id	sid	tid	token	lemma	pos
ejpam-7033	1	1	european	european	PROPN
ejpam-7033	1	2	journal	journal	PROPN
ejpam-7033	1	3	of	of	ADP
ejpam-7033	1	4	pure	pure	ADJ
ejpam-7033	1	5	and	and	CCONJ
ejpam-7033	1	6	applied	applied	ADJ
ejpam-7033	1	7	mathematics	mathematic	NOUN
ejpam-7033	1	8	2025	2025	NUM
ejpam-7033	1	9	,	,	PUNCT
ejpam-7033	1	10	vol	vol	NOUN
ejpam-7033	1	11	.	.	PROPN
ejpam-7033	1	12	18	18	NUM
ejpam-7033	1	13	,	,	PUNCT
ejpam-7033	1	14	issue	issue	NOUN
ejpam-7033	1	15	4	4	NUM
ejpam-7033	1	16	,	,	PUNCT
ejpam-7033	1	17	article	article	NOUN
ejpam-7033	1	18	number	number	NOUN
ejpam-7033	1	19	7033	7033	NUM
ejpam-7033	1	20	issn	issn	PROPN
ejpam-7033	1	21	1307	1307	NUM
ejpam-7033	1	22	-	-	SYM
ejpam-7033	1	23	5543	5543	NUM
ejpam-7033	1	24	–	–	PUNCT
ejpam-7033	1	25	ejpam.com	ejpam.com	X
ejpam-7033	1	26	published	publish	VERB
ejpam-7033	1	27	by	by	ADP
ejpam-7033	1	28	new	new	PROPN
ejpam-7033	1	29	york	york	PROPN
ejpam-7033	1	30	business	business	PROPN
ejpam-7033	1	31	global	global	PROPN
ejpam-7033	1	32	the	the	DET
ejpam-7033	1	33	ordered	order	VERB
ejpam-7033	1	34	implicit	implicit	ADJ
ejpam-7033	1	35	relations	relation	NOUN
ejpam-7033	1	36	:	:	PUNCT
ejpam-7033	1	37	fixed	fix	VERB
ejpam-7033	1	38	point	point	NOUN
ejpam-7033	1	39	problems	problem	NOUN
ejpam-7033	1	40	and	and	CCONJ
ejpam-7033	1	41	applications	application	NOUN
ejpam-7033	1	42	anam	anam	X
ejpam-7033	1	43	arif1	arif1	PROPN
ejpam-7033	1	44	,	,	PUNCT
ejpam-7033	1	45	muhammad	muhammad	PROPN
ejpam-7033	1	46	nazam2	nazam2	PROPN
ejpam-7033	1	47	,	,	PUNCT
ejpam-7033	1	48	hijaz	hijaz	PROPN
ejpam-7033	1	49	ahmad3,4,5,9,∗	ahmad3,4,5,9,∗	PROPN
ejpam-7033	1	50	,	,	PUNCT
ejpam-7033	1	51	ibrahim	ibrahim	PROPN
ejpam-7033	1	52	alraddadi3,∗	alraddadi3,∗	PROPN
ejpam-7033	1	53	,	,	PUNCT
ejpam-7033	1	54	changjin	changjin	PROPN
ejpam-7033	1	55	xu6	xu6	PROPN
ejpam-7033	1	56	,	,	PUNCT
ejpam-7033	1	57	waleed	waleed	PROPN
ejpam-7033	1	58	mohammed	mohammed	PROPN
ejpam-7033	1	59	abdelfattah7,8	abdelfattah7,8	PROPN
ejpam-7033	1	60	1	1	NUM
ejpam-7033	1	61	department	department	NOUN
ejpam-7033	1	62	of	of	ADP
ejpam-7033	1	63	mathematics	mathematic	NOUN
ejpam-7033	1	64	,	,	PUNCT
ejpam-7033	1	65	government	government	NOUN
ejpam-7033	1	66	college	college	NOUN
ejpam-7033	1	67	university	university	PROPN
ejpam-7033	1	68	,	,	PUNCT
ejpam-7033	1	69	lahore	lahore	PROPN
ejpam-7033	1	70	,	,	PUNCT
ejpam-7033	1	71	pakistan	pakistan	PROPN
ejpam-7033	1	72	2	2	NUM
ejpam-7033	1	73	department	department	NOUN
ejpam-7033	1	74	of	of	ADP
ejpam-7033	1	75	mathematics	mathematic	NOUN
ejpam-7033	1	76	,	,	PUNCT
ejpam-7033	1	77	allama	allama	PROPN
ejpam-7033	1	78	iqbal	iqbal	PROPN
ejpam-7033	1	79	open	open	PROPN
ejpam-7033	1	80	university	university	PROPN
ejpam-7033	1	81	,	,	PUNCT
ejpam-7033	1	82	h-8	h-8	NOUN
ejpam-7033	1	83	,	,	PUNCT
ejpam-7033	1	84	islamabad	islamabad	PROPN
ejpam-7033	1	85	,	,	PUNCT
ejpam-7033	1	86	pakistan	pakistan	PROPN
ejpam-7033	1	87	3	3	NUM
ejpam-7033	1	88	department	department	NOUN
ejpam-7033	1	89	of	of	ADP
ejpam-7033	1	90	mathematics	mathematic	NOUN
ejpam-7033	1	91	,	,	PUNCT
ejpam-7033	1	92	faculty	faculty	NOUN
ejpam-7033	1	93	of	of	ADP
ejpam-7033	1	94	science	science	NOUN
ejpam-7033	1	95	,	,	PUNCT
ejpam-7033	1	96	islamic	islamic	PROPN
ejpam-7033	1	97	university	university	PROPN
ejpam-7033	1	98	of	of	ADP
ejpam-7033	1	99	madinah	madinah	PROPN
ejpam-7033	1	100	,	,	PUNCT
ejpam-7033	1	101	madinah	madinah	PROPN
ejpam-7033	1	102	,	,	PUNCT
ejpam-7033	1	103	saudi	saudi	PROPN
ejpam-7033	1	104	arabia	arabia	PROPN
ejpam-7033	1	105	4	4	NUM
ejpam-7033	1	106	operational	operational	ADJ
ejpam-7033	1	107	research	research	NOUN
ejpam-7033	1	108	center	center	NOUN
ejpam-7033	1	109	in	in	ADP
ejpam-7033	1	110	healthcare	healthcare	PROPN
ejpam-7033	1	111	,	,	PUNCT
ejpam-7033	1	112	near	near	ADP
ejpam-7033	1	113	east	east	PROPN
ejpam-7033	1	114	university	university	PROPN
ejpam-7033	1	115	,	,	PUNCT
ejpam-7033	1	116	trnc	trnc	PROPN
ejpam-7033	1	117	mersin	mersin	PROPN
ejpam-7033	1	118	10	10	NUM
ejpam-7033	1	119	,	,	PUNCT
ejpam-7033	1	120	nicosia	nicosia	NOUN
ejpam-7033	1	121	,	,	PUNCT
ejpam-7033	1	122	99138	99138	NUM
ejpam-7033	1	123	,	,	PUNCT
ejpam-7033	1	124	turkey	turkey	PROPN
ejpam-7033	1	125	5	5	NUM
ejpam-7033	1	126	department	department	NOUN
ejpam-7033	1	127	of	of	ADP
ejpam-7033	1	128	mathematics	mathematic	NOUN
ejpam-7033	1	129	,	,	PUNCT
ejpam-7033	1	130	college	college	NOUN
ejpam-7033	1	131	of	of	ADP
ejpam-7033	1	132	science	science	PROPN
ejpam-7033	1	133	,	,	PUNCT
ejpam-7033	1	134	korea	korea	PROPN
ejpam-7033	1	135	university	university	PROPN
ejpam-7033	1	136	,	,	PUNCT
ejpam-7033	1	137	145	145	NUM
ejpam-7033	1	138	anam	anam	PROPN
ejpam-7033	1	139	-	-	PUNCT
ejpam-7033	1	140	ro	ro	ADJ
ejpam-7033	1	141	,	,	PUNCT
ejpam-7033	1	142	seongbuk	seongbuk	NOUN
ejpam-7033	1	143	-	-	PUNCT
ejpam-7033	1	144	gu	gu	NOUN
ejpam-7033	1	145	,	,	PUNCT
ejpam-7033	1	146	seoul	seoul	PROPN
ejpam-7033	1	147	02841	02841	PROPN
ejpam-7033	1	148	,	,	PUNCT
ejpam-7033	1	149	south	south	PROPN
ejpam-7033	1	150	korea	korea	PROPN
ejpam-7033	1	151	6	6	NUM
ejpam-7033	1	152	guizhou	guizhou	PROPN
ejpam-7033	1	153	key	key	ADJ
ejpam-7033	1	154	laboratory	laboratory	NOUN
ejpam-7033	1	155	of	of	ADP
ejpam-7033	1	156	economics	economic	NOUN
ejpam-7033	1	157	system	system	NOUN
ejpam-7033	1	158	simulation	simulation	NOUN
ejpam-7033	1	159	,	,	PUNCT
ejpam-7033	1	160	guizhou	guizhou	PROPN
ejpam-7033	1	161	university	university	PROPN
ejpam-7033	1	162	of	of	ADP
ejpam-7033	1	163	finance	finance	NOUN
ejpam-7033	1	164	and	and	CCONJ
ejpam-7033	1	165	economics	economic	NOUN
ejpam-7033	1	166	,	,	PUNCT
ejpam-7033	1	167	guiyang	guiyang	PROPN
ejpam-7033	1	168	,	,	PUNCT
ejpam-7033	1	169	p.r	p.r	PROPN
ejpam-7033	1	170	.	.	PROPN
ejpam-7033	1	171	china	china	PROPN
ejpam-7033	1	172	7	7	NUM
ejpam-7033	1	173	college	college	PROPN
ejpam-7033	1	174	of	of	ADP
ejpam-7033	1	175	engineering	engineering	NOUN
ejpam-7033	1	176	,	,	PUNCT
ejpam-7033	1	177	university	university	NOUN
ejpam-7033	1	178	of	of	ADP
ejpam-7033	1	179	business	business	NOUN
ejpam-7033	1	180	and	and	CCONJ
ejpam-7033	1	181	technology	technology	NOUN
ejpam-7033	1	182	,	,	PUNCT
ejpam-7033	1	183	jeddah	jeddah	PROPN
ejpam-7033	1	184	23435	23435	NUM
ejpam-7033	1	185	,	,	PUNCT
ejpam-7033	1	186	saudi	saudi	PROPN
ejpam-7033	1	187	arabia	arabia	PROPN
ejpam-7033	1	188	8	8	NUM
ejpam-7033	1	189	department	department	NOUN
ejpam-7033	1	190	of	of	ADP
ejpam-7033	1	191	engineering	engineering	NOUN
ejpam-7033	1	192	mathematics	mathematic	NOUN
ejpam-7033	1	193	and	and	CCONJ
ejpam-7033	1	194	physics	physics	NOUN
ejpam-7033	1	195	,	,	PUNCT
ejpam-7033	1	196	faculty	faculty	NOUN
ejpam-7033	1	197	of	of	ADP
ejpam-7033	1	198	engineering	engineering	PROPN
ejpam-7033	1	199	,	,	PUNCT
ejpam-7033	1	200	zagazig	zagazig	PROPN
ejpam-7033	1	201	university	university	PROPN
ejpam-7033	1	202	,	,	PUNCT
ejpam-7033	1	203	p.o	p.o	PROPN
ejpam-7033	1	204	.	.	PROPN
ejpam-7033	1	205	44519	44519	NUM
ejpam-7033	1	206	,	,	PUNCT
ejpam-7033	1	207	egypt	egypt	PROPN
ejpam-7033	1	208	9	9	NUM
ejpam-7033	1	209	jadara	jadara	PROPN
ejpam-7033	1	210	university	university	PROPN
ejpam-7033	1	211	research	research	NOUN
ejpam-7033	1	212	center	center	NOUN
ejpam-7033	1	213	,	,	PUNCT
ejpam-7033	1	214	jadara	jadara	PROPN
ejpam-7033	1	215	university	university	PROPN
ejpam-7033	1	216	,	,	PUNCT
ejpam-7033	1	217	irbid	irbid	PROPN
ejpam-7033	1	218	,	,	PUNCT
ejpam-7033	1	219	jordan	jordan	PROPN
ejpam-7033	1	220	abstract	abstract	PROPN
ejpam-7033	1	221	.	.	PUNCT
ejpam-7033	2	1	we	we	PRON
ejpam-7033	2	2	introduce	introduce	VERB
ejpam-7033	2	3	an	an	DET
ejpam-7033	2	4	ordered	order	VERB
ejpam-7033	2	5	implicit	implicit	ADJ
ejpam-7033	2	6	relation	relation	NOUN
ejpam-7033	2	7	and	and	CCONJ
ejpam-7033	2	8	obtain	obtain	VERB
ejpam-7033	2	9	fixed	fix	VERB
ejpam-7033	2	10	point	point	NOUN
ejpam-7033	2	11	theorems	theorem	NOUN
ejpam-7033	2	12	in	in	ADP
ejpam-7033	2	13	rectangular	rectangular	ADJ
ejpam-7033	2	14	cone	cone	NOUN
ejpam-7033	2	15	b	b	X
ejpam-7033	2	16	-	-	PUNCT
ejpam-7033	2	17	metric	metric	ADJ
ejpam-7033	2	18	space	space	NOUN
ejpam-7033	2	19	,	,	PUNCT
ejpam-7033	2	20	as	as	ADP
ejpam-7033	2	21	an	an	DET
ejpam-7033	2	22	extension	extension	NOUN
ejpam-7033	2	23	of	of	ADP
ejpam-7033	2	24	the	the	DET
ejpam-7033	2	25	results	result	NOUN
ejpam-7033	2	26	on	on	ADP
ejpam-7033	2	27	cone	cone	PROPN
ejpam-7033	2	28	metric	metric	NOUN
ejpam-7033	2	29	,	,	PUNCT
ejpam-7033	2	30	rectangular	rectangular	ADJ
ejpam-7033	2	31	cone	cone	NOUN
ejpam-7033	2	32	metric	metric	NOUN
ejpam-7033	2	33	and	and	CCONJ
ejpam-7033	2	34	cone	cone	NOUN
ejpam-7033	2	35	b	b	X
ejpam-7033	2	36	-	-	PUNCT
ejpam-7033	2	37	metric	metric	ADJ
ejpam-7033	2	38	space	space	NOUN
ejpam-7033	2	39	.	.	PUNCT
ejpam-7033	3	1	we	we	PRON
ejpam-7033	3	2	provide	provide	VERB
ejpam-7033	3	3	some	some	DET
ejpam-7033	3	4	examples	example	NOUN
ejpam-7033	3	5	as	as	ADP
ejpam-7033	3	6	an	an	DET
ejpam-7033	3	7	explanation	explanation	NOUN
ejpam-7033	3	8	of	of	ADP
ejpam-7033	3	9	established	establish	VERB
ejpam-7033	3	10	outcomes	outcome	NOUN
ejpam-7033	3	11	.	.	PUNCT
ejpam-7033	4	1	our	our	PRON
ejpam-7033	4	2	theorems	theorem	NOUN
ejpam-7033	4	3	universalize	universalize	VERB
ejpam-7033	4	4	many	many	ADJ
ejpam-7033	4	5	fixed	fix	VERB
ejpam-7033	4	6	point	point	NOUN
ejpam-7033	4	7	outcomes	outcome	NOUN
ejpam-7033	4	8	in	in	ADP
ejpam-7033	4	9	literature([1	literature([1	PROPN
ejpam-7033	4	10	]	]	PUNCT
ejpam-7033	4	11	,	,	PUNCT
ejpam-7033	4	12	[	[	X
ejpam-7033	4	13	2	2	NUM
ejpam-7033	4	14	]	]	NUM
ejpam-7033	4	15	)	)	PUNCT
ejpam-7033	4	16	.	.	PUNCT
ejpam-7033	5	1	a	a	DET
ejpam-7033	5	2	homotopy	homotopy	NOUN
ejpam-7033	5	3	result	result	NOUN
ejpam-7033	5	4	as	as	SCONJ
ejpam-7033	5	5	an	an	DET
ejpam-7033	5	6	application	application	NOUN
ejpam-7033	5	7	of	of	ADP
ejpam-7033	5	8	main	main	ADJ
ejpam-7033	5	9	theorem	theorem	NOUN
ejpam-7033	5	10	is	be	AUX
ejpam-7033	5	11	given	give	VERB
ejpam-7033	5	12	,	,	PUNCT
ejpam-7033	5	13	which	which	PRON
ejpam-7033	5	14	further	far	ADV
ejpam-7033	5	15	applied	apply	VERB
ejpam-7033	5	16	to	to	ADP
ejpam-7033	5	17	the	the	DET
ejpam-7033	5	18	human	human	ADJ
ejpam-7033	5	19	aging	age	VERB
ejpam-7033	5	20	process	process	NOUN
ejpam-7033	5	21	.	.	PUNCT
ejpam-7033	6	1	the	the	DET
ejpam-7033	6	2	obtained	obtain	VERB
ejpam-7033	6	3	fixed	fix	VERB
ejpam-7033	6	4	point	point	NOUN
ejpam-7033	6	5	results	result	NOUN
ejpam-7033	6	6	is	be	AUX
ejpam-7033	6	7	an	an	DET
ejpam-7033	6	8	extension	extension	NOUN
ejpam-7033	6	9	of	of	ADP
ejpam-7033	6	10	[	[	X
ejpam-7033	6	11	3	3	NUM
ejpam-7033	6	12	]	]	PUNCT
ejpam-7033	6	13	,	,	PUNCT
ejpam-7033	6	14	as	as	SCONJ
ejpam-7033	6	15	the	the	DET
ejpam-7033	6	16	present	present	ADJ
ejpam-7033	6	17	article	article	NOUN
ejpam-7033	6	18	deals	deal	VERB
ejpam-7033	6	19	with	with	ADP
ejpam-7033	6	20	nonlinear	nonlinear	ADJ
ejpam-7033	6	21	contractions	contraction	NOUN
ejpam-7033	6	22	.	.	PUNCT
ejpam-7033	7	1	the	the	DET
ejpam-7033	7	2	convergence	convergence	NOUN
ejpam-7033	7	3	of	of	ADP
ejpam-7033	7	4	the	the	DET
ejpam-7033	7	5	sequence	sequence	NOUN
ejpam-7033	7	6	generated	generate	VERB
ejpam-7033	7	7	by	by	ADP
ejpam-7033	7	8	urysohn	urysohn	PROPN
ejpam-7033	7	9	integral	integral	ADJ
ejpam-7033	7	10	operator	operator	NOUN
ejpam-7033	7	11	is	be	AUX
ejpam-7033	7	12	also	also	ADV
ejpam-7033	7	13	shown	show	VERB
ejpam-7033	7	14	by	by	ADP
ejpam-7033	7	15	using	use	VERB
ejpam-7033	7	16	fixed	fix	VERB
ejpam-7033	7	17	point	point	NOUN
ejpam-7033	7	18	technique	technique	NOUN
ejpam-7033	7	19	.	.	PUNCT
ejpam-7033	8	1	2020	2020	NUM
ejpam-7033	8	2	mathematics	mathematic	NOUN
ejpam-7033	8	3	subject	subject	NOUN
ejpam-7033	8	4	classifications	classification	NOUN
ejpam-7033	8	5	:	:	PUNCT
ejpam-7033	8	6	47h09	47h09	NUM
ejpam-7033	8	7	,	,	PUNCT
ejpam-7033	8	8	47h10	47h10	NUM
ejpam-7033	8	9	,	,	PUNCT
ejpam-7033	8	10	54h25	54h25	NUM
ejpam-7033	8	11	key	key	ADJ
ejpam-7033	8	12	words	word	NOUN
ejpam-7033	8	13	and	and	CCONJ
ejpam-7033	8	14	phrases	phrase	NOUN
ejpam-7033	8	15	:	:	PUNCT
ejpam-7033	8	16	fixed	fixed	ADJ
ejpam-7033	8	17	point	point	NOUN
ejpam-7033	8	18	,	,	PUNCT
ejpam-7033	8	19	implicit	implicit	ADJ
ejpam-7033	8	20	relation	relation	NOUN
ejpam-7033	8	21	,	,	PUNCT
ejpam-7033	8	22	cone	cone	NOUN
ejpam-7033	8	23	rectangular	rectangular	ADJ
ejpam-7033	8	24	b	b	X
ejpam-7033	8	25	-	-	PUNCT
ejpam-7033	8	26	metric	metric	ADJ
ejpam-7033	8	27	space	space	NOUN
ejpam-7033	8	28	,	,	PUNCT
ejpam-7033	8	29	contraction	contraction	NOUN
ejpam-7033	8	30	∗corresponding	∗corresponde	VERB
ejpam-7033	8	31	author	author	NOUN
ejpam-7033	8	32	.	.	PUNCT
ejpam-7033	9	1	∗corresponding	∗corresponde	VERB
ejpam-7033	9	2	author	author	NOUN
ejpam-7033	9	3	.	.	PUNCT
ejpam-7033	10	1	doi	doi	NOUN
ejpam-7033	10	2	:	:	PUNCT
ejpam-7033	10	3	https://doi.org/10.29020/nybg.ejpam.v18i4.7033	https://doi.org/10.29020/nybg.ejpam.v18i4.7033	VERB
ejpam-7033	10	4	email	email	NOUN
ejpam-7033	10	5	addresses	address	NOUN
ejpam-7033	10	6	:	:	PUNCT
ejpam-7033	10	7	amanarif970@gmail.com	amanarif970@gmail.com	X
ejpam-7033	10	8	(	(	PUNCT
ejpam-7033	10	9	a.	a.	PROPN
ejpam-7033	10	10	arif	arif	PROPN
ejpam-7033	10	11	)	)	PUNCT
ejpam-7033	10	12	,	,	PUNCT
ejpam-7033	10	13	muhammad.nazam@aiou.edu.pk	muhammad.nazam@aiou.edu.pk	PROPN
ejpam-7033	10	14	(	(	PUNCT
ejpam-7033	10	15	m.	m.	NOUN
ejpam-7033	10	16	nazam	nazam	PROPN
ejpam-7033	10	17	)	)	PUNCT
ejpam-7033	10	18	,	,	PUNCT
ejpam-7033	10	19	hijazahmad@korea.ac.kr	hijazahmad@korea.ac.kr	PROPN
ejpam-7033	10	20	(	(	PUNCT
ejpam-7033	10	21	h.	h.	PROPN
ejpam-7033	10	22	ahmad	ahmad	PROPN
ejpam-7033	10	23	)	)	PUNCT
ejpam-7033	10	24	,	,	PUNCT
ejpam-7033	10	25	ialraddadi@iu.edu.sa	ialraddadi@iu.edu.sa	PROPN
ejpam-7033	10	26	(	(	PUNCT
ejpam-7033	10	27	i.	i.	NOUN
ejpam-7033	10	28	alraddadi	alraddadi	PROPN
ejpam-7033	10	29	)	)	PUNCT
ejpam-7033	10	30	,	,	PUNCT
ejpam-7033	10	31	xcj403@126.com	xcj403@126.com	X
ejpam-7033	10	32	(	(	PUNCT
ejpam-7033	10	33	c.	c.	PROPN
ejpam-7033	10	34	xu	xu	PROPN
ejpam-7033	10	35	)	)	PUNCT
ejpam-7033	10	36	,	,	PUNCT
ejpam-7033	10	37	w.abdelfattah@ubt.edu.sa	w.abdelfattah@ubt.edu.sa	PROPN
ejpam-7033	10	38	(	(	PUNCT
ejpam-7033	10	39	w.	w.	PROPN
ejpam-7033	10	40	m.	m.	PROPN
ejpam-7033	10	41	abdelfattah	abdelfattah	PROPN
ejpam-7033	10	42	)	)	PUNCT
ejpam-7033	10	43	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-7033	11	1	1	1	NUM
ejpam-7033	11	2	copyright	copyright	NOUN
ejpam-7033	11	3	:	:	PUNCT
ejpam-7033	11	4	©	©	PROPN
ejpam-7033	11	5	2025	2025	NUM
ejpam-7033	11	6	the	the	DET
ejpam-7033	11	7	author(s	author(s	NOUN
ejpam-7033	11	8	)	)	PUNCT
ejpam-7033	11	9	.	.	PUNCT
ejpam-7033	12	1	(	(	PUNCT
ejpam-7033	12	2	cc	cc	NOUN
ejpam-7033	12	3	by	by	ADP
ejpam-7033	12	4	-	-	PUNCT
ejpam-7033	12	5	nc	nc	PROPN
ejpam-7033	12	6	4.0	4.0	NUM
ejpam-7033	12	7	)	)	PUNCT
ejpam-7033	12	8	a.	a.	NOUN
ejpam-7033	12	9	arif	arif	PROPN
ejpam-7033	12	10	et	et	PROPN
ejpam-7033	12	11	al	al	PROPN
ejpam-7033	12	12	.	.	PUNCT
ejpam-7033	12	13	/	/	SYM
ejpam-7033	12	14	eur	eur	PROPN
ejpam-7033	12	15	.	.	PUNCT
ejpam-7033	13	1	j.	j.	PROPN
ejpam-7033	13	2	pure	pure	PROPN
ejpam-7033	13	3	appl	appl	PROPN
ejpam-7033	13	4	.	.	PROPN
ejpam-7033	13	5	math	math	PROPN
ejpam-7033	13	6	,	,	PUNCT
ejpam-7033	13	7	18	18	NUM
ejpam-7033	13	8	(	(	PUNCT
ejpam-7033	13	9	4	4	NUM
ejpam-7033	13	10	)	)	PUNCT
ejpam-7033	13	11	(	(	PUNCT
ejpam-7033	13	12	2025	2025	NUM
ejpam-7033	13	13	)	)	PUNCT
ejpam-7033	13	14	,	,	PUNCT
ejpam-7033	13	15	7033	7033	NUM
ejpam-7033	13	16	2	2	NUM
ejpam-7033	13	17	of	of	ADP
ejpam-7033	13	18	29	29	NUM
ejpam-7033	13	19	1	1	NUM
ejpam-7033	13	20	.	.	PUNCT
ejpam-7033	14	1	introduction	introduction	NOUN
ejpam-7033	14	2	ran	run	VERB
ejpam-7033	14	3	[	[	X
ejpam-7033	14	4	4	4	X
ejpam-7033	14	5	]	]	PUNCT
ejpam-7033	14	6	applied	apply	VERB
ejpam-7033	14	7	the	the	DET
ejpam-7033	14	8	concept	concept	NOUN
ejpam-7033	14	9	of	of	ADP
ejpam-7033	14	10	partial	partial	ADJ
ejpam-7033	14	11	order	order	NOUN
ejpam-7033	14	12	to	to	PART
ejpam-7033	14	13	obtain	obtain	VERB
ejpam-7033	14	14	a	a	DET
ejpam-7033	14	15	new	new	ADJ
ejpam-7033	14	16	generalization	generalization	NOUN
ejpam-7033	14	17	of	of	ADP
ejpam-7033	14	18	bcp	bcp	PROPN
ejpam-7033	15	1	[	[	X
ejpam-7033	15	2	5	5	NUM
ejpam-7033	15	3	]	]	PUNCT
ejpam-7033	15	4	.	.	PUNCT
ejpam-7033	16	1	the	the	DET
ejpam-7033	16	2	appearance	appearance	NOUN
ejpam-7033	16	3	of	of	ADP
ejpam-7033	16	4	this	this	DET
ejpam-7033	16	5	idea	idea	NOUN
ejpam-7033	16	6	set	set	VERB
ejpam-7033	16	7	a	a	DET
ejpam-7033	16	8	new	new	ADJ
ejpam-7033	16	9	direction	direction	NOUN
ejpam-7033	16	10	in	in	ADP
ejpam-7033	16	11	metric	metric	ADJ
ejpam-7033	16	12	fixed	fix	VERB
ejpam-7033	16	13	point	point	NOUN
ejpam-7033	16	14	theory	theory	NOUN
ejpam-7033	16	15	,	,	PUNCT
ejpam-7033	16	16	and	and	CCONJ
ejpam-7033	16	17	many	many	ADJ
ejpam-7033	16	18	authors	author	NOUN
ejpam-7033	16	19	contributed	contribute	VERB
ejpam-7033	16	20	with	with	ADP
ejpam-7033	16	21	remarkable	remarkable	ADJ
ejpam-7033	16	22	research	research	NOUN
ejpam-7033	16	23	articles	article	NOUN
ejpam-7033	16	24	(	(	PUNCT
ejpam-7033	16	25	see	see	VERB
ejpam-7033	16	26	[	[	X
ejpam-7033	16	27	6	6	NUM
ejpam-7033	16	28	,	,	PUNCT
ejpam-7033	16	29	7	7	NUM
ejpam-7033	16	30	]	]	PUNCT
ejpam-7033	16	31	)	)	PUNCT
ejpam-7033	16	32	.	.	PUNCT
ejpam-7033	17	1	popa	popa	NOUN
ejpam-7033	18	1	[	[	X
ejpam-7033	18	2	1	1	X
ejpam-7033	18	3	]	]	PUNCT
ejpam-7033	18	4	introduced	introduce	VERB
ejpam-7033	18	5	the	the	DET
ejpam-7033	18	6	concept	concept	NOUN
ejpam-7033	18	7	of	of	ADP
ejpam-7033	18	8	an	an	DET
ejpam-7033	18	9	implicit	implicit	ADJ
ejpam-7033	18	10	relation	relation	NOUN
ejpam-7033	18	11	to	to	PART
ejpam-7033	18	12	present	present	VERB
ejpam-7033	18	13	generalization	generalization	NOUN
ejpam-7033	18	14	of	of	ADP
ejpam-7033	18	15	bcp	bcp	PROPN
ejpam-7033	18	16	.	.	PUNCT
ejpam-7033	19	1	beg	beg	VERB
ejpam-7033	19	2	et	et	PROPN
ejpam-7033	19	3	al	al	PROPN
ejpam-7033	19	4	.	.	PUNCT
ejpam-7033	20	1	[	[	X
ejpam-7033	20	2	8	8	NUM
ejpam-7033	20	3	,	,	PUNCT
ejpam-7033	20	4	9	9	NUM
ejpam-7033	20	5	]	]	PUNCT
ejpam-7033	20	6	,	,	PUNCT
ejpam-7033	20	7	berinde	berinde	VERB
ejpam-7033	20	8	et	et	PROPN
ejpam-7033	20	9	al	al	PROPN
ejpam-7033	20	10	.	.	PUNCT
ejpam-7033	21	1	[	[	X
ejpam-7033	21	2	10	10	NUM
ejpam-7033	21	3	,	,	PUNCT
ejpam-7033	21	4	11	11	NUM
ejpam-7033	21	5	]	]	PUNCT
ejpam-7033	21	6	and	and	CCONJ
ejpam-7033	21	7	sedghi	sedghi	VERB
ejpam-7033	21	8	et	et	PROPN
ejpam-7033	21	9	al	al	PROPN
ejpam-7033	21	10	.	.	PUNCT
ejpam-7033	22	1	[	[	X
ejpam-7033	22	2	12	12	NUM
ejpam-7033	22	3	]	]	PUNCT
ejpam-7033	22	4	contributed	contribute	VERB
ejpam-7033	22	5	with	with	ADP
ejpam-7033	22	6	several	several	ADJ
ejpam-7033	22	7	new	new	ADJ
ejpam-7033	22	8	fixed	fix	VERB
ejpam-7033	22	9	point	point	NOUN
ejpam-7033	22	10	results	result	NOUN
ejpam-7033	22	11	of	of	ADP
ejpam-7033	22	12	selfoperators	selfoperator	NOUN
ejpam-7033	22	13	satisfying	satisfy	VERB
ejpam-7033	22	14	implicit	implicit	ADJ
ejpam-7033	22	15	relations	relation	NOUN
ejpam-7033	22	16	.	.	PUNCT
ejpam-7033	23	1	altun	altun	NOUN
ejpam-7033	23	2	and	and	CCONJ
ejpam-7033	23	3	simsek	simsek	NOUN
ejpam-7033	23	4	applied	apply	VERB
ejpam-7033	23	5	the	the	DET
ejpam-7033	23	6	concept	concept	NOUN
ejpam-7033	23	7	of	of	ADP
ejpam-7033	23	8	implicit	implicit	ADJ
ejpam-7033	23	9	relation	relation	NOUN
ejpam-7033	23	10	(	(	PUNCT
ejpam-7033	23	11	see[13	see[13	PROPN
ejpam-7033	23	12	]	]	PUNCT
ejpam-7033	23	13	)	)	PUNCT
ejpam-7033	23	14	,	,	PUNCT
ejpam-7033	23	15	and	and	CCONJ
ejpam-7033	23	16	obtained	obtain	VERB
ejpam-7033	23	17	a	a	DET
ejpam-7033	23	18	generalization	generalization	NOUN
ejpam-7033	23	19	of	of	ADP
ejpam-7033	23	20	[	[	X
ejpam-7033	23	21	4	4	NUM
ejpam-7033	23	22	,	,	PUNCT
ejpam-7033	23	23	14	14	NUM
ejpam-7033	23	24	]	]	PUNCT
ejpam-7033	23	25	.	.	PUNCT
ejpam-7033	24	1	fixed	fix	VERB
ejpam-7033	24	2	point	point	NOUN
ejpam-7033	24	3	theory	theory	NOUN
ejpam-7033	24	4	deals	deal	VERB
ejpam-7033	24	5	with	with	ADP
ejpam-7033	24	6	metric	metric	ADJ
ejpam-7033	24	7	structures	structure	NOUN
ejpam-7033	24	8	and	and	CCONJ
ejpam-7033	24	9	their	their	PRON
ejpam-7033	24	10	generalizations	generalization	NOUN
ejpam-7033	24	11	.	.	PUNCT
ejpam-7033	25	1	recently	recently	ADV
ejpam-7033	25	2	,	,	PUNCT
ejpam-7033	25	3	jachymski	jachymski	PROPN
ejpam-7033	25	4	[	[	X
ejpam-7033	25	5	15	15	NUM
ejpam-7033	25	6	]	]	X
ejpam-7033	25	7	generalized	generalize	VERB
ejpam-7033	25	8	the	the	DET
ejpam-7033	25	9	bcp	bcp	NOUN
ejpam-7033	25	10	subject	subject	ADJ
ejpam-7033	25	11	to	to	ADP
ejpam-7033	25	12	a	a	DET
ejpam-7033	25	13	graphic	graphic	ADJ
ejpam-7033	25	14	metric	metric	ADJ
ejpam-7033	25	15	space	space	NOUN
ejpam-7033	25	16	,	,	PUNCT
ejpam-7033	25	17	nadler	nadler	PROPN
ejpam-7033	26	1	[	[	X
ejpam-7033	26	2	16	16	NUM
ejpam-7033	26	3	]	]	PUNCT
ejpam-7033	26	4	used	use	VERB
ejpam-7033	26	5	hausdorff	hausdorff	NOUN
ejpam-7033	26	6	metric	metric	ADJ
ejpam-7033	26	7	space	space	NOUN
ejpam-7033	26	8	to	to	PART
ejpam-7033	26	9	manifest	manifest	VERB
ejpam-7033	26	10	the	the	DET
ejpam-7033	26	11	fixed	fix	VERB
ejpam-7033	26	12	point	point	NOUN
ejpam-7033	26	13	results	result	NOUN
ejpam-7033	26	14	for	for	ADP
ejpam-7033	26	15	multivalued	multivalued	ADJ
ejpam-7033	26	16	mappings	mapping	NOUN
ejpam-7033	26	17	.	.	PUNCT
ejpam-7033	27	1	rashem	rashem	NOUN
ejpam-7033	27	2	at	at	ADP
ejpam-7033	27	3	al	al	PROPN
ejpam-7033	27	4	.	.	PUNCT
ejpam-7033	28	1	[	[	X
ejpam-7033	28	2	17	17	NUM
ejpam-7033	28	3	]	]	PUNCT
ejpam-7033	28	4	presented	present	VERB
ejpam-7033	28	5	some	some	DET
ejpam-7033	28	6	fixed	fix	VERB
ejpam-7033	28	7	point	point	NOUN
ejpam-7033	28	8	outcomes	outcome	NOUN
ejpam-7033	28	9	in	in	ADP
ejpam-7033	28	10	a	a	DET
ejpam-7033	28	11	modular	modular	ADJ
ejpam-7033	28	12	like	like	ADP
ejpam-7033	28	13	metric	metric	ADJ
ejpam-7033	28	14	structure	structure	NOUN
ejpam-7033	28	15	with	with	ADP
ejpam-7033	28	16	graph	graph	NOUN
ejpam-7033	28	17	.	.	PUNCT
ejpam-7033	29	1	hammad	hammad	PROPN
ejpam-7033	29	2	at	at	ADP
ejpam-7033	29	3	al	al	PROPN
ejpam-7033	29	4	.	.	PUNCT
ejpam-7033	30	1	[	[	X
ejpam-7033	30	2	18	18	NUM
ejpam-7033	30	3	]	]	PUNCT
ejpam-7033	30	4	,	,	PUNCT
ejpam-7033	30	5	contributed	contribute	VERB
ejpam-7033	30	6	some	some	DET
ejpam-7033	30	7	tripled	triple	VERB
ejpam-7033	30	8	fixed	fix	VERB
ejpam-7033	30	9	point	point	NOUN
ejpam-7033	30	10	techniques	technique	NOUN
ejpam-7033	30	11	in	in	ADP
ejpam-7033	30	12	partially	partially	ADV
ejpam-7033	30	13	ordered	order	VERB
ejpam-7033	30	14	metric	metric	ADJ
ejpam-7033	30	15	spaces	space	NOUN
ejpam-7033	30	16	(	(	PUNCT
ejpam-7033	30	17	see	see	VERB
ejpam-7033	30	18	[	[	X
ejpam-7033	30	19	19	19	NUM
ejpam-7033	30	20	,	,	PUNCT
ejpam-7033	30	21	20	20	NUM
ejpam-7033	30	22	]	]	PUNCT
ejpam-7033	30	23	)	)	PUNCT
ejpam-7033	30	24	.	.	PUNCT
ejpam-7033	31	1	huang	huang	PROPN
ejpam-7033	31	2	and	and	CCONJ
ejpam-7033	31	3	zhang	zhang	PROPN
ejpam-7033	32	1	[	[	X
ejpam-7033	32	2	21	21	NUM
ejpam-7033	32	3	]	]	PUNCT
ejpam-7033	32	4	proposed	propose	VERB
ejpam-7033	32	5	the	the	DET
ejpam-7033	32	6	idea	idea	NOUN
ejpam-7033	32	7	of	of	ADP
ejpam-7033	32	8	cone	cone	PROPN
ejpam-7033	32	9	metric	metric	NOUN
ejpam-7033	32	10	,	,	PUNCT
ejpam-7033	32	11	and	and	CCONJ
ejpam-7033	32	12	hence	hence	ADV
ejpam-7033	32	13	proved	prove	VERB
ejpam-7033	32	14	the	the	DET
ejpam-7033	32	15	bcp	bcp	PROPN
ejpam-7033	32	16	and	and	CCONJ
ejpam-7033	32	17	kannan	kannan	PROPN
ejpam-7033	32	18	fixed	fix	VERB
ejpam-7033	32	19	point	point	NOUN
ejpam-7033	32	20	theorem	theorem	VERB
ejpam-7033	32	21	in	in	ADP
ejpam-7033	32	22	this	this	DET
ejpam-7033	32	23	setting	setting	NOUN
ejpam-7033	32	24	.	.	PUNCT
ejpam-7033	33	1	they	they	PRON
ejpam-7033	33	2	used	use	VERB
ejpam-7033	33	3	the	the	DET
ejpam-7033	33	4	idea	idea	NOUN
ejpam-7033	33	5	of	of	ADP
ejpam-7033	33	6	normal	normal	ADJ
ejpam-7033	33	7	cones	cone	NOUN
ejpam-7033	33	8	in	in	ADP
ejpam-7033	33	9	their	their	PRON
ejpam-7033	33	10	work	work	NOUN
ejpam-7033	33	11	(	(	PUNCT
ejpam-7033	33	12	see	see	VERB
ejpam-7033	33	13	[	[	X
ejpam-7033	33	14	21	21	NUM
ejpam-7033	33	15	]	]	PUNCT
ejpam-7033	33	16	)	)	PUNCT
ejpam-7033	33	17	,	,	PUNCT
ejpam-7033	33	18	later	later	ADV
ejpam-7033	33	19	on	on	ADV
ejpam-7033	33	20	,	,	PUNCT
ejpam-7033	33	21	rezapour	rezapour	X
ejpam-7033	33	22	et	et	PROPN
ejpam-7033	33	23	al	al	PROPN
ejpam-7033	33	24	.	.	PUNCT
ejpam-7033	34	1	[	[	X
ejpam-7033	34	2	22	22	NUM
ejpam-7033	34	3	]	]	PUNCT
ejpam-7033	34	4	improved	improve	VERB
ejpam-7033	34	5	these	these	DET
ejpam-7033	34	6	results	result	NOUN
ejpam-7033	34	7	.	.	PUNCT
ejpam-7033	35	1	motivated	motivate	VERB
ejpam-7033	35	2	by	by	ADP
ejpam-7033	35	3	b	b	NOUN
ejpam-7033	35	4	-	-	PUNCT
ejpam-7033	35	5	metric	metric	ADJ
ejpam-7033	35	6	space	space	NOUN
ejpam-7033	35	7	[	[	X
ejpam-7033	35	8	23	23	NUM
ejpam-7033	35	9	]	]	PUNCT
ejpam-7033	35	10	,	,	PUNCT
ejpam-7033	35	11	hussain	hussain	PROPN
ejpam-7033	35	12	and	and	CCONJ
ejpam-7033	35	13	shah	shah	PROPN
ejpam-7033	36	1	[	[	X
ejpam-7033	36	2	24	24	NUM
ejpam-7033	36	3	]	]	PUNCT
ejpam-7033	36	4	inaugurated	inaugurate	VERB
ejpam-7033	36	5	the	the	DET
ejpam-7033	36	6	theory	theory	NOUN
ejpam-7033	36	7	of	of	ADP
ejpam-7033	36	8	cone	cone	PROPN
ejpam-7033	36	9	b	b	X
ejpam-7033	36	10	-	-	PUNCT
ejpam-7033	36	11	metric	metric	ADJ
ejpam-7033	36	12	structure	structure	NOUN
ejpam-7033	36	13	.	.	PUNCT
ejpam-7033	37	1	huang	huang	PROPN
ejpam-7033	37	2	and	and	CCONJ
ejpam-7033	37	3	xu	xu	PROPN
ejpam-7033	38	1	[	[	X
ejpam-7033	38	2	25	25	NUM
ejpam-7033	38	3	]	]	PUNCT
ejpam-7033	38	4	presented	present	VERB
ejpam-7033	38	5	some	some	DET
ejpam-7033	38	6	fixed	fix	VERB
ejpam-7033	38	7	point	point	NOUN
ejpam-7033	38	8	results	result	NOUN
ejpam-7033	38	9	in	in	ADP
ejpam-7033	38	10	the	the	DET
ejpam-7033	38	11	cone	cone	NOUN
ejpam-7033	38	12	b	b	X
ejpam-7033	38	13	-	-	PUNCT
ejpam-7033	38	14	metric	metric	ADJ
ejpam-7033	38	15	space	space	NOUN
ejpam-7033	38	16	.	.	PUNCT
ejpam-7033	39	1	recently	recently	ADV
ejpam-7033	39	2	,	,	PUNCT
ejpam-7033	39	3	anam	anam	PROPN
ejpam-7033	39	4	et	et	PROPN
ejpam-7033	39	5	al	al	PROPN
ejpam-7033	39	6	.	.	PROPN
ejpam-7033	39	7	investigated	investigate	VERB
ejpam-7033	39	8	some	some	DET
ejpam-7033	39	9	necessary	necessary	ADJ
ejpam-7033	39	10	conditions	condition	NOUN
ejpam-7033	39	11	for	for	ADP
ejpam-7033	39	12	the	the	DET
ejpam-7033	39	13	convergence	convergence	NOUN
ejpam-7033	39	14	of	of	ADP
ejpam-7033	39	15	a	a	DET
ejpam-7033	39	16	sequence	sequence	NOUN
ejpam-7033	39	17	generated	generate	VERB
ejpam-7033	39	18	by	by	ADP
ejpam-7033	39	19	implicit	implicit	ADJ
ejpam-7033	39	20	contraction	contraction	NOUN
ejpam-7033	39	21	in	in	ADP
ejpam-7033	39	22	cone	cone	PROPN
ejpam-7033	39	23	b	b	X
ejpam-7033	39	24	-	-	PUNCT
ejpam-7033	39	25	metric	metric	ADJ
ejpam-7033	39	26	space	space	NOUN
ejpam-7033	39	27	[	[	X
ejpam-7033	39	28	26	26	NUM
ejpam-7033	39	29	]	]	PUNCT
ejpam-7033	39	30	.	.	PUNCT
ejpam-7033	40	1	for	for	ADP
ejpam-7033	40	2	more	more	ADJ
ejpam-7033	40	3	information	information	NOUN
ejpam-7033	40	4	on	on	ADP
ejpam-7033	40	5	this	this	DET
ejpam-7033	40	6	direction	direction	NOUN
ejpam-7033	40	7	,	,	PUNCT
ejpam-7033	40	8	we	we	PRON
ejpam-7033	40	9	suggest	suggest	VERB
ejpam-7033	40	10	reading	reading	NOUN
ejpam-7033	40	11	of	of	ADP
ejpam-7033	40	12	(	(	PUNCT
ejpam-7033	40	13	[	[	X
ejpam-7033	40	14	23	23	NUM
ejpam-7033	40	15	,	,	PUNCT
ejpam-7033	40	16	27–35	27–35	NUM
ejpam-7033	40	17	]	]	PUNCT
ejpam-7033	40	18	)	)	PUNCT
ejpam-7033	40	19	.	.	PUNCT
ejpam-7033	41	1	george	george	PROPN
ejpam-7033	42	1	[	[	X
ejpam-7033	42	2	2	2	NUM
ejpam-7033	42	3	]	]	PUNCT
ejpam-7033	42	4	defined	define	VERB
ejpam-7033	42	5	the	the	DET
ejpam-7033	42	6	rectangular	rectangular	ADJ
ejpam-7033	42	7	cone	cone	NOUN
ejpam-7033	42	8	b	b	X
ejpam-7033	42	9	-	-	PUNCT
ejpam-7033	42	10	metric	metric	ADJ
ejpam-7033	42	11	space	space	NOUN
ejpam-7033	42	12	that	that	PRON
ejpam-7033	42	13	universalizes	universalize	VERB
ejpam-7033	42	14	the	the	DET
ejpam-7033	42	15	idea	idea	NOUN
ejpam-7033	42	16	of	of	ADP
ejpam-7033	42	17	[	[	X
ejpam-7033	42	18	36	36	NUM
ejpam-7033	42	19	]	]	PUNCT
ejpam-7033	42	20	,	,	PUNCT
ejpam-7033	42	21	and	and	CCONJ
ejpam-7033	42	22	established	establish	VERB
ejpam-7033	42	23	some	some	DET
ejpam-7033	42	24	well	well	ADV
ejpam-7033	42	25	-	-	PUNCT
ejpam-7033	42	26	known	know	VERB
ejpam-7033	42	27	consequences	consequence	NOUN
ejpam-7033	42	28	in	in	ADP
ejpam-7033	42	29	this	this	DET
ejpam-7033	42	30	setting	setting	NOUN
ejpam-7033	42	31	.	.	PUNCT
ejpam-7033	43	1	•	•	ADP
ejpam-7033	43	2	the	the	DET
ejpam-7033	43	3	fixed	fix	VERB
ejpam-7033	43	4	point	point	NOUN
ejpam-7033	43	5	theorem	theorem	NOUN
ejpam-7033	43	6	and	and	CCONJ
ejpam-7033	43	7	the	the	DET
ejpam-7033	43	8	variational	variational	ADJ
ejpam-7033	43	9	iteration	iteration	NOUN
ejpam-7033	43	10	method	method	NOUN
ejpam-7033	43	11	(	(	PUNCT
ejpam-7033	43	12	vim	vim	NOUN
ejpam-7033	43	13	)	)	PUNCT
ejpam-7033	43	14	are	be	AUX
ejpam-7033	43	15	related	relate	VERB
ejpam-7033	43	16	being	be	AUX
ejpam-7033	43	17	fundamental	fundamental	ADJ
ejpam-7033	43	18	tools	tool	NOUN
ejpam-7033	43	19	for	for	ADP
ejpam-7033	43	20	resolving	resolve	VERB
ejpam-7033	43	21	a	a	DET
ejpam-7033	43	22	variety	variety	NOUN
ejpam-7033	43	23	of	of	ADP
ejpam-7033	43	24	mathematical	mathematical	ADJ
ejpam-7033	43	25	issues	issue	NOUN
ejpam-7033	43	26	,	,	PUNCT
ejpam-7033	43	27	including	include	VERB
ejpam-7033	43	28	differential	differential	ADJ
ejpam-7033	43	29	and	and	CCONJ
ejpam-7033	43	30	integral	integral	ADJ
ejpam-7033	43	31	equations	equation	NOUN
ejpam-7033	43	32	.	.	PUNCT
ejpam-7033	44	1	(	(	PUNCT
ejpam-7033	44	2	a	a	X
ejpam-7033	44	3	)	)	PUNCT
ejpam-7033	44	4	iterative	iterative	NOUN
ejpam-7033	44	5	procedures	procedure	NOUN
ejpam-7033	44	6	are	be	AUX
ejpam-7033	44	7	the	the	DET
ejpam-7033	44	8	foundation	foundation	NOUN
ejpam-7033	44	9	of	of	ADP
ejpam-7033	44	10	both	both	CCONJ
ejpam-7033	44	11	vim	vim	NOUN
ejpam-7033	44	12	and	and	CCONJ
ejpam-7033	44	13	the	the	DET
ejpam-7033	44	14	fixed	fix	VERB
ejpam-7033	44	15	point	point	NOUN
ejpam-7033	44	16	theorem	theorem	VERB
ejpam-7033	44	17	.	.	PROPN
ejpam-7033	44	18	similar	similar	ADJ
ejpam-7033	44	19	to	to	ADP
ejpam-7033	44	20	finding	find	VERB
ejpam-7033	44	21	a	a	DET
ejpam-7033	44	22	fixed	fix	VERB
ejpam-7033	44	23	point	point	NOUN
ejpam-7033	44	24	,	,	PUNCT
ejpam-7033	44	25	the	the	DET
ejpam-7033	44	26	correction	correction	NOUN
ejpam-7033	44	27	process	process	NOUN
ejpam-7033	44	28	in	in	ADP
ejpam-7033	44	29	vim	vim	PROPN
ejpam-7033	44	30	can	can	AUX
ejpam-7033	44	31	be	be	AUX
ejpam-7033	44	32	thought	think	VERB
ejpam-7033	44	33	of	of	ADP
ejpam-7033	44	34	as	as	ADP
ejpam-7033	44	35	a	a	DET
ejpam-7033	44	36	mapping	mapping	NOUN
ejpam-7033	44	37	that	that	PRON
ejpam-7033	44	38	seeks	seek	VERB
ejpam-7033	44	39	to	to	PART
ejpam-7033	44	40	move	move	VERB
ejpam-7033	44	41	successive	successive	ADJ
ejpam-7033	44	42	approximations	approximation	NOUN
ejpam-7033	44	43	closer	close	ADV
ejpam-7033	44	44	to	to	ADP
ejpam-7033	44	45	the	the	DET
ejpam-7033	44	46	genuine	genuine	ADJ
ejpam-7033	44	47	solution	solution	NOUN
ejpam-7033	44	48	.	.	PUNCT
ejpam-7033	45	1	(	(	PUNCT
ejpam-7033	45	2	b	b	X
ejpam-7033	45	3	)	)	PUNCT
ejpam-7033	45	4	it	it	PRON
ejpam-7033	45	5	is	be	AUX
ejpam-7033	45	6	feasible	feasible	ADJ
ejpam-7033	45	7	to	to	PART
ejpam-7033	45	8	understand	understand	VERB
ejpam-7033	45	9	the	the	DET
ejpam-7033	45	10	convergence	convergence	NOUN
ejpam-7033	45	11	of	of	ADP
ejpam-7033	45	12	the	the	DET
ejpam-7033	45	13	vim	vim	PROPN
ejpam-7033	45	14	iterations	iteration	NOUN
ejpam-7033	45	15	as	as	ADP
ejpam-7033	45	16	the	the	DET
ejpam-7033	45	17	discovery	discovery	NOUN
ejpam-7033	45	18	of	of	ADP
ejpam-7033	45	19	a	a	DET
ejpam-7033	45	20	fixed	fix	VERB
ejpam-7033	45	21	point	point	NOUN
ejpam-7033	45	22	in	in	ADP
ejpam-7033	45	23	the	the	DET
ejpam-7033	45	24	space	space	NOUN
ejpam-7033	45	25	of	of	ADP
ejpam-7033	45	26	potential	potential	ADJ
ejpam-7033	45	27	solutions	solution	NOUN
ejpam-7033	45	28	.	.	PUNCT
ejpam-7033	46	1	in	in	ADP
ejpam-7033	46	2	particular	particular	ADJ
ejpam-7033	46	3	,	,	PUNCT
ejpam-7033	46	4	if	if	SCONJ
ejpam-7033	46	5	vim	vim	PROPN
ejpam-7033	46	6	’s	’s	ADJ
ejpam-7033	46	7	iterative	iterative	NOUN
ejpam-7033	46	8	process	process	NOUN
ejpam-7033	46	9	is	be	AUX
ejpam-7033	46	10	successful	successful	ADJ
ejpam-7033	46	11	,	,	PUNCT
ejpam-7033	46	12	it	it	PRON
ejpam-7033	46	13	indicates	indicate	VERB
ejpam-7033	46	14	that	that	SCONJ
ejpam-7033	46	15	,	,	PUNCT
ejpam-7033	46	16	much	much	ADV
ejpam-7033	46	17	like	like	INTJ
ejpam-7033	46	18	when	when	SCONJ
ejpam-7033	46	19	a	a	DET
ejpam-7033	46	20	fixed	fix	VERB
ejpam-7033	46	21	point	point	NOUN
ejpam-7033	46	22	is	be	AUX
ejpam-7033	46	23	found	find	VERB
ejpam-7033	46	24	,	,	PUNCT
ejpam-7033	46	25	the	the	DET
ejpam-7033	46	26	series	series	NOUN
ejpam-7033	46	27	of	of	ADP
ejpam-7033	46	28	approximations	approximation	NOUN
ejpam-7033	46	29	converges	converge	VERB
ejpam-7033	46	30	to	to	ADP
ejpam-7033	46	31	a	a	DET
ejpam-7033	46	32	point	point	NOUN
ejpam-7033	46	33	(	(	PUNCT
ejpam-7033	46	34	the	the	DET
ejpam-7033	46	35	solution	solution	NOUN
ejpam-7033	46	36	)	)	PUNCT
ejpam-7033	46	37	where	where	SCONJ
ejpam-7033	46	38	the	the	DET
ejpam-7033	46	39	correction	correction	NOUN
ejpam-7033	46	40	functional	functional	ADJ
ejpam-7033	46	41	no	no	ADV
ejpam-7033	46	42	longer	long	ADV
ejpam-7033	46	43	changes	change	NOUN
ejpam-7033	46	44	.	.	PUNCT
ejpam-7033	47	1	(	(	PUNCT
ejpam-7033	47	2	c	c	X
ejpam-7033	47	3	)	)	PUNCT
ejpam-7033	47	4	in	in	ADP
ejpam-7033	47	5	some	some	DET
ejpam-7033	47	6	vim	vim	NOUN
ejpam-7033	47	7	analysis	analysis	NOUN
ejpam-7033	47	8	,	,	PUNCT
ejpam-7033	47	9	by	by	ADP
ejpam-7033	47	10	proving	prove	VERB
ejpam-7033	47	11	that	that	SCONJ
ejpam-7033	47	12	the	the	DET
ejpam-7033	47	13	iterative	iterative	NOUN
ejpam-7033	47	14	process	process	NOUN
ejpam-7033	47	15	is	be	AUX
ejpam-7033	47	16	,	,	PUNCT
ejpam-7033	47	17	in	in	ADP
ejpam-7033	47	18	fact	fact	NOUN
ejpam-7033	47	19	,	,	PUNCT
ejpam-7033	47	20	a	a	DET
ejpam-7033	47	21	contraction	contraction	NOUN
ejpam-7033	47	22	mapping	mapping	NOUN
ejpam-7033	47	23	,	,	PUNCT
ejpam-7033	47	24	the	the	DET
ejpam-7033	47	25	fixed	fix	VERB
ejpam-7033	47	26	point	point	NOUN
ejpam-7033	47	27	theorem	theorem	ADJ
ejpam-7033	47	28	(	(	PUNCT
ejpam-7033	47	29	more	more	ADV
ejpam-7033	47	30	precisely	precisely	ADV
ejpam-7033	47	31	,	,	PUNCT
ejpam-7033	47	32	banach	banach	ADV
ejpam-7033	47	33	’s	’s	PART
ejpam-7033	47	34	fixed	fix	VERB
ejpam-7033	47	35	point	point	NOUN
ejpam-7033	47	36	theorem	theorem	VERB
ejpam-7033	47	37	)	)	PUNCT
ejpam-7033	47	38	can	can	AUX
ejpam-7033	47	39	be	be	AUX
ejpam-7033	47	40	used	use	VERB
ejpam-7033	47	41	to	to	PART
ejpam-7033	47	42	establish	establish	VERB
ejpam-7033	47	43	the	the	DET
ejpam-7033	47	44	existence	existence	NOUN
ejpam-7033	47	45	and	and	CCONJ
ejpam-7033	47	46	uniqueness	uniqueness	NOUN
ejpam-7033	47	47	of	of	ADP
ejpam-7033	47	48	the	the	DET
ejpam-7033	47	49	solution	solution	NOUN
ejpam-7033	47	50	to	to	ADP
ejpam-7033	47	51	the	the	DET
ejpam-7033	47	52	problem	problem	NOUN
ejpam-7033	47	53	.	.	PUNCT
ejpam-7033	48	1	a.	a.	PROPN
ejpam-7033	48	2	arif	arif	PROPN
ejpam-7033	48	3	et	et	PROPN
ejpam-7033	48	4	al	al	PROPN
ejpam-7033	48	5	.	.	PUNCT
ejpam-7033	48	6	/	/	SYM
ejpam-7033	48	7	eur	eur	PROPN
ejpam-7033	48	8	.	.	PUNCT
ejpam-7033	49	1	j.	j.	PROPN
ejpam-7033	49	2	pure	pure	PROPN
ejpam-7033	49	3	appl	appl	PROPN
ejpam-7033	49	4	.	.	PROPN
ejpam-7033	49	5	math	math	PROPN
ejpam-7033	49	6	,	,	PUNCT
ejpam-7033	49	7	18	18	NUM
ejpam-7033	49	8	(	(	PUNCT
ejpam-7033	49	9	4	4	NUM
ejpam-7033	49	10	)	)	PUNCT
ejpam-7033	49	11	(	(	PUNCT
ejpam-7033	49	12	2025	2025	NUM
ejpam-7033	49	13	)	)	PUNCT
ejpam-7033	49	14	,	,	PUNCT
ejpam-7033	49	15	7033	7033	NUM
ejpam-7033	49	16	3	3	NUM
ejpam-7033	49	17	of	of	ADP
ejpam-7033	49	18	29	29	NUM
ejpam-7033	49	19	we	we	PRON
ejpam-7033	49	20	observe	observe	VERB
ejpam-7033	49	21	that	that	SCONJ
ejpam-7033	49	22	the	the	DET
ejpam-7033	49	23	implicit	implicit	ADJ
ejpam-7033	49	24	relation	relation	NOUN
ejpam-7033	49	25	defined	define	VERB
ejpam-7033	49	26	by	by	ADP
ejpam-7033	49	27	popa	popa	NOUN
ejpam-7033	49	28	,	,	PUNCT
ejpam-7033	49	29	can	can	AUX
ejpam-7033	49	30	be	be	AUX
ejpam-7033	49	31	generalized	generalize	VERB
ejpam-7033	49	32	to	to	ADP
ejpam-7033	49	33	vector	vector	NOUN
ejpam-7033	49	34	spaces	space	NOUN
ejpam-7033	49	35	(	(	PUNCT
ejpam-7033	49	36	[	[	X
ejpam-7033	49	37	37	37	NUM
ejpam-7033	49	38	,	,	PUNCT
ejpam-7033	49	39	38	38	NUM
ejpam-7033	49	40	]	]	PUNCT
ejpam-7033	49	41	)	)	PUNCT
ejpam-7033	49	42	.	.	PUNCT
ejpam-7033	50	1	in	in	ADP
ejpam-7033	50	2	this	this	DET
ejpam-7033	50	3	research	research	NOUN
ejpam-7033	50	4	paper	paper	NOUN
ejpam-7033	50	5	,	,	PUNCT
ejpam-7033	50	6	motivated	motivate	VERB
ejpam-7033	50	7	by	by	ADP
ejpam-7033	50	8	beg	beg	VERB
ejpam-7033	50	9	et	et	PROPN
ejpam-7033	50	10	al	al	PROPN
ejpam-7033	50	11	.	.	PUNCT
ejpam-7033	51	1	[	[	X
ejpam-7033	51	2	8	8	NUM
ejpam-7033	51	3	,	,	PUNCT
ejpam-7033	51	4	9	9	NUM
ejpam-7033	51	5	]	]	PUNCT
ejpam-7033	51	6	,	,	PUNCT
ejpam-7033	51	7	berinde	berinde	VERB
ejpam-7033	51	8	et	et	PROPN
ejpam-7033	51	9	al	al	PROPN
ejpam-7033	51	10	.	.	PUNCT
ejpam-7033	52	1	[	[	X
ejpam-7033	52	2	10	10	NUM
ejpam-7033	52	3	,	,	PUNCT
ejpam-7033	52	4	11	11	NUM
ejpam-7033	52	5	]	]	PUNCT
ejpam-7033	53	1	and	and	CCONJ
ejpam-7033	53	2	sedghi	sedghi	VERB
ejpam-7033	53	3	[	[	X
ejpam-7033	53	4	12	12	NUM
ejpam-7033	53	5	]	]	PUNCT
ejpam-7033	53	6	,	,	PUNCT
ejpam-7033	53	7	we	we	PRON
ejpam-7033	53	8	define	define	VERB
ejpam-7033	53	9	an	an	DET
ejpam-7033	53	10	ordered	order	VERB
ejpam-7033	53	11	implicit	implicit	ADJ
ejpam-7033	53	12	relation	relation	NOUN
ejpam-7033	53	13	in	in	ADP
ejpam-7033	53	14	a	a	DET
ejpam-7033	53	15	rectangular	rectangular	ADJ
ejpam-7033	53	16	cone	cone	NOUN
ejpam-7033	53	17	b	b	NOUN
ejpam-7033	53	18	-	-	PUNCT
ejpam-7033	53	19	metric	metric	ADJ
ejpam-7033	53	20	space	space	NOUN
ejpam-7033	53	21	.	.	PUNCT
ejpam-7033	54	1	we	we	PRON
ejpam-7033	54	2	contribute	contribute	VERB
ejpam-7033	54	3	with	with	ADP
ejpam-7033	54	4	a	a	DET
ejpam-7033	54	5	fixed	fix	VERB
ejpam-7033	54	6	point	point	NOUN
ejpam-7033	54	7	problem	problem	NOUN
ejpam-7033	54	8	subject	subject	ADJ
ejpam-7033	54	9	to	to	ADP
ejpam-7033	54	10	monotone	monotone	ADJ
ejpam-7033	54	11	mappings	mapping	NOUN
ejpam-7033	54	12	,	,	PUNCT
ejpam-7033	54	13	satisfying	satisfy	VERB
ejpam-7033	54	14	an	an	DET
ejpam-7033	54	15	implicit	implicit	ADJ
ejpam-7033	54	16	contraction	contraction	NOUN
ejpam-7033	54	17	.	.	PUNCT
ejpam-7033	55	1	we	we	PRON
ejpam-7033	55	2	aslo	aslo	PROPN
ejpam-7033	55	3	solve	solve	VERB
ejpam-7033	55	4	a	a	DET
ejpam-7033	55	5	homotopy	homotopy	NOUN
ejpam-7033	55	6	problem	problem	NOUN
ejpam-7033	55	7	and	and	CCONJ
ejpam-7033	55	8	show	show	VERB
ejpam-7033	55	9	existence	existence	NOUN
ejpam-7033	55	10	of	of	ADP
ejpam-7033	55	11	solution	solution	NOUN
ejpam-7033	55	12	to	to	ADP
ejpam-7033	55	13	a	a	DET
ejpam-7033	55	14	urysohn	urysohn	ADJ
ejpam-7033	55	15	integral	integral	ADJ
ejpam-7033	55	16	equation	equation	NOUN
ejpam-7033	55	17	as	as	ADP
ejpam-7033	55	18	applications	application	NOUN
ejpam-7033	55	19	of	of	ADP
ejpam-7033	55	20	the	the	DET
ejpam-7033	55	21	obtained	obtain	VERB
ejpam-7033	55	22	fixed	fix	VERB
ejpam-7033	55	23	point	point	NOUN
ejpam-7033	55	24	theorems	theorem	NOUN
ejpam-7033	55	25	.	.	PUNCT
ejpam-7033	56	1	the	the	DET
ejpam-7033	56	2	obtained	obtain	VERB
ejpam-7033	56	3	fixed	fix	VERB
ejpam-7033	56	4	point	point	NOUN
ejpam-7033	56	5	theorems	theorem	NOUN
ejpam-7033	56	6	are	be	AUX
ejpam-7033	56	7	independent	independent	ADJ
ejpam-7033	56	8	of	of	ADP
ejpam-7033	56	9	the	the	DET
ejpam-7033	56	10	observations	observation	NOUN
ejpam-7033	56	11	presented	present	VERB
ejpam-7033	56	12	by	by	ADP
ejpam-7033	56	13	ercan	ercan	PROPN
ejpam-7033	56	14	[	[	X
ejpam-7033	56	15	3	3	NUM
ejpam-7033	56	16	]	]	PUNCT
ejpam-7033	56	17	.	.	PUNCT
ejpam-7033	57	1	ercan	ercan	PROPN
ejpam-7033	57	2	worked	work	VERB
ejpam-7033	57	3	on	on	ADP
ejpam-7033	57	4	linear	linear	ADJ
ejpam-7033	57	5	contractions	contraction	NOUN
ejpam-7033	57	6	only	only	ADV
ejpam-7033	57	7	,	,	PUNCT
ejpam-7033	57	8	while	while	SCONJ
ejpam-7033	57	9	in	in	ADP
ejpam-7033	57	10	this	this	DET
ejpam-7033	57	11	paper	paper	NOUN
ejpam-7033	57	12	,	,	PUNCT
ejpam-7033	57	13	we	we	PRON
ejpam-7033	57	14	considered	consider	VERB
ejpam-7033	57	15	nonlinear	nonlinear	ADJ
ejpam-7033	57	16	contractions	contraction	NOUN
ejpam-7033	57	17	.	.	PUNCT
ejpam-7033	58	1	so	so	ADV
ejpam-7033	58	2	,	,	PUNCT
ejpam-7033	58	3	the	the	DET
ejpam-7033	58	4	obtained	obtain	VERB
ejpam-7033	58	5	results	result	NOUN
ejpam-7033	58	6	are	be	AUX
ejpam-7033	58	7	real	real	ADJ
ejpam-7033	58	8	generalizations	generalization	NOUN
ejpam-7033	58	9	and	and	CCONJ
ejpam-7033	58	10	could	could	AUX
ejpam-7033	58	11	not	not	PART
ejpam-7033	58	12	be	be	AUX
ejpam-7033	58	13	followed	follow	VERB
ejpam-7033	58	14	from	from	ADP
ejpam-7033	58	15	known	know	VERB
ejpam-7033	58	16	ones	one	NOUN
ejpam-7033	58	17	in	in	ADP
ejpam-7033	58	18	literature	literature	NOUN
ejpam-7033	58	19	.	.	PUNCT
ejpam-7033	59	1	this	this	DET
ejpam-7033	59	2	paper	paper	NOUN
ejpam-7033	59	3	has	have	AUX
ejpam-7033	59	4	been	be	AUX
ejpam-7033	59	5	organized	organize	VERB
ejpam-7033	59	6	in	in	ADP
ejpam-7033	59	7	eight	eight	NUM
ejpam-7033	59	8	sections	section	NOUN
ejpam-7033	59	9	.	.	PUNCT
ejpam-7033	60	1	section	section	NOUN
ejpam-7033	60	2	1	1	NUM
ejpam-7033	60	3	,	,	PUNCT
ejpam-7033	60	4	contains	contain	VERB
ejpam-7033	60	5	the	the	DET
ejpam-7033	60	6	introduction	introduction	NOUN
ejpam-7033	60	7	of	of	ADP
ejpam-7033	60	8	the	the	DET
ejpam-7033	60	9	topic	topic	NOUN
ejpam-7033	60	10	and	and	CCONJ
ejpam-7033	60	11	motivation	motivation	NOUN
ejpam-7033	60	12	for	for	ADP
ejpam-7033	60	13	this	this	DET
ejpam-7033	60	14	research	research	NOUN
ejpam-7033	60	15	work	work	NOUN
ejpam-7033	60	16	.	.	PUNCT
ejpam-7033	61	1	section	section	NOUN
ejpam-7033	61	2	2	2	NUM
ejpam-7033	61	3	,	,	PUNCT
ejpam-7033	61	4	consists	consist	VERB
ejpam-7033	61	5	of	of	ADP
ejpam-7033	61	6	related	related	ADJ
ejpam-7033	61	7	basic	basic	ADJ
ejpam-7033	61	8	notions	notion	NOUN
ejpam-7033	61	9	and	and	CCONJ
ejpam-7033	61	10	results	result	NOUN
ejpam-7033	61	11	.	.	PUNCT
ejpam-7033	62	1	section	section	NOUN
ejpam-7033	62	2	3	3	NUM
ejpam-7033	62	3	,	,	PUNCT
ejpam-7033	62	4	shed	shed	VERB
ejpam-7033	62	5	light	light	NOUN
ejpam-7033	62	6	on	on	ADP
ejpam-7033	62	7	the	the	DET
ejpam-7033	62	8	notion	notion	NOUN
ejpam-7033	62	9	of	of	ADP
ejpam-7033	62	10	ordered	order	VERB
ejpam-7033	62	11	implicit	implicit	ADJ
ejpam-7033	62	12	relation	relation	NOUN
ejpam-7033	62	13	and	and	CCONJ
ejpam-7033	62	14	its	its	PRON
ejpam-7033	62	15	associated	associated	ADJ
ejpam-7033	62	16	properties	property	NOUN
ejpam-7033	62	17	.	.	PUNCT
ejpam-7033	63	1	section	section	NOUN
ejpam-7033	63	2	4	4	NUM
ejpam-7033	63	3	,	,	PUNCT
ejpam-7033	63	4	explains	explain	VERB
ejpam-7033	63	5	the	the	DET
ejpam-7033	63	6	methodology	methodology	NOUN
ejpam-7033	63	7	for	for	ADP
ejpam-7033	63	8	the	the	DET
ejpam-7033	63	9	existence	existence	NOUN
ejpam-7033	63	10	of	of	ADP
ejpam-7033	63	11	fixed	fix	VERB
ejpam-7033	63	12	points	point	NOUN
ejpam-7033	63	13	of	of	ADP
ejpam-7033	63	14	the	the	DET
ejpam-7033	63	15	self	self	NOUN
ejpam-7033	63	16	mapping	mapping	NOUN
ejpam-7033	63	17	satisfying	satisfy	VERB
ejpam-7033	63	18	an	an	DET
ejpam-7033	63	19	implicit	implicit	ADJ
ejpam-7033	63	20	contractive	contractive	ADJ
ejpam-7033	63	21	condition	condition	NOUN
ejpam-7033	63	22	under	under	ADP
ejpam-7033	63	23	ordered	order	VERB
ejpam-7033	63	24	implicit	implicit	ADJ
ejpam-7033	63	25	relation	relation	NOUN
ejpam-7033	63	26	.	.	PUNCT
ejpam-7033	64	1	section	section	NOUN
ejpam-7033	64	2	5	5	NUM
ejpam-7033	64	3	,	,	PUNCT
ejpam-7033	64	4	contains	contain	VERB
ejpam-7033	64	5	the	the	DET
ejpam-7033	64	6	examples	example	NOUN
ejpam-7033	64	7	that	that	PRON
ejpam-7033	64	8	explain	explain	VERB
ejpam-7033	64	9	the	the	DET
ejpam-7033	64	10	hypotheses	hypothesis	NOUN
ejpam-7033	64	11	of	of	ADP
ejpam-7033	64	12	the	the	DET
ejpam-7033	64	13	fixed	fix	VERB
ejpam-7033	64	14	point	point	NOUN
ejpam-7033	64	15	theorems	theorem	NOUN
ejpam-7033	64	16	stated	state	VERB
ejpam-7033	64	17	in	in	ADP
ejpam-7033	64	18	section	section	NOUN
ejpam-7033	64	19	4	4	NUM
ejpam-7033	64	20	.	.	PUNCT
ejpam-7033	65	1	it	it	PRON
ejpam-7033	65	2	also	also	ADV
ejpam-7033	65	3	contains	contain	VERB
ejpam-7033	65	4	the	the	DET
ejpam-7033	65	5	corollaries	corollary	NOUN
ejpam-7033	65	6	of	of	ADP
ejpam-7033	65	7	the	the	DET
ejpam-7033	65	8	main	main	ADJ
ejpam-7033	65	9	theorem	theorem	NOUN
ejpam-7033	65	10	.	.	PROPN
ejpam-7033	65	11	section	section	NOUN
ejpam-7033	65	12	6	6	NUM
ejpam-7033	65	13	,	,	PUNCT
ejpam-7033	65	14	consists	consist	VERB
ejpam-7033	65	15	of	of	ADP
ejpam-7033	65	16	a	a	DET
ejpam-7033	65	17	homotopy	homotopy	NOUN
ejpam-7033	65	18	result	result	NOUN
ejpam-7033	65	19	as	as	ADP
ejpam-7033	65	20	an	an	DET
ejpam-7033	65	21	application	application	NOUN
ejpam-7033	65	22	of	of	ADP
ejpam-7033	65	23	the	the	DET
ejpam-7033	65	24	main	main	ADJ
ejpam-7033	65	25	theorem	theorem	NOUN
ejpam-7033	65	26	and	and	CCONJ
ejpam-7033	65	27	a	a	DET
ejpam-7033	65	28	result	result	NOUN
ejpam-7033	65	29	about	about	ADP
ejpam-7033	65	30	human	human	ADJ
ejpam-7033	65	31	aging	age	VERB
ejpam-7033	65	32	process	process	NOUN
ejpam-7033	65	33	that	that	PRON
ejpam-7033	65	34	uses	use	VERB
ejpam-7033	65	35	homotopy	homotopy	NOUN
ejpam-7033	65	36	result	result	NOUN
ejpam-7033	65	37	.	.	PUNCT
ejpam-7033	66	1	section	section	NOUN
ejpam-7033	66	2	7	7	NUM
ejpam-7033	66	3	,	,	PUNCT
ejpam-7033	66	4	shed	shed	VERB
ejpam-7033	66	5	light	light	NOUN
ejpam-7033	66	6	on	on	ADP
ejpam-7033	66	7	the	the	DET
ejpam-7033	66	8	process	process	NOUN
ejpam-7033	66	9	of	of	ADP
ejpam-7033	66	10	application	application	NOUN
ejpam-7033	66	11	of	of	ADP
ejpam-7033	66	12	main	main	ADJ
ejpam-7033	66	13	theorem	theorem	NOUN
ejpam-7033	66	14	to	to	PART
ejpam-7033	66	15	show	show	VERB
ejpam-7033	66	16	the	the	DET
ejpam-7033	66	17	existence	existence	NOUN
ejpam-7033	66	18	of	of	ADP
ejpam-7033	66	19	solution	solution	NOUN
ejpam-7033	66	20	to	to	PART
ejpam-7033	66	21	urysohn	urysohn	VERB
ejpam-7033	66	22	integral	integral	ADJ
ejpam-7033	66	23	equation	equation	NOUN
ejpam-7033	66	24	.	.	PUNCT
ejpam-7033	67	1	section	section	NOUN
ejpam-7033	67	2	8	8	NUM
ejpam-7033	67	3	,	,	PUNCT
ejpam-7033	67	4	contains	contain	VERB
ejpam-7033	67	5	the	the	DET
ejpam-7033	67	6	conclusion	conclusion	NOUN
ejpam-7033	67	7	of	of	ADP
ejpam-7033	67	8	the	the	DET
ejpam-7033	67	9	research	research	NOUN
ejpam-7033	67	10	work	work	NOUN
ejpam-7033	67	11	done	do	VERB
ejpam-7033	67	12	in	in	ADP
ejpam-7033	67	13	this	this	DET
ejpam-7033	67	14	paper	paper	NOUN
ejpam-7033	67	15	.	.	PUNCT
ejpam-7033	68	1	2	2	X
ejpam-7033	68	2	.	.	X
ejpam-7033	68	3	preliminaries	preliminary	NOUN
ejpam-7033	68	4	this	this	DET
ejpam-7033	68	5	section	section	NOUN
ejpam-7033	68	6	consists	consist	VERB
ejpam-7033	68	7	of	of	ADP
ejpam-7033	68	8	some	some	DET
ejpam-7033	68	9	basic	basic	ADJ
ejpam-7033	68	10	notions	notion	NOUN
ejpam-7033	68	11	and	and	CCONJ
ejpam-7033	68	12	related	related	ADJ
ejpam-7033	68	13	axioms	axiom	NOUN
ejpam-7033	68	14	of	of	ADP
ejpam-7033	68	15	cone	cone	NOUN
ejpam-7033	68	16	,	,	PUNCT
ejpam-7033	68	17	cone	cone	NOUN
ejpam-7033	68	18	metric	metric	ADJ
ejpam-7033	68	19	space	space	NOUN
ejpam-7033	68	20	,	,	PUNCT
ejpam-7033	68	21	cone	cone	NOUN
ejpam-7033	68	22	b	b	X
ejpam-7033	68	23	-	-	PUNCT
ejpam-7033	68	24	metric	metric	ADJ
ejpam-7033	68	25	space	space	NOUN
ejpam-7033	68	26	,	,	PUNCT
ejpam-7033	68	27	rectangular	rectangular	ADJ
ejpam-7033	68	28	cone	cone	NOUN
ejpam-7033	68	29	metric	metric	ADJ
ejpam-7033	68	30	space	space	NOUN
ejpam-7033	68	31	and	and	CCONJ
ejpam-7033	68	32	rectangular	rectangular	ADJ
ejpam-7033	68	33	cone	cone	NOUN
ejpam-7033	68	34	b	b	NOUN
ejpam-7033	68	35	-	-	PUNCT
ejpam-7033	68	36	metric	metric	ADJ
ejpam-7033	68	37	space	space	NOUN
ejpam-7033	68	38	.	.	PUNCT
ejpam-7033	69	1	throughout	throughout	ADP
ejpam-7033	69	2	in	in	ADP
ejpam-7033	69	3	this	this	DET
ejpam-7033	69	4	article	article	NOUN
ejpam-7033	69	5	,	,	PUNCT
ejpam-7033	69	6	we	we	PRON
ejpam-7033	69	7	will	will	AUX
ejpam-7033	69	8	take	take	VERB
ejpam-7033	69	9	e	e	NOUN
ejpam-7033	69	10	as	as	ADP
ejpam-7033	69	11	a	a	DET
ejpam-7033	69	12	real	real	ADJ
ejpam-7033	69	13	banach	banach	NOUN
ejpam-7033	69	14	space	space	NOUN
ejpam-7033	69	15	.	.	PUNCT
ejpam-7033	70	1	definition	definition	NOUN
ejpam-7033	70	2	1	1	NUM
ejpam-7033	70	3	.	.	PUNCT
ejpam-7033	71	1	[	[	X
ejpam-7033	71	2	21	21	NUM
ejpam-7033	71	3	]	]	PUNCT
ejpam-7033	71	4	let	let	VERB
ejpam-7033	71	5	c	c	NOUN
ejpam-7033	71	6	⊆	⊆	NUM
ejpam-7033	71	7	e	e	NOUN
ejpam-7033	71	8	,	,	PUNCT
ejpam-7033	71	9	then	then	ADV
ejpam-7033	71	10	c	c	PROPN
ejpam-7033	71	11	is	be	AUX
ejpam-7033	71	12	said	say	VERB
ejpam-7033	71	13	to	to	PART
ejpam-7033	71	14	be	be	AUX
ejpam-7033	71	15	a	a	DET
ejpam-7033	71	16	cone	cone	NOUN
ejpam-7033	71	17	if	if	SCONJ
ejpam-7033	71	18	it	it	PRON
ejpam-7033	71	19	admits	admit	VERB
ejpam-7033	71	20	the	the	DET
ejpam-7033	71	21	following	following	ADJ
ejpam-7033	71	22	axioms	axiom	NOUN
ejpam-7033	71	23	:	:	PUNCT
ejpam-7033	71	24	(	(	PUNCT
ejpam-7033	71	25	1	1	X
ejpam-7033	71	26	)	)	PUNCT
ejpam-7033	71	27	c	c	NOUN
ejpam-7033	71	28	is	be	AUX
ejpam-7033	71	29	non	non	X
ejpam-7033	71	30	empty	empty	ADJ
ejpam-7033	71	31	and	and	CCONJ
ejpam-7033	71	32	closed	closed	ADJ
ejpam-7033	71	33	set	set	NOUN
ejpam-7033	71	34	,	,	PUNCT
ejpam-7033	71	35	and	and	CCONJ
ejpam-7033	72	1	c	c	PROPN
ejpam-7033	72	2	̸=	̸=	PROPN
ejpam-7033	72	3	{	{	PUNCT
ejpam-7033	72	4	0	0	NUM
ejpam-7033	72	5	}	}	PUNCT
ejpam-7033	72	6	;	;	PUNCT
ejpam-7033	72	7	(	(	PUNCT
ejpam-7033	72	8	2	2	X
ejpam-7033	72	9	)	)	PUNCT
ejpam-7033	72	10	px+	px+	NOUN
ejpam-7033	72	11	qy	qy	PROPN
ejpam-7033	72	12	∈	∈	PROPN
ejpam-7033	72	13	c	c	PROPN
ejpam-7033	72	14	,	,	PUNCT
ejpam-7033	72	15	∀	∀	X
ejpam-7033	72	16	x	x	NOUN
ejpam-7033	72	17	,	,	PUNCT
ejpam-7033	72	18	y	y	PROPN
ejpam-7033	72	19	∈	∈	PROPN
ejpam-7033	72	20	c	c	NOUN
ejpam-7033	72	21	where	where	SCONJ
ejpam-7033	72	22	p	p	X
ejpam-7033	72	23	,	,	PUNCT
ejpam-7033	72	24	q	q	PUNCT
ejpam-7033	72	25	∈	∈	PROPN
ejpam-7033	72	26	r	r	NOUN
ejpam-7033	72	27	and	and	CCONJ
ejpam-7033	72	28	a	a	PRON
ejpam-7033	72	29	,	,	PUNCT
ejpam-7033	72	30	b	b	PROPN
ejpam-7033	72	31	≥	≥	NOUN
ejpam-7033	72	32	0	0	NUM
ejpam-7033	72	33	;	;	PUNCT
ejpam-7033	72	34	(	(	PUNCT
ejpam-7033	72	35	3	3	X
ejpam-7033	72	36	)	)	PUNCT
ejpam-7033	72	37	c	c	NOUN
ejpam-7033	72	38	∩	∩	NOUN
ejpam-7033	72	39	(	(	PUNCT
ejpam-7033	72	40	−c	−c	NOUN
ejpam-7033	72	41	)	)	PUNCT
ejpam-7033	72	42	=	=	PUNCT
ejpam-7033	72	43	{	{	PUNCT
ejpam-7033	72	44	0	0	NUM
ejpam-7033	72	45	}	}	PUNCT
ejpam-7033	72	46	.	.	PUNCT
ejpam-7033	73	1	for	for	ADP
ejpam-7033	73	2	c	c	PROPN
ejpam-7033	73	3	⊂	⊂	PROPN
ejpam-7033	73	4	e	e	PROPN
ejpam-7033	73	5	,	,	PUNCT
ejpam-7033	73	6	the	the	DET
ejpam-7033	73	7	partial	partial	ADJ
ejpam-7033	73	8	order	order	NOUN
ejpam-7033	73	9	⪯	⪯	NOUN
ejpam-7033	73	10	in	in	ADP
ejpam-7033	73	11	c	c	PROPN
ejpam-7033	73	12	is	be	AUX
ejpam-7033	73	13	taken	take	VERB
ejpam-7033	73	14	as	as	ADP
ejpam-7033	73	15	:	:	PUNCT
ejpam-7033	73	16	x	x	PUNCT
ejpam-7033	73	17	⪯	⪯	PROPN
ejpam-7033	73	18	y	y	PROPN
ejpam-7033	73	19	⇔	⇔	PROPN
ejpam-7033	73	20	y	y	PROPN
ejpam-7033	73	21	−	−	PROPN
ejpam-7033	73	22	x	x	SYM
ejpam-7033	73	23	∈	∈	PROPN
ejpam-7033	73	24	cfor	cfor	ADP
ejpam-7033	73	25	allx	allx	NOUN
ejpam-7033	73	26	,	,	PUNCT
ejpam-7033	73	27	y	y	PROPN
ejpam-7033	73	28	∈	∈	PROPN
ejpam-7033	73	29	e	e	X
ejpam-7033	73	30	.	.	PUNCT
ejpam-7033	74	1	the	the	DET
ejpam-7033	74	2	expression	expression	NOUN
ejpam-7033	74	3	x≪	x≪	PROPN
ejpam-7033	75	1	y	y	PROPN
ejpam-7033	75	2	shows	show	VERB
ejpam-7033	75	3	that	that	SCONJ
ejpam-7033	75	4	y	y	PROPN
ejpam-7033	76	1	−	−	NOUN
ejpam-7033	76	2	x	x	SYM
ejpam-7033	76	3	∈	∈	PROPN
ejpam-7033	76	4	c	c	X
ejpam-7033	76	5	◦	◦	NOUN
ejpam-7033	76	6	(the	(the	DET
ejpam-7033	76	7	interior	interior	NOUN
ejpam-7033	76	8	of	of	ADP
ejpam-7033	76	9	c	c	PROPN
ejpam-7033	76	10	)	)	PUNCT
ejpam-7033	76	11	.	.	PUNCT
ejpam-7033	77	1	the	the	DET
ejpam-7033	77	2	cone	cone	NOUN
ejpam-7033	77	3	c	c	NOUN
ejpam-7033	77	4	⊆	⊆	NUM
ejpam-7033	77	5	e	e	NOUN
ejpam-7033	77	6	is	be	AUX
ejpam-7033	77	7	called	call	VERB
ejpam-7033	77	8	normal	normal	ADJ
ejpam-7033	77	9	,	,	PUNCT
ejpam-7033	77	10	if	if	SCONJ
ejpam-7033	77	11	there	there	PRON
ejpam-7033	77	12	exists	exist	VERB
ejpam-7033	77	13	k	k	PROPN
ejpam-7033	77	14	>	>	X
ejpam-7033	77	15	0	0	NUM
ejpam-7033	77	16	such	such	ADJ
ejpam-7033	77	17	that	that	PRON
ejpam-7033	77	18	0	0	NUM
ejpam-7033	77	19	⪯	⪯	NOUN
ejpam-7033	77	20	x	x	AUX
ejpam-7033	77	21	⪯	⪯	AUX
ejpam-7033	77	22	y	y	PROPN
ejpam-7033	77	23	⇒	⇒	VERB
ejpam-7033	77	24	∥x∥	∥x∥	NOUN
ejpam-7033	77	25	≤	≤	ADJ
ejpam-7033	77	26	k∥y∥.	k∥y∥.	NOUN
ejpam-7033	77	27	let	let	VERB
ejpam-7033	77	28	ℜ	ℜ	PROPN
ejpam-7033	77	29	denotes	denote	VERB
ejpam-7033	77	30	the	the	DET
ejpam-7033	77	31	partial	partial	ADJ
ejpam-7033	77	32	order	order	NOUN
ejpam-7033	77	33	in	in	ADP
ejpam-7033	77	34	an	an	DET
ejpam-7033	77	35	ordinary	ordinary	ADJ
ejpam-7033	77	36	set	set	NOUN
ejpam-7033	77	37	x	x	PUNCT
ejpam-7033	77	38	and	and	CCONJ
ejpam-7033	77	39	⪯	⪯	NOUN
ejpam-7033	77	40	be	be	AUX
ejpam-7033	77	41	a	a	DET
ejpam-7033	77	42	partial	partial	ADJ
ejpam-7033	77	43	order	order	NOUN
ejpam-7033	77	44	in	in	ADP
ejpam-7033	77	45	the	the	DET
ejpam-7033	77	46	cone	cone	NOUN
ejpam-7033	77	47	c	c	NOUN
ejpam-7033	77	48	⊆	⊆	NUM
ejpam-7033	77	49	e	e	X
ejpam-7033	77	50	.	.	PUNCT
ejpam-7033	78	1	for	for	SCONJ
ejpam-7033	78	2	x	x	SYM
ejpam-7033	78	3	⊆	⊆	NUM
ejpam-7033	78	4	e	e	NOUN
ejpam-7033	78	5	,	,	PUNCT
ejpam-7033	78	6	ℜ	ℜ	PROPN
ejpam-7033	78	7	and	and	CCONJ
ejpam-7033	78	8	⪯	⪯	PROPN
ejpam-7033	78	9	assumed	assume	VERB
ejpam-7033	78	10	to	to	PART
ejpam-7033	78	11	be	be	AUX
ejpam-7033	78	12	same	same	ADJ
ejpam-7033	78	13	.	.	PUNCT
ejpam-7033	79	1	a.	a.	PROPN
ejpam-7033	79	2	arif	arif	PROPN
ejpam-7033	79	3	et	et	PROPN
ejpam-7033	79	4	al	al	PROPN
ejpam-7033	79	5	.	.	PUNCT
ejpam-7033	79	6	/	/	SYM
ejpam-7033	79	7	eur	eur	PROPN
ejpam-7033	79	8	.	.	PUNCT
ejpam-7033	80	1	j.	j.	PROPN
ejpam-7033	80	2	pure	pure	PROPN
ejpam-7033	80	3	appl	appl	PROPN
ejpam-7033	80	4	.	.	PROPN
ejpam-7033	80	5	math	math	PROPN
ejpam-7033	80	6	,	,	PUNCT
ejpam-7033	80	7	18	18	NUM
ejpam-7033	80	8	(	(	PUNCT
ejpam-7033	80	9	4	4	NUM
ejpam-7033	80	10	)	)	PUNCT
ejpam-7033	80	11	(	(	PUNCT
ejpam-7033	80	12	2025	2025	NUM
ejpam-7033	80	13	)	)	PUNCT
ejpam-7033	80	14	,	,	PUNCT
ejpam-7033	80	15	7033	7033	NUM
ejpam-7033	80	16	4	4	NUM
ejpam-7033	80	17	of	of	ADP
ejpam-7033	80	18	29	29	NUM
ejpam-7033	80	19	definition	definition	NOUN
ejpam-7033	80	20	2	2	NUM
ejpam-7033	80	21	.	.	PUNCT
ejpam-7033	81	1	[	[	X
ejpam-7033	81	2	21	21	NUM
ejpam-7033	81	3	]	]	X
ejpam-7033	81	4	let	let	VERB
ejpam-7033	81	5	x	x	SYM
ejpam-7033	81	6	̸=	̸=	PROPN
ejpam-7033	81	7	∅	∅	NOUN
ejpam-7033	81	8	and	and	CCONJ
ejpam-7033	81	9	dc	dc	PROPN
ejpam-7033	81	10	:	:	PUNCT
ejpam-7033	81	11	x	x	X
ejpam-7033	81	12	×x	×x	VERB
ejpam-7033	81	13	7→	7→	NUM
ejpam-7033	81	14	e	e	NOUN
ejpam-7033	81	15	satisfies	satisfy	VERB
ejpam-7033	81	16	the	the	DET
ejpam-7033	81	17	following	follow	VERB
ejpam-7033	81	18	axioms	axiom	NOUN
ejpam-7033	81	19	:	:	PUNCT
ejpam-7033	81	20	(	(	PUNCT
ejpam-7033	81	21	d1	d1	NOUN
ejpam-7033	81	22	)	)	PUNCT
ejpam-7033	81	23	dc(ℓ	dc(ℓ	PUNCT
ejpam-7033	81	24	,	,	PUNCT
ejpam-7033	81	25	r	r	NOUN
ejpam-7033	81	26	)	)	PUNCT
ejpam-7033	81	27	⪰	⪰	NOUN
ejpam-7033	81	28	0	0	NUM
ejpam-7033	81	29	,	,	PUNCT
ejpam-7033	81	30	∀	∀	X
ejpam-7033	81	31	ℓ	ℓ	NOUN
ejpam-7033	81	32	,	,	PUNCT
ejpam-7033	81	33	r	r	NOUN
ejpam-7033	81	34	∈	∈	PROPN
ejpam-7033	81	35	x	x	X
ejpam-7033	81	36	and	and	CCONJ
ejpam-7033	81	37	dc(ℓ	dc(ℓ	NUM
ejpam-7033	81	38	,	,	PUNCT
ejpam-7033	81	39	r	r	NOUN
ejpam-7033	81	40	)	)	PUNCT
ejpam-7033	81	41	=	=	SYM
ejpam-7033	81	42	0	0	NUM
ejpam-7033	82	1	⇔	⇔	PROPN
ejpam-7033	82	2	ℓ	ℓ	PROPN
ejpam-7033	82	3	=	=	SYM
ejpam-7033	82	4	r	r	NOUN
ejpam-7033	82	5	;	;	PUNCT
ejpam-7033	82	6	(	(	PUNCT
ejpam-7033	82	7	d2	d2	PROPN
ejpam-7033	82	8	)	)	PUNCT
ejpam-7033	82	9	dc(ℓ	dc(ℓ	PUNCT
ejpam-7033	82	10	,	,	PUNCT
ejpam-7033	82	11	r	r	NOUN
ejpam-7033	82	12	)	)	PUNCT
ejpam-7033	82	13	=	=	SYM
ejpam-7033	82	14	dc(r	dc(r	NOUN
ejpam-7033	82	15	,	,	PUNCT
ejpam-7033	82	16	ℓ	ℓ	NOUN
ejpam-7033	82	17	)	)	PUNCT
ejpam-7033	82	18	;	;	PUNCT
ejpam-7033	82	19	(	(	PUNCT
ejpam-7033	82	20	d3	d3	PROPN
ejpam-7033	82	21	)	)	PUNCT
ejpam-7033	82	22	dc(ℓ	dc(ℓ	PUNCT
ejpam-7033	82	23	,	,	PUNCT
ejpam-7033	82	24	r1	r1	PROPN
ejpam-7033	82	25	)	)	PUNCT
ejpam-7033	82	26	⪯	⪯	NOUN
ejpam-7033	82	27	dc(ℓ	dc(ℓ	X
ejpam-7033	82	28	,	,	PUNCT
ejpam-7033	82	29	r	r	NOUN
ejpam-7033	82	30	)	)	PUNCT
ejpam-7033	82	31	+	+	CCONJ
ejpam-7033	82	32	dc(r	dc(r	NOUN
ejpam-7033	82	33	,	,	PUNCT
ejpam-7033	82	34	r1	r1	PROPN
ejpam-7033	82	35	)	)	PUNCT
ejpam-7033	82	36	,	,	PUNCT
ejpam-7033	82	37	∀	∀	X
ejpam-7033	82	38	ℓ	ℓ	NOUN
ejpam-7033	82	39	,	,	PUNCT
ejpam-7033	82	40	r	r	NOUN
ejpam-7033	82	41	,	,	PUNCT
ejpam-7033	82	42	r1	r1	PROPN
ejpam-7033	82	43	∈	∈	PROPN
ejpam-7033	82	44	x.	x.	NOUN
ejpam-7033	82	45	then	then	ADV
ejpam-7033	82	46	dc	dc	PROPN
ejpam-7033	82	47	is	be	AUX
ejpam-7033	82	48	called	call	VERB
ejpam-7033	82	49	cone	cone	NOUN
ejpam-7033	82	50	metric	metric	NOUN
ejpam-7033	82	51	and	and	CCONJ
ejpam-7033	82	52	the	the	DET
ejpam-7033	82	53	pair	pair	NOUN
ejpam-7033	82	54	(	(	PUNCT
ejpam-7033	82	55	x	x	NOUN
ejpam-7033	82	56	,	,	PUNCT
ejpam-7033	82	57	dc	dc	PROPN
ejpam-7033	82	58	)	)	PUNCT
ejpam-7033	82	59	represents	represent	VERB
ejpam-7033	82	60	a	a	DET
ejpam-7033	82	61	cone	cone	NOUN
ejpam-7033	82	62	metric	metric	ADJ
ejpam-7033	82	63	space	space	NOUN
ejpam-7033	82	64	.	.	PUNCT
ejpam-7033	82	65	example	example	NOUN
ejpam-7033	83	1	1	1	NUM
ejpam-7033	83	2	.	.	PUNCT
ejpam-7033	84	1	[	[	X
ejpam-7033	84	2	36	36	NUM
ejpam-7033	84	3	]	]	PUNCT
ejpam-7033	84	4	consider	consider	VERB
ejpam-7033	84	5	x	x	X
ejpam-7033	84	6	=	=	SYM
ejpam-7033	84	7	r	r	NOUN
ejpam-7033	84	8	,	,	PUNCT
ejpam-7033	84	9	e	e	NOUN
ejpam-7033	84	10	=	=	SYM
ejpam-7033	84	11	r2	r2	PROPN
ejpam-7033	84	12	with	with	ADP
ejpam-7033	84	13	cone	cone	NOUN
ejpam-7033	84	14	c	c	NOUN
ejpam-7033	84	15	=	=	SYM
ejpam-7033	84	16	{	{	PUNCT
ejpam-7033	84	17	(	(	PUNCT
ejpam-7033	84	18	ℓ	ℓ	INTJ
ejpam-7033	84	19	,	,	PUNCT
ejpam-7033	84	20	y	y	NOUN
ejpam-7033	84	21	)	)	PUNCT
ejpam-7033	84	22	∈	∈	PROPN
ejpam-7033	84	23	e	e	NOUN
ejpam-7033	84	24	:	:	PUNCT
ejpam-7033	84	25	ℓ	ℓ	X
ejpam-7033	84	26	,	,	PUNCT
ejpam-7033	84	27	y	y	PROPN
ejpam-7033	84	28	≥	≥	NUM
ejpam-7033	84	29	0	0	NUM
ejpam-7033	84	30	}	}	PUNCT
ejpam-7033	84	31	.	.	PUNCT
ejpam-7033	85	1	take	take	VERB
ejpam-7033	85	2	dc	dc	PROPN
ejpam-7033	85	3	:	:	PUNCT
ejpam-7033	85	4	x	x	X
ejpam-7033	85	5	×x	×x	ADP
ejpam-7033	85	6	→	→	SYM
ejpam-7033	85	7	e	e	NOUN
ejpam-7033	85	8	,	,	PUNCT
ejpam-7033	85	9	in	in	ADP
ejpam-7033	85	10	a	a	DET
ejpam-7033	85	11	way	way	NOUN
ejpam-7033	85	12	dc(ℓ	dc(ℓ	X
ejpam-7033	85	13	,	,	PUNCT
ejpam-7033	85	14	y	y	NOUN
ejpam-7033	85	15	)	)	PUNCT
ejpam-7033	85	16	=	=	SYM
ejpam-7033	86	1	(	(	PUNCT
ejpam-7033	86	2	|	|	ADV
ejpam-7033	86	3	ℓ−	ℓ−	PROPN
ejpam-7033	86	4	y	y	NOUN
ejpam-7033	86	5	|	|	NOUN
ejpam-7033	86	6	,	,	PUNCT
ejpam-7033	86	7	δ	δ	PROPN
ejpam-7033	86	8	|	|	ADV
ejpam-7033	86	9	ℓ−	ℓ−	VERB
ejpam-7033	86	10	y	y	PROPN
ejpam-7033	86	11	|	|	NOUN
ejpam-7033	86	12	)	)	PUNCT
ejpam-7033	86	13	,	,	PUNCT
ejpam-7033	86	14	here	here	ADV
ejpam-7033	86	15	δ	δ	PROPN
ejpam-7033	86	16	≥	≥	X
ejpam-7033	86	17	0	0	NUM
ejpam-7033	86	18	(	(	PUNCT
ejpam-7033	86	19	scalar	scalar	ADJ
ejpam-7033	86	20	)	)	PUNCT
ejpam-7033	86	21	.	.	PUNCT
ejpam-7033	87	1	subsequently	subsequently	ADV
ejpam-7033	87	2	dc	dc	PROPN
ejpam-7033	87	3	represents	represent	VERB
ejpam-7033	87	4	a	a	DET
ejpam-7033	87	5	cone	cone	NOUN
ejpam-7033	87	6	metric	metric	NOUN
ejpam-7033	87	7	,	,	PUNCT
ejpam-7033	87	8	and	and	CCONJ
ejpam-7033	87	9	(	(	PUNCT
ejpam-7033	87	10	x	x	X
ejpam-7033	87	11	,	,	PUNCT
ejpam-7033	87	12	dc	dc	PROPN
ejpam-7033	87	13	)	)	PUNCT
ejpam-7033	87	14	a	a	DET
ejpam-7033	87	15	cone	cone	NOUN
ejpam-7033	87	16	metric	metric	ADJ
ejpam-7033	87	17	space	space	NOUN
ejpam-7033	87	18	.	.	PUNCT
ejpam-7033	88	1	proposition	proposition	NOUN
ejpam-7033	88	2	3	3	NUM
ejpam-7033	88	3	.	.	PUNCT
ejpam-7033	89	1	[	[	X
ejpam-7033	89	2	36	36	NUM
ejpam-7033	89	3	]	]	PUNCT
ejpam-7033	89	4	let	let	VERB
ejpam-7033	89	5	c	c	PRON
ejpam-7033	89	6	be	be	AUX
ejpam-7033	89	7	a	a	DET
ejpam-7033	89	8	cone	cone	NOUN
ejpam-7033	89	9	with	with	ADP
ejpam-7033	89	10	cone	cone	NOUN
ejpam-7033	89	11	metric	metric	ADJ
ejpam-7033	89	12	space	space	NOUN
ejpam-7033	89	13	(	(	PUNCT
ejpam-7033	89	14	x	x	X
ejpam-7033	89	15	,	,	PUNCT
ejpam-7033	89	16	dc	dc	PROPN
ejpam-7033	89	17	)	)	PUNCT
ejpam-7033	89	18	.	.	PUNCT
ejpam-7033	90	1	then	then	ADV
ejpam-7033	90	2	for	for	ADP
ejpam-7033	90	3	x	x	PROPN
ejpam-7033	90	4	,	,	PUNCT
ejpam-7033	90	5	ℓ	ℓ	PROPN
ejpam-7033	90	6	,	,	PUNCT
ejpam-7033	90	7	ϱ	ϱ	ADP
ejpam-7033	90	8	∈	∈	PROPN
ejpam-7033	90	9	e	e	NOUN
ejpam-7033	90	10	,	,	PUNCT
ejpam-7033	90	11	we	we	PRON
ejpam-7033	90	12	have	have	VERB
ejpam-7033	90	13	(	(	PUNCT
ejpam-7033	90	14	1	1	X
ejpam-7033	90	15	)	)	PUNCT
ejpam-7033	90	16	if	if	SCONJ
ejpam-7033	90	17	x	x	PRON
ejpam-7033	90	18	⪯	⪯	VERB
ejpam-7033	90	19	αx	αx	ADV
ejpam-7033	90	20	and	and	CCONJ
ejpam-7033	90	21	α	α	PRON
ejpam-7033	90	22	∈	∈	PROPN
ejpam-7033	91	1	[	[	X
ejpam-7033	91	2	0	0	NUM
ejpam-7033	91	3	,	,	PUNCT
ejpam-7033	91	4	1	1	NUM
ejpam-7033	91	5	)	)	PUNCT
ejpam-7033	91	6	,	,	PUNCT
ejpam-7033	91	7	then	then	ADV
ejpam-7033	91	8	x	x	X
ejpam-7033	91	9	=	=	NOUN
ejpam-7033	92	1	0	0	NUM
ejpam-7033	92	2	.	.	PUNCT
ejpam-7033	93	1	(	(	PUNCT
ejpam-7033	93	2	2	2	X
ejpam-7033	93	3	)	)	PUNCT
ejpam-7033	93	4	if	if	SCONJ
ejpam-7033	93	5	0	0	NUM
ejpam-7033	93	6	⪯	⪯	X
ejpam-7033	93	7	x≪	x≪	PROPN
ejpam-7033	93	8	ℓ	ℓ	PROPN
ejpam-7033	93	9	for	for	ADP
ejpam-7033	93	10	each	each	DET
ejpam-7033	93	11	0	0	NUM
ejpam-7033	93	12	≪	≪	PROPN
ejpam-7033	93	13	ℓ	ℓ	NOUN
ejpam-7033	93	14	,	,	PUNCT
ejpam-7033	93	15	then	then	ADV
ejpam-7033	93	16	x	x	X
ejpam-7033	93	17	=	=	NOUN
ejpam-7033	93	18	0	0	NUM
ejpam-7033	93	19	.	.	PUNCT
ejpam-7033	94	1	(	(	PUNCT
ejpam-7033	94	2	3	3	X
ejpam-7033	94	3	)	)	PUNCT
ejpam-7033	94	4	if	if	SCONJ
ejpam-7033	94	5	x	x	X
ejpam-7033	94	6	⪯	⪯	PROPN
ejpam-7033	94	7	ℓ	ℓ	PROPN
ejpam-7033	94	8	and	and	CCONJ
ejpam-7033	94	9	ℓ≪	ℓ≪	PROPN
ejpam-7033	94	10	ϱ	ϱ	VERB
ejpam-7033	94	11	,	,	PUNCT
ejpam-7033	94	12	then	then	ADV
ejpam-7033	94	13	x≪	x≪	PROPN
ejpam-7033	94	14	ϱ.	ϱ.	PROPN
ejpam-7033	94	15	definition	definition	NOUN
ejpam-7033	94	16	4	4	NUM
ejpam-7033	94	17	.	.	PUNCT
ejpam-7033	95	1	[	[	X
ejpam-7033	95	2	34	34	NUM
ejpam-7033	95	3	]	]	PUNCT
ejpam-7033	95	4	let	let	VERB
ejpam-7033	95	5	db	db	VERB
ejpam-7033	95	6	:	:	PUNCT
ejpam-7033	95	7	x	x	PROPN
ejpam-7033	95	8	×x	×x	VERB
ejpam-7033	95	9	7→	7→	NUM
ejpam-7033	95	10	e	e	NOUN
ejpam-7033	95	11	fulfills	fulfill	VERB
ejpam-7033	95	12	the	the	DET
ejpam-7033	95	13	following	follow	VERB
ejpam-7033	95	14	axioms	axiom	NOUN
ejpam-7033	95	15	:	:	PUNCT
ejpam-7033	95	16	(	(	PUNCT
ejpam-7033	95	17	db1	db1	NOUN
ejpam-7033	95	18	)	)	PUNCT
ejpam-7033	95	19	0	0	NUM
ejpam-7033	96	1	⪯	⪯	PROPN
ejpam-7033	96	2	db(p	db(p	PROPN
ejpam-7033	96	3	,	,	PUNCT
ejpam-7033	96	4	y	y	NOUN
ejpam-7033	96	5	)	)	PUNCT
ejpam-7033	96	6	along	along	ADP
ejpam-7033	96	7	with	with	ADP
ejpam-7033	96	8	db(p	db(p	PROPN
ejpam-7033	96	9	,	,	PUNCT
ejpam-7033	96	10	y	y	NOUN
ejpam-7033	96	11	)	)	PUNCT
ejpam-7033	96	12	=	=	SYM
ejpam-7033	96	13	0	0	NUM
ejpam-7033	96	14	⇔	⇔	PROPN
ejpam-7033	96	15	p	p	PROPN
ejpam-7033	96	16	=	=	PROPN
ejpam-7033	96	17	y	y	PROPN
ejpam-7033	96	18	;	;	PUNCT
ejpam-7033	96	19	(	(	PUNCT
ejpam-7033	96	20	db2	db2	PROPN
ejpam-7033	96	21	)	)	PUNCT
ejpam-7033	96	22	db(p	db(p	PROPN
ejpam-7033	96	23	,	,	PUNCT
ejpam-7033	96	24	y	y	NOUN
ejpam-7033	96	25	)	)	PUNCT
ejpam-7033	96	26	=	=	PUNCT
ejpam-7033	97	1	db(y	db(y	ADJ
ejpam-7033	97	2	,	,	PUNCT
ejpam-7033	97	3	p	p	NOUN
ejpam-7033	97	4	)	)	PUNCT
ejpam-7033	97	5	;	;	PUNCT
ejpam-7033	97	6	(	(	PUNCT
ejpam-7033	97	7	db3	db3	PROPN
ejpam-7033	97	8	)	)	PUNCT
ejpam-7033	97	9	db(p	db(p	PROPN
ejpam-7033	97	10	,	,	PUNCT
ejpam-7033	97	11	r	r	NOUN
ejpam-7033	97	12	)	)	PUNCT
ejpam-7033	97	13	⪯	⪯	NOUN
ejpam-7033	97	14	α[db(p	α[db(p	NOUN
ejpam-7033	97	15	,	,	PUNCT
ejpam-7033	97	16	x	x	PRON
ejpam-7033	97	17	)	)	PUNCT
ejpam-7033	97	18	+	+	CCONJ
ejpam-7033	97	19	db(x	db(x	ADJ
ejpam-7033	97	20	,	,	PUNCT
ejpam-7033	97	21	r	r	NOUN
ejpam-7033	97	22	)	)	PUNCT
ejpam-7033	97	23	]	]	PUNCT
ejpam-7033	97	24	for	for	ADP
ejpam-7033	97	25	some	some	DET
ejpam-7033	97	26	α	α	PRON
ejpam-7033	97	27	≥	≥	NOUN
ejpam-7033	97	28	1	1	NUM
ejpam-7033	97	29	,	,	PUNCT
ejpam-7033	97	30	∀	∀	PUNCT
ejpam-7033	97	31	p	p	NOUN
ejpam-7033	97	32	,	,	PUNCT
ejpam-7033	97	33	x	x	X
ejpam-7033	97	34	,	,	PUNCT
ejpam-7033	97	35	r	r	NOUN
ejpam-7033	97	36	∈	∈	PROPN
ejpam-7033	97	37	x.	x.	NOUN
ejpam-7033	97	38	then	then	ADV
ejpam-7033	97	39	db	db	PROPN
ejpam-7033	97	40	is	be	AUX
ejpam-7033	97	41	called	call	VERB
ejpam-7033	97	42	a	a	DET
ejpam-7033	97	43	cone	cone	NOUN
ejpam-7033	97	44	b	b	NOUN
ejpam-7033	97	45	-	-	NOUN
ejpam-7033	97	46	metric	metric	ADJ
ejpam-7033	97	47	,	,	PUNCT
ejpam-7033	97	48	and	and	CCONJ
ejpam-7033	97	49	(	(	PUNCT
ejpam-7033	97	50	x	x	NOUN
ejpam-7033	97	51	,	,	PUNCT
ejpam-7033	97	52	db	db	PROPN
ejpam-7033	97	53	)	)	PUNCT
ejpam-7033	97	54	represents	represent	VERB
ejpam-7033	97	55	a	a	DET
ejpam-7033	97	56	cone	cone	NOUN
ejpam-7033	97	57	b	b	NOUN
ejpam-7033	97	58	-	-	PUNCT
ejpam-7033	97	59	metric	metric	ADJ
ejpam-7033	97	60	space	space	NOUN
ejpam-7033	97	61	.	.	PUNCT
ejpam-7033	98	1	it	it	PRON
ejpam-7033	98	2	is	be	AUX
ejpam-7033	98	3	observed	observe	VERB
ejpam-7033	98	4	that	that	SCONJ
ejpam-7033	98	5	every	every	DET
ejpam-7033	98	6	dc	dc	PROPN
ejpam-7033	98	7	is	be	AUX
ejpam-7033	98	8	a	a	DET
ejpam-7033	98	9	db	db	ADJ
ejpam-7033	98	10	metric	metric	ADJ
ejpam-7033	98	11	space	space	NOUN
ejpam-7033	98	12	,	,	PUNCT
ejpam-7033	98	13	but	but	CCONJ
ejpam-7033	98	14	converse	converse	NOUN
ejpam-7033	98	15	may	may	AUX
ejpam-7033	98	16	not	not	PART
ejpam-7033	98	17	be	be	AUX
ejpam-7033	98	18	true	true	ADJ
ejpam-7033	98	19	.	.	PUNCT
ejpam-7033	99	1	example	example	NOUN
ejpam-7033	100	1	2	2	NUM
ejpam-7033	100	2	.	.	PUNCT
ejpam-7033	101	1	[	[	X
ejpam-7033	101	2	36	36	NUM
ejpam-7033	101	3	]	]	X
ejpam-7033	101	4	let	let	VERB
ejpam-7033	101	5	e	e	NOUN
ejpam-7033	101	6	=	=	NOUN
ejpam-7033	101	7	r2	r2	PROPN
ejpam-7033	101	8	,	,	PUNCT
ejpam-7033	101	9	c	c	X
ejpam-7033	101	10	=	=	PRON
ejpam-7033	101	11	{	{	PUNCT
ejpam-7033	101	12	(	(	PUNCT
ejpam-7033	101	13	ℓ	ℓ	INTJ
ejpam-7033	101	14	,	,	PUNCT
ejpam-7033	101	15	r	r	NOUN
ejpam-7033	101	16	)	)	PUNCT
ejpam-7033	101	17	∈	∈	PROPN
ejpam-7033	101	18	e	e	NOUN
ejpam-7033	101	19	:	:	PUNCT
ejpam-7033	101	20	ℓ	ℓ	X
ejpam-7033	101	21	,	,	PUNCT
ejpam-7033	101	22	r	r	NOUN
ejpam-7033	101	23	≥	≥	NOUN
ejpam-7033	101	24	0	0	NUM
ejpam-7033	101	25	}	}	PUNCT
ejpam-7033	101	26	⊂	⊂	ADJ
ejpam-7033	101	27	r2	r2	NOUN
ejpam-7033	101	28	,	,	PUNCT
ejpam-7033	101	29	and	and	CCONJ
ejpam-7033	101	30	x	x	X
ejpam-7033	101	31	=	=	SYM
ejpam-7033	101	32	{	{	PUNCT
ejpam-7033	101	33	1	1	NUM
ejpam-7033	101	34	,	,	PUNCT
ejpam-7033	101	35	2	2	NUM
ejpam-7033	101	36	,	,	PUNCT
ejpam-7033	101	37	3	3	NUM
ejpam-7033	101	38	,	,	PUNCT
ejpam-7033	101	39	4	4	NUM
ejpam-7033	101	40	}	}	PUNCT
ejpam-7033	101	41	.	.	PUNCT
ejpam-7033	102	1	define	define	VERB
ejpam-7033	102	2	db(ℓ	db(ℓ	PROPN
ejpam-7033	102	3	,	,	PUNCT
ejpam-7033	102	4	r	r	NOUN
ejpam-7033	102	5	)	)	PUNCT
ejpam-7033	102	6	=	=	SYM
ejpam-7033	102	7	{	{	PUNCT
ejpam-7033	102	8	(	(	PUNCT
ejpam-7033	103	1	|ℓ−	|ℓ−	PRON
ejpam-7033	103	2	r|−1	r|−1	PROPN
ejpam-7033	103	3	,	,	PUNCT
ejpam-7033	103	4	|ℓ−	|ℓ−	VERB
ejpam-7033	103	5	r|−1	r|−1	VERB
ejpam-7033	103	6	)	)	PUNCT
ejpam-7033	104	1	if	if	SCONJ
ejpam-7033	104	2	ℓ	ℓ	NUM
ejpam-7033	104	3	̸=	̸=	PROPN
ejpam-7033	104	4	r	r	NOUN
ejpam-7033	104	5	0	0	NUM
ejpam-7033	104	6	if	if	SCONJ
ejpam-7033	104	7	ℓ	ℓ	NOUN
ejpam-7033	104	8	=	=	SYM
ejpam-7033	104	9	r.	r.	PROPN
ejpam-7033	104	10	here	here	ADV
ejpam-7033	104	11	(	(	PUNCT
ejpam-7033	104	12	x	x	NOUN
ejpam-7033	104	13	,	,	PUNCT
ejpam-7033	104	14	db	db	PROPN
ejpam-7033	104	15	)	)	PUNCT
ejpam-7033	104	16	represents	represent	VERB
ejpam-7033	104	17	a	a	DET
ejpam-7033	104	18	cone	cone	NOUN
ejpam-7033	104	19	b	b	X
ejpam-7033	104	20	-	-	PUNCT
ejpam-7033	104	21	metric	metric	ADJ
ejpam-7033	104	22	space	space	NOUN
ejpam-7033	104	23	for	for	ADP
ejpam-7033	104	24	s	s	NOUN
ejpam-7033	104	25	=	=	SYM
ejpam-7033	104	26	6	6	NUM
ejpam-7033	104	27	5	5	NUM
ejpam-7033	104	28	,	,	PUNCT
ejpam-7033	104	29	and	and	CCONJ
ejpam-7033	104	30	since	since	SCONJ
ejpam-7033	104	31	db(1	db(1	PROPN
ejpam-7033	104	32	,	,	PUNCT
ejpam-7033	104	33	2	2	NUM
ejpam-7033	104	34	)	)	PUNCT
ejpam-7033	104	35	≻	≻	NOUN
ejpam-7033	105	1	db(1	db(1	VERB
ejpam-7033	105	2	,	,	PUNCT
ejpam-7033	105	3	4	4	NUM
ejpam-7033	105	4	)	)	PUNCT
ejpam-7033	105	5	+	+	NUM
ejpam-7033	105	6	db(4	db(4	PROPN
ejpam-7033	105	7	,	,	PUNCT
ejpam-7033	105	8	2	2	NUM
ejpam-7033	105	9	)	)	PUNCT
ejpam-7033	105	10	,	,	PUNCT
ejpam-7033	105	11	db	db	PROPN
ejpam-7033	105	12	is	be	AUX
ejpam-7033	105	13	not	not	PART
ejpam-7033	105	14	a	a	DET
ejpam-7033	105	15	cone	cone	NOUN
ejpam-7033	105	16	metric	metric	NOUN
ejpam-7033	105	17	.	.	PUNCT
ejpam-7033	106	1	definition	definition	NOUN
ejpam-7033	106	2	5	5	NUM
ejpam-7033	106	3	.	.	PUNCT
ejpam-7033	107	1	[	[	X
ejpam-7033	107	2	34	34	NUM
ejpam-7033	107	3	]	]	PUNCT
ejpam-7033	107	4	let	let	VERB
ejpam-7033	107	5	dr	dr	PROPN
ejpam-7033	107	6	:	:	PUNCT
ejpam-7033	107	7	x×x	x×x	PROPN
ejpam-7033	107	8	7→	7→	NUM
ejpam-7033	107	9	e	e	NOUN
ejpam-7033	107	10	,	,	PUNCT
ejpam-7033	107	11	∀	∀	X
ejpam-7033	107	12	f1	f1	NOUN
ejpam-7033	107	13	,	,	PUNCT
ejpam-7033	107	14	f2	f2	PROPN
ejpam-7033	107	15	,	,	PUNCT
ejpam-7033	107	16	f3	f3	ADJ
ejpam-7033	107	17	,	,	PUNCT
ejpam-7033	107	18	f4	f4	PROPN
ejpam-7033	107	19	∈	∈	PROPN
ejpam-7033	107	20	x	x	NOUN
ejpam-7033	107	21	,	,	PUNCT
ejpam-7033	107	22	satisfies	satisfy	VERB
ejpam-7033	107	23	the	the	DET
ejpam-7033	107	24	following	follow	VERB
ejpam-7033	107	25	axioms	axiom	NOUN
ejpam-7033	107	26	:	:	PUNCT
ejpam-7033	107	27	(	(	PUNCT
ejpam-7033	107	28	dr1	dr1	PROPN
ejpam-7033	107	29	)	)	PUNCT
ejpam-7033	107	30	0	0	PROPN
ejpam-7033	108	1	⪯	⪯	PROPN
ejpam-7033	108	2	dr(f1	dr(f1	NOUN
ejpam-7033	108	3	,	,	PUNCT
ejpam-7033	108	4	f2	f2	PROPN
ejpam-7033	108	5	)	)	PUNCT
ejpam-7033	108	6	and	and	CCONJ
ejpam-7033	108	7	dr(f2	dr(f2	NOUN
ejpam-7033	108	8	,	,	PUNCT
ejpam-7033	108	9	f1	f1	NOUN
ejpam-7033	108	10	)	)	PUNCT
ejpam-7033	108	11	=	=	SYM
ejpam-7033	108	12	0	0	PUNCT
ejpam-7033	109	1	if	if	SCONJ
ejpam-7033	109	2	and	and	CCONJ
ejpam-7033	109	3	only	only	ADV
ejpam-7033	109	4	if	if	SCONJ
ejpam-7033	109	5	f1	f1	PROPN
ejpam-7033	109	6	=	=	SYM
ejpam-7033	109	7	f2	f2	PROPN
ejpam-7033	109	8	;	;	PUNCT
ejpam-7033	109	9	(	(	PUNCT
ejpam-7033	109	10	dr2	dr2	INTJ
ejpam-7033	109	11	)	)	PUNCT
ejpam-7033	109	12	dr(f1	dr(f1	NOUN
ejpam-7033	109	13	,	,	PUNCT
ejpam-7033	109	14	f2	f2	X
ejpam-7033	109	15	)	)	PUNCT
ejpam-7033	109	16	=	=	SYM
ejpam-7033	109	17	dr(f2	dr(f2	NOUN
ejpam-7033	109	18	,	,	PUNCT
ejpam-7033	109	19	f1	f1	NOUN
ejpam-7033	109	20	)	)	PUNCT
ejpam-7033	109	21	;	;	PUNCT
ejpam-7033	109	22	a.	a.	PROPN
ejpam-7033	109	23	arif	arif	PROPN
ejpam-7033	109	24	et	et	PROPN
ejpam-7033	109	25	al	al	PROPN
ejpam-7033	109	26	.	.	PUNCT
ejpam-7033	109	27	/	/	SYM
ejpam-7033	109	28	eur	eur	PROPN
ejpam-7033	109	29	.	.	PUNCT
ejpam-7033	110	1	j.	j.	PROPN
ejpam-7033	110	2	pure	pure	PROPN
ejpam-7033	110	3	appl	appl	PROPN
ejpam-7033	110	4	.	.	PROPN
ejpam-7033	110	5	math	math	PROPN
ejpam-7033	110	6	,	,	PUNCT
ejpam-7033	110	7	18	18	NUM
ejpam-7033	110	8	(	(	PUNCT
ejpam-7033	110	9	4	4	NUM
ejpam-7033	110	10	)	)	PUNCT
ejpam-7033	110	11	(	(	PUNCT
ejpam-7033	110	12	2025	2025	NUM
ejpam-7033	110	13	)	)	PUNCT
ejpam-7033	110	14	,	,	PUNCT
ejpam-7033	110	15	7033	7033	NUM
ejpam-7033	110	16	5	5	NUM
ejpam-7033	110	17	of	of	ADP
ejpam-7033	110	18	29	29	NUM
ejpam-7033	110	19	(	(	PUNCT
ejpam-7033	110	20	dr3	dr3	NOUN
ejpam-7033	110	21	)	)	PUNCT
ejpam-7033	110	22	dr(f1	dr(f1	NOUN
ejpam-7033	110	23	,	,	PUNCT
ejpam-7033	110	24	f4	f4	NOUN
ejpam-7033	110	25	)	)	PUNCT
ejpam-7033	110	26	⪯	⪯	NOUN
ejpam-7033	110	27	dr(f1	dr(f1	NOUN
ejpam-7033	110	28	,	,	PUNCT
ejpam-7033	110	29	f2	f2	PROPN
ejpam-7033	110	30	)	)	PUNCT
ejpam-7033	110	31	+	+	CCONJ
ejpam-7033	110	32	dr(f2	dr(f2	NOUN
ejpam-7033	110	33	,	,	PUNCT
ejpam-7033	110	34	f3	f3	ADJ
ejpam-7033	110	35	)	)	PUNCT
ejpam-7033	110	36	+	+	CCONJ
ejpam-7033	110	37	dr(f3	dr(f3	NOUN
ejpam-7033	110	38	,	,	PUNCT
ejpam-7033	110	39	f4	f4	PROPN
ejpam-7033	110	40	)	)	PUNCT
ejpam-7033	110	41	for	for	ADP
ejpam-7033	110	42	all	all	DET
ejpam-7033	110	43	distinct	distinct	ADJ
ejpam-7033	110	44	f3	f3	NOUN
ejpam-7033	110	45	,	,	PUNCT
ejpam-7033	110	46	f4	f4	PROPN
ejpam-7033	110	47	∈	∈	PROPN
ejpam-7033	110	48	x	x	SYM
ejpam-7033	110	49	\	\	PROPN
ejpam-7033	110	50	{	{	PUNCT
ejpam-7033	110	51	f1	f1	NOUN
ejpam-7033	110	52	,	,	PUNCT
ejpam-7033	110	53	f2	f2	PROPN
ejpam-7033	110	54	}	}	PUNCT
ejpam-7033	110	55	.	.	PUNCT
ejpam-7033	111	1	then	then	ADV
ejpam-7033	111	2	dr	dr	PROPN
ejpam-7033	111	3	is	be	AUX
ejpam-7033	111	4	known	know	VERB
ejpam-7033	111	5	as	as	ADP
ejpam-7033	111	6	rectangular	rectangular	ADJ
ejpam-7033	111	7	cone	cone	NOUN
ejpam-7033	111	8	metric	metric	NOUN
ejpam-7033	111	9	and	and	CCONJ
ejpam-7033	111	10	the	the	DET
ejpam-7033	111	11	pair	pair	NOUN
ejpam-7033	111	12	(	(	PUNCT
ejpam-7033	111	13	x	x	NOUN
ejpam-7033	111	14	,	,	PUNCT
ejpam-7033	111	15	dr	dr	PROPN
ejpam-7033	111	16	)	)	PUNCT
ejpam-7033	111	17	represents	represent	VERB
ejpam-7033	111	18	a	a	DET
ejpam-7033	111	19	rectangular	rectangular	ADJ
ejpam-7033	111	20	cone	cone	NOUN
ejpam-7033	111	21	metric	metric	ADJ
ejpam-7033	111	22	space	space	NOUN
ejpam-7033	111	23	.	.	PUNCT
ejpam-7033	112	1	remark	remark	PROPN
ejpam-7033	112	2	6	6	NUM
ejpam-7033	112	3	.	.	PUNCT
ejpam-7033	113	1	a	a	DET
ejpam-7033	113	2	cone	cone	NOUN
ejpam-7033	113	3	metric	metric	ADJ
ejpam-7033	113	4	space	space	NOUN
ejpam-7033	113	5	always	always	ADV
ejpam-7033	113	6	represents	represent	VERB
ejpam-7033	113	7	a	a	DET
ejpam-7033	113	8	rectangular	rectangular	ADJ
ejpam-7033	113	9	cone	cone	NOUN
ejpam-7033	113	10	metric	metric	ADJ
ejpam-7033	113	11	space	space	NOUN
ejpam-7033	113	12	,	,	PUNCT
ejpam-7033	113	13	but	but	CCONJ
ejpam-7033	113	14	converse	converse	NOUN
ejpam-7033	113	15	may	may	AUX
ejpam-7033	113	16	not	not	PART
ejpam-7033	113	17	hold	hold	VERB
ejpam-7033	113	18	.	.	PUNCT
ejpam-7033	114	1	definition	definition	NOUN
ejpam-7033	114	2	7	7	NUM
ejpam-7033	114	3	.	.	PUNCT
ejpam-7033	115	1	[	[	X
ejpam-7033	115	2	34	34	NUM
ejpam-7033	115	3	]	]	PUNCT
ejpam-7033	115	4	let	let	VERB
ejpam-7033	115	5	r	r	NOUN
ejpam-7033	115	6	:	:	PUNCT
ejpam-7033	115	7	x	x	PROPN
ejpam-7033	115	8	×x	×x	VERB
ejpam-7033	115	9	7→	7→	NUM
ejpam-7033	115	10	e	e	NOUN
ejpam-7033	115	11	,	,	PUNCT
ejpam-7033	115	12	∀	∀	X
ejpam-7033	115	13	ℓ	ℓ	NOUN
ejpam-7033	115	14	,	,	PUNCT
ejpam-7033	115	15	y	y	PROPN
ejpam-7033	115	16	,	,	PUNCT
ejpam-7033	115	17	x	x	NOUN
ejpam-7033	115	18	,	,	PUNCT
ejpam-7033	115	19	υ	υ	PROPN
ejpam-7033	115	20	∈	∈	PROPN
ejpam-7033	115	21	x	x	NOUN
ejpam-7033	115	22	,	,	PUNCT
ejpam-7033	115	23	satisfies	satisfy	VERB
ejpam-7033	115	24	the	the	DET
ejpam-7033	115	25	following	follow	VERB
ejpam-7033	115	26	axioms	axiom	NOUN
ejpam-7033	115	27	:	:	PUNCT
ejpam-7033	115	28	(	(	PUNCT
ejpam-7033	115	29	drb1	drb1	PROPN
ejpam-7033	115	30	)	)	PUNCT
ejpam-7033	115	31	0	0	NUM
ejpam-7033	116	1	⪯	⪯	PROPN
ejpam-7033	116	2	r(ℓ	r(ℓ	PROPN
ejpam-7033	116	3	,	,	PUNCT
ejpam-7033	116	4	y	y	PROPN
ejpam-7033	116	5	)	)	PUNCT
ejpam-7033	116	6	and	and	CCONJ
ejpam-7033	116	7	r(ℓ	r(ℓ	PROPN
ejpam-7033	116	8	,	,	PUNCT
ejpam-7033	116	9	y	y	PROPN
ejpam-7033	116	10	)	)	PUNCT
ejpam-7033	116	11	=	=	SYM
ejpam-7033	116	12	0	0	NUM
ejpam-7033	116	13	⇔	⇔	PROPN
ejpam-7033	116	14	ℓ	ℓ	PROPN
ejpam-7033	116	15	=	=	SYM
ejpam-7033	116	16	y	y	PROPN
ejpam-7033	116	17	;	;	PUNCT
ejpam-7033	116	18	(	(	PUNCT
ejpam-7033	116	19	drb2	drb2	PROPN
ejpam-7033	116	20	)	)	PUNCT
ejpam-7033	116	21	r(ℓ	r(ℓ	PROPN
ejpam-7033	116	22	,	,	PUNCT
ejpam-7033	116	23	y	y	NOUN
ejpam-7033	116	24	)	)	PUNCT
ejpam-7033	116	25	=	=	PUNCT
ejpam-7033	117	1	r(y	r(y	VERB
ejpam-7033	117	2	,	,	PUNCT
ejpam-7033	117	3	ℓ	ℓ	NOUN
ejpam-7033	117	4	)	)	PUNCT
ejpam-7033	117	5	;	;	PUNCT
ejpam-7033	117	6	(	(	PUNCT
ejpam-7033	117	7	drb3	drb3	PROPN
ejpam-7033	117	8	)	)	PUNCT
ejpam-7033	117	9	r(ℓ	r(ℓ	PROPN
ejpam-7033	117	10	,	,	PUNCT
ejpam-7033	117	11	υ	υ	NOUN
ejpam-7033	117	12	)	)	PUNCT
ejpam-7033	117	13	⪯	⪯	NOUN
ejpam-7033	117	14	s[r(ℓ	s[r(ℓ	PROPN
ejpam-7033	117	15	,	,	PUNCT
ejpam-7033	117	16	y)+r(y	y)+r(y	PROPN
ejpam-7033	117	17	,	,	PUNCT
ejpam-7033	117	18	x)+r(x	x)+r(x	PROPN
ejpam-7033	117	19	,	,	PUNCT
ejpam-7033	117	20	υ	υ	NOUN
ejpam-7033	117	21	)	)	PUNCT
ejpam-7033	117	22	]	]	PUNCT
ejpam-7033	117	23	for	for	ADP
ejpam-7033	117	24	all	all	DET
ejpam-7033	117	25	distinct	distinct	ADJ
ejpam-7033	117	26	y	y	NOUN
ejpam-7033	117	27	,	,	PUNCT
ejpam-7033	117	28	x	x	X
ejpam-7033	117	29	∈	∈	NOUN
ejpam-7033	117	30	x	x	SYM
ejpam-7033	117	31	\	\	X
ejpam-7033	117	32	{	{	PUNCT
ejpam-7033	117	33	ℓ	ℓ	NOUN
ejpam-7033	117	34	,	,	PUNCT
ejpam-7033	117	35	υ	υ	NOUN
ejpam-7033	117	36	}	}	PUNCT
ejpam-7033	117	37	,	,	PUNCT
ejpam-7033	117	38	where	where	SCONJ
ejpam-7033	117	39	s	s	VERB
ejpam-7033	117	40	≥	≥	NOUN
ejpam-7033	117	41	1	1	NUM
ejpam-7033	117	42	.	.	PUNCT
ejpam-7033	118	1	then	then	ADV
ejpam-7033	118	2	r	r	NOUN
ejpam-7033	118	3	stands	stand	VERB
ejpam-7033	118	4	for	for	ADP
ejpam-7033	118	5	rectangular	rectangular	ADJ
ejpam-7033	118	6	cone	cone	NOUN
ejpam-7033	118	7	b	b	NOUN
ejpam-7033	118	8	-	-	NOUN
ejpam-7033	118	9	metric	metric	ADJ
ejpam-7033	118	10	,	,	PUNCT
ejpam-7033	118	11	and	and	CCONJ
ejpam-7033	118	12	(	(	PUNCT
ejpam-7033	118	13	x	x	X
ejpam-7033	118	14	,	,	PUNCT
ejpam-7033	118	15	r	r	NOUN
ejpam-7033	118	16	)	)	PUNCT
ejpam-7033	118	17	represents	represent	VERB
ejpam-7033	118	18	a	a	DET
ejpam-7033	118	19	rectangular	rectangular	ADJ
ejpam-7033	118	20	cone	cone	NOUN
ejpam-7033	118	21	b	b	NOUN
ejpam-7033	118	22	-	-	PUNCT
ejpam-7033	118	23	metric	metric	ADJ
ejpam-7033	118	24	space	space	NOUN
ejpam-7033	118	25	(	(	PUNCT
ejpam-7033	118	26	rcbms	rcbms	NOUN
ejpam-7033	118	27	)	)	PUNCT
ejpam-7033	118	28	.	.	PUNCT
ejpam-7033	119	1	example	example	NOUN
ejpam-7033	120	1	3	3	NUM
ejpam-7033	120	2	.	.	PUNCT
ejpam-7033	121	1	[	[	X
ejpam-7033	121	2	36	36	NUM
ejpam-7033	121	3	]	]	PUNCT
ejpam-7033	121	4	consider	consider	VERB
ejpam-7033	121	5	x	x	X
ejpam-7033	121	6	=	=	PUNCT
ejpam-7033	122	1	[	[	X
ejpam-7033	122	2	0	0	NUM
ejpam-7033	122	3	,	,	PUNCT
ejpam-7033	122	4	2	2	NUM
ejpam-7033	122	5	]	]	PUNCT
ejpam-7033	122	6	and	and	CCONJ
ejpam-7033	122	7	e	e	X
ejpam-7033	122	8	=	=	PROPN
ejpam-7033	122	9	cr2(x	cr2(x	PROPN
ejpam-7033	122	10	)	)	PUNCT
ejpam-7033	122	11	.	.	PUNCT
ejpam-7033	123	1	for	for	ADP
ejpam-7033	123	2	x	x	SYM
ejpam-7033	123	3	=	=	SYM
ejpam-7033	123	4	(	(	PUNCT
ejpam-7033	123	5	ℓ	ℓ	PROPN
ejpam-7033	123	6	,	,	PUNCT
ejpam-7033	123	7	y	y	NOUN
ejpam-7033	123	8	)	)	PUNCT
ejpam-7033	123	9	and	and	CCONJ
ejpam-7033	123	10	℘	℘	PROPN
ejpam-7033	123	11	=	=	SYM
ejpam-7033	123	12	(	(	PUNCT
ejpam-7033	123	13	u	u	NOUN
ejpam-7033	123	14	,	,	PUNCT
ejpam-7033	123	15	v	v	NOUN
ejpam-7033	123	16	)	)	PUNCT
ejpam-7033	123	17	in	in	ADP
ejpam-7033	123	18	e	e	NOUN
ejpam-7033	123	19	,	,	PUNCT
ejpam-7033	123	20	we	we	PRON
ejpam-7033	123	21	define	define	VERB
ejpam-7033	123	22	x.℘	x.℘	NOUN
ejpam-7033	124	1	=	=	SYM
ejpam-7033	124	2	(	(	PUNCT
ejpam-7033	124	3	ℓu	ℓu	PROPN
ejpam-7033	124	4	,	,	PUNCT
ejpam-7033	124	5	yv	yv	NOUN
ejpam-7033	124	6	)	)	PUNCT
ejpam-7033	124	7	and	and	CCONJ
ejpam-7033	124	8	∥x∥	∥x∥	NOUN
ejpam-7033	124	9	=	=	SYM
ejpam-7033	124	10	max(∥ℓ∥	max(∥ℓ∥	PROPN
ejpam-7033	124	11	,	,	PUNCT
ejpam-7033	124	12	∥y∥	∥y∥	NOUN
ejpam-7033	124	13	)	)	PUNCT
ejpam-7033	124	14	,	,	PUNCT
ejpam-7033	124	15	where	where	SCONJ
ejpam-7033	124	16	∥℘∥	∥℘∥	PUNCT
ejpam-7033	124	17	=	=	PUNCT
ejpam-7033	124	18	supx∈x	supx∈x	NOUN
ejpam-7033	124	19	|	|	ADV
ejpam-7033	124	20	℘(x	℘(x	ADJ
ejpam-7033	124	21	)	)	PUNCT
ejpam-7033	124	22	|	|	ADV
ejpam-7033	124	23	.	.	PUNCT
ejpam-7033	125	1	then	then	ADV
ejpam-7033	125	2	e	e	PROPN
ejpam-7033	125	3	is	be	AUX
ejpam-7033	125	4	a	a	DET
ejpam-7033	125	5	banach	banach	NOUN
ejpam-7033	125	6	algebra	algebra	NOUN
ejpam-7033	125	7	with	with	ADP
ejpam-7033	125	8	unit	unit	NOUN
ejpam-7033	125	9	element	element	NOUN
ejpam-7033	125	10	e	e	NOUN
ejpam-7033	125	11	=	=	PUNCT
ejpam-7033	125	12	(	(	PUNCT
ejpam-7033	125	13	1	1	NUM
ejpam-7033	125	14	,	,	PUNCT
ejpam-7033	125	15	1	1	NUM
ejpam-7033	125	16	)	)	PUNCT
ejpam-7033	125	17	and	and	CCONJ
ejpam-7033	125	18	zero	zero	NUM
ejpam-7033	125	19	element	element	NOUN
ejpam-7033	125	20	ω	ω	PROPN
ejpam-7033	125	21	=	=	SYM
ejpam-7033	125	22	(	(	PUNCT
ejpam-7033	125	23	0	0	NUM
ejpam-7033	125	24	,	,	PUNCT
ejpam-7033	125	25	0	0	NUM
ejpam-7033	125	26	)	)	PUNCT
ejpam-7033	125	27	.	.	PUNCT
ejpam-7033	126	1	suppose	suppose	VERB
ejpam-7033	126	2	that	that	SCONJ
ejpam-7033	126	3	c	c	AUX
ejpam-7033	126	4	=	=	PRON
ejpam-7033	126	5	{	{	PUNCT
ejpam-7033	126	6	(	(	PUNCT
ejpam-7033	126	7	ℓ	ℓ	INTJ
ejpam-7033	126	8	,	,	PUNCT
ejpam-7033	127	1	y	y	NOUN
ejpam-7033	127	2	)	)	PUNCT
ejpam-7033	127	3	∈	∈	PROPN
ejpam-7033	127	4	e	e	NOUN
ejpam-7033	127	5	:	:	PUNCT
ejpam-7033	127	6	ℓ(x	ℓ(x	PROPN
ejpam-7033	127	7	)	)	PUNCT
ejpam-7033	127	8	,	,	PUNCT
ejpam-7033	127	9	y(x	y(x	PROPN
ejpam-7033	127	10	)	)	PUNCT
ejpam-7033	127	11	≥	≥	NOUN
ejpam-7033	127	12	0	0	NUM
ejpam-7033	127	13	,	,	PUNCT
ejpam-7033	127	14	x	x	X
ejpam-7033	127	15	∈	∈	NOUN
ejpam-7033	127	16	x	x	X
ejpam-7033	127	17	}	}	PUNCT
ejpam-7033	127	18	⊂	⊂	PROPN
ejpam-7033	127	19	cr2(x	cr2(x	PROPN
ejpam-7033	127	20	)	)	PUNCT
ejpam-7033	127	21	,	,	PUNCT
ejpam-7033	127	22	clearly	clearly	ADV
ejpam-7033	127	23	c	c	PROPN
ejpam-7033	127	24	represents	represent	VERB
ejpam-7033	127	25	a	a	DET
ejpam-7033	127	26	cone	cone	NOUN
ejpam-7033	127	27	in	in	ADP
ejpam-7033	127	28	e.	e.	PROPN
ejpam-7033	127	29	define	define	VERB
ejpam-7033	128	1	r	r	NOUN
ejpam-7033	128	2	:	:	PUNCT
ejpam-7033	128	3	x	x	PROPN
ejpam-7033	128	4	×x	×x	X
ejpam-7033	128	5	→	→	SYM
ejpam-7033	128	6	e	e	NOUN
ejpam-7033	128	7	,	,	PUNCT
ejpam-7033	128	8	such	such	ADJ
ejpam-7033	128	9	that	that	SCONJ
ejpam-7033	128	10	r(ℓ	r(ℓ	PROPN
ejpam-7033	128	11	,	,	PUNCT
ejpam-7033	128	12	y)(x	y)(x	PROPN
ejpam-7033	128	13	)	)	PUNCT
ejpam-7033	128	14	=	=	PUNCT
ejpam-7033	129	1			X
ejpam-7033	129	2	(	(	PUNCT
ejpam-7033	129	3	0	0	NUM
ejpam-7033	129	4	,	,	PUNCT
ejpam-7033	129	5	0	0	NUM
ejpam-7033	129	6	)	)	PUNCT
ejpam-7033	129	7	if	if	SCONJ
ejpam-7033	129	8	ℓ	ℓ	NOUN
ejpam-7033	129	9	=	=	SYM
ejpam-7033	129	10	y	y	PROPN
ejpam-7033	129	11	(	(	PUNCT
ejpam-7033	129	12	a+	a+	X
ejpam-7033	129	13	bx	bx	PROPN
ejpam-7033	129	14	,	,	PUNCT
ejpam-7033	129	15	c+	c+	X
ejpam-7033	129	16	dx2	dx2	PROPN
ejpam-7033	129	17	)	)	PUNCT
ejpam-7033	129	18	if	if	SCONJ
ejpam-7033	129	19	ℓ	ℓ	X
ejpam-7033	129	20	,	,	PUNCT
ejpam-7033	129	21	y	y	PROPN
ejpam-7033	129	22	∈	∈	PROPN
ejpam-7033	130	1	[	[	X
ejpam-7033	130	2	0	0	NUM
ejpam-7033	130	3	,	,	PUNCT
ejpam-7033	130	4	12	12	NUM
ejpam-7033	130	5	)	)	PUNCT
ejpam-7033	130	6	and	and	CCONJ
ejpam-7033	130	7	a	a	DET
ejpam-7033	130	8	,	,	PUNCT
ejpam-7033	130	9	b	b	NOUN
ejpam-7033	130	10	,	,	PUNCT
ejpam-7033	130	11	c	c	NOUN
ejpam-7033	130	12	,	,	PUNCT
ejpam-7033	130	13	d	d	X
ejpam-7033	130	14	are	be	AUX
ejpam-7033	130	15	some	some	DET
ejpam-7033	130	16	fixed	fix	VERB
ejpam-7033	130	17	real	real	ADJ
ejpam-7033	130	18	numbers	number	NOUN
ejpam-7033	130	19	.	.	PUNCT
ejpam-7033	131	1	(	(	PUNCT
ejpam-7033	131	2	a+bx	a+bx	PROPN
ejpam-7033	131	3	n3	n3	NOUN
ejpam-7033	131	4	,	,	PUNCT
ejpam-7033	131	5	c+dx2	c+dx2	NOUN
ejpam-7033	131	6	n3	n3	NOUN
ejpam-7033	131	7	)	)	PUNCT
ejpam-7033	131	8	if	if	SCONJ
ejpam-7033	131	9	ℓ	ℓ	NOUN
ejpam-7033	131	10	=	=	SYM
ejpam-7033	131	11	1	1	NUM
ejpam-7033	131	12	n(n	n(n	NOUN
ejpam-7033	131	13	≥	≥	NUM
ejpam-7033	131	14	2	2	NUM
ejpam-7033	131	15	)	)	PUNCT
ejpam-7033	131	16	∈	∈	NOUN
ejpam-7033	132	1	[	[	X
ejpam-7033	132	2	0	0	NUM
ejpam-7033	132	3	,	,	PUNCT
ejpam-7033	132	4	12	12	NUM
ejpam-7033	132	5	)	)	PUNCT
ejpam-7033	132	6	and	and	CCONJ
ejpam-7033	132	7	y	y	PROPN
ejpam-7033	132	8	∈	∈	PROPN
ejpam-7033	132	9	{	{	PUNCT
ejpam-7033	132	10	1	1	NUM
ejpam-7033	132	11	,	,	PUNCT
ejpam-7033	132	12	2	2	NUM
ejpam-7033	132	13	}	}	PUNCT
ejpam-7033	132	14	(	(	PUNCT
ejpam-7033	132	15	|ℓ−	|ℓ−	VERB
ejpam-7033	132	16	y|2(a+	y|2(a+	PROPN
ejpam-7033	132	17	bx	bx	NOUN
ejpam-7033	132	18	)	)	PUNCT
ejpam-7033	132	19	,	,	PUNCT
ejpam-7033	132	20	|ℓ−	|ℓ−	VERB
ejpam-7033	132	21	y|2(c+	y|2(c+	PROPN
ejpam-7033	132	22	dx2	dx2	PROPN
ejpam-7033	132	23	)	)	PUNCT
ejpam-7033	132	24	)	)	PUNCT
ejpam-7033	133	1	if	if	SCONJ
ejpam-7033	133	2	ℓ	ℓ	X
ejpam-7033	133	3	,	,	PUNCT
ejpam-7033	133	4	y	y	PROPN
ejpam-7033	133	5	∈	∈	PROPN
ejpam-7033	134	1	[	[	X
ejpam-7033	134	2	0	0	NUM
ejpam-7033	134	3	,	,	PUNCT
ejpam-7033	134	4	12	12	NUM
ejpam-7033	134	5	)	)	PUNCT
ejpam-7033	134	6	otherwise	otherwise	ADV
ejpam-7033	134	7	.	.	PUNCT
ejpam-7033	135	1	here	here	ADV
ejpam-7033	135	2	(	(	PUNCT
ejpam-7033	135	3	x	x	NOUN
ejpam-7033	135	4	,	,	PUNCT
ejpam-7033	135	5	r	r	NOUN
ejpam-7033	135	6	)	)	PUNCT
ejpam-7033	135	7	represents	represent	VERB
ejpam-7033	135	8	rectangular	rectangular	ADJ
ejpam-7033	135	9	cone	cone	NOUN
ejpam-7033	135	10	b	b	NOUN
ejpam-7033	135	11	-	-	PUNCT
ejpam-7033	135	12	metric	metric	ADJ
ejpam-7033	135	13	space	space	NOUN
ejpam-7033	135	14	with	with	ADP
ejpam-7033	135	15	s	s	NOUN
ejpam-7033	135	16	=	=	SYM
ejpam-7033	135	17	2	2	NUM
ejpam-7033	135	18	over	over	ADP
ejpam-7033	135	19	e	e	NOUN
ejpam-7033	135	20	,	,	PUNCT
ejpam-7033	135	21	but	but	CCONJ
ejpam-7033	135	22	is	be	AUX
ejpam-7033	135	23	not	not	PART
ejpam-7033	135	24	cone	cone	NOUN
ejpam-7033	135	25	b	b	X
ejpam-7033	135	26	-	-	PUNCT
ejpam-7033	135	27	metric	metric	ADJ
ejpam-7033	135	28	space	space	NOUN
ejpam-7033	135	29	.	.	PUNCT
ejpam-7033	136	1	remark	remark	PROPN
ejpam-7033	136	2	8	8	NUM
ejpam-7033	136	3	.	.	PUNCT
ejpam-7033	137	1	a	a	DET
ejpam-7033	137	2	cone	cone	NOUN
ejpam-7033	137	3	b	b	X
ejpam-7033	137	4	-	-	PUNCT
ejpam-7033	137	5	metric	metric	ADJ
ejpam-7033	137	6	space	space	NOUN
ejpam-7033	137	7	always	always	ADV
ejpam-7033	137	8	represents	represent	VERB
ejpam-7033	137	9	a	a	DET
ejpam-7033	137	10	rectangular	rectangular	ADJ
ejpam-7033	137	11	cone	cone	NOUN
ejpam-7033	137	12	b	b	NOUN
ejpam-7033	137	13	-	-	PUNCT
ejpam-7033	137	14	metric	metric	ADJ
ejpam-7033	137	15	space	space	NOUN
ejpam-7033	137	16	,	,	PUNCT
ejpam-7033	137	17	converse	converse	NOUN
ejpam-7033	137	18	may	may	AUX
ejpam-7033	137	19	not	not	PART
ejpam-7033	137	20	hold	hold	VERB
ejpam-7033	137	21	,	,	PUNCT
ejpam-7033	137	22	as	as	SCONJ
ejpam-7033	137	23	illustrated	illustrate	VERB
ejpam-7033	137	24	in	in	ADP
ejpam-7033	137	25	the	the	DET
ejpam-7033	137	26	above	above	ADJ
ejpam-7033	137	27	mentioned	mention	VERB
ejpam-7033	137	28	examples	example	NOUN
ejpam-7033	137	29	.	.	PUNCT
ejpam-7033	138	1	definition	definition	NOUN
ejpam-7033	138	2	9	9	NUM
ejpam-7033	138	3	.	.	PUNCT
ejpam-7033	139	1	[	[	X
ejpam-7033	139	2	36	36	NUM
ejpam-7033	139	3	]	]	PUNCT
ejpam-7033	139	4	let	let	VERB
ejpam-7033	139	5	e	e	PRON
ejpam-7033	139	6	be	be	AUX
ejpam-7033	139	7	a	a	DET
ejpam-7033	139	8	real	real	ADJ
ejpam-7033	139	9	banach	banach	NOUN
ejpam-7033	139	10	space	space	NOUN
ejpam-7033	139	11	,	,	PUNCT
ejpam-7033	139	12	(	(	PUNCT
ejpam-7033	139	13	x	x	NOUN
ejpam-7033	139	14	,	,	PUNCT
ejpam-7033	139	15	r	r	NOUN
ejpam-7033	139	16	)	)	PUNCT
ejpam-7033	139	17	is	be	AUX
ejpam-7033	139	18	taken	take	VERB
ejpam-7033	139	19	as	as	ADP
ejpam-7033	139	20	a	a	DET
ejpam-7033	139	21	rectangular	rectangular	ADJ
ejpam-7033	139	22	cone	cone	NOUN
ejpam-7033	139	23	b	b	NOUN
ejpam-7033	139	24	-	-	PUNCT
ejpam-7033	139	25	metric	metric	ADJ
ejpam-7033	139	26	space	space	NOUN
ejpam-7033	139	27	and	and	CCONJ
ejpam-7033	139	28	ϵ	ϵ	ADP
ejpam-7033	139	29	∈	∈	PROPN
ejpam-7033	139	30	e	e	NOUN
ejpam-7033	139	31	with	with	ADP
ejpam-7033	139	32	0	0	NUM
ejpam-7033	139	33	≪	≪	ADJ
ejpam-7033	139	34	ϵ(arbitrary	ϵ(arbitrary	NOUN
ejpam-7033	139	35	)	)	PUNCT
ejpam-7033	139	36	.	.	PUNCT
ejpam-7033	140	1	(	(	PUNCT
ejpam-7033	140	2	1	1	X
ejpam-7033	140	3	)	)	PUNCT
ejpam-7033	140	4	any	any	DET
ejpam-7033	140	5	sequence	sequence	NOUN
ejpam-7033	140	6	{	{	PUNCT
ejpam-7033	140	7	ℓn	ℓn	ADV
ejpam-7033	140	8	}	}	PUNCT
ejpam-7033	140	9	is	be	AUX
ejpam-7033	140	10	referred	refer	VERB
ejpam-7033	140	11	as	as	ADP
ejpam-7033	140	12	a	a	DET
ejpam-7033	140	13	cauchy	cauchy	ADJ
ejpam-7033	140	14	sequence	sequence	NOUN
ejpam-7033	140	15	(	(	PUNCT
ejpam-7033	140	16	cs	cs	PROPN
ejpam-7033	140	17	)	)	PUNCT
ejpam-7033	140	18	,	,	PUNCT
ejpam-7033	140	19	whenever	whenever	SCONJ
ejpam-7033	140	20	we	we	PRON
ejpam-7033	140	21	get	get	VERB
ejpam-7033	140	22	k	k	PRON
ejpam-7033	140	23	∈	∈	PROPN
ejpam-7033	140	24	n	n	X
ejpam-7033	140	25	with	with	ADP
ejpam-7033	140	26	r(ℓn	r(ℓn	NOUN
ejpam-7033	140	27	,	,	PUNCT
ejpam-7033	140	28	ℓm	ℓm	NOUN
ejpam-7033	140	29	)	)	PUNCT
ejpam-7033	140	30	≪	≪	PUNCT
ejpam-7033	140	31	c	c	X
ejpam-7033	140	32	∀	∀	X
ejpam-7033	140	33	n	n	CCONJ
ejpam-7033	140	34	,	,	PUNCT
ejpam-7033	140	35	m	m	VERB
ejpam-7033	140	36	>	>	X
ejpam-7033	140	37	k.	k.	PROPN
ejpam-7033	141	1	(	(	PUNCT
ejpam-7033	141	2	2	2	X
ejpam-7033	141	3	)	)	PUNCT
ejpam-7033	141	4	any	any	DET
ejpam-7033	141	5	sequence	sequence	NOUN
ejpam-7033	141	6	{	{	PUNCT
ejpam-7033	141	7	ℓn	ℓn	ADV
ejpam-7033	141	8	}	}	PUNCT
ejpam-7033	141	9	is	be	AUX
ejpam-7033	141	10	referred	refer	VERB
ejpam-7033	141	11	to	to	ADP
ejpam-7033	141	12	as	as	ADP
ejpam-7033	141	13	convergent	convergent	NOUN
ejpam-7033	141	14	if	if	SCONJ
ejpam-7033	141	15	we	we	PRON
ejpam-7033	141	16	have	have	VERB
ejpam-7033	141	17	an	an	DET
ejpam-7033	141	18	k	k	PROPN
ejpam-7033	141	19	∈	∈	PROPN
ejpam-7033	141	20	n	n	X
ejpam-7033	141	21	with	with	ADP
ejpam-7033	141	22	r(ℓn	r(ℓn	PROPN
ejpam-7033	141	23	,	,	PUNCT
ejpam-7033	141	24	ℓ	ℓ	NUM
ejpam-7033	141	25	)	)	PUNCT
ejpam-7033	141	26	≪	≪	PUNCT
ejpam-7033	141	27	ϵ	ϵ	ADP
ejpam-7033	141	28	∀	∀	X
ejpam-7033	141	29	n	n	PRON
ejpam-7033	141	30	≥	≥	NOUN
ejpam-7033	141	31	k	k	NOUN
ejpam-7033	141	32	and	and	CCONJ
ejpam-7033	141	33	ℓ	ℓ	PROPN
ejpam-7033	141	34	∈	∈	PROPN
ejpam-7033	141	35	x.	x.	NOUN
ejpam-7033	141	36	(	(	PUNCT
ejpam-7033	141	37	3	3	X
ejpam-7033	141	38	)	)	PUNCT
ejpam-7033	141	39	any	any	DET
ejpam-7033	141	40	(	(	PUNCT
ejpam-7033	141	41	rcbms	rcbms	NOUN
ejpam-7033	141	42	)	)	PUNCT
ejpam-7033	141	43	referred	refer	VERB
ejpam-7033	141	44	as	as	ADP
ejpam-7033	141	45	complete	complete	ADJ
ejpam-7033	141	46	,	,	PUNCT
ejpam-7033	141	47	whenever	whenever	SCONJ
ejpam-7033	141	48	every	every	DET
ejpam-7033	141	49	(	(	PUNCT
ejpam-7033	141	50	cs	cs	PROPN
ejpam-7033	141	51	)	)	PUNCT
ejpam-7033	141	52	has	have	VERB
ejpam-7033	141	53	a	a	DET
ejpam-7033	141	54	convergent	convergent	NOUN
ejpam-7033	141	55	point	point	NOUN
ejpam-7033	141	56	in	in	ADP
ejpam-7033	141	57	x.	x.	PROPN
ejpam-7033	141	58	a.	a.	PROPN
ejpam-7033	141	59	arif	arif	PROPN
ejpam-7033	141	60	et	et	PROPN
ejpam-7033	141	61	al	al	PROPN
ejpam-7033	141	62	.	.	PUNCT
ejpam-7033	141	63	/	/	SYM
ejpam-7033	141	64	eur	eur	PROPN
ejpam-7033	141	65	.	.	PUNCT
ejpam-7033	142	1	j.	j.	PROPN
ejpam-7033	142	2	pure	pure	PROPN
ejpam-7033	142	3	appl	appl	PROPN
ejpam-7033	142	4	.	.	PROPN
ejpam-7033	142	5	math	math	PROPN
ejpam-7033	142	6	,	,	PUNCT
ejpam-7033	142	7	18	18	NUM
ejpam-7033	142	8	(	(	PUNCT
ejpam-7033	142	9	4	4	NUM
ejpam-7033	142	10	)	)	PUNCT
ejpam-7033	142	11	(	(	PUNCT
ejpam-7033	142	12	2025	2025	NUM
ejpam-7033	142	13	)	)	PUNCT
ejpam-7033	142	14	,	,	PUNCT
ejpam-7033	142	15	7033	7033	NUM
ejpam-7033	142	16	6	6	NUM
ejpam-7033	142	17	of	of	ADP
ejpam-7033	142	18	29	29	NUM
ejpam-7033	142	19	the	the	DET
ejpam-7033	142	20	main	main	ADJ
ejpam-7033	142	21	theorem	theorem	NOUN
ejpam-7033	142	22	of	of	ADP
ejpam-7033	142	23	simsek	simsek	NOUN
ejpam-7033	142	24	[	[	X
ejpam-7033	142	25	13	13	NUM
ejpam-7033	142	26	]	]	X
ejpam-7033	142	27	paper	paper	NOUN
ejpam-7033	142	28	is	be	AUX
ejpam-7033	142	29	as	as	SCONJ
ejpam-7033	142	30	follows	follow	VERB
ejpam-7033	142	31	:	:	PUNCT
ejpam-7033	142	32	theorem	theorem	NOUN
ejpam-7033	142	33	10	10	NUM
ejpam-7033	142	34	.	.	PUNCT
ejpam-7033	143	1	[	[	X
ejpam-7033	143	2	13	13	NUM
ejpam-7033	143	3	]	]	PUNCT
ejpam-7033	143	4	let	let	VERB
ejpam-7033	143	5	(	(	PUNCT
ejpam-7033	143	6	y	y	NOUN
ejpam-7033	143	7	,	,	PUNCT
ejpam-7033	143	8	d,⪯	d,⪯	PRON
ejpam-7033	143	9	)	)	PUNCT
ejpam-7033	143	10	be	be	VERB
ejpam-7033	143	11	a	a	DET
ejpam-7033	143	12	partially	partially	ADV
ejpam-7033	143	13	ordered	order	VERB
ejpam-7033	143	14	metric	metric	ADJ
ejpam-7033	143	15	space	space	NOUN
ejpam-7033	143	16	,	,	PUNCT
ejpam-7033	143	17	and	and	CCONJ
ejpam-7033	143	18	l	l	NOUN
ejpam-7033	143	19	:	:	PUNCT
ejpam-7033	143	20	y	y	X
ejpam-7033	143	21	→	→	SYM
ejpam-7033	143	22	y	y	PROPN
ejpam-7033	143	23	satisfies	satisfy	VERB
ejpam-7033	143	24	the	the	DET
ejpam-7033	143	25	following	follow	VERB
ejpam-7033	143	26	inequality	inequality	NOUN
ejpam-7033	143	27	:	:	PUNCT
ejpam-7033	143	28	t	t	PROPN
ejpam-7033	143	29	(	(	PUNCT
ejpam-7033	143	30	d(lx	d(lx	PROPN
ejpam-7033	143	31	,	,	PUNCT
ejpam-7033	143	32	ly	ly	NOUN
ejpam-7033	143	33	)	)	PUNCT
ejpam-7033	143	34	,	,	PUNCT
ejpam-7033	143	35	d(x	d(x	PROPN
ejpam-7033	143	36	,	,	PUNCT
ejpam-7033	143	37	y	y	NOUN
ejpam-7033	143	38	)	)	PUNCT
ejpam-7033	143	39	,	,	PUNCT
ejpam-7033	143	40	d(x	d(x	PROPN
ejpam-7033	143	41	,	,	PUNCT
ejpam-7033	143	42	lx	lx	NOUN
ejpam-7033	143	43	)	)	PUNCT
ejpam-7033	143	44	,	,	PUNCT
ejpam-7033	143	45	d(y	d(y	PROPN
ejpam-7033	143	46	,	,	PUNCT
ejpam-7033	143	47	ly	ly	NOUN
ejpam-7033	143	48	)	)	PUNCT
ejpam-7033	143	49	,	,	PUNCT
ejpam-7033	143	50	d(x	d(x	PROPN
ejpam-7033	143	51	,	,	PUNCT
ejpam-7033	143	52	ly	ly	NOUN
ejpam-7033	143	53	)	)	PUNCT
ejpam-7033	143	54	,	,	PUNCT
ejpam-7033	143	55	d(y	d(y	NOUN
ejpam-7033	143	56	,	,	PUNCT
ejpam-7033	143	57	lx	lx	NOUN
ejpam-7033	143	58	)	)	PUNCT
ejpam-7033	143	59	)	)	PUNCT
ejpam-7033	143	60	≤	≤	ADV
ejpam-7033	143	61	0	0	NUM
ejpam-7033	143	62	,	,	PUNCT
ejpam-7033	143	63	(	(	PUNCT
ejpam-7033	143	64	1	1	X
ejpam-7033	143	65	)	)	PUNCT
ejpam-7033	143	66	∀	∀	PUNCT
ejpam-7033	144	1	x	x	NOUN
ejpam-7033	144	2	,	,	PUNCT
ejpam-7033	144	3	y	y	PROPN
ejpam-7033	144	4	∈	∈	PROPN
ejpam-7033	144	5	y	y	PROPN
ejpam-7033	144	6	with	with	ADP
ejpam-7033	144	7	x	x	X
ejpam-7033	144	8	⪯	⪯	PROPN
ejpam-7033	144	9	y	y	PROPN
ejpam-7033	144	10	,	,	PUNCT
ejpam-7033	144	11	where	where	SCONJ
ejpam-7033	144	12	t	t	NOUN
ejpam-7033	144	13	:	:	PUNCT
ejpam-7033	145	1	[	[	X
ejpam-7033	145	2	0,∞)6	0,∞)6	NUM
ejpam-7033	145	3	→	→	SYM
ejpam-7033	145	4	(	(	PUNCT
ejpam-7033	145	5	−∞,∞	−∞,∞	NOUN
ejpam-7033	145	6	)	)	PUNCT
ejpam-7033	145	7	.	.	PUNCT
ejpam-7033	146	1	then	then	ADV
ejpam-7033	146	2	l	l	PROPN
ejpam-7033	146	3	admits	admit	VERB
ejpam-7033	146	4	a	a	DET
ejpam-7033	146	5	fixed	fixed	ADJ
ejpam-7033	146	6	point	point	NOUN
ejpam-7033	146	7	in	in	ADP
ejpam-7033	146	8	y	y	PROPN
ejpam-7033	146	9	provided	provide	VERB
ejpam-7033	146	10	l	l	NOUN
ejpam-7033	146	11	is	be	AUX
ejpam-7033	146	12	continuous	continuous	ADJ
ejpam-7033	146	13	or	or	CCONJ
ejpam-7033	146	14	(	(	PUNCT
ejpam-7033	146	15	y	y	PROPN
ejpam-7033	146	16	,	,	PUNCT
ejpam-7033	146	17	d,⪯	d,⪯	NOUN
ejpam-7033	146	18	)	)	PUNCT
ejpam-7033	146	19	is	be	AUX
ejpam-7033	146	20	as	as	ADP
ejpam-7033	146	21	a	a	DET
ejpam-7033	146	22	regular	regular	ADJ
ejpam-7033	146	23	space	space	NOUN
ejpam-7033	146	24	.	.	PUNCT
ejpam-7033	147	1	a	a	DET
ejpam-7033	147	2	number	number	NOUN
ejpam-7033	147	3	of	of	ADP
ejpam-7033	147	4	contractive	contractive	ADJ
ejpam-7033	147	5	conditions	condition	NOUN
ejpam-7033	147	6	were	be	AUX
ejpam-7033	147	7	obtained	obtain	VERB
ejpam-7033	147	8	by	by	ADP
ejpam-7033	147	9	using	use	VERB
ejpam-7033	147	10	(	(	PUNCT
ejpam-7033	147	11	1	1	NUM
ejpam-7033	147	12	)	)	PUNCT
ejpam-7033	147	13	,	,	PUNCT
ejpam-7033	147	14	for	for	ADP
ejpam-7033	147	15	instance	instance	NOUN
ejpam-7033	147	16	,	,	PUNCT
ejpam-7033	147	17	define	define	VERB
ejpam-7033	147	18	t	t	NOUN
ejpam-7033	147	19	:	:	PUNCT
ejpam-7033	148	1	[	[	X
ejpam-7033	148	2	0,∞)6	0,∞)6	NUM
ejpam-7033	148	3	→	→	SYM
ejpam-7033	148	4	(	(	PUNCT
ejpam-7033	148	5	−∞,∞	−∞,∞	NOUN
ejpam-7033	148	6	)	)	PUNCT
ejpam-7033	148	7	such	such	ADJ
ejpam-7033	148	8	that	that	SCONJ
ejpam-7033	148	9	t	t	PROPN
ejpam-7033	148	10	(	(	PUNCT
ejpam-7033	148	11	f1	f1	PROPN
ejpam-7033	148	12	,	,	PUNCT
ejpam-7033	148	13	f2	f2	PROPN
ejpam-7033	148	14	,	,	PUNCT
ejpam-7033	148	15	f3	f3	ADJ
ejpam-7033	148	16	,	,	PUNCT
ejpam-7033	148	17	f4	f4	PROPN
ejpam-7033	148	18	,	,	PUNCT
ejpam-7033	148	19	f5	f5	PROPN
ejpam-7033	148	20	,	,	PUNCT
ejpam-7033	148	21	f6	f6	PROPN
ejpam-7033	148	22	)	)	PUNCT
ejpam-7033	148	23	=	=	SYM
ejpam-7033	148	24	f1	f1	NOUN
ejpam-7033	148	25	−	−	PROPN
ejpam-7033	148	26	ψ	ψ	PROPN
ejpam-7033	148	27	(	(	PUNCT
ejpam-7033	148	28	max	max	X
ejpam-7033	148	29	{	{	PUNCT
ejpam-7033	148	30	f2	f2	PROPN
ejpam-7033	148	31	,	,	PUNCT
ejpam-7033	148	32	f3	f3	ADJ
ejpam-7033	148	33	,	,	PUNCT
ejpam-7033	148	34	f4	f4	PROPN
ejpam-7033	148	35	,	,	PUNCT
ejpam-7033	148	36	1	1	NUM
ejpam-7033	148	37	2	2	NUM
ejpam-7033	148	38	(	(	PUNCT
ejpam-7033	148	39	f5	f5	PROPN
ejpam-7033	148	40	+	+	SYM
ejpam-7033	148	41	f6	f6	NUM
ejpam-7033	148	42	)	)	PUNCT
ejpam-7033	148	43	}	}	PUNCT
ejpam-7033	148	44	)	)	PUNCT
ejpam-7033	148	45	,	,	PUNCT
ejpam-7033	148	46	which	which	PRON
ejpam-7033	148	47	leads	lead	VERB
ejpam-7033	148	48	to	to	ADP
ejpam-7033	148	49	main	main	ADJ
ejpam-7033	148	50	theorems	theorem	NOUN
ejpam-7033	148	51	proved	prove	VERB
ejpam-7033	148	52	in	in	ADP
ejpam-7033	148	53	[	[	X
ejpam-7033	148	54	14	14	NUM
ejpam-7033	148	55	]	]	PUNCT
ejpam-7033	148	56	.	.	PUNCT
ejpam-7033	149	1	equivalently	equivalently	ADV
ejpam-7033	149	2	by	by	ADP
ejpam-7033	149	3	choosing	choose	VERB
ejpam-7033	149	4	t	t	PROPN
ejpam-7033	149	5	(	(	PUNCT
ejpam-7033	149	6	f1	f1	PROPN
ejpam-7033	149	7	,	,	PUNCT
ejpam-7033	149	8	f2	f2	PROPN
ejpam-7033	149	9	,	,	PUNCT
ejpam-7033	149	10	f3	f3	ADJ
ejpam-7033	149	11	,	,	PUNCT
ejpam-7033	149	12	f4	f4	PROPN
ejpam-7033	149	13	,	,	PUNCT
ejpam-7033	149	14	f5	f5	PROPN
ejpam-7033	149	15	,	,	PUNCT
ejpam-7033	149	16	f6	f6	PROPN
ejpam-7033	149	17	)	)	PUNCT
ejpam-7033	149	18	=	=	SYM
ejpam-7033	149	19	f1	f1	NOUN
ejpam-7033	149	20	−	−	PROPN
ejpam-7033	149	21	kf2	kf2	PROPN
ejpam-7033	149	22	;	;	PUNCT
ejpam-7033	149	23	k	k	PROPN
ejpam-7033	149	24	∈	∈	PROPN
ejpam-7033	150	1	[	[	X
ejpam-7033	150	2	0	0	NUM
ejpam-7033	150	3	,	,	PUNCT
ejpam-7033	150	4	1	1	NUM
ejpam-7033	150	5	)	)	PUNCT
ejpam-7033	150	6	,	,	PUNCT
ejpam-7033	150	7	in	in	ADP
ejpam-7033	150	8	(	(	PUNCT
ejpam-7033	150	9	1	1	NUM
ejpam-7033	150	10	)	)	PUNCT
ejpam-7033	150	11	,	,	PUNCT
ejpam-7033	150	12	we	we	PRON
ejpam-7033	150	13	get	get	VERB
ejpam-7033	150	14	results	result	NOUN
ejpam-7033	150	15	proved	prove	VERB
ejpam-7033	150	16	in	in	ADP
ejpam-7033	150	17	[	[	X
ejpam-7033	150	18	4	4	NUM
ejpam-7033	150	19	]	]	PUNCT
ejpam-7033	150	20	.	.	PUNCT
ejpam-7033	151	1	so	so	ADV
ejpam-7033	151	2	,	,	PUNCT
ejpam-7033	151	3	we	we	PRON
ejpam-7033	151	4	get	get	VERB
ejpam-7033	151	5	different	different	ADJ
ejpam-7033	151	6	contractive	contractive	ADJ
ejpam-7033	151	7	conditions	condition	NOUN
ejpam-7033	151	8	for	for	ADP
ejpam-7033	151	9	different	different	ADJ
ejpam-7033	151	10	definitions	definition	NOUN
ejpam-7033	151	11	of	of	ADP
ejpam-7033	151	12	t	t	NOUN
ejpam-7033	151	13	:	:	PUNCT
ejpam-7033	152	1	[	[	X
ejpam-7033	152	2	0,∞)6	0,∞)6	NUM
ejpam-7033	152	3	→	→	SYM
ejpam-7033	152	4	(	(	PUNCT
ejpam-7033	152	5	−∞,∞	−∞,∞	NOUN
ejpam-7033	152	6	)	)	PUNCT
ejpam-7033	152	7	.	.	PUNCT
ejpam-7033	153	1	note	note	NOUN
ejpam-7033	153	2	:	:	PUNCT
ejpam-7033	153	3	throughout	throughout	ADP
ejpam-7033	153	4	in	in	ADP
ejpam-7033	153	5	this	this	DET
ejpam-7033	153	6	article	article	NOUN
ejpam-7033	153	7	we	we	PRON
ejpam-7033	153	8	will	will	AUX
ejpam-7033	153	9	take	take	VERB
ejpam-7033	153	10	(	(	PUNCT
ejpam-7033	153	11	e	e	NOUN
ejpam-7033	153	12	,	,	PUNCT
ejpam-7033	153	13	∥.∥	∥.∥	PROPN
ejpam-7033	153	14	)	)	PUNCT
ejpam-7033	153	15	as	as	ADP
ejpam-7033	153	16	a	a	DET
ejpam-7033	153	17	real	real	ADJ
ejpam-7033	153	18	banach	banach	NOUN
ejpam-7033	153	19	space	space	NOUN
ejpam-7033	153	20	and	and	CCONJ
ejpam-7033	153	21	b(e	b(e	PROPN
ejpam-7033	153	22	,	,	PUNCT
ejpam-7033	153	23	e	e	X
ejpam-7033	153	24	)	)	PUNCT
ejpam-7033	153	25	taken	take	VERB
ejpam-7033	153	26	as	as	ADP
ejpam-7033	153	27	collection	collection	NOUN
ejpam-7033	153	28	of	of	ADP
ejpam-7033	153	29	all	all	DET
ejpam-7033	153	30	bounded	bounded	ADJ
ejpam-7033	153	31	linear	linear	ADJ
ejpam-7033	153	32	mappings	mapping	NOUN
ejpam-7033	153	33	.	.	PUNCT
ejpam-7033	154	1	3	3	X
ejpam-7033	154	2	.	.	NUM
ejpam-7033	154	3	ordered	order	VERB
ejpam-7033	154	4	implicit	implicit	ADJ
ejpam-7033	154	5	relations	relation	NOUN
ejpam-7033	154	6	motivated	motivate	VERB
ejpam-7033	154	7	by	by	ADP
ejpam-7033	154	8	[	[	X
ejpam-7033	154	9	8–11	8–11	NOUN
ejpam-7033	154	10	,	,	PUNCT
ejpam-7033	154	11	39	39	NUM
ejpam-7033	154	12	,	,	PUNCT
ejpam-7033	154	13	40	40	NUM
ejpam-7033	154	14	]	]	PUNCT
ejpam-7033	154	15	,	,	PUNCT
ejpam-7033	154	16	we	we	PRON
ejpam-7033	154	17	construct	construct	VERB
ejpam-7033	154	18	an	an	DET
ejpam-7033	154	19	ordered	order	VERB
ejpam-7033	154	20	implicit	implicit	ADJ
ejpam-7033	154	21	relation	relation	NOUN
ejpam-7033	154	22	as	as	SCONJ
ejpam-7033	154	23	follows	follow	VERB
ejpam-7033	154	24	:	:	PUNCT
ejpam-7033	154	25	definition	definition	NOUN
ejpam-7033	154	26	11	11	NUM
ejpam-7033	154	27	.	.	PUNCT
ejpam-7033	155	1	assume	assume	VERB
ejpam-7033	155	2	(	(	PUNCT
ejpam-7033	155	3	e	e	NOUN
ejpam-7033	155	4	,	,	PUNCT
ejpam-7033	155	5	∥.∥	∥.∥	PROPN
ejpam-7033	155	6	)	)	PUNCT
ejpam-7033	155	7	is	be	AUX
ejpam-7033	155	8	taken	take	VERB
ejpam-7033	155	9	as	as	ADP
ejpam-7033	155	10	a	a	DET
ejpam-7033	155	11	real	real	ADJ
ejpam-7033	155	12	banach	banach	NOUN
ejpam-7033	155	13	space	space	NOUN
ejpam-7033	155	14	,	,	PUNCT
ejpam-7033	155	15	along	along	ADP
ejpam-7033	155	16	with	with	ADP
ejpam-7033	155	17	b(e	b(e	PROPN
ejpam-7033	155	18	,	,	PUNCT
ejpam-7033	155	19	e	e	NOUN
ejpam-7033	155	20	)	)	PUNCT
ejpam-7033	155	21	(	(	PUNCT
ejpam-7033	155	22	the	the	DET
ejpam-7033	155	23	collection	collection	NOUN
ejpam-7033	155	24	of	of	ADP
ejpam-7033	155	25	all	all	DET
ejpam-7033	155	26	bounded	bound	VERB
ejpam-7033	155	27	linear	linear	PROPN
ejpam-7033	155	28	operators	operators	PROPN
ejpam-7033	155	29	t	t	PROPN
ejpam-7033	155	30	)	)	PUNCT
ejpam-7033	155	31	,	,	PUNCT
ejpam-7033	155	32	t	t	X
ejpam-7033	155	33	:	:	PUNCT
ejpam-7033	156	1	e	e	X
ejpam-7033	156	2	→	→	SYM
ejpam-7033	156	3	e	e	X
ejpam-7033	156	4	where	where	SCONJ
ejpam-7033	156	5	∥t	∥t	ADJ
ejpam-7033	156	6	∥1	∥1	NOUN
ejpam-7033	156	7	<	<	X
ejpam-7033	156	8	1	1	NUM
ejpam-7033	156	9	s	s	NOUN
ejpam-7033	156	10	for	for	ADP
ejpam-7033	156	11	s	s	PRON
ejpam-7033	156	12	≥	≥	NOUN
ejpam-7033	156	13	1	1	NUM
ejpam-7033	156	14	,	,	PUNCT
ejpam-7033	156	15	we	we	PRON
ejpam-7033	156	16	take	take	VERB
ejpam-7033	156	17	∥.∥1	∥.∥1	ADJ
ejpam-7033	156	18	as	as	ADP
ejpam-7033	156	19	the	the	DET
ejpam-7033	156	20	usual	usual	ADJ
ejpam-7033	156	21	norm	norm	NOUN
ejpam-7033	156	22	.	.	PUNCT
ejpam-7033	157	1	the	the	DET
ejpam-7033	157	2	mapping	mapping	NOUN
ejpam-7033	157	3	j	j	PROPN
ejpam-7033	157	4	:	:	PUNCT
ejpam-7033	157	5	e6	e6	PROPN
ejpam-7033	157	6	→	→	SYM
ejpam-7033	157	7	e	e	PROPN
ejpam-7033	157	8	will	will	AUX
ejpam-7033	157	9	define	define	VERB
ejpam-7033	157	10	an	an	DET
ejpam-7033	157	11	ordered	order	VERB
ejpam-7033	157	12	implicit	implicit	ADJ
ejpam-7033	157	13	relation	relation	NOUN
ejpam-7033	157	14	,	,	PUNCT
ejpam-7033	157	15	if	if	SCONJ
ejpam-7033	157	16	j	j	PROPN
ejpam-7033	157	17	taken	take	VERB
ejpam-7033	157	18	as	as	ADV
ejpam-7033	157	19	continuous	continuous	ADJ
ejpam-7033	157	20	on	on	ADP
ejpam-7033	157	21	e6	e6	PROPN
ejpam-7033	157	22	and	and	CCONJ
ejpam-7033	157	23	also	also	ADV
ejpam-7033	157	24	it	it	PRON
ejpam-7033	157	25	satisfy	satisfy	VERB
ejpam-7033	157	26	the	the	DET
ejpam-7033	157	27	given	give	VERB
ejpam-7033	157	28	conditions	condition	NOUN
ejpam-7033	157	29	:	:	PUNCT
ejpam-7033	157	30	(	(	PUNCT
ejpam-7033	157	31	j1	j1	PROPN
ejpam-7033	157	32	)	)	PUNCT
ejpam-7033	157	33	r1	r1	PROPN
ejpam-7033	157	34	⪯	⪯	PROPN
ejpam-7033	157	35	υ1	υ1	PROPN
ejpam-7033	157	36	,	,	PUNCT
ejpam-7033	157	37	r5	r5	PROPN
ejpam-7033	157	38	⪯	⪯	NOUN
ejpam-7033	157	39	υ5	υ5	VERB
ejpam-7033	157	40	and	and	CCONJ
ejpam-7033	157	41	r6	r6	PROPN
ejpam-7033	157	42	⪯	⪯	NOUN
ejpam-7033	157	43	υ6	υ6	PROPN
ejpam-7033	157	44	⇒	⇒	PROPN
ejpam-7033	157	45	j	j	PROPN
ejpam-7033	157	46	(	(	PUNCT
ejpam-7033	157	47	υ1	υ1	PROPN
ejpam-7033	157	48	,	,	PUNCT
ejpam-7033	157	49	r2	r2	PROPN
ejpam-7033	157	50	,	,	PUNCT
ejpam-7033	157	51	r3	r3	PROPN
ejpam-7033	157	52	,	,	PUNCT
ejpam-7033	157	53	r4	r4	NOUN
ejpam-7033	157	54	,	,	PUNCT
ejpam-7033	157	55	υ5	υ5	PROPN
ejpam-7033	157	56	,	,	PUNCT
ejpam-7033	157	57	υ6	υ6	PROPN
ejpam-7033	157	58	)	)	PUNCT
ejpam-7033	158	1	⪯	⪯	PROPN
ejpam-7033	158	2	j	j	PROPN
ejpam-7033	158	3	(	(	PUNCT
ejpam-7033	158	4	r1	r1	PROPN
ejpam-7033	158	5	,	,	PUNCT
ejpam-7033	158	6	r2	r2	PROPN
ejpam-7033	158	7	,	,	PUNCT
ejpam-7033	158	8	r3	r3	PROPN
ejpam-7033	158	9	,	,	PUNCT
ejpam-7033	158	10	r4	r4	NOUN
ejpam-7033	158	11	,	,	PUNCT
ejpam-7033	158	12	r5	r5	PROPN
ejpam-7033	158	13	,	,	PUNCT
ejpam-7033	158	14	r6	r6	NOUN
ejpam-7033	158	15	)	)	PUNCT
ejpam-7033	158	16	.	.	PUNCT
ejpam-7033	159	1	(	(	PUNCT
ejpam-7033	159	2	j2	j2	PROPN
ejpam-7033	159	3	)	)	PUNCT
ejpam-7033	159	4	if	if	SCONJ
ejpam-7033	159	5	j	j	PROPN
ejpam-7033	159	6	(	(	PUNCT
ejpam-7033	159	7	r1	r1	PROPN
ejpam-7033	159	8	,	,	PUNCT
ejpam-7033	159	9	r2	r2	PROPN
ejpam-7033	159	10	,	,	PUNCT
ejpam-7033	159	11	r2	r2	PROPN
ejpam-7033	159	12	,	,	PUNCT
ejpam-7033	159	13	r1	r1	NOUN
ejpam-7033	159	14	,	,	PUNCT
ejpam-7033	159	15	α[r1	α[r1	ADV
ejpam-7033	159	16	+	+	CCONJ
ejpam-7033	159	17	r2	r2	PROPN
ejpam-7033	159	18	+	+	CCONJ
ejpam-7033	159	19	r3	r3	PROPN
ejpam-7033	159	20	]	]	PUNCT
ejpam-7033	159	21	,	,	PUNCT
ejpam-7033	159	22	r1	r1	PROPN
ejpam-7033	159	23	)	)	PUNCT
ejpam-7033	159	24	⪯	⪯	NOUN
ejpam-7033	159	25	0e	0e	NOUN
ejpam-7033	159	26	or	or	CCONJ
ejpam-7033	159	27	if	if	SCONJ
ejpam-7033	159	28	j	j	PROPN
ejpam-7033	159	29	(	(	PUNCT
ejpam-7033	159	30	r1	r1	PROPN
ejpam-7033	159	31	,	,	PUNCT
ejpam-7033	159	32	r2	r2	PROPN
ejpam-7033	159	33	,	,	PUNCT
ejpam-7033	159	34	r1	r1	NOUN
ejpam-7033	159	35	,	,	PUNCT
ejpam-7033	159	36	r2	r2	PROPN
ejpam-7033	159	37	,	,	PUNCT
ejpam-7033	159	38	r1	r1	NOUN
ejpam-7033	159	39	,	,	PUNCT
ejpam-7033	159	40	α[r1	α[r1	ADV
ejpam-7033	159	41	+	+	CCONJ
ejpam-7033	159	42	r2	r2	PROPN
ejpam-7033	159	43	+	+	CCONJ
ejpam-7033	159	44	r3	r3	PROPN
ejpam-7033	159	45	]	]	PUNCT
ejpam-7033	159	46	)	)	PUNCT
ejpam-7033	159	47	⪯	⪯	NOUN
ejpam-7033	159	48	0e	0e	NOUN
ejpam-7033	159	49	,	,	PUNCT
ejpam-7033	159	50	then	then	ADV
ejpam-7033	159	51	∃	∃	PROPN
ejpam-7033	159	52	t	t	PROPN
ejpam-7033	159	53	∈	∈	PROPN
ejpam-7033	159	54	b(e	b(e	PROPN
ejpam-7033	159	55	,	,	PUNCT
ejpam-7033	159	56	e	e	X
ejpam-7033	159	57	)	)	PUNCT
ejpam-7033	159	58	so	so	SCONJ
ejpam-7033	159	59	that	that	SCONJ
ejpam-7033	159	60	r1	r1	PROPN
ejpam-7033	159	61	⪯	⪯	NOUN
ejpam-7033	159	62	1	1	NUM
ejpam-7033	159	63	αt	αt	PROPN
ejpam-7033	159	64	(	(	PUNCT
ejpam-7033	159	65	r2	r2	PROPN
ejpam-7033	159	66	)	)	PUNCT
ejpam-7033	159	67	and	and	CCONJ
ejpam-7033	159	68	r3	r3	PROPN
ejpam-7033	159	69	⪯	⪯	NOUN
ejpam-7033	159	70	1	1	NUM
ejpam-7033	159	71	αt	αt	PROPN
ejpam-7033	159	72	(	(	PUNCT
ejpam-7033	159	73	r1	r1	PROPN
ejpam-7033	159	74	)	)	PUNCT
ejpam-7033	159	75	(	(	PUNCT
ejpam-7033	159	76	∀	∀	X
ejpam-7033	159	77	r1	r1	NOUN
ejpam-7033	159	78	,	,	PUNCT
ejpam-7033	159	79	r2	r2	PROPN
ejpam-7033	159	80	∈	∈	PROPN
ejpam-7033	159	81	e	e	NOUN
ejpam-7033	159	82	)	)	PUNCT
ejpam-7033	159	83	for	for	ADP
ejpam-7033	159	84	some	some	DET
ejpam-7033	159	85	r	r	NOUN
ejpam-7033	159	86	∋	∋	NOUN
ejpam-7033	159	87	α	α	NOUN
ejpam-7033	159	88	≥	≥	NOUN
ejpam-7033	159	89	1	1	NUM
ejpam-7033	159	90	.	.	PUNCT
ejpam-7033	160	1	(	(	PUNCT
ejpam-7033	160	2	j3	j3	PROPN
ejpam-7033	160	3	)	)	PUNCT
ejpam-7033	160	4	j	j	PROPN
ejpam-7033	160	5	(	(	PUNCT
ejpam-7033	160	6	αr,0e	αr,0e	PROPN
ejpam-7033	160	7	,	,	PUNCT
ejpam-7033	160	8	0e	0e	NOUN
ejpam-7033	160	9	,	,	PUNCT
ejpam-7033	160	10	r	r	NOUN
ejpam-7033	160	11	,	,	PUNCT
ejpam-7033	160	12	αr,0e	αr,0e	NOUN
ejpam-7033	160	13	)	)	PUNCT
ejpam-7033	160	14	≻	≻	NOUN
ejpam-7033	160	15	0e	0e	NOUN
ejpam-7033	160	16	whenever	whenever	SCONJ
ejpam-7033	160	17	∥r∥	∥r∥	NOUN
ejpam-7033	160	18	>	>	SYM
ejpam-7033	160	19	0	0	NUM
ejpam-7033	160	20	and	and	CCONJ
ejpam-7033	160	21	α	α	PRON
ejpam-7033	160	22	≥	≥	NOUN
ejpam-7033	160	23	1	1	NUM
ejpam-7033	160	24	.	.	PUNCT
ejpam-7033	161	1	let	let	VERB
ejpam-7033	161	2	f	f	PROPN
ejpam-7033	161	3	=	=	PRON
ejpam-7033	161	4	{	{	PUNCT
ejpam-7033	161	5	j	j	NOUN
ejpam-7033	161	6	:	:	PUNCT
ejpam-7033	161	7	e6	e6	PROPN
ejpam-7033	161	8	→	→	SYM
ejpam-7033	161	9	e	e	PROPN
ejpam-7033	161	10	|j	|j	PROPN
ejpam-7033	161	11	owns	own	VERB
ejpam-7033	161	12	j1,j2,j3	j1,j2,j3	PROPN
ejpam-7033	161	13	}	}	PUNCT
ejpam-7033	161	14	.	.	PUNCT
ejpam-7033	162	1	a.	a.	PROPN
ejpam-7033	162	2	arif	arif	PROPN
ejpam-7033	162	3	et	et	PROPN
ejpam-7033	162	4	al	al	PROPN
ejpam-7033	162	5	.	.	PUNCT
ejpam-7033	162	6	/	/	SYM
ejpam-7033	162	7	eur	eur	PROPN
ejpam-7033	162	8	.	.	PUNCT
ejpam-7033	163	1	j.	j.	PROPN
ejpam-7033	163	2	pure	pure	PROPN
ejpam-7033	163	3	appl	appl	PROPN
ejpam-7033	163	4	.	.	PROPN
ejpam-7033	163	5	math	math	PROPN
ejpam-7033	163	6	,	,	PUNCT
ejpam-7033	163	7	18	18	NUM
ejpam-7033	163	8	(	(	PUNCT
ejpam-7033	163	9	4	4	NUM
ejpam-7033	163	10	)	)	PUNCT
ejpam-7033	163	11	(	(	PUNCT
ejpam-7033	163	12	2025	2025	NUM
ejpam-7033	163	13	)	)	PUNCT
ejpam-7033	163	14	,	,	PUNCT
ejpam-7033	163	15	7033	7033	NUM
ejpam-7033	163	16	7	7	NUM
ejpam-7033	163	17	of	of	ADP
ejpam-7033	163	18	29	29	NUM
ejpam-7033	163	19	example	example	NOUN
ejpam-7033	163	20	4	4	NUM
ejpam-7033	163	21	.	.	PUNCT
ejpam-7033	163	22	consider	consider	VERB
ejpam-7033	163	23	the	the	DET
ejpam-7033	163	24	partial	partial	ADJ
ejpam-7033	163	25	order	order	NOUN
ejpam-7033	163	26	⪯	⪯	NOUN
ejpam-7033	163	27	in	in	ADP
ejpam-7033	163	28	a	a	DET
ejpam-7033	163	29	cone	cone	NOUN
ejpam-7033	163	30	c.	c.	NOUN
ejpam-7033	163	31	for	for	ADP
ejpam-7033	163	32	all	all	DET
ejpam-7033	163	33	ri	ri	NOUN
ejpam-7033	163	34	∈	∈	PROPN
ejpam-7033	163	35	e	e	NOUN
ejpam-7033	163	36	(	(	PUNCT
ejpam-7033	163	37	for	for	ADP
ejpam-7033	163	38	all	all	DET
ejpam-7033	163	39	i	i	PRON
ejpam-7033	163	40	=	=	NOUN
ejpam-7033	163	41	1	1	NUM
ejpam-7033	163	42	to	to	PART
ejpam-7033	163	43	6	6	NUM
ejpam-7033	163	44	)	)	PUNCT
ejpam-7033	163	45	and	and	CCONJ
ejpam-7033	163	46	for	for	ADP
ejpam-7033	163	47	some	some	DET
ejpam-7033	163	48	α	α	NOUN
ejpam-7033	163	49	<	<	X
ejpam-7033	163	50	1	1	NUM
ejpam-7033	163	51	,	,	PUNCT
ejpam-7033	163	52	define	define	VERB
ejpam-7033	163	53	j	j	PROPN
ejpam-7033	163	54	:	:	PUNCT
ejpam-7033	163	55	e6	e6	PROPN
ejpam-7033	163	56	→	→	SYM
ejpam-7033	163	57	e	e	PROPN
ejpam-7033	163	58	such	such	ADJ
ejpam-7033	163	59	that	that	SCONJ
ejpam-7033	163	60	j	j	PROPN
ejpam-7033	163	61	(	(	PUNCT
ejpam-7033	163	62	r1	r1	PROPN
ejpam-7033	163	63	,	,	PUNCT
ejpam-7033	163	64	r2	r2	PROPN
ejpam-7033	163	65	,	,	PUNCT
ejpam-7033	163	66	r3	r3	PROPN
ejpam-7033	163	67	,	,	PUNCT
ejpam-7033	163	68	r4	r4	NOUN
ejpam-7033	163	69	,	,	PUNCT
ejpam-7033	163	70	r5	r5	PROPN
ejpam-7033	163	71	,	,	PUNCT
ejpam-7033	163	72	r6	r6	NOUN
ejpam-7033	163	73	)	)	PUNCT
ejpam-7033	163	74	=	=	SYM
ejpam-7033	163	75	r5	r5	PROPN
ejpam-7033	163	76	−	−	PROPN
ejpam-7033	163	77	α{r1	α{r1	NUM
ejpam-7033	163	78	+	+	NUM
ejpam-7033	163	79	r2	r2	NOUN
ejpam-7033	163	80	}	}	PUNCT
ejpam-7033	163	81	−	−	PROPN
ejpam-7033	163	82	r1	r1	PROPN
ejpam-7033	163	83	.	.	PUNCT
ejpam-7033	164	1	then	then	ADV
ejpam-7033	164	2	the	the	DET
ejpam-7033	164	3	operator	operator	NOUN
ejpam-7033	164	4	j	j	PROPN
ejpam-7033	164	5	∈	∈	PROPN
ejpam-7033	164	6	f	f	PROPN
ejpam-7033	164	7	.	.	PUNCT
ejpam-7033	165	1	indeed	indeed	ADV
ejpam-7033	165	2	(	(	PUNCT
ejpam-7033	165	3	j1	j1	PROPN
ejpam-7033	165	4	)	)	PUNCT
ejpam-7033	165	5	.	.	PUNCT
ejpam-7033	166	1	let	let	VERB
ejpam-7033	166	2	r1	r1	PROPN
ejpam-7033	166	3	⪯	⪯	PROPN
ejpam-7033	166	4	γ1	γ1	PROPN
ejpam-7033	166	5	,	,	PUNCT
ejpam-7033	166	6	r5	r5	PROPN
ejpam-7033	166	7	⪯	⪯	NOUN
ejpam-7033	166	8	γ5	γ5	PROPN
ejpam-7033	166	9	and	and	CCONJ
ejpam-7033	166	10	r6	r6	PROPN
ejpam-7033	166	11	⪯	⪯	PROPN
ejpam-7033	166	12	γ6	γ6	PROPN
ejpam-7033	166	13	,	,	PUNCT
ejpam-7033	166	14	then	then	ADV
ejpam-7033	166	15	γ1	γ1	PROPN
ejpam-7033	166	16	−	−	PROPN
ejpam-7033	166	17	r1	r1	PROPN
ejpam-7033	166	18	∈	∈	PROPN
ejpam-7033	166	19	c	c	NOUN
ejpam-7033	166	20	,	,	PUNCT
ejpam-7033	166	21	γ5	γ5	NOUN
ejpam-7033	166	22	−	−	PROPN
ejpam-7033	166	23	r5	r5	PROPN
ejpam-7033	166	24	∈	∈	PROPN
ejpam-7033	166	25	c	c	PROPN
ejpam-7033	166	26	and	and	CCONJ
ejpam-7033	166	27	γ6	γ6	PROPN
ejpam-7033	166	28	−	−	PROPN
ejpam-7033	166	29	r6	r6	PROPN
ejpam-7033	166	30	∈	∈	PROPN
ejpam-7033	166	31	c.	c.	NOUN
ejpam-7033	166	32	now	now	ADV
ejpam-7033	166	33	we	we	PRON
ejpam-7033	166	34	show	show	VERB
ejpam-7033	166	35	that	that	SCONJ
ejpam-7033	166	36	j	j	PROPN
ejpam-7033	166	37	(	(	PUNCT
ejpam-7033	166	38	r1	r1	PROPN
ejpam-7033	166	39	,	,	PUNCT
ejpam-7033	166	40	r2	r2	PROPN
ejpam-7033	166	41	,	,	PUNCT
ejpam-7033	166	42	r3	r3	PROPN
ejpam-7033	166	43	,	,	PUNCT
ejpam-7033	166	44	r4	r4	NOUN
ejpam-7033	166	45	,	,	PUNCT
ejpam-7033	166	46	r5	r5	PROPN
ejpam-7033	166	47	,	,	PUNCT
ejpam-7033	166	48	r6)−	r6)−	PROPN
ejpam-7033	166	49	j	j	PROPN
ejpam-7033	166	50	(	(	PUNCT
ejpam-7033	166	51	γ1	γ1	PROPN
ejpam-7033	166	52	,	,	PUNCT
ejpam-7033	166	53	r2	r2	PROPN
ejpam-7033	166	54	,	,	PUNCT
ejpam-7033	166	55	r3	r3	PROPN
ejpam-7033	166	56	,	,	PUNCT
ejpam-7033	166	57	r4	r4	NOUN
ejpam-7033	166	58	,	,	PUNCT
ejpam-7033	166	59	γ5	γ5	NOUN
ejpam-7033	166	60	,	,	PUNCT
ejpam-7033	166	61	γ6	γ6	PROPN
ejpam-7033	166	62	)	)	PUNCT
ejpam-7033	166	63	∈	∈	PROPN
ejpam-7033	166	64	c.	c.	PROPN
ejpam-7033	166	65	consider	consider	VERB
ejpam-7033	166	66	,	,	PUNCT
ejpam-7033	166	67	j	j	PROPN
ejpam-7033	166	68	(	(	PUNCT
ejpam-7033	166	69	r1	r1	PROPN
ejpam-7033	166	70	,	,	PUNCT
ejpam-7033	166	71	r2	r2	PROPN
ejpam-7033	166	72	,	,	PUNCT
ejpam-7033	166	73	r3	r3	PROPN
ejpam-7033	166	74	,	,	PUNCT
ejpam-7033	166	75	r4	r4	NOUN
ejpam-7033	166	76	,	,	PUNCT
ejpam-7033	166	77	r5	r5	PROPN
ejpam-7033	166	78	,	,	PUNCT
ejpam-7033	166	79	r6)−	r6)−	PROPN
ejpam-7033	166	80	j	j	PROPN
ejpam-7033	166	81	(	(	PUNCT
ejpam-7033	166	82	γ1	γ1	PROPN
ejpam-7033	166	83	,	,	PUNCT
ejpam-7033	166	84	r2	r2	PROPN
ejpam-7033	166	85	,	,	PUNCT
ejpam-7033	166	86	r3	r3	PROPN
ejpam-7033	166	87	,	,	PUNCT
ejpam-7033	166	88	r4	r4	NOUN
ejpam-7033	166	89	,	,	PUNCT
ejpam-7033	166	90	γ5	γ5	NOUN
ejpam-7033	166	91	,	,	PUNCT
ejpam-7033	166	92	γ6	γ6	PROPN
ejpam-7033	166	93	)	)	PUNCT
ejpam-7033	167	1	=	=	SYM
ejpam-7033	167	2	r5	r5	PROPN
ejpam-7033	167	3	−	−	PROPN
ejpam-7033	167	4	α{r1	α{r1	NUM
ejpam-7033	167	5	+	+	NUM
ejpam-7033	167	6	r2	r2	NOUN
ejpam-7033	167	7	}	}	PUNCT
ejpam-7033	167	8	−	−	PROPN
ejpam-7033	167	9	r1	r1	NOUN
ejpam-7033	167	10	−	−	PROPN
ejpam-7033	168	1	(	(	PUNCT
ejpam-7033	168	2	γ5	γ5	VERB
ejpam-7033	168	3	−	−	PROPN
ejpam-7033	168	4	α{γ1	α{γ1	NUM
ejpam-7033	168	5	+	+	CCONJ
ejpam-7033	168	6	r2}+	r2}+	NOUN
ejpam-7033	168	7	r1	r1	NOUN
ejpam-7033	168	8	)	)	PUNCT
ejpam-7033	168	9	=	=	PUNCT
ejpam-7033	168	10	−(γ5	−(γ5	NUM
ejpam-7033	168	11	−	−	PROPN
ejpam-7033	168	12	r5	r5	PROPN
ejpam-7033	168	13	)	)	PUNCT
ejpam-7033	169	1	+	+	NUM
ejpam-7033	169	2	α(γ1	α(γ1	PROPN
ejpam-7033	169	3	−	−	PROPN
ejpam-7033	169	4	r1	r1	PROPN
ejpam-7033	169	5	)	)	PUNCT
ejpam-7033	169	6	∈	∈	PROPN
ejpam-7033	169	7	c.	c.	PROPN
ejpam-7033	169	8	thus	thus	ADV
ejpam-7033	169	9	,	,	PUNCT
ejpam-7033	169	10	j	j	PROPN
ejpam-7033	169	11	(	(	PUNCT
ejpam-7033	169	12	γ1	γ1	PROPN
ejpam-7033	169	13	,	,	PUNCT
ejpam-7033	169	14	r2	r2	PROPN
ejpam-7033	169	15	,	,	PUNCT
ejpam-7033	169	16	r3	r3	PROPN
ejpam-7033	169	17	,	,	PUNCT
ejpam-7033	169	18	r4	r4	NOUN
ejpam-7033	169	19	,	,	PUNCT
ejpam-7033	169	20	γ5	γ5	NOUN
ejpam-7033	169	21	,	,	PUNCT
ejpam-7033	169	22	γ6	γ6	PROPN
ejpam-7033	169	23	)	)	PUNCT
ejpam-7033	169	24	⪯	⪯	PROPN
ejpam-7033	169	25	j	j	PROPN
ejpam-7033	169	26	(	(	PUNCT
ejpam-7033	169	27	r1	r1	PROPN
ejpam-7033	169	28	,	,	PUNCT
ejpam-7033	169	29	r2	r2	PROPN
ejpam-7033	169	30	,	,	PUNCT
ejpam-7033	169	31	r3	r3	PROPN
ejpam-7033	169	32	,	,	PUNCT
ejpam-7033	169	33	r4	r4	NOUN
ejpam-7033	169	34	,	,	PUNCT
ejpam-7033	169	35	r5	r5	PROPN
ejpam-7033	169	36	,	,	PUNCT
ejpam-7033	169	37	r6	r6	NOUN
ejpam-7033	169	38	)	)	PUNCT
ejpam-7033	169	39	.	.	PUNCT
ejpam-7033	170	1	(	(	PUNCT
ejpam-7033	170	2	j2	j2	PROPN
ejpam-7033	170	3	)	)	PUNCT
ejpam-7033	170	4	.	.	PUNCT
ejpam-7033	171	1	let	let	VERB
ejpam-7033	171	2	r1	r1	PROPN
ejpam-7033	171	3	,	,	PUNCT
ejpam-7033	171	4	r2	r2	PROPN
ejpam-7033	171	5	,	,	PUNCT
ejpam-7033	171	6	r3	r3	PROPN
ejpam-7033	171	7	∈	∈	PROPN
ejpam-7033	172	1	e	e	NOUN
ejpam-7033	172	2	be	be	VERB
ejpam-7033	172	3	such	such	ADJ
ejpam-7033	172	4	that	that	SCONJ
ejpam-7033	172	5	0e	0e	PROPN
ejpam-7033	172	6	⪯	⪯	PROPN
ejpam-7033	172	7	r1	r1	PROPN
ejpam-7033	172	8	,	,	PUNCT
ejpam-7033	172	9	0e	0e	PROPN
ejpam-7033	172	10	⪯	⪯	PROPN
ejpam-7033	172	11	r2	r2	PROPN
ejpam-7033	172	12	,	,	PUNCT
ejpam-7033	172	13	0e	0e	PROPN
ejpam-7033	172	14	⪯	⪯	PROPN
ejpam-7033	172	15	r3	r3	PROPN
ejpam-7033	172	16	.	.	PUNCT
ejpam-7033	173	1	if	if	SCONJ
ejpam-7033	173	2	j	j	PROPN
ejpam-7033	173	3	(	(	PUNCT
ejpam-7033	173	4	r1	r1	PROPN
ejpam-7033	173	5	,	,	PUNCT
ejpam-7033	173	6	r2	r2	PROPN
ejpam-7033	173	7	,	,	PUNCT
ejpam-7033	173	8	r1	r1	NOUN
ejpam-7033	173	9	,	,	PUNCT
ejpam-7033	173	10	r2	r2	PROPN
ejpam-7033	173	11	,	,	PUNCT
ejpam-7033	173	12	s[r1	s[r1	ADJ
ejpam-7033	173	13	+	+	CCONJ
ejpam-7033	173	14	r2	r2	PROPN
ejpam-7033	173	15	+	+	CCONJ
ejpam-7033	173	16	r3	r3	PROPN
ejpam-7033	173	17	]	]	PUNCT
ejpam-7033	173	18	,	,	PUNCT
ejpam-7033	173	19	r1	r1	PROPN
ejpam-7033	173	20	)	)	PUNCT
ejpam-7033	173	21	⪯	⪯	NOUN
ejpam-7033	173	22	0e	0e	NOUN
ejpam-7033	173	23	then	then	ADV
ejpam-7033	173	24	by	by	ADP
ejpam-7033	173	25	definition	definition	NOUN
ejpam-7033	173	26	of	of	ADP
ejpam-7033	173	27	j	j	PROPN
ejpam-7033	173	28	,	,	PUNCT
ejpam-7033	173	29	we	we	PRON
ejpam-7033	173	30	have	have	VERB
ejpam-7033	173	31	−s[r1	−s[r1	NUM
ejpam-7033	174	1	+	+	NUM
ejpam-7033	174	2	r2	r2	PROPN
ejpam-7033	174	3	+	+	CCONJ
ejpam-7033	174	4	r3	r3	PROPN
ejpam-7033	174	5	]	]	PUNCT
ejpam-7033	175	1	+	+	CCONJ
ejpam-7033	175	2	α(r1	α(r1	X
ejpam-7033	175	3	+	+	CCONJ
ejpam-7033	175	4	r2	r2	NOUN
ejpam-7033	175	5	)	)	PUNCT
ejpam-7033	176	1	+	+	CCONJ
ejpam-7033	176	2	r1	r1	PROPN
ejpam-7033	176	3	∈	∈	PROPN
ejpam-7033	176	4	c.	c.	NOUN
ejpam-7033	177	1	so	so	SCONJ
ejpam-7033	177	2	we	we	PRON
ejpam-7033	177	3	get	get	VERB
ejpam-7033	177	4	two	two	NUM
ejpam-7033	177	5	equations	equation	NOUN
ejpam-7033	177	6	,	,	PUNCT
ejpam-7033	177	7	αr2	αr2	NOUN
ejpam-7033	177	8	−	−	PROPN
ejpam-7033	177	9	(	(	PUNCT
ejpam-7033	177	10	s−	s−	PROPN
ejpam-7033	177	11	α−	α−	ADP
ejpam-7033	177	12	1)r1	1)r1	NUM
ejpam-7033	177	13	∈	∈	PROPN
ejpam-7033	177	14	c	c	NOUN
ejpam-7033	177	15	,	,	PUNCT
ejpam-7033	177	16	(	(	PUNCT
ejpam-7033	177	17	2	2	NUM
ejpam-7033	177	18	)	)	PUNCT
ejpam-7033	177	19	(	(	PUNCT
ejpam-7033	177	20	α+	α+	PROPN
ejpam-7033	177	21	1−	1−	NUM
ejpam-7033	177	22	s)r1	s)r1	PROPN
ejpam-7033	177	23	−	−	PROPN
ejpam-7033	177	24	sr3	sr3	PROPN
ejpam-7033	177	25	∈	∈	PROPN
ejpam-7033	177	26	c.	c.	PROPN
ejpam-7033	177	27	(	(	PUNCT
ejpam-7033	177	28	3	3	NUM
ejpam-7033	177	29	)	)	PUNCT
ejpam-7033	177	30	for	for	ADP
ejpam-7033	177	31	(	(	PUNCT
ejpam-7033	177	32	2	2	X
ejpam-7033	177	33	)	)	PUNCT
ejpam-7033	177	34	if	if	SCONJ
ejpam-7033	177	35	r1	r1	PROPN
ejpam-7033	177	36	=	=	PUNCT
ejpam-7033	177	37	0e	0e	NOUN
ejpam-7033	177	38	,	,	PUNCT
ejpam-7033	177	39	then	then	ADV
ejpam-7033	177	40	αr2	αr2	PROPN
ejpam-7033	177	41	∈	∈	PROPN
ejpam-7033	177	42	c.	c.	PROPN
ejpam-7033	178	1	so	so	ADV
ejpam-7033	178	2	,	,	PUNCT
ejpam-7033	178	3	we	we	PRON
ejpam-7033	178	4	get	get	VERB
ejpam-7033	178	5	a	a	DET
ejpam-7033	178	6	t	t	NOUN
ejpam-7033	178	7	:	:	PUNCT
ejpam-7033	178	8	e	e	X
ejpam-7033	178	9	→	→	PUNCT
ejpam-7033	178	10	e	e	X
ejpam-7033	178	11	such	such	ADJ
ejpam-7033	178	12	that	that	DET
ejpam-7033	178	13	t	t	PROPN
ejpam-7033	178	14	(	(	PUNCT
ejpam-7033	178	15	r2	r2	PROPN
ejpam-7033	178	16	)	)	PUNCT
ejpam-7033	178	17	=	=	SYM
ejpam-7033	178	18	αr2	αr2	NOUN
ejpam-7033	178	19	(	(	PUNCT
ejpam-7033	178	20	α	α	X
ejpam-7033	178	21	<	<	X
ejpam-7033	178	22	1	1	NUM
ejpam-7033	178	23	is	be	AUX
ejpam-7033	178	24	fixed	fix	VERB
ejpam-7033	178	25	)	)	PUNCT
ejpam-7033	178	26	and	and	CCONJ
ejpam-7033	178	27	∥	∥	SYM
ejpam-7033	178	28	t	t	NOUN
ejpam-7033	178	29	∥=	∥=	NOUN
ejpam-7033	178	30	α	α	X
ejpam-7033	178	31	<	<	X
ejpam-7033	178	32	1	1	NUM
ejpam-7033	178	33	.	.	PUNCT
ejpam-7033	179	1	if	if	SCONJ
ejpam-7033	179	2	r1	r1	PROPN
ejpam-7033	179	3	̸=	̸=	PROPN
ejpam-7033	179	4	0e	0e	NOUN
ejpam-7033	179	5	,	,	PUNCT
ejpam-7033	179	6	then	then	ADV
ejpam-7033	179	7	,	,	PUNCT
ejpam-7033	179	8	(	(	PUNCT
ejpam-7033	179	9	2	2	X
ejpam-7033	179	10	)	)	PUNCT
ejpam-7033	179	11	implies	imply	VERB
ejpam-7033	179	12	r1	r1	PROPN
ejpam-7033	179	13	⪯	⪯	PROPN
ejpam-7033	179	14	α	α	PROPN
ejpam-7033	179	15	(	(	PUNCT
ejpam-7033	179	16	s−α−1)r2	s−α−1)r2	PROPN
ejpam-7033	179	17	.	.	PUNCT
ejpam-7033	180	1	so	so	ADV
ejpam-7033	180	2	∃	∃	PROPN
ejpam-7033	180	3	,	,	PUNCT
ejpam-7033	180	4	t	t	X
ejpam-7033	180	5	:	:	PUNCT
ejpam-7033	180	6	e	e	X
ejpam-7033	180	7	→	→	PUNCT
ejpam-7033	180	8	e	e	X
ejpam-7033	180	9	such	such	ADJ
ejpam-7033	180	10	that	that	DET
ejpam-7033	180	11	t	t	PROPN
ejpam-7033	180	12	(	(	PUNCT
ejpam-7033	180	13	r2	r2	PROPN
ejpam-7033	180	14	)	)	PUNCT
ejpam-7033	180	15	=	=	PUNCT
ejpam-7033	181	1	yr2	yr2	NOUN
ejpam-7033	181	2	(	(	PUNCT
ejpam-7033	181	3	y	y	NOUN
ejpam-7033	181	4	=	=	SYM
ejpam-7033	181	5	α	α	PROPN
ejpam-7033	181	6	(	(	PUNCT
ejpam-7033	181	7	s−α−1	s−α−1	NOUN
ejpam-7033	181	8	)	)	PUNCT
ejpam-7033	181	9	is	be	AUX
ejpam-7033	181	10	a	a	DET
ejpam-7033	181	11	scalar	scalar	NOUN
ejpam-7033	181	12	)	)	PUNCT
ejpam-7033	181	13	such	such	ADJ
ejpam-7033	181	14	that	that	SCONJ
ejpam-7033	181	15	r1	r1	PROPN
ejpam-7033	181	16	⪯	⪯	PROPN
ejpam-7033	181	17	t	t	PROPN
ejpam-7033	181	18	(	(	PUNCT
ejpam-7033	181	19	r2	r2	PROPN
ejpam-7033	181	20	)	)	PUNCT
ejpam-7033	181	21	,	,	PUNCT
ejpam-7033	181	22	for	for	ADP
ejpam-7033	181	23	α	α	PRON
ejpam-7033	181	24	<	<	X
ejpam-7033	181	25	1	1	NUM
ejpam-7033	181	26	.	.	PUNCT
ejpam-7033	182	1	for	for	ADP
ejpam-7033	182	2	(	(	PUNCT
ejpam-7033	182	3	3	3	X
ejpam-7033	182	4	)	)	PUNCT
ejpam-7033	182	5	if	if	SCONJ
ejpam-7033	182	6	r3	r3	PROPN
ejpam-7033	182	7	=	=	SYM
ejpam-7033	182	8	0e	0e	NOUN
ejpam-7033	182	9	,	,	PUNCT
ejpam-7033	182	10	then	then	ADV
ejpam-7033	182	11	(	(	PUNCT
ejpam-7033	182	12	α	α	NOUN
ejpam-7033	182	13	+	+	X
ejpam-7033	182	14	1−	1−	NUM
ejpam-7033	182	15	s)r1	s)r1	PROPN
ejpam-7033	182	16	∈	∈	PROPN
ejpam-7033	182	17	c.	c.	NOUN
ejpam-7033	183	1	so	so	ADV
ejpam-7033	183	2	,	,	PUNCT
ejpam-7033	183	3	we	we	PRON
ejpam-7033	183	4	have	have	VERB
ejpam-7033	183	5	t	t	NOUN
ejpam-7033	183	6	:	:	PUNCT
ejpam-7033	184	1	e	e	X
ejpam-7033	184	2	→	→	SYM
ejpam-7033	184	3	e	e	X
ejpam-7033	184	4	taken	take	VERB
ejpam-7033	184	5	as	as	ADP
ejpam-7033	184	6	t	t	PROPN
ejpam-7033	184	7	(	(	PUNCT
ejpam-7033	184	8	r1	r1	PROPN
ejpam-7033	184	9	)	)	PUNCT
ejpam-7033	184	10	=	=	SYM
ejpam-7033	184	11	yr1	yr1	PROPN
ejpam-7033	184	12	(	(	PUNCT
ejpam-7033	184	13	where	where	SCONJ
ejpam-7033	184	14	y	y	PROPN
ejpam-7033	184	15	=	=	PRON
ejpam-7033	184	16	(	(	PUNCT
ejpam-7033	184	17	α	α	NOUN
ejpam-7033	184	18	+	+	NOUN
ejpam-7033	184	19	1	1	NUM
ejpam-7033	184	20	−	−	NOUN
ejpam-7033	184	21	s	s	NOUN
ejpam-7033	184	22	)	)	PUNCT
ejpam-7033	184	23	is	be	AUX
ejpam-7033	184	24	a	a	DET
ejpam-7033	184	25	scalar	scalar	NOUN
ejpam-7033	184	26	with	with	ADP
ejpam-7033	184	27	α	α	PROPN
ejpam-7033	184	28	<	<	X
ejpam-7033	184	29	1	1	NUM
ejpam-7033	184	30	≤	≤	NOUN
ejpam-7033	184	31	s	s	VERB
ejpam-7033	184	32	implies	imply	VERB
ejpam-7033	184	33	α	α	X
ejpam-7033	184	34	−	−	PROPN
ejpam-7033	184	35	s	s	PART
ejpam-7033	184	36	<	<	X
ejpam-7033	184	37	0	0	PROPN
ejpam-7033	184	38	and	and	CCONJ
ejpam-7033	184	39	α	α	NUM
ejpam-7033	184	40	−	−	PROPN
ejpam-7033	184	41	s	s	PART
ejpam-7033	184	42	+	+	CCONJ
ejpam-7033	184	43	1	1	NUM
ejpam-7033	184	44	<	<	SYM
ejpam-7033	184	45	1	1	NUM
ejpam-7033	184	46	)	)	PUNCT
ejpam-7033	184	47	such	such	ADJ
ejpam-7033	184	48	that	that	SCONJ
ejpam-7033	184	49	r3	r3	PROPN
ejpam-7033	184	50	⪯	⪯	PROPN
ejpam-7033	184	51	t	t	PROPN
ejpam-7033	184	52	(	(	PUNCT
ejpam-7033	184	53	r1	r1	PROPN
ejpam-7033	184	54	)	)	PUNCT
ejpam-7033	184	55	.	.	PUNCT
ejpam-7033	185	1	now	now	ADV
ejpam-7033	185	2	if	if	SCONJ
ejpam-7033	185	3	r3	r3	PROPN
ejpam-7033	185	4	̸=	̸=	PROPN
ejpam-7033	185	5	0e	0e	NOUN
ejpam-7033	185	6	,	,	PUNCT
ejpam-7033	185	7	then	then	ADV
ejpam-7033	185	8	,	,	PUNCT
ejpam-7033	185	9	r3	r3	PROPN
ejpam-7033	185	10	⪯	⪯	NOUN
ejpam-7033	185	11	(	(	PUNCT
ejpam-7033	185	12	1+α−s	1+α−s	NUM
ejpam-7033	185	13	)	)	PUNCT
ejpam-7033	185	14	s	s	PART
ejpam-7033	185	15	r1	r1	PROPN
ejpam-7033	185	16	.	.	PUNCT
ejpam-7033	186	1	so	so	ADV
ejpam-7033	186	2	,	,	PUNCT
ejpam-7033	186	3	we	we	PRON
ejpam-7033	186	4	get	get	VERB
ejpam-7033	186	5	t	t	NOUN
ejpam-7033	186	6	:	:	PUNCT
ejpam-7033	187	1	e	e	X
ejpam-7033	187	2	→	→	SYM
ejpam-7033	187	3	e	e	X
ejpam-7033	187	4	taken	take	VERB
ejpam-7033	187	5	as	as	ADP
ejpam-7033	187	6	t	t	PROPN
ejpam-7033	187	7	(	(	PUNCT
ejpam-7033	187	8	r2	r2	PROPN
ejpam-7033	187	9	)	)	PUNCT
ejpam-7033	187	10	=	=	PUNCT
ejpam-7033	188	1	yr2	yr2	NOUN
ejpam-7033	188	2	(	(	PUNCT
ejpam-7033	188	3	y	y	NOUN
ejpam-7033	188	4	=	=	SYM
ejpam-7033	188	5	(	(	PUNCT
ejpam-7033	188	6	1+α−s	1+α−s	NUM
ejpam-7033	188	7	)	)	PUNCT
ejpam-7033	188	8	s	s	VERB
ejpam-7033	188	9	is	be	AUX
ejpam-7033	188	10	fixed	fix	VERB
ejpam-7033	188	11	)	)	PUNCT
ejpam-7033	188	12	with	with	ADP
ejpam-7033	188	13	r3	r3	PROPN
ejpam-7033	188	14	⪯	⪯	NOUN
ejpam-7033	188	15	(	(	PUNCT
ejpam-7033	188	16	r1	r1	PROPN
ejpam-7033	188	17	)	)	PUNCT
ejpam-7033	188	18	,	,	PUNCT
ejpam-7033	188	19	for	for	ADP
ejpam-7033	188	20	α	α	PRON
ejpam-7033	188	21	<	<	X
ejpam-7033	188	22	1	1	NUM
ejpam-7033	188	23	.	.	PUNCT
ejpam-7033	188	24	(	(	PUNCT
ejpam-7033	188	25	j3	j3	PROPN
ejpam-7033	188	26	)	)	PUNCT
ejpam-7033	188	27	.	.	PUNCT
ejpam-7033	189	1	take	take	VERB
ejpam-7033	189	2	r	r	NOUN
ejpam-7033	189	3	∈	∈	NOUN
ejpam-7033	189	4	e	e	NOUN
ejpam-7033	189	5	and	and	CCONJ
ejpam-7033	189	6	∥r∥	∥r∥	NUM
ejpam-7033	189	7	>	>	SYM
ejpam-7033	189	8	0	0	PUNCT
ejpam-7033	190	1	with	with	ADP
ejpam-7033	190	2	,	,	PUNCT
ejpam-7033	190	3	0e	0e	PROPN
ejpam-7033	190	4	⪯	⪯	PROPN
ejpam-7033	190	5	j	j	PROPN
ejpam-7033	190	6	(	(	PUNCT
ejpam-7033	190	7	sr,0e	sr,0e	NOUN
ejpam-7033	190	8	,	,	PUNCT
ejpam-7033	190	9	0e	0e	NOUN
ejpam-7033	190	10	,	,	PUNCT
ejpam-7033	190	11	r	r	NOUN
ejpam-7033	190	12	,	,	PUNCT
ejpam-7033	190	13	sr,0e	sr,0e	NOUN
ejpam-7033	190	14	)	)	PUNCT
ejpam-7033	190	15	then	then	ADV
ejpam-7033	190	16	(	(	PUNCT
ejpam-7033	190	17	s	s	AUX
ejpam-7033	190	18	−	−	NOUN
ejpam-7033	190	19	αs	αs	INTJ
ejpam-7033	190	20	−	−	PROPN
ejpam-7033	190	21	1)r	1)r	NUM
ejpam-7033	190	22	∈	∈	PROPN
ejpam-7033	190	23	c	c	NOUN
ejpam-7033	190	24	,	,	PUNCT
ejpam-7033	190	25	which	which	PRON
ejpam-7033	190	26	is	be	AUX
ejpam-7033	190	27	true	true	ADJ
ejpam-7033	190	28	for	for	ADP
ejpam-7033	190	29	∥r∥	∥r∥	NUM
ejpam-7033	190	30	>	>	SYM
ejpam-7033	190	31	0	0	NUM
ejpam-7033	190	32	.	.	PUNCT
ejpam-7033	190	33	example	example	NOUN
ejpam-7033	190	34	5	5	NUM
ejpam-7033	190	35	.	.	PUNCT
ejpam-7033	190	36	similarly	similarly	ADV
ejpam-7033	190	37	,	,	PUNCT
ejpam-7033	190	38	the	the	DET
ejpam-7033	190	39	operator	operator	NOUN
ejpam-7033	190	40	j	j	PROPN
ejpam-7033	190	41	:	:	PUNCT
ejpam-7033	190	42	e6	e6	PROPN
ejpam-7033	190	43	→	→	SYM
ejpam-7033	190	44	e	e	PROPN
ejpam-7033	190	45	defined	define	VERB
ejpam-7033	190	46	by	by	ADP
ejpam-7033	190	47	(	(	PUNCT
ejpam-7033	190	48	i	i	NOUN
ejpam-7033	190	49	)	)	PUNCT
ejpam-7033	190	50	.	.	PUNCT
ejpam-7033	191	1	j	j	PROPN
ejpam-7033	191	2	∗	∗	NOUN
ejpam-7033	191	3	1	1	NUM
ejpam-7033	191	4	(	(	PUNCT
ejpam-7033	191	5	r1	r1	NOUN
ejpam-7033	191	6	,	,	PUNCT
ejpam-7033	191	7	r2	r2	PROPN
ejpam-7033	191	8	,	,	PUNCT
ejpam-7033	191	9	r3	r3	PROPN
ejpam-7033	191	10	,	,	PUNCT
ejpam-7033	191	11	r4	r4	NOUN
ejpam-7033	191	12	,	,	PUNCT
ejpam-7033	191	13	r5	r5	PROPN
ejpam-7033	191	14	,	,	PUNCT
ejpam-7033	191	15	r6	r6	NOUN
ejpam-7033	191	16	)	)	PUNCT
ejpam-7033	192	1	=	=	PROPN
ejpam-7033	192	2	r1	r1	PROPN
ejpam-7033	192	3	+	+	CCONJ
ejpam-7033	192	4	r5	r5	PROPN
ejpam-7033	192	5	−	−	PROPN
ejpam-7033	192	6	α(r2	α(r2	NOUN
ejpam-7033	192	7	+	+	CCONJ
ejpam-7033	192	8	r4);α	r4);α	X
ejpam-7033	192	9	<	<	X
ejpam-7033	192	10	1	1	NUM
ejpam-7033	192	11	2	2	NUM
ejpam-7033	192	12	.	.	PUNCT
ejpam-7033	192	13	(	(	PUNCT
ejpam-7033	192	14	ii	ii	NOUN
ejpam-7033	192	15	)	)	PUNCT
ejpam-7033	192	16	.	.	PUNCT
ejpam-7033	193	1	j	j	PROPN
ejpam-7033	193	2	∗	∗	NOUN
ejpam-7033	193	3	2	2	NUM
ejpam-7033	193	4	(	(	PUNCT
ejpam-7033	193	5	r1	r1	NOUN
ejpam-7033	193	6	,	,	PUNCT
ejpam-7033	193	7	r2	r2	PROPN
ejpam-7033	193	8	,	,	PUNCT
ejpam-7033	193	9	r3	r3	PROPN
ejpam-7033	193	10	,	,	PUNCT
ejpam-7033	193	11	r4	r4	NOUN
ejpam-7033	193	12	,	,	PUNCT
ejpam-7033	193	13	r5	r5	PROPN
ejpam-7033	193	14	,	,	PUNCT
ejpam-7033	193	15	r6	r6	NOUN
ejpam-7033	193	16	)	)	PUNCT
ejpam-7033	193	17	=	=	PUNCT
ejpam-7033	194	1	(	(	PUNCT
ejpam-7033	194	2	1−	1−	NUM
ejpam-7033	194	3	β)r5	β)r5	PROPN
ejpam-7033	194	4	−	−	NOUN
ejpam-7033	194	5	β(r3	β(r3	VERB
ejpam-7033	194	6	+	+	CCONJ
ejpam-7033	194	7	r4)−	r4)−	VERB
ejpam-7033	194	8	r3;β	r3;β	PROPN
ejpam-7033	194	9	∈	∈	PROPN
ejpam-7033	194	10	(	(	PUNCT
ejpam-7033	194	11	−∞	−∞	NOUN
ejpam-7033	194	12	,	,	PUNCT
ejpam-7033	194	13	14	14	NUM
ejpam-7033	194	14	)	)	PUNCT
ejpam-7033	194	15	.	.	PUNCT
ejpam-7033	195	1	(	(	PUNCT
ejpam-7033	195	2	iii	iii	NOUN
ejpam-7033	195	3	)	)	PUNCT
ejpam-7033	195	4	.	.	PUNCT
ejpam-7033	196	1	j	j	PROPN
ejpam-7033	196	2	∗	∗	NOUN
ejpam-7033	196	3	3	3	NUM
ejpam-7033	196	4	(	(	PUNCT
ejpam-7033	196	5	r1	r1	NOUN
ejpam-7033	196	6	,	,	PUNCT
ejpam-7033	196	7	r2	r2	PROPN
ejpam-7033	196	8	,	,	PUNCT
ejpam-7033	196	9	r3	r3	PROPN
ejpam-7033	196	10	,	,	PUNCT
ejpam-7033	196	11	r4	r4	NOUN
ejpam-7033	196	12	,	,	PUNCT
ejpam-7033	196	13	r5	r5	PROPN
ejpam-7033	196	14	,	,	PUNCT
ejpam-7033	196	15	r6	r6	NOUN
ejpam-7033	196	16	)	)	PUNCT
ejpam-7033	196	17	=	=	PUNCT
ejpam-7033	197	1	γr1	γr1	NOUN
ejpam-7033	197	2	−	−	NOUN
ejpam-7033	197	3	r2	r2	NOUN
ejpam-7033	197	4	;	;	PUNCT
ejpam-7033	197	5	γ	γ	X
ejpam-7033	197	6	>	>	X
ejpam-7033	197	7	1	1	NUM
ejpam-7033	197	8	.	.	PUNCT
ejpam-7033	197	9	(	(	PUNCT
ejpam-7033	197	10	iv	iv	X
ejpam-7033	197	11	)	)	PUNCT
ejpam-7033	197	12	.	.	PUNCT
ejpam-7033	198	1	j	j	PROPN
ejpam-7033	198	2	∗	∗	NOUN
ejpam-7033	198	3	4	4	NUM
ejpam-7033	198	4	(	(	PUNCT
ejpam-7033	198	5	r1	r1	NOUN
ejpam-7033	198	6	,	,	PUNCT
ejpam-7033	198	7	r2	r2	PROPN
ejpam-7033	198	8	,	,	PUNCT
ejpam-7033	198	9	r3	r3	PROPN
ejpam-7033	198	10	,	,	PUNCT
ejpam-7033	198	11	r4	r4	NOUN
ejpam-7033	198	12	,	,	PUNCT
ejpam-7033	198	13	r5	r5	PROPN
ejpam-7033	198	14	,	,	PUNCT
ejpam-7033	198	15	r6	r6	NOUN
ejpam-7033	198	16	)	)	PUNCT
ejpam-7033	199	1	=	=	PROPN
ejpam-7033	199	2	r1	r1	PROPN
ejpam-7033	199	3	+	+	CCONJ
ejpam-7033	199	4	r5	r5	PROPN
ejpam-7033	199	5	−	−	PROPN
ejpam-7033	199	6	ϱ{r2	ϱ{r2	PROPN
ejpam-7033	199	7	+	+	CCONJ
ejpam-7033	199	8	r4	r4	PROPN
ejpam-7033	199	9	}	}	PUNCT
ejpam-7033	199	10	;	;	PUNCT
ejpam-7033	199	11	ϱ	ϱ	ADP
ejpam-7033	199	12	<	<	X
ejpam-7033	199	13	3	3	NUM
ejpam-7033	199	14	2	2	NUM
ejpam-7033	199	15	.	.	PUNCT
ejpam-7033	200	1	then	then	ADV
ejpam-7033	200	2	j	j	PROPN
ejpam-7033	200	3	∗	∗	VERB
ejpam-7033	200	4	i	i	PRON
ejpam-7033	201	1	∈	∈	PROPN
ejpam-7033	201	2	f	f	PROPN
ejpam-7033	201	3	for	for	ADP
ejpam-7033	201	4	each	each	DET
ejpam-7033	201	5	i	i	NOUN
ejpam-7033	201	6	=	=	NOUN
ejpam-7033	201	7	1	1	NUM
ejpam-7033	201	8	,	,	PUNCT
ejpam-7033	201	9	2	2	NUM
ejpam-7033	201	10	,	,	PUNCT
ejpam-7033	201	11	3	3	NUM
ejpam-7033	201	12	,	,	PUNCT
ejpam-7033	201	13	4	4	NUM
ejpam-7033	201	14	.	.	X
ejpam-7033	202	1	we	we	PRON
ejpam-7033	202	2	will	will	AUX
ejpam-7033	202	3	apply	apply	VERB
ejpam-7033	202	4	this	this	DET
ejpam-7033	202	5	implicit	implicit	ADJ
ejpam-7033	202	6	relation	relation	NOUN
ejpam-7033	202	7	along	along	ADP
ejpam-7033	202	8	with	with	ADP
ejpam-7033	202	9	some	some	DET
ejpam-7033	202	10	additional	additional	ADJ
ejpam-7033	202	11	conditions	condition	NOUN
ejpam-7033	202	12	to	to	PART
ejpam-7033	202	13	construct	construct	VERB
ejpam-7033	202	14	a	a	DET
ejpam-7033	202	15	sequence	sequence	NOUN
ejpam-7033	202	16	,	,	PUNCT
ejpam-7033	202	17	and	and	CCONJ
ejpam-7033	202	18	to	to	PART
ejpam-7033	202	19	solve	solve	VERB
ejpam-7033	202	20	the	the	DET
ejpam-7033	202	21	following	following	ADJ
ejpam-7033	202	22	problem	problem	NOUN
ejpam-7033	202	23	fixed	fix	VERB
ejpam-7033	202	24	-	-	PUNCT
ejpam-7033	202	25	point	point	NOUN
ejpam-7033	202	26	problem	problem	NOUN
ejpam-7033	202	27	:	:	PUNCT
ejpam-7033	202	28	“	"	PUNCT
ejpam-7033	202	29	find	find	VERB
ejpam-7033	202	30	z∗	z∗	PROPN
ejpam-7033	202	31	∈	∈	PROPN
ejpam-7033	202	32	(	(	PUNCT
ejpam-7033	202	33	x	x	NOUN
ejpam-7033	202	34	,	,	PUNCT
ejpam-7033	202	35	r	r	NOUN
ejpam-7033	202	36	)	)	PUNCT
ejpam-7033	202	37	along	along	ADP
ejpam-7033	202	38	f(z∗	f(z∗	NOUN
ejpam-7033	202	39	)	)	PUNCT
ejpam-7033	202	40	=	=	SYM
ejpam-7033	202	41	z∗	z∗	NOUN
ejpam-7033	202	42	”	"	PUNCT
ejpam-7033	202	43	,	,	PUNCT
ejpam-7033	202	44	when	when	SCONJ
ejpam-7033	202	45	t	t	PROPN
ejpam-7033	202	46	∈	∈	PROPN
ejpam-7033	202	47	b(e	b(e	PROPN
ejpam-7033	202	48	,	,	PUNCT
ejpam-7033	202	49	e	e	NOUN
ejpam-7033	202	50	)	)	PUNCT
ejpam-7033	202	51	,	,	PUNCT
ejpam-7033	202	52	i	i	PRON
ejpam-7033	202	53	:	:	PUNCT
ejpam-7033	203	1	e	e	X
ejpam-7033	203	2	→	→	PUNCT
ejpam-7033	203	3	e	e	NOUN
ejpam-7033	203	4	considered	consider	VERB
ejpam-7033	203	5	as	as	ADP
ejpam-7033	203	6	a.	a.	PROPN
ejpam-7033	203	7	arif	arif	PROPN
ejpam-7033	203	8	et	et	PROPN
ejpam-7033	203	9	al	al	PROPN
ejpam-7033	203	10	.	.	PUNCT
ejpam-7033	203	11	/	/	SYM
ejpam-7033	203	12	eur	eur	PROPN
ejpam-7033	203	13	.	.	PUNCT
ejpam-7033	204	1	j.	j.	PROPN
ejpam-7033	204	2	pure	pure	PROPN
ejpam-7033	204	3	appl	appl	PROPN
ejpam-7033	204	4	.	.	PROPN
ejpam-7033	204	5	math	math	PROPN
ejpam-7033	204	6	,	,	PUNCT
ejpam-7033	204	7	18	18	NUM
ejpam-7033	204	8	(	(	PUNCT
ejpam-7033	204	9	4	4	NUM
ejpam-7033	204	10	)	)	PUNCT
ejpam-7033	204	11	(	(	PUNCT
ejpam-7033	204	12	2025	2025	NUM
ejpam-7033	204	13	)	)	PUNCT
ejpam-7033	204	14	,	,	PUNCT
ejpam-7033	204	15	7033	7033	NUM
ejpam-7033	204	16	8	8	NUM
ejpam-7033	204	17	of	of	ADP
ejpam-7033	204	18	29	29	NUM
ejpam-7033	204	19	an	an	DET
ejpam-7033	204	20	identity	identity	NOUN
ejpam-7033	204	21	operator	operator	NOUN
ejpam-7033	204	22	,	,	PUNCT
ejpam-7033	204	23	j	j	PROPN
ejpam-7033	204	24	∈	∈	PROPN
ejpam-7033	204	25	f	f	PROPN
ejpam-7033	204	26	and	and	CCONJ
ejpam-7033	204	27	𭟋	𭟋	ADP
ejpam-7033	204	28	:	:	PUNCT
ejpam-7033	204	29	x	x	X
ejpam-7033	204	30	→	→	SYM
ejpam-7033	204	31	x	x	PRON
ejpam-7033	204	32	admits	admit	NOUN
ejpam-7033	204	33	(	(	PUNCT
ejpam-7033	204	34	4	4	NUM
ejpam-7033	204	35	)	)	PUNCT
ejpam-7033	204	36	,	,	PUNCT
ejpam-7033	204	37	for	for	ADP
ejpam-7033	204	38	each	each	DET
ejpam-7033	204	39	pair	pair	NOUN
ejpam-7033	204	40	of	of	ADP
ejpam-7033	204	41	comparable	comparable	ADJ
ejpam-7033	204	42	elements	element	NOUN
ejpam-7033	204	43	r	r	NOUN
ejpam-7033	204	44	,	,	PUNCT
ejpam-7033	204	45	x	x	SYM
ejpam-7033	204	46	∈	∈	PROPN
ejpam-7033	204	47	x	x	INTJ
ejpam-7033	204	48	when	when	SCONJ
ejpam-7033	204	49	s	s	X
ejpam-7033	204	50	≥	≥	NOUN
ejpam-7033	204	51	1	1	NUM
ejpam-7033	204	52	.	.	PUNCT
ejpam-7033	205	1	(	(	PUNCT
ejpam-7033	205	2	i	i	PRON
ejpam-7033	205	3	−	−	PROPN
ejpam-7033	206	1	t	t	NOUN
ejpam-7033	206	2	)	)	PUNCT
ejpam-7033	206	3	2(i	2(i	NUM
ejpam-7033	207	1	+	+	NUM
ejpam-7033	207	2	t	t	NOUN
ejpam-7033	207	3	)	)	PUNCT
ejpam-7033	207	4	(	(	PUNCT
ejpam-7033	207	5	r(r	r(r	NOUN
ejpam-7033	207	6	,	,	PUNCT
ejpam-7033	207	7	𭟋(r	𭟋(r	NOUN
ejpam-7033	207	8	)	)	PUNCT
ejpam-7033	207	9	)	)	PUNCT
ejpam-7033	207	10	)	)	PUNCT
ejpam-7033	207	11	⪯	⪯	PROPN
ejpam-7033	207	12	sr(r	sr(r	NOUN
ejpam-7033	207	13	,	,	PUNCT
ejpam-7033	207	14	x	x	X
ejpam-7033	207	15	)	)	PUNCT
ejpam-7033	207	16	further	far	ADV
ejpam-7033	207	17	implies	imply	VERB
ejpam-7033	207	18	f	f	PROPN
ejpam-7033	207	19	(	(	PUNCT
ejpam-7033	207	20	r(𭟋(r),𭟋(x)),r(r	r(𭟋(r),𭟋(x)),r(r	PROPN
ejpam-7033	207	21	,	,	PUNCT
ejpam-7033	207	22	x),r(r	x),r(r	PROPN
ejpam-7033	207	23	,	,	PUNCT
ejpam-7033	207	24	𭟋(r)),r(x	𭟋(r)),r(x	PROPN
ejpam-7033	207	25	,	,	PUNCT
ejpam-7033	207	26	𭟋(x)),r(r	𭟋(x)),r(r	PROPN
ejpam-7033	207	27	,	,	PUNCT
ejpam-7033	207	28	𭟋(x)),r(x	𭟋(x)),r(x	PROPN
ejpam-7033	207	29	,	,	PUNCT
ejpam-7033	207	30	𭟋(r	𭟋(r	PROPN
ejpam-7033	207	31	)	)	PUNCT
ejpam-7033	207	32	)	)	PUNCT
ejpam-7033	207	33	)	)	PUNCT
ejpam-7033	208	1	⪯	⪯	NOUN
ejpam-7033	208	2	0e	0e	PROPN
ejpam-7033	208	3	.	.	PUNCT
ejpam-7033	209	1	(	(	PUNCT
ejpam-7033	209	2	4	4	X
ejpam-7033	209	3	)	)	PUNCT
ejpam-7033	209	4	remark	remark	NOUN
ejpam-7033	209	5	12	12	NUM
ejpam-7033	209	6	.	.	PUNCT
ejpam-7033	210	1	for	for	ADP
ejpam-7033	210	2	h	h	PROPN
ejpam-7033	210	3	∈	∈	PROPN
ejpam-7033	210	4	b(e	b(e	PROPN
ejpam-7033	210	5	,	,	PUNCT
ejpam-7033	210	6	e	e	NOUN
ejpam-7033	210	7	)	)	PUNCT
ejpam-7033	210	8	,	,	PUNCT
ejpam-7033	210	9	i	i	PRON
ejpam-7033	210	10	+	+	NUM
ejpam-7033	210	11	h	h	NOUN
ejpam-7033	210	12	+	+	CCONJ
ejpam-7033	210	13	h2	h2	NOUN
ejpam-7033	210	14	+	+	CCONJ
ejpam-7033	210	15	·	·	PUNCT
ejpam-7033	210	16	·	·	PUNCT
ejpam-7033	210	17	·	·	PUNCT
ejpam-7033	211	1	+	+	CCONJ
ejpam-7033	211	2	hn	hn	PROPN
ejpam-7033	211	3	+	+	PROPN
ejpam-7033	211	4	·	·	PUNCT
ejpam-7033	211	5	·	·	PUNCT
ejpam-7033	211	6	·	·	PUNCT
ejpam-7033	211	7	converges	converge	VERB
ejpam-7033	211	8	for	for	ADP
ejpam-7033	211	9	∥h∥1	∥h∥1	NOUN
ejpam-7033	211	10	<	<	X
ejpam-7033	211	11	1	1	NUM
ejpam-7033	211	12	,	,	PUNCT
ejpam-7033	211	13	otherwise	otherwise	ADV
ejpam-7033	211	14	diverge	diverge	VERB
ejpam-7033	211	15	.	.	PUNCT
ejpam-7033	212	1	in	in	ADP
ejpam-7033	212	2	addition	addition	NOUN
ejpam-7033	212	3	if	if	SCONJ
ejpam-7033	212	4	∥h∥1	∥h∥1	NOUN
ejpam-7033	212	5	<	<	X
ejpam-7033	212	6	1	1	NUM
ejpam-7033	212	7	,	,	PUNCT
ejpam-7033	212	8	then	then	ADV
ejpam-7033	212	9	we	we	PRON
ejpam-7033	212	10	get	get	VERB
ejpam-7033	212	11	a	a	DET
ejpam-7033	212	12	y	y	PROPN
ejpam-7033	212	13	>	>	X
ejpam-7033	212	14	0	0	PROPN
ejpam-7033	212	15	,	,	PUNCT
ejpam-7033	212	16	so	so	SCONJ
ejpam-7033	212	17	that	that	SCONJ
ejpam-7033	212	18	∥h∥1	∥h∥1	NOUN
ejpam-7033	212	19	<	<	X
ejpam-7033	212	20	y	y	X
ejpam-7033	212	21	<	<	X
ejpam-7033	212	22	1	1	NUM
ejpam-7033	212	23	along	along	ADP
ejpam-7033	212	24	with	with	ADP
ejpam-7033	212	25	∥hn∥1	∥hn∥1	NOUN
ejpam-7033	212	26	≤	≤	NUM
ejpam-7033	212	27	yn	yn	PROPN
ejpam-7033	212	28	<	<	X
ejpam-7033	212	29	1	1	NUM
ejpam-7033	212	30	.	.	NOUN
ejpam-7033	212	31	4	4	NUM
ejpam-7033	212	32	.	.	NOUN
ejpam-7033	212	33	results	result	NOUN
ejpam-7033	212	34	on	on	ADP
ejpam-7033	212	35	ordered	order	VERB
ejpam-7033	212	36	implicit	implicit	ADJ
ejpam-7033	212	37	contractions	contraction	NOUN
ejpam-7033	212	38	popa[1	popa[1	NOUN
ejpam-7033	212	39	]	]	PUNCT
ejpam-7033	212	40	considered	consider	VERB
ejpam-7033	212	41	a	a	DET
ejpam-7033	212	42	self	self	NOUN
ejpam-7033	212	43	-	-	PUNCT
ejpam-7033	212	44	mapping	mapping	NOUN
ejpam-7033	212	45	satisfying	satisfy	VERB
ejpam-7033	212	46	an	an	DET
ejpam-7033	212	47	implicit	implicit	ADJ
ejpam-7033	212	48	contractive	contractive	ADJ
ejpam-7033	212	49	conditions	condition	NOUN
ejpam-7033	212	50	and	and	CCONJ
ejpam-7033	212	51	established	establish	VERB
ejpam-7033	212	52	well	well	ADV
ejpam-7033	212	53	-	-	PUNCT
ejpam-7033	212	54	known	know	VERB
ejpam-7033	212	55	fixed	fix	VERB
ejpam-7033	212	56	point	point	NOUN
ejpam-7033	212	57	results	result	NOUN
ejpam-7033	212	58	.	.	PUNCT
ejpam-7033	213	1	ran	run	VERB
ejpam-7033	213	2	et	et	PROPN
ejpam-7033	213	3	al	al	PROPN
ejpam-7033	213	4	.	.	PUNCT
ejpam-7033	214	1	[	[	X
ejpam-7033	214	2	4	4	X
ejpam-7033	214	3	]	]	PUNCT
ejpam-7033	214	4	used	use	VERB
ejpam-7033	214	5	monotone	monotone	NOUN
ejpam-7033	214	6	functions	function	NOUN
ejpam-7033	214	7	to	to	PART
ejpam-7033	214	8	generalize	generalize	VERB
ejpam-7033	214	9	the	the	DET
ejpam-7033	214	10	famous	famous	ADJ
ejpam-7033	214	11	banach	banach	NOUN
ejpam-7033	214	12	fixed	fix	VERB
ejpam-7033	214	13	point	point	NOUN
ejpam-7033	214	14	theorem	theorem	VERB
ejpam-7033	214	15	in	in	ADP
ejpam-7033	214	16	partially	partially	ADV
ejpam-7033	214	17	ordered	order	VERB
ejpam-7033	214	18	metric	metric	ADJ
ejpam-7033	214	19	space	space	NOUN
ejpam-7033	214	20	.	.	PUNCT
ejpam-7033	215	1	haung	haung	PROPN
ejpam-7033	215	2	et	et	PROPN
ejpam-7033	215	3	al.[21	al.[21	PROPN
ejpam-7033	215	4	]	]	PUNCT
ejpam-7033	215	5	introduced	introduce	VERB
ejpam-7033	215	6	cone	cone	NOUN
ejpam-7033	215	7	metric	metric	ADJ
ejpam-7033	215	8	space	space	NOUN
ejpam-7033	215	9	,	,	PUNCT
ejpam-7033	215	10	hussain	hussain	NOUN
ejpam-7033	215	11	and	and	CCONJ
ejpam-7033	215	12	shah	shah	PROPN
ejpam-7033	216	1	[	[	X
ejpam-7033	216	2	24	24	NUM
ejpam-7033	216	3	]	]	PUNCT
ejpam-7033	216	4	introduced	introduce	VERB
ejpam-7033	216	5	cone	cone	PROPN
ejpam-7033	216	6	b	b	X
ejpam-7033	216	7	-	-	PUNCT
ejpam-7033	216	8	metric	metric	ADJ
ejpam-7033	216	9	space	space	NOUN
ejpam-7033	216	10	,	,	PUNCT
ejpam-7033	216	11	huang	huang	PROPN
ejpam-7033	216	12	and	and	CCONJ
ejpam-7033	216	13	xu	xu	PROPN
ejpam-7033	217	1	[	[	X
ejpam-7033	217	2	25	25	NUM
ejpam-7033	217	3	]	]	PUNCT
ejpam-7033	217	4	practiced	practice	VERB
ejpam-7033	217	5	with	with	ADP
ejpam-7033	217	6	cone	cone	NOUN
ejpam-7033	217	7	b	b	X
ejpam-7033	217	8	-	-	PUNCT
ejpam-7033	217	9	metric	metric	ADJ
ejpam-7033	217	10	structure	structure	NOUN
ejpam-7033	217	11	to	to	PART
ejpam-7033	217	12	establish	establish	VERB
ejpam-7033	217	13	new	new	ADJ
ejpam-7033	217	14	fixed	fix	VERB
ejpam-7033	217	15	point	point	NOUN
ejpam-7033	217	16	results	result	NOUN
ejpam-7033	217	17	.	.	PUNCT
ejpam-7033	218	1	azam	azam	PROPN
ejpam-7033	218	2	et	et	PROPN
ejpam-7033	218	3	al	al	PROPN
ejpam-7033	218	4	.	.	PUNCT
ejpam-7033	219	1	[	[	X
ejpam-7033	219	2	34	34	NUM
ejpam-7033	219	3	]	]	PUNCT
ejpam-7033	219	4	introduced	introduce	VERB
ejpam-7033	219	5	the	the	DET
ejpam-7033	219	6	concept	concept	NOUN
ejpam-7033	219	7	of	of	ADP
ejpam-7033	219	8	rectangular	rectangular	ADJ
ejpam-7033	219	9	cone	cone	NOUN
ejpam-7033	219	10	metric	metric	ADJ
ejpam-7033	219	11	space	space	NOUN
ejpam-7033	219	12	and	and	CCONJ
ejpam-7033	219	13	generalized	generalized	ADJ
ejpam-7033	219	14	bcp	bcp	PROPN
ejpam-7033	219	15	.	.	PUNCT
ejpam-7033	219	16	anam	anam	PROPN
ejpam-7033	219	17	et	et	PROPN
ejpam-7033	219	18	al.[26	al.[26	PROPN
ejpam-7033	219	19	]	]	PUNCT
ejpam-7033	219	20	investigated	investigate	VERB
ejpam-7033	219	21	necessary	necessary	ADJ
ejpam-7033	219	22	convergence	convergence	NOUN
ejpam-7033	219	23	axioms	axiom	NOUN
ejpam-7033	219	24	for	for	ADP
ejpam-7033	219	25	an	an	DET
ejpam-7033	219	26	implicit	implicit	ADJ
ejpam-7033	219	27	contraction	contraction	NOUN
ejpam-7033	219	28	in	in	ADP
ejpam-7033	219	29	a	a	DET
ejpam-7033	219	30	cone	cone	NOUN
ejpam-7033	219	31	b	b	X
ejpam-7033	219	32	-	-	PUNCT
ejpam-7033	219	33	metric	metric	ADJ
ejpam-7033	219	34	space	space	NOUN
ejpam-7033	219	35	.	.	PUNCT
ejpam-7033	220	1	motivated	motivate	VERB
ejpam-7033	220	2	by	by	ADP
ejpam-7033	220	3	[	[	X
ejpam-7033	220	4	34	34	NUM
ejpam-7033	220	5	,	,	PUNCT
ejpam-7033	220	6	36	36	NUM
ejpam-7033	220	7	]	]	PUNCT
ejpam-7033	220	8	,	,	PUNCT
ejpam-7033	220	9	george	george	PROPN
ejpam-7033	221	1	[	[	X
ejpam-7033	221	2	2	2	NUM
ejpam-7033	221	3	]	]	PUNCT
ejpam-7033	221	4	defined	define	VERB
ejpam-7033	221	5	the	the	DET
ejpam-7033	221	6	rectangular	rectangular	ADJ
ejpam-7033	221	7	cone	cone	NOUN
ejpam-7033	221	8	b	b	X
ejpam-7033	221	9	-	-	PUNCT
ejpam-7033	221	10	metric	metric	ADJ
ejpam-7033	221	11	space	space	NOUN
ejpam-7033	221	12	,	,	PUNCT
ejpam-7033	221	13	that	that	PRON
ejpam-7033	221	14	generalizes	generalize	VERB
ejpam-7033	221	15	the	the	DET
ejpam-7033	221	16	rectangular	rectangular	ADJ
ejpam-7033	221	17	b	b	X
ejpam-7033	221	18	-	-	PUNCT
ejpam-7033	221	19	metric	metric	ADJ
ejpam-7033	221	20	space	space	NOUN
ejpam-7033	221	21	and	and	CCONJ
ejpam-7033	221	22	established	establish	VERB
ejpam-7033	221	23	some	some	DET
ejpam-7033	221	24	well	well	ADV
ejpam-7033	221	25	-	-	PUNCT
ejpam-7033	221	26	known	know	VERB
ejpam-7033	221	27	theorems	theorem	NOUN
ejpam-7033	221	28	in	in	ADP
ejpam-7033	221	29	this	this	DET
ejpam-7033	221	30	setting	setting	NOUN
ejpam-7033	221	31	.	.	PUNCT
ejpam-7033	222	1	in	in	ADP
ejpam-7033	222	2	this	this	DET
ejpam-7033	222	3	section	section	NOUN
ejpam-7033	222	4	,	,	PUNCT
ejpam-7033	222	5	we	we	PRON
ejpam-7033	222	6	utilize	utilize	VERB
ejpam-7033	222	7	the	the	DET
ejpam-7033	222	8	ideas	idea	NOUN
ejpam-7033	222	9	of	of	ADP
ejpam-7033	222	10	popa[1	popa[1	NOUN
ejpam-7033	222	11	]	]	PUNCT
ejpam-7033	222	12	and	and	CCONJ
ejpam-7033	222	13	george	george	PROPN
ejpam-7033	222	14	[	[	X
ejpam-7033	222	15	2	2	NUM
ejpam-7033	222	16	]	]	PUNCT
ejpam-7033	222	17	to	to	PART
ejpam-7033	222	18	develop	develop	VERB
ejpam-7033	222	19	the	the	DET
ejpam-7033	222	20	notion	notion	NOUN
ejpam-7033	222	21	of	of	ADP
ejpam-7033	222	22	ordered	order	VERB
ejpam-7033	222	23	implicit	implicit	ADJ
ejpam-7033	222	24	relation	relation	NOUN
ejpam-7033	222	25	,	,	PUNCT
ejpam-7033	222	26	and	and	CCONJ
ejpam-7033	222	27	prove	prove	VERB
ejpam-7033	222	28	some	some	DET
ejpam-7033	222	29	fixed	fix	VERB
ejpam-7033	222	30	point	point	NOUN
ejpam-7033	222	31	results	result	NOUN
ejpam-7033	222	32	in	in	ADP
ejpam-7033	222	33	rectangular	rectangular	ADJ
ejpam-7033	222	34	cone	cone	NOUN
ejpam-7033	222	35	b	b	X
ejpam-7033	222	36	-	-	PUNCT
ejpam-7033	222	37	metric	metric	ADJ
ejpam-7033	222	38	spaces	space	NOUN
ejpam-7033	222	39	.	.	PUNCT
ejpam-7033	223	1	theorem	theorem	NOUN
ejpam-7033	223	2	13	13	NUM
ejpam-7033	223	3	.	.	PUNCT
ejpam-7033	224	1	let	let	AUX
ejpam-7033	224	2	(	(	PUNCT
ejpam-7033	224	3	w	w	NOUN
ejpam-7033	224	4	,	,	PUNCT
ejpam-7033	224	5	r	r	NOUN
ejpam-7033	224	6	)	)	PUNCT
ejpam-7033	224	7	be	be	AUX
ejpam-7033	224	8	a	a	DET
ejpam-7033	224	9	complete	complete	ADJ
ejpam-7033	224	10	rectangular	rectangular	ADJ
ejpam-7033	224	11	cone	cone	NOUN
ejpam-7033	224	12	b	b	NOUN
ejpam-7033	224	13	-	-	PUNCT
ejpam-7033	224	14	metric	metric	ADJ
ejpam-7033	224	15	space	space	NOUN
ejpam-7033	224	16	along	along	ADP
ejpam-7033	224	17	with	with	ADP
ejpam-7033	224	18	a	a	DET
ejpam-7033	224	19	cone	cone	NOUN
ejpam-7033	224	20	c	c	NOUN
ejpam-7033	224	21	⊂	⊂	PROPN
ejpam-7033	224	22	e	e	PROPN
ejpam-7033	224	23	and	and	CCONJ
ejpam-7033	224	24	ℏ	ℏ	X
ejpam-7033	224	25	:	:	PUNCT
ejpam-7033	224	26	w	w	X
ejpam-7033	224	27	→	→	SYM
ejpam-7033	224	28	w	w	X
ejpam-7033	224	29	.	.	PUNCT
ejpam-7033	225	1	let	let	VERB
ejpam-7033	225	2	t	t	PROPN
ejpam-7033	225	3	∈	∈	PROPN
ejpam-7033	225	4	b(e	b(e	PROPN
ejpam-7033	225	5	,	,	PUNCT
ejpam-7033	225	6	e	e	X
ejpam-7033	225	7	)	)	PUNCT
ejpam-7033	225	8	such	such	ADJ
ejpam-7033	225	9	that	that	SCONJ
ejpam-7033	225	10	∥t	∥t	VERB
ejpam-7033	225	11	∥1	∥1	PRON
ejpam-7033	225	12	<	<	X
ejpam-7033	225	13	1	1	NUM
ejpam-7033	225	14	s	s	PART
ejpam-7033	225	15	(	(	PUNCT
ejpam-7033	225	16	s	s	X
ejpam-7033	225	17	≥	≥	NOUN
ejpam-7033	225	18	1	1	NUM
ejpam-7033	225	19	)	)	PUNCT
ejpam-7033	225	20	,	,	PUNCT
ejpam-7033	226	1	i	i	PRON
ejpam-7033	226	2	:	:	PUNCT
ejpam-7033	226	3	e	e	X
ejpam-7033	226	4	→	→	SYM
ejpam-7033	226	5	e	e	PROPN
ejpam-7033	226	6	and	and	CCONJ
ejpam-7033	226	7	j	j	PROPN
ejpam-7033	226	8	∈	∈	PROPN
ejpam-7033	226	9	f	f	PROPN
ejpam-7033	226	10	such	such	ADJ
ejpam-7033	226	11	that	that	SCONJ
ejpam-7033	226	12	,	,	PUNCT
ejpam-7033	226	13	for	for	ADP
ejpam-7033	226	14	each	each	DET
ejpam-7033	226	15	pair	pair	NOUN
ejpam-7033	226	16	of	of	ADP
ejpam-7033	226	17	comparable	comparable	ADJ
ejpam-7033	226	18	elements	element	NOUN
ejpam-7033	226	19	f	f	NOUN
ejpam-7033	226	20	,	,	PUNCT
ejpam-7033	226	21	x	x	SYM
ejpam-7033	226	22	∈	∈	PROPN
ejpam-7033	226	23	w	w	NOUN
ejpam-7033	226	24	and	and	CCONJ
ejpam-7033	226	25	for	for	ADP
ejpam-7033	226	26	some	some	PRON
ejpam-7033	226	27	s	s	PART
ejpam-7033	226	28	≥	≥	NOUN
ejpam-7033	226	29	1	1	NUM
ejpam-7033	226	30	,	,	PUNCT
ejpam-7033	226	31	the	the	DET
ejpam-7033	226	32	following	follow	VERB
ejpam-7033	226	33	holds	hold	VERB
ejpam-7033	226	34	(	(	PUNCT
ejpam-7033	226	35	i	i	PRON
ejpam-7033	226	36	−	−	PROPN
ejpam-7033	226	37	t	t	NOUN
ejpam-7033	226	38	)	)	PUNCT
ejpam-7033	226	39	2(i	2(i	NUM
ejpam-7033	227	1	+	+	NUM
ejpam-7033	227	2	t	t	NOUN
ejpam-7033	227	3	)	)	PUNCT
ejpam-7033	227	4	(	(	PUNCT
ejpam-7033	227	5	r(f	r(f	PROPN
ejpam-7033	227	6	,	,	PUNCT
ejpam-7033	227	7	ℏ(f	ℏ(f	NOUN
ejpam-7033	227	8	)	)	PUNCT
ejpam-7033	227	9	)	)	PUNCT
ejpam-7033	227	10	)	)	PUNCT
ejpam-7033	228	1	⪯	⪯	NOUN
ejpam-7033	228	2	sr(f	sr(f	ADJ
ejpam-7033	228	3	,	,	PUNCT
ejpam-7033	228	4	x	x	PRON
ejpam-7033	228	5	)	)	PUNCT
ejpam-7033	228	6	implies	imply	VERB
ejpam-7033	228	7	j	j	PROPN
ejpam-7033	228	8	(	(	PUNCT
ejpam-7033	228	9	r(ℏ(f	r(ℏ(f	PROPN
ejpam-7033	228	10	)	)	PUNCT
ejpam-7033	228	11	,	,	PUNCT
ejpam-7033	228	12	ℏ(x)),r(f	ℏ(x)),r(f	NOUN
ejpam-7033	228	13	,	,	PUNCT
ejpam-7033	228	14	x),r(f	x),r(f	PROPN
ejpam-7033	228	15	,	,	PUNCT
ejpam-7033	228	16	ℏ(f)),r(x	ℏ(f)),r(x	NOUN
ejpam-7033	228	17	,	,	PUNCT
ejpam-7033	228	18	ℏ(x)),r(f	ℏ(x)),r(f	NOUN
ejpam-7033	228	19	,	,	PUNCT
ejpam-7033	228	20	ℏ2(x)),r(x	ℏ2(x)),r(x	NOUN
ejpam-7033	228	21	,	,	PUNCT
ejpam-7033	228	22	ℏ2(f	ℏ2(f	NOUN
ejpam-7033	228	23	)	)	PUNCT
ejpam-7033	228	24	)	)	PUNCT
ejpam-7033	228	25	)	)	PUNCT
ejpam-7033	229	1	⪯	⪯	NOUN
ejpam-7033	229	2	0e	0e	NOUN
ejpam-7033	229	3	,	,	PUNCT
ejpam-7033	229	4	(	(	PUNCT
ejpam-7033	229	5	5	5	NUM
ejpam-7033	229	6	)	)	PUNCT
ejpam-7033	229	7	and	and	CCONJ
ejpam-7033	229	8	(	(	PUNCT
ejpam-7033	229	9	1	1	X
ejpam-7033	229	10	)	)	PUNCT
ejpam-7033	229	11	there	there	PRON
ejpam-7033	229	12	exists	exist	VERB
ejpam-7033	229	13	f0	f0	PROPN
ejpam-7033	229	14	∈w	∈w	NOUN
ejpam-7033	229	15	satisfying	satisfy	VERB
ejpam-7033	229	16	f0ℜℏ(f0	f0ℜℏ(f0	NOUN
ejpam-7033	229	17	)	)	PUNCT
ejpam-7033	229	18	;	;	PUNCT
ejpam-7033	229	19	(	(	PUNCT
ejpam-7033	229	20	2	2	X
ejpam-7033	229	21	)	)	PUNCT
ejpam-7033	229	22	for	for	ADP
ejpam-7033	229	23	every	every	DET
ejpam-7033	229	24	pair	pair	NOUN
ejpam-7033	229	25	f	f	NOUN
ejpam-7033	229	26	,	,	PUNCT
ejpam-7033	229	27	x	x	SYM
ejpam-7033	229	28	∈w	∈w	NOUN
ejpam-7033	229	29	,	,	PUNCT
ejpam-7033	229	30	fℜx	fℜx	NOUN
ejpam-7033	229	31	⇒	⇒	NOUN
ejpam-7033	229	32	ℏ(f)ℜℏ(x	ℏ(f)ℜℏ(x	PROPN
ejpam-7033	229	33	)	)	PUNCT
ejpam-7033	229	34	;	;	PUNCT
ejpam-7033	229	35	(	(	PUNCT
ejpam-7033	229	36	3	3	X
ejpam-7033	229	37	)	)	PUNCT
ejpam-7033	229	38	for	for	ADP
ejpam-7033	229	39	any	any	DET
ejpam-7033	229	40	sequence	sequence	NOUN
ejpam-7033	229	41	{	{	PUNCT
ejpam-7033	229	42	fn	fn	NOUN
ejpam-7033	229	43	}	}	PUNCT
ejpam-7033	229	44	such	such	ADJ
ejpam-7033	229	45	that	that	DET
ejpam-7033	229	46	fnℜfn+1	fnℜfn+1	PROPN
ejpam-7033	229	47	and	and	CCONJ
ejpam-7033	229	48	fn	fn	NOUN
ejpam-7033	229	49	→	→	SYM
ejpam-7033	229	50	z∗	z∗	PROPN
ejpam-7033	229	51	,	,	PUNCT
ejpam-7033	229	52	we	we	PRON
ejpam-7033	229	53	have	have	VERB
ejpam-7033	229	54	fnℜz∗	fnℜz∗	X
ejpam-7033	229	55	∀	∀	X
ejpam-7033	229	56	n	n	ADP
ejpam-7033	229	57	∈	∈	PROPN
ejpam-7033	229	58	n	n	NOUN
ejpam-7033	229	59	and	and	CCONJ
ejpam-7033	229	60	r(z∗	r(z∗	NUM
ejpam-7033	229	61	,	,	PUNCT
ejpam-7033	229	62	ℏ(z∗	ℏ(z∗	NOUN
ejpam-7033	229	63	)	)	PUNCT
ejpam-7033	229	64	)	)	PUNCT
ejpam-7033	229	65	⪯	⪯	NOUN
ejpam-7033	229	66	r(z∗	r(z∗	NOUN
ejpam-7033	229	67	,	,	PUNCT
ejpam-7033	229	68	ℏ2(z∗	ℏ2(z∗	NUM
ejpam-7033	229	69	)	)	PUNCT
ejpam-7033	229	70	)	)	PUNCT
ejpam-7033	229	71	.	.	PUNCT
ejpam-7033	230	1	then	then	ADV
ejpam-7033	230	2	,	,	PUNCT
ejpam-7033	230	3	there	there	PRON
ejpam-7033	230	4	exists	exist	VERB
ejpam-7033	230	5	z∗	z∗	NOUN
ejpam-7033	230	6	∈w	∈w	NOUN
ejpam-7033	230	7	such	such	ADJ
ejpam-7033	230	8	that	that	DET
ejpam-7033	230	9	z∗	z∗	NOUN
ejpam-7033	230	10	=	=	PUNCT
ejpam-7033	230	11	ℏ(z∗	ℏ(z∗	NOUN
ejpam-7033	230	12	)	)	PUNCT
ejpam-7033	230	13	.	.	PUNCT
ejpam-7033	231	1	a.	a.	PROPN
ejpam-7033	231	2	arif	arif	PROPN
ejpam-7033	231	3	et	et	PROPN
ejpam-7033	231	4	al	al	PROPN
ejpam-7033	231	5	.	.	PUNCT
ejpam-7033	231	6	/	/	SYM
ejpam-7033	231	7	eur	eur	PROPN
ejpam-7033	231	8	.	.	PUNCT
ejpam-7033	232	1	j.	j.	PROPN
ejpam-7033	232	2	pure	pure	PROPN
ejpam-7033	232	3	appl	appl	PROPN
ejpam-7033	232	4	.	.	PROPN
ejpam-7033	232	5	math	math	PROPN
ejpam-7033	232	6	,	,	PUNCT
ejpam-7033	232	7	18	18	NUM
ejpam-7033	232	8	(	(	PUNCT
ejpam-7033	232	9	4	4	NUM
ejpam-7033	232	10	)	)	PUNCT
ejpam-7033	232	11	(	(	PUNCT
ejpam-7033	232	12	2025	2025	NUM
ejpam-7033	232	13	)	)	PUNCT
ejpam-7033	232	14	,	,	PUNCT
ejpam-7033	232	15	7033	7033	NUM
ejpam-7033	232	16	9	9	NUM
ejpam-7033	232	17	of	of	ADP
ejpam-7033	232	18	29	29	NUM
ejpam-7033	232	19	proof	proof	NOUN
ejpam-7033	232	20	.	.	PUNCT
ejpam-7033	233	1	let	let	VERB
ejpam-7033	233	2	f0	f0	PROPN
ejpam-7033	233	3	∈	∈	PROPN
ejpam-7033	233	4	w	w	NOUN
ejpam-7033	233	5	satisfying	satisfy	VERB
ejpam-7033	233	6	(	(	PUNCT
ejpam-7033	233	7	1	1	NUM
ejpam-7033	233	8	)	)	PUNCT
ejpam-7033	233	9	,	,	PUNCT
ejpam-7033	233	10	define	define	VERB
ejpam-7033	233	11	{	{	PUNCT
ejpam-7033	233	12	fn	fn	NOUN
ejpam-7033	233	13	}	}	PUNCT
ejpam-7033	233	14	by	by	ADP
ejpam-7033	233	15	ℏ(fn−1	ℏ(fn−1	NOUN
ejpam-7033	233	16	)	)	PUNCT
ejpam-7033	234	1	=	=	SYM
ejpam-7033	234	2	fn	fn	PROPN
ejpam-7033	234	3	,	,	PUNCT
ejpam-7033	234	4	then	then	ADV
ejpam-7033	234	5	f0ℜf1	f0ℜf1	PROPN
ejpam-7033	234	6	.	.	PUNCT
ejpam-7033	235	1	by	by	ADP
ejpam-7033	235	2	assumption	assumption	NOUN
ejpam-7033	235	3	(	(	PUNCT
ejpam-7033	235	4	2	2	NUM
ejpam-7033	235	5	)	)	PUNCT
ejpam-7033	235	6	,	,	PUNCT
ejpam-7033	235	7	we	we	PRON
ejpam-7033	235	8	get	get	VERB
ejpam-7033	235	9	f1ℜf2	f1ℜf2	PROPN
ejpam-7033	235	10	,	,	PUNCT
ejpam-7033	235	11	f2ℜf3	f2ℜf3	NOUN
ejpam-7033	235	12	,	,	PUNCT
ejpam-7033	235	13	·	·	PUNCT
ejpam-7033	235	14	·	·	PUNCT
ejpam-7033	235	15	·	·	PUNCT
ejpam-7033	235	16	,	,	PUNCT
ejpam-7033	235	17	fn−1ℜfn	fn−1ℜfn	PROPN
ejpam-7033	235	18	.	.	PUNCT
ejpam-7033	236	1	in	in	ADP
ejpam-7033	236	2	(	(	PUNCT
ejpam-7033	236	3	5	5	NUM
ejpam-7033	236	4	)	)	PUNCT
ejpam-7033	236	5	,	,	PUNCT
ejpam-7033	236	6	put	put	VERB
ejpam-7033	236	7	f	f	NOUN
ejpam-7033	236	8	=	=	SYM
ejpam-7033	236	9	f0	f0	PROPN
ejpam-7033	236	10	and	and	CCONJ
ejpam-7033	236	11	x	x	NOUN
ejpam-7033	236	12	=	=	SYM
ejpam-7033	236	13	f1	f1	NOUN
ejpam-7033	236	14	,	,	PUNCT
ejpam-7033	236	15	(	(	PUNCT
ejpam-7033	236	16	i	i	PRON
ejpam-7033	237	1	−	−	PROPN
ejpam-7033	237	2	t	t	NOUN
ejpam-7033	237	3	)	)	PUNCT
ejpam-7033	237	4	2(i	2(i	NUM
ejpam-7033	238	1	+	+	NUM
ejpam-7033	238	2	t	t	NOUN
ejpam-7033	238	3	)	)	PUNCT
ejpam-7033	238	4	(	(	PUNCT
ejpam-7033	238	5	r(f0	r(f0	NOUN
ejpam-7033	238	6	,	,	PUNCT
ejpam-7033	238	7	ℏ(f0	ℏ(f0	NOUN
ejpam-7033	238	8	)	)	PUNCT
ejpam-7033	238	9	)	)	PUNCT
ejpam-7033	238	10	)	)	PUNCT
ejpam-7033	239	1	=	=	PUNCT
ejpam-7033	239	2	(	(	PUNCT
ejpam-7033	239	3	i	i	PRON
ejpam-7033	239	4	−	−	PROPN
ejpam-7033	239	5	t	t	NOUN
ejpam-7033	239	6	)	)	PUNCT
ejpam-7033	239	7	2(i	2(i	NUM
ejpam-7033	240	1	+	+	NUM
ejpam-7033	240	2	t	t	NOUN
ejpam-7033	240	3	)	)	PUNCT
ejpam-7033	240	4	(	(	PUNCT
ejpam-7033	240	5	r(f0	r(f0	NOUN
ejpam-7033	240	6	,	,	PUNCT
ejpam-7033	240	7	f1	f1	NOUN
ejpam-7033	240	8	)	)	PUNCT
ejpam-7033	240	9	)	)	PUNCT
ejpam-7033	240	10	⪯	⪯	PROPN
ejpam-7033	240	11	sr(f0	sr(f0	PROPN
ejpam-7033	240	12	,	,	PUNCT
ejpam-7033	240	13	f1	f1	NOUN
ejpam-7033	240	14	)	)	PUNCT
ejpam-7033	240	15	implies	imply	VERB
ejpam-7033	240	16	j	j	PROPN
ejpam-7033	240	17	(	(	PUNCT
ejpam-7033	240	18	r(ℏ(f0	r(ℏ(f0	NOUN
ejpam-7033	240	19	)	)	PUNCT
ejpam-7033	240	20	,	,	PUNCT
ejpam-7033	240	21	ℏ(f1)),r(f0	ℏ(f1)),r(f0	NOUN
ejpam-7033	240	22	,	,	PUNCT
ejpam-7033	240	23	f1),r(f0	f1),r(f0	PROPN
ejpam-7033	240	24	,	,	PUNCT
ejpam-7033	240	25	ℏ(f0)),r(f1	ℏ(f0)),r(f1	PROPN
ejpam-7033	240	26	,	,	PUNCT
ejpam-7033	240	27	ℏ(f1)),r(f0	ℏ(f1)),r(f0	NOUN
ejpam-7033	240	28	,	,	PUNCT
ejpam-7033	240	29	ℏ2(f1)),r(f1	ℏ2(f1)),r(f1	PROPN
ejpam-7033	240	30	,	,	PUNCT
ejpam-7033	240	31	ℏ2(f0	ℏ2(f0	NOUN
ejpam-7033	240	32	)	)	PUNCT
ejpam-7033	240	33	)	)	PUNCT
ejpam-7033	240	34	)	)	PUNCT
ejpam-7033	241	1	⪯	⪯	NOUN
ejpam-7033	241	2	0e	0e	NOUN
ejpam-7033	241	3	,	,	PUNCT
ejpam-7033	241	4	that	that	ADV
ejpam-7033	241	5	is	is	ADV
ejpam-7033	241	6	,	,	PUNCT
ejpam-7033	241	7	j	j	PROPN
ejpam-7033	241	8	(	(	PUNCT
ejpam-7033	241	9	r(f1	r(f1	NOUN
ejpam-7033	241	10	,	,	PUNCT
ejpam-7033	241	11	f2),r(f0	f2),r(f0	NOUN
ejpam-7033	241	12	,	,	PUNCT
ejpam-7033	241	13	f1),r(f0	f1),r(f0	PROPN
ejpam-7033	241	14	,	,	PUNCT
ejpam-7033	241	15	f1),r(f1	f1),r(f1	PROPN
ejpam-7033	241	16	,	,	PUNCT
ejpam-7033	241	17	f2),r(f0	f2),r(f0	NOUN
ejpam-7033	241	18	,	,	PUNCT
ejpam-7033	241	19	f3),r(f1	f3),r(f1	NOUN
ejpam-7033	241	20	,	,	PUNCT
ejpam-7033	241	21	f2	f2	PROPN
ejpam-7033	241	22	)	)	PUNCT
ejpam-7033	241	23	)	)	PUNCT
ejpam-7033	242	1	⪯	⪯	NOUN
ejpam-7033	242	2	0e	0e	PROPN
ejpam-7033	242	3	.	.	PUNCT
ejpam-7033	243	1	(	(	PUNCT
ejpam-7033	243	2	6	6	NUM
ejpam-7033	243	3	)	)	PUNCT
ejpam-7033	243	4	by	by	ADP
ejpam-7033	243	5	(	(	PUNCT
ejpam-7033	243	6	dr3	dr3	PROPN
ejpam-7033	243	7	)	)	PUNCT
ejpam-7033	243	8	,	,	PUNCT
ejpam-7033	243	9	we	we	PRON
ejpam-7033	243	10	have	have	VERB
ejpam-7033	243	11	r(f0	r(f0	NOUN
ejpam-7033	243	12	,	,	PUNCT
ejpam-7033	243	13	f3	f3	PROPN
ejpam-7033	243	14	)	)	PUNCT
ejpam-7033	243	15	⪯	⪯	PROPN
ejpam-7033	243	16	s[r(f0	s[r(f0	NOUN
ejpam-7033	243	17	,	,	PUNCT
ejpam-7033	243	18	f1	f1	NOUN
ejpam-7033	243	19	)	)	PUNCT
ejpam-7033	244	1	+	+	SYM
ejpam-7033	244	2	r(f1	r(f1	NOUN
ejpam-7033	244	3	,	,	PUNCT
ejpam-7033	244	4	f2	f2	PROPN
ejpam-7033	244	5	)	)	PUNCT
ejpam-7033	244	6	+	+	SYM
ejpam-7033	244	7	r(f2	r(f2	NOUN
ejpam-7033	244	8	,	,	PUNCT
ejpam-7033	244	9	f3	f3	NOUN
ejpam-7033	244	10	)	)	PUNCT
ejpam-7033	244	11	]	]	PUNCT
ejpam-7033	244	12	.	.	PUNCT
ejpam-7033	245	1	by	by	ADP
ejpam-7033	245	2	(	(	PUNCT
ejpam-7033	245	3	j1	j1	PROPN
ejpam-7033	245	4	)	)	PUNCT
ejpam-7033	245	5	,	,	PUNCT
ejpam-7033	245	6	and	and	CCONJ
ejpam-7033	245	7	rewriting	rewrite	VERB
ejpam-7033	245	8	(	(	PUNCT
ejpam-7033	245	9	6	6	NUM
ejpam-7033	245	10	)	)	PUNCT
ejpam-7033	245	11	we	we	PRON
ejpam-7033	245	12	get	get	VERB
ejpam-7033	245	13	:	:	PUNCT
ejpam-7033	245	14	j	j	PROPN
ejpam-7033	245	15	(	(	PUNCT
ejpam-7033	245	16	r(f1	r(f1	NOUN
ejpam-7033	245	17	,	,	PUNCT
ejpam-7033	245	18	f2),r(f0	f2),r(f0	NOUN
ejpam-7033	245	19	,	,	PUNCT
ejpam-7033	245	20	f1),r(f0	f1),r(f0	PROPN
ejpam-7033	245	21	,	,	PUNCT
ejpam-7033	245	22	f1),r(f1	f1),r(f1	PROPN
ejpam-7033	245	23	,	,	PUNCT
ejpam-7033	245	24	f2	f2	PROPN
ejpam-7033	245	25	)	)	PUNCT
ejpam-7033	245	26	,	,	PUNCT
ejpam-7033	245	27	s[r(f0	s[r(f0	PROPN
ejpam-7033	245	28	,	,	PUNCT
ejpam-7033	245	29	f1	f1	NOUN
ejpam-7033	245	30	)	)	PUNCT
ejpam-7033	246	1	+	+	SYM
ejpam-7033	246	2	r(f1	r(f1	NOUN
ejpam-7033	246	3	,	,	PUNCT
ejpam-7033	246	4	f2	f2	PROPN
ejpam-7033	246	5	)	)	PUNCT
ejpam-7033	246	6	+	+	SYM
ejpam-7033	246	7	r(f2	r(f2	NOUN
ejpam-7033	246	8	,	,	PUNCT
ejpam-7033	246	9	f3)],r(f1	f3)],r(f1	NOUN
ejpam-7033	246	10	,	,	PUNCT
ejpam-7033	246	11	f2	f2	PROPN
ejpam-7033	246	12	)	)	PUNCT
ejpam-7033	246	13	)	)	PUNCT
ejpam-7033	246	14	⪯	⪯	NOUN
ejpam-7033	246	15	0e	0e	NOUN
ejpam-7033	246	16	.	.	PUNCT
ejpam-7033	247	1	by	by	ADP
ejpam-7033	247	2	(	(	PUNCT
ejpam-7033	247	3	j2	j2	PROPN
ejpam-7033	247	4	)	)	PUNCT
ejpam-7033	247	5	,	,	PUNCT
ejpam-7033	247	6	there	there	PRON
ejpam-7033	247	7	exists	exist	VERB
ejpam-7033	247	8	t	t	PROPN
ejpam-7033	247	9	∈	∈	PROPN
ejpam-7033	247	10	b(e	b(e	PROPN
ejpam-7033	247	11	,	,	PUNCT
ejpam-7033	247	12	e	e	NOUN
ejpam-7033	247	13	)	)	PUNCT
ejpam-7033	247	14	along	along	ADP
ejpam-7033	247	15	with	with	ADP
ejpam-7033	247	16	∥t	∥t	PROPN
ejpam-7033	247	17	∥1	∥1	NOUN
ejpam-7033	247	18	<	<	X
ejpam-7033	247	19	1	1	NUM
ejpam-7033	247	20	,	,	PUNCT
ejpam-7033	247	21	s	s	VERB
ejpam-7033	247	22	≥	≥	NOUN
ejpam-7033	247	23	1	1	NUM
ejpam-7033	247	24	,	,	PUNCT
ejpam-7033	247	25	so	so	SCONJ
ejpam-7033	247	26	that	that	SCONJ
ejpam-7033	247	27	r(f1	r(f1	NOUN
ejpam-7033	247	28	,	,	PUNCT
ejpam-7033	247	29	f2	f2	PROPN
ejpam-7033	247	30	)	)	PUNCT
ejpam-7033	247	31	⪯	⪯	NOUN
ejpam-7033	247	32	1	1	NUM
ejpam-7033	247	33	s	s	PART
ejpam-7033	247	34	t	t	PROPN
ejpam-7033	247	35	(	(	PUNCT
ejpam-7033	247	36	r(f0	r(f0	NOUN
ejpam-7033	247	37	,	,	PUNCT
ejpam-7033	247	38	f1	f1	NOUN
ejpam-7033	247	39	)	)	PUNCT
ejpam-7033	247	40	)	)	PUNCT
ejpam-7033	247	41	⪯	⪯	PROPN
ejpam-7033	247	42	t	t	PROPN
ejpam-7033	247	43	(	(	PUNCT
ejpam-7033	247	44	r(f0	r(f0	NOUN
ejpam-7033	247	45	,	,	PUNCT
ejpam-7033	247	46	f1	f1	NOUN
ejpam-7033	247	47	)	)	PUNCT
ejpam-7033	247	48	)	)	PUNCT
ejpam-7033	247	49	and	and	CCONJ
ejpam-7033	247	50	r(f2	r(f2	NOUN
ejpam-7033	247	51	,	,	PUNCT
ejpam-7033	247	52	f3	f3	ADJ
ejpam-7033	247	53	)	)	PUNCT
ejpam-7033	247	54	⪯	⪯	NOUN
ejpam-7033	247	55	1	1	NUM
ejpam-7033	247	56	s	s	PART
ejpam-7033	247	57	t	t	PROPN
ejpam-7033	247	58	(	(	PUNCT
ejpam-7033	247	59	r(f1	r(f1	NOUN
ejpam-7033	247	60	,	,	PUNCT
ejpam-7033	247	61	f2	f2	PROPN
ejpam-7033	247	62	)	)	PUNCT
ejpam-7033	247	63	)	)	PUNCT
ejpam-7033	247	64	⪯	⪯	PROPN
ejpam-7033	247	65	t	t	PROPN
ejpam-7033	247	66	(	(	PUNCT
ejpam-7033	247	67	r(f1	r(f1	NOUN
ejpam-7033	247	68	,	,	PUNCT
ejpam-7033	247	69	f2	f2	PROPN
ejpam-7033	247	70	)	)	PUNCT
ejpam-7033	247	71	)	)	PUNCT
ejpam-7033	247	72	.	.	PUNCT
ejpam-7033	248	1	now	now	ADV
ejpam-7033	248	2	put	put	VERB
ejpam-7033	248	3	f	f	NOUN
ejpam-7033	248	4	=	=	SYM
ejpam-7033	248	5	f1	f1	PROPN
ejpam-7033	248	6	and	and	CCONJ
ejpam-7033	248	7	x	x	X
ejpam-7033	248	8	=	=	X
ejpam-7033	248	9	f2	f2	PROPN
ejpam-7033	248	10	in	in	ADP
ejpam-7033	248	11	(	(	PUNCT
ejpam-7033	248	12	5	5	NUM
ejpam-7033	248	13	)	)	PUNCT
ejpam-7033	248	14	to	to	PART
ejpam-7033	248	15	have	have	VERB
ejpam-7033	248	16	(	(	PUNCT
ejpam-7033	248	17	i	i	PRON
ejpam-7033	248	18	−	−	PROPN
ejpam-7033	249	1	t	t	NOUN
ejpam-7033	249	2	)	)	PUNCT
ejpam-7033	249	3	2(i	2(i	NUM
ejpam-7033	250	1	+	+	NUM
ejpam-7033	250	2	t	t	NOUN
ejpam-7033	250	3	)	)	PUNCT
ejpam-7033	250	4	(	(	PUNCT
ejpam-7033	250	5	r(f1	r(f1	NOUN
ejpam-7033	250	6	,	,	PUNCT
ejpam-7033	250	7	ℏ(f1	ℏ(f1	NOUN
ejpam-7033	250	8	)	)	PUNCT
ejpam-7033	250	9	)	)	PUNCT
ejpam-7033	250	10	)	)	PUNCT
ejpam-7033	251	1	=	=	PUNCT
ejpam-7033	251	2	(	(	PUNCT
ejpam-7033	251	3	i	i	PRON
ejpam-7033	251	4	−	−	PROPN
ejpam-7033	251	5	t	t	NOUN
ejpam-7033	251	6	)	)	PUNCT
ejpam-7033	251	7	2(i	2(i	NUM
ejpam-7033	252	1	+	+	NUM
ejpam-7033	252	2	t	t	NOUN
ejpam-7033	252	3	)	)	PUNCT
ejpam-7033	252	4	(	(	PUNCT
ejpam-7033	252	5	r(f1	r(f1	NOUN
ejpam-7033	252	6	,	,	PUNCT
ejpam-7033	252	7	f2	f2	PROPN
ejpam-7033	252	8	)	)	PUNCT
ejpam-7033	252	9	)	)	PUNCT
ejpam-7033	252	10	⪯	⪯	PROPN
ejpam-7033	252	11	sr(f1	sr(f1	PROPN
ejpam-7033	252	12	,	,	PUNCT
ejpam-7033	252	13	f2	f2	PROPN
ejpam-7033	252	14	)	)	PUNCT
ejpam-7033	252	15	implies	imply	VERB
ejpam-7033	252	16	j	j	PROPN
ejpam-7033	252	17	(	(	PUNCT
ejpam-7033	252	18	r(ℏ(f1	r(ℏ(f1	PROPN
ejpam-7033	252	19	)	)	PUNCT
ejpam-7033	252	20	,	,	PUNCT
ejpam-7033	252	21	ℏ(f2)),r(f1	ℏ(f2)),r(f1	PROPN
ejpam-7033	252	22	,	,	PUNCT
ejpam-7033	252	23	f2),r(f1	f2),r(f1	PROPN
ejpam-7033	252	24	,	,	PUNCT
ejpam-7033	252	25	ℏ(f1)),r(f2	ℏ(f1)),r(f2	NOUN
ejpam-7033	252	26	,	,	PUNCT
ejpam-7033	252	27	ℏ(f2)),r(f1	ℏ(f2)),r(f1	PROPN
ejpam-7033	252	28	,	,	PUNCT
ejpam-7033	252	29	ℏ(f3)),r(f2	ℏ(f3)),r(f2	PROPN
ejpam-7033	252	30	,	,	PUNCT
ejpam-7033	252	31	ℏ(f2	ℏ(f2	NOUN
ejpam-7033	252	32	)	)	PUNCT
ejpam-7033	252	33	)	)	PUNCT
ejpam-7033	252	34	)	)	PUNCT
ejpam-7033	253	1	⪯	⪯	NOUN
ejpam-7033	253	2	0e	0e	NOUN
ejpam-7033	253	3	,	,	PUNCT
ejpam-7033	253	4	that	that	ADV
ejpam-7033	253	5	is	is	ADV
ejpam-7033	253	6	,	,	PUNCT
ejpam-7033	253	7	j	j	PROPN
ejpam-7033	253	8	(	(	PUNCT
ejpam-7033	253	9	r(f2	r(f2	NOUN
ejpam-7033	253	10	,	,	PUNCT
ejpam-7033	253	11	f3),r(f1	f3),r(f1	NOUN
ejpam-7033	253	12	,	,	PUNCT
ejpam-7033	253	13	f2),r(f1	f2),r(f1	PROPN
ejpam-7033	253	14	,	,	PUNCT
ejpam-7033	253	15	f2),r(f2	f2),r(f2	NOUN
ejpam-7033	253	16	,	,	PUNCT
ejpam-7033	253	17	f3),r(f1	f3),r(f1	NOUN
ejpam-7033	253	18	,	,	PUNCT
ejpam-7033	253	19	f4),r(f2	f4),r(f2	NOUN
ejpam-7033	253	20	,	,	PUNCT
ejpam-7033	253	21	f3	f3	ADJ
ejpam-7033	253	22	)	)	PUNCT
ejpam-7033	253	23	)	)	PUNCT
ejpam-7033	253	24	⪯	⪯	NOUN
ejpam-7033	253	25	0e	0e	NOUN
ejpam-7033	253	26	.	.	PUNCT
ejpam-7033	254	1	by	by	ADP
ejpam-7033	254	2	(	(	PUNCT
ejpam-7033	254	3	drb3	drb3	PROPN
ejpam-7033	254	4	)	)	PUNCT
ejpam-7033	254	5	,	,	PUNCT
ejpam-7033	254	6	we	we	PRON
ejpam-7033	254	7	get	get	VERB
ejpam-7033	254	8	r(f1	r(f1	NOUN
ejpam-7033	254	9	,	,	PUNCT
ejpam-7033	254	10	f4	f4	NUM
ejpam-7033	254	11	)	)	PUNCT
ejpam-7033	254	12	⪯	⪯	NOUN
ejpam-7033	254	13	s[r(f1	s[r(f1	PROPN
ejpam-7033	254	14	,	,	PUNCT
ejpam-7033	254	15	f2	f2	PROPN
ejpam-7033	254	16	)	)	PUNCT
ejpam-7033	254	17	+	+	SYM
ejpam-7033	254	18	r(f2	r(f2	NOUN
ejpam-7033	254	19	,	,	PUNCT
ejpam-7033	254	20	f3	f3	ADJ
ejpam-7033	254	21	)	)	PUNCT
ejpam-7033	255	1	+	+	SYM
ejpam-7033	255	2	r(f3	r(f3	NOUN
ejpam-7033	255	3	,	,	PUNCT
ejpam-7033	255	4	f4	f4	PROPN
ejpam-7033	255	5	)	)	PUNCT
ejpam-7033	255	6	]	]	PUNCT
ejpam-7033	255	7	,	,	PUNCT
ejpam-7033	255	8	(	(	PUNCT
ejpam-7033	255	9	j1	j1	PROPN
ejpam-7033	255	10	)	)	PUNCT
ejpam-7033	255	11	implies	imply	VERB
ejpam-7033	255	12	j	j	PROPN
ejpam-7033	255	13	(	(	PUNCT
ejpam-7033	255	14	r(f2	r(f2	NOUN
ejpam-7033	255	15	,	,	PUNCT
ejpam-7033	255	16	f3),r(f1	f3),r(f1	NOUN
ejpam-7033	255	17	,	,	PUNCT
ejpam-7033	255	18	f2),r(f1	f2),r(f1	PROPN
ejpam-7033	255	19	,	,	PUNCT
ejpam-7033	255	20	f2),r(f2	f2),r(f2	NOUN
ejpam-7033	255	21	,	,	PUNCT
ejpam-7033	255	22	f3	f3	NOUN
ejpam-7033	255	23	)	)	PUNCT
ejpam-7033	255	24	,	,	PUNCT
ejpam-7033	255	25	s[r(f1	s[r(f1	PROPN
ejpam-7033	255	26	,	,	PUNCT
ejpam-7033	255	27	f2	f2	PROPN
ejpam-7033	255	28	)	)	PUNCT
ejpam-7033	255	29	+	+	SYM
ejpam-7033	255	30	r(f2	r(f2	NOUN
ejpam-7033	255	31	,	,	PUNCT
ejpam-7033	255	32	f3	f3	ADJ
ejpam-7033	255	33	)	)	PUNCT
ejpam-7033	256	1	+	+	CCONJ
ejpam-7033	256	2	r(f3	r(f3	PROPN
ejpam-7033	256	3	,	,	PUNCT
ejpam-7033	256	4	f4)],r(f2	f4)],r(f2	NOUN
ejpam-7033	256	5	,	,	PUNCT
ejpam-7033	256	6	f3	f3	ADJ
ejpam-7033	256	7	)	)	PUNCT
ejpam-7033	256	8	)	)	PUNCT
ejpam-7033	257	1	⪯	⪯	NOUN
ejpam-7033	257	2	0e	0e	NOUN
ejpam-7033	257	3	.	.	PUNCT
ejpam-7033	258	1	now	now	ADV
ejpam-7033	258	2	(	(	PUNCT
ejpam-7033	258	3	j2	j2	PROPN
ejpam-7033	258	4	)	)	PUNCT
ejpam-7033	258	5	guarantees	guarantee	VERB
ejpam-7033	258	6	the	the	DET
ejpam-7033	258	7	existence	existence	NOUN
ejpam-7033	258	8	of	of	ADP
ejpam-7033	258	9	t	t	PROPN
ejpam-7033	258	10	∈	∈	PROPN
ejpam-7033	258	11	b(e	b(e	PROPN
ejpam-7033	258	12	,	,	PUNCT
ejpam-7033	258	13	e	e	NOUN
ejpam-7033	258	14	)	)	PUNCT
ejpam-7033	258	15	along	along	ADP
ejpam-7033	258	16	with	with	ADP
ejpam-7033	258	17	∥t	∥t	PROPN
ejpam-7033	258	18	∥1	∥1	NOUN
ejpam-7033	258	19	<	<	X
ejpam-7033	258	20	1	1	NUM
ejpam-7033	258	21	so	so	SCONJ
ejpam-7033	258	22	that	that	SCONJ
ejpam-7033	258	23	r(f3	r(f3	PROPN
ejpam-7033	258	24	,	,	PUNCT
ejpam-7033	258	25	f4	f4	PROPN
ejpam-7033	258	26	)	)	PUNCT
ejpam-7033	258	27	⪯	⪯	NOUN
ejpam-7033	258	28	1	1	NUM
ejpam-7033	258	29	s	s	PART
ejpam-7033	258	30	t	t	NOUN
ejpam-7033	258	31	(	(	PUNCT
ejpam-7033	258	32	r(f2	r(f2	NOUN
ejpam-7033	258	33	,	,	PUNCT
ejpam-7033	258	34	f3	f3	ADJ
ejpam-7033	258	35	)	)	PUNCT
ejpam-7033	258	36	)	)	PUNCT
ejpam-7033	258	37	⪯	⪯	NOUN
ejpam-7033	258	38	1	1	NUM
ejpam-7033	258	39	s2	s2	NOUN
ejpam-7033	258	40	t	t	NOUN
ejpam-7033	258	41	2(r(f2	2(r(f2	NUM
ejpam-7033	258	42	,	,	PUNCT
ejpam-7033	258	43	f3	f3	ADJ
ejpam-7033	258	44	)	)	PUNCT
ejpam-7033	258	45	)	)	PUNCT
ejpam-7033	259	1	⪯	⪯	NOUN
ejpam-7033	259	2	1	1	NUM
ejpam-7033	259	3	s3	s3	PROPN
ejpam-7033	259	4	t	t	PROPN
ejpam-7033	259	5	3(r(f0	3(r(f0	NUM
ejpam-7033	259	6	,	,	PUNCT
ejpam-7033	259	7	f1	f1	NOUN
ejpam-7033	259	8	)	)	PUNCT
ejpam-7033	259	9	)	)	PUNCT
ejpam-7033	259	10	⪯	⪯	PROPN
ejpam-7033	259	11	t	t	PROPN
ejpam-7033	259	12	3(r(f0	3(r(f0	NUM
ejpam-7033	259	13	,	,	PUNCT
ejpam-7033	259	14	f1	f1	NOUN
ejpam-7033	259	15	)	)	PUNCT
ejpam-7033	259	16	)	)	PUNCT
ejpam-7033	259	17	.	.	PUNCT
ejpam-7033	260	1	continuing	continue	VERB
ejpam-7033	260	2	,	,	PUNCT
ejpam-7033	260	3	we	we	PRON
ejpam-7033	260	4	construct	construct	VERB
ejpam-7033	260	5	a	a	DET
ejpam-7033	260	6	sequence	sequence	NOUN
ejpam-7033	260	7	{	{	PUNCT
ejpam-7033	260	8	fn	fn	NOUN
ejpam-7033	260	9	}	}	PUNCT
ejpam-7033	260	10	so	so	SCONJ
ejpam-7033	260	11	that	that	PRON
ejpam-7033	260	12	fnℜfn+1	fnℜfn+1	NOUN
ejpam-7033	260	13	with	with	ADP
ejpam-7033	260	14	fn+1	fn+1	NOUN
ejpam-7033	260	15	=	=	SYM
ejpam-7033	260	16	ℏ(fn	ℏ(fn	PROPN
ejpam-7033	260	17	)	)	PUNCT
ejpam-7033	260	18	,	,	PUNCT
ejpam-7033	260	19	hence	hence	ADV
ejpam-7033	260	20	for	for	ADP
ejpam-7033	260	21	(	(	PUNCT
ejpam-7033	260	22	i	i	PRON
ejpam-7033	260	23	−	−	PROPN
ejpam-7033	260	24	t	t	NOUN
ejpam-7033	260	25	)	)	PUNCT
ejpam-7033	260	26	2(i	2(i	NUM
ejpam-7033	261	1	+	+	NUM
ejpam-7033	261	2	t	t	NOUN
ejpam-7033	261	3	)	)	PUNCT
ejpam-7033	261	4	(	(	PUNCT
ejpam-7033	261	5	r(fn−1	r(fn−1	X
ejpam-7033	261	6	,	,	PUNCT
ejpam-7033	261	7	ℏ(fn−1	ℏ(fn−1	NOUN
ejpam-7033	261	8	)	)	PUNCT
ejpam-7033	261	9	)	)	PUNCT
ejpam-7033	261	10	)	)	PUNCT
ejpam-7033	262	1	=	=	PUNCT
ejpam-7033	262	2	(	(	PUNCT
ejpam-7033	262	3	i	i	PRON
ejpam-7033	262	4	−	−	PROPN
ejpam-7033	262	5	t	t	NOUN
ejpam-7033	262	6	)	)	PUNCT
ejpam-7033	262	7	2(i	2(i	NUM
ejpam-7033	263	1	+	+	NUM
ejpam-7033	263	2	t	t	NOUN
ejpam-7033	263	3	)	)	PUNCT
ejpam-7033	263	4	(	(	PUNCT
ejpam-7033	263	5	r(fn−1	r(fn−1	PROPN
ejpam-7033	263	6	,	,	PUNCT
ejpam-7033	263	7	fn	fn	NOUN
ejpam-7033	263	8	)	)	PUNCT
ejpam-7033	263	9	)	)	PUNCT
ejpam-7033	263	10	⪯	⪯	NOUN
ejpam-7033	263	11	sr(fn−1	sr(fn−1	PROPN
ejpam-7033	263	12	,	,	PUNCT
ejpam-7033	263	13	fn	fn	NOUN
ejpam-7033	263	14	)	)	PUNCT
ejpam-7033	263	15	,	,	PUNCT
ejpam-7033	263	16	a.	a.	PROPN
ejpam-7033	263	17	arif	arif	PROPN
ejpam-7033	263	18	et	et	PROPN
ejpam-7033	263	19	al	al	PROPN
ejpam-7033	263	20	.	.	PUNCT
ejpam-7033	263	21	/	/	SYM
ejpam-7033	263	22	eur	eur	PROPN
ejpam-7033	263	23	.	.	PUNCT
ejpam-7033	264	1	j.	j.	PROPN
ejpam-7033	264	2	pure	pure	PROPN
ejpam-7033	264	3	appl	appl	PROPN
ejpam-7033	264	4	.	.	PROPN
ejpam-7033	264	5	math	math	PROPN
ejpam-7033	264	6	,	,	PUNCT
ejpam-7033	264	7	18	18	NUM
ejpam-7033	264	8	(	(	PUNCT
ejpam-7033	264	9	4	4	NUM
ejpam-7033	264	10	)	)	PUNCT
ejpam-7033	264	11	(	(	PUNCT
ejpam-7033	264	12	2025	2025	NUM
ejpam-7033	264	13	)	)	PUNCT
ejpam-7033	264	14	,	,	PUNCT
ejpam-7033	264	15	7033	7033	NUM
ejpam-7033	264	16	10	10	NUM
ejpam-7033	264	17	of	of	ADP
ejpam-7033	264	18	29	29	NUM
ejpam-7033	264	19	we	we	PRON
ejpam-7033	264	20	get	get	VERB
ejpam-7033	264	21	r(fn	r(fn	NOUN
ejpam-7033	264	22	,	,	PUNCT
ejpam-7033	264	23	fn+1	fn+1	NUM
ejpam-7033	264	24	)	)	PUNCT
ejpam-7033	264	25	⪯	⪯	NOUN
ejpam-7033	264	26	1	1	NUM
ejpam-7033	264	27	s	s	PART
ejpam-7033	264	28	t	t	NOUN
ejpam-7033	264	29	(	(	PUNCT
ejpam-7033	264	30	r(fn−1	r(fn−1	PROPN
ejpam-7033	264	31	,	,	PUNCT
ejpam-7033	264	32	fn	fn	NOUN
ejpam-7033	264	33	)	)	PUNCT
ejpam-7033	264	34	)	)	PUNCT
ejpam-7033	264	35	⪯	⪯	NOUN
ejpam-7033	264	36	1	1	NUM
ejpam-7033	264	37	s2	s2	NOUN
ejpam-7033	264	38	t	t	PROPN
ejpam-7033	264	39	2(r(fn−2	2(r(fn−2	NUM
ejpam-7033	264	40	,	,	PUNCT
ejpam-7033	264	41	fn−1	fn−1	ADJ
ejpam-7033	264	42	)	)	PUNCT
ejpam-7033	264	43	)	)	PUNCT
ejpam-7033	264	44	⪯	⪯	NOUN
ejpam-7033	264	45	·	·	PUNCT
ejpam-7033	264	46	·	·	PUNCT
ejpam-7033	264	47	·	·	PUNCT
ejpam-7033	265	1	⪯	⪯	NOUN
ejpam-7033	265	2	1	1	NUM
ejpam-7033	265	3	sn	sn	NOUN
ejpam-7033	265	4	t	t	PROPN
ejpam-7033	265	5	n(r(f0	n(r(f0	NOUN
ejpam-7033	265	6	,	,	PUNCT
ejpam-7033	265	7	f1	f1	NOUN
ejpam-7033	265	8	)	)	PUNCT
ejpam-7033	265	9	)	)	PUNCT
ejpam-7033	265	10	⪯	⪯	PROPN
ejpam-7033	265	11	t	t	PROPN
ejpam-7033	265	12	n(r(f0	n(r(f0	PROPN
ejpam-7033	265	13	,	,	PUNCT
ejpam-7033	265	14	f1	f1	NOUN
ejpam-7033	265	15	)	)	PUNCT
ejpam-7033	265	16	)	)	PUNCT
ejpam-7033	265	17	.	.	PUNCT
ejpam-7033	266	1	assume	assume	VERB
ejpam-7033	266	2	two	two	NUM
ejpam-7033	266	3	situations	situation	NOUN
ejpam-7033	266	4	for	for	ADP
ejpam-7033	266	5	r(fn	r(fn	NOUN
ejpam-7033	266	6	,	,	PUNCT
ejpam-7033	266	7	fn+p	fn+p	PROPN
ejpam-7033	266	8	)	)	PUNCT
ejpam-7033	266	9	,	,	PUNCT
ejpam-7033	266	10	for	for	SCONJ
ejpam-7033	266	11	if	if	SCONJ
ejpam-7033	266	12	p	p	NOUN
ejpam-7033	266	13	is	be	AUX
ejpam-7033	266	14	odd	odd	ADJ
ejpam-7033	266	15	,	,	PUNCT
ejpam-7033	266	16	that	that	PRON
ejpam-7033	266	17	is	be	AUX
ejpam-7033	266	18	p	p	NOUN
ejpam-7033	266	19	=	=	VERB
ejpam-7033	266	20	2	2	NUM
ejpam-7033	266	21	m	m	NOUN
ejpam-7033	266	22	+	+	NUM
ejpam-7033	266	23	1	1	NUM
ejpam-7033	266	24	and	and	CCONJ
ejpam-7033	266	25	r∗	r∗	VERB
ejpam-7033	266	26	n	n	PROPN
ejpam-7033	266	27	=	=	SYM
ejpam-7033	266	28	r(fn	r(fn	PROPN
ejpam-7033	266	29	,	,	PUNCT
ejpam-7033	266	30	fn+1	fn+1	NUM
ejpam-7033	266	31	)	)	PUNCT
ejpam-7033	266	32	r(fn	r(fn	PROPN
ejpam-7033	266	33	,	,	PUNCT
ejpam-7033	266	34	fn+2m+1	fn+2m+1	PROPN
ejpam-7033	266	35	)	)	PUNCT
ejpam-7033	266	36	⪯	⪯	NOUN
ejpam-7033	266	37	s[r∗	s[r∗	PROPN
ejpam-7033	266	38	n	n	PROPN
ejpam-7033	266	39	+	+	CCONJ
ejpam-7033	266	40	r∗	r∗	VERB
ejpam-7033	266	41	n+1	n+1	PROPN
ejpam-7033	267	1	+	+	NUM
ejpam-7033	267	2	r(fn+2	r(fn+2	PROPN
ejpam-7033	267	3	,	,	PUNCT
ejpam-7033	267	4	fn+2m+1	fn+2m+1	PROPN
ejpam-7033	267	5	)	)	PUNCT
ejpam-7033	267	6	]	]	PUNCT
ejpam-7033	268	1	⪯	⪯	X
ejpam-7033	268	2	s[r∗	s[r∗	PROPN
ejpam-7033	268	3	n	n	PROPN
ejpam-7033	268	4	+	+	CCONJ
ejpam-7033	268	5	r∗	r∗	PROPN
ejpam-7033	268	6	n+1	n+1	PROPN
ejpam-7033	268	7	]	]	X
ejpam-7033	268	8	+	+	CCONJ
ejpam-7033	268	9	s2[r∗	s2[r∗	NOUN
ejpam-7033	268	10	n+2	n+2	NOUN
ejpam-7033	268	11	+	+	CCONJ
ejpam-7033	268	12	r∗	r∗	VERB
ejpam-7033	268	13	n+3	n+3	PROPN
ejpam-7033	268	14	+	+	CCONJ
ejpam-7033	268	15	r(fn+3	r(fn+3	PROPN
ejpam-7033	268	16	,	,	PUNCT
ejpam-7033	268	17	fn+2m+1	fn+2m+1	PROPN
ejpam-7033	268	18	)	)	PUNCT
ejpam-7033	268	19	]	]	PUNCT
ejpam-7033	269	1	⪯	⪯	X
ejpam-7033	269	2	s[r∗	s[r∗	PROPN
ejpam-7033	269	3	n	n	PROPN
ejpam-7033	269	4	+	+	CCONJ
ejpam-7033	269	5	r∗	r∗	PROPN
ejpam-7033	269	6	n+1	n+1	PROPN
ejpam-7033	269	7	]	]	X
ejpam-7033	269	8	+	+	CCONJ
ejpam-7033	269	9	s2[r∗	s2[r∗	NOUN
ejpam-7033	269	10	n+2	n+2	NOUN
ejpam-7033	269	11	+	+	CCONJ
ejpam-7033	269	12	r∗	r∗	PROPN
ejpam-7033	269	13	n+3	n+3	NUM
ejpam-7033	269	14	]	]	X
ejpam-7033	269	15	+	+	CCONJ
ejpam-7033	269	16	·	·	PUNCT
ejpam-7033	269	17	·	·	PUNCT
ejpam-7033	269	18	·	·	PUNCT
ejpam-7033	269	19	+	+	NUM
ejpam-7033	269	20	smr(fn+2	smr(fn+2	NUM
ejpam-7033	269	21	m	m	NOUN
ejpam-7033	269	22	,	,	PUNCT
ejpam-7033	269	23	fn+2m+1	fn+2m+1	PROPN
ejpam-7033	269	24	)	)	PUNCT
ejpam-7033	269	25	⪯	⪯	VERB
ejpam-7033	269	26	s[t	s[t	PROPN
ejpam-7033	269	27	nr∗	nr∗	NOUN
ejpam-7033	269	28	0	0	PUNCT
ejpam-7033	270	1	+	+	CCONJ
ejpam-7033	270	2	t	t	PROPN
ejpam-7033	270	3	n+1r∗	n+1r∗	NUM
ejpam-7033	270	4	1	1	NUM
ejpam-7033	270	5	]	]	PUNCT
ejpam-7033	270	6	+	+	CCONJ
ejpam-7033	270	7	s2[t	s2[t	NOUN
ejpam-7033	270	8	n+2r∗	n+2r∗	NUM
ejpam-7033	270	9	0	0	NUM
ejpam-7033	271	1	+	+	NUM
ejpam-7033	271	2	t	t	PROPN
ejpam-7033	271	3	n+3r∗	n+3r∗	NUM
ejpam-7033	271	4	0	0	NUM
ejpam-7033	271	5	]	]	X
ejpam-7033	271	6	+	+	CCONJ
ejpam-7033	271	7	·	·	PUNCT
ejpam-7033	271	8	·	·	PUNCT
ejpam-7033	271	9	·	·	PUNCT
ejpam-7033	271	10	+	+	NUM
ejpam-7033	271	11	smt	smt	PROPN
ejpam-7033	271	12	n+2mr∗	n+2mr∗	ADP
ejpam-7033	271	13	0	0	NUM
ejpam-7033	271	14	≺	≺	NOUN
ejpam-7033	271	15	st	st	PROPN
ejpam-7033	271	16	n(i	n(i	PROPN
ejpam-7033	271	17	+	+	CCONJ
ejpam-7033	271	18	st	st	PROPN
ejpam-7033	271	19	2	2	NUM
ejpam-7033	271	20	+	+	NOUN
ejpam-7033	271	21	s2	s2	PROPN
ejpam-7033	271	22	t	t	NOUN
ejpam-7033	271	23	4	4	NUM
ejpam-7033	271	24	+	+	CCONJ
ejpam-7033	271	25	·	·	PUNCT
ejpam-7033	272	1	·	·	PUNCT
ejpam-7033	272	2	·	·	PUNCT
ejpam-7033	272	3	)	)	PUNCT
ejpam-7033	272	4	r∗	r∗	VERB
ejpam-7033	272	5	0	0	NUM
ejpam-7033	273	1	+	+	CCONJ
ejpam-7033	273	2	st	st	PROPN
ejpam-7033	273	3	n+1(i	n+1(i	PROPN
ejpam-7033	273	4	+	+	CCONJ
ejpam-7033	273	5	st	st	PROPN
ejpam-7033	273	6	2	2	NUM
ejpam-7033	273	7	+	+	CCONJ
ejpam-7033	273	8	(	(	PUNCT
ejpam-7033	273	9	st	st	PROPN
ejpam-7033	273	10	2)2	2)2	NUM
ejpam-7033	273	11	+	+	CCONJ
ejpam-7033	273	12	·	·	PUNCT
ejpam-7033	273	13	·	·	PUNCT
ejpam-7033	273	14	·	·	PUNCT
ejpam-7033	273	15	)	)	PUNCT
ejpam-7033	273	16	r∗	r∗	VERB
ejpam-7033	273	17	0	0	NUM
ejpam-7033	274	1	=	=	SYM
ejpam-7033	274	2	st	st	PROPN
ejpam-7033	274	3	n(i	n(i	PROPN
ejpam-7033	274	4	−	−	PROPN
ejpam-7033	274	5	st	st	PROPN
ejpam-7033	274	6	2)−1r∗	2)−1r∗	PROPN
ejpam-7033	274	7	0	0	NUM
ejpam-7033	275	1	+	+	CCONJ
ejpam-7033	275	2	st	st	PROPN
ejpam-7033	275	3	n+1(i	n+1(i	PROPN
ejpam-7033	275	4	−	−	PROPN
ejpam-7033	275	5	st	st	PROPN
ejpam-7033	275	6	2)−1r∗	2)−1r∗	PROPN
ejpam-7033	275	7	0	0	NUM
ejpam-7033	275	8	=	=	SYM
ejpam-7033	275	9	st	st	PROPN
ejpam-7033	275	10	n(i	n(i	PROPN
ejpam-7033	275	11	−	−	PROPN
ejpam-7033	275	12	st	st	PROPN
ejpam-7033	275	13	2)−1r∗	2)−1r∗	PROPN
ejpam-7033	275	14	0(i	0(i	NUM
ejpam-7033	276	1	+	+	CCONJ
ejpam-7033	276	2	t	t	NOUN
ejpam-7033	276	3	)	)	PUNCT
ejpam-7033	276	4	.	.	PUNCT
ejpam-7033	277	1	(	(	PUNCT
ejpam-7033	277	2	by	by	ADP
ejpam-7033	277	3	remark	remark	NOUN
ejpam-7033	277	4	12	12	NUM
ejpam-7033	277	5	)	)	PUNCT
ejpam-7033	277	6	for	for	ADP
ejpam-7033	277	7	if	if	SCONJ
ejpam-7033	277	8	p	p	NOUN
ejpam-7033	277	9	is	be	AUX
ejpam-7033	277	10	even	even	ADV
ejpam-7033	277	11	,	,	PUNCT
ejpam-7033	277	12	that	that	PRON
ejpam-7033	277	13	is	be	AUX
ejpam-7033	277	14	p	p	NOUN
ejpam-7033	277	15	=	=	PROPN
ejpam-7033	277	16	2	2	NUM
ejpam-7033	277	17	m	m	NOUN
ejpam-7033	277	18	and	and	CCONJ
ejpam-7033	277	19	r∗	r∗	VERB
ejpam-7033	277	20	n	n	PROPN
ejpam-7033	277	21	=	=	SYM
ejpam-7033	277	22	r(fn	r(fn	PROPN
ejpam-7033	277	23	,	,	PUNCT
ejpam-7033	277	24	fn+1	fn+1	NUM
ejpam-7033	277	25	)	)	PUNCT
ejpam-7033	277	26	.	.	PUNCT
ejpam-7033	278	1	r(fn	r(fn	NOUN
ejpam-7033	278	2	,	,	PUNCT
ejpam-7033	278	3	fn+2	fn+2	PROPN
ejpam-7033	278	4	m	m	NOUN
ejpam-7033	278	5	)	)	PUNCT
ejpam-7033	278	6	⪯	⪯	NOUN
ejpam-7033	278	7	s[r∗	s[r∗	PROPN
ejpam-7033	278	8	n	n	PROPN
ejpam-7033	278	9	+	+	CCONJ
ejpam-7033	278	10	r∗	r∗	VERB
ejpam-7033	278	11	n+1	n+1	PROPN
ejpam-7033	278	12	+	+	NUM
ejpam-7033	278	13	r(fn+2	r(fn+2	PROPN
ejpam-7033	278	14	,	,	PUNCT
ejpam-7033	278	15	fn+2	fn+2	NOUN
ejpam-7033	278	16	m	m	NOUN
ejpam-7033	278	17	)	)	PUNCT
ejpam-7033	278	18	]	]	PUNCT
ejpam-7033	279	1	⪯	⪯	X
ejpam-7033	279	2	s[r∗	s[r∗	PROPN
ejpam-7033	279	3	n	n	PROPN
ejpam-7033	279	4	+	+	CCONJ
ejpam-7033	279	5	r∗	r∗	PROPN
ejpam-7033	279	6	n+1	n+1	PROPN
ejpam-7033	279	7	]	]	X
ejpam-7033	279	8	+	+	CCONJ
ejpam-7033	279	9	s2[r∗	s2[r∗	NOUN
ejpam-7033	279	10	n+2	n+2	NOUN
ejpam-7033	279	11	+	+	CCONJ
ejpam-7033	279	12	r∗	r∗	VERB
ejpam-7033	279	13	n+3	n+3	PROPN
ejpam-7033	279	14	+	+	CCONJ
ejpam-7033	279	15	r(fn+3	r(fn+3	PROPN
ejpam-7033	279	16	,	,	PUNCT
ejpam-7033	279	17	fn+2m+1	fn+2m+1	PROPN
ejpam-7033	279	18	)	)	PUNCT
ejpam-7033	279	19	]	]	PUNCT
ejpam-7033	280	1	⪯	⪯	X
ejpam-7033	280	2	s[r∗	s[r∗	PROPN
ejpam-7033	280	3	n	n	PROPN
ejpam-7033	280	4	+	+	CCONJ
ejpam-7033	280	5	r∗	r∗	PROPN
ejpam-7033	280	6	n+1	n+1	PROPN
ejpam-7033	280	7	]	]	X
ejpam-7033	280	8	+	+	CCONJ
ejpam-7033	280	9	s2[r∗	s2[r∗	NOUN
ejpam-7033	280	10	n+2	n+2	NOUN
ejpam-7033	280	11	+	+	CCONJ
ejpam-7033	280	12	r∗	r∗	PROPN
ejpam-7033	280	13	n+3	n+3	NUM
ejpam-7033	280	14	]	]	X
ejpam-7033	280	15	+	+	CCONJ
ejpam-7033	280	16	·	·	PUNCT
ejpam-7033	280	17	·	·	PUNCT
ejpam-7033	280	18	·	·	PUNCT
ejpam-7033	281	1	+	+	NUM
ejpam-7033	281	2	sm−1[r∗	sm−1[r∗	NOUN
ejpam-7033	281	3	2m−4	2m−4	PROPN
ejpam-7033	281	4	+	+	CCONJ
ejpam-7033	281	5	r∗	r∗	PROPN
ejpam-7033	281	6	2m−3	2m−3	NUM
ejpam-7033	281	7	]	]	X
ejpam-7033	281	8	+	+	CCONJ
ejpam-7033	281	9	sm−1r(fn+2m−2	sm−1r(fn+2m−2	PROPN
ejpam-7033	281	10	,	,	PUNCT
ejpam-7033	281	11	fn+2	fn+2	PROPN
ejpam-7033	281	12	m	m	NOUN
ejpam-7033	281	13	)	)	PUNCT
ejpam-7033	281	14	⪯	⪯	VERB
ejpam-7033	281	15	s[t	s[t	PROPN
ejpam-7033	281	16	nr∗	nr∗	NOUN
ejpam-7033	281	17	0	0	PUNCT
ejpam-7033	282	1	+	+	CCONJ
ejpam-7033	282	2	t	t	PROPN
ejpam-7033	282	3	n+1r∗	n+1r∗	NUM
ejpam-7033	282	4	1	1	NUM
ejpam-7033	282	5	]	]	PUNCT
ejpam-7033	282	6	+	+	CCONJ
ejpam-7033	282	7	s2[t	s2[t	NOUN
ejpam-7033	282	8	n+2r∗	n+2r∗	NUM
ejpam-7033	282	9	0	0	NUM
ejpam-7033	283	1	+	+	NUM
ejpam-7033	283	2	t	t	PROPN
ejpam-7033	283	3	n+3r∗	n+3r∗	NUM
ejpam-7033	283	4	0	0	NUM
ejpam-7033	283	5	]	]	X
ejpam-7033	283	6	+	+	CCONJ
ejpam-7033	283	7	·	·	PUNCT
ejpam-7033	283	8	·	·	PUNCT
ejpam-7033	283	9	·	·	PUNCT
ejpam-7033	283	10	+	+	NUM
ejpam-7033	283	11	sm−1	sm−1	NOUN
ejpam-7033	283	12	t	t	X
ejpam-7033	283	13	n+2m−2r∗	n+2m−2r∗	NOUN
ejpam-7033	283	14	0	0	NUM
ejpam-7033	283	15	≺	≺	NOUN
ejpam-7033	283	16	(	(	PUNCT
ejpam-7033	283	17	st	st	PROPN
ejpam-7033	283	18	n	n	PROPN
ejpam-7033	283	19	+	+	CCONJ
ejpam-7033	283	20	st	st	PROPN
ejpam-7033	283	21	n+1)(i	n+1)(i	PROPN
ejpam-7033	283	22	+	+	CCONJ
ejpam-7033	283	23	st	st	PROPN
ejpam-7033	283	24	2	2	NUM
ejpam-7033	283	25	+	+	NOUN
ejpam-7033	283	26	s2	s2	PROPN
ejpam-7033	283	27	t	t	NOUN
ejpam-7033	283	28	4	4	NUM
ejpam-7033	283	29	+	+	CCONJ
ejpam-7033	283	30	·	·	PUNCT
ejpam-7033	283	31	·	·	PUNCT
ejpam-7033	283	32	·	·	PUNCT
ejpam-7033	283	33	)	)	PUNCT
ejpam-7033	283	34	r∗	r∗	VERB
ejpam-7033	283	35	0	0	PUNCT
ejpam-7033	284	1	+	+	CCONJ
ejpam-7033	284	2	sm−1	sm−1	NOUN
ejpam-7033	284	3	t	t	NOUN
ejpam-7033	284	4	n+2m−2r∗	n+2m−2r∗	NOUN
ejpam-7033	284	5	0	0	PUNCT
ejpam-7033	285	1	=	=	SYM
ejpam-7033	285	2	(	(	PUNCT
ejpam-7033	285	3	st	st	PROPN
ejpam-7033	285	4	n	n	PROPN
ejpam-7033	285	5	+	+	CCONJ
ejpam-7033	285	6	st	st	PROPN
ejpam-7033	285	7	n+1)(i	n+1)(i	PROPN
ejpam-7033	285	8	−	−	PROPN
ejpam-7033	285	9	st	st	PROPN
ejpam-7033	285	10	2)−1r∗	2)−1r∗	PROPN
ejpam-7033	285	11	0	0	PUNCT
ejpam-7033	286	1	+	+	CCONJ
ejpam-7033	287	1	sm−1	sm−1	PROPN
ejpam-7033	287	2	t	t	PROPN
ejpam-7033	287	3	2m−2	2m−2	NUM
ejpam-7033	287	4	t	t	NOUN
ejpam-7033	287	5	nr∗	nr∗	NOUN
ejpam-7033	287	6	0	0	NUM
ejpam-7033	288	1	=	=	SYM
ejpam-7033	288	2	1	1	NUM
ejpam-7033	288	3	s	s	X
ejpam-7033	288	4	(	(	PUNCT
ejpam-7033	288	5	st	st	PROPN
ejpam-7033	288	6	n	n	PROPN
ejpam-7033	288	7	+	+	CCONJ
ejpam-7033	288	8	st	st	PROPN
ejpam-7033	288	9	n+1	n+1	PROPN
ejpam-7033	288	10	)	)	PUNCT
ejpam-7033	288	11	(	(	PUNCT
ejpam-7033	288	12	1	1	NUM
ejpam-7033	288	13	s	s	NOUN
ejpam-7033	288	14	−	−	PROPN
ejpam-7033	288	15	t	t	NOUN
ejpam-7033	288	16	2)−1r∗	2)−1r∗	NUM
ejpam-7033	288	17	0	0	PUNCT
ejpam-7033	289	1	+	+	CCONJ
ejpam-7033	289	2	sm−1	sm−1	PROPN
ejpam-7033	289	3	t	t	PROPN
ejpam-7033	289	4	2m−2	2m−2	NUM
ejpam-7033	289	5	t	t	PROPN
ejpam-7033	289	6	nr∗	nr∗	NOUN
ejpam-7033	289	7	0	0	NUM
ejpam-7033	289	8	.	.	PUNCT
ejpam-7033	290	1	here	here	ADV
ejpam-7033	290	2	∥t	∥t	VERB
ejpam-7033	290	3	∥1	∥1	PRON
ejpam-7033	290	4	<	<	X
ejpam-7033	290	5	1	1	NUM
ejpam-7033	290	6	s	s	NOUN
ejpam-7033	290	7	,	,	PUNCT
ejpam-7033	290	8	which	which	PRON
ejpam-7033	290	9	further	far	ADV
ejpam-7033	290	10	implies	imply	VERB
ejpam-7033	290	11	that	that	SCONJ
ejpam-7033	290	12	limn→∞	limn→∞	PROPN
ejpam-7033	290	13	t	t	NOUN
ejpam-7033	290	14	n	n	NOUN
ejpam-7033	290	15	=	=	SYM
ejpam-7033	290	16	0	0	NUM
ejpam-7033	290	17	.	.	PUNCT
ejpam-7033	291	1	hence	hence	ADV
ejpam-7033	291	2	,	,	PUNCT
ejpam-7033	291	3	limn→∞r(fn	limn→∞r(fn	NOUN
ejpam-7033	291	4	,	,	PUNCT
ejpam-7033	291	5	fn+p	fn+p	PROPN
ejpam-7033	291	6	)	)	PUNCT
ejpam-7033	291	7	=	=	SYM
ejpam-7033	291	8	0e	0e	NOUN
ejpam-7033	291	9	and	and	CCONJ
ejpam-7033	291	10	{	{	PUNCT
ejpam-7033	291	11	fn	fn	NOUN
ejpam-7033	291	12	}	}	PUNCT
ejpam-7033	291	13	is	be	AUX
ejpam-7033	291	14	a	a	DET
ejpam-7033	291	15	cauchy	cauchy	ADJ
ejpam-7033	291	16	sequence	sequence	NOUN
ejpam-7033	291	17	in	in	ADP
ejpam-7033	291	18	w	w	PROPN
ejpam-7033	291	19	.	.	PUNCT
ejpam-7033	292	1	now	now	ADV
ejpam-7033	292	2	(	(	PUNCT
ejpam-7033	292	3	w	w	NOUN
ejpam-7033	292	4	,	,	PUNCT
ejpam-7033	292	5	r	r	NOUN
ejpam-7033	292	6	)	)	PUNCT
ejpam-7033	292	7	is	be	AUX
ejpam-7033	292	8	a	a	DET
ejpam-7033	292	9	complete	complete	ADJ
ejpam-7033	292	10	rectangular	rectangular	ADJ
ejpam-7033	292	11	cone	cone	NOUN
ejpam-7033	292	12	bmetric	bmetric	ADJ
ejpam-7033	292	13	space	space	NOUN
ejpam-7033	292	14	,	,	PUNCT
ejpam-7033	292	15	so	so	SCONJ
ejpam-7033	292	16	fn	fn	PROPN
ejpam-7033	292	17	→	→	SYM
ejpam-7033	292	18	z∗	z∗	PROPN
ejpam-7033	292	19	for	for	ADP
ejpam-7033	292	20	some	some	DET
ejpam-7033	292	21	z∗	z∗	NOUN
ejpam-7033	292	22	∈w	∈w	NOUN
ejpam-7033	292	23	if	if	SCONJ
ejpam-7033	292	24	n	n	PRON
ejpam-7033	292	25	being	be	AUX
ejpam-7033	292	26	very	very	ADV
ejpam-7033	292	27	large	large	ADJ
ejpam-7033	292	28	.	.	PUNCT
ejpam-7033	293	1	so	so	ADV
ejpam-7033	293	2	r(fn	r(fn	PROPN
ejpam-7033	293	3	,	,	PUNCT
ejpam-7033	293	4	z	z	NOUN
ejpam-7033	293	5	∗	∗	NOUN
ejpam-7033	293	6	)	)	PUNCT
ejpam-7033	293	7	≪	≪	NOUN
ejpam-7033	293	8	ϵ	ϵ	X
ejpam-7033	293	9	for	for	ADP
ejpam-7033	293	10	all	all	DET
ejpam-7033	293	11	n	n	PRON
ejpam-7033	293	12	≥	≥	NOUN
ejpam-7033	293	13	n2	n2	PROPN
ejpam-7033	293	14	∈	∈	PROPN
ejpam-7033	293	15	n	n	CCONJ
ejpam-7033	293	16	and	and	CCONJ
ejpam-7033	293	17	0	0	NUM
ejpam-7033	293	18	≪	≪	PUNCT
ejpam-7033	293	19	ϵ.	ϵ.	NOUN
ejpam-7033	293	20	let	let	VERB
ejpam-7033	293	21	(	(	PUNCT
ejpam-7033	293	22	i	i	PRON
ejpam-7033	293	23	−	−	PROPN
ejpam-7033	293	24	t	t	NOUN
ejpam-7033	293	25	)	)	PUNCT
ejpam-7033	293	26	2(i	2(i	NUM
ejpam-7033	294	1	+	+	NUM
ejpam-7033	294	2	t	t	NOUN
ejpam-7033	294	3	)	)	PUNCT
ejpam-7033	294	4	(	(	PUNCT
ejpam-7033	294	5	r(fn	r(fn	NOUN
ejpam-7033	294	6	,	,	PUNCT
ejpam-7033	294	7	ℏ(fn	ℏ(fn	NOUN
ejpam-7033	294	8	)	)	PUNCT
ejpam-7033	294	9	)	)	PUNCT
ejpam-7033	294	10	)	)	PUNCT
ejpam-7033	294	11	≻	≻	PROPN
ejpam-7033	295	1	sr(fn	sr(fn	PROPN
ejpam-7033	295	2	,	,	PUNCT
ejpam-7033	295	3	z	z	NOUN
ejpam-7033	295	4	∗	∗	NOUN
ejpam-7033	295	5	)	)	PUNCT
ejpam-7033	295	6	and	and	CCONJ
ejpam-7033	295	7	(	(	PUNCT
ejpam-7033	295	8	i	i	PRON
ejpam-7033	295	9	−	−	PROPN
ejpam-7033	295	10	t	t	NOUN
ejpam-7033	295	11	)	)	PUNCT
ejpam-7033	295	12	2(i	2(i	NUM
ejpam-7033	296	1	+	+	NUM
ejpam-7033	296	2	t	t	NOUN
ejpam-7033	296	3	)	)	PUNCT
ejpam-7033	296	4	(	(	PUNCT
ejpam-7033	296	5	r(fn+2	r(fn+2	PROPN
ejpam-7033	296	6	,	,	PUNCT
ejpam-7033	296	7	ℏ(fn+2	ℏ(fn+2	NOUN
ejpam-7033	296	8	)	)	PUNCT
ejpam-7033	296	9	)	)	PUNCT
ejpam-7033	296	10	)	)	PUNCT
ejpam-7033	297	1	≻	≻	PROPN
ejpam-7033	298	1	sr(fn+2	sr(fn+2	PROPN
ejpam-7033	298	2	,	,	PUNCT
ejpam-7033	298	3	z	z	NOUN
ejpam-7033	298	4	∗	∗	NOUN
ejpam-7033	298	5	)	)	PUNCT
ejpam-7033	298	6	for	for	ADP
ejpam-7033	298	7	some	some	DET
ejpam-7033	298	8	n	n	PRON
ejpam-7033	298	9	∈	∈	PROPN
ejpam-7033	298	10	n	n	NOUN
ejpam-7033	298	11	and	and	CCONJ
ejpam-7033	298	12	s	s	X
ejpam-7033	298	13	≥	≥	NOUN
ejpam-7033	298	14	1	1	NUM
ejpam-7033	298	15	.	.	PUNCT
ejpam-7033	299	1	using	use	VERB
ejpam-7033	299	2	(	(	PUNCT
ejpam-7033	299	3	5	5	NUM
ejpam-7033	299	4	)	)	PUNCT
ejpam-7033	299	5	and	and	CCONJ
ejpam-7033	299	6	(	(	PUNCT
ejpam-7033	299	7	drb3	drb3	PROPN
ejpam-7033	299	8	)	)	PUNCT
ejpam-7033	299	9	,	,	PUNCT
ejpam-7033	299	10	implies	imply	VERB
ejpam-7033	299	11	r(fn	r(fn	NOUN
ejpam-7033	299	12	,	,	PUNCT
ejpam-7033	299	13	ℏ(fn	ℏ(fn	NOUN
ejpam-7033	299	14	)	)	PUNCT
ejpam-7033	299	15	)	)	PUNCT
ejpam-7033	299	16	⪯	⪯	PROPN
ejpam-7033	299	17	s[r(fn	s[r(fn	PROPN
ejpam-7033	299	18	,	,	PUNCT
ejpam-7033	299	19	z	z	NOUN
ejpam-7033	299	20	∗	∗	NOUN
ejpam-7033	299	21	)	)	PUNCT
ejpam-7033	300	1	+	+	CCONJ
ejpam-7033	300	2	r(z∗	r(z∗	NUM
ejpam-7033	300	3	,	,	PUNCT
ejpam-7033	300	4	fn+2	fn+2	X
ejpam-7033	300	5	)	)	PUNCT
ejpam-7033	300	6	+	+	SYM
ejpam-7033	300	7	r(fn+2	r(fn+2	PROPN
ejpam-7033	300	8	,	,	PUNCT
ejpam-7033	300	9	fn+1	fn+1	NOUN
ejpam-7033	300	10	)	)	PUNCT
ejpam-7033	300	11	]	]	PUNCT
ejpam-7033	300	12	≺	≺	NOUN
ejpam-7033	300	13	s	s	X
ejpam-7033	300	14	s	s	X
ejpam-7033	300	15	(	(	PUNCT
ejpam-7033	300	16	i	i	PRON
ejpam-7033	300	17	−	−	PROPN
ejpam-7033	300	18	t	t	NOUN
ejpam-7033	300	19	)	)	PUNCT
ejpam-7033	300	20	2(i	2(i	NUM
ejpam-7033	301	1	+	+	NUM
ejpam-7033	301	2	t	t	NOUN
ejpam-7033	301	3	)	)	PUNCT
ejpam-7033	301	4	(	(	PUNCT
ejpam-7033	301	5	r(fn	r(fn	NOUN
ejpam-7033	301	6	,	,	PUNCT
ejpam-7033	301	7	ℏ(fn	ℏ(fn	NOUN
ejpam-7033	301	8	)	)	PUNCT
ejpam-7033	301	9	)	)	PUNCT
ejpam-7033	301	10	)	)	PUNCT
ejpam-7033	302	1	+	+	CCONJ
ejpam-7033	302	2	s	s	X
ejpam-7033	302	3	s	s	X
ejpam-7033	302	4	(	(	PUNCT
ejpam-7033	302	5	i	i	PRON
ejpam-7033	302	6	−	−	PROPN
ejpam-7033	302	7	t	t	NOUN
ejpam-7033	302	8	)	)	PUNCT
ejpam-7033	302	9	2(i	2(i	NUM
ejpam-7033	303	1	+	+	NUM
ejpam-7033	303	2	t	t	NOUN
ejpam-7033	303	3	)	)	PUNCT
ejpam-7033	304	1	r(fn+2	r(fn+2	PROPN
ejpam-7033	304	2	,	,	PUNCT
ejpam-7033	304	3	ℏ(fn+2	ℏ(fn+2	NOUN
ejpam-7033	304	4	)	)	PUNCT
ejpam-7033	304	5	)	)	PUNCT
ejpam-7033	304	6	)	)	PUNCT
ejpam-7033	305	1	a.	a.	PROPN
ejpam-7033	305	2	arif	arif	PROPN
ejpam-7033	305	3	et	et	PROPN
ejpam-7033	305	4	al	al	PROPN
ejpam-7033	305	5	.	.	PUNCT
ejpam-7033	305	6	/	/	SYM
ejpam-7033	305	7	eur	eur	PROPN
ejpam-7033	305	8	.	.	PUNCT
ejpam-7033	306	1	j.	j.	PROPN
ejpam-7033	306	2	pure	pure	PROPN
ejpam-7033	306	3	appl	appl	PROPN
ejpam-7033	306	4	.	.	PROPN
ejpam-7033	306	5	math	math	PROPN
ejpam-7033	306	6	,	,	PUNCT
ejpam-7033	306	7	18	18	NUM
ejpam-7033	306	8	(	(	PUNCT
ejpam-7033	306	9	4	4	NUM
ejpam-7033	306	10	)	)	PUNCT
ejpam-7033	306	11	(	(	PUNCT
ejpam-7033	306	12	2025	2025	NUM
ejpam-7033	306	13	)	)	PUNCT
ejpam-7033	306	14	,	,	PUNCT
ejpam-7033	306	15	7033	7033	NUM
ejpam-7033	306	16	11	11	NUM
ejpam-7033	306	17	of	of	ADP
ejpam-7033	306	18	29	29	NUM
ejpam-7033	307	1	+	+	SYM
ejpam-7033	307	2	s	s	NOUN
ejpam-7033	307	3	1	1	NUM
ejpam-7033	307	4	s	s	PART
ejpam-7033	307	5	t	t	NOUN
ejpam-7033	307	6	(	(	PUNCT
ejpam-7033	307	7	r(fn	r(fn	PROPN
ejpam-7033	307	8	,	,	PUNCT
ejpam-7033	307	9	ℏ(fn	ℏ(fn	NOUN
ejpam-7033	307	10	)	)	PUNCT
ejpam-7033	307	11	)	)	PUNCT
ejpam-7033	307	12	)	)	PUNCT
ejpam-7033	307	13	≺	≺	NOUN
ejpam-7033	307	14	(	(	PUNCT
ejpam-7033	307	15	i	i	PRON
ejpam-7033	307	16	−	−	PROPN
ejpam-7033	307	17	t	t	NOUN
ejpam-7033	307	18	)	)	PUNCT
ejpam-7033	307	19	2(i	2(i	NUM
ejpam-7033	308	1	+	+	NUM
ejpam-7033	308	2	t	t	NOUN
ejpam-7033	308	3	)	)	PUNCT
ejpam-7033	308	4	(	(	PUNCT
ejpam-7033	308	5	r(fn	r(fn	NOUN
ejpam-7033	308	6	,	,	PUNCT
ejpam-7033	308	7	ℏ(fn	ℏ(fn	NOUN
ejpam-7033	308	8	)	)	PUNCT
ejpam-7033	308	9	)	)	PUNCT
ejpam-7033	308	10	)	)	PUNCT
ejpam-7033	309	1	+	+	CCONJ
ejpam-7033	309	2	(	(	PUNCT
ejpam-7033	309	3	i	i	PRON
ejpam-7033	309	4	−	−	PROPN
ejpam-7033	309	5	t	t	NOUN
ejpam-7033	309	6	)	)	PUNCT
ejpam-7033	309	7	2(i	2(i	NUM
ejpam-7033	310	1	+	+	CCONJ
ejpam-7033	310	2	t	t	PROPN
ejpam-7033	310	3	)	)	PUNCT
ejpam-7033	310	4	t	t	PROPN
ejpam-7033	310	5	2r(fn	2r(fn	NUM
ejpam-7033	310	6	,	,	PUNCT
ejpam-7033	310	7	ℏ(fn	ℏ(fn	NOUN
ejpam-7033	310	8	)	)	PUNCT
ejpam-7033	310	9	)	)	PUNCT
ejpam-7033	310	10	)	)	PUNCT
ejpam-7033	311	1	+	+	CCONJ
ejpam-7033	311	2	t	t	PROPN
ejpam-7033	311	3	(	(	PUNCT
ejpam-7033	311	4	r(fn	r(fn	PROPN
ejpam-7033	311	5	,	,	PUNCT
ejpam-7033	311	6	ℏ(fn	ℏ(fn	NOUN
ejpam-7033	311	7	)	)	PUNCT
ejpam-7033	311	8	)	)	PUNCT
ejpam-7033	311	9	)	)	PUNCT
ejpam-7033	312	1	(	(	PUNCT
ejpam-7033	312	2	i	i	PRON
ejpam-7033	312	3	−	−	PROPN
ejpam-7033	312	4	t	t	NOUN
ejpam-7033	312	5	)	)	PUNCT
ejpam-7033	312	6	r(fn	r(fn	PROPN
ejpam-7033	312	7	,	,	PUNCT
ejpam-7033	312	8	ℏ(fn	ℏ(fn	NOUN
ejpam-7033	312	9	)	)	PUNCT
ejpam-7033	312	10	)	)	PUNCT
ejpam-7033	312	11	⪯	⪯	NOUN
ejpam-7033	312	12	(	(	PUNCT
ejpam-7033	312	13	i	i	PRON
ejpam-7033	312	14	−	−	PROPN
ejpam-7033	312	15	t	t	NOUN
ejpam-7033	312	16	)	)	PUNCT
ejpam-7033	312	17	2(i	2(i	NUM
ejpam-7033	313	1	+	+	NUM
ejpam-7033	313	2	t	t	NOUN
ejpam-7033	313	3	)	)	PUNCT
ejpam-7033	313	4	(	(	PUNCT
ejpam-7033	313	5	i	i	PRON
ejpam-7033	313	6	+	+	X
ejpam-7033	313	7	t	t	PROPN
ejpam-7033	313	8	2)r(fn	2)r(fn	NUM
ejpam-7033	313	9	,	,	PUNCT
ejpam-7033	313	10	ℏ(fn	ℏ(fn	NOUN
ejpam-7033	313	11	)	)	PUNCT
ejpam-7033	313	12	)	)	PUNCT
ejpam-7033	313	13	)	)	PUNCT
ejpam-7033	313	14	.	.	PUNCT
ejpam-7033	314	1	thus	thus	ADV
ejpam-7033	314	2	t	t	PROPN
ejpam-7033	314	3	4(r(fn	4(r(fn	NUM
ejpam-7033	314	4	,	,	PUNCT
ejpam-7033	314	5	ℏ(fn	ℏ(fn	PROPN
ejpam-7033	314	6	)	)	PUNCT
ejpam-7033	314	7	)	)	PUNCT
ejpam-7033	314	8	)	)	PUNCT
ejpam-7033	315	1	≺	≺	NOUN
ejpam-7033	315	2	0e	0e	NOUN
ejpam-7033	315	3	,	,	PUNCT
ejpam-7033	315	4	that	that	SCONJ
ejpam-7033	315	5	steers	steer	NOUN
ejpam-7033	315	6	to	to	ADP
ejpam-7033	315	7	contradiction	contradiction	NOUN
ejpam-7033	315	8	.	.	PUNCT
ejpam-7033	316	1	thus	thus	ADV
ejpam-7033	316	2	,	,	PUNCT
ejpam-7033	316	3	for	for	ADP
ejpam-7033	316	4	every	every	DET
ejpam-7033	316	5	n	n	PRON
ejpam-7033	316	6	≥	≥	NOUN
ejpam-7033	316	7	1	1	NUM
ejpam-7033	316	8	and	and	CCONJ
ejpam-7033	316	9	for	for	ADP
ejpam-7033	316	10	some	some	PRON
ejpam-7033	316	11	s	s	PART
ejpam-7033	316	12	≥	≥	NOUN
ejpam-7033	316	13	1	1	NUM
ejpam-7033	316	14	(	(	PUNCT
ejpam-7033	316	15	i	i	PRON
ejpam-7033	316	16	−	−	PROPN
ejpam-7033	316	17	t	t	NOUN
ejpam-7033	316	18	)	)	PUNCT
ejpam-7033	316	19	2(i	2(i	NUM
ejpam-7033	317	1	+	+	NUM
ejpam-7033	317	2	t	t	NOUN
ejpam-7033	317	3	)	)	PUNCT
ejpam-7033	317	4	(	(	PUNCT
ejpam-7033	317	5	r(fn	r(fn	NOUN
ejpam-7033	317	6	,	,	PUNCT
ejpam-7033	317	7	ℏ(fn	ℏ(fn	NOUN
ejpam-7033	317	8	)	)	PUNCT
ejpam-7033	317	9	)	)	PUNCT
ejpam-7033	317	10	)	)	PUNCT
ejpam-7033	317	11	⪯	⪯	PROPN
ejpam-7033	317	12	sr(fn	sr(fn	PROPN
ejpam-7033	317	13	,	,	PUNCT
ejpam-7033	317	14	z	z	NOUN
ejpam-7033	317	15	∗	∗	NOUN
ejpam-7033	317	16	)	)	PUNCT
ejpam-7033	317	17	.	.	PUNCT
ejpam-7033	318	1	this	this	PRON
ejpam-7033	318	2	implies	imply	VERB
ejpam-7033	318	3	that	that	SCONJ
ejpam-7033	318	4	(	(	PUNCT
ejpam-7033	318	5	due	due	ADP
ejpam-7033	318	6	to	to	PART
ejpam-7033	318	7	(	(	PUNCT
ejpam-7033	318	8	5	5	NUM
ejpam-7033	318	9	)	)	PUNCT
ejpam-7033	318	10	)	)	PUNCT
ejpam-7033	318	11	j	j	PROPN
ejpam-7033	318	12	(	(	PUNCT
ejpam-7033	318	13	r(ℏ(fn	r(ℏ(fn	NOUN
ejpam-7033	318	14	)	)	PUNCT
ejpam-7033	318	15	,	,	PUNCT
ejpam-7033	318	16	ℏ(z∗)),r(fn	ℏ(z∗)),r(fn	PROPN
ejpam-7033	318	17	,	,	PUNCT
ejpam-7033	318	18	z∗),r(fn	z∗),r(fn	PROPN
ejpam-7033	318	19	,	,	PUNCT
ejpam-7033	318	20	ℏ(fn)),r(z∗	ℏ(fn)),r(z∗	NUM
ejpam-7033	318	21	,	,	PUNCT
ejpam-7033	318	22	ℏ(z∗	ℏ(z∗	NOUN
ejpam-7033	318	23	)	)	PUNCT
ejpam-7033	318	24	)	)	PUNCT
ejpam-7033	318	25	,	,	PUNCT
ejpam-7033	318	26	r(fn−1	r(fn−1	X
ejpam-7033	318	27	,	,	PUNCT
ejpam-7033	318	28	ℏ2(z∗)),r(ℏ2(fn	ℏ2(z∗)),r(ℏ2(fn	NOUN
ejpam-7033	318	29	)	)	PUNCT
ejpam-7033	318	30	,	,	PUNCT
ejpam-7033	318	31	ℏ(fn	ℏ(fn	NOUN
ejpam-7033	318	32	)	)	PUNCT
ejpam-7033	318	33	)	)	PUNCT
ejpam-7033	318	34	)	)	PUNCT
ejpam-7033	318	35	⪯	⪯	NOUN
ejpam-7033	318	36	0e	0e	PROPN
ejpam-7033	318	37	.	.	PUNCT
ejpam-7033	319	1	(	(	PUNCT
ejpam-7033	319	2	7	7	X
ejpam-7033	319	3	)	)	PUNCT
ejpam-7033	319	4	now	now	ADV
ejpam-7033	319	5	,	,	PUNCT
ejpam-7033	319	6	we	we	PRON
ejpam-7033	319	7	claim	claim	VERB
ejpam-7033	319	8	that	that	SCONJ
ejpam-7033	319	9	∥r(z∗	∥r(z∗	NUM
ejpam-7033	319	10	,	,	PUNCT
ejpam-7033	319	11	ℏ(z∗))∥	ℏ(z∗))∥	NOUN
ejpam-7033	319	12	=	=	NOUN
ejpam-7033	319	13	0	0	NUM
ejpam-7033	319	14	,	,	PUNCT
ejpam-7033	319	15	on	on	ADP
ejpam-7033	319	16	contrary	contrary	NOUN
ejpam-7033	319	17	suppose	suppose	VERB
ejpam-7033	319	18	that	that	SCONJ
ejpam-7033	319	19	∥r(z∗	∥r(z∗	NUM
ejpam-7033	319	20	,	,	PUNCT
ejpam-7033	319	21	ℏ(z∗))∥	ℏ(z∗))∥	PROPN
ejpam-7033	319	22	>	>	X
ejpam-7033	319	23	0	0	NUM
ejpam-7033	319	24	,	,	PUNCT
ejpam-7033	319	25	as	as	ADP
ejpam-7033	319	26	a	a	DET
ejpam-7033	319	27	result	result	NOUN
ejpam-7033	319	28	we	we	PRON
ejpam-7033	319	29	get	get	VERB
ejpam-7033	319	30	r(ℏ(fn	r(ℏ(fn	NOUN
ejpam-7033	319	31	)	)	PUNCT
ejpam-7033	319	32	,	,	PUNCT
ejpam-7033	319	33	ℏ(z∗	ℏ(z∗	NOUN
ejpam-7033	319	34	)	)	PUNCT
ejpam-7033	319	35	)	)	PUNCT
ejpam-7033	319	36	⪯	⪯	PROPN
ejpam-7033	319	37	s[r(ℏ(fn	s[r(ℏ(fn	PROPN
ejpam-7033	319	38	)	)	PUNCT
ejpam-7033	319	39	,	,	PUNCT
ejpam-7033	319	40	ℏ(fn+1	ℏ(fn+1	NOUN
ejpam-7033	319	41	)	)	PUNCT
ejpam-7033	319	42	)	)	PUNCT
ejpam-7033	320	1	+	+	PUNCT
ejpam-7033	320	2	r(ℏ(fn+1	r(ℏ(fn+1	NUM
ejpam-7033	320	3	)	)	PUNCT
ejpam-7033	320	4	,	,	PUNCT
ejpam-7033	320	5	z	z	NOUN
ejpam-7033	320	6	∗	∗	NOUN
ejpam-7033	320	7	)	)	PUNCT
ejpam-7033	320	8	)	)	PUNCT
ejpam-7033	321	1	+	+	CCONJ
ejpam-7033	321	2	r(z∗	r(z∗	NUM
ejpam-7033	321	3	,	,	PUNCT
ejpam-7033	321	4	ℏ(z∗	ℏ(z∗	NOUN
ejpam-7033	321	5	)	)	PUNCT
ejpam-7033	321	6	)	)	PUNCT
ejpam-7033	321	7	]	]	PUNCT
ejpam-7033	321	8	limn→∞r(ℏ(fn	limn→∞r(ℏ(fn	PROPN
ejpam-7033	321	9	)	)	PUNCT
ejpam-7033	321	10	,	,	PUNCT
ejpam-7033	321	11	ℏ(z∗	ℏ(z∗	NOUN
ejpam-7033	321	12	)	)	PUNCT
ejpam-7033	321	13	)	)	PUNCT
ejpam-7033	321	14	⪯	⪯	PROPN
ejpam-7033	321	15	sr(z∗	sr(z∗	NUM
ejpam-7033	321	16	,	,	PUNCT
ejpam-7033	321	17	ℏ(z∗	ℏ(z∗	NOUN
ejpam-7033	321	18	)	)	PUNCT
ejpam-7033	321	19	)	)	PUNCT
ejpam-7033	321	20	r(fn−1	r(fn−1	PROPN
ejpam-7033	321	21	,	,	PUNCT
ejpam-7033	321	22	ℏ2(z∗	ℏ2(z∗	NUM
ejpam-7033	321	23	)	)	PUNCT
ejpam-7033	321	24	)	)	PUNCT
ejpam-7033	321	25	⪯	⪯	PROPN
ejpam-7033	321	26	s[r(fn−1	s[r(fn−1	PROPN
ejpam-7033	321	27	,	,	PUNCT
ejpam-7033	321	28	fn	fn	NOUN
ejpam-7033	321	29	)	)	PUNCT
ejpam-7033	322	1	+	+	CCONJ
ejpam-7033	322	2	r(fn	r(fn	NOUN
ejpam-7033	322	3	,	,	PUNCT
ejpam-7033	322	4	z	z	NOUN
ejpam-7033	322	5	∗	∗	NOUN
ejpam-7033	322	6	)	)	PUNCT
ejpam-7033	322	7	+	+	CCONJ
ejpam-7033	322	8	r(z∗	r(z∗	NUM
ejpam-7033	322	9	,	,	PUNCT
ejpam-7033	322	10	ℏ2(z∗	ℏ2(z∗	NUM
ejpam-7033	322	11	)	)	PUNCT
ejpam-7033	322	12	)	)	PUNCT
ejpam-7033	322	13	]	]	PUNCT
ejpam-7033	323	1	limn→∞r(fn−1	limn→∞r(fn−1	PROPN
ejpam-7033	323	2	,	,	PUNCT
ejpam-7033	323	3	ℏ2(z∗	ℏ2(z∗	NUM
ejpam-7033	323	4	)	)	PUNCT
ejpam-7033	323	5	)	)	PUNCT
ejpam-7033	323	6	⪯	⪯	PROPN
ejpam-7033	323	7	sr(z∗	sr(z∗	NUM
ejpam-7033	323	8	,	,	PUNCT
ejpam-7033	323	9	ℏ2(z∗	ℏ2(z∗	NUM
ejpam-7033	323	10	)	)	PUNCT
ejpam-7033	323	11	)	)	PUNCT
ejpam-7033	323	12	taking	take	VERB
ejpam-7033	323	13	n→	n→	ADV
ejpam-7033	323	14	∞	∞	PROPN
ejpam-7033	323	15	,	,	PUNCT
ejpam-7033	323	16	and	and	CCONJ
ejpam-7033	323	17	in	in	ADP
ejpam-7033	323	18	view	view	NOUN
ejpam-7033	323	19	of	of	ADP
ejpam-7033	323	20	assumption	assumption	NOUN
ejpam-7033	323	21	(	(	PUNCT
ejpam-7033	323	22	3	3	NUM
ejpam-7033	323	23	)	)	PUNCT
ejpam-7033	323	24	and	and	CCONJ
ejpam-7033	323	25	(	(	PUNCT
ejpam-7033	323	26	7	7	NUM
ejpam-7033	323	27	)	)	PUNCT
ejpam-7033	323	28	,	,	PUNCT
ejpam-7033	323	29	we	we	PRON
ejpam-7033	323	30	get	get	VERB
ejpam-7033	323	31	j	j	PROPN
ejpam-7033	323	32	(	(	PUNCT
ejpam-7033	323	33	sr(z∗	sr(z∗	NUM
ejpam-7033	323	34	,	,	PUNCT
ejpam-7033	323	35	ℏ(z∗)),0e	ℏ(z∗)),0e	NOUN
ejpam-7033	323	36	,	,	PUNCT
ejpam-7033	323	37	0e	0e	NOUN
ejpam-7033	323	38	,	,	PUNCT
ejpam-7033	323	39	r(z∗	r(z∗	NOUN
ejpam-7033	323	40	,	,	PUNCT
ejpam-7033	323	41	ℏ(z∗	ℏ(z∗	NOUN
ejpam-7033	323	42	)	)	PUNCT
ejpam-7033	323	43	)	)	PUNCT
ejpam-7033	323	44	,	,	PUNCT
ejpam-7033	323	45	sr(z∗	sr(z∗	NUM
ejpam-7033	323	46	,	,	PUNCT
ejpam-7033	323	47	ℏ2(z∗)),0e	ℏ2(z∗)),0e	NOUN
ejpam-7033	323	48	)	)	PUNCT
ejpam-7033	323	49	⪯	⪯	NOUN
ejpam-7033	323	50	0e	0e	NOUN
ejpam-7033	323	51	.	.	PUNCT
ejpam-7033	324	1	by	by	ADP
ejpam-7033	324	2	(	(	PUNCT
ejpam-7033	324	3	j1	j1	PROPN
ejpam-7033	324	4	)	)	PUNCT
ejpam-7033	324	5	and	and	CCONJ
ejpam-7033	324	6	condition	condition	NOUN
ejpam-7033	324	7	(	(	PUNCT
ejpam-7033	324	8	3	3	NUM
ejpam-7033	324	9	)	)	PUNCT
ejpam-7033	324	10	,	,	PUNCT
ejpam-7033	324	11	we	we	PRON
ejpam-7033	324	12	have	have	VERB
ejpam-7033	324	13	j	j	PROPN
ejpam-7033	324	14	(	(	PUNCT
ejpam-7033	324	15	sr(z∗	sr(z∗	NUM
ejpam-7033	324	16	,	,	PUNCT
ejpam-7033	324	17	ℏ(z∗)),0e	ℏ(z∗)),0e	NOUN
ejpam-7033	324	18	,	,	PUNCT
ejpam-7033	324	19	0e	0e	NOUN
ejpam-7033	324	20	,	,	PUNCT
ejpam-7033	324	21	r(z∗	r(z∗	NOUN
ejpam-7033	324	22	,	,	PUNCT
ejpam-7033	324	23	ℏ(z∗	ℏ(z∗	NOUN
ejpam-7033	324	24	)	)	PUNCT
ejpam-7033	324	25	)	)	PUNCT
ejpam-7033	324	26	,	,	PUNCT
ejpam-7033	324	27	sr(z∗	sr(z∗	NUM
ejpam-7033	324	28	,	,	PUNCT
ejpam-7033	324	29	ℏ(z∗)),0e	ℏ(z∗)),0e	PROPN
ejpam-7033	324	30	)	)	PUNCT
ejpam-7033	324	31	⪯	⪯	NOUN
ejpam-7033	324	32	0e	0e	NOUN
ejpam-7033	324	33	.	.	PUNCT
ejpam-7033	325	1	this	this	PRON
ejpam-7033	325	2	contradicts	contradict	VERB
ejpam-7033	325	3	(	(	PUNCT
ejpam-7033	325	4	j3	j3	PROPN
ejpam-7033	325	5	)	)	PUNCT
ejpam-7033	325	6	.	.	PUNCT
ejpam-7033	326	1	thus	thus	ADV
ejpam-7033	326	2	,	,	PUNCT
ejpam-7033	326	3	∥r(z∗	∥r(z∗	NUM
ejpam-7033	326	4	,	,	PUNCT
ejpam-7033	326	5	ℏ(z∗))∥	ℏ(z∗))∥	NOUN
ejpam-7033	326	6	=	=	NOUN
ejpam-7033	326	7	0	0	NUM
ejpam-7033	326	8	.	.	PUNCT
ejpam-7033	327	1	hence	hence	ADV
ejpam-7033	327	2	,	,	PUNCT
ejpam-7033	327	3	r(z∗	r(z∗	PRON
ejpam-7033	327	4	,	,	PUNCT
ejpam-7033	327	5	ℏ(z∗	ℏ(z∗	NOUN
ejpam-7033	327	6	)	)	PUNCT
ejpam-7033	327	7	)	)	PUNCT
ejpam-7033	328	1	=	=	SYM
ejpam-7033	328	2	0e	0e	NOUN
ejpam-7033	328	3	and	and	CCONJ
ejpam-7033	328	4	by	by	ADP
ejpam-7033	328	5	(	(	PUNCT
ejpam-7033	328	6	drb1	drb1	PROPN
ejpam-7033	328	7	)	)	PUNCT
ejpam-7033	328	8	,	,	PUNCT
ejpam-7033	328	9	we	we	PRON
ejpam-7033	328	10	get	get	VERB
ejpam-7033	328	11	z∗	z∗	NOUN
ejpam-7033	328	12	=	=	PUNCT
ejpam-7033	328	13	ℏ(z∗	ℏ(z∗	NOUN
ejpam-7033	328	14	)	)	PUNCT
ejpam-7033	328	15	.	.	PUNCT
ejpam-7033	329	1	in	in	ADP
ejpam-7033	329	2	next	next	ADJ
ejpam-7033	329	3	theorem	theorem	NOUN
ejpam-7033	329	4	,	,	PUNCT
ejpam-7033	329	5	we	we	PRON
ejpam-7033	329	6	present	present	VERB
ejpam-7033	329	7	a	a	DET
ejpam-7033	329	8	result	result	NOUN
ejpam-7033	329	9	for	for	ADP
ejpam-7033	329	10	non	non	ADJ
ejpam-7033	329	11	-	-	ADJ
ejpam-7033	329	12	increasing	increase	VERB
ejpam-7033	329	13	self	self	NOUN
ejpam-7033	329	14	-	-	PUNCT
ejpam-7033	329	15	operators	operator	NOUN
ejpam-7033	329	16	.	.	PUNCT
ejpam-7033	330	1	theorem	theorem	NOUN
ejpam-7033	330	2	14	14	NUM
ejpam-7033	330	3	.	.	PUNCT
ejpam-7033	331	1	let	let	AUX
ejpam-7033	331	2	(	(	PUNCT
ejpam-7033	331	3	w	w	NOUN
ejpam-7033	331	4	,	,	PUNCT
ejpam-7033	331	5	r	r	NOUN
ejpam-7033	331	6	)	)	PUNCT
ejpam-7033	331	7	be	be	AUX
ejpam-7033	331	8	a	a	DET
ejpam-7033	331	9	complete	complete	ADJ
ejpam-7033	331	10	rectangular	rectangular	ADJ
ejpam-7033	331	11	cone	cone	NOUN
ejpam-7033	331	12	b	b	NOUN
ejpam-7033	331	13	-	-	PUNCT
ejpam-7033	331	14	metric	metric	ADJ
ejpam-7033	331	15	space	space	NOUN
ejpam-7033	331	16	along	along	ADP
ejpam-7033	331	17	with	with	ADP
ejpam-7033	331	18	a	a	DET
ejpam-7033	331	19	cone	cone	NOUN
ejpam-7033	331	20	c	c	NOUN
ejpam-7033	331	21	⊂	⊂	X
ejpam-7033	331	22	e	e	PROPN
ejpam-7033	331	23	and	and	CCONJ
ejpam-7033	331	24	let	let	VERB
ejpam-7033	331	25	ℏ	ℏ	PRON
ejpam-7033	331	26	:	:	PUNCT
ejpam-7033	331	27	w	w	PROPN
ejpam-7033	331	28	→	→	SYM
ejpam-7033	331	29	w	w	X
ejpam-7033	331	30	.	.	PUNCT
ejpam-7033	332	1	consider	consider	VERB
ejpam-7033	332	2	t	t	PROPN
ejpam-7033	332	3	∈	∈	PROPN
ejpam-7033	332	4	b(e	b(e	PROPN
ejpam-7033	332	5	,	,	PUNCT
ejpam-7033	332	6	e	e	X
ejpam-7033	332	7	)	)	PUNCT
ejpam-7033	332	8	with	with	ADP
ejpam-7033	332	9	∥t	∥t	ADJ
ejpam-7033	332	10	∥1	∥1	ADP
ejpam-7033	332	11	<	<	X
ejpam-7033	332	12	1	1	NUM
ejpam-7033	332	13	s	s	PART
ejpam-7033	332	14	(	(	PUNCT
ejpam-7033	332	15	s	s	X
ejpam-7033	332	16	≥	≥	NOUN
ejpam-7033	332	17	1	1	NUM
ejpam-7033	332	18	)	)	PUNCT
ejpam-7033	332	19	,	,	PUNCT
ejpam-7033	332	20	i	i	PRON
ejpam-7033	332	21	:	:	PUNCT
ejpam-7033	333	1	e	e	X
ejpam-7033	333	2	→	→	SYM
ejpam-7033	333	3	e	e	PROPN
ejpam-7033	333	4	and	and	CCONJ
ejpam-7033	333	5	j	j	PROPN
ejpam-7033	333	6	∈	∈	PROPN
ejpam-7033	333	7	f	f	PROPN
ejpam-7033	333	8	such	such	ADJ
ejpam-7033	333	9	that	that	SCONJ
ejpam-7033	333	10	,	,	PUNCT
ejpam-7033	333	11	for	for	ADP
ejpam-7033	333	12	each	each	DET
ejpam-7033	333	13	pair	pair	NOUN
ejpam-7033	333	14	of	of	ADP
ejpam-7033	333	15	comparable	comparable	ADJ
ejpam-7033	333	16	elements	element	NOUN
ejpam-7033	333	17	f	f	NOUN
ejpam-7033	333	18	,	,	PUNCT
ejpam-7033	333	19	x	x	SYM
ejpam-7033	333	20	∈	∈	PROPN
ejpam-7033	333	21	w	w	NOUN
ejpam-7033	333	22	with	with	ADP
ejpam-7033	333	23	s	s	PRON
ejpam-7033	333	24	≥	≥	NUM
ejpam-7033	333	25	1	1	NUM
ejpam-7033	333	26	,	,	PUNCT
ejpam-7033	333	27	following	follow	VERB
ejpam-7033	333	28	holds	hold	NOUN
ejpam-7033	333	29	(	(	PUNCT
ejpam-7033	333	30	i	i	PRON
ejpam-7033	333	31	−	−	PROPN
ejpam-7033	333	32	t	t	NOUN
ejpam-7033	333	33	)	)	PUNCT
ejpam-7033	333	34	2(i	2(i	NUM
ejpam-7033	334	1	+	+	NUM
ejpam-7033	334	2	t	t	NOUN
ejpam-7033	334	3	)	)	PUNCT
ejpam-7033	334	4	(	(	PUNCT
ejpam-7033	334	5	r(f	r(f	PROPN
ejpam-7033	334	6	,	,	PUNCT
ejpam-7033	334	7	ℏ(f	ℏ(f	NOUN
ejpam-7033	334	8	)	)	PUNCT
ejpam-7033	334	9	)	)	PUNCT
ejpam-7033	334	10	)	)	PUNCT
ejpam-7033	335	1	⪯	⪯	NOUN
ejpam-7033	335	2	sr(f	sr(f	ADJ
ejpam-7033	335	3	,	,	PUNCT
ejpam-7033	335	4	x	x	PRON
ejpam-7033	335	5	)	)	PUNCT
ejpam-7033	335	6	implies	imply	VERB
ejpam-7033	335	7	j	j	PROPN
ejpam-7033	335	8	(	(	PUNCT
ejpam-7033	335	9	r(ℏ(f	r(ℏ(f	PROPN
ejpam-7033	335	10	)	)	PUNCT
ejpam-7033	335	11	,	,	PUNCT
ejpam-7033	335	12	ℏ(x)),r(f	ℏ(x)),r(f	NOUN
ejpam-7033	335	13	,	,	PUNCT
ejpam-7033	335	14	x),r(f	x),r(f	PROPN
ejpam-7033	335	15	,	,	PUNCT
ejpam-7033	335	16	ℏ(f)),r(x	ℏ(f)),r(x	NOUN
ejpam-7033	335	17	,	,	PUNCT
ejpam-7033	335	18	ℏ(x)),r(f	ℏ(x)),r(f	NOUN
ejpam-7033	335	19	,	,	PUNCT
ejpam-7033	335	20	ℏ2(x)),r(x	ℏ2(x)),r(x	NOUN
ejpam-7033	335	21	,	,	PUNCT
ejpam-7033	335	22	ℏ2(f	ℏ2(f	NOUN
ejpam-7033	335	23	)	)	PUNCT
ejpam-7033	335	24	)	)	PUNCT
ejpam-7033	335	25	)	)	PUNCT
ejpam-7033	336	1	⪯	⪯	NOUN
ejpam-7033	336	2	0e	0e	NOUN
ejpam-7033	336	3	(	(	PUNCT
ejpam-7033	336	4	8)	8)	NUM
ejpam-7033	336	5	and	and	CCONJ
ejpam-7033	336	6	a.	a.	NOUN
ejpam-7033	336	7	arif	arif	PROPN
ejpam-7033	336	8	et	et	PROPN
ejpam-7033	337	1	al	al	PROPN
ejpam-7033	337	2	.	.	PUNCT
ejpam-7033	337	3	/	/	SYM
ejpam-7033	337	4	eur	eur	PROPN
ejpam-7033	337	5	.	.	PUNCT
ejpam-7033	338	1	j.	j.	PROPN
ejpam-7033	338	2	pure	pure	PROPN
ejpam-7033	338	3	appl	appl	PROPN
ejpam-7033	338	4	.	.	PROPN
ejpam-7033	338	5	math	math	PROPN
ejpam-7033	338	6	,	,	PUNCT
ejpam-7033	338	7	18	18	NUM
ejpam-7033	338	8	(	(	PUNCT
ejpam-7033	338	9	4	4	NUM
ejpam-7033	338	10	)	)	PUNCT
ejpam-7033	338	11	(	(	PUNCT
ejpam-7033	338	12	2025	2025	NUM
ejpam-7033	338	13	)	)	PUNCT
ejpam-7033	338	14	,	,	PUNCT
ejpam-7033	338	15	7033	7033	NUM
ejpam-7033	338	16	12	12	NUM
ejpam-7033	338	17	of	of	ADP
ejpam-7033	338	18	29	29	NUM
ejpam-7033	338	19	(	(	PUNCT
ejpam-7033	338	20	1	1	NUM
ejpam-7033	338	21	)	)	PUNCT
ejpam-7033	338	22	there	there	PRON
ejpam-7033	338	23	exists	exist	VERB
ejpam-7033	338	24	f0	f0	PROPN
ejpam-7033	338	25	∈w	∈w	NOUN
ejpam-7033	338	26	satisfying	satisfy	VERB
ejpam-7033	338	27	ℏ(f0)ℜf0	ℏ(f0)ℜf0	NOUN
ejpam-7033	338	28	;	;	PUNCT
ejpam-7033	338	29	(	(	PUNCT
ejpam-7033	338	30	2	2	X
ejpam-7033	338	31	)	)	PUNCT
ejpam-7033	338	32	for	for	ADP
ejpam-7033	338	33	every	every	DET
ejpam-7033	338	34	pair	pair	NOUN
ejpam-7033	338	35	of	of	ADP
ejpam-7033	338	36	f	f	PROPN
ejpam-7033	338	37	,	,	PUNCT
ejpam-7033	338	38	x	x	SYM
ejpam-7033	338	39	∈w	∈w	NOUN
ejpam-7033	338	40	,	,	PUNCT
ejpam-7033	338	41	fℜx	fℜx	NOUN
ejpam-7033	338	42	⇒	⇒	NOUN
ejpam-7033	338	43	ℏ(x)ℜℏ(f	ℏ(x)ℜℏ(f	PROPN
ejpam-7033	338	44	)	)	PUNCT
ejpam-7033	338	45	;	;	PUNCT
ejpam-7033	338	46	(	(	PUNCT
ejpam-7033	338	47	3	3	X
ejpam-7033	338	48	)	)	PUNCT
ejpam-7033	338	49	for	for	ADP
ejpam-7033	338	50	a	a	DET
ejpam-7033	338	51	sequence	sequence	NOUN
ejpam-7033	338	52	{	{	PUNCT
ejpam-7033	338	53	fn	fn	NOUN
ejpam-7033	338	54	}	}	PUNCT
ejpam-7033	338	55	satisfying	satisfy	VERB
ejpam-7033	338	56	fnℜfn+1	fnℜfn+1	NOUN
ejpam-7033	338	57	and	and	CCONJ
ejpam-7033	338	58	fn	fn	NOUN
ejpam-7033	338	59	→	→	SYM
ejpam-7033	338	60	z∗	z∗	PROPN
ejpam-7033	338	61	,	,	PUNCT
ejpam-7033	338	62	we	we	PRON
ejpam-7033	338	63	get	get	VERB
ejpam-7033	338	64	fnℜz∗	fnℜz∗	X
ejpam-7033	338	65	∀	∀	X
ejpam-7033	338	66	n	n	PRON
ejpam-7033	338	67	∈	∈	PROPN
ejpam-7033	338	68	n.	n.	NOUN
ejpam-7033	338	69	moreover	moreover	ADV
ejpam-7033	338	70	,	,	PUNCT
ejpam-7033	338	71	r(z∗	r(z∗	PRON
ejpam-7033	338	72	,	,	PUNCT
ejpam-7033	338	73	ℏ(z∗	ℏ(z∗	NOUN
ejpam-7033	338	74	)	)	PUNCT
ejpam-7033	338	75	)	)	PUNCT
ejpam-7033	338	76	⪯	⪯	NOUN
ejpam-7033	338	77	r(z∗	r(z∗	NOUN
ejpam-7033	338	78	,	,	PUNCT
ejpam-7033	338	79	ℏ2(z∗	ℏ2(z∗	NUM
ejpam-7033	338	80	)	)	PUNCT
ejpam-7033	338	81	)	)	PUNCT
ejpam-7033	338	82	.	.	PUNCT
ejpam-7033	339	1	then	then	ADV
ejpam-7033	339	2	,	,	PUNCT
ejpam-7033	339	3	ℏ	ℏ	PROPN
ejpam-7033	339	4	admits	admit	VERB
ejpam-7033	339	5	a	a	DET
ejpam-7033	339	6	fixed	fixed	ADJ
ejpam-7033	339	7	point	point	NOUN
ejpam-7033	339	8	z∗	z∗	NOUN
ejpam-7033	339	9	∈w	∈w	NOUN
ejpam-7033	339	10	.	.	PUNCT
ejpam-7033	340	1	proof	proof	NOUN
ejpam-7033	340	2	.	.	PUNCT
ejpam-7033	341	1	let	let	VERB
ejpam-7033	341	2	f0	f0	PROPN
ejpam-7033	341	3	∈w	∈w	PROPN
ejpam-7033	341	4	satisfies	satisfie	NOUN
ejpam-7033	341	5	assumtion	assumtion	NOUN
ejpam-7033	341	6	(	(	PUNCT
ejpam-7033	341	7	1	1	NUM
ejpam-7033	341	8	)	)	PUNCT
ejpam-7033	341	9	.	.	PUNCT
ejpam-7033	342	1	construct	construct	VERB
ejpam-7033	342	2	the	the	DET
ejpam-7033	342	3	sequence	sequence	NOUN
ejpam-7033	342	4	{	{	PUNCT
ejpam-7033	342	5	fn	fn	NOUN
ejpam-7033	342	6	}	}	PUNCT
ejpam-7033	342	7	such	such	ADJ
ejpam-7033	342	8	that	that	DET
ejpam-7033	342	9	fn	fn	NOUN
ejpam-7033	342	10	=	=	PUNCT
ejpam-7033	342	11	ℏ(fn−1	ℏ(fn−1	NOUN
ejpam-7033	342	12	)	)	PUNCT
ejpam-7033	342	13	∀	∀	X
ejpam-7033	343	1	n	n	PRON
ejpam-7033	343	2	∈	∈	NOUN
ejpam-7033	343	3	n	n	NOUN
ejpam-7033	343	4	.	.	PUNCT
ejpam-7033	344	1	since	since	SCONJ
ejpam-7033	344	2	f1	f1	PROPN
ejpam-7033	344	3	=	=	SYM
ejpam-7033	344	4	ℏ(f0)ℜf0	ℏ(f0)ℜf0	NOUN
ejpam-7033	344	5	and	and	CCONJ
ejpam-7033	344	6	by	by	ADP
ejpam-7033	344	7	using	use	VERB
ejpam-7033	344	8	condition	condition	NOUN
ejpam-7033	344	9	(	(	PUNCT
ejpam-7033	344	10	2	2	NUM
ejpam-7033	344	11	)	)	PUNCT
ejpam-7033	344	12	,	,	PUNCT
ejpam-7033	344	13	f1	f1	NOUN
ejpam-7033	344	14	=	=	SYM
ejpam-7033	344	15	ℏ(f0)ℜℏ(f1	ℏ(f0)ℜℏ(f1	PROPN
ejpam-7033	344	16	)	)	PUNCT
ejpam-7033	344	17	=	=	SYM
ejpam-7033	344	18	f2	f2	PROPN
ejpam-7033	344	19	,	,	PUNCT
ejpam-7033	344	20	and	and	CCONJ
ejpam-7033	344	21	assumption	assumption	NOUN
ejpam-7033	344	22	(	(	PUNCT
ejpam-7033	344	23	2	2	X
ejpam-7033	344	24	)	)	PUNCT
ejpam-7033	344	25	further	far	ADV
ejpam-7033	344	26	implies	imply	VERB
ejpam-7033	344	27	fn	fn	PROPN
ejpam-7033	344	28	⪯	⪯	PROPN
ejpam-7033	344	29	fn−1	fn−1	PROPN
ejpam-7033	344	30	.	.	PUNCT
ejpam-7033	345	1	letting	let	VERB
ejpam-7033	345	2	f	f	X
ejpam-7033	345	3	=	=	SYM
ejpam-7033	345	4	f1	f1	PROPN
ejpam-7033	345	5	and	and	CCONJ
ejpam-7033	345	6	x	x	SYM
ejpam-7033	345	7	=	=	SYM
ejpam-7033	345	8	f0	f0	PROPN
ejpam-7033	345	9	in	in	ADP
ejpam-7033	345	10	(	(	PUNCT
ejpam-7033	345	11	8)	8)	NUM
ejpam-7033	345	12	,	,	PUNCT
ejpam-7033	345	13	we	we	PRON
ejpam-7033	345	14	get	get	VERB
ejpam-7033	345	15	(	(	PUNCT
ejpam-7033	345	16	i	i	PRON
ejpam-7033	345	17	−	−	PROPN
ejpam-7033	345	18	t	t	NOUN
ejpam-7033	345	19	)	)	PUNCT
ejpam-7033	345	20	2(i	2(i	NUM
ejpam-7033	346	1	+	+	NUM
ejpam-7033	346	2	t	t	NOUN
ejpam-7033	346	3	)	)	PUNCT
ejpam-7033	346	4	(	(	PUNCT
ejpam-7033	346	5	r(ℏ(f0	r(ℏ(f0	NOUN
ejpam-7033	346	6	)	)	PUNCT
ejpam-7033	346	7	,	,	PUNCT
ejpam-7033	346	8	f0	f0	PROPN
ejpam-7033	346	9	)	)	PUNCT
ejpam-7033	346	10	=	=	PUNCT
ejpam-7033	347	1	(	(	PUNCT
ejpam-7033	347	2	i	i	PRON
ejpam-7033	347	3	−	−	PROPN
ejpam-7033	347	4	t	t	NOUN
ejpam-7033	347	5	)	)	PUNCT
ejpam-7033	347	6	2(i	2(i	NUM
ejpam-7033	348	1	+	+	NUM
ejpam-7033	348	2	t	t	NOUN
ejpam-7033	348	3	)	)	PUNCT
ejpam-7033	348	4	(	(	PUNCT
ejpam-7033	348	5	r(f1	r(f1	NOUN
ejpam-7033	348	6	,	,	PUNCT
ejpam-7033	348	7	f0	f0	PROPN
ejpam-7033	348	8	)	)	PUNCT
ejpam-7033	348	9	)	)	PUNCT
ejpam-7033	348	10	⪯	⪯	PROPN
ejpam-7033	348	11	sr(f1	sr(f1	PROPN
ejpam-7033	348	12	,	,	PUNCT
ejpam-7033	348	13	f0	f0	PROPN
ejpam-7033	348	14	)	)	PUNCT
ejpam-7033	348	15	implies	imply	VERB
ejpam-7033	348	16	j	j	PROPN
ejpam-7033	348	17	(	(	PUNCT
ejpam-7033	348	18	r(ℏ(f1	r(ℏ(f1	PROPN
ejpam-7033	348	19	)	)	PUNCT
ejpam-7033	348	20	,	,	PUNCT
ejpam-7033	348	21	ℏ(f0)),r(f1	ℏ(f0)),r(f1	PROPN
ejpam-7033	348	22	,	,	PUNCT
ejpam-7033	348	23	f0),r(f1	f0),r(f1	PROPN
ejpam-7033	348	24	,	,	PUNCT
ejpam-7033	348	25	ℏ(f1)),r(f0	ℏ(f1)),r(f0	NOUN
ejpam-7033	348	26	,	,	PUNCT
ejpam-7033	348	27	ℏ(f0)),r(f1	ℏ(f0)),r(f1	PROPN
ejpam-7033	348	28	,	,	PUNCT
ejpam-7033	348	29	ℏ2(f0)),r(f0	ℏ2(f0)),r(f0	NOUN
ejpam-7033	348	30	,	,	PUNCT
ejpam-7033	348	31	ℏ2(f1	ℏ2(f1	PROPN
ejpam-7033	348	32	)	)	PUNCT
ejpam-7033	348	33	)	)	PUNCT
ejpam-7033	348	34	)	)	PUNCT
ejpam-7033	349	1	⪯	⪯	VERB
ejpam-7033	349	2	0e	0e	PROPN
ejpam-7033	349	3	⇒	⇒	PROPN
ejpam-7033	349	4	j	j	PROPN
ejpam-7033	349	5	(	(	PUNCT
ejpam-7033	349	6	r(f1	r(f1	NOUN
ejpam-7033	349	7	,	,	PUNCT
ejpam-7033	349	8	f2),r(f0	f2),r(f0	NOUN
ejpam-7033	349	9	,	,	PUNCT
ejpam-7033	349	10	f1),r(f1	f1),r(f1	PROPN
ejpam-7033	349	11	,	,	PUNCT
ejpam-7033	349	12	f2),r(f0	f2),r(f0	NOUN
ejpam-7033	349	13	,	,	PUNCT
ejpam-7033	349	14	f1),r(f1	f1),r(f1	PROPN
ejpam-7033	349	15	,	,	PUNCT
ejpam-7033	349	16	f2),r(f0	f2),r(f0	NOUN
ejpam-7033	349	17	,	,	PUNCT
ejpam-7033	349	18	f3	f3	NOUN
ejpam-7033	349	19	)	)	PUNCT
ejpam-7033	349	20	)	)	PUNCT
ejpam-7033	349	21	⪯	⪯	NOUN
ejpam-7033	349	22	0e	0e	NOUN
ejpam-7033	349	23	.	.	PUNCT
ejpam-7033	350	1	by	by	ADP
ejpam-7033	350	2	(	(	PUNCT
ejpam-7033	350	3	dr3	dr3	PROPN
ejpam-7033	350	4	)	)	PUNCT
ejpam-7033	350	5	,	,	PUNCT
ejpam-7033	350	6	we	we	PRON
ejpam-7033	350	7	have	have	VERB
ejpam-7033	350	8	r(f0	r(f0	NOUN
ejpam-7033	350	9	,	,	PUNCT
ejpam-7033	350	10	f3	f3	PROPN
ejpam-7033	350	11	)	)	PUNCT
ejpam-7033	350	12	⪯	⪯	PROPN
ejpam-7033	350	13	s[r(f0	s[r(f0	NOUN
ejpam-7033	350	14	,	,	PUNCT
ejpam-7033	350	15	f1	f1	NOUN
ejpam-7033	350	16	)	)	PUNCT
ejpam-7033	351	1	+	+	SYM
ejpam-7033	351	2	r(f1	r(f1	NOUN
ejpam-7033	351	3	,	,	PUNCT
ejpam-7033	351	4	f2	f2	PROPN
ejpam-7033	351	5	)	)	PUNCT
ejpam-7033	351	6	+	+	SYM
ejpam-7033	351	7	r(f2	r(f2	NOUN
ejpam-7033	351	8	,	,	PUNCT
ejpam-7033	351	9	f3	f3	NOUN
ejpam-7033	351	10	)	)	PUNCT
ejpam-7033	351	11	]	]	PUNCT
ejpam-7033	351	12	and	and	CCONJ
ejpam-7033	351	13	then	then	ADV
ejpam-7033	351	14	using	use	VERB
ejpam-7033	351	15	j1	j1	PROPN
ejpam-7033	351	16	,	,	PUNCT
ejpam-7033	351	17	we	we	PRON
ejpam-7033	351	18	obtain	obtain	VERB
ejpam-7033	351	19	j	j	PROPN
ejpam-7033	351	20	(	(	PUNCT
ejpam-7033	351	21	r(f1	r(f1	NOUN
ejpam-7033	351	22	,	,	PUNCT
ejpam-7033	351	23	f2),r(f0	f2),r(f0	NOUN
ejpam-7033	351	24	,	,	PUNCT
ejpam-7033	351	25	f1),r(f1	f1),r(f1	PROPN
ejpam-7033	351	26	,	,	PUNCT
ejpam-7033	351	27	f2),r(f0	f2),r(f0	NOUN
ejpam-7033	351	28	,	,	PUNCT
ejpam-7033	351	29	f1),r(f1	f1),r(f1	PROPN
ejpam-7033	351	30	,	,	PUNCT
ejpam-7033	351	31	f2	f2	PROPN
ejpam-7033	351	32	)	)	PUNCT
ejpam-7033	351	33	,	,	PUNCT
ejpam-7033	351	34	s[r(f0	s[r(f0	PROPN
ejpam-7033	351	35	,	,	PUNCT
ejpam-7033	351	36	f1)+r(f1	f1)+r(f1	NOUN
ejpam-7033	351	37	,	,	PUNCT
ejpam-7033	351	38	f2)+r(f2	f2)+r(f2	NOUN
ejpam-7033	351	39	,	,	PUNCT
ejpam-7033	351	40	f3	f3	NOUN
ejpam-7033	351	41	)	)	PUNCT
ejpam-7033	351	42	]	]	PUNCT
ejpam-7033	351	43	)	)	PUNCT
ejpam-7033	351	44	⪯	⪯	NOUN
ejpam-7033	351	45	0e	0e	NOUN
ejpam-7033	351	46	.	.	PUNCT
ejpam-7033	352	1	by	by	ADP
ejpam-7033	352	2	(	(	PUNCT
ejpam-7033	352	3	j2	j2	PROPN
ejpam-7033	352	4	)	)	PUNCT
ejpam-7033	352	5	,	,	PUNCT
ejpam-7033	352	6	there	there	PRON
ejpam-7033	352	7	exists	exist	VERB
ejpam-7033	352	8	t	t	PROPN
ejpam-7033	352	9	∈	∈	PROPN
ejpam-7033	352	10	b(e	b(e	PROPN
ejpam-7033	352	11	,	,	PUNCT
ejpam-7033	352	12	e	e	X
ejpam-7033	352	13	)	)	PUNCT
ejpam-7033	352	14	with	with	ADP
ejpam-7033	352	15	∥t	∥t	ADJ
ejpam-7033	352	16	∥1	∥1	ADP
ejpam-7033	352	17	<	<	X
ejpam-7033	352	18	1	1	NUM
ejpam-7033	352	19	and	and	CCONJ
ejpam-7033	352	20	r(f1	r(f1	NOUN
ejpam-7033	352	21	,	,	PUNCT
ejpam-7033	352	22	f2	f2	PROPN
ejpam-7033	352	23	)	)	PUNCT
ejpam-7033	352	24	⪯	⪯	NOUN
ejpam-7033	352	25	1	1	NUM
ejpam-7033	352	26	s	s	PART
ejpam-7033	352	27	t	t	PROPN
ejpam-7033	352	28	(	(	PUNCT
ejpam-7033	352	29	r(f0	r(f0	NOUN
ejpam-7033	352	30	,	,	PUNCT
ejpam-7033	352	31	f1	f1	NOUN
ejpam-7033	352	32	)	)	PUNCT
ejpam-7033	352	33	)	)	PUNCT
ejpam-7033	352	34	⪯	⪯	PROPN
ejpam-7033	352	35	t	t	PROPN
ejpam-7033	352	36	(	(	PUNCT
ejpam-7033	352	37	r(f0	r(f0	NOUN
ejpam-7033	352	38	,	,	PUNCT
ejpam-7033	352	39	f1	f1	NOUN
ejpam-7033	352	40	)	)	PUNCT
ejpam-7033	352	41	)	)	PUNCT
ejpam-7033	352	42	and	and	CCONJ
ejpam-7033	352	43	r(f2	r(f2	NOUN
ejpam-7033	352	44	,	,	PUNCT
ejpam-7033	352	45	f3	f3	ADJ
ejpam-7033	352	46	)	)	PUNCT
ejpam-7033	352	47	⪯	⪯	NOUN
ejpam-7033	352	48	1	1	NUM
ejpam-7033	352	49	s	s	PART
ejpam-7033	352	50	t	t	PROPN
ejpam-7033	352	51	(	(	PUNCT
ejpam-7033	352	52	r(f1	r(f1	NOUN
ejpam-7033	352	53	,	,	PUNCT
ejpam-7033	352	54	f2	f2	PROPN
ejpam-7033	352	55	)	)	PUNCT
ejpam-7033	352	56	)	)	PUNCT
ejpam-7033	353	1	⪯	⪯	PROPN
ejpam-7033	353	2	t	t	PROPN
ejpam-7033	353	3	(	(	PUNCT
ejpam-7033	353	4	r(f1	r(f1	NOUN
ejpam-7033	353	5	,	,	PUNCT
ejpam-7033	353	6	f2	f2	PROPN
ejpam-7033	353	7	)	)	PUNCT
ejpam-7033	353	8	)	)	PUNCT
ejpam-7033	353	9	.	.	PUNCT
ejpam-7033	354	1	by	by	ADP
ejpam-7033	354	2	(	(	PUNCT
ejpam-7033	354	3	2	2	NUM
ejpam-7033	354	4	)	)	PUNCT
ejpam-7033	354	5	,	,	PUNCT
ejpam-7033	354	6	ℏ(f0)ℜℏ(f1	ℏ(f0)ℜℏ(f1	PROPN
ejpam-7033	354	7	)	)	PUNCT
ejpam-7033	354	8	,	,	PUNCT
ejpam-7033	354	9	letting	let	VERB
ejpam-7033	354	10	f	f	X
ejpam-7033	354	11	=	=	SYM
ejpam-7033	354	12	f1	f1	PROPN
ejpam-7033	354	13	and	and	CCONJ
ejpam-7033	354	14	x	x	X
ejpam-7033	354	15	=	=	X
ejpam-7033	354	16	f2	f2	PROPN
ejpam-7033	354	17	in	in	ADP
ejpam-7033	354	18	(	(	PUNCT
ejpam-7033	354	19	8)	8)	NUM
ejpam-7033	354	20	we	we	PRON
ejpam-7033	354	21	get	get	VERB
ejpam-7033	354	22	(	(	PUNCT
ejpam-7033	354	23	i	i	PRON
ejpam-7033	354	24	−	−	PROPN
ejpam-7033	354	25	t	t	NOUN
ejpam-7033	354	26	)	)	PUNCT
ejpam-7033	354	27	2(i	2(i	NUM
ejpam-7033	355	1	+	+	NUM
ejpam-7033	355	2	t	t	NOUN
ejpam-7033	355	3	)	)	PUNCT
ejpam-7033	355	4	(	(	PUNCT
ejpam-7033	355	5	r(f1	r(f1	NOUN
ejpam-7033	355	6	,	,	PUNCT
ejpam-7033	355	7	ℏ(f1	ℏ(f1	NOUN
ejpam-7033	355	8	)	)	PUNCT
ejpam-7033	355	9	)	)	PUNCT
ejpam-7033	356	1	=	=	PUNCT
ejpam-7033	356	2	(	(	PUNCT
ejpam-7033	356	3	i	i	PRON
ejpam-7033	356	4	−	−	PROPN
ejpam-7033	356	5	t	t	NOUN
ejpam-7033	356	6	)	)	PUNCT
ejpam-7033	356	7	2(i	2(i	NUM
ejpam-7033	357	1	+	+	NUM
ejpam-7033	357	2	t	t	NOUN
ejpam-7033	357	3	)	)	PUNCT
ejpam-7033	357	4	(	(	PUNCT
ejpam-7033	357	5	r(f1	r(f1	NOUN
ejpam-7033	357	6	,	,	PUNCT
ejpam-7033	357	7	f2	f2	PROPN
ejpam-7033	357	8	)	)	PUNCT
ejpam-7033	357	9	)	)	PUNCT
ejpam-7033	357	10	⪯	⪯	PROPN
ejpam-7033	357	11	sr(f1	sr(f1	PROPN
ejpam-7033	357	12	,	,	PUNCT
ejpam-7033	357	13	f2	f2	PROPN
ejpam-7033	357	14	)	)	PUNCT
ejpam-7033	357	15	implies	imply	VERB
ejpam-7033	357	16	j	j	PROPN
ejpam-7033	357	17	(	(	PUNCT
ejpam-7033	357	18	r(ℏ(f1	r(ℏ(f1	PROPN
ejpam-7033	357	19	)	)	PUNCT
ejpam-7033	357	20	,	,	PUNCT
ejpam-7033	357	21	ℏ(f2)),r(f1	ℏ(f2)),r(f1	PROPN
ejpam-7033	357	22	,	,	PUNCT
ejpam-7033	357	23	f2),r(f1	f2),r(f1	PROPN
ejpam-7033	357	24	,	,	PUNCT
ejpam-7033	357	25	ℏ(f1)),r(f2	ℏ(f1)),r(f2	NOUN
ejpam-7033	357	26	,	,	PUNCT
ejpam-7033	357	27	ℏ(f2)),r(f1	ℏ(f2)),r(f1	PROPN
ejpam-7033	357	28	,	,	PUNCT
ejpam-7033	357	29	ℏ2(f2)),r(f2	ℏ2(f2)),r(f2	PROPN
ejpam-7033	357	30	,	,	PUNCT
ejpam-7033	357	31	ℏ2(f1	ℏ2(f1	PROPN
ejpam-7033	357	32	)	)	PUNCT
ejpam-7033	357	33	)	)	PUNCT
ejpam-7033	357	34	)	)	PUNCT
ejpam-7033	358	1	⪯	⪯	VERB
ejpam-7033	358	2	0e	0e	PROPN
ejpam-7033	358	3	⇒	⇒	PROPN
ejpam-7033	358	4	j	j	PROPN
ejpam-7033	358	5	(	(	PUNCT
ejpam-7033	358	6	r(f2	r(f2	NOUN
ejpam-7033	358	7	,	,	PUNCT
ejpam-7033	358	8	f3),r(f1	f3),r(f1	NOUN
ejpam-7033	358	9	,	,	PUNCT
ejpam-7033	358	10	f2),r(f1	f2),r(f1	PROPN
ejpam-7033	358	11	,	,	PUNCT
ejpam-7033	358	12	f2),r(f2	f2),r(f2	NOUN
ejpam-7033	358	13	,	,	PUNCT
ejpam-7033	358	14	f3),r(f1	f3),r(f1	NOUN
ejpam-7033	358	15	,	,	PUNCT
ejpam-7033	358	16	f4),r(f2	f4),r(f2	NOUN
ejpam-7033	358	17	,	,	PUNCT
ejpam-7033	358	18	f3	f3	ADJ
ejpam-7033	358	19	)	)	PUNCT
ejpam-7033	358	20	)	)	PUNCT
ejpam-7033	359	1	⪯	⪯	NOUN
ejpam-7033	359	2	0e	0e	NOUN
ejpam-7033	359	3	.	.	PUNCT
ejpam-7033	360	1	by	by	ADP
ejpam-7033	360	2	(	(	PUNCT
ejpam-7033	360	3	dr3	dr3	PROPN
ejpam-7033	360	4	)	)	PUNCT
ejpam-7033	360	5	,	,	PUNCT
ejpam-7033	360	6	(	(	PUNCT
ejpam-7033	360	7	j1	j1	PROPN
ejpam-7033	360	8	)	)	PUNCT
ejpam-7033	360	9	and	and	CCONJ
ejpam-7033	360	10	(	(	PUNCT
ejpam-7033	360	11	j2	j2	PROPN
ejpam-7033	360	12	)	)	PUNCT
ejpam-7033	360	13	,	,	PUNCT
ejpam-7033	360	14	we	we	PRON
ejpam-7033	360	15	get	get	VERB
ejpam-7033	360	16	r(f3	r(f3	NOUN
ejpam-7033	360	17	,	,	PUNCT
ejpam-7033	360	18	f4	f4	PROPN
ejpam-7033	360	19	)	)	PUNCT
ejpam-7033	360	20	⪯	⪯	NOUN
ejpam-7033	360	21	1	1	NUM
ejpam-7033	360	22	s	s	PART
ejpam-7033	360	23	t	t	NOUN
ejpam-7033	360	24	(	(	PUNCT
ejpam-7033	360	25	r(f2	r(f2	NOUN
ejpam-7033	360	26	,	,	PUNCT
ejpam-7033	360	27	f3	f3	ADJ
ejpam-7033	360	28	)	)	PUNCT
ejpam-7033	360	29	)	)	PUNCT
ejpam-7033	360	30	⪯	⪯	NOUN
ejpam-7033	360	31	1	1	NUM
ejpam-7033	360	32	s2	s2	NOUN
ejpam-7033	360	33	t	t	PROPN
ejpam-7033	360	34	2(r(f1	2(r(f1	NUM
ejpam-7033	360	35	,	,	PUNCT
ejpam-7033	360	36	f2	f2	PROPN
ejpam-7033	360	37	)	)	PUNCT
ejpam-7033	360	38	)	)	PUNCT
ejpam-7033	361	1	⪯	⪯	NOUN
ejpam-7033	361	2	1	1	NUM
ejpam-7033	361	3	s3	s3	PROPN
ejpam-7033	361	4	t	t	PROPN
ejpam-7033	361	5	3(r(f0	3(r(f0	NUM
ejpam-7033	361	6	,	,	PUNCT
ejpam-7033	361	7	f1	f1	NOUN
ejpam-7033	361	8	)	)	PUNCT
ejpam-7033	361	9	)	)	PUNCT
ejpam-7033	361	10	⪯	⪯	PROPN
ejpam-7033	361	11	t	t	PROPN
ejpam-7033	361	12	3(r(f0	3(r(f0	NUM
ejpam-7033	361	13	,	,	PUNCT
ejpam-7033	361	14	f1	f1	NOUN
ejpam-7033	361	15	)	)	PUNCT
ejpam-7033	361	16	)	)	PUNCT
ejpam-7033	361	17	.	.	PUNCT
ejpam-7033	362	1	following	follow	VERB
ejpam-7033	362	2	this	this	DET
ejpam-7033	362	3	pattern	pattern	NOUN
ejpam-7033	362	4	,	,	PUNCT
ejpam-7033	362	5	we	we	PRON
ejpam-7033	362	6	get	get	VERB
ejpam-7033	362	7	a	a	DET
ejpam-7033	362	8	sequence	sequence	NOUN
ejpam-7033	362	9	{	{	PUNCT
ejpam-7033	362	10	fn	fn	NOUN
ejpam-7033	362	11	}	}	PUNCT
ejpam-7033	362	12	that	that	PRON
ejpam-7033	362	13	satisfies	satisfy	VERB
ejpam-7033	362	14	r(fn	r(fn	NOUN
ejpam-7033	362	15	,	,	PUNCT
ejpam-7033	362	16	fn+1	fn+1	NUM
ejpam-7033	362	17	)	)	PUNCT
ejpam-7033	362	18	⪯	⪯	NOUN
ejpam-7033	362	19	1	1	NUM
ejpam-7033	362	20	s	s	PART
ejpam-7033	362	21	t	t	NOUN
ejpam-7033	362	22	(	(	PUNCT
ejpam-7033	362	23	r(fn−1	r(fn−1	PROPN
ejpam-7033	362	24	,	,	PUNCT
ejpam-7033	362	25	fn	fn	NOUN
ejpam-7033	362	26	)	)	PUNCT
ejpam-7033	362	27	)	)	PUNCT
ejpam-7033	362	28	⪯	⪯	NOUN
ejpam-7033	362	29	1	1	NUM
ejpam-7033	362	30	s2	s2	NOUN
ejpam-7033	362	31	t	t	PROPN
ejpam-7033	362	32	2(r(fn−2	2(r(fn−2	NUM
ejpam-7033	362	33	,	,	PUNCT
ejpam-7033	362	34	fn−1	fn−1	ADJ
ejpam-7033	362	35	)	)	PUNCT
ejpam-7033	362	36	)	)	PUNCT
ejpam-7033	362	37	⪯	⪯	NOUN
ejpam-7033	362	38	·	·	PUNCT
ejpam-7033	362	39	·	·	PUNCT
ejpam-7033	363	1	·	·	PUNCT
ejpam-7033	363	2	⪯	⪯	NOUN
ejpam-7033	363	3	1	1	NUM
ejpam-7033	363	4	sn	sn	NOUN
ejpam-7033	363	5	t	t	PROPN
ejpam-7033	363	6	n(r(f0	n(r(f0	NOUN
ejpam-7033	363	7	,	,	PUNCT
ejpam-7033	363	8	f1	f1	NOUN
ejpam-7033	363	9	)	)	PUNCT
ejpam-7033	363	10	)	)	PUNCT
ejpam-7033	363	11	.	.	PUNCT
ejpam-7033	364	1	following	follow	VERB
ejpam-7033	364	2	the	the	DET
ejpam-7033	364	3	pattern	pattern	NOUN
ejpam-7033	364	4	for	for	ADP
ejpam-7033	364	5	the	the	DET
ejpam-7033	364	6	proof	proof	NOUN
ejpam-7033	364	7	of	of	ADP
ejpam-7033	364	8	theorem	theorem	ADJ
ejpam-7033	364	9	13	13	NUM
ejpam-7033	364	10	,	,	PUNCT
ejpam-7033	364	11	there	there	PRON
ejpam-7033	364	12	exists	exist	VERB
ejpam-7033	364	13	a	a	DET
ejpam-7033	364	14	convergence	convergence	NOUN
ejpam-7033	364	15	point	point	NOUN
ejpam-7033	364	16	z∗	z∗	NOUN
ejpam-7033	364	17	satisfying	satisfy	VERB
ejpam-7033	364	18	z∗	z∗	NOUN
ejpam-7033	364	19	=	=	PUNCT
ejpam-7033	364	20	ℏ(z∗	ℏ(z∗	NOUN
ejpam-7033	364	21	)	)	PUNCT
ejpam-7033	364	22	.	.	PUNCT
ejpam-7033	365	1	the	the	DET
ejpam-7033	365	2	next	next	ADJ
ejpam-7033	365	3	result	result	NOUN
ejpam-7033	365	4	summarizes	summarize	VERB
ejpam-7033	365	5	the	the	DET
ejpam-7033	365	6	results	result	NOUN
ejpam-7033	365	7	of	of	ADP
ejpam-7033	365	8	theorem	theorem	ADJ
ejpam-7033	365	9	13	13	NUM
ejpam-7033	365	10	and	and	CCONJ
ejpam-7033	365	11	theorem	theorem	VERB
ejpam-7033	365	12	14	14	NUM
ejpam-7033	365	13	.	.	PUNCT
ejpam-7033	365	14	a.	a.	PROPN
ejpam-7033	365	15	arif	arif	PROPN
ejpam-7033	365	16	et	et	PROPN
ejpam-7033	365	17	al	al	PROPN
ejpam-7033	365	18	.	.	PUNCT
ejpam-7033	365	19	/	/	SYM
ejpam-7033	365	20	eur	eur	PROPN
ejpam-7033	365	21	.	.	PUNCT
ejpam-7033	366	1	j.	j.	PROPN
ejpam-7033	366	2	pure	pure	PROPN
ejpam-7033	366	3	appl	appl	PROPN
ejpam-7033	366	4	.	.	PROPN
ejpam-7033	366	5	math	math	PROPN
ejpam-7033	366	6	,	,	PUNCT
ejpam-7033	366	7	18	18	NUM
ejpam-7033	366	8	(	(	PUNCT
ejpam-7033	366	9	4	4	NUM
ejpam-7033	366	10	)	)	PUNCT
ejpam-7033	366	11	(	(	PUNCT
ejpam-7033	366	12	2025	2025	NUM
ejpam-7033	366	13	)	)	PUNCT
ejpam-7033	366	14	,	,	PUNCT
ejpam-7033	366	15	7033	7033	NUM
ejpam-7033	366	16	13	13	NUM
ejpam-7033	366	17	of	of	ADP
ejpam-7033	366	18	29	29	NUM
ejpam-7033	366	19	theorem	theorem	NOUN
ejpam-7033	366	20	15	15	NUM
ejpam-7033	366	21	.	.	PUNCT
ejpam-7033	367	1	let	let	AUX
ejpam-7033	367	2	(	(	PUNCT
ejpam-7033	367	3	w	w	NOUN
ejpam-7033	367	4	,	,	PUNCT
ejpam-7033	367	5	r	r	NOUN
ejpam-7033	367	6	)	)	PUNCT
ejpam-7033	367	7	be	be	AUX
ejpam-7033	367	8	a	a	DET
ejpam-7033	367	9	complete	complete	ADJ
ejpam-7033	367	10	rectangular	rectangular	ADJ
ejpam-7033	367	11	cone	cone	NOUN
ejpam-7033	367	12	b	b	NOUN
ejpam-7033	367	13	-	-	PUNCT
ejpam-7033	367	14	metric	metric	ADJ
ejpam-7033	367	15	space	space	NOUN
ejpam-7033	367	16	with	with	ADP
ejpam-7033	367	17	c	c	PROPN
ejpam-7033	367	18	⊂	⊂	PROPN
ejpam-7033	367	19	e	e	PROPN
ejpam-7033	367	20	as	as	ADP
ejpam-7033	367	21	a	a	DET
ejpam-7033	367	22	cone	cone	NOUN
ejpam-7033	367	23	and	and	CCONJ
ejpam-7033	367	24	ℏ	ℏ	NOUN
ejpam-7033	367	25	:	:	PUNCT
ejpam-7033	367	26	w	w	PROPN
ejpam-7033	367	27	→w	→w	PROPN
ejpam-7033	367	28	.	.	PUNCT
ejpam-7033	368	1	if	if	SCONJ
ejpam-7033	368	2	t	t	PROPN
ejpam-7033	368	3	∈	∈	PROPN
ejpam-7033	368	4	b(e	b(e	PROPN
ejpam-7033	368	5	,	,	PUNCT
ejpam-7033	368	6	e	e	X
ejpam-7033	368	7	)	)	PUNCT
ejpam-7033	368	8	with	with	ADP
ejpam-7033	368	9	∥t	∥t	ADJ
ejpam-7033	368	10	∥1	∥1	ADP
ejpam-7033	368	11	<	<	X
ejpam-7033	368	12	1	1	NUM
ejpam-7033	368	13	s	s	PART
ejpam-7033	368	14	(	(	PUNCT
ejpam-7033	368	15	s	s	X
ejpam-7033	368	16	≥	≥	NOUN
ejpam-7033	368	17	1	1	NUM
ejpam-7033	368	18	)	)	PUNCT
ejpam-7033	368	19	,	,	PUNCT
ejpam-7033	368	20	i	i	PRON
ejpam-7033	368	21	:	:	PUNCT
ejpam-7033	368	22	e	e	X
ejpam-7033	368	23	→	→	SYM
ejpam-7033	368	24	e	e	PROPN
ejpam-7033	368	25	and	and	CCONJ
ejpam-7033	368	26	j	j	PROPN
ejpam-7033	368	27	∈	∈	PROPN
ejpam-7033	368	28	f	f	PROPN
ejpam-7033	368	29	.	.	PUNCT
ejpam-7033	368	30	also	also	ADV
ejpam-7033	368	31	let	let	VERB
ejpam-7033	368	32	,	,	PUNCT
ejpam-7033	368	33	for	for	SCONJ
ejpam-7033	368	34	each	each	DET
ejpam-7033	368	35	pair	pair	NOUN
ejpam-7033	368	36	of	of	ADP
ejpam-7033	368	37	comparable	comparable	ADJ
ejpam-7033	368	38	elements	element	NOUN
ejpam-7033	368	39	ϱ	ϱ	VERB
ejpam-7033	368	40	,	,	PUNCT
ejpam-7033	368	41	x	x	SYM
ejpam-7033	368	42	∈w	∈w	NOUN
ejpam-7033	368	43	and	and	CCONJ
ejpam-7033	368	44	for	for	ADP
ejpam-7033	368	45	some	some	PRON
ejpam-7033	368	46	s	s	PART
ejpam-7033	368	47	≥	≥	NOUN
ejpam-7033	368	48	1	1	NUM
ejpam-7033	368	49	,	,	PUNCT
ejpam-7033	368	50	the	the	DET
ejpam-7033	368	51	following	follow	VERB
ejpam-7033	368	52	holds	hold	VERB
ejpam-7033	368	53	(	(	PUNCT
ejpam-7033	368	54	i	i	PRON
ejpam-7033	368	55	−	−	PROPN
ejpam-7033	368	56	t	t	NOUN
ejpam-7033	368	57	)	)	PUNCT
ejpam-7033	368	58	2(i	2(i	NUM
ejpam-7033	369	1	+	+	NUM
ejpam-7033	369	2	t	t	NOUN
ejpam-7033	369	3	)	)	PUNCT
ejpam-7033	369	4	(	(	PUNCT
ejpam-7033	369	5	r(f	r(f	PROPN
ejpam-7033	369	6	,	,	PUNCT
ejpam-7033	369	7	ℏ(f	ℏ(f	NOUN
ejpam-7033	369	8	)	)	PUNCT
ejpam-7033	369	9	)	)	PUNCT
ejpam-7033	369	10	)	)	PUNCT
ejpam-7033	370	1	⪯	⪯	NOUN
ejpam-7033	370	2	sr(f	sr(f	ADJ
ejpam-7033	370	3	,	,	PUNCT
ejpam-7033	370	4	x	x	PRON
ejpam-7033	370	5	)	)	PUNCT
ejpam-7033	370	6	implies	imply	VERB
ejpam-7033	370	7	j	j	PROPN
ejpam-7033	370	8	(	(	PUNCT
ejpam-7033	370	9	r(ℏ(f	r(ℏ(f	PROPN
ejpam-7033	370	10	)	)	PUNCT
ejpam-7033	370	11	,	,	PUNCT
ejpam-7033	370	12	ℏ(x)),r(f	ℏ(x)),r(f	NOUN
ejpam-7033	370	13	,	,	PUNCT
ejpam-7033	370	14	x),r(f	x),r(f	PROPN
ejpam-7033	370	15	,	,	PUNCT
ejpam-7033	370	16	ℏ(f)),r(x	ℏ(f)),r(x	NOUN
ejpam-7033	370	17	,	,	PUNCT
ejpam-7033	370	18	ℏ(x)),r(f	ℏ(x)),r(f	NOUN
ejpam-7033	370	19	,	,	PUNCT
ejpam-7033	370	20	ℏ2(x)),r(k	ℏ2(x)),r(k	ADJ
ejpam-7033	370	21	,	,	PUNCT
ejpam-7033	370	22	ℏ2(f	ℏ2(f	NOUN
ejpam-7033	370	23	)	)	PUNCT
ejpam-7033	370	24	)	)	PUNCT
ejpam-7033	370	25	)	)	PUNCT
ejpam-7033	371	1	⪯	⪯	NOUN
ejpam-7033	371	2	0e	0e	NOUN
ejpam-7033	371	3	,	,	PUNCT
ejpam-7033	371	4	(	(	PUNCT
ejpam-7033	371	5	9	9	NUM
ejpam-7033	371	6	)	)	PUNCT
ejpam-7033	371	7	and	and	CCONJ
ejpam-7033	371	8	(	(	PUNCT
ejpam-7033	371	9	1	1	X
ejpam-7033	371	10	)	)	PUNCT
ejpam-7033	371	11	∃	∃	NOUN
ejpam-7033	371	12	f0	f0	PROPN
ejpam-7033	371	13	∈w	∈w	NOUN
ejpam-7033	371	14	with	with	ADP
ejpam-7033	371	15	f0ℜℏ(f0	f0ℜℏ(f0	NOUN
ejpam-7033	371	16	)	)	PUNCT
ejpam-7033	371	17	or	or	CCONJ
ejpam-7033	371	18	ℏ(f0)ℜf0	ℏ(f0)ℜf0	NOUN
ejpam-7033	371	19	;	;	PUNCT
ejpam-7033	371	20	(	(	PUNCT
ejpam-7033	371	21	2	2	X
ejpam-7033	371	22	)	)	PUNCT
ejpam-7033	371	23	for	for	ADP
ejpam-7033	371	24	a	a	DET
ejpam-7033	371	25	sequence	sequence	NOUN
ejpam-7033	371	26	{	{	PUNCT
ejpam-7033	371	27	fn	fn	NOUN
ejpam-7033	371	28	}	}	PUNCT
ejpam-7033	371	29	satisfying	satisfy	VERB
ejpam-7033	371	30	fnℜfn+1	fnℜfn+1	NOUN
ejpam-7033	371	31	and	and	CCONJ
ejpam-7033	371	32	fn	fn	NOUN
ejpam-7033	371	33	→	→	SYM
ejpam-7033	371	34	z∗	z∗	PROPN
ejpam-7033	371	35	,	,	PUNCT
ejpam-7033	371	36	we	we	PRON
ejpam-7033	371	37	get	get	VERB
ejpam-7033	371	38	fnℜz∗	fnℜz∗	X
ejpam-7033	371	39	∀	∀	X
ejpam-7033	371	40	n	n	PRON
ejpam-7033	371	41	∈	∈	NOUN
ejpam-7033	371	42	n	n	NOUN
ejpam-7033	371	43	and	and	CCONJ
ejpam-7033	371	44	let	let	VERB
ejpam-7033	371	45	r(z∗	r(z∗	NOUN
ejpam-7033	371	46	,	,	PUNCT
ejpam-7033	371	47	ℏ(z∗	ℏ(z∗	NOUN
ejpam-7033	371	48	)	)	PUNCT
ejpam-7033	371	49	)	)	PUNCT
ejpam-7033	371	50	⪯	⪯	NOUN
ejpam-7033	371	51	r(z∗	r(z∗	NOUN
ejpam-7033	371	52	,	,	PUNCT
ejpam-7033	371	53	ℏ2(z∗	ℏ2(z∗	NUM
ejpam-7033	371	54	)	)	PUNCT
ejpam-7033	371	55	)	)	PUNCT
ejpam-7033	371	56	.	.	PUNCT
ejpam-7033	372	1	then	then	ADV
ejpam-7033	372	2	,	,	PUNCT
ejpam-7033	372	3	ℏ	ℏ	PROPN
ejpam-7033	372	4	admits	admit	VERB
ejpam-7033	372	5	a	a	DET
ejpam-7033	372	6	fixed	fixed	ADJ
ejpam-7033	372	7	point	point	NOUN
ejpam-7033	372	8	z∗	z∗	NOUN
ejpam-7033	372	9	∈w	∈w	NOUN
ejpam-7033	372	10	.	.	PUNCT
ejpam-7033	373	1	proof	proof	NOUN
ejpam-7033	373	2	.	.	PUNCT
ejpam-7033	374	1	let	let	VERB
ejpam-7033	374	2	f0	f0	PROPN
ejpam-7033	374	3	∈	∈	PROPN
ejpam-7033	374	4	w	w	NOUN
ejpam-7033	374	5	and	and	CCONJ
ejpam-7033	374	6	define	define	VERB
ejpam-7033	374	7	the	the	DET
ejpam-7033	374	8	sequence	sequence	NOUN
ejpam-7033	374	9	{	{	PUNCT
ejpam-7033	374	10	fn	fn	NOUN
ejpam-7033	374	11	}	}	PUNCT
ejpam-7033	374	12	by	by	ADP
ejpam-7033	374	13	fn	fn	NOUN
ejpam-7033	374	14	=	=	PUNCT
ejpam-7033	374	15	ℏ(fn−1	ℏ(fn−1	NOUN
ejpam-7033	374	16	)	)	PUNCT
ejpam-7033	374	17	∀	∀	X
ejpam-7033	375	1	n	n	PRON
ejpam-7033	375	2	∈	∈	PROPN
ejpam-7033	375	3	n.	n.	NOUN
ejpam-7033	375	4	by	by	ADP
ejpam-7033	375	5	assumption	assumption	NOUN
ejpam-7033	375	6	(	(	PUNCT
ejpam-7033	375	7	1	1	NUM
ejpam-7033	375	8	)	)	PUNCT
ejpam-7033	375	9	,	,	PUNCT
ejpam-7033	375	10	we	we	PRON
ejpam-7033	375	11	get	get	VERB
ejpam-7033	375	12	f0ℜℏ(f0	f0ℜℏ(f0	NOUN
ejpam-7033	375	13	)	)	PUNCT
ejpam-7033	376	1	=	=	SYM
ejpam-7033	376	2	f1	f1	NOUN
ejpam-7033	376	3	.	.	PUNCT
ejpam-7033	377	1	also	also	ADV
ejpam-7033	377	2	f2ℜf1(as	f2ℜf1(as	PROPN
ejpam-7033	377	3	f	f	PROPN
ejpam-7033	377	4	is	be	AUX
ejpam-7033	377	5	order	order	NOUN
ejpam-7033	377	6	reversing	reversing	NOUN
ejpam-7033	377	7	)	)	PUNCT
ejpam-7033	377	8	.	.	PUNCT
ejpam-7033	378	1	by	by	ADP
ejpam-7033	378	2	(	(	PUNCT
ejpam-7033	378	3	9	9	NUM
ejpam-7033	378	4	)	)	PUNCT
ejpam-7033	378	5	,	,	PUNCT
ejpam-7033	378	6	we	we	PRON
ejpam-7033	378	7	obtain	obtain	VERB
ejpam-7033	378	8	(	(	PUNCT
ejpam-7033	378	9	i	i	PRON
ejpam-7033	378	10	−	−	PROPN
ejpam-7033	378	11	t	t	NOUN
ejpam-7033	378	12	)	)	PUNCT
ejpam-7033	378	13	2(i	2(i	NUM
ejpam-7033	379	1	+	+	NUM
ejpam-7033	379	2	t	t	NOUN
ejpam-7033	379	3	)	)	PUNCT
ejpam-7033	379	4	(	(	PUNCT
ejpam-7033	379	5	r(f0	r(f0	NOUN
ejpam-7033	379	6	,	,	PUNCT
ejpam-7033	379	7	ℏ(f0	ℏ(f0	NOUN
ejpam-7033	379	8	)	)	PUNCT
ejpam-7033	379	9	)	)	PUNCT
ejpam-7033	379	10	)	)	PUNCT
ejpam-7033	380	1	=	=	PUNCT
ejpam-7033	380	2	(	(	PUNCT
ejpam-7033	380	3	i	i	PRON
ejpam-7033	380	4	−	−	PROPN
ejpam-7033	380	5	t	t	NOUN
ejpam-7033	380	6	)	)	PUNCT
ejpam-7033	380	7	2(i	2(i	NUM
ejpam-7033	381	1	+	+	NUM
ejpam-7033	381	2	t	t	NOUN
ejpam-7033	381	3	)	)	PUNCT
ejpam-7033	381	4	(	(	PUNCT
ejpam-7033	381	5	r(f0	r(f0	NOUN
ejpam-7033	381	6	,	,	PUNCT
ejpam-7033	381	7	f1	f1	NOUN
ejpam-7033	381	8	)	)	PUNCT
ejpam-7033	381	9	)	)	PUNCT
ejpam-7033	381	10	⪯	⪯	PROPN
ejpam-7033	381	11	sr(f0	sr(f0	PROPN
ejpam-7033	381	12	,	,	PUNCT
ejpam-7033	381	13	f1	f1	NOUN
ejpam-7033	381	14	)	)	PUNCT
ejpam-7033	381	15	implies	imply	VERB
ejpam-7033	381	16	j	j	PROPN
ejpam-7033	381	17	(	(	PUNCT
ejpam-7033	381	18	r(ℏ(f0	r(ℏ(f0	NOUN
ejpam-7033	381	19	)	)	PUNCT
ejpam-7033	381	20	,	,	PUNCT
ejpam-7033	381	21	ℏ(f1)),r(f0	ℏ(f1)),r(f0	NOUN
ejpam-7033	381	22	,	,	PUNCT
ejpam-7033	381	23	f1),r(f0	f1),r(f0	PROPN
ejpam-7033	381	24	,	,	PUNCT
ejpam-7033	381	25	ℏ(f0	ℏ(f0	NOUN
ejpam-7033	381	26	)	)	PUNCT
ejpam-7033	381	27	)	)	PUNCT
ejpam-7033	381	28	,	,	PUNCT
ejpam-7033	381	29	r(f1	r(f1	NOUN
ejpam-7033	381	30	,	,	PUNCT
ejpam-7033	381	31	ℏ(f1)),r(f0	ℏ(f1)),r(f0	NOUN
ejpam-7033	381	32	,	,	PUNCT
ejpam-7033	381	33	ℏ(f2)),r(f1	ℏ(f2)),r(f1	PROPN
ejpam-7033	381	34	,	,	PUNCT
ejpam-7033	381	35	ℏ(f1	ℏ(f1	NOUN
ejpam-7033	381	36	)	)	PUNCT
ejpam-7033	381	37	)	)	PUNCT
ejpam-7033	381	38	)	)	PUNCT
ejpam-7033	382	1	⪯	⪯	NOUN
ejpam-7033	382	2	0e	0e	NOUN
ejpam-7033	382	3	,	,	PUNCT
ejpam-7033	382	4	that	that	ADV
ejpam-7033	382	5	is	is	ADV
ejpam-7033	382	6	,	,	PUNCT
ejpam-7033	382	7	j	j	PROPN
ejpam-7033	382	8	(	(	PUNCT
ejpam-7033	382	9	r(f1	r(f1	NOUN
ejpam-7033	382	10	,	,	PUNCT
ejpam-7033	382	11	f2),r(f0	f2),r(f0	NOUN
ejpam-7033	382	12	,	,	PUNCT
ejpam-7033	382	13	f1),r(f0	f1),r(f0	PROPN
ejpam-7033	382	14	,	,	PUNCT
ejpam-7033	382	15	f1),r(f1	f1),r(f1	PROPN
ejpam-7033	382	16	,	,	PUNCT
ejpam-7033	382	17	f2	f2	PROPN
ejpam-7033	382	18	)	)	PUNCT
ejpam-7033	382	19	,	,	PUNCT
ejpam-7033	382	20	r(f0	r(f0	NOUN
ejpam-7033	382	21	,	,	PUNCT
ejpam-7033	382	22	f3),r(f1	f3),r(f1	PROPN
ejpam-7033	382	23	,	,	PUNCT
ejpam-7033	382	24	f2	f2	PROPN
ejpam-7033	382	25	)	)	PUNCT
ejpam-7033	382	26	)	)	PUNCT
ejpam-7033	383	1	⪯	⪯	PROPN
ejpam-7033	383	2	0e	0e	PROPN
ejpam-7033	383	3	.	.	PUNCT
ejpam-7033	384	1	(	(	PUNCT
ejpam-7033	384	2	10	10	NUM
ejpam-7033	384	3	)	)	PUNCT
ejpam-7033	384	4	by	by	ADP
ejpam-7033	384	5	(	(	PUNCT
ejpam-7033	384	6	dr3	dr3	PROPN
ejpam-7033	384	7	)	)	PUNCT
ejpam-7033	384	8	and	and	CCONJ
ejpam-7033	384	9	(	(	PUNCT
ejpam-7033	384	10	j1	j1	PROPN
ejpam-7033	384	11	)	)	PUNCT
ejpam-7033	384	12	,	,	PUNCT
ejpam-7033	384	13	j	j	PROPN
ejpam-7033	384	14	(	(	PUNCT
ejpam-7033	384	15	r(f1	r(f1	NOUN
ejpam-7033	384	16	,	,	PUNCT
ejpam-7033	384	17	f2),r(f0	f2),r(f0	NOUN
ejpam-7033	384	18	,	,	PUNCT
ejpam-7033	384	19	f1),r(f0	f1),r(f0	PROPN
ejpam-7033	384	20	,	,	PUNCT
ejpam-7033	384	21	f1),r(f1	f1),r(f1	PROPN
ejpam-7033	384	22	,	,	PUNCT
ejpam-7033	384	23	f2	f2	PROPN
ejpam-7033	384	24	)	)	PUNCT
ejpam-7033	384	25	,	,	PUNCT
ejpam-7033	384	26	s[r(f0	s[r(f0	PROPN
ejpam-7033	384	27	,	,	PUNCT
ejpam-7033	384	28	f1)+r(f1	f1)+r(f1	PROPN
ejpam-7033	384	29	,	,	PUNCT
ejpam-7033	384	30	f2)+r(f2	f2)+r(f2	NOUN
ejpam-7033	384	31	,	,	PUNCT
ejpam-7033	384	32	f3)],r(f2	f3)],r(f2	NOUN
ejpam-7033	384	33	,	,	PUNCT
ejpam-7033	384	34	f1	f1	NOUN
ejpam-7033	384	35	)	)	PUNCT
ejpam-7033	384	36	⪯	⪯	NOUN
ejpam-7033	384	37	0e	0e	NOUN
ejpam-7033	384	38	.	.	PUNCT
ejpam-7033	385	1	by	by	ADP
ejpam-7033	385	2	(	(	PUNCT
ejpam-7033	385	3	j2	j2	PROPN
ejpam-7033	385	4	)	)	PUNCT
ejpam-7033	385	5	,	,	PUNCT
ejpam-7033	385	6	∃	∃	PROPN
ejpam-7033	385	7	t	t	PROPN
ejpam-7033	385	8	∈	∈	PROPN
ejpam-7033	385	9	b(e	b(e	PROPN
ejpam-7033	385	10	,	,	PUNCT
ejpam-7033	385	11	e	e	X
ejpam-7033	385	12	)	)	PUNCT
ejpam-7033	386	1	so	so	SCONJ
ejpam-7033	386	2	that	that	SCONJ
ejpam-7033	386	3	∥t	∥t	VERB
ejpam-7033	386	4	∥1	∥1	PRON
ejpam-7033	386	5	<	<	X
ejpam-7033	386	6	1	1	NUM
ejpam-7033	386	7	with	with	ADP
ejpam-7033	386	8	r(f1	r(f1	NOUN
ejpam-7033	386	9	,	,	PUNCT
ejpam-7033	386	10	f2	f2	PROPN
ejpam-7033	386	11	)	)	PUNCT
ejpam-7033	386	12	⪯	⪯	NOUN
ejpam-7033	386	13	1	1	NUM
ejpam-7033	386	14	s	s	PART
ejpam-7033	386	15	t	t	PROPN
ejpam-7033	386	16	(	(	PUNCT
ejpam-7033	386	17	r(f0	r(f0	NOUN
ejpam-7033	386	18	,	,	PUNCT
ejpam-7033	386	19	f1	f1	NOUN
ejpam-7033	386	20	)	)	PUNCT
ejpam-7033	386	21	)	)	PUNCT
ejpam-7033	386	22	⪯	⪯	PROPN
ejpam-7033	386	23	t	t	PROPN
ejpam-7033	386	24	(	(	PUNCT
ejpam-7033	386	25	r(f0	r(f0	NOUN
ejpam-7033	386	26	,	,	PUNCT
ejpam-7033	386	27	f1	f1	NOUN
ejpam-7033	386	28	)	)	PUNCT
ejpam-7033	386	29	)	)	PUNCT
ejpam-7033	386	30	,	,	PUNCT
ejpam-7033	386	31	and	and	CCONJ
ejpam-7033	386	32	r(f2	r(f2	NOUN
ejpam-7033	386	33	,	,	PUNCT
ejpam-7033	386	34	f3	f3	ADJ
ejpam-7033	386	35	)	)	PUNCT
ejpam-7033	386	36	⪯	⪯	NOUN
ejpam-7033	386	37	1	1	NUM
ejpam-7033	386	38	s	s	PART
ejpam-7033	386	39	t	t	PROPN
ejpam-7033	386	40	(	(	PUNCT
ejpam-7033	386	41	r(f1	r(f1	NOUN
ejpam-7033	386	42	,	,	PUNCT
ejpam-7033	386	43	f2	f2	PROPN
ejpam-7033	386	44	)	)	PUNCT
ejpam-7033	386	45	)	)	PUNCT
ejpam-7033	387	1	⪯	⪯	PROPN
ejpam-7033	387	2	t	t	PROPN
ejpam-7033	387	3	(	(	PUNCT
ejpam-7033	387	4	r(f1	r(f1	NOUN
ejpam-7033	387	5	,	,	PUNCT
ejpam-7033	387	6	f2	f2	PROPN
ejpam-7033	387	7	)	)	PUNCT
ejpam-7033	387	8	)	)	PUNCT
ejpam-7033	387	9	.	.	PUNCT
ejpam-7033	388	1	using	use	VERB
ejpam-7033	388	2	assumption	assumption	NOUN
ejpam-7033	388	3	(	(	PUNCT
ejpam-7033	388	4	2	2	NUM
ejpam-7033	388	5	)	)	PUNCT
ejpam-7033	388	6	,	,	PUNCT
ejpam-7033	388	7	we	we	PRON
ejpam-7033	388	8	get	get	VERB
ejpam-7033	388	9	f2ℜf1(f	f2ℜf1(f	NOUN
ejpam-7033	388	10	being	be	AUX
ejpam-7033	388	11	order	order	NOUN
ejpam-7033	388	12	preserving	preserve	VERB
ejpam-7033	388	13	)	)	PUNCT
ejpam-7033	388	14	,	,	PUNCT
ejpam-7033	388	15	hence	hence	ADV
ejpam-7033	388	16	using	use	VERB
ejpam-7033	388	17	(	(	PUNCT
ejpam-7033	388	18	9	9	NUM
ejpam-7033	388	19	)	)	PUNCT
ejpam-7033	389	1	(	(	PUNCT
ejpam-7033	389	2	i	i	PRON
ejpam-7033	389	3	−	−	PROPN
ejpam-7033	390	1	t	t	NOUN
ejpam-7033	390	2	)	)	PUNCT
ejpam-7033	390	3	2(i	2(i	NUM
ejpam-7033	391	1	+	+	NUM
ejpam-7033	391	2	t	t	NOUN
ejpam-7033	391	3	)	)	PUNCT
ejpam-7033	391	4	r(ℏ(f1	r(ℏ(f1	PROPN
ejpam-7033	391	5	)	)	PUNCT
ejpam-7033	391	6	,	,	PUNCT
ejpam-7033	391	7	f1	f1	NOUN
ejpam-7033	391	8	)	)	PUNCT
ejpam-7033	391	9	=	=	PUNCT
ejpam-7033	392	1	(	(	PUNCT
ejpam-7033	392	2	i	i	PRON
ejpam-7033	392	3	−	−	PROPN
ejpam-7033	392	4	t	t	NOUN
ejpam-7033	392	5	)	)	PUNCT
ejpam-7033	392	6	2(i	2(i	NUM
ejpam-7033	393	1	+	+	CCONJ
ejpam-7033	393	2	t	t	NOUN
ejpam-7033	393	3	)	)	PUNCT
ejpam-7033	393	4	r(f2	r(f2	NOUN
ejpam-7033	393	5	,	,	PUNCT
ejpam-7033	393	6	f1	f1	NOUN
ejpam-7033	393	7	)	)	PUNCT
ejpam-7033	393	8	⪯	⪯	PROPN
ejpam-7033	393	9	sr(f2	sr(f2	NOUN
ejpam-7033	393	10	,	,	PUNCT
ejpam-7033	393	11	f1	f1	NOUN
ejpam-7033	393	12	)	)	PUNCT
ejpam-7033	393	13	implies	imply	VERB
ejpam-7033	393	14	j	j	PROPN
ejpam-7033	393	15	(	(	PUNCT
ejpam-7033	393	16	r(ℏ(f2	r(ℏ(f2	NOUN
ejpam-7033	393	17	)	)	PUNCT
ejpam-7033	393	18	,	,	PUNCT
ejpam-7033	393	19	ℏ(f1)),r(f2	ℏ(f1)),r(f2	NOUN
ejpam-7033	393	20	,	,	PUNCT
ejpam-7033	393	21	f1),r(f2	f1),r(f2	NOUN
ejpam-7033	393	22	,	,	PUNCT
ejpam-7033	393	23	ℏ(f2)),r(f1	ℏ(f2)),r(f1	PROPN
ejpam-7033	393	24	,	,	PUNCT
ejpam-7033	393	25	ℏ(f1	ℏ(f1	PROPN
ejpam-7033	393	26	)	)	PUNCT
ejpam-7033	393	27	,	,	PUNCT
ejpam-7033	393	28	r(f2	r(f2	NOUN
ejpam-7033	393	29	,	,	PUNCT
ejpam-7033	393	30	ℏ2(f1)),r(f1	ℏ2(f1)),r(f1	NOUN
ejpam-7033	393	31	,	,	PUNCT
ejpam-7033	393	32	ℏ2(f2	ℏ2(f2	NOUN
ejpam-7033	393	33	)	)	PUNCT
ejpam-7033	393	34	)	)	PUNCT
ejpam-7033	393	35	)	)	PUNCT
ejpam-7033	394	1	⪯	⪯	NOUN
ejpam-7033	394	2	0e	0e	PROPN
ejpam-7033	394	3	.	.	PUNCT
ejpam-7033	395	1	a.	a.	PROPN
ejpam-7033	395	2	arif	arif	PROPN
ejpam-7033	395	3	et	et	PROPN
ejpam-7033	395	4	al	al	PROPN
ejpam-7033	395	5	.	.	PUNCT
ejpam-7033	395	6	/	/	SYM
ejpam-7033	395	7	eur	eur	PROPN
ejpam-7033	395	8	.	.	PUNCT
ejpam-7033	396	1	j.	j.	PROPN
ejpam-7033	396	2	pure	pure	PROPN
ejpam-7033	396	3	appl	appl	PROPN
ejpam-7033	396	4	.	.	PROPN
ejpam-7033	396	5	math	math	PROPN
ejpam-7033	396	6	,	,	PUNCT
ejpam-7033	396	7	18	18	NUM
ejpam-7033	396	8	(	(	PUNCT
ejpam-7033	396	9	4	4	NUM
ejpam-7033	396	10	)	)	PUNCT
ejpam-7033	396	11	(	(	PUNCT
ejpam-7033	396	12	2025	2025	NUM
ejpam-7033	396	13	)	)	PUNCT
ejpam-7033	396	14	,	,	PUNCT
ejpam-7033	396	15	7033	7033	NUM
ejpam-7033	396	16	14	14	NUM
ejpam-7033	396	17	of	of	ADP
ejpam-7033	396	18	29	29	NUM
ejpam-7033	396	19	by	by	ADP
ejpam-7033	396	20	(	(	PUNCT
ejpam-7033	396	21	dr3	dr3	PROPN
ejpam-7033	396	22	)	)	PUNCT
ejpam-7033	396	23	,	,	PUNCT
ejpam-7033	396	24	(	(	PUNCT
ejpam-7033	396	25	j1	j1	PROPN
ejpam-7033	396	26	)	)	PUNCT
ejpam-7033	396	27	and	and	CCONJ
ejpam-7033	396	28	(	(	PUNCT
ejpam-7033	396	29	j2	j2	PROPN
ejpam-7033	396	30	)	)	PUNCT
ejpam-7033	396	31	,	,	PUNCT
ejpam-7033	396	32	we	we	PRON
ejpam-7033	396	33	get	get	VERB
ejpam-7033	396	34	r(f3	r(f3	NOUN
ejpam-7033	396	35	,	,	PUNCT
ejpam-7033	396	36	f4	f4	PROPN
ejpam-7033	396	37	)	)	PUNCT
ejpam-7033	396	38	⪯	⪯	NOUN
ejpam-7033	396	39	1	1	NUM
ejpam-7033	396	40	s	s	PART
ejpam-7033	396	41	t	t	NOUN
ejpam-7033	396	42	(	(	PUNCT
ejpam-7033	396	43	r(f2	r(f2	NOUN
ejpam-7033	396	44	,	,	PUNCT
ejpam-7033	396	45	f3	f3	ADJ
ejpam-7033	396	46	)	)	PUNCT
ejpam-7033	396	47	)	)	PUNCT
ejpam-7033	396	48	⪯	⪯	NOUN
ejpam-7033	396	49	1	1	NUM
ejpam-7033	396	50	s2	s2	NOUN
ejpam-7033	396	51	t	t	PROPN
ejpam-7033	396	52	2(r(f1	2(r(f1	NUM
ejpam-7033	396	53	,	,	PUNCT
ejpam-7033	396	54	f2	f2	PROPN
ejpam-7033	396	55	)	)	PUNCT
ejpam-7033	396	56	)	)	PUNCT
ejpam-7033	397	1	⪯	⪯	NOUN
ejpam-7033	397	2	1	1	NUM
ejpam-7033	397	3	s3	s3	PROPN
ejpam-7033	397	4	t	t	PROPN
ejpam-7033	397	5	3(r(f0	3(r(f0	NUM
ejpam-7033	397	6	,	,	PUNCT
ejpam-7033	397	7	f1	f1	NOUN
ejpam-7033	397	8	)	)	PUNCT
ejpam-7033	397	9	)	)	PUNCT
ejpam-7033	397	10	⪯	⪯	PROPN
ejpam-7033	397	11	t	t	PROPN
ejpam-7033	397	12	3(r(f0	3(r(f0	NUM
ejpam-7033	397	13	,	,	PUNCT
ejpam-7033	397	14	f1	f1	NOUN
ejpam-7033	397	15	)	)	PUNCT
ejpam-7033	397	16	)	)	PUNCT
ejpam-7033	397	17	.	.	PUNCT
ejpam-7033	398	1	this	this	DET
ejpam-7033	398	2	pattern	pattern	NOUN
ejpam-7033	398	3	enable	enable	VERB
ejpam-7033	398	4	us	we	PRON
ejpam-7033	398	5	to	to	PART
ejpam-7033	398	6	construct	construct	VERB
ejpam-7033	398	7	a	a	DET
ejpam-7033	398	8	sequence	sequence	NOUN
ejpam-7033	398	9	{	{	PUNCT
ejpam-7033	398	10	fn	fn	NOUN
ejpam-7033	398	11	}	}	PUNCT
ejpam-7033	398	12	so	so	SCONJ
ejpam-7033	398	13	that	that	SCONJ
ejpam-7033	398	14	r(fn	r(fn	NOUN
ejpam-7033	398	15	,	,	PUNCT
ejpam-7033	398	16	fn+1	fn+1	NUM
ejpam-7033	398	17	)	)	PUNCT
ejpam-7033	398	18	⪯	⪯	NOUN
ejpam-7033	398	19	1	1	NUM
ejpam-7033	398	20	s	s	PART
ejpam-7033	398	21	t	t	NOUN
ejpam-7033	398	22	(	(	PUNCT
ejpam-7033	398	23	r(fn−1	r(fn−1	PROPN
ejpam-7033	398	24	,	,	PUNCT
ejpam-7033	398	25	fn	fn	NOUN
ejpam-7033	398	26	)	)	PUNCT
ejpam-7033	398	27	)	)	PUNCT
ejpam-7033	399	1	⪯	⪯	NOUN
ejpam-7033	399	2	1	1	NUM
ejpam-7033	399	3	s2	s2	NOUN
ejpam-7033	399	4	t	t	PROPN
ejpam-7033	399	5	2(r(fn−2	2(r(fn−2	NUM
ejpam-7033	399	6	,	,	PUNCT
ejpam-7033	399	7	fn−1	fn−1	ADJ
ejpam-7033	399	8	)	)	PUNCT
ejpam-7033	399	9	)	)	PUNCT
ejpam-7033	399	10	⪯	⪯	NOUN
ejpam-7033	399	11	·	·	PUNCT
ejpam-7033	399	12	·	·	PUNCT
ejpam-7033	399	13	·	·	PUNCT
ejpam-7033	400	1	⪯	⪯	NOUN
ejpam-7033	400	2	1	1	NUM
ejpam-7033	400	3	sn	sn	NOUN
ejpam-7033	400	4	t	t	PROPN
ejpam-7033	400	5	n(r(f0	n(r(f0	NOUN
ejpam-7033	400	6	,	,	PUNCT
ejpam-7033	400	7	f1	f1	NOUN
ejpam-7033	400	8	)	)	PUNCT
ejpam-7033	400	9	)	)	PUNCT
ejpam-7033	400	10	.	.	PUNCT
ejpam-7033	401	1	by	by	ADP
ejpam-7033	401	2	following	follow	VERB
ejpam-7033	401	3	same	same	ADJ
ejpam-7033	401	4	pattern	pattern	NOUN
ejpam-7033	401	5	as	as	ADP
ejpam-7033	401	6	for	for	ADP
ejpam-7033	401	7	the	the	DET
ejpam-7033	401	8	proof	proof	NOUN
ejpam-7033	401	9	of	of	ADP
ejpam-7033	401	10	theorem	theorem	ADJ
ejpam-7033	401	11	13	13	NUM
ejpam-7033	401	12	,	,	PUNCT
ejpam-7033	401	13	we	we	PRON
ejpam-7033	401	14	will	will	AUX
ejpam-7033	401	15	obtain	obtain	VERB
ejpam-7033	401	16	z∗	z∗	NOUN
ejpam-7033	401	17	=	=	SYM
ejpam-7033	401	18	ℏ(z∗	ℏ(z∗	NOUN
ejpam-7033	401	19	)	)	PUNCT
ejpam-7033	401	20	.	.	PUNCT
ejpam-7033	402	1	remark	remark	PROPN
ejpam-7033	402	2	16	16	NUM
ejpam-7033	402	3	.	.	PUNCT
ejpam-7033	403	1	we	we	PRON
ejpam-7033	403	2	get	get	VERB
ejpam-7033	403	3	different	different	ADJ
ejpam-7033	403	4	ordered	order	VERB
ejpam-7033	403	5	contractive	contractive	ADJ
ejpam-7033	403	6	conditions	condition	NOUN
ejpam-7033	403	7	for	for	ADP
ejpam-7033	403	8	different	different	ADJ
ejpam-7033	403	9	definitions	definition	NOUN
ejpam-7033	403	10	of	of	ADP
ejpam-7033	403	11	j	j	PROPN
ejpam-7033	403	12	.	.	PUNCT
ejpam-7033	404	1	also	also	ADV
ejpam-7033	404	2	,	,	PUNCT
ejpam-7033	404	3	theorem	theorem	VERB
ejpam-7033	404	4	15	15	NUM
ejpam-7033	404	5	generalizes	generalize	VERB
ejpam-7033	404	6	the	the	DET
ejpam-7033	404	7	results	result	NOUN
ejpam-7033	404	8	in	in	ADP
ejpam-7033	404	9	[	[	X
ejpam-7033	404	10	8–11	8–11	NOUN
ejpam-7033	404	11	,	,	PUNCT
ejpam-7033	404	12	37	37	NUM
ejpam-7033	404	13	,	,	PUNCT
ejpam-7033	404	14	38	38	NUM
ejpam-7033	404	15	]	]	PUNCT
ejpam-7033	404	16	.	.	PUNCT
ejpam-7033	405	1	remark	remark	PROPN
ejpam-7033	405	2	17	17	NUM
ejpam-7033	405	3	.	.	PUNCT
ejpam-7033	406	1	in	in	ADP
ejpam-7033	406	2	a	a	DET
ejpam-7033	406	3	non	non	ADJ
ejpam-7033	406	4	-	-	ADJ
ejpam-7033	406	5	normal	normal	ADJ
ejpam-7033	406	6	cone	cone	NOUN
ejpam-7033	406	7	,	,	PUNCT
ejpam-7033	406	8	by	by	ADP
ejpam-7033	406	9	taking	take	VERB
ejpam-7033	406	10	an	an	DET
ejpam-7033	406	11	“	"	PUNCT
ejpam-7033	406	12	upper	upper	ADJ
ejpam-7033	406	13	bound	bind	VERB
ejpam-7033	406	14	or	or	CCONJ
ejpam-7033	406	15	lower	low	ADJ
ejpam-7033	406	16	bound	bind	VERB
ejpam-7033	406	17	”	"	PUNCT
ejpam-7033	406	18	for	for	ADP
ejpam-7033	406	19	every	every	DET
ejpam-7033	406	20	pair	pair	NOUN
ejpam-7033	406	21	ϱ	ϱ	ADP
ejpam-7033	406	22	,	,	PUNCT
ejpam-7033	406	23	ω	ω	NUM
ejpam-7033	406	24	∈w	∈w	NOUN
ejpam-7033	406	25	,	,	PUNCT
ejpam-7033	406	26	one	one	PRON
ejpam-7033	406	27	may	may	AUX
ejpam-7033	406	28	find	find	VERB
ejpam-7033	406	29	a	a	DET
ejpam-7033	406	30	unique	unique	ADJ
ejpam-7033	406	31	fixed	fix	VERB
ejpam-7033	406	32	point	point	NOUN
ejpam-7033	406	33	in	in	ADP
ejpam-7033	406	34	theorem	theorem	ADJ
ejpam-7033	406	35	15	15	NUM
ejpam-7033	406	36	.	.	NOUN
ejpam-7033	406	37	5	5	NUM
ejpam-7033	406	38	.	.	PUNCT
ejpam-7033	406	39	examples	example	NOUN
ejpam-7033	406	40	and	and	CCONJ
ejpam-7033	406	41	consequences	consequence	NOUN
ejpam-7033	406	42	in	in	ADP
ejpam-7033	406	43	this	this	DET
ejpam-7033	406	44	section	section	NOUN
ejpam-7033	406	45	,	,	PUNCT
ejpam-7033	406	46	we	we	PRON
ejpam-7033	406	47	give	give	VERB
ejpam-7033	406	48	some	some	DET
ejpam-7033	406	49	examples	example	NOUN
ejpam-7033	406	50	for	for	ADP
ejpam-7033	406	51	the	the	DET
ejpam-7033	406	52	explanation	explanation	NOUN
ejpam-7033	406	53	of	of	ADP
ejpam-7033	406	54	hypotheses	hypothesis	NOUN
ejpam-7033	406	55	of	of	ADP
ejpam-7033	406	56	main	main	ADJ
ejpam-7033	406	57	theorem	theorem	NOUN
ejpam-7033	406	58	.	.	PROPN
ejpam-7033	406	59	example	example	NOUN
ejpam-7033	406	60	6	6	NUM
ejpam-7033	406	61	.	.	PUNCT
ejpam-7033	407	1	let	let	VERB
ejpam-7033	407	2	e	e	NOUN
ejpam-7033	407	3	=	=	SYM
ejpam-7033	407	4	(	(	PUNCT
ejpam-7033	407	5	r3	r3	PROPN
ejpam-7033	407	6	,	,	PUNCT
ejpam-7033	407	7	∥	∥	X
ejpam-7033	407	8	·	·	PUNCT
ejpam-7033	407	9	∥	∥	NUM
ejpam-7033	407	10	)	)	PUNCT
ejpam-7033	407	11	,	,	PUNCT
ejpam-7033	407	12	then	then	ADV
ejpam-7033	407	13	it	it	PRON
ejpam-7033	407	14	is	be	AUX
ejpam-7033	407	15	a	a	DET
ejpam-7033	407	16	real	real	ADJ
ejpam-7033	407	17	banach	banach	NOUN
ejpam-7033	407	18	space	space	NOUN
ejpam-7033	407	19	.	.	PUNCT
ejpam-7033	408	1	define	define	VERB
ejpam-7033	408	2	a	a	DET
ejpam-7033	408	3	cone	cone	NOUN
ejpam-7033	408	4	c	c	NOUN
ejpam-7033	408	5	∈	∈	PROPN
ejpam-7033	408	6	e	e	NOUN
ejpam-7033	408	7	such	such	ADJ
ejpam-7033	408	8	that	that	SCONJ
ejpam-7033	408	9	c	c	NOUN
ejpam-7033	408	10	=	=	PRON
ejpam-7033	408	11	{	{	PUNCT
ejpam-7033	408	12	(	(	PUNCT
ejpam-7033	408	13	ϑ	ϑ	X
ejpam-7033	408	14	,	,	PUNCT
ejpam-7033	408	15	x	x	NOUN
ejpam-7033	408	16	,	,	PUNCT
ejpam-7033	408	17	ν	ν	NOUN
ejpam-7033	408	18	)	)	PUNCT
ejpam-7033	408	19	∈	∈	PROPN
ejpam-7033	408	20	r3	r3	PROPN
ejpam-7033	408	21	:	:	PUNCT
ejpam-7033	408	22	ϑ	ϑ	X
ejpam-7033	408	23	,	,	PUNCT
ejpam-7033	408	24	x	x	X
ejpam-7033	408	25	,	,	PUNCT
ejpam-7033	408	26	ν	ν	X
ejpam-7033	408	27	≥	≥	NOUN
ejpam-7033	408	28	0	0	NUM
ejpam-7033	408	29	}	}	PUNCT
ejpam-7033	408	30	and	and	CCONJ
ejpam-7033	408	31	∥ϑ∥	∥ϑ∥	NOUN
ejpam-7033	408	32	=	=	SYM
ejpam-7033	408	33	max	max	X
ejpam-7033	408	34	{	{	PUNCT
ejpam-7033	408	35	(	(	PUNCT
ejpam-7033	408	36	|ϑ1|	|ϑ1|	NOUN
ejpam-7033	408	37	,	,	PUNCT
ejpam-7033	408	38	|ϑ2|	|ϑ2|	NOUN
ejpam-7033	408	39	,	,	PUNCT
ejpam-7033	408	40	|ϑ3|	|ϑ3|	NOUN
ejpam-7033	408	41	)	)	PUNCT
ejpam-7033	408	42	}	}	PUNCT
ejpam-7033	408	43	.	.	PUNCT
ejpam-7033	409	1	consider	consider	VERB
ejpam-7033	409	2	x	x	PRON
ejpam-7033	409	3	=	=	PRON
ejpam-7033	409	4	{	{	PUNCT
ejpam-7033	409	5	(	(	PUNCT
ejpam-7033	409	6	0	0	NUM
ejpam-7033	409	7	,	,	PUNCT
ejpam-7033	409	8	0	0	NUM
ejpam-7033	409	9	,	,	PUNCT
ejpam-7033	409	10	0	0	NUM
ejpam-7033	409	11	)	)	PUNCT
ejpam-7033	409	12	,	,	PUNCT
ejpam-7033	409	13	(	(	PUNCT
ejpam-7033	409	14	1	1	NUM
ejpam-7033	409	15	4	4	NUM
ejpam-7033	409	16	,	,	PUNCT
ejpam-7033	409	17	0	0	NUM
ejpam-7033	409	18	,	,	PUNCT
ejpam-7033	409	19	0	0	NUM
ejpam-7033	409	20	)	)	PUNCT
ejpam-7033	409	21	,	,	PUNCT
ejpam-7033	409	22	(	(	PUNCT
ejpam-7033	409	23	1	1	NUM
ejpam-7033	409	24	4	4	NUM
ejpam-7033	409	25	,	,	PUNCT
ejpam-7033	409	26	1	1	NUM
ejpam-7033	409	27	4	4	NUM
ejpam-7033	409	28	,	,	PUNCT
ejpam-7033	409	29	0	0	NUM
ejpam-7033	409	30	)	)	PUNCT
ejpam-7033	409	31	,	,	PUNCT
ejpam-7033	409	32	(	(	PUNCT
ejpam-7033	409	33	1	1	NUM
ejpam-7033	409	34	4	4	NUM
ejpam-7033	409	35	,	,	PUNCT
ejpam-7033	409	36	1	1	NUM
ejpam-7033	409	37	4	4	NUM
ejpam-7033	409	38	,	,	PUNCT
ejpam-7033	409	39	1	1	NUM
ejpam-7033	409	40	4	4	NUM
ejpam-7033	409	41	)	)	PUNCT
ejpam-7033	409	42	}	}	PUNCT
ejpam-7033	410	1	⊂	⊂	PROPN
ejpam-7033	410	2	e	e	NOUN
ejpam-7033	410	3	with	with	ADP
ejpam-7033	410	4	ℏ	ℏ	PROPN
ejpam-7033	410	5	:	:	PUNCT
ejpam-7033	410	6	x	x	SYM
ejpam-7033	410	7	→	→	SYM
ejpam-7033	410	8	x	x	PUNCT
ejpam-7033	410	9	defined	define	VERB
ejpam-7033	410	10	as	as	ADP
ejpam-7033	410	11	ℏ	ℏ	PROPN
ejpam-7033	410	12	(	(	PUNCT
ejpam-7033	410	13	0	0	NUM
ejpam-7033	410	14	,	,	PUNCT
ejpam-7033	410	15	0	0	NUM
ejpam-7033	410	16	,	,	PUNCT
ejpam-7033	410	17	0	0	NUM
ejpam-7033	410	18	)	)	PUNCT
ejpam-7033	410	19	=	=	SYM
ejpam-7033	410	20	ℏ	ℏ	PROPN
ejpam-7033	410	21	(	(	PUNCT
ejpam-7033	410	22	1	1	NUM
ejpam-7033	410	23	4	4	NUM
ejpam-7033	410	24	,	,	PUNCT
ejpam-7033	410	25	0	0	NUM
ejpam-7033	410	26	,	,	PUNCT
ejpam-7033	410	27	0	0	NUM
ejpam-7033	410	28	)	)	PUNCT
ejpam-7033	410	29	=	=	SYM
ejpam-7033	410	30	(	(	PUNCT
ejpam-7033	410	31	0	0	NUM
ejpam-7033	410	32	,	,	PUNCT
ejpam-7033	410	33	0	0	NUM
ejpam-7033	410	34	,	,	PUNCT
ejpam-7033	410	35	0	0	NUM
ejpam-7033	410	36	)	)	PUNCT
ejpam-7033	410	37	,	,	PUNCT
ejpam-7033	410	38	ℏ	ℏ	PROPN
ejpam-7033	410	39	(	(	PUNCT
ejpam-7033	410	40	1	1	NUM
ejpam-7033	410	41	4	4	NUM
ejpam-7033	410	42	,	,	PUNCT
ejpam-7033	410	43	1	1	NUM
ejpam-7033	410	44	4	4	NUM
ejpam-7033	410	45	,	,	PUNCT
ejpam-7033	410	46	0	0	NUM
ejpam-7033	410	47	)	)	PUNCT
ejpam-7033	411	1	=	=	PUNCT
ejpam-7033	411	2	(	(	PUNCT
ejpam-7033	411	3	1	1	NUM
ejpam-7033	411	4	4	4	NUM
ejpam-7033	411	5	,	,	PUNCT
ejpam-7033	411	6	0	0	NUM
ejpam-7033	411	7	,	,	PUNCT
ejpam-7033	411	8	0	0	NUM
ejpam-7033	411	9	)	)	PUNCT
ejpam-7033	411	10	,	,	PUNCT
ejpam-7033	411	11	ℏ	ℏ	PROPN
ejpam-7033	411	12	(	(	PUNCT
ejpam-7033	411	13	1	1	NUM
ejpam-7033	411	14	4	4	NUM
ejpam-7033	411	15	,	,	PUNCT
ejpam-7033	411	16	1	1	NUM
ejpam-7033	411	17	4	4	NUM
ejpam-7033	411	18	,	,	PUNCT
ejpam-7033	411	19	1	1	NUM
ejpam-7033	411	20	4	4	NUM
ejpam-7033	411	21	)	)	PUNCT
ejpam-7033	411	22	=	=	PUNCT
ejpam-7033	411	23	(	(	PUNCT
ejpam-7033	411	24	1	1	NUM
ejpam-7033	411	25	4	4	NUM
ejpam-7033	411	26	,	,	PUNCT
ejpam-7033	411	27	1	1	NUM
ejpam-7033	411	28	4	4	NUM
ejpam-7033	411	29	,	,	PUNCT
ejpam-7033	411	30	0	0	NUM
ejpam-7033	411	31	)	)	PUNCT
ejpam-7033	411	32	.	.	PUNCT
ejpam-7033	412	1	define	define	VERB
ejpam-7033	412	2	r	r	NOUN
ejpam-7033	412	3	:	:	PUNCT
ejpam-7033	412	4	x	x	PROPN
ejpam-7033	412	5	×x	×x	X
ejpam-7033	412	6	→	→	SYM
ejpam-7033	412	7	e	e	NOUN
ejpam-7033	412	8	,	,	PUNCT
ejpam-7033	412	9	r(ϑ1	r(ϑ1	ADJ
ejpam-7033	412	10	,	,	PUNCT
ejpam-7033	412	11	ϑ2	ϑ2	NOUN
ejpam-7033	412	12	)	)	PUNCT
ejpam-7033	412	13	=	=	SYM
ejpam-7033	412	14			X
ejpam-7033	412	15	(	(	PUNCT
ejpam-7033	412	16	0	0	NUM
ejpam-7033	412	17	,	,	PUNCT
ejpam-7033	412	18	0	0	NUM
ejpam-7033	412	19	,	,	PUNCT
ejpam-7033	412	20	0	0	NUM
ejpam-7033	412	21	)	)	PUNCT
ejpam-7033	412	22	if	if	SCONJ
ejpam-7033	412	23	ϑ1	ϑ1	NOUN
ejpam-7033	412	24	=	=	SYM
ejpam-7033	412	25	ϑ2	ϑ2	PROPN
ejpam-7033	412	26	(	(	PUNCT
ejpam-7033	412	27	3	3	NUM
ejpam-7033	412	28	4	4	NUM
ejpam-7033	412	29	,	,	PUNCT
ejpam-7033	412	30	3	3	NUM
ejpam-7033	412	31	4	4	NUM
ejpam-7033	412	32	,	,	PUNCT
ejpam-7033	412	33	3	3	NUM
ejpam-7033	412	34	4	4	NUM
ejpam-7033	412	35	)	)	PUNCT
ejpam-7033	412	36	if	if	SCONJ
ejpam-7033	412	37	ϑ1	ϑ1	PROPN
ejpam-7033	412	38	,	,	PUNCT
ejpam-7033	412	39	ϑ2	ϑ2	PROPN
ejpam-7033	412	40	∈	∈	PROPN
ejpam-7033	412	41	{	{	PUNCT
ejpam-7033	412	42	(	(	PUNCT
ejpam-7033	412	43	0	0	NUM
ejpam-7033	412	44	,	,	PUNCT
ejpam-7033	412	45	0	0	NUM
ejpam-7033	412	46	,	,	PUNCT
ejpam-7033	412	47	0	0	NUM
ejpam-7033	412	48	)	)	PUNCT
ejpam-7033	412	49	,	,	PUNCT
ejpam-7033	412	50	(	(	PUNCT
ejpam-7033	412	51	1	1	NUM
ejpam-7033	412	52	4	4	NUM
ejpam-7033	412	53	,	,	PUNCT
ejpam-7033	412	54	1	1	NUM
ejpam-7033	412	55	4	4	NUM
ejpam-7033	412	56	,	,	PUNCT
ejpam-7033	412	57	0	0	NUM
ejpam-7033	412	58	)	)	PUNCT
ejpam-7033	412	59	}	}	PUNCT
ejpam-7033	412	60	(	(	PUNCT
ejpam-7033	412	61	1	1	NUM
ejpam-7033	412	62	4	4	NUM
ejpam-7033	412	63	,	,	PUNCT
ejpam-7033	412	64	1	1	NUM
ejpam-7033	412	65	4	4	NUM
ejpam-7033	412	66	,	,	PUNCT
ejpam-7033	412	67	1	1	NUM
ejpam-7033	412	68	4	4	NUM
ejpam-7033	412	69	)	)	PUNCT
ejpam-7033	412	70	if	if	SCONJ
ejpam-7033	412	71	ϑ1	ϑ1	PROPN
ejpam-7033	412	72	,	,	PUNCT
ejpam-7033	412	73	ϑ2	ϑ2	PROPN
ejpam-7033	412	74	∈	∈	PROPN
ejpam-7033	412	75	{	{	PUNCT
ejpam-7033	412	76	(	(	PUNCT
ejpam-7033	412	77	1	1	NUM
ejpam-7033	412	78	4	4	NUM
ejpam-7033	412	79	,	,	PUNCT
ejpam-7033	412	80	1	1	NUM
ejpam-7033	412	81	4	4	NUM
ejpam-7033	412	82	,	,	PUNCT
ejpam-7033	412	83	1	1	NUM
ejpam-7033	412	84	4	4	NUM
ejpam-7033	412	85	)	)	PUNCT
ejpam-7033	412	86	,	,	PUNCT
ejpam-7033	412	87	(	(	PUNCT
ejpam-7033	412	88	1	1	NUM
ejpam-7033	412	89	4	4	NUM
ejpam-7033	412	90	,	,	PUNCT
ejpam-7033	412	91	1	1	NUM
ejpam-7033	412	92	4	4	NUM
ejpam-7033	412	93	,	,	PUNCT
ejpam-7033	412	94	0	0	NUM
ejpam-7033	412	95	)	)	PUNCT
ejpam-7033	412	96	}	}	PUNCT
ejpam-7033	412	97	(	(	PUNCT
ejpam-7033	412	98	0	0	NUM
ejpam-7033	412	99	,	,	PUNCT
ejpam-7033	412	100	14	14	NUM
ejpam-7033	412	101	,	,	PUNCT
ejpam-7033	412	102	1	1	NUM
ejpam-7033	412	103	4	4	NUM
ejpam-7033	412	104	)	)	PUNCT
ejpam-7033	412	105	otherwise	otherwise	ADV
ejpam-7033	412	106	.	.	PUNCT
ejpam-7033	413	1	define	define	VERB
ejpam-7033	413	2	t	t	NOUN
ejpam-7033	414	1	:	:	PUNCT
ejpam-7033	414	2	e	e	X
ejpam-7033	414	3	→	→	SYM
ejpam-7033	414	4	e	e	X
ejpam-7033	414	5	by	by	ADP
ejpam-7033	414	6	t	t	PROPN
ejpam-7033	414	7	(	(	PUNCT
ejpam-7033	414	8	ϑ	ϑ	X
ejpam-7033	414	9	)	)	PUNCT
ejpam-7033	414	10	=	=	SYM
ejpam-7033	414	11	ϑ	ϑ	X
ejpam-7033	414	12	2	2	NUM
ejpam-7033	414	13	,	,	PUNCT
ejpam-7033	414	14	clearly	clearly	ADV
ejpam-7033	414	15	∥t	∥t	VERB
ejpam-7033	414	16	∥1	∥1	PRON
ejpam-7033	414	17	<	<	X
ejpam-7033	414	18	1	1	NUM
ejpam-7033	414	19	.	.	PUNCT
ejpam-7033	415	1	(	(	PUNCT
ejpam-7033	415	2	3	3	NUM
ejpam-7033	415	3	4	4	NUM
ejpam-7033	415	4	,	,	PUNCT
ejpam-7033	415	5	3	3	NUM
ejpam-7033	415	6	4	4	NUM
ejpam-7033	415	7	,	,	PUNCT
ejpam-7033	415	8	3	3	NUM
ejpam-7033	415	9	4	4	NUM
ejpam-7033	415	10	)	)	PUNCT
ejpam-7033	416	1	=	=	SYM
ejpam-7033	416	2	r	r	NOUN
ejpam-7033	416	3	(	(	PUNCT
ejpam-7033	416	4	(	(	PUNCT
ejpam-7033	416	5	0	0	NUM
ejpam-7033	416	6	,	,	PUNCT
ejpam-7033	416	7	0	0	NUM
ejpam-7033	416	8	,	,	PUNCT
ejpam-7033	416	9	0	0	NUM
ejpam-7033	416	10	)	)	PUNCT
ejpam-7033	416	11	,	,	PUNCT
ejpam-7033	416	12	(	(	PUNCT
ejpam-7033	416	13	1	1	NUM
ejpam-7033	416	14	4	4	NUM
ejpam-7033	416	15	,	,	PUNCT
ejpam-7033	416	16	1	1	NUM
ejpam-7033	416	17	4	4	NUM
ejpam-7033	416	18	,	,	PUNCT
ejpam-7033	416	19	0	0	NUM
ejpam-7033	416	20	)	)	PUNCT
ejpam-7033	416	21	)	)	PUNCT
ejpam-7033	417	1	⪰	⪰	NOUN
ejpam-7033	417	2	r	r	NOUN
ejpam-7033	417	3	(	(	PUNCT
ejpam-7033	417	4	(	(	PUNCT
ejpam-7033	417	5	0	0	NUM
ejpam-7033	417	6	,	,	PUNCT
ejpam-7033	417	7	0	0	NUM
ejpam-7033	417	8	,	,	PUNCT
ejpam-7033	417	9	0	0	NUM
ejpam-7033	417	10	)	)	PUNCT
ejpam-7033	417	11	,	,	PUNCT
ejpam-7033	417	12	(	(	PUNCT
ejpam-7033	417	13	1	1	NUM
ejpam-7033	417	14	4	4	NUM
ejpam-7033	417	15	,	,	PUNCT
ejpam-7033	417	16	0	0	NUM
ejpam-7033	417	17	,	,	PUNCT
ejpam-7033	417	18	0	0	NUM
ejpam-7033	417	19	)	)	PUNCT
ejpam-7033	417	20	)	)	PUNCT
ejpam-7033	418	1	+	+	CCONJ
ejpam-7033	418	2	r	r	NOUN
ejpam-7033	418	3	(	(	PUNCT
ejpam-7033	418	4	(	(	PUNCT
ejpam-7033	418	5	1	1	NUM
ejpam-7033	418	6	4	4	NUM
ejpam-7033	418	7	,	,	PUNCT
ejpam-7033	418	8	0	0	NUM
ejpam-7033	418	9	,	,	PUNCT
ejpam-7033	418	10	0	0	NUM
ejpam-7033	418	11	)	)	PUNCT
ejpam-7033	418	12	,	,	PUNCT
ejpam-7033	418	13	(	(	PUNCT
ejpam-7033	418	14	1	1	NUM
ejpam-7033	418	15	4	4	NUM
ejpam-7033	418	16	,	,	PUNCT
ejpam-7033	418	17	1	1	NUM
ejpam-7033	418	18	4	4	NUM
ejpam-7033	418	19	,	,	PUNCT
ejpam-7033	418	20	1	1	NUM
ejpam-7033	418	21	4	4	NUM
ejpam-7033	418	22	)	)	PUNCT
ejpam-7033	418	23	)	)	PUNCT
ejpam-7033	419	1	+	+	CCONJ
ejpam-7033	419	2	r	r	NOUN
ejpam-7033	419	3	(	(	PUNCT
ejpam-7033	419	4	(	(	PUNCT
ejpam-7033	419	5	1	1	NUM
ejpam-7033	419	6	4	4	NUM
ejpam-7033	419	7	,	,	PUNCT
ejpam-7033	419	8	1	1	NUM
ejpam-7033	419	9	4	4	NUM
ejpam-7033	419	10	,	,	PUNCT
ejpam-7033	419	11	1	1	NUM
ejpam-7033	419	12	4	4	NUM
ejpam-7033	419	13	)	)	PUNCT
ejpam-7033	419	14	,	,	PUNCT
ejpam-7033	419	15	(	(	PUNCT
ejpam-7033	419	16	1	1	NUM
ejpam-7033	419	17	4	4	NUM
ejpam-7033	419	18	,	,	PUNCT
ejpam-7033	419	19	1	1	NUM
ejpam-7033	419	20	4	4	NUM
ejpam-7033	419	21	,	,	PUNCT
ejpam-7033	419	22	0	0	NUM
ejpam-7033	419	23	)	)	PUNCT
ejpam-7033	419	24	)	)	PUNCT
ejpam-7033	420	1	=	=	PUNCT
ejpam-7033	420	2	(	(	PUNCT
ejpam-7033	420	3	0	0	NUM
ejpam-7033	420	4	,	,	PUNCT
ejpam-7033	420	5	1	1	NUM
ejpam-7033	420	6	4	4	NUM
ejpam-7033	420	7	,	,	PUNCT
ejpam-7033	420	8	1	1	NUM
ejpam-7033	420	9	4	4	NUM
ejpam-7033	420	10	)	)	PUNCT
ejpam-7033	420	11	+	+	CCONJ
ejpam-7033	420	12	(	(	PUNCT
ejpam-7033	420	13	0	0	NUM
ejpam-7033	420	14	,	,	PUNCT
ejpam-7033	420	15	1	1	NUM
ejpam-7033	420	16	4	4	NUM
ejpam-7033	420	17	,	,	PUNCT
ejpam-7033	420	18	1	1	NUM
ejpam-7033	420	19	4	4	NUM
ejpam-7033	420	20	)	)	PUNCT
ejpam-7033	420	21	+	+	CCONJ
ejpam-7033	420	22	(	(	PUNCT
ejpam-7033	420	23	1	1	NUM
ejpam-7033	420	24	4	4	NUM
ejpam-7033	420	25	,	,	PUNCT
ejpam-7033	420	26	1	1	NUM
ejpam-7033	420	27	4	4	NUM
ejpam-7033	420	28	,	,	PUNCT
ejpam-7033	420	29	1	1	NUM
ejpam-7033	420	30	4	4	NUM
ejpam-7033	420	31	)	)	PUNCT
ejpam-7033	420	32	a.	a.	NOUN
ejpam-7033	420	33	arif	arif	PROPN
ejpam-7033	420	34	et	et	PROPN
ejpam-7033	420	35	al	al	PROPN
ejpam-7033	420	36	.	.	PUNCT
ejpam-7033	420	37	/	/	SYM
ejpam-7033	420	38	eur	eur	PROPN
ejpam-7033	420	39	.	.	PUNCT
ejpam-7033	421	1	j.	j.	PROPN
ejpam-7033	421	2	pure	pure	PROPN
ejpam-7033	421	3	appl	appl	PROPN
ejpam-7033	421	4	.	.	PROPN
ejpam-7033	421	5	math	math	PROPN
ejpam-7033	421	6	,	,	PUNCT
ejpam-7033	421	7	18	18	NUM
ejpam-7033	421	8	(	(	PUNCT
ejpam-7033	421	9	4	4	NUM
ejpam-7033	421	10	)	)	PUNCT
ejpam-7033	421	11	(	(	PUNCT
ejpam-7033	421	12	2025	2025	NUM
ejpam-7033	421	13	)	)	PUNCT
ejpam-7033	421	14	,	,	PUNCT
ejpam-7033	421	15	7033	7033	NUM
ejpam-7033	421	16	15	15	NUM
ejpam-7033	421	17	of	of	ADP
ejpam-7033	421	18	29	29	NUM
ejpam-7033	421	19	=	=	SYM
ejpam-7033	421	20	(	(	PUNCT
ejpam-7033	421	21	1	1	NUM
ejpam-7033	421	22	4	4	NUM
ejpam-7033	421	23	,	,	PUNCT
ejpam-7033	421	24	3	3	NUM
ejpam-7033	421	25	4	4	NUM
ejpam-7033	421	26	,	,	PUNCT
ejpam-7033	421	27	3	3	NUM
ejpam-7033	421	28	4	4	NUM
ejpam-7033	421	29	)	)	PUNCT
ejpam-7033	421	30	.	.	PUNCT
ejpam-7033	422	1	note	note	VERB
ejpam-7033	422	2	that	that	SCONJ
ejpam-7033	422	3	r	r	NOUN
ejpam-7033	422	4	is	be	AUX
ejpam-7033	422	5	rcbm	rcbm	ADJ
ejpam-7033	422	6	but	but	CCONJ
ejpam-7033	422	7	not	not	PART
ejpam-7033	422	8	rbm	rbm	PROPN
ejpam-7033	422	9	,	,	PUNCT
ejpam-7033	422	10	for	for	ADP
ejpam-7033	422	11	s	s	NOUN
ejpam-7033	422	12	=	=	SYM
ejpam-7033	422	13	3	3	X
ejpam-7033	422	14	.	.	PUNCT
ejpam-7033	422	15	consider	consider	VERB
ejpam-7033	422	16	ϑ	ϑ	X
ejpam-7033	422	17	=	=	X
ejpam-7033	422	18	(	(	PUNCT
ejpam-7033	422	19	0	0	NUM
ejpam-7033	422	20	,	,	PUNCT
ejpam-7033	422	21	0	0	NUM
ejpam-7033	422	22	,	,	PUNCT
ejpam-7033	422	23	0	0	NUM
ejpam-7033	422	24	)	)	PUNCT
ejpam-7033	422	25	and	and	CCONJ
ejpam-7033	422	26	ω	ω	NUM
ejpam-7033	422	27	=	=	SYM
ejpam-7033	422	28	(	(	PUNCT
ejpam-7033	422	29	1	1	NUM
ejpam-7033	422	30	4	4	NUM
ejpam-7033	422	31	,	,	PUNCT
ejpam-7033	422	32	0	0	NUM
ejpam-7033	422	33	,	,	PUNCT
ejpam-7033	422	34	0	0	NUM
ejpam-7033	422	35	)	)	PUNCT
ejpam-7033	422	36	.	.	PUNCT
ejpam-7033	423	1	then	then	ADV
ejpam-7033	423	2	ℏ(ϑ	ℏ(ϑ	PROPN
ejpam-7033	423	3	)	)	PUNCT
ejpam-7033	423	4	=	=	SYM
ejpam-7033	423	5	(	(	PUNCT
ejpam-7033	423	6	0	0	NUM
ejpam-7033	423	7	,	,	PUNCT
ejpam-7033	423	8	0	0	NUM
ejpam-7033	423	9	,	,	PUNCT
ejpam-7033	423	10	0	0	NUM
ejpam-7033	423	11	)	)	PUNCT
ejpam-7033	423	12	=	=	SYM
ejpam-7033	423	13	ℏ(ω	ℏ(ω	NOUN
ejpam-7033	423	14	)	)	PUNCT
ejpam-7033	423	15	=	=	SYM
ejpam-7033	424	1	ℏ2(ω	ℏ2(ω	ADJ
ejpam-7033	424	2	)	)	PUNCT
ejpam-7033	424	3	r(ϑ	r(ϑ	PROPN
ejpam-7033	424	4	,	,	PUNCT
ejpam-7033	424	5	ℏ(ϑ	ℏ(ϑ	PROPN
ejpam-7033	424	6	)	)	PUNCT
ejpam-7033	424	7	)	)	PUNCT
ejpam-7033	425	1	=	=	PUNCT
ejpam-7033	425	2	r(ϑ	r(ϑ	PROPN
ejpam-7033	425	3	,	,	PUNCT
ejpam-7033	425	4	ℏ2(ω	ℏ2(ω	ADJ
ejpam-7033	425	5	)	)	PUNCT
ejpam-7033	425	6	)	)	PUNCT
ejpam-7033	426	1	=	=	SYM
ejpam-7033	426	2	(	(	PUNCT
ejpam-7033	426	3	0	0	NUM
ejpam-7033	426	4	,	,	PUNCT
ejpam-7033	426	5	0	0	NUM
ejpam-7033	426	6	,	,	PUNCT
ejpam-7033	426	7	0	0	NUM
ejpam-7033	426	8	)	)	PUNCT
ejpam-7033	426	9	,	,	PUNCT
ejpam-7033	426	10	r(ϑ	r(ϑ	PROPN
ejpam-7033	426	11	,	,	PUNCT
ejpam-7033	426	12	ω	ω	NOUN
ejpam-7033	426	13	)	)	PUNCT
ejpam-7033	426	14	=	=	SYM
ejpam-7033	426	15	(	(	PUNCT
ejpam-7033	426	16	0	0	NUM
ejpam-7033	426	17	,	,	PUNCT
ejpam-7033	426	18	1	1	NUM
ejpam-7033	426	19	4	4	NUM
ejpam-7033	426	20	,	,	PUNCT
ejpam-7033	426	21	1	1	NUM
ejpam-7033	426	22	4	4	NUM
ejpam-7033	426	23	)	)	PUNCT
ejpam-7033	426	24	,	,	PUNCT
ejpam-7033	426	25	(	(	PUNCT
ejpam-7033	426	26	i	i	PRON
ejpam-7033	426	27	−	−	PROPN
ejpam-7033	427	1	t	t	NOUN
ejpam-7033	427	2	)	)	PUNCT
ejpam-7033	427	3	2(i	2(i	NUM
ejpam-7033	428	1	+	+	NUM
ejpam-7033	428	2	t	t	NOUN
ejpam-7033	428	3	)	)	PUNCT
ejpam-7033	428	4	r(ϑ	r(ϑ	PROPN
ejpam-7033	428	5	,	,	PUNCT
ejpam-7033	428	6	ℏ(ϑ	ℏ(ϑ	PROPN
ejpam-7033	428	7	)	)	PUNCT
ejpam-7033	428	8	)	)	PUNCT
ejpam-7033	429	1	=	=	PUNCT
ejpam-7033	429	2	(	(	PUNCT
ejpam-7033	429	3	0	0	NUM
ejpam-7033	429	4	,	,	PUNCT
ejpam-7033	429	5	0	0	NUM
ejpam-7033	429	6	,	,	PUNCT
ejpam-7033	429	7	0	0	NUM
ejpam-7033	429	8	)	)	PUNCT
ejpam-7033	429	9	.	.	PUNCT
ejpam-7033	430	1	take	take	VERB
ejpam-7033	430	2	ϑ	ϑ	NOUN
ejpam-7033	430	3	=	=	X
ejpam-7033	430	4	(	(	PUNCT
ejpam-7033	430	5	1	1	NUM
ejpam-7033	430	6	4	4	NUM
ejpam-7033	430	7	,	,	PUNCT
ejpam-7033	430	8	0	0	NUM
ejpam-7033	430	9	,	,	PUNCT
ejpam-7033	430	10	0	0	NUM
ejpam-7033	430	11	)	)	PUNCT
ejpam-7033	430	12	and	and	CCONJ
ejpam-7033	430	13	ω	ω	X
ejpam-7033	430	14	=	=	SYM
ejpam-7033	430	15	(	(	PUNCT
ejpam-7033	430	16	1	1	NUM
ejpam-7033	430	17	4	4	NUM
ejpam-7033	430	18	,	,	PUNCT
ejpam-7033	430	19	1	1	NUM
ejpam-7033	430	20	4	4	NUM
ejpam-7033	430	21	,	,	PUNCT
ejpam-7033	430	22	0	0	NUM
ejpam-7033	430	23	)	)	PUNCT
ejpam-7033	430	24	.	.	PUNCT
ejpam-7033	431	1	then	then	ADV
ejpam-7033	431	2	ℏ(ϑ	ℏ(ϑ	PROPN
ejpam-7033	431	3	)	)	PUNCT
ejpam-7033	431	4	=	=	SYM
ejpam-7033	431	5	(	(	PUNCT
ejpam-7033	431	6	0	0	NUM
ejpam-7033	431	7	,	,	PUNCT
ejpam-7033	431	8	0	0	NUM
ejpam-7033	431	9	,	,	PUNCT
ejpam-7033	431	10	0	0	NUM
ejpam-7033	431	11	)	)	PUNCT
ejpam-7033	431	12	=	=	SYM
ejpam-7033	432	1	ℏ2(ω	ℏ2(ω	ADJ
ejpam-7033	432	2	)	)	PUNCT
ejpam-7033	432	3	and	and	CCONJ
ejpam-7033	432	4	ℏ(ω	ℏ(ω	PROPN
ejpam-7033	432	5	)	)	PUNCT
ejpam-7033	432	6	=	=	PUNCT
ejpam-7033	433	1	(	(	PUNCT
ejpam-7033	433	2	1	1	NUM
ejpam-7033	433	3	4	4	NUM
ejpam-7033	433	4	,	,	PUNCT
ejpam-7033	433	5	0	0	NUM
ejpam-7033	433	6	,	,	PUNCT
ejpam-7033	433	7	0	0	NUM
ejpam-7033	433	8	)	)	PUNCT
ejpam-7033	433	9	.	.	PUNCT
ejpam-7033	434	1	r(ϑ	r(ϑ	PROPN
ejpam-7033	434	2	,	,	PUNCT
ejpam-7033	434	3	ℏ(ϑ	ℏ(ϑ	PROPN
ejpam-7033	434	4	)	)	PUNCT
ejpam-7033	434	5	)	)	PUNCT
ejpam-7033	435	1	=	=	PUNCT
ejpam-7033	435	2	r(ϑ	r(ϑ	PROPN
ejpam-7033	435	3	,	,	PUNCT
ejpam-7033	435	4	ℏ2(ω	ℏ2(ω	ADJ
ejpam-7033	435	5	)	)	PUNCT
ejpam-7033	435	6	)	)	PUNCT
ejpam-7033	436	1	=	=	SYM
ejpam-7033	436	2	r(ϑ	r(ϑ	PROPN
ejpam-7033	436	3	,	,	PUNCT
ejpam-7033	436	4	ω	ω	NUM
ejpam-7033	436	5	)	)	PUNCT
ejpam-7033	436	6	=	=	SYM
ejpam-7033	436	7	(	(	PUNCT
ejpam-7033	436	8	0	0	NUM
ejpam-7033	436	9	,	,	PUNCT
ejpam-7033	436	10	1	1	NUM
ejpam-7033	436	11	4	4	NUM
ejpam-7033	436	12	,	,	PUNCT
ejpam-7033	436	13	1	1	NUM
ejpam-7033	436	14	4	4	NUM
ejpam-7033	436	15	)	)	PUNCT
ejpam-7033	436	16	,	,	PUNCT
ejpam-7033	436	17	(	(	PUNCT
ejpam-7033	436	18	i	i	PRON
ejpam-7033	436	19	−	−	PROPN
ejpam-7033	436	20	t	t	NOUN
ejpam-7033	436	21	)	)	PUNCT
ejpam-7033	436	22	2(i	2(i	NUM
ejpam-7033	437	1	+	+	NUM
ejpam-7033	437	2	t	t	NOUN
ejpam-7033	437	3	)	)	PUNCT
ejpam-7033	437	4	r(ϑ	r(ϑ	PROPN
ejpam-7033	437	5	,	,	PUNCT
ejpam-7033	437	6	ℏ(ϑ	ℏ(ϑ	PROPN
ejpam-7033	437	7	)	)	PUNCT
ejpam-7033	437	8	)	)	PUNCT
ejpam-7033	438	1	=	=	PUNCT
ejpam-7033	438	2	(	(	PUNCT
ejpam-7033	438	3	0	0	NUM
ejpam-7033	438	4	,	,	PUNCT
ejpam-7033	438	5	3	3	NUM
ejpam-7033	438	6	32	32	NUM
ejpam-7033	438	7	,	,	PUNCT
ejpam-7033	438	8	3	3	NUM
ejpam-7033	438	9	32	32	NUM
ejpam-7033	438	10	)	)	PUNCT
ejpam-7033	438	11	.	.	PUNCT
ejpam-7033	439	1	for	for	ADP
ejpam-7033	439	2	ϑ	ϑ	X
ejpam-7033	439	3	=	=	X
ejpam-7033	439	4	(	(	PUNCT
ejpam-7033	439	5	1	1	NUM
ejpam-7033	439	6	4	4	NUM
ejpam-7033	439	7	,	,	PUNCT
ejpam-7033	439	8	1	1	NUM
ejpam-7033	439	9	4	4	NUM
ejpam-7033	439	10	,	,	PUNCT
ejpam-7033	439	11	0	0	NUM
ejpam-7033	439	12	)	)	PUNCT
ejpam-7033	439	13	and	and	CCONJ
ejpam-7033	439	14	ω	ω	X
ejpam-7033	439	15	=	=	SYM
ejpam-7033	439	16	(	(	PUNCT
ejpam-7033	439	17	1	1	NUM
ejpam-7033	439	18	4	4	NUM
ejpam-7033	439	19	,	,	PUNCT
ejpam-7033	439	20	1	1	NUM
ejpam-7033	439	21	4	4	NUM
ejpam-7033	439	22	,	,	PUNCT
ejpam-7033	439	23	1	1	NUM
ejpam-7033	439	24	4	4	NUM
ejpam-7033	439	25	)	)	PUNCT
ejpam-7033	439	26	.	.	PUNCT
ejpam-7033	440	1	then	then	ADV
ejpam-7033	440	2	ℏ(ϑ	ℏ(ϑ	PROPN
ejpam-7033	440	3	)	)	PUNCT
ejpam-7033	440	4	=	=	PUNCT
ejpam-7033	440	5	(	(	PUNCT
ejpam-7033	440	6	14	14	NUM
ejpam-7033	440	7	,	,	PUNCT
ejpam-7033	440	8	0	0	NUM
ejpam-7033	440	9	,	,	PUNCT
ejpam-7033	440	10	0	0	NUM
ejpam-7033	440	11	)	)	PUNCT
ejpam-7033	440	12	=	=	SYM
ejpam-7033	441	1	ℏ2(ω	ℏ2(ω	ADJ
ejpam-7033	441	2	)	)	PUNCT
ejpam-7033	441	3	and	and	CCONJ
ejpam-7033	441	4	ℏ(ω	ℏ(ω	PROPN
ejpam-7033	441	5	)	)	PUNCT
ejpam-7033	441	6	=	=	PUNCT
ejpam-7033	442	1	(	(	PUNCT
ejpam-7033	442	2	1	1	NUM
ejpam-7033	442	3	4	4	NUM
ejpam-7033	442	4	,	,	PUNCT
ejpam-7033	442	5	1	1	NUM
ejpam-7033	442	6	4	4	NUM
ejpam-7033	442	7	,	,	PUNCT
ejpam-7033	442	8	0	0	NUM
ejpam-7033	442	9	)	)	PUNCT
ejpam-7033	442	10	.	.	PUNCT
ejpam-7033	443	1	r(ℏ(ϑ	r(ℏ(ϑ	NUM
ejpam-7033	443	2	)	)	PUNCT
ejpam-7033	443	3	,	,	PUNCT
ejpam-7033	443	4	ℏ(ω	ℏ(ω	NOUN
ejpam-7033	443	5	)	)	PUNCT
ejpam-7033	443	6	)	)	PUNCT
ejpam-7033	444	1	=	=	PUNCT
ejpam-7033	444	2	r(ϑ	r(ϑ	PROPN
ejpam-7033	444	3	,	,	PUNCT
ejpam-7033	444	4	ℏ(ϑ	ℏ(ϑ	PROPN
ejpam-7033	444	5	)	)	PUNCT
ejpam-7033	444	6	)	)	PUNCT
ejpam-7033	445	1	=	=	PUNCT
ejpam-7033	445	2	r(ϑ	r(ϑ	PROPN
ejpam-7033	445	3	,	,	PUNCT
ejpam-7033	445	4	ℏ2(ω	ℏ2(ω	ADJ
ejpam-7033	445	5	)	)	PUNCT
ejpam-7033	445	6	)	)	PUNCT
ejpam-7033	446	1	=	=	PUNCT
ejpam-7033	446	2	(	(	PUNCT
ejpam-7033	446	3	0	0	NUM
ejpam-7033	446	4	,	,	PUNCT
ejpam-7033	446	5	1	1	NUM
ejpam-7033	446	6	4	4	NUM
ejpam-7033	446	7	,	,	PUNCT
ejpam-7033	446	8	1	1	NUM
ejpam-7033	446	9	4	4	NUM
ejpam-7033	446	10	)	)	PUNCT
ejpam-7033	446	11	,	,	PUNCT
ejpam-7033	446	12	r(ϑ	r(ϑ	PROPN
ejpam-7033	446	13	,	,	PUNCT
ejpam-7033	446	14	ω	ω	NOUN
ejpam-7033	446	15	)	)	PUNCT
ejpam-7033	446	16	=	=	PUNCT
ejpam-7033	446	17	(	(	PUNCT
ejpam-7033	446	18	1	1	NUM
ejpam-7033	446	19	4	4	NUM
ejpam-7033	446	20	,	,	PUNCT
ejpam-7033	446	21	1	1	NUM
ejpam-7033	446	22	4	4	NUM
ejpam-7033	446	23	,	,	PUNCT
ejpam-7033	446	24	1	1	NUM
ejpam-7033	446	25	4	4	NUM
ejpam-7033	446	26	)	)	PUNCT
ejpam-7033	446	27	,	,	PUNCT
ejpam-7033	446	28	(	(	PUNCT
ejpam-7033	446	29	i	i	PRON
ejpam-7033	446	30	−	−	PROPN
ejpam-7033	447	1	t	t	NOUN
ejpam-7033	447	2	)	)	PUNCT
ejpam-7033	447	3	2(i	2(i	NUM
ejpam-7033	448	1	+	+	NUM
ejpam-7033	448	2	t	t	NOUN
ejpam-7033	448	3	)	)	PUNCT
ejpam-7033	448	4	r(ϑ	r(ϑ	PROPN
ejpam-7033	448	5	,	,	PUNCT
ejpam-7033	448	6	ℏ(ϑ	ℏ(ϑ	PROPN
ejpam-7033	448	7	)	)	PUNCT
ejpam-7033	448	8	)	)	PUNCT
ejpam-7033	449	1	=	=	PUNCT
ejpam-7033	449	2	(	(	PUNCT
ejpam-7033	449	3	0	0	NUM
ejpam-7033	449	4	,	,	PUNCT
ejpam-7033	449	5	3	3	NUM
ejpam-7033	449	6	32	32	NUM
ejpam-7033	449	7	,	,	PUNCT
ejpam-7033	449	8	3	3	NUM
ejpam-7033	449	9	32	32	NUM
ejpam-7033	449	10	)	)	PUNCT
ejpam-7033	449	11	.	.	PUNCT
ejpam-7033	450	1	take	take	VERB
ejpam-7033	450	2	ϑ	ϑ	NOUN
ejpam-7033	450	3	=	=	X
ejpam-7033	450	4	(	(	PUNCT
ejpam-7033	450	5	0	0	NUM
ejpam-7033	450	6	,	,	PUNCT
ejpam-7033	450	7	0	0	NUM
ejpam-7033	450	8	,	,	PUNCT
ejpam-7033	450	9	0	0	NUM
ejpam-7033	450	10	)	)	PUNCT
ejpam-7033	450	11	and	and	CCONJ
ejpam-7033	450	12	ω	ω	NUM
ejpam-7033	450	13	=	=	SYM
ejpam-7033	450	14	(	(	PUNCT
ejpam-7033	450	15	1	1	NUM
ejpam-7033	450	16	4	4	NUM
ejpam-7033	450	17	,	,	PUNCT
ejpam-7033	450	18	1	1	NUM
ejpam-7033	450	19	4	4	NUM
ejpam-7033	450	20	,	,	PUNCT
ejpam-7033	450	21	0	0	NUM
ejpam-7033	450	22	)	)	PUNCT
ejpam-7033	450	23	.	.	PUNCT
ejpam-7033	451	1	then	then	ADV
ejpam-7033	451	2	ℏ(ϑ	ℏ(ϑ	PROPN
ejpam-7033	451	3	)	)	PUNCT
ejpam-7033	451	4	=	=	SYM
ejpam-7033	451	5	(	(	PUNCT
ejpam-7033	451	6	0	0	NUM
ejpam-7033	451	7	,	,	PUNCT
ejpam-7033	451	8	0	0	NUM
ejpam-7033	451	9	,	,	PUNCT
ejpam-7033	451	10	0	0	NUM
ejpam-7033	451	11	)	)	PUNCT
ejpam-7033	451	12	=	=	SYM
ejpam-7033	452	1	ℏ2(ω	ℏ2(ω	ADJ
ejpam-7033	452	2	)	)	PUNCT
ejpam-7033	452	3	and	and	CCONJ
ejpam-7033	452	4	ℏ(ω	ℏ(ω	PROPN
ejpam-7033	452	5	)	)	PUNCT
ejpam-7033	452	6	=	=	PUNCT
ejpam-7033	453	1	(	(	PUNCT
ejpam-7033	453	2	1	1	NUM
ejpam-7033	453	3	4	4	NUM
ejpam-7033	453	4	,	,	PUNCT
ejpam-7033	453	5	0	0	NUM
ejpam-7033	453	6	,	,	PUNCT
ejpam-7033	453	7	0	0	NUM
ejpam-7033	453	8	)	)	PUNCT
ejpam-7033	453	9	.	.	PUNCT
ejpam-7033	454	1	r(ℏ(ϑ	r(ℏ(ϑ	NUM
ejpam-7033	454	2	)	)	PUNCT
ejpam-7033	454	3	,	,	PUNCT
ejpam-7033	454	4	ℏ(ω	ℏ(ω	NOUN
ejpam-7033	454	5	)	)	PUNCT
ejpam-7033	454	6	)	)	PUNCT
ejpam-7033	455	1	=	=	PUNCT
ejpam-7033	455	2	r(ϑ	r(ϑ	PROPN
ejpam-7033	455	3	,	,	PUNCT
ejpam-7033	455	4	ω	ω	NUM
ejpam-7033	455	5	)	)	PUNCT
ejpam-7033	455	6	=	=	SYM
ejpam-7033	455	7	(	(	PUNCT
ejpam-7033	455	8	0	0	NUM
ejpam-7033	455	9	,	,	PUNCT
ejpam-7033	455	10	1	1	NUM
ejpam-7033	455	11	4	4	NUM
ejpam-7033	455	12	,	,	PUNCT
ejpam-7033	455	13	1	1	NUM
ejpam-7033	455	14	4	4	NUM
ejpam-7033	455	15	)	)	PUNCT
ejpam-7033	455	16	and	and	CCONJ
ejpam-7033	455	17	r(ϑ	r(ϑ	PROPN
ejpam-7033	455	18	,	,	PUNCT
ejpam-7033	455	19	ℏ2(ω	ℏ2(ω	ADJ
ejpam-7033	455	20	)	)	PUNCT
ejpam-7033	455	21	)	)	PUNCT
ejpam-7033	456	1	=	=	SYM
ejpam-7033	456	2	(	(	PUNCT
ejpam-7033	456	3	0	0	NUM
ejpam-7033	456	4	,	,	PUNCT
ejpam-7033	456	5	0	0	NUM
ejpam-7033	456	6	,	,	PUNCT
ejpam-7033	456	7	0	0	NUM
ejpam-7033	456	8	)	)	PUNCT
ejpam-7033	456	9	,	,	PUNCT
ejpam-7033	456	10	(	(	PUNCT
ejpam-7033	456	11	i	i	PRON
ejpam-7033	456	12	−	−	PROPN
ejpam-7033	457	1	t	t	NOUN
ejpam-7033	457	2	)	)	PUNCT
ejpam-7033	457	3	2(i	2(i	NUM
ejpam-7033	458	1	+	+	NUM
ejpam-7033	458	2	t	t	NOUN
ejpam-7033	458	3	)	)	PUNCT
ejpam-7033	458	4	r(ϑ	r(ϑ	PROPN
ejpam-7033	458	5	,	,	PUNCT
ejpam-7033	458	6	ℏ(ϑ	ℏ(ϑ	PROPN
ejpam-7033	458	7	)	)	PUNCT
ejpam-7033	458	8	)	)	PUNCT
ejpam-7033	459	1	=	=	PUNCT
ejpam-7033	459	2	(	(	PUNCT
ejpam-7033	459	3	0	0	NUM
ejpam-7033	459	4	,	,	PUNCT
ejpam-7033	459	5	0	0	NUM
ejpam-7033	459	6	,	,	PUNCT
ejpam-7033	459	7	0	0	NUM
ejpam-7033	459	8	)	)	PUNCT
ejpam-7033	459	9	.	.	PUNCT
ejpam-7033	460	1	take	take	VERB
ejpam-7033	460	2	ϑ	ϑ	NOUN
ejpam-7033	460	3	=	=	X
ejpam-7033	460	4	(	(	PUNCT
ejpam-7033	460	5	0	0	NUM
ejpam-7033	460	6	,	,	PUNCT
ejpam-7033	460	7	0	0	NUM
ejpam-7033	460	8	,	,	PUNCT
ejpam-7033	460	9	0	0	NUM
ejpam-7033	460	10	)	)	PUNCT
ejpam-7033	460	11	and	and	CCONJ
ejpam-7033	460	12	ω	ω	NUM
ejpam-7033	460	13	=	=	SYM
ejpam-7033	460	14	(	(	PUNCT
ejpam-7033	460	15	1	1	NUM
ejpam-7033	460	16	4	4	NUM
ejpam-7033	460	17	,	,	PUNCT
ejpam-7033	460	18	1	1	NUM
ejpam-7033	460	19	4	4	NUM
ejpam-7033	460	20	,	,	PUNCT
ejpam-7033	460	21	1	1	NUM
ejpam-7033	460	22	4	4	NUM
ejpam-7033	460	23	)	)	PUNCT
ejpam-7033	460	24	.	.	PUNCT
ejpam-7033	461	1	then	then	ADV
ejpam-7033	461	2	ℏ(ϑ	ℏ(ϑ	PROPN
ejpam-7033	461	3	)	)	PUNCT
ejpam-7033	461	4	=	=	SYM
ejpam-7033	461	5	(	(	PUNCT
ejpam-7033	461	6	0	0	NUM
ejpam-7033	461	7	,	,	PUNCT
ejpam-7033	461	8	0	0	NUM
ejpam-7033	461	9	,	,	PUNCT
ejpam-7033	461	10	0	0	NUM
ejpam-7033	461	11	)	)	PUNCT
ejpam-7033	461	12	=	=	SYM
ejpam-7033	462	1	ℏ2(ω	ℏ2(ω	ADJ
ejpam-7033	462	2	)	)	PUNCT
ejpam-7033	462	3	and	and	CCONJ
ejpam-7033	462	4	ℏ(ω	ℏ(ω	PROPN
ejpam-7033	462	5	)	)	PUNCT
ejpam-7033	462	6	=	=	PUNCT
ejpam-7033	463	1	(	(	PUNCT
ejpam-7033	463	2	1	1	NUM
ejpam-7033	463	3	4	4	NUM
ejpam-7033	463	4	,	,	PUNCT
ejpam-7033	463	5	1	1	NUM
ejpam-7033	463	6	4	4	NUM
ejpam-7033	463	7	,	,	PUNCT
ejpam-7033	463	8	0	0	NUM
ejpam-7033	463	9	)	)	PUNCT
ejpam-7033	463	10	.	.	PUNCT
ejpam-7033	464	1	r(ℏ(ϑ	r(ℏ(ϑ	NUM
ejpam-7033	464	2	)	)	PUNCT
ejpam-7033	464	3	,	,	PUNCT
ejpam-7033	464	4	ℏ(ω	ℏ(ω	NOUN
ejpam-7033	464	5	)	)	PUNCT
ejpam-7033	464	6	)	)	PUNCT
ejpam-7033	465	1	=	=	PUNCT
ejpam-7033	465	2	r(ϑ	r(ϑ	PROPN
ejpam-7033	465	3	,	,	PUNCT
ejpam-7033	465	4	ω	ω	NUM
ejpam-7033	465	5	)	)	PUNCT
ejpam-7033	465	6	=	=	SYM
ejpam-7033	465	7	(	(	PUNCT
ejpam-7033	465	8	0	0	NUM
ejpam-7033	465	9	,	,	PUNCT
ejpam-7033	465	10	1	1	NUM
ejpam-7033	465	11	4	4	NUM
ejpam-7033	465	12	,	,	PUNCT
ejpam-7033	465	13	1	1	NUM
ejpam-7033	465	14	4	4	NUM
ejpam-7033	465	15	)	)	PUNCT
ejpam-7033	465	16	and	and	CCONJ
ejpam-7033	465	17	r(ϑ	r(ϑ	PROPN
ejpam-7033	465	18	,	,	PUNCT
ejpam-7033	465	19	ℏ2(ω	ℏ2(ω	ADJ
ejpam-7033	465	20	)	)	PUNCT
ejpam-7033	465	21	)	)	PUNCT
ejpam-7033	466	1	=	=	SYM
ejpam-7033	466	2	(	(	PUNCT
ejpam-7033	466	3	0	0	NUM
ejpam-7033	466	4	,	,	PUNCT
ejpam-7033	466	5	0	0	NUM
ejpam-7033	466	6	,	,	PUNCT
ejpam-7033	466	7	0	0	NUM
ejpam-7033	466	8	)	)	PUNCT
ejpam-7033	466	9	,	,	PUNCT
ejpam-7033	466	10	(	(	PUNCT
ejpam-7033	466	11	i	i	PRON
ejpam-7033	466	12	−	−	PROPN
ejpam-7033	467	1	t	t	NOUN
ejpam-7033	467	2	)	)	PUNCT
ejpam-7033	467	3	2(i	2(i	NUM
ejpam-7033	468	1	+	+	NUM
ejpam-7033	468	2	t	t	NOUN
ejpam-7033	468	3	)	)	PUNCT
ejpam-7033	468	4	r(ϑ	r(ϑ	PROPN
ejpam-7033	468	5	,	,	PUNCT
ejpam-7033	468	6	ℏ(ϑ	ℏ(ϑ	PROPN
ejpam-7033	468	7	)	)	PUNCT
ejpam-7033	468	8	)	)	PUNCT
ejpam-7033	469	1	=	=	PUNCT
ejpam-7033	469	2	(	(	PUNCT
ejpam-7033	469	3	0	0	NUM
ejpam-7033	469	4	,	,	PUNCT
ejpam-7033	469	5	0	0	NUM
ejpam-7033	469	6	,	,	PUNCT
ejpam-7033	469	7	0	0	NUM
ejpam-7033	469	8	)	)	PUNCT
ejpam-7033	469	9	.	.	PUNCT
ejpam-7033	470	1	take	take	VERB
ejpam-7033	470	2	ϑ	ϑ	NOUN
ejpam-7033	470	3	=	=	X
ejpam-7033	470	4	(	(	PUNCT
ejpam-7033	470	5	1	1	NUM
ejpam-7033	470	6	4	4	NUM
ejpam-7033	470	7	,	,	PUNCT
ejpam-7033	470	8	0	0	NUM
ejpam-7033	470	9	,	,	PUNCT
ejpam-7033	470	10	0	0	NUM
ejpam-7033	470	11	)	)	PUNCT
ejpam-7033	470	12	and	and	CCONJ
ejpam-7033	470	13	ω	ω	X
ejpam-7033	470	14	=	=	SYM
ejpam-7033	470	15	(	(	PUNCT
ejpam-7033	470	16	1	1	NUM
ejpam-7033	470	17	4	4	NUM
ejpam-7033	470	18	,	,	PUNCT
ejpam-7033	470	19	1	1	NUM
ejpam-7033	470	20	4	4	NUM
ejpam-7033	470	21	,	,	PUNCT
ejpam-7033	470	22	1	1	NUM
ejpam-7033	470	23	4	4	NUM
ejpam-7033	470	24	)	)	PUNCT
ejpam-7033	470	25	.	.	PUNCT
ejpam-7033	471	1	then	then	ADV
ejpam-7033	471	2	ℏ(ϑ	ℏ(ϑ	PROPN
ejpam-7033	471	3	)	)	PUNCT
ejpam-7033	471	4	=	=	SYM
ejpam-7033	471	5	(	(	PUNCT
ejpam-7033	471	6	0	0	NUM
ejpam-7033	471	7	,	,	PUNCT
ejpam-7033	471	8	0	0	NUM
ejpam-7033	471	9	,	,	PUNCT
ejpam-7033	471	10	0	0	NUM
ejpam-7033	471	11	)	)	PUNCT
ejpam-7033	471	12	=	=	SYM
ejpam-7033	472	1	ℏ2(ω	ℏ2(ω	ADJ
ejpam-7033	472	2	)	)	PUNCT
ejpam-7033	472	3	and	and	CCONJ
ejpam-7033	472	4	ℏ(ω	ℏ(ω	PROPN
ejpam-7033	472	5	)	)	PUNCT
ejpam-7033	472	6	=	=	PUNCT
ejpam-7033	473	1	(	(	PUNCT
ejpam-7033	473	2	1	1	NUM
ejpam-7033	473	3	4	4	NUM
ejpam-7033	473	4	,	,	PUNCT
ejpam-7033	473	5	1	1	NUM
ejpam-7033	473	6	4	4	NUM
ejpam-7033	473	7	,	,	PUNCT
ejpam-7033	473	8	0	0	NUM
ejpam-7033	473	9	)	)	PUNCT
ejpam-7033	473	10	.	.	PUNCT
ejpam-7033	474	1	r(ℏ(ϑ	r(ℏ(ϑ	NUM
ejpam-7033	474	2	)	)	PUNCT
ejpam-7033	474	3	,	,	PUNCT
ejpam-7033	474	4	ℏ(ω	ℏ(ω	NOUN
ejpam-7033	474	5	)	)	PUNCT
ejpam-7033	474	6	)	)	PUNCT
ejpam-7033	475	1	=	=	PUNCT
ejpam-7033	475	2	r(ϑ	r(ϑ	PROPN
ejpam-7033	475	3	,	,	PUNCT
ejpam-7033	475	4	ω	ω	NUM
ejpam-7033	475	5	)	)	PUNCT
ejpam-7033	475	6	=	=	PUNCT
ejpam-7033	475	7	(	(	PUNCT
ejpam-7033	475	8	3	3	NUM
ejpam-7033	475	9	4	4	NUM
ejpam-7033	475	10	,	,	PUNCT
ejpam-7033	475	11	3	3	NUM
ejpam-7033	475	12	4	4	NUM
ejpam-7033	475	13	,	,	PUNCT
ejpam-7033	475	14	3	3	NUM
ejpam-7033	475	15	4	4	NUM
ejpam-7033	475	16	)	)	PUNCT
ejpam-7033	475	17	and	and	CCONJ
ejpam-7033	475	18	r(ϑ	r(ϑ	PROPN
ejpam-7033	475	19	,	,	PUNCT
ejpam-7033	475	20	ℏ2(ω	ℏ2(ω	ADJ
ejpam-7033	475	21	)	)	PUNCT
ejpam-7033	475	22	)	)	PUNCT
ejpam-7033	476	1	=	=	SYM
ejpam-7033	476	2	(	(	PUNCT
ejpam-7033	476	3	0	0	NUM
ejpam-7033	476	4	,	,	PUNCT
ejpam-7033	476	5	0	0	NUM
ejpam-7033	476	6	,	,	PUNCT
ejpam-7033	476	7	0	0	NUM
ejpam-7033	476	8	)	)	PUNCT
ejpam-7033	476	9	,	,	PUNCT
ejpam-7033	476	10	a.	a.	PROPN
ejpam-7033	476	11	arif	arif	PROPN
ejpam-7033	476	12	et	et	PROPN
ejpam-7033	476	13	al	al	PROPN
ejpam-7033	476	14	.	.	PUNCT
ejpam-7033	476	15	/	/	SYM
ejpam-7033	476	16	eur	eur	PROPN
ejpam-7033	476	17	.	.	PUNCT
ejpam-7033	477	1	j.	j.	PROPN
ejpam-7033	477	2	pure	pure	PROPN
ejpam-7033	477	3	appl	appl	PROPN
ejpam-7033	477	4	.	.	PROPN
ejpam-7033	477	5	math	math	PROPN
ejpam-7033	477	6	,	,	PUNCT
ejpam-7033	477	7	18	18	NUM
ejpam-7033	477	8	(	(	PUNCT
ejpam-7033	477	9	4	4	NUM
ejpam-7033	477	10	)	)	PUNCT
ejpam-7033	477	11	(	(	PUNCT
ejpam-7033	477	12	2025	2025	NUM
ejpam-7033	477	13	)	)	PUNCT
ejpam-7033	477	14	,	,	PUNCT
ejpam-7033	477	15	7033	7033	NUM
ejpam-7033	477	16	16	16	NUM
ejpam-7033	477	17	of	of	ADP
ejpam-7033	477	18	29	29	NUM
ejpam-7033	477	19	(	(	PUNCT
ejpam-7033	477	20	i	i	PRON
ejpam-7033	477	21	−	−	PROPN
ejpam-7033	478	1	t	t	NOUN
ejpam-7033	478	2	)	)	PUNCT
ejpam-7033	478	3	2(i	2(i	NUM
ejpam-7033	479	1	+	+	NUM
ejpam-7033	479	2	t	t	NOUN
ejpam-7033	479	3	)	)	PUNCT
ejpam-7033	479	4	r(ϑ	r(ϑ	PROPN
ejpam-7033	479	5	,	,	PUNCT
ejpam-7033	479	6	ℏ(ϑ	ℏ(ϑ	PROPN
ejpam-7033	479	7	)	)	PUNCT
ejpam-7033	479	8	)	)	PUNCT
ejpam-7033	480	1	=	=	PUNCT
ejpam-7033	480	2	(	(	PUNCT
ejpam-7033	480	3	0	0	NUM
ejpam-7033	480	4	,	,	PUNCT
ejpam-7033	480	5	3	3	NUM
ejpam-7033	480	6	32	32	NUM
ejpam-7033	480	7	,	,	PUNCT
ejpam-7033	480	8	3	3	NUM
ejpam-7033	480	9	32	32	NUM
ejpam-7033	480	10	)	)	PUNCT
ejpam-7033	480	11	.	.	PUNCT
ejpam-7033	481	1	define	define	VERB
ejpam-7033	481	2	for	for	ADP
ejpam-7033	481	3	α	α	PRON
ejpam-7033	481	4	∈	∈	PROPN
ejpam-7033	482	1	[	[	X
ejpam-7033	482	2	1,∞	1,∞	NUM
ejpam-7033	482	3	)	)	PUNCT
ejpam-7033	482	4	,	,	PUNCT
ejpam-7033	482	5	and	and	CCONJ
ejpam-7033	482	6	j	j	PROPN
ejpam-7033	482	7	∈	∈	PROPN
ejpam-7033	483	1	f	f	PROPN
ejpam-7033	483	2	j	j	PROPN
ejpam-7033	483	3	(	(	PUNCT
ejpam-7033	483	4	r(ℏ(ϑ	r(ℏ(ϑ	NOUN
ejpam-7033	483	5	)	)	PUNCT
ejpam-7033	483	6	,	,	PUNCT
ejpam-7033	483	7	ℏ(ω)),r(ϑ	ℏ(ω)),r(ϑ	PROPN
ejpam-7033	483	8	,	,	PUNCT
ejpam-7033	483	9	ω),r(ϑ	ω),r(ϑ	NUM
ejpam-7033	483	10	,	,	PUNCT
ejpam-7033	483	11	ℏ(ϑ	ℏ(ϑ	PROPN
ejpam-7033	483	12	)	)	PUNCT
ejpam-7033	483	13	)	)	PUNCT
ejpam-7033	483	14	,	,	PUNCT
ejpam-7033	483	15	r(ω	r(ω	ADV
ejpam-7033	483	16	,	,	PUNCT
ejpam-7033	483	17	ℏ(ω)),r(ϑ	ℏ(ω)),r(ϑ	PROPN
ejpam-7033	483	18	,	,	PUNCT
ejpam-7033	483	19	ℏ2(ω)),r(ω	ℏ2(ω)),r(ω	PROPN
ejpam-7033	483	20	,	,	PUNCT
ejpam-7033	483	21	ℏ2(ϑ	ℏ2(ϑ	NOUN
ejpam-7033	483	22	)	)	PUNCT
ejpam-7033	483	23	)	)	PUNCT
ejpam-7033	483	24	)	)	PUNCT
ejpam-7033	484	1	=	=	PUNCT
ejpam-7033	484	2	r(ϑ	r(ϑ	PROPN
ejpam-7033	484	3	,	,	PUNCT
ejpam-7033	484	4	ℏ2(ω))−	ℏ2(ω))−	VERB
ejpam-7033	485	1	[	[	X
ejpam-7033	485	2	αr(ℏ(ϑ	αr(ℏ(ϑ	NUM
ejpam-7033	485	3	)	)	PUNCT
ejpam-7033	485	4	,	,	PUNCT
ejpam-7033	485	5	ℏ(ω	ℏ(ω	PROPN
ejpam-7033	485	6	)	)	PUNCT
ejpam-7033	485	7	)	)	PUNCT
ejpam-7033	486	1	+	+	CCONJ
ejpam-7033	486	2	r(ϑ	r(ϑ	PROPN
ejpam-7033	486	3	,	,	PUNCT
ejpam-7033	486	4	ω	ω	NOUN
ejpam-7033	486	5	)	)	PUNCT
ejpam-7033	486	6	]	]	PUNCT
ejpam-7033	486	7	.	.	PUNCT
ejpam-7033	487	1	thus	thus	ADV
ejpam-7033	487	2	,	,	PUNCT
ejpam-7033	487	3	(	(	PUNCT
ejpam-7033	487	4	i	i	PRON
ejpam-7033	487	5	−	−	PROPN
ejpam-7033	487	6	t	t	NOUN
ejpam-7033	487	7	)	)	PUNCT
ejpam-7033	487	8	2(i	2(i	NUM
ejpam-7033	488	1	+	+	NUM
ejpam-7033	488	2	t	t	NOUN
ejpam-7033	488	3	)	)	PUNCT
ejpam-7033	489	1	r(ϑ	r(ϑ	PROPN
ejpam-7033	489	2	,	,	PUNCT
ejpam-7033	489	3	ℏ(ϑ	ℏ(ϑ	PROPN
ejpam-7033	489	4	)	)	PUNCT
ejpam-7033	489	5	)	)	PUNCT
ejpam-7033	490	1	⪯	⪯	PROPN
ejpam-7033	490	2	r(ϑ	r(ϑ	PROPN
ejpam-7033	490	3	,	,	PUNCT
ejpam-7033	490	4	ω	ω	NOUN
ejpam-7033	490	5	)	)	PUNCT
ejpam-7033	490	6	implies	imply	VERB
ejpam-7033	490	7	j	j	PROPN
ejpam-7033	490	8	(	(	PUNCT
ejpam-7033	490	9	r(ℏ(ϑ	r(ℏ(ϑ	NOUN
ejpam-7033	490	10	)	)	PUNCT
ejpam-7033	490	11	,	,	PUNCT
ejpam-7033	490	12	ℏ(ω)),r(ϑ	ℏ(ω)),r(ϑ	PROPN
ejpam-7033	490	13	,	,	PUNCT
ejpam-7033	490	14	ω),r(ϑ	ω),r(ϑ	NUM
ejpam-7033	490	15	,	,	PUNCT
ejpam-7033	490	16	ℏ(ϑ)),r(ω	ℏ(ϑ)),r(ω	PROPN
ejpam-7033	490	17	,	,	PUNCT
ejpam-7033	490	18	ℏ(ω	ℏ(ω	NOUN
ejpam-7033	490	19	)	)	PUNCT
ejpam-7033	490	20	)	)	PUNCT
ejpam-7033	490	21	,	,	PUNCT
ejpam-7033	490	22	r(ϑ	r(ϑ	PROPN
ejpam-7033	490	23	,	,	PUNCT
ejpam-7033	490	24	ℏ2(ω)),r(ω	ℏ2(ω)),r(ω	PROPN
ejpam-7033	490	25	,	,	PUNCT
ejpam-7033	490	26	ℏ2(ϑ	ℏ2(ϑ	NOUN
ejpam-7033	490	27	)	)	PUNCT
ejpam-7033	490	28	)	)	PUNCT
ejpam-7033	490	29	)	)	PUNCT
ejpam-7033	491	1	⪯	⪯	NOUN
ejpam-7033	491	2	0	0	NUM
ejpam-7033	491	3	.	.	PUNCT
ejpam-7033	492	1	so	so	ADV
ejpam-7033	492	2	all	all	DET
ejpam-7033	492	3	assumptions	assumption	NOUN
ejpam-7033	492	4	of	of	ADP
ejpam-7033	492	5	theorem	theorem	NOUN
ejpam-7033	492	6	15	15	NUM
ejpam-7033	492	7	are	be	AUX
ejpam-7033	492	8	justified	justify	VERB
ejpam-7033	492	9	and	and	CCONJ
ejpam-7033	492	10	ℏ(0	ℏ(0	PROPN
ejpam-7033	492	11	,	,	PUNCT
ejpam-7033	492	12	0	0	NUM
ejpam-7033	492	13	,	,	PUNCT
ejpam-7033	492	14	0	0	NUM
ejpam-7033	492	15	)	)	PUNCT
ejpam-7033	492	16	=	=	SYM
ejpam-7033	493	1	(	(	PUNCT
ejpam-7033	493	2	0	0	NUM
ejpam-7033	493	3	,	,	PUNCT
ejpam-7033	493	4	0	0	NUM
ejpam-7033	493	5	,	,	PUNCT
ejpam-7033	493	6	0	0	NUM
ejpam-7033	493	7	)	)	PUNCT
ejpam-7033	493	8	.	.	PUNCT
ejpam-7033	494	1	example	example	NOUN
ejpam-7033	495	1	7	7	NUM
ejpam-7033	495	2	.	.	PUNCT
ejpam-7033	496	1	let	let	VERB
ejpam-7033	496	2	e	e	NOUN
ejpam-7033	496	3	=	=	PUNCT
ejpam-7033	496	4	(	(	PUNCT
ejpam-7033	496	5	r	r	NOUN
ejpam-7033	496	6	,	,	PUNCT
ejpam-7033	496	7	∥	∥	X
ejpam-7033	496	8	·	·	PUNCT
ejpam-7033	496	9	∥	∥	NUM
ejpam-7033	496	10	)	)	PUNCT
ejpam-7033	496	11	,	,	PUNCT
ejpam-7033	496	12	then	then	ADV
ejpam-7033	496	13	it	it	PRON
ejpam-7033	496	14	is	be	AUX
ejpam-7033	496	15	a	a	DET
ejpam-7033	496	16	real	real	ADJ
ejpam-7033	496	17	banach	banach	NOUN
ejpam-7033	496	18	space	space	NOUN
ejpam-7033	496	19	and	and	CCONJ
ejpam-7033	496	20	c	c	NOUN
ejpam-7033	496	21	=	=	PUNCT
ejpam-7033	496	22	{	{	PUNCT
ejpam-7033	496	23	ϑ	ϑ	X
ejpam-7033	496	24	∈	∈	NOUN
ejpam-7033	496	25	r	r	NOUN
ejpam-7033	496	26	:	:	PUNCT
ejpam-7033	496	27	ϑ	ϑ	X
ejpam-7033	496	28	≥	≥	NOUN
ejpam-7033	496	29	0	0	NUM
ejpam-7033	496	30	}	}	PUNCT
ejpam-7033	496	31	is	be	AUX
ejpam-7033	496	32	a	a	DET
ejpam-7033	496	33	cone	cone	NOUN
ejpam-7033	496	34	in	in	ADP
ejpam-7033	496	35	e.	e.	PROPN
ejpam-7033	496	36	let	let	VERB
ejpam-7033	496	37	x	x	PUNCT
ejpam-7033	496	38	=	=	PRON
ejpam-7033	496	39	{	{	PUNCT
ejpam-7033	496	40	1	1	NUM
ejpam-7033	496	41	,	,	PUNCT
ejpam-7033	496	42	2	2	NUM
ejpam-7033	496	43	,	,	PUNCT
ejpam-7033	496	44	3	3	NUM
ejpam-7033	496	45	,	,	PUNCT
ejpam-7033	496	46	4	4	NUM
ejpam-7033	496	47	}	}	PUNCT
ejpam-7033	496	48	and	and	CCONJ
ejpam-7033	496	49	define	define	VERB
ejpam-7033	496	50	ℏ	ℏ	PROPN
ejpam-7033	496	51	:	:	PUNCT
ejpam-7033	496	52	x	x	SYM
ejpam-7033	496	53	→	→	SYM
ejpam-7033	496	54	x	x	PUNCT
ejpam-7033	496	55	by	by	ADP
ejpam-7033	496	56	ℏ(1	ℏ(1	NOUN
ejpam-7033	496	57	)	)	PUNCT
ejpam-7033	497	1	=	=	SYM
ejpam-7033	497	2	ℏ(2	ℏ(2	PROPN
ejpam-7033	497	3	)	)	PUNCT
ejpam-7033	497	4	=	=	SYM
ejpam-7033	497	5	1	1	NUM
ejpam-7033	497	6	and	and	CCONJ
ejpam-7033	497	7	ℏ(4	ℏ(4	NOUN
ejpam-7033	497	8	)	)	PUNCT
ejpam-7033	497	9	=	=	SYM
ejpam-7033	497	10	ℏ(3	ℏ(3	PROPN
ejpam-7033	497	11	)	)	PUNCT
ejpam-7033	497	12	=	=	SYM
ejpam-7033	497	13	2	2	X
ejpam-7033	497	14	.	.	X
ejpam-7033	497	15	define	define	VERB
ejpam-7033	497	16	r	r	NOUN
ejpam-7033	497	17	by	by	ADP
ejpam-7033	497	18	r(ϑ1	r(ϑ1	NOUN
ejpam-7033	497	19	,	,	PUNCT
ejpam-7033	497	20	ϑ2	ϑ2	NOUN
ejpam-7033	497	21	)	)	PUNCT
ejpam-7033	497	22	=	=	PUNCT
ejpam-7033	498	1			PUNCT
ejpam-7033	498	2	0	0	NUM
ejpam-7033	499	1	if	if	SCONJ
ejpam-7033	499	2	ϑ1	ϑ1	NOUN
ejpam-7033	499	3	=	=	SYM
ejpam-7033	499	4	ϑ2	ϑ2	NOUN
ejpam-7033	499	5	et	et	NOUN
ejpam-7033	499	6	3	3	NUM
ejpam-7033	499	7	if	if	SCONJ
ejpam-7033	499	8	ϑ1	ϑ1	PROPN
ejpam-7033	499	9	,	,	PUNCT
ejpam-7033	499	10	ϑ2	ϑ2	PROPN
ejpam-7033	499	11	∈	∈	PROPN
ejpam-7033	499	12	{	{	PUNCT
ejpam-7033	499	13	1	1	NUM
ejpam-7033	499	14	,	,	PUNCT
ejpam-7033	499	15	2	2	NUM
ejpam-7033	499	16	}	}	PUNCT
ejpam-7033	499	17	et	et	NOUN
ejpam-7033	499	18	2	2	NUM
ejpam-7033	499	19	if	if	SCONJ
ejpam-7033	499	20	(	(	PUNCT
ejpam-7033	499	21	ϑ1	ϑ1	NOUN
ejpam-7033	499	22	,	,	PUNCT
ejpam-7033	499	23	ϑ2	ϑ2	PROPN
ejpam-7033	499	24	)	)	PUNCT
ejpam-7033	499	25	∈	∈	PROPN
ejpam-7033	499	26	{	{	PUNCT
ejpam-7033	499	27	3	3	NUM
ejpam-7033	499	28	,	,	PUNCT
ejpam-7033	499	29	4	4	NUM
ejpam-7033	499	30	}	}	PUNCT
ejpam-7033	499	31	et	et	NOUN
ejpam-7033	499	32	otherwise	otherwise	ADV
ejpam-7033	499	33	.	.	PUNCT
ejpam-7033	500	1	note	note	VERB
ejpam-7033	500	2	that	that	SCONJ
ejpam-7033	500	3	et	et	PRON
ejpam-7033	500	4	=	=	PUNCT
ejpam-7033	500	5	r(2	r(2	PROPN
ejpam-7033	500	6	,	,	PUNCT
ejpam-7033	500	7	4	4	NUM
ejpam-7033	500	8	)	)	PUNCT
ejpam-7033	500	9	≥	≥	NOUN
ejpam-7033	500	10	r(2	r(2	NOUN
ejpam-7033	500	11	,	,	PUNCT
ejpam-7033	500	12	1	1	NUM
ejpam-7033	500	13	)	)	PUNCT
ejpam-7033	500	14	+	+	CCONJ
ejpam-7033	500	15	r(1	r(1	PROPN
ejpam-7033	500	16	,	,	PUNCT
ejpam-7033	500	17	3	3	NUM
ejpam-7033	500	18	)	)	PUNCT
ejpam-7033	500	19	+	+	CCONJ
ejpam-7033	501	1	r(3	r(3	PROPN
ejpam-7033	501	2	,	,	PUNCT
ejpam-7033	501	3	4	4	X
ejpam-7033	501	4	)	)	PUNCT
ejpam-7033	501	5	=	=	SYM
ejpam-7033	502	1	5et	5et	NOUN
ejpam-7033	502	2	6	6	NUM
ejpam-7033	502	3	.	.	PUNCT
ejpam-7033	503	1	for	for	ADP
ejpam-7033	503	2	s	s	NOUN
ejpam-7033	503	3	=	=	SYM
ejpam-7033	503	4	6	6	NUM
ejpam-7033	503	5	5	5	NUM
ejpam-7033	503	6	,	,	PUNCT
ejpam-7033	503	7	r	r	NOUN
ejpam-7033	503	8	represents	represent	VERB
ejpam-7033	503	9	rcbm	rcbm	ADJ
ejpam-7033	503	10	but	but	CCONJ
ejpam-7033	503	11	not	not	PART
ejpam-7033	503	12	rcm	rcm	PROPN
ejpam-7033	503	13	.	.	PUNCT
ejpam-7033	504	1	define	define	VERB
ejpam-7033	504	2	t	t	PROPN
ejpam-7033	504	3	:	:	PUNCT
ejpam-7033	504	4	e	e	X
ejpam-7033	504	5	→	→	SYM
ejpam-7033	504	6	e	e	X
ejpam-7033	504	7	by	by	ADP
ejpam-7033	504	8	t	t	PROPN
ejpam-7033	504	9	(	(	PUNCT
ejpam-7033	504	10	ϑ	ϑ	X
ejpam-7033	504	11	)	)	PUNCT
ejpam-7033	504	12	=	=	SYM
ejpam-7033	504	13	ϑ	ϑ	X
ejpam-7033	504	14	3	3	NUM
ejpam-7033	504	15	,	,	PUNCT
ejpam-7033	504	16	clearly	clearly	ADV
ejpam-7033	504	17	∥t	∥t	VERB
ejpam-7033	504	18	∥1	∥1	PRON
ejpam-7033	504	19	<	<	X
ejpam-7033	504	20	1	1	X
ejpam-7033	504	21	.	.	X
ejpam-7033	504	22	take	take	VERB
ejpam-7033	504	23	ϑ	ϑ	NOUN
ejpam-7033	504	24	=	=	SYM
ejpam-7033	504	25	1	1	NUM
ejpam-7033	504	26	and	and	CCONJ
ejpam-7033	504	27	ω	ω	NUM
ejpam-7033	504	28	=	=	SYM
ejpam-7033	504	29	2	2	NUM
ejpam-7033	504	30	,	,	PUNCT
ejpam-7033	504	31	then	then	ADV
ejpam-7033	504	32	r(ω	r(ω	ADV
ejpam-7033	504	33	,	,	PUNCT
ejpam-7033	504	34	ℏ(ω	ℏ(ω	NOUN
ejpam-7033	504	35	)	)	PUNCT
ejpam-7033	504	36	)	)	PUNCT
ejpam-7033	505	1	=	=	PUNCT
ejpam-7033	505	2	r(ϑ	r(ϑ	PROPN
ejpam-7033	505	3	,	,	PUNCT
ejpam-7033	505	4	ω	ω	NUM
ejpam-7033	505	5	)	)	PUNCT
ejpam-7033	505	6	=	=	SYM
ejpam-7033	505	7	r(ω	r(ω	ADJ
ejpam-7033	505	8	,	,	PUNCT
ejpam-7033	505	9	ℏ2(ϑ	ℏ2(ϑ	NOUN
ejpam-7033	505	10	)	)	PUNCT
ejpam-7033	505	11	)	)	PUNCT
ejpam-7033	506	1	=	=	SYM
ejpam-7033	506	2	et	et	NOUN
ejpam-7033	506	3	3	3	NUM
ejpam-7033	506	4	,	,	PUNCT
ejpam-7033	506	5	r(ϑ	r(ϑ	PROPN
ejpam-7033	506	6	,	,	PUNCT
ejpam-7033	506	7	ℏ(ϑ	ℏ(ϑ	PROPN
ejpam-7033	506	8	)	)	PUNCT
ejpam-7033	506	9	)	)	PUNCT
ejpam-7033	507	1	=	=	SYM
ejpam-7033	507	2	r(ℏ(ϑ	r(ℏ(ϑ	NUM
ejpam-7033	507	3	)	)	PUNCT
ejpam-7033	507	4	,	,	PUNCT
ejpam-7033	507	5	ℏ(ω	ℏ(ω	NOUN
ejpam-7033	507	6	)	)	PUNCT
ejpam-7033	507	7	)	)	PUNCT
ejpam-7033	508	1	=	=	PUNCT
ejpam-7033	508	2	0	0	X
ejpam-7033	508	3	.	.	X
ejpam-7033	508	4	take	take	VERB
ejpam-7033	508	5	ϑ	ϑ	NOUN
ejpam-7033	508	6	=	=	SYM
ejpam-7033	508	7	2	2	NUM
ejpam-7033	508	8	and	and	CCONJ
ejpam-7033	508	9	ω	ω	NUM
ejpam-7033	508	10	=	=	SYM
ejpam-7033	508	11	3	3	NUM
ejpam-7033	508	12	,	,	PUNCT
ejpam-7033	508	13	then	then	ADV
ejpam-7033	508	14	r(ϑ	r(ϑ	PROPN
ejpam-7033	508	15	,	,	PUNCT
ejpam-7033	508	16	ω	ω	NUM
ejpam-7033	508	17	)	)	PUNCT
ejpam-7033	509	1	=	=	SYM
ejpam-7033	509	2	r(ϑ	r(ϑ	PROPN
ejpam-7033	509	3	,	,	PUNCT
ejpam-7033	509	4	ℏ(ϑ	ℏ(ϑ	PROPN
ejpam-7033	509	5	)	)	PUNCT
ejpam-7033	509	6	)	)	PUNCT
ejpam-7033	510	1	=	=	PUNCT
ejpam-7033	510	2	r(ω	r(ω	ADV
ejpam-7033	510	3	,	,	PUNCT
ejpam-7033	510	4	ℏ2(ϑ	ℏ2(ϑ	NOUN
ejpam-7033	510	5	)	)	PUNCT
ejpam-7033	510	6	)	)	PUNCT
ejpam-7033	511	1	=	=	PUNCT
ejpam-7033	511	2	r(ω	r(ω	ADJ
ejpam-7033	511	3	,	,	PUNCT
ejpam-7033	511	4	ℏ(ω	ℏ(ω	NOUN
ejpam-7033	511	5	)	)	PUNCT
ejpam-7033	511	6	)	)	PUNCT
ejpam-7033	512	1	=	=	SYM
ejpam-7033	512	2	et	et	NOUN
ejpam-7033	512	3	3	3	NUM
ejpam-7033	512	4	.	.	PUNCT
ejpam-7033	513	1	as	as	ADP
ejpam-7033	513	2	(	(	PUNCT
ejpam-7033	513	3	i	i	PRON
ejpam-7033	513	4	+	+	X
ejpam-7033	513	5	t	t	NOUN
ejpam-7033	513	6	)	)	PUNCT
ejpam-7033	513	7	(	(	PUNCT
ejpam-7033	513	8	i	i	PRON
ejpam-7033	513	9	−	−	PROPN
ejpam-7033	513	10	t	t	NOUN
ejpam-7033	513	11	)	)	PUNCT
ejpam-7033	513	12	2r(ϑ	2r(ϑ	NUM
ejpam-7033	513	13	,	,	PUNCT
ejpam-7033	513	14	ℏ(ϑ	ℏ(ϑ	PROPN
ejpam-7033	513	15	)	)	PUNCT
ejpam-7033	513	16	)	)	PUNCT
ejpam-7033	514	1	=	=	PUNCT
ejpam-7033	515	1	(	(	PUNCT
ejpam-7033	515	2	i	i	PRON
ejpam-7033	515	3	−	−	PROPN
ejpam-7033	515	4	t	t	NOUN
ejpam-7033	515	5	)	)	PUNCT
ejpam-7033	515	6	(	(	PUNCT
ejpam-7033	515	7	i	i	PRON
ejpam-7033	515	8	−	−	PROPN
ejpam-7033	515	9	t	t	PROPN
ejpam-7033	515	10	2)r(ϑ	2)r(ϑ	NUM
ejpam-7033	515	11	,	,	PUNCT
ejpam-7033	515	12	ℏ(ϑ	ℏ(ϑ	PROPN
ejpam-7033	515	13	)	)	PUNCT
ejpam-7033	515	14	)	)	PUNCT
ejpam-7033	515	15	.	.	PUNCT
ejpam-7033	516	1	we	we	PRON
ejpam-7033	516	2	get	get	VERB
ejpam-7033	516	3	(	(	PUNCT
ejpam-7033	516	4	i	i	PRON
ejpam-7033	516	5	−	−	PROPN
ejpam-7033	516	6	t	t	NOUN
ejpam-7033	516	7	)	)	PUNCT
ejpam-7033	516	8	(	(	PUNCT
ejpam-7033	516	9	i	i	PRON
ejpam-7033	516	10	−	−	PROPN
ejpam-7033	516	11	t	t	PROPN
ejpam-7033	516	12	2)r(ϑ	2)r(ϑ	NUM
ejpam-7033	516	13	,	,	PUNCT
ejpam-7033	516	14	ℏ(ϑ	ℏ(ϑ	PROPN
ejpam-7033	516	15	)	)	PUNCT
ejpam-7033	516	16	)	)	PUNCT
ejpam-7033	516	17	=	=	PUNCT
ejpam-7033	517	1	17et	17et	ADJ
ejpam-7033	517	2	81	81	NUM
ejpam-7033	517	3	.	.	PUNCT
ejpam-7033	518	1	a.	a.	PROPN
ejpam-7033	518	2	arif	arif	PROPN
ejpam-7033	518	3	et	et	PROPN
ejpam-7033	518	4	al	al	PROPN
ejpam-7033	518	5	.	.	PUNCT
ejpam-7033	518	6	/	/	SYM
ejpam-7033	518	7	eur	eur	PROPN
ejpam-7033	518	8	.	.	PUNCT
ejpam-7033	519	1	j.	j.	PROPN
ejpam-7033	519	2	pure	pure	PROPN
ejpam-7033	519	3	appl	appl	PROPN
ejpam-7033	519	4	.	.	PROPN
ejpam-7033	519	5	math	math	PROPN
ejpam-7033	519	6	,	,	PUNCT
ejpam-7033	519	7	18	18	NUM
ejpam-7033	519	8	(	(	PUNCT
ejpam-7033	519	9	4	4	NUM
ejpam-7033	519	10	)	)	PUNCT
ejpam-7033	519	11	(	(	PUNCT
ejpam-7033	519	12	2025	2025	NUM
ejpam-7033	519	13	)	)	PUNCT
ejpam-7033	519	14	,	,	PUNCT
ejpam-7033	519	15	7033	7033	NUM
ejpam-7033	519	16	17	17	NUM
ejpam-7033	519	17	of	of	ADP
ejpam-7033	519	18	29	29	NUM
ejpam-7033	519	19	take	take	VERB
ejpam-7033	519	20	ϑ	ϑ	NOUN
ejpam-7033	519	21	=	=	SYM
ejpam-7033	519	22	3	3	NUM
ejpam-7033	519	23	and	and	CCONJ
ejpam-7033	519	24	ω	ω	NUM
ejpam-7033	519	25	=	=	SYM
ejpam-7033	519	26	4	4	NUM
ejpam-7033	519	27	,	,	PUNCT
ejpam-7033	519	28	then	then	ADV
ejpam-7033	519	29	r(ω	r(ω	ADV
ejpam-7033	519	30	,	,	PUNCT
ejpam-7033	519	31	ℏ(ω	ℏ(ω	NOUN
ejpam-7033	519	32	)	)	PUNCT
ejpam-7033	519	33	)	)	PUNCT
ejpam-7033	520	1	=	=	PUNCT
ejpam-7033	520	2	r(ω	r(ω	ADV
ejpam-7033	520	3	,	,	PUNCT
ejpam-7033	520	4	ℏ2(ϑ	ℏ2(ϑ	NOUN
ejpam-7033	520	5	)	)	PUNCT
ejpam-7033	520	6	)	)	PUNCT
ejpam-7033	520	7	=	=	SYM
ejpam-7033	520	8	et	et	NOUN
ejpam-7033	520	9	,	,	PUNCT
ejpam-7033	520	10	r(ϑ	r(ϑ	PROPN
ejpam-7033	520	11	,	,	PUNCT
ejpam-7033	520	12	ℏ(ϑ	ℏ(ϑ	PROPN
ejpam-7033	520	13	)	)	PUNCT
ejpam-7033	520	14	)	)	PUNCT
ejpam-7033	521	1	=	=	SYM
ejpam-7033	521	2	et	et	NOUN
ejpam-7033	521	3	3	3	NUM
ejpam-7033	521	4	,	,	PUNCT
ejpam-7033	521	5	r(ϑ	r(ϑ	PROPN
ejpam-7033	521	6	,	,	PUNCT
ejpam-7033	521	7	ω	ω	NOUN
ejpam-7033	521	8	)	)	PUNCT
ejpam-7033	521	9	=	=	SYM
ejpam-7033	521	10	et	et	NOUN
ejpam-7033	521	11	2	2	NUM
ejpam-7033	521	12	.	.	PUNCT
ejpam-7033	522	1	(	(	PUNCT
ejpam-7033	522	2	i	i	PRON
ejpam-7033	522	3	−	−	PROPN
ejpam-7033	523	1	t	t	NOUN
ejpam-7033	523	2	)	)	PUNCT
ejpam-7033	524	1	(	(	PUNCT
ejpam-7033	524	2	i	i	PRON
ejpam-7033	524	3	−	−	PROPN
ejpam-7033	524	4	t	t	PROPN
ejpam-7033	524	5	2)r(ϑ	2)r(ϑ	NUM
ejpam-7033	524	6	,	,	PUNCT
ejpam-7033	524	7	ℏ(ϑ	ℏ(ϑ	PROPN
ejpam-7033	524	8	)	)	PUNCT
ejpam-7033	524	9	)	)	PUNCT
ejpam-7033	525	1	=	=	PUNCT
ejpam-7033	525	2	17et	17et	ADJ
ejpam-7033	525	3	81	81	NUM
ejpam-7033	525	4	.	.	PUNCT
ejpam-7033	526	1	for	for	ADP
ejpam-7033	526	2	j	j	PROPN
ejpam-7033	526	3	∈	∈	PROPN
ejpam-7033	526	4	f	f	PROPN
ejpam-7033	526	5	,	,	PUNCT
ejpam-7033	526	6	define	define	VERB
ejpam-7033	526	7	j	j	PROPN
ejpam-7033	526	8	(	(	PUNCT
ejpam-7033	526	9	r(ℏ(ϑ	r(ℏ(ϑ	NOUN
ejpam-7033	526	10	)	)	PUNCT
ejpam-7033	526	11	,	,	PUNCT
ejpam-7033	526	12	ℏ(ω)),r(ϑ	ℏ(ω)),r(ϑ	PROPN
ejpam-7033	526	13	,	,	PUNCT
ejpam-7033	526	14	ω),r(ϑ	ω),r(ϑ	NUM
ejpam-7033	526	15	,	,	PUNCT
ejpam-7033	526	16	ℏ(ϑ	ℏ(ϑ	PROPN
ejpam-7033	526	17	)	)	PUNCT
ejpam-7033	526	18	)	)	PUNCT
ejpam-7033	526	19	,	,	PUNCT
ejpam-7033	526	20	r(ω	r(ω	ADV
ejpam-7033	526	21	,	,	PUNCT
ejpam-7033	526	22	ℏ(ω)),r(ϑ	ℏ(ω)),r(ϑ	PROPN
ejpam-7033	526	23	,	,	PUNCT
ejpam-7033	526	24	ℏ2(ω)),r(ω	ℏ2(ω)),r(ω	PROPN
ejpam-7033	526	25	,	,	PUNCT
ejpam-7033	526	26	ℏ2(ϑ	ℏ2(ϑ	NOUN
ejpam-7033	526	27	)	)	PUNCT
ejpam-7033	526	28	)	)	PUNCT
ejpam-7033	526	29	)	)	PUNCT
ejpam-7033	527	1	=	=	PUNCT
ejpam-7033	527	2	r(ω	r(ω	ADV
ejpam-7033	527	3	,	,	PUNCT
ejpam-7033	527	4	ℏ2(ϑ))−	ℏ2(ϑ))−	NOUN
ejpam-7033	528	1	[	[	X
ejpam-7033	528	2	r(ϑ	r(ϑ	PROPN
ejpam-7033	528	3	,	,	PUNCT
ejpam-7033	528	4	ℏ(ϑ	ℏ(ϑ	PROPN
ejpam-7033	528	5	)	)	PUNCT
ejpam-7033	528	6	)	)	PUNCT
ejpam-7033	529	1	+	+	PUNCT
ejpam-7033	529	2	r(ω	r(ω	ADV
ejpam-7033	529	3	,	,	PUNCT
ejpam-7033	529	4	ℏ(ω	ℏ(ω	NOUN
ejpam-7033	529	5	)	)	PUNCT
ejpam-7033	529	6	)	)	PUNCT
ejpam-7033	529	7	]	]	PUNCT
ejpam-7033	529	8	.	.	PUNCT
ejpam-7033	530	1	thus	thus	ADV
ejpam-7033	530	2	,	,	PUNCT
ejpam-7033	530	3	(	(	PUNCT
ejpam-7033	530	4	i	i	PRON
ejpam-7033	530	5	−	−	PROPN
ejpam-7033	530	6	t	t	NOUN
ejpam-7033	530	7	)	)	PUNCT
ejpam-7033	530	8	2(i	2(i	NUM
ejpam-7033	531	1	+	+	NUM
ejpam-7033	531	2	t	t	NOUN
ejpam-7033	531	3	)	)	PUNCT
ejpam-7033	532	1	r(ϑ	r(ϑ	PROPN
ejpam-7033	532	2	,	,	PUNCT
ejpam-7033	532	3	ℏ(ϑ	ℏ(ϑ	PROPN
ejpam-7033	532	4	)	)	PUNCT
ejpam-7033	532	5	)	)	PUNCT
ejpam-7033	533	1	⪯	⪯	PROPN
ejpam-7033	533	2	r(ϑ	r(ϑ	PROPN
ejpam-7033	533	3	,	,	PUNCT
ejpam-7033	533	4	ω	ω	NOUN
ejpam-7033	533	5	)	)	PUNCT
ejpam-7033	533	6	implies	imply	VERB
ejpam-7033	533	7	j	j	PROPN
ejpam-7033	533	8	(	(	PUNCT
ejpam-7033	533	9	r(ℏ(ϑ	r(ℏ(ϑ	NOUN
ejpam-7033	533	10	)	)	PUNCT
ejpam-7033	533	11	,	,	PUNCT
ejpam-7033	533	12	ℏ(ω)),r(ϑ	ℏ(ω)),r(ϑ	PROPN
ejpam-7033	533	13	,	,	PUNCT
ejpam-7033	533	14	ω),r(ϑ	ω),r(ϑ	NUM
ejpam-7033	533	15	,	,	PUNCT
ejpam-7033	533	16	ℏ(ϑ)),r(ω	ℏ(ϑ)),r(ω	PROPN
ejpam-7033	533	17	,	,	PUNCT
ejpam-7033	533	18	ℏ(ω	ℏ(ω	NOUN
ejpam-7033	533	19	)	)	PUNCT
ejpam-7033	533	20	)	)	PUNCT
ejpam-7033	533	21	,	,	PUNCT
ejpam-7033	533	22	r(ϑ	r(ϑ	PROPN
ejpam-7033	533	23	,	,	PUNCT
ejpam-7033	533	24	ℏ2(ω)),r(ω	ℏ2(ω)),r(ω	PROPN
ejpam-7033	533	25	,	,	PUNCT
ejpam-7033	533	26	ℏ2(ϑ	ℏ2(ϑ	NOUN
ejpam-7033	533	27	)	)	PUNCT
ejpam-7033	533	28	)	)	PUNCT
ejpam-7033	533	29	)	)	PUNCT
ejpam-7033	534	1	⪯	⪯	NOUN
ejpam-7033	534	2	0	0	NUM
ejpam-7033	534	3	.	.	PUNCT
ejpam-7033	535	1	note	note	VERB
ejpam-7033	535	2	that	that	SCONJ
ejpam-7033	535	3	ℏ(1	ℏ(1	NOUN
ejpam-7033	535	4	)	)	PUNCT
ejpam-7033	535	5	=	=	SYM
ejpam-7033	536	1	1	1	NUM
ejpam-7033	536	2	.	.	X
ejpam-7033	536	3	5.1	5.1	NUM
ejpam-7033	536	4	.	.	PUNCT
ejpam-7033	537	1	consequences	consequence	NOUN
ejpam-7033	537	2	of	of	ADP
ejpam-7033	537	3	the	the	DET
ejpam-7033	537	4	main	main	ADJ
ejpam-7033	537	5	theorem	theorem	NOUN
ejpam-7033	537	6	.	.	PUNCT
ejpam-7033	538	1	in	in	ADP
ejpam-7033	538	2	this	this	DET
ejpam-7033	538	3	subsection	subsection	NOUN
ejpam-7033	538	4	,	,	PUNCT
ejpam-7033	538	5	we	we	PRON
ejpam-7033	538	6	state	state	VERB
ejpam-7033	538	7	some	some	DET
ejpam-7033	538	8	corollaries	corollary	NOUN
ejpam-7033	538	9	that	that	PRON
ejpam-7033	538	10	can	can	AUX
ejpam-7033	538	11	be	be	AUX
ejpam-7033	538	12	deduced	deduce	VERB
ejpam-7033	538	13	directly	directly	ADV
ejpam-7033	538	14	from	from	ADP
ejpam-7033	538	15	the	the	DET
ejpam-7033	538	16	main	main	ADJ
ejpam-7033	538	17	theorem	theorem	NOUN
ejpam-7033	538	18	.	.	PUNCT
ejpam-7033	538	19	corollary	corollary	ADJ
ejpam-7033	538	20	18	18	NUM
ejpam-7033	538	21	.	.	PUNCT
ejpam-7033	539	1	let	let	AUX
ejpam-7033	539	2	(	(	PUNCT
ejpam-7033	539	3	x	x	NOUN
ejpam-7033	539	4	,	,	PUNCT
ejpam-7033	539	5	r	r	NOUN
ejpam-7033	539	6	)	)	PUNCT
ejpam-7033	539	7	be	be	AUX
ejpam-7033	539	8	a	a	DET
ejpam-7033	539	9	complete	complete	ADJ
ejpam-7033	539	10	rectangular	rectangular	ADJ
ejpam-7033	539	11	cone	cone	NOUN
ejpam-7033	539	12	b	b	NOUN
ejpam-7033	539	13	-	-	PUNCT
ejpam-7033	539	14	metric	metric	ADJ
ejpam-7033	539	15	space	space	NOUN
ejpam-7033	539	16	along	along	ADP
ejpam-7033	539	17	with	with	ADP
ejpam-7033	539	18	self	self	NOUN
ejpam-7033	539	19	mapping	map	VERB
ejpam-7033	539	20	ℏ	ℏ	NOUN
ejpam-7033	539	21	:	:	PUNCT
ejpam-7033	539	22	x	x	X
ejpam-7033	539	23	→	→	SYM
ejpam-7033	539	24	x	x	X
ejpam-7033	539	25	and	and	CCONJ
ejpam-7033	539	26	a	a	DET
ejpam-7033	539	27	cone	cone	NOUN
ejpam-7033	539	28	c.	c.	NOUN
ejpam-7033	539	29	let	let	VERB
ejpam-7033	539	30	t	t	PROPN
ejpam-7033	539	31	∈	∈	PROPN
ejpam-7033	539	32	b(e	b(e	PROPN
ejpam-7033	539	33	,	,	PUNCT
ejpam-7033	539	34	e	e	X
ejpam-7033	539	35	)	)	PUNCT
ejpam-7033	539	36	and	and	CCONJ
ejpam-7033	539	37	i	i	PRON
ejpam-7033	539	38	:	:	PUNCT
ejpam-7033	539	39	e	e	X
ejpam-7033	539	40	→	→	PUNCT
ejpam-7033	539	41	e	e	X
ejpam-7033	539	42	an	an	DET
ejpam-7033	539	43	identity	identity	NOUN
ejpam-7033	539	44	operator	operator	NOUN
ejpam-7033	539	45	,	,	PUNCT
ejpam-7033	539	46	s	s	VERB
ejpam-7033	539	47	≥	≥	NOUN
ejpam-7033	539	48	1	1	NUM
ejpam-7033	539	49	.	.	PUNCT
ejpam-7033	540	1	if	if	SCONJ
ejpam-7033	540	2	there	there	PRON
ejpam-7033	540	3	exists	exist	VERB
ejpam-7033	540	4	j	j	PROPN
ejpam-7033	540	5	∈	∈	PROPN
ejpam-7033	540	6	f	f	X
ejpam-7033	540	7	satisfying	satisfying	NOUN
ejpam-7033	540	8	,	,	PUNCT
ejpam-7033	540	9	for	for	ADP
ejpam-7033	540	10	each	each	DET
ejpam-7033	540	11	pair	pair	NOUN
ejpam-7033	540	12	of	of	ADP
ejpam-7033	540	13	comparable	comparable	ADJ
ejpam-7033	540	14	elements	element	NOUN
ejpam-7033	540	15	ϑ	ϑ	X
ejpam-7033	540	16	,	,	PUNCT
ejpam-7033	540	17	ω	ω	PROPN
ejpam-7033	540	18	∈	∈	PROPN
ejpam-7033	540	19	x	x	X
ejpam-7033	540	20	,	,	PUNCT
ejpam-7033	540	21	(	(	PUNCT
ejpam-7033	540	22	i	i	PRON
ejpam-7033	540	23	−	−	PROPN
ejpam-7033	540	24	t	t	NOUN
ejpam-7033	540	25	)	)	PUNCT
ejpam-7033	540	26	2(i	2(i	NUM
ejpam-7033	541	1	+	+	NUM
ejpam-7033	541	2	t	t	NOUN
ejpam-7033	541	3	)	)	PUNCT
ejpam-7033	541	4	(	(	PUNCT
ejpam-7033	541	5	r(ϑ	r(ϑ	PROPN
ejpam-7033	541	6	,	,	PUNCT
ejpam-7033	541	7	ℏ(ϑ	ℏ(ϑ	PROPN
ejpam-7033	541	8	)	)	PUNCT
ejpam-7033	541	9	)	)	PUNCT
ejpam-7033	541	10	)	)	PUNCT
ejpam-7033	541	11	⪯	⪯	PROPN
ejpam-7033	541	12	sr(ϑ	sr(ϑ	PROPN
ejpam-7033	541	13	,	,	PUNCT
ejpam-7033	541	14	ω	ω	NOUN
ejpam-7033	541	15	)	)	PUNCT
ejpam-7033	541	16	implies	imply	VERB
ejpam-7033	541	17	r(ℏ(ϑ	r(ℏ(ϑ	NOUN
ejpam-7033	541	18	)	)	PUNCT
ejpam-7033	541	19	,	,	PUNCT
ejpam-7033	541	20	ℏ(ω	ℏ(ω	PROPN
ejpam-7033	541	21	)	)	PUNCT
ejpam-7033	541	22	)	)	PUNCT
ejpam-7033	542	1	⪯	⪯	NOUN
ejpam-7033	542	2	1	1	NUM
ejpam-7033	542	3	s	s	PART
ejpam-7033	542	4	t	t	NOUN
ejpam-7033	542	5	(	(	PUNCT
ejpam-7033	542	6	r(ϑ	r(ϑ	PROPN
ejpam-7033	542	7	,	,	PUNCT
ejpam-7033	542	8	ω	ω	NOUN
ejpam-7033	542	9	)	)	PUNCT
ejpam-7033	542	10	)	)	PUNCT
ejpam-7033	542	11	,	,	PUNCT
ejpam-7033	542	12	(	(	PUNCT
ejpam-7033	542	13	11	11	NUM
ejpam-7033	542	14	)	)	PUNCT
ejpam-7033	542	15	and	and	CCONJ
ejpam-7033	542	16	(	(	PUNCT
ejpam-7033	542	17	1	1	X
ejpam-7033	542	18	)	)	PUNCT
ejpam-7033	542	19	∃	∃	PROPN
ejpam-7033	542	20	ϑ	ϑ	X
ejpam-7033	542	21	∈	∈	PROPN
ejpam-7033	542	22	x	x	PUNCT
ejpam-7033	542	23	so	so	ADV
ejpam-7033	542	24	that	that	SCONJ
ejpam-7033	542	25	ϑ0ℜℏ(ϑ0	ϑ0ℜℏ(ϑ0	NOUN
ejpam-7033	542	26	)	)	PUNCT
ejpam-7033	542	27	or	or	CCONJ
ejpam-7033	542	28	ℏ(ϑ0)ℜϑ0	ℏ(ϑ0)ℜϑ0	NOUN
ejpam-7033	542	29	;	;	PUNCT
ejpam-7033	542	30	(	(	PUNCT
ejpam-7033	542	31	2	2	X
ejpam-7033	542	32	)	)	PUNCT
ejpam-7033	542	33	∀	∀	X
ejpam-7033	542	34	ϑ	ϑ	X
ejpam-7033	542	35	,	,	PUNCT
ejpam-7033	542	36	ω	ω	PROPN
ejpam-7033	542	37	∈	∈	PROPN
ejpam-7033	542	38	x	x	X
ejpam-7033	542	39	,	,	PUNCT
ejpam-7033	542	40	ϑℜω	ϑℜω	ADJ
ejpam-7033	542	41	⇒	⇒	NOUN
ejpam-7033	542	42	ℏ(ϑ)ℜℏ(ω	ℏ(ϑ)ℜℏ(ω	PROPN
ejpam-7033	542	43	)	)	PUNCT
ejpam-7033	542	44	or	or	CCONJ
ejpam-7033	542	45	ℏ(ω)ℜℏ(ϑ	ℏ(ω)ℜℏ(ϑ	PROPN
ejpam-7033	542	46	)	)	PUNCT
ejpam-7033	542	47	;	;	PUNCT
ejpam-7033	542	48	(	(	PUNCT
ejpam-7033	542	49	3	3	X
ejpam-7033	542	50	)	)	PUNCT
ejpam-7033	542	51	for	for	ADP
ejpam-7033	542	52	a	a	DET
ejpam-7033	542	53	sequence	sequence	NOUN
ejpam-7033	542	54	{	{	PUNCT
ejpam-7033	542	55	ϑn	ϑn	NOUN
ejpam-7033	542	56	}	}	PUNCT
ejpam-7033	542	57	such	such	ADJ
ejpam-7033	542	58	that	that	SCONJ
ejpam-7033	542	59	ϑnℜϑn+1	ϑnℜϑn+1	PROPN
ejpam-7033	542	60	and	and	CCONJ
ejpam-7033	542	61	ϑn	ϑn	NOUN
ejpam-7033	542	62	→	→	SYM
ejpam-7033	542	63	z∗	z∗	PROPN
ejpam-7033	542	64	,	,	PUNCT
ejpam-7033	542	65	we	we	PRON
ejpam-7033	542	66	get	get	VERB
ejpam-7033	542	67	ϑnℜz∗	ϑnℜz∗	X
ejpam-7033	542	68	∀	∀	X
ejpam-7033	542	69	n	n	PRON
ejpam-7033	542	70	∈	∈	NOUN
ejpam-7033	542	71	n	n	NOUN
ejpam-7033	542	72	and	and	CCONJ
ejpam-7033	542	73	let	let	VERB
ejpam-7033	542	74	r(z∗	r(z∗	NOUN
ejpam-7033	542	75	,	,	PUNCT
ejpam-7033	542	76	ℏ(z∗	ℏ(z∗	NOUN
ejpam-7033	542	77	)	)	PUNCT
ejpam-7033	542	78	)	)	PUNCT
ejpam-7033	542	79	⪯	⪯	NOUN
ejpam-7033	542	80	r(z∗	r(z∗	NOUN
ejpam-7033	542	81	,	,	PUNCT
ejpam-7033	542	82	ℏ2(z∗	ℏ2(z∗	NUM
ejpam-7033	542	83	)	)	PUNCT
ejpam-7033	542	84	)	)	PUNCT
ejpam-7033	542	85	.	.	PUNCT
ejpam-7033	543	1	then	then	ADV
ejpam-7033	543	2	there	there	PRON
ejpam-7033	543	3	exists	exist	VERB
ejpam-7033	543	4	z∗	z∗	PROPN
ejpam-7033	543	5	∈	∈	PROPN
ejpam-7033	543	6	x	x	X
ejpam-7033	543	7	so	so	ADV
ejpam-7033	543	8	that	that	PRON
ejpam-7033	543	9	z∗	z∗	NOUN
ejpam-7033	543	10	=	=	PUNCT
ejpam-7033	543	11	ℏ(z∗	ℏ(z∗	NOUN
ejpam-7033	543	12	)	)	PUNCT
ejpam-7033	543	13	.	.	PUNCT
ejpam-7033	544	1	proof	proof	NOUN
ejpam-7033	544	2	.	.	PUNCT
ejpam-7033	545	1	define	define	VERB
ejpam-7033	545	2	j	j	PROPN
ejpam-7033	545	3	as	as	ADP
ejpam-7033	545	4	in	in	ADP
ejpam-7033	545	5	example	example	NOUN
ejpam-7033	545	6	5	5	NUM
ejpam-7033	545	7	(	(	PUNCT
ejpam-7033	545	8	iv	iv	NUM
ejpam-7033	545	9	)	)	PUNCT
ejpam-7033	545	10	,	,	PUNCT
ejpam-7033	545	11	and	and	CCONJ
ejpam-7033	545	12	t	t	X
ejpam-7033	546	1	:	:	PUNCT
ejpam-7033	546	2	e	e	X
ejpam-7033	546	3	→	→	SYM
ejpam-7033	546	4	e	e	X
ejpam-7033	546	5	by	by	ADP
ejpam-7033	546	6	t	t	PROPN
ejpam-7033	546	7	(	(	PUNCT
ejpam-7033	546	8	ϑ	ϑ	NOUN
ejpam-7033	546	9	)	)	PUNCT
ejpam-7033	546	10	=	=	SYM
ejpam-7033	547	1	βϑ	βϑ	ADJ
ejpam-7033	547	2	∀	∀	X
ejpam-7033	547	3	ϑ	ϑ	X
ejpam-7033	547	4	∈	∈	PROPN
ejpam-7033	547	5	e	e	NOUN
ejpam-7033	547	6	,	,	PUNCT
ejpam-7033	547	7	0	0	NUM
ejpam-7033	547	8	≤	≤	NUM
ejpam-7033	547	9	β	β	X
ejpam-7033	547	10	<	<	X
ejpam-7033	547	11	1	1	NUM
ejpam-7033	547	12	.	.	PUNCT
ejpam-7033	547	13	clearly	clearly	ADV
ejpam-7033	547	14	∥t	∥t	VERB
ejpam-7033	547	15	∥1	∥1	PRON
ejpam-7033	547	16	<	<	X
ejpam-7033	547	17	1	1	NUM
ejpam-7033	547	18	,	,	PUNCT
ejpam-7033	547	19	we	we	PRON
ejpam-7033	547	20	get	get	VERB
ejpam-7033	547	21	t	t	PROPN
ejpam-7033	547	22	∈	∈	PROPN
ejpam-7033	547	23	b(e	b(e	PROPN
ejpam-7033	547	24	,	,	PUNCT
ejpam-7033	547	25	e	e	NOUN
ejpam-7033	547	26	)	)	PUNCT
ejpam-7033	547	27	,	,	PUNCT
ejpam-7033	547	28	and	and	CCONJ
ejpam-7033	547	29	the	the	DET
ejpam-7033	547	30	proof	proof	NOUN
ejpam-7033	547	31	is	be	AUX
ejpam-7033	547	32	obvious	obvious	ADJ
ejpam-7033	547	33	as	as	ADP
ejpam-7033	547	34	an	an	DET
ejpam-7033	547	35	application	application	NOUN
ejpam-7033	547	36	of	of	ADP
ejpam-7033	547	37	theorem	theorem	NOUN
ejpam-7033	547	38	15	15	NUM
ejpam-7033	547	39	.	.	PUNCT
ejpam-7033	547	40	a.	a.	PROPN
ejpam-7033	547	41	arif	arif	PROPN
ejpam-7033	547	42	et	et	PROPN
ejpam-7033	547	43	al	al	PROPN
ejpam-7033	547	44	.	.	PUNCT
ejpam-7033	547	45	/	/	SYM
ejpam-7033	547	46	eur	eur	PROPN
ejpam-7033	547	47	.	.	PUNCT
ejpam-7033	548	1	j.	j.	PROPN
ejpam-7033	548	2	pure	pure	PROPN
ejpam-7033	548	3	appl	appl	PROPN
ejpam-7033	548	4	.	.	PROPN
ejpam-7033	548	5	math	math	PROPN
ejpam-7033	548	6	,	,	PUNCT
ejpam-7033	548	7	18	18	NUM
ejpam-7033	548	8	(	(	PUNCT
ejpam-7033	548	9	4	4	NUM
ejpam-7033	548	10	)	)	PUNCT
ejpam-7033	548	11	(	(	PUNCT
ejpam-7033	548	12	2025	2025	NUM
ejpam-7033	548	13	)	)	PUNCT
ejpam-7033	548	14	,	,	PUNCT
ejpam-7033	548	15	7033	7033	NUM
ejpam-7033	548	16	18	18	NUM
ejpam-7033	548	17	of	of	ADP
ejpam-7033	548	18	29	29	NUM
ejpam-7033	548	19	corollary	corollary	ADJ
ejpam-7033	548	20	19	19	NUM
ejpam-7033	548	21	.	.	PUNCT
ejpam-7033	549	1	let	let	AUX
ejpam-7033	549	2	(	(	PUNCT
ejpam-7033	549	3	x	x	NOUN
ejpam-7033	549	4	,	,	PUNCT
ejpam-7033	549	5	r	r	NOUN
ejpam-7033	549	6	)	)	PUNCT
ejpam-7033	549	7	be	be	AUX
ejpam-7033	549	8	a	a	DET
ejpam-7033	549	9	complete	complete	ADJ
ejpam-7033	549	10	rectangular	rectangular	ADJ
ejpam-7033	549	11	cone	cone	NOUN
ejpam-7033	549	12	b	b	NOUN
ejpam-7033	549	13	-	-	PUNCT
ejpam-7033	549	14	metric	metric	ADJ
ejpam-7033	549	15	space	space	NOUN
ejpam-7033	549	16	,	,	PUNCT
ejpam-7033	549	17	ℏ	ℏ	PROPN
ejpam-7033	549	18	:	:	PUNCT
ejpam-7033	549	19	x	x	X
ejpam-7033	549	20	→	→	SYM
ejpam-7033	549	21	x	x	X
ejpam-7033	549	22	,	,	PUNCT
ejpam-7033	549	23	c	c	X
ejpam-7033	549	24	be	be	AUX
ejpam-7033	549	25	a	a	DET
ejpam-7033	549	26	cone	cone	NOUN
ejpam-7033	549	27	,	,	PUNCT
ejpam-7033	549	28	t	t	X
ejpam-7033	549	29	:	:	PUNCT
ejpam-7033	549	30	e	e	X
ejpam-7033	549	31	→	→	PUNCT
ejpam-7033	549	32	e	e	X
ejpam-7033	549	33	such	such	ADJ
ejpam-7033	549	34	that	that	SCONJ
ejpam-7033	549	35	∥t	∥t	VERB
ejpam-7033	549	36	∥1	∥1	PRON
ejpam-7033	549	37	<	<	X
ejpam-7033	549	38	1	1	NUM
ejpam-7033	549	39	s	s	PART
ejpam-7033	549	40	,	,	PUNCT
ejpam-7033	549	41	i	i	PRON
ejpam-7033	549	42	:	:	PUNCT
ejpam-7033	549	43	e	e	X
ejpam-7033	549	44	→	→	PUNCT
ejpam-7033	549	45	e	e	X
ejpam-7033	549	46	ba	ba	PROPN
ejpam-7033	549	47	an	an	DET
ejpam-7033	549	48	identity	identity	NOUN
ejpam-7033	549	49	operator	operator	NOUN
ejpam-7033	549	50	and	and	CCONJ
ejpam-7033	549	51	s	s	NOUN
ejpam-7033	549	52	≥	≥	NOUN
ejpam-7033	549	53	1	1	NUM
ejpam-7033	549	54	.	.	PUNCT
ejpam-7033	550	1	if	if	SCONJ
ejpam-7033	550	2	there	there	PRON
ejpam-7033	550	3	exists	exist	VERB
ejpam-7033	550	4	j	j	PROPN
ejpam-7033	550	5	∈	∈	PROPN
ejpam-7033	550	6	f	f	PROPN
ejpam-7033	550	7	,	,	PUNCT
ejpam-7033	550	8	for	for	ADP
ejpam-7033	550	9	each	each	DET
ejpam-7033	550	10	pair	pair	NOUN
ejpam-7033	550	11	of	of	ADP
ejpam-7033	550	12	comparable	comparable	ADJ
ejpam-7033	550	13	elements	element	NOUN
ejpam-7033	550	14	ϑ	ϑ	X
ejpam-7033	550	15	,	,	PUNCT
ejpam-7033	550	16	ω	ω	PROPN
ejpam-7033	550	17	∈	∈	PROPN
ejpam-7033	550	18	x	x	X
ejpam-7033	550	19	,	,	PUNCT
ejpam-7033	550	20	satisfying	satisfy	VERB
ejpam-7033	550	21	(	(	PUNCT
ejpam-7033	550	22	i	i	PRON
ejpam-7033	550	23	−	−	PROPN
ejpam-7033	551	1	t	t	NOUN
ejpam-7033	551	2	)	)	PUNCT
ejpam-7033	551	3	2(i	2(i	NUM
ejpam-7033	552	1	+	+	NUM
ejpam-7033	552	2	t	t	NOUN
ejpam-7033	552	3	)	)	PUNCT
ejpam-7033	552	4	(	(	PUNCT
ejpam-7033	552	5	r(ϑ	r(ϑ	PROPN
ejpam-7033	552	6	,	,	PUNCT
ejpam-7033	552	7	ℏ(ϑ	ℏ(ϑ	PROPN
ejpam-7033	552	8	)	)	PUNCT
ejpam-7033	552	9	)	)	PUNCT
ejpam-7033	552	10	)	)	PUNCT
ejpam-7033	552	11	⪯	⪯	PROPN
ejpam-7033	552	12	sr(ϑ	sr(ϑ	PROPN
ejpam-7033	552	13	,	,	PUNCT
ejpam-7033	552	14	ω	ω	NOUN
ejpam-7033	552	15	)	)	PUNCT
ejpam-7033	552	16	implies	imply	VERB
ejpam-7033	552	17	r(ℏ(ϑ	r(ℏ(ϑ	NOUN
ejpam-7033	552	18	)	)	PUNCT
ejpam-7033	552	19	,	,	PUNCT
ejpam-7033	552	20	ℏ(ω	ℏ(ω	PROPN
ejpam-7033	552	21	)	)	PUNCT
ejpam-7033	552	22	)	)	PUNCT
ejpam-7033	553	1	⪯	⪯	PROPN
ejpam-7033	553	2	t	t	PROPN
ejpam-7033	553	3	s	s	PART
ejpam-7033	553	4	(	(	PUNCT
ejpam-7033	553	5	r(ϑ	r(ϑ	PROPN
ejpam-7033	553	6	,	,	PUNCT
ejpam-7033	553	7	ω	ω	NOUN
ejpam-7033	553	8	)	)	PUNCT
ejpam-7033	553	9	)	)	PUNCT
ejpam-7033	554	1	and	and	CCONJ
ejpam-7033	554	2	(	(	PUNCT
ejpam-7033	554	3	1	1	X
ejpam-7033	554	4	)	)	PUNCT
ejpam-7033	554	5	there	there	PRON
ejpam-7033	554	6	exists	exist	VERB
ejpam-7033	554	7	ϑ0	ϑ0	PROPN
ejpam-7033	554	8	∈	∈	PROPN
ejpam-7033	554	9	x	x	PUNCT
ejpam-7033	554	10	satisfying	satisfy	VERB
ejpam-7033	554	11	ϑ0ℜℏ(ϑ0	ϑ0ℜℏ(ϑ0	NOUN
ejpam-7033	554	12	)	)	PUNCT
ejpam-7033	554	13	or	or	CCONJ
ejpam-7033	554	14	ℏ(ϑ0)ℜϑ0	ℏ(ϑ0)ℜϑ0	NOUN
ejpam-7033	554	15	;	;	PUNCT
ejpam-7033	554	16	(	(	PUNCT
ejpam-7033	554	17	2	2	X
ejpam-7033	554	18	)	)	PUNCT
ejpam-7033	554	19	∀	∀	X
ejpam-7033	554	20	ϑ	ϑ	X
ejpam-7033	554	21	,	,	PUNCT
ejpam-7033	554	22	ω	ω	PROPN
ejpam-7033	554	23	∈	∈	PROPN
ejpam-7033	554	24	x	x	X
ejpam-7033	554	25	,	,	PUNCT
ejpam-7033	554	26	ϑℜω	ϑℜω	ADJ
ejpam-7033	554	27	⇒	⇒	NOUN
ejpam-7033	554	28	ℏ(ϑ)ℜℏ(ω	ℏ(ϑ)ℜℏ(ω	PROPN
ejpam-7033	554	29	)	)	PUNCT
ejpam-7033	554	30	or	or	CCONJ
ejpam-7033	554	31	ℏ(ω)ℜℏ(ϑ	ℏ(ω)ℜℏ(ϑ	PROPN
ejpam-7033	554	32	)	)	PUNCT
ejpam-7033	554	33	;	;	PUNCT
ejpam-7033	554	34	(	(	PUNCT
ejpam-7033	554	35	3	3	X
ejpam-7033	554	36	)	)	PUNCT
ejpam-7033	554	37	for	for	ADP
ejpam-7033	554	38	a	a	DET
ejpam-7033	554	39	sequence	sequence	NOUN
ejpam-7033	554	40	{	{	PUNCT
ejpam-7033	554	41	ϑn	ϑn	NOUN
ejpam-7033	554	42	}	}	PUNCT
ejpam-7033	554	43	such	such	ADJ
ejpam-7033	554	44	that	that	SCONJ
ejpam-7033	554	45	ϑnℜϑn+1	ϑnℜϑn+1	PROPN
ejpam-7033	554	46	and	and	CCONJ
ejpam-7033	554	47	ϑn	ϑn	NOUN
ejpam-7033	554	48	→	→	SYM
ejpam-7033	554	49	z∗	z∗	PROPN
ejpam-7033	554	50	,	,	PUNCT
ejpam-7033	554	51	we	we	PRON
ejpam-7033	554	52	get	get	VERB
ejpam-7033	554	53	ϑnℜz∗	ϑnℜz∗	NOUN
ejpam-7033	554	54	for	for	ADP
ejpam-7033	554	55	all	all	PRON
ejpam-7033	554	56	n	n	PRON
ejpam-7033	554	57	∈	∈	NOUN
ejpam-7033	554	58	n	n	NOUN
ejpam-7033	554	59	and	and	CCONJ
ejpam-7033	554	60	let	let	VERB
ejpam-7033	554	61	r(z∗	r(z∗	NOUN
ejpam-7033	554	62	,	,	PUNCT
ejpam-7033	554	63	ℏ(z∗	ℏ(z∗	NOUN
ejpam-7033	554	64	)	)	PUNCT
ejpam-7033	554	65	)	)	PUNCT
ejpam-7033	554	66	⪯	⪯	NOUN
ejpam-7033	554	67	r(z∗	r(z∗	NOUN
ejpam-7033	554	68	,	,	PUNCT
ejpam-7033	554	69	ℏ2(z∗	ℏ2(z∗	NUM
ejpam-7033	554	70	)	)	PUNCT
ejpam-7033	554	71	)	)	PUNCT
ejpam-7033	554	72	.	.	PUNCT
ejpam-7033	555	1	then	then	ADV
ejpam-7033	555	2	there	there	PRON
ejpam-7033	555	3	exists	exist	VERB
ejpam-7033	555	4	z∗	z∗	PROPN
ejpam-7033	555	5	∈	∈	PROPN
ejpam-7033	555	6	x	x	X
ejpam-7033	555	7	satisfying	satisfy	VERB
ejpam-7033	555	8	z∗	z∗	NOUN
ejpam-7033	555	9	=	=	PUNCT
ejpam-7033	555	10	ℏ(z∗	ℏ(z∗	NOUN
ejpam-7033	555	11	)	)	PUNCT
ejpam-7033	555	12	.	.	PUNCT
ejpam-7033	556	1	proof	proof	NOUN
ejpam-7033	556	2	.	.	PUNCT
ejpam-7033	557	1	define	define	VERB
ejpam-7033	557	2	t	t	NOUN
ejpam-7033	558	1	:	:	PUNCT
ejpam-7033	558	2	e	e	X
ejpam-7033	558	3	→	→	SYM
ejpam-7033	558	4	e	e	X
ejpam-7033	558	5	by	by	ADP
ejpam-7033	558	6	t	t	PROPN
ejpam-7033	558	7	(	(	PUNCT
ejpam-7033	558	8	ϑ	ϑ	X
ejpam-7033	558	9	)	)	PUNCT
ejpam-7033	558	10	=	=	SYM
ejpam-7033	558	11	ϑ	ϑ	X
ejpam-7033	558	12	∀	∀	X
ejpam-7033	558	13	ϑ	ϑ	X
ejpam-7033	558	14	∈	∈	PROPN
ejpam-7033	558	15	e	e	X
ejpam-7033	558	16	.	.	PUNCT
ejpam-7033	559	1	then	then	ADV
ejpam-7033	559	2	the	the	DET
ejpam-7033	559	3	proof	proof	NOUN
ejpam-7033	559	4	is	be	AUX
ejpam-7033	559	5	obvious	obvious	ADJ
ejpam-7033	559	6	from	from	ADP
ejpam-7033	559	7	corollary	corollary	ADJ
ejpam-7033	559	8	18	18	NUM
ejpam-7033	559	9	.	.	PUNCT
ejpam-7033	559	10	example	example	NOUN
ejpam-7033	559	11	8	8	NUM
ejpam-7033	559	12	.	.	PUNCT
ejpam-7033	560	1	let	let	VERB
ejpam-7033	560	2	e	e	NOUN
ejpam-7033	560	3	=	=	PUNCT
ejpam-7033	560	4	(	(	PUNCT
ejpam-7033	560	5	r	r	NOUN
ejpam-7033	560	6	,	,	PUNCT
ejpam-7033	560	7	∥	∥	X
ejpam-7033	560	8	·	·	PUNCT
ejpam-7033	560	9	∥	∥	NUM
ejpam-7033	560	10	)	)	PUNCT
ejpam-7033	560	11	,	,	PUNCT
ejpam-7033	560	12	then	then	ADV
ejpam-7033	560	13	it	it	PRON
ejpam-7033	560	14	is	be	AUX
ejpam-7033	560	15	real	real	ADJ
ejpam-7033	560	16	banach	banach	NOUN
ejpam-7033	560	17	space	space	NOUN
ejpam-7033	560	18	.	.	PUNCT
ejpam-7033	561	1	the	the	DET
ejpam-7033	561	2	set	set	NOUN
ejpam-7033	561	3	c	c	NOUN
ejpam-7033	561	4	=	=	SYM
ejpam-7033	561	5	{	{	PUNCT
ejpam-7033	561	6	ϑ	ϑ	X
ejpam-7033	561	7	∈	∈	NOUN
ejpam-7033	561	8	r	r	NOUN
ejpam-7033	561	9	:	:	PUNCT
ejpam-7033	561	10	ϑ	ϑ	X
ejpam-7033	561	11	≥	≥	NOUN
ejpam-7033	561	12	0	0	NUM
ejpam-7033	561	13	}	}	PUNCT
ejpam-7033	561	14	is	be	AUX
ejpam-7033	561	15	a	a	DET
ejpam-7033	561	16	cone	cone	NOUN
ejpam-7033	561	17	.	.	PUNCT
ejpam-7033	562	1	let	let	VERB
ejpam-7033	562	2	w	w	VERB
ejpam-7033	562	3	=	=	PUNCT
ejpam-7033	562	4	{	{	PUNCT
ejpam-7033	562	5	0	0	NUM
ejpam-7033	562	6	,	,	PUNCT
ejpam-7033	562	7	1	1	NUM
ejpam-7033	562	8	,	,	PUNCT
ejpam-7033	562	9	2	2	NUM
ejpam-7033	562	10	,	,	PUNCT
ejpam-7033	562	11	3	3	NUM
ejpam-7033	562	12	}	}	PUNCT
ejpam-7033	562	13	,	,	PUNCT
ejpam-7033	562	14	define	define	VERB
ejpam-7033	562	15	ℏ	ℏ	PROPN
ejpam-7033	562	16	:	:	PUNCT
ejpam-7033	562	17	w	w	PROPN
ejpam-7033	562	18	→w	→w	NUM
ejpam-7033	562	19	by	by	ADP
ejpam-7033	562	20	ℏ(0	ℏ(0	PROPN
ejpam-7033	562	21	)	)	PUNCT
ejpam-7033	562	22	=	=	SYM
ejpam-7033	562	23	ℏ(2	ℏ(2	PROPN
ejpam-7033	562	24	)	)	PUNCT
ejpam-7033	562	25	=	=	SYM
ejpam-7033	562	26	0	0	NUM
ejpam-7033	562	27	,	,	PUNCT
ejpam-7033	562	28	ℏ(1	ℏ(1	NOUN
ejpam-7033	562	29	)	)	PUNCT
ejpam-7033	562	30	=	=	SYM
ejpam-7033	562	31	2	2	NUM
ejpam-7033	562	32	,	,	PUNCT
ejpam-7033	562	33	ℏ(3	ℏ(3	PROPN
ejpam-7033	562	34	)	)	PUNCT
ejpam-7033	562	35	=	=	NOUN
ejpam-7033	562	36	1	1	NUM
ejpam-7033	562	37	and	and	CCONJ
ejpam-7033	562	38	r	r	NOUN
ejpam-7033	562	39	:	:	PUNCT
ejpam-7033	562	40	w	w	NOUN
ejpam-7033	562	41	×w	×w	NOUN
ejpam-7033	562	42	→	→	SYM
ejpam-7033	562	43	e	e	NOUN
ejpam-7033	562	44	by	by	ADP
ejpam-7033	562	45	r(ϑ1	r(ϑ1	NOUN
ejpam-7033	562	46	,	,	PUNCT
ejpam-7033	562	47	ϑ2	ϑ2	NOUN
ejpam-7033	562	48	)	)	PUNCT
ejpam-7033	562	49	=	=	PUNCT
ejpam-7033	563	1			NOUN
ejpam-7033	563	2	0	0	PUNCT
ejpam-7033	564	1	if	if	SCONJ
ejpam-7033	564	2	ϑ1	ϑ1	NOUN
ejpam-7033	564	3	=	=	SYM
ejpam-7033	564	4	ϑ2	ϑ2	PROPN
ejpam-7033	564	5	3	3	NUM
ejpam-7033	564	6	if	if	SCONJ
ejpam-7033	564	7	ϑ1	ϑ1	PROPN
ejpam-7033	564	8	,	,	PUNCT
ejpam-7033	564	9	ϑ2	ϑ2	PROPN
ejpam-7033	564	10	∈	∈	PROPN
ejpam-7033	564	11	{	{	PUNCT
ejpam-7033	564	12	1	1	NUM
ejpam-7033	564	13	,	,	PUNCT
ejpam-7033	564	14	2	2	NUM
ejpam-7033	564	15	}	}	SYM
ejpam-7033	564	16	10	10	NUM
ejpam-7033	564	17	if	if	SCONJ
ejpam-7033	564	18	ϑ1	ϑ1	NOUN
ejpam-7033	564	19	,	,	PUNCT
ejpam-7033	564	20	ϑ2	ϑ2	PROPN
ejpam-7033	564	21	∈	∈	PROPN
ejpam-7033	564	22	{	{	PUNCT
ejpam-7033	564	23	0	0	NUM
ejpam-7033	564	24	,	,	PUNCT
ejpam-7033	564	25	1	1	NUM
ejpam-7033	564	26	}	}	SYM
ejpam-7033	564	27	22	22	NUM
ejpam-7033	564	28	if	if	SCONJ
ejpam-7033	564	29	ϑ1	ϑ1	NOUN
ejpam-7033	564	30	,	,	PUNCT
ejpam-7033	564	31	ϑ2	ϑ2	PROPN
ejpam-7033	564	32	∈	∈	PROPN
ejpam-7033	564	33	{	{	PUNCT
ejpam-7033	564	34	2	2	NUM
ejpam-7033	564	35	,	,	PUNCT
ejpam-7033	564	36	3	3	NUM
ejpam-7033	564	37	}	}	SYM
ejpam-7033	564	38	0.5	0.5	NUM
ejpam-7033	564	39	otherwise	otherwise	ADV
ejpam-7033	564	40	.	.	PUNCT
ejpam-7033	565	1	22	22	NUM
ejpam-7033	565	2	=	=	SYM
ejpam-7033	565	3	r	r	NOUN
ejpam-7033	565	4	(	(	PUNCT
ejpam-7033	565	5	2	2	NUM
ejpam-7033	565	6	,	,	PUNCT
ejpam-7033	565	7	3	3	NUM
ejpam-7033	565	8	)	)	PUNCT
ejpam-7033	565	9	≥	≥	NOUN
ejpam-7033	565	10	r	r	NOUN
ejpam-7033	565	11	(	(	PUNCT
ejpam-7033	565	12	2	2	NUM
ejpam-7033	565	13	,	,	PUNCT
ejpam-7033	565	14	0	0	NUM
ejpam-7033	565	15	)	)	PUNCT
ejpam-7033	566	1	+	+	CCONJ
ejpam-7033	566	2	r	r	NOUN
ejpam-7033	566	3	(	(	PUNCT
ejpam-7033	566	4	0	0	NUM
ejpam-7033	566	5	,	,	PUNCT
ejpam-7033	566	6	1	1	NUM
ejpam-7033	566	7	)	)	PUNCT
ejpam-7033	566	8	+	+	CCONJ
ejpam-7033	566	9	r	r	NOUN
ejpam-7033	566	10	(	(	PUNCT
ejpam-7033	566	11	1	1	NUM
ejpam-7033	566	12	,	,	PUNCT
ejpam-7033	566	13	3	3	NUM
ejpam-7033	566	14	)	)	PUNCT
ejpam-7033	566	15	=	=	SYM
ejpam-7033	566	16	0.5	0.5	NUM
ejpam-7033	566	17	+	+	NUM
ejpam-7033	566	18	10	10	NUM
ejpam-7033	566	19	+	+	NUM
ejpam-7033	566	20	0.5	0.5	NUM
ejpam-7033	566	21	=	=	SYM
ejpam-7033	566	22	11	11	NUM
ejpam-7033	566	23	.	.	PUNCT
ejpam-7033	567	1	we	we	PRON
ejpam-7033	567	2	notice	notice	VERB
ejpam-7033	567	3	that	that	SCONJ
ejpam-7033	567	4	for	for	ADP
ejpam-7033	567	5	s	s	NOUN
ejpam-7033	567	6	=	=	SYM
ejpam-7033	567	7	2	2	NUM
ejpam-7033	567	8	,	,	PUNCT
ejpam-7033	567	9	r	r	NOUN
ejpam-7033	567	10	is	be	AUX
ejpam-7033	567	11	a	a	DET
ejpam-7033	567	12	rectangular	rectangular	ADJ
ejpam-7033	567	13	cone	cone	NOUN
ejpam-7033	567	14	b	b	NOUN
ejpam-7033	567	15	-	-	PUNCT
ejpam-7033	567	16	metric	metric	ADJ
ejpam-7033	567	17	space	space	NOUN
ejpam-7033	567	18	,	,	PUNCT
ejpam-7033	567	19	but	but	CCONJ
ejpam-7033	567	20	not	not	PART
ejpam-7033	567	21	cone	cone	NOUN
ejpam-7033	567	22	rectangular	rectangular	ADJ
ejpam-7033	567	23	metric	metric	ADJ
ejpam-7033	567	24	space	space	NOUN
ejpam-7033	567	25	.	.	PUNCT
ejpam-7033	568	1	define	define	VERB
ejpam-7033	568	2	t	t	NOUN
ejpam-7033	568	3	:	:	PUNCT
ejpam-7033	568	4	e	e	X
ejpam-7033	568	5	→	→	SYM
ejpam-7033	568	6	e	e	X
ejpam-7033	568	7	by	by	ADP
ejpam-7033	568	8	t	t	PROPN
ejpam-7033	568	9	(	(	PUNCT
ejpam-7033	568	10	ϑ	ϑ	X
ejpam-7033	568	11	)	)	PUNCT
ejpam-7033	568	12	=	=	SYM
ejpam-7033	568	13	ϑ	ϑ	X
ejpam-7033	568	14	2	2	NUM
ejpam-7033	568	15	,	,	PUNCT
ejpam-7033	568	16	clearly	clearly	ADV
ejpam-7033	568	17	∥t	∥t	VERB
ejpam-7033	568	18	∥1	∥1	PRON
ejpam-7033	568	19	<	<	X
ejpam-7033	568	20	1	1	X
ejpam-7033	568	21	.	.	PUNCT
ejpam-7033	569	1	for	for	ADP
ejpam-7033	569	2	if	if	SCONJ
ejpam-7033	569	3	ϑ	ϑ	X
ejpam-7033	569	4	=	=	SYM
ejpam-7033	569	5	0	0	PROPN
ejpam-7033	569	6	,	,	PUNCT
ejpam-7033	569	7	ω	ω	NOUN
ejpam-7033	569	8	=	=	SYM
ejpam-7033	569	9	1	1	NUM
ejpam-7033	569	10	,	,	PUNCT
ejpam-7033	569	11	then	then	ADV
ejpam-7033	569	12	r(ϑ	r(ϑ	PROPN
ejpam-7033	569	13	,	,	PUNCT
ejpam-7033	569	14	ω	ω	NUM
ejpam-7033	569	15	)	)	PUNCT
ejpam-7033	569	16	=	=	SYM
ejpam-7033	569	17	10	10	NUM
ejpam-7033	569	18	,	,	PUNCT
ejpam-7033	569	19	r(ℏ(ϑ	r(ℏ(ϑ	NUM
ejpam-7033	569	20	)	)	PUNCT
ejpam-7033	569	21	,	,	PUNCT
ejpam-7033	569	22	ℏ(ω	ℏ(ω	PROPN
ejpam-7033	569	23	)	)	PUNCT
ejpam-7033	569	24	)	)	PUNCT
ejpam-7033	569	25	=	=	SYM
ejpam-7033	569	26	0.5	0.5	NUM
ejpam-7033	569	27	,	,	PUNCT
ejpam-7033	569	28	r(ϑ	r(ϑ	PROPN
ejpam-7033	569	29	,	,	PUNCT
ejpam-7033	569	30	ℏ(ϑ	ℏ(ϑ	PROPN
ejpam-7033	569	31	)	)	PUNCT
ejpam-7033	569	32	)	)	PUNCT
ejpam-7033	570	1	=	=	PUNCT
ejpam-7033	570	2	0	0	X
ejpam-7033	570	3	.	.	PUNCT
ejpam-7033	571	1	t	t	PROPN
ejpam-7033	571	2	r(ϑ	r(ϑ	PROPN
ejpam-7033	571	3	,	,	PUNCT
ejpam-7033	571	4	ω	ω	NUM
ejpam-7033	571	5	)	)	PUNCT
ejpam-7033	571	6	=	=	SYM
ejpam-7033	571	7	10	10	NUM
ejpam-7033	571	8	2	2	NUM
ejpam-7033	571	9	=	=	SYM
ejpam-7033	571	10	5	5	NUM
ejpam-7033	571	11	.	.	PUNCT
ejpam-7033	572	1	for	for	ADP
ejpam-7033	572	2	if	if	SCONJ
ejpam-7033	572	3	ϑ	ϑ	X
ejpam-7033	572	4	=	=	SYM
ejpam-7033	572	5	1	1	NUM
ejpam-7033	572	6	,	,	PUNCT
ejpam-7033	572	7	ω	ω	NOUN
ejpam-7033	572	8	=	=	SYM
ejpam-7033	572	9	2	2	NUM
ejpam-7033	572	10	,	,	PUNCT
ejpam-7033	572	11	then	then	ADV
ejpam-7033	572	12	r(ϑ	r(ϑ	PROPN
ejpam-7033	572	13	,	,	PUNCT
ejpam-7033	572	14	ω	ω	NUM
ejpam-7033	572	15	)	)	PUNCT
ejpam-7033	572	16	=	=	SYM
ejpam-7033	572	17	r(ϑ	r(ϑ	PROPN
ejpam-7033	572	18	,	,	PUNCT
ejpam-7033	572	19	ℏ(ϑ	ℏ(ϑ	PROPN
ejpam-7033	572	20	)	)	PUNCT
ejpam-7033	572	21	)	)	PUNCT
ejpam-7033	572	22	=	=	SYM
ejpam-7033	572	23	3	3	X
ejpam-7033	572	24	,	,	PUNCT
ejpam-7033	572	25	r(ℏ(ϑ	r(ℏ(ϑ	NUM
ejpam-7033	572	26	)	)	PUNCT
ejpam-7033	572	27	,	,	PUNCT
ejpam-7033	572	28	ℏ(ω	ℏ(ω	NOUN
ejpam-7033	572	29	)	)	PUNCT
ejpam-7033	572	30	)	)	PUNCT
ejpam-7033	572	31	=	=	PUNCT
ejpam-7033	573	1	1.125	1.125	NUM
ejpam-7033	573	2	.	.	PUNCT
ejpam-7033	573	3	a.	a.	PROPN
ejpam-7033	573	4	arif	arif	PROPN
ejpam-7033	573	5	et	et	PROPN
ejpam-7033	573	6	al	al	PROPN
ejpam-7033	573	7	.	.	PUNCT
ejpam-7033	573	8	/	/	SYM
ejpam-7033	573	9	eur	eur	PROPN
ejpam-7033	573	10	.	.	PUNCT
ejpam-7033	574	1	j.	j.	PROPN
ejpam-7033	574	2	pure	pure	PROPN
ejpam-7033	574	3	appl	appl	PROPN
ejpam-7033	574	4	.	.	PROPN
ejpam-7033	574	5	math	math	PROPN
ejpam-7033	574	6	,	,	PUNCT
ejpam-7033	574	7	18	18	NUM
ejpam-7033	574	8	(	(	PUNCT
ejpam-7033	574	9	4	4	NUM
ejpam-7033	574	10	)	)	PUNCT
ejpam-7033	574	11	(	(	PUNCT
ejpam-7033	574	12	2025	2025	NUM
ejpam-7033	574	13	)	)	PUNCT
ejpam-7033	574	14	,	,	PUNCT
ejpam-7033	574	15	7033	7033	NUM
ejpam-7033	574	16	19	19	NUM
ejpam-7033	574	17	of	of	ADP
ejpam-7033	574	18	29	29	NUM
ejpam-7033	574	19	t	t	PROPN
ejpam-7033	574	20	r(ϑ	r(ϑ	PROPN
ejpam-7033	574	21	,	,	PUNCT
ejpam-7033	574	22	ω	ω	NUM
ejpam-7033	574	23	)	)	PUNCT
ejpam-7033	574	24	=	=	SYM
ejpam-7033	574	25	3	3	NUM
ejpam-7033	574	26	2	2	NUM
ejpam-7033	574	27	=	=	SYM
ejpam-7033	574	28	1.5	1.5	NUM
ejpam-7033	574	29	,	,	PUNCT
ejpam-7033	574	30	(	(	PUNCT
ejpam-7033	574	31	i	i	PRON
ejpam-7033	574	32	−	−	PROPN
ejpam-7033	575	1	t	t	NOUN
ejpam-7033	575	2	)	)	PUNCT
ejpam-7033	575	3	2(i	2(i	NUM
ejpam-7033	576	1	+	+	NUM
ejpam-7033	576	2	t	t	NOUN
ejpam-7033	576	3	)	)	PUNCT
ejpam-7033	576	4	r(ϑ	r(ϑ	PROPN
ejpam-7033	576	5	,	,	PUNCT
ejpam-7033	576	6	ℏ(ϑ	ℏ(ϑ	PROPN
ejpam-7033	576	7	)	)	PUNCT
ejpam-7033	576	8	)	)	PUNCT
ejpam-7033	577	1	=	=	PUNCT
ejpam-7033	577	2	0.25	0.25	NUM
ejpam-7033	577	3	.	.	PUNCT
ejpam-7033	578	1	for	for	ADP
ejpam-7033	578	2	if	if	SCONJ
ejpam-7033	578	3	ϑ	ϑ	X
ejpam-7033	578	4	=	=	SYM
ejpam-7033	578	5	2	2	NUM
ejpam-7033	578	6	,	,	PUNCT
ejpam-7033	578	7	ω	ω	X
ejpam-7033	578	8	=	=	SYM
ejpam-7033	578	9	3	3	NUM
ejpam-7033	578	10	,	,	PUNCT
ejpam-7033	578	11	then	then	ADV
ejpam-7033	578	12	r(ϑ	r(ϑ	PROPN
ejpam-7033	578	13	,	,	PUNCT
ejpam-7033	578	14	ω	ω	NUM
ejpam-7033	578	15	)	)	PUNCT
ejpam-7033	578	16	=	=	SYM
ejpam-7033	578	17	22	22	NUM
ejpam-7033	578	18	,	,	PUNCT
ejpam-7033	578	19	r(ℏ(ϑ	r(ℏ(ϑ	NUM
ejpam-7033	578	20	)	)	PUNCT
ejpam-7033	578	21	,	,	PUNCT
ejpam-7033	578	22	ℏ(ω	ℏ(ω	NOUN
ejpam-7033	578	23	)	)	PUNCT
ejpam-7033	578	24	)	)	PUNCT
ejpam-7033	578	25	=	=	SYM
ejpam-7033	578	26	10	10	NUM
ejpam-7033	578	27	,	,	PUNCT
ejpam-7033	578	28	r(ϑ	r(ϑ	PROPN
ejpam-7033	578	29	,	,	PUNCT
ejpam-7033	578	30	ℏ(ϑ	ℏ(ϑ	PROPN
ejpam-7033	578	31	)	)	PUNCT
ejpam-7033	578	32	)	)	PUNCT
ejpam-7033	578	33	=	=	SYM
ejpam-7033	578	34	0.5	0.5	NUM
ejpam-7033	578	35	.	.	PUNCT
ejpam-7033	578	36	t	t	PROPN
ejpam-7033	578	37	r(ϑ	r(ϑ	PROPN
ejpam-7033	578	38	,	,	PUNCT
ejpam-7033	578	39	ω	ω	NUM
ejpam-7033	578	40	)	)	PUNCT
ejpam-7033	578	41	=	=	SYM
ejpam-7033	578	42	0.5	0.5	NUM
ejpam-7033	578	43	2	2	NUM
ejpam-7033	578	44	=	=	SYM
ejpam-7033	578	45	0.25	0.25	NUM
ejpam-7033	578	46	,	,	PUNCT
ejpam-7033	578	47	(	(	PUNCT
ejpam-7033	578	48	i	i	PRON
ejpam-7033	578	49	−	−	PROPN
ejpam-7033	578	50	t	t	NOUN
ejpam-7033	578	51	)	)	PUNCT
ejpam-7033	578	52	2(i	2(i	NUM
ejpam-7033	579	1	+	+	NUM
ejpam-7033	579	2	t	t	NOUN
ejpam-7033	579	3	)	)	PUNCT
ejpam-7033	579	4	r(ϑ	r(ϑ	PROPN
ejpam-7033	579	5	,	,	PUNCT
ejpam-7033	579	6	ℏ(ϑ	ℏ(ϑ	PROPN
ejpam-7033	579	7	)	)	PUNCT
ejpam-7033	579	8	)	)	PUNCT
ejpam-7033	580	1	=	=	PUNCT
ejpam-7033	580	2	0.1875	0.1875	NUM
ejpam-7033	580	3	.	.	PUNCT
ejpam-7033	581	1	hence	hence	ADV
ejpam-7033	581	2	for	for	ADP
ejpam-7033	581	3	all	all	DET
ejpam-7033	581	4	ϑ	ϑ	X
ejpam-7033	581	5	,	,	PUNCT
ejpam-7033	581	6	ω	ω	NUM
ejpam-7033	581	7	∈w	∈w	NOUN
ejpam-7033	581	8	,	,	PUNCT
ejpam-7033	581	9	(	(	PUNCT
ejpam-7033	581	10	i	i	PRON
ejpam-7033	581	11	−	−	PROPN
ejpam-7033	581	12	t	t	NOUN
ejpam-7033	581	13	)	)	PUNCT
ejpam-7033	581	14	2(i	2(i	NUM
ejpam-7033	582	1	+	+	NUM
ejpam-7033	582	2	t	t	NOUN
ejpam-7033	582	3	)	)	PUNCT
ejpam-7033	583	1	r(ϑ	r(ϑ	PROPN
ejpam-7033	583	2	,	,	PUNCT
ejpam-7033	583	3	ℏ(ϑ	ℏ(ϑ	PROPN
ejpam-7033	583	4	)	)	PUNCT
ejpam-7033	583	5	)	)	PUNCT
ejpam-7033	584	1	⪯	⪯	PROPN
ejpam-7033	584	2	sr(ϑ	sr(ϑ	PROPN
ejpam-7033	584	3	,	,	PUNCT
ejpam-7033	584	4	ω	ω	NOUN
ejpam-7033	584	5	)	)	PUNCT
ejpam-7033	584	6	implies	imply	VERB
ejpam-7033	584	7	r(ℏ(ϑ	r(ℏ(ϑ	NOUN
ejpam-7033	584	8	)	)	PUNCT
ejpam-7033	584	9	,	,	PUNCT
ejpam-7033	584	10	ℏ(ω	ℏ(ω	PROPN
ejpam-7033	584	11	)	)	PUNCT
ejpam-7033	584	12	)	)	PUNCT
ejpam-7033	585	1	⪯	⪯	PROPN
ejpam-7033	585	2	t	t	PROPN
ejpam-7033	585	3	r(ϑ	r(ϑ	PROPN
ejpam-7033	585	4	,	,	PUNCT
ejpam-7033	585	5	ω	ω	NOUN
ejpam-7033	585	6	)	)	PUNCT
ejpam-7033	585	7	.	.	PUNCT
ejpam-7033	586	1	corollary	corollary	ADJ
ejpam-7033	586	2	18	18	NUM
ejpam-7033	586	3	leads	lead	VERB
ejpam-7033	586	4	us	we	PRON
ejpam-7033	586	5	to	to	PART
ejpam-7033	586	6	have	have	VERB
ejpam-7033	586	7	a	a	DET
ejpam-7033	586	8	point	point	NOUN
ejpam-7033	586	9	0	0	NUM
ejpam-7033	586	10	satisfying	satisfy	VERB
ejpam-7033	586	11	ℏ(0	ℏ(0	PROPN
ejpam-7033	586	12	)	)	PUNCT
ejpam-7033	586	13	=	=	SYM
ejpam-7033	586	14	0	0	X
ejpam-7033	586	15	.	.	NOUN
ejpam-7033	586	16	example	example	NOUN
ejpam-7033	587	1	9	9	NUM
ejpam-7033	587	2	.	.	PUNCT
ejpam-7033	588	1	let	let	VERB
ejpam-7033	588	2	e	e	NOUN
ejpam-7033	588	3	=	=	PROPN
ejpam-7033	588	4	c1	c1	PROPN
ejpam-7033	588	5	r[1	r[1	PROPN
ejpam-7033	588	6	,	,	PUNCT
ejpam-7033	588	7	2	2	NUM
ejpam-7033	588	8	]	]	PUNCT
ejpam-7033	588	9	,	,	PUNCT
ejpam-7033	588	10	and	and	CCONJ
ejpam-7033	588	11	∥ϑ∥	∥ϑ∥	NOUN
ejpam-7033	588	12	=	=	SYM
ejpam-7033	588	13	∥ϑ∥∞	∥ϑ∥∞	PUNCT
ejpam-7033	589	1	+	+	CCONJ
ejpam-7033	589	2	∥ϑ́∥∞	∥ϑ́∥∞	ADV
ejpam-7033	589	3	,	,	PUNCT
ejpam-7033	589	4	c	c	X
ejpam-7033	589	5	=	=	PRON
ejpam-7033	589	6	{	{	PUNCT
ejpam-7033	589	7	ϑ(s	ϑ(s	PROPN
ejpam-7033	589	8	)	)	PUNCT
ejpam-7033	589	9	∈	∈	PROPN
ejpam-7033	589	10	e	e	NOUN
ejpam-7033	589	11	:	:	PUNCT
ejpam-7033	589	12	ϑ(s	ϑ(s	VERB
ejpam-7033	589	13	)	)	PUNCT
ejpam-7033	589	14	>	>	X
ejpam-7033	589	15	0	0	NUM
ejpam-7033	589	16	,	,	PUNCT
ejpam-7033	589	17	s	s	VERB
ejpam-7033	589	18	∈	∈	X
ejpam-7033	590	1	[	[	X
ejpam-7033	590	2	1	1	NUM
ejpam-7033	590	3	,	,	PUNCT
ejpam-7033	590	4	2	2	NUM
ejpam-7033	590	5	]	]	PUNCT
ejpam-7033	590	6	}	}	PUNCT
ejpam-7033	590	7	.	.	PUNCT
ejpam-7033	591	1	for	for	ADP
ejpam-7033	591	2	q	q	PROPN
ejpam-7033	591	3	≥	≥	NUM
ejpam-7033	591	4	1	1	NUM
ejpam-7033	591	5	,	,	PUNCT
ejpam-7033	591	6	let	let	VERB
ejpam-7033	591	7	ϑ	ϑ	X
ejpam-7033	591	8	=	=	PUNCT
ejpam-7033	591	9	x	x	X
ejpam-7033	591	10	and	and	CCONJ
ejpam-7033	591	11	ω	ω	NUM
ejpam-7033	591	12	=	=	SYM
ejpam-7033	591	13	x2k	x2k	NOUN
ejpam-7033	591	14	.	.	PUNCT
ejpam-7033	592	1	by	by	ADP
ejpam-7033	592	2	definition	definition	NOUN
ejpam-7033	592	3	∥ϑ∥	∥ϑ∥	NOUN
ejpam-7033	592	4	=	=	SYM
ejpam-7033	592	5	2	2	NUM
ejpam-7033	592	6	and	and	CCONJ
ejpam-7033	592	7	∥ω∥	∥ω∥	NUM
ejpam-7033	592	8	=	=	SYM
ejpam-7033	592	9	2k	2k	NOUN
ejpam-7033	592	10	+	+	CCONJ
ejpam-7033	592	11	1	1	NUM
ejpam-7033	592	12	also	also	ADV
ejpam-7033	592	13	ϑ	ϑ	X
ejpam-7033	592	14	⪯	⪯	PROPN
ejpam-7033	592	15	ω	ω	PROPN
ejpam-7033	592	16	,	,	PUNCT
ejpam-7033	592	17	with	with	ADP
ejpam-7033	592	18	q∥ϑ∥	q∥ϑ∥	PROPN
ejpam-7033	592	19	≤	≤	PROPN
ejpam-7033	592	20	∥ω∥.	∥ω∥.	ADV
ejpam-7033	593	1	so	so	SCONJ
ejpam-7033	593	2	c	c	NOUN
ejpam-7033	593	3	represents	represent	VERB
ejpam-7033	593	4	a	a	DET
ejpam-7033	593	5	non	non	ADJ
ejpam-7033	593	6	normal	normal	ADJ
ejpam-7033	593	7	cone	cone	NOUN
ejpam-7033	593	8	.	.	PUNCT
ejpam-7033	594	1	define	define	VERB
ejpam-7033	594	2	t	t	PROPN
ejpam-7033	594	3	:	:	PUNCT
ejpam-7033	594	4	e	e	X
ejpam-7033	594	5	→	→	SYM
ejpam-7033	594	6	e	e	X
ejpam-7033	594	7	by	by	X
ejpam-7033	594	8	(	(	PUNCT
ejpam-7033	594	9	t	t	NOUN
ejpam-7033	594	10	ϑ)(t	ϑ)(t	PROPN
ejpam-7033	594	11	)	)	PUNCT
ejpam-7033	594	12	=	=	SYM
ejpam-7033	594	13	1	1	NUM
ejpam-7033	594	14	2	2	NUM
ejpam-7033	594	15	∫	∫	NOUN
ejpam-7033	594	16	t	t	PROPN
ejpam-7033	594	17	0	0	NUM
ejpam-7033	594	18	ϑ(t)ds	ϑ(t)ds	PROPN
ejpam-7033	594	19	.	.	PUNCT
ejpam-7033	595	1	(	(	PUNCT
ejpam-7033	595	2	t	t	PROPN
ejpam-7033	595	3	(	(	PUNCT
ejpam-7033	595	4	ϑ+	ϑ+	X
ejpam-7033	595	5	ω))(t	ω))(t	X
ejpam-7033	595	6	)	)	PUNCT
ejpam-7033	595	7	=	=	SYM
ejpam-7033	595	8	1	1	NUM
ejpam-7033	595	9	2	2	NUM
ejpam-7033	595	10	∫	∫	NOUN
ejpam-7033	595	11	t	t	NOUN
ejpam-7033	595	12	0	0	NUM
ejpam-7033	595	13	(	(	PUNCT
ejpam-7033	595	14	ϑ+	ϑ+	X
ejpam-7033	595	15	ω)(t)ds	ω)(t)ds	ADJ
ejpam-7033	595	16	=	=	SYM
ejpam-7033	595	17	1	1	NUM
ejpam-7033	595	18	2	2	NUM
ejpam-7033	595	19	∫	∫	NOUN
ejpam-7033	595	20	t	t	NOUN
ejpam-7033	595	21	0	0	NUM
ejpam-7033	595	22	ϑ(t)ds+	ϑ(t)ds+	NOUN
ejpam-7033	595	23	1	1	NUM
ejpam-7033	595	24	2	2	NUM
ejpam-7033	595	25	∫	∫	NOUN
ejpam-7033	595	26	t	t	PROPN
ejpam-7033	595	27	0	0	NUM
ejpam-7033	595	28	ω(t)ds	ω(t)ds	PROPN
ejpam-7033	595	29	.	.	PUNCT
ejpam-7033	595	30	(	(	PUNCT
ejpam-7033	595	31	t	t	PROPN
ejpam-7033	595	32	nϑ)(t	nϑ)(t	PROPN
ejpam-7033	595	33	)	)	PUNCT
ejpam-7033	595	34	⪯	⪯	PROPN
ejpam-7033	595	35	t	t	PROPN
ejpam-7033	595	36	n	n	ADV
ejpam-7033	595	37	2nn	2nn	ADJ
ejpam-7033	595	38	!	!	PUNCT
ejpam-7033	596	1	∥ϑ∥	∥ϑ∥	NOUN
ejpam-7033	596	2	1	1	NUM
ejpam-7033	596	3	2∞	2∞	NUM
ejpam-7033	596	4	⪯	⪯	NOUN
ejpam-7033	596	5	2n	2n	NUM
ejpam-7033	596	6	2nn	2nn	ADJ
ejpam-7033	596	7	!	!	PUNCT
ejpam-7033	597	1	∥ϑ∥	∥ϑ∥	VERB
ejpam-7033	597	2	1	1	NUM
ejpam-7033	597	3	2	2	NUM
ejpam-7033	597	4	for	for	ADP
ejpam-7033	597	5	each	each	DET
ejpam-7033	597	6	t	t	NOUN
ejpam-7033	597	7	∈	∈	PROPN
ejpam-7033	598	1	[	[	X
ejpam-7033	598	2	1	1	NUM
ejpam-7033	598	3	,	,	PUNCT
ejpam-7033	598	4	2	2	NUM
ejpam-7033	598	5	]	]	PUNCT
ejpam-7033	598	6	and	and	CCONJ
ejpam-7033	598	7	n	n	PRON
ejpam-7033	598	8	≥	≥	NOUN
ejpam-7033	598	9	1	1	NUM
ejpam-7033	598	10	.	.	PUNCT
ejpam-7033	598	11	so	so	ADV
ejpam-7033	598	12	∥(t	∥(t	VERB
ejpam-7033	598	13	nϑ)(t)∥∞	nϑ)(t)∥∞	NOUN
ejpam-7033	598	14	⪯	⪯	NOUN
ejpam-7033	598	15	1	1	NUM
ejpam-7033	598	16	n	n	CCONJ
ejpam-7033	598	17	!	!	NOUN
ejpam-7033	598	18	∥ϑ∥	∥ϑ∥	VERB
ejpam-7033	598	19	1	1	NUM
ejpam-7033	598	20	2	2	NUM
ejpam-7033	598	21	.	.	PUNCT
ejpam-7033	599	1	∥(t	∥(t	AUX
ejpam-7033	600	1	nϑ)′(t)∥∞	nϑ)′(t)∥∞	PROPN
ejpam-7033	600	2	⪯	⪯	VERB
ejpam-7033	600	3	1√	1√	PROPN
ejpam-7033	600	4	(	(	PUNCT
ejpam-7033	600	5	n−	n−	NOUN
ejpam-7033	600	6	1	1	NUM
ejpam-7033	600	7	)	)	PUNCT
ejpam-7033	600	8	!	!	PUNCT
ejpam-7033	601	1	∥ϑ∥	∥ϑ∥	NOUN
ejpam-7033	601	2	1	1	NUM
ejpam-7033	601	3	4	4	NUM
ejpam-7033	601	4	for	for	ADP
ejpam-7033	601	5	n	n	X
ejpam-7033	601	6	≥	≥	NUM
ejpam-7033	601	7	2	2	NUM
ejpam-7033	601	8	.	.	PUNCT
ejpam-7033	601	9	∥(t	∥(t	AUX
ejpam-7033	602	1	nϑ)(t)∥	nϑ)(t)∥	NOUN
ejpam-7033	602	2	=	=	PRON
ejpam-7033	602	3	∥(t	∥(t	VERB
ejpam-7033	602	4	nϑ)(t)∥∞	nϑ)(t)∥∞	PRON
ejpam-7033	602	5	+	+	CCONJ
ejpam-7033	602	6	∥(t	∥(t	VERB
ejpam-7033	602	7	nϑ)′(t)∥∞	nϑ)′(t)∥∞	PROPN
ejpam-7033	602	8	⪯	⪯	NOUN
ejpam-7033	602	9	1	1	NUM
ejpam-7033	602	10	n	n	CCONJ
ejpam-7033	602	11	!	!	NOUN
ejpam-7033	602	12	∥ϑ∥	∥ϑ∥	VERB
ejpam-7033	602	13	1	1	NUM
ejpam-7033	602	14	2	2	NUM
ejpam-7033	602	15	+	+	CCONJ
ejpam-7033	602	16	1√	1√	NUM
ejpam-7033	602	17	(	(	PUNCT
ejpam-7033	602	18	n−	n−	NOUN
ejpam-7033	602	19	1	1	NUM
ejpam-7033	602	20	)	)	PUNCT
ejpam-7033	602	21	!	!	PUNCT
ejpam-7033	603	1	∥ϑ∥	∥ϑ∥	NOUN
ejpam-7033	603	2	1	1	NUM
ejpam-7033	603	3	4	4	NUM
ejpam-7033	603	4	for	for	ADP
ejpam-7033	603	5	n	n	X
ejpam-7033	603	6	≥	≥	NOUN
ejpam-7033	603	7	2	2	NUM
ejpam-7033	603	8	,	,	PUNCT
ejpam-7033	603	9	∥(t	∥(t	X
ejpam-7033	604	1	nϑ)(t)∥	nϑ)(t)∥	NOUN
ejpam-7033	604	2	=	=	SYM
ejpam-7033	604	3	0	0	NUM
ejpam-7033	604	4	when	when	SCONJ
ejpam-7033	604	5	n	n	PRON
ejpam-7033	604	6	≥	≥	X
ejpam-7033	604	7	n1	n1	PROPN
ejpam-7033	604	8	for	for	ADP
ejpam-7033	604	9	n1	n1	PROPN
ejpam-7033	604	10	∈	∈	PROPN
ejpam-7033	604	11	n.	n.	NOUN
ejpam-7033	605	1	so	so	SCONJ
ejpam-7033	605	2	t	t	PROPN
ejpam-7033	605	3	∈	∈	PROPN
ejpam-7033	605	4	b(e	b(e	PROPN
ejpam-7033	605	5	,	,	PUNCT
ejpam-7033	605	6	e	e	NOUN
ejpam-7033	605	7	)	)	PUNCT
ejpam-7033	605	8	.	.	PUNCT
ejpam-7033	606	1	take	take	VERB
ejpam-7033	606	2	x	x	NOUN
ejpam-7033	606	3	=	=	PRON
ejpam-7033	606	4	{	{	PUNCT
ejpam-7033	606	5	et	et	NOUN
ejpam-7033	606	6	3	3	NUM
ejpam-7033	606	7	,	,	PUNCT
ejpam-7033	606	8	et	et	NOUN
ejpam-7033	606	9	2	2	NUM
ejpam-7033	606	10	,	,	PUNCT
ejpam-7033	606	11	e	e	PROPN
ejpam-7033	606	12	t	t	PROPN
ejpam-7033	606	13	,	,	PUNCT
ejpam-7033	606	14	2et	2et	NOUN
ejpam-7033	606	15	}	}	PUNCT
ejpam-7033	606	16	and	and	CCONJ
ejpam-7033	606	17	ℏ	ℏ	X
ejpam-7033	606	18	:	:	PUNCT
ejpam-7033	606	19	x	x	X
ejpam-7033	606	20	→	→	SYM
ejpam-7033	606	21	x	x	SYM
ejpam-7033	606	22	,	,	PUNCT
ejpam-7033	606	23	such	such	ADJ
ejpam-7033	606	24	that	that	SCONJ
ejpam-7033	606	25	ℏ	ℏ	PROPN
ejpam-7033	606	26	(	(	PUNCT
ejpam-7033	606	27	et3	et3	ADJ
ejpam-7033	606	28	)	)	PUNCT
ejpam-7033	606	29	=	=	SYM
ejpam-7033	606	30	ℏ	ℏ	PROPN
ejpam-7033	606	31	(	(	PUNCT
ejpam-7033	606	32	et2	et2	PROPN
ejpam-7033	606	33	)	)	PUNCT
ejpam-7033	606	34	=	=	SYM
ejpam-7033	606	35	et	et	NOUN
ejpam-7033	606	36	3	3	NUM
ejpam-7033	606	37	,	,	PUNCT
ejpam-7033	606	38	ℏ(et	ℏ(et	X
ejpam-7033	606	39	)	)	PUNCT
ejpam-7033	606	40	=	=	SYM
ejpam-7033	606	41	2et	2et	NOUN
ejpam-7033	606	42	and	and	CCONJ
ejpam-7033	606	43	ℏ(2et	ℏ(2et	ADJ
ejpam-7033	606	44	)	)	PUNCT
ejpam-7033	606	45	=	=	SYM
ejpam-7033	606	46	et	et	NOUN
ejpam-7033	606	47	2	2	NUM
ejpam-7033	606	48	.	.	PUNCT
ejpam-7033	607	1	define	define	VERB
ejpam-7033	607	2	r	r	NOUN
ejpam-7033	607	3	:	:	PUNCT
ejpam-7033	607	4	x	x	X
ejpam-7033	607	5	×x	×x	ADP
ejpam-7033	607	6	→	→	SYM
ejpam-7033	607	7	e	e	NOUN
ejpam-7033	607	8	by	by	ADP
ejpam-7033	607	9	r(ϑ1	r(ϑ1	NOUN
ejpam-7033	607	10	,	,	PUNCT
ejpam-7033	607	11	ϑ2	ϑ2	NOUN
ejpam-7033	607	12	)	)	PUNCT
ejpam-7033	607	13	=	=	PUNCT
ejpam-7033	608	1			NUM
ejpam-7033	608	2	0	0	PUNCT
ejpam-7033	609	1	if	if	SCONJ
ejpam-7033	609	2	ϑ1	ϑ1	NOUN
ejpam-7033	609	3	=	=	SYM
ejpam-7033	609	4	ϑ2	ϑ2	PROPN
ejpam-7033	609	5	10et	10et	PROPN
ejpam-7033	609	6	if	if	SCONJ
ejpam-7033	609	7	(	(	PUNCT
ejpam-7033	609	8	ϑ1	ϑ1	NOUN
ejpam-7033	609	9	,	,	PUNCT
ejpam-7033	609	10	ϑ2	ϑ2	PROPN
ejpam-7033	609	11	)	)	PUNCT
ejpam-7033	609	12	=	=	PUNCT
ejpam-7033	610	1	(	(	PUNCT
ejpam-7033	610	2	e	e	X
ejpam-7033	610	3	t	t	PROPN
ejpam-7033	610	4	3	3	NUM
ejpam-7033	610	5	,	,	PUNCT
ejpam-7033	610	6	e	e	PROPN
ejpam-7033	610	7	t	t	PROPN
ejpam-7033	610	8	)	)	PUNCT
ejpam-7033	610	9	,	,	PUNCT
ejpam-7033	610	10	et	et	NOUN
ejpam-7033	610	11	3	3	NUM
ejpam-7033	610	12	if	if	SCONJ
ejpam-7033	610	13	(	(	PUNCT
ejpam-7033	610	14	ϑ1	ϑ1	NOUN
ejpam-7033	610	15	,	,	PUNCT
ejpam-7033	610	16	ϑ2	ϑ2	PROPN
ejpam-7033	610	17	)	)	PUNCT
ejpam-7033	610	18	=	=	PUNCT
ejpam-7033	611	1	(	(	PUNCT
ejpam-7033	611	2	e	e	X
ejpam-7033	611	3	t	t	PROPN
ejpam-7033	611	4	2	2	NUM
ejpam-7033	611	5	,	,	PUNCT
ejpam-7033	611	6	2e	2e	PROPN
ejpam-7033	611	7	t	t	PROPN
ejpam-7033	611	8	)	)	PUNCT
ejpam-7033	611	9	,	,	PUNCT
ejpam-7033	611	10	6et	6et	ADJ
ejpam-7033	611	11	if	if	SCONJ
ejpam-7033	611	12	(	(	PUNCT
ejpam-7033	611	13	ϑ1	ϑ1	NOUN
ejpam-7033	611	14	,	,	PUNCT
ejpam-7033	611	15	ϑ2	ϑ2	PROPN
ejpam-7033	611	16	)	)	PUNCT
ejpam-7033	611	17	∈	∈	PROPN
ejpam-7033	611	18	{	{	PUNCT
ejpam-7033	611	19	(	(	PUNCT
ejpam-7033	611	20	et2	et2	PROPN
ejpam-7033	611	21	,	,	PUNCT
ejpam-7033	611	22	e	e	PROPN
ejpam-7033	611	23	t	t	PROPN
ejpam-7033	611	24	)	)	PUNCT
ejpam-7033	611	25	,	,	PUNCT
ejpam-7033	611	26	(	(	PUNCT
ejpam-7033	611	27	et	et	NOUN
ejpam-7033	611	28	,	,	PUNCT
ejpam-7033	611	29	2et	2et	NOUN
ejpam-7033	611	30	)	)	PUNCT
ejpam-7033	611	31	}	}	PUNCT
ejpam-7033	611	32	3et	3et	NOUN
ejpam-7033	611	33	2	2	NUM
ejpam-7033	611	34	otherwise	otherwise	ADV
ejpam-7033	611	35	.	.	PUNCT
ejpam-7033	612	1	a.	a.	PROPN
ejpam-7033	612	2	arif	arif	PROPN
ejpam-7033	612	3	et	et	PROPN
ejpam-7033	612	4	al	al	PROPN
ejpam-7033	612	5	.	.	PUNCT
ejpam-7033	612	6	/	/	SYM
ejpam-7033	612	7	eur	eur	PROPN
ejpam-7033	612	8	.	.	PUNCT
ejpam-7033	613	1	j.	j.	PROPN
ejpam-7033	613	2	pure	pure	PROPN
ejpam-7033	613	3	appl	appl	PROPN
ejpam-7033	613	4	.	.	PROPN
ejpam-7033	613	5	math	math	PROPN
ejpam-7033	613	6	,	,	PUNCT
ejpam-7033	613	7	18	18	NUM
ejpam-7033	613	8	(	(	PUNCT
ejpam-7033	613	9	4	4	NUM
ejpam-7033	613	10	)	)	PUNCT
ejpam-7033	613	11	(	(	PUNCT
ejpam-7033	613	12	2025	2025	NUM
ejpam-7033	613	13	)	)	PUNCT
ejpam-7033	613	14	,	,	PUNCT
ejpam-7033	613	15	7033	7033	NUM
ejpam-7033	613	16	20	20	NUM
ejpam-7033	613	17	of	of	ADP
ejpam-7033	613	18	29	29	NUM
ejpam-7033	613	19	10et	10et	NOUN
ejpam-7033	613	20	=	=	SYM
ejpam-7033	614	1	r	r	NOUN
ejpam-7033	614	2	(	(	PUNCT
ejpam-7033	614	3	et	et	NOUN
ejpam-7033	614	4	3	3	NUM
ejpam-7033	614	5	,	,	PUNCT
ejpam-7033	614	6	et	et	NOUN
ejpam-7033	614	7	)	)	PUNCT
ejpam-7033	614	8	≥	≥	PROPN
ejpam-7033	614	9	r	r	NOUN
ejpam-7033	614	10	(	(	PUNCT
ejpam-7033	614	11	et	et	NOUN
ejpam-7033	614	12	3	3	NUM
ejpam-7033	614	13	,	,	PUNCT
ejpam-7033	614	14	et	et	NOUN
ejpam-7033	614	15	2	2	NUM
ejpam-7033	614	16	)	)	PUNCT
ejpam-7033	615	1	+	+	CCONJ
ejpam-7033	615	2	r	r	NOUN
ejpam-7033	615	3	(	(	PUNCT
ejpam-7033	615	4	et	et	NOUN
ejpam-7033	615	5	2	2	NUM
ejpam-7033	615	6	,	,	PUNCT
ejpam-7033	615	7	2et	2et	NOUN
ejpam-7033	615	8	)	)	PUNCT
ejpam-7033	616	1	+	+	CCONJ
ejpam-7033	616	2	r	r	NOUN
ejpam-7033	616	3	(	(	PUNCT
ejpam-7033	616	4	2et	2et	NOUN
ejpam-7033	616	5	,	,	PUNCT
ejpam-7033	616	6	et	et	NOUN
ejpam-7033	616	7	)	)	PUNCT
ejpam-7033	616	8	=	=	PUNCT
ejpam-7033	617	1	3et	3et	NOUN
ejpam-7033	617	2	2	2	NUM
ejpam-7033	618	1	+	+	CCONJ
ejpam-7033	618	2	et	et	NOUN
ejpam-7033	618	3	3	3	NUM
ejpam-7033	618	4	+	+	NUM
ejpam-7033	618	5	6et	6et	ADJ
ejpam-7033	618	6	=	=	SYM
ejpam-7033	618	7	29et	29et	NOUN
ejpam-7033	618	8	6	6	NUM
ejpam-7033	618	9	.	.	PUNCT
ejpam-7033	619	1	one	one	PRON
ejpam-7033	619	2	can	can	AUX
ejpam-7033	619	3	easily	easily	ADV
ejpam-7033	619	4	check	check	VERB
ejpam-7033	619	5	that	that	PRON
ejpam-7033	619	6	(	(	PUNCT
ejpam-7033	619	7	db3	db3	PROPN
ejpam-7033	619	8	)	)	PUNCT
ejpam-7033	619	9	holds	hold	VERB
ejpam-7033	619	10	for	for	ADP
ejpam-7033	619	11	s	s	NOUN
ejpam-7033	619	12	=	=	SYM
ejpam-7033	619	13	3	3	NUM
ejpam-7033	619	14	,	,	PUNCT
ejpam-7033	619	15	so	so	SCONJ
ejpam-7033	619	16	r	r	NOUN
ejpam-7033	619	17	represents	represent	VERB
ejpam-7033	619	18	rectangular	rectangular	ADJ
ejpam-7033	619	19	cone	cone	NOUN
ejpam-7033	619	20	b	b	NOUN
ejpam-7033	619	21	-	-	PUNCT
ejpam-7033	619	22	metric	metric	ADJ
ejpam-7033	619	23	space	space	NOUN
ejpam-7033	619	24	,	,	PUNCT
ejpam-7033	619	25	but	but	CCONJ
ejpam-7033	619	26	not	not	PART
ejpam-7033	619	27	rectangular	rectangular	VERB
ejpam-7033	619	28	cone	cone	NOUN
ejpam-7033	619	29	metric	metric	ADJ
ejpam-7033	619	30	space	space	NOUN
ejpam-7033	619	31	.	.	PUNCT
ejpam-7033	620	1	for	for	ADP
ejpam-7033	620	2	if	if	SCONJ
ejpam-7033	620	3	ϑ	ϑ	X
ejpam-7033	620	4	=	=	X
ejpam-7033	620	5	et	et	NOUN
ejpam-7033	620	6	3	3	NUM
ejpam-7033	620	7	and	and	CCONJ
ejpam-7033	620	8	ω	ω	NUM
ejpam-7033	620	9	=	=	SYM
ejpam-7033	620	10	et	et	NOUN
ejpam-7033	620	11	2	2	NUM
ejpam-7033	620	12	,	,	PUNCT
ejpam-7033	620	13	then	then	ADV
ejpam-7033	620	14	r(ϑ	r(ϑ	PROPN
ejpam-7033	620	15	,	,	PUNCT
ejpam-7033	620	16	ℏ(ϑ	ℏ(ϑ	PROPN
ejpam-7033	620	17	)	)	PUNCT
ejpam-7033	620	18	)	)	PUNCT
ejpam-7033	620	19	=	=	SYM
ejpam-7033	620	20	r(ℏ(ϑ	r(ℏ(ϑ	NUM
ejpam-7033	620	21	)	)	PUNCT
ejpam-7033	620	22	,	,	PUNCT
ejpam-7033	620	23	ℏ(ω	ℏ(ω	NOUN
ejpam-7033	620	24	)	)	PUNCT
ejpam-7033	620	25	)	)	PUNCT
ejpam-7033	620	26	=	=	SYM
ejpam-7033	620	27	0	0	NUM
ejpam-7033	620	28	,	,	PUNCT
ejpam-7033	620	29	r(ϑ	r(ϑ	PROPN
ejpam-7033	620	30	,	,	PUNCT
ejpam-7033	620	31	ω	ω	NOUN
ejpam-7033	620	32	)	)	PUNCT
ejpam-7033	620	33	=	=	SYM
ejpam-7033	621	1	3et	3et	NOUN
ejpam-7033	621	2	2	2	NUM
ejpam-7033	621	3	(	(	PUNCT
ejpam-7033	621	4	i	i	PRON
ejpam-7033	621	5	−	−	PROPN
ejpam-7033	622	1	t	t	NOUN
ejpam-7033	622	2	)	)	PUNCT
ejpam-7033	622	3	2(i	2(i	NUM
ejpam-7033	623	1	+	+	NUM
ejpam-7033	623	2	t	t	NOUN
ejpam-7033	623	3	)	)	PUNCT
ejpam-7033	623	4	r(ϑ	r(ϑ	PROPN
ejpam-7033	623	5	,	,	PUNCT
ejpam-7033	623	6	ℏ(ϑ	ℏ(ϑ	PROPN
ejpam-7033	623	7	)	)	PUNCT
ejpam-7033	623	8	)	)	PUNCT
ejpam-7033	624	1	=	=	PUNCT
ejpam-7033	624	2	0	0	X
ejpam-7033	624	3	.	.	PUNCT
ejpam-7033	625	1	for	for	ADP
ejpam-7033	625	2	if	if	SCONJ
ejpam-7033	625	3	ϑ	ϑ	X
ejpam-7033	625	4	=	=	X
ejpam-7033	625	5	et	et	NOUN
ejpam-7033	625	6	2	2	NUM
ejpam-7033	625	7	and	and	CCONJ
ejpam-7033	625	8	ω	ω	NUM
ejpam-7033	625	9	=	=	SYM
ejpam-7033	625	10	et	et	PROPN
ejpam-7033	625	11	,	,	PUNCT
ejpam-7033	625	12	then	then	ADV
ejpam-7033	625	13	r(ϑ	r(ϑ	PROPN
ejpam-7033	625	14	,	,	PUNCT
ejpam-7033	625	15	ω	ω	NUM
ejpam-7033	625	16	)	)	PUNCT
ejpam-7033	625	17	=	=	SYM
ejpam-7033	625	18	6et	6et	NOUN
ejpam-7033	625	19	,	,	PUNCT
ejpam-7033	625	20	r(ℏ(ϑ	r(ℏ(ϑ	NOUN
ejpam-7033	625	21	)	)	PUNCT
ejpam-7033	625	22	,	,	PUNCT
ejpam-7033	625	23	ℏ(ω	ℏ(ω	NOUN
ejpam-7033	625	24	)	)	PUNCT
ejpam-7033	625	25	)	)	PUNCT
ejpam-7033	626	1	=	=	PUNCT
ejpam-7033	626	2	r(ϑ	r(ϑ	PROPN
ejpam-7033	626	3	,	,	PUNCT
ejpam-7033	626	4	ℏ(ϑ	ℏ(ϑ	PROPN
ejpam-7033	626	5	)	)	PUNCT
ejpam-7033	626	6	)	)	PUNCT
ejpam-7033	627	1	=	=	PUNCT
ejpam-7033	627	2	3et	3et	NOUN
ejpam-7033	627	3	2	2	NUM
ejpam-7033	627	4	,	,	PUNCT
ejpam-7033	627	5	t	t	PROPN
ejpam-7033	627	6	s	s	PART
ejpam-7033	627	7	r(ϑ	r(ϑ	PROPN
ejpam-7033	627	8	,	,	PUNCT
ejpam-7033	627	9	ω)(t	ω)(t	NUM
ejpam-7033	627	10	)	)	PUNCT
ejpam-7033	627	11	=	=	SYM
ejpam-7033	627	12	et	et	NOUN
ejpam-7033	627	13	.	.	PUNCT
ejpam-7033	628	1	(	(	PUNCT
ejpam-7033	628	2	i	i	PRON
ejpam-7033	628	3	−	−	PROPN
ejpam-7033	629	1	t	t	NOUN
ejpam-7033	629	2	)	)	PUNCT
ejpam-7033	629	3	2(i	2(i	NUM
ejpam-7033	630	1	+	+	NUM
ejpam-7033	630	2	t	t	NOUN
ejpam-7033	630	3	)	)	PUNCT
ejpam-7033	630	4	r(ϑ	r(ϑ	PROPN
ejpam-7033	630	5	,	,	PUNCT
ejpam-7033	630	6	ℏ(ϑ	ℏ(ϑ	PROPN
ejpam-7033	630	7	)	)	PUNCT
ejpam-7033	630	8	)	)	PUNCT
ejpam-7033	631	1	=	=	SYM
ejpam-7033	632	1	15et	15et	ADJ
ejpam-7033	632	2	4	4	X
ejpam-7033	632	3	.	.	PUNCT
ejpam-7033	633	1	for	for	ADP
ejpam-7033	633	2	if	if	SCONJ
ejpam-7033	633	3	ϑ	ϑ	X
ejpam-7033	633	4	=	=	X
ejpam-7033	633	5	et	et	NOUN
ejpam-7033	633	6	and	and	CCONJ
ejpam-7033	633	7	ω	ω	NUM
ejpam-7033	633	8	=	=	NOUN
ejpam-7033	633	9	2et	2et	PROPN
ejpam-7033	633	10	,	,	PUNCT
ejpam-7033	633	11	then	then	ADV
ejpam-7033	633	12	r(ϑ	r(ϑ	PROPN
ejpam-7033	633	13	,	,	PUNCT
ejpam-7033	633	14	ω	ω	NUM
ejpam-7033	633	15	)	)	PUNCT
ejpam-7033	633	16	=	=	SYM
ejpam-7033	633	17	6et	6et	NOUN
ejpam-7033	633	18	,	,	PUNCT
ejpam-7033	633	19	r(ℏ(ϑ	r(ℏ(ϑ	NOUN
ejpam-7033	633	20	)	)	PUNCT
ejpam-7033	633	21	,	,	PUNCT
ejpam-7033	633	22	ℏ(ω	ℏ(ω	NOUN
ejpam-7033	633	23	)	)	PUNCT
ejpam-7033	633	24	)	)	PUNCT
ejpam-7033	634	1	=	=	PUNCT
ejpam-7033	634	2	3et	3et	NOUN
ejpam-7033	634	3	2	2	NUM
ejpam-7033	634	4	,	,	PUNCT
ejpam-7033	634	5	r(ϑ	r(ϑ	PROPN
ejpam-7033	634	6	,	,	PUNCT
ejpam-7033	634	7	ℏ(ϑ	ℏ(ϑ	PROPN
ejpam-7033	634	8	)	)	PUNCT
ejpam-7033	634	9	)	)	PUNCT
ejpam-7033	635	1	=	=	PUNCT
ejpam-7033	635	2	et	et	X
ejpam-7033	635	3	t	t	NOUN
ejpam-7033	635	4	s	s	PART
ejpam-7033	635	5	r(ϑ	r(ϑ	PROPN
ejpam-7033	635	6	,	,	PUNCT
ejpam-7033	635	7	ω)(t	ω)(t	NUM
ejpam-7033	635	8	)	)	PUNCT
ejpam-7033	635	9	=	=	SYM
ejpam-7033	635	10	et	et	NOUN
ejpam-7033	635	11	.	.	PUNCT
ejpam-7033	636	1	(	(	PUNCT
ejpam-7033	636	2	i	i	PRON
ejpam-7033	636	3	−	−	PROPN
ejpam-7033	637	1	t	t	NOUN
ejpam-7033	637	2	)	)	PUNCT
ejpam-7033	637	3	2(i	2(i	NUM
ejpam-7033	638	1	+	+	NUM
ejpam-7033	638	2	t	t	NOUN
ejpam-7033	638	3	)	)	PUNCT
ejpam-7033	638	4	r(ϑ	r(ϑ	PROPN
ejpam-7033	638	5	,	,	PUNCT
ejpam-7033	638	6	ℏ(ϑ	ℏ(ϑ	PROPN
ejpam-7033	638	7	)	)	PUNCT
ejpam-7033	638	8	)	)	PUNCT
ejpam-7033	639	1	=	=	PUNCT
ejpam-7033	640	1	3et	3et	NOUN
ejpam-7033	640	2	8	8	NUM
ejpam-7033	640	3	.	.	PUNCT
ejpam-7033	641	1	now	now	ADV
ejpam-7033	641	2	if	if	SCONJ
ejpam-7033	641	3	t	t	PROPN
ejpam-7033	641	4	∈	∈	PROPN
ejpam-7033	641	5	[	[	X
ejpam-7033	641	6	1	1	NUM
ejpam-7033	641	7	,	,	PUNCT
ejpam-7033	641	8	2	2	NUM
ejpam-7033	641	9	]	]	PUNCT
ejpam-7033	641	10	,	,	PUNCT
ejpam-7033	641	11	and	and	CCONJ
ejpam-7033	641	12	s	s	AUX
ejpam-7033	641	13	=	=	SYM
ejpam-7033	641	14	3	3	NUM
ejpam-7033	641	15	,	,	PUNCT
ejpam-7033	641	16	then	then	ADV
ejpam-7033	641	17	(	(	PUNCT
ejpam-7033	641	18	i	i	PRON
ejpam-7033	641	19	−	−	PROPN
ejpam-7033	641	20	t	t	NOUN
ejpam-7033	641	21	)	)	PUNCT
ejpam-7033	641	22	2(i	2(i	NUM
ejpam-7033	642	1	+	+	NUM
ejpam-7033	642	2	t	t	NOUN
ejpam-7033	642	3	)	)	PUNCT
ejpam-7033	643	1	r(ϑ	r(ϑ	PROPN
ejpam-7033	643	2	,	,	PUNCT
ejpam-7033	643	3	ℏ(ϑ	ℏ(ϑ	PROPN
ejpam-7033	643	4	)	)	PUNCT
ejpam-7033	643	5	)	)	PUNCT
ejpam-7033	644	1	⪯	⪯	PROPN
ejpam-7033	644	2	sr(ϑ	sr(ϑ	PROPN
ejpam-7033	644	3	,	,	PUNCT
ejpam-7033	644	4	ω	ω	NOUN
ejpam-7033	644	5	)	)	PUNCT
ejpam-7033	644	6	implies	imply	VERB
ejpam-7033	644	7	r(ℏ(ϑ	r(ℏ(ϑ	NOUN
ejpam-7033	644	8	)	)	PUNCT
ejpam-7033	644	9	,	,	PUNCT
ejpam-7033	644	10	ℏ(ω	ℏ(ω	PROPN
ejpam-7033	644	11	)	)	PUNCT
ejpam-7033	644	12	)	)	PUNCT
ejpam-7033	644	13	⪯	⪯	NOUN
ejpam-7033	644	14	1	1	NUM
ejpam-7033	644	15	s	s	PART
ejpam-7033	644	16	t	t	PROPN
ejpam-7033	644	17	r(ϑ	r(ϑ	PROPN
ejpam-7033	644	18	,	,	PUNCT
ejpam-7033	644	19	ω	ω	NOUN
ejpam-7033	644	20	)	)	PUNCT
ejpam-7033	644	21	.	.	PUNCT
ejpam-7033	645	1	by	by	ADP
ejpam-7033	645	2	corollary	corollary	ADJ
ejpam-7033	645	3	19	19	NUM
ejpam-7033	645	4	,	,	PUNCT
ejpam-7033	645	5	we	we	PRON
ejpam-7033	645	6	get	get	VERB
ejpam-7033	645	7	ℏ	ℏ	PROPN
ejpam-7033	645	8	(	(	PUNCT
ejpam-7033	645	9	et3	et3	ADJ
ejpam-7033	645	10	)	)	PUNCT
ejpam-7033	646	1	=	=	SYM
ejpam-7033	646	2	et	et	NOUN
ejpam-7033	646	3	3	3	NUM
ejpam-7033	646	4	.	.	PUNCT
ejpam-7033	647	1	6	6	NUM
ejpam-7033	647	2	.	.	X
ejpam-7033	647	3	a	a	DET
ejpam-7033	647	4	homotopy	homotopy	NOUN
ejpam-7033	647	5	result	result	NOUN
ejpam-7033	647	6	in	in	ADP
ejpam-7033	647	7	this	this	DET
ejpam-7033	647	8	section	section	NOUN
ejpam-7033	647	9	,	,	PUNCT
ejpam-7033	647	10	we	we	PRON
ejpam-7033	647	11	apply	apply	VERB
ejpam-7033	647	12	corollary	corollary	ADJ
ejpam-7033	647	13	19	19	NUM
ejpam-7033	647	14	to	to	PART
ejpam-7033	647	15	obtain	obtain	VERB
ejpam-7033	647	16	the	the	DET
ejpam-7033	647	17	following	follow	VERB
ejpam-7033	647	18	homotopy	homotopy	NOUN
ejpam-7033	647	19	result	result	NOUN
ejpam-7033	647	20	.	.	PUNCT
ejpam-7033	648	1	theorem	theorem	ADJ
ejpam-7033	648	2	20	20	NUM
ejpam-7033	648	3	.	.	PUNCT
ejpam-7033	649	1	let	let	AUX
ejpam-7033	649	2	(	(	PUNCT
ejpam-7033	649	3	e	e	NOUN
ejpam-7033	649	4	,	,	PUNCT
ejpam-7033	649	5	∥.∥	∥.∥	PROPN
ejpam-7033	649	6	)	)	PUNCT
ejpam-7033	649	7	be	be	AUX
ejpam-7033	649	8	a	a	DET
ejpam-7033	649	9	real	real	ADJ
ejpam-7033	649	10	banach	banach	NOUN
ejpam-7033	649	11	space	space	NOUN
ejpam-7033	649	12	and	and	CCONJ
ejpam-7033	649	13	c	c	NOUN
ejpam-7033	649	14	⊂	⊂	PROPN
ejpam-7033	650	1	e	e	X
ejpam-7033	650	2	be	be	AUX
ejpam-7033	650	3	a	a	DET
ejpam-7033	650	4	cone	cone	NOUN
ejpam-7033	650	5	.	.	PUNCT
ejpam-7033	651	1	let	let	AUX
ejpam-7033	651	2	(	(	PUNCT
ejpam-7033	651	3	x	x	NOUN
ejpam-7033	651	4	,	,	PUNCT
ejpam-7033	651	5	r	r	NOUN
ejpam-7033	651	6	)	)	PUNCT
ejpam-7033	651	7	be	be	AUX
ejpam-7033	651	8	a	a	DET
ejpam-7033	651	9	complete	complete	ADJ
ejpam-7033	651	10	rectangular	rectangular	ADJ
ejpam-7033	651	11	cone	cone	NOUN
ejpam-7033	651	12	b	b	NOUN
ejpam-7033	651	13	-	-	PUNCT
ejpam-7033	651	14	metric	metric	ADJ
ejpam-7033	651	15	space	space	NOUN
ejpam-7033	651	16	.	.	PUNCT
ejpam-7033	652	1	assume	assume	VERB
ejpam-7033	652	2	an	an	DET
ejpam-7033	652	3	open	open	ADJ
ejpam-7033	652	4	set	set	NOUN
ejpam-7033	652	5	v	v	ADP
ejpam-7033	652	6	⊂	⊂	PROPN
ejpam-7033	652	7	x.	x.	PROPN
ejpam-7033	652	8	let	let	VERB
ejpam-7033	652	9	t	t	PROPN
ejpam-7033	652	10	∈	∈	PROPN
ejpam-7033	652	11	b(e	b(e	PROPN
ejpam-7033	652	12	,	,	PUNCT
ejpam-7033	652	13	e	e	X
ejpam-7033	652	14	)	)	PUNCT
ejpam-7033	652	15	with	with	ADP
ejpam-7033	652	16	∥t	∥t	ADJ
ejpam-7033	652	17	∥1	∥1	NOUN
ejpam-7033	652	18	<	<	X
ejpam-7033	652	19	1	1	NUM
ejpam-7033	652	20	and	and	CCONJ
ejpam-7033	652	21	t	t	PROPN
ejpam-7033	653	1	(	(	PUNCT
ejpam-7033	653	2	c	c	X
ejpam-7033	653	3	)	)	PUNCT
ejpam-7033	653	4	⊂	⊂	PROPN
ejpam-7033	653	5	c	c	PROPN
ejpam-7033	653	6	and	and	CCONJ
ejpam-7033	653	7	g	g	NOUN
ejpam-7033	653	8	:	:	PUNCT
ejpam-7033	653	9	v×	v×	NOUN
ejpam-7033	654	1	[	[	X
ejpam-7033	654	2	0	0	NUM
ejpam-7033	654	3	,	,	PUNCT
ejpam-7033	654	4	1	1	NUM
ejpam-7033	654	5	]	]	PUNCT
ejpam-7033	654	6	→	→	PUNCT
ejpam-7033	654	7	x	x	PART
ejpam-7033	654	8	be	be	AUX
ejpam-7033	654	9	a	a	DET
ejpam-7033	654	10	monotonic	monotonic	ADJ
ejpam-7033	654	11	mapping	mapping	NOUN
ejpam-7033	654	12	,	,	PUNCT
ejpam-7033	654	13	and	and	CCONJ
ejpam-7033	654	14	satisfies	satisfy	VERB
ejpam-7033	654	15	the	the	DET
ejpam-7033	654	16	axioms	axiom	NOUN
ejpam-7033	654	17	of	of	ADP
ejpam-7033	654	18	corollary	corollary	ADJ
ejpam-7033	654	19	19	19	NUM
ejpam-7033	654	20	in	in	ADP
ejpam-7033	654	21	the	the	DET
ejpam-7033	654	22	first	first	ADJ
ejpam-7033	654	23	variable	variable	NOUN
ejpam-7033	654	24	and	and	CCONJ
ejpam-7033	654	25	(	(	PUNCT
ejpam-7033	654	26	1	1	X
ejpam-7033	654	27	)	)	PUNCT
ejpam-7033	654	28	ϑ	ϑ	X
ejpam-7033	654	29	̸=	̸=	PROPN
ejpam-7033	654	30	g(ϑ	g(ϑ	PROPN
ejpam-7033	654	31	,	,	PUNCT
ejpam-7033	654	32	℘	℘	PROPN
ejpam-7033	654	33	)	)	PUNCT
ejpam-7033	654	34	for	for	ADP
ejpam-7033	654	35	each	each	DET
ejpam-7033	654	36	ϑ	ϑ	X
ejpam-7033	654	37	∈	∈	PROPN
ejpam-7033	654	38	∂v	∂v	PROPN
ejpam-7033	654	39	(	(	PUNCT
ejpam-7033	654	40	∂v	∂v	PROPN
ejpam-7033	654	41	stands	stand	VERB
ejpam-7033	654	42	for	for	ADP
ejpam-7033	654	43	the	the	DET
ejpam-7033	654	44	boundary	boundary	NOUN
ejpam-7033	654	45	of	of	ADP
ejpam-7033	654	46	v	v	NOUN
ejpam-7033	654	47	in	in	ADP
ejpam-7033	654	48	x	x	NOUN
ejpam-7033	654	49	)	)	PUNCT
ejpam-7033	654	50	;	;	PUNCT
ejpam-7033	654	51	(	(	PUNCT
ejpam-7033	654	52	2	2	X
ejpam-7033	654	53	)	)	PUNCT
ejpam-7033	654	54	we	we	PRON
ejpam-7033	654	55	have	have	VERB
ejpam-7033	654	56	m	m	PROPN
ejpam-7033	654	57	≥	≥	NOUN
ejpam-7033	654	58	0	0	NUM
ejpam-7033	654	59	with	with	ADP
ejpam-7033	654	60	∥r(g(ϑ	∥r(g(ϑ	PROPN
ejpam-7033	654	61	,	,	PUNCT
ejpam-7033	654	62	℘	℘	PROPN
ejpam-7033	654	63	)	)	PUNCT
ejpam-7033	654	64	,	,	PUNCT
ejpam-7033	654	65	g(ϑ	g(ϑ	PROPN
ejpam-7033	654	66	,	,	PUNCT
ejpam-7033	654	67	σ))∥	σ))∥	PROPN
ejpam-7033	654	68	≤m	≤m	NOUN
ejpam-7033	654	69	|℘−	|℘−	PUNCT
ejpam-7033	654	70	σ|	σ|	PROPN
ejpam-7033	654	71	,	,	PUNCT
ejpam-7033	654	72	for	for	ADP
ejpam-7033	654	73	some	some	DET
ejpam-7033	654	74	ϑ	ϑ	PRON
ejpam-7033	654	75	∈	∈	PROPN
ejpam-7033	654	76	v	v	NOUN
ejpam-7033	654	77	and	and	CCONJ
ejpam-7033	654	78	σ	σ	PROPN
ejpam-7033	654	79	,	,	PUNCT
ejpam-7033	654	80	℘	℘	X
ejpam-7033	654	81	∈	∈	PROPN
ejpam-7033	655	1	[	[	X
ejpam-7033	655	2	0	0	NUM
ejpam-7033	655	3	,	,	PUNCT
ejpam-7033	655	4	1	1	NUM
ejpam-7033	655	5	]	]	PUNCT
ejpam-7033	655	6	;	;	PUNCT
ejpam-7033	655	7	a.	a.	PROPN
ejpam-7033	655	8	arif	arif	PROPN
ejpam-7033	655	9	et	et	PROPN
ejpam-7033	655	10	al	al	PROPN
ejpam-7033	655	11	.	.	PUNCT
ejpam-7033	655	12	/	/	SYM
ejpam-7033	655	13	eur	eur	PROPN
ejpam-7033	655	14	.	.	PUNCT
ejpam-7033	656	1	j.	j.	PROPN
ejpam-7033	656	2	pure	pure	PROPN
ejpam-7033	656	3	appl	appl	PROPN
ejpam-7033	656	4	.	.	PROPN
ejpam-7033	656	5	math	math	PROPN
ejpam-7033	656	6	,	,	PUNCT
ejpam-7033	656	7	18	18	NUM
ejpam-7033	656	8	(	(	PUNCT
ejpam-7033	656	9	4	4	NUM
ejpam-7033	656	10	)	)	PUNCT
ejpam-7033	656	11	(	(	PUNCT
ejpam-7033	656	12	2025	2025	NUM
ejpam-7033	656	13	)	)	PUNCT
ejpam-7033	656	14	,	,	PUNCT
ejpam-7033	656	15	7033	7033	NUM
ejpam-7033	656	16	21	21	NUM
ejpam-7033	656	17	of	of	ADP
ejpam-7033	656	18	29	29	NUM
ejpam-7033	656	19	(	(	PUNCT
ejpam-7033	656	20	3	3	NUM
ejpam-7033	656	21	)	)	PUNCT
ejpam-7033	656	22	for	for	ADP
ejpam-7033	656	23	any	any	DET
ejpam-7033	656	24	ϑ	ϑ	X
ejpam-7033	656	25	∈	∈	NOUN
ejpam-7033	656	26	v	v	ADP
ejpam-7033	656	27	there	there	PRON
ejpam-7033	656	28	is	be	VERB
ejpam-7033	656	29	ω	ω	NUM
ejpam-7033	656	30	∈	∈	PROPN
ejpam-7033	656	31	x	x	X
ejpam-7033	656	32	so	so	SCONJ
ejpam-7033	656	33	that	that	SCONJ
ejpam-7033	656	34	∥r(ϑ	∥r(ϑ	PROPN
ejpam-7033	656	35	,	,	PUNCT
ejpam-7033	656	36	ω)∥	ω)∥	PUNCT
ejpam-7033	656	37	≤	≤	ADJ
ejpam-7033	656	38	r	r	NOUN
ejpam-7033	656	39	,	,	PUNCT
ejpam-7033	656	40	then	then	ADV
ejpam-7033	656	41	ϑℜω	ϑℜω	NOUN
ejpam-7033	656	42	,	,	PUNCT
ejpam-7033	656	43	r	r	NOUN
ejpam-7033	656	44	is	be	AUX
ejpam-7033	656	45	the	the	DET
ejpam-7033	656	46	radius	radius	NOUN
ejpam-7033	656	47	of	of	ADP
ejpam-7033	656	48	v.	v.	ADV
ejpam-7033	656	49	if	if	SCONJ
ejpam-7033	656	50	g	g	PROPN
ejpam-7033	656	51	(	(	PUNCT
ejpam-7033	656	52	·	·	PUNCT
ejpam-7033	656	53	,	,	PUNCT
ejpam-7033	656	54	0	0	NUM
ejpam-7033	656	55	)	)	PUNCT
ejpam-7033	656	56	admits	admit	VERB
ejpam-7033	656	57	a	a	DET
ejpam-7033	656	58	fixed	fixed	ADJ
ejpam-7033	656	59	point	point	NOUN
ejpam-7033	656	60	in	in	ADP
ejpam-7033	656	61	v	v	NOUN
ejpam-7033	656	62	,	,	PUNCT
ejpam-7033	656	63	then	then	ADV
ejpam-7033	656	64	g	g	PROPN
ejpam-7033	656	65	(	(	PUNCT
ejpam-7033	656	66	·	·	PUNCT
ejpam-7033	656	67	,	,	PUNCT
ejpam-7033	656	68	1	1	NUM
ejpam-7033	656	69	)	)	PUNCT
ejpam-7033	656	70	also	also	ADV
ejpam-7033	656	71	admits	admit	VERB
ejpam-7033	656	72	a	a	DET
ejpam-7033	656	73	fixed	fixed	ADJ
ejpam-7033	656	74	point	point	NOUN
ejpam-7033	656	75	in	in	ADP
ejpam-7033	656	76	v.	v.	ADP
ejpam-7033	656	77	proof	proof	NOUN
ejpam-7033	656	78	.	.	PUNCT
ejpam-7033	657	1	let	let	VERB
ejpam-7033	657	2	c	c	NOUN
ejpam-7033	657	3	=	=	PRON
ejpam-7033	657	4	{	{	PUNCT
ejpam-7033	657	5	℘	℘	PROPN
ejpam-7033	657	6	∈	∈	PROPN
ejpam-7033	658	1	[	[	X
ejpam-7033	658	2	0	0	NUM
ejpam-7033	658	3	,	,	PUNCT
ejpam-7033	658	4	1	1	NUM
ejpam-7033	658	5	]	]	PUNCT
ejpam-7033	658	6	|	|	ADV
ejpam-7033	658	7	ϑ	ϑ	X
ejpam-7033	658	8	=	=	X
ejpam-7033	658	9	g(ϑ	g(ϑ	PROPN
ejpam-7033	658	10	,	,	PUNCT
ejpam-7033	658	11	℘	℘	PROPN
ejpam-7033	658	12	)	)	PUNCT
ejpam-7033	658	13	;	;	PUNCT
ejpam-7033	658	14	for	for	ADP
ejpam-7033	658	15	ϑ	ϑ	PROPN
ejpam-7033	658	16	∈	∈	PROPN
ejpam-7033	658	17	v	v	NOUN
ejpam-7033	658	18	}	}	PUNCT
ejpam-7033	658	19	.	.	PUNCT
ejpam-7033	659	1	define	define	VERB
ejpam-7033	659	2	the	the	DET
ejpam-7033	659	3	partial	partial	ADJ
ejpam-7033	659	4	order	order	NOUN
ejpam-7033	659	5	⪯	⪯	NOUN
ejpam-7033	659	6	in	in	ADP
ejpam-7033	659	7	e	e	NOUN
ejpam-7033	659	8	by	by	ADP
ejpam-7033	659	9	p	p	PROPN
ejpam-7033	659	10	⪯	⪯	PROPN
ejpam-7033	659	11	h	h	PROPN
ejpam-7033	659	12	⇔	⇔	PROPN
ejpam-7033	659	13	∥p∥	∥p∥	PROPN
ejpam-7033	659	14	≤	≤	NUM
ejpam-7033	659	15	∥h∥	∥h∥	NOUN
ejpam-7033	659	16	∀	∀	X
ejpam-7033	659	17	p	p	NOUN
ejpam-7033	659	18	,	,	PUNCT
ejpam-7033	659	19	h	h	NOUN
ejpam-7033	659	20	∈	∈	NOUN
ejpam-7033	659	21	e	e	X
ejpam-7033	659	22	.	.	PUNCT
ejpam-7033	660	1	it	it	PRON
ejpam-7033	660	2	is	be	AUX
ejpam-7033	660	3	obvious	obvious	ADJ
ejpam-7033	660	4	that	that	SCONJ
ejpam-7033	660	5	0	0	NUM
ejpam-7033	660	6	∈	∈	PROPN
ejpam-7033	660	7	c	c	NOUN
ejpam-7033	660	8	,	,	PUNCT
ejpam-7033	660	9	because	because	SCONJ
ejpam-7033	660	10	g	g	PROPN
ejpam-7033	660	11	(	(	PUNCT
ejpam-7033	660	12	.	.	NUM
ejpam-7033	660	13	,	,	PUNCT
ejpam-7033	660	14	0	0	X
ejpam-7033	660	15	)	)	PUNCT
ejpam-7033	660	16	possesses	possess	VERB
ejpam-7033	660	17	a	a	DET
ejpam-7033	660	18	fixed	fix	VERB
ejpam-7033	660	19	point	point	NOUN
ejpam-7033	660	20	in	in	ADP
ejpam-7033	660	21	v.	v.	ADP
ejpam-7033	660	22	hence	hence	ADV
ejpam-7033	660	23	c	c	PROPN
ejpam-7033	660	24	̸=	̸=	PROPN
ejpam-7033	660	25	ϕ.	ϕ.	NOUN
ejpam-7033	660	26	defining	define	VERB
ejpam-7033	660	27	r(ϑ	r(ϑ	PROPN
ejpam-7033	660	28	,	,	PUNCT
ejpam-7033	660	29	g(ϑ	g(ϑ	PROPN
ejpam-7033	660	30	,	,	PUNCT
ejpam-7033	660	31	℘	℘	PROPN
ejpam-7033	660	32	)	)	PUNCT
ejpam-7033	660	33	)	)	PUNCT
ejpam-7033	661	1	=	=	SYM
ejpam-7033	661	2	r(ϑ	r(ϑ	PROPN
ejpam-7033	661	3	,	,	PUNCT
ejpam-7033	661	4	ω	ω	NOUN
ejpam-7033	661	5	)	)	PUNCT
ejpam-7033	661	6	,	,	PUNCT
ejpam-7033	661	7	(	(	PUNCT
ejpam-7033	661	8	i	i	PRON
ejpam-7033	661	9	−	−	PROPN
ejpam-7033	661	10	t	t	NOUN
ejpam-7033	661	11	)	)	PUNCT
ejpam-7033	661	12	2(i	2(i	NUM
ejpam-7033	662	1	+	+	NUM
ejpam-7033	662	2	t	t	NOUN
ejpam-7033	662	3	)	)	PUNCT
ejpam-7033	662	4	(	(	PUNCT
ejpam-7033	662	5	r(ϑ	r(ϑ	PROPN
ejpam-7033	662	6	,	,	PUNCT
ejpam-7033	662	7	g(ϑ	g(ϑ	PROPN
ejpam-7033	662	8	,	,	PUNCT
ejpam-7033	662	9	℘	℘	PROPN
ejpam-7033	662	10	)	)	PUNCT
ejpam-7033	662	11	)	)	PUNCT
ejpam-7033	662	12	)	)	PUNCT
ejpam-7033	662	13	⪯	⪯	PROPN
ejpam-7033	662	14	sr(ϑ	sr(ϑ	PROPN
ejpam-7033	662	15	,	,	PUNCT
ejpam-7033	662	16	ω	ω	NUM
ejpam-7033	662	17	)	)	PUNCT
ejpam-7033	662	18	∀	∀	PUNCT
ejpam-7033	663	1	ϑℜω	ϑℜω	NOUN
ejpam-7033	663	2	,	,	PUNCT
ejpam-7033	663	3	then	then	ADV
ejpam-7033	663	4	by	by	ADP
ejpam-7033	663	5	using	use	VERB
ejpam-7033	663	6	corollary	corollary	ADJ
ejpam-7033	663	7	19	19	NUM
ejpam-7033	663	8	,	,	PUNCT
ejpam-7033	663	9	we	we	PRON
ejpam-7033	663	10	get	get	VERB
ejpam-7033	663	11	r(g(ϑ	r(g(ϑ	NOUN
ejpam-7033	663	12	,	,	PUNCT
ejpam-7033	663	13	℘	℘	PROPN
ejpam-7033	663	14	)	)	PUNCT
ejpam-7033	663	15	,	,	PUNCT
ejpam-7033	663	16	g(ω	g(ω	PROPN
ejpam-7033	663	17	,	,	PUNCT
ejpam-7033	663	18	℘	℘	PROPN
ejpam-7033	663	19	)	)	PUNCT
ejpam-7033	663	20	)	)	PUNCT
ejpam-7033	663	21	⪯	⪯	NOUN
ejpam-7033	663	22	1	1	NUM
ejpam-7033	663	23	s	s	PART
ejpam-7033	663	24	t	t	NOUN
ejpam-7033	663	25	(	(	PUNCT
ejpam-7033	663	26	r(ϑ	r(ϑ	PROPN
ejpam-7033	663	27	,	,	PUNCT
ejpam-7033	663	28	ω	ω	NOUN
ejpam-7033	663	29	)	)	PUNCT
ejpam-7033	663	30	)	)	PUNCT
ejpam-7033	663	31	.	.	PUNCT
ejpam-7033	664	1	firstly	firstly	ADV
ejpam-7033	664	2	,	,	PUNCT
ejpam-7033	664	3	we	we	PRON
ejpam-7033	664	4	need	need	VERB
ejpam-7033	664	5	to	to	PART
ejpam-7033	664	6	show	show	VERB
ejpam-7033	664	7	that	that	SCONJ
ejpam-7033	664	8	c	c	PROPN
ejpam-7033	664	9	is	be	AUX
ejpam-7033	664	10	closed	close	VERB
ejpam-7033	664	11	in	in	ADP
ejpam-7033	664	12	[	[	X
ejpam-7033	664	13	0	0	NUM
ejpam-7033	664	14	,	,	PUNCT
ejpam-7033	664	15	1	1	NUM
ejpam-7033	664	16	]	]	PUNCT
ejpam-7033	664	17	.	.	PUNCT
ejpam-7033	665	1	take	take	VERB
ejpam-7033	665	2	{	{	PUNCT
ejpam-7033	665	3	℘n}∞n=1	℘n}∞n=1	PROPN
ejpam-7033	665	4	⊆	⊆	NUM
ejpam-7033	665	5	c	c	NOUN
ejpam-7033	665	6	along	along	ADV
ejpam-7033	665	7	with	with	ADP
ejpam-7033	665	8	limn→∞	limn→∞	ADJ
ejpam-7033	665	9	℘n	℘n	NOUN
ejpam-7033	665	10	→	→	SYM
ejpam-7033	665	11	℘	℘	NOUN
ejpam-7033	665	12	∈	∈	NOUN
ejpam-7033	666	1	[	[	X
ejpam-7033	666	2	0	0	NUM
ejpam-7033	666	3	,	,	PUNCT
ejpam-7033	666	4	1	1	NUM
ejpam-7033	666	5	]	]	PUNCT
ejpam-7033	666	6	.	.	PUNCT
ejpam-7033	667	1	to	to	PART
ejpam-7033	667	2	show	show	VERB
ejpam-7033	667	3	c	c	PROPN
ejpam-7033	667	4	is	be	AUX
ejpam-7033	667	5	closed	closed	ADJ
ejpam-7033	667	6	,	,	PUNCT
ejpam-7033	667	7	we	we	PRON
ejpam-7033	667	8	need	need	VERB
ejpam-7033	667	9	to	to	PART
ejpam-7033	667	10	show	show	VERB
ejpam-7033	667	11	that	that	SCONJ
ejpam-7033	667	12	℘	℘	PROPN
ejpam-7033	667	13	∈	∈	PROPN
ejpam-7033	667	14	c.	c.	NOUN
ejpam-7033	667	15	as	as	ADP
ejpam-7033	667	16	℘n	℘n	NOUN
ejpam-7033	667	17	∈	∈	PROPN
ejpam-7033	667	18	c	c	X
ejpam-7033	667	19	∀	∀	X
ejpam-7033	667	20	n	n	ADP
ejpam-7033	667	21	∈	∈	PROPN
ejpam-7033	667	22	n	n	CCONJ
ejpam-7033	667	23	,	,	PUNCT
ejpam-7033	667	24	so	so	ADV
ejpam-7033	667	25	we	we	PRON
ejpam-7033	667	26	have	have	VERB
ejpam-7033	667	27	ϑn	ϑn	NOUN
ejpam-7033	667	28	∈	∈	NOUN
ejpam-7033	667	29	v	v	NOUN
ejpam-7033	667	30	so	so	SCONJ
ejpam-7033	667	31	that	that	DET
ejpam-7033	667	32	ϑn	ϑn	NOUN
ejpam-7033	667	33	=	=	SYM
ejpam-7033	667	34	g(ϑn	g(ϑn	NOUN
ejpam-7033	667	35	,	,	PUNCT
ejpam-7033	667	36	℘n	℘n	NOUN
ejpam-7033	667	37	)	)	PUNCT
ejpam-7033	667	38	.	.	PUNCT
ejpam-7033	668	1	because	because	SCONJ
ejpam-7033	668	2	,	,	PUNCT
ejpam-7033	668	3	g(ϑ	g(ϑ	PROPN
ejpam-7033	668	4	,	,	PUNCT
ejpam-7033	668	5	·	·	PUNCT
ejpam-7033	668	6	)	)	PUNCT
ejpam-7033	668	7	is	be	AUX
ejpam-7033	668	8	monotone	monotone	ADJ
ejpam-7033	668	9	,	,	PUNCT
ejpam-7033	668	10	we	we	PRON
ejpam-7033	668	11	get	get	VERB
ejpam-7033	668	12	ϑmℜϑn	ϑmℜϑn	ADJ
ejpam-7033	668	13	∀	∀	NOUN
ejpam-7033	668	14	n	n	CCONJ
ejpam-7033	668	15	,	,	PUNCT
ejpam-7033	668	16	m	m	PROPN
ejpam-7033	668	17	∈	∈	NOUN
ejpam-7033	668	18	n.	n.	NOUN
ejpam-7033	668	19	also	also	ADV
ejpam-7033	668	20	for	for	ADP
ejpam-7033	668	21	s	s	PRON
ejpam-7033	668	22	≥	≥	NOUN
ejpam-7033	668	23	1	1	NUM
ejpam-7033	668	24	,	,	PUNCT
ejpam-7033	668	25	(	(	PUNCT
ejpam-7033	669	1	i	i	PRON
ejpam-7033	669	2	−	−	PROPN
ejpam-7033	669	3	t	t	NOUN
ejpam-7033	669	4	)	)	PUNCT
ejpam-7033	669	5	2(i	2(i	NUM
ejpam-7033	670	1	+	+	NUM
ejpam-7033	670	2	t	t	NOUN
ejpam-7033	670	3	)	)	PUNCT
ejpam-7033	670	4	(	(	PUNCT
ejpam-7033	670	5	r(ϑn	r(ϑn	PROPN
ejpam-7033	670	6	,	,	PUNCT
ejpam-7033	670	7	g(ϑm	g(ϑm	NOUN
ejpam-7033	670	8	,	,	PUNCT
ejpam-7033	670	9	℘m	℘m	NOUN
ejpam-7033	670	10	)	)	PUNCT
ejpam-7033	670	11	)	)	PUNCT
ejpam-7033	670	12	)	)	PUNCT
ejpam-7033	671	1	=	=	PUNCT
ejpam-7033	671	2	(	(	PUNCT
ejpam-7033	671	3	i	i	PRON
ejpam-7033	671	4	−	−	PROPN
ejpam-7033	671	5	t	t	NOUN
ejpam-7033	671	6	)	)	PUNCT
ejpam-7033	671	7	2(i	2(i	NUM
ejpam-7033	672	1	+	+	NUM
ejpam-7033	672	2	t	t	NOUN
ejpam-7033	672	3	)	)	PUNCT
ejpam-7033	672	4	(	(	PUNCT
ejpam-7033	672	5	r(ϑn	r(ϑn	PROPN
ejpam-7033	672	6	,	,	PUNCT
ejpam-7033	672	7	ϑm	ϑm	NOUN
ejpam-7033	672	8	)	)	PUNCT
ejpam-7033	672	9	)	)	PUNCT
ejpam-7033	672	10	⪯	⪯	PROPN
ejpam-7033	672	11	sr(ϑn	sr(ϑn	PROPN
ejpam-7033	672	12	,	,	PUNCT
ejpam-7033	672	13	ϑm	ϑm	PROPN
ejpam-7033	672	14	)	)	PUNCT
ejpam-7033	672	15	,	,	PUNCT
ejpam-7033	672	16	we	we	PRON
ejpam-7033	672	17	have	have	VERB
ejpam-7033	672	18	r(g(ϑn	r(g(ϑn	NOUN
ejpam-7033	672	19	,	,	PUNCT
ejpam-7033	672	20	℘m	℘m	NOUN
ejpam-7033	672	21	)	)	PUNCT
ejpam-7033	672	22	,	,	PUNCT
ejpam-7033	672	23	g(ϑm	g(ϑm	PROPN
ejpam-7033	672	24	,	,	PUNCT
ejpam-7033	672	25	℘m	℘m	NOUN
ejpam-7033	672	26	)	)	PUNCT
ejpam-7033	672	27	)	)	PUNCT
ejpam-7033	673	1	⪯	⪯	NOUN
ejpam-7033	673	2	1	1	NUM
ejpam-7033	673	3	s	s	PART
ejpam-7033	673	4	t	t	NOUN
ejpam-7033	673	5	(	(	PUNCT
ejpam-7033	673	6	r(ϑnϑm	r(ϑnϑm	NOUN
ejpam-7033	673	7	)	)	PUNCT
ejpam-7033	673	8	)	)	PUNCT
ejpam-7033	673	9	,	,	PUNCT
ejpam-7033	673	10	and	and	CCONJ
ejpam-7033	673	11	r(ϑn	r(ϑn	PROPN
ejpam-7033	673	12	,	,	PUNCT
ejpam-7033	673	13	ϑm+1	ϑm+1	X
ejpam-7033	673	14	)	)	PUNCT
ejpam-7033	673	15	=	=	SYM
ejpam-7033	673	16	r(g(ϑn	r(g(ϑn	ADJ
ejpam-7033	673	17	,	,	PUNCT
ejpam-7033	673	18	℘n	℘n	NOUN
ejpam-7033	673	19	)	)	PUNCT
ejpam-7033	673	20	,	,	PUNCT
ejpam-7033	673	21	g(ϑm+1	g(ϑm+1	PROPN
ejpam-7033	673	22	,	,	PUNCT
ejpam-7033	673	23	℘m+1	℘m+1	PROPN
ejpam-7033	673	24	)	)	PUNCT
ejpam-7033	673	25	)	)	PUNCT
ejpam-7033	673	26	⪯	⪯	PROPN
ejpam-7033	673	27	s[r(g(ϑn	s[r(g(ϑn	NOUN
ejpam-7033	673	28	,	,	PUNCT
ejpam-7033	673	29	℘n	℘n	NOUN
ejpam-7033	673	30	)	)	PUNCT
ejpam-7033	673	31	,	,	PUNCT
ejpam-7033	673	32	g(ϑn	g(ϑn	NOUN
ejpam-7033	673	33	,	,	PUNCT
ejpam-7033	673	34	℘m	℘m	NOUN
ejpam-7033	673	35	)	)	PUNCT
ejpam-7033	673	36	)	)	PUNCT
ejpam-7033	674	1	+	+	CCONJ
ejpam-7033	674	2	r(g(ϑn	r(g(ϑn	PRON
ejpam-7033	674	3	,	,	PUNCT
ejpam-7033	674	4	℘m	℘m	NOUN
ejpam-7033	674	5	)	)	PUNCT
ejpam-7033	674	6	,	,	PUNCT
ejpam-7033	674	7	g(ϑn	g(ϑn	PROPN
ejpam-7033	674	8	,	,	PUNCT
ejpam-7033	674	9	℘m+1	℘m+1	PROPN
ejpam-7033	674	10	)	)	PUNCT
ejpam-7033	674	11	)	)	PUNCT
ejpam-7033	674	12	]	]	PUNCT
ejpam-7033	675	1	+	+	CCONJ
ejpam-7033	675	2	sr(g(ϑn	sr(g(ϑn	PROPN
ejpam-7033	675	3	,	,	PUNCT
ejpam-7033	675	4	℘m+1	℘m+1	PROPN
ejpam-7033	675	5	)	)	PUNCT
ejpam-7033	675	6	,	,	PUNCT
ejpam-7033	675	7	g(ϑm+1	g(ϑm+1	PROPN
ejpam-7033	675	8	,	,	PUNCT
ejpam-7033	675	9	℘m+1	℘m+1	PROPN
ejpam-7033	675	10	)	)	PUNCT
ejpam-7033	675	11	)	)	PUNCT
ejpam-7033	676	1	∥r(ϑn	∥r(ϑn	PROPN
ejpam-7033	676	2	,	,	PUNCT
ejpam-7033	676	3	ϑm)∥	ϑm)∥	VERB
ejpam-7033	676	4	≤	≤	NUM
ejpam-7033	676	5	s	s	X
ejpam-7033	676	6	[	[	PUNCT
ejpam-7033	676	7	m	m	NOUN
ejpam-7033	676	8	|℘n	|℘n	ADJ
ejpam-7033	676	9	−	−	PROPN
ejpam-7033	676	10	℘m|+m	℘m|+m	NOUN
ejpam-7033	677	1	|℘m	|℘m	ADP
ejpam-7033	677	2	−	−	PUNCT
ejpam-7033	677	3	℘m+1|+	℘m+1|+	PROPN
ejpam-7033	677	4	∥∥∥∥1st	∥∥∥∥1st	PROPN
ejpam-7033	677	5	(	(	PUNCT
ejpam-7033	677	6	r(ϑn	r(ϑn	PROPN
ejpam-7033	677	7	,	,	PUNCT
ejpam-7033	677	8	ϑm	ϑm	NOUN
ejpam-7033	677	9	)	)	PUNCT
ejpam-7033	677	10	)	)	PUNCT
ejpam-7033	678	1	∥∥∥∥	∥∥∥∥	NUM
ejpam-7033	678	2	]	]	PUNCT
ejpam-7033	679	1	∥r(ϑn	∥r(ϑn	NOUN
ejpam-7033	679	2	,	,	PUNCT
ejpam-7033	679	3	ϑm)∥	ϑm)∥	VERB
ejpam-7033	679	4	≤	≤	PUNCT
ejpam-7033	680	1	sm	sm	PROPN
ejpam-7033	680	2	1−	1−	NUM
ejpam-7033	680	3	∥t	∥t	ADJ
ejpam-7033	680	4	∥	∥	PUNCT
ejpam-7033	681	1	[	[	X
ejpam-7033	681	2	|℘n	|℘n	NOUN
ejpam-7033	681	3	−	−	PROPN
ejpam-7033	681	4	℘m|+	℘m|+	PROPN
ejpam-7033	681	5	|℘m	|℘m	ADP
ejpam-7033	681	6	−	−	VERB
ejpam-7033	681	7	℘m+1|	℘m+1|	PROPN
ejpam-7033	681	8	]	]	PUNCT
ejpam-7033	681	9	.	.	PUNCT
ejpam-7033	682	1	since	since	SCONJ
ejpam-7033	682	2	{	{	PUNCT
ejpam-7033	682	3	ϑn}∞n=1	ϑn}∞n=1	PRON
ejpam-7033	682	4	is	be	AUX
ejpam-7033	682	5	a	a	DET
ejpam-7033	682	6	cauchy	cauchy	ADJ
ejpam-7033	682	7	sequence	sequence	NOUN
ejpam-7033	682	8	in	in	ADP
ejpam-7033	682	9	[	[	X
ejpam-7033	682	10	0	0	NUM
ejpam-7033	682	11	,	,	PUNCT
ejpam-7033	682	12	1	1	NUM
ejpam-7033	682	13	]	]	PUNCT
ejpam-7033	682	14	,	,	PUNCT
ejpam-7033	682	15	so	so	ADV
ejpam-7033	682	16	lim	lim	PROPN
ejpam-7033	682	17	n	n	CCONJ
ejpam-7033	682	18	,	,	PUNCT
ejpam-7033	682	19	m→∞	m→∞	NUM
ejpam-7033	682	20	r(ϑn	r(ϑn	PROPN
ejpam-7033	682	21	,	,	PUNCT
ejpam-7033	682	22	ϑm	ϑm	ADV
ejpam-7033	682	23	)	)	PUNCT
ejpam-7033	682	24	=	=	SYM
ejpam-7033	682	25	0e	0e	NOUN
ejpam-7033	682	26	.	.	PUNCT
ejpam-7033	683	1	this	this	PRON
ejpam-7033	683	2	shows	show	VERB
ejpam-7033	683	3	that	that	SCONJ
ejpam-7033	683	4	{	{	PUNCT
ejpam-7033	683	5	ϑn	ϑn	NOUN
ejpam-7033	683	6	}	}	PUNCT
ejpam-7033	683	7	represents	represent	VERB
ejpam-7033	683	8	a	a	DET
ejpam-7033	683	9	cauchy	cauchy	ADJ
ejpam-7033	683	10	sequence	sequence	NOUN
ejpam-7033	683	11	in	in	ADP
ejpam-7033	683	12	x.	x.	NOUN
ejpam-7033	683	13	since	since	SCONJ
ejpam-7033	683	14	x	x	PRON
ejpam-7033	683	15	is	be	AUX
ejpam-7033	683	16	a	a	DET
ejpam-7033	683	17	complete	complete	ADJ
ejpam-7033	683	18	rcbm	rcbm	ADJ
ejpam-7033	683	19	space	space	NOUN
ejpam-7033	683	20	,	,	PUNCT
ejpam-7033	683	21	hence	hence	ADV
ejpam-7033	683	22	limn→∞r(ϑn	limn→∞r(ϑn	PROPN
ejpam-7033	683	23	,	,	PUNCT
ejpam-7033	683	24	ϑ	ϑ	NOUN
ejpam-7033	683	25	)	)	PUNCT
ejpam-7033	683	26	≪	≪	PUNCT
ejpam-7033	683	27	c	c	NOUN
ejpam-7033	683	28	for	for	ADP
ejpam-7033	683	29	some	some	DET
ejpam-7033	683	30	ϑ	ϑ	PRON
ejpam-7033	683	31	∈	∈	PROPN
ejpam-7033	683	32	u	u	NOUN
ejpam-7033	683	33	.	.	PUNCT
ejpam-7033	684	1	as	as	ADP
ejpam-7033	684	2	a	a	DET
ejpam-7033	684	3	result	result	NOUN
ejpam-7033	684	4	ϑnℜϑ	ϑnℜϑ	VERB
ejpam-7033	684	5	∀	∀	X
ejpam-7033	684	6	n	n	PRON
ejpam-7033	684	7	∈	∈	PROPN
ejpam-7033	684	8	n.	n.	NOUN
ejpam-7033	684	9	by	by	ADP
ejpam-7033	684	10	(	(	PUNCT
ejpam-7033	684	11	drb3	drb3	PROPN
ejpam-7033	684	12	)	)	PUNCT
ejpam-7033	684	13	r(ϑ	r(ϑ	PROPN
ejpam-7033	684	14	,	,	PUNCT
ejpam-7033	684	15	g(ϑ	g(ϑ	PROPN
ejpam-7033	684	16	,	,	PUNCT
ejpam-7033	684	17	℘	℘	PROPN
ejpam-7033	684	18	)	)	PUNCT
ejpam-7033	684	19	)	)	PUNCT
ejpam-7033	684	20	⪯	⪯	PROPN
ejpam-7033	684	21	s[r(ϑ	s[r(ϑ	PROPN
ejpam-7033	684	22	,	,	PUNCT
ejpam-7033	684	23	ϑn	ϑn	NOUN
ejpam-7033	684	24	)	)	PUNCT
ejpam-7033	684	25	+	+	CCONJ
ejpam-7033	684	26	r(ϑn	r(ϑn	PROPN
ejpam-7033	684	27	,	,	PUNCT
ejpam-7033	684	28	g(ϑn	g(ϑn	NOUN
ejpam-7033	684	29	,	,	PUNCT
ejpam-7033	684	30	℘	℘	NUM
ejpam-7033	684	31	)	)	PUNCT
ejpam-7033	684	32	)	)	PUNCT
ejpam-7033	685	1	+	+	CCONJ
ejpam-7033	685	2	r(g(ϑn	r(g(ϑn	PRON
ejpam-7033	685	3	,	,	PUNCT
ejpam-7033	685	4	℘	℘	PROPN
ejpam-7033	685	5	)	)	PUNCT
ejpam-7033	685	6	,	,	PUNCT
ejpam-7033	685	7	g(ϑ	g(ϑ	PROPN
ejpam-7033	685	8	,	,	PUNCT
ejpam-7033	685	9	℘	℘	PROPN
ejpam-7033	685	10	)	)	PUNCT
ejpam-7033	685	11	)	)	PUNCT
ejpam-7033	685	12	]	]	PUNCT
ejpam-7033	685	13	⪯	⪯	PROPN
ejpam-7033	685	14	s[r(ϑ	s[r(ϑ	PROPN
ejpam-7033	685	15	,	,	PUNCT
ejpam-7033	685	16	ϑn	ϑn	NOUN
ejpam-7033	685	17	)	)	PUNCT
ejpam-7033	685	18	+	+	CCONJ
ejpam-7033	685	19	r(g(ϑn	r(g(ϑn	ADJ
ejpam-7033	685	20	,	,	PUNCT
ejpam-7033	685	21	℘n	℘n	NOUN
ejpam-7033	685	22	)	)	PUNCT
ejpam-7033	685	23	,	,	PUNCT
ejpam-7033	685	24	g(ϑn	g(ϑn	PROPN
ejpam-7033	685	25	,	,	PUNCT
ejpam-7033	685	26	℘	℘	NUM
ejpam-7033	685	27	)	)	PUNCT
ejpam-7033	685	28	)	)	PUNCT
ejpam-7033	686	1	+	+	CCONJ
ejpam-7033	686	2	r(g(ϑn	r(g(ϑn	PRON
ejpam-7033	686	3	,	,	PUNCT
ejpam-7033	686	4	℘	℘	PROPN
ejpam-7033	686	5	)	)	PUNCT
ejpam-7033	686	6	,	,	PUNCT
ejpam-7033	686	7	g(ϑ	g(ϑ	PROPN
ejpam-7033	686	8	,	,	PUNCT
ejpam-7033	686	9	℘	℘	PROPN
ejpam-7033	686	10	)	)	PUNCT
ejpam-7033	686	11	)	)	PUNCT
ejpam-7033	686	12	]	]	PUNCT
ejpam-7033	687	1	∥r(ϑ	∥r(ϑ	PROPN
ejpam-7033	687	2	,	,	PUNCT
ejpam-7033	687	3	g(ϑ	g(ϑ	PROPN
ejpam-7033	687	4	,	,	PUNCT
ejpam-7033	687	5	℘))∥	℘))∥	ADJ
ejpam-7033	687	6	≤	≤	NUM
ejpam-7033	687	7	sr(ϑ	sr(ϑ	NOUN
ejpam-7033	687	8	,	,	PUNCT
ejpam-7033	687	9	ϑn	ϑn	NOUN
ejpam-7033	687	10	)	)	PUNCT
ejpam-7033	687	11	+	+	SYM
ejpam-7033	687	12	s	s	X
ejpam-7033	687	13	[	[	PUNCT
ejpam-7033	687	14	m	m	NOUN
ejpam-7033	687	15	|℘n	|℘n	ADJ
ejpam-7033	687	16	−	−	PROPN
ejpam-7033	687	17	℘|+	℘|+	PROPN
ejpam-7033	687	18	∥∥∥∥1st	∥∥∥∥1st	NOUN
ejpam-7033	687	19	(	(	PUNCT
ejpam-7033	687	20	r(ϑn	r(ϑn	PROPN
ejpam-7033	687	21	,	,	PUNCT
ejpam-7033	687	22	ϑ	ϑ	NOUN
ejpam-7033	687	23	)	)	PUNCT
ejpam-7033	687	24	)	)	PUNCT
ejpam-7033	687	25	∥∥∥∥	∥∥∥∥	NUM
ejpam-7033	687	26	]	]	PUNCT
ejpam-7033	687	27	.	.	PUNCT
ejpam-7033	688	1	a.	a.	PROPN
ejpam-7033	688	2	arif	arif	PROPN
ejpam-7033	688	3	et	et	PROPN
ejpam-7033	688	4	al	al	PROPN
ejpam-7033	688	5	.	.	PUNCT
ejpam-7033	688	6	/	/	SYM
ejpam-7033	688	7	eur	eur	PROPN
ejpam-7033	688	8	.	.	PUNCT
ejpam-7033	689	1	j.	j.	PROPN
ejpam-7033	689	2	pure	pure	PROPN
ejpam-7033	689	3	appl	appl	PROPN
ejpam-7033	689	4	.	.	PROPN
ejpam-7033	689	5	math	math	PROPN
ejpam-7033	689	6	,	,	PUNCT
ejpam-7033	689	7	18	18	NUM
ejpam-7033	689	8	(	(	PUNCT
ejpam-7033	689	9	4	4	NUM
ejpam-7033	689	10	)	)	PUNCT
ejpam-7033	689	11	(	(	PUNCT
ejpam-7033	689	12	2025	2025	NUM
ejpam-7033	689	13	)	)	PUNCT
ejpam-7033	689	14	,	,	PUNCT
ejpam-7033	689	15	7033	7033	NUM
ejpam-7033	689	16	22	22	NUM
ejpam-7033	689	17	of	of	ADP
ejpam-7033	689	18	29	29	NUM
ejpam-7033	689	19	hence	hence	ADV
ejpam-7033	689	20	,	,	PUNCT
ejpam-7033	689	21	r(ϑ	r(ϑ	PROPN
ejpam-7033	689	22	,	,	PUNCT
ejpam-7033	689	23	g(ϑ	g(ϑ	PROPN
ejpam-7033	689	24	,	,	PUNCT
ejpam-7033	689	25	℘	℘	PROPN
ejpam-7033	689	26	)	)	PUNCT
ejpam-7033	689	27	)	)	PUNCT
ejpam-7033	690	1	=	=	SYM
ejpam-7033	690	2	0e	0e	NOUN
ejpam-7033	690	3	.	.	PUNCT
ejpam-7033	691	1	so	so	ADV
ejpam-7033	691	2	℘	℘	VERB
ejpam-7033	691	3	∈	∈	PROPN
ejpam-7033	691	4	c	c	NOUN
ejpam-7033	691	5	,	,	PUNCT
ejpam-7033	691	6	hence	hence	ADV
ejpam-7033	691	7	c	c	PROPN
ejpam-7033	691	8	is	be	AUX
ejpam-7033	691	9	closed	close	VERB
ejpam-7033	691	10	in	in	ADP
ejpam-7033	691	11	[	[	X
ejpam-7033	691	12	0	0	NUM
ejpam-7033	691	13	,	,	PUNCT
ejpam-7033	691	14	1	1	NUM
ejpam-7033	691	15	]	]	PUNCT
ejpam-7033	691	16	.	.	PUNCT
ejpam-7033	692	1	now	now	ADV
ejpam-7033	692	2	we	we	PRON
ejpam-7033	692	3	show	show	VERB
ejpam-7033	692	4	that	that	SCONJ
ejpam-7033	692	5	c	c	PROPN
ejpam-7033	692	6	is	be	AUX
ejpam-7033	692	7	open	open	ADJ
ejpam-7033	692	8	in	in	ADP
ejpam-7033	692	9	[	[	X
ejpam-7033	692	10	0	0	NUM
ejpam-7033	692	11	,	,	PUNCT
ejpam-7033	692	12	1	1	NUM
ejpam-7033	692	13	]	]	PUNCT
ejpam-7033	692	14	.	.	PUNCT
ejpam-7033	693	1	take	take	VERB
ejpam-7033	693	2	℘2	℘2	NOUN
ejpam-7033	693	3	∈	∈	PROPN
ejpam-7033	693	4	c	c	NOUN
ejpam-7033	693	5	with	with	ADP
ejpam-7033	693	6	g(℘2	g(℘2	PROPN
ejpam-7033	693	7	,	,	PUNCT
ejpam-7033	693	8	ϑ2	ϑ2	PROPN
ejpam-7033	693	9	)	)	PUNCT
ejpam-7033	693	10	=	=	SYM
ejpam-7033	693	11	ϑ2	ϑ2	NOUN
ejpam-7033	693	12	for	for	ADP
ejpam-7033	693	13	ϑ2	ϑ2	PROPN
ejpam-7033	693	14	∈	∈	PROPN
ejpam-7033	694	1	v.	v.	ADP
ejpam-7033	694	2	now	now	ADV
ejpam-7033	694	3	v	v	NOUN
ejpam-7033	694	4	is	be	AUX
ejpam-7033	694	5	open	open	ADJ
ejpam-7033	694	6	,	,	PUNCT
ejpam-7033	694	7	so	so	SCONJ
ejpam-7033	694	8	we	we	PRON
ejpam-7033	694	9	can	can	AUX
ejpam-7033	694	10	find	find	VERB
ejpam-7033	694	11	some	some	DET
ejpam-7033	694	12	r	r	NOUN
ejpam-7033	694	13	>	>	X
ejpam-7033	694	14	0	0	PUNCT
ejpam-7033	694	15	with	with	ADP
ejpam-7033	694	16	c(ϑ2	c(ϑ2	NOUN
ejpam-7033	694	17	,	,	PUNCT
ejpam-7033	694	18	r	r	NOUN
ejpam-7033	694	19	)	)	PUNCT
ejpam-7033	694	20	⊆	⊆	PROPN
ejpam-7033	694	21	v.	v.	ADP
ejpam-7033	694	22	assume	assume	PROPN
ejpam-7033	694	23	l	l	NOUN
ejpam-7033	694	24	=	=	PUNCT
ejpam-7033	694	25	r(ϑ2	r(ϑ2	NOUN
ejpam-7033	694	26	,	,	PUNCT
ejpam-7033	694	27	∂v	∂v	PROPN
ejpam-7033	694	28	)	)	PUNCT
ejpam-7033	695	1	=	=	PUNCT
ejpam-7033	695	2	inf{r(ϑ2	inf{r(ϑ2	NOUN
ejpam-7033	695	3	,	,	PUNCT
ejpam-7033	695	4	x	x	NOUN
ejpam-7033	695	5	)	)	PUNCT
ejpam-7033	695	6	:	:	PUNCT
ejpam-7033	695	7	x	x	X
ejpam-7033	695	8	∈	∈	PROPN
ejpam-7033	695	9	∂v	∂v	PROPN
ejpam-7033	695	10	}	}	PUNCT
ejpam-7033	695	11	.	.	PUNCT
ejpam-7033	696	1	we	we	PRON
ejpam-7033	696	2	get	get	VERB
ejpam-7033	696	3	r	r	NOUN
ejpam-7033	696	4	=	=	PUNCT
ejpam-7033	696	5	l	l	NOUN
ejpam-7033	696	6	>	>	X
ejpam-7033	696	7	0	0	X
ejpam-7033	696	8	.	.	PUNCT
ejpam-7033	697	1	given	give	VERB
ejpam-7033	697	2	ϵ	ϵ	ADP
ejpam-7033	697	3	>	>	X
ejpam-7033	697	4	0	0	PUNCT
ejpam-7033	698	1	taking	take	VERB
ejpam-7033	698	2	ϵ	ϵ	X
ejpam-7033	698	3	<	<	X
ejpam-7033	698	4	(	(	PUNCT
ejpam-7033	698	5	1−∥t	1−∥t	NUM
ejpam-7033	698	6	∥)l	∥)l	NOUN
ejpam-7033	698	7	2sm	2sm	NOUN
ejpam-7033	698	8	.	.	PUNCT
ejpam-7033	699	1	take	take	VERB
ejpam-7033	699	2	℘	℘	PROPN
ejpam-7033	699	3	∈	∈	PROPN
ejpam-7033	699	4	(	(	PUNCT
ejpam-7033	699	5	℘1	℘1	NOUN
ejpam-7033	699	6	−	−	PROPN
ejpam-7033	699	7	ϵ	ϵ	NOUN
ejpam-7033	699	8	,	,	PUNCT
ejpam-7033	699	9	℘1	℘1	VERB
ejpam-7033	699	10	+	+	CCONJ
ejpam-7033	699	11	ϵ	ϵ	X
ejpam-7033	699	12	)	)	PUNCT
ejpam-7033	699	13	with	with	ADP
ejpam-7033	699	14	℘1	℘1	ADJ
ejpam-7033	699	15	∈	∈	PROPN
ejpam-7033	699	16	(	(	PUNCT
ejpam-7033	699	17	℘2	℘2	NOUN
ejpam-7033	699	18	−	−	PROPN
ejpam-7033	699	19	ϵ	ϵ	NOUN
ejpam-7033	699	20	,	,	PUNCT
ejpam-7033	699	21	℘2	℘2	NOUN
ejpam-7033	699	22	+	+	PROPN
ejpam-7033	699	23	ϵ	ϵ	NUM
ejpam-7033	699	24	)	)	PUNCT
ejpam-7033	699	25	.	.	PUNCT
ejpam-7033	700	1	subsequently	subsequently	ADV
ejpam-7033	700	2	ϑ	ϑ	PROPN
ejpam-7033	700	3	∈	∈	PROPN
ejpam-7033	700	4	c(ϑ2	c(ϑ2	NOUN
ejpam-7033	700	5	,	,	PUNCT
ejpam-7033	700	6	r	r	NOUN
ejpam-7033	700	7	)	)	PUNCT
ejpam-7033	700	8	=	=	SYM
ejpam-7033	700	9	{	{	PUNCT
ejpam-7033	700	10	ϑ	ϑ	X
ejpam-7033	700	11	∈	∈	NOUN
ejpam-7033	700	12	x	x	X
ejpam-7033	700	13	:	:	PUNCT
ejpam-7033	700	14	∥r(ϑ	∥r(ϑ	PROPN
ejpam-7033	700	15	,	,	PUNCT
ejpam-7033	700	16	ϑ2)∥	ϑ2)∥	VERB
ejpam-7033	700	17	≤	≤	NOUN
ejpam-7033	700	18	r	r	NOUN
ejpam-7033	700	19	}	}	PUNCT
ejpam-7033	700	20	,	,	PUNCT
ejpam-7033	700	21	as	as	ADP
ejpam-7033	700	22	ϑℜϑ2	ϑℜϑ2	PROPN
ejpam-7033	700	23	.	.	PUNCT
ejpam-7033	701	1	consider	consider	VERB
ejpam-7033	701	2	r(g(ϑ	r(g(ϑ	NOUN
ejpam-7033	701	3	,	,	PUNCT
ejpam-7033	701	4	℘	℘	PROPN
ejpam-7033	701	5	)	)	PUNCT
ejpam-7033	701	6	,	,	PUNCT
ejpam-7033	701	7	ϑ2	ϑ2	PROPN
ejpam-7033	701	8	)	)	PUNCT
ejpam-7033	701	9	=	=	SYM
ejpam-7033	701	10	r(g(ϑ	r(g(ϑ	PROPN
ejpam-7033	701	11	,	,	PUNCT
ejpam-7033	701	12	℘	℘	PROPN
ejpam-7033	701	13	)	)	PUNCT
ejpam-7033	701	14	,	,	PUNCT
ejpam-7033	701	15	g(ϑ2	g(ϑ2	NOUN
ejpam-7033	701	16	,	,	PUNCT
ejpam-7033	701	17	℘2	℘2	PROPN
ejpam-7033	701	18	)	)	PUNCT
ejpam-7033	701	19	⪯	⪯	NOUN
ejpam-7033	701	20	s[r(g(ϑ	s[r(g(ϑ	PROPN
ejpam-7033	701	21	,	,	PUNCT
ejpam-7033	701	22	℘	℘	PROPN
ejpam-7033	701	23	)	)	PUNCT
ejpam-7033	701	24	,	,	PUNCT
ejpam-7033	701	25	g(ϑ	g(ϑ	PROPN
ejpam-7033	701	26	,	,	PUNCT
ejpam-7033	701	27	℘1	℘1	NOUN
ejpam-7033	701	28	)	)	PUNCT
ejpam-7033	701	29	+	+	CCONJ
ejpam-7033	701	30	r(g(ϑ	r(g(ϑ	ADJ
ejpam-7033	701	31	,	,	PUNCT
ejpam-7033	701	32	℘1	℘1	NOUN
ejpam-7033	701	33	)	)	PUNCT
ejpam-7033	701	34	,	,	PUNCT
ejpam-7033	701	35	g(ϑ	g(ϑ	PROPN
ejpam-7033	701	36	,	,	PUNCT
ejpam-7033	701	37	℘2	℘2	PROPN
ejpam-7033	701	38	)	)	PUNCT
ejpam-7033	701	39	+	+	NUM
ejpam-7033	702	1	r(g(ϑ	r(g(ϑ	ADJ
ejpam-7033	702	2	,	,	PUNCT
ejpam-7033	702	3	℘2	℘2	PROPN
ejpam-7033	702	4	)	)	PUNCT
ejpam-7033	702	5	,	,	PUNCT
ejpam-7033	702	6	g(ϑ2	g(ϑ2	NOUN
ejpam-7033	702	7	,	,	PUNCT
ejpam-7033	702	8	℘2	℘2	PROPN
ejpam-7033	702	9	)	)	PUNCT
ejpam-7033	702	10	)	)	PUNCT
ejpam-7033	702	11	]	]	PUNCT
ejpam-7033	703	1	∥r(g(ϑ	∥r(g(ϑ	PROPN
ejpam-7033	703	2	,	,	PUNCT
ejpam-7033	703	3	℘	℘	PROPN
ejpam-7033	703	4	)	)	PUNCT
ejpam-7033	703	5	,	,	PUNCT
ejpam-7033	703	6	ϑ2)∥	ϑ2)∥	VERB
ejpam-7033	703	7	≤	≤	PUNCT
ejpam-7033	703	8	sm	sm	PROPN
ejpam-7033	703	9	|℘1	|℘1	PROPN
ejpam-7033	704	1	−	−	PROPN
ejpam-7033	704	2	℘|+	℘|+	PROPN
ejpam-7033	704	3	sm	sm	PROPN
ejpam-7033	704	4	|℘2	|℘2	VERB
ejpam-7033	704	5	−	−	NOUN
ejpam-7033	704	6	℘1|+	℘1|+	ADV
ejpam-7033	704	7	∥t	∥t	ADJ
ejpam-7033	704	8	(	(	PUNCT
ejpam-7033	704	9	r(ϑ2	r(ϑ2	NOUN
ejpam-7033	704	10	,	,	PUNCT
ejpam-7033	704	11	ϑ))∥	ϑ))∥	ADJ
ejpam-7033	704	12	≤	≤	NOUN
ejpam-7033	704	13	smϵ+	smϵ+	ADJ
ejpam-7033	704	14	smϵ+	smϵ+	PROPN
ejpam-7033	704	15	∥t	∥t	ADJ
ejpam-7033	704	16	∥	∥	PRON
ejpam-7033	704	17	l	l	NOUN
ejpam-7033	704	18	=	=	SYM
ejpam-7033	704	19	2smϵ+	2smϵ+	NUM
ejpam-7033	704	20	∥t	∥t	ADJ
ejpam-7033	704	21	∥	∥	PUNCT
ejpam-7033	704	22	l	l	NOUN
ejpam-7033	704	23	<	<	X
ejpam-7033	704	24	l.	l.	X
ejpam-7033	704	25	thus	thus	ADV
ejpam-7033	704	26	for	for	ADP
ejpam-7033	704	27	each	each	DET
ejpam-7033	704	28	℘	℘	PROPN
ejpam-7033	704	29	∈	∈	PROPN
ejpam-7033	704	30	(	(	PUNCT
ejpam-7033	704	31	℘2	℘2	NOUN
ejpam-7033	704	32	−	−	PROPN
ejpam-7033	704	33	ϵ	ϵ	NOUN
ejpam-7033	704	34	,	,	PUNCT
ejpam-7033	704	35	℘2	℘2	NOUN
ejpam-7033	704	36	+	+	CCONJ
ejpam-7033	704	37	ϵ	ϵ	X
ejpam-7033	704	38	)	)	PUNCT
ejpam-7033	704	39	,	,	PUNCT
ejpam-7033	704	40	g	g	PROPN
ejpam-7033	704	41	(	(	PUNCT
ejpam-7033	704	42	·	·	PUNCT
ejpam-7033	704	43	,	,	PUNCT
ejpam-7033	704	44	℘	℘	PROPN
ejpam-7033	704	45	)	)	PUNCT
ejpam-7033	704	46	:	:	PUNCT
ejpam-7033	704	47	c(ϑ	c(ϑ	NOUN
ejpam-7033	704	48	,	,	PUNCT
ejpam-7033	704	49	r	r	NOUN
ejpam-7033	704	50	)	)	PUNCT
ejpam-7033	704	51	→	→	SYM
ejpam-7033	704	52	c(ϑ	c(ϑ	NOUN
ejpam-7033	704	53	,	,	PUNCT
ejpam-7033	704	54	r	r	NOUN
ejpam-7033	704	55	)	)	PUNCT
ejpam-7033	704	56	has	have	VERB
ejpam-7033	704	57	a	a	DET
ejpam-7033	704	58	fixed	fix	VERB
ejpam-7033	704	59	point	point	NOUN
ejpam-7033	704	60	in	in	ADP
ejpam-7033	704	61	v	v	NOUN
ejpam-7033	704	62	as	as	ADP
ejpam-7033	704	63	an	an	DET
ejpam-7033	704	64	implementation	implementation	NOUN
ejpam-7033	704	65	of	of	ADP
ejpam-7033	704	66	corollary	corollary	ADJ
ejpam-7033	704	67	19	19	NUM
ejpam-7033	704	68	.	.	PUNCT
ejpam-7033	705	1	so	so	ADV
ejpam-7033	705	2	℘	℘	VERB
ejpam-7033	705	3	∈	∈	PROPN
ejpam-7033	705	4	c	c	NOUN
ejpam-7033	705	5	,	,	PUNCT
ejpam-7033	705	6	for	for	ADP
ejpam-7033	705	7	every	every	DET
ejpam-7033	705	8	℘	℘	PROPN
ejpam-7033	705	9	∈	∈	PROPN
ejpam-7033	705	10	(	(	PUNCT
ejpam-7033	705	11	℘2	℘2	NOUN
ejpam-7033	705	12	−	−	PROPN
ejpam-7033	705	13	ϵ	ϵ	NOUN
ejpam-7033	705	14	,	,	PUNCT
ejpam-7033	705	15	℘2	℘2	NOUN
ejpam-7033	705	16	+	+	CCONJ
ejpam-7033	705	17	ϵ	ϵ	X
ejpam-7033	705	18	)	)	PUNCT
ejpam-7033	705	19	and	and	CCONJ
ejpam-7033	705	20	hence	hence	ADV
ejpam-7033	705	21	c	c	PROPN
ejpam-7033	705	22	is	be	AUX
ejpam-7033	705	23	open	open	ADJ
ejpam-7033	705	24	in	in	ADP
ejpam-7033	705	25	[	[	X
ejpam-7033	705	26	0	0	NUM
ejpam-7033	705	27	,	,	PUNCT
ejpam-7033	705	28	1	1	NUM
ejpam-7033	705	29	]	]	PUNCT
ejpam-7033	705	30	.	.	PUNCT
ejpam-7033	706	1	using	use	VERB
ejpam-7033	706	2	connectedness	connectedness	NOUN
ejpam-7033	706	3	,	,	PUNCT
ejpam-7033	706	4	c	c	NOUN
ejpam-7033	706	5	=	=	PUNCT
ejpam-7033	707	1	[	[	X
ejpam-7033	707	2	0	0	NUM
ejpam-7033	707	3	,	,	PUNCT
ejpam-7033	707	4	1	1	NUM
ejpam-7033	707	5	]	]	PUNCT
ejpam-7033	707	6	.	.	PUNCT
ejpam-7033	708	1	so	so	ADV
ejpam-7033	708	2	g	g	PROPN
ejpam-7033	708	3	(	(	PUNCT
ejpam-7033	708	4	·	·	PUNCT
ejpam-7033	708	5	,	,	PUNCT
ejpam-7033	708	6	1	1	NUM
ejpam-7033	708	7	)	)	PUNCT
ejpam-7033	708	8	has	have	VERB
ejpam-7033	708	9	a	a	DET
ejpam-7033	708	10	fixed	fix	VERB
ejpam-7033	708	11	point	point	NOUN
ejpam-7033	708	12	in	in	ADP
ejpam-7033	708	13	v.	v.	ADP
ejpam-7033	708	14	6.1	6.1	NUM
ejpam-7033	708	15	.	.	PUNCT
ejpam-7033	709	1	application	application	NOUN
ejpam-7033	709	2	of	of	ADP
ejpam-7033	709	3	homotopy	homotopy	NOUN
ejpam-7033	709	4	to	to	ADP
ejpam-7033	709	5	human	human	ADJ
ejpam-7033	709	6	aging	age	VERB
ejpam-7033	709	7	process	process	NOUN
ejpam-7033	709	8	this	this	DET
ejpam-7033	709	9	segment	segment	NOUN
ejpam-7033	709	10	use	use	VERB
ejpam-7033	709	11	homotopy	homotopy	NOUN
ejpam-7033	709	12	to	to	PART
ejpam-7033	709	13	explain	explain	VERB
ejpam-7033	709	14	the	the	DET
ejpam-7033	709	15	procedure	procedure	NOUN
ejpam-7033	709	16	of	of	ADP
ejpam-7033	709	17	aging	aging	NOUN
ejpam-7033	709	18	of	of	ADP
ejpam-7033	709	19	human	human	ADJ
ejpam-7033	709	20	body	body	NOUN
ejpam-7033	709	21	.	.	PUNCT
ejpam-7033	710	1	we	we	PRON
ejpam-7033	710	2	assume	assume	VERB
ejpam-7033	710	3	aging	aging	NOUN
ejpam-7033	710	4	process	process	NOUN
ejpam-7033	710	5	by	by	ADP
ejpam-7033	710	6	taking	take	VERB
ejpam-7033	710	7	appropriate	appropriate	ADJ
ejpam-7033	710	8	values	value	NOUN
ejpam-7033	710	9	for	for	ADP
ejpam-7033	710	10	the	the	DET
ejpam-7033	710	11	time	time	NOUN
ejpam-7033	710	12	parameters	parameter	NOUN
ejpam-7033	710	13	t	t	PROPN
ejpam-7033	710	14	of	of	ADP
ejpam-7033	710	15	the	the	DET
ejpam-7033	710	16	homotopy	homotopy	NOUN
ejpam-7033	710	17	η(t	η(t	NOUN
ejpam-7033	710	18	,	,	PUNCT
ejpam-7033	710	19	α	α	NOUN
ejpam-7033	710	20	)	)	PUNCT
ejpam-7033	710	21	.	.	PUNCT
ejpam-7033	711	1	here	here	ADV
ejpam-7033	711	2	t	t	PROPN
ejpam-7033	711	3	and	and	CCONJ
ejpam-7033	711	4	α	α	PRON
ejpam-7033	711	5	control	control	VERB
ejpam-7033	711	6	the	the	DET
ejpam-7033	711	7	procedure	procedure	NOUN
ejpam-7033	711	8	of	of	ADP
ejpam-7033	711	9	aging	aging	NOUN
ejpam-7033	711	10	.	.	PUNCT
ejpam-7033	712	1	human	human	ADJ
ejpam-7033	712	2	body	body	NOUN
ejpam-7033	712	3	will	will	AUX
ejpam-7033	712	4	be	be	AUX
ejpam-7033	712	5	considered	consider	VERB
ejpam-7033	712	6	as	as	ADP
ejpam-7033	712	7	one	one	NUM
ejpam-7033	712	8	year	year	NOUN
ejpam-7033	712	9	old	old	ADJ
ejpam-7033	712	10	,	,	PUNCT
ejpam-7033	712	11	if	if	SCONJ
ejpam-7033	712	12	we	we	PRON
ejpam-7033	712	13	have	have	VERB
ejpam-7033	712	14	a	a	DET
ejpam-7033	712	15	homotopy	homotopy	NOUN
ejpam-7033	712	16	η(t	η(t	NOUN
ejpam-7033	712	17	,	,	PUNCT
ejpam-7033	712	18	α	α	NOUN
ejpam-7033	712	19	)	)	PUNCT
ejpam-7033	712	20	:	:	PUNCT
ejpam-7033	712	21	ℏ(α	ℏ(α	NOUN
ejpam-7033	712	22	)	)	PUNCT
ejpam-7033	712	23	→	→	SYM
ejpam-7033	712	24	g(α	g(α	X
ejpam-7033	712	25	)	)	PUNCT
ejpam-7033	712	26	for	for	ADP
ejpam-7033	712	27	t	t	PROPN
ejpam-7033	712	28	∈	∈	PROPN
ejpam-7033	713	1	[	[	X
ejpam-7033	713	2	0	0	NUM
ejpam-7033	713	3	,	,	PUNCT
ejpam-7033	713	4	1	1	NUM
ejpam-7033	713	5	]	]	PUNCT
ejpam-7033	713	6	along	along	ADP
ejpam-7033	713	7	η(0	η(0	PROPN
ejpam-7033	713	8	,	,	PUNCT
ejpam-7033	713	9	α	α	NOUN
ejpam-7033	713	10	)	)	PUNCT
ejpam-7033	713	11	=	=	SYM
ejpam-7033	713	12	ℏ(α	ℏ(α	NOUN
ejpam-7033	713	13	)	)	PUNCT
ejpam-7033	713	14	and	and	CCONJ
ejpam-7033	713	15	η(1	η(1	NOUN
ejpam-7033	713	16	,	,	PUNCT
ejpam-7033	713	17	α	α	NOUN
ejpam-7033	713	18	)	)	PUNCT
ejpam-7033	713	19	=	=	SYM
ejpam-7033	713	20	g(α	g(α	PROPN
ejpam-7033	713	21	)	)	PUNCT
ejpam-7033	713	22	.	.	PUNCT
ejpam-7033	714	1	human	human	ADJ
ejpam-7033	714	2	body	body	NOUN
ejpam-7033	714	3	will	will	AUX
ejpam-7033	714	4	be	be	AUX
ejpam-7033	714	5	considered	consider	VERB
ejpam-7033	714	6	as	as	ADP
ejpam-7033	714	7	n	n	NUM
ejpam-7033	714	8	years	year	NOUN
ejpam-7033	714	9	old	old	ADJ
ejpam-7033	714	10	,	,	PUNCT
ejpam-7033	714	11	if	if	SCONJ
ejpam-7033	714	12	we	we	PRON
ejpam-7033	714	13	have	have	VERB
ejpam-7033	714	14	η(t	η(t	NOUN
ejpam-7033	714	15	,	,	PUNCT
ejpam-7033	714	16	α	α	NOUN
ejpam-7033	714	17	)	)	PUNCT
ejpam-7033	714	18	:	:	PUNCT
ejpam-7033	714	19	ℏ(α	ℏ(α	NOUN
ejpam-7033	714	20	)	)	PUNCT
ejpam-7033	714	21	→	→	SYM
ejpam-7033	714	22	w(α	w(α	NOUN
ejpam-7033	714	23	)	)	PUNCT
ejpam-7033	714	24	for	for	ADP
ejpam-7033	714	25	t	t	PROPN
ejpam-7033	714	26	∈	∈	PROPN
ejpam-7033	715	1	[	[	X
ejpam-7033	715	2	1	1	NUM
ejpam-7033	715	3	,	,	PUNCT
ejpam-7033	715	4	n	n	CCONJ
ejpam-7033	715	5	]	]	PUNCT
ejpam-7033	715	6	,	,	PUNCT
ejpam-7033	715	7	n	n	PROPN
ejpam-7033	715	8	>	>	X
ejpam-7033	715	9	l	l	NOUN
ejpam-7033	715	10	with	with	ADP
ejpam-7033	715	11	η(l	η(l	PROPN
ejpam-7033	715	12	,	,	PUNCT
ejpam-7033	715	13	α	α	NOUN
ejpam-7033	715	14	)	)	PUNCT
ejpam-7033	715	15	=	=	SYM
ejpam-7033	715	16	ℏ(α	ℏ(α	NOUN
ejpam-7033	715	17	)	)	PUNCT
ejpam-7033	715	18	and	and	CCONJ
ejpam-7033	715	19	η(n	η(n	NOUN
ejpam-7033	715	20	,	,	PUNCT
ejpam-7033	715	21	α	α	NOUN
ejpam-7033	715	22	)	)	PUNCT
ejpam-7033	715	23	=	=	PUNCT
ejpam-7033	715	24	w(α	w(α	NOUN
ejpam-7033	715	25	)	)	PUNCT
ejpam-7033	715	26	.	.	PUNCT
ejpam-7033	716	1	now	now	ADV
ejpam-7033	716	2	the	the	DET
ejpam-7033	716	3	true	true	ADJ
ejpam-7033	716	4	age	age	NOUN
ejpam-7033	716	5	of	of	ADP
ejpam-7033	716	6	human	human	ADJ
ejpam-7033	716	7	body	body	NOUN
ejpam-7033	716	8	is	be	AUX
ejpam-7033	716	9	the	the	DET
ejpam-7033	716	10	least	least	ADJ
ejpam-7033	716	11	upper	upper	ADJ
ejpam-7033	716	12	bound	bind	VERB
ejpam-7033	716	13	η(n	η(n	NOUN
ejpam-7033	716	14	,	,	PUNCT
ejpam-7033	716	15	α	α	NOUN
ejpam-7033	716	16	)	)	PUNCT
ejpam-7033	716	17	=	=	SYM
ejpam-7033	716	18	y(α	y(α	PROPN
ejpam-7033	716	19	)	)	PUNCT
ejpam-7033	716	20	,	,	PUNCT
ejpam-7033	716	21	where	where	SCONJ
ejpam-7033	716	22	t	t	PROPN
ejpam-7033	716	23	∈	∈	PROPN
ejpam-7033	717	1	[	[	X
ejpam-7033	717	2	l	l	NOUN
ejpam-7033	717	3	,	,	PUNCT
ejpam-7033	717	4	n	n	CCONJ
ejpam-7033	717	5	]	]	PUNCT
ejpam-7033	717	6	.	.	PUNCT
ejpam-7033	718	1	topologically	topologically	ADV
ejpam-7033	718	2	the	the	DET
ejpam-7033	718	3	toddler	toddler	NOUN
ejpam-7033	718	4	is	be	AUX
ejpam-7033	718	5	the	the	DET
ejpam-7033	718	6	same	same	ADJ
ejpam-7033	718	7	as	as	ADP
ejpam-7033	718	8	a	a	DET
ejpam-7033	718	9	fully	fully	ADV
ejpam-7033	718	10	grown	grown	ADJ
ejpam-7033	718	11	person	person	NOUN
ejpam-7033	718	12	,	,	PUNCT
ejpam-7033	718	13	because	because	SCONJ
ejpam-7033	718	14	the	the	DET
ejpam-7033	718	15	toddler	toddler	NOUN
ejpam-7033	718	16	constantly	constantly	ADV
ejpam-7033	718	17	becomes	become	VERB
ejpam-7033	718	18	an	an	DET
ejpam-7033	718	19	adult	adult	NOUN
ejpam-7033	718	20	.	.	PUNCT
ejpam-7033	719	1	we	we	PRON
ejpam-7033	719	2	establish	establish	VERB
ejpam-7033	719	3	an	an	DET
ejpam-7033	719	4	algebraic	algebraic	ADJ
ejpam-7033	719	5	method	method	NOUN
ejpam-7033	719	6	to	to	PART
ejpam-7033	719	7	relate	relate	VERB
ejpam-7033	719	8	homotopy	homotopy	NOUN
ejpam-7033	719	9	with	with	ADP
ejpam-7033	719	10	the	the	DET
ejpam-7033	719	11	procedure	procedure	NOUN
ejpam-7033	719	12	of	of	ADP
ejpam-7033	719	13	aging	aging	NOUN
ejpam-7033	719	14	of	of	ADP
ejpam-7033	719	15	human	human	ADJ
ejpam-7033	719	16	body	body	NOUN
ejpam-7033	719	17	.	.	PUNCT
ejpam-7033	720	1	the	the	DET
ejpam-7033	720	2	cylinder	cylinder	NOUN
ejpam-7033	720	3	x	x	PUNCT
ejpam-7033	721	1	=	=	SYM
ejpam-7033	721	2	s	s	PART
ejpam-7033	721	3	×	×	NOUN
ejpam-7033	721	4	i	i	PRON
ejpam-7033	721	5	is	be	AUX
ejpam-7033	721	6	to	to	PART
ejpam-7033	721	7	be	be	AUX
ejpam-7033	721	8	considered	consider	VERB
ejpam-7033	721	9	topologically	topologically	ADV
ejpam-7033	721	10	equivalent	equivalent	ADJ
ejpam-7033	721	11	to	to	ADP
ejpam-7033	721	12	a	a	DET
ejpam-7033	721	13	compact	compact	ADJ
ejpam-7033	721	14	connected	connect	VERB
ejpam-7033	721	15	human	human	ADJ
ejpam-7033	721	16	body	body	NOUN
ejpam-7033	721	17	,	,	PUNCT
ejpam-7033	721	18	when	when	SCONJ
ejpam-7033	721	19	s	s	NOUN
ejpam-7033	721	20	is	be	AUX
ejpam-7033	721	21	taken	take	VERB
ejpam-7033	721	22	as	as	ADP
ejpam-7033	721	23	circle	circle	NOUN
ejpam-7033	721	24	and	and	CCONJ
ejpam-7033	722	1	i	i	NOUN
ejpam-7033	722	2	=	=	PUNCT
ejpam-7033	723	1	[	[	X
ejpam-7033	723	2	0	0	NUM
ejpam-7033	723	3	,	,	PUNCT
ejpam-7033	723	4	β	β	NOUN
ejpam-7033	723	5	]	]	X
ejpam-7033	723	6	.	.	PUNCT
ejpam-7033	724	1	the	the	DET
ejpam-7033	724	2	infant	infant	NOUN
ejpam-7033	724	3	is	be	AUX
ejpam-7033	724	4	topologically	topologically	ADV
ejpam-7033	724	5	taken	take	VERB
ejpam-7033	724	6	as	as	ADP
ejpam-7033	724	7	x	x	X
ejpam-7033	724	8	=	=	SYM
ejpam-7033	724	9	s	s	PART
ejpam-7033	724	10	×	×	PROPN
ejpam-7033	724	11	i.	i.	NOUN
ejpam-7033	724	12	the	the	DET
ejpam-7033	724	13	family	family	NOUN
ejpam-7033	724	14	of	of	ADP
ejpam-7033	724	15	continuous	continuous	ADJ
ejpam-7033	724	16	functions	function	NOUN
ejpam-7033	724	17	η(t	η(t	NOUN
ejpam-7033	724	18	,	,	PUNCT
ejpam-7033	724	19	α	α	NOUN
ejpam-7033	724	20	)	)	PUNCT
ejpam-7033	724	21	on	on	ADP
ejpam-7033	724	22	the	the	DET
ejpam-7033	724	23	interval	interval	NOUN
ejpam-7033	725	1	i	i	PRON
ejpam-7033	725	2	=	=	PUNCT
ejpam-7033	726	1	[	[	X
ejpam-7033	726	2	0	0	NUM
ejpam-7033	726	3	,	,	PUNCT
ejpam-7033	726	4	β	β	X
ejpam-7033	726	5	]	]	PUNCT
ejpam-7033	726	6	is	be	AUX
ejpam-7033	726	7	called	call	VERB
ejpam-7033	726	8	homotopy	homotopy	NOUN
ejpam-7033	726	9	.	.	PUNCT
ejpam-7033	727	1	consider	consider	VERB
ejpam-7033	727	2	x	x	PRON
ejpam-7033	727	3	as	as	ADP
ejpam-7033	727	4	human	human	ADJ
ejpam-7033	727	5	body	body	NOUN
ejpam-7033	727	6	,	,	PUNCT
ejpam-7033	727	7	then	then	ADV
ejpam-7033	727	8	homotopy	homotopy	NOUN
ejpam-7033	727	9	is	be	AUX
ejpam-7033	727	10	an	an	DET
ejpam-7033	727	11	increasing	increase	VERB
ejpam-7033	727	12	sequence	sequence	NOUN
ejpam-7033	727	13	of	of	ADP
ejpam-7033	727	14	the	the	DET
ejpam-7033	727	15	function	function	NOUN
ejpam-7033	727	16	η(t	η(t	NOUN
ejpam-7033	727	17	,	,	PUNCT
ejpam-7033	727	18	α	α	NOUN
ejpam-7033	727	19	)	)	PUNCT
ejpam-7033	727	20	.	.	PUNCT
ejpam-7033	728	1	we	we	PRON
ejpam-7033	728	2	use	use	VERB
ejpam-7033	728	3	homotopy	homotopy	NOUN
ejpam-7033	728	4	to	to	PART
ejpam-7033	728	5	relate	relate	VERB
ejpam-7033	728	6	topologically	topologically	ADV
ejpam-7033	728	7	a	a	DET
ejpam-7033	728	8	toddler	toddler	NOUN
ejpam-7033	728	9	to	to	ADP
ejpam-7033	728	10	topologically	topologically	ADV
ejpam-7033	728	11	an	an	DET
ejpam-7033	728	12	adult	adult	NOUN
ejpam-7033	728	13	.	.	PUNCT
ejpam-7033	729	1	consider	consider	VERB
ejpam-7033	729	2	x	x	PRON
ejpam-7033	729	3	as	as	ADP
ejpam-7033	729	4	a	a	DET
ejpam-7033	729	5	human	human	ADJ
ejpam-7033	729	6	body	body	NOUN
ejpam-7033	729	7	,	,	PUNCT
ejpam-7033	729	8	assume	assume	VERB
ejpam-7033	729	9	α	α	NUM
ejpam-7033	729	10	∈	∈	PROPN
ejpam-7033	729	11	x	x	PUNCT
ejpam-7033	729	12	define	define	VERB
ejpam-7033	729	13	growth	growth	NOUN
ejpam-7033	729	14	of	of	ADP
ejpam-7033	729	15	the	the	DET
ejpam-7033	729	16	body	body	NOUN
ejpam-7033	729	17	and	and	CCONJ
ejpam-7033	729	18	t	t	NOUN
ejpam-7033	729	19	∈	∈	PROPN
ejpam-7033	729	20	i	i	PRON
ejpam-7033	729	21	define	define	VERB
ejpam-7033	729	22	age	age	NOUN
ejpam-7033	729	23	of	of	ADP
ejpam-7033	729	24	the	the	DET
ejpam-7033	729	25	body	body	NOUN
ejpam-7033	729	26	.	.	PUNCT
ejpam-7033	730	1	because	because	SCONJ
ejpam-7033	730	2	we	we	PRON
ejpam-7033	730	3	are	be	AUX
ejpam-7033	730	4	not	not	PART
ejpam-7033	730	5	sure	sure	ADJ
ejpam-7033	730	6	about	about	ADP
ejpam-7033	730	7	the	the	DET
ejpam-7033	730	8	life	life	NOUN
ejpam-7033	730	9	duration	duration	NOUN
ejpam-7033	730	10	of	of	ADP
ejpam-7033	730	11	human	human	ADJ
ejpam-7033	730	12	body	body	NOUN
ejpam-7033	730	13	,	,	PUNCT
ejpam-7033	730	14	consider	consider	VERB
ejpam-7033	730	15	t	t	NOUN
ejpam-7033	730	16	=	=	SYM
ejpam-7033	730	17	∞	∞	PROPN
ejpam-7033	730	18	as	as	ADP
ejpam-7033	730	19	the	the	DET
ejpam-7033	730	20	final	final	ADJ
ejpam-7033	730	21	age	age	NOUN
ejpam-7033	730	22	of	of	ADP
ejpam-7033	730	23	the	the	DET
ejpam-7033	730	24	body	body	NOUN
ejpam-7033	730	25	,	,	PUNCT
ejpam-7033	730	26	where	where	SCONJ
ejpam-7033	730	27	t	t	PROPN
ejpam-7033	730	28	∈	∈	PROPN
ejpam-7033	731	1	[	[	X
ejpam-7033	731	2	θ,∞	θ,∞	NOUN
ejpam-7033	731	3	]	]	PUNCT
ejpam-7033	731	4	represents	represent	VERB
ejpam-7033	731	5	the	the	DET
ejpam-7033	731	6	age	age	NOUN
ejpam-7033	731	7	interval	interval	NOUN
ejpam-7033	731	8	from	from	ADP
ejpam-7033	731	9	t	t	PROPN
ejpam-7033	731	10	=	=	PUNCT
ejpam-7033	731	11	θ	θ	NOUN
ejpam-7033	731	12	to	to	ADP
ejpam-7033	731	13	t	t	PROPN
ejpam-7033	731	14	=	=	SYM
ejpam-7033	731	15	∞.	∞.	PROPN
ejpam-7033	731	16	the	the	DET
ejpam-7033	731	17	aging	age	VERB
ejpam-7033	731	18	procedure	procedure	NOUN
ejpam-7033	731	19	is	be	AUX
ejpam-7033	731	20	the	the	DET
ejpam-7033	731	21	sequence	sequence	NOUN
ejpam-7033	731	22	of	of	ADP
ejpam-7033	731	23	the	the	DET
ejpam-7033	731	24	functions	function	NOUN
ejpam-7033	731	25	η(t	η(t	NOUN
ejpam-7033	731	26	,	,	PUNCT
ejpam-7033	731	27	α	α	NOUN
ejpam-7033	731	28	)	)	PUNCT
ejpam-7033	731	29	so	so	SCONJ
ejpam-7033	731	30	that	that	SCONJ
ejpam-7033	731	31	,	,	PUNCT
ejpam-7033	731	32	∀	∀	X
ejpam-7033	731	33	t	t	X
ejpam-7033	731	34	∈	∈	PROPN
ejpam-7033	731	35	[	[	X
ejpam-7033	731	36	0,∞	0,∞	X
ejpam-7033	731	37	]	]	X
ejpam-7033	731	38	η(0	η(0	PROPN
ejpam-7033	731	39	,	,	PUNCT
ejpam-7033	731	40	α	α	NOUN
ejpam-7033	731	41	)	)	PUNCT
ejpam-7033	731	42	=	=	SYM
ejpam-7033	731	43	ℏ(α	ℏ(α	NOUN
ejpam-7033	731	44	)	)	PUNCT
ejpam-7033	731	45	and	and	CCONJ
ejpam-7033	731	46	η(∞	η(∞	PROPN
ejpam-7033	731	47	,	,	PUNCT
ejpam-7033	731	48	α	α	NOUN
ejpam-7033	731	49	)	)	PUNCT
ejpam-7033	731	50	=	=	SYM
ejpam-7033	731	51	y(α	y(α	PROPN
ejpam-7033	731	52	)	)	PUNCT
ejpam-7033	731	53	.	.	PUNCT
ejpam-7033	732	1	a.	a.	PROPN
ejpam-7033	732	2	arif	arif	PROPN
ejpam-7033	732	3	et	et	PROPN
ejpam-7033	732	4	al	al	PROPN
ejpam-7033	732	5	.	.	PUNCT
ejpam-7033	732	6	/	/	SYM
ejpam-7033	732	7	eur	eur	PROPN
ejpam-7033	732	8	.	.	PUNCT
ejpam-7033	733	1	j.	j.	PROPN
ejpam-7033	733	2	pure	pure	PROPN
ejpam-7033	733	3	appl	appl	PROPN
ejpam-7033	733	4	.	.	PROPN
ejpam-7033	733	5	math	math	PROPN
ejpam-7033	733	6	,	,	PUNCT
ejpam-7033	733	7	18	18	NUM
ejpam-7033	733	8	(	(	PUNCT
ejpam-7033	733	9	4	4	NUM
ejpam-7033	733	10	)	)	PUNCT
ejpam-7033	733	11	(	(	PUNCT
ejpam-7033	733	12	2025	2025	NUM
ejpam-7033	733	13	)	)	PUNCT
ejpam-7033	733	14	,	,	PUNCT
ejpam-7033	733	15	7033	7033	NUM
ejpam-7033	733	16	23	23	NUM
ejpam-7033	733	17	of	of	ADP
ejpam-7033	733	18	29	29	NUM
ejpam-7033	733	19	theorem	theorem	NOUN
ejpam-7033	733	20	21	21	NUM
ejpam-7033	733	21	.	.	PUNCT
ejpam-7033	734	1	consider	consider	VERB
ejpam-7033	734	2	x	x	PUNCT
ejpam-7033	734	3	=	=	PRON
ejpam-7033	734	4	s	s	VERB
ejpam-7033	734	5	×	×	NOUN
ejpam-7033	734	6	i	i	PRON
ejpam-7033	734	7	as	as	ADP
ejpam-7033	734	8	a	a	DET
ejpam-7033	734	9	cylinder	cylinder	NOUN
ejpam-7033	734	10	.	.	PUNCT
ejpam-7033	735	1	take	take	VERB
ejpam-7033	735	2	a	a	DET
ejpam-7033	735	3	homotopy	homotopy	NOUN
ejpam-7033	735	4	η(t	η(t	NOUN
ejpam-7033	735	5	,	,	PUNCT
ejpam-7033	735	6	α	α	NOUN
ejpam-7033	735	7	)	)	PUNCT
ejpam-7033	735	8	,	,	PUNCT
ejpam-7033	735	9	if	if	SCONJ
ejpam-7033	735	10	we	we	PRON
ejpam-7033	735	11	have	have	VERB
ejpam-7033	735	12	a	a	DET
ejpam-7033	735	13	fixed	fix	VERB
ejpam-7033	735	14	point	point	NOUN
ejpam-7033	735	15	for	for	ADP
ejpam-7033	735	16	η(0	η(0	PROPN
ejpam-7033	735	17	,	,	PUNCT
ejpam-7033	735	18	α	α	NOUN
ejpam-7033	735	19	)	)	PUNCT
ejpam-7033	735	20	,	,	PUNCT
ejpam-7033	735	21	then	then	ADV
ejpam-7033	735	22	η(∞	η(∞	VERB
ejpam-7033	735	23	,	,	PUNCT
ejpam-7033	735	24	α	α	NOUN
ejpam-7033	735	25	)	)	PUNCT
ejpam-7033	735	26	also	also	ADV
ejpam-7033	735	27	has	have	AUX
ejpam-7033	735	28	fixed	fix	VERB
ejpam-7033	735	29	point	point	NOUN
ejpam-7033	735	30	.	.	PUNCT
ejpam-7033	736	1	proof	proof	NOUN
ejpam-7033	736	2	.	.	PUNCT
ejpam-7033	737	1	because	because	SCONJ
ejpam-7033	737	2	of	of	ADP
ejpam-7033	737	3	compactness	compactness	NOUN
ejpam-7033	737	4	and	and	CCONJ
ejpam-7033	737	5	connectedness	connectedness	NOUN
ejpam-7033	737	6	,	,	PUNCT
ejpam-7033	737	7	human	human	ADJ
ejpam-7033	737	8	body	body	NOUN
ejpam-7033	737	9	is	be	AUX
ejpam-7033	737	10	topologically	topologically	ADV
ejpam-7033	737	11	equivalent	equivalent	ADJ
ejpam-7033	737	12	to	to	ADP
ejpam-7033	737	13	a	a	DET
ejpam-7033	737	14	cylinder	cylinder	NOUN
ejpam-7033	737	15	x	x	PUNCT
ejpam-7033	738	1	=	=	SYM
ejpam-7033	738	2	s	s	PART
ejpam-7033	738	3	×	×	PROPN
ejpam-7033	738	4	i.	i.	NOUN
ejpam-7033	738	5	since	since	SCONJ
ejpam-7033	738	6	constant	constant	ADJ
ejpam-7033	738	7	changing	change	VERB
ejpam-7033	738	8	in	in	ADP
ejpam-7033	738	9	the	the	DET
ejpam-7033	738	10	shape	shape	NOUN
ejpam-7033	738	11	of	of	ADP
ejpam-7033	738	12	cylinder	cylinder	NOUN
ejpam-7033	738	13	has	have	VERB
ejpam-7033	738	14	many	many	ADJ
ejpam-7033	738	15	invariant	invariant	ADJ
ejpam-7033	738	16	points	point	NOUN
ejpam-7033	738	17	,	,	PUNCT
ejpam-7033	738	18	which	which	PRON
ejpam-7033	738	19	leads	lead	VERB
ejpam-7033	738	20	to	to	ADP
ejpam-7033	738	21	proof	proof	NOUN
ejpam-7033	738	22	.	.	PUNCT
ejpam-7033	739	1	7	7	X
ejpam-7033	739	2	.	.	X
ejpam-7033	739	3	the	the	DET
ejpam-7033	739	4	existence	existence	NOUN
ejpam-7033	739	5	of	of	ADP
ejpam-7033	739	6	a	a	DET
ejpam-7033	739	7	solution	solution	NOUN
ejpam-7033	739	8	to	to	PART
ejpam-7033	739	9	urysohn	urysohn	VERB
ejpam-7033	739	10	integral	integral	ADJ
ejpam-7033	739	11	equation	equation	NOUN
ejpam-7033	739	12	(	(	PUNCT
ejpam-7033	739	13	uie	uie	NOUN
ejpam-7033	739	14	)	)	PUNCT
ejpam-7033	739	15	in	in	ADP
ejpam-7033	739	16	this	this	DET
ejpam-7033	739	17	section	section	NOUN
ejpam-7033	739	18	,	,	PUNCT
ejpam-7033	739	19	we	we	PRON
ejpam-7033	739	20	will	will	AUX
ejpam-7033	739	21	get	get	VERB
ejpam-7033	739	22	a	a	DET
ejpam-7033	739	23	unique	unique	ADJ
ejpam-7033	739	24	solution	solution	NOUN
ejpam-7033	739	25	for	for	ADP
ejpam-7033	739	26	an	an	DET
ejpam-7033	739	27	uie	uie	NOUN
ejpam-7033	739	28	as	as	ADP
ejpam-7033	739	29	an	an	DET
ejpam-7033	739	30	application	application	NOUN
ejpam-7033	739	31	of	of	ADP
ejpam-7033	739	32	theorem	theorem	ADJ
ejpam-7033	739	33	13	13	NUM
ejpam-7033	739	34	:	:	SYM
ejpam-7033	739	35	ℓ(℘	ℓ(℘	NOUN
ejpam-7033	739	36	)	)	PUNCT
ejpam-7033	739	37	=	=	SYM
ejpam-7033	739	38	c(℘	c(℘	PROPN
ejpam-7033	739	39	)	)	PUNCT
ejpam-7033	740	1	+	+	NUM
ejpam-7033	740	2	∫	∫	PROPN
ejpam-7033	740	3	ir	ir	PROPN
ejpam-7033	740	4	k1(℘	k1(℘	PROPN
ejpam-7033	740	5	,	,	PUNCT
ejpam-7033	740	6	s,ϖ(s))ds	s,ϖ(s))ds	PROPN
ejpam-7033	740	7	.	.	PUNCT
ejpam-7033	741	1	(	(	PUNCT
ejpam-7033	741	2	12	12	NUM
ejpam-7033	741	3	)	)	PUNCT
ejpam-7033	741	4	above	above	ADP
ejpam-7033	741	5	mentioned	mention	VERB
ejpam-7033	741	6	equation	equation	NOUN
ejpam-7033	741	7	is	be	AUX
ejpam-7033	741	8	a	a	DET
ejpam-7033	741	9	summarization	summarization	NOUN
ejpam-7033	741	10	of	of	ADP
ejpam-7033	741	11	volterra	volterra	PROPN
ejpam-7033	741	12	integral	integral	ADJ
ejpam-7033	741	13	equation	equation	NOUN
ejpam-7033	741	14	(	(	PUNCT
ejpam-7033	741	15	vie	vie	NOUN
ejpam-7033	741	16	)	)	PUNCT
ejpam-7033	741	17	and	and	CCONJ
ejpam-7033	741	18	fredholm	fredholm	VERB
ejpam-7033	741	19	integral	integral	ADJ
ejpam-7033	741	20	equation	equation	NOUN
ejpam-7033	741	21	(	(	PUNCT
ejpam-7033	741	22	fie	fie	NOUN
ejpam-7033	741	23	)	)	PUNCT
ejpam-7033	741	24	.	.	PUNCT
ejpam-7033	742	1	this	this	DET
ejpam-7033	742	2	integral	integral	ADJ
ejpam-7033	742	3	equation	equation	NOUN
ejpam-7033	742	4	is	be	AUX
ejpam-7033	742	5	dependent	dependent	ADJ
ejpam-7033	742	6	on	on	ADP
ejpam-7033	742	7	the	the	DET
ejpam-7033	742	8	range	range	NOUN
ejpam-7033	742	9	of	of	ADP
ejpam-7033	742	10	integration	integration	NOUN
ejpam-7033	742	11	(	(	PUNCT
ejpam-7033	742	12	ir	ir	NOUN
ejpam-7033	742	13	)	)	PUNCT
ejpam-7033	742	14	.	.	PUNCT
ejpam-7033	743	1	uie	uie	PROPN
ejpam-7033	743	2	will	will	AUX
ejpam-7033	743	3	converted	convert	VERB
ejpam-7033	743	4	into	into	ADP
ejpam-7033	743	5	vie	vie	PROPN
ejpam-7033	743	6	by	by	ADP
ejpam-7033	743	7	fixing	fix	VERB
ejpam-7033	743	8	a	a	PRON
ejpam-7033	743	9	in	in	ADP
ejpam-7033	743	10	ir	ir	NOUN
ejpam-7033	743	11	=	=	PUNCT
ejpam-7033	743	12	(	(	PUNCT
ejpam-7033	743	13	a	a	DET
ejpam-7033	743	14	,	,	PUNCT
ejpam-7033	743	15	x	x	NOUN
ejpam-7033	743	16	)	)	PUNCT
ejpam-7033	743	17	and	and	CCONJ
ejpam-7033	743	18	uie	uie	PROPN
ejpam-7033	743	19	will	will	AUX
ejpam-7033	743	20	become	become	VERB
ejpam-7033	743	21	fie	fie	NOUN
ejpam-7033	743	22	by	by	ADP
ejpam-7033	743	23	fixing	fix	VERB
ejpam-7033	743	24	a	a	DET
ejpam-7033	743	25	,	,	PUNCT
ejpam-7033	743	26	b	b	NOUN
ejpam-7033	743	27	in	in	ADP
ejpam-7033	743	28	ir	ir	PROPN
ejpam-7033	743	29	=	=	PUNCT
ejpam-7033	743	30	(	(	PUNCT
ejpam-7033	743	31	a	a	DET
ejpam-7033	743	32	,	,	PUNCT
ejpam-7033	743	33	b	b	NOUN
ejpam-7033	743	34	)	)	PUNCT
ejpam-7033	743	35	.	.	PUNCT
ejpam-7033	744	1	many	many	ADJ
ejpam-7033	744	2	authors	author	NOUN
ejpam-7033	744	3	have	have	AUX
ejpam-7033	744	4	found	find	VERB
ejpam-7033	744	5	a	a	DET
ejpam-7033	744	6	unique	unique	ADJ
ejpam-7033	744	7	solution	solution	NOUN
ejpam-7033	744	8	to	to	ADP
ejpam-7033	744	9	uie	uie	PROPN
ejpam-7033	744	10	(	(	PUNCT
ejpam-7033	744	11	see	see	VERB
ejpam-7033	744	12	[	[	X
ejpam-7033	744	13	41–43	41–43	NUM
ejpam-7033	744	14	]	]	PUNCT
ejpam-7033	744	15	)	)	PUNCT
ejpam-7033	744	16	.	.	PUNCT
ejpam-7033	745	1	here	here	ADV
ejpam-7033	745	2	we	we	PRON
ejpam-7033	745	3	get	get	VERB
ejpam-7033	745	4	a	a	DET
ejpam-7033	745	5	unique	unique	ADJ
ejpam-7033	745	6	solution	solution	NOUN
ejpam-7033	745	7	to	to	ADP
ejpam-7033	745	8	uie	uie	NOUN
ejpam-7033	745	9	by	by	ADP
ejpam-7033	745	10	using	use	VERB
ejpam-7033	745	11	a	a	DET
ejpam-7033	745	12	fixed	fix	VERB
ejpam-7033	745	13	point	point	NOUN
ejpam-7033	745	14	way	way	NOUN
ejpam-7033	745	15	,	,	PUNCT
ejpam-7033	745	16	which	which	PRON
ejpam-7033	745	17	further	far	ADV
ejpam-7033	745	18	helps	help	VERB
ejpam-7033	745	19	to	to	PART
ejpam-7033	745	20	find	find	VERB
ejpam-7033	745	21	a	a	DET
ejpam-7033	745	22	convergence	convergence	NOUN
ejpam-7033	745	23	point	point	NOUN
ejpam-7033	745	24	to	to	ADP
ejpam-7033	745	25	many	many	ADJ
ejpam-7033	745	26	mathematical	mathematical	ADJ
ejpam-7033	745	27	structures	structure	NOUN
ejpam-7033	745	28	.	.	PUNCT
ejpam-7033	746	1	take	take	VERB
ejpam-7033	746	2	ir	ir	PROPN
ejpam-7033	746	3	as	as	ADP
ejpam-7033	746	4	the	the	DET
ejpam-7033	746	5	set	set	NOUN
ejpam-7033	746	6	with	with	ADP
ejpam-7033	746	7	finite	finite	ADJ
ejpam-7033	746	8	measure	measure	NOUN
ejpam-7033	746	9	along	along	ADP
ejpam-7033	746	10	j	j	PROPN
ejpam-7033	746	11	2	2	NUM
ejpam-7033	746	12	ir	ir	NOUN
ejpam-7033	746	13	=	=	PRON
ejpam-7033	746	14	{	{	PUNCT
ejpam-7033	746	15	ϖ	ϖ	INTJ
ejpam-7033	746	16	|	|	ADV
ejpam-7033	746	17	∫	∫	PROPN
ejpam-7033	746	18	ir	ir	PROPN
ejpam-7033	746	19	|ϖ(s)|2ds	|ϖ(s)|2ds	PROPN
ejpam-7033	746	20	<	<	X
ejpam-7033	746	21	∞	∞	NUM
ejpam-7033	746	22	}	}	PUNCT
ejpam-7033	746	23	.	.	PUNCT
ejpam-7033	747	1	take	take	VERB
ejpam-7033	747	2	the	the	DET
ejpam-7033	747	3	norm	norm	NOUN
ejpam-7033	747	4	∥.∥	∥.∥	PUNCT
ejpam-7033	747	5	:	:	PUNCT
ejpam-7033	748	1	j	j	PROPN
ejpam-7033	748	2	2	2	NUM
ejpam-7033	748	3	ir	ir	VERB
ejpam-7033	748	4	→	→	PUNCT
ejpam-7033	748	5	[	[	X
ejpam-7033	748	6	0,∞	0,∞	NOUN
ejpam-7033	748	7	)	)	PUNCT
ejpam-7033	748	8	such	such	ADJ
ejpam-7033	748	9	that	that	DET
ejpam-7033	748	10	∥ϖ∥2	∥ϖ∥2	NOUN
ejpam-7033	748	11	=	=	SYM
ejpam-7033	748	12	√∫	√∫	ADJ
ejpam-7033	748	13	ir	ir	NOUN
ejpam-7033	748	14	|ϖ(s)|2ds	|ϖ(s)|2ds	NOUN
ejpam-7033	748	15	,	,	PUNCT
ejpam-7033	748	16	for	for	ADP
ejpam-7033	748	17	all	all	DET
ejpam-7033	748	18	ϖ	ϖ	NOUN
ejpam-7033	748	19	,	,	PUNCT
ejpam-7033	748	20	r	r	NOUN
ejpam-7033	748	21	∈	∈	PROPN
ejpam-7033	748	22	j	j	PROPN
ejpam-7033	748	23	2	2	NUM
ejpam-7033	748	24	ir	ir	PROPN
ejpam-7033	748	25	.	.	PUNCT
ejpam-7033	749	1	equivalently	equivalently	ADV
ejpam-7033	749	2	we	we	PRON
ejpam-7033	749	3	define	define	VERB
ejpam-7033	749	4	the	the	DET
ejpam-7033	749	5	norm	norm	NOUN
ejpam-7033	749	6	in	in	ADP
ejpam-7033	749	7	the	the	DET
ejpam-7033	749	8	following	following	ADJ
ejpam-7033	749	9	manner	manner	NOUN
ejpam-7033	749	10	:	:	PUNCT
ejpam-7033	749	11	∥ϖ∥2,y	∥ϖ∥2,y	PROPN
ejpam-7033	749	12	=	=	NOUN
ejpam-7033	750	1	√	√	PROPN
ejpam-7033	750	2	sup{e−y	sup{e−y	NUM
ejpam-7033	750	3	∫	∫	PROPN
ejpam-7033	750	4	ir	ir	PROPN
ejpam-7033	750	5	α(s)ds	α(s)ds	NUM
ejpam-7033	750	6	∫	∫	PROPN
ejpam-7033	750	7	ir	ir	PROPN
ejpam-7033	750	8	|ϖ(s)|2ds	|ϖ(s)|2ds	PROPN
ejpam-7033	750	9	}	}	PUNCT
ejpam-7033	750	10	,	,	PUNCT
ejpam-7033	750	11	for	for	ADP
ejpam-7033	750	12	all	all	DET
ejpam-7033	750	13	ϖ	ϖ	PRON
ejpam-7033	750	14	∈	∈	PROPN
ejpam-7033	750	15	j	j	PROPN
ejpam-7033	750	16	2	2	NUM
ejpam-7033	750	17	ir	ir	PROPN
ejpam-7033	750	18	,	,	PUNCT
ejpam-7033	750	19	y	y	PROPN
ejpam-7033	750	20	>	>	X
ejpam-7033	750	21	1	1	X
ejpam-7033	750	22	.	.	PUNCT
ejpam-7033	751	1	then	then	ADV
ejpam-7033	751	2	e	e	PROPN
ejpam-7033	751	3	=	=	SYM
ejpam-7033	751	4	(	(	PUNCT
ejpam-7033	751	5	j	j	PROPN
ejpam-7033	751	6	2	2	NUM
ejpam-7033	751	7	ir	ir	PROPN
ejpam-7033	751	8	,	,	PUNCT
ejpam-7033	751	9	∥.∥2,y	∥.∥2,y	PROPN
ejpam-7033	751	10	)	)	PUNCT
ejpam-7033	751	11	represents	represent	VERB
ejpam-7033	751	12	a	a	DET
ejpam-7033	751	13	banach	banach	NOUN
ejpam-7033	751	14	space	space	NOUN
ejpam-7033	751	15	.	.	PUNCT
ejpam-7033	752	1	consider	consider	VERB
ejpam-7033	752	2	a	a	DET
ejpam-7033	752	3	cone	cone	NOUN
ejpam-7033	753	1	d	d	NOUN
ejpam-7033	753	2	=	=	SYM
ejpam-7033	753	3	{	{	PUNCT
ejpam-7033	753	4	ϖ	ϖ	X
ejpam-7033	753	5	∈	∈	PROPN
ejpam-7033	753	6	j	j	NOUN
ejpam-7033	753	7	2	2	NUM
ejpam-7033	753	8	ir	ir	NOUN
ejpam-7033	753	9	:	:	PUNCT
ejpam-7033	753	10	ϖ(s	ϖ(	NOUN
ejpam-7033	753	11	)	)	PUNCT
ejpam-7033	753	12	>	>	X
ejpam-7033	753	13	0	0	PUNCT
ejpam-7033	754	1	for	for	ADP
ejpam-7033	754	2	almost	almost	ADV
ejpam-7033	754	3	every	every	PRON
ejpam-7033	754	4	s	s	NOUN
ejpam-7033	754	5	}	}	PUNCT
ejpam-7033	754	6	.	.	PUNCT
ejpam-7033	755	1	the	the	DET
ejpam-7033	755	2	rectangular	rectangular	ADJ
ejpam-7033	755	3	cone	cone	NOUN
ejpam-7033	755	4	b	b	X
ejpam-7033	755	5	-	-	PUNCT
ejpam-7033	755	6	metric	metric	ADJ
ejpam-7033	755	7	ry	ry	NOUN
ejpam-7033	755	8	is	be	AUX
ejpam-7033	755	9	taken	take	VERB
ejpam-7033	755	10	as	as	ADP
ejpam-7033	755	11	ry(ϖ	ry(ϖ	NOUN
ejpam-7033	755	12	,	,	PUNCT
ejpam-7033	755	13	r	r	NOUN
ejpam-7033	755	14	)	)	PUNCT
ejpam-7033	755	15	=	=	PUNCT
ejpam-7033	756	1	ϖ	ϖ	PUNCT
ejpam-7033	756	2	∥ϖ	∥ϖ	NOUN
ejpam-7033	756	3	−	−	NOUN
ejpam-7033	756	4	r∥22,y	r∥22,y	VERB
ejpam-7033	756	5	∀	∀	NOUN
ejpam-7033	756	6	ϖ	ϖ	NOUN
ejpam-7033	756	7	,	,	PUNCT
ejpam-7033	756	8	r	r	PROPN
ejpam-7033	756	9	∈	∈	PROPN
ejpam-7033	756	10	d.	d.	NOUN
ejpam-7033	756	11	take	take	VERB
ejpam-7033	756	12	⪯	⪯	NOUN
ejpam-7033	756	13	as	as	ADP
ejpam-7033	756	14	a	a	DET
ejpam-7033	756	15	partial	partial	ADJ
ejpam-7033	756	16	order	order	NOUN
ejpam-7033	756	17	on	on	ADP
ejpam-7033	756	18	d	d	NOUN
ejpam-7033	756	19	,	,	PUNCT
ejpam-7033	756	20	so	so	SCONJ
ejpam-7033	756	21	that	that	SCONJ
ejpam-7033	756	22	a	a	DET
ejpam-7033	756	23	⪯	⪯	NOUN
ejpam-7033	756	24	υ	υ	PROPN
ejpam-7033	756	25	⇔	⇔	PROPN
ejpam-7033	756	26	a(s)υ(s	a(s)υ(s	PROPN
ejpam-7033	756	27	)	)	PUNCT
ejpam-7033	756	28	≥	≥	NOUN
ejpam-7033	756	29	υ(s	υ(s	PROPN
ejpam-7033	756	30	)	)	PUNCT
ejpam-7033	756	31	,	,	PUNCT
ejpam-7033	756	32	∀a	∀a	X
ejpam-7033	756	33	,	,	PUNCT
ejpam-7033	756	34	υ	υ	PROPN
ejpam-7033	756	35	∈	∈	PROPN
ejpam-7033	756	36	d.	d.	NOUN
ejpam-7033	756	37	subsequently	subsequently	ADV
ejpam-7033	756	38	(	(	PUNCT
ejpam-7033	756	39	e	e	X
ejpam-7033	756	40	,	,	PUNCT
ejpam-7033	756	41	⪯,ry	⪯,ry	PROPN
ejpam-7033	756	42	)	)	PUNCT
ejpam-7033	756	43	represents	represent	VERB
ejpam-7033	756	44	a	a	DET
ejpam-7033	756	45	complete	complete	ADJ
ejpam-7033	756	46	rcbm	rcbm	ADJ
ejpam-7033	756	47	space	space	NOUN
ejpam-7033	756	48	.	.	PUNCT
ejpam-7033	757	1	assume	assume	VERB
ejpam-7033	757	2	(	(	PUNCT
ejpam-7033	757	3	d1	d1	NOUN
ejpam-7033	757	4	)	)	PUNCT
ejpam-7033	757	5	the	the	DET
ejpam-7033	757	6	kernel	kernel	PROPN
ejpam-7033	757	7	k1	k1	PROPN
ejpam-7033	757	8	:	:	PUNCT
ejpam-7033	758	1	ir×	ir×	INTJ
ejpam-7033	758	2	ir×	ir×	ADV
ejpam-7033	759	1	r	r	NOUN
ejpam-7033	759	2	→	→	SYM
ejpam-7033	759	3	r	r	NOUN
ejpam-7033	759	4	holding	hold	VERB
ejpam-7033	759	5	carathéodory	carathéodory	NOUN
ejpam-7033	759	6	axioms	axiom	NOUN
ejpam-7033	759	7	along	along	ADP
ejpam-7033	759	8	with	with	ADP
ejpam-7033	759	9	|k1(c	|k1(c	NUM
ejpam-7033	759	10	,	,	PUNCT
ejpam-7033	759	11	s,ϖ(s))|	s,ϖ(s))|	VERB
ejpam-7033	759	12	≤	≤	PUNCT
ejpam-7033	760	1	w(℘	w(℘	PROPN
ejpam-7033	760	2	,	,	PUNCT
ejpam-7033	760	3	s	s	PART
ejpam-7033	760	4	)	)	PUNCT
ejpam-7033	760	5	+	+	CCONJ
ejpam-7033	760	6	e(℘	e(℘	NOUN
ejpam-7033	760	7	,	,	PUNCT
ejpam-7033	760	8	s	s	PART
ejpam-7033	760	9	)	)	PUNCT
ejpam-7033	760	10	|ϖ(s)|	|ϖ(s)|	ADP
ejpam-7033	760	11	;	;	PUNCT
ejpam-7033	760	12	w	w	X
ejpam-7033	760	13	,	,	PUNCT
ejpam-7033	760	14	e	e	PROPN
ejpam-7033	760	15	∈	∈	PROPN
ejpam-7033	760	16	j	j	PROPN
ejpam-7033	760	17	2(ir×	2(ir×	NUM
ejpam-7033	760	18	ir	ir	NOUN
ejpam-7033	760	19	)	)	PUNCT
ejpam-7033	760	20	,	,	PUNCT
ejpam-7033	760	21	e(℘	e(℘	NOUN
ejpam-7033	760	22	,	,	PUNCT
ejpam-7033	760	23	s	s	PROPN
ejpam-7033	760	24	)	)	PUNCT
ejpam-7033	760	25	>	>	X
ejpam-7033	760	26	0	0	X
ejpam-7033	760	27	.	.	PUNCT
ejpam-7033	760	28	d2	d2	PROPN
ejpam-7033	760	29	)	)	PUNCT
ejpam-7033	760	30	take	take	VERB
ejpam-7033	760	31	c	c	NOUN
ejpam-7033	760	32	:	:	PUNCT
ejpam-7033	760	33	ir	ir	PROPN
ejpam-7033	760	34	→	→	PUNCT
ejpam-7033	760	35	[	[	X
ejpam-7033	760	36	1,∞	1,∞	NUM
ejpam-7033	760	37	)	)	PUNCT
ejpam-7033	760	38	as	as	ADP
ejpam-7033	760	39	a	a	DET
ejpam-7033	760	40	continuous	continuous	ADJ
ejpam-7033	760	41	and	and	CCONJ
ejpam-7033	760	42	bounded	bounded	ADJ
ejpam-7033	760	43	function	function	NOUN
ejpam-7033	760	44	over	over	ADP
ejpam-7033	760	45	ir	ir	PROPN
ejpam-7033	760	46	.	.	PUNCT
ejpam-7033	760	47	a.	a.	PROPN
ejpam-7033	760	48	arif	arif	PROPN
ejpam-7033	760	49	et	et	PROPN
ejpam-7033	760	50	al	al	PROPN
ejpam-7033	760	51	.	.	PUNCT
ejpam-7033	760	52	/	/	SYM
ejpam-7033	760	53	eur	eur	PROPN
ejpam-7033	760	54	.	.	PUNCT
ejpam-7033	761	1	j.	j.	PROPN
ejpam-7033	761	2	pure	pure	PROPN
ejpam-7033	761	3	appl	appl	PROPN
ejpam-7033	761	4	.	.	PROPN
ejpam-7033	761	5	math	math	PROPN
ejpam-7033	761	6	,	,	PUNCT
ejpam-7033	761	7	18	18	NUM
ejpam-7033	761	8	(	(	PUNCT
ejpam-7033	761	9	4	4	NUM
ejpam-7033	761	10	)	)	PUNCT
ejpam-7033	761	11	(	(	PUNCT
ejpam-7033	761	12	2025	2025	NUM
ejpam-7033	761	13	)	)	PUNCT
ejpam-7033	761	14	,	,	PUNCT
ejpam-7033	761	15	7033	7033	NUM
ejpam-7033	761	16	24	24	NUM
ejpam-7033	761	17	of	of	ADP
ejpam-7033	761	18	29	29	NUM
ejpam-7033	761	19	(	(	PUNCT
ejpam-7033	761	20	d3	d3	PROPN
ejpam-7033	761	21	)	)	PUNCT
ejpam-7033	761	22	∃	∃	PROPN
ejpam-7033	761	23	a	a	DET
ejpam-7033	761	24	scalar	scalar	NOUN
ejpam-7033	762	1	c	c	NOUN
ejpam-7033	762	2	>	>	PUNCT
ejpam-7033	762	3	0	0	PUNCT
ejpam-7033	763	1	so	so	SCONJ
ejpam-7033	763	2	that	that	SCONJ
ejpam-7033	763	3	sup	sup	NOUN
ejpam-7033	763	4	℘∈ir	℘∈ir	NOUN
ejpam-7033	763	5	∫	∫	PROPN
ejpam-7033	763	6	ir	ir	PROPN
ejpam-7033	763	7	|k1(℘	|k1(℘	PROPN
ejpam-7033	763	8	,	,	PUNCT
ejpam-7033	763	9	s)|	s)|	NOUN
ejpam-7033	763	10	ds	ds	ADJ
ejpam-7033	763	11	≤	≤	PROPN
ejpam-7033	763	12	c.	c.	PROPN
ejpam-7033	763	13	(	(	PUNCT
ejpam-7033	763	14	d4	d4	PROPN
ejpam-7033	763	15	)	)	PUNCT
ejpam-7033	763	16	for	for	ADP
ejpam-7033	763	17	every	every	DET
ejpam-7033	763	18	ϖ0	ϖ0	NOUN
ejpam-7033	763	19	∈	∈	PROPN
ejpam-7033	763	20	j	j	PROPN
ejpam-7033	763	21	2	2	NUM
ejpam-7033	763	22	ir	ir	PROPN
ejpam-7033	763	23	,	,	PUNCT
ejpam-7033	763	24	∃	∃	PROPN
ejpam-7033	763	25	ϖ1	ϖ1	PROPN
ejpam-7033	763	26	=	=	SYM
ejpam-7033	763	27	r(ϖ0	r(ϖ0	NOUN
ejpam-7033	763	28	)	)	PUNCT
ejpam-7033	764	1	so	so	SCONJ
ejpam-7033	764	2	that	that	SCONJ
ejpam-7033	764	3	ϖ1	ϖ1	VERB
ejpam-7033	764	4	⪯	⪯	NOUN
ejpam-7033	764	5	ϖ0	ϖ0	NOUN
ejpam-7033	764	6	or	or	CCONJ
ejpam-7033	764	7	ϖ0	ϖ0	NOUN
ejpam-7033	764	8	⪯	⪯	AUX
ejpam-7033	764	9	ϖ1	ϖ1	VERB
ejpam-7033	764	10	.	.	PUNCT
ejpam-7033	765	1	(	(	PUNCT
ejpam-7033	765	2	d4	d4	PROPN
ejpam-7033	765	3	’	'	PUNCT
ejpam-7033	765	4	)	)	PUNCT
ejpam-7033	766	1	ϖn−1	ϖn−1	PROPN
ejpam-7033	766	2	⪯	⪯	NOUN
ejpam-7033	766	3	ϖn	ϖn	ADP
ejpam-7033	766	4	and	and	CCONJ
ejpam-7033	766	5	ϖn	ϖn	ADP
ejpam-7033	766	6	→	→	PUNCT
ejpam-7033	766	7	p	p	NOUN
ejpam-7033	766	8	holds	hold	VERB
ejpam-7033	766	9	for	for	ADP
ejpam-7033	766	10	any	any	DET
ejpam-7033	766	11	sequence	sequence	NOUN
ejpam-7033	766	12	{	{	PUNCT
ejpam-7033	766	13	ϖn	ϖn	NOUN
ejpam-7033	766	14	}	}	PUNCT
ejpam-7033	766	15	,	,	PUNCT
ejpam-7033	766	16	implies	imply	VERB
ejpam-7033	766	17	ϖn	ϖn	ADP
ejpam-7033	766	18	⪯	⪯	NOUN
ejpam-7033	766	19	p	p	NOUN
ejpam-7033	766	20	,	,	PUNCT
ejpam-7033	766	21	for	for	ADP
ejpam-7033	766	22	each	each	DET
ejpam-7033	766	23	natural	natural	ADJ
ejpam-7033	766	24	number	number	NOUN
ejpam-7033	766	25	n.	n.	NOUN
ejpam-7033	766	26	(	(	PUNCT
ejpam-7033	766	27	d5	d5	NOUN
ejpam-7033	766	28	)	)	PUNCT
ejpam-7033	766	29	we	we	PRON
ejpam-7033	766	30	get	get	VERB
ejpam-7033	766	31	a	a	DET
ejpam-7033	766	32	non	non	ADJ
ejpam-7033	766	33	-	-	ADJ
ejpam-7033	766	34	negative	negative	ADJ
ejpam-7033	766	35	integrable	integrable	ADJ
ejpam-7033	766	36	and	and	CCONJ
ejpam-7033	766	37	measurable	measurable	ADJ
ejpam-7033	766	38	operator	operator	NOUN
ejpam-7033	767	1	q	q	NOUN
ejpam-7033	767	2	:	:	PUNCT
ejpam-7033	767	3	ir×	ir×	INTJ
ejpam-7033	767	4	ir	ir	PROPN
ejpam-7033	768	1	→	→	SYM
ejpam-7033	768	2	r	r	NOUN
ejpam-7033	768	3	over	over	ADP
ejpam-7033	768	4	ir	ir	PROPN
ejpam-7033	768	5	,	,	PUNCT
ejpam-7033	768	6	so	so	SCONJ
ejpam-7033	768	7	that	that	SCONJ
ejpam-7033	768	8	α(℘	α(℘	NUM
ejpam-7033	768	9	)	)	PUNCT
ejpam-7033	768	10	:	:	PUNCT
ejpam-7033	768	11	=	=	SYM
ejpam-7033	768	12	∫	∫	PROPN
ejpam-7033	768	13	ir	ir	PROPN
ejpam-7033	768	14	q2(℘	q2(℘	PROPN
ejpam-7033	768	15	,	,	PUNCT
ejpam-7033	768	16	s	s	PART
ejpam-7033	768	17	)	)	PUNCT
ejpam-7033	768	18	ds	ds	ADJ
ejpam-7033	768	19	≤	≤	NUM
ejpam-7033	768	20	1	1	NUM
ejpam-7033	768	21	y	y	PROPN
ejpam-7033	768	22	,	,	PUNCT
ejpam-7033	768	23	where	where	SCONJ
ejpam-7033	768	24	y	y	PROPN
ejpam-7033	768	25	≥	≥	NUM
ejpam-7033	768	26	1	1	NUM
ejpam-7033	768	27	and	and	CCONJ
ejpam-7033	768	28	|k1(℘	|k1(℘	NOUN
ejpam-7033	768	29	,	,	PUNCT
ejpam-7033	768	30	s,ϖ(s))−k1(℘	s,ϖ(s))−k1(℘	NUM
ejpam-7033	768	31	,	,	PUNCT
ejpam-7033	768	32	s	s	PART
ejpam-7033	768	33	,	,	PUNCT
ejpam-7033	768	34	r(s))|	r(s))|	VERB
ejpam-7033	768	35	≤	≤	PROPN
ejpam-7033	768	36	q(℘	q(℘	PROPN
ejpam-7033	768	37	,	,	PUNCT
ejpam-7033	768	38	s)|ϖ(s)−	s)|ϖ(s)−	VERB
ejpam-7033	768	39	r(s)|	r(s)|	VERB
ejpam-7033	768	40	for	for	ADP
ejpam-7033	768	41	all	all	DET
ejpam-7033	768	42	℘	℘	NOUN
ejpam-7033	768	43	,	,	PUNCT
ejpam-7033	768	44	s	s	PART
ejpam-7033	768	45	∈	∈	PROPN
ejpam-7033	768	46	ir	ir	PROPN
ejpam-7033	768	47	and	and	CCONJ
ejpam-7033	768	48	ϖ	ϖ	NOUN
ejpam-7033	768	49	,	,	PUNCT
ejpam-7033	768	50	r	r	NOUN
ejpam-7033	768	51	∈	∈	NOUN
ejpam-7033	768	52	e	e	NOUN
ejpam-7033	768	53	with	with	ADP
ejpam-7033	768	54	ϖ	ϖ	PROPN
ejpam-7033	768	55	⪯	⪯	PROPN
ejpam-7033	768	56	r.	r.	PROPN
ejpam-7033	768	57	theorem	theorem	PROPN
ejpam-7033	768	58	22	22	PROPN
ejpam-7033	768	59	.	.	PUNCT
ejpam-7033	769	1	assume	assume	VERB
ejpam-7033	769	2	c	c	NOUN
ejpam-7033	769	3	and	and	CCONJ
ejpam-7033	769	4	k1	k1	PROPN
ejpam-7033	769	5	satisfying	satisfy	VERB
ejpam-7033	769	6	all	all	DET
ejpam-7033	769	7	axioms	axiom	NOUN
ejpam-7033	769	8	(	(	PUNCT
ejpam-7033	769	9	d1)-(d5	d1)-(d5	NOUN
ejpam-7033	769	10	)	)	PUNCT
ejpam-7033	769	11	,	,	PUNCT
ejpam-7033	769	12	then	then	ADV
ejpam-7033	769	13	we	we	PRON
ejpam-7033	769	14	get	get	VERB
ejpam-7033	769	15	a	a	DET
ejpam-7033	769	16	unique	unique	ADJ
ejpam-7033	769	17	solution	solution	NOUN
ejpam-7033	769	18	for	for	ADP
ejpam-7033	769	19	uie	uie	PROPN
ejpam-7033	769	20	.	.	PUNCT
ejpam-7033	770	1	proof	proof	NOUN
ejpam-7033	770	2	.	.	PUNCT
ejpam-7033	771	1	take	take	VERB
ejpam-7033	771	2	a	a	DET
ejpam-7033	771	3	function	function	NOUN
ejpam-7033	771	4	r	r	NOUN
ejpam-7033	771	5	:	:	PUNCT
ejpam-7033	771	6	e	e	X
ejpam-7033	771	7	→	→	SYM
ejpam-7033	771	8	e	e	PROPN
ejpam-7033	771	9	,	,	PUNCT
ejpam-7033	771	10	along	along	ADP
ejpam-7033	771	11	with	with	ADP
ejpam-7033	771	12	the	the	DET
ejpam-7033	771	13	mentioned	mention	VERB
ejpam-7033	771	14	symbols	symbol	NOUN
ejpam-7033	771	15	,	,	PUNCT
ejpam-7033	771	16	so	so	SCONJ
ejpam-7033	771	17	that	that	SCONJ
ejpam-7033	771	18	(	(	PUNCT
ejpam-7033	771	19	rϖ	rϖ	NOUN
ejpam-7033	771	20	)	)	PUNCT
ejpam-7033	771	21	(	(	PUNCT
ejpam-7033	771	22	℘	℘	PROPN
ejpam-7033	771	23	)	)	PUNCT
ejpam-7033	771	24	=	=	SYM
ejpam-7033	771	25	c(℘	c(℘	NOUN
ejpam-7033	771	26	)	)	PUNCT
ejpam-7033	772	1	+	+	NUM
ejpam-7033	772	2	∫	∫	PROPN
ejpam-7033	772	3	ir	ir	PROPN
ejpam-7033	772	4	k1(℘	k1(℘	PROPN
ejpam-7033	772	5	,	,	PUNCT
ejpam-7033	772	6	s,ϖ(s))ds	s,ϖ(s))ds	AUX
ejpam-7033	772	7	.	.	PUNCT
ejpam-7033	773	1	r	r	NOUN
ejpam-7033	773	2	is	be	AUX
ejpam-7033	773	3	taken	take	VERB
ejpam-7033	773	4	as	as	ADP
ejpam-7033	773	5	⪯-preserving	⪯-preserve	VERB
ejpam-7033	773	6	:	:	PUNCT
ejpam-7033	773	7	consider	consider	VERB
ejpam-7033	773	8	ϖ	ϖ	PRON
ejpam-7033	773	9	,	,	PUNCT
ejpam-7033	773	10	r	r	NOUN
ejpam-7033	773	11	∈	∈	PROPN
ejpam-7033	773	12	e	e	NOUN
ejpam-7033	773	13	such	such	ADJ
ejpam-7033	773	14	that	that	SCONJ
ejpam-7033	773	15	ϖ	ϖ	PROPN
ejpam-7033	773	16	⪯	⪯	NOUN
ejpam-7033	773	17	r	r	NOUN
ejpam-7033	773	18	,	,	PUNCT
ejpam-7033	773	19	then	then	ADV
ejpam-7033	773	20	ϖ(s)r(s	ϖ(s)r(s	NUM
ejpam-7033	773	21	)	)	PUNCT
ejpam-7033	773	22	≥	≥	NOUN
ejpam-7033	773	23	r(s	r(s	NUM
ejpam-7033	773	24	)	)	PUNCT
ejpam-7033	773	25	.	.	PUNCT
ejpam-7033	774	1	now	now	ADV
ejpam-7033	774	2	,	,	PUNCT
ejpam-7033	774	3	for	for	ADP
ejpam-7033	774	4	almost	almost	ADV
ejpam-7033	774	5	every	every	PRON
ejpam-7033	774	6	℘	℘	PROPN
ejpam-7033	774	7	∈	∈	PROPN
ejpam-7033	774	8	ir	ir	NOUN
ejpam-7033	774	9	,	,	PUNCT
ejpam-7033	774	10	(	(	PUNCT
ejpam-7033	774	11	rϖ	rϖ	ADP
ejpam-7033	774	12	)	)	PUNCT
ejpam-7033	774	13	(	(	PUNCT
ejpam-7033	774	14	℘	℘	PROPN
ejpam-7033	774	15	)	)	PUNCT
ejpam-7033	774	16	=	=	SYM
ejpam-7033	774	17	c(℘	c(℘	NOUN
ejpam-7033	774	18	)	)	PUNCT
ejpam-7033	775	1	+	+	NUM
ejpam-7033	775	2	∫	∫	PROPN
ejpam-7033	775	3	ir	ir	PROPN
ejpam-7033	775	4	k1(℘	k1(℘	PROPN
ejpam-7033	775	5	,	,	PUNCT
ejpam-7033	775	6	s,ϖ(s))ds	s,ϖ(s))d	VERB
ejpam-7033	775	7	≥	≥	PROPN
ejpam-7033	775	8	1	1	NUM
ejpam-7033	775	9	,	,	PUNCT
ejpam-7033	775	10	implies	imply	VERB
ejpam-7033	775	11	that	that	SCONJ
ejpam-7033	775	12	(	(	PUNCT
ejpam-7033	775	13	rϖ	rϖ	NOUN
ejpam-7033	775	14	)	)	PUNCT
ejpam-7033	775	15	(	(	PUNCT
ejpam-7033	775	16	℘	℘	PROPN
ejpam-7033	775	17	)	)	PUNCT
ejpam-7033	775	18	(	(	PUNCT
ejpam-7033	775	19	rr	rr	NOUN
ejpam-7033	775	20	)	)	PUNCT
ejpam-7033	775	21	(	(	PUNCT
ejpam-7033	775	22	℘	℘	PROPN
ejpam-7033	775	23	)	)	PUNCT
ejpam-7033	775	24	≥	≥	NOUN
ejpam-7033	775	25	(	(	PUNCT
ejpam-7033	775	26	rr	rr	NOUN
ejpam-7033	775	27	)	)	PUNCT
ejpam-7033	775	28	(	(	PUNCT
ejpam-7033	775	29	℘	℘	PROPN
ejpam-7033	775	30	)	)	PUNCT
ejpam-7033	775	31	.	.	PUNCT
ejpam-7033	776	1	so	so	ADV
ejpam-7033	776	2	,	,	PUNCT
ejpam-7033	776	3	(	(	PUNCT
ejpam-7033	776	4	rϖ	rϖ	ADP
ejpam-7033	776	5	)	)	PUNCT
ejpam-7033	776	6	⊥	⊥	PROPN
ejpam-7033	776	7	(	(	PUNCT
ejpam-7033	776	8	rr	rr	NOUN
ejpam-7033	776	9	)	)	PUNCT
ejpam-7033	776	10	.	.	PUNCT
ejpam-7033	777	1	self	self	NOUN
ejpam-7033	777	2	-	-	PUNCT
ejpam-7033	777	3	operator	operator	NOUN
ejpam-7033	777	4	:	:	PUNCT
ejpam-7033	777	5	using	use	VERB
ejpam-7033	777	6	(	(	PUNCT
ejpam-7033	777	7	d1	d1	NOUN
ejpam-7033	777	8	)	)	PUNCT
ejpam-7033	777	9	and	and	CCONJ
ejpam-7033	777	10	(	(	PUNCT
ejpam-7033	777	11	d3	d3	PROPN
ejpam-7033	777	12	)	)	PUNCT
ejpam-7033	777	13	we	we	PRON
ejpam-7033	777	14	get	get	VERB
ejpam-7033	777	15	r	r	NOUN
ejpam-7033	777	16	:	:	PUNCT
ejpam-7033	777	17	d	d	X
ejpam-7033	777	18	→	→	SYM
ejpam-7033	777	19	d	d	PROPN
ejpam-7033	777	20	as	as	ADP
ejpam-7033	777	21	continuous	continuous	ADJ
ejpam-7033	777	22	and	and	CCONJ
ejpam-7033	777	23	compact	compact	ADJ
ejpam-7033	777	24	function	function	NOUN
ejpam-7033	777	25	(	(	PUNCT
ejpam-7033	777	26	see	see	VERB
ejpam-7033	777	27	[	[	X
ejpam-7033	777	28	41	41	NUM
ejpam-7033	777	29	,	,	PUNCT
ejpam-7033	777	30	lemma	lemma	PROPN
ejpam-7033	777	31	3	3	NUM
ejpam-7033	777	32	]	]	PUNCT
ejpam-7033	777	33	)	)	PUNCT
ejpam-7033	777	34	.	.	PUNCT
ejpam-7033	778	1	using	use	VERB
ejpam-7033	778	2	(	(	PUNCT
ejpam-7033	778	3	d4	d4	PROPN
ejpam-7033	778	4	)	)	PUNCT
ejpam-7033	778	5	,	,	PUNCT
ejpam-7033	778	6	assures	assure	VERB
ejpam-7033	778	7	the	the	DET
ejpam-7033	778	8	existence	existence	NOUN
ejpam-7033	778	9	of	of	ADP
ejpam-7033	778	10	ϖ1	ϖ1	NOUN
ejpam-7033	778	11	=	=	SYM
ejpam-7033	778	12	r(ϖ0	r(ϖ0	NOUN
ejpam-7033	778	13	)	)	PUNCT
ejpam-7033	778	14	so	so	SCONJ
ejpam-7033	778	15	that	that	SCONJ
ejpam-7033	778	16	ϖ1	ϖ1	VERB
ejpam-7033	778	17	⪯	⪯	NOUN
ejpam-7033	778	18	ϖ0	ϖ0	NOUN
ejpam-7033	778	19	or	or	CCONJ
ejpam-7033	778	20	ϖ0	ϖ0	NOUN
ejpam-7033	778	21	⪯	⪯	AUX
ejpam-7033	778	22	ϖ1	ϖ1	VERB
ejpam-7033	778	23	,	,	PUNCT
ejpam-7033	778	24	for	for	ADP
ejpam-7033	778	25	every	every	DET
ejpam-7033	778	26	ϖ0	ϖ0	NOUN
ejpam-7033	778	27	∈	∈	NOUN
ejpam-7033	778	28	d	d	NOUN
ejpam-7033	778	29	and	and	CCONJ
ejpam-7033	778	30	r	r	NOUN
ejpam-7033	778	31	is	be	AUX
ejpam-7033	778	32	⪯-preserving	⪯-preserve	VERB
ejpam-7033	778	33	,	,	PUNCT
ejpam-7033	778	34	so	so	SCONJ
ejpam-7033	778	35	we	we	PRON
ejpam-7033	778	36	get	get	VERB
ejpam-7033	778	37	ϖn	ϖn	ADP
ejpam-7033	778	38	=	=	SYM
ejpam-7033	778	39	rn(ϖ0	rn(ϖ0	NOUN
ejpam-7033	778	40	)	)	PUNCT
ejpam-7033	778	41	with	with	ADP
ejpam-7033	778	42	ϖn	ϖn	NOUN
ejpam-7033	778	43	⪯	⪯	NOUN
ejpam-7033	778	44	ϖn+1	ϖn+1	ADJ
ejpam-7033	778	45	or	or	CCONJ
ejpam-7033	778	46	ϖn+1	ϖn+1	ADJ
ejpam-7033	778	47	⪯	⪯	NOUN
ejpam-7033	778	48	ϖn	ϖn	ADP
ejpam-7033	778	49	∀	∀	NOUN
ejpam-7033	778	50	n	n	PRON
ejpam-7033	778	51	≥	≥	NOUN
ejpam-7033	778	52	0	0	NUM
ejpam-7033	778	53	.	.	PUNCT
ejpam-7033	779	1	using	use	VERB
ejpam-7033	779	2	(	(	PUNCT
ejpam-7033	779	3	d5	d5	NOUN
ejpam-7033	779	4	)	)	PUNCT
ejpam-7033	779	5	and	and	CCONJ
ejpam-7033	779	6	holder	holder	NOUN
ejpam-7033	779	7	inequality	inequality	NOUN
ejpam-7033	779	8	will	will	AUX
ejpam-7033	779	9	lead	lead	VERB
ejpam-7033	779	10	us	we	PRON
ejpam-7033	779	11	to	to	ADP
ejpam-7033	779	12	the	the	DET
ejpam-7033	779	13	contractive	contractive	ADJ
ejpam-7033	779	14	condition	condition	NOUN
ejpam-7033	779	15	of	of	ADP
ejpam-7033	779	16	theorem	theorem	ADJ
ejpam-7033	779	17	13	13	NUM
ejpam-7033	779	18	.	.	PUNCT
ejpam-7033	780	1	ϖ	ϖ	X
ejpam-7033	780	2	|(rϖ)(℘)−	|(rϖ)(℘)−	NOUN
ejpam-7033	780	3	(	(	PUNCT
ejpam-7033	780	4	rr)(℘)|2	rr)(℘)|2	X
ejpam-7033	780	5	=	=	SYM
ejpam-7033	780	6	ϖ	ϖ	PROPN
ejpam-7033	780	7	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-7033	780	8	∫	∫	PROPN
ejpam-7033	780	9	ir	ir	PROPN
ejpam-7033	780	10	k1(℘	k1(℘	PROPN
ejpam-7033	780	11	,	,	PUNCT
ejpam-7033	780	12	s,ϖ(s	s,ϖ(	NOUN
ejpam-7033	780	13	)	)	PUNCT
ejpam-7033	780	14	)	)	PUNCT
ejpam-7033	781	1	ds−	ds−	PROPN
ejpam-7033	781	2	∫	∫	PROPN
ejpam-7033	781	3	ir	ir	PROPN
ejpam-7033	781	4	k1(℘	k1(℘	PROPN
ejpam-7033	781	5	,	,	PUNCT
ejpam-7033	781	6	s	s	NOUN
ejpam-7033	781	7	,	,	PUNCT
ejpam-7033	781	8	r(s	r(s	NOUN
ejpam-7033	781	9	)	)	PUNCT
ejpam-7033	781	10	)	)	PUNCT
ejpam-7033	781	11	ds	ds	ADP
ejpam-7033	781	12	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-7033	781	13	2	2	NUM
ejpam-7033	781	14	a.	a.	NOUN
ejpam-7033	781	15	arif	arif	PROPN
ejpam-7033	781	16	et	et	PROPN
ejpam-7033	781	17	al	al	PROPN
ejpam-7033	781	18	.	.	PUNCT
ejpam-7033	781	19	/	/	SYM
ejpam-7033	781	20	eur	eur	PROPN
ejpam-7033	781	21	.	.	PUNCT
ejpam-7033	782	1	j.	j.	PROPN
ejpam-7033	782	2	pure	pure	PROPN
ejpam-7033	782	3	appl	appl	PROPN
ejpam-7033	782	4	.	.	PROPN
ejpam-7033	782	5	math	math	PROPN
ejpam-7033	782	6	,	,	PUNCT
ejpam-7033	782	7	18	18	NUM
ejpam-7033	782	8	(	(	PUNCT
ejpam-7033	782	9	4	4	NUM
ejpam-7033	782	10	)	)	PUNCT
ejpam-7033	782	11	(	(	PUNCT
ejpam-7033	782	12	2025	2025	NUM
ejpam-7033	782	13	)	)	PUNCT
ejpam-7033	782	14	,	,	PUNCT
ejpam-7033	782	15	7033	7033	NUM
ejpam-7033	782	16	25	25	NUM
ejpam-7033	782	17	of	of	ADP
ejpam-7033	782	18	29	29	NUM
ejpam-7033	782	19	⪯	⪯	NOUN
ejpam-7033	782	20	ϖ	ϖ	X
ejpam-7033	782	21	∫	∫	NUM
ejpam-7033	782	22	ir	ir	NOUN
ejpam-7033	782	23	|k1(℘	|k1(℘	NOUN
ejpam-7033	782	24	,	,	PUNCT
ejpam-7033	782	25	s,ϖ(s))−k1(℘	s,ϖ(s))−k1(℘	NUM
ejpam-7033	782	26	,	,	PUNCT
ejpam-7033	782	27	s	s	PART
ejpam-7033	782	28	,	,	PUNCT
ejpam-7033	782	29	r(s))|	r(s))|	VERB
ejpam-7033	782	30	ds	ds	VERB
ejpam-7033	782	31	2	2	PROPN
ejpam-7033	782	32	⪯	⪯	X
ejpam-7033	782	33	ϖ	ϖ	PROPN
ejpam-7033	782	34	∫	∫	NUM
ejpam-7033	782	35	ir	ir	PROPN
ejpam-7033	782	36	q(℘	q(℘	PROPN
ejpam-7033	782	37	,	,	PUNCT
ejpam-7033	782	38	s)|ϖ(s)−	s)|ϖ(s)−	VERB
ejpam-7033	782	39	r(s)|	r(s)|	PROPN
ejpam-7033	782	40	ds	ds	PROPN
ejpam-7033	782	41	2	2	PROPN
ejpam-7033	782	42	⪯	⪯	PROPN
ejpam-7033	783	1	ϖ	ϖ	PROPN
ejpam-7033	783	2	∫	∫	PROPN
ejpam-7033	783	3	ir	ir	PROPN
ejpam-7033	783	4	q2(℘	q2(℘	PROPN
ejpam-7033	783	5	,	,	PUNCT
ejpam-7033	783	6	s	s	PART
ejpam-7033	783	7	)	)	PUNCT
ejpam-7033	783	8	ds	ds	ADJ
ejpam-7033	783	9	·	·	PUNCT
ejpam-7033	783	10	∫	∫	PROPN
ejpam-7033	783	11	ir	ir	PROPN
ejpam-7033	783	12	|ϖ(s)−	|ϖ(s)−	NOUN
ejpam-7033	783	13	r(s)|2	r(s)|2	PROPN
ejpam-7033	783	14	ds	ds	ADJ
ejpam-7033	783	15	=	=	SYM
ejpam-7033	783	16	ϖα(℘	ϖα(℘	NOUN
ejpam-7033	783	17	)	)	PUNCT
ejpam-7033	783	18	∫	∫	PROPN
ejpam-7033	784	1	ir	ir	PROPN
ejpam-7033	784	2	|ϖ(s)−	|ϖ(s)−	PROPN
ejpam-7033	784	3	r(s)|2	r(s)|2	PROPN
ejpam-7033	784	4	ds	ds	PROPN
ejpam-7033	784	5	.	.	PUNCT
ejpam-7033	784	6	by	by	ADP
ejpam-7033	784	7	integrating	integrate	VERB
ejpam-7033	784	8	with	with	ADP
ejpam-7033	784	9	respect	respect	NOUN
ejpam-7033	784	10	to	to	ADP
ejpam-7033	784	11	℘	℘	PROPN
ejpam-7033	784	12	,	,	PUNCT
ejpam-7033	784	13	we	we	PRON
ejpam-7033	784	14	get	get	VERB
ejpam-7033	784	15	ϖ	ϖ	INTJ
ejpam-7033	784	16	∫	∫	PROPN
ejpam-7033	784	17	ir	ir	PROPN
ejpam-7033	784	18	|(rϖ)(℘)−	|(rϖ)(℘)−	PROPN
ejpam-7033	784	19	(	(	PUNCT
ejpam-7033	784	20	rr)(℘)|2	rr)(℘)|2	NOUN
ejpam-7033	784	21	d℘	d℘	PROPN
ejpam-7033	784	22	⪯	⪯	PROPN
ejpam-7033	785	1	ϖ	ϖ	X
ejpam-7033	785	2	∫	∫	PROPN
ejpam-7033	785	3	ir	ir	PROPN
ejpam-7033	785	4	α(℘)∫	α(℘)∫	ADJ
ejpam-7033	785	5	ir	ir	X
ejpam-7033	785	6	|ϖ(s)−	|ϖ(s)−	NOUN
ejpam-7033	785	7	r(s)|2	r(s)|2	PROPN
ejpam-7033	785	8	ds	ds	PRON
ejpam-7033	785	9			PROPN
ejpam-7033	785	10	d℘	d℘	PROPN
ejpam-7033	785	11	=	=	SYM
ejpam-7033	786	1	ϖ	ϖ	X
ejpam-7033	786	2	∫	∫	PROPN
ejpam-7033	786	3	ir	ir	PROPN
ejpam-7033	786	4	α(℘)ey	α(℘)ey	PROPN
ejpam-7033	786	5	∫ir	∫ir	ADV
ejpam-7033	786	6	α(s)ds	α(s)ds	NUM
ejpam-7033	786	7	·	·	PUNCT
ejpam-7033	786	8	e−y	e−y	ADP
ejpam-7033	786	9	∫	∫	PROPN
ejpam-7033	786	10	ir	ir	PROPN
ejpam-7033	786	11	α(s)ds	α(s)ds	NUM
ejpam-7033	786	12	∫	∫	PROPN
ejpam-7033	786	13	ir	ir	PROPN
ejpam-7033	786	14	|ϖ(s)−	|ϖ(s)−	NOUN
ejpam-7033	786	15	r(s)|2	r(s)|2	PROPN
ejpam-7033	786	16	ds	ds	PRON
ejpam-7033	786	17			PROPN
ejpam-7033	786	18	d℘	d℘	PROPN
ejpam-7033	786	19	⪯	⪯	NOUN
ejpam-7033	787	1	ϖ	ϖ	INTJ
ejpam-7033	787	2	∥ϖ	∥ϖ	PROPN
ejpam-7033	787	3	−	−	PROPN
ejpam-7033	787	4	r∥22,y	r∥22,y	X
ejpam-7033	787	5	∫	∫	PROPN
ejpam-7033	788	1	ir	ir	PROPN
ejpam-7033	788	2	α(℘)ey	α(℘)ey	PROPN
ejpam-7033	788	3	∫	∫	PROPN
ejpam-7033	789	1	ir	ir	PROPN
ejpam-7033	789	2	α(s)ds	α(s)ds	NUM
ejpam-7033	789	3	d℘	d℘	PROPN
ejpam-7033	789	4	⪯	⪯	NOUN
ejpam-7033	789	5	ϖ	ϖ	NOUN
ejpam-7033	789	6	1	1	NUM
ejpam-7033	789	7	y	y	NOUN
ejpam-7033	789	8	∥ϖ	∥ϖ	PROPN
ejpam-7033	789	9	−	−	PROPN
ejpam-7033	789	10	r∥22,y	r∥22,y	NOUN
ejpam-7033	789	11	e	e	X
ejpam-7033	789	12	y	y	PROPN
ejpam-7033	789	13	∫	∫	PROPN
ejpam-7033	789	14	ir	ir	PROPN
ejpam-7033	789	15	α(s)ds	α(s)ds	PROPN
ejpam-7033	789	16	.	.	PUNCT
ejpam-7033	790	1	hence	hence	ADV
ejpam-7033	790	2	,	,	PUNCT
ejpam-7033	790	3	we	we	PRON
ejpam-7033	790	4	get	get	VERB
ejpam-7033	790	5	ϖe−y	ϖe−y	PROPN
ejpam-7033	790	6	∫	∫	PROPN
ejpam-7033	790	7	ir	ir	PROPN
ejpam-7033	790	8	α(s)ds	α(s)ds	NUM
ejpam-7033	790	9	∫	∫	PROPN
ejpam-7033	790	10	ir	ir	PROPN
ejpam-7033	790	11	|(rϖ)(℘)−	|(rϖ)(℘)−	PROPN
ejpam-7033	790	12	(	(	PUNCT
ejpam-7033	790	13	rr)(℘)|2	rr)(℘)|2	NOUN
ejpam-7033	790	14	d℘	d℘	PROPN
ejpam-7033	790	15	⪯	⪯	VERB
ejpam-7033	790	16	ϖ	ϖ	INTJ
ejpam-7033	791	1	1	1	NUM
ejpam-7033	791	2	y	y	PROPN
ejpam-7033	791	3	∥ϖ	∥ϖ	PROPN
ejpam-7033	791	4	−	−	PROPN
ejpam-7033	791	5	r∥22,y	r∥22,y	NOUN
ejpam-7033	791	6	.	.	PUNCT
ejpam-7033	792	1	which	which	PRON
ejpam-7033	792	2	further	far	ADV
ejpam-7033	792	3	implies	imply	VERB
ejpam-7033	792	4	that	that	SCONJ
ejpam-7033	792	5	ϖ	ϖ	PROPN
ejpam-7033	792	6	∥rϖ	∥rϖ	PROPN
ejpam-7033	792	7	−rr∥22,y	−rr∥22,y	PROPN
ejpam-7033	792	8	⪯	⪯	NOUN
ejpam-7033	792	9	ϖ	ϖ	NOUN
ejpam-7033	792	10	1	1	NUM
ejpam-7033	792	11	y	y	PROPN
ejpam-7033	792	12	∥ϖ	∥ϖ	PROPN
ejpam-7033	792	13	−	−	PROPN
ejpam-7033	792	14	r∥22,y	r∥22,y	NOUN
ejpam-7033	792	15	.	.	PUNCT
ejpam-7033	793	1	so	so	ADV
ejpam-7033	793	2	,	,	PUNCT
ejpam-7033	793	3	cy(rϖ,rr	cy(rϖ,rr	PROPN
ejpam-7033	793	4	)	)	PUNCT
ejpam-7033	793	5	⪯	⪯	NOUN
ejpam-7033	793	6	1	1	NUM
ejpam-7033	793	7	y	y	NOUN
ejpam-7033	793	8	cy(ϖ	cy(ϖ	NOUN
ejpam-7033	793	9	,	,	PUNCT
ejpam-7033	793	10	r	r	NOUN
ejpam-7033	793	11	)	)	PUNCT
ejpam-7033	793	12	implies	imply	VERB
ejpam-7033	793	13	ycy(rϖ,rr	ycy(rϖ,rr	NOUN
ejpam-7033	793	14	)	)	PUNCT
ejpam-7033	793	15	⪯	⪯	PROPN
ejpam-7033	793	16	cy(ϖ	cy(ϖ	NOUN
ejpam-7033	793	17	,	,	PUNCT
ejpam-7033	793	18	r	r	NOUN
ejpam-7033	793	19	)	)	PUNCT
ejpam-7033	793	20	define	define	VERB
ejpam-7033	793	21	j	j	PROPN
ejpam-7033	793	22	:	:	PUNCT
ejpam-7033	793	23	e6	e6	PROPN
ejpam-7033	793	24	→	→	SYM
ejpam-7033	793	25	e	e	PROPN
ejpam-7033	793	26	by	by	ADP
ejpam-7033	793	27	j	j	PROPN
ejpam-7033	793	28	(	(	PUNCT
ejpam-7033	793	29	p1	p1	PROPN
ejpam-7033	793	30	,	,	PUNCT
ejpam-7033	793	31	p2	p2	NOUN
ejpam-7033	793	32	,	,	PUNCT
ejpam-7033	793	33	p3	p3	NOUN
ejpam-7033	793	34	,	,	PUNCT
ejpam-7033	793	35	p4	p4	ADJ
ejpam-7033	793	36	,	,	PUNCT
ejpam-7033	793	37	p5	p5	ADJ
ejpam-7033	793	38	,	,	PUNCT
ejpam-7033	793	39	p6	p6	PROPN
ejpam-7033	793	40	)	)	PUNCT
ejpam-7033	794	1	=	=	PUNCT
ejpam-7033	794	2	kp1	kp1	NOUN
ejpam-7033	794	3	−	−	NOUN
ejpam-7033	794	4	p2	p2	NOUN
ejpam-7033	794	5	;	;	PUNCT
ejpam-7033	794	6	k	k	X
ejpam-7033	794	7	>	>	X
ejpam-7033	794	8	1	1	NUM
ejpam-7033	794	9	,	,	PUNCT
ejpam-7033	794	10	a.	a.	PROPN
ejpam-7033	794	11	arif	arif	PROPN
ejpam-7033	794	12	et	et	PROPN
ejpam-7033	794	13	al	al	PROPN
ejpam-7033	794	14	.	.	PUNCT
ejpam-7033	794	15	/	/	SYM
ejpam-7033	794	16	eur	eur	PROPN
ejpam-7033	794	17	.	.	PUNCT
ejpam-7033	795	1	j.	j.	PROPN
ejpam-7033	795	2	pure	pure	PROPN
ejpam-7033	795	3	appl	appl	PROPN
ejpam-7033	795	4	.	.	PROPN
ejpam-7033	795	5	math	math	PROPN
ejpam-7033	795	6	,	,	PUNCT
ejpam-7033	795	7	18	18	NUM
ejpam-7033	795	8	(	(	PUNCT
ejpam-7033	795	9	4	4	NUM
ejpam-7033	795	10	)	)	PUNCT
ejpam-7033	795	11	(	(	PUNCT
ejpam-7033	795	12	2025	2025	NUM
ejpam-7033	795	13	)	)	PUNCT
ejpam-7033	795	14	,	,	PUNCT
ejpam-7033	795	15	7033	7033	NUM
ejpam-7033	795	16	26	26	NUM
ejpam-7033	795	17	of	of	ADP
ejpam-7033	795	18	29	29	NUM
ejpam-7033	795	19	we	we	PRON
ejpam-7033	795	20	have	have	VERB
ejpam-7033	795	21	j	j	PROPN
ejpam-7033	795	22	(	(	PUNCT
ejpam-7033	795	23	c(rϖ,rr	c(rϖ,rr	PROPN
ejpam-7033	795	24	)	)	PUNCT
ejpam-7033	795	25	,	,	PUNCT
ejpam-7033	795	26	c(ϖ	c(ϖ	PROPN
ejpam-7033	795	27	,	,	PUNCT
ejpam-7033	795	28	r	r	NOUN
ejpam-7033	795	29	)	)	PUNCT
ejpam-7033	795	30	,	,	PUNCT
ejpam-7033	795	31	c(ϖ,rϖ	c(ϖ,rϖ	NOUN
ejpam-7033	795	32	)	)	PUNCT
ejpam-7033	795	33	,	,	PUNCT
ejpam-7033	795	34	c(r	c(r	PROPN
ejpam-7033	795	35	,	,	PUNCT
ejpam-7033	795	36	rr	rr	NOUN
ejpam-7033	795	37	)	)	PUNCT
ejpam-7033	795	38	,	,	PUNCT
ejpam-7033	795	39	c(ϖ,rr	c(ϖ,rr	NOUN
ejpam-7033	795	40	)	)	PUNCT
ejpam-7033	795	41	,	,	PUNCT
ejpam-7033	795	42	c(r	c(r	NOUN
ejpam-7033	795	43	,	,	PUNCT
ejpam-7033	795	44	rϖ	rϖ	NOUN
ejpam-7033	795	45	)	)	PUNCT
ejpam-7033	795	46	)	)	PUNCT
ejpam-7033	795	47	⪯	⪯	NOUN
ejpam-7033	795	48	0e	0e	NOUN
ejpam-7033	795	49	.	.	PUNCT
ejpam-7033	796	1	by	by	ADP
ejpam-7033	796	2	using	use	VERB
ejpam-7033	796	3	13	13	NUM
ejpam-7033	796	4	,	,	PUNCT
ejpam-7033	796	5	we	we	PRON
ejpam-7033	796	6	get	get	VERB
ejpam-7033	796	7	a	a	DET
ejpam-7033	796	8	unique	unique	ADJ
ejpam-7033	796	9	fixed	fix	VERB
ejpam-7033	796	10	point	point	NOUN
ejpam-7033	796	11	for	for	ADP
ejpam-7033	796	12	r	r	NOUN
ejpam-7033	796	13	,	,	PUNCT
ejpam-7033	796	14	which	which	PRON
ejpam-7033	796	15	implies	imply	VERB
ejpam-7033	796	16	uie	uie	PROPN
ejpam-7033	796	17	(	(	PUNCT
ejpam-7033	796	18	12	12	NUM
ejpam-7033	796	19	)	)	PUNCT
ejpam-7033	796	20	has	have	VERB
ejpam-7033	796	21	a	a	DET
ejpam-7033	796	22	unique	unique	ADJ
ejpam-7033	796	23	solution	solution	NOUN
ejpam-7033	796	24	.	.	PUNCT
ejpam-7033	797	1	8	8	X
ejpam-7033	797	2	.	.	X
ejpam-7033	797	3	conclusion	conclusion	NOUN
ejpam-7033	797	4	fixed	fix	VERB
ejpam-7033	797	5	point	point	NOUN
ejpam-7033	797	6	results	result	NOUN
ejpam-7033	797	7	show	show	VERB
ejpam-7033	797	8	that	that	SCONJ
ejpam-7033	797	9	rectangular	rectangular	ADJ
ejpam-7033	797	10	cone	cone	NOUN
ejpam-7033	797	11	b	b	NOUN
ejpam-7033	797	12	-	-	PUNCT
ejpam-7033	797	13	metric	metric	ADJ
ejpam-7033	797	14	space	space	NOUN
ejpam-7033	797	15	can	can	AUX
ejpam-7033	797	16	be	be	AUX
ejpam-7033	797	17	applied	apply	VERB
ejpam-7033	797	18	to	to	PART
ejpam-7033	797	19	obtain	obtain	VERB
ejpam-7033	797	20	the	the	DET
ejpam-7033	797	21	general	general	ADJ
ejpam-7033	797	22	existence	existence	NOUN
ejpam-7033	797	23	results	result	VERB
ejpam-7033	797	24	for	for	ADP
ejpam-7033	797	25	implicit	implicit	ADJ
ejpam-7033	797	26	contractions	contraction	NOUN
ejpam-7033	797	27	subject	subject	ADJ
ejpam-7033	797	28	to	to	ADP
ejpam-7033	797	29	implicit	implicit	ADJ
ejpam-7033	797	30	ordered	order	VERB
ejpam-7033	797	31	relation	relation	NOUN
ejpam-7033	797	32	.	.	PUNCT
ejpam-7033	798	1	these	these	DET
ejpam-7033	798	2	results	result	NOUN
ejpam-7033	798	3	generalize	generalize	VERB
ejpam-7033	798	4	many	many	ADJ
ejpam-7033	798	5	theorems	theorem	NOUN
ejpam-7033	798	6	in	in	ADP
ejpam-7033	798	7	[	[	X
ejpam-7033	798	8	1	1	NUM
ejpam-7033	798	9	,	,	PUNCT
ejpam-7033	798	10	4	4	NUM
ejpam-7033	798	11	,	,	PUNCT
ejpam-7033	798	12	34	34	NUM
ejpam-7033	798	13	]	]	PUNCT
ejpam-7033	798	14	.	.	PUNCT
ejpam-7033	799	1	the	the	DET
ejpam-7033	799	2	obtained	obtain	VERB
ejpam-7033	799	3	results	result	NOUN
ejpam-7033	799	4	can	can	AUX
ejpam-7033	799	5	be	be	AUX
ejpam-7033	799	6	applied	apply	VERB
ejpam-7033	799	7	to	to	PART
ejpam-7033	799	8	obtain	obtain	VERB
ejpam-7033	799	9	more	more	ADJ
ejpam-7033	799	10	general	general	ADJ
ejpam-7033	799	11	homotopy	homotopy	NOUN
ejpam-7033	799	12	results	result	NOUN
ejpam-7033	799	13	and	and	CCONJ
ejpam-7033	799	14	existence	existence	NOUN
ejpam-7033	799	15	results	result	VERB
ejpam-7033	799	16	for	for	ADP
ejpam-7033	799	17	integral	integral	ADJ
ejpam-7033	799	18	equations	equation	NOUN
ejpam-7033	799	19	.	.	PUNCT
ejpam-7033	800	1	this	this	DET
ejpam-7033	800	2	idea	idea	NOUN
ejpam-7033	800	3	can	can	AUX
ejpam-7033	800	4	be	be	AUX
ejpam-7033	800	5	further	far	ADV
ejpam-7033	800	6	applied	apply	VERB
ejpam-7033	800	7	to	to	PART
ejpam-7033	800	8	obtain	obtain	VERB
ejpam-7033	800	9	fixed	fix	VERB
ejpam-7033	800	10	point	point	NOUN
ejpam-7033	800	11	results	result	NOUN
ejpam-7033	800	12	in	in	ADP
ejpam-7033	800	13	cone	cone	NOUN
ejpam-7033	800	14	a	a	DET
ejpam-7033	800	15	-	-	PUNCT
ejpam-7033	800	16	metric	metric	ADJ
ejpam-7033	800	17	space	space	NOUN
ejpam-7033	800	18	.	.	PUNCT
ejpam-7033	801	1	we	we	PRON
ejpam-7033	801	2	refer	refer	VERB
ejpam-7033	801	3	a	a	DET
ejpam-7033	801	4	cmparison	cmparison	NOUN
ejpam-7033	801	5	between	between	ADP
ejpam-7033	801	6	this	this	DET
ejpam-7033	801	7	paper	paper	NOUN
ejpam-7033	801	8	and	and	CCONJ
ejpam-7033	801	9	[	[	X
ejpam-7033	801	10	44	44	NUM
ejpam-7033	801	11	]	]	PUNCT
ejpam-7033	801	12	for	for	ADP
ejpam-7033	801	13	further	further	ADJ
ejpam-7033	801	14	studies	study	NOUN
ejpam-7033	801	15	.	.	PUNCT
ejpam-7033	802	1	we	we	PRON
ejpam-7033	802	2	suggest	suggest	VERB
ejpam-7033	802	3	the	the	DET
ejpam-7033	802	4	readers	reader	NOUN
ejpam-7033	802	5	and	and	CCONJ
ejpam-7033	802	6	interested	interested	ADJ
ejpam-7033	802	7	researchers	researcher	NOUN
ejpam-7033	802	8	to	to	PART
ejpam-7033	802	9	compare	compare	VERB
ejpam-7033	802	10	the	the	DET
ejpam-7033	802	11	results	result	NOUN
ejpam-7033	802	12	presented	present	VERB
ejpam-7033	802	13	in	in	ADP
ejpam-7033	802	14	this	this	DET
ejpam-7033	802	15	paper	paper	NOUN
ejpam-7033	802	16	with	with	ADP
ejpam-7033	802	17	the	the	DET
ejpam-7033	802	18	results	result	NOUN
ejpam-7033	802	19	appearing	appear	VERB
ejpam-7033	802	20	in	in	ADP
ejpam-7033	802	21	[	[	X
ejpam-7033	802	22	44	44	NUM
ejpam-7033	802	23	]	]	PUNCT
ejpam-7033	802	24	for	for	ADP
ejpam-7033	802	25	further	further	ADJ
ejpam-7033	802	26	study	study	NOUN
ejpam-7033	802	27	.	.	PUNCT
ejpam-7033	803	1	acknowledgements	acknowledgement	NOUN
ejpam-7033	803	2	the	the	DET
ejpam-7033	803	3	authors	author	NOUN
ejpam-7033	803	4	extend	extend	VERB
ejpam-7033	803	5	their	their	PRON
ejpam-7033	803	6	appreciation	appreciation	NOUN
ejpam-7033	803	7	to	to	ADP
ejpam-7033	803	8	taif	taif	PROPN
ejpam-7033	803	9	university	university	PROPN
ejpam-7033	803	10	,	,	PUNCT
ejpam-7033	803	11	saudi	saudi	PROPN
ejpam-7033	803	12	arabia	arabia	PROPN
ejpam-7033	803	13	,	,	PUNCT
ejpam-7033	803	14	for	for	ADP
ejpam-7033	803	15	supporting	support	VERB
ejpam-7033	803	16	this	this	DET
ejpam-7033	803	17	work	work	NOUN
ejpam-7033	803	18	through	through	ADP
ejpam-7033	803	19	project	project	NOUN
ejpam-7033	803	20	number	number	NOUN
ejpam-7033	803	21	(	(	PUNCT
ejpam-7033	803	22	tu	tu	NOUN
ejpam-7033	803	23	-	-	PUNCT
ejpam-7033	803	24	dspp-2024	dspp-2024	NOUN
ejpam-7033	803	25	-	-	PUNCT
ejpam-7033	803	26	46	46	NUM
ejpam-7033	803	27	)	)	PUNCT
ejpam-7033	803	28	9	9	NUM
ejpam-7033	803	29	.	.	PUNCT
ejpam-7033	804	1	data	datum	NOUN
ejpam-7033	804	2	availability	availability	NOUN
ejpam-7033	804	3	no	no	DET
ejpam-7033	804	4	data	datum	NOUN
ejpam-7033	804	5	were	be	AUX
ejpam-7033	804	6	used	use	VERB
ejpam-7033	804	7	to	to	PART
ejpam-7033	804	8	support	support	VERB
ejpam-7033	804	9	this	this	DET
ejpam-7033	804	10	study	study	NOUN
ejpam-7033	804	11	.	.	PUNCT
ejpam-7033	805	1	competing	compete	VERB
ejpam-7033	805	2	interests	interest	NOUN
ejpam-7033	805	3	the	the	DET
ejpam-7033	805	4	authors	author	NOUN
ejpam-7033	805	5	declare	declare	VERB
ejpam-7033	805	6	that	that	SCONJ
ejpam-7033	805	7	they	they	PRON
ejpam-7033	805	8	have	have	VERB
ejpam-7033	805	9	no	no	DET
ejpam-7033	805	10	competing	compete	VERB
ejpam-7033	805	11	interests	interest	NOUN
ejpam-7033	805	12	.	.	PUNCT
ejpam-7033	806	1	10	10	NUM
ejpam-7033	806	2	.	.	PUNCT
ejpam-7033	807	1	author	author	NOUN
ejpam-7033	807	2	’s	’s	PART
ejpam-7033	807	3	contributions	contribution	NOUN
ejpam-7033	807	4	all	all	DET
ejpam-7033	807	5	authors	author	NOUN
ejpam-7033	807	6	contributed	contribute	VERB
ejpam-7033	807	7	equally	equally	ADV
ejpam-7033	807	8	to	to	ADP
ejpam-7033	807	9	this	this	DET
ejpam-7033	807	10	work	work	NOUN
ejpam-7033	807	11	.	.	PUNCT
ejpam-7033	808	1	references	reference	NOUN
ejpam-7033	808	2	[	[	X
ejpam-7033	808	3	1	1	X
ejpam-7033	808	4	]	]	PUNCT
ejpam-7033	808	5	v.	v.	CCONJ
ejpam-7033	808	6	popa	popa	NOUN
ejpam-7033	808	7	.	.	PUNCT
ejpam-7033	809	1	fixed	fix	VERB
ejpam-7033	809	2	point	point	NOUN
ejpam-7033	809	3	theorems	theorem	NOUN
ejpam-7033	809	4	for	for	ADP
ejpam-7033	809	5	implicit	implicit	ADJ
ejpam-7033	809	6	contractive	contractive	ADJ
ejpam-7033	809	7	mappings	mapping	NOUN
ejpam-7033	809	8	.	.	PUNCT
ejpam-7033	810	1	studii	studii	PROPN
ejpam-7033	810	2	şi	şi	PROPN
ejpam-7033	810	3	cercetări	cercetări	PROPN
ejpam-7033	810	4	ştiinţifice	ştiinţifice	PROPN
ejpam-7033	810	5	.	.	PUNCT
ejpam-7033	811	1	seria	seria	PROPN
ejpam-7033	811	2	matematică.	matematică.	PROPN
ejpam-7033	811	3	universitatea	universitatea	PROPN
ejpam-7033	811	4	bacău	bacău	PROPN
ejpam-7033	811	5	,	,	PUNCT
ejpam-7033	811	6	7:127–134	7:127–134	NUM
ejpam-7033	811	7	,	,	PUNCT
ejpam-7033	811	8	1997	1997	NUM
ejpam-7033	811	9	.	.	PUNCT
ejpam-7033	812	1	[	[	X
ejpam-7033	812	2	2	2	NUM
ejpam-7033	812	3	]	]	PUNCT
ejpam-7033	812	4	r.	r.	PROPN
ejpam-7033	812	5	george	george	PROPN
ejpam-7033	812	6	,	,	PUNCT
ejpam-7033	812	7	h.	h.	PROPN
ejpam-7033	812	8	a.	a.	PROPN
ejpam-7033	812	9	nabwey	nabwey	PROPN
ejpam-7033	812	10	,	,	PUNCT
ejpam-7033	812	11	r.	r.	PROPN
ejpam-7033	812	12	rajagopalan	rajagopalan	PROPN
ejpam-7033	812	13	,	,	PUNCT
ejpam-7033	812	14	s.	s.	PROPN
ejpam-7033	812	15	radenović	radenović	VERB
ejpam-7033	812	16	,	,	PUNCT
ejpam-7033	812	17	and	and	CCONJ
ejpam-7033	812	18	k.	k.	PROPN
ejpam-7033	812	19	p.	p.	PROPN
ejpam-7033	812	20	reshma	reshma	PROPN
ejpam-7033	812	21	.	.	PUNCT
ejpam-7033	813	1	rectangular	rectangular	ADJ
ejpam-7033	813	2	cone	cone	NOUN
ejpam-7033	813	3	b	b	X
ejpam-7033	813	4	-	-	ADJ
ejpam-7033	813	5	metric	metric	ADJ
ejpam-7033	813	6	spaces	space	NOUN
ejpam-7033	813	7	over	over	ADP
ejpam-7033	813	8	banach	banach	NOUN
ejpam-7033	813	9	algebra	algebra	NOUN
ejpam-7033	813	10	and	and	CCONJ
ejpam-7033	813	11	contraction	contraction	NOUN
ejpam-7033	813	12	principle	principle	NOUN
ejpam-7033	813	13	.	.	PUNCT
ejpam-7033	814	1	fixed	fix	VERB
ejpam-7033	814	2	point	point	NOUN
ejpam-7033	814	3	theory	theory	NOUN
ejpam-7033	814	4	and	and	CCONJ
ejpam-7033	814	5	applications	application	NOUN
ejpam-7033	814	6	,	,	PUNCT
ejpam-7033	814	7	page	page	NOUN
ejpam-7033	814	8	14	14	NUM
ejpam-7033	814	9	,	,	PUNCT
ejpam-7033	814	10	2017	2017	NUM
ejpam-7033	814	11	.	.	PUNCT
ejpam-7033	815	1	a.	a.	PROPN
ejpam-7033	815	2	arif	arif	PROPN
ejpam-7033	815	3	et	et	PROPN
ejpam-7033	815	4	al	al	PROPN
ejpam-7033	815	5	.	.	PUNCT
ejpam-7033	815	6	/	/	SYM
ejpam-7033	815	7	eur	eur	PROPN
ejpam-7033	815	8	.	.	PUNCT
ejpam-7033	816	1	j.	j.	PROPN
ejpam-7033	816	2	pure	pure	PROPN
ejpam-7033	816	3	appl	appl	PROPN
ejpam-7033	816	4	.	.	PROPN
ejpam-7033	816	5	math	math	PROPN
ejpam-7033	816	6	,	,	PUNCT
ejpam-7033	816	7	18	18	NUM
ejpam-7033	816	8	(	(	PUNCT
ejpam-7033	816	9	4	4	NUM
ejpam-7033	816	10	)	)	PUNCT
ejpam-7033	816	11	(	(	PUNCT
ejpam-7033	816	12	2025	2025	NUM
ejpam-7033	816	13	)	)	PUNCT
ejpam-7033	816	14	,	,	PUNCT
ejpam-7033	816	15	7033	7033	NUM
ejpam-7033	816	16	27	27	NUM
ejpam-7033	816	17	of	of	ADP
ejpam-7033	816	18	29	29	NUM
ejpam-7033	817	1	[	[	X
ejpam-7033	817	2	3	3	NUM
ejpam-7033	817	3	]	]	PUNCT
ejpam-7033	817	4	z.	z.	PROPN
ejpam-7033	817	5	ercan	ercan	PROPN
ejpam-7033	817	6	.	.	PUNCT
ejpam-7033	818	1	on	on	ADP
ejpam-7033	818	2	the	the	DET
ejpam-7033	818	3	end	end	NOUN
ejpam-7033	818	4	of	of	ADP
ejpam-7033	818	5	the	the	DET
ejpam-7033	818	6	cone	cone	NOUN
ejpam-7033	818	7	metric	metric	ADJ
ejpam-7033	818	8	spaces	space	NOUN
ejpam-7033	818	9	.	.	PUNCT
ejpam-7033	819	1	topology	topology	NOUN
ejpam-7033	819	2	and	and	CCONJ
ejpam-7033	819	3	its	its	PRON
ejpam-7033	819	4	applications	application	NOUN
ejpam-7033	819	5	,	,	PUNCT
ejpam-7033	819	6	166:10–14	166:10–14	NUM
ejpam-7033	819	7	,	,	PUNCT
ejpam-7033	819	8	2014	2014	NUM
ejpam-7033	819	9	.	.	PUNCT
ejpam-7033	820	1	[	[	X
ejpam-7033	820	2	4	4	NUM
ejpam-7033	820	3	]	]	PUNCT
ejpam-7033	820	4	a.	a.	NOUN
ejpam-7033	820	5	c.	c.	PROPN
ejpam-7033	820	6	m.	m.	PROPN
ejpam-7033	820	7	ran	run	VERB
ejpam-7033	820	8	and	and	CCONJ
ejpam-7033	820	9	m.	m.	PROPN
ejpam-7033	820	10	c.	c.	PROPN
ejpam-7033	820	11	b.	b.	PROPN
ejpam-7033	820	12	reurings	reurings	PROPN
ejpam-7033	820	13	.	.	PUNCT
ejpam-7033	821	1	a	a	DET
ejpam-7033	821	2	fixed	fix	VERB
ejpam-7033	821	3	point	point	NOUN
ejpam-7033	821	4	theorem	theorem	VERB
ejpam-7033	821	5	in	in	ADP
ejpam-7033	821	6	partially	partially	ADV
ejpam-7033	821	7	ordered	order	VERB
ejpam-7033	821	8	sets	set	NOUN
ejpam-7033	821	9	and	and	CCONJ
ejpam-7033	821	10	some	some	DET
ejpam-7033	821	11	applications	application	NOUN
ejpam-7033	821	12	to	to	PART
ejpam-7033	821	13	matrix	matrix	VERB
ejpam-7033	821	14	equations	equation	NOUN
ejpam-7033	821	15	.	.	PUNCT
ejpam-7033	822	1	proceedings	proceeding	NOUN
ejpam-7033	822	2	of	of	ADP
ejpam-7033	822	3	the	the	DET
ejpam-7033	822	4	american	american	PROPN
ejpam-7033	822	5	mathematical	mathematical	PROPN
ejpam-7033	822	6	society	society	NOUN
ejpam-7033	822	7	,	,	PUNCT
ejpam-7033	822	8	132:1435–1443	132:1435–1443	NUM
ejpam-7033	822	9	,	,	PUNCT
ejpam-7033	822	10	2004	2004	NUM
ejpam-7033	822	11	.	.	PUNCT
ejpam-7033	823	1	[	[	X
ejpam-7033	823	2	5	5	X
ejpam-7033	823	3	]	]	PUNCT
ejpam-7033	823	4	s.	s.	PROPN
ejpam-7033	823	5	banach	banach	PROPN
ejpam-7033	823	6	.	.	PUNCT
ejpam-7033	824	1	sur	sur	PROPN
ejpam-7033	824	2	les	les	X
ejpam-7033	824	3	opérations	opération	NOUN
ejpam-7033	824	4	dans	dan	NOUN
ejpam-7033	824	5	les	les	X
ejpam-7033	824	6	ensembles	ensemble	NOUN
ejpam-7033	824	7	abstraits	abstrait	NOUN
ejpam-7033	824	8	et	et	PROPN
ejpam-7033	824	9	leur	leur	X
ejpam-7033	824	10	application	application	PROPN
ejpam-7033	824	11	aux	aux	PROPN
ejpam-7033	824	12	équations	équations	PROPN
ejpam-7033	824	13	intégrales	intégrale	NOUN
ejpam-7033	824	14	.	.	PUNCT
ejpam-7033	825	1	fundamenta	fundamenta	PROPN
ejpam-7033	825	2	mathematicae	mathematicae	PROPN
ejpam-7033	825	3	,	,	PUNCT
ejpam-7033	825	4	3:133–181	3:133–181	NUM
ejpam-7033	825	5	,	,	PUNCT
ejpam-7033	825	6	1922	1922	NUM
ejpam-7033	825	7	.	.	PUNCT
ejpam-7033	826	1	[	[	X
ejpam-7033	826	2	6	6	NUM
ejpam-7033	826	3	]	]	PUNCT
ejpam-7033	826	4	j.	j.	PROPN
ejpam-7033	826	5	j.	j.	PROPN
ejpam-7033	826	6	nieto	nieto	PROPN
ejpam-7033	826	7	and	and	CCONJ
ejpam-7033	826	8	r.	r.	PROPN
ejpam-7033	826	9	rodŕıguez	rodŕıguez	PROPN
ejpam-7033	826	10	-	-	PUNCT
ejpam-7033	826	11	lópez	lópez	ADV
ejpam-7033	826	12	.	.	PUNCT
ejpam-7033	827	1	existence	existence	NOUN
ejpam-7033	827	2	and	and	CCONJ
ejpam-7033	827	3	uniqueness	uniqueness	NOUN
ejpam-7033	827	4	of	of	ADP
ejpam-7033	827	5	fixed	fix	VERB
ejpam-7033	827	6	point	point	NOUN
ejpam-7033	827	7	in	in	ADP
ejpam-7033	827	8	partially	partially	ADV
ejpam-7033	827	9	ordered	order	VERB
ejpam-7033	827	10	sets	set	NOUN
ejpam-7033	827	11	and	and	CCONJ
ejpam-7033	827	12	applications	application	NOUN
ejpam-7033	827	13	to	to	ADP
ejpam-7033	827	14	ordinary	ordinary	ADJ
ejpam-7033	827	15	differential	differential	ADJ
ejpam-7033	827	16	equations	equation	NOUN
ejpam-7033	827	17	.	.	PUNCT
ejpam-7033	828	1	acta	acta	PROPN
ejpam-7033	828	2	mathematica	mathematica	PROPN
ejpam-7033	828	3	sinica	sinica	PROPN
ejpam-7033	828	4	,	,	PUNCT
ejpam-7033	828	5	23:2205–2212	23:2205–2212	NUM
ejpam-7033	828	6	,	,	PUNCT
ejpam-7033	828	7	2007	2007	NUM
ejpam-7033	828	8	.	.	PUNCT
ejpam-7033	829	1	[	[	X
ejpam-7033	829	2	7	7	X
ejpam-7033	829	3	]	]	X
ejpam-7033	829	4	d.	d.	PROPN
ejpam-7033	829	5	o’regan	o’regan	PROPN
ejpam-7033	829	6	and	and	CCONJ
ejpam-7033	829	7	a.	a.	PROPN
ejpam-7033	829	8	petruşel	petruşel	PROPN
ejpam-7033	829	9	.	.	PUNCT
ejpam-7033	830	1	fixed	fix	VERB
ejpam-7033	830	2	point	point	NOUN
ejpam-7033	830	3	theorems	theorem	NOUN
ejpam-7033	830	4	for	for	ADP
ejpam-7033	830	5	generalized	generalized	ADJ
ejpam-7033	830	6	contractions	contraction	NOUN
ejpam-7033	830	7	in	in	ADP
ejpam-7033	830	8	ordered	order	VERB
ejpam-7033	830	9	metric	metric	ADJ
ejpam-7033	830	10	spaces	space	NOUN
ejpam-7033	830	11	.	.	PUNCT
ejpam-7033	831	1	journal	journal	PROPN
ejpam-7033	831	2	of	of	ADP
ejpam-7033	831	3	mathematical	mathematical	ADJ
ejpam-7033	831	4	analysis	analysis	NOUN
ejpam-7033	831	5	and	and	CCONJ
ejpam-7033	831	6	applications	application	NOUN
ejpam-7033	831	7	,	,	PUNCT
ejpam-7033	831	8	341:1241	341:1241	NUM
ejpam-7033	831	9	–	–	PUNCT
ejpam-7033	831	10	1252	1252	NUM
ejpam-7033	831	11	,	,	PUNCT
ejpam-7033	831	12	2008	2008	NUM
ejpam-7033	831	13	.	.	PUNCT
ejpam-7033	832	1	[	[	X
ejpam-7033	832	2	8	8	NUM
ejpam-7033	832	3	]	]	X
ejpam-7033	832	4	i.	i.	NOUN
ejpam-7033	832	5	beg	beg	PROPN
ejpam-7033	832	6	and	and	CCONJ
ejpam-7033	832	7	a.	a.	PROPN
ejpam-7033	832	8	r.	r.	PROPN
ejpam-7033	832	9	butt	butt	PROPN
ejpam-7033	832	10	.	.	PUNCT
ejpam-7033	833	1	fixed	fix	VERB
ejpam-7033	833	2	point	point	NOUN
ejpam-7033	833	3	for	for	ADP
ejpam-7033	833	4	set	set	ADJ
ejpam-7033	833	5	valued	value	VERB
ejpam-7033	833	6	mappings	mapping	NOUN
ejpam-7033	833	7	satisfying	satisfy	VERB
ejpam-7033	833	8	an	an	DET
ejpam-7033	833	9	implicit	implicit	ADJ
ejpam-7033	833	10	relation	relation	NOUN
ejpam-7033	833	11	in	in	ADP
ejpam-7033	833	12	partially	partially	ADV
ejpam-7033	833	13	ordered	order	VERB
ejpam-7033	833	14	metric	metric	ADJ
ejpam-7033	833	15	spaces	space	NOUN
ejpam-7033	833	16	.	.	PUNCT
ejpam-7033	834	1	nonlinear	nonlinear	ADJ
ejpam-7033	834	2	analysis	analysis	NOUN
ejpam-7033	834	3	:	:	PUNCT
ejpam-7033	834	4	theory	theory	NOUN
ejpam-7033	834	5	,	,	PUNCT
ejpam-7033	834	6	methods	method	NOUN
ejpam-7033	834	7	&	&	CCONJ
ejpam-7033	834	8	applications	application	NOUN
ejpam-7033	834	9	,	,	PUNCT
ejpam-7033	834	10	71:3699–3704	71:3699–3704	NUM
ejpam-7033	834	11	,	,	PUNCT
ejpam-7033	834	12	2009	2009	NUM
ejpam-7033	834	13	.	.	PUNCT
ejpam-7033	835	1	[	[	X
ejpam-7033	835	2	9	9	NUM
ejpam-7033	835	3	]	]	PUNCT
ejpam-7033	835	4	i.	i.	NOUN
ejpam-7033	835	5	beg	beg	PROPN
ejpam-7033	835	6	and	and	CCONJ
ejpam-7033	835	7	a.	a.	PROPN
ejpam-7033	835	8	r.	r.	PROPN
ejpam-7033	835	9	butt	butt	PROPN
ejpam-7033	835	10	.	.	PUNCT
ejpam-7033	836	1	fixed	fix	VERB
ejpam-7033	836	2	points	point	NOUN
ejpam-7033	836	3	for	for	ADP
ejpam-7033	836	4	weakly	weakly	ADJ
ejpam-7033	836	5	compatible	compatible	ADJ
ejpam-7033	836	6	mappings	mapping	NOUN
ejpam-7033	836	7	satisfying	satisfy	VERB
ejpam-7033	836	8	an	an	DET
ejpam-7033	836	9	implicit	implicit	ADJ
ejpam-7033	836	10	relation	relation	NOUN
ejpam-7033	836	11	in	in	ADP
ejpam-7033	836	12	partially	partially	ADV
ejpam-7033	836	13	ordered	order	VERB
ejpam-7033	836	14	metric	metric	ADJ
ejpam-7033	836	15	spaces	space	NOUN
ejpam-7033	836	16	.	.	PUNCT
ejpam-7033	837	1	carpathian	carpathian	ADJ
ejpam-7033	837	2	journal	journal	PROPN
ejpam-7033	837	3	of	of	ADP
ejpam-7033	837	4	mathematics	mathematic	NOUN
ejpam-7033	837	5	,	,	PUNCT
ejpam-7033	837	6	25:1–12	25:1–12	NUM
ejpam-7033	837	7	,	,	PUNCT
ejpam-7033	837	8	2009	2009	NUM
ejpam-7033	837	9	.	.	PUNCT
ejpam-7033	838	1	[	[	X
ejpam-7033	838	2	10	10	NUM
ejpam-7033	838	3	]	]	X
ejpam-7033	838	4	v.	v.	CCONJ
ejpam-7033	838	5	berinde	berinde	NOUN
ejpam-7033	838	6	.	.	PUNCT
ejpam-7033	839	1	stability	stability	NOUN
ejpam-7033	839	2	of	of	ADP
ejpam-7033	839	3	picard	picard	PROPN
ejpam-7033	839	4	iteration	iteration	NOUN
ejpam-7033	839	5	for	for	ADP
ejpam-7033	839	6	contractive	contractive	ADJ
ejpam-7033	839	7	mappings	mapping	NOUN
ejpam-7033	839	8	satisfying	satisfy	VERB
ejpam-7033	839	9	an	an	DET
ejpam-7033	839	10	implicit	implicit	ADJ
ejpam-7033	839	11	relation	relation	NOUN
ejpam-7033	839	12	.	.	PUNCT
ejpam-7033	840	1	carpathian	carpathian	ADJ
ejpam-7033	840	2	journal	journal	PROPN
ejpam-7033	840	3	of	of	ADP
ejpam-7033	840	4	mathematics	mathematics	PROPN
ejpam-7033	840	5	,	,	PUNCT
ejpam-7033	840	6	27:13–23	27:13–23	PROPN
ejpam-7033	840	7	,	,	PUNCT
ejpam-7033	840	8	2011	2011	NUM
ejpam-7033	840	9	.	.	PUNCT
ejpam-7033	841	1	[	[	X
ejpam-7033	841	2	11	11	NUM
ejpam-7033	841	3	]	]	X
ejpam-7033	841	4	v.	v.	ADP
ejpam-7033	841	5	berinde	berinde	PROPN
ejpam-7033	841	6	and	and	CCONJ
ejpam-7033	841	7	f.	f.	PROPN
ejpam-7033	841	8	vetro	vetro	PROPN
ejpam-7033	841	9	.	.	PUNCT
ejpam-7033	842	1	common	common	ADJ
ejpam-7033	842	2	fixed	fix	VERB
ejpam-7033	842	3	points	point	NOUN
ejpam-7033	842	4	of	of	ADP
ejpam-7033	842	5	mappings	mapping	NOUN
ejpam-7033	842	6	satisfying	satisfy	VERB
ejpam-7033	842	7	implicit	implicit	ADJ
ejpam-7033	842	8	contractive	contractive	ADJ
ejpam-7033	842	9	conditions	condition	NOUN
ejpam-7033	842	10	.	.	PUNCT
ejpam-7033	843	1	fixed	fix	VERB
ejpam-7033	843	2	point	point	NOUN
ejpam-7033	843	3	theory	theory	NOUN
ejpam-7033	843	4	and	and	CCONJ
ejpam-7033	843	5	applications	application	NOUN
ejpam-7033	843	6	,	,	PUNCT
ejpam-7033	843	7	page	page	NOUN
ejpam-7033	843	8	105	105	NUM
ejpam-7033	843	9	,	,	PUNCT
ejpam-7033	843	10	2012	2012	NUM
ejpam-7033	843	11	.	.	PUNCT
ejpam-7033	844	1	[	[	X
ejpam-7033	844	2	12	12	NUM
ejpam-7033	844	3	]	]	X
ejpam-7033	844	4	s.	s.	PROPN
ejpam-7033	844	5	sedghi	sedghi	PROPN
ejpam-7033	844	6	,	,	PUNCT
ejpam-7033	844	7	i.	i.	NOUN
ejpam-7033	844	8	altun	altun	PROPN
ejpam-7033	844	9	,	,	PUNCT
ejpam-7033	844	10	and	and	CCONJ
ejpam-7033	844	11	n.	n.	PROPN
ejpam-7033	844	12	shobe	shobe	PROPN
ejpam-7033	844	13	.	.	PUNCT
ejpam-7033	845	1	a	a	DET
ejpam-7033	845	2	fixed	fix	VERB
ejpam-7033	845	3	point	point	NOUN
ejpam-7033	845	4	theorem	theorem	NOUN
ejpam-7033	845	5	for	for	ADP
ejpam-7033	845	6	multi	multi	ADJ
ejpam-7033	845	7	maps	map	NOUN
ejpam-7033	845	8	satisfying	satisfy	VERB
ejpam-7033	845	9	an	an	DET
ejpam-7033	845	10	implicit	implicit	ADJ
ejpam-7033	845	11	relation	relation	NOUN
ejpam-7033	845	12	on	on	ADP
ejpam-7033	845	13	metric	metric	ADJ
ejpam-7033	845	14	spaces	space	NOUN
ejpam-7033	845	15	.	.	PUNCT
ejpam-7033	846	1	applicable	applicable	ADJ
ejpam-7033	846	2	analysis	analysis	NOUN
ejpam-7033	846	3	and	and	CCONJ
ejpam-7033	846	4	discrete	discrete	ADJ
ejpam-7033	846	5	mathematics	mathematic	NOUN
ejpam-7033	846	6	,	,	PUNCT
ejpam-7033	846	7	2:189–196	2:189–196	PROPN
ejpam-7033	846	8	,	,	PUNCT
ejpam-7033	846	9	2008	2008	NUM
ejpam-7033	846	10	.	.	PUNCT
ejpam-7033	847	1	[	[	X
ejpam-7033	847	2	13	13	NUM
ejpam-7033	847	3	]	]	PUNCT
ejpam-7033	847	4	i.	i.	NOUN
ejpam-7033	847	5	altun	altun	PROPN
ejpam-7033	847	6	and	and	CCONJ
ejpam-7033	847	7	h.	h.	PROPN
ejpam-7033	847	8	simsek	simsek	PROPN
ejpam-7033	847	9	.	.	PUNCT
ejpam-7033	848	1	some	some	DET
ejpam-7033	848	2	fixed	fix	VERB
ejpam-7033	848	3	point	point	NOUN
ejpam-7033	848	4	theorems	theorem	NOUN
ejpam-7033	848	5	on	on	ADP
ejpam-7033	848	6	ordered	order	VERB
ejpam-7033	848	7	metric	metric	ADJ
ejpam-7033	848	8	spaces	space	NOUN
ejpam-7033	848	9	and	and	CCONJ
ejpam-7033	848	10	application	application	NOUN
ejpam-7033	848	11	.	.	PUNCT
ejpam-7033	849	1	fixed	fix	VERB
ejpam-7033	849	2	point	point	NOUN
ejpam-7033	849	3	theory	theory	NOUN
ejpam-7033	849	4	and	and	CCONJ
ejpam-7033	849	5	applications	application	NOUN
ejpam-7033	849	6	,	,	PUNCT
ejpam-7033	849	7	page	page	NOUN
ejpam-7033	849	8	621469	621469	NUM
ejpam-7033	849	9	,	,	PUNCT
ejpam-7033	849	10	2010	2010	NUM
ejpam-7033	849	11	.	.	PUNCT
ejpam-7033	850	1	[	[	X
ejpam-7033	850	2	14	14	NUM
ejpam-7033	850	3	]	]	X
ejpam-7033	850	4	r.	r.	PROPN
ejpam-7033	850	5	p.	p.	PROPN
ejpam-7033	850	6	agarwal	agarwal	PROPN
ejpam-7033	850	7	,	,	PUNCT
ejpam-7033	850	8	m.	m.	NOUN
ejpam-7033	850	9	a.	a.	PROPN
ejpam-7033	850	10	el	el	PROPN
ejpam-7033	850	11	-	-	PROPN
ejpam-7033	850	12	gebeily	gebeily	ADV
ejpam-7033	850	13	,	,	PUNCT
ejpam-7033	850	14	and	and	CCONJ
ejpam-7033	850	15	d.	d.	PROPN
ejpam-7033	850	16	o’regan	o’regan	PROPN
ejpam-7033	850	17	.	.	PUNCT
ejpam-7033	851	1	generalized	generalized	ADJ
ejpam-7033	851	2	contractions	contraction	NOUN
ejpam-7033	851	3	in	in	ADP
ejpam-7033	851	4	partially	partially	ADV
ejpam-7033	851	5	ordered	order	VERB
ejpam-7033	851	6	metric	metric	ADJ
ejpam-7033	851	7	spaces	space	NOUN
ejpam-7033	851	8	.	.	PUNCT
ejpam-7033	852	1	applicable	applicable	ADJ
ejpam-7033	852	2	analysis	analysis	NOUN
ejpam-7033	852	3	,	,	PUNCT
ejpam-7033	852	4	87:1–8	87:1–8	NUM
ejpam-7033	852	5	,	,	PUNCT
ejpam-7033	852	6	2008	2008	NUM
ejpam-7033	852	7	.	.	PUNCT
ejpam-7033	853	1	[	[	X
ejpam-7033	853	2	15	15	NUM
ejpam-7033	853	3	]	]	X
ejpam-7033	853	4	j.	j.	PROPN
ejpam-7033	853	5	jachymski	jachymski	PROPN
ejpam-7033	853	6	.	.	PUNCT
ejpam-7033	854	1	the	the	DET
ejpam-7033	854	2	contraction	contraction	NOUN
ejpam-7033	854	3	principle	principle	NOUN
ejpam-7033	854	4	for	for	ADP
ejpam-7033	854	5	mappings	mapping	NOUN
ejpam-7033	854	6	on	on	ADP
ejpam-7033	854	7	a	a	DET
ejpam-7033	854	8	metric	metric	ADJ
ejpam-7033	854	9	space	space	NOUN
ejpam-7033	854	10	with	with	ADP
ejpam-7033	854	11	a	a	DET
ejpam-7033	854	12	graph	graph	NOUN
ejpam-7033	854	13	.	.	PUNCT
ejpam-7033	855	1	proceedings	proceeding	NOUN
ejpam-7033	855	2	of	of	ADP
ejpam-7033	855	3	the	the	DET
ejpam-7033	855	4	american	american	PROPN
ejpam-7033	855	5	mathematical	mathematical	PROPN
ejpam-7033	855	6	society	society	NOUN
ejpam-7033	855	7	,	,	PUNCT
ejpam-7033	855	8	136:1359–1373	136:1359–1373	NUM
ejpam-7033	855	9	,	,	PUNCT
ejpam-7033	855	10	2008	2008	NUM
ejpam-7033	855	11	.	.	PUNCT
ejpam-7033	856	1	[	[	X
ejpam-7033	856	2	16	16	NUM
ejpam-7033	856	3	]	]	PUNCT
ejpam-7033	856	4	s.	s.	PROPN
ejpam-7033	856	5	b.	b.	PROPN
ejpam-7033	856	6	nadler	nadler	PROPN
ejpam-7033	856	7	.	.	PUNCT
ejpam-7033	856	8	multivalued	multivalue	VERB
ejpam-7033	856	9	contraction	contraction	NOUN
ejpam-7033	856	10	mappings	mapping	NOUN
ejpam-7033	856	11	.	.	PUNCT
ejpam-7033	857	1	pacific	pacific	PROPN
ejpam-7033	857	2	journal	journal	PROPN
ejpam-7033	857	3	of	of	ADP
ejpam-7033	857	4	mathematics	mathematic	NOUN
ejpam-7033	857	5	,	,	PUNCT
ejpam-7033	857	6	30:475–488	30:475–488	NUM
ejpam-7033	857	7	,	,	PUNCT
ejpam-7033	857	8	1969	1969	NUM
ejpam-7033	857	9	.	.	PUNCT
ejpam-7033	858	1	[	[	X
ejpam-7033	858	2	17	17	NUM
ejpam-7033	858	3	]	]	X
ejpam-7033	858	4	t.	t.	NOUN
ejpam-7033	858	5	rasham	rasham	ADJ
ejpam-7033	858	6	,	,	PUNCT
ejpam-7033	858	7	p.	p.	PROPN
ejpam-7033	858	8	agarwal	agarwal	PROPN
ejpam-7033	858	9	,	,	PUNCT
ejpam-7033	858	10	l.	l.	PROPN
ejpam-7033	858	11	s.	s.	PROPN
ejpam-7033	858	12	abbasi	abbasi	PROPN
ejpam-7033	858	13	,	,	PUNCT
ejpam-7033	858	14	and	and	CCONJ
ejpam-7033	858	15	s.	s.	PROPN
ejpam-7033	858	16	jain	jain	PROPN
ejpam-7033	858	17	.	.	PUNCT
ejpam-7033	859	1	a	a	DET
ejpam-7033	859	2	study	study	NOUN
ejpam-7033	859	3	of	of	ADP
ejpam-7033	859	4	some	some	DET
ejpam-7033	859	5	new	new	ADJ
ejpam-7033	859	6	multivalued	multivalue	VERB
ejpam-7033	859	7	fixed	fix	VERB
ejpam-7033	859	8	point	point	NOUN
ejpam-7033	859	9	results	result	NOUN
ejpam-7033	859	10	in	in	ADP
ejpam-7033	859	11	a	a	DET
ejpam-7033	859	12	modular	modular	ADJ
ejpam-7033	859	13	like	like	ADP
ejpam-7033	859	14	metric	metric	ADJ
ejpam-7033	859	15	space	space	NOUN
ejpam-7033	859	16	with	with	ADP
ejpam-7033	859	17	graph	graph	NOUN
ejpam-7033	859	18	.	.	PUNCT
ejpam-7033	860	1	the	the	DET
ejpam-7033	860	2	journal	journal	NOUN
ejpam-7033	860	3	of	of	ADP
ejpam-7033	860	4	analysis	analysis	NOUN
ejpam-7033	860	5	,	,	PUNCT
ejpam-7033	860	6	30:833–844	30:833–844	NOUN
ejpam-7033	860	7	,	,	PUNCT
ejpam-7033	860	8	2022	2022	NUM
ejpam-7033	860	9	.	.	PUNCT
ejpam-7033	861	1	[	[	X
ejpam-7033	861	2	18	18	NUM
ejpam-7033	861	3	]	]	PUNCT
ejpam-7033	861	4	h.	h.	PROPN
ejpam-7033	861	5	a.	a.	PROPN
ejpam-7033	861	6	hammad	hammad	PROPN
ejpam-7033	861	7	,	,	PUNCT
ejpam-7033	861	8	p.	p.	PROPN
ejpam-7033	861	9	agarwal	agarwal	PROPN
ejpam-7033	861	10	,	,	PUNCT
ejpam-7033	861	11	and	and	CCONJ
ejpam-7033	861	12	juan	juan	PROPN
ejpam-7033	861	13	l.	l.	PROPN
ejpam-7033	861	14	g.	g.	PROPN
ejpam-7033	861	15	guirao	guirao	PROPN
ejpam-7033	861	16	.	.	PUNCT
ejpam-7033	862	1	applications	application	NOUN
ejpam-7033	862	2	to	to	ADP
ejpam-7033	862	3	boundary	boundary	ADJ
ejpam-7033	862	4	value	value	NOUN
ejpam-7033	862	5	problems	problem	NOUN
ejpam-7033	862	6	and	and	CCONJ
ejpam-7033	862	7	homotopy	homotopy	NOUN
ejpam-7033	862	8	theory	theory	NOUN
ejpam-7033	862	9	via	via	ADP
ejpam-7033	862	10	tripled	triple	VERB
ejpam-7033	862	11	fixed	fix	VERB
ejpam-7033	862	12	point	point	NOUN
ejpam-7033	862	13	techniques	technique	NOUN
ejpam-7033	862	14	in	in	ADP
ejpam-7033	862	15	partially	partially	ADV
ejpam-7033	862	16	metric	metric	ADJ
ejpam-7033	862	17	spaces	space	NOUN
ejpam-7033	862	18	.	.	PUNCT
ejpam-7033	863	1	mathematics	mathematic	NOUN
ejpam-7033	863	2	,	,	PUNCT
ejpam-7033	863	3	9:2012	9:2012	NUM
ejpam-7033	863	4	,	,	PUNCT
ejpam-7033	863	5	2021	2021	NUM
ejpam-7033	863	6	.	.	PUNCT
ejpam-7033	864	1	[	[	X
ejpam-7033	864	2	19	19	NUM
ejpam-7033	864	3	]	]	PUNCT
ejpam-7033	864	4	b.	b.	PROPN
ejpam-7033	864	5	samet	samet	PROPN
ejpam-7033	864	6	,	,	PUNCT
ejpam-7033	864	7	c.	c.	PROPN
ejpam-7033	864	8	vetro	vetro	PROPN
ejpam-7033	864	9	,	,	PUNCT
ejpam-7033	864	10	and	and	CCONJ
ejpam-7033	864	11	p.	p.	PROPN
ejpam-7033	864	12	vetro	vetro	PROPN
ejpam-7033	864	13	.	.	PUNCT
ejpam-7033	865	1	fixed	fix	VERB
ejpam-7033	865	2	point	point	NOUN
ejpam-7033	865	3	theorems	theorem	NOUN
ejpam-7033	865	4	for	for	ADP
ejpam-7033	865	5	(	(	PUNCT
ejpam-7033	865	6	α	α	NOUN
ejpam-7033	865	7	,	,	PUNCT
ejpam-7033	865	8	ψ)-contractive	ψ)-contractive	ADJ
ejpam-7033	865	9	type	type	NOUN
ejpam-7033	865	10	mappings	mapping	NOUN
ejpam-7033	865	11	.	.	PUNCT
ejpam-7033	866	1	nonlinear	nonlinear	ADJ
ejpam-7033	866	2	analysis	analysis	NOUN
ejpam-7033	866	3	:	:	PUNCT
ejpam-7033	866	4	theory	theory	NOUN
ejpam-7033	866	5	,	,	PUNCT
ejpam-7033	866	6	methods	method	NOUN
ejpam-7033	866	7	&	&	CCONJ
ejpam-7033	866	8	applications	application	NOUN
ejpam-7033	866	9	,	,	PUNCT
ejpam-7033	866	10	75:2154–2165	75:2154–2165	NUM
ejpam-7033	866	11	,	,	PUNCT
ejpam-7033	866	12	2012	2012	NUM
ejpam-7033	866	13	.	.	PUNCT
ejpam-7033	867	1	[	[	X
ejpam-7033	867	2	20	20	NUM
ejpam-7033	867	3	]	]	PUNCT
ejpam-7033	867	4	e.	e.	PROPN
ejpam-7033	867	5	karapinar	karapinar	PROPN
ejpam-7033	867	6	,	,	PUNCT
ejpam-7033	867	7	a.	a.	NOUN
ejpam-7033	867	8	fulga	fulga	NOUN
ejpam-7033	867	9	,	,	PUNCT
ejpam-7033	867	10	and	and	CCONJ
ejpam-7033	867	11	r.	r.	PROPN
ejpam-7033	867	12	p.	p.	PROPN
ejpam-7033	867	13	agarwal	agarwal	PROPN
ejpam-7033	867	14	.	.	PUNCT
ejpam-7033	868	1	a	a	DET
ejpam-7033	868	2	survey	survey	NOUN
ejpam-7033	868	3	:	:	PUNCT
ejpam-7033	868	4	f	f	X
ejpam-7033	868	5	-	-	PUNCT
ejpam-7033	868	6	contractions	contraction	NOUN
ejpam-7033	868	7	with	with	ADP
ejpam-7033	868	8	related	related	ADJ
ejpam-7033	868	9	a.	a.	NOUN
ejpam-7033	868	10	arif	arif	PROPN
ejpam-7033	868	11	et	et	PROPN
ejpam-7033	868	12	al	al	PROPN
ejpam-7033	868	13	.	.	PUNCT
ejpam-7033	868	14	/	/	SYM
ejpam-7033	868	15	eur	eur	PROPN
ejpam-7033	868	16	.	.	PUNCT
ejpam-7033	869	1	j.	j.	PROPN
ejpam-7033	869	2	pure	pure	PROPN
ejpam-7033	869	3	appl	appl	PROPN
ejpam-7033	869	4	.	.	PROPN
ejpam-7033	869	5	math	math	PROPN
ejpam-7033	869	6	,	,	PUNCT
ejpam-7033	869	7	18	18	NUM
ejpam-7033	869	8	(	(	PUNCT
ejpam-7033	869	9	4	4	NUM
ejpam-7033	869	10	)	)	PUNCT
ejpam-7033	869	11	(	(	PUNCT
ejpam-7033	869	12	2025	2025	NUM
ejpam-7033	869	13	)	)	PUNCT
ejpam-7033	869	14	,	,	PUNCT
ejpam-7033	869	15	7033	7033	NUM
ejpam-7033	869	16	28	28	NUM
ejpam-7033	869	17	of	of	ADP
ejpam-7033	869	18	29	29	NUM
ejpam-7033	869	19	fixed	fix	VERB
ejpam-7033	869	20	point	point	NOUN
ejpam-7033	869	21	results	result	NOUN
ejpam-7033	869	22	.	.	PUNCT
ejpam-7033	870	1	journal	journal	NOUN
ejpam-7033	870	2	of	of	ADP
ejpam-7033	870	3	fixed	fix	VERB
ejpam-7033	870	4	point	point	NOUN
ejpam-7033	870	5	theory	theory	NOUN
ejpam-7033	870	6	and	and	CCONJ
ejpam-7033	870	7	applications	application	NOUN
ejpam-7033	870	8	,	,	PUNCT
ejpam-7033	870	9	22:69	22:69	NUM
ejpam-7033	870	10	,	,	PUNCT
ejpam-7033	870	11	2020	2020	NUM
ejpam-7033	870	12	.	.	PUNCT
ejpam-7033	871	1	[	[	X
ejpam-7033	871	2	21	21	NUM
ejpam-7033	871	3	]	]	X
ejpam-7033	871	4	l.	l.	PROPN
ejpam-7033	871	5	g.	g.	PROPN
ejpam-7033	871	6	huang	huang	PROPN
ejpam-7033	871	7	and	and	CCONJ
ejpam-7033	871	8	x.	x.	PROPN
ejpam-7033	871	9	zhang	zhang	PROPN
ejpam-7033	871	10	.	.	PUNCT
ejpam-7033	872	1	cone	cone	PROPN
ejpam-7033	872	2	metric	metric	ADJ
ejpam-7033	872	3	spaces	space	NOUN
ejpam-7033	872	4	and	and	CCONJ
ejpam-7033	872	5	fixed	fix	VERB
ejpam-7033	872	6	point	point	NOUN
ejpam-7033	872	7	theorems	theorem	NOUN
ejpam-7033	872	8	of	of	ADP
ejpam-7033	872	9	contractive	contractive	ADJ
ejpam-7033	872	10	mappings	mapping	NOUN
ejpam-7033	872	11	.	.	PUNCT
ejpam-7033	873	1	journal	journal	PROPN
ejpam-7033	873	2	of	of	ADP
ejpam-7033	873	3	mathematical	mathematical	ADJ
ejpam-7033	873	4	analysis	analysis	NOUN
ejpam-7033	873	5	and	and	CCONJ
ejpam-7033	873	6	applications	application	NOUN
ejpam-7033	873	7	,	,	PUNCT
ejpam-7033	873	8	332(2):1468–1476	332(2):1468–1476	PROPN
ejpam-7033	873	9	,	,	PUNCT
ejpam-7033	873	10	2007	2007	NUM
ejpam-7033	873	11	.	.	PUNCT
ejpam-7033	874	1	[	[	X
ejpam-7033	874	2	22	22	NUM
ejpam-7033	874	3	]	]	X
ejpam-7033	874	4	s.	s.	PROPN
ejpam-7033	874	5	rezapour	rezapour	PROPN
ejpam-7033	874	6	and	and	CCONJ
ejpam-7033	874	7	r.	r.	PROPN
ejpam-7033	874	8	hamlbarani	hamlbarani	PROPN
ejpam-7033	874	9	.	.	PUNCT
ejpam-7033	875	1	some	some	DET
ejpam-7033	875	2	notes	note	NOUN
ejpam-7033	875	3	on	on	ADP
ejpam-7033	875	4	the	the	DET
ejpam-7033	875	5	paper	paper	NOUN
ejpam-7033	875	6	“	"	PUNCT
ejpam-7033	875	7	cone	cone	NOUN
ejpam-7033	875	8	metric	metric	ADJ
ejpam-7033	875	9	spaces	space	NOUN
ejpam-7033	875	10	and	and	CCONJ
ejpam-7033	875	11	fixed	fix	VERB
ejpam-7033	875	12	point	point	NOUN
ejpam-7033	875	13	theorems	theorem	NOUN
ejpam-7033	875	14	of	of	ADP
ejpam-7033	875	15	contractive	contractive	ADJ
ejpam-7033	875	16	mappings	mapping	NOUN
ejpam-7033	875	17	”	"	PUNCT
ejpam-7033	875	18	.	.	PUNCT
ejpam-7033	876	1	journal	journal	PROPN
ejpam-7033	876	2	of	of	ADP
ejpam-7033	876	3	mathematical	mathematical	ADJ
ejpam-7033	876	4	analysis	analysis	NOUN
ejpam-7033	876	5	and	and	CCONJ
ejpam-7033	876	6	applications	application	NOUN
ejpam-7033	876	7	,	,	PUNCT
ejpam-7033	876	8	345:719–724	345:719–724	NUM
ejpam-7033	876	9	,	,	PUNCT
ejpam-7033	876	10	2008	2008	NUM
ejpam-7033	876	11	.	.	PUNCT
ejpam-7033	877	1	[	[	X
ejpam-7033	877	2	23	23	NUM
ejpam-7033	877	3	]	]	X
ejpam-7033	877	4	s.	s.	PROPN
ejpam-7033	877	5	czerwik	czerwik	PROPN
ejpam-7033	877	6	.	.	PUNCT
ejpam-7033	878	1	nonlinear	nonlinear	ADJ
ejpam-7033	878	2	set	set	NOUN
ejpam-7033	878	3	-	-	PUNCT
ejpam-7033	878	4	valued	value	VERB
ejpam-7033	878	5	contraction	contraction	NOUN
ejpam-7033	878	6	mappings	mapping	NOUN
ejpam-7033	878	7	in	in	ADP
ejpam-7033	878	8	b	b	NOUN
ejpam-7033	878	9	-	-	ADJ
ejpam-7033	878	10	metric	metric	ADJ
ejpam-7033	878	11	spaces	space	NOUN
ejpam-7033	878	12	.	.	PUNCT
ejpam-7033	879	1	atti	atti	PROPN
ejpam-7033	879	2	del	del	PROPN
ejpam-7033	879	3	seminario	seminario	PROPN
ejpam-7033	879	4	matematico	matematico	PROPN
ejpam-7033	879	5	e	e	PROPN
ejpam-7033	879	6	fisico	fisico	PROPN
ejpam-7033	879	7	dell’università	dell’università	PROPN
ejpam-7033	879	8	di	di	PROPN
ejpam-7033	879	9	modena	modena	PROPN
ejpam-7033	879	10	,	,	PUNCT
ejpam-7033	879	11	46:263–276	46:263–276	PROPN
ejpam-7033	879	12	,	,	PUNCT
ejpam-7033	879	13	1998	1998	NUM
ejpam-7033	879	14	.	.	PUNCT
ejpam-7033	880	1	[	[	X
ejpam-7033	880	2	24	24	NUM
ejpam-7033	880	3	]	]	X
ejpam-7033	880	4	n.	n.	PROPN
ejpam-7033	880	5	hussian	hussian	PROPN
ejpam-7033	880	6	and	and	CCONJ
ejpam-7033	880	7	m.	m.	PROPN
ejpam-7033	880	8	h.	h.	PROPN
ejpam-7033	880	9	shah	shah	PROPN
ejpam-7033	880	10	.	.	PUNCT
ejpam-7033	881	1	kkm	kkm	PROPN
ejpam-7033	881	2	mappings	mapping	VERB
ejpam-7033	881	3	in	in	ADP
ejpam-7033	881	4	cone	cone	PROPN
ejpam-7033	881	5	b	b	X
ejpam-7033	881	6	-	-	PUNCT
ejpam-7033	881	7	metric	metric	ADJ
ejpam-7033	881	8	spaces	space	NOUN
ejpam-7033	881	9	.	.	PUNCT
ejpam-7033	882	1	computers	computer	NOUN
ejpam-7033	882	2	&	&	CCONJ
ejpam-7033	882	3	mathematics	mathematics	PROPN
ejpam-7033	882	4	with	with	ADP
ejpam-7033	882	5	applications	application	NOUN
ejpam-7033	882	6	,	,	PUNCT
ejpam-7033	882	7	62:1677–1684	62:1677–1684	NUM
ejpam-7033	882	8	,	,	PUNCT
ejpam-7033	882	9	2011	2011	NUM
ejpam-7033	882	10	.	.	PUNCT
ejpam-7033	883	1	[	[	X
ejpam-7033	883	2	25	25	NUM
ejpam-7033	883	3	]	]	X
ejpam-7033	883	4	h.	h.	PROPN
ejpam-7033	883	5	huang	huang	PROPN
ejpam-7033	883	6	and	and	CCONJ
ejpam-7033	883	7	s.	s.	PROPN
ejpam-7033	883	8	xu	xu	PROPN
ejpam-7033	883	9	.	.	PUNCT
ejpam-7033	884	1	fixed	fix	VERB
ejpam-7033	884	2	point	point	NOUN
ejpam-7033	884	3	theorems	theorem	NOUN
ejpam-7033	884	4	of	of	ADP
ejpam-7033	884	5	contractive	contractive	ADJ
ejpam-7033	884	6	mappings	mapping	NOUN
ejpam-7033	884	7	in	in	ADP
ejpam-7033	884	8	cone	cone	NOUN
ejpam-7033	884	9	b	b	X
ejpam-7033	884	10	-	-	PUNCT
ejpam-7033	884	11	metric	metric	ADJ
ejpam-7033	884	12	spaces	space	NOUN
ejpam-7033	884	13	and	and	CCONJ
ejpam-7033	884	14	applications	application	NOUN
ejpam-7033	884	15	.	.	PUNCT
ejpam-7033	885	1	fixed	fix	VERB
ejpam-7033	885	2	point	point	NOUN
ejpam-7033	885	3	theory	theory	NOUN
ejpam-7033	885	4	and	and	CCONJ
ejpam-7033	885	5	applications	application	NOUN
ejpam-7033	885	6	,	,	PUNCT
ejpam-7033	885	7	page	page	NOUN
ejpam-7033	885	8	112	112	NUM
ejpam-7033	885	9	,	,	PUNCT
ejpam-7033	885	10	2013	2013	NUM
ejpam-7033	885	11	.	.	PUNCT
ejpam-7033	886	1	[	[	X
ejpam-7033	886	2	26	26	NUM
ejpam-7033	886	3	]	]	X
ejpam-7033	886	4	a.	a.	NOUN
ejpam-7033	886	5	arif	arif	PROPN
ejpam-7033	886	6	,	,	PUNCT
ejpam-7033	886	7	m.	m.	NOUN
ejpam-7033	886	8	nazam	nazam	PROPN
ejpam-7033	886	9	,	,	PUNCT
ejpam-7033	886	10	a.	a.	NOUN
ejpam-7033	886	11	hussain	hussain	PROPN
ejpam-7033	886	12	,	,	PUNCT
ejpam-7033	886	13	and	and	CCONJ
ejpam-7033	886	14	m.	m.	NOUN
ejpam-7033	886	15	abbas	abbas	PROPN
ejpam-7033	886	16	.	.	PUNCT
ejpam-7033	887	1	the	the	DET
ejpam-7033	887	2	ordered	order	VERB
ejpam-7033	887	3	implicit	implicit	ADJ
ejpam-7033	887	4	relations	relation	NOUN
ejpam-7033	887	5	and	and	CCONJ
ejpam-7033	887	6	related	relate	VERB
ejpam-7033	887	7	fixed	fix	VERB
ejpam-7033	887	8	point	point	NOUN
ejpam-7033	887	9	problems	problem	NOUN
ejpam-7033	887	10	in	in	ADP
ejpam-7033	887	11	the	the	DET
ejpam-7033	887	12	cone	cone	NOUN
ejpam-7033	887	13	b	b	X
ejpam-7033	887	14	-	-	PUNCT
ejpam-7033	887	15	metric	metric	ADJ
ejpam-7033	887	16	spaces	space	NOUN
ejpam-7033	887	17	.	.	PUNCT
ejpam-7033	888	1	aims	aim	VERB
ejpam-7033	888	2	mathematics	mathematic	NOUN
ejpam-7033	888	3	,	,	PUNCT
ejpam-7033	888	4	7(4):5199	7(4):5199	NUM
ejpam-7033	888	5	–	–	PUNCT
ejpam-7033	888	6	5219	5219	NUM
ejpam-7033	888	7	,	,	PUNCT
ejpam-7033	888	8	2022	2022	NUM
ejpam-7033	888	9	.	.	PUNCT
ejpam-7033	889	1	[	[	X
ejpam-7033	889	2	27	27	NUM
ejpam-7033	889	3	]	]	X
ejpam-7033	889	4	s.	s.	PROPN
ejpam-7033	889	5	aleksić	aleksić	PROPN
ejpam-7033	889	6	,	,	PUNCT
ejpam-7033	889	7	z.	z.	PROPN
ejpam-7033	889	8	kadelburg	kadelburg	PROPN
ejpam-7033	889	9	,	,	PUNCT
ejpam-7033	889	10	z.	z.	PROPN
ejpam-7033	889	11	d.	d.	PROPN
ejpam-7033	889	12	mitrović	mitrović	PROPN
ejpam-7033	889	13	,	,	PUNCT
ejpam-7033	889	14	and	and	CCONJ
ejpam-7033	889	15	s.	s.	PROPN
ejpam-7033	890	1	radenović.	radenović.	PROPN
ejpam-7033	890	2	a	a	DET
ejpam-7033	890	3	new	new	ADJ
ejpam-7033	890	4	survey	survey	NOUN
ejpam-7033	890	5	:	:	PUNCT
ejpam-7033	890	6	cone	cone	NOUN
ejpam-7033	890	7	metric	metric	ADJ
ejpam-7033	890	8	spaces	space	NOUN
ejpam-7033	890	9	.	.	PUNCT
ejpam-7033	891	1	journal	journal	NOUN
ejpam-7033	891	2	of	of	ADP
ejpam-7033	891	3	the	the	DET
ejpam-7033	891	4	international	international	ADJ
ejpam-7033	891	5	mathematical	mathematical	ADJ
ejpam-7033	891	6	virtual	virtual	PROPN
ejpam-7033	891	7	institute	institute	PROPN
ejpam-7033	891	8	,	,	PUNCT
ejpam-7033	891	9	9:93–121	9:93–121	NUM
ejpam-7033	891	10	,	,	PUNCT
ejpam-7033	891	11	2019	2019	NUM
ejpam-7033	891	12	.	.	PUNCT
ejpam-7033	892	1	[	[	X
ejpam-7033	892	2	28	28	NUM
ejpam-7033	892	3	]	]	PUNCT
ejpam-7033	892	4	a.	a.	NOUN
ejpam-7033	892	5	bera	bera	NOUN
ejpam-7033	892	6	,	,	PUNCT
ejpam-7033	892	7	p.	p.	PROPN
ejpam-7033	892	8	mondal	mondal	PROPN
ejpam-7033	892	9	,	,	PUNCT
ejpam-7033	892	10	h.	h.	PROPN
ejpam-7033	892	11	garai	garai	PROPN
ejpam-7033	892	12	,	,	PUNCT
ejpam-7033	892	13	and	and	CCONJ
ejpam-7033	892	14	l.	l.	PROPN
ejpam-7033	892	15	k.	k.	PROPN
ejpam-7033	892	16	dey	dey	PROPN
ejpam-7033	892	17	.	.	PROPN
ejpam-7033	893	1	on	on	ADP
ejpam-7033	893	2	maia	maia	PROPN
ejpam-7033	893	3	type	type	PROPN
ejpam-7033	893	4	fixed	fix	VERB
ejpam-7033	893	5	point	point	NOUN
ejpam-7033	893	6	results	result	NOUN
ejpam-7033	893	7	via	via	ADP
ejpam-7033	893	8	implicit	implicit	ADJ
ejpam-7033	893	9	relation	relation	NOUN
ejpam-7033	893	10	.	.	PUNCT
ejpam-7033	894	1	aims	aim	VERB
ejpam-7033	894	2	mathematics	mathematic	NOUN
ejpam-7033	894	3	,	,	PUNCT
ejpam-7033	894	4	8(9):22067–22080	8(9):22067–22080	NOUN
ejpam-7033	894	5	,	,	PUNCT
ejpam-7033	894	6	2023	2023	NUM
ejpam-7033	894	7	.	.	PUNCT
ejpam-7033	895	1	[	[	X
ejpam-7033	895	2	29	29	NUM
ejpam-7033	895	3	]	]	X
ejpam-7033	895	4	m.	m.	NOUN
ejpam-7033	895	5	boriceanu	boriceanu	PROPN
ejpam-7033	895	6	,	,	PUNCT
ejpam-7033	895	7	m.	m.	NOUN
ejpam-7033	895	8	bota	bota	NOUN
ejpam-7033	895	9	,	,	PUNCT
ejpam-7033	895	10	and	and	CCONJ
ejpam-7033	895	11	a.	a.	PROPN
ejpam-7033	895	12	petruşel	petruşel	PROPN
ejpam-7033	895	13	.	.	PUNCT
ejpam-7033	896	1	multivalued	multivalue	VERB
ejpam-7033	896	2	fractals	fractal	NOUN
ejpam-7033	896	3	in	in	ADP
ejpam-7033	896	4	b	b	NOUN
ejpam-7033	896	5	-	-	PUNCT
ejpam-7033	896	6	metric	metric	ADJ
ejpam-7033	896	7	spaces	space	NOUN
ejpam-7033	896	8	.	.	PUNCT
ejpam-7033	897	1	central	central	ADJ
ejpam-7033	897	2	european	european	PROPN
ejpam-7033	897	3	journal	journal	PROPN
ejpam-7033	897	4	of	of	ADP
ejpam-7033	897	5	mathematics	mathematic	NOUN
ejpam-7033	897	6	,	,	PUNCT
ejpam-7033	897	7	8(2):367–377	8(2):367–377	NOUN
ejpam-7033	897	8	,	,	PUNCT
ejpam-7033	897	9	2010	2010	NUM
ejpam-7033	897	10	.	.	PUNCT
ejpam-7033	898	1	[	[	X
ejpam-7033	898	2	30	30	NUM
ejpam-7033	898	3	]	]	PUNCT
ejpam-7033	898	4	m.	m.	NOUN
ejpam-7033	898	5	bota	bota	NOUN
ejpam-7033	898	6	,	,	PUNCT
ejpam-7033	898	7	a.	a.	NOUN
ejpam-7033	898	8	molnár	molnár	NOUN
ejpam-7033	898	9	,	,	PUNCT
ejpam-7033	898	10	and	and	CCONJ
ejpam-7033	898	11	v.	v.	ADP
ejpam-7033	898	12	csaba	csaba	PROPN
ejpam-7033	898	13	.	.	PUNCT
ejpam-7033	899	1	on	on	ADP
ejpam-7033	899	2	ekeland	ekeland	PROPN
ejpam-7033	899	3	’s	’s	PART
ejpam-7033	899	4	variational	variational	ADJ
ejpam-7033	899	5	principle	principle	NOUN
ejpam-7033	899	6	in	in	ADP
ejpam-7033	899	7	b	b	NOUN
ejpam-7033	899	8	-	-	ADJ
ejpam-7033	899	9	metric	metric	ADJ
ejpam-7033	899	10	spaces	space	NOUN
ejpam-7033	899	11	.	.	PUNCT
ejpam-7033	900	1	fixed	fix	VERB
ejpam-7033	900	2	point	point	NOUN
ejpam-7033	900	3	theory	theory	NOUN
ejpam-7033	900	4	,	,	PUNCT
ejpam-7033	900	5	12:21–28	12:21–28	NUM
ejpam-7033	900	6	,	,	PUNCT
ejpam-7033	900	7	2011	2011	NUM
ejpam-7033	900	8	.	.	PUNCT
ejpam-7033	901	1	[	[	X
ejpam-7033	901	2	31	31	NUM
ejpam-7033	901	3	]	]	PUNCT
ejpam-7033	901	4	k.	k.	PROPN
ejpam-7033	901	5	javed	javed	PROPN
ejpam-7033	901	6	,	,	PUNCT
ejpam-7033	901	7	f.	f.	PROPN
ejpam-7033	901	8	uddin	uddin	PROPN
ejpam-7033	901	9	,	,	PUNCT
ejpam-7033	901	10	h.	h.	PROPN
ejpam-7033	901	11	aydi	aydi	PROPN
ejpam-7033	901	12	,	,	PUNCT
ejpam-7033	901	13	a.	a.	NOUN
ejpam-7033	901	14	mukheimer	mukheimer	NOUN
ejpam-7033	901	15	,	,	PUNCT
ejpam-7033	901	16	and	and	CCONJ
ejpam-7033	901	17	m.	m.	PROPN
ejpam-7033	901	18	arshad	arshad	PROPN
ejpam-7033	901	19	.	.	PUNCT
ejpam-7033	902	1	ordered	order	VERB
ejpam-7033	902	2	-	-	PUNCT
ejpam-7033	902	3	theoretic	theoretic	ADJ
ejpam-7033	902	4	fixed	fix	VERB
ejpam-7033	902	5	point	point	NOUN
ejpam-7033	902	6	results	result	NOUN
ejpam-7033	902	7	in	in	ADP
ejpam-7033	902	8	fuzzy	fuzzy	ADJ
ejpam-7033	902	9	b	b	X
ejpam-7033	902	10	-	-	ADJ
ejpam-7033	902	11	metric	metric	ADJ
ejpam-7033	902	12	spaces	space	NOUN
ejpam-7033	902	13	with	with	ADP
ejpam-7033	902	14	an	an	DET
ejpam-7033	902	15	application	application	NOUN
ejpam-7033	902	16	.	.	PUNCT
ejpam-7033	903	1	journal	journal	NOUN
ejpam-7033	903	2	of	of	ADP
ejpam-7033	903	3	mathematics	mathematic	NOUN
ejpam-7033	903	4	,	,	PUNCT
ejpam-7033	903	5	page	page	NOUN
ejpam-7033	903	6	6663707	6663707	NUM
ejpam-7033	903	7	,	,	PUNCT
ejpam-7033	903	8	2021	2021	NUM
ejpam-7033	903	9	.	.	PUNCT
ejpam-7033	904	1	[	[	X
ejpam-7033	904	2	32	32	NUM
ejpam-7033	904	3	]	]	PUNCT
ejpam-7033	904	4	k.	k.	PROPN
ejpam-7033	904	5	javed	javed	PROPN
ejpam-7033	904	6	,	,	PUNCT
ejpam-7033	904	7	h.	h.	PROPN
ejpam-7033	904	8	aydi	aydi	PROPN
ejpam-7033	904	9	,	,	PUNCT
ejpam-7033	904	10	f.	f.	PROPN
ejpam-7033	904	11	uddin	uddin	PROPN
ejpam-7033	904	12	,	,	PUNCT
ejpam-7033	904	13	and	and	CCONJ
ejpam-7033	904	14	m.	m.	PROPN
ejpam-7033	904	15	arshad	arshad	PROPN
ejpam-7033	904	16	.	.	PROPN
ejpam-7033	905	1	on	on	ADP
ejpam-7033	905	2	orthogonal	orthogonal	ADJ
ejpam-7033	905	3	partial	partial	ADJ
ejpam-7033	905	4	b	b	NOUN
ejpam-7033	905	5	-	-	ADJ
ejpam-7033	905	6	metric	metric	ADJ
ejpam-7033	905	7	spaces	space	NOUN
ejpam-7033	905	8	with	with	ADP
ejpam-7033	905	9	an	an	DET
ejpam-7033	905	10	application	application	NOUN
ejpam-7033	905	11	.	.	PUNCT
ejpam-7033	906	1	journal	journal	NOUN
ejpam-7033	906	2	of	of	ADP
ejpam-7033	906	3	mathematics	mathematic	NOUN
ejpam-7033	906	4	,	,	PUNCT
ejpam-7033	906	5	page	page	NOUN
ejpam-7033	906	6	6692063	6692063	NUM
ejpam-7033	906	7	,	,	PUNCT
ejpam-7033	906	8	2021	2021	NUM
ejpam-7033	906	9	.	.	PUNCT
ejpam-7033	907	1	[	[	X
ejpam-7033	907	2	33	33	NUM
ejpam-7033	907	3	]	]	PUNCT
ejpam-7033	907	4	e.	e.	PROPN
ejpam-7033	907	5	karapinar	karapinar	PROPN
ejpam-7033	907	6	,	,	PUNCT
ejpam-7033	907	7	s.	s.	PROPN
ejpam-7033	907	8	czerwik	czerwik	PROPN
ejpam-7033	907	9	,	,	PUNCT
ejpam-7033	907	10	and	and	CCONJ
ejpam-7033	907	11	h.	h.	PROPN
ejpam-7033	907	12	aydi	aydi	VERB
ejpam-7033	907	13	.	.	PUNCT
ejpam-7033	908	1	(	(	PUNCT
ejpam-7033	908	2	α	α	NOUN
ejpam-7033	908	3	,	,	PUNCT
ejpam-7033	908	4	ψ)-meir	ψ)-meir	ADJ
ejpam-7033	908	5	-	-	ADJ
ejpam-7033	908	6	keeler	keeler	ADJ
ejpam-7033	908	7	contraction	contraction	NOUN
ejpam-7033	908	8	mappings	mapping	NOUN
ejpam-7033	908	9	in	in	ADP
ejpam-7033	908	10	generalized	generalized	ADJ
ejpam-7033	908	11	b	b	X
ejpam-7033	908	12	-	-	ADJ
ejpam-7033	908	13	metric	metric	ADJ
ejpam-7033	908	14	spaces	space	NOUN
ejpam-7033	908	15	.	.	PUNCT
ejpam-7033	909	1	journal	journal	NOUN
ejpam-7033	909	2	of	of	ADP
ejpam-7033	909	3	function	function	NOUN
ejpam-7033	909	4	spaces	space	NOUN
ejpam-7033	909	5	,	,	PUNCT
ejpam-7033	909	6	page	page	NOUN
ejpam-7033	909	7	3264620	3264620	NUM
ejpam-7033	909	8	,	,	PUNCT
ejpam-7033	909	9	2018	2018	NUM
ejpam-7033	909	10	.	.	PUNCT
ejpam-7033	910	1	[	[	X
ejpam-7033	910	2	34	34	NUM
ejpam-7033	910	3	]	]	X
ejpam-7033	910	4	a.	a.	NOUN
ejpam-7033	910	5	azam	azam	PROPN
ejpam-7033	910	6	,	,	PUNCT
ejpam-7033	910	7	m.	m.	NOUN
ejpam-7033	910	8	arshad	arshad	PROPN
ejpam-7033	910	9	,	,	PUNCT
ejpam-7033	910	10	and	and	CCONJ
ejpam-7033	910	11	i.	i.	PROPN
ejpam-7033	910	12	beg	beg	PROPN
ejpam-7033	910	13	.	.	PUNCT
ejpam-7033	911	1	banach	banach	NOUN
ejpam-7033	911	2	contraction	contraction	NOUN
ejpam-7033	911	3	principle	principle	NOUN
ejpam-7033	911	4	on	on	ADP
ejpam-7033	911	5	cone	cone	NOUN
ejpam-7033	911	6	rectangular	rectangular	ADJ
ejpam-7033	911	7	metric	metric	ADJ
ejpam-7033	911	8	spaces	space	NOUN
ejpam-7033	911	9	.	.	PUNCT
ejpam-7033	912	1	applicable	applicable	ADJ
ejpam-7033	912	2	analysis	analysis	NOUN
ejpam-7033	912	3	and	and	CCONJ
ejpam-7033	912	4	discrete	discrete	ADJ
ejpam-7033	912	5	mathematics	mathematic	NOUN
ejpam-7033	912	6	,	,	PUNCT
ejpam-7033	912	7	3:236–241	3:236–241	NUM
ejpam-7033	912	8	,	,	PUNCT
ejpam-7033	912	9	2009	2009	NUM
ejpam-7033	912	10	.	.	PUNCT
ejpam-7033	913	1	[	[	X
ejpam-7033	913	2	35	35	NUM
ejpam-7033	913	3	]	]	X
ejpam-7033	913	4	sonam	sonam	PROPN
ejpam-7033	913	5	,	,	PUNCT
ejpam-7033	913	6	v.	v.	PROPN
ejpam-7033	913	7	rathore	rathore	PROPN
ejpam-7033	913	8	,	,	PUNCT
ejpam-7033	913	9	a.	a.	NOUN
ejpam-7033	913	10	pal	pal	NOUN
ejpam-7033	913	11	,	,	PUNCT
ejpam-7033	913	12	r.	r.	PROPN
ejpam-7033	913	13	bhardwaj	bhardwaj	PROPN
ejpam-7033	913	14	,	,	PUNCT
ejpam-7033	913	15	and	and	CCONJ
ejpam-7033	913	16	s.	s.	PROPN
ejpam-7033	913	17	narayan	narayan	PROPN
ejpam-7033	913	18	.	.	PUNCT
ejpam-7033	913	19	fixed	fix	VERB
ejpam-7033	913	20	-	-	PUNCT
ejpam-7033	913	21	point	point	NOUN
ejpam-7033	913	22	results	result	NOUN
ejpam-7033	913	23	for	for	ADP
ejpam-7033	913	24	mappings	mapping	NOUN
ejpam-7033	913	25	satisfying	satisfy	VERB
ejpam-7033	913	26	implicit	implicit	ADJ
ejpam-7033	913	27	relation	relation	NOUN
ejpam-7033	913	28	in	in	ADP
ejpam-7033	913	29	orthogonal	orthogonal	ADJ
ejpam-7033	913	30	fuzzy	fuzzy	ADJ
ejpam-7033	913	31	metric	metric	ADJ
ejpam-7033	913	32	spaces	space	NOUN
ejpam-7033	913	33	.	.	PUNCT
ejpam-7033	914	1	advances	advance	NOUN
ejpam-7033	914	2	in	in	ADP
ejpam-7033	914	3	fuzzy	fuzzy	ADJ
ejpam-7033	914	4	systems	system	NOUN
ejpam-7033	914	5	,	,	PUNCT
ejpam-7033	914	6	page	page	NOUN
ejpam-7033	914	7	5037401	5037401	NUM
ejpam-7033	914	8	,	,	PUNCT
ejpam-7033	914	9	2023	2023	NUM
ejpam-7033	914	10	.	.	PUNCT
ejpam-7033	915	1	[	[	X
ejpam-7033	915	2	36	36	NUM
ejpam-7033	915	3	]	]	X
ejpam-7033	915	4	r.	r.	PROPN
ejpam-7033	915	5	george	george	PROPN
ejpam-7033	915	6	,	,	PUNCT
ejpam-7033	915	7	s.	s.	PROPN
ejpam-7033	915	8	radenović	radenović	VERB
ejpam-7033	915	9	,	,	PUNCT
ejpam-7033	915	10	and	and	CCONJ
ejpam-7033	915	11	k.	k.	PROPN
ejpam-7033	915	12	p.	p.	PROPN
ejpam-7033	915	13	reshma	reshma	PROPN
ejpam-7033	915	14	.	.	PUNCT
ejpam-7033	916	1	rectangular	rectangular	ADJ
ejpam-7033	916	2	b	b	X
ejpam-7033	916	3	-	-	PUNCT
ejpam-7033	916	4	metric	metric	ADJ
ejpam-7033	916	5	space	space	NOUN
ejpam-7033	916	6	and	and	CCONJ
ejpam-7033	916	7	contraction	contraction	NOUN
ejpam-7033	916	8	principles	principle	NOUN
ejpam-7033	916	9	.	.	PUNCT
ejpam-7033	917	1	journal	journal	PROPN
ejpam-7033	917	2	of	of	ADP
ejpam-7033	917	3	nonlinear	nonlinear	ADJ
ejpam-7033	917	4	science	science	NOUN
ejpam-7033	917	5	and	and	CCONJ
ejpam-7033	917	6	applications	application	NOUN
ejpam-7033	917	7	,	,	PUNCT
ejpam-7033	917	8	8:1005–1013	8:1005–1013	NUM
ejpam-7033	917	9	,	,	PUNCT
ejpam-7033	917	10	2015	2015	NUM
ejpam-7033	917	11	.	.	PUNCT
ejpam-7033	918	1	[	[	X
ejpam-7033	918	2	37	37	NUM
ejpam-7033	918	3	]	]	PUNCT
ejpam-7033	918	4	v.	v.	CCONJ
ejpam-7033	918	5	popa	popa	NOUN
ejpam-7033	918	6	.	.	PUNCT
ejpam-7033	919	1	some	some	DET
ejpam-7033	919	2	fixed	fix	VERB
ejpam-7033	919	3	point	point	NOUN
ejpam-7033	919	4	theorems	theorem	NOUN
ejpam-7033	919	5	for	for	ADP
ejpam-7033	919	6	compatible	compatible	ADJ
ejpam-7033	919	7	mappings	mapping	NOUN
ejpam-7033	919	8	satisfying	satisfy	VERB
ejpam-7033	919	9	an	an	DET
ejpam-7033	919	10	implicit	implicit	ADJ
ejpam-7033	919	11	relation	relation	NOUN
ejpam-7033	919	12	.	.	PUNCT
ejpam-7033	920	1	demonstratio	demonstratio	PROPN
ejpam-7033	920	2	mathematica	mathematica	PROPN
ejpam-7033	920	3	,	,	PUNCT
ejpam-7033	920	4	32:157–163	32:157–163	PROPN
ejpam-7033	920	5	,	,	PUNCT
ejpam-7033	920	6	1999	1999	NUM
ejpam-7033	920	7	.	.	PUNCT
ejpam-7033	921	1	[	[	X
ejpam-7033	921	2	38	38	NUM
ejpam-7033	921	3	]	]	PUNCT
ejpam-7033	921	4	v.	v.	CCONJ
ejpam-7033	921	5	popa	popa	NOUN
ejpam-7033	921	6	.	.	PUNCT
ejpam-7033	922	1	a	a	DET
ejpam-7033	922	2	general	general	ADJ
ejpam-7033	922	3	coincidence	coincidence	NOUN
ejpam-7033	922	4	theorem	theorem	NOUN
ejpam-7033	922	5	for	for	ADP
ejpam-7033	922	6	compatible	compatible	ADJ
ejpam-7033	922	7	multivalued	multivalued	ADJ
ejpam-7033	922	8	mappings	mapping	NOUN
ejpam-7033	922	9	satisfying	satisfy	VERB
ejpam-7033	922	10	an	an	DET
ejpam-7033	922	11	implicit	implicit	ADJ
ejpam-7033	922	12	relation	relation	NOUN
ejpam-7033	922	13	.	.	PUNCT
ejpam-7033	923	1	demonstratio	demonstratio	PROPN
ejpam-7033	923	2	mathematica	mathematica	PROPN
ejpam-7033	923	3	,	,	PUNCT
ejpam-7033	923	4	33:159–164	33:159–164	NUM
ejpam-7033	923	5	,	,	PUNCT
ejpam-7033	923	6	2000	2000	NUM
ejpam-7033	923	7	.	.	PUNCT
ejpam-7033	924	1	a.	a.	PROPN
ejpam-7033	924	2	arif	arif	PROPN
ejpam-7033	924	3	et	et	PROPN
ejpam-7033	924	4	al	al	PROPN
ejpam-7033	924	5	.	.	PUNCT
ejpam-7033	924	6	/	/	SYM
ejpam-7033	924	7	eur	eur	PROPN
ejpam-7033	924	8	.	.	PUNCT
ejpam-7033	925	1	j.	j.	PROPN
ejpam-7033	925	2	pure	pure	PROPN
ejpam-7033	925	3	appl	appl	PROPN
ejpam-7033	925	4	.	.	PROPN
ejpam-7033	925	5	math	math	PROPN
ejpam-7033	925	6	,	,	PUNCT
ejpam-7033	925	7	18	18	NUM
ejpam-7033	925	8	(	(	PUNCT
ejpam-7033	925	9	4	4	NUM
ejpam-7033	925	10	)	)	PUNCT
ejpam-7033	925	11	(	(	PUNCT
ejpam-7033	925	12	2025	2025	NUM
ejpam-7033	925	13	)	)	PUNCT
ejpam-7033	925	14	,	,	PUNCT
ejpam-7033	925	15	7033	7033	NUM
ejpam-7033	925	16	29	29	NUM
ejpam-7033	925	17	of	of	ADP
ejpam-7033	925	18	29	29	NUM
ejpam-7033	925	19	[	[	SYM
ejpam-7033	925	20	39	39	NUM
ejpam-7033	925	21	]	]	PUNCT
ejpam-7033	925	22	i.	i.	NOUN
ejpam-7033	925	23	altun	altun	PROPN
ejpam-7033	925	24	,	,	PUNCT
ejpam-7033	925	25	f.	f.	PROPN
ejpam-7033	925	26	sola	sola	PROPN
ejpam-7033	925	27	,	,	PUNCT
ejpam-7033	925	28	and	and	CCONJ
ejpam-7033	925	29	h.	h.	PROPN
ejpam-7033	925	30	simsek	simsek	PROPN
ejpam-7033	925	31	.	.	PUNCT
ejpam-7033	926	1	generalized	generalized	ADJ
ejpam-7033	926	2	contractions	contraction	NOUN
ejpam-7033	926	3	on	on	ADP
ejpam-7033	926	4	partial	partial	ADJ
ejpam-7033	926	5	metric	metric	ADJ
ejpam-7033	926	6	spaces	space	NOUN
ejpam-7033	926	7	.	.	PUNCT
ejpam-7033	927	1	topology	topology	NOUN
ejpam-7033	927	2	and	and	CCONJ
ejpam-7033	927	3	its	its	PRON
ejpam-7033	927	4	applications	application	NOUN
ejpam-7033	927	5	,	,	PUNCT
ejpam-7033	927	6	157:2778–2785	157:2778–2785	NUM
ejpam-7033	927	7	,	,	PUNCT
ejpam-7033	927	8	2010	2010	NUM
ejpam-7033	927	9	.	.	PUNCT
ejpam-7033	928	1	[	[	X
ejpam-7033	928	2	40	40	NUM
ejpam-7033	928	3	]	]	PUNCT
ejpam-7033	928	4	i.	i.	NOUN
ejpam-7033	928	5	altun	altun	PROPN
ejpam-7033	928	6	and	and	CCONJ
ejpam-7033	928	7	d.	d.	PROPN
ejpam-7033	928	8	turkoglu	turkoglu	PROPN
ejpam-7033	928	9	.	.	PUNCT
ejpam-7033	929	1	some	some	DET
ejpam-7033	929	2	fixed	fix	VERB
ejpam-7033	929	3	point	point	NOUN
ejpam-7033	929	4	theorems	theorem	NOUN
ejpam-7033	929	5	for	for	ADP
ejpam-7033	929	6	weakly	weakly	ADJ
ejpam-7033	929	7	compatible	compatible	ADJ
ejpam-7033	929	8	mappings	mapping	NOUN
ejpam-7033	929	9	satisfying	satisfy	VERB
ejpam-7033	929	10	an	an	DET
ejpam-7033	929	11	implicit	implicit	ADJ
ejpam-7033	929	12	relation	relation	NOUN
ejpam-7033	929	13	.	.	PUNCT
ejpam-7033	930	1	taiwanese	taiwanese	ADJ
ejpam-7033	930	2	journal	journal	NOUN
ejpam-7033	930	3	of	of	ADP
ejpam-7033	930	4	mathematics	mathematic	NOUN
ejpam-7033	930	5	,	,	PUNCT
ejpam-7033	930	6	13:1291–1304	13:1291–1304	NUM
ejpam-7033	930	7	,	,	PUNCT
ejpam-7033	930	8	2009	2009	NUM
ejpam-7033	930	9	.	.	PUNCT
ejpam-7033	931	1	[	[	X
ejpam-7033	931	2	41	41	NUM
ejpam-7033	931	3	]	]	PUNCT
ejpam-7033	931	4	m.	m.	PROPN
ejpam-7033	931	5	joshi	joshi	PROPN
ejpam-7033	931	6	.	.	PUNCT
ejpam-7033	932	1	existence	existence	NOUN
ejpam-7033	932	2	theorems	theorem	VERB
ejpam-7033	932	3	for	for	ADP
ejpam-7033	932	4	urysohn	urysohn	PROPN
ejpam-7033	932	5	’s	’s	PART
ejpam-7033	932	6	integral	integral	ADJ
ejpam-7033	932	7	equation	equation	NOUN
ejpam-7033	932	8	.	.	PUNCT
ejpam-7033	933	1	proceedings	proceeding	NOUN
ejpam-7033	933	2	of	of	ADP
ejpam-7033	933	3	the	the	DET
ejpam-7033	933	4	american	american	PROPN
ejpam-7033	933	5	mathematical	mathematical	PROPN
ejpam-7033	933	6	society	society	NOUN
ejpam-7033	933	7	,	,	PUNCT
ejpam-7033	933	8	49(2):387–392	49(2):387–392	PROPN
ejpam-7033	933	9	,	,	PUNCT
ejpam-7033	933	10	1975	1975	NUM
ejpam-7033	933	11	.	.	PUNCT
ejpam-7033	934	1	[	[	X
ejpam-7033	934	2	42	42	NUM
ejpam-7033	934	3	]	]	PUNCT
ejpam-7033	934	4	k.	k.	PROPN
ejpam-7033	934	5	maleknejad	maleknejad	PROPN
ejpam-7033	934	6	,	,	PUNCT
ejpam-7033	934	7	h.	h.	PROPN
ejpam-7033	934	8	derili	derili	PROPN
ejpam-7033	934	9	,	,	PUNCT
ejpam-7033	934	10	and	and	CCONJ
ejpam-7033	934	11	s.	s.	PROPN
ejpam-7033	934	12	sohrabi	sohrabi	PROPN
ejpam-7033	934	13	.	.	PUNCT
ejpam-7033	935	1	numerical	numerical	ADJ
ejpam-7033	935	2	solution	solution	NOUN
ejpam-7033	935	3	of	of	ADP
ejpam-7033	935	4	urysohn	urysohn	PROPN
ejpam-7033	935	5	integral	integral	ADJ
ejpam-7033	935	6	equations	equation	NOUN
ejpam-7033	935	7	using	use	VERB
ejpam-7033	935	8	the	the	DET
ejpam-7033	935	9	iterated	iterated	ADJ
ejpam-7033	935	10	collocation	collocation	NOUN
ejpam-7033	935	11	method	method	NOUN
ejpam-7033	935	12	.	.	PUNCT
ejpam-7033	936	1	international	international	ADJ
ejpam-7033	936	2	journal	journal	PROPN
ejpam-7033	936	3	of	of	ADP
ejpam-7033	936	4	computer	computer	NOUN
ejpam-7033	936	5	mathematics	mathematic	NOUN
ejpam-7033	936	6	,	,	PUNCT
ejpam-7033	936	7	85(1):143–154	85(1):143–154	NOUN
ejpam-7033	936	8	,	,	PUNCT
ejpam-7033	936	9	2008	2008	NUM
ejpam-7033	936	10	.	.	PUNCT
ejpam-7033	937	1	[	[	X
ejpam-7033	937	2	43	43	NUM
ejpam-7033	937	3	]	]	X
ejpam-7033	937	4	r.	r.	PROPN
ejpam-7033	937	5	singh	singh	PROPN
ejpam-7033	937	6	,	,	PUNCT
ejpam-7033	937	7	g.	g.	PROPN
ejpam-7033	937	8	nelakanti	nelakanti	PROPN
ejpam-7033	937	9	,	,	PUNCT
ejpam-7033	937	10	and	and	CCONJ
ejpam-7033	937	11	j.	j.	PROPN
ejpam-7033	937	12	kumar	kumar	PROPN
ejpam-7033	937	13	.	.	PROPN
ejpam-7033	937	14	approximate	approximate	ADJ
ejpam-7033	937	15	solution	solution	NOUN
ejpam-7033	937	16	of	of	ADP
ejpam-7033	937	17	urysohn	urysohn	PROPN
ejpam-7033	937	18	integral	integral	ADJ
ejpam-7033	937	19	equations	equation	NOUN
ejpam-7033	937	20	using	use	VERB
ejpam-7033	937	21	the	the	DET
ejpam-7033	937	22	adomian	adomian	NOUN
ejpam-7033	937	23	decomposition	decomposition	NOUN
ejpam-7033	937	24	method	method	NOUN
ejpam-7033	937	25	.	.	PUNCT
ejpam-7033	938	1	the	the	DET
ejpam-7033	938	2	scientific	scientific	ADJ
ejpam-7033	938	3	world	world	NOUN
ejpam-7033	938	4	journal	journal	NOUN
ejpam-7033	938	5	,	,	PUNCT
ejpam-7033	938	6	page	page	NOUN
ejpam-7033	938	7	150483	150483	NUM
ejpam-7033	938	8	,	,	PUNCT
ejpam-7033	938	9	2014	2014	NUM
ejpam-7033	938	10	.	.	PUNCT
ejpam-7033	939	1	[	[	X
ejpam-7033	939	2	44	44	NUM
ejpam-7033	939	3	]	]	PUNCT
ejpam-7033	939	4	m.	m.	NOUN
ejpam-7033	939	5	nazam	nazam	PROPN
ejpam-7033	939	6	,	,	PUNCT
ejpam-7033	939	7	h.	h.	PROPN
ejpam-7033	939	8	aydi	aydi	PROPN
ejpam-7033	939	9	,	,	PUNCT
ejpam-7033	939	10	and	and	CCONJ
ejpam-7033	939	11	a.	a.	NOUN
ejpam-7033	939	12	hussain	hussain	PROPN
ejpam-7033	939	13	.	.	PUNCT
ejpam-7033	940	1	existence	existence	NOUN
ejpam-7033	940	2	theorems	theorem	VERB
ejpam-7033	940	3	for	for	ADP
ejpam-7033	940	4	(	(	PUNCT
ejpam-7033	940	5	ϕ	ϕ	NOUN
ejpam-7033	940	6	,	,	PUNCT
ejpam-7033	940	7	ψ)-orthogonal	ψ)-orthogonal	ADJ
ejpam-7033	940	8	interpolative	interpolative	ADJ
ejpam-7033	940	9	contractions	contraction	NOUN
ejpam-7033	940	10	and	and	CCONJ
ejpam-7033	940	11	an	an	DET
ejpam-7033	940	12	application	application	NOUN
ejpam-7033	940	13	to	to	ADP
ejpam-7033	940	14	fractional	fractional	ADJ
ejpam-7033	940	15	differential	differential	ADJ
ejpam-7033	940	16	equations	equation	NOUN
ejpam-7033	940	17	.	.	PUNCT
ejpam-7033	941	1	optimization	optimization	NOUN
ejpam-7033	941	2	,	,	PUNCT
ejpam-7033	941	3	71	71	NUM
ejpam-7033	941	4	,	,	PUNCT
ejpam-7033	941	5	2022	2022	NUM
ejpam-7033	941	6	.	.	PUNCT