id	sid	tid	token	lemma	pos
ejpam-6314	1	1	european	european	PROPN
ejpam-6314	1	2	journal	journal	PROPN
ejpam-6314	1	3	of	of	ADP
ejpam-6314	1	4	pure	pure	ADJ
ejpam-6314	1	5	and	and	CCONJ
ejpam-6314	1	6	applied	applied	ADJ
ejpam-6314	1	7	mathematics	mathematic	NOUN
ejpam-6314	1	8	2025	2025	NUM
ejpam-6314	1	9	,	,	PUNCT
ejpam-6314	1	10	vol	vol	NOUN
ejpam-6314	1	11	.	.	PROPN
ejpam-6314	1	12	18	18	NUM
ejpam-6314	1	13	,	,	PUNCT
ejpam-6314	1	14	issue	issue	NOUN
ejpam-6314	1	15	3	3	NUM
ejpam-6314	1	16	,	,	PUNCT
ejpam-6314	1	17	article	article	NOUN
ejpam-6314	1	18	number	number	NOUN
ejpam-6314	1	19	6314	6314	NUM
ejpam-6314	1	20	issn	issn	VERB
ejpam-6314	1	21	1307	1307	NUM
ejpam-6314	1	22	-	-	SYM
ejpam-6314	1	23	5543	5543	NUM
ejpam-6314	1	24	–	–	PUNCT
ejpam-6314	1	25	ejpam.com	ejpam.com	X
ejpam-6314	1	26	published	publish	VERB
ejpam-6314	1	27	by	by	ADP
ejpam-6314	1	28	new	new	PROPN
ejpam-6314	1	29	york	york	PROPN
ejpam-6314	1	30	business	business	PROPN
ejpam-6314	1	31	global	global	ADJ
ejpam-6314	1	32	on	on	ADP
ejpam-6314	1	33	rational	rational	ADJ
ejpam-6314	1	34	-	-	PUNCT
ejpam-6314	1	35	type	type	NOUN
ejpam-6314	1	36	contractive	contractive	ADJ
ejpam-6314	1	37	mappings	mapping	NOUN
ejpam-6314	1	38	in	in	ADP
ejpam-6314	1	39	bi	bi	ADJ
ejpam-6314	1	40	-	-	ADJ
ejpam-6314	1	41	complex	complex	ADJ
ejpam-6314	1	42	valued	value	VERB
ejpam-6314	1	43	control	control	NOUN
ejpam-6314	1	44	metric	metric	ADJ
ejpam-6314	1	45	spaces	space	NOUN
ejpam-6314	1	46	and	and	CCONJ
ejpam-6314	1	47	applications	application	NOUN
ejpam-6314	1	48	muhammad	muhammad	PROPN
ejpam-6314	1	49	sarwar1,2,∗	sarwar1,2,∗	PROPN
ejpam-6314	1	50	,	,	PUNCT
ejpam-6314	1	51	nahid	nahid	PROPN
ejpam-6314	1	52	fatima2	fatima2	PROPN
ejpam-6314	1	53	,	,	PUNCT
ejpam-6314	1	54	syed	syed	ADJ
ejpam-6314	1	55	khayyam	khayyam	PROPN
ejpam-6314	1	56	shah3	shah3	PROPN
ejpam-6314	1	57	,	,	PUNCT
ejpam-6314	1	58	asad	asad	PROPN
ejpam-6314	1	59	khan1	khan1	PROPN
ejpam-6314	1	60	,	,	PUNCT
ejpam-6314	1	61	kamaleldin	kamaleldin	VERB
ejpam-6314	1	62	abodayeh2	abodayeh2	PROPN
ejpam-6314	1	63	1	1	NUM
ejpam-6314	1	64	department	department	NOUN
ejpam-6314	1	65	of	of	ADP
ejpam-6314	1	66	mathematics	mathematic	NOUN
ejpam-6314	1	67	,	,	PUNCT
ejpam-6314	1	68	university	university	NOUN
ejpam-6314	1	69	of	of	ADP
ejpam-6314	1	70	malakand	malakand	PROPN
ejpam-6314	1	71	,	,	PUNCT
ejpam-6314	1	72	chakdara	chakdara	NOUN
ejpam-6314	1	73	dir(l	dir(l	PROPN
ejpam-6314	1	74	)	)	PUNCT
ejpam-6314	1	75	,	,	PUNCT
ejpam-6314	1	76	18000	18000	NUM
ejpam-6314	1	77	,	,	PUNCT
ejpam-6314	1	78	khyber	khyber	PROPN
ejpam-6314	1	79	pakhtunkhwa	pakhtunkhwa	PROPN
ejpam-6314	1	80	,	,	PUNCT
ejpam-6314	1	81	pakistan	pakistan	PROPN
ejpam-6314	1	82	2	2	NUM
ejpam-6314	1	83	department	department	NOUN
ejpam-6314	1	84	of	of	ADP
ejpam-6314	1	85	mathematics	mathematic	NOUN
ejpam-6314	1	86	and	and	CCONJ
ejpam-6314	1	87	sciences	science	NOUN
ejpam-6314	1	88	,	,	PUNCT
ejpam-6314	1	89	prince	prince	PROPN
ejpam-6314	1	90	sultan	sultan	PROPN
ejpam-6314	1	91	university	university	PROPN
ejpam-6314	1	92	,	,	PUNCT
ejpam-6314	1	93	riyadh	riyadh	PROPN
ejpam-6314	1	94	11586	11586	NUM
ejpam-6314	1	95	,	,	PUNCT
ejpam-6314	1	96	saudi	saudi	PROPN
ejpam-6314	1	97	arabia	arabia	PROPN
ejpam-6314	1	98	3	3	NUM
ejpam-6314	1	99	department	department	NOUN
ejpam-6314	1	100	of	of	ADP
ejpam-6314	1	101	sustainable	sustainable	ADJ
ejpam-6314	1	102	environment	environment	NOUN
ejpam-6314	1	103	and	and	CCONJ
ejpam-6314	1	104	energy	energy	NOUN
ejpam-6314	1	105	systems	system	NOUN
ejpam-6314	1	106	(	(	PUNCT
ejpam-6314	1	107	sees	see	VERB
ejpam-6314	1	108	)	)	PUNCT
ejpam-6314	1	109	,	,	PUNCT
ejpam-6314	1	110	middle	middle	PROPN
ejpam-6314	1	111	east	east	PROPN
ejpam-6314	1	112	technical	technical	PROPN
ejpam-6314	1	113	university	university	PROPN
ejpam-6314	1	114	,	,	PUNCT
ejpam-6314	1	115	northern	northern	ADJ
ejpam-6314	1	116	cyprus	cyprus	PROPN
ejpam-6314	1	117	campus	campus	PROPN
ejpam-6314	1	118	,	,	PUNCT
ejpam-6314	1	119	99738	99738	NUM
ejpam-6314	1	120	kalkanli	kalkanli	NOUN
ejpam-6314	1	121	,	,	PUNCT
ejpam-6314	1	122	guzelyurt	guzelyurt	PROPN
ejpam-6314	1	123	,	,	PUNCT
ejpam-6314	1	124	mersin	mersin	PROPN
ejpam-6314	1	125	10	10	NUM
ejpam-6314	1	126	,	,	PUNCT
ejpam-6314	1	127	turkey	turkey	NOUN
ejpam-6314	1	128	abstract	abstract	NOUN
ejpam-6314	1	129	.	.	PUNCT
ejpam-6314	2	1	this	this	DET
ejpam-6314	2	2	manuscript	manuscript	NOUN
ejpam-6314	2	3	studies	study	VERB
ejpam-6314	2	4	some	some	DET
ejpam-6314	2	5	unique	unique	ADJ
ejpam-6314	2	6	and	and	CCONJ
ejpam-6314	2	7	common	common	ADJ
ejpam-6314	2	8	fixed	fix	VERB
ejpam-6314	2	9	point	point	NOUN
ejpam-6314	2	10	results	result	NOUN
ejpam-6314	2	11	in	in	ADP
ejpam-6314	2	12	the	the	DET
ejpam-6314	2	13	context	context	NOUN
ejpam-6314	2	14	of	of	ADP
ejpam-6314	2	15	bi	bi	ADJ
ejpam-6314	2	16	-	-	ADJ
ejpam-6314	2	17	complex	complex	ADJ
ejpam-6314	2	18	valued	value	VERB
ejpam-6314	2	19	control	control	NOUN
ejpam-6314	2	20	metric	metric	PROPN
ejpam-6314	2	21	space(bvcms	space(bvcms	PROPN
ejpam-6314	2	22	)	)	PUNCT
ejpam-6314	2	23	using	use	VERB
ejpam-6314	2	24	rational	rational	ADJ
ejpam-6314	2	25	-	-	PUNCT
ejpam-6314	2	26	type	type	NOUN
ejpam-6314	2	27	inequalities	inequality	NOUN
ejpam-6314	2	28	.	.	PUNCT
ejpam-6314	3	1	the	the	DET
ejpam-6314	3	2	presented	present	VERB
ejpam-6314	3	3	work	work	NOUN
ejpam-6314	3	4	explains	explain	VERB
ejpam-6314	3	5	the	the	DET
ejpam-6314	3	6	idea	idea	NOUN
ejpam-6314	3	7	of	of	ADP
ejpam-6314	3	8	bvcms	bvcms	NOUN
ejpam-6314	3	9	and	and	CCONJ
ejpam-6314	3	10	then	then	ADV
ejpam-6314	3	11	shows	show	VERB
ejpam-6314	3	12	the	the	DET
ejpam-6314	3	13	necessary	necessary	ADJ
ejpam-6314	3	14	criteria	criterion	NOUN
ejpam-6314	3	15	for	for	ADP
ejpam-6314	3	16	a	a	DET
ejpam-6314	3	17	pair	pair	NOUN
ejpam-6314	3	18	of	of	ADP
ejpam-6314	3	19	contractive	contractive	ADJ
ejpam-6314	3	20	type	type	NOUN
ejpam-6314	3	21	mappings	mapping	NOUN
ejpam-6314	3	22	in	in	ADP
ejpam-6314	3	23	this	this	DET
ejpam-6314	3	24	space	space	NOUN
ejpam-6314	3	25	to	to	PART
ejpam-6314	3	26	have	have	VERB
ejpam-6314	3	27	common	common	ADJ
ejpam-6314	3	28	fixed	fix	VERB
ejpam-6314	3	29	points	point	NOUN
ejpam-6314	3	30	.	.	PUNCT
ejpam-6314	4	1	to	to	PART
ejpam-6314	4	2	show	show	VERB
ejpam-6314	4	3	how	how	SCONJ
ejpam-6314	4	4	applicable	applicable	ADJ
ejpam-6314	4	5	our	our	PRON
ejpam-6314	4	6	results	result	NOUN
ejpam-6314	4	7	are	be	AUX
ejpam-6314	4	8	,	,	PUNCT
ejpam-6314	4	9	we	we	PRON
ejpam-6314	4	10	also	also	ADV
ejpam-6314	4	11	give	give	VERB
ejpam-6314	4	12	an	an	DET
ejpam-6314	4	13	example	example	NOUN
ejpam-6314	4	14	.	.	PUNCT
ejpam-6314	5	1	finally	finally	ADV
ejpam-6314	5	2	,	,	PUNCT
ejpam-6314	5	3	the	the	DET
ejpam-6314	5	4	existence	existence	NOUN
ejpam-6314	5	5	of	of	ADP
ejpam-6314	5	6	solutions	solution	NOUN
ejpam-6314	5	7	of	of	ADP
ejpam-6314	5	8	a	a	DET
ejpam-6314	5	9	system	system	NOUN
ejpam-6314	5	10	of	of	ADP
ejpam-6314	5	11	fractional	fractional	ADJ
ejpam-6314	5	12	differential	differential	ADJ
ejpam-6314	5	13	equations	equation	NOUN
ejpam-6314	5	14	has	have	AUX
ejpam-6314	5	15	been	be	AUX
ejpam-6314	5	16	studied	study	VERB
ejpam-6314	5	17	using	use	VERB
ejpam-6314	5	18	the	the	DET
ejpam-6314	5	19	obtained	obtain	VERB
ejpam-6314	5	20	results	result	NOUN
ejpam-6314	5	21	.	.	PUNCT
ejpam-6314	6	1	2020	2020	NUM
ejpam-6314	6	2	mathematics	mathematic	NOUN
ejpam-6314	6	3	subject	subject	NOUN
ejpam-6314	6	4	classifications	classification	NOUN
ejpam-6314	6	5	:	:	PUNCT
ejpam-6314	6	6	47h10	47h10	NUM
ejpam-6314	6	7	,	,	PUNCT
ejpam-6314	6	8	54h25	54h25	NUM
ejpam-6314	6	9	,	,	PUNCT
ejpam-6314	6	10	34a08	34a08	DET
ejpam-6314	6	11	key	key	ADJ
ejpam-6314	6	12	words	word	NOUN
ejpam-6314	6	13	and	and	CCONJ
ejpam-6314	6	14	phrases	phrase	NOUN
ejpam-6314	6	15	:	:	PUNCT
ejpam-6314	6	16	bi	bi	ADJ
ejpam-6314	6	17	-	-	ADJ
ejpam-6314	6	18	complex	complex	ADJ
ejpam-6314	6	19	valued	value	VERB
ejpam-6314	6	20	controlled	control	VERB
ejpam-6314	6	21	metric	metric	ADJ
ejpam-6314	6	22	spaces	space	NOUN
ejpam-6314	6	23	,	,	PUNCT
ejpam-6314	6	24	fixed	fix	VERB
ejpam-6314	6	25	point	point	NOUN
ejpam-6314	6	26	,	,	PUNCT
ejpam-6314	6	27	rational	rational	ADJ
ejpam-6314	6	28	type	type	NOUN
ejpam-6314	6	29	contractions	contraction	NOUN
ejpam-6314	6	30	,	,	PUNCT
ejpam-6314	6	31	fractional	fractional	ADJ
ejpam-6314	6	32	differential	differential	ADJ
ejpam-6314	6	33	equations	equation	NOUN
ejpam-6314	6	34	1	1	NUM
ejpam-6314	6	35	.	.	PUNCT
ejpam-6314	7	1	introduction	introduction	NOUN
ejpam-6314	7	2	and	and	CCONJ
ejpam-6314	7	3	preliminaries	preliminary	NOUN
ejpam-6314	7	4	the	the	DET
ejpam-6314	7	5	notion	notion	NOUN
ejpam-6314	7	6	of	of	ADP
ejpam-6314	7	7	conventional	conventional	ADJ
ejpam-6314	7	8	differential	differential	ADJ
ejpam-6314	7	9	equations	equation	NOUN
ejpam-6314	7	10	may	may	AUX
ejpam-6314	7	11	be	be	AUX
ejpam-6314	7	12	extended	extend	VERB
ejpam-6314	7	13	to	to	ADP
ejpam-6314	7	14	non	non	ADJ
ejpam-6314	7	15	-	-	ADJ
ejpam-6314	7	16	integer	integer	ADJ
ejpam-6314	7	17	orders	order	NOUN
ejpam-6314	7	18	using	use	VERB
ejpam-6314	7	19	fractional	fractional	ADJ
ejpam-6314	7	20	differential	differential	ADJ
ejpam-6314	7	21	equations	equation	NOUN
ejpam-6314	7	22	(	(	PUNCT
ejpam-6314	7	23	fdes	fde	NOUN
ejpam-6314	7	24	)	)	PUNCT
ejpam-6314	7	25	,	,	PUNCT
ejpam-6314	7	26	an	an	DET
ejpam-6314	7	27	excellent	excellent	ADJ
ejpam-6314	7	28	mathematical	mathematical	ADJ
ejpam-6314	7	29	tool	tool	NOUN
ejpam-6314	7	30	.	.	PUNCT
ejpam-6314	8	1	unlike	unlike	ADP
ejpam-6314	8	2	fractional	fractional	ADJ
ejpam-6314	8	3	calculus	calculus	NOUN
ejpam-6314	8	4	,	,	PUNCT
ejpam-6314	8	5	which	which	PRON
ejpam-6314	8	6	introduces	introduce	VERB
ejpam-6314	8	7	the	the	DET
ejpam-6314	8	8	idea	idea	NOUN
ejpam-6314	8	9	of	of	ADP
ejpam-6314	8	10	fractional	fractional	ADJ
ejpam-6314	8	11	derivatives	derivative	NOUN
ejpam-6314	8	12	that	that	PRON
ejpam-6314	8	13	may	may	AUX
ejpam-6314	8	14	be	be	AUX
ejpam-6314	8	15	derived	derive	VERB
ejpam-6314	8	16	for	for	ADP
ejpam-6314	8	17	non	non	ADJ
ejpam-6314	8	18	-	-	ADJ
ejpam-6314	8	19	integer	integer	ADJ
ejpam-6314	8	20	orders	order	NOUN
ejpam-6314	8	21	,	,	PUNCT
ejpam-6314	8	22	conventional	conventional	ADJ
ejpam-6314	8	23	differential	differential	ADJ
ejpam-6314	8	24	equations	equation	NOUN
ejpam-6314	8	25	only	only	ADV
ejpam-6314	8	26	deal	deal	VERB
ejpam-6314	8	27	with	with	ADP
ejpam-6314	8	28	integer	integer	NOUN
ejpam-6314	8	29	-	-	PUNCT
ejpam-6314	8	30	order	order	NOUN
ejpam-6314	8	31	derivatives	derivative	NOUN
ejpam-6314	8	32	.	.	PUNCT
ejpam-6314	9	1	numerous	numerous	ADJ
ejpam-6314	9	2	scientific	scientific	ADJ
ejpam-6314	9	3	fields	field	NOUN
ejpam-6314	9	4	,	,	PUNCT
ejpam-6314	9	5	including	include	VERB
ejpam-6314	9	6	physics	physics	NOUN
ejpam-6314	9	7	,	,	PUNCT
ejpam-6314	9	8	engineering	engineering	NOUN
ejpam-6314	9	9	,	,	PUNCT
ejpam-6314	9	10	economics	economic	NOUN
ejpam-6314	9	11	,	,	PUNCT
ejpam-6314	9	12	biology	biology	NOUN
ejpam-6314	9	13	,	,	PUNCT
ejpam-6314	9	14	and	and	CCONJ
ejpam-6314	9	15	more	more	ADV
ejpam-6314	9	16	,	,	PUNCT
ejpam-6314	9	17	have	have	AUX
ejpam-6314	9	18	begun	begin	VERB
ejpam-6314	9	19	to	to	PART
ejpam-6314	9	20	pay	pay	VERB
ejpam-6314	9	21	close	close	ADJ
ejpam-6314	9	22	attention	attention	NOUN
ejpam-6314	9	23	to	to	ADP
ejpam-6314	9	24	the	the	DET
ejpam-6314	9	25	study	study	NOUN
ejpam-6314	9	26	of	of	ADP
ejpam-6314	9	27	fractional	fractional	ADJ
ejpam-6314	9	28	differential	differential	ADJ
ejpam-6314	9	29	equations	equation	NOUN
ejpam-6314	9	30	.	.	PUNCT
ejpam-6314	10	1	this	this	PRON
ejpam-6314	10	2	is	be	AUX
ejpam-6314	10	3	because	because	SCONJ
ejpam-6314	10	4	fdes	fde	NOUN
ejpam-6314	10	5	offer	offer	VERB
ejpam-6314	10	6	a	a	DET
ejpam-6314	10	7	more	more	ADV
ejpam-6314	10	8	precise	precise	ADJ
ejpam-6314	10	9	and	and	CCONJ
ejpam-6314	10	10	adaptable	adaptable	ADJ
ejpam-6314	10	11	method	method	NOUN
ejpam-6314	10	12	for	for	ADP
ejpam-6314	10	13	simulating	simulate	VERB
ejpam-6314	10	14	∗corresponding	∗corresponde	VERB
ejpam-6314	10	15	author	author	NOUN
ejpam-6314	10	16	.	.	PUNCT
ejpam-6314	11	1	doi	doi	NOUN
ejpam-6314	11	2	:	:	PUNCT
ejpam-6314	11	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6314	https://doi.org/10.29020/nybg.ejpam.v18i3.6314	NOUN
ejpam-6314	11	4	email	email	NOUN
ejpam-6314	11	5	addresses	address	VERB
ejpam-6314	11	6	:	:	PUNCT
ejpam-6314	11	7	sarwarswati@gmail.com	sarwarswati@gmail.com	X
ejpam-6314	11	8	(	(	PUNCT
ejpam-6314	11	9	m.	m.	NOUN
ejpam-6314	11	10	sarwar	sarwar	PROPN
ejpam-6314	11	11	)	)	PUNCT
ejpam-6314	11	12	,	,	PUNCT
ejpam-6314	11	13	nfatima@psu.edu.sa	nfatima@psu.edu.sa	PROPN
ejpam-6314	11	14	(	(	PUNCT
ejpam-6314	11	15	n.	n.	PROPN
ejpam-6314	11	16	fatima	fatima	PROPN
ejpam-6314	11	17	)	)	PUNCT
ejpam-6314	11	18	,	,	PUNCT
ejpam-6314	11	19	shah.syed@metu.edu.tr	shah.syed@metu.edu.tr	PROPN
ejpam-6314	11	20	(	(	PUNCT
ejpam-6314	11	21	s.	s.	PROPN
ejpam-6314	11	22	k.	k.	PROPN
ejpam-6314	11	23	shah	shah	PROPN
ejpam-6314	11	24	)	)	PUNCT
ejpam-6314	11	25	,	,	PUNCT
ejpam-6314	11	26	asad.ah.ak@gmail.com	asad.ah.ak@gmail.com	X
ejpam-6314	11	27	(	(	PUNCT
ejpam-6314	11	28	a.	a.	PROPN
ejpam-6314	11	29	khan	khan	PROPN
ejpam-6314	11	30	)	)	PUNCT
ejpam-6314	11	31	,	,	PUNCT
ejpam-6314	11	32	kamal@psu.edu.sa	kamal@psu.edu.sa	PROPN
ejpam-6314	11	33	(	(	PUNCT
ejpam-6314	11	34	k.	k.	PROPN
ejpam-6314	11	35	abodayeh	abodayeh	PROPN
ejpam-6314	11	36	)	)	PUNCT
ejpam-6314	11	37	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6314	12	1	1	1	NUM
ejpam-6314	12	2	copyright	copyright	NOUN
ejpam-6314	12	3	:	:	PUNCT
ejpam-6314	12	4	©	©	PROPN
ejpam-6314	12	5	2025	2025	NUM
ejpam-6314	12	6	the	the	DET
ejpam-6314	12	7	author(s	author(s	NOUN
ejpam-6314	12	8	)	)	PUNCT
ejpam-6314	12	9	.	.	PUNCT
ejpam-6314	13	1	(	(	PUNCT
ejpam-6314	13	2	cc	cc	NOUN
ejpam-6314	13	3	by	by	ADP
ejpam-6314	13	4	-	-	PUNCT
ejpam-6314	13	5	nc	nc	PROPN
ejpam-6314	13	6	4.0	4.0	NUM
ejpam-6314	13	7	)	)	PUNCT
ejpam-6314	13	8	m.	m.	NOUN
ejpam-6314	13	9	sarwar	sarwar	PROPN
ejpam-6314	13	10	et	et	PROPN
ejpam-6314	13	11	al	al	PROPN
ejpam-6314	13	12	.	.	PUNCT
ejpam-6314	13	13	/	/	SYM
ejpam-6314	13	14	eur	eur	PROPN
ejpam-6314	13	15	.	.	PUNCT
ejpam-6314	14	1	j.	j.	PROPN
ejpam-6314	14	2	pure	pure	PROPN
ejpam-6314	14	3	appl	appl	PROPN
ejpam-6314	14	4	.	.	PROPN
ejpam-6314	14	5	math	math	PROPN
ejpam-6314	14	6	,	,	PUNCT
ejpam-6314	14	7	18	18	NUM
ejpam-6314	14	8	(	(	PUNCT
ejpam-6314	14	9	3	3	NUM
ejpam-6314	14	10	)	)	PUNCT
ejpam-6314	14	11	(	(	PUNCT
ejpam-6314	14	12	2025	2025	NUM
ejpam-6314	14	13	)	)	PUNCT
ejpam-6314	14	14	,	,	PUNCT
ejpam-6314	14	15	6314	6314	NUM
ejpam-6314	14	16	2	2	NUM
ejpam-6314	14	17	of	of	ADP
ejpam-6314	14	18	28	28	NUM
ejpam-6314	14	19	complicated	complicated	ADJ
ejpam-6314	14	20	processes	process	NOUN
ejpam-6314	14	21	that	that	PRON
ejpam-6314	14	22	display	display	VERB
ejpam-6314	14	23	non	non	ADJ
ejpam-6314	14	24	-	-	ADJ
ejpam-6314	14	25	local	local	ADJ
ejpam-6314	14	26	and	and	CCONJ
ejpam-6314	14	27	memory	memory	NOUN
ejpam-6314	14	28	-	-	PUNCT
ejpam-6314	14	29	dependent	dependent	ADJ
ejpam-6314	14	30	behavior	behavior	NOUN
ejpam-6314	14	31	.	.	PUNCT
ejpam-6314	15	1	multiple	multiple	ADJ
ejpam-6314	15	2	applications	application	NOUN
ejpam-6314	15	3	of	of	ADP
ejpam-6314	15	4	fractional	fractional	ADJ
ejpam-6314	15	5	differential	differential	ADJ
ejpam-6314	15	6	equations	equation	NOUN
ejpam-6314	15	7	(	(	PUNCT
ejpam-6314	15	8	fdes	fde	NOUN
ejpam-6314	15	9	)	)	PUNCT
ejpam-6314	15	10	may	may	AUX
ejpam-6314	15	11	be	be	AUX
ejpam-6314	15	12	found	find	VERB
ejpam-6314	15	13	in	in	ADP
ejpam-6314	15	14	physics	physics	NOUN
ejpam-6314	15	15	,	,	PUNCT
ejpam-6314	15	16	engineering	engineering	NOUN
ejpam-6314	15	17	,	,	PUNCT
ejpam-6314	15	18	economics	economic	NOUN
ejpam-6314	15	19	,	,	PUNCT
ejpam-6314	15	20	and	and	CCONJ
ejpam-6314	15	21	biology	biology	NOUN
ejpam-6314	15	22	.	.	PUNCT
ejpam-6314	16	1	they	they	PRON
ejpam-6314	16	2	faithfully	faithfully	ADV
ejpam-6314	16	3	represent	represent	VERB
ejpam-6314	16	4	complex	complex	ADJ
ejpam-6314	16	5	systems	system	NOUN
ejpam-6314	16	6	with	with	ADP
ejpam-6314	16	7	anomalous	anomalous	ADJ
ejpam-6314	16	8	diffusion	diffusion	NOUN
ejpam-6314	16	9	,	,	PUNCT
ejpam-6314	16	10	long	long	ADJ
ejpam-6314	16	11	-	-	PUNCT
ejpam-6314	16	12	range	range	NOUN
ejpam-6314	16	13	interactions	interaction	NOUN
ejpam-6314	16	14	,	,	PUNCT
ejpam-6314	16	15	and	and	CCONJ
ejpam-6314	16	16	memory	memory	NOUN
ejpam-6314	16	17	dependence	dependence	NOUN
ejpam-6314	16	18	.	.	PUNCT
ejpam-6314	17	1	control	control	NOUN
ejpam-6314	17	2	systems	system	NOUN
ejpam-6314	17	3	,	,	PUNCT
ejpam-6314	17	4	the	the	DET
ejpam-6314	17	5	behavior	behavior	NOUN
ejpam-6314	17	6	of	of	ADP
ejpam-6314	17	7	viscoelastic	viscoelastic	ADJ
ejpam-6314	17	8	materials	material	NOUN
ejpam-6314	17	9	,	,	PUNCT
ejpam-6314	17	10	asset	asset	NOUN
ejpam-6314	17	11	pricing	pricing	NOUN
ejpam-6314	17	12	,	,	PUNCT
ejpam-6314	17	13	image	image	NOUN
ejpam-6314	17	14	processing	processing	NOUN
ejpam-6314	17	15	,	,	PUNCT
ejpam-6314	17	16	and	and	CCONJ
ejpam-6314	17	17	biomedicine	biomedicine	NOUN
ejpam-6314	17	18	are	be	AUX
ejpam-6314	17	19	all	all	PRON
ejpam-6314	17	20	improved	improve	VERB
ejpam-6314	17	21	by	by	ADP
ejpam-6314	17	22	fdes	fde	NOUN
ejpam-6314	17	23	.	.	PUNCT
ejpam-6314	18	1	in	in	ADP
ejpam-6314	18	2	the	the	DET
ejpam-6314	18	3	research	research	NOUN
ejpam-6314	18	4	of	of	ADP
ejpam-6314	18	5	fdes	fde	NOUN
ejpam-6314	18	6	,	,	PUNCT
ejpam-6314	18	7	[	[	X
ejpam-6314	18	8	1–4	1–4	NOUN
ejpam-6314	18	9	]	]	X
ejpam-6314	18	10	have	have	VERB
ejpam-6314	18	11	outstanding	outstanding	ADJ
ejpam-6314	18	12	data	datum	NOUN
ejpam-6314	18	13	.	.	PUNCT
ejpam-6314	19	1	furthermore	furthermore	ADV
ejpam-6314	19	2	,	,	PUNCT
ejpam-6314	19	3	fixed	fix	VERB
ejpam-6314	19	4	point	point	NOUN
ejpam-6314	19	5	theorems	theorem	NOUN
ejpam-6314	19	6	offer	offer	VERB
ejpam-6314	19	7	helpful	helpful	ADJ
ejpam-6314	19	8	methods	method	NOUN
ejpam-6314	19	9	for	for	ADP
ejpam-6314	19	10	demonstrating	demonstrate	VERB
ejpam-6314	19	11	that	that	SCONJ
ejpam-6314	19	12	solutions	solution	NOUN
ejpam-6314	19	13	to	to	ADP
ejpam-6314	19	14	specific	specific	ADJ
ejpam-6314	19	15	fractional	fractional	ADJ
ejpam-6314	19	16	differential	differential	ADJ
ejpam-6314	19	17	equations	equation	NOUN
ejpam-6314	19	18	exist	exist	VERB
ejpam-6314	19	19	,	,	PUNCT
ejpam-6314	19	20	supporting	support	VERB
ejpam-6314	19	21	the	the	DET
ejpam-6314	19	22	mathematical	mathematical	ADJ
ejpam-6314	19	23	study	study	NOUN
ejpam-6314	19	24	and	and	CCONJ
ejpam-6314	19	25	real	real	ADJ
ejpam-6314	19	26	-	-	PUNCT
ejpam-6314	19	27	world	world	NOUN
ejpam-6314	19	28	use	use	NOUN
ejpam-6314	19	29	of	of	ADP
ejpam-6314	19	30	these	these	DET
ejpam-6314	19	31	equations	equation	NOUN
ejpam-6314	19	32	in	in	ADP
ejpam-6314	19	33	various	various	ADJ
ejpam-6314	19	34	scientific	scientific	ADJ
ejpam-6314	19	35	and	and	CCONJ
ejpam-6314	19	36	technical	technical	ADJ
ejpam-6314	19	37	fields	field	NOUN
ejpam-6314	19	38	.	.	PUNCT
ejpam-6314	20	1	since	since	SCONJ
ejpam-6314	20	2	the	the	DET
ejpam-6314	20	3	proof	proof	NOUN
ejpam-6314	20	4	of	of	ADP
ejpam-6314	20	5	the	the	DET
ejpam-6314	20	6	well	well	ADV
ejpam-6314	20	7	-	-	PUNCT
ejpam-6314	20	8	known	know	VERB
ejpam-6314	20	9	banach	banach	NOUN
ejpam-6314	20	10	contraction	contraction	NOUN
ejpam-6314	20	11	theorem	theorem	VERB
ejpam-6314	20	12	,	,	PUNCT
ejpam-6314	20	13	the	the	DET
ejpam-6314	20	14	metric	metric	ADJ
ejpam-6314	20	15	fixed	fix	VERB
ejpam-6314	20	16	point	point	NOUN
ejpam-6314	20	17	theorem	theorem	NOUN
ejpam-6314	20	18	has	have	AUX
ejpam-6314	20	19	appeared	appear	VERB
ejpam-6314	20	20	.	.	PUNCT
ejpam-6314	21	1	since	since	SCONJ
ejpam-6314	21	2	then	then	ADV
ejpam-6314	21	3	,	,	PUNCT
ejpam-6314	21	4	there	there	PRON
ejpam-6314	21	5	have	have	AUX
ejpam-6314	21	6	been	be	AUX
ejpam-6314	21	7	numerous	numerous	ADJ
ejpam-6314	21	8	discoveries	discovery	NOUN
ejpam-6314	21	9	relating	relate	VERB
ejpam-6314	21	10	to	to	ADP
ejpam-6314	21	11	maps	map	NOUN
ejpam-6314	21	12	satisfying	satisfy	VERB
ejpam-6314	21	13	various	various	ADJ
ejpam-6314	21	14	contractive	contractive	ADJ
ejpam-6314	21	15	requirements	requirement	NOUN
ejpam-6314	21	16	and	and	CCONJ
ejpam-6314	21	17	different	different	ADJ
ejpam-6314	21	18	metric	metric	ADJ
ejpam-6314	21	19	spaces	space	NOUN
ejpam-6314	21	20	.	.	PUNCT
ejpam-6314	22	1	in	in	ADP
ejpam-6314	22	2	the	the	DET
ejpam-6314	22	3	context	context	NOUN
ejpam-6314	22	4	of	of	ADP
ejpam-6314	22	5	non	non	ADJ
ejpam-6314	22	6	-	-	ADJ
ejpam-6314	22	7	linear	linear	ADJ
ejpam-6314	22	8	analysis	analysis	NOUN
ejpam-6314	22	9	the	the	DET
ejpam-6314	22	10	theory	theory	NOUN
ejpam-6314	22	11	of	of	ADP
ejpam-6314	22	12	fixed	fix	VERB
ejpam-6314	22	13	point	point	NOUN
ejpam-6314	22	14	gained	gain	VERB
ejpam-6314	22	15	extraordinary	extraordinary	ADJ
ejpam-6314	22	16	importance	importance	NOUN
ejpam-6314	22	17	.	.	PUNCT
ejpam-6314	23	1	after	after	SCONJ
ejpam-6314	23	2	the	the	DET
ejpam-6314	23	3	famous	famous	ADJ
ejpam-6314	23	4	banach	banach	NOUN
ejpam-6314	23	5	presented	present	VERB
ejpam-6314	23	6	the	the	DET
ejpam-6314	23	7	very	very	ADV
ejpam-6314	23	8	first	first	ADJ
ejpam-6314	23	9	result	result	NOUN
ejpam-6314	23	10	in	in	ADP
ejpam-6314	23	11	metric	metric	ADJ
ejpam-6314	23	12	fixed	fix	VERB
ejpam-6314	23	13	point	point	NOUN
ejpam-6314	23	14	theory	theory	NOUN
ejpam-6314	23	15	[	[	X
ejpam-6314	23	16	5	5	NUM
ejpam-6314	23	17	]	]	PUNCT
ejpam-6314	23	18	,	,	PUNCT
ejpam-6314	23	19	many	many	ADJ
ejpam-6314	23	20	researchers	researcher	NOUN
ejpam-6314	23	21	in	in	ADP
ejpam-6314	23	22	this	this	DET
ejpam-6314	23	23	direction	direction	NOUN
ejpam-6314	23	24	put	put	VERB
ejpam-6314	23	25	forward	forward	ADP
ejpam-6314	23	26	the	the	DET
ejpam-6314	23	27	generalized	generalized	ADJ
ejpam-6314	23	28	structure	structure	NOUN
ejpam-6314	23	29	of	of	ADP
ejpam-6314	23	30	the	the	DET
ejpam-6314	23	31	contraction	contraction	NOUN
ejpam-6314	23	32	principle	principle	NOUN
ejpam-6314	23	33	.	.	PUNCT
ejpam-6314	24	1	one	one	NUM
ejpam-6314	24	2	of	of	ADP
ejpam-6314	24	3	the	the	DET
ejpam-6314	24	4	recent	recent	ADJ
ejpam-6314	24	5	generalizations	generalization	NOUN
ejpam-6314	24	6	in	in	ADP
ejpam-6314	24	7	this	this	DET
ejpam-6314	24	8	sequel	sequel	NOUN
ejpam-6314	24	9	was	be	AUX
ejpam-6314	24	10	the	the	DET
ejpam-6314	24	11	introduction	introduction	NOUN
ejpam-6314	24	12	of	of	ADP
ejpam-6314	24	13	b	b	NOUN
ejpam-6314	24	14	-	-	PUNCT
ejpam-6314	24	15	metric	metric	ADJ
ejpam-6314	24	16	space	space	NOUN
ejpam-6314	24	17	by	by	ADP
ejpam-6314	24	18	bakhtin	bakhtin	NOUN
ejpam-6314	24	19	[	[	X
ejpam-6314	24	20	6	6	NUM
ejpam-6314	24	21	]	]	PUNCT
ejpam-6314	24	22	.	.	PUNCT
ejpam-6314	25	1	in	in	ADP
ejpam-6314	25	2	generalizing	generalize	VERB
ejpam-6314	25	3	the	the	DET
ejpam-6314	25	4	metrix	metrix	NOUN
ejpam-6314	25	5	space	space	NOUN
ejpam-6314	25	6	the	the	DET
ejpam-6314	25	7	triangular	triangular	NOUN
ejpam-6314	25	8	inequality	inequality	NOUN
ejpam-6314	25	9	was	be	AUX
ejpam-6314	25	10	introduced	introduce	VERB
ejpam-6314	25	11	in	in	ADP
ejpam-6314	25	12	a	a	DET
ejpam-6314	25	13	different	different	ADJ
ejpam-6314	25	14	manner	manner	NOUN
ejpam-6314	25	15	by	by	ADP
ejpam-6314	25	16	introducing	introduce	VERB
ejpam-6314	25	17	s	s	PRON
ejpam-6314	25	18	≥	≥	NOUN
ejpam-6314	25	19	1	1	NUM
ejpam-6314	25	20	,	,	PUNCT
ejpam-6314	25	21	a	a	DET
ejpam-6314	25	22	constant	constant	ADJ
ejpam-6314	25	23	multiple	multiple	NOUN
ejpam-6314	25	24	.	.	PUNCT
ejpam-6314	26	1	this	this	DET
ejpam-6314	26	2	generalization	generalization	NOUN
ejpam-6314	26	3	leads	lead	VERB
ejpam-6314	26	4	to	to	ADP
ejpam-6314	26	5	some	some	DET
ejpam-6314	26	6	important	important	ADJ
ejpam-6314	26	7	developments	development	NOUN
ejpam-6314	26	8	notably	notably	ADV
ejpam-6314	26	9	,	,	PUNCT
ejpam-6314	26	10	extended	extended	ADJ
ejpam-6314	26	11	b	b	X
ejpam-6314	26	12	-	-	ADJ
ejpam-6314	26	13	metric	metric	ADJ
ejpam-6314	26	14	spaces	space	NOUN
ejpam-6314	26	15	,	,	PUNCT
ejpam-6314	26	16	which	which	PRON
ejpam-6314	26	17	was	be	AUX
ejpam-6314	26	18	developed	develop	VERB
ejpam-6314	26	19	by	by	ADP
ejpam-6314	26	20	kamran	kamran	PROPN
ejpam-6314	26	21	et	et	PROPN
ejpam-6314	26	22	al	al	PROPN
ejpam-6314	26	23	.	.	PUNCT
ejpam-6314	27	1	[	[	X
ejpam-6314	27	2	7	7	NUM
ejpam-6314	27	3	]	]	PUNCT
ejpam-6314	27	4	.	.	PUNCT
ejpam-6314	28	1	likewise	likewise	ADV
ejpam-6314	28	2	,	,	PUNCT
ejpam-6314	28	3	mlaiki	mlaiki	PROPN
ejpam-6314	28	4	et	et	PROPN
ejpam-6314	28	5	al.[8	al.[8	PROPN
ejpam-6314	28	6	]	]	PUNCT
ejpam-6314	28	7	presented	present	VERB
ejpam-6314	28	8	controlled	control	VERB
ejpam-6314	28	9	metric	metric	ADJ
ejpam-6314	28	10	spaces	space	NOUN
ejpam-6314	28	11	in	in	ADP
ejpam-6314	28	12	2018	2018	NUM
ejpam-6314	28	13	.	.	PUNCT
ejpam-6314	29	1	moreover	moreover	ADV
ejpam-6314	29	2	,	,	PUNCT
ejpam-6314	29	3	researcher	researcher	NOUN
ejpam-6314	29	4	expanded	expand	VERB
ejpam-6314	29	5	many	many	ADJ
ejpam-6314	29	6	results	result	NOUN
ejpam-6314	29	7	in	in	ADP
ejpam-6314	29	8	this	this	DET
ejpam-6314	29	9	space	space	NOUN
ejpam-6314	29	10	such	such	ADJ
ejpam-6314	29	11	as	as	ADP
ejpam-6314	29	12	[	[	X
ejpam-6314	29	13	9	9	NUM
ejpam-6314	29	14	,	,	PUNCT
ejpam-6314	29	15	10	10	NUM
ejpam-6314	29	16	]	]	PUNCT
ejpam-6314	29	17	in	in	ADP
ejpam-6314	29	18	this	this	DET
ejpam-6314	29	19	direction	direction	NOUN
ejpam-6314	29	20	,	,	PUNCT
ejpam-6314	29	21	the	the	DET
ejpam-6314	29	22	concept	concept	NOUN
ejpam-6314	29	23	of	of	ADP
ejpam-6314	29	24	complex	complex	ADV
ejpam-6314	29	25	-	-	PUNCT
ejpam-6314	29	26	valued	value	VERB
ejpam-6314	29	27	metric	metric	ADJ
ejpam-6314	29	28	spaces	space	NOUN
ejpam-6314	29	29	was	be	AUX
ejpam-6314	29	30	first	first	ADV
ejpam-6314	29	31	presented	present	VERB
ejpam-6314	29	32	by	by	ADP
ejpam-6314	29	33	azam	azam	PROPN
ejpam-6314	29	34	et	et	PROPN
ejpam-6314	29	35	al	al	PROPN
ejpam-6314	29	36	.	.	PUNCT
ejpam-6314	30	1	[	[	X
ejpam-6314	30	2	11	11	NUM
ejpam-6314	30	3	]	]	PUNCT
ejpam-6314	30	4	,	,	PUNCT
ejpam-6314	30	5	and	and	CCONJ
ejpam-6314	30	6	they	they	PRON
ejpam-6314	30	7	also	also	ADV
ejpam-6314	30	8	developed	develop	VERB
ejpam-6314	30	9	some	some	DET
ejpam-6314	30	10	fixed	fix	VERB
ejpam-6314	30	11	point	point	NOUN
ejpam-6314	30	12	results	result	NOUN
ejpam-6314	30	13	for	for	ADP
ejpam-6314	30	14	pairs	pair	NOUN
ejpam-6314	30	15	of	of	ADP
ejpam-6314	30	16	mappings	mapping	NOUN
ejpam-6314	30	17	that	that	PRON
ejpam-6314	30	18	fulfill	fulfill	VERB
ejpam-6314	30	19	the	the	DET
ejpam-6314	30	20	contraction	contraction	NOUN
ejpam-6314	30	21	requirement	requirement	NOUN
ejpam-6314	30	22	for	for	ADP
ejpam-6314	30	23	rational	rational	ADJ
ejpam-6314	30	24	expressions	expression	NOUN
ejpam-6314	30	25	.	.	PUNCT
ejpam-6314	31	1	furthermore	furthermore	ADV
ejpam-6314	31	2	,	,	PUNCT
ejpam-6314	31	3	segre	segre	VERB
ejpam-6314	31	4	[	[	X
ejpam-6314	31	5	12	12	NUM
ejpam-6314	31	6	]	]	PUNCT
ejpam-6314	31	7	established	establish	VERB
ejpam-6314	31	8	a	a	DET
ejpam-6314	31	9	base	base	NOUN
ejpam-6314	31	10	for	for	ADP
ejpam-6314	31	11	bi	bi	ADJ
ejpam-6314	31	12	-	-	ADJ
ejpam-6314	31	13	complex	complex	ADJ
ejpam-6314	31	14	numbers	number	NOUN
ejpam-6314	31	15	and	and	CCONJ
ejpam-6314	31	16	supported	support	VERB
ejpam-6314	31	17	a	a	DET
ejpam-6314	31	18	commutative	commutative	ADJ
ejpam-6314	31	19	replacement	replacement	NOUN
ejpam-6314	31	20	for	for	ADP
ejpam-6314	31	21	the	the	DET
ejpam-6314	31	22	skew	skew	ADJ
ejpam-6314	31	23	field	field	NOUN
ejpam-6314	31	24	of	of	ADP
ejpam-6314	31	25	quaternions	quaternion	NOUN
ejpam-6314	31	26	.	.	PUNCT
ejpam-6314	32	1	these	these	DET
ejpam-6314	32	2	numbers	number	NOUN
ejpam-6314	32	3	more	more	ADV
ejpam-6314	32	4	strongly	strongly	ADV
ejpam-6314	32	5	and	and	CCONJ
ejpam-6314	32	6	explicitly	explicitly	ADV
ejpam-6314	32	7	generalized	generalize	VERB
ejpam-6314	32	8	and	and	CCONJ
ejpam-6314	32	9	extended	extend	VERB
ejpam-6314	32	10	the	the	DET
ejpam-6314	32	11	complex	complex	ADJ
ejpam-6314	32	12	numbers	number	NOUN
ejpam-6314	32	13	to	to	ADP
ejpam-6314	32	14	quaternions	quaternion	NOUN
ejpam-6314	32	15	.	.	PUNCT
ejpam-6314	33	1	bi	bi	ADJ
ejpam-6314	33	2	-	-	ADJ
ejpam-6314	33	3	complex	complex	ADJ
ejpam-6314	33	4	valued	value	VERB
ejpam-6314	33	5	metric	metric	ADJ
ejpam-6314	33	6	spaces	space	NOUN
ejpam-6314	33	7	(	(	PUNCT
ejpam-6314	33	8	bcvms	bcvms	NOUN
ejpam-6314	33	9	)	)	PUNCT
ejpam-6314	33	10	were	be	AUX
ejpam-6314	33	11	first	first	ADV
ejpam-6314	33	12	proposed	propose	VERB
ejpam-6314	33	13	by	by	ADP
ejpam-6314	33	14	choi	choi	PROPN
ejpam-6314	33	15	et	et	PROPN
ejpam-6314	33	16	al	al	PROPN
ejpam-6314	33	17	.	.	PROPN
ejpam-6314	34	1	in	in	ADP
ejpam-6314	34	2	2017	2017	NUM
ejpam-6314	34	3	[	[	SYM
ejpam-6314	34	4	13	13	NUM
ejpam-6314	34	5	]	]	PUNCT
ejpam-6314	34	6	,	,	PUNCT
ejpam-6314	34	7	who	who	PRON
ejpam-6314	34	8	connected	connect	VERB
ejpam-6314	34	9	the	the	DET
ejpam-6314	34	10	two	two	NUM
ejpam-6314	34	11	ideas	idea	NOUN
ejpam-6314	34	12	,	,	PUNCT
ejpam-6314	34	13	bi	bi	ADJ
ejpam-6314	34	14	-	-	ADJ
ejpam-6314	34	15	complex	complex	ADJ
ejpam-6314	34	16	numbers	number	NOUN
ejpam-6314	34	17	and	and	CCONJ
ejpam-6314	34	18	complex	complex	ADV
ejpam-6314	34	19	-	-	PUNCT
ejpam-6314	34	20	valued	value	VERB
ejpam-6314	34	21	metric	metric	ADJ
ejpam-6314	34	22	spaces	space	NOUN
ejpam-6314	34	23	.	.	PUNCT
ejpam-6314	35	1	they	they	PRON
ejpam-6314	35	2	developed	develop	VERB
ejpam-6314	35	3	common	common	ADJ
ejpam-6314	35	4	fixedpoint	fixedpoint	NOUN
ejpam-6314	35	5	outcomes	outcome	NOUN
ejpam-6314	35	6	for	for	ADP
ejpam-6314	35	7	weakly	weakly	ADJ
ejpam-6314	35	8	compatible	compatible	ADJ
ejpam-6314	35	9	mappings	mapping	NOUN
ejpam-6314	35	10	.	.	PUNCT
ejpam-6314	36	1	a	a	DET
ejpam-6314	36	2	contractive	contractive	ADJ
ejpam-6314	36	3	type	type	NOUN
ejpam-6314	36	4	common	common	ADJ
ejpam-6314	36	5	fixed	fix	VERB
ejpam-6314	36	6	point	point	NOUN
ejpam-6314	36	7	for	for	ADP
ejpam-6314	36	8	two	two	NUM
ejpam-6314	36	9	maps	map	NOUN
ejpam-6314	36	10	in	in	ADP
ejpam-6314	36	11	bicomplex	bicomplex	NOUN
ejpam-6314	36	12	-	-	PUNCT
ejpam-6314	36	13	valued	value	VERB
ejpam-6314	36	14	metric	metric	ADJ
ejpam-6314	36	15	spaces	space	NOUN
ejpam-6314	36	16	was	be	AUX
ejpam-6314	36	17	established	establish	VERB
ejpam-6314	36	18	by	by	ADP
ejpam-6314	36	19	[	[	X
ejpam-6314	36	20	14	14	NUM
ejpam-6314	36	21	]	]	PUNCT
ejpam-6314	36	22	.	.	PUNCT
ejpam-6314	37	1	later	later	ADV
ejpam-6314	37	2	,	,	PUNCT
ejpam-6314	37	3	several	several	ADJ
ejpam-6314	37	4	researchers	researcher	NOUN
ejpam-6314	37	5	used	use	VERB
ejpam-6314	37	6	this	this	DET
ejpam-6314	37	7	notion	notion	NOUN
ejpam-6314	37	8	to	to	PART
ejpam-6314	37	9	describe	describe	VERB
ejpam-6314	37	10	their	their	PRON
ejpam-6314	37	11	results	result	NOUN
ejpam-6314	37	12	;	;	PUNCT
ejpam-6314	37	13	see	see	VERB
ejpam-6314	37	14	[	[	X
ejpam-6314	37	15	15–22	15–22	NUM
ejpam-6314	37	16	]	]	PUNCT
ejpam-6314	37	17	.	.	PUNCT
ejpam-6314	38	1	guechi	guechi	PROPN
ejpam-6314	38	2	[	[	X
ejpam-6314	38	3	23	23	NUM
ejpam-6314	38	4	]	]	PUNCT
ejpam-6314	38	5	first	first	ADV
ejpam-6314	38	6	discussed	discuss	VERB
ejpam-6314	38	7	the	the	DET
ejpam-6314	38	8	idea	idea	NOUN
ejpam-6314	38	9	of	of	ADP
ejpam-6314	38	10	optimum	optimum	ADJ
ejpam-6314	38	11	control	control	NOUN
ejpam-6314	38	12	for	for	ADP
ejpam-6314	38	13	hilfer	hilfer	NOUN
ejpam-6314	38	14	fractional	fractional	ADJ
ejpam-6314	38	15	equations	equation	NOUN
ejpam-6314	38	16	and	and	CCONJ
ejpam-6314	38	17	demonstrated	demonstrate	VERB
ejpam-6314	38	18	fixed	fix	VERB
ejpam-6314	38	19	-	-	PUNCT
ejpam-6314	38	20	point	point	NOUN
ejpam-6314	38	21	outcomes	outcome	NOUN
ejpam-6314	38	22	.	.	PUNCT
ejpam-6314	39	1	similarly	similarly	ADV
ejpam-6314	39	2	,	,	PUNCT
ejpam-6314	39	3	inspired	inspire	VERB
ejpam-6314	39	4	by	by	ADP
ejpam-6314	39	5	the	the	DET
ejpam-6314	39	6	above	above	ADJ
ejpam-6314	39	7	work	work	NOUN
ejpam-6314	39	8	,	,	PUNCT
ejpam-6314	39	9	g.mani	g.mani	NOUN
ejpam-6314	39	10	and	and	CCONJ
ejpam-6314	39	11	s.haque	s.haque	NOUN
ejpam-6314	39	12	at	at	ADP
ejpam-6314	39	13	[	[	X
ejpam-6314	39	14	24	24	NUM
ejpam-6314	39	15	]	]	PUNCT
ejpam-6314	39	16	investigate	investigate	VERB
ejpam-6314	39	17	the	the	DET
ejpam-6314	39	18	existence	existence	NOUN
ejpam-6314	39	19	of	of	ADP
ejpam-6314	39	20	a	a	DET
ejpam-6314	39	21	unique	unique	ADJ
ejpam-6314	39	22	solution	solution	NOUN
ejpam-6314	39	23	of	of	ADP
ejpam-6314	39	24	the	the	DET
ejpam-6314	39	25	fractional	fractional	ADJ
ejpam-6314	39	26	differential	differential	ADJ
ejpam-6314	39	27	equation	equation	NOUN
ejpam-6314	39	28	in	in	ADP
ejpam-6314	39	29	a	a	DET
ejpam-6314	39	30	bi	bi	NOUN
ejpam-6314	39	31	-	-	ADJ
ejpam-6314	39	32	complex	complex	ADJ
ejpam-6314	39	33	,	,	PUNCT
ejpam-6314	39	34	controlled	control	VERB
ejpam-6314	39	35	metric	metric	ADJ
ejpam-6314	39	36	space	space	NOUN
ejpam-6314	39	37	.	.	PUNCT
ejpam-6314	40	1	in	in	ADP
ejpam-6314	40	2	the	the	DET
ejpam-6314	40	3	realm	realm	NOUN
ejpam-6314	40	4	of	of	ADP
ejpam-6314	40	5	fixed	fix	VERB
ejpam-6314	40	6	point	point	NOUN
ejpam-6314	40	7	theory	theory	NOUN
ejpam-6314	40	8	,	,	PUNCT
ejpam-6314	40	9	the	the	DET
ejpam-6314	40	10	exploration	exploration	NOUN
ejpam-6314	40	11	of	of	ADP
ejpam-6314	40	12	results	result	NOUN
ejpam-6314	40	13	within	within	ADP
ejpam-6314	40	14	bi	bi	ADJ
ejpam-6314	40	15	-	-	ADJ
ejpam-6314	40	16	complex	complex	ADJ
ejpam-6314	40	17	valued	value	VERB
ejpam-6314	40	18	metric	metric	ADJ
ejpam-6314	40	19	spaces	space	NOUN
ejpam-6314	40	20	holds	hold	VERB
ejpam-6314	40	21	substantial	substantial	ADJ
ejpam-6314	40	22	significance	significance	NOUN
ejpam-6314	40	23	due	due	ADP
ejpam-6314	40	24	to	to	ADP
ejpam-6314	40	25	the	the	DET
ejpam-6314	40	26	enriched	enriched	ADJ
ejpam-6314	40	27	algebraic	algebraic	ADJ
ejpam-6314	40	28	and	and	CCONJ
ejpam-6314	40	29	topological	topological	ADJ
ejpam-6314	40	30	structures	structure	NOUN
ejpam-6314	40	31	these	these	DET
ejpam-6314	40	32	spaces	space	NOUN
ejpam-6314	40	33	exhibit	exhibit	VERB
ejpam-6314	40	34	in	in	ADP
ejpam-6314	40	35	comparison	comparison	NOUN
ejpam-6314	40	36	to	to	ADP
ejpam-6314	40	37	classical	classical	ADJ
ejpam-6314	40	38	and	and	CCONJ
ejpam-6314	40	39	even	even	ADV
ejpam-6314	40	40	complex	complex	ADV
ejpam-6314	40	41	-	-	PUNCT
ejpam-6314	40	42	valued	value	VERB
ejpam-6314	40	43	metric	metric	ADJ
ejpam-6314	40	44	spaces	space	NOUN
ejpam-6314	40	45	.	.	PUNCT
ejpam-6314	41	1	bi	bi	ADJ
ejpam-6314	41	2	-	-	ADJ
ejpam-6314	41	3	complex	complex	ADJ
ejpam-6314	41	4	numbers	number	NOUN
ejpam-6314	41	5	,	,	PUNCT
ejpam-6314	41	6	which	which	PRON
ejpam-6314	41	7	generalize	generalize	VERB
ejpam-6314	41	8	complex	complex	ADJ
ejpam-6314	41	9	numbers	number	NOUN
ejpam-6314	41	10	by	by	ADP
ejpam-6314	41	11	incorporating	incorporate	VERB
ejpam-6314	41	12	two	two	NUM
ejpam-6314	41	13	imaginary	imaginary	ADJ
ejpam-6314	41	14	units	unit	NOUN
ejpam-6314	41	15	,	,	PUNCT
ejpam-6314	41	16	provide	provide	VERB
ejpam-6314	41	17	a	a	DET
ejpam-6314	41	18	more	more	ADV
ejpam-6314	41	19	flexible	flexible	ADJ
ejpam-6314	41	20	and	and	CCONJ
ejpam-6314	41	21	comprehensive	comprehensive	ADJ
ejpam-6314	41	22	framework	framework	NOUN
ejpam-6314	41	23	for	for	ADP
ejpam-6314	41	24	analyzing	analyze	VERB
ejpam-6314	41	25	various	various	ADJ
ejpam-6314	41	26	mathematical	mathematical	ADJ
ejpam-6314	41	27	models	model	NOUN
ejpam-6314	41	28	.	.	PUNCT
ejpam-6314	42	1	this	this	DET
ejpam-6314	42	2	generalization	generalization	NOUN
ejpam-6314	42	3	is	be	AUX
ejpam-6314	42	4	particularly	particularly	ADV
ejpam-6314	42	5	beneficial	beneficial	ADJ
ejpam-6314	42	6	in	in	ADP
ejpam-6314	42	7	domains	domain	NOUN
ejpam-6314	42	8	m.	m.	NOUN
ejpam-6314	42	9	sarwar	sarwar	PROPN
ejpam-6314	42	10	et	et	PROPN
ejpam-6314	43	1	al	al	PROPN
ejpam-6314	43	2	.	.	PUNCT
ejpam-6314	43	3	/	/	SYM
ejpam-6314	43	4	eur	eur	PROPN
ejpam-6314	43	5	.	.	PUNCT
ejpam-6314	44	1	j.	j.	PROPN
ejpam-6314	44	2	pure	pure	PROPN
ejpam-6314	44	3	appl	appl	PROPN
ejpam-6314	44	4	.	.	PROPN
ejpam-6314	44	5	math	math	PROPN
ejpam-6314	44	6	,	,	PUNCT
ejpam-6314	44	7	18	18	NUM
ejpam-6314	44	8	(	(	PUNCT
ejpam-6314	44	9	3	3	NUM
ejpam-6314	44	10	)	)	PUNCT
ejpam-6314	44	11	(	(	PUNCT
ejpam-6314	44	12	2025	2025	NUM
ejpam-6314	44	13	)	)	PUNCT
ejpam-6314	44	14	,	,	PUNCT
ejpam-6314	44	15	6314	6314	NUM
ejpam-6314	44	16	3	3	NUM
ejpam-6314	44	17	of	of	ADP
ejpam-6314	44	18	28	28	NUM
ejpam-6314	44	19	involving	involve	VERB
ejpam-6314	44	20	multidimensional	multidimensional	ADJ
ejpam-6314	44	21	or	or	CCONJ
ejpam-6314	44	22	hyper	hyper	ADJ
ejpam-6314	44	23	-	-	ADJ
ejpam-6314	44	24	complex	complex	ADJ
ejpam-6314	44	25	systems	system	NOUN
ejpam-6314	44	26	,	,	PUNCT
ejpam-6314	44	27	such	such	ADJ
ejpam-6314	44	28	as	as	ADP
ejpam-6314	44	29	quantum	quantum	ADJ
ejpam-6314	44	30	mechanics	mechanic	NOUN
ejpam-6314	44	31	,	,	PUNCT
ejpam-6314	44	32	signal	signal	NOUN
ejpam-6314	44	33	processing	processing	NOUN
ejpam-6314	44	34	,	,	PUNCT
ejpam-6314	44	35	and	and	CCONJ
ejpam-6314	44	36	dynamic	dynamic	ADJ
ejpam-6314	44	37	systems	system	NOUN
ejpam-6314	44	38	analysis	analysis	NOUN
ejpam-6314	44	39	.	.	PUNCT
ejpam-6314	45	1	the	the	DET
ejpam-6314	45	2	inherent	inherent	ADJ
ejpam-6314	45	3	complexity	complexity	NOUN
ejpam-6314	45	4	of	of	ADP
ejpam-6314	45	5	bi	bi	ADJ
ejpam-6314	45	6	-	-	ADJ
ejpam-6314	45	7	complex	complex	ADJ
ejpam-6314	45	8	valued	value	VERB
ejpam-6314	45	9	metric	metric	ADJ
ejpam-6314	45	10	spaces	space	NOUN
ejpam-6314	45	11	allows	allow	VERB
ejpam-6314	45	12	researchers	researcher	NOUN
ejpam-6314	45	13	to	to	PART
ejpam-6314	45	14	investigate	investigate	VERB
ejpam-6314	45	15	more	more	ADV
ejpam-6314	45	16	intricate	intricate	ADJ
ejpam-6314	45	17	contraction	contraction	NOUN
ejpam-6314	45	18	mappings	mapping	NOUN
ejpam-6314	45	19	and	and	CCONJ
ejpam-6314	45	20	convergence	convergence	NOUN
ejpam-6314	45	21	behaviors	behavior	NOUN
ejpam-6314	45	22	that	that	PRON
ejpam-6314	45	23	may	may	AUX
ejpam-6314	45	24	not	not	PART
ejpam-6314	45	25	be	be	AUX
ejpam-6314	45	26	adequately	adequately	ADV
ejpam-6314	45	27	represented	represent	VERB
ejpam-6314	45	28	in	in	ADP
ejpam-6314	45	29	traditional	traditional	ADJ
ejpam-6314	45	30	settings	setting	NOUN
ejpam-6314	45	31	.	.	PUNCT
ejpam-6314	46	1	this	this	DET
ejpam-6314	46	2	adaptability	adaptability	NOUN
ejpam-6314	46	3	not	not	PART
ejpam-6314	46	4	only	only	ADV
ejpam-6314	46	5	broadens	broaden	VERB
ejpam-6314	46	6	the	the	DET
ejpam-6314	46	7	applicability	applicability	NOUN
ejpam-6314	46	8	of	of	ADP
ejpam-6314	46	9	fixed	fix	VERB
ejpam-6314	46	10	point	point	NOUN
ejpam-6314	46	11	results	result	NOUN
ejpam-6314	46	12	but	but	CCONJ
ejpam-6314	46	13	also	also	ADV
ejpam-6314	46	14	facilitates	facilitate	VERB
ejpam-6314	46	15	the	the	DET
ejpam-6314	46	16	development	development	NOUN
ejpam-6314	46	17	of	of	ADP
ejpam-6314	46	18	novel	novel	ADJ
ejpam-6314	46	19	theorems	theorem	NOUN
ejpam-6314	46	20	and	and	CCONJ
ejpam-6314	46	21	techniques	technique	NOUN
ejpam-6314	46	22	tailored	tailor	VERB
ejpam-6314	46	23	for	for	ADP
ejpam-6314	46	24	more	more	ADV
ejpam-6314	46	25	abstract	abstract	ADJ
ejpam-6314	46	26	and	and	CCONJ
ejpam-6314	46	27	challenging	challenging	ADJ
ejpam-6314	46	28	mathematical	mathematical	ADJ
ejpam-6314	46	29	problems	problem	NOUN
ejpam-6314	46	30	.	.	PUNCT
ejpam-6314	47	1	moreover	moreover	ADV
ejpam-6314	47	2	,	,	PUNCT
ejpam-6314	47	3	fixed	fixed	ADJ
ejpam-6314	47	4	point	point	NOUN
ejpam-6314	47	5	results	result	NOUN
ejpam-6314	47	6	in	in	ADP
ejpam-6314	47	7	bi	bi	ADJ
ejpam-6314	47	8	-	-	ADJ
ejpam-6314	47	9	complex	complex	ADJ
ejpam-6314	47	10	settings	setting	NOUN
ejpam-6314	47	11	serve	serve	VERB
ejpam-6314	47	12	to	to	PART
ejpam-6314	47	13	unify	unify	VERB
ejpam-6314	47	14	and	and	CCONJ
ejpam-6314	47	15	generalize	generalize	VERB
ejpam-6314	47	16	existing	exist	VERB
ejpam-6314	47	17	results	result	NOUN
ejpam-6314	47	18	in	in	ADP
ejpam-6314	47	19	real	real	ADJ
ejpam-6314	47	20	,	,	PUNCT
ejpam-6314	47	21	complex	complex	ADJ
ejpam-6314	47	22	,	,	PUNCT
ejpam-6314	47	23	and	and	CCONJ
ejpam-6314	47	24	complex	complex	ADV
ejpam-6314	47	25	-	-	PUNCT
ejpam-6314	47	26	valued	value	VERB
ejpam-6314	47	27	metric	metric	ADJ
ejpam-6314	47	28	spaces	space	NOUN
ejpam-6314	47	29	.	.	PUNCT
ejpam-6314	48	1	as	as	ADP
ejpam-6314	48	2	a	a	DET
ejpam-6314	48	3	result	result	NOUN
ejpam-6314	48	4	,	,	PUNCT
ejpam-6314	48	5	they	they	PRON
ejpam-6314	48	6	contribute	contribute	VERB
ejpam-6314	48	7	to	to	ADP
ejpam-6314	48	8	a	a	DET
ejpam-6314	48	9	deeper	deep	ADJ
ejpam-6314	48	10	understanding	understanding	NOUN
ejpam-6314	48	11	and	and	CCONJ
ejpam-6314	48	12	a	a	DET
ejpam-6314	48	13	more	more	ADV
ejpam-6314	48	14	universally	universally	ADV
ejpam-6314	48	15	applicable	applicable	ADJ
ejpam-6314	48	16	theoretical	theoretical	ADJ
ejpam-6314	48	17	foundation	foundation	NOUN
ejpam-6314	48	18	within	within	ADP
ejpam-6314	48	19	the	the	DET
ejpam-6314	48	20	scope	scope	NOUN
ejpam-6314	48	21	of	of	ADP
ejpam-6314	48	22	fixed	fix	VERB
ejpam-6314	48	23	point	point	NOUN
ejpam-6314	48	24	theory	theory	NOUN
ejpam-6314	48	25	.	.	PUNCT
ejpam-6314	49	1	the	the	DET
ejpam-6314	49	2	current	current	ADJ
ejpam-6314	49	3	manuscript	manuscript	NOUN
ejpam-6314	49	4	illustrates	illustrate	VERB
ejpam-6314	49	5	some	some	DET
ejpam-6314	49	6	unique	unique	ADJ
ejpam-6314	49	7	common	common	ADJ
ejpam-6314	49	8	fixed	fix	VERB
ejpam-6314	49	9	point	point	NOUN
ejpam-6314	49	10	results	result	NOUN
ejpam-6314	49	11	on	on	ADP
ejpam-6314	49	12	(	(	PUNCT
ejpam-6314	49	13	bcvms	bcvms	NOUN
ejpam-6314	49	14	)	)	PUNCT
ejpam-6314	49	15	.	.	PUNCT
ejpam-6314	50	1	then	then	ADV
ejpam-6314	50	2	,	,	PUNCT
ejpam-6314	50	3	we	we	PRON
ejpam-6314	50	4	provide	provide	VERB
ejpam-6314	50	5	an	an	DET
ejpam-6314	50	6	application	application	NOUN
ejpam-6314	50	7	to	to	PART
ejpam-6314	50	8	identify	identify	VERB
ejpam-6314	50	9	the	the	DET
ejpam-6314	50	10	unique	unique	ADJ
ejpam-6314	50	11	common	common	ADJ
ejpam-6314	50	12	solution	solution	NOUN
ejpam-6314	50	13	for	for	ADP
ejpam-6314	50	14	the	the	DET
ejpam-6314	50	15	fractional	fractional	ADJ
ejpam-6314	50	16	differential	differential	ADJ
ejpam-6314	50	17	equation	equation	NOUN
ejpam-6314	50	18	(	(	PUNCT
ejpam-6314	50	19	fde	fde	NOUN
ejpam-6314	50	20	)	)	PUNCT
ejpam-6314	50	21	system	system	NOUN
ejpam-6314	50	22	.	.	PUNCT
ejpam-6314	51	1	{	{	PUNCT
ejpam-6314	51	2	ϵdβℵ(y	ϵdβℵ(y	NOUN
ejpam-6314	51	3	)	)	PUNCT
ejpam-6314	51	4	+	+	CCONJ
ejpam-6314	51	5	ϑ(y	ϑ(y	PROPN
ejpam-6314	51	6	,	,	PUNCT
ejpam-6314	51	7	λ(y	λ(y	PROPN
ejpam-6314	51	8	)	)	PUNCT
ejpam-6314	51	9	)	)	PUNCT
ejpam-6314	52	1	=	=	SYM
ejpam-6314	52	2	0	0	NUM
ejpam-6314	52	3	,	,	PUNCT
ejpam-6314	52	4	ϵdβω(y	ϵdβω(y	NUM
ejpam-6314	52	5	)	)	PUNCT
ejpam-6314	53	1	+	+	CCONJ
ejpam-6314	53	2	υ(y	υ(y	PROPN
ejpam-6314	53	3	,	,	PUNCT
ejpam-6314	53	4	χ(y	χ(y	NOUN
ejpam-6314	53	5	)	)	PUNCT
ejpam-6314	53	6	)	)	PUNCT
ejpam-6314	54	1	=	=	SYM
ejpam-6314	54	2	0	0	NUM
ejpam-6314	54	3	,	,	PUNCT
ejpam-6314	54	4	1	1	NUM
ejpam-6314	54	5	<	<	X
ejpam-6314	54	6	ϵ	ϵ	X
ejpam-6314	54	7	≤	≤	NUM
ejpam-6314	54	8	2,y	2,y	NUM
ejpam-6314	54	9	∈	∈	PROPN
ejpam-6314	55	1	[	[	X
ejpam-6314	55	2	0	0	NUM
ejpam-6314	55	3	,	,	PUNCT
ejpam-6314	55	4	1	1	NUM
ejpam-6314	55	5	]	]	PUNCT
ejpam-6314	55	6	.	.	PUNCT
ejpam-6314	56	1	λ(0	λ(0	NOUN
ejpam-6314	56	2	)	)	PUNCT
ejpam-6314	56	3	=	=	SYM
ejpam-6314	56	4	ω(0	ω(0	PROPN
ejpam-6314	56	5	)	)	PUNCT
ejpam-6314	56	6	=	=	SYM
ejpam-6314	56	7	ℓ,λ(1	ℓ,λ(1	X
ejpam-6314	56	8	)	)	PUNCT
ejpam-6314	56	9	=	=	PUNCT
ejpam-6314	57	1	ω(1	ω(1	PROPN
ejpam-6314	57	2	)	)	PUNCT
ejpam-6314	57	3	=	=	SYM
ejpam-6314	57	4	ȷ	ȷ	NOUN
ejpam-6314	57	5	,	,	PUNCT
ejpam-6314	57	6	where	where	SCONJ
ejpam-6314	57	7	ℓ	ℓ	NOUN
ejpam-6314	57	8	and	and	CCONJ
ejpam-6314	57	9	ȷ	ȷ	PROPN
ejpam-6314	57	10	are	be	AUX
ejpam-6314	57	11	constant	constant	ADJ
ejpam-6314	57	12	.	.	PUNCT
ejpam-6314	58	1	where	where	SCONJ
ejpam-6314	58	2	ϵdβ	ϵdβ	PROPN
ejpam-6314	58	3	represent	represent	VERB
ejpam-6314	58	4	the	the	DET
ejpam-6314	58	5	order	order	NOUN
ejpam-6314	58	6	of	of	ADP
ejpam-6314	58	7	β	β	PRON
ejpam-6314	58	8	as	as	ADP
ejpam-6314	58	9	the	the	DET
ejpam-6314	58	10	caputo	caputo	PROPN
ejpam-6314	58	11	fractional	fractional	ADJ
ejpam-6314	58	12	derivatives	derivative	NOUN
ejpam-6314	58	13	and	and	CCONJ
ejpam-6314	58	14	λ.ω	λ.ω	NOUN
ejpam-6314	58	15	:	:	PUNCT
ejpam-6314	59	1	[	[	X
ejpam-6314	59	2	0	0	NUM
ejpam-6314	59	3	,	,	PUNCT
ejpam-6314	59	4	1]×	1]×	NUM
ejpam-6314	59	5	[	[	X
ejpam-6314	59	6	0,+∞	0,+∞	NUM
ejpam-6314	59	7	)	)	PUNCT
ejpam-6314	59	8	→	→	PUNCT
ejpam-6314	60	1	[	[	X
ejpam-6314	60	2	0,+∞	0,+∞	NUM
ejpam-6314	60	3	)	)	PUNCT
ejpam-6314	60	4	.	.	PUNCT
ejpam-6314	61	1	in	in	ADP
ejpam-6314	61	2	the	the	DET
ejpam-6314	61	3	subsequent	subsequent	ADJ
ejpam-6314	61	4	sections	section	NOUN
ejpam-6314	61	5	,	,	PUNCT
ejpam-6314	61	6	we	we	PRON
ejpam-6314	61	7	will	will	AUX
ejpam-6314	61	8	review	review	VERB
ejpam-6314	61	9	fundamental	fundamental	ADJ
ejpam-6314	61	10	definitions	definition	NOUN
ejpam-6314	61	11	and	and	CCONJ
ejpam-6314	61	12	notations	notation	NOUN
ejpam-6314	61	13	derived	derive	VERB
ejpam-6314	61	14	from	from	ADP
ejpam-6314	61	15	existing	exist	VERB
ejpam-6314	61	16	literature	literature	NOUN
ejpam-6314	61	17	,	,	PUNCT
ejpam-6314	61	18	which	which	PRON
ejpam-6314	61	19	will	will	AUX
ejpam-6314	61	20	be	be	AUX
ejpam-6314	61	21	employed	employ	VERB
ejpam-6314	61	22	throughout	throughout	ADP
ejpam-6314	61	23	the	the	DET
ejpam-6314	61	24	remainder	remainder	NOUN
ejpam-6314	61	25	of	of	ADP
ejpam-6314	61	26	this	this	DET
ejpam-6314	61	27	work	work	NOUN
ejpam-6314	61	28	.	.	PUNCT
ejpam-6314	62	1	throughout	throughout	ADP
ejpam-6314	62	2	the	the	DET
ejpam-6314	62	3	manuscript	manuscript	NOUN
ejpam-6314	62	4	,	,	PUNCT
ejpam-6314	62	5	we	we	PRON
ejpam-6314	62	6	represent	represent	VERB
ejpam-6314	62	7	the	the	DET
ejpam-6314	62	8	sets	set	NOUN
ejpam-6314	62	9	of	of	ADP
ejpam-6314	62	10	real	real	ADJ
ejpam-6314	62	11	,	,	PUNCT
ejpam-6314	62	12	complex	complex	ADJ
ejpam-6314	62	13	,	,	PUNCT
ejpam-6314	62	14	and	and	CCONJ
ejpam-6314	62	15	bi	bi	ADJ
ejpam-6314	62	16	-	-	ADJ
ejpam-6314	62	17	complex	complex	ADJ
ejpam-6314	62	18	numbers	number	NOUN
ejpam-6314	62	19	by	by	ADP
ejpam-6314	62	20	c0	c0	PROPN
ejpam-6314	62	21	,	,	PUNCT
ejpam-6314	62	22	c1	c1	PROPN
ejpam-6314	62	23	,	,	PUNCT
ejpam-6314	62	24	and	and	CCONJ
ejpam-6314	62	25	c2	c2	PROPN
ejpam-6314	62	26	,	,	PUNCT
ejpam-6314	62	27	respectively	respectively	ADV
ejpam-6314	62	28	.	.	PUNCT
ejpam-6314	63	1	segre	segre	VERB
ejpam-6314	64	1	[	[	X
ejpam-6314	64	2	12	12	NUM
ejpam-6314	64	3	]	]	PUNCT
ejpam-6314	64	4	provided	provide	VERB
ejpam-6314	64	5	the	the	DET
ejpam-6314	64	6	following	follow	VERB
ejpam-6314	64	7	list	list	NOUN
ejpam-6314	64	8	of	of	ADP
ejpam-6314	64	9	complex	complex	ADJ
ejpam-6314	64	10	numbers	number	NOUN
ejpam-6314	64	11	.	.	PUNCT
ejpam-6314	65	1	γ	γ	X
ejpam-6314	65	2	=	=	SYM
ejpam-6314	65	3	℘1	℘1	PROPN
ejpam-6314	65	4	+	+	CCONJ
ejpam-6314	65	5	℘2i1	℘2i1	NOUN
ejpam-6314	65	6	,	,	PUNCT
ejpam-6314	65	7	where	where	SCONJ
ejpam-6314	65	8	℘1	℘1	NOUN
ejpam-6314	65	9	,	,	PUNCT
ejpam-6314	65	10	℘2	℘2	PROPN
ejpam-6314	65	11	∈	∈	PROPN
ejpam-6314	65	12	c0	c0	NOUN
ejpam-6314	65	13	,	,	PUNCT
ejpam-6314	65	14	i	i	NOUN
ejpam-6314	65	15	2	2	NUM
ejpam-6314	65	16	1	1	NUM
ejpam-6314	65	17	=	=	SYM
ejpam-6314	65	18	−1	−1	NOUN
ejpam-6314	65	19	.	.	PUNCT
ejpam-6314	66	1	c1	c1	PROPN
ejpam-6314	66	2	is	be	AUX
ejpam-6314	66	3	represented	represent	VERB
ejpam-6314	66	4	as	as	SCONJ
ejpam-6314	66	5	follows	follow	VERB
ejpam-6314	66	6	:	:	PUNCT
ejpam-6314	66	7	c1	c1	PROPN
ejpam-6314	66	8	=	=	PROPN
ejpam-6314	66	9	{	{	PUNCT
ejpam-6314	66	10	γ	γ	X
ejpam-6314	66	11	:	:	PUNCT
ejpam-6314	66	12	γ	γ	X
ejpam-6314	66	13	=	=	SYM
ejpam-6314	66	14	℘1	℘1	PROPN
ejpam-6314	66	15	+	+	CCONJ
ejpam-6314	66	16	℘2i1	℘2i1	NOUN
ejpam-6314	66	17	,	,	PUNCT
ejpam-6314	66	18	℘1	℘1	NOUN
ejpam-6314	66	19	,	,	PUNCT
ejpam-6314	66	20	℘2	℘2	PROPN
ejpam-6314	66	21	∈	∈	PROPN
ejpam-6314	66	22	c0	c0	NOUN
ejpam-6314	66	23	}	}	PUNCT
ejpam-6314	66	24	.	.	PUNCT
ejpam-6314	67	1	let	let	VERB
ejpam-6314	67	2	γ	γ	PROPN
ejpam-6314	67	3	∈	∈	PROPN
ejpam-6314	67	4	c1	c1	NOUN
ejpam-6314	67	5	,	,	PUNCT
ejpam-6314	67	6	then	then	ADV
ejpam-6314	67	7	|γ|	|γ|	PROPN
ejpam-6314	67	8	=	=	SYM
ejpam-6314	67	9	(	(	PUNCT
ejpam-6314	67	10	℘2	℘2	NOUN
ejpam-6314	67	11	1	1	NUM
ejpam-6314	67	12	+	+	CCONJ
ejpam-6314	67	13	℘2	℘2	NOUN
ejpam-6314	67	14	2	2	NUM
ejpam-6314	67	15	)	)	PUNCT
ejpam-6314	67	16	1/2	1/2	NUM
ejpam-6314	67	17	.	.	PUNCT
ejpam-6314	68	1	all	all	DET
ejpam-6314	68	2	entries	entry	NOUN
ejpam-6314	68	3	in	in	ADP
ejpam-6314	68	4	c1	c1	PROPN
ejpam-6314	68	5	with	with	ADP
ejpam-6314	68	6	a	a	DET
ejpam-6314	68	7	real	real	ADV
ejpam-6314	68	8	-	-	PUNCT
ejpam-6314	68	9	valued	value	VERB
ejpam-6314	68	10	positive	positive	ADJ
ejpam-6314	68	11	norm	norm	NOUN
ejpam-6314	68	12	function	function	VERB
ejpam-6314	68	13	∥	∥	PUNCT
ejpam-6314	68	14	·	·	PUNCT
ejpam-6314	68	15	∥	∥	X
ejpam-6314	68	16	:	:	PUNCT
ejpam-6314	68	17	c1	c1	PROPN
ejpam-6314	68	18	→	→	SYM
ejpam-6314	68	19	c+	c+	X
ejpam-6314	68	20	0	0	NUM
ejpam-6314	68	21	is	be	AUX
ejpam-6314	68	22	defined	define	VERB
ejpam-6314	68	23	by	by	ADP
ejpam-6314	68	24	∥γ∥	∥γ∥	NOUN
ejpam-6314	68	25	=	=	SYM
ejpam-6314	68	26	(	(	PUNCT
ejpam-6314	68	27	℘2	℘2	NOUN
ejpam-6314	68	28	1	1	NUM
ejpam-6314	68	29	+	+	CCONJ
ejpam-6314	68	30	℘2	℘2	NOUN
ejpam-6314	68	31	2	2	NUM
ejpam-6314	68	32	)	)	PUNCT
ejpam-6314	68	33	1/2	1/2	NUM
ejpam-6314	68	34	.	.	PUNCT
ejpam-6314	69	1	segre	segre	VERB
ejpam-6314	69	2	[	[	X
ejpam-6314	69	3	12	12	NUM
ejpam-6314	69	4	]	]	PUNCT
ejpam-6314	69	5	described	describe	VERB
ejpam-6314	69	6	the	the	DET
ejpam-6314	69	7	bi	bi	ADJ
ejpam-6314	69	8	-	-	ADJ
ejpam-6314	69	9	complex	complex	ADJ
ejpam-6314	69	10	number	number	NOUN
ejpam-6314	69	11	(	(	PUNCT
ejpam-6314	69	12	bcn	bcn	PROPN
ejpam-6314	69	13	)	)	PUNCT
ejpam-6314	69	14	as	as	ADP
ejpam-6314	69	15	:	:	PUNCT
ejpam-6314	69	16	χ	χ	X
ejpam-6314	69	17	=	=	PUNCT
ejpam-6314	69	18	℘1	℘1	VERB
ejpam-6314	69	19	+	+	CCONJ
ejpam-6314	69	20	℘2i1	℘2i1	NOUN
ejpam-6314	69	21	+	+	CCONJ
ejpam-6314	69	22	℘3i2	℘3i2	PROPN
ejpam-6314	69	23	+	+	CCONJ
ejpam-6314	69	24	℘4i1i2	℘4i1i2	NUM
ejpam-6314	69	25	,	,	PUNCT
ejpam-6314	69	26	where	where	SCONJ
ejpam-6314	69	27	℘1	℘1	NOUN
ejpam-6314	69	28	,	,	PUNCT
ejpam-6314	69	29	℘2	℘2	PROPN
ejpam-6314	69	30	,	,	PUNCT
ejpam-6314	69	31	℘3	℘3	ADJ
ejpam-6314	69	32	,	,	PUNCT
ejpam-6314	69	33	℘4	℘4	PROPN
ejpam-6314	69	34	∈	∈	PROPN
ejpam-6314	69	35	c0	c0	NOUN
ejpam-6314	69	36	,	,	PUNCT
ejpam-6314	69	37	and	and	CCONJ
ejpam-6314	69	38	the	the	DET
ejpam-6314	69	39	independent	independent	ADJ
ejpam-6314	69	40	units	unit	NOUN
ejpam-6314	69	41	i1	i1	PROPN
ejpam-6314	69	42	,	,	PUNCT
ejpam-6314	69	43	i2	i2	PROPN
ejpam-6314	69	44	satisfy	satisfy	PROPN
ejpam-6314	69	45	i21	i21	NOUN
ejpam-6314	69	46	=	=	SYM
ejpam-6314	69	47	i22	i22	NOUN
ejpam-6314	69	48	=	=	SYM
ejpam-6314	69	49	−1	−1	NOUN
ejpam-6314	69	50	and	and	CCONJ
ejpam-6314	69	51	i1i2	i1i2	X
ejpam-6314	70	1	=	=	SYM
ejpam-6314	70	2	i2i1	i2i1	PROPN
ejpam-6314	70	3	.	.	NOUN
ejpam-6314	70	4	we	we	PRON
ejpam-6314	70	5	represent	represent	VERB
ejpam-6314	70	6	the	the	DET
ejpam-6314	70	7	bcn	bcn	PROPN
ejpam-6314	70	8	set	set	VERB
ejpam-6314	70	9	c2	c2	PROPN
ejpam-6314	70	10	as	as	ADP
ejpam-6314	70	11	:	:	PUNCT
ejpam-6314	70	12	c2	c2	PROPN
ejpam-6314	70	13	=	=	PUNCT
ejpam-6314	70	14	{	{	PUNCT
ejpam-6314	70	15	χ	χ	X
ejpam-6314	70	16	:	:	PUNCT
ejpam-6314	70	17	χ	χ	X
ejpam-6314	70	18	=	=	PUNCT
ejpam-6314	70	19	℘1	℘1	VERB
ejpam-6314	70	20	+	+	CCONJ
ejpam-6314	70	21	℘2i1	℘2i1	NOUN
ejpam-6314	70	22	+	+	CCONJ
ejpam-6314	70	23	℘3i2	℘3i2	PROPN
ejpam-6314	70	24	+	+	CCONJ
ejpam-6314	70	25	℘4i1i2	℘4i1i2	NUM
ejpam-6314	70	26	,	,	PUNCT
ejpam-6314	70	27	℘1	℘1	NOUN
ejpam-6314	70	28	,	,	PUNCT
ejpam-6314	70	29	℘2	℘2	PROPN
ejpam-6314	70	30	,	,	PUNCT
ejpam-6314	70	31	℘3	℘3	ADJ
ejpam-6314	70	32	,	,	PUNCT
ejpam-6314	70	33	℘4	℘4	PROPN
ejpam-6314	70	34	∈	∈	PROPN
ejpam-6314	70	35	c0	c0	NOUN
ejpam-6314	70	36	}	}	PUNCT
ejpam-6314	70	37	,	,	PUNCT
ejpam-6314	70	38	m.	m.	NOUN
ejpam-6314	70	39	sarwar	sarwar	PROPN
ejpam-6314	70	40	et	et	PROPN
ejpam-6314	70	41	al	al	PROPN
ejpam-6314	70	42	.	.	PUNCT
ejpam-6314	70	43	/	/	SYM
ejpam-6314	70	44	eur	eur	PROPN
ejpam-6314	70	45	.	.	PUNCT
ejpam-6314	71	1	j.	j.	PROPN
ejpam-6314	71	2	pure	pure	PROPN
ejpam-6314	71	3	appl	appl	PROPN
ejpam-6314	71	4	.	.	PROPN
ejpam-6314	71	5	math	math	PROPN
ejpam-6314	71	6	,	,	PUNCT
ejpam-6314	71	7	18	18	NUM
ejpam-6314	71	8	(	(	PUNCT
ejpam-6314	71	9	3	3	NUM
ejpam-6314	71	10	)	)	PUNCT
ejpam-6314	71	11	(	(	PUNCT
ejpam-6314	71	12	2025	2025	NUM
ejpam-6314	71	13	)	)	PUNCT
ejpam-6314	71	14	,	,	PUNCT
ejpam-6314	71	15	6314	6314	NUM
ejpam-6314	71	16	4	4	NUM
ejpam-6314	71	17	of	of	ADP
ejpam-6314	71	18	28	28	NUM
ejpam-6314	71	19	that	that	PRON
ejpam-6314	71	20	is	be	AUX
ejpam-6314	71	21	,	,	PUNCT
ejpam-6314	71	22	c2	c2	PROPN
ejpam-6314	71	23	=	=	PUNCT
ejpam-6314	71	24	{	{	PUNCT
ejpam-6314	71	25	χ	χ	X
ejpam-6314	71	26	:	:	PUNCT
ejpam-6314	71	27	χ	χ	X
ejpam-6314	71	28	=	=	PUNCT
ejpam-6314	71	29	γ1	γ1	PROPN
ejpam-6314	71	30	+	+	CCONJ
ejpam-6314	71	31	i2γ2	i2γ2	PROPN
ejpam-6314	71	32	,	,	PUNCT
ejpam-6314	71	33	γ1	γ1	NOUN
ejpam-6314	71	34	,	,	PUNCT
ejpam-6314	71	35	γ2	γ2	PROPN
ejpam-6314	71	36	∈	∈	PROPN
ejpam-6314	71	37	c1	c1	PROPN
ejpam-6314	71	38	}	}	PUNCT
ejpam-6314	71	39	,	,	PUNCT
ejpam-6314	71	40	where	where	SCONJ
ejpam-6314	71	41	γ1	γ1	PROPN
ejpam-6314	71	42	=	=	PUNCT
ejpam-6314	71	43	℘1	℘1	VERB
ejpam-6314	71	44	+	+	CCONJ
ejpam-6314	71	45	℘2i1	℘2i1	NOUN
ejpam-6314	71	46	∈	∈	PROPN
ejpam-6314	71	47	c1	c1	NOUN
ejpam-6314	71	48	and	and	CCONJ
ejpam-6314	71	49	γ2	γ2	PROPN
ejpam-6314	71	50	=	=	SYM
ejpam-6314	71	51	℘3	℘3	PROPN
ejpam-6314	71	52	+	+	NUM
ejpam-6314	71	53	℘4i1	℘4i1	VERB
ejpam-6314	71	54	∈	∈	PROPN
ejpam-6314	71	55	c1	c1	NOUN
ejpam-6314	71	56	.	.	PUNCT
ejpam-6314	72	1	if	if	SCONJ
ejpam-6314	72	2	χ	χ	PROPN
ejpam-6314	72	3	=	=	VERB
ejpam-6314	72	4	γ1	γ1	PROPN
ejpam-6314	72	5	+	+	CCONJ
ejpam-6314	72	6	i2γ2	i2γ2	X
ejpam-6314	72	7	and	and	CCONJ
ejpam-6314	72	8	ν	ν	X
ejpam-6314	72	9	=	=	SYM
ejpam-6314	72	10	ω1	ω1	PROPN
ejpam-6314	72	11	+	+	CCONJ
ejpam-6314	72	12	i2ω2	i2ω2	NOUN
ejpam-6314	72	13	are	be	AUX
ejpam-6314	72	14	any	any	DET
ejpam-6314	72	15	two	two	NUM
ejpam-6314	72	16	bcns	bcns	NOUN
ejpam-6314	72	17	,	,	PUNCT
ejpam-6314	72	18	then	then	ADV
ejpam-6314	72	19	their	their	PRON
ejpam-6314	72	20	sum	sum	NOUN
ejpam-6314	72	21	is	be	AUX
ejpam-6314	72	22	χ±	χ±	NOUN
ejpam-6314	72	23	ν	ν	NOUN
ejpam-6314	72	24	=	=	PUNCT
ejpam-6314	72	25	(	(	PUNCT
ejpam-6314	72	26	γ1	γ1	PROPN
ejpam-6314	72	27	+	+	CCONJ
ejpam-6314	72	28	i2γ2)±	i2γ2)±	PROPN
ejpam-6314	72	29	(	(	PUNCT
ejpam-6314	72	30	ω1	ω1	PROPN
ejpam-6314	72	31	+	+	CCONJ
ejpam-6314	72	32	i2ω2	i2ω2	NOUN
ejpam-6314	72	33	)	)	PUNCT
ejpam-6314	72	34	=	=	SYM
ejpam-6314	72	35	γ1	γ1	PROPN
ejpam-6314	72	36	±	±	PROPN
ejpam-6314	72	37	ω1	ω1	PROPN
ejpam-6314	72	38	+	+	CCONJ
ejpam-6314	72	39	i2(γ2	i2(γ2	SYM
ejpam-6314	72	40	±	±	NUM
ejpam-6314	72	41	ω2	ω2	ADJ
ejpam-6314	72	42	)	)	PUNCT
ejpam-6314	72	43	and	and	CCONJ
ejpam-6314	72	44	the	the	DET
ejpam-6314	72	45	product	product	NOUN
ejpam-6314	72	46	is	be	AUX
ejpam-6314	72	47	χ.ν	χ.ν	PROPN
ejpam-6314	72	48	=	=	SYM
ejpam-6314	72	49	(	(	PUNCT
ejpam-6314	72	50	γ1	γ1	NOUN
ejpam-6314	72	51	+	+	CCONJ
ejpam-6314	72	52	i2γ2)(ω1	i2γ2)(ω1	ADJ
ejpam-6314	72	53	+	+	X
ejpam-6314	72	54	i2ω2	i2ω2	X
ejpam-6314	72	55	)	)	PUNCT
ejpam-6314	72	56	=	=	SYM
ejpam-6314	73	1	(	(	PUNCT
ejpam-6314	73	2	γ1ω1	γ1ω1	NUM
ejpam-6314	73	3	−	−	NOUN
ejpam-6314	73	4	γ2ω2	γ2ω2	NOUN
ejpam-6314	73	5	)	)	PUNCT
ejpam-6314	73	6	+	+	CCONJ
ejpam-6314	73	7	i2(γ1ω2	i2(γ1ω2	ADJ
ejpam-6314	73	8	+	+	NUM
ejpam-6314	73	9	γ2ω1	γ2ω1	NOUN
ejpam-6314	73	10	)	)	PUNCT
ejpam-6314	73	11	.	.	PUNCT
ejpam-6314	74	1	in	in	ADP
ejpam-6314	74	2	c2	c2	PROPN
ejpam-6314	74	3	,	,	PUNCT
ejpam-6314	74	4	there	there	PRON
ejpam-6314	74	5	exist	exist	VERB
ejpam-6314	74	6	four	four	NUM
ejpam-6314	74	7	idempotent	idempotent	ADJ
ejpam-6314	74	8	elements	element	NOUN
ejpam-6314	74	9	,	,	PUNCT
ejpam-6314	74	10	they	they	PRON
ejpam-6314	74	11	are	be	AUX
ejpam-6314	74	12	0	0	NUM
ejpam-6314	74	13	,	,	PUNCT
ejpam-6314	74	14	1	1	NUM
ejpam-6314	74	15	,	,	PUNCT
ejpam-6314	74	16	ε1	ε1	PROPN
ejpam-6314	74	17	=	=	SYM
ejpam-6314	74	18	1+i1i2	1+i1i2	NUM
ejpam-6314	74	19	2	2	NUM
ejpam-6314	74	20	,	,	PUNCT
ejpam-6314	74	21	ε2	ε2	NOUN
ejpam-6314	74	22	=	=	PUNCT
ejpam-6314	74	23	1−i1i2	1−i1i2	NUM
ejpam-6314	74	24	2	2	NUM
ejpam-6314	74	25	of	of	ADP
ejpam-6314	74	26	which	which	PRON
ejpam-6314	74	27	ε1	ε1	PROPN
ejpam-6314	74	28	and	and	CCONJ
ejpam-6314	74	29	ε2	ε2	PROPN
ejpam-6314	74	30	are	be	AUX
ejpam-6314	74	31	non	non	ADJ
ejpam-6314	74	32	-	-	ADJ
ejpam-6314	74	33	trivial	trivial	ADJ
ejpam-6314	74	34	,	,	PUNCT
ejpam-6314	74	35	such	such	ADJ
ejpam-6314	74	36	that	that	DET
ejpam-6314	74	37	ε1	ε1	PROPN
ejpam-6314	74	38	+	+	CCONJ
ejpam-6314	74	39	ε2	ε2	ADJ
ejpam-6314	74	40	=	=	SYM
ejpam-6314	74	41	1	1	NUM
ejpam-6314	74	42	and	and	CCONJ
ejpam-6314	74	43	ε1ε2	ε1ε2	NOUN
ejpam-6314	74	44	=	=	NOUN
ejpam-6314	74	45	0	0	PROPN
ejpam-6314	74	46	.	.	PUNCT
ejpam-6314	75	1	every	every	DET
ejpam-6314	75	2	bcn	bcn	PROPN
ejpam-6314	75	3	γ1	γ1	PROPN
ejpam-6314	75	4	+	+	CCONJ
ejpam-6314	75	5	i2γ2	i2γ2	NOUN
ejpam-6314	75	6	may	may	AUX
ejpam-6314	75	7	be	be	AUX
ejpam-6314	75	8	written	write	VERB
ejpam-6314	75	9	in	in	ADP
ejpam-6314	75	10	a	a	DET
ejpam-6314	75	11	specific	specific	ADJ
ejpam-6314	75	12	way	way	NOUN
ejpam-6314	75	13	as	as	ADP
ejpam-6314	75	14	a	a	DET
ejpam-6314	75	15	combination	combination	NOUN
ejpam-6314	75	16	of	of	ADP
ejpam-6314	75	17	ε1	ε1	PROPN
ejpam-6314	75	18	and	and	CCONJ
ejpam-6314	75	19	ε2	ε2	PROPN
ejpam-6314	75	20	.	.	PUNCT
ejpam-6314	76	1	namely	namely	ADV
ejpam-6314	76	2	,	,	PUNCT
ejpam-6314	76	3	χ	χ	PROPN
ejpam-6314	76	4	=	=	PUNCT
ejpam-6314	76	5	γ1	γ1	PROPN
ejpam-6314	76	6	+	+	CCONJ
ejpam-6314	76	7	i2γ2	i2γ2	X
ejpam-6314	76	8	=	=	SYM
ejpam-6314	76	9	(	(	PUNCT
ejpam-6314	76	10	γ1	γ1	PROPN
ejpam-6314	76	11	−	−	PROPN
ejpam-6314	76	12	i1γ2)ε1	i1γ2)ε1	ADJ
ejpam-6314	76	13	+	+	CCONJ
ejpam-6314	76	14	(	(	PUNCT
ejpam-6314	76	15	γ1	γ1	PROPN
ejpam-6314	76	16	+	+	CCONJ
ejpam-6314	76	17	i1γ2)ε2	i1γ2)ε2	NUM
ejpam-6314	76	18	.	.	PUNCT
ejpam-6314	77	1	the	the	DET
ejpam-6314	77	2	complex	complex	ADJ
ejpam-6314	77	3	components	component	NOUN
ejpam-6314	77	4	χ1	χ1	NOUN
ejpam-6314	77	5	=	=	SYM
ejpam-6314	77	6	(	(	PUNCT
ejpam-6314	77	7	γ1	γ1	PROPN
ejpam-6314	77	8	−	−	PROPN
ejpam-6314	77	9	i1γ2	i1γ2	NOUN
ejpam-6314	77	10	)	)	PUNCT
ejpam-6314	77	11	and	and	CCONJ
ejpam-6314	77	12	χ2	χ2	PROPN
ejpam-6314	77	13	=	=	SYM
ejpam-6314	77	14	(	(	PUNCT
ejpam-6314	77	15	γ1	γ1	PROPN
ejpam-6314	77	16	+	+	CCONJ
ejpam-6314	77	17	i1γ2	i1γ2	AUX
ejpam-6314	77	18	)	)	PUNCT
ejpam-6314	77	19	are	be	AUX
ejpam-6314	77	20	referred	refer	VERB
ejpam-6314	77	21	to	to	ADP
ejpam-6314	77	22	as	as	ADP
ejpam-6314	77	23	the	the	DET
ejpam-6314	77	24	idempotent	idempotent	ADJ
ejpam-6314	77	25	components	component	NOUN
ejpam-6314	77	26	of	of	ADP
ejpam-6314	77	27	the	the	DET
ejpam-6314	77	28	bcn	bcn	PROPN
ejpam-6314	77	29	χ	χ	NOUN
ejpam-6314	77	30	,	,	PUNCT
ejpam-6314	77	31	and	and	CCONJ
ejpam-6314	77	32	this	this	DET
ejpam-6314	77	33	representation	representation	NOUN
ejpam-6314	77	34	of	of	ADP
ejpam-6314	77	35	χ	χ	PROPN
ejpam-6314	77	36	is	be	AUX
ejpam-6314	77	37	known	know	VERB
ejpam-6314	77	38	as	as	ADP
ejpam-6314	77	39	the	the	DET
ejpam-6314	77	40	idempotent	idempotent	ADJ
ejpam-6314	77	41	representation	representation	NOUN
ejpam-6314	77	42	of	of	ADP
ejpam-6314	77	43	a	a	DET
ejpam-6314	77	44	bcn	bcn	PROPN
ejpam-6314	77	45	.	.	PUNCT
ejpam-6314	78	1	each	each	DET
ejpam-6314	78	2	element	element	NOUN
ejpam-6314	78	3	in	in	ADP
ejpam-6314	78	4	c2	c2	PROPN
ejpam-6314	78	5	with	with	ADP
ejpam-6314	78	6	a	a	DET
ejpam-6314	78	7	positive	positive	ADJ
ejpam-6314	78	8	real	real	ADV
ejpam-6314	78	9	-	-	PUNCT
ejpam-6314	78	10	valued	value	VERB
ejpam-6314	78	11	norm	norm	NOUN
ejpam-6314	78	12	function	function	VERB
ejpam-6314	78	13	∥	∥	X
ejpam-6314	78	14	·	·	PUNCT
ejpam-6314	78	15	∥	∥	X
ejpam-6314	78	16	:	:	PUNCT
ejpam-6314	78	17	c2	c2	PROPN
ejpam-6314	78	18	→	→	SYM
ejpam-6314	78	19	c+	c+	X
ejpam-6314	78	20	0	0	NUM
ejpam-6314	78	21	is	be	AUX
ejpam-6314	78	22	defined	define	VERB
ejpam-6314	78	23	by	by	ADP
ejpam-6314	78	24	∥χ∥	∥χ∥	NOUN
ejpam-6314	78	25	=	=	X
ejpam-6314	78	26	∥γ1	∥γ1	NOUN
ejpam-6314	78	27	+	+	CCONJ
ejpam-6314	78	28	i2γ2∥	i2γ2∥	NOUN
ejpam-6314	78	29	=	=	NOUN
ejpam-6314	78	30	{	{	PUNCT
ejpam-6314	78	31	∥γ1∥2	∥γ1∥2	PROPN
ejpam-6314	79	1	+	+	PROPN
ejpam-6314	79	2	∥γ2∥2	∥γ2∥2	PROPN
ejpam-6314	79	3	}	}	PUNCT
ejpam-6314	79	4	1/2	1/2	NUM
ejpam-6314	79	5	=	=	PUNCT
ejpam-6314	79	6	[	[	PUNCT
ejpam-6314	79	7	|γ1	|γ1	NOUN
ejpam-6314	79	8	−	−	PROPN
ejpam-6314	79	9	i1γ2|2	i1γ2|2	ADV
ejpam-6314	79	10	+	+	CCONJ
ejpam-6314	79	11	|γ1	|γ1	NOUN
ejpam-6314	79	12	+	+	CCONJ
ejpam-6314	79	13	i1γ2|2	i1γ2|2	X
ejpam-6314	79	14	2	2	NUM
ejpam-6314	79	15	]	]	SYM
ejpam-6314	79	16	1/2	1/2	NUM
ejpam-6314	79	17	=	=	SYM
ejpam-6314	79	18	(	(	PUNCT
ejpam-6314	79	19	℘2	℘2	NOUN
ejpam-6314	79	20	1	1	NUM
ejpam-6314	79	21	+	+	CCONJ
ejpam-6314	79	22	℘2	℘2	NOUN
ejpam-6314	79	23	2	2	NUM
ejpam-6314	79	24	+	+	CCONJ
ejpam-6314	79	25	℘2	℘2	NOUN
ejpam-6314	79	26	3	3	NUM
ejpam-6314	79	27	+	+	CCONJ
ejpam-6314	79	28	θ24	θ24	ADJ
ejpam-6314	79	29	)	)	PUNCT
ejpam-6314	79	30	1/2	1/2	NUM
ejpam-6314	79	31	where	where	SCONJ
ejpam-6314	79	32	χ	χ	NOUN
ejpam-6314	79	33	=	=	PUNCT
ejpam-6314	79	34	℘1	℘1	VERB
ejpam-6314	79	35	+	+	CCONJ
ejpam-6314	79	36	℘2i1	℘2i1	NOUN
ejpam-6314	79	37	+	+	CCONJ
ejpam-6314	79	38	℘3i2	℘3i2	PROPN
ejpam-6314	79	39	+	+	NUM
ejpam-6314	79	40	℘4i1i2	℘4i1i2	NUM
ejpam-6314	79	41	=	=	SYM
ejpam-6314	79	42	γ1	γ1	PROPN
ejpam-6314	79	43	+	+	CCONJ
ejpam-6314	79	44	i2γ2	i2γ2	PROPN
ejpam-6314	79	45	∈	∈	PROPN
ejpam-6314	79	46	c2	c2	PROPN
ejpam-6314	79	47	.	.	PUNCT
ejpam-6314	80	1	the	the	DET
ejpam-6314	80	2	linear	linear	PROPN
ejpam-6314	80	3	space	space	NOUN
ejpam-6314	80	4	c2	c2	PROPN
ejpam-6314	80	5	with	with	ADP
ejpam-6314	80	6	respect	respect	NOUN
ejpam-6314	80	7	to	to	ADP
ejpam-6314	80	8	a	a	DET
ejpam-6314	80	9	defined	define	VERB
ejpam-6314	80	10	norm	norm	NOUN
ejpam-6314	80	11	is	be	AUX
ejpam-6314	80	12	a	a	DET
ejpam-6314	80	13	normed	normed	ADJ
ejpam-6314	80	14	linear	linear	ADJ
ejpam-6314	80	15	space	space	NOUN
ejpam-6314	80	16	,	,	PUNCT
ejpam-6314	80	17	and	and	CCONJ
ejpam-6314	80	18	c2	c2	PROPN
ejpam-6314	80	19	is	be	AUX
ejpam-6314	80	20	complete	complete	ADJ
ejpam-6314	80	21	.	.	PUNCT
ejpam-6314	81	1	therefore	therefore	ADV
ejpam-6314	81	2	,	,	PUNCT
ejpam-6314	81	3	c2	c2	PROPN
ejpam-6314	81	4	is	be	AUX
ejpam-6314	81	5	a	a	DET
ejpam-6314	81	6	banach	banach	NOUN
ejpam-6314	81	7	space	space	NOUN
ejpam-6314	81	8	.	.	PUNCT
ejpam-6314	82	1	if	if	SCONJ
ejpam-6314	82	2	χ	χ	X
ejpam-6314	82	3	,	,	PUNCT
ejpam-6314	82	4	ν	ν	PROPN
ejpam-6314	82	5	∈	∈	PROPN
ejpam-6314	82	6	c2	c2	PROPN
ejpam-6314	82	7	,	,	PUNCT
ejpam-6314	82	8	then	then	ADV
ejpam-6314	82	9	∥χν∥	∥χν∥	NOUN
ejpam-6314	82	10	≤	≤	NUM
ejpam-6314	82	11	√	√	NUM
ejpam-6314	82	12	2∥χ∥∥ν∥	2∥χ∥∥ν∥	NUM
ejpam-6314	82	13	holds	hold	VERB
ejpam-6314	82	14	instead	instead	ADV
ejpam-6314	82	15	of	of	ADP
ejpam-6314	82	16	∥fν∥	∥fν∥	NOUN
ejpam-6314	82	17	≤	≤	ADJ
ejpam-6314	82	18	∥χ∥∥ν∥	∥χ∥∥ν∥	PROPN
ejpam-6314	82	19	,	,	PUNCT
ejpam-6314	82	20	and	and	CCONJ
ejpam-6314	82	21	therefore	therefore	ADV
ejpam-6314	82	22	c2	c2	PROPN
ejpam-6314	82	23	is	be	AUX
ejpam-6314	82	24	not	not	PART
ejpam-6314	82	25	a	a	DET
ejpam-6314	82	26	banach	banach	NOUN
ejpam-6314	82	27	algebra	algebra	NOUN
ejpam-6314	82	28	.	.	PUNCT
ejpam-6314	83	1	for	for	ADP
ejpam-6314	83	2	any	any	DET
ejpam-6314	83	3	two	two	NUM
ejpam-6314	83	4	bcns	bcns	NOUN
ejpam-6314	83	5	χ	χ	NOUN
ejpam-6314	83	6	,	,	PUNCT
ejpam-6314	83	7	ν	ν	PROPN
ejpam-6314	83	8	∈	∈	PROPN
ejpam-6314	83	9	c2	c2	PROPN
ejpam-6314	83	10	,	,	PUNCT
ejpam-6314	83	11	then	then	ADV
ejpam-6314	83	12	(	(	PUNCT
ejpam-6314	83	13	i	i	NOUN
ejpam-6314	83	14	)	)	PUNCT
ejpam-6314	84	1	χ	χ	DET
ejpam-6314	84	2	⪯	⪯	NOUN
ejpam-6314	84	3	ν	ν	PROPN
ejpam-6314	84	4	⇔	⇔	PROPN
ejpam-6314	84	5	∥χ∥	∥χ∥	PROPN
ejpam-6314	84	6	≤	≤	PROPN
ejpam-6314	84	7	∥ν∥	∥ν∥	VERB
ejpam-6314	84	8	;	;	PUNCT
ejpam-6314	84	9	(	(	PUNCT
ejpam-6314	84	10	ii	ii	NOUN
ejpam-6314	84	11	)	)	PUNCT
ejpam-6314	84	12	∥χ+	∥χ+	NOUN
ejpam-6314	84	13	ν∥	ν∥	NOUN
ejpam-6314	84	14	≤	≤	NUM
ejpam-6314	84	15	∥χ∥+	∥χ∥+	ADP
ejpam-6314	84	16	∥ν∥	∥ν∥	NOUN
ejpam-6314	84	17	;	;	PUNCT
ejpam-6314	84	18	(	(	PUNCT
ejpam-6314	84	19	iii	iii	X
ejpam-6314	84	20	)	)	PUNCT
ejpam-6314	84	21	∥℘χ∥	∥℘χ∥	NOUN
ejpam-6314	84	22	=	=	SYM
ejpam-6314	84	23	|℘|∥χ∥	|℘|∥χ∥	PROPN
ejpam-6314	84	24	,	,	PUNCT
ejpam-6314	84	25	where	where	SCONJ
ejpam-6314	84	26	℘	℘	PROPN
ejpam-6314	84	27	is	be	AUX
ejpam-6314	84	28	in	in	ADP
ejpam-6314	84	29	c0	c0	NOUN
ejpam-6314	84	30	;	;	PUNCT
ejpam-6314	84	31	(	(	PUNCT
ejpam-6314	84	32	iv	iv	X
ejpam-6314	84	33	)	)	PUNCT
ejpam-6314	84	34	∥χν∥	∥χν∥	NOUN
ejpam-6314	84	35	≤	≤	NOUN
ejpam-6314	84	36	√	√	NUM
ejpam-6314	84	37	2∥χ∥∥ν∥	2∥χ∥∥ν∥	NUM
ejpam-6314	84	38	,	,	PUNCT
ejpam-6314	84	39	and	and	CCONJ
ejpam-6314	84	40	∥χν∥	∥χν∥	NOUN
ejpam-6314	84	41	=	=	SYM
ejpam-6314	84	42	√	√	NUM
ejpam-6314	84	43	2∥χ∥∥ν∥	2∥χ∥∥ν∥	NUM
ejpam-6314	84	44	holds	hold	VERB
ejpam-6314	84	45	if	if	SCONJ
ejpam-6314	84	46	just	just	ADV
ejpam-6314	84	47	one	one	NUM
ejpam-6314	84	48	of	of	ADP
ejpam-6314	84	49	χ	χ	NOUN
ejpam-6314	84	50	or	or	CCONJ
ejpam-6314	84	51	ν	ν	NOUN
ejpam-6314	84	52	is	be	AUX
ejpam-6314	84	53	degenerated	degenerated	ADJ
ejpam-6314	84	54	;	;	PUNCT
ejpam-6314	84	55	(	(	PUNCT
ejpam-6314	84	56	v	v	NOUN
ejpam-6314	84	57	)	)	PUNCT
ejpam-6314	84	58	∥χ−1∥	∥χ−1∥	X
ejpam-6314	85	1	=	=	PUNCT
ejpam-6314	85	2	∥χ∥−1	∥χ∥−1	PROPN
ejpam-6314	85	3	,	,	PUNCT
ejpam-6314	85	4	if	if	SCONJ
ejpam-6314	85	5	χ	χ	NOUN
ejpam-6314	85	6	is	be	AUX
ejpam-6314	85	7	degenerated	degenerate	VERB
ejpam-6314	85	8	with	with	ADP
ejpam-6314	85	9	χ	χ	PROPN
ejpam-6314	85	10	≻	≻	PROPN
ejpam-6314	85	11	0	0	NUM
ejpam-6314	85	12	;	;	PUNCT
ejpam-6314	85	13	m.	m.	NOUN
ejpam-6314	85	14	sarwar	sarwar	PROPN
ejpam-6314	85	15	et	et	PROPN
ejpam-6314	85	16	al	al	PROPN
ejpam-6314	85	17	.	.	PUNCT
ejpam-6314	85	18	/	/	SYM
ejpam-6314	85	19	eur	eur	PROPN
ejpam-6314	85	20	.	.	PUNCT
ejpam-6314	86	1	j.	j.	PROPN
ejpam-6314	86	2	pure	pure	PROPN
ejpam-6314	86	3	appl	appl	PROPN
ejpam-6314	86	4	.	.	PROPN
ejpam-6314	86	5	math	math	PROPN
ejpam-6314	86	6	,	,	PUNCT
ejpam-6314	86	7	18	18	NUM
ejpam-6314	86	8	(	(	PUNCT
ejpam-6314	86	9	3	3	NUM
ejpam-6314	86	10	)	)	PUNCT
ejpam-6314	86	11	(	(	PUNCT
ejpam-6314	86	12	2025	2025	NUM
ejpam-6314	86	13	)	)	PUNCT
ejpam-6314	86	14	,	,	PUNCT
ejpam-6314	86	15	6314	6314	NUM
ejpam-6314	86	16	5	5	NUM
ejpam-6314	86	17	of	of	ADP
ejpam-6314	86	18	28	28	NUM
ejpam-6314	86	19	(	(	PUNCT
ejpam-6314	86	20	vi	vi	NOUN
ejpam-6314	86	21	)	)	PUNCT
ejpam-6314	86	22	∥χν	∥χν	X
ejpam-6314	86	23	∥	∥	PROPN
ejpam-6314	86	24	=	=	PUNCT
ejpam-6314	86	25	∥χ∥	∥χ∥	NOUN
ejpam-6314	86	26	∥ν∥	∥ν∥	ADJ
ejpam-6314	86	27	,	,	PUNCT
ejpam-6314	86	28	if	if	SCONJ
ejpam-6314	86	29	ν	ν	NOUN
ejpam-6314	86	30	is	be	AUX
ejpam-6314	86	31	a	a	DET
ejpam-6314	86	32	degenerated	degenerated	ADJ
ejpam-6314	86	33	bcn	bcn	NOUN
ejpam-6314	86	34	.	.	PUNCT
ejpam-6314	87	1	the	the	DET
ejpam-6314	87	2	relation	relation	NOUN
ejpam-6314	87	3	⪯	⪯	NOUN
ejpam-6314	87	4	(	(	PUNCT
ejpam-6314	87	5	partial	partial	ADJ
ejpam-6314	87	6	order	order	NOUN
ejpam-6314	87	7	)	)	PUNCT
ejpam-6314	87	8	is	be	AUX
ejpam-6314	87	9	defined	define	VERB
ejpam-6314	87	10	on	on	ADP
ejpam-6314	87	11	c2	c2	PROPN
ejpam-6314	87	12	as	as	SCONJ
ejpam-6314	87	13	given	give	VERB
ejpam-6314	87	14	below	below	ADV
ejpam-6314	87	15	.	.	PUNCT
ejpam-6314	88	1	let	let	VERB
ejpam-6314	88	2	c2	c2	PROPN
ejpam-6314	88	3	be	be	AUX
ejpam-6314	88	4	a	a	DET
ejpam-6314	88	5	set	set	NOUN
ejpam-6314	88	6	of	of	ADP
ejpam-6314	88	7	bcns	bcns	NOUN
ejpam-6314	88	8	and	and	CCONJ
ejpam-6314	88	9	χ	χ	NOUN
ejpam-6314	88	10	=	=	PROPN
ejpam-6314	88	11	γ1	γ1	PROPN
ejpam-6314	88	12	+	+	CCONJ
ejpam-6314	88	13	i2γ2	i2γ2	X
ejpam-6314	88	14	and	and	CCONJ
ejpam-6314	88	15	ν	ν	X
ejpam-6314	88	16	=	=	SYM
ejpam-6314	88	17	ω1	ω1	PROPN
ejpam-6314	88	18	+	+	CCONJ
ejpam-6314	88	19	i2ω2	i2ω2	PROPN
ejpam-6314	88	20	∈	∈	PROPN
ejpam-6314	88	21	c2	c2	PROPN
ejpam-6314	88	22	.	.	PUNCT
ejpam-6314	89	1	then	then	ADV
ejpam-6314	89	2	,	,	PUNCT
ejpam-6314	89	3	χ	χ	DET
ejpam-6314	89	4	⪯	⪯	NOUN
ejpam-6314	89	5	ν	ν	X
ejpam-6314	89	6	if	if	SCONJ
ejpam-6314	89	7	and	and	CCONJ
ejpam-6314	89	8	only	only	ADV
ejpam-6314	89	9	if	if	SCONJ
ejpam-6314	89	10	γ1	γ1	PROPN
ejpam-6314	89	11	⪯	⪯	PROPN
ejpam-6314	89	12	ω1	ω1	PROPN
ejpam-6314	89	13	and	and	CCONJ
ejpam-6314	89	14	γ2	γ2	PROPN
ejpam-6314	89	15	⪯	⪯	PROPN
ejpam-6314	89	16	ω2	ω2	PROPN
ejpam-6314	89	17	,	,	PUNCT
ejpam-6314	89	18	i.e.	i.e.	X
ejpam-6314	89	19	,	,	PUNCT
ejpam-6314	89	20	χ	χ	DET
ejpam-6314	89	21	⪯	⪯	NOUN
ejpam-6314	89	22	ν	ν	NOUN
ejpam-6314	89	23	,	,	PUNCT
ejpam-6314	89	24	if	if	SCONJ
ejpam-6314	89	25	one	one	NUM
ejpam-6314	89	26	of	of	ADP
ejpam-6314	89	27	the	the	DET
ejpam-6314	89	28	following	follow	VERB
ejpam-6314	89	29	conditions	condition	NOUN
ejpam-6314	89	30	are	be	AUX
ejpam-6314	89	31	fulfilled	fulfil	VERB
ejpam-6314	89	32	:	:	PUNCT
ejpam-6314	89	33	(	(	PUNCT
ejpam-6314	89	34	i	i	NOUN
ejpam-6314	89	35	)	)	PUNCT
ejpam-6314	89	36	γ1	γ1	PROPN
ejpam-6314	89	37	=	=	SYM
ejpam-6314	89	38	ω1	ω1	PROPN
ejpam-6314	89	39	,	,	PUNCT
ejpam-6314	89	40	γ2	γ2	PROPN
ejpam-6314	89	41	=	=	SYM
ejpam-6314	89	42	ω2	ω2	PROPN
ejpam-6314	89	43	;	;	PUNCT
ejpam-6314	89	44	(	(	PUNCT
ejpam-6314	89	45	ii	ii	NOUN
ejpam-6314	89	46	)	)	PUNCT
ejpam-6314	89	47	γ1	γ1	PROPN
ejpam-6314	89	48	⪯	⪯	PROPN
ejpam-6314	89	49	ω1	ω1	PROPN
ejpam-6314	89	50	,	,	PUNCT
ejpam-6314	89	51	γ2	γ2	PROPN
ejpam-6314	89	52	=	=	SYM
ejpam-6314	89	53	ω2	ω2	PROPN
ejpam-6314	89	54	;	;	PUNCT
ejpam-6314	89	55	(	(	PUNCT
ejpam-6314	89	56	iii	iii	X
ejpam-6314	89	57	)	)	PUNCT
ejpam-6314	89	58	γ1	γ1	NOUN
ejpam-6314	89	59	=	=	SYM
ejpam-6314	89	60	ω1	ω1	PROPN
ejpam-6314	89	61	,	,	PUNCT
ejpam-6314	89	62	γ2	γ2	PROPN
ejpam-6314	89	63	⪯	⪯	PROPN
ejpam-6314	89	64	ω2	ω2	PROPN
ejpam-6314	89	65	;	;	PUNCT
ejpam-6314	89	66	(	(	PUNCT
ejpam-6314	89	67	iv	iv	X
ejpam-6314	89	68	)	)	PUNCT
ejpam-6314	89	69	γ1	γ1	PROPN
ejpam-6314	89	70	⪯	⪯	PROPN
ejpam-6314	89	71	ω1	ω1	PROPN
ejpam-6314	89	72	,	,	PUNCT
ejpam-6314	89	73	γ2	γ2	PROPN
ejpam-6314	89	74	⪯	⪯	PROPN
ejpam-6314	89	75	ω2	ω2	PROPN
ejpam-6314	89	76	.	.	PUNCT
ejpam-6314	90	1	it	it	PRON
ejpam-6314	90	2	is	be	AUX
ejpam-6314	90	3	obvious	obvious	ADJ
ejpam-6314	90	4	that	that	SCONJ
ejpam-6314	90	5	we	we	PRON
ejpam-6314	90	6	can	can	AUX
ejpam-6314	90	7	write	write	VERB
ejpam-6314	90	8	χ	χ	X
ejpam-6314	90	9	⋨	⋨	PROPN
ejpam-6314	90	10	ν	ν	X
ejpam-6314	90	11	if	if	SCONJ
ejpam-6314	90	12	χ	χ	PRON
ejpam-6314	90	13	⪯	⪯	NOUN
ejpam-6314	90	14	ν	ν	NOUN
ejpam-6314	90	15	and	and	CCONJ
ejpam-6314	90	16	χ	χ	DET
ejpam-6314	90	17	̸=	̸=	PROPN
ejpam-6314	90	18	ν	ν	PROPN
ejpam-6314	90	19	,	,	PUNCT
ejpam-6314	90	20	i.e.	i.e.	X
ejpam-6314	90	21	,	,	PUNCT
ejpam-6314	90	22	if	if	SCONJ
ejpam-6314	90	23	2	2	NUM
ejpam-6314	90	24	,	,	PUNCT
ejpam-6314	90	25	3	3	NUM
ejpam-6314	90	26	,	,	PUNCT
ejpam-6314	90	27	or	or	CCONJ
ejpam-6314	90	28	4	4	NUM
ejpam-6314	90	29	are	be	AUX
ejpam-6314	90	30	fulfilled	fulfil	VERB
ejpam-6314	90	31	,	,	PUNCT
ejpam-6314	90	32	and	and	CCONJ
ejpam-6314	90	33	we	we	PRON
ejpam-6314	90	34	will	will	AUX
ejpam-6314	90	35	write	write	VERB
ejpam-6314	90	36	χ	χ	DET
ejpam-6314	90	37	⪯	⪯	NOUN
ejpam-6314	90	38	ν	ν	NOUN
ejpam-6314	90	39	if	if	SCONJ
ejpam-6314	90	40	only	only	ADV
ejpam-6314	90	41	4	4	NUM
ejpam-6314	90	42	is	be	AUX
ejpam-6314	90	43	satisfied	satisfied	ADJ
ejpam-6314	90	44	.	.	PUNCT
ejpam-6314	91	1	definition	definition	NOUN
ejpam-6314	91	2	1	1	NUM
ejpam-6314	91	3	.	.	PUNCT
ejpam-6314	92	1	[	[	X
ejpam-6314	92	2	8	8	NUM
ejpam-6314	92	3	]	]	PUNCT
ejpam-6314	92	4	let	let	VERB
ejpam-6314	92	5	s	s	PRON
ejpam-6314	92	6	̸=	̸=	PROPN
ejpam-6314	92	7	∅	∅	NOUN
ejpam-6314	92	8	and	and	CCONJ
ejpam-6314	92	9	ϑ	ϑ	X
ejpam-6314	92	10	:	:	PUNCT
ejpam-6314	92	11	s	s	VERB
ejpam-6314	92	12	×	×	PROPN
ejpam-6314	92	13	s	s	X
ejpam-6314	92	14	→	→	SYM
ejpam-6314	92	15	[	[	X
ejpam-6314	92	16	1,+∞	1,+∞	NUM
ejpam-6314	92	17	)	)	PUNCT
ejpam-6314	92	18	.	.	PUNCT
ejpam-6314	93	1	the	the	DET
ejpam-6314	93	2	functional	functional	ADJ
ejpam-6314	93	3	mc	mc	NOUN
ejpam-6314	93	4	:	:	PUNCT
ejpam-6314	93	5	s	s	VERB
ejpam-6314	93	6	×	×	PROPN
ejpam-6314	93	7	s	s	X
ejpam-6314	93	8	→	→	SYM
ejpam-6314	93	9	[	[	X
ejpam-6314	93	10	0,+∞	0,+∞	NUM
ejpam-6314	93	11	)	)	PUNCT
ejpam-6314	93	12	is	be	AUX
ejpam-6314	93	13	called	call	VERB
ejpam-6314	93	14	controlled	control	VERB
ejpam-6314	93	15	-	-	PUNCT
ejpam-6314	93	16	type	type	NOUN
ejpam-6314	93	17	metric	metric	ADJ
ejpam-6314	93	18	(	(	PUNCT
ejpam-6314	93	19	cm	cm	NOUN
ejpam-6314	93	20	)	)	PUNCT
ejpam-6314	93	21	if	if	SCONJ
ejpam-6314	93	22	:	:	PUNCT
ejpam-6314	93	23	(	(	PUNCT
ejpam-6314	93	24	cm1	cm1	NOUN
ejpam-6314	93	25	)	)	PUNCT
ejpam-6314	93	26	mc(ς	mc(ς	PROPN
ejpam-6314	93	27	,	,	PUNCT
ejpam-6314	93	28	α	α	NOUN
ejpam-6314	93	29	)	)	PUNCT
ejpam-6314	93	30	=	=	SYM
ejpam-6314	93	31	0	0	NUM
ejpam-6314	94	1	⇐	⇐	ADJ
ejpam-6314	94	2	⇒	⇒	NOUN
ejpam-6314	94	3	ς	ς	PROPN
ejpam-6314	94	4	=	=	SYM
ejpam-6314	94	5	α	α	PROPN
ejpam-6314	94	6	,	,	PUNCT
ejpam-6314	94	7	(	(	PUNCT
ejpam-6314	94	8	cm2	cm2	NOUN
ejpam-6314	94	9	)	)	PUNCT
ejpam-6314	94	10	mc(ς	mc(ς	NOUN
ejpam-6314	94	11	,	,	PUNCT
ejpam-6314	94	12	α	α	NOUN
ejpam-6314	94	13	)	)	PUNCT
ejpam-6314	94	14	=	=	PUNCT
ejpam-6314	94	15	mc(α	mc(α	X
ejpam-6314	94	16	,	,	PUNCT
ejpam-6314	94	17	ς	ς	NOUN
ejpam-6314	94	18	)	)	PUNCT
ejpam-6314	94	19	,	,	PUNCT
ejpam-6314	94	20	(	(	PUNCT
ejpam-6314	94	21	cm3	cm3	NOUN
ejpam-6314	94	22	)	)	PUNCT
ejpam-6314	94	23	mc(ς	mc(ς	NOUN
ejpam-6314	94	24	,	,	PUNCT
ejpam-6314	94	25	β	β	NOUN
ejpam-6314	94	26	)	)	PUNCT
ejpam-6314	94	27	≤	≤	NOUN
ejpam-6314	94	28	ϑ(ς	ϑ(ς	PROPN
ejpam-6314	94	29	,	,	PUNCT
ejpam-6314	94	30	α)mc(ς	α)mc(ς	PROPN
ejpam-6314	94	31	,	,	PUNCT
ejpam-6314	94	32	α	α	NOUN
ejpam-6314	94	33	)	)	PUNCT
ejpam-6314	94	34	+	+	CCONJ
ejpam-6314	94	35	ϑ(α	ϑ(α	PROPN
ejpam-6314	94	36	,	,	PUNCT
ejpam-6314	94	37	β)mc(α	β)mc(α	PRON
ejpam-6314	94	38	,	,	PUNCT
ejpam-6314	94	39	β	β	NOUN
ejpam-6314	94	40	)	)	PUNCT
ejpam-6314	94	41	,	,	PUNCT
ejpam-6314	94	42	for	for	ADP
ejpam-6314	94	43	all	all	DET
ejpam-6314	94	44	ς	ς	PROPN
ejpam-6314	94	45	,	,	PUNCT
ejpam-6314	94	46	α	α	X
ejpam-6314	94	47	,	,	PUNCT
ejpam-6314	94	48	β	β	PROPN
ejpam-6314	94	49	∈	∈	PROPN
ejpam-6314	94	50	s.	s.	PROPN
ejpam-6314	94	51	then	then	ADV
ejpam-6314	94	52	,	,	PUNCT
ejpam-6314	94	53	the	the	DET
ejpam-6314	94	54	doublet	doublet	ADJ
ejpam-6314	94	55	(	(	PUNCT
ejpam-6314	94	56	s	s	PROPN
ejpam-6314	94	57	,	,	PUNCT
ejpam-6314	94	58	mc	mc	PROPN
ejpam-6314	94	59	)	)	PUNCT
ejpam-6314	94	60	is	be	AUX
ejpam-6314	94	61	called	call	VERB
ejpam-6314	94	62	a	a	DET
ejpam-6314	94	63	cm	cm	NOUN
ejpam-6314	94	64	space	space	NOUN
ejpam-6314	94	65	.	.	PUNCT
ejpam-6314	94	66	example	example	NOUN
ejpam-6314	95	1	1	1	NUM
ejpam-6314	95	2	.	.	PUNCT
ejpam-6314	96	1	[	[	X
ejpam-6314	96	2	8	8	NUM
ejpam-6314	96	3	]	]	X
ejpam-6314	96	4	choose	choose	NOUN
ejpam-6314	96	5	s	s	NOUN
ejpam-6314	96	6	=	=	PUNCT
ejpam-6314	96	7	{	{	PUNCT
ejpam-6314	96	8	1	1	NUM
ejpam-6314	96	9	,	,	PUNCT
ejpam-6314	96	10	2	2	NUM
ejpam-6314	96	11	,	,	PUNCT
ejpam-6314	96	12	.	.	PUNCT
ejpam-6314	96	13	.	.	PUNCT
ejpam-6314	96	14	.	.	PUNCT
ejpam-6314	97	1	,	,	PUNCT
ejpam-6314	97	2	}	}	PUNCT
ejpam-6314	97	3	.	.	PUNCT
ejpam-6314	98	1	take	take	VERB
ejpam-6314	98	2	mc	mc	PROPN
ejpam-6314	98	3	:	:	PUNCT
ejpam-6314	99	1	s	s	VERB
ejpam-6314	99	2	×	×	NOUN
ejpam-6314	99	3	s	s	PART
ejpam-6314	99	4	−→	−→	NOUN
ejpam-6314	99	5	[	[	X
ejpam-6314	99	6	0,+∞	0,+∞	NUM
ejpam-6314	99	7	)	)	PUNCT
ejpam-6314	99	8	such	such	ADJ
ejpam-6314	99	9	that	that	SCONJ
ejpam-6314	99	10	mc(ς	mc(ς	NOUN
ejpam-6314	99	11	,	,	PUNCT
ejpam-6314	99	12	α	α	NOUN
ejpam-6314	99	13	)	)	PUNCT
ejpam-6314	99	14	=	=	PUNCT
ejpam-6314	100	1			NOUN
ejpam-6314	100	2	0	0	PUNCT
ejpam-6314	101	1	if	if	SCONJ
ejpam-6314	101	2	and	and	CCONJ
ejpam-6314	101	3	only	only	ADV
ejpam-6314	101	4	if	if	SCONJ
ejpam-6314	101	5	ς	ς	PROPN
ejpam-6314	101	6	=	=	SYM
ejpam-6314	101	7	α	α	PROPN
ejpam-6314	101	8	1	1	NUM
ejpam-6314	101	9	ς	ς	NOUN
ejpam-6314	101	10	if	if	SCONJ
ejpam-6314	101	11	ς	ς	PROPN
ejpam-6314	101	12	=	=	SYM
ejpam-6314	101	13	2n	2n	NUM
ejpam-6314	101	14	and	and	CCONJ
ejpam-6314	101	15	α	α	NOUN
ejpam-6314	101	16	=	=	SYM
ejpam-6314	101	17	2n+	2n+	NUM
ejpam-6314	101	18	1	1	NUM
ejpam-6314	101	19	,	,	PUNCT
ejpam-6314	101	20	1	1	NUM
ejpam-6314	101	21	α	α	NOUN
ejpam-6314	101	22	if	if	SCONJ
ejpam-6314	101	23	ς	ς	PROPN
ejpam-6314	101	24	=	=	NOUN
ejpam-6314	101	25	2n+	2n+	NUM
ejpam-6314	101	26	1	1	NUM
ejpam-6314	101	27	and	and	CCONJ
ejpam-6314	101	28	α	α	NOUN
ejpam-6314	101	29	=	=	SYM
ejpam-6314	101	30	2n	2n	NUM
ejpam-6314	101	31	,	,	PUNCT
ejpam-6314	101	32	1	1	NUM
ejpam-6314	101	33	otherwise	otherwise	ADV
ejpam-6314	101	34	.	.	PUNCT
ejpam-6314	102	1	consider	consider	VERB
ejpam-6314	102	2	γ	γ	X
ejpam-6314	102	3	:	:	PUNCT
ejpam-6314	102	4	s	s	VERB
ejpam-6314	102	5	×	×	NOUN
ejpam-6314	102	6	s	s	PART
ejpam-6314	102	7	−→	−→	NOUN
ejpam-6314	102	8	[	[	X
ejpam-6314	102	9	1,+∞	1,+∞	NUM
ejpam-6314	102	10	)	)	PUNCT
ejpam-6314	102	11	as	as	ADP
ejpam-6314	102	12	γ(ς	γ(ς	NOUN
ejpam-6314	102	13	,	,	PUNCT
ejpam-6314	102	14	α	α	NOUN
ejpam-6314	102	15	)	)	PUNCT
ejpam-6314	102	16	=	=	SYM
ejpam-6314	103	1			NOUN
ejpam-6314	103	2	ς	ς	X
ejpam-6314	103	3	if	if	SCONJ
ejpam-6314	103	4	ς	ς	PROPN
ejpam-6314	103	5	=	=	SYM
ejpam-6314	103	6	2n	2n	NUM
ejpam-6314	103	7	and	and	CCONJ
ejpam-6314	103	8	α	α	NOUN
ejpam-6314	103	9	=	=	SYM
ejpam-6314	103	10	2n+	2n+	NUM
ejpam-6314	103	11	1	1	NUM
ejpam-6314	103	12	,	,	PUNCT
ejpam-6314	103	13	α	α	PRON
ejpam-6314	103	14	if	if	SCONJ
ejpam-6314	103	15	ς	ς	PROPN
ejpam-6314	103	16	=	=	NOUN
ejpam-6314	103	17	2n+	2n+	NUM
ejpam-6314	103	18	1	1	NUM
ejpam-6314	103	19	and	and	CCONJ
ejpam-6314	103	20	α	α	NOUN
ejpam-6314	103	21	=	=	SYM
ejpam-6314	103	22	2n	2n	NUM
ejpam-6314	103	23	,	,	PUNCT
ejpam-6314	103	24	1	1	NUM
ejpam-6314	103	25	otherwise	otherwise	ADV
ejpam-6314	103	26	.	.	PUNCT
ejpam-6314	104	1	it	it	PRON
ejpam-6314	104	2	is	be	AUX
ejpam-6314	104	3	clear	clear	ADJ
ejpam-6314	104	4	that	that	SCONJ
ejpam-6314	104	5	condition	condition	NOUN
ejpam-6314	104	6	(	(	PUNCT
ejpam-6314	104	7	cm1	cm1	NOUN
ejpam-6314	104	8	)	)	PUNCT
ejpam-6314	104	9	and	and	CCONJ
ejpam-6314	104	10	(	(	PUNCT
ejpam-6314	104	11	cm2	cm2	NOUN
ejpam-6314	104	12	)	)	PUNCT
ejpam-6314	104	13	are	be	AUX
ejpam-6314	104	14	satisfied	satisfied	ADJ
ejpam-6314	104	15	.	.	PUNCT
ejpam-6314	105	1	now	now	ADV
ejpam-6314	105	2	,	,	PUNCT
ejpam-6314	105	3	we	we	PRON
ejpam-6314	105	4	have	have	VERB
ejpam-6314	105	5	to	to	PART
ejpam-6314	105	6	investigate	investigate	VERB
ejpam-6314	105	7	condition	condition	NOUN
ejpam-6314	105	8	(	(	PUNCT
ejpam-6314	105	9	cm3	cm3	NOUN
ejpam-6314	105	10	)	)	PUNCT
ejpam-6314	105	11	case	case	NOUN
ejpam-6314	105	12	1	1	NUM
ejpam-6314	105	13	.	.	PUNCT
ejpam-6314	106	1	if	if	SCONJ
ejpam-6314	106	2	β	β	PRON
ejpam-6314	106	3	=	=	SYM
ejpam-6314	106	4	ς	ς	PROPN
ejpam-6314	106	5	or	or	CCONJ
ejpam-6314	106	6	β	β	X
ejpam-6314	106	7	=	=	SYM
ejpam-6314	106	8	α	α	PROPN
ejpam-6314	106	9	,	,	PUNCT
ejpam-6314	106	10	(	(	PUNCT
ejpam-6314	106	11	d3	d3	PROPN
ejpam-6314	106	12	)	)	PUNCT
ejpam-6314	106	13	is	be	AUX
ejpam-6314	106	14	satisfied	satisfied	ADJ
ejpam-6314	106	15	.	.	PUNCT
ejpam-6314	107	1	case	case	NOUN
ejpam-6314	107	2	2	2	NUM
ejpam-6314	107	3	.	.	PUNCT
ejpam-6314	108	1	if	if	SCONJ
ejpam-6314	108	2	β	β	PRON
ejpam-6314	108	3	̸=	̸=	PROPN
ejpam-6314	108	4	ς	ς	PROPN
ejpam-6314	108	5	and	and	CCONJ
ejpam-6314	108	6	β	β	NUM
ejpam-6314	108	7	̸=	̸=	PROPN
ejpam-6314	108	8	α	α	NUM
ejpam-6314	108	9	,	,	PUNCT
ejpam-6314	108	10	(	(	PUNCT
ejpam-6314	108	11	cm3	cm3	NOUN
ejpam-6314	108	12	)	)	PUNCT
ejpam-6314	108	13	is	be	AUX
ejpam-6314	108	14	true	true	ADJ
ejpam-6314	108	15	when	when	SCONJ
ejpam-6314	108	16	ς	ς	PROPN
ejpam-6314	108	17	=	=	SYM
ejpam-6314	108	18	α	α	PROPN
ejpam-6314	108	19	.	.	PUNCT
ejpam-6314	109	1	now	now	ADV
ejpam-6314	109	2	,	,	PUNCT
ejpam-6314	109	3	we	we	PRON
ejpam-6314	109	4	may	may	AUX
ejpam-6314	109	5	assume	assume	VERB
ejpam-6314	109	6	that	that	SCONJ
ejpam-6314	109	7	ς	ς	PROPN
ejpam-6314	109	8	̸=	̸=	PROPN
ejpam-6314	109	9	α	α	NOUN
ejpam-6314	109	10	.	.	PUNCT
ejpam-6314	110	1	then	then	ADV
ejpam-6314	110	2	,	,	PUNCT
ejpam-6314	110	3	we	we	PRON
ejpam-6314	110	4	have	have	VERB
ejpam-6314	110	5	ς	ς	PROPN
ejpam-6314	110	6	̸=	̸=	PROPN
ejpam-6314	110	7	α	α	PROPN
ejpam-6314	110	8	̸=	̸=	PROPN
ejpam-6314	110	9	β	β	X
ejpam-6314	110	10	.	.	PUNCT
ejpam-6314	111	1	it	it	PRON
ejpam-6314	111	2	is	be	AUX
ejpam-6314	111	3	clear	clear	ADJ
ejpam-6314	111	4	that	that	SCONJ
ejpam-6314	111	5	(	(	PUNCT
ejpam-6314	111	6	cm3	cm3	NOUN
ejpam-6314	111	7	)	)	PUNCT
ejpam-6314	111	8	holds	hold	VERB
ejpam-6314	111	9	in	in	ADP
ejpam-6314	111	10	all	all	PRON
ejpam-6314	111	11	of	of	ADP
ejpam-6314	111	12	the	the	DET
ejpam-6314	111	13	following	follow	VERB
ejpam-6314	111	14	possible	possible	ADJ
ejpam-6314	111	15	subcases	subcase	NOUN
ejpam-6314	111	16	:	:	PUNCT
ejpam-6314	111	17	m.	m.	NOUN
ejpam-6314	111	18	sarwar	sarwar	PROPN
ejpam-6314	111	19	et	et	PROPN
ejpam-6314	112	1	al	al	PROPN
ejpam-6314	112	2	.	.	PUNCT
ejpam-6314	112	3	/	/	SYM
ejpam-6314	112	4	eur	eur	PROPN
ejpam-6314	112	5	.	.	PUNCT
ejpam-6314	113	1	j.	j.	PROPN
ejpam-6314	113	2	pure	pure	PROPN
ejpam-6314	113	3	appl	appl	PROPN
ejpam-6314	113	4	.	.	PROPN
ejpam-6314	113	5	math	math	PROPN
ejpam-6314	113	6	,	,	PUNCT
ejpam-6314	113	7	18	18	NUM
ejpam-6314	113	8	(	(	PUNCT
ejpam-6314	113	9	3	3	NUM
ejpam-6314	113	10	)	)	PUNCT
ejpam-6314	113	11	(	(	PUNCT
ejpam-6314	113	12	2025	2025	NUM
ejpam-6314	113	13	)	)	PUNCT
ejpam-6314	113	14	,	,	PUNCT
ejpam-6314	113	15	6314	6314	NUM
ejpam-6314	113	16	6	6	NUM
ejpam-6314	113	17	of	of	ADP
ejpam-6314	113	18	28	28	NUM
ejpam-6314	113	19	(	(	PUNCT
ejpam-6314	113	20	i	i	NOUN
ejpam-6314	113	21	)	)	PUNCT
ejpam-6314	113	22	α	α	PROPN
ejpam-6314	113	23	is	be	AUX
ejpam-6314	113	24	odd	odd	ADJ
ejpam-6314	113	25	,	,	PUNCT
ejpam-6314	113	26	and	and	CCONJ
ejpam-6314	113	27	ς	ς	PROPN
ejpam-6314	113	28	,	,	PUNCT
ejpam-6314	113	29	β	β	X
ejpam-6314	113	30	are	be	AUX
ejpam-6314	113	31	even	even	ADV
ejpam-6314	113	32	.	.	PUNCT
ejpam-6314	114	1	(	(	PUNCT
ejpam-6314	114	2	ii	ii	X
ejpam-6314	114	3	)	)	PUNCT
ejpam-6314	114	4	α	α	PROPN
ejpam-6314	114	5	,	,	PUNCT
ejpam-6314	114	6	β	β	X
ejpam-6314	114	7	are	be	AUX
ejpam-6314	114	8	odd	odd	ADJ
ejpam-6314	114	9	,	,	PUNCT
ejpam-6314	114	10	and	and	CCONJ
ejpam-6314	114	11	ς	ς	PROPN
ejpam-6314	114	12	is	be	AUX
ejpam-6314	114	13	even	even	ADV
ejpam-6314	114	14	.	.	PUNCT
ejpam-6314	115	1	(	(	PUNCT
ejpam-6314	115	2	iii	iii	X
ejpam-6314	115	3	)	)	PUNCT
ejpam-6314	115	4	α	α	NOUN
ejpam-6314	115	5	is	be	AUX
ejpam-6314	115	6	even	even	ADV
ejpam-6314	115	7	,	,	PUNCT
ejpam-6314	115	8	and	and	CCONJ
ejpam-6314	115	9	ς	ς	PROPN
ejpam-6314	115	10	,	,	PUNCT
ejpam-6314	115	11	β	β	X
ejpam-6314	115	12	are	be	AUX
ejpam-6314	115	13	odd	odd	ADJ
ejpam-6314	115	14	.	.	PUNCT
ejpam-6314	116	1	(	(	PUNCT
ejpam-6314	116	2	iv	iv	X
ejpam-6314	116	3	)	)	PUNCT
ejpam-6314	116	4	ς	ς	PROPN
ejpam-6314	116	5	,	,	PUNCT
ejpam-6314	116	6	α	α	PROPN
ejpam-6314	116	7	,	,	PUNCT
ejpam-6314	116	8	β	β	X
ejpam-6314	116	9	are	be	AUX
ejpam-6314	116	10	even	even	ADV
ejpam-6314	116	11	.	.	PUNCT
ejpam-6314	117	1	(	(	PUNCT
ejpam-6314	117	2	v	v	NOUN
ejpam-6314	117	3	)	)	PUNCT
ejpam-6314	117	4	β	β	X
ejpam-6314	117	5	is	be	AUX
ejpam-6314	117	6	odd	odd	ADJ
ejpam-6314	117	7	,	,	PUNCT
ejpam-6314	117	8	and	and	CCONJ
ejpam-6314	117	9	ς	ς	PROPN
ejpam-6314	117	10	,	,	PUNCT
ejpam-6314	117	11	α	α	PROPN
ejpam-6314	117	12	are	be	AUX
ejpam-6314	117	13	even	even	ADV
ejpam-6314	117	14	.	.	PUNCT
ejpam-6314	118	1	(	(	PUNCT
ejpam-6314	118	2	vi	vi	X
ejpam-6314	118	3	)	)	PUNCT
ejpam-6314	118	4	β	β	X
ejpam-6314	118	5	is	be	AUX
ejpam-6314	118	6	even	even	ADV
ejpam-6314	118	7	,	,	PUNCT
ejpam-6314	118	8	and	and	CCONJ
ejpam-6314	118	9	ς	ς	PROPN
ejpam-6314	118	10	,	,	PUNCT
ejpam-6314	118	11	α	α	PROPN
ejpam-6314	118	12	are	be	AUX
ejpam-6314	118	13	odd	odd	ADJ
ejpam-6314	118	14	.	.	PUNCT
ejpam-6314	119	1	(	(	PUNCT
ejpam-6314	119	2	vii	vii	PROPN
ejpam-6314	119	3	)	)	PUNCT
ejpam-6314	119	4	ς	ς	PROPN
ejpam-6314	119	5	,	,	PUNCT
ejpam-6314	119	6	α	α	PROPN
ejpam-6314	119	7	,	,	PUNCT
ejpam-6314	119	8	β	β	X
ejpam-6314	119	9	are	be	AUX
ejpam-6314	119	10	odd	odd	ADJ
ejpam-6314	119	11	.	.	PUNCT
ejpam-6314	120	1	thus	thus	ADV
ejpam-6314	120	2	,	,	PUNCT
ejpam-6314	120	3	mc	mc	PROPN
ejpam-6314	120	4	is	be	AUX
ejpam-6314	120	5	a	a	DET
ejpam-6314	120	6	controlled	control	VERB
ejpam-6314	120	7	metric	metric	ADJ
ejpam-6314	120	8	type	type	NOUN
ejpam-6314	120	9	.	.	PUNCT
ejpam-6314	121	1	definition	definition	NOUN
ejpam-6314	121	2	2	2	NUM
ejpam-6314	121	3	.	.	PUNCT
ejpam-6314	122	1	[	[	X
ejpam-6314	122	2	25	25	NUM
ejpam-6314	122	3	]	]	PUNCT
ejpam-6314	122	4	let	let	VERB
ejpam-6314	122	5	s	s	PRON
ejpam-6314	122	6	̸=	̸=	PROPN
ejpam-6314	122	7	∅	∅	NOUN
ejpam-6314	122	8	and	and	CCONJ
ejpam-6314	122	9	ϑ	ϑ	X
ejpam-6314	122	10	:	:	PUNCT
ejpam-6314	122	11	s	s	VERB
ejpam-6314	122	12	×	×	PROPN
ejpam-6314	122	13	s	s	X
ejpam-6314	122	14	→	→	SYM
ejpam-6314	122	15	[	[	X
ejpam-6314	122	16	1,+∞	1,+∞	NUM
ejpam-6314	122	17	)	)	PUNCT
ejpam-6314	122	18	.	.	PUNCT
ejpam-6314	123	1	the	the	DET
ejpam-6314	123	2	functional	functional	ADJ
ejpam-6314	123	3	db	db	X
ejpam-6314	123	4	:	:	PUNCT
ejpam-6314	123	5	s	s	VERB
ejpam-6314	123	6	×	×	PROPN
ejpam-6314	123	7	s	s	X
ejpam-6314	123	8	→	→	PUNCT
ejpam-6314	123	9	c2	c2	PROPN
ejpam-6314	123	10	is	be	AUX
ejpam-6314	123	11	termed	term	VERB
ejpam-6314	123	12	the	the	DET
ejpam-6314	123	13	briefly	briefly	NOUN
ejpam-6314	123	14	bicomplex	bicomplex	NOUN
ejpam-6314	123	15	valued	value	VERB
ejpam-6314	123	16	controlled	control	VERB
ejpam-6314	123	17	-	-	PUNCT
ejpam-6314	123	18	type	type	NOUN
ejpam-6314	123	19	metric	metric	ADJ
ejpam-6314	123	20	(	(	PUNCT
ejpam-6314	123	21	bcvms	bcvms	NOUN
ejpam-6314	123	22	)	)	PUNCT
ejpam-6314	123	23	if	if	SCONJ
ejpam-6314	123	24	:	:	PUNCT
ejpam-6314	123	25	(	(	PUNCT
ejpam-6314	123	26	bvcm1	bvcm1	X
ejpam-6314	123	27	)	)	PUNCT
ejpam-6314	123	28	db(ς	db(ς	ADV
ejpam-6314	123	29	,	,	PUNCT
ejpam-6314	123	30	α	α	X
ejpam-6314	123	31	)	)	PUNCT
ejpam-6314	123	32	≾	≾	NOUN
ejpam-6314	123	33	0	0	NUM
ejpam-6314	123	34	,	,	PUNCT
ejpam-6314	123	35	(	(	PUNCT
ejpam-6314	123	36	bvcm2	bvcm2	NOUN
ejpam-6314	123	37	)	)	PUNCT
ejpam-6314	123	38	db(ς	db(ς	NOUN
ejpam-6314	123	39	,	,	PUNCT
ejpam-6314	123	40	α	α	NOUN
ejpam-6314	123	41	)	)	PUNCT
ejpam-6314	123	42	=	=	SYM
ejpam-6314	123	43	0	0	NUM
ejpam-6314	124	1	⇐	⇐	ADJ
ejpam-6314	124	2	⇒	⇒	NOUN
ejpam-6314	124	3	ς	ς	PROPN
ejpam-6314	124	4	=	=	SYM
ejpam-6314	124	5	α	α	PROPN
ejpam-6314	124	6	,	,	PUNCT
ejpam-6314	124	7	(	(	PUNCT
ejpam-6314	124	8	bvcm3	bvcm3	PROPN
ejpam-6314	124	9	)	)	PUNCT
ejpam-6314	124	10	db(ς	db(ς	ADV
ejpam-6314	124	11	,	,	PUNCT
ejpam-6314	124	12	α	α	NOUN
ejpam-6314	124	13	)	)	PUNCT
ejpam-6314	124	14	=	=	SYM
ejpam-6314	124	15	db(α	db(α	X
ejpam-6314	124	16	,	,	PUNCT
ejpam-6314	124	17	ς	ς	PROPN
ejpam-6314	124	18	)	)	PUNCT
ejpam-6314	124	19	,	,	PUNCT
ejpam-6314	124	20	(	(	PUNCT
ejpam-6314	124	21	bvcm4	bvcm4	NOUN
ejpam-6314	124	22	)	)	PUNCT
ejpam-6314	124	23	db(ς	db(ς	NOUN
ejpam-6314	124	24	,	,	PUNCT
ejpam-6314	124	25	β	β	X
ejpam-6314	124	26	)	)	PUNCT
ejpam-6314	124	27	≾	≾	PROPN
ejpam-6314	124	28	ϑ(ς	ϑ(ς	PROPN
ejpam-6314	124	29	,	,	PUNCT
ejpam-6314	124	30	α)db(ς	α)db(ς	PRON
ejpam-6314	124	31	,	,	PUNCT
ejpam-6314	124	32	α	α	X
ejpam-6314	124	33	)	)	PUNCT
ejpam-6314	124	34	+	+	CCONJ
ejpam-6314	124	35	ϑ(α	ϑ(α	PROPN
ejpam-6314	124	36	,	,	PUNCT
ejpam-6314	124	37	β)db(α	β)db(α	NOUN
ejpam-6314	124	38	,	,	PUNCT
ejpam-6314	124	39	β	β	NOUN
ejpam-6314	124	40	)	)	PUNCT
ejpam-6314	124	41	,	,	PUNCT
ejpam-6314	124	42	for	for	ADP
ejpam-6314	124	43	all	all	DET
ejpam-6314	124	44	ς	ς	PROPN
ejpam-6314	124	45	,	,	PUNCT
ejpam-6314	124	46	α	α	X
ejpam-6314	124	47	,	,	PUNCT
ejpam-6314	124	48	β	β	PROPN
ejpam-6314	124	49	∈	∈	PROPN
ejpam-6314	124	50	s.	s.	PROPN
ejpam-6314	124	51	then	then	ADV
ejpam-6314	124	52	,	,	PUNCT
ejpam-6314	124	53	the	the	DET
ejpam-6314	124	54	pair	pair	NOUN
ejpam-6314	124	55	(	(	PUNCT
ejpam-6314	124	56	s	s	X
ejpam-6314	124	57	,	,	PUNCT
ejpam-6314	124	58	db	db	PRON
ejpam-6314	124	59	)	)	PUNCT
ejpam-6314	124	60	is	be	AUX
ejpam-6314	124	61	termed	term	VERB
ejpam-6314	124	62	as	as	ADP
ejpam-6314	124	63	a	a	DET
ejpam-6314	124	64	bvcm	bvcm	NOUN
ejpam-6314	124	65	space	space	NOUN
ejpam-6314	124	66	.	.	PUNCT
ejpam-6314	125	1	example	example	NOUN
ejpam-6314	126	1	2	2	NUM
ejpam-6314	126	2	.	.	PUNCT
ejpam-6314	127	1	[	[	X
ejpam-6314	127	2	24	24	NUM
ejpam-6314	127	3	]	]	X
ejpam-6314	127	4	let	let	VERB
ejpam-6314	127	5	s	s	PRON
ejpam-6314	127	6	=	=	PUNCT
ejpam-6314	128	1	[	[	X
ejpam-6314	128	2	0	0	NUM
ejpam-6314	128	3	,	,	PUNCT
ejpam-6314	128	4	1	1	NUM
ejpam-6314	128	5	]	]	PUNCT
ejpam-6314	128	6	and	and	CCONJ
ejpam-6314	128	7	define	define	VERB
ejpam-6314	128	8	the	the	DET
ejpam-6314	128	9	function	function	NOUN
ejpam-6314	128	10	db	db	PROPN
ejpam-6314	128	11	:	:	PUNCT
ejpam-6314	128	12	s	s	VERB
ejpam-6314	128	13	×	×	PROPN
ejpam-6314	128	14	s	s	X
ejpam-6314	128	15	→	→	PUNCT
ejpam-6314	128	16	c2	c2	PROPN
ejpam-6314	128	17	by	by	ADP
ejpam-6314	128	18	db(σ	db(σ	NUM
ejpam-6314	128	19	,	,	PUNCT
ejpam-6314	128	20	v	v	NOUN
ejpam-6314	128	21	)	)	PUNCT
ejpam-6314	128	22	=	=	NOUN
ejpam-6314	128	23	|σ	|σ	NOUN
ejpam-6314	128	24	−	−	NOUN
ejpam-6314	128	25	v|2	v|2	PROPN
ejpam-6314	128	26	+	+	CCONJ
ejpam-6314	128	27	i2|σ	i2|σ	VERB
ejpam-6314	128	28	−	−	PROPN
ejpam-6314	128	29	v|2	v|2	PROPN
ejpam-6314	128	30	.	.	PUNCT
ejpam-6314	129	1	then	then	ADV
ejpam-6314	129	2	,	,	PUNCT
ejpam-6314	129	3	(	(	PUNCT
ejpam-6314	129	4	s	s	X
ejpam-6314	129	5	,	,	PUNCT
ejpam-6314	129	6	db	db	PRON
ejpam-6314	129	7	)	)	PUNCT
ejpam-6314	129	8	is	be	AUX
ejpam-6314	129	9	a	a	DET
ejpam-6314	129	10	complete	complete	ADJ
ejpam-6314	129	11	bi	bi	ADJ
ejpam-6314	129	12	-	-	ADJ
ejpam-6314	129	13	complex	complex	ADJ
ejpam-6314	129	14	b	b	X
ejpam-6314	129	15	-	-	PUNCT
ejpam-6314	129	16	metric	metric	ADJ
ejpam-6314	129	17	space	space	NOUN
ejpam-6314	129	18	with	with	ADP
ejpam-6314	129	19	ϑ(σ	ϑ(σ	PROPN
ejpam-6314	129	20	,	,	PUNCT
ejpam-6314	129	21	v	v	NOUN
ejpam-6314	129	22	)	)	PUNCT
ejpam-6314	129	23	=	=	SYM
ejpam-6314	129	24	2	2	X
ejpam-6314	129	25	.	.	NOUN
ejpam-6314	129	26	remark	remark	NOUN
ejpam-6314	129	27	1	1	NUM
ejpam-6314	129	28	.	.	PUNCT
ejpam-6314	130	1	[	[	X
ejpam-6314	130	2	24	24	NUM
ejpam-6314	130	3	]	]	PUNCT
ejpam-6314	130	4	every	every	DET
ejpam-6314	130	5	bicomplex	bicomplex	NOUN
ejpam-6314	130	6	-	-	PUNCT
ejpam-6314	130	7	valued	value	VERB
ejpam-6314	130	8	b	b	NOUN
ejpam-6314	130	9	-	-	PUNCT
ejpam-6314	130	10	metric	metric	ADJ
ejpam-6314	130	11	space	space	NOUN
ejpam-6314	130	12	is	be	AUX
ejpam-6314	130	13	a	a	DET
ejpam-6314	130	14	bvcm	bvcm	NOUN
ejpam-6314	130	15	space	space	NOUN
ejpam-6314	130	16	.	.	PUNCT
ejpam-6314	131	1	example	example	NOUN
ejpam-6314	132	1	3	3	NUM
ejpam-6314	132	2	.	.	PUNCT
ejpam-6314	133	1	[	[	X
ejpam-6314	133	2	25	25	NUM
ejpam-6314	133	3	]	]	PUNCT
ejpam-6314	133	4	let	let	VERB
ejpam-6314	133	5	s	s	PRON
ejpam-6314	133	6	=	=	VERB
ejpam-6314	133	7	{	{	PUNCT
ejpam-6314	133	8	1	1	NUM
ejpam-6314	133	9	,	,	PUNCT
ejpam-6314	133	10	2	2	NUM
ejpam-6314	133	11	,	,	PUNCT
ejpam-6314	133	12	3	3	NUM
ejpam-6314	133	13	}	}	PUNCT
ejpam-6314	133	14	and	and	CCONJ
ejpam-6314	133	15	b	b	X
ejpam-6314	133	16	:	:	PUNCT
ejpam-6314	133	17	s	s	VERB
ejpam-6314	133	18	×	×	PROPN
ejpam-6314	133	19	s	s	X
ejpam-6314	133	20	→	→	PUNCT
ejpam-6314	133	21	c2	c2	PROPN
ejpam-6314	133	22	be	be	AUX
ejpam-6314	133	23	defined	define	VERB
ejpam-6314	133	24	as	as	SCONJ
ejpam-6314	133	25	follows	follow	VERB
ejpam-6314	133	26	:	:	PUNCT
ejpam-6314	133	27	db(1	db(1	VERB
ejpam-6314	133	28	,	,	PUNCT
ejpam-6314	133	29	1	1	NUM
ejpam-6314	133	30	)	)	PUNCT
ejpam-6314	133	31	=	=	SYM
ejpam-6314	133	32	db(2	db(2	PROPN
ejpam-6314	133	33	,	,	PUNCT
ejpam-6314	133	34	2	2	NUM
ejpam-6314	133	35	)	)	PUNCT
ejpam-6314	133	36	=	=	SYM
ejpam-6314	133	37	db(3	db(3	NOUN
ejpam-6314	133	38	,	,	PUNCT
ejpam-6314	133	39	3	3	NUM
ejpam-6314	133	40	)	)	PUNCT
ejpam-6314	133	41	=	=	SYM
ejpam-6314	133	42	0	0	NUM
ejpam-6314	133	43	,	,	PUNCT
ejpam-6314	133	44	db(2	db(2	PROPN
ejpam-6314	133	45	,	,	PUNCT
ejpam-6314	133	46	1	1	NUM
ejpam-6314	133	47	)	)	PUNCT
ejpam-6314	133	48	=	=	VERB
ejpam-6314	133	49	db(1	db(1	VERB
ejpam-6314	133	50	,	,	PUNCT
ejpam-6314	133	51	2	2	NUM
ejpam-6314	133	52	)	)	PUNCT
ejpam-6314	133	53	=	=	SYM
ejpam-6314	133	54	4	4	NUM
ejpam-6314	133	55	+	+	SYM
ejpam-6314	133	56	4i2	4i2	NUM
ejpam-6314	133	57	,	,	PUNCT
ejpam-6314	133	58	db(3	db(3	NOUN
ejpam-6314	133	59	,	,	PUNCT
ejpam-6314	133	60	2	2	NUM
ejpam-6314	133	61	)	)	PUNCT
ejpam-6314	133	62	=	=	SYM
ejpam-6314	133	63	db(2	db(2	PROPN
ejpam-6314	133	64	,	,	PUNCT
ejpam-6314	133	65	3	3	NUM
ejpam-6314	133	66	)	)	PUNCT
ejpam-6314	133	67	=	=	SYM
ejpam-6314	133	68	1	1	NUM
ejpam-6314	133	69	+	+	NUM
ejpam-6314	133	70	2i2	2i2	NUM
ejpam-6314	133	71	,	,	PUNCT
ejpam-6314	133	72	db(3	db(3	NOUN
ejpam-6314	133	73	,	,	PUNCT
ejpam-6314	133	74	1	1	NUM
ejpam-6314	133	75	)	)	PUNCT
ejpam-6314	133	76	=	=	VERB
ejpam-6314	133	77	db(1	db(1	VERB
ejpam-6314	133	78	,	,	PUNCT
ejpam-6314	133	79	3	3	NUM
ejpam-6314	133	80	)	)	PUNCT
ejpam-6314	133	81	=	=	SYM
ejpam-6314	133	82	1−	1−	NUM
ejpam-6314	133	83	i2	i2	PROPN
ejpam-6314	133	84	.	.	PUNCT
ejpam-6314	134	1	also	also	ADV
ejpam-6314	134	2	,	,	PUNCT
ejpam-6314	134	3	let	let	VERB
ejpam-6314	134	4	ϑ	ϑ	X
ejpam-6314	134	5	:	:	PUNCT
ejpam-6314	134	6	s	s	VERB
ejpam-6314	134	7	×	×	PROPN
ejpam-6314	134	8	s	s	X
ejpam-6314	134	9	→	→	SYM
ejpam-6314	134	10	[	[	X
ejpam-6314	134	11	1,+∞	1,+∞	NUM
ejpam-6314	134	12	)	)	PUNCT
ejpam-6314	134	13	be	be	AUX
ejpam-6314	134	14	defined	define	VERB
ejpam-6314	134	15	as	as	SCONJ
ejpam-6314	134	16	follows	follow	VERB
ejpam-6314	134	17	:	:	PUNCT
ejpam-6314	135	1	ϑ(1	ϑ(1	NOUN
ejpam-6314	135	2	,	,	PUNCT
ejpam-6314	135	3	1	1	NUM
ejpam-6314	135	4	)	)	PUNCT
ejpam-6314	135	5	=	=	SYM
ejpam-6314	135	6	ϑ(2	ϑ(2	PROPN
ejpam-6314	135	7	,	,	PUNCT
ejpam-6314	135	8	2	2	NUM
ejpam-6314	135	9	)	)	PUNCT
ejpam-6314	135	10	=	=	SYM
ejpam-6314	135	11	ϑ(3	ϑ(3	PROPN
ejpam-6314	135	12	,	,	PUNCT
ejpam-6314	135	13	3	3	NUM
ejpam-6314	135	14	)	)	PUNCT
ejpam-6314	135	15	=	=	SYM
ejpam-6314	135	16	3	3	NUM
ejpam-6314	135	17	,	,	PUNCT
ejpam-6314	135	18	ϑ(1	ϑ(1	PROPN
ejpam-6314	135	19	,	,	PUNCT
ejpam-6314	135	20	2	2	NUM
ejpam-6314	135	21	)	)	PUNCT
ejpam-6314	135	22	=	=	SYM
ejpam-6314	135	23	ϑ(2	ϑ(2	PROPN
ejpam-6314	135	24	,	,	PUNCT
ejpam-6314	135	25	1	1	NUM
ejpam-6314	135	26	)	)	PUNCT
ejpam-6314	135	27	=	=	SYM
ejpam-6314	135	28	2	2	NUM
ejpam-6314	135	29	,	,	PUNCT
ejpam-6314	135	30	ϑ(2	ϑ(2	PROPN
ejpam-6314	135	31	,	,	PUNCT
ejpam-6314	135	32	3	3	NUM
ejpam-6314	135	33	)	)	PUNCT
ejpam-6314	135	34	=	=	PUNCT
ejpam-6314	135	35	ϑ(3	ϑ(3	PROPN
ejpam-6314	135	36	,	,	PUNCT
ejpam-6314	135	37	2	2	NUM
ejpam-6314	135	38	)	)	PUNCT
ejpam-6314	135	39	=	=	SYM
ejpam-6314	135	40	4	4	NUM
ejpam-6314	135	41	,	,	PUNCT
ejpam-6314	135	42	ϑ(1	ϑ(1	PROPN
ejpam-6314	135	43	,	,	PUNCT
ejpam-6314	135	44	3	3	NUM
ejpam-6314	135	45	)	)	PUNCT
ejpam-6314	135	46	=	=	PUNCT
ejpam-6314	135	47	ϑ(3	ϑ(3	PROPN
ejpam-6314	135	48	,	,	PUNCT
ejpam-6314	135	49	1	1	NUM
ejpam-6314	135	50	)	)	PUNCT
ejpam-6314	135	51	=	=	SYM
ejpam-6314	135	52	1	1	X
ejpam-6314	135	53	.	.	X
ejpam-6314	135	54	m.	m.	NOUN
ejpam-6314	135	55	sarwar	sarwar	PROPN
ejpam-6314	135	56	et	et	PROPN
ejpam-6314	136	1	al	al	PROPN
ejpam-6314	136	2	.	.	PUNCT
ejpam-6314	136	3	/	/	SYM
ejpam-6314	136	4	eur	eur	PROPN
ejpam-6314	136	5	.	.	PUNCT
ejpam-6314	137	1	j.	j.	PROPN
ejpam-6314	137	2	pure	pure	PROPN
ejpam-6314	137	3	appl	appl	PROPN
ejpam-6314	137	4	.	.	PROPN
ejpam-6314	137	5	math	math	PROPN
ejpam-6314	137	6	,	,	PUNCT
ejpam-6314	137	7	18	18	NUM
ejpam-6314	137	8	(	(	PUNCT
ejpam-6314	137	9	3	3	NUM
ejpam-6314	137	10	)	)	PUNCT
ejpam-6314	137	11	(	(	PUNCT
ejpam-6314	137	12	2025	2025	NUM
ejpam-6314	137	13	)	)	PUNCT
ejpam-6314	137	14	,	,	PUNCT
ejpam-6314	137	15	6314	6314	NUM
ejpam-6314	137	16	7	7	NUM
ejpam-6314	137	17	of	of	ADP
ejpam-6314	137	18	28	28	NUM
ejpam-6314	137	19	it	it	PRON
ejpam-6314	137	20	is	be	AUX
ejpam-6314	137	21	obvious	obvious	ADJ
ejpam-6314	137	22	that	that	SCONJ
ejpam-6314	137	23	the	the	DET
ejpam-6314	137	24	conditions	condition	NOUN
ejpam-6314	137	25	(	(	PUNCT
ejpam-6314	137	26	bvcm1	bvcm1	X
ejpam-6314	137	27	)	)	PUNCT
ejpam-6314	137	28	and	and	CCONJ
ejpam-6314	137	29	(	(	PUNCT
ejpam-6314	137	30	bvcm3	bvcm3	PROPN
ejpam-6314	137	31	)	)	PUNCT
ejpam-6314	137	32	fulfilled	fulfil	VERB
ejpam-6314	137	33	.	.	PUNCT
ejpam-6314	138	1	now	now	ADV
ejpam-6314	138	2	,	,	PUNCT
ejpam-6314	138	3	case	case	NOUN
ejpam-6314	138	4	1	1	X
ejpam-6314	138	5	.	.	PUNCT
ejpam-6314	139	1	if	if	SCONJ
ejpam-6314	139	2	ς	ς	PROPN
ejpam-6314	139	3	=	=	PUNCT
ejpam-6314	139	4	β	β	X
ejpam-6314	139	5	then	then	ADV
ejpam-6314	139	6	the	the	DET
ejpam-6314	139	7	condition	condition	NOUN
ejpam-6314	139	8	(	(	PUNCT
ejpam-6314	139	9	bvcm3	bvcm3	PROPN
ejpam-6314	139	10	)	)	PUNCT
ejpam-6314	139	11	fulfilled	fulfil	VERB
ejpam-6314	139	12	.	.	PUNCT
ejpam-6314	140	1	case	case	NOUN
ejpam-6314	140	2	2	2	NUM
ejpam-6314	140	3	.	.	PUNCT
ejpam-6314	141	1	if	if	SCONJ
ejpam-6314	141	2	ς	ς	PROPN
ejpam-6314	141	3	=	=	SYM
ejpam-6314	141	4	1	1	NUM
ejpam-6314	141	5	and	and	CCONJ
ejpam-6314	141	6	β	β	X
ejpam-6314	141	7	=	=	SYM
ejpam-6314	141	8	3	3	NUM
ejpam-6314	141	9	(	(	PUNCT
ejpam-6314	141	10	same	same	ADJ
ejpam-6314	141	11	as	as	ADP
ejpam-6314	141	12	β	β	NOUN
ejpam-6314	141	13	=	=	SYM
ejpam-6314	141	14	1	1	NUM
ejpam-6314	141	15	and	and	CCONJ
ejpam-6314	141	16	ς	ς	PROPN
ejpam-6314	141	17	=	=	SYM
ejpam-6314	141	18	3	3	NUM
ejpam-6314	141	19	)	)	PUNCT
ejpam-6314	141	20	and	and	CCONJ
ejpam-6314	141	21	α	α	NOUN
ejpam-6314	141	22	=	=	SYM
ejpam-6314	141	23	2	2	NUM
ejpam-6314	141	24	,	,	PUNCT
ejpam-6314	141	25	db(ς	db(ς	ADV
ejpam-6314	141	26	,	,	PUNCT
ejpam-6314	141	27	β	β	X
ejpam-6314	141	28	)	)	PUNCT
ejpam-6314	141	29	=	=	SYM
ejpam-6314	141	30	|db(1	|db(1	PROPN
ejpam-6314	141	31	,	,	PUNCT
ejpam-6314	141	32	3)|	3)|	NUM
ejpam-6314	141	33	=	=	SYM
ejpam-6314	141	34	|1−	|1−	PROPN
ejpam-6314	141	35	i2|	i2|	PROPN
ejpam-6314	141	36	≾	≾	PROPN
ejpam-6314	141	37	|12	|12	VERB
ejpam-6314	141	38	+	+	CCONJ
ejpam-6314	141	39	16i2|	16i2|	NUM
ejpam-6314	141	40	=	=	X
ejpam-6314	141	41	|2(4	|2(4	NOUN
ejpam-6314	141	42	+	+	NOUN
ejpam-6314	141	43	4i2	4i2	NUM
ejpam-6314	141	44	)	)	PUNCT
ejpam-6314	142	1	+	+	NUM
ejpam-6314	142	2	4(1	4(1	NUM
ejpam-6314	143	1	+	+	CCONJ
ejpam-6314	143	2	2i2)|	2i2)|	PROPN
ejpam-6314	143	3	≾	≾	NOUN
ejpam-6314	143	4	2	2	NUM
ejpam-6314	143	5	|4	|4	NUM
ejpam-6314	143	6	+	+	CCONJ
ejpam-6314	143	7	4i2|+	4i2|+	NUM
ejpam-6314	143	8	4	4	NUM
ejpam-6314	143	9	|1	|1	NUM
ejpam-6314	143	10	+	+	CCONJ
ejpam-6314	143	11	2i2|	2i2|	NOUN
ejpam-6314	143	12	=	=	NOUN
ejpam-6314	143	13	ϑ(1	ϑ(1	NOUN
ejpam-6314	143	14	,	,	PUNCT
ejpam-6314	143	15	2)db(1	2)db(1	NUM
ejpam-6314	143	16	,	,	PUNCT
ejpam-6314	143	17	2	2	NUM
ejpam-6314	143	18	)	)	PUNCT
ejpam-6314	143	19	+	+	X
ejpam-6314	143	20	ϑ(2	ϑ(2	PROPN
ejpam-6314	143	21	,	,	PUNCT
ejpam-6314	143	22	3)db(2	3)db(2	NUM
ejpam-6314	143	23	,	,	PUNCT
ejpam-6314	143	24	3	3	NUM
ejpam-6314	143	25	)	)	PUNCT
ejpam-6314	143	26	=	=	SYM
ejpam-6314	143	27	ϑ(ς	ϑ(ς	NOUN
ejpam-6314	143	28	,	,	PUNCT
ejpam-6314	143	29	α)db(ς	α)db(ς	PRON
ejpam-6314	143	30	,	,	PUNCT
ejpam-6314	143	31	α	α	X
ejpam-6314	143	32	)	)	PUNCT
ejpam-6314	143	33	+	+	CCONJ
ejpam-6314	143	34	ϑ(α	ϑ(α	PROPN
ejpam-6314	143	35	,	,	PUNCT
ejpam-6314	143	36	β)db(α	β)db(α	NOUN
ejpam-6314	143	37	,	,	PUNCT
ejpam-6314	143	38	β	β	NOUN
ejpam-6314	143	39	)	)	PUNCT
ejpam-6314	143	40	.	.	PUNCT
ejpam-6314	144	1	case	case	NOUN
ejpam-6314	145	1	3	3	X
ejpam-6314	145	2	.	.	PUNCT
ejpam-6314	146	1	if	if	SCONJ
ejpam-6314	146	2	ς	ς	PROPN
ejpam-6314	146	3	=	=	SYM
ejpam-6314	146	4	1	1	NUM
ejpam-6314	146	5	and	and	CCONJ
ejpam-6314	146	6	β	β	X
ejpam-6314	146	7	=	=	SYM
ejpam-6314	146	8	2	2	NUM
ejpam-6314	146	9	(	(	PUNCT
ejpam-6314	146	10	same	same	ADJ
ejpam-6314	146	11	as	as	ADP
ejpam-6314	146	12	β	β	NOUN
ejpam-6314	146	13	=	=	SYM
ejpam-6314	146	14	1	1	NUM
ejpam-6314	146	15	and	and	CCONJ
ejpam-6314	146	16	ς	ς	PROPN
ejpam-6314	146	17	=	=	SYM
ejpam-6314	146	18	2	2	NUM
ejpam-6314	146	19	)	)	PUNCT
ejpam-6314	146	20	and	and	CCONJ
ejpam-6314	146	21	α	α	NOUN
ejpam-6314	146	22	=	=	SYM
ejpam-6314	146	23	3	3	NUM
ejpam-6314	146	24	,	,	PUNCT
ejpam-6314	146	25	db(ς	db(ς	ADV
ejpam-6314	146	26	,	,	PUNCT
ejpam-6314	146	27	β	β	X
ejpam-6314	146	28	)	)	PUNCT
ejpam-6314	146	29	=	=	SYM
ejpam-6314	146	30	|db(1	|db(1	PROPN
ejpam-6314	146	31	,	,	PUNCT
ejpam-6314	146	32	2)|	2)|	NUM
ejpam-6314	146	33	=	=	SYM
ejpam-6314	146	34	|4	|4	NUM
ejpam-6314	146	35	+	+	SYM
ejpam-6314	146	36	4i2|	4i2|	NUM
ejpam-6314	146	37	≾	≾	NOUN
ejpam-6314	146	38	|5	|5	X
ejpam-6314	146	39	+	+	CCONJ
ejpam-6314	146	40	7i2|	7i2|	NUM
ejpam-6314	146	41	=	=	SYM
ejpam-6314	146	42	|1(1−	|1(1−	NOUN
ejpam-6314	146	43	i2	i2	PROPN
ejpam-6314	146	44	)	)	PUNCT
ejpam-6314	146	45	+	+	SYM
ejpam-6314	146	46	4(1	4(1	NUM
ejpam-6314	147	1	+	+	CCONJ
ejpam-6314	147	2	2i2)|	2i2)|	PROPN
ejpam-6314	147	3	≾	≾	PROPN
ejpam-6314	147	4	|1−	|1−	NOUN
ejpam-6314	147	5	i2|+	i2|+	NOUN
ejpam-6314	148	1	4|1	4|1	NUM
ejpam-6314	148	2	+	+	CCONJ
ejpam-6314	148	3	2i2|	2i2|	NOUN
ejpam-6314	148	4	=	=	NOUN
ejpam-6314	148	5	ϑ(1	ϑ(1	NOUN
ejpam-6314	148	6	,	,	PUNCT
ejpam-6314	148	7	3)db(1	3)db(1	NUM
ejpam-6314	148	8	,	,	PUNCT
ejpam-6314	148	9	3	3	NUM
ejpam-6314	148	10	)	)	PUNCT
ejpam-6314	148	11	+	+	CCONJ
ejpam-6314	148	12	ϑ(3	ϑ(3	PROPN
ejpam-6314	148	13	,	,	PUNCT
ejpam-6314	148	14	2)db(3	2)db(3	NUM
ejpam-6314	148	15	,	,	PUNCT
ejpam-6314	148	16	2	2	NUM
ejpam-6314	148	17	)	)	PUNCT
ejpam-6314	148	18	=	=	SYM
ejpam-6314	149	1	ϑ(ς	ϑ(ς	NOUN
ejpam-6314	149	2	,	,	PUNCT
ejpam-6314	149	3	α)db(ς	α)db(ς	PRON
ejpam-6314	149	4	,	,	PUNCT
ejpam-6314	149	5	α	α	X
ejpam-6314	149	6	)	)	PUNCT
ejpam-6314	149	7	+	+	CCONJ
ejpam-6314	149	8	ϑ(α	ϑ(α	PROPN
ejpam-6314	149	9	,	,	PUNCT
ejpam-6314	149	10	β)db(α	β)db(α	NOUN
ejpam-6314	149	11	,	,	PUNCT
ejpam-6314	149	12	β	β	NOUN
ejpam-6314	149	13	)	)	PUNCT
ejpam-6314	149	14	.	.	PUNCT
ejpam-6314	150	1	case	case	NOUN
ejpam-6314	150	2	4	4	NUM
ejpam-6314	150	3	.	.	PUNCT
ejpam-6314	151	1	if	if	SCONJ
ejpam-6314	151	2	ς	ς	PROPN
ejpam-6314	151	3	=	=	SYM
ejpam-6314	151	4	2	2	NUM
ejpam-6314	151	5	and	and	CCONJ
ejpam-6314	151	6	β	β	X
ejpam-6314	151	7	=	=	SYM
ejpam-6314	151	8	3	3	NUM
ejpam-6314	151	9	(	(	PUNCT
ejpam-6314	151	10	same	same	ADJ
ejpam-6314	151	11	as	as	ADP
ejpam-6314	151	12	β	β	X
ejpam-6314	151	13	=	=	SYM
ejpam-6314	151	14	3	3	NUM
ejpam-6314	151	15	and	and	CCONJ
ejpam-6314	151	16	ς	ς	PROPN
ejpam-6314	151	17	=	=	SYM
ejpam-6314	151	18	2	2	NUM
ejpam-6314	151	19	)	)	PUNCT
ejpam-6314	151	20	and	and	CCONJ
ejpam-6314	151	21	α	α	NOUN
ejpam-6314	151	22	=	=	SYM
ejpam-6314	151	23	1	1	NUM
ejpam-6314	151	24	,	,	PUNCT
ejpam-6314	151	25	db(ς	db(ς	ADV
ejpam-6314	151	26	,	,	PUNCT
ejpam-6314	151	27	β	β	X
ejpam-6314	152	1	)	)	PUNCT
ejpam-6314	152	2	=	=	SYM
ejpam-6314	152	3	|db(2	|db(2	PROPN
ejpam-6314	152	4	,	,	PUNCT
ejpam-6314	152	5	3)|	3)|	NUM
ejpam-6314	152	6	=	=	SYM
ejpam-6314	152	7	|1	|1	PRON
ejpam-6314	152	8	+	+	CCONJ
ejpam-6314	152	9	2i2|	2i2|	ADJ
ejpam-6314	152	10	≾	≾	PROPN
ejpam-6314	152	11	|9	|9	X
ejpam-6314	152	12	+	+	NUM
ejpam-6314	152	13	7i2|	7i2|	NUM
ejpam-6314	152	14	=	=	X
ejpam-6314	152	15	|2(4	|2(4	NOUN
ejpam-6314	152	16	+	+	NOUN
ejpam-6314	152	17	4i2	4i2	NUM
ejpam-6314	152	18	)	)	PUNCT
ejpam-6314	153	1	+	+	NUM
ejpam-6314	153	2	1(1−	1(1−	NUM
ejpam-6314	153	3	i2)|	i2)|	PROPN
ejpam-6314	153	4	≾	≾	PROPN
ejpam-6314	153	5	|4	|4	X
ejpam-6314	154	1	+	+	PROPN
ejpam-6314	155	1	4i2|+	4i2|+	NUM
ejpam-6314	155	2	1|1−	1|1−	NUM
ejpam-6314	155	3	i2|	i2|	PROPN
ejpam-6314	155	4	=	=	SYM
ejpam-6314	155	5	ϑ(2	ϑ(2	PROPN
ejpam-6314	155	6	,	,	PUNCT
ejpam-6314	155	7	1)db(2	1)db(2	NUM
ejpam-6314	155	8	,	,	PUNCT
ejpam-6314	155	9	1	1	NUM
ejpam-6314	155	10	)	)	PUNCT
ejpam-6314	155	11	+	+	CCONJ
ejpam-6314	155	12	ϑ(1	ϑ(1	PROPN
ejpam-6314	155	13	,	,	PUNCT
ejpam-6314	155	14	3)db(1	3)db(1	NUM
ejpam-6314	155	15	,	,	PUNCT
ejpam-6314	155	16	3	3	NUM
ejpam-6314	155	17	)	)	PUNCT
ejpam-6314	155	18	=	=	SYM
ejpam-6314	156	1	ϑ(ς	ϑ(ς	NOUN
ejpam-6314	156	2	,	,	PUNCT
ejpam-6314	156	3	α)db(ς	α)db(ς	PRON
ejpam-6314	156	4	,	,	PUNCT
ejpam-6314	156	5	α	α	X
ejpam-6314	156	6	)	)	PUNCT
ejpam-6314	156	7	+	+	CCONJ
ejpam-6314	156	8	ϑ(α	ϑ(α	PROPN
ejpam-6314	156	9	,	,	PUNCT
ejpam-6314	156	10	β)db(α	β)db(α	NOUN
ejpam-6314	156	11	,	,	PUNCT
ejpam-6314	156	12	β	β	NOUN
ejpam-6314	156	13	)	)	PUNCT
ejpam-6314	156	14	.	.	PUNCT
ejpam-6314	157	1	then	then	ADV
ejpam-6314	157	2	,	,	PUNCT
ejpam-6314	157	3	(	(	PUNCT
ejpam-6314	157	4	s	s	X
ejpam-6314	157	5	,	,	PUNCT
ejpam-6314	157	6	db	db	PRON
ejpam-6314	157	7	)	)	PUNCT
ejpam-6314	157	8	is	be	AUX
ejpam-6314	157	9	a	a	DET
ejpam-6314	157	10	(	(	PUNCT
ejpam-6314	157	11	bcvms	bcvms	NOUN
ejpam-6314	157	12	)	)	PUNCT
ejpam-6314	157	13	.	.	PUNCT
ejpam-6314	158	1	definition	definition	NOUN
ejpam-6314	158	2	3	3	NUM
ejpam-6314	158	3	.	.	PUNCT
ejpam-6314	159	1	[	[	X
ejpam-6314	159	2	25	25	NUM
ejpam-6314	159	3	]	]	X
ejpam-6314	159	4	let	let	VERB
ejpam-6314	159	5	(	(	PUNCT
ejpam-6314	159	6	s	s	X
ejpam-6314	159	7	,	,	PUNCT
ejpam-6314	159	8	db	db	PRON
ejpam-6314	159	9	)	)	PUNCT
ejpam-6314	159	10	be	be	AUX
ejpam-6314	159	11	a	a	DET
ejpam-6314	159	12	(	(	PUNCT
ejpam-6314	159	13	bcvms	bcvms	NOUN
ejpam-6314	159	14	)	)	PUNCT
ejpam-6314	159	15	with	with	ADP
ejpam-6314	159	16	a	a	DET
ejpam-6314	159	17	sequence	sequence	NOUN
ejpam-6314	159	18	{	{	PUNCT
ejpam-6314	159	19	κj	κj	PROPN
ejpam-6314	159	20	}	}	PUNCT
ejpam-6314	159	21	in	in	ADP
ejpam-6314	159	22	s	s	PRON
ejpam-6314	159	23	and	and	CCONJ
ejpam-6314	159	24	κ	κ	PROPN
ejpam-6314	159	25	∈	∈	PROPN
ejpam-6314	159	26	s.	s.	PROPN
ejpam-6314	159	27	then	then	ADV
ejpam-6314	159	28	,	,	PUNCT
ejpam-6314	159	29	[	[	X
ejpam-6314	159	30	i.	i.	NOUN
ejpam-6314	159	31	]	]	X
ejpam-6314	159	32	(	(	PUNCT
ejpam-6314	159	33	i	i	NOUN
ejpam-6314	159	34	)	)	PUNCT
ejpam-6314	159	35	a	a	DET
ejpam-6314	159	36	sequence	sequence	NOUN
ejpam-6314	159	37	{	{	PUNCT
ejpam-6314	159	38	κj	κj	PRON
ejpam-6314	159	39	}	}	PUNCT
ejpam-6314	159	40	in	in	ADP
ejpam-6314	159	41	s	s	PROPN
ejpam-6314	159	42	is	be	AUX
ejpam-6314	159	43	convergent	convergent	ADJ
ejpam-6314	159	44	to	to	ADP
ejpam-6314	159	45	κ	κ	PROPN
ejpam-6314	159	46	∈	∈	NOUN
ejpam-6314	159	47	s	s	PART
ejpam-6314	159	48	if	if	SCONJ
ejpam-6314	159	49	for	for	ADP
ejpam-6314	159	50	all	all	PRON
ejpam-6314	159	51	0	0	NUM
ejpam-6314	159	52	≾	≾	NOUN
ejpam-6314	159	53	α	α	NOUN
ejpam-6314	159	54	∈	∈	PROPN
ejpam-6314	159	55	c2	c2	PROPN
ejpam-6314	159	56	,	,	PUNCT
ejpam-6314	159	57	there	there	PRON
ejpam-6314	159	58	exists	exist	VERB
ejpam-6314	159	59	a	a	DET
ejpam-6314	159	60	natural	natural	ADJ
ejpam-6314	159	61	number	number	NOUN
ejpam-6314	159	62	n	n	ADP
ejpam-6314	159	63	such	such	ADJ
ejpam-6314	159	64	that	that	SCONJ
ejpam-6314	159	65	db(κj	db(κj	ADJ
ejpam-6314	159	66	,	,	PUNCT
ejpam-6314	159	67	κ	κ	NOUN
ejpam-6314	159	68	)	)	PUNCT
ejpam-6314	159	69	≾	≾	NOUN
ejpam-6314	159	70	α	α	NOUN
ejpam-6314	159	71	for	for	ADP
ejpam-6314	159	72	each	each	DET
ejpam-6314	159	73	j	j	PROPN
ejpam-6314	159	74	≥	≥	PROPN
ejpam-6314	159	75	n.	n.	NOUN
ejpam-6314	159	76	then	then	ADV
ejpam-6314	159	77	,	,	PUNCT
ejpam-6314	159	78	limj→+∞	limj→+∞	CCONJ
ejpam-6314	159	79	κj	κj	NOUN
ejpam-6314	159	80	=	=	PUNCT
ejpam-6314	159	81	κ	κ	NOUN
ejpam-6314	159	82	or	or	CCONJ
ejpam-6314	159	83	κj	κj	PROPN
ejpam-6314	159	84	→	→	SYM
ejpam-6314	159	85	κ	κ	NOUN
ejpam-6314	159	86	as	as	ADP
ejpam-6314	159	87	j	j	PROPN
ejpam-6314	159	88	→	→	SYM
ejpam-6314	159	89	+	+	PROPN
ejpam-6314	159	90	∞.	∞.	PROPN
ejpam-6314	159	91	(	(	PUNCT
ejpam-6314	159	92	ii	ii	NOUN
ejpam-6314	159	93	)	)	PUNCT
ejpam-6314	159	94	if	if	SCONJ
ejpam-6314	159	95	,	,	PUNCT
ejpam-6314	159	96	for	for	ADP
ejpam-6314	159	97	each	each	DET
ejpam-6314	159	98	0	0	NUM
ejpam-6314	159	99	≾	≾	NOUN
ejpam-6314	159	100	α	α	NOUN
ejpam-6314	159	101	where	where	SCONJ
ejpam-6314	159	102	α	α	PROPN
ejpam-6314	159	103	∈	∈	PROPN
ejpam-6314	159	104	c2	c2	PROPN
ejpam-6314	159	105	,	,	PUNCT
ejpam-6314	159	106	there	there	PRON
ejpam-6314	159	107	exists	exist	VERB
ejpam-6314	159	108	a	a	DET
ejpam-6314	159	109	natural	natural	ADJ
ejpam-6314	159	110	number	number	NOUN
ejpam-6314	159	111	n	n	ADP
ejpam-6314	159	112	such	such	ADJ
ejpam-6314	159	113	that	that	SCONJ
ejpam-6314	159	114	db(κj	db(κj	PROPN
ejpam-6314	159	115	,	,	PUNCT
ejpam-6314	159	116	κj+m	κj+m	NOUN
ejpam-6314	159	117	)	)	PUNCT
ejpam-6314	159	118	≾	≾	NOUN
ejpam-6314	159	119	α	α	NOUN
ejpam-6314	159	120	for	for	ADP
ejpam-6314	159	121	each	each	DET
ejpam-6314	159	122	m	m	PROPN
ejpam-6314	159	123	∈	∈	PROPN
ejpam-6314	159	124	n	n	NOUN
ejpam-6314	159	125	and	and	CCONJ
ejpam-6314	159	126	j	j	PROPN
ejpam-6314	159	127	>	>	X
ejpam-6314	159	128	n.	n.	PROPN
ejpam-6314	159	129	then	then	ADV
ejpam-6314	159	130	,	,	PUNCT
ejpam-6314	159	131	{	{	PUNCT
ejpam-6314	159	132	κj	κj	ADJ
ejpam-6314	159	133	}	}	PUNCT
ejpam-6314	159	134	is	be	AUX
ejpam-6314	159	135	referred	refer	VERB
ejpam-6314	159	136	to	to	ADP
ejpam-6314	159	137	as	as	ADP
ejpam-6314	159	138	a	a	DET
ejpam-6314	159	139	cauchy	cauchy	ADJ
ejpam-6314	159	140	sequence	sequence	NOUN
ejpam-6314	159	141	in	in	ADP
ejpam-6314	159	142	(	(	PUNCT
ejpam-6314	159	143	s	s	X
ejpam-6314	159	144	,	,	PUNCT
ejpam-6314	159	145	db	db	PROPN
ejpam-6314	159	146	)	)	PUNCT
ejpam-6314	159	147	.	.	PUNCT
ejpam-6314	160	1	(	(	PUNCT
ejpam-6314	160	2	iii	iii	X
ejpam-6314	160	3	)	)	PUNCT
ejpam-6314	160	4	if	if	SCONJ
ejpam-6314	160	5	each	each	DET
ejpam-6314	160	6	cauchy	cauchy	ADJ
ejpam-6314	160	7	sequence	sequence	NOUN
ejpam-6314	160	8	is	be	AUX
ejpam-6314	160	9	convergent	convergent	NOUN
ejpam-6314	160	10	in	in	ADP
ejpam-6314	160	11	s	s	PROPN
ejpam-6314	160	12	,	,	PUNCT
ejpam-6314	160	13	the	the	DET
ejpam-6314	160	14	(	(	PUNCT
ejpam-6314	160	15	bcvms	bcvms	NOUN
ejpam-6314	160	16	)	)	PUNCT
ejpam-6314	160	17	(	(	PUNCT
ejpam-6314	160	18	s,£bvc	s,£bvc	NUM
ejpam-6314	160	19	)	)	PUNCT
ejpam-6314	160	20	is	be	AUX
ejpam-6314	160	21	said	say	VERB
ejpam-6314	160	22	to	to	PART
ejpam-6314	160	23	be	be	AUX
ejpam-6314	160	24	complete	complete	ADJ
ejpam-6314	160	25	.	.	PUNCT
ejpam-6314	161	1	theorem	theorem	NOUN
ejpam-6314	161	2	1	1	NUM
ejpam-6314	161	3	.	.	PUNCT
ejpam-6314	162	1	[	[	X
ejpam-6314	162	2	25	25	NUM
ejpam-6314	162	3	]	]	PUNCT
ejpam-6314	162	4	suppose	suppose	VERB
ejpam-6314	162	5	that	that	SCONJ
ejpam-6314	162	6	(	(	PUNCT
ejpam-6314	162	7	s	s	X
ejpam-6314	162	8	,	,	PUNCT
ejpam-6314	162	9	db	db	PROPN
ejpam-6314	162	10	)	)	PUNCT
ejpam-6314	162	11	is	be	AUX
ejpam-6314	162	12	(	(	PUNCT
ejpam-6314	162	13	bcvms	bcvms	PROPN
ejpam-6314	162	14	)	)	PUNCT
ejpam-6314	162	15	which	which	PRON
ejpam-6314	162	16	is	be	AUX
ejpam-6314	162	17	complete	complete	ADJ
ejpam-6314	162	18	and	and	CCONJ
ejpam-6314	162	19	ψ	ψ	X
ejpam-6314	162	20	:	:	PUNCT
ejpam-6314	162	21	s	s	X
ejpam-6314	162	22	→	→	SYM
ejpam-6314	162	23	s	s	X
ejpam-6314	162	24	is	be	AUX
ejpam-6314	162	25	a	a	DET
ejpam-6314	162	26	map	map	NOUN
ejpam-6314	162	27	,	,	PUNCT
ejpam-6314	162	28	therefore	therefore	ADV
ejpam-6314	162	29	db(ψς	db(ψς	ADJ
ejpam-6314	162	30	,	,	PUNCT
ejpam-6314	162	31	ψα	ψα	ADP
ejpam-6314	162	32	)	)	PUNCT
ejpam-6314	162	33	≾	≾	PROPN
ejpam-6314	162	34	ωdb(ς	ωdb(ς	PROPN
ejpam-6314	162	35	,	,	PUNCT
ejpam-6314	162	36	α	α	NOUN
ejpam-6314	162	37	)	)	PUNCT
ejpam-6314	162	38	,	,	PUNCT
ejpam-6314	162	39	for	for	ADP
ejpam-6314	162	40	all	all	DET
ejpam-6314	162	41	ς	ς	PROPN
ejpam-6314	162	42	,	,	PUNCT
ejpam-6314	162	43	α	α	PROPN
ejpam-6314	162	44	∈	∈	PROPN
ejpam-6314	162	45	s	s	NOUN
ejpam-6314	162	46	,	,	PUNCT
ejpam-6314	162	47	where	where	SCONJ
ejpam-6314	162	48	0	0	X
ejpam-6314	162	49	<	<	X
ejpam-6314	162	50	ω	ω	X
ejpam-6314	162	51	<	<	X
ejpam-6314	162	52	1	1	NUM
ejpam-6314	162	53	.	.	PUNCT
ejpam-6314	163	1	for	for	ADP
ejpam-6314	163	2	ς0	ς0	PROPN
ejpam-6314	163	3	∈	∈	PROPN
ejpam-6314	163	4	s	s	NOUN
ejpam-6314	163	5	,	,	PUNCT
ejpam-6314	163	6	we	we	PRON
ejpam-6314	163	7	denote	denote	VERB
ejpam-6314	163	8	ςm	ςm	NOUN
ejpam-6314	163	9	=	=	PUNCT
ejpam-6314	163	10	ψmς0	ψmς0	PROPN
ejpam-6314	163	11	.	.	PUNCT
ejpam-6314	164	1	suppose	suppose	VERB
ejpam-6314	164	2	that	that	SCONJ
ejpam-6314	164	3	max	max	PROPN
ejpam-6314	164	4	m≥1	m≥1	PROPN
ejpam-6314	164	5	lim	lim	PROPN
ejpam-6314	164	6	i→+∞	i→+∞	PROPN
ejpam-6314	164	7	ϑ(ςi+1	ϑ(ςi+1	PROPN
ejpam-6314	164	8	,	,	PUNCT
ejpam-6314	164	9	ςi+2)ϑ(ςi+1	ςi+2)ϑ(ςi+1	NOUN
ejpam-6314	164	10	,	,	PUNCT
ejpam-6314	164	11	ςm	ςm	NOUN
ejpam-6314	164	12	)	)	PUNCT
ejpam-6314	164	13	ϑ(ςi	ϑ(ςi	PROPN
ejpam-6314	164	14	,	,	PUNCT
ejpam-6314	164	15	ςi+1	ςi+1	X
ejpam-6314	164	16	)	)	PUNCT
ejpam-6314	164	17	<	<	X
ejpam-6314	164	18	1	1	NUM
ejpam-6314	164	19	ω	ω	NOUN
ejpam-6314	164	20	.	.	PUNCT
ejpam-6314	165	1	in	in	ADP
ejpam-6314	165	2	addition	addition	NOUN
ejpam-6314	165	3	,	,	PUNCT
ejpam-6314	165	4	for	for	ADP
ejpam-6314	165	5	each	each	DET
ejpam-6314	165	6	ς	ς	PROPN
ejpam-6314	165	7	∈	∈	PROPN
ejpam-6314	165	8	s	s	PROPN
ejpam-6314	165	9	,	,	PUNCT
ejpam-6314	165	10	lim	lim	PROPN
ejpam-6314	165	11	η→+∞	η→+∞	PROPN
ejpam-6314	165	12	ϑ(ςη	ϑ(ςη	PROPN
ejpam-6314	165	13	,	,	PUNCT
ejpam-6314	165	14	ς	ς	NOUN
ejpam-6314	165	15	)	)	PUNCT
ejpam-6314	165	16	and	and	CCONJ
ejpam-6314	165	17	lim	lim	PROPN
ejpam-6314	165	18	η→+∞	η→+∞	PROPN
ejpam-6314	165	19	ϑ(ς	ϑ(ς	PROPN
ejpam-6314	165	20	,	,	PUNCT
ejpam-6314	165	21	ςη)∃	ςη)∃	NUM
ejpam-6314	165	22	and	and	CCONJ
ejpam-6314	165	23	is	be	AUX
ejpam-6314	165	24	finite	finite	ADJ
ejpam-6314	165	25	.	.	PUNCT
ejpam-6314	166	1	then	then	ADV
ejpam-6314	166	2	,	,	PUNCT
ejpam-6314	166	3	ψ	ψ	X
ejpam-6314	166	4	has	have	VERB
ejpam-6314	166	5	a	a	DET
ejpam-6314	166	6	ufp	ufp	NOUN
ejpam-6314	166	7	.	.	PUNCT
ejpam-6314	167	1	m.	m.	NOUN
ejpam-6314	167	2	sarwar	sarwar	PROPN
ejpam-6314	167	3	et	et	PROPN
ejpam-6314	167	4	al	al	PROPN
ejpam-6314	167	5	.	.	PUNCT
ejpam-6314	167	6	/	/	SYM
ejpam-6314	167	7	eur	eur	PROPN
ejpam-6314	167	8	.	.	PUNCT
ejpam-6314	168	1	j.	j.	PROPN
ejpam-6314	168	2	pure	pure	PROPN
ejpam-6314	168	3	appl	appl	PROPN
ejpam-6314	168	4	.	.	PROPN
ejpam-6314	168	5	math	math	PROPN
ejpam-6314	168	6	,	,	PUNCT
ejpam-6314	168	7	18	18	NUM
ejpam-6314	168	8	(	(	PUNCT
ejpam-6314	168	9	3	3	NUM
ejpam-6314	168	10	)	)	PUNCT
ejpam-6314	168	11	(	(	PUNCT
ejpam-6314	168	12	2025	2025	NUM
ejpam-6314	168	13	)	)	PUNCT
ejpam-6314	168	14	,	,	PUNCT
ejpam-6314	168	15	6314	6314	NUM
ejpam-6314	168	16	8	8	NUM
ejpam-6314	168	17	of	of	ADP
ejpam-6314	168	18	28	28	NUM
ejpam-6314	168	19	theorem	theorem	NOUN
ejpam-6314	168	20	2	2	NUM
ejpam-6314	168	21	.	.	PUNCT
ejpam-6314	169	1	[	[	X
ejpam-6314	169	2	25	25	NUM
ejpam-6314	169	3	]	]	PUNCT
ejpam-6314	169	4	suppose	suppose	VERB
ejpam-6314	169	5	that	that	SCONJ
ejpam-6314	169	6	(	(	PUNCT
ejpam-6314	169	7	s	s	X
ejpam-6314	169	8	,	,	PUNCT
ejpam-6314	169	9	db	db	PROPN
ejpam-6314	169	10	)	)	PUNCT
ejpam-6314	169	11	is	be	AUX
ejpam-6314	169	12	(	(	PUNCT
ejpam-6314	169	13	bcvms	bcvms	PROPN
ejpam-6314	169	14	)	)	PUNCT
ejpam-6314	169	15	which	which	PRON
ejpam-6314	169	16	is	be	AUX
ejpam-6314	169	17	complete	complete	ADJ
ejpam-6314	169	18	and	and	CCONJ
ejpam-6314	169	19	ψ	ψ	X
ejpam-6314	169	20	:	:	PUNCT
ejpam-6314	169	21	s	s	X
ejpam-6314	169	22	→	→	SYM
ejpam-6314	169	23	s	s	X
ejpam-6314	169	24	is	be	AUX
ejpam-6314	169	25	a	a	DET
ejpam-6314	169	26	map	map	NOUN
ejpam-6314	169	27	,	,	PUNCT
ejpam-6314	169	28	therefore	therefore	ADV
ejpam-6314	169	29	db(ψς	db(ψς	ADJ
ejpam-6314	169	30	,	,	PUNCT
ejpam-6314	169	31	ψi	ψi	ADJ
ejpam-6314	169	32	)	)	PUNCT
ejpam-6314	169	33	≾i2	≾i2	NOUN
ejpam-6314	169	34	κ(db(ψς	κ(db(ψς	NOUN
ejpam-6314	169	35	,	,	PUNCT
ejpam-6314	169	36	ς	ς	NOUN
ejpam-6314	169	37	)	)	PUNCT
ejpam-6314	170	1	+	+	SYM
ejpam-6314	170	2	db(ψα	db(ψα	PROPN
ejpam-6314	170	3	,	,	PUNCT
ejpam-6314	170	4	α	α	NOUN
ejpam-6314	170	5	)	)	PUNCT
ejpam-6314	170	6	)	)	PUNCT
ejpam-6314	170	7	.	.	PUNCT
ejpam-6314	171	1	for	for	ADP
ejpam-6314	171	2	all	all	DET
ejpam-6314	171	3	κ	κ	PROPN
ejpam-6314	171	4	,	,	PUNCT
ejpam-6314	171	5	σ	σ	PROPN
ejpam-6314	171	6	∈	∈	PROPN
ejpam-6314	171	7	s	s	NOUN
ejpam-6314	171	8	,	,	PUNCT
ejpam-6314	171	9	where	where	SCONJ
ejpam-6314	171	10	0	0	NUM
ejpam-6314	171	11	≤	≤	NUM
ejpam-6314	171	12	ω	ω	NOUN
ejpam-6314	171	13	<	<	X
ejpam-6314	171	14	1	1	NUM
ejpam-6314	171	15	2	2	NUM
ejpam-6314	171	16	.	.	PUNCT
ejpam-6314	172	1	for	for	ADP
ejpam-6314	172	2	ς0	ς0	PROPN
ejpam-6314	172	3	∈	∈	PROPN
ejpam-6314	172	4	s	s	NOUN
ejpam-6314	172	5	,	,	PUNCT
ejpam-6314	172	6	we	we	PRON
ejpam-6314	172	7	denote	denote	VERB
ejpam-6314	172	8	ςm	ςm	NOUN
ejpam-6314	172	9	=	=	PUNCT
ejpam-6314	172	10	ψmς0	ψmς0	PROPN
ejpam-6314	172	11	.	.	PUNCT
ejpam-6314	173	1	suppose	suppose	VERB
ejpam-6314	173	2	that	that	SCONJ
ejpam-6314	173	3	max	max	PROPN
ejpam-6314	173	4	m≥1	m≥1	PROPN
ejpam-6314	173	5	lim	lim	PROPN
ejpam-6314	173	6	i→+∞	i→+∞	PROPN
ejpam-6314	173	7	ϑ(ςi+1	ϑ(ςi+1	PROPN
ejpam-6314	173	8	,	,	PUNCT
ejpam-6314	173	9	ςi+2)ϑ(ςi	ςi+2)ϑ(ςi	NOUN
ejpam-6314	173	10	,	,	PUNCT
ejpam-6314	173	11	ςm	ςm	NOUN
ejpam-6314	173	12	)	)	PUNCT
ejpam-6314	173	13	ϑ(ςi	ϑ(ςi	PROPN
ejpam-6314	173	14	,	,	PUNCT
ejpam-6314	173	15	ςi+1	ςi+1	X
ejpam-6314	173	16	)	)	PUNCT
ejpam-6314	173	17	<	<	X
ejpam-6314	173	18	1	1	NUM
ejpam-6314	173	19	ω	ω	NUM
ejpam-6314	173	20	.	.	PUNCT
ejpam-6314	174	1	where	where	SCONJ
ejpam-6314	174	2	ω	ω	X
ejpam-6314	174	3	=	=	SYM
ejpam-6314	174	4	κ	κ	X
ejpam-6314	174	5	1−κ	1−κ	ADJ
ejpam-6314	174	6	in	in	ADP
ejpam-6314	174	7	addition	addition	NOUN
ejpam-6314	174	8	,	,	PUNCT
ejpam-6314	174	9	for	for	ADP
ejpam-6314	174	10	each	each	DET
ejpam-6314	174	11	ς	ς	PROPN
ejpam-6314	174	12	∈	∈	PROPN
ejpam-6314	174	13	s	s	PROPN
ejpam-6314	174	14	,	,	PUNCT
ejpam-6314	174	15	lim	lim	PROPN
ejpam-6314	174	16	η→+∞	η→+∞	PROPN
ejpam-6314	174	17	ϑ(ςη	ϑ(ςη	PROPN
ejpam-6314	174	18	,	,	PUNCT
ejpam-6314	174	19	ς	ς	NOUN
ejpam-6314	174	20	)	)	PUNCT
ejpam-6314	174	21	and	and	CCONJ
ejpam-6314	174	22	lim	lim	PROPN
ejpam-6314	174	23	η→+∞	η→+∞	PROPN
ejpam-6314	174	24	ϑ(ς	ϑ(ς	PROPN
ejpam-6314	174	25	,	,	PUNCT
ejpam-6314	174	26	ςη)exists	ςη)exist	NOUN
ejpam-6314	174	27	and	and	CCONJ
ejpam-6314	174	28	is	be	AUX
ejpam-6314	174	29	finite	finite	ADJ
ejpam-6314	174	30	.	.	PUNCT
ejpam-6314	175	1	then	then	ADV
ejpam-6314	175	2	,	,	PUNCT
ejpam-6314	175	3	ψ	ψ	X
ejpam-6314	175	4	has	have	VERB
ejpam-6314	175	5	a	a	DET
ejpam-6314	175	6	ufp	ufp	NOUN
ejpam-6314	175	7	.	.	PUNCT
ejpam-6314	176	1	2	2	X
ejpam-6314	176	2	.	.	X
ejpam-6314	176	3	main	main	ADJ
ejpam-6314	176	4	results	result	NOUN
ejpam-6314	176	5	in	in	ADP
ejpam-6314	176	6	this	this	DET
ejpam-6314	176	7	section	section	NOUN
ejpam-6314	176	8	,	,	PUNCT
ejpam-6314	176	9	we	we	PRON
ejpam-6314	176	10	provide	provide	VERB
ejpam-6314	176	11	the	the	DET
ejpam-6314	176	12	proof	proof	NOUN
ejpam-6314	176	13	of	of	ADP
ejpam-6314	176	14	the	the	DET
ejpam-6314	176	15	unique	unique	ADJ
ejpam-6314	176	16	and	and	CCONJ
ejpam-6314	176	17	common	common	ADJ
ejpam-6314	176	18	fixed	fix	VERB
ejpam-6314	176	19	point	point	NOUN
ejpam-6314	176	20	theorem	theorem	VERB
ejpam-6314	176	21	in	in	ADP
ejpam-6314	176	22	bi	bi	ADJ
ejpam-6314	176	23	-	-	ADJ
ejpam-6314	176	24	complex	complex	ADJ
ejpam-6314	176	25	valued	value	VERB
ejpam-6314	176	26	controlled	control	VERB
ejpam-6314	176	27	metric	metric	ADJ
ejpam-6314	176	28	space	space	NOUN
ejpam-6314	176	29	.	.	PUNCT
ejpam-6314	177	1	on	on	ADP
ejpam-6314	177	2	the	the	DET
ejpam-6314	177	3	basis	basis	NOUN
ejpam-6314	177	4	of	of	ADP
ejpam-6314	177	5	the	the	DET
ejpam-6314	177	6	theorems	theorem	NOUN
ejpam-6314	177	7	,	,	PUNCT
ejpam-6314	177	8	we	we	PRON
ejpam-6314	177	9	also	also	ADV
ejpam-6314	177	10	offer	offer	VERB
ejpam-6314	177	11	examples	example	NOUN
ejpam-6314	177	12	and	and	CCONJ
ejpam-6314	177	13	applications	application	NOUN
ejpam-6314	177	14	.	.	PUNCT
ejpam-6314	178	1	the	the	DET
ejpam-6314	178	2	following	follow	VERB
ejpam-6314	178	3	is	be	AUX
ejpam-6314	178	4	the	the	DET
ejpam-6314	178	5	first	first	ADJ
ejpam-6314	178	6	theorem	theorem	VERB
ejpam-6314	178	7	.	.	PUNCT
ejpam-6314	178	8	theorem	theorem	NOUN
ejpam-6314	178	9	3	3	X
ejpam-6314	178	10	.	.	PUNCT
ejpam-6314	179	1	let	let	AUX
ejpam-6314	179	2	(	(	PUNCT
ejpam-6314	179	3	s	s	X
ejpam-6314	179	4	,	,	PUNCT
ejpam-6314	179	5	db	db	PRON
ejpam-6314	179	6	)	)	PUNCT
ejpam-6314	179	7	be	be	AUX
ejpam-6314	179	8	a	a	DET
ejpam-6314	179	9	(	(	PUNCT
ejpam-6314	179	10	bcvms	bcvms	NOUN
ejpam-6314	179	11	)	)	PUNCT
ejpam-6314	179	12	which	which	PRON
ejpam-6314	179	13	is	be	AUX
ejpam-6314	179	14	complete	complete	ADJ
ejpam-6314	179	15	and	and	CCONJ
ejpam-6314	179	16	ψ	ψ	X
ejpam-6314	179	17	:	:	PUNCT
ejpam-6314	179	18	s	s	AUX
ejpam-6314	179	19	−→	−→	NOUN
ejpam-6314	179	20	s	s	AUX
ejpam-6314	179	21	be	be	AUX
ejpam-6314	179	22	such	such	ADJ
ejpam-6314	179	23	that	that	SCONJ
ejpam-6314	179	24	there	there	PRON
ejpam-6314	179	25	are	be	VERB
ejpam-6314	179	26	µ	µ	PRON
ejpam-6314	179	27	,	,	PUNCT
ejpam-6314	179	28	ν	ν	PROPN
ejpam-6314	179	29	,	,	PUNCT
ejpam-6314	179	30	γ	γ	X
ejpam-6314	179	31	∈	∈	PROPN
ejpam-6314	179	32	(	(	PUNCT
ejpam-6314	179	33	0	0	NUM
ejpam-6314	179	34	,	,	PUNCT
ejpam-6314	179	35	1	1	NUM
ejpam-6314	179	36	)	)	PUNCT
ejpam-6314	179	37	with	with	ADP
ejpam-6314	179	38	ω	ω	PROPN
ejpam-6314	179	39	=	=	SYM
ejpam-6314	179	40	µ+ν	µ+ν	NOUN
ejpam-6314	179	41	1−γ	1−γ	X
ejpam-6314	179	42	<	<	X
ejpam-6314	179	43	1	1	NUM
ejpam-6314	179	44	,	,	PUNCT
ejpam-6314	179	45	such	such	ADJ
ejpam-6314	179	46	that	that	SCONJ
ejpam-6314	179	47	db	db	PROPN
ejpam-6314	179	48	(	(	PUNCT
ejpam-6314	179	49	ψκ	ψκ	PROPN
ejpam-6314	179	50	,	,	PUNCT
ejpam-6314	179	51	ψσ	ψσ	ADJ
ejpam-6314	179	52	)	)	PUNCT
ejpam-6314	179	53	≾	≾	PROPN
ejpam-6314	179	54	µdb(κ	µdb(κ	PROPN
ejpam-6314	179	55	,	,	PUNCT
ejpam-6314	179	56	σ	σ	PROPN
ejpam-6314	179	57	)	)	PUNCT
ejpam-6314	180	1	+	+	NUM
ejpam-6314	180	2	νdb	νdb	NOUN
ejpam-6314	180	3	(	(	PUNCT
ejpam-6314	180	4	κ	κ	NOUN
ejpam-6314	180	5	,	,	PUNCT
ejpam-6314	180	6	ψκ	ψκ	PROPN
ejpam-6314	180	7	)	)	PUNCT
ejpam-6314	180	8	+	+	NUM
ejpam-6314	180	9	γdb	γdb	PROPN
ejpam-6314	180	10	(	(	PUNCT
ejpam-6314	180	11	σ	σ	NOUN
ejpam-6314	180	12	,	,	PUNCT
ejpam-6314	180	13	ψσ	ψσ	ADJ
ejpam-6314	180	14	)	)	PUNCT
ejpam-6314	180	15	,	,	PUNCT
ejpam-6314	180	16	(	(	PUNCT
ejpam-6314	180	17	1	1	X
ejpam-6314	180	18	)	)	PUNCT
ejpam-6314	180	19	for	for	ADP
ejpam-6314	180	20	all	all	DET
ejpam-6314	180	21	κ	κ	PROPN
ejpam-6314	180	22	,	,	PUNCT
ejpam-6314	180	23	σ	σ	PROPN
ejpam-6314	180	24	∈	∈	PROPN
ejpam-6314	180	25	s	s	NOUN
ejpam-6314	180	26	,	,	PUNCT
ejpam-6314	180	27	where	where	SCONJ
ejpam-6314	180	28	0	0	NUM
ejpam-6314	180	29	≤	≤	NUM
ejpam-6314	180	30	ω	ω	X
ejpam-6314	180	31	<	<	X
ejpam-6314	180	32	1	1	NUM
ejpam-6314	180	33	.	.	PUNCT
ejpam-6314	181	1	for	for	ADP
ejpam-6314	181	2	ς0	ς0	PROPN
ejpam-6314	181	3	∈	∈	PROPN
ejpam-6314	181	4	s	s	NOUN
ejpam-6314	181	5	,	,	PUNCT
ejpam-6314	181	6	we	we	PRON
ejpam-6314	181	7	assume	assume	VERB
ejpam-6314	181	8	that	that	SCONJ
ejpam-6314	181	9	ςm	ςm	NOUN
ejpam-6314	181	10	=	=	SYM
ejpam-6314	181	11	ψmς0	ψmς0	PROPN
ejpam-6314	181	12	.	.	PUNCT
ejpam-6314	182	1	let	let	VERB
ejpam-6314	182	2	max	max	PROPN
ejpam-6314	182	3	m≥1	m≥1	PROPN
ejpam-6314	182	4	lim	lim	PROPN
ejpam-6314	182	5	i→+∞	i→+∞	VERB
ejpam-6314	182	6	ϑ(κi+1,κi+2)ϑ(κi	ϑ(κi+1,κi+2)ϑ(κi	PROPN
ejpam-6314	182	7	,	,	PUNCT
ejpam-6314	182	8	κm	κm	NOUN
ejpam-6314	182	9	)	)	PUNCT
ejpam-6314	182	10	ϑ(κi	ϑ(κi	NOUN
ejpam-6314	182	11	,	,	PUNCT
ejpam-6314	182	12	κi+1	κi+1	X
ejpam-6314	182	13	)	)	PUNCT
ejpam-6314	182	14	<	<	X
ejpam-6314	182	15	1	1	NUM
ejpam-6314	182	16	ω	ω	NUM
ejpam-6314	182	17	.	.	PUNCT
ejpam-6314	183	1	(	(	PUNCT
ejpam-6314	183	2	2	2	X
ejpam-6314	183	3	)	)	PUNCT
ejpam-6314	183	4	suppose	suppose	VERB
ejpam-6314	183	5	that	that	SCONJ
ejpam-6314	183	6	,	,	PUNCT
ejpam-6314	183	7	lim	lim	PROPN
ejpam-6314	183	8	η→+∞	η→+∞	PROPN
ejpam-6314	183	9	ϑ(κη	ϑ(κη	PROPN
ejpam-6314	183	10	,	,	PUNCT
ejpam-6314	183	11	κ	κ	NOUN
ejpam-6314	183	12	)	)	PUNCT
ejpam-6314	183	13	and	and	CCONJ
ejpam-6314	183	14	lim	lim	PROPN
ejpam-6314	183	15	η→+∞	η→+∞	PROPN
ejpam-6314	183	16	ϑ(κ	ϑ(κ	PROPN
ejpam-6314	183	17	,	,	PUNCT
ejpam-6314	183	18	κη	κη	PROPN
ejpam-6314	183	19	)	)	PUNCT
ejpam-6314	183	20	exist	exist	VERB
ejpam-6314	183	21	and	and	CCONJ
ejpam-6314	183	22	are	be	AUX
ejpam-6314	183	23	finite	finite	ADJ
ejpam-6314	183	24	,	,	PUNCT
ejpam-6314	183	25	and	and	CCONJ
ejpam-6314	183	26	γ	γ	X
ejpam-6314	183	27	limη→+∞	limη→+∞	PROPN
ejpam-6314	183	28	ϑ(κη	ϑ(κη	PROPN
ejpam-6314	183	29	,	,	PUNCT
ejpam-6314	183	30	κ	κ	NOUN
ejpam-6314	183	31	)	)	PUNCT
ejpam-6314	183	32	<	<	X
ejpam-6314	183	33	1	1	NUM
ejpam-6314	183	34	for	for	ADP
ejpam-6314	183	35	every	every	DET
ejpam-6314	183	36	κ	κ	PROPN
ejpam-6314	183	37	∈	∈	PROPN
ejpam-6314	183	38	s	s	NOUN
ejpam-6314	183	39	,	,	PUNCT
ejpam-6314	183	40	then	then	ADV
ejpam-6314	183	41	ψ	ψ	AUX
ejpam-6314	183	42	have	have	VERB
ejpam-6314	183	43	a	a	DET
ejpam-6314	183	44	ufp	ufp	NOUN
ejpam-6314	183	45	.	.	PUNCT
ejpam-6314	184	1	proof	proof	NOUN
ejpam-6314	184	2	.	.	PUNCT
ejpam-6314	185	1	the	the	DET
ejpam-6314	185	2	examined	examine	VERB
ejpam-6314	185	3	sequence	sequence	NOUN
ejpam-6314	185	4	(	(	PUNCT
ejpam-6314	185	5	κn	κn	NOUN
ejpam-6314	185	6	)	)	PUNCT
ejpam-6314	185	7	verifies	verifie	NOUN
ejpam-6314	185	8	κn+1	κn+1	VERB
ejpam-6314	185	9	=	=	SYM
ejpam-6314	185	10	ψ(κn	ψ(κn	X
ejpam-6314	185	11	)	)	PUNCT
ejpam-6314	185	12	for	for	ADP
ejpam-6314	185	13	all	all	PRON
ejpam-6314	185	14	n	n	DET
ejpam-6314	185	15	∈	∈	PROPN
ejpam-6314	185	16	n.	n.	NOUN
ejpam-6314	185	17	clearly	clearly	ADV
ejpam-6314	185	18	,	,	PUNCT
ejpam-6314	185	19	if	if	SCONJ
ejpam-6314	185	20	there	there	PRON
ejpam-6314	185	21	exists	exist	VERB
ejpam-6314	185	22	n0	n0	PROPN
ejpam-6314	185	23	∈	∈	PROPN
ejpam-6314	185	24	n	n	X
ejpam-6314	185	25	for	for	ADP
ejpam-6314	185	26	which	which	PRON
ejpam-6314	185	27	κn0	κn0	NOUN
ejpam-6314	185	28	+	+	SYM
ejpam-6314	185	29	1	1	NUM
ejpam-6314	185	30	=	=	SYM
ejpam-6314	185	31	κn0	κn0	NOUN
ejpam-6314	185	32	,	,	PUNCT
ejpam-6314	185	33	then	then	ADV
ejpam-6314	185	34	ψ(κn0	ψ(κn0	NOUN
ejpam-6314	185	35	)	)	PUNCT
ejpam-6314	186	1	=	=	PUNCT
ejpam-6314	186	2	κn0	κn0	NOUN
ejpam-6314	186	3	,	,	PUNCT
ejpam-6314	186	4	and	and	CCONJ
ejpam-6314	186	5	the	the	DET
ejpam-6314	186	6	proof	proof	NOUN
ejpam-6314	186	7	is	be	AUX
ejpam-6314	186	8	complete	complete	ADJ
ejpam-6314	186	9	.	.	PUNCT
ejpam-6314	187	1	thus	thus	ADV
ejpam-6314	187	2	,	,	PUNCT
ejpam-6314	187	3	we	we	PRON
ejpam-6314	187	4	assume	assume	VERB
ejpam-6314	187	5	that	that	SCONJ
ejpam-6314	187	6	κn+1	κn+1	VERB
ejpam-6314	187	7	=	=	SYM
ejpam-6314	187	8	κn	κn	NOUN
ejpam-6314	187	9	for	for	ADP
ejpam-6314	187	10	every	every	DET
ejpam-6314	187	11	n	n	PRON
ejpam-6314	187	12	∈	∈	NOUN
ejpam-6314	187	13	n.	n.	NOUN
ejpam-6314	187	14	thus	thus	ADV
ejpam-6314	187	15	by	by	ADP
ejpam-6314	187	16	(	(	PUNCT
ejpam-6314	187	17	1	1	NUM
ejpam-6314	187	18	)	)	PUNCT
ejpam-6314	187	19	,	,	PUNCT
ejpam-6314	187	20	we	we	PRON
ejpam-6314	187	21	have	have	VERB
ejpam-6314	187	22	db(κn	db(κn	NOUN
ejpam-6314	187	23	,	,	PUNCT
ejpam-6314	187	24	κn+1	κn+1	NOUN
ejpam-6314	187	25	)	)	PUNCT
ejpam-6314	187	26	≾	≾	PROPN
ejpam-6314	187	27	db(ψ(κn−1),ψ(κn	db(ψ(κn−1),ψ(κn	PROPN
ejpam-6314	187	28	)	)	PUNCT
ejpam-6314	187	29	)	)	PUNCT
ejpam-6314	188	1	≾	≾	PROPN
ejpam-6314	188	2	µdb(κn−1,κn)+νdb(κn−1,ψ(κn−1))+γdb(κn	µdb(κn−1,κn)+νdb(κn−1,ψ(κn−1))+γdb(κn	NOUN
ejpam-6314	188	3	,	,	PUNCT
ejpam-6314	188	4	ψ(κn	ψ(κn	NOUN
ejpam-6314	188	5	)	)	PUNCT
ejpam-6314	188	6	)	)	PUNCT
ejpam-6314	188	7	,	,	PUNCT
ejpam-6314	188	8	which	which	PRON
ejpam-6314	188	9	implies	imply	VERB
ejpam-6314	188	10	that	that	SCONJ
ejpam-6314	188	11	db(κn	db(κn	NOUN
ejpam-6314	188	12	,	,	PUNCT
ejpam-6314	188	13	κn+1	κn+1	NOUN
ejpam-6314	188	14	)	)	PUNCT
ejpam-6314	188	15	≾	≾	NOUN
ejpam-6314	188	16	µdb(κn−1,κn	µdb(κn−1,κn	NOUN
ejpam-6314	188	17	)	)	PUNCT
ejpam-6314	188	18	+	+	CCONJ
ejpam-6314	188	19	νdb(κn−1,κn	νdb(κn−1,κn	X
ejpam-6314	188	20	)	)	PUNCT
ejpam-6314	189	1	+	+	CCONJ
ejpam-6314	189	2	γdb(κn	γdb(κn	ADJ
ejpam-6314	189	3	,	,	PUNCT
ejpam-6314	189	4	κn+1	κn+1	NOUN
ejpam-6314	189	5	)	)	PUNCT
ejpam-6314	189	6	,	,	PUNCT
ejpam-6314	189	7	m.	m.	NOUN
ejpam-6314	189	8	sarwar	sarwar	PROPN
ejpam-6314	189	9	et	et	PROPN
ejpam-6314	189	10	al	al	PROPN
ejpam-6314	189	11	.	.	PUNCT
ejpam-6314	189	12	/	/	SYM
ejpam-6314	189	13	eur	eur	PROPN
ejpam-6314	189	14	.	.	PUNCT
ejpam-6314	190	1	j.	j.	PROPN
ejpam-6314	190	2	pure	pure	PROPN
ejpam-6314	190	3	appl	appl	PROPN
ejpam-6314	190	4	.	.	PROPN
ejpam-6314	190	5	math	math	PROPN
ejpam-6314	190	6	,	,	PUNCT
ejpam-6314	190	7	18	18	NUM
ejpam-6314	190	8	(	(	PUNCT
ejpam-6314	190	9	3	3	NUM
ejpam-6314	190	10	)	)	PUNCT
ejpam-6314	190	11	(	(	PUNCT
ejpam-6314	190	12	2025	2025	NUM
ejpam-6314	190	13	)	)	PUNCT
ejpam-6314	190	14	,	,	PUNCT
ejpam-6314	190	15	6314	6314	NUM
ejpam-6314	190	16	9	9	NUM
ejpam-6314	190	17	of	of	ADP
ejpam-6314	190	18	28	28	NUM
ejpam-6314	190	19	db(κn	db(κn	NOUN
ejpam-6314	190	20	,	,	PUNCT
ejpam-6314	190	21	κn+1)−	κn+1)−	PROPN
ejpam-6314	190	22	γdb(κn	γdb(κn	PRON
ejpam-6314	190	23	,	,	PUNCT
ejpam-6314	190	24	κn+1	κn+1	NOUN
ejpam-6314	190	25	)	)	PUNCT
ejpam-6314	190	26	≾	≾	NOUN
ejpam-6314	190	27	µdb(κn−1,κn	µdb(κn−1,κn	NOUN
ejpam-6314	190	28	)	)	PUNCT
ejpam-6314	190	29	+	+	NUM
ejpam-6314	190	30	νdb(κn−1,κn	νdb(κn−1,κn	NOUN
ejpam-6314	190	31	)	)	PUNCT
ejpam-6314	190	32	,	,	PUNCT
ejpam-6314	190	33	(	(	PUNCT
ejpam-6314	190	34	1−	1−	NUM
ejpam-6314	190	35	γ)db(κn	γ)db(κn	NOUN
ejpam-6314	190	36	,	,	PUNCT
ejpam-6314	190	37	κn+1	κn+1	NOUN
ejpam-6314	190	38	)	)	PUNCT
ejpam-6314	190	39	≾	≾	PROPN
ejpam-6314	190	40	(	(	PUNCT
ejpam-6314	190	41	µ+	µ+	X
ejpam-6314	190	42	ν)db(κn−1,κn	ν)db(κn−1,κn	PROPN
ejpam-6314	190	43	)	)	PUNCT
ejpam-6314	190	44	,	,	PUNCT
ejpam-6314	190	45	db(κn	db(κn	NOUN
ejpam-6314	190	46	,	,	PUNCT
ejpam-6314	190	47	κn+1	κn+1	NOUN
ejpam-6314	190	48	)	)	PUNCT
ejpam-6314	190	49	≾	≾	PROPN
ejpam-6314	190	50	(	(	PUNCT
ejpam-6314	190	51	µ+	µ+	NOUN
ejpam-6314	190	52	ν	ν	NOUN
ejpam-6314	190	53	)	)	PUNCT
ejpam-6314	190	54	(	(	PUNCT
ejpam-6314	190	55	1−	1−	NUM
ejpam-6314	190	56	γ	γ	X
ejpam-6314	190	57	)	)	PUNCT
ejpam-6314	190	58	db(κn−1,κn	db(κn−1,κn	PROPN
ejpam-6314	190	59	)	)	PUNCT
ejpam-6314	190	60	,	,	PUNCT
ejpam-6314	190	61	db(κn	db(κn	NOUN
ejpam-6314	190	62	,	,	PUNCT
ejpam-6314	190	63	κn+1	κn+1	NOUN
ejpam-6314	190	64	)	)	PUNCT
ejpam-6314	190	65	≾	≾	PROPN
ejpam-6314	190	66	(	(	PUNCT
ejpam-6314	190	67	µ+	µ+	NOUN
ejpam-6314	190	68	ν	ν	NOUN
ejpam-6314	190	69	)	)	PUNCT
ejpam-6314	190	70	(	(	PUNCT
ejpam-6314	190	71	1−	1−	NUM
ejpam-6314	190	72	γ	γ	X
ejpam-6314	190	73	)	)	PUNCT
ejpam-6314	190	74	db(κn−1,κn	db(κn−1,κn	PROPN
ejpam-6314	190	75	)	)	PUNCT
ejpam-6314	190	76	=	=	SYM
ejpam-6314	190	77	ωdb(κn−1,κn	ωdb(κn−1,κn	X
ejpam-6314	190	78	)	)	PUNCT
ejpam-6314	190	79	.	.	PUNCT
ejpam-6314	191	1	thus	thus	ADV
ejpam-6314	191	2	,	,	PUNCT
ejpam-6314	191	3	we	we	PRON
ejpam-6314	191	4	have	have	VERB
ejpam-6314	191	5	db(κn	db(κn	NOUN
ejpam-6314	191	6	,	,	PUNCT
ejpam-6314	191	7	κn+1	κn+1	NOUN
ejpam-6314	191	8	)	)	PUNCT
ejpam-6314	191	9	≾	≾	NOUN
ejpam-6314	191	10	ωdb(κn−1,κn	ωdb(κn−1,κn	ADV
ejpam-6314	191	11	)	)	PUNCT
ejpam-6314	191	12	≾	≾	NOUN
ejpam-6314	191	13	ω2db(κn−2,κn−1	ω2db(κn−2,κn−1	NOUN
ejpam-6314	191	14	)	)	PUNCT
ejpam-6314	191	15	≾	≾	PROPN
ejpam-6314	191	16	·	·	PUNCT
ejpam-6314	191	17	·	·	PUNCT
ejpam-6314	191	18	·	·	PUNCT
ejpam-6314	192	1	≾	≾	NOUN
ejpam-6314	192	2	ωndb(κ0,κ1	ωndb(κ0,κ1	NOUN
ejpam-6314	192	3	)	)	PUNCT
ejpam-6314	192	4	.	.	PUNCT
ejpam-6314	193	1	for	for	ADP
ejpam-6314	193	2	all	all	DET
ejpam-6314	193	3	n	n	CCONJ
ejpam-6314	193	4	,	,	PUNCT
ejpam-6314	193	5	m	m	VERB
ejpam-6314	193	6	∈	∈	ADJ
ejpam-6314	193	7	n	n	CCONJ
ejpam-6314	193	8	(	(	PUNCT
ejpam-6314	193	9	n	n	X
ejpam-6314	193	10	<	<	X
ejpam-6314	193	11	m	m	PROPN
ejpam-6314	193	12	)	)	PUNCT
ejpam-6314	193	13	,	,	PUNCT
ejpam-6314	193	14	we	we	PRON
ejpam-6314	193	15	have	have	VERB
ejpam-6314	193	16	db(κn	db(κn	NOUN
ejpam-6314	193	17	,	,	PUNCT
ejpam-6314	193	18	κm	κm	NOUN
ejpam-6314	193	19	)	)	PUNCT
ejpam-6314	193	20	≾	≾	PROPN
ejpam-6314	193	21	ϑ(κn	ϑ(κn	PROPN
ejpam-6314	193	22	,	,	PUNCT
ejpam-6314	193	23	κn+1)db(κn	κn+1)db(κn	X
ejpam-6314	193	24	,	,	PUNCT
ejpam-6314	193	25	κn+1	κn+1	NOUN
ejpam-6314	193	26	)	)	PUNCT
ejpam-6314	194	1	+	+	CCONJ
ejpam-6314	194	2	ϑ(κn+1,κm)db(κn+1,κm	ϑ(κn+1,κm)db(κn+1,κm	X
ejpam-6314	194	3	)	)	PUNCT
ejpam-6314	194	4	≾	≾	PROPN
ejpam-6314	194	5	ϑ(κn	ϑ(κn	PROPN
ejpam-6314	194	6	,	,	PUNCT
ejpam-6314	194	7	κn+1)db(κn	κn+1)db(κn	X
ejpam-6314	194	8	,	,	PUNCT
ejpam-6314	194	9	κn+1	κn+1	NOUN
ejpam-6314	194	10	)	)	PUNCT
ejpam-6314	195	1	+	+	CCONJ
ejpam-6314	195	2	ϑ(κn+1,κm)ϑ(κn+1,κn+2	ϑ(κn+1,κm)ϑ(κn+1,κn+2	X
ejpam-6314	195	3	)	)	PUNCT
ejpam-6314	195	4	×	×	NOUN
ejpam-6314	195	5	db(κn+1,κn+2	db(κn+1,κn+2	ADV
ejpam-6314	195	6	)	)	PUNCT
ejpam-6314	196	1	+	+	CCONJ
ejpam-6314	196	2	ϑ(κn+1,κm)ϑ(κn+2,κm)db(κn+2,κm	ϑ(κn+1,κm)ϑ(κn+2,κm)db(κn+2,κm	X
ejpam-6314	196	3	)	)	PUNCT
ejpam-6314	196	4	≾	≾	PROPN
ejpam-6314	196	5	ϑ(κn	ϑ(κn	PROPN
ejpam-6314	196	6	,	,	PUNCT
ejpam-6314	196	7	κn+1)db(κn	κn+1)db(κn	X
ejpam-6314	196	8	,	,	PUNCT
ejpam-6314	196	9	κn+1	κn+1	NOUN
ejpam-6314	196	10	)	)	PUNCT
ejpam-6314	197	1	+	+	CCONJ
ejpam-6314	197	2	ϑ(κn+1,κm)ϑ(κn+1,κn+2	ϑ(κn+1,κm)ϑ(κn+1,κn+2	X
ejpam-6314	197	3	)	)	PUNCT
ejpam-6314	197	4	×	×	NOUN
ejpam-6314	197	5	db(κn+1,κn+2	db(κn+1,κn+2	ADV
ejpam-6314	197	6	)	)	PUNCT
ejpam-6314	198	1	+	+	NUM
ejpam-6314	198	2	ϑ(κn+1,κm)ϑ(κn+2,κm)ϑ(κn+2,κn+3	ϑ(κn+1,κm)ϑ(κn+2,κm)ϑ(κn+2,κn+3	NUM
ejpam-6314	198	3	)	)	PUNCT
ejpam-6314	198	4	×	×	NOUN
ejpam-6314	198	5	db(κn+3,κm	db(κn+3,κm	PROPN
ejpam-6314	198	6	)	)	PUNCT
ejpam-6314	198	7	≾	≾	PROPN
ejpam-6314	198	8	.	.	PUNCT
ejpam-6314	198	9	.	.	PUNCT
ejpam-6314	198	10	.	.	PUNCT
ejpam-6314	199	1	≾	≾	PROPN
ejpam-6314	199	2	ϑ(κn	ϑ(κn	PROPN
ejpam-6314	199	3	,	,	PUNCT
ejpam-6314	199	4	κn+1)db(κn	κn+1)db(κn	X
ejpam-6314	199	5	,	,	PUNCT
ejpam-6314	199	6	κn+1	κn+1	NOUN
ejpam-6314	199	7	)	)	PUNCT
ejpam-6314	200	1	+	+	CCONJ
ejpam-6314	200	2	m−2∑	m−2∑	NUM
ejpam-6314	201	1	i	i	PRON
ejpam-6314	201	2	=	=	NOUN
ejpam-6314	201	3	n+1	n+1	PRON
ejpam-6314	201	4			PROPN
ejpam-6314	201	5	i∏	i∏	PROPN
ejpam-6314	201	6	j	j	NOUN
ejpam-6314	201	7	=	=	NOUN
ejpam-6314	201	8	n+1	n+1	PROPN
ejpam-6314	201	9	ϑ(κj	ϑ(κj	PROPN
ejpam-6314	201	10	,	,	PUNCT
ejpam-6314	201	11	κm	κm	NOUN
ejpam-6314	201	12	)	)	PUNCT
ejpam-6314	201	13			NOUN
ejpam-6314	201	14	×	×	PROPN
ejpam-6314	201	15	ϑ(κi	ϑ(κi	NOUN
ejpam-6314	201	16	,	,	PUNCT
ejpam-6314	201	17	κi+1)db(κi	κi+1)db(κi	NOUN
ejpam-6314	201	18	,	,	PUNCT
ejpam-6314	201	19	κi+1	κi+1	X
ejpam-6314	201	20	)	)	PUNCT
ejpam-6314	202	1	+	+	CCONJ
ejpam-6314	202	2	m−1∏	m−1∏	PROPN
ejpam-6314	202	3	i	i	NOUN
ejpam-6314	202	4	=	=	NOUN
ejpam-6314	202	5	n+1	n+1	X
ejpam-6314	202	6	ϑ(κi	ϑ(κi	NOUN
ejpam-6314	202	7	,	,	PUNCT
ejpam-6314	202	8	κm)db(κm−1,κm	κm)db(κm−1,κm	ADJ
ejpam-6314	202	9	)	)	PUNCT
ejpam-6314	202	10	.	.	PUNCT
ejpam-6314	203	1	(	(	PUNCT
ejpam-6314	203	2	3	3	X
ejpam-6314	203	3	)	)	PUNCT
ejpam-6314	203	4	this	this	PRON
ejpam-6314	203	5	implies	imply	VERB
ejpam-6314	203	6	that	that	SCONJ
ejpam-6314	203	7	db(κn	db(κn	NOUN
ejpam-6314	203	8	,	,	PUNCT
ejpam-6314	203	9	κm	κm	NOUN
ejpam-6314	203	10	)	)	PUNCT
ejpam-6314	203	11	≾	≾	PROPN
ejpam-6314	203	12	ϑ(κn	ϑ(κn	PROPN
ejpam-6314	203	13	,	,	PUNCT
ejpam-6314	203	14	κn+1)db(κn	κn+1)db(κn	X
ejpam-6314	203	15	,	,	PUNCT
ejpam-6314	203	16	κn+1	κn+1	NOUN
ejpam-6314	203	17	)	)	PUNCT
ejpam-6314	204	1	+	+	CCONJ
ejpam-6314	204	2	m−2∑	m−2∑	NUM
ejpam-6314	205	1	i	i	PRON
ejpam-6314	205	2	=	=	NOUN
ejpam-6314	205	3	n+1	n+1	PRON
ejpam-6314	205	4			PROPN
ejpam-6314	205	5	i∏	i∏	PROPN
ejpam-6314	205	6	j	j	NOUN
ejpam-6314	205	7	=	=	NOUN
ejpam-6314	205	8	n+1	n+1	PROPN
ejpam-6314	205	9	ϑ(κj	ϑ(κj	PROPN
ejpam-6314	205	10	,	,	PUNCT
ejpam-6314	205	11	κm	κm	NOUN
ejpam-6314	205	12	)	)	PUNCT
ejpam-6314	205	13			NOUN
ejpam-6314	205	14	×	×	PROPN
ejpam-6314	205	15	ϑ(κi	ϑ(κi	NOUN
ejpam-6314	205	16	,	,	PUNCT
ejpam-6314	205	17	κi+1)db(κi	κi+1)db(κi	NOUN
ejpam-6314	205	18	,	,	PUNCT
ejpam-6314	205	19	κi+1	κi+1	X
ejpam-6314	205	20	)	)	PUNCT
ejpam-6314	206	1	+	+	CCONJ
ejpam-6314	206	2	[	[	PUNCT
ejpam-6314	206	3	m−1∏	m−1∏	PROPN
ejpam-6314	206	4	i	i	NOUN
ejpam-6314	206	5	=	=	NOUN
ejpam-6314	206	6	n+1	n+1	X
ejpam-6314	206	7	ϑ(κj	ϑ(κj	PROPN
ejpam-6314	206	8	,	,	PUNCT
ejpam-6314	206	9	κm	κm	PROPN
ejpam-6314	206	10	)	)	PUNCT
ejpam-6314	206	11	]	]	PUNCT
ejpam-6314	206	12	ϑ(κm−1,κm)db(κm−1,κm	ϑ(κm−1,κm)db(κm−1,κm	X
ejpam-6314	206	13	)	)	PUNCT
ejpam-6314	206	14	≾	≾	PROPN
ejpam-6314	206	15	ϑ(κn	ϑ(κn	PROPN
ejpam-6314	206	16	,	,	PUNCT
ejpam-6314	206	17	κn+1)ω	κn+1)ω	X
ejpam-6314	206	18	ndb(κn	ndb(κn	NUM
ejpam-6314	206	19	,	,	PUNCT
ejpam-6314	206	20	κn+1	κn+1	ADJ
ejpam-6314	206	21	)	)	PUNCT
ejpam-6314	207	1	+	+	CCONJ
ejpam-6314	207	2	m−2∑	m−2∑	NUM
ejpam-6314	208	1	i	i	PRON
ejpam-6314	208	2	=	=	NOUN
ejpam-6314	208	3	n+1	n+1	PRON
ejpam-6314	208	4			PROPN
ejpam-6314	208	5	i∏	i∏	PROPN
ejpam-6314	208	6	j	j	NOUN
ejpam-6314	208	7	=	=	NOUN
ejpam-6314	208	8	n+1	n+1	PROPN
ejpam-6314	208	9	ϑ(κj	ϑ(κj	PROPN
ejpam-6314	208	10	,	,	PUNCT
ejpam-6314	208	11	κm	κm	NOUN
ejpam-6314	208	12	)	)	PUNCT
ejpam-6314	209	1	ϑ(κi	ϑ(κi	NOUN
ejpam-6314	209	2	,	,	PUNCT
ejpam-6314	209	3	κi+1)ω	κi+1)ω	NOUN
ejpam-6314	209	4	idb(κ0,κ1	idb(κ0,κ1	ADJ
ejpam-6314	209	5	)	)	PUNCT
ejpam-6314	209	6	m.	m.	NOUN
ejpam-6314	209	7	sarwar	sarwar	PROPN
ejpam-6314	209	8	et	et	PROPN
ejpam-6314	210	1	al	al	PROPN
ejpam-6314	210	2	.	.	PUNCT
ejpam-6314	210	3	/	/	SYM
ejpam-6314	210	4	eur	eur	PROPN
ejpam-6314	210	5	.	.	PUNCT
ejpam-6314	211	1	j.	j.	PROPN
ejpam-6314	211	2	pure	pure	PROPN
ejpam-6314	211	3	appl	appl	PROPN
ejpam-6314	211	4	.	.	PROPN
ejpam-6314	211	5	math	math	PROPN
ejpam-6314	211	6	,	,	PUNCT
ejpam-6314	211	7	18	18	NUM
ejpam-6314	211	8	(	(	PUNCT
ejpam-6314	211	9	3	3	NUM
ejpam-6314	211	10	)	)	PUNCT
ejpam-6314	211	11	(	(	PUNCT
ejpam-6314	211	12	2025	2025	NUM
ejpam-6314	211	13	)	)	PUNCT
ejpam-6314	211	14	,	,	PUNCT
ejpam-6314	211	15	6314	6314	NUM
ejpam-6314	211	16	10	10	NUM
ejpam-6314	211	17	of	of	ADP
ejpam-6314	211	18	28	28	NUM
ejpam-6314	211	19	+	+	CCONJ
ejpam-6314	211	20	[	[	PUNCT
ejpam-6314	211	21	m−1∏	m−1∏	PROPN
ejpam-6314	211	22	i	i	NOUN
ejpam-6314	211	23	=	=	NOUN
ejpam-6314	211	24	n+1	n+1	X
ejpam-6314	211	25	ϑ(κj	ϑ(κj	PROPN
ejpam-6314	211	26	,	,	PUNCT
ejpam-6314	211	27	κm	κm	PROPN
ejpam-6314	211	28	)	)	PUNCT
ejpam-6314	211	29	]	]	PUNCT
ejpam-6314	211	30	ϑ(κm−1,κm)ωm−1db(κ0,κ1	ϑ(κm−1,κm)ωm−1db(κ0,κ1	X
ejpam-6314	211	31	)	)	PUNCT
ejpam-6314	211	32	=	=	SYM
ejpam-6314	211	33	ϑ(κn	ϑ(κn	PROPN
ejpam-6314	211	34	,	,	PUNCT
ejpam-6314	211	35	κn+1)ω	κn+1)ω	X
ejpam-6314	211	36	ndb(κ0,κ1	ndb(κ0,κ1	ADJ
ejpam-6314	211	37	)	)	PUNCT
ejpam-6314	211	38	+	+	CCONJ
ejpam-6314	211	39	m−1∑	m−1∑	NUM
ejpam-6314	211	40	i	i	NOUN
ejpam-6314	211	41	=	=	NOUN
ejpam-6314	211	42	n+1	n+1	PROPN
ejpam-6314	211	43			PROPN
ejpam-6314	211	44	i∏	i∏	PROPN
ejpam-6314	211	45	j	j	NOUN
ejpam-6314	211	46	=	=	NOUN
ejpam-6314	211	47	n+1	n+1	PROPN
ejpam-6314	211	48	ϑ(κj	ϑ(κj	PROPN
ejpam-6314	211	49	,	,	PUNCT
ejpam-6314	211	50	κm	κm	NOUN
ejpam-6314	211	51	)	)	PUNCT
ejpam-6314	211	52	ϑ(κi	ϑ(κi	NOUN
ejpam-6314	211	53	,	,	PUNCT
ejpam-6314	211	54	κi+1)ω	κi+1)ω	NOUN
ejpam-6314	211	55	idb(κ0,κ1	idb(κ0,κ1	ADJ
ejpam-6314	211	56	)	)	PUNCT
ejpam-6314	211	57	.	.	PUNCT
ejpam-6314	212	1	(	(	PUNCT
ejpam-6314	212	2	4	4	X
ejpam-6314	212	3	)	)	PUNCT
ejpam-6314	212	4	let	let	VERB
ejpam-6314	212	5	υℓ	υℓ	PRON
ejpam-6314	213	1	=	=	NOUN
ejpam-6314	213	2	ℓ∑	ℓ∑	INTJ
ejpam-6314	213	3	i=0	i=0	PROPN
ejpam-6314	213	4	[	[	PUNCT
ejpam-6314	213	5	i∏	i∏	VERB
ejpam-6314	213	6	j=0	j=0	VERB
ejpam-6314	213	7	ϑ(κj	ϑ(κj	PROPN
ejpam-6314	213	8	,	,	PUNCT
ejpam-6314	213	9	κm	κm	PROPN
ejpam-6314	213	10	)	)	PUNCT
ejpam-6314	213	11	]	]	PUNCT
ejpam-6314	213	12	ϑ(κi	ϑ(κi	NOUN
ejpam-6314	213	13	,	,	PUNCT
ejpam-6314	213	14	κi+1)ω	κi+1)ω	NOUN
ejpam-6314	213	15	idb(κ0,κ1	idb(κ0,κ1	ADJ
ejpam-6314	213	16	)	)	PUNCT
ejpam-6314	213	17	.	.	PUNCT
ejpam-6314	214	1	(	(	PUNCT
ejpam-6314	214	2	5	5	X
ejpam-6314	214	3	)	)	PUNCT
ejpam-6314	214	4	consider	consider	VERB
ejpam-6314	214	5	λi	λi	NOUN
ejpam-6314	214	6	=	=	PUNCT
ejpam-6314	214	7	[	[	PUNCT
ejpam-6314	214	8	i∏	i∏	AUX
ejpam-6314	214	9	j=0	j=0	VERB
ejpam-6314	214	10	ϑ(κj	ϑ(κj	PROPN
ejpam-6314	214	11	,	,	PUNCT
ejpam-6314	214	12	κm	κm	PROPN
ejpam-6314	214	13	)	)	PUNCT
ejpam-6314	214	14	]	]	PUNCT
ejpam-6314	215	1	ϑ(κi	ϑ(κi	NOUN
ejpam-6314	215	2	,	,	PUNCT
ejpam-6314	215	3	κi+1)ω	κi+1)ω	NOUN
ejpam-6314	215	4	idb(κ0,κ1	idb(κ0,κ1	ADJ
ejpam-6314	215	5	)	)	PUNCT
ejpam-6314	215	6	,	,	PUNCT
ejpam-6314	215	7	(	(	PUNCT
ejpam-6314	215	8	6	6	X
ejpam-6314	215	9	)	)	PUNCT
ejpam-6314	215	10	we	we	PRON
ejpam-6314	215	11	have	have	VERB
ejpam-6314	215	12	λi+1	λi+1	NOUN
ejpam-6314	215	13	λi	λi	NOUN
ejpam-6314	215	14	=	=	PUNCT
ejpam-6314	215	15	ϑ(κi+1,κm	ϑ(κi+1,κm	NOUN
ejpam-6314	215	16	)	)	PUNCT
ejpam-6314	215	17	ϑ(κi+1,κi+2	ϑ(κi+1,κi+2	NOUN
ejpam-6314	215	18	)	)	PUNCT
ejpam-6314	215	19	ϑ(κi	ϑ(κi	NOUN
ejpam-6314	215	20	,	,	PUNCT
ejpam-6314	215	21	κi+1	κi+1	NOUN
ejpam-6314	215	22	)	)	PUNCT
ejpam-6314	215	23	ω	ω	NOUN
ejpam-6314	215	24	.	.	PUNCT
ejpam-6314	216	1	(	(	PUNCT
ejpam-6314	216	2	7	7	X
ejpam-6314	216	3	)	)	PUNCT
ejpam-6314	216	4	we	we	PRON
ejpam-6314	216	5	make	make	VERB
ejpam-6314	216	6	sure	sure	ADJ
ejpam-6314	216	7	that	that	SCONJ
ejpam-6314	216	8	the	the	DET
ejpam-6314	216	9	series	series	NOUN
ejpam-6314	216	10	∑	∑	PROPN
ejpam-6314	216	11	i	i	PRON
ejpam-6314	216	12	λi	λi	VERB
ejpam-6314	216	13	converges	converge	NOUN
ejpam-6314	216	14	in	in	ADP
ejpam-6314	216	15	the	the	DET
ejpam-6314	216	16	context	context	NOUN
ejpam-6314	216	17	of	of	ADP
ejpam-6314	216	18	the	the	DET
ejpam-6314	216	19	condition	condition	NOUN
ejpam-6314	216	20	(	(	PUNCT
ejpam-6314	216	21	2	2	NUM
ejpam-6314	216	22	)	)	PUNCT
ejpam-6314	216	23	and	and	CCONJ
ejpam-6314	216	24	ratio	ratio	NOUN
ejpam-6314	216	25	test	test	NOUN
ejpam-6314	216	26	.	.	PUNCT
ejpam-6314	217	1	therefore	therefore	ADV
ejpam-6314	217	2	,	,	PUNCT
ejpam-6314	217	3	there	there	PRON
ejpam-6314	217	4	is	be	VERB
ejpam-6314	217	5	limn→+∞υℓ.	limn→+∞υℓ.	PROPN
ejpam-6314	217	6	thus	thus	ADV
ejpam-6314	217	7	the	the	DET
ejpam-6314	217	8	υℓ	υℓ	PROPN
ejpam-6314	217	9	is	be	AUX
ejpam-6314	217	10	cauchy	cauchy	ADJ
ejpam-6314	217	11	as	as	ADP
ejpam-6314	217	12	a	a	DET
ejpam-6314	217	13	result	result	NOUN
ejpam-6314	217	14	.	.	PUNCT
ejpam-6314	218	1	now	now	ADV
ejpam-6314	218	2	,	,	PUNCT
ejpam-6314	218	3	using	use	VERB
ejpam-6314	218	4	(	(	PUNCT
ejpam-6314	218	5	4	4	NUM
ejpam-6314	218	6	)	)	PUNCT
ejpam-6314	218	7	,	,	PUNCT
ejpam-6314	218	8	we	we	PRON
ejpam-6314	218	9	get	get	VERB
ejpam-6314	218	10	db(κn	db(κn	NOUN
ejpam-6314	218	11	,	,	PUNCT
ejpam-6314	218	12	κm	κm	NOUN
ejpam-6314	218	13	)	)	PUNCT
ejpam-6314	218	14	≾	≾	PROPN
ejpam-6314	218	15	db(κ0,κ1)[ω	db(κ0,κ1)[ω	NOUN
ejpam-6314	218	16	nϑ(κi	nϑ(κi	PROPN
ejpam-6314	218	17	,	,	PUNCT
ejpam-6314	218	18	κi+1	κi+1	X
ejpam-6314	218	19	)	)	PUNCT
ejpam-6314	219	1	+	+	CCONJ
ejpam-6314	219	2	(	(	PUNCT
ejpam-6314	219	3	υm−1	υm−1	PROPN
ejpam-6314	219	4	−υn	−υn	PROPN
ejpam-6314	219	5	)	)	PUNCT
ejpam-6314	219	6	]	]	PUNCT
ejpam-6314	219	7	.	.	PUNCT
ejpam-6314	220	1	(	(	PUNCT
ejpam-6314	220	2	8)	8)	NUM
ejpam-6314	220	3	above	above	ADV
ejpam-6314	220	4	,	,	PUNCT
ejpam-6314	220	5	we	we	PRON
ejpam-6314	220	6	used	use	VERB
ejpam-6314	220	7	ϑ(κ	ϑ(κ	PROPN
ejpam-6314	220	8	,	,	PUNCT
ejpam-6314	220	9	σ	σ	PROPN
ejpam-6314	220	10	)	)	PUNCT
ejpam-6314	220	11	≥	≥	NOUN
ejpam-6314	220	12	1	1	NUM
ejpam-6314	220	13	.	.	PUNCT
ejpam-6314	220	14	letting	let	VERB
ejpam-6314	220	15	n	n	CCONJ
ejpam-6314	220	16	,	,	PUNCT
ejpam-6314	220	17	m→	m→	PUNCT
ejpam-6314	221	1	+	+	NOUN
ejpam-6314	221	2	∞	∞	NUM
ejpam-6314	221	3	in	in	ADP
ejpam-6314	221	4	(	(	PUNCT
ejpam-6314	221	5	8)	8)	NUM
ejpam-6314	221	6	we	we	PRON
ejpam-6314	221	7	obtain	obtain	VERB
ejpam-6314	221	8	lim	lim	PROPN
ejpam-6314	221	9	n	n	CCONJ
ejpam-6314	221	10	,	,	PUNCT
ejpam-6314	221	11	m→+∞	m→+∞	PROPN
ejpam-6314	221	12	db(κn	db(κn	NOUN
ejpam-6314	221	13	,	,	PUNCT
ejpam-6314	221	14	κm	κm	PROPN
ejpam-6314	221	15	)	)	PUNCT
ejpam-6314	221	16	=	=	SYM
ejpam-6314	222	1	0	0	X
ejpam-6314	222	2	.	.	PUNCT
ejpam-6314	223	1	(	(	PUNCT
ejpam-6314	223	2	9	9	NUM
ejpam-6314	223	3	)	)	PUNCT
ejpam-6314	223	4	thus	thus	ADV
ejpam-6314	223	5	,	,	PUNCT
ejpam-6314	223	6	the	the	DET
ejpam-6314	223	7	sequence	sequence	NOUN
ejpam-6314	223	8	{	{	PUNCT
ejpam-6314	223	9	κn	κn	NOUN
ejpam-6314	223	10	}	}	PUNCT
ejpam-6314	223	11	is	be	AUX
ejpam-6314	223	12	a	a	DET
ejpam-6314	223	13	cauchy	cauchy	NOUN
ejpam-6314	223	14	in	in	ADP
ejpam-6314	223	15	bcvms	bcvms	PROPN
ejpam-6314	223	16	(	(	PUNCT
ejpam-6314	223	17	s	s	PROPN
ejpam-6314	223	18	,	,	PUNCT
ejpam-6314	223	19	db).for	db).for	ADP
ejpam-6314	223	20	some	some	DET
ejpam-6314	223	21	κ⋆	κ⋆	ADJ
ejpam-6314	223	22	∈	∈	PROPN
ejpam-6314	223	23	s	s	PART
ejpam-6314	223	24	so	so	SCONJ
ejpam-6314	224	1	that	that	SCONJ
ejpam-6314	224	2	lim	lim	PROPN
ejpam-6314	224	3	n→+∞	n→+∞	PROPN
ejpam-6314	224	4	db(κn	db(κn	PROPN
ejpam-6314	224	5	,	,	PUNCT
ejpam-6314	224	6	κ⋆	κ⋆	ADJ
ejpam-6314	224	7	)	)	PUNCT
ejpam-6314	224	8	=	=	SYM
ejpam-6314	224	9	0	0	NUM
ejpam-6314	224	10	,	,	PUNCT
ejpam-6314	224	11	(	(	PUNCT
ejpam-6314	224	12	10	10	NUM
ejpam-6314	224	13	)	)	PUNCT
ejpam-6314	224	14	that	that	PRON
ejpam-6314	224	15	is	be	AUX
ejpam-6314	224	16	κn	κn	NOUN
ejpam-6314	224	17	→	→	SYM
ejpam-6314	224	18	κ⋆	κ⋆	X
ejpam-6314	224	19	as	as	ADP
ejpam-6314	224	20	n→	n→	ADV
ejpam-6314	224	21	+	+	PROPN
ejpam-6314	224	22	∞.	∞.	PROPN
ejpam-6314	224	23	we	we	PRON
ejpam-6314	224	24	shall	shall	AUX
ejpam-6314	224	25	now	now	ADV
ejpam-6314	224	26	demonstrate	demonstrate	VERB
ejpam-6314	224	27	that	that	SCONJ
ejpam-6314	224	28	κ⋆	κ⋆	ADJ
ejpam-6314	224	29	is	be	AUX
ejpam-6314	224	30	a	a	DET
ejpam-6314	224	31	fixed	fix	VERB
ejpam-6314	224	32	point	point	NOUN
ejpam-6314	224	33	of	of	ADP
ejpam-6314	224	34	s.	s.	PROPN
ejpam-6314	224	35	by	by	ADP
ejpam-6314	224	36	applying	apply	VERB
ejpam-6314	224	37	condition	condition	NOUN
ejpam-6314	224	38	(	(	PUNCT
ejpam-6314	224	39	iii	iii	NOUN
ejpam-6314	224	40	)	)	PUNCT
ejpam-6314	224	41	and	and	CCONJ
ejpam-6314	224	42	using	use	VERB
ejpam-6314	224	43	(	(	PUNCT
ejpam-6314	224	44	1	1	NUM
ejpam-6314	224	45	)	)	PUNCT
ejpam-6314	224	46	,	,	PUNCT
ejpam-6314	224	47	we	we	PRON
ejpam-6314	224	48	obtain	obtain	VERB
ejpam-6314	224	49	db(κ⋆	db(κ⋆	NOUN
ejpam-6314	224	50	,	,	PUNCT
ejpam-6314	224	51	ψκ⋆	ψκ⋆	PROPN
ejpam-6314	224	52	)	)	PUNCT
ejpam-6314	224	53	≾	≾	PROPN
ejpam-6314	224	54	ϑ(κ⋆,κn+1)db(κ⋆,κn+1	ϑ(κ⋆,κn+1)db(κ⋆,κn+1	PROPN
ejpam-6314	224	55	)	)	PUNCT
ejpam-6314	225	1	+	+	NUM
ejpam-6314	225	2	ϑ(κn+1	ϑ(κn+1	NOUN
ejpam-6314	225	3	,	,	PUNCT
ejpam-6314	225	4	ψκ⋆)db(κn+1	ψκ⋆)db(κn+1	PROPN
ejpam-6314	225	5	,	,	PUNCT
ejpam-6314	225	6	ψκ⋆	ψκ⋆	PROPN
ejpam-6314	225	7	)	)	PUNCT
ejpam-6314	225	8	=	=	SYM
ejpam-6314	225	9	ϑ(κ⋆,κn+1)db(κ⋆,κn+1	ϑ(κ⋆,κn+1)db(κ⋆,κn+1	NOUN
ejpam-6314	225	10	)	)	PUNCT
ejpam-6314	226	1	+	+	CCONJ
ejpam-6314	226	2	ϑ(κn+1	ϑ(κn+1	NOUN
ejpam-6314	226	3	,	,	PUNCT
ejpam-6314	226	4	ψκ⋆)db(ψκn	ψκ⋆)db(ψκn	PROPN
ejpam-6314	226	5	,	,	PUNCT
ejpam-6314	226	6	ψκ⋆	ψκ⋆	PROPN
ejpam-6314	226	7	)	)	PUNCT
ejpam-6314	226	8	≾	≾	PROPN
ejpam-6314	226	9	ϑ(κ⋆,κn+1)db(κ⋆,κn+1	ϑ(κ⋆,κn+1)db(κ⋆,κn+1	PROPN
ejpam-6314	226	10	)	)	PUNCT
ejpam-6314	227	1	+	+	CCONJ
ejpam-6314	227	2	ϑ(κn+1	ϑ(κn+1	NOUN
ejpam-6314	227	3	,	,	PUNCT
ejpam-6314	227	4	ψκ⋆	ψκ⋆	PROPN
ejpam-6314	227	5	)	)	PUNCT
ejpam-6314	228	1	[	[	X
ejpam-6314	228	2	µdb(κn	µdb(κn	X
ejpam-6314	228	3	,	,	PUNCT
ejpam-6314	228	4	κ⋆	κ⋆	X
ejpam-6314	228	5	)	)	PUNCT
ejpam-6314	228	6	+	+	NOUN
ejpam-6314	228	7	νdb(κn	νdb(κn	ADJ
ejpam-6314	228	8	,	,	PUNCT
ejpam-6314	228	9	ψκn	ψκn	NOUN
ejpam-6314	228	10	)	)	PUNCT
ejpam-6314	229	1	+	+	CCONJ
ejpam-6314	229	2	γdb(κ⋆	γdb(κ⋆	ADJ
ejpam-6314	229	3	,	,	PUNCT
ejpam-6314	229	4	ψκ⋆	ψκ⋆	PROPN
ejpam-6314	229	5	)	)	PUNCT
ejpam-6314	229	6	]	]	PUNCT
ejpam-6314	229	7	=	=	PUNCT
ejpam-6314	229	8	ϑ(κ⋆,κn+1)db(κ⋆,κn+1	ϑ(κ⋆,κn+1)db(κ⋆,κn+1	X
ejpam-6314	229	9	)	)	PUNCT
ejpam-6314	229	10	+	+	CCONJ
ejpam-6314	229	11	ϑ(κn+1	ϑ(κn+1	NOUN
ejpam-6314	229	12	,	,	PUNCT
ejpam-6314	229	13	ψκ⋆	ψκ⋆	PROPN
ejpam-6314	229	14	)	)	PUNCT
ejpam-6314	230	1	[	[	X
ejpam-6314	230	2	µdb(κn	µdb(κn	X
ejpam-6314	230	3	,	,	PUNCT
ejpam-6314	230	4	κ⋆	κ⋆	X
ejpam-6314	230	5	)	)	PUNCT
ejpam-6314	230	6	+	+	NOUN
ejpam-6314	230	7	νdb(κn	νdb(κn	NUM
ejpam-6314	230	8	,	,	PUNCT
ejpam-6314	230	9	κn+1	κn+1	ADJ
ejpam-6314	230	10	)	)	PUNCT
ejpam-6314	231	1	+	+	CCONJ
ejpam-6314	231	2	γdb(κ⋆	γdb(κ⋆	ADJ
ejpam-6314	231	3	,	,	PUNCT
ejpam-6314	231	4	ψκ⋆	ψκ⋆	PROPN
ejpam-6314	231	5	)	)	PUNCT
ejpam-6314	231	6	]	]	PUNCT
ejpam-6314	231	7	(	(	PUNCT
ejpam-6314	231	8	11	11	NUM
ejpam-6314	231	9	)	)	PUNCT
ejpam-6314	231	10	m.	m.	NOUN
ejpam-6314	231	11	sarwar	sarwar	PROPN
ejpam-6314	231	12	et	et	PROPN
ejpam-6314	231	13	al	al	PROPN
ejpam-6314	231	14	.	.	PUNCT
ejpam-6314	231	15	/	/	SYM
ejpam-6314	231	16	eur	eur	PROPN
ejpam-6314	231	17	.	.	PUNCT
ejpam-6314	232	1	j.	j.	PROPN
ejpam-6314	232	2	pure	pure	PROPN
ejpam-6314	232	3	appl	appl	PROPN
ejpam-6314	232	4	.	.	PROPN
ejpam-6314	232	5	math	math	PROPN
ejpam-6314	232	6	,	,	PUNCT
ejpam-6314	232	7	18	18	NUM
ejpam-6314	232	8	(	(	PUNCT
ejpam-6314	232	9	3	3	NUM
ejpam-6314	232	10	)	)	PUNCT
ejpam-6314	232	11	(	(	PUNCT
ejpam-6314	232	12	2025	2025	NUM
ejpam-6314	232	13	)	)	PUNCT
ejpam-6314	232	14	,	,	PUNCT
ejpam-6314	232	15	6314	6314	NUM
ejpam-6314	232	16	11	11	NUM
ejpam-6314	232	17	of	of	ADP
ejpam-6314	232	18	28	28	NUM
ejpam-6314	232	19	employing	employ	VERB
ejpam-6314	232	20	the	the	DET
ejpam-6314	232	21	limit	limit	NOUN
ejpam-6314	232	22	,	,	PUNCT
ejpam-6314	232	23	n→	n→	PUNCT
ejpam-6314	232	24	+	+	ADJ
ejpam-6314	232	25	∞	∞	NUM
ejpam-6314	232	26	and	and	CCONJ
ejpam-6314	232	27	utilizing	utilize	VERB
ejpam-6314	232	28	(	(	PUNCT
ejpam-6314	232	29	3),(4	3),(4	NUM
ejpam-6314	232	30	)	)	PUNCT
ejpam-6314	232	31	and	and	CCONJ
ejpam-6314	232	32	the	the	DET
ejpam-6314	232	33	fact	fact	NOUN
ejpam-6314	232	34	that	that	SCONJ
ejpam-6314	232	35	limη→+∞	limη→+∞	PROPN
ejpam-6314	232	36	ϑ(κη	ϑ(κη	PROPN
ejpam-6314	232	37	,	,	PUNCT
ejpam-6314	232	38	κ	κ	NOUN
ejpam-6314	232	39	)	)	PUNCT
ejpam-6314	232	40	and	and	CCONJ
ejpam-6314	232	41	limη→+∞	limη→+∞	PROPN
ejpam-6314	232	42	ϑ(κ	ϑ(κ	PROPN
ejpam-6314	232	43	,	,	PUNCT
ejpam-6314	232	44	κη	κη	PROPN
ejpam-6314	232	45	)	)	PUNCT
ejpam-6314	232	46	exist	exist	VERB
ejpam-6314	232	47	and	and	CCONJ
ejpam-6314	232	48	are	be	AUX
ejpam-6314	232	49	finite	finite	ADJ
ejpam-6314	232	50	,	,	PUNCT
ejpam-6314	232	51	we	we	PRON
ejpam-6314	232	52	would	would	AUX
ejpam-6314	232	53	have	have	AUX
ejpam-6314	232	54	db(κ⋆	db(κ⋆	PROPN
ejpam-6314	232	55	,	,	PUNCT
ejpam-6314	232	56	ψκ⋆	ψκ⋆	PROPN
ejpam-6314	232	57	)	)	PUNCT
ejpam-6314	232	58	≾	≾	PROPN
ejpam-6314	232	59	[	[	PUNCT
ejpam-6314	232	60	γ	γ	PROPN
ejpam-6314	232	61	lim	lim	PROPN
ejpam-6314	232	62	n→+∞	n→+∞	VERB
ejpam-6314	232	63	ϑ(κ⋆,κψκ⋆	ϑ(κ⋆,κψκ⋆	NOUN
ejpam-6314	232	64	)	)	PUNCT
ejpam-6314	232	65	]	]	PUNCT
ejpam-6314	232	66	db(κ⋆,κψκ⋆	db(κ⋆,κψκ⋆	NOUN
ejpam-6314	232	67	)	)	PUNCT
ejpam-6314	232	68	.	.	PUNCT
ejpam-6314	233	1	(	(	PUNCT
ejpam-6314	233	2	12	12	X
ejpam-6314	233	3	)	)	PUNCT
ejpam-6314	233	4	suppose	suppose	VERB
ejpam-6314	233	5	that	that	SCONJ
ejpam-6314	233	6	κ⋆	κ⋆	ADJ
ejpam-6314	233	7	̸=	̸=	PROPN
ejpam-6314	233	8	ψκ⋆	ψκ⋆	PROPN
ejpam-6314	233	9	,	,	PUNCT
ejpam-6314	233	10	having	have	VERB
ejpam-6314	233	11	in	in	ADP
ejpam-6314	233	12	mind	mind	NOUN
ejpam-6314	233	13	that	that	SCONJ
ejpam-6314	233	14	[	[	PUNCT
ejpam-6314	233	15	γ	γ	X
ejpam-6314	233	16	limn→+∞	limn→+∞	X
ejpam-6314	233	17	ϑ(κ⋆,κψκ⋆	ϑ(κ⋆,κψκ⋆	NOUN
ejpam-6314	233	18	)	)	PUNCT
ejpam-6314	233	19	]	]	PUNCT
ejpam-6314	233	20	<	<	X
ejpam-6314	233	21	1	1	NUM
ejpam-6314	233	22	,	,	PUNCT
ejpam-6314	233	23	so	so	ADV
ejpam-6314	233	24	0	0	NUM
ejpam-6314	233	25	≺i2	≺i2	ADJ
ejpam-6314	233	26	db(κ⋆	db(κ⋆	PROPN
ejpam-6314	233	27	,	,	PUNCT
ejpam-6314	233	28	ψκ⋆	ψκ⋆	PROPN
ejpam-6314	233	29	)	)	PUNCT
ejpam-6314	233	30	≾	≾	PROPN
ejpam-6314	233	31	[	[	PUNCT
ejpam-6314	233	32	γ	γ	PROPN
ejpam-6314	233	33	lim	lim	PROPN
ejpam-6314	233	34	n→+∞	n→+∞	VERB
ejpam-6314	233	35	ϑ(κ⋆,κψκ⋆	ϑ(κ⋆,κψκ⋆	NOUN
ejpam-6314	233	36	)	)	PUNCT
ejpam-6314	233	37	]	]	PUNCT
ejpam-6314	233	38	db(κ⋆,κψκ⋆	db(κ⋆,κψκ⋆	X
ejpam-6314	233	39	)	)	PUNCT
ejpam-6314	233	40	≺i2	≺i2	DET
ejpam-6314	233	41	db(κ⋆,κψκ⋆	db(κ⋆,κψκ⋆	NOUN
ejpam-6314	233	42	)	)	PUNCT
ejpam-6314	233	43	.	.	PUNCT
ejpam-6314	234	1	(	(	PUNCT
ejpam-6314	234	2	13	13	NUM
ejpam-6314	234	3	)	)	PUNCT
ejpam-6314	234	4	it	it	PRON
ejpam-6314	234	5	is	be	AUX
ejpam-6314	234	6	a	a	DET
ejpam-6314	234	7	contradiction	contradiction	NOUN
ejpam-6314	234	8	.	.	PUNCT
ejpam-6314	235	1	this	this	DET
ejpam-6314	235	2	yields	yield	NOUN
ejpam-6314	235	3	that	that	PRON
ejpam-6314	235	4	κ⋆	κ⋆	ADJ
ejpam-6314	235	5	=	=	SYM
ejpam-6314	235	6	ψκ⋆.	ψκ⋆.	NOUN
ejpam-6314	235	7	uniqueness	uniqueness	NOUN
ejpam-6314	235	8	:	:	PUNCT
ejpam-6314	235	9	next	next	ADV
ejpam-6314	235	10	,	,	PUNCT
ejpam-6314	235	11	we	we	PRON
ejpam-6314	235	12	need	need	VERB
ejpam-6314	235	13	to	to	PART
ejpam-6314	235	14	justify	justify	VERB
ejpam-6314	235	15	that	that	SCONJ
ejpam-6314	235	16	κ⋆	κ⋆	ADJ
ejpam-6314	235	17	is	be	AUX
ejpam-6314	235	18	a	a	DET
ejpam-6314	235	19	unique	unique	ADJ
ejpam-6314	235	20	fixed	fix	VERB
ejpam-6314	235	21	point	point	NOUN
ejpam-6314	235	22	of	of	ADP
ejpam-6314	235	23	ψ	ψ	NOUN
ejpam-6314	235	24	.	.	PUNCT
ejpam-6314	235	25	suppose	suppose	VERB
ejpam-6314	235	26	that	that	SCONJ
ejpam-6314	235	27	there	there	PRON
ejpam-6314	235	28	is	be	VERB
ejpam-6314	235	29	one	one	NUM
ejpam-6314	235	30	more	more	ADV
ejpam-6314	235	31	fixed	fix	VERB
ejpam-6314	235	32	point	point	NOUN
ejpam-6314	235	33	κ•	κ•	ADJ
ejpam-6314	235	34	that	that	PRON
ejpam-6314	235	35	is	be	AUX
ejpam-6314	235	36	κ•	κ•	ADJ
ejpam-6314	235	37	=	=	PRON
ejpam-6314	235	38	ψκ•	ψκ•	NOUN
ejpam-6314	236	1	it	it	PRON
ejpam-6314	236	2	follows	follow	VERB
ejpam-6314	236	3	that	that	SCONJ
ejpam-6314	236	4	;	;	PUNCT
ejpam-6314	236	5	db(κ⋆,κ•	db(κ⋆,κ•	X
ejpam-6314	236	6	)	)	PUNCT
ejpam-6314	236	7	=	=	SYM
ejpam-6314	236	8	db(ψκ⋆	db(ψκ⋆	PROPN
ejpam-6314	236	9	,	,	PUNCT
ejpam-6314	236	10	ψκ•	ψκ•	NOUN
ejpam-6314	236	11	)	)	PUNCT
ejpam-6314	236	12	≾	≾	PROPN
ejpam-6314	236	13	µdb(κ⋆,κ•	µdb(κ⋆,κ•	PROPN
ejpam-6314	236	14	)	)	PUNCT
ejpam-6314	237	1	+	+	CCONJ
ejpam-6314	237	2	νdb(κ⋆,κ⋆	νdb(κ⋆,κ⋆	PROPN
ejpam-6314	237	3	)	)	PUNCT
ejpam-6314	237	4	+	+	NOUN
ejpam-6314	237	5	γdb(κ•,κ•	γdb(κ•,κ•	X
ejpam-6314	237	6	)	)	PUNCT
ejpam-6314	237	7	]	]	PUNCT
ejpam-6314	237	8	db(κ⋆,κ•	db(κ⋆,κ•	NOUN
ejpam-6314	237	9	)	)	PUNCT
ejpam-6314	237	10	≾	≾	PROPN
ejpam-6314	237	11	µdb(κ⋆,κ•	µdb(κ⋆,κ•	PROPN
ejpam-6314	237	12	)	)	PUNCT
ejpam-6314	237	13	.	.	PUNCT
ejpam-6314	238	1	since	since	SCONJ
ejpam-6314	238	2	µ	µ	NOUN
ejpam-6314	238	3	∈	∈	NOUN
ejpam-6314	238	4	(	(	PUNCT
ejpam-6314	238	5	0	0	NUM
ejpam-6314	238	6	,	,	PUNCT
ejpam-6314	238	7	1	1	NUM
ejpam-6314	238	8	)	)	PUNCT
ejpam-6314	238	9	,	,	PUNCT
ejpam-6314	238	10	so	so	ADV
ejpam-6314	238	11	we	we	PRON
ejpam-6314	238	12	have	have	VERB
ejpam-6314	238	13	db(κ⋆,κ•	db(κ⋆,κ•	NOUN
ejpam-6314	238	14	)	)	PUNCT
ejpam-6314	238	15	.	.	PUNCT
ejpam-6314	239	1	therefore	therefore	ADV
ejpam-6314	239	2	,	,	PUNCT
ejpam-6314	239	3	we	we	PRON
ejpam-6314	239	4	have	have	VERB
ejpam-6314	239	5	κ⋆	κ⋆	ADJ
ejpam-6314	239	6	=	=	SYM
ejpam-6314	239	7	κ•	κ•	PROPN
ejpam-6314	239	8	and	and	CCONJ
ejpam-6314	239	9	thus	thus	ADV
ejpam-6314	239	10	κ⋆	κ⋆	X
ejpam-6314	239	11	is	be	AUX
ejpam-6314	239	12	a	a	DET
ejpam-6314	239	13	unique	unique	ADJ
ejpam-6314	239	14	fixed	fix	VERB
ejpam-6314	239	15	point	point	NOUN
ejpam-6314	239	16	of	of	ADP
ejpam-6314	239	17	ψ	ψ	PROPN
ejpam-6314	239	18	.	.	PUNCT
ejpam-6314	239	19	theorem	theorem	ADJ
ejpam-6314	239	20	4	4	NUM
ejpam-6314	239	21	.	.	PUNCT
ejpam-6314	240	1	let	let	VERB
ejpam-6314	240	2	(	(	PUNCT
ejpam-6314	240	3	s	s	X
ejpam-6314	240	4	,	,	PUNCT
ejpam-6314	240	5	ϑ	ϑ	X
ejpam-6314	240	6	,	,	PUNCT
ejpam-6314	240	7	db	db	PRON
ejpam-6314	240	8	)	)	PUNCT
ejpam-6314	240	9	be	be	AUX
ejpam-6314	240	10	(	(	PUNCT
ejpam-6314	240	11	bcvms	bcvms	NOUN
ejpam-6314	240	12	)	)	PUNCT
ejpam-6314	240	13	which	which	PRON
ejpam-6314	240	14	is	be	AUX
ejpam-6314	240	15	complete	complete	ADJ
ejpam-6314	240	16	and	and	CCONJ
ejpam-6314	240	17	φ	φ	NUM
ejpam-6314	240	18	,	,	PUNCT
ejpam-6314	240	19	ψ	ψ	X
ejpam-6314	240	20	:	:	PUNCT
ejpam-6314	240	21	s	s	X
ejpam-6314	240	22	→	→	PUNCT
ejpam-6314	240	23	s.	s.	PROPN
ejpam-6314	240	24	if	if	SCONJ
ejpam-6314	240	25	there	there	PRON
ejpam-6314	240	26	exist	exist	VERB
ejpam-6314	240	27	µ	µ	NOUN
ejpam-6314	240	28	,	,	PUNCT
ejpam-6314	240	29	ν	ν	X
ejpam-6314	240	30	:	:	PUNCT
ejpam-6314	240	31	s	s	X
ejpam-6314	240	32	→	→	SYM
ejpam-6314	240	33	[	[	X
ejpam-6314	240	34	0	0	NUM
ejpam-6314	240	35	,	,	PUNCT
ejpam-6314	240	36	1	1	NUM
ejpam-6314	240	37	)	)	PUNCT
ejpam-6314	240	38	such	such	ADJ
ejpam-6314	240	39	that	that	PRON
ejpam-6314	240	40	:	:	PUNCT
ejpam-6314	240	41	(	(	PUNCT
ejpam-6314	240	42	i	i	NOUN
ejpam-6314	240	43	)	)	PUNCT
ejpam-6314	240	44	µ(φκ	µ(φκ	PROPN
ejpam-6314	240	45	)	)	PUNCT
ejpam-6314	240	46	≤	≤	NOUN
ejpam-6314	240	47	µ(κ	µ(κ	NOUN
ejpam-6314	240	48	)	)	PUNCT
ejpam-6314	240	49	and	and	CCONJ
ejpam-6314	240	50	ν(φκ	ν(φκ	NOUN
ejpam-6314	240	51	)	)	PUNCT
ejpam-6314	240	52	≤	≤	NUM
ejpam-6314	240	53	ν(κ	ν(κ	NOUN
ejpam-6314	240	54	)	)	PUNCT
ejpam-6314	240	55	;	;	PUNCT
ejpam-6314	240	56	(	(	PUNCT
ejpam-6314	240	57	ii	ii	NOUN
ejpam-6314	240	58	)	)	PUNCT
ejpam-6314	240	59	µ(ψκ	µ(ψκ	NOUN
ejpam-6314	240	60	)	)	PUNCT
ejpam-6314	240	61	≤	≤	NOUN
ejpam-6314	241	1	µ(κ	µ(κ	NOUN
ejpam-6314	241	2	)	)	PUNCT
ejpam-6314	241	3	and	and	CCONJ
ejpam-6314	241	4	ν(ψκ	ν(ψκ	NOUN
ejpam-6314	241	5	)	)	PUNCT
ejpam-6314	241	6	≤	≤	NUM
ejpam-6314	241	7	ν(κ	ν(κ	NOUN
ejpam-6314	241	8	)	)	PUNCT
ejpam-6314	241	9	;	;	PUNCT
ejpam-6314	241	10	(	(	PUNCT
ejpam-6314	241	11	iii	iii	X
ejpam-6314	241	12	)	)	PUNCT
ejpam-6314	241	13	(	(	PUNCT
ejpam-6314	241	14	µ+	µ+	X
ejpam-6314	241	15	ν)(κ	ν)(κ	NOUN
ejpam-6314	241	16	)	)	PUNCT
ejpam-6314	241	17	<	<	X
ejpam-6314	241	18	1	1	NUM
ejpam-6314	241	19	;	;	PUNCT
ejpam-6314	241	20	(	(	PUNCT
ejpam-6314	241	21	iv	iv	X
ejpam-6314	241	22	)	)	PUNCT
ejpam-6314	241	23	db(φκ	db(φκ	PROPN
ejpam-6314	241	24	,	,	PUNCT
ejpam-6314	241	25	ψσ	ψσ	ADJ
ejpam-6314	241	26	)	)	PUNCT
ejpam-6314	241	27	≾	≾	PROPN
ejpam-6314	241	28	µ(κ)db(κ	µ(κ)db(κ	NOUN
ejpam-6314	241	29	,	,	PUNCT
ejpam-6314	241	30	σ	σ	NOUN
ejpam-6314	241	31	)	)	PUNCT
ejpam-6314	241	32	+	+	NUM
ejpam-6314	241	33	ν(κ	ν(κ	NOUN
ejpam-6314	241	34	)	)	PUNCT
ejpam-6314	241	35	db(κ	db(κ	NOUN
ejpam-6314	241	36	,	,	PUNCT
ejpam-6314	241	37	φκ)db(σ	φκ)db(σ	NOUN
ejpam-6314	241	38	,	,	PUNCT
ejpam-6314	241	39	ψσ	ψσ	ADJ
ejpam-6314	241	40	)	)	PUNCT
ejpam-6314	241	41	1	1	NUM
ejpam-6314	241	42	+	+	CCONJ
ejpam-6314	241	43	db(κ	db(κ	NUM
ejpam-6314	241	44	,	,	PUNCT
ejpam-6314	241	45	σ	σ	PROPN
ejpam-6314	241	46	)	)	PUNCT
ejpam-6314	241	47	(	(	PUNCT
ejpam-6314	241	48	14	14	NUM
ejpam-6314	241	49	)	)	PUNCT
ejpam-6314	241	50	for	for	ADP
ejpam-6314	241	51	all	all	DET
ejpam-6314	241	52	κ	κ	PROPN
ejpam-6314	241	53	,	,	PUNCT
ejpam-6314	241	54	σ	σ	PROPN
ejpam-6314	241	55	∈	∈	PROPN
ejpam-6314	241	56	s.	s.	PROPN
ejpam-6314	241	57	for	for	ADP
ejpam-6314	241	58	κ0	κ0	PRON
ejpam-6314	241	59	∈	∈	PROPN
ejpam-6314	241	60	s	s	PART
ejpam-6314	241	61	,	,	PUNCT
ejpam-6314	241	62	we	we	PRON
ejpam-6314	241	63	set	set	VERB
ejpam-6314	241	64	µ(κ0	µ(κ0	ADJ
ejpam-6314	241	65	)	)	PUNCT
ejpam-6314	241	66	1−ν(κ0	1−ν(κ0	NUM
ejpam-6314	241	67	)	)	PUNCT
ejpam-6314	241	68	=	=	SYM
ejpam-6314	241	69	ω	ω	X
ejpam-6314	241	70	.	.	PUNCT
ejpam-6314	241	71	suppose	suppose	VERB
ejpam-6314	241	72	that	that	SCONJ
ejpam-6314	241	73	:	:	PUNCT
ejpam-6314	241	74	sup	sup	PROPN
ejpam-6314	241	75	m≥1	m≥1	PROPN
ejpam-6314	241	76	lim	lim	PROPN
ejpam-6314	241	77	i→+∞	i→+∞	PROPN
ejpam-6314	241	78	ϑ(κi+1,κi+2)ϑ(κi+1,κm	ϑ(κi+1,κi+2)ϑ(κi+1,κm	PUNCT
ejpam-6314	241	79	)	)	PUNCT
ejpam-6314	241	80	ϑ(κi	ϑ(κi	NOUN
ejpam-6314	241	81	,	,	PUNCT
ejpam-6314	241	82	κi+1	κi+1	X
ejpam-6314	241	83	)	)	PUNCT
ejpam-6314	241	84	<	<	X
ejpam-6314	241	85	1	1	NUM
ejpam-6314	241	86	ω	ω	NUM
ejpam-6314	241	87	(	(	PUNCT
ejpam-6314	241	88	15	15	NUM
ejpam-6314	241	89	)	)	PUNCT
ejpam-6314	241	90	where	where	SCONJ
ejpam-6314	241	91	κ2n+1	κ2n+1	NOUN
ejpam-6314	241	92	=	=	SYM
ejpam-6314	241	93	φκ2n	φκ2n	PROPN
ejpam-6314	241	94	and	and	CCONJ
ejpam-6314	241	95	κ2n+2	κ2n+2	PRON
ejpam-6314	241	96	=	=	PUNCT
ejpam-6314	241	97	ψκ2n+1	ψκ2n+1	VERB
ejpam-6314	241	98	for	for	ADP
ejpam-6314	241	99	each	each	DET
ejpam-6314	241	100	n	n	PRON
ejpam-6314	241	101	≥	≥	NOUN
ejpam-6314	241	102	0	0	NUM
ejpam-6314	241	103	.	.	PUNCT
ejpam-6314	241	104	assume	assume	VERB
ejpam-6314	241	105	further	far	ADV
ejpam-6314	241	106	,	,	PUNCT
ejpam-6314	241	107	that	that	SCONJ
ejpam-6314	241	108	for	for	ADP
ejpam-6314	241	109	every	every	DET
ejpam-6314	241	110	κ	κ	PROPN
ejpam-6314	241	111	∈	∈	PROPN
ejpam-6314	241	112	s	s	PART
ejpam-6314	241	113	,	,	PUNCT
ejpam-6314	241	114	we	we	PRON
ejpam-6314	241	115	have	have	AUX
ejpam-6314	241	116	limn→+∞	limn→+∞	VERB
ejpam-6314	241	117	ϑ(κn	ϑ(κn	PROPN
ejpam-6314	241	118	,	,	PUNCT
ejpam-6314	241	119	κ	κ	NOUN
ejpam-6314	241	120	)	)	PUNCT
ejpam-6314	241	121	and	and	CCONJ
ejpam-6314	241	122	limn→+∞	limn→+∞	PROPN
ejpam-6314	241	123	ϑ(κ	ϑ(κ	PROPN
ejpam-6314	241	124	,	,	PUNCT
ejpam-6314	241	125	κn	κn	NOUN
ejpam-6314	241	126	)	)	PUNCT
ejpam-6314	241	127	,	,	PUNCT
ejpam-6314	241	128	which	which	PRON
ejpam-6314	241	129	exist	exist	VERB
ejpam-6314	241	130	and	and	CCONJ
ejpam-6314	241	131	are	be	AUX
ejpam-6314	241	132	finite	finite	ADJ
ejpam-6314	241	133	.	.	PUNCT
ejpam-6314	242	1	then	then	ADV
ejpam-6314	242	2	,	,	PUNCT
ejpam-6314	242	3	φ	φ	PROPN
ejpam-6314	242	4	and	and	CCONJ
ejpam-6314	242	5	ψ	ψ	PROPN
ejpam-6314	242	6	have	have	VERB
ejpam-6314	242	7	a	a	DET
ejpam-6314	242	8	ucfp	ucfp	NOUN
ejpam-6314	242	9	.	.	PUNCT
ejpam-6314	243	1	proof	proof	NOUN
ejpam-6314	243	2	.	.	PUNCT
ejpam-6314	244	1	suppose	suppose	VERB
ejpam-6314	244	2	µ0	µ0	PROPN
ejpam-6314	244	3	∈	∈	PROPN
ejpam-6314	244	4	s.	s.	PROPN
ejpam-6314	244	5	we	we	PRON
ejpam-6314	244	6	find	find	VERB
ejpam-6314	244	7	{	{	PUNCT
ejpam-6314	244	8	κn	κn	NOUN
ejpam-6314	244	9	}	}	PUNCT
ejpam-6314	244	10	in	in	ADP
ejpam-6314	244	11	s	s	PRON
ejpam-6314	244	12	by	by	ADP
ejpam-6314	244	13	κ2n+1	κ2n+1	PROPN
ejpam-6314	244	14	=	=	SYM
ejpam-6314	244	15	φκ2n	φκ2n	PROPN
ejpam-6314	244	16	and	and	CCONJ
ejpam-6314	244	17	κ2n+2	κ2n+2	PRON
ejpam-6314	244	18	=	=	PUNCT
ejpam-6314	244	19	ψκ2n+1	ψκ2n+1	VERB
ejpam-6314	244	20	for	for	ADP
ejpam-6314	244	21	each	each	DET
ejpam-6314	244	22	n	n	PRON
ejpam-6314	244	23	≥	≥	NOUN
ejpam-6314	244	24	0	0	NUM
ejpam-6314	244	25	.	.	PUNCT
ejpam-6314	245	1	from	from	ADP
ejpam-6314	245	2	hypothesis	hypothesis	NOUN
ejpam-6314	245	3	and	and	CCONJ
ejpam-6314	245	4	(	(	PUNCT
ejpam-6314	245	5	14	14	NUM
ejpam-6314	245	6	)	)	PUNCT
ejpam-6314	245	7	we	we	PRON
ejpam-6314	245	8	get	get	VERB
ejpam-6314	245	9	:	:	PUNCT
ejpam-6314	245	10	db(κ2n+1,κ2n+2	db(κ2n+1,κ2n+2	X
ejpam-6314	245	11	)	)	PUNCT
ejpam-6314	246	1	=	=	SYM
ejpam-6314	246	2	db(φκ2n	db(φκ2n	PROPN
ejpam-6314	246	3	,	,	PUNCT
ejpam-6314	246	4	ψκ2n+1	ψκ2n+1	NOUN
ejpam-6314	246	5	)	)	PUNCT
ejpam-6314	246	6	m.	m.	NOUN
ejpam-6314	246	7	sarwar	sarwar	PROPN
ejpam-6314	246	8	et	et	PROPN
ejpam-6314	246	9	al	al	PROPN
ejpam-6314	246	10	.	.	PUNCT
ejpam-6314	246	11	/	/	SYM
ejpam-6314	246	12	eur	eur	PROPN
ejpam-6314	246	13	.	.	PUNCT
ejpam-6314	247	1	j.	j.	PROPN
ejpam-6314	247	2	pure	pure	PROPN
ejpam-6314	247	3	appl	appl	PROPN
ejpam-6314	247	4	.	.	PROPN
ejpam-6314	247	5	math	math	PROPN
ejpam-6314	247	6	,	,	PUNCT
ejpam-6314	247	7	18	18	NUM
ejpam-6314	247	8	(	(	PUNCT
ejpam-6314	247	9	3	3	NUM
ejpam-6314	247	10	)	)	PUNCT
ejpam-6314	247	11	(	(	PUNCT
ejpam-6314	247	12	2025	2025	NUM
ejpam-6314	247	13	)	)	PUNCT
ejpam-6314	247	14	,	,	PUNCT
ejpam-6314	247	15	6314	6314	NUM
ejpam-6314	247	16	12	12	NUM
ejpam-6314	247	17	of	of	ADP
ejpam-6314	247	18	28	28	NUM
ejpam-6314	247	19	≾	≾	PROPN
ejpam-6314	247	20	µ(κ2n)db(κ2n	µ(κ2n)db(κ2n	PROPN
ejpam-6314	247	21	,	,	PUNCT
ejpam-6314	247	22	κ2n+1	κ2n+1	PUNCT
ejpam-6314	247	23	)	)	PUNCT
ejpam-6314	247	24	+	+	CCONJ
ejpam-6314	247	25	ν(κ2n	ν(κ2n	X
ejpam-6314	247	26	)	)	PUNCT
ejpam-6314	247	27	db(κ2n	db(κ2n	PROPN
ejpam-6314	247	28	,	,	PUNCT
ejpam-6314	247	29	φκ2n)db(κ2n+1,ψκ2n+1	φκ2n)db(κ2n+1,ψκ2n+1	NOUN
ejpam-6314	247	30	)	)	PUNCT
ejpam-6314	247	31	1	1	NUM
ejpam-6314	248	1	+	+	CCONJ
ejpam-6314	248	2	db(κ2n	db(κ2n	PROPN
ejpam-6314	248	3	,	,	PUNCT
ejpam-6314	248	4	κ2n+1	κ2n+1	PROPN
ejpam-6314	248	5	)	)	PUNCT
ejpam-6314	248	6	=	=	SYM
ejpam-6314	248	7	µ(κ2n)db(κ2n	µ(κ2n)db(κ2n	PROPN
ejpam-6314	248	8	,	,	PUNCT
ejpam-6314	248	9	κ2n+1	κ2n+1	PUNCT
ejpam-6314	248	10	)	)	PUNCT
ejpam-6314	248	11	+	+	CCONJ
ejpam-6314	248	12	ν(κ2n	ν(κ2n	X
ejpam-6314	248	13	)	)	PUNCT
ejpam-6314	248	14	db(κ2n	db(κ2n	PROPN
ejpam-6314	248	15	,	,	PUNCT
ejpam-6314	248	16	κ2n+1)db(κ2n+1,κ2n+2	κ2n+1)db(κ2n+1,κ2n+2	PROPN
ejpam-6314	248	17	)	)	PUNCT
ejpam-6314	248	18	1	1	NUM
ejpam-6314	249	1	+	+	CCONJ
ejpam-6314	249	2	db(κ2n	db(κ2n	PROPN
ejpam-6314	249	3	,	,	PUNCT
ejpam-6314	249	4	κ2n+1	κ2n+1	NOUN
ejpam-6314	249	5	)	)	PUNCT
ejpam-6314	249	6	≾	≾	PROPN
ejpam-6314	249	7	µ(κ2n)db(κ2n	µ(κ2n)db(κ2n	PROPN
ejpam-6314	249	8	,	,	PUNCT
ejpam-6314	249	9	κ2n+1	κ2n+1	PUNCT
ejpam-6314	249	10	)	)	PUNCT
ejpam-6314	249	11	+	+	CCONJ
ejpam-6314	249	12	ν(κ2n)db(κ2n+1,κ2n+2	ν(κ2n)db(κ2n+1,κ2n+2	NOUN
ejpam-6314	249	13	)	)	PUNCT
ejpam-6314	249	14	=	=	SYM
ejpam-6314	249	15	µ(ψκ2n−1)db(κ2n	µ(ψκ2n−1)db(κ2n	PROPN
ejpam-6314	249	16	,	,	PUNCT
ejpam-6314	249	17	κ2n+1	κ2n+1	PROPN
ejpam-6314	249	18	)	)	PUNCT
ejpam-6314	249	19	+	+	SYM
ejpam-6314	249	20	ν(ψκ2n−1)db(κ2n+1,κ2n+2	ν(ψκ2n−1)db(κ2n+1,κ2n+2	NOUN
ejpam-6314	249	21	)	)	PUNCT
ejpam-6314	249	22	≾	≾	PROPN
ejpam-6314	249	23	µ(κ2n−1)db(κ2n	µ(κ2n−1)db(κ2n	PROPN
ejpam-6314	249	24	,	,	PUNCT
ejpam-6314	249	25	κ2n+1	κ2n+1	PROPN
ejpam-6314	249	26	)	)	PUNCT
ejpam-6314	249	27	+	+	CCONJ
ejpam-6314	249	28	ν(κ2n−1)db(κ2n+1,κ2n+2	ν(κ2n−1)db(κ2n+1,κ2n+2	NOUN
ejpam-6314	249	29	)	)	PUNCT
ejpam-6314	249	30	=	=	SYM
ejpam-6314	249	31	µ(φκ2n−2)db(κ2n	µ(φκ2n−2)db(κ2n	PROPN
ejpam-6314	249	32	,	,	PUNCT
ejpam-6314	249	33	κ2n+1	κ2n+1	PROPN
ejpam-6314	249	34	)	)	PUNCT
ejpam-6314	249	35	+	+	CCONJ
ejpam-6314	249	36	ν(φκ2n−2)db(κ2n+1,κ2n+2	ν(φκ2n−2)db(κ2n+1,κ2n+2	NOUN
ejpam-6314	249	37	)	)	PUNCT
ejpam-6314	249	38	≾	≾	PROPN
ejpam-6314	249	39	µ(κ2n−2)db(κ2n	µ(κ2n−2)db(κ2n	PROPN
ejpam-6314	249	40	,	,	PUNCT
ejpam-6314	249	41	κ2n+1	κ2n+1	PROPN
ejpam-6314	249	42	)	)	PUNCT
ejpam-6314	249	43	+	+	CCONJ
ejpam-6314	249	44	ν(κ2n−2)db(κ2n+1,κ2n+2	ν(κ2n−2)db(κ2n+1,κ2n+2	NOUN
ejpam-6314	249	45	)	)	PUNCT
ejpam-6314	249	46	·	·	PUNCT
ejpam-6314	249	47	·	·	PUNCT
ejpam-6314	249	48	·	·	PUNCT
ejpam-6314	250	1	≾	≾	NOUN
ejpam-6314	250	2	µ(κ0)db(κ2n	µ(κ0)db(κ2n	NUM
ejpam-6314	250	3	,	,	PUNCT
ejpam-6314	250	4	κ2n+1	κ2n+1	PUNCT
ejpam-6314	250	5	)	)	PUNCT
ejpam-6314	250	6	+	+	NUM
ejpam-6314	250	7	ν(κ0)db(κ2n+1,κ2n+2	ν(κ0)db(κ2n+1,κ2n+2	PROPN
ejpam-6314	250	8	)	)	PUNCT
ejpam-6314	250	9	.	.	PUNCT
ejpam-6314	251	1	which	which	PRON
ejpam-6314	251	2	implies	imply	VERB
ejpam-6314	251	3	that	that	SCONJ
ejpam-6314	251	4	,	,	PUNCT
ejpam-6314	251	5	db(κ2n+1,κ2n+2	db(κ2n+1,κ2n+2	PROPN
ejpam-6314	251	6	)	)	PUNCT
ejpam-6314	251	7	≾	≾	PROPN
ejpam-6314	251	8	(	(	PUNCT
ejpam-6314	251	9	µ(κ0	µ(κ0	ADJ
ejpam-6314	251	10	)	)	PUNCT
ejpam-6314	251	11	1−	1−	NUM
ejpam-6314	251	12	ν(κ0	ν(κ0	NOUN
ejpam-6314	251	13	)	)	PUNCT
ejpam-6314	251	14	)	)	PUNCT
ejpam-6314	252	1	db(κ2n	db(κ2n	PROPN
ejpam-6314	252	2	,	,	PUNCT
ejpam-6314	252	3	κ2n+1	κ2n+1	PROPN
ejpam-6314	252	4	)	)	PUNCT
ejpam-6314	252	5	.	.	PUNCT
ejpam-6314	253	1	similarly	similarly	ADV
ejpam-6314	253	2	,	,	PUNCT
ejpam-6314	253	3	db(κ2n+2,κ2n+3	db(κ2n+2,κ2n+3	PROPN
ejpam-6314	253	4	)	)	PUNCT
ejpam-6314	253	5	=	=	SYM
ejpam-6314	253	6	db(ψκ2n+1,φκ2n+2	db(ψκ2n+1,φκ2n+2	X
ejpam-6314	253	7	)	)	PUNCT
ejpam-6314	253	8	=	=	SYM
ejpam-6314	253	9	db(φκ2n+2,ψκ2n+1	db(φκ2n+2,ψκ2n+1	X
ejpam-6314	253	10	)	)	PUNCT
ejpam-6314	253	11	≾	≾	NOUN
ejpam-6314	253	12	µ(κ2n+2)db(κ2n+2,κ2n+1	µ(κ2n+2)db(κ2n+2,κ2n+1	NOUN
ejpam-6314	253	13	)	)	PUNCT
ejpam-6314	253	14	+	+	VERB
ejpam-6314	253	15	ν(κ2n+2	ν(κ2n+2	X
ejpam-6314	253	16	)	)	PUNCT
ejpam-6314	253	17	db(κ2n+2,φκ2n+2)db(κ2n+1,ψκ2n+1	db(κ2n+2,φκ2n+2)db(κ2n+1,ψκ2n+1	NOUN
ejpam-6314	253	18	)	)	PUNCT
ejpam-6314	253	19	1	1	NUM
ejpam-6314	254	1	+	+	CCONJ
ejpam-6314	254	2	db(κ2n+2,κ2n+1	db(κ2n+2,κ2n+1	ADJ
ejpam-6314	254	3	)	)	PUNCT
ejpam-6314	254	4	=	=	SYM
ejpam-6314	254	5	µ(κ2n+2)db(κ2n+2,κ2n+1	µ(κ2n+2)db(κ2n+2,κ2n+1	ADJ
ejpam-6314	254	6	)	)	PUNCT
ejpam-6314	255	1	+	+	VERB
ejpam-6314	255	2	ν(κ2n+2	ν(κ2n+2	X
ejpam-6314	255	3	)	)	PUNCT
ejpam-6314	256	1	db(κ2n+2,κ2n+3)db(κ2n+1,κ2n+2	db(κ2n+2,κ2n+3)db(κ2n+1,κ2n+2	NUM
ejpam-6314	256	2	)	)	PUNCT
ejpam-6314	256	3	1	1	NUM
ejpam-6314	257	1	+	+	PUNCT
ejpam-6314	257	2	db(κ2n+2,κ2n+1	db(κ2n+2,κ2n+1	ADJ
ejpam-6314	257	3	)	)	PUNCT
ejpam-6314	257	4	=	=	SYM
ejpam-6314	257	5	µ(κ2n+2)db(κ2n+2,κ2n+1	µ(κ2n+2)db(κ2n+2,κ2n+1	ADJ
ejpam-6314	257	6	)	)	PUNCT
ejpam-6314	258	1	+	+	CCONJ
ejpam-6314	258	2	ν(κ2n+2)db(κ2n+3,κ2n+2	ν(κ2n+2)db(κ2n+3,κ2n+2	NOUN
ejpam-6314	258	3	)	)	PUNCT
ejpam-6314	258	4	=	=	SYM
ejpam-6314	258	5	µ(ψκ2n+1)db(κ2n+2,κ2n+1	µ(ψκ2n+1)db(κ2n+2,κ2n+1	PROPN
ejpam-6314	258	6	)	)	PUNCT
ejpam-6314	258	7	+	+	CCONJ
ejpam-6314	258	8	ν(ψκ2n+1)db(κ2n+3,κ2n+2	ν(ψκ2n+1)db(κ2n+3,κ2n+2	X
ejpam-6314	258	9	)	)	PUNCT
ejpam-6314	258	10	µ(ψκ2n+1)db(κ2n+2,κ2n+1	µ(ψκ2n+1)db(κ2n+2,κ2n+1	PROPN
ejpam-6314	258	11	)	)	PUNCT
ejpam-6314	259	1	+	+	CCONJ
ejpam-6314	259	2	ν(ψκ2n+1)db(κ2n+3,κ2n+2	ν(ψκ2n+1)db(κ2n+3,κ2n+2	X
ejpam-6314	259	3	)	)	PUNCT
ejpam-6314	259	4	≾	≾	NOUN
ejpam-6314	259	5	µ(κ2n+1)db(κ2n+2,κ2n+1	µ(κ2n+1)db(κ2n+2,κ2n+1	NOUN
ejpam-6314	259	6	)	)	PUNCT
ejpam-6314	260	1	+	+	CCONJ
ejpam-6314	260	2	ν(κ2n+1)db(κ2n+3,κ2n+2	ν(κ2n+1)db(κ2n+3,κ2n+2	ADJ
ejpam-6314	260	3	)	)	PUNCT
ejpam-6314	260	4	=	=	PUNCT
ejpam-6314	260	5	µ(φκ2n)db(κ2n+2,κ2n+1	µ(φκ2n)db(κ2n+2,κ2n+1	X
ejpam-6314	260	6	)	)	PUNCT
ejpam-6314	260	7	+	+	CCONJ
ejpam-6314	260	8	ν(φκ2n)db(κ2n+3,κ2n+2	ν(φκ2n)db(κ2n+3,κ2n+2	NOUN
ejpam-6314	260	9	)	)	PUNCT
ejpam-6314	260	10	≾	≾	PROPN
ejpam-6314	260	11	µ(κ2n)db(κ2n+2,κ2n+3	µ(κ2n)db(κ2n+2,κ2n+3	NOUN
ejpam-6314	260	12	)	)	PUNCT
ejpam-6314	260	13	+	+	NUM
ejpam-6314	260	14	ν(κ2n)db(κ2n+3,κ2n+2	ν(κ2n)db(κ2n+3,κ2n+2	NOUN
ejpam-6314	260	15	)	)	PUNCT
ejpam-6314	260	16	.	.	PUNCT
ejpam-6314	260	17	.	.	PUNCT
ejpam-6314	260	18	.	.	PUNCT
ejpam-6314	261	1	≾	≾	NOUN
ejpam-6314	261	2	µ(κ0)db(κ2n+2,κ2n+1	µ(κ0)db(κ2n+2,κ2n+1	PROPN
ejpam-6314	261	3	)	)	PUNCT
ejpam-6314	262	1	+	+	CCONJ
ejpam-6314	262	2	ν(κ0)db(κ2n+3,κ2n+2	ν(κ0)db(κ2n+3,κ2n+2	ADV
ejpam-6314	262	3	)	)	PUNCT
ejpam-6314	262	4	.	.	PUNCT
ejpam-6314	263	1	m.	m.	NOUN
ejpam-6314	263	2	sarwar	sarwar	PROPN
ejpam-6314	263	3	et	et	PROPN
ejpam-6314	263	4	al	al	PROPN
ejpam-6314	263	5	.	.	PUNCT
ejpam-6314	263	6	/	/	SYM
ejpam-6314	263	7	eur	eur	PROPN
ejpam-6314	263	8	.	.	PUNCT
ejpam-6314	264	1	j.	j.	PROPN
ejpam-6314	264	2	pure	pure	PROPN
ejpam-6314	264	3	appl	appl	PROPN
ejpam-6314	264	4	.	.	PROPN
ejpam-6314	264	5	math	math	PROPN
ejpam-6314	264	6	,	,	PUNCT
ejpam-6314	264	7	18	18	NUM
ejpam-6314	264	8	(	(	PUNCT
ejpam-6314	264	9	3	3	NUM
ejpam-6314	264	10	)	)	PUNCT
ejpam-6314	264	11	(	(	PUNCT
ejpam-6314	264	12	2025	2025	NUM
ejpam-6314	264	13	)	)	PUNCT
ejpam-6314	264	14	,	,	PUNCT
ejpam-6314	264	15	6314	6314	NUM
ejpam-6314	264	16	13	13	NUM
ejpam-6314	264	17	of	of	ADP
ejpam-6314	264	18	28	28	NUM
ejpam-6314	264	19	which	which	PRON
ejpam-6314	264	20	implies	imply	VERB
ejpam-6314	264	21	that	that	SCONJ
ejpam-6314	264	22	db(κ2n+3,κ2n+2	db(κ2n+3,κ2n+2	PROPN
ejpam-6314	264	23	)	)	PUNCT
ejpam-6314	264	24	≾	≾	PROPN
ejpam-6314	264	25	(	(	PUNCT
ejpam-6314	264	26	µ(κ0	µ(κ0	ADJ
ejpam-6314	264	27	)	)	PUNCT
ejpam-6314	264	28	1−	1−	NUM
ejpam-6314	264	29	ν(κ0	ν(κ0	NOUN
ejpam-6314	264	30	)	)	PUNCT
ejpam-6314	264	31	)	)	PUNCT
ejpam-6314	265	1	db(κ2n+2,κ2n+1	db(κ2n+2,κ2n+1	PROPN
ejpam-6314	265	2	)	)	PUNCT
ejpam-6314	265	3	=	=	PUNCT
ejpam-6314	265	4	ωdb(κ2n+2,κ2n+1	ωdb(κ2n+2,κ2n+1	NOUN
ejpam-6314	265	5	.	.	NOUN
ejpam-6314	265	6	to	to	PART
ejpam-6314	265	7	continue	continue	VERB
ejpam-6314	265	8	the	the	DET
ejpam-6314	265	9	process	process	NOUN
ejpam-6314	265	10	in	in	ADP
ejpam-6314	265	11	this	this	DET
ejpam-6314	265	12	direction	direction	NOUN
ejpam-6314	265	13	,	,	PUNCT
ejpam-6314	265	14	we	we	PRON
ejpam-6314	265	15	obtain	obtain	VERB
ejpam-6314	265	16	,	,	PUNCT
ejpam-6314	265	17	db(κn	db(κn	NOUN
ejpam-6314	265	18	,	,	PUNCT
ejpam-6314	265	19	κn+1	κn+1	NOUN
ejpam-6314	265	20	)	)	PUNCT
ejpam-6314	266	1	≾	≾	NOUN
ejpam-6314	266	2	ωdb(κn−1,κn	ωdb(κn−1,κn	ADV
ejpam-6314	266	3	)	)	PUNCT
ejpam-6314	266	4	≾	≾	NOUN
ejpam-6314	266	5	ω2db(κn−2,κn−1	ω2db(κn−2,κn−1	NOUN
ejpam-6314	266	6	)	)	PUNCT
ejpam-6314	266	7	≾	≾	PROPN
ejpam-6314	266	8	·	·	PUNCT
ejpam-6314	266	9	·	·	PUNCT
ejpam-6314	266	10	·	·	PUNCT
ejpam-6314	266	11	ωndb(κ0,κ1	ωndb(κ0,κ1	X
ejpam-6314	266	12	)	)	PUNCT
ejpam-6314	266	13	.	.	PUNCT
ejpam-6314	267	1	thus	thus	ADV
ejpam-6314	267	2	,	,	PUNCT
ejpam-6314	267	3	db(κn	db(κn	NOUN
ejpam-6314	267	4	,	,	PUNCT
ejpam-6314	267	5	κn+1	κn+1	NOUN
ejpam-6314	267	6	)	)	PUNCT
ejpam-6314	267	7	≾	≾	PROPN
ejpam-6314	267	8	ωndb(κ0,κ0	ωndb(κ0,κ0	NOUN
ejpam-6314	267	9	)	)	PUNCT
ejpam-6314	267	10	.	.	PUNCT
ejpam-6314	268	1	(	(	PUNCT
ejpam-6314	268	2	16	16	NUM
ejpam-6314	268	3	)	)	PUNCT
ejpam-6314	268	4	for	for	ADP
ejpam-6314	268	5	all	all	DET
ejpam-6314	268	6	n	n	CCONJ
ejpam-6314	268	7	,	,	PUNCT
ejpam-6314	268	8	m	m	VERB
ejpam-6314	268	9	∈	∈	ADJ
ejpam-6314	268	10	n	n	CCONJ
ejpam-6314	268	11	(	(	PUNCT
ejpam-6314	268	12	n	n	X
ejpam-6314	268	13	<	<	X
ejpam-6314	268	14	m	m	PROPN
ejpam-6314	268	15	)	)	PUNCT
ejpam-6314	268	16	,	,	PUNCT
ejpam-6314	268	17	we	we	PRON
ejpam-6314	268	18	have	have	VERB
ejpam-6314	268	19	db(κn	db(κn	NOUN
ejpam-6314	268	20	,	,	PUNCT
ejpam-6314	268	21	κm	κm	NOUN
ejpam-6314	268	22	)	)	PUNCT
ejpam-6314	268	23	≾	≾	PROPN
ejpam-6314	268	24	ϑ(κn	ϑ(κn	PROPN
ejpam-6314	268	25	,	,	PUNCT
ejpam-6314	268	26	κn+1)db(κn	κn+1)db(κn	X
ejpam-6314	268	27	,	,	PUNCT
ejpam-6314	268	28	κn+1	κn+1	NOUN
ejpam-6314	268	29	)	)	PUNCT
ejpam-6314	269	1	+	+	CCONJ
ejpam-6314	269	2	ϑ(κn+1,κm)db(κn+1,κm	ϑ(κn+1,κm)db(κn+1,κm	X
ejpam-6314	269	3	)	)	PUNCT
ejpam-6314	269	4	≾	≾	PROPN
ejpam-6314	269	5	ϑ(κn	ϑ(κn	PROPN
ejpam-6314	269	6	,	,	PUNCT
ejpam-6314	269	7	κn+1)db(κn	κn+1)db(κn	X
ejpam-6314	269	8	,	,	PUNCT
ejpam-6314	269	9	κn+1	κn+1	NOUN
ejpam-6314	269	10	)	)	PUNCT
ejpam-6314	269	11	+	+	CCONJ
ejpam-6314	269	12	ϑ(κn+1,κm)ϑ(κn+1,κn+2	ϑ(κn+1,κm)ϑ(κn+1,κn+2	X
ejpam-6314	269	13	)	)	PUNCT
ejpam-6314	269	14	×	×	NOUN
ejpam-6314	269	15	db(κn	db(κn	NOUN
ejpam-6314	269	16	+	+	CCONJ
ejpam-6314	269	17	1,κn+2	1,κn+2	NUM
ejpam-6314	269	18	)	)	PUNCT
ejpam-6314	269	19	+	+	CCONJ
ejpam-6314	269	20	ϑ(κn+1,κm)ϑ(κn+2,κm)db(κn+2,κm	ϑ(κn+1,κm)ϑ(κn+2,κm)db(κn+2,κm	X
ejpam-6314	269	21	)	)	PUNCT
ejpam-6314	269	22	≾	≾	PROPN
ejpam-6314	269	23	ϑ(κn	ϑ(κn	PROPN
ejpam-6314	269	24	,	,	PUNCT
ejpam-6314	269	25	κn+1)db(κn	κn+1)db(κn	X
ejpam-6314	269	26	,	,	PUNCT
ejpam-6314	269	27	κn+1	κn+1	NOUN
ejpam-6314	269	28	)	)	PUNCT
ejpam-6314	269	29	+	+	CCONJ
ejpam-6314	269	30	ϑ(κn+1,κm)ϑ(κn+1,κn+2	ϑ(κn+1,κm)ϑ(κn+1,κn+2	X
ejpam-6314	269	31	)	)	PUNCT
ejpam-6314	269	32	×	×	NOUN
ejpam-6314	269	33	db(κn+1,κn+2	db(κn+1,κn+2	ADV
ejpam-6314	269	34	)	)	PUNCT
ejpam-6314	270	1	+	+	NUM
ejpam-6314	270	2	ϑ(κn+1,κm)ϑ(κn+2,κm)ϑ(κn+2,κn+3	ϑ(κn+1,κm)ϑ(κn+2,κm)ϑ(κn+2,κn+3	NUM
ejpam-6314	270	3	)	)	PUNCT
ejpam-6314	270	4	×	×	PROPN
ejpam-6314	270	5	db(κn+2,κn+3	db(κn+2,κn+3	PROPN
ejpam-6314	270	6	)	)	PUNCT
ejpam-6314	270	7	+	+	SYM
ejpam-6314	270	8	ϑ(κn+1,κm)ϑ(κn+2,κm	ϑ(κn+1,κm)ϑ(κn+2,κm	NOUN
ejpam-6314	270	9	)	)	PUNCT
ejpam-6314	270	10	×	×	NOUN
ejpam-6314	270	11	ϑ(κn+3,κm)db(κn+3,κm	ϑ(κn+3,κm)db(κn+3,κm	NOUN
ejpam-6314	270	12	)	)	PUNCT
ejpam-6314	270	13	≾	≾	PROPN
ejpam-6314	270	14	.	.	PUNCT
ejpam-6314	270	15	.	.	PUNCT
ejpam-6314	270	16	.	.	PUNCT
ejpam-6314	271	1	≾	≾	PROPN
ejpam-6314	271	2	ϑ(κn	ϑ(κn	PROPN
ejpam-6314	271	3	,	,	PUNCT
ejpam-6314	271	4	κn+1)db(κn	κn+1)db(κn	X
ejpam-6314	271	5	,	,	PUNCT
ejpam-6314	271	6	κn+1	κn+1	NOUN
ejpam-6314	271	7	)	)	PUNCT
ejpam-6314	272	1	+	+	CCONJ
ejpam-6314	272	2	m−2∑	m−2∑	NUM
ejpam-6314	273	1	i	i	PRON
ejpam-6314	273	2	=	=	NOUN
ejpam-6314	273	3	n+1	n+1	PRON
ejpam-6314	273	4			PROPN
ejpam-6314	273	5	i∏	i∏	PROPN
ejpam-6314	273	6	j	j	NOUN
ejpam-6314	273	7	=	=	NOUN
ejpam-6314	273	8	n+1	n+1	PROPN
ejpam-6314	273	9	ϑ(κj	ϑ(κj	PROPN
ejpam-6314	273	10	,	,	PUNCT
ejpam-6314	273	11	κm	κm	NOUN
ejpam-6314	273	12	)	)	PUNCT
ejpam-6314	273	13			NOUN
ejpam-6314	273	14	×	×	PROPN
ejpam-6314	273	15	ϑ(κi	ϑ(κi	NOUN
ejpam-6314	273	16	,	,	PUNCT
ejpam-6314	273	17	κi+1)db(κi	κi+1)db(κi	NOUN
ejpam-6314	273	18	,	,	PUNCT
ejpam-6314	273	19	κi+1	κi+1	X
ejpam-6314	273	20	)	)	PUNCT
ejpam-6314	274	1	+	+	CCONJ
ejpam-6314	274	2	m−1∏	m−1∏	PROPN
ejpam-6314	274	3	i	i	NOUN
ejpam-6314	274	4	=	=	NOUN
ejpam-6314	274	5	n+1	n+1	X
ejpam-6314	274	6	ϑ(κi	ϑ(κi	NOUN
ejpam-6314	274	7	,	,	PUNCT
ejpam-6314	274	8	κm)db(κm−1,κm	κm)db(κm−1,κm	NUM
ejpam-6314	274	9	)	)	PUNCT
ejpam-6314	274	10	(	(	PUNCT
ejpam-6314	274	11	17	17	NUM
ejpam-6314	274	12	)	)	PUNCT
ejpam-6314	274	13	this	this	PRON
ejpam-6314	274	14	implies	imply	VERB
ejpam-6314	274	15	that	that	SCONJ
ejpam-6314	274	16	db(κn	db(κn	NOUN
ejpam-6314	274	17	,	,	PUNCT
ejpam-6314	274	18	κm	κm	NOUN
ejpam-6314	274	19	)	)	PUNCT
ejpam-6314	274	20	≾	≾	PROPN
ejpam-6314	274	21	ϑ(κn	ϑ(κn	PROPN
ejpam-6314	274	22	,	,	PUNCT
ejpam-6314	274	23	κn+1)db(κn	κn+1)db(κn	X
ejpam-6314	274	24	,	,	PUNCT
ejpam-6314	274	25	κn+1	κn+1	NOUN
ejpam-6314	274	26	)	)	PUNCT
ejpam-6314	275	1	+	+	CCONJ
ejpam-6314	275	2	m−2∑	m−2∑	NUM
ejpam-6314	276	1	i	i	PRON
ejpam-6314	276	2	=	=	NOUN
ejpam-6314	276	3	n+1	n+1	PRON
ejpam-6314	276	4			PROPN
ejpam-6314	276	5	i∏	i∏	PROPN
ejpam-6314	276	6	j	j	NOUN
ejpam-6314	276	7	=	=	NOUN
ejpam-6314	276	8	n+1	n+1	PROPN
ejpam-6314	276	9	ϑ(κj	ϑ(κj	PROPN
ejpam-6314	276	10	,	,	PUNCT
ejpam-6314	276	11	κm	κm	NOUN
ejpam-6314	276	12	)	)	PUNCT
ejpam-6314	276	13			NOUN
ejpam-6314	276	14	×	×	PROPN
ejpam-6314	276	15	ϑ(κi	ϑ(κi	NOUN
ejpam-6314	276	16	,	,	PUNCT
ejpam-6314	276	17	κi+1)db(κi	κi+1)db(κi	NOUN
ejpam-6314	276	18	,	,	PUNCT
ejpam-6314	276	19	κi+1	κi+1	X
ejpam-6314	276	20	)	)	PUNCT
ejpam-6314	277	1	+	+	CCONJ
ejpam-6314	277	2	[	[	PUNCT
ejpam-6314	277	3	m−1∏	m−1∏	PROPN
ejpam-6314	277	4	i	i	NOUN
ejpam-6314	277	5	=	=	NOUN
ejpam-6314	277	6	n+1	n+1	X
ejpam-6314	277	7	ϑ(κj	ϑ(κj	PROPN
ejpam-6314	277	8	,	,	PUNCT
ejpam-6314	277	9	κm	κm	PROPN
ejpam-6314	277	10	)	)	PUNCT
ejpam-6314	277	11	]	]	PUNCT
ejpam-6314	277	12	×	×	PROPN
ejpam-6314	277	13	ϑ(κm−1,κm)db(κm−1,κm	ϑ(κm−1,κm)db(κm−1,κm	X
ejpam-6314	277	14	)	)	PUNCT
ejpam-6314	277	15	≾	≾	PROPN
ejpam-6314	277	16	ϑ(κn	ϑ(κn	PROPN
ejpam-6314	277	17	,	,	PUNCT
ejpam-6314	277	18	κn+1)ω	κn+1)ω	X
ejpam-6314	277	19	ndb(κn	ndb(κn	NUM
ejpam-6314	277	20	,	,	PUNCT
ejpam-6314	277	21	κn+1	κn+1	ADJ
ejpam-6314	277	22	)	)	PUNCT
ejpam-6314	278	1	+	+	CCONJ
ejpam-6314	278	2	m−2∑	m−2∑	NUM
ejpam-6314	279	1	i	i	PRON
ejpam-6314	279	2	=	=	NOUN
ejpam-6314	279	3	n+1	n+1	PRON
ejpam-6314	279	4			PROPN
ejpam-6314	279	5	i∏	i∏	PROPN
ejpam-6314	279	6	j	j	NOUN
ejpam-6314	279	7	=	=	NOUN
ejpam-6314	279	8	n+1	n+1	PROPN
ejpam-6314	279	9	ϑ(κj	ϑ(κj	PROPN
ejpam-6314	279	10	,	,	PUNCT
ejpam-6314	279	11	κm	κm	NOUN
ejpam-6314	279	12	)	)	PUNCT
ejpam-6314	279	13			NOUN
ejpam-6314	279	14	×	×	PROPN
ejpam-6314	279	15	ϑ(κi	ϑ(κi	NOUN
ejpam-6314	279	16	,	,	PUNCT
ejpam-6314	279	17	κi+1)ω	κi+1)ω	NOUN
ejpam-6314	279	18	idb(κ0,κ1	idb(κ0,κ1	ADJ
ejpam-6314	279	19	)	)	PUNCT
ejpam-6314	280	1	+	+	CCONJ
ejpam-6314	281	1	[	[	PUNCT
ejpam-6314	281	2	m−1∏	m−1∏	PROPN
ejpam-6314	281	3	i	i	NOUN
ejpam-6314	281	4	=	=	NOUN
ejpam-6314	281	5	n+1	n+1	X
ejpam-6314	281	6	ϑ(κj	ϑ(κj	PROPN
ejpam-6314	281	7	,	,	PUNCT
ejpam-6314	281	8	κm	κm	PROPN
ejpam-6314	281	9	)	)	PUNCT
ejpam-6314	281	10	]	]	PUNCT
ejpam-6314	281	11	m.	m.	NOUN
ejpam-6314	281	12	sarwar	sarwar	PROPN
ejpam-6314	281	13	et	et	PROPN
ejpam-6314	281	14	al	al	PROPN
ejpam-6314	281	15	.	.	PUNCT
ejpam-6314	281	16	/	/	SYM
ejpam-6314	281	17	eur	eur	PROPN
ejpam-6314	281	18	.	.	PUNCT
ejpam-6314	282	1	j.	j.	PROPN
ejpam-6314	282	2	pure	pure	PROPN
ejpam-6314	282	3	appl	appl	PROPN
ejpam-6314	282	4	.	.	PROPN
ejpam-6314	282	5	math	math	PROPN
ejpam-6314	282	6	,	,	PUNCT
ejpam-6314	282	7	18	18	NUM
ejpam-6314	282	8	(	(	PUNCT
ejpam-6314	282	9	3	3	NUM
ejpam-6314	282	10	)	)	PUNCT
ejpam-6314	282	11	(	(	PUNCT
ejpam-6314	282	12	2025	2025	NUM
ejpam-6314	282	13	)	)	PUNCT
ejpam-6314	282	14	,	,	PUNCT
ejpam-6314	282	15	6314	6314	NUM
ejpam-6314	282	16	14	14	NUM
ejpam-6314	282	17	of	of	ADP
ejpam-6314	282	18	28	28	NUM
ejpam-6314	282	19	×	×	NOUN
ejpam-6314	282	20	ϑ(κm−1,κm)ωm−1db(κ0,κ1	ϑ(κm−1,κm)ωm−1db(κ0,κ1	NOUN
ejpam-6314	282	21	)	)	PUNCT
ejpam-6314	282	22	=	=	SYM
ejpam-6314	282	23	ϑ(κn	ϑ(κn	PROPN
ejpam-6314	282	24	,	,	PUNCT
ejpam-6314	282	25	κn+1)ω	κn+1)ω	X
ejpam-6314	282	26	ndb(κ0,κ1	ndb(κ0,κ1	ADJ
ejpam-6314	282	27	)	)	PUNCT
ejpam-6314	282	28	+	+	CCONJ
ejpam-6314	282	29	m−1∑	m−1∑	NUM
ejpam-6314	282	30	i	i	NOUN
ejpam-6314	282	31	=	=	NOUN
ejpam-6314	282	32	n+1	n+1	PROPN
ejpam-6314	282	33			PROPN
ejpam-6314	282	34	i∏	i∏	PROPN
ejpam-6314	282	35	j	j	NOUN
ejpam-6314	282	36	=	=	NOUN
ejpam-6314	282	37	n+1	n+1	PROPN
ejpam-6314	282	38	ϑ(κj	ϑ(κj	PROPN
ejpam-6314	282	39	,	,	PUNCT
ejpam-6314	282	40	κm	κm	NOUN
ejpam-6314	282	41	)	)	PUNCT
ejpam-6314	282	42			NOUN
ejpam-6314	282	43	×	×	PROPN
ejpam-6314	282	44	ϑ(κi	ϑ(κi	NOUN
ejpam-6314	282	45	,	,	PUNCT
ejpam-6314	282	46	κi+1)ω	κi+1)ω	NOUN
ejpam-6314	282	47	idb(κ0,κ1	idb(κ0,κ1	ADJ
ejpam-6314	282	48	)	)	PUNCT
ejpam-6314	282	49	(	(	PUNCT
ejpam-6314	282	50	18	18	NUM
ejpam-6314	282	51	)	)	PUNCT
ejpam-6314	282	52	let	let	VERB
ejpam-6314	282	53	υℓ	υℓ	PRON
ejpam-6314	282	54	=	=	NOUN
ejpam-6314	282	55	ℓ∑	ℓ∑	INTJ
ejpam-6314	282	56	i=0	i=0	PROPN
ejpam-6314	282	57	[	[	PUNCT
ejpam-6314	282	58	i∏	i∏	VERB
ejpam-6314	282	59	j=0	j=0	VERB
ejpam-6314	282	60	ϑ(κj	ϑ(κj	PROPN
ejpam-6314	282	61	,	,	PUNCT
ejpam-6314	282	62	κm	κm	PROPN
ejpam-6314	282	63	)	)	PUNCT
ejpam-6314	282	64	]	]	PUNCT
ejpam-6314	283	1	ϑ(κi	ϑ(κi	NOUN
ejpam-6314	283	2	,	,	PUNCT
ejpam-6314	283	3	κi+1)ω	κi+1)ω	NOUN
ejpam-6314	283	4	idb(κ0,κ1	idb(κ0,κ1	ADJ
ejpam-6314	283	5	)	)	PUNCT
ejpam-6314	283	6	.	.	PUNCT
ejpam-6314	284	1	(	(	PUNCT
ejpam-6314	284	2	19	19	NUM
ejpam-6314	284	3	)	)	PUNCT
ejpam-6314	284	4	consider	consider	VERB
ejpam-6314	284	5	λi	λi	NOUN
ejpam-6314	284	6	=	=	PUNCT
ejpam-6314	284	7	[	[	PUNCT
ejpam-6314	284	8	i∏	i∏	AUX
ejpam-6314	284	9	j=0	j=0	VERB
ejpam-6314	284	10	ϑ(κj	ϑ(κj	PROPN
ejpam-6314	284	11	,	,	PUNCT
ejpam-6314	284	12	κm	κm	PROPN
ejpam-6314	284	13	)	)	PUNCT
ejpam-6314	284	14	]	]	PUNCT
ejpam-6314	285	1	ϑ(κi	ϑ(κi	NOUN
ejpam-6314	285	2	,	,	PUNCT
ejpam-6314	285	3	κi+1)ω	κi+1)ω	NOUN
ejpam-6314	285	4	idb(κ0,κ1	idb(κ0,κ1	ADJ
ejpam-6314	285	5	)	)	PUNCT
ejpam-6314	285	6	,	,	PUNCT
ejpam-6314	285	7	(	(	PUNCT
ejpam-6314	285	8	20	20	X
ejpam-6314	285	9	)	)	PUNCT
ejpam-6314	285	10	we	we	PRON
ejpam-6314	285	11	have	have	VERB
ejpam-6314	285	12	λi+1	λi+1	NOUN
ejpam-6314	285	13	λi	λi	NOUN
ejpam-6314	285	14	=	=	PUNCT
ejpam-6314	285	15	ϑ(κi+1,κm	ϑ(κi+1,κm	NOUN
ejpam-6314	285	16	)	)	PUNCT
ejpam-6314	285	17	ϑ(κi+1,κi+2	ϑ(κi+1,κi+2	NOUN
ejpam-6314	285	18	)	)	PUNCT
ejpam-6314	285	19	ϑ(κi	ϑ(κi	NOUN
ejpam-6314	285	20	,	,	PUNCT
ejpam-6314	285	21	κi+1	κi+1	NOUN
ejpam-6314	285	22	)	)	PUNCT
ejpam-6314	285	23	ω	ω	NOUN
ejpam-6314	285	24	.	.	PUNCT
ejpam-6314	286	1	(	(	PUNCT
ejpam-6314	286	2	21	21	NUM
ejpam-6314	286	3	)	)	PUNCT
ejpam-6314	286	4	we	we	PRON
ejpam-6314	286	5	make	make	VERB
ejpam-6314	286	6	sure	sure	ADJ
ejpam-6314	286	7	that	that	SCONJ
ejpam-6314	286	8	the	the	DET
ejpam-6314	286	9	series	series	NOUN
ejpam-6314	286	10	∑	∑	PROPN
ejpam-6314	286	11	i	i	PRON
ejpam-6314	286	12	λi	λi	VERB
ejpam-6314	286	13	converges	converge	NOUN
ejpam-6314	286	14	in	in	ADP
ejpam-6314	286	15	the	the	DET
ejpam-6314	286	16	context	context	NOUN
ejpam-6314	286	17	of	of	ADP
ejpam-6314	286	18	the	the	DET
ejpam-6314	286	19	condition	condition	NOUN
ejpam-6314	286	20	(	(	PUNCT
ejpam-6314	286	21	15	15	NUM
ejpam-6314	286	22	)	)	PUNCT
ejpam-6314	286	23	and	and	CCONJ
ejpam-6314	286	24	ratio	ratio	NOUN
ejpam-6314	286	25	test	test	NOUN
ejpam-6314	286	26	.	.	PUNCT
ejpam-6314	287	1	therefore	therefore	ADV
ejpam-6314	287	2	,	,	PUNCT
ejpam-6314	287	3	there	there	PRON
ejpam-6314	287	4	is	be	VERB
ejpam-6314	287	5	limn→+∞υℓ.	limn→+∞υℓ.	PROPN
ejpam-6314	287	6	thus	thus	ADV
ejpam-6314	287	7	the	the	DET
ejpam-6314	287	8	sequence	sequence	NOUN
ejpam-6314	287	9	υℓ	υℓ	PROPN
ejpam-6314	287	10	is	be	AUX
ejpam-6314	287	11	cauchy	cauchy	ADJ
ejpam-6314	287	12	as	as	ADP
ejpam-6314	287	13	a	a	DET
ejpam-6314	287	14	result	result	NOUN
ejpam-6314	287	15	.	.	PUNCT
ejpam-6314	288	1	now	now	ADV
ejpam-6314	288	2	,	,	PUNCT
ejpam-6314	288	3	using	use	VERB
ejpam-6314	288	4	(	(	PUNCT
ejpam-6314	288	5	18	18	NUM
ejpam-6314	288	6	)	)	PUNCT
ejpam-6314	288	7	,	,	PUNCT
ejpam-6314	288	8	we	we	PRON
ejpam-6314	288	9	get	get	VERB
ejpam-6314	288	10	db(κn	db(κn	NOUN
ejpam-6314	288	11	,	,	PUNCT
ejpam-6314	288	12	κm	κm	NOUN
ejpam-6314	288	13	)	)	PUNCT
ejpam-6314	288	14	≾	≾	PROPN
ejpam-6314	288	15	db(κ0,κ1)[ω	db(κ0,κ1)[ω	NOUN
ejpam-6314	288	16	nϑ(κi	nϑ(κi	PROPN
ejpam-6314	288	17	,	,	PUNCT
ejpam-6314	288	18	κi+1	κi+1	X
ejpam-6314	288	19	)	)	PUNCT
ejpam-6314	289	1	+	+	CCONJ
ejpam-6314	289	2	(	(	PUNCT
ejpam-6314	289	3	υm−1	υm−1	PROPN
ejpam-6314	289	4	−υn	−υn	PROPN
ejpam-6314	289	5	)	)	PUNCT
ejpam-6314	289	6	]	]	PUNCT
ejpam-6314	289	7	.	.	PUNCT
ejpam-6314	290	1	(	(	PUNCT
ejpam-6314	290	2	22	22	NUM
ejpam-6314	290	3	)	)	PUNCT
ejpam-6314	290	4	above	above	ADV
ejpam-6314	290	5	,	,	PUNCT
ejpam-6314	290	6	we	we	PRON
ejpam-6314	290	7	used	use	VERB
ejpam-6314	290	8	ϑ(κ	ϑ(κ	PROPN
ejpam-6314	290	9	,	,	PUNCT
ejpam-6314	290	10	σ	σ	PROPN
ejpam-6314	290	11	)	)	PUNCT
ejpam-6314	290	12	≥	≥	NOUN
ejpam-6314	290	13	1	1	NUM
ejpam-6314	290	14	.	.	PUNCT
ejpam-6314	290	15	letting	let	VERB
ejpam-6314	290	16	n	n	CCONJ
ejpam-6314	290	17	,	,	PUNCT
ejpam-6314	290	18	m→	m→	PUNCT
ejpam-6314	291	1	+	+	NOUN
ejpam-6314	291	2	∞	∞	NUM
ejpam-6314	291	3	in	in	ADP
ejpam-6314	291	4	(	(	PUNCT
ejpam-6314	291	5	22	22	NUM
ejpam-6314	291	6	)	)	PUNCT
ejpam-6314	291	7	we	we	PRON
ejpam-6314	291	8	obtain	obtain	VERB
ejpam-6314	291	9	lim	lim	PROPN
ejpam-6314	291	10	n	n	CCONJ
ejpam-6314	291	11	,	,	PUNCT
ejpam-6314	291	12	m→+∞	m→+∞	PROPN
ejpam-6314	291	13	db(κn	db(κn	NOUN
ejpam-6314	291	14	,	,	PUNCT
ejpam-6314	291	15	κm	κm	PROPN
ejpam-6314	291	16	)	)	PUNCT
ejpam-6314	291	17	=	=	SYM
ejpam-6314	292	1	0	0	X
ejpam-6314	292	2	.	.	PUNCT
ejpam-6314	293	1	(	(	PUNCT
ejpam-6314	293	2	23	23	NUM
ejpam-6314	293	3	)	)	PUNCT
ejpam-6314	293	4	thus	thus	ADV
ejpam-6314	293	5	,	,	PUNCT
ejpam-6314	293	6	the	the	DET
ejpam-6314	293	7	sequence	sequence	NOUN
ejpam-6314	293	8	{	{	PUNCT
ejpam-6314	293	9	κn	κn	NOUN
ejpam-6314	293	10	}	}	PUNCT
ejpam-6314	293	11	is	be	AUX
ejpam-6314	293	12	a	a	DET
ejpam-6314	293	13	cauchy	cauchy	NOUN
ejpam-6314	293	14	in	in	ADP
ejpam-6314	293	15	(	(	PUNCT
ejpam-6314	293	16	bcvms	bcvms	NOUN
ejpam-6314	293	17	)	)	PUNCT
ejpam-6314	293	18	(	(	PUNCT
ejpam-6314	293	19	s	s	X
ejpam-6314	293	20	,	,	PUNCT
ejpam-6314	293	21	db	db	PROPN
ejpam-6314	293	22	,	,	PUNCT
ejpam-6314	293	23	ϑ	ϑ	NOUN
ejpam-6314	293	24	)	)	PUNCT
ejpam-6314	293	25	.	.	PUNCT
ejpam-6314	294	1	thus	thus	ADV
ejpam-6314	294	2	for	for	SCONJ
ejpam-6314	294	3	all	all	DET
ejpam-6314	294	4	κ⋆	κ⋆	ADJ
ejpam-6314	294	5	∈	∈	PROPN
ejpam-6314	294	6	s	s	VERB
ejpam-6314	294	7	such	such	ADJ
ejpam-6314	294	8	that	that	SCONJ
ejpam-6314	294	9	lim	lim	PROPN
ejpam-6314	294	10	n→+∞	n→+∞	PROPN
ejpam-6314	294	11	db(κn	db(κn	PROPN
ejpam-6314	294	12	,	,	PUNCT
ejpam-6314	294	13	κ⋆	κ⋆	ADJ
ejpam-6314	294	14	)	)	PUNCT
ejpam-6314	294	15	=	=	SYM
ejpam-6314	294	16	0	0	NUM
ejpam-6314	294	17	,	,	PUNCT
ejpam-6314	294	18	(	(	PUNCT
ejpam-6314	294	19	24	24	NUM
ejpam-6314	294	20	)	)	PUNCT
ejpam-6314	294	21	that	that	PRON
ejpam-6314	294	22	is	be	AUX
ejpam-6314	294	23	κn	κn	NOUN
ejpam-6314	294	24	→	→	SYM
ejpam-6314	294	25	κ⋆	κ⋆	X
ejpam-6314	294	26	as	as	ADP
ejpam-6314	294	27	n→	n→	ADV
ejpam-6314	294	28	+	+	PROPN
ejpam-6314	294	29	∞.	∞.	PROPN
ejpam-6314	294	30	now	now	ADV
ejpam-6314	294	31	,	,	PUNCT
ejpam-6314	294	32	we	we	PRON
ejpam-6314	294	33	’ll	’ll	AUX
ejpam-6314	294	34	show	show	VERB
ejpam-6314	294	35	that	that	SCONJ
ejpam-6314	294	36	κ⋆	κ⋆	ADJ
ejpam-6314	294	37	is	be	AUX
ejpam-6314	294	38	a	a	DET
ejpam-6314	294	39	fixed	fix	VERB
ejpam-6314	294	40	point	point	NOUN
ejpam-6314	294	41	of	of	ADP
ejpam-6314	294	42	s.	s.	PROPN
ejpam-6314	294	43	by	by	ADP
ejpam-6314	294	44	using	use	VERB
ejpam-6314	294	45	(	(	PUNCT
ejpam-6314	294	46	14	14	NUM
ejpam-6314	294	47	)	)	PUNCT
ejpam-6314	294	48	and	and	CCONJ
ejpam-6314	294	49	condition	condition	NOUN
ejpam-6314	294	50	(	(	PUNCT
ejpam-6314	294	51	iii	iii	NOUN
ejpam-6314	294	52	)	)	PUNCT
ejpam-6314	294	53	,	,	PUNCT
ejpam-6314	294	54	we	we	PRON
ejpam-6314	294	55	get	get	VERB
ejpam-6314	294	56	db(κ⋆,φκ⋆	db(κ⋆,φκ⋆	NOUN
ejpam-6314	294	57	)	)	PUNCT
ejpam-6314	294	58	≾	≾	PROPN
ejpam-6314	294	59	ϑ(κ⋆,κ2n+2)db(κ⋆,κ2n+2	ϑ(κ⋆,κ2n+2)db(κ⋆,κ2n+2	PROPN
ejpam-6314	294	60	)	)	PUNCT
ejpam-6314	295	1	+	+	SYM
ejpam-6314	295	2	ϑ(κ2n+2,φκ⋆)db(κ2n+2,φκ⋆	ϑ(κ2n+2,φκ⋆)db(κ2n+2,φκ⋆	NOUN
ejpam-6314	295	3	)	)	PUNCT
ejpam-6314	295	4	=	=	PUNCT
ejpam-6314	295	5	ϑ(κ⋆,κ2n+2)db(κ⋆,κ2n+2	ϑ(κ⋆,κ2n+2)db(κ⋆,κ2n+2	NOUN
ejpam-6314	295	6	)	)	PUNCT
ejpam-6314	296	1	+	+	CCONJ
ejpam-6314	296	2	ϑ(κ2n+2,φκ⋆)db(ψκ2n+1,φκ⋆	ϑ(κ2n+2,φκ⋆)db(ψκ2n+1,φκ⋆	NOUN
ejpam-6314	296	3	)	)	PUNCT
ejpam-6314	296	4	=	=	PUNCT
ejpam-6314	296	5	ϑ(κ⋆,κ2n+2)db(κ⋆,κ2n+2	ϑ(κ⋆,κ2n+2)db(κ⋆,κ2n+2	PROPN
ejpam-6314	296	6	)	)	PUNCT
ejpam-6314	297	1	+	+	NUM
ejpam-6314	297	2	ϑ(κ2n+2,φκ⋆)db(φκ⋆	ϑ(κ2n+2,φκ⋆)db(φκ⋆	NOUN
ejpam-6314	297	3	,	,	PUNCT
ejpam-6314	297	4	ψκ2n+1	ψκ2n+1	NOUN
ejpam-6314	297	5	)	)	PUNCT
ejpam-6314	297	6	=	=	SYM
ejpam-6314	297	7	ϑ(κ⋆,κ2n+2)db(κ⋆,κ2n+2	ϑ(κ⋆,κ2n+2)db(κ⋆,κ2n+2	PROPN
ejpam-6314	297	8	)	)	PUNCT
ejpam-6314	298	1	+	+	NUM
ejpam-6314	298	2	ϑ(κ2n+2,φκ⋆	ϑ(κ2n+2,φκ⋆	NOUN
ejpam-6314	298	3	)	)	PUNCT
ejpam-6314	298	4	[	[	PUNCT
ejpam-6314	298	5	µ(κ⋆)db(κ⋆,κ2n+1	µ(κ⋆)db(κ⋆,κ2n+1	X
ejpam-6314	298	6	)	)	PUNCT
ejpam-6314	298	7	+	+	CCONJ
ejpam-6314	298	8	ν(κ⋆	ν(κ⋆	NOUN
ejpam-6314	298	9	)	)	PUNCT
ejpam-6314	298	10	db(κ⋆,φκ⋆)db(κ2n+1,κ2n+2	db(κ⋆,φκ⋆)db(κ2n+1,κ2n+2	NUM
ejpam-6314	298	11	)	)	PUNCT
ejpam-6314	298	12	1	1	NUM
ejpam-6314	299	1	+	+	NUM
ejpam-6314	299	2	db(κ⋆,κ2n+2	db(κ⋆,κ2n+2	NOUN
ejpam-6314	299	3	)	)	PUNCT
ejpam-6314	299	4	]	]	PUNCT
ejpam-6314	299	5	(	(	PUNCT
ejpam-6314	299	6	25	25	X
ejpam-6314	299	7	)	)	PUNCT
ejpam-6314	299	8	letting	let	VERB
ejpam-6314	299	9	n	n	X
ejpam-6314	299	10	→	→	SYM
ejpam-6314	299	11	+	+	NOUN
ejpam-6314	299	12	∞	∞	NUM
ejpam-6314	299	13	and	and	CCONJ
ejpam-6314	299	14	by	by	ADP
ejpam-6314	299	15	using	use	VERB
ejpam-6314	299	16	(	(	PUNCT
ejpam-6314	299	17	24	24	NUM
ejpam-6314	299	18	)	)	PUNCT
ejpam-6314	299	19	,	,	PUNCT
ejpam-6314	299	20	there	there	PRON
ejpam-6314	299	21	arise	arise	VERB
ejpam-6314	299	22	contradiction	contradiction	NOUN
ejpam-6314	299	23	to	to	ADP
ejpam-6314	299	24	db(κ⋆,φκ⋆	db(κ⋆,φκ⋆	NOUN
ejpam-6314	299	25	)	)	PUNCT
ejpam-6314	300	1	≺i2	≺i2	DET
ejpam-6314	300	2	0	0	NUM
ejpam-6314	300	3	.	.	PUNCT
ejpam-6314	301	1	thus	thus	ADV
ejpam-6314	301	2	,	,	PUNCT
ejpam-6314	301	3	db(κ⋆,φκ⋆	db(κ⋆,φκ⋆	NOUN
ejpam-6314	301	4	)	)	PUNCT
ejpam-6314	301	5	=	=	SYM
ejpam-6314	302	1	0	0	X
ejpam-6314	302	2	.	.	PUNCT
ejpam-6314	303	1	this	this	PRON
ejpam-6314	303	2	implies	imply	VERB
ejpam-6314	303	3	that	that	SCONJ
ejpam-6314	303	4	κ⋆	κ⋆	ADV
ejpam-6314	303	5	=	=	X
ejpam-6314	303	6	φκ⋆.	φκ⋆.	ADV
ejpam-6314	303	7	similarly	similarly	ADV
ejpam-6314	303	8	one	one	PRON
ejpam-6314	303	9	can	can	AUX
ejpam-6314	303	10	show	show	VERB
ejpam-6314	303	11	that	that	SCONJ
ejpam-6314	303	12	κ⋆	κ⋆	NOUN
ejpam-6314	303	13	=	=	PUNCT
ejpam-6314	303	14	m.	m.	NOUN
ejpam-6314	303	15	sarwar	sarwar	PROPN
ejpam-6314	303	16	et	et	PROPN
ejpam-6314	304	1	al	al	PROPN
ejpam-6314	304	2	.	.	PUNCT
ejpam-6314	304	3	/	/	SYM
ejpam-6314	304	4	eur	eur	PROPN
ejpam-6314	304	5	.	.	PUNCT
ejpam-6314	305	1	j.	j.	PROPN
ejpam-6314	305	2	pure	pure	PROPN
ejpam-6314	305	3	appl	appl	PROPN
ejpam-6314	305	4	.	.	PROPN
ejpam-6314	305	5	math	math	PROPN
ejpam-6314	305	6	,	,	PUNCT
ejpam-6314	305	7	18	18	NUM
ejpam-6314	305	8	(	(	PUNCT
ejpam-6314	305	9	3	3	NUM
ejpam-6314	305	10	)	)	PUNCT
ejpam-6314	305	11	(	(	PUNCT
ejpam-6314	305	12	2025	2025	NUM
ejpam-6314	305	13	)	)	PUNCT
ejpam-6314	305	14	,	,	PUNCT
ejpam-6314	305	15	6314	6314	NUM
ejpam-6314	305	16	15	15	NUM
ejpam-6314	305	17	of	of	ADP
ejpam-6314	305	18	28	28	NUM
ejpam-6314	305	19	ψκ⋆.	ψκ⋆.	NOUN
ejpam-6314	305	20	therefore	therefore	ADV
ejpam-6314	305	21	,	,	PUNCT
ejpam-6314	305	22	κ⋆	κ⋆	X
ejpam-6314	305	23	is	be	AUX
ejpam-6314	305	24	common	common	ADJ
ejpam-6314	305	25	fixed	fix	VERB
ejpam-6314	305	26	point	point	NOUN
ejpam-6314	305	27	of	of	ADP
ejpam-6314	305	28	φ	φ	PROPN
ejpam-6314	305	29	and	and	CCONJ
ejpam-6314	305	30	ψ	ψ	PROPN
ejpam-6314	305	31	.	.	PUNCT
ejpam-6314	305	32	uniqueness	uniqueness	NOUN
ejpam-6314	305	33	:	:	PUNCT
ejpam-6314	305	34	now	now	ADV
ejpam-6314	305	35	we	we	PRON
ejpam-6314	305	36	have	have	VERB
ejpam-6314	305	37	to	to	PART
ejpam-6314	305	38	show	show	VERB
ejpam-6314	305	39	that	that	SCONJ
ejpam-6314	305	40	κ⋆	κ⋆	ADJ
ejpam-6314	305	41	is	be	AUX
ejpam-6314	305	42	a	a	DET
ejpam-6314	305	43	unique	unique	ADJ
ejpam-6314	305	44	fixed	fix	VERB
ejpam-6314	305	45	point	point	NOUN
ejpam-6314	305	46	of	of	ADP
ejpam-6314	305	47	ψ	ψ	PROPN
ejpam-6314	305	48	and	and	CCONJ
ejpam-6314	305	49	φ	φ	PROPN
ejpam-6314	305	50	.	.	PROPN
ejpam-6314	306	1	assume	assume	VERB
ejpam-6314	306	2	that	that	SCONJ
ejpam-6314	306	3	there	there	PRON
ejpam-6314	306	4	exists	exist	VERB
ejpam-6314	306	5	another	another	DET
ejpam-6314	306	6	common	common	ADJ
ejpam-6314	306	7	fixed	fix	VERB
ejpam-6314	306	8	point	point	NOUN
ejpam-6314	306	9	κ•	κ•	ADJ
ejpam-6314	306	10	that	that	PRON
ejpam-6314	306	11	is	be	AUX
ejpam-6314	306	12	κ•	κ•	ADJ
ejpam-6314	306	13	=	=	PUNCT
ejpam-6314	306	14	ψκ•	ψκ•	PROPN
ejpam-6314	306	15	=	=	PUNCT
ejpam-6314	307	1	φκ•.	φκ•.	NOUN
ejpam-6314	307	2	it	it	PRON
ejpam-6314	307	3	follows	follow	VERB
ejpam-6314	307	4	that	that	SCONJ
ejpam-6314	307	5	:	:	PUNCT
ejpam-6314	307	6	db(κ⋆,κ•	db(κ⋆,κ•	X
ejpam-6314	307	7	)	)	PUNCT
ejpam-6314	307	8	=	=	SYM
ejpam-6314	307	9	db(φκ⋆,ψκ•	db(φκ⋆,ψκ•	ADJ
ejpam-6314	307	10	)	)	PUNCT
ejpam-6314	307	11	≾	≾	NOUN
ejpam-6314	307	12	µ(κ⋆)db(κ⋆,κ•	µ(κ⋆)db(κ⋆,κ•	NOUN
ejpam-6314	307	13	)	)	PUNCT
ejpam-6314	307	14	+	+	NUM
ejpam-6314	307	15	ν(κ⋆	ν(κ⋆	NOUN
ejpam-6314	307	16	)	)	PUNCT
ejpam-6314	307	17	db(κ⋆,φκ⋆)db(κ•,ψκ•	db(κ⋆,φκ⋆)db(κ•,ψκ•	PROPN
ejpam-6314	307	18	)	)	PUNCT
ejpam-6314	307	19	1	1	NUM
ejpam-6314	307	20	+	+	NUM
ejpam-6314	307	21	db(κ⋆,κ•	db(κ⋆,κ•	NOUN
ejpam-6314	307	22	)	)	PUNCT
ejpam-6314	307	23	db(κ⋆,κ•	db(κ⋆,κ•	NOUN
ejpam-6314	307	24	)	)	PUNCT
ejpam-6314	308	1	≾	≾	NOUN
ejpam-6314	308	2	µ(κ⋆)db(κ⋆,κ•	µ(κ⋆)db(κ⋆,κ•	NOUN
ejpam-6314	308	3	)	)	PUNCT
ejpam-6314	308	4	.	.	PUNCT
ejpam-6314	309	1	since	since	SCONJ
ejpam-6314	309	2	µ	µ	NOUN
ejpam-6314	309	3	∈	∈	NOUN
ejpam-6314	309	4	[	[	X
ejpam-6314	309	5	0	0	NUM
ejpam-6314	309	6	,	,	PUNCT
ejpam-6314	309	7	1	1	NUM
ejpam-6314	309	8	)	)	PUNCT
ejpam-6314	309	9	,	,	PUNCT
ejpam-6314	309	10	so	so	ADV
ejpam-6314	309	11	we	we	PRON
ejpam-6314	309	12	have	have	VERB
ejpam-6314	309	13	db(κ⋆,κ•	db(κ⋆,κ•	NOUN
ejpam-6314	309	14	)	)	PUNCT
ejpam-6314	309	15	.	.	PUNCT
ejpam-6314	310	1	therefore	therefore	ADV
ejpam-6314	310	2	,	,	PUNCT
ejpam-6314	310	3	we	we	PRON
ejpam-6314	310	4	have	have	VERB
ejpam-6314	310	5	κ⋆	κ⋆	ADJ
ejpam-6314	310	6	=	=	SYM
ejpam-6314	310	7	κ•	κ•	PROPN
ejpam-6314	310	8	and	and	CCONJ
ejpam-6314	310	9	thus	thus	ADV
ejpam-6314	310	10	κ⋆	κ⋆	X
ejpam-6314	310	11	is	be	AUX
ejpam-6314	310	12	a	a	DET
ejpam-6314	310	13	unique	unique	ADJ
ejpam-6314	310	14	common	common	ADJ
ejpam-6314	310	15	fixed	fix	VERB
ejpam-6314	310	16	point	point	NOUN
ejpam-6314	310	17	ofφ	ofφ	NUM
ejpam-6314	310	18	and	and	CCONJ
ejpam-6314	310	19	ψ	ψ	NOUN
ejpam-6314	310	20	.	.	NOUN
ejpam-6314	311	1	corollary	corollary	ADJ
ejpam-6314	311	2	1	1	NUM
ejpam-6314	311	3	.	.	PUNCT
ejpam-6314	312	1	let	let	VERB
ejpam-6314	312	2	(	(	PUNCT
ejpam-6314	312	3	s	s	X
ejpam-6314	312	4	,	,	PUNCT
ejpam-6314	312	5	ϑ	ϑ	X
ejpam-6314	312	6	,	,	PUNCT
ejpam-6314	312	7	db	db	PRON
ejpam-6314	312	8	)	)	PUNCT
ejpam-6314	312	9	be	be	AUX
ejpam-6314	312	10	a	a	DET
ejpam-6314	312	11	complete	complete	ADJ
ejpam-6314	312	12	controlled	control	VERB
ejpam-6314	312	13	metric	metric	ADJ
ejpam-6314	312	14	space	space	NOUN
ejpam-6314	312	15	and	and	CCONJ
ejpam-6314	312	16	φ	φ	NOUN
ejpam-6314	312	17	,	,	PUNCT
ejpam-6314	312	18	ψ	ψ	X
ejpam-6314	312	19	:	:	PUNCT
ejpam-6314	312	20	s	s	X
ejpam-6314	312	21	→	→	PUNCT
ejpam-6314	312	22	s.	s.	PROPN
ejpam-6314	312	23	if	if	SCONJ
ejpam-6314	312	24	there	there	PRON
ejpam-6314	312	25	exist	exist	VERB
ejpam-6314	312	26	µ	µ	NOUN
ejpam-6314	312	27	,	,	PUNCT
ejpam-6314	312	28	ν	ν	X
ejpam-6314	312	29	:	:	PUNCT
ejpam-6314	312	30	s	s	X
ejpam-6314	312	31	→	→	SYM
ejpam-6314	312	32	[	[	X
ejpam-6314	312	33	0	0	NUM
ejpam-6314	312	34	,	,	PUNCT
ejpam-6314	312	35	1	1	NUM
ejpam-6314	312	36	)	)	PUNCT
ejpam-6314	312	37	such	such	ADJ
ejpam-6314	312	38	that	that	SCONJ
ejpam-6314	312	39	:	:	PUNCT
ejpam-6314	312	40	db(φκ	db(φκ	NOUN
ejpam-6314	312	41	,	,	PUNCT
ejpam-6314	312	42	ψν	ψν	NOUN
ejpam-6314	312	43	)	)	PUNCT
ejpam-6314	312	44	≾	≾	PROPN
ejpam-6314	312	45	µdb(κ	µdb(κ	PROPN
ejpam-6314	312	46	,	,	PUNCT
ejpam-6314	312	47	σ	σ	PROPN
ejpam-6314	312	48	)	)	PUNCT
ejpam-6314	312	49	+	+	NUM
ejpam-6314	312	50	ν	ν	NOUN
ejpam-6314	312	51	db(κ	db(κ	NUM
ejpam-6314	312	52	,	,	PUNCT
ejpam-6314	312	53	φκ)db(σ	φκ)db(σ	NOUN
ejpam-6314	312	54	,	,	PUNCT
ejpam-6314	312	55	ψσ	ψσ	ADJ
ejpam-6314	312	56	)	)	PUNCT
ejpam-6314	312	57	1	1	NUM
ejpam-6314	312	58	+	+	CCONJ
ejpam-6314	312	59	db(κ	db(κ	NUM
ejpam-6314	312	60	,	,	PUNCT
ejpam-6314	312	61	σ	σ	NOUN
ejpam-6314	312	62	)	)	PUNCT
ejpam-6314	312	63	for	for	ADP
ejpam-6314	312	64	all	all	DET
ejpam-6314	312	65	κ	κ	PROPN
ejpam-6314	312	66	,	,	PUNCT
ejpam-6314	312	67	σ	σ	PROPN
ejpam-6314	312	68	∈	∈	PROPN
ejpam-6314	312	69	s.	s.	PROPN
ejpam-6314	312	70	for	for	ADP
ejpam-6314	312	71	κ0	κ0	PRON
ejpam-6314	312	72	∈	∈	PROPN
ejpam-6314	312	73	s	s	PART
ejpam-6314	312	74	,	,	PUNCT
ejpam-6314	312	75	we	we	PRON
ejpam-6314	312	76	set	set	VERB
ejpam-6314	312	77	µ(κ	µ(κ	PROPN
ejpam-6314	312	78	)	)	PUNCT
ejpam-6314	312	79	1−ν(κ	1−ν(κ	NUM
ejpam-6314	312	80	)	)	PUNCT
ejpam-6314	312	81	=	=	SYM
ejpam-6314	312	82	ω	ω	X
ejpam-6314	312	83	.	.	PROPN
ejpam-6314	312	84	suppose	suppose	VERB
ejpam-6314	312	85	that	that	SCONJ
ejpam-6314	312	86	,	,	PUNCT
ejpam-6314	312	87	sup	sup	NOUN
ejpam-6314	312	88	m≥1	m≥1	PROPN
ejpam-6314	312	89	lim	lim	PROPN
ejpam-6314	312	90	i→+∞	i→+∞	PROPN
ejpam-6314	312	91	ϑ(κi+1,κi+2)ϑ(κi+1,κm	ϑ(κi+1,κi+2)ϑ(κi+1,κm	PUNCT
ejpam-6314	312	92	)	)	PUNCT
ejpam-6314	312	93	ϑ(κi	ϑ(κi	NOUN
ejpam-6314	312	94	,	,	PUNCT
ejpam-6314	312	95	κi+1	κi+1	X
ejpam-6314	312	96	)	)	PUNCT
ejpam-6314	312	97	<	<	X
ejpam-6314	313	1	1	1	NUM
ejpam-6314	313	2	ω	ω	NUM
ejpam-6314	313	3	where	where	SCONJ
ejpam-6314	313	4	κ2n+1	κ2n+1	NOUN
ejpam-6314	313	5	=	=	SYM
ejpam-6314	313	6	φκ2n	φκ2n	PROPN
ejpam-6314	313	7	and	and	CCONJ
ejpam-6314	313	8	κ2n+2	κ2n+2	PRON
ejpam-6314	313	9	=	=	PUNCT
ejpam-6314	313	10	ψκ2n+1	ψκ2n+1	VERB
ejpam-6314	313	11	for	for	ADP
ejpam-6314	313	12	each	each	DET
ejpam-6314	313	13	n	n	PRON
ejpam-6314	313	14	≥	≥	NOUN
ejpam-6314	313	15	0	0	NUM
ejpam-6314	313	16	.	.	PUNCT
ejpam-6314	313	17	assume	assume	VERB
ejpam-6314	313	18	further	far	ADV
ejpam-6314	313	19	,	,	PUNCT
ejpam-6314	313	20	that	that	SCONJ
ejpam-6314	313	21	for	for	ADP
ejpam-6314	313	22	every	every	DET
ejpam-6314	313	23	κ	κ	PROPN
ejpam-6314	313	24	∈	∈	PROPN
ejpam-6314	313	25	s	s	PART
ejpam-6314	313	26	,	,	PUNCT
ejpam-6314	313	27	we	we	PRON
ejpam-6314	313	28	have	have	AUX
ejpam-6314	313	29	limn→+∞	limn→+∞	VERB
ejpam-6314	313	30	ϑ(κn	ϑ(κn	PROPN
ejpam-6314	313	31	,	,	PUNCT
ejpam-6314	313	32	κ	κ	NOUN
ejpam-6314	313	33	)	)	PUNCT
ejpam-6314	313	34	and	and	CCONJ
ejpam-6314	313	35	limn→+∞	limn→+∞	PROPN
ejpam-6314	313	36	ϑ(κ	ϑ(κ	PROPN
ejpam-6314	313	37	,	,	PUNCT
ejpam-6314	313	38	κn	κn	NOUN
ejpam-6314	313	39	)	)	PUNCT
ejpam-6314	313	40	,	,	PUNCT
ejpam-6314	313	41	which	which	PRON
ejpam-6314	313	42	are	be	AUX
ejpam-6314	313	43	finite	finite	ADJ
ejpam-6314	313	44	and	and	CCONJ
ejpam-6314	313	45	exist	exist	VERB
ejpam-6314	313	46	.	.	PUNCT
ejpam-6314	314	1	then	then	ADV
ejpam-6314	314	2	,	,	PUNCT
ejpam-6314	314	3	φ	φ	PROPN
ejpam-6314	314	4	and	and	CCONJ
ejpam-6314	314	5	ψ	ψ	PROPN
ejpam-6314	314	6	have	have	VERB
ejpam-6314	314	7	a	a	DET
ejpam-6314	314	8	ucfp	ucfp	NOUN
ejpam-6314	314	9	.	.	PUNCT
ejpam-6314	315	1	proof	proof	NOUN
ejpam-6314	315	2	.	.	PUNCT
ejpam-6314	316	1	the	the	DET
ejpam-6314	316	2	proof	proof	NOUN
ejpam-6314	316	3	is	be	AUX
ejpam-6314	316	4	trivial	trivial	ADJ
ejpam-6314	316	5	by	by	ADP
ejpam-6314	316	6	setting	set	VERB
ejpam-6314	316	7	µ(κ	µ(κ	NOUN
ejpam-6314	316	8	)	)	PUNCT
ejpam-6314	316	9	=	=	SYM
ejpam-6314	316	10	µ	µ	X
ejpam-6314	316	11	and	and	CCONJ
ejpam-6314	316	12	ν(κ	ν(κ	NOUN
ejpam-6314	316	13	)	)	PUNCT
ejpam-6314	317	1	=	=	PUNCT
ejpam-6314	318	1	ν	ν	NOUN
ejpam-6314	318	2	in	in	ADP
ejpam-6314	318	3	the	the	DET
ejpam-6314	318	4	theorem	theorem	NOUN
ejpam-6314	318	5	(	(	PUNCT
ejpam-6314	318	6	4	4	NUM
ejpam-6314	318	7	)	)	PUNCT
ejpam-6314	318	8	.	.	PUNCT
ejpam-6314	319	1	corollary	corollary	ADJ
ejpam-6314	319	2	2	2	NUM
ejpam-6314	319	3	.	.	PUNCT
ejpam-6314	320	1	let	let	VERB
ejpam-6314	320	2	(	(	PUNCT
ejpam-6314	320	3	s	s	X
ejpam-6314	320	4	,	,	PUNCT
ejpam-6314	320	5	ϑ	ϑ	NOUN
ejpam-6314	320	6	,	,	PUNCT
ejpam-6314	320	7	db)be	db)be	PROPN
ejpam-6314	320	8	a	a	DET
ejpam-6314	320	9	(	(	PUNCT
ejpam-6314	320	10	bcvms	bcvms	NOUN
ejpam-6314	320	11	)	)	PUNCT
ejpam-6314	320	12	which	which	PRON
ejpam-6314	320	13	is	be	AUX
ejpam-6314	320	14	complete	complete	ADJ
ejpam-6314	320	15	and	and	CCONJ
ejpam-6314	320	16	ψ	ψ	X
ejpam-6314	320	17	:	:	PUNCT
ejpam-6314	320	18	s	s	X
ejpam-6314	320	19	→	→	PUNCT
ejpam-6314	320	20	s.	s.	PROPN
ejpam-6314	320	21	if	if	SCONJ
ejpam-6314	320	22	there	there	PRON
ejpam-6314	320	23	exist	exist	VERB
ejpam-6314	320	24	µ	µ	NOUN
ejpam-6314	320	25	,	,	PUNCT
ejpam-6314	320	26	ν	ν	X
ejpam-6314	320	27	:	:	PUNCT
ejpam-6314	320	28	s	s	X
ejpam-6314	320	29	→	→	SYM
ejpam-6314	320	30	[	[	X
ejpam-6314	320	31	0	0	NUM
ejpam-6314	320	32	,	,	PUNCT
ejpam-6314	320	33	1	1	NUM
ejpam-6314	320	34	)	)	PUNCT
ejpam-6314	320	35	such	such	ADJ
ejpam-6314	320	36	that	that	PRON
ejpam-6314	320	37	:	:	PUNCT
ejpam-6314	320	38	(	(	PUNCT
ejpam-6314	320	39	i	i	NOUN
ejpam-6314	320	40	)	)	PUNCT
ejpam-6314	320	41	µ(ψκ	µ(ψκ	NOUN
ejpam-6314	320	42	)	)	PUNCT
ejpam-6314	320	43	≤	≤	NOUN
ejpam-6314	320	44	µ(κ	µ(κ	NOUN
ejpam-6314	320	45	)	)	PUNCT
ejpam-6314	320	46	and	and	CCONJ
ejpam-6314	320	47	ν(ψκ	ν(ψκ	NOUN
ejpam-6314	320	48	)	)	PUNCT
ejpam-6314	320	49	≤	≤	NUM
ejpam-6314	320	50	ν(κ	ν(κ	NOUN
ejpam-6314	320	51	)	)	PUNCT
ejpam-6314	320	52	;	;	PUNCT
ejpam-6314	320	53	(	(	PUNCT
ejpam-6314	320	54	ii	ii	NOUN
ejpam-6314	320	55	)	)	PUNCT
ejpam-6314	320	56	(	(	PUNCT
ejpam-6314	320	57	µ+	µ+	X
ejpam-6314	320	58	ν)(κ	ν)(κ	NOUN
ejpam-6314	320	59	)	)	PUNCT
ejpam-6314	320	60	<	<	X
ejpam-6314	320	61	1	1	NUM
ejpam-6314	320	62	;	;	PUNCT
ejpam-6314	320	63	(	(	PUNCT
ejpam-6314	320	64	iii	iii	NOUN
ejpam-6314	320	65	)	)	PUNCT
ejpam-6314	320	66	db(ψκ	db(ψκ	NOUN
ejpam-6314	320	67	,	,	PUNCT
ejpam-6314	320	68	ψν	ψν	NOUN
ejpam-6314	320	69	)	)	PUNCT
ejpam-6314	320	70	≾	≾	PROPN
ejpam-6314	320	71	µ(κ)db(κ	µ(κ)db(κ	NOUN
ejpam-6314	320	72	,	,	PUNCT
ejpam-6314	320	73	σ	σ	NOUN
ejpam-6314	320	74	)	)	PUNCT
ejpam-6314	320	75	+	+	NUM
ejpam-6314	320	76	ν(κ	ν(κ	NOUN
ejpam-6314	320	77	)	)	PUNCT
ejpam-6314	320	78	db(κ	db(κ	NOUN
ejpam-6314	320	79	,	,	PUNCT
ejpam-6314	320	80	ψκ)db(σ	ψκ)db(σ	NOUN
ejpam-6314	320	81	,	,	PUNCT
ejpam-6314	320	82	ψσ	ψσ	ADJ
ejpam-6314	320	83	)	)	PUNCT
ejpam-6314	320	84	1	1	NUM
ejpam-6314	320	85	+	+	CCONJ
ejpam-6314	320	86	db(κ	db(κ	NUM
ejpam-6314	320	87	,	,	PUNCT
ejpam-6314	320	88	σ	σ	NOUN
ejpam-6314	320	89	)	)	PUNCT
ejpam-6314	320	90	for	for	ADP
ejpam-6314	320	91	all	all	DET
ejpam-6314	320	92	κ	κ	PROPN
ejpam-6314	320	93	,	,	PUNCT
ejpam-6314	320	94	σ	σ	PROPN
ejpam-6314	320	95	∈	∈	PROPN
ejpam-6314	320	96	s.	s.	PROPN
ejpam-6314	320	97	for	for	ADP
ejpam-6314	320	98	κ0	κ0	PRON
ejpam-6314	320	99	∈	∈	PROPN
ejpam-6314	320	100	s	s	PART
ejpam-6314	320	101	,	,	PUNCT
ejpam-6314	320	102	we	we	PRON
ejpam-6314	320	103	set	set	VERB
ejpam-6314	320	104	µ(κ0	µ(κ0	ADJ
ejpam-6314	320	105	)	)	PUNCT
ejpam-6314	320	106	1−ν(κ0	1−ν(κ0	NUM
ejpam-6314	320	107	)	)	PUNCT
ejpam-6314	320	108	=	=	SYM
ejpam-6314	320	109	ω	ω	X
ejpam-6314	320	110	.	.	PROPN
ejpam-6314	320	111	suppose	suppose	VERB
ejpam-6314	320	112	that	that	SCONJ
ejpam-6314	320	113	,	,	PUNCT
ejpam-6314	320	114	sup	sup	NOUN
ejpam-6314	320	115	m≥1	m≥1	PROPN
ejpam-6314	320	116	lim	lim	PROPN
ejpam-6314	320	117	i→+∞	i→+∞	PROPN
ejpam-6314	320	118	ϑ(κi+1,κi+2)ϑ(κi+1,κm	ϑ(κi+1,κi+2)ϑ(κi+1,κm	PUNCT
ejpam-6314	320	119	)	)	PUNCT
ejpam-6314	320	120	ϑ(κi	ϑ(κi	NOUN
ejpam-6314	320	121	,	,	PUNCT
ejpam-6314	320	122	κi+1	κi+1	X
ejpam-6314	320	123	)	)	PUNCT
ejpam-6314	320	124	<	<	X
ejpam-6314	320	125	1	1	NUM
ejpam-6314	320	126	ω	ω	NUM
ejpam-6314	320	127	m.	m.	NOUN
ejpam-6314	320	128	sarwar	sarwar	PROPN
ejpam-6314	320	129	et	et	PROPN
ejpam-6314	321	1	al	al	PROPN
ejpam-6314	321	2	.	.	PUNCT
ejpam-6314	321	3	/	/	SYM
ejpam-6314	321	4	eur	eur	PROPN
ejpam-6314	321	5	.	.	PUNCT
ejpam-6314	322	1	j.	j.	PROPN
ejpam-6314	322	2	pure	pure	PROPN
ejpam-6314	322	3	appl	appl	PROPN
ejpam-6314	322	4	.	.	PROPN
ejpam-6314	322	5	math	math	PROPN
ejpam-6314	322	6	,	,	PUNCT
ejpam-6314	322	7	18	18	NUM
ejpam-6314	322	8	(	(	PUNCT
ejpam-6314	322	9	3	3	NUM
ejpam-6314	322	10	)	)	PUNCT
ejpam-6314	322	11	(	(	PUNCT
ejpam-6314	322	12	2025	2025	NUM
ejpam-6314	322	13	)	)	PUNCT
ejpam-6314	322	14	,	,	PUNCT
ejpam-6314	322	15	6314	6314	NUM
ejpam-6314	322	16	16	16	NUM
ejpam-6314	322	17	of	of	ADP
ejpam-6314	322	18	28	28	NUM
ejpam-6314	322	19	where	where	SCONJ
ejpam-6314	322	20	κn+1	κn+1	NOUN
ejpam-6314	322	21	=	=	PUNCT
ejpam-6314	322	22	ψκn	ψκn	NOUN
ejpam-6314	322	23	and	and	CCONJ
ejpam-6314	322	24	for	for	ADP
ejpam-6314	322	25	each	each	DET
ejpam-6314	322	26	n	n	PRON
ejpam-6314	322	27	≥	≥	NOUN
ejpam-6314	322	28	0	0	NUM
ejpam-6314	322	29	.	.	PUNCT
ejpam-6314	322	30	assume	assume	VERB
ejpam-6314	322	31	further	far	ADV
ejpam-6314	322	32	,	,	PUNCT
ejpam-6314	322	33	that	that	SCONJ
ejpam-6314	322	34	for	for	ADP
ejpam-6314	322	35	every	every	DET
ejpam-6314	322	36	κ	κ	PROPN
ejpam-6314	322	37	∈	∈	PROPN
ejpam-6314	322	38	s	s	PART
ejpam-6314	322	39	,	,	PUNCT
ejpam-6314	322	40	we	we	PRON
ejpam-6314	322	41	have	have	AUX
ejpam-6314	322	42	limn→+∞	limn→+∞	VERB
ejpam-6314	322	43	ϑ(κn	ϑ(κn	PROPN
ejpam-6314	322	44	,	,	PUNCT
ejpam-6314	322	45	κ	κ	NOUN
ejpam-6314	322	46	)	)	PUNCT
ejpam-6314	322	47	and	and	CCONJ
ejpam-6314	322	48	limn→+∞	limn→+∞	PROPN
ejpam-6314	322	49	ϑ(κ	ϑ(κ	PROPN
ejpam-6314	322	50	,	,	PUNCT
ejpam-6314	322	51	κn	κn	NOUN
ejpam-6314	322	52	)	)	PUNCT
ejpam-6314	322	53	,	,	PUNCT
ejpam-6314	322	54	which	which	PRON
ejpam-6314	322	55	exist	exist	VERB
ejpam-6314	322	56	and	and	CCONJ
ejpam-6314	322	57	are	be	AUX
ejpam-6314	322	58	finite	finite	ADJ
ejpam-6314	322	59	.	.	PUNCT
ejpam-6314	323	1	then	then	ADV
ejpam-6314	323	2	,	,	PUNCT
ejpam-6314	323	3	ψ	ψ	X
ejpam-6314	323	4	have	have	VERB
ejpam-6314	323	5	a	a	DET
ejpam-6314	323	6	ufp	ufp	NOUN
ejpam-6314	323	7	.	.	PUNCT
ejpam-6314	324	1	proof	proof	NOUN
ejpam-6314	324	2	.	.	PUNCT
ejpam-6314	325	1	the	the	DET
ejpam-6314	325	2	proof	proof	NOUN
ejpam-6314	325	3	is	be	AUX
ejpam-6314	325	4	trivial	trivial	ADJ
ejpam-6314	325	5	by	by	ADP
ejpam-6314	325	6	setting	set	VERB
ejpam-6314	325	7	ψ	ψ	X
ejpam-6314	325	8	=	=	SYM
ejpam-6314	325	9	φ	φ	PROPN
ejpam-6314	325	10	in	in	ADP
ejpam-6314	325	11	the	the	DET
ejpam-6314	325	12	theorem	theorem	NOUN
ejpam-6314	325	13	(	(	PUNCT
ejpam-6314	325	14	4	4	NUM
ejpam-6314	325	15	)	)	PUNCT
ejpam-6314	325	16	this	this	DET
ejpam-6314	325	17	result	result	NOUN
ejpam-6314	325	18	can	can	AUX
ejpam-6314	325	19	be	be	AUX
ejpam-6314	325	20	obtained	obtain	VERB
ejpam-6314	325	21	.	.	PUNCT
ejpam-6314	326	1	corollary	corollary	ADJ
ejpam-6314	326	2	3	3	X
ejpam-6314	326	3	.	.	PUNCT
ejpam-6314	327	1	let	let	VERB
ejpam-6314	327	2	(	(	PUNCT
ejpam-6314	327	3	s	s	X
ejpam-6314	327	4	,	,	PUNCT
ejpam-6314	327	5	ϑ	ϑ	NOUN
ejpam-6314	327	6	,	,	PUNCT
ejpam-6314	327	7	db)be	db)be	PROPN
ejpam-6314	327	8	a	a	DET
ejpam-6314	327	9	(	(	PUNCT
ejpam-6314	327	10	bcvms	bcvms	NOUN
ejpam-6314	327	11	)	)	PUNCT
ejpam-6314	327	12	which	which	PRON
ejpam-6314	327	13	is	be	AUX
ejpam-6314	327	14	complete	complete	ADJ
ejpam-6314	327	15	and	and	CCONJ
ejpam-6314	327	16	ψ	ψ	X
ejpam-6314	327	17	:	:	PUNCT
ejpam-6314	327	18	s	s	X
ejpam-6314	327	19	→	→	PUNCT
ejpam-6314	327	20	s.	s.	PROPN
ejpam-6314	327	21	if	if	SCONJ
ejpam-6314	327	22	there	there	PRON
ejpam-6314	327	23	exist	exist	VERB
ejpam-6314	327	24	µ	µ	NOUN
ejpam-6314	327	25	,	,	PUNCT
ejpam-6314	327	26	ν	ν	X
ejpam-6314	327	27	:	:	PUNCT
ejpam-6314	327	28	s	s	X
ejpam-6314	327	29	→	→	SYM
ejpam-6314	327	30	[	[	X
ejpam-6314	327	31	0	0	NUM
ejpam-6314	327	32	,	,	PUNCT
ejpam-6314	327	33	1	1	NUM
ejpam-6314	327	34	)	)	PUNCT
ejpam-6314	327	35	such	such	ADJ
ejpam-6314	327	36	that	that	PRON
ejpam-6314	327	37	:	:	PUNCT
ejpam-6314	327	38	(	(	PUNCT
ejpam-6314	327	39	i	i	NOUN
ejpam-6314	327	40	)	)	PUNCT
ejpam-6314	327	41	µ(ψκ	µ(ψκ	NOUN
ejpam-6314	327	42	)	)	PUNCT
ejpam-6314	327	43	≤	≤	NOUN
ejpam-6314	327	44	µ(κ	µ(κ	PROPN
ejpam-6314	327	45	)	)	PUNCT
ejpam-6314	327	46	;	;	PUNCT
ejpam-6314	327	47	(	(	PUNCT
ejpam-6314	327	48	ii	ii	NOUN
ejpam-6314	327	49	)	)	PUNCT
ejpam-6314	327	50	db(ψκ	db(ψκ	NOUN
ejpam-6314	327	51	,	,	PUNCT
ejpam-6314	327	52	ψν	ψν	NOUN
ejpam-6314	327	53	)	)	PUNCT
ejpam-6314	327	54	≾	≾	PROPN
ejpam-6314	327	55	µ(κ)db(κ	µ(κ)db(κ	NOUN
ejpam-6314	327	56	,	,	PUNCT
ejpam-6314	327	57	σ	σ	PROPN
ejpam-6314	327	58	)	)	PUNCT
ejpam-6314	327	59	for	for	ADP
ejpam-6314	327	60	all	all	DET
ejpam-6314	327	61	κ	κ	PROPN
ejpam-6314	327	62	,	,	PUNCT
ejpam-6314	327	63	σ	σ	PROPN
ejpam-6314	327	64	∈	∈	PROPN
ejpam-6314	327	65	s.	s.	PROPN
ejpam-6314	327	66	for	for	ADP
ejpam-6314	327	67	κ0	κ0	PROPN
ejpam-6314	327	68	∈	∈	PROPN
ejpam-6314	327	69	s.	s.	PROPN
ejpam-6314	327	70	suppose	suppose	VERB
ejpam-6314	327	71	that	that	SCONJ
ejpam-6314	327	72	:	:	PUNCT
ejpam-6314	327	73	sup	sup	PROPN
ejpam-6314	327	74	m≥1	m≥1	PROPN
ejpam-6314	327	75	lim	lim	PROPN
ejpam-6314	327	76	i→+∞	i→+∞	PROPN
ejpam-6314	327	77	ϑ(κi+1,κi+2)ϑ(κi+1,κm	ϑ(κi+1,κi+2)ϑ(κi+1,κm	PUNCT
ejpam-6314	327	78	)	)	PUNCT
ejpam-6314	327	79	ϑ(κi	ϑ(κi	NOUN
ejpam-6314	327	80	,	,	PUNCT
ejpam-6314	327	81	κi+1	κi+1	X
ejpam-6314	327	82	)	)	PUNCT
ejpam-6314	327	83	<	<	X
ejpam-6314	327	84	1	1	NUM
ejpam-6314	327	85	µ(κ0	µ(κ0	NOUN
ejpam-6314	327	86	)	)	PUNCT
ejpam-6314	327	87	where	where	SCONJ
ejpam-6314	327	88	κn+1	κn+1	NOUN
ejpam-6314	327	89	=	=	PUNCT
ejpam-6314	327	90	ψκn	ψκn	NOUN
ejpam-6314	327	91	and	and	CCONJ
ejpam-6314	327	92	for	for	ADP
ejpam-6314	327	93	each	each	DET
ejpam-6314	327	94	n	n	PRON
ejpam-6314	327	95	≥	≥	NOUN
ejpam-6314	327	96	0	0	NUM
ejpam-6314	327	97	.	.	PUNCT
ejpam-6314	327	98	assume	assume	VERB
ejpam-6314	327	99	further	far	ADV
ejpam-6314	327	100	,	,	PUNCT
ejpam-6314	327	101	that	that	SCONJ
ejpam-6314	327	102	for	for	ADP
ejpam-6314	327	103	every	every	DET
ejpam-6314	327	104	κ	κ	PROPN
ejpam-6314	327	105	∈	∈	PROPN
ejpam-6314	327	106	s	s	PART
ejpam-6314	327	107	,	,	PUNCT
ejpam-6314	327	108	we	we	PRON
ejpam-6314	327	109	have	have	AUX
ejpam-6314	327	110	limn→+∞	limn→+∞	VERB
ejpam-6314	327	111	ϑ(κn	ϑ(κn	PROPN
ejpam-6314	327	112	,	,	PUNCT
ejpam-6314	327	113	κ	κ	NOUN
ejpam-6314	327	114	)	)	PUNCT
ejpam-6314	327	115	and	and	CCONJ
ejpam-6314	327	116	limn→+∞	limn→+∞	PROPN
ejpam-6314	327	117	ϑ(κ	ϑ(κ	PROPN
ejpam-6314	327	118	,	,	PUNCT
ejpam-6314	327	119	κn	κn	NOUN
ejpam-6314	327	120	)	)	PUNCT
ejpam-6314	327	121	,	,	PUNCT
ejpam-6314	327	122	which	which	PRON
ejpam-6314	327	123	exist	exist	VERB
ejpam-6314	327	124	and	and	CCONJ
ejpam-6314	327	125	are	be	AUX
ejpam-6314	327	126	finite	finite	ADJ
ejpam-6314	327	127	.	.	PUNCT
ejpam-6314	328	1	then	then	ADV
ejpam-6314	328	2	,	,	PUNCT
ejpam-6314	328	3	ψ	ψ	X
ejpam-6314	328	4	have	have	VERB
ejpam-6314	328	5	a	a	DET
ejpam-6314	328	6	ufp	ufp	NOUN
ejpam-6314	328	7	.	.	PUNCT
ejpam-6314	329	1	proof	proof	NOUN
ejpam-6314	329	2	.	.	PUNCT
ejpam-6314	330	1	this	this	DET
ejpam-6314	330	2	result	result	NOUN
ejpam-6314	330	3	can	can	AUX
ejpam-6314	330	4	be	be	AUX
ejpam-6314	330	5	obtained	obtain	VERB
ejpam-6314	330	6	by	by	ADP
ejpam-6314	330	7	putting	put	VERB
ejpam-6314	330	8	ν(κ	ν(κ	NOUN
ejpam-6314	330	9	)	)	PUNCT
ejpam-6314	331	1	=	=	SYM
ejpam-6314	331	2	0	0	NUM
ejpam-6314	332	1	in	in	ADP
ejpam-6314	332	2	the	the	DET
ejpam-6314	332	3	corollary	corollary	ADJ
ejpam-6314	332	4	(	(	PUNCT
ejpam-6314	332	5	2	2	NUM
ejpam-6314	332	6	)	)	PUNCT
ejpam-6314	332	7	.	.	PUNCT
ejpam-6314	333	1	corollary	corollary	ADJ
ejpam-6314	333	2	4	4	NUM
ejpam-6314	333	3	.	.	PUNCT
ejpam-6314	334	1	let	let	VERB
ejpam-6314	334	2	(	(	PUNCT
ejpam-6314	334	3	s	s	X
ejpam-6314	334	4	,	,	PUNCT
ejpam-6314	334	5	ϑ	ϑ	NOUN
ejpam-6314	334	6	,	,	PUNCT
ejpam-6314	334	7	db)be	db)be	PROPN
ejpam-6314	334	8	a	a	DET
ejpam-6314	334	9	(	(	PUNCT
ejpam-6314	334	10	bcvms	bcvms	NOUN
ejpam-6314	334	11	)	)	PUNCT
ejpam-6314	334	12	which	which	PRON
ejpam-6314	334	13	is	be	AUX
ejpam-6314	334	14	complete	complete	ADJ
ejpam-6314	334	15	and	and	CCONJ
ejpam-6314	334	16	ψ	ψ	X
ejpam-6314	334	17	:	:	PUNCT
ejpam-6314	334	18	s	s	X
ejpam-6314	334	19	→	→	PUNCT
ejpam-6314	334	20	s.	s.	PROPN
ejpam-6314	334	21	if	if	SCONJ
ejpam-6314	334	22	there	there	PRON
ejpam-6314	334	23	exist	exist	VERB
ejpam-6314	334	24	µ	µ	NOUN
ejpam-6314	334	25	,	,	PUNCT
ejpam-6314	334	26	ν	ν	X
ejpam-6314	334	27	:	:	PUNCT
ejpam-6314	334	28	s	s	X
ejpam-6314	334	29	→	→	SYM
ejpam-6314	334	30	[	[	X
ejpam-6314	334	31	0	0	NUM
ejpam-6314	334	32	,	,	PUNCT
ejpam-6314	334	33	1	1	NUM
ejpam-6314	334	34	)	)	PUNCT
ejpam-6314	334	35	such	such	ADJ
ejpam-6314	334	36	that	that	SCONJ
ejpam-6314	334	37	:	:	PUNCT
ejpam-6314	334	38	db(ψκ	db(ψκ	NOUN
ejpam-6314	334	39	,	,	PUNCT
ejpam-6314	334	40	ψν	ψν	NOUN
ejpam-6314	334	41	)	)	PUNCT
ejpam-6314	334	42	≾	≾	PROPN
ejpam-6314	334	43	µdb(κ	µdb(κ	PROPN
ejpam-6314	334	44	,	,	PUNCT
ejpam-6314	334	45	σ	σ	PROPN
ejpam-6314	334	46	)	)	PUNCT
ejpam-6314	335	1	+	+	CCONJ
ejpam-6314	335	2	ν	ν	NOUN
ejpam-6314	335	3	db(κ	db(κ	X
ejpam-6314	335	4	,	,	PUNCT
ejpam-6314	335	5	ψκ)db(σ	ψκ)db(σ	NOUN
ejpam-6314	335	6	,	,	PUNCT
ejpam-6314	335	7	ψσ	ψσ	ADJ
ejpam-6314	335	8	)	)	PUNCT
ejpam-6314	335	9	1	1	NUM
ejpam-6314	335	10	+	+	CCONJ
ejpam-6314	335	11	db(κ	db(κ	NUM
ejpam-6314	335	12	,	,	PUNCT
ejpam-6314	335	13	σ	σ	NOUN
ejpam-6314	335	14	)	)	PUNCT
ejpam-6314	335	15	for	for	ADP
ejpam-6314	335	16	all	all	DET
ejpam-6314	335	17	κ	κ	PROPN
ejpam-6314	335	18	,	,	PUNCT
ejpam-6314	335	19	σ	σ	PROPN
ejpam-6314	335	20	∈	∈	PROPN
ejpam-6314	335	21	s.	s.	PROPN
ejpam-6314	335	22	for	for	ADP
ejpam-6314	335	23	κ0	κ0	PRON
ejpam-6314	335	24	∈	∈	PROPN
ejpam-6314	335	25	s	s	PART
ejpam-6314	335	26	,	,	PUNCT
ejpam-6314	335	27	we	we	PRON
ejpam-6314	335	28	set	set	VERB
ejpam-6314	335	29	µ(κ0	µ(κ0	ADJ
ejpam-6314	335	30	)	)	PUNCT
ejpam-6314	335	31	1−ν(κ0	1−ν(κ0	NUM
ejpam-6314	335	32	)	)	PUNCT
ejpam-6314	335	33	=	=	SYM
ejpam-6314	335	34	ω	ω	X
ejpam-6314	335	35	.	.	PROPN
ejpam-6314	335	36	suppose	suppose	VERB
ejpam-6314	335	37	that	that	SCONJ
ejpam-6314	335	38	,	,	PUNCT
ejpam-6314	335	39	sup	sup	NOUN
ejpam-6314	335	40	m≥1	m≥1	PROPN
ejpam-6314	335	41	lim	lim	PROPN
ejpam-6314	335	42	i→+∞	i→+∞	PROPN
ejpam-6314	335	43	ϑ(κi+1,κi+2)ϑ(κi+1,κm	ϑ(κi+1,κi+2)ϑ(κi+1,κm	PUNCT
ejpam-6314	335	44	)	)	PUNCT
ejpam-6314	335	45	ϑ(κi	ϑ(κi	NOUN
ejpam-6314	335	46	,	,	PUNCT
ejpam-6314	335	47	κi+1	κi+1	X
ejpam-6314	335	48	)	)	PUNCT
ejpam-6314	335	49	<	<	X
ejpam-6314	336	1	1	1	NUM
ejpam-6314	336	2	ω	ω	NUM
ejpam-6314	336	3	where	where	SCONJ
ejpam-6314	336	4	κn+1	κn+1	NOUN
ejpam-6314	336	5	=	=	PUNCT
ejpam-6314	336	6	ψκn	ψκn	NOUN
ejpam-6314	336	7	and	and	CCONJ
ejpam-6314	336	8	for	for	ADP
ejpam-6314	336	9	each	each	DET
ejpam-6314	336	10	n	n	PRON
ejpam-6314	336	11	≥	≥	NOUN
ejpam-6314	336	12	0	0	NUM
ejpam-6314	336	13	.	.	PUNCT
ejpam-6314	336	14	assume	assume	VERB
ejpam-6314	336	15	further	far	ADV
ejpam-6314	336	16	,	,	PUNCT
ejpam-6314	336	17	that	that	SCONJ
ejpam-6314	336	18	for	for	ADP
ejpam-6314	336	19	every	every	DET
ejpam-6314	336	20	κ	κ	PROPN
ejpam-6314	336	21	∈	∈	PROPN
ejpam-6314	336	22	s	s	PART
ejpam-6314	336	23	,	,	PUNCT
ejpam-6314	336	24	we	we	PRON
ejpam-6314	336	25	have	have	AUX
ejpam-6314	336	26	limn→+∞	limn→+∞	VERB
ejpam-6314	336	27	ϑ(κn	ϑ(κn	PROPN
ejpam-6314	336	28	,	,	PUNCT
ejpam-6314	336	29	κ	κ	NOUN
ejpam-6314	336	30	)	)	PUNCT
ejpam-6314	336	31	and	and	CCONJ
ejpam-6314	336	32	limn→+∞	limn→+∞	PROPN
ejpam-6314	336	33	ϑ(κ	ϑ(κ	PROPN
ejpam-6314	336	34	,	,	PUNCT
ejpam-6314	336	35	κn	κn	NOUN
ejpam-6314	336	36	)	)	PUNCT
ejpam-6314	336	37	,	,	PUNCT
ejpam-6314	336	38	which	which	PRON
ejpam-6314	336	39	exist	exist	VERB
ejpam-6314	336	40	and	and	CCONJ
ejpam-6314	336	41	are	be	AUX
ejpam-6314	336	42	finite	finite	ADJ
ejpam-6314	336	43	.	.	PUNCT
ejpam-6314	337	1	then	then	ADV
ejpam-6314	337	2	,	,	PUNCT
ejpam-6314	337	3	ψ	ψ	X
ejpam-6314	337	4	have	have	VERB
ejpam-6314	337	5	a	a	DET
ejpam-6314	337	6	ufp	ufp	NOUN
ejpam-6314	337	7	.	.	PUNCT
ejpam-6314	338	1	proof	proof	NOUN
ejpam-6314	338	2	.	.	PUNCT
ejpam-6314	339	1	by	by	ADP
ejpam-6314	339	2	setting	set	VERB
ejpam-6314	339	3	µ(κ	µ(κ	NOUN
ejpam-6314	339	4	)	)	PUNCT
ejpam-6314	339	5	=	=	SYM
ejpam-6314	339	6	µ	µ	X
ejpam-6314	339	7	and	and	CCONJ
ejpam-6314	339	8	ν(κ	ν(κ	NOUN
ejpam-6314	339	9	)	)	PUNCT
ejpam-6314	339	10	=	=	PUNCT
ejpam-6314	339	11	ν	ν	NOUN
ejpam-6314	339	12	in	in	ADP
ejpam-6314	339	13	the	the	DET
ejpam-6314	339	14	corollary	corollary	ADJ
ejpam-6314	339	15	(	(	PUNCT
ejpam-6314	339	16	2	2	NUM
ejpam-6314	339	17	)	)	PUNCT
ejpam-6314	339	18	this	this	DET
ejpam-6314	339	19	result	result	NOUN
ejpam-6314	339	20	can	can	AUX
ejpam-6314	339	21	be	be	AUX
ejpam-6314	339	22	obtained	obtain	VERB
ejpam-6314	339	23	.	.	PUNCT
ejpam-6314	340	1	corollary	corollary	ADJ
ejpam-6314	340	2	5	5	NUM
ejpam-6314	340	3	.	.	PUNCT
ejpam-6314	341	1	let	let	VERB
ejpam-6314	341	2	(	(	PUNCT
ejpam-6314	341	3	s	s	X
ejpam-6314	341	4	,	,	PUNCT
ejpam-6314	341	5	ϑ	ϑ	NOUN
ejpam-6314	341	6	,	,	PUNCT
ejpam-6314	341	7	db)be	db)be	PROPN
ejpam-6314	341	8	a	a	DET
ejpam-6314	341	9	(	(	PUNCT
ejpam-6314	341	10	bcvms	bcvms	NOUN
ejpam-6314	341	11	)	)	PUNCT
ejpam-6314	341	12	which	which	PRON
ejpam-6314	341	13	is	be	AUX
ejpam-6314	341	14	complete	complete	ADJ
ejpam-6314	341	15	and	and	CCONJ
ejpam-6314	341	16	ψ	ψ	X
ejpam-6314	341	17	:	:	PUNCT
ejpam-6314	341	18	s	s	X
ejpam-6314	341	19	→	→	PUNCT
ejpam-6314	341	20	s.	s.	PROPN
ejpam-6314	341	21	if	if	SCONJ
ejpam-6314	341	22	there	there	PRON
ejpam-6314	341	23	exist	exist	VERB
ejpam-6314	341	24	µ	µ	NOUN
ejpam-6314	341	25	,	,	PUNCT
ejpam-6314	341	26	ν	ν	X
ejpam-6314	341	27	:	:	PUNCT
ejpam-6314	341	28	s	s	X
ejpam-6314	341	29	→	→	SYM
ejpam-6314	341	30	[	[	X
ejpam-6314	341	31	0	0	NUM
ejpam-6314	341	32	,	,	PUNCT
ejpam-6314	341	33	1	1	NUM
ejpam-6314	341	34	)	)	PUNCT
ejpam-6314	341	35	such	such	ADJ
ejpam-6314	341	36	that	that	PRON
ejpam-6314	341	37	:	:	PUNCT
ejpam-6314	341	38	m.	m.	NOUN
ejpam-6314	341	39	sarwar	sarwar	PROPN
ejpam-6314	341	40	et	et	PROPN
ejpam-6314	341	41	al	al	PROPN
ejpam-6314	341	42	.	.	PUNCT
ejpam-6314	341	43	/	/	SYM
ejpam-6314	341	44	eur	eur	PROPN
ejpam-6314	341	45	.	.	PUNCT
ejpam-6314	342	1	j.	j.	PROPN
ejpam-6314	342	2	pure	pure	PROPN
ejpam-6314	342	3	appl	appl	PROPN
ejpam-6314	342	4	.	.	PROPN
ejpam-6314	342	5	math	math	PROPN
ejpam-6314	342	6	,	,	PUNCT
ejpam-6314	342	7	18	18	NUM
ejpam-6314	342	8	(	(	PUNCT
ejpam-6314	342	9	3	3	NUM
ejpam-6314	342	10	)	)	PUNCT
ejpam-6314	342	11	(	(	PUNCT
ejpam-6314	342	12	2025	2025	NUM
ejpam-6314	342	13	)	)	PUNCT
ejpam-6314	342	14	,	,	PUNCT
ejpam-6314	342	15	6314	6314	NUM
ejpam-6314	342	16	17	17	NUM
ejpam-6314	342	17	of	of	ADP
ejpam-6314	342	18	28	28	NUM
ejpam-6314	342	19	db(ψκ	db(ψκ	NOUN
ejpam-6314	342	20	,	,	PUNCT
ejpam-6314	342	21	ψν	ψν	NOUN
ejpam-6314	342	22	)	)	PUNCT
ejpam-6314	342	23	≾	≾	PROPN
ejpam-6314	342	24	µdb(κ	µdb(κ	PROPN
ejpam-6314	342	25	,	,	PUNCT
ejpam-6314	342	26	σ	σ	PROPN
ejpam-6314	342	27	)	)	PUNCT
ejpam-6314	342	28	for	for	ADP
ejpam-6314	342	29	all	all	DET
ejpam-6314	342	30	κ	κ	PROPN
ejpam-6314	342	31	,	,	PUNCT
ejpam-6314	342	32	σ	σ	PROPN
ejpam-6314	342	33	∈	∈	PROPN
ejpam-6314	342	34	s.	s.	PROPN
ejpam-6314	342	35	for	for	ADP
ejpam-6314	342	36	κ0	κ0	PROPN
ejpam-6314	342	37	∈	∈	PROPN
ejpam-6314	342	38	s.	s.	PROPN
ejpam-6314	342	39	suppose	suppose	VERB
ejpam-6314	342	40	that	that	SCONJ
ejpam-6314	342	41	,	,	PUNCT
ejpam-6314	342	42	sup	sup	NOUN
ejpam-6314	342	43	m≥1	m≥1	PROPN
ejpam-6314	342	44	lim	lim	PROPN
ejpam-6314	342	45	i→+∞	i→+∞	PROPN
ejpam-6314	342	46	ϑ(κi+1,κi+2)ϑ(κi+1,κm	ϑ(κi+1,κi+2)ϑ(κi+1,κm	PUNCT
ejpam-6314	342	47	)	)	PUNCT
ejpam-6314	342	48	ϑ(κi	ϑ(κi	NOUN
ejpam-6314	342	49	,	,	PUNCT
ejpam-6314	342	50	κi+1	κi+1	X
ejpam-6314	342	51	)	)	PUNCT
ejpam-6314	342	52	<	<	X
ejpam-6314	343	1	1	1	NUM
ejpam-6314	343	2	µ	µ	X
ejpam-6314	343	3	where	where	SCONJ
ejpam-6314	343	4	κn+1	κn+1	NOUN
ejpam-6314	343	5	=	=	PUNCT
ejpam-6314	343	6	ψκn	ψκn	NOUN
ejpam-6314	343	7	and	and	CCONJ
ejpam-6314	343	8	for	for	ADP
ejpam-6314	343	9	each	each	DET
ejpam-6314	343	10	n	n	PRON
ejpam-6314	343	11	≥	≥	NOUN
ejpam-6314	343	12	0	0	NUM
ejpam-6314	343	13	.	.	PUNCT
ejpam-6314	343	14	assume	assume	VERB
ejpam-6314	343	15	further	far	ADV
ejpam-6314	343	16	,	,	PUNCT
ejpam-6314	343	17	that	that	SCONJ
ejpam-6314	343	18	for	for	ADP
ejpam-6314	343	19	every	every	DET
ejpam-6314	343	20	κ	κ	PROPN
ejpam-6314	343	21	∈	∈	PROPN
ejpam-6314	343	22	s	s	PART
ejpam-6314	343	23	,	,	PUNCT
ejpam-6314	343	24	we	we	PRON
ejpam-6314	343	25	have	have	AUX
ejpam-6314	343	26	limn→+∞	limn→+∞	VERB
ejpam-6314	343	27	ϑ(κn	ϑ(κn	PROPN
ejpam-6314	343	28	,	,	PUNCT
ejpam-6314	343	29	κ	κ	NOUN
ejpam-6314	343	30	)	)	PUNCT
ejpam-6314	343	31	and	and	CCONJ
ejpam-6314	343	32	limn→+∞	limn→+∞	PROPN
ejpam-6314	343	33	ϑ(κ	ϑ(κ	PROPN
ejpam-6314	343	34	,	,	PUNCT
ejpam-6314	343	35	κn	κn	NOUN
ejpam-6314	343	36	)	)	PUNCT
ejpam-6314	343	37	,	,	PUNCT
ejpam-6314	343	38	which	which	PRON
ejpam-6314	343	39	exist	exist	VERB
ejpam-6314	343	40	and	and	CCONJ
ejpam-6314	343	41	are	be	AUX
ejpam-6314	343	42	finite	finite	ADJ
ejpam-6314	343	43	.	.	PUNCT
ejpam-6314	344	1	then	then	ADV
ejpam-6314	344	2	,	,	PUNCT
ejpam-6314	344	3	ψ	ψ	X
ejpam-6314	344	4	have	have	VERB
ejpam-6314	344	5	a	a	DET
ejpam-6314	344	6	ufp	ufp	NOUN
ejpam-6314	344	7	.	.	PUNCT
ejpam-6314	345	1	proof	proof	NOUN
ejpam-6314	345	2	.	.	PUNCT
ejpam-6314	346	1	this	this	DET
ejpam-6314	346	2	result	result	NOUN
ejpam-6314	346	3	can	can	AUX
ejpam-6314	346	4	be	be	AUX
ejpam-6314	346	5	obtained	obtain	VERB
ejpam-6314	346	6	by	by	ADP
ejpam-6314	346	7	putting	put	VERB
ejpam-6314	346	8	µ(κ	µ(κ	PROPN
ejpam-6314	346	9	)	)	PUNCT
ejpam-6314	347	1	=	=	SYM
ejpam-6314	347	2	µ	µ	X
ejpam-6314	347	3	in	in	ADP
ejpam-6314	347	4	corollary	corollary	ADJ
ejpam-6314	347	5	(	(	PUNCT
ejpam-6314	347	6	3	3	NUM
ejpam-6314	347	7	)	)	PUNCT
ejpam-6314	347	8	.	.	PUNCT
ejpam-6314	348	1	remark	remark	PROPN
ejpam-6314	348	2	2	2	NUM
ejpam-6314	348	3	.	.	PUNCT
ejpam-6314	348	4	corollary	corollary	ADJ
ejpam-6314	348	5	(	(	PUNCT
ejpam-6314	348	6	4	4	NUM
ejpam-6314	348	7	)	)	PUNCT
ejpam-6314	348	8	and	and	CCONJ
ejpam-6314	348	9	(	(	PUNCT
ejpam-6314	348	10	5	5	X
ejpam-6314	348	11	)	)	PUNCT
ejpam-6314	348	12	are	be	AUX
ejpam-6314	348	13	the	the	DET
ejpam-6314	348	14	outcomes	outcome	NOUN
ejpam-6314	348	15	of	of	ADP
ejpam-6314	348	16	paper	paper	NOUN
ejpam-6314	348	17	[	[	X
ejpam-6314	348	18	24	24	NUM
ejpam-6314	348	19	]	]	PUNCT
ejpam-6314	348	20	.	.	PUNCT
ejpam-6314	349	1	theorem	theorem	NOUN
ejpam-6314	349	2	5	5	NUM
ejpam-6314	349	3	.	.	PUNCT
ejpam-6314	350	1	let	let	VERB
ejpam-6314	350	2	(	(	PUNCT
ejpam-6314	350	3	s	s	X
ejpam-6314	350	4	,	,	PUNCT
ejpam-6314	350	5	ϑ	ϑ	NOUN
ejpam-6314	350	6	,	,	PUNCT
ejpam-6314	350	7	db)be	db)be	PROPN
ejpam-6314	350	8	a	a	DET
ejpam-6314	350	9	(	(	PUNCT
ejpam-6314	350	10	bcvms	bcvms	NOUN
ejpam-6314	350	11	)	)	PUNCT
ejpam-6314	350	12	which	which	PRON
ejpam-6314	350	13	is	be	AUX
ejpam-6314	350	14	complete	complete	ADJ
ejpam-6314	350	15	and	and	CCONJ
ejpam-6314	350	16	ψ	ψ	X
ejpam-6314	350	17	:	:	PUNCT
ejpam-6314	350	18	s	s	X
ejpam-6314	350	19	→	→	PUNCT
ejpam-6314	350	20	s.	s.	PROPN
ejpam-6314	350	21	if	if	SCONJ
ejpam-6314	350	22	there	there	PRON
ejpam-6314	350	23	exist	exist	VERB
ejpam-6314	350	24	µ	µ	NOUN
ejpam-6314	350	25	,	,	PUNCT
ejpam-6314	350	26	ν	ν	X
ejpam-6314	350	27	:	:	PUNCT
ejpam-6314	350	28	s	s	X
ejpam-6314	350	29	→	→	SYM
ejpam-6314	350	30	[	[	X
ejpam-6314	350	31	0	0	NUM
ejpam-6314	350	32	,	,	PUNCT
ejpam-6314	350	33	1	1	NUM
ejpam-6314	350	34	)	)	PUNCT
ejpam-6314	350	35	such	such	ADJ
ejpam-6314	350	36	that	that	PRON
ejpam-6314	350	37	:	:	PUNCT
ejpam-6314	350	38	(	(	PUNCT
ejpam-6314	350	39	i	i	NOUN
ejpam-6314	350	40	)	)	PUNCT
ejpam-6314	350	41	µ(ψnκ	µ(ψnκ	PROPN
ejpam-6314	350	42	)	)	PUNCT
ejpam-6314	350	43	≤	≤	NUM
ejpam-6314	350	44	µ(κ	µ(κ	NOUN
ejpam-6314	350	45	)	)	PUNCT
ejpam-6314	350	46	and	and	CCONJ
ejpam-6314	350	47	ν(ψnκ	ν(ψnκ	PROPN
ejpam-6314	350	48	)	)	PUNCT
ejpam-6314	350	49	≤	≤	NUM
ejpam-6314	350	50	ν(κ	ν(κ	NOUN
ejpam-6314	350	51	)	)	PUNCT
ejpam-6314	350	52	;	;	PUNCT
ejpam-6314	350	53	(	(	PUNCT
ejpam-6314	350	54	ii	ii	NOUN
ejpam-6314	350	55	)	)	PUNCT
ejpam-6314	350	56	(	(	PUNCT
ejpam-6314	350	57	µ+	µ+	X
ejpam-6314	350	58	ν)(κ	ν)(κ	NOUN
ejpam-6314	350	59	)	)	PUNCT
ejpam-6314	350	60	<	<	X
ejpam-6314	350	61	1	1	NUM
ejpam-6314	350	62	;	;	PUNCT
ejpam-6314	350	63	(	(	PUNCT
ejpam-6314	350	64	iii	iii	NOUN
ejpam-6314	350	65	)	)	PUNCT
ejpam-6314	350	66	db(ψ	db(ψ	PROPN
ejpam-6314	350	67	nκ	nκ	NOUN
ejpam-6314	350	68	,	,	PUNCT
ejpam-6314	350	69	ψnσ	ψnσ	NOUN
ejpam-6314	350	70	)	)	PUNCT
ejpam-6314	350	71	≾	≾	PROPN
ejpam-6314	350	72	µ(κ)db(κ	µ(κ)db(κ	NOUN
ejpam-6314	350	73	,	,	PUNCT
ejpam-6314	350	74	σ	σ	NOUN
ejpam-6314	350	75	)	)	PUNCT
ejpam-6314	350	76	+	+	NUM
ejpam-6314	350	77	ν(κ	ν(κ	NOUN
ejpam-6314	350	78	)	)	PUNCT
ejpam-6314	350	79	db(κ	db(κ	NOUN
ejpam-6314	350	80	,	,	PUNCT
ejpam-6314	350	81	ψnκ)db(σ	ψnκ)db(σ	NOUN
ejpam-6314	350	82	,	,	PUNCT
ejpam-6314	350	83	ψnσ	ψnσ	NOUN
ejpam-6314	350	84	)	)	PUNCT
ejpam-6314	350	85	1	1	NUM
ejpam-6314	350	86	+	+	CCONJ
ejpam-6314	350	87	db(κ	db(κ	NUM
ejpam-6314	350	88	,	,	PUNCT
ejpam-6314	350	89	σ	σ	PROPN
ejpam-6314	350	90	)	)	PUNCT
ejpam-6314	350	91	(	(	PUNCT
ejpam-6314	350	92	26	26	NUM
ejpam-6314	350	93	)	)	PUNCT
ejpam-6314	350	94	for	for	ADP
ejpam-6314	350	95	all	all	DET
ejpam-6314	350	96	κ	κ	PROPN
ejpam-6314	350	97	,	,	PUNCT
ejpam-6314	350	98	σ	σ	PROPN
ejpam-6314	350	99	∈	∈	PROPN
ejpam-6314	350	100	s.	s.	PROPN
ejpam-6314	350	101	for	for	ADP
ejpam-6314	350	102	κ0	κ0	PRON
ejpam-6314	350	103	∈	∈	PROPN
ejpam-6314	350	104	s	s	PART
ejpam-6314	350	105	,	,	PUNCT
ejpam-6314	350	106	we	we	PRON
ejpam-6314	350	107	set	set	VERB
ejpam-6314	350	108	µ(κ0	µ(κ0	ADJ
ejpam-6314	350	109	)	)	PUNCT
ejpam-6314	350	110	1−ν(κ0	1−ν(κ0	NUM
ejpam-6314	350	111	)	)	PUNCT
ejpam-6314	350	112	=	=	SYM
ejpam-6314	350	113	ω	ω	X
ejpam-6314	350	114	.	.	PROPN
ejpam-6314	350	115	suppose	suppose	VERB
ejpam-6314	350	116	that	that	SCONJ
ejpam-6314	350	117	,	,	PUNCT
ejpam-6314	350	118	sup	sup	NOUN
ejpam-6314	350	119	m≥1	m≥1	PROPN
ejpam-6314	350	120	lim	lim	PROPN
ejpam-6314	350	121	i→+∞	i→+∞	PROPN
ejpam-6314	350	122	ϑ(κi+1,κi+2)ϑ(κi+1,κm	ϑ(κi+1,κi+2)ϑ(κi+1,κm	PUNCT
ejpam-6314	350	123	)	)	PUNCT
ejpam-6314	350	124	ϑ(κi	ϑ(κi	NOUN
ejpam-6314	350	125	,	,	PUNCT
ejpam-6314	350	126	κi+1	κi+1	X
ejpam-6314	350	127	)	)	PUNCT
ejpam-6314	350	128	<	<	X
ejpam-6314	351	1	1	1	NUM
ejpam-6314	351	2	ω	ω	NUM
ejpam-6314	351	3	where	where	SCONJ
ejpam-6314	351	4	κn+1	κn+1	NOUN
ejpam-6314	351	5	=	=	PUNCT
ejpam-6314	351	6	ψκn	ψκn	NOUN
ejpam-6314	351	7	and	and	CCONJ
ejpam-6314	351	8	for	for	ADP
ejpam-6314	351	9	each	each	DET
ejpam-6314	351	10	n	n	PRON
ejpam-6314	351	11	≥	≥	NOUN
ejpam-6314	351	12	0	0	NUM
ejpam-6314	351	13	.	.	PUNCT
ejpam-6314	351	14	assume	assume	VERB
ejpam-6314	351	15	further	far	ADV
ejpam-6314	351	16	,	,	PUNCT
ejpam-6314	351	17	that	that	SCONJ
ejpam-6314	351	18	for	for	ADP
ejpam-6314	351	19	every	every	DET
ejpam-6314	351	20	κ	κ	PROPN
ejpam-6314	351	21	∈	∈	PROPN
ejpam-6314	351	22	s	s	PART
ejpam-6314	351	23	,	,	PUNCT
ejpam-6314	351	24	we	we	PRON
ejpam-6314	351	25	have	have	AUX
ejpam-6314	351	26	limn→+∞	limn→+∞	VERB
ejpam-6314	351	27	ϑ(κn	ϑ(κn	PROPN
ejpam-6314	351	28	,	,	PUNCT
ejpam-6314	351	29	κ	κ	NOUN
ejpam-6314	351	30	)	)	PUNCT
ejpam-6314	351	31	and	and	CCONJ
ejpam-6314	351	32	limn→+∞	limn→+∞	PROPN
ejpam-6314	351	33	ϑ(κ	ϑ(κ	PROPN
ejpam-6314	351	34	,	,	PUNCT
ejpam-6314	351	35	κn	κn	NOUN
ejpam-6314	351	36	)	)	PUNCT
ejpam-6314	351	37	,	,	PUNCT
ejpam-6314	351	38	which	which	PRON
ejpam-6314	351	39	exist	exist	VERB
ejpam-6314	351	40	and	and	CCONJ
ejpam-6314	351	41	are	be	AUX
ejpam-6314	351	42	finite	finite	ADJ
ejpam-6314	351	43	.	.	PUNCT
ejpam-6314	352	1	then	then	ADV
ejpam-6314	352	2	,	,	PUNCT
ejpam-6314	352	3	ψ	ψ	X
ejpam-6314	352	4	have	have	VERB
ejpam-6314	352	5	a	a	DET
ejpam-6314	352	6	ufp	ufp	NOUN
ejpam-6314	352	7	.	.	PUNCT
ejpam-6314	353	1	proof	proof	NOUN
ejpam-6314	353	2	.	.	PUNCT
ejpam-6314	354	1	by	by	ADP
ejpam-6314	354	2	the	the	DET
ejpam-6314	354	3	corollary	corollary	ADJ
ejpam-6314	354	4	(	(	PUNCT
ejpam-6314	354	5	2	2	NUM
ejpam-6314	354	6	)	)	PUNCT
ejpam-6314	354	7	,	,	PUNCT
ejpam-6314	354	8	ψn	ψn	PUNCT
ejpam-6314	354	9	possess	possess	VERB
ejpam-6314	354	10	a	a	DET
ejpam-6314	354	11	unique	unique	ADJ
ejpam-6314	354	12	fixed	fix	VERB
ejpam-6314	354	13	point	point	NOUN
ejpam-6314	354	14	κ⋆.	κ⋆.	ADV
ejpam-6314	354	15	it	it	PRON
ejpam-6314	354	16	can	can	AUX
ejpam-6314	354	17	be	be	AUX
ejpam-6314	354	18	deduced	deduce	VERB
ejpam-6314	354	19	from	from	ADP
ejpam-6314	354	20	,	,	PUNCT
ejpam-6314	354	21	ψn(ψκ⋆	ψn(ψκ⋆	NOUN
ejpam-6314	354	22	)	)	PUNCT
ejpam-6314	354	23	=	=	PUNCT
ejpam-6314	354	24	ψ(ψnκ⋆	ψ(ψnκ⋆	X
ejpam-6314	354	25	)	)	PUNCT
ejpam-6314	354	26	=	=	VERB
ejpam-6314	355	1	ψκ⋆	ψκ⋆	NOUN
ejpam-6314	355	2	that	that	PRON
ejpam-6314	355	3	ψκ⋆	ψκ⋆	PROPN
ejpam-6314	355	4	is	be	AUX
ejpam-6314	355	5	a	a	DET
ejpam-6314	355	6	fixed	fix	VERB
ejpam-6314	355	7	point	point	NOUN
ejpam-6314	355	8	of	of	ADP
ejpam-6314	355	9	ψn	ψn	NOUN
ejpam-6314	355	10	.	.	PUNCT
ejpam-6314	356	1	thus	thus	ADV
ejpam-6314	356	2	ψκ⋆	ψκ⋆	PROPN
ejpam-6314	356	3	=	=	SYM
ejpam-6314	356	4	κ⋆	κ⋆	X
ejpam-6314	356	5	by	by	ADP
ejpam-6314	356	6	the	the	DET
ejpam-6314	356	7	uniqueness	uniqueness	NOUN
ejpam-6314	356	8	of	of	ADP
ejpam-6314	356	9	a	a	DET
ejpam-6314	356	10	fixed	fix	VERB
ejpam-6314	356	11	point	point	NOUN
ejpam-6314	356	12	of	of	ADP
ejpam-6314	356	13	κn	κn	NOUN
ejpam-6314	356	14	and	and	CCONJ
ejpam-6314	356	15	then	then	ADV
ejpam-6314	356	16	κ⋆	κ⋆	VERB
ejpam-6314	356	17	is	be	AUX
ejpam-6314	356	18	also	also	ADV
ejpam-6314	356	19	fixed	fix	VERB
ejpam-6314	356	20	point	point	NOUN
ejpam-6314	356	21	of	of	ADP
ejpam-6314	356	22	ψ	ψ	NOUN
ejpam-6314	356	23	.	.	PUNCT
ejpam-6314	357	1	as	as	ADP
ejpam-6314	357	2	a	a	DET
ejpam-6314	357	3	result	result	NOUN
ejpam-6314	357	4	,	,	PUNCT
ejpam-6314	357	5	since	since	SCONJ
ejpam-6314	357	6	the	the	DET
ejpam-6314	357	7	fixed	fix	VERB
ejpam-6314	357	8	point	point	NOUN
ejpam-6314	357	9	is	be	AUX
ejpam-6314	357	10	unique	unique	ADJ
ejpam-6314	357	11	so	so	SCONJ
ejpam-6314	357	12	it	it	PRON
ejpam-6314	357	13	is	be	AUX
ejpam-6314	357	14	the	the	DET
ejpam-6314	357	15	fixed	fixed	ADJ
ejpam-6314	357	16	point	point	NOUN
ejpam-6314	357	17	of	of	ADP
ejpam-6314	357	18	both	both	DET
ejpam-6314	357	19	ψ	ψ	X
ejpam-6314	357	20	and	and	CCONJ
ejpam-6314	357	21	ψn	ψn	INTJ
ejpam-6314	357	22	.	.	PUNCT
ejpam-6314	358	1	corollary	corollary	ADJ
ejpam-6314	358	2	6	6	NUM
ejpam-6314	358	3	.	.	PUNCT
ejpam-6314	359	1	let	let	VERB
ejpam-6314	359	2	(	(	PUNCT
ejpam-6314	359	3	s	s	X
ejpam-6314	359	4	,	,	PUNCT
ejpam-6314	359	5	ϑ	ϑ	NOUN
ejpam-6314	359	6	,	,	PUNCT
ejpam-6314	359	7	db)be	db)be	PROPN
ejpam-6314	359	8	a	a	DET
ejpam-6314	359	9	(	(	PUNCT
ejpam-6314	359	10	bcvms	bcvms	NOUN
ejpam-6314	359	11	)	)	PUNCT
ejpam-6314	359	12	which	which	PRON
ejpam-6314	359	13	is	be	AUX
ejpam-6314	359	14	complete	complete	ADJ
ejpam-6314	359	15	and	and	CCONJ
ejpam-6314	359	16	ψ	ψ	X
ejpam-6314	359	17	:	:	PUNCT
ejpam-6314	359	18	s	s	X
ejpam-6314	359	19	→	→	PUNCT
ejpam-6314	359	20	s.	s.	PROPN
ejpam-6314	359	21	if	if	SCONJ
ejpam-6314	359	22	there	there	PRON
ejpam-6314	359	23	exist	exist	VERB
ejpam-6314	359	24	µ	µ	NOUN
ejpam-6314	359	25	,	,	PUNCT
ejpam-6314	359	26	ν	ν	X
ejpam-6314	359	27	:	:	PUNCT
ejpam-6314	359	28	s	s	X
ejpam-6314	359	29	→	→	SYM
ejpam-6314	359	30	[	[	X
ejpam-6314	359	31	0	0	NUM
ejpam-6314	359	32	,	,	PUNCT
ejpam-6314	359	33	1	1	NUM
ejpam-6314	359	34	)	)	PUNCT
ejpam-6314	359	35	such	such	ADJ
ejpam-6314	359	36	that	that	PRON
ejpam-6314	359	37	:	:	PUNCT
ejpam-6314	359	38	m.	m.	NOUN
ejpam-6314	359	39	sarwar	sarwar	PROPN
ejpam-6314	359	40	et	et	PROPN
ejpam-6314	359	41	al	al	PROPN
ejpam-6314	359	42	.	.	PUNCT
ejpam-6314	359	43	/	/	SYM
ejpam-6314	359	44	eur	eur	PROPN
ejpam-6314	359	45	.	.	PUNCT
ejpam-6314	360	1	j.	j.	PROPN
ejpam-6314	360	2	pure	pure	PROPN
ejpam-6314	360	3	appl	appl	PROPN
ejpam-6314	360	4	.	.	PROPN
ejpam-6314	360	5	math	math	PROPN
ejpam-6314	360	6	,	,	PUNCT
ejpam-6314	360	7	18	18	NUM
ejpam-6314	360	8	(	(	PUNCT
ejpam-6314	360	9	3	3	NUM
ejpam-6314	360	10	)	)	PUNCT
ejpam-6314	360	11	(	(	PUNCT
ejpam-6314	360	12	2025	2025	NUM
ejpam-6314	360	13	)	)	PUNCT
ejpam-6314	360	14	,	,	PUNCT
ejpam-6314	360	15	6314	6314	NUM
ejpam-6314	360	16	18	18	NUM
ejpam-6314	360	17	of	of	ADP
ejpam-6314	360	18	28	28	NUM
ejpam-6314	360	19	db(ψ	db(ψ	NOUN
ejpam-6314	360	20	nκ	nκ	NOUN
ejpam-6314	360	21	,	,	PUNCT
ejpam-6314	360	22	ψnσ	ψnσ	NOUN
ejpam-6314	360	23	)	)	PUNCT
ejpam-6314	360	24	≾	≾	PROPN
ejpam-6314	360	25	κdb(κ	κdb(κ	PROPN
ejpam-6314	360	26	,	,	PUNCT
ejpam-6314	360	27	σ	σ	PROPN
ejpam-6314	360	28	)	)	PUNCT
ejpam-6314	361	1	+	+	CCONJ
ejpam-6314	361	2	νκ	νκ	ADP
ejpam-6314	361	3	db(κ	db(κ	NOUN
ejpam-6314	361	4	,	,	PUNCT
ejpam-6314	361	5	ψnκ)db(σ	ψnκ)db(σ	NOUN
ejpam-6314	361	6	,	,	PUNCT
ejpam-6314	361	7	ψnσ	ψnσ	NOUN
ejpam-6314	361	8	)	)	PUNCT
ejpam-6314	361	9	1	1	NUM
ejpam-6314	362	1	+	+	CCONJ
ejpam-6314	362	2	db(κ	db(κ	NUM
ejpam-6314	362	3	,	,	PUNCT
ejpam-6314	362	4	σ	σ	NOUN
ejpam-6314	362	5	)	)	PUNCT
ejpam-6314	362	6	for	for	ADP
ejpam-6314	362	7	all	all	DET
ejpam-6314	362	8	κ	κ	PROPN
ejpam-6314	362	9	,	,	PUNCT
ejpam-6314	362	10	σ	σ	PROPN
ejpam-6314	362	11	∈	∈	PROPN
ejpam-6314	362	12	s.	s.	PROPN
ejpam-6314	362	13	for	for	ADP
ejpam-6314	362	14	κ0	κ0	PRON
ejpam-6314	362	15	∈	∈	PROPN
ejpam-6314	362	16	s	s	PART
ejpam-6314	362	17	,	,	PUNCT
ejpam-6314	362	18	we	we	PRON
ejpam-6314	362	19	set	set	VERB
ejpam-6314	362	20	κ	κ	PRON
ejpam-6314	362	21	1−κ	1−κ	PROPN
ejpam-6314	362	22	=	=	SYM
ejpam-6314	362	23	ω	ω	PROPN
ejpam-6314	362	24	.	.	PUNCT
ejpam-6314	362	25	suppose	suppose	VERB
ejpam-6314	362	26	that	that	SCONJ
ejpam-6314	362	27	,	,	PUNCT
ejpam-6314	362	28	sup	sup	NOUN
ejpam-6314	362	29	m≥1	m≥1	PROPN
ejpam-6314	362	30	lim	lim	PROPN
ejpam-6314	362	31	i→+∞	i→+∞	PROPN
ejpam-6314	362	32	ϑ(κi+1,κi+2)ϑ(κi+1,κm	ϑ(κi+1,κi+2)ϑ(κi+1,κm	PUNCT
ejpam-6314	362	33	)	)	PUNCT
ejpam-6314	362	34	ϑ(κi	ϑ(κi	NOUN
ejpam-6314	362	35	,	,	PUNCT
ejpam-6314	362	36	κi+1	κi+1	X
ejpam-6314	362	37	)	)	PUNCT
ejpam-6314	362	38	<	<	X
ejpam-6314	363	1	1	1	NUM
ejpam-6314	363	2	ω	ω	NUM
ejpam-6314	363	3	where	where	SCONJ
ejpam-6314	363	4	κn+1	κn+1	NOUN
ejpam-6314	363	5	=	=	PUNCT
ejpam-6314	363	6	ψκn	ψκn	NOUN
ejpam-6314	363	7	and	and	CCONJ
ejpam-6314	363	8	for	for	ADP
ejpam-6314	363	9	each	each	DET
ejpam-6314	363	10	n	n	PRON
ejpam-6314	363	11	≥	≥	NOUN
ejpam-6314	363	12	0	0	NUM
ejpam-6314	363	13	.	.	PUNCT
ejpam-6314	363	14	assume	assume	VERB
ejpam-6314	363	15	further	far	ADV
ejpam-6314	363	16	,	,	PUNCT
ejpam-6314	363	17	that	that	SCONJ
ejpam-6314	363	18	for	for	ADP
ejpam-6314	363	19	every	every	DET
ejpam-6314	363	20	κ	κ	PROPN
ejpam-6314	363	21	∈	∈	PROPN
ejpam-6314	363	22	s	s	PART
ejpam-6314	363	23	,	,	PUNCT
ejpam-6314	363	24	we	we	PRON
ejpam-6314	363	25	have	have	AUX
ejpam-6314	363	26	limn→+∞	limn→+∞	VERB
ejpam-6314	363	27	ϑ(κn	ϑ(κn	PROPN
ejpam-6314	363	28	,	,	PUNCT
ejpam-6314	363	29	κ	κ	NOUN
ejpam-6314	363	30	)	)	PUNCT
ejpam-6314	363	31	and	and	CCONJ
ejpam-6314	363	32	limn→+∞	limn→+∞	PROPN
ejpam-6314	363	33	ϑ(κ	ϑ(κ	PROPN
ejpam-6314	363	34	,	,	PUNCT
ejpam-6314	363	35	κn	κn	NOUN
ejpam-6314	363	36	)	)	PUNCT
ejpam-6314	363	37	,	,	PUNCT
ejpam-6314	363	38	which	which	PRON
ejpam-6314	363	39	exist	exist	VERB
ejpam-6314	363	40	and	and	CCONJ
ejpam-6314	363	41	are	be	AUX
ejpam-6314	363	42	finite	finite	ADJ
ejpam-6314	363	43	.	.	PUNCT
ejpam-6314	364	1	then	then	ADV
ejpam-6314	364	2	,	,	PUNCT
ejpam-6314	364	3	ψ	ψ	X
ejpam-6314	364	4	have	have	VERB
ejpam-6314	364	5	a	a	DET
ejpam-6314	364	6	ufp	ufp	NOUN
ejpam-6314	364	7	.	.	PUNCT
ejpam-6314	365	1	proof	proof	NOUN
ejpam-6314	365	2	.	.	PUNCT
ejpam-6314	366	1	this	this	DET
ejpam-6314	366	2	result	result	NOUN
ejpam-6314	366	3	can	can	AUX
ejpam-6314	366	4	be	be	AUX
ejpam-6314	366	5	obtained	obtain	VERB
ejpam-6314	366	6	by	by	ADP
ejpam-6314	366	7	setting	set	VERB
ejpam-6314	366	8	µ(κ	µ(κ	NOUN
ejpam-6314	366	9	)	)	PUNCT
ejpam-6314	366	10	=	=	SYM
ejpam-6314	366	11	µ	µ	X
ejpam-6314	366	12	and	and	CCONJ
ejpam-6314	366	13	ν(κ	ν(κ	NOUN
ejpam-6314	366	14	)	)	PUNCT
ejpam-6314	367	1	=	=	PUNCT
ejpam-6314	367	2	ν	ν	NOUN
ejpam-6314	367	3	in	in	ADP
ejpam-6314	367	4	theorem	theorem	NOUN
ejpam-6314	367	5	(	(	PUNCT
ejpam-6314	367	6	5	5	NUM
ejpam-6314	367	7	)	)	PUNCT
ejpam-6314	367	8	.	.	PUNCT
ejpam-6314	368	1	example	example	NOUN
ejpam-6314	369	1	4	4	X
ejpam-6314	369	2	.	.	PUNCT
ejpam-6314	369	3	let	let	VERB
ejpam-6314	369	4	db	db	PART
ejpam-6314	369	5	be	be	AUX
ejpam-6314	369	6	a	a	DET
ejpam-6314	369	7	(	(	PUNCT
ejpam-6314	369	8	bcvms	bcvms	NOUN
ejpam-6314	369	9	)	)	PUNCT
ejpam-6314	369	10	defined	define	VERB
ejpam-6314	369	11	on	on	ADP
ejpam-6314	369	12	s	s	NOUN
ejpam-6314	369	13	=	=	PUNCT
ejpam-6314	369	14	{	{	PUNCT
ejpam-6314	369	15	0	0	NUM
ejpam-6314	369	16	,	,	PUNCT
ejpam-6314	369	17	1	1	NUM
ejpam-6314	369	18	,	,	PUNCT
ejpam-6314	369	19	2	2	NUM
ejpam-6314	369	20	}	}	PUNCT
ejpam-6314	369	21	such	such	ADJ
ejpam-6314	369	22	that	that	SCONJ
ejpam-6314	369	23	,	,	PUNCT
ejpam-6314	369	24	db(0	db(0	NOUN
ejpam-6314	369	25	,	,	PUNCT
ejpam-6314	369	26	1	1	NUM
ejpam-6314	369	27	)	)	PUNCT
ejpam-6314	369	28	=	=	VERB
ejpam-6314	370	1	db(1	db(1	VERB
ejpam-6314	370	2	,	,	PUNCT
ejpam-6314	370	3	2	2	NUM
ejpam-6314	370	4	)	)	PUNCT
ejpam-6314	370	5	=	=	SYM
ejpam-6314	370	6	1	1	NUM
ejpam-6314	370	7	+	+	NUM
ejpam-6314	370	8	i2	i2	PROPN
ejpam-6314	370	9	,	,	PUNCT
ejpam-6314	370	10	db(0	db(0	NOUN
ejpam-6314	370	11	,	,	PUNCT
ejpam-6314	370	12	2	2	NUM
ejpam-6314	370	13	)	)	PUNCT
ejpam-6314	370	14	=	=	SYM
ejpam-6314	370	15	4	4	NUM
ejpam-6314	370	16	+	+	SYM
ejpam-6314	370	17	4i2	4i2	NUM
ejpam-6314	370	18	.	.	PUNCT
ejpam-6314	371	1	where	where	SCONJ
ejpam-6314	371	2	ϑ	ϑ	X
ejpam-6314	371	3	:	:	PUNCT
ejpam-6314	371	4	s	s	VERB
ejpam-6314	371	5	×	×	PROPN
ejpam-6314	371	6	s	s	X
ejpam-6314	371	7	→	→	SYM
ejpam-6314	371	8	[	[	X
ejpam-6314	371	9	1,+∞	1,+∞	NUM
ejpam-6314	371	10	)	)	PUNCT
ejpam-6314	371	11	such	such	ADJ
ejpam-6314	371	12	that	that	SCONJ
ejpam-6314	371	13	ϑ(0	ϑ(0	NOUN
ejpam-6314	371	14	,	,	PUNCT
ejpam-6314	371	15	0	0	NUM
ejpam-6314	371	16	)	)	PUNCT
ejpam-6314	371	17	=	=	PUNCT
ejpam-6314	372	1	ϑ(1	ϑ(1	NOUN
ejpam-6314	372	2	,	,	PUNCT
ejpam-6314	372	3	1	1	NUM
ejpam-6314	372	4	)	)	PUNCT
ejpam-6314	372	5	=	=	SYM
ejpam-6314	372	6	ϑ(2	ϑ(2	PROPN
ejpam-6314	372	7	,	,	PUNCT
ejpam-6314	372	8	2	2	NUM
ejpam-6314	372	9	)	)	PUNCT
ejpam-6314	372	10	=	=	PUNCT
ejpam-6314	372	11	ϑ(1	ϑ(1	NOUN
ejpam-6314	372	12	,	,	PUNCT
ejpam-6314	372	13	2	2	NUM
ejpam-6314	372	14	)	)	PUNCT
ejpam-6314	372	15	=	=	SYM
ejpam-6314	372	16	1	1	NUM
ejpam-6314	372	17	,	,	PUNCT
ejpam-6314	372	18	ϑ(0	ϑ(0	PROPN
ejpam-6314	372	19	,	,	PUNCT
ejpam-6314	372	20	2	2	NUM
ejpam-6314	372	21	)	)	PUNCT
ejpam-6314	372	22	=	=	SYM
ejpam-6314	372	23	2	2	NUM
ejpam-6314	372	24	,	,	PUNCT
ejpam-6314	372	25	ϑ(0	ϑ(0	PROPN
ejpam-6314	372	26	,	,	PUNCT
ejpam-6314	372	27	1	1	NUM
ejpam-6314	372	28	)	)	PUNCT
ejpam-6314	372	29	=	=	SYM
ejpam-6314	372	30	3	3	NUM
ejpam-6314	372	31	2	2	NUM
ejpam-6314	372	32	.	.	PUNCT
ejpam-6314	373	1	let	let	VERB
ejpam-6314	373	2	ψ	ψ	X
ejpam-6314	373	3	:	:	PUNCT
ejpam-6314	373	4	s	s	X
ejpam-6314	373	5	→	→	SYM
ejpam-6314	373	6	s	s	X
ejpam-6314	373	7	as	as	ADP
ejpam-6314	373	8	ψ(0	ψ(0	NOUN
ejpam-6314	373	9	)	)	PUNCT
ejpam-6314	373	10	=	=	SYM
ejpam-6314	373	11	2	2	NUM
ejpam-6314	373	12	and	and	CCONJ
ejpam-6314	373	13	ψ(1	ψ(1	PRON
ejpam-6314	373	14	)	)	PUNCT
ejpam-6314	373	15	=	=	SYM
ejpam-6314	374	1	ψ(2	ψ(2	NOUN
ejpam-6314	374	2	)	)	PUNCT
ejpam-6314	374	3	=	=	SYM
ejpam-6314	375	1	1	1	X
ejpam-6314	375	2	.	.	X
ejpam-6314	375	3	consider	consider	VERB
ejpam-6314	375	4	,	,	PUNCT
ejpam-6314	375	5	µ	µ	X
ejpam-6314	375	6	=	=	SYM
ejpam-6314	375	7	1	1	NUM
ejpam-6314	375	8	11	11	NUM
ejpam-6314	375	9	and	and	CCONJ
ejpam-6314	375	10	ν	ν	X
ejpam-6314	375	11	=	=	PUNCT
ejpam-6314	375	12	γ	γ	X
ejpam-6314	375	13	=	=	SYM
ejpam-6314	375	14	3	3	NUM
ejpam-6314	375	15	11	11	NUM
ejpam-6314	375	16	,	,	PUNCT
ejpam-6314	375	17	and	and	CCONJ
ejpam-6314	375	18	κ0	κ0	PRON
ejpam-6314	375	19	=	=	SYM
ejpam-6314	375	20	0	0	NUM
ejpam-6314	375	21	,	,	PUNCT
ejpam-6314	375	22	then	then	ADV
ejpam-6314	375	23	κ1	κ1	NOUN
ejpam-6314	375	24	=	=	SYM
ejpam-6314	375	25	2	2	NUM
ejpam-6314	375	26	and	and	CCONJ
ejpam-6314	375	27	κn	κn	NOUN
ejpam-6314	375	28	=	=	NOUN
ejpam-6314	375	29	1	1	NUM
ejpam-6314	375	30	for	for	ADP
ejpam-6314	375	31	all	all	DET
ejpam-6314	375	32	n	n	PRON
ejpam-6314	375	33	≥	≥	NOUN
ejpam-6314	375	34	2	2	NUM
ejpam-6314	375	35	.	.	PUNCT
ejpam-6314	376	1	clearly	clearly	ADV
ejpam-6314	376	2	,	,	PUNCT
ejpam-6314	376	3	(	(	PUNCT
ejpam-6314	376	4	2	2	X
ejpam-6314	376	5	)	)	PUNCT
ejpam-6314	376	6	is	be	AUX
ejpam-6314	376	7	satisfied	satisfied	ADJ
ejpam-6314	376	8	.	.	PUNCT
ejpam-6314	377	1	now	now	ADV
ejpam-6314	377	2	,	,	PUNCT
ejpam-6314	377	3	we	we	PRON
ejpam-6314	377	4	take	take	VERB
ejpam-6314	377	5	different	different	ADJ
ejpam-6314	377	6	cases	case	NOUN
ejpam-6314	377	7	to	to	PART
ejpam-6314	377	8	check	check	VERB
ejpam-6314	377	9	that	that	PRON
ejpam-6314	377	10	(	(	PUNCT
ejpam-6314	377	11	1	1	X
ejpam-6314	377	12	)	)	PUNCT
ejpam-6314	377	13	is	be	AUX
ejpam-6314	377	14	also	also	ADV
ejpam-6314	377	15	satisfied	satisfied	ADJ
ejpam-6314	377	16	.	.	PUNCT
ejpam-6314	378	1	case	case	NOUN
ejpam-6314	379	1	i	i	PRON
ejpam-6314	379	2	:	:	PUNCT
ejpam-6314	379	3	if	if	SCONJ
ejpam-6314	379	4	κ	κ	X
ejpam-6314	379	5	=	=	SYM
ejpam-6314	379	6	σ	σ	PROPN
ejpam-6314	379	7	=	=	SYM
ejpam-6314	379	8	0	0	NUM
ejpam-6314	379	9	,	,	PUNCT
ejpam-6314	379	10	κ	κ	X
ejpam-6314	379	11	=	=	SYM
ejpam-6314	379	12	σ	σ	PROPN
ejpam-6314	379	13	=	=	SYM
ejpam-6314	379	14	1	1	NUM
ejpam-6314	379	15	,	,	PUNCT
ejpam-6314	379	16	κ	κ	X
ejpam-6314	379	17	=	=	SYM
ejpam-6314	379	18	σ	σ	PROPN
ejpam-6314	379	19	=	=	SYM
ejpam-6314	379	20	2	2	X
ejpam-6314	379	21	.	.	PUNCT
ejpam-6314	379	22	then	then	ADV
ejpam-6314	379	23	clearly	clearly	ADV
ejpam-6314	379	24	our	our	PRON
ejpam-6314	379	25	result	result	NOUN
ejpam-6314	379	26	can	can	AUX
ejpam-6314	379	27	be	be	AUX
ejpam-6314	379	28	obtained	obtain	VERB
ejpam-6314	379	29	.	.	PUNCT
ejpam-6314	380	1	case	case	NOUN
ejpam-6314	380	2	ii	ii	NOUN
ejpam-6314	380	3	:	:	PUNCT
ejpam-6314	380	4	if	if	SCONJ
ejpam-6314	380	5	κ	κ	X
ejpam-6314	380	6	=	=	SYM
ejpam-6314	380	7	0	0	NUM
ejpam-6314	380	8	and	and	CCONJ
ejpam-6314	380	9	σ	σ	NUM
ejpam-6314	380	10	=	=	NOUN
ejpam-6314	380	11	1	1	NUM
ejpam-6314	380	12	then	then	ADV
ejpam-6314	380	13	we	we	PRON
ejpam-6314	380	14	obtain	obtain	VERB
ejpam-6314	380	15	,	,	PUNCT
ejpam-6314	380	16	db(ψκ	db(ψκ	NOUN
ejpam-6314	380	17	,	,	PUNCT
ejpam-6314	380	18	ψσ	ψσ	ADJ
ejpam-6314	380	19	)	)	PUNCT
ejpam-6314	380	20	=	=	SYM
ejpam-6314	380	21	db(ψ(0	db(ψ(0	NOUN
ejpam-6314	380	22	)	)	PUNCT
ejpam-6314	380	23	,	,	PUNCT
ejpam-6314	380	24	ψ(1	ψ(1	PROPN
ejpam-6314	380	25	)	)	PUNCT
ejpam-6314	380	26	)	)	PUNCT
ejpam-6314	381	1	=	=	SYM
ejpam-6314	381	2	1	1	NUM
ejpam-6314	381	3	+	+	NUM
ejpam-6314	381	4	i2	i2	NOUN
ejpam-6314	381	5	,	,	PUNCT
ejpam-6314	381	6	db(κ	db(κ	NOUN
ejpam-6314	381	7	,	,	PUNCT
ejpam-6314	381	8	σ	σ	X
ejpam-6314	381	9	)	)	PUNCT
ejpam-6314	381	10	=	=	SYM
ejpam-6314	382	1	db(0	db(0	NOUN
ejpam-6314	382	2	,	,	PUNCT
ejpam-6314	382	3	1	1	NUM
ejpam-6314	382	4	)	)	PUNCT
ejpam-6314	382	5	=	=	SYM
ejpam-6314	382	6	1	1	NUM
ejpam-6314	382	7	+	+	NUM
ejpam-6314	382	8	i2	i2	PROPN
ejpam-6314	382	9	db(κ	db(κ	NUM
ejpam-6314	382	10	,	,	PUNCT
ejpam-6314	382	11	ψκ	ψκ	PROPN
ejpam-6314	382	12	)	)	PUNCT
ejpam-6314	382	13	=	=	SYM
ejpam-6314	382	14	db(0	db(0	PROPN
ejpam-6314	382	15	,	,	PUNCT
ejpam-6314	382	16	ψ(0	ψ(0	NOUN
ejpam-6314	382	17	)	)	PUNCT
ejpam-6314	382	18	)	)	PUNCT
ejpam-6314	383	1	=	=	PUNCT
ejpam-6314	383	2	4	4	NUM
ejpam-6314	383	3	+	+	SYM
ejpam-6314	383	4	4i2	4i2	NUM
ejpam-6314	383	5	,	,	PUNCT
ejpam-6314	383	6	db(σ	db(σ	NUM
ejpam-6314	383	7	,	,	PUNCT
ejpam-6314	383	8	ψσ	ψσ	ADJ
ejpam-6314	383	9	)	)	PUNCT
ejpam-6314	383	10	=	=	SYM
ejpam-6314	383	11	db(1	db(1	ADJ
ejpam-6314	383	12	,	,	PUNCT
ejpam-6314	383	13	ψ(1	ψ(1	PROPN
ejpam-6314	383	14	)	)	PUNCT
ejpam-6314	383	15	)	)	PUNCT
ejpam-6314	384	1	=	=	PUNCT
ejpam-6314	384	2	0	0	NUM
ejpam-6314	385	1	+	+	NUM
ejpam-6314	385	2	0i2	0i2	NOUN
ejpam-6314	385	3	.	.	PUNCT
ejpam-6314	386	1	db	db	PROPN
ejpam-6314	386	2	(	(	PUNCT
ejpam-6314	386	3	ψκ	ψκ	PROPN
ejpam-6314	386	4	,	,	PUNCT
ejpam-6314	386	5	ψσ	ψσ	ADJ
ejpam-6314	386	6	)	)	PUNCT
ejpam-6314	386	7	≾	≾	PROPN
ejpam-6314	386	8	µdb(κ	µdb(κ	PROPN
ejpam-6314	386	9	,	,	PUNCT
ejpam-6314	386	10	σ	σ	PROPN
ejpam-6314	386	11	)	)	PUNCT
ejpam-6314	387	1	+	+	NUM
ejpam-6314	387	2	νdb	νdb	NOUN
ejpam-6314	387	3	(	(	PUNCT
ejpam-6314	387	4	κ	κ	NOUN
ejpam-6314	387	5	,	,	PUNCT
ejpam-6314	387	6	ψκ	ψκ	PROPN
ejpam-6314	387	7	)	)	PUNCT
ejpam-6314	387	8	+	+	NUM
ejpam-6314	387	9	γdb	γdb	PROPN
ejpam-6314	387	10	(	(	PUNCT
ejpam-6314	387	11	σ	σ	NOUN
ejpam-6314	387	12	,	,	PUNCT
ejpam-6314	387	13	ψσ	ψσ	ADJ
ejpam-6314	387	14	)	)	PUNCT
ejpam-6314	387	15	,	,	PUNCT
ejpam-6314	387	16	the	the	DET
ejpam-6314	387	17	above	above	ADJ
ejpam-6314	387	18	distances	distance	NOUN
ejpam-6314	387	19	contraction	contraction	NOUN
ejpam-6314	387	20	condition	condition	NOUN
ejpam-6314	387	21	of	of	ADP
ejpam-6314	387	22	theorem	theorem	NOUN
ejpam-6314	387	23	(	(	PUNCT
ejpam-6314	387	24	3	3	NUM
ejpam-6314	387	25	)	)	PUNCT
ejpam-6314	387	26	by	by	ADP
ejpam-6314	387	27	using	use	VERB
ejpam-6314	387	28	the	the	DET
ejpam-6314	387	29	partial	partial	ADJ
ejpam-6314	387	30	order	order	NOUN
ejpam-6314	387	31	for	for	ADP
ejpam-6314	387	32	bcns	bcns	NOUN
ejpam-6314	387	33	,	,	PUNCT
ejpam-6314	387	34	thus	thus	ADV
ejpam-6314	387	35	the	the	DET
ejpam-6314	387	36	result	result	NOUN
ejpam-6314	387	37	is	be	AUX
ejpam-6314	387	38	obvious	obvious	ADJ
ejpam-6314	387	39	for	for	ADP
ejpam-6314	387	40	case(ii	case(ii	NOUN
ejpam-6314	387	41	)	)	PUNCT
ejpam-6314	387	42	.	.	PUNCT
ejpam-6314	388	1	m.	m.	NOUN
ejpam-6314	388	2	sarwar	sarwar	PROPN
ejpam-6314	388	3	et	et	PROPN
ejpam-6314	388	4	al	al	PROPN
ejpam-6314	388	5	.	.	PUNCT
ejpam-6314	388	6	/	/	SYM
ejpam-6314	388	7	eur	eur	PROPN
ejpam-6314	388	8	.	.	PUNCT
ejpam-6314	389	1	j.	j.	PROPN
ejpam-6314	389	2	pure	pure	PROPN
ejpam-6314	389	3	appl	appl	PROPN
ejpam-6314	389	4	.	.	PROPN
ejpam-6314	389	5	math	math	PROPN
ejpam-6314	389	6	,	,	PUNCT
ejpam-6314	389	7	18	18	NUM
ejpam-6314	389	8	(	(	PUNCT
ejpam-6314	389	9	3	3	NUM
ejpam-6314	389	10	)	)	PUNCT
ejpam-6314	389	11	(	(	PUNCT
ejpam-6314	389	12	2025	2025	NUM
ejpam-6314	389	13	)	)	PUNCT
ejpam-6314	389	14	,	,	PUNCT
ejpam-6314	389	15	6314	6314	NUM
ejpam-6314	389	16	19	19	NUM
ejpam-6314	389	17	of	of	ADP
ejpam-6314	389	18	28	28	NUM
ejpam-6314	389	19	case	case	NOUN
ejpam-6314	389	20	iii	iii	NOUN
ejpam-6314	389	21	:	:	PUNCT
ejpam-6314	389	22	if	if	SCONJ
ejpam-6314	389	23	κ	κ	X
ejpam-6314	389	24	=	=	SYM
ejpam-6314	389	25	0	0	NUM
ejpam-6314	389	26	and	and	CCONJ
ejpam-6314	389	27	σ	σ	NUM
ejpam-6314	389	28	=	=	SYM
ejpam-6314	389	29	2	2	NUM
ejpam-6314	389	30	then	then	ADV
ejpam-6314	389	31	we	we	PRON
ejpam-6314	389	32	obtain	obtain	VERB
ejpam-6314	389	33	,	,	PUNCT
ejpam-6314	389	34	db(ψκ	db(ψκ	NOUN
ejpam-6314	389	35	,	,	PUNCT
ejpam-6314	389	36	ψσ	ψσ	ADJ
ejpam-6314	389	37	)	)	PUNCT
ejpam-6314	389	38	=	=	SYM
ejpam-6314	389	39	db(ψ(0	db(ψ(0	NOUN
ejpam-6314	389	40	)	)	PUNCT
ejpam-6314	389	41	,	,	PUNCT
ejpam-6314	389	42	ψ(2	ψ(2	NOUN
ejpam-6314	389	43	)	)	PUNCT
ejpam-6314	389	44	)	)	PUNCT
ejpam-6314	390	1	=	=	SYM
ejpam-6314	390	2	1	1	NUM
ejpam-6314	390	3	+	+	NUM
ejpam-6314	390	4	i2	i2	NOUN
ejpam-6314	390	5	,	,	PUNCT
ejpam-6314	390	6	db(κ	db(κ	NOUN
ejpam-6314	390	7	,	,	PUNCT
ejpam-6314	390	8	σ	σ	X
ejpam-6314	390	9	)	)	PUNCT
ejpam-6314	390	10	=	=	SYM
ejpam-6314	391	1	db(0	db(0	NOUN
ejpam-6314	391	2	,	,	PUNCT
ejpam-6314	391	3	2	2	NUM
ejpam-6314	391	4	)	)	PUNCT
ejpam-6314	391	5	=	=	SYM
ejpam-6314	391	6	4	4	NUM
ejpam-6314	391	7	+	+	SYM
ejpam-6314	391	8	4i2	4i2	NUM
ejpam-6314	391	9	,	,	PUNCT
ejpam-6314	391	10	db(κ	db(κ	NUM
ejpam-6314	391	11	,	,	PUNCT
ejpam-6314	391	12	ψκ	ψκ	PROPN
ejpam-6314	391	13	)	)	PUNCT
ejpam-6314	391	14	=	=	SYM
ejpam-6314	391	15	db(0	db(0	PROPN
ejpam-6314	391	16	,	,	PUNCT
ejpam-6314	391	17	ψ(0	ψ(0	NOUN
ejpam-6314	391	18	)	)	PUNCT
ejpam-6314	391	19	)	)	PUNCT
ejpam-6314	392	1	=	=	PUNCT
ejpam-6314	392	2	4	4	NUM
ejpam-6314	392	3	+	+	SYM
ejpam-6314	392	4	4i2	4i2	NUM
ejpam-6314	392	5	,	,	PUNCT
ejpam-6314	392	6	db(σ	db(σ	NUM
ejpam-6314	392	7	,	,	PUNCT
ejpam-6314	392	8	ψσ	ψσ	ADJ
ejpam-6314	392	9	)	)	PUNCT
ejpam-6314	392	10	=	=	SYM
ejpam-6314	392	11	db(2	db(2	PROPN
ejpam-6314	392	12	,	,	PUNCT
ejpam-6314	392	13	ψ(2	ψ(2	NOUN
ejpam-6314	392	14	)	)	PUNCT
ejpam-6314	392	15	)	)	PUNCT
ejpam-6314	393	1	=	=	SYM
ejpam-6314	393	2	1	1	NUM
ejpam-6314	393	3	+	+	NUM
ejpam-6314	393	4	i2	i2	NOUN
ejpam-6314	393	5	.	.	PUNCT
ejpam-6314	394	1	db	db	PROPN
ejpam-6314	394	2	(	(	PUNCT
ejpam-6314	394	3	ψκ	ψκ	PROPN
ejpam-6314	394	4	,	,	PUNCT
ejpam-6314	394	5	ψσ	ψσ	ADJ
ejpam-6314	394	6	)	)	PUNCT
ejpam-6314	394	7	≾	≾	PROPN
ejpam-6314	394	8	µdb(κ	µdb(κ	PROPN
ejpam-6314	394	9	,	,	PUNCT
ejpam-6314	394	10	σ	σ	PROPN
ejpam-6314	394	11	)	)	PUNCT
ejpam-6314	395	1	+	+	NUM
ejpam-6314	395	2	νdb	νdb	NOUN
ejpam-6314	395	3	(	(	PUNCT
ejpam-6314	395	4	κ	κ	NOUN
ejpam-6314	395	5	,	,	PUNCT
ejpam-6314	395	6	ψκ	ψκ	PROPN
ejpam-6314	395	7	)	)	PUNCT
ejpam-6314	395	8	+	+	NUM
ejpam-6314	395	9	γdb	γdb	PROPN
ejpam-6314	395	10	(	(	PUNCT
ejpam-6314	395	11	σ	σ	NOUN
ejpam-6314	395	12	,	,	PUNCT
ejpam-6314	395	13	ψσ	ψσ	ADJ
ejpam-6314	395	14	)	)	PUNCT
ejpam-6314	395	15	,	,	PUNCT
ejpam-6314	395	16	the	the	DET
ejpam-6314	395	17	above	above	ADJ
ejpam-6314	395	18	distances	distance	NOUN
ejpam-6314	395	19	contraction	contraction	NOUN
ejpam-6314	395	20	condition	condition	NOUN
ejpam-6314	395	21	of	of	ADP
ejpam-6314	395	22	theorem	theorem	NOUN
ejpam-6314	395	23	(	(	PUNCT
ejpam-6314	395	24	3	3	NUM
ejpam-6314	395	25	)	)	PUNCT
ejpam-6314	395	26	by	by	ADP
ejpam-6314	395	27	using	use	VERB
ejpam-6314	395	28	the	the	DET
ejpam-6314	395	29	partial	partial	ADJ
ejpam-6314	395	30	order	order	NOUN
ejpam-6314	395	31	for	for	ADP
ejpam-6314	395	32	bcns	bcns	NOUN
ejpam-6314	395	33	,	,	PUNCT
ejpam-6314	395	34	thus	thus	ADV
ejpam-6314	395	35	the	the	DET
ejpam-6314	395	36	result	result	NOUN
ejpam-6314	395	37	is	be	AUX
ejpam-6314	395	38	obvious	obvious	ADJ
ejpam-6314	395	39	for	for	ADP
ejpam-6314	395	40	case(iii	case(iii	NOUN
ejpam-6314	395	41	)	)	PUNCT
ejpam-6314	395	42	.	.	PUNCT
ejpam-6314	396	1	case	case	NOUN
ejpam-6314	396	2	iv	iv	X
ejpam-6314	396	3	:	:	PUNCT
ejpam-6314	396	4	if	if	SCONJ
ejpam-6314	396	5	κ	κ	X
ejpam-6314	396	6	=	=	SYM
ejpam-6314	396	7	1	1	NUM
ejpam-6314	396	8	and	and	CCONJ
ejpam-6314	396	9	σ	σ	NUM
ejpam-6314	396	10	=	=	SYM
ejpam-6314	396	11	2	2	NUM
ejpam-6314	396	12	then	then	ADV
ejpam-6314	396	13	we	we	PRON
ejpam-6314	396	14	obtain	obtain	VERB
ejpam-6314	396	15	,	,	PUNCT
ejpam-6314	396	16	db(ψκ	db(ψκ	NOUN
ejpam-6314	396	17	,	,	PUNCT
ejpam-6314	396	18	ψσ	ψσ	ADJ
ejpam-6314	396	19	)	)	PUNCT
ejpam-6314	396	20	=	=	SYM
ejpam-6314	396	21	db(ψ(1	db(ψ(1	NOUN
ejpam-6314	396	22	)	)	PUNCT
ejpam-6314	396	23	,	,	PUNCT
ejpam-6314	396	24	ψ(2	ψ(2	NOUN
ejpam-6314	396	25	)	)	PUNCT
ejpam-6314	396	26	)	)	PUNCT
ejpam-6314	397	1	=	=	PUNCT
ejpam-6314	397	2	0	0	PUNCT
ejpam-6314	398	1	+	+	NUM
ejpam-6314	398	2	0i2	0i2	NOUN
ejpam-6314	398	3	,	,	PUNCT
ejpam-6314	398	4	db(κ	db(κ	NUM
ejpam-6314	398	5	,	,	PUNCT
ejpam-6314	398	6	σ	σ	X
ejpam-6314	398	7	)	)	PUNCT
ejpam-6314	398	8	=	=	PUNCT
ejpam-6314	398	9	db(1	db(1	VERB
ejpam-6314	398	10	,	,	PUNCT
ejpam-6314	398	11	2	2	NUM
ejpam-6314	398	12	)	)	PUNCT
ejpam-6314	398	13	=	=	SYM
ejpam-6314	399	1	1	1	NUM
ejpam-6314	399	2	+	+	NUM
ejpam-6314	399	3	i2	i2	NOUN
ejpam-6314	399	4	,	,	PUNCT
ejpam-6314	399	5	db(κ	db(κ	NOUN
ejpam-6314	399	6	,	,	PUNCT
ejpam-6314	399	7	ψκ	ψκ	PROPN
ejpam-6314	399	8	)	)	PUNCT
ejpam-6314	399	9	=	=	SYM
ejpam-6314	399	10	db(1	db(1	ADJ
ejpam-6314	399	11	,	,	PUNCT
ejpam-6314	399	12	ψ(1	ψ(1	PROPN
ejpam-6314	399	13	)	)	PUNCT
ejpam-6314	399	14	)	)	PUNCT
ejpam-6314	400	1	=	=	PUNCT
ejpam-6314	400	2	0	0	NUM
ejpam-6314	401	1	+	+	NUM
ejpam-6314	401	2	0i2	0i2	NOUN
ejpam-6314	401	3	,	,	PUNCT
ejpam-6314	401	4	db(σ	db(σ	NUM
ejpam-6314	401	5	,	,	PUNCT
ejpam-6314	401	6	ψσ	ψσ	ADJ
ejpam-6314	401	7	)	)	PUNCT
ejpam-6314	401	8	=	=	SYM
ejpam-6314	401	9	db(2	db(2	PROPN
ejpam-6314	401	10	,	,	PUNCT
ejpam-6314	401	11	ψ(2	ψ(2	NOUN
ejpam-6314	401	12	)	)	PUNCT
ejpam-6314	401	13	)	)	PUNCT
ejpam-6314	402	1	=	=	SYM
ejpam-6314	402	2	1	1	NUM
ejpam-6314	402	3	+	+	NUM
ejpam-6314	402	4	i2	i2	NOUN
ejpam-6314	402	5	.	.	PUNCT
ejpam-6314	403	1	db	db	PROPN
ejpam-6314	403	2	(	(	PUNCT
ejpam-6314	403	3	ψκ	ψκ	PROPN
ejpam-6314	403	4	,	,	PUNCT
ejpam-6314	403	5	ψσ	ψσ	ADJ
ejpam-6314	403	6	)	)	PUNCT
ejpam-6314	403	7	≾	≾	PROPN
ejpam-6314	403	8	µdb(κ	µdb(κ	PROPN
ejpam-6314	403	9	,	,	PUNCT
ejpam-6314	403	10	σ	σ	PROPN
ejpam-6314	403	11	)	)	PUNCT
ejpam-6314	404	1	+	+	NUM
ejpam-6314	404	2	νdb	νdb	NOUN
ejpam-6314	404	3	(	(	PUNCT
ejpam-6314	404	4	κ	κ	NOUN
ejpam-6314	404	5	,	,	PUNCT
ejpam-6314	404	6	ψκ	ψκ	PROPN
ejpam-6314	404	7	)	)	PUNCT
ejpam-6314	404	8	+	+	NUM
ejpam-6314	404	9	γdb	γdb	PROPN
ejpam-6314	404	10	(	(	PUNCT
ejpam-6314	404	11	σ	σ	NOUN
ejpam-6314	404	12	,	,	PUNCT
ejpam-6314	404	13	ψσ	ψσ	ADJ
ejpam-6314	404	14	)	)	PUNCT
ejpam-6314	404	15	,	,	PUNCT
ejpam-6314	404	16	the	the	DET
ejpam-6314	404	17	above	above	ADJ
ejpam-6314	404	18	distances	distance	NOUN
ejpam-6314	404	19	satisfies	satisfie	NOUN
ejpam-6314	404	20	contraction	contraction	NOUN
ejpam-6314	404	21	condition	condition	NOUN
ejpam-6314	404	22	of	of	ADP
ejpam-6314	404	23	theorem	theorem	NOUN
ejpam-6314	404	24	(	(	PUNCT
ejpam-6314	404	25	3	3	NUM
ejpam-6314	404	26	)	)	PUNCT
ejpam-6314	404	27	by	by	ADP
ejpam-6314	404	28	using	use	VERB
ejpam-6314	404	29	the	the	DET
ejpam-6314	404	30	partial	partial	ADJ
ejpam-6314	404	31	order	order	NOUN
ejpam-6314	404	32	for	for	ADP
ejpam-6314	404	33	bcns	bcns	NOUN
ejpam-6314	404	34	,	,	PUNCT
ejpam-6314	404	35	thus	thus	ADV
ejpam-6314	404	36	the	the	DET
ejpam-6314	404	37	result	result	NOUN
ejpam-6314	404	38	is	be	AUX
ejpam-6314	404	39	also	also	ADV
ejpam-6314	404	40	obvious	obvious	ADJ
ejpam-6314	404	41	for	for	ADP
ejpam-6314	404	42	case(iv	case(iv	NOUN
ejpam-6314	404	43	)	)	PUNCT
ejpam-6314	404	44	.	.	PUNCT
ejpam-6314	405	1	therefore	therefore	ADV
ejpam-6314	405	2	,	,	PUNCT
ejpam-6314	405	3	all	all	DET
ejpam-6314	405	4	the	the	DET
ejpam-6314	405	5	necessities	necessity	NOUN
ejpam-6314	405	6	of	of	ADP
ejpam-6314	405	7	the	the	DET
ejpam-6314	405	8	theorem	theorem	NOUN
ejpam-6314	405	9	(	(	PUNCT
ejpam-6314	405	10	3	3	X
ejpam-6314	405	11	)	)	PUNCT
ejpam-6314	405	12	are	be	AUX
ejpam-6314	405	13	true	true	ADJ
ejpam-6314	405	14	for	for	SCONJ
ejpam-6314	405	15	all	all	DET
ejpam-6314	405	16	the	the	DET
ejpam-6314	405	17	cases	case	NOUN
ejpam-6314	405	18	so	so	SCONJ
ejpam-6314	405	19	ψ	ψ	NOUN
ejpam-6314	405	20	has	have	VERB
ejpam-6314	405	21	a	a	DET
ejpam-6314	405	22	unique	unique	ADJ
ejpam-6314	405	23	fixed	fix	VERB
ejpam-6314	405	24	point	point	NOUN
ejpam-6314	405	25	.	.	PUNCT
ejpam-6314	405	26	example	example	NOUN
ejpam-6314	406	1	5	5	NUM
ejpam-6314	406	2	.	.	PUNCT
ejpam-6314	406	3	let	let	VERB
ejpam-6314	406	4	db	db	PART
ejpam-6314	406	5	be	be	AUX
ejpam-6314	406	6	a	a	DET
ejpam-6314	406	7	(	(	PUNCT
ejpam-6314	406	8	bcvms	bcvms	NOUN
ejpam-6314	406	9	)	)	PUNCT
ejpam-6314	406	10	defined	define	VERB
ejpam-6314	406	11	on	on	ADP
ejpam-6314	406	12	s	s	NOUN
ejpam-6314	406	13	=	=	PUNCT
ejpam-6314	406	14	{	{	PUNCT
ejpam-6314	406	15	0	0	NUM
ejpam-6314	406	16	,	,	PUNCT
ejpam-6314	406	17	1	1	NUM
ejpam-6314	406	18	,	,	PUNCT
ejpam-6314	406	19	2	2	NUM
ejpam-6314	406	20	}	}	PUNCT
ejpam-6314	406	21	such	such	ADJ
ejpam-6314	406	22	that	that	SCONJ
ejpam-6314	406	23	,	,	PUNCT
ejpam-6314	406	24	db(0	db(0	NOUN
ejpam-6314	406	25	,	,	PUNCT
ejpam-6314	406	26	1	1	NUM
ejpam-6314	406	27	)	)	PUNCT
ejpam-6314	406	28	=	=	SYM
ejpam-6314	407	1	60	60	NUM
ejpam-6314	407	2	+	+	NUM
ejpam-6314	407	3	60i2	60i2	NUM
ejpam-6314	407	4	,	,	PUNCT
ejpam-6314	407	5	db(1	db(1	NOUN
ejpam-6314	407	6	,	,	PUNCT
ejpam-6314	407	7	2	2	NUM
ejpam-6314	407	8	)	)	PUNCT
ejpam-6314	407	9	=	=	SYM
ejpam-6314	408	1	1	1	NUM
ejpam-6314	408	2	+	+	NUM
ejpam-6314	408	3	i2	i2	PROPN
ejpam-6314	408	4	and	and	CCONJ
ejpam-6314	408	5	db(0	db(0	PROPN
ejpam-6314	408	6	,	,	PUNCT
ejpam-6314	408	7	2	2	NUM
ejpam-6314	408	8	)	)	PUNCT
ejpam-6314	408	9	=	=	SYM
ejpam-6314	408	10	90	90	NUM
ejpam-6314	409	1	+	+	NUM
ejpam-6314	409	2	90i2	90i2	NUM
ejpam-6314	409	3	.	.	PUNCT
ejpam-6314	410	1	where	where	SCONJ
ejpam-6314	410	2	ϑ	ϑ	X
ejpam-6314	410	3	:	:	PUNCT
ejpam-6314	410	4	s	s	VERB
ejpam-6314	410	5	×	×	PROPN
ejpam-6314	410	6	s	s	X
ejpam-6314	410	7	→	→	SYM
ejpam-6314	410	8	[	[	X
ejpam-6314	410	9	1,+∞	1,+∞	NUM
ejpam-6314	410	10	)	)	PUNCT
ejpam-6314	410	11	such	such	ADJ
ejpam-6314	410	12	that	that	SCONJ
ejpam-6314	410	13	,	,	PUNCT
ejpam-6314	410	14	ϑ(0	ϑ(0	PROPN
ejpam-6314	410	15	,	,	PUNCT
ejpam-6314	410	16	0	0	NUM
ejpam-6314	410	17	)	)	PUNCT
ejpam-6314	410	18	=	=	PUNCT
ejpam-6314	411	1	ϑ(1	ϑ(1	NOUN
ejpam-6314	411	2	,	,	PUNCT
ejpam-6314	411	3	1	1	NUM
ejpam-6314	411	4	)	)	PUNCT
ejpam-6314	411	5	=	=	SYM
ejpam-6314	411	6	ϑ(2	ϑ(2	PROPN
ejpam-6314	411	7	,	,	PUNCT
ejpam-6314	411	8	2	2	NUM
ejpam-6314	411	9	)	)	PUNCT
ejpam-6314	411	10	=	=	PUNCT
ejpam-6314	411	11	ϑ(1	ϑ(1	NOUN
ejpam-6314	411	12	,	,	PUNCT
ejpam-6314	411	13	2	2	NUM
ejpam-6314	411	14	)	)	PUNCT
ejpam-6314	411	15	=	=	SYM
ejpam-6314	411	16	1	1	NUM
ejpam-6314	411	17	,	,	PUNCT
ejpam-6314	411	18	ϑ(0	ϑ(0	PROPN
ejpam-6314	411	19	,	,	PUNCT
ejpam-6314	411	20	2	2	NUM
ejpam-6314	411	21	)	)	PUNCT
ejpam-6314	411	22	=	=	SYM
ejpam-6314	411	23	2	2	NUM
ejpam-6314	411	24	,	,	PUNCT
ejpam-6314	411	25	ϑ(0	ϑ(0	PROPN
ejpam-6314	411	26	,	,	PUNCT
ejpam-6314	411	27	1	1	NUM
ejpam-6314	411	28	)	)	PUNCT
ejpam-6314	411	29	=	=	SYM
ejpam-6314	411	30	3	3	NUM
ejpam-6314	411	31	2	2	NUM
ejpam-6314	411	32	.	.	PUNCT
ejpam-6314	412	1	let	let	VERB
ejpam-6314	412	2	φ	φ	NUM
ejpam-6314	412	3	,	,	PUNCT
ejpam-6314	412	4	ψ	ψ	X
ejpam-6314	412	5	:	:	PUNCT
ejpam-6314	412	6	s	s	X
ejpam-6314	412	7	→	→	SYM
ejpam-6314	412	8	s	s	X
ejpam-6314	412	9	as	as	ADP
ejpam-6314	412	10	ψ(0	ψ(0	NOUN
ejpam-6314	412	11	)	)	PUNCT
ejpam-6314	412	12	=	=	SYM
ejpam-6314	413	1	φ(0	φ(0	ADJ
ejpam-6314	413	2	)	)	PUNCT
ejpam-6314	413	3	=	=	SYM
ejpam-6314	413	4	1	1	NUM
ejpam-6314	413	5	and	and	CCONJ
ejpam-6314	413	6	ψ(1	ψ(1	PRON
ejpam-6314	413	7	)	)	PUNCT
ejpam-6314	413	8	=	=	SYM
ejpam-6314	413	9	φ(1	φ(1	PROPN
ejpam-6314	413	10	)	)	PUNCT
ejpam-6314	413	11	=	=	SYM
ejpam-6314	414	1	ψ(2	ψ(2	NOUN
ejpam-6314	414	2	)	)	PUNCT
ejpam-6314	414	3	=	=	SYM
ejpam-6314	414	4	φ(2	φ(2	PROPN
ejpam-6314	414	5	)	)	PUNCT
ejpam-6314	415	1	=	=	SYM
ejpam-6314	415	2	2	2	X
ejpam-6314	415	3	.	.	X
ejpam-6314	415	4	consider	consider	VERB
ejpam-6314	415	5	,	,	PUNCT
ejpam-6314	415	6	µ(κ	µ(κ	PROPN
ejpam-6314	415	7	)	)	PUNCT
ejpam-6314	415	8	=	=	PUNCT
ejpam-6314	415	9	(	(	PUNCT
ejpam-6314	415	10	κ−3)2	κ−3)2	PROPN
ejpam-6314	415	11	30	30	NUM
ejpam-6314	415	12	and	and	CCONJ
ejpam-6314	415	13	ν(κ	ν(κ	NOUN
ejpam-6314	415	14	)	)	PUNCT
ejpam-6314	416	1	=	=	PRON
ejpam-6314	416	2	(	(	PUNCT
ejpam-6314	416	3	κ−3)2	κ−3)2	PROPN
ejpam-6314	416	4	20	20	NUM
ejpam-6314	416	5	,	,	PUNCT
ejpam-6314	416	6	and	and	CCONJ
ejpam-6314	416	7	κ0	κ0	NOUN
ejpam-6314	416	8	=	=	SYM
ejpam-6314	416	9	0	0	NUM
ejpam-6314	416	10	,	,	PUNCT
ejpam-6314	416	11	then	then	ADV
ejpam-6314	416	12	κ1	κ1	NOUN
ejpam-6314	416	13	=	=	SYM
ejpam-6314	416	14	2	2	NUM
ejpam-6314	416	15	and	and	CCONJ
ejpam-6314	416	16	κn	κn	NOUN
ejpam-6314	416	17	=	=	NOUN
ejpam-6314	416	18	1	1	NUM
ejpam-6314	416	19	for	for	ADP
ejpam-6314	416	20	all	all	DET
ejpam-6314	416	21	n	n	PRON
ejpam-6314	416	22	≥	≥	NOUN
ejpam-6314	416	23	2	2	NUM
ejpam-6314	416	24	.	.	PUNCT
ejpam-6314	416	25	clearly	clearly	ADV
ejpam-6314	416	26	,	,	PUNCT
ejpam-6314	416	27	condition(i),(ii),(iii	condition(i),(ii),(iii	X
ejpam-6314	416	28	)	)	PUNCT
ejpam-6314	416	29	and	and	CCONJ
ejpam-6314	416	30	(	(	PUNCT
ejpam-6314	416	31	15	15	NUM
ejpam-6314	416	32	)	)	PUNCT
ejpam-6314	416	33	are	be	AUX
ejpam-6314	416	34	satisfied	satisfied	ADJ
ejpam-6314	416	35	.	.	PUNCT
ejpam-6314	417	1	now	now	ADV
ejpam-6314	417	2	,	,	PUNCT
ejpam-6314	417	3	we	we	PRON
ejpam-6314	417	4	take	take	VERB
ejpam-6314	417	5	different	different	ADJ
ejpam-6314	417	6	cases	case	NOUN
ejpam-6314	417	7	to	to	PART
ejpam-6314	417	8	check	check	VERB
ejpam-6314	417	9	that	that	PRON
ejpam-6314	417	10	(	(	PUNCT
ejpam-6314	417	11	14	14	NUM
ejpam-6314	417	12	)	)	PUNCT
ejpam-6314	417	13	is	be	AUX
ejpam-6314	417	14	also	also	ADV
ejpam-6314	417	15	satisfied	satisfied	ADJ
ejpam-6314	417	16	.	.	PUNCT
ejpam-6314	418	1	case	case	NOUN
ejpam-6314	419	1	i	i	PRON
ejpam-6314	419	2	:	:	PUNCT
ejpam-6314	419	3	m.	m.	PROPN
ejpam-6314	419	4	sarwar	sarwar	PROPN
ejpam-6314	419	5	et	et	PROPN
ejpam-6314	419	6	al	al	PROPN
ejpam-6314	419	7	.	.	PUNCT
ejpam-6314	419	8	/	/	SYM
ejpam-6314	419	9	eur	eur	PROPN
ejpam-6314	419	10	.	.	PUNCT
ejpam-6314	420	1	j.	j.	PROPN
ejpam-6314	420	2	pure	pure	PROPN
ejpam-6314	420	3	appl	appl	PROPN
ejpam-6314	420	4	.	.	PROPN
ejpam-6314	420	5	math	math	PROPN
ejpam-6314	420	6	,	,	PUNCT
ejpam-6314	420	7	18	18	NUM
ejpam-6314	420	8	(	(	PUNCT
ejpam-6314	420	9	3	3	NUM
ejpam-6314	420	10	)	)	PUNCT
ejpam-6314	420	11	(	(	PUNCT
ejpam-6314	420	12	2025	2025	NUM
ejpam-6314	420	13	)	)	PUNCT
ejpam-6314	420	14	,	,	PUNCT
ejpam-6314	420	15	6314	6314	NUM
ejpam-6314	420	16	20	20	NUM
ejpam-6314	420	17	of	of	ADP
ejpam-6314	420	18	28	28	NUM
ejpam-6314	420	19	if	if	SCONJ
ejpam-6314	420	20	κ	κ	X
ejpam-6314	420	21	=	=	SYM
ejpam-6314	420	22	σ	σ	PROPN
ejpam-6314	420	23	=	=	SYM
ejpam-6314	420	24	0	0	NUM
ejpam-6314	420	25	,	,	PUNCT
ejpam-6314	420	26	κ	κ	X
ejpam-6314	420	27	=	=	SYM
ejpam-6314	420	28	σ	σ	PROPN
ejpam-6314	420	29	=	=	SYM
ejpam-6314	420	30	1	1	NUM
ejpam-6314	420	31	,	,	PUNCT
ejpam-6314	420	32	κ	κ	X
ejpam-6314	420	33	=	=	SYM
ejpam-6314	420	34	σ	σ	PROPN
ejpam-6314	420	35	=	=	SYM
ejpam-6314	420	36	2	2	X
ejpam-6314	420	37	.	.	PUNCT
ejpam-6314	421	1	then	then	ADV
ejpam-6314	421	2	clearly	clearly	ADV
ejpam-6314	421	3	our	our	PRON
ejpam-6314	421	4	result	result	NOUN
ejpam-6314	421	5	can	can	AUX
ejpam-6314	421	6	be	be	AUX
ejpam-6314	421	7	obtained	obtain	VERB
ejpam-6314	421	8	.	.	PUNCT
ejpam-6314	422	1	case	case	NOUN
ejpam-6314	422	2	ii	ii	NOUN
ejpam-6314	422	3	:	:	PUNCT
ejpam-6314	422	4	if	if	SCONJ
ejpam-6314	422	5	κ	κ	X
ejpam-6314	422	6	=	=	SYM
ejpam-6314	422	7	0	0	NUM
ejpam-6314	422	8	and	and	CCONJ
ejpam-6314	422	9	σ	σ	NUM
ejpam-6314	422	10	=	=	NOUN
ejpam-6314	422	11	1	1	NUM
ejpam-6314	422	12	then	then	ADV
ejpam-6314	422	13	we	we	PRON
ejpam-6314	422	14	obtain	obtain	VERB
ejpam-6314	422	15	db(φκ	db(φκ	NOUN
ejpam-6314	422	16	,	,	PUNCT
ejpam-6314	422	17	ψσ	ψσ	ADJ
ejpam-6314	422	18	)	)	PUNCT
ejpam-6314	422	19	=	=	SYM
ejpam-6314	422	20	db(φ(0),ψ(1	db(φ(0),ψ(1	X
ejpam-6314	422	21	)	)	PUNCT
ejpam-6314	422	22	)	)	PUNCT
ejpam-6314	423	1	=	=	SYM
ejpam-6314	423	2	1	1	NUM
ejpam-6314	423	3	+	+	NUM
ejpam-6314	423	4	i2	i2	NOUN
ejpam-6314	423	5	,	,	PUNCT
ejpam-6314	423	6	db(κ	db(κ	NOUN
ejpam-6314	423	7	,	,	PUNCT
ejpam-6314	423	8	σ	σ	X
ejpam-6314	423	9	)	)	PUNCT
ejpam-6314	423	10	=	=	SYM
ejpam-6314	424	1	db(0	db(0	NOUN
ejpam-6314	424	2	,	,	PUNCT
ejpam-6314	424	3	1	1	NUM
ejpam-6314	424	4	)	)	PUNCT
ejpam-6314	424	5	=	=	SYM
ejpam-6314	425	1	60	60	NUM
ejpam-6314	425	2	+	+	NUM
ejpam-6314	425	3	60i2	60i2	NUM
ejpam-6314	425	4	,	,	PUNCT
ejpam-6314	425	5	db(σ	db(σ	NUM
ejpam-6314	425	6	,	,	PUNCT
ejpam-6314	425	7	ψσ	ψσ	ADJ
ejpam-6314	425	8	)	)	PUNCT
ejpam-6314	425	9	=	=	PRON
ejpam-6314	425	10	db(1,ψ(1	db(1,ψ(1	X
ejpam-6314	425	11	)	)	PUNCT
ejpam-6314	425	12	)	)	PUNCT
ejpam-6314	426	1	=	=	SYM
ejpam-6314	426	2	1	1	NUM
ejpam-6314	426	3	+	+	NUM
ejpam-6314	426	4	i2	i2	NOUN
ejpam-6314	426	5	,	,	PUNCT
ejpam-6314	426	6	db(κ	db(κ	NOUN
ejpam-6314	426	7	,	,	PUNCT
ejpam-6314	426	8	ϕκ	ϕκ	X
ejpam-6314	426	9	)	)	PUNCT
ejpam-6314	426	10	=	=	SYM
ejpam-6314	426	11	db(0,φ(0	db(0,φ(0	NOUN
ejpam-6314	426	12	)	)	PUNCT
ejpam-6314	426	13	)	)	PUNCT
ejpam-6314	427	1	=	=	PUNCT
ejpam-6314	428	1	60	60	NUM
ejpam-6314	428	2	+	+	NUM
ejpam-6314	428	3	60i2	60i2	NUM
ejpam-6314	428	4	.	.	PUNCT
ejpam-6314	429	1	db(φκ	db(φκ	NOUN
ejpam-6314	429	2	,	,	PUNCT
ejpam-6314	429	3	ψσ	ψσ	ADJ
ejpam-6314	429	4	)	)	PUNCT
ejpam-6314	429	5	≾	≾	PROPN
ejpam-6314	429	6	µ(κ)db(κ	µ(κ)db(κ	NOUN
ejpam-6314	429	7	,	,	PUNCT
ejpam-6314	429	8	σ	σ	NOUN
ejpam-6314	429	9	)	)	PUNCT
ejpam-6314	429	10	+	+	NUM
ejpam-6314	429	11	ν(κ	ν(κ	NOUN
ejpam-6314	429	12	)	)	PUNCT
ejpam-6314	429	13	db(κ	db(κ	NOUN
ejpam-6314	429	14	,	,	PUNCT
ejpam-6314	429	15	φκ)db(σ	φκ)db(σ	NOUN
ejpam-6314	429	16	,	,	PUNCT
ejpam-6314	429	17	ψσ	ψσ	ADJ
ejpam-6314	429	18	)	)	PUNCT
ejpam-6314	429	19	1	1	NUM
ejpam-6314	429	20	+	+	CCONJ
ejpam-6314	429	21	db(κ	db(κ	NUM
ejpam-6314	429	22	,	,	PUNCT
ejpam-6314	429	23	σ	σ	PROPN
ejpam-6314	429	24	)	)	PUNCT
ejpam-6314	429	25	the	the	DET
ejpam-6314	429	26	above	above	ADJ
ejpam-6314	429	27	distances	distance	NOUN
ejpam-6314	429	28	satisfies	satisfy	VERB
ejpam-6314	429	29	the	the	DET
ejpam-6314	429	30	contraction	contraction	NOUN
ejpam-6314	429	31	for	for	ADP
ejpam-6314	429	32	theorem	theorem	NOUN
ejpam-6314	429	33	(	(	PUNCT
ejpam-6314	429	34	4	4	NUM
ejpam-6314	429	35	)	)	PUNCT
ejpam-6314	429	36	by	by	ADP
ejpam-6314	429	37	using	use	VERB
ejpam-6314	429	38	type	type	NOUN
ejpam-6314	429	39	partial	partial	ADJ
ejpam-6314	429	40	order	order	NOUN
ejpam-6314	429	41	for	for	ADP
ejpam-6314	429	42	bcns	bcns	NOUN
ejpam-6314	429	43	,	,	PUNCT
ejpam-6314	429	44	thus	thus	ADV
ejpam-6314	429	45	the	the	DET
ejpam-6314	429	46	result	result	NOUN
ejpam-6314	429	47	is	be	AUX
ejpam-6314	429	48	obvious	obvious	ADJ
ejpam-6314	429	49	for	for	ADP
ejpam-6314	429	50	case(ii	case(ii	NOUN
ejpam-6314	429	51	)	)	PUNCT
ejpam-6314	429	52	.	.	PUNCT
ejpam-6314	430	1	case	case	NOUN
ejpam-6314	430	2	iii	iii	X
ejpam-6314	430	3	:	:	PUNCT
ejpam-6314	430	4	if	if	SCONJ
ejpam-6314	430	5	κ	κ	X
ejpam-6314	430	6	=	=	SYM
ejpam-6314	430	7	0	0	NUM
ejpam-6314	430	8	and	and	CCONJ
ejpam-6314	430	9	σ	σ	NUM
ejpam-6314	430	10	=	=	SYM
ejpam-6314	430	11	2	2	NUM
ejpam-6314	430	12	then	then	ADV
ejpam-6314	430	13	we	we	PRON
ejpam-6314	430	14	obtain	obtain	VERB
ejpam-6314	430	15	db(φκ	db(φκ	NOUN
ejpam-6314	430	16	,	,	PUNCT
ejpam-6314	430	17	ψσ	ψσ	ADJ
ejpam-6314	430	18	)	)	PUNCT
ejpam-6314	430	19	=	=	SYM
ejpam-6314	430	20	db(φ(0),ψ(2	db(φ(0),ψ(2	NOUN
ejpam-6314	430	21	)	)	PUNCT
ejpam-6314	430	22	)	)	PUNCT
ejpam-6314	431	1	=	=	SYM
ejpam-6314	431	2	1	1	NUM
ejpam-6314	431	3	+	+	NUM
ejpam-6314	431	4	i2	i2	NOUN
ejpam-6314	431	5	,	,	PUNCT
ejpam-6314	431	6	db(κ	db(κ	NOUN
ejpam-6314	431	7	,	,	PUNCT
ejpam-6314	431	8	σ	σ	X
ejpam-6314	431	9	)	)	PUNCT
ejpam-6314	431	10	=	=	SYM
ejpam-6314	432	1	db(0	db(0	NOUN
ejpam-6314	432	2	,	,	PUNCT
ejpam-6314	432	3	2	2	NUM
ejpam-6314	432	4	)	)	PUNCT
ejpam-6314	432	5	=	=	SYM
ejpam-6314	432	6	90	90	NUM
ejpam-6314	433	1	+	+	NUM
ejpam-6314	433	2	90i2	90i2	NUM
ejpam-6314	433	3	,	,	PUNCT
ejpam-6314	433	4	db(κ	db(κ	NOUN
ejpam-6314	433	5	,	,	PUNCT
ejpam-6314	433	6	φκ	φκ	ADJ
ejpam-6314	433	7	)	)	PUNCT
ejpam-6314	433	8	=	=	SYM
ejpam-6314	433	9	db(0,φ(0	db(0,φ(0	NOUN
ejpam-6314	433	10	)	)	PUNCT
ejpam-6314	433	11	)	)	PUNCT
ejpam-6314	434	1	=	=	PUNCT
ejpam-6314	435	1	60	60	NUM
ejpam-6314	435	2	+	+	NUM
ejpam-6314	435	3	60i2	60i2	NUM
ejpam-6314	435	4	,	,	PUNCT
ejpam-6314	435	5	db(σ	db(σ	NUM
ejpam-6314	435	6	,	,	PUNCT
ejpam-6314	435	7	ψσ	ψσ	ADJ
ejpam-6314	435	8	)	)	PUNCT
ejpam-6314	435	9	=	=	SYM
ejpam-6314	435	10	db(2	db(2	PROPN
ejpam-6314	435	11	,	,	PUNCT
ejpam-6314	435	12	ψ(2	ψ(2	NOUN
ejpam-6314	435	13	)	)	PUNCT
ejpam-6314	435	14	)	)	PUNCT
ejpam-6314	436	1	=	=	PUNCT
ejpam-6314	436	2	0	0	NUM
ejpam-6314	437	1	+	+	NUM
ejpam-6314	437	2	0i2	0i2	NOUN
ejpam-6314	437	3	.	.	PUNCT
ejpam-6314	438	1	db(φκ	db(φκ	NOUN
ejpam-6314	438	2	,	,	PUNCT
ejpam-6314	438	3	ψσ	ψσ	ADJ
ejpam-6314	438	4	)	)	PUNCT
ejpam-6314	438	5	≾	≾	PROPN
ejpam-6314	438	6	µ(κ)db(κ	µ(κ)db(κ	NOUN
ejpam-6314	438	7	,	,	PUNCT
ejpam-6314	438	8	σ	σ	NOUN
ejpam-6314	438	9	)	)	PUNCT
ejpam-6314	438	10	+	+	NUM
ejpam-6314	438	11	ν(κ	ν(κ	NOUN
ejpam-6314	438	12	)	)	PUNCT
ejpam-6314	438	13	db(κ	db(κ	NOUN
ejpam-6314	438	14	,	,	PUNCT
ejpam-6314	438	15	φκ)db(σ	φκ)db(σ	NOUN
ejpam-6314	438	16	,	,	PUNCT
ejpam-6314	438	17	ψσ	ψσ	ADJ
ejpam-6314	438	18	)	)	PUNCT
ejpam-6314	438	19	1	1	NUM
ejpam-6314	438	20	+	+	CCONJ
ejpam-6314	438	21	db(κ	db(κ	NUM
ejpam-6314	438	22	,	,	PUNCT
ejpam-6314	438	23	σ	σ	PROPN
ejpam-6314	438	24	)	)	PUNCT
ejpam-6314	438	25	the	the	DET
ejpam-6314	438	26	above	above	ADJ
ejpam-6314	438	27	distances	distance	NOUN
ejpam-6314	438	28	satisfies	satisfy	VERB
ejpam-6314	438	29	the	the	DET
ejpam-6314	438	30	contraction	contraction	NOUN
ejpam-6314	438	31	for	for	ADP
ejpam-6314	438	32	theorem	theorem	NOUN
ejpam-6314	438	33	(	(	PUNCT
ejpam-6314	438	34	4	4	NUM
ejpam-6314	438	35	)	)	PUNCT
ejpam-6314	438	36	by	by	ADP
ejpam-6314	438	37	using	use	VERB
ejpam-6314	438	38	type	type	NOUN
ejpam-6314	438	39	partial	partial	ADJ
ejpam-6314	438	40	order	order	NOUN
ejpam-6314	438	41	for	for	ADP
ejpam-6314	438	42	bcns	bcns	NOUN
ejpam-6314	438	43	,	,	PUNCT
ejpam-6314	438	44	thus	thus	ADV
ejpam-6314	438	45	the	the	DET
ejpam-6314	438	46	result	result	NOUN
ejpam-6314	438	47	is	be	AUX
ejpam-6314	438	48	obvious	obvious	ADJ
ejpam-6314	438	49	for	for	ADP
ejpam-6314	438	50	case(iii	case(iii	NOUN
ejpam-6314	438	51	)	)	PUNCT
ejpam-6314	438	52	.	.	PUNCT
ejpam-6314	439	1	case	case	NOUN
ejpam-6314	439	2	iv	iv	X
ejpam-6314	439	3	:	:	PUNCT
ejpam-6314	439	4	if	if	SCONJ
ejpam-6314	439	5	κ	κ	X
ejpam-6314	439	6	=	=	SYM
ejpam-6314	439	7	1	1	NUM
ejpam-6314	439	8	and	and	CCONJ
ejpam-6314	439	9	σ	σ	NUM
ejpam-6314	439	10	=	=	SYM
ejpam-6314	439	11	2	2	NUM
ejpam-6314	439	12	then	then	ADV
ejpam-6314	439	13	we	we	PRON
ejpam-6314	439	14	obtain	obtain	VERB
ejpam-6314	439	15	,	,	PUNCT
ejpam-6314	439	16	db(φκ	db(φκ	NOUN
ejpam-6314	439	17	,	,	PUNCT
ejpam-6314	439	18	ψσ	ψσ	ADJ
ejpam-6314	439	19	)	)	PUNCT
ejpam-6314	439	20	=	=	SYM
ejpam-6314	439	21	db(φ(1),ψ(2	db(φ(1),ψ(2	NOUN
ejpam-6314	439	22	)	)	PUNCT
ejpam-6314	439	23	)	)	PUNCT
ejpam-6314	440	1	=	=	PUNCT
ejpam-6314	440	2	0	0	NUM
ejpam-6314	441	1	+	+	NUM
ejpam-6314	441	2	0i2	0i2	NOUN
ejpam-6314	441	3	,	,	PUNCT
ejpam-6314	441	4	db(κ	db(κ	NUM
ejpam-6314	441	5	,	,	PUNCT
ejpam-6314	441	6	σ	σ	X
ejpam-6314	441	7	)	)	PUNCT
ejpam-6314	441	8	=	=	PUNCT
ejpam-6314	441	9	db(1	db(1	VERB
ejpam-6314	441	10	,	,	PUNCT
ejpam-6314	441	11	2	2	NUM
ejpam-6314	441	12	)	)	PUNCT
ejpam-6314	441	13	=	=	SYM
ejpam-6314	442	1	1	1	NUM
ejpam-6314	442	2	+	+	NUM
ejpam-6314	442	3	i2	i2	NOUN
ejpam-6314	442	4	,	,	PUNCT
ejpam-6314	442	5	db(κ	db(κ	NOUN
ejpam-6314	442	6	,	,	PUNCT
ejpam-6314	442	7	φκ	φκ	ADJ
ejpam-6314	442	8	)	)	PUNCT
ejpam-6314	442	9	=	=	PUNCT
ejpam-6314	442	10	db(1,φ(1	db(1,φ(1	NOUN
ejpam-6314	442	11	)	)	PUNCT
ejpam-6314	442	12	)	)	PUNCT
ejpam-6314	443	1	=	=	SYM
ejpam-6314	443	2	1	1	NUM
ejpam-6314	443	3	+	+	NUM
ejpam-6314	443	4	i2	i2	NOUN
ejpam-6314	443	5	,	,	PUNCT
ejpam-6314	443	6	db(σ	db(σ	NUM
ejpam-6314	443	7	,	,	PUNCT
ejpam-6314	443	8	ψσ	ψσ	ADJ
ejpam-6314	443	9	)	)	PUNCT
ejpam-6314	443	10	=	=	SYM
ejpam-6314	443	11	db(2,ψ(2	db(2,ψ(2	NOUN
ejpam-6314	443	12	)	)	PUNCT
ejpam-6314	443	13	)	)	PUNCT
ejpam-6314	444	1	=	=	PUNCT
ejpam-6314	444	2	0	0	NUM
ejpam-6314	445	1	+	+	NUM
ejpam-6314	445	2	0i2	0i2	NOUN
ejpam-6314	445	3	.	.	PUNCT
ejpam-6314	446	1	db(φκ	db(φκ	NOUN
ejpam-6314	446	2	,	,	PUNCT
ejpam-6314	446	3	ψσ	ψσ	ADJ
ejpam-6314	446	4	)	)	PUNCT
ejpam-6314	446	5	≾	≾	PROPN
ejpam-6314	446	6	µ(κ)db(κ	µ(κ)db(κ	NOUN
ejpam-6314	446	7	,	,	PUNCT
ejpam-6314	446	8	σ	σ	NOUN
ejpam-6314	446	9	)	)	PUNCT
ejpam-6314	446	10	+	+	NUM
ejpam-6314	446	11	ν(κ	ν(κ	NOUN
ejpam-6314	446	12	)	)	PUNCT
ejpam-6314	446	13	db(κ	db(κ	NOUN
ejpam-6314	446	14	,	,	PUNCT
ejpam-6314	446	15	φκ)db(σ	φκ)db(σ	NOUN
ejpam-6314	446	16	,	,	PUNCT
ejpam-6314	446	17	ψσ	ψσ	ADJ
ejpam-6314	446	18	)	)	PUNCT
ejpam-6314	446	19	1	1	NUM
ejpam-6314	446	20	+	+	CCONJ
ejpam-6314	446	21	db(κ	db(κ	NUM
ejpam-6314	446	22	,	,	PUNCT
ejpam-6314	446	23	σ	σ	PROPN
ejpam-6314	446	24	)	)	PUNCT
ejpam-6314	446	25	the	the	DET
ejpam-6314	446	26	above	above	ADJ
ejpam-6314	446	27	distances	distance	NOUN
ejpam-6314	446	28	satisfies	satisfy	VERB
ejpam-6314	446	29	the	the	DET
ejpam-6314	446	30	contraction	contraction	NOUN
ejpam-6314	446	31	for	for	ADP
ejpam-6314	446	32	theorem	theorem	NOUN
ejpam-6314	446	33	(	(	PUNCT
ejpam-6314	446	34	4	4	NUM
ejpam-6314	446	35	)	)	PUNCT
ejpam-6314	446	36	by	by	ADP
ejpam-6314	446	37	using	use	VERB
ejpam-6314	446	38	type	type	NOUN
ejpam-6314	446	39	partial	partial	ADJ
ejpam-6314	446	40	order	order	NOUN
ejpam-6314	446	41	for	for	ADP
ejpam-6314	446	42	bcns	bcns	NOUN
ejpam-6314	446	43	,	,	PUNCT
ejpam-6314	446	44	thus	thus	ADV
ejpam-6314	446	45	the	the	DET
ejpam-6314	446	46	result	result	NOUN
ejpam-6314	446	47	is	be	AUX
ejpam-6314	446	48	obvious	obvious	ADJ
ejpam-6314	446	49	for	for	ADP
ejpam-6314	446	50	case(iv	case(iv	NOUN
ejpam-6314	446	51	)	)	PUNCT
ejpam-6314	446	52	.	.	PUNCT
ejpam-6314	447	1	case	case	NOUN
ejpam-6314	447	2	v	v	ADP
ejpam-6314	447	3	:	:	PUNCT
ejpam-6314	447	4	if	if	SCONJ
ejpam-6314	447	5	κ	κ	X
ejpam-6314	447	6	=	=	SYM
ejpam-6314	447	7	1	1	NUM
ejpam-6314	447	8	and	and	CCONJ
ejpam-6314	447	9	σ	σ	NUM
ejpam-6314	447	10	=	=	SYM
ejpam-6314	447	11	0	0	PUNCT
ejpam-6314	448	1	then	then	ADV
ejpam-6314	448	2	we	we	PRON
ejpam-6314	448	3	obtain	obtain	VERB
ejpam-6314	448	4	,	,	PUNCT
ejpam-6314	448	5	db(φκ	db(φκ	NOUN
ejpam-6314	448	6	,	,	PUNCT
ejpam-6314	448	7	ψσ	ψσ	ADJ
ejpam-6314	448	8	)	)	PUNCT
ejpam-6314	448	9	=	=	SYM
ejpam-6314	448	10	db(φ(1),ψ(0	db(φ(1),ψ(0	NOUN
ejpam-6314	448	11	)	)	PUNCT
ejpam-6314	448	12	)	)	PUNCT
ejpam-6314	449	1	=	=	SYM
ejpam-6314	449	2	1	1	NUM
ejpam-6314	449	3	+	+	NUM
ejpam-6314	449	4	1i2	1i2	NUM
ejpam-6314	449	5	,	,	PUNCT
ejpam-6314	449	6	db(κ	db(κ	NOUN
ejpam-6314	449	7	,	,	PUNCT
ejpam-6314	449	8	σ	σ	X
ejpam-6314	449	9	)	)	PUNCT
ejpam-6314	449	10	=	=	PUNCT
ejpam-6314	449	11	db(1	db(1	VERB
ejpam-6314	449	12	,	,	PUNCT
ejpam-6314	449	13	0	0	NUM
ejpam-6314	449	14	)	)	PUNCT
ejpam-6314	449	15	=	=	SYM
ejpam-6314	450	1	60	60	NUM
ejpam-6314	450	2	+	+	NUM
ejpam-6314	450	3	60i2	60i2	NUM
ejpam-6314	450	4	,	,	PUNCT
ejpam-6314	450	5	db(κ	db(κ	NOUN
ejpam-6314	450	6	,	,	PUNCT
ejpam-6314	450	7	φκ	φκ	ADJ
ejpam-6314	450	8	)	)	PUNCT
ejpam-6314	450	9	=	=	PUNCT
ejpam-6314	450	10	db(1,φ(1	db(1,φ(1	NOUN
ejpam-6314	450	11	)	)	PUNCT
ejpam-6314	450	12	)	)	PUNCT
ejpam-6314	451	1	=	=	SYM
ejpam-6314	451	2	1	1	NUM
ejpam-6314	451	3	+	+	NUM
ejpam-6314	451	4	i2	i2	NOUN
ejpam-6314	451	5	,	,	PUNCT
ejpam-6314	451	6	db(σ	db(σ	NUM
ejpam-6314	451	7	,	,	PUNCT
ejpam-6314	451	8	ψσ	ψσ	ADJ
ejpam-6314	451	9	)	)	PUNCT
ejpam-6314	451	10	=	=	SYM
ejpam-6314	451	11	db(0,ψ(0	db(0,ψ(0	X
ejpam-6314	451	12	)	)	PUNCT
ejpam-6314	451	13	)	)	PUNCT
ejpam-6314	452	1	=	=	PUNCT
ejpam-6314	453	1	60	60	NUM
ejpam-6314	453	2	+	+	NUM
ejpam-6314	453	3	60i2	60i2	NUM
ejpam-6314	453	4	.	.	PUNCT
ejpam-6314	454	1	db(φκ	db(φκ	NOUN
ejpam-6314	454	2	,	,	PUNCT
ejpam-6314	454	3	ψσ	ψσ	ADJ
ejpam-6314	454	4	)	)	PUNCT
ejpam-6314	454	5	≾	≾	PROPN
ejpam-6314	454	6	µ(κ)db(κ	µ(κ)db(κ	NOUN
ejpam-6314	454	7	,	,	PUNCT
ejpam-6314	454	8	σ	σ	NOUN
ejpam-6314	454	9	)	)	PUNCT
ejpam-6314	454	10	+	+	NUM
ejpam-6314	454	11	ν(κ	ν(κ	NOUN
ejpam-6314	454	12	)	)	PUNCT
ejpam-6314	454	13	db(κ	db(κ	NOUN
ejpam-6314	454	14	,	,	PUNCT
ejpam-6314	454	15	φκ)db(σ	φκ)db(σ	NOUN
ejpam-6314	454	16	,	,	PUNCT
ejpam-6314	454	17	ψσ	ψσ	ADJ
ejpam-6314	454	18	)	)	PUNCT
ejpam-6314	454	19	1	1	NUM
ejpam-6314	454	20	+	+	CCONJ
ejpam-6314	454	21	db(κ	db(κ	NUM
ejpam-6314	454	22	,	,	PUNCT
ejpam-6314	454	23	σ	σ	X
ejpam-6314	454	24	)	)	PUNCT
ejpam-6314	454	25	m.	m.	NOUN
ejpam-6314	454	26	sarwar	sarwar	PROPN
ejpam-6314	454	27	et	et	PROPN
ejpam-6314	454	28	al	al	PROPN
ejpam-6314	454	29	.	.	PUNCT
ejpam-6314	454	30	/	/	SYM
ejpam-6314	454	31	eur	eur	PROPN
ejpam-6314	454	32	.	.	PUNCT
ejpam-6314	455	1	j.	j.	PROPN
ejpam-6314	455	2	pure	pure	PROPN
ejpam-6314	455	3	appl	appl	PROPN
ejpam-6314	455	4	.	.	PROPN
ejpam-6314	455	5	math	math	PROPN
ejpam-6314	455	6	,	,	PUNCT
ejpam-6314	455	7	18	18	NUM
ejpam-6314	455	8	(	(	PUNCT
ejpam-6314	455	9	3	3	NUM
ejpam-6314	455	10	)	)	PUNCT
ejpam-6314	455	11	(	(	PUNCT
ejpam-6314	455	12	2025	2025	NUM
ejpam-6314	455	13	)	)	PUNCT
ejpam-6314	455	14	,	,	PUNCT
ejpam-6314	455	15	6314	6314	NUM
ejpam-6314	455	16	21	21	NUM
ejpam-6314	455	17	of	of	ADP
ejpam-6314	455	18	28	28	NUM
ejpam-6314	455	19	the	the	DET
ejpam-6314	455	20	above	above	ADJ
ejpam-6314	455	21	distances	distance	NOUN
ejpam-6314	455	22	satisfies	satisfy	VERB
ejpam-6314	455	23	the	the	DET
ejpam-6314	455	24	contraction	contraction	NOUN
ejpam-6314	455	25	for	for	ADP
ejpam-6314	455	26	theorem	theorem	NOUN
ejpam-6314	455	27	(	(	PUNCT
ejpam-6314	455	28	4	4	NUM
ejpam-6314	455	29	)	)	PUNCT
ejpam-6314	455	30	by	by	ADP
ejpam-6314	455	31	using	use	VERB
ejpam-6314	455	32	type	type	NOUN
ejpam-6314	455	33	partial	partial	ADJ
ejpam-6314	455	34	order	order	NOUN
ejpam-6314	455	35	for	for	ADP
ejpam-6314	455	36	bcns	bcns	NOUN
ejpam-6314	455	37	,	,	PUNCT
ejpam-6314	455	38	thus	thus	ADV
ejpam-6314	455	39	the	the	DET
ejpam-6314	455	40	result	result	NOUN
ejpam-6314	455	41	is	be	AUX
ejpam-6314	455	42	obvious	obvious	ADJ
ejpam-6314	455	43	for	for	ADP
ejpam-6314	455	44	case(v	case(v	NOUN
ejpam-6314	455	45	)	)	PUNCT
ejpam-6314	455	46	.	.	PUNCT
ejpam-6314	456	1	case	case	NOUN
ejpam-6314	456	2	vi	vi	ADP
ejpam-6314	456	3	:	:	PUNCT
ejpam-6314	456	4	if	if	SCONJ
ejpam-6314	456	5	κ	κ	X
ejpam-6314	456	6	=	=	SYM
ejpam-6314	456	7	2	2	NUM
ejpam-6314	456	8	and	and	CCONJ
ejpam-6314	456	9	σ	σ	NUM
ejpam-6314	456	10	=	=	SYM
ejpam-6314	456	11	0	0	PUNCT
ejpam-6314	457	1	then	then	ADV
ejpam-6314	457	2	we	we	PRON
ejpam-6314	457	3	obtain	obtain	VERB
ejpam-6314	457	4	,	,	PUNCT
ejpam-6314	457	5	db(φκ	db(φκ	NOUN
ejpam-6314	457	6	,	,	PUNCT
ejpam-6314	457	7	ψσ	ψσ	ADJ
ejpam-6314	457	8	)	)	PUNCT
ejpam-6314	457	9	=	=	SYM
ejpam-6314	457	10	db(ψ(2),φ(0	db(ψ(2),φ(0	NOUN
ejpam-6314	457	11	)	)	PUNCT
ejpam-6314	457	12	)	)	PUNCT
ejpam-6314	458	1	=	=	SYM
ejpam-6314	458	2	1	1	NUM
ejpam-6314	458	3	+	+	NUM
ejpam-6314	458	4	i2	i2	NOUN
ejpam-6314	458	5	,	,	PUNCT
ejpam-6314	458	6	db(κ	db(κ	NOUN
ejpam-6314	458	7	,	,	PUNCT
ejpam-6314	458	8	σ	σ	NOUN
ejpam-6314	458	9	)	)	PUNCT
ejpam-6314	458	10	=	=	SYM
ejpam-6314	458	11	db(2	db(2	PROPN
ejpam-6314	458	12	,	,	PUNCT
ejpam-6314	458	13	0	0	NUM
ejpam-6314	458	14	)	)	PUNCT
ejpam-6314	458	15	=	=	SYM
ejpam-6314	459	1	90	90	NUM
ejpam-6314	459	2	+	+	NUM
ejpam-6314	459	3	90i2	90i2	NUM
ejpam-6314	459	4	,	,	PUNCT
ejpam-6314	459	5	db(κ	db(κ	NOUN
ejpam-6314	459	6	,	,	PUNCT
ejpam-6314	459	7	φκ	φκ	ADJ
ejpam-6314	459	8	)	)	PUNCT
ejpam-6314	459	9	=	=	PUNCT
ejpam-6314	459	10	db(2,φ(2	db(2,φ(2	NOUN
ejpam-6314	459	11	)	)	PUNCT
ejpam-6314	459	12	)	)	PUNCT
ejpam-6314	460	1	=	=	PUNCT
ejpam-6314	460	2	0	0	NUM
ejpam-6314	461	1	+	+	NUM
ejpam-6314	461	2	0i2	0i2	NOUN
ejpam-6314	461	3	,	,	PUNCT
ejpam-6314	461	4	db(σ	db(σ	NUM
ejpam-6314	461	5	,	,	PUNCT
ejpam-6314	461	6	ψσ	ψσ	ADJ
ejpam-6314	461	7	)	)	PUNCT
ejpam-6314	461	8	=	=	SYM
ejpam-6314	461	9	db(0,ψ(0	db(0,ψ(0	X
ejpam-6314	461	10	)	)	PUNCT
ejpam-6314	461	11	)	)	PUNCT
ejpam-6314	462	1	=	=	SYM
ejpam-6314	462	2	1	1	NUM
ejpam-6314	462	3	+	+	NUM
ejpam-6314	462	4	i2	i2	NOUN
ejpam-6314	462	5	.	.	PUNCT
ejpam-6314	463	1	db(φκ	db(φκ	NOUN
ejpam-6314	463	2	,	,	PUNCT
ejpam-6314	463	3	ψσ	ψσ	ADJ
ejpam-6314	463	4	)	)	PUNCT
ejpam-6314	463	5	≾	≾	PROPN
ejpam-6314	463	6	µ(κ)db(κ	µ(κ)db(κ	NOUN
ejpam-6314	463	7	,	,	PUNCT
ejpam-6314	463	8	σ	σ	NOUN
ejpam-6314	463	9	)	)	PUNCT
ejpam-6314	463	10	+	+	NUM
ejpam-6314	463	11	ν(κ	ν(κ	NOUN
ejpam-6314	463	12	)	)	PUNCT
ejpam-6314	463	13	db(κ	db(κ	NOUN
ejpam-6314	463	14	,	,	PUNCT
ejpam-6314	463	15	φκ)db(σ	φκ)db(σ	NOUN
ejpam-6314	463	16	,	,	PUNCT
ejpam-6314	463	17	ψσ	ψσ	ADJ
ejpam-6314	463	18	)	)	PUNCT
ejpam-6314	463	19	1	1	NUM
ejpam-6314	463	20	+	+	CCONJ
ejpam-6314	463	21	db(κ	db(κ	NUM
ejpam-6314	463	22	,	,	PUNCT
ejpam-6314	463	23	σ	σ	PROPN
ejpam-6314	463	24	)	)	PUNCT
ejpam-6314	463	25	the	the	DET
ejpam-6314	463	26	above	above	ADJ
ejpam-6314	463	27	distances	distance	NOUN
ejpam-6314	463	28	satisfies	satisfy	VERB
ejpam-6314	463	29	the	the	DET
ejpam-6314	463	30	contraction	contraction	NOUN
ejpam-6314	463	31	for	for	ADP
ejpam-6314	463	32	theorem	theorem	NOUN
ejpam-6314	463	33	(	(	PUNCT
ejpam-6314	463	34	4	4	NUM
ejpam-6314	463	35	)	)	PUNCT
ejpam-6314	463	36	by	by	ADP
ejpam-6314	463	37	using	use	VERB
ejpam-6314	463	38	type	type	NOUN
ejpam-6314	463	39	partial	partial	ADJ
ejpam-6314	463	40	order	order	NOUN
ejpam-6314	463	41	for	for	ADP
ejpam-6314	463	42	bcns	bcns	NOUN
ejpam-6314	463	43	,	,	PUNCT
ejpam-6314	463	44	thus	thus	ADV
ejpam-6314	463	45	the	the	DET
ejpam-6314	463	46	result	result	NOUN
ejpam-6314	463	47	is	be	AUX
ejpam-6314	463	48	obvious	obvious	ADJ
ejpam-6314	463	49	for	for	ADP
ejpam-6314	463	50	case(vi	case(vi	NOUN
ejpam-6314	463	51	)	)	PUNCT
ejpam-6314	463	52	.	.	PUNCT
ejpam-6314	464	1	case	case	NOUN
ejpam-6314	464	2	vii	vii	PROPN
ejpam-6314	464	3	:	:	PUNCT
ejpam-6314	464	4	if	if	SCONJ
ejpam-6314	464	5	κ	κ	X
ejpam-6314	464	6	=	=	SYM
ejpam-6314	464	7	2	2	NUM
ejpam-6314	464	8	and	and	CCONJ
ejpam-6314	464	9	σ	σ	NUM
ejpam-6314	464	10	=	=	NOUN
ejpam-6314	464	11	1	1	NUM
ejpam-6314	464	12	then	then	ADV
ejpam-6314	464	13	we	we	PRON
ejpam-6314	464	14	obtain	obtain	VERB
ejpam-6314	464	15	,	,	PUNCT
ejpam-6314	464	16	db(φκ	db(φκ	NOUN
ejpam-6314	464	17	,	,	PUNCT
ejpam-6314	464	18	ψσ	ψσ	ADJ
ejpam-6314	464	19	)	)	PUNCT
ejpam-6314	464	20	=	=	SYM
ejpam-6314	464	21	db(ψ(2),φ(1	db(ψ(2),φ(1	NOUN
ejpam-6314	464	22	)	)	PUNCT
ejpam-6314	464	23	)	)	PUNCT
ejpam-6314	465	1	=	=	PUNCT
ejpam-6314	465	2	0	0	PUNCT
ejpam-6314	466	1	+	+	NUM
ejpam-6314	466	2	0i2	0i2	NOUN
ejpam-6314	466	3	,	,	PUNCT
ejpam-6314	466	4	db(κ	db(κ	NUM
ejpam-6314	466	5	,	,	PUNCT
ejpam-6314	466	6	σ	σ	NOUN
ejpam-6314	466	7	)	)	PUNCT
ejpam-6314	466	8	=	=	SYM
ejpam-6314	466	9	db(2	db(2	PROPN
ejpam-6314	466	10	,	,	PUNCT
ejpam-6314	466	11	1	1	NUM
ejpam-6314	466	12	)	)	PUNCT
ejpam-6314	466	13	=	=	SYM
ejpam-6314	467	1	1	1	NUM
ejpam-6314	467	2	+	+	NUM
ejpam-6314	467	3	i2	i2	NOUN
ejpam-6314	467	4	,	,	PUNCT
ejpam-6314	467	5	db(κ	db(κ	NOUN
ejpam-6314	467	6	,	,	PUNCT
ejpam-6314	467	7	φκ	φκ	ADJ
ejpam-6314	467	8	)	)	PUNCT
ejpam-6314	467	9	=	=	PUNCT
ejpam-6314	467	10	db(2,φ(2	db(2,φ(2	NOUN
ejpam-6314	467	11	)	)	PUNCT
ejpam-6314	467	12	)	)	PUNCT
ejpam-6314	468	1	=	=	PUNCT
ejpam-6314	468	2	0	0	NUM
ejpam-6314	469	1	+	+	NUM
ejpam-6314	469	2	0i2	0i2	NOUN
ejpam-6314	469	3	,	,	PUNCT
ejpam-6314	469	4	db(σ	db(σ	NUM
ejpam-6314	469	5	,	,	PUNCT
ejpam-6314	469	6	ψσ	ψσ	ADJ
ejpam-6314	469	7	)	)	PUNCT
ejpam-6314	469	8	=	=	SYM
ejpam-6314	469	9	db(2,ψ(1	db(2,ψ(1	NOUN
ejpam-6314	469	10	)	)	PUNCT
ejpam-6314	469	11	)	)	PUNCT
ejpam-6314	470	1	=	=	PUNCT
ejpam-6314	470	2	0	0	NUM
ejpam-6314	471	1	+	+	NUM
ejpam-6314	471	2	0i2	0i2	NOUN
ejpam-6314	471	3	.	.	PUNCT
ejpam-6314	472	1	db(φκ	db(φκ	NOUN
ejpam-6314	472	2	,	,	PUNCT
ejpam-6314	472	3	ψσ	ψσ	ADJ
ejpam-6314	472	4	)	)	PUNCT
ejpam-6314	472	5	≾	≾	PROPN
ejpam-6314	472	6	µ(κ)db(κ	µ(κ)db(κ	NOUN
ejpam-6314	472	7	,	,	PUNCT
ejpam-6314	472	8	σ	σ	NOUN
ejpam-6314	472	9	)	)	PUNCT
ejpam-6314	472	10	+	+	NUM
ejpam-6314	472	11	ν(κ	ν(κ	NOUN
ejpam-6314	472	12	)	)	PUNCT
ejpam-6314	472	13	db(κ	db(κ	NOUN
ejpam-6314	472	14	,	,	PUNCT
ejpam-6314	472	15	φκ)db(σ	φκ)db(σ	NOUN
ejpam-6314	472	16	,	,	PUNCT
ejpam-6314	472	17	ψσ	ψσ	ADJ
ejpam-6314	472	18	)	)	PUNCT
ejpam-6314	472	19	1	1	NUM
ejpam-6314	472	20	+	+	CCONJ
ejpam-6314	472	21	db(κ	db(κ	NUM
ejpam-6314	472	22	,	,	PUNCT
ejpam-6314	472	23	σ	σ	PROPN
ejpam-6314	472	24	)	)	PUNCT
ejpam-6314	472	25	the	the	DET
ejpam-6314	472	26	above	above	ADJ
ejpam-6314	472	27	distances	distance	NOUN
ejpam-6314	472	28	satisfies	satisfy	VERB
ejpam-6314	472	29	the	the	DET
ejpam-6314	472	30	contraction	contraction	NOUN
ejpam-6314	472	31	for	for	ADP
ejpam-6314	472	32	theorem	theorem	NOUN
ejpam-6314	472	33	(	(	PUNCT
ejpam-6314	472	34	4	4	NUM
ejpam-6314	472	35	)	)	PUNCT
ejpam-6314	472	36	by	by	ADP
ejpam-6314	472	37	using	use	VERB
ejpam-6314	472	38	type	type	NOUN
ejpam-6314	472	39	partial	partial	ADJ
ejpam-6314	472	40	order	order	NOUN
ejpam-6314	472	41	for	for	ADP
ejpam-6314	472	42	bcns	bcns	NOUN
ejpam-6314	472	43	,	,	PUNCT
ejpam-6314	472	44	thus	thus	ADV
ejpam-6314	472	45	the	the	DET
ejpam-6314	472	46	result	result	NOUN
ejpam-6314	472	47	is	be	AUX
ejpam-6314	472	48	obvious	obvious	ADJ
ejpam-6314	472	49	for	for	ADP
ejpam-6314	472	50	case(vii	case(vii	NOUN
ejpam-6314	472	51	)	)	PUNCT
ejpam-6314	472	52	.	.	PUNCT
ejpam-6314	473	1	therefore	therefore	ADV
ejpam-6314	473	2	all	all	DET
ejpam-6314	473	3	the	the	DET
ejpam-6314	473	4	axioms	axiom	NOUN
ejpam-6314	473	5	of	of	ADP
ejpam-6314	473	6	theorem	theorem	NOUN
ejpam-6314	473	7	(	(	PUNCT
ejpam-6314	473	8	4	4	NUM
ejpam-6314	473	9	)	)	PUNCT
ejpam-6314	473	10	are	be	AUX
ejpam-6314	473	11	fulfilled	fulfil	VERB
ejpam-6314	473	12	for	for	ADP
ejpam-6314	473	13	all	all	DET
ejpam-6314	473	14	the	the	DET
ejpam-6314	473	15	cases	case	NOUN
ejpam-6314	473	16	,	,	PUNCT
ejpam-6314	473	17	so	so	SCONJ
ejpam-6314	473	18	φ	φ	PROPN
ejpam-6314	473	19	and	and	CCONJ
ejpam-6314	473	20	ψ	ψ	PROPN
ejpam-6314	473	21	have	have	VERB
ejpam-6314	473	22	a	a	DET
ejpam-6314	473	23	unique	unique	ADJ
ejpam-6314	473	24	common	common	ADJ
ejpam-6314	473	25	fixed	fix	VERB
ejpam-6314	473	26	point	point	NOUN
ejpam-6314	473	27	.	.	PUNCT
ejpam-6314	474	1	example	example	NOUN
ejpam-6314	475	1	6	6	NUM
ejpam-6314	475	2	.	.	PUNCT
ejpam-6314	475	3	let	let	VERB
ejpam-6314	475	4	db	db	PART
ejpam-6314	475	5	be	be	AUX
ejpam-6314	475	6	a	a	DET
ejpam-6314	475	7	bccm	bccm	NOUN
ejpam-6314	475	8	defined	define	VERB
ejpam-6314	475	9	on	on	ADP
ejpam-6314	475	10	s	s	NOUN
ejpam-6314	475	11	=	=	PUNCT
ejpam-6314	475	12	{	{	PUNCT
ejpam-6314	475	13	0	0	NUM
ejpam-6314	475	14	,	,	PUNCT
ejpam-6314	475	15	1	1	NUM
ejpam-6314	475	16	,	,	PUNCT
ejpam-6314	475	17	2	2	NUM
ejpam-6314	475	18	}	}	PUNCT
ejpam-6314	475	19	such	such	ADJ
ejpam-6314	475	20	that	that	PRON
ejpam-6314	475	21	;	;	PUNCT
ejpam-6314	475	22	db(0	db(0	NOUN
ejpam-6314	475	23	,	,	PUNCT
ejpam-6314	475	24	1	1	NUM
ejpam-6314	475	25	)	)	PUNCT
ejpam-6314	475	26	=	=	SYM
ejpam-6314	476	1	60	60	NUM
ejpam-6314	476	2	+	+	NUM
ejpam-6314	476	3	60i2	60i2	NUM
ejpam-6314	476	4	,	,	PUNCT
ejpam-6314	476	5	db(1	db(1	NOUN
ejpam-6314	476	6	,	,	PUNCT
ejpam-6314	476	7	2	2	NUM
ejpam-6314	476	8	)	)	PUNCT
ejpam-6314	476	9	=	=	SYM
ejpam-6314	477	1	1	1	NUM
ejpam-6314	477	2	+	+	NUM
ejpam-6314	477	3	i2	i2	PROPN
ejpam-6314	477	4	and	and	CCONJ
ejpam-6314	477	5	db(0	db(0	PROPN
ejpam-6314	477	6	,	,	PUNCT
ejpam-6314	477	7	2	2	NUM
ejpam-6314	477	8	)	)	PUNCT
ejpam-6314	477	9	=	=	SYM
ejpam-6314	477	10	90	90	NUM
ejpam-6314	478	1	+	+	NUM
ejpam-6314	478	2	90i2	90i2	NUM
ejpam-6314	478	3	.	.	PUNCT
ejpam-6314	479	1	where	where	SCONJ
ejpam-6314	479	2	ϑ	ϑ	X
ejpam-6314	479	3	:	:	PUNCT
ejpam-6314	479	4	s	s	VERB
ejpam-6314	479	5	×	×	PROPN
ejpam-6314	479	6	s	s	X
ejpam-6314	479	7	→	→	SYM
ejpam-6314	479	8	[	[	X
ejpam-6314	479	9	1,+∞	1,+∞	NUM
ejpam-6314	479	10	)	)	PUNCT
ejpam-6314	479	11	such	such	ADJ
ejpam-6314	479	12	that	that	SCONJ
ejpam-6314	479	13	ϑ(0	ϑ(0	NOUN
ejpam-6314	479	14	,	,	PUNCT
ejpam-6314	479	15	0	0	NUM
ejpam-6314	479	16	)	)	PUNCT
ejpam-6314	479	17	=	=	PUNCT
ejpam-6314	480	1	ϑ(1	ϑ(1	NOUN
ejpam-6314	480	2	,	,	PUNCT
ejpam-6314	480	3	1	1	NUM
ejpam-6314	480	4	)	)	PUNCT
ejpam-6314	480	5	=	=	SYM
ejpam-6314	480	6	ϑ(2	ϑ(2	PROPN
ejpam-6314	480	7	,	,	PUNCT
ejpam-6314	480	8	2	2	NUM
ejpam-6314	480	9	)	)	PUNCT
ejpam-6314	480	10	=	=	PUNCT
ejpam-6314	480	11	ϑ(1	ϑ(1	NOUN
ejpam-6314	480	12	,	,	PUNCT
ejpam-6314	480	13	2	2	NUM
ejpam-6314	480	14	)	)	PUNCT
ejpam-6314	480	15	=	=	SYM
ejpam-6314	480	16	1	1	NUM
ejpam-6314	480	17	,	,	PUNCT
ejpam-6314	480	18	ϑ(0	ϑ(0	PROPN
ejpam-6314	480	19	,	,	PUNCT
ejpam-6314	480	20	2	2	NUM
ejpam-6314	480	21	)	)	PUNCT
ejpam-6314	480	22	=	=	SYM
ejpam-6314	480	23	2	2	NUM
ejpam-6314	480	24	,	,	PUNCT
ejpam-6314	480	25	ϑ(0	ϑ(0	PROPN
ejpam-6314	480	26	,	,	PUNCT
ejpam-6314	480	27	1	1	NUM
ejpam-6314	480	28	)	)	PUNCT
ejpam-6314	480	29	=	=	SYM
ejpam-6314	480	30	3	3	NUM
ejpam-6314	480	31	2	2	NUM
ejpam-6314	480	32	.	.	PUNCT
ejpam-6314	481	1	let	let	VERB
ejpam-6314	481	2	ψ	ψ	X
ejpam-6314	481	3	:	:	PUNCT
ejpam-6314	481	4	s	s	X
ejpam-6314	481	5	→	→	SYM
ejpam-6314	481	6	s	s	X
ejpam-6314	481	7	as	as	ADP
ejpam-6314	481	8	ψn(0	ψn(0	NOUN
ejpam-6314	481	9	)	)	PUNCT
ejpam-6314	481	10	=	=	SYM
ejpam-6314	481	11	1	1	NUM
ejpam-6314	481	12	and	and	CCONJ
ejpam-6314	481	13	ψn(1	ψn(1	NOUN
ejpam-6314	481	14	)	)	PUNCT
ejpam-6314	481	15	=	=	SYM
ejpam-6314	481	16	ψn(2	ψn(2	NOUN
ejpam-6314	481	17	)	)	PUNCT
ejpam-6314	482	1	=	=	SYM
ejpam-6314	482	2	2	2	X
ejpam-6314	482	3	.	.	X
ejpam-6314	482	4	consider	consider	VERB
ejpam-6314	482	5	,	,	PUNCT
ejpam-6314	482	6	µ(κ	µ(κ	PROPN
ejpam-6314	482	7	)	)	PUNCT
ejpam-6314	482	8	=	=	PUNCT
ejpam-6314	482	9	(	(	PUNCT
ejpam-6314	482	10	κ−3)2	κ−3)2	PROPN
ejpam-6314	482	11	30	30	NUM
ejpam-6314	482	12	and	and	CCONJ
ejpam-6314	482	13	ν(κ	ν(κ	NOUN
ejpam-6314	482	14	)	)	PUNCT
ejpam-6314	483	1	=	=	PRON
ejpam-6314	483	2	(	(	PUNCT
ejpam-6314	483	3	κ−3)2	κ−3)2	PROPN
ejpam-6314	483	4	20	20	NUM
ejpam-6314	483	5	.	.	PUNCT
ejpam-6314	484	1	and	and	CCONJ
ejpam-6314	484	2	κ0	κ0	PRON
ejpam-6314	484	3	=	=	SYM
ejpam-6314	484	4	0	0	NUM
ejpam-6314	484	5	,	,	PUNCT
ejpam-6314	484	6	then	then	ADV
ejpam-6314	484	7	κ1	κ1	NOUN
ejpam-6314	484	8	=	=	SYM
ejpam-6314	484	9	2	2	NUM
ejpam-6314	484	10	and	and	CCONJ
ejpam-6314	484	11	κn	κn	NOUN
ejpam-6314	484	12	=	=	NOUN
ejpam-6314	484	13	1	1	NUM
ejpam-6314	484	14	for	for	ADP
ejpam-6314	484	15	all	all	DET
ejpam-6314	484	16	n	n	PRON
ejpam-6314	484	17	≥	≥	NOUN
ejpam-6314	484	18	2	2	NUM
ejpam-6314	484	19	.	.	PUNCT
ejpam-6314	484	20	clearly	clearly	ADV
ejpam-6314	484	21	,	,	PUNCT
ejpam-6314	484	22	condition(i),(ii),(iii	condition(i),(ii),(iii	X
ejpam-6314	484	23	)	)	PUNCT
ejpam-6314	484	24	and	and	CCONJ
ejpam-6314	484	25	(	(	PUNCT
ejpam-6314	484	26	5	5	X
ejpam-6314	484	27	)	)	PUNCT
ejpam-6314	484	28	are	be	AUX
ejpam-6314	484	29	satisfied	satisfied	ADJ
ejpam-6314	484	30	.	.	PUNCT
ejpam-6314	485	1	now	now	ADV
ejpam-6314	485	2	,	,	PUNCT
ejpam-6314	485	3	we	we	PRON
ejpam-6314	485	4	take	take	VERB
ejpam-6314	485	5	different	different	ADJ
ejpam-6314	485	6	cases	case	NOUN
ejpam-6314	485	7	to	to	PART
ejpam-6314	485	8	check	check	VERB
ejpam-6314	485	9	that	that	PRON
ejpam-6314	485	10	(	(	PUNCT
ejpam-6314	485	11	26	26	NUM
ejpam-6314	485	12	)	)	PUNCT
ejpam-6314	485	13	is	be	AUX
ejpam-6314	485	14	also	also	ADV
ejpam-6314	485	15	satisfied	satisfied	ADJ
ejpam-6314	485	16	.	.	PUNCT
ejpam-6314	486	1	case	case	NOUN
ejpam-6314	487	1	i	i	PRON
ejpam-6314	487	2	:	:	PUNCT
ejpam-6314	487	3	if	if	SCONJ
ejpam-6314	487	4	κ	κ	X
ejpam-6314	487	5	=	=	SYM
ejpam-6314	487	6	σ	σ	PROPN
ejpam-6314	487	7	=	=	SYM
ejpam-6314	487	8	0	0	NUM
ejpam-6314	487	9	,	,	PUNCT
ejpam-6314	487	10	κ	κ	X
ejpam-6314	487	11	=	=	SYM
ejpam-6314	487	12	σ	σ	PROPN
ejpam-6314	487	13	=	=	SYM
ejpam-6314	487	14	1	1	NUM
ejpam-6314	487	15	,	,	PUNCT
ejpam-6314	487	16	κ	κ	X
ejpam-6314	487	17	=	=	SYM
ejpam-6314	487	18	σ	σ	PROPN
ejpam-6314	487	19	=	=	SYM
ejpam-6314	487	20	2	2	X
ejpam-6314	487	21	.	.	PUNCT
ejpam-6314	487	22	m.	m.	NOUN
ejpam-6314	487	23	sarwar	sarwar	PROPN
ejpam-6314	487	24	et	et	PROPN
ejpam-6314	487	25	al	al	PROPN
ejpam-6314	487	26	.	.	PUNCT
ejpam-6314	487	27	/	/	SYM
ejpam-6314	487	28	eur	eur	PROPN
ejpam-6314	487	29	.	.	PUNCT
ejpam-6314	488	1	j.	j.	PROPN
ejpam-6314	488	2	pure	pure	PROPN
ejpam-6314	488	3	appl	appl	PROPN
ejpam-6314	488	4	.	.	PROPN
ejpam-6314	488	5	math	math	PROPN
ejpam-6314	488	6	,	,	PUNCT
ejpam-6314	488	7	18	18	NUM
ejpam-6314	488	8	(	(	PUNCT
ejpam-6314	488	9	3	3	NUM
ejpam-6314	488	10	)	)	PUNCT
ejpam-6314	488	11	(	(	PUNCT
ejpam-6314	488	12	2025	2025	NUM
ejpam-6314	488	13	)	)	PUNCT
ejpam-6314	488	14	,	,	PUNCT
ejpam-6314	488	15	6314	6314	NUM
ejpam-6314	488	16	22	22	NUM
ejpam-6314	488	17	of	of	ADP
ejpam-6314	488	18	28	28	NUM
ejpam-6314	488	19	then	then	ADV
ejpam-6314	488	20	clearly	clearly	ADV
ejpam-6314	488	21	our	our	PRON
ejpam-6314	488	22	result	result	NOUN
ejpam-6314	488	23	can	can	AUX
ejpam-6314	488	24	be	be	AUX
ejpam-6314	488	25	obtained	obtain	VERB
ejpam-6314	488	26	.	.	PUNCT
ejpam-6314	489	1	case	case	NOUN
ejpam-6314	489	2	ii	ii	NOUN
ejpam-6314	489	3	:	:	PUNCT
ejpam-6314	489	4	if	if	SCONJ
ejpam-6314	489	5	κ	κ	X
ejpam-6314	489	6	=	=	SYM
ejpam-6314	489	7	0	0	NUM
ejpam-6314	489	8	and	and	CCONJ
ejpam-6314	489	9	σ	σ	NUM
ejpam-6314	489	10	=	=	NOUN
ejpam-6314	489	11	1	1	NUM
ejpam-6314	489	12	then	then	ADV
ejpam-6314	489	13	we	we	PRON
ejpam-6314	489	14	obtain	obtain	VERB
ejpam-6314	489	15	,	,	PUNCT
ejpam-6314	489	16	db(ψ	db(ψ	X
ejpam-6314	489	17	nκ	nκ	NOUN
ejpam-6314	489	18	,	,	PUNCT
ejpam-6314	489	19	ψnσ	ψnσ	NOUN
ejpam-6314	489	20	)	)	PUNCT
ejpam-6314	489	21	=	=	SYM
ejpam-6314	489	22	db(ψ	db(ψ	X
ejpam-6314	489	23	n(0),ψn(1	n(0),ψn(1	NUM
ejpam-6314	489	24	)	)	PUNCT
ejpam-6314	489	25	)	)	PUNCT
ejpam-6314	490	1	=	=	SYM
ejpam-6314	490	2	1	1	NUM
ejpam-6314	490	3	+	+	NUM
ejpam-6314	490	4	i2	i2	NOUN
ejpam-6314	490	5	,	,	PUNCT
ejpam-6314	490	6	db(κ	db(κ	NOUN
ejpam-6314	490	7	,	,	PUNCT
ejpam-6314	490	8	σ	σ	X
ejpam-6314	490	9	)	)	PUNCT
ejpam-6314	490	10	=	=	SYM
ejpam-6314	491	1	db(0	db(0	NOUN
ejpam-6314	491	2	,	,	PUNCT
ejpam-6314	491	3	1	1	NUM
ejpam-6314	491	4	)	)	PUNCT
ejpam-6314	491	5	=	=	SYM
ejpam-6314	492	1	60	60	NUM
ejpam-6314	492	2	+	+	NUM
ejpam-6314	492	3	60i2	60i2	NUM
ejpam-6314	492	4	,	,	PUNCT
ejpam-6314	492	5	db(σ	db(σ	NUM
ejpam-6314	492	6	,	,	PUNCT
ejpam-6314	492	7	ψ	ψ	NOUN
ejpam-6314	492	8	nσ	nσ	NOUN
ejpam-6314	492	9	)	)	PUNCT
ejpam-6314	492	10	=	=	PUNCT
ejpam-6314	492	11	db(1,ψ	db(1,ψ	PRON
ejpam-6314	492	12	n(1	n(1	NOUN
ejpam-6314	492	13	)	)	PUNCT
ejpam-6314	492	14	)	)	PUNCT
ejpam-6314	493	1	=	=	SYM
ejpam-6314	493	2	1	1	NUM
ejpam-6314	493	3	+	+	NUM
ejpam-6314	493	4	i2	i2	NOUN
ejpam-6314	493	5	,	,	PUNCT
ejpam-6314	493	6	db(κ	db(κ	NOUN
ejpam-6314	493	7	,	,	PUNCT
ejpam-6314	493	8	ψnκ	ψnκ	PROPN
ejpam-6314	493	9	)	)	PUNCT
ejpam-6314	494	1	=	=	PUNCT
ejpam-6314	494	2	db(0,ψ	db(0,ψ	ADJ
ejpam-6314	494	3	n(0	n(0	PROPN
ejpam-6314	494	4	)	)	PUNCT
ejpam-6314	494	5	)	)	PUNCT
ejpam-6314	495	1	=	=	PUNCT
ejpam-6314	496	1	60	60	NUM
ejpam-6314	496	2	+	+	NUM
ejpam-6314	497	1	60i2	60i2	NUM
ejpam-6314	497	2	.	.	NOUN
ejpam-6314	497	3	db(ψ	db(ψ	PROPN
ejpam-6314	497	4	nκ	nκ	PROPN
ejpam-6314	497	5	,	,	PUNCT
ejpam-6314	497	6	ψnσ	ψnσ	NOUN
ejpam-6314	497	7	)	)	PUNCT
ejpam-6314	497	8	≾	≾	PROPN
ejpam-6314	497	9	µ(κ)db(κ	µ(κ)db(κ	NOUN
ejpam-6314	497	10	,	,	PUNCT
ejpam-6314	497	11	σ	σ	NOUN
ejpam-6314	497	12	)	)	PUNCT
ejpam-6314	497	13	+	+	NUM
ejpam-6314	497	14	ν(κ	ν(κ	NOUN
ejpam-6314	497	15	)	)	PUNCT
ejpam-6314	497	16	db(κ	db(κ	NOUN
ejpam-6314	497	17	,	,	PUNCT
ejpam-6314	497	18	ψnκ)db(σ	ψnκ)db(σ	NOUN
ejpam-6314	497	19	,	,	PUNCT
ejpam-6314	497	20	ψnσ	ψnσ	NOUN
ejpam-6314	497	21	)	)	PUNCT
ejpam-6314	497	22	1	1	NUM
ejpam-6314	497	23	+	+	CCONJ
ejpam-6314	497	24	db(κ	db(κ	NUM
ejpam-6314	497	25	,	,	PUNCT
ejpam-6314	497	26	σ	σ	PROPN
ejpam-6314	497	27	)	)	PUNCT
ejpam-6314	497	28	the	the	DET
ejpam-6314	497	29	above	above	ADJ
ejpam-6314	497	30	distances	distance	NOUN
ejpam-6314	497	31	satisfies	satisfie	NOUN
ejpam-6314	497	32	contraction	contraction	NOUN
ejpam-6314	497	33	condition	condition	NOUN
ejpam-6314	497	34	for	for	ADP
ejpam-6314	497	35	theorem	theorem	NOUN
ejpam-6314	497	36	(	(	PUNCT
ejpam-6314	497	37	5	5	NUM
ejpam-6314	497	38	)	)	PUNCT
ejpam-6314	497	39	by	by	ADP
ejpam-6314	497	40	using	use	VERB
ejpam-6314	497	41	type	type	NOUN
ejpam-6314	497	42	partial	partial	ADJ
ejpam-6314	497	43	order	order	NOUN
ejpam-6314	497	44	for	for	ADP
ejpam-6314	497	45	bcns	bcns	NOUN
ejpam-6314	497	46	,	,	PUNCT
ejpam-6314	497	47	thus	thus	ADV
ejpam-6314	497	48	the	the	DET
ejpam-6314	497	49	result	result	NOUN
ejpam-6314	497	50	is	be	AUX
ejpam-6314	497	51	obvious	obvious	ADJ
ejpam-6314	497	52	for	for	ADP
ejpam-6314	497	53	case(ii	case(ii	NOUN
ejpam-6314	497	54	)	)	PUNCT
ejpam-6314	497	55	.	.	PUNCT
ejpam-6314	498	1	case	case	NOUN
ejpam-6314	498	2	iii	iii	X
ejpam-6314	498	3	:	:	PUNCT
ejpam-6314	498	4	if	if	SCONJ
ejpam-6314	498	5	κ	κ	X
ejpam-6314	498	6	=	=	SYM
ejpam-6314	498	7	0	0	NUM
ejpam-6314	498	8	and	and	CCONJ
ejpam-6314	498	9	σ	σ	NUM
ejpam-6314	498	10	=	=	SYM
ejpam-6314	498	11	2	2	NUM
ejpam-6314	498	12	then	then	ADV
ejpam-6314	498	13	we	we	PRON
ejpam-6314	498	14	obtain	obtain	VERB
ejpam-6314	498	15	db(ψ	db(ψ	NOUN
ejpam-6314	498	16	nκ	nκ	NOUN
ejpam-6314	498	17	,	,	PUNCT
ejpam-6314	498	18	ψnσ	ψnσ	NOUN
ejpam-6314	498	19	)	)	PUNCT
ejpam-6314	498	20	=	=	SYM
ejpam-6314	498	21	db(ψ	db(ψ	X
ejpam-6314	498	22	n(0),ψn(2	n(0),ψn(2	NUM
ejpam-6314	498	23	)	)	PUNCT
ejpam-6314	498	24	)	)	PUNCT
ejpam-6314	499	1	=	=	SYM
ejpam-6314	499	2	1	1	NUM
ejpam-6314	499	3	+	+	NUM
ejpam-6314	499	4	i2	i2	NOUN
ejpam-6314	499	5	,	,	PUNCT
ejpam-6314	499	6	db(κ	db(κ	NOUN
ejpam-6314	499	7	,	,	PUNCT
ejpam-6314	499	8	σ	σ	X
ejpam-6314	499	9	)	)	PUNCT
ejpam-6314	499	10	=	=	SYM
ejpam-6314	500	1	db(0	db(0	NOUN
ejpam-6314	500	2	,	,	PUNCT
ejpam-6314	500	3	2	2	NUM
ejpam-6314	500	4	)	)	PUNCT
ejpam-6314	500	5	=	=	SYM
ejpam-6314	500	6	90	90	NUM
ejpam-6314	501	1	+	+	NUM
ejpam-6314	501	2	90i2	90i2	NUM
ejpam-6314	501	3	,	,	PUNCT
ejpam-6314	501	4	db(κ	db(κ	NOUN
ejpam-6314	501	5	,	,	PUNCT
ejpam-6314	501	6	ψnκ	ψnκ	PROPN
ejpam-6314	501	7	)	)	PUNCT
ejpam-6314	502	1	=	=	PUNCT
ejpam-6314	502	2	db(0,ψ	db(0,ψ	ADJ
ejpam-6314	502	3	n(0	n(0	PROPN
ejpam-6314	502	4	)	)	PUNCT
ejpam-6314	502	5	)	)	PUNCT
ejpam-6314	503	1	=	=	PUNCT
ejpam-6314	504	1	60	60	NUM
ejpam-6314	504	2	+	+	NUM
ejpam-6314	504	3	60i2	60i2	NUM
ejpam-6314	504	4	,	,	PUNCT
ejpam-6314	504	5	db(σ	db(σ	NUM
ejpam-6314	504	6	,	,	PUNCT
ejpam-6314	504	7	ψ	ψ	NOUN
ejpam-6314	504	8	nσ	nσ	NOUN
ejpam-6314	504	9	)	)	PUNCT
ejpam-6314	504	10	=	=	PUNCT
ejpam-6314	504	11	db(2,ψ	db(2,ψ	VERB
ejpam-6314	504	12	n(2	n(2	NOUN
ejpam-6314	504	13	)	)	PUNCT
ejpam-6314	504	14	)	)	PUNCT
ejpam-6314	505	1	=	=	PUNCT
ejpam-6314	505	2	0	0	PUNCT
ejpam-6314	506	1	+	+	NUM
ejpam-6314	506	2	0i2	0i2	NUM
ejpam-6314	506	3	.	.	PUNCT
ejpam-6314	507	1	db(ψ	db(ψ	PROPN
ejpam-6314	507	2	nκ	nκ	NOUN
ejpam-6314	507	3	,	,	PUNCT
ejpam-6314	507	4	ψnσ	ψnσ	NOUN
ejpam-6314	507	5	)	)	PUNCT
ejpam-6314	507	6	≾	≾	PROPN
ejpam-6314	507	7	µ(κ)db(κ	µ(κ)db(κ	NOUN
ejpam-6314	507	8	,	,	PUNCT
ejpam-6314	507	9	σ	σ	NOUN
ejpam-6314	507	10	)	)	PUNCT
ejpam-6314	507	11	+	+	NUM
ejpam-6314	507	12	ν(κ	ν(κ	NOUN
ejpam-6314	507	13	)	)	PUNCT
ejpam-6314	507	14	db(κ	db(κ	NOUN
ejpam-6314	507	15	,	,	PUNCT
ejpam-6314	507	16	ψnκ)db(σ	ψnκ)db(σ	NOUN
ejpam-6314	507	17	,	,	PUNCT
ejpam-6314	507	18	ψnσ	ψnσ	NOUN
ejpam-6314	507	19	)	)	PUNCT
ejpam-6314	507	20	1	1	NUM
ejpam-6314	507	21	+	+	CCONJ
ejpam-6314	507	22	db(κ	db(κ	NUM
ejpam-6314	507	23	,	,	PUNCT
ejpam-6314	507	24	σ	σ	PROPN
ejpam-6314	507	25	)	)	PUNCT
ejpam-6314	507	26	the	the	DET
ejpam-6314	507	27	above	above	ADJ
ejpam-6314	507	28	distances	distance	NOUN
ejpam-6314	507	29	satisfies	satisfie	NOUN
ejpam-6314	507	30	contraction	contraction	NOUN
ejpam-6314	507	31	condition	condition	NOUN
ejpam-6314	507	32	for	for	ADP
ejpam-6314	507	33	theorem	theorem	NOUN
ejpam-6314	507	34	(	(	PUNCT
ejpam-6314	507	35	5	5	NUM
ejpam-6314	507	36	)	)	PUNCT
ejpam-6314	507	37	by	by	ADP
ejpam-6314	507	38	using	use	VERB
ejpam-6314	507	39	type	type	NOUN
ejpam-6314	507	40	partial	partial	ADJ
ejpam-6314	507	41	order	order	NOUN
ejpam-6314	507	42	for	for	ADP
ejpam-6314	507	43	bcns	bcns	NOUN
ejpam-6314	507	44	,	,	PUNCT
ejpam-6314	507	45	thus	thus	ADV
ejpam-6314	507	46	the	the	DET
ejpam-6314	507	47	result	result	NOUN
ejpam-6314	507	48	is	be	AUX
ejpam-6314	507	49	obvious	obvious	ADJ
ejpam-6314	507	50	for	for	ADP
ejpam-6314	507	51	case(iii	case(iii	NOUN
ejpam-6314	507	52	)	)	PUNCT
ejpam-6314	507	53	.	.	PUNCT
ejpam-6314	508	1	case	case	NOUN
ejpam-6314	508	2	iv	iv	X
ejpam-6314	508	3	:	:	PUNCT
ejpam-6314	508	4	if	if	SCONJ
ejpam-6314	508	5	κ	κ	X
ejpam-6314	508	6	=	=	SYM
ejpam-6314	508	7	1	1	NUM
ejpam-6314	508	8	and	and	CCONJ
ejpam-6314	508	9	σ	σ	NUM
ejpam-6314	508	10	=	=	SYM
ejpam-6314	508	11	2	2	NUM
ejpam-6314	508	12	then	then	ADV
ejpam-6314	508	13	we	we	PRON
ejpam-6314	508	14	obtain	obtain	VERB
ejpam-6314	508	15	db(ψ	db(ψ	NOUN
ejpam-6314	508	16	nκ	nκ	NOUN
ejpam-6314	508	17	,	,	PUNCT
ejpam-6314	508	18	ψnσ	ψnσ	NOUN
ejpam-6314	508	19	)	)	PUNCT
ejpam-6314	508	20	=	=	SYM
ejpam-6314	508	21	db(ψ	db(ψ	NOUN
ejpam-6314	508	22	n(1),ψn(2	n(1),ψn(2	NUM
ejpam-6314	508	23	)	)	PUNCT
ejpam-6314	508	24	)	)	PUNCT
ejpam-6314	509	1	=	=	PUNCT
ejpam-6314	509	2	0	0	PUNCT
ejpam-6314	510	1	+	+	NUM
ejpam-6314	510	2	0i2	0i2	NOUN
ejpam-6314	510	3	,	,	PUNCT
ejpam-6314	510	4	db(κ	db(κ	NUM
ejpam-6314	510	5	,	,	PUNCT
ejpam-6314	510	6	σ	σ	X
ejpam-6314	510	7	)	)	PUNCT
ejpam-6314	510	8	=	=	PUNCT
ejpam-6314	510	9	db(1	db(1	VERB
ejpam-6314	510	10	,	,	PUNCT
ejpam-6314	510	11	2	2	NUM
ejpam-6314	510	12	)	)	PUNCT
ejpam-6314	510	13	=	=	SYM
ejpam-6314	511	1	1	1	NUM
ejpam-6314	511	2	+	+	NUM
ejpam-6314	511	3	i2	i2	NOUN
ejpam-6314	511	4	,	,	PUNCT
ejpam-6314	511	5	db(κ	db(κ	NOUN
ejpam-6314	511	6	,	,	PUNCT
ejpam-6314	511	7	ψnκ	ψnκ	PROPN
ejpam-6314	511	8	)	)	PUNCT
ejpam-6314	511	9	=	=	SYM
ejpam-6314	511	10	db(1,ψ	db(1,ψ	PRON
ejpam-6314	511	11	n(1	n(1	NOUN
ejpam-6314	511	12	)	)	PUNCT
ejpam-6314	511	13	)	)	PUNCT
ejpam-6314	512	1	=	=	SYM
ejpam-6314	512	2	1	1	NUM
ejpam-6314	512	3	+	+	NUM
ejpam-6314	512	4	i2	i2	NOUN
ejpam-6314	512	5	,	,	PUNCT
ejpam-6314	512	6	db(σ	db(σ	NUM
ejpam-6314	512	7	,	,	PUNCT
ejpam-6314	512	8	ψ	ψ	NOUN
ejpam-6314	512	9	nσ	nσ	NOUN
ejpam-6314	512	10	)	)	PUNCT
ejpam-6314	512	11	=	=	PUNCT
ejpam-6314	512	12	db(2,ψ	db(2,ψ	VERB
ejpam-6314	512	13	n(2	n(2	NOUN
ejpam-6314	512	14	)	)	PUNCT
ejpam-6314	512	15	)	)	PUNCT
ejpam-6314	513	1	=	=	PUNCT
ejpam-6314	513	2	0	0	PUNCT
ejpam-6314	514	1	+	+	NUM
ejpam-6314	514	2	0i2	0i2	NUM
ejpam-6314	514	3	.	.	PUNCT
ejpam-6314	515	1	db(ψ	db(ψ	PROPN
ejpam-6314	515	2	nκ	nκ	NOUN
ejpam-6314	515	3	,	,	PUNCT
ejpam-6314	515	4	ψnσ	ψnσ	NOUN
ejpam-6314	515	5	)	)	PUNCT
ejpam-6314	515	6	≾	≾	PROPN
ejpam-6314	515	7	µ(κ)db(κ	µ(κ)db(κ	NOUN
ejpam-6314	515	8	,	,	PUNCT
ejpam-6314	515	9	σ	σ	NOUN
ejpam-6314	515	10	)	)	PUNCT
ejpam-6314	515	11	+	+	NUM
ejpam-6314	515	12	ν(κ	ν(κ	NOUN
ejpam-6314	515	13	)	)	PUNCT
ejpam-6314	515	14	db(κ	db(κ	NOUN
ejpam-6314	515	15	,	,	PUNCT
ejpam-6314	515	16	ψnκ)db(σ	ψnκ)db(σ	NOUN
ejpam-6314	515	17	,	,	PUNCT
ejpam-6314	515	18	ψnσ	ψnσ	NOUN
ejpam-6314	515	19	)	)	PUNCT
ejpam-6314	515	20	1	1	NUM
ejpam-6314	515	21	+	+	CCONJ
ejpam-6314	515	22	db(κ	db(κ	NUM
ejpam-6314	515	23	,	,	PUNCT
ejpam-6314	515	24	σ	σ	PROPN
ejpam-6314	515	25	)	)	PUNCT
ejpam-6314	515	26	the	the	DET
ejpam-6314	515	27	above	above	ADJ
ejpam-6314	515	28	distances	distance	NOUN
ejpam-6314	515	29	satisfies	satisfie	NOUN
ejpam-6314	515	30	contraction	contraction	NOUN
ejpam-6314	515	31	condition	condition	NOUN
ejpam-6314	515	32	for	for	ADP
ejpam-6314	515	33	theorem	theorem	NOUN
ejpam-6314	515	34	(	(	PUNCT
ejpam-6314	515	35	5	5	NUM
ejpam-6314	515	36	)	)	PUNCT
ejpam-6314	515	37	by	by	ADP
ejpam-6314	515	38	using	use	VERB
ejpam-6314	515	39	type	type	NOUN
ejpam-6314	515	40	partial	partial	ADJ
ejpam-6314	515	41	order	order	NOUN
ejpam-6314	515	42	for	for	ADP
ejpam-6314	515	43	bcns	bcns	NOUN
ejpam-6314	515	44	,	,	PUNCT
ejpam-6314	515	45	thus	thus	ADV
ejpam-6314	515	46	the	the	DET
ejpam-6314	515	47	result	result	NOUN
ejpam-6314	515	48	is	be	AUX
ejpam-6314	515	49	obvious	obvious	ADJ
ejpam-6314	515	50	for	for	ADP
ejpam-6314	515	51	case(iv	case(iv	NOUN
ejpam-6314	515	52	)	)	PUNCT
ejpam-6314	515	53	.	.	PUNCT
ejpam-6314	516	1	case	case	NOUN
ejpam-6314	516	2	v	v	ADP
ejpam-6314	516	3	:	:	PUNCT
ejpam-6314	516	4	if	if	SCONJ
ejpam-6314	516	5	κ	κ	X
ejpam-6314	516	6	=	=	SYM
ejpam-6314	516	7	1	1	NUM
ejpam-6314	516	8	and	and	CCONJ
ejpam-6314	516	9	σ	σ	NUM
ejpam-6314	516	10	=	=	SYM
ejpam-6314	516	11	0	0	PUNCT
ejpam-6314	517	1	then	then	ADV
ejpam-6314	517	2	we	we	PRON
ejpam-6314	517	3	obtain	obtain	VERB
ejpam-6314	517	4	db(ψ	db(ψ	NOUN
ejpam-6314	517	5	nκ	nκ	NOUN
ejpam-6314	517	6	,	,	PUNCT
ejpam-6314	517	7	ψnσ	ψnσ	NOUN
ejpam-6314	517	8	)	)	PUNCT
ejpam-6314	517	9	=	=	SYM
ejpam-6314	517	10	db(ψ	db(ψ	X
ejpam-6314	517	11	n(1),ψn(0	n(1),ψn(0	NOUN
ejpam-6314	517	12	)	)	PUNCT
ejpam-6314	517	13	)	)	PUNCT
ejpam-6314	518	1	=	=	SYM
ejpam-6314	518	2	1	1	NUM
ejpam-6314	518	3	+	+	NUM
ejpam-6314	518	4	1i2	1i2	NUM
ejpam-6314	518	5	,	,	PUNCT
ejpam-6314	518	6	db(κ	db(κ	NOUN
ejpam-6314	518	7	,	,	PUNCT
ejpam-6314	518	8	σ	σ	X
ejpam-6314	518	9	)	)	PUNCT
ejpam-6314	518	10	=	=	PUNCT
ejpam-6314	518	11	db(1	db(1	VERB
ejpam-6314	518	12	,	,	PUNCT
ejpam-6314	518	13	0	0	NUM
ejpam-6314	518	14	)	)	PUNCT
ejpam-6314	518	15	=	=	SYM
ejpam-6314	519	1	60	60	NUM
ejpam-6314	519	2	+	+	NUM
ejpam-6314	519	3	60i2	60i2	NUM
ejpam-6314	519	4	,	,	PUNCT
ejpam-6314	519	5	db(κ	db(κ	NOUN
ejpam-6314	519	6	,	,	PUNCT
ejpam-6314	519	7	ψnκ	ψnκ	PROPN
ejpam-6314	519	8	)	)	PUNCT
ejpam-6314	519	9	=	=	SYM
ejpam-6314	519	10	db(1,ψ	db(1,ψ	PRON
ejpam-6314	519	11	n(1	n(1	NOUN
ejpam-6314	519	12	)	)	PUNCT
ejpam-6314	519	13	)	)	PUNCT
ejpam-6314	520	1	=	=	SYM
ejpam-6314	520	2	1	1	NUM
ejpam-6314	520	3	+	+	NUM
ejpam-6314	520	4	i2	i2	NOUN
ejpam-6314	520	5	,	,	PUNCT
ejpam-6314	520	6	db(σ	db(σ	NUM
ejpam-6314	520	7	,	,	PUNCT
ejpam-6314	520	8	ψ	ψ	NOUN
ejpam-6314	520	9	nσ	nσ	NOUN
ejpam-6314	520	10	)	)	PUNCT
ejpam-6314	520	11	=	=	PUNCT
ejpam-6314	520	12	db(0,ψ	db(0,ψ	ADJ
ejpam-6314	520	13	n(0	n(0	PROPN
ejpam-6314	520	14	)	)	PUNCT
ejpam-6314	520	15	)	)	PUNCT
ejpam-6314	521	1	=	=	PUNCT
ejpam-6314	522	1	60	60	NUM
ejpam-6314	522	2	+	+	NUM
ejpam-6314	523	1	60i2	60i2	NUM
ejpam-6314	523	2	.	.	NOUN
ejpam-6314	523	3	db(ψ	db(ψ	PROPN
ejpam-6314	523	4	nκ	nκ	PROPN
ejpam-6314	523	5	,	,	PUNCT
ejpam-6314	523	6	ψnσ	ψnσ	NOUN
ejpam-6314	523	7	)	)	PUNCT
ejpam-6314	523	8	≾	≾	PROPN
ejpam-6314	523	9	µ(κ)db(κ	µ(κ)db(κ	NOUN
ejpam-6314	523	10	,	,	PUNCT
ejpam-6314	523	11	σ	σ	NOUN
ejpam-6314	523	12	)	)	PUNCT
ejpam-6314	523	13	+	+	NUM
ejpam-6314	523	14	ν(κ	ν(κ	NOUN
ejpam-6314	523	15	)	)	PUNCT
ejpam-6314	523	16	db(κ	db(κ	NOUN
ejpam-6314	523	17	,	,	PUNCT
ejpam-6314	523	18	ψnκ)db(σ	ψnκ)db(σ	NOUN
ejpam-6314	523	19	,	,	PUNCT
ejpam-6314	523	20	ψnσ	ψnσ	NOUN
ejpam-6314	523	21	)	)	PUNCT
ejpam-6314	523	22	1	1	NUM
ejpam-6314	523	23	+	+	CCONJ
ejpam-6314	523	24	db(κ	db(κ	NUM
ejpam-6314	523	25	,	,	PUNCT
ejpam-6314	523	26	σ	σ	X
ejpam-6314	523	27	)	)	PUNCT
ejpam-6314	523	28	m.	m.	NOUN
ejpam-6314	523	29	sarwar	sarwar	PROPN
ejpam-6314	523	30	et	et	PROPN
ejpam-6314	523	31	al	al	PROPN
ejpam-6314	523	32	.	.	PUNCT
ejpam-6314	523	33	/	/	SYM
ejpam-6314	523	34	eur	eur	PROPN
ejpam-6314	523	35	.	.	PUNCT
ejpam-6314	524	1	j.	j.	PROPN
ejpam-6314	524	2	pure	pure	PROPN
ejpam-6314	524	3	appl	appl	PROPN
ejpam-6314	524	4	.	.	PROPN
ejpam-6314	524	5	math	math	PROPN
ejpam-6314	524	6	,	,	PUNCT
ejpam-6314	524	7	18	18	NUM
ejpam-6314	524	8	(	(	PUNCT
ejpam-6314	524	9	3	3	NUM
ejpam-6314	524	10	)	)	PUNCT
ejpam-6314	524	11	(	(	PUNCT
ejpam-6314	524	12	2025	2025	NUM
ejpam-6314	524	13	)	)	PUNCT
ejpam-6314	524	14	,	,	PUNCT
ejpam-6314	524	15	6314	6314	NUM
ejpam-6314	524	16	23	23	NUM
ejpam-6314	524	17	of	of	ADP
ejpam-6314	524	18	28	28	NUM
ejpam-6314	524	19	the	the	DET
ejpam-6314	524	20	above	above	ADJ
ejpam-6314	524	21	distances	distance	NOUN
ejpam-6314	524	22	satisfies	satisfie	NOUN
ejpam-6314	524	23	contraction	contraction	NOUN
ejpam-6314	524	24	condition	condition	NOUN
ejpam-6314	524	25	for	for	ADP
ejpam-6314	524	26	theorem	theorem	NOUN
ejpam-6314	524	27	(	(	PUNCT
ejpam-6314	524	28	5	5	NUM
ejpam-6314	524	29	)	)	PUNCT
ejpam-6314	524	30	by	by	ADP
ejpam-6314	524	31	using	use	VERB
ejpam-6314	524	32	type	type	NOUN
ejpam-6314	524	33	partial	partial	ADJ
ejpam-6314	524	34	order	order	NOUN
ejpam-6314	524	35	for	for	ADP
ejpam-6314	524	36	bcns	bcns	NOUN
ejpam-6314	524	37	,	,	PUNCT
ejpam-6314	524	38	thus	thus	ADV
ejpam-6314	524	39	the	the	DET
ejpam-6314	524	40	result	result	NOUN
ejpam-6314	524	41	is	be	AUX
ejpam-6314	524	42	obvious	obvious	ADJ
ejpam-6314	524	43	for	for	ADP
ejpam-6314	524	44	case(v	case(v	NOUN
ejpam-6314	524	45	)	)	PUNCT
ejpam-6314	524	46	.	.	PUNCT
ejpam-6314	525	1	case	case	NOUN
ejpam-6314	525	2	vi	vi	ADP
ejpam-6314	525	3	:	:	PUNCT
ejpam-6314	525	4	if	if	SCONJ
ejpam-6314	525	5	κ	κ	X
ejpam-6314	525	6	=	=	SYM
ejpam-6314	525	7	2	2	NUM
ejpam-6314	525	8	and	and	CCONJ
ejpam-6314	525	9	σ	σ	NUM
ejpam-6314	525	10	=	=	SYM
ejpam-6314	525	11	0	0	PUNCT
ejpam-6314	526	1	then	then	ADV
ejpam-6314	526	2	we	we	PRON
ejpam-6314	526	3	obtain	obtain	VERB
ejpam-6314	526	4	db(ψ	db(ψ	NOUN
ejpam-6314	526	5	nκ	nκ	NOUN
ejpam-6314	526	6	,	,	PUNCT
ejpam-6314	526	7	ψnσ	ψnσ	NOUN
ejpam-6314	526	8	)	)	PUNCT
ejpam-6314	526	9	=	=	SYM
ejpam-6314	526	10	db(ψ	db(ψ	X
ejpam-6314	526	11	n(2),ψn(0	n(2),ψn(0	NOUN
ejpam-6314	526	12	)	)	PUNCT
ejpam-6314	526	13	)	)	PUNCT
ejpam-6314	527	1	=	=	SYM
ejpam-6314	527	2	1	1	NUM
ejpam-6314	527	3	+	+	NUM
ejpam-6314	527	4	i2	i2	NOUN
ejpam-6314	527	5	,	,	PUNCT
ejpam-6314	527	6	db(κ	db(κ	NOUN
ejpam-6314	527	7	,	,	PUNCT
ejpam-6314	527	8	σ	σ	NOUN
ejpam-6314	527	9	)	)	PUNCT
ejpam-6314	527	10	=	=	SYM
ejpam-6314	527	11	db(2	db(2	PROPN
ejpam-6314	527	12	,	,	PUNCT
ejpam-6314	527	13	0	0	NUM
ejpam-6314	527	14	)	)	PUNCT
ejpam-6314	527	15	=	=	SYM
ejpam-6314	528	1	90	90	NUM
ejpam-6314	528	2	+	+	NUM
ejpam-6314	528	3	90i2	90i2	NUM
ejpam-6314	528	4	,	,	PUNCT
ejpam-6314	528	5	db(κ	db(κ	NOUN
ejpam-6314	528	6	,	,	PUNCT
ejpam-6314	528	7	ψnκ	ψnκ	PROPN
ejpam-6314	528	8	)	)	PUNCT
ejpam-6314	529	1	=	=	PRON
ejpam-6314	529	2	db(2,ψ	db(2,ψ	VERB
ejpam-6314	529	3	n(2	n(2	NOUN
ejpam-6314	529	4	)	)	PUNCT
ejpam-6314	529	5	)	)	PUNCT
ejpam-6314	530	1	=	=	PUNCT
ejpam-6314	530	2	0	0	NUM
ejpam-6314	531	1	+	+	NUM
ejpam-6314	531	2	0i2	0i2	NOUN
ejpam-6314	531	3	,	,	PUNCT
ejpam-6314	531	4	db(σ	db(σ	NUM
ejpam-6314	531	5	,	,	PUNCT
ejpam-6314	531	6	ψ	ψ	NOUN
ejpam-6314	531	7	nσ	nσ	NOUN
ejpam-6314	531	8	)	)	PUNCT
ejpam-6314	531	9	=	=	PUNCT
ejpam-6314	532	1	db(0,ψ	db(0,ψ	ADJ
ejpam-6314	532	2	n(0	n(0	PROPN
ejpam-6314	532	3	)	)	PUNCT
ejpam-6314	532	4	)	)	PUNCT
ejpam-6314	533	1	=	=	SYM
ejpam-6314	533	2	1	1	NUM
ejpam-6314	533	3	+	+	NUM
ejpam-6314	533	4	i2	i2	PROPN
ejpam-6314	533	5	.	.	PROPN
ejpam-6314	533	6	db(ψ	db(ψ	PROPN
ejpam-6314	533	7	nκ	nκ	PROPN
ejpam-6314	533	8	,	,	PUNCT
ejpam-6314	533	9	ψnσ	ψnσ	NOUN
ejpam-6314	533	10	)	)	PUNCT
ejpam-6314	533	11	≾	≾	PROPN
ejpam-6314	533	12	µ(κ)db(κ	µ(κ)db(κ	NOUN
ejpam-6314	533	13	,	,	PUNCT
ejpam-6314	533	14	σ	σ	NOUN
ejpam-6314	533	15	)	)	PUNCT
ejpam-6314	533	16	+	+	NUM
ejpam-6314	533	17	ν(κ	ν(κ	NOUN
ejpam-6314	533	18	)	)	PUNCT
ejpam-6314	533	19	db(κ	db(κ	NOUN
ejpam-6314	533	20	,	,	PUNCT
ejpam-6314	533	21	ψnκ)db(σ	ψnκ)db(σ	NOUN
ejpam-6314	533	22	,	,	PUNCT
ejpam-6314	533	23	ψnσ	ψnσ	NOUN
ejpam-6314	533	24	)	)	PUNCT
ejpam-6314	533	25	1	1	NUM
ejpam-6314	533	26	+	+	CCONJ
ejpam-6314	533	27	db(κ	db(κ	NUM
ejpam-6314	533	28	,	,	PUNCT
ejpam-6314	533	29	σ	σ	PROPN
ejpam-6314	533	30	)	)	PUNCT
ejpam-6314	533	31	the	the	DET
ejpam-6314	533	32	above	above	ADJ
ejpam-6314	533	33	distances	distance	NOUN
ejpam-6314	533	34	satisfies	satisfie	NOUN
ejpam-6314	533	35	contraction	contraction	NOUN
ejpam-6314	533	36	condition	condition	NOUN
ejpam-6314	533	37	for	for	ADP
ejpam-6314	533	38	theorem	theorem	NOUN
ejpam-6314	533	39	(	(	PUNCT
ejpam-6314	533	40	5	5	NUM
ejpam-6314	533	41	)	)	PUNCT
ejpam-6314	533	42	by	by	ADP
ejpam-6314	533	43	using	use	VERB
ejpam-6314	533	44	type	type	NOUN
ejpam-6314	533	45	partial	partial	ADJ
ejpam-6314	533	46	order	order	NOUN
ejpam-6314	533	47	for	for	ADP
ejpam-6314	533	48	bcns	bcns	NOUN
ejpam-6314	533	49	,	,	PUNCT
ejpam-6314	533	50	thus	thus	ADV
ejpam-6314	533	51	the	the	DET
ejpam-6314	533	52	result	result	NOUN
ejpam-6314	533	53	is	be	AUX
ejpam-6314	533	54	obvious	obvious	ADJ
ejpam-6314	533	55	for	for	ADP
ejpam-6314	533	56	case(vi	case(vi	NOUN
ejpam-6314	533	57	)	)	PUNCT
ejpam-6314	533	58	.	.	PUNCT
ejpam-6314	534	1	case	case	NOUN
ejpam-6314	534	2	vii	vii	PROPN
ejpam-6314	534	3	:	:	PUNCT
ejpam-6314	534	4	if	if	SCONJ
ejpam-6314	534	5	κ	κ	X
ejpam-6314	534	6	=	=	SYM
ejpam-6314	534	7	2	2	NUM
ejpam-6314	534	8	and	and	CCONJ
ejpam-6314	534	9	σ	σ	NUM
ejpam-6314	534	10	=	=	NOUN
ejpam-6314	534	11	1	1	NUM
ejpam-6314	534	12	then	then	ADV
ejpam-6314	534	13	we	we	PRON
ejpam-6314	534	14	obtain	obtain	VERB
ejpam-6314	534	15	db(ψ	db(ψ	NOUN
ejpam-6314	534	16	nκ	nκ	NOUN
ejpam-6314	534	17	,	,	PUNCT
ejpam-6314	534	18	ψnσ	ψnσ	NOUN
ejpam-6314	534	19	)	)	PUNCT
ejpam-6314	534	20	=	=	SYM
ejpam-6314	534	21	db(ψ	db(ψ	X
ejpam-6314	534	22	n(2),ψn(1	n(2),ψn(1	NUM
ejpam-6314	534	23	)	)	PUNCT
ejpam-6314	534	24	)	)	PUNCT
ejpam-6314	535	1	=	=	PUNCT
ejpam-6314	535	2	0	0	PUNCT
ejpam-6314	536	1	+	+	NUM
ejpam-6314	536	2	0i2	0i2	NOUN
ejpam-6314	536	3	,	,	PUNCT
ejpam-6314	536	4	db(κ	db(κ	NUM
ejpam-6314	536	5	,	,	PUNCT
ejpam-6314	536	6	σ	σ	NOUN
ejpam-6314	536	7	)	)	PUNCT
ejpam-6314	536	8	=	=	SYM
ejpam-6314	536	9	db(2	db(2	PROPN
ejpam-6314	536	10	,	,	PUNCT
ejpam-6314	536	11	1	1	NUM
ejpam-6314	536	12	)	)	PUNCT
ejpam-6314	536	13	=	=	SYM
ejpam-6314	537	1	1	1	NUM
ejpam-6314	537	2	+	+	NUM
ejpam-6314	537	3	i2	i2	NOUN
ejpam-6314	537	4	,	,	PUNCT
ejpam-6314	537	5	db(κ	db(κ	NOUN
ejpam-6314	537	6	,	,	PUNCT
ejpam-6314	537	7	ψnκ	ψnκ	PROPN
ejpam-6314	537	8	)	)	PUNCT
ejpam-6314	538	1	=	=	PRON
ejpam-6314	538	2	db(2,ψ	db(2,ψ	VERB
ejpam-6314	538	3	n(2	n(2	NOUN
ejpam-6314	538	4	)	)	PUNCT
ejpam-6314	538	5	)	)	PUNCT
ejpam-6314	539	1	=	=	PUNCT
ejpam-6314	539	2	0	0	NUM
ejpam-6314	540	1	+	+	NUM
ejpam-6314	540	2	0i2	0i2	NOUN
ejpam-6314	540	3	,	,	PUNCT
ejpam-6314	540	4	db(σ	db(σ	NUM
ejpam-6314	540	5	,	,	PUNCT
ejpam-6314	540	6	ψ	ψ	NOUN
ejpam-6314	540	7	nσ	nσ	NOUN
ejpam-6314	540	8	)	)	PUNCT
ejpam-6314	541	1	=	=	PRON
ejpam-6314	541	2	db(2,ψ	db(2,ψ	VERB
ejpam-6314	541	3	n(1	n(1	NOUN
ejpam-6314	541	4	)	)	PUNCT
ejpam-6314	541	5	)	)	PUNCT
ejpam-6314	542	1	=	=	PUNCT
ejpam-6314	542	2	0	0	PUNCT
ejpam-6314	543	1	+	+	NUM
ejpam-6314	543	2	0i2	0i2	NUM
ejpam-6314	543	3	.	.	PUNCT
ejpam-6314	544	1	db(ψ	db(ψ	PROPN
ejpam-6314	544	2	nκ	nκ	NOUN
ejpam-6314	544	3	,	,	PUNCT
ejpam-6314	544	4	ψnσ	ψnσ	NOUN
ejpam-6314	544	5	)	)	PUNCT
ejpam-6314	544	6	≾	≾	PROPN
ejpam-6314	544	7	µ(κ)db(κ	µ(κ)db(κ	NOUN
ejpam-6314	544	8	,	,	PUNCT
ejpam-6314	544	9	σ	σ	NOUN
ejpam-6314	544	10	)	)	PUNCT
ejpam-6314	544	11	+	+	NUM
ejpam-6314	544	12	ν(κ	ν(κ	NOUN
ejpam-6314	544	13	)	)	PUNCT
ejpam-6314	544	14	db(κ	db(κ	NOUN
ejpam-6314	544	15	,	,	PUNCT
ejpam-6314	544	16	ψnκ)db(σ	ψnκ)db(σ	NOUN
ejpam-6314	544	17	,	,	PUNCT
ejpam-6314	544	18	ψnσ	ψnσ	NOUN
ejpam-6314	544	19	)	)	PUNCT
ejpam-6314	544	20	1	1	NUM
ejpam-6314	544	21	+	+	CCONJ
ejpam-6314	544	22	db(κ	db(κ	NUM
ejpam-6314	544	23	,	,	PUNCT
ejpam-6314	544	24	σ	σ	PROPN
ejpam-6314	544	25	)	)	PUNCT
ejpam-6314	544	26	the	the	DET
ejpam-6314	544	27	above	above	ADJ
ejpam-6314	544	28	distances	distance	NOUN
ejpam-6314	544	29	satisfies	satisfie	NOUN
ejpam-6314	544	30	contraction	contraction	NOUN
ejpam-6314	544	31	condition	condition	NOUN
ejpam-6314	544	32	for	for	ADP
ejpam-6314	544	33	theorem	theorem	NOUN
ejpam-6314	544	34	(	(	PUNCT
ejpam-6314	544	35	5	5	NUM
ejpam-6314	544	36	)	)	PUNCT
ejpam-6314	544	37	by	by	ADP
ejpam-6314	544	38	using	use	VERB
ejpam-6314	544	39	type	type	NOUN
ejpam-6314	544	40	partial	partial	ADJ
ejpam-6314	544	41	order	order	NOUN
ejpam-6314	544	42	for	for	ADP
ejpam-6314	544	43	bcns	bcns	NOUN
ejpam-6314	544	44	,	,	PUNCT
ejpam-6314	544	45	thus	thus	ADV
ejpam-6314	544	46	the	the	DET
ejpam-6314	544	47	result	result	NOUN
ejpam-6314	544	48	is	be	AUX
ejpam-6314	544	49	obvious	obvious	ADJ
ejpam-6314	544	50	for	for	ADP
ejpam-6314	544	51	case(vii	case(vii	NOUN
ejpam-6314	544	52	)	)	PUNCT
ejpam-6314	544	53	.	.	PUNCT
ejpam-6314	545	1	therefore	therefore	ADV
ejpam-6314	545	2	all	all	DET
ejpam-6314	545	3	the	the	DET
ejpam-6314	545	4	axioms	axiom	NOUN
ejpam-6314	545	5	of	of	ADP
ejpam-6314	545	6	theorem	theorem	NOUN
ejpam-6314	545	7	(	(	PUNCT
ejpam-6314	545	8	5	5	NUM
ejpam-6314	545	9	)	)	PUNCT
ejpam-6314	545	10	are	be	AUX
ejpam-6314	545	11	fulfilled	fulfil	VERB
ejpam-6314	545	12	for	for	ADP
ejpam-6314	545	13	all	all	DET
ejpam-6314	545	14	the	the	DET
ejpam-6314	545	15	cases	case	NOUN
ejpam-6314	545	16	,	,	PUNCT
ejpam-6314	545	17	thus	thus	ADV
ejpam-6314	545	18	ψ	ψ	X
ejpam-6314	545	19	has	have	VERB
ejpam-6314	545	20	a	a	DET
ejpam-6314	545	21	ufp	ufp	NOUN
ejpam-6314	545	22	.	.	PUNCT
ejpam-6314	546	1	3	3	X
ejpam-6314	546	2	.	.	X
ejpam-6314	546	3	application	application	NOUN
ejpam-6314	546	4	in	in	ADP
ejpam-6314	546	5	this	this	DET
ejpam-6314	546	6	section	section	NOUN
ejpam-6314	546	7	we	we	PRON
ejpam-6314	546	8	solve	solve	VERB
ejpam-6314	546	9	the	the	DET
ejpam-6314	546	10	system	system	NOUN
ejpam-6314	546	11	of	of	ADP
ejpam-6314	546	12	fractional	fractional	ADJ
ejpam-6314	546	13	differential	differential	ADJ
ejpam-6314	546	14	equation	equation	NOUN
ejpam-6314	546	15	with	with	ADP
ejpam-6314	546	16	the	the	DET
ejpam-6314	546	17	help	help	NOUN
ejpam-6314	546	18	of	of	ADP
ejpam-6314	546	19	theorem(4	theorem(4	PROPN
ejpam-6314	546	20	)	)	PUNCT
ejpam-6314	546	21	{	{	PUNCT
ejpam-6314	546	22	ϵdβℵ(y	ϵdβℵ(y	NOUN
ejpam-6314	546	23	)	)	PUNCT
ejpam-6314	546	24	+	+	CCONJ
ejpam-6314	546	25	ϑ(y	ϑ(y	PROPN
ejpam-6314	546	26	,	,	PUNCT
ejpam-6314	546	27	λ(y	λ(y	PROPN
ejpam-6314	546	28	)	)	PUNCT
ejpam-6314	546	29	)	)	PUNCT
ejpam-6314	547	1	=	=	SYM
ejpam-6314	547	2	0	0	NUM
ejpam-6314	547	3	,	,	PUNCT
ejpam-6314	547	4	ϵdβω(y	ϵdβω(y	NUM
ejpam-6314	547	5	)	)	PUNCT
ejpam-6314	548	1	+	+	CCONJ
ejpam-6314	548	2	υ(y	υ(y	PROPN
ejpam-6314	548	3	,	,	PUNCT
ejpam-6314	548	4	χ(y	χ(y	NOUN
ejpam-6314	548	5	)	)	PUNCT
ejpam-6314	548	6	)	)	PUNCT
ejpam-6314	549	1	=	=	SYM
ejpam-6314	549	2	0	0	NUM
ejpam-6314	549	3	,	,	PUNCT
ejpam-6314	549	4	1	1	NUM
ejpam-6314	549	5	<	<	X
ejpam-6314	549	6	ϵ	ϵ	X
ejpam-6314	549	7	≤	≤	NUM
ejpam-6314	549	8	2,y	2,y	NUM
ejpam-6314	549	9	∈	∈	PROPN
ejpam-6314	550	1	[	[	X
ejpam-6314	550	2	0	0	NUM
ejpam-6314	550	3	,	,	PUNCT
ejpam-6314	550	4	1	1	NUM
ejpam-6314	550	5	]	]	PUNCT
ejpam-6314	550	6	.	.	PUNCT
ejpam-6314	551	1	λ(0	λ(0	NOUN
ejpam-6314	551	2	)	)	PUNCT
ejpam-6314	551	3	=	=	SYM
ejpam-6314	551	4	ω(0	ω(0	PROPN
ejpam-6314	551	5	)	)	PUNCT
ejpam-6314	551	6	=	=	SYM
ejpam-6314	551	7	ℓ,λ(1	ℓ,λ(1	X
ejpam-6314	551	8	)	)	PUNCT
ejpam-6314	551	9	=	=	PUNCT
ejpam-6314	552	1	ω(1	ω(1	PROPN
ejpam-6314	552	2	)	)	PUNCT
ejpam-6314	552	3	=	=	SYM
ejpam-6314	552	4	ȷ	ȷ	NOUN
ejpam-6314	552	5	,	,	PUNCT
ejpam-6314	552	6	where	where	SCONJ
ejpam-6314	552	7	ℓ	ℓ	NOUN
ejpam-6314	552	8	and	and	CCONJ
ejpam-6314	552	9	ȷ	ȷ	PROPN
ejpam-6314	552	10	are	be	AUX
ejpam-6314	552	11	constant	constant	ADJ
ejpam-6314	552	12	.	.	PUNCT
ejpam-6314	553	1	(	(	PUNCT
ejpam-6314	553	2	27	27	NUM
ejpam-6314	553	3	)	)	PUNCT
ejpam-6314	553	4	where	where	SCONJ
ejpam-6314	553	5	ϵdβ	ϵdβ	PROPN
ejpam-6314	553	6	represent	represent	VERB
ejpam-6314	553	7	the	the	DET
ejpam-6314	553	8	order	order	NOUN
ejpam-6314	553	9	of	of	ADP
ejpam-6314	553	10	β	β	PRON
ejpam-6314	553	11	as	as	ADP
ejpam-6314	553	12	the	the	DET
ejpam-6314	553	13	caputo	caputo	PROPN
ejpam-6314	553	14	fractional	fractional	ADJ
ejpam-6314	553	15	derivatives	derivative	NOUN
ejpam-6314	553	16	and	and	CCONJ
ejpam-6314	553	17	λ.ω	λ.ω	NOUN
ejpam-6314	553	18	:	:	PUNCT
ejpam-6314	554	1	[	[	X
ejpam-6314	554	2	0	0	NUM
ejpam-6314	554	3	,	,	PUNCT
ejpam-6314	554	4	1]×	1]×	NUM
ejpam-6314	554	5	[	[	X
ejpam-6314	554	6	0,+∞	0,+∞	NUM
ejpam-6314	554	7	)	)	PUNCT
ejpam-6314	554	8	→	→	PUNCT
ejpam-6314	555	1	[	[	X
ejpam-6314	555	2	0,+∞	0,+∞	NUM
ejpam-6314	555	3	)	)	PUNCT
ejpam-6314	555	4	.	.	PUNCT
ejpam-6314	556	1	by	by	ADP
ejpam-6314	556	2	using	use	VERB
ejpam-6314	556	3	the	the	DET
ejpam-6314	556	4	result	result	NOUN
ejpam-6314	556	5	of	of	ADP
ejpam-6314	556	6	[	[	X
ejpam-6314	556	7	26	26	NUM
ejpam-6314	556	8	]	]	X
ejpam-6314	556	9	we	we	PRON
ejpam-6314	556	10	have	have	AUX
ejpam-6314	556	11	,	,	PUNCT
ejpam-6314	556	12	iβ[dβℵ(y	iβ[dβℵ(y	PROPN
ejpam-6314	556	13	)	)	PUNCT
ejpam-6314	556	14	]	]	PUNCT
ejpam-6314	557	1	=	=	PUNCT
ejpam-6314	557	2	ℵ(y	ℵ(y	PROPN
ejpam-6314	557	3	)	)	PUNCT
ejpam-6314	558	1	+	+	CCONJ
ejpam-6314	558	2	c0	c0	NOUN
ejpam-6314	558	3	+	+	CCONJ
ejpam-6314	558	4	yc1	yc1	PRON
ejpam-6314	559	1	+	+	CCONJ
ejpam-6314	559	2	y2c2	y2c2	NUM
ejpam-6314	560	1	+	+	NUM
ejpam-6314	560	2	...	...	PUNCT
ejpam-6314	561	1	+	+	X
ejpam-6314	561	2	yn−	yn−	NOUN
ejpam-6314	562	1	+	+	CCONJ
ejpam-6314	562	2	cn−1y	cn−1y	PROPN
ejpam-6314	562	3	n−1	n−1	PROPN
ejpam-6314	562	4	,	,	PUNCT
ejpam-6314	562	5	where	where	SCONJ
ejpam-6314	562	6	n	n	NOUN
ejpam-6314	562	7	=	=	PUNCT
ejpam-6314	563	1	[	[	X
ejpam-6314	563	2	β	β	X
ejpam-6314	563	3	]	]	X
ejpam-6314	563	4	+	+	CCONJ
ejpam-6314	563	5	1	1	NUM
ejpam-6314	563	6	and	and	CCONJ
ejpam-6314	563	7	c	c	NOUN
ejpam-6314	563	8	∈	∈	PROPN
ejpam-6314	563	9	r+	r+	NOUN
ejpam-6314	563	10	and	and	CCONJ
ejpam-6314	563	11	iβ	iβ	X
ejpam-6314	563	12	is	be	AUX
ejpam-6314	563	13	the	the	DET
ejpam-6314	563	14	integral	integral	ADJ
ejpam-6314	563	15	operator	operator	NOUN
ejpam-6314	563	16	of	of	ADP
ejpam-6314	563	17	fractional	fractional	ADJ
ejpam-6314	563	18	order.the	order.the	DET
ejpam-6314	563	19	system	system	NOUN
ejpam-6314	563	20	of	of	ADP
ejpam-6314	563	21	integral	integral	ADJ
ejpam-6314	563	22	equations	equation	NOUN
ejpam-6314	563	23	then	then	ADV
ejpam-6314	563	24	provides	provide	VERB
ejpam-6314	563	25	the	the	DET
ejpam-6314	563	26	solution	solution	NOUN
ejpam-6314	563	27	to	to	ADP
ejpam-6314	563	28	(	(	PUNCT
ejpam-6314	563	29	27	27	NUM
ejpam-6314	563	30	)	)	PUNCT
ejpam-6314	563	31	;	;	PUNCT
ejpam-6314	563	32	{	{	PUNCT
ejpam-6314	563	33	ℵ(y	ℵ(y	NOUN
ejpam-6314	563	34	)	)	PUNCT
ejpam-6314	563	35	=	=	PUNCT
ejpam-6314	563	36	ℓ+	ℓ+	PUNCT
ejpam-6314	563	37	y(ȷ−	y(ȷ−	PROPN
ejpam-6314	563	38	ℓ	ℓ	NUM
ejpam-6314	563	39	)	)	PUNCT
ejpam-6314	564	1	+	+	NUM
ejpam-6314	564	2	∫	∫	PROPN
ejpam-6314	564	3	1	1	NUM
ejpam-6314	564	4	0	0	NUM
ejpam-6314	564	5	ℑ(y	ℑ(y	NOUN
ejpam-6314	564	6	,	,	PUNCT
ejpam-6314	564	7	s)∆(s	s)∆(s	PROPN
ejpam-6314	564	8	,	,	PUNCT
ejpam-6314	564	9	κ(s))ds	κ(s))ds	NOUN
ejpam-6314	564	10	,	,	PUNCT
ejpam-6314	564	11	ω(y	ω(y	PROPN
ejpam-6314	564	12	)	)	PUNCT
ejpam-6314	564	13	=	=	PROPN
ejpam-6314	564	14	ℓ+	ℓ+	PUNCT
ejpam-6314	564	15	y(ȷ−	y(ȷ−	PROPN
ejpam-6314	564	16	ℓ	ℓ	NUM
ejpam-6314	564	17	)	)	PUNCT
ejpam-6314	565	1	+	+	NUM
ejpam-6314	565	2	∫	∫	PROPN
ejpam-6314	565	3	1	1	NUM
ejpam-6314	565	4	0	0	NUM
ejpam-6314	565	5	ℑ(y	ℑ(y	NOUN
ejpam-6314	565	6	,	,	PUNCT
ejpam-6314	565	7	s)θ(s	s)θ(s	NUM
ejpam-6314	565	8	,	,	PUNCT
ejpam-6314	565	9	σ(s))ds	σ(s))ds	NOUN
ejpam-6314	565	10	(	(	PUNCT
ejpam-6314	565	11	28	28	NUM
ejpam-6314	565	12	)	)	PUNCT
ejpam-6314	565	13	m.	m.	NOUN
ejpam-6314	565	14	sarwar	sarwar	PROPN
ejpam-6314	565	15	et	et	PROPN
ejpam-6314	566	1	al	al	PROPN
ejpam-6314	566	2	.	.	PUNCT
ejpam-6314	566	3	/	/	SYM
ejpam-6314	566	4	eur	eur	PROPN
ejpam-6314	566	5	.	.	PUNCT
ejpam-6314	567	1	j.	j.	PROPN
ejpam-6314	567	2	pure	pure	PROPN
ejpam-6314	567	3	appl	appl	PROPN
ejpam-6314	567	4	.	.	PROPN
ejpam-6314	567	5	math	math	PROPN
ejpam-6314	567	6	,	,	PUNCT
ejpam-6314	567	7	18	18	NUM
ejpam-6314	567	8	(	(	PUNCT
ejpam-6314	567	9	3	3	NUM
ejpam-6314	567	10	)	)	PUNCT
ejpam-6314	567	11	(	(	PUNCT
ejpam-6314	567	12	2025	2025	NUM
ejpam-6314	567	13	)	)	PUNCT
ejpam-6314	567	14	,	,	PUNCT
ejpam-6314	567	15	6314	6314	NUM
ejpam-6314	567	16	24	24	NUM
ejpam-6314	567	17	of	of	ADP
ejpam-6314	567	18	28	28	NUM
ejpam-6314	567	19	where	where	SCONJ
ejpam-6314	567	20	ℑ(y	ℑ(y	X
ejpam-6314	567	21	,	,	PUNCT
ejpam-6314	567	22	s	s	PART
ejpam-6314	567	23	)	)	PUNCT
ejpam-6314	567	24	=	=	SYM
ejpam-6314	567	25	1	1	NUM
ejpam-6314	567	26	ℶ(β	ℶ(β	PROPN
ejpam-6314	567	27	)	)	PUNCT
ejpam-6314	567	28	{	{	PUNCT
ejpam-6314	567	29	y(1−	y(1−	PROPN
ejpam-6314	567	30	s)β−1	s)β−1	VERB
ejpam-6314	567	31	−	−	PROPN
ejpam-6314	567	32	(	(	PUNCT
ejpam-6314	567	33	y	y	PROPN
ejpam-6314	567	34	−	−	PROPN
ejpam-6314	567	35	s)β−1	s)β−1	VERB
ejpam-6314	567	36	,	,	PUNCT
ejpam-6314	567	37	0	0	NUM
ejpam-6314	567	38	≤	≤	NUM
ejpam-6314	567	39	s	s	PART
ejpam-6314	567	40	≤	≤	NUM
ejpam-6314	567	41	y	y	NOUN
ejpam-6314	567	42	≤	≤	NUM
ejpam-6314	567	43	1	1	NUM
ejpam-6314	567	44	,	,	PUNCT
ejpam-6314	567	45	y(1−	y(1−	PROPN
ejpam-6314	567	46	s)β−1	s)β−1	NOUN
ejpam-6314	567	47	,	,	PUNCT
ejpam-6314	567	48	0	0	NUM
ejpam-6314	567	49	≤	≤	NUM
ejpam-6314	567	50	s	s	PART
ejpam-6314	567	51	≤	≤	NUM
ejpam-6314	567	52	y	y	NOUN
ejpam-6314	567	53	≤	≤	NUM
ejpam-6314	567	54	1	1	NUM
ejpam-6314	567	55	.	.	PUNCT
ejpam-6314	568	1	in	in	ADP
ejpam-6314	568	2	the	the	DET
ejpam-6314	568	3	above	above	ADJ
ejpam-6314	568	4	system	system	NOUN
ejpam-6314	568	5	(	(	PUNCT
ejpam-6314	568	6	28	28	NUM
ejpam-6314	568	7	)	)	PUNCT
ejpam-6314	568	8	,	,	PUNCT
ejpam-6314	568	9	let	let	VERB
ejpam-6314	568	10	us	we	PRON
ejpam-6314	568	11	denote	denote	VERB
ejpam-6314	568	12	γ(y	γ(y	PROPN
ejpam-6314	568	13	)	)	PUNCT
ejpam-6314	569	1	=	=	PROPN
ejpam-6314	569	2	ℓ+	ℓ+	PUNCT
ejpam-6314	569	3	y(ȷ−	y(ȷ−	PROPN
ejpam-6314	569	4	ℓ	ℓ	NUM
ejpam-6314	569	5	)	)	PUNCT
ejpam-6314	569	6	,	,	PUNCT
ejpam-6314	569	7	rκ(y	rκ(y	NOUN
ejpam-6314	569	8	)	)	PUNCT
ejpam-6314	569	9	=	=	SYM
ejpam-6314	570	1	∫	∫	PROPN
ejpam-6314	570	2	1	1	NUM
ejpam-6314	570	3	0	0	NUM
ejpam-6314	570	4	ℑ(y	ℑ(y	NOUN
ejpam-6314	570	5	,	,	PUNCT
ejpam-6314	570	6	s)∆(s	s)∆(s	PROPN
ejpam-6314	570	7	,	,	PUNCT
ejpam-6314	570	8	κ(s))ds	κ(s))ds	NOUN
ejpam-6314	570	9	,	,	PUNCT
ejpam-6314	570	10	sσ(y	sσ(y	NOUN
ejpam-6314	570	11	)	)	PUNCT
ejpam-6314	571	1	=	=	SYM
ejpam-6314	571	2	∫	∫	PROPN
ejpam-6314	571	3	1	1	NUM
ejpam-6314	571	4	0	0	NUM
ejpam-6314	571	5	ℑ(y	ℑ(y	NOUN
ejpam-6314	571	6	,	,	PUNCT
ejpam-6314	571	7	s)θ(s	s)θ(s	NUM
ejpam-6314	571	8	,	,	PUNCT
ejpam-6314	571	9	σ(s))ds	σ(s))ds	PROPN
ejpam-6314	571	10	.	.	PUNCT
ejpam-6314	571	11	consider	consider	VERB
ejpam-6314	571	12	c([0	c([0	NOUN
ejpam-6314	571	13	,	,	PUNCT
ejpam-6314	571	14	1],r	1],r	NUM
ejpam-6314	571	15	)	)	PUNCT
ejpam-6314	572	1	=	=	PUNCT
ejpam-6314	572	2	s	s	VERB
ejpam-6314	572	3	is	be	AUX
ejpam-6314	572	4	a	a	DET
ejpam-6314	572	5	space	space	NOUN
ejpam-6314	572	6	described	describe	VERB
ejpam-6314	572	7	by	by	ADP
ejpam-6314	572	8	[	[	X
ejpam-6314	572	9	0	0	NUM
ejpam-6314	572	10	,	,	PUNCT
ejpam-6314	572	11	1	1	NUM
ejpam-6314	572	12	]	]	PUNCT
ejpam-6314	572	13	,	,	PUNCT
ejpam-6314	572	14	and	and	CCONJ
ejpam-6314	572	15	db	db	ADJ
ejpam-6314	572	16	:	:	PUNCT
ejpam-6314	572	17	s×s	s×s	PROPN
ejpam-6314	572	18	→	→	SYM
ejpam-6314	572	19	c2	c2	PROPN
ejpam-6314	572	20	is	be	AUX
ejpam-6314	572	21	a	a	DET
ejpam-6314	572	22	(	(	PUNCT
ejpam-6314	572	23	bcvms	bcvms	NOUN
ejpam-6314	572	24	)	)	PUNCT
ejpam-6314	572	25	,	,	PUNCT
ejpam-6314	572	26	such	such	ADJ
ejpam-6314	572	27	that	that	PRON
ejpam-6314	572	28	;	;	PUNCT
ejpam-6314	572	29	db(κ	db(κ	NUM
ejpam-6314	572	30	,	,	PUNCT
ejpam-6314	572	31	σ	σ	X
ejpam-6314	572	32	)	)	PUNCT
ejpam-6314	572	33	=	=	SYM
ejpam-6314	572	34	sup	sup	NOUN
ejpam-6314	572	35	m∈[0,1	m∈[0,1	NOUN
ejpam-6314	572	36	]	]	X
ejpam-6314	572	37	|	|	ADV
ejpam-6314	572	38	κ(m)−	κ(m)−	PROPN
ejpam-6314	572	39	σ(m	σ(m	NOUN
ejpam-6314	572	40	)	)	PUNCT
ejpam-6314	572	41	|2	|2	PUNCT
ejpam-6314	573	1	+	+	PROPN
ejpam-6314	573	2	i2	i2	PROPN
ejpam-6314	573	3	sup	sup	NOUN
ejpam-6314	573	4	m∈[0,1	m∈[0,1	NOUN
ejpam-6314	573	5	]	]	X
ejpam-6314	573	6	|	|	ADV
ejpam-6314	573	7	κ(m)−	κ(m)−	PROPN
ejpam-6314	573	8	σ(m	σ(m	NOUN
ejpam-6314	573	9	)	)	PUNCT
ejpam-6314	573	10	|2	|2	NUM
ejpam-6314	573	11	,	,	PUNCT
ejpam-6314	573	12	for	for	ADP
ejpam-6314	573	13	all	all	DET
ejpam-6314	573	14	κ	κ	NOUN
ejpam-6314	573	15	,	,	PUNCT
ejpam-6314	573	16	σ	σ	PROPN
ejpam-6314	573	17	∈	∈	PROPN
ejpam-6314	573	18	s.	s.	PROPN
ejpam-6314	573	19	let	let	VERB
ejpam-6314	573	20	ϑ	ϑ	X
ejpam-6314	573	21	:	:	PUNCT
ejpam-6314	573	22	s	s	VERB
ejpam-6314	573	23	×	×	PROPN
ejpam-6314	573	24	s	s	X
ejpam-6314	573	25	→	→	SYM
ejpam-6314	573	26	[	[	X
ejpam-6314	573	27	1,+∞	1,+∞	NUM
ejpam-6314	573	28	)	)	PUNCT
ejpam-6314	573	29	be	be	AUX
ejpam-6314	573	30	defined	define	VERB
ejpam-6314	573	31	by	by	ADP
ejpam-6314	573	32	ϑ(κ	ϑ(κ	PROPN
ejpam-6314	573	33	,	,	PUNCT
ejpam-6314	573	34	σ	σ	PROPN
ejpam-6314	573	35	)	)	PUNCT
ejpam-6314	573	36	=	=	SYM
ejpam-6314	573	37	2	2	NUM
ejpam-6314	573	38	,	,	PUNCT
ejpam-6314	573	39	for	for	ADP
ejpam-6314	573	40	all	all	DET
ejpam-6314	573	41	κ	κ	NOUN
ejpam-6314	573	42	,	,	PUNCT
ejpam-6314	573	43	σ	σ	PROPN
ejpam-6314	573	44	∈	∈	PROPN
ejpam-6314	573	45	s.	s.	PROPN
ejpam-6314	573	46	then	then	ADV
ejpam-6314	573	47	,	,	PUNCT
ejpam-6314	573	48	(	(	PUNCT
ejpam-6314	573	49	s	s	X
ejpam-6314	573	50	,	,	PUNCT
ejpam-6314	573	51	db	db	PROPN
ejpam-6314	573	52	)	)	PUNCT
ejpam-6314	573	53	is	be	AUX
ejpam-6314	573	54	(	(	PUNCT
ejpam-6314	573	55	bcvms	bcvms	NOUN
ejpam-6314	573	56	)	)	PUNCT
ejpam-6314	573	57	.	.	PUNCT
ejpam-6314	574	1	theorem	theorem	NOUN
ejpam-6314	574	2	6	6	NUM
ejpam-6314	574	3	.	.	PUNCT
ejpam-6314	574	4	consider	consider	VERB
ejpam-6314	574	5	a	a	DET
ejpam-6314	574	6	system	system	NOUN
ejpam-6314	574	7	of	of	ADP
ejpam-6314	574	8	non	non	ADJ
ejpam-6314	574	9	-	-	ADJ
ejpam-6314	574	10	linear	linear	ADJ
ejpam-6314	574	11	fractional	fractional	ADJ
ejpam-6314	574	12	differential	differential	ADJ
ejpam-6314	574	13	equations	equation	NOUN
ejpam-6314	574	14	(	(	PUNCT
ejpam-6314	574	15	27	27	NUM
ejpam-6314	574	16	)	)	PUNCT
ejpam-6314	574	17	.	.	PUNCT
ejpam-6314	575	1	assume	assume	VERB
ejpam-6314	575	2	that	that	SCONJ
ejpam-6314	575	3	the	the	DET
ejpam-6314	575	4	following	follow	VERB
ejpam-6314	575	5	claims	claim	NOUN
ejpam-6314	575	6	are	be	AUX
ejpam-6314	575	7	verified	verify	VERB
ejpam-6314	575	8	:	:	PUNCT
ejpam-6314	575	9	if	if	SCONJ
ejpam-6314	575	10	for	for	ADP
ejpam-6314	575	11	all	all	DET
ejpam-6314	575	12	y	y	PROPN
ejpam-6314	575	13	∈	∈	PROPN
ejpam-6314	576	1	[	[	X
ejpam-6314	576	2	0	0	NUM
ejpam-6314	576	3	,	,	PUNCT
ejpam-6314	576	4	1	1	NUM
ejpam-6314	576	5	]	]	PUNCT
ejpam-6314	576	6	there	there	PRON
ejpam-6314	576	7	exist	exist	VERB
ejpam-6314	576	8	µ	µ	NUM
ejpam-6314	576	9	,	,	PUNCT
ejpam-6314	576	10	ν	ν	X
ejpam-6314	576	11	:	:	PUNCT
ejpam-6314	576	12	s	s	X
ejpam-6314	576	13	→	→	SYM
ejpam-6314	576	14	[	[	X
ejpam-6314	576	15	0	0	NUM
ejpam-6314	576	16	,	,	PUNCT
ejpam-6314	576	17	1	1	NUM
ejpam-6314	576	18	)	)	PUNCT
ejpam-6314	576	19	such	such	ADJ
ejpam-6314	576	20	that	that	PRON
ejpam-6314	576	21	:	:	PUNCT
ejpam-6314	576	22	(	(	PUNCT
ejpam-6314	576	23	i	i	NOUN
ejpam-6314	576	24	)	)	PUNCT
ejpam-6314	577	1	µ(rκ	µ(rκ	PROPN
ejpam-6314	577	2	+	+	NUM
ejpam-6314	577	3	γ(y	γ(y	PROPN
ejpam-6314	577	4	)	)	PUNCT
ejpam-6314	577	5	)	)	PUNCT
ejpam-6314	578	1	≤	≤	NUM
ejpam-6314	578	2	µ(κ	µ(κ	NOUN
ejpam-6314	578	3	)	)	PUNCT
ejpam-6314	578	4	and	and	CCONJ
ejpam-6314	578	5	ν(rκ	ν(rκ	PROPN
ejpam-6314	578	6	+	+	CCONJ
ejpam-6314	578	7	γ(y	γ(y	PROPN
ejpam-6314	578	8	)	)	PUNCT
ejpam-6314	578	9	)	)	PUNCT
ejpam-6314	578	10	≤	≤	NUM
ejpam-6314	578	11	ν(κ	ν(κ	NOUN
ejpam-6314	578	12	)	)	PUNCT
ejpam-6314	578	13	;	;	PUNCT
ejpam-6314	578	14	(	(	PUNCT
ejpam-6314	578	15	ii	ii	NOUN
ejpam-6314	578	16	)	)	PUNCT
ejpam-6314	578	17	µ(sσ	µ(sσ	NOUN
ejpam-6314	578	18	+	+	NUM
ejpam-6314	578	19	γ(y	γ(y	PROPN
ejpam-6314	578	20	)	)	PUNCT
ejpam-6314	578	21	)	)	PUNCT
ejpam-6314	579	1	≤	≤	NUM
ejpam-6314	579	2	µ(σ	µ(σ	PROPN
ejpam-6314	579	3	)	)	PUNCT
ejpam-6314	579	4	and	and	CCONJ
ejpam-6314	579	5	ν(sσ	ν(sσ	ADJ
ejpam-6314	579	6	+	+	NOUN
ejpam-6314	579	7	γ(y	γ(y	PROPN
ejpam-6314	579	8	)	)	PUNCT
ejpam-6314	579	9	)	)	PUNCT
ejpam-6314	579	10	≤	≤	NUM
ejpam-6314	579	11	ν(σ	ν(σ	NOUN
ejpam-6314	579	12	)	)	PUNCT
ejpam-6314	579	13	;	;	PUNCT
ejpam-6314	579	14	(	(	PUNCT
ejpam-6314	579	15	iii	iii	X
ejpam-6314	579	16	)	)	PUNCT
ejpam-6314	579	17	(	(	PUNCT
ejpam-6314	579	18	µ+	µ+	X
ejpam-6314	579	19	ν)(κ	ν)(κ	NOUN
ejpam-6314	579	20	)	)	PUNCT
ejpam-6314	579	21	<	<	X
ejpam-6314	579	22	1	1	NUM
ejpam-6314	579	23	;	;	PUNCT
ejpam-6314	579	24	(	(	PUNCT
ejpam-6314	579	25	iv	iv	X
ejpam-6314	579	26	)	)	PUNCT
ejpam-6314	579	27	∥	∥	NOUN
ejpam-6314	579	28	rκ(y)−	rκ(y)−	VERB
ejpam-6314	579	29	sσ(y	sσ(y	NOUN
ejpam-6314	579	30	)	)	PUNCT
ejpam-6314	579	31	∥2≾	∥2≾	VERB
ejpam-6314	579	32	µ(κ)𭟋1(κ	µ(κ)𭟋1(κ	NOUN
ejpam-6314	579	33	,	,	PUNCT
ejpam-6314	579	34	σ)(y	σ)(y	PUNCT
ejpam-6314	579	35	)	)	PUNCT
ejpam-6314	580	1	+	+	CCONJ
ejpam-6314	580	2	ν(κ)𭟋2(κ	ν(κ)𭟋2(κ	PROPN
ejpam-6314	580	3	,	,	PUNCT
ejpam-6314	580	4	σ)(y	σ)(y	X
ejpam-6314	580	5	)	)	PUNCT
ejpam-6314	580	6	(	(	PUNCT
ejpam-6314	580	7	v	v	NOUN
ejpam-6314	580	8	)	)	PUNCT
ejpam-6314	580	9	supy∈[0,1	supy∈[0,1	PROPN
ejpam-6314	580	10	]	]	PUNCT
ejpam-6314	580	11	∫	∫	PROPN
ejpam-6314	580	12	1	1	NUM
ejpam-6314	580	13	0	0	NUM
ejpam-6314	580	14	ℑ(y	ℑ(y	NOUN
ejpam-6314	580	15	,	,	PUNCT
ejpam-6314	580	16	s)ds	s)ds	PROPN
ejpam-6314	580	17	<	<	X
ejpam-6314	580	18	1	1	X
ejpam-6314	580	19	.	.	PUNCT
ejpam-6314	581	1	for	for	ADP
ejpam-6314	581	2	all	all	DET
ejpam-6314	581	3	κ	κ	PROPN
ejpam-6314	581	4	,	,	PUNCT
ejpam-6314	581	5	σ	σ	PROPN
ejpam-6314	581	6	∈	∈	PROPN
ejpam-6314	581	7	s	s	NOUN
ejpam-6314	581	8	,	,	PUNCT
ejpam-6314	581	9	where	where	SCONJ
ejpam-6314	581	10	:	:	PUNCT
ejpam-6314	581	11	𭟋1(κ	𭟋1(κ	NOUN
ejpam-6314	581	12	,	,	PUNCT
ejpam-6314	581	13	σ)(y	σ)(y	PUNCT
ejpam-6314	581	14	)	)	PUNCT
ejpam-6314	582	1	=	=	X
ejpam-6314	582	2	∥	∥	PRON
ejpam-6314	582	3	κ(y)−	κ(y)−	VERB
ejpam-6314	582	4	σ(y	σ(y	NOUN
ejpam-6314	582	5	)	)	PUNCT
ejpam-6314	582	6	∥2	∥2	PROPN
ejpam-6314	582	7	,	,	PUNCT
ejpam-6314	582	8	and	and	CCONJ
ejpam-6314	582	9	𭟋2(κ	𭟋2(κ	NOUN
ejpam-6314	582	10	,	,	PUNCT
ejpam-6314	582	11	σ)(y	σ)(y	PUNCT
ejpam-6314	582	12	)	)	PUNCT
ejpam-6314	582	13	=	=	SYM
ejpam-6314	582	14	∥	∥	NOUN
ejpam-6314	582	15	rκ(y	rκ(y	NOUN
ejpam-6314	582	16	)	)	PUNCT
ejpam-6314	583	1	+	+	CCONJ
ejpam-6314	583	2	γ(y)−	γ(y)−	NUM
ejpam-6314	583	3	κ(y	κ(y	PROPN
ejpam-6314	583	4	)	)	PUNCT
ejpam-6314	583	5	∥2∥	∥2∥	NOUN
ejpam-6314	583	6	sσ(y	sσ(y	NOUN
ejpam-6314	583	7	)	)	PUNCT
ejpam-6314	584	1	+	+	CCONJ
ejpam-6314	584	2	γ(y)−	γ(y)−	PRON
ejpam-6314	584	3	σ(y	σ(y	NOUN
ejpam-6314	584	4	)	)	PUNCT
ejpam-6314	584	5	∥2	∥2	NOUN
ejpam-6314	585	1	1	1	NUM
ejpam-6314	585	2	+	+	NUM
ejpam-6314	585	3	∥	∥	PRON
ejpam-6314	585	4	κ(y)−	κ(y)−	VERB
ejpam-6314	585	5	σ(y	σ(y	NOUN
ejpam-6314	585	6	)	)	PUNCT
ejpam-6314	585	7	∥	∥	PUNCT
ejpam-6314	585	8	.	.	PUNCT
ejpam-6314	586	1	then	then	ADV
ejpam-6314	586	2	the	the	DET
ejpam-6314	586	3	system	system	NOUN
ejpam-6314	586	4	of	of	ADP
ejpam-6314	586	5	fde	fde	PROPN
ejpam-6314	586	6	(	(	PUNCT
ejpam-6314	586	7	27	27	NUM
ejpam-6314	586	8	)	)	PUNCT
ejpam-6314	586	9	has	have	VERB
ejpam-6314	586	10	a	a	DET
ejpam-6314	586	11	unique	unique	ADJ
ejpam-6314	586	12	common	common	ADJ
ejpam-6314	586	13	solution	solution	NOUN
ejpam-6314	586	14	.	.	PUNCT
ejpam-6314	587	1	proof	proof	NOUN
ejpam-6314	587	2	.	.	PUNCT
ejpam-6314	588	1	let	let	VERB
ejpam-6314	588	2	us	we	PRON
ejpam-6314	588	3	define	define	VERB
ejpam-6314	588	4	φ	φ	PROPN
ejpam-6314	588	5	,	,	PUNCT
ejpam-6314	588	6	ψ	ψ	X
ejpam-6314	588	7	:	:	PUNCT
ejpam-6314	588	8	s	s	X
ejpam-6314	588	9	→	→	SYM
ejpam-6314	588	10	s	s	X
ejpam-6314	588	11	by	by	ADP
ejpam-6314	588	12	φκ	φκ	NOUN
ejpam-6314	588	13	=	=	PUNCT
ejpam-6314	588	14	rκ	rκ	NOUN
ejpam-6314	588	15	+	+	X
ejpam-6314	588	16	γ	γ	X
ejpam-6314	588	17	,	,	PUNCT
ejpam-6314	588	18	and	and	CCONJ
ejpam-6314	588	19	ψσ	ψσ	ADP
ejpam-6314	588	20	=	=	PUNCT
ejpam-6314	588	21	sσ	sσ	NOUN
ejpam-6314	588	22	+	+	CCONJ
ejpam-6314	588	23	γ	γ	X
ejpam-6314	588	24	.	.	PROPN
ejpam-6314	588	25	then	then	ADV
ejpam-6314	588	26	db(φκ	db(φκ	PROPN
ejpam-6314	588	27	,	,	PUNCT
ejpam-6314	588	28	ψσ	ψσ	ADJ
ejpam-6314	588	29	)	)	PUNCT
ejpam-6314	588	30	=	=	SYM
ejpam-6314	588	31	sup	sup	NOUN
ejpam-6314	588	32	y∈[0,1	y∈[0,1	NUM
ejpam-6314	588	33	]	]	X
ejpam-6314	588	34	(	(	PUNCT
ejpam-6314	588	35	∥	∥	X
ejpam-6314	588	36	rκ(y)−	rκ(y)−	X
ejpam-6314	588	37	sσ(y	sσ(y	NOUN
ejpam-6314	588	38	)	)	PUNCT
ejpam-6314	589	1	+	+	CCONJ
ejpam-6314	589	2	γ(y)−	γ(y)−	PROPN
ejpam-6314	589	3	γ(y	γ(y	PROPN
ejpam-6314	589	4	)	)	PUNCT
ejpam-6314	589	5	∥2	∥2	NOUN
ejpam-6314	589	6	)	)	PUNCT
ejpam-6314	590	1	(	(	PUNCT
ejpam-6314	590	2	1	1	NUM
ejpam-6314	590	3	+	+	NUM
ejpam-6314	590	4	i2	i2	NOUN
ejpam-6314	590	5	)	)	PUNCT
ejpam-6314	591	1	=	=	SYM
ejpam-6314	591	2	sup	sup	NOUN
ejpam-6314	591	3	y∈[0,1	y∈[0,1	NUM
ejpam-6314	591	4	]	]	X
ejpam-6314	591	5	(	(	PUNCT
ejpam-6314	591	6	∥	∥	X
ejpam-6314	591	7	rκ(y)−	rκ(y)−	X
ejpam-6314	591	8	sσ(y	sσ(y	NOUN
ejpam-6314	591	9	)	)	PUNCT
ejpam-6314	591	10	∥2	∥2	NUM
ejpam-6314	591	11	)	)	PUNCT
ejpam-6314	592	1	(	(	PUNCT
ejpam-6314	592	2	1	1	NUM
ejpam-6314	592	3	+	+	NUM
ejpam-6314	592	4	i2	i2	NOUN
ejpam-6314	592	5	)	)	PUNCT
ejpam-6314	592	6	,	,	PUNCT
ejpam-6314	592	7	m.	m.	NOUN
ejpam-6314	592	8	sarwar	sarwar	PROPN
ejpam-6314	592	9	et	et	PROPN
ejpam-6314	593	1	al	al	PROPN
ejpam-6314	593	2	.	.	PUNCT
ejpam-6314	593	3	/	/	SYM
ejpam-6314	593	4	eur	eur	PROPN
ejpam-6314	593	5	.	.	PUNCT
ejpam-6314	594	1	j.	j.	PROPN
ejpam-6314	594	2	pure	pure	PROPN
ejpam-6314	594	3	appl	appl	PROPN
ejpam-6314	594	4	.	.	PROPN
ejpam-6314	594	5	math	math	PROPN
ejpam-6314	594	6	,	,	PUNCT
ejpam-6314	594	7	18	18	NUM
ejpam-6314	594	8	(	(	PUNCT
ejpam-6314	594	9	3	3	NUM
ejpam-6314	594	10	)	)	PUNCT
ejpam-6314	594	11	(	(	PUNCT
ejpam-6314	594	12	2025	2025	NUM
ejpam-6314	594	13	)	)	PUNCT
ejpam-6314	594	14	,	,	PUNCT
ejpam-6314	594	15	6314	6314	NUM
ejpam-6314	594	16	25	25	NUM
ejpam-6314	594	17	of	of	ADP
ejpam-6314	594	18	28	28	NUM
ejpam-6314	594	19	db(κ	db(κ	NUM
ejpam-6314	594	20	,	,	PUNCT
ejpam-6314	594	21	σ	σ	NOUN
ejpam-6314	594	22	)	)	PUNCT
ejpam-6314	594	23	=	=	SYM
ejpam-6314	594	24	sup	sup	NOUN
ejpam-6314	594	25	y∈[0,1	y∈[0,1	PROPN
ejpam-6314	594	26	]	]	X
ejpam-6314	594	27	(	(	PUNCT
ejpam-6314	594	28	∥	∥	X
ejpam-6314	594	29	κ(y)−	κ(y)−	PROPN
ejpam-6314	594	30	σ(y	σ(y	NOUN
ejpam-6314	594	31	)	)	PUNCT
ejpam-6314	594	32	∥2	∥2	PROPN
ejpam-6314	594	33	)	)	PUNCT
ejpam-6314	595	1	(	(	PUNCT
ejpam-6314	595	2	1	1	NUM
ejpam-6314	595	3	+	+	NUM
ejpam-6314	595	4	i2	i2	NOUN
ejpam-6314	595	5	)	)	PUNCT
ejpam-6314	595	6	,	,	PUNCT
ejpam-6314	595	7	db(κ	db(κ	NOUN
ejpam-6314	595	8	,	,	PUNCT
ejpam-6314	595	9	φκ	φκ	ADJ
ejpam-6314	595	10	)	)	PUNCT
ejpam-6314	595	11	=	=	SYM
ejpam-6314	595	12	sup	sup	NOUN
ejpam-6314	595	13	y∈[0,1	y∈[0,1	PROPN
ejpam-6314	595	14	]	]	X
ejpam-6314	595	15	(	(	PUNCT
ejpam-6314	595	16	∥	∥	X
ejpam-6314	595	17	rκ(y	rκ(y	NOUN
ejpam-6314	595	18	)	)	PUNCT
ejpam-6314	595	19	+	+	NUM
ejpam-6314	595	20	γ(y)−	γ(y)−	NUM
ejpam-6314	595	21	κ(y	κ(y	PROPN
ejpam-6314	595	22	)	)	PUNCT
ejpam-6314	595	23	∥2	∥2	NOUN
ejpam-6314	595	24	)	)	PUNCT
ejpam-6314	595	25	(	(	PUNCT
ejpam-6314	595	26	1	1	NUM
ejpam-6314	595	27	+	+	NUM
ejpam-6314	595	28	i2	i2	NOUN
ejpam-6314	595	29	)	)	PUNCT
ejpam-6314	595	30	,	,	PUNCT
ejpam-6314	595	31	and	and	CCONJ
ejpam-6314	595	32	db(σ	db(σ	NOUN
ejpam-6314	595	33	,	,	PUNCT
ejpam-6314	595	34	φσ	φσ	NOUN
ejpam-6314	595	35	)	)	PUNCT
ejpam-6314	595	36	=	=	SYM
ejpam-6314	595	37	sup	sup	NOUN
ejpam-6314	595	38	y∈[0,1	y∈[0,1	PROPN
ejpam-6314	595	39	]	]	X
ejpam-6314	595	40	(	(	PUNCT
ejpam-6314	595	41	∥	∥	X
ejpam-6314	595	42	sσ(y	sσ(y	X
ejpam-6314	595	43	)	)	PUNCT
ejpam-6314	596	1	+	+	CCONJ
ejpam-6314	596	2	γ(y)−	γ(y)−	PRON
ejpam-6314	596	3	σ(y	σ(y	NOUN
ejpam-6314	596	4	)	)	PUNCT
ejpam-6314	596	5	∥2	∥2	NOUN
ejpam-6314	596	6	)	)	PUNCT
ejpam-6314	596	7	(	(	PUNCT
ejpam-6314	596	8	1	1	NUM
ejpam-6314	596	9	+	+	NUM
ejpam-6314	596	10	i2	i2	NOUN
ejpam-6314	596	11	)	)	PUNCT
ejpam-6314	596	12	.	.	PUNCT
ejpam-6314	597	1	now	now	ADV
ejpam-6314	597	2	by	by	ADP
ejpam-6314	597	3	(	(	PUNCT
ejpam-6314	597	4	14	14	NUM
ejpam-6314	597	5	)	)	PUNCT
ejpam-6314	597	6	of	of	ADP
ejpam-6314	597	7	theorem	theorem	NOUN
ejpam-6314	597	8	(	(	PUNCT
ejpam-6314	597	9	4	4	NUM
ejpam-6314	597	10	)	)	PUNCT
ejpam-6314	597	11	we	we	PRON
ejpam-6314	597	12	obtain	obtain	VERB
ejpam-6314	597	13	,	,	PUNCT
ejpam-6314	597	14	∥	∥	X
ejpam-6314	597	15	rκ(y)−	rκ(y)−	VERB
ejpam-6314	597	16	sσ(y	sσ(y	NOUN
ejpam-6314	597	17	)	)	PUNCT
ejpam-6314	597	18	∥2	∥2	PROPN
ejpam-6314	598	1	≾	≾	PROPN
ejpam-6314	598	2	µ(κ	µ(κ	NOUN
ejpam-6314	598	3	)	)	PUNCT
ejpam-6314	598	4	∥	∥	PRON
ejpam-6314	598	5	κ(y)−	κ(y)−	VERB
ejpam-6314	598	6	σ(y	σ(y	NOUN
ejpam-6314	598	7	)	)	PUNCT
ejpam-6314	598	8	∥2	∥2	NOUN
ejpam-6314	599	1	+	+	NUM
ejpam-6314	599	2	ν(κ	ν(κ	NOUN
ejpam-6314	599	3	)	)	PUNCT
ejpam-6314	600	1	∥	∥	NOUN
ejpam-6314	600	2	rκ(y	rκ(y	NOUN
ejpam-6314	600	3	)	)	PUNCT
ejpam-6314	600	4	+	+	CCONJ
ejpam-6314	600	5	γ(y)−	γ(y)−	NUM
ejpam-6314	600	6	κ(y	κ(y	PROPN
ejpam-6314	600	7	)	)	PUNCT
ejpam-6314	600	8	∥2∥	∥2∥	NOUN
ejpam-6314	600	9	sσ(y	sσ(y	NOUN
ejpam-6314	600	10	)	)	PUNCT
ejpam-6314	601	1	+	+	CCONJ
ejpam-6314	601	2	γ(y)−	γ(y)−	PRON
ejpam-6314	601	3	σ(y	σ(y	NOUN
ejpam-6314	601	4	)	)	PUNCT
ejpam-6314	601	5	∥2	∥2	NOUN
ejpam-6314	601	6	(	(	PUNCT
ejpam-6314	601	7	1	1	NUM
ejpam-6314	601	8	+	+	NUM
ejpam-6314	601	9	i2	i2	NOUN
ejpam-6314	601	10	)	)	PUNCT
ejpam-6314	601	11	1	1	NUM
ejpam-6314	601	12	+	+	NUM
ejpam-6314	601	13	∥	∥	PRON
ejpam-6314	601	14	κ(y)−	κ(y)−	VERB
ejpam-6314	601	15	σ(y	σ(y	NOUN
ejpam-6314	601	16	)	)	PUNCT
ejpam-6314	601	17	∥2	∥2	NOUN
ejpam-6314	601	18	(	(	PUNCT
ejpam-6314	601	19	1	1	NUM
ejpam-6314	601	20	+	+	NUM
ejpam-6314	601	21	i2	i2	NOUN
ejpam-6314	601	22	)	)	PUNCT
ejpam-6314	601	23	≾	≾	PROPN
ejpam-6314	601	24	µ(κ	µ(κ	NOUN
ejpam-6314	601	25	)	)	PUNCT
ejpam-6314	601	26	∥	∥	PRON
ejpam-6314	601	27	κ(y)−	κ(y)−	VERB
ejpam-6314	601	28	σ(y	σ(y	NOUN
ejpam-6314	601	29	)	)	PUNCT
ejpam-6314	601	30	∥2	∥2	NOUN
ejpam-6314	602	1	+	+	NUM
ejpam-6314	602	2	ν(κ	ν(κ	NOUN
ejpam-6314	602	3	)	)	PUNCT
ejpam-6314	603	1	∥	∥	NOUN
ejpam-6314	603	2	rκ(y	rκ(y	NOUN
ejpam-6314	603	3	)	)	PUNCT
ejpam-6314	603	4	+	+	CCONJ
ejpam-6314	603	5	γ(y)−	γ(y)−	NUM
ejpam-6314	603	6	κ(y	κ(y	PROPN
ejpam-6314	603	7	)	)	PUNCT
ejpam-6314	603	8	∥2∥	∥2∥	NOUN
ejpam-6314	603	9	sσ(y	sσ(y	NOUN
ejpam-6314	603	10	)	)	PUNCT
ejpam-6314	604	1	+	+	CCONJ
ejpam-6314	604	2	γ(y)−	γ(y)−	PRON
ejpam-6314	604	3	σ(y	σ(y	NOUN
ejpam-6314	604	4	)	)	PUNCT
ejpam-6314	604	5	∥2	∥2	NOUN
ejpam-6314	605	1	1	1	NUM
ejpam-6314	605	2	+	+	NUM
ejpam-6314	605	3	∥	∥	PRON
ejpam-6314	605	4	κ(y)−	κ(y)−	VERB
ejpam-6314	605	5	σ(y	σ(y	NOUN
ejpam-6314	605	6	)	)	PUNCT
ejpam-6314	605	7	∥2	∥2	NOUN
ejpam-6314	605	8	=	=	SYM
ejpam-6314	605	9	µ(κ)𭟋1(κ	µ(κ)𭟋1(κ	NOUN
ejpam-6314	605	10	,	,	PUNCT
ejpam-6314	605	11	σ)(y	σ)(y	PUNCT
ejpam-6314	605	12	)	)	PUNCT
ejpam-6314	606	1	+	+	CCONJ
ejpam-6314	606	2	ν(κ)𭟋2(κ	ν(κ)𭟋2(κ	PROPN
ejpam-6314	606	3	,	,	PUNCT
ejpam-6314	606	4	σ)(y	σ)(y	NOUN
ejpam-6314	606	5	)	)	PUNCT
ejpam-6314	606	6	.	.	PUNCT
ejpam-6314	607	1	thus	thus	ADV
ejpam-6314	607	2	,	,	PUNCT
ejpam-6314	607	3	it	it	PRON
ejpam-6314	607	4	implies	imply	VERB
ejpam-6314	607	5	that	that	SCONJ
ejpam-6314	607	6	:	:	PUNCT
ejpam-6314	607	7	(	(	PUNCT
ejpam-6314	607	8	i	i	NOUN
ejpam-6314	607	9	)	)	PUNCT
ejpam-6314	607	10	µ(φκ	µ(φκ	PROPN
ejpam-6314	607	11	)	)	PUNCT
ejpam-6314	607	12	≤	≤	NOUN
ejpam-6314	607	13	µ(κ	µ(κ	NOUN
ejpam-6314	607	14	)	)	PUNCT
ejpam-6314	607	15	and	and	CCONJ
ejpam-6314	607	16	ν(φκ	ν(φκ	NOUN
ejpam-6314	607	17	)	)	PUNCT
ejpam-6314	607	18	≤	≤	NUM
ejpam-6314	607	19	ν(κ	ν(κ	NOUN
ejpam-6314	607	20	)	)	PUNCT
ejpam-6314	607	21	;	;	PUNCT
ejpam-6314	607	22	(	(	PUNCT
ejpam-6314	607	23	ii	ii	NOUN
ejpam-6314	607	24	)	)	PUNCT
ejpam-6314	607	25	µ(ψκ	µ(ψκ	NOUN
ejpam-6314	607	26	)	)	PUNCT
ejpam-6314	607	27	≤	≤	NOUN
ejpam-6314	607	28	µ(κ	µ(κ	NOUN
ejpam-6314	607	29	)	)	PUNCT
ejpam-6314	607	30	and	and	CCONJ
ejpam-6314	607	31	ν(ψκ	ν(ψκ	NOUN
ejpam-6314	607	32	)	)	PUNCT
ejpam-6314	607	33	≤	≤	NUM
ejpam-6314	607	34	ν(κ	ν(κ	NOUN
ejpam-6314	607	35	)	)	PUNCT
ejpam-6314	607	36	;	;	PUNCT
ejpam-6314	607	37	(	(	PUNCT
ejpam-6314	607	38	iii	iii	X
ejpam-6314	607	39	)	)	PUNCT
ejpam-6314	607	40	(	(	PUNCT
ejpam-6314	607	41	µ+	µ+	X
ejpam-6314	607	42	ν)(κ	ν)(κ	NOUN
ejpam-6314	607	43	)	)	PUNCT
ejpam-6314	607	44	<	<	X
ejpam-6314	607	45	1	1	NUM
ejpam-6314	607	46	;	;	PUNCT
ejpam-6314	607	47	(	(	PUNCT
ejpam-6314	607	48	iv	iv	X
ejpam-6314	607	49	)	)	PUNCT
ejpam-6314	607	50	db(φκ	db(φκ	PROPN
ejpam-6314	607	51	,	,	PUNCT
ejpam-6314	607	52	ψσ	ψσ	ADJ
ejpam-6314	607	53	)	)	PUNCT
ejpam-6314	607	54	≾	≾	PROPN
ejpam-6314	607	55	µ(κ)db(κ	µ(κ)db(κ	NOUN
ejpam-6314	607	56	,	,	PUNCT
ejpam-6314	607	57	σ	σ	NOUN
ejpam-6314	607	58	)	)	PUNCT
ejpam-6314	607	59	+	+	NUM
ejpam-6314	607	60	ν(κ	ν(κ	NOUN
ejpam-6314	607	61	)	)	PUNCT
ejpam-6314	607	62	db(κ	db(κ	NOUN
ejpam-6314	607	63	,	,	PUNCT
ejpam-6314	607	64	φκ)db(σ	φκ)db(σ	NOUN
ejpam-6314	607	65	,	,	PUNCT
ejpam-6314	607	66	ψσ	ψσ	ADJ
ejpam-6314	607	67	)	)	PUNCT
ejpam-6314	607	68	1	1	NUM
ejpam-6314	607	69	+	+	CCONJ
ejpam-6314	607	70	db(κ	db(κ	NUM
ejpam-6314	607	71	,	,	PUNCT
ejpam-6314	607	72	σ	σ	PROPN
ejpam-6314	607	73	)	)	PUNCT
ejpam-6314	607	74	,	,	PUNCT
ejpam-6314	607	75	(	(	PUNCT
ejpam-6314	607	76	29	29	NUM
ejpam-6314	607	77	)	)	PUNCT
ejpam-6314	607	78	for	for	ADP
ejpam-6314	607	79	all	all	DET
ejpam-6314	607	80	κ	κ	PROPN
ejpam-6314	607	81	,	,	PUNCT
ejpam-6314	607	82	σ	σ	PROPN
ejpam-6314	607	83	∈	∈	PROPN
ejpam-6314	607	84	s.	s.	PROPN
ejpam-6314	607	85	therefore	therefore	ADV
ejpam-6314	607	86	,	,	PUNCT
ejpam-6314	607	87	by	by	ADP
ejpam-6314	607	88	the	the	DET
ejpam-6314	607	89	theorem	theorem	NOUN
ejpam-6314	607	90	(	(	PUNCT
ejpam-6314	607	91	4	4	NUM
ejpam-6314	607	92	)	)	PUNCT
ejpam-6314	607	93	,	,	PUNCT
ejpam-6314	607	94	we	we	PRON
ejpam-6314	607	95	obtain	obtain	VERB
ejpam-6314	607	96	that	that	SCONJ
ejpam-6314	607	97	φ	φ	PROPN
ejpam-6314	607	98	and	and	CCONJ
ejpam-6314	607	99	ψ	ψ	X
ejpam-6314	607	100	have	have	VERB
ejpam-6314	607	101	a	a	DET
ejpam-6314	607	102	unique	unique	ADJ
ejpam-6314	607	103	common	common	ADJ
ejpam-6314	607	104	fixed	fix	VERB
ejpam-6314	607	105	point	point	NOUN
ejpam-6314	607	106	.	.	PUNCT
ejpam-6314	608	1	thus	thus	ADV
ejpam-6314	608	2	we	we	PRON
ejpam-6314	608	3	claim	claim	VERB
ejpam-6314	608	4	that	that	SCONJ
ejpam-6314	608	5	the	the	DET
ejpam-6314	608	6	system	system	NOUN
ejpam-6314	608	7	of	of	ADP
ejpam-6314	608	8	fde	fde	PROPN
ejpam-6314	608	9	(	(	PUNCT
ejpam-6314	608	10	27	27	NUM
ejpam-6314	608	11	)	)	PUNCT
ejpam-6314	608	12	have	have	VERB
ejpam-6314	608	13	a	a	DET
ejpam-6314	608	14	unique	unique	ADJ
ejpam-6314	608	15	common	common	ADJ
ejpam-6314	608	16	solution	solution	NOUN
ejpam-6314	608	17	.	.	PUNCT
ejpam-6314	609	1	4	4	X
ejpam-6314	609	2	.	.	X
ejpam-6314	609	3	conclusion	conclusion	NOUN
ejpam-6314	609	4	fractional	fractional	ADJ
ejpam-6314	609	5	differential	differential	ADJ
ejpam-6314	609	6	equations	equation	NOUN
ejpam-6314	609	7	(	(	PUNCT
ejpam-6314	609	8	fdes	fde	NOUN
ejpam-6314	609	9	)	)	PUNCT
ejpam-6314	609	10	have	have	AUX
ejpam-6314	609	11	emerged	emerge	VERB
ejpam-6314	609	12	as	as	ADP
ejpam-6314	609	13	powerful	powerful	ADJ
ejpam-6314	609	14	tools	tool	NOUN
ejpam-6314	609	15	for	for	ADP
ejpam-6314	609	16	modeling	model	VERB
ejpam-6314	609	17	a	a	DET
ejpam-6314	609	18	variety	variety	NOUN
ejpam-6314	609	19	of	of	ADP
ejpam-6314	609	20	complex	complex	ADJ
ejpam-6314	609	21	,	,	PUNCT
ejpam-6314	609	22	real	real	ADJ
ejpam-6314	609	23	-	-	PUNCT
ejpam-6314	609	24	world	world	NOUN
ejpam-6314	609	25	processes	process	NOUN
ejpam-6314	609	26	encountered	encounter	VERB
ejpam-6314	609	27	in	in	ADP
ejpam-6314	609	28	physics	physics	NOUN
ejpam-6314	609	29	,	,	PUNCT
ejpam-6314	609	30	engineering	engineering	NOUN
ejpam-6314	609	31	,	,	PUNCT
ejpam-6314	609	32	biology	biology	NOUN
ejpam-6314	609	33	,	,	PUNCT
ejpam-6314	609	34	and	and	CCONJ
ejpam-6314	609	35	finance	finance	NOUN
ejpam-6314	609	36	.	.	PUNCT
ejpam-6314	610	1	their	their	PRON
ejpam-6314	610	2	ability	ability	NOUN
ejpam-6314	610	3	to	to	PART
ejpam-6314	610	4	incorporate	incorporate	VERB
ejpam-6314	610	5	non	non	ADJ
ejpam-6314	610	6	-	-	ADJ
ejpam-6314	610	7	integer	integer	ADJ
ejpam-6314	610	8	order	order	NOUN
ejpam-6314	610	9	derivatives	derivative	NOUN
ejpam-6314	610	10	makes	make	VERB
ejpam-6314	610	11	them	they	PRON
ejpam-6314	610	12	particularly	particularly	ADV
ejpam-6314	610	13	effective	effective	ADJ
ejpam-6314	610	14	in	in	ADP
ejpam-6314	610	15	capturing	capture	VERB
ejpam-6314	610	16	memory	memory	NOUN
ejpam-6314	610	17	effects	effect	NOUN
ejpam-6314	610	18	and	and	CCONJ
ejpam-6314	610	19	hereditary	hereditary	ADJ
ejpam-6314	610	20	properties	property	NOUN
ejpam-6314	610	21	inherent	inherent	ADJ
ejpam-6314	610	22	in	in	ADP
ejpam-6314	610	23	many	many	ADJ
ejpam-6314	610	24	dynamic	dynamic	ADJ
ejpam-6314	610	25	systems	system	NOUN
ejpam-6314	610	26	.	.	PUNCT
ejpam-6314	611	1	analyzing	analyze	VERB
ejpam-6314	611	2	such	such	ADJ
ejpam-6314	611	3	equations	equation	NOUN
ejpam-6314	611	4	often	often	ADV
ejpam-6314	611	5	involves	involve	VERB
ejpam-6314	611	6	transforming	transform	VERB
ejpam-6314	611	7	them	they	PRON
ejpam-6314	611	8	into	into	ADP
ejpam-6314	611	9	equivalent	equivalent	ADJ
ejpam-6314	611	10	integral	integral	ADJ
ejpam-6314	611	11	formulations	formulation	NOUN
ejpam-6314	611	12	,	,	PUNCT
ejpam-6314	611	13	which	which	PRON
ejpam-6314	611	14	in	in	ADP
ejpam-6314	611	15	turn	turn	NOUN
ejpam-6314	611	16	require	require	VERB
ejpam-6314	611	17	robust	robust	ADJ
ejpam-6314	611	18	mathematical	mathematical	ADJ
ejpam-6314	611	19	frameworks	framework	NOUN
ejpam-6314	611	20	to	to	PART
ejpam-6314	611	21	examine	examine	VERB
ejpam-6314	611	22	the	the	DET
ejpam-6314	611	23	m.	m.	NOUN
ejpam-6314	611	24	sarwar	sarwar	PROPN
ejpam-6314	611	25	et	et	PROPN
ejpam-6314	612	1	al	al	PROPN
ejpam-6314	612	2	.	.	PUNCT
ejpam-6314	612	3	/	/	SYM
ejpam-6314	612	4	eur	eur	PROPN
ejpam-6314	612	5	.	.	PUNCT
ejpam-6314	613	1	j.	j.	PROPN
ejpam-6314	613	2	pure	pure	PROPN
ejpam-6314	613	3	appl	appl	PROPN
ejpam-6314	613	4	.	.	PROPN
ejpam-6314	613	5	math	math	PROPN
ejpam-6314	613	6	,	,	PUNCT
ejpam-6314	613	7	18	18	NUM
ejpam-6314	613	8	(	(	PUNCT
ejpam-6314	613	9	3	3	NUM
ejpam-6314	613	10	)	)	PUNCT
ejpam-6314	613	11	(	(	PUNCT
ejpam-6314	613	12	2025	2025	NUM
ejpam-6314	613	13	)	)	PUNCT
ejpam-6314	613	14	,	,	PUNCT
ejpam-6314	613	15	6314	6314	NUM
ejpam-6314	613	16	26	26	NUM
ejpam-6314	613	17	of	of	ADP
ejpam-6314	613	18	28	28	NUM
ejpam-6314	613	19	existence	existence	NOUN
ejpam-6314	613	20	,	,	PUNCT
ejpam-6314	613	21	uniqueness	uniqueness	NOUN
ejpam-6314	613	22	,	,	PUNCT
ejpam-6314	613	23	and	and	CCONJ
ejpam-6314	613	24	stability	stability	NOUN
ejpam-6314	613	25	of	of	ADP
ejpam-6314	613	26	their	their	PRON
ejpam-6314	613	27	solutions	solution	NOUN
ejpam-6314	613	28	.	.	PUNCT
ejpam-6314	614	1	fixed	fix	VERB
ejpam-6314	614	2	point	point	NOUN
ejpam-6314	614	3	theory	theory	NOUN
ejpam-6314	614	4	,	,	PUNCT
ejpam-6314	614	5	especially	especially	ADV
ejpam-6314	614	6	in	in	ADP
ejpam-6314	614	7	the	the	DET
ejpam-6314	614	8	context	context	NOUN
ejpam-6314	614	9	of	of	ADP
ejpam-6314	614	10	generalized	generalized	ADJ
ejpam-6314	614	11	metric	metric	ADJ
ejpam-6314	614	12	spaces	space	NOUN
ejpam-6314	614	13	and	and	CCONJ
ejpam-6314	614	14	non	non	ADJ
ejpam-6314	614	15	-	-	ADJ
ejpam-6314	614	16	traditional	traditional	ADJ
ejpam-6314	614	17	contraction	contraction	NOUN
ejpam-6314	614	18	principles	principle	NOUN
ejpam-6314	614	19	,	,	PUNCT
ejpam-6314	614	20	provides	provide	VERB
ejpam-6314	614	21	a	a	DET
ejpam-6314	614	22	foundational	foundational	ADJ
ejpam-6314	614	23	approach	approach	NOUN
ejpam-6314	614	24	in	in	ADP
ejpam-6314	614	25	this	this	DET
ejpam-6314	614	26	analytical	analytical	ADJ
ejpam-6314	614	27	endeavor	endeavor	NOUN
ejpam-6314	614	28	.	.	PUNCT
ejpam-6314	615	1	in	in	ADP
ejpam-6314	615	2	particular	particular	ADJ
ejpam-6314	615	3	,	,	PUNCT
ejpam-6314	615	4	rational	rational	ADJ
ejpam-6314	615	5	-	-	PUNCT
ejpam-6314	615	6	type	type	NOUN
ejpam-6314	615	7	contractive	contractive	ADJ
ejpam-6314	615	8	conditions	condition	NOUN
ejpam-6314	615	9	have	have	AUX
ejpam-6314	615	10	proven	prove	VERB
ejpam-6314	615	11	to	to	PART
ejpam-6314	615	12	be	be	AUX
ejpam-6314	615	13	especially	especially	ADV
ejpam-6314	615	14	useful	useful	ADJ
ejpam-6314	615	15	in	in	ADP
ejpam-6314	615	16	establishing	establish	VERB
ejpam-6314	615	17	strong	strong	ADJ
ejpam-6314	615	18	convergence	convergence	NOUN
ejpam-6314	615	19	results	result	NOUN
ejpam-6314	615	20	and	and	CCONJ
ejpam-6314	615	21	solution	solution	NOUN
ejpam-6314	615	22	behaviors	behavior	NOUN
ejpam-6314	615	23	.	.	PUNCT
ejpam-6314	616	1	in	in	ADP
ejpam-6314	616	2	this	this	DET
ejpam-6314	616	3	study	study	NOUN
ejpam-6314	616	4	,	,	PUNCT
ejpam-6314	616	5	we	we	PRON
ejpam-6314	616	6	investigated	investigate	VERB
ejpam-6314	616	7	unique	unique	ADJ
ejpam-6314	616	8	and	and	CCONJ
ejpam-6314	616	9	common	common	ADJ
ejpam-6314	616	10	fixed	fix	VERB
ejpam-6314	616	11	point	point	NOUN
ejpam-6314	616	12	results	result	NOUN
ejpam-6314	616	13	within	within	ADP
ejpam-6314	616	14	the	the	DET
ejpam-6314	616	15	setting	setting	NOUN
ejpam-6314	616	16	of	of	ADP
ejpam-6314	616	17	bi	bi	ADJ
ejpam-6314	616	18	-	-	ADJ
ejpam-6314	616	19	complex	complex	ADJ
ejpam-6314	616	20	valued	value	VERB
ejpam-6314	616	21	control	control	NOUN
ejpam-6314	616	22	metric	metric	ADJ
ejpam-6314	616	23	spaces	space	NOUN
ejpam-6314	616	24	using	use	VERB
ejpam-6314	616	25	rational	rational	ADJ
ejpam-6314	616	26	-	-	PUNCT
ejpam-6314	616	27	type	type	NOUN
ejpam-6314	616	28	inequalities	inequality	NOUN
ejpam-6314	616	29	.	.	PUNCT
ejpam-6314	617	1	the	the	DET
ejpam-6314	617	2	use	use	NOUN
ejpam-6314	617	3	of	of	ADP
ejpam-6314	617	4	bi	bi	ADJ
ejpam-6314	617	5	-	-	ADJ
ejpam-6314	617	6	complex	complex	ADJ
ejpam-6314	617	7	numbers	number	NOUN
ejpam-6314	617	8	,	,	PUNCT
ejpam-6314	617	9	which	which	PRON
ejpam-6314	617	10	extend	extend	VERB
ejpam-6314	617	11	complex	complex	ADJ
ejpam-6314	617	12	analysis	analysis	NOUN
ejpam-6314	617	13	through	through	ADP
ejpam-6314	617	14	the	the	DET
ejpam-6314	617	15	introduction	introduction	NOUN
ejpam-6314	617	16	of	of	ADP
ejpam-6314	617	17	two	two	NUM
ejpam-6314	617	18	imaginary	imaginary	ADJ
ejpam-6314	617	19	units	unit	NOUN
ejpam-6314	617	20	,	,	PUNCT
ejpam-6314	617	21	provides	provide	VERB
ejpam-6314	617	22	a	a	DET
ejpam-6314	617	23	richer	rich	ADJ
ejpam-6314	617	24	and	and	CCONJ
ejpam-6314	617	25	more	more	ADV
ejpam-6314	617	26	flexible	flexible	ADJ
ejpam-6314	617	27	algebraic	algebraic	ADJ
ejpam-6314	617	28	and	and	CCONJ
ejpam-6314	617	29	topological	topological	ADJ
ejpam-6314	617	30	structure	structure	NOUN
ejpam-6314	617	31	.	.	PUNCT
ejpam-6314	618	1	this	this	DET
ejpam-6314	618	2	enhanced	enhance	VERB
ejpam-6314	618	3	framework	framework	NOUN
ejpam-6314	618	4	enables	enable	VERB
ejpam-6314	618	5	the	the	DET
ejpam-6314	618	6	examination	examination	NOUN
ejpam-6314	618	7	of	of	ADP
ejpam-6314	618	8	more	more	ADV
ejpam-6314	618	9	generalized	generalized	ADJ
ejpam-6314	618	10	and	and	CCONJ
ejpam-6314	618	11	complex	complex	ADJ
ejpam-6314	618	12	contractive	contractive	ADJ
ejpam-6314	618	13	mappings	mapping	NOUN
ejpam-6314	618	14	that	that	PRON
ejpam-6314	618	15	can	can	AUX
ejpam-6314	618	16	not	not	PART
ejpam-6314	618	17	be	be	AUX
ejpam-6314	618	18	adequately	adequately	ADV
ejpam-6314	618	19	addressed	address	VERB
ejpam-6314	618	20	within	within	ADP
ejpam-6314	618	21	conventional	conventional	ADJ
ejpam-6314	618	22	real	real	ADJ
ejpam-6314	618	23	or	or	CCONJ
ejpam-6314	618	24	complex	complex	ADV
ejpam-6314	618	25	-	-	PUNCT
ejpam-6314	618	26	valued	value	VERB
ejpam-6314	618	27	metric	metric	ADJ
ejpam-6314	618	28	spaces	space	NOUN
ejpam-6314	618	29	.	.	PUNCT
ejpam-6314	619	1	the	the	DET
ejpam-6314	619	2	theoretical	theoretical	ADJ
ejpam-6314	619	3	results	result	NOUN
ejpam-6314	619	4	obtained	obtain	VERB
ejpam-6314	619	5	not	not	PART
ejpam-6314	619	6	only	only	ADV
ejpam-6314	619	7	contribute	contribute	VERB
ejpam-6314	619	8	meaningfully	meaningfully	ADV
ejpam-6314	619	9	to	to	ADP
ejpam-6314	619	10	the	the	DET
ejpam-6314	619	11	broader	broad	ADJ
ejpam-6314	619	12	field	field	NOUN
ejpam-6314	619	13	of	of	ADP
ejpam-6314	619	14	fixed	fix	VERB
ejpam-6314	619	15	point	point	NOUN
ejpam-6314	619	16	theory	theory	NOUN
ejpam-6314	619	17	but	but	CCONJ
ejpam-6314	619	18	also	also	ADV
ejpam-6314	619	19	have	have	VERB
ejpam-6314	619	20	direct	direct	ADJ
ejpam-6314	619	21	applications	application	NOUN
ejpam-6314	619	22	in	in	ADP
ejpam-6314	619	23	the	the	DET
ejpam-6314	619	24	analysis	analysis	NOUN
ejpam-6314	619	25	and	and	CCONJ
ejpam-6314	619	26	solution	solution	NOUN
ejpam-6314	619	27	of	of	ADP
ejpam-6314	619	28	fractional	fractional	ADJ
ejpam-6314	619	29	differential	differential	ADJ
ejpam-6314	619	30	equations	equation	NOUN
ejpam-6314	619	31	.	.	PUNCT
ejpam-6314	620	1	overall	overall	ADV
ejpam-6314	620	2	,	,	PUNCT
ejpam-6314	620	3	this	this	DET
ejpam-6314	620	4	work	work	NOUN
ejpam-6314	620	5	opens	open	VERB
ejpam-6314	620	6	up	up	ADP
ejpam-6314	620	7	new	new	ADJ
ejpam-6314	620	8	avenues	avenue	NOUN
ejpam-6314	620	9	for	for	ADP
ejpam-6314	620	10	the	the	DET
ejpam-6314	620	11	study	study	NOUN
ejpam-6314	620	12	of	of	ADP
ejpam-6314	620	13	intricate	intricate	ADJ
ejpam-6314	620	14	mathematical	mathematical	ADJ
ejpam-6314	620	15	models	model	NOUN
ejpam-6314	620	16	and	and	CCONJ
ejpam-6314	620	17	offers	offer	VERB
ejpam-6314	620	18	innovative	innovative	ADJ
ejpam-6314	620	19	tools	tool	NOUN
ejpam-6314	620	20	for	for	ADP
ejpam-6314	620	21	addressing	address	VERB
ejpam-6314	620	22	the	the	DET
ejpam-6314	620	23	analytical	analytical	ADJ
ejpam-6314	620	24	challenges	challenge	NOUN
ejpam-6314	620	25	presented	present	VERB
ejpam-6314	620	26	by	by	ADP
ejpam-6314	620	27	fractional	fractional	ADJ
ejpam-6314	620	28	systems	system	NOUN
ejpam-6314	620	29	in	in	ADP
ejpam-6314	620	30	higher	higher	ADV
ejpam-6314	620	31	-	-	PUNCT
ejpam-6314	620	32	dimensional	dimensional	ADJ
ejpam-6314	620	33	and	and	CCONJ
ejpam-6314	620	34	abstract	abstract	ADJ
ejpam-6314	620	35	settings	setting	NOUN
ejpam-6314	620	36	.	.	PUNCT
ejpam-6314	621	1	acknowledgements	acknowledgement	VERB
ejpam-6314	621	2	the	the	DET
ejpam-6314	621	3	authors	author	NOUN
ejpam-6314	621	4	m.	m.	PROPN
ejpam-6314	621	5	sarwar	sarwar	PROPN
ejpam-6314	621	6	,	,	PUNCT
ejpam-6314	621	7	n.	n.	PROPN
ejpam-6314	621	8	fatima	fatima	PROPN
ejpam-6314	621	9	and	and	CCONJ
ejpam-6314	621	10	k.	k.	PROPN
ejpam-6314	621	11	abodayeh	abodayeh	PROPN
ejpam-6314	621	12	would	would	AUX
ejpam-6314	621	13	like	like	VERB
ejpam-6314	621	14	to	to	PART
ejpam-6314	621	15	thank	thank	VERB
ejpam-6314	621	16	prince	prince	PROPN
ejpam-6314	621	17	sultan	sultan	PROPN
ejpam-6314	621	18	university	university	PROPN
ejpam-6314	621	19	for	for	ADP
ejpam-6314	621	20	apc	apc	PROPN
ejpam-6314	621	21	and	and	CCONJ
ejpam-6314	621	22	for	for	ADP
ejpam-6314	621	23	the	the	DET
ejpam-6314	621	24	support	support	NOUN
ejpam-6314	621	25	of	of	ADP
ejpam-6314	621	26	this	this	DET
ejpam-6314	621	27	work	work	NOUN
ejpam-6314	621	28	through	through	ADP
ejpam-6314	621	29	tas	ta	NOUN
ejpam-6314	621	30	research	research	NOUN
ejpam-6314	621	31	lab	lab	NOUN
ejpam-6314	621	32	.	.	PUNCT
ejpam-6314	622	1	author	author	NOUN
ejpam-6314	622	2	’s	’s	PART
ejpam-6314	622	3	contributions	contribution	NOUN
ejpam-6314	622	4	all	all	DET
ejpam-6314	622	5	authors	author	NOUN
ejpam-6314	622	6	contribute	contribute	VERB
ejpam-6314	622	7	equally	equally	ADV
ejpam-6314	622	8	to	to	ADP
ejpam-6314	622	9	the	the	DET
ejpam-6314	622	10	writing	writing	NOUN
ejpam-6314	622	11	of	of	ADP
ejpam-6314	622	12	this	this	DET
ejpam-6314	622	13	manuscript	manuscript	NOUN
ejpam-6314	622	14	.	.	PUNCT
ejpam-6314	623	1	all	all	DET
ejpam-6314	623	2	authors	author	NOUN
ejpam-6314	623	3	reads	read	VERB
ejpam-6314	623	4	and	and	CCONJ
ejpam-6314	623	5	approved	approve	VERB
ejpam-6314	623	6	the	the	DET
ejpam-6314	623	7	final	final	ADJ
ejpam-6314	623	8	version	version	NOUN
ejpam-6314	623	9	.	.	PUNCT
ejpam-6314	624	1	references	reference	NOUN
ejpam-6314	624	2	[	[	X
ejpam-6314	624	3	1	1	NUM
ejpam-6314	624	4	]	]	PUNCT
ejpam-6314	624	5	anatolii	anatolii	NOUN
ejpam-6314	624	6	a.	a.	NOUN
ejpam-6314	624	7	kilbas	kilbas	PROPN
ejpam-6314	624	8	,	,	PUNCT
ejpam-6314	624	9	hari	hari	PROPN
ejpam-6314	624	10	m.	m.	PROPN
ejpam-6314	624	11	srivastava	srivastava	PROPN
ejpam-6314	624	12	,	,	PUNCT
ejpam-6314	624	13	and	and	CCONJ
ejpam-6314	624	14	juan	juan	PROPN
ejpam-6314	624	15	j.	j.	PROPN
ejpam-6314	624	16	trujillo	trujillo	PROPN
ejpam-6314	624	17	.	.	PUNCT
ejpam-6314	625	1	theory	theory	NOUN
ejpam-6314	625	2	and	and	CCONJ
ejpam-6314	625	3	applications	application	NOUN
ejpam-6314	625	4	of	of	ADP
ejpam-6314	625	5	fractional	fractional	ADJ
ejpam-6314	625	6	differential	differential	ADJ
ejpam-6314	625	7	equations	equation	NOUN
ejpam-6314	625	8	,	,	PUNCT
ejpam-6314	625	9	volume	volume	NOUN
ejpam-6314	625	10	204	204	NUM
ejpam-6314	625	11	.	.	PUNCT
ejpam-6314	626	1	elsevier	elsevier	NOUN
ejpam-6314	626	2	,	,	PUNCT
ejpam-6314	626	3	2006	2006	NUM
ejpam-6314	626	4	.	.	PUNCT
ejpam-6314	627	1	[	[	X
ejpam-6314	627	2	2	2	NUM
ejpam-6314	627	3	]	]	PUNCT
ejpam-6314	627	4	igor	igor	NOUN
ejpam-6314	627	5	podlubny	podlubny	PROPN
ejpam-6314	627	6	.	.	PUNCT
ejpam-6314	628	1	fractional	fractional	ADJ
ejpam-6314	628	2	differential	differential	ADJ
ejpam-6314	628	3	equations	equation	NOUN
ejpam-6314	628	4	,	,	PUNCT
ejpam-6314	628	5	volume	volume	NOUN
ejpam-6314	628	6	198	198	NUM
ejpam-6314	628	7	of	of	ADP
ejpam-6314	628	8	.	.	PUNCT
ejpam-6314	629	1	mathematics	mathematic	NOUN
ejpam-6314	629	2	in	in	ADP
ejpam-6314	629	3	science	science	NOUN
ejpam-6314	629	4	and	and	CCONJ
ejpam-6314	629	5	engineering	engineering	NOUN
ejpam-6314	629	6	,	,	PUNCT
ejpam-6314	629	7	198:7–35	198:7–35	NUM
ejpam-6314	629	8	,	,	PUNCT
ejpam-6314	629	9	1999	1999	NUM
ejpam-6314	629	10	.	.	PUNCT
ejpam-6314	630	1	[	[	X
ejpam-6314	630	2	3	3	X
ejpam-6314	630	3	]	]	X
ejpam-6314	630	4	vangipuram	vangipuram	NOUN
ejpam-6314	630	5	lakshmikantham	lakshmikantham	PROPN
ejpam-6314	630	6	,	,	PUNCT
ejpam-6314	630	7	srinivasa	srinivasa	PROPN
ejpam-6314	630	8	leela	leela	PROPN
ejpam-6314	630	9	,	,	PUNCT
ejpam-6314	630	10	and	and	CCONJ
ejpam-6314	630	11	j	j	PROPN
ejpam-6314	630	12	vasundhara	vasundhara	PROPN
ejpam-6314	630	13	devi	devi	PROPN
ejpam-6314	630	14	.	.	PUNCT
ejpam-6314	631	1	theory	theory	NOUN
ejpam-6314	631	2	of	of	ADP
ejpam-6314	631	3	fractional	fractional	ADJ
ejpam-6314	631	4	dynamic	dynamic	ADJ
ejpam-6314	631	5	systems	system	NOUN
ejpam-6314	631	6	.	.	PUNCT
ejpam-6314	632	1	(	(	PUNCT
ejpam-6314	632	2	no	no	DET
ejpam-6314	632	3	title	title	NOUN
ejpam-6314	632	4	)	)	PUNCT
ejpam-6314	632	5	,	,	PUNCT
ejpam-6314	632	6	2009	2009	NUM
ejpam-6314	632	7	.	.	PUNCT
ejpam-6314	633	1	[	[	X
ejpam-6314	633	2	4	4	NUM
ejpam-6314	633	3	]	]	PUNCT
ejpam-6314	633	4	kenneth	kenneth	PROPN
ejpam-6314	633	5	s	s	PROPN
ejpam-6314	633	6	miller	miller	PROPN
ejpam-6314	633	7	and	and	CCONJ
ejpam-6314	633	8	bertram	bertram	PROPN
ejpam-6314	633	9	ross	ross	PROPN
ejpam-6314	633	10	.	.	PUNCT
ejpam-6314	634	1	an	an	DET
ejpam-6314	634	2	introduction	introduction	NOUN
ejpam-6314	634	3	to	to	ADP
ejpam-6314	634	4	the	the	DET
ejpam-6314	634	5	fractional	fractional	ADJ
ejpam-6314	634	6	calculus	calculus	NOUN
ejpam-6314	634	7	and	and	CCONJ
ejpam-6314	634	8	fractional	fractional	ADJ
ejpam-6314	634	9	differential	differential	ADJ
ejpam-6314	634	10	equations	equation	NOUN
ejpam-6314	634	11	.	.	PUNCT
ejpam-6314	635	1	(	(	PUNCT
ejpam-6314	635	2	no	no	DET
ejpam-6314	635	3	title	title	NOUN
ejpam-6314	635	4	)	)	PUNCT
ejpam-6314	635	5	,	,	PUNCT
ejpam-6314	635	6	1993	1993	NUM
ejpam-6314	635	7	.	.	PUNCT
ejpam-6314	636	1	[	[	X
ejpam-6314	636	2	5	5	X
ejpam-6314	636	3	]	]	X
ejpam-6314	636	4	stefan	stefan	PROPN
ejpam-6314	636	5	banach	banach	PROPN
ejpam-6314	636	6	.	.	PUNCT
ejpam-6314	637	1	sur	sur	PROPN
ejpam-6314	637	2	les	les	X
ejpam-6314	637	3	opérations	opération	NOUN
ejpam-6314	637	4	dans	dan	NOUN
ejpam-6314	637	5	les	les	X
ejpam-6314	637	6	ensembles	ensemble	NOUN
ejpam-6314	637	7	abstraits	abstrait	NOUN
ejpam-6314	637	8	et	et	PROPN
ejpam-6314	637	9	leur	leur	X
ejpam-6314	637	10	application	application	PROPN
ejpam-6314	637	11	aux	aux	PROPN
ejpam-6314	637	12	équations	équations	PROPN
ejpam-6314	637	13	intégrales	intégrale	NOUN
ejpam-6314	637	14	.	.	PUNCT
ejpam-6314	638	1	fundamenta	fundamenta	PROPN
ejpam-6314	638	2	mathematicae	mathematicae	PROPN
ejpam-6314	638	3	,	,	PUNCT
ejpam-6314	638	4	3(1):133–181	3(1):133–181	NUM
ejpam-6314	638	5	,	,	PUNCT
ejpam-6314	638	6	1922	1922	NUM
ejpam-6314	638	7	.	.	PUNCT
ejpam-6314	639	1	[	[	X
ejpam-6314	639	2	6	6	NUM
ejpam-6314	639	3	]	]	SYM
ejpam-6314	639	4	i.a	i.a	PROPN
ejpam-6314	639	5	.	.	PROPN
ejpam-6314	639	6	bakhtin	bakhtin	PROPN
ejpam-6314	639	7	.	.	PUNCT
ejpam-6314	640	1	the	the	DET
ejpam-6314	640	2	contraction	contraction	NOUN
ejpam-6314	640	3	mapping	map	VERB
ejpam-6314	640	4	principle	principle	NOUN
ejpam-6314	640	5	in	in	ADP
ejpam-6314	640	6	quasimetric	quasimetric	ADJ
ejpam-6314	640	7	spaces	space	NOUN
ejpam-6314	640	8	.	.	PUNCT
ejpam-6314	641	1	functional	functional	ADJ
ejpam-6314	641	2	analysis	analysis	NOUN
ejpam-6314	641	3	,	,	PUNCT
ejpam-6314	641	4	30:26–37	30:26–37	PROPN
ejpam-6314	641	5	,	,	PUNCT
ejpam-6314	641	6	1989	1989	NUM
ejpam-6314	641	7	.	.	PUNCT
ejpam-6314	642	1	in	in	ADP
ejpam-6314	642	2	russian	russian	PROPN
ejpam-6314	642	3	.	.	PUNCT
ejpam-6314	643	1	m.	m.	PROPN
ejpam-6314	643	2	sarwar	sarwar	PROPN
ejpam-6314	643	3	et	et	PROPN
ejpam-6314	643	4	al	al	PROPN
ejpam-6314	643	5	.	.	PUNCT
ejpam-6314	643	6	/	/	SYM
ejpam-6314	643	7	eur	eur	PROPN
ejpam-6314	643	8	.	.	PUNCT
ejpam-6314	644	1	j.	j.	PROPN
ejpam-6314	644	2	pure	pure	PROPN
ejpam-6314	644	3	appl	appl	PROPN
ejpam-6314	644	4	.	.	PROPN
ejpam-6314	644	5	math	math	PROPN
ejpam-6314	644	6	,	,	PUNCT
ejpam-6314	644	7	18	18	NUM
ejpam-6314	644	8	(	(	PUNCT
ejpam-6314	644	9	3	3	NUM
ejpam-6314	644	10	)	)	PUNCT
ejpam-6314	644	11	(	(	PUNCT
ejpam-6314	644	12	2025	2025	NUM
ejpam-6314	644	13	)	)	PUNCT
ejpam-6314	644	14	,	,	PUNCT
ejpam-6314	644	15	6314	6314	NUM
ejpam-6314	644	16	27	27	NUM
ejpam-6314	644	17	of	of	ADP
ejpam-6314	644	18	28	28	NUM
ejpam-6314	644	19	[	[	X
ejpam-6314	644	20	7	7	NUM
ejpam-6314	644	21	]	]	PUNCT
ejpam-6314	644	22	tayyab	tayyab	NOUN
ejpam-6314	644	23	kamran	kamran	PROPN
ejpam-6314	644	24	,	,	PUNCT
ejpam-6314	644	25	maria	maria	PROPN
ejpam-6314	644	26	samreen	samreen	PROPN
ejpam-6314	644	27	,	,	PUNCT
ejpam-6314	644	28	and	and	CCONJ
ejpam-6314	644	29	qurat	qurat	PROPN
ejpam-6314	644	30	ul	ul	PROPN
ejpam-6314	644	31	ain	ain	PROPN
ejpam-6314	644	32	.	.	PUNCT
ejpam-6314	645	1	a	a	DET
ejpam-6314	645	2	generalization	generalization	NOUN
ejpam-6314	645	3	of	of	ADP
ejpam-6314	645	4	b	b	NOUN
ejpam-6314	645	5	-	-	PUNCT
ejpam-6314	645	6	metric	metric	ADJ
ejpam-6314	645	7	space	space	NOUN
ejpam-6314	645	8	and	and	CCONJ
ejpam-6314	645	9	some	some	DET
ejpam-6314	645	10	fixed	fix	VERB
ejpam-6314	645	11	point	point	NOUN
ejpam-6314	645	12	theorems	theorem	NOUN
ejpam-6314	645	13	.	.	PUNCT
ejpam-6314	646	1	mathematics	mathematic	NOUN
ejpam-6314	646	2	,	,	PUNCT
ejpam-6314	646	3	5(2):19	5(2):19	NUM
ejpam-6314	646	4	,	,	PUNCT
ejpam-6314	646	5	2017	2017	NUM
ejpam-6314	646	6	.	.	PUNCT
ejpam-6314	647	1	[	[	X
ejpam-6314	647	2	8	8	NUM
ejpam-6314	647	3	]	]	X
ejpam-6314	647	4	nabil	nabil	PROPN
ejpam-6314	647	5	mlaiki	mlaiki	PROPN
ejpam-6314	647	6	,	,	PUNCT
ejpam-6314	647	7	hassen	hassen	PROPN
ejpam-6314	647	8	aydi	aydi	VERB
ejpam-6314	647	9	,	,	PUNCT
ejpam-6314	647	10	nizar	nizar	NOUN
ejpam-6314	647	11	souayah	souayah	NOUN
ejpam-6314	647	12	,	,	PUNCT
ejpam-6314	647	13	and	and	CCONJ
ejpam-6314	647	14	thabet	thabet	ADJ
ejpam-6314	647	15	abdeljawad	abdeljawad	NOUN
ejpam-6314	647	16	.	.	PUNCT
ejpam-6314	648	1	controlled	control	VERB
ejpam-6314	648	2	metric	metric	ADJ
ejpam-6314	648	3	type	type	NOUN
ejpam-6314	648	4	spaces	space	NOUN
ejpam-6314	648	5	and	and	CCONJ
ejpam-6314	648	6	the	the	DET
ejpam-6314	648	7	related	related	ADJ
ejpam-6314	648	8	contraction	contraction	NOUN
ejpam-6314	648	9	principle	principle	NOUN
ejpam-6314	648	10	.	.	PUNCT
ejpam-6314	649	1	mathematics	mathematic	NOUN
ejpam-6314	649	2	,	,	PUNCT
ejpam-6314	649	3	6(10):194	6(10):194	PROPN
ejpam-6314	649	4	,	,	PUNCT
ejpam-6314	649	5	2018	2018	NUM
ejpam-6314	649	6	.	.	PUNCT
ejpam-6314	650	1	[	[	X
ejpam-6314	650	2	9	9	NUM
ejpam-6314	650	3	]	]	PUNCT
ejpam-6314	650	4	bhawna	bhawna	NOUN
ejpam-6314	650	5	soni	soni	ADJ
ejpam-6314	650	6	and	and	CCONJ
ejpam-6314	650	7	abha	abha	NOUN
ejpam-6314	650	8	tenguria	tenguria	NOUN
ejpam-6314	650	9	.	.	PUNCT
ejpam-6314	651	1	expansion	expansion	NOUN
ejpam-6314	651	2	mapping	mapping	NOUN
ejpam-6314	651	3	in	in	ADP
ejpam-6314	651	4	controlled	control	VERB
ejpam-6314	651	5	metric	metric	ADJ
ejpam-6314	651	6	space	space	NOUN
ejpam-6314	651	7	and	and	CCONJ
ejpam-6314	651	8	extended	extend	VERB
ejpam-6314	651	9	b	b	X
ejpam-6314	651	10	-	-	PUNCT
ejpam-6314	651	11	metric	metric	ADJ
ejpam-6314	651	12	space	space	NOUN
ejpam-6314	651	13	.	.	PUNCT
ejpam-6314	652	1	2025	2025	NUM
ejpam-6314	652	2	.	.	PUNCT
ejpam-6314	653	1	[	[	X
ejpam-6314	653	2	10	10	NUM
ejpam-6314	653	3	]	]	X
ejpam-6314	653	4	thabet	thabet	ADJ
ejpam-6314	653	5	abdeljawad	abdeljawad	NOUN
ejpam-6314	653	6	,	,	PUNCT
ejpam-6314	653	7	nabil	nabil	PROPN
ejpam-6314	653	8	mlaiki	mlaiki	PROPN
ejpam-6314	653	9	,	,	PUNCT
ejpam-6314	653	10	hassen	hassen	PROPN
ejpam-6314	653	11	aydi	aydi	ADV
ejpam-6314	653	12	,	,	PUNCT
ejpam-6314	653	13	and	and	CCONJ
ejpam-6314	653	14	nizar	nizar	PROPN
ejpam-6314	653	15	souayah	souayah	NOUN
ejpam-6314	653	16	.	.	PUNCT
ejpam-6314	654	1	double	double	ADJ
ejpam-6314	654	2	controlled	control	VERB
ejpam-6314	654	3	metric	metric	ADJ
ejpam-6314	654	4	type	type	NOUN
ejpam-6314	654	5	spaces	space	NOUN
ejpam-6314	654	6	and	and	CCONJ
ejpam-6314	654	7	some	some	DET
ejpam-6314	654	8	fixed	fix	VERB
ejpam-6314	654	9	point	point	NOUN
ejpam-6314	654	10	results	result	NOUN
ejpam-6314	654	11	.	.	PUNCT
ejpam-6314	655	1	mathematics	mathematic	NOUN
ejpam-6314	655	2	,	,	PUNCT
ejpam-6314	655	3	6(12):320	6(12):320	PROPN
ejpam-6314	655	4	,	,	PUNCT
ejpam-6314	655	5	2018	2018	NUM
ejpam-6314	655	6	.	.	PUNCT
ejpam-6314	656	1	[	[	X
ejpam-6314	656	2	11	11	NUM
ejpam-6314	656	3	]	]	X
ejpam-6314	656	4	akbar	akbar	PROPN
ejpam-6314	656	5	azam	azam	PROPN
ejpam-6314	656	6	,	,	PUNCT
ejpam-6314	656	7	brian	brian	PROPN
ejpam-6314	656	8	fisher	fisher	PROPN
ejpam-6314	656	9	,	,	PUNCT
ejpam-6314	656	10	and	and	CCONJ
ejpam-6314	656	11	m	m	PROPN
ejpam-6314	656	12	khan	khan	PROPN
ejpam-6314	656	13	.	.	PUNCT
ejpam-6314	657	1	common	common	ADJ
ejpam-6314	657	2	fixed	fix	VERB
ejpam-6314	657	3	point	point	NOUN
ejpam-6314	657	4	theorems	theorem	NOUN
ejpam-6314	657	5	in	in	ADP
ejpam-6314	657	6	complex	complex	ADJ
ejpam-6314	657	7	valued	value	VERB
ejpam-6314	657	8	metric	metric	ADJ
ejpam-6314	657	9	spaces	space	NOUN
ejpam-6314	657	10	.	.	PUNCT
ejpam-6314	658	1	numerical	numerical	ADJ
ejpam-6314	658	2	functional	functional	ADJ
ejpam-6314	658	3	analysis	analysis	NOUN
ejpam-6314	658	4	and	and	CCONJ
ejpam-6314	658	5	optimization	optimization	NOUN
ejpam-6314	658	6	,	,	PUNCT
ejpam-6314	658	7	32(3):243	32(3):243	NUM
ejpam-6314	658	8	–	–	PUNCT
ejpam-6314	658	9	253	253	NUM
ejpam-6314	658	10	,	,	PUNCT
ejpam-6314	658	11	2011	2011	NUM
ejpam-6314	658	12	.	.	PUNCT
ejpam-6314	659	1	[	[	X
ejpam-6314	659	2	12	12	NUM
ejpam-6314	659	3	]	]	PUNCT
ejpam-6314	659	4	corrado	corrado	PROPN
ejpam-6314	659	5	segre	segre	PROPN
ejpam-6314	659	6	.	.	PUNCT
ejpam-6314	660	1	le	le	PROPN
ejpam-6314	660	2	rappresentazioni	rappresentazioni	PROPN
ejpam-6314	660	3	reali	reali	PROPN
ejpam-6314	660	4	delle	delle	PROPN
ejpam-6314	660	5	forme	forme	PROPN
ejpam-6314	660	6	complesse	complesse	PROPN
ejpam-6314	660	7	e	e	PROPN
ejpam-6314	660	8	gli	gli	NOUN
ejpam-6314	660	9	enti	enti	X
ejpam-6314	660	10	iperalgebrici	iperalgebrici	NOUN
ejpam-6314	660	11	.	.	PUNCT
ejpam-6314	661	1	mathematische	mathematische	PROPN
ejpam-6314	661	2	annalen	annalen	PROPN
ejpam-6314	661	3	,	,	PUNCT
ejpam-6314	661	4	40(3):413–467	40(3):413–467	PROPN
ejpam-6314	661	5	,	,	PUNCT
ejpam-6314	661	6	1892	1892	NUM
ejpam-6314	661	7	.	.	PUNCT
ejpam-6314	662	1	[	[	X
ejpam-6314	662	2	13	13	NUM
ejpam-6314	662	3	]	]	X
ejpam-6314	662	4	junesang	junesang	NOUN
ejpam-6314	662	5	choi	choi	PROPN
ejpam-6314	662	6	,	,	PUNCT
ejpam-6314	662	7	sanjib	sanjib	PROPN
ejpam-6314	662	8	kumar	kumar	PROPN
ejpam-6314	662	9	datta	datta	PROPN
ejpam-6314	662	10	,	,	PUNCT
ejpam-6314	662	11	tanmay	tanmay	PROPN
ejpam-6314	662	12	biswas	biswas	PROPN
ejpam-6314	662	13	,	,	PUNCT
ejpam-6314	662	14	and	and	CCONJ
ejpam-6314	662	15	md	md	PROPN
ejpam-6314	662	16	nazimul	nazimul	PROPN
ejpam-6314	662	17	islam	islam	PROPN
ejpam-6314	662	18	.	.	PUNCT
ejpam-6314	663	1	some	some	DET
ejpam-6314	663	2	fixed	fix	VERB
ejpam-6314	663	3	point	point	NOUN
ejpam-6314	663	4	theorems	theorem	NOUN
ejpam-6314	663	5	in	in	ADP
ejpam-6314	663	6	connection	connection	NOUN
ejpam-6314	663	7	with	with	ADP
ejpam-6314	663	8	two	two	NUM
ejpam-6314	663	9	weakly	weakly	ADJ
ejpam-6314	663	10	compatible	compatible	ADJ
ejpam-6314	663	11	mappings	mapping	NOUN
ejpam-6314	663	12	in	in	ADP
ejpam-6314	663	13	bicomplex	bicomplex	NOUN
ejpam-6314	663	14	valued	value	VERB
ejpam-6314	663	15	metric	metric	ADJ
ejpam-6314	663	16	spaces	space	NOUN
ejpam-6314	663	17	.	.	PUNCT
ejpam-6314	664	1	honam	honam	PROPN
ejpam-6314	664	2	mathematical	mathematical	PROPN
ejpam-6314	664	3	journal	journal	PROPN
ejpam-6314	664	4	,	,	PUNCT
ejpam-6314	664	5	39(1):115–126	39(1):115–126	PROPN
ejpam-6314	664	6	,	,	PUNCT
ejpam-6314	664	7	2017	2017	NUM
ejpam-6314	664	8	.	.	PUNCT
ejpam-6314	665	1	[	[	X
ejpam-6314	665	2	14	14	NUM
ejpam-6314	665	3	]	]	X
ejpam-6314	665	4	ismat	ismat	NOUN
ejpam-6314	665	5	beg	beg	PROPN
ejpam-6314	665	6	,	,	PUNCT
ejpam-6314	665	7	sanjib	sanjib	PROPN
ejpam-6314	665	8	kumar	kumar	PROPN
ejpam-6314	665	9	datta	datta	PROPN
ejpam-6314	665	10	,	,	PUNCT
ejpam-6314	665	11	and	and	CCONJ
ejpam-6314	665	12	dipankar	dipankar	PROPN
ejpam-6314	665	13	pal	pal	PROPN
ejpam-6314	665	14	.	.	PUNCT
ejpam-6314	666	1	fixed	fix	VERB
ejpam-6314	666	2	point	point	NOUN
ejpam-6314	666	3	in	in	ADP
ejpam-6314	666	4	bicomplex	bicomplex	NOUN
ejpam-6314	666	5	valued	value	VERB
ejpam-6314	666	6	metric	metric	ADJ
ejpam-6314	666	7	spaces	space	NOUN
ejpam-6314	666	8	.	.	PUNCT
ejpam-6314	667	1	international	international	ADJ
ejpam-6314	667	2	journal	journal	PROPN
ejpam-6314	667	3	of	of	ADP
ejpam-6314	667	4	nonlinear	nonlinear	ADJ
ejpam-6314	667	5	analysis	analysis	NOUN
ejpam-6314	667	6	and	and	CCONJ
ejpam-6314	667	7	applications	application	NOUN
ejpam-6314	667	8	,	,	PUNCT
ejpam-6314	667	9	12(2):717–727	12(2):717–727	NUM
ejpam-6314	667	10	,	,	PUNCT
ejpam-6314	667	11	2021	2021	NUM
ejpam-6314	667	12	.	.	PUNCT
ejpam-6314	668	1	[	[	X
ejpam-6314	668	2	15	15	NUM
ejpam-6314	668	3	]	]	X
ejpam-6314	668	4	ramaraj	ramaraj	VERB
ejpam-6314	668	5	hariharan	hariharan	PROPN
ejpam-6314	668	6	and	and	CCONJ
ejpam-6314	668	7	ramalingam	ramalingam	PROPN
ejpam-6314	668	8	udhayakumar	udhayakumar	PROPN
ejpam-6314	668	9	.	.	PUNCT
ejpam-6314	669	1	existence	existence	NOUN
ejpam-6314	669	2	of	of	ADP
ejpam-6314	669	3	mild	mild	ADJ
ejpam-6314	669	4	solution	solution	NOUN
ejpam-6314	669	5	for	for	ADP
ejpam-6314	669	6	fuzzy	fuzzy	ADJ
ejpam-6314	669	7	fractional	fractional	ADJ
ejpam-6314	669	8	differential	differential	NOUN
ejpam-6314	669	9	equation	equation	NOUN
ejpam-6314	669	10	utilizing	utilize	VERB
ejpam-6314	669	11	the	the	DET
ejpam-6314	669	12	hilfer	hilfer	NOUN
ejpam-6314	669	13	-	-	PUNCT
ejpam-6314	669	14	katugampola	katugampola	NOUN
ejpam-6314	669	15	fractional	fractional	ADJ
ejpam-6314	669	16	derivative	derivative	NOUN
ejpam-6314	669	17	.	.	PUNCT
ejpam-6314	670	1	an	an	DET
ejpam-6314	670	2	international	international	ADJ
ejpam-6314	670	3	journal	journal	NOUN
ejpam-6314	670	4	of	of	ADP
ejpam-6314	670	5	optimization	optimization	NOUN
ejpam-6314	670	6	and	and	CCONJ
ejpam-6314	670	7	control	control	NOUN
ejpam-6314	670	8	:	:	PUNCT
ejpam-6314	670	9	theories	theory	NOUN
ejpam-6314	670	10	&	&	CCONJ
ejpam-6314	670	11	applications	application	NOUN
ejpam-6314	670	12	,	,	PUNCT
ejpam-6314	670	13	15(1):82–91	15(1):82–91	NUM
ejpam-6314	670	14	,	,	PUNCT
ejpam-6314	670	15	2025	2025	NUM
ejpam-6314	670	16	.	.	PUNCT
ejpam-6314	671	1	[	[	X
ejpam-6314	671	2	16	16	NUM
ejpam-6314	671	3	]	]	X
ejpam-6314	671	4	s	s	VERB
ejpam-6314	671	5	sivasankar	sivasankar	NOUN
ejpam-6314	671	6	,	,	PUNCT
ejpam-6314	671	7	k	k	PROPN
ejpam-6314	671	8	nadhaprasadh	nadhaprasadh	NOUN
ejpam-6314	671	9	,	,	PUNCT
ejpam-6314	671	10	m	m	PROPN
ejpam-6314	671	11	sathish	sathish	PROPN
ejpam-6314	671	12	kumar	kumar	PROPN
ejpam-6314	671	13	,	,	PUNCT
ejpam-6314	671	14	shrideh	shrideh	PROPN
ejpam-6314	671	15	al	al	PROPN
ejpam-6314	671	16	-	-	PUNCT
ejpam-6314	671	17	omari	omari	PROPN
ejpam-6314	671	18	,	,	PUNCT
ejpam-6314	671	19	and	and	CCONJ
ejpam-6314	671	20	r	r	PROPN
ejpam-6314	671	21	udhayakumar	udhayakumar	NOUN
ejpam-6314	671	22	.	.	PUNCT
ejpam-6314	672	1	new	new	ADJ
ejpam-6314	672	2	study	study	NOUN
ejpam-6314	672	3	on	on	ADP
ejpam-6314	672	4	cauchy	cauchy	ADJ
ejpam-6314	672	5	problems	problem	NOUN
ejpam-6314	672	6	of	of	ADP
ejpam-6314	672	7	fractional	fractional	ADJ
ejpam-6314	672	8	stochastic	stochastic	ADJ
ejpam-6314	672	9	evolution	evolution	NOUN
ejpam-6314	672	10	systems	system	NOUN
ejpam-6314	672	11	on	on	ADP
ejpam-6314	672	12	an	an	DET
ejpam-6314	672	13	infinite	infinite	ADJ
ejpam-6314	672	14	interval	interval	NOUN
ejpam-6314	672	15	.	.	PUNCT
ejpam-6314	673	1	mathematical	mathematical	ADJ
ejpam-6314	673	2	methods	method	NOUN
ejpam-6314	673	3	in	in	ADP
ejpam-6314	673	4	the	the	DET
ejpam-6314	673	5	applied	apply	VERB
ejpam-6314	673	6	sciences	science	NOUN
ejpam-6314	673	7	,	,	PUNCT
ejpam-6314	673	8	48(1):890–904	48(1):890–904	PROPN
ejpam-6314	673	9	,	,	PUNCT
ejpam-6314	673	10	2025	2025	NUM
ejpam-6314	673	11	.	.	PUNCT
ejpam-6314	674	1	[	[	X
ejpam-6314	674	2	17	17	NUM
ejpam-6314	674	3	]	]	X
ejpam-6314	674	4	zhaohui	zhaohui	PROPN
ejpam-6314	674	5	gu	gu	PROPN
ejpam-6314	674	6	,	,	PUNCT
ejpam-6314	674	7	gunaseelan	gunaseelan	PROPN
ejpam-6314	674	8	mani	mani	PROPN
ejpam-6314	674	9	,	,	PUNCT
ejpam-6314	674	10	arul	arul	PROPN
ejpam-6314	674	11	joseph	joseph	PROPN
ejpam-6314	674	12	gnanaprakasam	gnanaprakasam	PROPN
ejpam-6314	674	13	,	,	PUNCT
ejpam-6314	674	14	and	and	CCONJ
ejpam-6314	674	15	yongjin	yongjin	PROPN
ejpam-6314	674	16	li	li	PROPN
ejpam-6314	674	17	.	.	PUNCT
ejpam-6314	675	1	solving	solve	VERB
ejpam-6314	675	2	a	a	DET
ejpam-6314	675	3	system	system	NOUN
ejpam-6314	675	4	of	of	ADP
ejpam-6314	675	5	nonlinear	nonlinear	ADJ
ejpam-6314	675	6	integral	integral	ADJ
ejpam-6314	675	7	equations	equation	NOUN
ejpam-6314	675	8	via	via	ADP
ejpam-6314	675	9	common	common	ADJ
ejpam-6314	675	10	fixed	fix	VERB
ejpam-6314	675	11	point	point	NOUN
ejpam-6314	675	12	theorems	theorem	NOUN
ejpam-6314	675	13	on	on	ADP
ejpam-6314	675	14	bicomplex	bicomplex	NOUN
ejpam-6314	675	15	partial	partial	ADJ
ejpam-6314	675	16	metric	metric	ADJ
ejpam-6314	675	17	space	space	NOUN
ejpam-6314	675	18	.	.	PUNCT
ejpam-6314	676	1	mathematics	mathematic	NOUN
ejpam-6314	676	2	,	,	PUNCT
ejpam-6314	676	3	9(14):1584	9(14):1584	NUM
ejpam-6314	676	4	,	,	PUNCT
ejpam-6314	676	5	2021	2021	NUM
ejpam-6314	676	6	.	.	PUNCT
ejpam-6314	677	1	[	[	X
ejpam-6314	677	2	18	18	NUM
ejpam-6314	677	3	]	]	PUNCT
ejpam-6314	677	4	gunaseelan	gunaseelan	PROPN
ejpam-6314	677	5	mani	mani	PROPN
ejpam-6314	677	6	,	,	PUNCT
ejpam-6314	677	7	arul	arul	PROPN
ejpam-6314	677	8	joseph	joseph	PROPN
ejpam-6314	677	9	gnanaprakasam	gnanaprakasam	PROPN
ejpam-6314	677	10	,	,	PUNCT
ejpam-6314	677	11	khalil	khalil	PROPN
ejpam-6314	677	12	javed	javed	PROPN
ejpam-6314	677	13	,	,	PUNCT
ejpam-6314	677	14	muhammad	muhammad	PROPN
ejpam-6314	677	15	arshad	arshad	PROPN
ejpam-6314	677	16	,	,	PUNCT
ejpam-6314	677	17	and	and	CCONJ
ejpam-6314	677	18	fahd	fahd	PROPN
ejpam-6314	677	19	jarad	jarad	PROPN
ejpam-6314	677	20	.	.	PUNCT
ejpam-6314	678	1	solving	solve	VERB
ejpam-6314	678	2	a	a	DET
ejpam-6314	678	3	fredholm	fredholm	ADJ
ejpam-6314	678	4	integral	integral	ADJ
ejpam-6314	678	5	equation	equation	NOUN
ejpam-6314	678	6	via	via	ADP
ejpam-6314	678	7	coupled	couple	VERB
ejpam-6314	678	8	fixed	fix	VERB
ejpam-6314	678	9	point	point	NOUN
ejpam-6314	678	10	on	on	ADP
ejpam-6314	678	11	bicomplex	bicomplex	NOUN
ejpam-6314	678	12	partial	partial	ADJ
ejpam-6314	678	13	metric	metric	ADJ
ejpam-6314	678	14	space	space	NOUN
ejpam-6314	678	15	.	.	PUNCT
ejpam-6314	679	1	2022	2022	NUM
ejpam-6314	679	2	.	.	PUNCT
ejpam-6314	680	1	[	[	X
ejpam-6314	680	2	19	19	NUM
ejpam-6314	680	3	]	]	X
ejpam-6314	680	4	sanjib	sanjib	PROPN
ejpam-6314	680	5	kumar	kumar	PROPN
ejpam-6314	680	6	datta	datta	PROPN
ejpam-6314	680	7	,	,	PUNCT
ejpam-6314	680	8	dipankar	dipankar	PROPN
ejpam-6314	680	9	pal	pal	PROPN
ejpam-6314	680	10	,	,	PUNCT
ejpam-6314	680	11	rakesh	rakesh	PROPN
ejpam-6314	680	12	sarkar	sarkar	PROPN
ejpam-6314	680	13	,	,	PUNCT
ejpam-6314	680	14	and	and	CCONJ
ejpam-6314	680	15	arghyatanu	arghyatanu	PROPN
ejpam-6314	680	16	manna	manna	PROPN
ejpam-6314	680	17	.	.	PUNCT
ejpam-6314	681	1	on	on	ADP
ejpam-6314	681	2	a	a	DET
ejpam-6314	681	3	common	common	ADJ
ejpam-6314	681	4	fixed	fix	VERB
ejpam-6314	681	5	point	point	NOUN
ejpam-6314	681	6	theorem	theorem	VERB
ejpam-6314	681	7	in	in	ADP
ejpam-6314	681	8	bicomplex	bicomplex	NOUN
ejpam-6314	681	9	valued	value	VERB
ejpam-6314	681	10	b	b	X
ejpam-6314	681	11	-	-	PUNCT
ejpam-6314	681	12	metric	metric	ADJ
ejpam-6314	681	13	space	space	NOUN
ejpam-6314	681	14	.	.	PUNCT
ejpam-6314	682	1	montes	montes	PROPN
ejpam-6314	682	2	taurus	taurus	PROPN
ejpam-6314	682	3	journal	journal	PROPN
ejpam-6314	682	4	of	of	ADP
ejpam-6314	682	5	pure	pure	ADJ
ejpam-6314	682	6	and	and	CCONJ
ejpam-6314	682	7	applied	applied	ADJ
ejpam-6314	682	8	mathematics	mathematic	NOUN
ejpam-6314	682	9	,	,	PUNCT
ejpam-6314	682	10	3(3):358–366	3(3):358–366	NUM
ejpam-6314	682	11	,	,	PUNCT
ejpam-6314	682	12	2021	2021	NUM
ejpam-6314	682	13	.	.	PUNCT
ejpam-6314	683	1	[	[	X
ejpam-6314	683	2	20	20	NUM
ejpam-6314	683	3	]	]	X
ejpam-6314	683	4	mohammad	mohammad	PROPN
ejpam-6314	683	5	esmael	esmael	PROPN
ejpam-6314	683	6	samei	samei	PROPN
ejpam-6314	683	7	.	.	PUNCT
ejpam-6314	684	1	convergence	convergence	NOUN
ejpam-6314	684	2	of	of	ADP
ejpam-6314	684	3	an	an	DET
ejpam-6314	684	4	iterative	iterative	NOUN
ejpam-6314	684	5	scheme	scheme	NOUN
ejpam-6314	684	6	for	for	ADP
ejpam-6314	684	7	multifunctions	multifunction	NOUN
ejpam-6314	684	8	on	on	ADP
ejpam-6314	684	9	fuzzy	fuzzy	ADJ
ejpam-6314	684	10	metric	metric	ADJ
ejpam-6314	684	11	spaces	space	NOUN
ejpam-6314	684	12	.	.	PUNCT
ejpam-6314	685	1	sahand	sahand	NOUN
ejpam-6314	685	2	communications	communication	NOUN
ejpam-6314	685	3	in	in	ADP
ejpam-6314	685	4	mathematical	mathematical	ADJ
ejpam-6314	685	5	analysis	analysis	NOUN
ejpam-6314	685	6	,	,	PUNCT
ejpam-6314	685	7	15(1):91	15(1):91	NUM
ejpam-6314	685	8	–	–	PUNCT
ejpam-6314	685	9	106	106	NUM
ejpam-6314	685	10	,	,	PUNCT
ejpam-6314	685	11	2019	2019	NUM
ejpam-6314	685	12	.	.	PUNCT
ejpam-6314	686	1	[	[	X
ejpam-6314	686	2	21	21	NUM
ejpam-6314	686	3	]	]	PUNCT
ejpam-6314	686	4	wasfi	wasfi	NOUN
ejpam-6314	686	5	shatanawi	shatanawi	ADJ
ejpam-6314	686	6	and	and	CCONJ
ejpam-6314	686	7	taqi	taqi	ADJ
ejpam-6314	686	8	am	be	AUX
ejpam-6314	686	9	shatnawi	shatnawi	ADJ
ejpam-6314	686	10	.	.	PUNCT
ejpam-6314	687	1	new	new	ADJ
ejpam-6314	687	2	fixed	fix	VERB
ejpam-6314	687	3	point	point	NOUN
ejpam-6314	687	4	results	result	NOUN
ejpam-6314	687	5	in	in	ADP
ejpam-6314	687	6	controlled	control	VERB
ejpam-6314	687	7	metric	metric	ADJ
ejpam-6314	687	8	type	type	NOUN
ejpam-6314	687	9	spaces	space	NOUN
ejpam-6314	687	10	based	base	VERB
ejpam-6314	687	11	on	on	ADP
ejpam-6314	687	12	new	new	ADJ
ejpam-6314	687	13	contractive	contractive	ADJ
ejpam-6314	687	14	conditions	condition	NOUN
ejpam-6314	687	15	.	.	PUNCT
ejpam-6314	688	1	aims	aim	VERB
ejpam-6314	688	2	math	math	NOUN
ejpam-6314	688	3	,	,	PUNCT
ejpam-6314	688	4	8(4):9314–9330	8(4):9314–9330	NUM
ejpam-6314	688	5	,	,	PUNCT
ejpam-6314	688	6	2023	2023	NUM
ejpam-6314	688	7	.	.	PUNCT
ejpam-6314	689	1	m.	m.	NOUN
ejpam-6314	689	2	sarwar	sarwar	PROPN
ejpam-6314	689	3	et	et	PROPN
ejpam-6314	689	4	al	al	PROPN
ejpam-6314	689	5	.	.	PUNCT
ejpam-6314	689	6	/	/	SYM
ejpam-6314	689	7	eur	eur	PROPN
ejpam-6314	689	8	.	.	PUNCT
ejpam-6314	690	1	j.	j.	PROPN
ejpam-6314	690	2	pure	pure	PROPN
ejpam-6314	690	3	appl	appl	PROPN
ejpam-6314	690	4	.	.	PROPN
ejpam-6314	690	5	math	math	PROPN
ejpam-6314	690	6	,	,	PUNCT
ejpam-6314	690	7	18	18	NUM
ejpam-6314	690	8	(	(	PUNCT
ejpam-6314	690	9	3	3	NUM
ejpam-6314	690	10	)	)	PUNCT
ejpam-6314	690	11	(	(	PUNCT
ejpam-6314	690	12	2025	2025	NUM
ejpam-6314	690	13	)	)	PUNCT
ejpam-6314	690	14	,	,	PUNCT
ejpam-6314	690	15	6314	6314	NUM
ejpam-6314	690	16	28	28	NUM
ejpam-6314	690	17	of	of	ADP
ejpam-6314	690	18	28	28	NUM
ejpam-6314	691	1	[	[	X
ejpam-6314	691	2	22	22	NUM
ejpam-6314	691	3	]	]	PUNCT
ejpam-6314	691	4	a	a	DET
ejpam-6314	691	5	murali	murali	ADJ
ejpam-6314	691	6	and	and	CCONJ
ejpam-6314	691	7	k	k	PROPN
ejpam-6314	691	8	muthunagai	muthunagai	NOUN
ejpam-6314	691	9	.	.	PUNCT
ejpam-6314	692	1	some	some	DET
ejpam-6314	692	2	theorems	theorem	NOUN
ejpam-6314	692	3	on	on	ADP
ejpam-6314	692	4	fixed	fix	VERB
ejpam-6314	692	5	points	point	NOUN
ejpam-6314	692	6	in	in	ADP
ejpam-6314	692	7	bi	bi	ADJ
ejpam-6314	692	8	-	-	ADJ
ejpam-6314	692	9	complex	complex	ADJ
ejpam-6314	692	10	valued	value	VERB
ejpam-6314	692	11	metric	metric	ADJ
ejpam-6314	692	12	spaces	space	NOUN
ejpam-6314	692	13	with	with	ADP
ejpam-6314	692	14	an	an	DET
ejpam-6314	692	15	application	application	NOUN
ejpam-6314	692	16	to	to	ADP
ejpam-6314	692	17	integral	integral	ADJ
ejpam-6314	692	18	equations	equation	NOUN
ejpam-6314	692	19	.	.	PUNCT
ejpam-6314	693	1	journal	journal	NOUN
ejpam-6314	693	2	of	of	ADP
ejpam-6314	693	3	the	the	DET
ejpam-6314	693	4	nigerian	nigerian	ADJ
ejpam-6314	693	5	society	society	NOUN
ejpam-6314	693	6	of	of	ADP
ejpam-6314	693	7	physical	physical	ADJ
ejpam-6314	693	8	sciences	science	NOUN
ejpam-6314	693	9	,	,	PUNCT
ejpam-6314	693	10	pages	page	NOUN
ejpam-6314	693	11	1750–1750	1750–1750	NUM
ejpam-6314	693	12	,	,	PUNCT
ejpam-6314	693	13	2024	2024	NUM
ejpam-6314	693	14	.	.	PUNCT
ejpam-6314	694	1	[	[	X
ejpam-6314	694	2	23	23	NUM
ejpam-6314	694	3	]	]	X
ejpam-6314	694	4	sarra	sarra	PROPN
ejpam-6314	694	5	guechi	guechi	PROPN
ejpam-6314	694	6	,	,	PUNCT
ejpam-6314	694	7	rajesh	rajesh	PROPN
ejpam-6314	694	8	dhayal	dhayal	PROPN
ejpam-6314	694	9	,	,	PUNCT
ejpam-6314	694	10	amar	amar	PROPN
ejpam-6314	694	11	debbouche	debbouche	PROPN
ejpam-6314	694	12	,	,	PUNCT
ejpam-6314	694	13	and	and	CCONJ
ejpam-6314	694	14	muslim	muslim	PROPN
ejpam-6314	694	15	malik	malik	PROPN
ejpam-6314	694	16	.	.	PUNCT
ejpam-6314	695	1	analysis	analysis	NOUN
ejpam-6314	695	2	and	and	CCONJ
ejpam-6314	695	3	optimal	optimal	ADJ
ejpam-6314	695	4	control	control	NOUN
ejpam-6314	695	5	of	of	ADP
ejpam-6314	695	6	φ	φ	PROPN
ejpam-6314	695	7	-	-	PUNCT
ejpam-6314	695	8	hilfer	hilfer	NOUN
ejpam-6314	695	9	fractional	fractional	ADJ
ejpam-6314	695	10	semilinear	semilinear	NOUN
ejpam-6314	695	11	equations	equation	NOUN
ejpam-6314	695	12	involving	involve	VERB
ejpam-6314	695	13	nonlocal	nonlocal	ADJ
ejpam-6314	695	14	impulsive	impulsive	ADJ
ejpam-6314	695	15	conditions	condition	NOUN
ejpam-6314	695	16	.	.	PUNCT
ejpam-6314	696	1	symmetry	symmetry	NOUN
ejpam-6314	696	2	,	,	PUNCT
ejpam-6314	696	3	13(11):2084	13(11):2084	NUM
ejpam-6314	696	4	,	,	PUNCT
ejpam-6314	696	5	2021	2021	NUM
ejpam-6314	696	6	.	.	PUNCT
ejpam-6314	697	1	[	[	X
ejpam-6314	697	2	24	24	NUM
ejpam-6314	697	3	]	]	PUNCT
ejpam-6314	697	4	gunaseelan	gunaseelan	PROPN
ejpam-6314	697	5	mani	mani	PROPN
ejpam-6314	697	6	,	,	PUNCT
ejpam-6314	697	7	salma	salma	PROPN
ejpam-6314	697	8	haque	haque	PROPN
ejpam-6314	697	9	,	,	PUNCT
ejpam-6314	697	10	arul	arul	PROPN
ejpam-6314	697	11	joseph	joseph	PROPN
ejpam-6314	697	12	gnanaprakasam	gnanaprakasam	PROPN
ejpam-6314	697	13	,	,	PUNCT
ejpam-6314	697	14	ozgur	ozgur	PROPN
ejpam-6314	697	15	ege	ege	PROPN
ejpam-6314	697	16	,	,	PUNCT
ejpam-6314	697	17	and	and	CCONJ
ejpam-6314	697	18	nabil	nabil	PROPN
ejpam-6314	697	19	mlaiki	mlaiki	PROPN
ejpam-6314	697	20	.	.	PUNCT
ejpam-6314	698	1	the	the	DET
ejpam-6314	698	2	study	study	NOUN
ejpam-6314	698	3	of	of	ADP
ejpam-6314	698	4	bicomplex	bicomplex	NOUN
ejpam-6314	698	5	-	-	PUNCT
ejpam-6314	698	6	valued	value	VERB
ejpam-6314	698	7	controlled	control	VERB
ejpam-6314	698	8	metric	metric	ADJ
ejpam-6314	698	9	spaces	space	NOUN
ejpam-6314	698	10	with	with	ADP
ejpam-6314	698	11	applications	application	NOUN
ejpam-6314	698	12	to	to	ADP
ejpam-6314	698	13	fractional	fractional	ADJ
ejpam-6314	698	14	differential	differential	ADJ
ejpam-6314	698	15	equations	equation	NOUN
ejpam-6314	698	16	.	.	PUNCT
ejpam-6314	699	1	mathematics	mathematic	NOUN
ejpam-6314	699	2	,	,	PUNCT
ejpam-6314	699	3	11(12):2742	11(12):2742	NUM
ejpam-6314	699	4	,	,	PUNCT
ejpam-6314	699	5	2023	2023	NUM
ejpam-6314	699	6	.	.	PUNCT
ejpam-6314	700	1	[	[	X
ejpam-6314	700	2	25	25	NUM
ejpam-6314	700	3	]	]	X
ejpam-6314	700	4	amer	amer	PROPN
ejpam-6314	700	5	hassan	hassan	PROPN
ejpam-6314	700	6	albargi	albargi	PROPN
ejpam-6314	700	7	,	,	PUNCT
ejpam-6314	700	8	amnah	amnah	PROPN
ejpam-6314	700	9	essa	essa	PROPN
ejpam-6314	700	10	shammaky	shammaky	PROPN
ejpam-6314	700	11	,	,	PUNCT
ejpam-6314	700	12	and	and	CCONJ
ejpam-6314	700	13	jamshaid	jamshaid	PROPN
ejpam-6314	700	14	ahmad	ahmad	PROPN
ejpam-6314	700	15	.	.	PUNCT
ejpam-6314	701	1	common	common	ADJ
ejpam-6314	701	2	fixed	fix	VERB
ejpam-6314	701	3	point	point	NOUN
ejpam-6314	701	4	results	result	NOUN
ejpam-6314	701	5	in	in	ADP
ejpam-6314	701	6	bicomplex	bicomplex	NOUN
ejpam-6314	701	7	valued	value	VERB
ejpam-6314	701	8	metric	metric	ADJ
ejpam-6314	701	9	spaces	space	NOUN
ejpam-6314	701	10	with	with	ADP
ejpam-6314	701	11	application	application	NOUN
ejpam-6314	701	12	.	.	PUNCT
ejpam-6314	702	1	mathematics	mathematic	NOUN
ejpam-6314	702	2	,	,	PUNCT
ejpam-6314	702	3	11(5):1207	11(5):1207	NUM
ejpam-6314	702	4	,	,	PUNCT
ejpam-6314	702	5	2023	2023	NUM
ejpam-6314	702	6	.	.	PUNCT
ejpam-6314	703	1	[	[	X
ejpam-6314	703	2	26	26	NUM
ejpam-6314	703	3	]	]	X
ejpam-6314	703	4	stefan	stefan	PROPN
ejpam-6314	703	5	g	g	PROPN
ejpam-6314	703	6	samko	samko	PROPN
ejpam-6314	703	7	.	.	PUNCT
ejpam-6314	704	1	fractional	fractional	ADJ
ejpam-6314	704	2	integrals	integral	NOUN
ejpam-6314	704	3	and	and	CCONJ
ejpam-6314	704	4	derivatives	derivative	NOUN
ejpam-6314	704	5	.	.	PUNCT
ejpam-6314	705	1	theory	theory	NOUN
ejpam-6314	705	2	and	and	CCONJ
ejpam-6314	705	3	applications	application	NOUN
ejpam-6314	705	4	,	,	PUNCT
ejpam-6314	705	5	1993	1993	NUM
ejpam-6314	705	6	.	.	PUNCT