id	sid	tid	token	lemma	pos
ejpam-6294	1	1	european	european	PROPN
ejpam-6294	1	2	journal	journal	PROPN
ejpam-6294	1	3	of	of	ADP
ejpam-6294	1	4	pure	pure	ADJ
ejpam-6294	1	5	and	and	CCONJ
ejpam-6294	1	6	applied	applied	ADJ
ejpam-6294	1	7	mathematics	mathematic	NOUN
ejpam-6294	1	8	2025	2025	NUM
ejpam-6294	1	9	,	,	PUNCT
ejpam-6294	1	10	vol	vol	NOUN
ejpam-6294	1	11	.	.	PROPN
ejpam-6294	1	12	18	18	NUM
ejpam-6294	1	13	,	,	PUNCT
ejpam-6294	1	14	issue	issue	NOUN
ejpam-6294	1	15	3	3	NUM
ejpam-6294	1	16	,	,	PUNCT
ejpam-6294	1	17	article	article	NOUN
ejpam-6294	1	18	number	number	NOUN
ejpam-6294	1	19	6294	6294	NUM
ejpam-6294	1	20	issn	issn	PROPN
ejpam-6294	1	21	1307	1307	NUM
ejpam-6294	1	22	-	-	SYM
ejpam-6294	1	23	5543	5543	NUM
ejpam-6294	1	24	–	–	PUNCT
ejpam-6294	1	25	ejpam.com	ejpam.com	X
ejpam-6294	1	26	published	publish	VERB
ejpam-6294	1	27	by	by	ADP
ejpam-6294	1	28	new	new	PROPN
ejpam-6294	1	29	york	york	PROPN
ejpam-6294	1	30	business	business	PROPN
ejpam-6294	1	31	global	global	ADJ
ejpam-6294	1	32	representation	representation	NOUN
ejpam-6294	1	33	of	of	ADP
ejpam-6294	1	34	bi	bi	ADJ
ejpam-6294	1	35	-	-	ADJ
ejpam-6294	1	36	univalent	univalent	ADJ
ejpam-6294	1	37	functions	function	NOUN
ejpam-6294	1	38	to	to	ADP
ejpam-6294	1	39	lucas	lucas	NOUN
ejpam-6294	1	40	balancing	balancing	NOUN
ejpam-6294	1	41	polynomials	polynomial	NOUN
ejpam-6294	1	42	with	with	ADP
ejpam-6294	1	43	geometric	geometric	ADJ
ejpam-6294	1	44	properties	property	NOUN
ejpam-6294	1	45	and	and	CCONJ
ejpam-6294	1	46	coefficient	coefficient	NOUN
ejpam-6294	1	47	bounds	bound	NOUN
ejpam-6294	1	48	stalin	stalin	PROPN
ejpam-6294	1	49	thangamani1	thangamani1	PROPN
ejpam-6294	1	50	,	,	PUNCT
ejpam-6294	1	51	pshtiwan	pshtiwan	PROPN
ejpam-6294	1	52	othman	othman	PROPN
ejpam-6294	1	53	mohammed2,3,∗	mohammed2,3,∗	PROPN
ejpam-6294	1	54	,	,	PUNCT
ejpam-6294	1	55	jeno	jeno	PROPN
ejpam-6294	1	56	francis	francis	PROPN
ejpam-6294	1	57	devadoss4	devadoss4	PROPN
ejpam-6294	1	58	,	,	PUNCT
ejpam-6294	1	59	majeed	majeed	PROPN
ejpam-6294	1	60	a.	a.	PROPN
ejpam-6294	1	61	yousif5	yousif5	PROPN
ejpam-6294	1	62	,	,	PUNCT
ejpam-6294	1	63	meraa	meraa	NOUN
ejpam-6294	1	64	arab6,∗	arab6,∗	NOUN
ejpam-6294	1	65	,	,	PUNCT
ejpam-6294	1	66	dumitru	dumitru	PROPN
ejpam-6294	1	67	baleanu7	baleanu7	PROPN
ejpam-6294	1	68	1	1	NUM
ejpam-6294	1	69	department	department	NOUN
ejpam-6294	1	70	of	of	ADP
ejpam-6294	1	71	mathematics	mathematic	NOUN
ejpam-6294	1	72	,	,	PUNCT
ejpam-6294	1	73	vel	vel	ADJ
ejpam-6294	1	74	tech	tech	NOUN
ejpam-6294	1	75	rangarajan	rangarajan	NOUN
ejpam-6294	1	76	dr.sagunthala	dr.sagunthala	NOUN
ejpam-6294	1	77	r	r	PROPN
ejpam-6294	1	78	&	&	CCONJ
ejpam-6294	1	79	d	d	PROPN
ejpam-6294	1	80	institute	institute	PROPN
ejpam-6294	1	81	of	of	ADP
ejpam-6294	1	82	science	science	NOUN
ejpam-6294	1	83	and	and	CCONJ
ejpam-6294	1	84	technology	technology	NOUN
ejpam-6294	1	85	,	,	PUNCT
ejpam-6294	1	86	avadi	avadi	NOUN
ejpam-6294	1	87	,	,	PUNCT
ejpam-6294	1	88	chennai	chennai	NOUN
ejpam-6294	1	89	600062	600062	NUM
ejpam-6294	1	90	,	,	PUNCT
ejpam-6294	1	91	india	india	PROPN
ejpam-6294	1	92	2	2	NUM
ejpam-6294	1	93	research	research	NOUN
ejpam-6294	1	94	and	and	CCONJ
ejpam-6294	1	95	development	development	NOUN
ejpam-6294	1	96	center	center	NOUN
ejpam-6294	1	97	,	,	PUNCT
ejpam-6294	1	98	university	university	NOUN
ejpam-6294	1	99	of	of	ADP
ejpam-6294	1	100	sulaimani	sulaimani	PROPN
ejpam-6294	1	101	,	,	PUNCT
ejpam-6294	1	102	sulaymaniyah	sulaymaniyah	NOUN
ejpam-6294	1	103	46001	46001	NUM
ejpam-6294	1	104	,	,	PUNCT
ejpam-6294	1	105	iraq	iraq	PROPN
ejpam-6294	1	106	3	3	NUM
ejpam-6294	1	107	research	research	NOUN
ejpam-6294	1	108	center	center	NOUN
ejpam-6294	1	109	,	,	PUNCT
ejpam-6294	1	110	university	university	NOUN
ejpam-6294	1	111	of	of	ADP
ejpam-6294	1	112	halabja	halabja	PROPN
ejpam-6294	1	113	,	,	PUNCT
ejpam-6294	1	114	halabja	halabja	PROPN
ejpam-6294	1	115	46018	46018	NUM
ejpam-6294	1	116	,	,	PUNCT
ejpam-6294	1	117	iraq	iraq	PROPN
ejpam-6294	1	118	4	4	NUM
ejpam-6294	1	119	department	department	NOUN
ejpam-6294	1	120	of	of	ADP
ejpam-6294	1	121	mathematics	mathematic	NOUN
ejpam-6294	1	122	,	,	PUNCT
ejpam-6294	1	123	prathyusha	prathyusha	PROPN
ejpam-6294	1	124	engineering	engineering	PROPN
ejpam-6294	1	125	college	college	PROPN
ejpam-6294	1	126	,	,	PUNCT
ejpam-6294	1	127	anna	anna	PROPN
ejpam-6294	1	128	university	university	PROPN
ejpam-6294	1	129	,	,	PUNCT
ejpam-6294	1	130	chennai	chennai	PROPN
ejpam-6294	1	131	602025	602025	NUM
ejpam-6294	1	132	,	,	PUNCT
ejpam-6294	1	133	india	india	PROPN
ejpam-6294	1	134	5	5	NUM
ejpam-6294	1	135	department	department	NOUN
ejpam-6294	1	136	of	of	ADP
ejpam-6294	1	137	mathematics	mathematic	NOUN
ejpam-6294	1	138	,	,	PUNCT
ejpam-6294	1	139	college	college	NOUN
ejpam-6294	1	140	of	of	ADP
ejpam-6294	1	141	education	education	NOUN
ejpam-6294	1	142	,	,	PUNCT
ejpam-6294	1	143	university	university	NOUN
ejpam-6294	1	144	of	of	ADP
ejpam-6294	1	145	zakho	zakho	PROPN
ejpam-6294	1	146	,	,	PUNCT
ejpam-6294	1	147	zakho	zakho	PROPN
ejpam-6294	1	148	42002	42002	NUM
ejpam-6294	1	149	,	,	PUNCT
ejpam-6294	1	150	iraq	iraq	PROPN
ejpam-6294	1	151	6	6	NUM
ejpam-6294	1	152	department	department	NOUN
ejpam-6294	1	153	of	of	ADP
ejpam-6294	1	154	mathematics	mathematic	NOUN
ejpam-6294	1	155	and	and	CCONJ
ejpam-6294	1	156	statistics	statistic	NOUN
ejpam-6294	1	157	,	,	PUNCT
ejpam-6294	1	158	college	college	NOUN
ejpam-6294	1	159	of	of	ADP
ejpam-6294	1	160	science	science	NOUN
ejpam-6294	1	161	,	,	PUNCT
ejpam-6294	1	162	king	king	NOUN
ejpam-6294	1	163	faisal	faisal	PROPN
ejpam-6294	1	164	university	university	PROPN
ejpam-6294	1	165	,	,	PUNCT
ejpam-6294	1	166	hofuf	hofuf	PROPN
ejpam-6294	1	167	31982	31982	NUM
ejpam-6294	1	168	,	,	PUNCT
ejpam-6294	1	169	al	al	PROPN
ejpam-6294	1	170	ahsa	ahsa	PROPN
ejpam-6294	1	171	,	,	PUNCT
ejpam-6294	1	172	saudi	saudi	PROPN
ejpam-6294	1	173	arabia	arabia	PROPN
ejpam-6294	1	174	7	7	NUM
ejpam-6294	1	175	department	department	NOUN
ejpam-6294	1	176	of	of	ADP
ejpam-6294	1	177	computer	computer	NOUN
ejpam-6294	1	178	science	science	NOUN
ejpam-6294	1	179	and	and	CCONJ
ejpam-6294	1	180	mathematics	mathematic	NOUN
ejpam-6294	1	181	,	,	PUNCT
ejpam-6294	1	182	lebanese	lebanese	ADJ
ejpam-6294	1	183	american	american	PROPN
ejpam-6294	1	184	university	university	PROPN
ejpam-6294	1	185	,	,	PUNCT
ejpam-6294	1	186	beirut	beirut	PROPN
ejpam-6294	1	187	11022801	11022801	NUM
ejpam-6294	1	188	,	,	PUNCT
ejpam-6294	1	189	lebanon	lebanon	PROPN
ejpam-6294	1	190	abstract	abstract	NOUN
ejpam-6294	1	191	.	.	PUNCT
ejpam-6294	2	1	in	in	ADP
ejpam-6294	2	2	this	this	DET
ejpam-6294	2	3	paper	paper	NOUN
ejpam-6294	2	4	,	,	PUNCT
ejpam-6294	2	5	we	we	PRON
ejpam-6294	2	6	introduce	introduce	VERB
ejpam-6294	2	7	and	and	CCONJ
ejpam-6294	2	8	analyze	analyze	VERB
ejpam-6294	2	9	a	a	DET
ejpam-6294	2	10	new	new	ADJ
ejpam-6294	2	11	subclass	subclass	NOUN
ejpam-6294	2	12	of	of	ADP
ejpam-6294	2	13	bi	bi	ADJ
ejpam-6294	2	14	-	-	ADJ
ejpam-6294	2	15	univalent	univalent	ADJ
ejpam-6294	2	16	functions	function	NOUN
ejpam-6294	2	17	defined	define	VERB
ejpam-6294	2	18	in	in	ADP
ejpam-6294	2	19	the	the	DET
ejpam-6294	2	20	open	open	ADJ
ejpam-6294	2	21	unit	unit	NOUN
ejpam-6294	2	22	disk	disk	NOUN
ejpam-6294	2	23	,	,	PUNCT
ejpam-6294	2	24	associated	associate	VERB
ejpam-6294	2	25	with	with	ADP
ejpam-6294	2	26	lucas	lucas	PROPN
ejpam-6294	2	27	and	and	CCONJ
ejpam-6294	2	28	lucas	lucas	PROPN
ejpam-6294	2	29	balancing	balancing	NOUN
ejpam-6294	2	30	polynomials	polynomial	NOUN
ejpam-6294	2	31	.	.	PUNCT
ejpam-6294	3	1	by	by	ADP
ejpam-6294	3	2	employing	employ	VERB
ejpam-6294	3	3	the	the	DET
ejpam-6294	3	4	taylor	taylor	PROPN
ejpam-6294	3	5	-	-	PUNCT
ejpam-6294	3	6	maclaurin	maclaurin	PROPN
ejpam-6294	3	7	series	series	NOUN
ejpam-6294	3	8	expansion	expansion	NOUN
ejpam-6294	3	9	,	,	PUNCT
ejpam-6294	3	10	precise	precise	ADJ
ejpam-6294	3	11	bounds	bound	NOUN
ejpam-6294	3	12	for	for	ADP
ejpam-6294	3	13	the	the	DET
ejpam-6294	3	14	second	second	ADJ
ejpam-6294	3	15	and	and	CCONJ
ejpam-6294	3	16	third	third	ADJ
ejpam-6294	3	17	coefficients	coefficient	NOUN
ejpam-6294	3	18	,	,	PUNCT
ejpam-6294	3	19	|a2|	|a2|	NOUN
ejpam-6294	3	20	and	and	CCONJ
ejpam-6294	3	21	|a3|	|a3|	NOUN
ejpam-6294	3	22	,	,	PUNCT
ejpam-6294	3	23	are	be	AUX
ejpam-6294	3	24	obtained	obtain	VERB
ejpam-6294	3	25	.	.	PUNCT
ejpam-6294	4	1	these	these	DET
ejpam-6294	4	2	estimates	estimate	NOUN
ejpam-6294	4	3	lead	lead	VERB
ejpam-6294	4	4	to	to	ADP
ejpam-6294	4	5	important	important	ADJ
ejpam-6294	4	6	geometric	geometric	ADJ
ejpam-6294	4	7	interpretations	interpretation	NOUN
ejpam-6294	4	8	related	relate	VERB
ejpam-6294	4	9	to	to	ADP
ejpam-6294	4	10	the	the	DET
ejpam-6294	4	11	distortion	distortion	NOUN
ejpam-6294	4	12	,	,	PUNCT
ejpam-6294	4	13	growth	growth	NOUN
ejpam-6294	4	14	,	,	PUNCT
ejpam-6294	4	15	and	and	CCONJ
ejpam-6294	4	16	structural	structural	ADJ
ejpam-6294	4	17	behavior	behavior	NOUN
ejpam-6294	4	18	of	of	ADP
ejpam-6294	4	19	the	the	DET
ejpam-6294	4	20	functions	function	NOUN
ejpam-6294	4	21	near	near	ADP
ejpam-6294	4	22	the	the	DET
ejpam-6294	4	23	origin	origin	NOUN
ejpam-6294	4	24	.	.	PUNCT
ejpam-6294	5	1	furthermore	furthermore	ADV
ejpam-6294	5	2	,	,	PUNCT
ejpam-6294	5	3	the	the	DET
ejpam-6294	5	4	mapping	mapping	NOUN
ejpam-6294	5	5	characteristics	characteristic	NOUN
ejpam-6294	5	6	of	of	ADP
ejpam-6294	5	7	these	these	DET
ejpam-6294	5	8	functions	function	NOUN
ejpam-6294	5	9	are	be	AUX
ejpam-6294	5	10	examined	examine	VERB
ejpam-6294	5	11	in	in	ADP
ejpam-6294	5	12	connection	connection	NOUN
ejpam-6294	5	13	with	with	ADP
ejpam-6294	5	14	existing	exist	VERB
ejpam-6294	5	15	bi	bi	ADJ
ejpam-6294	5	16	-	-	ADJ
ejpam-6294	5	17	univalent	univalent	ADJ
ejpam-6294	5	18	subclasses	subclass	NOUN
ejpam-6294	5	19	.	.	PUNCT
ejpam-6294	6	1	special	special	ADJ
ejpam-6294	6	2	emphasis	emphasis	NOUN
ejpam-6294	6	3	is	be	AUX
ejpam-6294	6	4	placed	place	VERB
ejpam-6294	6	5	on	on	ADP
ejpam-6294	6	6	deriving	derive	VERB
ejpam-6294	6	7	a	a	DET
ejpam-6294	6	8	fekete	fekete	ADJ
ejpam-6294	6	9	-	-	PUNCT
ejpam-6294	6	10	szegö	szegö	ADJ
ejpam-6294	6	11	type	type	NOUN
ejpam-6294	6	12	inequality	inequality	NOUN
ejpam-6294	6	13	for	for	ADP
ejpam-6294	6	14	the	the	DET
ejpam-6294	6	15	proposed	propose	VERB
ejpam-6294	6	16	class	class	NOUN
ejpam-6294	6	17	,	,	PUNCT
ejpam-6294	6	18	thereby	thereby	ADV
ejpam-6294	6	19	extending	extend	VERB
ejpam-6294	6	20	earlier	early	ADJ
ejpam-6294	6	21	contributions	contribution	NOUN
ejpam-6294	6	22	in	in	ADP
ejpam-6294	6	23	the	the	DET
ejpam-6294	6	24	field	field	NOUN
ejpam-6294	6	25	.	.	PUNCT
ejpam-6294	7	1	the	the	DET
ejpam-6294	7	2	findings	finding	NOUN
ejpam-6294	7	3	presented	present	VERB
ejpam-6294	7	4	here	here	ADV
ejpam-6294	7	5	are	be	AUX
ejpam-6294	7	6	valuable	valuable	ADJ
ejpam-6294	7	7	for	for	ADP
ejpam-6294	7	8	applications	application	NOUN
ejpam-6294	7	9	in	in	ADP
ejpam-6294	7	10	geometric	geometric	ADJ
ejpam-6294	7	11	function	function	NOUN
ejpam-6294	7	12	theory	theory	NOUN
ejpam-6294	7	13	and	and	CCONJ
ejpam-6294	7	14	areas	area	NOUN
ejpam-6294	7	15	like	like	ADP
ejpam-6294	7	16	fluid	fluid	NOUN
ejpam-6294	7	17	mechanics	mechanic	NOUN
ejpam-6294	7	18	,	,	PUNCT
ejpam-6294	7	19	conformal	conformal	NOUN
ejpam-6294	7	20	mappings	mapping	NOUN
ejpam-6294	7	21	,	,	PUNCT
ejpam-6294	7	22	and	and	CCONJ
ejpam-6294	7	23	engineering	engineering	NOUN
ejpam-6294	7	24	models	model	NOUN
ejpam-6294	7	25	where	where	SCONJ
ejpam-6294	7	26	the	the	DET
ejpam-6294	7	27	analytic	analytic	ADJ
ejpam-6294	7	28	structure	structure	NOUN
ejpam-6294	7	29	of	of	ADP
ejpam-6294	7	30	bi	bi	ADJ
ejpam-6294	7	31	-	-	ADJ
ejpam-6294	7	32	univalent	univalent	ADJ
ejpam-6294	7	33	functions	function	NOUN
ejpam-6294	7	34	plays	play	VERB
ejpam-6294	7	35	a	a	DET
ejpam-6294	7	36	significant	significant	ADJ
ejpam-6294	7	37	role	role	NOUN
ejpam-6294	7	38	.	.	PUNCT
ejpam-6294	8	1	2020	2020	NUM
ejpam-6294	8	2	mathematics	mathematic	NOUN
ejpam-6294	8	3	subject	subject	NOUN
ejpam-6294	8	4	classifications	classification	NOUN
ejpam-6294	8	5	:	:	PUNCT
ejpam-6294	8	6	30c45	30c45	NUM
ejpam-6294	8	7	,	,	PUNCT
ejpam-6294	8	8	30c50	30c50	DET
ejpam-6294	8	9	key	key	ADJ
ejpam-6294	8	10	words	word	NOUN
ejpam-6294	8	11	and	and	CCONJ
ejpam-6294	8	12	phrases	phrase	NOUN
ejpam-6294	8	13	:	:	PUNCT
ejpam-6294	8	14	bi	bi	ADJ
ejpam-6294	8	15	-	-	ADJ
ejpam-6294	8	16	univalent	univalent	ADJ
ejpam-6294	8	17	functions	function	NOUN
ejpam-6294	8	18	,	,	PUNCT
ejpam-6294	8	19	lucas	lucas	PROPN
ejpam-6294	8	20	polynomial	polynomial	PROPN
ejpam-6294	8	21	,	,	PUNCT
ejpam-6294	8	22	fekete	fekete	NOUN
ejpam-6294	8	23	-	-	PUNCT
ejpam-6294	8	24	szegö	szegö	PROPN
ejpam-6294	8	25	inequality	inequality	NOUN
ejpam-6294	8	26	∗corresponding	∗corresponde	VERB
ejpam-6294	8	27	author	author	NOUN
ejpam-6294	8	28	.	.	PUNCT
ejpam-6294	9	1	∗corresponding	∗corresponde	VERB
ejpam-6294	9	2	author	author	NOUN
ejpam-6294	9	3	.	.	PUNCT
ejpam-6294	10	1	doi	doi	NOUN
ejpam-6294	10	2	:	:	PUNCT
ejpam-6294	10	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6294	https://doi.org/10.29020/nybg.ejpam.v18i3.6294	NOUN
ejpam-6294	10	4	email	email	NOUN
ejpam-6294	10	5	addresses	address	NOUN
ejpam-6294	10	6	:	:	PUNCT
ejpam-6294	10	7	drstalint@veltech.edu.in	drstalint@veltech.edu.in	PROPN
ejpam-6294	10	8	(	(	PUNCT
ejpam-6294	10	9	s.	s.	PROPN
ejpam-6294	10	10	thangamani	thangamani	PROPN
ejpam-6294	10	11	)	)	PUNCT
ejpam-6294	10	12	,	,	PUNCT
ejpam-6294	11	1	pshtiwansangawi@gmail.com	pshtiwansangawi@gmail.com	X
ejpam-6294	11	2	(	(	PUNCT
ejpam-6294	11	3	p.o	p.o	PROPN
ejpam-6294	11	4	.	.	PROPN
ejpam-6294	11	5	mohammed	mohammed	PROPN
ejpam-6294	11	6	)	)	PUNCT
ejpam-6294	11	7	,	,	PUNCT
ejpam-6294	11	8	jenofrancis29@gmail.com	jenofrancis29@gmail.com	PROPN
ejpam-6294	11	9	(	(	PUNCT
ejpam-6294	11	10	j.	j.	PROPN
ejpam-6294	11	11	f.	f.	PROPN
ejpam-6294	11	12	devadoss	devadoss	PROPN
ejpam-6294	11	13	)	)	PUNCT
ejpam-6294	11	14	,	,	PUNCT
ejpam-6294	11	15	majeed.yousif@uoz.edu.krd	majeed.yousif@uoz.edu.krd	PROPN
ejpam-6294	11	16	(	(	PUNCT
ejpam-6294	11	17	m.a	m.a	PROPN
ejpam-6294	11	18	.	.	PROPN
ejpam-6294	11	19	yousif	yousif	PROPN
ejpam-6294	11	20	)	)	PUNCT
ejpam-6294	11	21	,	,	PUNCT
ejpam-6294	11	22	marab@kfu.edu.sa	marab@kfu.edu.sa	PROPN
ejpam-6294	11	23	(	(	PUNCT
ejpam-6294	11	24	m.	m.	PROPN
ejpam-6294	11	25	arab	arab	PROPN
ejpam-6294	11	26	)	)	PUNCT
ejpam-6294	11	27	,	,	PUNCT
ejpam-6294	11	28	dumitru.baleanu@lau.edu.lb	dumitru.baleanu@lau.edu.lb	PROPN
ejpam-6294	11	29	(	(	PUNCT
ejpam-6294	11	30	d.	d.	NOUN
ejpam-6294	11	31	baleanu	baleanu	PROPN
ejpam-6294	11	32	)	)	PUNCT
ejpam-6294	11	33	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6294	12	1	1	1	NUM
ejpam-6294	12	2	copyright	copyright	NOUN
ejpam-6294	12	3	:	:	PUNCT
ejpam-6294	12	4	©	©	PROPN
ejpam-6294	12	5	2025	2025	NUM
ejpam-6294	12	6	the	the	DET
ejpam-6294	12	7	author(s	author(s	NOUN
ejpam-6294	12	8	)	)	PUNCT
ejpam-6294	12	9	.	.	PUNCT
ejpam-6294	13	1	(	(	PUNCT
ejpam-6294	13	2	cc	cc	NOUN
ejpam-6294	13	3	by	by	ADP
ejpam-6294	13	4	-	-	PUNCT
ejpam-6294	13	5	nc	nc	PROPN
ejpam-6294	13	6	4.0	4.0	NUM
ejpam-6294	13	7	)	)	PUNCT
ejpam-6294	13	8	s.	s.	PROPN
ejpam-6294	13	9	thangamani	thangamani	PROPN
ejpam-6294	13	10	et	et	PROPN
ejpam-6294	13	11	al	al	PROPN
ejpam-6294	13	12	.	.	PUNCT
ejpam-6294	13	13	/	/	SYM
ejpam-6294	13	14	eur	eur	PROPN
ejpam-6294	13	15	.	.	PUNCT
ejpam-6294	14	1	j.	j.	PROPN
ejpam-6294	14	2	pure	pure	PROPN
ejpam-6294	14	3	appl	appl	PROPN
ejpam-6294	14	4	.	.	PROPN
ejpam-6294	14	5	math	math	PROPN
ejpam-6294	14	6	,	,	PUNCT
ejpam-6294	14	7	18	18	NUM
ejpam-6294	14	8	(	(	PUNCT
ejpam-6294	14	9	3	3	NUM
ejpam-6294	14	10	)	)	PUNCT
ejpam-6294	14	11	(	(	PUNCT
ejpam-6294	14	12	2025	2025	NUM
ejpam-6294	14	13	)	)	PUNCT
ejpam-6294	14	14	,	,	PUNCT
ejpam-6294	14	15	6294	6294	NUM
ejpam-6294	14	16	2	2	NUM
ejpam-6294	14	17	of	of	ADP
ejpam-6294	14	18	19	19	NUM
ejpam-6294	14	19	1	1	NUM
ejpam-6294	14	20	.	.	PUNCT
ejpam-6294	15	1	introduction	introduction	NOUN
ejpam-6294	15	2	in	in	ADP
ejpam-6294	15	3	the	the	DET
ejpam-6294	15	4	open	open	ADJ
ejpam-6294	15	5	unit	unit	NOUN
ejpam-6294	15	6	disk	disk	NOUN
ejpam-6294	15	7	d	d	NOUN
ejpam-6294	15	8	=	=	SYM
ejpam-6294	15	9	{	{	PUNCT
ejpam-6294	15	10	θ	θ	PROPN
ejpam-6294	15	11	∈	∈	PROPN
ejpam-6294	16	1	c	c	NOUN
ejpam-6294	16	2	:	:	PUNCT
ejpam-6294	16	3	|θ	|θ	VERB
ejpam-6294	16	4	|	|	ADV
ejpam-6294	16	5	<	<	X
ejpam-6294	16	6	1	1	NUM
ejpam-6294	16	7	}	}	PUNCT
ejpam-6294	16	8	,	,	PUNCT
ejpam-6294	16	9	a	a	PRON
ejpam-6294	16	10	often	often	ADV
ejpam-6294	16	11	denotes	denote	VERB
ejpam-6294	16	12	the	the	DET
ejpam-6294	16	13	class	class	NOUN
ejpam-6294	16	14	of	of	ADP
ejpam-6294	16	15	normalized	normalized	ADJ
ejpam-6294	16	16	and	and	CCONJ
ejpam-6294	16	17	analytic	analytic	ADJ
ejpam-6294	16	18	functions	function	NOUN
ejpam-6294	16	19	f	f	X
ejpam-6294	16	20	(	(	PUNCT
ejpam-6294	16	21	θ	θ	NOUN
ejpam-6294	16	22	)	)	PUNCT
ejpam-6294	16	23	of	of	ADP
ejpam-6294	16	24	the	the	DET
ejpam-6294	16	25	form	form	NOUN
ejpam-6294	16	26	f	f	PROPN
ejpam-6294	16	27	(	(	PUNCT
ejpam-6294	16	28	θ	θ	NOUN
ejpam-6294	16	29	)	)	PUNCT
ejpam-6294	16	30	=	=	SYM
ejpam-6294	16	31	θ	θ	NOUN
ejpam-6294	17	1	+	+	PUNCT
ejpam-6294	18	1	∞∑	∞∑	NUM
ejpam-6294	18	2	k=2	k=2	PROPN
ejpam-6294	18	3	akθ	akθ	NOUN
ejpam-6294	18	4	k	k	PROPN
ejpam-6294	18	5	(	(	PUNCT
ejpam-6294	18	6	1	1	NUM
ejpam-6294	18	7	)	)	PUNCT
ejpam-6294	18	8	and	and	CCONJ
ejpam-6294	18	9	s	s	NOUN
ejpam-6294	18	10	act	act	NOUN
ejpam-6294	18	11	as	as	ADP
ejpam-6294	18	12	a	a	DET
ejpam-6294	18	13	subclass	subclass	NOUN
ejpam-6294	18	14	of	of	ADP
ejpam-6294	18	15	all	all	DET
ejpam-6294	18	16	functions	function	NOUN
ejpam-6294	18	17	in	in	ADP
ejpam-6294	18	18	a.	a.	NOUN
ejpam-6294	18	19	as	as	SCONJ
ejpam-6294	18	20	stated	state	VERB
ejpam-6294	18	21	by	by	ADP
ejpam-6294	18	22	koebe	koebe	NOUN
ejpam-6294	18	23	one	one	NUM
ejpam-6294	18	24	-	-	PUNCT
ejpam-6294	18	25	quarter	quarter	NOUN
ejpam-6294	18	26	theorem	theorem	NOUN
ejpam-6294	18	27	[	[	X
ejpam-6294	18	28	1	1	NUM
ejpam-6294	18	29	]	]	PUNCT
ejpam-6294	18	30	,	,	PUNCT
ejpam-6294	18	31	if	if	SCONJ
ejpam-6294	18	32	f	f	PROPN
ejpam-6294	18	33	∈	∈	PROPN
ejpam-6294	18	34	s	s	VERB
ejpam-6294	18	35	is	be	AUX
ejpam-6294	18	36	a	a	DET
ejpam-6294	18	37	univalent	univalent	ADJ
ejpam-6294	18	38	function	function	NOUN
ejpam-6294	18	39	,	,	PUNCT
ejpam-6294	18	40	then	then	ADV
ejpam-6294	18	41	the	the	DET
ejpam-6294	18	42	image	image	NOUN
ejpam-6294	18	43	of	of	ADP
ejpam-6294	18	44	unit	unit	NOUN
ejpam-6294	18	45	disk	disk	NOUN
ejpam-6294	18	46	under	under	ADP
ejpam-6294	18	47	f	f	PROPN
ejpam-6294	18	48	will	will	AUX
ejpam-6294	18	49	contain	contain	VERB
ejpam-6294	18	50	a	a	DET
ejpam-6294	18	51	disk	disk	NOUN
ejpam-6294	18	52	of	of	ADP
ejpam-6294	18	53	radius	radius	NOUN
ejpam-6294	18	54	1	1	NUM
ejpam-6294	18	55	4	4	NUM
ejpam-6294	18	56	.	.	PUNCT
ejpam-6294	19	1	as	as	ADP
ejpam-6294	19	2	a	a	DET
ejpam-6294	19	3	results	result	NOUN
ejpam-6294	19	4	,	,	PUNCT
ejpam-6294	19	5	for	for	ADP
ejpam-6294	19	6	all	all	DET
ejpam-6294	19	7	univalent	univalent	ADJ
ejpam-6294	19	8	functions	function	NOUN
ejpam-6294	19	9	f	f	PROPN
ejpam-6294	19	10	∈	∈	PROPN
ejpam-6294	19	11	s	s	PART
ejpam-6294	19	12	,	,	PUNCT
ejpam-6294	19	13	there	there	PRON
ejpam-6294	19	14	exists	exist	VERB
ejpam-6294	19	15	an	an	DET
ejpam-6294	19	16	inverse	inverse	NOUN
ejpam-6294	19	17	function	function	NOUN
ejpam-6294	19	18	f	f	NOUN
ejpam-6294	19	19	−1	−1	NOUN
ejpam-6294	19	20	that	that	PRON
ejpam-6294	19	21	satisfies	satisfy	VERB
ejpam-6294	19	22	f	f	PROPN
ejpam-6294	19	23	−1[f	−1[f	PROPN
ejpam-6294	19	24	(	(	PUNCT
ejpam-6294	19	25	θ	θ	NOUN
ejpam-6294	19	26	)	)	PUNCT
ejpam-6294	19	27	]	]	PUNCT
ejpam-6294	20	1	=	=	SYM
ejpam-6294	20	2	θ	θ	PROPN
ejpam-6294	20	3	and	and	CCONJ
ejpam-6294	20	4	f	f	X
ejpam-6294	21	1	[	[	X
ejpam-6294	21	2	f	f	X
ejpam-6294	21	3	−1(φ	−1(φ	PROPN
ejpam-6294	21	4	)	)	PUNCT
ejpam-6294	21	5	]	]	PUNCT
ejpam-6294	22	1	=	=	SYM
ejpam-6294	22	2	g(φ	g(φ	PROPN
ejpam-6294	22	3	)	)	PUNCT
ejpam-6294	22	4	for	for	ADP
ejpam-6294	22	5	|φ|	|φ|	PROPN
ejpam-6294	22	6	<	<	X
ejpam-6294	22	7	r0	r0	PROPN
ejpam-6294	22	8	(	(	PUNCT
ejpam-6294	22	9	f	f	PROPN
ejpam-6294	22	10	)	)	PUNCT
ejpam-6294	22	11	:	:	PUNCT
ejpam-6294	22	12	r0	r0	NOUN
ejpam-6294	22	13	(	(	PUNCT
ejpam-6294	22	14	f	f	PROPN
ejpam-6294	22	15	)	)	PUNCT
ejpam-6294	22	16	≥	≥	NOUN
ejpam-6294	22	17	1	1	NUM
ejpam-6294	22	18	4	4	NUM
ejpam-6294	22	19	.	.	PUNCT
ejpam-6294	23	1	a	a	DET
ejpam-6294	23	2	power	power	NOUN
ejpam-6294	23	3	series	series	NOUN
ejpam-6294	23	4	in	in	ADP
ejpam-6294	23	5	f	f	PROPN
ejpam-6294	23	6	(	(	PUNCT
ejpam-6294	23	7	θ	θ	NOUN
ejpam-6294	23	8	)	)	PUNCT
ejpam-6294	23	9	given	give	VERB
ejpam-6294	23	10	by	by	ADP
ejpam-6294	23	11	equation	equation	NOUN
ejpam-6294	23	12	(	(	PUNCT
ejpam-6294	23	13	1	1	X
ejpam-6294	23	14	)	)	PUNCT
ejpam-6294	23	15	can	can	AUX
ejpam-6294	23	16	be	be	AUX
ejpam-6294	23	17	used	use	VERB
ejpam-6294	23	18	to	to	PART
ejpam-6294	23	19	define	define	VERB
ejpam-6294	23	20	the	the	DET
ejpam-6294	23	21	inverse	inverse	NOUN
ejpam-6294	23	22	function	function	NOUN
ejpam-6294	23	23	,	,	PUNCT
ejpam-6294	23	24	where	where	SCONJ
ejpam-6294	23	25	a2	a2	PROPN
ejpam-6294	23	26	,	,	PUNCT
ejpam-6294	23	27	a3	a3	NOUN
ejpam-6294	23	28	,	,	PUNCT
ejpam-6294	23	29	.	.	PUNCT
ejpam-6294	23	30	.	.	PUNCT
ejpam-6294	24	1	.	.	PUNCT
ejpam-6294	25	1	are	be	AUX
ejpam-6294	25	2	complex	complex	ADJ
ejpam-6294	25	3	coefficients	coefficient	NOUN
ejpam-6294	25	4	.	.	PUNCT
ejpam-6294	26	1	if	if	SCONJ
ejpam-6294	26	2	both	both	PRON
ejpam-6294	26	3	a	a	DET
ejpam-6294	26	4	function	function	NOUN
ejpam-6294	26	5	f	f	NOUN
ejpam-6294	26	6	and	and	CCONJ
ejpam-6294	26	7	a	a	DET
ejpam-6294	26	8	function	function	NOUN
ejpam-6294	26	9	f	f	PROPN
ejpam-6294	26	10	−1	−1	NOUN
ejpam-6294	26	11	are	be	AUX
ejpam-6294	26	12	univalent	univalent	ADJ
ejpam-6294	26	13	in	in	ADP
ejpam-6294	26	14	d	d	PROPN
ejpam-6294	26	15	,	,	PUNCT
ejpam-6294	26	16	the	the	DET
ejpam-6294	26	17	function	function	NOUN
ejpam-6294	26	18	is	be	AUX
ejpam-6294	26	19	said	say	VERB
ejpam-6294	26	20	to	to	PART
ejpam-6294	26	21	be	be	AUX
ejpam-6294	26	22	bi	bi	ADJ
ejpam-6294	26	23	-	-	ADJ
ejpam-6294	26	24	univalent	univalent	ADJ
ejpam-6294	26	25	in	in	ADP
ejpam-6294	26	26	the	the	DET
ejpam-6294	26	27	unit	unit	NOUN
ejpam-6294	26	28	disc	disc	NOUN
ejpam-6294	26	29	.	.	PUNCT
ejpam-6294	27	1	let	let	VERB
ejpam-6294	27	2	σ	σ	NOUN
ejpam-6294	27	3	signify	signify	VERB
ejpam-6294	27	4	the	the	DET
ejpam-6294	27	5	class	class	NOUN
ejpam-6294	27	6	of	of	ADP
ejpam-6294	27	7	bi	bi	ADJ
ejpam-6294	27	8	-	-	ADJ
ejpam-6294	27	9	univalent	univalent	ADJ
ejpam-6294	27	10	functions	function	NOUN
ejpam-6294	27	11	in	in	ADP
ejpam-6294	27	12	d	d	PROPN
ejpam-6294	27	13	written	write	VERB
ejpam-6294	27	14	by	by	ADP
ejpam-6294	27	15	(	(	PUNCT
ejpam-6294	27	16	1	1	NUM
ejpam-6294	27	17	)	)	PUNCT
ejpam-6294	27	18	.	.	PUNCT
ejpam-6294	28	1	some	some	DET
ejpam-6294	28	2	familiar	familiar	ADJ
ejpam-6294	28	3	function	function	NOUN
ejpam-6294	28	4	for	for	ADP
ejpam-6294	28	5	the	the	DET
ejpam-6294	28	6	class	class	NOUN
ejpam-6294	28	7	σ	σ	NOUN
ejpam-6294	28	8	are	be	AUX
ejpam-6294	28	9	specified	specify	VERB
ejpam-6294	28	10	below	below	ADV
ejpam-6294	28	11	:	:	PUNCT
ejpam-6294	28	12	θ	θ	PROPN
ejpam-6294	28	13	1−θ	1−θ	NUM
ejpam-6294	28	14	,	,	PUNCT
ejpam-6294	28	15	1	1	NUM
ejpam-6294	28	16	2	2	NUM
ejpam-6294	28	17	log	log	NOUN
ejpam-6294	28	18	(	(	PUNCT
ejpam-6294	28	19	1+θ	1+θ	NUM
ejpam-6294	28	20	1−θ	1−θ	NUM
ejpam-6294	28	21	)	)	PUNCT
ejpam-6294	28	22	,	,	PUNCT
ejpam-6294	28	23	−log(1	−log(1	NOUN
ejpam-6294	28	24	−θ	−θ	ADJ
ejpam-6294	28	25	)	)	PUNCT
ejpam-6294	28	26	.	.	PUNCT
ejpam-6294	29	1	lewin	lewin	PROPN
ejpam-6294	30	1	[	[	X
ejpam-6294	30	2	2	2	NUM
ejpam-6294	30	3	]	]	PUNCT
ejpam-6294	30	4	initially	initially	ADV
ejpam-6294	30	5	derived	derive	VERB
ejpam-6294	30	6	the	the	DET
ejpam-6294	30	7	bi	bi	ADJ
ejpam-6294	30	8	-	-	ADJ
ejpam-6294	30	9	univalent	univalent	ADJ
ejpam-6294	30	10	functions	function	NOUN
ejpam-6294	30	11	class	class	NOUN
ejpam-6294	30	12	σ	σ	PROPN
ejpam-6294	30	13	,	,	PUNCT
ejpam-6294	30	14	and	and	CCONJ
ejpam-6294	30	15	found	find	VERB
ejpam-6294	30	16	that	that	DET
ejpam-6294	30	17	|a2|	|a2|	NOUN
ejpam-6294	30	18	<	<	X
ejpam-6294	30	19	1.51	1.51	NUM
ejpam-6294	30	20	.	.	PUNCT
ejpam-6294	31	1	for	for	ADP
ejpam-6294	31	2	the	the	DET
ejpam-6294	31	3	generalized	generalized	ADJ
ejpam-6294	31	4	subclass	subclass	NOUN
ejpam-6294	31	5	of	of	ADP
ejpam-6294	31	6	class	class	NOUN
ejpam-6294	31	7	σ	σ	PROPN
ejpam-6294	31	8	brannan	brannan	PROPN
ejpam-6294	31	9	and	and	CCONJ
ejpam-6294	31	10	clunie	clunie	NOUN
ejpam-6294	31	11	[	[	X
ejpam-6294	31	12	3	3	NUM
ejpam-6294	31	13	]	]	PUNCT
ejpam-6294	31	14	later	later	ADV
ejpam-6294	31	15	enhanced	enhance	VERB
ejpam-6294	31	16	this	this	DET
ejpam-6294	31	17	outcome	outcome	NOUN
ejpam-6294	31	18	as	as	SCONJ
ejpam-6294	31	19	|a2|	|a2|	NOUN
ejpam-6294	31	20	≤	≤	NOUN
ejpam-6294	31	21	√	√	ADP
ejpam-6294	31	22	2	2	NUM
ejpam-6294	31	23	.	.	PUNCT
ejpam-6294	31	24	brannan	brannan	PROPN
ejpam-6294	31	25	and	and	CCONJ
ejpam-6294	31	26	taha	taha	PROPN
ejpam-6294	32	1	[	[	X
ejpam-6294	32	2	4	4	NUM
ejpam-6294	32	3	]	]	PUNCT
ejpam-6294	32	4	focused	focus	VERB
ejpam-6294	32	5	on	on	ADP
ejpam-6294	32	6	a	a	DET
ejpam-6294	32	7	specific	specific	ADJ
ejpam-6294	32	8	subclass	subclass	NOUN
ejpam-6294	32	9	of	of	ADP
ejpam-6294	32	10	class	class	NOUN
ejpam-6294	32	11	σ	σ	PROPN
ejpam-6294	32	12	,	,	PUNCT
ejpam-6294	32	13	also	also	ADV
ejpam-6294	32	14	estimate	estimate	VERB
ejpam-6294	32	15	the	the	DET
ejpam-6294	32	16	initial	initial	ADJ
ejpam-6294	32	17	coefficients	coefficient	NOUN
ejpam-6294	32	18	|a2|	|a2|	VERB
ejpam-6294	32	19	and	and	CCONJ
ejpam-6294	32	20	|a3|	|a3|	NOUN
ejpam-6294	32	21	.	.	PUNCT
ejpam-6294	33	1	for	for	ADP
ejpam-6294	33	2	convex	convex	NOUN
ejpam-6294	33	3	and	and	CCONJ
ejpam-6294	33	4	starlike	starlike	NOUN
ejpam-6294	33	5	functions	function	NOUN
ejpam-6294	33	6	,	,	PUNCT
ejpam-6294	33	7	ma	ma	PROPN
ejpam-6294	33	8	minda	minda	PROPN
ejpam-6294	34	1	[	[	X
ejpam-6294	34	2	5	5	NUM
ejpam-6294	34	3	]	]	PUNCT
ejpam-6294	34	4	employed	employ	VERB
ejpam-6294	34	5	a	a	DET
ejpam-6294	34	6	number	number	NOUN
ejpam-6294	34	7	of	of	ADP
ejpam-6294	34	8	subclasses	subclass	NOUN
ejpam-6294	34	9	that	that	PRON
ejpam-6294	34	10	meet	meet	VERB
ejpam-6294	34	11	the	the	DET
ejpam-6294	34	12	requirement	requirement	NOUN
ejpam-6294	34	13	that	that	SCONJ
ejpam-6294	34	14	either	either	CCONJ
ejpam-6294	34	15	1	1	NUM
ejpam-6294	34	16	+	+	NUM
ejpam-6294	34	17	θf	θf	NOUN
ejpam-6294	34	18	′′(θ	′′(θ	PROPN
ejpam-6294	34	19	)	)	PUNCT
ejpam-6294	34	20	f	f	PROPN
ejpam-6294	34	21	′(θ	′(θ	NOUN
ejpam-6294	34	22	)	)	PUNCT
ejpam-6294	34	23	or	or	CCONJ
ejpam-6294	34	24	θf	θf	ADP
ejpam-6294	34	25	′(θ	′(θ	NOUN
ejpam-6294	34	26	)	)	PUNCT
ejpam-6294	34	27	f(θ	f(θ	PROPN
ejpam-6294	34	28	)	)	PUNCT
ejpam-6294	34	29	is	be	AUX
ejpam-6294	34	30	subordinate	subordinate	ADJ
ejpam-6294	34	31	to	to	ADP
ejpam-6294	34	32	a	a	DET
ejpam-6294	34	33	more	more	ADV
ejpam-6294	34	34	comprehensive	comprehensive	ADJ
ejpam-6294	34	35	subordinate	subordinate	ADJ
ejpam-6294	34	36	function	function	NOUN
ejpam-6294	34	37	.	.	PUNCT
ejpam-6294	35	1	in	in	ADP
ejpam-6294	35	2	order	order	NOUN
ejpam-6294	35	3	to	to	PART
ejpam-6294	35	4	do	do	AUX
ejpam-6294	35	5	this	this	PRON
ejpam-6294	35	6	,	,	PUNCT
ejpam-6294	35	7	ma	ma	PROPN
ejpam-6294	35	8	minda	minda	PROPN
ejpam-6294	35	9	looked	look	VERB
ejpam-6294	35	10	at	at	ADP
ejpam-6294	35	11	an	an	DET
ejpam-6294	35	12	analytic	analytic	ADJ
ejpam-6294	35	13	function	function	NOUN
ejpam-6294	35	14	φ	φ	NOUN
ejpam-6294	35	15	,	,	PUNCT
ejpam-6294	35	16	it	it	PRON
ejpam-6294	35	17	uses	use	VERB
ejpam-6294	35	18	the	the	DET
ejpam-6294	35	19	unit	unit	NOUN
ejpam-6294	35	20	disk	disk	NOUN
ejpam-6294	35	21	to	to	PART
ejpam-6294	35	22	map	map	VERB
ejpam-6294	35	23	d	d	PROPN
ejpam-6294	35	24	onto	onto	ADP
ejpam-6294	35	25	an	an	DET
ejpam-6294	35	26	area	area	NOUN
ejpam-6294	35	27	that	that	PRON
ejpam-6294	35	28	is	be	AUX
ejpam-6294	35	29	starlike	starlike	NOUN
ejpam-6294	35	30	with	with	ADP
ejpam-6294	35	31	regard	regard	NOUN
ejpam-6294	35	32	to	to	ADP
ejpam-6294	35	33	1	1	NUM
ejpam-6294	35	34	and	and	CCONJ
ejpam-6294	35	35	also	also	ADV
ejpam-6294	35	36	meets	meet	VERB
ejpam-6294	35	37	the	the	DET
ejpam-6294	35	38	requirements	requirement	NOUN
ejpam-6294	35	39	given	give	VERB
ejpam-6294	35	40	that	that	SCONJ
ejpam-6294	35	41	it	it	PRON
ejpam-6294	35	42	is	be	AUX
ejpam-6294	35	43	symmetrical	symmetrical	ADJ
ejpam-6294	35	44	relating	relate	VERB
ejpam-6294	35	45	to	to	ADP
ejpam-6294	35	46	the	the	DET
ejpam-6294	35	47	real	real	ADJ
ejpam-6294	35	48	axis	axis	NOUN
ejpam-6294	35	49	,	,	PUNCT
ejpam-6294	35	50	also	also	ADV
ejpam-6294	35	51	full	full	ADJ
ejpam-6294	35	52	files	file	NOUN
ejpam-6294	35	53	the	the	DET
ejpam-6294	35	54	conditions	condition	NOUN
ejpam-6294	35	55	φ(0	φ(0	ADJ
ejpam-6294	35	56	)	)	PUNCT
ejpam-6294	35	57	=	=	SYM
ejpam-6294	35	58	1	1	NUM
ejpam-6294	35	59	and	and	CCONJ
ejpam-6294	35	60	φ′(0	φ′(0	NOUN
ejpam-6294	35	61	)	)	PUNCT
ejpam-6294	35	62	>	>	X
ejpam-6294	36	1	0	0	X
ejpam-6294	36	2	.	.	PUNCT
ejpam-6294	37	1	the	the	DET
ejpam-6294	37	2	function	function	NOUN
ejpam-6294	37	3	f	f	PROPN
ejpam-6294	37	4	in	in	ADP
ejpam-6294	37	5	the	the	DET
ejpam-6294	37	6	ma	ma	PROPN
ejpam-6294	37	7	minda	minda	PROPN
ejpam-6294	37	8	starlike	starlike	PROPN
ejpam-6294	37	9	class	class	PROPN
ejpam-6294	37	10	satisfies	satisfy	VERB
ejpam-6294	37	11	subordination	subordination	NOUN
ejpam-6294	37	12	θf	θf	NOUN
ejpam-6294	37	13	′(θ	′(θ	NOUN
ejpam-6294	37	14	)	)	PUNCT
ejpam-6294	37	15	f(θ	f(θ	PROPN
ejpam-6294	37	16	)	)	PUNCT
ejpam-6294	37	17	≺	≺	NOUN
ejpam-6294	37	18	φ(θ	φ(θ	PROPN
ejpam-6294	37	19	)	)	PUNCT
ejpam-6294	37	20	.	.	PUNCT
ejpam-6294	38	1	the	the	DET
ejpam-6294	38	2	ma	ma	PROPN
ejpam-6294	38	3	minda	minda	PROPN
ejpam-6294	38	4	convex	convex	PROPN
ejpam-6294	38	5	class	class	NOUN
ejpam-6294	38	6	,	,	PUNCT
ejpam-6294	38	7	in	in	ADP
ejpam-6294	38	8	a	a	DET
ejpam-6294	38	9	similar	similar	ADJ
ejpam-6294	38	10	vein	vein	NOUN
ejpam-6294	38	11	,	,	PUNCT
ejpam-6294	38	12	consists	consist	VERB
ejpam-6294	38	13	of	of	ADP
ejpam-6294	38	14	functions	function	NOUN
ejpam-6294	38	15	f	f	PROPN
ejpam-6294	38	16	that	that	PRON
ejpam-6294	38	17	fulfill	fulfill	VERB
ejpam-6294	38	18	the	the	DET
ejpam-6294	38	19	subordination	subordination	NOUN
ejpam-6294	38	20	1	1	NUM
ejpam-6294	38	21	+	+	CCONJ
ejpam-6294	38	22	θf	θf	NOUN
ejpam-6294	38	23	′′(θ	′′(θ	PROPN
ejpam-6294	38	24	)	)	PUNCT
ejpam-6294	38	25	f	f	PROPN
ejpam-6294	38	26	′(θ	′(θ	NOUN
ejpam-6294	38	27	)	)	PUNCT
ejpam-6294	38	28	≺	≺	NOUN
ejpam-6294	38	29	φ(θ	φ(θ	PROPN
ejpam-6294	38	30	)	)	PUNCT
ejpam-6294	38	31	.	.	PUNCT
ejpam-6294	39	1	a	a	DET
ejpam-6294	39	2	large	large	ADJ
ejpam-6294	39	3	number	number	NOUN
ejpam-6294	39	4	of	of	ADP
ejpam-6294	39	5	integer	integer	NOUN
ejpam-6294	39	6	number	number	NOUN
ejpam-6294	39	7	sequences	sequence	NOUN
ejpam-6294	39	8	have	have	AUX
ejpam-6294	39	9	surfaced	surface	VERB
ejpam-6294	39	10	due	due	ADP
ejpam-6294	39	11	to	to	ADP
ejpam-6294	39	12	the	the	DET
ejpam-6294	39	13	elegance	elegance	NOUN
ejpam-6294	39	14	of	of	ADP
ejpam-6294	39	15	their	their	PRON
ejpam-6294	39	16	recurrence	recurrence	NOUN
ejpam-6294	39	17	relations	relation	NOUN
ejpam-6294	39	18	,	,	PUNCT
ejpam-6294	39	19	including	include	VERB
ejpam-6294	39	20	fibonacci	fibonacci	NOUN
ejpam-6294	39	21	,	,	PUNCT
ejpam-6294	39	22	jacobsthal	jacobsthal	ADJ
ejpam-6294	39	23	,	,	PUNCT
ejpam-6294	39	24	lucas	lucas	PROPN
ejpam-6294	39	25	,	,	PUNCT
ejpam-6294	39	26	fermat	fermat	PROPN
ejpam-6294	39	27	,	,	PUNCT
ejpam-6294	39	28	pell	pell	PROPN
ejpam-6294	39	29	,	,	PUNCT
ejpam-6294	39	30	chebyshev	chebyshev	NOUN
ejpam-6294	39	31	,	,	PUNCT
ejpam-6294	39	32	telephone	telephone	NOUN
ejpam-6294	39	33	and	and	CCONJ
ejpam-6294	39	34	others	other	NOUN
ejpam-6294	39	35	.	.	PUNCT
ejpam-6294	40	1	the	the	DET
ejpam-6294	40	2	lucas	lucas	PROPN
ejpam-6294	40	3	numbers	number	NOUN
ejpam-6294	40	4	are	be	AUX
ejpam-6294	40	5	a	a	DET
ejpam-6294	40	6	brand	brand	NOUN
ejpam-6294	40	7	-	-	PUNCT
ejpam-6294	40	8	new	new	ADJ
ejpam-6294	40	9	integer	integer	NOUN
ejpam-6294	40	10	series	series	NOUN
ejpam-6294	40	11	that	that	SCONJ
ejpam-6294	40	12	behera	behera	NOUN
ejpam-6294	40	13	and	and	CCONJ
ejpam-6294	40	14	panda	panda	NOUN
ejpam-6294	40	15	[	[	X
ejpam-6294	40	16	6	6	NUM
ejpam-6294	40	17	]	]	PUNCT
ejpam-6294	40	18	revealed.in	revealed.in	X
ejpam-6294	40	19	recent	recent	ADJ
ejpam-6294	40	20	years,[7–11	years,[7–11	PROPN
ejpam-6294	40	21	]	]	PUNCT
ejpam-6294	40	22	several	several	ADJ
ejpam-6294	40	23	authors	author	NOUN
ejpam-6294	40	24	have	have	AUX
ejpam-6294	40	25	explored	explore	VERB
ejpam-6294	40	26	subclasses	subclass	NOUN
ejpam-6294	40	27	of	of	ADP
ejpam-6294	40	28	biunivalent	biunivalent	NOUN
ejpam-6294	40	29	(	(	PUNCT
ejpam-6294	40	30	or	or	CCONJ
ejpam-6294	40	31	univalent	univalent	ADJ
ejpam-6294	40	32	)	)	PUNCT
ejpam-6294	40	33	functions	function	NOUN
ejpam-6294	40	34	over	over	ADP
ejpam-6294	40	35	the	the	DET
ejpam-6294	40	36	past	past	ADJ
ejpam-6294	40	37	few	few	ADJ
ejpam-6294	40	38	decades	decade	NOUN
ejpam-6294	40	39	,	,	PUNCT
ejpam-6294	40	40	the	the	DET
ejpam-6294	40	41	features	feature	NOUN
ejpam-6294	40	42	of	of	ADP
ejpam-6294	40	43	this	this	DET
ejpam-6294	40	44	unique	unique	ADJ
ejpam-6294	40	45	number	number	NOUN
ejpam-6294	40	46	sequence	sequence	NOUN
ejpam-6294	40	47	have	have	AUX
ejpam-6294	40	48	been	be	AUX
ejpam-6294	40	49	intensively	intensively	ADV
ejpam-6294	40	50	investigated	investigate	VERB
ejpam-6294	40	51	,	,	PUNCT
ejpam-6294	40	52	and	and	CCONJ
ejpam-6294	40	53	certain	certain	ADJ
ejpam-6294	40	54	generalizations	generalization	NOUN
ejpam-6294	40	55	have	have	AUX
ejpam-6294	40	56	been	be	AUX
ejpam-6294	40	57	developed	develop	VERB
ejpam-6294	40	58	.	.	PUNCT
ejpam-6294	41	1	a	a	DET
ejpam-6294	41	2	definition	definition	NOUN
ejpam-6294	41	3	and	and	CCONJ
ejpam-6294	41	4	a	a	DET
ejpam-6294	41	5	number	number	NOUN
ejpam-6294	41	6	of	of	ADP
ejpam-6294	41	7	interesting	interesting	ADJ
ejpam-6294	41	8	properties	property	NOUN
ejpam-6294	41	9	of	of	ADP
ejpam-6294	41	10	the	the	DET
ejpam-6294	41	11	polynomials	polynomial	NOUN
ejpam-6294	41	12	are	be	AUX
ejpam-6294	41	13	given	give	VERB
ejpam-6294	41	14	by	by	ADP
ejpam-6294	41	15	lee	lee	PROPN
ejpam-6294	41	16	et	et	PROPN
ejpam-6294	41	17	al	al	PROPN
ejpam-6294	41	18	.	.	PUNCT
ejpam-6294	42	1	[	[	X
ejpam-6294	42	2	12	12	NUM
ejpam-6294	42	3	]	]	PUNCT
ejpam-6294	42	4	and	and	CCONJ
ejpam-6294	42	5	ray	ray	VERB
ejpam-6294	43	1	[	[	X
ejpam-6294	43	2	13	13	NUM
ejpam-6294	43	3	]	]	PUNCT
ejpam-6294	43	4	.	.	PUNCT
ejpam-6294	44	1	the	the	DET
ejpam-6294	44	2	polynomials	polynomial	NOUN
ejpam-6294	44	3	are	be	AUX
ejpam-6294	44	4	a	a	DET
ejpam-6294	44	5	innate	innate	ADJ
ejpam-6294	44	6	consequence	consequence	NOUN
ejpam-6294	44	7	of	of	ADP
ejpam-6294	44	8	the	the	DET
ejpam-6294	44	9	lucas	lucas	PROPN
ejpam-6294	44	10	numbers	number	NOUN
ejpam-6294	44	11	and	and	CCONJ
ejpam-6294	44	12	balancing	balance	VERB
ejpam-6294	44	13	lucas	lucas	NOUN
ejpam-6294	44	14	numbers	number	NOUN
ejpam-6294	44	15	.	.	PUNCT
ejpam-6294	45	1	due	due	ADP
ejpam-6294	45	2	to	to	ADP
ejpam-6294	45	3	their	their	PRON
ejpam-6294	45	4	applications	application	NOUN
ejpam-6294	45	5	in	in	ADP
ejpam-6294	45	6	fluid	fluid	ADJ
ejpam-6294	45	7	dynamics	dynamic	NOUN
ejpam-6294	45	8	,	,	PUNCT
ejpam-6294	45	9	geometric	geometric	ADJ
ejpam-6294	45	10	function	function	NOUN
ejpam-6294	45	11	theory	theory	NOUN
ejpam-6294	45	12	,	,	PUNCT
ejpam-6294	45	13	and	and	CCONJ
ejpam-6294	45	14	conformal	conformal	ADJ
ejpam-6294	45	15	mapping	mapping	NOUN
ejpam-6294	45	16	,	,	PUNCT
ejpam-6294	45	17	bi	bi	ADJ
ejpam-6294	45	18	-	-	ADJ
ejpam-6294	45	19	univalent	univalent	ADJ
ejpam-6294	45	20	functions	function	NOUN
ejpam-6294	45	21	have	have	AUX
ejpam-6294	45	22	attracted	attract	VERB
ejpam-6294	45	23	a	a	DET
ejpam-6294	45	24	lot	lot	NOUN
ejpam-6294	45	25	of	of	ADP
ejpam-6294	45	26	attention	attention	NOUN
ejpam-6294	45	27	in	in	ADP
ejpam-6294	45	28	complex	complex	ADJ
ejpam-6294	45	29	analysis	analysis	NOUN
ejpam-6294	45	30	.	.	PUNCT
ejpam-6294	46	1	these	these	DET
ejpam-6294	46	2	functions	function	NOUN
ejpam-6294	46	3	have	have	VERB
ejpam-6294	46	4	intriguing	intriguing	ADJ
ejpam-6294	46	5	geometric	geometric	ADJ
ejpam-6294	46	6	properties	property	NOUN
ejpam-6294	46	7	that	that	PRON
ejpam-6294	46	8	can	can	AUX
ejpam-6294	46	9	provide	provide	VERB
ejpam-6294	46	10	important	important	ADJ
ejpam-6294	46	11	information	information	NOUN
ejpam-6294	46	12	on	on	ADP
ejpam-6294	46	13	growth	growth	NOUN
ejpam-6294	46	14	behavior	behavior	NOUN
ejpam-6294	46	15	,	,	PUNCT
ejpam-6294	46	16	distortion	distortion	NOUN
ejpam-6294	46	17	,	,	PUNCT
ejpam-6294	46	18	and	and	CCONJ
ejpam-6294	46	19	mapping	mapping	NOUN
ejpam-6294	46	20	s.	s.	PROPN
ejpam-6294	46	21	thangamani	thangamani	PROPN
ejpam-6294	46	22	et	et	PROPN
ejpam-6294	46	23	al	al	PROPN
ejpam-6294	46	24	.	.	PUNCT
ejpam-6294	46	25	/	/	SYM
ejpam-6294	46	26	eur	eur	PROPN
ejpam-6294	46	27	.	.	PUNCT
ejpam-6294	47	1	j.	j.	PROPN
ejpam-6294	47	2	pure	pure	PROPN
ejpam-6294	47	3	appl	appl	PROPN
ejpam-6294	47	4	.	.	PROPN
ejpam-6294	47	5	math	math	PROPN
ejpam-6294	47	6	,	,	PUNCT
ejpam-6294	47	7	18	18	NUM
ejpam-6294	47	8	(	(	PUNCT
ejpam-6294	47	9	3	3	NUM
ejpam-6294	47	10	)	)	PUNCT
ejpam-6294	47	11	(	(	PUNCT
ejpam-6294	47	12	2025	2025	NUM
ejpam-6294	47	13	)	)	PUNCT
ejpam-6294	47	14	,	,	PUNCT
ejpam-6294	47	15	6294	6294	NUM
ejpam-6294	47	16	3	3	NUM
ejpam-6294	47	17	of	of	ADP
ejpam-6294	47	18	19	19	NUM
ejpam-6294	47	19	properties	property	NOUN
ejpam-6294	47	20	.	.	PUNCT
ejpam-6294	48	1	a	a	DET
ejpam-6294	48	2	greater	great	ADJ
ejpam-6294	48	3	comprehension	comprehension	NOUN
ejpam-6294	48	4	of	of	ADP
ejpam-6294	48	5	the	the	DET
ejpam-6294	48	6	structural	structural	ADJ
ejpam-6294	48	7	characteristics	characteristic	NOUN
ejpam-6294	48	8	of	of	ADP
ejpam-6294	48	9	bi	bi	ADJ
ejpam-6294	48	10	-	-	ADJ
ejpam-6294	48	11	univalent	univalent	ADJ
ejpam-6294	48	12	functions	function	NOUN
ejpam-6294	48	13	and	and	CCONJ
ejpam-6294	48	14	how	how	SCONJ
ejpam-6294	48	15	they	they	PRON
ejpam-6294	48	16	interact	interact	VERB
ejpam-6294	48	17	with	with	ADP
ejpam-6294	48	18	classical	classical	ADJ
ejpam-6294	48	19	inequalities	inequality	NOUN
ejpam-6294	48	20	can	can	AUX
ejpam-6294	48	21	be	be	AUX
ejpam-6294	48	22	gained	gain	VERB
ejpam-6294	48	23	by	by	ADP
ejpam-6294	48	24	studying	study	VERB
ejpam-6294	48	25	their	their	PRON
ejpam-6294	48	26	subclasses	subclass	NOUN
ejpam-6294	48	27	.	.	PUNCT
ejpam-6294	49	1	lucas	lucas	NOUN
ejpam-6294	49	2	polynomials	polynomial	NOUN
ejpam-6294	49	3	are	be	AUX
ejpam-6294	49	4	one	one	NUM
ejpam-6294	49	5	such	such	ADJ
ejpam-6294	49	6	class	class	NOUN
ejpam-6294	49	7	of	of	ADP
ejpam-6294	49	8	functions	function	NOUN
ejpam-6294	49	9	,	,	PUNCT
ejpam-6294	49	10	and	and	CCONJ
ejpam-6294	49	11	their	their	PRON
ejpam-6294	49	12	special	special	ADJ
ejpam-6294	49	13	characteristics	characteristic	NOUN
ejpam-6294	49	14	can	can	AUX
ejpam-6294	49	15	be	be	AUX
ejpam-6294	49	16	used	use	VERB
ejpam-6294	49	17	to	to	PART
ejpam-6294	49	18	study	study	VERB
ejpam-6294	49	19	how	how	SCONJ
ejpam-6294	49	20	these	these	DET
ejpam-6294	49	21	functions	function	NOUN
ejpam-6294	49	22	behave	behave	VERB
ejpam-6294	49	23	.	.	PUNCT
ejpam-6294	50	1	in	in	ADP
ejpam-6294	50	2	recent	recent	ADJ
ejpam-6294	50	3	years	year	NOUN
ejpam-6294	50	4	,	,	PUNCT
ejpam-6294	50	5	a	a	DET
ejpam-6294	50	6	multitude	multitude	NOUN
ejpam-6294	50	7	of	of	ADP
ejpam-6294	50	8	writers	writer	NOUN
ejpam-6294	50	9	have	have	AUX
ejpam-6294	50	10	made	make	VERB
ejpam-6294	50	11	great	great	ADJ
ejpam-6294	50	12	strides	stride	NOUN
ejpam-6294	50	13	in	in	ADP
ejpam-6294	50	14	implementing	implement	VERB
ejpam-6294	50	15	sharp	sharp	ADJ
ejpam-6294	50	16	bounds	bound	NOUN
ejpam-6294	50	17	for	for	ADP
ejpam-6294	50	18	a	a	DET
ejpam-6294	50	19	variety	variety	NOUN
ejpam-6294	50	20	of	of	ADP
ejpam-6294	50	21	bi	bi	ADJ
ejpam-6294	50	22	-	-	ADJ
ejpam-6294	50	23	univalent	univalent	ADJ
ejpam-6294	50	24	function	function	NOUN
ejpam-6294	50	25	subclasses	subclass	NOUN
ejpam-6294	50	26	that	that	PRON
ejpam-6294	50	27	commonly	commonly	ADV
ejpam-6294	50	28	interact	interact	VERB
ejpam-6294	50	29	with	with	ADP
ejpam-6294	50	30	specific	specific	ADJ
ejpam-6294	50	31	polynomial	polynomial	ADJ
ejpam-6294	50	32	families	family	NOUN
ejpam-6294	50	33	,	,	PUNCT
ejpam-6294	50	34	including	include	VERB
ejpam-6294	50	35	lucas	lucas	NOUN
ejpam-6294	50	36	and	and	CCONJ
ejpam-6294	50	37	balancing	balance	VERB
ejpam-6294	50	38	lucas	lucas	NOUN
ejpam-6294	50	39	polynomials	polynomial	NOUN
ejpam-6294	50	40	[	[	X
ejpam-6294	50	41	14–24	14–24	NUM
ejpam-6294	50	42	]	]	PUNCT
ejpam-6294	50	43	and	and	CCONJ
ejpam-6294	50	44	[	[	X
ejpam-6294	50	45	25	25	NUM
ejpam-6294	50	46	]	]	PUNCT
ejpam-6294	50	47	.	.	PUNCT
ejpam-6294	51	1	the	the	DET
ejpam-6294	51	2	primary	primary	ADJ
ejpam-6294	51	3	objective	objective	NOUN
ejpam-6294	51	4	of	of	ADP
ejpam-6294	51	5	this	this	DET
ejpam-6294	51	6	work	work	NOUN
ejpam-6294	51	7	is	be	AUX
ejpam-6294	51	8	to	to	PART
ejpam-6294	51	9	determine	determine	VERB
ejpam-6294	51	10	the	the	DET
ejpam-6294	51	11	taylor	taylor	PROPN
ejpam-6294	51	12	-	-	PUNCT
ejpam-6294	51	13	maclaurin	maclaurin	NOUN
ejpam-6294	51	14	coefficients	coefficient	NOUN
ejpam-6294	51	15	|a2|	|a2|	NOUN
ejpam-6294	51	16	and	and	CCONJ
ejpam-6294	51	17	|a3|	|a3|	NOUN
ejpam-6294	51	18	and	and	CCONJ
ejpam-6294	51	19	their	their	PRON
ejpam-6294	51	20	influence	influence	NOUN
ejpam-6294	51	21	on	on	ADP
ejpam-6294	51	22	the	the	DET
ejpam-6294	51	23	geometric	geometric	ADJ
ejpam-6294	51	24	and	and	CCONJ
ejpam-6294	51	25	analytic	analytic	ADJ
ejpam-6294	51	26	features	feature	NOUN
ejpam-6294	51	27	of	of	ADP
ejpam-6294	51	28	the	the	DET
ejpam-6294	51	29	bi	bi	ADJ
ejpam-6294	51	30	-	-	ADJ
ejpam-6294	51	31	univalent	univalent	ADJ
ejpam-6294	51	32	subclass	subclass	NOUN
ejpam-6294	51	33	of	of	ADP
ejpam-6294	51	34	lucas	lucas	PROPN
ejpam-6294	51	35	and	and	CCONJ
ejpam-6294	51	36	lucas	lucas	PROPN
ejpam-6294	51	37	balancing	balance	VERB
ejpam-6294	51	38	polynomial	polynomial	ADJ
ejpam-6294	51	39	functions	function	NOUN
ejpam-6294	51	40	.	.	PUNCT
ejpam-6294	52	1	by	by	ADP
ejpam-6294	52	2	presenting	present	VERB
ejpam-6294	52	3	new	new	ADJ
ejpam-6294	52	4	results	result	NOUN
ejpam-6294	52	5	and	and	CCONJ
ejpam-6294	52	6	building	build	VERB
ejpam-6294	52	7	on	on	ADP
ejpam-6294	52	8	previous	previous	ADJ
ejpam-6294	52	9	work	work	NOUN
ejpam-6294	52	10	,	,	PUNCT
ejpam-6294	52	11	this	this	DET
ejpam-6294	52	12	study	study	NOUN
ejpam-6294	52	13	contributes	contribute	VERB
ejpam-6294	52	14	to	to	ADP
ejpam-6294	52	15	our	our	PRON
ejpam-6294	52	16	understanding	understanding	NOUN
ejpam-6294	52	17	of	of	ADP
ejpam-6294	52	18	bi	bi	ADJ
ejpam-6294	52	19	-	-	ADJ
ejpam-6294	52	20	univalent	univalent	ADJ
ejpam-6294	52	21	functions	function	NOUN
ejpam-6294	52	22	.	.	PUNCT
ejpam-6294	53	1	the	the	DET
ejpam-6294	53	2	main	main	ADJ
ejpam-6294	53	3	objective	objective	NOUN
ejpam-6294	53	4	of	of	ADP
ejpam-6294	53	5	this	this	DET
ejpam-6294	53	6	study	study	NOUN
ejpam-6294	53	7	is	be	AUX
ejpam-6294	53	8	to	to	PART
ejpam-6294	53	9	provide	provide	VERB
ejpam-6294	53	10	upper	upper	ADJ
ejpam-6294	53	11	bounds	bound	NOUN
ejpam-6294	53	12	and	and	CCONJ
ejpam-6294	53	13	initial	initial	ADJ
ejpam-6294	53	14	coefficients	coefficient	NOUN
ejpam-6294	53	15	for	for	ADP
ejpam-6294	53	16	the	the	DET
ejpam-6294	53	17	taylor	taylor	PROPN
ejpam-6294	53	18	-	-	PUNCT
ejpam-6294	53	19	maclaurin	maclaurin	PROPN
ejpam-6294	53	20	and	and	CCONJ
ejpam-6294	53	21	fekete	fekete	NOUN
ejpam-6294	53	22	-	-	PUNCT
ejpam-6294	53	23	szegö	szegö	ADJ
ejpam-6294	53	24	functionals	functional	NOUN
ejpam-6294	53	25	of	of	ADP
ejpam-6294	53	26	the	the	DET
ejpam-6294	53	27	function	function	NOUN
ejpam-6294	53	28	of	of	ADP
ejpam-6294	53	29	the	the	DET
ejpam-6294	53	30	stated	state	VERB
ejpam-6294	53	31	subclass	subclass	NOUN
ejpam-6294	53	32	.	.	PUNCT
ejpam-6294	54	1	this	this	DET
ejpam-6294	54	2	research	research	NOUN
ejpam-6294	54	3	is	be	AUX
ejpam-6294	54	4	divided	divide	VERB
ejpam-6294	54	5	into	into	ADP
ejpam-6294	54	6	three	three	NUM
ejpam-6294	54	7	parts	part	NOUN
ejpam-6294	54	8	.	.	PUNCT
ejpam-6294	55	1	in	in	ADP
ejpam-6294	55	2	the	the	DET
ejpam-6294	55	3	first	first	ADJ
ejpam-6294	55	4	section	section	NOUN
ejpam-6294	55	5	,	,	PUNCT
ejpam-6294	55	6	some	some	DET
ejpam-6294	55	7	basic	basic	ADJ
ejpam-6294	55	8	concepts	concept	NOUN
ejpam-6294	55	9	of	of	ADP
ejpam-6294	55	10	bi	bi	ADJ
ejpam-6294	55	11	-	-	ADJ
ejpam-6294	55	12	univalent	univalent	ADJ
ejpam-6294	55	13	function	function	NOUN
ejpam-6294	55	14	theory	theory	NOUN
ejpam-6294	55	15	are	be	AUX
ejpam-6294	55	16	discussed	discuss	VERB
ejpam-6294	55	17	,	,	PUNCT
ejpam-6294	55	18	including	include	VERB
ejpam-6294	55	19	information	information	NOUN
ejpam-6294	55	20	on	on	ADP
ejpam-6294	55	21	lucas	lucas	PROPN
ejpam-6294	55	22	and	and	CCONJ
ejpam-6294	55	23	balancing	balance	VERB
ejpam-6294	55	24	lucas	lucas	NOUN
ejpam-6294	55	25	polynomials	polynomial	NOUN
ejpam-6294	55	26	.	.	PUNCT
ejpam-6294	56	1	parts	part	NOUN
ejpam-6294	56	2	two	two	NUM
ejpam-6294	56	3	and	and	CCONJ
ejpam-6294	56	4	three	three	NUM
ejpam-6294	56	5	introduce	introduce	VERB
ejpam-6294	56	6	new	new	ADJ
ejpam-6294	56	7	subclasses	subclass	NOUN
ejpam-6294	56	8	of	of	ADP
ejpam-6294	56	9	bi	bi	ADJ
ejpam-6294	56	10	-	-	ADJ
ejpam-6294	56	11	univalent	univalent	ADJ
ejpam-6294	56	12	functions	function	NOUN
ejpam-6294	56	13	using	use	VERB
ejpam-6294	56	14	the	the	DET
ejpam-6294	56	15	lucas	lucas	NOUN
ejpam-6294	56	16	and	and	CCONJ
ejpam-6294	56	17	balancing	balance	VERB
ejpam-6294	56	18	lucas	lucas	NOUN
ejpam-6294	56	19	polynomials	polynomial	NOUN
ejpam-6294	56	20	,	,	PUNCT
ejpam-6294	56	21	respectively	respectively	ADV
ejpam-6294	56	22	.	.	PUNCT
ejpam-6294	57	1	the	the	DET
ejpam-6294	57	2	motivation	motivation	NOUN
ejpam-6294	57	3	for	for	ADP
ejpam-6294	57	4	this	this	DET
ejpam-6294	57	5	study	study	NOUN
ejpam-6294	57	6	stems	stem	VERB
ejpam-6294	57	7	from	from	ADP
ejpam-6294	57	8	the	the	DET
ejpam-6294	57	9	need	need	NOUN
ejpam-6294	57	10	to	to	PART
ejpam-6294	57	11	better	well	ADV
ejpam-6294	57	12	understand	understand	VERB
ejpam-6294	57	13	the	the	DET
ejpam-6294	57	14	intricate	intricate	ADJ
ejpam-6294	57	15	geometric	geometric	ADJ
ejpam-6294	57	16	and	and	CCONJ
ejpam-6294	57	17	analytic	analytic	ADJ
ejpam-6294	57	18	properties	property	NOUN
ejpam-6294	57	19	of	of	ADP
ejpam-6294	57	20	bi	bi	ADJ
ejpam-6294	57	21	-	-	ADJ
ejpam-6294	57	22	univalent	univalent	ADJ
ejpam-6294	57	23	functions	function	NOUN
ejpam-6294	57	24	.	.	PUNCT
ejpam-6294	58	1	these	these	DET
ejpam-6294	58	2	functions	function	NOUN
ejpam-6294	58	3	play	play	VERB
ejpam-6294	58	4	a	a	DET
ejpam-6294	58	5	crucial	crucial	ADJ
ejpam-6294	58	6	role	role	NOUN
ejpam-6294	58	7	in	in	ADP
ejpam-6294	58	8	complex	complex	ADJ
ejpam-6294	58	9	analysis	analysis	NOUN
ejpam-6294	58	10	,	,	PUNCT
ejpam-6294	58	11	particularly	particularly	ADV
ejpam-6294	58	12	in	in	ADP
ejpam-6294	58	13	areas	area	NOUN
ejpam-6294	58	14	such	such	ADJ
ejpam-6294	58	15	as	as	ADP
ejpam-6294	58	16	conformal	conformal	ADJ
ejpam-6294	58	17	mappings	mapping	NOUN
ejpam-6294	58	18	and	and	CCONJ
ejpam-6294	58	19	fluid	fluid	ADJ
ejpam-6294	58	20	dynamics	dynamic	NOUN
ejpam-6294	58	21	,	,	PUNCT
ejpam-6294	58	22	where	where	SCONJ
ejpam-6294	58	23	the	the	DET
ejpam-6294	58	24	behavior	behavior	NOUN
ejpam-6294	58	25	of	of	ADP
ejpam-6294	58	26	functions	function	NOUN
ejpam-6294	58	27	near	near	ADP
ejpam-6294	58	28	boundaries	boundary	NOUN
ejpam-6294	58	29	and	and	CCONJ
ejpam-6294	58	30	their	their	PRON
ejpam-6294	58	31	growth	growth	NOUN
ejpam-6294	58	32	rates	rate	NOUN
ejpam-6294	58	33	are	be	AUX
ejpam-6294	58	34	of	of	ADP
ejpam-6294	58	35	significant	significant	ADJ
ejpam-6294	58	36	importance	importance	NOUN
ejpam-6294	58	37	.	.	PUNCT
ejpam-6294	59	1	by	by	ADP
ejpam-6294	59	2	focusing	focus	VERB
ejpam-6294	59	3	on	on	ADP
ejpam-6294	59	4	the	the	DET
ejpam-6294	59	5	taylor	taylor	PROPN
ejpam-6294	59	6	-	-	PUNCT
ejpam-6294	59	7	maclaurin	maclaurin	NOUN
ejpam-6294	59	8	coefficients	coefficient	NOUN
ejpam-6294	59	9	and	and	CCONJ
ejpam-6294	59	10	their	their	PRON
ejpam-6294	59	11	implications	implication	NOUN
ejpam-6294	59	12	,	,	PUNCT
ejpam-6294	59	13	this	this	DET
ejpam-6294	59	14	work	work	NOUN
ejpam-6294	59	15	aims	aim	VERB
ejpam-6294	59	16	to	to	PART
ejpam-6294	59	17	provide	provide	VERB
ejpam-6294	59	18	deeper	deep	ADJ
ejpam-6294	59	19	insights	insight	NOUN
ejpam-6294	59	20	into	into	ADP
ejpam-6294	59	21	how	how	SCONJ
ejpam-6294	59	22	these	these	DET
ejpam-6294	59	23	functions	function	NOUN
ejpam-6294	59	24	behave	behave	VERB
ejpam-6294	59	25	in	in	ADP
ejpam-6294	59	26	the	the	DET
ejpam-6294	59	27	unit	unit	NOUN
ejpam-6294	59	28	disk	disk	NOUN
ejpam-6294	59	29	and	and	CCONJ
ejpam-6294	59	30	their	their	PRON
ejpam-6294	59	31	connections	connection	NOUN
ejpam-6294	59	32	to	to	ADP
ejpam-6294	59	33	other	other	ADJ
ejpam-6294	59	34	classes	class	NOUN
ejpam-6294	59	35	of	of	ADP
ejpam-6294	59	36	functions	function	NOUN
ejpam-6294	59	37	.	.	PUNCT
ejpam-6294	60	1	in	in	ADP
ejpam-6294	60	2	addition	addition	NOUN
ejpam-6294	60	3	to	to	ADP
ejpam-6294	60	4	their	their	PRON
ejpam-6294	60	5	theoretical	theoretical	ADJ
ejpam-6294	60	6	significance	significance	NOUN
ejpam-6294	60	7	,	,	PUNCT
ejpam-6294	60	8	the	the	DET
ejpam-6294	60	9	initial	initial	ADJ
ejpam-6294	60	10	coefficients	coefficient	NOUN
ejpam-6294	60	11	have	have	VERB
ejpam-6294	60	12	practical	practical	ADJ
ejpam-6294	60	13	implications	implication	NOUN
ejpam-6294	60	14	.	.	PUNCT
ejpam-6294	61	1	these	these	PRON
ejpam-6294	61	2	include	include	VERB
ejpam-6294	61	3	calculating	calculate	VERB
ejpam-6294	61	4	the	the	DET
ejpam-6294	61	5	degree	degree	NOUN
ejpam-6294	61	6	to	to	PART
ejpam-6294	61	7	which	which	PRON
ejpam-6294	61	8	bi	bi	ADJ
ejpam-6294	61	9	-	-	ADJ
ejpam-6294	61	10	univalent	univalent	ADJ
ejpam-6294	61	11	functions	function	NOUN
ejpam-6294	61	12	can	can	AUX
ejpam-6294	61	13	resemble	resemble	VERB
ejpam-6294	61	14	other	other	ADJ
ejpam-6294	61	15	kinds	kind	NOUN
ejpam-6294	61	16	of	of	ADP
ejpam-6294	61	17	functions	function	NOUN
ejpam-6294	61	18	,	,	PUNCT
ejpam-6294	61	19	creating	create	VERB
ejpam-6294	61	20	numerical	numerical	ADJ
ejpam-6294	61	21	algorithms	algorithm	NOUN
ejpam-6294	61	22	to	to	PART
ejpam-6294	61	23	find	find	VERB
ejpam-6294	61	24	bi	bi	ADJ
ejpam-6294	61	25	-	-	ADJ
ejpam-6294	61	26	univalent	univalent	ADJ
ejpam-6294	61	27	functions	function	NOUN
ejpam-6294	61	28	using	use	VERB
ejpam-6294	61	29	the	the	DET
ejpam-6294	61	30	initial	initial	ADJ
ejpam-6294	61	31	coefficients	coefficient	NOUN
ejpam-6294	61	32	,	,	PUNCT
ejpam-6294	61	33	and	and	CCONJ
ejpam-6294	61	34	using	use	VERB
ejpam-6294	61	35	these	these	DET
ejpam-6294	61	36	functions	function	NOUN
ejpam-6294	61	37	in	in	ADP
ejpam-6294	61	38	complex	complex	ADJ
ejpam-6294	61	39	analysis	analysis	NOUN
ejpam-6294	61	40	,	,	PUNCT
ejpam-6294	61	41	particularly	particularly	ADV
ejpam-6294	61	42	when	when	SCONJ
ejpam-6294	61	43	examining	examine	VERB
ejpam-6294	61	44	boundary	boundary	ADJ
ejpam-6294	61	45	behavior	behavior	NOUN
ejpam-6294	61	46	of	of	ADP
ejpam-6294	61	47	mappings	mapping	NOUN
ejpam-6294	61	48	from	from	ADP
ejpam-6294	61	49	the	the	DET
ejpam-6294	61	50	unit	unit	NOUN
ejpam-6294	61	51	disk	disk	NOUN
ejpam-6294	61	52	and	and	CCONJ
ejpam-6294	61	53	conformal	conformal	NOUN
ejpam-6294	61	54	mappings	mapping	NOUN
ejpam-6294	61	55	.	.	PUNCT
ejpam-6294	62	1	furthermore	furthermore	ADV
ejpam-6294	62	2	,	,	PUNCT
ejpam-6294	62	3	a	a	DET
ejpam-6294	62	4	function	function	NOUN
ejpam-6294	62	5	’s	’s	PART
ejpam-6294	62	6	growth	growth	NOUN
ejpam-6294	62	7	rate	rate	NOUN
ejpam-6294	62	8	is	be	AUX
ejpam-6294	62	9	frequently	frequently	ADV
ejpam-6294	62	10	estimated	estimate	VERB
ejpam-6294	62	11	using	use	VERB
ejpam-6294	62	12	the	the	DET
ejpam-6294	62	13	initial	initial	ADJ
ejpam-6294	62	14	coefficients	coefficient	NOUN
ejpam-6294	62	15	.	.	PUNCT
ejpam-6294	63	1	in	in	ADP
ejpam-6294	63	2	particular	particular	ADJ
ejpam-6294	63	3	,	,	PUNCT
ejpam-6294	63	4	they	they	PRON
ejpam-6294	63	5	help	help	VERB
ejpam-6294	63	6	define	define	VERB
ejpam-6294	63	7	limits	limit	NOUN
ejpam-6294	63	8	on	on	ADP
ejpam-6294	63	9	the	the	DET
ejpam-6294	63	10	function	function	NOUN
ejpam-6294	63	11	’s	’s	PART
ejpam-6294	63	12	maximum	maximum	ADJ
ejpam-6294	63	13	modulus	modulus	NOUN
ejpam-6294	63	14	and	and	CCONJ
ejpam-6294	63	15	behavior	behavior	NOUN
ejpam-6294	63	16	near	near	ADP
ejpam-6294	63	17	the	the	DET
ejpam-6294	63	18	unit	unit	NOUN
ejpam-6294	63	19	disk	disk	NOUN
ejpam-6294	63	20	’s	’s	PART
ejpam-6294	63	21	edge	edge	NOUN
ejpam-6294	63	22	.	.	PUNCT
ejpam-6294	64	1	by	by	ADP
ejpam-6294	64	2	setting	set	VERB
ejpam-6294	64	3	upper	upper	ADJ
ejpam-6294	64	4	constraints	constraint	NOUN
ejpam-6294	64	5	for	for	ADP
ejpam-6294	64	6	these	these	DET
ejpam-6294	64	7	coefficients	coefficient	NOUN
ejpam-6294	64	8	,	,	PUNCT
ejpam-6294	64	9	we	we	PRON
ejpam-6294	64	10	can	can	AUX
ejpam-6294	64	11	regulate	regulate	VERB
ejpam-6294	64	12	how	how	SCONJ
ejpam-6294	64	13	much	much	ADJ
ejpam-6294	64	14	the	the	DET
ejpam-6294	64	15	function	function	NOUN
ejpam-6294	64	16	”	"	PUNCT
ejpam-6294	64	17	spreads	spread	NOUN
ejpam-6294	64	18	”	"	PUNCT
ejpam-6294	64	19	or	or	CCONJ
ejpam-6294	64	20	”	"	PUNCT
ejpam-6294	64	21	compresses	compress	VERB
ejpam-6294	64	22	”	"	PUNCT
ejpam-6294	64	23	inside	inside	ADP
ejpam-6294	64	24	the	the	DET
ejpam-6294	64	25	unit	unit	NOUN
ejpam-6294	64	26	disk	disk	NOUN
ejpam-6294	64	27	.	.	PUNCT
ejpam-6294	65	1	the	the	DET
ejpam-6294	65	2	structure	structure	NOUN
ejpam-6294	65	3	of	of	ADP
ejpam-6294	65	4	the	the	DET
ejpam-6294	65	5	paper	paper	NOUN
ejpam-6294	65	6	is	be	AUX
ejpam-6294	65	7	organized	organize	VERB
ejpam-6294	65	8	systematically	systematically	ADV
ejpam-6294	65	9	to	to	PART
ejpam-6294	65	10	facilitate	facilitate	VERB
ejpam-6294	65	11	a	a	DET
ejpam-6294	65	12	coherent	coherent	ADJ
ejpam-6294	65	13	flow	flow	NOUN
ejpam-6294	65	14	of	of	ADP
ejpam-6294	65	15	ideas	idea	NOUN
ejpam-6294	65	16	and	and	CCONJ
ejpam-6294	65	17	results	result	NOUN
ejpam-6294	65	18	.	.	PUNCT
ejpam-6294	66	1	section	section	NOUN
ejpam-6294	66	2	2	2	NUM
ejpam-6294	66	3	presents	present	VERB
ejpam-6294	66	4	the	the	DET
ejpam-6294	66	5	initial	initial	ADJ
ejpam-6294	66	6	coefficient	coefficient	NOUN
ejpam-6294	66	7	estimates	estimate	NOUN
ejpam-6294	66	8	for	for	ADP
ejpam-6294	66	9	the	the	DET
ejpam-6294	66	10	subclass	subclass	NOUN
ejpam-6294	66	11	gς	gς	NOUN
ejpam-6294	66	12	,	,	PUNCT
ejpam-6294	66	13	g	g	PROPN
ejpam-6294	66	14	u	u	PROPN
ejpam-6294	66	15	,	,	PUNCT
ejpam-6294	66	16	v	v	PROPN
ejpam-6294	66	17	(	(	PUNCT
ejpam-6294	66	18	τ	τ	PROPN
ejpam-6294	66	19	)	)	PUNCT
ejpam-6294	66	20	,	,	PUNCT
ejpam-6294	66	21	laying	lay	VERB
ejpam-6294	66	22	the	the	DET
ejpam-6294	66	23	foundation	foundation	NOUN
ejpam-6294	66	24	for	for	ADP
ejpam-6294	66	25	the	the	DET
ejpam-6294	66	26	subsequent	subsequent	ADJ
ejpam-6294	66	27	analysis	analysis	NOUN
ejpam-6294	66	28	.	.	PUNCT
ejpam-6294	67	1	building	build	VERB
ejpam-6294	67	2	on	on	ADP
ejpam-6294	67	3	this	this	PRON
ejpam-6294	67	4	,	,	PUNCT
ejpam-6294	67	5	section	section	NOUN
ejpam-6294	67	6	3	3	NUM
ejpam-6294	67	7	derives	derive	VERB
ejpam-6294	67	8	the	the	DET
ejpam-6294	67	9	fekete	fekete	PROPN
ejpam-6294	67	10	-	-	PUNCT
ejpam-6294	67	11	szegö	szegö	PROPN
ejpam-6294	67	12	inequality	inequality	NOUN
ejpam-6294	67	13	for	for	ADP
ejpam-6294	67	14	the	the	DET
ejpam-6294	67	15	same	same	ADJ
ejpam-6294	67	16	subclass	subclass	NOUN
ejpam-6294	67	17	,	,	PUNCT
ejpam-6294	67	18	highlighting	highlight	VERB
ejpam-6294	67	19	important	important	ADJ
ejpam-6294	67	20	functional	functional	ADJ
ejpam-6294	67	21	bounds	bound	NOUN
ejpam-6294	67	22	.	.	PUNCT
ejpam-6294	68	1	in	in	ADP
ejpam-6294	68	2	section	section	NOUN
ejpam-6294	68	3	4	4	NUM
ejpam-6294	68	4	,	,	PUNCT
ejpam-6294	68	5	attention	attention	NOUN
ejpam-6294	68	6	shifts	shift	NOUN
ejpam-6294	68	7	to	to	ADP
ejpam-6294	68	8	a	a	DET
ejpam-6294	68	9	related	relate	VERB
ejpam-6294	68	10	subclass	subclass	NOUN
ejpam-6294	68	11	gς	gς	NOUN
ejpam-6294	68	12	,	,	PUNCT
ejpam-6294	68	13	g(τ	g(τ	PROPN
ejpam-6294	68	14	)	)	PUNCT
ejpam-6294	68	15	,	,	PUNCT
ejpam-6294	68	16	where	where	SCONJ
ejpam-6294	68	17	initial	initial	ADJ
ejpam-6294	68	18	coefficient	coefficient	NOUN
ejpam-6294	68	19	estimates	estimate	NOUN
ejpam-6294	68	20	are	be	AUX
ejpam-6294	68	21	again	again	ADV
ejpam-6294	68	22	established	establish	VERB
ejpam-6294	68	23	.	.	PUNCT
ejpam-6294	69	1	following	follow	VERB
ejpam-6294	69	2	this	this	PRON
ejpam-6294	69	3	,	,	PUNCT
ejpam-6294	69	4	section	section	NOUN
ejpam-6294	69	5	5	5	NUM
ejpam-6294	69	6	investigates	investigate	VERB
ejpam-6294	69	7	the	the	DET
ejpam-6294	69	8	fekete	fekete	PROPN
ejpam-6294	69	9	-	-	PUNCT
ejpam-6294	69	10	szegö	szegö	PROPN
ejpam-6294	69	11	s.	s.	PROPN
ejpam-6294	69	12	thangamani	thangamani	PROPN
ejpam-6294	69	13	et	et	PROPN
ejpam-6294	69	14	al	al	PROPN
ejpam-6294	69	15	.	.	PUNCT
ejpam-6294	69	16	/	/	SYM
ejpam-6294	69	17	eur	eur	PROPN
ejpam-6294	69	18	.	.	PUNCT
ejpam-6294	70	1	j.	j.	PROPN
ejpam-6294	70	2	pure	pure	PROPN
ejpam-6294	70	3	appl	appl	PROPN
ejpam-6294	70	4	.	.	PROPN
ejpam-6294	70	5	math	math	PROPN
ejpam-6294	70	6	,	,	PUNCT
ejpam-6294	70	7	18	18	NUM
ejpam-6294	70	8	(	(	PUNCT
ejpam-6294	70	9	3	3	NUM
ejpam-6294	70	10	)	)	PUNCT
ejpam-6294	70	11	(	(	PUNCT
ejpam-6294	70	12	2025	2025	NUM
ejpam-6294	70	13	)	)	PUNCT
ejpam-6294	70	14	,	,	PUNCT
ejpam-6294	70	15	6294	6294	NUM
ejpam-6294	70	16	4	4	NUM
ejpam-6294	70	17	of	of	ADP
ejpam-6294	70	18	19	19	NUM
ejpam-6294	70	19	inequality	inequality	NOUN
ejpam-6294	70	20	for	for	ADP
ejpam-6294	70	21	gς	gς	NOUN
ejpam-6294	70	22	,	,	PUNCT
ejpam-6294	70	23	g(τ	g(τ	PROPN
ejpam-6294	70	24	)	)	PUNCT
ejpam-6294	70	25	,	,	PUNCT
ejpam-6294	70	26	offering	offer	VERB
ejpam-6294	70	27	a	a	DET
ejpam-6294	70	28	comparative	comparative	ADJ
ejpam-6294	70	29	view	view	NOUN
ejpam-6294	70	30	of	of	ADP
ejpam-6294	70	31	the	the	DET
ejpam-6294	70	32	functional	functional	ADJ
ejpam-6294	70	33	behavior	behavior	NOUN
ejpam-6294	70	34	.	.	PUNCT
ejpam-6294	71	1	section	section	NOUN
ejpam-6294	71	2	6	6	NUM
ejpam-6294	71	3	is	be	AUX
ejpam-6294	71	4	dedicated	dedicate	VERB
ejpam-6294	71	5	to	to	ADP
ejpam-6294	71	6	a	a	DET
ejpam-6294	71	7	discussion	discussion	NOUN
ejpam-6294	71	8	on	on	ADP
ejpam-6294	71	9	the	the	DET
ejpam-6294	71	10	influence	influence	NOUN
ejpam-6294	71	11	of	of	ADP
ejpam-6294	71	12	the	the	DET
ejpam-6294	71	13	parameter	parameter	NOUN
ejpam-6294	71	14	s	s	PROPN
ejpam-6294	71	15	,	,	PUNCT
ejpam-6294	71	16	supported	support	VERB
ejpam-6294	71	17	by	by	ADP
ejpam-6294	71	18	surface	surface	NOUN
ejpam-6294	71	19	plot	plot	NOUN
ejpam-6294	71	20	interpretations	interpretation	NOUN
ejpam-6294	71	21	that	that	PRON
ejpam-6294	71	22	provide	provide	VERB
ejpam-6294	71	23	visual	visual	ADJ
ejpam-6294	71	24	insights	insight	NOUN
ejpam-6294	71	25	into	into	ADP
ejpam-6294	71	26	the	the	DET
ejpam-6294	71	27	parameter	parameter	NOUN
ejpam-6294	71	28	’s	’s	PART
ejpam-6294	71	29	effect	effect	NOUN
ejpam-6294	71	30	.	.	PUNCT
ejpam-6294	72	1	finally	finally	ADV
ejpam-6294	72	2	,	,	PUNCT
ejpam-6294	72	3	section	section	NOUN
ejpam-6294	72	4	7	7	NUM
ejpam-6294	72	5	concludes	conclude	VERB
ejpam-6294	72	6	the	the	DET
ejpam-6294	72	7	paper	paper	NOUN
ejpam-6294	72	8	by	by	ADP
ejpam-6294	72	9	summarizing	summarize	VERB
ejpam-6294	72	10	the	the	DET
ejpam-6294	72	11	key	key	ADJ
ejpam-6294	72	12	findings	finding	NOUN
ejpam-6294	72	13	and	and	CCONJ
ejpam-6294	72	14	highlighting	highlight	VERB
ejpam-6294	72	15	potential	potential	ADJ
ejpam-6294	72	16	directions	direction	NOUN
ejpam-6294	72	17	for	for	ADP
ejpam-6294	72	18	future	future	ADJ
ejpam-6294	72	19	research	research	NOUN
ejpam-6294	72	20	.	.	PUNCT
ejpam-6294	73	1	2	2	X
ejpam-6294	73	2	.	.	X
ejpam-6294	73	3	the	the	DET
ejpam-6294	73	4	initial	initial	ADJ
ejpam-6294	73	5	coefficient	coefficient	NOUN
ejpam-6294	73	6	estimates	estimate	NOUN
ejpam-6294	73	7	for	for	ADP
ejpam-6294	73	8	the	the	DET
ejpam-6294	73	9	subclass	subclass	NOUN
ejpam-6294	73	10	gς	gς	NOUN
ejpam-6294	73	11	,	,	PUNCT
ejpam-6294	73	12	g	g	PROPN
ejpam-6294	73	13	u	u	PROPN
ejpam-6294	73	14	,	,	PUNCT
ejpam-6294	73	15	v	v	PROPN
ejpam-6294	73	16	(	(	PUNCT
ejpam-6294	73	17	τ	τ	X
ejpam-6294	73	18	)	)	PUNCT
ejpam-6294	73	19	the	the	DET
ejpam-6294	73	20	lucas	lucas	PROPN
ejpam-6294	73	21	polynomials	polynomial	NOUN
ejpam-6294	73	22	ln(u(s	ln(u(s	PRON
ejpam-6294	73	23	)	)	PUNCT
ejpam-6294	73	24	,	,	PUNCT
ejpam-6294	73	25	v(s	v(s	PROPN
ejpam-6294	73	26	)	)	PUNCT
ejpam-6294	73	27	,	,	PUNCT
ejpam-6294	73	28	s	s	X
ejpam-6294	73	29	)	)	PUNCT
ejpam-6294	73	30	are	be	AUX
ejpam-6294	73	31	defined	define	VERB
ejpam-6294	73	32	by	by	ADP
ejpam-6294	73	33	the	the	DET
ejpam-6294	73	34	recurrence	recurrence	NOUN
ejpam-6294	73	35	relation	relation	NOUN
ejpam-6294	73	36	that	that	PRON
ejpam-6294	73	37	follows	follow	VERB
ejpam-6294	73	38	:	:	PUNCT
ejpam-6294	73	39	ln(s	ln(s	X
ejpam-6294	73	40	)	)	PUNCT
ejpam-6294	73	41	=	=	SYM
ejpam-6294	73	42	u(s)ln−1(s	u(s)ln−1(	NOUN
ejpam-6294	73	43	)	)	PUNCT
ejpam-6294	73	44	+	+	NOUN
ejpam-6294	73	45	v(s)ln−2(s	v(s)ln−2(s	ADJ
ejpam-6294	73	46	)	)	PUNCT
ejpam-6294	73	47	with	with	ADP
ejpam-6294	73	48	initial	initial	ADJ
ejpam-6294	73	49	conditions	condition	NOUN
ejpam-6294	73	50	:	:	PUNCT
ejpam-6294	73	51	l0(s	l0(s	PROPN
ejpam-6294	73	52	)	)	PUNCT
ejpam-6294	73	53	=	=	SYM
ejpam-6294	73	54	2	2	NUM
ejpam-6294	73	55	,	,	PUNCT
ejpam-6294	73	56	l1(s	l1(s	PROPN
ejpam-6294	73	57	)	)	PUNCT
ejpam-6294	73	58	=	=	PUNCT
ejpam-6294	73	59	u(s	u(s	PROPN
ejpam-6294	73	60	)	)	PUNCT
ejpam-6294	73	61	,	,	PUNCT
ejpam-6294	73	62	the	the	DET
ejpam-6294	73	63	generating	generate	VERB
ejpam-6294	73	64	function	function	NOUN
ejpam-6294	73	65	for	for	ADP
ejpam-6294	73	66	ln(s	ln(	NOUN
ejpam-6294	73	67	)	)	PUNCT
ejpam-6294	73	68	is	be	AUX
ejpam-6294	73	69	given	give	VERB
ejpam-6294	73	70	by	by	ADP
ejpam-6294	73	71	:	:	PUNCT
ejpam-6294	73	72	g(s	g(s	PROPN
ejpam-6294	73	73	,	,	PUNCT
ejpam-6294	73	74	θ	θ	NOUN
ejpam-6294	73	75	)	)	PUNCT
ejpam-6294	73	76	=	=	SYM
ejpam-6294	74	1	2−	2−	NUM
ejpam-6294	74	2	u(s)θ	u(s)θ	PROPN
ejpam-6294	74	3	1−	1−	NUM
ejpam-6294	74	4	u(s)θ−	u(s)θ−	ADJ
ejpam-6294	74	5	v(s)θ2	v(s)θ2	PROPN
ejpam-6294	74	6	.	.	PUNCT
ejpam-6294	75	1	the	the	DET
ejpam-6294	75	2	generating	generate	VERB
ejpam-6294	75	3	function	function	NOUN
ejpam-6294	75	4	g(s	g(s	PROPN
ejpam-6294	75	5	,	,	PUNCT
ejpam-6294	75	6	θ	θ	NOUN
ejpam-6294	75	7	)	)	PUNCT
ejpam-6294	75	8	is	be	AUX
ejpam-6294	75	9	related	relate	VERB
ejpam-6294	75	10	to	to	ADP
ejpam-6294	75	11	the	the	DET
ejpam-6294	75	12	sequence	sequence	NOUN
ejpam-6294	75	13	ln(u(s	ln(u(s	NUM
ejpam-6294	75	14	)	)	PUNCT
ejpam-6294	75	15	,	,	PUNCT
ejpam-6294	75	16	v(s	v(s	PROPN
ejpam-6294	75	17	)	)	PUNCT
ejpam-6294	75	18	,	,	PUNCT
ejpam-6294	75	19	s	s	X
ejpam-6294	75	20	)	)	PUNCT
ejpam-6294	75	21	by	by	ADP
ejpam-6294	75	22	the	the	DET
ejpam-6294	75	23	expansion	expansion	NOUN
ejpam-6294	75	24	:	:	PUNCT
ejpam-6294	75	25	g(s	g(s	NOUN
ejpam-6294	75	26	,	,	PUNCT
ejpam-6294	75	27	θ	θ	NOUN
ejpam-6294	75	28	)	)	PUNCT
ejpam-6294	75	29	=	=	PUNCT
ejpam-6294	76	1	∞∑	∞∑	PRON
ejpam-6294	76	2	n=0	n=0	NUM
ejpam-6294	76	3	ln(u(s	ln(u(s	NUM
ejpam-6294	76	4	)	)	PUNCT
ejpam-6294	76	5	,	,	PUNCT
ejpam-6294	76	6	v(s	v(s	PROPN
ejpam-6294	76	7	)	)	PUNCT
ejpam-6294	76	8	,	,	PUNCT
ejpam-6294	76	9	s)θ	s)θ	X
ejpam-6294	76	10	n	n	CCONJ
ejpam-6294	76	11	thus	thus	ADV
ejpam-6294	76	12	,	,	PUNCT
ejpam-6294	76	13	we	we	PRON
ejpam-6294	76	14	can	can	AUX
ejpam-6294	76	15	express	express	VERB
ejpam-6294	76	16	the	the	DET
ejpam-6294	76	17	generating	generate	VERB
ejpam-6294	76	18	function	function	NOUN
ejpam-6294	76	19	as	as	ADP
ejpam-6294	76	20	:	:	PUNCT
ejpam-6294	76	21	g(s	g(s	PROPN
ejpam-6294	76	22	,	,	PUNCT
ejpam-6294	76	23	θ	θ	NOUN
ejpam-6294	76	24	)	)	PUNCT
ejpam-6294	76	25	=	=	SYM
ejpam-6294	76	26	2−	2−	NUM
ejpam-6294	76	27	u(s)θ	u(s)θ	PROPN
ejpam-6294	76	28	1−	1−	NUM
ejpam-6294	76	29	u(s)θ−	u(s)θ−	ADJ
ejpam-6294	76	30	v(s)θ2	v(s)θ2	PROPN
ejpam-6294	76	31	=	=	SYM
ejpam-6294	76	32	2+u(s)θ+(2v(s)+u2	2+u(s)θ+(2v(s)+u2	NUM
ejpam-6294	76	33	(	(	PUNCT
ejpam-6294	76	34	s))θ2+(3u(s)v(s)+u3	s))θ2+(3u(s)v(s)+u3	NOUN
ejpam-6294	76	35	(	(	PUNCT
ejpam-6294	76	36	s))θ3	s))θ3	NOUN
ejpam-6294	76	37	+	+	NOUN
ejpam-6294	76	38	...	...	PUNCT
ejpam-6294	76	39	,	,	PUNCT
ejpam-6294	76	40	(	(	PUNCT
ejpam-6294	76	41	2	2	X
ejpam-6294	76	42	)	)	PUNCT
ejpam-6294	76	43	∴	∴	PROPN
ejpam-6294	76	44	g(s	g(s	PROPN
ejpam-6294	76	45	,	,	PUNCT
ejpam-6294	76	46	θ	θ	NOUN
ejpam-6294	76	47	)	)	PUNCT
ejpam-6294	76	48	=	=	PUNCT
ejpam-6294	77	1	∞∑	∞∑	PRON
ejpam-6294	77	2	n=0	n=0	NUM
ejpam-6294	77	3	ln(u(s	ln(u(s	NUM
ejpam-6294	77	4	)	)	PUNCT
ejpam-6294	77	5	,	,	PUNCT
ejpam-6294	77	6	v(s	v(s	PROPN
ejpam-6294	77	7	)	)	PUNCT
ejpam-6294	77	8	,	,	PUNCT
ejpam-6294	77	9	s)θ	s)θ	X
ejpam-6294	77	10	n.	n.	NOUN
ejpam-6294	77	11	where	where	SCONJ
ejpam-6294	77	12	l0(s	l0(s	PROPN
ejpam-6294	77	13	)	)	PUNCT
ejpam-6294	77	14	=	=	SYM
ejpam-6294	77	15	2	2	NUM
ejpam-6294	77	16	,	,	PUNCT
ejpam-6294	77	17	l1(s	l1(s	PROPN
ejpam-6294	77	18	)	)	PUNCT
ejpam-6294	77	19	=	=	PUNCT
ejpam-6294	77	20	u(s	u(s	PROPN
ejpam-6294	77	21	)	)	PUNCT
ejpam-6294	77	22	,	,	PUNCT
ejpam-6294	77	23	l2(s	l2(s	NOUN
ejpam-6294	77	24	)	)	PUNCT
ejpam-6294	77	25	=	=	SYM
ejpam-6294	77	26	2v(s	2v(s	NUM
ejpam-6294	77	27	)	)	PUNCT
ejpam-6294	78	1	+	+	CCONJ
ejpam-6294	78	2	u2	u2	PROPN
ejpam-6294	78	3	(	(	PUNCT
ejpam-6294	78	4	s	s	NOUN
ejpam-6294	78	5	)	)	PUNCT
ejpam-6294	78	6	l3(s	l3(s	PROPN
ejpam-6294	78	7	)	)	PUNCT
ejpam-6294	78	8	=	=	NOUN
ejpam-6294	78	9	u3	u3	NOUN
ejpam-6294	78	10	(	(	PUNCT
ejpam-6294	78	11	s	s	NOUN
ejpam-6294	78	12	)	)	PUNCT
ejpam-6294	78	13	+	+	NUM
ejpam-6294	78	14	3u(s)v(s	3u(s)v(s	NOUN
ejpam-6294	78	15	)	)	PUNCT
ejpam-6294	78	16	,	,	PUNCT
ejpam-6294	78	17	...	...	PUNCT
ejpam-6294	78	18	remark	remark	NOUN
ejpam-6294	78	19	1	1	NUM
ejpam-6294	78	20	.	.	PUNCT
ejpam-6294	79	1	it	it	PRON
ejpam-6294	79	2	should	should	AUX
ejpam-6294	79	3	be	be	AUX
ejpam-6294	79	4	noted	note	VERB
ejpam-6294	79	5	that	that	SCONJ
ejpam-6294	79	6	the	the	DET
ejpam-6294	79	7	(	(	PUNCT
ejpam-6294	79	8	u	u	NOUN
ejpam-6294	79	9	,	,	PUNCT
ejpam-6294	79	10	v)-polynomial	v)-polynomial	NOUN
ejpam-6294	79	11	ln(s	ln(s	X
ejpam-6294	79	12	)	)	PUNCT
ejpam-6294	79	13	leads	lead	VERB
ejpam-6294	79	14	to	to	ADP
ejpam-6294	79	15	different	different	ADJ
ejpam-6294	79	16	polynomials	polynomial	NOUN
ejpam-6294	79	17	for	for	ADP
ejpam-6294	79	18	certain	certain	ADJ
ejpam-6294	79	19	values	value	NOUN
ejpam-6294	79	20	of	of	ADP
ejpam-6294	79	21	u	u	NOUN
ejpam-6294	79	22	and	and	CCONJ
ejpam-6294	79	23	v.	v.	CCONJ
ejpam-6294	79	24	here	here	ADV
ejpam-6294	79	25	,	,	PUNCT
ejpam-6294	79	26	we	we	PRON
ejpam-6294	79	27	highlight	highlight	VERB
ejpam-6294	79	28	a	a	DET
ejpam-6294	79	29	few	few	ADJ
ejpam-6294	79	30	examples	example	NOUN
ejpam-6294	79	31	from	from	ADP
ejpam-6294	79	32	those	those	PRON
ejpam-6294	79	33	:	:	PUNCT
ejpam-6294	79	34	(	(	PUNCT
ejpam-6294	79	35	i	i	NOUN
ejpam-6294	79	36	)	)	PUNCT
ejpam-6294	79	37	for	for	ADP
ejpam-6294	79	38	u(s	u(s	NUM
ejpam-6294	79	39	)	)	PUNCT
ejpam-6294	79	40	=	=	SYM
ejpam-6294	80	1	2s	2s	NUM
ejpam-6294	80	2	and	and	CCONJ
ejpam-6294	80	3	v(s	v(s	NUM
ejpam-6294	80	4	)	)	PUNCT
ejpam-6294	80	5	=	=	SYM
ejpam-6294	81	1	1	1	NUM
ejpam-6294	81	2	,	,	PUNCT
ejpam-6294	81	3	then	then	ADV
ejpam-6294	81	4	obtain	obtain	VERB
ejpam-6294	81	5	the	the	DET
ejpam-6294	81	6	polynomials	polynomial	NOUN
ejpam-6294	81	7	of	of	ADP
ejpam-6294	81	8	pell	pell	NOUN
ejpam-6294	81	9	-	-	PUNCT
ejpam-6294	81	10	lucas	lucas	NOUN
ejpam-6294	81	11	qn(s	qn(s	NUM
ejpam-6294	81	12	)	)	PUNCT
ejpam-6294	81	13	.	.	PUNCT
ejpam-6294	82	1	(	(	PUNCT
ejpam-6294	82	2	ii	ii	NOUN
ejpam-6294	82	3	)	)	PUNCT
ejpam-6294	82	4	for	for	ADP
ejpam-6294	82	5	u(s	u(s	PROPN
ejpam-6294	82	6	)	)	PUNCT
ejpam-6294	82	7	=	=	SYM
ejpam-6294	82	8	1	1	NUM
ejpam-6294	82	9	and	and	CCONJ
ejpam-6294	82	10	v(s	v(s	NOUN
ejpam-6294	82	11	)	)	PUNCT
ejpam-6294	83	1	=	=	SYM
ejpam-6294	84	1	2s	2s	NUM
ejpam-6294	84	2	,	,	PUNCT
ejpam-6294	84	3	then	then	ADV
ejpam-6294	84	4	acquire	acquire	VERB
ejpam-6294	84	5	polynomials	polynomial	NOUN
ejpam-6294	84	6	of	of	ADP
ejpam-6294	84	7	jacobsthal	jacobsthal	ADJ
ejpam-6294	84	8	-	-	PUNCT
ejpam-6294	84	9	lucas	lucas	NOUN
ejpam-6294	84	10	jn(s	jn(s	NOUN
ejpam-6294	84	11	)	)	PUNCT
ejpam-6294	84	12	.	.	PUNCT
ejpam-6294	85	1	(	(	PUNCT
ejpam-6294	85	2	iii	iii	NOUN
ejpam-6294	85	3	)	)	PUNCT
ejpam-6294	85	4	for	for	ADP
ejpam-6294	85	5	u(s	u(s	ADJ
ejpam-6294	85	6	)	)	PUNCT
ejpam-6294	85	7	=	=	SYM
ejpam-6294	85	8	3s	3s	NUM
ejpam-6294	85	9	and	and	CCONJ
ejpam-6294	85	10	v(s	v(s	NOUN
ejpam-6294	85	11	)	)	PUNCT
ejpam-6294	86	1	=	=	SYM
ejpam-6294	86	2	−2	−2	NOUN
ejpam-6294	86	3	,	,	PUNCT
ejpam-6294	86	4	then	then	ADV
ejpam-6294	86	5	obtain	obtain	VERB
ejpam-6294	86	6	the	the	DET
ejpam-6294	86	7	polynomials	polynomial	NOUN
ejpam-6294	86	8	of	of	ADP
ejpam-6294	86	9	fermat	fermat	PROPN
ejpam-6294	86	10	-	-	PUNCT
ejpam-6294	86	11	lucas	lucas	PROPN
ejpam-6294	86	12	fn(s	fn(s	NOUN
ejpam-6294	86	13	)	)	PUNCT
ejpam-6294	86	14	.	.	PUNCT
ejpam-6294	87	1	s.	s.	PROPN
ejpam-6294	87	2	thangamani	thangamani	PROPN
ejpam-6294	87	3	et	et	PROPN
ejpam-6294	87	4	al	al	PROPN
ejpam-6294	87	5	.	.	PUNCT
ejpam-6294	87	6	/	/	SYM
ejpam-6294	87	7	eur	eur	PROPN
ejpam-6294	87	8	.	.	PUNCT
ejpam-6294	88	1	j.	j.	PROPN
ejpam-6294	88	2	pure	pure	PROPN
ejpam-6294	88	3	appl	appl	PROPN
ejpam-6294	88	4	.	.	PROPN
ejpam-6294	88	5	math	math	PROPN
ejpam-6294	88	6	,	,	PUNCT
ejpam-6294	88	7	18	18	NUM
ejpam-6294	88	8	(	(	PUNCT
ejpam-6294	88	9	3	3	NUM
ejpam-6294	88	10	)	)	PUNCT
ejpam-6294	88	11	(	(	PUNCT
ejpam-6294	88	12	2025	2025	NUM
ejpam-6294	88	13	)	)	PUNCT
ejpam-6294	88	14	,	,	PUNCT
ejpam-6294	88	15	6294	6294	NUM
ejpam-6294	88	16	5	5	NUM
ejpam-6294	88	17	of	of	ADP
ejpam-6294	88	18	19	19	NUM
ejpam-6294	88	19	(	(	PUNCT
ejpam-6294	88	20	iv	iv	NOUN
ejpam-6294	88	21	)	)	PUNCT
ejpam-6294	88	22	for	for	ADP
ejpam-6294	88	23	u(s	u(s	NUM
ejpam-6294	88	24	)	)	PUNCT
ejpam-6294	88	25	=	=	SYM
ejpam-6294	89	1	2s	2s	NUM
ejpam-6294	89	2	and	and	CCONJ
ejpam-6294	89	3	v(s	v(s	NUM
ejpam-6294	89	4	)	)	PUNCT
ejpam-6294	89	5	=	=	SYM
ejpam-6294	89	6	−1	−1	NOUN
ejpam-6294	89	7	,	,	PUNCT
ejpam-6294	89	8	then	then	ADV
ejpam-6294	89	9	acquire	acquire	VERB
ejpam-6294	89	10	first	first	ADJ
ejpam-6294	89	11	kind	kind	ADJ
ejpam-6294	89	12	chebyshev	chebyshev	NOUN
ejpam-6294	89	13	polynomials	polynomial	NOUN
ejpam-6294	89	14	tn(s	tn(s	PUNCT
ejpam-6294	89	15	)	)	PUNCT
ejpam-6294	89	16	.	.	PUNCT
ejpam-6294	90	1	the	the	DET
ejpam-6294	90	2	following	follow	VERB
ejpam-6294	90	3	lemma	lemma	PROPN
ejpam-6294	90	4	is	be	AUX
ejpam-6294	90	5	to	to	PART
ejpam-6294	90	6	be	be	AUX
ejpam-6294	90	7	kept	keep	VERB
ejpam-6294	90	8	forefront	forefront	ADJ
ejpam-6294	90	9	in	in	ADP
ejpam-6294	90	10	order	order	NOUN
ejpam-6294	90	11	to	to	PART
ejpam-6294	90	12	get	get	VERB
ejpam-6294	90	13	at	at	ADP
ejpam-6294	90	14	our	our	PRON
ejpam-6294	90	15	primary	primary	ADJ
ejpam-6294	90	16	conclusions	conclusion	NOUN
ejpam-6294	90	17	.	.	PUNCT
ejpam-6294	91	1	lemma	lemma	PROPN
ejpam-6294	91	2	1	1	NUM
ejpam-6294	91	3	.	.	PUNCT
ejpam-6294	92	1	[	[	X
ejpam-6294	92	2	26	26	NUM
ejpam-6294	92	3	]	]	X
ejpam-6294	92	4	if	if	SCONJ
ejpam-6294	92	5	p(θ	p(θ	PROPN
ejpam-6294	92	6	)	)	PUNCT
ejpam-6294	92	7	∈	∈	PROPN
ejpam-6294	92	8	p	p	NOUN
ejpam-6294	92	9	,	,	PUNCT
ejpam-6294	92	10	then	then	ADV
ejpam-6294	92	11	|pn	|pn	X
ejpam-6294	92	12	|	|	ADV
ejpam-6294	92	13	≤	≤	ADJ
ejpam-6294	92	14	2	2	NUM
ejpam-6294	92	15	for	for	ADP
ejpam-6294	92	16	each	each	DET
ejpam-6294	92	17	n	n	CCONJ
ejpam-6294	92	18	,	,	PUNCT
ejpam-6294	92	19	where	where	SCONJ
ejpam-6294	92	20	p	p	NOUN
ejpam-6294	92	21	is	be	AUX
ejpam-6294	92	22	the	the	DET
ejpam-6294	92	23	family	family	NOUN
ejpam-6294	92	24	of	of	ADP
ejpam-6294	92	25	all	all	DET
ejpam-6294	92	26	functions	function	NOUN
ejpam-6294	92	27	p	p	NOUN
ejpam-6294	92	28	analytic	analytic	NOUN
ejpam-6294	92	29	in	in	ADP
ejpam-6294	92	30	d	d	PROPN
ejpam-6294	92	31	for	for	ADP
ejpam-6294	92	32	which	which	PRON
ejpam-6294	92	33	re	re	ADP
ejpam-6294	92	34	(	(	PUNCT
ejpam-6294	92	35	p(θ	p(θ	PROPN
ejpam-6294	92	36	)	)	PUNCT
ejpam-6294	92	37	)	)	PUNCT
ejpam-6294	93	1	>	>	X
ejpam-6294	93	2	0	0	NUM
ejpam-6294	93	3	,	,	PUNCT
ejpam-6294	93	4	p(θ	p(θ	PROPN
ejpam-6294	93	5	)	)	PUNCT
ejpam-6294	93	6	=	=	SYM
ejpam-6294	94	1	1	1	NUM
ejpam-6294	94	2	+	+	CCONJ
ejpam-6294	94	3	p1θ	p1θ	ADP
ejpam-6294	94	4	+	+	CCONJ
ejpam-6294	94	5	p2θ	p2θ	NOUN
ejpam-6294	94	6	2	2	NUM
ejpam-6294	94	7	+	+	CCONJ
ejpam-6294	94	8	...	...	PUNCT
ejpam-6294	94	9	;	;	PUNCT
ejpam-6294	94	10	θ	θ	PROPN
ejpam-6294	94	11	∈	∈	PROPN
ejpam-6294	94	12	d.	d.	PROPN
ejpam-6294	94	13	in	in	ADP
ejpam-6294	94	14	the	the	DET
ejpam-6294	94	15	following	following	NOUN
ejpam-6294	94	16	,	,	PUNCT
ejpam-6294	94	17	it	it	PRON
ejpam-6294	94	18	is	be	AUX
ejpam-6294	94	19	assumed	assume	VERB
ejpam-6294	94	20	that	that	SCONJ
ejpam-6294	94	21	g(s	g(s	PROPN
ejpam-6294	94	22	,	,	PUNCT
ejpam-6294	94	23	θ	θ	NOUN
ejpam-6294	94	24	)	)	PUNCT
ejpam-6294	94	25	is	be	AUX
ejpam-6294	94	26	form	form	NOUN
ejpam-6294	94	27	of	of	ADP
ejpam-6294	94	28	taylor	taylor	PROPN
ejpam-6294	94	29	series	series	PROPN
ejpam-6294	94	30	nature	nature	PROPN
ejpam-6294	94	31	g(s	g(s	PROPN
ejpam-6294	94	32	,	,	PUNCT
ejpam-6294	94	33	θ)−1	θ)−1	NOUN
ejpam-6294	94	34	=	=	SYM
ejpam-6294	94	35	1+u(s)θ+2v(s)+u2	1+u(s)θ+2v(s)+u2	NUM
ejpam-6294	94	36	(	(	PUNCT
ejpam-6294	94	37	s))θ2+(3u(s)v(s)+u3	s))θ2+(3u(s)v(s)+u3	NOUN
ejpam-6294	94	38	(	(	PUNCT
ejpam-6294	94	39	s))θ3+(u4	s))θ3+(u4	PROPN
ejpam-6294	94	40	(	(	PUNCT
ejpam-6294	94	41	s)+4u2	s)+4u2	X
ejpam-6294	94	42	(	(	PUNCT
ejpam-6294	94	43	s)+2v(s))θ4	s)+2v(s))θ4	NOUN
ejpam-6294	94	44	+	+	NOUN
ejpam-6294	94	45	...	...	PUNCT
ejpam-6294	94	46	,	,	PUNCT
ejpam-6294	94	47	(	(	PUNCT
ejpam-6294	94	48	3	3	X
ejpam-6294	94	49	)	)	PUNCT
ejpam-6294	94	50	g(t	g(t	PROPN
ejpam-6294	94	51	,	,	PUNCT
ejpam-6294	94	52	φ)−1	φ)−1	NOUN
ejpam-6294	94	53	=	=	SYM
ejpam-6294	94	54	1+u(t)φ+2v(t)+u2	1+u(t)φ+2v(t)+u2	NUM
ejpam-6294	94	55	(	(	PUNCT
ejpam-6294	94	56	t))φ2+(3u(t)v(t)+u3	t))φ2+(3u(t)v(t)+u3	PROPN
ejpam-6294	94	57	(	(	PUNCT
ejpam-6294	94	58	t))φ3+(u4	t))φ3+(u4	PROPN
ejpam-6294	94	59	(	(	PUNCT
ejpam-6294	94	60	t)+4u2	t)+4u2	NUM
ejpam-6294	94	61	(	(	PUNCT
ejpam-6294	94	62	t)+2v(t))φ4	t)+2v(t))φ4	NOUN
ejpam-6294	94	63	+	+	NOUN
ejpam-6294	94	64	...	...	PUNCT
ejpam-6294	94	65	,	,	PUNCT
ejpam-6294	94	66	(	(	PUNCT
ejpam-6294	94	67	4	4	X
ejpam-6294	94	68	)	)	PUNCT
ejpam-6294	94	69	definition	definition	NOUN
ejpam-6294	94	70	1	1	NUM
ejpam-6294	94	71	.	.	PUNCT
ejpam-6294	95	1	if	if	SCONJ
ejpam-6294	95	2	the	the	DET
ejpam-6294	95	3	function	function	NOUN
ejpam-6294	95	4	f	f	PROPN
ejpam-6294	95	5	∈	∈	PROPN
ejpam-6294	95	6	σ	σ	PROPN
ejpam-6294	95	7	is	be	AUX
ejpam-6294	95	8	considered	consider	VERB
ejpam-6294	95	9	to	to	PART
ejpam-6294	95	10	be	be	AUX
ejpam-6294	95	11	in	in	ADP
ejpam-6294	95	12	the	the	DET
ejpam-6294	95	13	class	class	NOUN
ejpam-6294	95	14	gς	gς	NOUN
ejpam-6294	95	15	,	,	PUNCT
ejpam-6294	95	16	g	g	PROPN
ejpam-6294	95	17	u	u	PROPN
ejpam-6294	95	18	,	,	PUNCT
ejpam-6294	95	19	v	v	PROPN
ejpam-6294	95	20	(	(	PUNCT
ejpam-6294	95	21	τ	τ	PROPN
ejpam-6294	95	22	)	)	PUNCT
ejpam-6294	95	23	,	,	PUNCT
ejpam-6294	95	24	then	then	ADV
ejpam-6294	95	25	the	the	DET
ejpam-6294	95	26	resulting	result	VERB
ejpam-6294	95	27	subordination	subordination	NOUN
ejpam-6294	95	28	holds	hold	VERB
ejpam-6294	95	29	,	,	PUNCT
ejpam-6294	95	30	(	(	PUNCT
ejpam-6294	95	31	1−	1−	NUM
ejpam-6294	95	32	τ	τ	X
ejpam-6294	95	33	)	)	PUNCT
ejpam-6294	95	34	(	(	PUNCT
ejpam-6294	95	35	θf	θf	NOUN
ejpam-6294	95	36	′(θ	′(θ	NOUN
ejpam-6294	95	37	)	)	PUNCT
ejpam-6294	95	38	f(θ	f(θ	PROPN
ejpam-6294	95	39	)	)	PUNCT
ejpam-6294	95	40	)	)	PUNCT
ejpam-6294	96	1	+	+	CCONJ
ejpam-6294	96	2	τ	τ	X
ejpam-6294	96	3	(	(	PUNCT
ejpam-6294	96	4	1	1	NUM
ejpam-6294	96	5	+	+	CCONJ
ejpam-6294	96	6	θf	θf	NOUN
ejpam-6294	96	7	′′(θ	′′(θ	PROPN
ejpam-6294	96	8	)	)	PUNCT
ejpam-6294	96	9	f	f	PROPN
ejpam-6294	96	10	′(θ	′(θ	NOUN
ejpam-6294	96	11	)	)	PUNCT
ejpam-6294	96	12	)	)	PUNCT
ejpam-6294	96	13	≺	≺	VERB
ejpam-6294	96	14	g(s	g(s	PROPN
ejpam-6294	96	15	,	,	PUNCT
ejpam-6294	96	16	θ)−	θ)−	PROPN
ejpam-6294	96	17	1	1	NUM
ejpam-6294	96	18	(	(	PUNCT
ejpam-6294	96	19	5	5	NUM
ejpam-6294	96	20	)	)	PUNCT
ejpam-6294	96	21	and	and	CCONJ
ejpam-6294	96	22	(	(	PUNCT
ejpam-6294	96	23	1−	1−	NUM
ejpam-6294	96	24	τ	τ	NOUN
ejpam-6294	96	25	)	)	PUNCT
ejpam-6294	96	26	(	(	PUNCT
ejpam-6294	96	27	φf	φf	ADP
ejpam-6294	96	28	′(φ	′(φ	NOUN
ejpam-6294	96	29	)	)	PUNCT
ejpam-6294	96	30	f(φ	f(φ	PROPN
ejpam-6294	96	31	)	)	PUNCT
ejpam-6294	96	32	)	)	PUNCT
ejpam-6294	97	1	+	+	CCONJ
ejpam-6294	97	2	τ	τ	X
ejpam-6294	97	3	(	(	PUNCT
ejpam-6294	97	4	1	1	NUM
ejpam-6294	97	5	+	+	CCONJ
ejpam-6294	97	6	φf	φf	ADP
ejpam-6294	97	7	′′(φ	′′(φ	NOUN
ejpam-6294	97	8	)	)	PUNCT
ejpam-6294	97	9	)	)	PUNCT
ejpam-6294	98	1	f	f	PROPN
ejpam-6294	98	2	′(φ	′(φ	NOUN
ejpam-6294	98	3	)	)	PUNCT
ejpam-6294	98	4	)	)	PUNCT
ejpam-6294	99	1	≺	≺	NOUN
ejpam-6294	99	2	g(t	g(t	PROPN
ejpam-6294	99	3	,	,	PUNCT
ejpam-6294	99	4	φ)−	φ)−	PROPN
ejpam-6294	99	5	1	1	NUM
ejpam-6294	99	6	(	(	PUNCT
ejpam-6294	99	7	6	6	NUM
ejpam-6294	99	8	)	)	PUNCT
ejpam-6294	99	9	example	example	NOUN
ejpam-6294	99	10	1	1	NUM
ejpam-6294	99	11	.	.	PUNCT
ejpam-6294	99	12	when	when	SCONJ
ejpam-6294	99	13	replacing	replace	VERB
ejpam-6294	99	14	τ	τ	X
ejpam-6294	99	15	=	=	SYM
ejpam-6294	99	16	0	0	NUM
ejpam-6294	99	17	in	in	ADP
ejpam-6294	99	18	definition	definition	NOUN
ejpam-6294	99	19	(	(	PUNCT
ejpam-6294	99	20	1	1	NUM
ejpam-6294	99	21	)	)	PUNCT
ejpam-6294	99	22	then	then	ADV
ejpam-6294	99	23	the	the	DET
ejpam-6294	99	24	particular	particular	ADJ
ejpam-6294	99	25	subordination	subordination	NOUN
ejpam-6294	99	26	is	be	AUX
ejpam-6294	99	27	hold	hold	NOUN
ejpam-6294	99	28	for	for	ADP
ejpam-6294	99	29	the	the	DET
ejpam-6294	99	30	class	class	NOUN
ejpam-6294	99	31	gς	gς	NOUN
ejpam-6294	99	32	,	,	PUNCT
ejpam-6294	99	33	g	g	PROPN
ejpam-6294	99	34	u	u	PROPN
ejpam-6294	99	35	,	,	PUNCT
ejpam-6294	99	36	v	v	PROPN
ejpam-6294	99	37	(	(	PUNCT
ejpam-6294	99	38	0	0	NUM
ejpam-6294	99	39	)	)	PUNCT
ejpam-6294	99	40	.	.	PUNCT
ejpam-6294	100	1	(	(	PUNCT
ejpam-6294	100	2	θf	θf	NOUN
ejpam-6294	100	3	′(θ	′(θ	NOUN
ejpam-6294	100	4	)	)	PUNCT
ejpam-6294	100	5	f(θ	f(θ	PROPN
ejpam-6294	100	6	)	)	PUNCT
ejpam-6294	100	7	)	)	PUNCT
ejpam-6294	101	1	≺	≺	NOUN
ejpam-6294	101	2	g(s	g(s	PROPN
ejpam-6294	101	3	,	,	PUNCT
ejpam-6294	101	4	θ)−	θ)−	PROPN
ejpam-6294	101	5	1	1	NUM
ejpam-6294	101	6	(	(	PUNCT
ejpam-6294	101	7	φf	φf	ADP
ejpam-6294	101	8	′(φ	′(φ	NOUN
ejpam-6294	101	9	)	)	PUNCT
ejpam-6294	101	10	f(φ	f(φ	PROPN
ejpam-6294	101	11	)	)	PUNCT
ejpam-6294	101	12	)	)	PUNCT
ejpam-6294	102	1	≺	≺	NOUN
ejpam-6294	102	2	g(t	g(t	PROPN
ejpam-6294	102	3	,	,	PUNCT
ejpam-6294	102	4	φ)−	φ)−	PROPN
ejpam-6294	102	5	1	1	NUM
ejpam-6294	102	6	example	example	NOUN
ejpam-6294	102	7	2	2	NUM
ejpam-6294	102	8	.	.	PUNCT
ejpam-6294	103	1	when	when	SCONJ
ejpam-6294	103	2	replacing	replace	VERB
ejpam-6294	103	3	τ	τ	X
ejpam-6294	103	4	=	=	SYM
ejpam-6294	103	5	1	1	NUM
ejpam-6294	103	6	in	in	ADP
ejpam-6294	103	7	definition	definition	NOUN
ejpam-6294	103	8	(	(	PUNCT
ejpam-6294	103	9	1	1	NUM
ejpam-6294	103	10	)	)	PUNCT
ejpam-6294	103	11	then	then	ADV
ejpam-6294	103	12	the	the	DET
ejpam-6294	103	13	particular	particular	ADJ
ejpam-6294	103	14	subordination	subordination	NOUN
ejpam-6294	103	15	is	be	AUX
ejpam-6294	103	16	hold	hold	NOUN
ejpam-6294	103	17	for	for	ADP
ejpam-6294	103	18	the	the	DET
ejpam-6294	103	19	class	class	NOUN
ejpam-6294	103	20	gς	gς	NOUN
ejpam-6294	103	21	,	,	PUNCT
ejpam-6294	103	22	g	g	PROPN
ejpam-6294	103	23	u	u	PROPN
ejpam-6294	103	24	,	,	PUNCT
ejpam-6294	103	25	v	v	X
ejpam-6294	103	26	(	(	PUNCT
ejpam-6294	103	27	1	1	NUM
ejpam-6294	103	28	)	)	PUNCT
ejpam-6294	103	29	.	.	PUNCT
ejpam-6294	104	1	(	(	PUNCT
ejpam-6294	104	2	1	1	X
ejpam-6294	104	3	+	+	CCONJ
ejpam-6294	104	4	θf	θf	NOUN
ejpam-6294	104	5	′′(θ	′′(θ	PROPN
ejpam-6294	104	6	)	)	PUNCT
ejpam-6294	104	7	f	f	PROPN
ejpam-6294	104	8	′(θ	′(θ	NOUN
ejpam-6294	104	9	)	)	PUNCT
ejpam-6294	104	10	)	)	PUNCT
ejpam-6294	104	11	≺	≺	VERB
ejpam-6294	104	12	g(s	g(s	PROPN
ejpam-6294	104	13	,	,	PUNCT
ejpam-6294	104	14	θ)−	θ)−	PROPN
ejpam-6294	104	15	1	1	NUM
ejpam-6294	104	16	(	(	PUNCT
ejpam-6294	104	17	1	1	NUM
ejpam-6294	104	18	+	+	CCONJ
ejpam-6294	104	19	φf	φf	ADP
ejpam-6294	104	20	′′(φ	′′(φ	NOUN
ejpam-6294	104	21	)	)	PUNCT
ejpam-6294	104	22	)	)	PUNCT
ejpam-6294	104	23	f	f	PROPN
ejpam-6294	104	24	′(φ	′(φ	NOUN
ejpam-6294	104	25	)	)	PUNCT
ejpam-6294	104	26	)	)	PUNCT
ejpam-6294	105	1	≺	≺	NOUN
ejpam-6294	105	2	g(t	g(t	PROPN
ejpam-6294	105	3	,	,	PUNCT
ejpam-6294	105	4	φ)−	φ)−	PROPN
ejpam-6294	105	5	1	1	NUM
ejpam-6294	105	6	s.	s.	PROPN
ejpam-6294	105	7	thangamani	thangamani	PROPN
ejpam-6294	105	8	et	et	PROPN
ejpam-6294	105	9	al	al	PROPN
ejpam-6294	105	10	.	.	PUNCT
ejpam-6294	105	11	/	/	SYM
ejpam-6294	105	12	eur	eur	PROPN
ejpam-6294	105	13	.	.	PUNCT
ejpam-6294	106	1	j.	j.	PROPN
ejpam-6294	106	2	pure	pure	PROPN
ejpam-6294	106	3	appl	appl	PROPN
ejpam-6294	106	4	.	.	PROPN
ejpam-6294	106	5	math	math	PROPN
ejpam-6294	106	6	,	,	PUNCT
ejpam-6294	106	7	18	18	NUM
ejpam-6294	106	8	(	(	PUNCT
ejpam-6294	106	9	3	3	NUM
ejpam-6294	106	10	)	)	PUNCT
ejpam-6294	106	11	(	(	PUNCT
ejpam-6294	106	12	2025	2025	NUM
ejpam-6294	106	13	)	)	PUNCT
ejpam-6294	106	14	,	,	PUNCT
ejpam-6294	106	15	6294	6294	NUM
ejpam-6294	106	16	6	6	NUM
ejpam-6294	106	17	of	of	ADP
ejpam-6294	106	18	19	19	NUM
ejpam-6294	106	19	theorem	theorem	NOUN
ejpam-6294	106	20	1	1	NUM
ejpam-6294	106	21	.	.	PUNCT
ejpam-6294	107	1	if	if	SCONJ
ejpam-6294	107	2	f	f	PROPN
ejpam-6294	107	3	(	(	PUNCT
ejpam-6294	107	4	θ	θ	NOUN
ejpam-6294	107	5	)	)	PUNCT
ejpam-6294	107	6	defined	define	VERB
ejpam-6294	107	7	by	by	ADP
ejpam-6294	107	8	the	the	DET
ejpam-6294	107	9	equation	equation	NOUN
ejpam-6294	107	10	(	(	PUNCT
ejpam-6294	107	11	1	1	X
ejpam-6294	107	12	)	)	PUNCT
ejpam-6294	107	13	is	be	AUX
ejpam-6294	107	14	belongs	belong	VERB
ejpam-6294	107	15	to	to	ADP
ejpam-6294	107	16	the	the	DET
ejpam-6294	107	17	class	class	NOUN
ejpam-6294	107	18	gς	gς	NOUN
ejpam-6294	107	19	,	,	PUNCT
ejpam-6294	107	20	g	g	PROPN
ejpam-6294	107	21	u	u	PROPN
ejpam-6294	107	22	,	,	PUNCT
ejpam-6294	107	23	v	v	PROPN
ejpam-6294	107	24	(	(	PUNCT
ejpam-6294	107	25	τ	τ	PROPN
ejpam-6294	107	26	)	)	PUNCT
ejpam-6294	107	27	.	.	PUNCT
ejpam-6294	108	1	then	then	ADV
ejpam-6294	108	2	|a2|	|a2|	VERB
ejpam-6294	108	3	≤	≤	ADJ
ejpam-6294	108	4	√	√	ADP
ejpam-6294	108	5	u2	u2	PROPN
ejpam-6294	108	6	(	(	PUNCT
ejpam-6294	108	7	s	s	NOUN
ejpam-6294	108	8	)	)	PUNCT
ejpam-6294	108	9	+	+	CCONJ
ejpam-6294	108	10	u2	u2	PROPN
ejpam-6294	108	11	(	(	PUNCT
ejpam-6294	108	12	t	t	PROPN
ejpam-6294	108	13	)	)	PUNCT
ejpam-6294	108	14	+	+	NUM
ejpam-6294	108	15	2(v(s	2(v(s	NUM
ejpam-6294	108	16	)	)	PUNCT
ejpam-6294	109	1	+	+	CCONJ
ejpam-6294	109	2	v(t	v(t	NOUN
ejpam-6294	109	3	)	)	PUNCT
ejpam-6294	109	4	)	)	PUNCT
ejpam-6294	109	5	(	(	PUNCT
ejpam-6294	109	6	2	2	NUM
ejpam-6294	109	7	+	+	NUM
ejpam-6294	109	8	2τ	2τ	NUM
ejpam-6294	109	9	)	)	PUNCT
ejpam-6294	109	10	and	and	CCONJ
ejpam-6294	109	11	|a3|	|a3|	VERB
ejpam-6294	109	12	≤	≤	ADJ
ejpam-6294	109	13	u2	u2	PROPN
ejpam-6294	109	14	(	(	PUNCT
ejpam-6294	109	15	s	s	NOUN
ejpam-6294	109	16	)	)	PUNCT
ejpam-6294	110	1	+	+	CCONJ
ejpam-6294	110	2	u2	u2	PROPN
ejpam-6294	110	3	(	(	PUNCT
ejpam-6294	110	4	t	t	PROPN
ejpam-6294	110	5	)	)	PUNCT
ejpam-6294	110	6	2(1	2(1	NUM
ejpam-6294	111	1	+	+	CCONJ
ejpam-6294	111	2	τ)2	τ)2	NOUN
ejpam-6294	111	3	+	+	CCONJ
ejpam-6294	111	4	u2	u2	NOUN
ejpam-6294	111	5	(	(	PUNCT
ejpam-6294	111	6	s)−	s)−	PROPN
ejpam-6294	111	7	u2	u2	PROPN
ejpam-6294	111	8	(	(	PUNCT
ejpam-6294	111	9	t	t	PROPN
ejpam-6294	111	10	)	)	PUNCT
ejpam-6294	111	11	+	+	NUM
ejpam-6294	112	1	2(v(s)−	2(v(s)−	NUM
ejpam-6294	112	2	v(t	v(t	NUM
ejpam-6294	112	3	)	)	PUNCT
ejpam-6294	112	4	)	)	PUNCT
ejpam-6294	112	5	4(1	4(1	X
ejpam-6294	113	1	+	+	CCONJ
ejpam-6294	113	2	2τ	2τ	NUM
ejpam-6294	113	3	)	)	PUNCT
ejpam-6294	113	4	(	(	PUNCT
ejpam-6294	113	5	7	7	X
ejpam-6294	113	6	)	)	PUNCT
ejpam-6294	113	7	proof	proof	NOUN
ejpam-6294	113	8	.	.	PUNCT
ejpam-6294	114	1	let	let	VERB
ejpam-6294	114	2	f	f	PROPN
ejpam-6294	114	3	∈	∈	PROPN
ejpam-6294	114	4	gς	gς	PROPN
ejpam-6294	114	5	,	,	PUNCT
ejpam-6294	114	6	g	g	PROPN
ejpam-6294	114	7	u	u	PROPN
ejpam-6294	114	8	,	,	PUNCT
ejpam-6294	114	9	v	v	PROPN
ejpam-6294	114	10	(	(	PUNCT
ejpam-6294	114	11	τ	τ	PROPN
ejpam-6294	114	12	)	)	PUNCT
ejpam-6294	114	13	.	.	PUNCT
ejpam-6294	115	1	then	then	ADV
ejpam-6294	115	2	there	there	PRON
ejpam-6294	115	3	are	be	VERB
ejpam-6294	115	4	two	two	NUM
ejpam-6294	115	5	analytic	analytic	ADJ
ejpam-6294	115	6	functions	function	NOUN
ejpam-6294	115	7	f	f	NOUN
ejpam-6294	115	8	,	,	PUNCT
ejpam-6294	115	9	g	g	NOUN
ejpam-6294	115	10	:	:	PUNCT
ejpam-6294	115	11	d	d	X
ejpam-6294	115	12	→	→	SYM
ejpam-6294	115	13	d	d	X
ejpam-6294	115	14	given	give	VERB
ejpam-6294	115	15	by	by	ADP
ejpam-6294	115	16	(	(	PUNCT
ejpam-6294	115	17	5	5	NUM
ejpam-6294	115	18	)	)	PUNCT
ejpam-6294	115	19	and	and	CCONJ
ejpam-6294	115	20	(	(	PUNCT
ejpam-6294	115	21	6	6	NUM
ejpam-6294	115	22	)	)	PUNCT
ejpam-6294	115	23	such	such	ADJ
ejpam-6294	115	24	that	that	SCONJ
ejpam-6294	115	25	(	(	PUNCT
ejpam-6294	115	26	1−	1−	NUM
ejpam-6294	115	27	τ	τ	X
ejpam-6294	115	28	)	)	PUNCT
ejpam-6294	115	29	(	(	PUNCT
ejpam-6294	115	30	θf	θf	NOUN
ejpam-6294	115	31	′(θ	′(θ	NOUN
ejpam-6294	115	32	)	)	PUNCT
ejpam-6294	115	33	f(θ	f(θ	PROPN
ejpam-6294	115	34	)	)	PUNCT
ejpam-6294	115	35	)	)	PUNCT
ejpam-6294	116	1	+	+	CCONJ
ejpam-6294	116	2	τ	τ	X
ejpam-6294	116	3	(	(	PUNCT
ejpam-6294	116	4	1	1	NUM
ejpam-6294	116	5	+	+	CCONJ
ejpam-6294	116	6	θf	θf	NOUN
ejpam-6294	116	7	′′(θ	′′(θ	PROPN
ejpam-6294	116	8	)	)	PUNCT
ejpam-6294	116	9	f	f	PROPN
ejpam-6294	116	10	′(θ	′(θ	NOUN
ejpam-6294	116	11	)	)	PUNCT
ejpam-6294	116	12	)	)	PUNCT
ejpam-6294	117	1	=	=	SYM
ejpam-6294	117	2	g(s	g(s	PROPN
ejpam-6294	117	3	,	,	PUNCT
ejpam-6294	117	4	θ)−	θ)−	PROPN
ejpam-6294	117	5	1	1	NUM
ejpam-6294	117	6	and	and	CCONJ
ejpam-6294	117	7	(	(	PUNCT
ejpam-6294	117	8	1−	1−	NUM
ejpam-6294	117	9	τ	τ	NOUN
ejpam-6294	117	10	)	)	PUNCT
ejpam-6294	117	11	(	(	PUNCT
ejpam-6294	117	12	φf	φf	ADP
ejpam-6294	117	13	′(φ	′(φ	NOUN
ejpam-6294	117	14	)	)	PUNCT
ejpam-6294	117	15	f(φ	f(φ	PROPN
ejpam-6294	117	16	)	)	PUNCT
ejpam-6294	117	17	)	)	PUNCT
ejpam-6294	118	1	+	+	CCONJ
ejpam-6294	118	2	τ	τ	X
ejpam-6294	118	3	(	(	PUNCT
ejpam-6294	118	4	1	1	NUM
ejpam-6294	118	5	+	+	CCONJ
ejpam-6294	118	6	φf	φf	ADP
ejpam-6294	118	7	′′(φ	′′(φ	NOUN
ejpam-6294	118	8	)	)	PUNCT
ejpam-6294	118	9	)	)	PUNCT
ejpam-6294	119	1	f	f	PROPN
ejpam-6294	119	2	′(φ	′(φ	NOUN
ejpam-6294	119	3	)	)	PUNCT
ejpam-6294	119	4	)	)	PUNCT
ejpam-6294	120	1	=	=	SYM
ejpam-6294	120	2	g(t	g(t	PROPN
ejpam-6294	120	3	,	,	PUNCT
ejpam-6294	120	4	φ)−	φ)−	PROPN
ejpam-6294	120	5	1	1	NUM
ejpam-6294	120	6	since	since	SCONJ
ejpam-6294	120	7	(	(	PUNCT
ejpam-6294	120	8	1−τ	1−τ	NUM
ejpam-6294	120	9	)	)	PUNCT
ejpam-6294	120	10	(	(	PUNCT
ejpam-6294	120	11	θf	θf	NOUN
ejpam-6294	120	12	′(θ	′(θ	NOUN
ejpam-6294	120	13	)	)	PUNCT
ejpam-6294	120	14	f(θ	f(θ	PROPN
ejpam-6294	120	15	)	)	PUNCT
ejpam-6294	120	16	)	)	PUNCT
ejpam-6294	121	1	+	+	X
ejpam-6294	121	2	τ	τ	X
ejpam-6294	121	3	(	(	PUNCT
ejpam-6294	121	4	1	1	NUM
ejpam-6294	121	5	+	+	CCONJ
ejpam-6294	121	6	θf	θf	NOUN
ejpam-6294	121	7	′′(θ	′′(θ	PROPN
ejpam-6294	121	8	)	)	PUNCT
ejpam-6294	121	9	f	f	PROPN
ejpam-6294	121	10	′(θ	′(θ	NOUN
ejpam-6294	121	11	)	)	PUNCT
ejpam-6294	121	12	)	)	PUNCT
ejpam-6294	122	1	=	=	PUNCT
ejpam-6294	123	1	1+(1+τ)a2θ+(2(1	1+(1+τ)a2θ+(2(1	NUM
ejpam-6294	123	2	+	+	NOUN
ejpam-6294	123	3	2τ)a3−	2τ)a3−	NOUN
ejpam-6294	123	4	(	(	PUNCT
ejpam-6294	123	5	1	1	NUM
ejpam-6294	123	6	+	+	NOUN
ejpam-6294	123	7	3τ)a22)θ	3τ)a22)θ	NUM
ejpam-6294	123	8	2	2	NUM
ejpam-6294	123	9	+	+	NUM
ejpam-6294	123	10	...	...	PUNCT
ejpam-6294	123	11	(	(	PUNCT
ejpam-6294	123	12	8)	8)	NUM
ejpam-6294	123	13	and	and	CCONJ
ejpam-6294	123	14	(	(	PUNCT
ejpam-6294	123	15	1−τ	1−τ	NUM
ejpam-6294	123	16	)	)	PUNCT
ejpam-6294	123	17	(	(	PUNCT
ejpam-6294	123	18	φf	φf	ADP
ejpam-6294	123	19	′(φ	′(φ	NOUN
ejpam-6294	123	20	)	)	PUNCT
ejpam-6294	123	21	f(φ	f(φ	PROPN
ejpam-6294	123	22	)	)	PUNCT
ejpam-6294	123	23	)	)	PUNCT
ejpam-6294	124	1	+	+	X
ejpam-6294	124	2	τ	τ	X
ejpam-6294	124	3	(	(	PUNCT
ejpam-6294	124	4	1	1	NUM
ejpam-6294	124	5	+	+	CCONJ
ejpam-6294	124	6	φf	φf	ADP
ejpam-6294	124	7	′′(φ	′′(φ	NOUN
ejpam-6294	124	8	)	)	PUNCT
ejpam-6294	124	9	)	)	PUNCT
ejpam-6294	124	10	f	f	PROPN
ejpam-6294	124	11	′(φ	′(φ	NOUN
ejpam-6294	124	12	)	)	PUNCT
ejpam-6294	124	13	)	)	PUNCT
ejpam-6294	125	1	=	=	SYM
ejpam-6294	125	2	1−	1−	NUM
ejpam-6294	125	3	(	(	PUNCT
ejpam-6294	125	4	1+τ)a2φ+((3	1+τ)a2φ+((3	NUM
ejpam-6294	125	5	+	+	NOUN
ejpam-6294	125	6	5τ)a22−2(1	5τ)a22−2(1	NOUN
ejpam-6294	125	7	+	+	ADJ
ejpam-6294	125	8	2τ)a3)φ	2τ)a3)φ	NUM
ejpam-6294	125	9	2	2	NUM
ejpam-6294	125	10	+	+	NUM
ejpam-6294	125	11	...	...	PUNCT
ejpam-6294	125	12	(	(	PUNCT
ejpam-6294	125	13	9	9	NUM
ejpam-6294	125	14	)	)	PUNCT
ejpam-6294	125	15	from	from	ADP
ejpam-6294	125	16	the	the	DET
ejpam-6294	125	17	equations	equation	NOUN
ejpam-6294	125	18	(	(	PUNCT
ejpam-6294	125	19	3	3	NUM
ejpam-6294	125	20	)	)	PUNCT
ejpam-6294	125	21	and	and	CCONJ
ejpam-6294	125	22	(	(	PUNCT
ejpam-6294	125	23	8)	8)	NUM
ejpam-6294	125	24	,	,	PUNCT
ejpam-6294	125	25	by	by	ADP
ejpam-6294	125	26	comparing	compare	VERB
ejpam-6294	125	27	coefficients	coefficient	NOUN
ejpam-6294	125	28	of	of	ADP
ejpam-6294	125	29	θ	θ	PROPN
ejpam-6294	125	30	and	and	CCONJ
ejpam-6294	125	31	θ2	θ2	PROPN
ejpam-6294	125	32	respectively	respectively	ADV
ejpam-6294	125	33	,	,	PUNCT
ejpam-6294	125	34	we	we	PRON
ejpam-6294	125	35	get	get	VERB
ejpam-6294	125	36	coefficient	coefficient	NOUN
ejpam-6294	125	37	of	of	ADP
ejpam-6294	125	38	θ	θ	PROPN
ejpam-6294	125	39	:	:	PUNCT
ejpam-6294	125	40	(	(	PUNCT
ejpam-6294	125	41	1	1	NUM
ejpam-6294	125	42	+	+	NUM
ejpam-6294	125	43	τ)a2	τ)a2	NOUN
ejpam-6294	125	44	=	=	PUNCT
ejpam-6294	125	45	u(s	u(s	PROPN
ejpam-6294	125	46	)	)	PUNCT
ejpam-6294	125	47	(	(	PUNCT
ejpam-6294	125	48	10	10	NUM
ejpam-6294	125	49	)	)	PUNCT
ejpam-6294	125	50	coefficient	coefficient	NOUN
ejpam-6294	125	51	of	of	ADP
ejpam-6294	125	52	θ2	θ2	PROPN
ejpam-6294	125	53	:	:	PUNCT
ejpam-6294	125	54	2(1	2(1	NUM
ejpam-6294	125	55	+	+	CCONJ
ejpam-6294	125	56	2τ)a3	2τ)a3	NUM
ejpam-6294	125	57	−	−	NOUN
ejpam-6294	125	58	(	(	PUNCT
ejpam-6294	125	59	1	1	NUM
ejpam-6294	125	60	+	+	NUM
ejpam-6294	125	61	3τ)a22	3τ)a22	NUM
ejpam-6294	125	62	=	=	SYM
ejpam-6294	125	63	u2	u2	PROPN
ejpam-6294	125	64	(	(	PUNCT
ejpam-6294	125	65	s	s	NOUN
ejpam-6294	125	66	)	)	PUNCT
ejpam-6294	125	67	+	+	CCONJ
ejpam-6294	126	1	2v(s	2v(s	NUM
ejpam-6294	126	2	)	)	PUNCT
ejpam-6294	127	1	(	(	PUNCT
ejpam-6294	127	2	11	11	NUM
ejpam-6294	127	3	)	)	PUNCT
ejpam-6294	127	4	from	from	ADP
ejpam-6294	127	5	the	the	DET
ejpam-6294	127	6	equations	equation	NOUN
ejpam-6294	127	7	(	(	PUNCT
ejpam-6294	127	8	4	4	NUM
ejpam-6294	127	9	)	)	PUNCT
ejpam-6294	127	10	and	and	CCONJ
ejpam-6294	127	11	(	(	PUNCT
ejpam-6294	127	12	9	9	NUM
ejpam-6294	127	13	)	)	PUNCT
ejpam-6294	127	14	,	,	PUNCT
ejpam-6294	127	15	equating	equate	VERB
ejpam-6294	127	16	the	the	DET
ejpam-6294	127	17	coefficients	coefficient	NOUN
ejpam-6294	127	18	of	of	ADP
ejpam-6294	127	19	φ	φ	PROPN
ejpam-6294	127	20	and	and	CCONJ
ejpam-6294	127	21	φ2	φ2	PROPN
ejpam-6294	127	22	respectively	respectively	ADV
ejpam-6294	127	23	,	,	PUNCT
ejpam-6294	127	24	we	we	PRON
ejpam-6294	127	25	get	get	VERB
ejpam-6294	127	26	coefficient	coefficient	NOUN
ejpam-6294	127	27	of	of	ADP
ejpam-6294	127	28	φ	φ	PROPN
ejpam-6294	127	29	:	:	PUNCT
ejpam-6294	128	1	−(1	−(1	NOUN
ejpam-6294	128	2	+	+	PUNCT
ejpam-6294	128	3	τ)a2	τ)a2	NOUN
ejpam-6294	128	4	=	=	SYM
ejpam-6294	128	5	u(t	u(t	PROPN
ejpam-6294	128	6	)	)	PUNCT
ejpam-6294	128	7	(	(	PUNCT
ejpam-6294	128	8	12	12	X
ejpam-6294	128	9	)	)	PUNCT
ejpam-6294	128	10	coefficient	coefficient	NOUN
ejpam-6294	128	11	of	of	ADP
ejpam-6294	128	12	φ2	φ2	PROPN
ejpam-6294	128	13	:	:	PUNCT
ejpam-6294	128	14	(	(	PUNCT
ejpam-6294	128	15	3	3	NUM
ejpam-6294	128	16	+	+	NUM
ejpam-6294	128	17	5τ)a22	5τ)a22	NUM
ejpam-6294	128	18	−	−	NOUN
ejpam-6294	128	19	2(1	2(1	NUM
ejpam-6294	128	20	+	+	CCONJ
ejpam-6294	128	21	2τ)a3	2τ)a3	NUM
ejpam-6294	128	22	=	=	SYM
ejpam-6294	128	23	u2	u2	PROPN
ejpam-6294	128	24	(	(	PUNCT
ejpam-6294	128	25	t	t	PROPN
ejpam-6294	128	26	)	)	PUNCT
ejpam-6294	128	27	+	+	CCONJ
ejpam-6294	128	28	2v(t	2v(t	NUM
ejpam-6294	128	29	)	)	PUNCT
ejpam-6294	128	30	(	(	PUNCT
ejpam-6294	128	31	13	13	NUM
ejpam-6294	128	32	)	)	PUNCT
ejpam-6294	128	33	now	now	ADV
ejpam-6294	128	34	,	,	PUNCT
ejpam-6294	128	35	adding	add	VERB
ejpam-6294	128	36	the	the	DET
ejpam-6294	128	37	equations	equation	NOUN
ejpam-6294	128	38	(	(	PUNCT
ejpam-6294	128	39	10	10	NUM
ejpam-6294	128	40	)	)	PUNCT
ejpam-6294	128	41	and	and	CCONJ
ejpam-6294	128	42	(	(	PUNCT
ejpam-6294	128	43	12	12	NUM
ejpam-6294	128	44	)	)	PUNCT
ejpam-6294	128	45	,	,	PUNCT
ejpam-6294	128	46	we	we	PRON
ejpam-6294	128	47	have	have	VERB
ejpam-6294	128	48	u(s	u(s	ADJ
ejpam-6294	128	49	)	)	PUNCT
ejpam-6294	128	50	=	=	SYM
ejpam-6294	128	51	−u(t	−u(t	ADJ
ejpam-6294	128	52	)	)	PUNCT
ejpam-6294	128	53	(	(	PUNCT
ejpam-6294	128	54	14	14	NUM
ejpam-6294	128	55	)	)	PUNCT
ejpam-6294	128	56	squaring	square	VERB
ejpam-6294	128	57	and	and	CCONJ
ejpam-6294	128	58	adding	add	VERB
ejpam-6294	128	59	the	the	DET
ejpam-6294	128	60	equations	equation	NOUN
ejpam-6294	128	61	(	(	PUNCT
ejpam-6294	128	62	10	10	NUM
ejpam-6294	128	63	)	)	PUNCT
ejpam-6294	128	64	and	and	CCONJ
ejpam-6294	128	65	(	(	PUNCT
ejpam-6294	128	66	12	12	NUM
ejpam-6294	128	67	)	)	PUNCT
ejpam-6294	128	68	,	,	PUNCT
ejpam-6294	128	69	we	we	PRON
ejpam-6294	128	70	get	get	VERB
ejpam-6294	128	71	2(1	2(1	NUM
ejpam-6294	128	72	+	+	CCONJ
ejpam-6294	128	73	τ)2a22	τ)2a22	PUNCT
ejpam-6294	128	74	=	=	SYM
ejpam-6294	128	75	u2	u2	PROPN
ejpam-6294	128	76	(	(	PUNCT
ejpam-6294	128	77	s	s	NOUN
ejpam-6294	128	78	)	)	PUNCT
ejpam-6294	129	1	+	+	CCONJ
ejpam-6294	129	2	u2	u2	PROPN
ejpam-6294	129	3	(	(	PUNCT
ejpam-6294	129	4	t	t	PROPN
ejpam-6294	129	5	)	)	PUNCT
ejpam-6294	129	6	s.	s.	PROPN
ejpam-6294	129	7	thangamani	thangamani	PROPN
ejpam-6294	129	8	et	et	PROPN
ejpam-6294	129	9	al	al	PROPN
ejpam-6294	129	10	.	.	PUNCT
ejpam-6294	129	11	/	/	SYM
ejpam-6294	129	12	eur	eur	PROPN
ejpam-6294	129	13	.	.	PUNCT
ejpam-6294	130	1	j.	j.	PROPN
ejpam-6294	130	2	pure	pure	PROPN
ejpam-6294	130	3	appl	appl	PROPN
ejpam-6294	130	4	.	.	PROPN
ejpam-6294	130	5	math	math	PROPN
ejpam-6294	130	6	,	,	PUNCT
ejpam-6294	130	7	18	18	NUM
ejpam-6294	130	8	(	(	PUNCT
ejpam-6294	130	9	3	3	NUM
ejpam-6294	130	10	)	)	PUNCT
ejpam-6294	130	11	(	(	PUNCT
ejpam-6294	130	12	2025	2025	NUM
ejpam-6294	130	13	)	)	PUNCT
ejpam-6294	130	14	,	,	PUNCT
ejpam-6294	130	15	6294	6294	NUM
ejpam-6294	130	16	7	7	NUM
ejpam-6294	130	17	of	of	ADP
ejpam-6294	130	18	19	19	NUM
ejpam-6294	130	19	a22	a22	NOUN
ejpam-6294	130	20	=	=	PROPN
ejpam-6294	130	21	u2	u2	PROPN
ejpam-6294	130	22	(	(	PUNCT
ejpam-6294	130	23	s	s	NOUN
ejpam-6294	130	24	)	)	PUNCT
ejpam-6294	130	25	+	+	CCONJ
ejpam-6294	130	26	u2	u2	PROPN
ejpam-6294	130	27	(	(	PUNCT
ejpam-6294	130	28	t	t	PROPN
ejpam-6294	130	29	)	)	PUNCT
ejpam-6294	130	30	2(1	2(1	NUM
ejpam-6294	131	1	+	+	CCONJ
ejpam-6294	131	2	τ)2	τ)2	NOUN
ejpam-6294	131	3	(	(	PUNCT
ejpam-6294	131	4	15	15	NUM
ejpam-6294	131	5	)	)	PUNCT
ejpam-6294	131	6	subtracting	subtract	VERB
ejpam-6294	131	7	the	the	DET
ejpam-6294	131	8	equations	equation	NOUN
ejpam-6294	131	9	(	(	PUNCT
ejpam-6294	131	10	11	11	NUM
ejpam-6294	131	11	)	)	PUNCT
ejpam-6294	131	12	and	and	CCONJ
ejpam-6294	131	13	(	(	PUNCT
ejpam-6294	131	14	13	13	NUM
ejpam-6294	131	15	)	)	PUNCT
ejpam-6294	131	16	,	,	PUNCT
ejpam-6294	131	17	we	we	PRON
ejpam-6294	131	18	get	get	VERB
ejpam-6294	131	19	2(1	2(1	NUM
ejpam-6294	131	20	+	+	CCONJ
ejpam-6294	131	21	2τ)a3	2τ)a3	NUM
ejpam-6294	131	22	−	−	NUM
ejpam-6294	131	23	4(1	4(1	NUM
ejpam-6294	132	1	+	+	CCONJ
ejpam-6294	132	2	2τ)a22	2τ)a22	NUM
ejpam-6294	132	3	+	+	SYM
ejpam-6294	132	4	2(1	2(1	NUM
ejpam-6294	132	5	+	+	CCONJ
ejpam-6294	132	6	2τ)a3	2τ)a3	NUM
ejpam-6294	132	7	=	=	SYM
ejpam-6294	132	8	u2	u2	NOUN
ejpam-6294	132	9	(	(	PUNCT
ejpam-6294	132	10	s)−	s)−	PROPN
ejpam-6294	132	11	u2	u2	PROPN
ejpam-6294	132	12	(	(	PUNCT
ejpam-6294	132	13	t	t	PROPN
ejpam-6294	132	14	)	)	PUNCT
ejpam-6294	132	15	+	+	NUM
ejpam-6294	132	16	2(v(s)−	2(v(s)−	NUM
ejpam-6294	132	17	v(t	v(t	NUM
ejpam-6294	132	18	)	)	PUNCT
ejpam-6294	132	19	)	)	PUNCT
ejpam-6294	132	20	4(1	4(1	X
ejpam-6294	133	1	+	+	CCONJ
ejpam-6294	133	2	2τ)a3	2τ)a3	NUM
ejpam-6294	133	3	=	=	SYM
ejpam-6294	133	4	4(1	4(1	NOUN
ejpam-6294	134	1	+	+	CCONJ
ejpam-6294	134	2	2τ)a22	2τ)a22	NUM
ejpam-6294	134	3	−	−	NOUN
ejpam-6294	135	1	u(t)2	u(t)2	PROPN
ejpam-6294	135	2	+	+	CCONJ
ejpam-6294	135	3	u2	u2	PROPN
ejpam-6294	135	4	(	(	PUNCT
ejpam-6294	135	5	s	s	NOUN
ejpam-6294	135	6	)	)	PUNCT
ejpam-6294	135	7	+	+	CCONJ
ejpam-6294	135	8	2(v(s)−	2(v(s)−	NUM
ejpam-6294	135	9	v(t	v(t	NUM
ejpam-6294	135	10	)	)	PUNCT
ejpam-6294	135	11	)	)	PUNCT
ejpam-6294	135	12	a3	a3	NOUN
ejpam-6294	135	13	=	=	SYM
ejpam-6294	135	14	a22	a22	PROPN
ejpam-6294	135	15	+	+	CCONJ
ejpam-6294	135	16	u2	u2	PROPN
ejpam-6294	135	17	(	(	PUNCT
ejpam-6294	135	18	s)−	s)−	PROPN
ejpam-6294	135	19	u2	u2	PROPN
ejpam-6294	135	20	(	(	PUNCT
ejpam-6294	135	21	t	t	PROPN
ejpam-6294	135	22	)	)	PUNCT
ejpam-6294	136	1	+	+	NUM
ejpam-6294	136	2	2(v(s)−	2(v(s)−	NUM
ejpam-6294	136	3	v(t	v(t	NUM
ejpam-6294	136	4	)	)	PUNCT
ejpam-6294	136	5	)	)	PUNCT
ejpam-6294	136	6	4(1	4(1	X
ejpam-6294	137	1	+	+	CCONJ
ejpam-6294	137	2	2τ	2τ	NUM
ejpam-6294	137	3	)	)	PUNCT
ejpam-6294	137	4	(	(	PUNCT
ejpam-6294	137	5	16	16	NUM
ejpam-6294	137	6	)	)	PUNCT
ejpam-6294	137	7	substituting	substitute	VERB
ejpam-6294	137	8	the	the	DET
ejpam-6294	137	9	equations	equation	NOUN
ejpam-6294	137	10	(	(	PUNCT
ejpam-6294	137	11	11	11	NUM
ejpam-6294	137	12	)	)	PUNCT
ejpam-6294	137	13	in	in	ADP
ejpam-6294	137	14	equation	equation	NOUN
ejpam-6294	137	15	(	(	PUNCT
ejpam-6294	137	16	13	13	NUM
ejpam-6294	137	17	)	)	PUNCT
ejpam-6294	137	18	,	,	PUNCT
ejpam-6294	137	19	we	we	PRON
ejpam-6294	137	20	get	get	VERB
ejpam-6294	137	21	(	(	PUNCT
ejpam-6294	137	22	2	2	NUM
ejpam-6294	137	23	+	+	NUM
ejpam-6294	137	24	2τ)a22	2τ)a22	NUM
ejpam-6294	137	25	=	=	SYM
ejpam-6294	137	26	u2	u2	PROPN
ejpam-6294	137	27	(	(	PUNCT
ejpam-6294	137	28	s	s	NOUN
ejpam-6294	137	29	)	)	PUNCT
ejpam-6294	137	30	+	+	CCONJ
ejpam-6294	137	31	2v(s	2v(s	NUM
ejpam-6294	137	32	)	)	PUNCT
ejpam-6294	138	1	+	+	CCONJ
ejpam-6294	138	2	u2	u2	PROPN
ejpam-6294	138	3	(	(	PUNCT
ejpam-6294	138	4	t	t	PROPN
ejpam-6294	138	5	)	)	PUNCT
ejpam-6294	138	6	+	+	CCONJ
ejpam-6294	138	7	2v(t	2v(t	NUM
ejpam-6294	138	8	)	)	PUNCT
ejpam-6294	138	9	a22	a22	PROPN
ejpam-6294	138	10	=	=	PROPN
ejpam-6294	138	11	u2	u2	PROPN
ejpam-6294	138	12	(	(	PUNCT
ejpam-6294	138	13	s	s	NOUN
ejpam-6294	138	14	)	)	PUNCT
ejpam-6294	138	15	+	+	CCONJ
ejpam-6294	138	16	u2	u2	PROPN
ejpam-6294	138	17	(	(	PUNCT
ejpam-6294	138	18	t	t	PROPN
ejpam-6294	138	19	)	)	PUNCT
ejpam-6294	138	20	+	+	NUM
ejpam-6294	138	21	2(v(s	2(v(s	NUM
ejpam-6294	138	22	)	)	PUNCT
ejpam-6294	138	23	+	+	CCONJ
ejpam-6294	138	24	v(t	v(t	NOUN
ejpam-6294	138	25	)	)	PUNCT
ejpam-6294	138	26	)	)	PUNCT
ejpam-6294	138	27	(	(	PUNCT
ejpam-6294	138	28	2	2	NUM
ejpam-6294	138	29	+	+	NUM
ejpam-6294	138	30	2τ	2τ	NUM
ejpam-6294	138	31	)	)	PUNCT
ejpam-6294	138	32	(	(	PUNCT
ejpam-6294	138	33	17	17	NUM
ejpam-6294	138	34	)	)	PUNCT
ejpam-6294	138	35	|a2|	|a2|	NOUN
ejpam-6294	138	36	≤	≤	ADJ
ejpam-6294	138	37	√	√	ADP
ejpam-6294	138	38	u2	u2	PROPN
ejpam-6294	138	39	(	(	PUNCT
ejpam-6294	138	40	s	s	NOUN
ejpam-6294	138	41	)	)	PUNCT
ejpam-6294	139	1	+	+	CCONJ
ejpam-6294	139	2	u2	u2	PROPN
ejpam-6294	139	3	(	(	PUNCT
ejpam-6294	139	4	t	t	PROPN
ejpam-6294	139	5	)	)	PUNCT
ejpam-6294	139	6	+	+	NUM
ejpam-6294	140	1	2(v(s	2(v(s	NUM
ejpam-6294	140	2	)	)	PUNCT
ejpam-6294	141	1	+	+	CCONJ
ejpam-6294	141	2	v(t	v(t	NOUN
ejpam-6294	141	3	)	)	PUNCT
ejpam-6294	141	4	)	)	PUNCT
ejpam-6294	141	5	(	(	PUNCT
ejpam-6294	141	6	2	2	NUM
ejpam-6294	141	7	+	+	NUM
ejpam-6294	141	8	2τ	2τ	NUM
ejpam-6294	141	9	)	)	PUNCT
ejpam-6294	141	10	(	(	PUNCT
ejpam-6294	141	11	18	18	NUM
ejpam-6294	141	12	)	)	PUNCT
ejpam-6294	141	13	substituting	substitute	VERB
ejpam-6294	141	14	the	the	DET
ejpam-6294	141	15	equations	equation	NOUN
ejpam-6294	141	16	(	(	PUNCT
ejpam-6294	141	17	15	15	NUM
ejpam-6294	141	18	)	)	PUNCT
ejpam-6294	141	19	in	in	ADP
ejpam-6294	141	20	equation	equation	NOUN
ejpam-6294	141	21	(	(	PUNCT
ejpam-6294	141	22	16	16	NUM
ejpam-6294	141	23	)	)	PUNCT
ejpam-6294	141	24	,	,	PUNCT
ejpam-6294	141	25	we	we	PRON
ejpam-6294	141	26	get	get	AUX
ejpam-6294	141	27	|a3|	|a3|	VERB
ejpam-6294	141	28	≤	≤	ADJ
ejpam-6294	141	29	u2	u2	PROPN
ejpam-6294	141	30	(	(	PUNCT
ejpam-6294	141	31	s	s	NOUN
ejpam-6294	141	32	)	)	PUNCT
ejpam-6294	142	1	+	+	CCONJ
ejpam-6294	142	2	u2	u2	PROPN
ejpam-6294	142	3	(	(	PUNCT
ejpam-6294	142	4	t	t	PROPN
ejpam-6294	142	5	)	)	PUNCT
ejpam-6294	142	6	2(1	2(1	NUM
ejpam-6294	143	1	+	+	CCONJ
ejpam-6294	143	2	τ)2	τ)2	NOUN
ejpam-6294	143	3	+	+	CCONJ
ejpam-6294	143	4	u2	u2	NOUN
ejpam-6294	143	5	(	(	PUNCT
ejpam-6294	143	6	s)−	s)−	PROPN
ejpam-6294	143	7	u2	u2	PROPN
ejpam-6294	143	8	(	(	PUNCT
ejpam-6294	143	9	t	t	PROPN
ejpam-6294	143	10	)	)	PUNCT
ejpam-6294	143	11	+	+	NUM
ejpam-6294	144	1	2(v(s)−	2(v(s)−	NUM
ejpam-6294	144	2	v(t	v(t	NUM
ejpam-6294	144	3	)	)	PUNCT
ejpam-6294	144	4	)	)	PUNCT
ejpam-6294	144	5	4(1	4(1	X
ejpam-6294	145	1	+	+	CCONJ
ejpam-6294	145	2	2τ	2τ	NUM
ejpam-6294	145	3	)	)	PUNCT
ejpam-6294	145	4	(	(	PUNCT
ejpam-6294	145	5	19	19	NUM
ejpam-6294	145	6	)	)	PUNCT
ejpam-6294	145	7	substituting	substitute	VERB
ejpam-6294	145	8	the	the	DET
ejpam-6294	145	9	equation	equation	NOUN
ejpam-6294	145	10	(	(	PUNCT
ejpam-6294	145	11	17	17	NUM
ejpam-6294	145	12	)	)	PUNCT
ejpam-6294	145	13	in	in	ADP
ejpam-6294	145	14	(	(	PUNCT
ejpam-6294	145	15	16	16	NUM
ejpam-6294	145	16	)	)	PUNCT
ejpam-6294	145	17	,	,	PUNCT
ejpam-6294	145	18	we	we	PRON
ejpam-6294	145	19	attain	attain	VERB
ejpam-6294	145	20	a3	a3	NOUN
ejpam-6294	145	21	=	=	PROPN
ejpam-6294	145	22	u2	u2	PROPN
ejpam-6294	145	23	(	(	PUNCT
ejpam-6294	145	24	s	s	NOUN
ejpam-6294	145	25	)	)	PUNCT
ejpam-6294	145	26	+	+	CCONJ
ejpam-6294	145	27	u2	u2	PROPN
ejpam-6294	145	28	(	(	PUNCT
ejpam-6294	145	29	t	t	PROPN
ejpam-6294	145	30	)	)	PUNCT
ejpam-6294	145	31	+	+	NUM
ejpam-6294	146	1	2(v(s	2(v(s	NUM
ejpam-6294	146	2	)	)	PUNCT
ejpam-6294	147	1	+	+	CCONJ
ejpam-6294	147	2	v(t	v(t	NOUN
ejpam-6294	147	3	)	)	PUNCT
ejpam-6294	147	4	)	)	PUNCT
ejpam-6294	147	5	(	(	PUNCT
ejpam-6294	147	6	2	2	NUM
ejpam-6294	147	7	+	+	NUM
ejpam-6294	147	8	2τ	2τ	NUM
ejpam-6294	147	9	)	)	PUNCT
ejpam-6294	148	1	+	+	CCONJ
ejpam-6294	148	2	u2	u2	PROPN
ejpam-6294	148	3	(	(	PUNCT
ejpam-6294	148	4	s)−	s)−	PROPN
ejpam-6294	148	5	u2	u2	PROPN
ejpam-6294	148	6	(	(	PUNCT
ejpam-6294	148	7	t	t	PROPN
ejpam-6294	148	8	)	)	PUNCT
ejpam-6294	148	9	+	+	NUM
ejpam-6294	148	10	2(v(s)−	2(v(s)−	NUM
ejpam-6294	148	11	v(t	v(t	NUM
ejpam-6294	148	12	)	)	PUNCT
ejpam-6294	148	13	)	)	PUNCT
ejpam-6294	148	14	4(1	4(1	X
ejpam-6294	149	1	+	+	NUM
ejpam-6294	149	2	2τ	2τ	NOUN
ejpam-6294	149	3	)	)	PUNCT
ejpam-6294	149	4	|a3|	|a3|	VERB
ejpam-6294	149	5	≤	≤	ADJ
ejpam-6294	149	6	u2	u2	PROPN
ejpam-6294	149	7	(	(	PUNCT
ejpam-6294	149	8	s	s	NOUN
ejpam-6294	149	9	)	)	PUNCT
ejpam-6294	149	10	+	+	CCONJ
ejpam-6294	149	11	2v(s	2v(s	NUM
ejpam-6294	149	12	)	)	PUNCT
ejpam-6294	149	13	(	(	PUNCT
ejpam-6294	149	14	2	2	NUM
ejpam-6294	149	15	+	+	NUM
ejpam-6294	149	16	2τ	2τ	NUM
ejpam-6294	149	17	)	)	PUNCT
ejpam-6294	149	18	(	(	PUNCT
ejpam-6294	149	19	20	20	NUM
ejpam-6294	149	20	)	)	PUNCT
ejpam-6294	149	21	hence	hence	ADV
ejpam-6294	149	22	,	,	PUNCT
ejpam-6294	149	23	|a2|	|a2|	VERB
ejpam-6294	149	24	≤	≤	ADJ
ejpam-6294	149	25	√	√	ADP
ejpam-6294	149	26	u2	u2	PROPN
ejpam-6294	149	27	(	(	PUNCT
ejpam-6294	149	28	s	s	NOUN
ejpam-6294	149	29	)	)	PUNCT
ejpam-6294	150	1	+	+	CCONJ
ejpam-6294	150	2	u2	u2	PROPN
ejpam-6294	150	3	(	(	PUNCT
ejpam-6294	150	4	t	t	PROPN
ejpam-6294	150	5	)	)	PUNCT
ejpam-6294	150	6	+	+	NUM
ejpam-6294	151	1	2(v(s	2(v(s	NUM
ejpam-6294	151	2	)	)	PUNCT
ejpam-6294	152	1	+	+	CCONJ
ejpam-6294	152	2	v(t	v(t	NOUN
ejpam-6294	152	3	)	)	PUNCT
ejpam-6294	152	4	)	)	PUNCT
ejpam-6294	152	5	(	(	PUNCT
ejpam-6294	152	6	2	2	NUM
ejpam-6294	152	7	+	+	NUM
ejpam-6294	152	8	2τ	2τ	NUM
ejpam-6294	152	9	)	)	PUNCT
ejpam-6294	152	10	and	and	CCONJ
ejpam-6294	152	11	|a3|	|a3|	VERB
ejpam-6294	152	12	≤	≤	ADJ
ejpam-6294	152	13	u2	u2	PROPN
ejpam-6294	152	14	(	(	PUNCT
ejpam-6294	152	15	s	s	NOUN
ejpam-6294	152	16	)	)	PUNCT
ejpam-6294	153	1	+	+	CCONJ
ejpam-6294	153	2	u2	u2	PROPN
ejpam-6294	153	3	(	(	PUNCT
ejpam-6294	153	4	t	t	PROPN
ejpam-6294	153	5	)	)	PUNCT
ejpam-6294	153	6	2(1	2(1	NUM
ejpam-6294	154	1	+	+	CCONJ
ejpam-6294	154	2	τ)2	τ)2	NOUN
ejpam-6294	154	3	+	+	CCONJ
ejpam-6294	154	4	u2	u2	NOUN
ejpam-6294	154	5	(	(	PUNCT
ejpam-6294	154	6	s)−	s)−	PROPN
ejpam-6294	154	7	u2	u2	PROPN
ejpam-6294	154	8	(	(	PUNCT
ejpam-6294	154	9	t	t	PROPN
ejpam-6294	154	10	)	)	PUNCT
ejpam-6294	154	11	+	+	NUM
ejpam-6294	155	1	2(v(s)−	2(v(s)−	NUM
ejpam-6294	155	2	v(t	v(t	NUM
ejpam-6294	155	3	)	)	PUNCT
ejpam-6294	155	4	)	)	PUNCT
ejpam-6294	155	5	4(1	4(1	X
ejpam-6294	156	1	+	+	NUM
ejpam-6294	156	2	2τ	2τ	NOUN
ejpam-6294	156	3	)	)	PUNCT
ejpam-6294	156	4	specializing	specialize	VERB
ejpam-6294	156	5	the	the	DET
ejpam-6294	156	6	parameter	parameter	NOUN
ejpam-6294	156	7	values	value	NOUN
ejpam-6294	156	8	of	of	ADP
ejpam-6294	156	9	τ	τ	PROPN
ejpam-6294	156	10	=	=	SYM
ejpam-6294	156	11	0	0	PROPN
ejpam-6294	156	12	and	and	CCONJ
ejpam-6294	156	13	τ	τ	X
ejpam-6294	156	14	=	=	NOUN
ejpam-6294	156	15	1	1	NUM
ejpam-6294	156	16	in	in	ADP
ejpam-6294	156	17	the	the	DET
ejpam-6294	156	18	above	above	ADJ
ejpam-6294	156	19	theorem	theorem	NOUN
ejpam-6294	156	20	(	(	PUNCT
ejpam-6294	156	21	1	1	NUM
ejpam-6294	156	22	)	)	PUNCT
ejpam-6294	156	23	,	,	PUNCT
ejpam-6294	156	24	then	then	ADV
ejpam-6294	156	25	the	the	DET
ejpam-6294	156	26	subsequent	subsequent	ADJ
ejpam-6294	156	27	corollaries	corollary	NOUN
ejpam-6294	156	28	are	be	AUX
ejpam-6294	156	29	obtained	obtain	VERB
ejpam-6294	156	30	,	,	PUNCT
ejpam-6294	156	31	in	in	ADP
ejpam-6294	156	32	that	that	DET
ejpam-6294	156	33	order	order	NOUN
ejpam-6294	156	34	.	.	PUNCT
ejpam-6294	157	1	s.	s.	PROPN
ejpam-6294	157	2	thangamani	thangamani	PROPN
ejpam-6294	157	3	et	et	PROPN
ejpam-6294	157	4	al	al	PROPN
ejpam-6294	157	5	.	.	PUNCT
ejpam-6294	157	6	/	/	SYM
ejpam-6294	157	7	eur	eur	PROPN
ejpam-6294	157	8	.	.	PUNCT
ejpam-6294	158	1	j.	j.	PROPN
ejpam-6294	158	2	pure	pure	PROPN
ejpam-6294	158	3	appl	appl	PROPN
ejpam-6294	158	4	.	.	PROPN
ejpam-6294	158	5	math	math	PROPN
ejpam-6294	158	6	,	,	PUNCT
ejpam-6294	158	7	18	18	NUM
ejpam-6294	158	8	(	(	PUNCT
ejpam-6294	158	9	3	3	NUM
ejpam-6294	158	10	)	)	PUNCT
ejpam-6294	158	11	(	(	PUNCT
ejpam-6294	158	12	2025	2025	NUM
ejpam-6294	158	13	)	)	PUNCT
ejpam-6294	158	14	,	,	PUNCT
ejpam-6294	158	15	6294	6294	NUM
ejpam-6294	158	16	8	8	NUM
ejpam-6294	158	17	of	of	ADP
ejpam-6294	158	18	19	19	NUM
ejpam-6294	158	19	corollary	corollary	ADJ
ejpam-6294	158	20	1	1	NUM
ejpam-6294	158	21	.	.	PUNCT
ejpam-6294	159	1	if	if	SCONJ
ejpam-6294	159	2	f	f	PROPN
ejpam-6294	159	3	(	(	PUNCT
ejpam-6294	159	4	θ	θ	NOUN
ejpam-6294	159	5	)	)	PUNCT
ejpam-6294	159	6	is	be	AUX
ejpam-6294	159	7	derived	derive	VERB
ejpam-6294	159	8	by	by	ADP
ejpam-6294	159	9	(	(	PUNCT
ejpam-6294	159	10	1	1	X
ejpam-6294	159	11	)	)	PUNCT
ejpam-6294	159	12	which	which	PRON
ejpam-6294	159	13	is	be	AUX
ejpam-6294	159	14	belongs	belong	VERB
ejpam-6294	159	15	to	to	ADP
ejpam-6294	159	16	class	class	NOUN
ejpam-6294	159	17	gς	gς	PROPN
ejpam-6294	159	18	,	,	PUNCT
ejpam-6294	159	19	g	g	PROPN
ejpam-6294	159	20	u	u	PROPN
ejpam-6294	159	21	,	,	PUNCT
ejpam-6294	159	22	v	v	PROPN
ejpam-6294	159	23	(	(	PUNCT
ejpam-6294	159	24	τ	τ	PROPN
ejpam-6294	159	25	)	)	PUNCT
ejpam-6294	159	26	.	.	PUNCT
ejpam-6294	160	1	then	then	ADV
ejpam-6294	160	2	|a2|	|a2|	VERB
ejpam-6294	160	3	≤	≤	ADJ
ejpam-6294	160	4	√	√	ADP
ejpam-6294	160	5	u2	u2	PROPN
ejpam-6294	160	6	(	(	PUNCT
ejpam-6294	160	7	s	s	NOUN
ejpam-6294	160	8	)	)	PUNCT
ejpam-6294	160	9	+	+	CCONJ
ejpam-6294	160	10	u2	u2	PROPN
ejpam-6294	160	11	(	(	PUNCT
ejpam-6294	160	12	t	t	PROPN
ejpam-6294	160	13	)	)	PUNCT
ejpam-6294	160	14	+	+	NUM
ejpam-6294	160	15	2(v(s	2(v(s	NUM
ejpam-6294	160	16	)	)	PUNCT
ejpam-6294	161	1	+	+	CCONJ
ejpam-6294	161	2	v(t	v(t	NOUN
ejpam-6294	161	3	)	)	PUNCT
ejpam-6294	161	4	)	)	PUNCT
ejpam-6294	161	5	2	2	NUM
ejpam-6294	161	6	and	and	CCONJ
ejpam-6294	161	7	|a3|	|a3|	VERB
ejpam-6294	161	8	≤	≤	ADJ
ejpam-6294	161	9	u2	u2	PROPN
ejpam-6294	161	10	(	(	PUNCT
ejpam-6294	161	11	s	s	NOUN
ejpam-6294	161	12	)	)	PUNCT
ejpam-6294	162	1	+	+	CCONJ
ejpam-6294	162	2	u2	u2	PROPN
ejpam-6294	162	3	(	(	PUNCT
ejpam-6294	162	4	t	t	PROPN
ejpam-6294	162	5	)	)	PUNCT
ejpam-6294	162	6	2	2	NUM
ejpam-6294	162	7	+	+	CCONJ
ejpam-6294	162	8	u2	u2	PROPN
ejpam-6294	162	9	(	(	PUNCT
ejpam-6294	162	10	s)−	s)−	PROPN
ejpam-6294	162	11	u2	u2	PROPN
ejpam-6294	162	12	(	(	PUNCT
ejpam-6294	162	13	t	t	PROPN
ejpam-6294	162	14	)	)	PUNCT
ejpam-6294	162	15	+	+	NUM
ejpam-6294	162	16	2(v(s)−	2(v(s)−	NUM
ejpam-6294	162	17	v(t	v(t	NUM
ejpam-6294	162	18	)	)	PUNCT
ejpam-6294	162	19	)	)	PUNCT
ejpam-6294	162	20	4	4	NUM
ejpam-6294	162	21	corollary	corollary	NOUN
ejpam-6294	162	22	2	2	NUM
ejpam-6294	162	23	.	.	PUNCT
ejpam-6294	163	1	if	if	SCONJ
ejpam-6294	163	2	the	the	DET
ejpam-6294	163	3	function	function	NOUN
ejpam-6294	163	4	f	f	X
ejpam-6294	163	5	(	(	PUNCT
ejpam-6294	163	6	θ	θ	NOUN
ejpam-6294	163	7	)	)	PUNCT
ejpam-6294	163	8	∈	∈	PROPN
ejpam-6294	163	9	gς	gς	NOUN
ejpam-6294	163	10	,	,	PUNCT
ejpam-6294	163	11	g	g	PROPN
ejpam-6294	163	12	u	u	PROPN
ejpam-6294	163	13	,	,	PUNCT
ejpam-6294	163	14	v	v	PROPN
ejpam-6294	163	15	(	(	PUNCT
ejpam-6294	163	16	τ	τ	PROPN
ejpam-6294	163	17	)	)	PUNCT
ejpam-6294	163	18	.	.	PUNCT
ejpam-6294	164	1	then	then	ADV
ejpam-6294	164	2	|a2|	|a2|	VERB
ejpam-6294	164	3	≤	≤	ADJ
ejpam-6294	164	4	√	√	ADP
ejpam-6294	164	5	u2	u2	PROPN
ejpam-6294	164	6	(	(	PUNCT
ejpam-6294	164	7	s	s	NOUN
ejpam-6294	164	8	)	)	PUNCT
ejpam-6294	164	9	+	+	CCONJ
ejpam-6294	164	10	u2	u2	PROPN
ejpam-6294	164	11	(	(	PUNCT
ejpam-6294	164	12	t	t	PROPN
ejpam-6294	164	13	)	)	PUNCT
ejpam-6294	164	14	+	+	NUM
ejpam-6294	164	15	2(v(s	2(v(s	NUM
ejpam-6294	164	16	)	)	PUNCT
ejpam-6294	165	1	+	+	CCONJ
ejpam-6294	165	2	v(t	v(t	NOUN
ejpam-6294	165	3	)	)	PUNCT
ejpam-6294	165	4	)	)	PUNCT
ejpam-6294	165	5	4	4	NUM
ejpam-6294	165	6	and	and	CCONJ
ejpam-6294	165	7	|a3|	|a3|	VERB
ejpam-6294	165	8	≤	≤	ADJ
ejpam-6294	165	9	u2	u2	PROPN
ejpam-6294	165	10	(	(	PUNCT
ejpam-6294	165	11	s	s	NOUN
ejpam-6294	165	12	)	)	PUNCT
ejpam-6294	166	1	+	+	CCONJ
ejpam-6294	166	2	u2	u2	PROPN
ejpam-6294	166	3	(	(	PUNCT
ejpam-6294	166	4	t	t	PROPN
ejpam-6294	166	5	)	)	PUNCT
ejpam-6294	166	6	8	8	NUM
ejpam-6294	167	1	+	+	CCONJ
ejpam-6294	167	2	u2	u2	PROPN
ejpam-6294	167	3	(	(	PUNCT
ejpam-6294	167	4	s)−	s)−	PROPN
ejpam-6294	167	5	u2	u2	PROPN
ejpam-6294	167	6	(	(	PUNCT
ejpam-6294	167	7	t	t	PROPN
ejpam-6294	167	8	)	)	PUNCT
ejpam-6294	167	9	+	+	NUM
ejpam-6294	167	10	2(v(s)−	2(v(s)−	NUM
ejpam-6294	167	11	v(t	v(t	NUM
ejpam-6294	167	12	)	)	PUNCT
ejpam-6294	167	13	)	)	PUNCT
ejpam-6294	167	14	12	12	NUM
ejpam-6294	167	15	3	3	NUM
ejpam-6294	167	16	.	.	PUNCT
ejpam-6294	167	17	fekete	fekete	NOUN
ejpam-6294	167	18	-	-	PUNCT
ejpam-6294	167	19	szegö	szegö	PROPN
ejpam-6294	167	20	inequality	inequality	NOUN
ejpam-6294	167	21	for	for	ADP
ejpam-6294	167	22	the	the	DET
ejpam-6294	167	23	subclass	subclass	NOUN
ejpam-6294	167	24	gς	gς	NOUN
ejpam-6294	167	25	,	,	PUNCT
ejpam-6294	167	26	g	g	PROPN
ejpam-6294	167	27	u	u	PROPN
ejpam-6294	167	28	,	,	PUNCT
ejpam-6294	167	29	v	v	PROPN
ejpam-6294	167	30	(	(	PUNCT
ejpam-6294	167	31	τ	τ	NOUN
ejpam-6294	167	32	)	)	PUNCT
ejpam-6294	167	33	theorem	theorem	NOUN
ejpam-6294	167	34	2	2	NUM
ejpam-6294	167	35	.	.	X
ejpam-6294	167	36	assume	assume	VERB
ejpam-6294	167	37	f	f	PROPN
ejpam-6294	167	38	(	(	PUNCT
ejpam-6294	167	39	θ	θ	NOUN
ejpam-6294	167	40	)	)	PUNCT
ejpam-6294	167	41	is	be	AUX
ejpam-6294	167	42	provided	provide	VERB
ejpam-6294	167	43	by	by	ADP
ejpam-6294	167	44	(	(	PUNCT
ejpam-6294	167	45	1	1	NUM
ejpam-6294	167	46	)	)	PUNCT
ejpam-6294	167	47	and	and	CCONJ
ejpam-6294	167	48	is	be	AUX
ejpam-6294	167	49	a	a	DET
ejpam-6294	167	50	member	member	NOUN
ejpam-6294	167	51	of	of	ADP
ejpam-6294	167	52	the	the	DET
ejpam-6294	167	53	class	class	NOUN
ejpam-6294	167	54	gς	gς	PROPN
ejpam-6294	167	55	,	,	PUNCT
ejpam-6294	167	56	g	g	PROPN
ejpam-6294	167	57	u	u	PROPN
ejpam-6294	167	58	,	,	PUNCT
ejpam-6294	167	59	v	v	PROPN
ejpam-6294	167	60	(	(	PUNCT
ejpam-6294	167	61	τ	τ	PROPN
ejpam-6294	167	62	)	)	PUNCT
ejpam-6294	167	63	.	.	PUNCT
ejpam-6294	168	1	then	then	ADV
ejpam-6294	168	2	|a3	|a3	VERB
ejpam-6294	168	3	−	−	PROPN
ejpam-6294	168	4	ηa22|	ηa22|	NOUN
ejpam-6294	168	5	≤	≤	NUM
ejpam-6294	168	6	{	{	PUNCT
ejpam-6294	168	7	v(s	v(s	NOUN
ejpam-6294	168	8	)	)	PUNCT
ejpam-6294	168	9	(	(	PUNCT
ejpam-6294	168	10	2	2	NUM
ejpam-6294	168	11	+	+	NOUN
ejpam-6294	168	12	2τ	2τ	NUM
ejpam-6294	168	13	)	)	PUNCT
ejpam-6294	168	14	if	if	SCONJ
ejpam-6294	168	15	0	0	NUM
ejpam-6294	168	16	≤	≤	NUM
ejpam-6294	168	17	|h1(η)|	|h1(η)|	NOUN
ejpam-6294	168	18	≤	≤	NUM
ejpam-6294	168	19	1	1	NUM
ejpam-6294	168	20	(	(	PUNCT
ejpam-6294	168	21	2	2	NUM
ejpam-6294	168	22	+	+	NUM
ejpam-6294	168	23	2τ	2τ	NUM
ejpam-6294	168	24	)	)	PUNCT
ejpam-6294	168	25	,	,	PUNCT
ejpam-6294	168	26	v(s)|	v(s)|	X
ejpam-6294	168	27	2(1−η	2(1−η	NUM
ejpam-6294	168	28	)	)	PUNCT
ejpam-6294	168	29	(	(	PUNCT
ejpam-6294	168	30	2	2	NUM
ejpam-6294	168	31	+	+	NOUN
ejpam-6294	168	32	2τ)−4(1+τ)2	2τ)−4(1+τ)2	NOUN
ejpam-6294	168	33	|	|	ADV
ejpam-6294	168	34	if	if	SCONJ
ejpam-6294	168	35	|h1(η)|	|h1(η)|	NUM
ejpam-6294	168	36	≥	≥	NOUN
ejpam-6294	168	37	1	1	NUM
ejpam-6294	168	38	(	(	PUNCT
ejpam-6294	168	39	2	2	NUM
ejpam-6294	168	40	+	+	NUM
ejpam-6294	168	41	2τ	2τ	NUM
ejpam-6294	168	42	)	)	PUNCT
ejpam-6294	168	43	,	,	PUNCT
ejpam-6294	168	44	(	(	PUNCT
ejpam-6294	168	45	21	21	NUM
ejpam-6294	168	46	)	)	PUNCT
ejpam-6294	168	47	where	where	SCONJ
ejpam-6294	168	48	h1(η	h1(η	X
ejpam-6294	168	49	)	)	PUNCT
ejpam-6294	168	50	=	=	SYM
ejpam-6294	168	51	(	(	PUNCT
ejpam-6294	168	52	1−	1−	NUM
ejpam-6294	168	53	η	η	NOUN
ejpam-6294	168	54	)	)	PUNCT
ejpam-6294	168	55	(	(	PUNCT
ejpam-6294	168	56	2	2	NUM
ejpam-6294	168	57	+	+	NUM
ejpam-6294	168	58	2τ)−	2τ)−	NUM
ejpam-6294	168	59	4(1	4(1	NOUN
ejpam-6294	168	60	+	+	CCONJ
ejpam-6294	168	61	τ)2	τ)2	NOUN
ejpam-6294	168	62	.	.	PUNCT
ejpam-6294	169	1	proof	proof	NOUN
ejpam-6294	169	2	.	.	PUNCT
ejpam-6294	170	1	from	from	ADP
ejpam-6294	170	2	the	the	DET
ejpam-6294	170	3	equation	equation	NOUN
ejpam-6294	170	4	(	(	PUNCT
ejpam-6294	170	5	16	16	NUM
ejpam-6294	170	6	)	)	PUNCT
ejpam-6294	170	7	and	and	CCONJ
ejpam-6294	170	8	(	(	PUNCT
ejpam-6294	170	9	17	17	NUM
ejpam-6294	170	10	)	)	PUNCT
ejpam-6294	170	11	,	,	PUNCT
ejpam-6294	170	12	we	we	PRON
ejpam-6294	170	13	get	get	VERB
ejpam-6294	170	14	a3	a3	NOUN
ejpam-6294	170	15	−	−	PROPN
ejpam-6294	171	1	ηa22	ηa22	PROPN
ejpam-6294	171	2	=	=	PUNCT
ejpam-6294	171	3	a22	a22	PROPN
ejpam-6294	171	4	+	+	CCONJ
ejpam-6294	171	5	u2	u2	PROPN
ejpam-6294	171	6	(	(	PUNCT
ejpam-6294	171	7	s)−	s)−	PROPN
ejpam-6294	171	8	u2	u2	PROPN
ejpam-6294	171	9	(	(	PUNCT
ejpam-6294	171	10	t	t	PROPN
ejpam-6294	171	11	)	)	PUNCT
ejpam-6294	171	12	+	+	NUM
ejpam-6294	171	13	2(v(s)−	2(v(s)−	NUM
ejpam-6294	171	14	v(t	v(t	NUM
ejpam-6294	171	15	)	)	PUNCT
ejpam-6294	171	16	)	)	PUNCT
ejpam-6294	171	17	4(1	4(1	NOUN
ejpam-6294	172	1	+	+	CCONJ
ejpam-6294	172	2	τ)2	τ)2	NOUN
ejpam-6294	172	3	−	−	PROPN
ejpam-6294	172	4	ηa22	ηa22	PROPN
ejpam-6294	172	5	a3	a3	NOUN
ejpam-6294	172	6	−	−	PROPN
ejpam-6294	173	1	ηa22	ηa22	PROPN
ejpam-6294	173	2	=	=	SYM
ejpam-6294	173	3	(	(	PUNCT
ejpam-6294	173	4	1−	1−	NUM
ejpam-6294	173	5	η)a22	η)a22	PROPN
ejpam-6294	173	6	+	+	NUM
ejpam-6294	173	7	u2	u2	PROPN
ejpam-6294	173	8	(	(	PUNCT
ejpam-6294	173	9	s)−	s)−	PROPN
ejpam-6294	173	10	u2	u2	PROPN
ejpam-6294	173	11	(	(	PUNCT
ejpam-6294	173	12	t	t	PROPN
ejpam-6294	173	13	)	)	PUNCT
ejpam-6294	173	14	+	+	NUM
ejpam-6294	173	15	2(v(s)−	2(v(s)−	NUM
ejpam-6294	173	16	v(t	v(t	NUM
ejpam-6294	173	17	)	)	PUNCT
ejpam-6294	173	18	)	)	PUNCT
ejpam-6294	173	19	4(1	4(1	NOUN
ejpam-6294	174	1	+	+	CCONJ
ejpam-6294	174	2	τ)2	τ)2	PROPN
ejpam-6294	174	3	a3	a3	NOUN
ejpam-6294	174	4	−	−	PROPN
ejpam-6294	175	1	ηa22	ηa22	PROPN
ejpam-6294	175	2	=	=	SYM
ejpam-6294	175	3	(	(	PUNCT
ejpam-6294	175	4	1−	1−	NUM
ejpam-6294	175	5	η	η	NOUN
ejpam-6294	175	6	)	)	PUNCT
ejpam-6294	175	7	2(v(s	2(v(s	NUM
ejpam-6294	175	8	)	)	PUNCT
ejpam-6294	175	9	+	+	CCONJ
ejpam-6294	175	10	v(t	v(t	NUM
ejpam-6294	175	11	)	)	PUNCT
ejpam-6294	175	12	(	(	PUNCT
ejpam-6294	175	13	2	2	NUM
ejpam-6294	175	14	+	+	SYM
ejpam-6294	175	15	2τ))−	2τ))−	NUM
ejpam-6294	175	16	4(1	4(1	NOUN
ejpam-6294	175	17	+	+	CCONJ
ejpam-6294	175	18	τ)2	τ)2	NOUN
ejpam-6294	175	19	+	+	CCONJ
ejpam-6294	175	20	u2	u2	NOUN
ejpam-6294	175	21	(	(	PUNCT
ejpam-6294	175	22	s)−	s)−	PROPN
ejpam-6294	175	23	u2	u2	PROPN
ejpam-6294	175	24	(	(	PUNCT
ejpam-6294	175	25	t	t	PROPN
ejpam-6294	175	26	)	)	PUNCT
ejpam-6294	175	27	+	+	NUM
ejpam-6294	175	28	2(v(s)−	2(v(s)−	NUM
ejpam-6294	175	29	v(t	v(t	NUM
ejpam-6294	175	30	)	)	PUNCT
ejpam-6294	175	31	)	)	PUNCT
ejpam-6294	175	32	4(1	4(1	NOUN
ejpam-6294	176	1	+	+	CCONJ
ejpam-6294	176	2	τ)2	τ)2	PROPN
ejpam-6294	176	3	a3	a3	NOUN
ejpam-6294	176	4	−	−	PROPN
ejpam-6294	177	1	ηa22	ηa22	PROPN
ejpam-6294	177	2	=	=	SYM
ejpam-6294	177	3	(	(	PUNCT
ejpam-6294	177	4	1−	1−	NUM
ejpam-6294	177	5	η	η	NOUN
ejpam-6294	177	6	)	)	PUNCT
ejpam-6294	177	7	2v(s	2v(s	NUM
ejpam-6294	177	8	)	)	PUNCT
ejpam-6294	177	9	(	(	PUNCT
ejpam-6294	177	10	2	2	NUM
ejpam-6294	177	11	+	+	NUM
ejpam-6294	177	12	2τ)−	2τ)−	NUM
ejpam-6294	177	13	4(1	4(1	NOUN
ejpam-6294	177	14	+	+	CCONJ
ejpam-6294	177	15	τ)2	τ)2	NOUN
ejpam-6294	177	16	+	+	CCONJ
ejpam-6294	177	17	u2	u2	NOUN
ejpam-6294	177	18	(	(	PUNCT
ejpam-6294	177	19	s)−	s)−	PROPN
ejpam-6294	177	20	u2	u2	PROPN
ejpam-6294	177	21	(	(	PUNCT
ejpam-6294	177	22	t	t	PROPN
ejpam-6294	177	23	)	)	PUNCT
ejpam-6294	177	24	4(1	4(1	NOUN
ejpam-6294	178	1	+	+	CCONJ
ejpam-6294	178	2	τ)2	τ)2	NOUN
ejpam-6294	178	3	+	+	CCONJ
ejpam-6294	178	4	2(v(s)−	2(v(s)−	NUM
ejpam-6294	178	5	v(t	v(t	NUM
ejpam-6294	178	6	)	)	PUNCT
ejpam-6294	178	7	)	)	PUNCT
ejpam-6294	178	8	4(1	4(1	NOUN
ejpam-6294	179	1	+	+	CCONJ
ejpam-6294	179	2	τ)2	τ)2	PROPN
ejpam-6294	179	3	a3	a3	NOUN
ejpam-6294	179	4	−	−	PROPN
ejpam-6294	179	5	ηa22	ηa22	PROPN
ejpam-6294	179	6	=	=	SYM
ejpam-6294	179	7	v(s	v(s	PROPN
ejpam-6294	179	8	)	)	PUNCT
ejpam-6294	179	9	(	(	PUNCT
ejpam-6294	179	10	2(1−	2(1−	NUM
ejpam-6294	179	11	η	η	NOUN
ejpam-6294	179	12	)	)	PUNCT
ejpam-6294	179	13	(	(	PUNCT
ejpam-6294	179	14	2	2	NUM
ejpam-6294	179	15	+	+	NUM
ejpam-6294	179	16	2τ)−	2τ)−	NUM
ejpam-6294	179	17	4(1	4(1	NOUN
ejpam-6294	179	18	+	+	CCONJ
ejpam-6294	179	19	τ)2	τ)2	NOUN
ejpam-6294	179	20	+	+	CCONJ
ejpam-6294	179	21	1	1	NUM
ejpam-6294	179	22	2(1	2(1	NUM
ejpam-6294	179	23	+	+	CCONJ
ejpam-6294	179	24	τ)2	τ)2	NOUN
ejpam-6294	179	25	)	)	PUNCT
ejpam-6294	180	1	+	+	CCONJ
ejpam-6294	180	2	v(t	v(t	NUM
ejpam-6294	180	3	)	)	PUNCT
ejpam-6294	180	4	(	(	PUNCT
ejpam-6294	180	5	2(1−	2(1−	NUM
ejpam-6294	180	6	η	η	NOUN
ejpam-6294	180	7	)	)	PUNCT
ejpam-6294	180	8	(	(	PUNCT
ejpam-6294	180	9	2	2	NUM
ejpam-6294	180	10	+	+	NUM
ejpam-6294	180	11	2τ)−	2τ)−	NUM
ejpam-6294	180	12	4(1	4(1	NOUN
ejpam-6294	180	13	+	+	CCONJ
ejpam-6294	180	14	τ)2	τ)2	NOUN
ejpam-6294	180	15	−	−	NUM
ejpam-6294	180	16	1	1	NUM
ejpam-6294	180	17	2(1	2(1	NUM
ejpam-6294	180	18	+	+	CCONJ
ejpam-6294	180	19	τ)2	τ)2	NOUN
ejpam-6294	180	20	)	)	PUNCT
ejpam-6294	180	21	s.	s.	PROPN
ejpam-6294	180	22	thangamani	thangamani	PROPN
ejpam-6294	180	23	et	et	PROPN
ejpam-6294	180	24	al	al	PROPN
ejpam-6294	180	25	.	.	PUNCT
ejpam-6294	180	26	/	/	SYM
ejpam-6294	180	27	eur	eur	PROPN
ejpam-6294	180	28	.	.	PUNCT
ejpam-6294	181	1	j.	j.	PROPN
ejpam-6294	181	2	pure	pure	PROPN
ejpam-6294	181	3	appl	appl	PROPN
ejpam-6294	181	4	.	.	PROPN
ejpam-6294	181	5	math	math	PROPN
ejpam-6294	181	6	,	,	PUNCT
ejpam-6294	181	7	18	18	NUM
ejpam-6294	181	8	(	(	PUNCT
ejpam-6294	181	9	3	3	NUM
ejpam-6294	181	10	)	)	PUNCT
ejpam-6294	181	11	(	(	PUNCT
ejpam-6294	181	12	2025	2025	NUM
ejpam-6294	181	13	)	)	PUNCT
ejpam-6294	181	14	,	,	PUNCT
ejpam-6294	181	15	6294	6294	NUM
ejpam-6294	181	16	9	9	NUM
ejpam-6294	181	17	of	of	ADP
ejpam-6294	181	18	19	19	NUM
ejpam-6294	181	19	+	+	CCONJ
ejpam-6294	181	20	u2	u2	PROPN
ejpam-6294	181	21	(	(	PUNCT
ejpam-6294	181	22	s)−	s)−	PROPN
ejpam-6294	181	23	u2	u2	PROPN
ejpam-6294	181	24	(	(	PUNCT
ejpam-6294	181	25	t	t	PROPN
ejpam-6294	181	26	)	)	PUNCT
ejpam-6294	181	27	4(1	4(1	NOUN
ejpam-6294	182	1	+	+	CCONJ
ejpam-6294	182	2	τ)2	τ)2	PROPN
ejpam-6294	182	3	a3	a3	NOUN
ejpam-6294	182	4	−	−	PROPN
ejpam-6294	182	5	ηa22	ηa22	PROPN
ejpam-6294	182	6	=	=	SYM
ejpam-6294	182	7	v(s	v(s	PROPN
ejpam-6294	182	8	)	)	PUNCT
ejpam-6294	182	9	(	(	PUNCT
ejpam-6294	182	10	h1(η	h1(η	PROPN
ejpam-6294	182	11	)	)	PUNCT
ejpam-6294	182	12	+	+	CCONJ
ejpam-6294	182	13	1	1	NUM
ejpam-6294	182	14	2(1	2(1	NUM
ejpam-6294	182	15	+	+	CCONJ
ejpam-6294	182	16	τ)2	τ)2	NOUN
ejpam-6294	182	17	)	)	PUNCT
ejpam-6294	183	1	+	+	CCONJ
ejpam-6294	184	1	v(t	v(t	NUM
ejpam-6294	184	2	)	)	PUNCT
ejpam-6294	184	3	(	(	PUNCT
ejpam-6294	184	4	h1(η)−	h1(η)−	NOUN
ejpam-6294	184	5	1	1	NUM
ejpam-6294	184	6	2(1	2(1	NUM
ejpam-6294	184	7	+	+	CCONJ
ejpam-6294	184	8	τ)2	τ)2	NOUN
ejpam-6294	184	9	)	)	PUNCT
ejpam-6294	185	1	where	where	SCONJ
ejpam-6294	185	2	h1(η	h1(η	X
ejpam-6294	185	3	)	)	PUNCT
ejpam-6294	185	4	=	=	SYM
ejpam-6294	186	1	2(1−	2(1−	NUM
ejpam-6294	186	2	η	η	NOUN
ejpam-6294	186	3	)	)	PUNCT
ejpam-6294	186	4	(	(	PUNCT
ejpam-6294	186	5	2	2	NUM
ejpam-6294	186	6	+	+	NUM
ejpam-6294	186	7	2τ)−	2τ)−	NUM
ejpam-6294	186	8	4(1	4(1	NOUN
ejpam-6294	186	9	+	+	CCONJ
ejpam-6294	186	10	τ)2	τ)2	NOUN
ejpam-6294	186	11	(	(	PUNCT
ejpam-6294	186	12	22	22	NUM
ejpam-6294	186	13	)	)	PUNCT
ejpam-6294	186	14	hence	hence	ADV
ejpam-6294	186	15	,	,	PUNCT
ejpam-6294	186	16	|a3	|a3	VERB
ejpam-6294	186	17	−	−	PROPN
ejpam-6294	186	18	ηa22|	ηa22|	NOUN
ejpam-6294	186	19	≤	≤	NUM
ejpam-6294	186	20	{	{	PUNCT
ejpam-6294	186	21	v(s	v(s	NOUN
ejpam-6294	186	22	)	)	PUNCT
ejpam-6294	186	23	(	(	PUNCT
ejpam-6294	187	1	2	2	NUM
ejpam-6294	187	2	+	+	NOUN
ejpam-6294	187	3	2τ	2τ	NUM
ejpam-6294	187	4	)	)	PUNCT
ejpam-6294	188	1	if	if	SCONJ
ejpam-6294	188	2	0	0	NUM
ejpam-6294	188	3	≤	≤	NUM
ejpam-6294	188	4	|h1(η)|	|h1(η)|	NOUN
ejpam-6294	188	5	≤	≤	NUM
ejpam-6294	188	6	1	1	NUM
ejpam-6294	188	7	(	(	PUNCT
ejpam-6294	188	8	2	2	NUM
ejpam-6294	188	9	+	+	NUM
ejpam-6294	188	10	2τ	2τ	NUM
ejpam-6294	188	11	)	)	PUNCT
ejpam-6294	188	12	,	,	PUNCT
ejpam-6294	188	13	v(s)|	v(s)|	X
ejpam-6294	188	14	2(1−η	2(1−η	NUM
ejpam-6294	188	15	)	)	PUNCT
ejpam-6294	188	16	(	(	PUNCT
ejpam-6294	188	17	2	2	NUM
ejpam-6294	188	18	+	+	NOUN
ejpam-6294	188	19	2τ)−4(1+τ)2	2τ)−4(1+τ)2	NOUN
ejpam-6294	188	20	|	|	ADV
ejpam-6294	188	21	if	if	SCONJ
ejpam-6294	188	22	|h1(η)|	|h1(η)|	NUM
ejpam-6294	188	23	≥	≥	NOUN
ejpam-6294	188	24	1	1	NUM
ejpam-6294	188	25	(	(	PUNCT
ejpam-6294	188	26	2	2	NUM
ejpam-6294	188	27	+	+	NUM
ejpam-6294	188	28	2τ	2τ	NUM
ejpam-6294	188	29	)	)	PUNCT
ejpam-6294	188	30	.	.	PUNCT
ejpam-6294	189	1	specializing	specialize	VERB
ejpam-6294	189	2	the	the	DET
ejpam-6294	189	3	parameter	parameter	NOUN
ejpam-6294	189	4	values	value	NOUN
ejpam-6294	189	5	of	of	ADP
ejpam-6294	189	6	τ	τ	PROPN
ejpam-6294	189	7	=	=	SYM
ejpam-6294	189	8	0	0	PROPN
ejpam-6294	189	9	and	and	CCONJ
ejpam-6294	189	10	τ	τ	X
ejpam-6294	189	11	=	=	NOUN
ejpam-6294	189	12	1	1	NUM
ejpam-6294	189	13	in	in	ADP
ejpam-6294	189	14	the	the	DET
ejpam-6294	189	15	theorem	theorem	NOUN
ejpam-6294	189	16	(	(	PUNCT
ejpam-6294	189	17	2	2	NUM
ejpam-6294	189	18	)	)	PUNCT
ejpam-6294	189	19	,	,	PUNCT
ejpam-6294	189	20	we	we	PRON
ejpam-6294	189	21	obtain	obtain	VERB
ejpam-6294	189	22	the	the	DET
ejpam-6294	189	23	following	follow	VERB
ejpam-6294	189	24	corollaries	corollary	NOUN
ejpam-6294	189	25	respectively	respectively	ADV
ejpam-6294	189	26	.	.	PUNCT
ejpam-6294	190	1	corollary	corollary	ADJ
ejpam-6294	190	2	3	3	PROPN
ejpam-6294	190	3	.	.	PUNCT
ejpam-6294	190	4	suppose	suppose	VERB
ejpam-6294	190	5	that	that	SCONJ
ejpam-6294	190	6	f	f	PROPN
ejpam-6294	190	7	(	(	PUNCT
ejpam-6294	190	8	θ	θ	NOUN
ejpam-6294	190	9	)	)	PUNCT
ejpam-6294	190	10	belongs	belong	VERB
ejpam-6294	190	11	to	to	ADP
ejpam-6294	190	12	the	the	DET
ejpam-6294	190	13	class	class	NOUN
ejpam-6294	190	14	gς	gς	NOUN
ejpam-6294	190	15	,	,	PUNCT
ejpam-6294	190	16	g	g	PROPN
ejpam-6294	190	17	u	u	PROPN
ejpam-6294	190	18	,	,	PUNCT
ejpam-6294	190	19	v	v	PROPN
ejpam-6294	190	20	(	(	PUNCT
ejpam-6294	190	21	τ	τ	X
ejpam-6294	190	22	)	)	PUNCT
ejpam-6294	190	23	and	and	CCONJ
ejpam-6294	190	24	is	be	AUX
ejpam-6294	190	25	provided	provide	VERB
ejpam-6294	190	26	by	by	ADP
ejpam-6294	190	27	(	(	PUNCT
ejpam-6294	190	28	1	1	NUM
ejpam-6294	190	29	)	)	PUNCT
ejpam-6294	190	30	.	.	PUNCT
ejpam-6294	191	1	then	then	ADV
ejpam-6294	191	2	|a3	|a3	VERB
ejpam-6294	191	3	−	−	PROPN
ejpam-6294	191	4	ηa22|	ηa22|	NOUN
ejpam-6294	191	5	≤	≤	NUM
ejpam-6294	191	6	{	{	PUNCT
ejpam-6294	191	7	v(s	v(s	NOUN
ejpam-6294	191	8	)	)	PUNCT
ejpam-6294	191	9	if	if	SCONJ
ejpam-6294	191	10	0	0	NUM
ejpam-6294	191	11	≤	≤	NUM
ejpam-6294	191	12	|h1(η)|	|h1(η)|	NOUN
ejpam-6294	191	13	≤	≤	NUM
ejpam-6294	191	14	1	1	NUM
ejpam-6294	191	15	2	2	NUM
ejpam-6294	191	16	,	,	PUNCT
ejpam-6294	191	17	v(s)|(1−	v(s)|(1−	VERB
ejpam-6294	191	18	η)|	η)|	PROPN
ejpam-6294	191	19	if	if	SCONJ
ejpam-6294	191	20	|h1(η)|	|h1(η)|	NUM
ejpam-6294	191	21	≥	≥	NOUN
ejpam-6294	191	22	1	1	NUM
ejpam-6294	191	23	2	2	NUM
ejpam-6294	191	24	,	,	PUNCT
ejpam-6294	191	25	where	where	SCONJ
ejpam-6294	191	26	|h1(η)|	|h1(η)|	NOUN
ejpam-6294	191	27	=	=	SYM
ejpam-6294	191	28	(	(	PUNCT
ejpam-6294	191	29	1−	1−	NUM
ejpam-6294	191	30	η	η	NOUN
ejpam-6294	191	31	)	)	PUNCT
ejpam-6294	191	32	2	2	NUM
ejpam-6294	191	33	.	.	PUNCT
ejpam-6294	192	1	corollary	corollary	ADJ
ejpam-6294	192	2	4	4	NUM
ejpam-6294	192	3	.	.	PUNCT
ejpam-6294	192	4	suppose	suppose	VERB
ejpam-6294	192	5	that	that	SCONJ
ejpam-6294	192	6	f	f	PROPN
ejpam-6294	192	7	(	(	PUNCT
ejpam-6294	192	8	θ	θ	NOUN
ejpam-6294	192	9	)	)	PUNCT
ejpam-6294	192	10	is	be	AUX
ejpam-6294	192	11	belonging	belong	VERB
ejpam-6294	192	12	to	to	ADP
ejpam-6294	192	13	the	the	DET
ejpam-6294	192	14	class	class	NOUN
ejpam-6294	192	15	gς	gς	NOUN
ejpam-6294	192	16	,	,	PUNCT
ejpam-6294	192	17	g	g	PROPN
ejpam-6294	192	18	u	u	PROPN
ejpam-6294	192	19	,	,	PUNCT
ejpam-6294	192	20	v	v	PROPN
ejpam-6294	192	21	(	(	PUNCT
ejpam-6294	192	22	τ	τ	X
ejpam-6294	192	23	)	)	PUNCT
ejpam-6294	192	24	and	and	CCONJ
ejpam-6294	192	25	is	be	AUX
ejpam-6294	192	26	provided	provide	VERB
ejpam-6294	192	27	by	by	ADP
ejpam-6294	192	28	(	(	PUNCT
ejpam-6294	192	29	1	1	NUM
ejpam-6294	192	30	)	)	PUNCT
ejpam-6294	192	31	.	.	PUNCT
ejpam-6294	193	1	then	then	ADV
ejpam-6294	193	2	|a3	|a3	VERB
ejpam-6294	193	3	−	−	PROPN
ejpam-6294	193	4	ηa22|	ηa22|	NOUN
ejpam-6294	193	5	≤	≤	NUM
ejpam-6294	193	6	{	{	PUNCT
ejpam-6294	193	7	v(s	v(s	NOUN
ejpam-6294	193	8	)	)	PUNCT
ejpam-6294	193	9	4	4	NUM
ejpam-6294	193	10	if	if	SCONJ
ejpam-6294	193	11	0	0	NUM
ejpam-6294	193	12	≤	≤	NUM
ejpam-6294	193	13	|h1(η)|	|h1(η)|	NOUN
ejpam-6294	193	14	≤	≤	NUM
ejpam-6294	193	15	1	1	NUM
ejpam-6294	193	16	4	4	NUM
ejpam-6294	193	17	,	,	PUNCT
ejpam-6294	193	18	v(s)|	v(s)|	PROPN
ejpam-6294	193	19	(	(	PUNCT
ejpam-6294	193	20	1−η	1−η	NUM
ejpam-6294	193	21	)	)	PUNCT
ejpam-6294	193	22	6	6	NUM
ejpam-6294	194	1	|	|	ADV
ejpam-6294	194	2	if	if	SCONJ
ejpam-6294	194	3	|h1(η)|	|h1(η)|	NUM
ejpam-6294	194	4	≥	≥	NOUN
ejpam-6294	194	5	1	1	NUM
ejpam-6294	194	6	4	4	NUM
ejpam-6294	194	7	,	,	PUNCT
ejpam-6294	194	8	where	where	SCONJ
ejpam-6294	194	9	|h1(η)|	|h1(η)|	NOUN
ejpam-6294	194	10	=	=	SYM
ejpam-6294	194	11	(	(	PUNCT
ejpam-6294	194	12	1−	1−	NUM
ejpam-6294	194	13	η	η	NOUN
ejpam-6294	194	14	)	)	PUNCT
ejpam-6294	194	15	6	6	NUM
ejpam-6294	194	16	.	.	NOUN
ejpam-6294	195	1	4	4	X
ejpam-6294	195	2	.	.	X
ejpam-6294	196	1	the	the	DET
ejpam-6294	196	2	initial	initial	ADJ
ejpam-6294	196	3	coefficient	coefficient	NOUN
ejpam-6294	196	4	estimates	estimate	NOUN
ejpam-6294	196	5	for	for	ADP
ejpam-6294	196	6	the	the	DET
ejpam-6294	196	7	subclass	subclass	ADJ
ejpam-6294	196	8	gς	gς	PROPN
ejpam-6294	196	9	,	,	PUNCT
ejpam-6294	196	10	g(τ	g(τ	PROPN
ejpam-6294	196	11	)	)	PUNCT
ejpam-6294	196	12	for	for	ADP
ejpam-6294	196	13	u(s	u(s	ADJ
ejpam-6294	196	14	)	)	PUNCT
ejpam-6294	196	15	=	=	SYM
ejpam-6294	196	16	s	s	PROPN
ejpam-6294	196	17	and	and	CCONJ
ejpam-6294	196	18	v(s	v(s	NUM
ejpam-6294	196	19	)	)	PUNCT
ejpam-6294	196	20	=	=	SYM
ejpam-6294	196	21	1	1	NUM
ejpam-6294	196	22	in	in	ADP
ejpam-6294	196	23	(	(	PUNCT
ejpam-6294	196	24	2	2	NUM
ejpam-6294	196	25	)	)	PUNCT
ejpam-6294	196	26	,	,	PUNCT
ejpam-6294	196	27	the	the	DET
ejpam-6294	196	28	following	follow	VERB
ejpam-6294	196	29	lucas	lucas	PROPN
ejpam-6294	196	30	polynomials	polynomial	NOUN
ejpam-6294	196	31	ln(s	ln(	NOUN
ejpam-6294	196	32	)	)	PUNCT
ejpam-6294	196	33	were	be	AUX
ejpam-6294	196	34	produced	produce	VERB
ejpam-6294	196	35	.	.	PUNCT
ejpam-6294	197	1	in	in	ADP
ejpam-6294	197	2	the	the	DET
ejpam-6294	197	3	following	following	NOUN
ejpam-6294	197	4	,	,	PUNCT
ejpam-6294	197	5	it	it	PRON
ejpam-6294	197	6	is	be	AUX
ejpam-6294	197	7	assumed	assume	VERB
ejpam-6294	197	8	that	that	SCONJ
ejpam-6294	197	9	g(s	g(s	PROPN
ejpam-6294	197	10	,	,	PUNCT
ejpam-6294	197	11	θ	θ	NOUN
ejpam-6294	197	12	)	)	PUNCT
ejpam-6294	197	13	is	be	AUX
ejpam-6294	197	14	a	a	DET
ejpam-6294	197	15	taylor	taylor	PROPN
ejpam-6294	197	16	series	series	NOUN
ejpam-6294	197	17	of	of	ADP
ejpam-6294	197	18	the	the	DET
ejpam-6294	197	19	form	form	NOUN
ejpam-6294	197	20	g(s	g(s	PROPN
ejpam-6294	197	21	,	,	PUNCT
ejpam-6294	197	22	θ)−	θ)−	PROPN
ejpam-6294	197	23	1	1	NUM
ejpam-6294	197	24	=	=	SYM
ejpam-6294	197	25	1	1	NUM
ejpam-6294	197	26	+	+	NUM
ejpam-6294	197	27	sθ+	sθ+	NOUN
ejpam-6294	197	28	(	(	PUNCT
ejpam-6294	197	29	2	2	NUM
ejpam-6294	197	30	+	+	NUM
ejpam-6294	197	31	s2)θ2	s2)θ2	NOUN
ejpam-6294	197	32	+	+	CCONJ
ejpam-6294	197	33	(	(	PUNCT
ejpam-6294	197	34	3s+	3s+	NUM
ejpam-6294	197	35	s3)θ3	s3)θ3	NOUN
ejpam-6294	197	36	+	+	CCONJ
ejpam-6294	197	37	(	(	PUNCT
ejpam-6294	197	38	s4	s4	PROPN
ejpam-6294	197	39	+	+	CCONJ
ejpam-6294	197	40	4s2	4s2	NUM
ejpam-6294	197	41	+	+	CCONJ
ejpam-6294	197	42	2)θ4	2)θ4	NUM
ejpam-6294	197	43	+	+	CCONJ
ejpam-6294	197	44	...	...	PUNCT
ejpam-6294	197	45	,	,	PUNCT
ejpam-6294	197	46	(	(	PUNCT
ejpam-6294	197	47	23	23	NUM
ejpam-6294	197	48	)	)	PUNCT
ejpam-6294	197	49	g(t	g(t	PROPN
ejpam-6294	197	50	,	,	PUNCT
ejpam-6294	197	51	φ)−	φ)−	PROPN
ejpam-6294	197	52	1	1	NUM
ejpam-6294	197	53	=	=	SYM
ejpam-6294	197	54	1	1	NUM
ejpam-6294	197	55	+	+	CCONJ
ejpam-6294	197	56	tφ+	tφ+	PROPN
ejpam-6294	197	57	(	(	PUNCT
ejpam-6294	197	58	2	2	NUM
ejpam-6294	197	59	+	+	NUM
ejpam-6294	197	60	t2)φ2	t2)φ2	NOUN
ejpam-6294	197	61	+	+	CCONJ
ejpam-6294	197	62	(	(	PUNCT
ejpam-6294	197	63	3t+	3t+	NUM
ejpam-6294	197	64	t3)φ3	t3)φ3	NOUN
ejpam-6294	197	65	+	+	X
ejpam-6294	197	66	(	(	PUNCT
ejpam-6294	197	67	t4	t4	PROPN
ejpam-6294	197	68	+	+	PROPN
ejpam-6294	197	69	4t2	4t2	NUM
ejpam-6294	198	1	+	+	CCONJ
ejpam-6294	198	2	2)φ4	2)φ4	NUM
ejpam-6294	198	3	+	+	CCONJ
ejpam-6294	198	4	...	...	PUNCT
ejpam-6294	198	5	,	,	PUNCT
ejpam-6294	198	6	(	(	PUNCT
ejpam-6294	198	7	24	24	NUM
ejpam-6294	198	8	)	)	PUNCT
ejpam-6294	198	9	s.	s.	PROPN
ejpam-6294	198	10	thangamani	thangamani	PROPN
ejpam-6294	198	11	et	et	PROPN
ejpam-6294	198	12	al	al	PROPN
ejpam-6294	198	13	.	.	PUNCT
ejpam-6294	198	14	/	/	SYM
ejpam-6294	198	15	eur	eur	PROPN
ejpam-6294	198	16	.	.	PUNCT
ejpam-6294	199	1	j.	j.	PROPN
ejpam-6294	199	2	pure	pure	PROPN
ejpam-6294	199	3	appl	appl	PROPN
ejpam-6294	199	4	.	.	PROPN
ejpam-6294	199	5	math	math	PROPN
ejpam-6294	199	6	,	,	PUNCT
ejpam-6294	199	7	18	18	NUM
ejpam-6294	199	8	(	(	PUNCT
ejpam-6294	199	9	3	3	NUM
ejpam-6294	199	10	)	)	PUNCT
ejpam-6294	199	11	(	(	PUNCT
ejpam-6294	199	12	2025	2025	NUM
ejpam-6294	199	13	)	)	PUNCT
ejpam-6294	199	14	,	,	PUNCT
ejpam-6294	199	15	6294	6294	NUM
ejpam-6294	199	16	10	10	NUM
ejpam-6294	199	17	of	of	ADP
ejpam-6294	199	18	19	19	NUM
ejpam-6294	199	19	definition	definition	NOUN
ejpam-6294	199	20	2	2	NUM
ejpam-6294	199	21	.	.	PUNCT
ejpam-6294	200	1	if	if	SCONJ
ejpam-6294	200	2	a	a	DET
ejpam-6294	200	3	function	function	NOUN
ejpam-6294	200	4	f	f	PROPN
ejpam-6294	200	5	∈	∈	PROPN
ejpam-6294	200	6	σ	σ	PROPN
ejpam-6294	200	7	is	be	AUX
ejpam-6294	200	8	regarded	regard	VERB
ejpam-6294	200	9	as	as	ADP
ejpam-6294	200	10	a	a	DET
ejpam-6294	200	11	member	member	NOUN
ejpam-6294	200	12	of	of	ADP
ejpam-6294	200	13	the	the	DET
ejpam-6294	200	14	class	class	NOUN
ejpam-6294	200	15	gς	gς	PROPN
ejpam-6294	200	16	,	,	PUNCT
ejpam-6294	200	17	g(τ	g(τ	PROPN
ejpam-6294	200	18	)	)	PUNCT
ejpam-6294	200	19	,	,	PUNCT
ejpam-6294	200	20	then	then	ADV
ejpam-6294	200	21	the	the	DET
ejpam-6294	200	22	resulting	result	VERB
ejpam-6294	200	23	subordination	subordination	NOUN
ejpam-6294	200	24	is	be	AUX
ejpam-6294	200	25	valid	valid	ADJ
ejpam-6294	200	26	.	.	PUNCT
ejpam-6294	201	1	(	(	PUNCT
ejpam-6294	201	2	1−	1−	NUM
ejpam-6294	201	3	τ	τ	X
ejpam-6294	201	4	)	)	PUNCT
ejpam-6294	201	5	(	(	PUNCT
ejpam-6294	201	6	θf	θf	NOUN
ejpam-6294	201	7	′(θ	′(θ	NOUN
ejpam-6294	201	8	)	)	PUNCT
ejpam-6294	201	9	f(θ	f(θ	PROPN
ejpam-6294	201	10	)	)	PUNCT
ejpam-6294	201	11	)	)	PUNCT
ejpam-6294	202	1	+	+	CCONJ
ejpam-6294	202	2	τ	τ	X
ejpam-6294	202	3	(	(	PUNCT
ejpam-6294	202	4	1	1	NUM
ejpam-6294	202	5	+	+	CCONJ
ejpam-6294	202	6	θf	θf	NOUN
ejpam-6294	202	7	′′(θ	′′(θ	PROPN
ejpam-6294	202	8	)	)	PUNCT
ejpam-6294	202	9	f	f	PROPN
ejpam-6294	202	10	′(θ	′(θ	NOUN
ejpam-6294	202	11	)	)	PUNCT
ejpam-6294	202	12	)	)	PUNCT
ejpam-6294	202	13	≺	≺	VERB
ejpam-6294	202	14	g(s	g(s	PROPN
ejpam-6294	202	15	,	,	PUNCT
ejpam-6294	202	16	θ)−	θ)−	PROPN
ejpam-6294	202	17	1	1	NUM
ejpam-6294	202	18	(	(	PUNCT
ejpam-6294	202	19	25	25	NUM
ejpam-6294	202	20	)	)	PUNCT
ejpam-6294	202	21	and	and	CCONJ
ejpam-6294	202	22	(	(	PUNCT
ejpam-6294	202	23	1−	1−	NUM
ejpam-6294	202	24	τ	τ	NOUN
ejpam-6294	202	25	)	)	PUNCT
ejpam-6294	202	26	(	(	PUNCT
ejpam-6294	202	27	φf	φf	ADP
ejpam-6294	202	28	′(φ	′(φ	NOUN
ejpam-6294	202	29	)	)	PUNCT
ejpam-6294	202	30	f(φ	f(φ	PROPN
ejpam-6294	202	31	)	)	PUNCT
ejpam-6294	202	32	)	)	PUNCT
ejpam-6294	203	1	+	+	CCONJ
ejpam-6294	203	2	τ	τ	X
ejpam-6294	203	3	(	(	PUNCT
ejpam-6294	203	4	1	1	NUM
ejpam-6294	203	5	+	+	CCONJ
ejpam-6294	203	6	φf	φf	ADP
ejpam-6294	203	7	′′(φ	′′(φ	NOUN
ejpam-6294	203	8	)	)	PUNCT
ejpam-6294	203	9	)	)	PUNCT
ejpam-6294	204	1	f	f	PROPN
ejpam-6294	204	2	′(φ	′(φ	NOUN
ejpam-6294	204	3	)	)	PUNCT
ejpam-6294	204	4	)	)	PUNCT
ejpam-6294	205	1	≺	≺	NOUN
ejpam-6294	205	2	g(t	g(t	PROPN
ejpam-6294	205	3	,	,	PUNCT
ejpam-6294	205	4	φ)−	φ)−	PROPN
ejpam-6294	205	5	1	1	NUM
ejpam-6294	205	6	(	(	PUNCT
ejpam-6294	205	7	26	26	NUM
ejpam-6294	205	8	)	)	PUNCT
ejpam-6294	205	9	example	example	NOUN
ejpam-6294	205	10	3	3	NUM
ejpam-6294	205	11	.	.	X
ejpam-6294	205	12	for	for	ADP
ejpam-6294	205	13	the	the	DET
ejpam-6294	205	14	function	function	NOUN
ejpam-6294	205	15	f	f	PROPN
ejpam-6294	205	16	to	to	PART
ejpam-6294	205	17	be	be	AUX
ejpam-6294	205	18	classified	classify	VERB
ejpam-6294	205	19	as	as	ADP
ejpam-6294	205	20	belonging	belong	VERB
ejpam-6294	205	21	to	to	ADP
ejpam-6294	205	22	the	the	DET
ejpam-6294	205	23	class	class	NOUN
ejpam-6294	205	24	gς	gς	NOUN
ejpam-6294	205	25	,	,	PUNCT
ejpam-6294	205	26	g(τ	g(τ	PROPN
ejpam-6294	205	27	)	)	PUNCT
ejpam-6294	205	28	when	when	SCONJ
ejpam-6294	205	29	τ	τ	PROPN
ejpam-6294	205	30	=	=	SYM
ejpam-6294	205	31	0	0	PROPN
ejpam-6294	205	32	,	,	PUNCT
ejpam-6294	205	33	it	it	PRON
ejpam-6294	205	34	must	must	AUX
ejpam-6294	205	35	meet	meet	VERB
ejpam-6294	205	36	a	a	DET
ejpam-6294	205	37	subordination	subordination	NOUN
ejpam-6294	205	38	condition	condition	NOUN
ejpam-6294	205	39	.	.	PUNCT
ejpam-6294	206	1	this	this	PRON
ejpam-6294	206	2	constrains	constrain	VERB
ejpam-6294	206	3	how	how	SCONJ
ejpam-6294	206	4	f	f	PROPN
ejpam-6294	206	5	behaves	behave	VERB
ejpam-6294	206	6	in	in	ADP
ejpam-6294	206	7	relation	relation	NOUN
ejpam-6294	206	8	to	to	ADP
ejpam-6294	206	9	other	other	ADJ
ejpam-6294	206	10	functions	function	NOUN
ejpam-6294	206	11	,	,	PUNCT
ejpam-6294	206	12	frequently	frequently	ADV
ejpam-6294	206	13	in	in	ADP
ejpam-6294	206	14	terms	term	NOUN
ejpam-6294	206	15	of	of	ADP
ejpam-6294	206	16	growth	growth	NOUN
ejpam-6294	206	17	,	,	PUNCT
ejpam-6294	206	18	distortion	distortion	NOUN
ejpam-6294	206	19	,	,	PUNCT
ejpam-6294	206	20	or	or	CCONJ
ejpam-6294	206	21	mapping	mapping	NOUN
ejpam-6294	206	22	properties	property	NOUN
ejpam-6294	206	23	in	in	ADP
ejpam-6294	206	24	the	the	DET
ejpam-6294	206	25	unit	unit	NOUN
ejpam-6294	206	26	disc	disc	NOUN
ejpam-6294	206	27	.	.	PUNCT
ejpam-6294	207	1	(	(	PUNCT
ejpam-6294	207	2	θf	θf	NOUN
ejpam-6294	207	3	′(θ	′(θ	NOUN
ejpam-6294	207	4	)	)	PUNCT
ejpam-6294	207	5	f(θ	f(θ	PROPN
ejpam-6294	207	6	)	)	PUNCT
ejpam-6294	207	7	)	)	PUNCT
ejpam-6294	207	8	)	)	PUNCT
ejpam-6294	208	1	≺	≺	NOUN
ejpam-6294	208	2	g(s	g(s	PROPN
ejpam-6294	208	3	,	,	PUNCT
ejpam-6294	208	4	θ)−	θ)−	PROPN
ejpam-6294	208	5	1	1	NUM
ejpam-6294	208	6	and	and	CCONJ
ejpam-6294	208	7	(	(	PUNCT
ejpam-6294	208	8	φf	φf	DET
ejpam-6294	208	9	′(φ	′(φ	NOUN
ejpam-6294	208	10	)	)	PUNCT
ejpam-6294	208	11	f(φ	f(φ	PROPN
ejpam-6294	208	12	)	)	PUNCT
ejpam-6294	208	13	)	)	PUNCT
ejpam-6294	209	1	≺	≺	NOUN
ejpam-6294	209	2	g(t	g(t	PROPN
ejpam-6294	209	3	,	,	PUNCT
ejpam-6294	209	4	φ)−	φ)−	PROPN
ejpam-6294	209	5	1	1	NUM
ejpam-6294	209	6	example	example	NOUN
ejpam-6294	209	7	4	4	NUM
ejpam-6294	209	8	.	.	PUNCT
ejpam-6294	210	1	a	a	DET
ejpam-6294	210	2	function	function	NOUN
ejpam-6294	210	3	f	f	PROPN
ejpam-6294	210	4	∈	∈	PROPN
ejpam-6294	210	5	σ	σ	PROPN
ejpam-6294	210	6	is	be	AUX
ejpam-6294	210	7	regarded	regard	VERB
ejpam-6294	210	8	as	as	ADP
ejpam-6294	210	9	belonging	belong	VERB
ejpam-6294	210	10	to	to	ADP
ejpam-6294	210	11	the	the	DET
ejpam-6294	210	12	class	class	NOUN
ejpam-6294	210	13	gς	gς	NOUN
ejpam-6294	210	14	,	,	PUNCT
ejpam-6294	210	15	g(τ	g(τ	PROPN
ejpam-6294	210	16	)	)	PUNCT
ejpam-6294	210	17	when	when	SCONJ
ejpam-6294	210	18	τ	τ	PROPN
ejpam-6294	210	19	=	=	SYM
ejpam-6294	210	20	1	1	NUM
ejpam-6294	210	21	in	in	ADP
ejpam-6294	210	22	definition	definition	NOUN
ejpam-6294	210	23	(	(	PUNCT
ejpam-6294	210	24	2	2	X
ejpam-6294	210	25	)	)	PUNCT
ejpam-6294	210	26	if	if	SCONJ
ejpam-6294	210	27	it	it	PRON
ejpam-6294	210	28	meets	meet	VERB
ejpam-6294	210	29	the	the	DET
ejpam-6294	210	30	subsequent	subsequent	ADJ
ejpam-6294	210	31	subordination	subordination	NOUN
ejpam-6294	210	32	condition	condition	NOUN
ejpam-6294	210	33	:(	:(	X
ejpam-6294	210	34	1	1	NUM
ejpam-6294	210	35	+	+	CCONJ
ejpam-6294	210	36	θf	θf	NOUN
ejpam-6294	210	37	′′(θ	′′(θ	PROPN
ejpam-6294	210	38	)	)	PUNCT
ejpam-6294	210	39	f	f	PROPN
ejpam-6294	210	40	′(θ	′(θ	NOUN
ejpam-6294	210	41	)	)	PUNCT
ejpam-6294	210	42	)	)	PUNCT
ejpam-6294	211	1	≺	≺	VERB
ejpam-6294	211	2	g(s	g(s	PROPN
ejpam-6294	211	3	,	,	PUNCT
ejpam-6294	211	4	θ)−	θ)−	PROPN
ejpam-6294	211	5	1	1	NUM
ejpam-6294	211	6	and	and	CCONJ
ejpam-6294	211	7	(	(	PUNCT
ejpam-6294	211	8	1	1	NUM
ejpam-6294	211	9	+	+	CCONJ
ejpam-6294	211	10	φf	φf	ADP
ejpam-6294	211	11	′′(φ	′′(φ	NOUN
ejpam-6294	211	12	)	)	PUNCT
ejpam-6294	211	13	)	)	PUNCT
ejpam-6294	211	14	f	f	PROPN
ejpam-6294	211	15	′(φ	′(φ	NOUN
ejpam-6294	211	16	)	)	PUNCT
ejpam-6294	211	17	)	)	PUNCT
ejpam-6294	212	1	≺	≺	NOUN
ejpam-6294	212	2	g(t	g(t	PROPN
ejpam-6294	212	3	,	,	PUNCT
ejpam-6294	212	4	φ)−	φ)−	PROPN
ejpam-6294	212	5	1	1	NUM
ejpam-6294	212	6	theorem	theorem	NOUN
ejpam-6294	212	7	3	3	NUM
ejpam-6294	212	8	.	.	PUNCT
ejpam-6294	213	1	if	if	SCONJ
ejpam-6294	213	2	a	a	DET
ejpam-6294	213	3	function	function	NOUN
ejpam-6294	213	4	f	f	PROPN
ejpam-6294	213	5	∈	∈	PROPN
ejpam-6294	213	6	σ	σ	PROPN
ejpam-6294	213	7	is	be	AUX
ejpam-6294	213	8	regarded	regard	VERB
ejpam-6294	213	9	as	as	ADP
ejpam-6294	213	10	belonging	belong	VERB
ejpam-6294	213	11	to	to	ADP
ejpam-6294	213	12	the	the	DET
ejpam-6294	213	13	class	class	NOUN
ejpam-6294	213	14	gς	gς	NOUN
ejpam-6294	213	15	,	,	PUNCT
ejpam-6294	213	16	g(τ	g(τ	PROPN
ejpam-6294	213	17	)	)	PUNCT
ejpam-6294	213	18	,	,	PUNCT
ejpam-6294	213	19	then	then	ADV
ejpam-6294	213	20	the	the	DET
ejpam-6294	213	21	resulting	result	VERB
ejpam-6294	213	22	subordination	subordination	NOUN
ejpam-6294	213	23	condition	condition	NOUN
ejpam-6294	213	24	is	be	AUX
ejpam-6294	213	25	valid	valid	ADJ
ejpam-6294	213	26	:	:	PUNCT
ejpam-6294	213	27	|a2|	|a2|	VERB
ejpam-6294	213	28	≤	≤	ADJ
ejpam-6294	213	29	√	√	PROPN
ejpam-6294	213	30	s2	s2	VERB
ejpam-6294	213	31	+	+	CCONJ
ejpam-6294	213	32	t2	t2	NOUN
ejpam-6294	213	33	+	+	CCONJ
ejpam-6294	213	34	4	4	NUM
ejpam-6294	213	35	4(1	4(1	NUM
ejpam-6294	213	36	+	+	CCONJ
ejpam-6294	213	37	2τ	2τ	NUM
ejpam-6294	213	38	)	)	PUNCT
ejpam-6294	213	39	(	(	PUNCT
ejpam-6294	213	40	27	27	NUM
ejpam-6294	213	41	)	)	PUNCT
ejpam-6294	213	42	and	and	CCONJ
ejpam-6294	213	43	|a3|	|a3|	VERB
ejpam-6294	213	44	≤	≤	PUNCT
ejpam-6294	213	45	s2	s2	PROPN
ejpam-6294	213	46	+	+	CCONJ
ejpam-6294	213	47	t2	t2	PROPN
ejpam-6294	213	48	8(1	8(1	NOUN
ejpam-6294	213	49	+	+	CCONJ
ejpam-6294	213	50	τ)2	τ)2	PROPN
ejpam-6294	213	51	+	+	CCONJ
ejpam-6294	213	52	s2	s2	PROPN
ejpam-6294	214	1	−	−	PROPN
ejpam-6294	214	2	t2	t2	NOUN
ejpam-6294	214	3	4(1	4(1	X
ejpam-6294	214	4	+	+	CCONJ
ejpam-6294	214	5	2τ	2τ	NUM
ejpam-6294	214	6	)	)	PUNCT
ejpam-6294	214	7	(	(	PUNCT
ejpam-6294	214	8	28	28	X
ejpam-6294	214	9	)	)	PUNCT
ejpam-6294	214	10	proof	proof	NOUN
ejpam-6294	214	11	:	:	PUNCT
ejpam-6294	214	12	let	let	VERB
ejpam-6294	214	13	f	f	PROPN
ejpam-6294	214	14	∈	∈	PROPN
ejpam-6294	214	15	gς	gς	PROPN
ejpam-6294	214	16	,	,	PUNCT
ejpam-6294	214	17	g(τ	g(τ	PROPN
ejpam-6294	214	18	)	)	PUNCT
ejpam-6294	214	19	.	.	PUNCT
ejpam-6294	215	1	then	then	ADV
ejpam-6294	215	2	f	f	X
ejpam-6294	215	3	,	,	PUNCT
ejpam-6294	215	4	g	g	NOUN
ejpam-6294	215	5	:	:	PUNCT
ejpam-6294	215	6	d	d	X
ejpam-6294	215	7	→	→	SYM
ejpam-6294	215	8	d	d	X
ejpam-6294	215	9	given	give	VERB
ejpam-6294	215	10	by	by	ADP
ejpam-6294	215	11	(	(	PUNCT
ejpam-6294	215	12	25	25	NUM
ejpam-6294	215	13	)	)	PUNCT
ejpam-6294	215	14	and	and	CCONJ
ejpam-6294	215	15	(	(	PUNCT
ejpam-6294	215	16	26	26	NUM
ejpam-6294	215	17	)	)	PUNCT
ejpam-6294	215	18	such	such	ADJ
ejpam-6294	215	19	that	that	SCONJ
ejpam-6294	215	20	(	(	PUNCT
ejpam-6294	215	21	1−	1−	NUM
ejpam-6294	215	22	τ	τ	X
ejpam-6294	215	23	)	)	PUNCT
ejpam-6294	215	24	(	(	PUNCT
ejpam-6294	215	25	θf	θf	NOUN
ejpam-6294	215	26	′(θ	′(θ	NOUN
ejpam-6294	215	27	)	)	PUNCT
ejpam-6294	215	28	f(θ	f(θ	PROPN
ejpam-6294	215	29	)	)	PUNCT
ejpam-6294	215	30	)	)	PUNCT
ejpam-6294	216	1	+	+	CCONJ
ejpam-6294	216	2	τ	τ	X
ejpam-6294	216	3	(	(	PUNCT
ejpam-6294	216	4	1	1	NUM
ejpam-6294	216	5	+	+	CCONJ
ejpam-6294	216	6	θf	θf	NOUN
ejpam-6294	216	7	′′(θ	′′(θ	PROPN
ejpam-6294	216	8	)	)	PUNCT
ejpam-6294	216	9	f	f	PROPN
ejpam-6294	216	10	′(θ	′(θ	NOUN
ejpam-6294	216	11	)	)	PUNCT
ejpam-6294	216	12	)	)	PUNCT
ejpam-6294	217	1	=	=	SYM
ejpam-6294	217	2	g(s	g(s	PROPN
ejpam-6294	217	3	,	,	PUNCT
ejpam-6294	217	4	θ)−	θ)−	PROPN
ejpam-6294	217	5	1	1	NUM
ejpam-6294	217	6	(	(	PUNCT
ejpam-6294	217	7	29	29	NUM
ejpam-6294	217	8	)	)	PUNCT
ejpam-6294	217	9	s.	s.	PROPN
ejpam-6294	217	10	thangamani	thangamani	PROPN
ejpam-6294	217	11	et	et	PROPN
ejpam-6294	217	12	al	al	PROPN
ejpam-6294	217	13	.	.	PUNCT
ejpam-6294	217	14	/	/	SYM
ejpam-6294	217	15	eur	eur	PROPN
ejpam-6294	217	16	.	.	PUNCT
ejpam-6294	218	1	j.	j.	PROPN
ejpam-6294	218	2	pure	pure	PROPN
ejpam-6294	218	3	appl	appl	PROPN
ejpam-6294	218	4	.	.	PROPN
ejpam-6294	218	5	math	math	PROPN
ejpam-6294	218	6	,	,	PUNCT
ejpam-6294	218	7	18	18	NUM
ejpam-6294	218	8	(	(	PUNCT
ejpam-6294	218	9	3	3	NUM
ejpam-6294	218	10	)	)	PUNCT
ejpam-6294	218	11	(	(	PUNCT
ejpam-6294	218	12	2025	2025	NUM
ejpam-6294	218	13	)	)	PUNCT
ejpam-6294	218	14	,	,	PUNCT
ejpam-6294	218	15	6294	6294	NUM
ejpam-6294	218	16	11	11	NUM
ejpam-6294	218	17	of	of	ADP
ejpam-6294	218	18	19	19	NUM
ejpam-6294	218	19	and	and	CCONJ
ejpam-6294	218	20	(	(	PUNCT
ejpam-6294	218	21	1−	1−	NUM
ejpam-6294	218	22	τ	τ	NOUN
ejpam-6294	218	23	)	)	PUNCT
ejpam-6294	218	24	(	(	PUNCT
ejpam-6294	218	25	φf	φf	ADP
ejpam-6294	218	26	′(φ	′(φ	NOUN
ejpam-6294	218	27	)	)	PUNCT
ejpam-6294	218	28	f(φ	f(φ	PROPN
ejpam-6294	218	29	)	)	PUNCT
ejpam-6294	218	30	)	)	PUNCT
ejpam-6294	219	1	+	+	CCONJ
ejpam-6294	219	2	τ	τ	X
ejpam-6294	219	3	(	(	PUNCT
ejpam-6294	219	4	1	1	NUM
ejpam-6294	219	5	+	+	CCONJ
ejpam-6294	219	6	φf	φf	ADP
ejpam-6294	219	7	′′(φ	′′(φ	NOUN
ejpam-6294	219	8	)	)	PUNCT
ejpam-6294	219	9	)	)	PUNCT
ejpam-6294	220	1	f	f	PROPN
ejpam-6294	220	2	′(φ	′(φ	NOUN
ejpam-6294	220	3	)	)	PUNCT
ejpam-6294	220	4	)	)	PUNCT
ejpam-6294	221	1	=	=	SYM
ejpam-6294	221	2	l(t	l(t	PROPN
ejpam-6294	221	3	,	,	PUNCT
ejpam-6294	221	4	φ)−	φ)−	PROPN
ejpam-6294	221	5	1	1	NUM
ejpam-6294	221	6	(	(	PUNCT
ejpam-6294	221	7	30	30	NUM
ejpam-6294	221	8	)	)	PUNCT
ejpam-6294	221	9	since	since	SCONJ
ejpam-6294	221	10	(	(	PUNCT
ejpam-6294	221	11	1−τ	1−τ	NUM
ejpam-6294	221	12	)	)	PUNCT
ejpam-6294	221	13	(	(	PUNCT
ejpam-6294	221	14	θf	θf	NOUN
ejpam-6294	221	15	′(θ	′(θ	NOUN
ejpam-6294	221	16	)	)	PUNCT
ejpam-6294	221	17	f(θ	f(θ	PROPN
ejpam-6294	221	18	)	)	PUNCT
ejpam-6294	221	19	)	)	PUNCT
ejpam-6294	222	1	+	+	X
ejpam-6294	222	2	τ	τ	X
ejpam-6294	222	3	(	(	PUNCT
ejpam-6294	222	4	1	1	NUM
ejpam-6294	222	5	+	+	CCONJ
ejpam-6294	222	6	θf	θf	NOUN
ejpam-6294	222	7	′′(θ	′′(θ	PROPN
ejpam-6294	222	8	)	)	PUNCT
ejpam-6294	222	9	f	f	PROPN
ejpam-6294	222	10	′(θ	′(θ	NOUN
ejpam-6294	222	11	)	)	PUNCT
ejpam-6294	222	12	)	)	PUNCT
ejpam-6294	223	1	=	=	PUNCT
ejpam-6294	224	1	1+(1+τ)a2θ+(2(1	1+(1+τ)a2θ+(2(1	NUM
ejpam-6294	224	2	+	+	NOUN
ejpam-6294	224	3	2τ)a3−	2τ)a3−	NOUN
ejpam-6294	224	4	(	(	PUNCT
ejpam-6294	224	5	1	1	NUM
ejpam-6294	224	6	+	+	NOUN
ejpam-6294	224	7	3τ)a22)θ	3τ)a22)θ	NUM
ejpam-6294	224	8	2	2	NUM
ejpam-6294	224	9	+	+	NUM
ejpam-6294	224	10	...	...	PUNCT
ejpam-6294	224	11	(	(	PUNCT
ejpam-6294	224	12	31	31	NUM
ejpam-6294	224	13	)	)	PUNCT
ejpam-6294	224	14	and	and	CCONJ
ejpam-6294	224	15	(	(	PUNCT
ejpam-6294	224	16	1−τ	1−τ	NUM
ejpam-6294	224	17	)	)	PUNCT
ejpam-6294	224	18	(	(	PUNCT
ejpam-6294	224	19	φf	φf	ADP
ejpam-6294	224	20	′(φ	′(φ	NOUN
ejpam-6294	224	21	)	)	PUNCT
ejpam-6294	224	22	f(φ	f(φ	PROPN
ejpam-6294	224	23	)	)	PUNCT
ejpam-6294	224	24	)	)	PUNCT
ejpam-6294	225	1	+	+	X
ejpam-6294	225	2	τ	τ	X
ejpam-6294	225	3	(	(	PUNCT
ejpam-6294	225	4	1	1	NUM
ejpam-6294	225	5	+	+	CCONJ
ejpam-6294	225	6	φf	φf	ADP
ejpam-6294	225	7	′′(φ	′′(φ	NOUN
ejpam-6294	225	8	)	)	PUNCT
ejpam-6294	225	9	)	)	PUNCT
ejpam-6294	225	10	f	f	PROPN
ejpam-6294	225	11	′(φ	′(φ	NOUN
ejpam-6294	225	12	)	)	PUNCT
ejpam-6294	225	13	)	)	PUNCT
ejpam-6294	226	1	=	=	SYM
ejpam-6294	226	2	1−	1−	NUM
ejpam-6294	226	3	(	(	PUNCT
ejpam-6294	226	4	1+τ)a2φ+((3	1+τ)a2φ+((3	NUM
ejpam-6294	226	5	+	+	NOUN
ejpam-6294	226	6	5τ)a22−2(1	5τ)a22−2(1	NOUN
ejpam-6294	226	7	+	+	ADJ
ejpam-6294	226	8	2τ)a3)φ	2τ)a3)φ	NUM
ejpam-6294	226	9	2	2	NUM
ejpam-6294	226	10	+	+	NUM
ejpam-6294	226	11	...	...	PUNCT
ejpam-6294	226	12	(	(	PUNCT
ejpam-6294	226	13	32	32	NUM
ejpam-6294	226	14	)	)	PUNCT
ejpam-6294	226	15	from	from	ADP
ejpam-6294	226	16	the	the	DET
ejpam-6294	226	17	equations	equation	NOUN
ejpam-6294	226	18	(	(	PUNCT
ejpam-6294	226	19	23	23	NUM
ejpam-6294	226	20	)	)	PUNCT
ejpam-6294	226	21	and	and	CCONJ
ejpam-6294	226	22	(	(	PUNCT
ejpam-6294	226	23	31	31	NUM
ejpam-6294	226	24	)	)	PUNCT
ejpam-6294	226	25	,	,	PUNCT
ejpam-6294	226	26	by	by	ADP
ejpam-6294	226	27	comparing	compare	VERB
ejpam-6294	226	28	coefficients	coefficient	NOUN
ejpam-6294	226	29	of	of	ADP
ejpam-6294	226	30	θ	θ	PROPN
ejpam-6294	226	31	and	and	CCONJ
ejpam-6294	226	32	θ2	θ2	PROPN
ejpam-6294	226	33	respectively	respectively	ADV
ejpam-6294	226	34	,	,	PUNCT
ejpam-6294	226	35	we	we	PRON
ejpam-6294	226	36	get	get	VERB
ejpam-6294	226	37	coefficient	coefficient	NOUN
ejpam-6294	226	38	of	of	ADP
ejpam-6294	226	39	θ	θ	PROPN
ejpam-6294	226	40	:	:	PUNCT
ejpam-6294	226	41	(	(	PUNCT
ejpam-6294	226	42	1	1	NUM
ejpam-6294	226	43	+	+	NUM
ejpam-6294	226	44	τ)a2	τ)a2	NOUN
ejpam-6294	226	45	=	=	SYM
ejpam-6294	226	46	s	s	X
ejpam-6294	226	47	(	(	PUNCT
ejpam-6294	226	48	33	33	NUM
ejpam-6294	226	49	)	)	PUNCT
ejpam-6294	226	50	coefficient	coefficient	NOUN
ejpam-6294	226	51	of	of	ADP
ejpam-6294	226	52	θ2	θ2	PROPN
ejpam-6294	226	53	:	:	PUNCT
ejpam-6294	226	54	2(1	2(1	NUM
ejpam-6294	226	55	+	+	CCONJ
ejpam-6294	226	56	2τ)a3	2τ)a3	NUM
ejpam-6294	226	57	−	−	NOUN
ejpam-6294	226	58	(	(	PUNCT
ejpam-6294	226	59	1	1	NUM
ejpam-6294	226	60	+	+	NUM
ejpam-6294	226	61	3τ)a22	3τ)a22	NUM
ejpam-6294	226	62	=	=	SYM
ejpam-6294	226	63	2	2	NUM
ejpam-6294	226	64	+	+	NUM
ejpam-6294	226	65	s2	s2	X
ejpam-6294	226	66	(	(	PUNCT
ejpam-6294	226	67	34	34	NUM
ejpam-6294	226	68	)	)	PUNCT
ejpam-6294	226	69	from	from	ADP
ejpam-6294	226	70	the	the	DET
ejpam-6294	226	71	equations	equation	NOUN
ejpam-6294	226	72	(	(	PUNCT
ejpam-6294	226	73	24	24	NUM
ejpam-6294	226	74	)	)	PUNCT
ejpam-6294	226	75	and	and	CCONJ
ejpam-6294	226	76	(	(	PUNCT
ejpam-6294	226	77	32	32	NUM
ejpam-6294	226	78	)	)	PUNCT
ejpam-6294	226	79	,	,	PUNCT
ejpam-6294	226	80	equating	equate	VERB
ejpam-6294	226	81	the	the	DET
ejpam-6294	226	82	coefficients	coefficient	NOUN
ejpam-6294	226	83	of	of	ADP
ejpam-6294	226	84	φ	φ	PROPN
ejpam-6294	226	85	and	and	CCONJ
ejpam-6294	226	86	φ2	φ2	PROPN
ejpam-6294	226	87	respectively	respectively	ADV
ejpam-6294	226	88	,	,	PUNCT
ejpam-6294	226	89	we	we	PRON
ejpam-6294	226	90	get	get	VERB
ejpam-6294	226	91	coefficient	coefficient	NOUN
ejpam-6294	226	92	of	of	ADP
ejpam-6294	226	93	φ	φ	PROPN
ejpam-6294	226	94	:	:	PUNCT
ejpam-6294	227	1	−(1	−(1	NOUN
ejpam-6294	227	2	+	+	PUNCT
ejpam-6294	227	3	τ)a2	τ)a2	PROPN
ejpam-6294	227	4	=	=	SYM
ejpam-6294	227	5	t	t	PROPN
ejpam-6294	227	6	(	(	PUNCT
ejpam-6294	227	7	35	35	NUM
ejpam-6294	227	8	)	)	PUNCT
ejpam-6294	227	9	coefficient	coefficient	NOUN
ejpam-6294	227	10	of	of	ADP
ejpam-6294	227	11	φ2	φ2	PROPN
ejpam-6294	227	12	:	:	PUNCT
ejpam-6294	227	13	(	(	PUNCT
ejpam-6294	227	14	3	3	NUM
ejpam-6294	227	15	+	+	NUM
ejpam-6294	227	16	5τ)a22	5τ)a22	NUM
ejpam-6294	227	17	−	−	NOUN
ejpam-6294	227	18	2(1	2(1	NUM
ejpam-6294	228	1	+	+	CCONJ
ejpam-6294	228	2	2τ)a3	2τ)a3	NUM
ejpam-6294	228	3	=	=	SYM
ejpam-6294	228	4	2	2	NUM
ejpam-6294	228	5	+	+	NUM
ejpam-6294	228	6	t2	t2	PROPN
ejpam-6294	228	7	(	(	PUNCT
ejpam-6294	228	8	36	36	NUM
ejpam-6294	228	9	)	)	PUNCT
ejpam-6294	228	10	now	now	ADV
ejpam-6294	228	11	,	,	PUNCT
ejpam-6294	228	12	adding	add	VERB
ejpam-6294	228	13	the	the	DET
ejpam-6294	228	14	equations	equation	NOUN
ejpam-6294	228	15	(	(	PUNCT
ejpam-6294	228	16	33	33	NUM
ejpam-6294	228	17	)	)	PUNCT
ejpam-6294	228	18	and	and	CCONJ
ejpam-6294	228	19	(	(	PUNCT
ejpam-6294	228	20	35	35	NUM
ejpam-6294	228	21	)	)	PUNCT
ejpam-6294	228	22	,	,	PUNCT
ejpam-6294	228	23	we	we	PRON
ejpam-6294	228	24	have	have	VERB
ejpam-6294	228	25	s	s	NOUN
ejpam-6294	228	26	=	=	NOUN
ejpam-6294	228	27	−t	−t	NOUN
ejpam-6294	228	28	(	(	PUNCT
ejpam-6294	228	29	37	37	NUM
ejpam-6294	228	30	)	)	PUNCT
ejpam-6294	228	31	squaring	square	VERB
ejpam-6294	228	32	and	and	CCONJ
ejpam-6294	228	33	adding	add	VERB
ejpam-6294	228	34	the	the	DET
ejpam-6294	228	35	equations	equation	NOUN
ejpam-6294	228	36	(	(	PUNCT
ejpam-6294	228	37	33	33	NUM
ejpam-6294	228	38	)	)	PUNCT
ejpam-6294	228	39	and	and	CCONJ
ejpam-6294	228	40	(	(	PUNCT
ejpam-6294	228	41	35	35	NUM
ejpam-6294	228	42	)	)	PUNCT
ejpam-6294	228	43	,	,	PUNCT
ejpam-6294	228	44	we	we	PRON
ejpam-6294	228	45	get	get	VERB
ejpam-6294	228	46	2(1	2(1	NUM
ejpam-6294	228	47	+	+	CCONJ
ejpam-6294	228	48	τ)2a22	τ)2a22	PUNCT
ejpam-6294	228	49	=	=	SYM
ejpam-6294	228	50	s2	s2	PROPN
ejpam-6294	228	51	+	+	CCONJ
ejpam-6294	228	52	t2	t2	NOUN
ejpam-6294	228	53	a22	a22	NOUN
ejpam-6294	228	54	=	=	SYM
ejpam-6294	228	55	s2	s2	PROPN
ejpam-6294	228	56	+	+	CCONJ
ejpam-6294	228	57	t2	t2	PROPN
ejpam-6294	228	58	2(1	2(1	NUM
ejpam-6294	229	1	+	+	CCONJ
ejpam-6294	229	2	τ)2	τ)2	NOUN
ejpam-6294	229	3	(	(	PUNCT
ejpam-6294	229	4	38	38	NUM
ejpam-6294	229	5	)	)	PUNCT
ejpam-6294	229	6	subtracting	subtract	VERB
ejpam-6294	229	7	the	the	DET
ejpam-6294	229	8	equations	equation	NOUN
ejpam-6294	229	9	(	(	PUNCT
ejpam-6294	229	10	34	34	NUM
ejpam-6294	229	11	)	)	PUNCT
ejpam-6294	229	12	and	and	CCONJ
ejpam-6294	229	13	(	(	PUNCT
ejpam-6294	229	14	36	36	NUM
ejpam-6294	229	15	)	)	PUNCT
ejpam-6294	229	16	,	,	PUNCT
ejpam-6294	229	17	we	we	PRON
ejpam-6294	229	18	get	get	VERB
ejpam-6294	229	19	2(1	2(1	NUM
ejpam-6294	229	20	+	+	CCONJ
ejpam-6294	229	21	2τ)a3	2τ)a3	NUM
ejpam-6294	229	22	−	−	NOUN
ejpam-6294	229	23	(	(	PUNCT
ejpam-6294	229	24	1	1	NUM
ejpam-6294	229	25	+	+	NUM
ejpam-6294	229	26	3τ)a22	3τ)a22	NUM
ejpam-6294	229	27	−	−	NOUN
ejpam-6294	229	28	(	(	PUNCT
ejpam-6294	229	29	3	3	NUM
ejpam-6294	229	30	+	+	NUM
ejpam-6294	229	31	5τ)a22	5τ)a22	NUM
ejpam-6294	229	32	+	+	CCONJ
ejpam-6294	229	33	2(1	2(1	NUM
ejpam-6294	229	34	+	+	CCONJ
ejpam-6294	229	35	2τ)a3	2τ)a3	NUM
ejpam-6294	229	36	=	=	SYM
ejpam-6294	229	37	s2	s2	NOUN
ejpam-6294	229	38	−	−	PROPN
ejpam-6294	229	39	t2	t2	NOUN
ejpam-6294	229	40	4(1	4(1	NUM
ejpam-6294	229	41	+	+	CCONJ
ejpam-6294	229	42	2τ)a3	2τ)a3	NUM
ejpam-6294	229	43	=	=	SYM
ejpam-6294	229	44	s2	s2	NOUN
ejpam-6294	229	45	−	−	NOUN
ejpam-6294	229	46	t2	t2	PROPN
ejpam-6294	229	47	+	+	CCONJ
ejpam-6294	229	48	(	(	PUNCT
ejpam-6294	229	49	4	4	NUM
ejpam-6294	229	50	+	+	NUM
ejpam-6294	229	51	8τ)a22	8τ)a22	NUM
ejpam-6294	229	52	a3	a3	NOUN
ejpam-6294	229	53	=	=	SYM
ejpam-6294	229	54	a22	a22	PROPN
ejpam-6294	229	55	+	+	CCONJ
ejpam-6294	229	56	s2	s2	PROPN
ejpam-6294	229	57	−	−	PROPN
ejpam-6294	229	58	t2	t2	NOUN
ejpam-6294	229	59	4(1	4(1	X
ejpam-6294	229	60	+	+	CCONJ
ejpam-6294	229	61	2τ	2τ	NUM
ejpam-6294	229	62	)	)	PUNCT
ejpam-6294	229	63	(	(	PUNCT
ejpam-6294	229	64	39	39	NUM
ejpam-6294	229	65	)	)	PUNCT
ejpam-6294	229	66	substituting	substitute	VERB
ejpam-6294	229	67	the	the	DET
ejpam-6294	229	68	equations	equation	NOUN
ejpam-6294	229	69	(	(	PUNCT
ejpam-6294	229	70	38	38	NUM
ejpam-6294	229	71	)	)	PUNCT
ejpam-6294	229	72	in	in	ADP
ejpam-6294	229	73	equation	equation	NOUN
ejpam-6294	229	74	(	(	PUNCT
ejpam-6294	229	75	39	39	NUM
ejpam-6294	229	76	)	)	PUNCT
ejpam-6294	229	77	,	,	PUNCT
ejpam-6294	229	78	we	we	PRON
ejpam-6294	229	79	get	get	VERB
ejpam-6294	229	80	a3	a3	NOUN
ejpam-6294	229	81	=	=	SYM
ejpam-6294	229	82	s2	s2	NOUN
ejpam-6294	229	83	−	−	PROPN
ejpam-6294	229	84	t2	t2	PROPN
ejpam-6294	229	85	4(1	4(1	NUM
ejpam-6294	229	86	+	+	CCONJ
ejpam-6294	229	87	2τ	2τ	NUM
ejpam-6294	229	88	)	)	PUNCT
ejpam-6294	230	1	+	+	CCONJ
ejpam-6294	230	2	s2	s2	NOUN
ejpam-6294	230	3	+	+	CCONJ
ejpam-6294	230	4	t2	t2	PROPN
ejpam-6294	230	5	2(1	2(1	NUM
ejpam-6294	230	6	+	+	CCONJ
ejpam-6294	230	7	τ)2	τ)2	NOUN
ejpam-6294	230	8	(	(	PUNCT
ejpam-6294	230	9	40	40	NUM
ejpam-6294	230	10	)	)	PUNCT
ejpam-6294	230	11	s.	s.	PROPN
ejpam-6294	230	12	thangamani	thangamani	PROPN
ejpam-6294	230	13	et	et	PROPN
ejpam-6294	230	14	al	al	PROPN
ejpam-6294	230	15	.	.	PUNCT
ejpam-6294	230	16	/	/	SYM
ejpam-6294	230	17	eur	eur	PROPN
ejpam-6294	230	18	.	.	PUNCT
ejpam-6294	231	1	j.	j.	PROPN
ejpam-6294	231	2	pure	pure	PROPN
ejpam-6294	231	3	appl	appl	PROPN
ejpam-6294	231	4	.	.	PROPN
ejpam-6294	231	5	math	math	PROPN
ejpam-6294	231	6	,	,	PUNCT
ejpam-6294	231	7	18	18	NUM
ejpam-6294	231	8	(	(	PUNCT
ejpam-6294	231	9	3	3	NUM
ejpam-6294	231	10	)	)	PUNCT
ejpam-6294	231	11	(	(	PUNCT
ejpam-6294	231	12	2025	2025	NUM
ejpam-6294	231	13	)	)	PUNCT
ejpam-6294	231	14	,	,	PUNCT
ejpam-6294	231	15	6294	6294	NUM
ejpam-6294	231	16	12	12	NUM
ejpam-6294	231	17	of	of	ADP
ejpam-6294	231	18	19	19	NUM
ejpam-6294	231	19	substituting	substitute	VERB
ejpam-6294	231	20	the	the	DET
ejpam-6294	231	21	equations	equation	NOUN
ejpam-6294	231	22	(	(	PUNCT
ejpam-6294	231	23	34	34	NUM
ejpam-6294	231	24	)	)	PUNCT
ejpam-6294	231	25	in	in	ADP
ejpam-6294	231	26	equation	equation	NOUN
ejpam-6294	231	27	(	(	PUNCT
ejpam-6294	231	28	36	36	NUM
ejpam-6294	231	29	)	)	PUNCT
ejpam-6294	231	30	,	,	PUNCT
ejpam-6294	231	31	we	we	PRON
ejpam-6294	231	32	get	get	VERB
ejpam-6294	231	33	2(1	2(1	NUM
ejpam-6294	231	34	+	+	CCONJ
ejpam-6294	231	35	2τ)a3	2τ)a3	NUM
ejpam-6294	231	36	−	−	NOUN
ejpam-6294	232	1	(	(	PUNCT
ejpam-6294	232	2	1	1	NUM
ejpam-6294	232	3	+	+	NUM
ejpam-6294	232	4	3τ)a22	3τ)a22	NUM
ejpam-6294	232	5	+	+	CCONJ
ejpam-6294	232	6	(	(	PUNCT
ejpam-6294	232	7	3	3	NUM
ejpam-6294	232	8	+	+	NUM
ejpam-6294	232	9	5τ)a22	5τ)a22	NUM
ejpam-6294	232	10	+	+	CCONJ
ejpam-6294	232	11	(	(	PUNCT
ejpam-6294	232	12	2	2	NUM
ejpam-6294	232	13	+	+	SYM
ejpam-6294	232	14	2τ)a3	2τ)a3	NUM
ejpam-6294	232	15	=	=	SYM
ejpam-6294	232	16	2	2	NUM
ejpam-6294	232	17	+	+	NUM
ejpam-6294	232	18	t2	t2	NOUN
ejpam-6294	232	19	(	(	PUNCT
ejpam-6294	232	20	2	2	NUM
ejpam-6294	232	21	+	+	NUM
ejpam-6294	232	22	2τ)a22	2τ)a22	NUM
ejpam-6294	232	23	=	=	SYM
ejpam-6294	232	24	2	2	NUM
ejpam-6294	232	25	+	+	NUM
ejpam-6294	232	26	t2	t2	NOUN
ejpam-6294	232	27	+	+	CCONJ
ejpam-6294	232	28	2	2	NUM
ejpam-6294	232	29	+	+	NUM
ejpam-6294	232	30	s2	s2	NOUN
ejpam-6294	232	31	a22	a22	NOUN
ejpam-6294	232	32	=	=	SYM
ejpam-6294	232	33	s2	s2	PROPN
ejpam-6294	232	34	+	+	CCONJ
ejpam-6294	232	35	t2	t2	NOUN
ejpam-6294	232	36	+	+	CCONJ
ejpam-6294	232	37	4	4	NUM
ejpam-6294	232	38	2(1	2(1	NUM
ejpam-6294	232	39	+	+	CCONJ
ejpam-6294	232	40	τ	τ	X
ejpam-6294	232	41	)	)	PUNCT
ejpam-6294	232	42	(	(	PUNCT
ejpam-6294	232	43	41	41	NUM
ejpam-6294	232	44	)	)	PUNCT
ejpam-6294	232	45	substituting	substitute	VERB
ejpam-6294	232	46	the	the	DET
ejpam-6294	232	47	equation	equation	NOUN
ejpam-6294	232	48	(	(	PUNCT
ejpam-6294	232	49	41	41	NUM
ejpam-6294	232	50	)	)	PUNCT
ejpam-6294	232	51	in	in	ADP
ejpam-6294	232	52	(	(	PUNCT
ejpam-6294	232	53	39	39	NUM
ejpam-6294	232	54	)	)	PUNCT
ejpam-6294	232	55	,	,	PUNCT
ejpam-6294	232	56	we	we	PRON
ejpam-6294	232	57	get	get	VERB
ejpam-6294	232	58	a3	a3	NOUN
ejpam-6294	232	59	=	=	SYM
ejpam-6294	232	60	s2	s2	NOUN
ejpam-6294	232	61	+	+	CCONJ
ejpam-6294	232	62	t2	t2	NOUN
ejpam-6294	232	63	+	+	CCONJ
ejpam-6294	232	64	4	4	NUM
ejpam-6294	232	65	(	(	PUNCT
ejpam-6294	232	66	2	2	NUM
ejpam-6294	232	67	+	+	NUM
ejpam-6294	232	68	2τ	2τ	NUM
ejpam-6294	232	69	)	)	PUNCT
ejpam-6294	233	1	+	+	CCONJ
ejpam-6294	233	2	s2	s2	NOUN
ejpam-6294	233	3	−	−	PROPN
ejpam-6294	233	4	t2	t2	NOUN
ejpam-6294	233	5	4(1	4(1	X
ejpam-6294	233	6	+	+	CCONJ
ejpam-6294	233	7	2τ	2τ	NOUN
ejpam-6294	233	8	)	)	PUNCT
ejpam-6294	233	9	|a3|	|a3|	VERB
ejpam-6294	233	10	≤	≤	PUNCT
ejpam-6294	233	11	s2	s2	NOUN
ejpam-6294	233	12	+	+	CCONJ
ejpam-6294	233	13	2	2	NUM
ejpam-6294	233	14	2(1	2(1	NUM
ejpam-6294	233	15	+	+	CCONJ
ejpam-6294	233	16	τ	τ	X
ejpam-6294	233	17	)	)	PUNCT
ejpam-6294	233	18	(	(	PUNCT
ejpam-6294	233	19	42	42	NUM
ejpam-6294	233	20	)	)	PUNCT
ejpam-6294	233	21	hence	hence	ADV
ejpam-6294	233	22	,	,	PUNCT
ejpam-6294	233	23	|a2|	|a2|	VERB
ejpam-6294	233	24	≤	≤	ADJ
ejpam-6294	233	25	√	√	CCONJ
ejpam-6294	233	26	s2	s2	NOUN
ejpam-6294	233	27	+	+	CCONJ
ejpam-6294	233	28	t2	t2	NOUN
ejpam-6294	233	29	+	+	CCONJ
ejpam-6294	233	30	4	4	NUM
ejpam-6294	233	31	(	(	PUNCT
ejpam-6294	233	32	2	2	NUM
ejpam-6294	233	33	+	+	NUM
ejpam-6294	233	34	2τ	2τ	NUM
ejpam-6294	233	35	)	)	PUNCT
ejpam-6294	233	36	|a3|	|a3|	VERB
ejpam-6294	233	37	≤	≤	PUNCT
ejpam-6294	233	38	s2	s2	PROPN
ejpam-6294	233	39	+	+	CCONJ
ejpam-6294	233	40	t2	t2	PROPN
ejpam-6294	233	41	2(1	2(1	NUM
ejpam-6294	233	42	+	+	CCONJ
ejpam-6294	233	43	τ)2	τ)2	NOUN
ejpam-6294	233	44	+	+	CCONJ
ejpam-6294	233	45	s2	s2	PROPN
ejpam-6294	233	46	−	−	PROPN
ejpam-6294	233	47	t2	t2	NOUN
ejpam-6294	233	48	4(1	4(1	X
ejpam-6294	233	49	+	+	CCONJ
ejpam-6294	233	50	2τ	2τ	NOUN
ejpam-6294	233	51	)	)	PUNCT
ejpam-6294	233	52	the	the	DET
ejpam-6294	233	53	next	next	ADJ
ejpam-6294	233	54	couple	couple	NOUN
ejpam-6294	233	55	of	of	ADP
ejpam-6294	233	56	consequences	consequence	NOUN
ejpam-6294	233	57	are	be	AUX
ejpam-6294	233	58	obtained	obtain	VERB
ejpam-6294	233	59	by	by	ADP
ejpam-6294	233	60	specializing	specialize	VERB
ejpam-6294	233	61	the	the	DET
ejpam-6294	233	62	parameter	parameter	NOUN
ejpam-6294	233	63	values	value	NOUN
ejpam-6294	233	64	of	of	ADP
ejpam-6294	233	65	τ	τ	PROPN
ejpam-6294	233	66	=	=	SYM
ejpam-6294	233	67	0	0	PROPN
ejpam-6294	233	68	and	and	CCONJ
ejpam-6294	233	69	τ	τ	X
ejpam-6294	233	70	=	=	NOUN
ejpam-6294	233	71	1	1	NUM
ejpam-6294	233	72	in	in	ADP
ejpam-6294	233	73	the	the	DET
ejpam-6294	233	74	theorem	theorem	NOUN
ejpam-6294	233	75	(	(	PUNCT
ejpam-6294	233	76	3	3	NUM
ejpam-6294	233	77	)	)	PUNCT
ejpam-6294	233	78	,	,	PUNCT
ejpam-6294	233	79	respectively	respectively	ADV
ejpam-6294	233	80	.	.	PUNCT
ejpam-6294	234	1	corollary	corollary	ADJ
ejpam-6294	234	2	5	5	NUM
ejpam-6294	234	3	.	.	PUNCT
ejpam-6294	235	1	the	the	DET
ejpam-6294	235	2	function	function	NOUN
ejpam-6294	235	3	f	f	PROPN
ejpam-6294	235	4	(	(	PUNCT
ejpam-6294	235	5	θ	θ	NOUN
ejpam-6294	235	6	)	)	PUNCT
ejpam-6294	235	7	satisfies	satisfy	VERB
ejpam-6294	235	8	a	a	DET
ejpam-6294	235	9	couple	couple	NOUN
ejpam-6294	235	10	of	of	ADP
ejpam-6294	235	11	conditions	condition	NOUN
ejpam-6294	235	12	to	to	PART
ejpam-6294	235	13	be	be	AUX
ejpam-6294	235	14	included	include	VERB
ejpam-6294	235	15	in	in	ADP
ejpam-6294	235	16	this	this	DET
ejpam-6294	235	17	subclass	subclass	NOUN
ejpam-6294	235	18	of	of	ADP
ejpam-6294	235	19	bi	bi	ADJ
ejpam-6294	235	20	-	-	ADJ
ejpam-6294	235	21	univalent	univalent	ADJ
ejpam-6294	235	22	functions	function	NOUN
ejpam-6294	235	23	if	if	SCONJ
ejpam-6294	235	24	it	it	PRON
ejpam-6294	235	25	is	be	AUX
ejpam-6294	235	26	provided	provide	VERB
ejpam-6294	235	27	by	by	ADP
ejpam-6294	235	28	(	(	PUNCT
ejpam-6294	235	29	1	1	NUM
ejpam-6294	235	30	)	)	PUNCT
ejpam-6294	235	31	and	and	CCONJ
ejpam-6294	235	32	is	be	AUX
ejpam-6294	235	33	a	a	DET
ejpam-6294	235	34	member	member	NOUN
ejpam-6294	235	35	of	of	ADP
ejpam-6294	235	36	the	the	DET
ejpam-6294	235	37	class	class	NOUN
ejpam-6294	235	38	gς	gς	PROPN
ejpam-6294	235	39	,	,	PUNCT
ejpam-6294	235	40	g(τ	g(τ	PROPN
ejpam-6294	235	41	)	)	PUNCT
ejpam-6294	235	42	.	.	PUNCT
ejpam-6294	236	1	then	then	ADV
ejpam-6294	236	2	|a2|	|a2|	VERB
ejpam-6294	236	3	≤	≤	ADJ
ejpam-6294	236	4	√	√	PROPN
ejpam-6294	236	5	s2	s2	VERB
ejpam-6294	236	6	+	+	CCONJ
ejpam-6294	236	7	t2	t2	NOUN
ejpam-6294	236	8	+	+	CCONJ
ejpam-6294	236	9	4	4	NUM
ejpam-6294	236	10	2	2	NUM
ejpam-6294	236	11	and	and	CCONJ
ejpam-6294	236	12	|a3|	|a3|	VERB
ejpam-6294	236	13	≤	≤	PUNCT
ejpam-6294	236	14	s2	s2	PROPN
ejpam-6294	236	15	+	+	CCONJ
ejpam-6294	236	16	t2	t2	PROPN
ejpam-6294	236	17	2	2	NUM
ejpam-6294	236	18	+	+	CCONJ
ejpam-6294	236	19	s2	s2	NOUN
ejpam-6294	236	20	−	−	PROPN
ejpam-6294	236	21	t2	t2	NOUN
ejpam-6294	236	22	4	4	NUM
ejpam-6294	236	23	corollary	corollary	ADJ
ejpam-6294	236	24	6	6	NUM
ejpam-6294	236	25	.	.	PUNCT
ejpam-6294	237	1	the	the	DET
ejpam-6294	237	2	function	function	NOUN
ejpam-6294	237	3	f	f	PROPN
ejpam-6294	237	4	(	(	PUNCT
ejpam-6294	237	5	θ	θ	NOUN
ejpam-6294	237	6	)	)	PUNCT
ejpam-6294	237	7	satisfies	satisfy	VERB
ejpam-6294	237	8	a	a	DET
ejpam-6294	237	9	couple	couple	NOUN
ejpam-6294	237	10	of	of	ADP
ejpam-6294	237	11	conditions	condition	NOUN
ejpam-6294	237	12	to	to	PART
ejpam-6294	237	13	be	be	AUX
ejpam-6294	237	14	included	include	VERB
ejpam-6294	237	15	in	in	ADP
ejpam-6294	237	16	this	this	DET
ejpam-6294	237	17	subclass	subclass	NOUN
ejpam-6294	237	18	of	of	ADP
ejpam-6294	237	19	bi	bi	ADJ
ejpam-6294	237	20	-	-	ADJ
ejpam-6294	237	21	univalent	univalent	ADJ
ejpam-6294	237	22	functions	function	NOUN
ejpam-6294	237	23	if	if	SCONJ
ejpam-6294	237	24	it	it	PRON
ejpam-6294	237	25	is	be	AUX
ejpam-6294	237	26	provided	provide	VERB
ejpam-6294	237	27	by	by	ADP
ejpam-6294	237	28	(	(	PUNCT
ejpam-6294	237	29	1	1	NUM
ejpam-6294	237	30	)	)	PUNCT
ejpam-6294	237	31	and	and	CCONJ
ejpam-6294	237	32	is	be	AUX
ejpam-6294	237	33	a	a	DET
ejpam-6294	237	34	member	member	NOUN
ejpam-6294	237	35	of	of	ADP
ejpam-6294	237	36	the	the	DET
ejpam-6294	237	37	class	class	NOUN
ejpam-6294	237	38	gς	gς	PROPN
ejpam-6294	237	39	,	,	PUNCT
ejpam-6294	237	40	g(τ	g(τ	PROPN
ejpam-6294	237	41	)	)	PUNCT
ejpam-6294	237	42	.	.	PUNCT
ejpam-6294	238	1	then	then	ADV
ejpam-6294	238	2	|a2|	|a2|	VERB
ejpam-6294	238	3	≤	≤	ADJ
ejpam-6294	238	4	√	√	PROPN
ejpam-6294	238	5	s2	s2	VERB
ejpam-6294	238	6	+	+	CCONJ
ejpam-6294	238	7	t2	t2	NOUN
ejpam-6294	238	8	+	+	CCONJ
ejpam-6294	238	9	4	4	NUM
ejpam-6294	238	10	4	4	NUM
ejpam-6294	238	11	and	and	CCONJ
ejpam-6294	238	12	|a3|	|a3|	VERB
ejpam-6294	238	13	≤	≤	PROPN
ejpam-6294	238	14	s2	s2	PROPN
ejpam-6294	238	15	+	+	CCONJ
ejpam-6294	238	16	t2	t2	PROPN
ejpam-6294	238	17	8	8	NUM
ejpam-6294	238	18	+	+	NUM
ejpam-6294	238	19	s2	s2	PROPN
ejpam-6294	238	20	−	−	PROPN
ejpam-6294	238	21	t2	t2	PROPN
ejpam-6294	238	22	12	12	NUM
ejpam-6294	238	23	s.	s.	PROPN
ejpam-6294	238	24	thangamani	thangamani	PROPN
ejpam-6294	238	25	et	et	PROPN
ejpam-6294	238	26	al	al	PROPN
ejpam-6294	238	27	.	.	PUNCT
ejpam-6294	238	28	/	/	SYM
ejpam-6294	238	29	eur	eur	PROPN
ejpam-6294	238	30	.	.	PUNCT
ejpam-6294	239	1	j.	j.	PROPN
ejpam-6294	239	2	pure	pure	PROPN
ejpam-6294	239	3	appl	appl	PROPN
ejpam-6294	239	4	.	.	PROPN
ejpam-6294	239	5	math	math	PROPN
ejpam-6294	239	6	,	,	PUNCT
ejpam-6294	239	7	18	18	NUM
ejpam-6294	239	8	(	(	PUNCT
ejpam-6294	239	9	3	3	NUM
ejpam-6294	239	10	)	)	PUNCT
ejpam-6294	239	11	(	(	PUNCT
ejpam-6294	239	12	2025	2025	NUM
ejpam-6294	239	13	)	)	PUNCT
ejpam-6294	239	14	,	,	PUNCT
ejpam-6294	239	15	6294	6294	NUM
ejpam-6294	239	16	13	13	NUM
ejpam-6294	239	17	of	of	ADP
ejpam-6294	239	18	19	19	NUM
ejpam-6294	239	19	5	5	NUM
ejpam-6294	239	20	.	.	PUNCT
ejpam-6294	240	1	fekete	fekete	NOUN
ejpam-6294	240	2	-	-	PUNCT
ejpam-6294	240	3	szegö	szegö	PROPN
ejpam-6294	240	4	inequality	inequality	NOUN
ejpam-6294	240	5	for	for	ADP
ejpam-6294	240	6	the	the	DET
ejpam-6294	240	7	subclass	subclass	ADJ
ejpam-6294	240	8	gς	gς	PROPN
ejpam-6294	240	9	,	,	PUNCT
ejpam-6294	240	10	g(τ	g(τ	PROPN
ejpam-6294	240	11	)	)	PUNCT
ejpam-6294	240	12	theorem	theorem	NOUN
ejpam-6294	240	13	4	4	NUM
ejpam-6294	240	14	.	.	PUNCT
ejpam-6294	241	1	if	if	SCONJ
ejpam-6294	241	2	f	f	PROPN
ejpam-6294	241	3	(	(	PUNCT
ejpam-6294	241	4	θ	θ	NOUN
ejpam-6294	241	5	)	)	PUNCT
ejpam-6294	241	6	is	be	AUX
ejpam-6294	241	7	given	give	VERB
ejpam-6294	241	8	by	by	ADP
ejpam-6294	241	9	(	(	PUNCT
ejpam-6294	241	10	1	1	X
ejpam-6294	241	11	)	)	PUNCT
ejpam-6294	241	12	be	be	AUX
ejpam-6294	241	13	in	in	ADP
ejpam-6294	241	14	the	the	DET
ejpam-6294	241	15	class	class	NOUN
ejpam-6294	241	16	gς	gς	NOUN
ejpam-6294	241	17	,	,	PUNCT
ejpam-6294	241	18	g(τ	g(τ	PROPN
ejpam-6294	241	19	)	)	PUNCT
ejpam-6294	241	20	.	.	PUNCT
ejpam-6294	242	1	then	then	ADV
ejpam-6294	242	2	|a3	|a3	VERB
ejpam-6294	242	3	−	−	PROPN
ejpam-6294	242	4	ηa22|	ηa22|	NOUN
ejpam-6294	242	5	≤	≤	NOUN
ejpam-6294	242	6	{	{	PUNCT
ejpam-6294	242	7	s2	s2	PROPN
ejpam-6294	242	8	(	(	PUNCT
ejpam-6294	242	9	1	1	NUM
ejpam-6294	242	10	+	+	NOUN
ejpam-6294	242	11	2τ	2τ	NUM
ejpam-6294	242	12	)	)	PUNCT
ejpam-6294	242	13	if	if	SCONJ
ejpam-6294	242	14	0	0	NUM
ejpam-6294	242	15	≤	≤	NUM
ejpam-6294	242	16	|h1(η)|	|h1(η)|	NOUN
ejpam-6294	242	17	≤	≤	NUM
ejpam-6294	242	18	1	1	NUM
ejpam-6294	242	19	4(1	4(1	NOUN
ejpam-6294	242	20	+	+	NOUN
ejpam-6294	242	21	2τ	2τ	NOUN
ejpam-6294	242	22	)	)	PUNCT
ejpam-6294	242	23	,	,	PUNCT
ejpam-6294	242	24	2s2|	2s2|	NUM
ejpam-6294	242	25	(	(	PUNCT
ejpam-6294	242	26	1−η	1−η	NUM
ejpam-6294	242	27	)	)	PUNCT
ejpam-6294	242	28	2(1+τ)2	2(1+τ)2	NUM
ejpam-6294	243	1	|	|	ADV
ejpam-6294	243	2	if	if	SCONJ
ejpam-6294	243	3	|h1(η)|	|h1(η)|	NUM
ejpam-6294	243	4	≥	≥	NOUN
ejpam-6294	243	5	1	1	NUM
ejpam-6294	243	6	4(1	4(1	NOUN
ejpam-6294	243	7	+	+	NOUN
ejpam-6294	243	8	2τ	2τ	NOUN
ejpam-6294	243	9	)	)	PUNCT
ejpam-6294	243	10	,	,	PUNCT
ejpam-6294	243	11	(	(	PUNCT
ejpam-6294	243	12	43	43	NUM
ejpam-6294	243	13	)	)	PUNCT
ejpam-6294	243	14	where	where	SCONJ
ejpam-6294	243	15	h1(η	h1(η	X
ejpam-6294	243	16	)	)	PUNCT
ejpam-6294	243	17	=	=	SYM
ejpam-6294	243	18	(	(	PUNCT
ejpam-6294	243	19	1−	1−	NUM
ejpam-6294	243	20	η	η	NOUN
ejpam-6294	243	21	)	)	PUNCT
ejpam-6294	243	22	2(1	2(1	NUM
ejpam-6294	244	1	+	+	CCONJ
ejpam-6294	244	2	τ)2	τ)2	NOUN
ejpam-6294	244	3	.	.	PUNCT
ejpam-6294	245	1	proof	proof	NOUN
ejpam-6294	245	2	.	.	PUNCT
ejpam-6294	246	1	from	from	ADP
ejpam-6294	246	2	the	the	DET
ejpam-6294	246	3	equations	equation	NOUN
ejpam-6294	246	4	(	(	PUNCT
ejpam-6294	246	5	38	38	NUM
ejpam-6294	246	6	)	)	PUNCT
ejpam-6294	246	7	and	and	CCONJ
ejpam-6294	246	8	(	(	PUNCT
ejpam-6294	246	9	39	39	NUM
ejpam-6294	246	10	)	)	PUNCT
ejpam-6294	246	11	,	,	PUNCT
ejpam-6294	246	12	we	we	PRON
ejpam-6294	246	13	get	get	VERB
ejpam-6294	246	14	a3	a3	NOUN
ejpam-6294	246	15	−	−	PROPN
ejpam-6294	247	1	ηa22	ηa22	PROPN
ejpam-6294	247	2	=	=	PUNCT
ejpam-6294	247	3	a22	a22	PROPN
ejpam-6294	247	4	+	+	CCONJ
ejpam-6294	247	5	s2	s2	PROPN
ejpam-6294	247	6	−	−	PROPN
ejpam-6294	247	7	t2	t2	NOUN
ejpam-6294	247	8	4(1	4(1	X
ejpam-6294	247	9	+	+	CCONJ
ejpam-6294	247	10	2τ	2τ	NUM
ejpam-6294	247	11	)	)	PUNCT
ejpam-6294	248	1	−	−	PROPN
ejpam-6294	249	1	ηa22	ηa22	PROPN
ejpam-6294	249	2	a3	a3	NOUN
ejpam-6294	249	3	−	−	PROPN
ejpam-6294	249	4	ηa22	ηa22	PROPN
ejpam-6294	249	5	=	=	SYM
ejpam-6294	249	6	(	(	PUNCT
ejpam-6294	249	7	1−	1−	NUM
ejpam-6294	249	8	η)a22	η)a22	SYM
ejpam-6294	249	9	+	+	NUM
ejpam-6294	249	10	s2	s2	PROPN
ejpam-6294	249	11	−	−	PROPN
ejpam-6294	249	12	t2	t2	NOUN
ejpam-6294	249	13	4(1	4(1	X
ejpam-6294	249	14	+	+	CCONJ
ejpam-6294	249	15	2τ	2τ	NOUN
ejpam-6294	249	16	)	)	PUNCT
ejpam-6294	249	17	a3	a3	NOUN
ejpam-6294	249	18	−	−	PROPN
ejpam-6294	250	1	ηa22	ηa22	PROPN
ejpam-6294	250	2	=	=	SYM
ejpam-6294	250	3	(	(	PUNCT
ejpam-6294	250	4	1−	1−	NUM
ejpam-6294	250	5	η	η	NOUN
ejpam-6294	250	6	)	)	PUNCT
ejpam-6294	250	7	s2	s2	NOUN
ejpam-6294	250	8	+	+	CCONJ
ejpam-6294	250	9	t2	t2	PROPN
ejpam-6294	250	10	2(1	2(1	NUM
ejpam-6294	250	11	+	+	CCONJ
ejpam-6294	250	12	τ2	τ2	NOUN
ejpam-6294	250	13	)	)	PUNCT
ejpam-6294	250	14	+	+	CCONJ
ejpam-6294	250	15	s2	s2	NOUN
ejpam-6294	250	16	−	−	PROPN
ejpam-6294	250	17	t2	t2	NOUN
ejpam-6294	250	18	4(1	4(1	X
ejpam-6294	250	19	+	+	CCONJ
ejpam-6294	250	20	2τ	2τ	NOUN
ejpam-6294	250	21	)	)	PUNCT
ejpam-6294	250	22	a3	a3	NOUN
ejpam-6294	250	23	−	−	PROPN
ejpam-6294	251	1	ηa22	ηa22	PROPN
ejpam-6294	251	2	=	=	SYM
ejpam-6294	251	3	s2	s2	PROPN
ejpam-6294	251	4	(	(	PUNCT
ejpam-6294	251	5	(	(	PUNCT
ejpam-6294	251	6	1−	1−	NUM
ejpam-6294	251	7	η	η	NOUN
ejpam-6294	251	8	)	)	PUNCT
ejpam-6294	251	9	2(1	2(1	NUM
ejpam-6294	252	1	+	+	CCONJ
ejpam-6294	252	2	τ)2	τ)2	NOUN
ejpam-6294	252	3	+	+	CCONJ
ejpam-6294	252	4	1	1	NUM
ejpam-6294	252	5	4(1	4(1	NUM
ejpam-6294	252	6	+	+	CCONJ
ejpam-6294	252	7	2τ	2τ	NUM
ejpam-6294	252	8	)	)	PUNCT
ejpam-6294	252	9	)	)	PUNCT
ejpam-6294	253	1	+	+	CCONJ
ejpam-6294	253	2	t2	t2	NOUN
ejpam-6294	253	3	(	(	PUNCT
ejpam-6294	253	4	(	(	PUNCT
ejpam-6294	253	5	1−	1−	NUM
ejpam-6294	253	6	η	η	NOUN
ejpam-6294	253	7	)	)	PUNCT
ejpam-6294	253	8	2(1	2(1	NUM
ejpam-6294	254	1	+	+	CCONJ
ejpam-6294	254	2	τ)2	τ)2	NOUN
ejpam-6294	254	3	−	−	PROPN
ejpam-6294	254	4	1	1	NUM
ejpam-6294	254	5	4(1	4(1	NOUN
ejpam-6294	254	6	+	+	CCONJ
ejpam-6294	254	7	2τ	2τ	NUM
ejpam-6294	254	8	)	)	PUNCT
ejpam-6294	254	9	)	)	PUNCT
ejpam-6294	254	10	a3	a3	NOUN
ejpam-6294	254	11	−	−	PROPN
ejpam-6294	255	1	ηa22	ηa22	PROPN
ejpam-6294	255	2	=	=	SYM
ejpam-6294	255	3	s2	s2	PROPN
ejpam-6294	255	4	(	(	PUNCT
ejpam-6294	255	5	h1(η	h1(η	PROPN
ejpam-6294	255	6	)	)	PUNCT
ejpam-6294	255	7	+	+	CCONJ
ejpam-6294	255	8	1	1	NUM
ejpam-6294	255	9	4(1	4(1	NUM
ejpam-6294	255	10	+	+	CCONJ
ejpam-6294	255	11	2τ	2τ	NUM
ejpam-6294	255	12	)	)	PUNCT
ejpam-6294	255	13	)	)	PUNCT
ejpam-6294	256	1	+	+	CCONJ
ejpam-6294	256	2	t2	t2	NOUN
ejpam-6294	256	3	(	(	PUNCT
ejpam-6294	256	4	h1(η)−	h1(η)−	NOUN
ejpam-6294	256	5	1	1	NUM
ejpam-6294	256	6	4(1	4(1	NUM
ejpam-6294	256	7	+	+	CCONJ
ejpam-6294	256	8	2τ	2τ	NUM
ejpam-6294	256	9	)	)	PUNCT
ejpam-6294	256	10	)	)	PUNCT
ejpam-6294	257	1	where	where	SCONJ
ejpam-6294	257	2	h1(η	h1(η	X
ejpam-6294	257	3	)	)	PUNCT
ejpam-6294	257	4	=	=	SYM
ejpam-6294	257	5	(	(	PUNCT
ejpam-6294	257	6	1−	1−	NUM
ejpam-6294	257	7	η	η	NOUN
ejpam-6294	257	8	)	)	PUNCT
ejpam-6294	257	9	2(1	2(1	NUM
ejpam-6294	258	1	+	+	CCONJ
ejpam-6294	258	2	τ)2	τ)2	NOUN
ejpam-6294	258	3	(	(	PUNCT
ejpam-6294	258	4	44	44	NUM
ejpam-6294	258	5	)	)	PUNCT
ejpam-6294	258	6	hence	hence	ADV
ejpam-6294	258	7	,	,	PUNCT
ejpam-6294	258	8	|a3	|a3	VERB
ejpam-6294	258	9	−	−	PROPN
ejpam-6294	258	10	ηa22|	ηa22|	NOUN
ejpam-6294	258	11	≤	≤	NOUN
ejpam-6294	258	12	{	{	PUNCT
ejpam-6294	258	13	s2	s2	PROPN
ejpam-6294	258	14	(	(	PUNCT
ejpam-6294	258	15	1	1	NUM
ejpam-6294	258	16	+	+	NOUN
ejpam-6294	258	17	2τ	2τ	NUM
ejpam-6294	258	18	)	)	PUNCT
ejpam-6294	258	19	if	if	SCONJ
ejpam-6294	258	20	0	0	NUM
ejpam-6294	258	21	≤	≤	NUM
ejpam-6294	258	22	|h1(η)|	|h1(η)|	NOUN
ejpam-6294	258	23	≤	≤	NUM
ejpam-6294	258	24	1	1	NUM
ejpam-6294	258	25	4(1	4(1	NOUN
ejpam-6294	258	26	+	+	NOUN
ejpam-6294	258	27	2τ	2τ	NOUN
ejpam-6294	258	28	)	)	PUNCT
ejpam-6294	258	29	,	,	PUNCT
ejpam-6294	258	30	2s2|	2s2|	NUM
ejpam-6294	258	31	(	(	PUNCT
ejpam-6294	258	32	1−η	1−η	NUM
ejpam-6294	258	33	)	)	PUNCT
ejpam-6294	258	34	2(1+τ)2	2(1+τ)2	NUM
ejpam-6294	259	1	|	|	ADV
ejpam-6294	259	2	if	if	SCONJ
ejpam-6294	259	3	|h1(η)|	|h1(η)|	NUM
ejpam-6294	259	4	≥	≥	NOUN
ejpam-6294	259	5	1	1	NUM
ejpam-6294	259	6	4(1	4(1	NOUN
ejpam-6294	259	7	+	+	NOUN
ejpam-6294	259	8	2τ	2τ	NOUN
ejpam-6294	259	9	)	)	PUNCT
ejpam-6294	259	10	.	.	PUNCT
ejpam-6294	260	1	the	the	DET
ejpam-6294	260	2	two	two	NUM
ejpam-6294	260	3	subsequent	subsequent	ADJ
ejpam-6294	260	4	consequences	consequence	NOUN
ejpam-6294	260	5	are	be	AUX
ejpam-6294	260	6	obtained	obtain	VERB
ejpam-6294	260	7	by	by	ADP
ejpam-6294	260	8	changing	change	VERB
ejpam-6294	260	9	the	the	DET
ejpam-6294	260	10	parameter	parameter	NOUN
ejpam-6294	260	11	values	value	NOUN
ejpam-6294	260	12	in	in	ADP
ejpam-6294	260	13	the	the	DET
ejpam-6294	260	14	theorem	theorem	NOUN
ejpam-6294	260	15	(	(	PUNCT
ejpam-6294	260	16	4	4	NUM
ejpam-6294	260	17	)	)	PUNCT
ejpam-6294	260	18	to	to	ADP
ejpam-6294	260	19	τ	τ	PROPN
ejpam-6294	260	20	=	=	SYM
ejpam-6294	260	21	0	0	PROPN
ejpam-6294	260	22	and	and	CCONJ
ejpam-6294	260	23	τ	τ	X
ejpam-6294	260	24	=	=	SYM
ejpam-6294	260	25	1	1	NUM
ejpam-6294	260	26	,	,	PUNCT
ejpam-6294	260	27	respectively	respectively	ADV
ejpam-6294	260	28	.	.	PUNCT
ejpam-6294	261	1	s.	s.	PROPN
ejpam-6294	261	2	thangamani	thangamani	PROPN
ejpam-6294	261	3	et	et	PROPN
ejpam-6294	261	4	al	al	PROPN
ejpam-6294	261	5	.	.	PUNCT
ejpam-6294	261	6	/	/	SYM
ejpam-6294	261	7	eur	eur	PROPN
ejpam-6294	261	8	.	.	PUNCT
ejpam-6294	262	1	j.	j.	PROPN
ejpam-6294	262	2	pure	pure	PROPN
ejpam-6294	262	3	appl	appl	PROPN
ejpam-6294	262	4	.	.	PROPN
ejpam-6294	262	5	math	math	PROPN
ejpam-6294	262	6	,	,	PUNCT
ejpam-6294	262	7	18	18	NUM
ejpam-6294	262	8	(	(	PUNCT
ejpam-6294	262	9	3	3	NUM
ejpam-6294	262	10	)	)	PUNCT
ejpam-6294	262	11	(	(	PUNCT
ejpam-6294	262	12	2025	2025	NUM
ejpam-6294	262	13	)	)	PUNCT
ejpam-6294	262	14	,	,	PUNCT
ejpam-6294	262	15	6294	6294	NUM
ejpam-6294	262	16	14	14	NUM
ejpam-6294	262	17	of	of	ADP
ejpam-6294	262	18	19	19	NUM
ejpam-6294	262	19	corollary	corollary	ADJ
ejpam-6294	262	20	7	7	NUM
ejpam-6294	262	21	.	.	PUNCT
ejpam-6294	263	1	if	if	SCONJ
ejpam-6294	263	2	the	the	DET
ejpam-6294	263	3	function	function	NOUN
ejpam-6294	263	4	f	f	X
ejpam-6294	263	5	(	(	PUNCT
ejpam-6294	263	6	θ	θ	NOUN
ejpam-6294	263	7	)	)	PUNCT
ejpam-6294	263	8	is	be	AUX
ejpam-6294	263	9	defined	define	VERB
ejpam-6294	263	10	by	by	ADP
ejpam-6294	263	11	(	(	PUNCT
ejpam-6294	263	12	1	1	NUM
ejpam-6294	263	13	)	)	PUNCT
ejpam-6294	263	14	and	and	CCONJ
ejpam-6294	263	15	belongs	belong	VERB
ejpam-6294	263	16	to	to	ADP
ejpam-6294	263	17	the	the	DET
ejpam-6294	263	18	class	class	NOUN
ejpam-6294	263	19	gς	gς	PROPN
ejpam-6294	263	20	,	,	PUNCT
ejpam-6294	263	21	g(τ	g(τ	PROPN
ejpam-6294	263	22	)	)	PUNCT
ejpam-6294	263	23	,	,	PUNCT
ejpam-6294	263	24	then	then	ADV
ejpam-6294	263	25	it	it	PRON
ejpam-6294	263	26	exhibits	exhibit	VERB
ejpam-6294	263	27	specific	specific	ADJ
ejpam-6294	263	28	geometric	geometric	ADJ
ejpam-6294	263	29	and	and	CCONJ
ejpam-6294	263	30	analytic	analytic	ADJ
ejpam-6294	263	31	property	property	NOUN
ejpam-6294	263	32	|a3−ηa22|	|a3−ηa22|	NOUN
ejpam-6294	263	33	that	that	PRON
ejpam-6294	263	34	characterize	characterize	VERB
ejpam-6294	263	35	this	this	DET
ejpam-6294	263	36	subclass	subclass	NOUN
ejpam-6294	263	37	of	of	ADP
ejpam-6294	263	38	functions	function	NOUN
ejpam-6294	263	39	.	.	PUNCT
ejpam-6294	264	1	i.e.	i.e.	X
ejpam-6294	264	2	,	,	PUNCT
ejpam-6294	264	3	|a3	|a3	NOUN
ejpam-6294	264	4	−	−	PROPN
ejpam-6294	264	5	ηa22|	ηa22|	NOUN
ejpam-6294	264	6	≤	≤	NOUN
ejpam-6294	264	7	{	{	PUNCT
ejpam-6294	264	8	s2	s2	VERB
ejpam-6294	264	9	if	if	SCONJ
ejpam-6294	264	10	0	0	NUM
ejpam-6294	264	11	≤	≤	NUM
ejpam-6294	264	12	|h1(η)|	|h1(η)|	NOUN
ejpam-6294	264	13	≤	≤	NUM
ejpam-6294	264	14	1	1	NUM
ejpam-6294	264	15	4	4	NUM
ejpam-6294	264	16	,	,	PUNCT
ejpam-6294	264	17	2s2|	2s2|	NUM
ejpam-6294	264	18	(	(	PUNCT
ejpam-6294	264	19	1−η	1−η	NUM
ejpam-6294	264	20	)	)	PUNCT
ejpam-6294	264	21	2	2	NUM
ejpam-6294	265	1	|	|	ADV
ejpam-6294	265	2	if	if	SCONJ
ejpam-6294	265	3	|h1(η)|	|h1(η)|	NUM
ejpam-6294	265	4	≥	≥	NOUN
ejpam-6294	265	5	1	1	NUM
ejpam-6294	265	6	4	4	NUM
ejpam-6294	265	7	,	,	PUNCT
ejpam-6294	265	8	this	this	PRON
ejpam-6294	265	9	implies	imply	VERB
ejpam-6294	265	10	|a3	|a3	NOUN
ejpam-6294	265	11	−	−	PROPN
ejpam-6294	265	12	ηa22|	ηa22|	NOUN
ejpam-6294	265	13	≤	≤	NOUN
ejpam-6294	265	14	{	{	PUNCT
ejpam-6294	265	15	s2	s2	VERB
ejpam-6294	265	16	if	if	SCONJ
ejpam-6294	265	17	0	0	NUM
ejpam-6294	265	18	≤	≤	NUM
ejpam-6294	265	19	|h1(η)|	|h1(η)|	NOUN
ejpam-6294	265	20	≤	≤	NUM
ejpam-6294	265	21	3	3	NUM
ejpam-6294	265	22	4	4	NUM
ejpam-6294	265	23	,	,	PUNCT
ejpam-6294	265	24	s2|(1−	s2|(1−	VERB
ejpam-6294	265	25	η)|	η)|	PROPN
ejpam-6294	265	26	if	if	SCONJ
ejpam-6294	265	27	|h1(η)|	|h1(η)|	NUM
ejpam-6294	265	28	≥	≥	NOUN
ejpam-6294	265	29	3	3	NUM
ejpam-6294	265	30	4	4	NUM
ejpam-6294	265	31	,	,	PUNCT
ejpam-6294	265	32	where	where	SCONJ
ejpam-6294	265	33	h1(η	h1(η	PROPN
ejpam-6294	265	34	)	)	PUNCT
ejpam-6294	265	35	=	=	SYM
ejpam-6294	265	36	(	(	PUNCT
ejpam-6294	265	37	1−	1−	NUM
ejpam-6294	265	38	η	η	NOUN
ejpam-6294	265	39	)	)	PUNCT
ejpam-6294	265	40	2	2	NUM
ejpam-6294	265	41	.	.	PUNCT
ejpam-6294	266	1	corollary	corollary	ADJ
ejpam-6294	266	2	8	8	NUM
ejpam-6294	266	3	.	.	PUNCT
ejpam-6294	267	1	the	the	DET
ejpam-6294	267	2	function	function	NOUN
ejpam-6294	267	3	f	f	PROPN
ejpam-6294	267	4	(	(	PUNCT
ejpam-6294	267	5	θ	θ	NOUN
ejpam-6294	267	6	)	)	PUNCT
ejpam-6294	267	7	possesses	possess	VERB
ejpam-6294	267	8	particular	particular	ADJ
ejpam-6294	267	9	geometric	geometric	ADJ
ejpam-6294	267	10	feature	feature	NOUN
ejpam-6294	267	11	|a3	|a3	NOUN
ejpam-6294	267	12	−	−	PROPN
ejpam-6294	267	13	ηa22|	ηa22|	NOUN
ejpam-6294	267	14	of	of	ADP
ejpam-6294	267	15	function	function	PROPN
ejpam-6294	267	16	f	f	PROPN
ejpam-6294	267	17	(	(	PUNCT
ejpam-6294	267	18	θ	θ	PROPN
ejpam-6294	267	19	)	)	PUNCT
ejpam-6294	267	20	,	,	PUNCT
ejpam-6294	267	21	it	it	PRON
ejpam-6294	267	22	is	be	AUX
ejpam-6294	267	23	defined	define	VERB
ejpam-6294	267	24	by	by	ADP
ejpam-6294	267	25	(	(	PUNCT
ejpam-6294	267	26	1	1	NUM
ejpam-6294	267	27	)	)	PUNCT
ejpam-6294	267	28	and	and	CCONJ
ejpam-6294	267	29	it	it	PRON
ejpam-6294	267	30	is	be	AUX
ejpam-6294	267	31	a	a	DET
ejpam-6294	267	32	member	member	NOUN
ejpam-6294	267	33	of	of	ADP
ejpam-6294	267	34	the	the	DET
ejpam-6294	267	35	class	class	NOUN
ejpam-6294	267	36	gς	gς	PROPN
ejpam-6294	267	37	,	,	PUNCT
ejpam-6294	267	38	g(τ	g(τ	PROPN
ejpam-6294	267	39	)	)	PUNCT
ejpam-6294	267	40	.	.	PUNCT
ejpam-6294	268	1	then	then	ADV
ejpam-6294	268	2	|a3	|a3	VERB
ejpam-6294	268	3	−	−	PROPN
ejpam-6294	268	4	ηa22|	ηa22|	NOUN
ejpam-6294	268	5	≤	≤	PROPN
ejpam-6294	268	6	{	{	PUNCT
ejpam-6294	268	7	s2	s2	NOUN
ejpam-6294	268	8	3	3	NUM
ejpam-6294	268	9	if	if	SCONJ
ejpam-6294	268	10	0	0	NUM
ejpam-6294	268	11	≤	≤	NUM
ejpam-6294	268	12	|h1(η)|	|h1(η)|	NOUN
ejpam-6294	268	13	≤	≤	NUM
ejpam-6294	268	14	1	1	NUM
ejpam-6294	268	15	12	12	NUM
ejpam-6294	268	16	,	,	PUNCT
ejpam-6294	268	17	2s2|	2s2|	NUM
ejpam-6294	268	18	(	(	PUNCT
ejpam-6294	268	19	1−η	1−η	NUM
ejpam-6294	268	20	)	)	PUNCT
ejpam-6294	268	21	8	8	NUM
ejpam-6294	268	22	|	|	ADV
ejpam-6294	268	23	if	if	SCONJ
ejpam-6294	268	24	|h1(η)|	|h1(η)|	NUM
ejpam-6294	268	25	≥	≥	NOUN
ejpam-6294	268	26	1	1	NUM
ejpam-6294	268	27	12	12	NUM
ejpam-6294	268	28	,	,	PUNCT
ejpam-6294	268	29	this	this	PRON
ejpam-6294	268	30	implies	imply	VERB
ejpam-6294	268	31	|a3	|a3	NOUN
ejpam-6294	268	32	−	−	PROPN
ejpam-6294	268	33	ηa22|	ηa22|	NOUN
ejpam-6294	268	34	≤	≤	PROPN
ejpam-6294	268	35	{	{	PUNCT
ejpam-6294	268	36	s2	s2	NOUN
ejpam-6294	268	37	3	3	NUM
ejpam-6294	268	38	if	if	SCONJ
ejpam-6294	268	39	0	0	NUM
ejpam-6294	268	40	≤	≤	NUM
ejpam-6294	268	41	|h1(η)|	|h1(η)|	NOUN
ejpam-6294	268	42	≤	≤	NUM
ejpam-6294	268	43	7	7	NUM
ejpam-6294	268	44	8	8	NUM
ejpam-6294	268	45	,	,	PUNCT
ejpam-6294	268	46	s2|	s2|	PROPN
ejpam-6294	268	47	(	(	PUNCT
ejpam-6294	268	48	1−η	1−η	NUM
ejpam-6294	268	49	)	)	PUNCT
ejpam-6294	268	50	4	4	NUM
ejpam-6294	268	51	|	|	ADV
ejpam-6294	268	52	if	if	SCONJ
ejpam-6294	268	53	|h1(η)|	|h1(η)|	NUM
ejpam-6294	268	54	≥	≥	NOUN
ejpam-6294	268	55	7	7	NUM
ejpam-6294	268	56	8	8	NUM
ejpam-6294	268	57	,	,	PUNCT
ejpam-6294	268	58	where	where	SCONJ
ejpam-6294	268	59	h1(η	h1(η	X
ejpam-6294	268	60	)	)	PUNCT
ejpam-6294	268	61	=	=	SYM
ejpam-6294	268	62	(	(	PUNCT
ejpam-6294	268	63	1−	1−	NUM
ejpam-6294	268	64	η	η	NOUN
ejpam-6294	268	65	)	)	PUNCT
ejpam-6294	268	66	8	8	NUM
ejpam-6294	268	67	.	.	PUNCT
ejpam-6294	269	1	6	6	X
ejpam-6294	269	2	.	.	X
ejpam-6294	269	3	discussion	discussion	NOUN
ejpam-6294	269	4	:	:	PUNCT
ejpam-6294	269	5	influence	influence	NOUN
ejpam-6294	269	6	of	of	ADP
ejpam-6294	269	7	parameter	parameter	NOUN
ejpam-6294	269	8	s	s	PART
ejpam-6294	269	9	and	and	CCONJ
ejpam-6294	269	10	surface	surface	NOUN
ejpam-6294	269	11	plot	plot	NOUN
ejpam-6294	269	12	interpretation	interpretation	NOUN
ejpam-6294	269	13	for	for	ADP
ejpam-6294	269	14	special	special	ADJ
ejpam-6294	269	15	values	value	NOUN
ejpam-6294	269	16	of	of	ADP
ejpam-6294	269	17	s	s	PROPN
ejpam-6294	269	18	,	,	PUNCT
ejpam-6294	269	19	the	the	DET
ejpam-6294	269	20	expansion	expansion	NOUN
ejpam-6294	269	21	may	may	AUX
ejpam-6294	269	22	reduce	reduce	VERB
ejpam-6294	269	23	to	to	ADP
ejpam-6294	269	24	well	well	ADV
ejpam-6294	269	25	-	-	PUNCT
ejpam-6294	269	26	known	know	VERB
ejpam-6294	269	27	families	family	NOUN
ejpam-6294	269	28	of	of	ADP
ejpam-6294	269	29	polynomials	polynomial	NOUN
ejpam-6294	269	30	:	:	PUNCT
ejpam-6294	269	31	•	•	ADP
ejpam-6294	269	32	when	when	SCONJ
ejpam-6294	269	33	s	s	VERB
ejpam-6294	269	34	=	=	NOUN
ejpam-6294	269	35	0	0	NUM
ejpam-6294	269	36	:	:	PUNCT
ejpam-6294	269	37	only	only	ADV
ejpam-6294	269	38	even	even	ADV
ejpam-6294	269	39	powers	power	NOUN
ejpam-6294	269	40	of	of	ADP
ejpam-6294	269	41	θ	θ	PROPN
ejpam-6294	269	42	survive	survive	VERB
ejpam-6294	269	43	with	with	ADP
ejpam-6294	269	44	relatively	relatively	ADV
ejpam-6294	269	45	simple	simple	ADJ
ejpam-6294	269	46	coefficients	coefficient	NOUN
ejpam-6294	269	47	—	—	PUNCT
ejpam-6294	269	48	suggesting	suggest	VERB
ejpam-6294	269	49	a	a	DET
ejpam-6294	269	50	resemblance	resemblance	NOUN
ejpam-6294	269	51	to	to	PART
ejpam-6294	269	52	chebyshev	chebyshev	VERB
ejpam-6294	269	53	-	-	PUNCT
ejpam-6294	269	54	type	type	NOUN
ejpam-6294	269	55	behavior	behavior	NOUN
ejpam-6294	269	56	.	.	PUNCT
ejpam-6294	270	1	•	•	ADV
ejpam-6294	270	2	when	when	SCONJ
ejpam-6294	270	3	s	s	VERB
ejpam-6294	270	4	=	=	NOUN
ejpam-6294	270	5	1	1	NUM
ejpam-6294	270	6	:	:	PUNCT
ejpam-6294	270	7	the	the	DET
ejpam-6294	270	8	sequence	sequence	NOUN
ejpam-6294	270	9	does	do	AUX
ejpam-6294	270	10	not	not	PART
ejpam-6294	270	11	exactly	exactly	ADV
ejpam-6294	270	12	match	match	VERB
ejpam-6294	270	13	fibonacci	fibonacci	NOUN
ejpam-6294	270	14	or	or	CCONJ
ejpam-6294	270	15	lucas	lucas	NOUN
ejpam-6294	270	16	,	,	PUNCT
ejpam-6294	270	17	but	but	CCONJ
ejpam-6294	270	18	the	the	DET
ejpam-6294	270	19	structure	structure	NOUN
ejpam-6294	270	20	mimics	mimic	VERB
ejpam-6294	270	21	a	a	DET
ejpam-6294	270	22	nonlinear	nonlinear	ADJ
ejpam-6294	270	23	recurrence	recurrence	NOUN
ejpam-6294	270	24	.	.	PUNCT
ejpam-6294	271	1	•	•	NUM
ejpam-6294	271	2	when	when	SCONJ
ejpam-6294	271	3	s	s	VERB
ejpam-6294	271	4	=	=	NOUN
ejpam-6294	271	5	2	2	NUM
ejpam-6294	271	6	:	:	PUNCT
ejpam-6294	271	7	the	the	DET
ejpam-6294	271	8	pattern	pattern	NOUN
ejpam-6294	271	9	aligns	align	VERB
ejpam-6294	271	10	closely	closely	ADV
ejpam-6294	271	11	with	with	ADP
ejpam-6294	271	12	growth	growth	NOUN
ejpam-6294	271	13	seen	see	VERB
ejpam-6294	271	14	in	in	ADP
ejpam-6294	271	15	bell	bell	NOUN
ejpam-6294	271	16	or	or	CCONJ
ejpam-6294	271	17	motzkin	motzkin	ADJ
ejpam-6294	271	18	-	-	PUNCT
ejpam-6294	271	19	like	like	ADJ
ejpam-6294	271	20	structures	structure	NOUN
ejpam-6294	271	21	,	,	PUNCT
ejpam-6294	271	22	potentially	potentially	ADV
ejpam-6294	271	23	capturing	capture	VERB
ejpam-6294	271	24	partition	partition	NOUN
ejpam-6294	271	25	-	-	PUNCT
ejpam-6294	271	26	related	relate	VERB
ejpam-6294	271	27	or	or	CCONJ
ejpam-6294	271	28	moment	moment	NOUN
ejpam-6294	271	29	-	-	PUNCT
ejpam-6294	271	30	generating	generate	VERB
ejpam-6294	271	31	behavior	behavior	NOUN
ejpam-6294	271	32	.	.	PUNCT
ejpam-6294	272	1	from	from	ADP
ejpam-6294	272	2	a	a	DET
ejpam-6294	272	3	generating	generate	VERB
ejpam-6294	272	4	function	function	NOUN
ejpam-6294	272	5	perspective	perspective	NOUN
ejpam-6294	272	6	,	,	PUNCT
ejpam-6294	272	7	the	the	DET
ejpam-6294	272	8	parameter	parameter	NOUN
ejpam-6294	272	9	s	s	PART
ejpam-6294	272	10	may	may	AUX
ejpam-6294	272	11	encode	encode	VERB
ejpam-6294	272	12	a	a	DET
ejpam-6294	272	13	deformation	deformation	NOUN
ejpam-6294	272	14	,	,	PUNCT
ejpam-6294	272	15	weight	weight	NOUN
ejpam-6294	272	16	,	,	PUNCT
ejpam-6294	272	17	or	or	CCONJ
ejpam-6294	272	18	even	even	ADV
ejpam-6294	272	19	a	a	DET
ejpam-6294	272	20	flow	flow	NOUN
ejpam-6294	272	21	parameter	parameter	NOUN
ejpam-6294	272	22	in	in	ADP
ejpam-6294	272	23	a	a	DET
ejpam-6294	272	24	functional	functional	ADJ
ejpam-6294	272	25	or	or	CCONJ
ejpam-6294	272	26	combinatorial	combinatorial	ADJ
ejpam-6294	272	27	system	system	NOUN
ejpam-6294	272	28	.	.	PUNCT
ejpam-6294	273	1	however	however	ADV
ejpam-6294	273	2	,	,	PUNCT
ejpam-6294	273	3	because	because	SCONJ
ejpam-6294	273	4	the	the	DET
ejpam-6294	273	5	expansion	expansion	NOUN
ejpam-6294	273	6	is	be	AUX
ejpam-6294	273	7	polynomial	polynomial	ADJ
ejpam-6294	273	8	in	in	ADP
ejpam-6294	273	9	s	s	PROPN
ejpam-6294	273	10	,	,	PUNCT
ejpam-6294	273	11	the	the	DET
ejpam-6294	273	12	fibonacci	fibonacci	NOUN
ejpam-6294	273	13	sequence	sequence	NOUN
ejpam-6294	273	14	is	be	AUX
ejpam-6294	273	15	not	not	PART
ejpam-6294	273	16	recovered	recover	VERB
ejpam-6294	273	17	directly	directly	ADV
ejpam-6294	273	18	for	for	ADP
ejpam-6294	273	19	any	any	DET
ejpam-6294	273	20	constant	constant	ADJ
ejpam-6294	273	21	value	value	NOUN
ejpam-6294	273	22	of	of	ADP
ejpam-6294	273	23	s.	s.	PROPN
ejpam-6294	273	24	moreover	moreover	ADV
ejpam-6294	273	25	,	,	PUNCT
ejpam-6294	273	26	the	the	DET
ejpam-6294	273	27	appearance	appearance	NOUN
ejpam-6294	273	28	of	of	ADP
ejpam-6294	273	29	higher	high	ADJ
ejpam-6294	273	30	powers	power	NOUN
ejpam-6294	273	31	of	of	ADP
ejpam-6294	273	32	s	s	PRON
ejpam-6294	273	33	than	than	SCONJ
ejpam-6294	273	34	allowed	allow	VERB
ejpam-6294	273	35	in	in	ADP
ejpam-6294	273	36	classical	classical	ADJ
ejpam-6294	273	37	recursions	recursion	NOUN
ejpam-6294	273	38	indicates	indicate	VERB
ejpam-6294	273	39	that	that	SCONJ
ejpam-6294	273	40	the	the	DET
ejpam-6294	273	41	structure	structure	NOUN
ejpam-6294	273	42	diverges	diverge	VERB
ejpam-6294	273	43	from	from	ADP
ejpam-6294	273	44	a	a	DET
ejpam-6294	273	45	standard	standard	ADJ
ejpam-6294	273	46	lucas	lucas	NOUN
ejpam-6294	273	47	recurrence	recurrence	NOUN
ejpam-6294	273	48	.	.	PUNCT
ejpam-6294	274	1	s.	s.	PROPN
ejpam-6294	274	2	thangamani	thangamani	PROPN
ejpam-6294	274	3	et	et	PROPN
ejpam-6294	274	4	al	al	PROPN
ejpam-6294	274	5	.	.	PUNCT
ejpam-6294	274	6	/	/	SYM
ejpam-6294	274	7	eur	eur	PROPN
ejpam-6294	274	8	.	.	PUNCT
ejpam-6294	275	1	j.	j.	PROPN
ejpam-6294	275	2	pure	pure	PROPN
ejpam-6294	275	3	appl	appl	PROPN
ejpam-6294	275	4	.	.	PROPN
ejpam-6294	275	5	math	math	PROPN
ejpam-6294	275	6	,	,	PUNCT
ejpam-6294	275	7	18	18	NUM
ejpam-6294	275	8	(	(	PUNCT
ejpam-6294	275	9	3	3	NUM
ejpam-6294	275	10	)	)	PUNCT
ejpam-6294	275	11	(	(	PUNCT
ejpam-6294	275	12	2025	2025	NUM
ejpam-6294	275	13	)	)	PUNCT
ejpam-6294	275	14	,	,	PUNCT
ejpam-6294	275	15	6294	6294	NUM
ejpam-6294	275	16	15	15	NUM
ejpam-6294	275	17	of	of	ADP
ejpam-6294	275	18	19	19	NUM
ejpam-6294	275	19	the	the	DET
ejpam-6294	275	20	parameter	parameter	NOUN
ejpam-6294	275	21	s	s	PROPN
ejpam-6294	275	22	plays	play	VERB
ejpam-6294	275	23	a	a	DET
ejpam-6294	275	24	crucial	crucial	ADJ
ejpam-6294	275	25	role	role	NOUN
ejpam-6294	275	26	in	in	ADP
ejpam-6294	275	27	shaping	shape	VERB
ejpam-6294	275	28	the	the	DET
ejpam-6294	275	29	behavior	behavior	NOUN
ejpam-6294	275	30	of	of	ADP
ejpam-6294	275	31	the	the	DET
ejpam-6294	275	32	fekete	fekete	PROPN
ejpam-6294	275	33	–	–	PUNCT
ejpam-6294	275	34	szegö	szegö	ADJ
ejpam-6294	275	35	inequality	inequality	NOUN
ejpam-6294	275	36	,	,	PUNCT
ejpam-6294	275	37	particularly	particularly	ADV
ejpam-6294	275	38	in	in	ADP
ejpam-6294	275	39	its	its	PRON
ejpam-6294	275	40	effect	effect	NOUN
ejpam-6294	275	41	on	on	ADP
ejpam-6294	275	42	the	the	DET
ejpam-6294	275	43	sharpness	sharpness	NOUN
ejpam-6294	275	44	and	and	CCONJ
ejpam-6294	275	45	structure	structure	NOUN
ejpam-6294	275	46	of	of	ADP
ejpam-6294	275	47	the	the	DET
ejpam-6294	275	48	bound	bind	VERB
ejpam-6294	275	49	for	for	ADP
ejpam-6294	275	50	the	the	DET
ejpam-6294	275	51	third	third	ADJ
ejpam-6294	275	52	coefficient	coefficient	NOUN
ejpam-6294	275	53	.	.	PUNCT
ejpam-6294	276	1	from	from	ADP
ejpam-6294	276	2	the	the	DET
ejpam-6294	276	3	theorem	theorem	NOUN
ejpam-6294	276	4	(	(	PUNCT
ejpam-6294	276	5	4	4	X
ejpam-6294	276	6	)	)	PUNCT
ejpam-6294	276	7	bound	bind	VERB
ejpam-6294	276	8	is	be	AUX
ejpam-6294	276	9	given	give	VERB
ejpam-6294	276	10	by	by	ADP
ejpam-6294	276	11	:	:	PUNCT
ejpam-6294	276	12	|a3	|a3	PROPN
ejpam-6294	276	13	−	−	PROPN
ejpam-6294	276	14	ηa22|	ηa22|	NOUN
ejpam-6294	276	15	≤	≤	NUM
ejpam-6294	276	16			PUNCT
ejpam-6294	276	17	s2	s2	VERB
ejpam-6294	276	18	1	1	NUM
ejpam-6294	276	19	+	+	NUM
ejpam-6294	276	20	2τ	2τ	NUM
ejpam-6294	276	21	,	,	PUNCT
ejpam-6294	276	22	if	if	SCONJ
ejpam-6294	276	23	|h1(η)|	|h1(η)|	NUM
ejpam-6294	276	24	≤	≤	NUM
ejpam-6294	276	25	1	1	NUM
ejpam-6294	276	26	4(1	4(1	NUM
ejpam-6294	276	27	+	+	CCONJ
ejpam-6294	276	28	2τ	2τ	NUM
ejpam-6294	276	29	)	)	PUNCT
ejpam-6294	276	30	,	,	PUNCT
ejpam-6294	276	31	2s2	2s2	NUM
ejpam-6294	276	32	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6294	276	33	1−	1−	NUM
ejpam-6294	276	34	η	η	PROPN
ejpam-6294	276	35	2(1	2(1	NUM
ejpam-6294	276	36	+	+	CCONJ
ejpam-6294	276	37	τ)2	τ)2	PROPN
ejpam-6294	276	38	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6294	276	39	,	,	PUNCT
ejpam-6294	276	40	if	if	SCONJ
ejpam-6294	276	41	|h1(η)|	|h1(η)|	NUM
ejpam-6294	276	42	≥	≥	NOUN
ejpam-6294	276	43	1	1	NUM
ejpam-6294	276	44	4(1	4(1	NUM
ejpam-6294	276	45	+	+	CCONJ
ejpam-6294	276	46	2τ	2τ	NUM
ejpam-6294	276	47	)	)	PUNCT
ejpam-6294	276	48	,	,	PUNCT
ejpam-6294	276	49	where	where	SCONJ
ejpam-6294	276	50	h1(η	h1(η	X
ejpam-6294	276	51	)	)	PUNCT
ejpam-6294	276	52	=	=	SYM
ejpam-6294	276	53	1−	1−	NUM
ejpam-6294	276	54	η	η	X
ejpam-6294	276	55	2(1	2(1	NUM
ejpam-6294	276	56	+	+	CCONJ
ejpam-6294	276	57	τ)2	τ)2	NOUN
ejpam-6294	276	58	.	.	PUNCT
ejpam-6294	277	1	the	the	DET
ejpam-6294	277	2	corresponding	correspond	VERB
ejpam-6294	277	3	surface	surface	NOUN
ejpam-6294	277	4	plot	plot	NOUN
ejpam-6294	277	5	of	of	ADP
ejpam-6294	277	6	the	the	DET
ejpam-6294	277	7	bound	bind	VERB
ejpam-6294	277	8	|a3−ηa22|	|a3−ηa22|	NOUN
ejpam-6294	277	9	over	over	ADP
ejpam-6294	277	10	the	the	DET
ejpam-6294	277	11	complex	complex	ADJ
ejpam-6294	277	12	η	η	PROPN
ejpam-6294	277	13	-	-	NOUN
ejpam-6294	277	14	plane	plane	NOUN
ejpam-6294	277	15	reveals	reveal	VERB
ejpam-6294	277	16	a	a	DET
ejpam-6294	277	17	piecewise	piecewise	NOUN
ejpam-6294	277	18	smooth	smooth	ADJ
ejpam-6294	277	19	,	,	PUNCT
ejpam-6294	277	20	radially	radially	ADV
ejpam-6294	277	21	structured	structure	VERB
ejpam-6294	277	22	surface	surface	NOUN
ejpam-6294	277	23	centered	center	VERB
ejpam-6294	277	24	at	at	ADP
ejpam-6294	277	25	η	η	PROPN
ejpam-6294	277	26	=	=	PROPN
ejpam-6294	277	27	1	1	NUM
ejpam-6294	277	28	.	.	PUNCT
ejpam-6294	278	1	the	the	DET
ejpam-6294	278	2	height	height	NOUN
ejpam-6294	278	3	of	of	ADP
ejpam-6294	278	4	the	the	DET
ejpam-6294	278	5	surface	surface	NOUN
ejpam-6294	278	6	at	at	ADP
ejpam-6294	278	7	each	each	DET
ejpam-6294	278	8	point	point	NOUN
ejpam-6294	278	9	corresponds	correspond	VERB
ejpam-6294	278	10	to	to	ADP
ejpam-6294	278	11	the	the	DET
ejpam-6294	278	12	maximum	maximum	ADJ
ejpam-6294	278	13	allowable	allowable	ADJ
ejpam-6294	278	14	deviation	deviation	NOUN
ejpam-6294	278	15	of	of	ADP
ejpam-6294	278	16	the	the	DET
ejpam-6294	278	17	coefficient	coefficient	NOUN
ejpam-6294	278	18	a3	a3	NOUN
ejpam-6294	278	19	in	in	ADP
ejpam-6294	278	20	terms	term	NOUN
ejpam-6294	278	21	of	of	ADP
ejpam-6294	278	22	a2	a2	PROPN
ejpam-6294	278	23	,	,	PUNCT
ejpam-6294	278	24	modulated	modulate	VERB
ejpam-6294	278	25	by	by	ADP
ejpam-6294	278	26	the	the	DET
ejpam-6294	278	27	geometry	geometry	NOUN
ejpam-6294	278	28	of	of	ADP
ejpam-6294	278	29	η	η	PROPN
ejpam-6294	278	30	and	and	CCONJ
ejpam-6294	278	31	the	the	DET
ejpam-6294	278	32	analytic	analytic	ADJ
ejpam-6294	278	33	parameter	parameter	NOUN
ejpam-6294	278	34	τ	τ	PROPN
ejpam-6294	278	35	.	.	PUNCT
ejpam-6294	279	1	the	the	DET
ejpam-6294	279	2	region	region	NOUN
ejpam-6294	279	3	defined	define	VERB
ejpam-6294	279	4	by	by	ADP
ejpam-6294	279	5	:	:	PUNCT
ejpam-6294	279	6	|1−	|1−	INTJ
ejpam-6294	279	7	η|	η|	ADJ
ejpam-6294	279	8	≤	≤	NUM
ejpam-6294	279	9	1	1	NUM
ejpam-6294	279	10	2	2	NUM
ejpam-6294	279	11	marks	mark	NOUN
ejpam-6294	279	12	a	a	DET
ejpam-6294	279	13	flat	flat	ADJ
ejpam-6294	279	14	plateau	plateau	NOUN
ejpam-6294	279	15	where	where	SCONJ
ejpam-6294	279	16	the	the	DET
ejpam-6294	279	17	bound	bind	VERB
ejpam-6294	279	18	remains	remain	VERB
ejpam-6294	279	19	constant	constant	ADJ
ejpam-6294	279	20	.	.	PUNCT
ejpam-6294	280	1	beyond	beyond	ADP
ejpam-6294	280	2	this	this	DET
ejpam-6294	280	3	threshold	threshold	NOUN
ejpam-6294	280	4	,	,	PUNCT
ejpam-6294	280	5	the	the	DET
ejpam-6294	280	6	bound	bind	VERB
ejpam-6294	280	7	increases	increase	NOUN
ejpam-6294	280	8	linearly	linearly	ADV
ejpam-6294	280	9	with	with	ADP
ejpam-6294	280	10	|1−	|1−	ADJ
ejpam-6294	280	11	η|	η|	PROPN
ejpam-6294	280	12	,	,	PUNCT
ejpam-6294	280	13	creating	create	VERB
ejpam-6294	280	14	a	a	DET
ejpam-6294	280	15	rising	rise	VERB
ejpam-6294	280	16	surface	surface	NOUN
ejpam-6294	280	17	outward	outward	ADV
ejpam-6294	280	18	from	from	ADP
ejpam-6294	280	19	η	η	PROPN
ejpam-6294	280	20	=	=	PROPN
ejpam-6294	280	21	1	1	NUM
ejpam-6294	280	22	.	.	X
ejpam-6294	280	23	for	for	ADP
ejpam-6294	280	24	a	a	DET
ejpam-6294	280	25	fixed	fix	VERB
ejpam-6294	280	26	value	value	NOUN
ejpam-6294	280	27	of	of	ADP
ejpam-6294	280	28	τ	τ	PROPN
ejpam-6294	280	29	=	=	SYM
ejpam-6294	280	30	1	1	NUM
ejpam-6294	280	31	,	,	PUNCT
ejpam-6294	280	32	the	the	DET
ejpam-6294	280	33	shape	shape	NOUN
ejpam-6294	280	34	and	and	CCONJ
ejpam-6294	280	35	scale	scale	NOUN
ejpam-6294	280	36	of	of	ADP
ejpam-6294	280	37	the	the	DET
ejpam-6294	280	38	surface	surface	NOUN
ejpam-6294	280	39	are	be	AUX
ejpam-6294	280	40	strongly	strongly	ADV
ejpam-6294	280	41	influenced	influence	VERB
ejpam-6294	280	42	by	by	ADP
ejpam-6294	280	43	the	the	DET
ejpam-6294	280	44	parameter	parameter	NOUN
ejpam-6294	280	45	s.	s.	PROPN
ejpam-6294	281	1	this	this	DET
ejpam-6294	281	2	dependency	dependency	NOUN
ejpam-6294	281	3	is	be	AUX
ejpam-6294	281	4	clearly	clearly	ADV
ejpam-6294	281	5	shown	show	VERB
ejpam-6294	281	6	in	in	ADP
ejpam-6294	281	7	figures	figure	NOUN
ejpam-6294	281	8	1	1	NUM
ejpam-6294	281	9	-	-	SYM
ejpam-6294	281	10	3	3	NUM
ejpam-6294	281	11	,	,	PUNCT
ejpam-6294	281	12	where	where	SCONJ
ejpam-6294	281	13	the	the	DET
ejpam-6294	281	14	behavior	behavior	NOUN
ejpam-6294	281	15	of	of	ADP
ejpam-6294	281	16	the	the	DET
ejpam-6294	281	17	surface	surface	NOUN
ejpam-6294	281	18	is	be	AUX
ejpam-6294	281	19	illustrated	illustrate	VERB
ejpam-6294	281	20	for	for	ADP
ejpam-6294	281	21	different	different	ADJ
ejpam-6294	281	22	values	value	NOUN
ejpam-6294	281	23	of	of	ADP
ejpam-6294	281	24	s.	s.	PROPN
ejpam-6294	281	25	variations	variation	NOUN
ejpam-6294	281	26	in	in	ADP
ejpam-6294	281	27	s	s	PRON
ejpam-6294	281	28	significantly	significantly	ADV
ejpam-6294	281	29	alter	alter	VERB
ejpam-6294	281	30	the	the	DET
ejpam-6294	281	31	surface	surface	NOUN
ejpam-6294	281	32	characteristics	characteristic	NOUN
ejpam-6294	281	33	,	,	PUNCT
ejpam-6294	281	34	showcasing	showcase	VERB
ejpam-6294	281	35	how	how	SCONJ
ejpam-6294	281	36	the	the	DET
ejpam-6294	281	37	bound	bind	VERB
ejpam-6294	281	38	’s	’s	PART
ejpam-6294	281	39	structure	structure	NOUN
ejpam-6294	281	40	evolves	evolve	VERB
ejpam-6294	281	41	as	as	ADP
ejpam-6294	281	42	the	the	DET
ejpam-6294	281	43	parameter	parameter	NOUN
ejpam-6294	281	44	changes	change	NOUN
ejpam-6294	281	45	.	.	PUNCT
ejpam-6294	282	1	the	the	DET
ejpam-6294	282	2	surface	surface	NOUN
ejpam-6294	282	3	plot	plot	NOUN
ejpam-6294	282	4	of	of	ADP
ejpam-6294	282	5	the	the	DET
ejpam-6294	282	6	bound	bind	VERB
ejpam-6294	282	7	|a3	|a3	NOUN
ejpam-6294	282	8	−	−	PROPN
ejpam-6294	282	9	ηa22|	ηa22|	NOUN
ejpam-6294	282	10	provides	provide	VERB
ejpam-6294	282	11	a	a	DET
ejpam-6294	282	12	clear	clear	ADJ
ejpam-6294	282	13	visual	visual	ADJ
ejpam-6294	282	14	interpretation	interpretation	NOUN
ejpam-6294	282	15	of	of	ADP
ejpam-6294	282	16	this	this	DET
ejpam-6294	282	17	analytic	analytic	ADJ
ejpam-6294	282	18	bound	bind	VERB
ejpam-6294	282	19	.	.	PUNCT
ejpam-6294	283	1	when	when	SCONJ
ejpam-6294	283	2	s	s	VERB
ejpam-6294	283	3	=	=	SYM
ejpam-6294	283	4	0	0	NUM
ejpam-6294	283	5	,	,	PUNCT
ejpam-6294	283	6	the	the	DET
ejpam-6294	283	7	bound	bind	VERB
ejpam-6294	283	8	becomes	become	VERB
ejpam-6294	283	9	zero	zero	NUM
ejpam-6294	283	10	,	,	PUNCT
ejpam-6294	283	11	reflecting	reflect	VERB
ejpam-6294	283	12	a	a	DET
ejpam-6294	283	13	highly	highly	ADV
ejpam-6294	283	14	constrained	constrain	VERB
ejpam-6294	283	15	structure	structure	NOUN
ejpam-6294	283	16	similar	similar	ADJ
ejpam-6294	283	17	to	to	ADP
ejpam-6294	283	18	chebyshev	chebyshev	VERB
ejpam-6294	283	19	-	-	PUNCT
ejpam-6294	283	20	like	like	ADJ
ejpam-6294	283	21	behavior	behavior	NOUN
ejpam-6294	283	22	in	in	ADP
ejpam-6294	283	23	the	the	DET
ejpam-6294	283	24	generating	generate	VERB
ejpam-6294	283	25	function	function	NOUN
ejpam-6294	283	26	.	.	PUNCT
ejpam-6294	284	1	as	as	SCONJ
ejpam-6294	284	2	s	s	NOUN
ejpam-6294	284	3	increases	increase	NOUN
ejpam-6294	284	4	to	to	ADP
ejpam-6294	284	5	1	1	NUM
ejpam-6294	284	6	,	,	PUNCT
ejpam-6294	284	7	the	the	DET
ejpam-6294	284	8	surface	surface	NOUN
ejpam-6294	284	9	shows	show	VERB
ejpam-6294	284	10	a	a	DET
ejpam-6294	284	11	mild	mild	ADJ
ejpam-6294	284	12	elevation	elevation	NOUN
ejpam-6294	284	13	and	and	CCONJ
ejpam-6294	284	14	nonlinear	nonlinear	ADJ
ejpam-6294	284	15	coefficient	coefficient	NOUN
ejpam-6294	284	16	growth	growth	NOUN
ejpam-6294	284	17	,	,	PUNCT
ejpam-6294	284	18	but	but	CCONJ
ejpam-6294	284	19	it	it	PRON
ejpam-6294	284	20	does	do	AUX
ejpam-6294	284	21	not	not	PART
ejpam-6294	284	22	align	align	VERB
ejpam-6294	284	23	with	with	ADP
ejpam-6294	284	24	fibonacci	fibonacci	NOUN
ejpam-6294	284	25	or	or	CCONJ
ejpam-6294	284	26	lucas	lucas	PROPN
ejpam-6294	284	27	forms	form	NOUN
ejpam-6294	284	28	.	.	PUNCT
ejpam-6294	285	1	for	for	ADP
ejpam-6294	285	2	s	s	NOUN
ejpam-6294	285	3	=	=	SYM
ejpam-6294	285	4	2	2	NUM
ejpam-6294	285	5	,	,	PUNCT
ejpam-6294	285	6	the	the	DET
ejpam-6294	285	7	surface	surface	NOUN
ejpam-6294	285	8	rises	rise	VERB
ejpam-6294	285	9	more	more	ADV
ejpam-6294	285	10	sharply	sharply	ADV
ejpam-6294	285	11	,	,	PUNCT
ejpam-6294	285	12	exhibiting	exhibit	VERB
ejpam-6294	285	13	coefficient	coefficient	ADJ
ejpam-6294	285	14	growth	growth	NOUN
ejpam-6294	285	15	that	that	PRON
ejpam-6294	285	16	resembles	resemble	VERB
ejpam-6294	285	17	bell	bell	NOUN
ejpam-6294	285	18	or	or	CCONJ
ejpam-6294	285	19	motzkin	motzkin	ADJ
ejpam-6294	285	20	-	-	PUNCT
ejpam-6294	285	21	like	like	ADJ
ejpam-6294	285	22	structures	structure	NOUN
ejpam-6294	285	23	.	.	PUNCT
ejpam-6294	286	1	the	the	DET
ejpam-6294	286	2	interaction	interaction	NOUN
ejpam-6294	286	3	between	between	ADP
ejpam-6294	286	4	s	s	NOUN
ejpam-6294	286	5	and	and	CCONJ
ejpam-6294	286	6	η	η	PROPN
ejpam-6294	286	7	demonstrates	demonstrate	VERB
ejpam-6294	286	8	how	how	SCONJ
ejpam-6294	286	9	geometric	geometric	ADJ
ejpam-6294	286	10	deviations	deviation	NOUN
ejpam-6294	286	11	and	and	CCONJ
ejpam-6294	286	12	deformations	deformation	NOUN
ejpam-6294	286	13	control	control	VERB
ejpam-6294	286	14	the	the	DET
ejpam-6294	286	15	flexibility	flexibility	NOUN
ejpam-6294	286	16	and	and	CCONJ
ejpam-6294	286	17	complexity	complexity	NOUN
ejpam-6294	286	18	of	of	ADP
ejpam-6294	286	19	the	the	DET
ejpam-6294	286	20	function	function	NOUN
ejpam-6294	286	21	class	class	NOUN
ejpam-6294	286	22	gς	gς	PROPN
ejpam-6294	286	23	,	,	PUNCT
ejpam-6294	286	24	g(τ	g(τ	PROPN
ejpam-6294	286	25	)	)	PUNCT
ejpam-6294	286	26	.	.	PUNCT
ejpam-6294	287	1	this	this	DET
ejpam-6294	287	2	interplay	interplay	NOUN
ejpam-6294	287	3	is	be	AUX
ejpam-6294	287	4	crucial	crucial	ADJ
ejpam-6294	287	5	in	in	ADP
ejpam-6294	287	6	determining	determine	VERB
ejpam-6294	287	7	the	the	DET
ejpam-6294	287	8	structure	structure	NOUN
ejpam-6294	287	9	of	of	ADP
ejpam-6294	287	10	the	the	DET
ejpam-6294	287	11	function	function	NOUN
ejpam-6294	287	12	,	,	PUNCT
ejpam-6294	287	13	providing	provide	VERB
ejpam-6294	287	14	a	a	DET
ejpam-6294	287	15	deeper	deep	ADJ
ejpam-6294	287	16	understanding	understanding	NOUN
ejpam-6294	287	17	of	of	ADP
ejpam-6294	287	18	the	the	DET
ejpam-6294	287	19	role	role	NOUN
ejpam-6294	287	20	of	of	ADP
ejpam-6294	287	21	second	second	ADJ
ejpam-6294	287	22	-	-	PUNCT
ejpam-6294	287	23	order	order	NOUN
ejpam-6294	287	24	coefficient	coefficient	NOUN
ejpam-6294	287	25	bounds	bound	NOUN
ejpam-6294	287	26	in	in	ADP
ejpam-6294	287	27	geometric	geometric	ADJ
ejpam-6294	287	28	function	function	NOUN
ejpam-6294	287	29	theory	theory	NOUN
ejpam-6294	287	30	.	.	PUNCT
ejpam-6294	288	1	s.	s.	PROPN
ejpam-6294	288	2	thangamani	thangamani	PROPN
ejpam-6294	288	3	et	et	PROPN
ejpam-6294	288	4	al	al	PROPN
ejpam-6294	288	5	.	.	PUNCT
ejpam-6294	288	6	/	/	SYM
ejpam-6294	288	7	eur	eur	PROPN
ejpam-6294	288	8	.	.	PUNCT
ejpam-6294	289	1	j.	j.	PROPN
ejpam-6294	289	2	pure	pure	PROPN
ejpam-6294	289	3	appl	appl	PROPN
ejpam-6294	289	4	.	.	PROPN
ejpam-6294	289	5	math	math	PROPN
ejpam-6294	289	6	,	,	PUNCT
ejpam-6294	289	7	18	18	NUM
ejpam-6294	289	8	(	(	PUNCT
ejpam-6294	289	9	3	3	NUM
ejpam-6294	289	10	)	)	PUNCT
ejpam-6294	289	11	(	(	PUNCT
ejpam-6294	289	12	2025	2025	NUM
ejpam-6294	289	13	)	)	PUNCT
ejpam-6294	289	14	,	,	PUNCT
ejpam-6294	289	15	6294	6294	NUM
ejpam-6294	289	16	16	16	NUM
ejpam-6294	289	17	of	of	ADP
ejpam-6294	289	18	19	19	NUM
ejpam-6294	289	19	-1	-1	SYM
ejpam-6294	289	20	0	0	NUM
ejpam-6294	289	21	1	1	NUM
ejpam-6294	289	22	2	2	NUM
ejpam-6294	289	23	3	3	NUM
ejpam-6294	289	24	-2	-2	NOUN
ejpam-6294	289	25	-1	-1	NOUN
ejpam-6294	289	26	0	0	NUM
ejpam-6294	289	27	1	1	NUM
ejpam-6294	289	28	2	2	NUM
ejpam-6294	289	29	-1	-1	SYM
ejpam-6294	289	30	-0.5	-0.5	X
ejpam-6294	289	31	0	0	NUM
ejpam-6294	289	32	0.5	0.5	NUM
ejpam-6294	289	33	1	1	NUM
ejpam-6294	289	34	figure	figure	NOUN
ejpam-6294	289	35	1	1	NUM
ejpam-6294	289	36	:	:	PUNCT
ejpam-6294	289	37	for	for	ADP
ejpam-6294	289	38	s	s	NOUN
ejpam-6294	289	39	=	=	SYM
ejpam-6294	289	40	0	0	NUM
ejpam-6294	289	41	,	,	PUNCT
ejpam-6294	289	42	the	the	DET
ejpam-6294	289	43	bound	bind	VERB
ejpam-6294	289	44	is	be	AUX
ejpam-6294	289	45	zero	zero	NUM
ejpam-6294	289	46	,	,	PUNCT
ejpam-6294	289	47	indicating	indicate	VERB
ejpam-6294	289	48	constrained	constrained	ADJ
ejpam-6294	289	49	geometry	geometry	NOUN
ejpam-6294	289	50	with	with	ADP
ejpam-6294	289	51	a	a	DET
ejpam-6294	289	52	chebyshev	chebyshev	VERB
ejpam-6294	289	53	-	-	PUNCT
ejpam-6294	289	54	like	like	ADJ
ejpam-6294	289	55	generating	generating	NOUN
ejpam-6294	289	56	function	function	NOUN
ejpam-6294	289	57	.	.	PUNCT
ejpam-6294	290	1	0	0	NUM
ejpam-6294	291	1	2	2	NUM
ejpam-6294	291	2	0.2	0.2	NUM
ejpam-6294	291	3	1	1	NUM
ejpam-6294	291	4	3	3	NUM
ejpam-6294	291	5	0.4	0.4	NUM
ejpam-6294	291	6	2	2	NUM
ejpam-6294	291	7	0.6	0.6	NUM
ejpam-6294	291	8	0	0	NUM
ejpam-6294	291	9	0.8	0.8	NUM
ejpam-6294	291	10	1	1	NUM
ejpam-6294	291	11	-1	-1	SYM
ejpam-6294	291	12	0	0	NUM
ejpam-6294	292	1	-2	-2	NOUN
ejpam-6294	292	2	-1	-1	INTJ
ejpam-6294	292	3	figure	figure	NOUN
ejpam-6294	292	4	2	2	NUM
ejpam-6294	292	5	:	:	PUNCT
ejpam-6294	292	6	for	for	ADP
ejpam-6294	292	7	s	s	NOUN
ejpam-6294	292	8	=	=	SYM
ejpam-6294	292	9	1	1	NUM
ejpam-6294	292	10	,	,	PUNCT
ejpam-6294	292	11	the	the	DET
ejpam-6294	292	12	surface	surface	NOUN
ejpam-6294	292	13	shows	show	VERB
ejpam-6294	292	14	mild	mild	ADJ
ejpam-6294	292	15	elevation	elevation	NOUN
ejpam-6294	292	16	and	and	CCONJ
ejpam-6294	292	17	nonlinear	nonlinear	ADJ
ejpam-6294	292	18	coefficient	coefficient	NOUN
ejpam-6294	292	19	growth	growth	NOUN
ejpam-6294	292	20	,	,	PUNCT
ejpam-6294	292	21	without	without	ADP
ejpam-6294	292	22	matching	match	VERB
ejpam-6294	292	23	fibonacci	fibonacci	NOUN
ejpam-6294	292	24	or	or	CCONJ
ejpam-6294	292	25	lucas	lucas	PROPN
ejpam-6294	292	26	forms	form	NOUN
ejpam-6294	292	27	.	.	PUNCT
ejpam-6294	293	1	s.	s.	PROPN
ejpam-6294	293	2	thangamani	thangamani	PROPN
ejpam-6294	293	3	et	et	PROPN
ejpam-6294	293	4	al	al	PROPN
ejpam-6294	293	5	.	.	PUNCT
ejpam-6294	293	6	/	/	SYM
ejpam-6294	293	7	eur	eur	PROPN
ejpam-6294	293	8	.	.	PUNCT
ejpam-6294	294	1	j.	j.	PROPN
ejpam-6294	294	2	pure	pure	PROPN
ejpam-6294	294	3	appl	appl	PROPN
ejpam-6294	294	4	.	.	PROPN
ejpam-6294	294	5	math	math	PROPN
ejpam-6294	294	6	,	,	PUNCT
ejpam-6294	294	7	18	18	NUM
ejpam-6294	294	8	(	(	PUNCT
ejpam-6294	294	9	3	3	NUM
ejpam-6294	294	10	)	)	PUNCT
ejpam-6294	294	11	(	(	PUNCT
ejpam-6294	294	12	2025	2025	NUM
ejpam-6294	294	13	)	)	PUNCT
ejpam-6294	294	14	,	,	PUNCT
ejpam-6294	294	15	6294	6294	NUM
ejpam-6294	294	16	17	17	NUM
ejpam-6294	294	17	of	of	ADP
ejpam-6294	294	18	19	19	NUM
ejpam-6294	295	1	0.5	0.5	NUM
ejpam-6294	295	2	2	2	NUM
ejpam-6294	295	3	1	1	NUM
ejpam-6294	295	4	1.5	1.5	NUM
ejpam-6294	295	5	1	1	NUM
ejpam-6294	295	6	3	3	NUM
ejpam-6294	295	7	2	2	NUM
ejpam-6294	295	8	2	2	NUM
ejpam-6294	295	9	2.5	2.5	NUM
ejpam-6294	295	10	0	0	NUM
ejpam-6294	295	11	3	3	NUM
ejpam-6294	295	12	1	1	NUM
ejpam-6294	295	13	-1	-1	SYM
ejpam-6294	295	14	0	0	NUM
ejpam-6294	295	15	-2	-2	NOUN
ejpam-6294	295	16	-1	-1	INTJ
ejpam-6294	295	17	figure	figure	NOUN
ejpam-6294	295	18	3	3	NUM
ejpam-6294	295	19	:	:	PUNCT
ejpam-6294	295	20	for	for	ADP
ejpam-6294	295	21	s	s	NOUN
ejpam-6294	295	22	=	=	SYM
ejpam-6294	295	23	2	2	NUM
ejpam-6294	295	24	,	,	PUNCT
ejpam-6294	295	25	the	the	DET
ejpam-6294	295	26	surface	surface	NOUN
ejpam-6294	295	27	rises	rise	VERB
ejpam-6294	295	28	steeply	steeply	ADV
ejpam-6294	295	29	,	,	PUNCT
ejpam-6294	295	30	resembling	resemble	VERB
ejpam-6294	295	31	coefficient	coefficient	ADJ
ejpam-6294	295	32	behavior	behavior	NOUN
ejpam-6294	295	33	in	in	ADP
ejpam-6294	295	34	bell	bell	NOUN
ejpam-6294	295	35	or	or	CCONJ
ejpam-6294	295	36	motzkin	motzkin	ADJ
ejpam-6294	295	37	-	-	PUNCT
ejpam-6294	295	38	like	like	ADJ
ejpam-6294	295	39	structures	structure	NOUN
ejpam-6294	295	40	.	.	PUNCT
ejpam-6294	296	1	7	7	X
ejpam-6294	296	2	.	.	X
ejpam-6294	296	3	conclusion	conclusion	NOUN
ejpam-6294	296	4	in	in	ADP
ejpam-6294	296	5	conclusion	conclusion	NOUN
ejpam-6294	296	6	,	,	PUNCT
ejpam-6294	296	7	the	the	DET
ejpam-6294	296	8	taylor	taylor	PROPN
ejpam-6294	296	9	-	-	PUNCT
ejpam-6294	296	10	maclaurin	maclaurin	NOUN
ejpam-6294	296	11	coefficients	coefficient	NOUN
ejpam-6294	296	12	|a2|	|a2|	NOUN
ejpam-6294	296	13	and	and	CCONJ
ejpam-6294	296	14	|a3|	|a3|	VERB
ejpam-6294	296	15	for	for	ADP
ejpam-6294	296	16	two	two	NUM
ejpam-6294	296	17	new	new	ADJ
ejpam-6294	296	18	subclasses	subclass	NOUN
ejpam-6294	296	19	of	of	ADP
ejpam-6294	296	20	bi	bi	ADJ
ejpam-6294	296	21	-	-	ADJ
ejpam-6294	296	22	univalent	univalent	ADJ
ejpam-6294	296	23	functions	function	NOUN
ejpam-6294	296	24	related	relate	VERB
ejpam-6294	296	25	to	to	ADP
ejpam-6294	296	26	lucas	lucas	PROPN
ejpam-6294	296	27	polynomial	polynomial	ADJ
ejpam-6294	296	28	functions	function	NOUN
ejpam-6294	296	29	are	be	AUX
ejpam-6294	296	30	precisely	precisely	ADV
ejpam-6294	296	31	determined	determined	ADJ
ejpam-6294	296	32	in	in	ADP
ejpam-6294	296	33	this	this	DET
ejpam-6294	296	34	study	study	NOUN
ejpam-6294	296	35	.	.	PUNCT
ejpam-6294	297	1	the	the	DET
ejpam-6294	297	2	obtained	obtain	VERB
ejpam-6294	297	3	coefficients	coefficient	NOUN
ejpam-6294	297	4	and	and	CCONJ
ejpam-6294	297	5	fekete	fekete	NOUN
ejpam-6294	297	6	-	-	PUNCT
ejpam-6294	297	7	szegö	szegö	ADJ
ejpam-6294	297	8	estimates	estimate	NOUN
ejpam-6294	297	9	reveal	reveal	VERB
ejpam-6294	297	10	that	that	SCONJ
ejpam-6294	297	11	our	our	PRON
ejpam-6294	297	12	subclass	subclass	NOUN
ejpam-6294	297	13	of	of	ADP
ejpam-6294	297	14	bi	bi	ADJ
ejpam-6294	297	15	-	-	ADJ
ejpam-6294	297	16	univalent	univalent	ADJ
ejpam-6294	297	17	functions	function	NOUN
ejpam-6294	297	18	demonstrates	demonstrate	VERB
ejpam-6294	297	19	improved	improved	ADJ
ejpam-6294	297	20	control	control	NOUN
ejpam-6294	297	21	over	over	ADP
ejpam-6294	297	22	its	its	PRON
ejpam-6294	297	23	first	first	ADJ
ejpam-6294	297	24	few	few	ADJ
ejpam-6294	297	25	coefficients	coefficient	NOUN
ejpam-6294	297	26	compared	compare	VERB
ejpam-6294	297	27	to	to	ADP
ejpam-6294	297	28	the	the	DET
ejpam-6294	297	29	previously	previously	ADV
ejpam-6294	297	30	studied	study	VERB
ejpam-6294	297	31	subclasses	subclass	NOUN
ejpam-6294	297	32	.	.	PUNCT
ejpam-6294	298	1	this	this	PRON
ejpam-6294	298	2	has	have	VERB
ejpam-6294	298	3	implications	implication	NOUN
ejpam-6294	298	4	for	for	ADP
ejpam-6294	298	5	understanding	understand	VERB
ejpam-6294	298	6	the	the	DET
ejpam-6294	298	7	geometric	geometric	ADJ
ejpam-6294	298	8	properties	property	NOUN
ejpam-6294	298	9	of	of	ADP
ejpam-6294	298	10	these	these	DET
ejpam-6294	298	11	functions	function	NOUN
ejpam-6294	298	12	,	,	PUNCT
ejpam-6294	298	13	particularly	particularly	ADV
ejpam-6294	298	14	in	in	ADP
ejpam-6294	298	15	their	their	PRON
ejpam-6294	298	16	growth	growth	NOUN
ejpam-6294	298	17	and	and	CCONJ
ejpam-6294	298	18	distortion	distortion	NOUN
ejpam-6294	298	19	behavior	behavior	NOUN
ejpam-6294	298	20	.	.	PUNCT
ejpam-6294	299	1	the	the	DET
ejpam-6294	299	2	classical	classical	ADJ
ejpam-6294	299	3	theory	theory	NOUN
ejpam-6294	299	4	is	be	AUX
ejpam-6294	299	5	interestingly	interestingly	ADV
ejpam-6294	299	6	improved	improve	VERB
ejpam-6294	299	7	by	by	ADP
ejpam-6294	299	8	the	the	DET
ejpam-6294	299	9	novel	novel	ADJ
ejpam-6294	299	10	subclass	subclass	NOUN
ejpam-6294	299	11	of	of	ADP
ejpam-6294	299	12	bi	bi	ADJ
ejpam-6294	299	13	-	-	ADJ
ejpam-6294	299	14	univalent	univalent	ADJ
ejpam-6294	299	15	functions	function	NOUN
ejpam-6294	299	16	,	,	PUNCT
ejpam-6294	299	17	especially	especially	ADV
ejpam-6294	299	18	in	in	ADP
ejpam-6294	299	19	relation	relation	NOUN
ejpam-6294	299	20	to	to	ADP
ejpam-6294	299	21	initial	initial	ADJ
ejpam-6294	299	22	coefficients	coefficient	NOUN
ejpam-6294	299	23	and	and	CCONJ
ejpam-6294	299	24	the	the	DET
ejpam-6294	299	25	fekete	fekete	NOUN
ejpam-6294	299	26	-	-	PUNCT
ejpam-6294	299	27	szegö	szegö	NOUN
ejpam-6294	299	28	inequality	inequality	NOUN
ejpam-6294	299	29	.	.	PUNCT
ejpam-6294	300	1	future	future	ADJ
ejpam-6294	300	2	studies	study	NOUN
ejpam-6294	300	3	might	might	AUX
ejpam-6294	300	4	concentrate	concentrate	VERB
ejpam-6294	300	5	on	on	ADP
ejpam-6294	300	6	applying	apply	VERB
ejpam-6294	300	7	these	these	DET
ejpam-6294	300	8	discoveries	discovery	NOUN
ejpam-6294	300	9	to	to	ADP
ejpam-6294	300	10	particular	particular	ADJ
ejpam-6294	300	11	geometric	geometric	ADJ
ejpam-6294	300	12	issues	issue	NOUN
ejpam-6294	300	13	in	in	ADP
ejpam-6294	300	14	univalent	univalent	ADJ
ejpam-6294	300	15	function	function	NOUN
ejpam-6294	300	16	theory	theory	NOUN
ejpam-6294	300	17	or	or	CCONJ
ejpam-6294	300	18	expanding	expand	VERB
ejpam-6294	300	19	them	they	PRON
ejpam-6294	300	20	to	to	ADP
ejpam-6294	300	21	higher	high	ADJ
ejpam-6294	300	22	-	-	PUNCT
ejpam-6294	300	23	order	order	NOUN
ejpam-6294	300	24	coefficients	coefficient	NOUN
ejpam-6294	300	25	.	.	PUNCT
ejpam-6294	301	1	analyzing	analyze	VERB
ejpam-6294	301	2	these	these	DET
ejpam-6294	301	3	initial	initial	ADJ
ejpam-6294	301	4	coefficients	coefficient	NOUN
ejpam-6294	301	5	helps	help	VERB
ejpam-6294	301	6	us	we	PRON
ejpam-6294	301	7	better	well	ADV
ejpam-6294	301	8	understand	understand	VERB
ejpam-6294	301	9	these	these	DET
ejpam-6294	301	10	functions	function	NOUN
ejpam-6294	301	11	’	'	PUNCT
ejpam-6294	301	12	geometric	geometric	ADJ
ejpam-6294	301	13	,	,	PUNCT
ejpam-6294	301	14	growth	growth	NOUN
ejpam-6294	301	15	,	,	PUNCT
ejpam-6294	301	16	and	and	CCONJ
ejpam-6294	301	17	distortion	distortion	NOUN
ejpam-6294	301	18	characteristics	characteristic	NOUN
ejpam-6294	301	19	,	,	PUNCT
ejpam-6294	301	20	as	as	ADV
ejpam-6294	301	21	well	well	ADV
ejpam-6294	301	22	as	as	ADP
ejpam-6294	301	23	how	how	SCONJ
ejpam-6294	301	24	they	they	PRON
ejpam-6294	301	25	behave	behave	VERB
ejpam-6294	301	26	close	close	ADV
ejpam-6294	301	27	to	to	ADP
ejpam-6294	301	28	the	the	DET
ejpam-6294	301	29	origin	origin	NOUN
ejpam-6294	301	30	and	and	CCONJ
ejpam-6294	301	31	relate	relate	VERB
ejpam-6294	301	32	to	to	ADP
ejpam-6294	301	33	other	other	ADJ
ejpam-6294	301	34	bi	bi	ADJ
ejpam-6294	301	35	-	-	ADJ
ejpam-6294	301	36	univalent	univalent	ADJ
ejpam-6294	301	37	subclasses	subclass	NOUN
ejpam-6294	301	38	.	.	PUNCT
ejpam-6294	302	1	this	this	DET
ejpam-6294	302	2	work	work	NOUN
ejpam-6294	302	3	builds	build	VERB
ejpam-6294	302	4	upon	upon	SCONJ
ejpam-6294	302	5	and	and	CCONJ
ejpam-6294	302	6	improves	improve	VERB
ejpam-6294	302	7	upon	upon	SCONJ
ejpam-6294	302	8	earlier	early	ADJ
ejpam-6294	302	9	studies	study	NOUN
ejpam-6294	302	10	by	by	ADP
ejpam-6294	302	11	using	use	VERB
ejpam-6294	302	12	the	the	DET
ejpam-6294	302	13	fekete	fekete	NOUN
ejpam-6294	302	14	-	-	PUNCT
ejpam-6294	302	15	szegö	szegö	NOUN
ejpam-6294	302	16	inequality	inequality	NOUN
ejpam-6294	302	17	,	,	PUNCT
ejpam-6294	302	18	providing	provide	VERB
ejpam-6294	302	19	a	a	DET
ejpam-6294	302	20	better	well	ADJ
ejpam-6294	302	21	understanding	understanding	NOUN
ejpam-6294	302	22	of	of	ADP
ejpam-6294	302	23	the	the	DET
ejpam-6294	302	24	functional	functional	ADJ
ejpam-6294	302	25	and	and	CCONJ
ejpam-6294	302	26	mapping	mapping	NOUN
ejpam-6294	302	27	properties	property	NOUN
ejpam-6294	302	28	.	.	PUNCT
ejpam-6294	303	1	these	these	DET
ejpam-6294	303	2	results	result	NOUN
ejpam-6294	303	3	have	have	VERB
ejpam-6294	303	4	wide	wide	ADV
ejpam-6294	303	5	-	-	PUNCT
ejpam-6294	303	6	ranging	range	VERB
ejpam-6294	303	7	implications	implication	NOUN
ejpam-6294	303	8	in	in	ADP
ejpam-6294	303	9	fields	field	NOUN
ejpam-6294	303	10	where	where	SCONJ
ejpam-6294	303	11	the	the	DET
ejpam-6294	303	12	exact	exact	ADJ
ejpam-6294	303	13	behavior	behavior	NOUN
ejpam-6294	303	14	of	of	ADP
ejpam-6294	303	15	bi	bi	ADJ
ejpam-6294	303	16	-	-	ADJ
ejpam-6294	303	17	univalent	univalent	ADJ
ejpam-6294	303	18	functions	function	NOUN
ejpam-6294	303	19	is	be	AUX
ejpam-6294	303	20	crucial	crucial	ADJ
ejpam-6294	303	21	,	,	PUNCT
ejpam-6294	303	22	such	such	ADJ
ejpam-6294	303	23	as	as	ADP
ejpam-6294	303	24	engineering	engineering	NOUN
ejpam-6294	303	25	,	,	PUNCT
ejpam-6294	303	26	fluid	fluid	ADJ
ejpam-6294	303	27	dynamics	dynamic	NOUN
ejpam-6294	303	28	,	,	PUNCT
ejpam-6294	303	29	and	and	CCONJ
ejpam-6294	303	30	complex	complex	ADJ
ejpam-6294	303	31	analysis	analysis	NOUN
ejpam-6294	303	32	.	.	PUNCT
ejpam-6294	304	1	acknowledgements	acknowledgement	NOUN
ejpam-6294	304	2	this	this	DET
ejpam-6294	304	3	work	work	NOUN
ejpam-6294	304	4	was	be	AUX
ejpam-6294	304	5	supported	support	VERB
ejpam-6294	304	6	by	by	ADP
ejpam-6294	304	7	the	the	DET
ejpam-6294	304	8	deanship	deanship	NOUN
ejpam-6294	304	9	of	of	ADP
ejpam-6294	304	10	scientific	scientific	ADJ
ejpam-6294	304	11	research	research	NOUN
ejpam-6294	304	12	,	,	PUNCT
ejpam-6294	304	13	vice	vice	NOUN
ejpam-6294	304	14	presidency	presidency	NOUN
ejpam-6294	304	15	for	for	ADP
ejpam-6294	304	16	graduate	graduate	NOUN
ejpam-6294	304	17	studies	study	NOUN
ejpam-6294	304	18	and	and	CCONJ
ejpam-6294	304	19	scientific	scientific	ADJ
ejpam-6294	304	20	research	research	NOUN
ejpam-6294	304	21	,	,	PUNCT
ejpam-6294	304	22	king	king	PROPN
ejpam-6294	304	23	faisal	faisal	PROPN
ejpam-6294	304	24	university	university	PROPN
ejpam-6294	304	25	,	,	PUNCT
ejpam-6294	304	26	saudi	saudi	PROPN
ejpam-6294	304	27	arabia	arabia	PROPN
ejpam-6294	305	1	[	[	X
ejpam-6294	305	2	grant	grant	PROPN
ejpam-6294	305	3	s.	s.	PROPN
ejpam-6294	305	4	thangamani	thangamani	PROPN
ejpam-6294	305	5	et	et	PROPN
ejpam-6294	305	6	al	al	PROPN
ejpam-6294	305	7	.	.	PUNCT
ejpam-6294	305	8	/	/	SYM
ejpam-6294	305	9	eur	eur	PROPN
ejpam-6294	305	10	.	.	PUNCT
ejpam-6294	306	1	j.	j.	PROPN
ejpam-6294	306	2	pure	pure	PROPN
ejpam-6294	306	3	appl	appl	PROPN
ejpam-6294	306	4	.	.	PROPN
ejpam-6294	306	5	math	math	PROPN
ejpam-6294	306	6	,	,	PUNCT
ejpam-6294	306	7	18	18	NUM
ejpam-6294	306	8	(	(	PUNCT
ejpam-6294	306	9	3	3	NUM
ejpam-6294	306	10	)	)	PUNCT
ejpam-6294	306	11	(	(	PUNCT
ejpam-6294	306	12	2025	2025	NUM
ejpam-6294	306	13	)	)	PUNCT
ejpam-6294	306	14	,	,	PUNCT
ejpam-6294	306	15	6294	6294	NUM
ejpam-6294	306	16	18	18	NUM
ejpam-6294	306	17	of	of	ADP
ejpam-6294	306	18	19	19	NUM
ejpam-6294	306	19	no	no	NOUN
ejpam-6294	306	20	.	.	PUNCT
ejpam-6294	306	21	kfu252106	kfu252106	NOUN
ejpam-6294	306	22	]	]	PUNCT
ejpam-6294	306	23	.	.	PUNCT
ejpam-6294	307	1	credit	credit	NOUN
ejpam-6294	307	2	authorship	authorship	NOUN
ejpam-6294	307	3	contribution	contribution	NOUN
ejpam-6294	307	4	statement	statement	NOUN
ejpam-6294	307	5	stalin	stalin	PROPN
ejpam-6294	307	6	thangamani	thangamani	PROPN
ejpam-6294	307	7	:	:	PUNCT
ejpam-6294	307	8	investigation	investigation	NOUN
ejpam-6294	307	9	,	,	PUNCT
ejpam-6294	307	10	writing	write	VERB
ejpam-6294	307	11	–	–	PUNCT
ejpam-6294	307	12	review	review	NOUN
ejpam-6294	307	13	&	&	CCONJ
ejpam-6294	307	14	editing	editing	NOUN
ejpam-6294	307	15	.	.	PUNCT
ejpam-6294	308	1	dumitru	dumitru	ADJ
ejpam-6294	308	2	baleanu	baleanu	NOUN
ejpam-6294	308	3	:	:	PUNCT
ejpam-6294	308	4	conceptualization	conceptualization	NOUN
ejpam-6294	308	5	,	,	PUNCT
ejpam-6294	308	6	project	project	NOUN
ejpam-6294	308	7	administration	administration	NOUN
ejpam-6294	308	8	,	,	PUNCT
ejpam-6294	308	9	software	software	NOUN
ejpam-6294	308	10	.	.	PUNCT
ejpam-6294	309	1	jeno	jeno	PROPN
ejpam-6294	309	2	francis	francis	PROPN
ejpam-6294	309	3	:	:	PUNCT
ejpam-6294	309	4	conceptualization	conceptualization	NOUN
ejpam-6294	309	5	,	,	PUNCT
ejpam-6294	309	6	project	project	NOUN
ejpam-6294	309	7	administration	administration	NOUN
ejpam-6294	309	8	.	.	PUNCT
ejpam-6294	310	1	majeed	majeed	PROPN
ejpam-6294	310	2	ahmad	ahmad	PROPN
ejpam-6294	310	3	yousif	yousif	PROPN
ejpam-6294	310	4	:	:	PUNCT
ejpam-6294	310	5	software	software	PROPN
ejpam-6294	310	6	,	,	PUNCT
ejpam-6294	310	7	writing	writing	NOUN
ejpam-6294	310	8	–	–	PUNCT
ejpam-6294	310	9	review	review	NOUN
ejpam-6294	310	10	&	&	CCONJ
ejpam-6294	310	11	editing	editing	NOUN
ejpam-6294	310	12	.	.	PUNCT
ejpam-6294	311	1	meraa	meraa	NOUN
ejpam-6294	311	2	arab	arab	PROPN
ejpam-6294	311	3	:	:	PUNCT
ejpam-6294	311	4	funding	funding	NOUN
ejpam-6294	311	5	acquisition	acquisition	NOUN
ejpam-6294	311	6	,	,	PUNCT
ejpam-6294	311	7	methodology	methodology	NOUN
ejpam-6294	311	8	,	,	PUNCT
ejpam-6294	311	9	writing	write	VERB
ejpam-6294	311	10	–	–	PUNCT
ejpam-6294	311	11	review	review	NOUN
ejpam-6294	311	12	&	&	CCONJ
ejpam-6294	311	13	editing	editing	PROPN
ejpam-6294	311	14	.	.	PUNCT
ejpam-6294	312	1	pshtiwan	pshtiwan	PROPN
ejpam-6294	312	2	othman	othman	PROPN
ejpam-6294	312	3	mohammed	mohammed	PROPN
ejpam-6294	312	4	:	:	PUNCT
ejpam-6294	312	5	conceptualization	conceptualization	NOUN
ejpam-6294	312	6	,	,	PUNCT
ejpam-6294	312	7	writing	writing	NOUN
ejpam-6294	312	8	–	–	PUNCT
ejpam-6294	312	9	original	original	ADJ
ejpam-6294	312	10	draft	draft	NOUN
ejpam-6294	312	11	.	.	PUNCT
ejpam-6294	313	1	declaration	declaration	NOUN
ejpam-6294	313	2	of	of	ADP
ejpam-6294	313	3	competing	compete	VERB
ejpam-6294	313	4	interest	interest	NOUN
ejpam-6294	313	5	the	the	DET
ejpam-6294	313	6	authors	author	NOUN
ejpam-6294	313	7	declare	declare	VERB
ejpam-6294	313	8	that	that	SCONJ
ejpam-6294	313	9	they	they	PRON
ejpam-6294	313	10	have	have	VERB
ejpam-6294	313	11	no	no	DET
ejpam-6294	313	12	known	know	VERB
ejpam-6294	313	13	competing	compete	VERB
ejpam-6294	313	14	financial	financial	ADJ
ejpam-6294	313	15	interests	interest	NOUN
ejpam-6294	313	16	or	or	CCONJ
ejpam-6294	313	17	personal	personal	ADJ
ejpam-6294	313	18	relationships	relationship	NOUN
ejpam-6294	313	19	that	that	PRON
ejpam-6294	313	20	could	could	AUX
ejpam-6294	313	21	have	have	AUX
ejpam-6294	313	22	appeared	appear	VERB
ejpam-6294	313	23	to	to	PART
ejpam-6294	313	24	influence	influence	VERB
ejpam-6294	313	25	the	the	DET
ejpam-6294	313	26	work	work	NOUN
ejpam-6294	313	27	reported	report	VERB
ejpam-6294	313	28	in	in	ADP
ejpam-6294	313	29	this	this	DET
ejpam-6294	313	30	paper	paper	NOUN
ejpam-6294	313	31	.	.	PUNCT
ejpam-6294	314	1	availability	availability	NOUN
ejpam-6294	314	2	of	of	ADP
ejpam-6294	314	3	data	datum	NOUN
ejpam-6294	314	4	and	and	CCONJ
ejpam-6294	314	5	material	material	NOUN
ejpam-6294	314	6	no	no	DET
ejpam-6294	314	7	data	datum	NOUN
ejpam-6294	314	8	was	be	AUX
ejpam-6294	314	9	used	use	VERB
ejpam-6294	314	10	for	for	ADP
ejpam-6294	314	11	the	the	DET
ejpam-6294	314	12	research	research	NOUN
ejpam-6294	314	13	described	describe	VERB
ejpam-6294	314	14	in	in	ADP
ejpam-6294	314	15	the	the	DET
ejpam-6294	314	16	article	article	NOUN
ejpam-6294	314	17	.	.	PUNCT
ejpam-6294	315	1	references	reference	NOUN
ejpam-6294	315	2	[	[	X
ejpam-6294	315	3	1	1	NUM
ejpam-6294	315	4	]	]	PUNCT
ejpam-6294	315	5	p.	p.	NOUN
ejpam-6294	315	6	koebe	koebe	NOUN
ejpam-6294	315	7	.	.	PUNCT
ejpam-6294	316	1	ueber	ueber	PROPN
ejpam-6294	316	2	die	die	VERB
ejpam-6294	316	3	uniformisierung	uniformisierung	PROPN
ejpam-6294	316	4	beliebiger	beliebiger	PROPN
ejpam-6294	316	5	analytischer	analytischer	PROPN
ejpam-6294	316	6	kurven	kurven	PROPN
ejpam-6294	316	7	ii	ii	PROPN
ejpam-6294	316	8	.	.	PUNCT
ejpam-6294	316	9	nachr	nachr	PROPN
ejpam-6294	316	10	.	.	PUNCT
ejpam-6294	317	1	k.	k.	PROPN
ejpam-6294	317	2	ges	ges	PROPN
ejpam-6294	317	3	.	.	PROPN
ejpam-6294	317	4	wissenschaft	wissenschaft	PROPN
ejpam-6294	317	5	.	.	PUNCT
ejpam-6294	318	1	gottinger	gottinger	ADP
ejpam-6294	318	2	math	math	NOUN
ejpam-6294	318	3	.	.	PUNCT
ejpam-6294	319	1	phys	phy	NOUN
ejpam-6294	319	2	.	.	PUNCT
ejpam-6294	319	3	,	,	PUNCT
ejpam-6294	319	4	pages	page	NOUN
ejpam-6294	319	5	177–198	177–198	NUM
ejpam-6294	319	6	,	,	PUNCT
ejpam-6294	319	7	1907	1907	NUM
ejpam-6294	319	8	.	.	PUNCT
ejpam-6294	320	1	[	[	X
ejpam-6294	320	2	2	2	NUM
ejpam-6294	320	3	]	]	PUNCT
ejpam-6294	320	4	m.	m.	NOUN
ejpam-6294	320	5	lewin	lewin	PROPN
ejpam-6294	320	6	.	.	PUNCT
ejpam-6294	321	1	on	on	ADP
ejpam-6294	321	2	a	a	DET
ejpam-6294	321	3	coefficient	coefficient	NOUN
ejpam-6294	321	4	problem	problem	NOUN
ejpam-6294	321	5	for	for	ADP
ejpam-6294	321	6	bi	bi	ADJ
ejpam-6294	321	7	-	-	ADJ
ejpam-6294	321	8	univalent	univalent	ADJ
ejpam-6294	321	9	functions	function	NOUN
ejpam-6294	321	10	.	.	PUNCT
ejpam-6294	322	1	proc	proc	NOUN
ejpam-6294	322	2	.	.	PUNCT
ejpam-6294	323	1	amer	amer	PROPN
ejpam-6294	323	2	.	.	PUNCT
ejpam-6294	323	3	math	math	PROPN
ejpam-6294	323	4	.	.	PUNCT
ejpam-6294	324	1	soc	soc	PROPN
ejpam-6294	324	2	.	.	PUNCT
ejpam-6294	324	3	,	,	PUNCT
ejpam-6294	324	4	18:63–68	18:63–68	NUM
ejpam-6294	324	5	,	,	PUNCT
ejpam-6294	324	6	1967	1967	NUM
ejpam-6294	324	7	.	.	PUNCT
ejpam-6294	325	1	[	[	X
ejpam-6294	325	2	3	3	X
ejpam-6294	325	3	]	]	X
ejpam-6294	325	4	d.	d.	PROPN
ejpam-6294	325	5	a.	a.	PROPN
ejpam-6294	325	6	brannan	brannan	PROPN
ejpam-6294	325	7	and	and	CCONJ
ejpam-6294	325	8	j.	j.	PROPN
ejpam-6294	325	9	g.	g.	PROPN
ejpam-6294	325	10	clunie	clunie	PROPN
ejpam-6294	325	11	.	.	PUNCT
ejpam-6294	326	1	aspects	aspect	NOUN
ejpam-6294	326	2	of	of	ADP
ejpam-6294	326	3	contemporary	contemporary	ADJ
ejpam-6294	326	4	complex	complex	ADJ
ejpam-6294	326	5	analysis	analysis	NOUN
ejpam-6294	326	6	.	.	PUNCT
ejpam-6294	327	1	academic	academic	ADJ
ejpam-6294	327	2	press	press	NOUN
ejpam-6294	327	3	,	,	PUNCT
ejpam-6294	327	4	new	new	PROPN
ejpam-6294	327	5	york	york	PROPN
ejpam-6294	327	6	and	and	CCONJ
ejpam-6294	327	7	london	london	PROPN
ejpam-6294	327	8	,	,	PUNCT
ejpam-6294	327	9	1980	1980	NUM
ejpam-6294	327	10	.	.	PUNCT
ejpam-6294	328	1	[	[	X
ejpam-6294	328	2	4	4	X
ejpam-6294	328	3	]	]	X
ejpam-6294	328	4	d.	d.	PROPN
ejpam-6294	328	5	a.	a.	PROPN
ejpam-6294	328	6	brannan	brannan	PROPN
ejpam-6294	328	7	and	and	CCONJ
ejpam-6294	328	8	t.	t.	PROPN
ejpam-6294	328	9	s.	s.	PROPN
ejpam-6294	328	10	taha	taha	PROPN
ejpam-6294	328	11	.	.	PUNCT
ejpam-6294	329	1	on	on	ADP
ejpam-6294	329	2	some	some	DET
ejpam-6294	329	3	classes	class	NOUN
ejpam-6294	329	4	of	of	ADP
ejpam-6294	329	5	bi	bi	ADJ
ejpam-6294	329	6	-	-	ADJ
ejpam-6294	329	7	valent	valent	NOUN
ejpam-6294	329	8	functions	function	NOUN
ejpam-6294	329	9	.	.	PUNCT
ejpam-6294	330	1	studia	studia	PROPN
ejpam-6294	330	2	univ	univ	PROPN
ejpam-6294	330	3	.	.	PUNCT
ejpam-6294	331	1	babes	babe	NOUN
ejpam-6294	331	2	-	-	PUNCT
ejpam-6294	331	3	bolyai	bolyai	NOUN
ejpam-6294	331	4	math	math	NOUN
ejpam-6294	331	5	.	.	PUNCT
ejpam-6294	331	6	,	,	PUNCT
ejpam-6294	331	7	31:70–77	31:70–77	NUM
ejpam-6294	331	8	,	,	PUNCT
ejpam-6294	331	9	1986	1986	NUM
ejpam-6294	331	10	.	.	PUNCT
ejpam-6294	332	1	[	[	X
ejpam-6294	332	2	5	5	X
ejpam-6294	332	3	]	]	PUNCT
ejpam-6294	332	4	w.	w.	PROPN
ejpam-6294	332	5	c.	c.	PROPN
ejpam-6294	332	6	ma	ma	PROPN
ejpam-6294	332	7	and	and	CCONJ
ejpam-6294	332	8	d.	d.	PROPN
ejpam-6294	332	9	minda	minda	PROPN
ejpam-6294	332	10	.	.	PUNCT
ejpam-6294	333	1	a	a	DET
ejpam-6294	333	2	unified	unified	ADJ
ejpam-6294	333	3	treatment	treatment	NOUN
ejpam-6294	333	4	of	of	ADP
ejpam-6294	333	5	some	some	DET
ejpam-6294	333	6	special	special	ADJ
ejpam-6294	333	7	classes	class	NOUN
ejpam-6294	333	8	of	of	ADP
ejpam-6294	333	9	univalent	univalent	ADJ
ejpam-6294	333	10	functions	function	NOUN
ejpam-6294	333	11	.	.	PUNCT
ejpam-6294	334	1	in	in	ADP
ejpam-6294	334	2	proceedings	proceeding	NOUN
ejpam-6294	334	3	of	of	ADP
ejpam-6294	334	4	the	the	DET
ejpam-6294	334	5	conference	conference	NOUN
ejpam-6294	334	6	on	on	ADP
ejpam-6294	334	7	complex	complex	ADJ
ejpam-6294	334	8	analysis	analysis	NOUN
ejpam-6294	334	9	,	,	PUNCT
ejpam-6294	334	10	tianjin	tianjin	NOUN
ejpam-6294	334	11	,	,	PUNCT
ejpam-6294	334	12	conf	conf	NOUN
ejpam-6294	334	13	.	.	PUNCT
ejpam-6294	334	14	proc	proc	PROPN
ejpam-6294	334	15	.	.	PUNCT
ejpam-6294	335	1	lecture	lecture	NOUN
ejpam-6294	335	2	notes	note	VERB
ejpam-6294	335	3	anal	anal	ADJ
ejpam-6294	335	4	.	.	PUNCT
ejpam-6294	335	5	,	,	PUNCT
ejpam-6294	335	6	pages	page	NOUN
ejpam-6294	335	7	157–169	157–169	NUM
ejpam-6294	335	8	,	,	PUNCT
ejpam-6294	335	9	cambridge	cambridge	PROPN
ejpam-6294	335	10	,	,	PUNCT
ejpam-6294	335	11	ma	ma	PROPN
ejpam-6294	335	12	,	,	PUNCT
ejpam-6294	335	13	1992	1992	NUM
ejpam-6294	335	14	.	.	PUNCT
ejpam-6294	336	1	[	[	X
ejpam-6294	336	2	6	6	NUM
ejpam-6294	336	3	]	]	PUNCT
ejpam-6294	336	4	a.	a.	NOUN
ejpam-6294	336	5	behera	behera	PROPN
ejpam-6294	336	6	and	and	CCONJ
ejpam-6294	336	7	g.	g.	PROPN
ejpam-6294	336	8	k.	k.	PROPN
ejpam-6294	336	9	panda	panda	PROPN
ejpam-6294	336	10	.	.	PUNCT
ejpam-6294	337	1	on	on	ADP
ejpam-6294	337	2	the	the	DET
ejpam-6294	337	3	square	square	ADJ
ejpam-6294	337	4	roots	root	NOUN
ejpam-6294	337	5	of	of	ADP
ejpam-6294	337	6	triangular	triangular	NOUN
ejpam-6294	337	7	numbers	number	NOUN
ejpam-6294	337	8	.	.	PUNCT
ejpam-6294	338	1	fibonacci	fibonacci	NOUN
ejpam-6294	338	2	quart	quart	PROPN
ejpam-6294	338	3	.	.	PUNCT
ejpam-6294	338	4	,	,	PUNCT
ejpam-6294	338	5	37:98–105	37:98–105	NUM
ejpam-6294	338	6	,	,	PUNCT
ejpam-6294	338	7	1999	1999	NUM
ejpam-6294	338	8	.	.	PUNCT
ejpam-6294	339	1	[	[	X
ejpam-6294	339	2	7	7	X
ejpam-6294	339	3	]	]	X
ejpam-6294	339	4	b.	b.	PROPN
ejpam-6294	339	5	a.	a.	PROPN
ejpam-6294	339	6	frasin	frasin	PROPN
ejpam-6294	339	7	and	and	CCONJ
ejpam-6294	339	8	m.	m.	PROPN
ejpam-6294	339	9	k.	k.	PROPN
ejpam-6294	339	10	aouf	aouf	PROPN
ejpam-6294	339	11	.	.	PUNCT
ejpam-6294	340	1	new	new	ADJ
ejpam-6294	340	2	subclasses	subclass	NOUN
ejpam-6294	340	3	of	of	ADP
ejpam-6294	340	4	bi	bi	ADJ
ejpam-6294	340	5	-	-	ADJ
ejpam-6294	340	6	univalent	univalent	ADJ
ejpam-6294	340	7	functions	function	NOUN
ejpam-6294	340	8	.	.	PUNCT
ejpam-6294	341	1	appl	appl	PROPN
ejpam-6294	341	2	.	.	PROPN
ejpam-6294	341	3	math	math	PROPN
ejpam-6294	341	4	.	.	PUNCT
ejpam-6294	342	1	lett	lett	PROPN
ejpam-6294	342	2	.	.	PROPN
ejpam-6294	342	3	,	,	PUNCT
ejpam-6294	342	4	24:1569–1573	24:1569–1573	NUM
ejpam-6294	342	5	,	,	PUNCT
ejpam-6294	342	6	2011	2011	NUM
ejpam-6294	342	7	.	.	PUNCT
ejpam-6294	343	1	[	[	X
ejpam-6294	343	2	8	8	NUM
ejpam-6294	343	3	]	]	X
ejpam-6294	343	4	d.	d.	PROPN
ejpam-6294	343	5	bansal	bansal	PROPN
ejpam-6294	343	6	and	and	CCONJ
ejpam-6294	343	7	j.	j.	PROPN
ejpam-6294	343	8	sokol	sokol	PROPN
ejpam-6294	343	9	.	.	PUNCT
ejpam-6294	344	1	coefficient	coefficient	PROPN
ejpam-6294	344	2	bound	bind	VERB
ejpam-6294	344	3	for	for	ADP
ejpam-6294	344	4	a	a	DET
ejpam-6294	344	5	new	new	ADJ
ejpam-6294	344	6	class	class	NOUN
ejpam-6294	344	7	of	of	ADP
ejpam-6294	344	8	analytic	analytic	ADJ
ejpam-6294	344	9	and	and	CCONJ
ejpam-6294	344	10	bi	bi	ADJ
ejpam-6294	344	11	-	-	ADJ
ejpam-6294	344	12	univalent	univalent	ADJ
ejpam-6294	344	13	functions	function	NOUN
ejpam-6294	344	14	.	.	PUNCT
ejpam-6294	345	1	j.	j.	PROPN
ejpam-6294	345	2	fract	fract	PROPN
ejpam-6294	345	3	.	.	PUNCT
ejpam-6294	346	1	calc	calc	PROPN
ejpam-6294	346	2	.	.	PUNCT
ejpam-6294	347	1	appl	appl	PROPN
ejpam-6294	347	2	.	.	PROPN
ejpam-6294	347	3	,	,	PUNCT
ejpam-6294	347	4	5(1):122–128	5(1):122–128	ADJ
ejpam-6294	347	5	,	,	PUNCT
ejpam-6294	347	6	2014	2014	NUM
ejpam-6294	347	7	.	.	PUNCT
ejpam-6294	348	1	[	[	X
ejpam-6294	348	2	9	9	NUM
ejpam-6294	348	3	]	]	PUNCT
ejpam-6294	348	4	a.	a.	NOUN
ejpam-6294	348	5	y.	y.	PROPN
ejpam-6294	348	6	lashin	lashin	PROPN
ejpam-6294	348	7	.	.	PUNCT
ejpam-6294	349	1	on	on	ADP
ejpam-6294	349	2	certain	certain	ADJ
ejpam-6294	349	3	subclasses	subclass	NOUN
ejpam-6294	349	4	of	of	ADP
ejpam-6294	349	5	analytic	analytic	ADJ
ejpam-6294	349	6	and	and	CCONJ
ejpam-6294	349	7	bi	bi	ADJ
ejpam-6294	349	8	-	-	ADJ
ejpam-6294	349	9	univalent	univalent	ADJ
ejpam-6294	349	10	functions	function	NOUN
ejpam-6294	349	11	.	.	PUNCT
ejpam-6294	350	1	j.	j.	PROPN
ejpam-6294	350	2	egyptian	egyptian	PROPN
ejpam-6294	350	3	math	math	PROPN
ejpam-6294	350	4	.	.	PUNCT
ejpam-6294	351	1	soc	soc	PROPN
ejpam-6294	351	2	.	.	PUNCT
ejpam-6294	351	3	,	,	PUNCT
ejpam-6294	351	4	24:220–225	24:220–225	PROPN
ejpam-6294	351	5	,	,	PUNCT
ejpam-6294	351	6	2016	2016	NUM
ejpam-6294	351	7	.	.	PUNCT
ejpam-6294	352	1	[	[	X
ejpam-6294	352	2	10	10	NUM
ejpam-6294	352	3	]	]	PUNCT
ejpam-6294	352	4	a.	a.	NOUN
ejpam-6294	352	5	o.	o.	NOUN
ejpam-6294	352	6	pall	pall	PROPN
ejpam-6294	352	7	-	-	PUNCT
ejpam-6294	352	8	szabo	szabo	PROPN
ejpam-6294	352	9	and	and	CCONJ
ejpam-6294	352	10	g.	g.	PROPN
ejpam-6294	352	11	i.	i.	PROPN
ejpam-6294	352	12	oros	oros	PROPN
ejpam-6294	352	13	.	.	PUNCT
ejpam-6294	353	1	coefficient	coefficient	PROPN
ejpam-6294	353	2	related	relate	VERB
ejpam-6294	353	3	studies	study	NOUN
ejpam-6294	353	4	for	for	ADP
ejpam-6294	353	5	new	new	ADJ
ejpam-6294	353	6	classes	class	NOUN
ejpam-6294	353	7	of	of	ADP
ejpam-6294	353	8	biunivalent	biunivalent	NOUN
ejpam-6294	353	9	functions	function	NOUN
ejpam-6294	353	10	.	.	PUNCT
ejpam-6294	354	1	mathematics	mathematic	NOUN
ejpam-6294	354	2	,	,	PUNCT
ejpam-6294	354	3	8:1110	8:1110	NUM
ejpam-6294	354	4	,	,	PUNCT
ejpam-6294	354	5	2020	2020	NUM
ejpam-6294	354	6	.	.	PUNCT
ejpam-6294	355	1	s.	s.	PROPN
ejpam-6294	355	2	thangamani	thangamani	PROPN
ejpam-6294	355	3	et	et	PROPN
ejpam-6294	355	4	al	al	PROPN
ejpam-6294	355	5	.	.	PUNCT
ejpam-6294	355	6	/	/	SYM
ejpam-6294	355	7	eur	eur	PROPN
ejpam-6294	355	8	.	.	PUNCT
ejpam-6294	356	1	j.	j.	PROPN
ejpam-6294	356	2	pure	pure	PROPN
ejpam-6294	356	3	appl	appl	PROPN
ejpam-6294	356	4	.	.	PROPN
ejpam-6294	356	5	math	math	PROPN
ejpam-6294	356	6	,	,	PUNCT
ejpam-6294	356	7	18	18	NUM
ejpam-6294	356	8	(	(	PUNCT
ejpam-6294	356	9	3	3	NUM
ejpam-6294	356	10	)	)	PUNCT
ejpam-6294	356	11	(	(	PUNCT
ejpam-6294	356	12	2025	2025	NUM
ejpam-6294	356	13	)	)	PUNCT
ejpam-6294	356	14	,	,	PUNCT
ejpam-6294	356	15	6294	6294	NUM
ejpam-6294	356	16	19	19	NUM
ejpam-6294	356	17	of	of	ADP
ejpam-6294	356	18	19	19	NUM
ejpam-6294	356	19	[	[	SYM
ejpam-6294	356	20	11	11	NUM
ejpam-6294	356	21	]	]	PUNCT
ejpam-6294	356	22	k.	k.	PROPN
ejpam-6294	356	23	a.	a.	PROPN
ejpam-6294	356	24	jassim	jassim	PROPN
ejpam-6294	356	25	,	,	PUNCT
ejpam-6294	356	26	r.	r.	PROPN
ejpam-6294	356	27	o.	o.	PROPN
ejpam-6294	356	28	rasheed	rasheed	PROPN
ejpam-6294	356	29	,	,	PUNCT
ejpam-6294	356	30	and	and	CCONJ
ejpam-6294	356	31	r.	r.	PROPN
ejpam-6294	356	32	h.	h.	PROPN
ejpam-6294	356	33	jassim	jassim	PROPN
ejpam-6294	356	34	.	.	PUNCT
ejpam-6294	357	1	generalized	generalized	ADJ
ejpam-6294	357	2	subclass	subclass	NOUN
ejpam-6294	357	3	of	of	ADP
ejpam-6294	357	4	analytic	analytic	ADJ
ejpam-6294	357	5	biunivalent	biunivalent	NOUN
ejpam-6294	357	6	functions	function	NOUN
ejpam-6294	357	7	defined	define	VERB
ejpam-6294	357	8	by	by	ADP
ejpam-6294	357	9	differential	differential	ADJ
ejpam-6294	357	10	operator	operator	NOUN
ejpam-6294	357	11	.	.	PUNCT
ejpam-6294	358	1	j.	j.	PROPN
ejpam-6294	358	2	interdiscip	interdiscip	PROPN
ejpam-6294	358	3	.	.	PUNCT
ejpam-6294	359	1	math	math	NOUN
ejpam-6294	359	2	.	.	PUNCT
ejpam-6294	359	3	,	,	PUNCT
ejpam-6294	360	1	24:961–970	24:961–970	PROPN
ejpam-6294	360	2	,	,	PUNCT
ejpam-6294	360	3	2021	2021	NUM
ejpam-6294	360	4	.	.	PUNCT
ejpam-6294	361	1	[	[	X
ejpam-6294	361	2	12	12	NUM
ejpam-6294	361	3	]	]	X
ejpam-6294	361	4	g.	g.	PROPN
ejpam-6294	361	5	lee	lee	PROPN
ejpam-6294	361	6	and	and	CCONJ
ejpam-6294	361	7	m.	m.	PROPN
ejpam-6294	361	8	asci	asci	PROPN
ejpam-6294	361	9	.	.	PUNCT
ejpam-6294	362	1	some	some	DET
ejpam-6294	362	2	properties	property	NOUN
ejpam-6294	362	3	of	of	ADP
ejpam-6294	362	4	the	the	DET
ejpam-6294	362	5	(	(	PUNCT
ejpam-6294	362	6	p	p	NOUN
ejpam-6294	362	7	,	,	PUNCT
ejpam-6294	362	8	q)-fibonacci	q)-fibonacci	NOUN
ejpam-6294	362	9	and	and	CCONJ
ejpam-6294	362	10	(	(	PUNCT
ejpam-6294	362	11	p	p	X
ejpam-6294	362	12	,	,	PUNCT
ejpam-6294	362	13	q)-lucas	q)-lucas	DET
ejpam-6294	362	14	polynomials	polynomial	NOUN
ejpam-6294	362	15	.	.	PUNCT
ejpam-6294	363	1	journal	journal	NOUN
ejpam-6294	363	2	of	of	ADP
ejpam-6294	363	3	applied	apply	VERB
ejpam-6294	363	4	mathematics	mathematic	NOUN
ejpam-6294	363	5	,	,	PUNCT
ejpam-6294	363	6	2012:264842	2012:264842	NUM
ejpam-6294	363	7	,	,	PUNCT
ejpam-6294	363	8	2012	2012	NUM
ejpam-6294	363	9	.	.	PUNCT
ejpam-6294	364	1	[	[	X
ejpam-6294	364	2	13	13	NUM
ejpam-6294	364	3	]	]	PUNCT
ejpam-6294	364	4	p.	p.	PROPN
ejpam-6294	364	5	k.	k.	PROPN
ejpam-6294	364	6	ray	ray	PROPN
ejpam-6294	364	7	.	.	PUNCT
ejpam-6294	365	1	certain	certain	ADJ
ejpam-6294	365	2	matrices	matrix	NOUN
ejpam-6294	365	3	associated	associate	VERB
ejpam-6294	365	4	with	with	ADP
ejpam-6294	365	5	balancing	balancing	NOUN
ejpam-6294	365	6	and	and	CCONJ
ejpam-6294	365	7	lucas	lucas	NOUN
ejpam-6294	365	8	-	-	PUNCT
ejpam-6294	365	9	balancing	balance	VERB
ejpam-6294	365	10	numbers	number	NOUN
ejpam-6294	365	11	.	.	PUNCT
ejpam-6294	366	1	matematika	matematika	ADJ
ejpam-6294	366	2	,	,	PUNCT
ejpam-6294	366	3	28:15–22	28:15–22	NUM
ejpam-6294	366	4	,	,	PUNCT
ejpam-6294	366	5	2012	2012	NUM
ejpam-6294	366	6	.	.	PUNCT
ejpam-6294	367	1	[	[	X
ejpam-6294	367	2	14	14	NUM
ejpam-6294	367	3	]	]	X
ejpam-6294	367	4	s.	s.	PROPN
ejpam-6294	367	5	altinkaya	altinkaya	PROPN
ejpam-6294	367	6	and	and	CCONJ
ejpam-6294	367	7	s.	s.	PROPN
ejpam-6294	367	8	yacin	yacin	PROPN
ejpam-6294	367	9	.	.	PUNCT
ejpam-6294	368	1	on	on	ADP
ejpam-6294	368	2	the	the	DET
ejpam-6294	368	3	(	(	PUNCT
ejpam-6294	368	4	p	p	NOUN
ejpam-6294	368	5	,	,	PUNCT
ejpam-6294	368	6	q)-lucas	q)-lucas	DET
ejpam-6294	368	7	polynomial	polynomial	ADJ
ejpam-6294	368	8	coefficient	coefficient	NOUN
ejpam-6294	368	9	bounds	bound	NOUN
ejpam-6294	368	10	of	of	ADP
ejpam-6294	368	11	biunivalent	biunivalent	NOUN
ejpam-6294	368	12	function	function	NOUN
ejpam-6294	368	13	class	class	NOUN
ejpam-6294	368	14	.	.	PUNCT
ejpam-6294	369	1	boletín	boletín	PROPN
ejpam-6294	369	2	de	de	PROPN
ejpam-6294	369	3	la	la	PROPN
ejpam-6294	369	4	sociedad	sociedad	PROPN
ejpam-6294	369	5	matemática	matemática	PROPN
ejpam-6294	369	6	mexicana	mexicana	PROPN
ejpam-6294	369	7	,	,	PUNCT
ejpam-6294	369	8	25:567–575	25:567–575	PROPN
ejpam-6294	369	9	,	,	PUNCT
ejpam-6294	369	10	2019	2019	NUM
ejpam-6294	369	11	.	.	PUNCT
ejpam-6294	370	1	[	[	X
ejpam-6294	370	2	15	15	NUM
ejpam-6294	370	3	]	]	X
ejpam-6294	370	4	y.	y.	PROPN
ejpam-6294	370	5	almalki	almalki	PROPN
ejpam-6294	370	6	,	,	PUNCT
ejpam-6294	370	7	a.	a.	PROPN
ejpam-6294	370	8	k.	k.	PROPN
ejpam-6294	370	9	wanas	wanas	PROPN
ejpam-6294	370	10	,	,	PUNCT
ejpam-6294	370	11	t.	t.	PROPN
ejpam-6294	370	12	g.	g.	PROPN
ejpam-6294	370	13	shaba	shaba	PROPN
ejpam-6294	370	14	,	,	PUNCT
ejpam-6294	370	15	a.	a.	PROPN
ejpam-6294	370	16	alb	alb	PROPN
ejpam-6294	370	17	lupaş	lupaş	PROPN
ejpam-6294	370	18	,	,	PUNCT
ejpam-6294	370	19	and	and	CCONJ
ejpam-6294	370	20	m.	m.	PROPN
ejpam-6294	370	21	abdalla	abdalla	PROPN
ejpam-6294	370	22	.	.	PUNCT
ejpam-6294	371	1	coefficient	coefficient	NOUN
ejpam-6294	371	2	bounds	bound	NOUN
ejpam-6294	371	3	and	and	CCONJ
ejpam-6294	371	4	fekete	fekete	PROPN
ejpam-6294	371	5	–	–	PUNCT
ejpam-6294	371	6	szegö	szegö	ADJ
ejpam-6294	371	7	inequalities	inequality	NOUN
ejpam-6294	371	8	for	for	ADP
ejpam-6294	371	9	a	a	DET
ejpam-6294	371	10	two	two	NUM
ejpam-6294	371	11	families	family	NOUN
ejpam-6294	371	12	of	of	ADP
ejpam-6294	371	13	bi	bi	ADJ
ejpam-6294	371	14	-	-	ADJ
ejpam-6294	371	15	univalent	univalent	ADJ
ejpam-6294	371	16	functions	function	NOUN
ejpam-6294	371	17	related	relate	VERB
ejpam-6294	371	18	to	to	ADP
ejpam-6294	371	19	gegenbauer	gegenbauer	NOUN
ejpam-6294	371	20	polynomials	polynomial	NOUN
ejpam-6294	371	21	.	.	PUNCT
ejpam-6294	372	1	axioms	axiom	NOUN
ejpam-6294	372	2	,	,	PUNCT
ejpam-6294	372	3	12:1018	12:1018	NUM
ejpam-6294	372	4	,	,	PUNCT
ejpam-6294	372	5	2023	2023	NUM
ejpam-6294	372	6	.	.	PUNCT
ejpam-6294	373	1	[	[	X
ejpam-6294	373	2	16	16	NUM
ejpam-6294	373	3	]	]	PUNCT
ejpam-6294	373	4	arzu	arzu	NOUN
ejpam-6294	373	5	akgül	akgül	NOUN
ejpam-6294	373	6	.	.	PUNCT
ejpam-6294	374	1	(	(	PUNCT
ejpam-6294	374	2	p	p	X
ejpam-6294	374	3	,	,	PUNCT
ejpam-6294	374	4	q)-lucas	q)-lucas	DET
ejpam-6294	374	5	polynomial	polynomial	ADJ
ejpam-6294	374	6	coefficient	coefficient	NOUN
ejpam-6294	374	7	inequalities	inequality	NOUN
ejpam-6294	374	8	of	of	ADP
ejpam-6294	374	9	the	the	DET
ejpam-6294	374	10	bi	bi	ADJ
ejpam-6294	374	11	-	-	ADJ
ejpam-6294	374	12	univalent	univalent	ADJ
ejpam-6294	374	13	function	function	NOUN
ejpam-6294	374	14	class	class	NOUN
ejpam-6294	374	15	.	.	PUNCT
ejpam-6294	375	1	turkish	turkish	ADJ
ejpam-6294	375	2	journal	journal	NOUN
ejpam-6294	375	3	of	of	ADP
ejpam-6294	375	4	mathematics	mathematic	NOUN
ejpam-6294	375	5	,	,	PUNCT
ejpam-6294	375	6	43(5):2170–2176	43(5):2170–2176	PROPN
ejpam-6294	375	7	,	,	PUNCT
ejpam-6294	375	8	2019	2019	NUM
ejpam-6294	375	9	.	.	PUNCT
ejpam-6294	376	1	[	[	X
ejpam-6294	376	2	17	17	NUM
ejpam-6294	376	3	]	]	PUNCT
ejpam-6294	376	4	s.	s.	PROPN
ejpam-6294	376	5	r.	r.	PROPN
ejpam-6294	376	6	swamy	swamy	PROPN
ejpam-6294	376	7	,	,	PUNCT
ejpam-6294	376	8	a.	a.	PROPN
ejpam-6294	376	9	k.	k.	PROPN
ejpam-6294	376	10	wanas	wanas	PROPN
ejpam-6294	376	11	,	,	PUNCT
ejpam-6294	376	12	and	and	CCONJ
ejpam-6294	376	13	y.	y.	PROPN
ejpam-6294	376	14	sailaja	sailaja	PROPN
ejpam-6294	376	15	.	.	PUNCT
ejpam-6294	377	1	some	some	DET
ejpam-6294	377	2	special	special	ADJ
ejpam-6294	377	3	families	family	NOUN
ejpam-6294	377	4	of	of	ADP
ejpam-6294	377	5	holomorphic	holomorphic	ADJ
ejpam-6294	377	6	and	and	CCONJ
ejpam-6294	377	7	salagean	salagean	ADJ
ejpam-6294	377	8	type	type	NOUN
ejpam-6294	377	9	bi	bi	ADJ
ejpam-6294	377	10	-	-	ADJ
ejpam-6294	377	11	univalent	univalent	ADJ
ejpam-6294	377	12	functions	function	NOUN
ejpam-6294	377	13	associated	associate	VERB
ejpam-6294	377	14	with	with	ADP
ejpam-6294	377	15	(	(	PUNCT
ejpam-6294	377	16	m	m	PROPN
ejpam-6294	377	17	,	,	PUNCT
ejpam-6294	377	18	n)-lucas	n)-luca	NOUN
ejpam-6294	377	19	polynomials	polynomial	NOUN
ejpam-6294	377	20	.	.	PUNCT
ejpam-6294	378	1	mathematics	mathematic	NOUN
ejpam-6294	378	2	,	,	PUNCT
ejpam-6294	378	3	11(4):563–574	11(4):563–574	NUM
ejpam-6294	378	4	,	,	PUNCT
ejpam-6294	378	5	2020	2020	NUM
ejpam-6294	378	6	.	.	PUNCT
ejpam-6294	379	1	[	[	X
ejpam-6294	379	2	18	18	NUM
ejpam-6294	379	3	]	]	X
ejpam-6294	379	4	n.	n.	NOUN
ejpam-6294	379	5	magesh	magesh	PROPN
ejpam-6294	379	6	,	,	PUNCT
ejpam-6294	379	7	c.	c.	PROPN
ejpam-6294	379	8	abirami	abirami	PROPN
ejpam-6294	379	9	,	,	PUNCT
ejpam-6294	379	10	and	and	CCONJ
ejpam-6294	379	11	ş	ş	X
ejpam-6294	379	12	.	.	PUNCT
ejpam-6294	379	13	altınkaya	altınkaya	NOUN
ejpam-6294	379	14	.	.	PUNCT
ejpam-6294	380	1	initial	initial	ADJ
ejpam-6294	380	2	bounds	bound	NOUN
ejpam-6294	380	3	for	for	ADP
ejpam-6294	380	4	certain	certain	ADJ
ejpam-6294	380	5	classes	class	NOUN
ejpam-6294	380	6	of	of	ADP
ejpam-6294	380	7	biunivalent	biunivalent	NOUN
ejpam-6294	380	8	functions	function	NOUN
ejpam-6294	380	9	defined	define	VERB
ejpam-6294	380	10	by	by	ADP
ejpam-6294	380	11	the	the	DET
ejpam-6294	380	12	(	(	PUNCT
ejpam-6294	380	13	p	p	NOUN
ejpam-6294	380	14	,	,	PUNCT
ejpam-6294	380	15	q)-lucas	q)-lucas	DET
ejpam-6294	380	16	polynomials	polynomial	NOUN
ejpam-6294	380	17	.	.	PUNCT
ejpam-6294	381	1	twms	twms	PROPN
ejpam-6294	381	2	journal	journal	PROPN
ejpam-6294	381	3	of	of	ADP
ejpam-6294	381	4	applied	apply	VERB
ejpam-6294	381	5	and	and	CCONJ
ejpam-6294	381	6	engineering	engineering	NOUN
ejpam-6294	381	7	mathematics	mathematic	NOUN
ejpam-6294	381	8	,	,	PUNCT
ejpam-6294	381	9	11(1):282–288	11(1):282–288	NUM
ejpam-6294	381	10	,	,	PUNCT
ejpam-6294	381	11	2021	2021	NUM
ejpam-6294	381	12	.	.	PUNCT
ejpam-6294	382	1	[	[	X
ejpam-6294	382	2	19	19	NUM
ejpam-6294	382	3	]	]	PUNCT
ejpam-6294	382	4	a.	a.	NOUN
ejpam-6294	382	5	k.	k.	PROPN
ejpam-6294	382	6	wanas	wanas	PROPN
ejpam-6294	382	7	and	and	CCONJ
ejpam-6294	382	8	l.	l.	PROPN
ejpam-6294	382	9	i.	i.	PROPN
ejpam-6294	382	10	cotîrlă	cotîrlă	PROPN
ejpam-6294	382	11	.	.	PUNCT
ejpam-6294	383	1	applications	application	NOUN
ejpam-6294	383	2	of	of	ADP
ejpam-6294	383	3	(	(	PUNCT
ejpam-6294	383	4	m	m	PROPN
ejpam-6294	383	5	,	,	PUNCT
ejpam-6294	383	6	n)-lucas	n)-luca	NOUN
ejpam-6294	383	7	polynomials	polynomial	NOUN
ejpam-6294	383	8	on	on	ADP
ejpam-6294	383	9	a	a	DET
ejpam-6294	383	10	certain	certain	ADJ
ejpam-6294	383	11	family	family	NOUN
ejpam-6294	383	12	of	of	ADP
ejpam-6294	383	13	bi	bi	ADJ
ejpam-6294	383	14	-	-	ADJ
ejpam-6294	383	15	univalent	univalent	ADJ
ejpam-6294	383	16	functions	function	NOUN
ejpam-6294	383	17	.	.	PUNCT
ejpam-6294	384	1	mathematics	mathematic	NOUN
ejpam-6294	384	2	,	,	PUNCT
ejpam-6294	384	3	10(4):595	10(4):595	PROPN
ejpam-6294	384	4	,	,	PUNCT
ejpam-6294	384	5	2022	2022	NUM
ejpam-6294	384	6	.	.	PUNCT
ejpam-6294	385	1	[	[	X
ejpam-6294	385	2	20	20	NUM
ejpam-6294	385	3	]	]	PUNCT
ejpam-6294	385	4	a.	a.	NOUN
ejpam-6294	385	5	hussen	hussen	PROPN
ejpam-6294	385	6	and	and	CCONJ
ejpam-6294	385	7	m.	m.	NOUN
ejpam-6294	385	8	illafe	illafe	ADJ
ejpam-6294	385	9	.	.	PUNCT
ejpam-6294	386	1	coefficient	coefficient	NOUN
ejpam-6294	386	2	bounds	bound	VERB
ejpam-6294	386	3	for	for	ADP
ejpam-6294	386	4	a	a	DET
ejpam-6294	386	5	certain	certain	ADJ
ejpam-6294	386	6	subclass	subclass	NOUN
ejpam-6294	386	7	of	of	ADP
ejpam-6294	386	8	bi	bi	ADJ
ejpam-6294	386	9	-	-	ADJ
ejpam-6294	386	10	univalent	univalent	ADJ
ejpam-6294	386	11	functions	function	NOUN
ejpam-6294	386	12	associated	associate	VERB
ejpam-6294	386	13	with	with	ADP
ejpam-6294	386	14	lucas	lucas	NOUN
ejpam-6294	386	15	-	-	PUNCT
ejpam-6294	386	16	balancing	balance	VERB
ejpam-6294	386	17	polynomials	polynomial	NOUN
ejpam-6294	386	18	.	.	PUNCT
ejpam-6294	387	1	mathematics	mathematic	NOUN
ejpam-6294	387	2	,	,	PUNCT
ejpam-6294	387	3	11:4941	11:4941	NUM
ejpam-6294	387	4	,	,	PUNCT
ejpam-6294	387	5	2023	2023	NUM
ejpam-6294	387	6	.	.	PUNCT
ejpam-6294	388	1	[	[	X
ejpam-6294	388	2	21	21	NUM
ejpam-6294	388	3	]	]	PUNCT
ejpam-6294	388	4	i̇.	i̇.	X
ejpam-6294	388	5	aktaş	aktaş	NOUN
ejpam-6294	388	6	and	and	CCONJ
ejpam-6294	388	7	i̇.	i̇.	NOUN
ejpam-6294	388	8	karaman	karaman	NOUN
ejpam-6294	388	9	.	.	PUNCT
ejpam-6294	389	1	on	on	ADP
ejpam-6294	389	2	some	some	DET
ejpam-6294	389	3	new	new	ADJ
ejpam-6294	389	4	subclasses	subclass	NOUN
ejpam-6294	389	5	of	of	ADP
ejpam-6294	389	6	bi	bi	ADJ
ejpam-6294	389	7	-	-	ADJ
ejpam-6294	389	8	univalent	univalent	ADJ
ejpam-6294	389	9	functions	function	NOUN
ejpam-6294	389	10	defined	define	VERB
ejpam-6294	389	11	by	by	ADP
ejpam-6294	389	12	balancing	balance	VERB
ejpam-6294	389	13	polynomials	polynomial	NOUN
ejpam-6294	389	14	.	.	PUNCT
ejpam-6294	390	1	karamanoğlu	karamanoğlu	PROPN
ejpam-6294	390	2	mehmetbey	mehmetbey	PROPN
ejpam-6294	390	3	univ	univ	PROPN
ejpam-6294	390	4	.	.	PUNCT
ejpam-6294	391	1	journal	journal	PROPN
ejpam-6294	391	2	of	of	ADP
ejpam-6294	391	3	engineering	engineering	NOUN
ejpam-6294	391	4	and	and	CCONJ
ejpam-6294	391	5	natural	natural	ADJ
ejpam-6294	391	6	sciences	science	NOUN
ejpam-6294	391	7	,	,	PUNCT
ejpam-6294	391	8	5:25–32	5:25–32	NUM
ejpam-6294	391	9	,	,	PUNCT
ejpam-6294	391	10	2023	2023	NUM
ejpam-6294	391	11	.	.	PUNCT
ejpam-6294	392	1	[	[	X
ejpam-6294	392	2	22	22	NUM
ejpam-6294	392	3	]	]	PUNCT
ejpam-6294	392	4	a.	a.	NOUN
ejpam-6294	392	5	k.	k.	PROPN
ejpam-6294	392	6	wanas	wanas	PROPN
ejpam-6294	392	7	,	,	PUNCT
ejpam-6294	392	8	g.	g.	PROPN
ejpam-6294	392	9	ş	ş	PROPN
ejpam-6294	392	10	.	.	PUNCT
ejpam-6294	393	1	sălăgean	sălăgean	ADJ
ejpam-6294	393	2	,	,	PUNCT
ejpam-6294	393	3	and	and	CCONJ
ejpam-6294	393	4	á	á	X
ejpam-6294	393	5	.	.	PUNCT
ejpam-6294	394	1	p.	p.	PROPN
ejpam-6294	394	2	s.	s.	PROPN
ejpam-6294	394	3	orsolya	orsolya	PROPN
ejpam-6294	394	4	.	.	PUNCT
ejpam-6294	395	1	coefficient	coefficient	NOUN
ejpam-6294	395	2	bounds	bound	NOUN
ejpam-6294	395	3	and	and	CCONJ
ejpam-6294	395	4	feketeszegő	feketeszegő	NOUN
ejpam-6294	395	5	inequality	inequality	NOUN
ejpam-6294	395	6	for	for	ADP
ejpam-6294	395	7	a	a	DET
ejpam-6294	395	8	certain	certain	ADJ
ejpam-6294	395	9	family	family	NOUN
ejpam-6294	395	10	of	of	ADP
ejpam-6294	395	11	holomorphic	holomorphic	ADJ
ejpam-6294	395	12	and	and	CCONJ
ejpam-6294	395	13	bi	bi	ADJ
ejpam-6294	395	14	-	-	ADJ
ejpam-6294	395	15	univalent	univalent	ADJ
ejpam-6294	395	16	functions	function	NOUN
ejpam-6294	395	17	defined	define	VERB
ejpam-6294	395	18	by	by	ADP
ejpam-6294	395	19	(	(	PUNCT
ejpam-6294	395	20	m	m	PROPN
ejpam-6294	395	21	,	,	PUNCT
ejpam-6294	395	22	n)-lucas	n)-luca	NOUN
ejpam-6294	395	23	polynomials	polynomial	NOUN
ejpam-6294	395	24	.	.	PUNCT
ejpam-6294	396	1	filomat	filomat	PROPN
ejpam-6294	396	2	,	,	PUNCT
ejpam-6294	396	3	37(4):1037–1044	37(4):1037–1044	PROPN
ejpam-6294	396	4	,	,	PUNCT
ejpam-6294	396	5	2023	2023	NUM
ejpam-6294	396	6	.	.	PUNCT
ejpam-6294	397	1	[	[	X
ejpam-6294	397	2	23	23	NUM
ejpam-6294	397	3	]	]	PUNCT
ejpam-6294	397	4	a.	a.	NOUN
ejpam-6294	397	5	k.	k.	PROPN
ejpam-6294	397	6	wanas	wanas	PROPN
ejpam-6294	397	7	,	,	PUNCT
ejpam-6294	397	8	e.	e.	PROPN
ejpam-6294	397	9	k.	k.	PROPN
ejpam-6294	397	10	wanas	wanas	PROPN
ejpam-6294	397	11	,	,	PUNCT
ejpam-6294	397	12	a.	a.	NOUN
ejpam-6294	397	13	cătaş	cătaş	NOUN
ejpam-6294	397	14	,	,	PUNCT
ejpam-6294	397	15	and	and	CCONJ
ejpam-6294	397	16	m.	m.	PROPN
ejpam-6294	397	17	abdalla	abdalla	PROPN
ejpam-6294	397	18	.	.	PUNCT
ejpam-6294	398	1	applications	application	NOUN
ejpam-6294	398	2	of	of	ADP
ejpam-6294	398	3	(	(	PUNCT
ejpam-6294	398	4	m	m	PROPN
ejpam-6294	398	5	,	,	PUNCT
ejpam-6294	398	6	n)-lucas	n)-luca	NOUN
ejpam-6294	398	7	polynomials	polynomial	NOUN
ejpam-6294	398	8	for	for	ADP
ejpam-6294	398	9	a	a	DET
ejpam-6294	398	10	certain	certain	ADJ
ejpam-6294	398	11	family	family	NOUN
ejpam-6294	398	12	of	of	ADP
ejpam-6294	398	13	bi	bi	ADJ
ejpam-6294	398	14	-	-	ADJ
ejpam-6294	398	15	univalent	univalent	ADJ
ejpam-6294	398	16	functions	function	NOUN
ejpam-6294	398	17	associating	associate	VERB
ejpam-6294	398	18	λ	λ	NOUN
ejpam-6294	398	19	-	-	PUNCT
ejpam-6294	398	20	pseudo	pseudo	ADJ
ejpam-6294	398	21	-	-	ADJ
ejpam-6294	398	22	starlike	starlike	ADJ
ejpam-6294	398	23	functions	function	NOUN
ejpam-6294	398	24	with	with	ADP
ejpam-6294	398	25	sakaguchi	sakaguchi	ADJ
ejpam-6294	398	26	type	type	NOUN
ejpam-6294	398	27	functions	function	NOUN
ejpam-6294	398	28	.	.	PUNCT
ejpam-6294	399	1	earthline	earthline	PROPN
ejpam-6294	399	2	journal	journal	PROPN
ejpam-6294	399	3	of	of	ADP
ejpam-6294	399	4	mathematical	mathematical	ADJ
ejpam-6294	399	5	sciences	sciences	PROPN
ejpam-6294	399	6	,	,	PUNCT
ejpam-6294	399	7	15(1):1–10	15(1):1–10	NUM
ejpam-6294	399	8	,	,	PUNCT
ejpam-6294	399	9	2024	2024	NUM
ejpam-6294	399	10	.	.	PUNCT
ejpam-6294	400	1	[	[	X
ejpam-6294	400	2	24	24	NUM
ejpam-6294	400	3	]	]	PUNCT
ejpam-6294	400	4	a.	a.	NOUN
ejpam-6294	400	5	hussen	hussen	PROPN
ejpam-6294	400	6	,	,	PUNCT
ejpam-6294	400	7	m.	m.	NOUN
ejpam-6294	400	8	s.	s.	PROPN
ejpam-6294	400	9	a.	a.	PROPN
ejpam-6294	400	10	madi	madi	PROPN
ejpam-6294	400	11	,	,	PUNCT
ejpam-6294	400	12	and	and	CCONJ
ejpam-6294	400	13	a.	a.	NOUN
ejpam-6294	400	14	m.	m.	PROPN
ejpam-6294	400	15	m.	m.	PROPN
ejpam-6294	400	16	abominjil	abominjil	PROPN
ejpam-6294	400	17	.	.	PUNCT
ejpam-6294	401	1	bounding	bound	VERB
ejpam-6294	401	2	coefficients	coefficient	NOUN
ejpam-6294	401	3	for	for	ADP
ejpam-6294	401	4	certain	certain	ADJ
ejpam-6294	401	5	subclasses	subclass	NOUN
ejpam-6294	401	6	of	of	ADP
ejpam-6294	401	7	bi	bi	ADJ
ejpam-6294	401	8	-	-	ADJ
ejpam-6294	401	9	univalent	univalent	ADJ
ejpam-6294	401	10	functions	function	NOUN
ejpam-6294	401	11	related	relate	VERB
ejpam-6294	401	12	to	to	ADP
ejpam-6294	401	13	lucas	lucas	NOUN
ejpam-6294	401	14	-	-	PUNCT
ejpam-6294	401	15	balancing	balance	VERB
ejpam-6294	401	16	polynomials	polynomial	NOUN
ejpam-6294	401	17	.	.	PUNCT
ejpam-6294	402	1	aims	aim	VERB
ejpam-6294	402	2	mathematics	mathematic	NOUN
ejpam-6294	402	3	,	,	PUNCT
ejpam-6294	402	4	9(7):18034–18047	9(7):18034–18047	NUM
ejpam-6294	402	5	,	,	PUNCT
ejpam-6294	402	6	2024	2024	NUM
ejpam-6294	402	7	.	.	PUNCT
ejpam-6294	403	1	[	[	X
ejpam-6294	403	2	25	25	NUM
ejpam-6294	403	3	]	]	PUNCT
ejpam-6294	403	4	m.	m.	NOUN
ejpam-6294	403	5	buyankara	buyankara	NOUN
ejpam-6294	403	6	and	and	CCONJ
ejpam-6294	403	7	m.	m.	NOUN
ejpam-6294	403	8	çağlar	çağlar	NOUN
ejpam-6294	403	9	.	.	PUNCT
ejpam-6294	404	1	coefficient	coefficient	NOUN
ejpam-6294	404	2	inequalities	inequality	NOUN
ejpam-6294	404	3	for	for	ADP
ejpam-6294	404	4	two	two	NUM
ejpam-6294	404	5	new	new	ADJ
ejpam-6294	404	6	subclasses	subclass	NOUN
ejpam-6294	404	7	of	of	ADP
ejpam-6294	404	8	biunivalent	biunivalent	NOUN
ejpam-6294	404	9	functions	function	NOUN
ejpam-6294	404	10	involving	involve	VERB
ejpam-6294	404	11	lucas	lucas	NOUN
ejpam-6294	404	12	-	-	PUNCT
ejpam-6294	404	13	balancing	balance	VERB
ejpam-6294	404	14	polynomials	polynomial	NOUN
ejpam-6294	404	15	.	.	PUNCT
ejpam-6294	405	1	eastern	eastern	ADJ
ejpam-6294	405	2	anatolian	anatolian	PROPN
ejpam-6294	405	3	journal	journal	PROPN
ejpam-6294	405	4	of	of	ADP
ejpam-6294	405	5	science	science	PROPN
ejpam-6294	405	6	,	,	PUNCT
ejpam-6294	405	7	10(2):5–11	10(2):5–11	NOUN
ejpam-6294	405	8	,	,	PUNCT
ejpam-6294	405	9	2024	2024	NUM
ejpam-6294	405	10	.	.	PUNCT
ejpam-6294	406	1	[	[	X
ejpam-6294	406	2	26	26	NUM
ejpam-6294	406	3	]	]	X
ejpam-6294	407	1	p.	p.	NOUN
ejpam-6294	407	2	l.	l.	PROPN
ejpam-6294	407	3	duren	duren	PROPN
ejpam-6294	407	4	.	.	PUNCT
ejpam-6294	408	1	univalent	univalent	ADJ
ejpam-6294	408	2	functions	function	NOUN
ejpam-6294	408	3	,	,	PUNCT
ejpam-6294	408	4	volume	volume	NOUN
ejpam-6294	408	5	259	259	NUM
ejpam-6294	408	6	of	of	ADP
ejpam-6294	408	7	grundlehren	grundlehren	PROPN
ejpam-6294	408	8	der	der	PROPN
ejpam-6294	408	9	mathematischen	mathematischen	PROPN
ejpam-6294	408	10	wissenschaften	wissenschaften	PROPN
ejpam-6294	408	11	.	.	PUNCT
ejpam-6294	409	1	springer	springer	NOUN
ejpam-6294	409	2	-	-	PUNCT
ejpam-6294	409	3	verlag	verlag	PROPN
ejpam-6294	409	4	,	,	PUNCT
ejpam-6294	409	5	new	new	PROPN
ejpam-6294	409	6	york	york	PROPN
ejpam-6294	409	7	,	,	PUNCT
ejpam-6294	409	8	1983	1983	NUM
ejpam-6294	409	9	.	.	PUNCT