id	sid	tid	token	lemma	pos
ejpam-6793	1	1	european	european	PROPN
ejpam-6793	1	2	journal	journal	PROPN
ejpam-6793	1	3	of	of	ADP
ejpam-6793	1	4	pure	pure	ADJ
ejpam-6793	1	5	and	and	CCONJ
ejpam-6793	1	6	applied	applied	ADJ
ejpam-6793	1	7	mathematics	mathematic	NOUN
ejpam-6793	1	8	2025	2025	NUM
ejpam-6793	1	9	,	,	PUNCT
ejpam-6793	1	10	vol	vol	NOUN
ejpam-6793	1	11	.	.	PROPN
ejpam-6793	1	12	18	18	NUM
ejpam-6793	1	13	,	,	PUNCT
ejpam-6793	1	14	issue	issue	NOUN
ejpam-6793	1	15	4	4	NUM
ejpam-6793	1	16	,	,	PUNCT
ejpam-6793	1	17	article	article	NOUN
ejpam-6793	1	18	number	number	NOUN
ejpam-6793	1	19	6793	6793	NUM
ejpam-6793	1	20	issn	issn	PROPN
ejpam-6793	1	21	1307	1307	NUM
ejpam-6793	1	22	-	-	SYM
ejpam-6793	1	23	5543	5543	NUM
ejpam-6793	1	24	–	–	PUNCT
ejpam-6793	1	25	ejpam.com	ejpam.com	X
ejpam-6793	1	26	published	publish	VERB
ejpam-6793	1	27	by	by	ADP
ejpam-6793	1	28	new	new	PROPN
ejpam-6793	1	29	york	york	PROPN
ejpam-6793	1	30	business	business	PROPN
ejpam-6793	1	31	global	global	ADJ
ejpam-6793	1	32	exponential	exponential	ADJ
ejpam-6793	1	33	bases	basis	NOUN
ejpam-6793	1	34	of	of	ADP
ejpam-6793	1	35	cliffordian	cliffordian	ADJ
ejpam-6793	1	36	polynomials	polynomial	NOUN
ejpam-6793	1	37	in	in	ADP
ejpam-6793	1	38	fréchet	fréchet	NOUN
ejpam-6793	1	39	modules	module	NOUN
ejpam-6793	1	40	mohra	mohra	NOUN
ejpam-6793	1	41	zayed1,∗	zayed1,∗	NOUN
ejpam-6793	1	42	1	1	NUM
ejpam-6793	1	43	mathematics	mathematics	PROPN
ejpam-6793	1	44	department	department	NOUN
ejpam-6793	1	45	,	,	PUNCT
ejpam-6793	1	46	college	college	NOUN
ejpam-6793	1	47	of	of	ADP
ejpam-6793	1	48	science	science	NOUN
ejpam-6793	1	49	,	,	PUNCT
ejpam-6793	1	50	king	king	PROPN
ejpam-6793	1	51	khalid	khalid	PROPN
ejpam-6793	1	52	university	university	PROPN
ejpam-6793	1	53	,	,	PUNCT
ejpam-6793	1	54	abha	abha	NOUN
ejpam-6793	1	55	61413	61413	NUM
ejpam-6793	1	56	,	,	PUNCT
ejpam-6793	1	57	saudi	saudi	PROPN
ejpam-6793	1	58	arabia	arabia	PROPN
ejpam-6793	1	59	abstract	abstract	NOUN
ejpam-6793	1	60	.	.	PUNCT
ejpam-6793	2	1	this	this	DET
ejpam-6793	2	2	paper	paper	NOUN
ejpam-6793	2	3	presents	present	VERB
ejpam-6793	2	4	a	a	DET
ejpam-6793	2	5	generalization	generalization	NOUN
ejpam-6793	2	6	of	of	ADP
ejpam-6793	2	7	the	the	DET
ejpam-6793	2	8	exponential	exponential	ADJ
ejpam-6793	2	9	base	base	NOUN
ejpam-6793	2	10	of	of	ADP
ejpam-6793	2	11	special	special	ADJ
ejpam-6793	2	12	monogenic	monogenic	ADJ
ejpam-6793	2	13	polynomials	polynomial	NOUN
ejpam-6793	2	14	within	within	ADP
ejpam-6793	2	15	the	the	DET
ejpam-6793	2	16	framework	framework	NOUN
ejpam-6793	2	17	of	of	ADP
ejpam-6793	2	18	fréchet	fréchet	NOUN
ejpam-6793	2	19	modules	module	NOUN
ejpam-6793	2	20	(	(	PUNCT
ejpam-6793	2	21	f	f	NOUN
ejpam-6793	2	22	-	-	PUNCT
ejpam-6793	2	23	modules	module	NOUN
ejpam-6793	2	24	)	)	PUNCT
ejpam-6793	2	25	.	.	PUNCT
ejpam-6793	3	1	the	the	DET
ejpam-6793	3	2	study	study	NOUN
ejpam-6793	3	3	focuses	focus	VERB
ejpam-6793	3	4	on	on	ADP
ejpam-6793	3	5	examining	examine	VERB
ejpam-6793	3	6	the	the	DET
ejpam-6793	3	7	convergence	convergence	NOUN
ejpam-6793	3	8	properties	property	NOUN
ejpam-6793	3	9	,	,	PUNCT
ejpam-6793	3	10	specifically	specifically	ADV
ejpam-6793	3	11	the	the	DET
ejpam-6793	3	12	effectiveness	effectiveness	NOUN
ejpam-6793	3	13	,	,	PUNCT
ejpam-6793	3	14	of	of	ADP
ejpam-6793	3	15	both	both	CCONJ
ejpam-6793	3	16	the	the	DET
ejpam-6793	3	17	exponential	exponential	ADJ
ejpam-6793	3	18	simple	simple	ADJ
ejpam-6793	3	19	base	base	NOUN
ejpam-6793	3	20	of	of	ADP
ejpam-6793	3	21	special	special	ADJ
ejpam-6793	3	22	monogenic	monogenic	ADJ
ejpam-6793	3	23	polynomials	polynomial	NOUN
ejpam-6793	3	24	(	(	PUNCT
ejpam-6793	3	25	esbsmps	esbsmp	NOUN
ejpam-6793	3	26	)	)	PUNCT
ejpam-6793	3	27	and	and	CCONJ
ejpam-6793	3	28	the	the	DET
ejpam-6793	3	29	exponential	exponential	ADJ
ejpam-6793	3	30	cannon	cannon	NOUN
ejpam-6793	3	31	base	base	NOUN
ejpam-6793	3	32	of	of	ADP
ejpam-6793	3	33	special	special	ADJ
ejpam-6793	3	34	monogenic	monogenic	ADJ
ejpam-6793	3	35	polynomials	polynomial	NOUN
ejpam-6793	3	36	(	(	PUNCT
ejpam-6793	3	37	ecbsmps	ecbsmp	NOUN
ejpam-6793	3	38	)	)	PUNCT
ejpam-6793	3	39	in	in	ADP
ejpam-6793	3	40	fréchet	fréchet	NOUN
ejpam-6793	3	41	modules	module	NOUN
ejpam-6793	3	42	.	.	PUNCT
ejpam-6793	4	1	these	these	DET
ejpam-6793	4	2	properties	property	NOUN
ejpam-6793	4	3	are	be	AUX
ejpam-6793	4	4	investigated	investigate	VERB
ejpam-6793	4	5	on	on	ADP
ejpam-6793	4	6	hyper	hyper	ADJ
ejpam-6793	4	7	-	-	ADJ
ejpam-6793	4	8	closed	closed	ADJ
ejpam-6793	4	9	and	and	CCONJ
ejpam-6793	4	10	open	open	ADJ
ejpam-6793	4	11	balls	ball	NOUN
ejpam-6793	4	12	,	,	PUNCT
ejpam-6793	4	13	in	in	ADP
ejpam-6793	4	14	open	open	ADJ
ejpam-6793	4	15	regions	region	NOUN
ejpam-6793	4	16	surrounding	surround	VERB
ejpam-6793	4	17	hyper	hyper	ADJ
ejpam-6793	4	18	-	-	ADJ
ejpam-6793	4	19	closed	closed	ADJ
ejpam-6793	4	20	balls	ball	NOUN
ejpam-6793	4	21	,	,	PUNCT
ejpam-6793	4	22	for	for	ADP
ejpam-6793	4	23	all	all	DET
ejpam-6793	4	24	entire	entire	ADJ
ejpam-6793	4	25	special	special	ADJ
ejpam-6793	4	26	monogenic	monogenic	ADJ
ejpam-6793	4	27	functions	function	NOUN
ejpam-6793	4	28	,	,	PUNCT
ejpam-6793	4	29	as	as	ADV
ejpam-6793	4	30	well	well	ADV
ejpam-6793	4	31	as	as	ADP
ejpam-6793	4	32	at	at	ADP
ejpam-6793	4	33	the	the	DET
ejpam-6793	4	34	origin	origin	NOUN
ejpam-6793	4	35	.	.	PUNCT
ejpam-6793	5	1	furthermore	furthermore	ADV
ejpam-6793	5	2	,	,	PUNCT
ejpam-6793	5	3	an	an	DET
ejpam-6793	5	4	explicit	explicit	ADJ
ejpam-6793	5	5	upper	upper	ADJ
ejpam-6793	5	6	bound	bind	VERB
ejpam-6793	5	7	for	for	ADP
ejpam-6793	5	8	the	the	DET
ejpam-6793	5	9	order	order	NOUN
ejpam-6793	5	10	of	of	ADP
ejpam-6793	5	11	the	the	DET
ejpam-6793	5	12	exponential	exponential	ADJ
ejpam-6793	5	13	simple	simple	ADJ
ejpam-6793	5	14	base	base	NOUN
ejpam-6793	5	15	is	be	AUX
ejpam-6793	5	16	established	establish	VERB
ejpam-6793	5	17	and	and	CCONJ
ejpam-6793	5	18	shown	show	VERB
ejpam-6793	5	19	to	to	PART
ejpam-6793	5	20	be	be	AUX
ejpam-6793	5	21	attainable	attainable	ADJ
ejpam-6793	5	22	.	.	PUNCT
ejpam-6793	6	1	finally	finally	ADV
ejpam-6793	6	2	,	,	PUNCT
ejpam-6793	6	3	we	we	PRON
ejpam-6793	6	4	extend	extend	VERB
ejpam-6793	6	5	the	the	DET
ejpam-6793	6	6	discussion	discussion	NOUN
ejpam-6793	6	7	to	to	ADP
ejpam-6793	6	8	equivalent	equivalent	ADJ
ejpam-6793	6	9	and	and	CCONJ
ejpam-6793	6	10	similar	similar	ADJ
ejpam-6793	6	11	bases	basis	NOUN
ejpam-6793	6	12	,	,	PUNCT
ejpam-6793	6	13	verifying	verify	VERB
ejpam-6793	6	14	that	that	SCONJ
ejpam-6793	6	15	the	the	DET
ejpam-6793	6	16	derived	derive	VERB
ejpam-6793	6	17	results	result	NOUN
ejpam-6793	6	18	remain	remain	VERB
ejpam-6793	6	19	valid	valid	ADJ
ejpam-6793	6	20	under	under	ADP
ejpam-6793	6	21	such	such	ADJ
ejpam-6793	6	22	transformations	transformation	NOUN
ejpam-6793	6	23	,	,	PUNCT
ejpam-6793	6	24	which	which	PRON
ejpam-6793	6	25	confirms	confirm	VERB
ejpam-6793	6	26	the	the	DET
ejpam-6793	6	27	robustness	robustness	NOUN
ejpam-6793	6	28	and	and	CCONJ
ejpam-6793	6	29	general	general	ADJ
ejpam-6793	6	30	applicability	applicability	NOUN
ejpam-6793	6	31	of	of	ADP
ejpam-6793	6	32	the	the	DET
ejpam-6793	6	33	findings	finding	NOUN
ejpam-6793	6	34	.	.	PUNCT
ejpam-6793	7	1	2020	2020	NUM
ejpam-6793	7	2	mathematics	mathematic	NOUN
ejpam-6793	7	3	subject	subject	NOUN
ejpam-6793	7	4	classifications	classification	NOUN
ejpam-6793	7	5	:	:	PUNCT
ejpam-6793	7	6	30g35	30g35	NUM
ejpam-6793	7	7	,	,	PUNCT
ejpam-6793	7	8	30d15	30d15	NUM
ejpam-6793	7	9	,	,	PUNCT
ejpam-6793	7	10	41a10	41a10	NUM
ejpam-6793	7	11	key	key	ADJ
ejpam-6793	7	12	words	word	NOUN
ejpam-6793	7	13	and	and	CCONJ
ejpam-6793	7	14	phrases	phrase	NOUN
ejpam-6793	7	15	:	:	PUNCT
ejpam-6793	7	16	clifford	clifford	PROPN
ejpam-6793	7	17	analysis	analysis	NOUN
ejpam-6793	7	18	,	,	PUNCT
ejpam-6793	7	19	special	special	ADJ
ejpam-6793	7	20	monogenic	monogenic	ADJ
ejpam-6793	7	21	polynomials	polynomial	NOUN
ejpam-6793	7	22	,	,	PUNCT
ejpam-6793	7	23	fréchet	fréchet	NOUN
ejpam-6793	7	24	modules	module	NOUN
ejpam-6793	7	25	,	,	PUNCT
ejpam-6793	7	26	bases	basis	NOUN
ejpam-6793	7	27	of	of	ADP
ejpam-6793	7	28	polynomials	polynomial	NOUN
ejpam-6793	7	29	,	,	PUNCT
ejpam-6793	7	30	growth	growth	NOUN
ejpam-6793	7	31	of	of	ADP
ejpam-6793	7	32	bases	basis	NOUN
ejpam-6793	7	33	,	,	PUNCT
ejpam-6793	7	34	effectiveness	effectiveness	NOUN
ejpam-6793	7	35	1	1	NUM
ejpam-6793	7	36	.	.	PUNCT
ejpam-6793	7	37	introduction	introduction	NOUN
ejpam-6793	7	38	the	the	DET
ejpam-6793	7	39	development	development	NOUN
ejpam-6793	7	40	of	of	ADP
ejpam-6793	7	41	bases	basis	NOUN
ejpam-6793	7	42	theories	theory	NOUN
ejpam-6793	7	43	in	in	ADP
ejpam-6793	7	44	functional	functional	ADJ
ejpam-6793	7	45	spaces	space	NOUN
ejpam-6793	7	46	has	have	AUX
ejpam-6793	7	47	gained	gain	VERB
ejpam-6793	7	48	increasing	increase	VERB
ejpam-6793	7	49	importance	importance	NOUN
ejpam-6793	7	50	in	in	ADP
ejpam-6793	7	51	diverse	diverse	ADJ
ejpam-6793	7	52	mathematical	mathematical	ADJ
ejpam-6793	7	53	areas	area	NOUN
ejpam-6793	7	54	including	include	VERB
ejpam-6793	7	55	approximation	approximation	NOUN
ejpam-6793	7	56	theory	theory	NOUN
ejpam-6793	7	57	,	,	PUNCT
ejpam-6793	7	58	partial	partial	ADJ
ejpam-6793	7	59	differential	differential	NOUN
ejpam-6793	7	60	equations	equation	NOUN
ejpam-6793	7	61	,	,	PUNCT
ejpam-6793	7	62	and	and	CCONJ
ejpam-6793	7	63	mathematical	mathematical	ADJ
ejpam-6793	7	64	physics	physics	NOUN
ejpam-6793	7	65	.	.	PUNCT
ejpam-6793	8	1	approximation	approximation	NOUN
ejpam-6793	8	2	theory	theory	NOUN
ejpam-6793	8	3	has	have	VERB
ejpam-6793	8	4	a	a	DET
ejpam-6793	8	5	crucial	crucial	ADJ
ejpam-6793	8	6	role	role	NOUN
ejpam-6793	8	7	providing	provide	VERB
ejpam-6793	8	8	tools	tool	NOUN
ejpam-6793	8	9	for	for	ADP
ejpam-6793	8	10	analyzing	analyze	VERB
ejpam-6793	8	11	and	and	CCONJ
ejpam-6793	8	12	solving	solve	VERB
ejpam-6793	8	13	problems	problem	NOUN
ejpam-6793	8	14	arising	arise	VERB
ejpam-6793	8	15	in	in	ADP
ejpam-6793	8	16	applied	applied	ADJ
ejpam-6793	8	17	sciences	science	NOUN
ejpam-6793	8	18	and	and	CCONJ
ejpam-6793	8	19	engineering	engineering	NOUN
ejpam-6793	8	20	.	.	PUNCT
ejpam-6793	9	1	recent	recent	ADJ
ejpam-6793	9	2	developments	development	NOUN
ejpam-6793	9	3	demonstrate	demonstrate	VERB
ejpam-6793	9	4	the	the	DET
ejpam-6793	9	5	diversity	diversity	NOUN
ejpam-6793	9	6	of	of	ADP
ejpam-6793	9	7	its	its	PRON
ejpam-6793	9	8	applications	application	NOUN
ejpam-6793	9	9	.	.	PUNCT
ejpam-6793	10	1	the	the	DET
ejpam-6793	10	2	authors	author	NOUN
ejpam-6793	10	3	of	of	ADP
ejpam-6793	10	4	[	[	X
ejpam-6793	10	5	1	1	NUM
ejpam-6793	10	6	]	]	PUNCT
ejpam-6793	10	7	addressed	address	VERB
ejpam-6793	10	8	approximate	approximate	ADJ
ejpam-6793	10	9	numerical	numerical	ADJ
ejpam-6793	10	10	solutions	solution	NOUN
ejpam-6793	10	11	of	of	ADP
ejpam-6793	10	12	time	time	NOUN
ejpam-6793	10	13	-	-	PUNCT
ejpam-6793	10	14	fractional	fractional	ADJ
ejpam-6793	10	15	partial	partial	ADJ
ejpam-6793	10	16	differential	differential	NOUN
ejpam-6793	10	17	equations	equation	NOUN
ejpam-6793	10	18	in	in	ADP
ejpam-6793	10	19	three	three	NUM
ejpam-6793	10	20	dimensions	dimension	NOUN
ejpam-6793	10	21	,	,	PUNCT
ejpam-6793	10	22	achieving	achieve	VERB
ejpam-6793	10	23	high	high	ADJ
ejpam-6793	10	24	accuracy	accuracy	NOUN
ejpam-6793	10	25	even	even	ADV
ejpam-6793	10	26	on	on	ADP
ejpam-6793	10	27	irregular	irregular	ADJ
ejpam-6793	10	28	domains	domain	NOUN
ejpam-6793	10	29	.	.	PUNCT
ejpam-6793	11	1	in	in	ADP
ejpam-6793	11	2	[	[	X
ejpam-6793	11	3	2	2	NUM
ejpam-6793	11	4	]	]	PUNCT
ejpam-6793	11	5	,	,	PUNCT
ejpam-6793	11	6	the	the	DET
ejpam-6793	11	7	authors	author	NOUN
ejpam-6793	11	8	proposed	propose	VERB
ejpam-6793	11	9	a	a	DET
ejpam-6793	11	10	derivative	derivative	ADJ
ejpam-6793	11	11	-	-	PUNCT
ejpam-6793	11	12	free	free	ADJ
ejpam-6793	11	13	iterative	iterative	NOUN
ejpam-6793	11	14	method	method	NOUN
ejpam-6793	11	15	with	with	ADP
ejpam-6793	11	16	optimal	optimal	ADJ
ejpam-6793	11	17	fourth-order.convergence	fourth-order.convergence	NOUN
ejpam-6793	11	18	for	for	ADP
ejpam-6793	11	19	finding	find	VERB
ejpam-6793	11	20	multiple	multiple	ADJ
ejpam-6793	11	21	roots	root	NOUN
ejpam-6793	11	22	.	.	PUNCT
ejpam-6793	12	1	∗corresponding	∗corresponde	VERB
ejpam-6793	12	2	author	author	NOUN
ejpam-6793	12	3	.	.	PUNCT
ejpam-6793	13	1	doi	doi	NOUN
ejpam-6793	13	2	:	:	PUNCT
ejpam-6793	13	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6793	https://doi.org/10.29020/nybg.ejpam.v18i4.6793	ADJ
ejpam-6793	13	4	email	email	NOUN
ejpam-6793	13	5	addresses	address	NOUN
ejpam-6793	13	6	:	:	PUNCT
ejpam-6793	13	7	mzayed@kku.edu.sa	mzayed@kku.edu.sa	PROPN
ejpam-6793	13	8	(	(	PUNCT
ejpam-6793	13	9	m.	m.	NOUN
ejpam-6793	13	10	zayed	zaye	VERB
ejpam-6793	13	11	)	)	PUNCT
ejpam-6793	13	12	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6793	14	1	1	1	NUM
ejpam-6793	14	2	copyright	copyright	NOUN
ejpam-6793	14	3	:	:	PUNCT
ejpam-6793	14	4	©	©	PROPN
ejpam-6793	14	5	2025	2025	NUM
ejpam-6793	14	6	the	the	DET
ejpam-6793	14	7	author(s	author(s	NOUN
ejpam-6793	14	8	)	)	PUNCT
ejpam-6793	14	9	.	.	PUNCT
ejpam-6793	15	1	(	(	PUNCT
ejpam-6793	15	2	cc	cc	NOUN
ejpam-6793	15	3	by	by	ADP
ejpam-6793	15	4	-	-	PUNCT
ejpam-6793	15	5	nc	nc	PROPN
ejpam-6793	15	6	4.0	4.0	NUM
ejpam-6793	15	7	)	)	PUNCT
ejpam-6793	15	8	m.	m.	NOUN
ejpam-6793	15	9	zayed	zayed	PROPN
ejpam-6793	15	10	/	/	SYM
ejpam-6793	15	11	eur	eur	PROPN
ejpam-6793	15	12	.	.	PUNCT
ejpam-6793	16	1	j.	j.	PROPN
ejpam-6793	16	2	pure	pure	PROPN
ejpam-6793	16	3	appl	appl	PROPN
ejpam-6793	16	4	.	.	PROPN
ejpam-6793	16	5	math	math	PROPN
ejpam-6793	16	6	,	,	PUNCT
ejpam-6793	16	7	18	18	NUM
ejpam-6793	16	8	(	(	PUNCT
ejpam-6793	16	9	4	4	NUM
ejpam-6793	16	10	)	)	PUNCT
ejpam-6793	16	11	(	(	PUNCT
ejpam-6793	16	12	2025	2025	NUM
ejpam-6793	16	13	)	)	PUNCT
ejpam-6793	16	14	,	,	PUNCT
ejpam-6793	16	15	6793	6793	NUM
ejpam-6793	16	16	2	2	NUM
ejpam-6793	16	17	of	of	ADP
ejpam-6793	16	18	19	19	NUM
ejpam-6793	16	19	clifford	clifford	PROPN
ejpam-6793	16	20	analysis	analysis	NOUN
ejpam-6793	16	21	is	be	AUX
ejpam-6793	16	22	considered	consider	VERB
ejpam-6793	16	23	as	as	ADP
ejpam-6793	16	24	an	an	DET
ejpam-6793	16	25	elegant	elegant	ADJ
ejpam-6793	16	26	higher	high	ADJ
ejpam-6793	16	27	dimensional	dimensional	ADJ
ejpam-6793	16	28	analogy	analogy	NOUN
ejpam-6793	16	29	to	to	ADP
ejpam-6793	16	30	complex	complex	ADJ
ejpam-6793	16	31	analysis	analysis	NOUN
ejpam-6793	16	32	.	.	PUNCT
ejpam-6793	17	1	it	it	PRON
ejpam-6793	17	2	allow	allow	VERB
ejpam-6793	17	3	an	an	DET
ejpam-6793	17	4	extension	extension	NOUN
ejpam-6793	17	5	of	of	ADP
ejpam-6793	17	6	the	the	DET
ejpam-6793	17	7	theory	theory	NOUN
ejpam-6793	17	8	of	of	ADP
ejpam-6793	17	9	holomorphic	holomorphic	ADJ
ejpam-6793	17	10	functions	function	NOUN
ejpam-6793	17	11	to	to	ADP
ejpam-6793	17	12	higher	high	ADJ
ejpam-6793	17	13	dimensional	dimensional	ADJ
ejpam-6793	17	14	setting	setting	NOUN
ejpam-6793	17	15	by	by	ADP
ejpam-6793	17	16	using	use	VERB
ejpam-6793	17	17	clifford	clifford	PROPN
ejpam-6793	17	18	algebra	algebra	PROPN
ejpam-6793	17	19	valued	value	VERB
ejpam-6793	17	20	functions	function	NOUN
ejpam-6793	17	21	which	which	PRON
ejpam-6793	17	22	are	be	AUX
ejpam-6793	17	23	the	the	DET
ejpam-6793	17	24	solutions	solution	NOUN
ejpam-6793	17	25	the	the	DET
ejpam-6793	17	26	generalized	generalized	ADJ
ejpam-6793	17	27	cauchy	cauchy	PROPN
ejpam-6793	17	28	–	–	PUNCT
ejpam-6793	17	29	riemann	riemann	PROPN
ejpam-6793	17	30	system	system	NOUN
ejpam-6793	17	31	(	(	PUNCT
ejpam-6793	17	32	dirac	dirac	NOUN
ejpam-6793	17	33	operator	operator	NOUN
ejpam-6793	17	34	)	)	PUNCT
ejpam-6793	17	35	.	.	PUNCT
ejpam-6793	18	1	these	these	DET
ejpam-6793	18	2	functions	function	NOUN
ejpam-6793	18	3	are	be	AUX
ejpam-6793	18	4	known	know	VERB
ejpam-6793	18	5	as	as	ADP
ejpam-6793	18	6	clifford	clifford	PROPN
ejpam-6793	18	7	holomorphic	holomorphic	PROPN
ejpam-6793	18	8	functions	function	NOUN
ejpam-6793	18	9	(	(	PUNCT
ejpam-6793	18	10	monogenic	monogenic	ADJ
ejpam-6793	18	11	functions	function	NOUN
ejpam-6793	18	12	)	)	PUNCT
ejpam-6793	18	13	.	.	PUNCT
ejpam-6793	19	1	in	in	ADP
ejpam-6793	19	2	the	the	DET
ejpam-6793	19	3	context	context	NOUN
ejpam-6793	19	4	of	of	ADP
ejpam-6793	19	5	single	single	ADJ
ejpam-6793	19	6	complex	complex	ADJ
ejpam-6793	19	7	variable	variable	NOUN
ejpam-6793	19	8	,	,	PUNCT
ejpam-6793	19	9	the	the	DET
ejpam-6793	19	10	topic	topic	NOUN
ejpam-6793	19	11	of	of	ADP
ejpam-6793	19	12	basic	basic	ADJ
ejpam-6793	19	13	sets	set	NOUN
ejpam-6793	19	14	was	be	AUX
ejpam-6793	19	15	introduced	introduce	VERB
ejpam-6793	19	16	by	by	ADP
ejpam-6793	19	17	whittaker	whittaker	PROPN
ejpam-6793	20	1	[	[	X
ejpam-6793	20	2	3	3	NUM
ejpam-6793	20	3	,	,	PUNCT
ejpam-6793	20	4	4	4	NUM
ejpam-6793	20	5	]	]	PUNCT
ejpam-6793	20	6	and	and	CCONJ
ejpam-6793	20	7	cannon	cannon	NOUN
ejpam-6793	20	8	[	[	X
ejpam-6793	20	9	5	5	NUM
ejpam-6793	20	10	,	,	PUNCT
ejpam-6793	20	11	6	6	NUM
ejpam-6793	20	12	]	]	PUNCT
ejpam-6793	20	13	.	.	PUNCT
ejpam-6793	21	1	in	in	ADP
ejpam-6793	21	2	[	[	X
ejpam-6793	21	3	7	7	NUM
ejpam-6793	21	4	,	,	PUNCT
ejpam-6793	21	5	8	8	NUM
ejpam-6793	21	6	]	]	PUNCT
ejpam-6793	21	7	,	,	PUNCT
ejpam-6793	21	8	the	the	DET
ejpam-6793	21	9	authors	author	NOUN
ejpam-6793	21	10	proposed	propose	VERB
ejpam-6793	21	11	an	an	DET
ejpam-6793	21	12	extended	extended	ADJ
ejpam-6793	21	13	adaptation	adaptation	NOUN
ejpam-6793	21	14	of	of	ADP
ejpam-6793	21	15	whittaker	whittaker	NOUN
ejpam-6793	21	16	-	-	PUNCT
ejpam-6793	21	17	cannon	cannon	NOUN
ejpam-6793	21	18	theory	theory	NOUN
ejpam-6793	21	19	of	of	ADP
ejpam-6793	21	20	bases	basis	NOUN
ejpam-6793	21	21	of	of	ADP
ejpam-6793	21	22	polynomial	polynomial	NOUN
ejpam-6793	21	23	in	in	ADP
ejpam-6793	21	24	the	the	DET
ejpam-6793	21	25	complex	complex	ADJ
ejpam-6793	21	26	setting	setting	NOUN
ejpam-6793	21	27	to	to	ADP
ejpam-6793	21	28	the	the	DET
ejpam-6793	21	29	framework	framework	NOUN
ejpam-6793	21	30	of	of	ADP
ejpam-6793	21	31	clifford	clifford	PROPN
ejpam-6793	21	32	algebra	algebra	PROPN
ejpam-6793	21	33	.	.	PUNCT
ejpam-6793	22	1	they	they	PRON
ejpam-6793	22	2	provided	provide	VERB
ejpam-6793	22	3	the	the	DET
ejpam-6793	22	4	effectiveness	effectiveness	NOUN
ejpam-6793	22	5	criteria	criterion	NOUN
ejpam-6793	22	6	in	in	ADP
ejpam-6793	22	7	the	the	DET
ejpam-6793	22	8	convergence	convergence	NOUN
ejpam-6793	22	9	domain	domain	NOUN
ejpam-6793	22	10	which	which	PRON
ejpam-6793	22	11	means	mean	VERB
ejpam-6793	22	12	the	the	DET
ejpam-6793	22	13	action	action	NOUN
ejpam-6793	22	14	of	of	ADP
ejpam-6793	22	15	approximating	approximate	VERB
ejpam-6793	22	16	special	special	ADJ
ejpam-6793	22	17	monogenic	monogenic	ADJ
ejpam-6793	22	18	functions	function	NOUN
ejpam-6793	22	19	(	(	PUNCT
ejpam-6793	22	20	smfs	smfs	PROPN
ejpam-6793	22	21	)	)	PUNCT
ejpam-6793	22	22	via	via	ADP
ejpam-6793	22	23	bases	basis	NOUN
ejpam-6793	22	24	of	of	ADP
ejpam-6793	22	25	special	special	ADJ
ejpam-6793	22	26	monogenic	monogenic	ADJ
ejpam-6793	22	27	polynomials	polynomial	NOUN
ejpam-6793	22	28	(	(	PUNCT
ejpam-6793	22	29	smps	smp	NOUN
ejpam-6793	22	30	)	)	PUNCT
ejpam-6793	22	31	with	with	ADP
ejpam-6793	22	32	or	or	CCONJ
ejpam-6793	22	33	without	without	ADP
ejpam-6793	22	34	some	some	DET
ejpam-6793	22	35	restrictions	restriction	NOUN
ejpam-6793	22	36	.	.	PUNCT
ejpam-6793	23	1	their	their	PRON
ejpam-6793	23	2	study	study	NOUN
ejpam-6793	23	3	was	be	AUX
ejpam-6793	23	4	concerned	concern	VERB
ejpam-6793	23	5	with	with	ADP
ejpam-6793	23	6	the	the	DET
ejpam-6793	23	7	approximation	approximation	NOUN
ejpam-6793	23	8	of	of	ADP
ejpam-6793	23	9	subclass	subclass	NOUN
ejpam-6793	23	10	of	of	ADP
ejpam-6793	23	11	mfs	mfs	NOUN
ejpam-6793	23	12	which	which	PRON
ejpam-6793	23	13	are	be	AUX
ejpam-6793	23	14	generated	generate	VERB
ejpam-6793	23	15	by	by	ADP
ejpam-6793	23	16	a	a	DET
ejpam-6793	23	17	particular	particular	ADJ
ejpam-6793	23	18	special	special	ADJ
ejpam-6793	23	19	polynomials	polynomial	NOUN
ejpam-6793	23	20	in	in	ADP
ejpam-6793	23	21	axially	axially	ADV
ejpam-6793	23	22	symmetric	symmetric	ADJ
ejpam-6793	23	23	domains	domain	NOUN
ejpam-6793	23	24	.	.	PUNCT
ejpam-6793	24	1	subsequent	subsequent	ADJ
ejpam-6793	24	2	papers	paper	NOUN
ejpam-6793	24	3	proposed	propose	VERB
ejpam-6793	24	4	by	by	ADP
ejpam-6793	24	5	several	several	ADJ
ejpam-6793	24	6	authors	author	NOUN
ejpam-6793	24	7	which	which	PRON
ejpam-6793	24	8	expose	expose	VERB
ejpam-6793	24	9	the	the	DET
ejpam-6793	24	10	significant	significant	NOUN
ejpam-6793	24	11	of	of	ADP
ejpam-6793	24	12	this	this	DET
ejpam-6793	24	13	approach	approach	NOUN
ejpam-6793	24	14	.	.	PUNCT
ejpam-6793	25	1	the	the	DET
ejpam-6793	25	2	construction	construction	NOUN
ejpam-6793	25	3	and	and	CCONJ
ejpam-6793	25	4	effectiveness	effectiveness	NOUN
ejpam-6793	25	5	of	of	ADP
ejpam-6793	25	6	certain	certain	ADJ
ejpam-6793	25	7	derived	derive	VERB
ejpam-6793	25	8	bases	basis	NOUN
ejpam-6793	25	9	of	of	ADP
ejpam-6793	25	10	smps	smp	NOUN
ejpam-6793	25	11	were	be	AUX
ejpam-6793	25	12	studied	study	VERB
ejpam-6793	25	13	in	in	ADP
ejpam-6793	25	14	[	[	X
ejpam-6793	25	15	9–11	9–11	NOUN
ejpam-6793	25	16	]	]	PUNCT
ejpam-6793	25	17	.	.	PUNCT
ejpam-6793	26	1	the	the	DET
ejpam-6793	26	2	convergence	convergence	NOUN
ejpam-6793	26	3	properties	property	NOUN
ejpam-6793	26	4	for	for	ADP
ejpam-6793	26	5	the	the	DET
ejpam-6793	26	6	bernoulli	bernoulli	PROPN
ejpam-6793	26	7	polynomials	polynomial	NOUN
ejpam-6793	26	8	,	,	PUNCT
ejpam-6793	26	9	euler	euler	NOUN
ejpam-6793	26	10	polynomials	polynomial	NOUN
ejpam-6793	26	11	,	,	PUNCT
ejpam-6793	26	12	bessel	bessel	NOUN
ejpam-6793	26	13	polynomials	polynomial	NOUN
ejpam-6793	26	14	,	,	PUNCT
ejpam-6793	26	15	and	and	CCONJ
ejpam-6793	26	16	chebyshev	chebyshev	VERB
ejpam-6793	26	17	in	in	ADP
ejpam-6793	26	18	clifford	clifford	PROPN
ejpam-6793	26	19	analysis	analysis	NOUN
ejpam-6793	26	20	[	[	X
ejpam-6793	26	21	12–15	12–15	NUM
ejpam-6793	26	22	]	]	PUNCT
ejpam-6793	26	23	.	.	PUNCT
ejpam-6793	27	1	constructing	construct	VERB
ejpam-6793	27	2	bases	basis	NOUN
ejpam-6793	27	3	of	of	ADP
ejpam-6793	27	4	smps	smp	NOUN
ejpam-6793	27	5	by	by	ADP
ejpam-6793	27	6	the	the	DET
ejpam-6793	27	7	utilization	utilization	NOUN
ejpam-6793	27	8	the	the	DET
ejpam-6793	27	9	fundamentals	fundamental	NOUN
ejpam-6793	27	10	of	of	ADP
ejpam-6793	27	11	the	the	DET
ejpam-6793	27	12	functional	functional	ADJ
ejpam-6793	27	13	analysis	analysis	NOUN
ejpam-6793	27	14	was	be	AUX
ejpam-6793	27	15	proposed	propose	VERB
ejpam-6793	27	16	in	in	ADP
ejpam-6793	27	17	[	[	X
ejpam-6793	27	18	16	16	NUM
ejpam-6793	27	19	]	]	PUNCT
ejpam-6793	27	20	where	where	SCONJ
ejpam-6793	27	21	the	the	DET
ejpam-6793	27	22	authors	author	NOUN
ejpam-6793	27	23	characterized	characterize	VERB
ejpam-6793	27	24	the	the	DET
ejpam-6793	27	25	convergence	convergence	NOUN
ejpam-6793	27	26	of	of	ADP
ejpam-6793	27	27	certain	certain	ADJ
ejpam-6793	27	28	classes	class	NOUN
ejpam-6793	27	29	of	of	ADP
ejpam-6793	27	30	bases	basis	NOUN
ejpam-6793	27	31	for	for	ADP
ejpam-6793	27	32	various	various	ADJ
ejpam-6793	27	33	f	f	NOUN
ejpam-6793	27	34	-	-	PUNCT
ejpam-6793	27	35	modules	module	NOUN
ejpam-6793	27	36	.	.	PUNCT
ejpam-6793	28	1	the	the	DET
ejpam-6793	28	2	effectiveness	effectiveness	NOUN
ejpam-6793	28	3	and	and	CCONJ
ejpam-6793	28	4	the	the	DET
ejpam-6793	28	5	growth	growth	NOUN
ejpam-6793	28	6	of	of	ADP
ejpam-6793	28	7	the	the	DET
ejpam-6793	28	8	equivalent	equivalent	ADJ
ejpam-6793	28	9	base	base	NOUN
ejpam-6793	28	10	constructed	construct	VERB
ejpam-6793	28	11	with	with	ADP
ejpam-6793	28	12	smps	smp	NOUN
ejpam-6793	28	13	in	in	ADP
ejpam-6793	28	14	f	f	NOUN
ejpam-6793	28	15	-	-	PUNCT
ejpam-6793	28	16	modules	module	NOUN
ejpam-6793	28	17	were	be	AUX
ejpam-6793	28	18	studied	study	VERB
ejpam-6793	28	19	in	in	ADP
ejpam-6793	28	20	[	[	X
ejpam-6793	28	21	17	17	NUM
ejpam-6793	28	22	]	]	PUNCT
ejpam-6793	28	23	.	.	PUNCT
ejpam-6793	29	1	recently	recently	ADV
ejpam-6793	29	2	,	,	PUNCT
ejpam-6793	29	3	the	the	DET
ejpam-6793	29	4	authors	author	NOUN
ejpam-6793	29	5	in	in	ADP
ejpam-6793	29	6	[	[	X
ejpam-6793	29	7	18	18	NUM
ejpam-6793	29	8	]	]	PUNCT
ejpam-6793	29	9	deduced	deduce	VERB
ejpam-6793	29	10	the	the	DET
ejpam-6793	29	11	extended	extended	ADJ
ejpam-6793	29	12	ruscheweyh	ruscheweyh	NOUN
ejpam-6793	29	13	differential	differential	ADJ
ejpam-6793	29	14	operator	operator	NOUN
ejpam-6793	29	15	and	and	CCONJ
ejpam-6793	29	16	examined	examine	VERB
ejpam-6793	29	17	the	the	DET
ejpam-6793	29	18	representation	representation	NOUN
ejpam-6793	29	19	of	of	ADP
ejpam-6793	29	20	its	its	PRON
ejpam-6793	29	21	derived	derive	VERB
ejpam-6793	29	22	bases	basis	NOUN
ejpam-6793	29	23	of	of	ADP
ejpam-6793	29	24	smps	smp	NOUN
ejpam-6793	29	25	in	in	ADP
ejpam-6793	29	26	different	different	ADJ
ejpam-6793	29	27	convergence	convergence	NOUN
ejpam-6793	29	28	regions	region	NOUN
ejpam-6793	29	29	.	.	PUNCT
ejpam-6793	30	1	recently	recently	ADV
ejpam-6793	30	2	in	in	ADP
ejpam-6793	30	3	[	[	X
ejpam-6793	30	4	19	19	NUM
ejpam-6793	30	5	]	]	PUNCT
ejpam-6793	30	6	,	,	PUNCT
ejpam-6793	30	7	the	the	DET
ejpam-6793	30	8	authors	author	NOUN
ejpam-6793	30	9	investigated	investigate	VERB
ejpam-6793	30	10	the	the	DET
ejpam-6793	30	11	representation	representation	NOUN
ejpam-6793	30	12	of	of	ADP
ejpam-6793	30	13	a	a	DET
ejpam-6793	30	14	smfs	smfs	NOUN
ejpam-6793	30	15	in	in	ADP
ejpam-6793	30	16	terms	term	NOUN
ejpam-6793	30	17	of	of	ADP
ejpam-6793	30	18	infinite	infinite	ADJ
ejpam-6793	30	19	series	series	NOUN
ejpam-6793	30	20	of	of	ADP
ejpam-6793	30	21	cliffordian	cliffordian	PROPN
ejpam-6793	30	22	hasse	hasse	PROPN
ejpam-6793	30	23	derivative	derivative	ADJ
ejpam-6793	30	24	bases	basis	NOUN
ejpam-6793	30	25	in	in	ADP
ejpam-6793	30	26	hyper	hyper	ADJ
ejpam-6793	30	27	regions	region	NOUN
ejpam-6793	30	28	was	be	AUX
ejpam-6793	30	29	introduced	introduce	VERB
ejpam-6793	30	30	.	.	PUNCT
ejpam-6793	31	1	the	the	DET
ejpam-6793	31	2	representation	representation	NOUN
ejpam-6793	31	3	of	of	ADP
ejpam-6793	31	4	regular	regular	ADJ
ejpam-6793	31	5	functions	function	NOUN
ejpam-6793	31	6	of	of	ADP
ejpam-6793	31	7	several	several	ADJ
ejpam-6793	31	8	complex	complex	ADJ
ejpam-6793	31	9	variables	variable	NOUN
ejpam-6793	31	10	by	by	ADP
ejpam-6793	31	11	means	mean	NOUN
ejpam-6793	31	12	of	of	ADP
ejpam-6793	31	13	exponential	exponential	ADJ
ejpam-6793	31	14	base	base	NOUN
ejpam-6793	31	15	of	of	ADP
ejpam-6793	31	16	polynomials	polynomial	NOUN
ejpam-6793	31	17	in	in	ADP
ejpam-6793	31	18	hyperelliptical	hyperelliptical	ADJ
ejpam-6793	31	19	regions	region	NOUN
ejpam-6793	31	20	were	be	AUX
ejpam-6793	31	21	discussed	discuss	VERB
ejpam-6793	31	22	in	in	ADP
ejpam-6793	31	23	[	[	X
ejpam-6793	31	24	20	20	NUM
ejpam-6793	31	25	]	]	PUNCT
ejpam-6793	31	26	.	.	PUNCT
ejpam-6793	32	1	in	in	ADP
ejpam-6793	32	2	the	the	DET
ejpam-6793	32	3	clifford	clifford	PROPN
ejpam-6793	32	4	context	context	NOUN
ejpam-6793	32	5	,	,	PUNCT
ejpam-6793	32	6	the	the	DET
ejpam-6793	32	7	exponential	exponential	ADJ
ejpam-6793	32	8	function	function	NOUN
ejpam-6793	32	9	exp(x	exp(x	PROPN
ejpam-6793	32	10	)	)	PUNCT
ejpam-6793	32	11	,	,	PUNCT
ejpam-6793	32	12	x	x	PROPN
ejpam-6793	32	13	a	a	DET
ejpam-6793	32	14	clifford	clifford	PROPN
ejpam-6793	32	15	variable	variable	NOUN
ejpam-6793	32	16	was	be	AUX
ejpam-6793	32	17	introduced	introduce	VERB
ejpam-6793	32	18	in	in	ADP
ejpam-6793	32	19	[	[	X
ejpam-6793	32	20	21	21	NUM
ejpam-6793	32	21	]	]	PUNCT
ejpam-6793	32	22	as	as	ADP
ejpam-6793	32	23	an	an	DET
ejpam-6793	32	24	extension	extension	NOUN
ejpam-6793	32	25	of	of	ADP
ejpam-6793	32	26	the	the	DET
ejpam-6793	32	27	classical	classical	ADJ
ejpam-6793	32	28	complex	complex	ADJ
ejpam-6793	32	29	function	function	NOUN
ejpam-6793	32	30	ez	ez	PROPN
ejpam-6793	32	31	.	.	PUNCT
ejpam-6793	33	1	in	in	ADP
ejpam-6793	33	2	[	[	X
ejpam-6793	33	3	21	21	NUM
ejpam-6793	33	4	]	]	PUNCT
ejpam-6793	33	5	,	,	PUNCT
ejpam-6793	33	6	the	the	DET
ejpam-6793	33	7	author	author	NOUN
ejpam-6793	33	8	discussed	discuss	VERB
ejpam-6793	33	9	the	the	DET
ejpam-6793	33	10	convergence	convergence	NOUN
ejpam-6793	33	11	properties	property	NOUN
ejpam-6793	33	12	of	of	ADP
ejpam-6793	33	13	the	the	DET
ejpam-6793	33	14	exponential	exponential	ADJ
ejpam-6793	33	15	base	base	NOUN
ejpam-6793	33	16	of	of	ADP
ejpam-6793	33	17	smps	smp	NOUN
ejpam-6793	33	18	with	with	ADP
ejpam-6793	33	19	the	the	DET
ejpam-6793	33	20	bases	basis	NOUN
ejpam-6793	33	21	associated	associate	VERB
ejpam-6793	33	22	with	with	ADP
ejpam-6793	33	23	the	the	DET
ejpam-6793	33	24	base	base	NOUN
ejpam-6793	33	25	of	of	ADP
ejpam-6793	33	26	polynomials	polynomial	NOUN
ejpam-6793	33	27	{	{	PUNCT
ejpam-6793	33	28	qn(x	qn(x	NOUN
ejpam-6793	33	29	)	)	PUNCT
ejpam-6793	33	30	}	}	PUNCT
ejpam-6793	34	1	=	=	SYM
ejpam-6793	34	2	{	{	PUNCT
ejpam-6793	34	3	∑	∑	PUNCT
ejpam-6793	34	4	k	k	PROPN
ejpam-6793	34	5	qk(x)qn	qk(x)qn	PROPN
ejpam-6793	34	6	,	,	PUNCT
ejpam-6793	34	7	k	k	NOUN
ejpam-6793	34	8	}	}	PUNCT
ejpam-6793	34	9	,	,	PUNCT
ejpam-6793	34	10	where	where	SCONJ
ejpam-6793	34	11	the	the	DET
ejpam-6793	34	12	qn	qn	NOUN
ejpam-6793	34	13	,	,	PUNCT
ejpam-6793	34	14	k	k	PROPN
ejpam-6793	34	15	are	be	AUX
ejpam-6793	34	16	real	real	ADJ
ejpam-6793	34	17	clifford	clifford	PROPN
ejpam-6793	34	18	coefficients	coefficient	NOUN
ejpam-6793	34	19	.	.	PUNCT
ejpam-6793	35	1	precisely	precisely	ADV
ejpam-6793	35	2	,	,	PUNCT
ejpam-6793	35	3	the	the	DET
ejpam-6793	35	4	restriction	restriction	NOUN
ejpam-6793	35	5	qn	qn	NOUN
ejpam-6793	35	6	,	,	PUNCT
ejpam-6793	35	7	n	n	NOUN
ejpam-6793	35	8	=	=	SYM
ejpam-6793	35	9	1	1	NUM
ejpam-6793	35	10	for	for	ADP
ejpam-6793	35	11	n	n	PRON
ejpam-6793	35	12	∈	∈	NOUN
ejpam-6793	35	13	n	n	NOUN
ejpam-6793	35	14	was	be	AUX
ejpam-6793	35	15	imposed	impose	VERB
ejpam-6793	35	16	on	on	ADP
ejpam-6793	35	17	the	the	DET
ejpam-6793	35	18	diagonal	diagonal	NOUN
ejpam-6793	35	19	of	of	ADP
ejpam-6793	35	20	the	the	DET
ejpam-6793	35	21	matrix	matrix	NOUN
ejpam-6793	35	22	of	of	ADP
ejpam-6793	35	23	entries	entry	NOUN
ejpam-6793	35	24	of	of	ADP
ejpam-6793	35	25	the	the	DET
ejpam-6793	35	26	matrix	matrix	NOUN
ejpam-6793	35	27	q	q	NOUN
ejpam-6793	36	1	=	=	PUNCT
ejpam-6793	36	2	(	(	PUNCT
ejpam-6793	36	3	qn	qn	INTJ
ejpam-6793	36	4	,	,	PUNCT
ejpam-6793	36	5	k	k	NOUN
ejpam-6793	36	6	)	)	PUNCT
ejpam-6793	36	7	.	.	PUNCT
ejpam-6793	37	1	in	in	ADP
ejpam-6793	37	2	the	the	DET
ejpam-6793	37	3	current	current	ADJ
ejpam-6793	37	4	study	study	NOUN
ejpam-6793	37	5	,	,	PUNCT
ejpam-6793	37	6	we	we	PRON
ejpam-6793	37	7	relinquish	relinquish	VERB
ejpam-6793	37	8	the	the	DET
ejpam-6793	37	9	aforementioned	aforementioned	ADJ
ejpam-6793	37	10	condition	condition	NOUN
ejpam-6793	37	11	and	and	CCONJ
ejpam-6793	37	12	consider	consider	VERB
ejpam-6793	37	13	a	a	DET
ejpam-6793	37	14	more	more	ADV
ejpam-6793	37	15	generalized	generalized	ADJ
ejpam-6793	37	16	form	form	NOUN
ejpam-6793	37	17	for	for	ADP
ejpam-6793	37	18	these	these	DET
ejpam-6793	37	19	diagonal	diagonal	ADJ
ejpam-6793	37	20	elements	element	NOUN
ejpam-6793	37	21	to	to	PART
ejpam-6793	37	22	be	be	AUX
ejpam-6793	37	23	qn	qn	NOUN
ejpam-6793	37	24	,	,	PUNCT
ejpam-6793	37	25	n	n	NOUN
ejpam-6793	37	26	=	=	SYM
ejpam-6793	37	27	αn	αn	NOUN
ejpam-6793	37	28	for	for	ADP
ejpam-6793	37	29	all	all	PRON
ejpam-6793	37	30	n	n	PRON
ejpam-6793	37	31	∈	∈	PROPN
ejpam-6793	37	32	n	n	CCONJ
ejpam-6793	37	33	,	,	PUNCT
ejpam-6793	37	34	where	where	SCONJ
ejpam-6793	37	35	{	{	PUNCT
ejpam-6793	37	36	αn	αn	NOUN
ejpam-6793	37	37	}	}	PUNCT
ejpam-6793	37	38	is	be	AUX
ejpam-6793	37	39	a	a	DET
ejpam-6793	37	40	bounded	bounded	ADJ
ejpam-6793	37	41	sequence	sequence	NOUN
ejpam-6793	37	42	of	of	ADP
ejpam-6793	37	43	the	the	DET
ejpam-6793	37	44	positive	positive	ADJ
ejpam-6793	37	45	numbers	number	NOUN
ejpam-6793	37	46	.	.	PUNCT
ejpam-6793	38	1	we	we	PRON
ejpam-6793	38	2	assign	assign	VERB
ejpam-6793	38	3	certain	certain	ADJ
ejpam-6793	38	4	conditions	condition	NOUN
ejpam-6793	38	5	to	to	ADP
ejpam-6793	38	6	the	the	DET
ejpam-6793	38	7	coefficients	coefficient	NOUN
ejpam-6793	38	8	of	of	ADP
ejpam-6793	38	9	the	the	DET
ejpam-6793	38	10	power	power	NOUN
ejpam-6793	38	11	associated	associate	VERB
ejpam-6793	38	12	infinite	infinite	ADJ
ejpam-6793	38	13	matrices	matrix	NOUN
ejpam-6793	38	14	of	of	ADP
ejpam-6793	38	15	an	an	DET
ejpam-6793	38	16	original	original	ADJ
ejpam-6793	38	17	base	base	NOUN
ejpam-6793	38	18	.	.	PUNCT
ejpam-6793	39	1	consequently	consequently	ADV
ejpam-6793	39	2	,	,	PUNCT
ejpam-6793	39	3	the	the	DET
ejpam-6793	39	4	representation	representation	NOUN
ejpam-6793	39	5	of	of	ADP
ejpam-6793	39	6	a	a	DET
ejpam-6793	39	7	smf	smf	NOUN
ejpam-6793	39	8	is	be	AUX
ejpam-6793	39	9	provided	provide	VERB
ejpam-6793	39	10	in	in	ADP
ejpam-6793	39	11	terms	term	NOUN
ejpam-6793	39	12	of	of	ADP
ejpam-6793	39	13	esbsmps	esbsmp	NOUN
ejpam-6793	39	14	.	.	PUNCT
ejpam-6793	40	1	we	we	PRON
ejpam-6793	40	2	show	show	VERB
ejpam-6793	40	3	that	that	SCONJ
ejpam-6793	40	4	exponential	exponential	ADJ
ejpam-6793	40	5	base	base	NOUN
ejpam-6793	40	6	satisfies	satisfy	VERB
ejpam-6793	40	7	the	the	DET
ejpam-6793	40	8	higher	higher	ADV
ejpam-6793	40	9	-	-	PUNCT
ejpam-6793	40	10	dimensional	dimensional	ADJ
ejpam-6793	40	11	effectiveness	effectiveness	NOUN
ejpam-6793	40	12	criteria	criterion	NOUN
ejpam-6793	40	13	for	for	ADP
ejpam-6793	40	14	the	the	DET
ejpam-6793	40	15	f	f	NOUN
ejpam-6793	40	16	-	-	PUNCT
ejpam-6793	40	17	module	module	NOUN
ejpam-6793	40	18	wb̄(r	wb̄(r	NOUN
ejpam-6793	40	19	)	)	PUNCT
ejpam-6793	40	20	.	.	PUNCT
ejpam-6793	41	1	furthermore	furthermore	ADV
ejpam-6793	41	2	,	,	PUNCT
ejpam-6793	41	3	we	we	PRON
ejpam-6793	41	4	find	find	VERB
ejpam-6793	41	5	that	that	SCONJ
ejpam-6793	41	6	the	the	DET
ejpam-6793	41	7	order	order	NOUN
ejpam-6793	41	8	of	of	ADP
ejpam-6793	41	9	the	the	DET
ejpam-6793	41	10	esbsmps	esbsmp	NOUN
ejpam-6793	41	11	is	be	AUX
ejpam-6793	41	12	bounded	bound	VERB
ejpam-6793	41	13	above	above	ADV
ejpam-6793	41	14	by	by	ADP
ejpam-6793	41	15	an	an	DET
ejpam-6793	41	16	attainable	attainable	ADJ
ejpam-6793	41	17	upper	upper	ADJ
ejpam-6793	41	18	bound	bind	VERB
ejpam-6793	41	19	.	.	PUNCT
ejpam-6793	42	1	moreover	moreover	ADV
ejpam-6793	42	2	,	,	PUNCT
ejpam-6793	42	3	we	we	PRON
ejpam-6793	42	4	investigate	investigate	VERB
ejpam-6793	42	5	the	the	DET
ejpam-6793	42	6	convergence	convergence	NOUN
ejpam-6793	42	7	properties	property	NOUN
ejpam-6793	42	8	of	of	ADP
ejpam-6793	42	9	the	the	DET
ejpam-6793	42	10	ecbsmps	ecbsmp	NOUN
ejpam-6793	42	11	for	for	ADP
ejpam-6793	42	12	the	the	DET
ejpam-6793	42	13	f	f	NOUN
ejpam-6793	42	14	-	-	PUNCT
ejpam-6793	42	15	modules	module	NOUN
ejpam-6793	42	16	m.	m.	NOUN
ejpam-6793	42	17	zayed	zayed	PROPN
ejpam-6793	42	18	/	/	SYM
ejpam-6793	42	19	eur	eur	PROPN
ejpam-6793	42	20	.	.	PUNCT
ejpam-6793	43	1	j.	j.	PROPN
ejpam-6793	43	2	pure	pure	PROPN
ejpam-6793	43	3	appl	appl	PROPN
ejpam-6793	43	4	.	.	PROPN
ejpam-6793	43	5	math	math	PROPN
ejpam-6793	43	6	,	,	PUNCT
ejpam-6793	43	7	18	18	NUM
ejpam-6793	43	8	(	(	PUNCT
ejpam-6793	43	9	4	4	NUM
ejpam-6793	43	10	)	)	PUNCT
ejpam-6793	43	11	(	(	PUNCT
ejpam-6793	43	12	2025	2025	NUM
ejpam-6793	43	13	)	)	PUNCT
ejpam-6793	43	14	,	,	PUNCT
ejpam-6793	43	15	6793	6793	NUM
ejpam-6793	43	16	3	3	NUM
ejpam-6793	43	17	of	of	ADP
ejpam-6793	43	18	19	19	NUM
ejpam-6793	43	19	wb̄(r	wb̄(r	NUM
ejpam-6793	43	20	)	)	PUNCT
ejpam-6793	43	21	,	,	PUNCT
ejpam-6793	43	22	wb(r	wb(r	NUM
ejpam-6793	43	23	)	)	PUNCT
ejpam-6793	43	24	,	,	PUNCT
ejpam-6793	43	25	wb+(r	wb+(r	PROPN
ejpam-6793	43	26	)	)	PUNCT
ejpam-6793	43	27	,	,	PUNCT
ejpam-6793	43	28	w∞	w∞	PROPN
ejpam-6793	43	29	,	,	PUNCT
ejpam-6793	43	30	w0	w0	PROPN
ejpam-6793	43	31	+	+	X
ejpam-6793	43	32	which	which	PRON
ejpam-6793	43	33	will	will	AUX
ejpam-6793	43	34	be	be	AUX
ejpam-6793	43	35	defined	define	VERB
ejpam-6793	43	36	in	in	ADP
ejpam-6793	43	37	section	section	NOUN
ejpam-6793	43	38	2	2	NUM
ejpam-6793	43	39	.	.	NOUN
ejpam-6793	43	40	2	2	NUM
ejpam-6793	43	41	.	.	NOUN
ejpam-6793	43	42	notations	notation	NOUN
ejpam-6793	43	43	and	and	CCONJ
ejpam-6793	43	44	basic	basic	ADJ
ejpam-6793	43	45	results	result	NOUN
ejpam-6793	43	46	the	the	DET
ejpam-6793	43	47	associated	associated	ADJ
ejpam-6793	43	48	2m	2m	ADJ
ejpam-6793	43	49	-	-	PUNCT
ejpam-6793	43	50	dimensional	dimensional	ADJ
ejpam-6793	43	51	real	real	ADJ
ejpam-6793	43	52	algebra	algebra	NOUN
ejpam-6793	43	53	am	be	AUX
ejpam-6793	43	54	constructed	construct	VERB
ejpam-6793	43	55	from	from	ADP
ejpam-6793	43	56	the	the	DET
ejpam-6793	43	57	space	space	NOUN
ejpam-6793	43	58	rm	rm	NOUN
ejpam-6793	43	59	with	with	ADP
ejpam-6793	43	60	an	an	DET
ejpam-6793	43	61	orthogonal	orthogonal	ADJ
ejpam-6793	43	62	base	base	NOUN
ejpam-6793	43	63	{	{	PUNCT
ejpam-6793	43	64	e1	e1	PROPN
ejpam-6793	43	65	,	,	PUNCT
ejpam-6793	43	66	e2	e2	PROPN
ejpam-6793	43	67	,	,	PUNCT
ejpam-6793	43	68	.	.	PUNCT
ejpam-6793	43	69	.	.	PUNCT
ejpam-6793	44	1	.	.	PUNCT
ejpam-6793	45	1	,	,	PUNCT
ejpam-6793	45	2	em	em	PRON
ejpam-6793	45	3	}	}	PUNCT
ejpam-6793	45	4	is	be	AUX
ejpam-6793	45	5	identified	identify	VERB
ejpam-6793	45	6	such	such	ADJ
ejpam-6793	45	7	that	that	SCONJ
ejpam-6793	45	8	rm	rm	PROPN
ejpam-6793	45	9	⊂	⊂	PROPN
ejpam-6793	45	10	am	be	AUX
ejpam-6793	45	11	.	.	PUNCT
ejpam-6793	46	1	suppose	suppose	VERB
ejpam-6793	46	2	that	that	SCONJ
ejpam-6793	46	3	{	{	PUNCT
ejpam-6793	46	4	ej}mj=1	ej}mj=1	PROPN
ejpam-6793	46	5	is	be	AUX
ejpam-6793	46	6	an	an	DET
ejpam-6793	46	7	orthonormal	orthonormal	ADJ
ejpam-6793	46	8	base	base	NOUN
ejpam-6793	46	9	of	of	ADP
ejpam-6793	46	10	rm	rm	PROPN
ejpam-6793	46	11	.	.	PUNCT
ejpam-6793	47	1	then	then	ADV
ejpam-6793	47	2	the	the	DET
ejpam-6793	47	3	non	non	ADJ
ejpam-6793	47	4	-	-	ADJ
ejpam-6793	47	5	commutative	commutative	ADJ
ejpam-6793	47	6	multiplication	multiplication	NOUN
ejpam-6793	47	7	in	in	ADP
ejpam-6793	47	8	rm	rm	PROPN
ejpam-6793	47	9	is	be	AUX
ejpam-6793	47	10	subjected	subject	VERB
ejpam-6793	47	11	to	to	PART
ejpam-6793	47	12	ekeℓ	ekeℓ	VERB
ejpam-6793	47	13	+	+	CCONJ
ejpam-6793	47	14	eℓek	eℓek	NOUN
ejpam-6793	47	15	=	=	SYM
ejpam-6793	47	16	−2δkℓ	−2δkℓ	NOUN
ejpam-6793	47	17	,	,	PUNCT
ejpam-6793	47	18	where	where	SCONJ
ejpam-6793	47	19	k	k	NOUN
ejpam-6793	47	20	,	,	PUNCT
ejpam-6793	47	21	ℓ	ℓ	NOUN
ejpam-6793	47	22	=	=	SYM
ejpam-6793	47	23	1	1	NUM
ejpam-6793	47	24	,	,	PUNCT
ejpam-6793	47	25	.	.	PUNCT
ejpam-6793	47	26	.	.	PUNCT
ejpam-6793	48	1	.	.	PUNCT
ejpam-6793	49	1	,	,	PUNCT
ejpam-6793	49	2	m	m	NOUN
ejpam-6793	49	3	and	and	CCONJ
ejpam-6793	49	4	δkℓ	δkℓ	PROPN
ejpam-6793	49	5	stands	stand	VERB
ejpam-6793	49	6	for	for	ADP
ejpam-6793	49	7	the	the	DET
ejpam-6793	49	8	kronecker	kronecker	NOUN
ejpam-6793	49	9	symbol	symbol	NOUN
ejpam-6793	49	10	(	(	PUNCT
ejpam-6793	49	11	for	for	ADP
ejpam-6793	49	12	details	detail	NOUN
ejpam-6793	49	13	on	on	ADP
ejpam-6793	49	14	the	the	DET
ejpam-6793	49	15	main	main	ADJ
ejpam-6793	49	16	concepts	concept	NOUN
ejpam-6793	49	17	of	of	ADP
ejpam-6793	49	18	am	am	NOUN
ejpam-6793	49	19	,	,	PUNCT
ejpam-6793	49	20	see	see	VERB
ejpam-6793	49	21	[	[	X
ejpam-6793	49	22	22	22	NUM
ejpam-6793	49	23	]	]	PUNCT
ejpam-6793	49	24	)	)	PUNCT
ejpam-6793	49	25	.	.	PUNCT
ejpam-6793	50	1	the	the	DET
ejpam-6793	50	2	set	set	NOUN
ejpam-6793	50	3	{	{	PUNCT
ejpam-6793	50	4	es	es	X
ejpam-6793	50	5	:	:	PUNCT
ejpam-6793	50	6	s	s	X
ejpam-6793	50	7	⊂	⊂	X
ejpam-6793	50	8	{	{	PUNCT
ejpam-6793	50	9	0	0	NUM
ejpam-6793	50	10	,	,	PUNCT
ejpam-6793	50	11	1	1	NUM
ejpam-6793	50	12	,	,	PUNCT
ejpam-6793	50	13	.	.	PUNCT
ejpam-6793	50	14	.	.	PUNCT
ejpam-6793	50	15	.	.	PUNCT
ejpam-6793	51	1	,	,	PUNCT
ejpam-6793	51	2	m	m	NOUN
ejpam-6793	51	3	}	}	PUNCT
ejpam-6793	51	4	}	}	PUNCT
ejpam-6793	51	5	where	where	SCONJ
ejpam-6793	51	6	s	s	VERB
ejpam-6793	51	7	=	=	SYM
ejpam-6793	51	8	{	{	PUNCT
ejpam-6793	51	9	s1	s1	NOUN
ejpam-6793	51	10	,	,	PUNCT
ejpam-6793	51	11	s2	s2	NOUN
ejpam-6793	51	12	,	,	PUNCT
ejpam-6793	51	13	.	.	PUNCT
ejpam-6793	51	14	.	.	PUNCT
ejpam-6793	51	15	.	.	PUNCT
ejpam-6793	52	1	sh	sh	INTJ
ejpam-6793	52	2	}	}	PUNCT
ejpam-6793	52	3	,	,	PUNCT
ejpam-6793	52	4	0	0	NUM
ejpam-6793	52	5	≤	≤	NUM
ejpam-6793	52	6	s1	s1	NOUN
ejpam-6793	52	7	<	<	X
ejpam-6793	52	8	s2	s2	X
ejpam-6793	52	9	<	<	X
ejpam-6793	52	10	·	·	PUNCT
ejpam-6793	52	11	·	·	PUNCT
ejpam-6793	52	12	·	·	PUNCT
ejpam-6793	53	1	<	<	X
ejpam-6793	53	2	sh	sh	X
ejpam-6793	53	3	≤	≤	NUM
ejpam-6793	53	4	m	m	PROPN
ejpam-6793	53	5	,	,	PUNCT
ejpam-6793	53	6	es	es	X
ejpam-6793	53	7	=	=	PUNCT
ejpam-6793	53	8	es1es2	es1es2	PROPN
ejpam-6793	53	9	.	.	PUNCT
ejpam-6793	53	10	.	.	PUNCT
ejpam-6793	53	11	.	.	PUNCT
ejpam-6793	54	1	esh	esh	PROPN
ejpam-6793	54	2	,	,	PUNCT
ejpam-6793	54	3	eϕ	eϕ	PROPN
ejpam-6793	54	4	,	,	PUNCT
ejpam-6793	54	5	e0	e0	PROPN
ejpam-6793	54	6	=	=	SYM
ejpam-6793	54	7	1	1	NUM
ejpam-6793	54	8	,	,	PUNCT
ejpam-6793	54	9	creates	create	VERB
ejpam-6793	54	10	a	a	DET
ejpam-6793	54	11	base	base	NOUN
ejpam-6793	54	12	of	of	ADP
ejpam-6793	54	13	r0,m	r0,m	PROPN
ejpam-6793	54	14	.	.	PUNCT
ejpam-6793	55	1	embedding	embed	VERB
ejpam-6793	55	2	rm+1	rm+1	PRON
ejpam-6793	55	3	in	in	ADP
ejpam-6793	55	4	r0,m	r0,m	PROPN
ejpam-6793	55	5	.	.	PUNCT
ejpam-6793	56	1	it	it	PRON
ejpam-6793	56	2	is	be	AUX
ejpam-6793	56	3	identified	identify	VERB
ejpam-6793	56	4	that	that	SCONJ
ejpam-6793	56	5	x	x	X
ejpam-6793	56	6	=	=	PRON
ejpam-6793	56	7	(	(	PUNCT
ejpam-6793	56	8	x0	x0	PROPN
ejpam-6793	56	9	,	,	PUNCT
ejpam-6793	56	10	x1	x1	PROPN
ejpam-6793	56	11	,	,	PUNCT
ejpam-6793	56	12	.	.	PUNCT
ejpam-6793	56	13	.	.	PUNCT
ejpam-6793	57	1	.	.	PUNCT
ejpam-6793	58	1	,	,	PUNCT
ejpam-6793	58	2	xm	xm	X
ejpam-6793	58	3	)	)	PUNCT
ejpam-6793	58	4	∈	∈	PROPN
ejpam-6793	58	5	rm+1	rm+1	PRON
ejpam-6793	58	6	corresponds	correspond	VERB
ejpam-6793	58	7	to	to	ADP
ejpam-6793	58	8	x	x	SYM
ejpam-6793	58	9	=	=	PUNCT
ejpam-6793	58	10	∑m	∑m	PROPN
ejpam-6793	58	11	i=0	i=0	PROPN
ejpam-6793	58	12	xiei	xiei	PROPN
ejpam-6793	58	13	.	.	PUNCT
ejpam-6793	59	1	conjugation	conjugation	NOUN
ejpam-6793	59	2	in	in	ADP
ejpam-6793	59	3	r0,m	r0,m	PROPN
ejpam-6793	59	4	is	be	AUX
ejpam-6793	59	5	defined	define	VERB
ejpam-6793	59	6	as	as	ADP
ejpam-6793	59	7	the	the	DET
ejpam-6793	59	8	anti	anti	NOUN
ejpam-6793	59	9	-	-	NOUN
ejpam-6793	59	10	involution	involution	NOUN
ejpam-6793	59	11	for	for	ADP
ejpam-6793	59	12	which	which	PRON
ejpam-6793	59	13	ek	ek	NOUN
ejpam-6793	59	14	=	=	SYM
ejpam-6793	59	15	−ek	−ek	PROPN
ejpam-6793	59	16	(	(	PUNCT
ejpam-6793	59	17	1	1	NUM
ejpam-6793	59	18	≤	≤	NUM
ejpam-6793	59	19	k	k	X
ejpam-6793	59	20	≤	≤	NUM
ejpam-6793	59	21	m	m	PROPN
ejpam-6793	59	22	)	)	PUNCT
ejpam-6793	59	23	.	.	PUNCT
ejpam-6793	60	1	the	the	DET
ejpam-6793	60	2	norm	norm	NOUN
ejpam-6793	60	3	of	of	ADP
ejpam-6793	60	4	an	an	DET
ejpam-6793	60	5	element	element	NOUN
ejpam-6793	60	6	u	u	NOUN
ejpam-6793	60	7	∈	∈	NOUN
ejpam-6793	60	8	am	be	AUX
ejpam-6793	60	9	is	be	AUX
ejpam-6793	60	10	defined	define	VERB
ejpam-6793	60	11	by	by	ADP
ejpam-6793	60	12	(	(	PUNCT
ejpam-6793	60	13	∑	∑	PROPN
ejpam-6793	60	14	a	a	DET
ejpam-6793	60	15	|ua|2	|ua|2	PUNCT
ejpam-6793	60	16	)	)	PUNCT
ejpam-6793	60	17	1	1	NUM
ejpam-6793	60	18	2	2	NUM
ejpam-6793	61	1	and	and	CCONJ
ejpam-6793	61	2	we	we	PRON
ejpam-6793	61	3	have	have	AUX
ejpam-6793	61	4	always	always	ADV
ejpam-6793	61	5	use	use	VERB
ejpam-6793	61	6	the	the	DET
ejpam-6793	61	7	formula	formula	NOUN
ejpam-6793	61	8	|uv|	|uv|	PROPN
ejpam-6793	61	9	≤	≤	NUM
ejpam-6793	61	10	2	2	NUM
ejpam-6793	61	11	m	m	NUM
ejpam-6793	61	12	2	2	NUM
ejpam-6793	61	13	|u|	|u|	NOUN
ejpam-6793	61	14	|v|	|v|	NUM
ejpam-6793	61	15	where	where	SCONJ
ejpam-6793	61	16	the	the	DET
ejpam-6793	61	17	products	product	NOUN
ejpam-6793	61	18	uu	uu	X
ejpam-6793	61	19	or	or	CCONJ
ejpam-6793	61	20	vv	vv	ADP
ejpam-6793	61	21	produce	produce	VERB
ejpam-6793	61	22	real	real	ADJ
ejpam-6793	61	23	numbers	number	NOUN
ejpam-6793	61	24	.	.	PUNCT
ejpam-6793	62	1	clifford	clifford	PROPN
ejpam-6793	62	2	analysis	analysis	NOUN
ejpam-6793	62	3	provide	provide	VERB
ejpam-6793	62	4	a	a	DET
ejpam-6793	62	5	function	function	NOUN
ejpam-6793	62	6	theory	theory	NOUN
ejpam-6793	62	7	that	that	PRON
ejpam-6793	62	8	is	be	AUX
ejpam-6793	62	9	a	a	DET
ejpam-6793	62	10	higher	high	ADJ
ejpam-6793	62	11	dimensional	dimensional	ADJ
ejpam-6793	62	12	analog	analog	NOUN
ejpam-6793	62	13	of	of	ADP
ejpam-6793	62	14	functions	function	NOUN
ejpam-6793	62	15	theory	theory	NOUN
ejpam-6793	62	16	of	of	ADP
ejpam-6793	62	17	single	single	ADJ
ejpam-6793	62	18	complex	complex	ADJ
ejpam-6793	62	19	variable	variable	NOUN
ejpam-6793	62	20	(	(	PUNCT
ejpam-6793	62	21	see	see	VERB
ejpam-6793	63	1	e.g.	e.g.	ADV
ejpam-6793	63	2	[	[	X
ejpam-6793	63	3	22	22	NUM
ejpam-6793	63	4	,	,	PUNCT
ejpam-6793	63	5	23	23	NUM
ejpam-6793	63	6	]	]	PUNCT
ejpam-6793	63	7	)	)	PUNCT
ejpam-6793	63	8	.	.	PUNCT
ejpam-6793	64	1	in	in	ADP
ejpam-6793	64	2	this	this	DET
ejpam-6793	64	3	context	context	NOUN
ejpam-6793	64	4	,	,	PUNCT
ejpam-6793	64	5	a	a	DET
ejpam-6793	64	6	monogenic	monogenic	ADJ
ejpam-6793	64	7	functions	function	NOUN
ejpam-6793	64	8	is	be	AUX
ejpam-6793	64	9	a	a	DET
ejpam-6793	64	10	null	null	ADJ
ejpam-6793	64	11	solution	solution	NOUN
ejpam-6793	64	12	of	of	ADP
ejpam-6793	64	13	the	the	DET
ejpam-6793	64	14	dirac	dirac	NOUN
ejpam-6793	64	15	operator	operator	NOUN
ejpam-6793	65	1	d	d	NOUN
ejpam-6793	65	2	=	=	PROPN
ejpam-6793	65	3	∑m	∑m	PROPN
ejpam-6793	65	4	i=0	i=0	PROPN
ejpam-6793	65	5	ei	ei	NOUN
ejpam-6793	65	6	∂	∂	NUM
ejpam-6793	65	7	∂xi	∂xi	NOUN
ejpam-6793	65	8	,	,	PUNCT
ejpam-6793	65	9	in	in	ADP
ejpam-6793	65	10	rm+1	rm+1	PROPN
ejpam-6793	65	11	(	(	PUNCT
ejpam-6793	65	12	see	see	VERB
ejpam-6793	65	13	[	[	X
ejpam-6793	65	14	24	24	NUM
ejpam-6793	65	15	]	]	PUNCT
ejpam-6793	65	16	)	)	PUNCT
ejpam-6793	65	17	.	.	PUNCT
ejpam-6793	66	1	consider	consider	VERB
ejpam-6793	66	2	a	a	DET
ejpam-6793	66	3	regular	regular	ADJ
ejpam-6793	66	4	function	function	NOUN
ejpam-6793	66	5	φ	φ	NOUN
ejpam-6793	66	6	having	have	VERB
ejpam-6793	66	7	values	value	NOUN
ejpam-6793	66	8	in	in	ADP
ejpam-6793	66	9	am	be	AUX
ejpam-6793	66	10	defined	define	VERB
ejpam-6793	66	11	in	in	ADP
ejpam-6793	66	12	some	some	DET
ejpam-6793	66	13	open	open	ADJ
ejpam-6793	66	14	subset	subset	NOUN
ejpam-6793	66	15	m	m	NOUN
ejpam-6793	66	16	of	of	ADP
ejpam-6793	66	17	rm+1	rm+1	PRON
ejpam-6793	66	18	.	.	PUNCT
ejpam-6793	67	1	if	if	SCONJ
ejpam-6793	67	2	dφ	dφ	ADV
ejpam-6793	67	3	=	=	SYM
ejpam-6793	67	4	0	0	NUM
ejpam-6793	67	5	or	or	CCONJ
ejpam-6793	67	6	φd	φd	PUNCT
ejpam-6793	67	7	=	=	ADJ
ejpam-6793	67	8	0	0	PROPN
ejpam-6793	67	9	,	,	PUNCT
ejpam-6793	67	10	then	then	ADV
ejpam-6793	67	11	φ	φ	PROPN
ejpam-6793	67	12	is	be	AUX
ejpam-6793	67	13	called	call	VERB
ejpam-6793	67	14	left	left	ADJ
ejpam-6793	67	15	-	-	PUNCT
ejpam-6793	67	16	monogenic	monogenic	ADJ
ejpam-6793	67	17	or	or	CCONJ
ejpam-6793	67	18	right	right	ADJ
ejpam-6793	67	19	-	-	PUNCT
ejpam-6793	67	20	monogenic	monogenic	NOUN
ejpam-6793	67	21	respectively	respectively	ADV
ejpam-6793	67	22	.	.	PUNCT
ejpam-6793	68	1	definition	definition	NOUN
ejpam-6793	68	2	1	1	NUM
ejpam-6793	68	3	.	.	PUNCT
ejpam-6793	68	4	let	let	VERB
ejpam-6793	68	5	q(x	q(x	NOUN
ejpam-6793	68	6	)	)	PUNCT
ejpam-6793	68	7	be	be	AUX
ejpam-6793	68	8	mp	mp	PROPN
ejpam-6793	68	9	.	.	PUNCT
ejpam-6793	69	1	then	then	ADV
ejpam-6793	69	2	q(x	q(x	NOUN
ejpam-6793	69	3	)	)	PUNCT
ejpam-6793	69	4	is	be	AUX
ejpam-6793	69	5	smp	smp	NOUN
ejpam-6793	69	6	if	if	SCONJ
ejpam-6793	69	7	there	there	PRON
ejpam-6793	69	8	exist	exist	VERB
ejpam-6793	69	9	uk,ℓ	uk,ℓ	X
ejpam-6793	69	10	∈	∈	PROPN
ejpam-6793	69	11	am	am	NOUN
ejpam-6793	69	12	,	,	PUNCT
ejpam-6793	69	13	and	and	CCONJ
ejpam-6793	69	14	we	we	PRON
ejpam-6793	69	15	have	have	VERB
ejpam-6793	69	16	q(x	q(x	NOUN
ejpam-6793	69	17	)	)	PUNCT
ejpam-6793	70	1	=	=	SYM
ejpam-6793	70	2	finite∑	finite∑	NOUN
ejpam-6793	70	3	k,ℓ	k,ℓ	NOUN
ejpam-6793	70	4	xkxℓuk,ℓ.	xkxℓuk,ℓ.	PROPN
ejpam-6793	70	5	definition	definition	NOUN
ejpam-6793	70	6	2	2	NUM
ejpam-6793	70	7	.	.	PUNCT
ejpam-6793	71	1	let	let	VERB
ejpam-6793	71	2	φ	φ	PROPN
ejpam-6793	71	3	be	be	AUX
ejpam-6793	71	4	a	a	DET
ejpam-6793	71	5	mf	mf	NOUN
ejpam-6793	71	6	in	in	ADP
ejpam-6793	71	7	m	m	ADP
ejpam-6793	71	8	where	where	SCONJ
ejpam-6793	71	9	m	m	VERB
ejpam-6793	71	10	⊂	⊂	VERB
ejpam-6793	71	11	rm+1	rm+1	PROPN
ejpam-6793	71	12	is	be	AUX
ejpam-6793	71	13	an	an	DET
ejpam-6793	71	14	open	open	ADJ
ejpam-6793	71	15	and	and	CCONJ
ejpam-6793	71	16	connected	connect	VERB
ejpam-6793	71	17	.	.	PUNCT
ejpam-6793	72	1	which	which	PRON
ejpam-6793	72	2	contain	contain	VERB
ejpam-6793	72	3	0	0	NUM
ejpam-6793	72	4	.	.	PUNCT
ejpam-6793	73	1	the	the	DET
ejpam-6793	73	2	function	function	NOUN
ejpam-6793	73	3	φ	φ	PROPN
ejpam-6793	73	4	is	be	AUX
ejpam-6793	73	5	smf	smf	PROPN
ejpam-6793	73	6	in	in	ADP
ejpam-6793	73	7	m	m	PROPN
ejpam-6793	73	8	iff	iff	NOUN
ejpam-6793	73	9	it	it	PRON
ejpam-6793	73	10	has	have	VERB
ejpam-6793	73	11	taylor	taylor	PROPN
ejpam-6793	73	12	expansion	expansion	NOUN
ejpam-6793	73	13	near	near	ADP
ejpam-6793	73	14	zero	zero	NUM
ejpam-6793	73	15	and	and	CCONJ
ejpam-6793	73	16	can	can	AUX
ejpam-6793	73	17	be	be	AUX
ejpam-6793	73	18	written	write	VERB
ejpam-6793	73	19	in	in	ADP
ejpam-6793	73	20	the	the	DET
ejpam-6793	73	21	form	form	NOUN
ejpam-6793	73	22	φ(x	φ(x	NOUN
ejpam-6793	73	23	)	)	PUNCT
ejpam-6793	73	24	=	=	SYM
ejpam-6793	74	1	∞∑	∞∑	NUM
ejpam-6793	74	2	ℓ=0	ℓ=0	NOUN
ejpam-6793	74	3	qℓ(x)uℓ	qℓ(x)uℓ	NOUN
ejpam-6793	74	4	for	for	ADP
ejpam-6793	74	5	some	some	DET
ejpam-6793	74	6	smps	smp	NOUN
ejpam-6793	74	7	qℓ(x	qℓ(x	NOUN
ejpam-6793	74	8	)	)	PUNCT
ejpam-6793	74	9	where	where	SCONJ
ejpam-6793	74	10	uℓ	uℓ	X
ejpam-6793	74	11	∈	∈	PROPN
ejpam-6793	74	12	am	be	AUX
ejpam-6793	74	13	.	.	PUNCT
ejpam-6793	75	1	the	the	DET
ejpam-6793	75	2	right	right	ADJ
ejpam-6793	75	3	am	be	AUX
ejpam-6793	75	4	module	module	NOUN
ejpam-6793	75	5	has	have	VERB
ejpam-6793	75	6	the	the	DET
ejpam-6793	75	7	the	the	DET
ejpam-6793	75	8	following	follow	VERB
ejpam-6793	75	9	form	form	NOUN
ejpam-6793	75	10	:	:	PUNCT
ejpam-6793	75	11	am[x	am[x	NOUN
ejpam-6793	75	12	]	]	X
ejpam-6793	75	13	=	=	PUNCT
ejpam-6793	75	14	spanam	spanam	X
ejpam-6793	75	15	{	{	PUNCT
ejpam-6793	75	16	qℓ(x	qℓ(x	NOUN
ejpam-6793	75	17	)	)	PUNCT
ejpam-6793	75	18	:	:	PUNCT
ejpam-6793	75	19	ℓ	ℓ	PROPN
ejpam-6793	75	20	∈	∈	PROPN
ejpam-6793	75	21	n	n	CCONJ
ejpam-6793	75	22	}	}	PUNCT
ejpam-6793	75	23	,	,	PUNCT
ejpam-6793	75	24	where	where	SCONJ
ejpam-6793	75	25	qℓ(x	qℓ(x	NOUN
ejpam-6793	75	26	)	)	PUNCT
ejpam-6793	75	27	was	be	AUX
ejpam-6793	75	28	first	first	ADV
ejpam-6793	75	29	constructed	construct	VERB
ejpam-6793	75	30	in	in	ADP
ejpam-6793	75	31	[	[	X
ejpam-6793	75	32	7	7	NUM
ejpam-6793	75	33	]	]	PUNCT
ejpam-6793	75	34	as	as	SCONJ
ejpam-6793	75	35	follows	follow	VERB
ejpam-6793	75	36	:	:	PUNCT
ejpam-6793	75	37	qℓ(x	qℓ(x	NOUN
ejpam-6793	75	38	)	)	PUNCT
ejpam-6793	76	1	=	=	PUNCT
ejpam-6793	76	2	ℓ	ℓ	X
ejpam-6793	76	3	!	!	PUNCT
ejpam-6793	76	4	(	(	PUNCT
ejpam-6793	76	5	m)ℓ	m)ℓ	ADJ
ejpam-6793	76	6	∑	∑	ADV
ejpam-6793	76	7	s+t=ℓ	s+t=ℓ	NOUN
ejpam-6793	76	8	(	(	PUNCT
ejpam-6793	76	9	m−1	m−1	PROPN
ejpam-6793	76	10	2	2	NUM
ejpam-6793	76	11	)	)	PUNCT
ejpam-6793	76	12	s	s	PROPN
ejpam-6793	76	13	(	(	PUNCT
ejpam-6793	76	14	m+1	m+1	NUM
ejpam-6793	76	15	2	2	NUM
ejpam-6793	76	16	)	)	PUNCT
ejpam-6793	76	17	t	t	PROPN
ejpam-6793	76	18	s!t	s!t	PROPN
ejpam-6793	76	19	!	!	PUNCT
ejpam-6793	76	20	xsxt	xsxt	PROPN
ejpam-6793	76	21	,	,	PUNCT
ejpam-6793	76	22	(	(	PUNCT
ejpam-6793	76	23	1	1	X
ejpam-6793	76	24	)	)	PUNCT
ejpam-6793	76	25	where	where	SCONJ
ejpam-6793	76	26	(	(	PUNCT
ejpam-6793	76	27	a)h	a)h	X
ejpam-6793	76	28	=	=	SYM
ejpam-6793	76	29	a(a+	a(a+	NOUN
ejpam-6793	76	30	1	1	NUM
ejpam-6793	76	31	)	)	PUNCT
ejpam-6793	76	32	.	.	PUNCT
ejpam-6793	76	33	.	.	PUNCT
ejpam-6793	76	34	.	.	PUNCT
ejpam-6793	77	1	(	(	PUNCT
ejpam-6793	77	2	a+	a+	X
ejpam-6793	77	3	h−	h−	PROPN
ejpam-6793	77	4	1	1	NUM
ejpam-6793	77	5	)	)	PUNCT
ejpam-6793	77	6	is	be	AUX
ejpam-6793	77	7	the	the	DET
ejpam-6793	77	8	pochhamer	pochhamer	ADJ
ejpam-6793	77	9	symbol	symbol	NOUN
ejpam-6793	77	10	for	for	ADP
ejpam-6793	77	11	a	a	DET
ejpam-6793	77	12	∈	∈	PROPN
ejpam-6793	77	13	r.	r.	PROPN
ejpam-6793	77	14	m.	m.	PROPN
ejpam-6793	77	15	zayed	zayed	PROPN
ejpam-6793	77	16	/	/	SYM
ejpam-6793	77	17	eur	eur	PROPN
ejpam-6793	77	18	.	.	PUNCT
ejpam-6793	78	1	j.	j.	PROPN
ejpam-6793	78	2	pure	pure	PROPN
ejpam-6793	78	3	appl	appl	PROPN
ejpam-6793	78	4	.	.	PROPN
ejpam-6793	78	5	math	math	PROPN
ejpam-6793	78	6	,	,	PUNCT
ejpam-6793	78	7	18	18	NUM
ejpam-6793	78	8	(	(	PUNCT
ejpam-6793	78	9	4	4	NUM
ejpam-6793	78	10	)	)	PUNCT
ejpam-6793	78	11	(	(	PUNCT
ejpam-6793	78	12	2025	2025	NUM
ejpam-6793	78	13	)	)	PUNCT
ejpam-6793	78	14	,	,	PUNCT
ejpam-6793	78	15	6793	6793	NUM
ejpam-6793	78	16	4	4	NUM
ejpam-6793	78	17	of	of	ADP
ejpam-6793	78	18	19	19	NUM
ejpam-6793	78	19	remark	remark	NOUN
ejpam-6793	78	20	1	1	NUM
ejpam-6793	78	21	.	.	PUNCT
ejpam-6793	79	1	if	if	SCONJ
ejpam-6793	79	2	qℓ(x	qℓ(x	NOUN
ejpam-6793	79	3	)	)	PUNCT
ejpam-6793	80	1	is	be	AUX
ejpam-6793	80	2	a	a	DET
ejpam-6793	80	3	smp	smp	NOUN
ejpam-6793	80	4	which	which	PRON
ejpam-6793	80	5	is	be	AUX
ejpam-6793	80	6	homogeneous	homogeneous	ADJ
ejpam-6793	80	7	and	and	CCONJ
ejpam-6793	80	8	of	of	ADP
ejpam-6793	80	9	degree	degree	NOUN
ejpam-6793	80	10	ℓ	ℓ	PROPN
ejpam-6793	80	11	and	and	CCONJ
ejpam-6793	80	12	qℓ(x	qℓ(x	NOUN
ejpam-6793	80	13	)	)	PUNCT
ejpam-6793	81	1	=	=	SYM
ejpam-6793	81	2	qℓ(x)u	qℓ(x)u	NOUN
ejpam-6793	81	3	,	,	PUNCT
ejpam-6793	81	4	for	for	ADP
ejpam-6793	81	5	u	u	PROPN
ejpam-6793	81	6	∈	∈	PROPN
ejpam-6793	81	7	am	be	AUX
ejpam-6793	81	8	(	(	PUNCT
ejpam-6793	81	9	[	[	X
ejpam-6793	81	10	7	7	NUM
ejpam-6793	81	11	]	]	NUM
ejpam-6793	81	12	)	)	PUNCT
ejpam-6793	81	13	,	,	PUNCT
ejpam-6793	81	14	then	then	ADV
ejpam-6793	81	15	∥qℓ∥r	∥qℓ∥r	PROPN
ejpam-6793	81	16	=	=	SYM
ejpam-6793	81	17	sup	sup	NOUN
ejpam-6793	81	18	b(r	b(r	NOUN
ejpam-6793	81	19	)	)	PUNCT
ejpam-6793	81	20	|qℓ(x)|	|qℓ(x)|	VERB
ejpam-6793	81	21	=	=	SYM
ejpam-6793	81	22	rℓ.	rℓ.	ADJ
ejpam-6793	81	23	definition	definition	NOUN
ejpam-6793	81	24	3	3	NUM
ejpam-6793	81	25	.	.	PUNCT
ejpam-6793	82	1	a	a	DET
ejpam-6793	82	2	space	space	NOUN
ejpam-6793	82	3	f	f	NOUN
ejpam-6793	82	4	is	be	AUX
ejpam-6793	82	5	called	call	VERB
ejpam-6793	82	6	an	an	DET
ejpam-6793	82	7	f	f	NOUN
ejpam-6793	82	8	-	-	PUNCT
ejpam-6793	82	9	module	module	NOUN
ejpam-6793	82	10	over	over	ADP
ejpam-6793	82	11	am	be	AUX
ejpam-6793	82	12	if	if	SCONJ
ejpam-6793	82	13	f	f	PROPN
ejpam-6793	82	14	is	be	AUX
ejpam-6793	82	15	a	a	DET
ejpam-6793	82	16	hausdorff	hausdorff	NOUN
ejpam-6793	82	17	space	space	NOUN
ejpam-6793	82	18	associated	associate	VERB
ejpam-6793	82	19	with	with	ADP
ejpam-6793	82	20	a	a	DET
ejpam-6793	82	21	countable	countable	ADJ
ejpam-6793	82	22	proper	proper	ADJ
ejpam-6793	82	23	sets	set	NOUN
ejpam-6793	82	24	of	of	ADP
ejpam-6793	82	25	seminorms	seminorm	NOUN
ejpam-6793	82	26	n	n	AUX
ejpam-6793	82	27	=	=	PUNCT
ejpam-6793	82	28	{	{	PUNCT
ejpam-6793	82	29	∥.∥k}k≥0	∥.∥k}k≥0	ADP
ejpam-6793	82	30	such	such	ADJ
ejpam-6793	82	31	that	that	PRON
ejpam-6793	82	32	:	:	PUNCT
ejpam-6793	82	33	(	(	PUNCT
ejpam-6793	82	34	i	i	NOUN
ejpam-6793	82	35	)	)	PUNCT
ejpam-6793	82	36	for	for	ADP
ejpam-6793	82	37	φ	φ	PROPN
ejpam-6793	82	38	∈	∈	PROPN
ejpam-6793	82	39	f	f	X
ejpam-6793	82	40	,	,	PUNCT
ejpam-6793	82	41	and	and	CCONJ
ejpam-6793	82	42	k	k	X
ejpam-6793	82	43	<	<	X
ejpam-6793	82	44	l	l	NOUN
ejpam-6793	82	45	,	,	PUNCT
ejpam-6793	82	46	we	we	PRON
ejpam-6793	82	47	have	have	AUX
ejpam-6793	82	48	∥φ∥k	∥φ∥k	NOUN
ejpam-6793	82	49	≤	≤	NUM
ejpam-6793	82	50	∥φ∥l	∥φ∥l	NOUN
ejpam-6793	82	51	.	.	PUNCT
ejpam-6793	83	1	(	(	PUNCT
ejpam-6793	83	2	ii	ii	NOUN
ejpam-6793	83	3	)	)	PUNCT
ejpam-6793	83	4	a	a	DET
ejpam-6793	83	5	subset	subset	NOUN
ejpam-6793	83	6	w	w	ADP
ejpam-6793	83	7	⊂	⊂	PROPN
ejpam-6793	83	8	f	f	PROPN
ejpam-6793	83	9	is	be	AUX
ejpam-6793	83	10	open	open	ADJ
ejpam-6793	83	11	if	if	SCONJ
ejpam-6793	83	12	for	for	ADP
ejpam-6793	83	13	all	all	DET
ejpam-6793	83	14	φ	φ	NOUN
ejpam-6793	83	15	∈	∈	PROPN
ejpam-6793	83	16	w	w	NOUN
ejpam-6793	83	17	,	,	PUNCT
ejpam-6793	83	18	there	there	PRON
ejpam-6793	83	19	exists	exist	VERB
ejpam-6793	83	20	ϵ	ϵ	X
ejpam-6793	83	21	>	>	X
ejpam-6793	83	22	0	0	PROPN
ejpam-6793	83	23	,	,	PUNCT
ejpam-6793	83	24	l	l	NOUN
ejpam-6793	83	25	≥	≥	NOUN
ejpam-6793	83	26	0	0	NUM
ejpam-6793	83	27	such	such	ADJ
ejpam-6793	83	28	that	that	SCONJ
ejpam-6793	83	29	{	{	PUNCT
ejpam-6793	83	30	ψ	ψ	X
ejpam-6793	83	31	∈	∈	X
ejpam-6793	83	32	f	f	X
ejpam-6793	83	33	:	:	PUNCT
ejpam-6793	83	34	∥φ−	∥φ−	NUM
ejpam-6793	83	35	ψ∥k	ψ∥k	NOUN
ejpam-6793	83	36	)	)	PUNCT
ejpam-6793	83	37	≤	≤	NUM
ejpam-6793	84	1	ϵ	ϵ	X
ejpam-6793	84	2	}	}	PUNCT
ejpam-6793	84	3	⊂w	⊂w	PROPN
ejpam-6793	84	4	,	,	PUNCT
ejpam-6793	84	5	for	for	ADP
ejpam-6793	84	6	all	all	DET
ejpam-6793	84	7	k	k	PROPN
ejpam-6793	84	8	≤	≤	PROPN
ejpam-6793	84	9	l.	l.	PROPN
ejpam-6793	84	10	(	(	PUNCT
ejpam-6793	84	11	iii	iii	PROPN
ejpam-6793	84	12	)	)	PUNCT
ejpam-6793	84	13	f	f	PROPN
ejpam-6793	84	14	is	be	AUX
ejpam-6793	84	15	complete	complete	ADJ
ejpam-6793	84	16	regarding	regard	VERB
ejpam-6793	84	17	the	the	DET
ejpam-6793	84	18	topology	topology	NOUN
ejpam-6793	84	19	determined	determine	VERB
ejpam-6793	84	20	by	by	ADP
ejpam-6793	84	21	the	the	DET
ejpam-6793	84	22	family	family	NOUN
ejpam-6793	84	23	n.	n.	NOUN
ejpam-6793	84	24	definition	definition	NOUN
ejpam-6793	84	25	4	4	X
ejpam-6793	84	26	.	.	PUNCT
ejpam-6793	85	1	let	let	AUX
ejpam-6793	85	2	{	{	PUNCT
ejpam-6793	85	3	un	un	AUX
ejpam-6793	85	4	}	}	PUNCT
ejpam-6793	85	5	be	be	AUX
ejpam-6793	85	6	sequence	sequence	NOUN
ejpam-6793	85	7	in	in	ADP
ejpam-6793	85	8	an	an	DET
ejpam-6793	85	9	f	f	NOUN
ejpam-6793	85	10	-	-	PUNCT
ejpam-6793	85	11	module	module	NOUN
ejpam-6793	85	12	f	f	NOUN
ejpam-6793	85	13	.	.	PUNCT
ejpam-6793	86	1	then	then	ADV
ejpam-6793	86	2	,	,	PUNCT
ejpam-6793	86	3	the	the	DET
ejpam-6793	86	4	sequence	sequence	NOUN
ejpam-6793	86	5	{	{	PUNCT
ejpam-6793	86	6	un	un	PROPN
ejpam-6793	86	7	}	}	PUNCT
ejpam-6793	86	8	converges	converge	NOUN
ejpam-6793	86	9	to	to	ADP
ejpam-6793	86	10	φ	φ	PROPN
ejpam-6793	86	11	in	in	ADP
ejpam-6793	86	12	f	f	PROPN
ejpam-6793	86	13	iff	iff	PROPN
ejpam-6793	86	14	limn→∞	limn→∞	PROPN
ejpam-6793	86	15	∥un	∥un	PROPN
ejpam-6793	86	16	−	−	PROPN
ejpam-6793	86	17	φ∥k	φ∥k	NOUN
ejpam-6793	86	18	=	=	SYM
ejpam-6793	86	19	0	0	NUM
ejpam-6793	86	20	for	for	SCONJ
ejpam-6793	86	21	all	all	PRON
ejpam-6793	86	22	∥.∥k	∥.∥k	PROPN
ejpam-6793	86	23	∈	∈	PROPN
ejpam-6793	86	24	n.	n.	NOUN
ejpam-6793	86	25	let	let	VERB
ejpam-6793	86	26	φ(x	φ(x	NOUN
ejpam-6793	86	27	)	)	PUNCT
ejpam-6793	86	28	where	where	SCONJ
ejpam-6793	86	29	x	x	SYM
ejpam-6793	86	30	∈	∈	PROPN
ejpam-6793	86	31	rm+1	rm+1	PROPN
ejpam-6793	86	32	be	be	VERB
ejpam-6793	86	33	a	a	DET
ejpam-6793	86	34	smf	smf	PROPN
ejpam-6793	86	35	.	.	PUNCT
ejpam-6793	87	1	each	each	DET
ejpam-6793	87	2	notation	notation	NOUN
ejpam-6793	87	3	in	in	ADP
ejpam-6793	87	4	table	table	NOUN
ejpam-6793	87	5	1	1	NUM
ejpam-6793	87	6	below	below	ADV
ejpam-6793	87	7	expresses	express	VERB
ejpam-6793	87	8	a	a	DET
ejpam-6793	87	9	class	class	NOUN
ejpam-6793	87	10	of	of	ADP
ejpam-6793	87	11	smfs	smfs	NOUN
ejpam-6793	87	12	in	in	ADP
ejpam-6793	87	13	the	the	DET
ejpam-6793	87	14	indicated	indicate	VERB
ejpam-6793	87	15	regions	region	NOUN
ejpam-6793	87	16	including	include	VERB
ejpam-6793	87	17	:	:	PUNCT
ejpam-6793	87	18	hyper	hyper	ADJ
ejpam-6793	87	19	open	open	PROPN
ejpam-6793	87	20	ball	ball	PROPN
ejpam-6793	87	21	b(r	b(r	PROPN
ejpam-6793	87	22	)	)	PUNCT
ejpam-6793	87	23	,	,	PUNCT
ejpam-6793	87	24	hyper	hyper	NOUN
ejpam-6793	87	25	closed	close	VERB
ejpam-6793	87	26	ball	ball	PROPN
ejpam-6793	87	27	b(r	b(r	PROPN
ejpam-6793	87	28	)	)	PUNCT
ejpam-6793	87	29	,	,	PUNCT
ejpam-6793	87	30	any	any	DET
ejpam-6793	87	31	hyper	hyper	ADJ
ejpam-6793	87	32	open	open	ADJ
ejpam-6793	87	33	ball	ball	NOUN
ejpam-6793	87	34	enclosing	enclose	VERB
ejpam-6793	87	35	hyper	hyper	NOUN
ejpam-6793	87	36	closed	close	VERB
ejpam-6793	87	37	ball	ball	PROPN
ejpam-6793	87	38	b+(r	b+(r	PROPN
ejpam-6793	87	39	)	)	PUNCT
ejpam-6793	87	40	,	,	PUNCT
ejpam-6793	87	41	for	for	ADP
ejpam-6793	87	42	all	all	DET
ejpam-6793	87	43	entire	entire	ADJ
ejpam-6793	87	44	special	special	ADJ
ejpam-6793	87	45	monogenic	monogenic	ADJ
ejpam-6793	87	46	functions	function	NOUN
ejpam-6793	87	47	and	and	CCONJ
ejpam-6793	87	48	at	at	ADP
ejpam-6793	87	49	the	the	DET
ejpam-6793	87	50	origin	origin	NOUN
ejpam-6793	87	51	.	.	PUNCT
ejpam-6793	88	1	note	note	VERB
ejpam-6793	88	2	that	that	SCONJ
ejpam-6793	88	3	all	all	DET
ejpam-6793	88	4	these	these	DET
ejpam-6793	88	5	spaces	space	NOUN
ejpam-6793	88	6	are	be	AUX
ejpam-6793	88	7	actually	actually	ADV
ejpam-6793	88	8	f	f	NOUN
ejpam-6793	88	9	-	-	PUNCT
ejpam-6793	88	10	modules	module	NOUN
ejpam-6793	88	11	associated	associate	VERB
ejpam-6793	88	12	with	with	ADP
ejpam-6793	88	13	the	the	DET
ejpam-6793	88	14	corresponding	corresponding	ADJ
ejpam-6793	88	15	semi	semi	ADJ
ejpam-6793	88	16	-	-	ADJ
ejpam-6793	88	17	norms	norms	ADJ
ejpam-6793	88	18	system	system	NOUN
ejpam-6793	88	19	.	.	PUNCT
ejpam-6793	89	1	table	table	NOUN
ejpam-6793	89	2	1	1	NUM
ejpam-6793	89	3	:	:	PUNCT
ejpam-6793	89	4	types	type	NOUN
ejpam-6793	89	5	of	of	ADP
ejpam-6793	89	6	f	f	NOUN
ejpam-6793	89	7	-	-	PUNCT
ejpam-6793	89	8	modules	module	NOUN
ejpam-6793	89	9	f	f	NOUN
ejpam-6793	89	10	-	-	PUNCT
ejpam-6793	89	11	module	module	NOUN
ejpam-6793	89	12	notation	notation	NOUN
ejpam-6793	89	13	associated	associate	VERB
ejpam-6793	89	14	semi	semi	ADJ
ejpam-6793	89	15	-	-	ADJ
ejpam-6793	89	16	norms	norms	ADJ
ejpam-6793	89	17	space	space	NOUN
ejpam-6793	89	18	containing	contain	VERB
ejpam-6793	89	19	smfs	smfs	NOUN
ejpam-6793	89	20	in	in	ADP
ejpam-6793	89	21	b(r	b(r	PROPN
ejpam-6793	89	22	):	):	PUNCT
ejpam-6793	89	23	wb(r	wb(r	X
ejpam-6793	89	24	)	)	PUNCT
ejpam-6793	89	25	∥φ∥r	∥φ∥r	NOUN
ejpam-6793	89	26	=	=	SYM
ejpam-6793	89	27	supb̄(r	supb̄(r	PROPN
ejpam-6793	89	28	)	)	PUNCT
ejpam-6793	89	29	|φ(x)|	|φ(x)|	PROPN
ejpam-6793	89	30	,	,	PUNCT
ejpam-6793	89	31	∀r	∀r	X
ejpam-6793	89	32	<	<	X
ejpam-6793	89	33	r	r	NOUN
ejpam-6793	89	34	space	space	NOUN
ejpam-6793	89	35	containing	contain	VERB
ejpam-6793	89	36	smfs	smfs	PROPN
ejpam-6793	89	37	b(r	b(r	PROPN
ejpam-6793	89	38	):	):	PUNCT
ejpam-6793	89	39	wb̄(r	wb̄(r	NOUN
ejpam-6793	89	40	)	)	PUNCT
ejpam-6793	89	41	∥φ∥r	∥φ∥r	PROPN
ejpam-6793	89	42	=	=	SYM
ejpam-6793	89	43	supb̄(r	supb̄(r	PROPN
ejpam-6793	89	44	)	)	PUNCT
ejpam-6793	89	45	|φ(x)|	|φ(x)|	PROPN
ejpam-6793	89	46	space	space	NOUN
ejpam-6793	89	47	containing	contain	VERB
ejpam-6793	89	48	smfs	smfs	NOUN
ejpam-6793	89	49	in	in	ADP
ejpam-6793	89	50	b+(r	b+(r	PROPN
ejpam-6793	89	51	)	)	PUNCT
ejpam-6793	89	52	wb+(r	wb+(r	PROPN
ejpam-6793	89	53	)	)	PUNCT
ejpam-6793	89	54	∥φ∥r	∥φ∥r	PROPN
ejpam-6793	89	55	=	=	SYM
ejpam-6793	89	56	supb̄(r	supb̄(r	PROPN
ejpam-6793	89	57	)	)	PUNCT
ejpam-6793	89	58	|φ(x)|	|φ(x)|	PROPN
ejpam-6793	89	59	,	,	PUNCT
ejpam-6793	89	60	∀r	∀r	X
ejpam-6793	89	61	<	<	X
ejpam-6793	89	62	r	r	NOUN
ejpam-6793	89	63	}	}	PUNCT
ejpam-6793	89	64	space	space	NOUN
ejpam-6793	89	65	of	of	ADP
ejpam-6793	89	66	entire	entire	ADJ
ejpam-6793	89	67	smfs	smfs	NOUN
ejpam-6793	89	68	w∞	w∞	X
ejpam-6793	89	69	∥φ∥n	∥φ∥n	ADV
ejpam-6793	89	70	=	=	SYM
ejpam-6793	89	71	supb(n	supb(n	NOUN
ejpam-6793	89	72	)	)	PUNCT
ejpam-6793	89	73	|φ(x)|	|φ(x)|	PROPN
ejpam-6793	89	74	,	,	PUNCT
ejpam-6793	89	75	n	n	CCONJ
ejpam-6793	89	76	<	<	NOUN
ejpam-6793	89	77	∞	∞	PROPN
ejpam-6793	89	78	space	space	NOUN
ejpam-6793	89	79	of	of	ADP
ejpam-6793	89	80	smfs	smfs	NOUN
ejpam-6793	89	81	at	at	ADP
ejpam-6793	89	82	0	0	NUM
ejpam-6793	89	83	w0	w0	PROPN
ejpam-6793	89	84	+	+	CCONJ
ejpam-6793	89	85	∥φ∥ϵ	∥φ∥ϵ	ADJ
ejpam-6793	89	86	=	=	SYM
ejpam-6793	89	87	supb̄(ϵ	supb̄(ϵ	NOUN
ejpam-6793	89	88	)	)	PUNCT
ejpam-6793	89	89	|φ(x)|	|φ(x)|	PROPN
ejpam-6793	89	90	,	,	PUNCT
ejpam-6793	89	91	ϵ	ϵ	X
ejpam-6793	89	92	>	>	X
ejpam-6793	89	93	0	0	NUM
ejpam-6793	89	94	definition	definition	NOUN
ejpam-6793	89	95	5	5	NUM
ejpam-6793	89	96	.	.	PUNCT
ejpam-6793	90	1	let	let	VERB
ejpam-6793	90	2	{	{	PUNCT
ejpam-6793	90	3	qn(x	qn(x	X
ejpam-6793	90	4	)	)	PUNCT
ejpam-6793	90	5	}	}	PUNCT
ejpam-6793	90	6	be	be	AUX
ejpam-6793	90	7	a	a	DET
ejpam-6793	90	8	sequence	sequence	NOUN
ejpam-6793	90	9	of	of	ADP
ejpam-6793	90	10	an	an	DET
ejpam-6793	90	11	f	f	NOUN
ejpam-6793	90	12	-	-	PUNCT
ejpam-6793	90	13	module	module	NOUN
ejpam-6793	90	14	f	f	NOUN
ejpam-6793	90	15	.	.	PUNCT
ejpam-6793	91	1	then	then	ADV
ejpam-6793	91	2	{	{	PUNCT
ejpam-6793	91	3	qn(x	qn(x	X
ejpam-6793	91	4	)	)	PUNCT
ejpam-6793	91	5	}	}	PUNCT
ejpam-6793	91	6	forms	form	VERB
ejpam-6793	91	7	a	a	DET
ejpam-6793	91	8	base	base	NOUN
ejpam-6793	91	9	if	if	SCONJ
ejpam-6793	91	10	qn(x	qn(x	PUNCT
ejpam-6793	91	11	)	)	PUNCT
ejpam-6793	91	12	is	be	AUX
ejpam-6793	91	13	given	give	VERB
ejpam-6793	91	14	in	in	ADP
ejpam-6793	91	15	the	the	DET
ejpam-6793	91	16	form	form	NOUN
ejpam-6793	91	17	:	:	PUNCT
ejpam-6793	91	18	qn(x	qn(x	X
ejpam-6793	91	19	)	)	PUNCT
ejpam-6793	91	20	=	=	PUNCT
ejpam-6793	92	1	∞∑	∞∑	NUM
ejpam-6793	92	2	k=0	k=0	PROPN
ejpam-6793	92	3	qk(x	qk(x	NOUN
ejpam-6793	92	4	)	)	PUNCT
ejpam-6793	92	5	q̃n	q̃n	PROPN
ejpam-6793	92	6	,	,	PUNCT
ejpam-6793	92	7	k	k	NOUN
ejpam-6793	92	8	,	,	PUNCT
ejpam-6793	92	9	q̃n	q̃n	PROPN
ejpam-6793	92	10	,	,	PUNCT
ejpam-6793	92	11	k	k	PROPN
ejpam-6793	92	12	∈	∈	PROPN
ejpam-6793	92	13	am	be	AUX
ejpam-6793	92	14	,	,	PUNCT
ejpam-6793	92	15	(	(	PUNCT
ejpam-6793	92	16	2	2	X
ejpam-6793	92	17	)	)	PUNCT
ejpam-6793	92	18	where	where	SCONJ
ejpam-6793	92	19	q̃	q̃	PROPN
ejpam-6793	92	20	=	=	SYM
ejpam-6793	92	21	(	(	PUNCT
ejpam-6793	92	22	q̃n	q̃n	PROPN
ejpam-6793	92	23	,	,	PUNCT
ejpam-6793	92	24	k	k	NOUN
ejpam-6793	92	25	)	)	PUNCT
ejpam-6793	92	26	is	be	AUX
ejpam-6793	92	27	the	the	DET
ejpam-6793	92	28	clifford	clifford	PROPN
ejpam-6793	92	29	matrix	matrix	NOUN
ejpam-6793	92	30	of	of	ADP
ejpam-6793	92	31	operators	operator	NOUN
ejpam-6793	92	32	of	of	ADP
ejpam-6793	92	33	the	the	DET
ejpam-6793	92	34	base	base	NOUN
ejpam-6793	92	35	{	{	PUNCT
ejpam-6793	92	36	qn(x	qn(x	NOUN
ejpam-6793	92	37	)	)	PUNCT
ejpam-6793	92	38	}	}	PUNCT
ejpam-6793	92	39	which	which	PRON
ejpam-6793	92	40	has	have	VERB
ejpam-6793	92	41	the	the	DET
ejpam-6793	92	42	form	form	NOUN
ejpam-6793	92	43	:	:	PUNCT
ejpam-6793	92	44	qn(x	qn(x	X
ejpam-6793	92	45	)	)	PUNCT
ejpam-6793	92	46	=	=	PUNCT
ejpam-6793	93	1	∞∑	∞∑	NUM
ejpam-6793	93	2	k=0	k=0	PROPN
ejpam-6793	93	3	qk(x	qk(x	X
ejpam-6793	93	4	)	)	PUNCT
ejpam-6793	93	5	qn	qn	NOUN
ejpam-6793	93	6	,	,	PUNCT
ejpam-6793	93	7	k	k	PROPN
ejpam-6793	93	8	,	,	PUNCT
ejpam-6793	93	9	qn	qn	INTJ
ejpam-6793	93	10	,	,	PUNCT
ejpam-6793	93	11	k	k	PROPN
ejpam-6793	93	12	∈	∈	PROPN
ejpam-6793	93	13	am	be	AUX
ejpam-6793	93	14	.	.	PUNCT
ejpam-6793	94	1	(	(	PUNCT
ejpam-6793	94	2	3	3	X
ejpam-6793	94	3	)	)	PUNCT
ejpam-6793	94	4	m.	m.	NOUN
ejpam-6793	94	5	zayed	zayed	PROPN
ejpam-6793	94	6	/	/	SYM
ejpam-6793	94	7	eur	eur	PROPN
ejpam-6793	94	8	.	.	PUNCT
ejpam-6793	95	1	j.	j.	PROPN
ejpam-6793	95	2	pure	pure	PROPN
ejpam-6793	95	3	appl	appl	PROPN
ejpam-6793	95	4	.	.	PROPN
ejpam-6793	95	5	math	math	PROPN
ejpam-6793	95	6	,	,	PUNCT
ejpam-6793	95	7	18	18	NUM
ejpam-6793	95	8	(	(	PUNCT
ejpam-6793	95	9	4	4	NUM
ejpam-6793	95	10	)	)	PUNCT
ejpam-6793	95	11	(	(	PUNCT
ejpam-6793	95	12	2025	2025	NUM
ejpam-6793	95	13	)	)	PUNCT
ejpam-6793	95	14	,	,	PUNCT
ejpam-6793	95	15	6793	6793	NUM
ejpam-6793	95	16	5	5	NUM
ejpam-6793	95	17	of	of	ADP
ejpam-6793	95	18	19	19	NUM
ejpam-6793	95	19	the	the	DET
ejpam-6793	95	20	matrix	matrix	NOUN
ejpam-6793	95	21	q	q	NOUN
ejpam-6793	96	1	=	=	PUNCT
ejpam-6793	96	2	(	(	PUNCT
ejpam-6793	96	3	qn	qn	INTJ
ejpam-6793	96	4	,	,	PUNCT
ejpam-6793	96	5	k	k	NOUN
ejpam-6793	96	6	)	)	PUNCT
ejpam-6793	96	7	is	be	AUX
ejpam-6793	96	8	the	the	DET
ejpam-6793	96	9	clifford	clifford	PROPN
ejpam-6793	96	10	matrix	matrix	NOUN
ejpam-6793	96	11	of	of	ADP
ejpam-6793	96	12	coefficient	coefficient	NOUN
ejpam-6793	96	13	of	of	ADP
ejpam-6793	96	14	{	{	PUNCT
ejpam-6793	96	15	qn(x	qn(x	NOUN
ejpam-6793	96	16	)	)	PUNCT
ejpam-6793	96	17	}	}	PUNCT
ejpam-6793	96	18	.	.	PUNCT
ejpam-6793	97	1	as	as	SCONJ
ejpam-6793	97	2	deduced	deduce	VERB
ejpam-6793	97	3	in	in	ADP
ejpam-6793	97	4	[	[	X
ejpam-6793	97	5	7	7	NUM
ejpam-6793	97	6	]	]	PUNCT
ejpam-6793	97	7	,	,	PUNCT
ejpam-6793	97	8	the	the	DET
ejpam-6793	97	9	set	set	NOUN
ejpam-6793	97	10	{	{	PUNCT
ejpam-6793	97	11	qn(x	qn(x	NOUN
ejpam-6793	97	12	)	)	PUNCT
ejpam-6793	97	13	}	}	PUNCT
ejpam-6793	97	14	form	form	VERB
ejpam-6793	97	15	a	a	DET
ejpam-6793	97	16	base	base	NOUN
ejpam-6793	97	17	iff	iff	PROPN
ejpam-6793	97	18	qq̃	qq̃	PROPN
ejpam-6793	98	1	=	=	SYM
ejpam-6793	98	2	q̃q	q̃q	PROPN
ejpam-6793	99	1	=	=	SYM
ejpam-6793	99	2	i	i	PROPN
ejpam-6793	99	3	,	,	PUNCT
ejpam-6793	99	4	(	(	PUNCT
ejpam-6793	99	5	4	4	X
ejpam-6793	99	6	)	)	PUNCT
ejpam-6793	99	7	where	where	SCONJ
ejpam-6793	99	8	i	i	PRON
ejpam-6793	99	9	is	be	AUX
ejpam-6793	99	10	the	the	DET
ejpam-6793	99	11	identity	identity	NOUN
ejpam-6793	99	12	matrix	matrix	NOUN
ejpam-6793	99	13	.	.	PUNCT
ejpam-6793	100	1	suppose	suppose	VERB
ejpam-6793	100	2	that	that	SCONJ
ejpam-6793	100	3	φ(x	φ(x	NOUN
ejpam-6793	100	4	)	)	PUNCT
ejpam-6793	100	5	=	=	PUNCT
ejpam-6793	101	1	∞∑	∞∑	NOUN
ejpam-6793	101	2	n=0	n=0	NUM
ejpam-6793	101	3	qn(x	qn(x	X
ejpam-6793	101	4	)	)	PUNCT
ejpam-6793	101	5	un(g	un(g	PUNCT
ejpam-6793	101	6	)	)	PUNCT
ejpam-6793	101	7	is	be	AUX
ejpam-6793	101	8	any	any	DET
ejpam-6793	101	9	smf	smf	NOUN
ejpam-6793	101	10	of	of	ADP
ejpam-6793	101	11	f	f	PROPN
ejpam-6793	101	12	.	.	PUNCT
ejpam-6793	102	1	by	by	ADP
ejpam-6793	102	2	using	use	VERB
ejpam-6793	102	3	the	the	DET
ejpam-6793	102	4	formula	formula	NOUN
ejpam-6793	102	5	of	of	ADP
ejpam-6793	102	6	qn(x	qn(x	NOUN
ejpam-6793	102	7	)	)	PUNCT
ejpam-6793	102	8	as	as	ADP
ejpam-6793	102	9	in	in	ADP
ejpam-6793	102	10	(	(	PUNCT
ejpam-6793	102	11	2	2	NUM
ejpam-6793	102	12	)	)	PUNCT
ejpam-6793	102	13	,	,	PUNCT
ejpam-6793	102	14	the	the	DET
ejpam-6793	102	15	basic	basic	ADJ
ejpam-6793	102	16	series	series	NOUN
ejpam-6793	102	17	g(x	g(x	NOUN
ejpam-6793	102	18	)	)	PUNCT
ejpam-6793	102	19	∼	∼	VERB
ejpam-6793	102	20	∞∑	∞∑	NOUN
ejpam-6793	102	21	n=0	n=0	NUM
ejpam-6793	102	22	qn(x	qn(x	X
ejpam-6793	102	23	)	)	PUNCT
ejpam-6793	102	24	πn(g	πn(g	NOUN
ejpam-6793	102	25	)	)	PUNCT
ejpam-6793	102	26	,	,	PUNCT
ejpam-6793	102	27	(	(	PUNCT
ejpam-6793	102	28	5	5	X
ejpam-6793	102	29	)	)	PUNCT
ejpam-6793	102	30	follows	follow	VERB
ejpam-6793	102	31	,	,	PUNCT
ejpam-6793	102	32	where	where	SCONJ
ejpam-6793	102	33	πn(g	πn(g	VERB
ejpam-6793	102	34	)	)	PUNCT
ejpam-6793	102	35	=	=	SYM
ejpam-6793	103	1	∞∑	∞∑	PRON
ejpam-6793	103	2	k=0	k=0	PROPN
ejpam-6793	103	3	q̃k	q̃k	PROPN
ejpam-6793	103	4	,	,	PUNCT
ejpam-6793	103	5	n	n	PRON
ejpam-6793	103	6	ak(g	ak(g	PROPN
ejpam-6793	103	7	)	)	PUNCT
ejpam-6793	103	8	.	.	PUNCT
ejpam-6793	104	1	(	(	PUNCT
ejpam-6793	104	2	6	6	X
ejpam-6793	104	3	)	)	PUNCT
ejpam-6793	104	4	definition	definition	NOUN
ejpam-6793	104	5	6	6	NUM
ejpam-6793	104	6	.	.	PUNCT
ejpam-6793	105	1	if	if	SCONJ
ejpam-6793	105	2	the	the	DET
ejpam-6793	105	3	associated	associated	ADJ
ejpam-6793	105	4	basic	basic	ADJ
ejpam-6793	105	5	series	series	NOUN
ejpam-6793	105	6	(	(	PUNCT
ejpam-6793	105	7	5	5	NUM
ejpam-6793	105	8	)	)	PUNCT
ejpam-6793	105	9	is	be	AUX
ejpam-6793	105	10	normally	normally	ADV
ejpam-6793	105	11	convergent	convergent	ADJ
ejpam-6793	105	12	to	to	ADP
ejpam-6793	105	13	every	every	DET
ejpam-6793	105	14	φ(x	φ(x	NOUN
ejpam-6793	105	15	)	)	PUNCT
ejpam-6793	105	16	in	in	ADP
ejpam-6793	105	17	an	an	DET
ejpam-6793	105	18	f	f	NOUN
ejpam-6793	105	19	-	-	PUNCT
ejpam-6793	105	20	module	module	NOUN
ejpam-6793	105	21	f	f	NOUN
ejpam-6793	105	22	,	,	PUNCT
ejpam-6793	105	23	then	then	ADV
ejpam-6793	105	24	the	the	DET
ejpam-6793	105	25	base	base	NOUN
ejpam-6793	105	26	{	{	PUNCT
ejpam-6793	105	27	qn(x	qn(x	NOUN
ejpam-6793	105	28	)	)	PUNCT
ejpam-6793	105	29	}	}	PUNCT
ejpam-6793	105	30	is	be	AUX
ejpam-6793	105	31	called	call	VERB
ejpam-6793	105	32	effective	effective	ADJ
ejpam-6793	105	33	for	for	ADP
ejpam-6793	105	34	f	f	PROPN
ejpam-6793	105	35	.	.	PUNCT
ejpam-6793	106	1	more	more	ADJ
ejpam-6793	106	2	details	detail	NOUN
ejpam-6793	106	3	on	on	ADP
ejpam-6793	106	4	the	the	DET
ejpam-6793	106	5	convergence	convergence	NOUN
ejpam-6793	106	6	properties	property	NOUN
ejpam-6793	106	7	of	of	ADP
ejpam-6793	106	8	bases	basis	NOUN
ejpam-6793	106	9	{	{	PUNCT
ejpam-6793	106	10	qn(x	qn(x	NOUN
ejpam-6793	106	11	)	)	PUNCT
ejpam-6793	106	12	}	}	PUNCT
ejpam-6793	106	13	in	in	ADP
ejpam-6793	106	14	the	the	DET
ejpam-6793	106	15	sense	sense	NOUN
ejpam-6793	106	16	of	of	ADP
ejpam-6793	106	17	f	f	NOUN
ejpam-6793	106	18	-	-	PUNCT
ejpam-6793	106	19	modules	module	NOUN
ejpam-6793	106	20	can	can	AUX
ejpam-6793	106	21	be	be	AUX
ejpam-6793	106	22	found	find	VERB
ejpam-6793	106	23	in	in	ADP
ejpam-6793	106	24	[	[	X
ejpam-6793	106	25	16	16	NUM
ejpam-6793	106	26	,	,	PUNCT
ejpam-6793	106	27	17	17	NUM
ejpam-6793	106	28	]	]	PUNCT
ejpam-6793	106	29	.	.	PUNCT
ejpam-6793	107	1	∥qn∥r	∥qn∥r	X
ejpam-6793	107	2	=	=	SYM
ejpam-6793	107	3	sup	sup	NUM
ejpam-6793	107	4	b(r	b(r	NOUN
ejpam-6793	107	5	)	)	PUNCT
ejpam-6793	107	6	|qn(x)|	|qn(x)|	NOUN
ejpam-6793	107	7	,	,	PUNCT
ejpam-6793	107	8	(	(	PUNCT
ejpam-6793	107	9	7	7	X
ejpam-6793	107	10	)	)	PUNCT
ejpam-6793	108	1	where	where	SCONJ
ejpam-6793	108	2	∥qk	∥qk	PROPN
ejpam-6793	108	3	q̃n	q̃n	PROPN
ejpam-6793	108	4	,	,	PUNCT
ejpam-6793	108	5	k∥r	k∥r	NOUN
ejpam-6793	108	6	=	=	SYM
ejpam-6793	108	7	sup	sup	NOUN
ejpam-6793	108	8	b(r	b(r	PROPN
ejpam-6793	108	9	)	)	PUNCT
ejpam-6793	108	10	|qk(x	|qk(x	SYM
ejpam-6793	108	11	)	)	PUNCT
ejpam-6793	108	12	q̃n	q̃n	PROPN
ejpam-6793	108	13	,	,	PUNCT
ejpam-6793	108	14	k|	k|	NOUN
ejpam-6793	108	15	.	.	PUNCT
ejpam-6793	109	1	examining	examine	VERB
ejpam-6793	109	2	the	the	DET
ejpam-6793	109	3	effectiveness	effectiveness	NOUN
ejpam-6793	109	4	of	of	ADP
ejpam-6793	109	5	bases	basis	NOUN
ejpam-6793	109	6	throughout	throughout	ADP
ejpam-6793	109	7	this	this	DET
ejpam-6793	109	8	study	study	NOUN
ejpam-6793	109	9	is	be	AUX
ejpam-6793	109	10	mainly	mainly	ADV
ejpam-6793	109	11	conducted	conduct	VERB
ejpam-6793	109	12	using	use	VERB
ejpam-6793	109	13	the	the	DET
ejpam-6793	109	14	value	value	NOUN
ejpam-6793	109	15	of	of	ADP
ejpam-6793	109	16	the	the	DET
ejpam-6793	109	17	cannon	cannon	NOUN
ejpam-6793	109	18	function	function	NOUN
ejpam-6793	109	19	ω(q	ω(q	PROPN
ejpam-6793	109	20	,	,	PUNCT
ejpam-6793	109	21	r	r	NOUN
ejpam-6793	109	22	)	)	PUNCT
ejpam-6793	109	23	=	=	SYM
ejpam-6793	109	24	lim	lim	PROPN
ejpam-6793	109	25	sup	sup	PROPN
ejpam-6793	109	26	n→∞	n→∞	X
ejpam-6793	109	27	{	{	PUNCT
ejpam-6793	109	28	ω(qn	ω(qn	NUM
ejpam-6793	109	29	,	,	PUNCT
ejpam-6793	109	30	r	r	NOUN
ejpam-6793	109	31	)	)	PUNCT
ejpam-6793	109	32	}	}	PUNCT
ejpam-6793	109	33	1	1	NUM
ejpam-6793	109	34	n	n	NOUN
ejpam-6793	109	35	,	,	PUNCT
ejpam-6793	109	36	(	(	PUNCT
ejpam-6793	109	37	8)	8)	NUM
ejpam-6793	109	38	where	where	SCONJ
ejpam-6793	109	39	ω(qn	ω(qn	NOUN
ejpam-6793	109	40	,	,	PUNCT
ejpam-6793	109	41	r	r	NOUN
ejpam-6793	109	42	)	)	PUNCT
ejpam-6793	109	43	=	=	PUNCT
ejpam-6793	109	44	∑	∑	PUNCT
ejpam-6793	109	45	k	k	PROPN
ejpam-6793	109	46	∥qk	∥qk	PROPN
ejpam-6793	109	47	q̃n	q̃n	PROPN
ejpam-6793	109	48	,	,	PUNCT
ejpam-6793	109	49	k∥r	k∥r	NOUN
ejpam-6793	109	50	,	,	PUNCT
ejpam-6793	109	51	(	(	PUNCT
ejpam-6793	109	52	9	9	X
ejpam-6793	109	53	)	)	PUNCT
ejpam-6793	109	54	is	be	AUX
ejpam-6793	109	55	called	call	VERB
ejpam-6793	109	56	the	the	DET
ejpam-6793	109	57	cannon	cannon	NOUN
ejpam-6793	109	58	sum	sum	NOUN
ejpam-6793	109	59	as	as	SCONJ
ejpam-6793	109	60	we	we	PRON
ejpam-6793	109	61	shall	shall	AUX
ejpam-6793	109	62	see	see	VERB
ejpam-6793	109	63	in	in	ADP
ejpam-6793	109	64	the	the	DET
ejpam-6793	109	65	following	following	NOUN
ejpam-6793	109	66	theorem	theorem	NOUN
ejpam-6793	109	67	which	which	PRON
ejpam-6793	109	68	determines	determine	VERB
ejpam-6793	109	69	the	the	DET
ejpam-6793	109	70	effectiveness	effectiveness	NOUN
ejpam-6793	109	71	criteria	criterion	NOUN
ejpam-6793	109	72	(	(	PUNCT
ejpam-6793	109	73	see	see	VERB
ejpam-6793	109	74	[	[	X
ejpam-6793	109	75	16	16	NUM
ejpam-6793	109	76	,	,	PUNCT
ejpam-6793	109	77	17	17	NUM
ejpam-6793	109	78	]	]	PUNCT
ejpam-6793	109	79	)	)	PUNCT
ejpam-6793	109	80	.	.	PUNCT
ejpam-6793	110	1	theorem	theorem	NOUN
ejpam-6793	110	2	1	1	NUM
ejpam-6793	110	3	.	.	PUNCT
ejpam-6793	111	1	(	(	PUNCT
ejpam-6793	111	2	i	i	NOUN
ejpam-6793	111	3	)	)	PUNCT
ejpam-6793	111	4	a	a	DET
ejpam-6793	111	5	base	base	NOUN
ejpam-6793	111	6	{	{	PUNCT
ejpam-6793	111	7	qn(x	qn(x	NOUN
ejpam-6793	111	8	)	)	PUNCT
ejpam-6793	111	9	}	}	PUNCT
ejpam-6793	111	10	is	be	AUX
ejpam-6793	111	11	effective	effective	ADJ
ejpam-6793	111	12	for	for	ADP
ejpam-6793	111	13	wb̄(r	wb̄(r	NOUN
ejpam-6793	111	14	)	)	PUNCT
ejpam-6793	111	15	,	,	PUNCT
ejpam-6793	111	16	iff	iff	PROPN
ejpam-6793	111	17	ω(q	ω(q	PROPN
ejpam-6793	111	18	,	,	PUNCT
ejpam-6793	111	19	r	r	NOUN
ejpam-6793	111	20	)	)	PUNCT
ejpam-6793	111	21	=	=	SYM
ejpam-6793	111	22	r	r	NOUN
ejpam-6793	111	23	;	;	PUNCT
ejpam-6793	111	24	(	(	PUNCT
ejpam-6793	111	25	ii	ii	NOUN
ejpam-6793	111	26	)	)	PUNCT
ejpam-6793	111	27	a	a	DET
ejpam-6793	111	28	base	base	NOUN
ejpam-6793	111	29	{	{	PUNCT
ejpam-6793	111	30	qn(x	qn(x	NOUN
ejpam-6793	111	31	)	)	PUNCT
ejpam-6793	111	32	}	}	PUNCT
ejpam-6793	111	33	is	be	AUX
ejpam-6793	111	34	effective	effective	ADJ
ejpam-6793	111	35	for	for	ADP
ejpam-6793	111	36	wb+(r	wb+(r	NOUN
ejpam-6793	111	37	)	)	PUNCT
ejpam-6793	111	38	,	,	PUNCT
ejpam-6793	111	39	iff	iff	PROPN
ejpam-6793	111	40	ω(q	ω(q	PROPN
ejpam-6793	111	41	,	,	PUNCT
ejpam-6793	111	42	r+	r+	X
ejpam-6793	111	43	)	)	PUNCT
ejpam-6793	111	44	=	=	SYM
ejpam-6793	111	45	r	r	NOUN
ejpam-6793	111	46	;	;	PUNCT
ejpam-6793	111	47	m.	m.	NOUN
ejpam-6793	111	48	zayed	zayed	PROPN
ejpam-6793	111	49	/	/	SYM
ejpam-6793	111	50	eur	eur	PROPN
ejpam-6793	111	51	.	.	PUNCT
ejpam-6793	112	1	j.	j.	PROPN
ejpam-6793	112	2	pure	pure	PROPN
ejpam-6793	112	3	appl	appl	PROPN
ejpam-6793	112	4	.	.	PROPN
ejpam-6793	112	5	math	math	PROPN
ejpam-6793	112	6	,	,	PUNCT
ejpam-6793	112	7	18	18	NUM
ejpam-6793	112	8	(	(	PUNCT
ejpam-6793	112	9	4	4	NUM
ejpam-6793	112	10	)	)	PUNCT
ejpam-6793	112	11	(	(	PUNCT
ejpam-6793	112	12	2025	2025	NUM
ejpam-6793	112	13	)	)	PUNCT
ejpam-6793	112	14	,	,	PUNCT
ejpam-6793	112	15	6793	6793	NUM
ejpam-6793	112	16	6	6	NUM
ejpam-6793	112	17	of	of	ADP
ejpam-6793	112	18	19	19	NUM
ejpam-6793	112	19	(	(	PUNCT
ejpam-6793	112	20	iii	iii	NOUN
ejpam-6793	112	21	)	)	PUNCT
ejpam-6793	112	22	a	a	DET
ejpam-6793	112	23	base	base	NOUN
ejpam-6793	112	24	{	{	PUNCT
ejpam-6793	112	25	qn(x	qn(x	NOUN
ejpam-6793	112	26	)	)	PUNCT
ejpam-6793	112	27	}	}	PUNCT
ejpam-6793	112	28	is	be	AUX
ejpam-6793	112	29	effective	effective	ADJ
ejpam-6793	112	30	for	for	ADP
ejpam-6793	112	31	wb(r	wb(r	NUM
ejpam-6793	112	32	)	)	PUNCT
ejpam-6793	112	33	iff	iff	PROPN
ejpam-6793	112	34	ω(q	ω(q	PROPN
ejpam-6793	112	35	,	,	PUNCT
ejpam-6793	112	36	r	r	NOUN
ejpam-6793	112	37	)	)	PUNCT
ejpam-6793	112	38	<	<	X
ejpam-6793	112	39	r	r	NOUN
ejpam-6793	112	40	∀	∀	NOUN
ejpam-6793	112	41	r	r	NOUN
ejpam-6793	112	42	<	<	X
ejpam-6793	112	43	r	r	NOUN
ejpam-6793	112	44	;	;	PUNCT
ejpam-6793	112	45	(	(	PUNCT
ejpam-6793	112	46	iv	iv	X
ejpam-6793	112	47	)	)	PUNCT
ejpam-6793	112	48	a	a	DET
ejpam-6793	112	49	base	base	NOUN
ejpam-6793	112	50	{	{	PUNCT
ejpam-6793	112	51	qn(x	qn(x	NOUN
ejpam-6793	112	52	)	)	PUNCT
ejpam-6793	112	53	}	}	PUNCT
ejpam-6793	112	54	is	be	AUX
ejpam-6793	112	55	effective	effective	ADJ
ejpam-6793	112	56	for	for	ADP
ejpam-6793	112	57	w∞	w∞	PROPN
ejpam-6793	112	58	iff	iff	PROPN
ejpam-6793	112	59	ω(q	ω(q	PROPN
ejpam-6793	112	60	,	,	PUNCT
ejpam-6793	112	61	r	r	NOUN
ejpam-6793	112	62	)	)	PUNCT
ejpam-6793	112	63	<	<	X
ejpam-6793	112	64	∞	∞	NUM
ejpam-6793	112	65	∀	∀	X
ejpam-6793	112	66	r	r	NOUN
ejpam-6793	112	67	<	<	X
ejpam-6793	112	68	∞	∞	PROPN
ejpam-6793	112	69	;	;	PUNCT
ejpam-6793	112	70	(	(	PUNCT
ejpam-6793	112	71	v	v	NOUN
ejpam-6793	112	72	)	)	PUNCT
ejpam-6793	112	73	a	a	DET
ejpam-6793	112	74	base	base	NOUN
ejpam-6793	112	75	{	{	PUNCT
ejpam-6793	112	76	qn(x	qn(x	NOUN
ejpam-6793	112	77	)	)	PUNCT
ejpam-6793	112	78	}	}	PUNCT
ejpam-6793	112	79	is	be	AUX
ejpam-6793	112	80	effective	effective	ADJ
ejpam-6793	112	81	for	for	ADP
ejpam-6793	112	82	w0	w0	PROPN
ejpam-6793	112	83	+	+	CCONJ
ejpam-6793	112	84	iff	iff	PROPN
ejpam-6793	112	85	ω(q	ω(q	PROPN
ejpam-6793	112	86	,	,	PUNCT
ejpam-6793	112	87	0	0	PUNCT
ejpam-6793	113	1	+	+	NUM
ejpam-6793	113	2	)	)	PUNCT
ejpam-6793	113	3	=	=	SYM
ejpam-6793	113	4	0	0	X
ejpam-6793	113	5	.	.	PUNCT
ejpam-6793	114	1	for	for	ADP
ejpam-6793	114	2	the	the	DET
ejpam-6793	114	3	base	base	NOUN
ejpam-6793	114	4	defined	define	VERB
ejpam-6793	114	5	in	in	ADP
ejpam-6793	114	6	(	(	PUNCT
ejpam-6793	114	7	3	3	NUM
ejpam-6793	114	8	)	)	PUNCT
ejpam-6793	114	9	,	,	PUNCT
ejpam-6793	114	10	we	we	PRON
ejpam-6793	114	11	have	have	VERB
ejpam-6793	114	12	the	the	DET
ejpam-6793	114	13	clifford	clifford	PROPN
ejpam-6793	114	14	version	version	PROPN
ejpam-6793	114	15	cauchy	cauchy	PROPN
ejpam-6793	114	16	inequality	inequality	NOUN
ejpam-6793	115	1	[	[	X
ejpam-6793	115	2	16	16	NUM
ejpam-6793	115	3	]	]	X
ejpam-6793	115	4	:	:	PUNCT
ejpam-6793	115	5	|qn	|qn	NUM
ejpam-6793	115	6	,	,	PUNCT
ejpam-6793	115	7	k|	k|	NOUN
ejpam-6793	115	8	≤	≤	NOUN
ejpam-6793	116	1	∥qn∥r	∥qn∥r	NUM
ejpam-6793	116	2	rk	rk	NOUN
ejpam-6793	116	3	.	.	PUNCT
ejpam-6793	117	1	(	(	PUNCT
ejpam-6793	117	2	10	10	NUM
ejpam-6793	117	3	)	)	PUNCT
ejpam-6793	117	4	definition	definition	NOUN
ejpam-6793	117	5	7	7	NUM
ejpam-6793	117	6	.	.	PUNCT
ejpam-6793	118	1	if	if	SCONJ
ejpam-6793	118	2	{	{	PUNCT
ejpam-6793	118	3	qn(x	qn(x	X
ejpam-6793	118	4	)	)	PUNCT
ejpam-6793	118	5	}	}	PUNCT
ejpam-6793	118	6	be	be	AUX
ejpam-6793	118	7	a	a	DET
ejpam-6793	118	8	base	base	NOUN
ejpam-6793	118	9	of	of	ADP
ejpam-6793	118	10	smps	smp	NOUN
ejpam-6793	118	11	,	,	PUNCT
ejpam-6793	118	12	then	then	ADV
ejpam-6793	118	13	the	the	DET
ejpam-6793	118	14	series	series	NOUN
ejpam-6793	118	15	in	in	ADP
ejpam-6793	118	16	(	(	PUNCT
ejpam-6793	118	17	2	2	NUM
ejpam-6793	118	18	)	)	PUNCT
ejpam-6793	118	19	is	be	AUX
ejpam-6793	118	20	finite	finite	ADJ
ejpam-6793	118	21	.	.	PUNCT
ejpam-6793	119	1	let	let	VERB
ejpam-6793	119	2	n(n	n(n	NUM
ejpam-6793	119	3	)	)	PUNCT
ejpam-6793	120	1	denote	denote	VERB
ejpam-6793	120	2	the	the	DET
ejpam-6793	120	3	number	number	NOUN
ejpam-6793	120	4	of	of	ADP
ejpam-6793	120	5	terms	term	NOUN
ejpam-6793	120	6	in	in	ADP
ejpam-6793	120	7	(	(	PUNCT
ejpam-6793	120	8	2	2	NUM
ejpam-6793	120	9	)	)	PUNCT
ejpam-6793	120	10	for	for	ADP
ejpam-6793	120	11	which	which	PRON
ejpam-6793	120	12	qn	qn	PROPN
ejpam-6793	120	13	,	,	PUNCT
ejpam-6793	120	14	k	k	PROPN
ejpam-6793	120	15	̸=	̸=	PROPN
ejpam-6793	120	16	0	0	NUM
ejpam-6793	121	1	and	and	CCONJ
ejpam-6793	121	2	lim	lim	PROPN
ejpam-6793	121	3	supn→∞{n(n	supn→∞{n(n	PROPN
ejpam-6793	121	4	)	)	PUNCT
ejpam-6793	121	5	}	}	PUNCT
ejpam-6793	122	1	1	1	NUM
ejpam-6793	122	2	n	n	NOUN
ejpam-6793	122	3	=	=	SYM
ejpam-6793	122	4	1	1	NUM
ejpam-6793	122	5	.	.	PUNCT
ejpam-6793	123	1	then	then	ADV
ejpam-6793	123	2	,	,	PUNCT
ejpam-6793	123	3	the	the	DET
ejpam-6793	123	4	base	base	NOUN
ejpam-6793	123	5	{	{	PUNCT
ejpam-6793	123	6	qn(x	qn(x	NOUN
ejpam-6793	123	7	)	)	PUNCT
ejpam-6793	123	8	}	}	PUNCT
ejpam-6793	123	9	is	be	AUX
ejpam-6793	123	10	said	say	VERB
ejpam-6793	123	11	to	to	PART
ejpam-6793	123	12	be	be	AUX
ejpam-6793	123	13	a	a	DET
ejpam-6793	123	14	cannon	cannon	NOUN
ejpam-6793	123	15	base	base	NOUN
ejpam-6793	123	16	of	of	ADP
ejpam-6793	123	17	smps	smp	NOUN
ejpam-6793	123	18	(	(	PUNCT
ejpam-6793	123	19	cbsmps	cbsmp	NOUN
ejpam-6793	123	20	)	)	PUNCT
ejpam-6793	123	21	.	.	PUNCT
ejpam-6793	124	1	definition	definition	NOUN
ejpam-6793	124	2	8	8	NUM
ejpam-6793	124	3	.	.	PUNCT
ejpam-6793	125	1	any	any	DET
ejpam-6793	125	2	base	base	NOUN
ejpam-6793	125	3	qn(x	qn(x	PUNCT
ejpam-6793	125	4	)	)	PUNCT
ejpam-6793	125	5	is	be	AUX
ejpam-6793	125	6	simple	simple	ADJ
ejpam-6793	125	7	it	it	PRON
ejpam-6793	125	8	has	have	VERB
ejpam-6793	125	9	degree	degree	NOUN
ejpam-6793	125	10	n.	n.	NOUN
ejpam-6793	125	11	in	in	ADP
ejpam-6793	125	12	a	a	DET
ejpam-6793	125	13	particular	particular	ADJ
ejpam-6793	125	14	case	case	NOUN
ejpam-6793	125	15	when	when	SCONJ
ejpam-6793	125	16	qn	qn	NOUN
ejpam-6793	125	17	,	,	PUNCT
ejpam-6793	125	18	n	n	NOUN
ejpam-6793	125	19	=	=	SYM
ejpam-6793	125	20	1	1	NUM
ejpam-6793	125	21	for	for	ADP
ejpam-6793	125	22	all	all	PRON
ejpam-6793	125	23	n	n	PRON
ejpam-6793	125	24	∈	∈	PROPN
ejpam-6793	125	25	n	n	CCONJ
ejpam-6793	125	26	,	,	PUNCT
ejpam-6793	125	27	then	then	ADV
ejpam-6793	125	28	qn(x	qn(x	PUNCT
ejpam-6793	125	29	)	)	PUNCT
ejpam-6793	126	1	i	i	PRON
ejpam-6793	126	2	a	a	DET
ejpam-6793	126	3	simple	simple	ADJ
ejpam-6793	126	4	monic	monic	ADJ
ejpam-6793	126	5	base	base	NOUN
ejpam-6793	126	6	now	now	ADV
ejpam-6793	126	7	,	,	PUNCT
ejpam-6793	126	8	we	we	PRON
ejpam-6793	126	9	characterize	characterize	VERB
ejpam-6793	126	10	the	the	DET
ejpam-6793	126	11	growth	growth	NOUN
ejpam-6793	126	12	of	of	ADP
ejpam-6793	126	13	a	a	DET
ejpam-6793	126	14	base	base	NOUN
ejpam-6793	126	15	as	as	SCONJ
ejpam-6793	126	16	introduced	introduce	VERB
ejpam-6793	126	17	in	in	ADP
ejpam-6793	126	18	[	[	X
ejpam-6793	126	19	7	7	NUM
ejpam-6793	126	20	,	,	PUNCT
ejpam-6793	126	21	8	8	NUM
ejpam-6793	126	22	]	]	PUNCT
ejpam-6793	126	23	where	where	SCONJ
ejpam-6793	126	24	the	the	DET
ejpam-6793	126	25	order	order	NOUN
ejpam-6793	126	26	in	in	ADP
ejpam-6793	126	27	clifford	clifford	PROPN
ejpam-6793	126	28	setting	setting	NOUN
ejpam-6793	126	29	was	be	AUX
ejpam-6793	126	30	given	give	VERB
ejpam-6793	126	31	by	by	ADP
ejpam-6793	126	32	:	:	PUNCT
ejpam-6793	126	33	ρ	ρ	PROPN
ejpam-6793	126	34	=	=	PROPN
ejpam-6793	126	35	lim	lim	PROPN
ejpam-6793	126	36	r→∞	r→∞	NUM
ejpam-6793	126	37	lim	lim	PROPN
ejpam-6793	126	38	sup	sup	VERB
ejpam-6793	126	39	n→∞	n→∞	NUM
ejpam-6793	126	40	log	log	NOUN
ejpam-6793	126	41	ω(qn	ω(qn	NOUN
ejpam-6793	126	42	,	,	PUNCT
ejpam-6793	126	43	r	r	NOUN
ejpam-6793	126	44	)	)	PUNCT
ejpam-6793	126	45	n	n	NOUN
ejpam-6793	126	46	log	log	VERB
ejpam-6793	126	47	n	n	INTJ
ejpam-6793	126	48	.	.	PUNCT
ejpam-6793	127	1	(	(	PUNCT
ejpam-6793	127	2	11	11	NUM
ejpam-6793	127	3	)	)	PUNCT
ejpam-6793	127	4	remark	remark	NOUN
ejpam-6793	127	5	2	2	NUM
ejpam-6793	127	6	.	.	PUNCT
ejpam-6793	128	1	a	a	DET
ejpam-6793	128	2	significant	significant	ADJ
ejpam-6793	128	3	relation	relation	NOUN
ejpam-6793	128	4	between	between	ADP
ejpam-6793	128	5	the	the	DET
ejpam-6793	128	6	order	order	NOUN
ejpam-6793	128	7	of	of	ADP
ejpam-6793	128	8	base	base	NOUN
ejpam-6793	128	9	and	and	CCONJ
ejpam-6793	128	10	the	the	DET
ejpam-6793	128	11	entire	entire	ADJ
ejpam-6793	128	12	functions	function	NOUN
ejpam-6793	128	13	be	be	AUX
ejpam-6793	128	14	represented	represent	VERB
ejpam-6793	128	15	in	in	ADP
ejpam-6793	128	16	the	the	DET
ejpam-6793	128	17	sense	sense	NOUN
ejpam-6793	128	18	that	that	SCONJ
ejpam-6793	128	19	if	if	SCONJ
ejpam-6793	128	20	the	the	DET
ejpam-6793	128	21	base	base	NOUN
ejpam-6793	128	22	{	{	PUNCT
ejpam-6793	128	23	qn(x	qn(x	NOUN
ejpam-6793	128	24	)	)	PUNCT
ejpam-6793	128	25	}	}	PUNCT
ejpam-6793	128	26	is	be	AUX
ejpam-6793	128	27	of	of	ADP
ejpam-6793	128	28	order	order	NOUN
ejpam-6793	128	29	ρ	ρ	NOUN
ejpam-6793	128	30	,	,	PUNCT
ejpam-6793	128	31	then	then	ADV
ejpam-6793	128	32	it	it	PRON
ejpam-6793	128	33	will	will	AUX
ejpam-6793	128	34	represent	represent	VERB
ejpam-6793	128	35	every	every	DET
ejpam-6793	128	36	entire	entire	ADJ
ejpam-6793	128	37	smf	smf	NOUN
ejpam-6793	128	38	which	which	PRON
ejpam-6793	128	39	has	have	VERB
ejpam-6793	128	40	order	order	NOUN
ejpam-6793	128	41	ρ′	ρ′	X
ejpam-6793	128	42	<	<	X
ejpam-6793	128	43	1	1	NUM
ejpam-6793	128	44	ρ	ρ	NOUN
ejpam-6793	128	45	in	in	ADP
ejpam-6793	128	46	any	any	DET
ejpam-6793	128	47	finite	finite	ADJ
ejpam-6793	128	48	ball	ball	NOUN
ejpam-6793	128	49	.	.	PUNCT
ejpam-6793	129	1	3	3	NUM
ejpam-6793	129	2	.	.	NOUN
ejpam-6793	129	3	effectiveness	effectiveness	NOUN
ejpam-6793	129	4	and	and	CCONJ
ejpam-6793	129	5	order	order	NOUN
ejpam-6793	129	6	of	of	ADP
ejpam-6793	129	7	the	the	DET
ejpam-6793	129	8	exponential	exponential	ADJ
ejpam-6793	129	9	simple	simple	ADJ
ejpam-6793	129	10	base	base	NOUN
ejpam-6793	129	11	of	of	ADP
ejpam-6793	129	12	special	special	ADJ
ejpam-6793	129	13	monogenic	monogenic	ADJ
ejpam-6793	129	14	polynomials	polynomial	NOUN
ejpam-6793	129	15	in	in	ADP
ejpam-6793	129	16	this	this	DET
ejpam-6793	129	17	section	section	NOUN
ejpam-6793	129	18	,	,	PUNCT
ejpam-6793	129	19	we	we	PRON
ejpam-6793	129	20	investigate	investigate	VERB
ejpam-6793	129	21	the	the	DET
ejpam-6793	129	22	convergence	convergence	NOUN
ejpam-6793	129	23	properties	property	NOUN
ejpam-6793	129	24	of	of	ADP
ejpam-6793	129	25	the	the	DET
ejpam-6793	129	26	esbsmps	esbsmp	NOUN
ejpam-6793	129	27	for	for	ADP
ejpam-6793	129	28	the	the	DET
ejpam-6793	129	29	f	f	NOUN
ejpam-6793	129	30	-	-	PUNCT
ejpam-6793	129	31	module	module	NOUN
ejpam-6793	129	32	wb̄(r	wb̄(r	NOUN
ejpam-6793	129	33	)	)	PUNCT
ejpam-6793	129	34	as	as	SCONJ
ejpam-6793	129	35	follows	follow	VERB
ejpam-6793	129	36	.	.	PUNCT
ejpam-6793	130	1	3.1	3.1	NUM
ejpam-6793	130	2	.	.	PUNCT
ejpam-6793	130	3	effectiveness	effectiveness	NOUN
ejpam-6793	130	4	of	of	ADP
ejpam-6793	130	5	the	the	DET
ejpam-6793	130	6	exponential	exponential	ADJ
ejpam-6793	130	7	simple	simple	ADJ
ejpam-6793	130	8	base	base	NOUN
ejpam-6793	130	9	of	of	ADP
ejpam-6793	130	10	special	special	ADJ
ejpam-6793	130	11	monogenic	monogenic	ADJ
ejpam-6793	130	12	polynomials	polynomial	NOUN
ejpam-6793	130	13	for	for	ADP
ejpam-6793	130	14	the	the	DET
ejpam-6793	130	15	f	f	NOUN
ejpam-6793	130	16	-	-	PUNCT
ejpam-6793	130	17	module	module	NOUN
ejpam-6793	130	18	w	w	PROPN
ejpam-6793	130	19	b̄(r	b̄(r	NOUN
ejpam-6793	130	20	)	)	PUNCT
ejpam-6793	130	21	let	let	VERB
ejpam-6793	130	22	{	{	PUNCT
ejpam-6793	130	23	qn(x	qn(x	X
ejpam-6793	130	24	)	)	PUNCT
ejpam-6793	130	25	}	}	PUNCT
ejpam-6793	130	26	be	be	AUX
ejpam-6793	130	27	a	a	DET
ejpam-6793	130	28	simple	simple	ADJ
ejpam-6793	130	29	base	base	NOUN
ejpam-6793	130	30	of	of	ADP
ejpam-6793	130	31	smps	smp	NOUN
ejpam-6793	130	32	(	(	PUNCT
ejpam-6793	130	33	sbsmps	sbsmp	NOUN
ejpam-6793	130	34	)	)	PUNCT
ejpam-6793	130	35	of	of	ADP
ejpam-6793	130	36	a	a	DET
ejpam-6793	130	37	clifford	clifford	PROPN
ejpam-6793	130	38	variable	variable	NOUN
ejpam-6793	130	39	x	x	X
ejpam-6793	130	40	∈	∈	PROPN
ejpam-6793	130	41	rm+1	rm+1	PRON
ejpam-6793	130	42	,	,	PUNCT
ejpam-6793	130	43	whose	whose	DET
ejpam-6793	130	44	clifford	clifford	PROPN
ejpam-6793	130	45	matrix	matrix	NOUN
ejpam-6793	130	46	of	of	ADP
ejpam-6793	130	47	coefficients	coefficient	NOUN
ejpam-6793	130	48	is	be	AUX
ejpam-6793	130	49	q.	q.	PROPN
ejpam-6793	130	50	then	then	ADV
ejpam-6793	130	51	the	the	DET
ejpam-6793	130	52	set	set	NOUN
ejpam-6793	130	53	{	{	PUNCT
ejpam-6793	130	54	qen(x	qen(x	X
ejpam-6793	130	55	)	)	PUNCT
ejpam-6793	130	56	}	}	PUNCT
ejpam-6793	130	57	,	,	PUNCT
ejpam-6793	130	58	whose	whose	DET
ejpam-6793	130	59	clifford	clifford	PROPN
ejpam-6793	130	60	matrices	matrix	NOUN
ejpam-6793	130	61	of	of	ADP
ejpam-6793	130	62	coefficients	coefficient	NOUN
ejpam-6793	130	63	and	and	CCONJ
ejpam-6793	130	64	operators	operator	NOUN
ejpam-6793	130	65	are	be	AUX
ejpam-6793	130	66	e	e	NOUN
ejpam-6793	130	67	=	=	PUNCT
ejpam-6793	130	68	eq	eq	NOUN
ejpam-6793	130	69	and	and	CCONJ
ejpam-6793	130	70	ẽ	ẽ	PROPN
ejpam-6793	130	71	=	=	SYM
ejpam-6793	130	72	e−q	e−q	NOUN
ejpam-6793	130	73	is	be	AUX
ejpam-6793	130	74	a	a	DET
ejpam-6793	130	75	base	base	NOUN
ejpam-6793	130	76	.	.	PUNCT
ejpam-6793	131	1	this	this	DET
ejpam-6793	131	2	base	base	NOUN
ejpam-6793	131	3	was	be	AUX
ejpam-6793	131	4	defined	define	VERB
ejpam-6793	131	5	in	in	ADP
ejpam-6793	131	6	[	[	X
ejpam-6793	131	7	21	21	NUM
ejpam-6793	131	8	]	]	PUNCT
ejpam-6793	131	9	as	as	ADP
ejpam-6793	131	10	the	the	DET
ejpam-6793	131	11	esbsmp	esbsmp	NOUN
ejpam-6793	131	12	.	.	PUNCT
ejpam-6793	132	1	suppose	suppose	VERB
ejpam-6793	132	2	that	that	SCONJ
ejpam-6793	132	3	the	the	DET
ejpam-6793	132	4	elements	element	NOUN
ejpam-6793	132	5	{	{	PUNCT
ejpam-6793	132	6	qn	qn	NOUN
ejpam-6793	132	7	,	,	PUNCT
ejpam-6793	132	8	k	k	NOUN
ejpam-6793	132	9	}	}	PUNCT
ejpam-6793	132	10	of	of	ADP
ejpam-6793	132	11	the	the	DET
ejpam-6793	132	12	clifford	clifford	PROPN
ejpam-6793	132	13	matrix	matrix	NOUN
ejpam-6793	132	14	of	of	ADP
ejpam-6793	132	15	coefficients	coefficient	NOUN
ejpam-6793	132	16	of	of	ADP
ejpam-6793	132	17	the	the	DET
ejpam-6793	132	18	sbsmps	sbsmp	NOUN
ejpam-6793	132	19	{	{	PUNCT
ejpam-6793	132	20	qn(x	qn(x	X
ejpam-6793	132	21	)	)	PUNCT
ejpam-6793	132	22	}	}	PUNCT
ejpam-6793	132	23	satisfy	satisfy	VERB
ejpam-6793	132	24	{	{	PUNCT
ejpam-6793	132	25	|qn	|qn	NUM
ejpam-6793	132	26	,	,	PUNCT
ejpam-6793	132	27	k|	k|	NOUN
ejpam-6793	132	28	≤m	≤m	NOUN
ejpam-6793	132	29	bn−k	bn−k	PROPN
ejpam-6793	132	30	n+1	n+1	PROPN
ejpam-6793	132	31	αk	αk	NOUN
ejpam-6793	132	32	,	,	PUNCT
ejpam-6793	132	33	0	0	NUM
ejpam-6793	132	34	≤	≤	NUM
ejpam-6793	133	1	k	k	X
ejpam-6793	133	2	<	<	X
ejpam-6793	133	3	n	n	CCONJ
ejpam-6793	133	4	,	,	PUNCT
ejpam-6793	133	5	m	m	VERB
ejpam-6793	133	6	≥	≥	NOUN
ejpam-6793	133	7	1	1	NUM
ejpam-6793	133	8	qn	qn	NOUN
ejpam-6793	133	9	,	,	PUNCT
ejpam-6793	133	10	n	n	NOUN
ejpam-6793	133	11	=	=	SYM
ejpam-6793	133	12	αn	αn	NOUN
ejpam-6793	133	13	,	,	PUNCT
ejpam-6793	133	14	(	(	PUNCT
ejpam-6793	133	15	12	12	NUM
ejpam-6793	133	16	)	)	PUNCT
ejpam-6793	133	17	where	where	SCONJ
ejpam-6793	133	18	{	{	PUNCT
ejpam-6793	133	19	αn	αn	NOUN
ejpam-6793	133	20	}	}	PUNCT
ejpam-6793	133	21	is	be	AUX
ejpam-6793	133	22	a	a	DET
ejpam-6793	133	23	bounded	bounded	ADJ
ejpam-6793	133	24	sequence	sequence	NOUN
ejpam-6793	133	25	of	of	ADP
ejpam-6793	133	26	positive	positive	ADJ
ejpam-6793	133	27	numbers	number	NOUN
ejpam-6793	133	28	,	,	PUNCT
ejpam-6793	133	29	k	k	PROPN
ejpam-6793	133	30	and	and	CCONJ
ejpam-6793	133	31	b	b	PROPN
ejpam-6793	133	32	are	be	AUX
ejpam-6793	133	33	finite	finite	ADJ
ejpam-6793	133	34	positive	positive	ADJ
ejpam-6793	133	35	numbers	number	NOUN
ejpam-6793	133	36	.	.	PUNCT
ejpam-6793	134	1	before	before	SCONJ
ejpam-6793	134	2	we	we	PRON
ejpam-6793	134	3	proceed	proceed	VERB
ejpam-6793	134	4	with	with	ADP
ejpam-6793	134	5	our	our	PRON
ejpam-6793	134	6	results	result	NOUN
ejpam-6793	134	7	,	,	PUNCT
ejpam-6793	134	8	we	we	PRON
ejpam-6793	134	9	state	state	VERB
ejpam-6793	134	10	and	and	CCONJ
ejpam-6793	134	11	prove	prove	VERB
ejpam-6793	134	12	the	the	DET
ejpam-6793	134	13	following	follow	VERB
ejpam-6793	134	14	important	important	ADJ
ejpam-6793	134	15	lemma	lemma	PROPN
ejpam-6793	134	16	.	.	PUNCT
ejpam-6793	134	17	m.	m.	PROPN
ejpam-6793	134	18	zayed	zayed	PROPN
ejpam-6793	134	19	/	/	SYM
ejpam-6793	134	20	eur	eur	PROPN
ejpam-6793	134	21	.	.	PUNCT
ejpam-6793	135	1	j.	j.	PROPN
ejpam-6793	135	2	pure	pure	PROPN
ejpam-6793	135	3	appl	appl	PROPN
ejpam-6793	135	4	.	.	PROPN
ejpam-6793	135	5	math	math	PROPN
ejpam-6793	135	6	,	,	PUNCT
ejpam-6793	135	7	18	18	NUM
ejpam-6793	135	8	(	(	PUNCT
ejpam-6793	135	9	4	4	NUM
ejpam-6793	135	10	)	)	PUNCT
ejpam-6793	135	11	(	(	PUNCT
ejpam-6793	135	12	2025	2025	NUM
ejpam-6793	135	13	)	)	PUNCT
ejpam-6793	135	14	,	,	PUNCT
ejpam-6793	135	15	6793	6793	NUM
ejpam-6793	135	16	7	7	NUM
ejpam-6793	135	17	of	of	ADP
ejpam-6793	135	18	19	19	NUM
ejpam-6793	135	19	lemma	lemma	PROPN
ejpam-6793	135	20	1	1	NUM
ejpam-6793	135	21	.	.	PUNCT
ejpam-6793	136	1	if	if	SCONJ
ejpam-6793	136	2	q(j	q(j	PROPN
ejpam-6793	136	3	)	)	PUNCT
ejpam-6793	136	4	n	n	CCONJ
ejpam-6793	136	5	,	,	PUNCT
ejpam-6793	136	6	k	k	PROPN
ejpam-6793	136	7	∈	∈	PROPN
ejpam-6793	136	8	am	be	AUX
ejpam-6793	136	9	are	be	AUX
ejpam-6793	136	10	the	the	DET
ejpam-6793	136	11	elements	element	NOUN
ejpam-6793	136	12	of	of	ADP
ejpam-6793	136	13	the	the	DET
ejpam-6793	136	14	power	power	NOUN
ejpam-6793	136	15	clifford	clifford	PROPN
ejpam-6793	136	16	matrix	matrix	PROPN
ejpam-6793	136	17	q(j	q(j	PROPN
ejpam-6793	136	18	)	)	PUNCT
ejpam-6793	136	19	,	,	PUNCT
ejpam-6793	137	1	j	j	PROPN
ejpam-6793	137	2	≥	≥	NUM
ejpam-6793	137	3	1	1	NUM
ejpam-6793	137	4	and	and	CCONJ
ejpam-6793	137	5	satisfying	satisfying	ADJ
ejpam-6793	137	6	(	(	PUNCT
ejpam-6793	137	7	12	12	NUM
ejpam-6793	137	8	)	)	PUNCT
ejpam-6793	137	9	,	,	PUNCT
ejpam-6793	137	10	then	then	ADV
ejpam-6793	137	11	∣∣∣q(j	∣∣∣q(j	NOUN
ejpam-6793	137	12	)	)	PUNCT
ejpam-6793	137	13	n	n	CCONJ
ejpam-6793	137	14	,	,	PUNCT
ejpam-6793	137	15	x	x	X
ejpam-6793	137	16	∣∣∣	∣∣∣	ADJ
ejpam-6793	137	17	≤	≤	NUM
ejpam-6793	137	18	2−	2−	NUM
ejpam-6793	137	19	m	m	NOUN
ejpam-6793	137	20	2	2	NUM
ejpam-6793	137	21	(	(	PUNCT
ejpam-6793	137	22	2	2	NUM
ejpam-6793	137	23	m	m	NUM
ejpam-6793	137	24	2	2	NUM
ejpam-6793	137	25	mc	mc	NOUN
ejpam-6793	137	26	)	)	PUNCT
ejpam-6793	137	27	j	j	PROPN
ejpam-6793	137	28	bn−k	bn−k	PROPN
ejpam-6793	137	29	,	,	PUNCT
ejpam-6793	137	30	0	0	NUM
ejpam-6793	137	31	≤	≤	PUNCT
ejpam-6793	138	1	k	k	X
ejpam-6793	138	2	<	<	X
ejpam-6793	138	3	n	n	CCONJ
ejpam-6793	138	4	,	,	PUNCT
ejpam-6793	138	5	(	(	PUNCT
ejpam-6793	138	6	13	13	NUM
ejpam-6793	138	7	)	)	PUNCT
ejpam-6793	138	8	where	where	SCONJ
ejpam-6793	138	9	c	c	NOUN
ejpam-6793	138	10	is	be	AUX
ejpam-6793	138	11	a	a	DET
ejpam-6793	138	12	real	real	ADJ
ejpam-6793	138	13	number	number	NOUN
ejpam-6793	138	14	such	such	ADJ
ejpam-6793	138	15	that	that	DET
ejpam-6793	138	16	αk	αk	NOUN
ejpam-6793	138	17	≤	≤	NUM
ejpam-6793	138	18	c	c	NOUN
ejpam-6793	138	19	,	,	PUNCT
ejpam-6793	138	20	0	0	NUM
ejpam-6793	138	21	≤	≤	NOUN
ejpam-6793	139	1	k	k	X
ejpam-6793	139	2	<	<	X
ejpam-6793	139	3	n.	n.	PROPN
ejpam-6793	139	4	proof	proof	NOUN
ejpam-6793	139	5	.	.	PUNCT
ejpam-6793	140	1	the	the	DET
ejpam-6793	140	2	elements	elements	PROPN
ejpam-6793	140	3	q(j	q(j	PROPN
ejpam-6793	140	4	)	)	PUNCT
ejpam-6793	140	5	n	n	CCONJ
ejpam-6793	140	6	,	,	PUNCT
ejpam-6793	140	7	k	k	PROPN
ejpam-6793	140	8	of	of	ADP
ejpam-6793	140	9	the	the	DET
ejpam-6793	140	10	power	power	NOUN
ejpam-6793	140	11	clifford	clifford	PROPN
ejpam-6793	140	12	matrix	matrix	PROPN
ejpam-6793	140	13	qj	qj	PROPN
ejpam-6793	140	14	,	,	PUNCT
ejpam-6793	140	15	j	j	PROPN
ejpam-6793	140	16	≥	≥	NUM
ejpam-6793	140	17	1	1	NUM
ejpam-6793	140	18	are	be	AUX
ejpam-6793	140	19	given	give	VERB
ejpam-6793	140	20	as	as	ADP
ejpam-6793	140	21	q(j	q(j	PROPN
ejpam-6793	140	22	)	)	PUNCT
ejpam-6793	140	23	n	n	CCONJ
ejpam-6793	140	24	,	,	PUNCT
ejpam-6793	140	25	k	k	PROPN
ejpam-6793	140	26	=	=	PROPN
ejpam-6793	140	27	n∑	n∑	PROPN
ejpam-6793	140	28	t	t	PROPN
ejpam-6793	140	29	=	=	SYM
ejpam-6793	140	30	k	k	PROPN
ejpam-6793	140	31	q(j−1	q(j−1	PROPN
ejpam-6793	140	32	)	)	PUNCT
ejpam-6793	140	33	t	t	PROPN
ejpam-6793	140	34	,	,	PUNCT
ejpam-6793	140	35	k	k	PROPN
ejpam-6793	140	36	qn	qn	PROPN
ejpam-6793	140	37	,	,	PUNCT
ejpam-6793	140	38	t	t	PROPN
ejpam-6793	140	39	(	(	PUNCT
ejpam-6793	140	40	14	14	NUM
ejpam-6793	140	41	)	)	PUNCT
ejpam-6793	140	42	assume	assume	VERB
ejpam-6793	140	43	that	that	SCONJ
ejpam-6793	140	44	j	j	PROPN
ejpam-6793	140	45	=	=	NOUN
ejpam-6793	140	46	2	2	NUM
ejpam-6793	140	47	in	in	ADP
ejpam-6793	140	48	(	(	PUNCT
ejpam-6793	140	49	14	14	NUM
ejpam-6793	140	50	)	)	PUNCT
ejpam-6793	140	51	and	and	CCONJ
ejpam-6793	140	52	by	by	ADP
ejpam-6793	140	53	using	use	VERB
ejpam-6793	140	54	(	(	PUNCT
ejpam-6793	140	55	12	12	NUM
ejpam-6793	140	56	)	)	PUNCT
ejpam-6793	140	57	,	,	PUNCT
ejpam-6793	140	58	we	we	PRON
ejpam-6793	140	59	obtain	obtain	VERB
ejpam-6793	140	60	that	that	DET
ejpam-6793	140	61	∣∣∣q(2	∣∣∣q(2	NOUN
ejpam-6793	140	62	)	)	PUNCT
ejpam-6793	140	63	n	n	CCONJ
ejpam-6793	140	64	,	,	PUNCT
ejpam-6793	140	65	k	k	PROPN
ejpam-6793	140	66	∣∣∣	∣∣∣	NOUN
ejpam-6793	140	67	=	=	PUNCT
ejpam-6793	140	68	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-6793	140	69	n∑	n∑	PROPN
ejpam-6793	140	70	t	t	PROPN
ejpam-6793	140	71	=	=	SYM
ejpam-6793	140	72	k	k	PROPN
ejpam-6793	140	73	qt	qt	PROPN
ejpam-6793	140	74	,	,	PUNCT
ejpam-6793	140	75	kqn	kqn	PROPN
ejpam-6793	140	76	,	,	PUNCT
ejpam-6793	140	77	t	t	X
ejpam-6793	140	78	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-6793	140	79	≤	≤	ADV
ejpam-6793	140	80	2	2	NUM
ejpam-6793	140	81	m	m	NUM
ejpam-6793	140	82	2	2	NUM
ejpam-6793	140	83	n∑	n∑	NOUN
ejpam-6793	140	84	t	t	PROPN
ejpam-6793	141	1	=	=	PROPN
ejpam-6793	141	2	k	k	PROPN
ejpam-6793	141	3	|qt	|qt	PROPN
ejpam-6793	141	4	,	,	PUNCT
ejpam-6793	141	5	k|	k|	NOUN
ejpam-6793	141	6	|qn	|qn	NUM
ejpam-6793	141	7	,	,	PUNCT
ejpam-6793	141	8	t|	t|	NOUN
ejpam-6793	141	9	≤	≤	ADV
ejpam-6793	142	1	2	2	NUM
ejpam-6793	142	2	m	m	NUM
ejpam-6793	142	3	2	2	NUM
ejpam-6793	142	4	n∑	n∑	NOUN
ejpam-6793	142	5	t	t	PROPN
ejpam-6793	142	6	=	=	SYM
ejpam-6793	142	7	k	k	PROPN
ejpam-6793	142	8	m	m	VERB
ejpam-6793	142	9	bt−k	bt−k	NOUN
ejpam-6793	142	10	t+	t+	NOUN
ejpam-6793	142	11	1	1	NUM
ejpam-6793	142	12	αk	αk	NOUN
ejpam-6793	142	13	·	·	NOUN
ejpam-6793	142	14	m	m	NOUN
ejpam-6793	142	15	bn−t	bn−t	ADJ
ejpam-6793	142	16	n+	n+	ADP
ejpam-6793	142	17	1	1	NUM
ejpam-6793	142	18	αt	αt	NOUN
ejpam-6793	142	19	=	=	SYM
ejpam-6793	142	20	2	2	NUM
ejpam-6793	142	21	m	m	NOUN
ejpam-6793	142	22	2	2	NUM
ejpam-6793	142	23	(	(	PUNCT
ejpam-6793	142	24	mc)2	mc)2	NOUN
ejpam-6793	142	25	·	·	PUNCT
ejpam-6793	142	26	bn−k	bn−k	NOUN
ejpam-6793	142	27	n+	n+	ADP
ejpam-6793	142	28	1	1	NUM
ejpam-6793	142	29	n∑	n∑	NOUN
ejpam-6793	142	30	t	t	PROPN
ejpam-6793	142	31	=	=	SYM
ejpam-6793	142	32	k	k	PROPN
ejpam-6793	142	33	1	1	NUM
ejpam-6793	142	34	t+	t+	NUM
ejpam-6793	142	35	1	1	NUM
ejpam-6793	142	36	≤	≤	NUM
ejpam-6793	142	37	2	2	NUM
ejpam-6793	142	38	m	m	NOUN
ejpam-6793	142	39	2	2	NUM
ejpam-6793	142	40	(	(	PUNCT
ejpam-6793	142	41	mc)2bn−k	mc)2bn−k	PUNCT
ejpam-6793	142	42	=	=	PUNCT
ejpam-6793	143	1	2−	2−	NUM
ejpam-6793	143	2	m	m	NOUN
ejpam-6793	143	3	2	2	NUM
ejpam-6793	143	4	(	(	PUNCT
ejpam-6793	143	5	2	2	NUM
ejpam-6793	143	6	m	m	NUM
ejpam-6793	143	7	2	2	NUM
ejpam-6793	143	8	mc	mc	NOUN
ejpam-6793	143	9	)	)	PUNCT
ejpam-6793	143	10	2	2	NUM
ejpam-6793	143	11	bn−k	bn−k	NOUN
ejpam-6793	143	12	,	,	PUNCT
ejpam-6793	143	13	where	where	SCONJ
ejpam-6793	143	14	0	0	NUM
ejpam-6793	143	15	≤	≤	NOUN
ejpam-6793	144	1	k	k	X
ejpam-6793	144	2	<	<	X
ejpam-6793	144	3	n.	n.	X
ejpam-6793	144	4	we	we	PRON
ejpam-6793	144	5	assume	assume	VERB
ejpam-6793	144	6	that∣∣∣q(j	that∣∣∣q(j	PROPN
ejpam-6793	144	7	)	)	PUNCT
ejpam-6793	144	8	n	n	CCONJ
ejpam-6793	144	9	,	,	PUNCT
ejpam-6793	144	10	k	k	PROPN
ejpam-6793	144	11	∣∣∣	∣∣∣	PROPN
ejpam-6793	144	12	⩽	⩽	PROPN
ejpam-6793	144	13	2−	2−	NUM
ejpam-6793	144	14	m	m	NOUN
ejpam-6793	144	15	2	2	NUM
ejpam-6793	144	16	(	(	PUNCT
ejpam-6793	144	17	2	2	NUM
ejpam-6793	144	18	m	m	NUM
ejpam-6793	144	19	2	2	NUM
ejpam-6793	144	20	mαk	mαk	NOUN
ejpam-6793	144	21	)	)	PUNCT
ejpam-6793	144	22	j	j	PROPN
ejpam-6793	144	23	bn−k	bn−k	PROPN
ejpam-6793	144	24	(	(	PUNCT
ejpam-6793	144	25	15	15	NUM
ejpam-6793	144	26	)	)	PUNCT
ejpam-6793	144	27	applying	apply	VERB
ejpam-6793	144	28	(	(	PUNCT
ejpam-6793	144	29	12	12	NUM
ejpam-6793	144	30	)	)	PUNCT
ejpam-6793	144	31	,	,	PUNCT
ejpam-6793	144	32	(	(	PUNCT
ejpam-6793	144	33	14	14	NUM
ejpam-6793	144	34	)	)	PUNCT
ejpam-6793	144	35	and	and	CCONJ
ejpam-6793	144	36	(	(	PUNCT
ejpam-6793	144	37	15	15	NUM
ejpam-6793	144	38	)	)	PUNCT
ejpam-6793	144	39	implies	imply	VERB
ejpam-6793	144	40	that	that	SCONJ
ejpam-6793	144	41	∣∣∣q(j+1	∣∣∣q(j+1	X
ejpam-6793	144	42	)	)	PUNCT
ejpam-6793	144	43	n	n	CCONJ
ejpam-6793	144	44	,	,	PUNCT
ejpam-6793	145	1	k	k	PROPN
ejpam-6793	145	2	∣∣∣	∣∣∣	NOUN
ejpam-6793	145	3	≤	≤	NUM
ejpam-6793	145	4	2	2	NUM
ejpam-6793	145	5	m	m	NUM
ejpam-6793	145	6	2	2	NUM
ejpam-6793	145	7	n∑	n∑	NOUN
ejpam-6793	145	8	t	t	PROPN
ejpam-6793	145	9	=	=	SYM
ejpam-6793	145	10	k	k	PROPN
ejpam-6793	145	11	∣∣∣q(j	∣∣∣q(j	PROPN
ejpam-6793	145	12	)	)	PUNCT
ejpam-6793	145	13	t	t	PROPN
ejpam-6793	145	14	,	,	PUNCT
ejpam-6793	145	15	k	k	PROPN
ejpam-6793	145	16	∣∣∣	∣∣∣	PROPN
ejpam-6793	145	17	|qn	|qn	NUM
ejpam-6793	145	18	,	,	PUNCT
ejpam-6793	145	19	t|	t|	PROPN
ejpam-6793	145	20	⩽	⩽	NOUN
ejpam-6793	145	21	2	2	NUM
ejpam-6793	145	22	m	m	NUM
ejpam-6793	145	23	2	2	NUM
ejpam-6793	145	24	n∑	n∑	NOUN
ejpam-6793	145	25	t	t	PROPN
ejpam-6793	145	26	=	=	PROPN
ejpam-6793	145	27	k	k	PROPN
ejpam-6793	145	28	2−	2−	NUM
ejpam-6793	145	29	m	m	NOUN
ejpam-6793	145	30	2	2	NUM
ejpam-6793	145	31	(	(	PUNCT
ejpam-6793	145	32	2	2	NUM
ejpam-6793	145	33	m	m	NUM
ejpam-6793	145	34	2	2	NUM
ejpam-6793	145	35	mc	mc	NOUN
ejpam-6793	145	36	)	)	PUNCT
ejpam-6793	145	37	j	j	PROPN
ejpam-6793	145	38	bt−k	bt−k	PROPN
ejpam-6793	145	39	·	·	PUNCT
ejpam-6793	145	40	mbn−t	mbn−t	NOUN
ejpam-6793	145	41	n+	n+	ADP
ejpam-6793	145	42	1	1	NUM
ejpam-6793	145	43	αt	αt	NOUN
ejpam-6793	145	44	⩽	⩽	NOUN
ejpam-6793	145	45	2−	2−	NUM
ejpam-6793	145	46	m	m	NOUN
ejpam-6793	145	47	2	2	NUM
ejpam-6793	145	48	(	(	PUNCT
ejpam-6793	145	49	2	2	NUM
ejpam-6793	145	50	m	m	NUM
ejpam-6793	145	51	2	2	NUM
ejpam-6793	145	52	mc	mc	NOUN
ejpam-6793	145	53	)	)	PUNCT
ejpam-6793	145	54	j+1	j+1	NUM
ejpam-6793	145	55	bn−k	bn−k	NOUN
ejpam-6793	145	56	.	.	PUNCT
ejpam-6793	146	1	which	which	PRON
ejpam-6793	146	2	gives	give	VERB
ejpam-6793	146	3	the	the	DET
ejpam-6793	146	4	desire	desire	NOUN
ejpam-6793	146	5	result	result	NOUN
ejpam-6793	146	6	by	by	ADP
ejpam-6793	146	7	mathematical	mathematical	ADJ
ejpam-6793	146	8	induction	induction	NOUN
ejpam-6793	146	9	.	.	PUNCT
ejpam-6793	147	1	m.	m.	NOUN
ejpam-6793	147	2	zayed	zayed	PROPN
ejpam-6793	147	3	/	/	SYM
ejpam-6793	147	4	eur	eur	PROPN
ejpam-6793	147	5	.	.	PUNCT
ejpam-6793	148	1	j.	j.	PROPN
ejpam-6793	148	2	pure	pure	PROPN
ejpam-6793	148	3	appl	appl	PROPN
ejpam-6793	148	4	.	.	PROPN
ejpam-6793	148	5	math	math	PROPN
ejpam-6793	148	6	,	,	PUNCT
ejpam-6793	148	7	18	18	NUM
ejpam-6793	148	8	(	(	PUNCT
ejpam-6793	148	9	4	4	NUM
ejpam-6793	148	10	)	)	PUNCT
ejpam-6793	148	11	(	(	PUNCT
ejpam-6793	148	12	2025	2025	NUM
ejpam-6793	148	13	)	)	PUNCT
ejpam-6793	148	14	,	,	PUNCT
ejpam-6793	148	15	6793	6793	NUM
ejpam-6793	148	16	8	8	NUM
ejpam-6793	148	17	of	of	ADP
ejpam-6793	148	18	19	19	NUM
ejpam-6793	148	19	theorem	theorem	NOUN
ejpam-6793	148	20	2	2	NUM
ejpam-6793	148	21	.	.	PUNCT
ejpam-6793	148	22	suppose	suppose	VERB
ejpam-6793	148	23	that	that	SCONJ
ejpam-6793	148	24	{	{	PUNCT
ejpam-6793	148	25	qn(x	qn(x	NOUN
ejpam-6793	148	26	)	)	PUNCT
ejpam-6793	148	27	}	}	PUNCT
ejpam-6793	148	28	is	be	AUX
ejpam-6793	148	29	a	a	DET
ejpam-6793	148	30	sbsmps	sbsmp	NOUN
ejpam-6793	148	31	satisfying	satisfy	VERB
ejpam-6793	148	32	(	(	PUNCT
ejpam-6793	148	33	12	12	NUM
ejpam-6793	148	34	)	)	PUNCT
ejpam-6793	148	35	.	.	PUNCT
ejpam-6793	149	1	then	then	ADV
ejpam-6793	149	2	the	the	DET
ejpam-6793	149	3	esbsmps	esbsmp	NOUN
ejpam-6793	149	4	{	{	PUNCT
ejpam-6793	149	5	qen(x	qen(x	PROPN
ejpam-6793	149	6	)	)	PUNCT
ejpam-6793	149	7	}	}	PUNCT
ejpam-6793	149	8	is	be	AUX
ejpam-6793	149	9	effective	effective	ADJ
ejpam-6793	149	10	for	for	ADP
ejpam-6793	149	11	wb̄(r	wb̄(r	NOUN
ejpam-6793	149	12	)	)	PUNCT
ejpam-6793	149	13	,	,	PUNCT
ejpam-6793	149	14	where	where	SCONJ
ejpam-6793	149	15	r	r	NOUN
ejpam-6793	149	16	≥	≥	NOUN
ejpam-6793	149	17	b	b	NOUN
ejpam-6793	149	18	,	,	PUNCT
ejpam-6793	149	19	however	however	ADV
ejpam-6793	149	20	,	,	PUNCT
ejpam-6793	149	21	it	it	PRON
ejpam-6793	149	22	may	may	AUX
ejpam-6793	149	23	not	not	PART
ejpam-6793	149	24	be	be	AUX
ejpam-6793	149	25	effective	effective	ADJ
ejpam-6793	149	26	for	for	ADP
ejpam-6793	149	27	wb̄(r	wb̄(r	NOUN
ejpam-6793	149	28	)	)	PUNCT
ejpam-6793	149	29	when	when	SCONJ
ejpam-6793	149	30	r	r	NOUN
ejpam-6793	149	31	<	<	X
ejpam-6793	149	32	b.	b.	PROPN
ejpam-6793	149	33	proof	proof	NOUN
ejpam-6793	149	34	.	.	PUNCT
ejpam-6793	150	1	since	since	SCONJ
ejpam-6793	150	2	qe	qe	PROPN
ejpam-6793	150	3	=	=	PUNCT
ejpam-6793	150	4	eq	eq	PROPN
ejpam-6793	150	5	is	be	AUX
ejpam-6793	150	6	the	the	DET
ejpam-6793	150	7	clifford	clifford	PROPN
ejpam-6793	150	8	matrix	matrix	NOUN
ejpam-6793	150	9	of	of	ADP
ejpam-6793	150	10	coefficients	coefficient	NOUN
ejpam-6793	150	11	of	of	ADP
ejpam-6793	150	12	the	the	DET
ejpam-6793	150	13	esbsmps	esbsmp	NOUN
ejpam-6793	150	14	{	{	PUNCT
ejpam-6793	150	15	qen(x	qen(x	X
ejpam-6793	150	16	)	)	PUNCT
ejpam-6793	150	17	}	}	PUNCT
ejpam-6793	150	18	,	,	PUNCT
ejpam-6793	150	19	then	then	ADV
ejpam-6793	150	20	it	it	PRON
ejpam-6793	150	21	follows	follow	VERB
ejpam-6793	150	22	that	that	SCONJ
ejpam-6793	150	23	qen(x	qen(x	X
ejpam-6793	150	24	)	)	PUNCT
ejpam-6793	150	25	=	=	SYM
ejpam-6793	151	1	n∑	n∑	PROPN
ejpam-6793	151	2	k=0	k=0	PROPN
ejpam-6793	151	3	qk(x	qk(x	NOUN
ejpam-6793	151	4	)	)	PUNCT
ejpam-6793	151	5	qen	qen	PROPN
ejpam-6793	151	6	,	,	PUNCT
ejpam-6793	151	7	k	k	PROPN
ejpam-6793	151	8	=	=	PROPN
ejpam-6793	151	9	n∑	n∑	PROPN
ejpam-6793	151	10	k=0	k=0	PROPN
ejpam-6793	151	11	qk(x	qk(x	NOUN
ejpam-6793	151	12	)	)	PUNCT
ejpam-6793	151	13			PROPN
ejpam-6793	151	14	∞∑	∞∑	NUM
ejpam-6793	151	15	j=0	j=0	PROPN
ejpam-6793	151	16	q(j	q(j	PROPN
ejpam-6793	151	17	)	)	PUNCT
ejpam-6793	151	18	n	n	CCONJ
ejpam-6793	151	19	,	,	PUNCT
ejpam-6793	151	20	k	k	PROPN
ejpam-6793	151	21	j	j	PROPN
ejpam-6793	151	22	!	!	PUNCT
ejpam-6793	152	1			PROPN
ejpam-6793	152	2	(	(	PUNCT
ejpam-6793	152	3	16	16	NUM
ejpam-6793	152	4	)	)	PUNCT
ejpam-6793	152	5	applying	apply	VERB
ejpam-6793	152	6	(	(	PUNCT
ejpam-6793	152	7	13	13	NUM
ejpam-6793	152	8	)	)	PUNCT
ejpam-6793	152	9	in	in	ADP
ejpam-6793	152	10	(	(	PUNCT
ejpam-6793	152	11	16	16	NUM
ejpam-6793	152	12	)	)	PUNCT
ejpam-6793	152	13	,	,	PUNCT
ejpam-6793	152	14	it	it	PRON
ejpam-6793	152	15	follows	follow	VERB
ejpam-6793	152	16	that	that	SCONJ
ejpam-6793	152	17	∥qen∥r	∥qen∥r	PROPN
ejpam-6793	152	18	=	=	SYM
ejpam-6793	152	19	sup	sup	NOUN
ejpam-6793	152	20	b̄(r	b̄(r	NOUN
ejpam-6793	152	21	)	)	PUNCT
ejpam-6793	152	22	|qen(x)|	|qen(x)|	VERB
ejpam-6793	152	23	≤	≤	NUM
ejpam-6793	152	24	2	2	NUM
ejpam-6793	152	25	m	m	NUM
ejpam-6793	152	26	2	2	NUM
ejpam-6793	152	27	n∑	n∑	NOUN
ejpam-6793	152	28	k=0	k=0	PROPN
ejpam-6793	152	29	rk	rk	VERB
ejpam-6793	152	30			PROPN
ejpam-6793	152	31	∞∑	∞∑	NUM
ejpam-6793	152	32	j=0	j=0	PROPN
ejpam-6793	152	33	∣∣∣q(j	∣∣∣q(j	PROPN
ejpam-6793	152	34	)	)	PUNCT
ejpam-6793	152	35	n	n	CCONJ
ejpam-6793	152	36	,	,	PUNCT
ejpam-6793	152	37	k	k	PROPN
ejpam-6793	152	38	∣∣∣	∣∣∣	PROPN
ejpam-6793	152	39	j	j	PROPN
ejpam-6793	152	40	!	!	PUNCT
ejpam-6793	153	1			PROPN
ejpam-6793	153	2	⩽	⩽	NOUN
ejpam-6793	153	3	n∑	n∑	PUNCT
ejpam-6793	153	4	k=0	k=0	PROPN
ejpam-6793	153	5	rkbn−k	rkbn−k	VERB
ejpam-6793	153	6	∞∑	∞∑	NUM
ejpam-6793	153	7	j=0	j=0	PROPN
ejpam-6793	153	8	(	(	PUNCT
ejpam-6793	153	9	2	2	NUM
ejpam-6793	153	10	m	m	NUM
ejpam-6793	153	11	2	2	NUM
ejpam-6793	153	12	mc)j	mc)j	PROPN
ejpam-6793	153	13	j	j	PROPN
ejpam-6793	153	14	!	!	PUNCT
ejpam-6793	154	1	⩽	⩽	ADJ
ejpam-6793	154	2	rne2	rne2	PROPN
ejpam-6793	154	3	m	m	VERB
ejpam-6793	154	4	2	2	NUM
ejpam-6793	154	5	mc	mc	PROPN
ejpam-6793	154	6	n∑	n∑	PROPN
ejpam-6793	154	7	k=0	k=0	PROPN
ejpam-6793	155	1	(	(	PUNCT
ejpam-6793	155	2	b	b	X
ejpam-6793	155	3	r	r	NOUN
ejpam-6793	155	4	)	)	PUNCT
ejpam-6793	155	5	n−k	n−k	NOUN
ejpam-6793	155	6	≤	≤	NUM
ejpam-6793	155	7	e2	e2	PROPN
ejpam-6793	155	8	m	m	VERB
ejpam-6793	155	9	2	2	NUM
ejpam-6793	155	10	mc(n+	mc(n+	NOUN
ejpam-6793	155	11	1)rn	1)rn	NOUN
ejpam-6793	155	12	,	,	PUNCT
ejpam-6793	155	13	for	for	ADP
ejpam-6793	155	14	all	all	DET
ejpam-6793	155	15	r	r	NOUN
ejpam-6793	155	16	≥	≥	PROPN
ejpam-6793	155	17	b.	b.	NOUN
ejpam-6793	155	18	(	(	PUNCT
ejpam-6793	155	19	17	17	NUM
ejpam-6793	155	20	)	)	PUNCT
ejpam-6793	155	21	moreover	moreover	ADV
ejpam-6793	155	22	,	,	PUNCT
ejpam-6793	155	23	since	since	SCONJ
ejpam-6793	155	24	the	the	DET
ejpam-6793	155	25	clifford	clifford	PROPN
ejpam-6793	155	26	matrix	matrix	NOUN
ejpam-6793	155	27	of	of	ADP
ejpam-6793	155	28	operators	operator	NOUN
ejpam-6793	155	29	of	of	ADP
ejpam-6793	155	30	the	the	DET
ejpam-6793	155	31	esbsmps	esbsmp	NOUN
ejpam-6793	155	32	is	be	AUX
ejpam-6793	155	33	{	{	PUNCT
ejpam-6793	155	34	qen(x	qen(x	X
ejpam-6793	155	35	)	)	PUNCT
ejpam-6793	155	36	}	}	PUNCT
ejpam-6793	155	37	is	be	AUX
ejpam-6793	155	38	qē	qē	NOUN
ejpam-6793	155	39	=	=	SYM
ejpam-6793	155	40	e−q	e−q	NOUN
ejpam-6793	155	41	,	,	PUNCT
ejpam-6793	155	42	hence	hence	ADV
ejpam-6793	155	43	by	by	ADP
ejpam-6793	155	44	using	use	VERB
ejpam-6793	155	45	(	(	PUNCT
ejpam-6793	155	46	13	13	NUM
ejpam-6793	155	47	)	)	PUNCT
ejpam-6793	155	48	and	and	CCONJ
ejpam-6793	155	49	(	(	PUNCT
ejpam-6793	155	50	17	17	NUM
ejpam-6793	155	51	)	)	PUNCT
ejpam-6793	155	52	in	in	ADP
ejpam-6793	155	53	the	the	DET
ejpam-6793	155	54	cannon	cannon	NOUN
ejpam-6793	155	55	sum	sum	NOUN
ejpam-6793	155	56	of	of	ADP
ejpam-6793	155	57	{	{	PUNCT
ejpam-6793	155	58	qen(x	qen(x	X
ejpam-6793	155	59	)	)	PUNCT
ejpam-6793	155	60	}	}	PUNCT
ejpam-6793	155	61	yields	yield	NOUN
ejpam-6793	155	62	:	:	PUNCT
ejpam-6793	155	63	ω	ω	PROPN
ejpam-6793	155	64	(	(	PUNCT
ejpam-6793	155	65	qen	qen	PROPN
ejpam-6793	155	66	,	,	PUNCT
ejpam-6793	155	67	b̄(r	b̄(r	NOUN
ejpam-6793	155	68	)	)	PUNCT
ejpam-6793	155	69	)	)	PUNCT
ejpam-6793	156	1	=	=	PUNCT
ejpam-6793	156	2	n∑	n∑	PROPN
ejpam-6793	156	3	k=0	k=0	PROPN
ejpam-6793	156	4	∥∥qekqēn	∥∥qekqēn	PROPN
ejpam-6793	156	5	,	,	PUNCT
ejpam-6793	156	6	k	k	X
ejpam-6793	156	7	∥∥	∥∥	PUNCT
ejpam-6793	156	8	r	r	NOUN
ejpam-6793	156	9	=	=	SYM
ejpam-6793	156	10	n∑	n∑	PROPN
ejpam-6793	156	11	k=0	k=0	PROPN
ejpam-6793	156	12	sup	sup	NOUN
ejpam-6793	156	13	b̄(r	b̄(r	NOUN
ejpam-6793	156	14	)	)	PUNCT
ejpam-6793	156	15	∣∣qek(x)qēn	∣∣qek(x)qēn	PROPN
ejpam-6793	156	16	,	,	PUNCT
ejpam-6793	156	17	k	k	X
ejpam-6793	156	18	∣∣	∣∣	X
ejpam-6793	156	19	≤	≤	ADV
ejpam-6793	156	20	2	2	NUM
ejpam-6793	156	21	m	m	NUM
ejpam-6793	156	22	2	2	NUM
ejpam-6793	156	23	n∑	n∑	NOUN
ejpam-6793	156	24	k=0	k=0	PROPN
ejpam-6793	156	25	∥qek∥r	∥qek∥r	NUM
ejpam-6793	156	26	∣∣qēn	∣∣qēn	PROPN
ejpam-6793	156	27	,	,	PUNCT
ejpam-6793	156	28	k	k	X
ejpam-6793	156	29	∣∣	∣∣	X
ejpam-6793	156	30	=	=	SYM
ejpam-6793	156	31	2	2	NUM
ejpam-6793	156	32	m	m	NUM
ejpam-6793	156	33	2	2	NUM
ejpam-6793	156	34	n∑	n∑	NOUN
ejpam-6793	156	35	k=0	k=0	PROPN
ejpam-6793	156	36	∥qek∥r	∥qek∥r	ADP
ejpam-6793	156	37	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-6793	156	38	∞∑	∞∑	NUM
ejpam-6793	156	39	j=0	j=0	PROPN
ejpam-6793	156	40	(	(	PUNCT
ejpam-6793	156	41	−1)j	−1)j	NOUN
ejpam-6793	156	42	q(j	q(j	PROPN
ejpam-6793	156	43	)	)	PUNCT
ejpam-6793	156	44	n	n	CCONJ
ejpam-6793	156	45	,	,	PUNCT
ejpam-6793	156	46	k	k	PROPN
ejpam-6793	156	47	j	j	PROPN
ejpam-6793	156	48	!	!	PUNCT
ejpam-6793	157	1	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-6793	157	2	≤	≤	ADV
ejpam-6793	157	3	2	2	NUM
ejpam-6793	157	4	m	m	NUM
ejpam-6793	157	5	2	2	NUM
ejpam-6793	157	6	n∑	n∑	NOUN
ejpam-6793	157	7	k=0	k=0	PROPN
ejpam-6793	157	8	∥qek∥r	∥qek∥r	VERB
ejpam-6793	157	9	∞∑	∞∑	NUM
ejpam-6793	157	10	j=0	j=0	PROPN
ejpam-6793	157	11	∣∣∣q(j	∣∣∣q(j	PROPN
ejpam-6793	157	12	)	)	PUNCT
ejpam-6793	157	13	n	n	CCONJ
ejpam-6793	157	14	,	,	PUNCT
ejpam-6793	158	1	k	k	PROPN
ejpam-6793	158	2	∣∣∣	∣∣∣	PROPN
ejpam-6793	158	3	j	j	PROPN
ejpam-6793	158	4	!	!	PUNCT
ejpam-6793	158	5	m.	m.	PROPN
ejpam-6793	158	6	zayed	zayed	PROPN
ejpam-6793	158	7	/	/	SYM
ejpam-6793	158	8	eur	eur	PROPN
ejpam-6793	158	9	.	.	PUNCT
ejpam-6793	159	1	j.	j.	PROPN
ejpam-6793	159	2	pure	pure	PROPN
ejpam-6793	159	3	appl	appl	PROPN
ejpam-6793	159	4	.	.	PROPN
ejpam-6793	159	5	math	math	PROPN
ejpam-6793	159	6	,	,	PUNCT
ejpam-6793	159	7	18	18	NUM
ejpam-6793	159	8	(	(	PUNCT
ejpam-6793	159	9	4	4	NUM
ejpam-6793	159	10	)	)	PUNCT
ejpam-6793	159	11	(	(	PUNCT
ejpam-6793	159	12	2025	2025	NUM
ejpam-6793	159	13	)	)	PUNCT
ejpam-6793	159	14	,	,	PUNCT
ejpam-6793	159	15	6793	6793	NUM
ejpam-6793	159	16	9	9	NUM
ejpam-6793	159	17	of	of	ADP
ejpam-6793	159	18	19	19	NUM
ejpam-6793	159	19	≤	≤	NUM
ejpam-6793	159	20	e2	e2	PROPN
ejpam-6793	159	21	m	m	VERB
ejpam-6793	159	22	2	2	NUM
ejpam-6793	159	23	mc	mc	PROPN
ejpam-6793	159	24	n∑	n∑	PROPN
ejpam-6793	159	25	k=0	k=0	PROPN
ejpam-6793	160	1	(	(	PUNCT
ejpam-6793	160	2	k	k	PROPN
ejpam-6793	160	3	+	+	PROPN
ejpam-6793	160	4	1)rk	1)rk	PROPN
ejpam-6793	160	5	∞∑	∞∑	NUM
ejpam-6793	160	6	j=0	j=0	PROPN
ejpam-6793	160	7	bn−k	bn−k	PROPN
ejpam-6793	160	8	(	(	PUNCT
ejpam-6793	160	9	2	2	NUM
ejpam-6793	160	10	m	m	NUM
ejpam-6793	160	11	2	2	NUM
ejpam-6793	160	12	mc)j	mc)j	PROPN
ejpam-6793	160	13	j	j	PROPN
ejpam-6793	160	14	!	!	PUNCT
ejpam-6793	160	15	≤	≤	PROPN
ejpam-6793	160	16	e2	e2	PROPN
ejpam-6793	160	17	(	(	PUNCT
ejpam-6793	160	18	m2	m2	PROPN
ejpam-6793	160	19	+1)mc	+1)mc	PROPN
ejpam-6793	160	20	n∑	n∑	PROPN
ejpam-6793	160	21	k=0	k=0	PROPN
ejpam-6793	160	22	(	(	PUNCT
ejpam-6793	160	23	k	k	PROPN
ejpam-6793	160	24	+	+	PROPN
ejpam-6793	160	25	1)rkbn−k	1)rkbn−k	NUM
ejpam-6793	160	26	=	=	SYM
ejpam-6793	160	27	e2	e2	PROPN
ejpam-6793	160	28	(	(	PUNCT
ejpam-6793	160	29	m2	m2	PROPN
ejpam-6793	160	30	+1)mcrn	+1)mcrn	PROPN
ejpam-6793	160	31	n∑	n∑	PROPN
ejpam-6793	160	32	k=0	k=0	PROPN
ejpam-6793	160	33	(	(	PUNCT
ejpam-6793	160	34	k	k	X
ejpam-6793	160	35	+	+	PROPN
ejpam-6793	160	36	1	1	X
ejpam-6793	160	37	)	)	PUNCT
ejpam-6793	160	38	(	(	PUNCT
ejpam-6793	160	39	b	b	NOUN
ejpam-6793	160	40	r	r	NOUN
ejpam-6793	160	41	)	)	PUNCT
ejpam-6793	160	42	n−k	n−k	NOUN
ejpam-6793	160	43	≤	≤	PROPN
ejpam-6793	160	44	e2	e2	PROPN
ejpam-6793	160	45	(	(	PUNCT
ejpam-6793	160	46	m2	m2	PROPN
ejpam-6793	160	47	+1)mc(n+	+1)mc(n+	PRON
ejpam-6793	160	48	1)2rn	1)2rn	NUM
ejpam-6793	160	49	for	for	ADP
ejpam-6793	160	50	all	all	DET
ejpam-6793	160	51	r	r	NOUN
ejpam-6793	160	52	≥	≥	NOUN
ejpam-6793	160	53	b.	b.	NOUN
ejpam-6793	161	1	it	it	PRON
ejpam-6793	161	2	follows	follow	VERB
ejpam-6793	161	3	that	that	SCONJ
ejpam-6793	162	1	ω	ω	PROPN
ejpam-6793	162	2	(	(	PUNCT
ejpam-6793	162	3	qe	qe	PROPN
ejpam-6793	162	4	,	,	PUNCT
ejpam-6793	162	5	b̄(r	b̄(r	NOUN
ejpam-6793	162	6	)	)	PUNCT
ejpam-6793	162	7	)	)	PUNCT
ejpam-6793	163	1	=	=	SYM
ejpam-6793	163	2	lim	lim	PROPN
ejpam-6793	163	3	sup	sup	PROPN
ejpam-6793	163	4	n→∞	n→∞	X
ejpam-6793	163	5	{	{	PUNCT
ejpam-6793	163	6	ω	ω	PROPN
ejpam-6793	163	7	(	(	PUNCT
ejpam-6793	163	8	qen	qen	PROPN
ejpam-6793	163	9	,	,	PUNCT
ejpam-6793	163	10	b̄(r	b̄(r	NOUN
ejpam-6793	163	11	)	)	PUNCT
ejpam-6793	163	12	)	)	PUNCT
ejpam-6793	163	13	}	}	PUNCT
ejpam-6793	163	14	1	1	NUM
ejpam-6793	163	15	n	n	DET
ejpam-6793	163	16	≤	≤	NOUN
ejpam-6793	163	17	r	r	NOUN
ejpam-6793	163	18	for	for	ADP
ejpam-6793	163	19	all	all	DET
ejpam-6793	163	20	r	r	NOUN
ejpam-6793	163	21	≥	≥	NOUN
ejpam-6793	163	22	b.	b.	PROPN
ejpam-6793	163	23	as	as	ADP
ejpam-6793	163	24	ω	ω	PROPN
ejpam-6793	163	25	(	(	PUNCT
ejpam-6793	163	26	qe	qe	PROPN
ejpam-6793	163	27	,	,	PUNCT
ejpam-6793	163	28	b̄(r	b̄(r	NOUN
ejpam-6793	163	29	)	)	PUNCT
ejpam-6793	163	30	)	)	PUNCT
ejpam-6793	163	31	≥	≥	NOUN
ejpam-6793	164	1	r	r	NOUN
ejpam-6793	164	2	,	,	PUNCT
ejpam-6793	164	3	then	then	ADV
ejpam-6793	164	4	ω	ω	PROPN
ejpam-6793	164	5	(	(	PUNCT
ejpam-6793	164	6	qe	qe	PROPN
ejpam-6793	164	7	,	,	PUNCT
ejpam-6793	164	8	b̄(r	b̄(r	NOUN
ejpam-6793	164	9	)	)	PUNCT
ejpam-6793	164	10	)	)	PUNCT
ejpam-6793	165	1	=	=	PUNCT
ejpam-6793	165	2	r.	r.	PROPN
ejpam-6793	165	3	and	and	CCONJ
ejpam-6793	165	4	therefore	therefore	ADV
ejpam-6793	165	5	the	the	DET
ejpam-6793	165	6	esbsmps	esbsmp	NOUN
ejpam-6793	165	7	{	{	PUNCT
ejpam-6793	165	8	qen(x	qen(x	X
ejpam-6793	165	9	)	)	PUNCT
ejpam-6793	165	10	}	}	PUNCT
ejpam-6793	165	11	will	will	AUX
ejpam-6793	165	12	be	be	AUX
ejpam-6793	165	13	effective	effective	ADJ
ejpam-6793	165	14	for	for	ADP
ejpam-6793	165	15	wb̄(r	wb̄(r	NOUN
ejpam-6793	165	16	)	)	PUNCT
ejpam-6793	165	17	for	for	ADP
ejpam-6793	165	18	all	all	DET
ejpam-6793	165	19	r	r	NOUN
ejpam-6793	165	20	≥	≥	NOUN
ejpam-6793	165	21	b.	b.	NOUN
ejpam-6793	165	22	when	when	SCONJ
ejpam-6793	165	23	r	r	NOUN
ejpam-6793	165	24	<	<	X
ejpam-6793	165	25	b	b	X
ejpam-6793	165	26	the	the	DET
ejpam-6793	165	27	esbshps	esbshps	NOUN
ejpam-6793	165	28	{	{	PUNCT
ejpam-6793	165	29	qen(x	qen(x	X
ejpam-6793	165	30	)	)	PUNCT
ejpam-6793	165	31	}	}	PUNCT
ejpam-6793	165	32	may	may	AUX
ejpam-6793	165	33	not	not	PART
ejpam-6793	165	34	be	be	AUX
ejpam-6793	165	35	effective	effective	ADJ
ejpam-6793	165	36	for	for	ADP
ejpam-6793	165	37	wb̄(r	wb̄(r	NOUN
ejpam-6793	165	38	)	)	PUNCT
ejpam-6793	165	39	where	where	SCONJ
ejpam-6793	165	40	r	r	NOUN
ejpam-6793	165	41	<	<	X
ejpam-6793	165	42	b.	b.	PROPN
ejpam-6793	165	43	to	to	PART
ejpam-6793	165	44	show	show	VERB
ejpam-6793	165	45	this	this	DET
ejpam-6793	165	46	fact	fact	NOUN
ejpam-6793	165	47	,	,	PUNCT
ejpam-6793	165	48	we	we	PRON
ejpam-6793	165	49	illustrate	illustrate	VERB
ejpam-6793	165	50	the	the	DET
ejpam-6793	165	51	following	follow	VERB
ejpam-6793	165	52	example	example	NOUN
ejpam-6793	165	53	example	example	NOUN
ejpam-6793	165	54	1	1	X
ejpam-6793	165	55	.	.	X
ejpam-6793	165	56	consider	consider	VERB
ejpam-6793	165	57	the	the	DET
ejpam-6793	165	58	sbsmps	sbsmp	NOUN
ejpam-6793	165	59	{	{	PUNCT
ejpam-6793	165	60	qn(x	qn(x	NOUN
ejpam-6793	165	61	)	)	PUNCT
ejpam-6793	165	62	}	}	PUNCT
ejpam-6793	165	63	for	for	ADP
ejpam-6793	165	64	which	which	PRON
ejpam-6793	165	65	qn	qn	PROPN
ejpam-6793	165	66	,	,	PUNCT
ejpam-6793	165	67	k	k	NOUN
ejpam-6793	166	1	=	=	PRON
ejpam-6793	167	1	{	{	PUNCT
ejpam-6793	168	1	αn	αn	NOUN
ejpam-6793	168	2	,	,	PUNCT
ejpam-6793	168	3	k	k	NOUN
ejpam-6793	168	4	=	=	SYM
ejpam-6793	168	5	n	n	CCONJ
ejpam-6793	168	6	,	,	PUNCT
ejpam-6793	168	7	bn−k	bn−k	VERB
ejpam-6793	168	8	n+1	n+1	NUM
ejpam-6793	168	9	αk	αk	NOUN
ejpam-6793	168	10	,	,	PUNCT
ejpam-6793	168	11	0	0	NUM
ejpam-6793	168	12	≤	≤	NUM
ejpam-6793	169	1	k	k	X
ejpam-6793	169	2	<	<	X
ejpam-6793	169	3	n	n	CCONJ
ejpam-6793	169	4	,	,	PUNCT
ejpam-6793	169	5	(	(	PUNCT
ejpam-6793	169	6	18	18	NUM
ejpam-6793	169	7	)	)	PUNCT
ejpam-6793	169	8	where	where	SCONJ
ejpam-6793	169	9	αi	αi	ADV
ejpam-6793	169	10	=	=	SYM
ejpam-6793	169	11	1	1	NUM
ejpam-6793	169	12	i+1	i+1	NOUN
ejpam-6793	169	13	for	for	ADP
ejpam-6793	169	14	i	i	PRON
ejpam-6793	169	15	=	=	SYM
ejpam-6793	169	16	k	k	PROPN
ejpam-6793	169	17	,	,	PUNCT
ejpam-6793	169	18	n.	n.	NOUN
ejpam-6793	169	19	as	as	ADP
ejpam-6793	169	20	in	in	ADP
ejpam-6793	169	21	(	(	PUNCT
ejpam-6793	169	22	13	13	NUM
ejpam-6793	169	23	)	)	PUNCT
ejpam-6793	169	24	we	we	PRON
ejpam-6793	169	25	can	can	AUX
ejpam-6793	169	26	apply	apply	VERB
ejpam-6793	169	27	(	(	PUNCT
ejpam-6793	169	28	18	18	NUM
ejpam-6793	169	29	)	)	PUNCT
ejpam-6793	169	30	to	to	PART
ejpam-6793	169	31	prove	prove	VERB
ejpam-6793	169	32	by	by	ADP
ejpam-6793	169	33	mathematical	mathematical	ADJ
ejpam-6793	169	34	induction	induction	NOUN
ejpam-6793	169	35	that	that	SCONJ
ejpam-6793	169	36	q(j	q(j	PROPN
ejpam-6793	169	37	)	)	PUNCT
ejpam-6793	169	38	n,0	n,0	NOUN
ejpam-6793	169	39	≥	≥	PROPN
ejpam-6793	169	40	bnαj	bnαj	PROPN
ejpam-6793	169	41	n.	n.	PROPN
ejpam-6793	169	42	(	(	PUNCT
ejpam-6793	169	43	19	19	NUM
ejpam-6793	169	44	)	)	PUNCT
ejpam-6793	169	45	now	now	ADV
ejpam-6793	169	46	,	,	PUNCT
ejpam-6793	169	47	the	the	DET
ejpam-6793	169	48	cannon	cannon	NOUN
ejpam-6793	169	49	sum	sum	NOUN
ejpam-6793	169	50	for	for	ADP
ejpam-6793	169	51	esbsmps	esbsmp	NOUN
ejpam-6793	169	52	{	{	PUNCT
ejpam-6793	169	53	qen(x	qen(x	X
ejpam-6793	169	54	)	)	PUNCT
ejpam-6793	169	55	}	}	PUNCT
ejpam-6793	169	56	is	be	AUX
ejpam-6793	169	57	given	give	VERB
ejpam-6793	169	58	as	as	ADP
ejpam-6793	169	59	ωn	ωn	PROPN
ejpam-6793	169	60	(	(	PUNCT
ejpam-6793	169	61	qen	qen	PROPN
ejpam-6793	169	62	,	,	PUNCT
ejpam-6793	169	63	b̄(r	b̄(r	NOUN
ejpam-6793	169	64	)	)	PUNCT
ejpam-6793	169	65	)	)	PUNCT
ejpam-6793	170	1	=	=	PUNCT
ejpam-6793	170	2	n∑	n∑	PROPN
ejpam-6793	170	3	k=0	k=0	PROPN
ejpam-6793	170	4	∥∥∥qek	∥∥∥qek	VERB
ejpam-6793	170	5	qẽn	qẽn	PROPN
ejpam-6793	170	6	,	,	PUNCT
ejpam-6793	170	7	k	k	PROPN
ejpam-6793	170	8	∥∥∥	∥∥∥	PROPN
ejpam-6793	170	9	r	r	NOUN
ejpam-6793	170	10	≥	≥	NOUN
ejpam-6793	170	11	∥∥∥qenqẽn	∥∥∥qenqẽn	PROPN
ejpam-6793	170	12	,	,	PUNCT
ejpam-6793	170	13	n	n	PRON
ejpam-6793	170	14	∥∥∥	∥∥∥	PROPN
ejpam-6793	170	15	r	r	NOUN
ejpam-6793	170	16	=	=	SYM
ejpam-6793	170	17	eαn	eαn	X
ejpam-6793	171	1	∥qen∥r	∥qen∥r	X
ejpam-6793	171	2	≥	≥	X
ejpam-6793	171	3	eαn	eαn	X
ejpam-6793	171	4	|qen,0|	|qen,0|	ADV
ejpam-6793	171	5	=	=	PUNCT
ejpam-6793	171	6	eαn	eαn	VERB
ejpam-6793	171	7	∞∑	∞∑	NUM
ejpam-6793	171	8	j=0	j=0	PROPN
ejpam-6793	171	9	q(j	q(j	PROPN
ejpam-6793	171	10	)	)	PUNCT
ejpam-6793	171	11	n,0	n,0	NOUN
ejpam-6793	172	1	j	j	PROPN
ejpam-6793	172	2	!	!	PROPN
ejpam-6793	172	3	≥	≥	PROPN
ejpam-6793	172	4	eαnbn	eαnbn	PROPN
ejpam-6793	172	5	∞∑	∞∑	NUM
ejpam-6793	172	6	j=0	j=0	PROPN
ejpam-6793	172	7	αj	αj	PROPN
ejpam-6793	172	8	n	n	PRON
ejpam-6793	172	9	j	j	PROPN
ejpam-6793	172	10	!	!	PUNCT
ejpam-6793	173	1	=	=	PRON
ejpam-6793	173	2	e2αnbn	e2αnbn	VERB
ejpam-6793	173	3	≥	≥	NOUN
ejpam-6793	173	4	bn	bn	NOUN
ejpam-6793	173	5	.	.	PUNCT
ejpam-6793	174	1	(	(	PUNCT
ejpam-6793	174	2	20	20	NUM
ejpam-6793	174	3	)	)	PUNCT
ejpam-6793	174	4	m.	m.	NOUN
ejpam-6793	174	5	zayed	zayed	PROPN
ejpam-6793	174	6	/	/	SYM
ejpam-6793	174	7	eur	eur	PROPN
ejpam-6793	174	8	.	.	PUNCT
ejpam-6793	175	1	j.	j.	PROPN
ejpam-6793	175	2	pure	pure	PROPN
ejpam-6793	175	3	appl	appl	PROPN
ejpam-6793	175	4	.	.	PROPN
ejpam-6793	175	5	math	math	PROPN
ejpam-6793	175	6	,	,	PUNCT
ejpam-6793	175	7	18	18	NUM
ejpam-6793	175	8	(	(	PUNCT
ejpam-6793	175	9	4	4	NUM
ejpam-6793	175	10	)	)	PUNCT
ejpam-6793	175	11	(	(	PUNCT
ejpam-6793	175	12	2025	2025	NUM
ejpam-6793	175	13	)	)	PUNCT
ejpam-6793	175	14	,	,	PUNCT
ejpam-6793	175	15	6793	6793	NUM
ejpam-6793	175	16	10	10	NUM
ejpam-6793	175	17	of	of	ADP
ejpam-6793	175	18	19	19	NUM
ejpam-6793	175	19	thus	thus	ADV
ejpam-6793	175	20	ω	ω	PROPN
ejpam-6793	175	21	(	(	PUNCT
ejpam-6793	175	22	qe	qe	PROPN
ejpam-6793	175	23	,	,	PUNCT
ejpam-6793	175	24	b̄(r	b̄(r	NOUN
ejpam-6793	175	25	)	)	PUNCT
ejpam-6793	175	26	)	)	PUNCT
ejpam-6793	175	27	≥	≥	PROPN
ejpam-6793	176	1	b	b	X
ejpam-6793	176	2	>	>	X
ejpam-6793	176	3	r	r	NOUN
ejpam-6793	176	4	for	for	ADP
ejpam-6793	176	5	r	r	NOUN
ejpam-6793	176	6	<	<	X
ejpam-6793	176	7	b	b	NOUN
ejpam-6793	176	8	,	,	PUNCT
ejpam-6793	176	9	and	and	CCONJ
ejpam-6793	176	10	the	the	DET
ejpam-6793	176	11	esbsmps	esbsmp	NOUN
ejpam-6793	176	12	is	be	AUX
ejpam-6793	176	13	not	not	PART
ejpam-6793	176	14	effective	effective	ADJ
ejpam-6793	176	15	for	for	ADP
ejpam-6793	176	16	wb̄(r	wb̄(r	NOUN
ejpam-6793	176	17	)	)	PUNCT
ejpam-6793	176	18	for	for	ADP
ejpam-6793	176	19	r	r	NOUN
ejpam-6793	176	20	<	<	X
ejpam-6793	176	21	b	b	NOUN
ejpam-6793	176	22	as	as	SCONJ
ejpam-6793	176	23	required	require	VERB
ejpam-6793	176	24	.	.	PUNCT
ejpam-6793	177	1	remark	remark	PROPN
ejpam-6793	177	2	3	3	NUM
ejpam-6793	177	3	.	.	PUNCT
ejpam-6793	177	4	in	in	ADP
ejpam-6793	177	5	theorem	theorem	NOUN
ejpam-6793	177	6	2	2	NUM
ejpam-6793	177	7	,	,	PUNCT
ejpam-6793	177	8	if	if	SCONJ
ejpam-6793	177	9	{	{	PUNCT
ejpam-6793	177	10	qn(x	qn(x	X
ejpam-6793	177	11	)	)	PUNCT
ejpam-6793	177	12	}	}	PUNCT
ejpam-6793	177	13	is	be	AUX
ejpam-6793	177	14	taken	take	VERB
ejpam-6793	177	15	to	to	PART
ejpam-6793	177	16	be	be	AUX
ejpam-6793	177	17	a	a	DET
ejpam-6793	177	18	simple	simple	ADJ
ejpam-6793	177	19	monic	monic	ADJ
ejpam-6793	177	20	base	base	NOUN
ejpam-6793	177	21	(	(	PUNCT
ejpam-6793	177	22	qn	qn	NOUN
ejpam-6793	177	23	,	,	PUNCT
ejpam-6793	177	24	n	n	NOUN
ejpam-6793	177	25	=	=	SYM
ejpam-6793	177	26	1	1	NUM
ejpam-6793	177	27	for	for	ADP
ejpam-6793	177	28	n	n	PRON
ejpam-6793	177	29	∈	∈	PROPN
ejpam-6793	177	30	n	n	CCONJ
ejpam-6793	177	31	)	)	PUNCT
ejpam-6793	177	32	,	,	PUNCT
ejpam-6793	178	1	then	then	ADV
ejpam-6793	178	2	the	the	DET
ejpam-6793	178	3	results	result	NOUN
ejpam-6793	178	4	in	in	ADP
ejpam-6793	178	5	[	[	X
ejpam-6793	178	6	21	21	NUM
ejpam-6793	178	7	]	]	PUNCT
ejpam-6793	178	8	becomes	become	VERB
ejpam-6793	178	9	a	a	DET
ejpam-6793	178	10	particular	particular	ADJ
ejpam-6793	178	11	case	case	NOUN
ejpam-6793	178	12	of	of	ADP
ejpam-6793	178	13	our	our	PRON
ejpam-6793	178	14	theorem	theorem	NOUN
ejpam-6793	178	15	2	2	NUM
ejpam-6793	178	16	.	.	NOUN
ejpam-6793	178	17	3.2	3.2	NUM
ejpam-6793	178	18	.	.	PUNCT
ejpam-6793	179	1	the	the	DET
ejpam-6793	179	2	order	order	NOUN
ejpam-6793	179	3	of	of	ADP
ejpam-6793	179	4	the	the	DET
ejpam-6793	179	5	exponential	exponential	ADJ
ejpam-6793	179	6	simple	simple	ADJ
ejpam-6793	179	7	base	base	NOUN
ejpam-6793	179	8	of	of	ADP
ejpam-6793	179	9	special	special	ADJ
ejpam-6793	179	10	monogenic	monogenic	ADJ
ejpam-6793	179	11	polynomials	polynomial	NOUN
ejpam-6793	179	12	let	let	VERB
ejpam-6793	179	13	{	{	PUNCT
ejpam-6793	179	14	qn(x	qn(x	X
ejpam-6793	179	15	)	)	PUNCT
ejpam-6793	179	16	}	}	PUNCT
ejpam-6793	179	17	be	be	AUX
ejpam-6793	179	18	a	a	DET
ejpam-6793	179	19	sbsmp	sbsmp	NOUN
ejpam-6793	179	20	for	for	ADP
ejpam-6793	179	21	which	which	PRON
ejpam-6793	179	22	{	{	PUNCT
ejpam-6793	179	23	|qn	|qn	NUM
ejpam-6793	179	24	,	,	PUNCT
ejpam-6793	179	25	k|	k|	NOUN
ejpam-6793	179	26	≤m	≤m	NOUN
ejpam-6793	179	27	nλ(n−k	nλ(n−k	PROPN
ejpam-6793	179	28	)	)	PUNCT
ejpam-6793	180	1	n+1	n+1	NUM
ejpam-6793	180	2	αk	αk	ADP
ejpam-6793	180	3	0	0	NUM
ejpam-6793	180	4	⩽	⩽	PROPN
ejpam-6793	181	1	k	k	PROPN
ejpam-6793	181	2	<	<	X
ejpam-6793	181	3	n	n	X
ejpam-6793	181	4	qn	qn	NOUN
ejpam-6793	181	5	,	,	PUNCT
ejpam-6793	181	6	n	n	NOUN
ejpam-6793	181	7	=	=	SYM
ejpam-6793	181	8	αn	αn	NOUN
ejpam-6793	181	9	,	,	PUNCT
ejpam-6793	181	10	n	n	PROPN
ejpam-6793	181	11	∈	∈	PROPN
ejpam-6793	181	12	n	n	CCONJ
ejpam-6793	181	13	(	(	PUNCT
ejpam-6793	181	14	21	21	NUM
ejpam-6793	181	15	)	)	PUNCT
ejpam-6793	181	16	where	where	SCONJ
ejpam-6793	181	17	λ	λ	NOUN
ejpam-6793	181	18	is	be	AUX
ejpam-6793	181	19	positive	positive	ADJ
ejpam-6793	181	20	constant	constant	ADJ
ejpam-6793	181	21	and	and	CCONJ
ejpam-6793	181	22	1	1	NUM
ejpam-6793	181	23	≤	≤	NUM
ejpam-6793	181	24	m	m	VERB
ejpam-6793	181	25	<	<	X
ejpam-6793	181	26	∞.	∞.	PROPN
ejpam-6793	181	27	to	to	PART
ejpam-6793	181	28	justify	justify	VERB
ejpam-6793	181	29	the	the	DET
ejpam-6793	181	30	main	main	ADJ
ejpam-6793	181	31	result	result	NOUN
ejpam-6793	181	32	of	of	ADP
ejpam-6793	181	33	this	this	DET
ejpam-6793	181	34	section	section	NOUN
ejpam-6793	181	35	,	,	PUNCT
ejpam-6793	181	36	we	we	PRON
ejpam-6793	181	37	first	first	ADV
ejpam-6793	181	38	introduce	introduce	VERB
ejpam-6793	181	39	the	the	DET
ejpam-6793	181	40	following	follow	VERB
ejpam-6793	181	41	lemma	lemma	PROPN
ejpam-6793	181	42	.	.	PUNCT
ejpam-6793	182	1	lemma	lemma	PROPN
ejpam-6793	182	2	2	2	NUM
ejpam-6793	182	3	.	.	PUNCT
ejpam-6793	183	1	if	if	SCONJ
ejpam-6793	183	2	q(j	q(j	PROPN
ejpam-6793	183	3	)	)	PUNCT
ejpam-6793	183	4	n	n	CCONJ
ejpam-6793	183	5	,	,	PUNCT
ejpam-6793	183	6	k	k	PROPN
ejpam-6793	183	7	∈	∈	PROPN
ejpam-6793	183	8	am	be	AUX
ejpam-6793	183	9	are	be	AUX
ejpam-6793	183	10	the	the	DET
ejpam-6793	183	11	elements	element	NOUN
ejpam-6793	183	12	of	of	ADP
ejpam-6793	183	13	the	the	DET
ejpam-6793	183	14	power	power	NOUN
ejpam-6793	183	15	clifford	clifford	PROPN
ejpam-6793	183	16	matrix	matrix	PROPN
ejpam-6793	183	17	q(j	q(j	PROPN
ejpam-6793	183	18	)	)	PUNCT
ejpam-6793	183	19	,	,	PUNCT
ejpam-6793	184	1	j	j	PROPN
ejpam-6793	184	2	≥	≥	NOUN
ejpam-6793	184	3	1	1	NUM
ejpam-6793	184	4	satisfying	satisfy	VERB
ejpam-6793	184	5	(	(	PUNCT
ejpam-6793	184	6	21	21	NUM
ejpam-6793	184	7	)	)	PUNCT
ejpam-6793	184	8	,	,	PUNCT
ejpam-6793	184	9	then	then	ADV
ejpam-6793	184	10	∣∣∣q(j	∣∣∣q(j	PROPN
ejpam-6793	184	11	)	)	PUNCT
ejpam-6793	184	12	n	n	CCONJ
ejpam-6793	184	13	,	,	PUNCT
ejpam-6793	184	14	k	k	PROPN
ejpam-6793	184	15	∣∣∣	∣∣∣	PROPN
ejpam-6793	184	16	⩽	⩽	PROPN
ejpam-6793	184	17	2−	2−	NUM
ejpam-6793	184	18	m	m	NOUN
ejpam-6793	184	19	2	2	NUM
ejpam-6793	184	20	(	(	PUNCT
ejpam-6793	184	21	2	2	NUM
ejpam-6793	184	22	m	m	NUM
ejpam-6793	184	23	2	2	NUM
ejpam-6793	184	24	mc	mc	NOUN
ejpam-6793	184	25	)	)	PUNCT
ejpam-6793	184	26	j	j	PROPN
ejpam-6793	184	27	nλ(n−k	nλ(n−k	PROPN
ejpam-6793	184	28	)	)	PUNCT
ejpam-6793	184	29	,	,	PUNCT
ejpam-6793	184	30	0	0	NUM
ejpam-6793	184	31	⩽	⩽	PROPN
ejpam-6793	184	32	k	k	PROPN
ejpam-6793	184	33	<	<	X
ejpam-6793	184	34	n.	n.	PROPN
ejpam-6793	184	35	(	(	PUNCT
ejpam-6793	184	36	22	22	NUM
ejpam-6793	184	37	)	)	PUNCT
ejpam-6793	184	38	proof	proof	NOUN
ejpam-6793	184	39	.	.	PUNCT
ejpam-6793	185	1	as	as	SCONJ
ejpam-6793	185	2	proceed	procee	VERB
ejpam-6793	185	3	in	in	ADP
ejpam-6793	185	4	the	the	DET
ejpam-6793	185	5	proof	proof	NOUN
ejpam-6793	185	6	of	of	ADP
ejpam-6793	185	7	lemma	lemma	PROPN
ejpam-6793	185	8	(	(	PUNCT
ejpam-6793	185	9	1	1	NUM
ejpam-6793	185	10	)	)	PUNCT
ejpam-6793	185	11	,	,	PUNCT
ejpam-6793	185	12	the	the	DET
ejpam-6793	185	13	inequality	inequality	NOUN
ejpam-6793	185	14	(	(	PUNCT
ejpam-6793	185	15	22	22	NUM
ejpam-6793	185	16	)	)	PUNCT
ejpam-6793	185	17	.	.	PUNCT
ejpam-6793	186	1	can	can	AUX
ejpam-6793	186	2	be	be	AUX
ejpam-6793	186	3	verified	verify	VERB
ejpam-6793	186	4	.	.	PUNCT
ejpam-6793	187	1	theorem	theorem	NOUN
ejpam-6793	187	2	3	3	X
ejpam-6793	187	3	.	.	PUNCT
ejpam-6793	188	1	let	let	VERB
ejpam-6793	188	2	{	{	PUNCT
ejpam-6793	188	3	qn(x	qn(x	X
ejpam-6793	188	4	)	)	PUNCT
ejpam-6793	188	5	}	}	PUNCT
ejpam-6793	188	6	be	be	AUX
ejpam-6793	188	7	a	a	DET
ejpam-6793	188	8	sbsmp	sbsmp	ADJ
ejpam-6793	188	9	satisfies	satisfie	NOUN
ejpam-6793	188	10	(	(	PUNCT
ejpam-6793	188	11	21	21	NUM
ejpam-6793	188	12	)	)	PUNCT
ejpam-6793	188	13	.	.	PUNCT
ejpam-6793	189	1	then	then	ADV
ejpam-6793	189	2	the	the	DET
ejpam-6793	189	3	esbsmps	esbsmp	NOUN
ejpam-6793	189	4	{	{	PUNCT
ejpam-6793	189	5	qen(x	qen(x	PROPN
ejpam-6793	189	6	)	)	PUNCT
ejpam-6793	189	7	}	}	PUNCT
ejpam-6793	189	8	is	be	AUX
ejpam-6793	189	9	of	of	ADP
ejpam-6793	189	10	order	order	NOUN
ejpam-6793	189	11	γ	γ	X
ejpam-6793	189	12	≤	≤	NUM
ejpam-6793	189	13	λ	λ	PROPN
ejpam-6793	189	14	.	.	PUNCT
ejpam-6793	190	1	moreover	moreover	ADV
ejpam-6793	190	2	,	,	PUNCT
ejpam-6793	190	3	the	the	DET
ejpam-6793	190	4	value	value	NOUN
ejpam-6793	190	5	λ	λ	NOUN
ejpam-6793	190	6	is	be	AUX
ejpam-6793	190	7	attainable	attainable	ADJ
ejpam-6793	190	8	.	.	PUNCT
ejpam-6793	191	1	proof	proof	NOUN
ejpam-6793	191	2	.	.	PUNCT
ejpam-6793	192	1	applying	apply	VERB
ejpam-6793	192	2	(	(	PUNCT
ejpam-6793	192	3	22	22	NUM
ejpam-6793	192	4	)	)	PUNCT
ejpam-6793	192	5	in	in	ADP
ejpam-6793	192	6	(	(	PUNCT
ejpam-6793	192	7	16	16	NUM
ejpam-6793	192	8	)	)	PUNCT
ejpam-6793	192	9	,	,	PUNCT
ejpam-6793	192	10	we	we	PRON
ejpam-6793	192	11	get	get	VERB
ejpam-6793	192	12	∥qen∥r	∥qen∥r	PRON
ejpam-6793	192	13	≤	≤	ADJ
ejpam-6793	192	14	2	2	NUM
ejpam-6793	192	15	m	m	NUM
ejpam-6793	192	16	2	2	NUM
ejpam-6793	192	17	n∑	n∑	NOUN
ejpam-6793	192	18	k=0	k=0	PROPN
ejpam-6793	192	19	rk	rk	VERB
ejpam-6793	192	20			PROPN
ejpam-6793	192	21	∞∑	∞∑	NUM
ejpam-6793	192	22	j=0	j=0	PROPN
ejpam-6793	192	23	∣∣∣q(j	∣∣∣q(j	PROPN
ejpam-6793	192	24	)	)	PUNCT
ejpam-6793	192	25	n	n	CCONJ
ejpam-6793	192	26	,	,	PUNCT
ejpam-6793	192	27	k	k	PROPN
ejpam-6793	192	28	∣∣∣	∣∣∣	PROPN
ejpam-6793	192	29	j	j	PROPN
ejpam-6793	192	30	!	!	PUNCT
ejpam-6793	193	1			PROPN
ejpam-6793	193	2	≤	≤	NUM
ejpam-6793	194	1	n∑	n∑	PUNCT
ejpam-6793	194	2	k=0	k=0	PROPN
ejpam-6793	194	3	rk	rk	PROPN
ejpam-6793	194	4			NOUN
ejpam-6793	194	5	∞∑	∞∑	NUM
ejpam-6793	194	6	j=0	j=0	PROPN
ejpam-6793	194	7	(	(	PUNCT
ejpam-6793	194	8	2	2	NUM
ejpam-6793	194	9	m	m	NOUN
ejpam-6793	194	10	2	2	NUM
ejpam-6793	194	11	mc	mc	NOUN
ejpam-6793	194	12	)	)	PUNCT
ejpam-6793	195	1	j	j	PROPN
ejpam-6793	195	2	j	j	PROPN
ejpam-6793	195	3	!	!	PUNCT
ejpam-6793	195	4	nλ(n−k	nλ(n−k	PROPN
ejpam-6793	195	5	)	)	PUNCT
ejpam-6793	195	6			PROPN
ejpam-6793	195	7	≤	≤	PROPN
ejpam-6793	195	8	e2	e2	PROPN
ejpam-6793	195	9	m	m	VERB
ejpam-6793	195	10	2	2	NUM
ejpam-6793	195	11	mcnλn	mcnλn	NOUN
ejpam-6793	195	12	n∑	n∑	NOUN
ejpam-6793	195	13	k=0	k=0	PROPN
ejpam-6793	195	14	(	(	PUNCT
ejpam-6793	195	15	r	r	NOUN
ejpam-6793	195	16	nλ	nλ	NOUN
ejpam-6793	195	17	)	)	PUNCT
ejpam-6793	195	18	k	k	PROPN
ejpam-6793	195	19	≤	≤	PROPN
ejpam-6793	195	20	e2	e2	PROPN
ejpam-6793	195	21	m	m	PROPN
ejpam-6793	195	22	2	2	NUM
ejpam-6793	195	23	mcnλn(n+	mcnλn(n+	NOUN
ejpam-6793	195	24	1	1	NUM
ejpam-6793	195	25	)	)	PUNCT
ejpam-6793	195	26	=	=	SYM
ejpam-6793	195	27	k1(m	k1(m	PROPN
ejpam-6793	195	28	)	)	PUNCT
ejpam-6793	195	29	nλn(n+	nλn(n+	NOUN
ejpam-6793	195	30	1	1	NUM
ejpam-6793	195	31	)	)	PUNCT
ejpam-6793	195	32	,	,	PUNCT
ejpam-6793	195	33	for	for	ADP
ejpam-6793	195	34	nλ	nλ	INTJ
ejpam-6793	195	35	>	>	X
ejpam-6793	195	36	r.	r.	PROPN
ejpam-6793	195	37	(	(	PUNCT
ejpam-6793	195	38	23	23	NUM
ejpam-6793	195	39	)	)	PUNCT
ejpam-6793	195	40	where	where	SCONJ
ejpam-6793	195	41	k1(m	k1(m	X
ejpam-6793	195	42	)	)	PUNCT
ejpam-6793	195	43	=	=	SYM
ejpam-6793	195	44	e2	e2	PROPN
ejpam-6793	195	45	m	m	VERB
ejpam-6793	195	46	2	2	NUM
ejpam-6793	195	47	mc	mc	NOUN
ejpam-6793	195	48	.	.	PUNCT
ejpam-6793	196	1	introducing	introduce	VERB
ejpam-6793	196	2	(	(	PUNCT
ejpam-6793	196	3	22	22	NUM
ejpam-6793	196	4	)	)	PUNCT
ejpam-6793	196	5	and	and	CCONJ
ejpam-6793	196	6	(	(	PUNCT
ejpam-6793	196	7	23	23	NUM
ejpam-6793	196	8	)	)	PUNCT
ejpam-6793	196	9	in	in	ADP
ejpam-6793	196	10	the	the	DET
ejpam-6793	196	11	cannon	cannon	NOUN
ejpam-6793	196	12	sum	sum	NOUN
ejpam-6793	196	13	of	of	ADP
ejpam-6793	196	14	the	the	DET
ejpam-6793	196	15	esbsmp	esbsmp	NOUN
ejpam-6793	196	16	{	{	PUNCT
ejpam-6793	196	17	qen(x	qen(x	X
ejpam-6793	196	18	)	)	PUNCT
ejpam-6793	196	19	}	}	PUNCT
ejpam-6793	196	20	we	we	PRON
ejpam-6793	196	21	have	have	VERB
ejpam-6793	196	22	m.	m.	NOUN
ejpam-6793	196	23	zayed	zayed	PROPN
ejpam-6793	196	24	/	/	SYM
ejpam-6793	196	25	eur	eur	PROPN
ejpam-6793	196	26	.	.	PUNCT
ejpam-6793	197	1	j.	j.	PROPN
ejpam-6793	197	2	pure	pure	PROPN
ejpam-6793	197	3	appl	appl	PROPN
ejpam-6793	197	4	.	.	PROPN
ejpam-6793	197	5	math	math	PROPN
ejpam-6793	197	6	,	,	PUNCT
ejpam-6793	197	7	18	18	NUM
ejpam-6793	197	8	(	(	PUNCT
ejpam-6793	197	9	4	4	NUM
ejpam-6793	197	10	)	)	PUNCT
ejpam-6793	197	11	(	(	PUNCT
ejpam-6793	197	12	2025	2025	NUM
ejpam-6793	197	13	)	)	PUNCT
ejpam-6793	197	14	,	,	PUNCT
ejpam-6793	197	15	6793	6793	NUM
ejpam-6793	197	16	11	11	NUM
ejpam-6793	197	17	of	of	ADP
ejpam-6793	197	18	19	19	NUM
ejpam-6793	197	19	ω	ω	NOUN
ejpam-6793	197	20	(	(	PUNCT
ejpam-6793	197	21	qen	qen	PROPN
ejpam-6793	197	22	,	,	PUNCT
ejpam-6793	197	23	b̄(r	b̄(r	NOUN
ejpam-6793	197	24	)	)	PUNCT
ejpam-6793	197	25	)	)	PUNCT
ejpam-6793	198	1	≤	≤	ADV
ejpam-6793	198	2	2	2	NUM
ejpam-6793	198	3	m	m	NUM
ejpam-6793	198	4	2	2	NUM
ejpam-6793	198	5	n∑	n∑	NOUN
ejpam-6793	198	6	k=0	k=0	PROPN
ejpam-6793	198	7	∥qek∥r	∥qek∥r	VERB
ejpam-6793	198	8	∞∑	∞∑	NUM
ejpam-6793	198	9	j=0	j=0	PROPN
ejpam-6793	198	10	∣∣∣q(j	∣∣∣q(j	PROPN
ejpam-6793	198	11	)	)	PUNCT
ejpam-6793	198	12	n	n	CCONJ
ejpam-6793	198	13	,	,	PUNCT
ejpam-6793	198	14	k	k	PROPN
ejpam-6793	198	15	∣∣∣	∣∣∣	PROPN
ejpam-6793	198	16	j	j	PROPN
ejpam-6793	198	17	!	!	PUNCT
ejpam-6793	198	18	≤	≤	NUM
ejpam-6793	198	19	2	2	NUM
ejpam-6793	198	20	m	m	NUM
ejpam-6793	198	21	2	2	NUM
ejpam-6793	198	22	n∑	n∑	NOUN
ejpam-6793	198	23	k=0	k=0	PROPN
ejpam-6793	199	1	k1(m)kλk(k	k1(m)kλk(k	PROPN
ejpam-6793	200	1	+	+	CCONJ
ejpam-6793	200	2	1	1	X
ejpam-6793	200	3	)	)	PUNCT
ejpam-6793	200	4	∞∑	∞∑	NUM
ejpam-6793	200	5	j=0	j=0	PROPN
ejpam-6793	200	6	2−m/2	2−m/2	NUM
ejpam-6793	200	7			NOUN
ejpam-6793	200	8	(	(	PUNCT
ejpam-6793	200	9	2	2	NUM
ejpam-6793	200	10	m	m	NOUN
ejpam-6793	200	11	2	2	NUM
ejpam-6793	200	12	mc	mc	NOUN
ejpam-6793	200	13	)	)	PUNCT
ejpam-6793	200	14	j	j	PROPN
ejpam-6793	200	15	j	j	PROPN
ejpam-6793	200	16	!	!	PUNCT
ejpam-6793	200	17	nλ(n−k	nλ(n−k	PROPN
ejpam-6793	200	18	)	)	PUNCT
ejpam-6793	200	19			PROPN
ejpam-6793	200	20	≤	≤	PROPN
ejpam-6793	200	21	k2	k2	X
ejpam-6793	200	22	1	1	NUM
ejpam-6793	200	23	(	(	PUNCT
ejpam-6793	200	24	m)(n+	m)(n+	PROPN
ejpam-6793	200	25	1)2nλn	1)2nλn	NUM
ejpam-6793	200	26	(	(	PUNCT
ejpam-6793	200	27	24	24	NUM
ejpam-6793	200	28	)	)	PUNCT
ejpam-6793	200	29	when	when	SCONJ
ejpam-6793	200	30	n	n	NUM
ejpam-6793	200	31	approaches	approach	VERB
ejpam-6793	200	32	infinity	infinity	NOUN
ejpam-6793	200	33	,	,	PUNCT
ejpam-6793	200	34	and	and	CCONJ
ejpam-6793	200	35	using	use	VERB
ejpam-6793	200	36	the	the	DET
ejpam-6793	200	37	definition	definition	NOUN
ejpam-6793	200	38	of	of	ADP
ejpam-6793	200	39	the	the	DET
ejpam-6793	200	40	order	order	NOUN
ejpam-6793	200	41	,	,	PUNCT
ejpam-6793	200	42	it	it	PRON
ejpam-6793	200	43	follows	follow	VERB
ejpam-6793	200	44	that	that	SCONJ
ejpam-6793	200	45	the	the	DET
ejpam-6793	200	46	order	order	NOUN
ejpam-6793	200	47	γ	γ	X
ejpam-6793	200	48	of	of	ADP
ejpam-6793	200	49	esbsmps	esbsmp	NOUN
ejpam-6793	200	50	{	{	PUNCT
ejpam-6793	200	51	qen(x	qen(x	X
ejpam-6793	200	52	)	)	PUNCT
ejpam-6793	200	53	}	}	PUNCT
ejpam-6793	200	54	is	be	AUX
ejpam-6793	200	55	at	at	ADP
ejpam-6793	200	56	most	most	ADJ
ejpam-6793	200	57	λ	λ	NOUN
ejpam-6793	200	58	.	.	PUNCT
ejpam-6793	201	1	the	the	DET
ejpam-6793	201	2	following	follow	VERB
ejpam-6793	201	3	example	example	NOUN
ejpam-6793	201	4	demonstrates	demonstrate	VERB
ejpam-6793	201	5	the	the	DET
ejpam-6793	201	6	fact	fact	NOUN
ejpam-6793	201	7	that	that	SCONJ
ejpam-6793	201	8	the	the	DET
ejpam-6793	201	9	bound	bind	VERB
ejpam-6793	201	10	λ	λ	NOUN
ejpam-6793	201	11	is	be	AUX
ejpam-6793	201	12	attainable	attainable	ADJ
ejpam-6793	201	13	.	.	PUNCT
ejpam-6793	202	1	example	example	NOUN
ejpam-6793	202	2	2	2	NUM
ejpam-6793	202	3	.	.	X
ejpam-6793	203	1	consider	consider	VERB
ejpam-6793	203	2	the	the	DET
ejpam-6793	203	3	sbsmps	sbsmp	NOUN
ejpam-6793	203	4	{	{	PUNCT
ejpam-6793	203	5	qn(x	qn(x	X
ejpam-6793	203	6	)	)	PUNCT
ejpam-6793	203	7	}	}	PUNCT
ejpam-6793	203	8	given	give	VERB
ejpam-6793	203	9	by	by	ADP
ejpam-6793	203	10	qn	qn	PROPN
ejpam-6793	203	11	,	,	PUNCT
ejpam-6793	203	12	k	k	PROPN
ejpam-6793	203	13	=	=	PUNCT
ejpam-6793	203	14	{	{	PUNCT
ejpam-6793	203	15	m	m	NOUN
ejpam-6793	203	16	nλ(n−k	nλ(n−k	PROPN
ejpam-6793	203	17	)	)	PUNCT
ejpam-6793	203	18	n+1	n+1	NUM
ejpam-6793	203	19	αk	αk	NOUN
ejpam-6793	203	20	,	,	PUNCT
ejpam-6793	203	21	0	0	NUM
ejpam-6793	204	1	⩽	⩽	PROPN
ejpam-6793	205	1	k	k	X
ejpam-6793	205	2	<	<	X
ejpam-6793	205	3	n	n	PROPN
ejpam-6793	205	4	αn	αn	NOUN
ejpam-6793	205	5	,	,	PUNCT
ejpam-6793	205	6	k	k	PROPN
ejpam-6793	205	7	=	=	SYM
ejpam-6793	205	8	n	n	PROPN
ejpam-6793	205	9	(	(	PUNCT
ejpam-6793	205	10	25	25	NUM
ejpam-6793	205	11	)	)	PUNCT
ejpam-6793	205	12	where	where	SCONJ
ejpam-6793	205	13	αk	αk	NOUN
ejpam-6793	205	14	=	=	SYM
ejpam-6793	205	15	1	1	NUM
ejpam-6793	205	16	k+1	k+1	NOUN
ejpam-6793	205	17	and	and	CCONJ
ejpam-6793	205	18	αn	αn	NOUN
ejpam-6793	205	19	=	=	SYM
ejpam-6793	205	20	1	1	NUM
ejpam-6793	205	21	n+1	n+1	NUM
ejpam-6793	205	22	.	.	PUNCT
ejpam-6793	206	1	as	as	ADP
ejpam-6793	206	2	in	in	ADP
ejpam-6793	206	3	(	(	PUNCT
ejpam-6793	206	4	19	19	NUM
ejpam-6793	206	5	)	)	PUNCT
ejpam-6793	206	6	we	we	PRON
ejpam-6793	206	7	can	can	AUX
ejpam-6793	206	8	use	use	VERB
ejpam-6793	206	9	(	(	PUNCT
ejpam-6793	206	10	25	25	NUM
ejpam-6793	206	11	)	)	PUNCT
ejpam-6793	206	12	to	to	PART
ejpam-6793	206	13	prove	prove	VERB
ejpam-6793	206	14	by	by	ADP
ejpam-6793	206	15	mathematical	mathematical	ADJ
ejpam-6793	206	16	induction	induction	NOUN
ejpam-6793	206	17	that	that	SCONJ
ejpam-6793	206	18	q(j	q(j	PROPN
ejpam-6793	206	19	)	)	PUNCT
ejpam-6793	206	20	n,0	n,0	X
ejpam-6793	207	1	⩾	⩾	NOUN
ejpam-6793	207	2	nλn	nλn	NOUN
ejpam-6793	207	3	(	(	PUNCT
ejpam-6793	207	4	mαn	mαn	PROPN
ejpam-6793	207	5	)	)	PUNCT
ejpam-6793	207	6	j	j	PROPN
ejpam-6793	207	7	.	.	PUNCT
ejpam-6793	208	1	now	now	ADV
ejpam-6793	208	2	,	,	PUNCT
ejpam-6793	208	3	it	it	PRON
ejpam-6793	208	4	can	can	AUX
ejpam-6793	208	5	be	be	AUX
ejpam-6793	208	6	verified	verify	VERB
ejpam-6793	208	7	,	,	PUNCT
ejpam-6793	208	8	as	as	ADP
ejpam-6793	208	9	in	in	ADP
ejpam-6793	208	10	(	(	PUNCT
ejpam-6793	208	11	20	20	NUM
ejpam-6793	208	12	)	)	PUNCT
ejpam-6793	209	1	that	that	PRON
ejpam-6793	209	2	ω	ω	PROPN
ejpam-6793	209	3	(	(	PUNCT
ejpam-6793	209	4	qen	qen	PROPN
ejpam-6793	209	5	,	,	PUNCT
ejpam-6793	209	6	b̄(r	b̄(r	NOUN
ejpam-6793	209	7	)	)	PUNCT
ejpam-6793	209	8	)	)	PUNCT
ejpam-6793	209	9	⩾	⩾	PROPN
ejpam-6793	209	10	eαn	eαn	ADV
ejpam-6793	209	11	∑	∑	PUNCT
ejpam-6793	209	12	j=0	j=0	PROPN
ejpam-6793	209	13	q(j	q(j	PROPN
ejpam-6793	209	14	)	)	PUNCT
ejpam-6793	209	15	n,0	n,0	NOUN
ejpam-6793	210	1	j	j	PROPN
ejpam-6793	210	2	!	!	PROPN
ejpam-6793	210	3	≥	≥	PROPN
ejpam-6793	210	4	eαnnλn	eαnnλn	PROPN
ejpam-6793	210	5	∞∑	∞∑	NUM
ejpam-6793	210	6	j=0	j=0	PROPN
ejpam-6793	210	7	(	(	PUNCT
ejpam-6793	210	8	mαn	mαn	PROPN
ejpam-6793	210	9	)	)	PUNCT
ejpam-6793	210	10	j	j	PROPN
ejpam-6793	211	1	j	j	PROPN
ejpam-6793	211	2	!	!	PROPN
ejpam-6793	211	3	≥	≥	PROPN
ejpam-6793	212	1	e	e	X
ejpam-6793	212	2	1+m	1+m	NUM
ejpam-6793	212	3	1+n	1+n	NUM
ejpam-6793	212	4	nλn	nλn	NOUN
ejpam-6793	212	5	.	.	PUNCT
ejpam-6793	213	1	thus	thus	ADV
ejpam-6793	213	2	,	,	PUNCT
ejpam-6793	213	3	γ	γ	X
ejpam-6793	213	4	≥	≥	NOUN
ejpam-6793	213	5	λ	λ	PROPN
ejpam-6793	213	6	,	,	PUNCT
ejpam-6793	213	7	but	but	CCONJ
ejpam-6793	213	8	γ	γ	X
ejpam-6793	213	9	≤	≤	PROPN
ejpam-6793	213	10	λ	λ	NOUN
ejpam-6793	213	11	which	which	PRON
ejpam-6793	213	12	means	mean	VERB
ejpam-6793	213	13	that	that	SCONJ
ejpam-6793	213	14	γ	γ	PROPN
ejpam-6793	213	15	=	=	SYM
ejpam-6793	213	16	λ	λ	PROPN
ejpam-6793	213	17	and	and	CCONJ
ejpam-6793	213	18	the	the	DET
ejpam-6793	213	19	bound	bind	VERB
ejpam-6793	213	20	is	be	AUX
ejpam-6793	213	21	λ	λ	PROPN
ejpam-6793	213	22	is	be	AUX
ejpam-6793	213	23	attainable	attainable	ADJ
ejpam-6793	213	24	.	.	PUNCT
ejpam-6793	214	1	this	this	PRON
ejpam-6793	214	2	completes	complete	VERB
ejpam-6793	214	3	the	the	DET
ejpam-6793	214	4	proof	proof	NOUN
ejpam-6793	214	5	.	.	PUNCT
ejpam-6793	215	1	remark	remark	VERB
ejpam-6793	215	2	4	4	NUM
ejpam-6793	215	3	.	.	PUNCT
ejpam-6793	215	4	in	in	ADP
ejpam-6793	215	5	theorem	theorem	NOUN
ejpam-6793	215	6	3	3	NUM
ejpam-6793	215	7	,	,	PUNCT
ejpam-6793	215	8	if	if	SCONJ
ejpam-6793	215	9	{	{	PUNCT
ejpam-6793	215	10	qn(x	qn(x	X
ejpam-6793	215	11	)	)	PUNCT
ejpam-6793	215	12	}	}	PUNCT
ejpam-6793	215	13	is	be	AUX
ejpam-6793	215	14	a	a	DET
ejpam-6793	215	15	simple	simple	ADJ
ejpam-6793	215	16	monic	monic	ADJ
ejpam-6793	215	17	base	base	NOUN
ejpam-6793	215	18	(	(	PUNCT
ejpam-6793	215	19	qn	qn	NOUN
ejpam-6793	215	20	,	,	PUNCT
ejpam-6793	215	21	n	n	NOUN
ejpam-6793	215	22	=	=	SYM
ejpam-6793	215	23	1	1	NUM
ejpam-6793	215	24	for	for	ADP
ejpam-6793	215	25	n	n	PRON
ejpam-6793	215	26	∈	∈	PROPN
ejpam-6793	215	27	n	n	CCONJ
ejpam-6793	215	28	)	)	PUNCT
ejpam-6793	215	29	,	,	PUNCT
ejpam-6793	215	30	then	then	ADV
ejpam-6793	215	31	the	the	DET
ejpam-6793	215	32	result	result	NOUN
ejpam-6793	215	33	in	in	ADP
ejpam-6793	215	34	[	[	X
ejpam-6793	215	35	21	21	NUM
ejpam-6793	215	36	]	]	PUNCT
ejpam-6793	215	37	becomes	become	VERB
ejpam-6793	215	38	a	a	DET
ejpam-6793	215	39	particular	particular	ADJ
ejpam-6793	215	40	case	case	NOUN
ejpam-6793	215	41	of	of	ADP
ejpam-6793	215	42	our	our	PRON
ejpam-6793	215	43	theorem	theorem	ADJ
ejpam-6793	215	44	3	3	PROPN
ejpam-6793	215	45	.	.	PUNCT
ejpam-6793	215	46	m.	m.	NOUN
ejpam-6793	215	47	zayed	zayed	PROPN
ejpam-6793	215	48	/	/	SYM
ejpam-6793	215	49	eur	eur	PROPN
ejpam-6793	215	50	.	.	PUNCT
ejpam-6793	216	1	j.	j.	PROPN
ejpam-6793	216	2	pure	pure	PROPN
ejpam-6793	216	3	appl	appl	PROPN
ejpam-6793	216	4	.	.	PROPN
ejpam-6793	216	5	math	math	PROPN
ejpam-6793	216	6	,	,	PUNCT
ejpam-6793	216	7	18	18	NUM
ejpam-6793	216	8	(	(	PUNCT
ejpam-6793	216	9	4	4	NUM
ejpam-6793	216	10	)	)	PUNCT
ejpam-6793	216	11	(	(	PUNCT
ejpam-6793	216	12	2025	2025	NUM
ejpam-6793	216	13	)	)	PUNCT
ejpam-6793	216	14	,	,	PUNCT
ejpam-6793	216	15	6793	6793	NUM
ejpam-6793	216	16	12	12	NUM
ejpam-6793	216	17	of	of	ADP
ejpam-6793	216	18	19	19	NUM
ejpam-6793	216	19	4	4	NUM
ejpam-6793	216	20	.	.	PUNCT
ejpam-6793	216	21	effectiveness	effectiveness	NOUN
ejpam-6793	216	22	of	of	ADP
ejpam-6793	216	23	the	the	DET
ejpam-6793	216	24	the	the	DET
ejpam-6793	216	25	exponential	exponential	ADJ
ejpam-6793	216	26	cannon	cannon	NOUN
ejpam-6793	216	27	base	base	NOUN
ejpam-6793	216	28	of	of	ADP
ejpam-6793	216	29	special	special	ADJ
ejpam-6793	216	30	monogenic	monogenic	ADJ
ejpam-6793	216	31	polynomials	polynomial	NOUN
ejpam-6793	216	32	in	in	ADP
ejpam-6793	216	33	the	the	DET
ejpam-6793	216	34	current	current	ADJ
ejpam-6793	216	35	section	section	NOUN
ejpam-6793	217	1	,	,	PUNCT
ejpam-6793	217	2	we	we	PRON
ejpam-6793	217	3	study	study	VERB
ejpam-6793	217	4	the	the	DET
ejpam-6793	217	5	convergence	convergence	NOUN
ejpam-6793	217	6	properties	property	NOUN
ejpam-6793	217	7	of	of	ADP
ejpam-6793	217	8	the	the	DET
ejpam-6793	217	9	ecbsmps	ecbsmp	NOUN
ejpam-6793	217	10	for	for	ADP
ejpam-6793	217	11	the	the	DET
ejpam-6793	217	12	f	f	NOUN
ejpam-6793	217	13	-	-	PUNCT
ejpam-6793	217	14	modules	module	NOUN
ejpam-6793	217	15	wb̄(r	wb̄(r	NOUN
ejpam-6793	217	16	)	)	PUNCT
ejpam-6793	217	17	,	,	PUNCT
ejpam-6793	217	18	wb(r	wb(r	NUM
ejpam-6793	217	19	)	)	PUNCT
ejpam-6793	217	20	,	,	PUNCT
ejpam-6793	217	21	wb+(r	wb+(r	PROPN
ejpam-6793	217	22	)	)	PUNCT
ejpam-6793	217	23	,	,	PUNCT
ejpam-6793	217	24	w0	w0	PROPN
ejpam-6793	217	25	+	+	CCONJ
ejpam-6793	217	26	and	and	CCONJ
ejpam-6793	217	27	w∞.	w∞.	NOUN
ejpam-6793	217	28	theorem	theorem	ADJ
ejpam-6793	217	29	4	4	NUM
ejpam-6793	217	30	.	.	PUNCT
ejpam-6793	218	1	the	the	DET
ejpam-6793	218	2	ecbsmps	ecbsmp	NOUN
ejpam-6793	218	3	{	{	PUNCT
ejpam-6793	218	4	qen(x	qen(x	X
ejpam-6793	218	5	)	)	PUNCT
ejpam-6793	218	6	}	}	PUNCT
ejpam-6793	218	7	is	be	AUX
ejpam-6793	218	8	effective	effective	ADJ
ejpam-6793	218	9	for	for	ADP
ejpam-6793	218	10	wb̄(r	wb̄(r	NOUN
ejpam-6793	218	11	)	)	PUNCT
ejpam-6793	218	12	for	for	ADP
ejpam-6793	218	13	all	all	DET
ejpam-6793	218	14	b	b	NOUN
ejpam-6793	218	15	⩽	⩽	NOUN
ejpam-6793	218	16	r	r	NOUN
ejpam-6793	218	17	<	<	X
ejpam-6793	218	18	b	b	X
ejpam-6793	218	19	a	a	PRON
ejpam-6793	218	20	if	if	SCONJ
ejpam-6793	218	21	the	the	DET
ejpam-6793	218	22	cannon	cannon	NOUN
ejpam-6793	218	23	base	base	NOUN
ejpam-6793	218	24	{	{	PUNCT
ejpam-6793	218	25	qn(x	qn(x	NOUN
ejpam-6793	218	26	)	)	PUNCT
ejpam-6793	218	27	}	}	PUNCT
ejpam-6793	218	28	satisfy	satisfy	VERB
ejpam-6793	218	29	|qn	|qn	NUM
ejpam-6793	218	30	,	,	PUNCT
ejpam-6793	218	31	k|	k|	NOUN
ejpam-6793	218	32	≤m	≤m	NOUN
ejpam-6793	218	33	bn−kak	bn−kak	PROPN
ejpam-6793	218	34	,	,	PUNCT
ejpam-6793	218	35	0	0	PUNCT
ejpam-6793	218	36	<	<	X
ejpam-6793	218	37	a	a	DET
ejpam-6793	218	38	<	<	X
ejpam-6793	218	39	1	1	NUM
ejpam-6793	218	40	(	(	PUNCT
ejpam-6793	218	41	26	26	NUM
ejpam-6793	218	42	)	)	PUNCT
ejpam-6793	218	43	and	and	CCONJ
ejpam-6793	218	44	may	may	AUX
ejpam-6793	218	45	not	not	PART
ejpam-6793	218	46	be	be	AUX
ejpam-6793	218	47	effective	effective	ADJ
ejpam-6793	218	48	for	for	ADP
ejpam-6793	218	49	wb̄(r	wb̄(r	NOUN
ejpam-6793	218	50	)	)	PUNCT
ejpam-6793	218	51	for	for	ADP
ejpam-6793	218	52	all	all	DET
ejpam-6793	218	53	r	r	NOUN
ejpam-6793	218	54	<	<	X
ejpam-6793	218	55	b	b	NOUN
ejpam-6793	218	56	or	or	CCONJ
ejpam-6793	218	57	r	r	NOUN
ejpam-6793	218	58	⩾	⩾	PROPN
ejpam-6793	218	59	b	b	NOUN
ejpam-6793	218	60	a	a	PRON
ejpam-6793	218	61	.	.	PUNCT
ejpam-6793	219	1	proof	proof	NOUN
ejpam-6793	219	2	.	.	PUNCT
ejpam-6793	220	1	suppose	suppose	VERB
ejpam-6793	220	2	that	that	SCONJ
ejpam-6793	220	3	{	{	PUNCT
ejpam-6793	220	4	qn(x	qn(x	NOUN
ejpam-6793	220	5	)	)	PUNCT
ejpam-6793	220	6	}	}	PUNCT
ejpam-6793	220	7	is	be	AUX
ejpam-6793	220	8	a	a	DET
ejpam-6793	220	9	cannon	cannon	NOUN
ejpam-6793	220	10	base	base	NOUN
ejpam-6793	220	11	,	,	PUNCT
ejpam-6793	220	12	the	the	DET
ejpam-6793	220	13	relation	relation	NOUN
ejpam-6793	220	14	(	(	PUNCT
ejpam-6793	220	15	14	14	NUM
ejpam-6793	220	16	)	)	PUNCT
ejpam-6793	220	17	has	have	VERB
ejpam-6793	220	18	the	the	DET
ejpam-6793	220	19	form	form	NOUN
ejpam-6793	220	20	q(j	q(j	PROPN
ejpam-6793	220	21	)	)	PUNCT
ejpam-6793	220	22	n	n	CCONJ
ejpam-6793	220	23	,	,	PUNCT
ejpam-6793	220	24	k	k	X
ejpam-6793	220	25	=	=	PUNCT
ejpam-6793	220	26	∞∑	∞∑	NUM
ejpam-6793	220	27	t=0	t=0	PUNCT
ejpam-6793	220	28	q(j−1	q(j−1	PROPN
ejpam-6793	220	29	)	)	PUNCT
ejpam-6793	220	30	t	t	PROPN
ejpam-6793	220	31	,	,	PUNCT
ejpam-6793	220	32	k	k	PROPN
ejpam-6793	220	33	qn	qn	PROPN
ejpam-6793	220	34	,	,	PUNCT
ejpam-6793	220	35	t	t	PROPN
ejpam-6793	220	36	(	(	PUNCT
ejpam-6793	220	37	27	27	NUM
ejpam-6793	220	38	)	)	PUNCT
ejpam-6793	220	39	thus	thus	ADV
ejpam-6793	220	40	,	,	PUNCT
ejpam-6793	220	41	as	as	ADP
ejpam-6793	220	42	in	in	ADP
ejpam-6793	220	43	(	(	PUNCT
ejpam-6793	220	44	13	13	NUM
ejpam-6793	220	45	)	)	PUNCT
ejpam-6793	220	46	,	,	PUNCT
ejpam-6793	220	47	applying	apply	VERB
ejpam-6793	220	48	(	(	PUNCT
ejpam-6793	220	49	26	26	NUM
ejpam-6793	220	50	)	)	PUNCT
ejpam-6793	220	51	,	,	PUNCT
ejpam-6793	220	52	we	we	PRON
ejpam-6793	220	53	obtain	obtain	VERB
ejpam-6793	220	54	the	the	DET
ejpam-6793	220	55	following	follow	VERB
ejpam-6793	220	56	inequality∣∣∣q(j	inequality∣∣∣q(j	NOUN
ejpam-6793	220	57	)	)	PUNCT
ejpam-6793	220	58	n	n	CCONJ
ejpam-6793	220	59	,	,	PUNCT
ejpam-6793	220	60	k	k	PROPN
ejpam-6793	220	61	∣∣∣	∣∣∣	PROPN
ejpam-6793	220	62	⩽m	⩽m	PROPN
ejpam-6793	220	63	j(1−	j(1−	ADJ
ejpam-6793	220	64	a)−(j−1)bn−kak	a)−(j−1)bn−kak	ADJ
ejpam-6793	220	65	.	.	PUNCT
ejpam-6793	221	1	(	(	PUNCT
ejpam-6793	221	2	28	28	NUM
ejpam-6793	221	3	)	)	PUNCT
ejpam-6793	221	4	using	use	VERB
ejpam-6793	221	5	(	(	PUNCT
ejpam-6793	221	6	28	28	NUM
ejpam-6793	221	7	)	)	PUNCT
ejpam-6793	221	8	,	,	PUNCT
ejpam-6793	221	9	we	we	PRON
ejpam-6793	221	10	get	get	VERB
ejpam-6793	221	11	∥qen∥r	∥qen∥r	PRON
ejpam-6793	221	12	≤	≤	ADJ
ejpam-6793	221	13	2	2	NUM
ejpam-6793	221	14	m	m	NOUN
ejpam-6793	221	15	2	2	NUM
ejpam-6793	221	16	∑	∑	PART
ejpam-6793	221	17	k	k	PROPN
ejpam-6793	221	18	rk	rk	NOUN
ejpam-6793	221	19			PROPN
ejpam-6793	221	20	∞∑	∞∑	NUM
ejpam-6793	221	21	j=0	j=0	PROPN
ejpam-6793	221	22	∣∣∣q(j	∣∣∣q(j	PROPN
ejpam-6793	221	23	)	)	PUNCT
ejpam-6793	221	24	n	n	CCONJ
ejpam-6793	221	25	,	,	PUNCT
ejpam-6793	221	26	k	k	PROPN
ejpam-6793	221	27	∣∣∣	∣∣∣	PROPN
ejpam-6793	221	28	j	j	PROPN
ejpam-6793	221	29	!	!	PUNCT
ejpam-6793	222	1			PROPN
ejpam-6793	222	2	≤	≤	ADJ
ejpam-6793	222	3	2	2	NUM
ejpam-6793	222	4	m	m	NOUN
ejpam-6793	222	5	2	2	NUM
ejpam-6793	222	6	em(1−a)−1	em(1−a)−1	NOUN
ejpam-6793	222	7	(	(	PUNCT
ejpam-6793	222	8	1−	1−	NUM
ejpam-6793	222	9	a	a	NOUN
ejpam-6793	222	10	)	)	PUNCT
ejpam-6793	222	11	∑	∑	PUNCT
ejpam-6793	222	12	k	k	PROPN
ejpam-6793	222	13	rkbn−kak	rkbn−kak	PROPN
ejpam-6793	222	14	=	=	PUNCT
ejpam-6793	222	15	2	2	NUM
ejpam-6793	222	16	m	m	NOUN
ejpam-6793	222	17	2	2	NUM
ejpam-6793	222	18	em(1−a)−1	em(1−a)−1	NOUN
ejpam-6793	222	19	(	(	PUNCT
ejpam-6793	222	20	1−	1−	NUM
ejpam-6793	222	21	a	a	NOUN
ejpam-6793	222	22	)	)	PUNCT
ejpam-6793	222	23	∑	∑	ADJ
ejpam-6793	222	24	k≤n	k≤n	NOUN
ejpam-6793	222	25	(	(	PUNCT
ejpam-6793	222	26	b	b	NOUN
ejpam-6793	222	27	r	r	NOUN
ejpam-6793	222	28	)	)	PUNCT
ejpam-6793	222	29	n−k	n−k	NOUN
ejpam-6793	222	30	ak	ak	PROPN
ejpam-6793	222	31	+	+	PROPN
ejpam-6793	222	32	∑	∑	PROPN
ejpam-6793	222	33	k	k	X
ejpam-6793	222	34	>	>	X
ejpam-6793	222	35	n	n	PROPN
ejpam-6793	222	36	(	(	PUNCT
ejpam-6793	222	37	b	b	NOUN
ejpam-6793	222	38	r	r	NOUN
ejpam-6793	222	39	)	)	PUNCT
ejpam-6793	222	40	n(ra	n(ra	PROPN
ejpam-6793	222	41	b	b	PROPN
ejpam-6793	222	42	)	)	PUNCT
ejpam-6793	222	43	k	k	X
ejpam-6793	222	44	]	]	PUNCT
ejpam-6793	222	45	rn	rn	PROPN
ejpam-6793	222	46	=	=	PRON
ejpam-6793	222	47	k2r	k2r	PROPN
ejpam-6793	222	48	n	n	CCONJ
ejpam-6793	222	49	,	,	PUNCT
ejpam-6793	222	50	for	for	ADP
ejpam-6793	222	51	all	all	DET
ejpam-6793	222	52	b	b	NOUN
ejpam-6793	222	53	≤	≤	NUM
ejpam-6793	222	54	r	r	NOUN
ejpam-6793	222	55	<	<	X
ejpam-6793	222	56	b	b	X
ejpam-6793	222	57	a	a	PRON
ejpam-6793	222	58	.	.	PUNCT
ejpam-6793	223	1	(	(	PUNCT
ejpam-6793	223	2	29	29	NUM
ejpam-6793	223	3	)	)	PUNCT
ejpam-6793	223	4	where	where	SCONJ
ejpam-6793	223	5	k2	k2	NOUN
ejpam-6793	223	6	=	=	SYM
ejpam-6793	223	7	2	2	NUM
ejpam-6793	223	8	m	m	NOUN
ejpam-6793	223	9	2	2	NUM
ejpam-6793	223	10	em(1−a)−1	em(1−a)−1	NOUN
ejpam-6793	223	11	(	(	PUNCT
ejpam-6793	223	12	1−	1−	NUM
ejpam-6793	223	13	a	a	NOUN
ejpam-6793	223	14	)	)	PUNCT
ejpam-6793	223	15	∑	∑	ADJ
ejpam-6793	223	16	k≤n	k≤n	NOUN
ejpam-6793	223	17	(	(	PUNCT
ejpam-6793	223	18	b	b	NOUN
ejpam-6793	223	19	r	r	NOUN
ejpam-6793	223	20	)	)	PUNCT
ejpam-6793	223	21	n−k	n−k	NOUN
ejpam-6793	223	22	ak	ak	PROPN
ejpam-6793	223	23	+	+	PROPN
ejpam-6793	223	24	∑	∑	PROPN
ejpam-6793	223	25	k	k	X
ejpam-6793	223	26	>	>	X
ejpam-6793	223	27	n	n	PROPN
ejpam-6793	223	28	(	(	PUNCT
ejpam-6793	223	29	b	b	NOUN
ejpam-6793	223	30	r	r	NOUN
ejpam-6793	223	31	)	)	PUNCT
ejpam-6793	223	32	n(ra	n(ra	PROPN
ejpam-6793	223	33	b	b	PROPN
ejpam-6793	223	34	)	)	PUNCT
ejpam-6793	223	35	k	k	PROPN
ejpam-6793	223	36			NOUN
ejpam-6793	223	37	.	.	PUNCT
ejpam-6793	224	1	hence	hence	ADV
ejpam-6793	224	2	,	,	PUNCT
ejpam-6793	224	3	making	make	VERB
ejpam-6793	224	4	use	use	NOUN
ejpam-6793	224	5	of	of	ADP
ejpam-6793	224	6	of	of	ADP
ejpam-6793	224	7	(	(	PUNCT
ejpam-6793	224	8	28	28	NUM
ejpam-6793	224	9	)	)	PUNCT
ejpam-6793	224	10	and	and	CCONJ
ejpam-6793	224	11	(	(	PUNCT
ejpam-6793	224	12	29	29	NUM
ejpam-6793	224	13	)	)	PUNCT
ejpam-6793	224	14	in	in	ADP
ejpam-6793	224	15	ωn	ωn	ADP
ejpam-6793	224	16	(	(	PUNCT
ejpam-6793	224	17	qen	qen	PROPN
ejpam-6793	224	18	,	,	PUNCT
ejpam-6793	224	19	b̄(r	b̄(r	NOUN
ejpam-6793	224	20	)	)	PUNCT
ejpam-6793	224	21	)	)	PUNCT
ejpam-6793	224	22	of	of	ADP
ejpam-6793	224	23	the	the	DET
ejpam-6793	224	24	exponential	exponential	ADJ
ejpam-6793	224	25	base	base	NOUN
ejpam-6793	224	26	{	{	PUNCT
ejpam-6793	224	27	qen(x	qen(x	X
ejpam-6793	224	28	)	)	PUNCT
ejpam-6793	224	29	}	}	PUNCT
ejpam-6793	224	30	associated	associate	VERB
ejpam-6793	224	31	with	with	ADP
ejpam-6793	224	32	the	the	DET
ejpam-6793	224	33	cannon	cannon	NOUN
ejpam-6793	224	34	base	base	NOUN
ejpam-6793	224	35	{	{	PUNCT
ejpam-6793	224	36	qn(x	qn(x	NOUN
ejpam-6793	224	37	)	)	PUNCT
ejpam-6793	224	38	}	}	PUNCT
ejpam-6793	224	39	yields	yield	NOUN
ejpam-6793	224	40	.	.	PUNCT
ejpam-6793	225	1	ωn	ωn	PRON
ejpam-6793	225	2	(	(	PUNCT
ejpam-6793	225	3	qen	qen	PROPN
ejpam-6793	225	4	,	,	PUNCT
ejpam-6793	225	5	b̄(r	b̄(r	NOUN
ejpam-6793	225	6	)	)	PUNCT
ejpam-6793	225	7	)	)	PUNCT
ejpam-6793	225	8	≤	≤	ADV
ejpam-6793	226	1	2	2	NUM
ejpam-6793	226	2	m	m	NOUN
ejpam-6793	226	3	2	2	NUM
ejpam-6793	226	4	∑	∑	PUNCT
ejpam-6793	226	5	k	k	PROPN
ejpam-6793	226	6	∥qek∥r	∥qek∥r	PROPN
ejpam-6793	226	7	∣∣qēn	∣∣qēn	PROPN
ejpam-6793	226	8	,	,	PUNCT
ejpam-6793	226	9	k	k	X
ejpam-6793	226	10	∣∣	∣∣	X
ejpam-6793	226	11	m.	m.	NOUN
ejpam-6793	226	12	zayed	zayed	PROPN
ejpam-6793	226	13	/	/	SYM
ejpam-6793	226	14	eur	eur	PROPN
ejpam-6793	226	15	.	.	PUNCT
ejpam-6793	227	1	j.	j.	PROPN
ejpam-6793	227	2	pure	pure	PROPN
ejpam-6793	227	3	appl	appl	PROPN
ejpam-6793	227	4	.	.	PROPN
ejpam-6793	227	5	math	math	PROPN
ejpam-6793	227	6	,	,	PUNCT
ejpam-6793	227	7	18	18	NUM
ejpam-6793	227	8	(	(	PUNCT
ejpam-6793	227	9	4	4	NUM
ejpam-6793	227	10	)	)	PUNCT
ejpam-6793	227	11	(	(	PUNCT
ejpam-6793	227	12	2025	2025	NUM
ejpam-6793	227	13	)	)	PUNCT
ejpam-6793	227	14	,	,	PUNCT
ejpam-6793	227	15	6793	6793	NUM
ejpam-6793	227	16	13	13	NUM
ejpam-6793	227	17	of	of	ADP
ejpam-6793	227	18	19	19	NUM
ejpam-6793	227	19	≤	≤	NUM
ejpam-6793	227	20	2	2	NUM
ejpam-6793	227	21	m	m	NOUN
ejpam-6793	227	22	2	2	NUM
ejpam-6793	227	23	∑	∑	PUNCT
ejpam-6793	227	24	k	k	PROPN
ejpam-6793	227	25	∥qek∥r	∥qek∥r	VERB
ejpam-6793	227	26	∞∑	∞∑	NUM
ejpam-6793	227	27	j=0	j=0	PROPN
ejpam-6793	227	28	∣∣∣q(j	∣∣∣q(j	PROPN
ejpam-6793	227	29	)	)	PUNCT
ejpam-6793	227	30	n	n	CCONJ
ejpam-6793	227	31	,	,	PUNCT
ejpam-6793	227	32	k	k	PROPN
ejpam-6793	227	33	∣∣∣	∣∣∣	PROPN
ejpam-6793	227	34	j	j	PROPN
ejpam-6793	227	35	!	!	PUNCT
ejpam-6793	227	36	≤	≤	PROPN
ejpam-6793	228	1	k2	k2	PROPN
ejpam-6793	228	2	e	e	PROPN
ejpam-6793	228	3	m(1−a)−1	m(1−a)−1	PROPN
ejpam-6793	228	4	(	(	PUNCT
ejpam-6793	228	5	1−	1−	NUM
ejpam-6793	228	6	a	a	NOUN
ejpam-6793	228	7	)	)	PUNCT
ejpam-6793	228	8	∑	∑	PUNCT
ejpam-6793	228	9	k	k	PROPN
ejpam-6793	228	10	rkbn−kak	rkbn−kak	PROPN
ejpam-6793	228	11	≤	≤	PROPN
ejpam-6793	228	12	k2	k2	ADJ
ejpam-6793	228	13	2	2	NUM
ejpam-6793	228	14	r	r	NOUN
ejpam-6793	228	15	n	n	NOUN
ejpam-6793	228	16	for	for	ADP
ejpam-6793	228	17	all	all	DET
ejpam-6793	228	18	b	b	NOUN
ejpam-6793	228	19	≤	≤	NUM
ejpam-6793	228	20	r	r	NOUN
ejpam-6793	228	21	<	<	X
ejpam-6793	228	22	b	b	X
ejpam-6793	228	23	a	a	NOUN
ejpam-6793	228	24	.	.	PUNCT
ejpam-6793	229	1	thus	thus	ADV
ejpam-6793	229	2	,	,	PUNCT
ejpam-6793	229	3	the	the	DET
ejpam-6793	229	4	cannon	cannon	NOUN
ejpam-6793	229	5	function	function	NOUN
ejpam-6793	229	6	for	for	ADP
ejpam-6793	229	7	{	{	PUNCT
ejpam-6793	229	8	qen(x	qen(x	NOUN
ejpam-6793	229	9	)	)	PUNCT
ejpam-6793	229	10	}	}	PUNCT
ejpam-6793	229	11	satisfies	satisfy	VERB
ejpam-6793	229	12	ω	ω	PROPN
ejpam-6793	229	13	(	(	PUNCT
ejpam-6793	229	14	qe	qe	PROPN
ejpam-6793	229	15	,	,	PUNCT
ejpam-6793	229	16	b̄(r	b̄(r	NOUN
ejpam-6793	229	17	)	)	PUNCT
ejpam-6793	229	18	)	)	PUNCT
ejpam-6793	229	19	≤	≤	NOUN
ejpam-6793	229	20	r	r	NOUN
ejpam-6793	229	21	,	,	PUNCT
ejpam-6793	229	22	but	but	CCONJ
ejpam-6793	229	23	ω	ω	NUM
ejpam-6793	229	24	(	(	PUNCT
ejpam-6793	229	25	qe	qe	PROPN
ejpam-6793	229	26	,	,	PUNCT
ejpam-6793	229	27	b̄(r	b̄(r	NOUN
ejpam-6793	229	28	)	)	PUNCT
ejpam-6793	229	29	)	)	PUNCT
ejpam-6793	229	30	≥	≥	PROPN
ejpam-6793	229	31	r.	r.	PROPN
ejpam-6793	229	32	therefore	therefore	ADV
ejpam-6793	229	33	,	,	PUNCT
ejpam-6793	229	34	ω	ω	PROPN
ejpam-6793	229	35	(	(	PUNCT
ejpam-6793	229	36	qe	qe	PROPN
ejpam-6793	229	37	,	,	PUNCT
ejpam-6793	229	38	b̄(r	b̄(r	NOUN
ejpam-6793	229	39	)	)	PUNCT
ejpam-6793	229	40	)	)	PUNCT
ejpam-6793	230	1	=	=	SYM
ejpam-6793	230	2	r	r	NOUN
ejpam-6793	230	3	,	,	PUNCT
ejpam-6793	230	4	for	for	ADP
ejpam-6793	230	5	b	b	NOUN
ejpam-6793	230	6	≤	≤	NUM
ejpam-6793	230	7	r	r	NOUN
ejpam-6793	230	8	<	<	X
ejpam-6793	230	9	b	b	X
ejpam-6793	230	10	a	a	NOUN
ejpam-6793	230	11	,	,	PUNCT
ejpam-6793	230	12	and	and	CCONJ
ejpam-6793	230	13	the	the	DET
ejpam-6793	230	14	ecbsmps	ecbsmp	NOUN
ejpam-6793	230	15	{	{	PUNCT
ejpam-6793	230	16	qen(x	qen(x	X
ejpam-6793	230	17	)	)	PUNCT
ejpam-6793	230	18	}	}	PUNCT
ejpam-6793	230	19	is	be	AUX
ejpam-6793	230	20	effective	effective	ADJ
ejpam-6793	230	21	for	for	ADP
ejpam-6793	230	22	wb̄(r	wb̄(r	NOUN
ejpam-6793	230	23	)	)	PUNCT
ejpam-6793	230	24	for	for	ADP
ejpam-6793	230	25	b	b	NOUN
ejpam-6793	230	26	≤	≤	NUM
ejpam-6793	230	27	r	r	NOUN
ejpam-6793	230	28	<	<	X
ejpam-6793	230	29	b	b	X
ejpam-6793	230	30	a	a	NOUN
ejpam-6793	230	31	.	.	PUNCT
ejpam-6793	231	1	when	when	SCONJ
ejpam-6793	231	2	r	r	NOUN
ejpam-6793	231	3	<	<	X
ejpam-6793	231	4	b	b	NOUN
ejpam-6793	231	5	or	or	CCONJ
ejpam-6793	231	6	r	r	NOUN
ejpam-6793	231	7	⩾	⩾	PROPN
ejpam-6793	231	8	b	b	NOUN
ejpam-6793	231	9	a	a	PRON
ejpam-6793	231	10	,	,	PUNCT
ejpam-6793	231	11	the	the	DET
ejpam-6793	231	12	ecbsmps	ecbsmp	NOUN
ejpam-6793	231	13	{	{	PUNCT
ejpam-6793	231	14	qen(x	qen(x	X
ejpam-6793	231	15	)	)	PUNCT
ejpam-6793	231	16	}	}	PUNCT
ejpam-6793	231	17	may	may	AUX
ejpam-6793	231	18	not	not	PART
ejpam-6793	231	19	be	be	AUX
ejpam-6793	231	20	effective	effective	ADJ
ejpam-6793	231	21	in	in	ADP
ejpam-6793	231	22	for	for	ADP
ejpam-6793	231	23	wb̄(r	wb̄(r	NOUN
ejpam-6793	231	24	)	)	PUNCT
ejpam-6793	231	25	.	.	PUNCT
ejpam-6793	232	1	to	to	PART
ejpam-6793	232	2	show	show	VERB
ejpam-6793	232	3	this	this	DET
ejpam-6793	232	4	fact	fact	NOUN
ejpam-6793	232	5	consider	consider	VERB
ejpam-6793	232	6	the	the	DET
ejpam-6793	232	7	cbsmps	cbsmp	NOUN
ejpam-6793	232	8	{	{	PUNCT
ejpam-6793	232	9	qn(x	qn(x	NOUN
ejpam-6793	232	10	)	)	PUNCT
ejpam-6793	232	11	}	}	PUNCT
ejpam-6793	232	12	for	for	ADP
ejpam-6793	232	13	which	which	PRON
ejpam-6793	232	14	qn	qn	PROPN
ejpam-6793	232	15	,	,	PUNCT
ejpam-6793	232	16	k	k	NOUN
ejpam-6793	232	17	=	=	X
ejpam-6793	232	18	{	{	PUNCT
ejpam-6793	232	19	1	1	NUM
ejpam-6793	232	20	,	,	PUNCT
ejpam-6793	232	21	k	k	NOUN
ejpam-6793	232	22	=	=	PUNCT
ejpam-6793	232	23	0	0	NUM
ejpam-6793	232	24	mbn−kak	mbn−kak	NOUN
ejpam-6793	232	25	,	,	PUNCT
ejpam-6793	232	26	k	k	PROPN
ejpam-6793	232	27	̸=	̸=	PROPN
ejpam-6793	232	28	0	0	NUM
ejpam-6793	232	29	.	.	PUNCT
ejpam-6793	233	1	similar	similar	ADJ
ejpam-6793	233	2	steps	step	NOUN
ejpam-6793	233	3	as	as	ADP
ejpam-6793	233	4	in	in	ADP
ejpam-6793	233	5	(	(	PUNCT
ejpam-6793	233	6	20	20	NUM
ejpam-6793	233	7	)	)	PUNCT
ejpam-6793	233	8	can	can	AUX
ejpam-6793	233	9	be	be	AUX
ejpam-6793	233	10	obtained	obtain	VERB
ejpam-6793	233	11	ω	ω	PROPN
ejpam-6793	233	12	(	(	PUNCT
ejpam-6793	233	13	qe	qe	PROPN
ejpam-6793	233	14	,	,	PUNCT
ejpam-6793	233	15	b̄(r	b̄(r	NOUN
ejpam-6793	233	16	)	)	PUNCT
ejpam-6793	233	17	)	)	PUNCT
ejpam-6793	234	1	>	>	PUNCT
ejpam-6793	235	1	r	r	NOUN
ejpam-6793	235	2	for	for	ADP
ejpam-6793	235	3	r	r	NOUN
ejpam-6793	235	4	<	<	X
ejpam-6793	235	5	b	b	NOUN
ejpam-6793	235	6	,	,	PUNCT
ejpam-6793	235	7	and	and	CCONJ
ejpam-6793	235	8	the	the	DET
ejpam-6793	235	9	ecbsmps	ecbsmp	NOUN
ejpam-6793	235	10	{	{	PUNCT
ejpam-6793	235	11	qen(x	qen(x	X
ejpam-6793	235	12	)	)	PUNCT
ejpam-6793	235	13	}	}	PUNCT
ejpam-6793	235	14	is	be	AUX
ejpam-6793	235	15	not	not	PART
ejpam-6793	235	16	effective	effective	ADJ
ejpam-6793	235	17	for	for	ADP
ejpam-6793	235	18	wb̄(r	wb̄(r	NOUN
ejpam-6793	235	19	)	)	PUNCT
ejpam-6793	235	20	.	.	PUNCT
ejpam-6793	236	1	also	also	ADV
ejpam-6793	236	2	,	,	PUNCT
ejpam-6793	236	3	ω	ω	PROPN
ejpam-6793	236	4	(	(	PUNCT
ejpam-6793	236	5	qe	qe	PROPN
ejpam-6793	236	6	,	,	PUNCT
ejpam-6793	236	7	b̄(r	b̄(r	NOUN
ejpam-6793	236	8	)	)	PUNCT
ejpam-6793	236	9	)	)	PUNCT
ejpam-6793	237	1	=	=	PUNCT
ejpam-6793	237	2	∞	∞	PROPN
ejpam-6793	237	3	for	for	ADP
ejpam-6793	237	4	r	r	PROPN
ejpam-6793	237	5	≥	≥	PROPN
ejpam-6793	237	6	b	b	NOUN
ejpam-6793	237	7	a	a	NOUN
ejpam-6793	237	8	and	and	CCONJ
ejpam-6793	237	9	the	the	DET
ejpam-6793	237	10	ecbsmps	ecbsmp	NOUN
ejpam-6793	237	11	{	{	PUNCT
ejpam-6793	237	12	qn(x	qn(x	NOUN
ejpam-6793	237	13	)	)	PUNCT
ejpam-6793	237	14	}	}	PUNCT
ejpam-6793	237	15	is	be	AUX
ejpam-6793	237	16	not	not	PART
ejpam-6793	237	17	effective	effective	ADJ
ejpam-6793	237	18	for	for	ADP
ejpam-6793	237	19	wb̄(r	wb̄(r	NOUN
ejpam-6793	237	20	)	)	PUNCT
ejpam-6793	237	21	for	for	ADP
ejpam-6793	237	22	r	r	NOUN
ejpam-6793	237	23	≥	≥	PROPN
ejpam-6793	237	24	b	b	NOUN
ejpam-6793	237	25	a	a	PRON
ejpam-6793	237	26	.	.	PUNCT
ejpam-6793	238	1	in	in	ADP
ejpam-6793	238	2	examining	examine	VERB
ejpam-6793	238	3	the	the	DET
ejpam-6793	238	4	effectiveness	effectiveness	NOUN
ejpam-6793	238	5	of	of	ADP
ejpam-6793	238	6	the	the	DET
ejpam-6793	238	7	ecbsmps	ecbsmp	NOUN
ejpam-6793	238	8	{	{	PUNCT
ejpam-6793	238	9	qen(x	qen(x	X
ejpam-6793	238	10	)	)	PUNCT
ejpam-6793	238	11	}	}	PUNCT
ejpam-6793	238	12	for	for	ADP
ejpam-6793	238	13	the	the	DET
ejpam-6793	238	14	f	f	NOUN
ejpam-6793	238	15	-	-	PUNCT
ejpam-6793	238	16	module	module	NOUN
ejpam-6793	238	17	wb+(r	wb+(r	NOUN
ejpam-6793	238	18	)	)	PUNCT
ejpam-6793	238	19	,	,	PUNCT
ejpam-6793	238	20	we	we	PRON
ejpam-6793	238	21	assume	assume	VERB
ejpam-6793	238	22	that	that	SCONJ
ejpam-6793	238	23	the	the	DET
ejpam-6793	238	24	base	base	NOUN
ejpam-6793	238	25	qn(x	qn(x	PUNCT
ejpam-6793	238	26	)	)	PUNCT
ejpam-6793	238	27	satisfies	satisfy	VERB
ejpam-6793	238	28	the	the	DET
ejpam-6793	238	29	prescribed	prescribed	ADJ
ejpam-6793	238	30	condition	condition	NOUN
ejpam-6793	238	31	.	.	PUNCT
ejpam-6793	239	1	µ(q	µ(q	ADV
ejpam-6793	239	2	,	,	PUNCT
ejpam-6793	239	3	r+	r+	X
ejpam-6793	239	4	)	)	PUNCT
ejpam-6793	239	5	≤	≤	NOUN
ejpam-6793	239	6	r	r	NOUN
ejpam-6793	239	7	,	,	PUNCT
ejpam-6793	239	8	(	(	PUNCT
ejpam-6793	239	9	30	30	NUM
ejpam-6793	239	10	)	)	PUNCT
ejpam-6793	239	11	where	where	SCONJ
ejpam-6793	239	12	µ(q	µ(q	PROPN
ejpam-6793	239	13	,	,	PUNCT
ejpam-6793	239	14	r+	r+	X
ejpam-6793	239	15	)	)	PUNCT
ejpam-6793	239	16	=	=	SYM
ejpam-6793	239	17	lim	lim	PROPN
ejpam-6793	239	18	sup	sup	PROPN
ejpam-6793	239	19	n→∞	n→∞	X
ejpam-6793	239	20	{	{	PUNCT
ejpam-6793	239	21	∥qn∥r+	∥qn∥r+	X
ejpam-6793	239	22	}	}	SYM
ejpam-6793	239	23	1	1	NUM
ejpam-6793	239	24	n	n	NOUN
ejpam-6793	239	25	.	.	PUNCT
ejpam-6793	240	1	and	and	CCONJ
ejpam-6793	240	2	∥qn∥r+	∥qn∥r+	NUM
ejpam-6793	240	3	=	=	SYM
ejpam-6793	240	4	sup	sup	PROPN
ejpam-6793	240	5	b+(r	b+(r	NOUN
ejpam-6793	240	6	)	)	PUNCT
ejpam-6793	240	7	|qn(x)|	|qn(x)|	NOUN
ejpam-6793	240	8	.	.	PUNCT
ejpam-6793	241	1	in	in	ADP
ejpam-6793	241	2	the	the	DET
ejpam-6793	241	3	sequel	sequel	NOUN
ejpam-6793	241	4	,	,	PUNCT
ejpam-6793	241	5	we	we	PRON
ejpam-6793	241	6	present	present	VERB
ejpam-6793	241	7	a	a	DET
ejpam-6793	241	8	proof	proof	NOUN
ejpam-6793	241	9	for	for	ADP
ejpam-6793	241	10	the	the	DET
ejpam-6793	241	11	following	follow	VERB
ejpam-6793	241	12	theorem	theorem	NOUN
ejpam-6793	241	13	theorem	theorem	NOUN
ejpam-6793	241	14	5	5	X
ejpam-6793	241	15	.	.	PUNCT
ejpam-6793	242	1	if	if	SCONJ
ejpam-6793	242	2	the	the	DET
ejpam-6793	242	3	cbsmps	cbsmp	NOUN
ejpam-6793	242	4	{	{	PUNCT
ejpam-6793	242	5	qn(x	qn(x	NOUN
ejpam-6793	242	6	)	)	PUNCT
ejpam-6793	242	7	}	}	PUNCT
ejpam-6793	242	8	satisfying	satisfy	VERB
ejpam-6793	242	9	(	(	PUNCT
ejpam-6793	242	10	30	30	NUM
ejpam-6793	242	11	)	)	PUNCT
ejpam-6793	242	12	,	,	PUNCT
ejpam-6793	242	13	then	then	ADV
ejpam-6793	242	14	the	the	DET
ejpam-6793	242	15	ecbsmps	ecbsmp	NOUN
ejpam-6793	242	16	{	{	PUNCT
ejpam-6793	242	17	qen(x	qen(x	X
ejpam-6793	242	18	)	)	PUNCT
ejpam-6793	242	19	}	}	PUNCT
ejpam-6793	242	20	associated	associate	VERB
ejpam-6793	242	21	with	with	ADP
ejpam-6793	242	22	{	{	PUNCT
ejpam-6793	242	23	qn(x	qn(x	NOUN
ejpam-6793	242	24	)	)	PUNCT
ejpam-6793	242	25	}	}	PUNCT
ejpam-6793	242	26	is	be	AUX
ejpam-6793	242	27	effectiveness	effectiveness	NOUN
ejpam-6793	242	28	for	for	ADP
ejpam-6793	242	29	wb+(r	wb+(r	NOUN
ejpam-6793	242	30	)	)	PUNCT
ejpam-6793	242	31	.	.	PUNCT
ejpam-6793	243	1	proof	proof	NOUN
ejpam-6793	243	2	.	.	PUNCT
ejpam-6793	244	1	suppose	suppose	VERB
ejpam-6793	244	2	that	that	SCONJ
ejpam-6793	244	3	ρ1	ρ1	NOUN
ejpam-6793	244	4	,	,	PUNCT
ejpam-6793	244	5	ρ2	ρ2	NOUN
ejpam-6793	244	6	and	and	CCONJ
ejpam-6793	244	7	r	r	NOUN
ejpam-6793	244	8	are	be	AUX
ejpam-6793	244	9	chosen	choose	VERB
ejpam-6793	244	10	such	such	ADJ
ejpam-6793	244	11	that	that	SCONJ
ejpam-6793	244	12	r	r	NOUN
ejpam-6793	244	13	<	<	X
ejpam-6793	244	14	ρ1	ρ1	NOUN
ejpam-6793	244	15	<	<	X
ejpam-6793	244	16	ρ2	ρ2	NOUN
ejpam-6793	244	17	<	<	X
ejpam-6793	244	18	r.	r.	PROPN
ejpam-6793	244	19	then	then	ADV
ejpam-6793	244	20	one	one	PRON
ejpam-6793	244	21	can	can	AUX
ejpam-6793	244	22	construct	construct	VERB
ejpam-6793	244	23	a	a	DET
ejpam-6793	244	24	sequence	sequence	NOUN
ejpam-6793	244	25	(	(	PUNCT
ejpam-6793	244	26	rj	rj	PROPN
ejpam-6793	244	27	)	)	PUNCT
ejpam-6793	244	28	of	of	ADP
ejpam-6793	244	29	positive	positive	ADJ
ejpam-6793	244	30	numbers	number	NOUN
ejpam-6793	244	31	satisfying	satisfy	VERB
ejpam-6793	244	32	r	r	NOUN
ejpam-6793	244	33	<	<	X
ejpam-6793	244	34	ρ1	ρ1	NOUN
ejpam-6793	244	35	<	<	X
ejpam-6793	244	36	ρ2	ρ2	PROPN
ejpam-6793	244	37	<	<	X
ejpam-6793	244	38	r1	r1	PROPN
ejpam-6793	244	39	<	<	X
ejpam-6793	244	40	r2	r2	PROPN
ejpam-6793	244	41	<	<	X
ejpam-6793	244	42	·	·	PUNCT
ejpam-6793	244	43	·	·	PUNCT
ejpam-6793	244	44	·	·	PUNCT
ejpam-6793	244	45	<	<	X
ejpam-6793	244	46	rj	rj	X
ejpam-6793	244	47	<	<	X
ejpam-6793	244	48	·	·	PUNCT
ejpam-6793	244	49	·	·	PUNCT
ejpam-6793	244	50	·	·	PUNCT
ejpam-6793	244	51	<	<	X
ejpam-6793	244	52	r	r	NOUN
ejpam-6793	244	53	and	and	CCONJ
ejpam-6793	244	54	∥qn∥ri	∥qn∥ri	NOUN
ejpam-6793	244	55	<	<	X
ejpam-6793	244	56	krn	krn	PROPN
ejpam-6793	244	57	i+1;n	i+1;n	PROPN
ejpam-6793	244	58	≥	≥	NOUN
ejpam-6793	244	59	0	0	NUM
ejpam-6793	244	60	(	(	PUNCT
ejpam-6793	244	61	31	31	NUM
ejpam-6793	244	62	)	)	PUNCT
ejpam-6793	244	63	m.	m.	NOUN
ejpam-6793	244	64	zayed	zayed	PROPN
ejpam-6793	244	65	/	/	SYM
ejpam-6793	244	66	eur	eur	PROPN
ejpam-6793	244	67	.	.	PUNCT
ejpam-6793	245	1	j.	j.	PROPN
ejpam-6793	245	2	pure	pure	PROPN
ejpam-6793	245	3	appl	appl	PROPN
ejpam-6793	245	4	.	.	PROPN
ejpam-6793	245	5	math	math	PROPN
ejpam-6793	245	6	,	,	PUNCT
ejpam-6793	245	7	18	18	NUM
ejpam-6793	245	8	(	(	PUNCT
ejpam-6793	245	9	4	4	NUM
ejpam-6793	245	10	)	)	PUNCT
ejpam-6793	245	11	(	(	PUNCT
ejpam-6793	245	12	2025	2025	NUM
ejpam-6793	245	13	)	)	PUNCT
ejpam-6793	245	14	,	,	PUNCT
ejpam-6793	245	15	6793	6793	NUM
ejpam-6793	245	16	14	14	NUM
ejpam-6793	245	17	of	of	ADP
ejpam-6793	245	18	19	19	NUM
ejpam-6793	245	19	where	where	SCONJ
ejpam-6793	245	20	k	k	PROPN
ejpam-6793	245	21	is	be	AUX
ejpam-6793	245	22	a	a	DET
ejpam-6793	245	23	positive	positive	ADJ
ejpam-6793	245	24	finite	finite	NOUN
ejpam-6793	245	25	constant	constant	ADJ
ejpam-6793	245	26	.	.	PUNCT
ejpam-6793	246	1	for	for	ADP
ejpam-6793	246	2	the	the	DET
ejpam-6793	246	3	power	power	NOUN
ejpam-6793	246	4	base	base	NOUN
ejpam-6793	246	5	{	{	PUNCT
ejpam-6793	246	6	q(j	q(j	PROPN
ejpam-6793	246	7	)	)	PUNCT
ejpam-6793	246	8	n	n	CCONJ
ejpam-6793	246	9	(	(	PUNCT
ejpam-6793	246	10	x	x	X
ejpam-6793	246	11	)	)	PUNCT
ejpam-6793	246	12	}	}	PUNCT
ejpam-6793	246	13	corresponding	correspond	VERB
ejpam-6793	246	14	to	to	ADP
ejpam-6793	246	15	the	the	DET
ejpam-6793	246	16	original	original	ADJ
ejpam-6793	246	17	base	base	NOUN
ejpam-6793	246	18	{	{	PUNCT
ejpam-6793	246	19	qn(x	qn(x	NOUN
ejpam-6793	246	20	)	)	PUNCT
ejpam-6793	246	21	}	}	PUNCT
ejpam-6793	246	22	,	,	PUNCT
ejpam-6793	246	23	it	it	PRON
ejpam-6793	246	24	follows	follow	VERB
ejpam-6793	246	25	that	that	SCONJ
ejpam-6793	246	26	q(j	q(j	PROPN
ejpam-6793	246	27	)	)	PUNCT
ejpam-6793	246	28	n	n	CCONJ
ejpam-6793	246	29	(	(	PUNCT
ejpam-6793	246	30	x	x	X
ejpam-6793	246	31	)	)	PUNCT
ejpam-6793	246	32	=	=	SYM
ejpam-6793	246	33	∑	∑	PUNCT
ejpam-6793	246	34	k	k	PROPN
ejpam-6793	246	35	q(j−1	q(j−1	PROPN
ejpam-6793	246	36	)	)	PUNCT
ejpam-6793	246	37	k	k	NOUN
ejpam-6793	246	38	(	(	PUNCT
ejpam-6793	246	39	x)qn	x)qn	PROPN
ejpam-6793	246	40	,	,	PUNCT
ejpam-6793	246	41	k	k	PROPN
ejpam-6793	246	42	,	,	PUNCT
ejpam-6793	246	43	(	(	PUNCT
ejpam-6793	246	44	32	32	NUM
ejpam-6793	246	45	)	)	PUNCT
ejpam-6793	246	46	where	where	SCONJ
ejpam-6793	246	47	{	{	PUNCT
ejpam-6793	246	48	qn	qn	NOUN
ejpam-6793	246	49	,	,	PUNCT
ejpam-6793	246	50	k	k	NOUN
ejpam-6793	246	51	}	}	PUNCT
ejpam-6793	246	52	represent	represent	VERB
ejpam-6793	246	53	the	the	DET
ejpam-6793	246	54	elements	element	NOUN
ejpam-6793	246	55	of	of	ADP
ejpam-6793	246	56	the	the	DET
ejpam-6793	246	57	matrix	matrix	NOUN
ejpam-6793	246	58	q	q	NOUN
ejpam-6793	246	59	,	,	PUNCT
ejpam-6793	246	60	and	and	CCONJ
ejpam-6793	246	61	by	by	ADP
ejpam-6793	246	62	substituting	substitute	VERB
ejpam-6793	246	63	s	s	NOUN
ejpam-6793	246	64	=	=	SYM
ejpam-6793	246	65	2	2	NUM
ejpam-6793	246	66	into	into	ADP
ejpam-6793	246	67	(	(	PUNCT
ejpam-6793	246	68	32	32	NUM
ejpam-6793	246	69	)	)	PUNCT
ejpam-6793	246	70	,	,	PUNCT
ejpam-6793	246	71	then	then	ADV
ejpam-6793	246	72	applying	apply	VERB
ejpam-6793	246	73	cauchy	cauchy	PROPN
ejpam-6793	246	74	’s	’s	PART
ejpam-6793	246	75	inequality	inequality	NOUN
ejpam-6793	246	76	together	together	ADV
ejpam-6793	246	77	with	with	ADP
ejpam-6793	246	78	relation	relation	NOUN
ejpam-6793	246	79	(	(	PUNCT
ejpam-6793	246	80	31	31	NUM
ejpam-6793	246	81	)	)	PUNCT
ejpam-6793	246	82	,	,	PUNCT
ejpam-6793	246	83	one	one	PRON
ejpam-6793	246	84	obtains	obtain	VERB
ejpam-6793	246	85	∥∥∥q(2	∥∥∥q(2	ADJ
ejpam-6793	246	86	)	)	PUNCT
ejpam-6793	246	87	n	n	DET
ejpam-6793	246	88	∥∥∥	∥∥∥	PROPN
ejpam-6793	246	89	r1	r1	NOUN
ejpam-6793	246	90	=	=	PUNCT
ejpam-6793	246	91	sup	sup	NUM
ejpam-6793	246	92	b̄(r1	b̄(r1	NOUN
ejpam-6793	246	93	)	)	PUNCT
ejpam-6793	246	94	∣∣∣q(2	∣∣∣q(2	NOUN
ejpam-6793	246	95	)	)	PUNCT
ejpam-6793	246	96	n	n	CCONJ
ejpam-6793	246	97	(	(	PUNCT
ejpam-6793	246	98	x	x	NOUN
ejpam-6793	246	99	)	)	PUNCT
ejpam-6793	246	100	∣∣∣	∣∣∣	ADJ
ejpam-6793	246	101	≤	≤	NUM
ejpam-6793	247	1	2	2	NUM
ejpam-6793	247	2	m	m	NOUN
ejpam-6793	247	3	2	2	NUM
ejpam-6793	247	4	∥qn∥r3	∥qn∥r3	X
ejpam-6793	247	5	∑	∑	PROPN
ejpam-6793	247	6	k	k	PROPN
ejpam-6793	247	7	∥qk∥r1	∥qk∥r1	PROPN
ejpam-6793	247	8	rk	rk	NOUN
ejpam-6793	247	9	3	3	NUM
ejpam-6793	247	10	<	<	X
ejpam-6793	247	11	k2	k2	PROPN
ejpam-6793	247	12	m	m	PROPN
ejpam-6793	247	13	2	2	NUM
ejpam-6793	247	14	∑	∑	PROPN
ejpam-6793	247	15	k	k	PROPN
ejpam-6793	247	16	(	(	PUNCT
ejpam-6793	247	17	r2	r2	PROPN
ejpam-6793	247	18	r3	r3	PROPN
ejpam-6793	247	19	)	)	PUNCT
ejpam-6793	247	20	k	k	PROPN
ejpam-6793	247	21	∥qn∥r3	∥qn∥r3	X
ejpam-6793	247	22	=	=	PROPN
ejpam-6793	247	23	k2	k2	PROPN
ejpam-6793	247	24	m	m	PROPN
ejpam-6793	247	25	2	2	NUM
ejpam-6793	247	26	s	s	PART
ejpam-6793	247	27	(	(	PUNCT
ejpam-6793	247	28	r2	r2	PROPN
ejpam-6793	247	29	,	,	PUNCT
ejpam-6793	247	30	r3	r3	PROPN
ejpam-6793	247	31	)	)	PUNCT
ejpam-6793	247	32	∥qn∥r3	∥qn∥r3	X
ejpam-6793	247	33	.	.	PUNCT
ejpam-6793	248	1	throughout	throughout	ADP
ejpam-6793	248	2	the	the	DET
ejpam-6793	248	3	following	follow	VERB
ejpam-6793	248	4	discussion	discussion	NOUN
ejpam-6793	248	5	,	,	PUNCT
ejpam-6793	248	6	we	we	PRON
ejpam-6793	248	7	assume	assume	VERB
ejpam-6793	248	8	that	that	SCONJ
ejpam-6793	248	9	∥∥∥q(j	∥∥∥q(j	NOUN
ejpam-6793	248	10	)	)	PUNCT
ejpam-6793	248	11	n	n	NUM
ejpam-6793	248	12	∥∥∥	∥∥∥	PROPN
ejpam-6793	248	13	r1	r1	NOUN
ejpam-6793	248	14	<	<	X
ejpam-6793	249	1	(	(	PUNCT
ejpam-6793	249	2	k	k	PROPN
ejpam-6793	249	3	2	2	NUM
ejpam-6793	249	4	m	m	NOUN
ejpam-6793	249	5	2	2	NUM
ejpam-6793	249	6	)	)	PUNCT
ejpam-6793	249	7	j−1	j−1	PROPN
ejpam-6793	249	8	j−1∏	j−1∏	VERB
ejpam-6793	249	9	n=1	n=1	PROPN
ejpam-6793	249	10	s	s	PART
ejpam-6793	249	11	(	(	PUNCT
ejpam-6793	249	12	r2n	r2n	NOUN
ejpam-6793	249	13	,	,	PUNCT
ejpam-6793	249	14	r2n+1	r2n+1	PROPN
ejpam-6793	249	15	)	)	PUNCT
ejpam-6793	249	16	∥qn∥r2j−1	∥qn∥r2j−1	NOUN
ejpam-6793	249	17	(	(	PUNCT
ejpam-6793	249	18	33	33	NUM
ejpam-6793	249	19	)	)	PUNCT
ejpam-6793	249	20	from	from	ADP
ejpam-6793	249	21	(	(	PUNCT
ejpam-6793	249	22	31	31	NUM
ejpam-6793	249	23	)	)	PUNCT
ejpam-6793	249	24	,	,	PUNCT
ejpam-6793	249	25	(	(	PUNCT
ejpam-6793	249	26	32	32	NUM
ejpam-6793	249	27	)	)	PUNCT
ejpam-6793	249	28	,	,	PUNCT
ejpam-6793	249	29	and	and	CCONJ
ejpam-6793	249	30	(	(	PUNCT
ejpam-6793	249	31	33	33	NUM
ejpam-6793	249	32	)	)	PUNCT
ejpam-6793	249	33	,	,	PUNCT
ejpam-6793	249	34	together	together	ADV
ejpam-6793	249	35	with	with	ADP
ejpam-6793	249	36	an	an	DET
ejpam-6793	249	37	application	application	NOUN
ejpam-6793	249	38	of	of	ADP
ejpam-6793	249	39	cauchy	cauchy	PROPN
ejpam-6793	249	40	’s	’s	PART
ejpam-6793	249	41	inequality	inequality	NOUN
ejpam-6793	249	42	,	,	PUNCT
ejpam-6793	249	43	it	it	PRON
ejpam-6793	249	44	follows	follow	VERB
ejpam-6793	249	45	that	that	SCONJ
ejpam-6793	249	46	∥∥∥q(j+1	∥∥∥q(j+1	NOUN
ejpam-6793	249	47	)	)	PUNCT
ejpam-6793	249	48	n	n	PRON
ejpam-6793	249	49	∥∥∥	∥∥∥	PROPN
ejpam-6793	249	50	r1	r1	PROPN
ejpam-6793	249	51	≤	≤	ADJ
ejpam-6793	249	52	2	2	NUM
ejpam-6793	249	53	m	m	NUM
ejpam-6793	249	54	2	2	NUM
ejpam-6793	249	55	∥∥qn∥r2j+1	∥∥qn∥r2j+1	NOUN
ejpam-6793	249	56	∥∥∑	∥∥∑	NUM
ejpam-6793	249	57	k	k	PROPN
ejpam-6793	249	58	∥∥∥q(j	∥∥∥q(j	PROPN
ejpam-6793	249	59	)	)	PUNCT
ejpam-6793	250	1	k	k	PROPN
ejpam-6793	250	2	∥∥∥	∥∥∥	PROPN
ejpam-6793	250	3	r1	r1	PROPN
ejpam-6793	250	4	rk	rk	NOUN
ejpam-6793	250	5	2j+1	2j+1	PROPN
ejpam-6793	250	6	<	<	X
ejpam-6793	250	7	2	2	NUM
ejpam-6793	250	8	m	m	NUM
ejpam-6793	250	9	2	2	NUM
ejpam-6793	250	10	(	(	PUNCT
ejpam-6793	250	11	k	k	PROPN
ejpam-6793	250	12	2	2	NUM
ejpam-6793	250	13	m	m	NOUN
ejpam-6793	250	14	2	2	NUM
ejpam-6793	250	15	)	)	PUNCT
ejpam-6793	250	16	j−1	j−1	PROPN
ejpam-6793	250	17	j−1∏	j−1∏	VERB
ejpam-6793	250	18	n=1	n=1	PROPN
ejpam-6793	250	19	s	s	PART
ejpam-6793	250	20	(	(	PUNCT
ejpam-6793	250	21	r2n	r2n	NOUN
ejpam-6793	250	22	,	,	PUNCT
ejpam-6793	250	23	r2n+1	r2n+1	PROPN
ejpam-6793	250	24	)	)	PUNCT
ejpam-6793	250	25	∥qn∥r2j+1	∥qn∥r2j+1	VERB
ejpam-6793	251	1	∑	∑	PUNCT
ejpam-6793	251	2	k	k	PROPN
ejpam-6793	251	3	∥qk∥r2j−1	∥qk∥r2j−1	PROPN
ejpam-6793	251	4	rk	rk	NOUN
ejpam-6793	251	5	2j−1	2j−1	NUM
ejpam-6793	251	6	<	<	X
ejpam-6793	251	7	(	(	PUNCT
ejpam-6793	251	8	k	k	PROPN
ejpam-6793	251	9	2	2	NUM
ejpam-6793	251	10	m	m	NOUN
ejpam-6793	251	11	2	2	NUM
ejpam-6793	251	12	)	)	PUNCT
ejpam-6793	252	1	j	j	PROPN
ejpam-6793	252	2	j∏	j∏	PROPN
ejpam-6793	252	3	n=1	n=1	PROPN
ejpam-6793	252	4	s	s	PART
ejpam-6793	252	5	(	(	PUNCT
ejpam-6793	252	6	r2n	r2n	NOUN
ejpam-6793	252	7	,	,	PUNCT
ejpam-6793	252	8	r2n+1	r2n+1	PROPN
ejpam-6793	252	9	)	)	PUNCT
ejpam-6793	252	10	∥qn∥r2j+1	∥qn∥r2j+1	VERB
ejpam-6793	253	1	hence	hence	ADV
ejpam-6793	253	2	,	,	PUNCT
ejpam-6793	253	3	the	the	DET
ejpam-6793	253	4	validity	validity	NOUN
ejpam-6793	253	5	of	of	ADP
ejpam-6793	253	6	assumption	assumption	NOUN
ejpam-6793	253	7	(	(	PUNCT
ejpam-6793	253	8	33	33	NUM
ejpam-6793	253	9	)	)	PUNCT
ejpam-6793	253	10	is	be	AUX
ejpam-6793	253	11	established	establish	VERB
ejpam-6793	253	12	by	by	ADP
ejpam-6793	253	13	induction	induction	NOUN
ejpam-6793	253	14	.	.	PUNCT
ejpam-6793	254	1	defining	define	VERB
ejpam-6793	254	2	k1	k1	NOUN
ejpam-6793	254	3	=	=	SYM
ejpam-6793	254	4	max1≤n≤j−1k	max1≤n≤j−1k	PROPN
ejpam-6793	254	5	2	2	NUM
ejpam-6793	254	6	m	m	PROPN
ejpam-6793	254	7	2	2	NUM
ejpam-6793	254	8	s	s	PART
ejpam-6793	254	9	(	(	PUNCT
ejpam-6793	254	10	r2n	r2n	NOUN
ejpam-6793	254	11	,	,	PUNCT
ejpam-6793	254	12	r2n+1	r2n+1	PROPN
ejpam-6793	254	13	)	)	PUNCT
ejpam-6793	254	14	,	,	PUNCT
ejpam-6793	254	15	relation	relation	NOUN
ejpam-6793	254	16	(	(	PUNCT
ejpam-6793	254	17	33	33	NUM
ejpam-6793	254	18	)	)	PUNCT
ejpam-6793	254	19	takes	take	VERB
ejpam-6793	254	20	the	the	DET
ejpam-6793	254	21	form∥∥∥q(j	form∥∥∥q(j	NOUN
ejpam-6793	254	22	)	)	PUNCT
ejpam-6793	254	23	n	n	NUM
ejpam-6793	254	24	∥∥∥	∥∥∥	PROPN
ejpam-6793	254	25	r1	r1	PROPN
ejpam-6793	254	26	<	<	X
ejpam-6793	254	27	kj−1	kj−1	PROPN
ejpam-6793	254	28	1	1	NUM
ejpam-6793	254	29	∥qn∥r2j−1	∥qn∥r2j−1	PROPN
ejpam-6793	254	30	(	(	PUNCT
ejpam-6793	254	31	34	34	NUM
ejpam-6793	254	32	)	)	PUNCT
ejpam-6793	254	33	observing	observe	VERB
ejpam-6793	254	34	that	that	PRON
ejpam-6793	254	35	qe	qe	PROPN
ejpam-6793	254	36	=	=	PUNCT
ejpam-6793	254	37	eq	eq	NOUN
ejpam-6793	254	38	serves	serve	VERB
ejpam-6793	254	39	as	as	ADP
ejpam-6793	254	40	the	the	DET
ejpam-6793	254	41	coefficient	coefficient	NOUN
ejpam-6793	254	42	matrix	matrix	NOUN
ejpam-6793	254	43	associated	associate	VERB
ejpam-6793	254	44	with	with	ADP
ejpam-6793	254	45	the	the	DET
ejpam-6793	254	46	exponential	exponential	ADJ
ejpam-6793	254	47	basis	basis	NOUN
ejpam-6793	254	48	{	{	PUNCT
ejpam-6793	254	49	qen(x	qen(x	X
ejpam-6793	254	50	)	)	PUNCT
ejpam-6793	254	51	}	}	PUNCT
ejpam-6793	254	52	,	,	PUNCT
ejpam-6793	254	53	we	we	PRON
ejpam-6793	254	54	deduce	deduce	VERB
ejpam-6793	254	55	that	that	DET
ejpam-6793	254	56	m.	m.	NOUN
ejpam-6793	254	57	zayed	zayed	PROPN
ejpam-6793	254	58	/	/	SYM
ejpam-6793	254	59	eur	eur	PROPN
ejpam-6793	254	60	.	.	PUNCT
ejpam-6793	255	1	j.	j.	PROPN
ejpam-6793	255	2	pure	pure	PROPN
ejpam-6793	255	3	appl	appl	PROPN
ejpam-6793	255	4	.	.	PROPN
ejpam-6793	255	5	math	math	PROPN
ejpam-6793	255	6	,	,	PUNCT
ejpam-6793	255	7	18	18	NUM
ejpam-6793	255	8	(	(	PUNCT
ejpam-6793	255	9	4	4	NUM
ejpam-6793	255	10	)	)	PUNCT
ejpam-6793	255	11	(	(	PUNCT
ejpam-6793	255	12	2025	2025	NUM
ejpam-6793	255	13	)	)	PUNCT
ejpam-6793	255	14	,	,	PUNCT
ejpam-6793	255	15	6793	6793	NUM
ejpam-6793	255	16	15	15	NUM
ejpam-6793	255	17	of	of	ADP
ejpam-6793	255	18	19	19	NUM
ejpam-6793	255	19	qen(x	qen(x	NOUN
ejpam-6793	255	20	)	)	PUNCT
ejpam-6793	255	21	=	=	PUNCT
ejpam-6793	256	1	∑	∑	PUNCT
ejpam-6793	256	2	k	k	PROPN
ejpam-6793	256	3	qk(x)qen	qk(x)qen	PROPN
ejpam-6793	256	4	,	,	PUNCT
ejpam-6793	256	5	k	k	PROPN
ejpam-6793	257	1	=	=	PUNCT
ejpam-6793	257	2	∑	∑	PUNCT
ejpam-6793	257	3	k	k	PROPN
ejpam-6793	257	4	qk(x	qk(x	NOUN
ejpam-6793	257	5	)	)	PUNCT
ejpam-6793	257	6			PROPN
ejpam-6793	257	7	∞∑	∞∑	NUM
ejpam-6793	257	8	j=0	j=0	PROPN
ejpam-6793	257	9	q(j	q(j	PROPN
ejpam-6793	257	10	)	)	PUNCT
ejpam-6793	257	11	n	n	CCONJ
ejpam-6793	257	12	,	,	PUNCT
ejpam-6793	257	13	k	k	PROPN
ejpam-6793	257	14	u	u	PROPN
ejpam-6793	257	15	!	!	PUNCT
ejpam-6793	258	1			PROPN
ejpam-6793	258	2	(	(	PUNCT
ejpam-6793	258	3	35	35	NUM
ejpam-6793	258	4	)	)	PUNCT
ejpam-6793	258	5	from	from	ADP
ejpam-6793	258	6	(	(	PUNCT
ejpam-6793	258	7	31	31	NUM
ejpam-6793	258	8	)	)	PUNCT
ejpam-6793	258	9	,	,	PUNCT
ejpam-6793	258	10	(	(	PUNCT
ejpam-6793	258	11	34	34	NUM
ejpam-6793	258	12	)	)	PUNCT
ejpam-6793	258	13	,	,	PUNCT
ejpam-6793	258	14	together	together	ADV
ejpam-6793	258	15	with	with	ADP
ejpam-6793	258	16	cauchy	cauchy	PROPN
ejpam-6793	258	17	’s	’s	PART
ejpam-6793	258	18	inequality	inequality	NOUN
ejpam-6793	258	19	applied	apply	VERB
ejpam-6793	258	20	in	in	ADP
ejpam-6793	258	21	(	(	PUNCT
ejpam-6793	258	22	35	35	NUM
ejpam-6793	258	23	)	)	PUNCT
ejpam-6793	258	24	,	,	PUNCT
ejpam-6793	258	25	we	we	PRON
ejpam-6793	258	26	obtain	obtain	VERB
ejpam-6793	258	27	∥qen∥ρ1	∥qen∥ρ1	ADJ
ejpam-6793	258	28	=	=	SYM
ejpam-6793	258	29	sup	sup	NOUN
ejpam-6793	258	30	b̄(ρ1	b̄(ρ1	NOUN
ejpam-6793	258	31	)	)	PUNCT
ejpam-6793	259	1	|qen(x)|	|qen(x)|	VERB
ejpam-6793	259	2	≤	≤	NUM
ejpam-6793	259	3	2	2	NUM
ejpam-6793	259	4	m	m	NOUN
ejpam-6793	259	5	2	2	NUM
ejpam-6793	259	6	∑	∑	SYM
ejpam-6793	259	7	k	k	X
ejpam-6793	259	8	ρk1	ρk1	X
ejpam-6793	259	9	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-6793	259	10	∞∑	∞∑	NUM
ejpam-6793	259	11	j=0	j=0	PROPN
ejpam-6793	259	12	q(j	q(j	PROPN
ejpam-6793	259	13	)	)	PUNCT
ejpam-6793	259	14	n	n	CCONJ
ejpam-6793	259	15	,	,	PUNCT
ejpam-6793	259	16	k	k	PROPN
ejpam-6793	259	17	j	j	PROPN
ejpam-6793	259	18	!	!	PUNCT
ejpam-6793	260	1	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-6793	260	2	<	<	X
ejpam-6793	260	3	2	2	NUM
ejpam-6793	260	4	m	m	NUM
ejpam-6793	260	5	2	2	NUM
ejpam-6793	260	6	∑	∑	PUNCT
ejpam-6793	260	7	k	k	PROPN
ejpam-6793	260	8	∞∑	∞∑	PROPN
ejpam-6793	260	9	j=0	j=0	PROPN
ejpam-6793	260	10	∥qn∥r1	∥qn∥r1	PROPN
ejpam-6793	260	11	j	j	PROPN
ejpam-6793	260	12	!	!	PUNCT
ejpam-6793	261	1	(	(	PUNCT
ejpam-6793	261	2	ρ1	ρ1	NOUN
ejpam-6793	261	3	r1	r1	PROPN
ejpam-6793	261	4	)	)	PUNCT
ejpam-6793	262	1	k	k	X
ejpam-6793	262	2	<	<	X
ejpam-6793	262	3	2	2	NUM
ejpam-6793	262	4	m	m	NUM
ejpam-6793	262	5	2	2	NUM
ejpam-6793	262	6	∑	∑	PROPN
ejpam-6793	262	7	k	k	PROPN
ejpam-6793	262	8	∞∑	∞∑	NUM
ejpam-6793	262	9	j=0	j=0	ADJ
ejpam-6793	262	10	kj−1	kj−1	PROPN
ejpam-6793	262	11	1	1	NUM
ejpam-6793	262	12	∥qn∥r2j−1	∥qn∥r2j−1	PROPN
ejpam-6793	262	13	j	j	PROPN
ejpam-6793	262	14	!	!	PUNCT
ejpam-6793	262	15	(	(	PUNCT
ejpam-6793	262	16	ρ1	ρ1	NOUN
ejpam-6793	262	17	r1	r1	PROPN
ejpam-6793	262	18	)	)	PUNCT
ejpam-6793	263	1	k	k	X
ejpam-6793	263	2	<	<	X
ejpam-6793	263	3	2	2	NUM
ejpam-6793	263	4	m	m	NUM
ejpam-6793	263	5	2	2	NUM
ejpam-6793	263	6	rn	rn	PROPN
ejpam-6793	263	7	∑	∑	PROPN
ejpam-6793	263	8	k	k	PROPN
ejpam-6793	263	9			PUNCT
ejpam-6793	263	10	∞∑	∞∑	PROPN
ejpam-6793	263	11	j=0	j=0	PROPN
ejpam-6793	263	12	kj	kj	PROPN
ejpam-6793	263	13	1	1	NUM
ejpam-6793	263	14	j	j	PROPN
ejpam-6793	263	15	!	!	PUNCT
ejpam-6793	264	1	(ρ1	(ρ1	PROPN
ejpam-6793	264	2	r	r	NOUN
ejpam-6793	264	3	)	)	PUNCT
ejpam-6793	265	1	k	k	X
ejpam-6793	265	2	=	=	SYM
ejpam-6793	265	3	2	2	NUM
ejpam-6793	265	4	m	m	NOUN
ejpam-6793	265	5	2	2	NUM
ejpam-6793	265	6	ek1s	ek1s	NOUN
ejpam-6793	265	7	(	(	PUNCT
ejpam-6793	265	8	ρ1	ρ1	PROPN
ejpam-6793	265	9	,	,	PUNCT
ejpam-6793	265	10	r1	r1	NOUN
ejpam-6793	265	11	)	)	PUNCT
ejpam-6793	265	12	r	r	NOUN
ejpam-6793	265	13	n.	n.	NOUN
ejpam-6793	265	14	it	it	PRON
ejpam-6793	265	15	can	can	AUX
ejpam-6793	265	16	be	be	AUX
ejpam-6793	265	17	concluded	conclude	VERB
ejpam-6793	265	18	that	that	SCONJ
ejpam-6793	265	19	∥qe∥ρ1	∥qe∥ρ1	NOUN
ejpam-6793	265	20	=	=	SYM
ejpam-6793	265	21	lim	lim	PROPN
ejpam-6793	265	22	sup	sup	PROPN
ejpam-6793	265	23	n→∞	n→∞	X
ejpam-6793	265	24	{	{	PUNCT
ejpam-6793	265	25	∥qen∥ρ1	∥qen∥ρ1	PROPN
ejpam-6793	265	26	}	}	PUNCT
ejpam-6793	265	27	1	1	NUM
ejpam-6793	265	28	n	n	NOUN
ejpam-6793	265	29	≤	≤	NOUN
ejpam-6793	265	30	r	r	NOUN
ejpam-6793	265	31	taking	take	VERB
ejpam-6793	265	32	the	the	DET
ejpam-6793	265	33	limit	limit	NOUN
ejpam-6793	265	34	as	as	ADP
ejpam-6793	265	35	r	r	NOUN
ejpam-6793	265	36	→	→	SYM
ejpam-6793	265	37	r+	r+	NOUN
ejpam-6793	265	38	,	,	PUNCT
ejpam-6793	265	39	we	we	PRON
ejpam-6793	265	40	obtain	obtain	VERB
ejpam-6793	265	41	∥qe∥r+	∥qe∥r+	NUM
ejpam-6793	265	42	≤	≤	PROPN
ejpam-6793	265	43	r.	r.	PROPN
ejpam-6793	265	44	then	then	ADV
ejpam-6793	265	45	,	,	PUNCT
ejpam-6793	265	46	for	for	ADP
ejpam-6793	265	47	any	any	DET
ejpam-6793	265	48	number	number	NOUN
ejpam-6793	265	49	ρ1	ρ1	NOUN
ejpam-6793	265	50	>	>	X
ejpam-6793	266	1	r	r	NOUN
ejpam-6793	266	2	,	,	PUNCT
ejpam-6793	266	3	one	one	PRON
ejpam-6793	266	4	can	can	AUX
ejpam-6793	266	5	choose	choose	VERB
ejpam-6793	266	6	ρ2	ρ2	PROPN
ejpam-6793	266	7	>	>	SYM
ejpam-6793	266	8	ρ1	ρ1	NOUN
ejpam-6793	266	9	>	>	PUNCT
ejpam-6793	266	10	r	r	NOUN
ejpam-6793	266	11	such	such	ADJ
ejpam-6793	266	12	that	that	SCONJ
ejpam-6793	266	13	∥qe∥ρ1	∥qe∥ρ1	NOUN
ejpam-6793	266	14	<	<	X
ejpam-6793	266	15	ρ2	ρ2	PROPN
ejpam-6793	266	16	.	.	PUNCT
ejpam-6793	267	1	consequently	consequently	ADV
ejpam-6793	267	2	,	,	PUNCT
ejpam-6793	267	3	it	it	PRON
ejpam-6793	267	4	follows	follow	VERB
ejpam-6793	267	5	that	that	SCONJ
ejpam-6793	267	6	∥qen∥ρ1	∥qen∥ρ1	PROPN
ejpam-6793	267	7	<	<	X
ejpam-6793	267	8	k2ρ	k2ρ	PROPN
ejpam-6793	267	9	n	n	CCONJ
ejpam-6793	267	10	2	2	NUM
ejpam-6793	267	11	,	,	PUNCT
ejpam-6793	267	12	∀	∀	NOUN
ejpam-6793	267	13	n	n	PRON
ejpam-6793	267	14	≥	≥	NOUN
ejpam-6793	267	15	0	0	NUM
ejpam-6793	267	16	,	,	PUNCT
ejpam-6793	267	17	where	where	SCONJ
ejpam-6793	267	18	k2	k2	PROPN
ejpam-6793	267	19	≥	≥	NOUN
ejpam-6793	267	20	1	1	NUM
ejpam-6793	267	21	.	.	PUNCT
ejpam-6793	267	22	from	from	ADP
ejpam-6793	267	23	the	the	DET
ejpam-6793	267	24	definition	definition	NOUN
ejpam-6793	267	25	of	of	ADP
ejpam-6793	267	26	the	the	DET
ejpam-6793	267	27	exponential	exponential	ADJ
ejpam-6793	267	28	base	base	NOUN
ejpam-6793	267	29	{	{	PUNCT
ejpam-6793	267	30	qen(x	qen(x	X
ejpam-6793	267	31	)	)	PUNCT
ejpam-6793	267	32	}	}	PUNCT
ejpam-6793	267	33	,	,	PUNCT
ejpam-6793	267	34	its	its	PRON
ejpam-6793	267	35	cannon	cannon	NOUN
ejpam-6793	267	36	sum	sum	NOUN
ejpam-6793	267	37	is	be	AUX
ejpam-6793	267	38	given	give	VERB
ejpam-6793	267	39	by	by	ADP
ejpam-6793	267	40	ω	ω	PROPN
ejpam-6793	267	41	(	(	PUNCT
ejpam-6793	267	42	qen	qen	PROPN
ejpam-6793	267	43	,	,	PUNCT
ejpam-6793	267	44	b̄	b̄	PROPN
ejpam-6793	267	45	(	(	PUNCT
ejpam-6793	267	46	ρ1	ρ1	PROPN
ejpam-6793	267	47	)	)	PUNCT
ejpam-6793	267	48	)	)	PUNCT
ejpam-6793	268	1	=	=	PUNCT
ejpam-6793	268	2	∑	∑	PUNCT
ejpam-6793	268	3	k	k	X
ejpam-6793	268	4	∥∥	∥∥	PRON
ejpam-6793	268	5	qek	qek	PROPN
ejpam-6793	268	6	qēn	qēn	PROPN
ejpam-6793	268	7	,	,	PUNCT
ejpam-6793	268	8	k	k	PROPN
ejpam-6793	268	9	∥∥	∥∥	PRON
ejpam-6793	268	10	ρ1	ρ1	VERB
ejpam-6793	268	11	≤	≤	NUM
ejpam-6793	268	12	2	2	NUM
ejpam-6793	268	13	m	m	NOUN
ejpam-6793	268	14	2	2	NUM
ejpam-6793	268	15	∑	∑	SYM
ejpam-6793	268	16	k	k	PROPN
ejpam-6793	268	17	∥qek∥ρ1	∥qek∥ρ1	PROPN
ejpam-6793	268	18	∞∑	∞∑	NUM
ejpam-6793	268	19	j=0	j=0	PROPN
ejpam-6793	268	20	∣∣∣q(j	∣∣∣q(j	PROPN
ejpam-6793	268	21	)	)	PUNCT
ejpam-6793	268	22	n	n	CCONJ
ejpam-6793	268	23	,	,	PUNCT
ejpam-6793	268	24	k	k	PROPN
ejpam-6793	268	25	∣∣∣	∣∣∣	PROPN
ejpam-6793	268	26	j	j	PROPN
ejpam-6793	268	27	!	!	PUNCT
ejpam-6793	268	28	m.	m.	PROPN
ejpam-6793	268	29	zayed	zayed	PROPN
ejpam-6793	268	30	/	/	SYM
ejpam-6793	268	31	eur	eur	PROPN
ejpam-6793	268	32	.	.	PUNCT
ejpam-6793	269	1	j.	j.	PROPN
ejpam-6793	269	2	pure	pure	PROPN
ejpam-6793	269	3	appl	appl	PROPN
ejpam-6793	269	4	.	.	PROPN
ejpam-6793	269	5	math	math	PROPN
ejpam-6793	269	6	,	,	PUNCT
ejpam-6793	269	7	18	18	NUM
ejpam-6793	269	8	(	(	PUNCT
ejpam-6793	269	9	4	4	NUM
ejpam-6793	269	10	)	)	PUNCT
ejpam-6793	269	11	(	(	PUNCT
ejpam-6793	269	12	2025	2025	NUM
ejpam-6793	269	13	)	)	PUNCT
ejpam-6793	269	14	,	,	PUNCT
ejpam-6793	269	15	6793	6793	NUM
ejpam-6793	269	16	16	16	NUM
ejpam-6793	269	17	of	of	ADP
ejpam-6793	269	18	19	19	NUM
ejpam-6793	269	19	≤	≤	NUM
ejpam-6793	269	20	2	2	NUM
ejpam-6793	269	21	m	m	NOUN
ejpam-6793	269	22	2	2	NUM
ejpam-6793	269	23	∑	∑	SYM
ejpam-6793	269	24	k	k	PROPN
ejpam-6793	269	25	∥qek∥ρ1	∥qek∥ρ1	PROPN
ejpam-6793	269	26	∞∑	∞∑	NUM
ejpam-6793	269	27	j=0	j=0	PROPN
ejpam-6793	269	28	∥∥∥q(j	∥∥∥q(j	NOUN
ejpam-6793	269	29	)	)	PUNCT
ejpam-6793	269	30	n	n	NUM
ejpam-6793	269	31	∥∥∥	∥∥∥	PROPN
ejpam-6793	269	32	r1	r1	NOUN
ejpam-6793	269	33	j!rk	j!rk	ADP
ejpam-6793	269	34	1	1	NUM
ejpam-6793	269	35	<	<	X
ejpam-6793	269	36	k2	k2	PROPN
ejpam-6793	269	37	2	2	NUM
ejpam-6793	269	38	m	m	NOUN
ejpam-6793	269	39	2	2	NUM
ejpam-6793	269	40	∑	∑	PUNCT
ejpam-6793	269	41	k	k	PROPN
ejpam-6793	269	42	∞∑	∞∑	NUM
ejpam-6793	269	43	j=0	j=0	PROPN
ejpam-6793	269	44	∥qn∥r2j−1	∥qn∥r2j−1	PROPN
ejpam-6793	269	45	hj−1	hj−1	PROPN
ejpam-6793	269	46	1	1	NUM
ejpam-6793	269	47	j	j	NOUN
ejpam-6793	269	48	!	!	PUNCT
ejpam-6793	270	1	(	(	PUNCT
ejpam-6793	270	2	ρ2	ρ2	NOUN
ejpam-6793	270	3	r1	r1	NOUN
ejpam-6793	270	4	)	)	PUNCT
ejpam-6793	271	1	k	k	X
ejpam-6793	271	2	<	<	X
ejpam-6793	271	3	k2	k2	PROPN
ejpam-6793	271	4	2	2	NUM
ejpam-6793	271	5	m	m	NOUN
ejpam-6793	271	6	2	2	NUM
ejpam-6793	271	7	·	·	PUNCT
ejpam-6793	271	8	ek1s	ek1s	X
ejpam-6793	271	9	(	(	PUNCT
ejpam-6793	271	10	ρ2	ρ2	PROPN
ejpam-6793	271	11	,	,	PUNCT
ejpam-6793	271	12	r1	r1	PROPN
ejpam-6793	271	13	)	)	PUNCT
ejpam-6793	271	14	r	r	NOUN
ejpam-6793	271	15	n.	n.	NOUN
ejpam-6793	271	16	taking	take	VERB
ejpam-6793	271	17	the	the	DET
ejpam-6793	271	18	limit	limit	NOUN
ejpam-6793	271	19	as	as	SCONJ
ejpam-6793	271	20	n	n	PRON
ejpam-6793	271	21	tend	tend	VERB
ejpam-6793	271	22	to	to	PART
ejpam-6793	271	23	infinity	infinity	VERB
ejpam-6793	271	24	,	,	PUNCT
ejpam-6793	271	25	we	we	PRON
ejpam-6793	271	26	obtain	obtain	VERB
ejpam-6793	271	27	ω	ω	PROPN
ejpam-6793	271	28	(	(	PUNCT
ejpam-6793	271	29	qe	qe	PROPN
ejpam-6793	271	30	,	,	PUNCT
ejpam-6793	271	31	b̄	b̄	PROPN
ejpam-6793	271	32	(	(	PUNCT
ejpam-6793	271	33	ρ1	ρ1	PROPN
ejpam-6793	271	34	)	)	PUNCT
ejpam-6793	271	35	)	)	PUNCT
ejpam-6793	272	1	=	=	SYM
ejpam-6793	272	2	lim	lim	PROPN
ejpam-6793	272	3	sup	sup	PROPN
ejpam-6793	272	4	n→∞	n→∞	X
ejpam-6793	272	5	{	{	PUNCT
ejpam-6793	272	6	ω	ω	PROPN
ejpam-6793	272	7	(	(	PUNCT
ejpam-6793	272	8	qen	qen	PROPN
ejpam-6793	272	9	,	,	PUNCT
ejpam-6793	272	10	b̄	b̄	PROPN
ejpam-6793	272	11	(	(	PUNCT
ejpam-6793	272	12	ρ1	ρ1	PROPN
ejpam-6793	272	13	)	)	PUNCT
ejpam-6793	272	14	)	)	PUNCT
ejpam-6793	272	15	}	}	PUNCT
ejpam-6793	273	1	≤	≤	NUM
ejpam-6793	274	1	r	r	NOUN
ejpam-6793	274	2	which	which	PRON
ejpam-6793	274	3	yields	yield	VERB
ejpam-6793	274	4	ω	ω	PROPN
ejpam-6793	274	5	(	(	PUNCT
ejpam-6793	274	6	qe	qe	PROPN
ejpam-6793	274	7	,	,	PUNCT
ejpam-6793	274	8	r	r	NOUN
ejpam-6793	274	9	+	+	NOUN
ejpam-6793	274	10	)	)	PUNCT
ejpam-6793	274	11	≤	≤	NOUN
ejpam-6793	274	12	r	r	NOUN
ejpam-6793	274	13	as	as	ADP
ejpam-6793	274	14	r	r	NOUN
ejpam-6793	274	15	→	→	SYM
ejpam-6793	274	16	r+	r+	X
ejpam-6793	274	17	.	.	PUNCT
ejpam-6793	275	1	however	however	ADV
ejpam-6793	275	2	,	,	PUNCT
ejpam-6793	275	3	since	since	SCONJ
ejpam-6793	275	4	ω	ω	PROPN
ejpam-6793	275	5	(	(	PUNCT
ejpam-6793	275	6	qe	qe	PROPN
ejpam-6793	275	7	,	,	PUNCT
ejpam-6793	275	8	r	r	NOUN
ejpam-6793	275	9	+	+	NOUN
ejpam-6793	275	10	)	)	PUNCT
ejpam-6793	275	11	≥	≥	NOUN
ejpam-6793	275	12	r	r	NOUN
ejpam-6793	275	13	,	,	PUNCT
ejpam-6793	275	14	it	it	PRON
ejpam-6793	275	15	follows	follow	VERB
ejpam-6793	275	16	that	that	SCONJ
ejpam-6793	275	17	ω	ω	PROPN
ejpam-6793	275	18	(	(	PUNCT
ejpam-6793	275	19	qe	qe	PROPN
ejpam-6793	275	20	,	,	PUNCT
ejpam-6793	275	21	r	r	NOUN
ejpam-6793	275	22	+	+	NOUN
ejpam-6793	275	23	)	)	PUNCT
ejpam-6793	275	24	=	=	SYM
ejpam-6793	275	25	r.	r.	PROPN
ejpam-6793	275	26	r.	r.	PROPN
ejpam-6793	275	27	consequently	consequently	ADV
ejpam-6793	275	28	,	,	PUNCT
ejpam-6793	275	29	the	the	DET
ejpam-6793	275	30	exponential	exponential	ADJ
ejpam-6793	275	31	base	base	NOUN
ejpam-6793	275	32	{	{	PUNCT
ejpam-6793	275	33	qen(x	qen(x	X
ejpam-6793	275	34	)	)	PUNCT
ejpam-6793	275	35	}	}	PUNCT
ejpam-6793	275	36	is	be	AUX
ejpam-6793	275	37	effective	effective	ADJ
ejpam-6793	275	38	for	for	ADP
ejpam-6793	275	39	wb+(r	wb+(r	NOUN
ejpam-6793	275	40	)	)	PUNCT
ejpam-6793	275	41	.	.	PUNCT
ejpam-6793	276	1	remark	remark	PROPN
ejpam-6793	276	2	5	5	NUM
ejpam-6793	276	3	.	.	PUNCT
ejpam-6793	277	1	when	when	SCONJ
ejpam-6793	277	2	r→	r→	PROPN
ejpam-6793	277	3	0	0	NUM
ejpam-6793	277	4	in	in	ADP
ejpam-6793	277	5	condition	condition	NOUN
ejpam-6793	277	6	(	(	PUNCT
ejpam-6793	277	7	30	30	NUM
ejpam-6793	277	8	)	)	PUNCT
ejpam-6793	277	9	we	we	PRON
ejpam-6793	277	10	obtain	obtain	VERB
ejpam-6793	277	11	the	the	DET
ejpam-6793	277	12	effectiveness	effectiveness	NOUN
ejpam-6793	277	13	of	of	ADP
ejpam-6793	277	14	the	the	DET
ejpam-6793	277	15	ecbsmps	ecbsmp	NOUN
ejpam-6793	277	16	,	,	PUNCT
ejpam-6793	277	17	{	{	PUNCT
ejpam-6793	277	18	qen(x	qen(x	X
ejpam-6793	277	19	)	)	PUNCT
ejpam-6793	277	20	}	}	PUNCT
ejpam-6793	277	21	for	for	ADP
ejpam-6793	277	22	the	the	DET
ejpam-6793	277	23	space	space	NOUN
ejpam-6793	277	24	w0	w0	PROPN
ejpam-6793	277	25	+	+	PROPN
ejpam-6793	277	26	.	.	PUNCT
ejpam-6793	278	1	in	in	ADP
ejpam-6793	278	2	order	order	NOUN
ejpam-6793	278	3	to	to	PART
ejpam-6793	278	4	examine	examine	VERB
ejpam-6793	278	5	the	the	DET
ejpam-6793	278	6	effectiveness	effectiveness	NOUN
ejpam-6793	278	7	of	of	ADP
ejpam-6793	278	8	the	the	DET
ejpam-6793	278	9	ecbsmps	ecbsmp	NOUN
ejpam-6793	278	10	{	{	PUNCT
ejpam-6793	278	11	qen(x	qen(x	X
ejpam-6793	278	12	)	)	PUNCT
ejpam-6793	278	13	}	}	PUNCT
ejpam-6793	278	14	for	for	ADP
ejpam-6793	278	15	the	the	DET
ejpam-6793	278	16	f	f	NOUN
ejpam-6793	278	17	-	-	PUNCT
ejpam-6793	278	18	module	module	NOUN
ejpam-6793	278	19	wb(r	wb(r	NOUN
ejpam-6793	278	20	)	)	PUNCT
ejpam-6793	278	21	,	,	PUNCT
ejpam-6793	278	22	we	we	PRON
ejpam-6793	278	23	assume	assume	VERB
ejpam-6793	278	24	that	that	SCONJ
ejpam-6793	278	25	the	the	DET
ejpam-6793	278	26	base	base	NOUN
ejpam-6793	278	27	{	{	PUNCT
ejpam-6793	278	28	qn(x	qn(x	NOUN
ejpam-6793	278	29	)	)	PUNCT
ejpam-6793	278	30	}	}	PUNCT
ejpam-6793	278	31	fulfills	fulfill	VERB
ejpam-6793	278	32	the	the	DET
ejpam-6793	278	33	condition	condition	NOUN
ejpam-6793	278	34	µ(q	µ(q	PROPN
ejpam-6793	278	35	,	,	PUNCT
ejpam-6793	278	36	r	r	NOUN
ejpam-6793	278	37	)	)	PUNCT
ejpam-6793	278	38	<	<	X
ejpam-6793	278	39	r	r	NOUN
ejpam-6793	278	40	,	,	PUNCT
ejpam-6793	278	41	∀r	∀r	X
ejpam-6793	278	42	<	<	X
ejpam-6793	278	43	r	r	NOUN
ejpam-6793	278	44	,	,	PUNCT
ejpam-6793	278	45	(	(	PUNCT
ejpam-6793	278	46	36	36	NUM
ejpam-6793	278	47	)	)	PUNCT
ejpam-6793	278	48	with	with	ADP
ejpam-6793	278	49	µ(q	µ(q	PROPN
ejpam-6793	278	50	,	,	PUNCT
ejpam-6793	278	51	r	r	NOUN
ejpam-6793	278	52	)	)	PUNCT
ejpam-6793	278	53	=	=	SYM
ejpam-6793	278	54	lim	lim	PROPN
ejpam-6793	278	55	sup	sup	PROPN
ejpam-6793	278	56	n→∞	n→∞	X
ejpam-6793	278	57	{	{	PUNCT
ejpam-6793	278	58	∥qn∥r	∥qn∥r	NOUN
ejpam-6793	278	59	}	}	SYM
ejpam-6793	278	60	1	1	NUM
ejpam-6793	278	61	n	n	NOUN
ejpam-6793	278	62	.	.	PUNCT
ejpam-6793	279	1	theorem	theorem	ADJ
ejpam-6793	279	2	6	6	NUM
ejpam-6793	279	3	.	.	PUNCT
ejpam-6793	280	1	if	if	SCONJ
ejpam-6793	280	2	the	the	DET
ejpam-6793	280	3	cbsmps	cbsmp	NOUN
ejpam-6793	280	4	{	{	PUNCT
ejpam-6793	280	5	qn(x	qn(x	NOUN
ejpam-6793	280	6	)	)	PUNCT
ejpam-6793	280	7	}	}	PUNCT
ejpam-6793	280	8	satisfying	satisfy	VERB
ejpam-6793	280	9	(	(	PUNCT
ejpam-6793	280	10	36	36	NUM
ejpam-6793	280	11	)	)	PUNCT
ejpam-6793	280	12	,	,	PUNCT
ejpam-6793	280	13	then	then	ADV
ejpam-6793	280	14	the	the	DET
ejpam-6793	280	15	ecbsmps	ecbsmp	NOUN
ejpam-6793	280	16	{	{	PUNCT
ejpam-6793	280	17	qen(x	qen(x	X
ejpam-6793	280	18	)	)	PUNCT
ejpam-6793	280	19	}	}	PUNCT
ejpam-6793	280	20	associated	associate	VERB
ejpam-6793	280	21	with	with	ADP
ejpam-6793	280	22	{	{	PUNCT
ejpam-6793	280	23	qn(x	qn(x	NOUN
ejpam-6793	280	24	)	)	PUNCT
ejpam-6793	280	25	}	}	PUNCT
ejpam-6793	280	26	is	be	AUX
ejpam-6793	280	27	effectiveness	effectiveness	NOUN
ejpam-6793	280	28	for	for	ADP
ejpam-6793	280	29	wb(r	wb(r	NOUN
ejpam-6793	280	30	)	)	PUNCT
ejpam-6793	280	31	.	.	PUNCT
ejpam-6793	281	1	proof	proof	NOUN
ejpam-6793	281	2	.	.	PUNCT
ejpam-6793	282	1	the	the	DET
ejpam-6793	282	2	proof	proof	NOUN
ejpam-6793	282	3	of	of	ADP
ejpam-6793	282	4	the	the	DET
ejpam-6793	282	5	following	following	ADJ
ejpam-6793	282	6	theorem	theorem	NOUN
ejpam-6793	282	7	is	be	AUX
ejpam-6793	282	8	omitted	omit	VERB
ejpam-6793	282	9	,	,	PUNCT
ejpam-6793	282	10	as	as	SCONJ
ejpam-6793	282	11	it	it	PRON
ejpam-6793	282	12	can	can	AUX
ejpam-6793	282	13	be	be	AUX
ejpam-6793	282	14	established	establish	VERB
ejpam-6793	282	15	by	by	ADP
ejpam-6793	282	16	arguments	argument	NOUN
ejpam-6793	282	17	analogous	analogous	ADJ
ejpam-6793	282	18	to	to	ADP
ejpam-6793	282	19	those	those	PRON
ejpam-6793	282	20	employed	employ	VERB
ejpam-6793	282	21	in	in	ADP
ejpam-6793	282	22	theorem	theorem	ADJ
ejpam-6793	282	23	4	4	NUM
ejpam-6793	282	24	,	,	PUNCT
ejpam-6793	282	25	together	together	ADV
ejpam-6793	282	26	with	with	ADP
ejpam-6793	282	27	the	the	DET
ejpam-6793	282	28	aid	aid	NOUN
ejpam-6793	282	29	of	of	ADP
ejpam-6793	282	30	theorem	theorem	ADJ
ejpam-6793	282	31	1	1	NUM
ejpam-6793	282	32	(	(	PUNCT
ejpam-6793	282	33	see	see	VERB
ejpam-6793	282	34	[	[	X
ejpam-6793	282	35	16	16	NUM
ejpam-6793	282	36	]	]	SYM
ejpam-6793	282	37	)	)	PUNCT
ejpam-6793	282	38	.	.	PUNCT
ejpam-6793	283	1	remark	remark	NOUN
ejpam-6793	283	2	6	6	NUM
ejpam-6793	283	3	.	.	PUNCT
ejpam-6793	284	1	if	if	SCONJ
ejpam-6793	284	2	r→	r→	PROPN
ejpam-6793	284	3	∞	∞	PROPN
ejpam-6793	284	4	then	then	ADV
ejpam-6793	284	5	condition	condition	NOUN
ejpam-6793	284	6	(	(	PUNCT
ejpam-6793	284	7	36	36	NUM
ejpam-6793	284	8	)	)	PUNCT
ejpam-6793	284	9	will	will	AUX
ejpam-6793	284	10	be	be	AUX
ejpam-6793	284	11	replaced	replace	VERB
ejpam-6793	284	12	by	by	ADP
ejpam-6793	284	13	the	the	DET
ejpam-6793	284	14	condition	condition	NOUN
ejpam-6793	284	15	µ(q	µ(q	PROPN
ejpam-6793	284	16	,	,	PUNCT
ejpam-6793	284	17	r	r	NOUN
ejpam-6793	284	18	)	)	PUNCT
ejpam-6793	284	19	<	<	X
ejpam-6793	284	20	∞	∞	PROPN
ejpam-6793	284	21	,	,	PUNCT
ejpam-6793	284	22	∀r	∀r	X
ejpam-6793	284	23	<	<	X
ejpam-6793	284	24	∞	∞	PROPN
ejpam-6793	284	25	,	,	PUNCT
ejpam-6793	284	26	(	(	PUNCT
ejpam-6793	284	27	37	37	NUM
ejpam-6793	284	28	)	)	PUNCT
ejpam-6793	284	29	and	and	CCONJ
ejpam-6793	284	30	we	we	PRON
ejpam-6793	284	31	have	have	VERB
ejpam-6793	284	32	the	the	DET
ejpam-6793	284	33	effectiveness	effectiveness	NOUN
ejpam-6793	284	34	for	for	ADP
ejpam-6793	284	35	the	the	DET
ejpam-6793	284	36	ecbsmps	ecbsmp	NOUN
ejpam-6793	284	37	{	{	PUNCT
ejpam-6793	284	38	qen(x	qen(x	X
ejpam-6793	284	39	)	)	PUNCT
ejpam-6793	284	40	}	}	PUNCT
ejpam-6793	284	41	for	for	ADP
ejpam-6793	284	42	w∞.	w∞.	NOUN
ejpam-6793	284	43	m.	m.	NOUN
ejpam-6793	284	44	zayed	zayed	PROPN
ejpam-6793	284	45	/	/	SYM
ejpam-6793	284	46	eur	eur	PROPN
ejpam-6793	284	47	.	.	PUNCT
ejpam-6793	285	1	j.	j.	PROPN
ejpam-6793	285	2	pure	pure	PROPN
ejpam-6793	285	3	appl	appl	PROPN
ejpam-6793	285	4	.	.	PROPN
ejpam-6793	285	5	math	math	PROPN
ejpam-6793	285	6	,	,	PUNCT
ejpam-6793	285	7	18	18	NUM
ejpam-6793	285	8	(	(	PUNCT
ejpam-6793	285	9	4	4	NUM
ejpam-6793	285	10	)	)	PUNCT
ejpam-6793	285	11	(	(	PUNCT
ejpam-6793	285	12	2025	2025	NUM
ejpam-6793	285	13	)	)	PUNCT
ejpam-6793	285	14	,	,	PUNCT
ejpam-6793	285	15	6793	6793	NUM
ejpam-6793	285	16	17	17	NUM
ejpam-6793	285	17	of	of	ADP
ejpam-6793	285	18	19	19	NUM
ejpam-6793	285	19	now	now	ADV
ejpam-6793	285	20	,	,	PUNCT
ejpam-6793	285	21	let	let	VERB
ejpam-6793	285	22	{	{	PUNCT
ejpam-6793	285	23	qs	qs	VERB
ejpam-6793	285	24	,	,	PUNCT
ejpam-6793	285	25	n(x	n(x	PROPN
ejpam-6793	285	26	)	)	PUNCT
ejpam-6793	285	27	}	}	PUNCT
ejpam-6793	285	28	,	,	PUNCT
ejpam-6793	285	29	s	s	NOUN
ejpam-6793	285	30	=	=	SYM
ejpam-6793	285	31	1	1	NUM
ejpam-6793	285	32	,	,	PUNCT
ejpam-6793	285	33	2	2	NUM
ejpam-6793	285	34	,	,	PUNCT
ejpam-6793	285	35	3	3	NUM
ejpam-6793	285	36	be	be	AUX
ejpam-6793	285	37	three	three	NUM
ejpam-6793	285	38	bases	basis	NOUN
ejpam-6793	285	39	of	of	ADP
ejpam-6793	285	40	smps	smp	NOUN
ejpam-6793	285	41	where	where	SCONJ
ejpam-6793	285	42	x	x	SYM
ejpam-6793	285	43	∈	∈	PROPN
ejpam-6793	285	44	rm+1	rm+1	PROPN
ejpam-6793	285	45	.	.	PUNCT
ejpam-6793	286	1	the	the	DET
ejpam-6793	286	2	equivalent	equivalent	ADJ
ejpam-6793	286	3	base	base	NOUN
ejpam-6793	286	4	{	{	PUNCT
ejpam-6793	286	5	tn(x	tn(x	ADJ
ejpam-6793	286	6	)	)	PUNCT
ejpam-6793	286	7	}	}	PUNCT
ejpam-6793	286	8	defined	define	VERB
ejpam-6793	286	9	by	by	ADP
ejpam-6793	286	10	{	{	PUNCT
ejpam-6793	286	11	tn(x	tn(x	ADJ
ejpam-6793	286	12	)	)	PUNCT
ejpam-6793	286	13	}	}	PUNCT
ejpam-6793	286	14	=	=	SYM
ejpam-6793	286	15	{	{	PUNCT
ejpam-6793	286	16	q̃3,n(x)}{q2,n(x)}{q1,n(x	q̃3,n(x)}{q2,n(x)}{q1,n(x	NOUN
ejpam-6793	286	17	)	)	PUNCT
ejpam-6793	286	18	}	}	PUNCT
ejpam-6793	286	19	(	(	PUNCT
ejpam-6793	286	20	38	38	NUM
ejpam-6793	286	21	)	)	PUNCT
ejpam-6793	286	22	where	where	SCONJ
ejpam-6793	286	23	{	{	PUNCT
ejpam-6793	286	24	q̃3,n(x	q̃3,n(x	NOUN
ejpam-6793	286	25	)	)	PUNCT
ejpam-6793	286	26	}	}	PUNCT
ejpam-6793	286	27	is	be	AUX
ejpam-6793	286	28	the	the	DET
ejpam-6793	286	29	inverse	inverse	ADJ
ejpam-6793	286	30	base	base	NOUN
ejpam-6793	286	31	of	of	ADP
ejpam-6793	286	32	{	{	PUNCT
ejpam-6793	286	33	q3,n(x	q3,n(x	NOUN
ejpam-6793	286	34	)	)	PUNCT
ejpam-6793	286	35	}	}	PUNCT
ejpam-6793	286	36	.	.	PUNCT
ejpam-6793	287	1	in	in	ADP
ejpam-6793	287	2	a	a	DET
ejpam-6793	287	3	recent	recent	ADJ
ejpam-6793	287	4	paper	paper	NOUN
ejpam-6793	287	5	[	[	X
ejpam-6793	287	6	17	17	NUM
ejpam-6793	287	7	]	]	PUNCT
ejpam-6793	287	8	the	the	DET
ejpam-6793	287	9	authors	author	NOUN
ejpam-6793	287	10	prove	prove	VERB
ejpam-6793	287	11	that	that	SCONJ
ejpam-6793	287	12	the	the	DET
ejpam-6793	287	13	equivalent	equivalent	ADJ
ejpam-6793	287	14	base	base	NOUN
ejpam-6793	287	15	{	{	PUNCT
ejpam-6793	287	16	tn(x	tn(x	ADJ
ejpam-6793	287	17	)	)	PUNCT
ejpam-6793	287	18	}	}	PUNCT
ejpam-6793	287	19	satisfy	satisfy	VERB
ejpam-6793	287	20	the	the	DET
ejpam-6793	287	21	conditions	condition	NOUN
ejpam-6793	287	22	µ(t	µ(t	ADJ
ejpam-6793	287	23	,	,	PUNCT
ejpam-6793	287	24	r	r	NOUN
ejpam-6793	287	25	)	)	PUNCT
ejpam-6793	287	26	<	<	X
ejpam-6793	287	27	r	r	NOUN
ejpam-6793	287	28	,	,	PUNCT
ejpam-6793	287	29	∀r	∀r	X
ejpam-6793	287	30	<	<	X
ejpam-6793	287	31	r	r	NOUN
ejpam-6793	287	32	,	,	PUNCT
ejpam-6793	287	33	(	(	PUNCT
ejpam-6793	287	34	39	39	NUM
ejpam-6793	287	35	)	)	PUNCT
ejpam-6793	287	36	and	and	CCONJ
ejpam-6793	287	37	µ(t	µ(t	ADJ
ejpam-6793	287	38	,	,	PUNCT
ejpam-6793	287	39	r+	r+	X
ejpam-6793	287	40	)	)	PUNCT
ejpam-6793	287	41	≤	≤	NOUN
ejpam-6793	287	42	r	r	NOUN
ejpam-6793	287	43	,	,	PUNCT
ejpam-6793	287	44	(	(	PUNCT
ejpam-6793	287	45	40	40	NUM
ejpam-6793	287	46	)	)	PUNCT
ejpam-6793	287	47	when	when	SCONJ
ejpam-6793	287	48	the	the	DET
ejpam-6793	287	49	bases	basis	NOUN
ejpam-6793	287	50	{	{	PUNCT
ejpam-6793	287	51	qs	qs	NOUN
ejpam-6793	287	52	,	,	PUNCT
ejpam-6793	287	53	n(x	n(x	PROPN
ejpam-6793	287	54	)	)	PUNCT
ejpam-6793	287	55	}	}	PUNCT
ejpam-6793	287	56	,	,	PUNCT
ejpam-6793	287	57	s	s	NOUN
ejpam-6793	287	58	=	=	SYM
ejpam-6793	287	59	1	1	NUM
ejpam-6793	287	60	,	,	PUNCT
ejpam-6793	287	61	2	2	NUM
ejpam-6793	287	62	,	,	PUNCT
ejpam-6793	287	63	3	3	NUM
ejpam-6793	287	64	is	be	AUX
ejpam-6793	287	65	algebraic	algebraic	ADJ
ejpam-6793	287	66	according	accord	VERB
ejpam-6793	287	67	to	to	ADP
ejpam-6793	287	68	[	[	X
ejpam-6793	287	69	10	10	NUM
ejpam-6793	287	70	]	]	PUNCT
ejpam-6793	287	71	and	and	CCONJ
ejpam-6793	287	72	satisfying	satisfy	VERB
ejpam-6793	287	73	the	the	DET
ejpam-6793	287	74	following	follow	VERB
ejpam-6793	287	75	conditions	condition	NOUN
ejpam-6793	287	76	,	,	PUNCT
ejpam-6793	287	77	respectively	respectively	ADV
ejpam-6793	287	78	µ(qs	µ(qs	PROPN
ejpam-6793	287	79	,	,	PUNCT
ejpam-6793	287	80	r	r	NOUN
ejpam-6793	287	81	)	)	PUNCT
ejpam-6793	287	82	<	<	X
ejpam-6793	287	83	r	r	NOUN
ejpam-6793	287	84	,	,	PUNCT
ejpam-6793	287	85	∀r	∀r	X
ejpam-6793	287	86	<	<	X
ejpam-6793	287	87	r	r	NOUN
ejpam-6793	287	88	,	,	PUNCT
ejpam-6793	287	89	(	(	PUNCT
ejpam-6793	287	90	41	41	NUM
ejpam-6793	287	91	)	)	PUNCT
ejpam-6793	287	92	and	and	CCONJ
ejpam-6793	287	93	µ(qs	µ(qs	PROPN
ejpam-6793	287	94	,	,	PUNCT
ejpam-6793	287	95	r	r	NOUN
ejpam-6793	287	96	+	+	NOUN
ejpam-6793	287	97	)	)	PUNCT
ejpam-6793	287	98	≤	≤	NOUN
ejpam-6793	287	99	r	r	NOUN
ejpam-6793	287	100	,	,	PUNCT
ejpam-6793	287	101	(	(	PUNCT
ejpam-6793	287	102	42	42	X
ejpam-6793	287	103	)	)	PUNCT
ejpam-6793	287	104	applying	apply	VERB
ejpam-6793	287	105	theorems	theorem	NOUN
ejpam-6793	287	106	5	5	NUM
ejpam-6793	287	107	and	and	CCONJ
ejpam-6793	287	108	6	6	NUM
ejpam-6793	287	109	,	,	PUNCT
ejpam-6793	287	110	we	we	PRON
ejpam-6793	287	111	conclude	conclude	VERB
ejpam-6793	287	112	the	the	DET
ejpam-6793	287	113	following	follow	VERB
ejpam-6793	287	114	result	result	NOUN
ejpam-6793	287	115	.	.	PUNCT
ejpam-6793	288	1	corollary	corollary	ADJ
ejpam-6793	288	2	1	1	NUM
ejpam-6793	288	3	.	.	PUNCT
ejpam-6793	289	1	let	let	VERB
ejpam-6793	289	2	{	{	PUNCT
ejpam-6793	289	3	qs	qs	VERB
ejpam-6793	289	4	,	,	PUNCT
ejpam-6793	289	5	n(x	n(x	PROPN
ejpam-6793	289	6	)	)	PUNCT
ejpam-6793	289	7	}	}	PUNCT
ejpam-6793	289	8	,	,	PUNCT
ejpam-6793	289	9	s	s	NOUN
ejpam-6793	289	10	=	=	SYM
ejpam-6793	289	11	1	1	NUM
ejpam-6793	289	12	,	,	PUNCT
ejpam-6793	289	13	2	2	NUM
ejpam-6793	289	14	,	,	PUNCT
ejpam-6793	289	15	3	3	NUM
ejpam-6793	289	16	be	be	AUX
ejpam-6793	289	17	three	three	NUM
ejpam-6793	289	18	algebraic	algebraic	ADJ
ejpam-6793	289	19	bases	basis	NOUN
ejpam-6793	289	20	of	of	ADP
ejpam-6793	289	21	smps	smp	NOUN
ejpam-6793	289	22	satisfying	satisfy	VERB
ejpam-6793	289	23	the	the	DET
ejpam-6793	289	24	conditions	condition	NOUN
ejpam-6793	289	25	(	(	PUNCT
ejpam-6793	289	26	41	41	NUM
ejpam-6793	289	27	)	)	PUNCT
ejpam-6793	289	28	and	and	CCONJ
ejpam-6793	289	29	(	(	PUNCT
ejpam-6793	289	30	42	42	NUM
ejpam-6793	289	31	)	)	PUNCT
ejpam-6793	289	32	,	,	PUNCT
ejpam-6793	289	33	then	then	ADV
ejpam-6793	289	34	the	the	DET
ejpam-6793	289	35	ecbsmps	ecbsmp	NOUN
ejpam-6793	289	36	{	{	PUNCT
ejpam-6793	289	37	ten(x	ten(x	PROPN
ejpam-6793	289	38	)	)	PUNCT
ejpam-6793	289	39	}	}	PUNCT
ejpam-6793	289	40	associated	associate	VERB
ejpam-6793	289	41	with	with	ADP
ejpam-6793	289	42	the	the	DET
ejpam-6793	289	43	equivalent	equivalent	ADJ
ejpam-6793	289	44	base	base	NOUN
ejpam-6793	289	45	{	{	PUNCT
ejpam-6793	289	46	tn(x	tn(x	ADJ
ejpam-6793	289	47	)	)	PUNCT
ejpam-6793	289	48	}	}	PUNCT
ejpam-6793	289	49	are	be	AUX
ejpam-6793	289	50	effectiveness	effectiveness	NOUN
ejpam-6793	289	51	for	for	ADP
ejpam-6793	289	52	the	the	DET
ejpam-6793	289	53	spaces	space	NOUN
ejpam-6793	289	54	wb(r	wb(r	NOUN
ejpam-6793	289	55	)	)	PUNCT
ejpam-6793	289	56	,	,	PUNCT
ejpam-6793	289	57	wb+(r	wb+(r	PROPN
ejpam-6793	289	58	)	)	PUNCT
ejpam-6793	289	59	,	,	PUNCT
ejpam-6793	289	60	w0	w0	PROPN
ejpam-6793	289	61	+	+	CCONJ
ejpam-6793	289	62	and	and	CCONJ
ejpam-6793	289	63	w∞.	w∞.	X
ejpam-6793	289	64	looking	look	VERB
ejpam-6793	289	65	back	back	ADV
ejpam-6793	289	66	to	to	ADP
ejpam-6793	289	67	the	the	DET
ejpam-6793	289	68	equivalent	equivalent	ADJ
ejpam-6793	289	69	base	base	NOUN
ejpam-6793	289	70	{	{	PUNCT
ejpam-6793	289	71	tn(x	tn(x	ADJ
ejpam-6793	289	72	)	)	PUNCT
ejpam-6793	289	73	}	}	PUNCT
ejpam-6793	289	74	and	and	CCONJ
ejpam-6793	289	75	by	by	ADP
ejpam-6793	289	76	taking	take	VERB
ejpam-6793	289	77	{	{	PUNCT
ejpam-6793	289	78	q3,n(x	q3,n(x	NOUN
ejpam-6793	289	79	)	)	PUNCT
ejpam-6793	289	80	}	}	PUNCT
ejpam-6793	289	81	=	=	SYM
ejpam-6793	289	82	{	{	PUNCT
ejpam-6793	289	83	q1,n(x	q1,n(x	NOUN
ejpam-6793	289	84	)	)	PUNCT
ejpam-6793	289	85	}	}	PUNCT
ejpam-6793	289	86	,	,	PUNCT
ejpam-6793	289	87	we	we	PRON
ejpam-6793	289	88	get	get	VERB
ejpam-6793	289	89	the	the	DET
ejpam-6793	289	90	similar	similar	ADJ
ejpam-6793	289	91	base	base	NOUN
ejpam-6793	289	92	{	{	PUNCT
ejpam-6793	289	93	sn(x	sn(x	ADJ
ejpam-6793	289	94	)	)	PUNCT
ejpam-6793	289	95	}	}	PUNCT
ejpam-6793	289	96	as	as	SCONJ
ejpam-6793	289	97	studied	study	VERB
ejpam-6793	289	98	in	in	ADP
ejpam-6793	289	99	[	[	X
ejpam-6793	289	100	25	25	NUM
ejpam-6793	289	101	]	]	PUNCT
ejpam-6793	289	102	.	.	PUNCT
ejpam-6793	290	1	therefore	therefore	ADV
ejpam-6793	290	2	all	all	DET
ejpam-6793	290	3	the	the	DET
ejpam-6793	290	4	results	result	NOUN
ejpam-6793	290	5	of	of	ADP
ejpam-6793	290	6	corollary	corollary	ADJ
ejpam-6793	290	7	1	1	NUM
ejpam-6793	290	8	will	will	AUX
ejpam-6793	290	9	be	be	AUX
ejpam-6793	290	10	satisfied	satisfied	ADJ
ejpam-6793	290	11	but	but	CCONJ
ejpam-6793	290	12	for	for	ADP
ejpam-6793	290	13	the	the	DET
ejpam-6793	290	14	similar	similar	ADJ
ejpam-6793	290	15	base	base	NOUN
ejpam-6793	290	16	{	{	PUNCT
ejpam-6793	290	17	sn(x	sn(x	ADJ
ejpam-6793	290	18	)	)	PUNCT
ejpam-6793	290	19	}	}	PUNCT
ejpam-6793	290	20	instead	instead	ADV
ejpam-6793	290	21	of	of	ADP
ejpam-6793	290	22	equivalent	equivalent	ADJ
ejpam-6793	290	23	base	base	NOUN
ejpam-6793	290	24	{	{	PUNCT
ejpam-6793	290	25	tn(x	tn(x	ADJ
ejpam-6793	290	26	)	)	PUNCT
ejpam-6793	290	27	}	}	PUNCT
ejpam-6793	290	28	.	.	PUNCT
ejpam-6793	291	1	5	5	X
ejpam-6793	291	2	.	.	X
ejpam-6793	291	3	conclusions	conclusion	NOUN
ejpam-6793	291	4	the	the	DET
ejpam-6793	291	5	current	current	ADJ
ejpam-6793	291	6	study	study	NOUN
ejpam-6793	291	7	discusses	discuss	VERB
ejpam-6793	291	8	the	the	DET
ejpam-6793	291	9	representation	representation	NOUN
ejpam-6793	291	10	of	of	ADP
ejpam-6793	291	11	the	the	DET
ejpam-6793	291	12	exponential	exponential	ADJ
ejpam-6793	291	13	base	base	NOUN
ejpam-6793	291	14	of	of	ADP
ejpam-6793	291	15	special	special	ADJ
ejpam-6793	291	16	monogenic	monogenic	ADJ
ejpam-6793	291	17	polynomials	polynomial	NOUN
ejpam-6793	291	18	(	(	PUNCT
ejpam-6793	291	19	ebsmps	ebsmp	NOUN
ejpam-6793	291	20	)	)	PUNCT
ejpam-6793	291	21	in	in	ADP
ejpam-6793	291	22	fréchet	fréchet	NOUN
ejpam-6793	291	23	modules	module	NOUN
ejpam-6793	291	24	.	.	PUNCT
ejpam-6793	292	1	the	the	DET
ejpam-6793	292	2	coefficients	coefficient	NOUN
ejpam-6793	292	3	of	of	ADP
ejpam-6793	292	4	the	the	DET
ejpam-6793	292	5	power	power	NOUN
ejpam-6793	292	6	associated	associate	VERB
ejpam-6793	292	7	infinite	infinite	ADJ
ejpam-6793	292	8	matrices	matrix	NOUN
ejpam-6793	292	9	of	of	ADP
ejpam-6793	292	10	an	an	DET
ejpam-6793	292	11	original	original	ADJ
ejpam-6793	292	12	base	base	NOUN
ejpam-6793	292	13	have	have	VERB
ejpam-6793	292	14	some	some	DET
ejpam-6793	292	15	restriction	restriction	NOUN
ejpam-6793	292	16	for	for	ADP
ejpam-6793	292	17	which	which	PRON
ejpam-6793	292	18	certain	certain	ADJ
ejpam-6793	292	19	classes	class	NOUN
ejpam-6793	292	20	of	of	ADP
ejpam-6793	292	21	smfs	smfs	NOUN
ejpam-6793	292	22	can	can	AUX
ejpam-6793	292	23	be	be	AUX
ejpam-6793	292	24	represented	represent	VERB
ejpam-6793	292	25	by	by	ADP
ejpam-6793	292	26	esbsmps	esbsmp	NOUN
ejpam-6793	292	27	in	in	ADP
ejpam-6793	292	28	hyber	hyber	PROPN
ejpam-6793	292	29	closed	close	VERB
ejpam-6793	292	30	ball	ball	NOUN
ejpam-6793	292	31	.	.	PUNCT
ejpam-6793	293	1	the	the	DET
ejpam-6793	293	2	upper	upper	ADJ
ejpam-6793	293	3	bound	bound	NOUN
ejpam-6793	293	4	of	of	ADP
ejpam-6793	293	5	the	the	DET
ejpam-6793	293	6	order	order	NOUN
ejpam-6793	293	7	of	of	ADP
ejpam-6793	293	8	the	the	DET
ejpam-6793	293	9	esbsmps	esbsmp	NOUN
ejpam-6793	293	10	is	be	AUX
ejpam-6793	293	11	is	be	AUX
ejpam-6793	293	12	determined	determine	VERB
ejpam-6793	293	13	.	.	PUNCT
ejpam-6793	294	1	moreover	moreover	ADV
ejpam-6793	294	2	,	,	PUNCT
ejpam-6793	294	3	the	the	DET
ejpam-6793	294	4	effectiveness	effectiveness	NOUN
ejpam-6793	294	5	of	of	ADP
ejpam-6793	294	6	the	the	DET
ejpam-6793	294	7	exponential	exponential	ADJ
ejpam-6793	294	8	base	base	NOUN
ejpam-6793	294	9	associated	associate	VERB
ejpam-6793	294	10	with	with	ADP
ejpam-6793	294	11	cannon	cannon	NOUN
ejpam-6793	294	12	sets	set	NOUN
ejpam-6793	294	13	is	be	AUX
ejpam-6793	294	14	studied	study	VERB
ejpam-6793	294	15	in	in	ADP
ejpam-6793	294	16	different	different	ADJ
ejpam-6793	294	17	hyper	hyper	ADJ
ejpam-6793	294	18	regions	region	NOUN
ejpam-6793	294	19	.	.	PUNCT
ejpam-6793	295	1	in	in	ADP
ejpam-6793	295	2	the	the	DET
ejpam-6793	295	3	previous	previous	ADJ
ejpam-6793	295	4	studies	study	NOUN
ejpam-6793	295	5	[	[	X
ejpam-6793	295	6	9–11	9–11	NOUN
ejpam-6793	295	7	,	,	PUNCT
ejpam-6793	295	8	20	20	NUM
ejpam-6793	295	9	,	,	PUNCT
ejpam-6793	295	10	25–27	25–27	NUM
ejpam-6793	295	11	]	]	PUNCT
ejpam-6793	295	12	in	in	ADP
ejpam-6793	295	13	complex	complex	ADJ
ejpam-6793	295	14	and	and	CCONJ
ejpam-6793	295	15	clifford	clifford	PROPN
ejpam-6793	295	16	analysis	analysis	NOUN
ejpam-6793	295	17	the	the	DET
ejpam-6793	295	18	convergence	convergence	NOUN
ejpam-6793	295	19	properties	property	NOUN
ejpam-6793	295	20	(	(	PUNCT
ejpam-6793	295	21	effectiveness	effectiveness	NOUN
ejpam-6793	295	22	,	,	PUNCT
ejpam-6793	295	23	order	order	NOUN
ejpam-6793	295	24	,	,	PUNCT
ejpam-6793	295	25	type	type	NOUN
ejpam-6793	295	26	,	,	PUNCT
ejpam-6793	295	27	and	and	CCONJ
ejpam-6793	295	28	the	the	DET
ejpam-6793	295	29	tρ	tρ	NOUN
ejpam-6793	295	30	-	-	PUNCT
ejpam-6793	295	31	property	property	NOUN
ejpam-6793	295	32	)	)	PUNCT
ejpam-6793	295	33	of	of	ADP
ejpam-6793	295	34	some	some	DET
ejpam-6793	295	35	associated	associated	ADJ
ejpam-6793	295	36	bases	basis	NOUN
ejpam-6793	295	37	of	of	ADP
ejpam-6793	295	38	polynomials	polynomial	NOUN
ejpam-6793	295	39	have	have	AUX
ejpam-6793	295	40	been	be	AUX
ejpam-6793	295	41	examined	examine	VERB
ejpam-6793	295	42	,	,	PUNCT
ejpam-6793	295	43	such	such	ADJ
ejpam-6793	295	44	as	as	ADP
ejpam-6793	295	45	,	,	PUNCT
ejpam-6793	295	46	hadamard	hadamard	ADJ
ejpam-6793	295	47	product	product	NOUN
ejpam-6793	295	48	base	base	NOUN
ejpam-6793	295	49	,	,	PUNCT
ejpam-6793	295	50	product	product	NOUN
ejpam-6793	295	51	base	base	NOUN
ejpam-6793	295	52	,	,	PUNCT
ejpam-6793	295	53	inverse	inverse	NOUN
ejpam-6793	295	54	base	base	NOUN
ejpam-6793	295	55	,	,	PUNCT
ejpam-6793	295	56	square	square	ADJ
ejpam-6793	295	57	root	root	NOUN
ejpam-6793	295	58	base	base	NOUN
ejpam-6793	295	59	,	,	PUNCT
ejpam-6793	295	60	m.	m.	NOUN
ejpam-6793	295	61	zayed	zayed	PROPN
ejpam-6793	295	62	/	/	SYM
ejpam-6793	295	63	eur	eur	PROPN
ejpam-6793	295	64	.	.	PUNCT
ejpam-6793	296	1	j.	j.	PROPN
ejpam-6793	296	2	pure	pure	PROPN
ejpam-6793	296	3	appl	appl	PROPN
ejpam-6793	296	4	.	.	PROPN
ejpam-6793	296	5	math	math	PROPN
ejpam-6793	296	6	,	,	PUNCT
ejpam-6793	296	7	18	18	NUM
ejpam-6793	296	8	(	(	PUNCT
ejpam-6793	296	9	4	4	NUM
ejpam-6793	296	10	)	)	PUNCT
ejpam-6793	296	11	(	(	PUNCT
ejpam-6793	296	12	2025	2025	NUM
ejpam-6793	296	13	)	)	PUNCT
ejpam-6793	296	14	,	,	PUNCT
ejpam-6793	296	15	6793	6793	NUM
ejpam-6793	296	16	18	18	NUM
ejpam-6793	296	17	of	of	ADP
ejpam-6793	296	18	19	19	NUM
ejpam-6793	296	19	similar	similar	ADJ
ejpam-6793	296	20	base	base	NOUN
ejpam-6793	296	21	and	and	CCONJ
ejpam-6793	296	22	similar	similar	ADJ
ejpam-6793	296	23	transposed	transpose	VERB
ejpam-6793	296	24	base	base	NOUN
ejpam-6793	296	25	.	.	PUNCT
ejpam-6793	297	1	theses	these	VERB
ejpam-6793	297	2	constituents	constituent	NOUN
ejpam-6793	297	3	are	be	AUX
ejpam-6793	297	4	simple	simple	ADJ
ejpam-6793	297	5	monic	monic	ADJ
ejpam-6793	297	6	bases	basis	NOUN
ejpam-6793	297	7	.	.	PUNCT
ejpam-6793	298	1	it	it	PRON
ejpam-6793	298	2	is	be	AUX
ejpam-6793	298	3	interesting	interesting	ADJ
ejpam-6793	298	4	to	to	PART
ejpam-6793	298	5	explore	explore	VERB
ejpam-6793	298	6	more	more	ADV
ejpam-6793	298	7	extended	extended	ADJ
ejpam-6793	298	8	associated	associate	VERB
ejpam-6793	298	9	bases	basis	NOUN
ejpam-6793	298	10	from	from	ADP
ejpam-6793	298	11	those	those	PRON
ejpam-6793	298	12	obtained	obtain	VERB
ejpam-6793	298	13	in	in	ADP
ejpam-6793	298	14	the	the	DET
ejpam-6793	298	15	existing	exist	VERB
ejpam-6793	298	16	by	by	ADP
ejpam-6793	298	17	considering	consider	VERB
ejpam-6793	298	18	the	the	DET
ejpam-6793	298	19	constituents	constituent	NOUN
ejpam-6793	298	20	to	to	PART
ejpam-6793	298	21	be	be	AUX
ejpam-6793	298	22	general	general	ADJ
ejpam-6793	298	23	bases	basis	NOUN
ejpam-6793	298	24	.	.	PUNCT
ejpam-6793	299	1	as	as	ADV
ejpam-6793	299	2	far	far	ADV
ejpam-6793	299	3	as	as	SCONJ
ejpam-6793	299	4	we	we	PRON
ejpam-6793	299	5	know	know	VERB
ejpam-6793	299	6	from	from	ADP
ejpam-6793	299	7	the	the	DET
ejpam-6793	299	8	literature	literature	NOUN
ejpam-6793	299	9	that	that	SCONJ
ejpam-6793	299	10	one	one	NUM
ejpam-6793	299	11	of	of	ADP
ejpam-6793	299	12	the	the	DET
ejpam-6793	299	13	untouched	untouched	ADJ
ejpam-6793	299	14	problems	problem	NOUN
ejpam-6793	299	15	in	in	ADP
ejpam-6793	299	16	clifford	clifford	PROPN
ejpam-6793	299	17	context	context	NOUN
ejpam-6793	299	18	,	,	PUNCT
ejpam-6793	299	19	is	be	AUX
ejpam-6793	299	20	to	to	PART
ejpam-6793	299	21	represent	represent	VERB
ejpam-6793	299	22	any	any	DET
ejpam-6793	299	23	entire	entire	ADJ
ejpam-6793	299	24	monogenic	monogenic	ADJ
ejpam-6793	299	25	functions	function	NOUN
ejpam-6793	299	26	by	by	ADP
ejpam-6793	299	27	a	a	DET
ejpam-6793	299	28	set	set	NOUN
ejpam-6793	299	29	of	of	ADP
ejpam-6793	299	30	polynomials	polynomial	NOUN
ejpam-6793	299	31	,	,	PUNCT
ejpam-6793	299	32	in	in	ADP
ejpam-6793	299	33	non	non	ADJ
ejpam-6793	299	34	-	-	ADJ
ejpam-6793	299	35	spherical	spherical	ADJ
ejpam-6793	299	36	regions	region	NOUN
ejpam-6793	299	37	,	,	PUNCT
ejpam-6793	299	38	such	such	ADJ
ejpam-6793	299	39	as	as	ADP
ejpam-6793	299	40	faber	faber	NOUN
ejpam-6793	299	41	regions	region	NOUN
ejpam-6793	299	42	.	.	PUNCT
ejpam-6793	300	1	having	have	VERB
ejpam-6793	300	2	such	such	ADJ
ejpam-6793	300	3	tools	tool	NOUN
ejpam-6793	300	4	would	would	AUX
ejpam-6793	300	5	pave	pave	VERB
ejpam-6793	300	6	the	the	DET
ejpam-6793	300	7	way	way	NOUN
ejpam-6793	300	8	to	to	PART
ejpam-6793	300	9	explore	explore	VERB
ejpam-6793	300	10	these	these	DET
ejpam-6793	300	11	problems	problem	NOUN
ejpam-6793	300	12	and	and	CCONJ
ejpam-6793	300	13	may	may	AUX
ejpam-6793	300	14	be	be	AUX
ejpam-6793	300	15	fruitful	fruitful	ADJ
ejpam-6793	300	16	to	to	PART
ejpam-6793	300	17	enrich	enrich	VERB
ejpam-6793	300	18	the	the	DET
ejpam-6793	300	19	approximation	approximation	NOUN
ejpam-6793	300	20	theory	theory	NOUN
ejpam-6793	300	21	in	in	ADP
ejpam-6793	300	22	clifford	clifford	PROPN
ejpam-6793	300	23	setting	setting	NOUN
ejpam-6793	300	24	.	.	PUNCT
ejpam-6793	301	1	acknowledgements	acknowledgement	VERB
ejpam-6793	301	2	the	the	DET
ejpam-6793	301	3	author	author	NOUN
ejpam-6793	301	4	thanks	thank	NOUN
ejpam-6793	301	5	the	the	DET
ejpam-6793	301	6	anonymous	anonymous	ADJ
ejpam-6793	301	7	reviewers	reviewer	NOUN
ejpam-6793	301	8	and	and	CCONJ
ejpam-6793	301	9	the	the	DET
ejpam-6793	301	10	handling	handling	NOUN
ejpam-6793	301	11	editor	editor	NOUN
ejpam-6793	301	12	for	for	ADP
ejpam-6793	301	13	their	their	PRON
ejpam-6793	301	14	constructive	constructive	ADJ
ejpam-6793	301	15	comments	comment	NOUN
ejpam-6793	301	16	,	,	PUNCT
ejpam-6793	301	17	which	which	PRON
ejpam-6793	301	18	significantly	significantly	ADV
ejpam-6793	301	19	improved	improve	VERB
ejpam-6793	301	20	the	the	DET
ejpam-6793	301	21	paper	paper	NOUN
ejpam-6793	301	22	.	.	PUNCT
ejpam-6793	302	1	references	reference	NOUN
ejpam-6793	302	2	[	[	X
ejpam-6793	302	3	1	1	NUM
ejpam-6793	302	4	]	]	X
ejpam-6793	302	5	fuzhang	fuzhang	PROPN
ejpam-6793	302	6	wang	wang	PROPN
ejpam-6793	302	7	,	,	PUNCT
ejpam-6793	302	8	imtiaz	imtiaz	PROPN
ejpam-6793	302	9	ahmad	ahmad	PROPN
ejpam-6793	302	10	,	,	PUNCT
ejpam-6793	302	11	hijaz	hijaz	PROPN
ejpam-6793	302	12	ahmad	ahmad	PROPN
ejpam-6793	302	13	,	,	PUNCT
ejpam-6793	302	14	m.d	m.d	PROPN
ejpam-6793	302	15	.	.	PROPN
ejpam-6793	302	16	alsulami	alsulami	PROPN
ejpam-6793	302	17	,	,	PUNCT
ejpam-6793	302	18	k.s	k.s	PROPN
ejpam-6793	302	19	.	.	PROPN
ejpam-6793	302	20	alimgeer	alimgeer	PROPN
ejpam-6793	302	21	,	,	PUNCT
ejpam-6793	302	22	clemente	clemente	PROPN
ejpam-6793	302	23	cesarano	cesarano	PROPN
ejpam-6793	302	24	,	,	PUNCT
ejpam-6793	302	25	and	and	CCONJ
ejpam-6793	302	26	taher	taher	ADJ
ejpam-6793	302	27	a.	a.	NOUN
ejpam-6793	302	28	nofal	nofal	PROPN
ejpam-6793	302	29	.	.	PUNCT
ejpam-6793	303	1	meshless	meshless	ADJ
ejpam-6793	303	2	method	method	NOUN
ejpam-6793	303	3	based	base	VERB
ejpam-6793	303	4	on	on	ADP
ejpam-6793	303	5	rbfs	rbfs	NOUN
ejpam-6793	303	6	for	for	ADP
ejpam-6793	303	7	solving	solve	VERB
ejpam-6793	303	8	three	three	NUM
ejpam-6793	303	9	-	-	PUNCT
ejpam-6793	303	10	dimensional	dimensional	ADJ
ejpam-6793	303	11	multi	multi	ADJ
ejpam-6793	303	12	-	-	ADJ
ejpam-6793	303	13	term	term	ADJ
ejpam-6793	303	14	time	time	NOUN
ejpam-6793	303	15	fractional	fractional	ADJ
ejpam-6793	303	16	pdes	pde	NOUN
ejpam-6793	303	17	arising	arise	VERB
ejpam-6793	303	18	in	in	ADP
ejpam-6793	303	19	engineering	engineering	NOUN
ejpam-6793	303	20	phenomenons	phenomenon	NOUN
ejpam-6793	303	21	.	.	PUNCT
ejpam-6793	304	1	journal	journal	PROPN
ejpam-6793	304	2	of	of	ADP
ejpam-6793	304	3	king	king	PROPN
ejpam-6793	304	4	saud	saud	PROPN
ejpam-6793	304	5	university	university	PROPN
ejpam-6793	304	6	science	science	NOUN
ejpam-6793	304	7	,	,	PUNCT
ejpam-6793	304	8	33(8):101604	33(8):101604	NUM
ejpam-6793	304	9	,	,	PUNCT
ejpam-6793	304	10	2021	2021	NUM
ejpam-6793	304	11	.	.	PUNCT
ejpam-6793	305	1	[	[	X
ejpam-6793	305	2	2	2	NUM
ejpam-6793	305	3	]	]	PUNCT
ejpam-6793	305	4	sunil	sunil	PROPN
ejpam-6793	305	5	kumar	kumar	PROPN
ejpam-6793	305	6	,	,	PUNCT
ejpam-6793	305	7	deepak	deepak	PROPN
ejpam-6793	305	8	kumar	kumar	PROPN
ejpam-6793	305	9	,	,	PUNCT
ejpam-6793	305	10	janak	janak	PROPN
ejpam-6793	305	11	raj	raj	PROPN
ejpam-6793	305	12	sharma	sharma	PROPN
ejpam-6793	305	13	,	,	PUNCT
ejpam-6793	305	14	clemente	clemente	PROPN
ejpam-6793	305	15	cesarano	cesarano	PROPN
ejpam-6793	305	16	,	,	PUNCT
ejpam-6793	305	17	praveen	praveen	PROPN
ejpam-6793	305	18	agarwal	agarwal	PROPN
ejpam-6793	305	19	,	,	PUNCT
ejpam-6793	305	20	and	and	CCONJ
ejpam-6793	305	21	yu	yu	PROPN
ejpam-6793	305	22	-	-	PROPN
ejpam-6793	305	23	ming	ming	PROPN
ejpam-6793	305	24	chu	chu	PROPN
ejpam-6793	305	25	.	.	PUNCT
ejpam-6793	306	1	an	an	DET
ejpam-6793	306	2	optimal	optimal	ADJ
ejpam-6793	306	3	fourth	fourth	ADJ
ejpam-6793	306	4	order	order	NOUN
ejpam-6793	306	5	derivative	derivative	ADJ
ejpam-6793	306	6	-	-	PUNCT
ejpam-6793	306	7	free	free	ADJ
ejpam-6793	306	8	numerical	numerical	ADJ
ejpam-6793	306	9	algorithm	algorithm	NOUN
ejpam-6793	306	10	for	for	ADP
ejpam-6793	306	11	multiple	multiple	ADJ
ejpam-6793	306	12	roots	root	NOUN
ejpam-6793	306	13	.	.	PUNCT
ejpam-6793	307	1	symmetry	symmetry	NOUN
ejpam-6793	307	2	,	,	PUNCT
ejpam-6793	307	3	12(6	12(6	NUM
ejpam-6793	307	4	)	)	PUNCT
ejpam-6793	307	5	,	,	PUNCT
ejpam-6793	307	6	2020	2020	NUM
ejpam-6793	307	7	.	.	PUNCT
ejpam-6793	308	1	[	[	X
ejpam-6793	308	2	3	3	X
ejpam-6793	308	3	]	]	X
ejpam-6793	308	4	j.	j.	PROPN
ejpam-6793	308	5	m.	m.	PROPN
ejpam-6793	308	6	whittaker	whittaker	PROPN
ejpam-6793	308	7	.	.	PUNCT
ejpam-6793	309	1	on	on	ADP
ejpam-6793	309	2	the	the	DET
ejpam-6793	309	3	uniqueness	uniqueness	NOUN
ejpam-6793	309	4	of	of	ADP
ejpam-6793	309	5	expansion	expansion	NOUN
ejpam-6793	309	6	in	in	ADP
ejpam-6793	309	7	polynomials	polynomial	NOUN
ejpam-6793	309	8	.	.	PUNCT
ejpam-6793	310	1	journal	journal	NOUN
ejpam-6793	310	2	of	of	ADP
ejpam-6793	310	3	the	the	DET
ejpam-6793	310	4	london	london	PROPN
ejpam-6793	310	5	mathematical	mathematical	ADJ
ejpam-6793	310	6	society	society	NOUN
ejpam-6793	310	7	,	,	PUNCT
ejpam-6793	310	8	volume	volume	NOUN
ejpam-6793	310	9	s1	s1	NOUN
ejpam-6793	310	10	-	-	PUNCT
ejpam-6793	310	11	10:108–111	10:108–111	NUM
ejpam-6793	310	12	,	,	PUNCT
ejpam-6793	310	13	1935	1935	NUM
ejpam-6793	310	14	.	.	PUNCT
ejpam-6793	311	1	[	[	X
ejpam-6793	311	2	4	4	X
ejpam-6793	311	3	]	]	PUNCT
ejpam-6793	311	4	j.	j.	PROPN
ejpam-6793	311	5	m.	m.	PROPN
ejpam-6793	311	6	whittaker	whittaker	PROPN
ejpam-6793	311	7	and	and	CCONJ
ejpam-6793	311	8	c.	c.	PROPN
ejpam-6793	311	9	gattegno	gattegno	PROPN
ejpam-6793	311	10	.	.	PUNCT
ejpam-6793	312	1	sur	sur	PROPN
ejpam-6793	312	2	les	les	PROPN
ejpam-6793	312	3	s’eries	s’eries	PROPN
ejpam-6793	312	4	de	de	X
ejpam-6793	312	5	base	base	X
ejpam-6793	312	6	de	de	X
ejpam-6793	312	7	polynômes	polynôme	NOUN
ejpam-6793	312	8	quelconques	quelconque	NOUN
ejpam-6793	312	9	.	.	PUNCT
ejpam-6793	313	1	gauthier	gauthier	NOUN
ejpam-6793	313	2	-	-	PUNCT
ejpam-6793	313	3	villars	villars	PROPN
ejpam-6793	313	4	,	,	PUNCT
ejpam-6793	313	5	paris	paris	PROPN
ejpam-6793	313	6	,	,	PUNCT
ejpam-6793	313	7	1949	1949	NUM
ejpam-6793	313	8	.	.	PUNCT
ejpam-6793	314	1	[	[	X
ejpam-6793	314	2	5	5	X
ejpam-6793	314	3	]	]	PUNCT
ejpam-6793	314	4	b.	b.	NOUN
ejpam-6793	314	5	cannon	cannon	NOUN
ejpam-6793	314	6	.	.	PUNCT
ejpam-6793	315	1	on	on	ADP
ejpam-6793	315	2	the	the	DET
ejpam-6793	315	3	convergence	convergence	NOUN
ejpam-6793	315	4	of	of	ADP
ejpam-6793	315	5	series	series	NOUN
ejpam-6793	315	6	of	of	ADP
ejpam-6793	315	7	polynomials	polynomial	NOUN
ejpam-6793	315	8	.	.	PUNCT
ejpam-6793	316	1	proceedings	proceeding	NOUN
ejpam-6793	316	2	of	of	ADP
ejpam-6793	316	3	the	the	DET
ejpam-6793	316	4	london	london	PROPN
ejpam-6793	316	5	mathematical	mathematical	ADJ
ejpam-6793	316	6	society	society	NOUN
ejpam-6793	316	7	,	,	PUNCT
ejpam-6793	316	8	43:348–364	43:348–364	PROPN
ejpam-6793	316	9	,	,	PUNCT
ejpam-6793	316	10	1937	1937	NUM
ejpam-6793	316	11	.	.	PUNCT
ejpam-6793	317	1	[	[	X
ejpam-6793	317	2	6	6	NUM
ejpam-6793	317	3	]	]	PUNCT
ejpam-6793	317	4	b.	b.	NOUN
ejpam-6793	317	5	cannon	cannon	NOUN
ejpam-6793	317	6	.	.	PUNCT
ejpam-6793	318	1	on	on	ADP
ejpam-6793	318	2	the	the	DET
ejpam-6793	318	3	representation	representation	NOUN
ejpam-6793	318	4	of	of	ADP
ejpam-6793	318	5	integral	integral	ADJ
ejpam-6793	318	6	functions	function	NOUN
ejpam-6793	318	7	by	by	ADP
ejpam-6793	318	8	general	general	ADJ
ejpam-6793	318	9	basic	basic	ADJ
ejpam-6793	318	10	series	series	NOUN
ejpam-6793	318	11	.	.	PUNCT
ejpam-6793	319	1	mathematische	mathematische	PROPN
ejpam-6793	319	2	zeitschrift	zeitschrift	PROPN
ejpam-6793	319	3	,	,	PUNCT
ejpam-6793	319	4	45:185–208	45:185–208	PROPN
ejpam-6793	319	5	,	,	PUNCT
ejpam-6793	319	6	1939	1939	NUM
ejpam-6793	319	7	.	.	PUNCT
ejpam-6793	320	1	[	[	X
ejpam-6793	320	2	7	7	X
ejpam-6793	320	3	]	]	PUNCT
ejpam-6793	320	4	m.	m.	NOUN
ejpam-6793	320	5	abul	abul	PROPN
ejpam-6793	320	6	-	-	PUNCT
ejpam-6793	320	7	ez	ez	PROPN
ejpam-6793	320	8	and	and	CCONJ
ejpam-6793	320	9	d.	d.	PROPN
ejpam-6793	320	10	constales	constale	NOUN
ejpam-6793	320	11	.	.	PUNCT
ejpam-6793	321	1	basic	basic	ADJ
ejpam-6793	321	2	sets	set	NOUN
ejpam-6793	321	3	of	of	ADP
ejpam-6793	321	4	polynomials	polynomial	NOUN
ejpam-6793	321	5	in	in	ADP
ejpam-6793	321	6	clifford	clifford	PROPN
ejpam-6793	321	7	analysis	analysis	NOUN
ejpam-6793	321	8	.	.	PUNCT
ejpam-6793	322	1	complex	complex	ADJ
ejpam-6793	322	2	variables	variable	NOUN
ejpam-6793	322	3	,	,	PUNCT
ejpam-6793	322	4	14:177–185	14:177–185	NUM
ejpam-6793	322	5	,	,	PUNCT
ejpam-6793	322	6	1990	1990	NUM
ejpam-6793	322	7	.	.	PUNCT
ejpam-6793	323	1	[	[	X
ejpam-6793	323	2	8	8	NUM
ejpam-6793	323	3	]	]	PUNCT
ejpam-6793	323	4	m.	m.	NOUN
ejpam-6793	323	5	abul	abul	PROPN
ejpam-6793	323	6	-	-	PUNCT
ejpam-6793	323	7	ez	ez	PROPN
ejpam-6793	323	8	and	and	CCONJ
ejpam-6793	323	9	d.	d.	PROPN
ejpam-6793	323	10	constales	constale	NOUN
ejpam-6793	323	11	.	.	PUNCT
ejpam-6793	324	1	linear	linear	ADJ
ejpam-6793	324	2	substitution	substitution	NOUN
ejpam-6793	324	3	for	for	ADP
ejpam-6793	324	4	basic	basic	ADJ
ejpam-6793	324	5	sets	set	NOUN
ejpam-6793	324	6	of	of	ADP
ejpam-6793	324	7	polynomials	polynomial	NOUN
ejpam-6793	324	8	in	in	ADP
ejpam-6793	324	9	clifford	clifford	PROPN
ejpam-6793	324	10	analysis	analysis	NOUN
ejpam-6793	324	11	.	.	PUNCT
ejpam-6793	325	1	portugaliae	portugaliae	PROPN
ejpam-6793	325	2	mathematica	mathematica	PROPN
ejpam-6793	325	3	,	,	PUNCT
ejpam-6793	325	4	48:143–154	48:143–154	PROPN
ejpam-6793	325	5	,	,	PUNCT
ejpam-6793	325	6	1990	1990	NUM
ejpam-6793	325	7	.	.	PUNCT
ejpam-6793	326	1	[	[	X
ejpam-6793	326	2	9	9	NUM
ejpam-6793	326	3	]	]	PUNCT
ejpam-6793	326	4	m.	m.	NOUN
ejpam-6793	326	5	abul	abul	PROPN
ejpam-6793	326	6	-	-	PUNCT
ejpam-6793	326	7	ez	ez	PROPN
ejpam-6793	326	8	.	.	PROPN
ejpam-6793	326	9	inverse	inverse	NOUN
ejpam-6793	326	10	sets	set	NOUN
ejpam-6793	326	11	of	of	ADP
ejpam-6793	326	12	polynomials	polynomial	NOUN
ejpam-6793	326	13	in	in	ADP
ejpam-6793	326	14	clifford	clifford	PROPN
ejpam-6793	326	15	analysis	analysis	NOUN
ejpam-6793	326	16	.	.	PUNCT
ejpam-6793	327	1	archiv	archiv	PROPN
ejpam-6793	327	2	der	der	PROPN
ejpam-6793	327	3	mathematik	mathematik	PROPN
ejpam-6793	327	4	,	,	PUNCT
ejpam-6793	327	5	58:561–567	58:561–567	NUM
ejpam-6793	327	6	,	,	PUNCT
ejpam-6793	327	7	1992	1992	NUM
ejpam-6793	327	8	.	.	PUNCT
ejpam-6793	328	1	[	[	X
ejpam-6793	328	2	10	10	NUM
ejpam-6793	328	3	]	]	PUNCT
ejpam-6793	328	4	m.	m.	NOUN
ejpam-6793	328	5	abul	abul	PROPN
ejpam-6793	328	6	-	-	PUNCT
ejpam-6793	328	7	ez	ez	PROPN
ejpam-6793	328	8	.	.	PUNCT
ejpam-6793	328	9	hadamard	hadamard	ADJ
ejpam-6793	328	10	product	product	NOUN
ejpam-6793	328	11	of	of	ADP
ejpam-6793	328	12	bases	basis	NOUN
ejpam-6793	328	13	of	of	ADP
ejpam-6793	328	14	polynomials	polynomial	NOUN
ejpam-6793	328	15	in	in	ADP
ejpam-6793	328	16	clifford	clifford	PROPN
ejpam-6793	328	17	analysis	analysis	NOUN
ejpam-6793	328	18	.	.	PUNCT
ejpam-6793	329	1	complex	complex	ADJ
ejpam-6793	329	2	variables	variable	NOUN
ejpam-6793	329	3	and	and	CCONJ
ejpam-6793	329	4	elliptic	elliptic	ADJ
ejpam-6793	329	5	equations	equation	NOUN
ejpam-6793	329	6	,	,	PUNCT
ejpam-6793	329	7	43(2):109–128	43(2):109–128	NUM
ejpam-6793	329	8	,	,	PUNCT
ejpam-6793	329	9	2000	2000	NUM
ejpam-6793	329	10	.	.	PUNCT
ejpam-6793	330	1	[	[	X
ejpam-6793	330	2	11	11	NUM
ejpam-6793	330	3	]	]	PUNCT
ejpam-6793	330	4	m.	m.	NOUN
ejpam-6793	330	5	abul	abul	PROPN
ejpam-6793	330	6	-	-	PUNCT
ejpam-6793	330	7	ez	ez	PROPN
ejpam-6793	330	8	and	and	CCONJ
ejpam-6793	330	9	d.	d.	PROPN
ejpam-6793	330	10	constales	constale	NOUN
ejpam-6793	330	11	.	.	PUNCT
ejpam-6793	331	1	the	the	DET
ejpam-6793	331	2	square	square	ADJ
ejpam-6793	331	3	root	root	NOUN
ejpam-6793	331	4	base	base	NOUN
ejpam-6793	331	5	of	of	ADP
ejpam-6793	331	6	polynomials	polynomial	NOUN
ejpam-6793	331	7	in	in	ADP
ejpam-6793	331	8	clifford	clifford	PROPN
ejpam-6793	331	9	analysis	analysis	NOUN
ejpam-6793	331	10	.	.	PUNCT
ejpam-6793	332	1	archiv	archiv	PROPN
ejpam-6793	332	2	der	der	PROPN
ejpam-6793	332	3	mathematik	mathematik	PROPN
ejpam-6793	332	4	,	,	PUNCT
ejpam-6793	332	5	80(5):486–495	80(5):486–495	NUM
ejpam-6793	332	6	,	,	PUNCT
ejpam-6793	332	7	2003	2003	NUM
ejpam-6793	332	8	.	.	PUNCT
ejpam-6793	333	1	[	[	X
ejpam-6793	333	2	12	12	NUM
ejpam-6793	333	3	]	]	PUNCT
ejpam-6793	333	4	m.	m.	NOUN
ejpam-6793	333	5	abdalla	abdalla	PROPN
ejpam-6793	333	6	,	,	PUNCT
ejpam-6793	333	7	m.	m.	PROPN
ejpam-6793	333	8	abul	abul	PROPN
ejpam-6793	333	9	-	-	PUNCT
ejpam-6793	333	10	ez	ez	PROPN
ejpam-6793	333	11	,	,	PUNCT
ejpam-6793	333	12	and	and	CCONJ
ejpam-6793	333	13	j.	j.	PROPN
ejpam-6793	333	14	morais	morais	PROPN
ejpam-6793	333	15	.	.	PUNCT
ejpam-6793	334	1	on	on	ADP
ejpam-6793	334	2	the	the	DET
ejpam-6793	334	3	construction	construction	NOUN
ejpam-6793	334	4	of	of	ADP
ejpam-6793	334	5	generalized	generalized	ADJ
ejpam-6793	334	6	monogenic	monogenic	ADJ
ejpam-6793	334	7	bessel	bessel	NOUN
ejpam-6793	334	8	polynomials	polynomial	NOUN
ejpam-6793	334	9	.	.	PUNCT
ejpam-6793	335	1	mathematical	mathematical	ADJ
ejpam-6793	335	2	methods	method	NOUN
ejpam-6793	335	3	in	in	ADP
ejpam-6793	335	4	the	the	DET
ejpam-6793	335	5	applied	apply	VERB
ejpam-6793	335	6	sciences	science	NOUN
ejpam-6793	335	7	,	,	PUNCT
ejpam-6793	335	8	41:9335–9348	41:9335–9348	NUM
ejpam-6793	335	9	,	,	PUNCT
ejpam-6793	335	10	2018	2018	NUM
ejpam-6793	335	11	.	.	PUNCT
ejpam-6793	336	1	m.	m.	NOUN
ejpam-6793	336	2	zayed	zayed	PROPN
ejpam-6793	336	3	/	/	SYM
ejpam-6793	336	4	eur	eur	PROPN
ejpam-6793	336	5	.	.	PUNCT
ejpam-6793	337	1	j.	j.	PROPN
ejpam-6793	337	2	pure	pure	PROPN
ejpam-6793	337	3	appl	appl	PROPN
ejpam-6793	337	4	.	.	PROPN
ejpam-6793	337	5	math	math	PROPN
ejpam-6793	337	6	,	,	PUNCT
ejpam-6793	337	7	18	18	NUM
ejpam-6793	337	8	(	(	PUNCT
ejpam-6793	337	9	4	4	NUM
ejpam-6793	337	10	)	)	PUNCT
ejpam-6793	337	11	(	(	PUNCT
ejpam-6793	337	12	2025	2025	NUM
ejpam-6793	337	13	)	)	PUNCT
ejpam-6793	337	14	,	,	PUNCT
ejpam-6793	337	15	6793	6793	NUM
ejpam-6793	337	16	19	19	NUM
ejpam-6793	337	17	of	of	ADP
ejpam-6793	337	18	19	19	NUM
ejpam-6793	337	19	[	[	SYM
ejpam-6793	337	20	13	13	NUM
ejpam-6793	337	21	]	]	PUNCT
ejpam-6793	337	22	m.	m.	NOUN
ejpam-6793	337	23	abul	abul	PROPN
ejpam-6793	337	24	-	-	PUNCT
ejpam-6793	337	25	ez	ez	PROPN
ejpam-6793	337	26	and	and	CCONJ
ejpam-6793	337	27	m.	m.	NOUN
ejpam-6793	337	28	zayed	zayed	PROPN
ejpam-6793	337	29	.	.	PUNCT
ejpam-6793	337	30	criteria	criterion	NOUN
ejpam-6793	337	31	in	in	ADP
ejpam-6793	337	32	nuclear	nuclear	ADJ
ejpam-6793	337	33	fréchet	fréchet	NOUN
ejpam-6793	337	34	spaces	space	NOUN
ejpam-6793	337	35	and	and	CCONJ
ejpam-6793	337	36	silva	silva	NOUN
ejpam-6793	337	37	spaces	space	NOUN
ejpam-6793	337	38	with	with	ADP
ejpam-6793	337	39	refinement	refinement	NOUN
ejpam-6793	337	40	of	of	ADP
ejpam-6793	337	41	the	the	DET
ejpam-6793	337	42	cannon	cannon	NOUN
ejpam-6793	337	43	–	–	PUNCT
ejpam-6793	337	44	whittaker	whittaker	PROPN
ejpam-6793	337	45	theory	theory	NOUN
ejpam-6793	337	46	.	.	PUNCT
ejpam-6793	338	1	journal	journal	PROPN
ejpam-6793	338	2	of	of	ADP
ejpam-6793	338	3	function	function	NOUN
ejpam-6793	338	4	spaces	space	NOUN
ejpam-6793	338	5	,	,	PUNCT
ejpam-6793	338	6	2020:15	2020:15	NUM
ejpam-6793	338	7	,	,	PUNCT
ejpam-6793	338	8	2020	2020	NUM
ejpam-6793	338	9	.	.	PUNCT
ejpam-6793	339	1	[	[	X
ejpam-6793	339	2	14	14	NUM
ejpam-6793	339	3	]	]	PUNCT
ejpam-6793	339	4	m.	m.	NOUN
ejpam-6793	339	5	abul	abul	PROPN
ejpam-6793	339	6	-	-	PUNCT
ejpam-6793	339	7	ez	ez	PROPN
ejpam-6793	339	8	.	.	PROPN
ejpam-6793	339	9	bessel	bessel	ADJ
ejpam-6793	339	10	polynomial	polynomial	ADJ
ejpam-6793	339	11	expansions	expansion	NOUN
ejpam-6793	339	12	in	in	ADP
ejpam-6793	339	13	spaces	space	NOUN
ejpam-6793	339	14	of	of	ADP
ejpam-6793	339	15	holomorphic	holomorphic	ADJ
ejpam-6793	339	16	functions	function	NOUN
ejpam-6793	339	17	.	.	PUNCT
ejpam-6793	340	1	journal	journal	NOUN
ejpam-6793	340	2	of	of	ADP
ejpam-6793	340	3	mathematical	mathematical	ADJ
ejpam-6793	340	4	analysis	analysis	NOUN
ejpam-6793	340	5	and	and	CCONJ
ejpam-6793	340	6	applications	application	NOUN
ejpam-6793	340	7	,	,	PUNCT
ejpam-6793	340	8	221:177–190	221:177–190	NUM
ejpam-6793	340	9	,	,	PUNCT
ejpam-6793	340	10	1998	1998	NUM
ejpam-6793	340	11	.	.	PUNCT
ejpam-6793	341	1	[	[	X
ejpam-6793	341	2	15	15	NUM
ejpam-6793	341	3	]	]	X
ejpam-6793	341	4	g.	g.	PROPN
ejpam-6793	341	5	f.	f.	PROPN
ejpam-6793	341	6	hassan	hassan	PROPN
ejpam-6793	341	7	and	and	CCONJ
ejpam-6793	341	8	l.	l.	PROPN
ejpam-6793	341	9	aloui	aloui	PROPN
ejpam-6793	341	10	.	.	PUNCT
ejpam-6793	342	1	bernoulli	bernoulli	PROPN
ejpam-6793	342	2	and	and	CCONJ
ejpam-6793	342	3	euler	euler	NOUN
ejpam-6793	342	4	polynomials	polynomial	NOUN
ejpam-6793	342	5	in	in	ADP
ejpam-6793	342	6	clifford	clifford	PROPN
ejpam-6793	342	7	analysis	analysis	NOUN
ejpam-6793	342	8	.	.	PUNCT
ejpam-6793	343	1	advances	advance	NOUN
ejpam-6793	343	2	in	in	ADP
ejpam-6793	343	3	applied	apply	VERB
ejpam-6793	343	4	clifford	clifford	PROPN
ejpam-6793	343	5	algebras	algebra	NOUN
ejpam-6793	343	6	,	,	PUNCT
ejpam-6793	343	7	25:351–376	25:351–376	NUM
ejpam-6793	343	8	,	,	PUNCT
ejpam-6793	343	9	2015	2015	NUM
ejpam-6793	343	10	.	.	PUNCT
ejpam-6793	344	1	[	[	X
ejpam-6793	344	2	16	16	NUM
ejpam-6793	344	3	]	]	X
ejpam-6793	344	4	g.	g.	PROPN
ejpam-6793	344	5	f.	f.	PROPN
ejpam-6793	344	6	hassan	hassan	PROPN
ejpam-6793	344	7	,	,	PUNCT
ejpam-6793	344	8	l.	l.	PROPN
ejpam-6793	344	9	aloui	aloui	PROPN
ejpam-6793	344	10	,	,	PUNCT
ejpam-6793	344	11	and	and	CCONJ
ejpam-6793	344	12	a.	a.	PROPN
ejpam-6793	344	13	bakali	bakali	PROPN
ejpam-6793	344	14	.	.	PUNCT
ejpam-6793	345	1	basic	basic	ADJ
ejpam-6793	345	2	sets	set	NOUN
ejpam-6793	345	3	of	of	ADP
ejpam-6793	345	4	special	special	ADJ
ejpam-6793	345	5	monogenic	monogenic	ADJ
ejpam-6793	345	6	polynomials	polynomial	NOUN
ejpam-6793	345	7	in	in	ADP
ejpam-6793	345	8	fréchet	fréchet	NOUN
ejpam-6793	345	9	modules	module	NOUN
ejpam-6793	345	10	.	.	PUNCT
ejpam-6793	346	1	journal	journal	NOUN
ejpam-6793	346	2	of	of	ADP
ejpam-6793	346	3	complex	complex	ADJ
ejpam-6793	346	4	analysis	analysis	NOUN
ejpam-6793	346	5	,	,	PUNCT
ejpam-6793	346	6	pages	page	NOUN
ejpam-6793	346	7	article	article	NOUN
ejpam-6793	346	8	i	i	PROPN
ejpam-6793	346	9	d	d	PROPN
ejpam-6793	346	10	2075938	2075938	NUM
ejpam-6793	346	11	,	,	PUNCT
ejpam-6793	346	12	11	11	NUM
ejpam-6793	346	13	pages	page	NOUN
ejpam-6793	346	14	,	,	PUNCT
ejpam-6793	346	15	2017	2017	NUM
ejpam-6793	346	16	.	.	PUNCT
ejpam-6793	347	1	[	[	X
ejpam-6793	347	2	17	17	NUM
ejpam-6793	347	3	]	]	PUNCT
ejpam-6793	347	4	m.	m.	NOUN
ejpam-6793	347	5	zayed	zayed	PROPN
ejpam-6793	347	6	and	and	CCONJ
ejpam-6793	347	7	g.	g.	PROPN
ejpam-6793	347	8	hassan	hassan	PROPN
ejpam-6793	347	9	.	.	PUNCT
ejpam-6793	348	1	equivalent	equivalent	ADJ
ejpam-6793	348	2	base	base	NOUN
ejpam-6793	348	3	expansions	expansion	NOUN
ejpam-6793	348	4	in	in	ADP
ejpam-6793	348	5	the	the	DET
ejpam-6793	348	6	space	space	NOUN
ejpam-6793	348	7	of	of	ADP
ejpam-6793	348	8	cliffordian	cliffordian	ADJ
ejpam-6793	348	9	functions	function	NOUN
ejpam-6793	348	10	.	.	PUNCT
ejpam-6793	349	1	axioms	axiom	NOUN
ejpam-6793	349	2	,	,	PUNCT
ejpam-6793	349	3	12(6):544	12(6):544	PROPN
ejpam-6793	349	4	,	,	PUNCT
ejpam-6793	349	5	2023	2023	NUM
ejpam-6793	349	6	.	.	PUNCT
ejpam-6793	350	1	[	[	X
ejpam-6793	350	2	18	18	NUM
ejpam-6793	350	3	]	]	X
ejpam-6793	350	4	g.	g.	PROPN
ejpam-6793	350	5	hassan	hassan	PROPN
ejpam-6793	350	6	and	and	CCONJ
ejpam-6793	350	7	m.	m.	PROPN
ejpam-6793	350	8	zayed	zayed	PROPN
ejpam-6793	350	9	.	.	PUNCT
ejpam-6793	351	1	approximation	approximation	NOUN
ejpam-6793	351	2	of	of	ADP
ejpam-6793	351	3	monogenic	monogenic	ADJ
ejpam-6793	351	4	functions	function	NOUN
ejpam-6793	351	5	by	by	ADP
ejpam-6793	351	6	hypercomplex	hypercomplex	NOUN
ejpam-6793	351	7	ruscheweyh	ruscheweyh	NOUN
ejpam-6793	351	8	derivative	derivative	ADJ
ejpam-6793	351	9	bases	basis	NOUN
ejpam-6793	351	10	.	.	PUNCT
ejpam-6793	352	1	complex	complex	ADJ
ejpam-6793	352	2	variables	variable	NOUN
ejpam-6793	352	3	and	and	CCONJ
ejpam-6793	352	4	elliptic	elliptic	ADJ
ejpam-6793	352	5	equations	equation	NOUN
ejpam-6793	352	6	,	,	PUNCT
ejpam-6793	352	7	68:2073	68:2073	NUM
ejpam-6793	352	8	–	–	PUNCT
ejpam-6793	352	9	2092	2092	NUM
ejpam-6793	352	10	,	,	PUNCT
ejpam-6793	352	11	2023	2023	NUM
ejpam-6793	352	12	.	.	PUNCT
ejpam-6793	353	1	[	[	X
ejpam-6793	353	2	19	19	NUM
ejpam-6793	353	3	]	]	PUNCT
ejpam-6793	353	4	m.	m.	NOUN
ejpam-6793	353	5	zayed	zayed	PROPN
ejpam-6793	353	6	and	and	CCONJ
ejpam-6793	353	7	g.	g.	PROPN
ejpam-6793	353	8	hassan	hassan	PROPN
ejpam-6793	353	9	.	.	PUNCT
ejpam-6793	354	1	expansions	expansion	NOUN
ejpam-6793	354	2	of	of	ADP
ejpam-6793	354	3	generalized	generalized	ADJ
ejpam-6793	354	4	bases	basis	NOUN
ejpam-6793	354	5	constructed	construct	VERB
ejpam-6793	354	6	via	via	ADP
ejpam-6793	354	7	hasse	hasse	ADJ
ejpam-6793	354	8	derivative	derivative	ADJ
ejpam-6793	354	9	operator	operator	NOUN
ejpam-6793	354	10	in	in	ADP
ejpam-6793	354	11	clifford	clifford	PROPN
ejpam-6793	354	12	analysis	analysis	NOUN
ejpam-6793	354	13	.	.	PUNCT
ejpam-6793	355	1	aims	aim	VERB
ejpam-6793	355	2	mathematics	mathematic	NOUN
ejpam-6793	355	3	,	,	PUNCT
ejpam-6793	355	4	8(11):26115–26133	8(11):26115–26133	NUM
ejpam-6793	355	5	,	,	PUNCT
ejpam-6793	355	6	2023	2023	NUM
ejpam-6793	355	7	.	.	PUNCT
ejpam-6793	356	1	[	[	X
ejpam-6793	356	2	20	20	NUM
ejpam-6793	356	3	]	]	PUNCT
ejpam-6793	356	4	z.	z.	PROPN
ejpam-6793	356	5	g.	g.	PROPN
ejpam-6793	356	6	kishka	kishka	PROPN
ejpam-6793	356	7	,	,	PUNCT
ejpam-6793	356	8	m.	m.	NOUN
ejpam-6793	356	9	a.	a.	PROPN
ejpam-6793	356	10	saleem	saleem	PROPN
ejpam-6793	356	11	,	,	PUNCT
ejpam-6793	356	12	and	and	CCONJ
ejpam-6793	356	13	m.	m.	PROPN
ejpam-6793	356	14	a.	a.	PROPN
ejpam-6793	356	15	abul	abul	PROPN
ejpam-6793	356	16	-	-	PUNCT
ejpam-6793	356	17	dahab	dahab	PROPN
ejpam-6793	356	18	.	.	PUNCT
ejpam-6793	357	1	on	on	ADP
ejpam-6793	357	2	simple	simple	ADJ
ejpam-6793	357	3	exponential	exponential	ADJ
ejpam-6793	357	4	sets	set	NOUN
ejpam-6793	357	5	of	of	ADP
ejpam-6793	357	6	polynomials	polynomial	NOUN
ejpam-6793	357	7	.	.	PUNCT
ejpam-6793	358	1	mediterranean	mediterranean	PROPN
ejpam-6793	358	2	journal	journal	PROPN
ejpam-6793	358	3	of	of	ADP
ejpam-6793	358	4	mathematics	mathematic	NOUN
ejpam-6793	358	5	,	,	PUNCT
ejpam-6793	358	6	11:337–347	11:337–347	PROPN
ejpam-6793	358	7	,	,	PUNCT
ejpam-6793	358	8	2014	2014	NUM
ejpam-6793	358	9	.	.	PUNCT
ejpam-6793	359	1	[	[	X
ejpam-6793	359	2	21	21	NUM
ejpam-6793	359	3	]	]	PUNCT
ejpam-6793	359	4	m.	m.	NOUN
ejpam-6793	359	5	a.	a.	PROPN
ejpam-6793	359	6	abul	abul	PROPN
ejpam-6793	359	7	-	-	PUNCT
ejpam-6793	359	8	ez	ez	PROPN
ejpam-6793	359	9	.	.	PROPN
ejpam-6793	359	10	exponential	exponential	ADJ
ejpam-6793	359	11	base	base	NOUN
ejpam-6793	359	12	of	of	ADP
ejpam-6793	359	13	special	special	ADJ
ejpam-6793	359	14	monogenic	monogenic	ADJ
ejpam-6793	359	15	polynomials	polynomial	NOUN
ejpam-6793	359	16	.	.	PUNCT
ejpam-6793	360	1	pure	pure	ADJ
ejpam-6793	360	2	mathematics	mathematic	NOUN
ejpam-6793	360	3	and	and	CCONJ
ejpam-6793	360	4	applications	application	NOUN
ejpam-6793	360	5	,	,	PUNCT
ejpam-6793	360	6	8(2	8(2	NUM
ejpam-6793	360	7	-	-	SYM
ejpam-6793	360	8	4):137–146	4):137–146	NUM
ejpam-6793	360	9	,	,	PUNCT
ejpam-6793	360	10	1997	1997	NUM
ejpam-6793	360	11	.	.	PUNCT
ejpam-6793	361	1	[	[	X
ejpam-6793	361	2	22	22	NUM
ejpam-6793	361	3	]	]	X
ejpam-6793	361	4	f.	f.	PROPN
ejpam-6793	361	5	brackx	brackx	PROPN
ejpam-6793	361	6	,	,	PUNCT
ejpam-6793	361	7	r.	r.	PROPN
ejpam-6793	361	8	delanghe	delanghe	PROPN
ejpam-6793	361	9	,	,	PUNCT
ejpam-6793	361	10	and	and	CCONJ
ejpam-6793	361	11	f.	f.	PROPN
ejpam-6793	361	12	sommen	sommen	PROPN
ejpam-6793	361	13	.	.	PUNCT
ejpam-6793	362	1	clifford	clifford	PROPN
ejpam-6793	362	2	analysis	analysis	PROPN
ejpam-6793	362	3	,	,	PUNCT
ejpam-6793	362	4	volume	volume	NOUN
ejpam-6793	362	5	76	76	NUM
ejpam-6793	362	6	of	of	ADP
ejpam-6793	362	7	research	research	NOUN
ejpam-6793	362	8	notes	note	NOUN
ejpam-6793	362	9	in	in	ADP
ejpam-6793	362	10	mathematics	mathematic	NOUN
ejpam-6793	362	11	.	.	PUNCT
ejpam-6793	363	1	pitman	pitman	PROPN
ejpam-6793	363	2	,	,	PUNCT
ejpam-6793	363	3	london	london	PROPN
ejpam-6793	363	4	,	,	PUNCT
ejpam-6793	363	5	1982	1982	NUM
ejpam-6793	363	6	.	.	PUNCT
ejpam-6793	364	1	[	[	X
ejpam-6793	364	2	23	23	NUM
ejpam-6793	364	3	]	]	PUNCT
ejpam-6793	364	4	k.	k.	PROPN
ejpam-6793	364	5	gürlebeck	gürlebeck	PROPN
ejpam-6793	364	6	,	,	PUNCT
ejpam-6793	364	7	k.	k.	PROPN
ejpam-6793	364	8	habetha	habetha	PROPN
ejpam-6793	364	9	,	,	PUNCT
ejpam-6793	364	10	and	and	CCONJ
ejpam-6793	364	11	w.	w.	PROPN
ejpam-6793	364	12	sprößig	sprößig	PROPN
ejpam-6793	364	13	.	.	PUNCT
ejpam-6793	365	1	holomorphic	holomorphic	ADJ
ejpam-6793	365	2	functions	function	NOUN
ejpam-6793	365	3	in	in	ADP
ejpam-6793	365	4	the	the	DET
ejpam-6793	365	5	plane	plane	NOUN
ejpam-6793	365	6	and	and	CCONJ
ejpam-6793	365	7	n	n	CCONJ
ejpam-6793	365	8	-	-	PUNCT
ejpam-6793	365	9	dimensional	dimensional	ADJ
ejpam-6793	365	10	space	space	NOUN
ejpam-6793	365	11	.	.	PUNCT
ejpam-6793	366	1	birkh”auser	birkh”auser	PROPN
ejpam-6793	366	2	,	,	PUNCT
ejpam-6793	366	3	basel	basel	PROPN
ejpam-6793	366	4	,	,	PUNCT
ejpam-6793	366	5	2008	2008	NUM
ejpam-6793	366	6	.	.	PUNCT
ejpam-6793	367	1	[	[	X
ejpam-6793	367	2	24	24	NUM
ejpam-6793	367	3	]	]	X
ejpam-6793	367	4	e.	e.	PROPN
ejpam-6793	367	5	m.	m.	PROPN
ejpam-6793	367	6	stein	stein	PROPN
ejpam-6793	367	7	and	and	CCONJ
ejpam-6793	367	8	g.	g.	PROPN
ejpam-6793	367	9	i.	i.	PROPN
ejpam-6793	367	10	weiss	weiss	PROPN
ejpam-6793	367	11	.	.	PUNCT
ejpam-6793	368	1	generalization	generalization	NOUN
ejpam-6793	368	2	of	of	ADP
ejpam-6793	368	3	the	the	DET
ejpam-6793	368	4	cauchy	cauchy	PROPN
ejpam-6793	368	5	–	–	PUNCT
ejpam-6793	368	6	riemann	riemann	PROPN
ejpam-6793	368	7	equations	equation	NOUN
ejpam-6793	368	8	and	and	CCONJ
ejpam-6793	368	9	representation	representation	NOUN
ejpam-6793	368	10	of	of	ADP
ejpam-6793	368	11	the	the	DET
ejpam-6793	368	12	rotation	rotation	NOUN
ejpam-6793	368	13	group	group	NOUN
ejpam-6793	368	14	.	.	PUNCT
ejpam-6793	369	1	american	american	PROPN
ejpam-6793	369	2	journal	journal	PROPN
ejpam-6793	369	3	of	of	ADP
ejpam-6793	369	4	mathematics	mathematic	NOUN
ejpam-6793	369	5	,	,	PUNCT
ejpam-6793	369	6	90:163–196	90:163–196	NUM
ejpam-6793	369	7	,	,	PUNCT
ejpam-6793	369	8	1968	1968	NUM
ejpam-6793	369	9	.	.	PUNCT
ejpam-6793	370	1	[	[	X
ejpam-6793	370	2	25	25	NUM
ejpam-6793	370	3	]	]	PUNCT
ejpam-6793	370	4	m.	m.	NOUN
ejpam-6793	370	5	abul	abul	PROPN
ejpam-6793	370	6	-	-	PUNCT
ejpam-6793	370	7	ez	ez	PROPN
ejpam-6793	370	8	and	and	CCONJ
ejpam-6793	370	9	d.	d.	PROPN
ejpam-6793	370	10	constales	constale	NOUN
ejpam-6793	370	11	.	.	PUNCT
ejpam-6793	371	1	similar	similar	ADJ
ejpam-6793	371	2	functions	function	NOUN
ejpam-6793	371	3	and	and	CCONJ
ejpam-6793	371	4	similar	similar	ADJ
ejpam-6793	371	5	bases	basis	NOUN
ejpam-6793	371	6	of	of	ADP
ejpam-6793	371	7	polynomials	polynomial	NOUN
ejpam-6793	371	8	in	in	ADP
ejpam-6793	371	9	clifford	clifford	PROPN
ejpam-6793	371	10	setting	setting	NOUN
ejpam-6793	371	11	.	.	PUNCT
ejpam-6793	372	1	complex	complex	ADJ
ejpam-6793	372	2	variables	variable	NOUN
ejpam-6793	372	3	,	,	PUNCT
ejpam-6793	372	4	theory	theory	NOUN
ejpam-6793	372	5	and	and	CCONJ
ejpam-6793	372	6	application	application	NOUN
ejpam-6793	372	7	:	:	PUNCT
ejpam-6793	372	8	an	an	DET
ejpam-6793	372	9	international	international	ADJ
ejpam-6793	372	10	journal	journal	NOUN
ejpam-6793	372	11	,	,	PUNCT
ejpam-6793	372	12	48(12):1055–1070	48(12):1055–1070	PROPN
ejpam-6793	372	13	,	,	PUNCT
ejpam-6793	372	14	2003	2003	NUM
ejpam-6793	372	15	.	.	PUNCT
ejpam-6793	373	1	[	[	X
ejpam-6793	373	2	26	26	NUM
ejpam-6793	373	3	]	]	PUNCT
ejpam-6793	373	4	m.	m.	NOUN
ejpam-6793	373	5	abul	abul	PROPN
ejpam-6793	373	6	-	-	PUNCT
ejpam-6793	373	7	ez	ez	PROPN
ejpam-6793	373	8	.	.	PROPN
ejpam-6793	373	9	product	product	NOUN
ejpam-6793	373	10	simple	simple	ADJ
ejpam-6793	373	11	sets	set	NOUN
ejpam-6793	373	12	of	of	ADP
ejpam-6793	373	13	polynomials	polynomial	NOUN
ejpam-6793	373	14	in	in	ADP
ejpam-6793	373	15	clifford	clifford	PROPN
ejpam-6793	373	16	analysis	analysis	NOUN
ejpam-6793	373	17	.	.	PUNCT
ejpam-6793	374	1	rivista	rivista	PROPN
ejpam-6793	374	2	di	di	PROPN
ejpam-6793	374	3	matematica	matematica	PROPN
ejpam-6793	374	4	della	della	PROPN
ejpam-6793	374	5	università	università	PROPN
ejpam-6793	374	6	di	di	X
ejpam-6793	374	7	parma	parma	PROPN
ejpam-6793	374	8	,	,	PUNCT
ejpam-6793	374	9	3(5):283–293	3(5):283–293	NUM
ejpam-6793	374	10	,	,	PUNCT
ejpam-6793	374	11	1994	1994	NUM
ejpam-6793	374	12	.	.	PUNCT
ejpam-6793	375	1	[	[	X
ejpam-6793	375	2	27	27	NUM
ejpam-6793	375	3	]	]	PUNCT
ejpam-6793	375	4	m.	m.	NOUN
ejpam-6793	375	5	abul	abul	PROPN
ejpam-6793	375	6	-	-	PUNCT
ejpam-6793	375	7	ez	ez	PROPN
ejpam-6793	375	8	and	and	CCONJ
ejpam-6793	375	9	m.	m.	NOUN
ejpam-6793	375	10	zayed	zaye	VERB
ejpam-6793	375	11	.	.	PUNCT
ejpam-6793	376	1	similar	similar	ADJ
ejpam-6793	376	2	transposed	transpose	VERB
ejpam-6793	376	3	bases	basis	NOUN
ejpam-6793	376	4	of	of	ADP
ejpam-6793	376	5	polynomials	polynomial	NOUN
ejpam-6793	376	6	in	in	ADP
ejpam-6793	376	7	clifford	clifford	PROPN
ejpam-6793	376	8	analysis	analysis	NOUN
ejpam-6793	376	9	.	.	PUNCT
ejpam-6793	377	1	applied	apply	VERB
ejpam-6793	377	2	mathematics	mathematic	NOUN
ejpam-6793	377	3	and	and	CCONJ
ejpam-6793	377	4	information	information	NOUN
ejpam-6793	377	5	sciences	science	NOUN
ejpam-6793	377	6	,	,	PUNCT
ejpam-6793	377	7	4:63–78	4:63–78	NUM
ejpam-6793	377	8	,	,	PUNCT
ejpam-6793	377	9	2010	2010	NUM
ejpam-6793	377	10	.	.	PUNCT