id	sid	tid	token	lemma	pos
ejpam-6841	1	1	european	european	PROPN
ejpam-6841	1	2	journal	journal	PROPN
ejpam-6841	1	3	of	of	ADP
ejpam-6841	1	4	pure	pure	ADJ
ejpam-6841	1	5	and	and	CCONJ
ejpam-6841	1	6	applied	applied	ADJ
ejpam-6841	1	7	mathematics	mathematic	NOUN
ejpam-6841	1	8	2025	2025	NUM
ejpam-6841	1	9	,	,	PUNCT
ejpam-6841	1	10	vol	vol	NOUN
ejpam-6841	1	11	.	.	PROPN
ejpam-6841	1	12	18	18	NUM
ejpam-6841	1	13	,	,	PUNCT
ejpam-6841	1	14	issue	issue	NOUN
ejpam-6841	1	15	4	4	NUM
ejpam-6841	1	16	,	,	PUNCT
ejpam-6841	1	17	article	article	NOUN
ejpam-6841	1	18	number	number	NOUN
ejpam-6841	1	19	6841	6841	NUM
ejpam-6841	1	20	issn	issn	PROPN
ejpam-6841	1	21	1307	1307	NUM
ejpam-6841	1	22	-	-	SYM
ejpam-6841	1	23	5543	5543	NUM
ejpam-6841	1	24	–	–	PUNCT
ejpam-6841	1	25	ejpam.com	ejpam.com	X
ejpam-6841	1	26	published	publish	VERB
ejpam-6841	1	27	by	by	ADP
ejpam-6841	1	28	new	new	PROPN
ejpam-6841	1	29	york	york	PROPN
ejpam-6841	1	30	business	business	PROPN
ejpam-6841	1	31	global	global	ADJ
ejpam-6841	1	32	applications	application	NOUN
ejpam-6841	1	33	and	and	CCONJ
ejpam-6841	1	34	theoretical	theoretical	ADJ
ejpam-6841	1	35	foundations	foundation	NOUN
ejpam-6841	1	36	of	of	ADP
ejpam-6841	1	37	best	good	ADJ
ejpam-6841	1	38	proximity	proximity	NOUN
ejpam-6841	1	39	points	point	NOUN
ejpam-6841	1	40	in	in	ADP
ejpam-6841	1	41	generalized	generalized	ADJ
ejpam-6841	1	42	interpolative	interpolative	ADJ
ejpam-6841	1	43	proximal	proximal	ADJ
ejpam-6841	1	44	contractions	contraction	NOUN
ejpam-6841	1	45	khalil	khalil	PROPN
ejpam-6841	1	46	javed	javed	PROPN
ejpam-6841	1	47	1,∗	1,∗	PROPN
ejpam-6841	1	48	,	,	PUNCT
ejpam-6841	1	49	muhammad	muhammad	PROPN
ejpam-6841	1	50	nazam2	nazam2	PROPN
ejpam-6841	1	51	,	,	PUNCT
ejpam-6841	1	52	muhammad	muhammad	PROPN
ejpam-6841	1	53	arshad1	arshad1	PROPN
ejpam-6841	1	54	,	,	PUNCT
ejpam-6841	1	55	manuel	manuel	PROPN
ejpam-6841	1	56	de	de	X
ejpam-6841	1	57	la	la	X
ejpam-6841	1	58	sen3,∗	sen3,∗	PROPN
ejpam-6841	1	59	1	1	NUM
ejpam-6841	1	60	department	department	NOUN
ejpam-6841	1	61	of	of	ADP
ejpam-6841	1	62	mathematics	mathematics	PROPN
ejpam-6841	1	63	&	&	CCONJ
ejpam-6841	1	64	statistics	statistic	NOUN
ejpam-6841	1	65	,	,	PUNCT
ejpam-6841	1	66	international	international	ADJ
ejpam-6841	1	67	islamic	islamic	PROPN
ejpam-6841	1	68	university	university	PROPN
ejpam-6841	1	69	,	,	PUNCT
ejpam-6841	1	70	islamabad	islamabad	PROPN
ejpam-6841	1	71	,	,	PUNCT
ejpam-6841	1	72	pakistan	pakistan	PROPN
ejpam-6841	1	73	2	2	NUM
ejpam-6841	1	74	department	department	NOUN
ejpam-6841	1	75	of	of	ADP
ejpam-6841	1	76	mathematics	mathematic	NOUN
ejpam-6841	1	77	,	,	PUNCT
ejpam-6841	1	78	allama	allama	PROPN
ejpam-6841	1	79	iqbal	iqbal	PROPN
ejpam-6841	1	80	open	open	PROPN
ejpam-6841	1	81	university	university	PROPN
ejpam-6841	1	82	,	,	PUNCT
ejpam-6841	1	83	islamabad	islamabad	PROPN
ejpam-6841	1	84	,	,	PUNCT
ejpam-6841	1	85	pakistan	pakistan	PROPN
ejpam-6841	1	86	3	3	NUM
ejpam-6841	1	87	department	department	NOUN
ejpam-6841	1	88	of	of	ADP
ejpam-6841	1	89	electricity	electricity	NOUN
ejpam-6841	1	90	and	and	CCONJ
ejpam-6841	1	91	electronics	electronic	NOUN
ejpam-6841	1	92	,	,	PUNCT
ejpam-6841	1	93	faculty	faculty	NOUN
ejpam-6841	1	94	of	of	ADP
ejpam-6841	1	95	science	science	NOUN
ejpam-6841	1	96	and	and	CCONJ
ejpam-6841	1	97	technology	technology	NOUN
ejpam-6841	1	98	,	,	PUNCT
ejpam-6841	1	99	university	university	NOUN
ejpam-6841	1	100	of	of	ADP
ejpam-6841	1	101	the	the	DET
ejpam-6841	1	102	basque	basque	ADJ
ejpam-6841	1	103	country	country	NOUN
ejpam-6841	1	104	campus	campus	NOUN
ejpam-6841	1	105	of	of	ADP
ejpam-6841	1	106	leioa	leioa	ADJ
ejpam-6841	1	107	leioa	leioa	PROPN
ejpam-6841	1	108	(	(	PUNCT
ejpam-6841	1	109	bizkaia	bizkaia	PROPN
ejpam-6841	1	110	)	)	PUNCT
ejpam-6841	1	111	,	,	PUNCT
ejpam-6841	1	112	leioa	leioa	PROPN
ejpam-6841	1	113	48940	48940	NUM
ejpam-6841	1	114	spain	spain	PROPN
ejpam-6841	1	115	abstract	abstract	NOUN
ejpam-6841	1	116	.	.	PUNCT
ejpam-6841	2	1	this	this	DET
ejpam-6841	2	2	paper	paper	NOUN
ejpam-6841	2	3	investigates	investigate	VERB
ejpam-6841	2	4	optimal	optimal	ADJ
ejpam-6841	2	5	solutions	solution	NOUN
ejpam-6841	2	6	for	for	ADP
ejpam-6841	2	7	best	good	ADJ
ejpam-6841	2	8	proximity	proximity	NOUN
ejpam-6841	2	9	points	point	NOUN
ejpam-6841	2	10	through	through	ADP
ejpam-6841	2	11	the	the	DET
ejpam-6841	2	12	framework	framework	NOUN
ejpam-6841	2	13	of	of	ADP
ejpam-6841	2	14	generalized	generalized	ADJ
ejpam-6841	2	15	interpolative	interpolative	ADJ
ejpam-6841	2	16	proximal	proximal	ADJ
ejpam-6841	2	17	contractions	contraction	NOUN
ejpam-6841	2	18	.	.	PUNCT
ejpam-6841	3	1	we	we	PRON
ejpam-6841	3	2	introduce	introduce	VERB
ejpam-6841	3	3	a	a	DET
ejpam-6841	3	4	new	new	ADJ
ejpam-6841	3	5	method	method	NOUN
ejpam-6841	3	6	that	that	PRON
ejpam-6841	3	7	uses	use	VERB
ejpam-6841	3	8	interpolation	interpolation	NOUN
ejpam-6841	3	9	techniques	technique	NOUN
ejpam-6841	3	10	to	to	PART
ejpam-6841	3	11	handle	handle	VERB
ejpam-6841	3	12	a	a	DET
ejpam-6841	3	13	wider	wide	ADJ
ejpam-6841	3	14	class	class	NOUN
ejpam-6841	3	15	of	of	ADP
ejpam-6841	3	16	mappings	mapping	NOUN
ejpam-6841	3	17	by	by	ADP
ejpam-6841	3	18	expanding	expand	VERB
ejpam-6841	3	19	the	the	DET
ejpam-6841	3	20	concepts	concept	NOUN
ejpam-6841	3	21	of	of	ADP
ejpam-6841	3	22	classical	classical	ADJ
ejpam-6841	3	23	proximal	proximal	ADJ
ejpam-6841	3	24	contraction	contraction	NOUN
ejpam-6841	3	25	.	.	PUNCT
ejpam-6841	4	1	in	in	ADP
ejpam-6841	4	2	the	the	DET
ejpam-6841	4	3	absence	absence	NOUN
ejpam-6841	4	4	of	of	ADP
ejpam-6841	4	5	a	a	DET
ejpam-6841	4	6	precise	precise	ADJ
ejpam-6841	4	7	solution	solution	NOUN
ejpam-6841	4	8	,	,	PUNCT
ejpam-6841	4	9	best	good	ADJ
ejpam-6841	4	10	proximity	proximity	NOUN
ejpam-6841	4	11	point	point	NOUN
ejpam-6841	4	12	theorems	theorem	NOUN
ejpam-6841	4	13	investigate	investigate	VERB
ejpam-6841	4	14	the	the	DET
ejpam-6841	4	15	existence	existence	NOUN
ejpam-6841	4	16	of	of	ADP
ejpam-6841	4	17	such	such	ADJ
ejpam-6841	4	18	best	good	ADJ
ejpam-6841	4	19	proximity	proximity	NOUN
ejpam-6841	4	20	points	point	NOUN
ejpam-6841	4	21	for	for	ADP
ejpam-6841	4	22	approximate	approximate	ADJ
ejpam-6841	4	23	solutions	solution	NOUN
ejpam-6841	4	24	to	to	ADP
ejpam-6841	4	25	the	the	DET
ejpam-6841	4	26	fixed	fix	VERB
ejpam-6841	4	27	point	point	NOUN
ejpam-6841	4	28	problem	problem	NOUN
ejpam-6841	4	29	.	.	PUNCT
ejpam-6841	5	1	this	this	DET
ejpam-6841	5	2	article	article	NOUN
ejpam-6841	5	3	aims	aim	VERB
ejpam-6841	5	4	to	to	PART
ejpam-6841	5	5	develop	develop	VERB
ejpam-6841	5	6	the	the	DET
ejpam-6841	5	7	best	good	ADJ
ejpam-6841	5	8	proximity	proximity	NOUN
ejpam-6841	5	9	point	point	NOUN
ejpam-6841	5	10	theorems	theorem	NOUN
ejpam-6841	5	11	for	for	ADP
ejpam-6841	5	12	contractive	contractive	ADJ
ejpam-6841	5	13	non	non	ADJ
ejpam-6841	5	14	-	-	ADJ
ejpam-6841	5	15	self	self	ADJ
ejpam-6841	5	16	mappings	mapping	NOUN
ejpam-6841	5	17	via	via	ADP
ejpam-6841	5	18	interpolation	interpolation	NOUN
ejpam-6841	5	19	to	to	PART
ejpam-6841	5	20	generate	generate	VERB
ejpam-6841	5	21	global	global	ADJ
ejpam-6841	5	22	optimal	optimal	ADJ
ejpam-6841	5	23	approximate	approximate	ADJ
ejpam-6841	5	24	solutions	solution	NOUN
ejpam-6841	5	25	to	to	ADP
ejpam-6841	5	26	particular	particular	ADJ
ejpam-6841	5	27	fixed	fix	VERB
ejpam-6841	5	28	point	point	NOUN
ejpam-6841	5	29	equations	equation	NOUN
ejpam-6841	5	30	.	.	PUNCT
ejpam-6841	6	1	in	in	ADP
ejpam-6841	6	2	addition	addition	NOUN
ejpam-6841	6	3	to	to	ADP
ejpam-6841	6	4	demonstrating	demonstrate	VERB
ejpam-6841	6	5	the	the	DET
ejpam-6841	6	6	existence	existence	NOUN
ejpam-6841	6	7	of	of	ADP
ejpam-6841	6	8	the	the	DET
ejpam-6841	6	9	optimal	optimal	ADJ
ejpam-6841	6	10	proximity	proximity	NOUN
ejpam-6841	6	11	points	point	NOUN
ejpam-6841	6	12	,	,	PUNCT
ejpam-6841	6	13	iterative	iterative	NOUN
ejpam-6841	6	14	techniques	technique	NOUN
ejpam-6841	6	15	are	be	AUX
ejpam-6841	6	16	also	also	ADV
ejpam-6841	6	17	offered	offer	VERB
ejpam-6841	6	18	to	to	PART
ejpam-6841	6	19	locate	locate	VERB
ejpam-6841	6	20	such	such	ADJ
ejpam-6841	6	21	optimal	optimal	ADJ
ejpam-6841	6	22	approximative	approximative	ADJ
ejpam-6841	6	23	solutions	solution	NOUN
ejpam-6841	6	24	.	.	PUNCT
ejpam-6841	7	1	we	we	PRON
ejpam-6841	7	2	illustrate	illustrate	VERB
ejpam-6841	7	3	the	the	DET
ejpam-6841	7	4	utility	utility	NOUN
ejpam-6841	7	5	of	of	ADP
ejpam-6841	7	6	our	our	PRON
ejpam-6841	7	7	findings	finding	NOUN
ejpam-6841	7	8	with	with	ADP
ejpam-6841	7	9	a	a	DET
ejpam-6841	7	10	few	few	ADJ
ejpam-6841	7	11	instances	instance	NOUN
ejpam-6841	7	12	.	.	PUNCT
ejpam-6841	8	1	the	the	DET
ejpam-6841	8	2	value	value	NOUN
ejpam-6841	8	3	of	of	ADP
ejpam-6841	8	4	our	our	PRON
ejpam-6841	8	5	research	research	NOUN
ejpam-6841	8	6	is	be	AUX
ejpam-6841	8	7	illustrated	illustrate	VERB
ejpam-6841	8	8	with	with	ADP
ejpam-6841	8	9	a	a	DET
ejpam-6841	8	10	few	few	ADJ
ejpam-6841	8	11	examples	example	NOUN
ejpam-6841	8	12	and	and	CCONJ
ejpam-6841	8	13	applications	application	NOUN
ejpam-6841	8	14	.	.	PUNCT
ejpam-6841	9	1	2020	2020	NUM
ejpam-6841	9	2	mathematics	mathematic	NOUN
ejpam-6841	9	3	subject	subject	NOUN
ejpam-6841	9	4	classifications	classification	NOUN
ejpam-6841	9	5	:	:	PUNCT
ejpam-6841	9	6	47h10	47h10	NUM
ejpam-6841	9	7	,	,	PUNCT
ejpam-6841	9	8	26e05	26e05	NUM
ejpam-6841	9	9	,	,	PUNCT
ejpam-6841	9	10	26e25	26e25	NUM
ejpam-6841	9	11	key	key	ADJ
ejpam-6841	9	12	words	word	NOUN
ejpam-6841	9	13	and	and	CCONJ
ejpam-6841	9	14	phrases	phrase	NOUN
ejpam-6841	9	15	:	:	PUNCT
ejpam-6841	9	16	nonlinear	nonlinear	ADJ
ejpam-6841	9	17	equations	equation	NOUN
ejpam-6841	9	18	;	;	PUNCT
ejpam-6841	9	19	best	good	ADJ
ejpam-6841	9	20	proximity	proximity	NOUN
ejpam-6841	9	21	point	point	NOUN
ejpam-6841	9	22	;	;	PUNCT
ejpam-6841	9	23	generalized	generalize	VERB
ejpam-6841	9	24	interpolative	interpolative	ADJ
ejpam-6841	9	25	proximal	proximal	ADJ
ejpam-6841	9	26	contractions	contraction	NOUN
ejpam-6841	9	27	;	;	PUNCT
ejpam-6841	9	28	mathematical	mathematical	ADJ
ejpam-6841	9	29	operators	operator	NOUN
ejpam-6841	9	30	;	;	PUNCT
ejpam-6841	9	31	complete	complete	ADJ
ejpam-6841	9	32	metric	metric	ADJ
ejpam-6841	9	33	space	space	NOUN
ejpam-6841	9	34	.	.	PUNCT
ejpam-6841	10	1	1	1	X
ejpam-6841	10	2	.	.	X
ejpam-6841	10	3	introduction	introduction	NOUN
ejpam-6841	10	4	best	good	ADJ
ejpam-6841	10	5	proximity	proximity	NOUN
ejpam-6841	10	6	points	point	NOUN
ejpam-6841	10	7	have	have	VERB
ejpam-6841	10	8	widespread	widespread	ADJ
ejpam-6841	10	9	applications	application	NOUN
ejpam-6841	10	10	in	in	ADP
ejpam-6841	10	11	optimization	optimization	NOUN
ejpam-6841	10	12	,	,	PUNCT
ejpam-6841	10	13	economics	economic	NOUN
ejpam-6841	10	14	,	,	PUNCT
ejpam-6841	10	15	and	and	CCONJ
ejpam-6841	10	16	various	various	ADJ
ejpam-6841	10	17	engineering	engineering	NOUN
ejpam-6841	10	18	disciplines	discipline	NOUN
ejpam-6841	10	19	,	,	PUNCT
ejpam-6841	10	20	where	where	SCONJ
ejpam-6841	10	21	exact	exact	ADJ
ejpam-6841	10	22	fixed	fix	VERB
ejpam-6841	10	23	points	point	NOUN
ejpam-6841	10	24	are	be	AUX
ejpam-6841	10	25	elusive	elusive	ADJ
ejpam-6841	10	26	,	,	PUNCT
ejpam-6841	10	27	and	and	CCONJ
ejpam-6841	10	28	optimal	optimal	ADJ
ejpam-6841	10	29	approximations	approximation	NOUN
ejpam-6841	10	30	are	be	AUX
ejpam-6841	10	31	sought	seek	VERB
ejpam-6841	10	32	.	.	PUNCT
ejpam-6841	11	1	future	future	ADJ
ejpam-6841	11	2	research	research	NOUN
ejpam-6841	11	3	may	may	AUX
ejpam-6841	11	4	extend	extend	VERB
ejpam-6841	11	5	these	these	DET
ejpam-6841	11	6	concepts	concept	NOUN
ejpam-6841	11	7	to	to	ADP
ejpam-6841	11	8	more	more	ADJ
ejpam-6841	11	9	complex	complex	ADJ
ejpam-6841	11	10	structures	structure	NOUN
ejpam-6841	11	11	,	,	PUNCT
ejpam-6841	11	12	such	such	ADJ
ejpam-6841	11	13	as	as	ADP
ejpam-6841	11	14	partial	partial	ADJ
ejpam-6841	11	15	metric	metric	ADJ
ejpam-6841	11	16	spaces	space	NOUN
ejpam-6841	11	17	or	or	CCONJ
ejpam-6841	11	18	ordered	order	VERB
ejpam-6841	11	19	metric	metric	ADJ
ejpam-6841	11	20	spaces	space	NOUN
ejpam-6841	11	21	,	,	PUNCT
ejpam-6841	11	22	broadening	broaden	VERB
ejpam-6841	11	23	the	the	DET
ejpam-6841	11	24	scope	scope	NOUN
ejpam-6841	11	25	and	and	CCONJ
ejpam-6841	11	26	∗corresponding	∗corresponde	VERB
ejpam-6841	11	27	author	author	NOUN
ejpam-6841	11	28	.	.	PUNCT
ejpam-6841	12	1	∗corresponding	∗corresponde	VERB
ejpam-6841	12	2	author	author	NOUN
ejpam-6841	12	3	.	.	PUNCT
ejpam-6841	13	1	doi	doi	NOUN
ejpam-6841	13	2	:	:	PUNCT
ejpam-6841	13	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6841	https://doi.org/10.29020/nybg.ejpam.v18i4.6841	NOUN
ejpam-6841	13	4	email	email	NOUN
ejpam-6841	13	5	addresses	address	NOUN
ejpam-6841	13	6	:	:	PUNCT
ejpam-6841	13	7	khalil.phdma127@iiu.edu.pk	khalil.phdma127@iiu.edu.pk	X
ejpam-6841	13	8	(	(	PUNCT
ejpam-6841	13	9	k.	k.	PROPN
ejpam-6841	13	10	javed	javed	PROPN
ejpam-6841	13	11	)	)	PUNCT
ejpam-6841	13	12	,	,	PUNCT
ejpam-6841	13	13	muhammad.nazam@aiou.edu.pk	muhammad.nazam@aiou.edu.pk	PROPN
ejpam-6841	13	14	(	(	PUNCT
ejpam-6841	13	15	m.	m.	NOUN
ejpam-6841	13	16	nazam	nazam	PROPN
ejpam-6841	13	17	)	)	PUNCT
ejpam-6841	13	18	,	,	PUNCT
ejpam-6841	13	19	marshadzia@iiu.edu.pk	marshadzia@iiu.edu.pk	NOUN
ejpam-6841	13	20	(	(	PUNCT
ejpam-6841	13	21	m.	m.	PROPN
ejpam-6841	13	22	arshad	arshad	PROPN
ejpam-6841	13	23	)	)	PUNCT
ejpam-6841	13	24	,	,	PUNCT
ejpam-6841	13	25	manuel.delasen@ehu.eus	manuel.delasen@ehu.eus	PROPN
ejpam-6841	13	26	(	(	PUNCT
ejpam-6841	13	27	m.	m.	NOUN
ejpam-6841	13	28	de	de	X
ejpam-6841	13	29	la	la	X
ejpam-6841	13	30	sen	sen	PROPN
ejpam-6841	13	31	)	)	PUNCT
ejpam-6841	13	32	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6841	13	33	1	1	NUM
ejpam-6841	13	34	copyright	copyright	NOUN
ejpam-6841	13	35	:	:	PUNCT
ejpam-6841	14	1	©	©	PROPN
ejpam-6841	14	2	2025	2025	NUM
ejpam-6841	14	3	the	the	DET
ejpam-6841	14	4	author(s	author(s	NOUN
ejpam-6841	14	5	)	)	PUNCT
ejpam-6841	14	6	.	.	PUNCT
ejpam-6841	15	1	(	(	PUNCT
ejpam-6841	15	2	cc	cc	NOUN
ejpam-6841	15	3	by	by	ADP
ejpam-6841	15	4	-	-	PUNCT
ejpam-6841	15	5	nc	nc	PROPN
ejpam-6841	15	6	4.0	4.0	NUM
ejpam-6841	15	7	)	)	PUNCT
ejpam-6841	15	8	k.	k.	PROPN
ejpam-6841	15	9	javed	javed	PROPN
ejpam-6841	15	10	,	,	PUNCT
ejpam-6841	15	11	m.	m.	NOUN
ejpam-6841	15	12	nazam	nazam	PROPN
ejpam-6841	15	13	,	,	PUNCT
ejpam-6841	15	14	m.	m.	PROPN
ejpam-6841	15	15	arshad	arshad	PROPN
ejpam-6841	15	16	,	,	PUNCT
ejpam-6841	15	17	m.	m.	NOUN
ejpam-6841	15	18	de	de	X
ejpam-6841	15	19	la	la	PROPN
ejpam-6841	15	20	sen	sen	PROPN
ejpam-6841	15	21	/	/	SYM
ejpam-6841	15	22	eur	eur	PROPN
ejpam-6841	15	23	.	.	PUNCT
ejpam-6841	16	1	j.	j.	PROPN
ejpam-6841	16	2	pure	pure	PROPN
ejpam-6841	16	3	appl	appl	PROPN
ejpam-6841	16	4	.	.	PROPN
ejpam-6841	16	5	math	math	PROPN
ejpam-6841	16	6	,	,	PUNCT
ejpam-6841	16	7	18	18	NUM
ejpam-6841	16	8	(	(	PUNCT
ejpam-6841	16	9	4	4	NUM
ejpam-6841	16	10	)	)	PUNCT
ejpam-6841	16	11	(	(	PUNCT
ejpam-6841	16	12	2025	2025	NUM
ejpam-6841	16	13	)	)	PUNCT
ejpam-6841	16	14	,	,	PUNCT
ejpam-6841	16	15	6841	6841	NUM
ejpam-6841	16	16	2	2	NUM
ejpam-6841	16	17	of	of	ADP
ejpam-6841	16	18	23	23	NUM
ejpam-6841	16	19	applicability	applicability	NOUN
ejpam-6841	16	20	of	of	ADP
ejpam-6841	16	21	these	these	DET
ejpam-6841	16	22	results	result	NOUN
ejpam-6841	16	23	.	.	PUNCT
ejpam-6841	17	1	in	in	ADP
ejpam-6841	17	2	optimization	optimization	NOUN
ejpam-6841	17	3	and	and	CCONJ
ejpam-6841	17	4	fixed	fix	VERB
ejpam-6841	17	5	point	point	NOUN
ejpam-6841	17	6	theory	theory	NOUN
ejpam-6841	17	7	,	,	PUNCT
ejpam-6841	17	8	best	good	ADJ
ejpam-6841	17	9	proximity	proximity	NOUN
ejpam-6841	17	10	points	point	NOUN
ejpam-6841	17	11	are	be	AUX
ejpam-6841	17	12	crucial	crucial	ADJ
ejpam-6841	17	13	when	when	SCONJ
ejpam-6841	17	14	dealing	deal	VERB
ejpam-6841	17	15	with	with	ADP
ejpam-6841	17	16	non	non	ADJ
ejpam-6841	17	17	-	-	ADJ
ejpam-6841	17	18	self	self	ADJ
ejpam-6841	17	19	mappings	mapping	NOUN
ejpam-6841	17	20	where	where	SCONJ
ejpam-6841	17	21	fixed	fix	VERB
ejpam-6841	17	22	points	point	NOUN
ejpam-6841	17	23	do	do	AUX
ejpam-6841	17	24	not	not	PART
ejpam-6841	17	25	exist	exist	VERB
ejpam-6841	17	26	.	.	PUNCT
ejpam-6841	18	1	the	the	DET
ejpam-6841	18	2	classical	classical	ADJ
ejpam-6841	18	3	banach	banach	NOUN
ejpam-6841	18	4	contraction	contraction	NOUN
ejpam-6841	18	5	principle	principle	NOUN
ejpam-6841	18	6	has	have	AUX
ejpam-6841	18	7	seen	see	VERB
ejpam-6841	18	8	various	various	ADJ
ejpam-6841	18	9	extensions	extension	NOUN
ejpam-6841	18	10	to	to	PART
ejpam-6841	18	11	accommodate	accommodate	VERB
ejpam-6841	18	12	different	different	ADJ
ejpam-6841	18	13	contractions	contraction	NOUN
ejpam-6841	18	14	and	and	CCONJ
ejpam-6841	18	15	more	more	ADJ
ejpam-6841	18	16	general	general	ADJ
ejpam-6841	18	17	settings	setting	NOUN
ejpam-6841	18	18	.	.	PUNCT
ejpam-6841	19	1	this	this	DET
ejpam-6841	19	2	note	note	NOUN
ejpam-6841	19	3	focuses	focus	VERB
ejpam-6841	19	4	on	on	ADP
ejpam-6841	19	5	a	a	DET
ejpam-6841	19	6	specific	specific	ADJ
ejpam-6841	19	7	generalization	generalization	NOUN
ejpam-6841	19	8	:	:	PUNCT
ejpam-6841	19	9	generalized	generalize	VERB
ejpam-6841	19	10	interpolative	interpolative	ADJ
ejpam-6841	19	11	proximal	proximal	ADJ
ejpam-6841	19	12	contractions	contraction	NOUN
ejpam-6841	19	13	.	.	PUNCT
ejpam-6841	20	1	best	good	ADJ
ejpam-6841	20	2	proximity	proximity	NOUN
ejpam-6841	20	3	point	point	NOUN
ejpam-6841	20	4	theory	theory	NOUN
ejpam-6841	20	5	is	be	AUX
ejpam-6841	20	6	an	an	DET
ejpam-6841	20	7	area	area	NOUN
ejpam-6841	20	8	of	of	ADP
ejpam-6841	20	9	mathematical	mathematical	ADJ
ejpam-6841	20	10	analysis	analysis	NOUN
ejpam-6841	20	11	and	and	CCONJ
ejpam-6841	20	12	optimization	optimization	NOUN
ejpam-6841	20	13	that	that	PRON
ejpam-6841	20	14	focuses	focus	VERB
ejpam-6841	20	15	on	on	ADP
ejpam-6841	20	16	finding	find	VERB
ejpam-6841	20	17	points	point	NOUN
ejpam-6841	20	18	in	in	ADP
ejpam-6841	20	19	one	one	NUM
ejpam-6841	20	20	set	set	NOUN
ejpam-6841	20	21	that	that	PRON
ejpam-6841	20	22	are	be	AUX
ejpam-6841	20	23	closest	close	ADJ
ejpam-6841	20	24	to	to	ADP
ejpam-6841	20	25	points	point	NOUN
ejpam-6841	20	26	in	in	ADP
ejpam-6841	20	27	another	another	DET
ejpam-6841	20	28	set	set	NOUN
ejpam-6841	20	29	when	when	SCONJ
ejpam-6841	20	30	a	a	DET
ejpam-6841	20	31	contractive	contractive	ADJ
ejpam-6841	20	32	mapping	mapping	NOUN
ejpam-6841	20	33	is	be	AUX
ejpam-6841	20	34	involved	involve	VERB
ejpam-6841	20	35	.	.	PUNCT
ejpam-6841	21	1	in	in	ADP
ejpam-6841	21	2	metric	metric	ADJ
ejpam-6841	21	3	fixed	fix	VERB
ejpam-6841	21	4	point	point	NOUN
ejpam-6841	21	5	theory	theory	NOUN
ejpam-6841	21	6	,	,	PUNCT
ejpam-6841	21	7	the	the	DET
ejpam-6841	21	8	concept	concept	NOUN
ejpam-6841	21	9	of	of	ADP
ejpam-6841	21	10	best	good	ADJ
ejpam-6841	21	11	proximity	proximity	NOUN
ejpam-6841	21	12	points	point	NOUN
ejpam-6841	21	13	plays	play	VERB
ejpam-6841	21	14	a	a	DET
ejpam-6841	21	15	crucial	crucial	ADJ
ejpam-6841	21	16	role	role	NOUN
ejpam-6841	21	17	,	,	PUNCT
ejpam-6841	21	18	particularly	particularly	ADV
ejpam-6841	21	19	when	when	SCONJ
ejpam-6841	21	20	dealing	deal	VERB
ejpam-6841	21	21	with	with	ADP
ejpam-6841	21	22	mappings	mapping	NOUN
ejpam-6841	21	23	that	that	PRON
ejpam-6841	21	24	do	do	AUX
ejpam-6841	21	25	not	not	PART
ejpam-6841	21	26	necessarily	necessarily	ADV
ejpam-6841	21	27	have	have	VERB
ejpam-6841	21	28	fixed	fix	VERB
ejpam-6841	21	29	points	point	NOUN
ejpam-6841	21	30	.	.	PUNCT
ejpam-6841	22	1	this	this	DET
ejpam-6841	22	2	note	note	NOUN
ejpam-6841	22	3	delves	delve	VERB
ejpam-6841	22	4	into	into	ADP
ejpam-6841	22	5	the	the	DET
ejpam-6841	22	6	best	good	ADJ
ejpam-6841	22	7	proximity	proximity	NOUN
ejpam-6841	22	8	points	point	NOUN
ejpam-6841	22	9	for	for	ADP
ejpam-6841	22	10	generalized	generalized	ADJ
ejpam-6841	22	11	interpolative	interpolative	ADJ
ejpam-6841	22	12	proximal	proximal	ADJ
ejpam-6841	22	13	contractions	contraction	NOUN
ejpam-6841	22	14	,	,	PUNCT
ejpam-6841	22	15	an	an	DET
ejpam-6841	22	16	important	important	ADJ
ejpam-6841	22	17	class	class	NOUN
ejpam-6841	22	18	of	of	ADP
ejpam-6841	22	19	mappings	mapping	NOUN
ejpam-6841	22	20	in	in	ADP
ejpam-6841	22	21	metric	metric	ADJ
ejpam-6841	22	22	spaces	space	NOUN
ejpam-6841	22	23	.	.	PUNCT
ejpam-6841	23	1	the	the	DET
ejpam-6841	23	2	fundamentals	fundamental	NOUN
ejpam-6841	23	3	of	of	ADP
ejpam-6841	23	4	interpolative	interpolative	ADJ
ejpam-6841	23	5	contraction	contraction	NOUN
ejpam-6841	23	6	are	be	AUX
ejpam-6841	23	7	the	the	DET
ejpam-6841	23	8	product	product	NOUN
ejpam-6841	23	9	of	of	ADP
ejpam-6841	23	10	distances	distance	NOUN
ejpam-6841	23	11	with	with	ADP
ejpam-6841	23	12	exponents	exponent	NOUN
ejpam-6841	23	13	that	that	PRON
ejpam-6841	23	14	satisfy	satisfy	VERB
ejpam-6841	23	15	certain	certain	ADJ
ejpam-6841	23	16	conditions	condition	NOUN
ejpam-6841	23	17	.	.	PUNCT
ejpam-6841	24	1	the	the	DET
ejpam-6841	24	2	prominent	prominent	ADJ
ejpam-6841	24	3	mathematician	mathematician	ADJ
ejpam-6841	24	4	erdal	erdal	PROPN
ejpam-6841	24	5	karapinar	karapinar	PROPN
ejpam-6841	24	6	first	first	ADV
ejpam-6841	24	7	used	use	VERB
ejpam-6841	24	8	the	the	DET
ejpam-6841	24	9	word	word	NOUN
ejpam-6841	24	10	”	"	PUNCT
ejpam-6841	24	11	interpolative	interpolative	ADJ
ejpam-6841	24	12	contraction	contraction	NOUN
ejpam-6841	24	13	”	"	PUNCT
ejpam-6841	24	14	in	in	ADP
ejpam-6841	24	15	his	his	PRON
ejpam-6841	24	16	paper	paper	NOUN
ejpam-6841	25	1	[	[	X
ejpam-6841	25	2	1	1	NUM
ejpam-6841	25	3	]	]	PUNCT
ejpam-6841	25	4	,	,	PUNCT
ejpam-6841	25	5	which	which	PRON
ejpam-6841	25	6	was	be	AUX
ejpam-6841	25	7	published	publish	VERB
ejpam-6841	25	8	in	in	ADP
ejpam-6841	25	9	2018	2018	NUM
ejpam-6841	25	10	.	.	PUNCT
ejpam-6841	26	1	the	the	DET
ejpam-6841	26	2	following	follow	VERB
ejpam-6841	26	3	is	be	AUX
ejpam-6841	26	4	the	the	DET
ejpam-6841	26	5	definition	definition	NOUN
ejpam-6841	26	6	of	of	ADP
ejpam-6841	26	7	an	an	DET
ejpam-6841	26	8	interpolative	interpolative	ADJ
ejpam-6841	26	9	contraction	contraction	NOUN
ejpam-6841	26	10	:	:	PUNCT
ejpam-6841	26	11	a	a	DET
ejpam-6841	26	12	self	self	NOUN
ejpam-6841	26	13	-	-	PUNCT
ejpam-6841	26	14	mapping	mapping	NOUN
ejpam-6841	26	15	p	p	NOUN
ejpam-6841	26	16	,	,	PUNCT
ejpam-6841	26	17	defined	define	VERB
ejpam-6841	26	18	on	on	ADP
ejpam-6841	26	19	a	a	DET
ejpam-6841	26	20	metric	metric	ADJ
ejpam-6841	26	21	space	space	NOUN
ejpam-6841	26	22	(	(	PUNCT
ejpam-6841	26	23	w	w	NOUN
ejpam-6841	26	24	,	,	PUNCT
ejpam-6841	26	25	ϑ	ϑ	NOUN
ejpam-6841	26	26	)	)	PUNCT
ejpam-6841	26	27	,	,	PUNCT
ejpam-6841	26	28	satisfying	satisfy	VERB
ejpam-6841	26	29	the	the	DET
ejpam-6841	26	30	following	follow	VERB
ejpam-6841	26	31	inequality	inequality	NOUN
ejpam-6841	26	32	ϑ(pb	ϑ(pb	PROPN
ejpam-6841	26	33	,	,	PUNCT
ejpam-6841	26	34	pm	pm	NOUN
ejpam-6841	26	35	)	)	PUNCT
ejpam-6841	26	36	≤	≤	NUM
ejpam-6841	26	37	k	k	X
ejpam-6841	26	38	(	(	PUNCT
ejpam-6841	26	39	ϑ(b	ϑ(b	PROPN
ejpam-6841	26	40	,	,	PUNCT
ejpam-6841	26	41	m))ν	m))ν	NOUN
ejpam-6841	26	42	,	,	PUNCT
ejpam-6841	26	43	∀b	∀b	NOUN
ejpam-6841	26	44	,	,	PUNCT
ejpam-6841	26	45	m	m	PROPN
ejpam-6841	26	46	∈	∈	PROPN
ejpam-6841	26	47	w	w	PROPN
ejpam-6841	26	48	,	,	PUNCT
ejpam-6841	26	49	(	(	PUNCT
ejpam-6841	26	50	1	1	X
ejpam-6841	26	51	)	)	PUNCT
ejpam-6841	26	52	is	be	AUX
ejpam-6841	26	53	called	call	VERB
ejpam-6841	26	54	an	an	DET
ejpam-6841	26	55	interpolative	interpolative	ADJ
ejpam-6841	26	56	contraction	contraction	NOUN
ejpam-6841	26	57	,	,	PUNCT
ejpam-6841	26	58	where	where	SCONJ
ejpam-6841	26	59	ν	ν	PROPN
ejpam-6841	26	60	∈	∈	PROPN
ejpam-6841	26	61	(	(	PUNCT
ejpam-6841	26	62	0	0	NUM
ejpam-6841	26	63	,	,	PUNCT
ejpam-6841	26	64	1	1	NUM
ejpam-6841	26	65	]	]	PUNCT
ejpam-6841	26	66	and	and	CCONJ
ejpam-6841	26	67	k	k	PROPN
ejpam-6841	26	68	∈	∈	PROPN
ejpam-6841	27	1	[	[	X
ejpam-6841	27	2	0	0	NUM
ejpam-6841	27	3	,	,	PUNCT
ejpam-6841	27	4	1	1	NUM
ejpam-6841	27	5	)	)	PUNCT
ejpam-6841	27	6	.	.	PUNCT
ejpam-6841	28	1	since	since	SCONJ
ejpam-6841	28	2	ν	ν	PROPN
ejpam-6841	28	3	=	=	SYM
ejpam-6841	28	4	1	1	NUM
ejpam-6841	28	5	,	,	PUNCT
ejpam-6841	28	6	p	p	PRON
ejpam-6841	28	7	is	be	AUX
ejpam-6841	28	8	a	a	DET
ejpam-6841	28	9	banach	banach	NOUN
ejpam-6841	28	10	contraction	contraction	NOUN
ejpam-6841	28	11	.	.	PUNCT
ejpam-6841	29	1	if	if	SCONJ
ejpam-6841	29	2	p	p	PRON
ejpam-6841	29	3	defined	define	VERB
ejpam-6841	29	4	on	on	ADP
ejpam-6841	29	5	a	a	DET
ejpam-6841	29	6	metric	metric	ADJ
ejpam-6841	29	7	space	space	NOUN
ejpam-6841	29	8	(	(	PUNCT
ejpam-6841	29	9	w	w	NOUN
ejpam-6841	29	10	,	,	PUNCT
ejpam-6841	29	11	ϑ	ϑ	NOUN
ejpam-6841	29	12	)	)	PUNCT
ejpam-6841	29	13	the	the	DET
ejpam-6841	29	14	followings	following	NOUN
ejpam-6841	29	15	axioms	axiom	NOUN
ejpam-6841	29	16	are	be	AUX
ejpam-6841	29	17	holds	hold	NOUN
ejpam-6841	29	18	:	:	PUNCT
ejpam-6841	29	19	ϑ(pb	ϑ(pb	NOUN
ejpam-6841	29	20	,	,	PUNCT
ejpam-6841	29	21	pm	pm	NOUN
ejpam-6841	29	22	)	)	PUNCT
ejpam-6841	29	23	≤	≤	NUM
ejpam-6841	30	1	k	k	X
ejpam-6841	30	2	(	(	PUNCT
ejpam-6841	30	3	ϑ(b	ϑ(b	PROPN
ejpam-6841	30	4	,	,	PUNCT
ejpam-6841	30	5	pb))ν	pb))ν	PROPN
ejpam-6841	30	6	(	(	PUNCT
ejpam-6841	30	7	ϑ(b	ϑ(b	ADJ
ejpam-6841	30	8	,	,	PUNCT
ejpam-6841	30	9	pm))1−ν	pm))1−ν	NOUN
ejpam-6841	30	10	,	,	PUNCT
ejpam-6841	30	11	ϑ(pb	ϑ(pb	PROPN
ejpam-6841	30	12	,	,	PUNCT
ejpam-6841	30	13	pm	pm	NOUN
ejpam-6841	30	14	)	)	PUNCT
ejpam-6841	30	15	≤	≤	NUM
ejpam-6841	31	1	k	k	X
ejpam-6841	31	2	(	(	PUNCT
ejpam-6841	31	3	ϑ(b	ϑ(b	PROPN
ejpam-6841	31	4	,	,	PUNCT
ejpam-6841	31	5	pm))ν	pm))ν	NOUN
ejpam-6841	31	6	(	(	PUNCT
ejpam-6841	31	7	ϑ(b	ϑ(b	ADJ
ejpam-6841	31	8	,	,	PUNCT
ejpam-6841	31	9	pm))1−ν	pm))1−ν	NOUN
ejpam-6841	31	10	,	,	PUNCT
ejpam-6841	31	11	ϑ(pb	ϑ(pb	PROPN
ejpam-6841	31	12	,	,	PUNCT
ejpam-6841	31	13	pm	pm	NOUN
ejpam-6841	31	14	)	)	PUNCT
ejpam-6841	31	15	≤	≤	NUM
ejpam-6841	32	1	k	k	X
ejpam-6841	32	2	(	(	PUNCT
ejpam-6841	32	3	ϑ(b	ϑ(b	PROPN
ejpam-6841	32	4	,	,	PUNCT
ejpam-6841	32	5	w))η	w))η	NOUN
ejpam-6841	32	6	(	(	PUNCT
ejpam-6841	32	7	ϑ(b	ϑ(b	ADJ
ejpam-6841	32	8	,	,	PUNCT
ejpam-6841	32	9	pb))ν	pb))ν	PROPN
ejpam-6841	32	10	(	(	PUNCT
ejpam-6841	32	11	ϑ(m	ϑ(m	NOUN
ejpam-6841	32	12	,	,	PUNCT
ejpam-6841	32	13	pm))1−ν−η	pm))1−ν−η	NOUN
ejpam-6841	32	14	,	,	PUNCT
ejpam-6841	32	15	ν	ν	X
ejpam-6841	32	16	+	+	CCONJ
ejpam-6841	32	17	η	η	X
ejpam-6841	32	18	<	<	X
ejpam-6841	32	19	1	1	NUM
ejpam-6841	32	20	ϑ(pb	ϑ(pb	PROPN
ejpam-6841	32	21	,	,	PUNCT
ejpam-6841	32	22	pm	pm	NOUN
ejpam-6841	32	23	)	)	PUNCT
ejpam-6841	32	24	≤	≤	NUM
ejpam-6841	33	1	k	k	X
ejpam-6841	33	2	(	(	PUNCT
ejpam-6841	33	3	ϑ(b	ϑ(b	PROPN
ejpam-6841	33	4	,	,	PUNCT
ejpam-6841	33	5	w))ν	w))ν	NOUN
ejpam-6841	33	6	(	(	PUNCT
ejpam-6841	33	7	ϑ(b	ϑ(b	PROPN
ejpam-6841	33	8	,	,	PUNCT
ejpam-6841	33	9	pb))η	pb))η	PROPN
ejpam-6841	33	10	(	(	PUNCT
ejpam-6841	33	11	ϑ(m	ϑ(m	NOUN
ejpam-6841	33	12	,	,	PUNCT
ejpam-6841	33	13	pm))γ	pm))γ	PROPN
ejpam-6841	33	14	(	(	PUNCT
ejpam-6841	33	15	1	1	NUM
ejpam-6841	33	16	2	2	NUM
ejpam-6841	33	17	(	(	PUNCT
ejpam-6841	33	18	ϑ(b	ϑ(b	ADJ
ejpam-6841	33	19	,	,	PUNCT
ejpam-6841	33	20	pm	pm	NOUN
ejpam-6841	33	21	)	)	PUNCT
ejpam-6841	33	22	·	·	PUNCT
ejpam-6841	33	23	ϑ(m	ϑ(m	NOUN
ejpam-6841	33	24	,	,	PUNCT
ejpam-6841	33	25	pb	pb	NOUN
ejpam-6841	33	26	)	)	PUNCT
ejpam-6841	33	27	)	)	PUNCT
ejpam-6841	33	28	)	)	PUNCT
ejpam-6841	33	29	1−η−ν−γ	1−η−ν−γ	NUM
ejpam-6841	33	30	,	,	PUNCT
ejpam-6841	33	31	ν	ν	X
ejpam-6841	33	32	+	+	CCONJ
ejpam-6841	33	33	η	η	PROPN
ejpam-6841	33	34	+	+	X
ejpam-6841	33	35	γ	γ	X
ejpam-6841	33	36	<	<	X
ejpam-6841	33	37	1	1	NUM
ejpam-6841	33	38	for	for	ADP
ejpam-6841	33	39	all	all	DET
ejpam-6841	33	40	b	b	NOUN
ejpam-6841	33	41	,	,	PUNCT
ejpam-6841	33	42	m	m	PROPN
ejpam-6841	33	43	∈	∈	PROPN
ejpam-6841	33	44	w	w	PROPN
ejpam-6841	33	45	,	,	PUNCT
ejpam-6841	33	46	then	then	ADV
ejpam-6841	33	47	p	p	PROPN
ejpam-6841	33	48	is	be	AUX
ejpam-6841	33	49	called	call	VERB
ejpam-6841	33	50	kannan	kannan	PROPN
ejpam-6841	33	51	type	type	NOUN
ejpam-6841	33	52	interpolative	interpolative	ADJ
ejpam-6841	33	53	contraction	contraction	NOUN
ejpam-6841	33	54	,	,	PUNCT
ejpam-6841	33	55	chatterjea	chatterjea	ADJ
ejpam-6841	33	56	type	type	NOUN
ejpam-6841	33	57	interpolative	interpolative	ADJ
ejpam-6841	33	58	contraction	contraction	NOUN
ejpam-6841	33	59	,	,	PUNCT
ejpam-6841	33	60	ćirić	ćirić	NOUN
ejpam-6841	33	61	-	-	PUNCT
ejpam-6841	33	62	reich	reich	NOUN
ejpam-6841	33	63	-	-	PUNCT
ejpam-6841	33	64	rus	rus	NOUN
ejpam-6841	33	65	type	type	NOUN
ejpam-6841	33	66	interpolative	interpolative	ADJ
ejpam-6841	33	67	contraction	contraction	NOUN
ejpam-6841	33	68	and	and	CCONJ
ejpam-6841	33	69	hardy	hardy	ADJ
ejpam-6841	33	70	rogers	roger	NOUN
ejpam-6841	33	71	type	type	VERB
ejpam-6841	33	72	interpolative	interpolative	ADJ
ejpam-6841	33	73	contractions	contraction	NOUN
ejpam-6841	33	74	,	,	PUNCT
ejpam-6841	33	75	respectively	respectively	ADV
ejpam-6841	33	76	.	.	PUNCT
ejpam-6841	34	1	through	through	ADP
ejpam-6841	34	2	interpolation	interpolation	NOUN
ejpam-6841	34	3	,	,	PUNCT
ejpam-6841	34	4	numerous	numerous	ADJ
ejpam-6841	34	5	complex	complex	ADJ
ejpam-6841	34	6	and	and	CCONJ
ejpam-6841	34	7	conventional	conventional	ADJ
ejpam-6841	34	8	contractions	contraction	NOUN
ejpam-6841	34	9	have	have	AUX
ejpam-6841	34	10	lately	lately	ADV
ejpam-6841	34	11	been	be	AUX
ejpam-6841	34	12	reexamined	reexamine	VERB
ejpam-6841	34	13	(	(	PUNCT
ejpam-6841	34	14	see	see	VERB
ejpam-6841	34	15	[	[	X
ejpam-6841	34	16	2–6	2–6	NOUN
ejpam-6841	34	17	]	]	X
ejpam-6841	34	18	and	and	CCONJ
ejpam-6841	34	19	references	reference	NOUN
ejpam-6841	34	20	therein	therein	ADV
ejpam-6841	34	21	)	)	PUNCT
ejpam-6841	34	22	.	.	PUNCT
ejpam-6841	35	1	the	the	DET
ejpam-6841	35	2	proximal	proximal	ADJ
ejpam-6841	35	3	contraction	contraction	NOUN
ejpam-6841	35	4	principle	principle	NOUN
ejpam-6841	35	5	appeared	appear	VERB
ejpam-6841	35	6	in	in	ADP
ejpam-6841	35	7	[	[	X
ejpam-6841	35	8	7	7	NUM
ejpam-6841	35	9	]	]	PUNCT
ejpam-6841	35	10	.	.	PUNCT
ejpam-6841	36	1	proinov	proinov	VERB
ejpam-6841	37	1	[	[	X
ejpam-6841	37	2	8](2020	8](2020	NUM
ejpam-6841	37	3	)	)	PUNCT
ejpam-6841	37	4	offered	offer	VERB
ejpam-6841	37	5	various	various	ADJ
ejpam-6841	37	6	fixed	fix	VERB
ejpam-6841	37	7	-	-	PUNCT
ejpam-6841	37	8	point	point	NOUN
ejpam-6841	37	9	theorems	theorem	NOUN
ejpam-6841	37	10	that	that	PRON
ejpam-6841	37	11	built	build	VERB
ejpam-6841	37	12	on	on	ADP
ejpam-6841	37	13	previous	previous	ADJ
ejpam-6841	37	14	work	work	NOUN
ejpam-6841	37	15	in	in	ADP
ejpam-6841	37	16	[	[	X
ejpam-6841	37	17	9	9	NUM
ejpam-6841	37	18	]	]	PUNCT
ejpam-6841	37	19	.	.	PUNCT
ejpam-6841	38	1	first	first	ADV
ejpam-6841	38	2	,	,	PUNCT
ejpam-6841	38	3	erdal	erdal	PROPN
ejpam-6841	38	4	karapinar	karapinar	PROPN
ejpam-6841	38	5	introduced	introduce	VERB
ejpam-6841	38	6	the	the	DET
ejpam-6841	38	7	idea	idea	NOUN
ejpam-6841	38	8	of	of	ADP
ejpam-6841	38	9	interpolation	interpolation	NOUN
ejpam-6841	38	10	contraction	contraction	NOUN
ejpam-6841	38	11	in	in	ADP
ejpam-6841	38	12	his	his	PRON
ejpam-6841	38	13	work	work	NOUN
ejpam-6841	38	14	[	[	X
ejpam-6841	38	15	1	1	X
ejpam-6841	38	16	]	]	PUNCT
ejpam-6841	38	17	published	publish	VERB
ejpam-6841	38	18	in	in	ADP
ejpam-6841	38	19	2018	2018	NUM
ejpam-6841	38	20	,	,	PUNCT
ejpam-6841	38	21	then	then	ADV
ejpam-6841	38	22	proinov	proinov	PROPN
ejpam-6841	38	23	gave	give	VERB
ejpam-6841	38	24	the	the	DET
ejpam-6841	38	25	second	second	ADJ
ejpam-6841	38	26	idea	idea	NOUN
ejpam-6841	38	27	in	in	ADP
ejpam-6841	38	28	his	his	PRON
ejpam-6841	38	29	paper	paper	NOUN
ejpam-6841	38	30	[	[	X
ejpam-6841	38	31	8	8	NUM
ejpam-6841	38	32	]	]	PUNCT
ejpam-6841	38	33	published	publish	VERB
ejpam-6841	38	34	in	in	ADP
ejpam-6841	38	35	2020	2020	NUM
ejpam-6841	38	36	.	.	PUNCT
ejpam-6841	39	1	best	good	ADJ
ejpam-6841	39	2	proximity	proximity	NOUN
ejpam-6841	39	3	points	point	NOUN
ejpam-6841	39	4	are	be	AUX
ejpam-6841	39	5	optimal	optimal	ADJ
ejpam-6841	39	6	points	point	NOUN
ejpam-6841	39	7	that	that	PRON
ejpam-6841	39	8	minimize	minimize	VERB
ejpam-6841	39	9	the	the	DET
ejpam-6841	39	10	distance	distance	NOUN
ejpam-6841	39	11	between	between	ADP
ejpam-6841	39	12	two	two	NUM
ejpam-6841	39	13	sets	set	NOUN
ejpam-6841	39	14	when	when	SCONJ
ejpam-6841	39	15	fixed	fix	VERB
ejpam-6841	39	16	points	point	NOUN
ejpam-6841	39	17	may	may	AUX
ejpam-6841	39	18	not	not	PART
ejpam-6841	39	19	exist	exist	VERB
ejpam-6841	39	20	.	.	PUNCT
ejpam-6841	40	1	a	a	DET
ejpam-6841	40	2	best	good	ADJ
ejpam-6841	40	3	proximity	proximity	NOUN
ejpam-6841	40	4	point	point	NOUN
ejpam-6841	40	5	theorem	theorem	NOUN
ejpam-6841	40	6	achieves	achieve	VERB
ejpam-6841	40	7	a	a	DET
ejpam-6841	40	8	global	global	ADJ
ejpam-6841	40	9	minimum	minimum	NOUN
ejpam-6841	40	10	of	of	ADP
ejpam-6841	40	11	ϑ(b	ϑ(b	ADJ
ejpam-6841	40	12	,	,	PUNCT
ejpam-6841	40	13	p(b	p(b	PROPN
ejpam-6841	40	14	)	)	PUNCT
ejpam-6841	40	15	)	)	PUNCT
ejpam-6841	40	16	by	by	ADP
ejpam-6841	40	17	specifying	specify	VERB
ejpam-6841	40	18	an	an	DET
ejpam-6841	40	19	approximate	approximate	ADJ
ejpam-6841	40	20	solution	solution	NOUN
ejpam-6841	40	21	b	b	PROPN
ejpam-6841	40	22	of	of	ADP
ejpam-6841	40	23	the	the	DET
ejpam-6841	40	24	fixed	fix	VERB
ejpam-6841	40	25	point	point	NOUN
ejpam-6841	40	26	equation	equation	NOUN
ejpam-6841	40	27	k.	k.	PROPN
ejpam-6841	40	28	javed	javed	PROPN
ejpam-6841	40	29	,	,	PUNCT
ejpam-6841	40	30	m.	m.	NOUN
ejpam-6841	40	31	nazam	nazam	PROPN
ejpam-6841	40	32	,	,	PUNCT
ejpam-6841	40	33	m.	m.	PROPN
ejpam-6841	40	34	arshad	arshad	PROPN
ejpam-6841	40	35	,	,	PUNCT
ejpam-6841	40	36	m.	m.	NOUN
ejpam-6841	40	37	de	de	X
ejpam-6841	40	38	la	la	PROPN
ejpam-6841	40	39	sen	sen	PROPN
ejpam-6841	40	40	/	/	SYM
ejpam-6841	40	41	eur	eur	PROPN
ejpam-6841	40	42	.	.	PUNCT
ejpam-6841	41	1	j.	j.	PROPN
ejpam-6841	41	2	pure	pure	PROPN
ejpam-6841	41	3	appl	appl	PROPN
ejpam-6841	41	4	.	.	PROPN
ejpam-6841	41	5	math	math	PROPN
ejpam-6841	41	6	,	,	PUNCT
ejpam-6841	41	7	18	18	NUM
ejpam-6841	41	8	(	(	PUNCT
ejpam-6841	41	9	4	4	NUM
ejpam-6841	41	10	)	)	PUNCT
ejpam-6841	41	11	(	(	PUNCT
ejpam-6841	41	12	2025	2025	NUM
ejpam-6841	41	13	)	)	PUNCT
ejpam-6841	41	14	,	,	PUNCT
ejpam-6841	41	15	6841	6841	NUM
ejpam-6841	41	16	3	3	NUM
ejpam-6841	41	17	of	of	ADP
ejpam-6841	41	18	23	23	NUM
ejpam-6841	41	19	p(b	p(b	NOUN
ejpam-6841	41	20	)	)	PUNCT
ejpam-6841	42	1	=	=	SYM
ejpam-6841	42	2	b	b	X
ejpam-6841	42	3	to	to	PART
ejpam-6841	42	4	satisfy	satisfy	VERB
ejpam-6841	42	5	the	the	DET
ejpam-6841	42	6	requirement	requirement	NOUN
ejpam-6841	42	7	that	that	SCONJ
ejpam-6841	42	8	ϑ(b	ϑ(b	PROPN
ejpam-6841	42	9	,	,	PUNCT
ejpam-6841	42	10	p(b	p(b	NOUN
ejpam-6841	42	11	)	)	PUNCT
ejpam-6841	42	12	)	)	PUNCT
ejpam-6841	43	1	=	=	PUNCT
ejpam-6841	43	2	ϑ(c	ϑ(c	PROPN
ejpam-6841	43	3	,	,	PUNCT
ejpam-6841	43	4	d	d	NOUN
ejpam-6841	43	5	)	)	PUNCT
ejpam-6841	43	6	because	because	SCONJ
ejpam-6841	43	7	the	the	DET
ejpam-6841	43	8	distance	distance	NOUN
ejpam-6841	43	9	between	between	ADP
ejpam-6841	43	10	any	any	DET
ejpam-6841	43	11	element	element	NOUN
ejpam-6841	43	12	b	b	NOUN
ejpam-6841	43	13	in	in	ADP
ejpam-6841	43	14	c	c	PROPN
ejpam-6841	43	15	and	and	CCONJ
ejpam-6841	43	16	its	its	PRON
ejpam-6841	43	17	image	image	NOUN
ejpam-6841	43	18	p(b	p(b	NOUN
ejpam-6841	43	19	)	)	PUNCT
ejpam-6841	43	20	in	in	ADP
ejpam-6841	43	21	d	d	NOUN
ejpam-6841	43	22	is	be	AUX
ejpam-6841	43	23	at	at	ADP
ejpam-6841	43	24	least	least	ADJ
ejpam-6841	43	25	the	the	DET
ejpam-6841	43	26	distance	distance	NOUN
ejpam-6841	43	27	between	between	ADP
ejpam-6841	43	28	the	the	DET
ejpam-6841	43	29	sets	set	NOUN
ejpam-6841	43	30	c	c	PROPN
ejpam-6841	43	31	and	and	CCONJ
ejpam-6841	43	32	d.	d.	PROPN
ejpam-6841	43	33	recently	recently	ADV
ejpam-6841	43	34	,	,	PUNCT
ejpam-6841	43	35	altun	altun	NOUN
ejpam-6841	43	36	and	and	CCONJ
ejpam-6841	43	37	taşdemir	taşdemir	NOUN
ejpam-6841	43	38	[	[	X
ejpam-6841	43	39	10	10	NUM
ejpam-6841	43	40	]	]	PUNCT
ejpam-6841	43	41	have	have	AUX
ejpam-6841	43	42	utilized	utilize	VERB
ejpam-6841	43	43	the	the	DET
ejpam-6841	43	44	interpolative	interpolative	ADJ
ejpam-6841	43	45	proximal	proximal	ADJ
ejpam-6841	43	46	contraction	contraction	NOUN
ejpam-6841	43	47	to	to	PART
ejpam-6841	43	48	produce	produce	VERB
ejpam-6841	43	49	some	some	DET
ejpam-6841	43	50	best	good	ADJ
ejpam-6841	43	51	proximity	proximity	NOUN
ejpam-6841	43	52	point	point	NOUN
ejpam-6841	43	53	theorems	theorem	NOUN
ejpam-6841	43	54	.	.	PUNCT
ejpam-6841	44	1	let	let	VERB
ejpam-6841	45	1	c	c	NOUN
ejpam-6841	46	1	and	and	CCONJ
ejpam-6841	46	2	d	d	AUX
ejpam-6841	46	3	be	be	AUX
ejpam-6841	46	4	metric	metric	ADJ
ejpam-6841	46	5	space	space	NOUN
ejpam-6841	46	6	subsets	subset	NOUN
ejpam-6841	46	7	that	that	PRON
ejpam-6841	46	8	are	be	AUX
ejpam-6841	46	9	non	non	ADJ
ejpam-6841	46	10	-	-	ADJ
ejpam-6841	46	11	empty	empty	ADJ
ejpam-6841	46	12	.	.	PUNCT
ejpam-6841	47	1	finding	find	VERB
ejpam-6841	47	2	an	an	DET
ejpam-6841	47	3	element	element	NOUN
ejpam-6841	47	4	b	b	NOUN
ejpam-6841	47	5	in	in	ADP
ejpam-6841	47	6	c	c	NOUN
ejpam-6841	47	7	that	that	PRON
ejpam-6841	47	8	is	be	AUX
ejpam-6841	47	9	as	as	ADV
ejpam-6841	47	10	close	close	ADJ
ejpam-6841	47	11	to	to	ADP
ejpam-6841	47	12	p(b	p(b	NOUN
ejpam-6841	47	13	)	)	PUNCT
ejpam-6841	47	14	in	in	ADP
ejpam-6841	47	15	d	d	PROPN
ejpam-6841	47	16	as	as	ADP
ejpam-6841	47	17	possible	possible	ADJ
ejpam-6841	47	18	,	,	PUNCT
ejpam-6841	47	19	is	be	AUX
ejpam-6841	47	20	of	of	ADP
ejpam-6841	47	21	great	great	ADJ
ejpam-6841	47	22	interest	interest	NOUN
ejpam-6841	47	23	,	,	PUNCT
ejpam-6841	47	24	since	since	SCONJ
ejpam-6841	47	25	a	a	DET
ejpam-6841	47	26	non	non	ADJ
ejpam-6841	47	27	-	-	ADJ
ejpam-6841	47	28	self	self	ADJ
ejpam-6841	47	29	mapping	mapping	NOUN
ejpam-6841	47	30	p	p	NOUN
ejpam-6841	47	31	:	:	PUNCT
ejpam-6841	47	32	c	c	X
ejpam-6841	47	33	→	→	PUNCT
ejpam-6841	47	34	d	d	NOUN
ejpam-6841	47	35	need	need	AUX
ejpam-6841	47	36	not	not	PART
ejpam-6841	47	37	have	have	AUX
ejpam-6841	47	38	a	a	DET
ejpam-6841	47	39	fixed	fix	VERB
ejpam-6841	47	40	point	point	NOUN
ejpam-6841	47	41	.	.	PUNCT
ejpam-6841	48	1	in	in	ADP
ejpam-6841	48	2	other	other	ADJ
ejpam-6841	48	3	words	word	NOUN
ejpam-6841	48	4	,	,	PUNCT
ejpam-6841	48	5	it	it	PRON
ejpam-6841	48	6	is	be	AUX
ejpam-6841	48	7	considered	consider	VERB
ejpam-6841	48	8	to	to	PART
ejpam-6841	48	9	find	find	VERB
ejpam-6841	48	10	an	an	DET
ejpam-6841	48	11	approximation	approximation	NOUN
ejpam-6841	48	12	solution	solution	NOUN
ejpam-6841	48	13	b	b	NOUN
ejpam-6841	48	14	in	in	ADP
ejpam-6841	48	15	c	c	PROPN
ejpam-6841	48	16	such	such	ADJ
ejpam-6841	48	17	that	that	SCONJ
ejpam-6841	48	18	the	the	DET
ejpam-6841	48	19	error	error	NOUN
ejpam-6841	48	20	ϑ(b	ϑ(b	VERB
ejpam-6841	48	21	,	,	PUNCT
ejpam-6841	48	22	p(b	p(b	PROPN
ejpam-6841	48	23	)	)	PUNCT
ejpam-6841	48	24	)	)	PUNCT
ejpam-6841	48	25	is	be	AUX
ejpam-6841	48	26	smallest	small	ADJ
ejpam-6841	48	27	,	,	PUNCT
ejpam-6841	48	28	where	where	SCONJ
ejpam-6841	48	29	ϑ	ϑ	PROPN
ejpam-6841	48	30	is	be	AUX
ejpam-6841	48	31	the	the	DET
ejpam-6841	48	32	distance	distance	NOUN
ejpam-6841	48	33	function	function	NOUN
ejpam-6841	48	34	,	,	PUNCT
ejpam-6841	48	35	if	if	SCONJ
ejpam-6841	48	36	the	the	DET
ejpam-6841	48	37	fixed	fix	VERB
ejpam-6841	48	38	point	point	NOUN
ejpam-6841	48	39	equation	equation	NOUN
ejpam-6841	48	40	p(b	p(b	NOUN
ejpam-6841	48	41	)	)	PUNCT
ejpam-6841	49	1	=	=	SYM
ejpam-6841	49	2	b	b	X
ejpam-6841	49	3	has	have	VERB
ejpam-6841	49	4	no	no	DET
ejpam-6841	49	5	exact	exact	ADJ
ejpam-6841	49	6	solution	solution	NOUN
ejpam-6841	49	7	.	.	PUNCT
ejpam-6841	50	1	in	in	ADP
ejpam-6841	50	2	fact	fact	NOUN
ejpam-6841	50	3	,	,	PUNCT
ejpam-6841	50	4	best	good	ADJ
ejpam-6841	50	5	proximity	proximity	NOUN
ejpam-6841	50	6	point	point	NOUN
ejpam-6841	50	7	theorems	theorem	NOUN
ejpam-6841	50	8	look	look	VERB
ejpam-6841	50	9	into	into	ADP
ejpam-6841	50	10	the	the	DET
ejpam-6841	50	11	possibility	possibility	NOUN
ejpam-6841	50	12	of	of	ADP
ejpam-6841	50	13	such	such	ADJ
ejpam-6841	50	14	best	good	ADJ
ejpam-6841	50	15	proximity	proximity	NOUN
ejpam-6841	50	16	point	point	NOUN
ejpam-6841	50	17	for	for	ADP
ejpam-6841	50	18	approximate	approximate	ADJ
ejpam-6841	50	19	solutions	solution	NOUN
ejpam-6841	50	20	to	to	ADP
ejpam-6841	50	21	the	the	DET
ejpam-6841	50	22	fixed	fix	VERB
ejpam-6841	50	23	point	point	NOUN
ejpam-6841	50	24	equation	equation	NOUN
ejpam-6841	50	25	p(b	p(b	NOUN
ejpam-6841	50	26	)	)	PUNCT
ejpam-6841	51	1	=	=	SYM
ejpam-6841	51	2	b	b	X
ejpam-6841	51	3	in	in	ADP
ejpam-6841	51	4	the	the	DET
ejpam-6841	51	5	absence	absence	NOUN
ejpam-6841	51	6	of	of	ADP
ejpam-6841	51	7	a	a	DET
ejpam-6841	51	8	precise	precise	ADJ
ejpam-6841	51	9	solution	solution	NOUN
ejpam-6841	51	10	.	.	PUNCT
ejpam-6841	52	1	in	in	ADP
ejpam-6841	52	2	order	order	NOUN
ejpam-6841	52	3	to	to	PART
ejpam-6841	52	4	produce	produce	VERB
ejpam-6841	52	5	global	global	ADJ
ejpam-6841	52	6	optimal	optimal	ADJ
ejpam-6841	52	7	approximate	approximate	ADJ
ejpam-6841	52	8	solutions	solution	NOUN
ejpam-6841	52	9	to	to	ADP
ejpam-6841	52	10	some	some	DET
ejpam-6841	52	11	fixed	fix	VERB
ejpam-6841	52	12	point	point	NOUN
ejpam-6841	52	13	equations	equation	NOUN
ejpam-6841	52	14	,	,	PUNCT
ejpam-6841	52	15	this	this	DET
ejpam-6841	52	16	article	article	NOUN
ejpam-6841	52	17	aims	aim	VERB
ejpam-6841	52	18	to	to	PART
ejpam-6841	52	19	establish	establish	VERB
ejpam-6841	52	20	best	good	ADJ
ejpam-6841	52	21	proximity	proximity	NOUN
ejpam-6841	52	22	point	point	NOUN
ejpam-6841	52	23	theorems	theorem	NOUN
ejpam-6841	52	24	for	for	ADP
ejpam-6841	52	25	contractive	contractive	ADJ
ejpam-6841	52	26	non	non	ADJ
ejpam-6841	52	27	-	-	ADJ
ejpam-6841	52	28	self	self	ADJ
ejpam-6841	52	29	mappings	mapping	NOUN
ejpam-6841	52	30	via	via	ADP
ejpam-6841	52	31	interpolation	interpolation	NOUN
ejpam-6841	52	32	.	.	PUNCT
ejpam-6841	53	1	iterative	iterative	NOUN
ejpam-6841	53	2	strategies	strategy	NOUN
ejpam-6841	53	3	are	be	AUX
ejpam-6841	53	4	also	also	ADV
ejpam-6841	53	5	provided	provide	VERB
ejpam-6841	53	6	to	to	PART
ejpam-6841	53	7	find	find	VERB
ejpam-6841	53	8	such	such	ADJ
ejpam-6841	53	9	ideal	ideal	ADJ
ejpam-6841	53	10	approximative	approximative	ADJ
ejpam-6841	53	11	solutions	solution	NOUN
ejpam-6841	53	12	in	in	ADP
ejpam-6841	53	13	addition	addition	NOUN
ejpam-6841	53	14	to	to	ADP
ejpam-6841	53	15	proving	prove	VERB
ejpam-6841	53	16	the	the	DET
ejpam-6841	53	17	presence	presence	NOUN
ejpam-6841	53	18	of	of	ADP
ejpam-6841	53	19	best	good	ADJ
ejpam-6841	53	20	proximity	proximity	NOUN
ejpam-6841	53	21	points	point	NOUN
ejpam-6841	53	22	.	.	PUNCT
ejpam-6841	54	1	also	also	ADV
ejpam-6841	54	2	,	,	PUNCT
ejpam-6841	54	3	we	we	PRON
ejpam-6841	54	4	extend	extend	VERB
ejpam-6841	54	5	the	the	DET
ejpam-6841	54	6	results	result	NOUN
ejpam-6841	54	7	appeared	appear	VERB
ejpam-6841	54	8	in	in	ADP
ejpam-6841	54	9	[	[	X
ejpam-6841	54	10	8	8	NUM
ejpam-6841	54	11	,	,	PUNCT
ejpam-6841	54	12	10	10	NUM
ejpam-6841	54	13	]	]	PUNCT
ejpam-6841	54	14	by	by	ADP
ejpam-6841	54	15	introducing	introduce	VERB
ejpam-6841	54	16	(	(	PUNCT
ejpam-6841	54	17	j,£)-interpolative	j,£)-interpolative	ADJ
ejpam-6841	54	18	proximal	proximal	ADJ
ejpam-6841	54	19	contractions	contraction	NOUN
ejpam-6841	54	20	,	,	PUNCT
ejpam-6841	54	21	which	which	PRON
ejpam-6841	54	22	generalize	generalize	VERB
ejpam-6841	54	23	and	and	CCONJ
ejpam-6841	54	24	establishing	establish	VERB
ejpam-6841	54	25	the	the	DET
ejpam-6841	54	26	optimal	optimal	ADJ
ejpam-6841	54	27	proximity	proximity	NOUN
ejpam-6841	54	28	point	point	NOUN
ejpam-6841	54	29	theorems	theorem	NOUN
ejpam-6841	54	30	for	for	ADP
ejpam-6841	54	31	them	they	PRON
ejpam-6841	54	32	.	.	PUNCT
ejpam-6841	55	1	to	to	PART
ejpam-6841	55	2	ascertain	ascertain	VERB
ejpam-6841	55	3	the	the	DET
ejpam-6841	55	4	generalized	generalized	ADJ
ejpam-6841	55	5	interpolative	interpolative	ADJ
ejpam-6841	55	6	proximal	proximal	ADJ
ejpam-6841	55	7	contractions	contraction	NOUN
ejpam-6841	55	8	that	that	PRON
ejpam-6841	55	9	produce	produce	VERB
ejpam-6841	55	10	interpolative	interpolative	ADJ
ejpam-6841	55	11	proximal	proximal	ADJ
ejpam-6841	55	12	contractions	contraction	NOUN
ejpam-6841	55	13	and	and	CCONJ
ejpam-6841	55	14	proximal	proximal	ADJ
ejpam-6841	55	15	contractions	contraction	NOUN
ejpam-6841	55	16	as	as	ADP
ejpam-6841	55	17	special	special	ADJ
ejpam-6841	55	18	cases	case	NOUN
ejpam-6841	55	19	.	.	PUNCT
ejpam-6841	56	1	we	we	PRON
ejpam-6841	56	2	extend	extend	VERB
ejpam-6841	56	3	classical	classical	ADJ
ejpam-6841	56	4	fixed	fix	VERB
ejpam-6841	56	5	point	point	NOUN
ejpam-6841	56	6	results	result	NOUN
ejpam-6841	56	7	by	by	ADP
ejpam-6841	56	8	considering	consider	VERB
ejpam-6841	56	9	a	a	DET
ejpam-6841	56	10	generalized	generalized	ADJ
ejpam-6841	56	11	class	class	NOUN
ejpam-6841	56	12	of	of	ADP
ejpam-6841	56	13	contractions	contraction	NOUN
ejpam-6841	56	14	known	know	VERB
ejpam-6841	56	15	as	as	ADP
ejpam-6841	56	16	generalized	generalize	VERB
ejpam-6841	56	17	interpolative	interpolative	ADJ
ejpam-6841	56	18	proximal	proximal	ADJ
ejpam-6841	56	19	contractions	contraction	NOUN
ejpam-6841	56	20	and	and	CCONJ
ejpam-6841	56	21	provide	provide	VERB
ejpam-6841	56	22	conditions	condition	NOUN
ejpam-6841	56	23	under	under	ADP
ejpam-6841	56	24	which	which	PRON
ejpam-6841	56	25	best	good	ADJ
ejpam-6841	56	26	proximity	proximity	NOUN
ejpam-6841	56	27	points	point	NOUN
ejpam-6841	56	28	are	be	AUX
ejpam-6841	56	29	guaranteed	guarantee	VERB
ejpam-6841	56	30	.	.	PUNCT
ejpam-6841	57	1	the	the	DET
ejpam-6841	57	2	interpolative	interpolative	ADJ
ejpam-6841	57	3	proximal	proximal	ADJ
ejpam-6841	57	4	contraction	contraction	NOUN
ejpam-6841	57	5	introduced	introduce	VERB
ejpam-6841	57	6	in	in	ADP
ejpam-6841	57	7	[	[	X
ejpam-6841	57	8	10	10	NUM
ejpam-6841	57	9	]	]	PUNCT
ejpam-6841	57	10	are	be	AUX
ejpam-6841	57	11	generalized	generalize	VERB
ejpam-6841	57	12	by	by	ADP
ejpam-6841	57	13	the	the	DET
ejpam-6841	57	14	(	(	PUNCT
ejpam-6841	57	15	j,£)-interpolative	j,£)-interpolative	ADJ
ejpam-6841	57	16	proximal	proximal	ADJ
ejpam-6841	57	17	contraction	contraction	NOUN
ejpam-6841	57	18	.	.	PUNCT
ejpam-6841	58	1	we	we	PRON
ejpam-6841	58	2	look	look	VERB
ejpam-6841	58	3	for	for	ADP
ejpam-6841	58	4	various	various	ADJ
ejpam-6841	58	5	conditions	condition	NOUN
ejpam-6841	58	6	on	on	ADP
ejpam-6841	58	7	the	the	DET
ejpam-6841	58	8	functions	function	NOUN
ejpam-6841	58	9	j,£	j,£	ADJ
ejpam-6841	58	10	to	to	PART
ejpam-6841	58	11	prove	prove	VERB
ejpam-6841	58	12	the	the	DET
ejpam-6841	58	13	presence	presence	NOUN
ejpam-6841	58	14	of	of	ADP
ejpam-6841	58	15	best	good	ADJ
ejpam-6841	58	16	proximity	proximity	NOUN
ejpam-6841	58	17	points	point	NOUN
ejpam-6841	58	18	of	of	ADP
ejpam-6841	58	19	(	(	PUNCT
ejpam-6841	58	20	j,£)-proximal	j,£)-proximal	ADJ
ejpam-6841	58	21	contraction	contraction	NOUN
ejpam-6841	58	22	,	,	PUNCT
ejpam-6841	58	23	(	(	PUNCT
ejpam-6841	58	24	j,£)-ćirić	j,£)-ćirić	PROPN
ejpam-6841	58	25	-	-	PUNCT
ejpam-6841	58	26	reich	reich	NOUN
ejpam-6841	58	27	-	-	PUNCT
ejpam-6841	58	28	rus	rus	NOUN
ejpam-6841	58	29	type	type	NOUN
ejpam-6841	58	30	interpolative	interpolative	ADJ
ejpam-6841	58	31	proximal	proximal	ADJ
ejpam-6841	58	32	contraction	contraction	NOUN
ejpam-6841	58	33	,	,	PUNCT
ejpam-6841	58	34	(	(	PUNCT
ejpam-6841	58	35	j,£)-hardy	j,£)-hardy	PROPN
ejpam-6841	58	36	rogers	rogers	PROPN
ejpam-6841	58	37	type	type	VERB
ejpam-6841	58	38	interpolative	interpolative	ADJ
ejpam-6841	58	39	proximal	proximal	ADJ
ejpam-6841	58	40	contraction	contraction	NOUN
ejpam-6841	58	41	.	.	PUNCT
ejpam-6841	59	1	we	we	PRON
ejpam-6841	59	2	also	also	ADV
ejpam-6841	59	3	show	show	VERB
ejpam-6841	59	4	non	non	ADJ
ejpam-6841	59	5	-	-	ADJ
ejpam-6841	59	6	trivial	trivial	ADJ
ejpam-6841	59	7	examples	example	NOUN
ejpam-6841	59	8	and	and	CCONJ
ejpam-6841	59	9	applications	application	NOUN
ejpam-6841	59	10	are	be	AUX
ejpam-6841	59	11	given	give	VERB
ejpam-6841	59	12	to	to	PART
ejpam-6841	59	13	demonstrate	demonstrate	VERB
ejpam-6841	59	14	the	the	DET
ejpam-6841	59	15	usefulness	usefulness	NOUN
ejpam-6841	59	16	of	of	ADP
ejpam-6841	59	17	our	our	PRON
ejpam-6841	59	18	results	result	NOUN
ejpam-6841	59	19	.	.	PUNCT
ejpam-6841	60	1	the	the	DET
ejpam-6841	60	2	structure	structure	NOUN
ejpam-6841	60	3	of	of	ADP
ejpam-6841	60	4	the	the	DET
ejpam-6841	60	5	paper	paper	NOUN
ejpam-6841	60	6	is	be	AUX
ejpam-6841	60	7	as	as	SCONJ
ejpam-6841	60	8	follows	follow	VERB
ejpam-6841	60	9	:	:	PUNCT
ejpam-6841	60	10	we	we	PRON
ejpam-6841	60	11	begin	begin	VERB
ejpam-6841	60	12	by	by	ADP
ejpam-6841	60	13	reviewing	review	VERB
ejpam-6841	60	14	key	key	ADJ
ejpam-6841	60	15	concepts	concept	NOUN
ejpam-6841	60	16	and	and	CCONJ
ejpam-6841	60	17	preliminary	preliminary	ADJ
ejpam-6841	60	18	results	result	NOUN
ejpam-6841	60	19	related	relate	VERB
ejpam-6841	60	20	to	to	ADP
ejpam-6841	60	21	proximal	proximal	ADJ
ejpam-6841	60	22	contractions	contraction	NOUN
ejpam-6841	60	23	and	and	CCONJ
ejpam-6841	60	24	best	good	ADJ
ejpam-6841	60	25	proximity	proximity	NOUN
ejpam-6841	60	26	points	point	NOUN
ejpam-6841	60	27	.	.	PUNCT
ejpam-6841	61	1	we	we	PRON
ejpam-6841	61	2	then	then	ADV
ejpam-6841	61	3	introduce	introduce	VERB
ejpam-6841	61	4	the	the	DET
ejpam-6841	61	5	concept	concept	NOUN
ejpam-6841	61	6	of	of	ADP
ejpam-6841	61	7	generalized	generalized	ADJ
ejpam-6841	61	8	interpolative	interpolative	ADJ
ejpam-6841	61	9	proximal	proximal	ADJ
ejpam-6841	61	10	contractions	contraction	NOUN
ejpam-6841	61	11	and	and	CCONJ
ejpam-6841	61	12	establish	establish	VERB
ejpam-6841	61	13	the	the	DET
ejpam-6841	61	14	necessary	necessary	ADJ
ejpam-6841	61	15	theoretical	theoretical	ADJ
ejpam-6841	61	16	foundations	foundation	NOUN
ejpam-6841	61	17	.	.	PUNCT
ejpam-6841	62	1	subsequent	subsequent	ADJ
ejpam-6841	62	2	sections	section	NOUN
ejpam-6841	62	3	are	be	AUX
ejpam-6841	62	4	dedicated	dedicate	VERB
ejpam-6841	62	5	to	to	ADP
ejpam-6841	62	6	proving	prove	VERB
ejpam-6841	62	7	essential	essential	ADJ
ejpam-6841	62	8	theorems	theorem	NOUN
ejpam-6841	62	9	and	and	CCONJ
ejpam-6841	62	10	demonstrating	demonstrate	VERB
ejpam-6841	62	11	their	their	PRON
ejpam-6841	62	12	practical	practical	ADJ
ejpam-6841	62	13	implications	implication	NOUN
ejpam-6841	62	14	through	through	ADP
ejpam-6841	62	15	detailed	detailed	ADJ
ejpam-6841	62	16	examples	example	NOUN
ejpam-6841	62	17	.	.	PUNCT
ejpam-6841	63	1	finally	finally	ADV
ejpam-6841	63	2	,	,	PUNCT
ejpam-6841	63	3	we	we	PRON
ejpam-6841	63	4	explore	explore	VERB
ejpam-6841	63	5	applications	application	NOUN
ejpam-6841	63	6	of	of	ADP
ejpam-6841	63	7	our	our	PRON
ejpam-6841	63	8	findings	finding	NOUN
ejpam-6841	63	9	in	in	ADP
ejpam-6841	63	10	optimization	optimization	NOUN
ejpam-6841	63	11	and	and	CCONJ
ejpam-6841	63	12	equilibrium	equilibrium	NOUN
ejpam-6841	63	13	problems	problem	NOUN
ejpam-6841	63	14	,	,	PUNCT
ejpam-6841	63	15	showcasing	showcase	VERB
ejpam-6841	63	16	the	the	DET
ejpam-6841	63	17	practical	practical	ADJ
ejpam-6841	63	18	significance	significance	NOUN
ejpam-6841	63	19	and	and	CCONJ
ejpam-6841	63	20	potential	potential	ADJ
ejpam-6841	63	21	impact	impact	NOUN
ejpam-6841	63	22	of	of	ADP
ejpam-6841	63	23	our	our	PRON
ejpam-6841	63	24	research	research	NOUN
ejpam-6841	63	25	.	.	PUNCT
ejpam-6841	64	1	by	by	ADP
ejpam-6841	64	2	advancing	advance	VERB
ejpam-6841	64	3	the	the	DET
ejpam-6841	64	4	theoretical	theoretical	ADJ
ejpam-6841	64	5	framework	framework	NOUN
ejpam-6841	64	6	of	of	ADP
ejpam-6841	64	7	best	good	ADJ
ejpam-6841	64	8	proximity	proximity	NOUN
ejpam-6841	64	9	points	point	NOUN
ejpam-6841	64	10	and	and	CCONJ
ejpam-6841	64	11	providing	provide	VERB
ejpam-6841	64	12	practical	practical	ADJ
ejpam-6841	64	13	solutions	solution	NOUN
ejpam-6841	64	14	to	to	ADP
ejpam-6841	64	15	complex	complex	ADJ
ejpam-6841	64	16	problems	problem	NOUN
ejpam-6841	64	17	,	,	PUNCT
ejpam-6841	64	18	this	this	DET
ejpam-6841	64	19	paper	paper	NOUN
ejpam-6841	64	20	aims	aim	VERB
ejpam-6841	64	21	to	to	PART
ejpam-6841	64	22	contribute	contribute	VERB
ejpam-6841	64	23	to	to	ADP
ejpam-6841	64	24	both	both	DET
ejpam-6841	64	25	the	the	DET
ejpam-6841	64	26	academic	academic	ADJ
ejpam-6841	64	27	literature	literature	NOUN
ejpam-6841	64	28	and	and	CCONJ
ejpam-6841	64	29	real	real	ADJ
ejpam-6841	64	30	-	-	PUNCT
ejpam-6841	64	31	world	world	NOUN
ejpam-6841	64	32	applications	application	NOUN
ejpam-6841	64	33	.	.	PUNCT
ejpam-6841	65	1	k.	k.	PROPN
ejpam-6841	65	2	javed	javed	PROPN
ejpam-6841	65	3	,	,	PUNCT
ejpam-6841	65	4	m.	m.	NOUN
ejpam-6841	65	5	nazam	nazam	PROPN
ejpam-6841	65	6	,	,	PUNCT
ejpam-6841	65	7	m.	m.	PROPN
ejpam-6841	65	8	arshad	arshad	PROPN
ejpam-6841	65	9	,	,	PUNCT
ejpam-6841	65	10	m.	m.	NOUN
ejpam-6841	65	11	de	de	X
ejpam-6841	65	12	la	la	PROPN
ejpam-6841	65	13	sen	sen	PROPN
ejpam-6841	65	14	/	/	SYM
ejpam-6841	65	15	eur	eur	PROPN
ejpam-6841	65	16	.	.	PUNCT
ejpam-6841	66	1	j.	j.	PROPN
ejpam-6841	66	2	pure	pure	PROPN
ejpam-6841	66	3	appl	appl	PROPN
ejpam-6841	66	4	.	.	PROPN
ejpam-6841	66	5	math	math	PROPN
ejpam-6841	66	6	,	,	PUNCT
ejpam-6841	66	7	18	18	NUM
ejpam-6841	66	8	(	(	PUNCT
ejpam-6841	66	9	4	4	NUM
ejpam-6841	66	10	)	)	PUNCT
ejpam-6841	66	11	(	(	PUNCT
ejpam-6841	66	12	2025	2025	NUM
ejpam-6841	66	13	)	)	PUNCT
ejpam-6841	66	14	,	,	PUNCT
ejpam-6841	66	15	6841	6841	NUM
ejpam-6841	66	16	4	4	NUM
ejpam-6841	66	17	of	of	ADP
ejpam-6841	66	18	23	23	NUM
ejpam-6841	66	19	2	2	NUM
ejpam-6841	66	20	.	.	PUNCT
ejpam-6841	67	1	preliminaries	preliminary	NOUN
ejpam-6841	67	2	let	let	VERB
ejpam-6841	67	3	(	(	PUNCT
ejpam-6841	67	4	w	w	NOUN
ejpam-6841	67	5	,	,	PUNCT
ejpam-6841	67	6	ϑ	ϑ	NOUN
ejpam-6841	67	7	)	)	PUNCT
ejpam-6841	67	8	be	be	AUX
ejpam-6841	67	9	a	a	DET
ejpam-6841	67	10	metric	metric	ADJ
ejpam-6841	67	11	space	space	NOUN
ejpam-6841	67	12	and	and	CCONJ
ejpam-6841	67	13	c	c	NOUN
ejpam-6841	67	14	,	,	PUNCT
ejpam-6841	67	15	d	d	X
ejpam-6841	67	16	be	be	AUX
ejpam-6841	67	17	two	two	NUM
ejpam-6841	67	18	subsets	subset	NOUN
ejpam-6841	67	19	of	of	ADP
ejpam-6841	67	20	(	(	PUNCT
ejpam-6841	67	21	w	w	PROPN
ejpam-6841	67	22	,	,	PUNCT
ejpam-6841	67	23	ϑ	ϑ	NOUN
ejpam-6841	67	24	)	)	PUNCT
ejpam-6841	67	25	.	.	PUNCT
ejpam-6841	68	1	the	the	DET
ejpam-6841	68	2	following	follow	VERB
ejpam-6841	68	3	information	information	NOUN
ejpam-6841	68	4	is	be	AUX
ejpam-6841	68	5	needed	need	VERB
ejpam-6841	68	6	throughout	throughout	ADP
ejpam-6841	68	7	this	this	DET
ejpam-6841	68	8	paper	paper	NOUN
ejpam-6841	68	9	.	.	PUNCT
ejpam-6841	69	1	ϑ(c	ϑ(c	NOUN
ejpam-6841	69	2	,	,	PUNCT
ejpam-6841	69	3	d	d	NOUN
ejpam-6841	69	4	)	)	PUNCT
ejpam-6841	69	5	=	=	SYM
ejpam-6841	69	6	inf{ϑ(b	inf{ϑ(b	PROPN
ejpam-6841	69	7	,	,	PUNCT
ejpam-6841	69	8	m	m	NOUN
ejpam-6841	69	9	)	)	PUNCT
ejpam-6841	69	10	:	:	PUNCT
ejpam-6841	69	11	b	b	X
ejpam-6841	69	12	∈	∈	NOUN
ejpam-6841	69	13	c	c	X
ejpam-6841	69	14	∧m	∧m	PROPN
ejpam-6841	69	15	∈	∈	PROPN
ejpam-6841	69	16	d	d	NOUN
ejpam-6841	69	17	}	}	PUNCT
ejpam-6841	69	18	.	.	PUNCT
ejpam-6841	70	1	c0	c0	PROPN
ejpam-6841	70	2	=	=	PUNCT
ejpam-6841	70	3	{	{	PUNCT
ejpam-6841	70	4	b	b	PROPN
ejpam-6841	70	5	∈	∈	PROPN
ejpam-6841	70	6	c	c	NOUN
ejpam-6841	70	7	:	:	PUNCT
ejpam-6841	70	8	ϑ(b	ϑ(b	PROPN
ejpam-6841	70	9	,	,	PUNCT
ejpam-6841	70	10	m	m	NOUN
ejpam-6841	70	11	)	)	PUNCT
ejpam-6841	70	12	=	=	PUNCT
ejpam-6841	70	13	ϑ(c	ϑ(c	PROPN
ejpam-6841	70	14	,	,	PUNCT
ejpam-6841	70	15	d	d	NOUN
ejpam-6841	70	16	)	)	PUNCT
ejpam-6841	70	17	for	for	ADP
ejpam-6841	70	18	some	some	DET
ejpam-6841	70	19	m	m	NOUN
ejpam-6841	70	20	∈	∈	NOUN
ejpam-6841	70	21	d	d	NOUN
ejpam-6841	70	22	}	}	PUNCT
ejpam-6841	70	23	.	.	PUNCT
ejpam-6841	71	1	d0	d0	PROPN
ejpam-6841	71	2	=	=	SYM
ejpam-6841	71	3	{	{	PUNCT
ejpam-6841	71	4	m	m	NOUN
ejpam-6841	71	5	∈	∈	PROPN
ejpam-6841	71	6	d	d	NOUN
ejpam-6841	71	7	:	:	PUNCT
ejpam-6841	71	8	ϑ(b	ϑ(b	PROPN
ejpam-6841	71	9	,	,	PUNCT
ejpam-6841	71	10	m	m	NOUN
ejpam-6841	71	11	)	)	PUNCT
ejpam-6841	72	1	=	=	PUNCT
ejpam-6841	72	2	ϑ(c	ϑ(c	PROPN
ejpam-6841	72	3	,	,	PUNCT
ejpam-6841	72	4	d	d	NOUN
ejpam-6841	72	5	)	)	PUNCT
ejpam-6841	72	6	for	for	ADP
ejpam-6841	72	7	some	some	DET
ejpam-6841	72	8	b	b	NOUN
ejpam-6841	72	9	∈	∈	PROPN
ejpam-6841	72	10	c	c	NOUN
ejpam-6841	72	11	}	}	PUNCT
ejpam-6841	72	12	.	.	PUNCT
ejpam-6841	73	1	definition	definition	NOUN
ejpam-6841	73	2	1	1	NUM
ejpam-6841	73	3	.	.	PUNCT
ejpam-6841	74	1	[	[	X
ejpam-6841	74	2	11	11	NUM
ejpam-6841	74	3	]	]	X
ejpam-6841	74	4	let	let	AUX
ejpam-6841	74	5	(	(	PUNCT
ejpam-6841	74	6	w	w	NOUN
ejpam-6841	74	7	,	,	PUNCT
ejpam-6841	74	8	ϑ	ϑ	NOUN
ejpam-6841	74	9	)	)	PUNCT
ejpam-6841	74	10	be	be	AUX
ejpam-6841	74	11	a	a	DET
ejpam-6841	74	12	metric	metric	ADJ
ejpam-6841	74	13	space	space	NOUN
ejpam-6841	74	14	and	and	CCONJ
ejpam-6841	74	15	c	c	NOUN
ejpam-6841	74	16	,	,	PUNCT
ejpam-6841	74	17	d	d	X
ejpam-6841	74	18	be	be	AUX
ejpam-6841	74	19	any	any	DET
ejpam-6841	74	20	nonvoid	nonvoid	ADJ
ejpam-6841	74	21	subsets	subset	NOUN
ejpam-6841	74	22	of	of	ADP
ejpam-6841	74	23	w.	w.	PROPN
ejpam-6841	75	1	a	a	DET
ejpam-6841	75	2	mapping	mapping	NOUN
ejpam-6841	75	3	p	p	X
ejpam-6841	75	4	:	:	PUNCT
ejpam-6841	75	5	c	c	X
ejpam-6841	75	6	→	→	PUNCT
ejpam-6841	75	7	d	d	NOUN
ejpam-6841	75	8	is	be	AUX
ejpam-6841	75	9	said	say	VERB
ejpam-6841	75	10	to	to	PART
ejpam-6841	75	11	be	be	AUX
ejpam-6841	75	12	a	a	DET
ejpam-6841	75	13	proximal	proximal	ADJ
ejpam-6841	75	14	contraction	contraction	NOUN
ejpam-6841	75	15	,	,	PUNCT
ejpam-6841	75	16	if	if	SCONJ
ejpam-6841	75	17	there	there	PRON
ejpam-6841	75	18	exists	exist	VERB
ejpam-6841	75	19	a	a	DET
ejpam-6841	75	20	real	real	ADJ
ejpam-6841	75	21	number	number	NOUN
ejpam-6841	75	22	k	k	PROPN
ejpam-6841	75	23	∈	∈	PROPN
ejpam-6841	76	1	[	[	X
ejpam-6841	76	2	0	0	NUM
ejpam-6841	76	3	,	,	PUNCT
ejpam-6841	76	4	1	1	NUM
ejpam-6841	76	5	)	)	PUNCT
ejpam-6841	76	6	such	such	ADJ
ejpam-6841	76	7	that	that	SCONJ
ejpam-6841	76	8	ϑ(b1,p(m1	ϑ(b1,p(m1	NOUN
ejpam-6841	76	9	)	)	PUNCT
ejpam-6841	76	10	)	)	PUNCT
ejpam-6841	77	1	=	=	SYM
ejpam-6841	77	2	ϑ	ϑ	X
ejpam-6841	77	3	(	(	PUNCT
ejpam-6841	77	4	c	c	X
ejpam-6841	77	5	,	,	PUNCT
ejpam-6841	77	6	d	d	NOUN
ejpam-6841	77	7	)	)	PUNCT
ejpam-6841	77	8	ϑ(b2,p(m2	ϑ(b2,p(m2	NOUN
ejpam-6841	77	9	)	)	PUNCT
ejpam-6841	77	10	)	)	PUNCT
ejpam-6841	78	1	=	=	SYM
ejpam-6841	78	2	ϑ	ϑ	X
ejpam-6841	78	3	(	(	PUNCT
ejpam-6841	78	4	c	c	X
ejpam-6841	78	5	,	,	PUNCT
ejpam-6841	78	6	d	d	NOUN
ejpam-6841	78	7	)	)	PUNCT
ejpam-6841	78	8	}	}	PUNCT
ejpam-6841	78	9	⇒	⇒	PROPN
ejpam-6841	78	10	ϑ(b1	ϑ(b1	VERB
ejpam-6841	78	11	,	,	PUNCT
ejpam-6841	78	12	b2	b2	NOUN
ejpam-6841	78	13	)	)	PUNCT
ejpam-6841	78	14	≤	≤	NUM
ejpam-6841	78	15	kϑ	kϑ	NOUN
ejpam-6841	78	16	(	(	PUNCT
ejpam-6841	78	17	m1,m2	m1,m2	PROPN
ejpam-6841	78	18	)	)	PUNCT
ejpam-6841	78	19	for	for	ADP
ejpam-6841	78	20	all	all	DET
ejpam-6841	78	21	b1	b1	NOUN
ejpam-6841	78	22	,	,	PUNCT
ejpam-6841	78	23	b2,m1,m2	b2,m1,m2	NOUN
ejpam-6841	78	24	∈	∈	PROPN
ejpam-6841	78	25	c	c	PROPN
ejpam-6841	78	26	and	and	CCONJ
ejpam-6841	78	27	b1	b1	PROPN
ejpam-6841	78	28	6=	6=	PROPN
ejpam-6841	78	29	b2	b2	NOUN
ejpam-6841	78	30	.	.	PUNCT
ejpam-6841	79	1	it	it	PRON
ejpam-6841	79	2	is	be	AUX
ejpam-6841	79	3	easy	easy	ADJ
ejpam-6841	79	4	to	to	PART
ejpam-6841	79	5	observe	observe	VERB
ejpam-6841	79	6	that	that	SCONJ
ejpam-6841	79	7	a	a	DET
ejpam-6841	79	8	self	self	NOUN
ejpam-6841	79	9	-	-	PUNCT
ejpam-6841	79	10	mapping	mapping	NOUN
ejpam-6841	79	11	that	that	PRON
ejpam-6841	79	12	is	be	AUX
ejpam-6841	79	13	a	a	DET
ejpam-6841	79	14	proximal	proximal	ADJ
ejpam-6841	79	15	contraction	contraction	NOUN
ejpam-6841	79	16	of	of	ADP
ejpam-6841	79	17	the	the	DET
ejpam-6841	79	18	first	first	ADJ
ejpam-6841	79	19	kind	kind	NOUN
ejpam-6841	79	20	reduces	reduce	VERB
ejpam-6841	79	21	to	to	ADP
ejpam-6841	79	22	a	a	DET
ejpam-6841	79	23	contraction	contraction	NOUN
ejpam-6841	79	24	.	.	PUNCT
ejpam-6841	80	1	definition	definition	NOUN
ejpam-6841	80	2	2	2	NUM
ejpam-6841	80	3	.	.	PUNCT
ejpam-6841	81	1	[	[	X
ejpam-6841	81	2	11	11	NUM
ejpam-6841	81	3	]	]	X
ejpam-6841	81	4	let	let	AUX
ejpam-6841	81	5	(	(	PUNCT
ejpam-6841	81	6	w	w	NOUN
ejpam-6841	81	7	,	,	PUNCT
ejpam-6841	81	8	ϑ	ϑ	NOUN
ejpam-6841	81	9	)	)	PUNCT
ejpam-6841	81	10	be	be	AUX
ejpam-6841	81	11	a	a	DET
ejpam-6841	81	12	metric	metric	ADJ
ejpam-6841	81	13	space	space	NOUN
ejpam-6841	81	14	and	and	CCONJ
ejpam-6841	81	15	c	c	NOUN
ejpam-6841	81	16	,	,	PUNCT
ejpam-6841	81	17	d	d	X
ejpam-6841	81	18	be	be	AUX
ejpam-6841	81	19	any	any	DET
ejpam-6841	81	20	nonvoid	nonvoid	ADJ
ejpam-6841	81	21	subsets	subset	NOUN
ejpam-6841	81	22	of	of	ADP
ejpam-6841	81	23	w.	w.	PROPN
ejpam-6841	82	1	a	a	DET
ejpam-6841	82	2	mapping	mapping	NOUN
ejpam-6841	82	3	p	p	X
ejpam-6841	82	4	:	:	PUNCT
ejpam-6841	82	5	c	c	X
ejpam-6841	82	6	→	→	PUNCT
ejpam-6841	82	7	d	d	NOUN
ejpam-6841	82	8	is	be	AUX
ejpam-6841	82	9	said	say	VERB
ejpam-6841	82	10	to	to	PART
ejpam-6841	82	11	be	be	AUX
ejpam-6841	82	12	a	a	DET
ejpam-6841	82	13	proximal	proximal	ADJ
ejpam-6841	82	14	contraction	contraction	NOUN
ejpam-6841	82	15	of	of	ADP
ejpam-6841	82	16	second	second	ADJ
ejpam-6841	82	17	kind	kind	NOUN
ejpam-6841	82	18	,	,	PUNCT
ejpam-6841	82	19	if	if	SCONJ
ejpam-6841	82	20	there	there	PRON
ejpam-6841	82	21	exists	exist	VERB
ejpam-6841	82	22	a	a	DET
ejpam-6841	82	23	real	real	ADJ
ejpam-6841	82	24	number	number	NOUN
ejpam-6841	82	25	k	k	PROPN
ejpam-6841	82	26	∈	∈	PROPN
ejpam-6841	83	1	[	[	X
ejpam-6841	83	2	0	0	NUM
ejpam-6841	83	3	,	,	PUNCT
ejpam-6841	83	4	1	1	NUM
ejpam-6841	83	5	)	)	PUNCT
ejpam-6841	83	6	such	such	ADJ
ejpam-6841	83	7	that	that	SCONJ
ejpam-6841	83	8	ϑ(b1,p(m1	ϑ(b1,p(m1	NOUN
ejpam-6841	83	9	)	)	PUNCT
ejpam-6841	83	10	)	)	PUNCT
ejpam-6841	84	1	=	=	SYM
ejpam-6841	84	2	ϑ	ϑ	X
ejpam-6841	84	3	(	(	PUNCT
ejpam-6841	84	4	c	c	X
ejpam-6841	84	5	,	,	PUNCT
ejpam-6841	84	6	d	d	NOUN
ejpam-6841	84	7	)	)	PUNCT
ejpam-6841	84	8	ϑ(b2,p(m2	ϑ(b2,p(m2	NOUN
ejpam-6841	84	9	)	)	PUNCT
ejpam-6841	84	10	)	)	PUNCT
ejpam-6841	85	1	=	=	SYM
ejpam-6841	85	2	ϑ	ϑ	X
ejpam-6841	85	3	(	(	PUNCT
ejpam-6841	85	4	c	c	X
ejpam-6841	85	5	,	,	PUNCT
ejpam-6841	85	6	d	d	NOUN
ejpam-6841	85	7	)	)	PUNCT
ejpam-6841	85	8	}	}	PUNCT
ejpam-6841	85	9	⇒	⇒	VERB
ejpam-6841	85	10	ϑ	ϑ	X
ejpam-6841	85	11	(	(	PUNCT
ejpam-6841	85	12	pb1,pb2	pb1,pb2	PROPN
ejpam-6841	85	13	)	)	PUNCT
ejpam-6841	85	14	≤	≤	NUM
ejpam-6841	85	15	kϑ	kϑ	NOUN
ejpam-6841	85	16	(	(	PUNCT
ejpam-6841	85	17	pm1,pm2	pm1,pm2	PROPN
ejpam-6841	85	18	)	)	PUNCT
ejpam-6841	85	19	for	for	ADP
ejpam-6841	85	20	all	all	DET
ejpam-6841	85	21	b1	b1	NOUN
ejpam-6841	85	22	,	,	PUNCT
ejpam-6841	85	23	b2,m1,m2	b2,m1,m2	NOUN
ejpam-6841	85	24	∈	∈	PROPN
ejpam-6841	85	25	c	c	NOUN
ejpam-6841	85	26	and	and	CCONJ
ejpam-6841	85	27	pb1	pb1	PROPN
ejpam-6841	85	28	6=	6=	PROPN
ejpam-6841	85	29	pb2	pb2	PROPN
ejpam-6841	85	30	.	.	PUNCT
ejpam-6841	86	1	for	for	ADP
ejpam-6841	86	2	a	a	DET
ejpam-6841	86	3	self	self	NOUN
ejpam-6841	86	4	-	-	PUNCT
ejpam-6841	86	5	mapping	mapping	NOUN
ejpam-6841	86	6	p	p	NOUN
ejpam-6841	86	7	:	:	PUNCT
ejpam-6841	86	8	c	c	X
ejpam-6841	86	9	→	→	SYM
ejpam-6841	86	10	c	c	NOUN
ejpam-6841	86	11	to	to	PART
ejpam-6841	86	12	be	be	AUX
ejpam-6841	86	13	a	a	DET
ejpam-6841	86	14	proximal	proximal	ADJ
ejpam-6841	86	15	contraction	contraction	NOUN
ejpam-6841	86	16	of	of	ADP
ejpam-6841	86	17	second	second	ADJ
ejpam-6841	86	18	kind	kind	NOUN
ejpam-6841	86	19	,	,	PUNCT
ejpam-6841	86	20	it	it	PRON
ejpam-6841	86	21	needs	need	VERB
ejpam-6841	86	22	to	to	PART
ejpam-6841	86	23	satisfy	satisfy	VERB
ejpam-6841	86	24	the	the	DET
ejpam-6841	86	25	following	follow	VERB
ejpam-6841	86	26	inequality	inequality	NOUN
ejpam-6841	86	27	:	:	PUNCT
ejpam-6841	86	28	ϑ	ϑ	X
ejpam-6841	86	29	(	(	PUNCT
ejpam-6841	86	30	p2m1,p	p2m1,p	NOUN
ejpam-6841	86	31	2m2	2m2	NUM
ejpam-6841	86	32	)	)	PUNCT
ejpam-6841	86	33	≤	≤	NUM
ejpam-6841	86	34	kϑ	kϑ	NOUN
ejpam-6841	86	35	(	(	PUNCT
ejpam-6841	86	36	pm1,pm2	pm1,pm2	PROPN
ejpam-6841	86	37	)	)	PUNCT
ejpam-6841	86	38	,	,	PUNCT
ejpam-6841	86	39	for	for	ADP
ejpam-6841	86	40	all	all	DET
ejpam-6841	86	41	m1,m2	m1,m2	PROPN
ejpam-6841	86	42	∈	∈	PROPN
ejpam-6841	86	43	c.	c.	NOUN
ejpam-6841	86	44	remark	remark	NOUN
ejpam-6841	86	45	1	1	NUM
ejpam-6841	86	46	.	.	PUNCT
ejpam-6841	87	1	every	every	DET
ejpam-6841	87	2	contrs	contrs	PROPN
ejpam-6841	87	3	is	be	AUX
ejpam-6841	87	4	a	a	DET
ejpam-6841	87	5	proximal	proximal	ADJ
ejpam-6841	87	6	contraction	contraction	NOUN
ejpam-6841	87	7	of	of	ADP
ejpam-6841	87	8	the	the	DET
ejpam-6841	87	9	second	second	ADJ
ejpam-6841	87	10	kind	kind	NOUN
ejpam-6841	87	11	but	but	CCONJ
ejpam-6841	87	12	the	the	DET
ejpam-6841	87	13	converse	converse	NOUN
ejpam-6841	87	14	is	be	AUX
ejpam-6841	87	15	not	not	PART
ejpam-6841	87	16	true	true	ADJ
ejpam-6841	87	17	.	.	PUNCT
ejpam-6841	88	1	let	let	AUX
ejpam-6841	88	2	be	be	AUX
ejpam-6841	88	3	a	a	DET
ejpam-6841	88	4	metric	metric	ADJ
ejpam-6841	88	5	space	space	NOUN
ejpam-6841	88	6	indeed	indeed	ADV
ejpam-6841	88	7	,	,	PUNCT
ejpam-6841	88	8	the	the	DET
ejpam-6841	88	9	mapping	mapping	NOUN
ejpam-6841	88	10	p	p	X
ejpam-6841	88	11	:	:	PUNCT
ejpam-6841	89	1	[	[	X
ejpam-6841	89	2	0	0	NUM
ejpam-6841	89	3	,	,	PUNCT
ejpam-6841	89	4	1	1	NUM
ejpam-6841	89	5	]	]	PUNCT
ejpam-6841	89	6	→	→	PUNCT
ejpam-6841	90	1	[	[	X
ejpam-6841	90	2	0	0	NUM
ejpam-6841	90	3	,	,	PUNCT
ejpam-6841	90	4	1	1	NUM
ejpam-6841	90	5	]	]	PUNCT
ejpam-6841	90	6	defined	define	VERB
ejpam-6841	90	7	by	by	ADP
ejpam-6841	90	8	p	p	PROPN
ejpam-6841	90	9	(	(	PUNCT
ejpam-6841	90	10	b	b	NOUN
ejpam-6841	90	11	)	)	PUNCT
ejpam-6841	90	12	=	=	PUNCT
ejpam-6841	90	13			PUNCT
ejpam-6841	90	14	0	0	NUM
ejpam-6841	90	15	if	if	SCONJ
ejpam-6841	90	16	b	b	NOUN
ejpam-6841	90	17	is	be	AUX
ejpam-6841	90	18	rational	rational	ADJ
ejpam-6841	90	19	1	1	NUM
ejpam-6841	90	20	otherwise	otherwise	ADV
ejpam-6841	90	21	is	be	AUX
ejpam-6841	90	22	a	a	DET
ejpam-6841	90	23	proximal	proximal	ADJ
ejpam-6841	90	24	contraction	contraction	NOUN
ejpam-6841	90	25	of	of	ADP
ejpam-6841	90	26	the	the	DET
ejpam-6841	90	27	second	second	ADJ
ejpam-6841	90	28	kind	kind	NOUN
ejpam-6841	90	29	but	but	CCONJ
ejpam-6841	90	30	not	not	PART
ejpam-6841	90	31	a	a	DET
ejpam-6841	90	32	contrs	contrs	NOUN
ejpam-6841	90	33	in	in	ADP
ejpam-6841	90	34	(	(	PUNCT
ejpam-6841	90	35	r	r	NOUN
ejpam-6841	90	36	,	,	PUNCT
ejpam-6841	90	37	ϑ	ϑ	NOUN
ejpam-6841	90	38	)	)	PUNCT
ejpam-6841	90	39	.	.	PUNCT
ejpam-6841	91	1	definition	definition	NOUN
ejpam-6841	91	2	3	3	NUM
ejpam-6841	91	3	.	.	PUNCT
ejpam-6841	92	1	[	[	X
ejpam-6841	92	2	10	10	NUM
ejpam-6841	92	3	]	]	X
ejpam-6841	92	4	let	let	VERB
ejpam-6841	92	5	(	(	PUNCT
ejpam-6841	92	6	w	w	NOUN
ejpam-6841	92	7	,	,	PUNCT
ejpam-6841	92	8	ϑ	ϑ	NOUN
ejpam-6841	92	9	)	)	PUNCT
ejpam-6841	92	10	be	be	AUX
ejpam-6841	92	11	a	a	DET
ejpam-6841	92	12	metric	metric	ADJ
ejpam-6841	92	13	space	space	NOUN
ejpam-6841	92	14	and	and	CCONJ
ejpam-6841	92	15	c	c	NOUN
ejpam-6841	92	16	,	,	PUNCT
ejpam-6841	92	17	d	d	X
ejpam-6841	92	18	be	be	AUX
ejpam-6841	92	19	any	any	DET
ejpam-6841	92	20	nonvoid	nonvoid	ADJ
ejpam-6841	92	21	subsets	subset	NOUN
ejpam-6841	92	22	of	of	ADP
ejpam-6841	92	23	w.	w.	NOUN
ejpam-6841	92	24	we	we	PRON
ejpam-6841	92	25	say	say	VERB
ejpam-6841	92	26	that	that	SCONJ
ejpam-6841	92	27	d	d	NOUN
ejpam-6841	92	28	is	be	AUX
ejpam-6841	92	29	approximately	approximately	ADV
ejpam-6841	92	30	compact	compact	ADJ
ejpam-6841	92	31	with	with	ADP
ejpam-6841	92	32	respect	respect	NOUN
ejpam-6841	92	33	to	to	ADP
ejpam-6841	92	34	c	c	NOUN
ejpam-6841	92	35	,	,	PUNCT
ejpam-6841	92	36	if	if	SCONJ
ejpam-6841	92	37	every	every	DET
ejpam-6841	92	38	sequence	sequence	NOUN
ejpam-6841	92	39	{	{	PUNCT
ejpam-6841	92	40	bn	bn	ADP
ejpam-6841	92	41	}	}	PUNCT
ejpam-6841	92	42	in	in	ADP
ejpam-6841	92	43	d	d	ADP
ejpam-6841	92	44	satisfying	satisfy	VERB
ejpam-6841	92	45	the	the	DET
ejpam-6841	92	46	following	follow	VERB
ejpam-6841	92	47	condition	condition	NOUN
ejpam-6841	92	48	ϑ	ϑ	X
ejpam-6841	92	49	(	(	PUNCT
ejpam-6841	92	50	m	m	PROPN
ejpam-6841	92	51	,	,	PUNCT
ejpam-6841	92	52	bn	bn	ADJ
ejpam-6841	92	53	)	)	PUNCT
ejpam-6841	92	54	→	→	SYM
ejpam-6841	92	55	ϑ	ϑ	X
ejpam-6841	92	56	(	(	PUNCT
ejpam-6841	92	57	m	m	PROPN
ejpam-6841	92	58	,	,	PUNCT
ejpam-6841	92	59	d	d	NOUN
ejpam-6841	92	60	)	)	PUNCT
ejpam-6841	92	61	for	for	ADP
ejpam-6841	92	62	some	some	DET
ejpam-6841	92	63	m	m	NOUN
ejpam-6841	92	64	∈	∈	ADJ
ejpam-6841	92	65	c	c	NOUN
ejpam-6841	92	66	,	,	PUNCT
ejpam-6841	92	67	has	have	VERB
ejpam-6841	92	68	a	a	DET
ejpam-6841	92	69	convergent	convergent	ADJ
ejpam-6841	92	70	sub	sub	NOUN
ejpam-6841	92	71	-	-	NOUN
ejpam-6841	92	72	sequence	sequence	NOUN
ejpam-6841	92	73	.	.	PUNCT
ejpam-6841	93	1	k.	k.	PROPN
ejpam-6841	93	2	javed	javed	PROPN
ejpam-6841	93	3	,	,	PUNCT
ejpam-6841	93	4	m.	m.	NOUN
ejpam-6841	93	5	nazam	nazam	PROPN
ejpam-6841	93	6	,	,	PUNCT
ejpam-6841	93	7	m.	m.	PROPN
ejpam-6841	93	8	arshad	arshad	PROPN
ejpam-6841	93	9	,	,	PUNCT
ejpam-6841	93	10	m.	m.	NOUN
ejpam-6841	93	11	de	de	X
ejpam-6841	93	12	la	la	PROPN
ejpam-6841	93	13	sen	sen	PROPN
ejpam-6841	93	14	/	/	SYM
ejpam-6841	93	15	eur	eur	PROPN
ejpam-6841	93	16	.	.	PUNCT
ejpam-6841	94	1	j.	j.	PROPN
ejpam-6841	94	2	pure	pure	PROPN
ejpam-6841	94	3	appl	appl	PROPN
ejpam-6841	94	4	.	.	PROPN
ejpam-6841	94	5	math	math	PROPN
ejpam-6841	94	6	,	,	PUNCT
ejpam-6841	94	7	18	18	NUM
ejpam-6841	94	8	(	(	PUNCT
ejpam-6841	94	9	4	4	NUM
ejpam-6841	94	10	)	)	PUNCT
ejpam-6841	94	11	(	(	PUNCT
ejpam-6841	94	12	2025	2025	NUM
ejpam-6841	94	13	)	)	PUNCT
ejpam-6841	94	14	,	,	PUNCT
ejpam-6841	94	15	6841	6841	NUM
ejpam-6841	94	16	5	5	NUM
ejpam-6841	94	17	of	of	ADP
ejpam-6841	94	18	23	23	NUM
ejpam-6841	94	19	definition	definition	NOUN
ejpam-6841	94	20	4	4	NUM
ejpam-6841	94	21	.	.	PUNCT
ejpam-6841	95	1	[	[	X
ejpam-6841	95	2	10	10	NUM
ejpam-6841	95	3	]	]	X
ejpam-6841	95	4	let	let	VERB
ejpam-6841	95	5	(	(	PUNCT
ejpam-6841	95	6	w	w	NOUN
ejpam-6841	95	7	,	,	PUNCT
ejpam-6841	95	8	ϑ	ϑ	NOUN
ejpam-6841	95	9	)	)	PUNCT
ejpam-6841	95	10	be	be	AUX
ejpam-6841	95	11	a	a	DET
ejpam-6841	95	12	metric	metric	ADJ
ejpam-6841	95	13	space	space	NOUN
ejpam-6841	95	14	and	and	CCONJ
ejpam-6841	95	15	c	c	NOUN
ejpam-6841	95	16	,	,	PUNCT
ejpam-6841	95	17	d	d	NOUN
ejpam-6841	95	18	be	be	AUX
ejpam-6841	95	19	nonvoid	nonvoid	ADJ
ejpam-6841	95	20	subsets	subset	NOUN
ejpam-6841	95	21	of	of	ADP
ejpam-6841	95	22	w.	w.	PROPN
ejpam-6841	95	23	an	an	DET
ejpam-6841	95	24	element	element	NOUN
ejpam-6841	95	25	b∗	b∗	ADJ
ejpam-6841	95	26	in	in	ADP
ejpam-6841	95	27	c	c	PROPN
ejpam-6841	95	28	is	be	AUX
ejpam-6841	95	29	called	call	VERB
ejpam-6841	95	30	a	a	DET
ejpam-6841	95	31	best	good	ADJ
ejpam-6841	95	32	proximity	proximity	NOUN
ejpam-6841	95	33	point	point	NOUN
ejpam-6841	95	34	of	of	ADP
ejpam-6841	95	35	the	the	DET
ejpam-6841	95	36	mapping	mapping	NOUN
ejpam-6841	95	37	p	p	NOUN
ejpam-6841	95	38	:	:	PUNCT
ejpam-6841	95	39	c	c	X
ejpam-6841	95	40	→	→	SYM
ejpam-6841	95	41	d	d	X
ejpam-6841	95	42	,	,	PUNCT
ejpam-6841	95	43	if	if	SCONJ
ejpam-6841	95	44	it	it	PRON
ejpam-6841	95	45	satisfies	satisfy	VERB
ejpam-6841	95	46	the	the	DET
ejpam-6841	95	47	equation	equation	NOUN
ejpam-6841	95	48	:	:	PUNCT
ejpam-6841	95	49	ϑ	ϑ	X
ejpam-6841	95	50	(	(	PUNCT
ejpam-6841	95	51	b∗,pb∗	b∗,pb∗	PROPN
ejpam-6841	95	52	)	)	PUNCT
ejpam-6841	95	53	=	=	SYM
ejpam-6841	95	54	ϑ	ϑ	X
ejpam-6841	95	55	(	(	PUNCT
ejpam-6841	95	56	c	c	X
ejpam-6841	95	57	,	,	PUNCT
ejpam-6841	95	58	d	d	NOUN
ejpam-6841	95	59	)	)	PUNCT
ejpam-6841	95	60	.	.	PUNCT
ejpam-6841	96	1	3	3	X
ejpam-6841	96	2	.	.	X
ejpam-6841	96	3	main	main	ADJ
ejpam-6841	96	4	results	result	NOUN
ejpam-6841	96	5	in	in	ADP
ejpam-6841	96	6	this	this	DET
ejpam-6841	96	7	section	section	NOUN
ejpam-6841	96	8	,	,	PUNCT
ejpam-6841	96	9	we	we	PRON
ejpam-6841	96	10	define	define	VERB
ejpam-6841	96	11	(	(	PUNCT
ejpam-6841	96	12	j,£)-proximal	j,£)-proximal	ADJ
ejpam-6841	96	13	contraction	contraction	NOUN
ejpam-6841	96	14	and	and	CCONJ
ejpam-6841	96	15	show	show	VERB
ejpam-6841	96	16	that	that	SCONJ
ejpam-6841	96	17	it	it	PRON
ejpam-6841	96	18	generalizes	generalize	VERB
ejpam-6841	96	19	proximal	proximal	ADJ
ejpam-6841	96	20	contraction	contraction	NOUN
ejpam-6841	96	21	1	1	X
ejpam-6841	96	22	.	.	PUNCT
ejpam-6841	97	1	we	we	PRON
ejpam-6841	97	2	prove	prove	VERB
ejpam-6841	97	3	the	the	DET
ejpam-6841	97	4	existence	existence	NOUN
ejpam-6841	97	5	of	of	ADP
ejpam-6841	97	6	the	the	DET
ejpam-6841	97	7	best	good	ADJ
ejpam-6841	97	8	proximity	proximity	NOUN
ejpam-6841	97	9	points	point	NOUN
ejpam-6841	97	10	of	of	ADP
ejpam-6841	97	11	(	(	PUNCT
ejpam-6841	97	12	j,£)proximal	j,£)proximal	ADJ
ejpam-6841	97	13	contraction	contraction	NOUN
ejpam-6841	97	14	and	and	CCONJ
ejpam-6841	97	15	(	(	PUNCT
ejpam-6841	97	16	j,£)-interpolative	j,£)-interpolative	ADJ
ejpam-6841	97	17	proximal	proximal	ADJ
ejpam-6841	97	18	contraction	contraction	NOUN
ejpam-6841	97	19	in	in	ADP
ejpam-6841	97	20	a	a	DET
ejpam-6841	97	21	complete	complete	ADJ
ejpam-6841	97	22	metric	metric	ADJ
ejpam-6841	97	23	space	space	NOUN
ejpam-6841	97	24	.	.	PUNCT
ejpam-6841	98	1	3.1	3.1	NUM
ejpam-6841	98	2	.	.	PUNCT
ejpam-6841	99	1	(	(	PUNCT
ejpam-6841	99	2	j,£)-proximal	j,£)-proximal	ADJ
ejpam-6841	99	3	contraction	contraction	NOUN
ejpam-6841	99	4	let	let	VERB
ejpam-6841	99	5	(	(	PUNCT
ejpam-6841	99	6	w	w	NOUN
ejpam-6841	99	7	,	,	PUNCT
ejpam-6841	99	8	ϑ	ϑ	NOUN
ejpam-6841	99	9	)	)	PUNCT
ejpam-6841	99	10	be	be	AUX
ejpam-6841	99	11	a	a	DET
ejpam-6841	99	12	complete	complete	ADJ
ejpam-6841	99	13	metric	metric	ADJ
ejpam-6841	99	14	space	space	NOUN
ejpam-6841	99	15	,	,	PUNCT
ejpam-6841	99	16	and	and	CCONJ
ejpam-6841	99	17	c	c	X
ejpam-6841	99	18	,	,	PUNCT
ejpam-6841	99	19	d	d	X
ejpam-6841	99	20	are	be	AUX
ejpam-6841	99	21	subsets	subset	NOUN
ejpam-6841	99	22	of	of	ADP
ejpam-6841	99	23	w.	w.	PROPN
ejpam-6841	99	24	a	a	DET
ejpam-6841	99	25	mapping	mapping	NOUN
ejpam-6841	99	26	p	p	X
ejpam-6841	99	27	:	:	PUNCT
ejpam-6841	99	28	c	c	X
ejpam-6841	99	29	→	→	PUNCT
ejpam-6841	99	30	d	d	NOUN
ejpam-6841	99	31	is	be	AUX
ejpam-6841	99	32	said	say	VERB
ejpam-6841	99	33	to	to	PART
ejpam-6841	99	34	be	be	AUX
ejpam-6841	99	35	a	a	DET
ejpam-6841	99	36	(	(	PUNCT
ejpam-6841	99	37	j,£)-proximal	j,£)-proximal	ADJ
ejpam-6841	99	38	contraction	contraction	NOUN
ejpam-6841	99	39	if	if	SCONJ
ejpam-6841	99	40	ϑ	ϑ	X
ejpam-6841	99	41	(	(	PUNCT
ejpam-6841	99	42	b1,pm1	b1,pm1	PROPN
ejpam-6841	99	43	)	)	PUNCT
ejpam-6841	100	1	=	=	SYM
ejpam-6841	100	2	ϑ	ϑ	X
ejpam-6841	100	3	(	(	PUNCT
ejpam-6841	100	4	c	c	X
ejpam-6841	100	5	,	,	PUNCT
ejpam-6841	100	6	d	d	NOUN
ejpam-6841	100	7	)	)	PUNCT
ejpam-6841	100	8	ϑ	ϑ	X
ejpam-6841	100	9	(	(	PUNCT
ejpam-6841	100	10	b2,pm2	b2,pm2	NOUN
ejpam-6841	100	11	)	)	PUNCT
ejpam-6841	100	12	=	=	SYM
ejpam-6841	100	13	ϑ	ϑ	X
ejpam-6841	100	14	(	(	PUNCT
ejpam-6841	100	15	c	c	X
ejpam-6841	100	16	,	,	PUNCT
ejpam-6841	100	17	d	d	NOUN
ejpam-6841	100	18	)	)	PUNCT
ejpam-6841	100	19	}	}	PUNCT
ejpam-6841	100	20	⇒	⇒	VERB
ejpam-6841	100	21	j	j	PROPN
ejpam-6841	100	22	(	(	PUNCT
ejpam-6841	100	23	ϑ	ϑ	X
ejpam-6841	100	24	(	(	PUNCT
ejpam-6841	100	25	b1	b1	NOUN
ejpam-6841	100	26	,	,	PUNCT
ejpam-6841	100	27	b2	b2	NOUN
ejpam-6841	100	28	)	)	PUNCT
ejpam-6841	100	29	)	)	PUNCT
ejpam-6841	101	1	≤	≤	NUM
ejpam-6841	101	2	£	£	NOUN
ejpam-6841	101	3	(	(	PUNCT
ejpam-6841	101	4	ϑ	ϑ	X
ejpam-6841	101	5	(	(	PUNCT
ejpam-6841	101	6	m1,m2	m1,m2	PROPN
ejpam-6841	101	7	)	)	PUNCT
ejpam-6841	101	8	)	)	PUNCT
ejpam-6841	101	9	(	(	PUNCT
ejpam-6841	101	10	2	2	X
ejpam-6841	101	11	)	)	PUNCT
ejpam-6841	101	12	for	for	ADP
ejpam-6841	101	13	all	all	DET
ejpam-6841	101	14	b1	b1	NOUN
ejpam-6841	101	15	,	,	PUNCT
ejpam-6841	101	16	b2,m1,m2	b2,m1,m2	NOUN
ejpam-6841	101	17	∈	∈	PROPN
ejpam-6841	101	18	c	c	NOUN
ejpam-6841	101	19	with	with	ADP
ejpam-6841	101	20	b1	b1	PROPN
ejpam-6841	101	21	6=	6=	SYM
ejpam-6841	101	22	b2	b2	NOUN
ejpam-6841	101	23	,	,	PUNCT
ejpam-6841	101	24	where	where	SCONJ
ejpam-6841	101	25	j,£	j,£	ADV
ejpam-6841	101	26	:	:	PUNCT
ejpam-6841	101	27	r+	r+	X
ejpam-6841	101	28	→	→	PUNCT
ejpam-6841	101	29	r	r	NOUN
ejpam-6841	101	30	are	be	AUX
ejpam-6841	101	31	two	two	NUM
ejpam-6841	101	32	mappings	mapping	NOUN
ejpam-6841	101	33	.	.	PUNCT
ejpam-6841	101	34	example	example	NOUN
ejpam-6841	102	1	1	1	NUM
ejpam-6841	102	2	.	.	PUNCT
ejpam-6841	102	3	let	let	VERB
ejpam-6841	102	4	w	w	NOUN
ejpam-6841	102	5	=	=	NOUN
ejpam-6841	102	6	r2	r2	PROPN
ejpam-6841	102	7	and	and	CCONJ
ejpam-6841	102	8	define	define	VERB
ejpam-6841	102	9	the	the	DET
ejpam-6841	102	10	function	function	NOUN
ejpam-6841	102	11	ϑ	ϑ	X
ejpam-6841	102	12	:	:	PUNCT
ejpam-6841	102	13	w×w	w×w	NOUN
ejpam-6841	102	14	→	→	SYM
ejpam-6841	102	15	[	[	X
ejpam-6841	102	16	0,∞	0,∞	NOUN
ejpam-6841	102	17	)	)	PUNCT
ejpam-6841	102	18	by	by	ADP
ejpam-6841	102	19	ϑ((b	ϑ((b	NOUN
ejpam-6841	102	20	,	,	PUNCT
ejpam-6841	102	21	m	m	NOUN
ejpam-6841	102	22	)	)	PUNCT
ejpam-6841	102	23	,	,	PUNCT
ejpam-6841	102	24	(	(	PUNCT
ejpam-6841	102	25	u	u	NOUN
ejpam-6841	102	26	,	,	PUNCT
ejpam-6841	102	27	v	v	NOUN
ejpam-6841	102	28	)	)	PUNCT
ejpam-6841	102	29	)	)	PUNCT
ejpam-6841	103	1	=	=	SYM
ejpam-6841	103	2	|b−	|b−	PROPN
ejpam-6841	103	3	u|+	u|+	PROPN
ejpam-6841	103	4	|m−	|m−	ADJ
ejpam-6841	103	5	v|	v|	ADV
ejpam-6841	103	6	for	for	ADP
ejpam-6841	103	7	all	all	DET
ejpam-6841	103	8	(	(	PUNCT
ejpam-6841	103	9	b	b	NOUN
ejpam-6841	103	10	,	,	PUNCT
ejpam-6841	103	11	m	m	NOUN
ejpam-6841	103	12	)	)	PUNCT
ejpam-6841	103	13	,	,	PUNCT
ejpam-6841	103	14	(	(	PUNCT
ejpam-6841	103	15	u	u	NOUN
ejpam-6841	103	16	,	,	PUNCT
ejpam-6841	103	17	v	v	NOUN
ejpam-6841	103	18	)	)	PUNCT
ejpam-6841	103	19	∈	∈	PROPN
ejpam-6841	103	20	w.	w.	NOUN
ejpam-6841	103	21	then	then	ADV
ejpam-6841	103	22	(	(	PUNCT
ejpam-6841	103	23	w	w	PROPN
ejpam-6841	103	24	,	,	PUNCT
ejpam-6841	103	25	ϑ	ϑ	NOUN
ejpam-6841	103	26	)	)	PUNCT
ejpam-6841	103	27	is	be	AUX
ejpam-6841	103	28	a	a	DET
ejpam-6841	103	29	metric	metric	ADJ
ejpam-6841	103	30	space	space	NOUN
ejpam-6841	103	31	.	.	PUNCT
ejpam-6841	104	1	let	let	VERB
ejpam-6841	104	2	c	c	X
ejpam-6841	104	3	,	,	PUNCT
ejpam-6841	104	4	d	d	X
ejpam-6841	104	5	be	be	AUX
ejpam-6841	104	6	the	the	DET
ejpam-6841	104	7	subsets	subset	NOUN
ejpam-6841	104	8	of	of	ADP
ejpam-6841	104	9	w	w	PROPN
ejpam-6841	104	10	defined	define	VERB
ejpam-6841	104	11	by	by	ADP
ejpam-6841	104	12	c	c	NOUN
ejpam-6841	104	13	=	=	SYM
ejpam-6841	104	14	{	{	PUNCT
ejpam-6841	104	15	(	(	PUNCT
ejpam-6841	104	16	0,m	0,m	NUM
ejpam-6841	104	17	)	)	PUNCT
ejpam-6841	104	18	;	;	PUNCT
ejpam-6841	104	19	0	0	NUM
ejpam-6841	104	20	≤	≤	NUM
ejpam-6841	104	21	m	m	VERB
ejpam-6841	104	22	≤	≤	NOUN
ejpam-6841	104	23	1	1	NUM
ejpam-6841	104	24	}	}	PUNCT
ejpam-6841	104	25	,	,	PUNCT
ejpam-6841	104	26	d	d	PROPN
ejpam-6841	104	27	=	=	PRON
ejpam-6841	104	28	{	{	PUNCT
ejpam-6841	104	29	(	(	PUNCT
ejpam-6841	104	30	1,m	1,m	PROPN
ejpam-6841	104	31	)	)	PUNCT
ejpam-6841	104	32	;	;	PUNCT
ejpam-6841	104	33	0	0	NUM
ejpam-6841	104	34	≤	≤	NUM
ejpam-6841	104	35	m	m	VERB
ejpam-6841	104	36	≤	≤	NOUN
ejpam-6841	104	37	1	1	NUM
ejpam-6841	104	38	}	}	PUNCT
ejpam-6841	104	39	,	,	PUNCT
ejpam-6841	104	40	then	then	ADV
ejpam-6841	104	41	ϑ(c	ϑ(c	VERB
ejpam-6841	104	42	,	,	PUNCT
ejpam-6841	104	43	d	d	NOUN
ejpam-6841	104	44	)	)	PUNCT
ejpam-6841	104	45	=	=	SYM
ejpam-6841	104	46	1	1	X
ejpam-6841	104	47	.	.	X
ejpam-6841	104	48	define	define	VERB
ejpam-6841	104	49	the	the	DET
ejpam-6841	104	50	functions	function	NOUN
ejpam-6841	104	51	j,£	j,£	ADV
ejpam-6841	104	52	:	:	PUNCT
ejpam-6841	104	53	r+	r+	X
ejpam-6841	104	54	→	→	PUNCT
ejpam-6841	104	55	r	r	NOUN
ejpam-6841	104	56	by	by	ADP
ejpam-6841	104	57	j(z	j(z	PROPN
ejpam-6841	104	58	)	)	PUNCT
ejpam-6841	104	59	=	=	SYM
ejpam-6841	104	60	z	z	NOUN
ejpam-6841	104	61	and	and	CCONJ
ejpam-6841	104	62	£	£	SYM
ejpam-6841	104	63	(	(	PUNCT
ejpam-6841	104	64	z	z	NOUN
ejpam-6841	104	65	)	)	PUNCT
ejpam-6841	104	66	=	=	SYM
ejpam-6841	104	67	z−	z−	PROPN
ejpam-6841	104	68	z2	z2	PROPN
ejpam-6841	104	69	2	2	NUM
ejpam-6841	104	70	,	,	PUNCT
ejpam-6841	104	71	z	z	NOUN
ejpam-6841	104	72	∈	∈	PROPN
ejpam-6841	104	73	r+	r+	X
ejpam-6841	104	74	.	.	PUNCT
ejpam-6841	105	1	define	define	VERB
ejpam-6841	105	2	the	the	DET
ejpam-6841	105	3	mapping	mapping	NOUN
ejpam-6841	105	4	p	p	NOUN
ejpam-6841	105	5	:	:	PUNCT
ejpam-6841	105	6	c	c	X
ejpam-6841	105	7	→	→	SYM
ejpam-6841	105	8	d	d	NOUN
ejpam-6841	105	9	by	by	ADP
ejpam-6841	105	10	p((0	p((0	PROPN
ejpam-6841	105	11	,	,	PUNCT
ejpam-6841	105	12	r	r	NOUN
ejpam-6841	105	13	)	)	PUNCT
ejpam-6841	105	14	)	)	PUNCT
ejpam-6841	106	1	=	=	PUNCT
ejpam-6841	106	2	(	(	PUNCT
ejpam-6841	106	3	1	1	NUM
ejpam-6841	106	4	,	,	PUNCT
ejpam-6841	106	5	r	r	NOUN
ejpam-6841	106	6	−	−	PROPN
ejpam-6841	106	7	r2	r2	PROPN
ejpam-6841	106	8	2	2	NUM
ejpam-6841	106	9	)	)	PUNCT
ejpam-6841	106	10	for	for	ADP
ejpam-6841	106	11	all	all	DET
ejpam-6841	106	12	(	(	PUNCT
ejpam-6841	106	13	0	0	NUM
ejpam-6841	106	14	,	,	PUNCT
ejpam-6841	106	15	r	r	NOUN
ejpam-6841	106	16	)	)	PUNCT
ejpam-6841	106	17	∈	∈	PROPN
ejpam-6841	106	18	c.	c.	NOUN
ejpam-6841	106	19	we	we	PRON
ejpam-6841	106	20	show	show	VERB
ejpam-6841	106	21	that	that	SCONJ
ejpam-6841	106	22	p	p	NOUN
ejpam-6841	106	23	is	be	AUX
ejpam-6841	106	24	a	a	DET
ejpam-6841	106	25	(	(	PUNCT
ejpam-6841	106	26	j,£)-proximal	j,£)-proximal	ADJ
ejpam-6841	106	27	contraction	contraction	NOUN
ejpam-6841	106	28	.	.	PUNCT
ejpam-6841	107	1	for	for	ADP
ejpam-6841	107	2	b	b	NOUN
ejpam-6841	107	3	=	=	SYM
ejpam-6841	107	4	(	(	PUNCT
ejpam-6841	107	5	0	0	NUM
ejpam-6841	107	6	,	,	PUNCT
ejpam-6841	107	7	b1	b1	NOUN
ejpam-6841	107	8	)	)	PUNCT
ejpam-6841	107	9	,	,	PUNCT
ejpam-6841	107	10	u	u	NOUN
ejpam-6841	107	11	=	=	SYM
ejpam-6841	107	12	(	(	PUNCT
ejpam-6841	107	13	0	0	NUM
ejpam-6841	107	14	,	,	PUNCT
ejpam-6841	107	15	b2	b2	NOUN
ejpam-6841	107	16	)	)	PUNCT
ejpam-6841	107	17	and	and	CCONJ
ejpam-6841	107	18	m1	m1	PROPN
ejpam-6841	107	19	=	=	SYM
ejpam-6841	107	20	(	(	PUNCT
ejpam-6841	107	21	0	0	NUM
ejpam-6841	107	22	,	,	PUNCT
ejpam-6841	107	23	a1	a1	NOUN
ejpam-6841	107	24	)	)	PUNCT
ejpam-6841	107	25	,	,	PUNCT
ejpam-6841	107	26	m2	m2	PROPN
ejpam-6841	107	27	=	=	SYM
ejpam-6841	107	28	(	(	PUNCT
ejpam-6841	107	29	0	0	NUM
ejpam-6841	107	30	,	,	PUNCT
ejpam-6841	107	31	a2	a2	PROPN
ejpam-6841	107	32	)	)	PUNCT
ejpam-6841	107	33	(	(	PUNCT
ejpam-6841	107	34	let	let	VERB
ejpam-6841	107	35	a1	a1	VERB
ejpam-6841	107	36	>	>	X
ejpam-6841	107	37	a2	a2	PROPN
ejpam-6841	107	38	)	)	PUNCT
ejpam-6841	107	39	,	,	PUNCT
ejpam-6841	107	40	we	we	PRON
ejpam-6841	107	41	have	have	AUX
ejpam-6841	107	42	ϑ(b	ϑ(b	PROPN
ejpam-6841	107	43	,	,	PUNCT
ejpam-6841	107	44	pm1	pm1	NUM
ejpam-6841	107	45	)	)	PUNCT
ejpam-6841	108	1	=	=	PUNCT
ejpam-6841	108	2	ϑ(c	ϑ(c	NOUN
ejpam-6841	108	3	,	,	PUNCT
ejpam-6841	108	4	d	d	NOUN
ejpam-6841	108	5	)	)	PUNCT
ejpam-6841	108	6	(	(	PUNCT
ejpam-6841	108	7	3	3	NUM
ejpam-6841	108	8	)	)	PUNCT
ejpam-6841	108	9	ϑ(u	ϑ(u	VERB
ejpam-6841	108	10	,	,	PUNCT
ejpam-6841	108	11	pm2	pm2	NOUN
ejpam-6841	108	12	)	)	PUNCT
ejpam-6841	108	13	=	=	PUNCT
ejpam-6841	109	1	ϑ(c	ϑ(c	PROPN
ejpam-6841	109	2	,	,	PUNCT
ejpam-6841	109	3	d	d	NOUN
ejpam-6841	109	4	)	)	PUNCT
ejpam-6841	109	5	.	.	PUNCT
ejpam-6841	110	1	(	(	PUNCT
ejpam-6841	110	2	4	4	X
ejpam-6841	110	3	)	)	PUNCT
ejpam-6841	110	4	we	we	PRON
ejpam-6841	110	5	note	note	VERB
ejpam-6841	110	6	that	that	SCONJ
ejpam-6841	110	7	the	the	DET
ejpam-6841	110	8	equations	equation	NOUN
ejpam-6841	110	9	(	(	PUNCT
ejpam-6841	110	10	3	3	NUM
ejpam-6841	110	11	)	)	PUNCT
ejpam-6841	110	12	and	and	CCONJ
ejpam-6841	110	13	(	(	PUNCT
ejpam-6841	110	14	4	4	X
ejpam-6841	110	15	)	)	PUNCT
ejpam-6841	110	16	can	can	AUX
ejpam-6841	110	17	further	far	ADV
ejpam-6841	110	18	be	be	AUX
ejpam-6841	110	19	simplified	simplify	VERB
ejpam-6841	110	20	to	to	PART
ejpam-6841	110	21	have	have	VERB
ejpam-6841	110	22	the	the	DET
ejpam-6841	110	23	following	follow	VERB
ejpam-6841	110	24	information	information	NOUN
ejpam-6841	110	25	:	:	PUNCT
ejpam-6841	110	26	b1	b1	NOUN
ejpam-6841	110	27	=	=	SYM
ejpam-6841	110	28	a1	a1	PROPN
ejpam-6841	110	29	−	−	PROPN
ejpam-6841	110	30	a21	a21	NOUN
ejpam-6841	110	31	2	2	NUM
ejpam-6841	110	32	,	,	PUNCT
ejpam-6841	110	33	k.	k.	PROPN
ejpam-6841	110	34	javed	javed	PROPN
ejpam-6841	110	35	,	,	PUNCT
ejpam-6841	110	36	m.	m.	NOUN
ejpam-6841	110	37	nazam	nazam	PROPN
ejpam-6841	110	38	,	,	PUNCT
ejpam-6841	110	39	m.	m.	PROPN
ejpam-6841	110	40	arshad	arshad	PROPN
ejpam-6841	110	41	,	,	PUNCT
ejpam-6841	110	42	m.	m.	NOUN
ejpam-6841	110	43	de	de	X
ejpam-6841	110	44	la	la	PROPN
ejpam-6841	110	45	sen	sen	PROPN
ejpam-6841	110	46	/	/	SYM
ejpam-6841	110	47	eur	eur	PROPN
ejpam-6841	110	48	.	.	PUNCT
ejpam-6841	111	1	j.	j.	PROPN
ejpam-6841	111	2	pure	pure	PROPN
ejpam-6841	111	3	appl	appl	PROPN
ejpam-6841	111	4	.	.	PROPN
ejpam-6841	111	5	math	math	PROPN
ejpam-6841	111	6	,	,	PUNCT
ejpam-6841	111	7	18	18	NUM
ejpam-6841	111	8	(	(	PUNCT
ejpam-6841	111	9	4	4	NUM
ejpam-6841	111	10	)	)	PUNCT
ejpam-6841	111	11	(	(	PUNCT
ejpam-6841	111	12	2025	2025	NUM
ejpam-6841	111	13	)	)	PUNCT
ejpam-6841	111	14	,	,	PUNCT
ejpam-6841	111	15	6841	6841	NUM
ejpam-6841	111	16	6	6	NUM
ejpam-6841	111	17	of	of	ADP
ejpam-6841	111	18	23	23	NUM
ejpam-6841	111	19	b2	b2	NOUN
ejpam-6841	111	20	=	=	SYM
ejpam-6841	111	21	a2	a2	PROPN
ejpam-6841	111	22	−	−	PROPN
ejpam-6841	111	23	a22	a22	PROPN
ejpam-6841	111	24	2	2	NUM
ejpam-6841	111	25	.	.	PUNCT
ejpam-6841	112	1	this	this	PRON
ejpam-6841	112	2	implies	imply	VERB
ejpam-6841	112	3	that	that	SCONJ
ejpam-6841	112	4	j(ϑ(b	j(ϑ(b	PROPN
ejpam-6841	112	5	,	,	PUNCT
ejpam-6841	112	6	u	u	NOUN
ejpam-6841	112	7	)	)	PUNCT
ejpam-6841	112	8	)	)	PUNCT
ejpam-6841	113	1	=	=	SYM
ejpam-6841	113	2	j(ϑ((0	j(ϑ((0	PROPN
ejpam-6841	113	3	,	,	PUNCT
ejpam-6841	113	4	b1	b1	NOUN
ejpam-6841	113	5	)	)	PUNCT
ejpam-6841	113	6	,	,	PUNCT
ejpam-6841	113	7	(	(	PUNCT
ejpam-6841	113	8	0	0	NUM
ejpam-6841	113	9	,	,	PUNCT
ejpam-6841	113	10	b2	b2	NOUN
ejpam-6841	113	11	)	)	PUNCT
ejpam-6841	113	12	)	)	PUNCT
ejpam-6841	113	13	)	)	PUNCT
ejpam-6841	114	1	=	=	PRON
ejpam-6841	114	2	(	(	PUNCT
ejpam-6841	114	3	|	|	ADV
ejpam-6841	114	4	0−	0−	NUM
ejpam-6841	114	5	0	0	NUM
ejpam-6841	115	1	|	|	ADV
ejpam-6841	115	2	+	+	CCONJ
ejpam-6841	115	3	|	|	ADV
ejpam-6841	115	4	b1	b1	NOUN
ejpam-6841	115	5	−	−	PROPN
ejpam-6841	115	6	b2	b2	NOUN
ejpam-6841	115	7	|	|	NOUN
ejpam-6841	115	8	)	)	PUNCT
ejpam-6841	115	9	≤	≤	NOUN
ejpam-6841	115	10	(	(	PUNCT
ejpam-6841	115	11	a1	a1	NOUN
ejpam-6841	115	12	−	−	PROPN
ejpam-6841	115	13	a2)−	a2)−	PROPN
ejpam-6841	115	14	1	1	NUM
ejpam-6841	115	15	2	2	NUM
ejpam-6841	115	16	(	(	PUNCT
ejpam-6841	115	17	a1	a1	NOUN
ejpam-6841	115	18	−	−	PROPN
ejpam-6841	115	19	a2	a2	PROPN
ejpam-6841	115	20	)	)	PUNCT
ejpam-6841	115	21	2	2	NUM
ejpam-6841	115	22	=	=	SYM
ejpam-6841	115	23	ϑ(m1,m2)−	ϑ(m1,m2)−	PRON
ejpam-6841	115	24	1	1	NUM
ejpam-6841	115	25	2	2	NUM
ejpam-6841	115	26	(	(	PUNCT
ejpam-6841	115	27	ϑ(m1,m2	ϑ(m1,m2	NOUN
ejpam-6841	115	28	)	)	PUNCT
ejpam-6841	115	29	)	)	PUNCT
ejpam-6841	115	30	2	2	NUM
ejpam-6841	115	31	=	=	SYM
ejpam-6841	115	32	£	£	SYM
ejpam-6841	115	33	(	(	PUNCT
ejpam-6841	115	34	ϑ(m1,m2	ϑ(m1,m2	NOUN
ejpam-6841	115	35	)	)	PUNCT
ejpam-6841	115	36	)	)	PUNCT
ejpam-6841	116	1	this	this	PRON
ejpam-6841	116	2	shows	show	VERB
ejpam-6841	116	3	that	that	SCONJ
ejpam-6841	116	4	p	p	NOUN
ejpam-6841	116	5	is	be	AUX
ejpam-6841	116	6	a	a	DET
ejpam-6841	116	7	(	(	PUNCT
ejpam-6841	116	8	j,£)-proximal	j,£)-proximal	ADJ
ejpam-6841	116	9	contraction	contraction	NOUN
ejpam-6841	116	10	.	.	PUNCT
ejpam-6841	117	1	next	next	ADV
ejpam-6841	117	2	,	,	PUNCT
ejpam-6841	117	3	we	we	PRON
ejpam-6841	117	4	show	show	VERB
ejpam-6841	117	5	that	that	SCONJ
ejpam-6841	117	6	it	it	PRON
ejpam-6841	117	7	is	be	AUX
ejpam-6841	117	8	not	not	PART
ejpam-6841	117	9	a	a	DET
ejpam-6841	117	10	proximal	proximal	ADJ
ejpam-6841	117	11	contraction	contraction	NOUN
ejpam-6841	117	12	.	.	PUNCT
ejpam-6841	118	1	since	since	SCONJ
ejpam-6841	118	2	ϑ(b	ϑ(b	PROPN
ejpam-6841	118	3	,	,	PUNCT
ejpam-6841	118	4	pm1	pm1	NUM
ejpam-6841	118	5	)	)	PUNCT
ejpam-6841	118	6	=	=	PUNCT
ejpam-6841	118	7	ϑ(c	ϑ(c	NOUN
ejpam-6841	118	8	,	,	PUNCT
ejpam-6841	118	9	d	d	NOUN
ejpam-6841	118	10	)	)	PUNCT
ejpam-6841	118	11	ϑ(u	ϑ(u	VERB
ejpam-6841	118	12	,	,	PUNCT
ejpam-6841	118	13	pm2	pm2	NOUN
ejpam-6841	118	14	)	)	PUNCT
ejpam-6841	118	15	=	=	PUNCT
ejpam-6841	118	16	ϑ(c	ϑ(c	PROPN
ejpam-6841	118	17	,	,	PUNCT
ejpam-6841	118	18	d	d	NOUN
ejpam-6841	118	19	)	)	PUNCT
ejpam-6841	118	20	.	.	PUNCT
ejpam-6841	119	1	if	if	SCONJ
ejpam-6841	119	2	there	there	PRON
ejpam-6841	119	3	exists	exist	VERB
ejpam-6841	119	4	k	k	PROPN
ejpam-6841	119	5	∈	∈	PROPN
ejpam-6841	119	6	(	(	PUNCT
ejpam-6841	119	7	0	0	NUM
ejpam-6841	119	8	,	,	PUNCT
ejpam-6841	119	9	1	1	NUM
ejpam-6841	119	10	)	)	PUNCT
ejpam-6841	119	11	such	such	ADJ
ejpam-6841	119	12	that	that	SCONJ
ejpam-6841	119	13	ϑ	ϑ	PROPN
ejpam-6841	119	14	(	(	PUNCT
ejpam-6841	119	15	b	b	NOUN
ejpam-6841	119	16	,	,	PUNCT
ejpam-6841	119	17	u	u	NOUN
ejpam-6841	119	18	)	)	PUNCT
ejpam-6841	119	19	≤	≤	NUM
ejpam-6841	119	20	kϑ	kϑ	PROPN
ejpam-6841	119	21	(	(	PUNCT
ejpam-6841	119	22	m1,m2	m1,m2	PROPN
ejpam-6841	119	23	)	)	PUNCT
ejpam-6841	119	24	.	.	PUNCT
ejpam-6841	120	1	then	then	ADV
ejpam-6841	120	2	,	,	PUNCT
ejpam-6841	120	3	ϑ((0	ϑ((0	PROPN
ejpam-6841	120	4	,	,	PUNCT
ejpam-6841	120	5	b1	b1	NOUN
ejpam-6841	120	6	)	)	PUNCT
ejpam-6841	120	7	,	,	PUNCT
ejpam-6841	120	8	(	(	PUNCT
ejpam-6841	120	9	0	0	NUM
ejpam-6841	120	10	,	,	PUNCT
ejpam-6841	120	11	b2	b2	NOUN
ejpam-6841	120	12	)	)	PUNCT
ejpam-6841	120	13	)	)	PUNCT
ejpam-6841	121	1	≤	≤	NUM
ejpam-6841	122	1	kϑ((0	kϑ((0	ADV
ejpam-6841	122	2	,	,	PUNCT
ejpam-6841	122	3	a1	a1	NOUN
ejpam-6841	122	4	)	)	PUNCT
ejpam-6841	122	5	,	,	PUNCT
ejpam-6841	122	6	(	(	PUNCT
ejpam-6841	122	7	0	0	NUM
ejpam-6841	122	8	,	,	PUNCT
ejpam-6841	122	9	a2	a2	PROPN
ejpam-6841	122	10	)	)	PUNCT
ejpam-6841	122	11	(	(	PUNCT
ejpam-6841	122	12	|	|	ADV
ejpam-6841	122	13	0−	0−	NUM
ejpam-6841	122	14	0	0	NUM
ejpam-6841	123	1	|	|	ADV
ejpam-6841	123	2	+	+	CCONJ
ejpam-6841	123	3	|	|	ADV
ejpam-6841	123	4	b1	b1	NOUN
ejpam-6841	123	5	−	−	PROPN
ejpam-6841	123	6	b2	b2	NOUN
ejpam-6841	123	7	|	|	NOUN
ejpam-6841	123	8	)	)	PUNCT
ejpam-6841	123	9	≤	≤	NOUN
ejpam-6841	123	10	k(|	k(|	PROPN
ejpam-6841	123	11	0−	0−	NUM
ejpam-6841	123	12	0	0	NUM
ejpam-6841	124	1	|	|	ADV
ejpam-6841	125	1	+	+	CCONJ
ejpam-6841	125	2	|	|	ADV
ejpam-6841	125	3	a1	a1	NOUN
ejpam-6841	125	4	−	−	PROPN
ejpam-6841	125	5	a2	a2	PROPN
ejpam-6841	125	6	|	|	NOUN
ejpam-6841	125	7	)	)	PUNCT
ejpam-6841	125	8	a1	a1	NOUN
ejpam-6841	125	9	−	−	PROPN
ejpam-6841	125	10	a21	a21	NOUN
ejpam-6841	125	11	2	2	NUM
ejpam-6841	125	12	−	−	PROPN
ejpam-6841	125	13	a2	a2	PROPN
ejpam-6841	125	14	+	+	CCONJ
ejpam-6841	125	15	a22	a22	PROPN
ejpam-6841	125	16	2	2	NUM
ejpam-6841	125	17	≤	≤	PROPN
ejpam-6841	125	18	k(a1	k(a1	NOUN
ejpam-6841	125	19	−	−	PROPN
ejpam-6841	125	20	a2	a2	PROPN
ejpam-6841	125	21	)	)	PUNCT
ejpam-6841	125	22	1	1	NUM
ejpam-6841	126	1	+	+	CCONJ
ejpam-6841	126	2	a1	a1	NOUN
ejpam-6841	126	3	+	+	CCONJ
ejpam-6841	126	4	a2	a2	PROPN
ejpam-6841	126	5	2	2	NUM
ejpam-6841	126	6	≤	≤	NUM
ejpam-6841	126	7	k.	k.	NOUN
ejpam-6841	127	1	this	this	PRON
ejpam-6841	127	2	is	be	AUX
ejpam-6841	127	3	a	a	DET
ejpam-6841	127	4	contradiction	contradiction	NOUN
ejpam-6841	127	5	.	.	PUNCT
ejpam-6841	128	1	hence	hence	ADV
ejpam-6841	128	2	,	,	PUNCT
ejpam-6841	128	3	p	p	PRON
ejpam-6841	128	4	is	be	AUX
ejpam-6841	128	5	not	not	PART
ejpam-6841	128	6	a	a	DET
ejpam-6841	128	7	proximal	proximal	ADJ
ejpam-6841	128	8	contraction	contraction	NOUN
ejpam-6841	128	9	.	.	PUNCT
ejpam-6841	129	1	the	the	DET
ejpam-6841	129	2	following	follow	VERB
ejpam-6841	129	3	lemmas	lemmas	PROPN
ejpam-6841	129	4	are	be	AUX
ejpam-6841	129	5	integral	integral	ADJ
ejpam-6841	129	6	part	part	NOUN
ejpam-6841	129	7	of	of	ADP
ejpam-6841	129	8	this	this	DET
ejpam-6841	129	9	paper	paper	NOUN
ejpam-6841	129	10	and	and	CCONJ
ejpam-6841	129	11	have	have	VERB
ejpam-6841	129	12	an	an	DET
ejpam-6841	129	13	impact	impact	NOUN
ejpam-6841	129	14	on	on	ADP
ejpam-6841	129	15	further	further	ADJ
ejpam-6841	129	16	investigations	investigation	NOUN
ejpam-6841	129	17	.	.	PUNCT
ejpam-6841	130	1	lemma	lemma	PROPN
ejpam-6841	130	2	1	1	NUM
ejpam-6841	130	3	.	.	PUNCT
ejpam-6841	131	1	[	[	X
ejpam-6841	131	2	8	8	NUM
ejpam-6841	131	3	]	]	X
ejpam-6841	131	4	let	let	AUX
ejpam-6841	131	5	{	{	PUNCT
ejpam-6841	131	6	bn	bn	PART
ejpam-6841	131	7	}	}	PUNCT
ejpam-6841	131	8	be	be	AUX
ejpam-6841	131	9	a	a	DET
ejpam-6841	131	10	sequence	sequence	NOUN
ejpam-6841	131	11	in	in	ADP
ejpam-6841	131	12	(	(	PUNCT
ejpam-6841	131	13	w	w	PROPN
ejpam-6841	131	14	,	,	PUNCT
ejpam-6841	131	15	ϑ	ϑ	NOUN
ejpam-6841	131	16	)	)	PUNCT
ejpam-6841	131	17	verifying	verify	VERB
ejpam-6841	131	18	limn→∞	limn→∞	PROPN
ejpam-6841	131	19	ϑ(bn	ϑ(bn	X
ejpam-6841	131	20	,	,	PUNCT
ejpam-6841	131	21	bn+1	bn+1	NUM
ejpam-6841	131	22	)	)	PUNCT
ejpam-6841	131	23	=	=	SYM
ejpam-6841	132	1	0	0	X
ejpam-6841	132	2	.	.	PUNCT
ejpam-6841	133	1	if	if	SCONJ
ejpam-6841	133	2	the	the	DET
ejpam-6841	133	3	sequence	sequence	NOUN
ejpam-6841	133	4	{	{	PUNCT
ejpam-6841	133	5	bn	bn	NOUN
ejpam-6841	133	6	}	}	PUNCT
ejpam-6841	133	7	is	be	AUX
ejpam-6841	133	8	not	not	PART
ejpam-6841	133	9	cauchy	cauchy	ADJ
ejpam-6841	133	10	,	,	PUNCT
ejpam-6841	133	11	then	then	ADV
ejpam-6841	133	12	there	there	PRON
ejpam-6841	133	13	are	be	VERB
ejpam-6841	133	14	subsequences	subsequence	NOUN
ejpam-6841	133	15	{	{	PUNCT
ejpam-6841	133	16	bnk	bnk	PROPN
ejpam-6841	133	17	}	}	PUNCT
ejpam-6841	133	18	,	,	PUNCT
ejpam-6841	133	19	{	{	PUNCT
ejpam-6841	133	20	bmk	bmk	NOUN
ejpam-6841	133	21	}	}	PUNCT
ejpam-6841	133	22	and	and	CCONJ
ejpam-6841	133	23	p	p	X
ejpam-6841	133	24	>	>	X
ejpam-6841	133	25	0	0	NUM
ejpam-6841	133	26	such	such	ADJ
ejpam-6841	133	27	that	that	SCONJ
ejpam-6841	133	28	lim	lim	PROPN
ejpam-6841	133	29	k→∞	k→∞	NOUN
ejpam-6841	133	30	ϑ(bnk+1	ϑ(bnk+1	PROPN
ejpam-6841	133	31	,	,	PUNCT
ejpam-6841	133	32	bmk+1	bmk+1	X
ejpam-6841	133	33	)	)	PUNCT
ejpam-6841	133	34	=	=	PROPN
ejpam-6841	133	35	p+	p+	NOUN
ejpam-6841	133	36	.	.	PUNCT
ejpam-6841	134	1	(	(	PUNCT
ejpam-6841	134	2	5	5	X
ejpam-6841	134	3	)	)	PUNCT
ejpam-6841	134	4	lim	lim	NOUN
ejpam-6841	134	5	k→∞	k→∞	NOUN
ejpam-6841	134	6	ϑ(bnk	ϑ(bnk	PROPN
ejpam-6841	134	7	,	,	PUNCT
ejpam-6841	134	8	bmk	bmk	PROPN
ejpam-6841	134	9	)	)	PUNCT
ejpam-6841	135	1	=	=	SYM
ejpam-6841	135	2	ϑ(bnk+1	ϑ(bnk+1	NOUN
ejpam-6841	135	3	,	,	PUNCT
ejpam-6841	135	4	bmk	bmk	PROPN
ejpam-6841	135	5	)	)	PUNCT
ejpam-6841	136	1	=	=	NOUN
ejpam-6841	136	2	ϑ(bnk	ϑ(bnk	NOUN
ejpam-6841	136	3	,	,	PUNCT
ejpam-6841	136	4	bmk+1	bmk+1	PROPN
ejpam-6841	136	5	)	)	PUNCT
ejpam-6841	136	6	=	=	SYM
ejpam-6841	137	1	p.	p.	NOUN
ejpam-6841	137	2	(	(	PUNCT
ejpam-6841	137	3	6	6	NUM
ejpam-6841	137	4	)	)	PUNCT
ejpam-6841	137	5	lemma	lemma	PROPN
ejpam-6841	137	6	2	2	NUM
ejpam-6841	137	7	.	.	PUNCT
ejpam-6841	138	1	[	[	X
ejpam-6841	138	2	8]let	8]let	PROPN
ejpam-6841	138	3	j	j	NOUN
ejpam-6841	138	4	:	:	PUNCT
ejpam-6841	138	5	(	(	PUNCT
ejpam-6841	138	6	0,∞	0,∞	NOUN
ejpam-6841	138	7	)	)	PUNCT
ejpam-6841	138	8	→	→	PUNCT
ejpam-6841	138	9	r	r	NOUN
ejpam-6841	138	10	be	be	AUX
ejpam-6841	138	11	a	a	DET
ejpam-6841	138	12	function	function	NOUN
ejpam-6841	138	13	.	.	PUNCT
ejpam-6841	139	1	then	then	ADV
ejpam-6841	139	2	the	the	DET
ejpam-6841	139	3	statements	statement	NOUN
ejpam-6841	139	4	(	(	PUNCT
ejpam-6841	139	5	i	i	NOUN
ejpam-6841	139	6	)	)	PUNCT
ejpam-6841	139	7	−	−	PROPN
ejpam-6841	139	8	(	(	PUNCT
ejpam-6841	139	9	iii	iii	NOUN
ejpam-6841	139	10	)	)	PUNCT
ejpam-6841	139	11	are	be	AUX
ejpam-6841	139	12	equivalent	equivalent	ADJ
ejpam-6841	139	13	:	:	PUNCT
ejpam-6841	139	14	(	(	PUNCT
ejpam-6841	139	15	i	i	NOUN
ejpam-6841	139	16	)	)	PUNCT
ejpam-6841	139	17	infz	infz	PROPN
ejpam-6841	139	18	>	>	X
ejpam-6841	140	1	ε	ε	PROPN
ejpam-6841	140	2	j	j	PROPN
ejpam-6841	140	3	(	(	PUNCT
ejpam-6841	140	4	z	z	PROPN
ejpam-6841	140	5	)	)	PUNCT
ejpam-6841	140	6	>	>	PUNCT
ejpam-6841	141	1	−∞	−∞	X
ejpam-6841	141	2	for	for	ADP
ejpam-6841	141	3	every	every	DET
ejpam-6841	141	4	ε	ε	PROPN
ejpam-6841	141	5	>	>	X
ejpam-6841	141	6	0	0	PROPN
ejpam-6841	141	7	.	.	PUNCT
ejpam-6841	142	1	k.	k.	PROPN
ejpam-6841	142	2	javed	javed	PROPN
ejpam-6841	142	3	,	,	PUNCT
ejpam-6841	142	4	m.	m.	NOUN
ejpam-6841	142	5	nazam	nazam	PROPN
ejpam-6841	142	6	,	,	PUNCT
ejpam-6841	142	7	m.	m.	PROPN
ejpam-6841	142	8	arshad	arshad	PROPN
ejpam-6841	142	9	,	,	PUNCT
ejpam-6841	142	10	m.	m.	NOUN
ejpam-6841	142	11	de	de	X
ejpam-6841	142	12	la	la	PROPN
ejpam-6841	142	13	sen	sen	PROPN
ejpam-6841	142	14	/	/	SYM
ejpam-6841	142	15	eur	eur	PROPN
ejpam-6841	142	16	.	.	PUNCT
ejpam-6841	143	1	j.	j.	PROPN
ejpam-6841	143	2	pure	pure	PROPN
ejpam-6841	143	3	appl	appl	PROPN
ejpam-6841	143	4	.	.	PROPN
ejpam-6841	143	5	math	math	PROPN
ejpam-6841	143	6	,	,	PUNCT
ejpam-6841	143	7	18	18	NUM
ejpam-6841	143	8	(	(	PUNCT
ejpam-6841	143	9	4	4	NUM
ejpam-6841	143	10	)	)	PUNCT
ejpam-6841	143	11	(	(	PUNCT
ejpam-6841	143	12	2025	2025	NUM
ejpam-6841	143	13	)	)	PUNCT
ejpam-6841	143	14	,	,	PUNCT
ejpam-6841	143	15	6841	6841	NUM
ejpam-6841	143	16	7	7	NUM
ejpam-6841	143	17	of	of	ADP
ejpam-6841	143	18	23	23	NUM
ejpam-6841	143	19	(	(	PUNCT
ejpam-6841	143	20	ii	ii	NOUN
ejpam-6841	143	21	)	)	PUNCT
ejpam-6841	143	22	limz→ε+	limz→ε+	PUNCT
ejpam-6841	143	23	inf	inf	NOUN
ejpam-6841	143	24	j	j	PROPN
ejpam-6841	143	25	(	(	PUNCT
ejpam-6841	143	26	z	z	PROPN
ejpam-6841	143	27	)	)	PUNCT
ejpam-6841	143	28	>	>	PUNCT
ejpam-6841	144	1	−∞	−∞	X
ejpam-6841	144	2	for	for	ADP
ejpam-6841	144	3	every	every	DET
ejpam-6841	144	4	ε	ε	PROPN
ejpam-6841	144	5	>	>	X
ejpam-6841	144	6	0	0	PROPN
ejpam-6841	144	7	.	.	PUNCT
ejpam-6841	144	8	(	(	PUNCT
ejpam-6841	144	9	iii	iii	X
ejpam-6841	144	10	)	)	PUNCT
ejpam-6841	144	11	limn→∞	limn→∞	PROPN
ejpam-6841	144	12	j	j	PROPN
ejpam-6841	144	13	(	(	PUNCT
ejpam-6841	144	14	zn	zn	NOUN
ejpam-6841	144	15	)	)	PUNCT
ejpam-6841	144	16	=	=	PUNCT
ejpam-6841	145	1	−∞	−∞	ADP
ejpam-6841	145	2	implies	imply	VERB
ejpam-6841	145	3	that	that	SCONJ
ejpam-6841	145	4	limn→∞	limn→∞	PROPN
ejpam-6841	145	5	zn	zn	X
ejpam-6841	145	6	=	=	SYM
ejpam-6841	145	7	0	0	PROPN
ejpam-6841	145	8	.	.	PUNCT
ejpam-6841	146	1	lemma	lemma	PROPN
ejpam-6841	146	2	3	3	X
ejpam-6841	146	3	.	.	PUNCT
ejpam-6841	147	1	let	let	AUX
ejpam-6841	147	2	{	{	PUNCT
ejpam-6841	147	3	bn	bn	PART
ejpam-6841	147	4	}	}	PUNCT
ejpam-6841	147	5	be	be	AUX
ejpam-6841	147	6	a	a	DET
ejpam-6841	147	7	sequence	sequence	NOUN
ejpam-6841	147	8	in	in	ADP
ejpam-6841	147	9	(	(	PUNCT
ejpam-6841	147	10	w	w	PROPN
ejpam-6841	147	11	,	,	PUNCT
ejpam-6841	147	12	ϑ	ϑ	NOUN
ejpam-6841	147	13	)	)	PUNCT
ejpam-6841	147	14	obeying	obey	VERB
ejpam-6841	147	15	the	the	DET
ejpam-6841	147	16	equation	equation	NOUN
ejpam-6841	147	17	limn→∞	limn→∞	PRON
ejpam-6841	147	18	ϑ(bn	ϑ(bn	X
ejpam-6841	147	19	,	,	PUNCT
ejpam-6841	147	20	bn+1	bn+1	NUM
ejpam-6841	147	21	)	)	PUNCT
ejpam-6841	148	1	=	=	SYM
ejpam-6841	148	2	0	0	X
ejpam-6841	148	3	.	.	PUNCT
ejpam-6841	148	4	suppose	suppose	VERB
ejpam-6841	148	5	that	that	SCONJ
ejpam-6841	148	6	the	the	DET
ejpam-6841	148	7	mapping	mapping	NOUN
ejpam-6841	148	8	and	and	CCONJ
ejpam-6841	148	9	p	p	NOUN
ejpam-6841	148	10	:	:	PUNCT
ejpam-6841	148	11	c	c	X
ejpam-6841	148	12	→	→	PUNCT
ejpam-6841	148	13	d	d	X
ejpam-6841	148	14	satisfying	satisfy	VERB
ejpam-6841	148	15	the	the	DET
ejpam-6841	148	16	condition	condition	NOUN
ejpam-6841	148	17	(	(	PUNCT
ejpam-6841	148	18	2	2	NUM
ejpam-6841	148	19	)	)	PUNCT
ejpam-6841	148	20	.	.	PUNCT
ejpam-6841	149	1	if	if	SCONJ
ejpam-6841	149	2	j,£	j,£	PROPN
ejpam-6841	149	3	:	:	PUNCT
ejpam-6841	149	4	(	(	PUNCT
ejpam-6841	149	5	0,∞	0,∞	NUM
ejpam-6841	149	6	)	)	PUNCT
ejpam-6841	149	7	→	→	SYM
ejpam-6841	149	8	r	r	NOUN
ejpam-6841	149	9	are	be	AUX
ejpam-6841	149	10	such	such	ADJ
ejpam-6841	149	11	that	that	SCONJ
ejpam-6841	149	12	(	(	PUNCT
ejpam-6841	149	13	1	1	X
ejpam-6841	149	14	)	)	PUNCT
ejpam-6841	149	15	lim	lim	PROPN
ejpam-6841	149	16	supz→ε+£	supz→ε+£	PROPN
ejpam-6841	149	17	(	(	PUNCT
ejpam-6841	149	18	z	z	NOUN
ejpam-6841	149	19	)	)	PUNCT
ejpam-6841	149	20	<	<	X
ejpam-6841	149	21	j(∈	j(∈	ADV
ejpam-6841	150	1	+	+	PUNCT
ejpam-6841	150	2	)	)	PUNCT
ejpam-6841	151	1	for	for	ADP
ejpam-6841	151	2	any	any	DET
ejpam-6841	151	3	ε	ε	PROPN
ejpam-6841	151	4	>	>	X
ejpam-6841	151	5	0	0	PROPN
ejpam-6841	151	6	.	.	PUNCT
ejpam-6841	152	1	then	then	ADV
ejpam-6841	152	2	{	{	PUNCT
ejpam-6841	152	3	bn	bn	NOUN
ejpam-6841	152	4	}	}	PUNCT
ejpam-6841	152	5	is	be	AUX
ejpam-6841	152	6	cauchy	cauchy	NOUN
ejpam-6841	152	7	.	.	PUNCT
ejpam-6841	153	1	proof	proof	NOUN
ejpam-6841	153	2	.	.	PUNCT
ejpam-6841	154	1	consider	consider	VERB
ejpam-6841	154	2	sequence	sequence	NOUN
ejpam-6841	154	3	{	{	PUNCT
ejpam-6841	154	4	bn	bn	NOUN
ejpam-6841	154	5	}	}	PUNCT
ejpam-6841	154	6	is	be	AUX
ejpam-6841	154	7	not	not	PART
ejpam-6841	154	8	cauchy	cauchy	ADJ
ejpam-6841	154	9	,	,	PUNCT
ejpam-6841	154	10	then	then	ADV
ejpam-6841	154	11	by	by	ADP
ejpam-6841	154	12	lemma	lemma	PROPN
ejpam-6841	154	13	1	1	NUM
ejpam-6841	154	14	,	,	PUNCT
ejpam-6841	154	15	then	then	ADV
ejpam-6841	154	16	two	two	NUM
ejpam-6841	154	17	subsequences	subsequence	NOUN
ejpam-6841	154	18	{	{	PUNCT
ejpam-6841	154	19	bnk	bnk	PROPN
ejpam-6841	154	20	}	}	PUNCT
ejpam-6841	154	21	,	,	PUNCT
ejpam-6841	154	22	{	{	PUNCT
ejpam-6841	154	23	bmk	bmk	NOUN
ejpam-6841	154	24	}	}	PUNCT
ejpam-6841	154	25	of	of	ADP
ejpam-6841	154	26	{	{	PUNCT
ejpam-6841	154	27	bn	bn	NOUN
ejpam-6841	154	28	}	}	PUNCT
ejpam-6841	154	29	and	and	CCONJ
ejpam-6841	154	30	ε	ε	PROPN
ejpam-6841	154	31	>	>	X
ejpam-6841	154	32	0	0	NUM
ejpam-6841	155	1	such	such	ADJ
ejpam-6841	155	2	that	that	SCONJ
ejpam-6841	155	3	the	the	DET
ejpam-6841	155	4	equations	equation	NOUN
ejpam-6841	155	5	(	(	PUNCT
ejpam-6841	155	6	5	5	NUM
ejpam-6841	155	7	)	)	PUNCT
ejpam-6841	155	8	and	and	CCONJ
ejpam-6841	155	9	(	(	PUNCT
ejpam-6841	155	10	6	6	X
ejpam-6841	155	11	)	)	PUNCT
ejpam-6841	155	12	hold	hold	NOUN
ejpam-6841	155	13	.	.	PUNCT
ejpam-6841	156	1	by	by	ADP
ejpam-6841	156	2	(	(	PUNCT
ejpam-6841	156	3	5	5	NUM
ejpam-6841	156	4	)	)	PUNCT
ejpam-6841	156	5	,	,	PUNCT
ejpam-6841	156	6	we	we	PRON
ejpam-6841	156	7	get	get	VERB
ejpam-6841	156	8	that	that	SCONJ
ejpam-6841	156	9	ϑ(bnk+1	ϑ(bnk+1	NOUN
ejpam-6841	156	10	,	,	PUNCT
ejpam-6841	156	11	bmk+1	bmk+1	PROPN
ejpam-6841	156	12	)	)	PUNCT
ejpam-6841	156	13	>	>	PUNCT
ejpam-6841	157	1	ε	ε	PROPN
ejpam-6841	157	2	.	.	PUNCT
ejpam-6841	157	3	since	since	SCONJ
ejpam-6841	157	4	,	,	PUNCT
ejpam-6841	157	5	for	for	ADP
ejpam-6841	157	6	bnk	bnk	PROPN
ejpam-6841	157	7	,	,	PUNCT
ejpam-6841	157	8	bmk	bmk	PROPN
ejpam-6841	157	9	,	,	PUNCT
ejpam-6841	157	10	bmk+1	bmk+1	PROPN
ejpam-6841	157	11	,	,	PUNCT
ejpam-6841	157	12	bnk+1	bnk+1	NOUN
ejpam-6841	157	13	∈	∈	NOUN
ejpam-6841	157	14	c	c	NOUN
ejpam-6841	157	15	,	,	PUNCT
ejpam-6841	157	16	we	we	PRON
ejpam-6841	157	17	have	have	VERB
ejpam-6841	157	18	ϑ(bnk+1,p(bmk	ϑ(bnk+1,p(bmk	PUNCT
ejpam-6841	157	19	)	)	PUNCT
ejpam-6841	157	20	)	)	PUNCT
ejpam-6841	158	1	=	=	PUNCT
ejpam-6841	158	2	ϑ(c	ϑ(c	PROPN
ejpam-6841	158	3	,	,	PUNCT
ejpam-6841	158	4	d	d	NOUN
ejpam-6841	158	5	)	)	PUNCT
ejpam-6841	158	6	,	,	PUNCT
ejpam-6841	158	7	ϑ(bmk+1,p(bnk	ϑ(bmk+1,p(bnk	NOUN
ejpam-6841	158	8	)	)	PUNCT
ejpam-6841	158	9	)	)	PUNCT
ejpam-6841	159	1	=	=	PUNCT
ejpam-6841	159	2	ϑ(c	ϑ(c	PROPN
ejpam-6841	159	3	,	,	PUNCT
ejpam-6841	159	4	d	d	NOUN
ejpam-6841	159	5	)	)	PUNCT
ejpam-6841	159	6	,	,	PUNCT
ejpam-6841	159	7	for	for	ADP
ejpam-6841	159	8	all	all	DET
ejpam-6841	159	9	k	k	PROPN
ejpam-6841	159	10	≥	≥	NUM
ejpam-6841	159	11	1	1	NUM
ejpam-6841	159	12	.	.	PUNCT
ejpam-6841	159	13	thus	thus	ADV
ejpam-6841	159	14	,	,	PUNCT
ejpam-6841	159	15	by	by	ADP
ejpam-6841	159	16	(	(	PUNCT
ejpam-6841	159	17	2	2	NUM
ejpam-6841	159	18	)	)	PUNCT
ejpam-6841	159	19	,	,	PUNCT
ejpam-6841	159	20	we	we	PRON
ejpam-6841	159	21	have	have	VERB
ejpam-6841	159	22	j(ϑ(bnk+1	j(ϑ(bnk+1	NOUN
ejpam-6841	159	23	,	,	PUNCT
ejpam-6841	159	24	bmk+1	bmk+1	NOUN
ejpam-6841	159	25	)	)	PUNCT
ejpam-6841	159	26	)	)	PUNCT
ejpam-6841	160	1	≤	≤	NUM
ejpam-6841	160	2	£	£	SYM
ejpam-6841	160	3	(	(	PUNCT
ejpam-6841	160	4	ϑ(bnk	ϑ(bnk	NOUN
ejpam-6841	160	5	,	,	PUNCT
ejpam-6841	160	6	bmk	bmk	PROPN
ejpam-6841	160	7	)	)	PUNCT
ejpam-6841	160	8	)	)	PUNCT
ejpam-6841	160	9	,	,	PUNCT
ejpam-6841	160	10	for	for	ADP
ejpam-6841	160	11	any	any	DET
ejpam-6841	160	12	k	k	PROPN
ejpam-6841	160	13	≥	≥	NUM
ejpam-6841	160	14	1	1	NUM
ejpam-6841	160	15	.	.	PUNCT
ejpam-6841	161	1	for	for	ADP
ejpam-6841	161	2	if	if	SCONJ
ejpam-6841	161	3	ck	ck	NOUN
ejpam-6841	161	4	=	=	SYM
ejpam-6841	161	5	ϑ(bnk+1	ϑ(bnk+1	NOUN
ejpam-6841	161	6	,	,	PUNCT
ejpam-6841	161	7	bmk+1	bmk+1	NOUN
ejpam-6841	161	8	)	)	PUNCT
ejpam-6841	161	9	and	and	CCONJ
ejpam-6841	161	10	jk	jk	NOUN
ejpam-6841	161	11	=	=	PROPN
ejpam-6841	161	12	ϑ(bnk	ϑ(bnk	NOUN
ejpam-6841	161	13	,	,	PUNCT
ejpam-6841	161	14	bmk	bmk	PROPN
ejpam-6841	161	15	)	)	PUNCT
ejpam-6841	161	16	,	,	PUNCT
ejpam-6841	161	17	we	we	PRON
ejpam-6841	161	18	have	have	VERB
ejpam-6841	161	19	j(ck	j(ck	NOUN
ejpam-6841	161	20	)	)	PUNCT
ejpam-6841	161	21	≤	≤	NOUN
ejpam-6841	161	22	£	£	SYM
ejpam-6841	161	23	(	(	PUNCT
ejpam-6841	161	24	jk	jk	PROPN
ejpam-6841	161	25	)	)	PUNCT
ejpam-6841	161	26	,	,	PUNCT
ejpam-6841	161	27	for	for	ADP
ejpam-6841	161	28	any	any	DET
ejpam-6841	161	29	k	k	PROPN
ejpam-6841	161	30	≥	≥	NUM
ejpam-6841	161	31	1	1	NUM
ejpam-6841	161	32	.	.	PUNCT
ejpam-6841	162	1	(	(	PUNCT
ejpam-6841	162	2	7	7	NUM
ejpam-6841	162	3	)	)	PUNCT
ejpam-6841	162	4	by	by	ADP
ejpam-6841	162	5	(	(	PUNCT
ejpam-6841	162	6	5	5	NUM
ejpam-6841	162	7	)	)	PUNCT
ejpam-6841	162	8	and	and	CCONJ
ejpam-6841	162	9	(	(	PUNCT
ejpam-6841	162	10	6	6	NUM
ejpam-6841	162	11	)	)	PUNCT
ejpam-6841	162	12	,	,	PUNCT
ejpam-6841	162	13	we	we	PRON
ejpam-6841	162	14	have	have	VERB
ejpam-6841	162	15	limk→∞	limk→∞	ADV
ejpam-6841	162	16	ck	ck	VERB
ejpam-6841	162	17	=	=	SYM
ejpam-6841	162	18	ε+	ε+	NOUN
ejpam-6841	162	19	and	and	CCONJ
ejpam-6841	162	20	limk→∞	limk→∞	ADJ
ejpam-6841	162	21	jk	jk	PROPN
ejpam-6841	162	22	=	=	SYM
ejpam-6841	162	23	ε	ε	PROPN
ejpam-6841	162	24	.	.	PUNCT
ejpam-6841	163	1	by	by	ADP
ejpam-6841	163	2	(	(	PUNCT
ejpam-6841	163	3	7	7	NUM
ejpam-6841	163	4	)	)	PUNCT
ejpam-6841	163	5	,	,	PUNCT
ejpam-6841	163	6	we	we	PRON
ejpam-6841	163	7	get	get	VERB
ejpam-6841	163	8	that	that	DET
ejpam-6841	163	9	j(ε+	j(ε+	NOUN
ejpam-6841	163	10	)	)	PUNCT
ejpam-6841	164	1	=	=	SYM
ejpam-6841	164	2	lim	lim	PROPN
ejpam-6841	164	3	k→∞	k→∞	NOUN
ejpam-6841	164	4	j(ck	j(ck	ADJ
ejpam-6841	164	5	)	)	PUNCT
ejpam-6841	164	6	≤	≤	NOUN
ejpam-6841	164	7	lim	lim	PROPN
ejpam-6841	164	8	sup	sup	VERB
ejpam-6841	164	9	k→∞	k→∞	NOUN
ejpam-6841	164	10	£	£	PROPN
ejpam-6841	164	11	(	(	PUNCT
ejpam-6841	164	12	jk	jk	NOUN
ejpam-6841	164	13	)	)	PUNCT
ejpam-6841	164	14	≤	≤	NOUN
ejpam-6841	164	15	lim	lim	PROPN
ejpam-6841	164	16	sup	sup	VERB
ejpam-6841	164	17	c→ε	c→ε	PROPN
ejpam-6841	164	18	£	£	SYM
ejpam-6841	164	19	(	(	PUNCT
ejpam-6841	164	20	c	c	NOUN
ejpam-6841	164	21	)	)	PUNCT
ejpam-6841	164	22	.	.	PUNCT
ejpam-6841	165	1	(	(	PUNCT
ejpam-6841	165	2	8)	8)	NUM
ejpam-6841	165	3	this	this	PRON
ejpam-6841	165	4	is	be	AUX
ejpam-6841	165	5	a	a	DET
ejpam-6841	165	6	contradiction	contradiction	NOUN
ejpam-6841	165	7	to	to	ADP
ejpam-6841	165	8	the	the	DET
ejpam-6841	165	9	assumption	assumption	NOUN
ejpam-6841	165	10	(	(	PUNCT
ejpam-6841	165	11	1	1	NUM
ejpam-6841	165	12	)	)	PUNCT
ejpam-6841	165	13	.	.	PUNCT
ejpam-6841	166	1	consequently	consequently	ADV
ejpam-6841	166	2	,	,	PUNCT
ejpam-6841	166	3	{	{	PUNCT
ejpam-6841	166	4	bn	bn	X
ejpam-6841	166	5	}	}	PUNCT
ejpam-6841	166	6	is	be	AUX
ejpam-6841	166	7	a	a	DET
ejpam-6841	166	8	cauchy	cauchy	ADJ
ejpam-6841	166	9	sequence	sequence	NOUN
ejpam-6841	166	10	in	in	ADP
ejpam-6841	166	11	c.	c.	PROPN
ejpam-6841	166	12	theorem	theorem	PROPN
ejpam-6841	166	13	1	1	X
ejpam-6841	166	14	.	.	PUNCT
ejpam-6841	167	1	let	let	VERB
ejpam-6841	167	2	p	p	NOUN
ejpam-6841	167	3	:	:	PUNCT
ejpam-6841	167	4	c	c	X
ejpam-6841	167	5	→	→	PUNCT
ejpam-6841	167	6	d	d	X
ejpam-6841	167	7	be	be	AUX
ejpam-6841	167	8	a	a	DET
ejpam-6841	167	9	(	(	PUNCT
ejpam-6841	167	10	j,£)-proximal	j,£)-proximal	ADJ
ejpam-6841	167	11	contraction	contraction	NOUN
ejpam-6841	167	12	defined	define	VERB
ejpam-6841	167	13	on	on	ADP
ejpam-6841	167	14	a	a	DET
ejpam-6841	167	15	complete	complete	ADJ
ejpam-6841	167	16	metric	metric	ADJ
ejpam-6841	167	17	space	space	NOUN
ejpam-6841	167	18	(	(	PUNCT
ejpam-6841	167	19	w	w	NOUN
ejpam-6841	167	20	,	,	PUNCT
ejpam-6841	167	21	ϑ	ϑ	NOUN
ejpam-6841	167	22	)	)	PUNCT
ejpam-6841	167	23	and	and	CCONJ
ejpam-6841	167	24	c	c	X
ejpam-6841	167	25	,	,	PUNCT
ejpam-6841	167	26	d	d	NOUN
ejpam-6841	167	27	be	be	AUX
ejpam-6841	167	28	nonvoid	nonvoid	ADJ
ejpam-6841	167	29	,	,	PUNCT
ejpam-6841	167	30	closed	closed	ADJ
ejpam-6841	167	31	subsets	subset	NOUN
ejpam-6841	167	32	of	of	ADP
ejpam-6841	167	33	w	w	ADP
ejpam-6841	167	34	such	such	ADJ
ejpam-6841	167	35	that	that	SCONJ
ejpam-6841	167	36	d	d	NOUN
ejpam-6841	167	37	is	be	AUX
ejpam-6841	167	38	approximately	approximately	ADV
ejpam-6841	167	39	compact	compact	ADJ
ejpam-6841	167	40	with	with	ADP
ejpam-6841	167	41	respect	respect	NOUN
ejpam-6841	167	42	to	to	ADP
ejpam-6841	167	43	c.	c.	NOUN
ejpam-6841	167	44	if	if	SCONJ
ejpam-6841	167	45	(	(	PUNCT
ejpam-6841	167	46	i	i	NOUN
ejpam-6841	167	47	)	)	PUNCT
ejpam-6841	167	48	j	j	PROPN
ejpam-6841	167	49	is	be	AUX
ejpam-6841	167	50	non	non	ADJ
ejpam-6841	167	51	-	-	ADJ
ejpam-6841	167	52	decreasing	decrease	VERB
ejpam-6841	167	53	function	function	NOUN
ejpam-6841	167	54	and	and	CCONJ
ejpam-6841	167	55	lim	lim	PROPN
ejpam-6841	167	56	supt→ε+£	supt→ε+£	PROPN
ejpam-6841	167	57	(	(	PUNCT
ejpam-6841	167	58	t	t	PROPN
ejpam-6841	167	59	)	)	PUNCT
ejpam-6841	167	60	<	<	X
ejpam-6841	167	61	j(ε+	j(ε+	NOUN
ejpam-6841	167	62	)	)	PUNCT
ejpam-6841	167	63	for	for	ADP
ejpam-6841	167	64	any	any	DET
ejpam-6841	167	65	ε	ε	PROPN
ejpam-6841	167	66	>	>	X
ejpam-6841	167	67	0	0	PROPN
ejpam-6841	167	68	.	.	PUNCT
ejpam-6841	168	1	(	(	PUNCT
ejpam-6841	168	2	ii	ii	X
ejpam-6841	168	3	)	)	PUNCT
ejpam-6841	168	4	c0	c0	PROPN
ejpam-6841	168	5	is	be	AUX
ejpam-6841	168	6	non	non	ADJ
ejpam-6841	168	7	-	-	ADJ
ejpam-6841	168	8	void	void	ADJ
ejpam-6841	168	9	subset	subset	NOUN
ejpam-6841	168	10	of	of	ADP
ejpam-6841	168	11	c	c	PROPN
ejpam-6841	168	12	such	such	ADJ
ejpam-6841	168	13	that	that	DET
ejpam-6841	168	14	p(c0	p(c0	NOUN
ejpam-6841	168	15	)	)	PUNCT
ejpam-6841	168	16	⊆	⊆	NUM
ejpam-6841	168	17	d0	d0	NOUN
ejpam-6841	168	18	.	.	PUNCT
ejpam-6841	169	1	then	then	ADV
ejpam-6841	169	2	p	p	X
ejpam-6841	169	3	has	have	VERB
ejpam-6841	169	4	a	a	DET
ejpam-6841	169	5	best	good	ADJ
ejpam-6841	169	6	proximity	proximity	NOUN
ejpam-6841	169	7	point	point	NOUN
ejpam-6841	169	8	.	.	PUNCT
ejpam-6841	170	1	k.	k.	PROPN
ejpam-6841	170	2	javed	javed	PROPN
ejpam-6841	170	3	,	,	PUNCT
ejpam-6841	170	4	m.	m.	NOUN
ejpam-6841	170	5	nazam	nazam	PROPN
ejpam-6841	170	6	,	,	PUNCT
ejpam-6841	170	7	m.	m.	PROPN
ejpam-6841	170	8	arshad	arshad	PROPN
ejpam-6841	170	9	,	,	PUNCT
ejpam-6841	170	10	m.	m.	NOUN
ejpam-6841	170	11	de	de	X
ejpam-6841	170	12	la	la	PROPN
ejpam-6841	170	13	sen	sen	PROPN
ejpam-6841	170	14	/	/	SYM
ejpam-6841	170	15	eur	eur	PROPN
ejpam-6841	170	16	.	.	PUNCT
ejpam-6841	171	1	j.	j.	PROPN
ejpam-6841	171	2	pure	pure	PROPN
ejpam-6841	171	3	appl	appl	PROPN
ejpam-6841	171	4	.	.	PROPN
ejpam-6841	171	5	math	math	PROPN
ejpam-6841	171	6	,	,	PUNCT
ejpam-6841	171	7	18	18	NUM
ejpam-6841	171	8	(	(	PUNCT
ejpam-6841	171	9	4	4	NUM
ejpam-6841	171	10	)	)	PUNCT
ejpam-6841	171	11	(	(	PUNCT
ejpam-6841	171	12	2025	2025	NUM
ejpam-6841	171	13	)	)	PUNCT
ejpam-6841	171	14	,	,	PUNCT
ejpam-6841	171	15	6841	6841	NUM
ejpam-6841	171	16	8	8	NUM
ejpam-6841	171	17	of	of	ADP
ejpam-6841	171	18	23	23	NUM
ejpam-6841	171	19	proof	proof	NOUN
ejpam-6841	171	20	.	.	PUNCT
ejpam-6841	172	1	let	let	VERB
ejpam-6841	172	2	b0	b0	VERB
ejpam-6841	172	3	∈	∈	PROPN
ejpam-6841	172	4	c0	c0	NOUN
ejpam-6841	172	5	.	.	PUNCT
ejpam-6841	173	1	since	since	SCONJ
ejpam-6841	173	2	p(b0	p(b0	NOUN
ejpam-6841	173	3	)	)	PUNCT
ejpam-6841	173	4	∈	∈	PROPN
ejpam-6841	173	5	p(c0	p(c0	NOUN
ejpam-6841	173	6	)	)	PUNCT
ejpam-6841	173	7	⊆	⊆	NUM
ejpam-6841	173	8	d0	d0	NOUN
ejpam-6841	173	9	,	,	PUNCT
ejpam-6841	173	10	there	there	PRON
ejpam-6841	173	11	exists	exist	VERB
ejpam-6841	173	12	b1	b1	PROPN
ejpam-6841	173	13	∈	∈	PROPN
ejpam-6841	173	14	c0	c0	NOUN
ejpam-6841	173	15	such	such	ADJ
ejpam-6841	173	16	that	that	SCONJ
ejpam-6841	173	17	,	,	PUNCT
ejpam-6841	173	18	ϑ(b1,p(b0	ϑ(b1,p(b0	NOUN
ejpam-6841	173	19	)	)	PUNCT
ejpam-6841	173	20	)	)	PUNCT
ejpam-6841	174	1	=	=	PUNCT
ejpam-6841	174	2	ϑ(c	ϑ(c	PROPN
ejpam-6841	174	3	,	,	PUNCT
ejpam-6841	174	4	d	d	NOUN
ejpam-6841	174	5	)	)	PUNCT
ejpam-6841	174	6	.	.	PUNCT
ejpam-6841	175	1	also	also	ADV
ejpam-6841	175	2	we	we	PRON
ejpam-6841	175	3	have	have	VERB
ejpam-6841	175	4	p(b1	p(b1	NOUN
ejpam-6841	175	5	)	)	PUNCT
ejpam-6841	175	6	∈	∈	PROPN
ejpam-6841	175	7	p(c0	p(c0	NOUN
ejpam-6841	175	8	)	)	PUNCT
ejpam-6841	175	9	⊆	⊆	NUM
ejpam-6841	175	10	d0	d0	NOUN
ejpam-6841	175	11	,	,	PUNCT
ejpam-6841	175	12	so	so	ADV
ejpam-6841	175	13	,	,	PUNCT
ejpam-6841	175	14	there	there	PRON
ejpam-6841	175	15	exist	exist	VERB
ejpam-6841	175	16	b2	b2	NOUN
ejpam-6841	175	17	∈	∈	NOUN
ejpam-6841	175	18	c0	c0	NOUN
ejpam-6841	175	19	such	such	ADJ
ejpam-6841	175	20	that	that	DET
ejpam-6841	175	21	ϑ(b2,p(b1	ϑ(b2,p(b1	NOUN
ejpam-6841	175	22	)	)	PUNCT
ejpam-6841	175	23	)	)	PUNCT
ejpam-6841	176	1	=	=	PUNCT
ejpam-6841	176	2	ϑ(c	ϑ(c	PROPN
ejpam-6841	176	3	,	,	PUNCT
ejpam-6841	176	4	d	d	NOUN
ejpam-6841	176	5	)	)	PUNCT
ejpam-6841	176	6	.	.	PUNCT
ejpam-6841	177	1	then	then	ADV
ejpam-6841	177	2	c0	c0	PROPN
ejpam-6841	177	3	implies	imply	VERB
ejpam-6841	177	4	to	to	PART
ejpam-6841	177	5	have	have	VERB
ejpam-6841	177	6	a	a	DET
ejpam-6841	177	7	sequence	sequence	NOUN
ejpam-6841	177	8	{	{	PUNCT
ejpam-6841	177	9	bn	bn	NOUN
ejpam-6841	177	10	}	}	PUNCT
ejpam-6841	177	11	⊆	⊆	NUM
ejpam-6841	177	12	c0	c0	NOUN
ejpam-6841	177	13	such	such	ADJ
ejpam-6841	177	14	that	that	SCONJ
ejpam-6841	177	15	ϑ(bn	ϑ(bn	NOUN
ejpam-6841	177	16	,	,	PUNCT
ejpam-6841	177	17	p(bn−1	p(bn−1	NUM
ejpam-6841	177	18	)	)	PUNCT
ejpam-6841	177	19	)	)	PUNCT
ejpam-6841	178	1	=	=	PUNCT
ejpam-6841	178	2	ϑ(c	ϑ(c	PROPN
ejpam-6841	178	3	,	,	PUNCT
ejpam-6841	178	4	d	d	NOUN
ejpam-6841	178	5	)	)	PUNCT
ejpam-6841	178	6	,	,	PUNCT
ejpam-6841	178	7	for	for	ADP
ejpam-6841	178	8	all	all	DET
ejpam-6841	178	9	n	n	PRON
ejpam-6841	178	10	∈	∈	PROPN
ejpam-6841	178	11	n.	n.	NOUN
ejpam-6841	178	12	(	(	PUNCT
ejpam-6841	178	13	9	9	NUM
ejpam-6841	178	14	)	)	PUNCT
ejpam-6841	178	15	if	if	SCONJ
ejpam-6841	178	16	∃	∃	PROPN
ejpam-6841	178	17	n	n	PROPN
ejpam-6841	178	18	∈	∈	PROPN
ejpam-6841	178	19	n	n	PRON
ejpam-6841	178	20	such	such	ADJ
ejpam-6841	178	21	that	that	PRON
ejpam-6841	178	22	bn	bn	NOUN
ejpam-6841	178	23	=	=	SYM
ejpam-6841	178	24	bn+1	bn+1	PROPN
ejpam-6841	178	25	,	,	PUNCT
ejpam-6841	178	26	then	then	ADV
ejpam-6841	178	27	by	by	ADP
ejpam-6841	178	28	(	(	PUNCT
ejpam-6841	178	29	9	9	NUM
ejpam-6841	178	30	)	)	PUNCT
ejpam-6841	178	31	,	,	PUNCT
ejpam-6841	178	32	then	then	ADV
ejpam-6841	178	33	bn	bn	PRON
ejpam-6841	178	34	is	be	AUX
ejpam-6841	178	35	a	a	DET
ejpam-6841	178	36	best	good	ADJ
ejpam-6841	178	37	proximity	proximity	NOUN
ejpam-6841	178	38	point	point	NOUN
ejpam-6841	178	39	of	of	ADP
ejpam-6841	178	40	the	the	DET
ejpam-6841	178	41	mapping	mapping	NOUN
ejpam-6841	178	42	p.	p.	NOUN
ejpam-6841	179	1	if	if	SCONJ
ejpam-6841	179	2	bn−1	bn−1	PROPN
ejpam-6841	179	3	6=	6=	NUM
ejpam-6841	179	4	bn	bn	NOUN
ejpam-6841	179	5	∀	∀	NOUN
ejpam-6841	179	6	n	n	ADP
ejpam-6841	179	7	∈	∈	PROPN
ejpam-6841	179	8	n	n	CCONJ
ejpam-6841	179	9	,	,	PUNCT
ejpam-6841	179	10	then	then	ADV
ejpam-6841	179	11	by	by	ADP
ejpam-6841	179	12	(	(	PUNCT
ejpam-6841	179	13	9	9	NUM
ejpam-6841	179	14	)	)	PUNCT
ejpam-6841	179	15	,	,	PUNCT
ejpam-6841	179	16	we	we	PRON
ejpam-6841	179	17	have	have	VERB
ejpam-6841	179	18	ϑ(bn	ϑ(bn	NOUN
ejpam-6841	179	19	,	,	PUNCT
ejpam-6841	179	20	p(bn−1	p(bn−1	NUM
ejpam-6841	179	21	)	)	PUNCT
ejpam-6841	179	22	)	)	PUNCT
ejpam-6841	180	1	=	=	PUNCT
ejpam-6841	180	2	ϑ(c	ϑ(c	PROPN
ejpam-6841	180	3	,	,	PUNCT
ejpam-6841	180	4	d	d	NOUN
ejpam-6841	180	5	)	)	PUNCT
ejpam-6841	180	6	,	,	PUNCT
ejpam-6841	180	7	ϑ(bn+1,p(bn	ϑ(bn+1,p(bn	X
ejpam-6841	180	8	)	)	PUNCT
ejpam-6841	180	9	)	)	PUNCT
ejpam-6841	181	1	=	=	PUNCT
ejpam-6841	181	2	ϑ(c	ϑ(c	PROPN
ejpam-6841	181	3	,	,	PUNCT
ejpam-6841	181	4	d	d	NOUN
ejpam-6841	181	5	)	)	PUNCT
ejpam-6841	181	6	,	,	PUNCT
ejpam-6841	181	7	for	for	ADP
ejpam-6841	181	8	all	all	DET
ejpam-6841	181	9	n	n	PRON
ejpam-6841	181	10	≥	≥	NOUN
ejpam-6841	181	11	1	1	NUM
ejpam-6841	181	12	.	.	PUNCT
ejpam-6841	181	13	thus	thus	ADV
ejpam-6841	181	14	,	,	PUNCT
ejpam-6841	181	15	by	by	ADP
ejpam-6841	181	16	(	(	PUNCT
ejpam-6841	181	17	2	2	NUM
ejpam-6841	181	18	)	)	PUNCT
ejpam-6841	181	19	,	,	PUNCT
ejpam-6841	181	20	we	we	PRON
ejpam-6841	181	21	have	have	VERB
ejpam-6841	181	22	j(ϑ(bn	j(ϑ(bn	PROPN
ejpam-6841	181	23	,	,	PUNCT
ejpam-6841	181	24	bn+1	bn+1	NUM
ejpam-6841	181	25	)	)	PUNCT
ejpam-6841	181	26	)	)	PUNCT
ejpam-6841	182	1	≤	≤	NUM
ejpam-6841	182	2	£	£	SYM
ejpam-6841	182	3	(	(	PUNCT
ejpam-6841	182	4	ϑ(bn−1	ϑ(bn−1	NOUN
ejpam-6841	182	5	,	,	PUNCT
ejpam-6841	182	6	bn	bn	NOUN
ejpam-6841	182	7	)	)	PUNCT
ejpam-6841	182	8	)	)	PUNCT
ejpam-6841	182	9	,	,	PUNCT
ejpam-6841	182	10	for	for	ADP
ejpam-6841	182	11	all	all	PRON
ejpam-6841	182	12	bn−1	bn−1	ADJ
ejpam-6841	182	13	,	,	PUNCT
ejpam-6841	182	14	bn	bn	ADJ
ejpam-6841	182	15	,	,	PUNCT
ejpam-6841	182	16	bn+1	bn+1	PROPN
ejpam-6841	182	17	∈	∈	PROPN
ejpam-6841	182	18	c.	c.	PROPN
ejpam-6841	182	19	let	let	VERB
ejpam-6841	182	20	ϑ(bn	ϑ(bn	PROPN
ejpam-6841	182	21	,	,	PUNCT
ejpam-6841	182	22	bn+1	bn+1	NUM
ejpam-6841	182	23	)	)	PUNCT
ejpam-6841	183	1	=	=	SYM
ejpam-6841	183	2	θn	θn	PROPN
ejpam-6841	183	3	,	,	PUNCT
ejpam-6841	183	4	we	we	PRON
ejpam-6841	183	5	have	have	VERB
ejpam-6841	183	6	j(θn	j(θn	NOUN
ejpam-6841	183	7	)	)	PUNCT
ejpam-6841	183	8	≤	≤	NOUN
ejpam-6841	183	9	f(θn−1	f(θn−1	PUNCT
ejpam-6841	183	10	)	)	PUNCT
ejpam-6841	183	11	<	<	X
ejpam-6841	183	12	j(θn−1	j(θn−1	PROPN
ejpam-6841	183	13	)	)	PUNCT
ejpam-6841	183	14	.	.	PUNCT
ejpam-6841	184	1	(	(	PUNCT
ejpam-6841	184	2	10	10	NUM
ejpam-6841	184	3	)	)	PUNCT
ejpam-6841	184	4	since	since	SCONJ
ejpam-6841	184	5	j	j	PROPN
ejpam-6841	184	6	is	be	AUX
ejpam-6841	184	7	non	non	ADJ
ejpam-6841	184	8	-	-	ADJ
ejpam-6841	184	9	decreasing	decrease	VERB
ejpam-6841	184	10	,	,	PUNCT
ejpam-6841	184	11	so	so	ADV
ejpam-6841	184	12	,	,	PUNCT
ejpam-6841	184	13	by	by	ADP
ejpam-6841	184	14	(	(	PUNCT
ejpam-6841	184	15	10	10	NUM
ejpam-6841	184	16	)	)	PUNCT
ejpam-6841	184	17	,	,	PUNCT
ejpam-6841	184	18	we	we	PRON
ejpam-6841	184	19	have	have	VERB
ejpam-6841	184	20	θn	θn	VERB
ejpam-6841	184	21	<	<	X
ejpam-6841	184	22	θn−1	θn−1	PROPN
ejpam-6841	184	23	for	for	ADP
ejpam-6841	184	24	all	all	PRON
ejpam-6841	184	25	n	n	PRON
ejpam-6841	184	26	∈	∈	NOUN
ejpam-6841	184	27	n	n	NOUN
ejpam-6841	184	28	.	.	PUNCT
ejpam-6841	185	1	if	if	SCONJ
ejpam-6841	185	2	θ	θ	PROPN
ejpam-6841	185	3	>	>	X
ejpam-6841	185	4	0	0	NUM
ejpam-6841	185	5	,	,	PUNCT
ejpam-6841	185	6	so	so	SCONJ
ejpam-6841	185	7	that	that	SCONJ
ejpam-6841	185	8	,	,	PUNCT
ejpam-6841	185	9	by	by	ADP
ejpam-6841	185	10	(	(	PUNCT
ejpam-6841	185	11	10	10	NUM
ejpam-6841	185	12	)	)	PUNCT
ejpam-6841	185	13	,	,	PUNCT
ejpam-6841	185	14	we	we	PRON
ejpam-6841	185	15	obtain	obtain	VERB
ejpam-6841	185	16	the	the	DET
ejpam-6841	185	17	following	following	NOUN
ejpam-6841	185	18	:	:	PUNCT
ejpam-6841	185	19	j	j	PROPN
ejpam-6841	185	20	(	(	PUNCT
ejpam-6841	185	21	θ+	θ+	X
ejpam-6841	185	22	)	)	PUNCT
ejpam-6841	186	1	=	=	VERB
ejpam-6841	186	2	lim	lim	PROPN
ejpam-6841	186	3	n→∞	n→∞	X
ejpam-6841	186	4	j	j	PROPN
ejpam-6841	186	5	(	(	PUNCT
ejpam-6841	186	6	θn	θn	NOUN
ejpam-6841	186	7	)	)	PUNCT
ejpam-6841	186	8	≤	≤	NOUN
ejpam-6841	186	9	lim	lim	PROPN
ejpam-6841	186	10	n→∞	n→∞	PROPN
ejpam-6841	186	11	f	f	PROPN
ejpam-6841	186	12	(	(	PUNCT
ejpam-6841	186	13	θn−1	θn−1	PROPN
ejpam-6841	186	14	)	)	PUNCT
ejpam-6841	186	15	≤	≤	PROPN
ejpam-6841	186	16	lim	lim	PROPN
ejpam-6841	186	17	t→θ+	t→θ+	PROPN
ejpam-6841	186	18	supf	supf	PROPN
ejpam-6841	186	19	(	(	PUNCT
ejpam-6841	186	20	t	t	PROPN
ejpam-6841	186	21	)	)	PUNCT
ejpam-6841	186	22	.	.	PUNCT
ejpam-6841	187	1	this	this	PRON
ejpam-6841	187	2	defies	defy	VERB
ejpam-6841	187	3	presumption	presumption	NOUN
ejpam-6841	187	4	(	(	PUNCT
ejpam-6841	187	5	i	i	NOUN
ejpam-6841	187	6	)	)	PUNCT
ejpam-6841	187	7	,	,	PUNCT
ejpam-6841	187	8	hence	hence	ADV
ejpam-6841	187	9	,	,	PUNCT
ejpam-6841	187	10	θ	θ	PROPN
ejpam-6841	187	11	=	=	SYM
ejpam-6841	187	12	0	0	NUM
ejpam-6841	187	13	and	and	CCONJ
ejpam-6841	187	14	limn→∞	limn→∞	PRON
ejpam-6841	187	15	ϑ(bn	ϑ(bn	NOUN
ejpam-6841	187	16	,	,	PUNCT
ejpam-6841	187	17	bn+1	bn+1	NUM
ejpam-6841	187	18	)	)	PUNCT
ejpam-6841	188	1	=	=	SYM
ejpam-6841	188	2	0	0	X
ejpam-6841	188	3	.	.	PUNCT
ejpam-6841	189	1	now	now	ADV
ejpam-6841	189	2	(	(	PUNCT
ejpam-6841	189	3	i	i	NOUN
ejpam-6841	189	4	)	)	PUNCT
ejpam-6841	189	5	and	and	CCONJ
ejpam-6841	189	6	lemma	lemma	PROPN
ejpam-6841	189	7	3	3	NUM
ejpam-6841	189	8	,	,	PUNCT
ejpam-6841	189	9	we	we	PRON
ejpam-6841	189	10	conclude	conclude	VERB
ejpam-6841	189	11	that	that	SCONJ
ejpam-6841	189	12	{	{	PUNCT
ejpam-6841	189	13	bn	bn	NOUN
ejpam-6841	189	14	}	}	PUNCT
ejpam-6841	189	15	is	be	AUX
ejpam-6841	189	16	a	a	DET
ejpam-6841	189	17	cauchy	cauchy	ADJ
ejpam-6841	189	18	sequence	sequence	NOUN
ejpam-6841	189	19	.	.	PUNCT
ejpam-6841	190	1	since	since	SCONJ
ejpam-6841	190	2	(	(	PUNCT
ejpam-6841	190	3	w	w	PROPN
ejpam-6841	190	4	,	,	PUNCT
ejpam-6841	190	5	ϑ	ϑ	NOUN
ejpam-6841	190	6	)	)	PUNCT
ejpam-6841	190	7	is	be	AUX
ejpam-6841	190	8	a	a	DET
ejpam-6841	190	9	complete	complete	ADJ
ejpam-6841	190	10	metric	metric	ADJ
ejpam-6841	190	11	space	space	NOUN
ejpam-6841	190	12	and	and	CCONJ
ejpam-6841	190	13	c	c	NOUN
ejpam-6841	190	14	is	be	AUX
ejpam-6841	190	15	a	a	DET
ejpam-6841	190	16	closed	closed	ADJ
ejpam-6841	190	17	subset	subset	NOUN
ejpam-6841	190	18	of	of	ADP
ejpam-6841	190	19	w.	w.	PROPN
ejpam-6841	190	20	then	then	ADV
ejpam-6841	190	21	there	there	PRON
ejpam-6841	190	22	exists	exist	VERB
ejpam-6841	190	23	b∗	b∗	ADJ
ejpam-6841	190	24	∈	∈	PROPN
ejpam-6841	190	25	c	c	NOUN
ejpam-6841	190	26	,	,	PUNCT
ejpam-6841	190	27	such	such	ADJ
ejpam-6841	190	28	that	that	SCONJ
ejpam-6841	190	29	limn→∞	limn→∞	PROPN
ejpam-6841	190	30	ϑ(bn	ϑ(bn	PROPN
ejpam-6841	190	31	,	,	PUNCT
ejpam-6841	190	32	b	b	NOUN
ejpam-6841	190	33	∗	∗	NOUN
ejpam-6841	190	34	)	)	PUNCT
ejpam-6841	191	1	=	=	SYM
ejpam-6841	191	2	0	0	X
ejpam-6841	191	3	.	.	PUNCT
ejpam-6841	192	1	moreover	moreover	ADV
ejpam-6841	192	2	,	,	PUNCT
ejpam-6841	192	3	ϑ(b∗,p(bn	ϑ(b∗,p(bn	PROPN
ejpam-6841	192	4	)	)	PUNCT
ejpam-6841	192	5	)	)	PUNCT
ejpam-6841	192	6	≤	≤	PROPN
ejpam-6841	192	7	ϑ(b∗	ϑ(b∗	X
ejpam-6841	192	8	,	,	PUNCT
ejpam-6841	192	9	bn+1	bn+1	NUM
ejpam-6841	192	10	)	)	PUNCT
ejpam-6841	192	11	+	+	CCONJ
ejpam-6841	192	12	ϑ(bn+1,p(bn	ϑ(bn+1,p(bn	NOUN
ejpam-6841	192	13	)	)	PUNCT
ejpam-6841	192	14	)	)	PUNCT
ejpam-6841	192	15	≤	≤	PROPN
ejpam-6841	192	16	ϑ(b∗	ϑ(b∗	X
ejpam-6841	192	17	,	,	PUNCT
ejpam-6841	192	18	bn+1	bn+1	NUM
ejpam-6841	192	19	)	)	PUNCT
ejpam-6841	193	1	+	+	CCONJ
ejpam-6841	193	2	ϑ(c	ϑ(c	PROPN
ejpam-6841	193	3	,	,	PUNCT
ejpam-6841	193	4	d	d	NOUN
ejpam-6841	193	5	)	)	PUNCT
ejpam-6841	193	6	≤	≤	PROPN
ejpam-6841	193	7	ϑ(b∗	ϑ(b∗	X
ejpam-6841	193	8	,	,	PUNCT
ejpam-6841	193	9	bn+1	bn+1	NUM
ejpam-6841	193	10	)	)	PUNCT
ejpam-6841	193	11	+	+	CCONJ
ejpam-6841	193	12	ϑ(b∗,d	ϑ(b∗,d	NUM
ejpam-6841	193	13	)	)	PUNCT
ejpam-6841	193	14	.	.	PUNCT
ejpam-6841	194	1	therefore	therefore	ADV
ejpam-6841	194	2	,	,	PUNCT
ejpam-6841	194	3	ϑ(b∗,p(bn	ϑ(b∗,p(bn	PROPN
ejpam-6841	194	4	)	)	PUNCT
ejpam-6841	194	5	)	)	PUNCT
ejpam-6841	194	6	→	→	SYM
ejpam-6841	194	7	ϑ(b∗,d	ϑ(b∗,d	NUM
ejpam-6841	194	8	)	)	PUNCT
ejpam-6841	194	9	as	as	ADP
ejpam-6841	194	10	n	n	PROPN
ejpam-6841	194	11	→	→	SYM
ejpam-6841	194	12	∞.	∞.	PROPN
ejpam-6841	194	13	since	since	SCONJ
ejpam-6841	194	14	d	d	PROPN
ejpam-6841	194	15	is	be	AUX
ejpam-6841	194	16	approximately	approximately	ADV
ejpam-6841	194	17	compact	compact	ADJ
ejpam-6841	194	18	with	with	ADP
ejpam-6841	194	19	respect	respect	NOUN
ejpam-6841	194	20	to	to	ADP
ejpam-6841	194	21	c	c	NOUN
ejpam-6841	194	22	,	,	PUNCT
ejpam-6841	194	23	there	there	PRON
ejpam-6841	194	24	exists	exist	VERB
ejpam-6841	194	25	a	a	DET
ejpam-6841	194	26	subsequence	subsequence	NOUN
ejpam-6841	194	27	{	{	PUNCT
ejpam-6841	194	28	p(bnk	p(bnk	NOUN
ejpam-6841	194	29	)	)	PUNCT
ejpam-6841	194	30	}	}	PUNCT
ejpam-6841	194	31	of	of	ADP
ejpam-6841	194	32	{	{	PUNCT
ejpam-6841	194	33	p(bn	p(bn	NOUN
ejpam-6841	194	34	)	)	PUNCT
ejpam-6841	194	35	}	}	PUNCT
ejpam-6841	194	36	.	.	PUNCT
ejpam-6841	195	1	such	such	ADJ
ejpam-6841	195	2	that	that	SCONJ
ejpam-6841	195	3	p(bnk	p(bnk	NOUN
ejpam-6841	195	4	)	)	PUNCT
ejpam-6841	195	5	→	→	SYM
ejpam-6841	195	6	m∗	m∗	VERB
ejpam-6841	195	7	∈	∈	PROPN
ejpam-6841	195	8	d	d	NOUN
ejpam-6841	195	9	as	as	ADP
ejpam-6841	195	10	k	k	PROPN
ejpam-6841	195	11	→	→	SYM
ejpam-6841	195	12	∞.	∞.	PROPN
ejpam-6841	195	13	thus	thus	ADV
ejpam-6841	195	14	,	,	PUNCT
ejpam-6841	195	15	by	by	ADP
ejpam-6841	195	16	solving	solve	VERB
ejpam-6841	195	17	the	the	DET
ejpam-6841	195	18	following	follow	VERB
ejpam-6841	195	19	equation	equation	NOUN
ejpam-6841	195	20	with	with	ADP
ejpam-6841	195	21	k	k	PROPN
ejpam-6841	195	22	→	→	SYM
ejpam-6841	195	23	∞	∞	PROPN
ejpam-6841	195	24	,	,	PUNCT
ejpam-6841	195	25	ϑ(bnk+1	ϑ(bnk+1	NOUN
ejpam-6841	195	26	,	,	PUNCT
ejpam-6841	195	27	p(bnk	p(bnk	NOUN
ejpam-6841	195	28	)	)	PUNCT
ejpam-6841	195	29	)	)	PUNCT
ejpam-6841	196	1	=	=	PUNCT
ejpam-6841	196	2	ϑ(c	ϑ(c	PROPN
ejpam-6841	196	3	,	,	PUNCT
ejpam-6841	196	4	d	d	NOUN
ejpam-6841	196	5	)	)	PUNCT
ejpam-6841	196	6	,	,	PUNCT
ejpam-6841	196	7	(	(	PUNCT
ejpam-6841	196	8	11	11	X
ejpam-6841	196	9	)	)	PUNCT
ejpam-6841	196	10	we	we	PRON
ejpam-6841	196	11	have	have	VERB
ejpam-6841	196	12	,	,	PUNCT
ejpam-6841	196	13	ϑ(b∗	ϑ(b∗	NOUN
ejpam-6841	196	14	,	,	PUNCT
ejpam-6841	196	15	θ∗	θ∗	NOUN
ejpam-6841	196	16	)	)	PUNCT
ejpam-6841	196	17	=	=	PUNCT
ejpam-6841	197	1	ϑ(c	ϑ(c	NOUN
ejpam-6841	197	2	,	,	PUNCT
ejpam-6841	197	3	d	d	NOUN
ejpam-6841	197	4	)	)	PUNCT
ejpam-6841	197	5	.	.	PUNCT
ejpam-6841	198	1	since	since	ADV
ejpam-6841	198	2	,	,	PUNCT
ejpam-6841	198	3	l∗	l∗	PROPN
ejpam-6841	198	4	∈	∈	PROPN
ejpam-6841	198	5	c0	c0	PROPN
ejpam-6841	198	6	,	,	PUNCT
ejpam-6841	198	7	so	so	ADV
ejpam-6841	198	8	,	,	PUNCT
ejpam-6841	198	9	p(b∗	p(b∗	NOUN
ejpam-6841	198	10	)	)	PUNCT
ejpam-6841	198	11	∈	∈	PROPN
ejpam-6841	198	12	p(c0	p(c0	NOUN
ejpam-6841	198	13	)	)	PUNCT
ejpam-6841	198	14	⊆	⊆	NUM
ejpam-6841	198	15	d0	d0	NOUN
ejpam-6841	198	16	and	and	CCONJ
ejpam-6841	198	17	p	p	PROPN
ejpam-6841	198	18	∈	∈	PROPN
ejpam-6841	198	19	c0	c0	PROPN
ejpam-6841	198	20	ϑ(p	ϑ(p	PROPN
ejpam-6841	198	21	,	,	PUNCT
ejpam-6841	198	22	p(b∗	p(b∗	NOUN
ejpam-6841	198	23	)	)	PUNCT
ejpam-6841	198	24	)	)	PUNCT
ejpam-6841	199	1	=	=	PUNCT
ejpam-6841	199	2	ϑ(c	ϑ(c	PROPN
ejpam-6841	199	3	,	,	PUNCT
ejpam-6841	199	4	d	d	NOUN
ejpam-6841	199	5	)	)	PUNCT
ejpam-6841	199	6	.	.	PUNCT
ejpam-6841	200	1	(	(	PUNCT
ejpam-6841	200	2	12	12	NUM
ejpam-6841	200	3	)	)	PUNCT
ejpam-6841	200	4	k.	k.	PROPN
ejpam-6841	200	5	javed	javed	PROPN
ejpam-6841	200	6	,	,	PUNCT
ejpam-6841	200	7	m.	m.	NOUN
ejpam-6841	200	8	nazam	nazam	PROPN
ejpam-6841	200	9	,	,	PUNCT
ejpam-6841	200	10	m.	m.	PROPN
ejpam-6841	200	11	arshad	arshad	PROPN
ejpam-6841	200	12	,	,	PUNCT
ejpam-6841	200	13	m.	m.	NOUN
ejpam-6841	200	14	de	de	X
ejpam-6841	200	15	la	la	PROPN
ejpam-6841	200	16	sen	sen	PROPN
ejpam-6841	200	17	/	/	SYM
ejpam-6841	200	18	eur	eur	PROPN
ejpam-6841	200	19	.	.	PUNCT
ejpam-6841	201	1	j.	j.	PROPN
ejpam-6841	201	2	pure	pure	PROPN
ejpam-6841	201	3	appl	appl	PROPN
ejpam-6841	201	4	.	.	PROPN
ejpam-6841	201	5	math	math	PROPN
ejpam-6841	201	6	,	,	PUNCT
ejpam-6841	201	7	18	18	NUM
ejpam-6841	201	8	(	(	PUNCT
ejpam-6841	201	9	4	4	NUM
ejpam-6841	201	10	)	)	PUNCT
ejpam-6841	201	11	(	(	PUNCT
ejpam-6841	201	12	2025	2025	NUM
ejpam-6841	201	13	)	)	PUNCT
ejpam-6841	201	14	,	,	PUNCT
ejpam-6841	201	15	6841	6841	NUM
ejpam-6841	201	16	9	9	NUM
ejpam-6841	201	17	of	of	ADP
ejpam-6841	201	18	23	23	NUM
ejpam-6841	201	19	now	now	ADV
ejpam-6841	201	20	,	,	PUNCT
ejpam-6841	201	21	(	(	PUNCT
ejpam-6841	201	22	11	11	NUM
ejpam-6841	201	23	)	)	PUNCT
ejpam-6841	201	24	and	and	CCONJ
ejpam-6841	201	25	(	(	PUNCT
ejpam-6841	201	26	12	12	NUM
ejpam-6841	201	27	)	)	PUNCT
ejpam-6841	201	28	,	,	PUNCT
ejpam-6841	201	29	by	by	ADP
ejpam-6841	201	30	(	(	PUNCT
ejpam-6841	201	31	2	2	X
ejpam-6841	201	32	)	)	PUNCT
ejpam-6841	201	33	we	we	PRON
ejpam-6841	201	34	have	have	VERB
ejpam-6841	201	35	j(ϑ(bnk+1	j(ϑ(bnk+1	NOUN
ejpam-6841	201	36	,	,	PUNCT
ejpam-6841	201	37	p	p	NOUN
ejpam-6841	201	38	)	)	PUNCT
ejpam-6841	201	39	)	)	PUNCT
ejpam-6841	202	1	≤	≤	ADV
ejpam-6841	202	2	b(ϑ(bnk	b(ϑ(bnk	NUM
ejpam-6841	202	3	,	,	PUNCT
ejpam-6841	202	4	b∗	b∗	ADJ
ejpam-6841	202	5	)	)	PUNCT
ejpam-6841	202	6	)	)	PUNCT
ejpam-6841	203	1	<	<	X
ejpam-6841	203	2	j(ϑ(bnk	j(ϑ(bnk	NOUN
ejpam-6841	203	3	,	,	PUNCT
ejpam-6841	203	4	b∗	b∗	ADJ
ejpam-6841	203	5	)	)	PUNCT
ejpam-6841	203	6	)	)	PUNCT
ejpam-6841	203	7	,	,	PUNCT
ejpam-6841	203	8	for	for	ADP
ejpam-6841	203	9	all	all	DET
ejpam-6841	203	10	k	k	PROPN
ejpam-6841	203	11	∈	∈	PROPN
ejpam-6841	203	12	n.	n.	NOUN
ejpam-6841	203	13	since	since	SCONJ
ejpam-6841	203	14	,	,	PUNCT
ejpam-6841	203	15	j	j	PROPN
ejpam-6841	203	16	is	be	AUX
ejpam-6841	203	17	non	non	ADJ
ejpam-6841	203	18	-	-	ADJ
ejpam-6841	203	19	decreasing	decrease	VERB
ejpam-6841	203	20	function	function	NOUN
ejpam-6841	203	21	,	,	PUNCT
ejpam-6841	203	22	so	so	ADV
ejpam-6841	203	23	,	,	PUNCT
ejpam-6841	203	24	we	we	PRON
ejpam-6841	203	25	have	have	VERB
ejpam-6841	203	26	ϑ(bnk+1	ϑ(bnk+1	NOUN
ejpam-6841	203	27	,	,	PUNCT
ejpam-6841	203	28	p	p	X
ejpam-6841	203	29	)	)	PUNCT
ejpam-6841	203	30	<	<	X
ejpam-6841	203	31	ϑ(bnk	ϑ(bnk	NOUN
ejpam-6841	203	32	,	,	PUNCT
ejpam-6841	203	33	b∗	b∗	ADJ
ejpam-6841	203	34	)	)	PUNCT
ejpam-6841	203	35	thus	thus	ADV
ejpam-6841	203	36	,	,	PUNCT
ejpam-6841	203	37	as	as	ADP
ejpam-6841	203	38	k	k	PROPN
ejpam-6841	203	39	→	→	SYM
ejpam-6841	203	40	∞	∞	PROPN
ejpam-6841	203	41	,	,	PUNCT
ejpam-6841	203	42	we	we	PRON
ejpam-6841	203	43	have	have	VERB
ejpam-6841	203	44	ϑ(b∗	ϑ(b∗	PROPN
ejpam-6841	203	45	,	,	PUNCT
ejpam-6841	203	46	p	p	X
ejpam-6841	203	47	)	)	PUNCT
ejpam-6841	203	48	=	=	SYM
ejpam-6841	203	49	0	0	NUM
ejpam-6841	203	50	or	or	CCONJ
ejpam-6841	203	51	b∗	b∗	ADJ
ejpam-6841	203	52	=	=	SYM
ejpam-6841	204	1	p.	p.	NOUN
ejpam-6841	204	2	finally	finally	ADV
ejpam-6841	204	3	,	,	PUNCT
ejpam-6841	204	4	by	by	ADP
ejpam-6841	204	5	(	(	PUNCT
ejpam-6841	204	6	12	12	NUM
ejpam-6841	204	7	)	)	PUNCT
ejpam-6841	204	8	we	we	PRON
ejpam-6841	204	9	have	have	VERB
ejpam-6841	204	10	ϑ(b∗,p(b∗	ϑ(b∗,p(b∗	PROPN
ejpam-6841	204	11	)	)	PUNCT
ejpam-6841	204	12	)	)	PUNCT
ejpam-6841	205	1	=	=	PUNCT
ejpam-6841	205	2	ϑ(c	ϑ(c	PROPN
ejpam-6841	205	3	,	,	PUNCT
ejpam-6841	205	4	d	d	NOUN
ejpam-6841	205	5	)	)	PUNCT
ejpam-6841	205	6	.	.	PUNCT
ejpam-6841	206	1	hence	hence	ADV
ejpam-6841	206	2	,	,	PUNCT
ejpam-6841	206	3	b∗	b∗	ADV
ejpam-6841	206	4	is	be	AUX
ejpam-6841	206	5	a	a	DET
ejpam-6841	206	6	best	good	ADJ
ejpam-6841	206	7	proximity	proximity	NOUN
ejpam-6841	206	8	point	point	NOUN
ejpam-6841	206	9	of	of	ADP
ejpam-6841	206	10	the	the	DET
ejpam-6841	206	11	mapping	mapping	NOUN
ejpam-6841	206	12	p.	p.	NOUN
ejpam-6841	206	13	theorem	theorem	NOUN
ejpam-6841	206	14	2	2	X
ejpam-6841	206	15	.	.	PUNCT
ejpam-6841	207	1	let	let	VERB
ejpam-6841	207	2	p	p	NOUN
ejpam-6841	207	3	:	:	PUNCT
ejpam-6841	207	4	c	c	X
ejpam-6841	207	5	→	→	PUNCT
ejpam-6841	207	6	d	d	X
ejpam-6841	207	7	be	be	AUX
ejpam-6841	207	8	a	a	DET
ejpam-6841	207	9	(	(	PUNCT
ejpam-6841	207	10	j,£)-proximal	j,£)-proximal	ADJ
ejpam-6841	207	11	contraction	contraction	NOUN
ejpam-6841	207	12	defined	define	VERB
ejpam-6841	207	13	on	on	ADP
ejpam-6841	207	14	a	a	DET
ejpam-6841	207	15	complete	complete	ADJ
ejpam-6841	207	16	metric	metric	ADJ
ejpam-6841	207	17	space	space	NOUN
ejpam-6841	207	18	(	(	PUNCT
ejpam-6841	207	19	w	w	NOUN
ejpam-6841	207	20	,	,	PUNCT
ejpam-6841	207	21	ϑ	ϑ	NOUN
ejpam-6841	207	22	)	)	PUNCT
ejpam-6841	207	23	and	and	CCONJ
ejpam-6841	207	24	c	c	X
ejpam-6841	207	25	,	,	PUNCT
ejpam-6841	207	26	d	d	NOUN
ejpam-6841	207	27	be	be	AUX
ejpam-6841	207	28	nonvoid	nonvoid	ADJ
ejpam-6841	207	29	,	,	PUNCT
ejpam-6841	207	30	closed	closed	ADJ
ejpam-6841	207	31	subsets	subset	NOUN
ejpam-6841	207	32	of	of	ADP
ejpam-6841	207	33	w	w	ADP
ejpam-6841	207	34	such	such	ADJ
ejpam-6841	207	35	that	that	SCONJ
ejpam-6841	207	36	d	d	NOUN
ejpam-6841	207	37	is	be	AUX
ejpam-6841	207	38	approximately	approximately	ADV
ejpam-6841	207	39	compact	compact	ADJ
ejpam-6841	207	40	with	with	ADP
ejpam-6841	207	41	respect	respect	NOUN
ejpam-6841	207	42	to	to	ADP
ejpam-6841	207	43	c.	c.	NOUN
ejpam-6841	207	44	if	if	SCONJ
ejpam-6841	207	45	(	(	PUNCT
ejpam-6841	207	46	i	i	NOUN
ejpam-6841	207	47	)	)	PUNCT
ejpam-6841	207	48	j	j	PROPN
ejpam-6841	207	49	is	be	AUX
ejpam-6841	207	50	non	non	ADJ
ejpam-6841	207	51	-	-	ADJ
ejpam-6841	207	52	decreasing	decrease	VERB
ejpam-6841	207	53	and	and	CCONJ
ejpam-6841	207	54	{	{	PUNCT
ejpam-6841	207	55	j(tn	j(tn	PROPN
ejpam-6841	207	56	)	)	PUNCT
ejpam-6841	207	57	}	}	PUNCT
ejpam-6841	207	58	and	and	CCONJ
ejpam-6841	207	59	{	{	PUNCT
ejpam-6841	207	60	£	£	NOUN
ejpam-6841	207	61	(	(	PUNCT
ejpam-6841	207	62	tn	tn	NOUN
ejpam-6841	207	63	)	)	PUNCT
ejpam-6841	207	64	}	}	PUNCT
ejpam-6841	207	65	are	be	AUX
ejpam-6841	207	66	convergent	convergent	ADJ
ejpam-6841	207	67	sequence	sequence	NOUN
ejpam-6841	207	68	such	such	ADJ
ejpam-6841	207	69	that	that	SCONJ
ejpam-6841	207	70	limn→∞	limn→∞	PROPN
ejpam-6841	207	71	j(tn	j(tn	NOUN
ejpam-6841	207	72	)	)	PUNCT
ejpam-6841	207	73	=	=	SYM
ejpam-6841	207	74	limn→∞£(tn	limn→∞£(tn	NOUN
ejpam-6841	207	75	)	)	PUNCT
ejpam-6841	207	76	,	,	PUNCT
ejpam-6841	207	77	then	then	ADV
ejpam-6841	207	78	limn→∞	limn→∞	PROPN
ejpam-6841	207	79	tn	tn	NOUN
ejpam-6841	207	80	=	=	SYM
ejpam-6841	207	81	0	0	PROPN
ejpam-6841	207	82	.	.	PUNCT
ejpam-6841	207	83	(	(	PUNCT
ejpam-6841	207	84	ii	ii	X
ejpam-6841	207	85	)	)	PUNCT
ejpam-6841	207	86	c0	c0	PROPN
ejpam-6841	207	87	is	be	AUX
ejpam-6841	207	88	non	non	ADJ
ejpam-6841	207	89	-	-	ADJ
ejpam-6841	207	90	empty	empty	ADJ
ejpam-6841	207	91	subset	subset	NOUN
ejpam-6841	207	92	of	of	ADP
ejpam-6841	207	93	c	c	PROPN
ejpam-6841	207	94	such	such	ADJ
ejpam-6841	207	95	that	that	DET
ejpam-6841	207	96	p(c0	p(c0	NOUN
ejpam-6841	207	97	)	)	PUNCT
ejpam-6841	207	98	⊆	⊆	NUM
ejpam-6841	207	99	d0	d0	NOUN
ejpam-6841	207	100	.	.	PUNCT
ejpam-6841	208	1	then	then	ADV
ejpam-6841	208	2	p	p	NOUN
ejpam-6841	208	3	admits	admit	VERB
ejpam-6841	208	4	a	a	DET
ejpam-6841	208	5	best	good	ADJ
ejpam-6841	208	6	proximity	proximity	NOUN
ejpam-6841	208	7	point	point	NOUN
ejpam-6841	208	8	.	.	PUNCT
ejpam-6841	209	1	proof	proof	NOUN
ejpam-6841	209	2	.	.	PUNCT
ejpam-6841	210	1	as	as	ADP
ejpam-6841	210	2	in	in	ADP
ejpam-6841	210	3	the	the	DET
ejpam-6841	210	4	proof	proof	NOUN
ejpam-6841	210	5	of	of	ADP
ejpam-6841	210	6	theorem	theorem	NOUN
ejpam-6841	210	7	1	1	NUM
ejpam-6841	210	8	,	,	PUNCT
ejpam-6841	210	9	we	we	PRON
ejpam-6841	210	10	have	have	VERB
ejpam-6841	210	11	j(θn	j(θn	NOUN
ejpam-6841	210	12	)	)	PUNCT
ejpam-6841	210	13	≤	≤	NOUN
ejpam-6841	210	14	£	£	SYM
ejpam-6841	210	15	(	(	PUNCT
ejpam-6841	210	16	θn−1	θn−1	PROPN
ejpam-6841	210	17	)	)	PUNCT
ejpam-6841	210	18	<	<	X
ejpam-6841	210	19	j(θn−1	j(θn−1	PROPN
ejpam-6841	210	20	)	)	PUNCT
ejpam-6841	210	21	.	.	PUNCT
ejpam-6841	211	1	(	(	PUNCT
ejpam-6841	211	2	13	13	NUM
ejpam-6841	211	3	)	)	PUNCT
ejpam-6841	211	4	by	by	ADP
ejpam-6841	211	5	(	(	PUNCT
ejpam-6841	211	6	13	13	NUM
ejpam-6841	211	7	)	)	PUNCT
ejpam-6841	211	8	,	,	PUNCT
ejpam-6841	211	9	then	then	ADV
ejpam-6841	211	10	{	{	PUNCT
ejpam-6841	211	11	j	j	PROPN
ejpam-6841	211	12	(	(	PUNCT
ejpam-6841	211	13	θn	θn	NOUN
ejpam-6841	211	14	)	)	PUNCT
ejpam-6841	211	15	}	}	PUNCT
ejpam-6841	211	16	is	be	AUX
ejpam-6841	211	17	a	a	DET
ejpam-6841	211	18	strictly	strictly	ADV
ejpam-6841	211	19	decreasing	decrease	VERB
ejpam-6841	211	20	sequence	sequence	NOUN
ejpam-6841	211	21	.	.	PUNCT
ejpam-6841	212	1	we	we	PRON
ejpam-6841	212	2	have	have	VERB
ejpam-6841	212	3	two	two	NUM
ejpam-6841	212	4	cases	case	NOUN
ejpam-6841	212	5	here	here	ADV
ejpam-6841	212	6	;	;	PUNCT
ejpam-6841	212	7	either	either	CCONJ
ejpam-6841	212	8	the	the	DET
ejpam-6841	212	9	sequence	sequence	NOUN
ejpam-6841	212	10	{	{	PUNCT
ejpam-6841	212	11	j	j	PROPN
ejpam-6841	212	12	(	(	PUNCT
ejpam-6841	212	13	θn	θn	NOUN
ejpam-6841	212	14	)	)	PUNCT
ejpam-6841	212	15	}	}	PUNCT
ejpam-6841	212	16	is	be	AUX
ejpam-6841	212	17	bounded	bound	VERB
ejpam-6841	212	18	below	below	ADP
ejpam-6841	212	19	or	or	CCONJ
ejpam-6841	212	20	not	not	PART
ejpam-6841	212	21	.	.	PUNCT
ejpam-6841	213	1	if	if	SCONJ
ejpam-6841	213	2	{	{	PUNCT
ejpam-6841	213	3	j	j	PROPN
ejpam-6841	213	4	(	(	PUNCT
ejpam-6841	213	5	θn	θn	NOUN
ejpam-6841	213	6	)	)	PUNCT
ejpam-6841	213	7	}	}	PUNCT
ejpam-6841	213	8	is	be	AUX
ejpam-6841	213	9	not	not	PART
ejpam-6841	213	10	bounded	bound	VERB
ejpam-6841	213	11	below	below	ADV
ejpam-6841	213	12	,	,	PUNCT
ejpam-6841	213	13	then	then	ADV
ejpam-6841	213	14	inf	inf	PROPN
ejpam-6841	213	15	θn	θn	PROPN
ejpam-6841	213	16	>	>	PROPN
ejpam-6841	213	17	ε	ε	PROPN
ejpam-6841	213	18	j	j	PROPN
ejpam-6841	213	19	(	(	PUNCT
ejpam-6841	213	20	θn	θn	NOUN
ejpam-6841	213	21	)	)	PUNCT
ejpam-6841	213	22	>	>	PUNCT
ejpam-6841	214	1	−∞	−∞	X
ejpam-6841	214	2	for	for	ADP
ejpam-6841	214	3	every	every	DET
ejpam-6841	214	4	ε	ε	PROPN
ejpam-6841	214	5	>	>	X
ejpam-6841	214	6	0	0	PROPN
ejpam-6841	214	7	,	,	PUNCT
ejpam-6841	214	8	n	n	PROPN
ejpam-6841	214	9	∈	∈	PROPN
ejpam-6841	214	10	n.	n.	NOUN
ejpam-6841	214	11	from	from	ADP
ejpam-6841	214	12	lemma	lemma	PROPN
ejpam-6841	214	13	2	2	NUM
ejpam-6841	214	14	,	,	PUNCT
ejpam-6841	214	15	indicated	indicate	VERB
ejpam-6841	214	16	that	that	SCONJ
ejpam-6841	214	17	θn	θn	NOUN
ejpam-6841	214	18	→	→	SYM
ejpam-6841	214	19	0	0	PROPN
ejpam-6841	214	20	as	as	ADP
ejpam-6841	214	21	n	n	PROPN
ejpam-6841	214	22	→	→	SYM
ejpam-6841	214	23	∞.	∞.	PROPN
ejpam-6841	214	24	second	second	NOUN
ejpam-6841	214	25	,	,	PUNCT
ejpam-6841	214	26	the	the	DET
ejpam-6841	214	27	sequence	sequence	NOUN
ejpam-6841	214	28	{	{	PUNCT
ejpam-6841	214	29	j(θn	j(θn	PROPN
ejpam-6841	214	30	)	)	PUNCT
ejpam-6841	214	31	}	}	PUNCT
ejpam-6841	214	32	is	be	AUX
ejpam-6841	214	33	convergent	convergent	ADJ
ejpam-6841	214	34	if	if	SCONJ
ejpam-6841	214	35	it	it	PRON
ejpam-6841	214	36	is	be	AUX
ejpam-6841	214	37	bounded	bound	VERB
ejpam-6841	214	38	below	below	ADV
ejpam-6841	214	39	.	.	PUNCT
ejpam-6841	215	1	the	the	DET
ejpam-6841	215	2	sequence	sequence	NOUN
ejpam-6841	215	3	{	{	PUNCT
ejpam-6841	215	4	£	£	PROPN
ejpam-6841	215	5	(	(	PUNCT
ejpam-6841	215	6	θn	θn	NOUN
ejpam-6841	215	7	)	)	PUNCT
ejpam-6841	215	8	}	}	PUNCT
ejpam-6841	215	9	likewise	likewise	ADV
ejpam-6841	215	10	converges	converge	VERB
ejpam-6841	215	11	by	by	ADP
ejpam-6841	215	12	(	(	PUNCT
ejpam-6841	215	13	13	13	NUM
ejpam-6841	215	14	)	)	PUNCT
ejpam-6841	215	15	,	,	PUNCT
ejpam-6841	215	16	and	and	CCONJ
ejpam-6841	215	17	,	,	PUNCT
ejpam-6841	215	18	both	both	PRON
ejpam-6841	215	19	have	have	VERB
ejpam-6841	215	20	the	the	DET
ejpam-6841	215	21	same	same	ADJ
ejpam-6841	215	22	limit	limit	NOUN
ejpam-6841	215	23	.	.	PUNCT
ejpam-6841	216	1	using	use	VERB
ejpam-6841	216	2	(	(	PUNCT
ejpam-6841	216	3	i	i	NOUN
ejpam-6841	216	4	)	)	PUNCT
ejpam-6841	216	5	,	,	PUNCT
ejpam-6841	216	6	we	we	PRON
ejpam-6841	216	7	have	have	VERB
ejpam-6841	216	8	limn→∞	limn→∞	PRON
ejpam-6841	216	9	θn	θn	X
ejpam-6841	216	10	=	=	NOUN
ejpam-6841	216	11	0	0	PROPN
ejpam-6841	216	12	,	,	PUNCT
ejpam-6841	216	13	for	for	ADP
ejpam-6841	216	14	any	any	DET
ejpam-6841	216	15	sequence	sequence	NOUN
ejpam-6841	216	16	{	{	PUNCT
ejpam-6841	216	17	bn	bn	NOUN
ejpam-6841	216	18	}	}	PUNCT
ejpam-6841	216	19	in	in	ADP
ejpam-6841	216	20	c.	c.	PROPN
ejpam-6841	216	21	now	now	ADV
ejpam-6841	216	22	,	,	PUNCT
ejpam-6841	216	23	the	the	DET
ejpam-6841	216	24	rest	rest	NOUN
ejpam-6841	216	25	of	of	ADP
ejpam-6841	216	26	the	the	DET
ejpam-6841	216	27	proof	proof	NOUN
ejpam-6841	216	28	aligns	align	VERB
ejpam-6841	216	29	with	with	ADP
ejpam-6841	216	30	the	the	DET
ejpam-6841	216	31	methodology	methodology	NOUN
ejpam-6841	216	32	outlined	outline	VERB
ejpam-6841	216	33	in	in	ADP
ejpam-6841	216	34	theorem	theorem	NOUN
ejpam-6841	216	35	1	1	NUM
ejpam-6841	216	36	,	,	PUNCT
ejpam-6841	216	37	we	we	PRON
ejpam-6841	216	38	have	have	VERB
ejpam-6841	216	39	ϑ(b∗,p(b∗	ϑ(b∗,p(b∗	PROPN
ejpam-6841	216	40	)	)	PUNCT
ejpam-6841	216	41	)	)	PUNCT
ejpam-6841	217	1	=	=	PUNCT
ejpam-6841	217	2	ϑ(c	ϑ(c	PROPN
ejpam-6841	217	3	,	,	PUNCT
ejpam-6841	217	4	d	d	NOUN
ejpam-6841	217	5	)	)	PUNCT
ejpam-6841	217	6	.	.	PUNCT
ejpam-6841	218	1	hence	hence	ADV
ejpam-6841	218	2	,	,	PUNCT
ejpam-6841	218	3	b∗	b∗	ADV
ejpam-6841	218	4	is	be	AUX
ejpam-6841	218	5	a	a	DET
ejpam-6841	218	6	best	good	ADJ
ejpam-6841	218	7	proximity	proximity	NOUN
ejpam-6841	218	8	point	point	NOUN
ejpam-6841	218	9	of	of	ADP
ejpam-6841	218	10	the	the	DET
ejpam-6841	218	11	mapping	mapping	NOUN
ejpam-6841	219	1	p.	p.	PROPN
ejpam-6841	219	2	k.	k.	PROPN
ejpam-6841	219	3	javed	javed	PROPN
ejpam-6841	219	4	,	,	PUNCT
ejpam-6841	219	5	m.	m.	NOUN
ejpam-6841	219	6	nazam	nazam	PROPN
ejpam-6841	219	7	,	,	PUNCT
ejpam-6841	219	8	m.	m.	PROPN
ejpam-6841	219	9	arshad	arshad	PROPN
ejpam-6841	219	10	,	,	PUNCT
ejpam-6841	219	11	m.	m.	NOUN
ejpam-6841	219	12	de	de	X
ejpam-6841	219	13	la	la	PROPN
ejpam-6841	219	14	sen	sen	PROPN
ejpam-6841	219	15	/	/	SYM
ejpam-6841	219	16	eur	eur	PROPN
ejpam-6841	219	17	.	.	PUNCT
ejpam-6841	220	1	j.	j.	PROPN
ejpam-6841	220	2	pure	pure	PROPN
ejpam-6841	220	3	appl	appl	PROPN
ejpam-6841	220	4	.	.	PROPN
ejpam-6841	220	5	math	math	PROPN
ejpam-6841	220	6	,	,	PUNCT
ejpam-6841	220	7	18	18	NUM
ejpam-6841	220	8	(	(	PUNCT
ejpam-6841	220	9	4	4	NUM
ejpam-6841	220	10	)	)	PUNCT
ejpam-6841	220	11	(	(	PUNCT
ejpam-6841	220	12	2025	2025	NUM
ejpam-6841	220	13	)	)	PUNCT
ejpam-6841	220	14	,	,	PUNCT
ejpam-6841	220	15	6841	6841	NUM
ejpam-6841	220	16	10	10	NUM
ejpam-6841	220	17	of	of	ADP
ejpam-6841	220	18	23	23	NUM
ejpam-6841	220	19	example	example	NOUN
ejpam-6841	220	20	2	2	NUM
ejpam-6841	220	21	.	.	PUNCT
ejpam-6841	221	1	let	let	VERB
ejpam-6841	221	2	w	w	NOUN
ejpam-6841	221	3	=	=	NOUN
ejpam-6841	221	4	r2	r2	PROPN
ejpam-6841	221	5	and	and	CCONJ
ejpam-6841	221	6	define	define	VERB
ejpam-6841	221	7	the	the	DET
ejpam-6841	221	8	function	function	NOUN
ejpam-6841	221	9	ϑ	ϑ	X
ejpam-6841	221	10	:	:	PUNCT
ejpam-6841	221	11	w×w	w×w	NOUN
ejpam-6841	221	12	→	→	SYM
ejpam-6841	221	13	[	[	X
ejpam-6841	221	14	0,∞	0,∞	NOUN
ejpam-6841	221	15	)	)	PUNCT
ejpam-6841	221	16	by	by	ADP
ejpam-6841	221	17	ϑ((b	ϑ((b	NOUN
ejpam-6841	221	18	,	,	PUNCT
ejpam-6841	221	19	m	m	NOUN
ejpam-6841	221	20	)	)	PUNCT
ejpam-6841	221	21	,	,	PUNCT
ejpam-6841	221	22	(	(	PUNCT
ejpam-6841	221	23	u	u	NOUN
ejpam-6841	221	24	,	,	PUNCT
ejpam-6841	221	25	v	v	NOUN
ejpam-6841	221	26	)	)	PUNCT
ejpam-6841	221	27	)	)	PUNCT
ejpam-6841	222	1	=	=	SYM
ejpam-6841	222	2	|b−	|b−	PROPN
ejpam-6841	222	3	u|+	u|+	PROPN
ejpam-6841	222	4	|m−	|m−	ADJ
ejpam-6841	222	5	v|	v|	ADV
ejpam-6841	222	6	for	for	ADP
ejpam-6841	222	7	all	all	DET
ejpam-6841	222	8	(	(	PUNCT
ejpam-6841	222	9	b	b	NOUN
ejpam-6841	222	10	,	,	PUNCT
ejpam-6841	222	11	m	m	NOUN
ejpam-6841	222	12	)	)	PUNCT
ejpam-6841	222	13	,	,	PUNCT
ejpam-6841	222	14	(	(	PUNCT
ejpam-6841	222	15	u	u	NOUN
ejpam-6841	222	16	,	,	PUNCT
ejpam-6841	222	17	v	v	NOUN
ejpam-6841	222	18	)	)	PUNCT
ejpam-6841	222	19	∈	∈	PROPN
ejpam-6841	222	20	w.	w.	NOUN
ejpam-6841	222	21	then	then	ADV
ejpam-6841	222	22	(	(	PUNCT
ejpam-6841	222	23	w	w	PROPN
ejpam-6841	222	24	,	,	PUNCT
ejpam-6841	222	25	ϑ	ϑ	NOUN
ejpam-6841	222	26	)	)	PUNCT
ejpam-6841	222	27	is	be	AUX
ejpam-6841	222	28	a	a	DET
ejpam-6841	222	29	complete	complete	ADJ
ejpam-6841	222	30	metric	metric	ADJ
ejpam-6841	222	31	space	space	NOUN
ejpam-6841	222	32	.	.	PUNCT
ejpam-6841	223	1	let	let	VERB
ejpam-6841	223	2	c	c	X
ejpam-6841	223	3	,	,	PUNCT
ejpam-6841	223	4	d	d	X
ejpam-6841	223	5	be	be	AUX
ejpam-6841	223	6	the	the	DET
ejpam-6841	223	7	subsets	subset	NOUN
ejpam-6841	223	8	of	of	ADP
ejpam-6841	223	9	w	w	PROPN
ejpam-6841	223	10	defined	define	VERB
ejpam-6841	223	11	by	by	ADP
ejpam-6841	223	12	c	c	NOUN
ejpam-6841	223	13	=	=	SYM
ejpam-6841	223	14	{	{	PUNCT
ejpam-6841	223	15	(	(	PUNCT
ejpam-6841	223	16	0,m	0,m	NUM
ejpam-6841	223	17	)	)	PUNCT
ejpam-6841	223	18	;	;	PUNCT
ejpam-6841	223	19	0	0	NUM
ejpam-6841	223	20	≤	≤	NUM
ejpam-6841	223	21	m	m	VERB
ejpam-6841	223	22	≤	≤	NOUN
ejpam-6841	223	23	1	1	NUM
ejpam-6841	223	24	}	}	PUNCT
ejpam-6841	223	25	,	,	PUNCT
ejpam-6841	223	26	d	d	PROPN
ejpam-6841	223	27	=	=	PRON
ejpam-6841	223	28	{	{	PUNCT
ejpam-6841	223	29	(	(	PUNCT
ejpam-6841	223	30	1,m	1,m	PROPN
ejpam-6841	223	31	)	)	PUNCT
ejpam-6841	223	32	;	;	PUNCT
ejpam-6841	223	33	0	0	NUM
ejpam-6841	223	34	≤	≤	NUM
ejpam-6841	223	35	m	m	VERB
ejpam-6841	223	36	≤	≤	NOUN
ejpam-6841	223	37	1	1	NUM
ejpam-6841	223	38	}	}	PUNCT
ejpam-6841	223	39	,	,	PUNCT
ejpam-6841	223	40	then	then	ADV
ejpam-6841	223	41	ϑ(c	ϑ(c	VERB
ejpam-6841	223	42	,	,	PUNCT
ejpam-6841	223	43	d	d	NOUN
ejpam-6841	223	44	)	)	PUNCT
ejpam-6841	223	45	=	=	SYM
ejpam-6841	223	46	1	1	X
ejpam-6841	223	47	.	.	X
ejpam-6841	223	48	here	here	ADV
ejpam-6841	223	49	c0	c0	PROPN
ejpam-6841	223	50	=	=	PROPN
ejpam-6841	223	51	c	c	PROPN
ejpam-6841	223	52	and	and	CCONJ
ejpam-6841	223	53	d0	d0	PROPN
ejpam-6841	223	54	=	=	SYM
ejpam-6841	223	55	d.	d.	PROPN
ejpam-6841	223	56	define	define	VERB
ejpam-6841	223	57	the	the	DET
ejpam-6841	223	58	mapping	mapping	NOUN
ejpam-6841	223	59	p	p	NOUN
ejpam-6841	223	60	:	:	PUNCT
ejpam-6841	223	61	c	c	X
ejpam-6841	223	62	→	→	SYM
ejpam-6841	223	63	d	d	NOUN
ejpam-6841	223	64	by	by	ADP
ejpam-6841	223	65	p((0	p((0	PROPN
ejpam-6841	223	66	,	,	PUNCT
ejpam-6841	223	67	r	r	NOUN
ejpam-6841	223	68	)	)	PUNCT
ejpam-6841	223	69	)	)	PUNCT
ejpam-6841	224	1	=	=	PUNCT
ejpam-6841	224	2	(	(	PUNCT
ejpam-6841	224	3	1	1	NUM
ejpam-6841	224	4	,	,	PUNCT
ejpam-6841	224	5	r2	r2	PROPN
ejpam-6841	224	6	)	)	PUNCT
ejpam-6841	224	7	for	for	ADP
ejpam-6841	224	8	all	all	DET
ejpam-6841	224	9	(	(	PUNCT
ejpam-6841	224	10	0	0	NUM
ejpam-6841	224	11	,	,	PUNCT
ejpam-6841	224	12	r	r	NOUN
ejpam-6841	224	13	)	)	PUNCT
ejpam-6841	224	14	∈	∈	PROPN
ejpam-6841	224	15	c.	c.	NOUN
ejpam-6841	224	16	thus	thus	ADV
ejpam-6841	224	17	p	p	X
ejpam-6841	224	18	(	(	PUNCT
ejpam-6841	224	19	c0	c0	NOUN
ejpam-6841	224	20	)	)	PUNCT
ejpam-6841	224	21	=	=	SYM
ejpam-6841	224	22	d0	d0	NOUN
ejpam-6841	224	23	.	.	PUNCT
ejpam-6841	225	1	define	define	VERB
ejpam-6841	225	2	the	the	DET
ejpam-6841	225	3	functions	function	NOUN
ejpam-6841	225	4	j,£	j,£	ADV
ejpam-6841	225	5	:	:	PUNCT
ejpam-6841	225	6	r+	r+	X
ejpam-6841	225	7	→	→	PUNCT
ejpam-6841	225	8	r	r	NOUN
ejpam-6841	225	9	by	by	ADP
ejpam-6841	225	10	j	j	PROPN
ejpam-6841	225	11	(	(	PUNCT
ejpam-6841	225	12	b	b	NOUN
ejpam-6841	225	13	)	)	PUNCT
ejpam-6841	225	14	=	=	SYM
ejpam-6841	225	15	2b	2b	NOUN
ejpam-6841	225	16	and	and	CCONJ
ejpam-6841	225	17	£	£	SYM
ejpam-6841	225	18	(	(	PUNCT
ejpam-6841	225	19	b	b	NOUN
ejpam-6841	225	20	)	)	PUNCT
ejpam-6841	225	21	=	=	SYM
ejpam-6841	225	22	b	b	NOUN
ejpam-6841	225	23	;	;	PUNCT
ejpam-6841	225	24	b	b	X
ejpam-6841	225	25	∈	∈	PROPN
ejpam-6841	225	26	r+	r+	NOUN
ejpam-6841	225	27	.	.	PUNCT
ejpam-6841	226	1	as	as	ADP
ejpam-6841	226	2	j	j	PROPN
ejpam-6841	226	3	(	(	PUNCT
ejpam-6841	226	4	b	b	NOUN
ejpam-6841	226	5	)	)	PUNCT
ejpam-6841	226	6	>	>	PUNCT
ejpam-6841	226	7	£	£	PROPN
ejpam-6841	226	8	(	(	PUNCT
ejpam-6841	226	9	b	b	NOUN
ejpam-6841	226	10	)	)	PUNCT
ejpam-6841	226	11	for	for	ADP
ejpam-6841	226	12	every	every	DET
ejpam-6841	226	13	b	b	PROPN
ejpam-6841	226	14	≥	≥	X
ejpam-6841	226	15	t	t	PROPN
ejpam-6841	226	16	>	>	X
ejpam-6841	226	17	0	0	X
ejpam-6841	226	18	.	.	PUNCT
ejpam-6841	226	19	also	also	ADV
ejpam-6841	226	20	lims→ε+	lims→ε+	VERB
ejpam-6841	226	21	j	j	PROPN
ejpam-6841	226	22	(	(	PUNCT
ejpam-6841	226	23	b	b	NOUN
ejpam-6841	226	24	)	)	PUNCT
ejpam-6841	226	25	>	>	X
ejpam-6841	227	1	limb→ε+	limb→ε+	PROPN
ejpam-6841	227	2	sup£	sup£	X
ejpam-6841	227	3	(	(	PUNCT
ejpam-6841	227	4	b	b	NOUN
ejpam-6841	227	5	)	)	PUNCT
ejpam-6841	227	6	.	.	PUNCT
ejpam-6841	228	1	we	we	PRON
ejpam-6841	228	2	need	need	VERB
ejpam-6841	228	3	to	to	PART
ejpam-6841	228	4	check	check	VERB
ejpam-6841	228	5	whether	whether	SCONJ
ejpam-6841	228	6	p	p	NOUN
ejpam-6841	228	7	is	be	AUX
ejpam-6841	228	8	a	a	DET
ejpam-6841	228	9	(	(	PUNCT
ejpam-6841	228	10	j,£)-proximal	j,£)-proximal	ADJ
ejpam-6841	228	11	contraction	contraction	NOUN
ejpam-6841	228	12	or	or	CCONJ
ejpam-6841	228	13	not	not	PART
ejpam-6841	228	14	.	.	PUNCT
ejpam-6841	229	1	for	for	ADP
ejpam-6841	229	2	u1	u1	NOUN
ejpam-6841	229	3	=	=	SYM
ejpam-6841	229	4	(	(	PUNCT
ejpam-6841	229	5	0	0	NUM
ejpam-6841	229	6	,	,	PUNCT
ejpam-6841	229	7	b	b	NOUN
ejpam-6841	229	8	)	)	PUNCT
ejpam-6841	229	9	,	,	PUNCT
ejpam-6841	229	10	u2	u2	NOUN
ejpam-6841	229	11	=	=	SYM
ejpam-6841	229	12	(	(	PUNCT
ejpam-6841	229	13	0,m	0,m	NUM
ejpam-6841	229	14	)	)	PUNCT
ejpam-6841	229	15	and	and	CCONJ
ejpam-6841	229	16	v1	v1	NOUN
ejpam-6841	229	17	=	=	SYM
ejpam-6841	229	18	(	(	PUNCT
ejpam-6841	229	19	0	0	NUM
ejpam-6841	229	20	,	,	PUNCT
ejpam-6841	229	21	2b),v2	2b),v2	NUM
ejpam-6841	229	22	=	=	SYM
ejpam-6841	229	23	(	(	PUNCT
ejpam-6841	229	24	0	0	NUM
ejpam-6841	229	25	,	,	PUNCT
ejpam-6841	229	26	2	2	NUM
ejpam-6841	229	27	m	m	NOUN
ejpam-6841	229	28	)	)	PUNCT
ejpam-6841	229	29	ϑ	ϑ	X
ejpam-6841	229	30	(	(	PUNCT
ejpam-6841	229	31	u1,pv1	u1,pv1	NOUN
ejpam-6841	229	32	)	)	PUNCT
ejpam-6841	229	33	=	=	SYM
ejpam-6841	229	34	ϑ	ϑ	X
ejpam-6841	229	35	(	(	PUNCT
ejpam-6841	229	36	(	(	PUNCT
ejpam-6841	229	37	0	0	NUM
ejpam-6841	229	38	,	,	PUNCT
ejpam-6841	229	39	b	b	NOUN
ejpam-6841	229	40	)	)	PUNCT
ejpam-6841	229	41	,	,	PUNCT
ejpam-6841	229	42	p	p	X
ejpam-6841	229	43	(	(	PUNCT
ejpam-6841	229	44	0	0	NUM
ejpam-6841	229	45	,	,	PUNCT
ejpam-6841	229	46	2b	2b	NUM
ejpam-6841	229	47	)	)	PUNCT
ejpam-6841	229	48	)	)	PUNCT
ejpam-6841	230	1	=	=	SYM
ejpam-6841	230	2	ϑ	ϑ	X
ejpam-6841	230	3	(	(	PUNCT
ejpam-6841	230	4	c	c	X
ejpam-6841	230	5	,	,	PUNCT
ejpam-6841	230	6	d	d	NOUN
ejpam-6841	230	7	)	)	PUNCT
ejpam-6841	230	8	,	,	PUNCT
ejpam-6841	230	9	ϑ	ϑ	X
ejpam-6841	230	10	(	(	PUNCT
ejpam-6841	230	11	u2,pv2	u2,pv2	NUM
ejpam-6841	230	12	)	)	PUNCT
ejpam-6841	230	13	=	=	SYM
ejpam-6841	230	14	ϑ	ϑ	X
ejpam-6841	230	15	(	(	PUNCT
ejpam-6841	230	16	(	(	PUNCT
ejpam-6841	230	17	0,m	0,m	NUM
ejpam-6841	230	18	)	)	PUNCT
ejpam-6841	230	19	,	,	PUNCT
ejpam-6841	230	20	p	p	X
ejpam-6841	230	21	(	(	PUNCT
ejpam-6841	230	22	0	0	NUM
ejpam-6841	230	23	,	,	PUNCT
ejpam-6841	230	24	2	2	NUM
ejpam-6841	230	25	m	m	NOUN
ejpam-6841	230	26	)	)	PUNCT
ejpam-6841	230	27	)	)	PUNCT
ejpam-6841	231	1	=	=	SYM
ejpam-6841	231	2	ϑ	ϑ	X
ejpam-6841	231	3	(	(	PUNCT
ejpam-6841	231	4	c	c	X
ejpam-6841	231	5	,	,	PUNCT
ejpam-6841	231	6	d	d	NOUN
ejpam-6841	231	7	)	)	PUNCT
ejpam-6841	231	8	.	.	PUNCT
ejpam-6841	232	1	this	this	PRON
ejpam-6841	232	2	implies	imply	VERB
ejpam-6841	232	3	that	that	SCONJ
ejpam-6841	232	4	,	,	PUNCT
ejpam-6841	232	5	j	j	PROPN
ejpam-6841	232	6	(	(	PUNCT
ejpam-6841	232	7	ϑ	ϑ	X
ejpam-6841	232	8	(	(	PUNCT
ejpam-6841	232	9	u1	u1	NOUN
ejpam-6841	232	10	,	,	PUNCT
ejpam-6841	232	11	u2	u2	NOUN
ejpam-6841	232	12	)	)	PUNCT
ejpam-6841	232	13	)	)	PUNCT
ejpam-6841	232	14	≤	≤	NUM
ejpam-6841	232	15	£	£	NOUN
ejpam-6841	232	16	(	(	PUNCT
ejpam-6841	232	17	ϑ	ϑ	X
ejpam-6841	232	18	(	(	PUNCT
ejpam-6841	232	19	v1	v1	NOUN
ejpam-6841	232	20	,	,	PUNCT
ejpam-6841	232	21	v2	v2	NOUN
ejpam-6841	232	22	)	)	PUNCT
ejpam-6841	232	23	)	)	PUNCT
ejpam-6841	232	24	therefore	therefore	ADV
ejpam-6841	232	25	,	,	PUNCT
ejpam-6841	232	26	the	the	DET
ejpam-6841	232	27	(	(	PUNCT
ejpam-6841	232	28	j,£)-proximal	j,£)-proximal	ADJ
ejpam-6841	232	29	contraction	contraction	NOUN
ejpam-6841	232	30	is	be	AUX
ejpam-6841	232	31	fulfilled	fulfil	VERB
ejpam-6841	232	32	.	.	PUNCT
ejpam-6841	233	1	also	also	ADV
ejpam-6841	233	2	,	,	PUNCT
ejpam-6841	233	3	(	(	PUNCT
ejpam-6841	233	4	0	0	NUM
ejpam-6841	233	5	,	,	PUNCT
ejpam-6841	233	6	0	0	NUM
ejpam-6841	233	7	)	)	PUNCT
ejpam-6841	233	8	is	be	AUX
ejpam-6841	233	9	the	the	DET
ejpam-6841	233	10	best	good	ADJ
ejpam-6841	233	11	proximity	proximity	NOUN
ejpam-6841	233	12	point	point	NOUN
ejpam-6841	233	13	of	of	ADP
ejpam-6841	233	14	the	the	DET
ejpam-6841	233	15	mapping	mapping	NOUN
ejpam-6841	233	16	p.	p.	NOUN
ejpam-6841	233	17	hence	hence	ADV
ejpam-6841	233	18	,	,	PUNCT
ejpam-6841	233	19	all	all	DET
ejpam-6841	233	20	the	the	DET
ejpam-6841	233	21	conditions	condition	NOUN
ejpam-6841	233	22	of	of	ADP
ejpam-6841	233	23	the	the	DET
ejpam-6841	233	24	theorem	theorem	NOUN
ejpam-6841	233	25	1	1	NUM
ejpam-6841	233	26	are	be	AUX
ejpam-6841	233	27	hold	hold	NOUN
ejpam-6841	233	28	.	.	PUNCT
ejpam-6841	234	1	3.2	3.2	NUM
ejpam-6841	234	2	.	.	PUNCT
ejpam-6841	235	1	(	(	PUNCT
ejpam-6841	235	2	j,£)-ćirić	j,£)-ćirić	PROPN
ejpam-6841	235	3	-	-	PUNCT
ejpam-6841	235	4	reich	reich	NOUN
ejpam-6841	235	5	-	-	PUNCT
ejpam-6841	235	6	rus	rus	NOUN
ejpam-6841	235	7	type	type	NOUN
ejpam-6841	235	8	interpolative	interpolative	ADJ
ejpam-6841	235	9	proximal	proximal	ADJ
ejpam-6841	235	10	contraction	contraction	NOUN
ejpam-6841	235	11	let	let	VERB
ejpam-6841	235	12	(	(	PUNCT
ejpam-6841	235	13	w	w	NOUN
ejpam-6841	235	14	,	,	PUNCT
ejpam-6841	235	15	ϑ	ϑ	NOUN
ejpam-6841	235	16	)	)	PUNCT
ejpam-6841	235	17	be	be	AUX
ejpam-6841	235	18	a	a	DET
ejpam-6841	235	19	complete	complete	ADJ
ejpam-6841	235	20	metric	metric	ADJ
ejpam-6841	235	21	space	space	NOUN
ejpam-6841	235	22	,	,	PUNCT
ejpam-6841	235	23	and	and	CCONJ
ejpam-6841	235	24	c	c	X
ejpam-6841	235	25	,	,	PUNCT
ejpam-6841	235	26	d	d	X
ejpam-6841	235	27	be	be	AUX
ejpam-6841	235	28	a	a	DET
ejpam-6841	235	29	pair	pair	NOUN
ejpam-6841	235	30	of	of	ADP
ejpam-6841	235	31	nonvoid	nonvoid	ADJ
ejpam-6841	235	32	subsets	subset	NOUN
ejpam-6841	235	33	of	of	ADP
ejpam-6841	235	34	w.	w.	PROPN
ejpam-6841	235	35	let	let	VERB
ejpam-6841	235	36	j,£	j,£	ADV
ejpam-6841	235	37	:	:	PUNCT
ejpam-6841	235	38	(	(	PUNCT
ejpam-6841	235	39	0,∞	0,∞	NUM
ejpam-6841	235	40	)	)	PUNCT
ejpam-6841	236	1	→	→	PUNCT
ejpam-6841	236	2	r	r	NOUN
ejpam-6841	236	3	be	be	VERB
ejpam-6841	236	4	two	two	NUM
ejpam-6841	236	5	functions	function	NOUN
ejpam-6841	236	6	.	.	PUNCT
ejpam-6841	237	1	a	a	DET
ejpam-6841	237	2	mapping	mapping	NOUN
ejpam-6841	237	3	p	p	NOUN
ejpam-6841	237	4	:	:	PUNCT
ejpam-6841	237	5	c	c	X
ejpam-6841	237	6	→	→	PUNCT
ejpam-6841	237	7	d	d	NOUN
ejpam-6841	237	8	is	be	AUX
ejpam-6841	237	9	said	say	VERB
ejpam-6841	237	10	to	to	PART
ejpam-6841	237	11	be	be	AUX
ejpam-6841	237	12	a	a	DET
ejpam-6841	237	13	(	(	PUNCT
ejpam-6841	237	14	j,£)-ćirićreich	j,£)-ćirićreich	NOUN
ejpam-6841	237	15	-	-	PUNCT
ejpam-6841	237	16	rus	rus	NOUN
ejpam-6841	237	17	type	type	NOUN
ejpam-6841	237	18	interpolative	interpolative	ADJ
ejpam-6841	237	19	proximal	proximal	ADJ
ejpam-6841	237	20	contraction	contraction	NOUN
ejpam-6841	237	21	if	if	SCONJ
ejpam-6841	237	22	there	there	PRON
ejpam-6841	237	23	exist	exist	VERB
ejpam-6841	237	24	α	α	PRON
ejpam-6841	237	25	,	,	PUNCT
ejpam-6841	237	26	β	β	X
ejpam-6841	237	27	∈	∈	PROPN
ejpam-6841	237	28	(	(	PUNCT
ejpam-6841	237	29	0	0	NUM
ejpam-6841	237	30	,	,	PUNCT
ejpam-6841	237	31	1	1	NUM
ejpam-6841	237	32	)	)	PUNCT
ejpam-6841	237	33	;	;	PUNCT
ejpam-6841	238	1	α	α	X
ejpam-6841	238	2	+	+	X
ejpam-6841	238	3	β	β	X
ejpam-6841	238	4	<	<	X
ejpam-6841	238	5	1	1	NUM
ejpam-6841	238	6	satisfying	satisfy	VERB
ejpam-6841	238	7	ϑ	ϑ	X
ejpam-6841	238	8	(	(	PUNCT
ejpam-6841	238	9	b1,pm1	b1,pm1	PROPN
ejpam-6841	238	10	)	)	PUNCT
ejpam-6841	238	11	=	=	SYM
ejpam-6841	238	12	ϑ	ϑ	X
ejpam-6841	238	13	(	(	PUNCT
ejpam-6841	238	14	c	c	X
ejpam-6841	238	15	,	,	PUNCT
ejpam-6841	238	16	d	d	NOUN
ejpam-6841	238	17	)	)	PUNCT
ejpam-6841	238	18	ϑ	ϑ	X
ejpam-6841	238	19	(	(	PUNCT
ejpam-6841	238	20	b2,pm2	b2,pm2	NOUN
ejpam-6841	238	21	)	)	PUNCT
ejpam-6841	238	22	=	=	SYM
ejpam-6841	238	23	ϑ	ϑ	X
ejpam-6841	238	24	(	(	PUNCT
ejpam-6841	238	25	c	c	X
ejpam-6841	238	26	,	,	PUNCT
ejpam-6841	238	27	d	d	NOUN
ejpam-6841	238	28	)	)	PUNCT
ejpam-6841	238	29	}	}	PUNCT
ejpam-6841	238	30	⇒	⇒	VERB
ejpam-6841	238	31	j	j	PROPN
ejpam-6841	238	32	(	(	PUNCT
ejpam-6841	238	33	ϑ	ϑ	X
ejpam-6841	238	34	(	(	PUNCT
ejpam-6841	238	35	b1	b1	NOUN
ejpam-6841	238	36	,	,	PUNCT
ejpam-6841	238	37	b2	b2	NOUN
ejpam-6841	238	38	)	)	PUNCT
ejpam-6841	238	39	)	)	PUNCT
ejpam-6841	239	1	≤	≤	NUM
ejpam-6841	239	2	£	£	NOUN
ejpam-6841	239	3	(	(	PUNCT
ejpam-6841	239	4	(	(	PUNCT
ejpam-6841	239	5	ϑ	ϑ	X
ejpam-6841	239	6	(	(	PUNCT
ejpam-6841	239	7	m1,m2	m1,m2	PROPN
ejpam-6841	239	8	)	)	PUNCT
ejpam-6841	239	9	)	)	PUNCT
ejpam-6841	239	10	α	α	PROPN
ejpam-6841	239	11	(	(	PUNCT
ejpam-6841	239	12	ϑ	ϑ	X
ejpam-6841	239	13	(	(	PUNCT
ejpam-6841	239	14	m1	m1	NOUN
ejpam-6841	239	15	,	,	PUNCT
ejpam-6841	239	16	b1	b1	NOUN
ejpam-6841	239	17	)	)	PUNCT
ejpam-6841	239	18	)	)	PUNCT
ejpam-6841	240	1	β	β	X
ejpam-6841	240	2	(	(	PUNCT
ejpam-6841	240	3	ϑ	ϑ	X
ejpam-6841	240	4	(	(	PUNCT
ejpam-6841	240	5	m2	m2	PROPN
ejpam-6841	240	6	,	,	PUNCT
ejpam-6841	240	7	b2	b2	NOUN
ejpam-6841	240	8	)	)	PUNCT
ejpam-6841	240	9	)	)	PUNCT
ejpam-6841	240	10	1−α−β	1−α−β	PROPN
ejpam-6841	240	11	)	)	PUNCT
ejpam-6841	240	12	,	,	PUNCT
ejpam-6841	240	13	(	(	PUNCT
ejpam-6841	240	14	14	14	NUM
ejpam-6841	240	15	)	)	PUNCT
ejpam-6841	240	16	for	for	ADP
ejpam-6841	240	17	all	all	DET
ejpam-6841	240	18	distinct	distinct	ADJ
ejpam-6841	240	19	b1	b1	NOUN
ejpam-6841	240	20	,	,	PUNCT
ejpam-6841	240	21	b2,m1,m2	b2,m1,m2	PROPN
ejpam-6841	240	22	∈	∈	PROPN
ejpam-6841	240	23	c.	c.	NOUN
ejpam-6841	241	1	the	the	DET
ejpam-6841	241	2	following	follow	VERB
ejpam-6841	241	3	example	example	NOUN
ejpam-6841	241	4	shows	show	VERB
ejpam-6841	241	5	that	that	SCONJ
ejpam-6841	241	6	ćirić	ćirić	NOUN
ejpam-6841	241	7	-	-	PUNCT
ejpam-6841	241	8	reich	reich	NOUN
ejpam-6841	241	9	-	-	PUNCT
ejpam-6841	241	10	rus	rus	NOUN
ejpam-6841	241	11	type	type	NOUN
ejpam-6841	241	12	interpolative	interpolative	ADJ
ejpam-6841	241	13	proximal	proximal	ADJ
ejpam-6841	241	14	contracion	contracion	NOUN
ejpam-6841	241	15	generalizes	generalize	VERB
ejpam-6841	241	16	ćirić	ćirić	NOUN
ejpam-6841	241	17	-	-	PUNCT
ejpam-6841	241	18	reich	reich	NOUN
ejpam-6841	241	19	-	-	PUNCT
ejpam-6841	241	20	rus	rus	NOUN
ejpam-6841	241	21	type	type	NOUN
ejpam-6841	241	22	interpolative	interpolative	ADJ
ejpam-6841	241	23	proximal	proximal	ADJ
ejpam-6841	241	24	contraction	contraction	NOUN
ejpam-6841	241	25	.	.	PUNCT
ejpam-6841	242	1	example	example	NOUN
ejpam-6841	243	1	3	3	X
ejpam-6841	243	2	.	.	PUNCT
ejpam-6841	243	3	let	let	AUX
ejpam-6841	243	4	w	w	NOUN
ejpam-6841	243	5	=	=	SYM
ejpam-6841	243	6	r	r	NOUN
ejpam-6841	243	7	and	and	CCONJ
ejpam-6841	243	8	(	(	PUNCT
ejpam-6841	243	9	w	w	PROPN
ejpam-6841	243	10	,	,	PUNCT
ejpam-6841	243	11	ϑ	ϑ	NOUN
ejpam-6841	243	12	)	)	PUNCT
ejpam-6841	243	13	be	be	AUX
ejpam-6841	243	14	a	a	DET
ejpam-6841	243	15	usual	usual	ADJ
ejpam-6841	243	16	metric	metric	ADJ
ejpam-6841	243	17	space	space	NOUN
ejpam-6841	243	18	.	.	PUNCT
ejpam-6841	244	1	let	let	VERB
ejpam-6841	244	2	c	c	NOUN
ejpam-6841	244	3	=	=	PUNCT
ejpam-6841	244	4	{	{	PUNCT
ejpam-6841	244	5	1	1	NUM
ejpam-6841	244	6	,	,	PUNCT
ejpam-6841	244	7	2	2	NUM
ejpam-6841	244	8	,	,	PUNCT
ejpam-6841	244	9	3	3	NUM
ejpam-6841	244	10	,	,	PUNCT
ejpam-6841	244	11	4	4	NUM
ejpam-6841	244	12	,	,	PUNCT
ejpam-6841	244	13	5	5	NUM
ejpam-6841	244	14	}	}	PUNCT
ejpam-6841	244	15	,	,	PUNCT
ejpam-6841	244	16	d	d	PROPN
ejpam-6841	244	17	=	=	PUNCT
ejpam-6841	244	18	{	{	PUNCT
ejpam-6841	244	19	1	1	NUM
ejpam-6841	244	20	,	,	PUNCT
ejpam-6841	244	21	2	2	NUM
ejpam-6841	244	22	,	,	PUNCT
ejpam-6841	244	23	3	3	NUM
ejpam-6841	244	24	,	,	PUNCT
ejpam-6841	244	25	4	4	NUM
ejpam-6841	244	26	,	,	PUNCT
ejpam-6841	244	27	5	5	NUM
ejpam-6841	244	28	,	,	PUNCT
ejpam-6841	244	29	6	6	NUM
ejpam-6841	244	30	,	,	PUNCT
ejpam-6841	244	31	7	7	NUM
ejpam-6841	244	32	}	}	PUNCT
ejpam-6841	244	33	and	and	CCONJ
ejpam-6841	244	34	define	define	VERB
ejpam-6841	244	35	p	p	X
ejpam-6841	244	36	:	:	PUNCT
ejpam-6841	244	37	c	c	NOUN
ejpam-6841	244	38	→	→	SYM
ejpam-6841	244	39	d	d	NOUN
ejpam-6841	244	40	by	by	ADP
ejpam-6841	244	41	p(b	p(b	NOUN
ejpam-6841	244	42	)	)	PUNCT
ejpam-6841	244	43	=	=	PUNCT
ejpam-6841	244	44	b+	b+	PUNCT
ejpam-6841	244	45	1	1	NUM
ejpam-6841	244	46	.	.	PUNCT
ejpam-6841	245	1	then	then	ADV
ejpam-6841	245	2	,	,	PUNCT
ejpam-6841	245	3	for	for	ADP
ejpam-6841	245	4	`	`	PUNCT
ejpam-6841	245	5	1	1	NUM
ejpam-6841	245	6	,	,	PUNCT
ejpam-6841	245	7	`	`	PUNCT
ejpam-6841	245	8	2	2	NUM
ejpam-6841	245	9	,	,	PUNCT
ejpam-6841	245	10	ν1	ν1	NOUN
ejpam-6841	245	11	,	,	PUNCT
ejpam-6841	245	12	ν2	ν2	NOUN
ejpam-6841	245	13	∈	∈	PROPN
ejpam-6841	245	14	c	c	X
ejpam-6841	245	15	,	,	PUNCT
ejpam-6841	245	16	ϑ(`1,p(v1	ϑ(`1,p(v1	NOUN
ejpam-6841	245	17	)	)	PUNCT
ejpam-6841	245	18	)	)	PUNCT
ejpam-6841	246	1	=	=	SYM
ejpam-6841	246	2	ϑ	ϑ	X
ejpam-6841	246	3	(	(	PUNCT
ejpam-6841	246	4	c	c	X
ejpam-6841	246	5	,	,	PUNCT
ejpam-6841	246	6	d	d	NOUN
ejpam-6841	246	7	)	)	PUNCT
ejpam-6841	246	8	ϑ(`2,p(v2	ϑ(`2,p(v2	NOUN
ejpam-6841	246	9	)	)	PUNCT
ejpam-6841	246	10	)	)	PUNCT
ejpam-6841	247	1	=	=	SYM
ejpam-6841	247	2	ϑ	ϑ	X
ejpam-6841	247	3	(	(	PUNCT
ejpam-6841	247	4	c	c	X
ejpam-6841	247	5	,	,	PUNCT
ejpam-6841	247	6	d	d	NOUN
ejpam-6841	247	7	)	)	PUNCT
ejpam-6841	247	8	.	.	PUNCT
ejpam-6841	248	1	k.	k.	PROPN
ejpam-6841	248	2	javed	javed	PROPN
ejpam-6841	248	3	,	,	PUNCT
ejpam-6841	248	4	m.	m.	NOUN
ejpam-6841	248	5	nazam	nazam	PROPN
ejpam-6841	248	6	,	,	PUNCT
ejpam-6841	248	7	m.	m.	PROPN
ejpam-6841	248	8	arshad	arshad	PROPN
ejpam-6841	248	9	,	,	PUNCT
ejpam-6841	248	10	m.	m.	NOUN
ejpam-6841	248	11	de	de	X
ejpam-6841	248	12	la	la	PROPN
ejpam-6841	248	13	sen	sen	PROPN
ejpam-6841	248	14	/	/	SYM
ejpam-6841	248	15	eur	eur	PROPN
ejpam-6841	248	16	.	.	PUNCT
ejpam-6841	249	1	j.	j.	PROPN
ejpam-6841	249	2	pure	pure	PROPN
ejpam-6841	249	3	appl	appl	PROPN
ejpam-6841	249	4	.	.	PROPN
ejpam-6841	249	5	math	math	PROPN
ejpam-6841	249	6	,	,	PUNCT
ejpam-6841	249	7	18	18	NUM
ejpam-6841	249	8	(	(	PUNCT
ejpam-6841	249	9	4	4	NUM
ejpam-6841	249	10	)	)	PUNCT
ejpam-6841	249	11	(	(	PUNCT
ejpam-6841	249	12	2025	2025	NUM
ejpam-6841	249	13	)	)	PUNCT
ejpam-6841	249	14	,	,	PUNCT
ejpam-6841	249	15	6841	6841	NUM
ejpam-6841	249	16	11	11	NUM
ejpam-6841	249	17	of	of	ADP
ejpam-6841	249	18	23	23	NUM
ejpam-6841	249	19	let	let	VERB
ejpam-6841	249	20	α	α	NOUN
ejpam-6841	249	21	=	=	SYM
ejpam-6841	249	22	1	1	NUM
ejpam-6841	249	23	2	2	NUM
ejpam-6841	249	24	,	,	PUNCT
ejpam-6841	249	25	β	β	X
ejpam-6841	249	26	=	=	SYM
ejpam-6841	249	27	1	1	NUM
ejpam-6841	249	28	3	3	NUM
ejpam-6841	249	29	,	,	PUNCT
ejpam-6841	249	30	and	and	CCONJ
ejpam-6841	249	31	suppose	suppose	VERB
ejpam-6841	249	32	that	that	SCONJ
ejpam-6841	249	33	the	the	DET
ejpam-6841	249	34	following	follow	VERB
ejpam-6841	249	35	inequality	inequality	NOUN
ejpam-6841	249	36	holds	hold	VERB
ejpam-6841	249	37	:	:	PUNCT
ejpam-6841	249	38	(	(	PUNCT
ejpam-6841	249	39	ϑ	ϑ	X
ejpam-6841	249	40	(	(	PUNCT
ejpam-6841	249	41	`	`	PUNCT
ejpam-6841	249	42	1	1	NUM
ejpam-6841	249	43	,	,	PUNCT
ejpam-6841	249	44	`	`	PUNCT
ejpam-6841	249	45	2	2	NUM
ejpam-6841	249	46	)	)	PUNCT
ejpam-6841	249	47	)	)	PUNCT
ejpam-6841	249	48	≤	≤	NUM
ejpam-6841	250	1	λ	λ	X
ejpam-6841	250	2	(	(	PUNCT
ejpam-6841	250	3	ϑ	ϑ	X
ejpam-6841	250	4	(	(	PUNCT
ejpam-6841	250	5	v1	v1	NOUN
ejpam-6841	250	6	,	,	PUNCT
ejpam-6841	250	7	v2	v2	NOUN
ejpam-6841	250	8	)	)	PUNCT
ejpam-6841	250	9	)	)	PUNCT
ejpam-6841	251	1	α	α	PROPN
ejpam-6841	251	2	(	(	PUNCT
ejpam-6841	251	3	ϑ	ϑ	X
ejpam-6841	251	4	(	(	PUNCT
ejpam-6841	251	5	v1	v1	NOUN
ejpam-6841	251	6	,	,	PUNCT
ejpam-6841	251	7	`	`	PUNCT
ejpam-6841	251	8	1	1	NUM
ejpam-6841	251	9	)	)	PUNCT
ejpam-6841	251	10	)	)	PUNCT
ejpam-6841	252	1	β	β	X
ejpam-6841	252	2	(	(	PUNCT
ejpam-6841	252	3	ϑ	ϑ	X
ejpam-6841	252	4	(	(	PUNCT
ejpam-6841	252	5	v2	v2	PROPN
ejpam-6841	252	6	,	,	PUNCT
ejpam-6841	252	7	`	`	PUNCT
ejpam-6841	252	8	2	2	NUM
ejpam-6841	252	9	)	)	PUNCT
ejpam-6841	252	10	)	)	PUNCT
ejpam-6841	252	11	1−α−β	1−α−β	NOUN
ejpam-6841	252	12	.	.	PUNCT
ejpam-6841	253	1	then	then	ADV
ejpam-6841	253	2	(	(	PUNCT
ejpam-6841	253	3	ϑ	ϑ	X
ejpam-6841	253	4	(	(	PUNCT
ejpam-6841	253	5	4	4	NUM
ejpam-6841	253	6	,	,	PUNCT
ejpam-6841	253	7	2	2	NUM
ejpam-6841	253	8	)	)	PUNCT
ejpam-6841	253	9	)	)	PUNCT
ejpam-6841	253	10	≤	≤	NUM
ejpam-6841	253	11	λ	λ	X
ejpam-6841	253	12	(	(	PUNCT
ejpam-6841	253	13	ϑ	ϑ	X
ejpam-6841	253	14	(	(	PUNCT
ejpam-6841	253	15	3	3	NUM
ejpam-6841	253	16	,	,	PUNCT
ejpam-6841	253	17	1))α	1))α	NUM
ejpam-6841	253	18	(	(	PUNCT
ejpam-6841	253	19	ϑ	ϑ	X
ejpam-6841	253	20	(	(	PUNCT
ejpam-6841	253	21	3	3	NUM
ejpam-6841	253	22	,	,	PUNCT
ejpam-6841	253	23	4))β	4))β	NUM
ejpam-6841	253	24	(	(	PUNCT
ejpam-6841	253	25	ϑ	ϑ	X
ejpam-6841	253	26	(	(	PUNCT
ejpam-6841	253	27	1	1	NUM
ejpam-6841	253	28	,	,	PUNCT
ejpam-6841	253	29	2))1−α−β	2))1−α−β	NUM
ejpam-6841	253	30	(	(	PUNCT
ejpam-6841	253	31	2	2	NUM
ejpam-6841	253	32	)	)	PUNCT
ejpam-6841	253	33	≤	≤	NOUN
ejpam-6841	253	34	λ((2)α	λ((2)α	PUNCT
ejpam-6841	253	35	(	(	PUNCT
ejpam-6841	253	36	1)β	1)β	NUM
ejpam-6841	253	37	(	(	PUNCT
ejpam-6841	253	38	1)1−α−β	1)1−α−β	NUM
ejpam-6841	253	39	)	)	PUNCT
ejpam-6841	253	40	(	(	PUNCT
ejpam-6841	253	41	2	2	X
ejpam-6841	253	42	)	)	PUNCT
ejpam-6841	253	43	≤	≤	NOUN
ejpam-6841	253	44	λ((2	λ((2	PROPN
ejpam-6841	253	45	)	)	PUNCT
ejpam-6841	253	46	1	1	NUM
ejpam-6841	253	47	2	2	NUM
ejpam-6841	253	48	(	(	PUNCT
ejpam-6841	253	49	1	1	NUM
ejpam-6841	253	50	)	)	PUNCT
ejpam-6841	253	51	1	1	NUM
ejpam-6841	253	52	3	3	NUM
ejpam-6841	253	53	(	(	PUNCT
ejpam-6841	253	54	1)1−	1)1−	NUM
ejpam-6841	253	55	1	1	NUM
ejpam-6841	253	56	2	2	NUM
ejpam-6841	253	57	−	−	NUM
ejpam-6841	253	58	1	1	NUM
ejpam-6841	253	59	3	3	NUM
ejpam-6841	253	60	)	)	PUNCT
ejpam-6841	253	61	(	(	PUNCT
ejpam-6841	253	62	2	2	X
ejpam-6841	253	63	)	)	PUNCT
ejpam-6841	253	64	≤	≤	NOUN
ejpam-6841	253	65	λ((2	λ((2	PROPN
ejpam-6841	253	66	)	)	PUNCT
ejpam-6841	253	67	1	1	NUM
ejpam-6841	253	68	2	2	NUM
ejpam-6841	253	69	(	(	PUNCT
ejpam-6841	253	70	1	1	NUM
ejpam-6841	253	71	)	)	PUNCT
ejpam-6841	253	72	1	1	NUM
ejpam-6841	253	73	3	3	NUM
ejpam-6841	253	74	(	(	PUNCT
ejpam-6841	253	75	1)0.166	1)0.166	NUM
ejpam-6841	253	76	)	)	PUNCT
ejpam-6841	253	77	2	2	NUM
ejpam-6841	253	78	1.4142	1.4142	NUM
ejpam-6841	253	79	≤	≤	NUM
ejpam-6841	253	80	λ	λ	X
ejpam-6841	253	81	(	(	PUNCT
ejpam-6841	253	82	a	a	DET
ejpam-6841	253	83	contradiction	contradiction	NOUN
ejpam-6841	253	84	to	to	ADP
ejpam-6841	253	85	λ	λ	X
ejpam-6841	253	86	∈	∈	PROPN
ejpam-6841	253	87	(	(	PUNCT
ejpam-6841	253	88	0	0	NUM
ejpam-6841	253	89	,	,	PUNCT
ejpam-6841	253	90	1	1	NUM
ejpam-6841	253	91	)	)	PUNCT
ejpam-6841	253	92	)	)	PUNCT
ejpam-6841	253	93	.	.	PUNCT
ejpam-6841	254	1	this	this	PRON
ejpam-6841	254	2	shows	show	VERB
ejpam-6841	254	3	that	that	SCONJ
ejpam-6841	254	4	p	p	NOUN
ejpam-6841	254	5	is	be	AUX
ejpam-6841	254	6	not	not	PART
ejpam-6841	254	7	a	a	DET
ejpam-6841	254	8	ćirić	ćirić	NOUN
ejpam-6841	254	9	-	-	PUNCT
ejpam-6841	254	10	reich	reich	NOUN
ejpam-6841	254	11	-	-	PUNCT
ejpam-6841	254	12	rus	rus	NOUN
ejpam-6841	254	13	type	type	NOUN
ejpam-6841	254	14	interpolative	interpolative	ADJ
ejpam-6841	254	15	proximal	proximal	ADJ
ejpam-6841	254	16	contraction	contraction	NOUN
ejpam-6841	254	17	,	,	PUNCT
ejpam-6841	254	18	however	however	ADV
ejpam-6841	254	19	,	,	PUNCT
ejpam-6841	254	20	for	for	SCONJ
ejpam-6841	254	21	the	the	DET
ejpam-6841	254	22	functions	function	NOUN
ejpam-6841	254	23	j,£	j,£	ADV
ejpam-6841	254	24	:	:	PUNCT
ejpam-6841	254	25	(	(	PUNCT
ejpam-6841	254	26	0,∞	0,∞	NUM
ejpam-6841	254	27	)	)	PUNCT
ejpam-6841	254	28	→	→	SYM
ejpam-6841	255	1	r	r	NOUN
ejpam-6841	255	2	defined	define	VERB
ejpam-6841	255	3	by	by	ADP
ejpam-6841	255	4	j	j	PROPN
ejpam-6841	255	5	(	(	PUNCT
ejpam-6841	255	6	`	`	PUNCT
ejpam-6841	255	7	)	)	PUNCT
ejpam-6841	255	8	=	=	PRON
ejpam-6841	255	9	{	{	PUNCT
ejpam-6841	255	10	`	`	PUNCT
ejpam-6841	255	11	+	+	NUM
ejpam-6841	255	12	1	1	NUM
ejpam-6841	255	13	for	for	ADP
ejpam-6841	255	14	`	`	PUNCT
ejpam-6841	255	15	=	=	SYM
ejpam-6841	255	16	2	2	NUM
ejpam-6841	255	17	`	`	PUNCT
ejpam-6841	255	18	+	+	NUM
ejpam-6841	255	19	4	4	NUM
ejpam-6841	255	20	for	for	ADP
ejpam-6841	255	21	`	`	PUNCT
ejpam-6841	255	22	6=	6=	SYM
ejpam-6841	255	23	2	2	NUM
ejpam-6841	255	24	£	£	PROPN
ejpam-6841	255	25	(	(	PUNCT
ejpam-6841	255	26	`	`	PUNCT
ejpam-6841	255	27	)	)	PUNCT
ejpam-6841	255	28	=	=	PRON
ejpam-6841	255	29	{	{	PUNCT
ejpam-6841	255	30	`	`	PUNCT
ejpam-6841	255	31	2	2	NUM
ejpam-6841	255	32	for	for	ADP
ejpam-6841	255	33	`	`	PUNCT
ejpam-6841	255	34	=	=	SYM
ejpam-6841	255	35	2	2	NUM
ejpam-6841	255	36	`	`	PUNCT
ejpam-6841	255	37	+	+	NUM
ejpam-6841	255	38	3	3	NUM
ejpam-6841	255	39	for	for	ADP
ejpam-6841	255	40	`	`	PUNCT
ejpam-6841	255	41	6=	6=	ADP
ejpam-6841	255	42	2	2	NUM
ejpam-6841	255	43	the	the	DET
ejpam-6841	255	44	mapping	mapping	NOUN
ejpam-6841	255	45	p	p	NOUN
ejpam-6841	255	46	satisfies	satisfie	NOUN
ejpam-6841	255	47	(	(	PUNCT
ejpam-6841	255	48	j	j	NOUN
ejpam-6841	255	49	,	,	PUNCT
ejpam-6841	255	50	b)-ćirić	b)-ćirić	NOUN
ejpam-6841	255	51	-	-	PUNCT
ejpam-6841	255	52	reich	reich	NOUN
ejpam-6841	255	53	-	-	PUNCT
ejpam-6841	255	54	rus	rus	NOUN
ejpam-6841	255	55	type	type	NOUN
ejpam-6841	255	56	interpolative	interpolative	ADJ
ejpam-6841	255	57	proximal	proximal	ADJ
ejpam-6841	255	58	contraction	contraction	NOUN
ejpam-6841	255	59	.	.	PUNCT
ejpam-6841	256	1	indeed	indeed	ADV
ejpam-6841	256	2	,	,	PUNCT
ejpam-6841	256	3	j	j	PROPN
ejpam-6841	256	4	(	(	PUNCT
ejpam-6841	256	5	ϑ	ϑ	X
ejpam-6841	256	6	(	(	PUNCT
ejpam-6841	256	7	b1	b1	NOUN
ejpam-6841	256	8	,	,	PUNCT
ejpam-6841	256	9	b2	b2	NOUN
ejpam-6841	256	10	)	)	PUNCT
ejpam-6841	256	11	)	)	PUNCT
ejpam-6841	256	12	≤	≤	NUM
ejpam-6841	256	13	f	f	X
ejpam-6841	256	14	(	(	PUNCT
ejpam-6841	256	15	(	(	PUNCT
ejpam-6841	256	16	ϑ	ϑ	X
ejpam-6841	256	17	(	(	PUNCT
ejpam-6841	256	18	m1,m2	m1,m2	PROPN
ejpam-6841	256	19	)	)	PUNCT
ejpam-6841	256	20	)	)	PUNCT
ejpam-6841	257	1	α	α	PROPN
ejpam-6841	257	2	(	(	PUNCT
ejpam-6841	257	3	ϑ	ϑ	X
ejpam-6841	257	4	(	(	PUNCT
ejpam-6841	257	5	m1	m1	NOUN
ejpam-6841	257	6	,	,	PUNCT
ejpam-6841	257	7	b1	b1	NOUN
ejpam-6841	257	8	)	)	PUNCT
ejpam-6841	257	9	)	)	PUNCT
ejpam-6841	258	1	β	β	X
ejpam-6841	258	2	(	(	PUNCT
ejpam-6841	258	3	ϑ	ϑ	X
ejpam-6841	258	4	(	(	PUNCT
ejpam-6841	258	5	m2	m2	PROPN
ejpam-6841	258	6	,	,	PUNCT
ejpam-6841	258	7	b2	b2	NOUN
ejpam-6841	258	8	)	)	PUNCT
ejpam-6841	258	9	)	)	PUNCT
ejpam-6841	258	10	1−α−β	1−α−β	PROPN
ejpam-6841	258	11	)	)	PUNCT
ejpam-6841	258	12	implies	imply	VERB
ejpam-6841	258	13	j	j	PROPN
ejpam-6841	258	14	(	(	PUNCT
ejpam-6841	258	15	2	2	NUM
ejpam-6841	258	16	)	)	PUNCT
ejpam-6841	258	17	≤	≤	NUM
ejpam-6841	258	18	f	f	X
ejpam-6841	258	19	(	(	PUNCT
ejpam-6841	258	20	1.4142	1.4142	NUM
ejpam-6841	258	21	)	)	PUNCT
ejpam-6841	258	22	3	3	NUM
ejpam-6841	258	23	≤	≤	NUM
ejpam-6841	258	24	4.4142	4.4142	NUM
ejpam-6841	258	25	.	.	PUNCT
ejpam-6841	259	1	theorem	theorem	NOUN
ejpam-6841	259	2	3	3	X
ejpam-6841	259	3	.	.	PUNCT
ejpam-6841	260	1	let	let	VERB
ejpam-6841	260	2	p	p	NOUN
ejpam-6841	260	3	:	:	PUNCT
ejpam-6841	260	4	c	c	X
ejpam-6841	260	5	→	→	PUNCT
ejpam-6841	260	6	d	d	X
ejpam-6841	260	7	be	be	AUX
ejpam-6841	260	8	an	an	DET
ejpam-6841	260	9	(	(	PUNCT
ejpam-6841	260	10	j,£)-interpolativw	j,£)-interpolativw	PROPN
ejpam-6841	260	11	ćirić	ćirić	NOUN
ejpam-6841	260	12	-	-	PUNCT
ejpam-6841	260	13	reich	reich	NOUN
ejpam-6841	260	14	-	-	PUNCT
ejpam-6841	260	15	rus	rus	NOUN
ejpam-6841	260	16	proximal	proximal	ADJ
ejpam-6841	260	17	contraction	contraction	NOUN
ejpam-6841	260	18	defined	define	VERB
ejpam-6841	260	19	on	on	ADP
ejpam-6841	260	20	a	a	DET
ejpam-6841	260	21	complete	complete	ADJ
ejpam-6841	260	22	metric	metric	ADJ
ejpam-6841	260	23	space	space	NOUN
ejpam-6841	260	24	(	(	PUNCT
ejpam-6841	260	25	w	w	NOUN
ejpam-6841	260	26	,	,	PUNCT
ejpam-6841	260	27	ϑ	ϑ	NOUN
ejpam-6841	260	28	)	)	PUNCT
ejpam-6841	260	29	and	and	CCONJ
ejpam-6841	260	30	c	c	X
ejpam-6841	260	31	,	,	PUNCT
ejpam-6841	260	32	d	d	NOUN
ejpam-6841	260	33	be	be	AUX
ejpam-6841	260	34	nonvoid	nonvoid	ADJ
ejpam-6841	260	35	,	,	PUNCT
ejpam-6841	260	36	closed	closed	ADJ
ejpam-6841	260	37	subsets	subset	NOUN
ejpam-6841	260	38	of	of	ADP
ejpam-6841	260	39	w	w	ADP
ejpam-6841	260	40	such	such	ADJ
ejpam-6841	260	41	that	that	SCONJ
ejpam-6841	260	42	d	d	NOUN
ejpam-6841	260	43	is	be	AUX
ejpam-6841	260	44	approximately	approximately	ADV
ejpam-6841	260	45	compact	compact	ADJ
ejpam-6841	260	46	with	with	ADP
ejpam-6841	260	47	respect	respect	NOUN
ejpam-6841	260	48	to	to	ADP
ejpam-6841	260	49	c.	c.	NOUN
ejpam-6841	260	50	if	if	SCONJ
ejpam-6841	260	51	(	(	PUNCT
ejpam-6841	260	52	i	i	NOUN
ejpam-6841	260	53	)	)	PUNCT
ejpam-6841	260	54	j	j	PROPN
ejpam-6841	260	55	is	be	AUX
ejpam-6841	260	56	non	non	ADJ
ejpam-6841	260	57	-	-	ADJ
ejpam-6841	260	58	decreasing	decrease	VERB
ejpam-6841	260	59	function	function	NOUN
ejpam-6841	260	60	and	and	CCONJ
ejpam-6841	260	61	for	for	ADP
ejpam-6841	260	62	any	any	DET
ejpam-6841	260	63	ε	ε	PROPN
ejpam-6841	260	64	>	>	X
ejpam-6841	260	65	0	0	PUNCT
ejpam-6841	261	1	lim	lim	PROPN
ejpam-6841	261	2	sup	sup	PROPN
ejpam-6841	261	3	t→ε+	t→ε+	VERB
ejpam-6841	261	4	£	£	PROPN
ejpam-6841	261	5	(	(	PUNCT
ejpam-6841	261	6	t	t	PROPN
ejpam-6841	261	7	)	)	PUNCT
ejpam-6841	261	8	<	<	X
ejpam-6841	261	9	j(ε+	j(ε+	NOUN
ejpam-6841	261	10	)	)	PUNCT
ejpam-6841	261	11	.	.	PUNCT
ejpam-6841	262	1	(	(	PUNCT
ejpam-6841	262	2	ii	ii	X
ejpam-6841	262	3	)	)	PUNCT
ejpam-6841	262	4	c0	c0	PROPN
ejpam-6841	262	5	is	be	AUX
ejpam-6841	262	6	nonvoid	nonvoid	PROPN
ejpam-6841	262	7	subset	subset	NOUN
ejpam-6841	262	8	of	of	ADP
ejpam-6841	262	9	c	c	PROPN
ejpam-6841	262	10	such	such	ADJ
ejpam-6841	262	11	that	that	DET
ejpam-6841	262	12	p(c0	p(c0	NOUN
ejpam-6841	262	13	)	)	PUNCT
ejpam-6841	262	14	⊆	⊆	NUM
ejpam-6841	262	15	d0	d0	NOUN
ejpam-6841	262	16	.	.	PUNCT
ejpam-6841	263	1	then	then	ADV
ejpam-6841	263	2	p	p	X
ejpam-6841	263	3	has	have	VERB
ejpam-6841	263	4	a	a	DET
ejpam-6841	263	5	best	good	ADJ
ejpam-6841	263	6	proximity	proximity	NOUN
ejpam-6841	263	7	point	point	NOUN
ejpam-6841	263	8	.	.	PUNCT
ejpam-6841	264	1	proof	proof	NOUN
ejpam-6841	264	2	.	.	PUNCT
ejpam-6841	265	1	let	let	VERB
ejpam-6841	265	2	b0	b0	VERB
ejpam-6841	265	3	∈	∈	PROPN
ejpam-6841	265	4	c0	c0	NOUN
ejpam-6841	265	5	.	.	PUNCT
ejpam-6841	266	1	since	since	SCONJ
ejpam-6841	266	2	p(b0	p(b0	NOUN
ejpam-6841	266	3	)	)	PUNCT
ejpam-6841	266	4	∈	∈	PROPN
ejpam-6841	266	5	p(c0	p(c0	NOUN
ejpam-6841	266	6	)	)	PUNCT
ejpam-6841	266	7	⊆	⊆	NUM
ejpam-6841	266	8	d0	d0	NOUN
ejpam-6841	266	9	,	,	PUNCT
ejpam-6841	266	10	there	there	PRON
ejpam-6841	266	11	exists	exist	VERB
ejpam-6841	266	12	b1	b1	PROPN
ejpam-6841	266	13	∈	∈	PROPN
ejpam-6841	266	14	c0	c0	NOUN
ejpam-6841	266	15	such	such	ADJ
ejpam-6841	266	16	that	that	SCONJ
ejpam-6841	266	17	ϑ(b1,p(b0	ϑ(b1,p(b0	NOUN
ejpam-6841	266	18	)	)	PUNCT
ejpam-6841	266	19	)	)	PUNCT
ejpam-6841	267	1	=	=	PUNCT
ejpam-6841	267	2	ϑ(c	ϑ(c	PROPN
ejpam-6841	267	3	,	,	PUNCT
ejpam-6841	267	4	d	d	NOUN
ejpam-6841	267	5	)	)	PUNCT
ejpam-6841	267	6	.	.	PUNCT
ejpam-6841	268	1	also	also	ADV
ejpam-6841	268	2	,	,	PUNCT
ejpam-6841	268	3	p(b1	p(b1	NOUN
ejpam-6841	268	4	)	)	PUNCT
ejpam-6841	268	5	∈	∈	PROPN
ejpam-6841	268	6	p(c0	p(c0	NOUN
ejpam-6841	268	7	)	)	PUNCT
ejpam-6841	268	8	⊆	⊆	NUM
ejpam-6841	268	9	d0	d0	NOUN
ejpam-6841	268	10	,	,	PUNCT
ejpam-6841	268	11	there	there	PRON
ejpam-6841	268	12	exists	exist	VERB
ejpam-6841	268	13	b2	b2	NOUN
ejpam-6841	268	14	∈	∈	PROPN
ejpam-6841	268	15	c0	c0	NOUN
ejpam-6841	268	16	such	such	ADJ
ejpam-6841	268	17	that	that	DET
ejpam-6841	268	18	ϑ(b2,p(b1	ϑ(b2,p(b1	NOUN
ejpam-6841	268	19	)	)	PUNCT
ejpam-6841	268	20	)	)	PUNCT
ejpam-6841	269	1	=	=	PUNCT
ejpam-6841	269	2	ϑ(c	ϑ(c	PROPN
ejpam-6841	269	3	,	,	PUNCT
ejpam-6841	269	4	d	d	NOUN
ejpam-6841	269	5	)	)	PUNCT
ejpam-6841	269	6	.	.	PUNCT
ejpam-6841	270	1	k.	k.	PROPN
ejpam-6841	270	2	javed	javed	PROPN
ejpam-6841	270	3	,	,	PUNCT
ejpam-6841	270	4	m.	m.	NOUN
ejpam-6841	270	5	nazam	nazam	PROPN
ejpam-6841	270	6	,	,	PUNCT
ejpam-6841	270	7	m.	m.	PROPN
ejpam-6841	270	8	arshad	arshad	PROPN
ejpam-6841	270	9	,	,	PUNCT
ejpam-6841	270	10	m.	m.	NOUN
ejpam-6841	270	11	de	de	X
ejpam-6841	270	12	la	la	PROPN
ejpam-6841	270	13	sen	sen	PROPN
ejpam-6841	270	14	/	/	SYM
ejpam-6841	270	15	eur	eur	PROPN
ejpam-6841	270	16	.	.	PUNCT
ejpam-6841	271	1	j.	j.	PROPN
ejpam-6841	271	2	pure	pure	PROPN
ejpam-6841	271	3	appl	appl	PROPN
ejpam-6841	271	4	.	.	PROPN
ejpam-6841	271	5	math	math	PROPN
ejpam-6841	271	6	,	,	PUNCT
ejpam-6841	271	7	18	18	NUM
ejpam-6841	271	8	(	(	PUNCT
ejpam-6841	271	9	4	4	NUM
ejpam-6841	271	10	)	)	PUNCT
ejpam-6841	271	11	(	(	PUNCT
ejpam-6841	271	12	2025	2025	NUM
ejpam-6841	271	13	)	)	PUNCT
ejpam-6841	271	14	,	,	PUNCT
ejpam-6841	271	15	6841	6841	NUM
ejpam-6841	271	16	12	12	NUM
ejpam-6841	271	17	of	of	ADP
ejpam-6841	271	18	23	23	NUM
ejpam-6841	271	19	continuing	continue	VERB
ejpam-6841	271	20	this	this	DET
ejpam-6841	271	21	process	process	NOUN
ejpam-6841	271	22	,	,	PUNCT
ejpam-6841	271	23	we	we	PRON
ejpam-6841	271	24	construct	construct	VERB
ejpam-6841	271	25	a	a	DET
ejpam-6841	271	26	sequence	sequence	NOUN
ejpam-6841	271	27	{	{	PUNCT
ejpam-6841	271	28	bn	bn	NOUN
ejpam-6841	271	29	}	}	PUNCT
ejpam-6841	271	30	in	in	ADP
ejpam-6841	271	31	c0	c0	PROPN
ejpam-6841	271	32	such	such	ADJ
ejpam-6841	271	33	that	that	DET
ejpam-6841	271	34	ϑ(bn+1,p(bn	ϑ(bn+1,p(bn	NOUN
ejpam-6841	271	35	)	)	PUNCT
ejpam-6841	271	36	)	)	PUNCT
ejpam-6841	272	1	=	=	PUNCT
ejpam-6841	272	2	ϑ(c	ϑ(c	PROPN
ejpam-6841	272	3	,	,	PUNCT
ejpam-6841	272	4	d	d	NOUN
ejpam-6841	272	5	)	)	PUNCT
ejpam-6841	272	6	,	,	PUNCT
ejpam-6841	272	7	for	for	ADP
ejpam-6841	272	8	all	all	DET
ejpam-6841	272	9	n	n	PRON
ejpam-6841	272	10	∈	∈	PROPN
ejpam-6841	272	11	n.	n.	NOUN
ejpam-6841	272	12	(	(	PUNCT
ejpam-6841	272	13	15	15	NUM
ejpam-6841	272	14	)	)	PUNCT
ejpam-6841	272	15	now	now	ADV
ejpam-6841	272	16	,	,	PUNCT
ejpam-6841	272	17	if	if	SCONJ
ejpam-6841	272	18	there	there	PRON
ejpam-6841	272	19	exists	exist	VERB
ejpam-6841	272	20	some	some	DET
ejpam-6841	272	21	n	n	PRON
ejpam-6841	272	22	∈	∈	PROPN
ejpam-6841	272	23	n	n	PRON
ejpam-6841	272	24	such	such	ADJ
ejpam-6841	272	25	that	that	PRON
ejpam-6841	272	26	bn	bn	NOUN
ejpam-6841	272	27	=	=	SYM
ejpam-6841	272	28	bn+1	bn+1	PROPN
ejpam-6841	272	29	,	,	PUNCT
ejpam-6841	272	30	then	then	ADV
ejpam-6841	272	31	by	by	ADP
ejpam-6841	272	32	(	(	PUNCT
ejpam-6841	272	33	15	15	NUM
ejpam-6841	272	34	)	)	PUNCT
ejpam-6841	272	35	,	,	PUNCT
ejpam-6841	272	36	then	then	ADV
ejpam-6841	272	37	bn	bn	PRON
ejpam-6841	272	38	is	be	AUX
ejpam-6841	272	39	a	a	DET
ejpam-6841	272	40	best	good	ADJ
ejpam-6841	272	41	proximity	proximity	NOUN
ejpam-6841	272	42	point	point	NOUN
ejpam-6841	272	43	of	of	ADP
ejpam-6841	272	44	the	the	DET
ejpam-6841	272	45	mapping	mapping	NOUN
ejpam-6841	273	1	p.	p.	NOUN
ejpam-6841	273	2	if	if	SCONJ
ejpam-6841	273	3	bn	bn	PROPN
ejpam-6841	273	4	6=	6=	ADP
ejpam-6841	273	5	bn+1	bn+1	NUM
ejpam-6841	273	6	for	for	ADP
ejpam-6841	273	7	all	all	PRON
ejpam-6841	273	8	n	n	PRON
ejpam-6841	273	9	∈	∈	NOUN
ejpam-6841	273	10	n	n	NOUN
ejpam-6841	273	11	and	and	CCONJ
ejpam-6841	273	12	using	use	VERB
ejpam-6841	273	13	(	(	PUNCT
ejpam-6841	273	14	15	15	NUM
ejpam-6841	273	15	)	)	PUNCT
ejpam-6841	273	16	,	,	PUNCT
ejpam-6841	273	17	we	we	PRON
ejpam-6841	273	18	have	have	VERB
ejpam-6841	273	19	ϑ(bn	ϑ(bn	NOUN
ejpam-6841	273	20	,	,	PUNCT
ejpam-6841	273	21	p(bn−1	p(bn−1	NUM
ejpam-6841	273	22	)	)	PUNCT
ejpam-6841	273	23	)	)	PUNCT
ejpam-6841	274	1	=	=	PUNCT
ejpam-6841	274	2	ϑ(c	ϑ(c	PROPN
ejpam-6841	274	3	,	,	PUNCT
ejpam-6841	274	4	d	d	NOUN
ejpam-6841	274	5	)	)	PUNCT
ejpam-6841	274	6	,	,	PUNCT
ejpam-6841	274	7	and	and	CCONJ
ejpam-6841	274	8	ϑ(bn+1,p(bn	ϑ(bn+1,p(bn	NOUN
ejpam-6841	274	9	)	)	PUNCT
ejpam-6841	274	10	)	)	PUNCT
ejpam-6841	275	1	=	=	PUNCT
ejpam-6841	275	2	ϑ(c	ϑ(c	PROPN
ejpam-6841	275	3	,	,	PUNCT
ejpam-6841	275	4	d	d	NOUN
ejpam-6841	275	5	)	)	PUNCT
ejpam-6841	275	6	,	,	PUNCT
ejpam-6841	275	7	for	for	ADP
ejpam-6841	275	8	all	all	DET
ejpam-6841	275	9	n	n	PRON
ejpam-6841	275	10	≥	≥	NOUN
ejpam-6841	275	11	1	1	NUM
ejpam-6841	275	12	.	.	PUNCT
ejpam-6841	275	13	thus	thus	ADV
ejpam-6841	275	14	,	,	PUNCT
ejpam-6841	275	15	by	by	ADP
ejpam-6841	275	16	(	(	PUNCT
ejpam-6841	275	17	14	14	NUM
ejpam-6841	275	18	)	)	PUNCT
ejpam-6841	275	19	,	,	PUNCT
ejpam-6841	275	20	we	we	PRON
ejpam-6841	275	21	have	have	VERB
ejpam-6841	275	22	j(ϑ(bn	j(ϑ(bn	PROPN
ejpam-6841	275	23	,	,	PUNCT
ejpam-6841	275	24	bn+1	bn+1	NUM
ejpam-6841	275	25	)	)	PUNCT
ejpam-6841	275	26	)	)	PUNCT
ejpam-6841	276	1	≤	≤	ADV
ejpam-6841	276	2	£	£	SYM
ejpam-6841	276	3	(	(	PUNCT
ejpam-6841	276	4	(	(	PUNCT
ejpam-6841	276	5	ϑ	ϑ	X
ejpam-6841	276	6	(	(	PUNCT
ejpam-6841	276	7	bn−1,bn	bn−1,bn	NOUN
ejpam-6841	276	8	)	)	PUNCT
ejpam-6841	276	9	)	)	PUNCT
ejpam-6841	277	1	α	α	X
ejpam-6841	277	2	(	(	PUNCT
ejpam-6841	277	3	ϑ	ϑ	X
ejpam-6841	277	4	(	(	PUNCT
ejpam-6841	277	5	bn−1	bn−1	ADJ
ejpam-6841	277	6	,	,	PUNCT
ejpam-6841	277	7	bn	bn	NOUN
ejpam-6841	277	8	)	)	PUNCT
ejpam-6841	277	9	)	)	PUNCT
ejpam-6841	278	1	β	β	X
ejpam-6841	278	2	(	(	PUNCT
ejpam-6841	278	3	ϑ	ϑ	X
ejpam-6841	278	4	(	(	PUNCT
ejpam-6841	278	5	bn	bn	X
ejpam-6841	278	6	,	,	PUNCT
ejpam-6841	278	7	bn+1	bn+1	NUM
ejpam-6841	278	8	)	)	PUNCT
ejpam-6841	278	9	)	)	PUNCT
ejpam-6841	278	10	1−α−β	1−α−β	NUM
ejpam-6841	278	11	)	)	PUNCT
ejpam-6841	278	12	(	(	PUNCT
ejpam-6841	278	13	16	16	NUM
ejpam-6841	278	14	)	)	PUNCT
ejpam-6841	278	15	for	for	ADP
ejpam-6841	278	16	all	all	DET
ejpam-6841	278	17	distinct	distinct	ADJ
ejpam-6841	278	18	bn−1	bn−1	ADJ
ejpam-6841	278	19	,	,	PUNCT
ejpam-6841	278	20	bn	bn	ADJ
ejpam-6841	278	21	,	,	PUNCT
ejpam-6841	278	22	bn+1	bn+1	PROPN
ejpam-6841	278	23	∈	∈	PROPN
ejpam-6841	278	24	c.	c.	PROPN
ejpam-6841	278	25	since	since	SCONJ
ejpam-6841	278	26	,	,	PUNCT
ejpam-6841	278	27	£	£	PROPN
ejpam-6841	278	28	(	(	PUNCT
ejpam-6841	278	29	t	t	PROPN
ejpam-6841	278	30	)	)	PUNCT
ejpam-6841	278	31	<	<	X
ejpam-6841	278	32	j(t	j(t	PROPN
ejpam-6841	278	33	)	)	PUNCT
ejpam-6841	278	34	for	for	ADP
ejpam-6841	278	35	all	all	DET
ejpam-6841	278	36	t	t	PROPN
ejpam-6841	278	37	>	>	X
ejpam-6841	278	38	0	0	NUM
ejpam-6841	278	39	,	,	PUNCT
ejpam-6841	278	40	by	by	ADP
ejpam-6841	278	41	(	(	PUNCT
ejpam-6841	278	42	16	16	NUM
ejpam-6841	278	43	)	)	PUNCT
ejpam-6841	278	44	,	,	PUNCT
ejpam-6841	278	45	we	we	PRON
ejpam-6841	278	46	have	have	VERB
ejpam-6841	278	47	j(ϑ(bn	j(ϑ(bn	PROPN
ejpam-6841	278	48	,	,	PUNCT
ejpam-6841	278	49	bn+1	bn+1	NUM
ejpam-6841	278	50	)	)	PUNCT
ejpam-6841	278	51	)	)	PUNCT
ejpam-6841	279	1	<	<	X
ejpam-6841	279	2	j((ϑ	j((ϑ	PROPN
ejpam-6841	279	3	(	(	PUNCT
ejpam-6841	279	4	bn−1,bn	bn−1,bn	NOUN
ejpam-6841	279	5	)	)	PUNCT
ejpam-6841	279	6	)	)	PUNCT
ejpam-6841	280	1	α	α	X
ejpam-6841	280	2	(	(	PUNCT
ejpam-6841	280	3	ϑ	ϑ	X
ejpam-6841	280	4	(	(	PUNCT
ejpam-6841	280	5	bn−1	bn−1	ADJ
ejpam-6841	280	6	,	,	PUNCT
ejpam-6841	280	7	bn	bn	NOUN
ejpam-6841	280	8	)	)	PUNCT
ejpam-6841	280	9	)	)	PUNCT
ejpam-6841	281	1	β	β	X
ejpam-6841	281	2	(	(	PUNCT
ejpam-6841	281	3	ϑ	ϑ	X
ejpam-6841	281	4	(	(	PUNCT
ejpam-6841	281	5	bn	bn	X
ejpam-6841	281	6	,	,	PUNCT
ejpam-6841	281	7	bn+1	bn+1	NUM
ejpam-6841	281	8	)	)	PUNCT
ejpam-6841	281	9	)	)	PUNCT
ejpam-6841	281	10	1−α−β	1−α−β	NUM
ejpam-6841	281	11	)	)	PUNCT
ejpam-6841	281	12	.	.	PUNCT
ejpam-6841	282	1	since	since	SCONJ
ejpam-6841	282	2	,	,	PUNCT
ejpam-6841	282	3	j	j	PROPN
ejpam-6841	282	4	is	be	AUX
ejpam-6841	282	5	a	a	DET
ejpam-6841	282	6	non	non	ADJ
ejpam-6841	282	7	-	-	ADJ
ejpam-6841	282	8	decreasing	decrease	VERB
ejpam-6841	282	9	function	function	NOUN
ejpam-6841	282	10	,	,	PUNCT
ejpam-6841	282	11	then	then	ADV
ejpam-6841	282	12	ϑ(bn	ϑ(bn	PROPN
ejpam-6841	282	13	,	,	PUNCT
ejpam-6841	282	14	bn+1	bn+1	NUM
ejpam-6841	282	15	)	)	PUNCT
ejpam-6841	282	16	<	<	X
ejpam-6841	282	17	(	(	PUNCT
ejpam-6841	282	18	ϑ	ϑ	X
ejpam-6841	282	19	(	(	PUNCT
ejpam-6841	282	20	bn−1,bn	bn−1,bn	NOUN
ejpam-6841	282	21	)	)	PUNCT
ejpam-6841	282	22	)	)	PUNCT
ejpam-6841	283	1	α+β	α+β	PROPN
ejpam-6841	283	2	(	(	PUNCT
ejpam-6841	283	3	ϑ(bn	ϑ(bn	PROPN
ejpam-6841	283	4	,	,	PUNCT
ejpam-6841	283	5	bn+1	bn+1	NUM
ejpam-6841	283	6	)	)	PUNCT
ejpam-6841	283	7	)	)	PUNCT
ejpam-6841	283	8	1−α−β	1−α−β	NOUN
ejpam-6841	283	9	.	.	PUNCT
ejpam-6841	284	1	this	this	PRON
ejpam-6841	284	2	implies	imply	VERB
ejpam-6841	284	3	that	that	SCONJ
ejpam-6841	284	4	(	(	PUNCT
ejpam-6841	284	5	ϑ(bn	ϑ(bn	PROPN
ejpam-6841	284	6	,	,	PUNCT
ejpam-6841	284	7	bn+1	bn+1	NUM
ejpam-6841	284	8	)	)	PUNCT
ejpam-6841	284	9	α+β	α+β	NUM
ejpam-6841	284	10	)	)	PUNCT
ejpam-6841	284	11	<	<	X
ejpam-6841	284	12	(	(	PUNCT
ejpam-6841	284	13	ϑ	ϑ	X
ejpam-6841	284	14	(	(	PUNCT
ejpam-6841	284	15	bn−1,bn	bn−1,bn	NOUN
ejpam-6841	284	16	)	)	PUNCT
ejpam-6841	284	17	)	)	PUNCT
ejpam-6841	284	18	α+β	α+β	PROPN
ejpam-6841	284	19	.	.	PUNCT
ejpam-6841	285	1	this	this	PRON
ejpam-6841	285	2	implies	imply	VERB
ejpam-6841	285	3	θn	θn	ADP
ejpam-6841	285	4	<	<	X
ejpam-6841	285	5	θn−1	θn−1	PROPN
ejpam-6841	285	6	for	for	ADP
ejpam-6841	285	7	all	all	PRON
ejpam-6841	285	8	n	n	DET
ejpam-6841	285	9	∈	∈	PROPN
ejpam-6841	285	10	n.	n.	NOUN
ejpam-6841	285	11	suppose	suppose	VERB
ejpam-6841	285	12	on	on	ADP
ejpam-6841	285	13	contrary	contrary	ADJ
ejpam-6841	285	14	that	that	SCONJ
ejpam-6841	285	15	θ	θ	PROPN
ejpam-6841	285	16	>	>	X
ejpam-6841	285	17	0	0	NUM
ejpam-6841	285	18	,	,	PUNCT
ejpam-6841	285	19	so	so	SCONJ
ejpam-6841	285	20	that	that	SCONJ
ejpam-6841	285	21	,	,	PUNCT
ejpam-6841	285	22	by	by	ADP
ejpam-6841	285	23	(	(	PUNCT
ejpam-6841	285	24	16	16	NUM
ejpam-6841	285	25	)	)	PUNCT
ejpam-6841	285	26	,	,	PUNCT
ejpam-6841	285	27	we	we	PRON
ejpam-6841	285	28	have	have	VERB
ejpam-6841	285	29	:	:	PUNCT
ejpam-6841	285	30	j	j	X
ejpam-6841	285	31	(	(	PUNCT
ejpam-6841	285	32	θ+	θ+	X
ejpam-6841	285	33	)	)	PUNCT
ejpam-6841	285	34	=	=	VERB
ejpam-6841	285	35	lim	lim	PROPN
ejpam-6841	285	36	n→∞	n→∞	X
ejpam-6841	285	37	j	j	PROPN
ejpam-6841	285	38	(	(	PUNCT
ejpam-6841	285	39	θn	θn	NOUN
ejpam-6841	285	40	)	)	PUNCT
ejpam-6841	285	41	≤	≤	NOUN
ejpam-6841	285	42	lim	lim	PROPN
ejpam-6841	285	43	n→∞	n→∞	PRON
ejpam-6841	285	44	£	£	PROPN
ejpam-6841	285	45	(	(	PUNCT
ejpam-6841	285	46	(	(	PUNCT
ejpam-6841	285	47	θn−1	θn−1	PROPN
ejpam-6841	285	48	)	)	PUNCT
ejpam-6841	285	49	α+β(θn	α+β(θn	PROPN
ejpam-6841	285	50	)	)	PUNCT
ejpam-6841	285	51	1−α−β	1−α−β	PROPN
ejpam-6841	285	52	)	)	PUNCT
ejpam-6841	285	53	≤	≤	PROPN
ejpam-6841	286	1	lim	lim	PROPN
ejpam-6841	286	2	t→θ+	t→θ+	PROPN
ejpam-6841	286	3	sup£	sup£	X
ejpam-6841	286	4	(	(	PUNCT
ejpam-6841	286	5	t	t	PROPN
ejpam-6841	286	6	)	)	PUNCT
ejpam-6841	286	7	.	.	PUNCT
ejpam-6841	287	1	this	this	PRON
ejpam-6841	287	2	defies	defy	VERB
ejpam-6841	287	3	presumption	presumption	NOUN
ejpam-6841	287	4	(	(	PUNCT
ejpam-6841	287	5	i	i	NOUN
ejpam-6841	287	6	)	)	PUNCT
ejpam-6841	287	7	,	,	PUNCT
ejpam-6841	287	8	hence	hence	ADV
ejpam-6841	287	9	,	,	PUNCT
ejpam-6841	287	10	θ	θ	PROPN
ejpam-6841	287	11	=	=	SYM
ejpam-6841	287	12	0	0	NUM
ejpam-6841	287	13	and	and	CCONJ
ejpam-6841	287	14	limn→∞	limn→∞	PRON
ejpam-6841	287	15	ϑ(bn	ϑ(bn	NOUN
ejpam-6841	287	16	,	,	PUNCT
ejpam-6841	287	17	bn+1	bn+1	NUM
ejpam-6841	287	18	)	)	PUNCT
ejpam-6841	288	1	=	=	SYM
ejpam-6841	288	2	0	0	X
ejpam-6841	288	3	.	.	PUNCT
ejpam-6841	289	1	now	now	ADV
ejpam-6841	289	2	,	,	PUNCT
ejpam-6841	289	3	(	(	PUNCT
ejpam-6841	289	4	i	i	NOUN
ejpam-6841	289	5	)	)	PUNCT
ejpam-6841	289	6	and	and	CCONJ
ejpam-6841	289	7	lemma	lemma	PROPN
ejpam-6841	289	8	3	3	NUM
ejpam-6841	289	9	,	,	PUNCT
ejpam-6841	289	10	we	we	PRON
ejpam-6841	289	11	conclude	conclude	VERB
ejpam-6841	289	12	that	that	SCONJ
ejpam-6841	289	13	{	{	PUNCT
ejpam-6841	289	14	bn	bn	NOUN
ejpam-6841	289	15	}	}	PUNCT
ejpam-6841	289	16	is	be	AUX
ejpam-6841	289	17	a	a	DET
ejpam-6841	289	18	cauchy	cauchy	ADJ
ejpam-6841	289	19	sequence	sequence	NOUN
ejpam-6841	289	20	.	.	PUNCT
ejpam-6841	290	1	since	since	SCONJ
ejpam-6841	290	2	(	(	PUNCT
ejpam-6841	290	3	w	w	PROPN
ejpam-6841	290	4	,	,	PUNCT
ejpam-6841	290	5	ϑ	ϑ	NOUN
ejpam-6841	290	6	)	)	PUNCT
ejpam-6841	290	7	is	be	AUX
ejpam-6841	290	8	a	a	DET
ejpam-6841	290	9	complete	complete	ADJ
ejpam-6841	290	10	metric	metric	ADJ
ejpam-6841	290	11	space	space	NOUN
ejpam-6841	290	12	and	and	CCONJ
ejpam-6841	290	13	c	c	NOUN
ejpam-6841	290	14	is	be	AUX
ejpam-6841	290	15	a	a	DET
ejpam-6841	290	16	closed	closed	ADJ
ejpam-6841	290	17	subset	subset	NOUN
ejpam-6841	290	18	of	of	ADP
ejpam-6841	290	19	w.	w.	PROPN
ejpam-6841	290	20	then	then	ADV
ejpam-6841	290	21	there	there	PRON
ejpam-6841	290	22	exists	exist	VERB
ejpam-6841	290	23	b∗	b∗	ADJ
ejpam-6841	290	24	∈	∈	PROPN
ejpam-6841	290	25	c	c	NOUN
ejpam-6841	290	26	,	,	PUNCT
ejpam-6841	290	27	such	such	ADJ
ejpam-6841	290	28	that	that	SCONJ
ejpam-6841	290	29	limn→∞	limn→∞	PROPN
ejpam-6841	290	30	ϑ(bn	ϑ(bn	PROPN
ejpam-6841	290	31	,	,	PUNCT
ejpam-6841	290	32	b	b	NOUN
ejpam-6841	290	33	∗	∗	NOUN
ejpam-6841	290	34	)	)	PUNCT
ejpam-6841	291	1	=	=	SYM
ejpam-6841	291	2	0	0	X
ejpam-6841	291	3	.	.	PUNCT
ejpam-6841	292	1	further	far	ADV
ejpam-6841	292	2	,	,	PUNCT
ejpam-6841	292	3	ϑ(b∗,p(bn	ϑ(b∗,p(bn	PROPN
ejpam-6841	292	4	)	)	PUNCT
ejpam-6841	292	5	)	)	PUNCT
ejpam-6841	293	1	≤	≤	PROPN
ejpam-6841	293	2	ϑ(b∗	ϑ(b∗	X
ejpam-6841	293	3	,	,	PUNCT
ejpam-6841	293	4	bn+1	bn+1	NUM
ejpam-6841	293	5	)	)	PUNCT
ejpam-6841	293	6	+	+	CCONJ
ejpam-6841	293	7	ϑ(bn+1,p(bn	ϑ(bn+1,p(bn	NOUN
ejpam-6841	293	8	)	)	PUNCT
ejpam-6841	293	9	)	)	PUNCT
ejpam-6841	293	10	≤	≤	PROPN
ejpam-6841	293	11	ϑ(b∗	ϑ(b∗	X
ejpam-6841	293	12	,	,	PUNCT
ejpam-6841	293	13	bn+1	bn+1	NUM
ejpam-6841	293	14	)	)	PUNCT
ejpam-6841	293	15	+	+	CCONJ
ejpam-6841	293	16	ϑ(c	ϑ(c	PROPN
ejpam-6841	293	17	,	,	PUNCT
ejpam-6841	293	18	d	d	NOUN
ejpam-6841	293	19	)	)	PUNCT
ejpam-6841	293	20	≤	≤	PROPN
ejpam-6841	293	21	ϑ(b∗	ϑ(b∗	X
ejpam-6841	293	22	,	,	PUNCT
ejpam-6841	293	23	bn+1	bn+1	NUM
ejpam-6841	293	24	)	)	PUNCT
ejpam-6841	293	25	+	+	CCONJ
ejpam-6841	293	26	ϑ(b∗,d	ϑ(b∗,d	NUM
ejpam-6841	293	27	)	)	PUNCT
ejpam-6841	293	28	.	.	PUNCT
ejpam-6841	294	1	therefore	therefore	ADV
ejpam-6841	294	2	,	,	PUNCT
ejpam-6841	294	3	ϑ(b∗,p(bn	ϑ(b∗,p(bn	PROPN
ejpam-6841	294	4	)	)	PUNCT
ejpam-6841	294	5	)	)	PUNCT
ejpam-6841	294	6	→	→	SYM
ejpam-6841	294	7	ϑ(b∗,d	ϑ(b∗,d	NUM
ejpam-6841	294	8	)	)	PUNCT
ejpam-6841	294	9	as	as	ADP
ejpam-6841	294	10	n	n	PROPN
ejpam-6841	294	11	→	→	SYM
ejpam-6841	294	12	∞.	∞.	PROPN
ejpam-6841	294	13	since	since	SCONJ
ejpam-6841	294	14	d	d	PROPN
ejpam-6841	294	15	is	be	AUX
ejpam-6841	294	16	approximately	approximately	ADV
ejpam-6841	294	17	compact	compact	ADJ
ejpam-6841	294	18	with	with	ADP
ejpam-6841	294	19	respect	respect	NOUN
ejpam-6841	294	20	to	to	ADP
ejpam-6841	294	21	c	c	NOUN
ejpam-6841	294	22	,	,	PUNCT
ejpam-6841	294	23	there	there	PRON
ejpam-6841	294	24	exists	exist	VERB
ejpam-6841	294	25	a	a	DET
ejpam-6841	294	26	subsequence	subsequence	NOUN
ejpam-6841	294	27	{	{	PUNCT
ejpam-6841	294	28	p(bnk	p(bnk	NOUN
ejpam-6841	294	29	)	)	PUNCT
ejpam-6841	294	30	}	}	PUNCT
ejpam-6841	294	31	of	of	ADP
ejpam-6841	294	32	{	{	PUNCT
ejpam-6841	294	33	p(bn	p(bn	NOUN
ejpam-6841	294	34	)	)	PUNCT
ejpam-6841	294	35	}	}	PUNCT
ejpam-6841	294	36	.	.	PUNCT
ejpam-6841	295	1	such	such	ADJ
ejpam-6841	295	2	that	that	SCONJ
ejpam-6841	295	3	p(bnk	p(bnk	NOUN
ejpam-6841	295	4	)	)	PUNCT
ejpam-6841	295	5	→	→	SYM
ejpam-6841	295	6	m∗	m∗	VERB
ejpam-6841	295	7	∈	∈	PROPN
ejpam-6841	295	8	d	d	NOUN
ejpam-6841	295	9	as	as	ADP
ejpam-6841	295	10	k	k	PROPN
ejpam-6841	295	11	→	→	SYM
ejpam-6841	295	12	∞.	∞.	PROPN
ejpam-6841	295	13	thus	thus	ADV
ejpam-6841	295	14	,	,	PUNCT
ejpam-6841	295	15	by	by	ADP
ejpam-6841	295	16	solving	solve	VERB
ejpam-6841	295	17	the	the	DET
ejpam-6841	295	18	following	follow	VERB
ejpam-6841	295	19	equation	equation	NOUN
ejpam-6841	295	20	with	with	ADP
ejpam-6841	295	21	k	k	PROPN
ejpam-6841	295	22	→	→	SYM
ejpam-6841	295	23	∞	∞	PROPN
ejpam-6841	295	24	,	,	PUNCT
ejpam-6841	295	25	ϑ(bnk+1	ϑ(bnk+1	NOUN
ejpam-6841	295	26	,	,	PUNCT
ejpam-6841	295	27	p(bnk	p(bnk	NOUN
ejpam-6841	295	28	)	)	PUNCT
ejpam-6841	295	29	)	)	PUNCT
ejpam-6841	296	1	=	=	PUNCT
ejpam-6841	296	2	ϑ(c	ϑ(c	PROPN
ejpam-6841	296	3	,	,	PUNCT
ejpam-6841	296	4	d	d	NOUN
ejpam-6841	296	5	)	)	PUNCT
ejpam-6841	296	6	,	,	PUNCT
ejpam-6841	296	7	(	(	PUNCT
ejpam-6841	296	8	17	17	NUM
ejpam-6841	296	9	)	)	PUNCT
ejpam-6841	296	10	k.	k.	PROPN
ejpam-6841	296	11	javed	javed	PROPN
ejpam-6841	296	12	,	,	PUNCT
ejpam-6841	296	13	m.	m.	NOUN
ejpam-6841	296	14	nazam	nazam	PROPN
ejpam-6841	296	15	,	,	PUNCT
ejpam-6841	296	16	m.	m.	PROPN
ejpam-6841	296	17	arshad	arshad	PROPN
ejpam-6841	296	18	,	,	PUNCT
ejpam-6841	296	19	m.	m.	NOUN
ejpam-6841	296	20	de	de	X
ejpam-6841	296	21	la	la	PROPN
ejpam-6841	296	22	sen	sen	PROPN
ejpam-6841	296	23	/	/	SYM
ejpam-6841	296	24	eur	eur	PROPN
ejpam-6841	296	25	.	.	PUNCT
ejpam-6841	297	1	j.	j.	PROPN
ejpam-6841	297	2	pure	pure	PROPN
ejpam-6841	297	3	appl	appl	PROPN
ejpam-6841	297	4	.	.	PROPN
ejpam-6841	297	5	math	math	PROPN
ejpam-6841	297	6	,	,	PUNCT
ejpam-6841	297	7	18	18	NUM
ejpam-6841	297	8	(	(	PUNCT
ejpam-6841	297	9	4	4	NUM
ejpam-6841	297	10	)	)	PUNCT
ejpam-6841	297	11	(	(	PUNCT
ejpam-6841	297	12	2025	2025	NUM
ejpam-6841	297	13	)	)	PUNCT
ejpam-6841	297	14	,	,	PUNCT
ejpam-6841	297	15	6841	6841	NUM
ejpam-6841	297	16	13	13	NUM
ejpam-6841	297	17	of	of	ADP
ejpam-6841	297	18	23	23	NUM
ejpam-6841	297	19	we	we	PRON
ejpam-6841	297	20	have	have	VERB
ejpam-6841	297	21	,	,	PUNCT
ejpam-6841	297	22	ϑ(b∗	ϑ(b∗	NOUN
ejpam-6841	297	23	,	,	PUNCT
ejpam-6841	297	24	y∗	y∗	PROPN
ejpam-6841	297	25	)	)	PUNCT
ejpam-6841	298	1	=	=	PUNCT
ejpam-6841	298	2	ϑ(c	ϑ(c	PROPN
ejpam-6841	298	3	,	,	PUNCT
ejpam-6841	298	4	d	d	NOUN
ejpam-6841	298	5	)	)	PUNCT
ejpam-6841	298	6	.	.	PUNCT
ejpam-6841	299	1	since	since	SCONJ
ejpam-6841	299	2	,	,	PUNCT
ejpam-6841	299	3	b∗	b∗	PROPN
ejpam-6841	299	4	∈	∈	PROPN
ejpam-6841	299	5	c0	c0	NOUN
ejpam-6841	299	6	,	,	PUNCT
ejpam-6841	299	7	so	so	ADV
ejpam-6841	299	8	,	,	PUNCT
ejpam-6841	299	9	p(b∗	p(b∗	NOUN
ejpam-6841	299	10	)	)	PUNCT
ejpam-6841	299	11	∈	∈	PROPN
ejpam-6841	299	12	p(c0	p(c0	NOUN
ejpam-6841	299	13	)	)	PUNCT
ejpam-6841	299	14	⊆	⊆	NUM
ejpam-6841	299	15	d0	d0	NOUN
ejpam-6841	299	16	and	and	CCONJ
ejpam-6841	299	17	there	there	PRON
ejpam-6841	299	18	exists	exist	VERB
ejpam-6841	299	19	p	p	PROPN
ejpam-6841	299	20	∈	∈	PROPN
ejpam-6841	299	21	c0	c0	NOUN
ejpam-6841	299	22	such	such	ADJ
ejpam-6841	299	23	that	that	PRON
ejpam-6841	299	24	ϑ(p	ϑ(p	PROPN
ejpam-6841	299	25	,	,	PUNCT
ejpam-6841	299	26	p(b∗	p(b∗	NOUN
ejpam-6841	299	27	)	)	PUNCT
ejpam-6841	299	28	)	)	PUNCT
ejpam-6841	300	1	=	=	PUNCT
ejpam-6841	300	2	ϑ(c	ϑ(c	PROPN
ejpam-6841	300	3	,	,	PUNCT
ejpam-6841	300	4	d	d	NOUN
ejpam-6841	300	5	)	)	PUNCT
ejpam-6841	300	6	.	.	PUNCT
ejpam-6841	301	1	(	(	PUNCT
ejpam-6841	301	2	18	18	NUM
ejpam-6841	301	3	)	)	PUNCT
ejpam-6841	301	4	now	now	ADV
ejpam-6841	301	5	,	,	PUNCT
ejpam-6841	301	6	(	(	PUNCT
ejpam-6841	301	7	17	17	NUM
ejpam-6841	301	8	)	)	PUNCT
ejpam-6841	301	9	and	and	CCONJ
ejpam-6841	301	10	(	(	PUNCT
ejpam-6841	301	11	18	18	NUM
ejpam-6841	301	12	)	)	PUNCT
ejpam-6841	301	13	,	,	PUNCT
ejpam-6841	301	14	by	by	ADP
ejpam-6841	301	15	(	(	PUNCT
ejpam-6841	301	16	14	14	NUM
ejpam-6841	301	17	)	)	PUNCT
ejpam-6841	301	18	we	we	PRON
ejpam-6841	301	19	have	have	VERB
ejpam-6841	301	20	j(ϑ(bnk+1	j(ϑ(bnk+1	NOUN
ejpam-6841	301	21	,	,	PUNCT
ejpam-6841	301	22	p	p	NOUN
ejpam-6841	301	23	)	)	PUNCT
ejpam-6841	301	24	)	)	PUNCT
ejpam-6841	302	1	≤	≤	NUM
ejpam-6841	302	2	£	£	NOUN
ejpam-6841	302	3	(	(	PUNCT
ejpam-6841	302	4	(	(	PUNCT
ejpam-6841	302	5	ϑ(bnk	ϑ(bnk	NOUN
ejpam-6841	302	6	,	,	PUNCT
ejpam-6841	302	7	b∗))α	b∗))α	PROPN
ejpam-6841	302	8	·	·	PUNCT
ejpam-6841	302	9	(	(	PUNCT
ejpam-6841	302	10	ϑ(bnk	ϑ(bnk	NOUN
ejpam-6841	302	11	,	,	PUNCT
ejpam-6841	302	12	bnk+1	bnk+1	NOUN
ejpam-6841	302	13	)	)	PUNCT
ejpam-6841	302	14	)	)	PUNCT
ejpam-6841	303	1	β	β	X
ejpam-6841	303	2	·	·	PUNCT
ejpam-6841	303	3	(	(	PUNCT
ejpam-6841	303	4	ϑ(b∗	ϑ(b∗	X
ejpam-6841	303	5	,	,	PUNCT
ejpam-6841	303	6	p))1−α−β	p))1−α−β	PRON
ejpam-6841	303	7	)	)	PUNCT
ejpam-6841	303	8	<	<	X
ejpam-6841	303	9	j	j	X
ejpam-6841	303	10	(	(	PUNCT
ejpam-6841	303	11	(	(	PUNCT
ejpam-6841	303	12	ϑ(bnk	ϑ(bnk	NOUN
ejpam-6841	303	13	,	,	PUNCT
ejpam-6841	303	14	b∗))α	b∗))α	PROPN
ejpam-6841	303	15	·	·	PUNCT
ejpam-6841	303	16	(	(	PUNCT
ejpam-6841	303	17	ϑ(bnk	ϑ(bnk	NOUN
ejpam-6841	303	18	,	,	PUNCT
ejpam-6841	303	19	bnk+1	bnk+1	NOUN
ejpam-6841	303	20	)	)	PUNCT
ejpam-6841	303	21	)	)	PUNCT
ejpam-6841	303	22	β	β	X
ejpam-6841	303	23	·	·	PUNCT
ejpam-6841	303	24	(	(	PUNCT
ejpam-6841	303	25	ϑ(b∗	ϑ(b∗	X
ejpam-6841	303	26	,	,	PUNCT
ejpam-6841	303	27	p))1−α−β	p))1−α−β	PRON
ejpam-6841	303	28	)	)	PUNCT
ejpam-6841	303	29	,	,	PUNCT
ejpam-6841	303	30	for	for	ADP
ejpam-6841	303	31	all	all	DET
ejpam-6841	303	32	k	k	PROPN
ejpam-6841	303	33	∈	∈	PROPN
ejpam-6841	303	34	n.	n.	NOUN
ejpam-6841	303	35	since	since	SCONJ
ejpam-6841	303	36	,	,	PUNCT
ejpam-6841	303	37	j	j	PROPN
ejpam-6841	303	38	is	be	AUX
ejpam-6841	303	39	non	non	ADJ
ejpam-6841	303	40	-	-	ADJ
ejpam-6841	303	41	decreasing	decrease	VERB
ejpam-6841	303	42	function	function	NOUN
ejpam-6841	303	43	,	,	PUNCT
ejpam-6841	303	44	so	so	ADV
ejpam-6841	303	45	,	,	PUNCT
ejpam-6841	303	46	we	we	PRON
ejpam-6841	303	47	have	have	VERB
ejpam-6841	303	48	ϑ(bnk+1	ϑ(bnk+1	NOUN
ejpam-6841	303	49	,	,	PUNCT
ejpam-6841	303	50	p	p	X
ejpam-6841	303	51	)	)	PUNCT
ejpam-6841	303	52	<	<	X
ejpam-6841	303	53	(	(	PUNCT
ejpam-6841	303	54	ϑ(bnk	ϑ(bnk	NOUN
ejpam-6841	303	55	,	,	PUNCT
ejpam-6841	303	56	b∗))α	b∗))α	PROPN
ejpam-6841	303	57	·	·	PUNCT
ejpam-6841	304	1	(	(	PUNCT
ejpam-6841	304	2	ϑ(bnk	ϑ(bnk	NOUN
ejpam-6841	304	3	,	,	PUNCT
ejpam-6841	304	4	bnk+1	bnk+1	NOUN
ejpam-6841	304	5	)	)	PUNCT
ejpam-6841	304	6	)	)	PUNCT
ejpam-6841	304	7	β	β	X
ejpam-6841	304	8	·	·	PUNCT
ejpam-6841	304	9	(	(	PUNCT
ejpam-6841	304	10	ϑ(b∗	ϑ(b∗	PROPN
ejpam-6841	304	11	,	,	PUNCT
ejpam-6841	304	12	p))1−α−β	p))1−α−β	PRON
ejpam-6841	304	13	,	,	PUNCT
ejpam-6841	304	14	for	for	ADP
ejpam-6841	304	15	all	all	DET
ejpam-6841	304	16	k	k	PROPN
ejpam-6841	304	17	∈	∈	PROPN
ejpam-6841	304	18	n.	n.	NOUN
ejpam-6841	304	19	thus	thus	ADV
ejpam-6841	304	20	,	,	PUNCT
ejpam-6841	304	21	as	as	SCONJ
ejpam-6841	304	22	k	k	PROPN
ejpam-6841	304	23	→	→	SYM
ejpam-6841	304	24	∞	∞	PROPN
ejpam-6841	304	25	,	,	PUNCT
ejpam-6841	304	26	we	we	PRON
ejpam-6841	304	27	have	have	VERB
ejpam-6841	304	28	b∗	b∗	ADJ
ejpam-6841	304	29	=	=	SYM
ejpam-6841	305	1	p.	p.	NOUN
ejpam-6841	305	2	finally	finally	ADV
ejpam-6841	305	3	,	,	PUNCT
ejpam-6841	305	4	by	by	ADP
ejpam-6841	305	5	(	(	PUNCT
ejpam-6841	305	6	18	18	NUM
ejpam-6841	305	7	)	)	PUNCT
ejpam-6841	305	8	we	we	PRON
ejpam-6841	305	9	have	have	VERB
ejpam-6841	305	10	ϑ(b∗,p(b∗	ϑ(b∗,p(b∗	PROPN
ejpam-6841	305	11	)	)	PUNCT
ejpam-6841	305	12	)	)	PUNCT
ejpam-6841	306	1	=	=	PUNCT
ejpam-6841	306	2	ϑ(c	ϑ(c	PROPN
ejpam-6841	306	3	,	,	PUNCT
ejpam-6841	306	4	d	d	NOUN
ejpam-6841	306	5	)	)	PUNCT
ejpam-6841	306	6	.	.	PUNCT
ejpam-6841	307	1	hence	hence	ADV
ejpam-6841	307	2	,	,	PUNCT
ejpam-6841	307	3	b∗	b∗	ADV
ejpam-6841	307	4	is	be	AUX
ejpam-6841	307	5	a	a	DET
ejpam-6841	307	6	best	good	ADJ
ejpam-6841	307	7	proximity	proximity	NOUN
ejpam-6841	307	8	point	point	NOUN
ejpam-6841	307	9	of	of	ADP
ejpam-6841	307	10	the	the	DET
ejpam-6841	307	11	mapping	mapping	NOUN
ejpam-6841	307	12	p.	p.	NOUN
ejpam-6841	307	13	theorem	theorem	NOUN
ejpam-6841	307	14	4	4	NUM
ejpam-6841	307	15	.	.	PUNCT
ejpam-6841	308	1	let	let	VERB
ejpam-6841	308	2	p	p	NOUN
ejpam-6841	308	3	:	:	PUNCT
ejpam-6841	308	4	c	c	X
ejpam-6841	308	5	→	→	PUNCT
ejpam-6841	308	6	d	d	X
ejpam-6841	308	7	be	be	AUX
ejpam-6841	308	8	an	an	DET
ejpam-6841	308	9	(	(	PUNCT
ejpam-6841	308	10	j,£)-ćirić	j,£)-ćirić	PROPN
ejpam-6841	308	11	-	-	PUNCT
ejpam-6841	308	12	reich	reich	NOUN
ejpam-6841	308	13	-	-	PUNCT
ejpam-6841	308	14	rus	rus	NOUN
ejpam-6841	308	15	type	type	NOUN
ejpam-6841	308	16	interpolative	interpolative	ADJ
ejpam-6841	308	17	proximal	proximal	ADJ
ejpam-6841	308	18	contraction	contraction	NOUN
ejpam-6841	308	19	defined	define	VERB
ejpam-6841	308	20	on	on	ADP
ejpam-6841	308	21	a	a	DET
ejpam-6841	308	22	complete	complete	ADJ
ejpam-6841	308	23	metric	metric	ADJ
ejpam-6841	308	24	space	space	NOUN
ejpam-6841	308	25	(	(	PUNCT
ejpam-6841	308	26	w	w	NOUN
ejpam-6841	308	27	,	,	PUNCT
ejpam-6841	308	28	ϑ	ϑ	NOUN
ejpam-6841	308	29	)	)	PUNCT
ejpam-6841	308	30	and	and	CCONJ
ejpam-6841	308	31	c	c	X
ejpam-6841	308	32	,	,	PUNCT
ejpam-6841	308	33	d	d	NOUN
ejpam-6841	308	34	be	be	AUX
ejpam-6841	308	35	nonvoid	nonvoid	ADJ
ejpam-6841	308	36	,	,	PUNCT
ejpam-6841	308	37	closed	closed	ADJ
ejpam-6841	308	38	subsets	subset	NOUN
ejpam-6841	308	39	of	of	ADP
ejpam-6841	308	40	w	w	ADP
ejpam-6841	308	41	such	such	ADJ
ejpam-6841	308	42	that	that	SCONJ
ejpam-6841	308	43	d	d	NOUN
ejpam-6841	308	44	is	be	AUX
ejpam-6841	308	45	approximately	approximately	ADV
ejpam-6841	308	46	compact	compact	ADJ
ejpam-6841	308	47	with	with	ADP
ejpam-6841	308	48	respect	respect	NOUN
ejpam-6841	308	49	to	to	ADP
ejpam-6841	308	50	c.	c.	NOUN
ejpam-6841	308	51	if	if	SCONJ
ejpam-6841	308	52	(	(	PUNCT
ejpam-6841	308	53	i	i	NOUN
ejpam-6841	308	54	)	)	PUNCT
ejpam-6841	308	55	j	j	PROPN
ejpam-6841	308	56	is	be	AUX
ejpam-6841	308	57	non	non	ADJ
ejpam-6841	308	58	-	-	ADJ
ejpam-6841	308	59	decreasing	decrease	VERB
ejpam-6841	308	60	and	and	CCONJ
ejpam-6841	308	61	{	{	PUNCT
ejpam-6841	308	62	j	j	PROPN
ejpam-6841	308	63	(	(	PUNCT
ejpam-6841	308	64	tn	tn	PROPN
ejpam-6841	308	65	)	)	PUNCT
ejpam-6841	308	66	}	}	PUNCT
ejpam-6841	308	67	and	and	CCONJ
ejpam-6841	308	68	{	{	PUNCT
ejpam-6841	308	69	b	b	PROPN
ejpam-6841	308	70	(	(	PUNCT
ejpam-6841	308	71	tn	tn	NOUN
ejpam-6841	308	72	)	)	PUNCT
ejpam-6841	308	73	}	}	PUNCT
ejpam-6841	308	74	are	be	AUX
ejpam-6841	308	75	convergent	convergent	ADJ
ejpam-6841	308	76	sequences	sequence	NOUN
ejpam-6841	308	77	such	such	ADJ
ejpam-6841	308	78	that	that	SCONJ
ejpam-6841	308	79	limn→∞	limn→∞	PROPN
ejpam-6841	308	80	j	j	PROPN
ejpam-6841	308	81	(	(	PUNCT
ejpam-6841	308	82	tn	tn	PROPN
ejpam-6841	308	83	)	)	PUNCT
ejpam-6841	308	84	then	then	ADV
ejpam-6841	308	85	limn→∞	limn→∞	PROPN
ejpam-6841	308	86	tn	tn	NOUN
ejpam-6841	308	87	=	=	SYM
ejpam-6841	308	88	0	0	PROPN
ejpam-6841	308	89	.	.	PUNCT
ejpam-6841	308	90	(	(	PUNCT
ejpam-6841	308	91	ii	ii	X
ejpam-6841	308	92	)	)	PUNCT
ejpam-6841	308	93	c0	c0	PROPN
ejpam-6841	308	94	is	be	AUX
ejpam-6841	308	95	non	non	ADJ
ejpam-6841	308	96	-	-	ADJ
ejpam-6841	308	97	void	void	ADJ
ejpam-6841	308	98	subset	subset	NOUN
ejpam-6841	308	99	of	of	ADP
ejpam-6841	308	100	c	c	PROPN
ejpam-6841	308	101	such	such	ADJ
ejpam-6841	308	102	that	that	SCONJ
ejpam-6841	308	103	p	p	PROPN
ejpam-6841	308	104	(	(	PUNCT
ejpam-6841	308	105	c0	c0	NOUN
ejpam-6841	308	106	)	)	PUNCT
ejpam-6841	308	107	⊆	⊆	NUM
ejpam-6841	308	108	d0	d0	NOUN
ejpam-6841	308	109	.	.	PUNCT
ejpam-6841	309	1	then	then	ADV
ejpam-6841	309	2	p	p	X
ejpam-6841	309	3	has	have	VERB
ejpam-6841	309	4	a	a	DET
ejpam-6841	309	5	best	good	ADJ
ejpam-6841	309	6	proximity	proximity	NOUN
ejpam-6841	309	7	point	point	NOUN
ejpam-6841	309	8	.	.	PUNCT
ejpam-6841	310	1	proof	proof	NOUN
ejpam-6841	310	2	.	.	PUNCT
ejpam-6841	311	1	as	as	ADP
ejpam-6841	311	2	in	in	ADP
ejpam-6841	311	3	the	the	DET
ejpam-6841	311	4	proof	proof	NOUN
ejpam-6841	311	5	of	of	ADP
ejpam-6841	311	6	theorem	theorem	NOUN
ejpam-6841	311	7	3	3	NUM
ejpam-6841	311	8	,	,	PUNCT
ejpam-6841	311	9	we	we	PRON
ejpam-6841	311	10	have	have	VERB
ejpam-6841	311	11	j	j	PROPN
ejpam-6841	311	12	(	(	PUNCT
ejpam-6841	311	13	θn	θn	NOUN
ejpam-6841	311	14	)	)	PUNCT
ejpam-6841	311	15	≤	≤	NOUN
ejpam-6841	311	16	£	£	PROPN
ejpam-6841	311	17	(	(	PUNCT
ejpam-6841	311	18	(	(	PUNCT
ejpam-6841	311	19	θn−1	θn−1	PROPN
ejpam-6841	311	20	)	)	PUNCT
ejpam-6841	311	21	α+β	α+β	PROPN
ejpam-6841	311	22	(	(	PUNCT
ejpam-6841	311	23	θn	θn	NOUN
ejpam-6841	311	24	)	)	PUNCT
ejpam-6841	311	25	1−α−β	1−α−β	PROPN
ejpam-6841	311	26	)	)	PUNCT
ejpam-6841	312	1	<	<	X
ejpam-6841	312	2	j	j	X
ejpam-6841	312	3	(	(	PUNCT
ejpam-6841	312	4	(	(	PUNCT
ejpam-6841	312	5	θn−1	θn−1	PROPN
ejpam-6841	312	6	)	)	PUNCT
ejpam-6841	312	7	α+β	α+β	PROPN
ejpam-6841	312	8	(	(	PUNCT
ejpam-6841	312	9	θn	θn	NOUN
ejpam-6841	312	10	)	)	PUNCT
ejpam-6841	312	11	1−α−β	1−α−β	PROPN
ejpam-6841	312	12	)	)	PUNCT
ejpam-6841	312	13	(	(	PUNCT
ejpam-6841	312	14	19	19	NUM
ejpam-6841	312	15	)	)	PUNCT
ejpam-6841	312	16	by	by	ADP
ejpam-6841	312	17	(	(	PUNCT
ejpam-6841	312	18	19	19	NUM
ejpam-6841	312	19	)	)	PUNCT
ejpam-6841	312	20	,	,	PUNCT
ejpam-6841	312	21	we	we	PRON
ejpam-6841	312	22	have	have	VERB
ejpam-6841	312	23	{	{	PUNCT
ejpam-6841	312	24	j	j	PROPN
ejpam-6841	312	25	(	(	PUNCT
ejpam-6841	312	26	θn	θn	NOUN
ejpam-6841	312	27	)	)	PUNCT
ejpam-6841	312	28	}	}	PUNCT
ejpam-6841	312	29	is	be	AUX
ejpam-6841	312	30	strictly	strictly	ADV
ejpam-6841	312	31	decreasing	decrease	VERB
ejpam-6841	312	32	sequence	sequence	NOUN
ejpam-6841	312	33	.	.	PUNCT
ejpam-6841	313	1	we	we	PRON
ejpam-6841	313	2	have	have	VERB
ejpam-6841	313	3	two	two	NUM
ejpam-6841	313	4	cases	case	NOUN
ejpam-6841	313	5	here	here	ADV
ejpam-6841	313	6	;	;	PUNCT
ejpam-6841	313	7	either	either	CCONJ
ejpam-6841	313	8	the	the	DET
ejpam-6841	313	9	sequence	sequence	NOUN
ejpam-6841	313	10	{	{	PUNCT
ejpam-6841	313	11	j	j	PROPN
ejpam-6841	313	12	(	(	PUNCT
ejpam-6841	313	13	θn	θn	NOUN
ejpam-6841	313	14	)	)	PUNCT
ejpam-6841	313	15	}	}	PUNCT
ejpam-6841	313	16	is	be	AUX
ejpam-6841	313	17	bounded	bound	VERB
ejpam-6841	313	18	below	below	ADP
ejpam-6841	313	19	or	or	CCONJ
ejpam-6841	313	20	not	not	PART
ejpam-6841	313	21	.	.	PUNCT
ejpam-6841	314	1	if	if	SCONJ
ejpam-6841	314	2	{	{	PUNCT
ejpam-6841	314	3	j	j	PROPN
ejpam-6841	314	4	(	(	PUNCT
ejpam-6841	314	5	θn	θn	NOUN
ejpam-6841	314	6	)	)	PUNCT
ejpam-6841	314	7	}	}	PUNCT
ejpam-6841	314	8	is	be	AUX
ejpam-6841	314	9	not	not	PART
ejpam-6841	314	10	bounded	bound	VERB
ejpam-6841	314	11	below	below	ADV
ejpam-6841	314	12	,	,	PUNCT
ejpam-6841	314	13	then	then	ADV
ejpam-6841	314	14	inf	inf	PROPN
ejpam-6841	314	15	θn	θn	PROPN
ejpam-6841	314	16	>	>	PROPN
ejpam-6841	314	17	ε	ε	PROPN
ejpam-6841	314	18	j	j	PROPN
ejpam-6841	314	19	(	(	PUNCT
ejpam-6841	314	20	θn	θn	NOUN
ejpam-6841	314	21	)	)	PUNCT
ejpam-6841	314	22	>	>	PUNCT
ejpam-6841	315	1	−∞	−∞	X
ejpam-6841	315	2	for	for	ADP
ejpam-6841	315	3	every	every	DET
ejpam-6841	315	4	ε	ε	PROPN
ejpam-6841	315	5	>	>	X
ejpam-6841	315	6	0	0	PROPN
ejpam-6841	315	7	,	,	PUNCT
ejpam-6841	315	8	n	n	PRON
ejpam-6841	315	9	∈	∈	PROPN
ejpam-6841	315	10	n	n	CCONJ
ejpam-6841	315	11	lemma	lemma	PROPN
ejpam-6841	315	12	2	2	NUM
ejpam-6841	315	13	,	,	PUNCT
ejpam-6841	315	14	indicates	indicate	VERB
ejpam-6841	315	15	that	that	SCONJ
ejpam-6841	315	16	θn	θn	PROPN
ejpam-6841	315	17	→	→	SYM
ejpam-6841	315	18	0	0	PROPN
ejpam-6841	315	19	as	as	ADP
ejpam-6841	315	20	n	n	PRON
ejpam-6841	315	21	approaches	approach	NOUN
ejpam-6841	315	22	to	to	ADP
ejpam-6841	315	23	∞.	∞.	PROPN
ejpam-6841	315	24	second	second	ADJ
ejpam-6841	315	25	,	,	PUNCT
ejpam-6841	315	26	the	the	DET
ejpam-6841	315	27	sequence	sequence	NOUN
ejpam-6841	315	28	{	{	PUNCT
ejpam-6841	315	29	j	j	PROPN
ejpam-6841	315	30	(	(	PUNCT
ejpam-6841	315	31	θn	θn	NOUN
ejpam-6841	315	32	)	)	PUNCT
ejpam-6841	315	33	}	}	PUNCT
ejpam-6841	315	34	is	be	AUX
ejpam-6841	315	35	convergent	convergent	ADJ
ejpam-6841	315	36	if	if	SCONJ
ejpam-6841	315	37	it	it	PRON
ejpam-6841	315	38	is	be	AUX
ejpam-6841	315	39	bounded	bound	VERB
ejpam-6841	315	40	below	below	ADV
ejpam-6841	315	41	.	.	PUNCT
ejpam-6841	316	1	the	the	DET
ejpam-6841	316	2	sequence	sequence	NOUN
ejpam-6841	316	3	{	{	PUNCT
ejpam-6841	316	4	b	b	PROPN
ejpam-6841	316	5	(	(	PUNCT
ejpam-6841	316	6	θn	θn	NOUN
ejpam-6841	316	7	)	)	PUNCT
ejpam-6841	316	8	}	}	PUNCT
ejpam-6841	316	9	likewise	likewise	ADV
ejpam-6841	316	10	cgs	cgs	NOUN
ejpam-6841	316	11	by	by	ADP
ejpam-6841	316	12	(	(	PUNCT
ejpam-6841	316	13	25	25	NUM
ejpam-6841	316	14	)	)	PUNCT
ejpam-6841	316	15	,	,	PUNCT
ejpam-6841	316	16	and	and	CCONJ
ejpam-6841	316	17	,	,	PUNCT
ejpam-6841	316	18	k.	k.	PROPN
ejpam-6841	316	19	javed	javed	PROPN
ejpam-6841	316	20	,	,	PUNCT
ejpam-6841	316	21	m.	m.	NOUN
ejpam-6841	316	22	nazam	nazam	PROPN
ejpam-6841	316	23	,	,	PUNCT
ejpam-6841	316	24	m.	m.	PROPN
ejpam-6841	316	25	arshad	arshad	PROPN
ejpam-6841	316	26	,	,	PUNCT
ejpam-6841	316	27	m.	m.	NOUN
ejpam-6841	316	28	de	de	X
ejpam-6841	316	29	la	la	PROPN
ejpam-6841	316	30	sen	sen	PROPN
ejpam-6841	316	31	/	/	SYM
ejpam-6841	316	32	eur	eur	PROPN
ejpam-6841	316	33	.	.	PUNCT
ejpam-6841	317	1	j.	j.	PROPN
ejpam-6841	317	2	pure	pure	PROPN
ejpam-6841	317	3	appl	appl	PROPN
ejpam-6841	317	4	.	.	PROPN
ejpam-6841	317	5	math	math	PROPN
ejpam-6841	317	6	,	,	PUNCT
ejpam-6841	317	7	18	18	NUM
ejpam-6841	317	8	(	(	PUNCT
ejpam-6841	317	9	4	4	NUM
ejpam-6841	317	10	)	)	PUNCT
ejpam-6841	317	11	(	(	PUNCT
ejpam-6841	317	12	2025	2025	NUM
ejpam-6841	317	13	)	)	PUNCT
ejpam-6841	317	14	,	,	PUNCT
ejpam-6841	317	15	6841	6841	NUM
ejpam-6841	317	16	14	14	NUM
ejpam-6841	317	17	of	of	ADP
ejpam-6841	317	18	23	23	NUM
ejpam-6841	317	19	both	both	PRON
ejpam-6841	317	20	have	have	VERB
ejpam-6841	317	21	the	the	DET
ejpam-6841	317	22	same	same	ADJ
ejpam-6841	317	23	limit	limit	NOUN
ejpam-6841	317	24	.	.	PUNCT
ejpam-6841	318	1	for	for	ADP
ejpam-6841	318	2	each	each	DET
ejpam-6841	318	3	sequence	sequence	NOUN
ejpam-6841	318	4	{	{	PUNCT
ejpam-6841	318	5	bn	bn	ADP
ejpam-6841	318	6	}	}	PUNCT
ejpam-6841	318	7	in	in	ADP
ejpam-6841	318	8	c	c	NOUN
ejpam-6841	318	9	we	we	PRON
ejpam-6841	318	10	have	have	VERB
ejpam-6841	318	11	limn→∞	limn→∞	PROPN
ejpam-6841	318	12	ϑ	ϑ	X
ejpam-6841	318	13	(	(	PUNCT
ejpam-6841	318	14	bn	bn	X
ejpam-6841	318	15	,	,	PUNCT
ejpam-6841	318	16	bn+1	bn+1	NUM
ejpam-6841	318	17	)	)	PUNCT
ejpam-6841	318	18	=	=	PUNCT
ejpam-6841	318	19	0	0	NUM
ejpam-6841	319	1	according	accord	VERB
ejpam-6841	319	2	to	to	ADP
ejpam-6841	319	3	(	(	PUNCT
ejpam-6841	319	4	i	i	NOUN
ejpam-6841	319	5	)	)	PUNCT
ejpam-6841	319	6	.now	.now	PROPN
ejpam-6841	319	7	,	,	PUNCT
ejpam-6841	319	8	theorem	theorem	VERB
ejpam-6841	319	9	3	3	NUM
ejpam-6841	319	10	,	,	PUNCT
ejpam-6841	319	11	we	we	PRON
ejpam-6841	319	12	have	have	VERB
ejpam-6841	319	13	ϑ	ϑ	X
ejpam-6841	319	14	(	(	PUNCT
ejpam-6841	319	15	b∗,pb∗	b∗,pb∗	PROPN
ejpam-6841	319	16	)	)	PUNCT
ejpam-6841	319	17	=	=	SYM
ejpam-6841	319	18	ϑ	ϑ	X
ejpam-6841	319	19	(	(	PUNCT
ejpam-6841	319	20	c	c	X
ejpam-6841	319	21	,	,	PUNCT
ejpam-6841	319	22	d	d	NOUN
ejpam-6841	319	23	)	)	PUNCT
ejpam-6841	319	24	.	.	PUNCT
ejpam-6841	320	1	hence	hence	ADV
ejpam-6841	320	2	,	,	PUNCT
ejpam-6841	320	3	b∗	b∗	ADV
ejpam-6841	320	4	is	be	AUX
ejpam-6841	320	5	a	a	DET
ejpam-6841	320	6	best	good	ADJ
ejpam-6841	320	7	proximity	proximity	NOUN
ejpam-6841	320	8	point	point	NOUN
ejpam-6841	320	9	of	of	ADP
ejpam-6841	320	10	the	the	DET
ejpam-6841	320	11	mapping	mapping	NOUN
ejpam-6841	320	12	p.	p.	NOUN
ejpam-6841	320	13	note	note	VERB
ejpam-6841	320	14	that	that	SCONJ
ejpam-6841	320	15	,	,	PUNCT
ejpam-6841	320	16	if	if	SCONJ
ejpam-6841	320	17	p	p	NOUN
ejpam-6841	320	18	is	be	AUX
ejpam-6841	320	19	a	a	DET
ejpam-6841	320	20	self	self	NOUN
ejpam-6841	320	21	-	-	PUNCT
ejpam-6841	320	22	mapping	mapping	NOUN
ejpam-6841	320	23	defined	define	VERB
ejpam-6841	320	24	on	on	ADP
ejpam-6841	320	25	c	c	NOUN
ejpam-6841	320	26	,	,	PUNCT
ejpam-6841	320	27	then	then	ADV
ejpam-6841	320	28	best	good	ADJ
ejpam-6841	320	29	proximity	proximity	NOUN
ejpam-6841	320	30	point	point	NOUN
ejpam-6841	320	31	is	be	AUX
ejpam-6841	320	32	a	a	DET
ejpam-6841	320	33	fixed	fix	VERB
ejpam-6841	320	34	point	point	NOUN
ejpam-6841	320	35	of	of	ADP
ejpam-6841	320	36	p.	p.	NOUN
ejpam-6841	320	37	remark	remark	NOUN
ejpam-6841	320	38	2	2	NUM
ejpam-6841	320	39	.	.	PUNCT
ejpam-6841	320	40	the	the	DET
ejpam-6841	320	41	generality	generality	NOUN
ejpam-6841	320	42	of	of	ADP
ejpam-6841	320	43	ćirić	ćirić	NOUN
ejpam-6841	320	44	-	-	PUNCT
ejpam-6841	320	45	reich	reich	NOUN
ejpam-6841	320	46	-	-	PUNCT
ejpam-6841	320	47	rus	rus	NOUN
ejpam-6841	320	48	type	type	NOUN
ejpam-6841	320	49	(	(	PUNCT
ejpam-6841	320	50	j,£	j,£	ADJ
ejpam-6841	320	51	)	)	PUNCT
ejpam-6841	320	52	interpolative	interpolative	ADJ
ejpam-6841	320	53	proximal	proximal	ADJ
ejpam-6841	320	54	contraction	contraction	NOUN
ejpam-6841	320	55	for	for	ADP
ejpam-6841	320	56	the	the	DET
ejpam-6841	320	57	particular	particular	ADJ
ejpam-6841	320	58	definitions	definition	NOUN
ejpam-6841	320	59	of	of	ADP
ejpam-6841	320	60	the	the	DET
ejpam-6841	320	61	mappings	mapping	NOUN
ejpam-6841	320	62	j,£	j,£	PROPN
ejpam-6841	320	63	is	be	AUX
ejpam-6841	320	64	demonstrated	demonstrate	VERB
ejpam-6841	320	65	by	by	ADP
ejpam-6841	320	66	the	the	DET
ejpam-6841	320	67	observation	observation	NOUN
ejpam-6841	320	68	that	that	PRON
ejpam-6841	320	69	follows	follow	VERB
ejpam-6841	320	70	.	.	PUNCT
ejpam-6841	321	1	1	1	X
ejpam-6841	321	2	.	.	X
ejpam-6841	321	3	defining	define	VERB
ejpam-6841	321	4	£	£	SYM
ejpam-6841	321	5	(	(	PUNCT
ejpam-6841	321	6	b	b	NOUN
ejpam-6841	321	7	)	)	PUNCT
ejpam-6841	321	8	=	=	SYM
ejpam-6841	321	9	j(b	j(b	NOUN
ejpam-6841	321	10	)	)	PUNCT
ejpam-6841	321	11	−	−	PROPN
ejpam-6841	321	12	τ	τ	PROPN
ejpam-6841	321	13	for	for	ADP
ejpam-6841	321	14	all	all	DET
ejpam-6841	321	15	b	b	PROPN
ejpam-6841	321	16	∈	∈	NOUN
ejpam-6841	321	17	(	(	PUNCT
ejpam-6841	321	18	0,∞	0,∞	NOUN
ejpam-6841	321	19	)	)	PUNCT
ejpam-6841	321	20	,	,	PUNCT
ejpam-6841	321	21	in	in	ADP
ejpam-6841	321	22	theorem	theorem	NOUN
ejpam-6841	321	23	3	3	NUM
ejpam-6841	321	24	and	and	CCONJ
ejpam-6841	321	25	theorem	theorem	VERB
ejpam-6841	321	26	4	4	NUM
ejpam-6841	321	27	,	,	PUNCT
ejpam-6841	321	28	we	we	PRON
ejpam-6841	321	29	obtain	obtain	VERB
ejpam-6841	321	30	the	the	DET
ejpam-6841	321	31	existence	existence	NOUN
ejpam-6841	321	32	of	of	ADP
ejpam-6841	321	33	best	good	ADJ
ejpam-6841	321	34	proximity	proximity	NOUN
ejpam-6841	321	35	points	point	NOUN
ejpam-6841	321	36	of	of	ADP
ejpam-6841	321	37	the	the	DET
ejpam-6841	321	38	ćirić	ćirić	NOUN
ejpam-6841	321	39	-	-	PUNCT
ejpam-6841	321	40	reich	reich	NOUN
ejpam-6841	321	41	-	-	PUNCT
ejpam-6841	321	42	rus	rus	NOUN
ejpam-6841	321	43	type	type	NOUN
ejpam-6841	321	44	interpolative	interpolative	ADJ
ejpam-6841	321	45	proximal	proximal	ADJ
ejpam-6841	321	46	contractions	contraction	NOUN
ejpam-6841	322	1	[	[	X
ejpam-6841	322	2	12	12	NUM
ejpam-6841	322	3	]	]	PUNCT
ejpam-6841	322	4	.	.	PUNCT
ejpam-6841	322	5	2	2	X
ejpam-6841	322	6	.	.	X
ejpam-6841	322	7	theorem	theorem	VERB
ejpam-6841	322	8	3	3	NUM
ejpam-6841	322	9	and	and	CCONJ
ejpam-6841	322	10	theorem	theorem	VERB
ejpam-6841	322	11	4	4	NUM
ejpam-6841	322	12	,	,	PUNCT
ejpam-6841	322	13	produce	produce	VERB
ejpam-6841	322	14	the	the	DET
ejpam-6841	322	15	existence	existence	NOUN
ejpam-6841	322	16	of	of	ADP
ejpam-6841	322	17	best	good	ADJ
ejpam-6841	322	18	proximity	proximity	NOUN
ejpam-6841	322	19	points	point	NOUN
ejpam-6841	322	20	of	of	ADP
ejpam-6841	322	21	the	the	DET
ejpam-6841	322	22	ćirićreich	ćirićreich	NOUN
ejpam-6841	322	23	-	-	PUNCT
ejpam-6841	322	24	rus	rus	NOUN
ejpam-6841	322	25	interpolative	interpolative	ADJ
ejpam-6841	322	26	type	type	NOUN
ejpam-6841	322	27	(	(	PUNCT
ejpam-6841	322	28	τ	τ	PROPN
ejpam-6841	322	29	,	,	PUNCT
ejpam-6841	322	30	jp)-proximal	jp)-proximal	ADJ
ejpam-6841	322	31	contraction	contraction	NOUN
ejpam-6841	322	32	if	if	SCONJ
ejpam-6841	322	33	£	£	SYM
ejpam-6841	322	34	(	(	PUNCT
ejpam-6841	322	35	b	b	NOUN
ejpam-6841	322	36	)	)	PUNCT
ejpam-6841	322	37	=	=	SYM
ejpam-6841	322	38	j(b	j(b	NOUN
ejpam-6841	322	39	)	)	PUNCT
ejpam-6841	322	40	−	−	PROPN
ejpam-6841	322	41	τ(b	τ(b	NOUN
ejpam-6841	322	42	)	)	PUNCT
ejpam-6841	322	43	for	for	ADP
ejpam-6841	322	44	all	all	DET
ejpam-6841	322	45	b	b	PROPN
ejpam-6841	322	46	∈	∈	NOUN
ejpam-6841	322	47	(	(	PUNCT
ejpam-6841	322	48	0,∞	0,∞	NOUN
ejpam-6841	322	49	)	)	PUNCT
ejpam-6841	322	50	.	.	PUNCT
ejpam-6841	323	1	3	3	X
ejpam-6841	323	2	.	.	X
ejpam-6841	323	3	letting	let	VERB
ejpam-6841	323	4	j	j	PROPN
ejpam-6841	323	5	as	as	ADP
ejpam-6841	323	6	an	an	DET
ejpam-6841	323	7	identity	identity	NOUN
ejpam-6841	323	8	mapping	mapping	NOUN
ejpam-6841	323	9	and	and	CCONJ
ejpam-6841	323	10	£	£	PROPN
ejpam-6841	323	11	(	(	PUNCT
ejpam-6841	323	12	t	t	NOUN
ejpam-6841	323	13	)	)	PUNCT
ejpam-6841	323	14	=	=	NOUN
ejpam-6841	323	15	λt	λt	ADP
ejpam-6841	323	16	for	for	ADP
ejpam-6841	323	17	all	all	DET
ejpam-6841	323	18	t	t	NOUN
ejpam-6841	323	19	>	>	X
ejpam-6841	323	20	0	0	PUNCT
ejpam-6841	323	21	and	and	CCONJ
ejpam-6841	323	22	λ	λ	PROPN
ejpam-6841	323	23	∈	∈	PROPN
ejpam-6841	323	24	(	(	PUNCT
ejpam-6841	323	25	0	0	NUM
ejpam-6841	323	26	,	,	PUNCT
ejpam-6841	323	27	1	1	NUM
ejpam-6841	323	28	)	)	PUNCT
ejpam-6841	323	29	,	,	PUNCT
ejpam-6841	323	30	in	in	ADP
ejpam-6841	323	31	theorem	theorem	NOUN
ejpam-6841	323	32	3	3	NUM
ejpam-6841	323	33	and	and	CCONJ
ejpam-6841	323	34	theorem	theorem	VERB
ejpam-6841	323	35	4	4	NUM
ejpam-6841	323	36	,	,	PUNCT
ejpam-6841	323	37	we	we	PRON
ejpam-6841	323	38	receive	receive	VERB
ejpam-6841	323	39	the	the	DET
ejpam-6841	323	40	existence	existence	NOUN
ejpam-6841	323	41	of	of	ADP
ejpam-6841	323	42	best	good	ADJ
ejpam-6841	323	43	proximity	proximity	NOUN
ejpam-6841	323	44	points	point	NOUN
ejpam-6841	323	45	of	of	ADP
ejpam-6841	323	46	the	the	DET
ejpam-6841	323	47	ćirić	ćirić	NOUN
ejpam-6841	323	48	-	-	PUNCT
ejpam-6841	323	49	reich	reich	NOUN
ejpam-6841	323	50	-	-	PUNCT
ejpam-6841	323	51	rus	rus	NOUN
ejpam-6841	323	52	type	type	NOUN
ejpam-6841	323	53	interpolative	interpolative	ADJ
ejpam-6841	323	54	proximal	proximal	ADJ
ejpam-6841	323	55	contraction	contraction	NOUN
ejpam-6841	324	1	[	[	X
ejpam-6841	324	2	10	10	NUM
ejpam-6841	324	3	]	]	PUNCT
ejpam-6841	324	4	.	.	PUNCT
ejpam-6841	325	1	4	4	X
ejpam-6841	325	2	.	.	X
ejpam-6841	325	3	if	if	SCONJ
ejpam-6841	325	4	we	we	PRON
ejpam-6841	325	5	define	define	VERB
ejpam-6841	325	6	£	£	SYM
ejpam-6841	325	7	(	(	PUNCT
ejpam-6841	325	8	b	b	NOUN
ejpam-6841	325	9	)	)	PUNCT
ejpam-6841	325	10	=	=	SYM
ejpam-6841	325	11	β(b)b	β(b)b	NOUN
ejpam-6841	325	12	and	and	CCONJ
ejpam-6841	325	13	j(b	j(b	PROPN
ejpam-6841	325	14	)	)	PUNCT
ejpam-6841	326	1	=	=	SYM
ejpam-6841	326	2	b	b	NOUN
ejpam-6841	326	3	for	for	ADP
ejpam-6841	326	4	all	all	DET
ejpam-6841	326	5	b	b	NOUN
ejpam-6841	326	6	>	>	X
ejpam-6841	326	7	0	0	PUNCT
ejpam-6841	326	8	and	and	CCONJ
ejpam-6841	326	9	β	β	X
ejpam-6841	326	10	:	:	PUNCT
ejpam-6841	326	11	(	(	PUNCT
ejpam-6841	326	12	0,∞	0,∞	NOUN
ejpam-6841	326	13	)	)	PUNCT
ejpam-6841	326	14	→	→	SYM
ejpam-6841	326	15	(	(	PUNCT
ejpam-6841	326	16	0	0	NUM
ejpam-6841	326	17	,	,	PUNCT
ejpam-6841	326	18	1	1	X
ejpam-6841	326	19	)	)	PUNCT
ejpam-6841	326	20	verifying	verifying	NOUN
ejpam-6841	326	21	lim	lim	PROPN
ejpam-6841	326	22	sup	sup	PROPN
ejpam-6841	326	23	b→p+	b→p+	NOUN
ejpam-6841	326	24	β(b	β(b	PUNCT
ejpam-6841	326	25	)	)	PUNCT
ejpam-6841	326	26	<	<	X
ejpam-6841	326	27	1	1	NUM
ejpam-6841	326	28	for	for	ADP
ejpam-6841	326	29	each	each	DET
ejpam-6841	326	30	p	p	X
ejpam-6841	326	31	>	>	X
ejpam-6841	326	32	0	0	PUNCT
ejpam-6841	326	33	in	in	ADP
ejpam-6841	326	34	theorem	theorem	ADJ
ejpam-6841	326	35	3	3	NUM
ejpam-6841	326	36	and	and	CCONJ
ejpam-6841	326	37	theorem	theorem	VERB
ejpam-6841	326	38	4	4	NUM
ejpam-6841	326	39	,	,	PUNCT
ejpam-6841	326	40	we	we	PRON
ejpam-6841	326	41	receive	receive	VERB
ejpam-6841	326	42	the	the	DET
ejpam-6841	326	43	existence	existence	NOUN
ejpam-6841	326	44	of	of	ADP
ejpam-6841	326	45	best	good	ADJ
ejpam-6841	326	46	proximity	proximity	NOUN
ejpam-6841	326	47	points	point	NOUN
ejpam-6841	326	48	of	of	ADP
ejpam-6841	326	49	the	the	DET
ejpam-6841	326	50	ćirić	ćirić	NOUN
ejpam-6841	326	51	-	-	PUNCT
ejpam-6841	326	52	reich	reich	NOUN
ejpam-6841	326	53	-	-	PUNCT
ejpam-6841	326	54	rus	rus	NOUN
ejpam-6841	326	55	type	type	NOUN
ejpam-6841	326	56	interpolative	interpolative	PROPN
ejpam-6841	326	57	geraghty	geraghty	PROPN
ejpam-6841	326	58	’s	’s	PART
ejpam-6841	326	59	proximal	proximal	ADJ
ejpam-6841	326	60	contraction	contraction	NOUN
ejpam-6841	326	61	.	.	PUNCT
ejpam-6841	327	1	5	5	X
ejpam-6841	327	2	.	.	X
ejpam-6841	327	3	for	for	ADP
ejpam-6841	327	4	v	v	NOUN
ejpam-6841	327	5	=	=	SYM
ejpam-6841	327	6	0	0	NUM
ejpam-6841	327	7	,	,	PUNCT
ejpam-6841	327	8	we	we	PRON
ejpam-6841	327	9	obtain	obtain	VERB
ejpam-6841	327	10	(	(	PUNCT
ejpam-6841	327	11	j,£)-interpolative	j,£)-interpolative	PROPN
ejpam-6841	327	12	kannan	kannan	PROPN
ejpam-6841	327	13	type	type	NOUN
ejpam-6841	327	14	proximal	proximal	ADJ
ejpam-6841	327	15	contraction	contraction	NOUN
ejpam-6841	327	16	from	from	ADP
ejpam-6841	327	17	(	(	PUNCT
ejpam-6841	327	18	14	14	NUM
ejpam-6841	327	19	)	)	PUNCT
ejpam-6841	327	20	.	.	PUNCT
ejpam-6841	328	1	example	example	NOUN
ejpam-6841	329	1	4	4	X
ejpam-6841	329	2	.	.	PUNCT
ejpam-6841	329	3	let	let	VERB
ejpam-6841	329	4	b	b	NOUN
ejpam-6841	329	5	=	=	SYM
ejpam-6841	329	6	r2	r2	PROPN
ejpam-6841	329	7	with	with	ADP
ejpam-6841	329	8	euclidean	euclidean	ADJ
ejpam-6841	329	9	metric	metric	PROPN
ejpam-6841	329	10	ϑ	ϑ	X
ejpam-6841	329	11	on	on	ADP
ejpam-6841	329	12	r2	r2	PROPN
ejpam-6841	329	13	and	and	CCONJ
ejpam-6841	329	14	c	c	NOUN
ejpam-6841	329	15	=	=	SYM
ejpam-6841	329	16	{	{	PUNCT
ejpam-6841	329	17	(	(	PUNCT
ejpam-6841	329	18	b	b	NOUN
ejpam-6841	329	19	,	,	PUNCT
ejpam-6841	329	20	m	m	NOUN
ejpam-6841	329	21	)	)	PUNCT
ejpam-6841	329	22	:	:	PUNCT
ejpam-6841	330	1	m	m	VERB
ejpam-6841	330	2	=	=	SYM
ejpam-6841	330	3	2	2	NUM
ejpam-6841	330	4	√	√	NUM
ejpam-6841	330	5	9−	9−	NUM
ejpam-6841	330	6	b2	b2	NOUN
ejpam-6841	330	7	}	}	PUNCT
ejpam-6841	330	8	d	d	NOUN
ejpam-6841	330	9	=	=	SYM
ejpam-6841	330	10	{	{	PUNCT
ejpam-6841	330	11	(	(	PUNCT
ejpam-6841	330	12	b	b	NOUN
ejpam-6841	330	13	,	,	PUNCT
ejpam-6841	330	14	m	m	NOUN
ejpam-6841	330	15	)	)	PUNCT
ejpam-6841	330	16	:	:	PUNCT
ejpam-6841	330	17	m	m	AUX
ejpam-6841	330	18	=	=	SYM
ejpam-6841	330	19	2	2	NUM
ejpam-6841	330	20	√	√	NUM
ejpam-6841	330	21	16−	16−	NUM
ejpam-6841	330	22	b2	b2	NOUN
ejpam-6841	330	23	}	}	PUNCT
ejpam-6841	330	24	be	be	VERB
ejpam-6841	330	25	two	two	NUM
ejpam-6841	330	26	subsets	subset	NOUN
ejpam-6841	330	27	of	of	ADP
ejpam-6841	330	28	w.	w.	PROPN
ejpam-6841	330	29	then	then	ADV
ejpam-6841	330	30	ϑ	ϑ	X
ejpam-6841	330	31	(	(	PUNCT
ejpam-6841	330	32	c	c	X
ejpam-6841	330	33	,	,	PUNCT
ejpam-6841	330	34	d	d	NOUN
ejpam-6841	330	35	)	)	PUNCT
ejpam-6841	330	36	=	=	SYM
ejpam-6841	330	37	1	1	NUM
ejpam-6841	330	38	,	,	PUNCT
ejpam-6841	330	39	c0	c0	NOUN
ejpam-6841	330	40	and	and	CCONJ
ejpam-6841	330	41	d0	d0	NOUN
ejpam-6841	330	42	are	be	AUX
ejpam-6841	330	43	nonvoid	nonvoid	ADJ
ejpam-6841	330	44	subsets	subset	NOUN
ejpam-6841	330	45	of	of	ADP
ejpam-6841	330	46	c	c	PROPN
ejpam-6841	330	47	and	and	CCONJ
ejpam-6841	330	48	d	d	NOUN
ejpam-6841	330	49	respectively	respectively	ADV
ejpam-6841	330	50	.	.	PUNCT
ejpam-6841	331	1	define	define	VERB
ejpam-6841	331	2	a	a	DET
ejpam-6841	331	3	mapping	mapping	NOUN
ejpam-6841	331	4	p	p	NOUN
ejpam-6841	331	5	:	:	PUNCT
ejpam-6841	331	6	c	c	X
ejpam-6841	331	7	→	→	SYM
ejpam-6841	331	8	d	d	NOUN
ejpam-6841	331	9	by	by	ADP
ejpam-6841	331	10	p(ζ	p(ζ	PROPN
ejpam-6841	331	11	)	)	PUNCT
ejpam-6841	332	1	=	=	SYM
ejpam-6841	332	2	p	p	X
ejpam-6841	332	3	(	(	PUNCT
ejpam-6841	332	4	b	b	PROPN
ejpam-6841	332	5	,	,	PUNCT
ejpam-6841	332	6	m	m	NOUN
ejpam-6841	332	7	)	)	PUNCT
ejpam-6841	332	8	=	=	PRON
ejpam-6841	332	9	{	{	PUNCT
ejpam-6841	332	10	(	(	PUNCT
ejpam-6841	332	11	b	b	PROPN
ejpam-6841	332	12	2	2	NUM
ejpam-6841	332	13	,	,	PUNCT
ejpam-6841	332	14	m	m	PROPN
ejpam-6841	332	15	2	2	NUM
ejpam-6841	332	16	)	)	PUNCT
ejpam-6841	332	17	for	for	ADP
ejpam-6841	332	18	b	b	PROPN
ejpam-6841	332	19	≥	≥	NOUN
ejpam-6841	332	20	0	0	NUM
ejpam-6841	332	21	(	(	PUNCT
ejpam-6841	332	22	−1	−1	NOUN
ejpam-6841	332	23	,	,	PUNCT
ejpam-6841	332	24	0	0	NUM
ejpam-6841	332	25	)	)	PUNCT
ejpam-6841	332	26	for	for	ADP
ejpam-6841	332	27	b	b	NOUN
ejpam-6841	332	28	<	<	X
ejpam-6841	332	29	0	0	NUM
ejpam-6841	332	30	.	.	PUNCT
ejpam-6841	333	1	we	we	PRON
ejpam-6841	333	2	note	note	VERB
ejpam-6841	333	3	that	that	SCONJ
ejpam-6841	333	4	for	for	ADP
ejpam-6841	333	5	b	b	PROPN
ejpam-6841	333	6	≥	≥	NOUN
ejpam-6841	333	7	0	0	NUM
ejpam-6841	333	8	,	,	PUNCT
ejpam-6841	333	9	there	there	PRON
ejpam-6841	333	10	is	be	VERB
ejpam-6841	333	11	ζ	ζ	NOUN
ejpam-6841	333	12	=	=	SYM
ejpam-6841	333	13	(	(	PUNCT
ejpam-6841	333	14	b	b	NOUN
ejpam-6841	333	15	,	,	PUNCT
ejpam-6841	333	16	m	m	NOUN
ejpam-6841	333	17	)	)	PUNCT
ejpam-6841	333	18	∈	∈	PROPN
ejpam-6841	333	19	c	c	NOUN
ejpam-6841	333	20	such	such	ADJ
ejpam-6841	333	21	that	that	SCONJ
ejpam-6841	333	22	ϑ(ζ	ϑ(ζ	NOUN
ejpam-6841	333	23	,	,	PUNCT
ejpam-6841	333	24	p	p	X
ejpam-6841	333	25	(	(	PUNCT
ejpam-6841	333	26	ζ	ζ	NOUN
ejpam-6841	333	27	)	)	PUNCT
ejpam-6841	333	28	)	)	PUNCT
ejpam-6841	334	1	=	=	PUNCT
ejpam-6841	334	2	ϑ(c	ϑ(c	PROPN
ejpam-6841	334	3	,	,	PUNCT
ejpam-6841	334	4	d	d	NOUN
ejpam-6841	334	5	)	)	PUNCT
ejpam-6841	334	6	=	=	SYM
ejpam-6841	334	7	1	1	X
ejpam-6841	334	8	.	.	PUNCT
ejpam-6841	335	1	the	the	DET
ejpam-6841	335	2	following	follow	VERB
ejpam-6841	335	3	information	information	NOUN
ejpam-6841	335	4	shows	show	VERB
ejpam-6841	335	5	that	that	SCONJ
ejpam-6841	335	6	p	p	PROPN
ejpam-6841	335	7	generalizes	generalize	VERB
ejpam-6841	335	8	the	the	DET
ejpam-6841	335	9	ćirić	ćirić	NOUN
ejpam-6841	335	10	-	-	PUNCT
ejpam-6841	335	11	reich	reich	NOUN
ejpam-6841	335	12	-	-	PUNCT
ejpam-6841	335	13	rus	rus	NOUN
ejpam-6841	335	14	type	type	NOUN
ejpam-6841	335	15	interpolative	interpolative	ADJ
ejpam-6841	335	16	proximal	proximal	ADJ
ejpam-6841	335	17	contraction	contraction	NOUN
ejpam-6841	336	1	[	[	X
ejpam-6841	336	2	10	10	NUM
ejpam-6841	336	3	]	]	PUNCT
ejpam-6841	336	4	.	.	PUNCT
ejpam-6841	337	1	for	for	ADP
ejpam-6841	337	2	b1	b1	NOUN
ejpam-6841	337	3	,	,	PUNCT
ejpam-6841	337	4	b2,m1,m2	b2,m1,m2	NOUN
ejpam-6841	337	5	∈	∈	PROPN
ejpam-6841	337	6	c	c	X
ejpam-6841	337	7	,	,	PUNCT
ejpam-6841	337	8	we	we	PRON
ejpam-6841	337	9	have	have	VERB
ejpam-6841	337	10	ϑ(b1,pm1	ϑ(b1,pm1	NOUN
ejpam-6841	337	11	)	)	PUNCT
ejpam-6841	338	1	=	=	PUNCT
ejpam-6841	338	2	ϑ(c	ϑ(c	NOUN
ejpam-6841	338	3	,	,	PUNCT
ejpam-6841	338	4	d	d	PROPN
ejpam-6841	338	5	)	)	PUNCT
ejpam-6841	338	6	k.	k.	PROPN
ejpam-6841	338	7	javed	javed	PROPN
ejpam-6841	338	8	,	,	PUNCT
ejpam-6841	338	9	m.	m.	NOUN
ejpam-6841	338	10	nazam	nazam	PROPN
ejpam-6841	338	11	,	,	PUNCT
ejpam-6841	338	12	m.	m.	PROPN
ejpam-6841	338	13	arshad	arshad	PROPN
ejpam-6841	338	14	,	,	PUNCT
ejpam-6841	338	15	m.	m.	NOUN
ejpam-6841	338	16	de	de	X
ejpam-6841	338	17	la	la	PROPN
ejpam-6841	338	18	sen	sen	PROPN
ejpam-6841	338	19	/	/	SYM
ejpam-6841	338	20	eur	eur	PROPN
ejpam-6841	338	21	.	.	PUNCT
ejpam-6841	339	1	j.	j.	PROPN
ejpam-6841	339	2	pure	pure	PROPN
ejpam-6841	339	3	appl	appl	PROPN
ejpam-6841	339	4	.	.	PROPN
ejpam-6841	339	5	math	math	PROPN
ejpam-6841	339	6	,	,	PUNCT
ejpam-6841	339	7	18	18	NUM
ejpam-6841	339	8	(	(	PUNCT
ejpam-6841	339	9	4	4	NUM
ejpam-6841	339	10	)	)	PUNCT
ejpam-6841	339	11	(	(	PUNCT
ejpam-6841	339	12	2025	2025	NUM
ejpam-6841	339	13	)	)	PUNCT
ejpam-6841	339	14	,	,	PUNCT
ejpam-6841	339	15	6841	6841	NUM
ejpam-6841	339	16	15	15	NUM
ejpam-6841	339	17	of	of	ADP
ejpam-6841	339	18	23	23	NUM
ejpam-6841	339	19	ϑ(b2,pm2	ϑ(b2,pm2	NOUN
ejpam-6841	339	20	)	)	PUNCT
ejpam-6841	339	21	=	=	PUNCT
ejpam-6841	340	1	ϑ(c	ϑ(c	PROPN
ejpam-6841	340	2	,	,	PUNCT
ejpam-6841	340	3	d	d	NOUN
ejpam-6841	340	4	)	)	PUNCT
ejpam-6841	340	5	.	.	PUNCT
ejpam-6841	341	1	let	let	VERB
ejpam-6841	341	2	α	α	NOUN
ejpam-6841	341	3	=	=	SYM
ejpam-6841	341	4	1	1	NUM
ejpam-6841	341	5	2	2	NUM
ejpam-6841	341	6	,	,	PUNCT
ejpam-6841	341	7	β	β	X
ejpam-6841	341	8	=	=	SYM
ejpam-6841	341	9	1	1	NUM
ejpam-6841	341	10	3	3	NUM
ejpam-6841	341	11	with	with	ADP
ejpam-6841	341	12	α+β	α+β	PROPN
ejpam-6841	341	13	<	<	X
ejpam-6841	341	14	1	1	NUM
ejpam-6841	341	15	,	,	PUNCT
ejpam-6841	341	16	and	and	CCONJ
ejpam-6841	341	17	suppose	suppose	VERB
ejpam-6841	341	18	on	on	ADP
ejpam-6841	341	19	contrary	contrary	ADJ
ejpam-6841	341	20	that	that	SCONJ
ejpam-6841	341	21	p	p	PROPN
ejpam-6841	341	22	satisfies	satisfy	VERB
ejpam-6841	341	23	the	the	DET
ejpam-6841	341	24	interpolative	interpolative	ADJ
ejpam-6841	341	25	ćirić	ćirić	NOUN
ejpam-6841	341	26	-	-	PUNCT
ejpam-6841	341	27	reich	reich	NOUN
ejpam-6841	341	28	-	-	PUNCT
ejpam-6841	341	29	rus	rus	NOUN
ejpam-6841	341	30	type	type	NOUN
ejpam-6841	341	31	proximal	proximal	ADJ
ejpam-6841	341	32	contraction	contraction	NOUN
ejpam-6841	341	33	,	,	PUNCT
ejpam-6841	341	34	then	then	ADV
ejpam-6841	341	35	ϑ	ϑ	X
ejpam-6841	341	36	(	(	PUNCT
ejpam-6841	341	37	b1	b1	NOUN
ejpam-6841	341	38	,	,	PUNCT
ejpam-6841	341	39	b2	b2	NOUN
ejpam-6841	341	40	)	)	PUNCT
ejpam-6841	341	41	≤	≤	NOUN
ejpam-6841	342	1	λ(ϑ	λ(ϑ	NOUN
ejpam-6841	342	2	(	(	PUNCT
ejpam-6841	342	3	m1,m2	m1,m2	PROPN
ejpam-6841	342	4	)	)	PUNCT
ejpam-6841	342	5	)	)	PUNCT
ejpam-6841	343	1	α(ϑ	α(ϑ	PROPN
ejpam-6841	343	2	(	(	PUNCT
ejpam-6841	343	3	m1	m1	PROPN
ejpam-6841	343	4	,	,	PUNCT
ejpam-6841	343	5	b1	b1	NOUN
ejpam-6841	343	6	)	)	PUNCT
ejpam-6841	343	7	)	)	PUNCT
ejpam-6841	344	1	β(ϑ	β(ϑ	PUNCT
ejpam-6841	344	2	(	(	PUNCT
ejpam-6841	344	3	m2	m2	PROPN
ejpam-6841	344	4	,	,	PUNCT
ejpam-6841	344	5	b2	b2	NOUN
ejpam-6841	344	6	)	)	PUNCT
ejpam-6841	344	7	)	)	PUNCT
ejpam-6841	344	8	1−α−β	1−α−β	PROPN
ejpam-6841	344	9	ϑ	ϑ	X
ejpam-6841	344	10	(	(	PUNCT
ejpam-6841	344	11	(	(	PUNCT
ejpam-6841	344	12	1	1	NUM
ejpam-6841	344	13	,	,	PUNCT
ejpam-6841	344	14	0	0	NUM
ejpam-6841	344	15	)	)	PUNCT
ejpam-6841	344	16	,	,	PUNCT
ejpam-6841	344	17	(	(	PUNCT
ejpam-6841	344	18	1	1	NUM
ejpam-6841	344	19	,	,	PUNCT
ejpam-6841	344	20	2	2	NUM
ejpam-6841	344	21	)	)	PUNCT
ejpam-6841	344	22	)	)	PUNCT
ejpam-6841	344	23	≤	≤	NUM
ejpam-6841	345	1	λ	λ	X
ejpam-6841	345	2	(	(	PUNCT
ejpam-6841	345	3	ϑ	ϑ	X
ejpam-6841	345	4	(	(	PUNCT
ejpam-6841	345	5	1	1	NUM
ejpam-6841	345	6	,	,	PUNCT
ejpam-6841	345	7	2	2	NUM
ejpam-6841	345	8	)	)	PUNCT
ejpam-6841	345	9	,	,	PUNCT
ejpam-6841	345	10	(	(	PUNCT
ejpam-6841	345	11	0	0	NUM
ejpam-6841	345	12	,	,	PUNCT
ejpam-6841	345	13	1))α	1))α	NUM
ejpam-6841	345	14	(	(	PUNCT
ejpam-6841	345	15	ϑ	ϑ	X
ejpam-6841	345	16	(	(	PUNCT
ejpam-6841	345	17	2	2	NUM
ejpam-6841	345	18	,	,	PUNCT
ejpam-6841	345	19	2	2	NUM
ejpam-6841	345	20	)	)	PUNCT
ejpam-6841	345	21	,	,	PUNCT
ejpam-6841	345	22	(	(	PUNCT
ejpam-6841	345	23	1	1	NUM
ejpam-6841	345	24	,	,	PUNCT
ejpam-6841	345	25	0))β	0))β	NUM
ejpam-6841	345	26	(	(	PUNCT
ejpam-6841	345	27	ϑ	ϑ	X
ejpam-6841	345	28	(	(	PUNCT
ejpam-6841	345	29	0	0	NUM
ejpam-6841	345	30	,	,	PUNCT
ejpam-6841	345	31	4	4	NUM
ejpam-6841	345	32	)	)	PUNCT
ejpam-6841	345	33	,	,	PUNCT
ejpam-6841	345	34	(	(	PUNCT
ejpam-6841	345	35	1	1	NUM
ejpam-6841	345	36	,	,	PUNCT
ejpam-6841	345	37	2	2	NUM
ejpam-6841	345	38	)	)	PUNCT
ejpam-6841	345	39	)	)	PUNCT
ejpam-6841	345	40	1−α−β	1−α−β	NOUN
ejpam-6841	345	41	.	.	PUNCT
ejpam-6841	346	1	this	this	DET
ejpam-6841	346	2	implies√	implies√	NOUN
ejpam-6841	346	3	(	(	PUNCT
ejpam-6841	346	4	1−	1−	NUM
ejpam-6841	346	5	1)2	1)2	NUM
ejpam-6841	346	6	+	+	CCONJ
ejpam-6841	346	7	(	(	PUNCT
ejpam-6841	346	8	2−	2−	NUM
ejpam-6841	346	9	0)2	0)2	NUM
ejpam-6841	346	10	≤	≤	NUM
ejpam-6841	346	11	λ	λ	NOUN
ejpam-6841	346	12	(	(	PUNCT
ejpam-6841	346	13	2	2	NUM
ejpam-6841	346	14	√	√	NUM
ejpam-6841	346	15	(	(	PUNCT
ejpam-6841	346	16	0−	0−	NUM
ejpam-6841	346	17	2)2	2)2	NUM
ejpam-6841	346	18	+	+	CCONJ
ejpam-6841	346	19	(	(	PUNCT
ejpam-6841	346	20	4−	4−	NOUN
ejpam-6841	346	21	2)2	2)2	NUM
ejpam-6841	346	22	)	)	PUNCT
ejpam-6841	346	23	α	α	PROPN
ejpam-6841	346	24	(	(	PUNCT
ejpam-6841	346	25	2	2	NUM
ejpam-6841	346	26	√	√	NUM
ejpam-6841	346	27	(	(	PUNCT
ejpam-6841	346	28	1−	1−	NUM
ejpam-6841	346	29	2)2	2)2	NUM
ejpam-6841	346	30	+	+	CCONJ
ejpam-6841	346	31	(	(	PUNCT
ejpam-6841	346	32	0−	0−	NUM
ejpam-6841	346	33	2)2)β	2)2)β	NUM
ejpam-6841	346	34	(	(	PUNCT
ejpam-6841	346	35	2	2	NUM
ejpam-6841	346	36	√	√	NUM
ejpam-6841	346	37	(	(	PUNCT
ejpam-6841	346	38	1−	1−	NUM
ejpam-6841	346	39	0)2	0)2	NUM
ejpam-6841	347	1	+	+	CCONJ
ejpam-6841	347	2	(	(	PUNCT
ejpam-6841	347	3	2−	2−	NUM
ejpam-6841	347	4	4)2	4)2	NUM
ejpam-6841	347	5	)	)	PUNCT
ejpam-6841	347	6	1−α−β	1−α−β	NOUN
ejpam-6841	347	7	]	]	PUNCT
ejpam-6841	348	1	2	2	NUM
ejpam-6841	348	2	≤	≤	NUM
ejpam-6841	348	3	λ	λ	PROPN
ejpam-6841	348	4	[	[	PUNCT
ejpam-6841	348	5	(	(	PUNCT
ejpam-6841	348	6	2	2	NUM
ejpam-6841	348	7	√	√	NUM
ejpam-6841	348	8	8	8	NUM
ejpam-6841	348	9	)	)	PUNCT
ejpam-6841	348	10	1	1	NUM
ejpam-6841	348	11	2	2	NUM
ejpam-6841	348	12	(	(	PUNCT
ejpam-6841	348	13	2	2	NUM
ejpam-6841	348	14	√	√	NUM
ejpam-6841	348	15	5	5	NUM
ejpam-6841	348	16	)	)	PUNCT
ejpam-6841	348	17	1	1	NUM
ejpam-6841	348	18	3	3	NUM
ejpam-6841	348	19	(	(	PUNCT
ejpam-6841	348	20	2	2	NUM
ejpam-6841	348	21	√	√	NUM
ejpam-6841	348	22	5	5	NUM
ejpam-6841	348	23	)	)	PUNCT
ejpam-6841	348	24	1−	1−	NUM
ejpam-6841	348	25	1	1	NUM
ejpam-6841	348	26	2	2	NUM
ejpam-6841	348	27	−	−	NOUN
ejpam-6841	348	28	1	1	NUM
ejpam-6841	348	29	3	3	NUM
ejpam-6841	348	30	]	]	SYM
ejpam-6841	348	31	2	2	NUM
ejpam-6841	348	32	≤	≤	NUM
ejpam-6841	348	33	λ[(1.6817)(1.3076)(1.1435	λ[(1.6817)(1.3076)(1.1435	PROPN
ejpam-6841	348	34	)	)	PUNCT
ejpam-6841	348	35	]	]	PUNCT
ejpam-6841	348	36	.	.	PUNCT
ejpam-6841	349	1	this	this	PRON
ejpam-6841	349	2	implies	imply	VERB
ejpam-6841	349	3	that	that	SCONJ
ejpam-6841	349	4	λ	λ	PROPN
ejpam-6841	349	5	≥	≥	NOUN
ejpam-6841	349	6	1	1	NUM
ejpam-6841	349	7	,	,	PUNCT
ejpam-6841	349	8	a	a	DET
ejpam-6841	349	9	contradiction	contradiction	NOUN
ejpam-6841	349	10	.	.	PUNCT
ejpam-6841	350	1	hence	hence	ADV
ejpam-6841	350	2	,	,	PUNCT
ejpam-6841	350	3	p	p	PROPN
ejpam-6841	350	4	does	do	AUX
ejpam-6841	350	5	not	not	PART
ejpam-6841	350	6	satisfy	satisfy	VERB
ejpam-6841	350	7	the	the	DET
ejpam-6841	350	8	intplv	intplv	ADJ
ejpam-6841	350	9	ćirićreich	ćirićreich	NOUN
ejpam-6841	350	10	-	-	PUNCT
ejpam-6841	350	11	rus	rus	NOUN
ejpam-6841	350	12	type	type	NOUN
ejpam-6841	350	13	proximal	proximal	ADJ
ejpam-6841	350	14	contraction	contraction	NOUN
ejpam-6841	350	15	.	.	PUNCT
ejpam-6841	351	1	however	however	ADV
ejpam-6841	351	2	p	p	X
ejpam-6841	351	3	satisfies	satisfie	NOUN
ejpam-6841	351	4	(	(	PUNCT
ejpam-6841	351	5	j,£)-ćirić	j,£)-ćirić	PROPN
ejpam-6841	351	6	-	-	PUNCT
ejpam-6841	351	7	reich	reich	NOUN
ejpam-6841	351	8	-	-	PUNCT
ejpam-6841	351	9	rus	rus	NOUN
ejpam-6841	351	10	type	type	NOUN
ejpam-6841	351	11	interpolative	interpolative	ADJ
ejpam-6841	351	12	proximal	proximal	ADJ
ejpam-6841	351	13	contraction	contraction	NOUN
ejpam-6841	351	14	.	.	PUNCT
ejpam-6841	352	1	indeed	indeed	ADV
ejpam-6841	352	2	,	,	PUNCT
ejpam-6841	352	3	define	define	VERB
ejpam-6841	352	4	the	the	DET
ejpam-6841	352	5	functions	function	NOUN
ejpam-6841	352	6	j,£	j,£	ADV
ejpam-6841	352	7	:	:	PUNCT
ejpam-6841	352	8	(	(	PUNCT
ejpam-6841	352	9	0,∞	0,∞	NUM
ejpam-6841	352	10	)	)	PUNCT
ejpam-6841	353	1	→	→	PUNCT
ejpam-6841	353	2	r	r	NOUN
ejpam-6841	353	3	by	by	ADP
ejpam-6841	353	4	£	£	SYM
ejpam-6841	353	5	(	(	PUNCT
ejpam-6841	353	6	b	b	NOUN
ejpam-6841	353	7	)	)	PUNCT
ejpam-6841	353	8	=	=	NOUN
ejpam-6841	353	9	{	{	PUNCT
ejpam-6841	353	10	b	b	NOUN
ejpam-6841	353	11	2	2	NUM
ejpam-6841	353	12	for	for	ADP
ejpam-6841	353	13	b	b	NOUN
ejpam-6841	353	14	=	=	SYM
ejpam-6841	353	15	1	1	NUM
ejpam-6841	353	16	b	b	SYM
ejpam-6841	353	17	10	10	NUM
ejpam-6841	353	18	otherwise	otherwise	ADV
ejpam-6841	353	19	j(b	j(b	NOUN
ejpam-6841	353	20	)	)	PUNCT
ejpam-6841	353	21	=	=	PRON
ejpam-6841	353	22	{	{	PUNCT
ejpam-6841	353	23	b	b	PROPN
ejpam-6841	353	24	for	for	ADP
ejpam-6841	353	25	b	b	NOUN
ejpam-6841	353	26	=	=	SYM
ejpam-6841	353	27	1	1	NUM
ejpam-6841	353	28	b	b	SYM
ejpam-6841	353	29	8	8	NUM
ejpam-6841	353	30	otherwise	otherwise	ADV
ejpam-6841	353	31	.	.	PUNCT
ejpam-6841	354	1	then	then	ADV
ejpam-6841	354	2	£	£	PROPN
ejpam-6841	354	3	(	(	PUNCT
ejpam-6841	354	4	t	t	PROPN
ejpam-6841	354	5	)	)	PUNCT
ejpam-6841	354	6	<	<	X
ejpam-6841	354	7	j(t	j(t	PROPN
ejpam-6841	354	8	)	)	PUNCT
ejpam-6841	354	9	for	for	ADP
ejpam-6841	354	10	all	all	DET
ejpam-6841	354	11	t	t	PROPN
ejpam-6841	354	12	>	>	X
ejpam-6841	354	13	0	0	PUNCT
ejpam-6841	354	14	and	and	CCONJ
ejpam-6841	354	15	satisfies	satisfy	VERB
ejpam-6841	354	16	assumption	assumption	NOUN
ejpam-6841	354	17	(	(	PUNCT
ejpam-6841	354	18	i	i	NOUN
ejpam-6841	354	19	)	)	PUNCT
ejpam-6841	354	20	and	and	CCONJ
ejpam-6841	354	21	since	since	SCONJ
ejpam-6841	354	22	j	j	PROPN
ejpam-6841	354	23	(	(	PUNCT
ejpam-6841	354	24	2	2	NUM
ejpam-6841	354	25	)	)	PUNCT
ejpam-6841	354	26	≤	≤	NUM
ejpam-6841	354	27	£	£	SYM
ejpam-6841	354	28	(	(	PUNCT
ejpam-6841	354	29	2.5145	2.5145	NUM
ejpam-6841	354	30	)	)	PUNCT
ejpam-6841	354	31	2	2	NUM
ejpam-6841	354	32	10	10	NUM
ejpam-6841	354	33	≤	≤	NUM
ejpam-6841	354	34	2.5145	2.5145	NUM
ejpam-6841	354	35	8	8	NUM
ejpam-6841	354	36	0.2	0.2	NUM
ejpam-6841	354	37	≤	≤	NUM
ejpam-6841	354	38	0.3143	0.3143	NUM
ejpam-6841	354	39	,	,	PUNCT
ejpam-6841	354	40	so	so	ADV
ejpam-6841	354	41	,	,	PUNCT
ejpam-6841	354	42	p	p	NOUN
ejpam-6841	354	43	satisfies	satisfie	NOUN
ejpam-6841	354	44	(	(	PUNCT
ejpam-6841	354	45	j,£)-ćirić	j,£)-ćirić	PROPN
ejpam-6841	354	46	-	-	PUNCT
ejpam-6841	354	47	reich	reich	NOUN
ejpam-6841	354	48	-	-	PUNCT
ejpam-6841	354	49	rus	rus	NOUN
ejpam-6841	354	50	type	type	NOUN
ejpam-6841	354	51	interpolative	interpolative	ADJ
ejpam-6841	354	52	proximal	proximal	ADJ
ejpam-6841	354	53	contraction	contraction	NOUN
ejpam-6841	354	54	.	.	PUNCT
ejpam-6841	355	1	3.3	3.3	NUM
ejpam-6841	355	2	.	.	PUNCT
ejpam-6841	356	1	(	(	PUNCT
ejpam-6841	356	2	j,£)-hardy	j,£)-hardy	PROPN
ejpam-6841	356	3	rogers	rogers	PROPN
ejpam-6841	356	4	type	type	VERB
ejpam-6841	356	5	interpolative	interpolative	ADJ
ejpam-6841	356	6	proximal	proximal	ADJ
ejpam-6841	356	7	contraction	contraction	NOUN
ejpam-6841	356	8	let	let	VERB
ejpam-6841	356	9	(	(	PUNCT
ejpam-6841	356	10	w	w	NOUN
ejpam-6841	356	11	,	,	PUNCT
ejpam-6841	356	12	ϑ	ϑ	NOUN
ejpam-6841	356	13	)	)	PUNCT
ejpam-6841	356	14	be	be	AUX
ejpam-6841	356	15	a	a	DET
ejpam-6841	356	16	complete	complete	ADJ
ejpam-6841	356	17	metric	metric	ADJ
ejpam-6841	356	18	space	space	NOUN
ejpam-6841	356	19	,	,	PUNCT
ejpam-6841	356	20	and	and	CCONJ
ejpam-6841	356	21	c	c	X
ejpam-6841	356	22	,	,	PUNCT
ejpam-6841	356	23	d	d	X
ejpam-6841	356	24	be	be	AUX
ejpam-6841	356	25	a	a	DET
ejpam-6841	356	26	pair	pair	NOUN
ejpam-6841	356	27	of	of	ADP
ejpam-6841	356	28	nonvoid	nonvoid	ADJ
ejpam-6841	356	29	subsets	subset	NOUN
ejpam-6841	356	30	of	of	ADP
ejpam-6841	356	31	w.	w.	PROPN
ejpam-6841	357	1	a	a	DET
ejpam-6841	357	2	mapping	mapping	NOUN
ejpam-6841	357	3	p	p	X
ejpam-6841	357	4	:	:	PUNCT
ejpam-6841	357	5	c	c	X
ejpam-6841	357	6	→	→	PUNCT
ejpam-6841	357	7	d	d	NOUN
ejpam-6841	357	8	is	be	AUX
ejpam-6841	357	9	said	say	VERB
ejpam-6841	357	10	to	to	PART
ejpam-6841	357	11	be	be	AUX
ejpam-6841	357	12	a	a	DET
ejpam-6841	357	13	(	(	PUNCT
ejpam-6841	357	14	j,£)-interpolative	j,£)-interpolative	ADJ
ejpam-6841	357	15	hardy	hardy	ADJ
ejpam-6841	357	16	rogers	roger	NOUN
ejpam-6841	357	17	type	type	VERB
ejpam-6841	357	18	proximal	proximal	ADJ
ejpam-6841	357	19	contraction	contraction	NOUN
ejpam-6841	357	20	if	if	SCONJ
ejpam-6841	357	21	there	there	PRON
ejpam-6841	357	22	exist	exist	VERB
ejpam-6841	357	23	α	α	PRON
ejpam-6841	357	24	,	,	PUNCT
ejpam-6841	357	25	β	β	X
ejpam-6841	357	26	,	,	PUNCT
ejpam-6841	357	27	γ	γ	PROPN
ejpam-6841	357	28	,	,	PUNCT
ejpam-6841	357	29	δ	δ	PROPN
ejpam-6841	357	30	∈	∈	PROPN
ejpam-6841	357	31	(	(	PUNCT
ejpam-6841	357	32	0	0	NUM
ejpam-6841	357	33	,	,	PUNCT
ejpam-6841	357	34	1	1	X
ejpam-6841	357	35	)	)	PUNCT
ejpam-6841	357	36	satisfying	satisfy	VERB
ejpam-6841	357	37	α+	α+	PRON
ejpam-6841	357	38	β	β	NOUN
ejpam-6841	357	39	+	+	CCONJ
ejpam-6841	357	40	γ	γ	PROPN
ejpam-6841	357	41	+	+	PROPN
ejpam-6841	357	42	δ	δ	PROPN
ejpam-6841	357	43	<	<	X
ejpam-6841	357	44	1	1	NUM
ejpam-6841	357	45	such	such	ADJ
ejpam-6841	357	46	that	that	SCONJ
ejpam-6841	357	47	ϑ	ϑ	X
ejpam-6841	357	48	(	(	PUNCT
ejpam-6841	357	49	b1,pm1	b1,pm1	PROPN
ejpam-6841	357	50	)	)	PUNCT
ejpam-6841	358	1	=	=	SYM
ejpam-6841	358	2	ϑ	ϑ	X
ejpam-6841	358	3	(	(	PUNCT
ejpam-6841	358	4	c	c	X
ejpam-6841	358	5	,	,	PUNCT
ejpam-6841	358	6	d	d	NOUN
ejpam-6841	358	7	)	)	PUNCT
ejpam-6841	358	8	ϑ	ϑ	X
ejpam-6841	358	9	(	(	PUNCT
ejpam-6841	358	10	b2,pm2	b2,pm2	NOUN
ejpam-6841	358	11	)	)	PUNCT
ejpam-6841	358	12	=	=	SYM
ejpam-6841	358	13	ϑ	ϑ	X
ejpam-6841	358	14	(	(	PUNCT
ejpam-6841	358	15	c	c	X
ejpam-6841	358	16	,	,	PUNCT
ejpam-6841	358	17	d	d	NOUN
ejpam-6841	358	18	)	)	PUNCT
ejpam-6841	358	19	}	}	PUNCT
ejpam-6841	358	20	⇒	⇒	VERB
ejpam-6841	358	21	j	j	PROPN
ejpam-6841	358	22	(	(	PUNCT
ejpam-6841	358	23	ϑ	ϑ	X
ejpam-6841	358	24	(	(	PUNCT
ejpam-6841	358	25	b1	b1	NOUN
ejpam-6841	358	26	,	,	PUNCT
ejpam-6841	358	27	b2	b2	NOUN
ejpam-6841	358	28	)	)	PUNCT
ejpam-6841	358	29	)	)	PUNCT
ejpam-6841	359	1	≤	≤	NUM
ejpam-6841	359	2	£	£	NOUN
ejpam-6841	359	3	(	(	PUNCT
ejpam-6841	359	4	ϑ	ϑ	X
ejpam-6841	359	5	(	(	PUNCT
ejpam-6841	359	6	m1,m2	m1,m2	PROPN
ejpam-6841	359	7	)	)	PUNCT
ejpam-6841	359	8	α	α	PROPN
ejpam-6841	359	9	ϑ	ϑ	X
ejpam-6841	359	10	(	(	PUNCT
ejpam-6841	359	11	m1	m1	NOUN
ejpam-6841	359	12	,	,	PUNCT
ejpam-6841	359	13	b1	b1	PROPN
ejpam-6841	359	14	)	)	PUNCT
ejpam-6841	359	15	β	β	PROPN
ejpam-6841	359	16	ϑ	ϑ	X
ejpam-6841	359	17	(	(	PUNCT
ejpam-6841	359	18	m2	m2	PROPN
ejpam-6841	359	19	,	,	PUNCT
ejpam-6841	359	20	b2	b2	NOUN
ejpam-6841	359	21	)	)	PUNCT
ejpam-6841	359	22	γ	γ	X
ejpam-6841	359	23	(	(	PUNCT
ejpam-6841	359	24	1	1	NUM
ejpam-6841	359	25	2	2	NUM
ejpam-6841	359	26	(	(	PUNCT
ejpam-6841	359	27	ϑ	ϑ	X
ejpam-6841	359	28	(	(	PUNCT
ejpam-6841	359	29	m1	m1	NOUN
ejpam-6841	359	30	,	,	PUNCT
ejpam-6841	359	31	b2	b2	NOUN
ejpam-6841	359	32	)	)	PUNCT
ejpam-6841	359	33	+	+	CCONJ
ejpam-6841	359	34	ϑ	ϑ	X
ejpam-6841	359	35	(	(	PUNCT
ejpam-6841	359	36	m2	m2	PROPN
ejpam-6841	359	37	,	,	PUNCT
ejpam-6841	359	38	b1	b1	NOUN
ejpam-6841	359	39	)	)	PUNCT
ejpam-6841	359	40	)	)	PUNCT
ejpam-6841	359	41	)	)	PUNCT
ejpam-6841	360	1	1−α−β−γ	1−α−β−γ	NUM
ejpam-6841	360	2	)	)	PUNCT
ejpam-6841	360	3	,	,	PUNCT
ejpam-6841	360	4	(	(	PUNCT
ejpam-6841	360	5	20	20	NUM
ejpam-6841	360	6	)	)	PUNCT
ejpam-6841	360	7	for	for	ADP
ejpam-6841	360	8	all	all	DET
ejpam-6841	360	9	distinct	distinct	ADJ
ejpam-6841	360	10	b1	b1	NOUN
ejpam-6841	360	11	,	,	PUNCT
ejpam-6841	360	12	b2,m1,m2	b2,m1,m2	NOUN
ejpam-6841	360	13	∈	∈	PROPN
ejpam-6841	360	14	c	c	PROPN
ejpam-6841	360	15	and	and	CCONJ
ejpam-6841	360	16	bi	bi	PROPN
ejpam-6841	360	17	6=	6=	PROPN
ejpam-6841	360	18	mi	mi	PROPN
ejpam-6841	360	19	,	,	PUNCT
ejpam-6841	360	20	i	i	PRON
ejpam-6841	360	21	∈	∈	PROPN
ejpam-6841	360	22	{	{	PUNCT
ejpam-6841	360	23	1	1	NUM
ejpam-6841	360	24	,	,	PUNCT
ejpam-6841	360	25	2	2	NUM
ejpam-6841	360	26	}	}	PUNCT
ejpam-6841	360	27	with	with	ADP
ejpam-6841	360	28	ϑ	ϑ	X
ejpam-6841	360	29	(	(	PUNCT
ejpam-6841	360	30	pb	pb	ADP
ejpam-6841	360	31	,	,	PUNCT
ejpam-6841	360	32	pm	pm	NOUN
ejpam-6841	360	33	)	)	PUNCT
ejpam-6841	360	34	>	>	X
ejpam-6841	360	35	0	0	NUM
ejpam-6841	360	36	;	;	PUNCT
ejpam-6841	360	37	j,£	j,£	ADV
ejpam-6841	360	38	:	:	PUNCT
ejpam-6841	360	39	r+	r+	X
ejpam-6841	360	40	→	→	PUNCT
ejpam-6841	360	41	r	r	NOUN
ejpam-6841	360	42	are	be	AUX
ejpam-6841	360	43	two	two	NUM
ejpam-6841	360	44	functions	function	NOUN
ejpam-6841	360	45	.	.	PUNCT
ejpam-6841	361	1	k.	k.	PROPN
ejpam-6841	361	2	javed	javed	PROPN
ejpam-6841	361	3	,	,	PUNCT
ejpam-6841	361	4	m.	m.	NOUN
ejpam-6841	361	5	nazam	nazam	PROPN
ejpam-6841	361	6	,	,	PUNCT
ejpam-6841	361	7	m.	m.	PROPN
ejpam-6841	361	8	arshad	arshad	PROPN
ejpam-6841	361	9	,	,	PUNCT
ejpam-6841	361	10	m.	m.	NOUN
ejpam-6841	361	11	de	de	X
ejpam-6841	361	12	la	la	PROPN
ejpam-6841	361	13	sen	sen	PROPN
ejpam-6841	361	14	/	/	SYM
ejpam-6841	361	15	eur	eur	PROPN
ejpam-6841	361	16	.	.	PUNCT
ejpam-6841	362	1	j.	j.	PROPN
ejpam-6841	362	2	pure	pure	PROPN
ejpam-6841	362	3	appl	appl	PROPN
ejpam-6841	362	4	.	.	PROPN
ejpam-6841	362	5	math	math	PROPN
ejpam-6841	362	6	,	,	PUNCT
ejpam-6841	362	7	18	18	NUM
ejpam-6841	362	8	(	(	PUNCT
ejpam-6841	362	9	4	4	NUM
ejpam-6841	362	10	)	)	PUNCT
ejpam-6841	362	11	(	(	PUNCT
ejpam-6841	362	12	2025	2025	NUM
ejpam-6841	362	13	)	)	PUNCT
ejpam-6841	362	14	,	,	PUNCT
ejpam-6841	362	15	6841	6841	NUM
ejpam-6841	362	16	16	16	NUM
ejpam-6841	362	17	of	of	ADP
ejpam-6841	362	18	23	23	NUM
ejpam-6841	362	19	remark	remark	NOUN
ejpam-6841	362	20	3	3	NUM
ejpam-6841	362	21	.	.	PUNCT
ejpam-6841	362	22	defining	define	VERB
ejpam-6841	362	23	£	£	SYM
ejpam-6841	362	24	(	(	PUNCT
ejpam-6841	362	25	b	b	NOUN
ejpam-6841	362	26	)	)	PUNCT
ejpam-6841	362	27	=	=	SYM
ejpam-6841	362	28	j(b	j(b	NOUN
ejpam-6841	362	29	)	)	PUNCT
ejpam-6841	363	1	−	−	PROPN
ejpam-6841	363	2	τ	τ	PROPN
ejpam-6841	363	3	for	for	ADP
ejpam-6841	363	4	all	all	DET
ejpam-6841	363	5	b	b	PROPN
ejpam-6841	363	6	∈	∈	NOUN
ejpam-6841	363	7	(	(	PUNCT
ejpam-6841	363	8	0,∞	0,∞	NOUN
ejpam-6841	363	9	)	)	PUNCT
ejpam-6841	363	10	;	;	PUNCT
ejpam-6841	363	11	£	£	PROPN
ejpam-6841	363	12	(	(	PUNCT
ejpam-6841	363	13	b	b	NOUN
ejpam-6841	363	14	)	)	PUNCT
ejpam-6841	363	15	=	=	SYM
ejpam-6841	363	16	j(b	j(b	NOUN
ejpam-6841	363	17	)	)	PUNCT
ejpam-6841	363	18	−	−	PROPN
ejpam-6841	363	19	τ(b	τ(b	NOUN
ejpam-6841	363	20	)	)	PUNCT
ejpam-6841	363	21	for	for	ADP
ejpam-6841	363	22	all	all	DET
ejpam-6841	363	23	b	b	PROPN
ejpam-6841	363	24	∈	∈	NOUN
ejpam-6841	363	25	(	(	PUNCT
ejpam-6841	363	26	0,∞	0,∞	NOUN
ejpam-6841	363	27	)	)	PUNCT
ejpam-6841	363	28	;	;	PUNCT
ejpam-6841	363	29	letting	let	VERB
ejpam-6841	363	30	j	j	PROPN
ejpam-6841	363	31	is	be	AUX
ejpam-6841	363	32	a	a	DET
ejpam-6841	363	33	identity	identity	NOUN
ejpam-6841	363	34	mapping	mapping	NOUN
ejpam-6841	363	35	and	and	CCONJ
ejpam-6841	363	36	£	£	PROPN
ejpam-6841	363	37	(	(	PUNCT
ejpam-6841	363	38	t	t	NOUN
ejpam-6841	363	39	)	)	PUNCT
ejpam-6841	363	40	=	=	NOUN
ejpam-6841	363	41	λt	λt	ADP
ejpam-6841	363	42	for	for	ADP
ejpam-6841	363	43	all	all	DET
ejpam-6841	363	44	t	t	NOUN
ejpam-6841	363	45	>	>	X
ejpam-6841	363	46	0	0	PUNCT
ejpam-6841	363	47	and	and	CCONJ
ejpam-6841	363	48	λ	λ	PROPN
ejpam-6841	363	49	∈	∈	PROPN
ejpam-6841	363	50	(	(	PUNCT
ejpam-6841	363	51	0	0	NUM
ejpam-6841	363	52	,	,	PUNCT
ejpam-6841	363	53	1	1	NUM
ejpam-6841	363	54	)	)	PUNCT
ejpam-6841	363	55	;	;	PUNCT
ejpam-6841	363	56	£	£	PROPN
ejpam-6841	363	57	(	(	PUNCT
ejpam-6841	363	58	b	b	NOUN
ejpam-6841	363	59	)	)	PUNCT
ejpam-6841	363	60	=	=	SYM
ejpam-6841	363	61	β(b)b	β(b)b	NOUN
ejpam-6841	363	62	and	and	CCONJ
ejpam-6841	363	63	j(b	j(b	PROPN
ejpam-6841	363	64	)	)	PUNCT
ejpam-6841	364	1	=	=	SYM
ejpam-6841	364	2	b	b	NOUN
ejpam-6841	364	3	for	for	ADP
ejpam-6841	364	4	all	all	DET
ejpam-6841	364	5	b	b	NOUN
ejpam-6841	364	6	>	>	X
ejpam-6841	364	7	0	0	PUNCT
ejpam-6841	364	8	and	and	CCONJ
ejpam-6841	364	9	β	β	X
ejpam-6841	364	10	:	:	PUNCT
ejpam-6841	364	11	(	(	PUNCT
ejpam-6841	364	12	0,∞	0,∞	NOUN
ejpam-6841	364	13	)	)	PUNCT
ejpam-6841	364	14	→	→	SYM
ejpam-6841	364	15	(	(	PUNCT
ejpam-6841	364	16	0	0	NUM
ejpam-6841	364	17	,	,	PUNCT
ejpam-6841	364	18	1	1	X
ejpam-6841	364	19	)	)	PUNCT
ejpam-6841	364	20	verifying	verifying	NOUN
ejpam-6841	364	21	lim	lim	PROPN
ejpam-6841	364	22	sup	sup	PROPN
ejpam-6841	364	23	b→p+	b→p+	NOUN
ejpam-6841	364	24	β(b	β(b	PUNCT
ejpam-6841	364	25	)	)	PUNCT
ejpam-6841	364	26	<	<	X
ejpam-6841	364	27	1	1	NUM
ejpam-6841	364	28	for	for	ADP
ejpam-6841	364	29	each	each	DET
ejpam-6841	364	30	p	p	X
ejpam-6841	364	31	>	>	X
ejpam-6841	364	32	0	0	PUNCT
ejpam-6841	365	1	in	in	ADP
ejpam-6841	365	2	(	(	PUNCT
ejpam-6841	365	3	20	20	NUM
ejpam-6841	365	4	)	)	PUNCT
ejpam-6841	365	5	,	,	PUNCT
ejpam-6841	365	6	we	we	PRON
ejpam-6841	365	7	obtain	obtain	VERB
ejpam-6841	365	8	the	the	DET
ejpam-6841	365	9	interpolative	interpolative	ADJ
ejpam-6841	365	10	hardy	hardy	ADJ
ejpam-6841	365	11	rogers	roger	NOUN
ejpam-6841	365	12	type	type	NOUN
ejpam-6841	365	13	f	f	X
ejpam-6841	365	14	-	-	PUNCT
ejpam-6841	365	15	proximal	proximal	ADJ
ejpam-6841	365	16	contrs	contrs	X
ejpam-6841	366	1	[	[	X
ejpam-6841	366	2	12	12	NUM
ejpam-6841	366	3	]	]	X
ejpam-6841	366	4	;	;	PUNCT
ejpam-6841	366	5	intplv	intplv	ADJ
ejpam-6841	366	6	h	h	NOUN
ejpam-6841	366	7	-	-	PUNCT
ejpam-6841	366	8	r	r	NOUN
ejpam-6841	366	9	type	type	NOUN
ejpam-6841	366	10	(	(	PUNCT
ejpam-6841	366	11	τ	τ	PROPN
ejpam-6841	366	12	,	,	PUNCT
ejpam-6841	366	13	fp)-prox	fp)-prox	PROPN
ejpam-6841	366	14	contrs	contrs	PROPN
ejpam-6841	366	15	;	;	PUNCT
ejpam-6841	366	16	interpolative	interpolative	ADJ
ejpam-6841	366	17	hardy	hardy	ADJ
ejpam-6841	366	18	rogers	roger	NOUN
ejpam-6841	366	19	type	type	NOUN
ejpam-6841	366	20	proximal	proximal	ADJ
ejpam-6841	366	21	contraction	contraction	NOUN
ejpam-6841	366	22	[	[	X
ejpam-6841	366	23	10	10	NUM
ejpam-6841	366	24	]	]	PUNCT
ejpam-6841	366	25	and	and	CCONJ
ejpam-6841	366	26	interpolative	interpolative	ADJ
ejpam-6841	366	27	hardy	hardy	ADJ
ejpam-6841	366	28	rogers	roger	NOUN
ejpam-6841	366	29	type	type	NOUN
ejpam-6841	366	30	geraghty	geraghty	PROPN
ejpam-6841	366	31	’s	’s	PART
ejpam-6841	366	32	proximal	proximal	ADJ
ejpam-6841	366	33	contraction	contraction	NOUN
ejpam-6841	366	34	respectively	respectively	ADV
ejpam-6841	366	35	.	.	PUNCT
ejpam-6841	367	1	the	the	DET
ejpam-6841	367	2	following	follow	VERB
ejpam-6841	367	3	example	example	NOUN
ejpam-6841	367	4	shows	show	VERB
ejpam-6841	367	5	that	that	SCONJ
ejpam-6841	367	6	(	(	PUNCT
ejpam-6841	367	7	j,£)-hardy	j,£)-hardy	PROPN
ejpam-6841	367	8	rogers	rogers	PROPN
ejpam-6841	367	9	type	type	VERB
ejpam-6841	367	10	interpoative	interpoative	ADJ
ejpam-6841	367	11	proximal	proximal	ADJ
ejpam-6841	367	12	contraction	contraction	NOUN
ejpam-6841	367	13	generalizes	generalize	VERB
ejpam-6841	367	14	the	the	DET
ejpam-6841	367	15	hardy	hardy	ADJ
ejpam-6841	367	16	rogers	roger	NOUN
ejpam-6841	367	17	type	type	VERB
ejpam-6841	367	18	interpolative	interpolative	ADJ
ejpam-6841	367	19	proximal	proximal	ADJ
ejpam-6841	367	20	contraction	contraction	NOUN
ejpam-6841	368	1	[	[	X
ejpam-6841	368	2	10	10	NUM
ejpam-6841	368	3	]	]	PUNCT
ejpam-6841	368	4	.	.	PUNCT
ejpam-6841	369	1	example	example	NOUN
ejpam-6841	369	2	5	5	NUM
ejpam-6841	369	3	.	.	PUNCT
ejpam-6841	370	1	let	let	VERB
ejpam-6841	370	2	w	w	NOUN
ejpam-6841	370	3	=	=	SYM
ejpam-6841	370	4	r	r	NOUN
ejpam-6841	370	5	and	and	CCONJ
ejpam-6841	370	6	define	define	VERB
ejpam-6841	370	7	the	the	DET
ejpam-6841	370	8	function	function	NOUN
ejpam-6841	370	9	ϑ	ϑ	X
ejpam-6841	370	10	:	:	PUNCT
ejpam-6841	370	11	w×w	w×w	NOUN
ejpam-6841	370	12	→	→	SYM
ejpam-6841	370	13	r	r	NOUN
ejpam-6841	370	14	by	by	ADP
ejpam-6841	370	15	ϑ	ϑ	PROPN
ejpam-6841	370	16	(	(	PUNCT
ejpam-6841	370	17	b	b	PROPN
ejpam-6841	370	18	,	,	PUNCT
ejpam-6841	370	19	m	m	NOUN
ejpam-6841	370	20	)	)	PUNCT
ejpam-6841	370	21	=|	=|	NOUN
ejpam-6841	370	22	b−m	b−m	NOUN
ejpam-6841	370	23	|	|	ADV
ejpam-6841	370	24	then	then	ADV
ejpam-6841	370	25	(	(	PUNCT
ejpam-6841	370	26	w	w	PROPN
ejpam-6841	370	27	,	,	PUNCT
ejpam-6841	370	28	ϑ	ϑ	NOUN
ejpam-6841	370	29	)	)	PUNCT
ejpam-6841	370	30	is	be	AUX
ejpam-6841	370	31	a	a	DET
ejpam-6841	370	32	metric	metric	ADJ
ejpam-6841	370	33	space	space	NOUN
ejpam-6841	370	34	.	.	PUNCT
ejpam-6841	371	1	let	let	VERB
ejpam-6841	371	2	c	c	X
ejpam-6841	371	3	,	,	PUNCT
ejpam-6841	371	4	d	d	X
ejpam-6841	371	5	be	be	AUX
ejpam-6841	371	6	the	the	DET
ejpam-6841	371	7	subsets	subset	NOUN
ejpam-6841	371	8	of	of	ADP
ejpam-6841	371	9	w	w	ADV
ejpam-6841	371	10	defined	define	VERB
ejpam-6841	371	11	as	as	ADP
ejpam-6841	371	12	c	c	NOUN
ejpam-6841	371	13	=	=	PUNCT
ejpam-6841	371	14	{	{	PUNCT
ejpam-6841	371	15	1	1	NUM
ejpam-6841	371	16	,	,	PUNCT
ejpam-6841	371	17	2	2	NUM
ejpam-6841	371	18	,	,	PUNCT
ejpam-6841	371	19	3	3	NUM
ejpam-6841	371	20	,	,	PUNCT
ejpam-6841	371	21	4	4	NUM
ejpam-6841	371	22	,	,	PUNCT
ejpam-6841	371	23	5},d	5},d	NUM
ejpam-6841	371	24	=	=	SYM
ejpam-6841	371	25	{	{	PUNCT
ejpam-6841	371	26	1	1	NUM
ejpam-6841	371	27	,	,	PUNCT
ejpam-6841	371	28	2	2	NUM
ejpam-6841	371	29	,	,	PUNCT
ejpam-6841	371	30	3	3	NUM
ejpam-6841	371	31	,	,	PUNCT
ejpam-6841	371	32	4	4	NUM
ejpam-6841	371	33	,	,	PUNCT
ejpam-6841	371	34	5	5	NUM
ejpam-6841	371	35	,	,	PUNCT
ejpam-6841	371	36	6	6	NUM
ejpam-6841	371	37	,	,	PUNCT
ejpam-6841	371	38	7	7	NUM
ejpam-6841	371	39	}	}	PUNCT
ejpam-6841	371	40	then	then	ADV
ejpam-6841	371	41	ϑ	ϑ	X
ejpam-6841	371	42	(	(	PUNCT
ejpam-6841	371	43	c	c	X
ejpam-6841	371	44	,	,	PUNCT
ejpam-6841	371	45	d	d	NOUN
ejpam-6841	371	46	)	)	PUNCT
ejpam-6841	371	47	=	=	SYM
ejpam-6841	371	48	0	0	NUM
ejpam-6841	371	49	define	define	VERB
ejpam-6841	371	50	the	the	DET
ejpam-6841	371	51	functions	function	NOUN
ejpam-6841	371	52	j,£	j,£	ADV
ejpam-6841	371	53	:	:	PUNCT
ejpam-6841	371	54	r+	r+	X
ejpam-6841	371	55	→	→	PUNCT
ejpam-6841	371	56	r	r	NOUN
ejpam-6841	371	57	j	j	PROPN
ejpam-6841	371	58	(	(	PUNCT
ejpam-6841	371	59	b	b	NOUN
ejpam-6841	371	60	)	)	PUNCT
ejpam-6841	371	61	=	=	NOUN
ejpam-6841	371	62	{	{	PUNCT
ejpam-6841	371	63	b+	b+	ADP
ejpam-6841	371	64	1	1	NUM
ejpam-6841	371	65	for	for	ADP
ejpam-6841	371	66	b	b	NOUN
ejpam-6841	371	67	=	=	SYM
ejpam-6841	371	68	2	2	NUM
ejpam-6841	371	69	b+	b+	ADP
ejpam-6841	371	70	10	10	NUM
ejpam-6841	371	71	for	for	ADP
ejpam-6841	371	72	b	b	PROPN
ejpam-6841	371	73	6=	6=	ADP
ejpam-6841	371	74	2	2	NUM
ejpam-6841	371	75	and	and	CCONJ
ejpam-6841	371	76	£	£	SYM
ejpam-6841	371	77	(	(	PUNCT
ejpam-6841	371	78	b	b	NOUN
ejpam-6841	371	79	)	)	PUNCT
ejpam-6841	371	80	=	=	NOUN
ejpam-6841	371	81	{	{	PUNCT
ejpam-6841	371	82	b	b	NOUN
ejpam-6841	371	83	2	2	NUM
ejpam-6841	371	84	for	for	ADP
ejpam-6841	371	85	b	b	NOUN
ejpam-6841	371	86	=	=	SYM
ejpam-6841	371	87	2	2	NUM
ejpam-6841	371	88	b+	b+	ADP
ejpam-6841	371	89	5	5	NUM
ejpam-6841	371	90	otherwise	otherwise	ADV
ejpam-6841	371	91	}	}	PUNCT
ejpam-6841	371	92	define	define	VERB
ejpam-6841	371	93	the	the	DET
ejpam-6841	371	94	mapping	mapping	NOUN
ejpam-6841	371	95	p	p	NOUN
ejpam-6841	371	96	:	:	PUNCT
ejpam-6841	372	1	c	c	X
ejpam-6841	372	2	→	→	SYM
ejpam-6841	372	3	d	d	NOUN
ejpam-6841	372	4	by	by	ADP
ejpam-6841	372	5	p	p	PROPN
ejpam-6841	372	6	(	(	PUNCT
ejpam-6841	372	7	b	b	NOUN
ejpam-6841	372	8	)	)	PUNCT
ejpam-6841	372	9	=	=	SYM
ejpam-6841	373	1	b	b	PROPN
ejpam-6841	373	2	+	+	CCONJ
ejpam-6841	373	3	1	1	NUM
ejpam-6841	373	4	for	for	ADP
ejpam-6841	373	5	all	all	DET
ejpam-6841	373	6	b	b	PROPN
ejpam-6841	373	7	∈	∈	PROPN
ejpam-6841	373	8	c.	c.	NOUN
ejpam-6841	373	9	we	we	PRON
ejpam-6841	373	10	show	show	VERB
ejpam-6841	373	11	that	that	SCONJ
ejpam-6841	373	12	p	p	NOUN
ejpam-6841	373	13	is	be	AUX
ejpam-6841	373	14	a	a	DET
ejpam-6841	373	15	(	(	PUNCT
ejpam-6841	373	16	j,£)-interpolative	j,£)-interpolative	ADJ
ejpam-6841	373	17	hardy	hardy	ADJ
ejpam-6841	373	18	rogers	roger	NOUN
ejpam-6841	373	19	type	type	VERB
ejpam-6841	373	20	proximal	proximal	ADJ
ejpam-6841	373	21	contraction	contraction	NOUN
ejpam-6841	373	22	.	.	PUNCT
ejpam-6841	374	1	for	for	ADP
ejpam-6841	374	2	b1	b1	NOUN
ejpam-6841	374	3	,	,	PUNCT
ejpam-6841	374	4	b2	b2	NOUN
ejpam-6841	374	5	,	,	PUNCT
ejpam-6841	374	6	m1	m1	PROPN
ejpam-6841	374	7	,	,	PUNCT
ejpam-6841	374	8	m2	m2	PROPN
ejpam-6841	374	9	∈	∈	PROPN
ejpam-6841	374	10	c	c	PROPN
ejpam-6841	374	11	,	,	PUNCT
ejpam-6841	374	12	and	and	CCONJ
ejpam-6841	374	13	α	α	NOUN
ejpam-6841	374	14	=	=	SYM
ejpam-6841	374	15	1	1	NUM
ejpam-6841	374	16	8	8	NUM
ejpam-6841	374	17	,	,	PUNCT
ejpam-6841	374	18	β	β	X
ejpam-6841	374	19	=	=	SYM
ejpam-6841	374	20	1	1	NUM
ejpam-6841	374	21	7	7	NUM
ejpam-6841	374	22	,	,	PUNCT
ejpam-6841	374	23	γ	γ	NOUN
ejpam-6841	374	24	=	=	SYM
ejpam-6841	374	25	1	1	NUM
ejpam-6841	374	26	6	6	NUM
ejpam-6841	374	27	ϑ	ϑ	X
ejpam-6841	374	28	(	(	PUNCT
ejpam-6841	374	29	b1,pm1	b1,pm1	PROPN
ejpam-6841	374	30	)	)	PUNCT
ejpam-6841	375	1	=	=	SYM
ejpam-6841	375	2	ϑ	ϑ	X
ejpam-6841	375	3	(	(	PUNCT
ejpam-6841	375	4	c	c	X
ejpam-6841	375	5	,	,	PUNCT
ejpam-6841	375	6	d	d	NOUN
ejpam-6841	375	7	)	)	PUNCT
ejpam-6841	375	8	ϑ	ϑ	X
ejpam-6841	375	9	(	(	PUNCT
ejpam-6841	375	10	b2,pm2	b2,pm2	NOUN
ejpam-6841	375	11	)	)	PUNCT
ejpam-6841	375	12	=	=	SYM
ejpam-6841	375	13	ϑ	ϑ	X
ejpam-6841	375	14	(	(	PUNCT
ejpam-6841	375	15	c	c	X
ejpam-6841	375	16	,	,	PUNCT
ejpam-6841	375	17	d	d	NOUN
ejpam-6841	375	18	)	)	PUNCT
ejpam-6841	375	19	implies	imply	VERB
ejpam-6841	375	20	j	j	PROPN
ejpam-6841	375	21	(	(	PUNCT
ejpam-6841	375	22	ϑ	ϑ	X
ejpam-6841	375	23	(	(	PUNCT
ejpam-6841	375	24	b1	b1	NOUN
ejpam-6841	375	25	,	,	PUNCT
ejpam-6841	375	26	b2	b2	NOUN
ejpam-6841	375	27	)	)	PUNCT
ejpam-6841	375	28	)	)	PUNCT
ejpam-6841	375	29	≤	≤	NUM
ejpam-6841	375	30	£	£	NOUN
ejpam-6841	375	31	(	(	PUNCT
ejpam-6841	375	32	ϑ	ϑ	X
ejpam-6841	375	33	(	(	PUNCT
ejpam-6841	375	34	m1,m2	m1,m2	PROPN
ejpam-6841	375	35	)	)	PUNCT
ejpam-6841	375	36	α	α	PROPN
ejpam-6841	375	37	ϑ	ϑ	X
ejpam-6841	375	38	(	(	PUNCT
ejpam-6841	375	39	m1	m1	NOUN
ejpam-6841	375	40	,	,	PUNCT
ejpam-6841	375	41	b1	b1	PROPN
ejpam-6841	375	42	)	)	PUNCT
ejpam-6841	375	43	β	β	PROPN
ejpam-6841	375	44	ϑ	ϑ	X
ejpam-6841	375	45	(	(	PUNCT
ejpam-6841	375	46	m2	m2	PROPN
ejpam-6841	375	47	,	,	PUNCT
ejpam-6841	375	48	b2	b2	NOUN
ejpam-6841	375	49	)	)	PUNCT
ejpam-6841	375	50	γ	γ	X
ejpam-6841	375	51	(	(	PUNCT
ejpam-6841	375	52	1	1	NUM
ejpam-6841	375	53	2	2	NUM
ejpam-6841	375	54	(	(	PUNCT
ejpam-6841	375	55	ϑ	ϑ	X
ejpam-6841	375	56	(	(	PUNCT
ejpam-6841	375	57	m1	m1	NOUN
ejpam-6841	375	58	,	,	PUNCT
ejpam-6841	375	59	b2	b2	NOUN
ejpam-6841	375	60	)	)	PUNCT
ejpam-6841	376	1	+	+	CCONJ
ejpam-6841	376	2	ϑ	ϑ	X
ejpam-6841	376	3	(	(	PUNCT
ejpam-6841	376	4	m2	m2	PROPN
ejpam-6841	376	5	,	,	PUNCT
ejpam-6841	376	6	b1	b1	NOUN
ejpam-6841	376	7	)	)	PUNCT
ejpam-6841	376	8	)	)	PUNCT
ejpam-6841	376	9	)	)	PUNCT
ejpam-6841	376	10	1−α−β−γ	1−α−β−γ	NUM
ejpam-6841	376	11	)	)	PUNCT
ejpam-6841	376	12	.	.	PUNCT
ejpam-6841	377	1	this	this	PRON
ejpam-6841	377	2	shows	show	VERB
ejpam-6841	377	3	that	that	SCONJ
ejpam-6841	377	4	p	p	NOUN
ejpam-6841	377	5	is	be	AUX
ejpam-6841	377	6	a	a	DET
ejpam-6841	377	7	(	(	PUNCT
ejpam-6841	377	8	j,£)-hardy	j,£)-hardy	PROPN
ejpam-6841	377	9	rogers	rogers	PROPN
ejpam-6841	377	10	interpoative	interpoative	ADJ
ejpam-6841	377	11	type	type	NOUN
ejpam-6841	377	12	proximal	proximal	ADJ
ejpam-6841	377	13	contraction	contraction	NOUN
ejpam-6841	377	14	.	.	PUNCT
ejpam-6841	378	1	however	however	ADV
ejpam-6841	378	2	,	,	PUNCT
ejpam-6841	378	3	the	the	DET
ejpam-6841	378	4	following	follow	VERB
ejpam-6841	378	5	calculation	calculation	NOUN
ejpam-6841	378	6	shows	show	VERB
ejpam-6841	378	7	that	that	SCONJ
ejpam-6841	378	8	it	it	PRON
ejpam-6841	378	9	is	be	AUX
ejpam-6841	378	10	not	not	PART
ejpam-6841	378	11	an	an	DET
ejpam-6841	378	12	interpolative	interpolative	ADJ
ejpam-6841	378	13	hardy	hardy	ADJ
ejpam-6841	378	14	rogers	roger	NOUN
ejpam-6841	378	15	type	type	NOUN
ejpam-6841	378	16	proximal	proximal	ADJ
ejpam-6841	378	17	contraction	contraction	NOUN
ejpam-6841	378	18	.	.	PUNCT
ejpam-6841	379	1	we	we	PRON
ejpam-6841	379	2	know	know	VERB
ejpam-6841	379	3	that	that	SCONJ
ejpam-6841	379	4	ϑ	ϑ	X
ejpam-6841	379	5	(	(	PUNCT
ejpam-6841	379	6	b1,pm1	b1,pm1	PROPN
ejpam-6841	379	7	)	)	PUNCT
ejpam-6841	380	1	=	=	SYM
ejpam-6841	380	2	ϑ	ϑ	X
ejpam-6841	380	3	(	(	PUNCT
ejpam-6841	380	4	c	c	X
ejpam-6841	380	5	,	,	PUNCT
ejpam-6841	380	6	d	d	NOUN
ejpam-6841	380	7	)	)	PUNCT
ejpam-6841	380	8	ϑ	ϑ	X
ejpam-6841	380	9	(	(	PUNCT
ejpam-6841	380	10	b2,pm2	b2,pm2	NOUN
ejpam-6841	380	11	)	)	PUNCT
ejpam-6841	380	12	=	=	SYM
ejpam-6841	380	13	ϑ	ϑ	X
ejpam-6841	380	14	(	(	PUNCT
ejpam-6841	380	15	c	c	X
ejpam-6841	380	16	,	,	PUNCT
ejpam-6841	380	17	d	d	NOUN
ejpam-6841	380	18	)	)	PUNCT
ejpam-6841	380	19	if	if	SCONJ
ejpam-6841	380	20	there	there	PRON
ejpam-6841	380	21	exists	exist	VERB
ejpam-6841	380	22	k	k	PROPN
ejpam-6841	380	23	∈	∈	PROPN
ejpam-6841	380	24	(	(	PUNCT
ejpam-6841	380	25	0	0	NUM
ejpam-6841	380	26	,	,	PUNCT
ejpam-6841	380	27	1	1	NUM
ejpam-6841	380	28	)	)	PUNCT
ejpam-6841	380	29	such	such	ADJ
ejpam-6841	380	30	that	that	SCONJ
ejpam-6841	380	31	ϑ	ϑ	PROPN
ejpam-6841	380	32	(	(	PUNCT
ejpam-6841	380	33	b1	b1	NOUN
ejpam-6841	380	34	,	,	PUNCT
ejpam-6841	380	35	b2	b2	NOUN
ejpam-6841	380	36	)	)	PUNCT
ejpam-6841	380	37	≤	≤	PUNCT
ejpam-6841	381	1	k	k	X
ejpam-6841	381	2	(	(	PUNCT
ejpam-6841	381	3	ϑ	ϑ	X
ejpam-6841	381	4	(	(	PUNCT
ejpam-6841	381	5	m1,m2	m1,m2	PROPN
ejpam-6841	381	6	)	)	PUNCT
ejpam-6841	381	7	α	α	PROPN
ejpam-6841	381	8	ϑ	ϑ	X
ejpam-6841	381	9	(	(	PUNCT
ejpam-6841	381	10	m1	m1	NOUN
ejpam-6841	381	11	,	,	PUNCT
ejpam-6841	381	12	b1	b1	PROPN
ejpam-6841	381	13	)	)	PUNCT
ejpam-6841	381	14	β	β	PROPN
ejpam-6841	381	15	ϑ	ϑ	X
ejpam-6841	381	16	(	(	PUNCT
ejpam-6841	381	17	m2	m2	PROPN
ejpam-6841	381	18	,	,	PUNCT
ejpam-6841	381	19	b2	b2	NOUN
ejpam-6841	381	20	)	)	PUNCT
ejpam-6841	381	21	γ	γ	X
ejpam-6841	381	22	(	(	PUNCT
ejpam-6841	381	23	1	1	NUM
ejpam-6841	381	24	2	2	NUM
ejpam-6841	381	25	(	(	PUNCT
ejpam-6841	381	26	ϑ	ϑ	X
ejpam-6841	381	27	(	(	PUNCT
ejpam-6841	381	28	m1	m1	NOUN
ejpam-6841	381	29	,	,	PUNCT
ejpam-6841	381	30	b2	b2	NOUN
ejpam-6841	381	31	)	)	PUNCT
ejpam-6841	381	32	+	+	CCONJ
ejpam-6841	381	33	ϑ	ϑ	X
ejpam-6841	381	34	(	(	PUNCT
ejpam-6841	381	35	m2	m2	PROPN
ejpam-6841	381	36	,	,	PUNCT
ejpam-6841	381	37	b1	b1	NOUN
ejpam-6841	381	38	)	)	PUNCT
ejpam-6841	381	39	)	)	PUNCT
ejpam-6841	381	40	)	)	PUNCT
ejpam-6841	382	1	1−α−β−γ	1−α−β−γ	X
ejpam-6841	382	2	)	)	PUNCT
ejpam-6841	383	1	k.	k.	PROPN
ejpam-6841	383	2	javed	javed	PROPN
ejpam-6841	383	3	,	,	PUNCT
ejpam-6841	383	4	m.	m.	NOUN
ejpam-6841	383	5	nazam	nazam	PROPN
ejpam-6841	383	6	,	,	PUNCT
ejpam-6841	383	7	m.	m.	PROPN
ejpam-6841	383	8	arshad	arshad	PROPN
ejpam-6841	383	9	,	,	PUNCT
ejpam-6841	383	10	m.	m.	NOUN
ejpam-6841	383	11	de	de	X
ejpam-6841	383	12	la	la	PROPN
ejpam-6841	383	13	sen	sen	PROPN
ejpam-6841	383	14	/	/	SYM
ejpam-6841	383	15	eur	eur	PROPN
ejpam-6841	383	16	.	.	PUNCT
ejpam-6841	384	1	j.	j.	PROPN
ejpam-6841	384	2	pure	pure	PROPN
ejpam-6841	384	3	appl	appl	PROPN
ejpam-6841	384	4	.	.	PROPN
ejpam-6841	384	5	math	math	PROPN
ejpam-6841	384	6	,	,	PUNCT
ejpam-6841	384	7	18	18	NUM
ejpam-6841	384	8	(	(	PUNCT
ejpam-6841	384	9	4	4	NUM
ejpam-6841	384	10	)	)	PUNCT
ejpam-6841	384	11	(	(	PUNCT
ejpam-6841	384	12	2025	2025	NUM
ejpam-6841	384	13	)	)	PUNCT
ejpam-6841	384	14	,	,	PUNCT
ejpam-6841	384	15	6841	6841	NUM
ejpam-6841	384	16	17	17	NUM
ejpam-6841	384	17	of	of	ADP
ejpam-6841	384	18	23	23	NUM
ejpam-6841	384	19	2	2	NUM
ejpam-6841	384	20	≤	≤	NOUN
ejpam-6841	384	21	k	k	X
ejpam-6841	384	22	(	(	PUNCT
ejpam-6841	384	23	(	(	PUNCT
ejpam-6841	384	24	2	2	NUM
ejpam-6841	384	25	)	)	PUNCT
ejpam-6841	384	26	1	1	NUM
ejpam-6841	384	27	8	8	NUM
ejpam-6841	384	28	(	(	PUNCT
ejpam-6841	384	29	1	1	NUM
ejpam-6841	384	30	)	)	PUNCT
ejpam-6841	384	31	1	1	NUM
ejpam-6841	384	32	7	7	NUM
ejpam-6841	384	33	(	(	PUNCT
ejpam-6841	384	34	1	1	NUM
ejpam-6841	384	35	)	)	PUNCT
ejpam-6841	384	36	1	1	NUM
ejpam-6841	384	37	6	6	NUM
ejpam-6841	384	38	(	(	PUNCT
ejpam-6841	384	39	1	1	NUM
ejpam-6841	384	40	2	2	NUM
ejpam-6841	384	41	(	(	PUNCT
ejpam-6841	384	42	3	3	NUM
ejpam-6841	384	43	+	+	NUM
ejpam-6841	384	44	1	1	NUM
ejpam-6841	384	45	)	)	PUNCT
ejpam-6841	384	46	)	)	PUNCT
ejpam-6841	385	1	1−	1−	NUM
ejpam-6841	386	1	1	1	NUM
ejpam-6841	386	2	8	8	NUM
ejpam-6841	386	3	−	−	NUM
ejpam-6841	386	4	1	1	NUM
ejpam-6841	386	5	7	7	NUM
ejpam-6841	386	6	−	−	NUM
ejpam-6841	386	7	1	1	NUM
ejpam-6841	386	8	6	6	NUM
ejpam-6841	386	9	)	)	PUNCT
ejpam-6841	386	10	2	2	NUM
ejpam-6841	386	11	≤	≤	NUM
ejpam-6841	386	12	k	k	X
ejpam-6841	386	13	(	(	PUNCT
ejpam-6841	386	14	1.6138	1.6138	NUM
ejpam-6841	386	15	)	)	PUNCT
ejpam-6841	386	16	,	,	PUNCT
ejpam-6841	386	17	a	a	DET
ejpam-6841	386	18	contradiction	contradiction	NOUN
ejpam-6841	386	19	.	.	PUNCT
ejpam-6841	387	1	hence	hence	ADV
ejpam-6841	387	2	,	,	PUNCT
ejpam-6841	387	3	p	p	PRON
ejpam-6841	387	4	is	be	AUX
ejpam-6841	387	5	not	not	PART
ejpam-6841	387	6	an	an	DET
ejpam-6841	387	7	interpolative	interpolative	ADJ
ejpam-6841	387	8	hardy	hardy	ADJ
ejpam-6841	387	9	rogers	roger	NOUN
ejpam-6841	387	10	type	type	NOUN
ejpam-6841	387	11	proximal	proximal	ADJ
ejpam-6841	387	12	contraction	contraction	NOUN
ejpam-6841	387	13	.	.	PUNCT
ejpam-6841	388	1	theorem	theorem	NOUN
ejpam-6841	388	2	5	5	NUM
ejpam-6841	388	3	.	.	PUNCT
ejpam-6841	389	1	let	let	AUX
ejpam-6841	389	2	(	(	PUNCT
ejpam-6841	389	3	w	w	NOUN
ejpam-6841	389	4	,	,	PUNCT
ejpam-6841	389	5	ϑ	ϑ	NOUN
ejpam-6841	389	6	)	)	PUNCT
ejpam-6841	389	7	be	be	AUX
ejpam-6841	389	8	a	a	DET
ejpam-6841	389	9	complete	complete	ADJ
ejpam-6841	389	10	metric	metric	ADJ
ejpam-6841	389	11	space	space	NOUN
ejpam-6841	389	12	and	and	CCONJ
ejpam-6841	389	13	c	c	NOUN
ejpam-6841	389	14	,	,	PUNCT
ejpam-6841	389	15	d	d	NOUN
ejpam-6841	389	16	be	be	AUX
ejpam-6841	389	17	nonvoid	nonvoid	ADJ
ejpam-6841	389	18	,	,	PUNCT
ejpam-6841	389	19	closed	closed	ADJ
ejpam-6841	389	20	subsets	subset	NOUN
ejpam-6841	389	21	of	of	ADP
ejpam-6841	389	22	w	w	ADP
ejpam-6841	389	23	such	such	ADJ
ejpam-6841	389	24	that	that	SCONJ
ejpam-6841	389	25	d	d	NOUN
ejpam-6841	389	26	is	be	AUX
ejpam-6841	389	27	approximately	approximately	ADV
ejpam-6841	389	28	compact	compact	ADJ
ejpam-6841	389	29	with	with	ADP
ejpam-6841	389	30	respect	respect	NOUN
ejpam-6841	389	31	to	to	ADP
ejpam-6841	389	32	c.	c.	NOUN
ejpam-6841	389	33	let	let	VERB
ejpam-6841	389	34	p	p	NOUN
ejpam-6841	389	35	:	:	PUNCT
ejpam-6841	389	36	c	c	X
ejpam-6841	389	37	→	→	PUNCT
ejpam-6841	389	38	d	d	X
ejpam-6841	389	39	be	be	AUX
ejpam-6841	389	40	an	an	DET
ejpam-6841	389	41	(	(	PUNCT
ejpam-6841	389	42	j,£)−	j,£)−	NOUN
ejpam-6841	389	43	interpolative	interpolative	ADJ
ejpam-6841	389	44	hardy	hardy	ADJ
ejpam-6841	389	45	rogers	roger	NOUN
ejpam-6841	389	46	type	type	NOUN
ejpam-6841	389	47	proximal	proximal	ADJ
ejpam-6841	389	48	contraction	contraction	NOUN
ejpam-6841	389	49	.	.	PUNCT
ejpam-6841	390	1	if	if	SCONJ
ejpam-6841	390	2	(	(	PUNCT
ejpam-6841	390	3	i	i	NOUN
ejpam-6841	390	4	)	)	PUNCT
ejpam-6841	390	5	j	j	PROPN
ejpam-6841	390	6	is	be	AUX
ejpam-6841	390	7	non	non	ADJ
ejpam-6841	390	8	-	-	ADJ
ejpam-6841	390	9	decreasing	decrease	VERB
ejpam-6841	390	10	function	function	NOUN
ejpam-6841	390	11	and	and	CCONJ
ejpam-6841	390	12	for	for	ADP
ejpam-6841	390	13	any	any	DET
ejpam-6841	390	14	ε	ε	PROPN
ejpam-6841	390	15	>	>	X
ejpam-6841	390	16	0	0	PROPN
ejpam-6841	390	17	,	,	PUNCT
ejpam-6841	390	18	lim	lim	PROPN
ejpam-6841	390	19	t→ε+	t→ε+	VERB
ejpam-6841	390	20	sup£	sup£	X
ejpam-6841	390	21	(	(	PUNCT
ejpam-6841	390	22	t	t	NOUN
ejpam-6841	390	23	)	)	PUNCT
ejpam-6841	390	24	<	<	X
ejpam-6841	390	25	j	j	PROPN
ejpam-6841	390	26	(	(	PUNCT
ejpam-6841	390	27	ε+	ε+	NOUN
ejpam-6841	390	28	)	)	PUNCT
ejpam-6841	390	29	.	.	PUNCT
ejpam-6841	391	1	(	(	PUNCT
ejpam-6841	391	2	ii	ii	X
ejpam-6841	391	3	)	)	PUNCT
ejpam-6841	391	4	c0	c0	PROPN
ejpam-6841	391	5	is	be	AUX
ejpam-6841	391	6	nonvoid	nonvoid	PROPN
ejpam-6841	391	7	subset	subset	NOUN
ejpam-6841	391	8	of	of	ADP
ejpam-6841	391	9	c	c	PROPN
ejpam-6841	391	10	such	such	ADJ
ejpam-6841	391	11	that	that	SCONJ
ejpam-6841	391	12	p	p	PROPN
ejpam-6841	391	13	(	(	PUNCT
ejpam-6841	391	14	c0	c0	NOUN
ejpam-6841	391	15	)	)	PUNCT
ejpam-6841	391	16	⊆	⊆	NUM
ejpam-6841	391	17	d0	d0	NOUN
ejpam-6841	391	18	.	.	PUNCT
ejpam-6841	392	1	then	then	ADV
ejpam-6841	392	2	p	p	X
ejpam-6841	392	3	has	have	VERB
ejpam-6841	392	4	a	a	DET
ejpam-6841	392	5	best	good	ADJ
ejpam-6841	392	6	proximity	proximity	NOUN
ejpam-6841	392	7	point	point	NOUN
ejpam-6841	392	8	.	.	PUNCT
ejpam-6841	393	1	proof	proof	NOUN
ejpam-6841	393	2	.	.	PUNCT
ejpam-6841	394	1	let	let	VERB
ejpam-6841	394	2	b0	b0	VERB
ejpam-6841	394	3	∈	∈	PROPN
ejpam-6841	394	4	c0	c0	NOUN
ejpam-6841	394	5	.	.	PUNCT
ejpam-6841	395	1	since	since	SCONJ
ejpam-6841	395	2	p(b0	p(b0	NOUN
ejpam-6841	395	3	)	)	PUNCT
ejpam-6841	395	4	∈	∈	PROPN
ejpam-6841	395	5	p(c0	p(c0	NOUN
ejpam-6841	395	6	)	)	PUNCT
ejpam-6841	395	7	⊆	⊆	NUM
ejpam-6841	395	8	d0	d0	NOUN
ejpam-6841	395	9	,	,	PUNCT
ejpam-6841	395	10	there	there	PRON
ejpam-6841	395	11	exist	exist	VERB
ejpam-6841	395	12	b1	b1	NOUN
ejpam-6841	395	13	∈	∈	PROPN
ejpam-6841	395	14	c0	c0	NOUN
ejpam-6841	395	15	such	such	ADJ
ejpam-6841	395	16	that	that	SCONJ
ejpam-6841	395	17	,	,	PUNCT
ejpam-6841	395	18	ϑ(b1,p(b0	ϑ(b1,p(b0	NOUN
ejpam-6841	395	19	)	)	PUNCT
ejpam-6841	395	20	)	)	PUNCT
ejpam-6841	396	1	=	=	PUNCT
ejpam-6841	396	2	ϑ(c	ϑ(c	NOUN
ejpam-6841	396	3	,	,	PUNCT
ejpam-6841	396	4	d).similarly	d).similarly	ADV
ejpam-6841	396	5	,	,	PUNCT
ejpam-6841	396	6	for	for	ADP
ejpam-6841	396	7	p(b1	p(b1	NOUN
ejpam-6841	396	8	)	)	PUNCT
ejpam-6841	396	9	∈	∈	PROPN
ejpam-6841	396	10	p(c0	p(c0	NOUN
ejpam-6841	396	11	)	)	PUNCT
ejpam-6841	396	12	⊆	⊆	NUM
ejpam-6841	396	13	d0	d0	NOUN
ejpam-6841	396	14	,	,	PUNCT
ejpam-6841	396	15	there	there	PRON
ejpam-6841	396	16	exists	exist	VERB
ejpam-6841	396	17	b2	b2	NOUN
ejpam-6841	396	18	∈	∈	PROPN
ejpam-6841	396	19	c0	c0	NOUN
ejpam-6841	396	20	such	such	ADJ
ejpam-6841	396	21	that	that	DET
ejpam-6841	396	22	ϑ(b2,p(b1	ϑ(b2,p(b1	NOUN
ejpam-6841	396	23	)	)	PUNCT
ejpam-6841	396	24	)	)	PUNCT
ejpam-6841	397	1	=	=	PUNCT
ejpam-6841	397	2	ϑ(c	ϑ(c	PROPN
ejpam-6841	397	3	,	,	PUNCT
ejpam-6841	397	4	d	d	NOUN
ejpam-6841	397	5	)	)	PUNCT
ejpam-6841	397	6	.	.	PUNCT
ejpam-6841	398	1	then	then	ADV
ejpam-6841	398	2	c0	c0	PROPN
ejpam-6841	398	3	implies	imply	VERB
ejpam-6841	398	4	to	to	PART
ejpam-6841	398	5	have	have	VERB
ejpam-6841	398	6	a	a	DET
ejpam-6841	398	7	sequence	sequence	NOUN
ejpam-6841	398	8	{	{	PUNCT
ejpam-6841	398	9	bn	bn	NOUN
ejpam-6841	398	10	}	}	PUNCT
ejpam-6841	398	11	⊆	⊆	NUM
ejpam-6841	398	12	c0	c0	NOUN
ejpam-6841	398	13	such	such	ADJ
ejpam-6841	398	14	that	that	DET
ejpam-6841	398	15	ϑ(bn+1,p(bn	ϑ(bn+1,p(bn	NOUN
ejpam-6841	398	16	)	)	PUNCT
ejpam-6841	398	17	)	)	PUNCT
ejpam-6841	399	1	=	=	PUNCT
ejpam-6841	399	2	ϑ(c	ϑ(c	PROPN
ejpam-6841	399	3	,	,	PUNCT
ejpam-6841	399	4	d	d	NOUN
ejpam-6841	399	5	)	)	PUNCT
ejpam-6841	399	6	(	(	PUNCT
ejpam-6841	399	7	21	21	NUM
ejpam-6841	399	8	)	)	PUNCT
ejpam-6841	399	9	if	if	SCONJ
ejpam-6841	399	10	there	there	PRON
ejpam-6841	399	11	exists	exist	VERB
ejpam-6841	399	12	some	some	DET
ejpam-6841	399	13	n	n	PRON
ejpam-6841	399	14	∈	∈	PROPN
ejpam-6841	399	15	n	n	PRON
ejpam-6841	399	16	such	such	ADJ
ejpam-6841	399	17	that	that	PRON
ejpam-6841	399	18	bn	bn	NOUN
ejpam-6841	399	19	=	=	SYM
ejpam-6841	399	20	bn+1	bn+1	PROPN
ejpam-6841	399	21	,	,	PUNCT
ejpam-6841	399	22	then	then	ADV
ejpam-6841	399	23	bn	bn	PROPN
ejpam-6841	399	24	is	be	AUX
ejpam-6841	399	25	a	a	DET
ejpam-6841	399	26	best	good	ADJ
ejpam-6841	399	27	proximity	proximity	NOUN
ejpam-6841	399	28	point	point	NOUN
ejpam-6841	399	29	of	of	ADP
ejpam-6841	399	30	the	the	DET
ejpam-6841	399	31	mapping	mapping	NOUN
ejpam-6841	399	32	p	p	NOUN
ejpam-6841	399	33	(	(	PUNCT
ejpam-6841	399	34	see	see	PROPN
ejpam-6841	399	35	(	(	PUNCT
ejpam-6841	399	36	21	21	NUM
ejpam-6841	399	37	)	)	PUNCT
ejpam-6841	399	38	)	)	PUNCT
ejpam-6841	399	39	.	.	PUNCT
ejpam-6841	400	1	assume	assume	VERB
ejpam-6841	400	2	that	that	SCONJ
ejpam-6841	400	3	bn+1	bn+1	PROPN
ejpam-6841	400	4	6=	6=	ADP
ejpam-6841	400	5	bn	bn	ADP
ejpam-6841	400	6	for	for	ADP
ejpam-6841	400	7	all	all	PRON
ejpam-6841	400	8	n	n	PRON
ejpam-6841	400	9	∈	∈	PROPN
ejpam-6841	400	10	n	n	CCONJ
ejpam-6841	400	11	,	,	PUNCT
ejpam-6841	400	12	then	then	ADV
ejpam-6841	400	13	by	by	ADP
ejpam-6841	400	14	(	(	PUNCT
ejpam-6841	400	15	21	21	NUM
ejpam-6841	400	16	)	)	PUNCT
ejpam-6841	400	17	we	we	PRON
ejpam-6841	400	18	have	have	VERB
ejpam-6841	400	19	ϑ(bn	ϑ(bn	NOUN
ejpam-6841	400	20	,	,	PUNCT
ejpam-6841	400	21	p(bn−1	p(bn−1	NUM
ejpam-6841	400	22	)	)	PUNCT
ejpam-6841	400	23	)	)	PUNCT
ejpam-6841	401	1	=	=	PUNCT
ejpam-6841	401	2	ϑ(c	ϑ(c	PROPN
ejpam-6841	401	3	,	,	PUNCT
ejpam-6841	401	4	d	d	NOUN
ejpam-6841	401	5	)	)	PUNCT
ejpam-6841	401	6	,	,	PUNCT
ejpam-6841	401	7	ϑ(bn+1,p(bn	ϑ(bn+1,p(bn	X
ejpam-6841	401	8	)	)	PUNCT
ejpam-6841	401	9	)	)	PUNCT
ejpam-6841	402	1	=	=	PUNCT
ejpam-6841	402	2	ϑ(c	ϑ(c	PROPN
ejpam-6841	402	3	,	,	PUNCT
ejpam-6841	402	4	d	d	NOUN
ejpam-6841	402	5	)	)	PUNCT
ejpam-6841	402	6	,	,	PUNCT
ejpam-6841	402	7	for	for	ADP
ejpam-6841	402	8	all	all	DET
ejpam-6841	402	9	n	n	PRON
ejpam-6841	402	10	≥	≥	NOUN
ejpam-6841	402	11	1	1	NUM
ejpam-6841	402	12	.	.	PUNCT
ejpam-6841	402	13	thus	thus	ADV
ejpam-6841	402	14	by	by	ADP
ejpam-6841	402	15	(	(	PUNCT
ejpam-6841	402	16	20	20	NUM
ejpam-6841	402	17	)	)	PUNCT
ejpam-6841	402	18	,	,	PUNCT
ejpam-6841	402	19	we	we	PRON
ejpam-6841	402	20	have	have	VERB
ejpam-6841	402	21	j(ϑ(bn	j(ϑ(bn	PROPN
ejpam-6841	402	22	,	,	PUNCT
ejpam-6841	402	23	bn+1	bn+1	NUM
ejpam-6841	402	24	)	)	PUNCT
ejpam-6841	402	25	)	)	PUNCT
ejpam-6841	403	1	≤	≤	NUM
ejpam-6841	403	2	£	£	NOUN
ejpam-6841	403	3	(	(	PUNCT
ejpam-6841	403	4	(	(	PUNCT
ejpam-6841	403	5	ϑ	ϑ	X
ejpam-6841	403	6	(	(	PUNCT
ejpam-6841	403	7	bn−1,bn	bn−1,bn	NOUN
ejpam-6841	403	8	)	)	PUNCT
ejpam-6841	403	9	)	)	PUNCT
ejpam-6841	404	1	α	α	PROPN
ejpam-6841	404	2	(	(	PUNCT
ejpam-6841	404	3	ϑ(bn−1	ϑ(bn−1	PROPN
ejpam-6841	404	4	,	,	PUNCT
ejpam-6841	404	5	bn	bn	ADJ
ejpam-6841	404	6	)	)	PUNCT
ejpam-6841	404	7	)	)	PUNCT
ejpam-6841	405	1	β	β	X
ejpam-6841	405	2	(	(	PUNCT
ejpam-6841	405	3	ϑ	ϑ	X
ejpam-6841	405	4	(	(	PUNCT
ejpam-6841	405	5	bn	bn	X
ejpam-6841	405	6	,	,	PUNCT
ejpam-6841	405	7	bn+1	bn+1	NUM
ejpam-6841	405	8	)	)	PUNCT
ejpam-6841	405	9	)	)	PUNCT
ejpam-6841	406	1	γ	γ	X
ejpam-6841	406	2	(	(	PUNCT
ejpam-6841	406	3	1	1	NUM
ejpam-6841	406	4	2	2	NUM
ejpam-6841	406	5	(	(	PUNCT
ejpam-6841	406	6	ϑ	ϑ	X
ejpam-6841	406	7	(	(	PUNCT
ejpam-6841	406	8	bn−1	bn−1	ADJ
ejpam-6841	406	9	,	,	PUNCT
ejpam-6841	406	10	bn+1	bn+1	NUM
ejpam-6841	406	11	)	)	PUNCT
ejpam-6841	406	12	+	+	CCONJ
ejpam-6841	406	13	ϑ	ϑ	X
ejpam-6841	406	14	(	(	PUNCT
ejpam-6841	406	15	bn	bn	INTJ
ejpam-6841	406	16	,	,	PUNCT
ejpam-6841	406	17	bn	bn	NOUN
ejpam-6841	406	18	)	)	PUNCT
ejpam-6841	406	19	)	)	PUNCT
ejpam-6841	406	20	)	)	PUNCT
ejpam-6841	406	21	1−α−β−γ	1−α−β−γ	X
ejpam-6841	406	22	)	)	PUNCT
ejpam-6841	406	23	j	j	NOUN
ejpam-6841	406	24	(	(	PUNCT
ejpam-6841	406	25	ϑ	ϑ	X
ejpam-6841	406	26	(	(	PUNCT
ejpam-6841	406	27	bn	bn	X
ejpam-6841	406	28	,	,	PUNCT
ejpam-6841	406	29	bn+1	bn+1	NUM
ejpam-6841	406	30	)	)	PUNCT
ejpam-6841	406	31	)	)	PUNCT
ejpam-6841	407	1	=	=	PUNCT
ejpam-6841	407	2	£	£	PROPN
ejpam-6841	407	3	(	(	PUNCT
ejpam-6841	407	4	(	(	PUNCT
ejpam-6841	407	5	ϑ	ϑ	X
ejpam-6841	407	6	(	(	PUNCT
ejpam-6841	407	7	bn−1,bn	bn−1,bn	NOUN
ejpam-6841	407	8	)	)	PUNCT
ejpam-6841	407	9	)	)	PUNCT
ejpam-6841	408	1	α	α	PROPN
ejpam-6841	408	2	(	(	PUNCT
ejpam-6841	408	3	ϑ(bn−1	ϑ(bn−1	PROPN
ejpam-6841	408	4	,	,	PUNCT
ejpam-6841	408	5	bn	bn	ADJ
ejpam-6841	408	6	)	)	PUNCT
ejpam-6841	408	7	)	)	PUNCT
ejpam-6841	409	1	β	β	X
ejpam-6841	409	2	(	(	PUNCT
ejpam-6841	409	3	ϑ	ϑ	X
ejpam-6841	409	4	(	(	PUNCT
ejpam-6841	409	5	bn	bn	X
ejpam-6841	409	6	,	,	PUNCT
ejpam-6841	409	7	bn+1	bn+1	NUM
ejpam-6841	409	8	)	)	PUNCT
ejpam-6841	409	9	)	)	PUNCT
ejpam-6841	410	1	γ	γ	X
ejpam-6841	410	2	(	(	PUNCT
ejpam-6841	410	3	1	1	NUM
ejpam-6841	410	4	2	2	NUM
ejpam-6841	410	5	(	(	PUNCT
ejpam-6841	410	6	ϑ	ϑ	X
ejpam-6841	410	7	(	(	PUNCT
ejpam-6841	410	8	bn−1	bn−1	ADJ
ejpam-6841	410	9	,	,	PUNCT
ejpam-6841	410	10	bn+1	bn+1	NUM
ejpam-6841	410	11	)	)	PUNCT
ejpam-6841	410	12	)	)	PUNCT
ejpam-6841	410	13	)	)	PUNCT
ejpam-6841	411	1	1−α−β−γ	1−α−β−γ	X
ejpam-6841	411	2	)	)	PUNCT
ejpam-6841	411	3	j	j	NOUN
ejpam-6841	411	4	(	(	PUNCT
ejpam-6841	411	5	ϑ	ϑ	X
ejpam-6841	411	6	(	(	PUNCT
ejpam-6841	411	7	bn	bn	X
ejpam-6841	411	8	,	,	PUNCT
ejpam-6841	411	9	bn+1	bn+1	NUM
ejpam-6841	411	10	)	)	PUNCT
ejpam-6841	411	11	)	)	PUNCT
ejpam-6841	412	1	≤	≤	NUM
ejpam-6841	412	2	£	£	NOUN
ejpam-6841	412	3	(	(	PUNCT
ejpam-6841	412	4	(	(	PUNCT
ejpam-6841	412	5	ϑ	ϑ	X
ejpam-6841	412	6	(	(	PUNCT
ejpam-6841	412	7	bn−1,bn	bn−1,bn	NOUN
ejpam-6841	412	8	)	)	PUNCT
ejpam-6841	412	9	)	)	PUNCT
ejpam-6841	413	1	α	α	PROPN
ejpam-6841	413	2	(	(	PUNCT
ejpam-6841	413	3	ϑ(bn−1	ϑ(bn−1	PROPN
ejpam-6841	413	4	,	,	PUNCT
ejpam-6841	413	5	bn	bn	ADJ
ejpam-6841	413	6	)	)	PUNCT
ejpam-6841	413	7	)	)	PUNCT
ejpam-6841	414	1	β	β	X
ejpam-6841	414	2	(	(	PUNCT
ejpam-6841	414	3	ϑ	ϑ	X
ejpam-6841	414	4	(	(	PUNCT
ejpam-6841	414	5	bn	bn	X
ejpam-6841	414	6	,	,	PUNCT
ejpam-6841	414	7	bn+1	bn+1	NUM
ejpam-6841	414	8	)	)	PUNCT
ejpam-6841	414	9	)	)	PUNCT
ejpam-6841	415	1	γ	γ	X
ejpam-6841	415	2	(	(	PUNCT
ejpam-6841	415	3	1	1	NUM
ejpam-6841	415	4	2	2	NUM
ejpam-6841	415	5	(	(	PUNCT
ejpam-6841	415	6	ϑ	ϑ	X
ejpam-6841	415	7	(	(	PUNCT
ejpam-6841	415	8	bn−1	bn−1	ADJ
ejpam-6841	415	9	,	,	PUNCT
ejpam-6841	415	10	bn	bn	ADJ
ejpam-6841	415	11	)	)	PUNCT
ejpam-6841	415	12	+	+	CCONJ
ejpam-6841	415	13	ϑ	ϑ	X
ejpam-6841	415	14	(	(	PUNCT
ejpam-6841	415	15	bn	bn	X
ejpam-6841	415	16	,	,	PUNCT
ejpam-6841	415	17	bn+1	bn+1	NUM
ejpam-6841	415	18	)	)	PUNCT
ejpam-6841	415	19	)	)	PUNCT
ejpam-6841	415	20	)	)	PUNCT
ejpam-6841	416	1	1−α−β−γ	1−α−β−γ	X
ejpam-6841	416	2	)	)	PUNCT
ejpam-6841	416	3	j	j	NOUN
ejpam-6841	416	4	(	(	PUNCT
ejpam-6841	416	5	ϑ	ϑ	X
ejpam-6841	416	6	(	(	PUNCT
ejpam-6841	416	7	bn	bn	X
ejpam-6841	416	8	,	,	PUNCT
ejpam-6841	416	9	bn+1	bn+1	NUM
ejpam-6841	416	10	)	)	PUNCT
ejpam-6841	416	11	)	)	PUNCT
ejpam-6841	417	1	≤	≤	NUM
ejpam-6841	417	2	£	£	NOUN
ejpam-6841	417	3	(	(	PUNCT
ejpam-6841	417	4	(	(	PUNCT
ejpam-6841	417	5	ϑ	ϑ	X
ejpam-6841	417	6	(	(	PUNCT
ejpam-6841	417	7	bn−1,bn	bn−1,bn	NOUN
ejpam-6841	417	8	)	)	PUNCT
ejpam-6841	417	9	)	)	PUNCT
ejpam-6841	417	10	α+β	α+β	PROPN
ejpam-6841	417	11	(	(	PUNCT
ejpam-6841	417	12	ϑ	ϑ	X
ejpam-6841	417	13	(	(	PUNCT
ejpam-6841	417	14	bn	bn	X
ejpam-6841	417	15	,	,	PUNCT
ejpam-6841	417	16	bn+1	bn+1	NUM
ejpam-6841	417	17	)	)	PUNCT
ejpam-6841	417	18	)	)	PUNCT
ejpam-6841	417	19	γ	γ	X
ejpam-6841	417	20	(	(	PUNCT
ejpam-6841	417	21	1	1	NUM
ejpam-6841	417	22	2	2	NUM
ejpam-6841	417	23	(	(	PUNCT
ejpam-6841	417	24	ϑ	ϑ	X
ejpam-6841	417	25	(	(	PUNCT
ejpam-6841	417	26	bn−1	bn−1	ADJ
ejpam-6841	417	27	,	,	PUNCT
ejpam-6841	417	28	bn	bn	ADJ
ejpam-6841	417	29	)	)	PUNCT
ejpam-6841	417	30	+	+	CCONJ
ejpam-6841	417	31	ϑ	ϑ	X
ejpam-6841	417	32	(	(	PUNCT
ejpam-6841	417	33	bn	bn	X
ejpam-6841	417	34	,	,	PUNCT
ejpam-6841	417	35	bn+1	bn+1	NUM
ejpam-6841	417	36	)	)	PUNCT
ejpam-6841	417	37	)	)	PUNCT
ejpam-6841	417	38	)	)	PUNCT
ejpam-6841	418	1	1−α−β−γ	1−α−β−γ	NUM
ejpam-6841	418	2	)	)	PUNCT
ejpam-6841	418	3	,	,	PUNCT
ejpam-6841	418	4	k.	k.	PROPN
ejpam-6841	418	5	javed	javed	PROPN
ejpam-6841	418	6	,	,	PUNCT
ejpam-6841	418	7	m.	m.	NOUN
ejpam-6841	418	8	nazam	nazam	PROPN
ejpam-6841	418	9	,	,	PUNCT
ejpam-6841	418	10	m.	m.	PROPN
ejpam-6841	418	11	arshad	arshad	PROPN
ejpam-6841	418	12	,	,	PUNCT
ejpam-6841	418	13	m.	m.	NOUN
ejpam-6841	418	14	de	de	X
ejpam-6841	418	15	la	la	PROPN
ejpam-6841	418	16	sen	sen	PROPN
ejpam-6841	418	17	/	/	SYM
ejpam-6841	418	18	eur	eur	PROPN
ejpam-6841	418	19	.	.	PUNCT
ejpam-6841	419	1	j.	j.	PROPN
ejpam-6841	419	2	pure	pure	PROPN
ejpam-6841	419	3	appl	appl	PROPN
ejpam-6841	419	4	.	.	PROPN
ejpam-6841	419	5	math	math	PROPN
ejpam-6841	419	6	,	,	PUNCT
ejpam-6841	419	7	18	18	NUM
ejpam-6841	419	8	(	(	PUNCT
ejpam-6841	419	9	4	4	NUM
ejpam-6841	419	10	)	)	PUNCT
ejpam-6841	419	11	(	(	PUNCT
ejpam-6841	419	12	2025	2025	NUM
ejpam-6841	419	13	)	)	PUNCT
ejpam-6841	419	14	,	,	PUNCT
ejpam-6841	419	15	6841	6841	NUM
ejpam-6841	419	16	18	18	NUM
ejpam-6841	419	17	of	of	ADP
ejpam-6841	419	18	23	23	NUM
ejpam-6841	419	19	for	for	ADP
ejpam-6841	419	20	all	all	DET
ejpam-6841	419	21	distinct	distinct	ADJ
ejpam-6841	419	22	bn−1	bn−1	ADJ
ejpam-6841	419	23	,	,	PUNCT
ejpam-6841	419	24	bn	bn	ADJ
ejpam-6841	419	25	,	,	PUNCT
ejpam-6841	419	26	bn+1	bn+1	PROPN
ejpam-6841	419	27	∈	∈	PROPN
ejpam-6841	419	28	c.	c.	PROPN
ejpam-6841	419	29	let	let	VERB
ejpam-6841	419	30	ϑ(bn	ϑ(bn	PROPN
ejpam-6841	419	31	,	,	PUNCT
ejpam-6841	419	32	bn+1	bn+1	NUM
ejpam-6841	419	33	)	)	PUNCT
ejpam-6841	419	34	=	=	SYM
ejpam-6841	420	1	θn	θn	PROPN
ejpam-6841	420	2	.	.	PROPN
ejpam-6841	420	3	since	since	SCONJ
ejpam-6841	420	4	,	,	PUNCT
ejpam-6841	420	5	£	£	PROPN
ejpam-6841	420	6	(	(	PUNCT
ejpam-6841	420	7	t	t	PROPN
ejpam-6841	420	8	)	)	PUNCT
ejpam-6841	420	9	<	<	X
ejpam-6841	420	10	j	j	PROPN
ejpam-6841	420	11	(	(	PUNCT
ejpam-6841	420	12	t	t	PROPN
ejpam-6841	420	13	)	)	PUNCT
ejpam-6841	420	14	for	for	ADP
ejpam-6841	420	15	all	all	DET
ejpam-6841	420	16	t	t	PROPN
ejpam-6841	420	17	>	>	X
ejpam-6841	420	18	0	0	NUM
ejpam-6841	420	19	,	,	PUNCT
ejpam-6841	420	20	so	so	SCONJ
ejpam-6841	420	21	we	we	PRON
ejpam-6841	420	22	get	get	VERB
ejpam-6841	420	23	j	j	PROPN
ejpam-6841	420	24	(	(	PUNCT
ejpam-6841	420	25	θn	θn	NOUN
ejpam-6841	420	26	)	)	PUNCT
ejpam-6841	420	27	<	<	X
ejpam-6841	420	28	j	j	PROPN
ejpam-6841	420	29	(	(	PUNCT
ejpam-6841	420	30	(	(	PUNCT
ejpam-6841	420	31	θn−1	θn−1	PROPN
ejpam-6841	420	32	)	)	PUNCT
ejpam-6841	420	33	α+β	α+β	PROPN
ejpam-6841	420	34	(	(	PUNCT
ejpam-6841	420	35	θn	θn	NOUN
ejpam-6841	420	36	)	)	PUNCT
ejpam-6841	420	37	γ	γ	NOUN
ejpam-6841	420	38	(	(	PUNCT
ejpam-6841	420	39	1	1	NUM
ejpam-6841	420	40	2	2	NUM
ejpam-6841	420	41	(	(	PUNCT
ejpam-6841	420	42	θn	θn	NOUN
ejpam-6841	420	43	+	+	X
ejpam-6841	420	44	θn−1	θn−1	PROPN
ejpam-6841	420	45	)	)	PUNCT
ejpam-6841	420	46	)	)	PUNCT
ejpam-6841	420	47	1−α−β−γ	1−α−β−γ	NUM
ejpam-6841	420	48	)	)	PUNCT
ejpam-6841	420	49	.	.	PUNCT
ejpam-6841	421	1	(	(	PUNCT
ejpam-6841	421	2	22	22	X
ejpam-6841	421	3	)	)	PUNCT
ejpam-6841	421	4	assume	assume	VERB
ejpam-6841	421	5	that	that	SCONJ
ejpam-6841	421	6	for	for	ADP
ejpam-6841	421	7	some	some	DET
ejpam-6841	421	8	n	n	PRON
ejpam-6841	421	9	≥	≥	NOUN
ejpam-6841	421	10	1	1	NUM
ejpam-6841	421	11	,	,	PUNCT
ejpam-6841	421	12	θn−1	θn−1	PROPN
ejpam-6841	421	13	<	<	X
ejpam-6841	421	14	θn	θn	NOUN
ejpam-6841	421	15	.	.	PROPN
ejpam-6841	421	16	according	accord	VERB
ejpam-6841	421	17	to	to	ADP
ejpam-6841	421	18	(	(	PUNCT
ejpam-6841	421	19	22	22	NUM
ejpam-6841	421	20	)	)	PUNCT
ejpam-6841	421	21	,	,	PUNCT
ejpam-6841	421	22	we	we	PRON
ejpam-6841	421	23	have	have	VERB
ejpam-6841	421	24	(	(	PUNCT
ejpam-6841	421	25	θn	θn	NOUN
ejpam-6841	421	26	)	)	PUNCT
ejpam-6841	421	27	α+β	α+β	PROPN
ejpam-6841	421	28	<	<	X
ejpam-6841	421	29	(	(	PUNCT
ejpam-6841	421	30	θn	θn	NOUN
ejpam-6841	421	31	)	)	PUNCT
ejpam-6841	421	32	α+β	α+β	PROPN
ejpam-6841	421	33	since	since	SCONJ
ejpam-6841	421	34	j	j	PROPN
ejpam-6841	421	35	is	be	AUX
ejpam-6841	421	36	nondecreasing	nondecrease	VERB
ejpam-6841	421	37	.	.	PUNCT
ejpam-6841	422	1	as	as	ADP
ejpam-6841	422	2	a	a	DET
ejpam-6841	422	3	result	result	NOUN
ejpam-6841	422	4	,	,	PUNCT
ejpam-6841	422	5	for	for	ADP
ejpam-6841	422	6	every	every	DET
ejpam-6841	422	7	n	n	PRON
ejpam-6841	422	8	∈	∈	PROPN
ejpam-6841	422	9	n	n	CCONJ
ejpam-6841	422	10	,	,	PUNCT
ejpam-6841	422	11	we	we	PRON
ejpam-6841	422	12	obtain	obtain	VERB
ejpam-6841	422	13	θn	θn	ADP
ejpam-6841	422	14	<	<	X
ejpam-6841	422	15	θn−1	θn−1	PROPN
ejpam-6841	422	16	.	.	PUNCT
ejpam-6841	423	1	this	this	PRON
ejpam-6841	423	2	indicates	indicate	VERB
ejpam-6841	423	3	a	a	DET
ejpam-6841	423	4	strictly	strictly	ADV
ejpam-6841	423	5	decreasing	decrease	VERB
ejpam-6841	423	6	sequence	sequence	NOUN
ejpam-6841	423	7	{	{	PUNCT
ejpam-6841	423	8	θn	θn	NOUN
ejpam-6841	423	9	}	}	PUNCT
ejpam-6841	423	10	.	.	PUNCT
ejpam-6841	424	1	as	as	ADP
ejpam-6841	424	2	a	a	DET
ejpam-6841	424	3	result	result	NOUN
ejpam-6841	424	4	,	,	PUNCT
ejpam-6841	424	5	it	it	PRON
ejpam-6841	424	6	approaches	approach	VERB
ejpam-6841	424	7	an	an	DET
ejpam-6841	424	8	element	element	NOUN
ejpam-6841	424	9	θ	θ	PROPN
ejpam-6841	424	10	≥	≥	NOUN
ejpam-6841	424	11	0	0	NUM
ejpam-6841	424	12	.	.	PUNCT
ejpam-6841	425	1	consequently	consequently	ADV
ejpam-6841	425	2	,	,	PUNCT
ejpam-6841	425	3	θ	θ	PROPN
ejpam-6841	425	4	=	=	SYM
ejpam-6841	425	5	0	0	NUM
ejpam-6841	425	6	,	,	PUNCT
ejpam-6841	425	7	in	in	ADP
ejpam-6841	425	8	case	case	NOUN
ejpam-6841	425	9	θ	θ	X
ejpam-6841	425	10	>	>	X
ejpam-6841	425	11	0	0	NUM
ejpam-6841	425	12	,	,	PUNCT
ejpam-6841	425	13	we	we	PRON
ejpam-6841	425	14	can	can	AUX
ejpam-6841	425	15	derive	derive	VERB
ejpam-6841	425	16	the	the	DET
ejpam-6841	425	17	following	following	NOUN
ejpam-6841	425	18	via	via	ADP
ejpam-6841	425	19	(	(	PUNCT
ejpam-6841	425	20	22	22	NUM
ejpam-6841	425	21	):	):	PUNCT
ejpam-6841	425	22	j(θ+	j(θ+	NOUN
ejpam-6841	425	23	)	)	PUNCT
ejpam-6841	426	1	=	=	SYM
ejpam-6841	426	2	lim	lim	PROPN
ejpam-6841	426	3	n→∞	n→∞	X
ejpam-6841	426	4	j	j	PROPN
ejpam-6841	426	5	(	(	PUNCT
ejpam-6841	426	6	θn	θn	NOUN
ejpam-6841	426	7	)	)	PUNCT
ejpam-6841	426	8	≤	≤	NOUN
ejpam-6841	426	9	lim	lim	PROPN
ejpam-6841	426	10	n→∞	n→∞	PRON
ejpam-6841	426	11	£	£	PROPN
ejpam-6841	426	12	(	(	PUNCT
ejpam-6841	426	13	(	(	PUNCT
ejpam-6841	426	14	θn−1	θn−1	PROPN
ejpam-6841	426	15	)	)	PUNCT
ejpam-6841	426	16	α+β	α+β	PROPN
ejpam-6841	426	17	(	(	PUNCT
ejpam-6841	426	18	θn	θn	NOUN
ejpam-6841	426	19	)	)	PUNCT
ejpam-6841	426	20	γ	γ	NOUN
ejpam-6841	426	21	(	(	PUNCT
ejpam-6841	426	22	1	1	NUM
ejpam-6841	426	23	2	2	NUM
ejpam-6841	426	24	(	(	PUNCT
ejpam-6841	426	25	θn	θn	NOUN
ejpam-6841	426	26	+	+	X
ejpam-6841	426	27	θn−1	θn−1	PROPN
ejpam-6841	426	28	)	)	PUNCT
ejpam-6841	426	29	)	)	PUNCT
ejpam-6841	426	30	1−α−β−γ	1−α−β−γ	X
ejpam-6841	426	31	)	)	PUNCT
ejpam-6841	426	32	≤	≤	PROPN
ejpam-6841	426	33	lim	lim	PROPN
ejpam-6841	426	34	t→θ+	t→θ+	PROPN
ejpam-6841	426	35	b(t	b(t	PROPN
ejpam-6841	426	36	)	)	PUNCT
ejpam-6841	426	37	this	this	PRON
ejpam-6841	426	38	contradicts	contradict	VERB
ejpam-6841	426	39	(	(	PUNCT
ejpam-6841	426	40	i	i	NOUN
ejpam-6841	426	41	)	)	PUNCT
ejpam-6841	426	42	,	,	PUNCT
ejpam-6841	426	43	hence	hence	ADV
ejpam-6841	426	44	,	,	PUNCT
ejpam-6841	426	45	θ	θ	PROPN
ejpam-6841	426	46	=	=	SYM
ejpam-6841	426	47	0	0	NUM
ejpam-6841	426	48	and	and	CCONJ
ejpam-6841	426	49	limn→∞	limn→∞	PRON
ejpam-6841	426	50	ϑ(bn	ϑ(bn	NOUN
ejpam-6841	426	51	,	,	PUNCT
ejpam-6841	426	52	bn+1	bn+1	NUM
ejpam-6841	426	53	)	)	PUNCT
ejpam-6841	426	54	=	=	SYM
ejpam-6841	427	1	0	0	X
ejpam-6841	427	2	.	.	PUNCT
ejpam-6841	428	1	now	now	ADV
ejpam-6841	428	2	,	,	PUNCT
ejpam-6841	428	3	(	(	PUNCT
ejpam-6841	428	4	i	i	NOUN
ejpam-6841	428	5	)	)	PUNCT
ejpam-6841	428	6	and	and	CCONJ
ejpam-6841	428	7	lemma	lemma	PROPN
ejpam-6841	428	8	3	3	NUM
ejpam-6841	428	9	,	,	PUNCT
ejpam-6841	428	10	we	we	PRON
ejpam-6841	428	11	conclude	conclude	VERB
ejpam-6841	428	12	that	that	SCONJ
ejpam-6841	428	13	{	{	PUNCT
ejpam-6841	428	14	bn	bn	NOUN
ejpam-6841	428	15	}	}	PUNCT
ejpam-6841	428	16	is	be	AUX
ejpam-6841	428	17	a	a	DET
ejpam-6841	428	18	cauchy	cauchy	ADJ
ejpam-6841	428	19	sequence	sequence	NOUN
ejpam-6841	428	20	.	.	PUNCT
ejpam-6841	429	1	since	since	SCONJ
ejpam-6841	429	2	(	(	PUNCT
ejpam-6841	429	3	w	w	PROPN
ejpam-6841	429	4	,	,	PUNCT
ejpam-6841	429	5	ϑ	ϑ	NOUN
ejpam-6841	429	6	)	)	PUNCT
ejpam-6841	429	7	is	be	AUX
ejpam-6841	429	8	a	a	DET
ejpam-6841	429	9	complete	complete	ADJ
ejpam-6841	429	10	metric	metric	ADJ
ejpam-6841	429	11	space	space	NOUN
ejpam-6841	429	12	and	and	CCONJ
ejpam-6841	429	13	c	c	NOUN
ejpam-6841	429	14	is	be	AUX
ejpam-6841	429	15	a	a	DET
ejpam-6841	429	16	closed	closed	ADJ
ejpam-6841	429	17	subset	subset	NOUN
ejpam-6841	429	18	of	of	ADP
ejpam-6841	429	19	w	w	PROPN
ejpam-6841	429	20	,	,	PUNCT
ejpam-6841	429	21	so	so	ADV
ejpam-6841	429	22	,	,	PUNCT
ejpam-6841	429	23	there	there	PRON
ejpam-6841	429	24	exists	exist	VERB
ejpam-6841	429	25	b∗	b∗	ADJ
ejpam-6841	429	26	∈	∈	PROPN
ejpam-6841	429	27	c	c	NOUN
ejpam-6841	429	28	,	,	PUNCT
ejpam-6841	429	29	such	such	ADJ
ejpam-6841	429	30	that	that	SCONJ
ejpam-6841	429	31	limn→∞	limn→∞	PROPN
ejpam-6841	429	32	ϑ	ϑ	X
ejpam-6841	429	33	(	(	PUNCT
ejpam-6841	429	34	bn	bn	PROPN
ejpam-6841	429	35	,	,	PUNCT
ejpam-6841	429	36	b	b	NOUN
ejpam-6841	429	37	∗	∗	NOUN
ejpam-6841	429	38	)	)	PUNCT
ejpam-6841	430	1	=	=	SYM
ejpam-6841	430	2	0	0	X
ejpam-6841	430	3	.	.	PUNCT
ejpam-6841	431	1	moreover	moreover	ADV
ejpam-6841	431	2	,	,	PUNCT
ejpam-6841	431	3	ϑ(b∗,p	ϑ(b∗,p	PROPN
ejpam-6841	431	4	(	(	PUNCT
ejpam-6841	431	5	bn	bn	NOUN
ejpam-6841	431	6	)	)	PUNCT
ejpam-6841	431	7	)	)	PUNCT
ejpam-6841	431	8	≤	≤	PROPN
ejpam-6841	431	9	ϑ(b∗	ϑ(b∗	X
ejpam-6841	431	10	,	,	PUNCT
ejpam-6841	431	11	bn+1	bn+1	NUM
ejpam-6841	431	12	)	)	PUNCT
ejpam-6841	431	13	+	+	CCONJ
ejpam-6841	431	14	ϑ(bn+1,p(bn	ϑ(bn+1,p(bn	NOUN
ejpam-6841	431	15	)	)	PUNCT
ejpam-6841	431	16	)	)	PUNCT
ejpam-6841	431	17	≤	≤	PROPN
ejpam-6841	431	18	ϑ(b∗	ϑ(b∗	X
ejpam-6841	431	19	,	,	PUNCT
ejpam-6841	431	20	bn+1	bn+1	NUM
ejpam-6841	431	21	)	)	PUNCT
ejpam-6841	432	1	+	+	CCONJ
ejpam-6841	432	2	ϑ(c	ϑ(c	PROPN
ejpam-6841	432	3	,	,	PUNCT
ejpam-6841	432	4	d	d	NOUN
ejpam-6841	432	5	)	)	PUNCT
ejpam-6841	432	6	≤	≤	PROPN
ejpam-6841	432	7	ϑ(b∗	ϑ(b∗	X
ejpam-6841	432	8	,	,	PUNCT
ejpam-6841	432	9	bn+1	bn+1	NUM
ejpam-6841	432	10	)	)	PUNCT
ejpam-6841	432	11	+	+	CCONJ
ejpam-6841	432	12	ϑ(b∗,d	ϑ(b∗,d	NUM
ejpam-6841	432	13	)	)	PUNCT
ejpam-6841	432	14	.	.	PUNCT
ejpam-6841	433	1	thus	thus	ADV
ejpam-6841	433	2	,	,	PUNCT
ejpam-6841	433	3	ϑ(b∗,p(bn	ϑ(b∗,p(bn	PROPN
ejpam-6841	433	4	)	)	PUNCT
ejpam-6841	433	5	)	)	PUNCT
ejpam-6841	434	1	→	→	SYM
ejpam-6841	434	2	ϑ(b∗,d	ϑ(b∗,d	NUM
ejpam-6841	434	3	)	)	PUNCT
ejpam-6841	434	4	as	as	ADP
ejpam-6841	434	5	n	n	PROPN
ejpam-6841	434	6	→	→	SYM
ejpam-6841	434	7	∞.	∞.	PROPN
ejpam-6841	434	8	since	since	SCONJ
ejpam-6841	434	9	d	d	PROPN
ejpam-6841	434	10	is	be	AUX
ejpam-6841	434	11	approximately	approximately	ADV
ejpam-6841	434	12	compact	compact	ADJ
ejpam-6841	434	13	with	with	ADP
ejpam-6841	434	14	respect	respect	NOUN
ejpam-6841	434	15	to	to	ADP
ejpam-6841	434	16	c	c	NOUN
ejpam-6841	434	17	,	,	PUNCT
ejpam-6841	434	18	there	there	PRON
ejpam-6841	434	19	exists	exist	VERB
ejpam-6841	434	20	a	a	DET
ejpam-6841	434	21	subsequence	subsequence	NOUN
ejpam-6841	434	22	{	{	PUNCT
ejpam-6841	434	23	p(bnk	p(bnk	NOUN
ejpam-6841	434	24	)	)	PUNCT
ejpam-6841	434	25	}	}	PUNCT
ejpam-6841	434	26	of	of	ADP
ejpam-6841	434	27	{	{	PUNCT
ejpam-6841	434	28	p(bn	p(bn	NOUN
ejpam-6841	434	29	)	)	PUNCT
ejpam-6841	434	30	}	}	PUNCT
ejpam-6841	434	31	such	such	ADJ
ejpam-6841	434	32	that	that	SCONJ
ejpam-6841	434	33	p(bnk	p(bnk	NOUN
ejpam-6841	434	34	)	)	PUNCT
ejpam-6841	434	35	→	→	SYM
ejpam-6841	434	36	m∗	m∗	VERB
ejpam-6841	434	37	∈	∈	PROPN
ejpam-6841	434	38	d	d	NOUN
ejpam-6841	434	39	as	as	SCONJ
ejpam-6841	434	40	k	k	PROPN
ejpam-6841	434	41	→	→	SYM
ejpam-6841	434	42	∞.	∞.	PROPN
ejpam-6841	434	43	letting	let	VERB
ejpam-6841	434	44	k	k	X
ejpam-6841	434	45	→	→	SYM
ejpam-6841	434	46	∞	∞	PROPN
ejpam-6841	434	47	in	in	ADP
ejpam-6841	434	48	the	the	DET
ejpam-6841	434	49	following	follow	VERB
ejpam-6841	434	50	equation	equation	NOUN
ejpam-6841	434	51	:	:	PUNCT
ejpam-6841	434	52	ϑ(bnk+1	ϑ(bnk+1	NOUN
ejpam-6841	434	53	,	,	PUNCT
ejpam-6841	434	54	p(bnk	p(bnk	NOUN
ejpam-6841	434	55	)	)	PUNCT
ejpam-6841	434	56	)	)	PUNCT
ejpam-6841	435	1	=	=	PUNCT
ejpam-6841	435	2	ϑ(c	ϑ(c	PROPN
ejpam-6841	435	3	,	,	PUNCT
ejpam-6841	435	4	d	d	NOUN
ejpam-6841	435	5	)	)	PUNCT
ejpam-6841	435	6	,	,	PUNCT
ejpam-6841	435	7	(	(	PUNCT
ejpam-6841	435	8	23	23	NUM
ejpam-6841	435	9	)	)	PUNCT
ejpam-6841	435	10	we	we	PRON
ejpam-6841	435	11	have	have	VERB
ejpam-6841	435	12	,	,	PUNCT
ejpam-6841	435	13	ϑ(b∗,m∗	ϑ(b∗,m∗	PROPN
ejpam-6841	435	14	)	)	PUNCT
ejpam-6841	435	15	=	=	PUNCT
ejpam-6841	435	16	ϑ(c	ϑ(c	NOUN
ejpam-6841	435	17	,	,	PUNCT
ejpam-6841	435	18	d	d	NOUN
ejpam-6841	435	19	)	)	PUNCT
ejpam-6841	435	20	.	.	PUNCT
ejpam-6841	436	1	since	since	SCONJ
ejpam-6841	436	2	,	,	PUNCT
ejpam-6841	436	3	b∗	b∗	PROPN
ejpam-6841	436	4	∈	∈	PROPN
ejpam-6841	436	5	c0	c0	NOUN
ejpam-6841	436	6	,	,	PUNCT
ejpam-6841	436	7	so	so	ADV
ejpam-6841	436	8	p(b∗	p(b∗	NOUN
ejpam-6841	436	9	)	)	PUNCT
ejpam-6841	436	10	∈	∈	PROPN
ejpam-6841	436	11	p(c0	p(c0	NOUN
ejpam-6841	436	12	)	)	PUNCT
ejpam-6841	436	13	⊆	⊆	NUM
ejpam-6841	436	14	d0	d0	NOUN
ejpam-6841	436	15	,	,	PUNCT
ejpam-6841	436	16	there	there	PRON
ejpam-6841	436	17	exists	exist	VERB
ejpam-6841	436	18	p	p	PROPN
ejpam-6841	436	19	∈	∈	PROPN
ejpam-6841	436	20	c0	c0	NOUN
ejpam-6841	436	21	such	such	ADJ
ejpam-6841	436	22	that	that	PRON
ejpam-6841	436	23	ϑ(p	ϑ(p	PROPN
ejpam-6841	436	24	,	,	PUNCT
ejpam-6841	436	25	p(b∗	p(b∗	NOUN
ejpam-6841	436	26	)	)	PUNCT
ejpam-6841	436	27	)	)	PUNCT
ejpam-6841	437	1	=	=	PUNCT
ejpam-6841	437	2	ϑ(c	ϑ(c	PROPN
ejpam-6841	437	3	,	,	PUNCT
ejpam-6841	437	4	d	d	NOUN
ejpam-6841	437	5	)	)	PUNCT
ejpam-6841	437	6	.	.	PUNCT
ejpam-6841	438	1	(	(	PUNCT
ejpam-6841	438	2	24	24	NUM
ejpam-6841	438	3	)	)	PUNCT
ejpam-6841	438	4	now	now	ADV
ejpam-6841	438	5	,	,	PUNCT
ejpam-6841	438	6	using	use	VERB
ejpam-6841	438	7	(	(	PUNCT
ejpam-6841	438	8	20	20	NUM
ejpam-6841	438	9	)	)	PUNCT
ejpam-6841	438	10	in	in	ADP
ejpam-6841	438	11	association	association	NOUN
ejpam-6841	438	12	with	with	ADP
ejpam-6841	438	13	(	(	PUNCT
ejpam-6841	438	14	21	21	NUM
ejpam-6841	438	15	)	)	PUNCT
ejpam-6841	438	16	and	and	CCONJ
ejpam-6841	438	17	(	(	PUNCT
ejpam-6841	438	18	22	22	NUM
ejpam-6841	438	19	)	)	PUNCT
ejpam-6841	438	20	,	,	PUNCT
ejpam-6841	438	21	for	for	ADP
ejpam-6841	438	22	all	all	DET
ejpam-6841	438	23	k	k	PROPN
ejpam-6841	438	24	∈	∈	PROPN
ejpam-6841	438	25	n	n	CCONJ
ejpam-6841	438	26	,	,	PUNCT
ejpam-6841	438	27	we	we	PRON
ejpam-6841	438	28	have	have	VERB
ejpam-6841	438	29	j	j	PROPN
ejpam-6841	438	30	(	(	PUNCT
ejpam-6841	438	31	ϑ	ϑ	X
ejpam-6841	438	32	(	(	PUNCT
ejpam-6841	438	33	bnk+1	bnk+1	NOUN
ejpam-6841	438	34	,	,	PUNCT
ejpam-6841	438	35	p	p	NOUN
ejpam-6841	438	36	)	)	PUNCT
ejpam-6841	438	37	)	)	PUNCT
ejpam-6841	439	1	≤	≤	NUM
ejpam-6841	439	2	£	£	NOUN
ejpam-6841	439	3	(	(	PUNCT
ejpam-6841	439	4	(	(	PUNCT
ejpam-6841	439	5	ϑ	ϑ	X
ejpam-6841	439	6	(	(	PUNCT
ejpam-6841	439	7	bnk	bnk	PROPN
ejpam-6841	439	8	,	,	PUNCT
ejpam-6841	439	9	b∗))α	b∗))α	PROPN
ejpam-6841	439	10	(	(	PUNCT
ejpam-6841	439	11	ϑ	ϑ	X
ejpam-6841	439	12	(	(	PUNCT
ejpam-6841	439	13	bnk	bnk	NOUN
ejpam-6841	439	14	,	,	PUNCT
ejpam-6841	439	15	bnk+1	bnk+1	NOUN
ejpam-6841	439	16	)	)	PUNCT
ejpam-6841	439	17	)	)	PUNCT
ejpam-6841	440	1	β	β	X
ejpam-6841	440	2	(	(	PUNCT
ejpam-6841	440	3	ϑ	ϑ	X
ejpam-6841	440	4	(	(	PUNCT
ejpam-6841	440	5	b∗	b∗	ADJ
ejpam-6841	440	6	,	,	PUNCT
ejpam-6841	440	7	p))γ	p))γ	PROPN
ejpam-6841	440	8	(	(	PUNCT
ejpam-6841	440	9	1	1	NUM
ejpam-6841	440	10	2	2	NUM
ejpam-6841	440	11	(	(	PUNCT
ejpam-6841	440	12	ϑ	ϑ	X
ejpam-6841	440	13	(	(	PUNCT
ejpam-6841	440	14	bnk	bnk	PROPN
ejpam-6841	440	15	,	,	PUNCT
ejpam-6841	440	16	p	p	NOUN
ejpam-6841	440	17	)	)	PUNCT
ejpam-6841	441	1	+	+	CCONJ
ejpam-6841	441	2	ϑ	ϑ	X
ejpam-6841	441	3	(	(	PUNCT
ejpam-6841	441	4	b∗	b∗	ADJ
ejpam-6841	441	5	,	,	PUNCT
ejpam-6841	441	6	bnk+1	bnk+1	NOUN
ejpam-6841	441	7	)	)	PUNCT
ejpam-6841	441	8	)	)	PUNCT
ejpam-6841	441	9	)	)	PUNCT
ejpam-6841	442	1	1−α−β−γ	1−α−β−γ	NUM
ejpam-6841	442	2	)	)	PUNCT
ejpam-6841	443	1	<	<	X
ejpam-6841	443	2	j	j	PROPN
ejpam-6841	443	3	(	(	PUNCT
ejpam-6841	443	4	(	(	PUNCT
ejpam-6841	443	5	ϑ	ϑ	X
ejpam-6841	443	6	(	(	PUNCT
ejpam-6841	443	7	bnk	bnk	PROPN
ejpam-6841	443	8	,	,	PUNCT
ejpam-6841	443	9	b∗))α	b∗))α	PROPN
ejpam-6841	443	10	(	(	PUNCT
ejpam-6841	443	11	ϑ	ϑ	X
ejpam-6841	443	12	(	(	PUNCT
ejpam-6841	443	13	bnk	bnk	NOUN
ejpam-6841	443	14	,	,	PUNCT
ejpam-6841	443	15	bnk+1	bnk+1	NOUN
ejpam-6841	443	16	)	)	PUNCT
ejpam-6841	443	17	)	)	PUNCT
ejpam-6841	444	1	β	β	X
ejpam-6841	444	2	(	(	PUNCT
ejpam-6841	444	3	ϑ	ϑ	X
ejpam-6841	444	4	(	(	PUNCT
ejpam-6841	444	5	b∗	b∗	ADJ
ejpam-6841	444	6	,	,	PUNCT
ejpam-6841	444	7	p))γ	p))γ	PROPN
ejpam-6841	444	8	(	(	PUNCT
ejpam-6841	444	9	1	1	NUM
ejpam-6841	444	10	2	2	NUM
ejpam-6841	444	11	(	(	PUNCT
ejpam-6841	444	12	ϑ	ϑ	X
ejpam-6841	444	13	(	(	PUNCT
ejpam-6841	444	14	bnk	bnk	PROPN
ejpam-6841	444	15	,	,	PUNCT
ejpam-6841	444	16	p	p	NOUN
ejpam-6841	444	17	)	)	PUNCT
ejpam-6841	445	1	+	+	CCONJ
ejpam-6841	445	2	ϑ	ϑ	X
ejpam-6841	445	3	(	(	PUNCT
ejpam-6841	445	4	b∗	b∗	ADJ
ejpam-6841	445	5	,	,	PUNCT
ejpam-6841	445	6	bnk+1	bnk+1	NOUN
ejpam-6841	445	7	)	)	PUNCT
ejpam-6841	445	8	)	)	PUNCT
ejpam-6841	445	9	)	)	PUNCT
ejpam-6841	446	1	1−α−β−γ	1−α−β−γ	NUM
ejpam-6841	446	2	)	)	PUNCT
ejpam-6841	446	3	.	.	PUNCT
ejpam-6841	447	1	by	by	ADP
ejpam-6841	447	2	using	use	VERB
ejpam-6841	447	3	the	the	DET
ejpam-6841	447	4	monotonicity	monotonicity	NOUN
ejpam-6841	447	5	of	of	ADP
ejpam-6841	447	6	j	j	PROPN
ejpam-6841	447	7	,	,	PUNCT
ejpam-6841	447	8	for	for	ADP
ejpam-6841	447	9	all	all	DET
ejpam-6841	447	10	k	k	PROPN
ejpam-6841	447	11	∈	∈	PROPN
ejpam-6841	447	12	n	n	CCONJ
ejpam-6841	447	13	,	,	PUNCT
ejpam-6841	447	14	we	we	PRON
ejpam-6841	447	15	have	have	VERB
ejpam-6841	447	16	ϑ	ϑ	X
ejpam-6841	447	17	(	(	PUNCT
ejpam-6841	447	18	bnk+1	bnk+1	NOUN
ejpam-6841	447	19	,	,	PUNCT
ejpam-6841	447	20	p	p	NOUN
ejpam-6841	447	21	)	)	PUNCT
ejpam-6841	447	22	≤	≤	NOUN
ejpam-6841	447	23	(	(	PUNCT
ejpam-6841	447	24	ϑ	ϑ	X
ejpam-6841	447	25	(	(	PUNCT
ejpam-6841	447	26	bnk	bnk	PROPN
ejpam-6841	447	27	,	,	PUNCT
ejpam-6841	447	28	b∗))α	b∗))α	PROPN
ejpam-6841	447	29	(	(	PUNCT
ejpam-6841	447	30	ϑ	ϑ	X
ejpam-6841	447	31	(	(	PUNCT
ejpam-6841	447	32	bnk	bnk	NOUN
ejpam-6841	447	33	,	,	PUNCT
ejpam-6841	447	34	bnk+1	bnk+1	NOUN
ejpam-6841	447	35	)	)	PUNCT
ejpam-6841	447	36	)	)	PUNCT
ejpam-6841	448	1	β	β	X
ejpam-6841	448	2	(	(	PUNCT
ejpam-6841	448	3	ϑ	ϑ	X
ejpam-6841	448	4	(	(	PUNCT
ejpam-6841	448	5	b∗	b∗	ADJ
ejpam-6841	448	6	,	,	PUNCT
ejpam-6841	448	7	p))γ	p))γ	PROPN
ejpam-6841	448	8	(	(	PUNCT
ejpam-6841	448	9	1	1	NUM
ejpam-6841	448	10	2	2	NUM
ejpam-6841	448	11	(	(	PUNCT
ejpam-6841	448	12	ϑ	ϑ	X
ejpam-6841	448	13	(	(	PUNCT
ejpam-6841	448	14	bnk	bnk	PROPN
ejpam-6841	448	15	,	,	PUNCT
ejpam-6841	448	16	p	p	NOUN
ejpam-6841	448	17	)	)	PUNCT
ejpam-6841	449	1	+	+	CCONJ
ejpam-6841	449	2	ϑ	ϑ	X
ejpam-6841	449	3	(	(	PUNCT
ejpam-6841	449	4	b∗	b∗	ADJ
ejpam-6841	449	5	,	,	PUNCT
ejpam-6841	449	6	bnk+1	bnk+1	NOUN
ejpam-6841	449	7	)	)	PUNCT
ejpam-6841	449	8	)	)	PUNCT
ejpam-6841	449	9	)	)	PUNCT
ejpam-6841	450	1	1−α−β−γ	1−α−β−γ	PROPN
ejpam-6841	450	2	.	.	PUNCT
ejpam-6841	451	1	k.	k.	PROPN
ejpam-6841	451	2	javed	javed	PROPN
ejpam-6841	451	3	,	,	PUNCT
ejpam-6841	451	4	m.	m.	NOUN
ejpam-6841	451	5	nazam	nazam	PROPN
ejpam-6841	451	6	,	,	PUNCT
ejpam-6841	451	7	m.	m.	PROPN
ejpam-6841	451	8	arshad	arshad	PROPN
ejpam-6841	451	9	,	,	PUNCT
ejpam-6841	451	10	m.	m.	NOUN
ejpam-6841	451	11	de	de	X
ejpam-6841	451	12	la	la	PROPN
ejpam-6841	451	13	sen	sen	PROPN
ejpam-6841	451	14	/	/	SYM
ejpam-6841	451	15	eur	eur	PROPN
ejpam-6841	451	16	.	.	PUNCT
ejpam-6841	452	1	j.	j.	PROPN
ejpam-6841	452	2	pure	pure	PROPN
ejpam-6841	452	3	appl	appl	PROPN
ejpam-6841	452	4	.	.	PROPN
ejpam-6841	452	5	math	math	PROPN
ejpam-6841	452	6	,	,	PUNCT
ejpam-6841	452	7	18	18	NUM
ejpam-6841	452	8	(	(	PUNCT
ejpam-6841	452	9	4	4	NUM
ejpam-6841	452	10	)	)	PUNCT
ejpam-6841	452	11	(	(	PUNCT
ejpam-6841	452	12	2025	2025	NUM
ejpam-6841	452	13	)	)	PUNCT
ejpam-6841	452	14	,	,	PUNCT
ejpam-6841	452	15	6841	6841	NUM
ejpam-6841	452	16	19	19	NUM
ejpam-6841	452	17	of	of	ADP
ejpam-6841	452	18	23	23	NUM
ejpam-6841	452	19	thus	thus	ADV
ejpam-6841	452	20	,	,	PUNCT
ejpam-6841	452	21	as	as	ADP
ejpam-6841	452	22	k	k	PROPN
ejpam-6841	452	23	→	→	SYM
ejpam-6841	452	24	∞	∞	PROPN
ejpam-6841	452	25	,	,	PUNCT
ejpam-6841	452	26	b∗	b∗	PROPN
ejpam-6841	452	27	=	=	SYM
ejpam-6841	453	1	p.	p.	NOUN
ejpam-6841	453	2	finally	finally	ADV
ejpam-6841	453	3	,	,	PUNCT
ejpam-6841	453	4	by	by	ADP
ejpam-6841	453	5	(	(	PUNCT
ejpam-6841	453	6	24	24	NUM
ejpam-6841	453	7	)	)	PUNCT
ejpam-6841	453	8	we	we	PRON
ejpam-6841	453	9	have	have	VERB
ejpam-6841	453	10	ϑ	ϑ	X
ejpam-6841	453	11	(	(	PUNCT
ejpam-6841	453	12	b∗,p	b∗,p	X
ejpam-6841	453	13	(	(	PUNCT
ejpam-6841	453	14	b∗	b∗	ADJ
ejpam-6841	453	15	)	)	PUNCT
ejpam-6841	453	16	)	)	PUNCT
ejpam-6841	454	1	=	=	SYM
ejpam-6841	454	2	ϑ	ϑ	X
ejpam-6841	454	3	(	(	PUNCT
ejpam-6841	454	4	c	c	X
ejpam-6841	454	5	,	,	PUNCT
ejpam-6841	454	6	d	d	NOUN
ejpam-6841	454	7	)	)	PUNCT
ejpam-6841	454	8	.	.	PUNCT
ejpam-6841	455	1	hence	hence	ADV
ejpam-6841	455	2	,	,	PUNCT
ejpam-6841	455	3	b∗	b∗	ADV
ejpam-6841	455	4	is	be	AUX
ejpam-6841	455	5	a	a	DET
ejpam-6841	455	6	best	good	ADJ
ejpam-6841	455	7	proximity	proximity	NOUN
ejpam-6841	455	8	point	point	NOUN
ejpam-6841	455	9	of	of	ADP
ejpam-6841	455	10	the	the	DET
ejpam-6841	455	11	mapping	mapping	NOUN
ejpam-6841	455	12	p.	p.	NOUN
ejpam-6841	455	13	theorem	theorem	NOUN
ejpam-6841	455	14	6	6	NUM
ejpam-6841	455	15	.	.	PUNCT
ejpam-6841	456	1	let	let	AUX
ejpam-6841	456	2	(	(	PUNCT
ejpam-6841	456	3	w	w	NOUN
ejpam-6841	456	4	,	,	PUNCT
ejpam-6841	456	5	ϑ	ϑ	NOUN
ejpam-6841	456	6	)	)	PUNCT
ejpam-6841	456	7	be	be	AUX
ejpam-6841	456	8	a	a	DET
ejpam-6841	456	9	complete	complete	ADJ
ejpam-6841	456	10	metric	metric	ADJ
ejpam-6841	456	11	space	space	NOUN
ejpam-6841	456	12	and	and	CCONJ
ejpam-6841	456	13	c	c	NOUN
ejpam-6841	456	14	,	,	PUNCT
ejpam-6841	456	15	d	d	NOUN
ejpam-6841	456	16	be	be	AUX
ejpam-6841	456	17	nonvoid	nonvoid	ADJ
ejpam-6841	456	18	,	,	PUNCT
ejpam-6841	456	19	closed	closed	ADJ
ejpam-6841	456	20	subsets	subset	NOUN
ejpam-6841	456	21	of	of	ADP
ejpam-6841	456	22	w	w	ADP
ejpam-6841	456	23	such	such	ADJ
ejpam-6841	456	24	that	that	SCONJ
ejpam-6841	456	25	d	d	NOUN
ejpam-6841	456	26	is	be	AUX
ejpam-6841	456	27	approximately	approximately	ADV
ejpam-6841	456	28	compact	compact	ADJ
ejpam-6841	456	29	with	with	ADP
ejpam-6841	456	30	respect	respect	NOUN
ejpam-6841	456	31	to	to	ADP
ejpam-6841	456	32	c.	c.	NOUN
ejpam-6841	456	33	let	let	VERB
ejpam-6841	456	34	p	p	NOUN
ejpam-6841	456	35	:	:	PUNCT
ejpam-6841	456	36	c	c	X
ejpam-6841	456	37	→	→	PUNCT
ejpam-6841	456	38	d	d	X
ejpam-6841	456	39	be	be	AUX
ejpam-6841	456	40	an	an	DET
ejpam-6841	456	41	(	(	PUNCT
ejpam-6841	456	42	j,£)-interpolative	j,£)-interpolative	ADJ
ejpam-6841	456	43	hardy	hardy	ADJ
ejpam-6841	456	44	rogers	roger	NOUN
ejpam-6841	456	45	type	type	VERB
ejpam-6841	456	46	proximal	proximal	ADJ
ejpam-6841	456	47	contraction	contraction	NOUN
ejpam-6841	456	48	.	.	PUNCT
ejpam-6841	457	1	if	if	SCONJ
ejpam-6841	457	2	(	(	PUNCT
ejpam-6841	457	3	i	i	NOUN
ejpam-6841	457	4	)	)	PUNCT
ejpam-6841	457	5	j	j	PROPN
ejpam-6841	457	6	is	be	AUX
ejpam-6841	457	7	non	non	ADJ
ejpam-6841	457	8	-	-	ADJ
ejpam-6841	457	9	decreasing	decrease	VERB
ejpam-6841	457	10	and	and	CCONJ
ejpam-6841	457	11	{	{	PUNCT
ejpam-6841	457	12	j	j	PROPN
ejpam-6841	457	13	(	(	PUNCT
ejpam-6841	457	14	tn	tn	PROPN
ejpam-6841	457	15	)	)	PUNCT
ejpam-6841	457	16	}	}	PUNCT
ejpam-6841	457	17	and	and	CCONJ
ejpam-6841	457	18	{	{	PUNCT
ejpam-6841	457	19	b	b	PROPN
ejpam-6841	457	20	(	(	PUNCT
ejpam-6841	457	21	tn	tn	NOUN
ejpam-6841	457	22	)	)	PUNCT
ejpam-6841	457	23	}	}	PUNCT
ejpam-6841	457	24	are	be	AUX
ejpam-6841	457	25	convergent	convergent	ADJ
ejpam-6841	457	26	sequences	sequence	NOUN
ejpam-6841	457	27	such	such	ADJ
ejpam-6841	457	28	that	that	SCONJ
ejpam-6841	457	29	lim	lim	PROPN
ejpam-6841	457	30	n→∞	n→∞	PROPN
ejpam-6841	457	31	j	j	PROPN
ejpam-6841	457	32	(	(	PUNCT
ejpam-6841	457	33	tn	tn	PROPN
ejpam-6841	457	34	)	)	PUNCT
ejpam-6841	457	35	=	=	VERB
ejpam-6841	458	1	lim	lim	PROPN
ejpam-6841	458	2	n→∞	n→∞	NUM
ejpam-6841	458	3	b	b	PROPN
ejpam-6841	458	4	(	(	PUNCT
ejpam-6841	458	5	tn	tn	PROPN
ejpam-6841	458	6	)	)	PUNCT
ejpam-6841	458	7	,	,	PUNCT
ejpam-6841	458	8	then	then	ADV
ejpam-6841	458	9	limn→∞	limn→∞	PROPN
ejpam-6841	458	10	tn	tn	NOUN
ejpam-6841	458	11	=	=	SYM
ejpam-6841	458	12	0	0	PROPN
ejpam-6841	458	13	.	.	PUNCT
ejpam-6841	458	14	(	(	PUNCT
ejpam-6841	458	15	ii	ii	X
ejpam-6841	458	16	)	)	PUNCT
ejpam-6841	458	17	c0	c0	PROPN
ejpam-6841	458	18	is	be	AUX
ejpam-6841	458	19	nonvoid	nonvoid	PROPN
ejpam-6841	458	20	subset	subset	NOUN
ejpam-6841	458	21	of	of	ADP
ejpam-6841	458	22	c	c	PROPN
ejpam-6841	458	23	such	such	ADJ
ejpam-6841	458	24	that	that	SCONJ
ejpam-6841	458	25	p	p	PROPN
ejpam-6841	458	26	(	(	PUNCT
ejpam-6841	458	27	c0	c0	NOUN
ejpam-6841	458	28	)	)	PUNCT
ejpam-6841	458	29	⊆	⊆	NUM
ejpam-6841	458	30	d0	d0	NOUN
ejpam-6841	458	31	.	.	PUNCT
ejpam-6841	459	1	then	then	ADV
ejpam-6841	459	2	p	p	X
ejpam-6841	459	3	has	have	VERB
ejpam-6841	459	4	a	a	DET
ejpam-6841	459	5	best	good	ADJ
ejpam-6841	459	6	proximity	proximity	NOUN
ejpam-6841	459	7	point	point	NOUN
ejpam-6841	459	8	.	.	PUNCT
ejpam-6841	460	1	proof	proof	NOUN
ejpam-6841	460	2	.	.	PUNCT
ejpam-6841	461	1	the	the	DET
ejpam-6841	461	2	proof	proof	NOUN
ejpam-6841	461	3	aligns	align	VERB
ejpam-6841	461	4	with	with	ADP
ejpam-6841	461	5	the	the	DET
ejpam-6841	461	6	methodology	methodology	NOUN
ejpam-6841	461	7	outlined	outline	VERB
ejpam-6841	461	8	in	in	ADP
ejpam-6841	461	9	theorem	theorem	NOUN
ejpam-6841	461	10	5	5	NUM
ejpam-6841	461	11	,	,	PUNCT
ejpam-6841	461	12	we	we	PRON
ejpam-6841	461	13	have	have	VERB
ejpam-6841	461	14	j	j	PROPN
ejpam-6841	461	15	(	(	PUNCT
ejpam-6841	461	16	θn	θn	NOUN
ejpam-6841	461	17	)	)	PUNCT
ejpam-6841	461	18	≤	≤	NOUN
ejpam-6841	461	19	£	£	PROPN
ejpam-6841	461	20	(	(	PUNCT
ejpam-6841	461	21	(	(	PUNCT
ejpam-6841	461	22	θn−1	θn−1	PROPN
ejpam-6841	461	23	)	)	PUNCT
ejpam-6841	461	24	α+β	α+β	PROPN
ejpam-6841	461	25	(	(	PUNCT
ejpam-6841	461	26	θn	θn	NOUN
ejpam-6841	461	27	)	)	PUNCT
ejpam-6841	461	28	γ	γ	NOUN
ejpam-6841	461	29	(	(	PUNCT
ejpam-6841	461	30	1	1	NUM
ejpam-6841	461	31	2	2	NUM
ejpam-6841	461	32	(	(	PUNCT
ejpam-6841	461	33	θn	θn	NOUN
ejpam-6841	461	34	+	+	X
ejpam-6841	461	35	θn−1	θn−1	PROPN
ejpam-6841	461	36	)	)	PUNCT
ejpam-6841	461	37	)	)	PUNCT
ejpam-6841	461	38	1−α−β−γ	1−α−β−γ	NUM
ejpam-6841	461	39	)	)	PUNCT
ejpam-6841	462	1	<	<	X
ejpam-6841	462	2	j	j	PROPN
ejpam-6841	462	3	(	(	PUNCT
ejpam-6841	462	4	(	(	PUNCT
ejpam-6841	462	5	θn−1	θn−1	PROPN
ejpam-6841	462	6	)	)	PUNCT
ejpam-6841	462	7	α+β	α+β	PROPN
ejpam-6841	462	8	(	(	PUNCT
ejpam-6841	462	9	θn	θn	NOUN
ejpam-6841	462	10	)	)	PUNCT
ejpam-6841	462	11	γ	γ	NOUN
ejpam-6841	462	12	(	(	PUNCT
ejpam-6841	462	13	1	1	NUM
ejpam-6841	462	14	2	2	NUM
ejpam-6841	462	15	(	(	PUNCT
ejpam-6841	462	16	θn	θn	NOUN
ejpam-6841	462	17	+	+	X
ejpam-6841	462	18	θn−1	θn−1	PROPN
ejpam-6841	462	19	)	)	PUNCT
ejpam-6841	462	20	)	)	PUNCT
ejpam-6841	462	21	1−α−β−γ	1−α−β−γ	NUM
ejpam-6841	462	22	)	)	PUNCT
ejpam-6841	462	23	.	.	PUNCT
ejpam-6841	463	1	(	(	PUNCT
ejpam-6841	463	2	25	25	NUM
ejpam-6841	463	3	)	)	PUNCT
ejpam-6841	463	4	we	we	PRON
ejpam-6841	463	5	establish	establish	VERB
ejpam-6841	463	6	that	that	SCONJ
ejpam-6841	463	7	{	{	PUNCT
ejpam-6841	463	8	j	j	PROPN
ejpam-6841	463	9	(	(	PUNCT
ejpam-6841	463	10	θn	θn	NOUN
ejpam-6841	463	11	)	)	PUNCT
ejpam-6841	463	12	}	}	PUNCT
ejpam-6841	463	13	is	be	AUX
ejpam-6841	463	14	a	a	DET
ejpam-6841	463	15	strictly	strictly	ADV
ejpam-6841	463	16	decreasing	decrease	VERB
ejpam-6841	463	17	sequence	sequence	NOUN
ejpam-6841	463	18	by	by	ADP
ejpam-6841	463	19	(	(	PUNCT
ejpam-6841	463	20	25	25	NUM
ejpam-6841	463	21	)	)	PUNCT
ejpam-6841	463	22	.	.	PUNCT
ejpam-6841	464	1	this	this	PRON
ejpam-6841	464	2	presents	present	VERB
ejpam-6841	464	3	two	two	NUM
ejpam-6841	464	4	scenarios	scenario	NOUN
ejpam-6841	464	5	:	:	PUNCT
ejpam-6841	464	6	either	either	CCONJ
ejpam-6841	464	7	the	the	DET
ejpam-6841	464	8	sequence	sequence	NOUN
ejpam-6841	464	9	{	{	PUNCT
ejpam-6841	464	10	j	j	PROPN
ejpam-6841	464	11	(	(	PUNCT
ejpam-6841	464	12	θn	θn	NOUN
ejpam-6841	464	13	)	)	PUNCT
ejpam-6841	464	14	}	}	PUNCT
ejpam-6841	464	15	is	be	AUX
ejpam-6841	464	16	bounded	bound	VERB
ejpam-6841	464	17	below	below	ADV
ejpam-6841	464	18	,	,	PUNCT
ejpam-6841	464	19	or	or	CCONJ
ejpam-6841	464	20	it	it	PRON
ejpam-6841	464	21	is	be	AUX
ejpam-6841	464	22	not	not	PART
ejpam-6841	464	23	.	.	PUNCT
ejpam-6841	465	1	if	if	SCONJ
ejpam-6841	465	2	{	{	PUNCT
ejpam-6841	465	3	j	j	PROPN
ejpam-6841	465	4	(	(	PUNCT
ejpam-6841	465	5	θn	θn	NOUN
ejpam-6841	465	6	)	)	PUNCT
ejpam-6841	465	7	}	}	PUNCT
ejpam-6841	465	8	is	be	AUX
ejpam-6841	465	9	not	not	PART
ejpam-6841	465	10	have	have	VERB
ejpam-6841	465	11	a	a	DET
ejpam-6841	465	12	lower	low	ADJ
ejpam-6841	465	13	bounded	bound	VERB
ejpam-6841	465	14	,	,	PUNCT
ejpam-6841	465	15	then	then	ADV
ejpam-6841	465	16	inf	inf	PROPN
ejpam-6841	465	17	θn	θn	PROPN
ejpam-6841	465	18	>	>	PROPN
ejpam-6841	465	19	ε	ε	PROPN
ejpam-6841	465	20	j	j	PROPN
ejpam-6841	465	21	(	(	PUNCT
ejpam-6841	465	22	θn	θn	NOUN
ejpam-6841	465	23	)	)	PUNCT
ejpam-6841	465	24	>	>	PUNCT
ejpam-6841	466	1	−∞	−∞	X
ejpam-6841	466	2	for	for	ADP
ejpam-6841	466	3	every	every	DET
ejpam-6841	466	4	ε	ε	PROPN
ejpam-6841	466	5	>	>	X
ejpam-6841	466	6	0	0	PROPN
ejpam-6841	466	7	,	,	PUNCT
ejpam-6841	466	8	n	n	PRON
ejpam-6841	466	9	∈	∈	PROPN
ejpam-6841	466	10	n.	n.	NOUN
ejpam-6841	466	11	lemma	lemma	PROPN
ejpam-6841	466	12	2	2	NUM
ejpam-6841	466	13	,	,	PUNCT
ejpam-6841	466	14	indicates	indicate	VERB
ejpam-6841	466	15	that	that	SCONJ
ejpam-6841	466	16	θn	θn	PROPN
ejpam-6841	466	17	→	→	SYM
ejpam-6841	466	18	0	0	PROPN
ejpam-6841	466	19	as	as	ADP
ejpam-6841	466	20	n	n	PRON
ejpam-6841	466	21	approaches	approach	NOUN
ejpam-6841	466	22	to	to	ADP
ejpam-6841	466	23	∞.	∞.	PROPN
ejpam-6841	466	24	second	second	ADJ
ejpam-6841	466	25	,	,	PUNCT
ejpam-6841	466	26	the	the	DET
ejpam-6841	466	27	sequence	sequence	NOUN
ejpam-6841	466	28	{	{	PUNCT
ejpam-6841	466	29	j	j	PROPN
ejpam-6841	466	30	(	(	PUNCT
ejpam-6841	466	31	θn	θn	NOUN
ejpam-6841	466	32	)	)	PUNCT
ejpam-6841	466	33	}	}	PUNCT
ejpam-6841	466	34	is	be	AUX
ejpam-6841	466	35	convergent	convergent	ADJ
ejpam-6841	466	36	if	if	SCONJ
ejpam-6841	466	37	it	it	PRON
ejpam-6841	466	38	is	be	AUX
ejpam-6841	466	39	bounded	bound	VERB
ejpam-6841	466	40	below	below	ADV
ejpam-6841	466	41	.	.	PUNCT
ejpam-6841	467	1	the	the	DET
ejpam-6841	467	2	sequence	sequence	NOUN
ejpam-6841	467	3	{	{	PUNCT
ejpam-6841	467	4	b	b	PROPN
ejpam-6841	467	5	(	(	PUNCT
ejpam-6841	467	6	θn	θn	NOUN
ejpam-6841	467	7	)	)	PUNCT
ejpam-6841	467	8	}	}	PUNCT
ejpam-6841	467	9	likewise	likewise	ADV
ejpam-6841	467	10	converges	converge	VERB
ejpam-6841	467	11	by	by	ADP
ejpam-6841	467	12	(	(	PUNCT
ejpam-6841	467	13	25	25	NUM
ejpam-6841	467	14	)	)	PUNCT
ejpam-6841	467	15	,	,	PUNCT
ejpam-6841	467	16	and	and	CCONJ
ejpam-6841	467	17	,	,	PUNCT
ejpam-6841	467	18	both	both	PRON
ejpam-6841	467	19	have	have	VERB
ejpam-6841	467	20	the	the	DET
ejpam-6841	467	21	same	same	ADJ
ejpam-6841	467	22	limit	limit	NOUN
ejpam-6841	467	23	.	.	PUNCT
ejpam-6841	468	1	for	for	ADP
ejpam-6841	468	2	each	each	DET
ejpam-6841	468	3	sequence	sequence	NOUN
ejpam-6841	468	4	{	{	PUNCT
ejpam-6841	468	5	bn	bn	ADP
ejpam-6841	468	6	}	}	PUNCT
ejpam-6841	468	7	in	in	ADP
ejpam-6841	468	8	c	c	NOUN
ejpam-6841	468	9	we	we	PRON
ejpam-6841	468	10	have	have	VERB
ejpam-6841	468	11	limn→∞	limn→∞	PROPN
ejpam-6841	468	12	ϑ	ϑ	X
ejpam-6841	468	13	(	(	PUNCT
ejpam-6841	468	14	bn	bn	X
ejpam-6841	468	15	,	,	PUNCT
ejpam-6841	468	16	bn+1	bn+1	NUM
ejpam-6841	468	17	)	)	PUNCT
ejpam-6841	468	18	=	=	PUNCT
ejpam-6841	468	19	0	0	NUM
ejpam-6841	469	1	according	accord	VERB
ejpam-6841	469	2	to	to	ADP
ejpam-6841	469	3	(	(	PUNCT
ejpam-6841	469	4	i	i	NOUN
ejpam-6841	469	5	)	)	PUNCT
ejpam-6841	469	6	.	.	PUNCT
ejpam-6841	470	1	now	now	ADV
ejpam-6841	470	2	,	,	PUNCT
ejpam-6841	470	3	according	accord	VERB
ejpam-6841	470	4	to	to	ADP
ejpam-6841	470	5	theorem	theorem	ADJ
ejpam-6841	470	6	5	5	NUM
ejpam-6841	470	7	proof	proof	NOUN
ejpam-6841	470	8	,	,	PUNCT
ejpam-6841	470	9	we	we	PRON
ejpam-6841	470	10	have	have	VERB
ejpam-6841	470	11	ϑ	ϑ	X
ejpam-6841	470	12	(	(	PUNCT
ejpam-6841	470	13	b∗,pb∗	b∗,pb∗	PROPN
ejpam-6841	470	14	)	)	PUNCT
ejpam-6841	470	15	=	=	SYM
ejpam-6841	470	16	ϑ	ϑ	X
ejpam-6841	470	17	(	(	PUNCT
ejpam-6841	470	18	c	c	X
ejpam-6841	470	19	,	,	PUNCT
ejpam-6841	470	20	d	d	NOUN
ejpam-6841	470	21	)	)	PUNCT
ejpam-6841	470	22	.	.	PUNCT
ejpam-6841	471	1	hence	hence	ADV
ejpam-6841	471	2	,	,	PUNCT
ejpam-6841	471	3	b∗	b∗	ADV
ejpam-6841	471	4	is	be	AUX
ejpam-6841	471	5	a	a	DET
ejpam-6841	471	6	best	good	ADJ
ejpam-6841	471	7	proximity	proximity	NOUN
ejpam-6841	471	8	point	point	NOUN
ejpam-6841	471	9	of	of	ADP
ejpam-6841	471	10	the	the	DET
ejpam-6841	471	11	mapping	mapping	NOUN
ejpam-6841	472	1	p.	p.	PROPN
ejpam-6841	472	2	k.	k.	PROPN
ejpam-6841	472	3	javed	javed	PROPN
ejpam-6841	472	4	,	,	PUNCT
ejpam-6841	472	5	m.	m.	NOUN
ejpam-6841	472	6	nazam	nazam	PROPN
ejpam-6841	472	7	,	,	PUNCT
ejpam-6841	472	8	m.	m.	PROPN
ejpam-6841	472	9	arshad	arshad	PROPN
ejpam-6841	472	10	,	,	PUNCT
ejpam-6841	472	11	m.	m.	NOUN
ejpam-6841	472	12	de	de	X
ejpam-6841	472	13	la	la	PROPN
ejpam-6841	472	14	sen	sen	PROPN
ejpam-6841	472	15	/	/	SYM
ejpam-6841	472	16	eur	eur	PROPN
ejpam-6841	472	17	.	.	PUNCT
ejpam-6841	473	1	j.	j.	PROPN
ejpam-6841	473	2	pure	pure	PROPN
ejpam-6841	473	3	appl	appl	PROPN
ejpam-6841	473	4	.	.	PROPN
ejpam-6841	473	5	math	math	PROPN
ejpam-6841	473	6	,	,	PUNCT
ejpam-6841	473	7	18	18	NUM
ejpam-6841	473	8	(	(	PUNCT
ejpam-6841	473	9	4	4	NUM
ejpam-6841	473	10	)	)	PUNCT
ejpam-6841	473	11	(	(	PUNCT
ejpam-6841	473	12	2025	2025	NUM
ejpam-6841	473	13	)	)	PUNCT
ejpam-6841	473	14	,	,	PUNCT
ejpam-6841	473	15	6841	6841	NUM
ejpam-6841	473	16	20	20	NUM
ejpam-6841	473	17	of	of	ADP
ejpam-6841	473	18	23	23	NUM
ejpam-6841	473	19	4	4	NUM
ejpam-6841	473	20	.	.	PUNCT
ejpam-6841	473	21	application	application	NOUN
ejpam-6841	473	22	to	to	ADP
ejpam-6841	473	23	integral	integral	ADJ
ejpam-6841	473	24	equations	equation	NOUN
ejpam-6841	473	25	the	the	DET
ejpam-6841	473	26	theory	theory	NOUN
ejpam-6841	473	27	of	of	ADP
ejpam-6841	473	28	integral	integral	ADJ
ejpam-6841	473	29	equations	equation	NOUN
ejpam-6841	473	30	is	be	AUX
ejpam-6841	473	31	essentially	essentially	ADV
ejpam-6841	473	32	credited	credit	VERB
ejpam-6841	473	33	to	to	ADP
ejpam-6841	473	34	fourier	fourier	PROPN
ejpam-6841	473	35	’s	’s	PART
ejpam-6841	473	36	exploration	exploration	NOUN
ejpam-6841	473	37	of	of	ADP
ejpam-6841	473	38	the	the	DET
ejpam-6841	473	39	theory	theory	NOUN
ejpam-6841	473	40	about	about	ADP
ejpam-6841	473	41	fundamentals	fundamental	NOUN
ejpam-6841	473	42	that	that	PRON
ejpam-6841	473	43	bears	bear	VERB
ejpam-6841	473	44	his	his	PRON
ejpam-6841	473	45	name	name	NOUN
ejpam-6841	473	46	;	;	PUNCT
ejpam-6841	473	47	in	in	ADP
ejpam-6841	473	48	fact	fact	NOUN
ejpam-6841	473	49	,	,	PUNCT
ejpam-6841	473	50	this	this	PRON
ejpam-6841	473	51	theorem	theorem	VERB
ejpam-6841	473	52	,	,	PUNCT
ejpam-6841	473	53	although	although	SCONJ
ejpam-6841	473	54	it	it	PRON
ejpam-6841	473	55	is	be	AUX
ejpam-6841	473	56	not	not	PART
ejpam-6841	473	57	consistent	consistent	ADJ
ejpam-6841	473	58	with	with	ADP
ejpam-6841	473	59	fourier	fourier	PROPN
ejpam-6841	473	60	’s	’s	PART
ejpam-6841	473	61	perspective	perspective	NOUN
ejpam-6841	473	62	,	,	PUNCT
ejpam-6841	473	63	can	can	AUX
ejpam-6841	473	64	be	be	AUX
ejpam-6841	473	65	understood	understand	VERB
ejpam-6841	473	66	as	as	ADP
ejpam-6841	473	67	a	a	DET
ejpam-6841	473	68	statement	statement	NOUN
ejpam-6841	473	69	of	of	ADP
ejpam-6841	473	70	the	the	DET
ejpam-6841	473	71	solution	solution	NOUN
ejpam-6841	473	72	to	to	ADP
ejpam-6841	473	73	a	a	DET
ejpam-6841	473	74	specific	specific	ADJ
ejpam-6841	473	75	first	first	ADJ
ejpam-6841	473	76	-	-	PUNCT
ejpam-6841	473	77	order	order	NOUN
ejpam-6841	473	78	integral	integral	ADJ
ejpam-6841	473	79	equation	equation	NOUN
ejpam-6841	473	80	.	.	PUNCT
ejpam-6841	474	1	however	however	ADV
ejpam-6841	474	2	,	,	PUNCT
ejpam-6841	474	3	abel	abel	PROPN
ejpam-6841	474	4	,	,	PUNCT
ejpam-6841	474	5	liouville	liouville	NOUN
ejpam-6841	474	6	,	,	PUNCT
ejpam-6841	474	7	and	and	CCONJ
ejpam-6841	474	8	several	several	ADJ
ejpam-6841	474	9	others	other	NOUN
ejpam-6841	474	10	who	who	PRON
ejpam-6841	474	11	came	come	VERB
ejpam-6841	474	12	behind	behind	ADP
ejpam-6841	474	13	them	they	PRON
ejpam-6841	474	14	began	begin	VERB
ejpam-6841	474	15	to	to	PART
ejpam-6841	474	16	consciously	consciously	ADV
ejpam-6841	474	17	explore	explore	VERB
ejpam-6841	474	18	incredible	incredible	ADJ
ejpam-6841	474	19	integral	integral	ADJ
ejpam-6841	474	20	equations	equation	NOUN
ejpam-6841	474	21	,	,	PUNCT
ejpam-6841	474	22	and	and	CCONJ
ejpam-6841	474	23	many	many	ADJ
ejpam-6841	474	24	of	of	ADP
ejpam-6841	474	25	them	they	PRON
ejpam-6841	474	26	came	come	VERB
ejpam-6841	474	27	to	to	ADP
ejpam-6841	474	28	the	the	DET
ejpam-6841	474	29	realisation	realisation	NOUN
ejpam-6841	474	30	that	that	SCONJ
ejpam-6841	474	31	the	the	DET
ejpam-6841	474	32	theory	theory	NOUN
ejpam-6841	474	33	might	might	AUX
ejpam-6841	474	34	be	be	AUX
ejpam-6841	474	35	necessary	necessary	ADJ
ejpam-6841	474	36	.	.	PUNCT
ejpam-6841	475	1	the	the	DET
ejpam-6841	475	2	objective	objective	NOUN
ejpam-6841	475	3	is	be	AUX
ejpam-6841	475	4	to	to	PART
ejpam-6841	475	5	use	use	VERB
ejpam-6841	475	6	theorem	theorem	NOUN
ejpam-6841	475	7	1	1	NUM
ejpam-6841	475	8	(	(	PUNCT
ejpam-6841	475	9	for	for	ADP
ejpam-6841	475	10	c	c	NOUN
ejpam-6841	475	11	⊆	⊆	NUM
ejpam-6841	475	12	d	d	NOUN
ejpam-6841	475	13	)	)	PUNCT
ejpam-6841	475	14	to	to	PART
ejpam-6841	475	15	show	show	VERB
ejpam-6841	475	16	that	that	SCONJ
ejpam-6841	475	17	the	the	DET
ejpam-6841	475	18	following	follow	VERB
ejpam-6841	475	19	nonlinear	nonlinear	PROPN
ejpam-6841	475	20	volterra	volterra	NOUN
ejpam-6841	475	21	-	-	PUNCT
ejpam-6841	475	22	type	type	NOUN
ejpam-6841	475	23	integral	integral	ADJ
ejpam-6841	475	24	equations	equation	NOUN
ejpam-6841	475	25	have	have	VERB
ejpam-6841	475	26	a	a	DET
ejpam-6841	475	27	solution	solution	NOUN
ejpam-6841	475	28	.	.	PUNCT
ejpam-6841	476	1	f(k	f(k	VERB
ejpam-6841	476	2	)	)	PUNCT
ejpam-6841	477	1	=	=	SYM
ejpam-6841	477	2	k∫	k∫	X
ejpam-6841	477	3	0	0	NUM
ejpam-6841	477	4	hς(k	hς(k	NOUN
ejpam-6841	477	5	,	,	PUNCT
ejpam-6841	477	6	h	h	NOUN
ejpam-6841	477	7	,	,	PUNCT
ejpam-6841	477	8	f	f	X
ejpam-6841	477	9	)	)	PUNCT
ejpam-6841	477	10	dh	dh	NOUN
ejpam-6841	477	11	,	,	PUNCT
ejpam-6841	477	12	(	(	PUNCT
ejpam-6841	477	13	26	26	NUM
ejpam-6841	477	14	)	)	PUNCT
ejpam-6841	477	15	for	for	ADP
ejpam-6841	477	16	all	all	DET
ejpam-6841	477	17	k	k	PROPN
ejpam-6841	477	18	∈	∈	PROPN
ejpam-6841	478	1	[	[	X
ejpam-6841	478	2	0	0	NUM
ejpam-6841	478	3	,	,	PUNCT
ejpam-6841	478	4	1	1	NUM
ejpam-6841	478	5	]	]	PUNCT
ejpam-6841	478	6	,	,	PUNCT
ejpam-6841	478	7	ς	ς	PROPN
ejpam-6841	478	8	∈	∈	PROPN
ejpam-6841	478	9	θ	θ	PROPN
ejpam-6841	478	10	,	,	PUNCT
ejpam-6841	478	11	and	and	CCONJ
ejpam-6841	478	12	hς	hς	ADV
ejpam-6841	478	13	is	be	AUX
ejpam-6841	478	14	a	a	DET
ejpam-6841	478	15	function	function	NOUN
ejpam-6841	478	16	defined	define	VERB
ejpam-6841	478	17	on	on	ADP
ejpam-6841	478	18	[	[	X
ejpam-6841	478	19	0	0	NUM
ejpam-6841	478	20	,	,	PUNCT
ejpam-6841	478	21	1]2	1]2	NUM
ejpam-6841	478	22	×	×	PROPN
ejpam-6841	478	23	c([0	c([0	PROPN
ejpam-6841	478	24	,	,	PUNCT
ejpam-6841	478	25	1],r+	1],r+	NUM
ejpam-6841	478	26	)	)	PUNCT
ejpam-6841	478	27	to	to	PART
ejpam-6841	478	28	r.	r.	VERB
ejpam-6841	478	29	we	we	PRON
ejpam-6841	478	30	demonstrate	demonstrate	VERB
ejpam-6841	478	31	that	that	SCONJ
ejpam-6841	478	32	the	the	DET
ejpam-6841	478	33	solution	solution	NOUN
ejpam-6841	478	34	to	to	ADP
ejpam-6841	478	35	(	(	PUNCT
ejpam-6841	478	36	26	26	NUM
ejpam-6841	478	37	)	)	PUNCT
ejpam-6841	478	38	exists	exist	VERB
ejpam-6841	478	39	.	.	PUNCT
ejpam-6841	479	1	for	for	ADP
ejpam-6841	479	2	f	f	PROPN
ejpam-6841	479	3	∈	∈	PROPN
ejpam-6841	479	4	c([0	c([0	NOUN
ejpam-6841	479	5	,	,	PUNCT
ejpam-6841	479	6	1],r+	1],r+	NUM
ejpam-6841	479	7	)	)	PUNCT
ejpam-6841	479	8	,	,	PUNCT
ejpam-6841	479	9	define	define	VERB
ejpam-6841	479	10	norm	norm	NOUN
ejpam-6841	479	11	as	as	ADP
ejpam-6841	479	12	:	:	PUNCT
ejpam-6841	479	13	‖f‖τ	‖f‖τ	NOUN
ejpam-6841	479	14	=	=	NOUN
ejpam-6841	479	15	sup	sup	NOUN
ejpam-6841	479	16	k∈[0,1	k∈[0,1	NOUN
ejpam-6841	479	17	]	]	PUNCT
ejpam-6841	479	18	|f(k)|	|f(k)|	VERB
ejpam-6841	479	19	e−τk	e−τk	NOUN
ejpam-6841	479	20	,	,	PUNCT
ejpam-6841	479	21	τ	τ	X
ejpam-6841	479	22	>	>	X
ejpam-6841	479	23	0	0	X
ejpam-6841	479	24	.	.	PUNCT
ejpam-6841	480	1	define	define	VERB
ejpam-6841	480	2	ητ	ητ	NOUN
ejpam-6841	480	3	(	(	PUNCT
ejpam-6841	480	4	f	f	X
ejpam-6841	480	5	,	,	PUNCT
ejpam-6841	480	6	κ	κ	NOUN
ejpam-6841	480	7	)	)	PUNCT
ejpam-6841	480	8	=	=	PUNCT
ejpam-6841	481	1	[	[	PUNCT
ejpam-6841	481	2	sup	sup	NOUN
ejpam-6841	481	3	k∈[0,1	k∈[0,1	NOUN
ejpam-6841	481	4	]	]	PUNCT
ejpam-6841	481	5	|f(k)−	|f(k)−	ADJ
ejpam-6841	481	6	κ(k)|	κ(k)|	NOUN
ejpam-6841	481	7	e−τk	e−τk	NOUN
ejpam-6841	481	8	]	]	PUNCT
ejpam-6841	482	1	=	=	PUNCT
ejpam-6841	482	2	‖f	‖f	ADP
ejpam-6841	482	3	−	−	NOUN
ejpam-6841	482	4	κ‖τ	κ‖τ	NOUN
ejpam-6841	482	5	for	for	ADP
ejpam-6841	482	6	all	all	DET
ejpam-6841	482	7	f	f	NOUN
ejpam-6841	482	8	,	,	PUNCT
ejpam-6841	482	9	κ	κ	PROPN
ejpam-6841	482	10	∈	∈	PROPN
ejpam-6841	482	11	c([0	c([0	NOUN
ejpam-6841	482	12	,	,	PUNCT
ejpam-6841	482	13	1],r+	1],r+	NUM
ejpam-6841	482	14	)	)	PUNCT
ejpam-6841	482	15	,	,	PUNCT
ejpam-6841	482	16	with	with	ADP
ejpam-6841	482	17	these	these	DET
ejpam-6841	482	18	settings	setting	NOUN
ejpam-6841	482	19	,	,	PUNCT
ejpam-6841	482	20	(	(	PUNCT
ejpam-6841	482	21	c([0	c([0	PROPN
ejpam-6841	482	22	,	,	PUNCT
ejpam-6841	482	23	1],r+	1],r+	NUM
ejpam-6841	482	24	)	)	PUNCT
ejpam-6841	482	25	,	,	PUNCT
ejpam-6841	482	26	ητ	ητ	PROPN
ejpam-6841	482	27	)	)	PUNCT
ejpam-6841	482	28	represents	represent	VERB
ejpam-6841	482	29	a	a	DET
ejpam-6841	482	30	complete	complete	ADJ
ejpam-6841	482	31	metric	metric	ADJ
ejpam-6841	482	32	space	space	NOUN
ejpam-6841	482	33	.	.	PUNCT
ejpam-6841	483	1	now	now	ADV
ejpam-6841	483	2	,	,	PUNCT
ejpam-6841	483	3	we	we	PRON
ejpam-6841	483	4	show	show	VERB
ejpam-6841	483	5	the	the	DET
ejpam-6841	483	6	following	following	NOUN
ejpam-6841	483	7	theorem	theorem	NOUN
ejpam-6841	483	8	to	to	PART
ejpam-6841	483	9	clarify	clarify	VERB
ejpam-6841	483	10	that	that	SCONJ
ejpam-6841	483	11	the	the	DET
ejpam-6841	483	12	solution	solution	NOUN
ejpam-6841	483	13	of	of	ADP
ejpam-6841	483	14	integral	integral	ADJ
ejpam-6841	483	15	equation	equation	NOUN
ejpam-6841	483	16	exists	exist	VERB
ejpam-6841	483	17	.	.	PUNCT
ejpam-6841	484	1	theorem	theorem	ADJ
ejpam-6841	484	2	7	7	NUM
ejpam-6841	484	3	.	.	PUNCT
ejpam-6841	484	4	suppose	suppose	VERB
ejpam-6841	484	5	that	that	SCONJ
ejpam-6841	484	6	the	the	DET
ejpam-6841	484	7	mapping	mapping	NOUN
ejpam-6841	484	8	hς	hς	ADP
ejpam-6841	484	9	:	:	PUNCT
ejpam-6841	485	1	[	[	X
ejpam-6841	485	2	0	0	NUM
ejpam-6841	485	3	,	,	PUNCT
ejpam-6841	485	4	1]×[0	1]×[0	NUM
ejpam-6841	485	5	,	,	PUNCT
ejpam-6841	485	6	1]×c([0	1]×c([0	NUM
ejpam-6841	485	7	,	,	PUNCT
ejpam-6841	485	8	1],r+	1],r+	NUM
ejpam-6841	485	9	)	)	PUNCT
ejpam-6841	485	10	→	→	PUNCT
ejpam-6841	485	11	r	r	NOUN
ejpam-6841	485	12	is	be	AUX
ejpam-6841	485	13	a	a	DET
ejpam-6841	485	14	continuous	continuous	ADJ
ejpam-6841	485	15	satisfying	satisfying	NOUN
ejpam-6841	485	16	:	:	PUNCT
ejpam-6841	485	17	|hς(k	|hς(k	ADJ
ejpam-6841	485	18	,	,	PUNCT
ejpam-6841	485	19	h	h	NOUN
ejpam-6841	485	20	,	,	PUNCT
ejpam-6841	485	21	f)−hς(k	f)−hς(k	NUM
ejpam-6841	485	22	,	,	PUNCT
ejpam-6841	485	23	h	h	NOUN
ejpam-6841	485	24	,	,	PUNCT
ejpam-6841	485	25	c)|	c)|	PROPN
ejpam-6841	485	26	≤	≤	NUM
ejpam-6841	485	27	τητ	τητ	NOUN
ejpam-6841	486	1	(	(	PUNCT
ejpam-6841	486	2	f	f	X
ejpam-6841	486	3	,	,	PUNCT
ejpam-6841	486	4	c	c	NOUN
ejpam-6841	486	5	)	)	PUNCT
ejpam-6841	486	6	τητ	τητ	NOUN
ejpam-6841	487	1	(	(	PUNCT
ejpam-6841	487	2	f	f	X
ejpam-6841	487	3	,	,	PUNCT
ejpam-6841	487	4	c	c	NOUN
ejpam-6841	487	5	)	)	PUNCT
ejpam-6841	487	6	+	+	CCONJ
ejpam-6841	487	7	1	1	NUM
ejpam-6841	487	8	eτh	eτh	NOUN
ejpam-6841	487	9	(	(	PUNCT
ejpam-6841	487	10	27	27	NUM
ejpam-6841	487	11	)	)	PUNCT
ejpam-6841	487	12	for	for	ADP
ejpam-6841	487	13	every	every	DET
ejpam-6841	487	14	h	h	NOUN
ejpam-6841	487	15	,	,	PUNCT
ejpam-6841	487	16	k	k	PROPN
ejpam-6841	487	17	∈	∈	PROPN
ejpam-6841	488	1	[	[	X
ejpam-6841	488	2	0	0	NUM
ejpam-6841	488	3	,	,	PUNCT
ejpam-6841	488	4	1	1	NUM
ejpam-6841	488	5	]	]	PUNCT
ejpam-6841	488	6	and	and	CCONJ
ejpam-6841	488	7	f	f	X
ejpam-6841	488	8	,	,	PUNCT
ejpam-6841	488	9	c	c	PROPN
ejpam-6841	488	10	∈	∈	PROPN
ejpam-6841	488	11	c([0	c([0	NOUN
ejpam-6841	488	12	,	,	PUNCT
ejpam-6841	488	13	1],r	1],r	NUM
ejpam-6841	488	14	)	)	PUNCT
ejpam-6841	488	15	.	.	PUNCT
ejpam-6841	489	1	then	then	ADV
ejpam-6841	489	2	,	,	PUNCT
ejpam-6841	489	3	integral	integral	ADJ
ejpam-6841	489	4	equation	equation	NOUN
ejpam-6841	489	5	(	(	PUNCT
ejpam-6841	489	6	26	26	NUM
ejpam-6841	489	7	)	)	PUNCT
ejpam-6841	489	8	have	have	VERB
ejpam-6841	489	9	at	at	ADP
ejpam-6841	489	10	most	most	ADV
ejpam-6841	489	11	one	one	NUM
ejpam-6841	489	12	solution	solution	NOUN
ejpam-6841	489	13	in	in	ADP
ejpam-6841	489	14	c([0	c([0	PROPN
ejpam-6841	489	15	,	,	PUNCT
ejpam-6841	489	16	1],r+	1],r+	NUM
ejpam-6841	489	17	)	)	PUNCT
ejpam-6841	489	18	or	or	CCONJ
ejpam-6841	489	19	equivalently	equivalently	ADV
ejpam-6841	489	20	the	the	DET
ejpam-6841	489	21	associated	associated	ADJ
ejpam-6841	489	22	operator	operator	NOUN
ejpam-6841	489	23	lς	lς	AUX
ejpam-6841	489	24	:	:	PUNCT
ejpam-6841	490	1	r	r	NOUN
ejpam-6841	490	2	→	→	SYM
ejpam-6841	490	3	r	r	NOUN
ejpam-6841	490	4	defined	define	VERB
ejpam-6841	490	5	by	by	ADP
ejpam-6841	490	6	(	(	PUNCT
ejpam-6841	490	7	lςf)(k	lςf)(k	NOUN
ejpam-6841	490	8	)	)	PUNCT
ejpam-6841	490	9	=	=	SYM
ejpam-6841	490	10	k∫	k∫	X
ejpam-6841	490	11	0	0	NUM
ejpam-6841	490	12	hς(k	hς(k	NOUN
ejpam-6841	490	13	,	,	PUNCT
ejpam-6841	490	14	h	h	NOUN
ejpam-6841	490	15	,	,	PUNCT
ejpam-6841	490	16	f	f	X
ejpam-6841	490	17	)	)	PUNCT
ejpam-6841	490	18	dh	dh	NOUN
ejpam-6841	490	19	,	,	PUNCT
ejpam-6841	490	20	(	(	PUNCT
ejpam-6841	490	21	28	28	NUM
ejpam-6841	490	22	)	)	PUNCT
ejpam-6841	490	23	admits	admit	VERB
ejpam-6841	490	24	a	a	DET
ejpam-6841	490	25	best	good	ADJ
ejpam-6841	490	26	proximity	proximity	NOUN
ejpam-6841	490	27	point	point	NOUN
ejpam-6841	490	28	.	.	PUNCT
ejpam-6841	491	1	proof	proof	NOUN
ejpam-6841	491	2	.	.	PUNCT
ejpam-6841	492	1	by	by	ADP
ejpam-6841	492	2	(	(	PUNCT
ejpam-6841	492	3	27	27	NUM
ejpam-6841	492	4	)	)	PUNCT
ejpam-6841	492	5	and	and	CCONJ
ejpam-6841	492	6	(	(	PUNCT
ejpam-6841	492	7	28	28	NUM
ejpam-6841	492	8	)	)	PUNCT
ejpam-6841	492	9	,	,	PUNCT
ejpam-6841	492	10	we	we	PRON
ejpam-6841	492	11	have	have	VERB
ejpam-6841	492	12	the	the	DET
ejpam-6841	492	13	following	follow	VERB
ejpam-6841	492	14	information	information	NOUN
ejpam-6841	492	15	.	.	PUNCT
ejpam-6841	493	1	|lςf	|lςf	NOUN
ejpam-6841	494	1	−	−	NOUN
ejpam-6841	494	2	lςκ|	lςκ|	PROPN
ejpam-6841	494	3	=	=	PUNCT
ejpam-6841	494	4	k∫	k∫	X
ejpam-6841	494	5	0	0	PUNCT
ejpam-6841	495	1	|hς(k	|hς(k	ADJ
ejpam-6841	495	2	,	,	PUNCT
ejpam-6841	495	3	h	h	NOUN
ejpam-6841	495	4	,	,	PUNCT
ejpam-6841	495	5	f)−hς(k	f)−hς(k	NUM
ejpam-6841	495	6	,	,	PUNCT
ejpam-6841	495	7	h	h	NOUN
ejpam-6841	495	8	,	,	PUNCT
ejpam-6841	495	9	κ)|	κ)|	PROPN
ejpam-6841	495	10	dh	dh	PROPN
ejpam-6841	495	11	,	,	PUNCT
ejpam-6841	495	12	k.	k.	PROPN
ejpam-6841	495	13	javed	javed	PROPN
ejpam-6841	495	14	,	,	PUNCT
ejpam-6841	495	15	m.	m.	NOUN
ejpam-6841	495	16	nazam	nazam	PROPN
ejpam-6841	495	17	,	,	PUNCT
ejpam-6841	495	18	m.	m.	PROPN
ejpam-6841	495	19	arshad	arshad	PROPN
ejpam-6841	495	20	,	,	PUNCT
ejpam-6841	495	21	m.	m.	NOUN
ejpam-6841	495	22	de	de	X
ejpam-6841	495	23	la	la	PROPN
ejpam-6841	495	24	sen	sen	PROPN
ejpam-6841	495	25	/	/	SYM
ejpam-6841	495	26	eur	eur	PROPN
ejpam-6841	495	27	.	.	PUNCT
ejpam-6841	496	1	j.	j.	PROPN
ejpam-6841	496	2	pure	pure	PROPN
ejpam-6841	496	3	appl	appl	PROPN
ejpam-6841	496	4	.	.	PROPN
ejpam-6841	496	5	math	math	PROPN
ejpam-6841	496	6	,	,	PUNCT
ejpam-6841	496	7	18	18	NUM
ejpam-6841	496	8	(	(	PUNCT
ejpam-6841	496	9	4	4	NUM
ejpam-6841	496	10	)	)	PUNCT
ejpam-6841	496	11	(	(	PUNCT
ejpam-6841	496	12	2025	2025	NUM
ejpam-6841	496	13	)	)	PUNCT
ejpam-6841	496	14	,	,	PUNCT
ejpam-6841	496	15	6841	6841	NUM
ejpam-6841	496	16	21	21	NUM
ejpam-6841	496	17	of	of	ADP
ejpam-6841	496	18	23	23	NUM
ejpam-6841	496	19	≤	≤	NUM
ejpam-6841	496	20	k∫	k∫	X
ejpam-6841	496	21	0	0	PUNCT
ejpam-6841	497	1	τητ	τητ	INTJ
ejpam-6841	497	2	(	(	PUNCT
ejpam-6841	497	3	f	f	X
ejpam-6841	497	4	,	,	PUNCT
ejpam-6841	497	5	κ	κ	NOUN
ejpam-6841	497	6	)	)	PUNCT
ejpam-6841	497	7	τητ	τητ	NOUN
ejpam-6841	498	1	(	(	PUNCT
ejpam-6841	498	2	f	f	X
ejpam-6841	498	3	,	,	PUNCT
ejpam-6841	498	4	κ	κ	NOUN
ejpam-6841	498	5	)	)	PUNCT
ejpam-6841	498	6	+	+	CCONJ
ejpam-6841	498	7	1	1	NUM
ejpam-6841	498	8	eτhdh	eτhdh	VERB
ejpam-6841	498	9	≤	≤	NUM
ejpam-6841	498	10	τητ	τητ	NOUN
ejpam-6841	499	1	(	(	PUNCT
ejpam-6841	499	2	f	f	X
ejpam-6841	499	3	,	,	PUNCT
ejpam-6841	499	4	κ	κ	NOUN
ejpam-6841	499	5	)	)	PUNCT
ejpam-6841	499	6	τητ	τητ	NOUN
ejpam-6841	500	1	(	(	PUNCT
ejpam-6841	500	2	f	f	X
ejpam-6841	500	3	,	,	PUNCT
ejpam-6841	500	4	κ	κ	NOUN
ejpam-6841	500	5	)	)	PUNCT
ejpam-6841	500	6	+	+	CCONJ
ejpam-6841	500	7	1	1	NUM
ejpam-6841	500	8	k∫	k∫	X
ejpam-6841	500	9	0	0	NUM
ejpam-6841	500	10	eτhdh	eτhdh	VERB
ejpam-6841	500	11	≤	≤	NUM
ejpam-6841	500	12	ητ	ητ	NOUN
ejpam-6841	500	13	(	(	PUNCT
ejpam-6841	500	14	f	f	X
ejpam-6841	500	15	,	,	PUNCT
ejpam-6841	500	16	κ	κ	NOUN
ejpam-6841	500	17	)	)	PUNCT
ejpam-6841	500	18	τητ	τητ	NOUN
ejpam-6841	501	1	(	(	PUNCT
ejpam-6841	501	2	f	f	X
ejpam-6841	501	3	,	,	PUNCT
ejpam-6841	501	4	κ	κ	NOUN
ejpam-6841	501	5	)	)	PUNCT
ejpam-6841	501	6	+	+	CCONJ
ejpam-6841	501	7	1	1	NUM
ejpam-6841	501	8	eτk	eτk	NOUN
ejpam-6841	501	9	.	.	PUNCT
ejpam-6841	502	1	this	this	PRON
ejpam-6841	502	2	implies	imply	VERB
ejpam-6841	502	3	|lςf	|lςf	PUNCT
ejpam-6841	502	4	−	−	PROPN
ejpam-6841	502	5	lςκ|	lςκ|	ADJ
ejpam-6841	502	6	e−τk	e−τk	NOUN
ejpam-6841	502	7	≤	≤	PUNCT
ejpam-6841	502	8	ητ	ητ	NOUN
ejpam-6841	502	9	(	(	PUNCT
ejpam-6841	502	10	f	f	X
ejpam-6841	502	11	,	,	PUNCT
ejpam-6841	502	12	κ	κ	NOUN
ejpam-6841	502	13	)	)	PUNCT
ejpam-6841	502	14	τητ	τητ	NOUN
ejpam-6841	502	15	(	(	PUNCT
ejpam-6841	502	16	f	f	X
ejpam-6841	502	17	,	,	PUNCT
ejpam-6841	502	18	κ	κ	NOUN
ejpam-6841	502	19	)	)	PUNCT
ejpam-6841	503	1	+	+	CCONJ
ejpam-6841	503	2	1	1	X
ejpam-6841	503	3	.	.	PUNCT
ejpam-6841	504	1	‖lςf	‖lςf	NOUN
ejpam-6841	504	2	−	−	NOUN
ejpam-6841	504	3	lςκ‖τ	lςκ‖τ	SYM
ejpam-6841	504	4	≤	≤	NUM
ejpam-6841	505	1	ητ	ητ	NOUN
ejpam-6841	505	2	(	(	PUNCT
ejpam-6841	505	3	f	f	X
ejpam-6841	505	4	,	,	PUNCT
ejpam-6841	505	5	κ	κ	NOUN
ejpam-6841	505	6	)	)	PUNCT
ejpam-6841	505	7	τητ	τητ	NOUN
ejpam-6841	506	1	(	(	PUNCT
ejpam-6841	506	2	f	f	X
ejpam-6841	506	3	,	,	PUNCT
ejpam-6841	506	4	κ	κ	NOUN
ejpam-6841	506	5	)	)	PUNCT
ejpam-6841	506	6	+	+	CCONJ
ejpam-6841	506	7	1	1	X
ejpam-6841	506	8	.	.	PUNCT
ejpam-6841	507	1	τητ	τητ	INTJ
ejpam-6841	508	1	(	(	PUNCT
ejpam-6841	508	2	f	f	X
ejpam-6841	508	3	,	,	PUNCT
ejpam-6841	508	4	κ	κ	NOUN
ejpam-6841	508	5	)	)	PUNCT
ejpam-6841	508	6	+	+	CCONJ
ejpam-6841	508	7	1	1	NUM
ejpam-6841	508	8	ητ	ητ	NOUN
ejpam-6841	508	9	(	(	PUNCT
ejpam-6841	508	10	f	f	X
ejpam-6841	508	11	,	,	PUNCT
ejpam-6841	508	12	κ	κ	NOUN
ejpam-6841	508	13	)	)	PUNCT
ejpam-6841	508	14	≤	≤	NUM
ejpam-6841	508	15	1	1	NUM
ejpam-6841	508	16	‖lςf	‖lςf	NOUN
ejpam-6841	508	17	−	−	NOUN
ejpam-6841	508	18	lςκ‖τ	lςκ‖τ	PUNCT
ejpam-6841	508	19	.	.	PUNCT
ejpam-6841	509	1	τ	τ	X
ejpam-6841	510	1	+	+	NOUN
ejpam-6841	510	2	1	1	NUM
ejpam-6841	510	3	ητ	ητ	NOUN
ejpam-6841	510	4	(	(	PUNCT
ejpam-6841	510	5	f	f	X
ejpam-6841	510	6	,	,	PUNCT
ejpam-6841	510	7	κ	κ	NOUN
ejpam-6841	510	8	)	)	PUNCT
ejpam-6841	510	9	≤	≤	NUM
ejpam-6841	510	10	1	1	NUM
ejpam-6841	510	11	‖lςf	‖lςf	NOUN
ejpam-6841	510	12	−	−	NOUN
ejpam-6841	510	13	lςκ‖τ	lςκ‖τ	PUNCT
ejpam-6841	510	14	.	.	PUNCT
ejpam-6841	511	1	which	which	PRON
ejpam-6841	511	2	further	far	ADV
ejpam-6841	511	3	implies	imply	VERB
ejpam-6841	511	4	τ	τ	PROPN
ejpam-6841	511	5	−	−	PROPN
ejpam-6841	511	6	1	1	NUM
ejpam-6841	511	7	‖lςf	‖lςf	NOUN
ejpam-6841	511	8	−	−	NOUN
ejpam-6841	511	9	lςκ‖τ	lςκ‖τ	SYM
ejpam-6841	511	10	≤	≤	NUM
ejpam-6841	511	11	−1	−1	NOUN
ejpam-6841	511	12	ητ	ητ	NOUN
ejpam-6841	511	13	(	(	PUNCT
ejpam-6841	511	14	f	f	X
ejpam-6841	511	15	,	,	PUNCT
ejpam-6841	511	16	κ	κ	NOUN
ejpam-6841	511	17	)	)	PUNCT
ejpam-6841	511	18	.	.	PUNCT
ejpam-6841	512	1	so	so	ADV
ejpam-6841	512	2	all	all	DET
ejpam-6841	512	3	the	the	DET
ejpam-6841	512	4	conditions	condition	NOUN
ejpam-6841	512	5	of	of	ADP
ejpam-6841	512	6	theorem	theorem	NOUN
ejpam-6841	512	7	1	1	NUM
ejpam-6841	512	8	are	be	AUX
ejpam-6841	512	9	satisfied	satisfied	ADJ
ejpam-6841	512	10	for	for	ADP
ejpam-6841	512	11	j(κ	j(κ	PROPN
ejpam-6841	512	12	)	)	PUNCT
ejpam-6841	513	1	=	=	SYM
ejpam-6841	513	2	−1	−1	NOUN
ejpam-6841	513	3	κ	κ	NOUN
ejpam-6841	513	4	;	;	PUNCT
ejpam-6841	513	5	κ	κ	X
ejpam-6841	513	6	>	>	X
ejpam-6841	513	7	0	0	NUM
ejpam-6841	513	8	and	and	CCONJ
ejpam-6841	513	9	£	£	SYM
ejpam-6841	513	10	(	(	PUNCT
ejpam-6841	513	11	κ	κ	NOUN
ejpam-6841	513	12	)	)	PUNCT
ejpam-6841	513	13	=	=	SYM
ejpam-6841	514	1	j(κ)−τ	j(κ)−τ	PROPN
ejpam-6841	514	2	.	.	PUNCT
ejpam-6841	515	1	hence	hence	ADV
ejpam-6841	515	2	,	,	PUNCT
ejpam-6841	515	3	the	the	DET
ejpam-6841	515	4	integral	integral	ADJ
ejpam-6841	515	5	equation	equation	NOUN
ejpam-6841	515	6	(	(	PUNCT
ejpam-6841	515	7	26	26	NUM
ejpam-6841	515	8	)	)	PUNCT
ejpam-6841	515	9	admits	admit	VERB
ejpam-6841	515	10	a	a	DET
ejpam-6841	515	11	solution	solution	NOUN
ejpam-6841	515	12	.	.	PUNCT
ejpam-6841	516	1	5	5	X
ejpam-6841	516	2	.	.	X
ejpam-6841	516	3	conclusion	conclusion	NOUN
ejpam-6841	516	4	generalized	generalize	VERB
ejpam-6841	516	5	interpolative	interpolative	ADJ
ejpam-6841	516	6	proximal	proximal	ADJ
ejpam-6841	516	7	contractions	contraction	NOUN
ejpam-6841	516	8	provide	provide	VERB
ejpam-6841	516	9	a	a	DET
ejpam-6841	516	10	robust	robust	ADJ
ejpam-6841	516	11	framework	framework	NOUN
ejpam-6841	516	12	for	for	ADP
ejpam-6841	516	13	solving	solve	VERB
ejpam-6841	516	14	proximity	proximity	NOUN
ejpam-6841	516	15	problems	problem	NOUN
ejpam-6841	516	16	in	in	ADP
ejpam-6841	516	17	various	various	ADJ
ejpam-6841	516	18	mathematical	mathematical	ADJ
ejpam-6841	516	19	and	and	CCONJ
ejpam-6841	516	20	applied	applied	ADJ
ejpam-6841	516	21	contexts	contexts	NOUN
ejpam-6841	516	22	.	.	PUNCT
ejpam-6841	517	1	the	the	DET
ejpam-6841	517	2	established	establish	VERB
ejpam-6841	517	3	existence	existence	NOUN
ejpam-6841	517	4	and	and	CCONJ
ejpam-6841	517	5	uniqueness	uniqueness	NOUN
ejpam-6841	517	6	results	result	NOUN
ejpam-6841	517	7	facilitate	facilitate	VERB
ejpam-6841	517	8	their	their	PRON
ejpam-6841	517	9	practical	practical	ADJ
ejpam-6841	517	10	use	use	NOUN
ejpam-6841	517	11	,	,	PUNCT
ejpam-6841	517	12	offering	offer	VERB
ejpam-6841	517	13	significant	significant	ADJ
ejpam-6841	517	14	insights	insight	NOUN
ejpam-6841	517	15	and	and	CCONJ
ejpam-6841	517	16	solutions	solution	NOUN
ejpam-6841	517	17	in	in	ADP
ejpam-6841	517	18	various	various	ADJ
ejpam-6841	517	19	applied	apply	VERB
ejpam-6841	517	20	mathematics	mathematic	NOUN
ejpam-6841	517	21	and	and	CCONJ
ejpam-6841	517	22	engineering	engineering	NOUN
ejpam-6841	517	23	fields	field	NOUN
ejpam-6841	517	24	.	.	PUNCT
ejpam-6841	518	1	acknowledgements	acknowledgement	NOUN
ejpam-6841	518	2	the	the	DET
ejpam-6841	518	3	authors	author	NOUN
ejpam-6841	518	4	would	would	AUX
ejpam-6841	518	5	like	like	VERB
ejpam-6841	518	6	to	to	PART
ejpam-6841	518	7	thank	thank	VERB
ejpam-6841	518	8	the	the	DET
ejpam-6841	518	9	basque	basque	ADJ
ejpam-6841	518	10	government	government	NOUN
ejpam-6841	518	11	for	for	ADP
ejpam-6841	518	12	funding	fund	VERB
ejpam-6841	518	13	this	this	DET
ejpam-6841	518	14	research	research	NOUN
ejpam-6841	518	15	work	work	NOUN
ejpam-6841	518	16	through	through	ADP
ejpam-6841	518	17	grant	grant	VERB
ejpam-6841	518	18	it1555	it1555	NOUN
ejpam-6841	518	19	-	-	PUNCT
ejpam-6841	518	20	22	22	NUM
ejpam-6841	518	21	.	.	PUNCT
ejpam-6841	519	1	they	they	PRON
ejpam-6841	519	2	also	also	ADV
ejpam-6841	519	3	thank	thank	VERB
ejpam-6841	519	4	miciu	miciu	PROPN
ejpam-6841	519	5	/	/	SYM
ejpam-6841	519	6	aei/10.13039/501100011033	aei/10.13039/501100011033	PROPN
ejpam-6841	519	7	939	939	NUM
ejpam-6841	519	8	and	and	CCONJ
ejpam-6841	519	9	feder	feder	PROPN
ejpam-6841	519	10	/	/	SYM
ejpam-6841	519	11	ue	ue	PROPN
ejpam-6841	519	12	for	for	ADP
ejpam-6841	519	13	partially	partially	ADV
ejpam-6841	519	14	funding	fund	VERB
ejpam-6841	519	15	their	their	PRON
ejpam-6841	519	16	research	research	NOUN
ejpam-6841	519	17	work	work	NOUN
ejpam-6841	519	18	through	through	ADP
ejpam-6841	519	19	grants	grant	NOUN
ejpam-6841	519	20	pid2021123543ob	pid2021123543ob	NOUN
ejpam-6841	519	21	-	-	PUNCT
ejpam-6841	519	22	c21	c21	NOUN
ejpam-6841	519	23	940	940	NUM
ejpam-6841	519	24	and	and	CCONJ
ejpam-6841	519	25	pid2021	pid2021	NOUN
ejpam-6841	519	26	-	-	PUNCT
ejpam-6841	519	27	123543ob	123543ob	VERB
ejpam-6841	519	28	-	-	PUNCT
ejpam-6841	519	29	c22	c22	NOUN
ejpam-6841	519	30	.	.	PUNCT
ejpam-6841	520	1	k.	k.	PROPN
ejpam-6841	520	2	javed	javed	PROPN
ejpam-6841	520	3	,	,	PUNCT
ejpam-6841	520	4	m.	m.	NOUN
ejpam-6841	520	5	nazam	nazam	PROPN
ejpam-6841	520	6	,	,	PUNCT
ejpam-6841	520	7	m.	m.	PROPN
ejpam-6841	520	8	arshad	arshad	PROPN
ejpam-6841	520	9	,	,	PUNCT
ejpam-6841	520	10	m.	m.	NOUN
ejpam-6841	520	11	de	de	X
ejpam-6841	520	12	la	la	PROPN
ejpam-6841	520	13	sen	sen	PROPN
ejpam-6841	520	14	/	/	SYM
ejpam-6841	520	15	eur	eur	PROPN
ejpam-6841	520	16	.	.	PUNCT
ejpam-6841	521	1	j.	j.	PROPN
ejpam-6841	521	2	pure	pure	PROPN
ejpam-6841	521	3	appl	appl	PROPN
ejpam-6841	521	4	.	.	PROPN
ejpam-6841	521	5	math	math	PROPN
ejpam-6841	521	6	,	,	PUNCT
ejpam-6841	521	7	18	18	NUM
ejpam-6841	521	8	(	(	PUNCT
ejpam-6841	521	9	4	4	NUM
ejpam-6841	521	10	)	)	PUNCT
ejpam-6841	521	11	(	(	PUNCT
ejpam-6841	521	12	2025	2025	NUM
ejpam-6841	521	13	)	)	PUNCT
ejpam-6841	521	14	,	,	PUNCT
ejpam-6841	521	15	6841	6841	NUM
ejpam-6841	521	16	22	22	NUM
ejpam-6841	521	17	of	of	ADP
ejpam-6841	521	18	23	23	NUM
ejpam-6841	521	19	6	6	NUM
ejpam-6841	521	20	.	.	PUNCT
ejpam-6841	522	1	authors	author	NOUN
ejpam-6841	522	2	’	’	PART
ejpam-6841	522	3	contributions	contribution	NOUN
ejpam-6841	522	4	m.n	m.n	PROPN
ejpam-6841	522	5	.	.	PROPN
ejpam-6841	522	6	tabled	table	VERB
ejpam-6841	522	7	the	the	DET
ejpam-6841	522	8	main	main	ADJ
ejpam-6841	522	9	idea	idea	NOUN
ejpam-6841	522	10	of	of	ADP
ejpam-6841	522	11	this	this	DET
ejpam-6841	522	12	paper	paper	NOUN
ejpam-6841	522	13	;	;	PUNCT
ejpam-6841	522	14	k.	k.	PROPN
ejpam-6841	522	15	j.	j.	PROPN
ejpam-6841	522	16	wrote	write	VERB
ejpam-6841	522	17	the	the	DET
ejpam-6841	522	18	first	first	ADJ
ejpam-6841	522	19	draft	draft	NOUN
ejpam-6841	522	20	of	of	ADP
ejpam-6841	522	21	this	this	DET
ejpam-6841	522	22	paper	paper	NOUN
ejpam-6841	522	23	;	;	PUNCT
ejpam-6841	522	24	m.n	m.n	PROPN
ejpam-6841	522	25	.	.	PROPN
ejpam-6841	522	26	,	,	PUNCT
ejpam-6841	522	27	m.	m.	NOUN
ejpam-6841	522	28	a.	a.	PROPN
ejpam-6841	522	29	and	and	CCONJ
ejpam-6841	522	30	m.	m.	PROPN
ejpam-6841	522	31	d.	d.	PROPN
ejpam-6841	522	32	s.	s.	PROPN
ejpam-6841	522	33	reviewed	review	VERB
ejpam-6841	522	34	and	and	CCONJ
ejpam-6841	522	35	prepared	prepare	VERB
ejpam-6841	522	36	the	the	DET
ejpam-6841	522	37	second	second	ADJ
ejpam-6841	522	38	draft	draft	NOUN
ejpam-6841	522	39	;	;	PUNCT
ejpam-6841	522	40	m.	m.	PROPN
ejpam-6841	522	41	d.	d.	PROPN
ejpam-6841	522	42	s.	s.	PROPN
ejpam-6841	522	43	supervised	supervise	VERB
ejpam-6841	522	44	the	the	DET
ejpam-6841	522	45	project	project	NOUN
ejpam-6841	522	46	.	.	PUNCT
ejpam-6841	523	1	all	all	DET
ejpam-6841	523	2	authors	author	NOUN
ejpam-6841	523	3	have	have	AUX
ejpam-6841	523	4	read	read	VERB
ejpam-6841	523	5	and	and	CCONJ
ejpam-6841	523	6	agreed	agree	VERB
ejpam-6841	523	7	to	to	ADP
ejpam-6841	523	8	the	the	DET
ejpam-6841	523	9	published	publish	VERB
ejpam-6841	523	10	version	version	NOUN
ejpam-6841	523	11	of	of	ADP
ejpam-6841	523	12	the	the	DET
ejpam-6841	523	13	manuscript	manuscript	NOUN
ejpam-6841	523	14	.	.	PUNCT
ejpam-6841	524	1	funding	fund	VERB
ejpam-6841	524	2	no	no	DET
ejpam-6841	524	3	funding	funding	NOUN
ejpam-6841	524	4	received	receive	VERB
ejpam-6841	524	5	for	for	ADP
ejpam-6841	524	6	this	this	DET
ejpam-6841	524	7	paper	paper	NOUN
ejpam-6841	524	8	.	.	PUNCT
ejpam-6841	525	1	availability	availability	NOUN
ejpam-6841	525	2	of	of	ADP
ejpam-6841	525	3	data	datum	NOUN
ejpam-6841	525	4	and	and	CCONJ
ejpam-6841	525	5	materials	material	NOUN
ejpam-6841	525	6	data	datum	NOUN
ejpam-6841	525	7	sharing	share	VERB
ejpam-6841	525	8	not	not	PART
ejpam-6841	525	9	applicable	applicable	ADJ
ejpam-6841	525	10	to	to	ADP
ejpam-6841	525	11	this	this	DET
ejpam-6841	525	12	article	article	NOUN
ejpam-6841	525	13	as	as	SCONJ
ejpam-6841	525	14	no	no	DET
ejpam-6841	525	15	datasets	dataset	NOUN
ejpam-6841	525	16	were	be	AUX
ejpam-6841	525	17	generated	generate	VERB
ejpam-6841	525	18	or	or	CCONJ
ejpam-6841	525	19	analyzed	analyze	VERB
ejpam-6841	525	20	during	during	ADP
ejpam-6841	525	21	the	the	DET
ejpam-6841	525	22	current	current	ADJ
ejpam-6841	525	23	study	study	NOUN
ejpam-6841	525	24	.	.	PUNCT
ejpam-6841	526	1	competing	compete	VERB
ejpam-6841	526	2	interests	interest	NOUN
ejpam-6841	526	3	the	the	DET
ejpam-6841	526	4	authors	author	NOUN
ejpam-6841	526	5	declare	declare	VERB
ejpam-6841	526	6	that	that	SCONJ
ejpam-6841	526	7	they	they	PRON
ejpam-6841	526	8	do	do	AUX
ejpam-6841	526	9	not	not	PART
ejpam-6841	526	10	have	have	VERB
ejpam-6841	526	11	any	any	DET
ejpam-6841	526	12	competing	compete	VERB
ejpam-6841	526	13	interests	interest	NOUN
ejpam-6841	526	14	.	.	PUNCT
ejpam-6841	527	1	all	all	DET
ejpam-6841	527	2	authors	author	NOUN
ejpam-6841	527	3	read	read	VERB
ejpam-6841	527	4	and	and	CCONJ
ejpam-6841	527	5	approved	approve	VERB
ejpam-6841	527	6	the	the	DET
ejpam-6841	527	7	final	final	ADJ
ejpam-6841	527	8	manuscript	manuscript	NOUN
ejpam-6841	527	9	.	.	PUNCT
ejpam-6841	528	1	references	reference	NOUN
ejpam-6841	528	2	[	[	X
ejpam-6841	528	3	1	1	NUM
ejpam-6841	528	4	]	]	PUNCT
ejpam-6841	528	5	erdal	erdal	X
ejpam-6841	528	6	karapinar	karapinar	PROPN
ejpam-6841	528	7	.	.	PUNCT
ejpam-6841	529	1	revisiting	revisit	VERB
ejpam-6841	529	2	the	the	DET
ejpam-6841	529	3	kannan	kannan	PROPN
ejpam-6841	529	4	type	type	NOUN
ejpam-6841	529	5	contraction	contraction	NOUN
ejpam-6841	529	6	via	via	ADP
ejpam-6841	529	7	interpolation	interpolation	NOUN
ejpam-6841	529	8	.	.	PUNCT
ejpam-6841	530	1	advances	advance	NOUN
ejpam-6841	530	2	in	in	ADP
ejpam-6841	530	3	theory	theory	NOUN
ejpam-6841	530	4	of	of	ADP
ejpam-6841	530	5	nonlinear	nonlinear	ADJ
ejpam-6841	530	6	analysis	analysis	NOUN
ejpam-6841	530	7	and	and	CCONJ
ejpam-6841	530	8	applications	application	NOUN
ejpam-6841	530	9	,	,	PUNCT
ejpam-6841	530	10	2:85–87	2:85–87	NUM
ejpam-6841	530	11	,	,	PUNCT
ejpam-6841	530	12	2018	2018	NUM
ejpam-6841	530	13	.	.	PUNCT
ejpam-6841	531	1	[	[	X
ejpam-6841	531	2	2	2	NUM
ejpam-6841	531	3	]	]	PUNCT
ejpam-6841	531	4	erdal	erdal	X
ejpam-6841	531	5	karapinar	karapinar	PROPN
ejpam-6841	531	6	and	and	CCONJ
ejpam-6841	531	7	ravi	ravi	PROPN
ejpam-6841	531	8	p.	p.	PROPN
ejpam-6841	531	9	agarwal	agarwal	PROPN
ejpam-6841	531	10	.	.	PUNCT
ejpam-6841	532	1	interpolative	interpolative	ADJ
ejpam-6841	532	2	rus	rus	PROPN
ejpam-6841	532	3	–	–	PUNCT
ejpam-6841	532	4	reich	reich	NOUN
ejpam-6841	532	5	–	–	PUNCT
ejpam-6841	532	6	ćirić	ćirić	NOUN
ejpam-6841	532	7	type	type	NOUN
ejpam-6841	532	8	contraction	contraction	NOUN
ejpam-6841	532	9	via	via	ADP
ejpam-6841	532	10	simulation	simulation	NOUN
ejpam-6841	532	11	functions	function	NOUN
ejpam-6841	532	12	.	.	PUNCT
ejpam-6841	533	1	analele	analele	PROPN
ejpam-6841	533	2	universitatii	universitatii	PROPN
ejpam-6841	533	3	ovidius	ovidius	PROPN
ejpam-6841	533	4	constanta	constanta	PROPN
ejpam-6841	533	5	,	,	PUNCT
ejpam-6841	533	6	27:137–152	27:137–152	PROPN
ejpam-6841	533	7	,	,	PUNCT
ejpam-6841	533	8	2019	2019	NUM
ejpam-6841	533	9	.	.	PUNCT
ejpam-6841	534	1	[	[	X
ejpam-6841	534	2	3	3	X
ejpam-6841	534	3	]	]	PUNCT
ejpam-6841	534	4	erdal	erdal	X
ejpam-6841	534	5	karapinar	karapinar	PROPN
ejpam-6841	534	6	,	,	PUNCT
ejpam-6841	534	7	omar	omar	PROPN
ejpam-6841	534	8	alqahtani	alqahtani	PROPN
ejpam-6841	534	9	,	,	PUNCT
ejpam-6841	534	10	and	and	CCONJ
ejpam-6841	534	11	hassen	hassen	PROPN
ejpam-6841	534	12	aydi	aydi	VERB
ejpam-6841	534	13	.	.	PUNCT
ejpam-6841	535	1	on	on	ADP
ejpam-6841	535	2	interpolative	interpolative	ADJ
ejpam-6841	535	3	hardy	hardy	ADJ
ejpam-6841	535	4	–	–	PUNCT
ejpam-6841	535	5	rogers	rogers	NOUN
ejpam-6841	535	6	type	type	NOUN
ejpam-6841	535	7	contraction	contraction	NOUN
ejpam-6841	535	8	.	.	PUNCT
ejpam-6841	536	1	symmetry	symmetry	NOUN
ejpam-6841	536	2	,	,	PUNCT
ejpam-6841	536	3	11(8	11(8	NUM
ejpam-6841	536	4	)	)	PUNCT
ejpam-6841	536	5	,	,	PUNCT
ejpam-6841	536	6	2019	2019	NUM
ejpam-6841	536	7	.	.	PUNCT
ejpam-6841	537	1	[	[	X
ejpam-6841	537	2	4	4	X
ejpam-6841	537	3	]	]	X
ejpam-6841	537	4	muhammad	muhammad	PROPN
ejpam-6841	537	5	nazam	nazam	PROPN
ejpam-6841	537	6	,	,	PUNCT
ejpam-6841	537	7	hassen	hassen	PROPN
ejpam-6841	537	8	aydi	aydi	ADV
ejpam-6841	537	9	,	,	PUNCT
ejpam-6841	537	10	and	and	CCONJ
ejpam-6841	537	11	aftab	aftab	PROPN
ejpam-6841	537	12	hussain	hussain	PROPN
ejpam-6841	537	13	.	.	PUNCT
ejpam-6841	538	1	generalized	generalize	VERB
ejpam-6841	538	2	interpolative	interpolative	ADJ
ejpam-6841	538	3	contraction	contraction	NOUN
ejpam-6841	538	4	and	and	CCONJ
ejpam-6841	538	5	an	an	DET
ejpam-6841	538	6	application	application	NOUN
ejpam-6841	538	7	.	.	PUNCT
ejpam-6841	539	1	journal	journal	NOUN
ejpam-6841	539	2	of	of	ADP
ejpam-6841	539	3	mathematics	mathematic	NOUN
ejpam-6841	539	4	,	,	PUNCT
ejpam-6841	539	5	2021	2021	NUM
ejpam-6841	539	6	.	.	PUNCT
ejpam-6841	540	1	article	article	NOUN
ejpam-6841	540	2	i	i	PROPN
ejpam-6841	540	3	d	d	PROPN
ejpam-6841	540	4	6461477	6461477	NUM
ejpam-6841	540	5	.	.	PUNCT
ejpam-6841	541	1	[	[	X
ejpam-6841	541	2	5	5	NUM
ejpam-6841	541	3	]	]	X
ejpam-6841	541	4	khalil	khalil	PROPN
ejpam-6841	541	5	javed	javed	PROPN
ejpam-6841	541	6	,	,	PUNCT
ejpam-6841	541	7	muhammad	muhammad	PROPN
ejpam-6841	541	8	nazam	nazam	PROPN
ejpam-6841	541	9	,	,	PUNCT
ejpam-6841	541	10	özlem	özlem	NOUN
ejpam-6841	541	11	acar	acar	NOUN
ejpam-6841	541	12	,	,	PUNCT
ejpam-6841	541	13	and	and	CCONJ
ejpam-6841	541	14	muhammad	muhammad	PROPN
ejpam-6841	541	15	arshad	arshad	PROPN
ejpam-6841	541	16	.	.	PROPN
ejpam-6841	542	1	on	on	ADP
ejpam-6841	542	2	the	the	DET
ejpam-6841	542	3	best	good	ADJ
ejpam-6841	542	4	proximity	proximity	NOUN
ejpam-6841	542	5	point	point	NOUN
ejpam-6841	542	6	theorems	theorem	NOUN
ejpam-6841	542	7	for	for	ADP
ejpam-6841	542	8	interpolative	interpolative	ADJ
ejpam-6841	542	9	proximal	proximal	ADJ
ejpam-6841	542	10	contractions	contraction	NOUN
ejpam-6841	542	11	with	with	ADP
ejpam-6841	542	12	applications	application	NOUN
ejpam-6841	542	13	.	.	PUNCT
ejpam-6841	543	1	filomat	filomat	NOUN
ejpam-6841	543	2	,	,	PUNCT
ejpam-6841	543	3	39(8):2817–2830	39(8):2817–2830	NUM
ejpam-6841	543	4	,	,	PUNCT
ejpam-6841	543	5	2025	2025	NUM
ejpam-6841	543	6	.	.	PUNCT
ejpam-6841	544	1	[	[	X
ejpam-6841	544	2	6	6	X
ejpam-6841	544	3	]	]	PUNCT
ejpam-6841	544	4	muhammad	muhammad	PROPN
ejpam-6841	544	5	nazam	nazam	PROPN
ejpam-6841	544	6	,	,	PUNCT
ejpam-6841	544	7	hassen	hassen	PROPN
ejpam-6841	544	8	aydi	aydi	ADV
ejpam-6841	544	9	,	,	PUNCT
ejpam-6841	544	10	and	and	CCONJ
ejpam-6841	544	11	aftab	aftab	PROPN
ejpam-6841	544	12	hussain	hussain	PROPN
ejpam-6841	544	13	.	.	PUNCT
ejpam-6841	545	1	existence	existence	NOUN
ejpam-6841	545	2	theorems	theorem	VERB
ejpam-6841	545	3	for	for	ADP
ejpam-6841	545	4	(	(	PUNCT
ejpam-6841	545	5	phi	phi	NOUN
ejpam-6841	545	6	,	,	PUNCT
ejpam-6841	545	7	psi)orthogonal	psi)orthogonal	ADJ
ejpam-6841	545	8	interpolative	interpolative	ADJ
ejpam-6841	545	9	contractions	contraction	NOUN
ejpam-6841	545	10	and	and	CCONJ
ejpam-6841	545	11	an	an	DET
ejpam-6841	545	12	application	application	NOUN
ejpam-6841	545	13	to	to	ADP
ejpam-6841	545	14	fractional	fractional	ADJ
ejpam-6841	545	15	differential	differential	ADJ
ejpam-6841	545	16	equations	equation	NOUN
ejpam-6841	545	17	.	.	PUNCT
ejpam-6841	546	1	optimization	optimization	NOUN
ejpam-6841	546	2	,	,	PUNCT
ejpam-6841	546	3	72(7):1899–1929	72(7):1899–1929	NOUN
ejpam-6841	546	4	,	,	PUNCT
ejpam-6841	546	5	2023	2023	NUM
ejpam-6841	546	6	.	.	PUNCT
ejpam-6841	547	1	[	[	X
ejpam-6841	547	2	7	7	X
ejpam-6841	547	3	]	]	PUNCT
ejpam-6841	547	4	s.	s.	PROPN
ejpam-6841	547	5	s.	s.	PROPN
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ejpam-6841	547	10	banach	banach	NOUN
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ejpam-6841	547	12	contraction	contraction	NOUN
ejpam-6841	547	13	principle	principle	PROPN
ejpam-6841	547	14	.	.	PUNCT
ejpam-6841	548	1	numerical	numerical	ADJ
ejpam-6841	548	2	functional	functional	ADJ
ejpam-6841	548	3	analysis	analysis	NOUN
ejpam-6841	548	4	and	and	CCONJ
ejpam-6841	548	5	optimization	optimization	NOUN
ejpam-6841	548	6	,	,	PUNCT
ejpam-6841	548	7	31(5):569–576	31(5):569–576	PROPN
ejpam-6841	548	8	,	,	PUNCT
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ejpam-6841	548	10	.	.	PUNCT
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ejpam-6841	549	5	d.	d.	PROPN
ejpam-6841	549	6	proinov	proinov	PROPN
ejpam-6841	549	7	.	.	PUNCT
ejpam-6841	550	1	fixed	fix	VERB
ejpam-6841	550	2	point	point	NOUN
ejpam-6841	550	3	theorems	theorem	NOUN
ejpam-6841	550	4	for	for	ADP
ejpam-6841	550	5	generalized	generalized	ADJ
ejpam-6841	550	6	contractive	contractive	ADJ
ejpam-6841	550	7	mappings	mapping	NOUN
ejpam-6841	550	8	in	in	ADP
ejpam-6841	550	9	metric	metric	ADJ
ejpam-6841	550	10	spaces	space	NOUN
ejpam-6841	550	11	.	.	PUNCT
ejpam-6841	551	1	journal	journal	NOUN
ejpam-6841	551	2	of	of	ADP
ejpam-6841	551	3	fixed	fix	VERB
ejpam-6841	551	4	point	point	NOUN
ejpam-6841	551	5	theory	theory	NOUN
ejpam-6841	551	6	and	and	CCONJ
ejpam-6841	551	7	applications	application	NOUN
ejpam-6841	551	8	,	,	PUNCT
ejpam-6841	551	9	22:21	22:21	NUM
ejpam-6841	551	10	,	,	PUNCT
ejpam-6841	551	11	2020	2020	NUM
ejpam-6841	551	12	.	.	PUNCT
ejpam-6841	552	1	[	[	X
ejpam-6841	552	2	9	9	NUM
ejpam-6841	552	3	]	]	PUNCT
ejpam-6841	552	4	erdal	erdal	X
ejpam-6841	552	5	karapinar	karapinar	PROPN
ejpam-6841	552	6	and	and	CCONJ
ejpam-6841	552	7	bessem	bessem	NOUN
ejpam-6841	552	8	samet	samet	NOUN
ejpam-6841	552	9	.	.	PUNCT
ejpam-6841	553	1	generalized	generalize	VERB
ejpam-6841	553	2	(	(	PUNCT
ejpam-6841	553	3	α	α	NOUN
ejpam-6841	553	4	,	,	PUNCT
ejpam-6841	553	5	ψ)-contractive	ψ)-contractive	ADJ
ejpam-6841	553	6	type	type	NOUN
ejpam-6841	553	7	mappings	mapping	NOUN
ejpam-6841	553	8	and	and	CCONJ
ejpam-6841	553	9	related	relate	VERB
ejpam-6841	553	10	fixed	fix	VERB
ejpam-6841	553	11	point	point	NOUN
ejpam-6841	553	12	theorems	theorem	NOUN
ejpam-6841	553	13	with	with	ADP
ejpam-6841	553	14	applications	application	NOUN
ejpam-6841	553	15	.	.	PUNCT
ejpam-6841	554	1	abstract	abstract	ADJ
ejpam-6841	554	2	and	and	CCONJ
ejpam-6841	554	3	applied	apply	VERB
ejpam-6841	554	4	analysis	analysis	NOUN
ejpam-6841	554	5	,	,	PUNCT
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ejpam-6841	554	7	,	,	PUNCT
ejpam-6841	554	8	2012	2012	NUM
ejpam-6841	554	9	.	.	PUNCT
ejpam-6841	555	1	article	article	NOUN
ejpam-6841	555	2	i	i	PROPN
ejpam-6841	555	3	d	d	PROPN
ejpam-6841	555	4	793486	793486	NUM
ejpam-6841	555	5	.	.	PUNCT
ejpam-6841	556	1	k.	k.	PROPN
ejpam-6841	556	2	javed	javed	PROPN
ejpam-6841	556	3	,	,	PUNCT
ejpam-6841	556	4	m.	m.	NOUN
ejpam-6841	556	5	nazam	nazam	PROPN
ejpam-6841	556	6	,	,	PUNCT
ejpam-6841	556	7	m.	m.	PROPN
ejpam-6841	556	8	arshad	arshad	PROPN
ejpam-6841	556	9	,	,	PUNCT
ejpam-6841	556	10	m.	m.	NOUN
ejpam-6841	556	11	de	de	X
ejpam-6841	556	12	la	la	PROPN
ejpam-6841	556	13	sen	sen	PROPN
ejpam-6841	556	14	/	/	SYM
ejpam-6841	556	15	eur	eur	PROPN
ejpam-6841	556	16	.	.	PUNCT
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ejpam-6841	557	2	pure	pure	PROPN
ejpam-6841	557	3	appl	appl	PROPN
ejpam-6841	557	4	.	.	PROPN
ejpam-6841	557	5	math	math	PROPN
ejpam-6841	557	6	,	,	PUNCT
ejpam-6841	557	7	18	18	NUM
ejpam-6841	557	8	(	(	PUNCT
ejpam-6841	557	9	4	4	NUM
ejpam-6841	557	10	)	)	PUNCT
ejpam-6841	557	11	(	(	PUNCT
ejpam-6841	557	12	2025	2025	NUM
ejpam-6841	557	13	)	)	PUNCT
ejpam-6841	557	14	,	,	PUNCT
ejpam-6841	557	15	6841	6841	NUM
ejpam-6841	557	16	23	23	NUM
ejpam-6841	557	17	of	of	ADP
ejpam-6841	557	18	23	23	NUM
ejpam-6841	558	1	[	[	SYM
ejpam-6841	558	2	10	10	NUM
ejpam-6841	558	3	]	]	X
ejpam-6841	558	4	i.	i.	NOUN
ejpam-6841	558	5	altun	altun	PROPN
ejpam-6841	558	6	and	and	CCONJ
ejpam-6841	558	7	a.	a.	NOUN
ejpam-6841	558	8	taşdemir	taşdemir	PROPN
ejpam-6841	558	9	.	.	PUNCT
ejpam-6841	559	1	on	on	ADP
ejpam-6841	559	2	best	good	ADJ
ejpam-6841	559	3	proximity	proximity	NOUN
ejpam-6841	559	4	points	point	NOUN
ejpam-6841	559	5	of	of	ADP
ejpam-6841	559	6	interpolative	interpolative	ADJ
ejpam-6841	559	7	proximal	proximal	ADJ
ejpam-6841	559	8	contraction	contraction	NOUN
ejpam-6841	559	9	.	.	PUNCT
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ejpam-6841	560	2	mathematicae	mathematicae	PROPN
ejpam-6841	560	3	,	,	PUNCT
ejpam-6841	560	4	44(9):1233–1241	44(9):1233–1241	NUM
ejpam-6841	560	5	,	,	PUNCT
ejpam-6841	560	6	2020	2020	NUM
ejpam-6841	560	7	.	.	PUNCT
ejpam-6841	561	1	[	[	X
ejpam-6841	561	2	11	11	NUM
ejpam-6841	561	3	]	]	PUNCT
ejpam-6841	561	4	s.	s.	PROPN
ejpam-6841	561	5	s.	s.	PROPN
ejpam-6841	561	6	basha	basha	PROPN
ejpam-6841	561	7	.	.	PUNCT
ejpam-6841	562	1	best	good	ADJ
ejpam-6841	562	2	proximity	proximity	NOUN
ejpam-6841	562	3	point	point	NOUN
ejpam-6841	562	4	theorems	theorem	NOUN
ejpam-6841	562	5	.	.	PUNCT
ejpam-6841	563	1	journal	journal	PROPN
ejpam-6841	563	2	of	of	ADP
ejpam-6841	563	3	approximation	approximation	NOUN
ejpam-6841	563	4	theory	theory	NOUN
ejpam-6841	563	5	,	,	PUNCT
ejpam-6841	563	6	163:1772–1781	163:1772–1781	NUM
ejpam-6841	563	7	,	,	PUNCT
ejpam-6841	563	8	2011	2011	NUM
ejpam-6841	563	9	.	.	PUNCT
ejpam-6841	564	1	[	[	X
ejpam-6841	564	2	12	12	NUM
ejpam-6841	564	3	]	]	X
ejpam-6841	564	4	iqbal	iqbal	PROPN
ejpam-6841	564	5	beg	beg	PROPN
ejpam-6841	564	6	,	,	PUNCT
ejpam-6841	564	7	g.	g.	PROPN
ejpam-6841	564	8	mani	mani	PROPN
ejpam-6841	564	9	,	,	PUNCT
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ejpam-6841	564	11	a.	a.	PROPN
ejpam-6841	564	12	j.	j.	PROPN
ejpam-6841	564	13	gnanaprakasam	gnanaprakasam	PROPN
ejpam-6841	564	14	.	.	PUNCT
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ejpam-6841	565	2	proximity	proximity	NOUN
ejpam-6841	565	3	points	point	NOUN
ejpam-6841	565	4	of	of	ADP
ejpam-6841	565	5	generalized	generalized	ADJ
ejpam-6841	565	6	f	f	ADJ
ejpam-6841	565	7	-	-	ADJ
ejpam-6841	565	8	proximal	proximal	ADJ
ejpam-6841	565	9	non	non	ADJ
ejpam-6841	565	10	-	-	ADJ
ejpam-6841	565	11	self	self	ADJ
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ejpam-6841	565	13	.	.	PUNCT
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ejpam-6841	566	3	fixed	fix	VERB
ejpam-6841	566	4	point	point	NOUN
ejpam-6841	566	5	theory	theory	NOUN
ejpam-6841	566	6	and	and	CCONJ
ejpam-6841	566	7	applications	application	NOUN
ejpam-6841	566	8	,	,	PUNCT
ejpam-6841	566	9	23:49	23:49	NUM
ejpam-6841	566	10	,	,	PUNCT
ejpam-6841	566	11	2021	2021	NUM
ejpam-6841	566	12	.	.	PUNCT