6	1996	1996	NUM
ejpam-5897	372	7	.	.	PUNCT
ejpam-5897	373	1	[	[	X
ejpam-5897	373	2	17	17	NUM
ejpam-5897	373	3	]	]	X
ejpam-5897	373	4	h	h	NOUN
ejpam-5897	373	5	zettl	zettl	NOUN
ejpam-5897	373	6	.	.	PUNCT
ejpam-5897	374	1	a	a	DET
ejpam-5897	374	2	characterization	characterization	NOUN
ejpam-5897	374	3	of	of	ADP
ejpam-5897	374	4	ternary	ternary	ADJ
ejpam-5897	374	5	ring	ring	NOUN
ejpam-5897	374	6	of	of	ADP
ejpam-5897	374	7	operators	operator	NOUN
ejpam-5897	374	8	.	.	PUNCT
ejpam-5897	375	1	adv	adv	PROPN
ejpam-5897	375	2	.	.	PUNCT
ejpam-5897	375	3	math	math	PROPN
ejpam-5897	375	4	.	.	PUNCT
ejpam-5897	375	5	,	,	PUNCT
ejpam-5897	376	1	48(2):117–143	48(2):117–143	PROPN
ejpam-5897	376	2	,	,	PUNCT
ejpam-5897	376	3	1983	1983	NUM
ejpam-5897	376	4	.	.	PUNCT
ejpam-5897	377	1	[	[	X
ejpam-5897	377	2	18	18	NUM
ejpam-5897	377	3	]	]	X
ejpam-5897	377	4	c	c	NOUN
ejpam-5897	377	5	park	park	NOUN
ejpam-5897	377	6	.	.	PUNCT
ejpam-5897	378	1	isomorphisms	isomorphism	NOUN
ejpam-5897	378	2	between	between	ADP
ejpam-5897	378	3	c∗-ternary	c∗-ternary	ADJ
ejpam-5897	378	4	algebras	algebras	PROPN
ejpam-5897	378	5	.	.	PUNCT
ejpam-5897	379	1	j.	j.	PROPN
ejpam-5897	379	2	math	math	PROPN
ejpam-5897	379	3	.	.	PUNCT
ejpam-5897	380	1	anal	anal	PROPN
ejpam-5897	380	2	.	.	PUNCT
ejpam-5897	381	1	appl	appl	PROPN
ejpam-5897	381	2	.	.	PROPN
ejpam-5897	382	1	,	,	PUNCT
ejpam-5897	382	2	327:101	327:101	PROPN
ejpam-5897	382	3	–	–	PUNCT
ejpam-5897	382	4	115	115	NUM
ejpam-5897	382	5	,	,	PUNCT
ejpam-5897	382	6	2007	2007	NUM
ejpam-5897	382	7	.	.	PUNCT
ejpam-5897	383	1	[	[	X
ejpam-5897	383	2	19	19	NUM
ejpam-5897	383	3	]	]	X
ejpam-5897	383	4	m	m	PROPN
ejpam-5897	383	5	s	s	NOUN
ejpam-5897	383	6	moslehian	moslehian	NOUN
ejpam-5897	383	7	.	.	PUNCT
ejpam-5897	384	1	almost	almost	ADV
ejpam-5897	384	2	derivations	derivation	NOUN
ejpam-5897	384	3	on	on	ADP
ejpam-5897	384	4	c∗-ternary	c∗-ternary	ADJ
ejpam-5897	384	5	rings	ring	NOUN
ejpam-5897	384	6	.	.	PUNCT
ejpam-5897	385	1	bull	bull	NOUN
ejpam-5897	385	2	.	.	PUNCT
ejpam-5897	386	1	belg	belg	PROPN
ejpam-5897	386	2	.	.	PUNCT
ejpam-5897	387	1	math	math	NOUN
ejpam-5897	387	2	.	.	PUNCT
ejpam-5897	388	1	soc.-simon	soc.-simon	PROPN
ejpam-5897	388	2	e.	e.	PROPN
ejpam-5897	388	3	shim	shim	PROPN
ejpam-5897	388	4	,	,	PUNCT
ejpam-5897	388	5	s.	s.	PROPN
ejpam-5897	388	6	donganont	donganont	PROPN
ejpam-5897	388	7	,	,	PUNCT
ejpam-5897	388	8	c.	c.	PROPN
ejpam-5897	388	9	park	park	PROPN
ejpam-5897	388	10	/	/	SYM
ejpam-5897	388	11	eur	eur	PROPN
ejpam-5897	388	12	.	.	PUNCT
ejpam-5897	389	1	j.	j.	PROPN
ejpam-5897	389	2	pure	pure	PROPN
ejpam-5897	389	3	appl	appl	PROPN
ejpam-5897	389	4	.	.	PROPN
ejpam-5897	389	5	math	math	PROPN
ejpam-5897	389	6	,	,	PUNCT
ejpam-5897	389	7	18	18	NUM
ejpam-5897	389	8	(	(	PUNCT
ejpam-5897	389	9	2	2	NUM
ejpam-5897	389	10	)	)	PUNCT
ejpam-5897	389	11	(	(	PUNCT
ejpam-5897	389	12	2025	2025	NUM
ejpam-5897	389	13	)	)	PUNCT
ejpam-5897	389	14	,	,	PUNCT
ejpam-5897	389	15	5897	5897	NUM
ejpam-5897	389	16	14	14	NUM
ejpam-5897	389	17	of	of	ADP
ejpam-5897	389	18	14	14	NUM
ejpam-5897	389	19	stevin	stevin	NOUN
ejpam-5897	389	20	,	,	PUNCT
ejpam-5897	389	21	14:135–142	14:135–142	PROPN
ejpam-5897	389	22	,	,	PUNCT
ejpam-5897	389	23	2007	2007	NUM
ejpam-5897	389	24	.	.	PUNCT
ejpam-5897	390	1	[	[	X
ejpam-5897	390	2	20	20	NUM
ejpam-5897	390	3	]	]	X
ejpam-5897	390	4	m	m	PROPN
ejpam-5897	390	5	b	b	NOUN
ejpam-5897	390	6	savadkouhi	savadkouhi	NOUN
ejpam-5897	390	7	,	,	PUNCT
ejpam-5897	390	8	m	m	PROPN
ejpam-5897	390	9	e	e	NOUN
ejpam-5897	390	10	gordji	gordji	PROPN
ejpam-5897	390	11	,	,	PUNCT
ejpam-5897	390	12	j	j	PROPN
ejpam-5897	390	13	m	m	PROPN
ejpam-5897	390	14	rassias	rassias	PROPN
ejpam-5897	390	15	,	,	PUNCT
ejpam-5897	390	16	and	and	CCONJ
ejpam-5897	390	17	n	n	PRON
ejpam-5897	390	18	ghobadipour	ghobadipour	NOUN
ejpam-5897	390	19	.	.	PUNCT
ejpam-5897	391	1	approximate	approximate	ADJ
ejpam-5897	391	2	ternary	ternary	PROPN
ejpam-5897	391	3	jordan	jordan	PROPN
ejpam-5897	391	4	derivations	derivation	NOUN
ejpam-5897	391	5	on	on	ADP
ejpam-5897	391	6	banach	banach	ADV
ejpam-5897	391	7	ternary	ternary	ADJ
ejpam-5897	391	8	algebras	algebra	NOUN
ejpam-5897	391	9	.	.	PUNCT
ejpam-5897	392	1	j.	j.	PROPN
ejpam-5897	392	2	math	math	PROPN
ejpam-5897	392	3	.	.	PUNCT
ejpam-5897	393	1	phys	phy	NOUN
ejpam-5897	393	2	.	.	PUNCT
ejpam-5897	393	3	,	,	PUNCT
ejpam-5897	393	4	50(4(042303)):1–9	50(4(042303)):1–9	NUM
ejpam-5897	393	5	,	,	PUNCT
ejpam-5897	393	6	2009	2009	NUM
ejpam-5897	393	7	.	.	PUNCT
ejpam-5897	394	1	[	[	X
ejpam-5897	394	2	21	21	NUM
ejpam-5897	394	3	]	]	X
ejpam-5897	394	4	j	j	PROPN
ejpam-5897	394	5	h	h	PROPN
ejpam-5897	394	6	bae	bae	PROPN
ejpam-5897	394	7	and	and	CCONJ
ejpam-5897	394	8	w	w	PROPN
ejpam-5897	394	9	g	g	PROPN
ejpam-5897	394	10	park	park	NOUN
ejpam-5897	394	11	.	.	PUNCT
ejpam-5897	395	1	approximate	approximate	ADJ
ejpam-5897	395	2	bi	bi	NOUN
ejpam-5897	395	3	-	-	ADJ
ejpam-5897	395	4	homomorphisms	homomorphism	NOUN
ejpam-5897	395	5	and	and	CCONJ
ejpam-5897	395	6	bi	bi	NOUN
ejpam-5897	395	7	-	-	NOUN
ejpam-5897	395	8	derivations	derivation	NOUN
ejpam-5897	395	9	in	in	ADP
ejpam-5897	395	10	c∗ternary	c∗ternary	ADJ
ejpam-5897	395	11	algebras	algebra	NOUN
ejpam-5897	395	12	.	.	PUNCT
ejpam-5897	396	1	bull	bull	NOUN
ejpam-5897	396	2	.	.	PUNCT
ejpam-5897	397	1	korean	korean	ADJ
ejpam-5897	397	2	math	math	PROPN
ejpam-5897	397	3	.	.	PUNCT
ejpam-5897	398	1	soc	soc	PROPN
ejpam-5897	398	2	.	.	PUNCT
ejpam-5897	398	3	,	,	PUNCT
ejpam-5897	398	4	47(1):195–209	47(1):195–209	NOUN
ejpam-5897	398	5	,	,	PUNCT
ejpam-5897	398	6	2010	2010	NUM
ejpam-5897	398	7	.	.	PUNCT
ejpam-5897	399	1	[	[	X
ejpam-5897	399	2	22	22	NUM
ejpam-5897	399	3	]	]	X
ejpam-5897	399	4	m	m	VERB
ejpam-5897	399	5	dehghanian	dehghanian	ADJ
ejpam-5897	399	6	,	,	PUNCT
ejpam-5897	399	7	s	s	VERB
ejpam-5897	399	8	m	m	NOUN
ejpam-5897	399	9	s	s	NOUN
ejpam-5897	399	10	m	m	NOUN
ejpam-5897	399	11	mosadegh	mosadegh	ADJ
ejpam-5897	399	12	,	,	PUNCT
ejpam-5897	399	13	and	and	CCONJ
ejpam-5897	399	14	c	c	PROPN
ejpam-5897	399	15	park	park	NOUN
ejpam-5897	399	16	.	.	PUNCT
ejpam-5897	400	1	c∗-ternary	c∗-ternary	ADJ
ejpam-5897	400	2	3	3	NUM
ejpam-5897	400	3	-	-	PUNCT
ejpam-5897	400	4	derivations	derivation	NOUN
ejpam-5897	400	5	on	on	ADP
ejpam-5897	400	6	c∗ternary	c∗ternary	ADJ
ejpam-5897	400	7	algebras	algebra	NOUN
ejpam-5897	400	8	.	.	PUNCT
ejpam-5897	401	1	j.	j.	PROPN
ejpam-5897	401	2	inequal	inequal	PROPN
ejpam-5897	401	3	.	.	PUNCT
ejpam-5897	402	1	appl	appl	PROPN
ejpam-5897	402	2	.	.	PROPN
ejpam-5897	402	3	,	,	PUNCT
ejpam-5897	402	4	2013(1(124)):1–9	2013(1(124)):1–9	NOUN
ejpam-5897	402	5	,	,	PUNCT
ejpam-5897	402	6	2013	2013	NUM
ejpam-5897	402	7	.	.	PUNCT
ejpam-5897	403	1	[	[	X
ejpam-5897	403	2	23	23	NUM
ejpam-5897	403	3	]	]	X
ejpam-5897	403	4	g	g	PROPN
ejpam-5897	403	5	isac	isac	PROPN
ejpam-5897	403	6	and	and	CCONJ
ejpam-5897	403	7	t	t	PROPN
ejpam-5897	403	8	m	m	PROPN
ejpam-5897	403	9	rassias	rassias	PROPN
ejpam-5897	403	10	.	.	PUNCT
ejpam-5897	404	1	stability	stability	NOUN
ejpam-5897	404	2	of	of	ADP
ejpam-5897	404	3	ψ	ψ	ADJ
ejpam-5897	404	4	-	-	ADJ
ejpam-5897	404	5	additive	additive	ADJ
ejpam-5897	404	6	mappings	mapping	NOUN
ejpam-5897	404	7	:	:	PUNCT
ejpam-5897	404	8	applications	application	NOUN
ejpam-5897	404	9	to	to	PART
ejpam-5897	404	10	nonlinear	nonlinear	ADJ
ejpam-5897	404	11	analysis	analysis	NOUN
ejpam-5897	404	12	.	.	PUNCT
ejpam-5897	405	1	int	int	NOUN
ejpam-5897	405	2	.	.	PUNCT
ejpam-5897	406	1	j.	j.	PROPN
ejpam-5897	406	2	math	math	PROPN
ejpam-5897	406	3	.	.	PUNCT
ejpam-5897	407	1	math	math	NOUN
ejpam-5897	407	2	.	.	PUNCT
ejpam-5897	408	1	sci	sci	PROPN
ejpam-5897	408	2	.	.	PROPN
ejpam-5897	408	3	,	,	PUNCT
ejpam-5897	408	4	19:219–228	19:219–228	PROPN
ejpam-5897	408	5	,	,	PUNCT
ejpam-5897	408	6	1996	1996	NUM
ejpam-5897	408	7	.	.	PUNCT
ejpam-5897	409	1	[	[	X
ejpam-5897	409	2	24	24	NUM
ejpam-5897	409	3	]	]	PUNCT
ejpam-5897	409	4	a	a	DET
ejpam-5897	409	5	najati	najati	NOUN
ejpam-5897	409	6	and	and	CCONJ
ejpam-5897	409	7	a	a	DET
ejpam-5897	409	8	ranjbari	ranjbari	NOUN
ejpam-5897	409	9	.	.	PUNCT
ejpam-5897	410	1	on	on	ADP
ejpam-5897	410	2	homomorphisms	homomorphism	NOUN
ejpam-5897	410	3	between	between	ADP
ejpam-5897	410	4	c∗-ternary	c∗-ternary	ADJ
ejpam-5897	410	5	algebras	algebra	NOUN
ejpam-5897	410	6	.	.	PUNCT
ejpam-5897	411	1	j.	j.	PROPN
ejpam-5897	411	2	math	math	PROPN
ejpam-5897	411	3	.	.	PUNCT
ejpam-5897	412	1	inequal	inequal	ADJ
ejpam-5897	412	2	.	.	PUNCT
ejpam-5897	412	3	,	,	PUNCT
ejpam-5897	412	4	1(3):387–407	1(3):387–407	NUM
ejpam-5897	412	5	,	,	PUNCT
ejpam-5897	412	6	2007	2007	NUM
ejpam-5897	412	7	.	.	PUNCT
ejpam-5897	413	1	[	[	X
ejpam-5897	413	2	25	25	NUM
ejpam-5897	413	3	]	]	X
ejpam-5897	413	4	m	m	VERB
ejpam-5897	413	5	osbouei	osbouei	PROPN
ejpam-5897	413	6	,	,	PUNCT
ejpam-5897	413	7	m	m	PROPN
ejpam-5897	413	8	e	e	NOUN
ejpam-5897	413	9	gordji	gordji	NOUN
ejpam-5897	413	10	,	,	PUNCT
ejpam-5897	413	11	a	a	DET
ejpam-5897	413	12	ebadian	ebadian	NOUN
ejpam-5897	413	13	,	,	PUNCT
ejpam-5897	413	14	g	g	PROPN
ejpam-5897	413	15	asgari	asgari	NOUN
ejpam-5897	413	16	,	,	PUNCT
ejpam-5897	413	17	and	and	CCONJ
ejpam-5897	413	18	h	h	DET
ejpam-5897	413	19	a	a	DET
ejpam-5897	413	20	kenary	kenary	ADJ
ejpam-5897	413	21	.	.	PUNCT
ejpam-5897	414	1	stability	stability	NOUN
ejpam-5897	414	2	and	and	CCONJ
ejpam-5897	414	3	superstability	superstability	NOUN
ejpam-5897	414	4	of	of	ADP
ejpam-5897	414	5	ternary	ternary	ADJ
ejpam-5897	414	6	homomorphisms	homomorphism	NOUN
ejpam-5897	414	7	and	and	CCONJ
ejpam-5897	414	8	ternary	ternary	ADJ
ejpam-5897	414	9	derivations	derivation	NOUN
ejpam-5897	414	10	on	on	ADP
ejpam-5897	414	11	ternary	ternary	ADJ
ejpam-5897	414	12	quasibanach	quasibanach	NOUN
ejpam-5897	414	13	algebras	algebra	NOUN
ejpam-5897	414	14	.	.	PUNCT
ejpam-5897	415	1	adv	adv	PROPN
ejpam-5897	415	2	.	.	PUNCT
ejpam-5897	415	3	difference	difference	PROPN
ejpam-5897	415	4	equ	equ	PROPN
ejpam-5897	415	5	.	.	PROPN
ejpam-5897	415	6	,	,	PUNCT
ejpam-5897	415	7	2012(80):1–11	2012(80):1–11	NUM
ejpam-5897	415	8	,	,	PUNCT
ejpam-5897	415	9	2012	2012	NUM
ejpam-5897	415	10	.	.	PUNCT
ejpam-5897	416	1	[	[	X
ejpam-5897	416	2	26	26	NUM
ejpam-5897	416	3	]	]	X
ejpam-5897	416	4	j	j	PROPN
ejpam-5897	416	5	m	m	VERB
ejpam-5897	416	6	rassias	rassias	PROPN
ejpam-5897	416	7	and	and	CCONJ
ejpam-5897	416	8	h	h	PROPN
ejpam-5897	416	9	m	m	PROPN
ejpam-5897	416	10	kim	kim	PROPN
ejpam-5897	416	11	.	.	PUNCT
ejpam-5897	416	12	approximate	approximate	PROPN
ejpam-5897	416	13	homomorphisms	homomorphism	NOUN
ejpam-5897	416	14	and	and	CCONJ
ejpam-5897	416	15	derivations	derivation	NOUN
ejpam-5897	416	16	between	between	ADP
ejpam-5897	416	17	c∗-ternary	c∗-ternary	ADJ
ejpam-5897	416	18	algebras	algebra	NOUN
ejpam-5897	416	19	.	.	PUNCT
ejpam-5897	417	1	j.	j.	PROPN
ejpam-5897	417	2	math	math	PROPN
ejpam-5897	417	3	.	.	PUNCT
ejpam-5897	418	1	phys	phy	NOUN
ejpam-5897	418	2	.	.	PUNCT
ejpam-5897	418	3	,	,	PUNCT
ejpam-5897	418	4	49(6(063507)):1–10	49(6(063507)):1–10	ADV
ejpam-5897	418	5	,	,	PUNCT
ejpam-5897	418	6	2008	2008	NUM
ejpam-5897	418	7	.	.	PUNCT
ejpam-5897	419	1	[	[	X
ejpam-5897	419	2	27	27	NUM
ejpam-5897	419	3	]	]	PUNCT
ejpam-5897	419	4	n	n	PRON
ejpam-5897	419	5	bazunova	bazunova	PROPN
ejpam-5897	419	6	,	,	PUNCT
ejpam-5897	419	7	a	a	DET
ejpam-5897	419	8	borowiec	borowiec	NOUN
ejpam-5897	419	9	,	,	PUNCT
ejpam-5897	419	10	and	and	CCONJ
ejpam-5897	419	11	r	r	PROPN
ejpam-5897	419	12	kerner	kerner	PROPN
ejpam-5897	419	13	.	.	PUNCT
ejpam-5897	420	1	universal	universal	PROPN
ejpam-5897	420	2	differential	differential	ADJ
ejpam-5897	420	3	calculus	calculus	NOUN
ejpam-5897	420	4	on	on	ADP
ejpam-5897	420	5	ternary	ternary	ADJ
ejpam-5897	420	6	algebras	algebra	NOUN
ejpam-5897	420	7	.	.	PUNCT
ejpam-5897	421	1	lett	lett	PROPN
ejpam-5897	421	2	.	.	PUNCT
ejpam-5897	421	3	math	math	NOUN
ejpam-5897	421	4	.	.	PUNCT
ejpam-5897	422	1	phys	phy	NOUN
ejpam-5897	422	2	.	.	PUNCT
ejpam-5897	422	3	,	,	PUNCT
ejpam-5897	422	4	67(3):195–206	67(3):195–206	NOUN
ejpam-5897	422	5	,	,	PUNCT
ejpam-5897	422	6	2004	2004	NUM
ejpam-5897	422	7	.	.	PUNCT
ejpam-5897	423	1	[	[	X
ejpam-5897	423	2	28	28	NUM
ejpam-5897	423	3	]	]	X
ejpam-5897	423	4	r	r	NOUN
ejpam-5897	423	5	farokhzad	farokhzad	NOUN
ejpam-5897	423	6	and	and	CCONJ
ejpam-5897	423	7	s	s	VERB
ejpam-5897	423	8	a	a	DET
ejpam-5897	423	9	r	r	NOUN
ejpam-5897	423	10	hosseinioun	hosseinioun	NOUN
ejpam-5897	423	11	.	.	PUNCT
ejpam-5897	424	1	perturbations	perturbation	NOUN
ejpam-5897	424	2	of	of	ADP
ejpam-5897	424	3	jordan	jordan	PROPN
ejpam-5897	424	4	higher	high	ADJ
ejpam-5897	424	5	derivations	derivation	NOUN
ejpam-5897	424	6	in	in	ADP
ejpam-5897	424	7	banach	banach	ADV
ejpam-5897	424	8	ternary	ternary	ADJ
ejpam-5897	424	9	algebras	algebra	NOUN
ejpam-5897	424	10	:	:	PUNCT
ejpam-5897	424	11	an	an	DET
ejpam-5897	424	12	alternative	alternative	ADJ
ejpam-5897	424	13	fixed	fix	VERB
ejpam-5897	424	14	point	point	NOUN
ejpam-5897	424	15	approach	approach	NOUN
ejpam-5897	424	16	.	.	PUNCT
ejpam-5897	425	1	int	int	NOUN
ejpam-5897	425	2	.	.	PUNCT
ejpam-5897	426	1	j.	j.	PROPN
ejpam-5897	426	2	nonlinear	nonlinear	PROPN
ejpam-5897	426	3	anal	anal	PROPN
ejpam-5897	426	4	.	.	PUNCT
ejpam-5897	427	1	appl	appl	PROPN
ejpam-5897	427	2	.	.	PROPN
ejpam-5897	427	3	,	,	PUNCT
ejpam-5897	427	4	1(1):42–53	1(1):42–53	NUM
ejpam-5897	427	5	,	,	PUNCT
ejpam-5897	427	6	2010	2010	NUM
ejpam-5897	427	7	.	.	PUNCT
ejpam-5897	428	1	[	[	X
ejpam-5897	428	2	29	29	NUM
ejpam-5897	428	3	]	]	SYM
ejpam-5897	428	4	m	m	PROPN
ejpam-5897	428	5	e	e	NOUN
ejpam-5897	428	6	gordji	gordji	NOUN
ejpam-5897	428	7	.	.	PUNCT
ejpam-5897	429	1	nearly	nearly	ADV
ejpam-5897	429	2	ring	ring	NOUN
ejpam-5897	429	3	homomorphisms	homomorphism	NOUN
ejpam-5897	429	4	and	and	CCONJ
ejpam-5897	429	5	nearly	nearly	ADV
ejpam-5897	429	6	ring	ring	NOUN
ejpam-5897	429	7	derivations	derivation	NOUN
ejpam-5897	429	8	on	on	ADP
ejpam-5897	429	9	nonarchimedean	nonarchimedean	ADJ
ejpam-5897	429	10	banach	banach	NOUN
ejpam-5897	429	11	algebras	algebra	NOUN
ejpam-5897	429	12	.	.	PUNCT
ejpam-5897	430	1	abstr	abstr	PROPN
ejpam-5897	430	2	.	.	PUNCT
ejpam-5897	430	3	appl	appl	PROPN
ejpam-5897	430	4	.	.	PUNCT
ejpam-5897	431	1	anal	anal	PROPN
ejpam-5897	431	2	.	.	PROPN
ejpam-5897	431	3	,	,	PUNCT
ejpam-5897	431	4	2010(1(393247)):1–12	2010(1(393247)):1–12	NUM
ejpam-5897	431	5	,	,	PUNCT
ejpam-5897	431	6	2010	2010	NUM
ejpam-5897	431	7	.	.	PUNCT
ejpam-5897	432	1	[	[	X
ejpam-5897	432	2	30	30	NUM
ejpam-5897	432	3	]	]	X
ejpam-5897	432	4	c	c	NOUN
ejpam-5897	432	5	park	park	NOUN
ejpam-5897	432	6	and	and	CCONJ
ejpam-5897	432	7	m	m	PROPN
ejpam-5897	432	8	e	e	NOUN
ejpam-5897	432	9	gordji	gordji	NOUN
ejpam-5897	432	10	.	.	PUNCT
ejpam-5897	433	1	comment	comment	NOUN
ejpam-5897	433	2	on	on	ADP
ejpam-5897	433	3	“	"	PUNCT
ejpam-5897	433	4	approximate	approximate	ADJ
ejpam-5897	433	5	ternary	ternary	ADJ
ejpam-5897	433	6	jordan	jordan	PROPN
ejpam-5897	433	7	derivations	derivation	NOUN
ejpam-5897	433	8	on	on	ADP
ejpam-5897	433	9	banach	banach	ADV
ejpam-5897	433	10	ternary	ternary	ADJ
ejpam-5897	433	11	algebras	algebra	NOUN
ejpam-5897	433	12	”	"	PUNCT
ejpam-5897	433	13	[	[	X
ejpam-5897	433	14	bavand	bavand	NOUN
ejpam-5897	433	15	savadkouhi	savadkouhi	VERB
ejpam-5897	433	16	et	et	PROPN
ejpam-5897	433	17	al	al	PROPN
ejpam-5897	433	18	.	.	PROPN
ejpam-5897	433	19	,	,	PUNCT
ejpam-5897	433	20	j.	j.	PROPN
ejpam-5897	433	21	math	math	PROPN
ejpam-5897	433	22	.	.	PUNCT
ejpam-5897	434	1	phys	phy	NOUN
ejpam-5897	434	2	.	.	PUNCT
ejpam-5897	435	1	50	50	NUM
ejpam-5897	435	2	,	,	PUNCT
ejpam-5897	435	3	042303	042303	NUM
ejpam-5897	435	4	(	(	PUNCT
ejpam-5897	435	5	2009	2009	NUM
ejpam-5897	435	6	)	)	PUNCT
ejpam-5897	435	7	]	]	PUNCT
ejpam-5897	435	8	.	.	PUNCT
ejpam-5897	436	1	j.	j.	PROPN
ejpam-5897	436	2	math	math	PROPN
ejpam-5897	436	3	.	.	PUNCT
ejpam-5897	437	1	phys	phy	NOUN
ejpam-5897	437	2	.	.	PUNCT
ejpam-5897	437	3	,	,	PUNCT
ejpam-5897	437	4	51(4(044102)):1–7	51(4(044102)):1–7	NUM
ejpam-5897	437	5	,	,	PUNCT
ejpam-5897	437	6	2010	2010	NUM
ejpam-5897	437	7	.	.	PUNCT
ejpam-5897	438	1	[	[	X
ejpam-5897	438	2	31	31	NUM
ejpam-5897	438	3	]	]	X
ejpam-5897	438	4	j	j	PROPN
ejpam-5897	438	5	h	h	PROPN
ejpam-5897	438	6	bae	bae	PROPN
ejpam-5897	438	7	and	and	CCONJ
ejpam-5897	438	8	w	w	PROPN
ejpam-5897	438	9	g	g	PROPN
ejpam-5897	438	10	park	park	NOUN
ejpam-5897	438	11	.	.	PUNCT
ejpam-5897	439	1	generalized	generalize	VERB
ejpam-5897	439	2	ulam	ulam	PROPN
ejpam-5897	439	3	-	-	PUNCT
ejpam-5897	439	4	hyers	hyer	NOUN
ejpam-5897	439	5	stability	stability	NOUN
ejpam-5897	439	6	of	of	ADP
ejpam-5897	439	7	c∗-ternary	c∗-ternary	ADJ
ejpam-5897	439	8	algebra	algebra	NOUN
ejpam-5897	439	9	3	3	NOUN
ejpam-5897	439	10	-	-	PUNCT
ejpam-5897	439	11	homomorphisms	homomorphism	NOUN
ejpam-5897	439	12	for	for	ADP
ejpam-5897	439	13	a	a	DET
ejpam-5897	439	14	functional	functional	ADJ
ejpam-5897	439	15	equation	equation	NOUN
ejpam-5897	439	16	.	.	PUNCT
ejpam-5897	440	1	j.	j.	PROPN
ejpam-5897	440	2	chungcheong	chungcheong	PROPN
ejpam-5897	440	3	math	math	PROPN
ejpam-5897	440	4	.	.	PUNCT
ejpam-5897	441	1	soc	soc	PROPN
ejpam-5897	441	2	.	.	PUNCT
ejpam-5897	441	3	,	,	PUNCT
ejpam-5897	441	4	24(2):147	24(2):147	PROPN
ejpam-5897	441	5	–	–	PUNCT
ejpam-5897	441	6	162	162	NUM
ejpam-5897	441	7	,	,	PUNCT
ejpam-5897	441	8	2011	2011	NUM
ejpam-5897	441	9	.	.	PUNCT