id	sid	tid	token	lemma	pos
ejpam-3949	1	1	european	european	PROPN
ejpam-3949	1	2	journal	journal	PROPN
ejpam-3949	1	3	of	of	ADP
ejpam-3949	1	4	pure	pure	ADJ
ejpam-3949	1	5	and	and	CCONJ
ejpam-3949	1	6	applied	apply	VERB
ejpam-3949	1	7	mathematics	mathematic	NOUN
ejpam-3949	1	8	vol	vol	NOUN
ejpam-3949	1	9	.	.	PUNCT
ejpam-3949	2	1	14	14	NUM
ejpam-3949	2	2	,	,	PUNCT
ejpam-3949	2	3	no	no	INTJ
ejpam-3949	2	4	.	.	NOUN
ejpam-3949	2	5	2	2	NUM
ejpam-3949	2	6	,	,	PUNCT
ejpam-3949	2	7	2021	2021	NUM
ejpam-3949	2	8	,	,	PUNCT
ejpam-3949	2	9	506	506	NUM
ejpam-3949	2	10	-	-	SYM
ejpam-3949	2	11	520	520	NUM
ejpam-3949	2	12	issn	issn	PROPN
ejpam-3949	2	13	1307	1307	NUM
ejpam-3949	2	14	-	-	SYM
ejpam-3949	2	15	5543	5543	NUM
ejpam-3949	2	16	–	–	PUNCT
ejpam-3949	2	17	ejpam.com	ejpam.com	X
ejpam-3949	2	18	published	publish	VERB
ejpam-3949	2	19	by	by	ADP
ejpam-3949	2	20	new	new	PROPN
ejpam-3949	2	21	york	york	PROPN
ejpam-3949	2	22	business	business	PROPN
ejpam-3949	2	23	global	global	ADJ
ejpam-3949	2	24	translated	translate	VERB
ejpam-3949	2	25	logarithmic	logarithmic	PROPN
ejpam-3949	2	26	lambert	lambert	PROPN
ejpam-3949	2	27	function	function	NOUN
ejpam-3949	2	28	and	and	CCONJ
ejpam-3949	2	29	its	its	PRON
ejpam-3949	2	30	applications	application	NOUN
ejpam-3949	2	31	to	to	ADP
ejpam-3949	2	32	three	three	NUM
ejpam-3949	2	33	-	-	PUNCT
ejpam-3949	2	34	parameter	parameter	NOUN
ejpam-3949	2	35	entropy	entropy	PROPN
ejpam-3949	2	36	cristina	cristina	PROPN
ejpam-3949	2	37	b.	b.	PROPN
ejpam-3949	2	38	corcino1,2	corcino1,2	PROPN
ejpam-3949	2	39	,	,	PUNCT
ejpam-3949	2	40	roberto	roberto	PROPN
ejpam-3949	2	41	b.	b.	PROPN
ejpam-3949	2	42	corcino1,2,∗	corcino1,2,∗	PROPN
ejpam-3949	2	43	1	1	NUM
ejpam-3949	2	44	research	research	NOUN
ejpam-3949	2	45	institute	institute	NOUN
ejpam-3949	2	46	for	for	ADP
ejpam-3949	2	47	computational	computational	ADJ
ejpam-3949	2	48	mathematics	mathematic	NOUN
ejpam-3949	2	49	and	and	CCONJ
ejpam-3949	2	50	physics	physics	NOUN
ejpam-3949	2	51	,	,	PUNCT
ejpam-3949	2	52	cebu	cebu	NOUN
ejpam-3949	2	53	normal	normal	ADJ
ejpam-3949	2	54	university	university	NOUN
ejpam-3949	2	55	,	,	PUNCT
ejpam-3949	2	56	6000	6000	NUM
ejpam-3949	2	57	cebu	cebu	NOUN
ejpam-3949	2	58	city	city	NOUN
ejpam-3949	2	59	,	,	PUNCT
ejpam-3949	2	60	philippines	philippine	NOUN
ejpam-3949	2	61	2	2	NUM
ejpam-3949	2	62	mathematics	mathematics	NOUN
ejpam-3949	2	63	department	department	NOUN
ejpam-3949	2	64	,	,	PUNCT
ejpam-3949	2	65	cebu	cebu	NOUN
ejpam-3949	2	66	normal	normal	ADJ
ejpam-3949	2	67	university	university	NOUN
ejpam-3949	2	68	,	,	PUNCT
ejpam-3949	2	69	6000	6000	NUM
ejpam-3949	2	70	cebu	cebu	NOUN
ejpam-3949	2	71	city	city	NOUN
ejpam-3949	2	72	,	,	PUNCT
ejpam-3949	2	73	philippines	philippine	NOUN
ejpam-3949	2	74	abstract	abstract	ADJ
ejpam-3949	2	75	.	.	PUNCT
ejpam-3949	3	1	the	the	DET
ejpam-3949	3	2	translated	translate	VERB
ejpam-3949	3	3	logarithmic	logarithmic	PROPN
ejpam-3949	3	4	lambert	lambert	PROPN
ejpam-3949	3	5	function	function	NOUN
ejpam-3949	3	6	is	be	AUX
ejpam-3949	3	7	defined	define	VERB
ejpam-3949	3	8	and	and	CCONJ
ejpam-3949	3	9	basic	basic	ADJ
ejpam-3949	3	10	analytic	analytic	ADJ
ejpam-3949	3	11	properties	property	NOUN
ejpam-3949	3	12	of	of	ADP
ejpam-3949	3	13	the	the	DET
ejpam-3949	3	14	function	function	NOUN
ejpam-3949	3	15	are	be	AUX
ejpam-3949	3	16	obtained	obtain	VERB
ejpam-3949	3	17	including	include	VERB
ejpam-3949	3	18	the	the	DET
ejpam-3949	3	19	derivative	derivative	ADJ
ejpam-3949	3	20	,	,	PUNCT
ejpam-3949	3	21	real	real	ADJ
ejpam-3949	3	22	branches	branch	NOUN
ejpam-3949	3	23	and	and	CCONJ
ejpam-3949	3	24	asymptotic	asymptotic	ADJ
ejpam-3949	3	25	approximation	approximation	NOUN
ejpam-3949	3	26	of	of	ADP
ejpam-3949	3	27	the	the	DET
ejpam-3949	3	28	function	function	NOUN
ejpam-3949	3	29	.	.	PUNCT
ejpam-3949	4	1	moreover	moreover	ADV
ejpam-3949	4	2	,	,	PUNCT
ejpam-3949	4	3	the	the	DET
ejpam-3949	4	4	probability	probability	NOUN
ejpam-3949	4	5	distribution	distribution	NOUN
ejpam-3949	4	6	of	of	ADP
ejpam-3949	4	7	the	the	DET
ejpam-3949	4	8	three	three	NUM
ejpam-3949	4	9	-	-	PUNCT
ejpam-3949	4	10	parameter	parameter	NOUN
ejpam-3949	4	11	entropy	entropy	NOUN
ejpam-3949	4	12	is	be	AUX
ejpam-3949	4	13	derived	derive	VERB
ejpam-3949	4	14	which	which	PRON
ejpam-3949	4	15	is	be	AUX
ejpam-3949	4	16	expressed	express	VERB
ejpam-3949	4	17	in	in	ADP
ejpam-3949	4	18	terms	term	NOUN
ejpam-3949	4	19	of	of	ADP
ejpam-3949	4	20	the	the	DET
ejpam-3949	4	21	translated	translate	VERB
ejpam-3949	4	22	logarithmic	logarithmic	ADJ
ejpam-3949	4	23	lambert	lambert	PROPN
ejpam-3949	4	24	function	function	NOUN
ejpam-3949	4	25	.	.	PUNCT
ejpam-3949	5	1	2020	2020	NUM
ejpam-3949	5	2	mathematics	mathematic	NOUN
ejpam-3949	5	3	subject	subject	NOUN
ejpam-3949	5	4	classifications	classification	NOUN
ejpam-3949	5	5	:	:	PUNCT
ejpam-3949	5	6	33e20	33e20	NUM
ejpam-3949	5	7	,	,	PUNCT
ejpam-3949	5	8	33f05	33f05	NUM
ejpam-3949	5	9	key	key	ADJ
ejpam-3949	5	10	words	word	NOUN
ejpam-3949	5	11	and	and	CCONJ
ejpam-3949	5	12	phrases	phrase	NOUN
ejpam-3949	5	13	:	:	PUNCT
ejpam-3949	5	14	lambert	lambert	PROPN
ejpam-3949	5	15	function	function	PROPN
ejpam-3949	5	16	,	,	PUNCT
ejpam-3949	5	17	entropy	entropy	PROPN
ejpam-3949	5	18	,	,	PUNCT
ejpam-3949	5	19	logarithmic	logarithmic	ADJ
ejpam-3949	5	20	function	function	NOUN
ejpam-3949	5	21	,	,	PUNCT
ejpam-3949	5	22	tsallis	tsalli	NOUN
ejpam-3949	5	23	entropy	entropy	VERB
ejpam-3949	5	24	1	1	NUM
ejpam-3949	5	25	.	.	PUNCT
ejpam-3949	6	1	introduction	introduction	NOUN
ejpam-3949	6	2	the	the	DET
ejpam-3949	6	3	first	first	ADJ
ejpam-3949	6	4	definition	definition	NOUN
ejpam-3949	6	5	of	of	ADP
ejpam-3949	6	6	entropy	entropy	NOUN
ejpam-3949	6	7	that	that	PRON
ejpam-3949	6	8	appeared	appear	VERB
ejpam-3949	6	9	in	in	ADP
ejpam-3949	6	10	the	the	DET
ejpam-3949	6	11	literature	literature	NOUN
ejpam-3949	6	12	is	be	AUX
ejpam-3949	6	13	in	in	ADP
ejpam-3949	6	14	the	the	DET
ejpam-3949	6	15	context	context	NOUN
ejpam-3949	6	16	of	of	ADP
ejpam-3949	6	17	thermodynamics	thermodynamic	NOUN
ejpam-3949	6	18	.	.	PUNCT
ejpam-3949	7	1	being	be	AUX
ejpam-3949	7	2	commonly	commonly	ADV
ejpam-3949	7	3	understood	understand	VERB
ejpam-3949	7	4	as	as	ADP
ejpam-3949	7	5	a	a	DET
ejpam-3949	7	6	measure	measure	NOUN
ejpam-3949	7	7	of	of	ADP
ejpam-3949	7	8	disorder	disorder	NOUN
ejpam-3949	7	9	,	,	PUNCT
ejpam-3949	7	10	entropy	entropy	PROPN
ejpam-3949	7	11	is	be	AUX
ejpam-3949	7	12	defined	define	VERB
ejpam-3949	7	13	in	in	ADP
ejpam-3949	7	14	thermodynamics	thermodynamic	NOUN
ejpam-3949	7	15	viewpoint	viewpoint	NOUN
ejpam-3949	7	16	as	as	ADP
ejpam-3949	7	17	a	a	DET
ejpam-3949	7	18	measure	measure	NOUN
ejpam-3949	7	19	of	of	ADP
ejpam-3949	7	20	the	the	DET
ejpam-3949	7	21	number	number	NOUN
ejpam-3949	7	22	of	of	ADP
ejpam-3949	7	23	specific	specific	ADJ
ejpam-3949	7	24	ways	way	NOUN
ejpam-3949	7	25	in	in	ADP
ejpam-3949	7	26	which	which	PRON
ejpam-3949	7	27	a	a	DET
ejpam-3949	7	28	thermodynamic	thermodynamic	ADJ
ejpam-3949	7	29	system	system	NOUN
ejpam-3949	7	30	may	may	AUX
ejpam-3949	7	31	be	be	AUX
ejpam-3949	7	32	arranged	arrange	VERB
ejpam-3949	7	33	.	.	PUNCT
ejpam-3949	8	1	however	however	ADV
ejpam-3949	8	2	,	,	PUNCT
ejpam-3949	8	3	the	the	DET
ejpam-3949	8	4	microscopic	microscopic	ADJ
ejpam-3949	8	5	details	detail	NOUN
ejpam-3949	8	6	of	of	ADP
ejpam-3949	8	7	a	a	DET
ejpam-3949	8	8	system	system	NOUN
ejpam-3949	8	9	are	be	AUX
ejpam-3949	8	10	not	not	PART
ejpam-3949	8	11	considered	consider	VERB
ejpam-3949	8	12	in	in	ADP
ejpam-3949	8	13	this	this	DET
ejpam-3949	8	14	context	context	NOUN
ejpam-3949	8	15	.	.	PUNCT
ejpam-3949	9	1	the	the	DET
ejpam-3949	9	2	definition	definition	NOUN
ejpam-3949	9	3	of	of	ADP
ejpam-3949	9	4	entropy	entropy	NOUN
ejpam-3949	9	5	in	in	ADP
ejpam-3949	9	6	the	the	DET
ejpam-3949	9	7	statistical	statistical	ADJ
ejpam-3949	9	8	mechanics	mechanic	NOUN
ejpam-3949	9	9	point	point	NOUN
ejpam-3949	9	10	of	of	ADP
ejpam-3949	9	11	view	view	NOUN
ejpam-3949	9	12	appeared	appear	VERB
ejpam-3949	9	13	later	later	ADV
ejpam-3949	9	14	along	along	ADV
ejpam-3949	9	15	with	with	ADP
ejpam-3949	9	16	other	other	ADJ
ejpam-3949	9	17	thermodynamic	thermodynamic	ADJ
ejpam-3949	9	18	properties	property	NOUN
ejpam-3949	9	19	.	.	PUNCT
ejpam-3949	10	1	in	in	ADP
ejpam-3949	10	2	this	this	DET
ejpam-3949	10	3	context	context	NOUN
ejpam-3949	10	4	,	,	PUNCT
ejpam-3949	10	5	entropy	entropy	PROPN
ejpam-3949	10	6	is	be	AUX
ejpam-3949	10	7	considered	consider	VERB
ejpam-3949	10	8	as	as	ADP
ejpam-3949	10	9	an	an	DET
ejpam-3949	10	10	extensive	extensive	ADJ
ejpam-3949	10	11	property	property	NOUN
ejpam-3949	10	12	of	of	ADP
ejpam-3949	10	13	a	a	DET
ejpam-3949	10	14	thermodynamic	thermodynamic	ADJ
ejpam-3949	10	15	system	system	NOUN
ejpam-3949	10	16	wherein	wherein	SCONJ
ejpam-3949	10	17	thermodynamic	thermodynamic	ADJ
ejpam-3949	10	18	properties	property	NOUN
ejpam-3949	10	19	are	be	AUX
ejpam-3949	10	20	defined	define	VERB
ejpam-3949	10	21	in	in	ADP
ejpam-3949	10	22	terms	term	NOUN
ejpam-3949	10	23	of	of	ADP
ejpam-3949	10	24	the	the	DET
ejpam-3949	10	25	statistics	statistic	NOUN
ejpam-3949	10	26	of	of	ADP
ejpam-3949	10	27	the	the	DET
ejpam-3949	10	28	motions	motion	NOUN
ejpam-3949	10	29	of	of	ADP
ejpam-3949	10	30	the	the	DET
ejpam-3949	10	31	microscopic	microscopic	ADJ
ejpam-3949	10	32	constituents	constituent	NOUN
ejpam-3949	10	33	of	of	ADP
ejpam-3949	10	34	a	a	DET
ejpam-3949	10	35	system	system	NOUN
ejpam-3949	10	36	.	.	PUNCT
ejpam-3949	11	1	it	it	PRON
ejpam-3949	11	2	is	be	AUX
ejpam-3949	11	3	known	know	VERB
ejpam-3949	11	4	that	that	SCONJ
ejpam-3949	11	5	the	the	DET
ejpam-3949	11	6	entropy	entropy	NOUN
ejpam-3949	11	7	of	of	ADP
ejpam-3949	11	8	an	an	DET
ejpam-3949	11	9	isolated	isolated	ADJ
ejpam-3949	11	10	system	system	NOUN
ejpam-3949	11	11	never	never	ADV
ejpam-3949	11	12	decreases	decrease	VERB
ejpam-3949	11	13	,	,	PUNCT
ejpam-3949	11	14	which	which	PRON
ejpam-3949	11	15	is	be	AUX
ejpam-3949	11	16	the	the	DET
ejpam-3949	11	17	essence	essence	NOUN
ejpam-3949	11	18	of	of	ADP
ejpam-3949	11	19	the	the	DET
ejpam-3949	11	20	second	second	ADJ
ejpam-3949	11	21	law	law	NOUN
ejpam-3949	11	22	of	of	ADP
ejpam-3949	11	23	thermodynamics	thermodynamic	NOUN
ejpam-3949	11	24	.	.	PUNCT
ejpam-3949	12	1	such	such	DET
ejpam-3949	12	2	a	a	DET
ejpam-3949	12	3	system	system	NOUN
ejpam-3949	12	4	will	will	AUX
ejpam-3949	12	5	spontaneously	spontaneously	ADV
ejpam-3949	12	6	proceed	proceed	VERB
ejpam-3949	12	7	towards	towards	ADP
ejpam-3949	12	8	thermodynamic	thermodynamic	ADJ
ejpam-3949	12	9	equilibrium	equilibrium	NOUN
ejpam-3949	12	10	,	,	PUNCT
ejpam-3949	12	11	the	the	DET
ejpam-3949	12	12	configuration	configuration	NOUN
ejpam-3949	12	13	with	with	ADP
ejpam-3949	12	14	maximum	maximum	ADJ
ejpam-3949	12	15	entropy	entropy	NOUN
ejpam-3949	12	16	[	[	X
ejpam-3949	12	17	6	6	NUM
ejpam-3949	12	18	]	]	PUNCT
ejpam-3949	12	19	.	.	PUNCT
ejpam-3949	13	1	there	there	PRON
ejpam-3949	13	2	are	be	VERB
ejpam-3949	13	3	three	three	NUM
ejpam-3949	13	4	macroscopic	macroscopic	ADJ
ejpam-3949	13	5	variables	variable	NOUN
ejpam-3949	13	6	that	that	PRON
ejpam-3949	13	7	describe	describe	VERB
ejpam-3949	13	8	a	a	DET
ejpam-3949	13	9	system	system	NOUN
ejpam-3949	13	10	in	in	ADP
ejpam-3949	13	11	thermodynamic	thermodynamic	ADJ
ejpam-3949	13	12	equilibrium	equilibrium	NOUN
ejpam-3949	13	13	which	which	PRON
ejpam-3949	13	14	correspond	correspond	VERB
ejpam-3949	13	15	to	to	ADP
ejpam-3949	13	16	thermal	thermal	ADJ
ejpam-3949	13	17	,	,	PUNCT
ejpam-3949	13	18	mechanical	mechanical	ADJ
ejpam-3949	13	19	and	and	CCONJ
ejpam-3949	13	20	the	the	DET
ejpam-3949	13	21	chemical	chemical	NOUN
ejpam-3949	13	22	equilibrium	equilibrium	NOUN
ejpam-3949	13	23	.	.	PUNCT
ejpam-3949	14	1	to	to	ADP
ejpam-3949	14	2	each	each	DET
ejpam-3949	14	3	value	value	NOUN
ejpam-3949	14	4	of	of	ADP
ejpam-3949	14	5	these	these	DET
ejpam-3949	14	6	macroscopic	macroscopic	ADJ
ejpam-3949	14	7	variables	variable	NOUN
ejpam-3949	14	8	,	,	PUNCT
ejpam-3949	14	9	there	there	PRON
ejpam-3949	14	10	exist	exist	VERB
ejpam-3949	14	11	several	several	ADJ
ejpam-3949	14	12	possible	possible	ADJ
ejpam-3949	14	13	microscopic	microscopic	ADJ
ejpam-3949	14	14	configurations	configuration	NOUN
ejpam-3949	14	15	.	.	PUNCT
ejpam-3949	15	1	these	these	PRON
ejpam-3949	15	2	will	will	AUX
ejpam-3949	15	3	then	then	ADV
ejpam-3949	15	4	entail	entail	VERB
ejpam-3949	15	5	different	different	ADJ
ejpam-3949	15	6	systems	system	NOUN
ejpam-3949	15	7	and	and	CCONJ
ejpam-3949	15	8	the	the	DET
ejpam-3949	15	9	collection	collection	NOUN
ejpam-3949	15	10	of	of	ADP
ejpam-3949	15	11	these	these	DET
ejpam-3949	15	12	systems	system	NOUN
ejpam-3949	15	13	is	be	AUX
ejpam-3949	15	14	called	call	VERB
ejpam-3949	15	15	an	an	DET
ejpam-3949	15	16	ensemble	ensemble	ADJ
ejpam-3949	15	17	.	.	PUNCT
ejpam-3949	16	1	∗corresponding	∗corresponde	VERB
ejpam-3949	16	2	author	author	NOUN
ejpam-3949	16	3	.	.	PUNCT
ejpam-3949	17	1	doi	doi	NOUN
ejpam-3949	17	2	:	:	PUNCT
ejpam-3949	17	3	https://doi.org/10.29020/nybg.ejpam.v14i2.3949	https://doi.org/10.29020/nybg.ejpam.v14i2.3949	NUM
ejpam-3949	17	4	email	email	NOUN
ejpam-3949	17	5	addresses	address	NOUN
ejpam-3949	17	6	:	:	PUNCT
ejpam-3949	17	7	corcinoc@cnu.edu.ph	corcinoc@cnu.edu.ph	PROPN
ejpam-3949	17	8	(	(	PUNCT
ejpam-3949	17	9	c.	c.	PROPN
ejpam-3949	17	10	corcino	corcino	PROPN
ejpam-3949	17	11	)	)	PUNCT
ejpam-3949	17	12	,	,	PUNCT
ejpam-3949	17	13	rcorcino@yahoo.com	rcorcino@yahoo.com	X
ejpam-3949	17	14	(	(	PUNCT
ejpam-3949	17	15	r.	r.	PROPN
ejpam-3949	17	16	corcino	corcino	PROPN
ejpam-3949	17	17	)	)	PUNCT
ejpam-3949	17	18	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3949	18	1	506	506	NUM
ejpam-3949	18	2	c	c	X
ejpam-3949	18	3	©	©	PROPN
ejpam-3949	18	4	2021	2021	NUM
ejpam-3949	18	5	ejpam	ejpam	VERB
ejpam-3949	18	6	all	all	DET
ejpam-3949	18	7	rights	right	NOUN
ejpam-3949	18	8	reserved	reserve	VERB
ejpam-3949	18	9	.	.	PUNCT
ejpam-3949	19	1	c.	c.	PROPN
ejpam-3949	19	2	corcino	corcino	PROPN
ejpam-3949	19	3	,	,	PUNCT
ejpam-3949	19	4	r.	r.	PROPN
ejpam-3949	19	5	corcino	corcino	PROPN
ejpam-3949	19	6	/	/	SYM
ejpam-3949	19	7	eur	eur	PROPN
ejpam-3949	19	8	.	.	PUNCT
ejpam-3949	20	1	j.	j.	PROPN
ejpam-3949	20	2	pure	pure	PROPN
ejpam-3949	20	3	appl	appl	PROPN
ejpam-3949	20	4	.	.	PROPN
ejpam-3949	20	5	math	math	PROPN
ejpam-3949	20	6	,	,	PUNCT
ejpam-3949	20	7	14	14	NUM
ejpam-3949	20	8	(	(	PUNCT
ejpam-3949	20	9	2	2	NUM
ejpam-3949	20	10	)	)	PUNCT
ejpam-3949	20	11	(	(	PUNCT
ejpam-3949	20	12	2021	2021	NUM
ejpam-3949	20	13	)	)	PUNCT
ejpam-3949	20	14	,	,	PUNCT
ejpam-3949	20	15	506	506	NUM
ejpam-3949	20	16	-	-	SYM
ejpam-3949	20	17	520	520	NUM
ejpam-3949	20	18	507	507	NUM
ejpam-3949	20	19	one	one	NUM
ejpam-3949	20	20	of	of	ADP
ejpam-3949	20	21	the	the	DET
ejpam-3949	20	22	popular	popular	ADJ
ejpam-3949	20	23	ensembles	ensemble	NOUN
ejpam-3949	20	24	is	be	AUX
ejpam-3949	20	25	the	the	DET
ejpam-3949	20	26	canonical	canonical	ADJ
ejpam-3949	20	27	ensemble	ensemble	NOUN
ejpam-3949	20	28	,	,	PUNCT
ejpam-3949	20	29	which	which	PRON
ejpam-3949	20	30	is	be	AUX
ejpam-3949	20	31	statistical	statistical	ADJ
ejpam-3949	20	32	in	in	ADP
ejpam-3949	20	33	nature	nature	NOUN
ejpam-3949	20	34	that	that	PRON
ejpam-3949	20	35	represents	represent	VERB
ejpam-3949	20	36	the	the	DET
ejpam-3949	20	37	possible	possible	ADJ
ejpam-3949	20	38	states	state	NOUN
ejpam-3949	20	39	of	of	ADP
ejpam-3949	20	40	a	a	DET
ejpam-3949	20	41	mechanical	mechanical	ADJ
ejpam-3949	20	42	system	system	NOUN
ejpam-3949	20	43	in	in	ADP
ejpam-3949	20	44	thermal	thermal	ADJ
ejpam-3949	20	45	equilibrium	equilibrium	NOUN
ejpam-3949	20	46	with	with	ADP
ejpam-3949	20	47	a	a	DET
ejpam-3949	20	48	heat	heat	NOUN
ejpam-3949	20	49	bath	bath	NOUN
ejpam-3949	20	50	at	at	ADP
ejpam-3949	20	51	a	a	DET
ejpam-3949	20	52	fixed	fix	VERB
ejpam-3949	20	53	temperature	temperature	NOUN
ejpam-3949	20	54	.	.	PUNCT
ejpam-3949	21	1	some	some	PRON
ejpam-3949	21	2	of	of	ADP
ejpam-3949	21	3	the	the	DET
ejpam-3949	21	4	physical	physical	ADJ
ejpam-3949	21	5	systems	system	NOUN
ejpam-3949	21	6	can	can	AUX
ejpam-3949	21	7	not	not	PART
ejpam-3949	21	8	be	be	AUX
ejpam-3949	21	9	described	describe	VERB
ejpam-3949	21	10	by	by	ADP
ejpam-3949	21	11	boltzmann	boltzmann	PROPN
ejpam-3949	21	12	-	-	PUNCT
ejpam-3949	21	13	gibbs(bg	gibbs(bg	PROPN
ejpam-3949	21	14	)	)	PUNCT
ejpam-3949	21	15	statistical	statistical	ADJ
ejpam-3949	21	16	mechanics	mechanic	NOUN
ejpam-3949	21	17	[	[	X
ejpam-3949	21	18	1	1	NUM
ejpam-3949	21	19	,	,	PUNCT
ejpam-3949	21	20	2	2	NUM
ejpam-3949	21	21	,	,	PUNCT
ejpam-3949	21	22	9	9	NUM
ejpam-3949	21	23	,	,	PUNCT
ejpam-3949	21	24	11–14	11–14	NUM
ejpam-3949	21	25	]	]	PUNCT
ejpam-3949	21	26	.	.	PUNCT
ejpam-3949	22	1	however	however	ADV
ejpam-3949	22	2	,	,	PUNCT
ejpam-3949	22	3	tsallis	tsalli	NOUN
ejpam-3949	23	1	[	[	X
ejpam-3949	23	2	8	8	NUM
ejpam-3949	23	3	]	]	PUNCT
ejpam-3949	23	4	has	have	AUX
ejpam-3949	23	5	overcome	overcome	VERB
ejpam-3949	23	6	some	some	PRON
ejpam-3949	23	7	of	of	ADP
ejpam-3949	23	8	these	these	DET
ejpam-3949	23	9	difficulties	difficulty	NOUN
ejpam-3949	23	10	by	by	ADP
ejpam-3949	23	11	introducing	introduce	VERB
ejpam-3949	23	12	the	the	DET
ejpam-3949	23	13	following	follow	VERB
ejpam-3949	23	14	q	q	NOUN
ejpam-3949	23	15	-	-	PUNCT
ejpam-3949	23	16	entropy	entropy	NOUN
ejpam-3949	23	17	sq	sq	PROPN
ejpam-3949	23	18	=	=	SYM
ejpam-3949	23	19	k	k	PROPN
ejpam-3949	23	20	ω∑	ω∑	PROPN
ejpam-3949	23	21	i=1	i=1	PROPN
ejpam-3949	23	22	pi	pi	NOUN
ejpam-3949	23	23	lnq	lnq	PROPN
ejpam-3949	23	24	1	1	NUM
ejpam-3949	23	25	pi	pi	NOUN
ejpam-3949	23	26	,	,	PUNCT
ejpam-3949	23	27	(	(	PUNCT
ejpam-3949	23	28	1	1	X
ejpam-3949	23	29	)	)	PUNCT
ejpam-3949	23	30	where	where	SCONJ
ejpam-3949	23	31	k	k	PROPN
ejpam-3949	23	32	is	be	AUX
ejpam-3949	23	33	a	a	DET
ejpam-3949	23	34	positive	positive	ADJ
ejpam-3949	23	35	constant	constant	NOUN
ejpam-3949	23	36	and	and	CCONJ
ejpam-3949	23	37	ω	ω	PROPN
ejpam-3949	23	38	is	be	AUX
ejpam-3949	23	39	the	the	DET
ejpam-3949	23	40	total	total	ADJ
ejpam-3949	23	41	number	number	NOUN
ejpam-3949	23	42	of	of	ADP
ejpam-3949	23	43	microscopic	microscopic	ADJ
ejpam-3949	23	44	states	state	NOUN
ejpam-3949	23	45	.	.	PUNCT
ejpam-3949	24	1	for	for	ADP
ejpam-3949	24	2	any	any	DET
ejpam-3949	24	3	real	real	ADJ
ejpam-3949	24	4	number	number	NOUN
ejpam-3949	24	5	x	x	PUNCT
ejpam-3949	24	6	and	and	CCONJ
ejpam-3949	24	7	q	q	ADJ
ejpam-3949	24	8	>	>	X
ejpam-3949	24	9	0	0	PROPN
ejpam-3949	24	10	,	,	PUNCT
ejpam-3949	24	11	lnq	lnq	PROPN
ejpam-3949	24	12	x	x	PUNCT
ejpam-3949	24	13	called	call	VERB
ejpam-3949	24	14	the	the	DET
ejpam-3949	24	15	q	q	NOUN
ejpam-3949	24	16	-	-	PUNCT
ejpam-3949	24	17	logarithm	logarithm	NOUN
ejpam-3949	24	18	is	be	AUX
ejpam-3949	24	19	defined	define	VERB
ejpam-3949	24	20	by	by	ADP
ejpam-3949	24	21	lnq	lnq	PROPN
ejpam-3949	24	22	x	x	X
ejpam-3949	25	1	=	=	PUNCT
ejpam-3949	25	2	x1−q	x1−q	PROPN
ejpam-3949	25	3	−	−	NOUN
ejpam-3949	25	4	1	1	NUM
ejpam-3949	25	5	1−	1−	NUM
ejpam-3949	25	6	q	q	NOUN
ejpam-3949	25	7	,	,	PUNCT
ejpam-3949	25	8	ln1	ln1	NOUN
ejpam-3949	25	9	x	x	X
ejpam-3949	25	10	=	=	SYM
ejpam-3949	25	11	lnx	lnx	PROPN
ejpam-3949	25	12	.	.	PUNCT
ejpam-3949	26	1	(	(	PUNCT
ejpam-3949	26	2	2	2	X
ejpam-3949	26	3	)	)	PUNCT
ejpam-3949	26	4	the	the	DET
ejpam-3949	26	5	inverse	inverse	NOUN
ejpam-3949	26	6	function	function	NOUN
ejpam-3949	26	7	of	of	ADP
ejpam-3949	26	8	the	the	DET
ejpam-3949	26	9	q	q	NOUN
ejpam-3949	26	10	-	-	PUNCT
ejpam-3949	26	11	logarithm	logarithm	NOUN
ejpam-3949	26	12	is	be	AUX
ejpam-3949	26	13	called	call	VERB
ejpam-3949	26	14	q	q	ADJ
ejpam-3949	26	15	-	-	PUNCT
ejpam-3949	26	16	exponential	exponential	ADJ
ejpam-3949	26	17	and	and	CCONJ
ejpam-3949	26	18	is	be	AUX
ejpam-3949	26	19	given	give	VERB
ejpam-3949	26	20	by	by	ADP
ejpam-3949	26	21	expq	expq	ADJ
ejpam-3949	26	22	x	x	X
ejpam-3949	27	1	=	=	PUNCT
ejpam-3949	28	1	[	[	X
ejpam-3949	28	2	1	1	NUM
ejpam-3949	28	3	+	+	CCONJ
ejpam-3949	28	4	(	(	PUNCT
ejpam-3949	28	5	1−	1−	NUM
ejpam-3949	28	6	q)x	q)x	NOUN
ejpam-3949	28	7	]	]	PUNCT
ejpam-3949	28	8	1	1	NUM
ejpam-3949	28	9	1−q	1−q	NUM
ejpam-3949	28	10	,	,	PUNCT
ejpam-3949	28	11	exp1	exp1	PROPN
ejpam-3949	28	12	x	x	PUNCT
ejpam-3949	28	13	=	=	PUNCT
ejpam-3949	28	14	expx	expx	PROPN
ejpam-3949	28	15	.	.	PUNCT
ejpam-3949	29	1	(	(	PUNCT
ejpam-3949	29	2	3	3	X
ejpam-3949	29	3	)	)	PUNCT
ejpam-3949	29	4	in	in	ADP
ejpam-3949	29	5	the	the	DET
ejpam-3949	29	6	case	case	NOUN
ejpam-3949	29	7	of	of	ADP
ejpam-3949	29	8	equiprobability	equiprobability	NOUN
ejpam-3949	29	9	,	,	PUNCT
ejpam-3949	29	10	bg	bg	PROPN
ejpam-3949	29	11	is	be	AUX
ejpam-3949	29	12	recovered	recover	VERB
ejpam-3949	29	13	in	in	ADP
ejpam-3949	29	14	the	the	DET
ejpam-3949	29	15	limit	limit	NOUN
ejpam-3949	29	16	q	q	X
ejpam-3949	30	1	→	→	SYM
ejpam-3949	30	2	1	1	NUM
ejpam-3949	30	3	.	.	PUNCT
ejpam-3949	31	1	a	a	DET
ejpam-3949	31	2	two	two	NUM
ejpam-3949	31	3	-	-	PUNCT
ejpam-3949	31	4	parameter	parameter	NOUN
ejpam-3949	31	5	entropy	entropy	PROPN
ejpam-3949	31	6	sq	sq	PROPN
ejpam-3949	31	7	,	,	PUNCT
ejpam-3949	31	8	q′	q′	NOUN
ejpam-3949	31	9	that	that	PRON
ejpam-3949	31	10	recovered	recover	VERB
ejpam-3949	31	11	the	the	DET
ejpam-3949	31	12	q	q	NOUN
ejpam-3949	31	13	-	-	PUNCT
ejpam-3949	31	14	entropy	entropy	NOUN
ejpam-3949	31	15	sq	sq	INTJ
ejpam-3949	31	16	in	in	ADP
ejpam-3949	31	17	the	the	DET
ejpam-3949	31	18	limit	limit	NOUN
ejpam-3949	31	19	q′	q′	NOUN
ejpam-3949	31	20	→	→	SYM
ejpam-3949	31	21	1	1	NUM
ejpam-3949	31	22	was	be	AUX
ejpam-3949	31	23	defined	define	VERB
ejpam-3949	31	24	in	in	ADP
ejpam-3949	31	25	[	[	X
ejpam-3949	31	26	7	7	NUM
ejpam-3949	31	27	]	]	PUNCT
ejpam-3949	31	28	as	as	ADP
ejpam-3949	31	29	sq	sq	PROPN
ejpam-3949	31	30	,	,	PUNCT
ejpam-3949	31	31	q′	q′	PUNCT
ejpam-3949	31	32	≡	≡	PROPN
ejpam-3949	31	33	ω∑	ω∑	PROPN
ejpam-3949	31	34	i=1	i=1	PROPN
ejpam-3949	31	35	pi	pi	PROPN
ejpam-3949	31	36	lnq	lnq	PROPN
ejpam-3949	31	37	,	,	PUNCT
ejpam-3949	31	38	q′	q′	NOUN
ejpam-3949	31	39	1	1	NUM
ejpam-3949	31	40	pi	pi	NOUN
ejpam-3949	31	41	=	=	SYM
ejpam-3949	31	42	1	1	NUM
ejpam-3949	31	43	1−	1−	NUM
ejpam-3949	31	44	q′	q′	NOUN
ejpam-3949	31	45	ω∑	ω∑	ADP
ejpam-3949	32	1	i=1	i=1	PROPN
ejpam-3949	32	2	pi	pi	NOUN
ejpam-3949	32	3	[	[	PUNCT
ejpam-3949	32	4	exp	exp	NOUN
ejpam-3949	32	5	(	(	PUNCT
ejpam-3949	32	6	1−	1−	NUM
ejpam-3949	32	7	q′	q′	NOUN
ejpam-3949	32	8	1−	1−	NUM
ejpam-3949	32	9	q	q	NOUN
ejpam-3949	32	10	(	(	PUNCT
ejpam-3949	32	11	pq−1i	pq−1i	NOUN
ejpam-3949	32	12	−	−	NOUN
ejpam-3949	32	13	1	1	NUM
ejpam-3949	32	14	)	)	PUNCT
ejpam-3949	32	15	)	)	PUNCT
ejpam-3949	33	1	−	−	PROPN
ejpam-3949	33	2	1	1	NUM
ejpam-3949	33	3	]	]	PUNCT
ejpam-3949	33	4	.	.	PUNCT
ejpam-3949	34	1	(	(	PUNCT
ejpam-3949	34	2	4	4	X
ejpam-3949	34	3	)	)	PUNCT
ejpam-3949	34	4	applications	application	NOUN
ejpam-3949	34	5	of	of	ADP
ejpam-3949	34	6	sq	sq	NUM
ejpam-3949	34	7	to	to	ADP
ejpam-3949	34	8	a	a	DET
ejpam-3949	34	9	class	class	NOUN
ejpam-3949	34	10	of	of	ADP
ejpam-3949	34	11	energy	energy	NOUN
ejpam-3949	34	12	based	base	VERB
ejpam-3949	34	13	ensembles	ensemble	NOUN
ejpam-3949	34	14	were	be	AUX
ejpam-3949	34	15	done	do	VERB
ejpam-3949	34	16	in	in	ADP
ejpam-3949	34	17	[	[	X
ejpam-3949	34	18	4	4	X
ejpam-3949	34	19	]	]	PUNCT
ejpam-3949	34	20	while	while	SCONJ
ejpam-3949	34	21	applications	application	NOUN
ejpam-3949	34	22	of	of	ADP
ejpam-3949	34	23	sq	sq	NOUN
ejpam-3949	34	24	,	,	PUNCT
ejpam-3949	34	25	q′	q′	NOUN
ejpam-3949	34	26	to	to	ADP
ejpam-3949	34	27	adiabatic	adiabatic	ADJ
ejpam-3949	34	28	ensembles	ensemble	NOUN
ejpam-3949	34	29	were	be	AUX
ejpam-3949	34	30	done	do	VERB
ejpam-3949	34	31	in	in	ADP
ejpam-3949	34	32	[	[	X
ejpam-3949	34	33	3	3	NUM
ejpam-3949	34	34	]	]	PUNCT
ejpam-3949	34	35	.	.	PUNCT
ejpam-3949	35	1	results	result	NOUN
ejpam-3949	35	2	in	in	ADP
ejpam-3949	35	3	the	the	DET
ejpam-3949	35	4	applications	application	NOUN
ejpam-3949	35	5	of	of	ADP
ejpam-3949	35	6	sq	sq	NOUN
ejpam-3949	35	7	,	,	PUNCT
ejpam-3949	35	8	q′	q′	NOUN
ejpam-3949	35	9	involved	involve	VERB
ejpam-3949	35	10	the	the	DET
ejpam-3949	35	11	well	well	ADV
ejpam-3949	35	12	-	-	PUNCT
ejpam-3949	35	13	known	know	VERB
ejpam-3949	35	14	lambert	lambert	PROPN
ejpam-3949	35	15	w	w	PROPN
ejpam-3949	35	16	function	function	PROPN
ejpam-3949	35	17	.	.	PUNCT
ejpam-3949	36	1	a	a	DET
ejpam-3949	36	2	three	three	NUM
ejpam-3949	36	3	-	-	PUNCT
ejpam-3949	36	4	parameter	parameter	NOUN
ejpam-3949	36	5	entropy	entropy	PROPN
ejpam-3949	36	6	sq	sq	PROPN
ejpam-3949	36	7	,	,	PUNCT
ejpam-3949	36	8	q′,r	q′,r	VERB
ejpam-3949	36	9	that	that	SCONJ
ejpam-3949	36	10	recovers	recover	VERB
ejpam-3949	36	11	sq	sq	PROPN
ejpam-3949	36	12	,	,	PUNCT
ejpam-3949	36	13	q′	q′	NOUN
ejpam-3949	36	14	in	in	ADP
ejpam-3949	36	15	the	the	DET
ejpam-3949	36	16	limit	limit	NOUN
ejpam-3949	36	17	r	r	NOUN
ejpam-3949	36	18	→	→	SYM
ejpam-3949	36	19	1	1	NUM
ejpam-3949	36	20	was	be	AUX
ejpam-3949	36	21	defined	define	VERB
ejpam-3949	36	22	in	in	ADP
ejpam-3949	36	23	[	[	X
ejpam-3949	36	24	5	5	NUM
ejpam-3949	36	25	]	]	PUNCT
ejpam-3949	36	26	as	as	ADP
ejpam-3949	36	27	sq	sq	PROPN
ejpam-3949	36	28	,	,	PUNCT
ejpam-3949	37	1	q′,r	q′,r	PROPN
ejpam-3949	37	2	≡	≡	PROPN
ejpam-3949	37	3	k	k	PROPN
ejpam-3949	37	4	w∑	w∑	PROPN
ejpam-3949	37	5	i=1	i=1	PROPN
ejpam-3949	37	6	pi	pi	PROPN
ejpam-3949	37	7	lnq	lnq	PROPN
ejpam-3949	37	8	,	,	PUNCT
ejpam-3949	37	9	q′,r	q′,r	PROPN
ejpam-3949	37	10	1	1	NUM
ejpam-3949	37	11	pi	pi	NOUN
ejpam-3949	37	12	,	,	PUNCT
ejpam-3949	37	13	(	(	PUNCT
ejpam-3949	37	14	5	5	NUM
ejpam-3949	37	15	)	)	PUNCT
ejpam-3949	37	16	where	where	SCONJ
ejpam-3949	37	17	k	k	PROPN
ejpam-3949	37	18	is	be	AUX
ejpam-3949	37	19	a	a	DET
ejpam-3949	37	20	positive	positive	ADJ
ejpam-3949	37	21	constant	constant	NOUN
ejpam-3949	37	22	and	and	CCONJ
ejpam-3949	37	23	lnq	lnq	PROPN
ejpam-3949	37	24	,	,	PUNCT
ejpam-3949	37	25	q′,r	q′,r	PROPN
ejpam-3949	37	26	x	x	PROPN
ejpam-3949	37	27	≡	≡	PROPN
ejpam-3949	37	28	1	1	NUM
ejpam-3949	37	29	1−	1−	NUM
ejpam-3949	37	30	r	r	NOUN
ejpam-3949	37	31	(	(	PUNCT
ejpam-3949	37	32	exp	exp	NOUN
ejpam-3949	37	33	(	(	PUNCT
ejpam-3949	37	34	1−	1−	NUM
ejpam-3949	37	35	r	r	NOUN
ejpam-3949	37	36	1−	1−	NUM
ejpam-3949	37	37	q′	q′	NOUN
ejpam-3949	37	38	(	(	PUNCT
ejpam-3949	38	1	e(1−q	e(1−q	PROPN
ejpam-3949	38	2	′	′	PROPN
ejpam-3949	38	3	)	)	PUNCT
ejpam-3949	38	4	lnq	lnq	NOUN
ejpam-3949	39	1	x	x	X
ejpam-3949	39	2	−	−	PROPN
ejpam-3949	39	3	1	1	NUM
ejpam-3949	39	4	)	)	PUNCT
ejpam-3949	39	5	−	−	PROPN
ejpam-3949	39	6	1	1	NUM
ejpam-3949	39	7	)	)	PUNCT
ejpam-3949	39	8	)	)	PUNCT
ejpam-3949	39	9	.	.	PUNCT
ejpam-3949	40	1	(	(	PUNCT
ejpam-3949	40	2	6	6	X
ejpam-3949	40	3	)	)	PUNCT
ejpam-3949	40	4	the	the	DET
ejpam-3949	40	5	three	three	NUM
ejpam-3949	40	6	-	-	PUNCT
ejpam-3949	40	7	parameter	parameter	NOUN
ejpam-3949	40	8	entropic	entropic	ADJ
ejpam-3949	40	9	function	function	NOUN
ejpam-3949	40	10	(	(	PUNCT
ejpam-3949	40	11	5	5	NUM
ejpam-3949	40	12	)	)	PUNCT
ejpam-3949	40	13	was	be	AUX
ejpam-3949	40	14	shown	show	VERB
ejpam-3949	40	15	to	to	PART
ejpam-3949	40	16	be	be	AUX
ejpam-3949	40	17	analytic	analytic	ADJ
ejpam-3949	40	18	(	(	PUNCT
ejpam-3949	40	19	hence	hence	ADV
ejpam-3949	40	20	,	,	PUNCT
ejpam-3949	40	21	lesche	lesche	NOUN
ejpam-3949	40	22	-	-	PUNCT
ejpam-3949	40	23	stable	stable	ADJ
ejpam-3949	40	24	)	)	PUNCT
ejpam-3949	40	25	,	,	PUNCT
ejpam-3949	40	26	concave	concave	NOUN
ejpam-3949	40	27	and	and	CCONJ
ejpam-3949	40	28	convex	convex	VERB
ejpam-3949	40	29	in	in	ADP
ejpam-3949	40	30	specified	specified	ADJ
ejpam-3949	40	31	ranges	range	NOUN
ejpam-3949	40	32	of	of	ADP
ejpam-3949	40	33	the	the	DET
ejpam-3949	40	34	parameters	parameter	NOUN
ejpam-3949	40	35	(	(	PUNCT
ejpam-3949	40	36	see	see	VERB
ejpam-3949	40	37	[	[	X
ejpam-3949	40	38	5	5	NUM
ejpam-3949	40	39	]	]	NUM
ejpam-3949	40	40	)	)	PUNCT
ejpam-3949	40	41	.	.	PUNCT
ejpam-3949	41	1	in	in	ADP
ejpam-3949	41	2	this	this	DET
ejpam-3949	41	3	paper	paper	NOUN
ejpam-3949	41	4	another	another	DET
ejpam-3949	41	5	variation	variation	NOUN
ejpam-3949	41	6	of	of	ADP
ejpam-3949	41	7	lambert	lambert	PROPN
ejpam-3949	41	8	w	w	PROPN
ejpam-3949	41	9	function	function	PROPN
ejpam-3949	41	10	called	call	VERB
ejpam-3949	41	11	the	the	DET
ejpam-3949	41	12	translated	translate	VERB
ejpam-3949	41	13	logarithmic	logarithmic	ADJ
ejpam-3949	41	14	lambert	lambert	PROPN
ejpam-3949	41	15	function	function	NOUN
ejpam-3949	41	16	will	will	AUX
ejpam-3949	41	17	be	be	AUX
ejpam-3949	41	18	introduced	introduce	VERB
ejpam-3949	41	19	.	.	PUNCT
ejpam-3949	42	1	moreover	moreover	ADV
ejpam-3949	42	2	,	,	PUNCT
ejpam-3949	42	3	the	the	DET
ejpam-3949	42	4	probability	probability	NOUN
ejpam-3949	42	5	distribution	distribution	NOUN
ejpam-3949	42	6	of	of	ADP
ejpam-3949	42	7	the	the	DET
ejpam-3949	42	8	threeparameter	threeparameter	NOUN
ejpam-3949	42	9	entropy	entropy	NOUN
ejpam-3949	42	10	is	be	AUX
ejpam-3949	42	11	derived	derive	VERB
ejpam-3949	42	12	and	and	CCONJ
ejpam-3949	42	13	expressed	express	VERB
ejpam-3949	42	14	in	in	ADP
ejpam-3949	42	15	terms	term	NOUN
ejpam-3949	42	16	of	of	ADP
ejpam-3949	42	17	the	the	DET
ejpam-3949	42	18	translated	translate	VERB
ejpam-3949	42	19	logarithmic	logarithmic	ADJ
ejpam-3949	42	20	lambert	lambert	PROPN
ejpam-3949	42	21	function	function	NOUN
ejpam-3949	42	22	.	.	PUNCT
ejpam-3949	43	1	c.	c.	PROPN
ejpam-3949	43	2	corcino	corcino	PROPN
ejpam-3949	43	3	,	,	PUNCT
ejpam-3949	43	4	r.	r.	PROPN
ejpam-3949	43	5	corcino	corcino	PROPN
ejpam-3949	43	6	/	/	SYM
ejpam-3949	43	7	eur	eur	PROPN
ejpam-3949	43	8	.	.	PUNCT
ejpam-3949	44	1	j.	j.	PROPN
ejpam-3949	44	2	pure	pure	PROPN
ejpam-3949	44	3	appl	appl	PROPN
ejpam-3949	44	4	.	.	PROPN
ejpam-3949	44	5	math	math	PROPN
ejpam-3949	44	6	,	,	PUNCT
ejpam-3949	44	7	14	14	NUM
ejpam-3949	44	8	(	(	PUNCT
ejpam-3949	44	9	2	2	NUM
ejpam-3949	44	10	)	)	PUNCT
ejpam-3949	44	11	(	(	PUNCT
ejpam-3949	44	12	2021	2021	NUM
ejpam-3949	44	13	)	)	PUNCT
ejpam-3949	44	14	,	,	PUNCT
ejpam-3949	44	15	506	506	NUM
ejpam-3949	44	16	-	-	SYM
ejpam-3949	44	17	520	520	NUM
ejpam-3949	44	18	508	508	NUM
ejpam-3949	44	19	2	2	NUM
ejpam-3949	44	20	.	.	PUNCT
ejpam-3949	45	1	translated	translate	VERB
ejpam-3949	45	2	logarithmic	logarithmic	PROPN
ejpam-3949	45	3	lambert	lambert	PROPN
ejpam-3949	45	4	function	function	VERB
ejpam-3949	45	5	the	the	DET
ejpam-3949	45	6	generalization	generalization	NOUN
ejpam-3949	45	7	of	of	ADP
ejpam-3949	45	8	the	the	DET
ejpam-3949	45	9	lambert	lambert	PROPN
ejpam-3949	45	10	w	w	PROPN
ejpam-3949	45	11	function	function	PROPN
ejpam-3949	45	12	introduced	introduce	VERB
ejpam-3949	45	13	here	here	ADV
ejpam-3949	45	14	is	be	AUX
ejpam-3949	45	15	the	the	DET
ejpam-3949	45	16	translated	translate	VERB
ejpam-3949	45	17	logarithmic	logarithmic	ADJ
ejpam-3949	45	18	lambert	lambert	PROPN
ejpam-3949	45	19	function	function	NOUN
ejpam-3949	45	20	denoted	denote	VERB
ejpam-3949	45	21	by	by	ADP
ejpam-3949	45	22	wlt	wlt	PROPN
ejpam-3949	45	23	(	(	PUNCT
ejpam-3949	45	24	x	x	NOUN
ejpam-3949	45	25	)	)	PUNCT
ejpam-3949	45	26	and	and	CCONJ
ejpam-3949	45	27	is	be	AUX
ejpam-3949	45	28	defined	define	VERB
ejpam-3949	45	29	as	as	SCONJ
ejpam-3949	45	30	follows	follow	VERB
ejpam-3949	45	31	:	:	PUNCT
ejpam-3949	45	32	definition	definition	NOUN
ejpam-3949	45	33	2.1	2.1	NUM
ejpam-3949	45	34	.	.	PUNCT
ejpam-3949	46	1	for	for	ADP
ejpam-3949	46	2	any	any	DET
ejpam-3949	46	3	real	real	ADJ
ejpam-3949	46	4	number	number	NOUN
ejpam-3949	46	5	x	x	PUNCT
ejpam-3949	46	6	and	and	CCONJ
ejpam-3949	46	7	constant	constant	ADJ
ejpam-3949	46	8	b	b	NOUN
ejpam-3949	46	9	,	,	PUNCT
ejpam-3949	46	10	the	the	DET
ejpam-3949	46	11	translated	translate	VERB
ejpam-3949	46	12	logarithmic	logarithmic	PROPN
ejpam-3949	46	13	lambert	lambert	PROPN
ejpam-3949	46	14	function	function	PROPN
ejpam-3949	46	15	wlt	wlt	PROPN
ejpam-3949	46	16	(	(	PUNCT
ejpam-3949	46	17	x	x	X
ejpam-3949	46	18	)	)	PUNCT
ejpam-3949	46	19	is	be	AUX
ejpam-3949	46	20	defined	define	VERB
ejpam-3949	46	21	to	to	PART
ejpam-3949	46	22	be	be	AUX
ejpam-3949	46	23	the	the	DET
ejpam-3949	46	24	solution	solution	NOUN
ejpam-3949	46	25	to	to	ADP
ejpam-3949	46	26	the	the	DET
ejpam-3949	46	27	equation	equation	NOUN
ejpam-3949	46	28	(	(	PUNCT
ejpam-3949	46	29	ay	ay	NOUN
ejpam-3949	46	30	ln(by	ln(by	PROPN
ejpam-3949	46	31	)	)	PUNCT
ejpam-3949	47	1	+	+	CCONJ
ejpam-3949	47	2	y	y	PROPN
ejpam-3949	47	3	+	+	NUM
ejpam-3949	48	1	c)ey	c)ey	PROPN
ejpam-3949	48	2	=	=	PUNCT
ejpam-3949	48	3	x.	x.	NOUN
ejpam-3949	48	4	(	(	PUNCT
ejpam-3949	48	5	7	7	X
ejpam-3949	48	6	)	)	PUNCT
ejpam-3949	48	7	observe	observe	VERB
ejpam-3949	48	8	that	that	SCONJ
ejpam-3949	48	9	y	y	PROPN
ejpam-3949	48	10	can	can	AUX
ejpam-3949	48	11	not	not	PART
ejpam-3949	48	12	be	be	AUX
ejpam-3949	48	13	zero	zero	NUM
ejpam-3949	48	14	.	.	PUNCT
ejpam-3949	49	1	moreover	moreover	ADV
ejpam-3949	49	2	,	,	PUNCT
ejpam-3949	49	3	by	by	ADP
ejpam-3949	49	4	must	must	AUX
ejpam-3949	49	5	be	be	AUX
ejpam-3949	49	6	positive	positive	ADJ
ejpam-3949	49	7	.	.	PUNCT
ejpam-3949	50	1	by	by	ADP
ejpam-3949	50	2	definition	definition	NOUN
ejpam-3949	50	3	2.1	2.1	NUM
ejpam-3949	50	4	,	,	PUNCT
ejpam-3949	50	5	y	y	PROPN
ejpam-3949	50	6	=	=	SYM
ejpam-3949	50	7	wlt	wlt	PROPN
ejpam-3949	50	8	(	(	PUNCT
ejpam-3949	50	9	x	x	NOUN
ejpam-3949	50	10	)	)	PUNCT
ejpam-3949	50	11	.	.	PUNCT
ejpam-3949	51	1	the	the	DET
ejpam-3949	51	2	derivative	derivative	NOUN
ejpam-3949	51	3	of	of	ADP
ejpam-3949	51	4	wlt	wlt	PROPN
ejpam-3949	51	5	(	(	PUNCT
ejpam-3949	51	6	x	x	NOUN
ejpam-3949	51	7	)	)	PUNCT
ejpam-3949	51	8	with	with	ADP
ejpam-3949	51	9	respect	respect	NOUN
ejpam-3949	51	10	to	to	ADP
ejpam-3949	51	11	x	x	PUNCT
ejpam-3949	51	12	can	can	AUX
ejpam-3949	51	13	be	be	AUX
ejpam-3949	51	14	readily	readily	ADV
ejpam-3949	51	15	determined	determine	VERB
ejpam-3949	51	16	as	as	ADP
ejpam-3949	51	17	the	the	DET
ejpam-3949	51	18	following	follow	VERB
ejpam-3949	51	19	theorem	theorem	ADJ
ejpam-3949	51	20	shows	show	NOUN
ejpam-3949	51	21	.	.	PUNCT
ejpam-3949	52	1	theorem	theorem	VERB
ejpam-3949	52	2	2.2	2.2	NUM
ejpam-3949	52	3	.	.	PUNCT
ejpam-3949	53	1	the	the	DET
ejpam-3949	53	2	derivative	derivative	NOUN
ejpam-3949	53	3	of	of	ADP
ejpam-3949	53	4	the	the	DET
ejpam-3949	53	5	translated	translate	VERB
ejpam-3949	53	6	logarithmic	logarithmic	PROPN
ejpam-3949	53	7	lambert	lambert	PROPN
ejpam-3949	53	8	function	function	NOUN
ejpam-3949	53	9	is	be	AUX
ejpam-3949	53	10	given	give	VERB
ejpam-3949	53	11	by	by	ADP
ejpam-3949	53	12	dwlt	dwlt	PROPN
ejpam-3949	53	13	(	(	PUNCT
ejpam-3949	53	14	x	x	NOUN
ejpam-3949	53	15	)	)	PUNCT
ejpam-3949	53	16	dx	dx	PROPN
ejpam-3949	54	1	=	=	PUNCT
ejpam-3949	54	2	e−wlt	e−wlt	NOUN
ejpam-3949	54	3	(	(	PUNCT
ejpam-3949	54	4	x	x	X
ejpam-3949	54	5	)	)	PUNCT
ejpam-3949	55	1	[	[	X
ejpam-3949	55	2	wlt	wlt	X
ejpam-3949	55	3	(	(	PUNCT
ejpam-3949	55	4	x	x	NOUN
ejpam-3949	55	5	)	)	PUNCT
ejpam-3949	55	6	+	+	CCONJ
ejpam-3949	55	7	1]a	1]a	NUM
ejpam-3949	55	8	lnbwlt	lnbwlt	NOUN
ejpam-3949	55	9	(	(	PUNCT
ejpam-3949	55	10	x	x	X
ejpam-3949	55	11	)	)	PUNCT
ejpam-3949	55	12	+	+	NUM
ejpam-3949	55	13	wlt	wlt	PROPN
ejpam-3949	55	14	(	(	PUNCT
ejpam-3949	55	15	x	x	X
ejpam-3949	55	16	)	)	PUNCT
ejpam-3949	55	17	+	+	NOUN
ejpam-3949	55	18	a+	a+	PUNCT
ejpam-3949	55	19	c	c	NOUN
ejpam-3949	55	20	+	+	NOUN
ejpam-3949	55	21	1	1	NUM
ejpam-3949	55	22	.	.	PUNCT
ejpam-3949	56	1	(	(	PUNCT
ejpam-3949	56	2	8)	8)	NUM
ejpam-3949	56	3	proof	proof	NOUN
ejpam-3949	56	4	.	.	PUNCT
ejpam-3949	57	1	taking	take	VERB
ejpam-3949	57	2	the	the	DET
ejpam-3949	57	3	derivative	derivative	NOUN
ejpam-3949	57	4	of	of	ADP
ejpam-3949	57	5	both	both	DET
ejpam-3949	57	6	sides	side	NOUN
ejpam-3949	57	7	of	of	ADP
ejpam-3949	57	8	(	(	PUNCT
ejpam-3949	57	9	7	7	X
ejpam-3949	57	10	)	)	PUNCT
ejpam-3949	57	11	gives	give	VERB
ejpam-3949	57	12	(	(	PUNCT
ejpam-3949	57	13	ay	ay	NOUN
ejpam-3949	57	14	ln(by	ln(by	PROPN
ejpam-3949	57	15	)	)	PUNCT
ejpam-3949	58	1	+	+	CCONJ
ejpam-3949	58	2	y	y	PROPN
ejpam-3949	58	3	+	+	NOUN
ejpam-3949	58	4	c)ey	c)ey	PROPN
ejpam-3949	58	5	dy	dy	VERB
ejpam-3949	58	6	dx	dx	PROPN
ejpam-3949	59	1	+	+	CCONJ
ejpam-3949	59	2	(	(	PUNCT
ejpam-3949	59	3	a+a	a+a	X
ejpam-3949	59	4	ln(by	ln(by	NOUN
ejpam-3949	59	5	)	)	PUNCT
ejpam-3949	60	1	+	+	CCONJ
ejpam-3949	60	2	1	1	X
ejpam-3949	60	3	)	)	PUNCT
ejpam-3949	60	4	ey	ey	PROPN
ejpam-3949	60	5	dy	dy	X
ejpam-3949	60	6	dx	dx	PROPN
ejpam-3949	60	7	=	=	PROPN
ejpam-3949	60	8	1	1	NUM
ejpam-3949	60	9	,	,	PUNCT
ejpam-3949	60	10	from	from	ADP
ejpam-3949	60	11	which	which	PRON
ejpam-3949	60	12	dy	dy	X
ejpam-3949	60	13	dx	dx	PROPN
ejpam-3949	60	14	=	=	SYM
ejpam-3949	61	1	1	1	NUM
ejpam-3949	61	2	[	[	X
ejpam-3949	61	3	ay	ay	X
ejpam-3949	61	4	ln(by	ln(by	NOUN
ejpam-3949	61	5	)	)	PUNCT
ejpam-3949	62	1	+	+	PUNCT
ejpam-3949	62	2	y	y	PROPN
ejpam-3949	63	1	+	+	NOUN
ejpam-3949	63	2	c	c	NOUN
ejpam-3949	64	1	+	+	PROPN
ejpam-3949	64	2	a+a	a+a	X
ejpam-3949	64	3	ln(by	ln(by	NOUN
ejpam-3949	64	4	)	)	PUNCT
ejpam-3949	65	1	+	+	CCONJ
ejpam-3949	65	2	1	1	X
ejpam-3949	65	3	]	]	X
ejpam-3949	65	4	ey	ey	X
ejpam-3949	65	5	.	.	PUNCT
ejpam-3949	66	1	(	(	PUNCT
ejpam-3949	66	2	9	9	NUM
ejpam-3949	66	3	)	)	PUNCT
ejpam-3949	66	4	with	with	ADP
ejpam-3949	66	5	y	y	PROPN
ejpam-3949	66	6	=	=	SYM
ejpam-3949	66	7	wlt	wlt	PROPN
ejpam-3949	66	8	(	(	PUNCT
ejpam-3949	66	9	x	x	NOUN
ejpam-3949	66	10	)	)	PUNCT
ejpam-3949	66	11	,	,	PUNCT
ejpam-3949	66	12	(	(	PUNCT
ejpam-3949	66	13	9	9	X
ejpam-3949	66	14	)	)	PUNCT
ejpam-3949	66	15	reduces	reduce	VERB
ejpam-3949	66	16	to	to	ADP
ejpam-3949	66	17	(	(	PUNCT
ejpam-3949	66	18	8)	8)	NUM
ejpam-3949	66	19	.	.	PUNCT
ejpam-3949	67	1	the	the	DET
ejpam-3949	67	2	integral	integral	NOUN
ejpam-3949	67	3	of	of	ADP
ejpam-3949	67	4	the	the	DET
ejpam-3949	67	5	translated	translate	VERB
ejpam-3949	67	6	logarithmic	logarithmic	PROPN
ejpam-3949	67	7	lambert	lambert	PROPN
ejpam-3949	67	8	function	function	NOUN
ejpam-3949	67	9	is	be	AUX
ejpam-3949	67	10	given	give	VERB
ejpam-3949	67	11	in	in	ADP
ejpam-3949	67	12	the	the	DET
ejpam-3949	67	13	next	next	ADJ
ejpam-3949	67	14	theorem	theorem	PROPN
ejpam-3949	67	15	.	.	PUNCT
ejpam-3949	67	16	theorem	theorem	VERB
ejpam-3949	67	17	2.3	2.3	NUM
ejpam-3949	67	18	.	.	PUNCT
ejpam-3949	68	1	the	the	DET
ejpam-3949	68	2	integral	integral	NOUN
ejpam-3949	68	3	of	of	ADP
ejpam-3949	68	4	wlt	wlt	PROPN
ejpam-3949	68	5	(	(	PUNCT
ejpam-3949	68	6	x	x	NOUN
ejpam-3949	68	7	)	)	PUNCT
ejpam-3949	68	8	is∫	is∫	PROPN
ejpam-3949	68	9	wlt	wlt	PROPN
ejpam-3949	68	10	(	(	PUNCT
ejpam-3949	68	11	x	x	NOUN
ejpam-3949	68	12	)	)	PUNCT
ejpam-3949	68	13	dx	dx	PROPN
ejpam-3949	68	14	=	=	SYM
ejpam-3949	68	15	ewlt	ewlt	PROPN
ejpam-3949	68	16	(	(	PUNCT
ejpam-3949	68	17	x	x	X
ejpam-3949	68	18	)	)	PUNCT
ejpam-3949	69	1	[	[	X
ejpam-3949	69	2	(	(	PUNCT
ejpam-3949	69	3	w	w	PROPN
ejpam-3949	69	4	2	2	NUM
ejpam-3949	69	5	lt	lt	PRON
ejpam-3949	69	6	(	(	PUNCT
ejpam-3949	69	7	x)−wlt	x)−wlt	PROPN
ejpam-3949	69	8	(	(	PUNCT
ejpam-3949	69	9	x	x	X
ejpam-3949	69	10	)	)	PUNCT
ejpam-3949	69	11	+	+	CCONJ
ejpam-3949	69	12	1	1	X
ejpam-3949	69	13	)	)	PUNCT
ejpam-3949	69	14	a	a	DET
ejpam-3949	69	15	ln	ln	ADJ
ejpam-3949	69	16	(	(	PUNCT
ejpam-3949	69	17	bwlt	bwlt	NOUN
ejpam-3949	69	18	(	(	PUNCT
ejpam-3949	69	19	x	x	NOUN
ejpam-3949	69	20	)	)	PUNCT
ejpam-3949	69	21	)	)	PUNCT
ejpam-3949	70	1	+	+	ADP
ejpam-3949	70	2	w	w	PROPN
ejpam-3949	70	3	2	2	NUM
ejpam-3949	70	4	lt	lt	PRON
ejpam-3949	70	5	(	(	PUNCT
ejpam-3949	70	6	x	x	X
ejpam-3949	70	7	)	)	PUNCT
ejpam-3949	70	8	+	+	PROPN
ejpam-3949	70	9	(	(	PUNCT
ejpam-3949	70	10	c	c	PROPN
ejpam-3949	70	11	−	−	PROPN
ejpam-3949	70	12	1)wlt	1)wlt	NUM
ejpam-3949	70	13	(	(	PUNCT
ejpam-3949	70	14	x	x	X
ejpam-3949	70	15	)	)	PUNCT
ejpam-3949	70	16	+	+	CCONJ
ejpam-3949	70	17	1	1	NUM
ejpam-3949	70	18	+	+	ADJ
ejpam-3949	70	19	a−	a−	NOUN
ejpam-3949	70	20	c]−	c]−	VERB
ejpam-3949	70	21	2ei	2ei	NOUN
ejpam-3949	70	22	(	(	PUNCT
ejpam-3949	70	23	wlt	wlt	PROPN
ejpam-3949	70	24	(	(	PUNCT
ejpam-3949	70	25	x	x	NOUN
ejpam-3949	70	26	)	)	PUNCT
ejpam-3949	70	27	)	)	PUNCT
ejpam-3949	71	1	+	+	CCONJ
ejpam-3949	71	2	c	c	NOUN
ejpam-3949	71	3	′	′	NOUN
ejpam-3949	71	4	,	,	PUNCT
ejpam-3949	71	5	(	(	PUNCT
ejpam-3949	71	6	10	10	NUM
ejpam-3949	71	7	)	)	PUNCT
ejpam-3949	71	8	where	where	SCONJ
ejpam-3949	71	9	ei(x	ei(x	NUM
ejpam-3949	71	10	)	)	PUNCT
ejpam-3949	71	11	is	be	AUX
ejpam-3949	71	12	the	the	DET
ejpam-3949	71	13	exponential	exponential	ADJ
ejpam-3949	71	14	integral	integral	NOUN
ejpam-3949	71	15	given	give	VERB
ejpam-3949	71	16	by	by	ADP
ejpam-3949	71	17	ei(x	ei(x	NUM
ejpam-3949	71	18	)	)	PUNCT
ejpam-3949	72	1	=	=	SYM
ejpam-3949	73	1	∫	∫	PROPN
ejpam-3949	73	2	ex	ex	X
ejpam-3949	74	1	x	x	PROPN
ejpam-3949	74	2	dx	dx	PROPN
ejpam-3949	74	3	.	.	PUNCT
ejpam-3949	74	4	proof	proof	NOUN
ejpam-3949	74	5	.	.	PUNCT
ejpam-3949	75	1	from	from	ADP
ejpam-3949	75	2	(	(	PUNCT
ejpam-3949	75	3	7	7	NUM
ejpam-3949	75	4	)	)	PUNCT
ejpam-3949	75	5	,	,	PUNCT
ejpam-3949	75	6	dx	dx	PROPN
ejpam-3949	75	7	=	=	PUNCT
ejpam-3949	76	1	[	[	X
ejpam-3949	76	2	ay	ay	X
ejpam-3949	76	3	ln(by	ln(by	NOUN
ejpam-3949	76	4	)	)	PUNCT
ejpam-3949	77	1	+	+	PUNCT
ejpam-3949	77	2	y	y	PROPN
ejpam-3949	78	1	+	+	NOUN
ejpam-3949	78	2	c	c	NOUN
ejpam-3949	79	1	+	+	PROPN
ejpam-3949	79	2	a+a	a+a	X
ejpam-3949	79	3	ln(by	ln(by	NOUN
ejpam-3949	79	4	)	)	PUNCT
ejpam-3949	80	1	+	+	CCONJ
ejpam-3949	80	2	1	1	X
ejpam-3949	80	3	]	]	PUNCT
ejpam-3949	80	4	ey	ey	PRON
ejpam-3949	80	5	dy	dy	X
ejpam-3949	80	6	.	.	PROPN
ejpam-3949	80	7	c.	c.	PROPN
ejpam-3949	80	8	corcino	corcino	PROPN
ejpam-3949	80	9	,	,	PUNCT
ejpam-3949	80	10	r.	r.	PROPN
ejpam-3949	80	11	corcino	corcino	PROPN
ejpam-3949	80	12	/	/	SYM
ejpam-3949	80	13	eur	eur	PROPN
ejpam-3949	80	14	.	.	PUNCT
ejpam-3949	81	1	j.	j.	PROPN
ejpam-3949	81	2	pure	pure	PROPN
ejpam-3949	81	3	appl	appl	PROPN
ejpam-3949	81	4	.	.	PROPN
ejpam-3949	81	5	math	math	PROPN
ejpam-3949	81	6	,	,	PUNCT
ejpam-3949	81	7	14	14	NUM
ejpam-3949	81	8	(	(	PUNCT
ejpam-3949	81	9	2	2	NUM
ejpam-3949	81	10	)	)	PUNCT
ejpam-3949	81	11	(	(	PUNCT
ejpam-3949	81	12	2021	2021	NUM
ejpam-3949	81	13	)	)	PUNCT
ejpam-3949	81	14	,	,	PUNCT
ejpam-3949	81	15	506	506	NUM
ejpam-3949	81	16	-	-	SYM
ejpam-3949	81	17	520	520	NUM
ejpam-3949	81	18	509	509	NUM
ejpam-3949	81	19	thus	thus	ADV
ejpam-3949	81	20	,	,	PUNCT
ejpam-3949	81	21	∫	∫	PROPN
ejpam-3949	81	22	y	y	PROPN
ejpam-3949	81	23	dx	dx	PROPN
ejpam-3949	82	1	=	=	SYM
ejpam-3949	82	2	∫	∫	PROPN
ejpam-3949	83	1	y	y	PROPN
ejpam-3949	83	2	[	[	X
ejpam-3949	83	3	ay	ay	X
ejpam-3949	83	4	ln(by	ln(by	PROPN
ejpam-3949	83	5	)	)	PUNCT
ejpam-3949	84	1	+	+	PUNCT
ejpam-3949	84	2	y	y	PROPN
ejpam-3949	85	1	+	+	NOUN
ejpam-3949	85	2	c	c	NOUN
ejpam-3949	86	1	+	+	PROPN
ejpam-3949	86	2	a+a	a+a	X
ejpam-3949	86	3	ln(by	ln(by	NOUN
ejpam-3949	86	4	)	)	PUNCT
ejpam-3949	87	1	+	+	CCONJ
ejpam-3949	87	2	1	1	X
ejpam-3949	87	3	]	]	SYM
ejpam-3949	87	4	ey	ey	X
ejpam-3949	87	5	dy	dy	NOUN
ejpam-3949	87	6	=	=	PUNCT
ejpam-3949	87	7	a	a	DET
ejpam-3949	87	8	∫	∫	PROPN
ejpam-3949	87	9	y2ey	y2ey	PROPN
ejpam-3949	87	10	ln(by	ln(by	NOUN
ejpam-3949	87	11	)	)	PUNCT
ejpam-3949	87	12	dy	dy	NOUN
ejpam-3949	88	1	+	+	NOUN
ejpam-3949	88	2	a	a	DET
ejpam-3949	88	3	∫	∫	PROPN
ejpam-3949	88	4	yey	yey	NOUN
ejpam-3949	88	5	ln(by	ln(by	PROPN
ejpam-3949	88	6	)	)	PUNCT
ejpam-3949	89	1	dy	dy	NOUN
ejpam-3949	89	2	+	+	CCONJ
ejpam-3949	89	3	∫	∫	PROPN
ejpam-3949	89	4	y2ey	y2ey	PROPN
ejpam-3949	90	1	dy	dy	NOUN
ejpam-3949	90	2	+	+	X
ejpam-3949	90	3	(	(	PUNCT
ejpam-3949	90	4	c	c	X
ejpam-3949	90	5	+	+	NOUN
ejpam-3949	90	6	a+	a+	PRON
ejpam-3949	90	7	1	1	NUM
ejpam-3949	90	8	)	)	PUNCT
ejpam-3949	90	9	∫	∫	PROPN
ejpam-3949	90	10	yeydy	yeydy	NOUN
ejpam-3949	90	11	.	.	PUNCT
ejpam-3949	91	1	(	(	PUNCT
ejpam-3949	91	2	11	11	X
ejpam-3949	91	3	)	)	PUNCT
ejpam-3949	91	4	these	these	DET
ejpam-3949	91	5	integrals	integral	NOUN
ejpam-3949	91	6	can	can	AUX
ejpam-3949	91	7	be	be	AUX
ejpam-3949	91	8	computed	compute	VERB
ejpam-3949	91	9	using	use	VERB
ejpam-3949	91	10	integration	integration	NOUN
ejpam-3949	91	11	by	by	ADP
ejpam-3949	91	12	parts	part	NOUN
ejpam-3949	91	13	to	to	PART
ejpam-3949	91	14	obtain	obtain	VERB
ejpam-3949	91	15	(	(	PUNCT
ejpam-3949	91	16	a+	a+	PUNCT
ejpam-3949	91	17	c	c	NOUN
ejpam-3949	92	1	+	+	NOUN
ejpam-3949	92	2	1	1	X
ejpam-3949	92	3	)	)	PUNCT
ejpam-3949	92	4	∫	∫	PROPN
ejpam-3949	92	5	yey	yey	NOUN
ejpam-3949	92	6	dy	dy	NOUN
ejpam-3949	92	7	=	=	SYM
ejpam-3949	92	8	(	(	PUNCT
ejpam-3949	92	9	a+	a+	PUNCT
ejpam-3949	92	10	c	c	NOUN
ejpam-3949	93	1	+	+	NOUN
ejpam-3949	94	1	1)(y	1)(y	NUM
ejpam-3949	94	2	−	−	PROPN
ejpam-3949	94	3	1)ey	1)ey	PROPN
ejpam-3949	94	4	+	+	NUM
ejpam-3949	94	5	c1	c1	PROPN
ejpam-3949	94	6	,	,	PUNCT
ejpam-3949	94	7	(	(	PUNCT
ejpam-3949	94	8	12)∫	12)∫	NUM
ejpam-3949	94	9	y2ey	y2ey	NOUN
ejpam-3949	94	10	dy	dy	NOUN
ejpam-3949	94	11	=	=	SYM
ejpam-3949	94	12	(	(	PUNCT
ejpam-3949	94	13	y2	y2	INTJ
ejpam-3949	94	14	−	−	PROPN
ejpam-3949	94	15	2y	2y	PROPN
ejpam-3949	94	16	+	+	CCONJ
ejpam-3949	94	17	2)ey	2)ey	PROPN
ejpam-3949	94	18	+	+	CCONJ
ejpam-3949	94	19	c2	c2	PROPN
ejpam-3949	94	20	,	,	PUNCT
ejpam-3949	94	21	(	(	PUNCT
ejpam-3949	94	22	13	13	NUM
ejpam-3949	94	23	)	)	PUNCT
ejpam-3949	94	24	a	a	DET
ejpam-3949	94	25	∫	∫	PROPN
ejpam-3949	94	26	yey	yey	PROPN
ejpam-3949	94	27	ln(by	ln(by	PROPN
ejpam-3949	94	28	)	)	PUNCT
ejpam-3949	94	29	dy	dy	NOUN
ejpam-3949	94	30	=	=	SYM
ejpam-3949	94	31	aey	aey	PROPN
ejpam-3949	94	32	(	(	PUNCT
ejpam-3949	94	33	(	(	PUNCT
ejpam-3949	94	34	y	y	PROPN
ejpam-3949	94	35	−	−	PROPN
ejpam-3949	94	36	1	1	NUM
ejpam-3949	94	37	)	)	PUNCT
ejpam-3949	94	38	ln(by)−	ln(by)−	NOUN
ejpam-3949	94	39	1	1	X
ejpam-3949	94	40	)	)	PUNCT
ejpam-3949	94	41	+	+	CCONJ
ejpam-3949	94	42	ei(y	ei(y	NOUN
ejpam-3949	94	43	)	)	PUNCT
ejpam-3949	94	44	+	+	CCONJ
ejpam-3949	94	45	c3	c3	PROPN
ejpam-3949	94	46	,	,	PUNCT
ejpam-3949	94	47	(	(	PUNCT
ejpam-3949	94	48	14	14	NUM
ejpam-3949	94	49	)	)	PUNCT
ejpam-3949	94	50	a	a	DET
ejpam-3949	94	51	∫	∫	PROPN
ejpam-3949	94	52	y2ey	y2ey	PROPN
ejpam-3949	94	53	ln(by	ln(by	NOUN
ejpam-3949	94	54	)	)	PUNCT
ejpam-3949	94	55	dy	dy	NOUN
ejpam-3949	94	56	=	=	SYM
ejpam-3949	94	57	aey	aey	PROPN
ejpam-3949	94	58	[	[	PUNCT
ejpam-3949	94	59	(	(	PUNCT
ejpam-3949	94	60	y2	y2	INTJ
ejpam-3949	94	61	−	−	PROPN
ejpam-3949	94	62	2y	2y	PROPN
ejpam-3949	94	63	+	+	CCONJ
ejpam-3949	94	64	2	2	X
ejpam-3949	94	65	)	)	PUNCT
ejpam-3949	94	66	ln(by)−	ln(by)−	PUNCT
ejpam-3949	95	1	y	y	PROPN
ejpam-3949	95	2	+	+	CCONJ
ejpam-3949	95	3	3	3	NUM
ejpam-3949	95	4	]	]	PUNCT
ejpam-3949	95	5	−	−	PROPN
ejpam-3949	95	6	2ei(y	2ei(y	NUM
ejpam-3949	95	7	)	)	PUNCT
ejpam-3949	95	8	+	+	NUM
ejpam-3949	95	9	c4	c4	NOUN
ejpam-3949	95	10	,	,	PUNCT
ejpam-3949	95	11	(	(	PUNCT
ejpam-3949	95	12	15	15	NUM
ejpam-3949	95	13	)	)	PUNCT
ejpam-3949	95	14	where	where	SCONJ
ejpam-3949	95	15	c1	c1	PROPN
ejpam-3949	95	16	,	,	PUNCT
ejpam-3949	95	17	c2	c2	PROPN
ejpam-3949	95	18	,	,	PUNCT
ejpam-3949	95	19	c3	c3	PROPN
ejpam-3949	95	20	are	be	AUX
ejpam-3949	95	21	constants	constant	NOUN
ejpam-3949	95	22	.	.	PUNCT
ejpam-3949	96	1	substitution	substitution	NOUN
ejpam-3949	96	2	of	of	ADP
ejpam-3949	96	3	(	(	PUNCT
ejpam-3949	96	4	12	12	NUM
ejpam-3949	96	5	)	)	PUNCT
ejpam-3949	96	6	,	,	PUNCT
ejpam-3949	96	7	(	(	PUNCT
ejpam-3949	96	8	13	13	NUM
ejpam-3949	96	9	)	)	PUNCT
ejpam-3949	96	10	,	,	PUNCT
ejpam-3949	96	11	(	(	PUNCT
ejpam-3949	96	12	15	15	NUM
ejpam-3949	96	13	)	)	PUNCT
ejpam-3949	96	14	and	and	CCONJ
ejpam-3949	96	15	(	(	PUNCT
ejpam-3949	96	16	14	14	NUM
ejpam-3949	96	17	)	)	PUNCT
ejpam-3949	96	18	to	to	ADP
ejpam-3949	96	19	(	(	PUNCT
ejpam-3949	96	20	11	11	NUM
ejpam-3949	96	21	)	)	PUNCT
ejpam-3949	96	22	with	with	ADP
ejpam-3949	96	23	c	c	NOUN
ejpam-3949	96	24	′	′	NOUN
ejpam-3949	96	25	=	=	PUNCT
ejpam-3949	96	26	c1	c1	PROPN
ejpam-3949	96	27	+	+	CCONJ
ejpam-3949	96	28	c2	c2	PROPN
ejpam-3949	96	29	+	+	CCONJ
ejpam-3949	96	30	c3	c3	PROPN
ejpam-3949	96	31	+	+	CCONJ
ejpam-3949	96	32	c4	c4	NOUN
ejpam-3949	96	33	,	,	PUNCT
ejpam-3949	96	34	and	and	CCONJ
ejpam-3949	96	35	writing	write	VERB
ejpam-3949	96	36	wlt	wlt	PROPN
ejpam-3949	96	37	(	(	PUNCT
ejpam-3949	96	38	x	x	NOUN
ejpam-3949	96	39	)	)	PUNCT
ejpam-3949	96	40	for	for	ADP
ejpam-3949	96	41	y	y	PROPN
ejpam-3949	96	42	will	will	AUX
ejpam-3949	96	43	give	give	VERB
ejpam-3949	96	44	(	(	PUNCT
ejpam-3949	96	45	10	10	NUM
ejpam-3949	96	46	)	)	PUNCT
ejpam-3949	96	47	.	.	PUNCT
ejpam-3949	97	1	the	the	DET
ejpam-3949	97	2	next	next	ADJ
ejpam-3949	97	3	theorem	theorem	NOUN
ejpam-3949	97	4	contains	contain	VERB
ejpam-3949	97	5	the	the	DET
ejpam-3949	97	6	taylor	taylor	PROPN
ejpam-3949	97	7	series	series	PROPN
ejpam-3949	97	8	expansion	expansion	NOUN
ejpam-3949	97	9	of	of	ADP
ejpam-3949	97	10	wlt	wlt	PROPN
ejpam-3949	97	11	(	(	PUNCT
ejpam-3949	97	12	x	x	NOUN
ejpam-3949	97	13	)	)	PUNCT
ejpam-3949	97	14	.	.	PUNCT
ejpam-3949	98	1	theorem	theorem	VERB
ejpam-3949	98	2	2.4	2.4	NUM
ejpam-3949	98	3	.	.	PUNCT
ejpam-3949	99	1	few	few	ADJ
ejpam-3949	99	2	terms	term	NOUN
ejpam-3949	99	3	of	of	ADP
ejpam-3949	99	4	the	the	DET
ejpam-3949	99	5	taylor	taylor	PROPN
ejpam-3949	99	6	series	series	NOUN
ejpam-3949	99	7	of	of	ADP
ejpam-3949	99	8	wlt	wlt	PROPN
ejpam-3949	99	9	(	(	PUNCT
ejpam-3949	99	10	x	x	NOUN
ejpam-3949	99	11	)	)	PUNCT
ejpam-3949	99	12	about	about	ADV
ejpam-3949	99	13	0	0	NUM
ejpam-3949	99	14	are	be	AUX
ejpam-3949	99	15	given	give	VERB
ejpam-3949	99	16	below	below	ADP
ejpam-3949	99	17	:	:	PUNCT
ejpam-3949	99	18	wlt	wlt	PROPN
ejpam-3949	99	19	(	(	PUNCT
ejpam-3949	99	20	x	x	NOUN
ejpam-3949	99	21	)	)	PUNCT
ejpam-3949	99	22	=	=	SYM
ejpam-3949	99	23	1	1	NUM
ejpam-3949	99	24	b	b	X
ejpam-3949	99	25	e	e	X
ejpam-3949	99	26	w	w	X
ejpam-3949	99	27	(	(	PUNCT
ejpam-3949	99	28	−bce1	−bce1	PROPN
ejpam-3949	99	29	/	/	SYM
ejpam-3949	99	30	a	a	DET
ejpam-3949	99	31	a	a	NOUN
ejpam-3949	99	32	)	)	PUNCT
ejpam-3949	99	33	−	−	PROPN
ejpam-3949	99	34	1	1	NUM
ejpam-3949	99	35	a	a	DET
ejpam-3949	99	36	+	+	NOUN
ejpam-3949	99	37	e	e	NOUN
ejpam-3949	99	38	−1	−1	NOUN
ejpam-3949	99	39	b	b	PROPN
ejpam-3949	99	40	e	e	X
ejpam-3949	99	41	w	w	PROPN
ejpam-3949	99	42	(	(	PUNCT
ejpam-3949	99	43	−bce1	−bce1	PROPN
ejpam-3949	99	44	/	/	SYM
ejpam-3949	99	45	a	a	DET
ejpam-3949	99	46	a	a	NOUN
ejpam-3949	99	47	)	)	PUNCT
ejpam-3949	99	48	−	−	PROPN
ejpam-3949	99	49	1	1	NUM
ejpam-3949	99	50	a	a	DET
ejpam-3949	99	51	a	a	DET
ejpam-3949	99	52	[	[	PUNCT
ejpam-3949	99	53	w	w	NOUN
ejpam-3949	99	54	(	(	PUNCT
ejpam-3949	99	55	−bce1	−bce1	PROPN
ejpam-3949	99	56	/	/	SYM
ejpam-3949	99	57	a	a	DET
ejpam-3949	99	58	a	a	NOUN
ejpam-3949	99	59	)	)	PUNCT
ejpam-3949	99	60	+	+	CCONJ
ejpam-3949	99	61	1	1	X
ejpam-3949	99	62	]	]	PUNCT
ejpam-3949	99	63	x+	x+	X
ejpam-3949	99	64	·	·	PUNCT
ejpam-3949	99	65	·	·	PUNCT
ejpam-3949	99	66	·	·	PUNCT
ejpam-3949	99	67	(	(	PUNCT
ejpam-3949	99	68	16	16	NUM
ejpam-3949	99	69	)	)	PUNCT
ejpam-3949	99	70	where	where	SCONJ
ejpam-3949	99	71	w	w	X
ejpam-3949	99	72	(	(	PUNCT
ejpam-3949	99	73	x	x	X
ejpam-3949	99	74	)	)	PUNCT
ejpam-3949	99	75	is	be	AUX
ejpam-3949	99	76	the	the	DET
ejpam-3949	99	77	classical	classical	ADJ
ejpam-3949	99	78	lambert	lambert	PROPN
ejpam-3949	99	79	w	w	PROPN
ejpam-3949	99	80	function	function	NOUN
ejpam-3949	99	81	.	.	PUNCT
ejpam-3949	100	1	proof	proof	NOUN
ejpam-3949	100	2	.	.	PUNCT
ejpam-3949	101	1	being	be	AUX
ejpam-3949	101	2	the	the	DET
ejpam-3949	101	3	inverse	inverse	NOUN
ejpam-3949	101	4	of	of	ADP
ejpam-3949	101	5	the	the	DET
ejpam-3949	101	6	function	function	NOUN
ejpam-3949	101	7	defined	define	VERB
ejpam-3949	101	8	by	by	ADP
ejpam-3949	101	9	x	x	X
ejpam-3949	101	10	=	=	SYM
ejpam-3949	101	11	y	y	PROPN
ejpam-3949	101	12	ln(by)ey	ln(by)ey	PROPN
ejpam-3949	101	13	,	,	PUNCT
ejpam-3949	101	14	the	the	DET
ejpam-3949	101	15	lagrange	lagrange	NOUN
ejpam-3949	101	16	inversion	inversion	NOUN
ejpam-3949	101	17	theorem	theorem	NOUN
ejpam-3949	101	18	is	be	AUX
ejpam-3949	101	19	the	the	DET
ejpam-3949	101	20	key	key	NOUN
ejpam-3949	101	21	to	to	PART
ejpam-3949	101	22	obtain	obtain	VERB
ejpam-3949	101	23	the	the	DET
ejpam-3949	101	24	taylor	taylor	PROPN
ejpam-3949	101	25	series	series	NOUN
ejpam-3949	101	26	of	of	ADP
ejpam-3949	101	27	the	the	DET
ejpam-3949	101	28	function	function	NOUN
ejpam-3949	101	29	wlt	wlt	PROPN
ejpam-3949	101	30	(	(	PUNCT
ejpam-3949	101	31	x	x	NOUN
ejpam-3949	101	32	)	)	PUNCT
ejpam-3949	101	33	.	.	PUNCT
ejpam-3949	102	1	let	let	VERB
ejpam-3949	102	2	f(y	f(y	NOUN
ejpam-3949	102	3	)	)	PUNCT
ejpam-3949	102	4	=	=	PUNCT
ejpam-3949	103	1	(	(	PUNCT
ejpam-3949	103	2	ay	ay	INTJ
ejpam-3949	103	3	ln(by	ln(by	PROPN
ejpam-3949	103	4	)	)	PUNCT
ejpam-3949	104	1	+	+	CCONJ
ejpam-3949	104	2	y	y	PROPN
ejpam-3949	104	3	+	+	PROPN
ejpam-3949	104	4	c)ey	c)ey	PROPN
ejpam-3949	104	5	.	.	PUNCT
ejpam-3949	105	1	the	the	DET
ejpam-3949	105	2	function	function	NOUN
ejpam-3949	105	3	f	f	PROPN
ejpam-3949	105	4	is	be	AUX
ejpam-3949	105	5	analytic	analytic	ADJ
ejpam-3949	105	6	for	for	ADP
ejpam-3949	105	7	by	by	ADP
ejpam-3949	105	8	>	>	X
ejpam-3949	105	9	0	0	X
ejpam-3949	105	10	.	.	PUNCT
ejpam-3949	106	1	moreover	moreover	ADV
ejpam-3949	106	2	,	,	PUNCT
ejpam-3949	106	3	f	f	PROPN
ejpam-3949	106	4	′(y	′(y	NOUN
ejpam-3949	106	5	)	)	PUNCT
ejpam-3949	106	6	=	=	PUNCT
ejpam-3949	107	1	[	[	X
ejpam-3949	107	2	a(y	a(y	NOUN
ejpam-3949	107	3	+	+	CCONJ
ejpam-3949	107	4	1	1	X
ejpam-3949	107	5	)	)	PUNCT
ejpam-3949	107	6	ln(by	ln(by	NOUN
ejpam-3949	107	7	)	)	PUNCT
ejpam-3949	108	1	+	+	CCONJ
ejpam-3949	108	2	y	y	PROPN
ejpam-3949	108	3	+	+	NOUN
ejpam-3949	108	4	a+	a+	X
ejpam-3949	108	5	c	c	NOUN
ejpam-3949	108	6	+	+	NOUN
ejpam-3949	108	7	1	1	X
ejpam-3949	108	8	]	]	X
ejpam-3949	108	9	ey	ey	PROPN
ejpam-3949	108	10	,	,	PUNCT
ejpam-3949	108	11	f	f	NOUN
ejpam-3949	108	12	′	′	NUM
ejpam-3949	108	13	(	(	PUNCT
ejpam-3949	108	14	1	1	NUM
ejpam-3949	108	15	b	b	X
ejpam-3949	108	16	e	e	ADP
ejpam-3949	108	17	w	w	X
ejpam-3949	108	18	(	(	PUNCT
ejpam-3949	108	19	−bce1	−bce1	PROPN
ejpam-3949	108	20	/	/	SYM
ejpam-3949	108	21	a	a	DET
ejpam-3949	108	22	a	a	NOUN
ejpam-3949	108	23	)	)	PUNCT
ejpam-3949	108	24	−	−	PROPN
ejpam-3949	108	25	1	1	NUM
ejpam-3949	108	26	a	a	NOUN
ejpam-3949	108	27	)	)	PUNCT
ejpam-3949	108	28	=	=	SYM
ejpam-3949	108	29	ae	ae	PROPN
ejpam-3949	108	30	1	1	NUM
ejpam-3949	108	31	b	b	PROPN
ejpam-3949	108	32	e	e	ADP
ejpam-3949	108	33	w	w	X
ejpam-3949	108	34	(	(	PUNCT
ejpam-3949	108	35	−bce1	−bce1	PROPN
ejpam-3949	108	36	/	/	SYM
ejpam-3949	108	37	a	a	DET
ejpam-3949	108	38	a	a	NOUN
ejpam-3949	108	39	)	)	PUNCT
ejpam-3949	108	40	−	−	PROPN
ejpam-3949	108	41	1	1	NUM
ejpam-3949	108	42	a	a	PRON
ejpam-3949	108	43	[	[	PUNCT
ejpam-3949	108	44	w	w	NOUN
ejpam-3949	108	45	(	(	PUNCT
ejpam-3949	108	46	−bce1	−bce1	PROPN
ejpam-3949	108	47	/	/	SYM
ejpam-3949	108	48	a	a	DET
ejpam-3949	108	49	a	a	NOUN
ejpam-3949	108	50	)	)	PUNCT
ejpam-3949	108	51	+	+	CCONJ
ejpam-3949	108	52	1	1	NUM
ejpam-3949	108	53	]	]	PUNCT
ejpam-3949	108	54	6=	6=	ADP
ejpam-3949	108	55	0	0	NUM
ejpam-3949	108	56	,	,	PUNCT
ejpam-3949	108	57	where	where	SCONJ
ejpam-3949	108	58	w	w	X
ejpam-3949	108	59	(	(	PUNCT
ejpam-3949	108	60	−bce1	−bce1	PROPN
ejpam-3949	108	61	/	/	SYM
ejpam-3949	108	62	a	a	DET
ejpam-3949	108	63	a	a	NOUN
ejpam-3949	108	64	)	)	PUNCT
ejpam-3949	108	65	6=	6=	ADP
ejpam-3949	108	66	−1	−1	NOUN
ejpam-3949	108	67	(	(	PUNCT
ejpam-3949	108	68	a	a	PRON
ejpam-3949	108	69	6=	6=	NUM
ejpam-3949	108	70	0	0	NUM
ejpam-3949	108	71	)	)	PUNCT
ejpam-3949	108	72	,	,	PUNCT
ejpam-3949	108	73	and	and	CCONJ
ejpam-3949	108	74	for	for	ADP
ejpam-3949	108	75	finite	finite	NOUN
ejpam-3949	108	76	b	b	PROPN
ejpam-3949	108	77	,	,	PUNCT
ejpam-3949	108	78	f	f	PROPN
ejpam-3949	108	79	(	(	PUNCT
ejpam-3949	108	80	1	1	NUM
ejpam-3949	108	81	b	b	X
ejpam-3949	108	82	e	e	ADP
ejpam-3949	108	83	w	w	X
ejpam-3949	108	84	(	(	PUNCT
ejpam-3949	108	85	−bce1	−bce1	PROPN
ejpam-3949	108	86	/	/	SYM
ejpam-3949	108	87	a	a	DET
ejpam-3949	108	88	a	a	NOUN
ejpam-3949	108	89	)	)	PUNCT
ejpam-3949	108	90	−	−	PROPN
ejpam-3949	108	91	1	1	NUM
ejpam-3949	108	92	a	a	NOUN
ejpam-3949	108	93	)	)	PUNCT
ejpam-3949	108	94	=	=	SYM
ejpam-3949	108	95	0	0	X
ejpam-3949	108	96	.	.	PUNCT
ejpam-3949	109	1	c.	c.	PROPN
ejpam-3949	109	2	corcino	corcino	PROPN
ejpam-3949	109	3	,	,	PUNCT
ejpam-3949	109	4	r.	r.	PROPN
ejpam-3949	109	5	corcino	corcino	PROPN
ejpam-3949	109	6	/	/	SYM
ejpam-3949	109	7	eur	eur	PROPN
ejpam-3949	109	8	.	.	PUNCT
ejpam-3949	110	1	j.	j.	PROPN
ejpam-3949	110	2	pure	pure	PROPN
ejpam-3949	110	3	appl	appl	PROPN
ejpam-3949	110	4	.	.	PROPN
ejpam-3949	110	5	math	math	PROPN
ejpam-3949	110	6	,	,	PUNCT
ejpam-3949	110	7	14	14	NUM
ejpam-3949	110	8	(	(	PUNCT
ejpam-3949	110	9	2	2	NUM
ejpam-3949	110	10	)	)	PUNCT
ejpam-3949	110	11	(	(	PUNCT
ejpam-3949	110	12	2021	2021	NUM
ejpam-3949	110	13	)	)	PUNCT
ejpam-3949	110	14	,	,	PUNCT
ejpam-3949	110	15	506	506	NUM
ejpam-3949	110	16	-	-	SYM
ejpam-3949	110	17	520	520	NUM
ejpam-3949	110	18	510	510	NUM
ejpam-3949	110	19	by	by	ADP
ejpam-3949	110	20	the	the	DET
ejpam-3949	110	21	lagrange	lagrange	NOUN
ejpam-3949	110	22	inversion	inversion	NOUN
ejpam-3949	110	23	theorem	theorem	NOUN
ejpam-3949	110	24	,	,	PUNCT
ejpam-3949	110	25	taking	take	VERB
ejpam-3949	110	26	a	a	DET
ejpam-3949	110	27	=	=	SYM
ejpam-3949	110	28	1	1	NUM
ejpam-3949	110	29	b	b	PROPN
ejpam-3949	110	30	e	e	ADP
ejpam-3949	110	31	w	w	X
ejpam-3949	110	32	(	(	PUNCT
ejpam-3949	110	33	−bce1	−bce1	PROPN
ejpam-3949	110	34	/	/	SYM
ejpam-3949	110	35	a	a	DET
ejpam-3949	110	36	a	a	NOUN
ejpam-3949	110	37	)	)	PUNCT
ejpam-3949	110	38	−	−	PROPN
ejpam-3949	110	39	1	1	NUM
ejpam-3949	110	40	a	a	PRON
ejpam-3949	110	41	,	,	PUNCT
ejpam-3949	110	42	we	we	PRON
ejpam-3949	110	43	have	have	VERB
ejpam-3949	110	44	wlt	wlt	NOUN
ejpam-3949	110	45	(	(	PUNCT
ejpam-3949	110	46	x	x	NOUN
ejpam-3949	110	47	)	)	PUNCT
ejpam-3949	110	48	=	=	SYM
ejpam-3949	110	49	1	1	NUM
ejpam-3949	110	50	b	b	X
ejpam-3949	110	51	e	e	X
ejpam-3949	110	52	w	w	X
ejpam-3949	110	53	(	(	PUNCT
ejpam-3949	110	54	−bce1	−bce1	PROPN
ejpam-3949	110	55	/	/	SYM
ejpam-3949	110	56	a	a	DET
ejpam-3949	110	57	a	a	NOUN
ejpam-3949	110	58	)	)	PUNCT
ejpam-3949	110	59	−	−	PROPN
ejpam-3949	110	60	1	1	NUM
ejpam-3949	110	61	a	a	DET
ejpam-3949	110	62	+	+	NOUN
ejpam-3949	110	63	∞∑	∞∑	PROPN
ejpam-3949	110	64	n=1	n=1	PROPN
ejpam-3949	110	65	gn	gn	PROPN
ejpam-3949	110	66	xn	xn	PROPN
ejpam-3949	110	67	n	n	PROPN
ejpam-3949	110	68	!	!	NUM
ejpam-3949	110	69	,	,	PUNCT
ejpam-3949	110	70	(	(	PUNCT
ejpam-3949	110	71	17	17	NUM
ejpam-3949	110	72	)	)	PUNCT
ejpam-3949	110	73	where	where	SCONJ
ejpam-3949	110	74	gn	gn	PROPN
ejpam-3949	110	75	=	=	PROPN
ejpam-3949	110	76	lim	lim	PROPN
ejpam-3949	110	77	y→a	y→a	PROPN
ejpam-3949	110	78	dn−1	dn−1	PROPN
ejpam-3949	110	79	dyn−1	dyn−1	PROPN
ejpam-3949	111	1	y	y	PROPN
ejpam-3949	111	2	−	−	PROPN
ejpam-3949	111	3	1	1	NUM
ejpam-3949	111	4	b	b	PROPN
ejpam-3949	111	5	e	e	ADP
ejpam-3949	111	6	w	w	X
ejpam-3949	111	7	(	(	PUNCT
ejpam-3949	111	8	−bce1	−bce1	PROPN
ejpam-3949	111	9	/	/	SYM
ejpam-3949	111	10	a	a	DET
ejpam-3949	111	11	a	a	NOUN
ejpam-3949	111	12	)	)	PUNCT
ejpam-3949	111	13	−	−	PROPN
ejpam-3949	111	14	1	1	NUM
ejpam-3949	111	15	a	a	DET
ejpam-3949	111	16	f(y	f(y	NOUN
ejpam-3949	111	17	)	)	PUNCT
ejpam-3949	111	18			NOUN
ejpam-3949	111	19	n	n	NOUN
ejpam-3949	111	20	.	.	PUNCT
ejpam-3949	112	1	(	(	PUNCT
ejpam-3949	112	2	18	18	NUM
ejpam-3949	112	3	)	)	PUNCT
ejpam-3949	112	4	that	that	PRON
ejpam-3949	112	5	is	be	AUX
ejpam-3949	112	6	,	,	PUNCT
ejpam-3949	112	7	when	when	SCONJ
ejpam-3949	112	8	n	n	X
ejpam-3949	112	9	=	=	SYM
ejpam-3949	112	10	1	1	NUM
ejpam-3949	112	11	,	,	PUNCT
ejpam-3949	112	12	g1	g1	NOUN
ejpam-3949	112	13	=	=	SYM
ejpam-3949	113	1	e	e	PROPN
ejpam-3949	113	2	−1	−1	NOUN
ejpam-3949	113	3	b	b	PROPN
ejpam-3949	113	4	e	e	X
ejpam-3949	113	5	w	w	PROPN
ejpam-3949	113	6	(	(	PUNCT
ejpam-3949	113	7	−bce1	−bce1	PROPN
ejpam-3949	113	8	/	/	SYM
ejpam-3949	113	9	a	a	DET
ejpam-3949	113	10	a	a	NOUN
ejpam-3949	113	11	)	)	PUNCT
ejpam-3949	113	12	−	−	PROPN
ejpam-3949	113	13	1	1	NUM
ejpam-3949	113	14	a	a	DET
ejpam-3949	113	15	a	a	DET
ejpam-3949	113	16	[	[	PUNCT
ejpam-3949	113	17	w	w	NOUN
ejpam-3949	113	18	(	(	PUNCT
ejpam-3949	113	19	−bce1	−bce1	PROPN
ejpam-3949	113	20	/	/	SYM
ejpam-3949	113	21	a	a	DET
ejpam-3949	113	22	a	a	NOUN
ejpam-3949	113	23	)	)	PUNCT
ejpam-3949	113	24	+	+	CCONJ
ejpam-3949	113	25	1	1	NUM
ejpam-3949	113	26	]	]	PUNCT
ejpam-3949	113	27	.	.	PUNCT
ejpam-3949	114	1	substituting	substitute	VERB
ejpam-3949	114	2	to	to	ADP
ejpam-3949	114	3	(	(	PUNCT
ejpam-3949	114	4	17	17	NUM
ejpam-3949	114	5	)	)	PUNCT
ejpam-3949	114	6	will	will	AUX
ejpam-3949	114	7	yield	yield	VERB
ejpam-3949	114	8	(	(	PUNCT
ejpam-3949	114	9	16	16	NUM
ejpam-3949	114	10	)	)	PUNCT
ejpam-3949	114	11	.	.	PUNCT
ejpam-3949	115	1	an	an	DET
ejpam-3949	115	2	approximation	approximation	NOUN
ejpam-3949	115	3	formula	formula	NOUN
ejpam-3949	115	4	for	for	ADP
ejpam-3949	115	5	wlt	wlt	PROPN
ejpam-3949	115	6	(	(	PUNCT
ejpam-3949	115	7	x	x	X
ejpam-3949	115	8	)	)	PUNCT
ejpam-3949	115	9	expressed	express	VERB
ejpam-3949	115	10	in	in	ADP
ejpam-3949	115	11	terms	term	NOUN
ejpam-3949	115	12	of	of	ADP
ejpam-3949	115	13	the	the	DET
ejpam-3949	115	14	classical	classical	ADJ
ejpam-3949	115	15	lambert	lambert	PROPN
ejpam-3949	115	16	w	w	PROPN
ejpam-3949	115	17	function	function	NOUN
ejpam-3949	115	18	is	be	AUX
ejpam-3949	115	19	proved	prove	VERB
ejpam-3949	115	20	in	in	ADP
ejpam-3949	115	21	the	the	DET
ejpam-3949	115	22	next	next	ADJ
ejpam-3949	115	23	theorem	theorem	PROPN
ejpam-3949	115	24	.	.	PUNCT
ejpam-3949	115	25	theorem	theorem	VERB
ejpam-3949	115	26	2.5	2.5	NUM
ejpam-3949	115	27	.	.	PUNCT
ejpam-3949	116	1	for	for	ADP
ejpam-3949	116	2	large	large	ADJ
ejpam-3949	116	3	x	x	NOUN
ejpam-3949	116	4	,	,	PUNCT
ejpam-3949	116	5	wlt	wlt	PROPN
ejpam-3949	116	6	(	(	PUNCT
ejpam-3949	116	7	x	x	NOUN
ejpam-3949	116	8	)	)	PUNCT
ejpam-3949	116	9	∼w	∼w	NOUN
ejpam-3949	116	10	(	(	PUNCT
ejpam-3949	116	11	xe	xe	PROPN
ejpam-3949	116	12	c	c	PROPN
ejpam-3949	116	13	a+1	a+1	PROPN
ejpam-3949	116	14	a+	a+	PUNCT
ejpam-3949	116	15	1	1	NUM
ejpam-3949	116	16	)	)	PUNCT
ejpam-3949	116	17	−	−	PROPN
ejpam-3949	116	18	ln	ln	INTJ
ejpam-3949	116	19	{	{	PUNCT
ejpam-3949	116	20	(	(	PUNCT
ejpam-3949	116	21	e	e	PROPN
ejpam-3949	116	22	c	c	NOUN
ejpam-3949	116	23	a+1	a+1	PROPN
ejpam-3949	116	24	a+	a+	PUNCT
ejpam-3949	116	25	1	1	NUM
ejpam-3949	116	26	)	)	PUNCT
ejpam-3949	116	27	[	[	PUNCT
ejpam-3949	116	28	a	a	PRON
ejpam-3949	116	29	ln	ln	NOUN
ejpam-3949	116	30	(	(	PUNCT
ejpam-3949	116	31	bw	bw	PROPN
ejpam-3949	116	32	(	(	PUNCT
ejpam-3949	116	33	xe	xe	PROPN
ejpam-3949	116	34	c	c	PROPN
ejpam-3949	116	35	a+1	a+1	PROPN
ejpam-3949	116	36	a+	a+	PUNCT
ejpam-3949	116	37	1	1	NUM
ejpam-3949	116	38	)	)	PUNCT
ejpam-3949	116	39	)	)	PUNCT
ejpam-3949	117	1	+	+	CCONJ
ejpam-3949	117	2	1	1	X
ejpam-3949	117	3	]	]	PUNCT
ejpam-3949	117	4	+	+	PUNCT
ejpam-3949	117	5	c	c	NOUN
ejpam-3949	117	6	x	x	X
ejpam-3949	117	7	e	e	X
ejpam-3949	117	8	w	w	PROPN
ejpam-3949	117	9	(	(	PUNCT
ejpam-3949	117	10	xe	xe	PROPN
ejpam-3949	117	11	c	c	PROPN
ejpam-3949	117	12	a+1	a+1	PROPN
ejpam-3949	117	13	a+1	a+1	PROPN
ejpam-3949	117	14	)	)	PUNCT
ejpam-3949	117	15	−	−	PROPN
ejpam-3949	117	16	c	c	NOUN
ejpam-3949	117	17	a+	a+	SYM
ejpam-3949	117	18	1	1	NUM
ejpam-3949	117	19	.	.	PUNCT
ejpam-3949	117	20	(	(	PUNCT
ejpam-3949	117	21	19	19	NUM
ejpam-3949	117	22	)	)	PUNCT
ejpam-3949	117	23	where	where	SCONJ
ejpam-3949	117	24	w	w	X
ejpam-3949	117	25	(	(	PUNCT
ejpam-3949	117	26	x	x	NOUN
ejpam-3949	117	27	)	)	PUNCT
ejpam-3949	117	28	denotes	denote	VERB
ejpam-3949	117	29	the	the	DET
ejpam-3949	117	30	lambert	lambert	PROPN
ejpam-3949	117	31	w	w	PROPN
ejpam-3949	117	32	function	function	NOUN
ejpam-3949	117	33	.	.	PUNCT
ejpam-3949	118	1	proof	proof	NOUN
ejpam-3949	118	2	.	.	PUNCT
ejpam-3949	119	1	from	from	ADP
ejpam-3949	119	2	(	(	PUNCT
ejpam-3949	119	3	7	7	NUM
ejpam-3949	119	4	)	)	PUNCT
ejpam-3949	119	5	,	,	PUNCT
ejpam-3949	119	6	y	y	PROPN
ejpam-3949	119	7	=	=	SYM
ejpam-3949	119	8	wlt	wlt	PROPN
ejpam-3949	119	9	(	(	PUNCT
ejpam-3949	119	10	x	x	NOUN
ejpam-3949	119	11	)	)	PUNCT
ejpam-3949	119	12	satisfies	satisfie	NOUN
ejpam-3949	119	13	x	x	PUNCT
ejpam-3949	119	14	=	=	PUNCT
ejpam-3949	120	1	[	[	X
ejpam-3949	120	2	ay(lnby	ay(lnby	PROPN
ejpam-3949	120	3	)	)	PUNCT
ejpam-3949	121	1	+	+	CCONJ
ejpam-3949	121	2	y	y	PROPN
ejpam-3949	121	3	+	+	CCONJ
ejpam-3949	121	4	c]ey	c]ey	PROPN
ejpam-3949	121	5	∼	∼	NOUN
ejpam-3949	121	6	[	[	X
ejpam-3949	121	7	(	(	PUNCT
ejpam-3949	121	8	a+	a+	PRON
ejpam-3949	121	9	1)y	1)y	NUM
ejpam-3949	121	10	+	+	CCONJ
ejpam-3949	121	11	c]ey	c]ey	PROPN
ejpam-3949	121	12	.	.	PUNCT
ejpam-3949	122	1	then	then	ADV
ejpam-3949	122	2	y	y	PROPN
ejpam-3949	122	3	=	=	SYM
ejpam-3949	122	4	w	w	PROPN
ejpam-3949	123	1	(	(	PUNCT
ejpam-3949	123	2	xe	xe	PROPN
ejpam-3949	123	3	c	c	PROPN
ejpam-3949	123	4	a+1	a+1	PROPN
ejpam-3949	123	5	a+	a+	PUNCT
ejpam-3949	123	6	1	1	NUM
ejpam-3949	123	7	)	)	PUNCT
ejpam-3949	123	8	−	−	PROPN
ejpam-3949	124	1	c	c	NOUN
ejpam-3949	124	2	a+	a+	SYM
ejpam-3949	124	3	1	1	NUM
ejpam-3949	124	4	+	+	NUM
ejpam-3949	124	5	u(x	u(x	NOUN
ejpam-3949	124	6	)	)	PUNCT
ejpam-3949	124	7	(	(	PUNCT
ejpam-3949	124	8	20	20	NUM
ejpam-3949	124	9	)	)	PUNCT
ejpam-3949	124	10	=	=	SYM
ejpam-3949	125	1	w	w	PROPN
ejpam-3949	125	2	(	(	PUNCT
ejpam-3949	125	3	xe	xe	PROPN
ejpam-3949	125	4	c	c	PROPN
ejpam-3949	125	5	a+1	a+1	PROPN
ejpam-3949	125	6	a+	a+	PUNCT
ejpam-3949	125	7	1	1	NUM
ejpam-3949	125	8	)	)	PUNCT
ejpam-3949	125	9	1−	1−	VERB
ejpam-3949	125	10	c	c	NOUN
ejpam-3949	125	11	a+1	a+1	PROPN
ejpam-3949	125	12	w	w	PROPN
ejpam-3949	125	13	(	(	PUNCT
ejpam-3949	125	14	xe	xe	PROPN
ejpam-3949	125	15	c	c	PROPN
ejpam-3949	125	16	a+1	a+1	PROPN
ejpam-3949	125	17	a+1	a+1	PROPN
ejpam-3949	125	18	)	)	PUNCT
ejpam-3949	125	19	+	+	CCONJ
ejpam-3949	125	20	u(x	u(x	NOUN
ejpam-3949	125	21	)	)	PUNCT
ejpam-3949	125	22	w	w	PROPN
ejpam-3949	126	1	(	(	PUNCT
ejpam-3949	126	2	xe	xe	PROPN
ejpam-3949	126	3	c	c	PROPN
ejpam-3949	126	4	a+1	a+1	PROPN
ejpam-3949	126	5	a+1	a+1	PROPN
ejpam-3949	126	6	)	)	PUNCT
ejpam-3949	126	7			PROPN
ejpam-3949	126	8	,	,	PUNCT
ejpam-3949	126	9	(	(	PUNCT
ejpam-3949	126	10	21	21	NUM
ejpam-3949	126	11	)	)	PUNCT
ejpam-3949	126	12	c.	c.	NOUN
ejpam-3949	126	13	corcino	corcino	PROPN
ejpam-3949	126	14	,	,	PUNCT
ejpam-3949	126	15	r.	r.	PROPN
ejpam-3949	126	16	corcino	corcino	PROPN
ejpam-3949	126	17	/	/	SYM
ejpam-3949	126	18	eur	eur	PROPN
ejpam-3949	126	19	.	.	PUNCT
ejpam-3949	127	1	j.	j.	PROPN
ejpam-3949	127	2	pure	pure	PROPN
ejpam-3949	127	3	appl	appl	PROPN
ejpam-3949	127	4	.	.	PROPN
ejpam-3949	127	5	math	math	PROPN
ejpam-3949	127	6	,	,	PUNCT
ejpam-3949	127	7	14	14	NUM
ejpam-3949	127	8	(	(	PUNCT
ejpam-3949	127	9	2	2	NUM
ejpam-3949	127	10	)	)	PUNCT
ejpam-3949	127	11	(	(	PUNCT
ejpam-3949	127	12	2021	2021	NUM
ejpam-3949	127	13	)	)	PUNCT
ejpam-3949	127	14	,	,	PUNCT
ejpam-3949	127	15	506	506	NUM
ejpam-3949	127	16	-	-	SYM
ejpam-3949	127	17	520	520	NUM
ejpam-3949	127	18	511	511	NUM
ejpam-3949	127	19	where	where	SCONJ
ejpam-3949	127	20	u(x	u(x	NOUN
ejpam-3949	127	21	)	)	PUNCT
ejpam-3949	127	22	is	be	AUX
ejpam-3949	127	23	a	a	DET
ejpam-3949	127	24	function	function	NOUN
ejpam-3949	127	25	to	to	PART
ejpam-3949	127	26	be	be	AUX
ejpam-3949	127	27	determined	determine	VERB
ejpam-3949	127	28	.	.	PUNCT
ejpam-3949	128	1	substituting	substitute	VERB
ejpam-3949	128	2	(	(	PUNCT
ejpam-3949	128	3	21	21	NUM
ejpam-3949	128	4	)	)	PUNCT
ejpam-3949	128	5	to	to	ADP
ejpam-3949	128	6	(	(	PUNCT
ejpam-3949	128	7	7	7	X
ejpam-3949	128	8	)	)	PUNCT
ejpam-3949	128	9	yieldsaw	yieldsaw	PROPN
ejpam-3949	128	10	(	(	PUNCT
ejpam-3949	128	11	xe	xe	PROPN
ejpam-3949	128	12	c	c	PROPN
ejpam-3949	128	13	a+1	a+1	PROPN
ejpam-3949	128	14	a+	a+	PUNCT
ejpam-3949	128	15	1	1	NUM
ejpam-3949	128	16	)	)	PUNCT
ejpam-3949	128	17	1−	1−	VERB
ejpam-3949	128	18	c	c	NOUN
ejpam-3949	128	19	a+1	a+1	PROPN
ejpam-3949	128	20	w	w	PROPN
ejpam-3949	128	21	(	(	PUNCT
ejpam-3949	128	22	xe	xe	PROPN
ejpam-3949	128	23	c	c	PROPN
ejpam-3949	128	24	a+1	a+1	PROPN
ejpam-3949	128	25	a+1	a+1	PROPN
ejpam-3949	128	26	)	)	PUNCT
ejpam-3949	128	27	+	+	CCONJ
ejpam-3949	128	28	u(x	u(x	NOUN
ejpam-3949	128	29	)	)	PUNCT
ejpam-3949	128	30	w	w	PROPN
ejpam-3949	129	1	(	(	PUNCT
ejpam-3949	129	2	xe	xe	PROPN
ejpam-3949	129	3	c	c	PROPN
ejpam-3949	129	4	a+1	a+1	PROPN
ejpam-3949	129	5	a+1	a+1	PROPN
ejpam-3949	129	6	)	)	PUNCT
ejpam-3949	129	7	×	×	NOUN
ejpam-3949	129	8	ln	ln	ADJ
ejpam-3949	129	9	bw	bw	NOUN
ejpam-3949	129	10	(	(	PUNCT
ejpam-3949	129	11	xe	xe	PROPN
ejpam-3949	129	12	c	c	PROPN
ejpam-3949	129	13	a+1	a+1	PROPN
ejpam-3949	129	14	a+	a+	PUNCT
ejpam-3949	129	15	1	1	NUM
ejpam-3949	129	16	)	)	PUNCT
ejpam-3949	129	17	1−	1−	VERB
ejpam-3949	129	18	c	c	NOUN
ejpam-3949	129	19	a+1	a+1	PROPN
ejpam-3949	129	20	w	w	PROPN
ejpam-3949	129	21	(	(	PUNCT
ejpam-3949	129	22	xe	xe	PROPN
ejpam-3949	129	23	c	c	PROPN
ejpam-3949	129	24	a+1	a+1	PROPN
ejpam-3949	129	25	a+1	a+1	PROPN
ejpam-3949	129	26	)	)	PUNCT
ejpam-3949	129	27	+	+	CCONJ
ejpam-3949	129	28	u(x	u(x	NOUN
ejpam-3949	129	29	)	)	PUNCT
ejpam-3949	129	30	w	w	PROPN
ejpam-3949	129	31	(	(	PUNCT
ejpam-3949	129	32	xe	xe	PROPN
ejpam-3949	129	33	c	c	PROPN
ejpam-3949	129	34	a+1	a+1	PROPN
ejpam-3949	129	35	a+1	a+1	PROPN
ejpam-3949	129	36	)	)	PUNCT
ejpam-3949	129	37			PROPN
ejpam-3949	129	38	+	+	NOUN
ejpam-3949	129	39	w	w	PROPN
ejpam-3949	129	40	(	(	PUNCT
ejpam-3949	129	41	xe	xe	PROPN
ejpam-3949	129	42	c	c	PROPN
ejpam-3949	129	43	a+1	a+1	PROPN
ejpam-3949	129	44	a+	a+	PUNCT
ejpam-3949	129	45	1	1	NUM
ejpam-3949	129	46	)	)	PUNCT
ejpam-3949	129	47	1−	1−	VERB
ejpam-3949	129	48	c	c	NOUN
ejpam-3949	129	49	a+1	a+1	PROPN
ejpam-3949	129	50	w	w	PROPN
ejpam-3949	129	51	(	(	PUNCT
ejpam-3949	129	52	xe	xe	PROPN
ejpam-3949	129	53	c	c	PROPN
ejpam-3949	129	54	a+1	a+1	PROPN
ejpam-3949	129	55	a+1	a+1	PROPN
ejpam-3949	129	56	)	)	PUNCT
ejpam-3949	129	57	+	+	CCONJ
ejpam-3949	129	58	u(x	u(x	NOUN
ejpam-3949	129	59	)	)	PUNCT
ejpam-3949	129	60	w	w	PROPN
ejpam-3949	130	1	(	(	PUNCT
ejpam-3949	130	2	xe	xe	PROPN
ejpam-3949	130	3	c	c	PROPN
ejpam-3949	130	4	a+1	a+1	PROPN
ejpam-3949	130	5	a+1	a+1	PROPN
ejpam-3949	130	6	)	)	PUNCT
ejpam-3949	131	1	+	+	PROPN
ejpam-3949	131	2	c	c	NOUN
ejpam-3949	131	3	×	×	NUM
ejpam-3949	131	4	e	e	X
ejpam-3949	131	5	w	w	PROPN
ejpam-3949	131	6	(	(	PUNCT
ejpam-3949	131	7	xe	xe	PROPN
ejpam-3949	131	8	c	c	PROPN
ejpam-3949	131	9	a+1	a+1	PROPN
ejpam-3949	131	10	a+1	a+1	PROPN
ejpam-3949	131	11	)	)	PUNCT
ejpam-3949	131	12	·	·	PUNCT
ejpam-3949	131	13	eu(x	eu(x	ADV
ejpam-3949	131	14	)	)	PUNCT
ejpam-3949	132	1	=	=	PUNCT
ejpam-3949	132	2	x.	x.	NOUN
ejpam-3949	132	3	(	(	PUNCT
ejpam-3949	132	4	22	22	NUM
ejpam-3949	132	5	)	)	PUNCT
ejpam-3949	132	6	with	with	ADP
ejpam-3949	132	7	c	c	PROPN
ejpam-3949	132	8	a+1	a+1	PROPN
ejpam-3949	132	9	,	,	PUNCT
ejpam-3949	132	10	u(x	u(x	PROPN
ejpam-3949	132	11	)	)	PUNCT
ejpam-3949	133	1	<	<	X
ejpam-3949	133	2	<	<	X
ejpam-3949	133	3	w	w	X
ejpam-3949	133	4	(	(	PUNCT
ejpam-3949	133	5	xe	xe	PROPN
ejpam-3949	133	6	c	c	PROPN
ejpam-3949	133	7	a+1	a+1	PROPN
ejpam-3949	133	8	a+1	a+1	PROPN
ejpam-3949	133	9	)	)	PUNCT
ejpam-3949	133	10	,	,	PUNCT
ejpam-3949	133	11	(	(	PUNCT
ejpam-3949	133	12	22	22	NUM
ejpam-3949	133	13	)	)	PUNCT
ejpam-3949	133	14	becomes	become	VERB
ejpam-3949	133	15	aw	aw	PROPN
ejpam-3949	133	16	(	(	PUNCT
ejpam-3949	133	17	xe	xe	PROPN
ejpam-3949	133	18	c	c	PROPN
ejpam-3949	133	19	a+1	a+1	PROPN
ejpam-3949	133	20	a+	a+	PUNCT
ejpam-3949	133	21	1	1	NUM
ejpam-3949	133	22	)	)	PUNCT
ejpam-3949	133	23	e	e	X
ejpam-3949	133	24	w	w	PROPN
ejpam-3949	134	1	(	(	PUNCT
ejpam-3949	134	2	xe	xe	PROPN
ejpam-3949	134	3	c	c	PROPN
ejpam-3949	134	4	a+1	a+1	PROPN
ejpam-3949	134	5	a+1	a+1	PROPN
ejpam-3949	134	6	)	)	PUNCT
ejpam-3949	134	7	ln	ln	NOUN
ejpam-3949	134	8	(	(	PUNCT
ejpam-3949	134	9	bw	bw	PROPN
ejpam-3949	134	10	(	(	PUNCT
ejpam-3949	134	11	xe	xe	PROPN
ejpam-3949	134	12	c	c	PROPN
ejpam-3949	134	13	a+1	a+1	PROPN
ejpam-3949	134	14	a+	a+	PUNCT
ejpam-3949	134	15	1	1	NUM
ejpam-3949	134	16	)	)	PUNCT
ejpam-3949	134	17	)	)	PUNCT
ejpam-3949	135	1	+	+	CCONJ
ejpam-3949	135	2	[	[	PUNCT
ejpam-3949	135	3	w	w	X
ejpam-3949	135	4	(	(	PUNCT
ejpam-3949	135	5	xe	xe	PROPN
ejpam-3949	135	6	c	c	PROPN
ejpam-3949	135	7	a+1	a+1	PROPN
ejpam-3949	135	8	a+	a+	PUNCT
ejpam-3949	135	9	1	1	NUM
ejpam-3949	135	10	)	)	PUNCT
ejpam-3949	135	11	+	+	PUNCT
ejpam-3949	135	12	c	c	NOUN
ejpam-3949	135	13	]	]	X
ejpam-3949	135	14	e	e	X
ejpam-3949	135	15	w	w	PROPN
ejpam-3949	135	16	(	(	PUNCT
ejpam-3949	135	17	xe	xe	PROPN
ejpam-3949	135	18	c	c	PROPN
ejpam-3949	135	19	a+1	a+1	PROPN
ejpam-3949	135	20	a+1	a+1	PROPN
ejpam-3949	135	21	)	)	PUNCT
ejpam-3949	135	22			X
ejpam-3949	135	23	eu(x	eu(x	ADV
ejpam-3949	135	24	)	)	PUNCT
ejpam-3949	135	25	=	=	PUNCT
ejpam-3949	135	26	x.	x.	NOUN
ejpam-3949	136	1			PROPN
ejpam-3949	136	2	(	(	PUNCT
ejpam-3949	136	3	xe	xe	PROPN
ejpam-3949	136	4	c	c	PROPN
ejpam-3949	136	5	a+1	a+1	PROPN
ejpam-3949	136	6	a+	a+	PUNCT
ejpam-3949	136	7	1	1	NUM
ejpam-3949	136	8	)	)	PUNCT
ejpam-3949	136	9	a	a	VERB
ejpam-3949	136	10	ln	ln	ADJ
ejpam-3949	136	11	(	(	PUNCT
ejpam-3949	136	12	bw	bw	PROPN
ejpam-3949	136	13	(	(	PUNCT
ejpam-3949	136	14	xe	xe	PROPN
ejpam-3949	136	15	c	c	PROPN
ejpam-3949	136	16	a+1	a+1	PROPN
ejpam-3949	136	17	a+	a+	PUNCT
ejpam-3949	136	18	1	1	NUM
ejpam-3949	136	19	)	)	PUNCT
ejpam-3949	137	1	+	+	CCONJ
ejpam-3949	137	2	1	1	X
ejpam-3949	137	3	]	]	PUNCT
ejpam-3949	137	4	+	+	CCONJ
ejpam-3949	137	5	ce	ce	PROPN
ejpam-3949	137	6	w	w	PROPN
ejpam-3949	137	7	(	(	PUNCT
ejpam-3949	137	8	xe	xe	PROPN
ejpam-3949	137	9	c	c	PROPN
ejpam-3949	137	10	a+1	a+1	PROPN
ejpam-3949	137	11	a+1	a+1	PROPN
ejpam-3949	137	12	)	)	PUNCT
ejpam-3949	137	13			NUM
ejpam-3949	137	14			NOUN
ejpam-3949	137	15	eu(x	eu(x	ADV
ejpam-3949	137	16	)	)	PUNCT
ejpam-3949	137	17	=	=	PUNCT
ejpam-3949	137	18	x.	x.	NOUN
ejpam-3949	137	19			PROPN
ejpam-3949	137	20	(	(	PUNCT
ejpam-3949	137	21	e	e	PROPN
ejpam-3949	137	22	c	c	PROPN
ejpam-3949	137	23	a+1	a+1	PROPN
ejpam-3949	137	24	a+	a+	PUNCT
ejpam-3949	137	25	1	1	NUM
ejpam-3949	137	26	)	)	PUNCT
ejpam-3949	137	27	a	a	VERB
ejpam-3949	137	28	ln	ln	ADJ
ejpam-3949	137	29	(	(	PUNCT
ejpam-3949	137	30	bw	bw	PROPN
ejpam-3949	137	31	(	(	PUNCT
ejpam-3949	137	32	xe	xe	PROPN
ejpam-3949	137	33	c	c	PROPN
ejpam-3949	137	34	a+1	a+1	PROPN
ejpam-3949	137	35	a+	a+	PUNCT
ejpam-3949	137	36	1	1	NUM
ejpam-3949	137	37	)	)	PUNCT
ejpam-3949	138	1	+	+	CCONJ
ejpam-3949	138	2	1	1	NUM
ejpam-3949	138	3	]	]	PUNCT
ejpam-3949	138	4	+	+	PUNCT
ejpam-3949	138	5	c	c	NOUN
ejpam-3949	138	6	x	x	X
ejpam-3949	138	7	e	e	X
ejpam-3949	138	8	w	w	PROPN
ejpam-3949	138	9	(	(	PUNCT
ejpam-3949	138	10	xe	xe	PROPN
ejpam-3949	138	11	c	c	PROPN
ejpam-3949	138	12	a+1	a+1	PROPN
ejpam-3949	138	13	a+1	a+1	PROPN
ejpam-3949	138	14	)	)	PUNCT
ejpam-3949	138	15			NUM
ejpam-3949	138	16			NOUN
ejpam-3949	138	17	eu(x	eu(x	ADV
ejpam-3949	138	18	)	)	PUNCT
ejpam-3949	138	19	=	=	SYM
ejpam-3949	139	1	1	1	X
ejpam-3949	139	2	.	.	PUNCT
ejpam-3949	139	3	thus	thus	ADV
ejpam-3949	139	4	,	,	PUNCT
ejpam-3949	139	5	u(x	u(x	X
ejpam-3949	139	6	)	)	PUNCT
ejpam-3949	139	7	=	=	SYM
ejpam-3949	140	1	−	−	PROPN
ejpam-3949	140	2	ln	ln	ADJ
ejpam-3949	140	3			PROPN
ejpam-3949	140	4	(	(	PUNCT
ejpam-3949	140	5	e	e	NOUN
ejpam-3949	140	6	c	c	PROPN
ejpam-3949	140	7	a+1	a+1	PROPN
ejpam-3949	140	8	a+	a+	PUNCT
ejpam-3949	140	9	1	1	NUM
ejpam-3949	140	10	)	)	PUNCT
ejpam-3949	140	11	[	[	PUNCT
ejpam-3949	140	12	a	a	DET
ejpam-3949	140	13	ln	ln	NOUN
ejpam-3949	140	14	(	(	PUNCT
ejpam-3949	140	15	bw	bw	PROPN
ejpam-3949	140	16	(	(	PUNCT
ejpam-3949	140	17	xe	xe	PROPN
ejpam-3949	140	18	c	c	PROPN
ejpam-3949	140	19	a+1	a+1	PROPN
ejpam-3949	140	20	a+	a+	PUNCT
ejpam-3949	140	21	1	1	NUM
ejpam-3949	140	22	)	)	PUNCT
ejpam-3949	140	23	)	)	PUNCT
ejpam-3949	141	1	+	+	CCONJ
ejpam-3949	141	2	1	1	X
ejpam-3949	141	3	]	]	PUNCT
ejpam-3949	141	4	+	+	PUNCT
ejpam-3949	141	5	c	c	NOUN
ejpam-3949	141	6	x	x	X
ejpam-3949	141	7	e	e	X
ejpam-3949	141	8	w	w	PROPN
ejpam-3949	141	9	(	(	PUNCT
ejpam-3949	141	10	xe	xe	PROPN
ejpam-3949	141	11	c	c	PROPN
ejpam-3949	141	12	a+1	a+1	PROPN
ejpam-3949	141	13	a+1	a+1	PROPN
ejpam-3949	141	14	)	)	PUNCT
ejpam-3949	141	15			PROPN
ejpam-3949	141	16	.	.	PUNCT
ejpam-3949	142	1	c.	c.	PROPN
ejpam-3949	142	2	corcino	corcino	PROPN
ejpam-3949	142	3	,	,	PUNCT
ejpam-3949	142	4	r.	r.	PROPN
ejpam-3949	142	5	corcino	corcino	PROPN
ejpam-3949	142	6	/	/	SYM
ejpam-3949	142	7	eur	eur	PROPN
ejpam-3949	142	8	.	.	PUNCT
ejpam-3949	143	1	j.	j.	PROPN
ejpam-3949	143	2	pure	pure	PROPN
ejpam-3949	143	3	appl	appl	PROPN
ejpam-3949	143	4	.	.	PROPN
ejpam-3949	143	5	math	math	PROPN
ejpam-3949	143	6	,	,	PUNCT
ejpam-3949	143	7	14	14	NUM
ejpam-3949	143	8	(	(	PUNCT
ejpam-3949	143	9	2	2	NUM
ejpam-3949	143	10	)	)	PUNCT
ejpam-3949	143	11	(	(	PUNCT
ejpam-3949	143	12	2021	2021	NUM
ejpam-3949	143	13	)	)	PUNCT
ejpam-3949	143	14	,	,	PUNCT
ejpam-3949	143	15	506	506	NUM
ejpam-3949	143	16	-	-	SYM
ejpam-3949	143	17	520	520	NUM
ejpam-3949	143	18	512	512	NUM
ejpam-3949	143	19	substituting	substitute	VERB
ejpam-3949	143	20	this	this	PRON
ejpam-3949	143	21	to	to	ADP
ejpam-3949	143	22	(	(	PUNCT
ejpam-3949	143	23	20	20	NUM
ejpam-3949	143	24	)	)	PUNCT
ejpam-3949	143	25	yields	yield	NOUN
ejpam-3949	143	26	(	(	PUNCT
ejpam-3949	143	27	19	19	NUM
ejpam-3949	143	28	)	)	PUNCT
ejpam-3949	143	29	.	.	PUNCT
ejpam-3949	144	1	the	the	DET
ejpam-3949	144	2	table	table	NOUN
ejpam-3949	144	3	below	below	ADV
ejpam-3949	144	4	illustrates	illustrate	VERB
ejpam-3949	144	5	the	the	DET
ejpam-3949	144	6	accuracy	accuracy	NOUN
ejpam-3949	144	7	of	of	ADP
ejpam-3949	144	8	the	the	DET
ejpam-3949	144	9	approximation	approximation	NOUN
ejpam-3949	144	10	formula	formula	NOUN
ejpam-3949	144	11	in	in	ADP
ejpam-3949	144	12	(	(	PUNCT
ejpam-3949	144	13	19	19	NUM
ejpam-3949	144	14	)	)	PUNCT
ejpam-3949	144	15	with	with	ADP
ejpam-3949	144	16	a	a	PRON
ejpam-3949	144	17	=	=	SYM
ejpam-3949	144	18	b	b	NOUN
ejpam-3949	144	19	=	=	SYM
ejpam-3949	144	20	c	c	NOUN
ejpam-3949	144	21	=	=	SYM
ejpam-3949	144	22	1	1	X
ejpam-3949	144	23	.	.	PUNCT
ejpam-3949	145	1	x	x	X
ejpam-3949	145	2	wlt	wlt	PROPN
ejpam-3949	145	3	(	(	PUNCT
ejpam-3949	145	4	x	x	NOUN
ejpam-3949	145	5	)	)	PUNCT
ejpam-3949	145	6	approximate	approximate	ADJ
ejpam-3949	145	7	relative	relative	ADJ
ejpam-3949	145	8	error	error	NOUN
ejpam-3949	145	9	value	value	NOUN
ejpam-3949	145	10	3575.7472	3575.7472	NUM
ejpam-3949	145	11	4	4	NUM
ejpam-3949	145	12	3.3121	3.3121	NUM
ejpam-3949	145	13	1.71987×	1.71987×	NUM
ejpam-3949	145	14	10−1	10−1	NUM
ejpam-3949	145	15	2084.7878	2084.7878	NUM
ejpam-3949	145	16	5	5	NUM
ejpam-3949	145	17	4.3301	4.3301	NUM
ejpam-3949	145	18	1.33982×	1.33982×	NUM
ejpam-3949	145	19	10−1	10−1	PROPN
ejpam-3949	145	20	7161.0857	7161.0857	PROPN
ejpam-3949	145	21	6	6	NUM
ejpam-3949	145	22	5.3453	5.3453	NUM
ejpam-3949	145	23	1.09116×	1.09116×	NUM
ejpam-3949	145	24	10−1	10−1	NUM
ejpam-3949	146	1	23710.7124	23710.7124	NUM
ejpam-3949	146	2	7	7	NUM
ejpam-3949	146	3	6.3581	6.3581	NUM
ejpam-3949	146	4	9.16961×	9.16961×	NUM
ejpam-3949	146	5	10−2	10−2	NUM
ejpam-3949	147	1	76418.4449	76418.4449	NOUN
ejpam-3949	147	2	8	8	NUM
ejpam-3949	147	3	7.3690	7.3690	NUM
ejpam-3949	147	4	7.88738×	7.88738×	NUM
ejpam-3949	147	5	10−2	10−2	NUM
ejpam-3949	147	6	241269.4957	241269.4957	NUM
ejpam-3949	147	7	9	9	NUM
ejpam-3949	147	8	8.3783	8.3783	NUM
ejpam-3949	147	9	6.90741×	6.90741×	NOUN
ejpam-3949	147	10	10−2	10−2	NUM
ejpam-3949	147	11	749469.2416	749469.2416	NUM
ejpam-3949	147	12	10	10	NUM
ejpam-3949	147	13	9.3864	9.3864	NUM
ejpam-3949	147	14	6.13602×	6.13602×	NUM
ejpam-3949	147	15	10−2	10−2	NUM
ejpam-3949	147	16	the	the	DET
ejpam-3949	147	17	next	next	ADJ
ejpam-3949	147	18	theorem	theorem	NOUN
ejpam-3949	147	19	describes	describe	VERB
ejpam-3949	147	20	the	the	DET
ejpam-3949	147	21	branches	branch	NOUN
ejpam-3949	147	22	of	of	ADP
ejpam-3949	147	23	the	the	DET
ejpam-3949	147	24	translated	translate	VERB
ejpam-3949	147	25	logarithmic	logarithmic	ADJ
ejpam-3949	147	26	lambert	lambert	PROPN
ejpam-3949	147	27	function	function	PROPN
ejpam-3949	147	28	.	.	PUNCT
ejpam-3949	148	1	theorem	theorem	VERB
ejpam-3949	148	2	2.6	2.6	NUM
ejpam-3949	148	3	.	.	PUNCT
ejpam-3949	149	1	let	let	VERB
ejpam-3949	149	2	x	x	SYM
ejpam-3949	149	3	=	=	SYM
ejpam-3949	149	4	f(y	f(y	NOUN
ejpam-3949	149	5	)	)	PUNCT
ejpam-3949	149	6	=	=	PUNCT
ejpam-3949	150	1	[	[	X
ejpam-3949	150	2	ay	ay	X
ejpam-3949	150	3	ln(by)+y+c]ey	ln(by)+y+c]ey	NOUN
ejpam-3949	150	4	.	.	PUNCT
ejpam-3949	151	1	then	then	ADV
ejpam-3949	151	2	the	the	DET
ejpam-3949	151	3	branches	branch	NOUN
ejpam-3949	151	4	of	of	ADP
ejpam-3949	151	5	the	the	DET
ejpam-3949	151	6	translated	translate	VERB
ejpam-3949	151	7	logarithmic	logarithmic	PROPN
ejpam-3949	151	8	lambert	lambert	PROPN
ejpam-3949	151	9	function	function	PROPN
ejpam-3949	151	10	y	y	PROPN
ejpam-3949	151	11	=	=	SYM
ejpam-3949	151	12	wlt	wlt	PROPN
ejpam-3949	151	13	(	(	PUNCT
ejpam-3949	151	14	x	x	X
ejpam-3949	151	15	)	)	PUNCT
ejpam-3949	151	16	can	can	AUX
ejpam-3949	151	17	be	be	AUX
ejpam-3949	151	18	described	describe	VERB
ejpam-3949	151	19	as	as	SCONJ
ejpam-3949	151	20	follows	follow	VERB
ejpam-3949	151	21	:	:	PUNCT
ejpam-3949	151	22	(	(	PUNCT
ejpam-3949	151	23	i	i	NOUN
ejpam-3949	151	24	)	)	PUNCT
ejpam-3949	151	25	when	when	SCONJ
ejpam-3949	151	26	b	b	X
ejpam-3949	151	27	>	>	X
ejpam-3949	151	28	0	0	PROPN
ejpam-3949	151	29	,	,	PUNCT
ejpam-3949	151	30	a	a	DET
ejpam-3949	151	31	>	>	X
ejpam-3949	151	32	0	0	NUM
ejpam-3949	151	33	,	,	PUNCT
ejpam-3949	151	34	the	the	DET
ejpam-3949	151	35	branches	branch	NOUN
ejpam-3949	151	36	are	be	AUX
ejpam-3949	151	37	•	•	PROPN
ejpam-3949	151	38	w	w	PROPN
ejpam-3949	151	39	0	0	NUM
ejpam-3949	151	40	lt	lt	DET
ejpam-3949	151	41	(	(	PUNCT
ejpam-3949	151	42	x	x	NOUN
ejpam-3949	151	43	)	)	PUNCT
ejpam-3949	151	44	:	:	PUNCT
ejpam-3949	152	1	[	[	X
ejpam-3949	152	2	f(δ	f(δ	NOUN
ejpam-3949	152	3	)	)	PUNCT
ejpam-3949	152	4	,	,	PUNCT
ejpam-3949	152	5	f(0))→	f(0))→	PROPN
ejpam-3949	152	6	(	(	PUNCT
ejpam-3949	152	7	0	0	NUM
ejpam-3949	152	8	,	,	PUNCT
ejpam-3949	152	9	δ	δ	PROPN
ejpam-3949	152	10	]	]	PUNCT
ejpam-3949	152	11	is	be	AUX
ejpam-3949	152	12	strictly	strictly	ADV
ejpam-3949	152	13	decreasing	decrease	VERB
ejpam-3949	152	14	;	;	PUNCT
ejpam-3949	153	1	•	•	X
ejpam-3949	153	2	w	w	PROPN
ejpam-3949	153	3	1	1	NUM
ejpam-3949	153	4	lt	lt	PRON
ejpam-3949	153	5	(	(	PUNCT
ejpam-3949	153	6	x	x	NOUN
ejpam-3949	153	7	)	)	PUNCT
ejpam-3949	153	8	:	:	PUNCT
ejpam-3949	154	1	[	[	X
ejpam-3949	154	2	f(δ),+∞)→	f(δ),+∞)→	NOUN
ejpam-3949	154	3	[	[	X
ejpam-3949	154	4	δ,+∞	δ,+∞	NOUN
ejpam-3949	154	5	)	)	PUNCT
ejpam-3949	154	6	is	be	AUX
ejpam-3949	154	7	strictly	strictly	ADV
ejpam-3949	154	8	increasing	increase	VERB
ejpam-3949	154	9	,	,	PUNCT
ejpam-3949	154	10	(	(	PUNCT
ejpam-3949	154	11	ii	ii	NOUN
ejpam-3949	154	12	)	)	PUNCT
ejpam-3949	154	13	when	when	SCONJ
ejpam-3949	154	14	b	b	X
ejpam-3949	154	15	>	>	X
ejpam-3949	154	16	0	0	PROPN
ejpam-3949	154	17	,	,	PUNCT
ejpam-3949	154	18	a	a	DET
ejpam-3949	154	19	<	<	X
ejpam-3949	154	20	0	0	NUM
ejpam-3949	154	21	,	,	PUNCT
ejpam-3949	154	22	the	the	DET
ejpam-3949	154	23	branches	branch	NOUN
ejpam-3949	154	24	are	be	AUX
ejpam-3949	154	25	•	•	PROPN
ejpam-3949	154	26	w	w	PROPN
ejpam-3949	154	27	0	0	NUM
ejpam-3949	154	28	lt	lt	PRON
ejpam-3949	154	29	(	(	PUNCT
ejpam-3949	154	30	x	x	NOUN
ejpam-3949	154	31	)	)	PUNCT
ejpam-3949	154	32	:	:	PUNCT
ejpam-3949	155	1	[	[	X
ejpam-3949	155	2	f(0	f(0	NOUN
ejpam-3949	155	3	)	)	PUNCT
ejpam-3949	155	4	,	,	PUNCT
ejpam-3949	155	5	f(δ))→	f(δ))→	NOUN
ejpam-3949	155	6	(	(	PUNCT
ejpam-3949	155	7	0	0	NUM
ejpam-3949	155	8	,	,	PUNCT
ejpam-3949	155	9	δ	δ	PROPN
ejpam-3949	155	10	]	]	PUNCT
ejpam-3949	155	11	is	be	AUX
ejpam-3949	155	12	strictly	strictly	ADV
ejpam-3949	155	13	increasing	increase	VERB
ejpam-3949	155	14	;	;	PUNCT
ejpam-3949	155	15	•	•	NUM
ejpam-3949	155	16	w	w	PROPN
ejpam-3949	155	17	1	1	NUM
ejpam-3949	155	18	lt	lt	PRON
ejpam-3949	155	19	(	(	PUNCT
ejpam-3949	155	20	x	x	NOUN
ejpam-3949	155	21	)	)	PUNCT
ejpam-3949	155	22	:	:	PUNCT
ejpam-3949	155	23	(	(	PUNCT
ejpam-3949	155	24	−∞	−∞	NOUN
ejpam-3949	155	25	,	,	PUNCT
ejpam-3949	155	26	f(δ)]→	f(δ)]→	PROPN
ejpam-3949	156	1	[	[	X
ejpam-3949	156	2	δ,+∞	δ,+∞	NOUN
ejpam-3949	156	3	)	)	PUNCT
ejpam-3949	156	4	is	be	AUX
ejpam-3949	156	5	strictly	strictly	ADV
ejpam-3949	156	6	decreasing	decrease	VERB
ejpam-3949	156	7	,	,	PUNCT
ejpam-3949	156	8	where	where	SCONJ
ejpam-3949	156	9	δ	δ	PROPN
ejpam-3949	156	10	is	be	AUX
ejpam-3949	156	11	the	the	DET
ejpam-3949	156	12	unique	unique	ADJ
ejpam-3949	156	13	solution	solution	NOUN
ejpam-3949	156	14	to	to	ADP
ejpam-3949	156	15	ay	ay	PROPN
ejpam-3949	156	16	ln(by	ln(by	PROPN
ejpam-3949	156	17	)	)	PUNCT
ejpam-3949	157	1	+	+	PUNCT
ejpam-3949	157	2	y	y	PROPN
ejpam-3949	158	1	+	+	NOUN
ejpam-3949	158	2	c	c	NOUN
ejpam-3949	159	1	+	+	PROPN
ejpam-3949	159	2	a+a	a+a	X
ejpam-3949	159	3	ln(by	ln(by	NOUN
ejpam-3949	159	4	)	)	PUNCT
ejpam-3949	159	5	=	=	PUNCT
ejpam-3949	159	6	−1	−1	NOUN
ejpam-3949	159	7	.	.	PUNCT
ejpam-3949	160	1	(	(	PUNCT
ejpam-3949	160	2	23	23	NUM
ejpam-3949	160	3	)	)	PUNCT
ejpam-3949	160	4	(	(	PUNCT
ejpam-3949	160	5	iii	iii	NOUN
ejpam-3949	160	6	)	)	PUNCT
ejpam-3949	160	7	when	when	SCONJ
ejpam-3949	160	8	b	b	X
ejpam-3949	160	9	<	<	X
ejpam-3949	160	10	0	0	NUM
ejpam-3949	160	11	,	,	PUNCT
ejpam-3949	160	12	a	a	DET
ejpam-3949	160	13	>	>	X
ejpam-3949	160	14	0	0	NUM
ejpam-3949	160	15	,	,	PUNCT
ejpam-3949	160	16	|c|	|c|	PROPN
ejpam-3949	160	17	≤	≤	PROPN
ejpam-3949	160	18	a	a	PRON
ejpam-3949	160	19	,	,	PUNCT
ejpam-3949	160	20	the	the	DET
ejpam-3949	160	21	branches	branch	NOUN
ejpam-3949	160	22	are	be	AUX
ejpam-3949	160	23	•	•	PROPN
ejpam-3949	160	24	w	w	PROPN
ejpam-3949	160	25	0	0	NUM
ejpam-3949	160	26	lt	lt	INTJ
ejpam-3949	160	27	,	,	PUNCT
ejpam-3949	160	28	<	<	X
ejpam-3949	160	29	(	(	PUNCT
ejpam-3949	160	30	x	x	X
ejpam-3949	160	31	)	)	PUNCT
ejpam-3949	160	32	:	:	PUNCT
ejpam-3949	160	33	(	(	PUNCT
ejpam-3949	160	34	f(0	f(0	NOUN
ejpam-3949	160	35	)	)	PUNCT
ejpam-3949	160	36	,	,	PUNCT
ejpam-3949	160	37	f(δ1)]→	f(δ1)]→	VERB
ejpam-3949	161	1	[	[	X
ejpam-3949	161	2	δ1	δ1	NOUN
ejpam-3949	161	3	,	,	PUNCT
ejpam-3949	161	4	0	0	NUM
ejpam-3949	161	5	)	)	PUNCT
ejpam-3949	161	6	is	be	AUX
ejpam-3949	161	7	strictly	strictly	ADV
ejpam-3949	161	8	decreasing	decrease	VERB
ejpam-3949	161	9	;	;	PUNCT
ejpam-3949	161	10	c.	c.	PROPN
ejpam-3949	161	11	corcino	corcino	PROPN
ejpam-3949	161	12	,	,	PUNCT
ejpam-3949	161	13	r.	r.	PROPN
ejpam-3949	161	14	corcino	corcino	PROPN
ejpam-3949	161	15	/	/	SYM
ejpam-3949	161	16	eur	eur	PROPN
ejpam-3949	161	17	.	.	PUNCT
ejpam-3949	162	1	j.	j.	PROPN
ejpam-3949	162	2	pure	pure	PROPN
ejpam-3949	162	3	appl	appl	PROPN
ejpam-3949	162	4	.	.	PROPN
ejpam-3949	162	5	math	math	PROPN
ejpam-3949	162	6	,	,	PUNCT
ejpam-3949	162	7	14	14	NUM
ejpam-3949	162	8	(	(	PUNCT
ejpam-3949	162	9	2	2	NUM
ejpam-3949	162	10	)	)	PUNCT
ejpam-3949	162	11	(	(	PUNCT
ejpam-3949	162	12	2021	2021	NUM
ejpam-3949	162	13	)	)	PUNCT
ejpam-3949	162	14	,	,	PUNCT
ejpam-3949	162	15	506	506	NUM
ejpam-3949	162	16	-	-	SYM
ejpam-3949	162	17	520	520	NUM
ejpam-3949	162	18	513	513	NUM
ejpam-3949	162	19	•	•	NOUN
ejpam-3949	162	20	w	w	PROPN
ejpam-3949	162	21	1	1	NUM
ejpam-3949	162	22	lt	lt	NOUN
ejpam-3949	162	23	,	,	PUNCT
ejpam-3949	162	24	<	<	X
ejpam-3949	162	25	(	(	PUNCT
ejpam-3949	162	26	x	x	X
ejpam-3949	162	27	)	)	PUNCT
ejpam-3949	162	28	:	:	PUNCT
ejpam-3949	163	1	[	[	X
ejpam-3949	163	2	f(δ2	f(δ2	NOUN
ejpam-3949	163	3	)	)	PUNCT
ejpam-3949	163	4	,	,	PUNCT
ejpam-3949	163	5	f(δ1)]→	f(δ1)]→	VERB
ejpam-3949	163	6	[	[	X
ejpam-3949	163	7	δ2	δ2	ADJ
ejpam-3949	163	8	,	,	PUNCT
ejpam-3949	163	9	δ1	δ1	NOUN
ejpam-3949	163	10	]	]	PUNCT
ejpam-3949	163	11	is	be	AUX
ejpam-3949	163	12	strictly	strictly	ADV
ejpam-3949	163	13	increasing	increase	VERB
ejpam-3949	163	14	,	,	PUNCT
ejpam-3949	163	15	•	•	PROPN
ejpam-3949	163	16	w	w	PROPN
ejpam-3949	163	17	2	2	NUM
ejpam-3949	163	18	lt	lt	NOUN
ejpam-3949	163	19	,	,	PUNCT
ejpam-3949	163	20	<	<	X
ejpam-3949	163	21	(	(	PUNCT
ejpam-3949	163	22	x	x	X
ejpam-3949	163	23	)	)	PUNCT
ejpam-3949	163	24	:	:	PUNCT
ejpam-3949	164	1	[	[	X
ejpam-3949	164	2	f(δ2	f(δ2	NOUN
ejpam-3949	164	3	)	)	PUNCT
ejpam-3949	164	4	,	,	PUNCT
ejpam-3949	164	5	0)→	0)→	NUM
ejpam-3949	164	6	(	(	PUNCT
ejpam-3949	164	7	−∞	−∞	NOUN
ejpam-3949	164	8	,	,	PUNCT
ejpam-3949	164	9	δ2	δ2	VERB
ejpam-3949	164	10	]	]	PUNCT
ejpam-3949	164	11	is	be	AUX
ejpam-3949	164	12	strictly	strictly	ADV
ejpam-3949	164	13	decreasing	decrease	VERB
ejpam-3949	164	14	,	,	PUNCT
ejpam-3949	164	15	(	(	PUNCT
ejpam-3949	164	16	iv	iv	X
ejpam-3949	164	17	)	)	PUNCT
ejpam-3949	164	18	when	when	SCONJ
ejpam-3949	164	19	b	b	X
ejpam-3949	164	20	<	<	X
ejpam-3949	164	21	0	0	NUM
ejpam-3949	164	22	,	,	PUNCT
ejpam-3949	164	23	a	a	DET
ejpam-3949	164	24	<	<	X
ejpam-3949	164	25	0	0	NUM
ejpam-3949	164	26	,	,	PUNCT
ejpam-3949	164	27	c	c	NOUN
ejpam-3949	164	28	≤	≤	NUM
ejpam-3949	164	29	|a|	|a|	PROPN
ejpam-3949	164	30	,	,	PUNCT
ejpam-3949	164	31	the	the	DET
ejpam-3949	164	32	branches	branch	NOUN
ejpam-3949	164	33	are	be	AUX
ejpam-3949	164	34	•	•	PROPN
ejpam-3949	164	35	w	w	PROPN
ejpam-3949	164	36	0	0	NUM
ejpam-3949	164	37	lt	lt	INTJ
ejpam-3949	164	38	,	,	PUNCT
ejpam-3949	164	39	<	<	X
ejpam-3949	164	40	(	(	PUNCT
ejpam-3949	164	41	x	x	X
ejpam-3949	164	42	)	)	PUNCT
ejpam-3949	164	43	:	:	PUNCT
ejpam-3949	165	1	[	[	X
ejpam-3949	165	2	f(δ1	f(δ1	NOUN
ejpam-3949	165	3	)	)	PUNCT
ejpam-3949	165	4	,	,	PUNCT
ejpam-3949	165	5	f(0)]→	f(0)]→	X
ejpam-3949	165	6	[	[	X
ejpam-3949	165	7	δ1	δ1	NOUN
ejpam-3949	165	8	,	,	PUNCT
ejpam-3949	165	9	0	0	NUM
ejpam-3949	165	10	)	)	PUNCT
ejpam-3949	165	11	is	be	AUX
ejpam-3949	165	12	strictly	strictly	ADV
ejpam-3949	165	13	increasing	increase	VERB
ejpam-3949	165	14	;	;	PUNCT
ejpam-3949	166	1	•	•	NUM
ejpam-3949	166	2	w	w	PROPN
ejpam-3949	166	3	1	1	NUM
ejpam-3949	166	4	lt	lt	NOUN
ejpam-3949	166	5	,	,	PUNCT
ejpam-3949	166	6	<	<	X
ejpam-3949	166	7	(	(	PUNCT
ejpam-3949	166	8	x	x	X
ejpam-3949	166	9	)	)	PUNCT
ejpam-3949	166	10	:	:	PUNCT
ejpam-3949	167	1	[	[	X
ejpam-3949	167	2	f(δ1	f(δ1	NOUN
ejpam-3949	167	3	)	)	PUNCT
ejpam-3949	167	4	,	,	PUNCT
ejpam-3949	167	5	f(δ2)]→	f(δ2)]→	ADJ
ejpam-3949	167	6	[	[	X
ejpam-3949	167	7	δ2	δ2	ADJ
ejpam-3949	167	8	,	,	PUNCT
ejpam-3949	167	9	δ1	δ1	NOUN
ejpam-3949	167	10	]	]	PUNCT
ejpam-3949	167	11	is	be	AUX
ejpam-3949	167	12	strictly	strictly	ADV
ejpam-3949	167	13	decreasing	decrease	VERB
ejpam-3949	167	14	,	,	PUNCT
ejpam-3949	168	1	•	•	PROPN
ejpam-3949	168	2	w	w	PROPN
ejpam-3949	168	3	2	2	NUM
ejpam-3949	168	4	lt	lt	NOUN
ejpam-3949	168	5	,	,	PUNCT
ejpam-3949	168	6	<	<	X
ejpam-3949	168	7	(	(	PUNCT
ejpam-3949	168	8	x	x	X
ejpam-3949	168	9	)	)	PUNCT
ejpam-3949	168	10	:	:	PUNCT
ejpam-3949	168	11	(	(	PUNCT
ejpam-3949	168	12	0	0	NUM
ejpam-3949	168	13	,	,	PUNCT
ejpam-3949	168	14	f(δ2)]→	f(δ2)]→	ADJ
ejpam-3949	168	15	(	(	PUNCT
ejpam-3949	168	16	−∞	−∞	NOUN
ejpam-3949	168	17	,	,	PUNCT
ejpam-3949	168	18	δ2	δ2	VERB
ejpam-3949	168	19	]	]	PUNCT
ejpam-3949	168	20	is	be	AUX
ejpam-3949	168	21	strictly	strictly	ADV
ejpam-3949	168	22	increasing	increase	VERB
ejpam-3949	168	23	,	,	PUNCT
ejpam-3949	168	24	where	where	SCONJ
ejpam-3949	168	25	δ1	δ1	NOUN
ejpam-3949	168	26	and	and	CCONJ
ejpam-3949	168	27	δ2	δ2	PROPN
ejpam-3949	168	28	are	be	AUX
ejpam-3949	168	29	the	the	DET
ejpam-3949	168	30	two	two	NUM
ejpam-3949	168	31	solutions	solution	NOUN
ejpam-3949	168	32	to	to	ADP
ejpam-3949	168	33	(	(	PUNCT
ejpam-3949	168	34	23	23	NUM
ejpam-3949	168	35	)	)	PUNCT
ejpam-3949	168	36	with	with	ADP
ejpam-3949	168	37	δ2	δ2	VERB
ejpam-3949	168	38	<	<	X
ejpam-3949	168	39	1	1	NUM
ejpam-3949	168	40	b	b	PROPN
ejpam-3949	168	41	e	e	ADP
ejpam-3949	168	42	w	w	X
ejpam-3949	168	43	(	(	PUNCT
ejpam-3949	168	44	−bce1	−bce1	PROPN
ejpam-3949	168	45	/	/	SYM
ejpam-3949	168	46	a	a	DET
ejpam-3949	168	47	a	a	NOUN
ejpam-3949	168	48	)	)	PUNCT
ejpam-3949	168	49	−	−	PROPN
ejpam-3949	168	50	1	1	NUM
ejpam-3949	168	51	a	a	DET
ejpam-3949	168	52	<	<	X
ejpam-3949	168	53	δ1	δ1	NOUN
ejpam-3949	168	54	<	<	X
ejpam-3949	168	55	0	0	X
ejpam-3949	168	56	.	.	PUNCT
ejpam-3949	169	1	proof	proof	NOUN
ejpam-3949	169	2	.	.	PUNCT
ejpam-3949	170	1	consider	consider	VERB
ejpam-3949	170	2	the	the	DET
ejpam-3949	170	3	case	case	NOUN
ejpam-3949	170	4	when	when	SCONJ
ejpam-3949	170	5	b	b	X
ejpam-3949	170	6	>	>	X
ejpam-3949	170	7	0	0	PROPN
ejpam-3949	170	8	,	,	PUNCT
ejpam-3949	170	9	a	a	PRON
ejpam-3949	170	10	>	>	X
ejpam-3949	170	11	0	0	X
ejpam-3949	170	12	.	.	PUNCT
ejpam-3949	171	1	let	let	VERB
ejpam-3949	171	2	x	x	SYM
ejpam-3949	171	3	=	=	SYM
ejpam-3949	171	4	f(y	f(y	NOUN
ejpam-3949	171	5	)	)	PUNCT
ejpam-3949	171	6	=	=	PUNCT
ejpam-3949	172	1	[	[	X
ejpam-3949	172	2	ay	ay	X
ejpam-3949	172	3	ln(by	ln(by	NOUN
ejpam-3949	172	4	)	)	PUNCT
ejpam-3949	173	1	+	+	CCONJ
ejpam-3949	173	2	y	y	PROPN
ejpam-3949	173	3	+	+	PROPN
ejpam-3949	173	4	c]ey	c]ey	PROPN
ejpam-3949	173	5	.	.	PUNCT
ejpam-3949	174	1	from	from	ADP
ejpam-3949	174	2	equation	equation	NOUN
ejpam-3949	174	3	(	(	PUNCT
ejpam-3949	174	4	8)	8)	NUM
ejpam-3949	174	5	,	,	PUNCT
ejpam-3949	174	6	the	the	DET
ejpam-3949	174	7	derivative	derivative	NOUN
ejpam-3949	174	8	of	of	ADP
ejpam-3949	174	9	y	y	PROPN
ejpam-3949	174	10	=	=	SYM
ejpam-3949	174	11	wlt	wlt	PROPN
ejpam-3949	174	12	(	(	PUNCT
ejpam-3949	174	13	x	x	X
ejpam-3949	174	14	)	)	PUNCT
ejpam-3949	174	15	is	be	AUX
ejpam-3949	174	16	not	not	PART
ejpam-3949	174	17	defined	define	VERB
ejpam-3949	174	18	when	when	SCONJ
ejpam-3949	174	19	y	y	PROPN
ejpam-3949	174	20	satisfies	satisfy	VERB
ejpam-3949	174	21	(	(	PUNCT
ejpam-3949	174	22	23	23	NUM
ejpam-3949	174	23	)	)	PUNCT
ejpam-3949	174	24	.	.	PUNCT
ejpam-3949	175	1	the	the	DET
ejpam-3949	175	2	solution	solution	NOUN
ejpam-3949	175	3	y	y	PROPN
ejpam-3949	175	4	=	=	PUNCT
ejpam-3949	175	5	δ	δ	PROPN
ejpam-3949	175	6	to	to	ADP
ejpam-3949	175	7	(	(	PUNCT
ejpam-3949	175	8	23	23	NUM
ejpam-3949	175	9	)	)	PUNCT
ejpam-3949	175	10	can	can	AUX
ejpam-3949	175	11	be	be	AUX
ejpam-3949	175	12	viewed	view	VERB
ejpam-3949	175	13	as	as	ADP
ejpam-3949	175	14	the	the	DET
ejpam-3949	175	15	intersection	intersection	NOUN
ejpam-3949	175	16	of	of	ADP
ejpam-3949	175	17	the	the	DET
ejpam-3949	175	18	functions	function	NOUN
ejpam-3949	175	19	g(y	g(y	NOUN
ejpam-3949	175	20	)	)	PUNCT
ejpam-3949	175	21	=	=	PUNCT
ejpam-3949	175	22	−y	−y	VERB
ejpam-3949	175	23	−	−	NOUN
ejpam-3949	175	24	c	c	NOUN
ejpam-3949	176	1	−a−	−a−	NOUN
ejpam-3949	176	2	1	1	NUM
ejpam-3949	176	3	y	y	NOUN
ejpam-3949	176	4	+	+	CCONJ
ejpam-3949	176	5	1	1	NUM
ejpam-3949	176	6	and	and	CCONJ
ejpam-3949	176	7	h(y	h(y	NOUN
ejpam-3949	176	8	)	)	PUNCT
ejpam-3949	177	1	=	=	SYM
ejpam-3949	177	2	a	a	DET
ejpam-3949	177	3	ln(by	ln(by	NOUN
ejpam-3949	177	4	)	)	PUNCT
ejpam-3949	177	5	.	.	PUNCT
ejpam-3949	178	1	clearly	clearly	ADV
ejpam-3949	178	2	,	,	PUNCT
ejpam-3949	178	3	the	the	DET
ejpam-3949	178	4	solution	solution	NOUN
ejpam-3949	178	5	is	be	AUX
ejpam-3949	178	6	unique	unique	ADJ
ejpam-3949	178	7	.	.	PUNCT
ejpam-3949	179	1	thus	thus	ADV
ejpam-3949	179	2	,	,	PUNCT
ejpam-3949	179	3	the	the	DET
ejpam-3949	179	4	derivative	derivative	ADJ
ejpam-3949	179	5	dwlt	dwlt	NOUN
ejpam-3949	179	6	(	(	PUNCT
ejpam-3949	179	7	x	x	X
ejpam-3949	179	8	)	)	PUNCT
ejpam-3949	179	9	dx	dx	PROPN
ejpam-3949	179	10	is	be	AUX
ejpam-3949	179	11	not	not	PART
ejpam-3949	179	12	defined	define	VERB
ejpam-3949	179	13	for	for	ADP
ejpam-3949	179	14	x	x	SYM
ejpam-3949	179	15	=	=	SYM
ejpam-3949	179	16	f(δ	f(δ	NOUN
ejpam-3949	179	17	)	)	PUNCT
ejpam-3949	179	18	=	=	PUNCT
ejpam-3949	180	1	[	[	X
ejpam-3949	180	2	aδ	aδ	PROPN
ejpam-3949	180	3	ln(bδ	ln(bδ	PROPN
ejpam-3949	180	4	)	)	PUNCT
ejpam-3949	181	1	+	+	NUM
ejpam-3949	181	2	δ	δ	PROPN
ejpam-3949	181	3	+	+	NUM
ejpam-3949	181	4	c]eδ	c]eδ	NOUN
ejpam-3949	181	5	.	.	PUNCT
ejpam-3949	182	1	the	the	DET
ejpam-3949	182	2	value	value	NOUN
ejpam-3949	182	3	of	of	ADP
ejpam-3949	182	4	f(δ	f(δ	NOUN
ejpam-3949	182	5	)	)	PUNCT
ejpam-3949	182	6	can	can	AUX
ejpam-3949	182	7	then	then	ADV
ejpam-3949	182	8	be	be	AUX
ejpam-3949	182	9	used	use	VERB
ejpam-3949	182	10	to	to	PART
ejpam-3949	182	11	determine	determine	VERB
ejpam-3949	182	12	the	the	DET
ejpam-3949	182	13	branches	branch	NOUN
ejpam-3949	182	14	of	of	ADP
ejpam-3949	182	15	wlt	wlt	PROPN
ejpam-3949	182	16	(	(	PUNCT
ejpam-3949	182	17	x	x	NOUN
ejpam-3949	182	18	)	)	PUNCT
ejpam-3949	182	19	.	.	PUNCT
ejpam-3949	183	1	to	to	PART
ejpam-3949	183	2	explicitly	explicitly	ADV
ejpam-3949	183	3	identify	identify	VERB
ejpam-3949	183	4	the	the	DET
ejpam-3949	183	5	said	say	VERB
ejpam-3949	183	6	branches	branch	NOUN
ejpam-3949	183	7	,	,	PUNCT
ejpam-3949	183	8	the	the	DET
ejpam-3949	183	9	following	follow	VERB
ejpam-3949	183	10	information	information	NOUN
ejpam-3949	183	11	are	be	AUX
ejpam-3949	183	12	important	important	ADJ
ejpam-3949	183	13	:	:	PUNCT
ejpam-3949	183	14	(	(	PUNCT
ejpam-3949	183	15	i	i	NOUN
ejpam-3949	183	16	)	)	PUNCT
ejpam-3949	183	17	the	the	DET
ejpam-3949	183	18	value	value	NOUN
ejpam-3949	183	19	of	of	ADP
ejpam-3949	183	20	y	y	PROPN
ejpam-3949	183	21	must	must	AUX
ejpam-3949	183	22	always	always	ADV
ejpam-3949	183	23	be	be	AUX
ejpam-3949	183	24	positive	positive	ADJ
ejpam-3949	183	25	,	,	PUNCT
ejpam-3949	183	26	otherwise	otherwise	ADV
ejpam-3949	183	27	,	,	PUNCT
ejpam-3949	183	28	ln(by	ln(by	PROPN
ejpam-3949	183	29	)	)	PUNCT
ejpam-3949	183	30	is	be	AUX
ejpam-3949	183	31	undefined	undefined	ADJ
ejpam-3949	183	32	;	;	PUNCT
ejpam-3949	183	33	(	(	PUNCT
ejpam-3949	183	34	ii	ii	NOUN
ejpam-3949	183	35	)	)	PUNCT
ejpam-3949	183	36	the	the	DET
ejpam-3949	183	37	function	function	NOUN
ejpam-3949	183	38	y	y	PROPN
ejpam-3949	183	39	=	=	PUNCT
ejpam-3949	183	40	wlt	wlt	PROPN
ejpam-3949	183	41	(	(	PUNCT
ejpam-3949	183	42	x	x	X
ejpam-3949	183	43	)	)	PUNCT
ejpam-3949	183	44	has	have	VERB
ejpam-3949	183	45	only	only	ADV
ejpam-3949	183	46	one	one	NUM
ejpam-3949	183	47	y	y	PROPN
ejpam-3949	183	48	-	-	PUNCT
ejpam-3949	183	49	intercept	intercept	NOUN
ejpam-3949	183	50	,	,	PUNCT
ejpam-3949	183	51	i.e.	i.e.	X
ejpam-3949	183	52	,	,	PUNCT
ejpam-3949	183	53	y	y	PROPN
ejpam-3949	183	54	=	=	SYM
ejpam-3949	183	55	1	1	NUM
ejpam-3949	183	56	b	b	NOUN
ejpam-3949	183	57	;	;	PUNCT
ejpam-3949	183	58	(	(	PUNCT
ejpam-3949	183	59	iii	iii	X
ejpam-3949	183	60	)	)	PUNCT
ejpam-3949	183	61	if	if	SCONJ
ejpam-3949	183	62	y	y	PROPN
ejpam-3949	183	63	<	<	X
ejpam-3949	183	64	δ	δ	PROPN
ejpam-3949	183	65	,	,	PUNCT
ejpam-3949	183	66	a(y	a(y	PROPN
ejpam-3949	183	67	+	+	CCONJ
ejpam-3949	183	68	1	1	X
ejpam-3949	183	69	)	)	PUNCT
ejpam-3949	183	70	ln(by	ln(by	NOUN
ejpam-3949	183	71	)	)	PUNCT
ejpam-3949	184	1	+	+	CCONJ
ejpam-3949	184	2	y	y	PROPN
ejpam-3949	184	3	+	+	NOUN
ejpam-3949	184	4	a+	a+	X
ejpam-3949	184	5	c	c	NOUN
ejpam-3949	184	6	+	+	ADP
ejpam-3949	184	7	1	1	NUM
ejpam-3949	184	8	>	>	SYM
ejpam-3949	184	9	0	0	NUM
ejpam-3949	184	10	which	which	PRON
ejpam-3949	184	11	gives	give	VERB
ejpam-3949	184	12	dy	dy	PROPN
ejpam-3949	184	13	dx	dx	PROPN
ejpam-3949	184	14	>	>	X
ejpam-3949	184	15	0	0	NUM
ejpam-3949	184	16	;	;	PUNCT
ejpam-3949	184	17	(	(	PUNCT
ejpam-3949	184	18	iv	iv	X
ejpam-3949	184	19	)	)	PUNCT
ejpam-3949	184	20	if	if	SCONJ
ejpam-3949	184	21	y	y	PROPN
ejpam-3949	184	22	>	>	X
ejpam-3949	184	23	δ	δ	PROPN
ejpam-3949	184	24	,	,	PUNCT
ejpam-3949	184	25	a(y	a(y	PROPN
ejpam-3949	184	26	+	+	CCONJ
ejpam-3949	184	27	1	1	X
ejpam-3949	184	28	)	)	PUNCT
ejpam-3949	184	29	ln(by	ln(by	NOUN
ejpam-3949	184	30	)	)	PUNCT
ejpam-3949	185	1	+	+	CCONJ
ejpam-3949	185	2	y	y	PROPN
ejpam-3949	185	3	+	+	NOUN
ejpam-3949	185	4	a+	a+	X
ejpam-3949	185	5	c	c	NOUN
ejpam-3949	185	6	+	+	CCONJ
ejpam-3949	185	7	1	1	NUM
ejpam-3949	185	8	<	<	X
ejpam-3949	185	9	0	0	NUM
ejpam-3949	185	10	which	which	PRON
ejpam-3949	185	11	gives	give	VERB
ejpam-3949	185	12	dy	dy	NOUN
ejpam-3949	185	13	dx	dx	PROPN
ejpam-3949	185	14	<	<	X
ejpam-3949	185	15	0	0	NUM
ejpam-3949	185	16	;	;	PUNCT
ejpam-3949	185	17	(	(	PUNCT
ejpam-3949	185	18	v	v	NOUN
ejpam-3949	185	19	)	)	PUNCT
ejpam-3949	185	20	if	if	SCONJ
ejpam-3949	185	21	y	y	PROPN
ejpam-3949	185	22	=	=	SYM
ejpam-3949	185	23	δ	δ	PROPN
ejpam-3949	185	24	,	,	PUNCT
ejpam-3949	185	25	a(y	a(y	PROPN
ejpam-3949	185	26	+	+	CCONJ
ejpam-3949	185	27	1	1	X
ejpam-3949	185	28	)	)	PUNCT
ejpam-3949	185	29	ln(by	ln(by	NOUN
ejpam-3949	185	30	)	)	PUNCT
ejpam-3949	186	1	+	+	CCONJ
ejpam-3949	186	2	y	y	PROPN
ejpam-3949	186	3	+	+	NOUN
ejpam-3949	186	4	a+	a+	X
ejpam-3949	186	5	c	c	NOUN
ejpam-3949	186	6	+	+	NOUN
ejpam-3949	186	7	1	1	NUM
ejpam-3949	186	8	=	=	SYM
ejpam-3949	186	9	0	0	NUM
ejpam-3949	186	10	and	and	CCONJ
ejpam-3949	186	11	dy	dy	NOUN
ejpam-3949	186	12	dx	dx	PROPN
ejpam-3949	186	13	does	do	AUX
ejpam-3949	186	14	not	not	PART
ejpam-3949	186	15	exist	exist	VERB
ejpam-3949	186	16	these	these	PRON
ejpam-3949	186	17	imply	imply	NOUN
ejpam-3949	186	18	that	that	SCONJ
ejpam-3949	186	19	(	(	PUNCT
ejpam-3949	186	20	i	i	NOUN
ejpam-3949	186	21	)	)	PUNCT
ejpam-3949	186	22	when	when	SCONJ
ejpam-3949	186	23	y	y	PROPN
ejpam-3949	186	24	<	<	X
ejpam-3949	186	25	δ	δ	PROPN
ejpam-3949	186	26	,	,	PUNCT
ejpam-3949	186	27	the	the	DET
ejpam-3949	186	28	function	function	NOUN
ejpam-3949	186	29	y	y	PROPN
ejpam-3949	186	30	=	=	PUNCT
ejpam-3949	186	31	wlt	wlt	PROPN
ejpam-3949	186	32	(	(	PUNCT
ejpam-3949	186	33	x	x	X
ejpam-3949	186	34	)	)	PUNCT
ejpam-3949	186	35	is	be	AUX
ejpam-3949	186	36	increasing	increase	VERB
ejpam-3949	186	37	in	in	ADP
ejpam-3949	186	38	the	the	DET
ejpam-3949	186	39	domain	domain	NOUN
ejpam-3949	186	40	[	[	X
ejpam-3949	186	41	f(δ	f(δ	NOUN
ejpam-3949	186	42	)	)	PUNCT
ejpam-3949	186	43	,	,	PUNCT
ejpam-3949	186	44	0	0	NUM
ejpam-3949	186	45	)	)	PUNCT
ejpam-3949	186	46	with	with	ADP
ejpam-3949	186	47	range	range	NOUN
ejpam-3949	186	48	(	(	PUNCT
ejpam-3949	186	49	0	0	NUM
ejpam-3949	186	50	,	,	PUNCT
ejpam-3949	186	51	δ	δ	PROPN
ejpam-3949	186	52	]	]	PUNCT
ejpam-3949	186	53	and	and	CCONJ
ejpam-3949	186	54	the	the	DET
ejpam-3949	186	55	function	function	NOUN
ejpam-3949	186	56	crosses	cross	VERB
ejpam-3949	186	57	the	the	DET
ejpam-3949	186	58	y	y	NOUN
ejpam-3949	186	59	-	-	PUNCT
ejpam-3949	186	60	axis	axis	NOUN
ejpam-3949	186	61	only	only	ADV
ejpam-3949	186	62	at	at	ADP
ejpam-3949	186	63	y	y	PROPN
ejpam-3949	186	64	=	=	SYM
ejpam-3949	186	65	1	1	NUM
ejpam-3949	186	66	b	b	X
ejpam-3949	186	67	e	e	ADP
ejpam-3949	186	68	w	w	X
ejpam-3949	186	69	(	(	PUNCT
ejpam-3949	186	70	−bce1	−bce1	PROPN
ejpam-3949	186	71	/	/	SYM
ejpam-3949	186	72	a	a	DET
ejpam-3949	186	73	a	a	NOUN
ejpam-3949	186	74	)	)	PUNCT
ejpam-3949	186	75	−	−	PROPN
ejpam-3949	186	76	1	1	NUM
ejpam-3949	186	77	a	a	PRON
ejpam-3949	186	78	;	;	PUNCT
ejpam-3949	186	79	c.	c.	PROPN
ejpam-3949	186	80	corcino	corcino	PROPN
ejpam-3949	186	81	,	,	PUNCT
ejpam-3949	186	82	r.	r.	PROPN
ejpam-3949	186	83	corcino	corcino	PROPN
ejpam-3949	186	84	/	/	SYM
ejpam-3949	186	85	eur	eur	PROPN
ejpam-3949	186	86	.	.	PUNCT
ejpam-3949	187	1	j.	j.	PROPN
ejpam-3949	187	2	pure	pure	PROPN
ejpam-3949	187	3	appl	appl	PROPN
ejpam-3949	187	4	.	.	PROPN
ejpam-3949	187	5	math	math	PROPN
ejpam-3949	187	6	,	,	PUNCT
ejpam-3949	187	7	14	14	NUM
ejpam-3949	187	8	(	(	PUNCT
ejpam-3949	187	9	2	2	NUM
ejpam-3949	187	10	)	)	PUNCT
ejpam-3949	187	11	(	(	PUNCT
ejpam-3949	187	12	2021	2021	NUM
ejpam-3949	187	13	)	)	PUNCT
ejpam-3949	187	14	,	,	PUNCT
ejpam-3949	187	15	506	506	NUM
ejpam-3949	187	16	-	-	SYM
ejpam-3949	187	17	520	520	NUM
ejpam-3949	187	18	514	514	NUM
ejpam-3949	187	19	(	(	PUNCT
ejpam-3949	187	20	ii	ii	NOUN
ejpam-3949	187	21	)	)	PUNCT
ejpam-3949	187	22	when	when	SCONJ
ejpam-3949	187	23	y	y	PROPN
ejpam-3949	187	24	>	>	X
ejpam-3949	187	25	δ	δ	PROPN
ejpam-3949	187	26	,	,	PUNCT
ejpam-3949	187	27	the	the	DET
ejpam-3949	187	28	function	function	NOUN
ejpam-3949	187	29	y	y	PROPN
ejpam-3949	187	30	=	=	PUNCT
ejpam-3949	187	31	wlt	wlt	PROPN
ejpam-3949	187	32	(	(	PUNCT
ejpam-3949	187	33	x	x	X
ejpam-3949	187	34	)	)	PUNCT
ejpam-3949	187	35	is	be	AUX
ejpam-3949	187	36	decreasing	decrease	VERB
ejpam-3949	187	37	,	,	PUNCT
ejpam-3949	187	38	the	the	DET
ejpam-3949	187	39	domain	domain	NOUN
ejpam-3949	187	40	is	be	AUX
ejpam-3949	187	41	[	[	X
ejpam-3949	187	42	f(δ),+∞	f(δ),+∞	X
ejpam-3949	187	43	)	)	PUNCT
ejpam-3949	187	44	and	and	CCONJ
ejpam-3949	187	45	the	the	DET
ejpam-3949	187	46	range	range	NOUN
ejpam-3949	187	47	is	be	AUX
ejpam-3949	187	48	[	[	X
ejpam-3949	187	49	δ,+∞	δ,+∞	NOUN
ejpam-3949	187	50	)	)	PUNCT
ejpam-3949	187	51	because	because	SCONJ
ejpam-3949	187	52	this	this	DET
ejpam-3949	187	53	part	part	NOUN
ejpam-3949	187	54	of	of	ADP
ejpam-3949	187	55	the	the	DET
ejpam-3949	187	56	graph	graph	NOUN
ejpam-3949	187	57	does	do	AUX
ejpam-3949	187	58	not	not	PART
ejpam-3949	187	59	cross	cross	VERB
ejpam-3949	187	60	the	the	DET
ejpam-3949	187	61	x	x	NOUN
ejpam-3949	187	62	-	-	NOUN
ejpam-3949	187	63	axis	axis	ADJ
ejpam-3949	187	64	and	and	CCONJ
ejpam-3949	187	65	y	y	NOUN
ejpam-3949	187	66	-	-	PUNCT
ejpam-3949	187	67	axis	axis	NOUN
ejpam-3949	187	68	;	;	PUNCT
ejpam-3949	187	69	(	(	PUNCT
ejpam-3949	187	70	iii	iii	X
ejpam-3949	187	71	)	)	PUNCT
ejpam-3949	187	72	when	when	SCONJ
ejpam-3949	187	73	y	y	PROPN
ejpam-3949	187	74	=	=	SYM
ejpam-3949	187	75	δ	δ	PROPN
ejpam-3949	187	76	,	,	PUNCT
ejpam-3949	187	77	the	the	DET
ejpam-3949	187	78	line	line	NOUN
ejpam-3949	187	79	tangent	tangent	NOUN
ejpam-3949	187	80	to	to	ADP
ejpam-3949	187	81	the	the	DET
ejpam-3949	187	82	curve	curve	NOUN
ejpam-3949	187	83	at	at	ADP
ejpam-3949	187	84	the	the	DET
ejpam-3949	187	85	point	point	NOUN
ejpam-3949	187	86	(	(	PUNCT
ejpam-3949	187	87	f(δ	f(δ	NOUN
ejpam-3949	187	88	)	)	PUNCT
ejpam-3949	187	89	,	,	PUNCT
ejpam-3949	187	90	δ	δ	PROPN
ejpam-3949	187	91	)	)	PUNCT
ejpam-3949	187	92	is	be	AUX
ejpam-3949	187	93	a	a	DET
ejpam-3949	187	94	vertical	vertical	ADJ
ejpam-3949	187	95	line	line	NOUN
ejpam-3949	187	96	.	.	PUNCT
ejpam-3949	188	1	these	these	PRON
ejpam-3949	188	2	proved	prove	VERB
ejpam-3949	188	3	the	the	DET
ejpam-3949	188	4	case	case	NOUN
ejpam-3949	188	5	when	when	SCONJ
ejpam-3949	188	6	b	b	X
ejpam-3949	188	7	>	>	X
ejpam-3949	188	8	0	0	PROPN
ejpam-3949	188	9	,	,	PUNCT
ejpam-3949	188	10	a	a	PRON
ejpam-3949	188	11	>	>	X
ejpam-3949	188	12	0	0	NUM
ejpam-3949	188	13	.	.	PUNCT
ejpam-3949	189	1	the	the	DET
ejpam-3949	189	2	case	case	NOUN
ejpam-3949	189	3	where	where	SCONJ
ejpam-3949	189	4	b	b	X
ejpam-3949	189	5	>	>	X
ejpam-3949	189	6	0	0	PROPN
ejpam-3949	189	7	,	,	PUNCT
ejpam-3949	189	8	a	a	DET
ejpam-3949	189	9	<	<	X
ejpam-3949	189	10	0	0	NUM
ejpam-3949	189	11	can	can	AUX
ejpam-3949	189	12	be	be	AUX
ejpam-3949	189	13	proved	prove	VERB
ejpam-3949	189	14	similarly	similarly	ADV
ejpam-3949	189	15	.	.	PUNCT
ejpam-3949	190	1	for	for	ADP
ejpam-3949	190	2	the	the	DET
ejpam-3949	190	3	case	case	NOUN
ejpam-3949	190	4	b	b	X
ejpam-3949	190	5	<	<	X
ejpam-3949	190	6	0	0	NUM
ejpam-3949	190	7	,	,	PUNCT
ejpam-3949	190	8	a	a	DET
ejpam-3949	190	9	>	>	X
ejpam-3949	190	10	0	0	NUM
ejpam-3949	190	11	,	,	PUNCT
ejpam-3949	190	12	|c|	|c|	PROPN
ejpam-3949	190	13	≤	≤	PROPN
ejpam-3949	190	14	a	a	PRON
ejpam-3949	190	15	,	,	PUNCT
ejpam-3949	190	16	the	the	DET
ejpam-3949	190	17	solution	solution	NOUN
ejpam-3949	190	18	to	to	ADP
ejpam-3949	190	19	(	(	PUNCT
ejpam-3949	190	20	23	23	NUM
ejpam-3949	190	21	)	)	PUNCT
ejpam-3949	190	22	can	can	AUX
ejpam-3949	190	23	be	be	AUX
ejpam-3949	190	24	viewed	view	VERB
ejpam-3949	190	25	as	as	ADP
ejpam-3949	190	26	the	the	DET
ejpam-3949	190	27	intersection	intersection	NOUN
ejpam-3949	190	28	of	of	ADP
ejpam-3949	190	29	the	the	DET
ejpam-3949	190	30	functions	function	NOUN
ejpam-3949	190	31	g(y	g(y	NOUN
ejpam-3949	190	32	)	)	PUNCT
ejpam-3949	190	33	=	=	PUNCT
ejpam-3949	190	34	−y	−y	VERB
ejpam-3949	190	35	−	−	NOUN
ejpam-3949	190	36	c	c	NOUN
ejpam-3949	191	1	−a−	−a−	NOUN
ejpam-3949	191	2	1	1	NUM
ejpam-3949	191	3	y	y	NOUN
ejpam-3949	191	4	+	+	CCONJ
ejpam-3949	191	5	1	1	NUM
ejpam-3949	191	6	and	and	CCONJ
ejpam-3949	191	7	h(y	h(y	NOUN
ejpam-3949	191	8	)	)	PUNCT
ejpam-3949	192	1	=	=	SYM
ejpam-3949	192	2	a	a	DET
ejpam-3949	192	3	ln(by	ln(by	NOUN
ejpam-3949	192	4	)	)	PUNCT
ejpam-3949	192	5	.	.	PUNCT
ejpam-3949	193	1	these	these	DET
ejpam-3949	193	2	graphs	graph	NOUN
ejpam-3949	193	3	intersect	intersect	ADJ
ejpam-3949	193	4	at	at	ADP
ejpam-3949	193	5	two	two	NUM
ejpam-3949	193	6	points	point	NOUN
ejpam-3949	193	7	δ1	δ1	NOUN
ejpam-3949	193	8	and	and	CCONJ
ejpam-3949	193	9	δ2	δ2	PROPN
ejpam-3949	193	10	.	.	PUNCT
ejpam-3949	194	1	thus	thus	ADV
ejpam-3949	194	2	,	,	PUNCT
ejpam-3949	194	3	the	the	DET
ejpam-3949	194	4	derivative	derivative	ADJ
ejpam-3949	194	5	dwlt	dwlt	NOUN
ejpam-3949	194	6	(	(	PUNCT
ejpam-3949	194	7	x	x	X
ejpam-3949	194	8	)	)	PUNCT
ejpam-3949	194	9	dx	dx	PROPN
ejpam-3949	194	10	is	be	AUX
ejpam-3949	194	11	not	not	PART
ejpam-3949	194	12	defined	define	VERB
ejpam-3949	194	13	for	for	ADP
ejpam-3949	194	14	x1	x1	PROPN
ejpam-3949	194	15	=	=	SYM
ejpam-3949	194	16	f(δ1	f(δ1	NOUN
ejpam-3949	194	17	)	)	PUNCT
ejpam-3949	194	18	=	=	PUNCT
ejpam-3949	195	1	[	[	X
ejpam-3949	195	2	aδ1	aδ1	NOUN
ejpam-3949	195	3	ln(bδ1	ln(bδ1	PROPN
ejpam-3949	195	4	)	)	PUNCT
ejpam-3949	195	5	+	+	NUM
ejpam-3949	195	6	δ1	δ1	NOUN
ejpam-3949	195	7	+	+	CCONJ
ejpam-3949	195	8	c]eδ1	c]eδ1	PROPN
ejpam-3949	195	9	,	,	PUNCT
ejpam-3949	195	10	x2	x2	NOUN
ejpam-3949	195	11	=	=	PUNCT
ejpam-3949	195	12	f(δ2	f(δ2	NOUN
ejpam-3949	195	13	)	)	PUNCT
ejpam-3949	195	14	=	=	PUNCT
ejpam-3949	196	1	[	[	X
ejpam-3949	196	2	aδ2	aδ2	NOUN
ejpam-3949	196	3	ln(bδ2	ln(bδ2	NUM
ejpam-3949	196	4	)	)	PUNCT
ejpam-3949	196	5	+	+	CCONJ
ejpam-3949	196	6	δ2	δ2	VERB
ejpam-3949	196	7	+	+	CCONJ
ejpam-3949	196	8	c]eδ2	c]eδ2	PROPN
ejpam-3949	196	9	.	.	PUNCT
ejpam-3949	197	1	note	note	VERB
ejpam-3949	197	2	that	that	SCONJ
ejpam-3949	197	3	(	(	PUNCT
ejpam-3949	197	4	i	i	NOUN
ejpam-3949	197	5	)	)	PUNCT
ejpam-3949	197	6	the	the	DET
ejpam-3949	197	7	value	value	NOUN
ejpam-3949	197	8	of	of	ADP
ejpam-3949	197	9	y	y	PROPN
ejpam-3949	197	10	must	must	AUX
ejpam-3949	197	11	always	always	ADV
ejpam-3949	197	12	be	be	AUX
ejpam-3949	197	13	negative	negative	ADJ
ejpam-3949	197	14	,	,	PUNCT
ejpam-3949	197	15	otherwise	otherwise	ADV
ejpam-3949	197	16	,	,	PUNCT
ejpam-3949	197	17	ln(by	ln(by	PROPN
ejpam-3949	197	18	)	)	PUNCT
ejpam-3949	198	1	is	be	AUX
ejpam-3949	198	2	undefined	undefined	ADJ
ejpam-3949	198	3	;	;	PUNCT
ejpam-3949	198	4	(	(	PUNCT
ejpam-3949	198	5	ii	ii	NOUN
ejpam-3949	198	6	)	)	PUNCT
ejpam-3949	198	7	the	the	DET
ejpam-3949	198	8	function	function	NOUN
ejpam-3949	198	9	y	y	PROPN
ejpam-3949	198	10	=	=	PUNCT
ejpam-3949	198	11	wlt	wlt	PROPN
ejpam-3949	198	12	(	(	PUNCT
ejpam-3949	198	13	x	x	X
ejpam-3949	198	14	)	)	PUNCT
ejpam-3949	198	15	has	have	VERB
ejpam-3949	198	16	only	only	ADV
ejpam-3949	198	17	one	one	NUM
ejpam-3949	198	18	y	y	PROPN
ejpam-3949	198	19	-	-	PUNCT
ejpam-3949	198	20	intercept	intercept	NOUN
ejpam-3949	198	21	,	,	PUNCT
ejpam-3949	198	22	i.e.	i.e.	X
ejpam-3949	198	23	,	,	PUNCT
ejpam-3949	198	24	y	y	PROPN
ejpam-3949	198	25	=	=	SYM
ejpam-3949	199	1	1	1	NUM
ejpam-3949	199	2	b	b	X
ejpam-3949	199	3	e	e	ADP
ejpam-3949	199	4	w	w	X
ejpam-3949	199	5	(	(	PUNCT
ejpam-3949	199	6	−bce1	−bce1	PROPN
ejpam-3949	199	7	/	/	SYM
ejpam-3949	199	8	a	a	DET
ejpam-3949	199	9	a	a	NOUN
ejpam-3949	199	10	)	)	PUNCT
ejpam-3949	199	11	−	−	PROPN
ejpam-3949	199	12	1	1	NUM
ejpam-3949	199	13	a	a	PRON
ejpam-3949	199	14	;	;	PUNCT
ejpam-3949	199	15	(	(	PUNCT
ejpam-3949	199	16	iii	iii	X
ejpam-3949	199	17	)	)	PUNCT
ejpam-3949	199	18	g(y	g(y	NOUN
ejpam-3949	199	19	)	)	PUNCT
ejpam-3949	199	20	is	be	AUX
ejpam-3949	199	21	not	not	PART
ejpam-3949	199	22	defined	define	VERB
ejpam-3949	199	23	at	at	ADP
ejpam-3949	199	24	y	y	PROPN
ejpam-3949	199	25	=	=	SYM
ejpam-3949	199	26	−1	−1	NOUN
ejpam-3949	199	27	.	.	PUNCT
ejpam-3949	200	1	the	the	DET
ejpam-3949	200	2	desired	desire	VERB
ejpam-3949	200	3	branches	branch	NOUN
ejpam-3949	200	4	are	be	AUX
ejpam-3949	200	5	completely	completely	ADV
ejpam-3949	200	6	determined	determined	ADJ
ejpam-3949	200	7	as	as	SCONJ
ejpam-3949	200	8	follows	follow	VERB
ejpam-3949	200	9	:	:	PUNCT
ejpam-3949	200	10	(	(	PUNCT
ejpam-3949	200	11	i	i	NOUN
ejpam-3949	200	12	)	)	PUNCT
ejpam-3949	200	13	if	if	SCONJ
ejpam-3949	200	14	δ1	δ1	VERB
ejpam-3949	200	15	<	<	X
ejpam-3949	200	16	y	y	X
ejpam-3949	200	17	<	<	X
ejpam-3949	200	18	0	0	PROPN
ejpam-3949	200	19	,	,	PUNCT
ejpam-3949	200	20	then	then	ADV
ejpam-3949	200	21	a(y+1	a(y+1	PROPN
ejpam-3949	200	22	)	)	PUNCT
ejpam-3949	200	23	ln(by)+y+a+c+1	ln(by)+y+a+c+1	NOUN
ejpam-3949	200	24	<	<	X
ejpam-3949	200	25	0	0	X
ejpam-3949	200	26	.	.	PUNCT
ejpam-3949	201	1	this	this	PRON
ejpam-3949	201	2	gives	give	VERB
ejpam-3949	201	3	dy	dy	ADP
ejpam-3949	201	4	dx	dx	PROPN
ejpam-3949	201	5	<	<	X
ejpam-3949	201	6	0	0	NUM
ejpam-3949	201	7	.	.	PUNCT
ejpam-3949	202	1	thus	thus	ADV
ejpam-3949	202	2	,	,	PUNCT
ejpam-3949	202	3	the	the	DET
ejpam-3949	202	4	function	function	NOUN
ejpam-3949	202	5	y	y	PROPN
ejpam-3949	202	6	=	=	PUNCT
ejpam-3949	202	7	wlt	wlt	PROPN
ejpam-3949	202	8	(	(	PUNCT
ejpam-3949	202	9	x	x	X
ejpam-3949	202	10	)	)	PUNCT
ejpam-3949	202	11	is	be	AUX
ejpam-3949	202	12	a	a	DET
ejpam-3949	202	13	decreasing	decrease	VERB
ejpam-3949	202	14	function	function	NOUN
ejpam-3949	202	15	with	with	ADP
ejpam-3949	202	16	domain	domain	NOUN
ejpam-3949	202	17	[	[	X
ejpam-3949	202	18	f(0	f(0	NOUN
ejpam-3949	202	19	)	)	PUNCT
ejpam-3949	202	20	,	,	PUNCT
ejpam-3949	202	21	f(δ1	f(δ1	NOUN
ejpam-3949	202	22	)	)	PUNCT
ejpam-3949	202	23	]	]	PUNCT
ejpam-3949	202	24	with	with	ADP
ejpam-3949	202	25	range	range	NOUN
ejpam-3949	202	26	[	[	X
ejpam-3949	202	27	δ1	δ1	NOUN
ejpam-3949	202	28	,	,	PUNCT
ejpam-3949	202	29	0	0	NUM
ejpam-3949	202	30	]	]	PUNCT
ejpam-3949	202	31	;	;	PUNCT
ejpam-3949	202	32	(	(	PUNCT
ejpam-3949	202	33	ii	ii	NOUN
ejpam-3949	202	34	)	)	PUNCT
ejpam-3949	202	35	if	if	SCONJ
ejpam-3949	202	36	δ2	δ2	VERB
ejpam-3949	202	37	≤	≤	PROPN
ejpam-3949	202	38	y	y	PROPN
ejpam-3949	202	39	≤	≤	NUM
ejpam-3949	202	40	δ1	δ1	NOUN
ejpam-3949	202	41	,	,	PUNCT
ejpam-3949	202	42	then	then	ADV
ejpam-3949	202	43	a(y	a(y	PROPN
ejpam-3949	202	44	+	+	CCONJ
ejpam-3949	202	45	1	1	X
ejpam-3949	202	46	)	)	PUNCT
ejpam-3949	202	47	ln(by	ln(by	NOUN
ejpam-3949	202	48	)	)	PUNCT
ejpam-3949	203	1	+	+	CCONJ
ejpam-3949	203	2	y	y	PROPN
ejpam-3949	203	3	+	+	NOUN
ejpam-3949	203	4	a+	a+	X
ejpam-3949	203	5	c	c	NOUN
ejpam-3949	203	6	+	+	ADP
ejpam-3949	203	7	1	1	NUM
ejpam-3949	203	8	>	>	SYM
ejpam-3949	203	9	0	0	NUM
ejpam-3949	203	10	.	.	PUNCT
ejpam-3949	204	1	this	this	PRON
ejpam-3949	204	2	gives	give	VERB
ejpam-3949	204	3	dy	dy	ADP
ejpam-3949	204	4	dx	dx	PROPN
ejpam-3949	204	5	>	>	X
ejpam-3949	204	6	0	0	PROPN
ejpam-3949	204	7	.	.	PUNCT
ejpam-3949	205	1	thus	thus	ADV
ejpam-3949	205	2	,	,	PUNCT
ejpam-3949	205	3	the	the	DET
ejpam-3949	205	4	function	function	NOUN
ejpam-3949	205	5	y	y	PROPN
ejpam-3949	205	6	=	=	PUNCT
ejpam-3949	205	7	wlt	wlt	PROPN
ejpam-3949	205	8	(	(	PUNCT
ejpam-3949	205	9	x	x	X
ejpam-3949	205	10	)	)	PUNCT
ejpam-3949	205	11	is	be	AUX
ejpam-3949	205	12	increasing	increase	VERB
ejpam-3949	205	13	function	function	NOUN
ejpam-3949	205	14	with	with	ADP
ejpam-3949	205	15	domain	domain	NOUN
ejpam-3949	205	16	[	[	X
ejpam-3949	205	17	f(δ2	f(δ2	NOUN
ejpam-3949	205	18	)	)	PUNCT
ejpam-3949	205	19	,	,	PUNCT
ejpam-3949	205	20	f(δ1	f(δ1	NOUN
ejpam-3949	205	21	)	)	PUNCT
ejpam-3949	205	22	]	]	PUNCT
ejpam-3949	205	23	and	and	CCONJ
ejpam-3949	205	24	range	range	VERB
ejpam-3949	205	25	[	[	X
ejpam-3949	205	26	δ2	δ2	VERB
ejpam-3949	205	27	,	,	PUNCT
ejpam-3949	205	28	δ1	δ1	NOUN
ejpam-3949	205	29	]	]	X
ejpam-3949	205	30	;	;	PUNCT
ejpam-3949	205	31	(	(	PUNCT
ejpam-3949	205	32	iii	iii	X
ejpam-3949	205	33	)	)	PUNCT
ejpam-3949	205	34	if	if	SCONJ
ejpam-3949	205	35	−∞	−∞	ADP
ejpam-3949	205	36	<	<	X
ejpam-3949	205	37	y	y	X
ejpam-3949	205	38	<	<	X
ejpam-3949	205	39	δ2	δ2	PROPN
ejpam-3949	205	40	,	,	PUNCT
ejpam-3949	205	41	then	then	ADV
ejpam-3949	205	42	a(y+	a(y+	PROPN
ejpam-3949	205	43	1	1	X
ejpam-3949	205	44	)	)	PUNCT
ejpam-3949	205	45	ln(by	ln(by	PROPN
ejpam-3949	205	46	)	)	PUNCT
ejpam-3949	206	1	+	+	CCONJ
ejpam-3949	206	2	y+a+c	y+a+c	NUM
ejpam-3949	206	3	+	+	SYM
ejpam-3949	206	4	1	1	NUM
ejpam-3949	206	5	<	<	X
ejpam-3949	206	6	0	0	NUM
ejpam-3949	206	7	.	.	PUNCT
ejpam-3949	207	1	this	this	PRON
ejpam-3949	207	2	gives	give	VERB
ejpam-3949	207	3	dy	dy	ADP
ejpam-3949	207	4	dx	dx	PROPN
ejpam-3949	207	5	<	<	X
ejpam-3949	207	6	0	0	NUM
ejpam-3949	207	7	.	.	PUNCT
ejpam-3949	208	1	thus	thus	ADV
ejpam-3949	208	2	y	y	PROPN
ejpam-3949	208	3	=	=	SYM
ejpam-3949	208	4	wlt	wlt	PROPN
ejpam-3949	208	5	(	(	PUNCT
ejpam-3949	208	6	x	x	X
ejpam-3949	208	7	)	)	PUNCT
ejpam-3949	208	8	is	be	AUX
ejpam-3949	208	9	a	a	DET
ejpam-3949	208	10	decreasing	decrease	VERB
ejpam-3949	208	11	function	function	NOUN
ejpam-3949	208	12	with	with	ADP
ejpam-3949	208	13	domain	domain	NOUN
ejpam-3949	208	14	[	[	X
ejpam-3949	208	15	f(δ2	f(δ2	NOUN
ejpam-3949	208	16	)	)	PUNCT
ejpam-3949	208	17	,	,	PUNCT
ejpam-3949	208	18	0	0	NUM
ejpam-3949	208	19	)	)	PUNCT
ejpam-3949	208	20	and	and	CCONJ
ejpam-3949	208	21	range	range	NOUN
ejpam-3949	208	22	(	(	PUNCT
ejpam-3949	208	23	−∞	−∞	NOUN
ejpam-3949	208	24	,	,	PUNCT
ejpam-3949	208	25	δ2	δ2	VERB
ejpam-3949	208	26	]	]	PUNCT
ejpam-3949	208	27	.	.	PUNCT
ejpam-3949	209	1	the	the	DET
ejpam-3949	209	2	case	case	NOUN
ejpam-3949	209	3	where	where	SCONJ
ejpam-3949	209	4	b	b	X
ejpam-3949	209	5	<	<	X
ejpam-3949	209	6	0	0	NUM
ejpam-3949	209	7	,	,	PUNCT
ejpam-3949	209	8	a	a	DET
ejpam-3949	209	9	<	<	X
ejpam-3949	209	10	0	0	NUM
ejpam-3949	209	11	,	,	PUNCT
ejpam-3949	209	12	c	c	NOUN
ejpam-3949	209	13	≤	≤	NUM
ejpam-3949	209	14	|a|	|a|	NOUN
ejpam-3949	209	15	can	can	AUX
ejpam-3949	209	16	be	be	AUX
ejpam-3949	209	17	proved	prove	VERB
ejpam-3949	209	18	similarly	similarly	ADV
ejpam-3949	209	19	.	.	PUNCT
ejpam-3949	210	1	figures	figure	NOUN
ejpam-3949	210	2	1	1	NUM
ejpam-3949	210	3	and	and	CCONJ
ejpam-3949	210	4	2	2	NUM
ejpam-3949	210	5	depict	depict	VERB
ejpam-3949	210	6	the	the	DET
ejpam-3949	210	7	graphs	graph	NOUN
ejpam-3949	210	8	of	of	ADP
ejpam-3949	210	9	the	the	DET
ejpam-3949	210	10	translated	translate	VERB
ejpam-3949	210	11	logarithmic	logarithmic	ADJ
ejpam-3949	210	12	lambert	lambert	PROPN
ejpam-3949	210	13	function	function	PROPN
ejpam-3949	210	14	(	(	PUNCT
ejpam-3949	210	15	red	red	ADJ
ejpam-3949	210	16	color	color	NOUN
ejpam-3949	210	17	graphs	graph	NOUN
ejpam-3949	210	18	)	)	PUNCT
ejpam-3949	210	19	when	when	SCONJ
ejpam-3949	210	20	b	b	X
ejpam-3949	210	21	=	=	SYM
ejpam-3949	210	22	1	1	NUM
ejpam-3949	210	23	and	and	CCONJ
ejpam-3949	210	24	b	b	NOUN
ejpam-3949	210	25	=	=	SYM
ejpam-3949	210	26	−1	−1	NOUN
ejpam-3949	210	27	.	.	PUNCT
ejpam-3949	211	1	the	the	DET
ejpam-3949	211	2	y	y	NOUN
ejpam-3949	211	3	-	-	PUNCT
ejpam-3949	211	4	coordinates	coordinate	NOUN
ejpam-3949	211	5	of	of	ADP
ejpam-3949	211	6	the	the	DET
ejpam-3949	211	7	points	point	NOUN
ejpam-3949	211	8	of	of	ADP
ejpam-3949	211	9	intersection	intersection	NOUN
ejpam-3949	211	10	of	of	ADP
ejpam-3949	211	11	the	the	DET
ejpam-3949	211	12	blue	blue	ADJ
ejpam-3949	211	13	and	and	CCONJ
ejpam-3949	211	14	black	black	ADJ
ejpam-3949	211	15	colored	colored	ADJ
ejpam-3949	211	16	graphs	graph	NOUN
ejpam-3949	211	17	correspond	correspond	VERB
ejpam-3949	211	18	to	to	ADP
ejpam-3949	211	19	the	the	DET
ejpam-3949	211	20	value	value	NOUN
ejpam-3949	211	21	of	of	ADP
ejpam-3949	211	22	δ	δ	PROPN
ejpam-3949	211	23	,	,	PUNCT
ejpam-3949	211	24	δ1	δ1	NOUN
ejpam-3949	211	25	and	and	CCONJ
ejpam-3949	211	26	δ2	δ2	PROPN
ejpam-3949	211	27	.	.	PUNCT
ejpam-3949	212	1	c.	c.	PROPN
ejpam-3949	212	2	corcino	corcino	PROPN
ejpam-3949	212	3	,	,	PUNCT
ejpam-3949	212	4	r.	r.	PROPN
ejpam-3949	212	5	corcino	corcino	PROPN
ejpam-3949	212	6	/	/	SYM
ejpam-3949	212	7	eur	eur	PROPN
ejpam-3949	212	8	.	.	PUNCT
ejpam-3949	213	1	j.	j.	PROPN
ejpam-3949	213	2	pure	pure	PROPN
ejpam-3949	213	3	appl	appl	PROPN
ejpam-3949	213	4	.	.	PROPN
ejpam-3949	213	5	math	math	PROPN
ejpam-3949	213	6	,	,	PUNCT
ejpam-3949	213	7	14	14	NUM
ejpam-3949	213	8	(	(	PUNCT
ejpam-3949	213	9	2	2	NUM
ejpam-3949	213	10	)	)	PUNCT
ejpam-3949	213	11	(	(	PUNCT
ejpam-3949	213	12	2021	2021	NUM
ejpam-3949	213	13	)	)	PUNCT
ejpam-3949	213	14	,	,	PUNCT
ejpam-3949	213	15	506	506	NUM
ejpam-3949	213	16	-	-	SYM
ejpam-3949	213	17	520	520	NUM
ejpam-3949	213	18	515	515	NUM
ejpam-3949	213	19	figure	figure	NOUN
ejpam-3949	213	20	1	1	NUM
ejpam-3949	213	21	.	.	PUNCT
ejpam-3949	214	1	graph	graph	NOUN
ejpam-3949	214	2	of	of	ADP
ejpam-3949	214	3	translated	translate	VERB
ejpam-3949	214	4	logarithmic	logarithmic	ADJ
ejpam-3949	214	5	lambert	lambert	PROPN
ejpam-3949	214	6	function	function	NOUN
ejpam-3949	214	7	with	with	ADP
ejpam-3949	214	8	b	b	NOUN
ejpam-3949	214	9	=	=	SYM
ejpam-3949	214	10	1	1	NUM
ejpam-3949	214	11	,	,	PUNCT
ejpam-3949	214	12	a	a	DET
ejpam-3949	214	13	=	=	SYM
ejpam-3949	214	14	2	2	NUM
ejpam-3949	214	15	,	,	PUNCT
ejpam-3949	214	16	c	c	NOUN
ejpam-3949	214	17	=	=	SYM
ejpam-3949	214	18	1	1	X
ejpam-3949	214	19	.	.	PUNCT
ejpam-3949	215	1	the	the	DET
ejpam-3949	215	2	graphs	graph	NOUN
ejpam-3949	215	3	with	with	ADP
ejpam-3949	215	4	red	red	ADJ
ejpam-3949	215	5	,	,	PUNCT
ejpam-3949	215	6	blue	blue	ADJ
ejpam-3949	215	7	and	and	CCONJ
ejpam-3949	215	8	black	black	ADJ
ejpam-3949	215	9	colors	color	NOUN
ejpam-3949	215	10	are	be	AUX
ejpam-3949	215	11	the	the	DET
ejpam-3949	215	12	graphs	graph	NOUN
ejpam-3949	215	13	of	of	ADP
ejpam-3949	215	14	x	x	X
ejpam-3949	215	15	=	=	SYM
ejpam-3949	215	16	f(y	f(y	NOUN
ejpam-3949	215	17	)	)	PUNCT
ejpam-3949	215	18	,	,	PUNCT
ejpam-3949	215	19	x	x	X
ejpam-3949	215	20	=	=	PUNCT
ejpam-3949	215	21	g(y	g(y	NOUN
ejpam-3949	215	22	)	)	PUNCT
ejpam-3949	215	23	and	and	CCONJ
ejpam-3949	215	24	x	x	X
ejpam-3949	215	25	=	=	PUNCT
ejpam-3949	215	26	h(y	h(y	NOUN
ejpam-3949	215	27	)	)	PUNCT
ejpam-3949	215	28	,	,	PUNCT
ejpam-3949	215	29	respectively	respectively	ADV
ejpam-3949	215	30	.	.	PUNCT
ejpam-3949	216	1	figure	figure	NOUN
ejpam-3949	216	2	2	2	NUM
ejpam-3949	216	3	.	.	PUNCT
ejpam-3949	216	4	graph	graph	NOUN
ejpam-3949	216	5	of	of	ADP
ejpam-3949	216	6	translated	translate	VERB
ejpam-3949	216	7	logarithmic	logarithmic	ADJ
ejpam-3949	216	8	lambert	lambert	PROPN
ejpam-3949	216	9	function	function	NOUN
ejpam-3949	216	10	with	with	ADP
ejpam-3949	216	11	b	b	PROPN
ejpam-3949	216	12	=	=	SYM
ejpam-3949	216	13	−1	−1	NOUN
ejpam-3949	216	14	,	,	PUNCT
ejpam-3949	216	15	a	a	DET
ejpam-3949	216	16	=	=	ADJ
ejpam-3949	216	17	−2	−2	NOUN
ejpam-3949	216	18	,	,	PUNCT
ejpam-3949	216	19	c	c	NOUN
ejpam-3949	216	20	=	=	SYM
ejpam-3949	216	21	1	1	X
ejpam-3949	216	22	.	.	PUNCT
ejpam-3949	217	1	the	the	DET
ejpam-3949	217	2	graphs	graph	NOUN
ejpam-3949	217	3	with	with	ADP
ejpam-3949	217	4	red	red	ADJ
ejpam-3949	217	5	,	,	PUNCT
ejpam-3949	217	6	blue	blue	ADJ
ejpam-3949	217	7	and	and	CCONJ
ejpam-3949	217	8	black	black	ADJ
ejpam-3949	217	9	colors	color	NOUN
ejpam-3949	217	10	are	be	AUX
ejpam-3949	217	11	the	the	DET
ejpam-3949	217	12	graphs	graph	NOUN
ejpam-3949	217	13	of	of	ADP
ejpam-3949	217	14	x	x	X
ejpam-3949	217	15	=	=	SYM
ejpam-3949	217	16	f(y	f(y	NOUN
ejpam-3949	217	17	)	)	PUNCT
ejpam-3949	217	18	,	,	PUNCT
ejpam-3949	217	19	x	x	X
ejpam-3949	217	20	=	=	PUNCT
ejpam-3949	217	21	g(y	g(y	NOUN
ejpam-3949	217	22	)	)	PUNCT
ejpam-3949	217	23	and	and	CCONJ
ejpam-3949	217	24	x	x	X
ejpam-3949	217	25	=	=	PUNCT
ejpam-3949	217	26	h(y	h(y	NOUN
ejpam-3949	217	27	)	)	PUNCT
ejpam-3949	217	28	,	,	PUNCT
ejpam-3949	217	29	respectively	respectively	ADV
ejpam-3949	217	30	.	.	PUNCT
ejpam-3949	218	1	3	3	X
ejpam-3949	218	2	.	.	X
ejpam-3949	218	3	applications	application	NOUN
ejpam-3949	218	4	to	to	PART
ejpam-3949	218	5	entropy	entropy	VERB
ejpam-3949	218	6	in	in	ADP
ejpam-3949	218	7	this	this	DET
ejpam-3949	218	8	section	section	NOUN
ejpam-3949	218	9	,	,	PUNCT
ejpam-3949	218	10	application	application	NOUN
ejpam-3949	218	11	of	of	ADP
ejpam-3949	218	12	the	the	DET
ejpam-3949	218	13	translated	translate	VERB
ejpam-3949	218	14	logarithmic	logarithmic	ADJ
ejpam-3949	218	15	lambert	lambert	PROPN
ejpam-3949	218	16	function	function	NOUN
ejpam-3949	218	17	to	to	PART
ejpam-3949	218	18	entropy	entropy	VERB
ejpam-3949	218	19	in	in	ADP
ejpam-3949	218	20	canonical	canonical	ADJ
ejpam-3949	218	21	ensemble	ensemble	ADJ
ejpam-3949	218	22	is	be	AUX
ejpam-3949	218	23	derived	derive	VERB
ejpam-3949	218	24	.	.	PUNCT
ejpam-3949	219	1	parallel	parallel	ADJ
ejpam-3949	219	2	to	to	ADP
ejpam-3949	219	3	the	the	DET
ejpam-3949	219	4	two	two	NUM
ejpam-3949	219	5	-	-	PUNCT
ejpam-3949	219	6	parameter	parameter	NOUN
ejpam-3949	219	7	entropy	entropy	NOUN
ejpam-3949	219	8	in	in	ADP
ejpam-3949	219	9	(	(	PUNCT
ejpam-3949	219	10	4	4	NUM
ejpam-3949	219	11	)	)	PUNCT
ejpam-3949	219	12	,	,	PUNCT
ejpam-3949	219	13	the	the	DET
ejpam-3949	219	14	three	three	NUM
ejpam-3949	219	15	-	-	PUNCT
ejpam-3949	219	16	parameter	parameter	NOUN
ejpam-3949	219	17	entropy	entropy	NOUN
ejpam-3949	219	18	,	,	PUNCT
ejpam-3949	219	19	denoted	denote	VERB
ejpam-3949	219	20	by	by	ADP
ejpam-3949	219	21	sq	sq	PROPN
ejpam-3949	219	22	,	,	PUNCT
ejpam-3949	219	23	q′,r	q′,r	PROPN
ejpam-3949	219	24	,	,	PUNCT
ejpam-3949	219	25	can	can	AUX
ejpam-3949	219	26	also	also	ADV
ejpam-3949	219	27	be	be	AUX
ejpam-3949	219	28	constructed	construct	VERB
ejpam-3949	219	29	based	base	VERB
ejpam-3949	219	30	on	on	ADP
ejpam-3949	219	31	the	the	DET
ejpam-3949	219	32	c.	c.	PROPN
ejpam-3949	219	33	corcino	corcino	PROPN
ejpam-3949	219	34	,	,	PUNCT
ejpam-3949	219	35	r.	r.	PROPN
ejpam-3949	219	36	corcino	corcino	PROPN
ejpam-3949	219	37	/	/	SYM
ejpam-3949	219	38	eur	eur	PROPN
ejpam-3949	219	39	.	.	PUNCT
ejpam-3949	220	1	j.	j.	PROPN
ejpam-3949	220	2	pure	pure	PROPN
ejpam-3949	220	3	appl	appl	PROPN
ejpam-3949	220	4	.	.	PROPN
ejpam-3949	220	5	math	math	PROPN
ejpam-3949	220	6	,	,	PUNCT
ejpam-3949	220	7	14	14	NUM
ejpam-3949	220	8	(	(	PUNCT
ejpam-3949	220	9	2	2	NUM
ejpam-3949	220	10	)	)	PUNCT
ejpam-3949	220	11	(	(	PUNCT
ejpam-3949	220	12	2021	2021	NUM
ejpam-3949	220	13	)	)	PUNCT
ejpam-3949	220	14	,	,	PUNCT
ejpam-3949	220	15	506	506	NUM
ejpam-3949	220	16	-	-	SYM
ejpam-3949	220	17	520	520	NUM
ejpam-3949	220	18	516	516	NUM
ejpam-3949	220	19	three	three	NUM
ejpam-3949	220	20	-	-	PUNCT
ejpam-3949	220	21	parameter	parameter	NOUN
ejpam-3949	220	22	logarithm	logarithm	NOUN
ejpam-3949	220	23	as	as	SCONJ
ejpam-3949	220	24	follows	follow	VERB
ejpam-3949	220	25	:	:	PUNCT
ejpam-3949	220	26	sq	sq	ADJ
ejpam-3949	220	27	,	,	PUNCT
ejpam-3949	220	28	q′,r	q′,r	PROPN
ejpam-3949	220	29	=	=	PROPN
ejpam-3949	220	30	k	k	PROPN
ejpam-3949	220	31	ω∑	ω∑	PROPN
ejpam-3949	220	32	i=1	i=1	PROPN
ejpam-3949	221	1	pi	pi	PROPN
ejpam-3949	221	2	lnq	lnq	PROPN
ejpam-3949	221	3	,	,	PUNCT
ejpam-3949	221	4	q′,r	q′,r	PROPN
ejpam-3949	221	5	1	1	NUM
ejpam-3949	221	6	pi	pi	NOUN
ejpam-3949	221	7	(	(	PUNCT
ejpam-3949	221	8	24	24	NUM
ejpam-3949	221	9	)	)	PUNCT
ejpam-3949	221	10	=	=	PUNCT
ejpam-3949	222	1	k	k	PROPN
ejpam-3949	222	2	ω∑	ω∑	PUNCT
ejpam-3949	222	3	i=1	i=1	PROPN
ejpam-3949	222	4	pi	pi	NOUN
ejpam-3949	222	5	1	1	NUM
ejpam-3949	222	6	1−	1−	NUM
ejpam-3949	222	7	r	r	NOUN
ejpam-3949	222	8	(	(	PUNCT
ejpam-3949	222	9	exp	exp	NOUN
ejpam-3949	222	10	(	(	PUNCT
ejpam-3949	222	11	1−	1−	NUM
ejpam-3949	222	12	r	r	NOUN
ejpam-3949	222	13	1−	1−	NUM
ejpam-3949	222	14	q′	q′	NOUN
ejpam-3949	222	15	(	(	PUNCT
ejpam-3949	222	16	e(1−q	e(1−q	PROPN
ejpam-3949	222	17	′	′	PROPN
ejpam-3949	222	18	)	)	PUNCT
ejpam-3949	222	19	lnq	lnq	NOUN
ejpam-3949	223	1	x	x	X
ejpam-3949	223	2	−	−	PROPN
ejpam-3949	223	3	1	1	NUM
ejpam-3949	223	4	)	)	PUNCT
ejpam-3949	223	5	−	−	PROPN
ejpam-3949	223	6	1	1	NUM
ejpam-3949	223	7	)	)	PUNCT
ejpam-3949	223	8	)	)	PUNCT
ejpam-3949	223	9	(	(	PUNCT
ejpam-3949	223	10	25	25	NUM
ejpam-3949	223	11	)	)	PUNCT
ejpam-3949	223	12	where	where	SCONJ
ejpam-3949	223	13	x	x	SYM
ejpam-3949	223	14	=	=	SYM
ejpam-3949	223	15	1	1	NUM
ejpam-3949	223	16	pi	pi	NOUN
ejpam-3949	223	17	.	.	PUNCT
ejpam-3949	224	1	in	in	ADP
ejpam-3949	224	2	maximizing	maximize	VERB
ejpam-3949	224	3	sq	sq	PROPN
ejpam-3949	224	4	,	,	PUNCT
ejpam-3949	224	5	q′,r	q′,r	PROPN
ejpam-3949	224	6	,	,	PUNCT
ejpam-3949	224	7	the	the	DET
ejpam-3949	224	8	following	follow	VERB
ejpam-3949	224	9	constraints	constraint	NOUN
ejpam-3949	224	10	are	be	AUX
ejpam-3949	224	11	to	to	PART
ejpam-3949	224	12	be	be	AUX
ejpam-3949	224	13	considered	consider	VERB
ejpam-3949	224	14	:	:	PUNCT
ejpam-3949	225	1	ω∑	ω∑	ADP
ejpam-3949	225	2	i=1	i=1	PROPN
ejpam-3949	225	3	pi	pi	NOUN
ejpam-3949	225	4	−	−	PROPN
ejpam-3949	226	1	1	1	NUM
ejpam-3949	226	2	=	=	SYM
ejpam-3949	226	3	0	0	NUM
ejpam-3949	226	4	(	(	PUNCT
ejpam-3949	226	5	26	26	NUM
ejpam-3949	226	6	)	)	PUNCT
ejpam-3949	226	7	ω∑	ω∑	ADP
ejpam-3949	226	8	i=1	i=1	PROPN
ejpam-3949	226	9	piεi	piεi	VERB
ejpam-3949	226	10	−	−	NOUN
ejpam-3949	226	11	e	e	NOUN
ejpam-3949	226	12	=	=	NOUN
ejpam-3949	226	13	0	0	PROPN
ejpam-3949	226	14	.	.	PUNCT
ejpam-3949	227	1	(	(	PUNCT
ejpam-3949	227	2	27	27	NUM
ejpam-3949	227	3	)	)	PUNCT
ejpam-3949	227	4	now	now	ADV
ejpam-3949	227	5	,	,	PUNCT
ejpam-3949	227	6	we	we	PRON
ejpam-3949	227	7	construct	construct	VERB
ejpam-3949	227	8	the	the	DET
ejpam-3949	227	9	three	three	NUM
ejpam-3949	227	10	-	-	PUNCT
ejpam-3949	227	11	parameter	parameter	NOUN
ejpam-3949	227	12	entropic	entropic	ADJ
ejpam-3949	227	13	functional	functional	ADJ
ejpam-3949	227	14	,	,	PUNCT
ejpam-3949	227	15	denoted	denote	VERB
ejpam-3949	227	16	by	by	ADP
ejpam-3949	227	17	φq	φq	NOUN
ejpam-3949	227	18	,	,	PUNCT
ejpam-3949	227	19	q′,r	q′,r	PROPN
ejpam-3949	227	20	,	,	PUNCT
ejpam-3949	227	21	by	by	ADP
ejpam-3949	227	22	adding	add	VERB
ejpam-3949	227	23	the	the	DET
ejpam-3949	227	24	above	above	ADJ
ejpam-3949	227	25	constraints	constraint	NOUN
ejpam-3949	227	26	(	(	PUNCT
ejpam-3949	227	27	26	26	NUM
ejpam-3949	227	28	)	)	PUNCT
ejpam-3949	227	29	and	and	CCONJ
ejpam-3949	227	30	(	(	PUNCT
ejpam-3949	227	31	27	27	NUM
ejpam-3949	227	32	)	)	PUNCT
ejpam-3949	227	33	to	to	ADP
ejpam-3949	227	34	the	the	DET
ejpam-3949	227	35	entropy	entropy	PROPN
ejpam-3949	227	36	sq	sq	PROPN
ejpam-3949	227	37	,	,	PUNCT
ejpam-3949	227	38	q′,r	q′,r	VERB
ejpam-3949	227	39	with	with	ADP
ejpam-3949	227	40	lagrange	lagrange	NOUN
ejpam-3949	227	41	multipliers	multiplier	NOUN
ejpam-3949	227	42	.	.	PUNCT
ejpam-3949	228	1	that	that	PRON
ejpam-3949	228	2	is	is	ADV
ejpam-3949	228	3	,	,	PUNCT
ejpam-3949	228	4	φq	φq	ADP
ejpam-3949	228	5	,	,	PUNCT
ejpam-3949	228	6	q′,r(pi	q′,r(pi	NOUN
ejpam-3949	228	7	,	,	PUNCT
ejpam-3949	228	8	α	α	NOUN
ejpam-3949	228	9	,	,	PUNCT
ejpam-3949	228	10	β	β	NOUN
ejpam-3949	228	11	)	)	PUNCT
ejpam-3949	228	12	=	=	SYM
ejpam-3949	229	1	1	1	NUM
ejpam-3949	229	2	k	k	PROPN
ejpam-3949	229	3	sq	sq	PROPN
ejpam-3949	229	4	,	,	PUNCT
ejpam-3949	229	5	q′,r	q′,r	PROPN
ejpam-3949	229	6	+	+	X
ejpam-3949	229	7	α	α	PROPN
ejpam-3949	229	8	(	(	PUNCT
ejpam-3949	229	9	ω∑	ω∑	ADP
ejpam-3949	229	10	i=1	i=1	PROPN
ejpam-3949	229	11	pi	pi	NOUN
ejpam-3949	229	12	−	−	PROPN
ejpam-3949	229	13	1	1	NUM
ejpam-3949	229	14	)	)	PUNCT
ejpam-3949	229	15	+	+	CCONJ
ejpam-3949	229	16	β	β	X
ejpam-3949	229	17	(	(	PUNCT
ejpam-3949	229	18	ω∑	ω∑	ADP
ejpam-3949	229	19	i=1	i=1	PROPN
ejpam-3949	229	20	piεi	piεi	VERB
ejpam-3949	229	21	−	−	PROPN
ejpam-3949	229	22	e	e	NOUN
ejpam-3949	229	23	)	)	PUNCT
ejpam-3949	229	24	.	.	PUNCT
ejpam-3949	230	1	(	(	PUNCT
ejpam-3949	230	2	28	28	NUM
ejpam-3949	230	3	)	)	PUNCT
ejpam-3949	230	4	the	the	DET
ejpam-3949	230	5	entropic	entropic	ADJ
ejpam-3949	230	6	functional	functional	ADJ
ejpam-3949	230	7	φq	φq	ADP
ejpam-3949	230	8	,	,	PUNCT
ejpam-3949	230	9	q′,r	q′,r	PROPN
ejpam-3949	230	10	should	should	AUX
ejpam-3949	230	11	be	be	AUX
ejpam-3949	230	12	maximized	maximize	VERB
ejpam-3949	230	13	in	in	ADP
ejpam-3949	230	14	order	order	NOUN
ejpam-3949	230	15	to	to	PART
ejpam-3949	230	16	reach	reach	VERB
ejpam-3949	230	17	the	the	DET
ejpam-3949	230	18	equilibrium	equilibrium	NOUN
ejpam-3949	230	19	state	state	NOUN
ejpam-3949	230	20	.	.	PUNCT
ejpam-3949	231	1	hence	hence	ADV
ejpam-3949	231	2	,	,	PUNCT
ejpam-3949	231	3	∂φq	∂φq	PROPN
ejpam-3949	231	4	,	,	PUNCT
ejpam-3949	231	5	q′,r(pi	q′,r(pi	PROPN
ejpam-3949	231	6	,	,	PUNCT
ejpam-3949	231	7	α	α	NOUN
ejpam-3949	231	8	,	,	PUNCT
ejpam-3949	231	9	β	β	NOUN
ejpam-3949	231	10	)	)	PUNCT
ejpam-3949	231	11	∂pi	∂pi	NOUN
ejpam-3949	231	12	=	=	NOUN
ejpam-3949	231	13	1	1	NUM
ejpam-3949	231	14	k	k	PROPN
ejpam-3949	231	15	∂sq	∂sq	PROPN
ejpam-3949	231	16	,	,	PUNCT
ejpam-3949	231	17	q′,r	q′,r	PROPN
ejpam-3949	231	18	∂pi	∂pi	PROPN
ejpam-3949	231	19	+	+	CCONJ
ejpam-3949	231	20	α+	α+	PUNCT
ejpam-3949	231	21	βεi	βεi	NOUN
ejpam-3949	231	22	=	=	NOUN
ejpam-3949	231	23	0	0	X
ejpam-3949	231	24	.	.	PUNCT
ejpam-3949	232	1	(	(	PUNCT
ejpam-3949	232	2	29	29	NUM
ejpam-3949	232	3	)	)	PUNCT
ejpam-3949	232	4	note	note	VERB
ejpam-3949	232	5	that	that	SCONJ
ejpam-3949	232	6	1	1	NUM
ejpam-3949	232	7	k	k	PROPN
ejpam-3949	232	8	∂sq	∂sq	PROPN
ejpam-3949	232	9	,	,	PUNCT
ejpam-3949	232	10	q′,r	q′,r	PROPN
ejpam-3949	232	11	∂pi	∂pi	PROPN
ejpam-3949	232	12	=	=	PROPN
ejpam-3949	232	13	pi	pi	PROPN
ejpam-3949	232	14	∂	∂	NUM
ejpam-3949	232	15	lnq	lnq	NOUN
ejpam-3949	232	16	,	,	PUNCT
ejpam-3949	232	17	q′,r	q′,r	PROPN
ejpam-3949	232	18	1	1	NUM
ejpam-3949	232	19	pi	pi	NOUN
ejpam-3949	232	20	∂pi	∂pi	PROPN
ejpam-3949	233	1	+	+	CCONJ
ejpam-3949	233	2	lnq	lnq	PROPN
ejpam-3949	233	3	,	,	PUNCT
ejpam-3949	233	4	q′,r	q′,r	PROPN
ejpam-3949	233	5	1	1	NUM
ejpam-3949	233	6	pi	pi	NOUN
ejpam-3949	233	7	(	(	PUNCT
ejpam-3949	233	8	30	30	NUM
ejpam-3949	233	9	)	)	PUNCT
ejpam-3949	233	10	with	with	ADP
ejpam-3949	233	11	∂	∂	PROPN
ejpam-3949	233	12	lnq	lnq	NOUN
ejpam-3949	233	13	,	,	PUNCT
ejpam-3949	233	14	q′,r	q′,r	PROPN
ejpam-3949	233	15	1	1	NUM
ejpam-3949	233	16	pi	pi	NOUN
ejpam-3949	233	17	∂pi	∂pi	NOUN
ejpam-3949	233	18	=	=	NOUN
ejpam-3949	233	19	1	1	NUM
ejpam-3949	233	20	1−	1−	NUM
ejpam-3949	233	21	r	r	NOUN
ejpam-3949	233	22	exp	exp	NOUN
ejpam-3949	233	23	(	(	PUNCT
ejpam-3949	233	24	1−	1−	NUM
ejpam-3949	233	25	r	r	NOUN
ejpam-3949	233	26	1−	1−	NUM
ejpam-3949	233	27	q′	q′	NOUN
ejpam-3949	233	28	(	(	PUNCT
ejpam-3949	233	29	exp	exp	NOUN
ejpam-3949	233	30	(	(	PUNCT
ejpam-3949	233	31	1−	1−	NUM
ejpam-3949	233	32	q′	q′	NOUN
ejpam-3949	233	33	1−	1−	NUM
ejpam-3949	234	1	q	q	NOUN
ejpam-3949	235	1	(	(	PUNCT
ejpam-3949	235	2	pq−1i	pq−1i	NOUN
ejpam-3949	235	3	−	−	NOUN
ejpam-3949	235	4	1	1	NUM
ejpam-3949	235	5	)	)	PUNCT
ejpam-3949	235	6	)	)	PUNCT
ejpam-3949	236	1	−	−	PROPN
ejpam-3949	236	2	1	1	NUM
ejpam-3949	236	3	)	)	PUNCT
ejpam-3949	236	4	)	)	PUNCT
ejpam-3949	237	1	×	×	NOUN
ejpam-3949	237	2	1−	1−	NUM
ejpam-3949	237	3	r	r	NOUN
ejpam-3949	237	4	1−	1−	NUM
ejpam-3949	237	5	q′	q′	NOUN
ejpam-3949	237	6	exp	exp	NOUN
ejpam-3949	237	7	(	(	PUNCT
ejpam-3949	237	8	1−	1−	NUM
ejpam-3949	237	9	q′	q′	NOUN
ejpam-3949	237	10	1−	1−	NUM
ejpam-3949	238	1	q	q	NOUN
ejpam-3949	239	1	(	(	PUNCT
ejpam-3949	239	2	pq−1i	pq−1i	NOUN
ejpam-3949	239	3	−	−	NOUN
ejpam-3949	239	4	1	1	NUM
ejpam-3949	239	5	)	)	PUNCT
ejpam-3949	239	6	)	)	PUNCT
ejpam-3949	240	1	1−	1−	NUM
ejpam-3949	240	2	q′	q′	NOUN
ejpam-3949	240	3	1−	1−	NUM
ejpam-3949	240	4	q	q	NOUN
ejpam-3949	240	5	(	(	PUNCT
ejpam-3949	240	6	q	q	NOUN
ejpam-3949	240	7	−	−	PROPN
ejpam-3949	240	8	1)pq−2i	1)pq−2i	NUM
ejpam-3949	240	9	=	=	SYM
ejpam-3949	240	10	e−	e−	PROPN
ejpam-3949	240	11	1	1	NUM
ejpam-3949	240	12	1−r	1−r	NUM
ejpam-3949	240	13	exp	exp	NOUN
ejpam-3949	240	14	(	(	PUNCT
ejpam-3949	240	15	1−	1−	NUM
ejpam-3949	240	16	r	r	NOUN
ejpam-3949	240	17	1−	1−	NUM
ejpam-3949	240	18	q′	q′	NOUN
ejpam-3949	240	19	exp	exp	NOUN
ejpam-3949	240	20	(	(	PUNCT
ejpam-3949	240	21	1−	1−	NUM
ejpam-3949	240	22	q′	q′	NOUN
ejpam-3949	240	23	1−	1−	NUM
ejpam-3949	240	24	q	q	NOUN
ejpam-3949	240	25	(	(	PUNCT
ejpam-3949	240	26	pq−1i	pq−1i	NOUN
ejpam-3949	240	27	−	−	NOUN
ejpam-3949	240	28	1	1	NUM
ejpam-3949	240	29	)	)	PUNCT
ejpam-3949	240	30	)	)	PUNCT
ejpam-3949	240	31	)	)	PUNCT
ejpam-3949	241	1	×	×	NOUN
ejpam-3949	241	2	exp	exp	NOUN
ejpam-3949	241	3	(	(	PUNCT
ejpam-3949	241	4	1−	1−	NUM
ejpam-3949	241	5	q′	q′	NOUN
ejpam-3949	241	6	1−	1−	NUM
ejpam-3949	241	7	q	q	NOUN
ejpam-3949	241	8	(	(	PUNCT
ejpam-3949	241	9	pq−1i	pq−1i	NOUN
ejpam-3949	241	10	−	−	NOUN
ejpam-3949	241	11	1	1	NUM
ejpam-3949	241	12	)	)	PUNCT
ejpam-3949	241	13	)	)	PUNCT
ejpam-3949	241	14	(	(	PUNCT
ejpam-3949	241	15	−pq−2i	−pq−2i	NOUN
ejpam-3949	241	16	)	)	PUNCT
ejpam-3949	241	17	.	.	PUNCT
ejpam-3949	242	1	letting	let	VERB
ejpam-3949	242	2	u	u	NOUN
ejpam-3949	242	3	=	=	NOUN
ejpam-3949	242	4	exp	exp	X
ejpam-3949	242	5	(	(	PUNCT
ejpam-3949	242	6	1−	1−	NUM
ejpam-3949	242	7	q′	q′	NOUN
ejpam-3949	242	8	1−	1−	NUM
ejpam-3949	242	9	q	q	NOUN
ejpam-3949	242	10	(	(	PUNCT
ejpam-3949	242	11	pq−1i	pq−1i	NOUN
ejpam-3949	242	12	−	−	NOUN
ejpam-3949	242	13	1	1	NUM
ejpam-3949	242	14	)	)	PUNCT
ejpam-3949	242	15	)	)	PUNCT
ejpam-3949	242	16	(	(	PUNCT
ejpam-3949	242	17	31	31	NUM
ejpam-3949	242	18	)	)	PUNCT
ejpam-3949	242	19	c.	c.	NOUN
ejpam-3949	242	20	corcino	corcino	PROPN
ejpam-3949	242	21	,	,	PUNCT
ejpam-3949	242	22	r.	r.	PROPN
ejpam-3949	242	23	corcino	corcino	PROPN
ejpam-3949	242	24	/	/	SYM
ejpam-3949	242	25	eur	eur	PROPN
ejpam-3949	242	26	.	.	PUNCT
ejpam-3949	243	1	j.	j.	PROPN
ejpam-3949	243	2	pure	pure	PROPN
ejpam-3949	243	3	appl	appl	PROPN
ejpam-3949	243	4	.	.	PROPN
ejpam-3949	243	5	math	math	PROPN
ejpam-3949	243	6	,	,	PUNCT
ejpam-3949	243	7	14	14	NUM
ejpam-3949	243	8	(	(	PUNCT
ejpam-3949	243	9	2	2	NUM
ejpam-3949	243	10	)	)	PUNCT
ejpam-3949	243	11	(	(	PUNCT
ejpam-3949	243	12	2021	2021	NUM
ejpam-3949	243	13	)	)	PUNCT
ejpam-3949	243	14	,	,	PUNCT
ejpam-3949	243	15	506	506	NUM
ejpam-3949	243	16	-	-	SYM
ejpam-3949	243	17	520	520	NUM
ejpam-3949	243	18	517	517	NUM
ejpam-3949	243	19	yields	yield	NOUN
ejpam-3949	243	20	∂	∂	NUM
ejpam-3949	244	1	lnq	lnq	NOUN
ejpam-3949	245	1	,	,	PUNCT
ejpam-3949	245	2	q′,r	q′,r	PROPN
ejpam-3949	245	3	1	1	NUM
ejpam-3949	245	4	pi	pi	NOUN
ejpam-3949	245	5	∂pi	∂pi	NOUN
ejpam-3949	245	6	=	=	SYM
ejpam-3949	246	1	e	e	X
ejpam-3949	246	2	−	−	PROPN
ejpam-3949	246	3	1−r	1−r	NUM
ejpam-3949	246	4	1−q′	1−q′	NUM
ejpam-3949	246	5	e	e	SYM
ejpam-3949	246	6	1−r	1−r	PROPN
ejpam-3949	246	7	1−q′	1−q′	NUM
ejpam-3949	246	8	uu(−pq−2i	uu(−pq−2i	PROPN
ejpam-3949	246	9	)	)	PUNCT
ejpam-3949	246	10	.	.	PUNCT
ejpam-3949	247	1	then	then	ADV
ejpam-3949	247	2	∂φq	∂φq	PROPN
ejpam-3949	247	3	,	,	PUNCT
ejpam-3949	247	4	q′,r(pi	q′,r(pi	PROPN
ejpam-3949	247	5	,	,	PUNCT
ejpam-3949	247	6	α	α	NOUN
ejpam-3949	247	7	,	,	PUNCT
ejpam-3949	247	8	β	β	NOUN
ejpam-3949	247	9	)	)	PUNCT
ejpam-3949	247	10	∂pi	∂pi	NOUN
ejpam-3949	247	11	=	=	SYM
ejpam-3949	247	12	−pq−1i	−pq−1i	PROPN
ejpam-3949	247	13	e	e	NOUN
ejpam-3949	247	14	−	−	PROPN
ejpam-3949	247	15	1−r	1−r	NUM
ejpam-3949	247	16	1−q′	1−q′	NUM
ejpam-3949	247	17	e	e	SYM
ejpam-3949	247	18	1−r	1−r	NUM
ejpam-3949	247	19	1−q′	1−q′	NUM
ejpam-3949	247	20	uu+	uu+	NOUN
ejpam-3949	247	21	1	1	NUM
ejpam-3949	247	22	1−	1−	NUM
ejpam-3949	247	23	r	r	NOUN
ejpam-3949	247	24	[	[	PUNCT
ejpam-3949	247	25	e	e	NOUN
ejpam-3949	247	26	−	−	PROPN
ejpam-3949	247	27	1−r	1−r	NUM
ejpam-3949	248	1	1−q′	1−q′	NUM
ejpam-3949	248	2	e	e	SYM
ejpam-3949	248	3	1−r	1−r	NUM
ejpam-3949	248	4	1−q′	1−q′	NUM
ejpam-3949	248	5	u	u	NOUN
ejpam-3949	248	6	−	−	PROPN
ejpam-3949	248	7	1	1	NUM
ejpam-3949	248	8	]	]	PUNCT
ejpam-3949	249	1	+	+	CCONJ
ejpam-3949	249	2	α+	α+	PRON
ejpam-3949	249	3	βεi	βεi	NOUN
ejpam-3949	249	4	=	=	NOUN
ejpam-3949	249	5	0	0	X
ejpam-3949	249	6	.	.	PUNCT
ejpam-3949	250	1	−pq−1i	−pq−1i	PROPN
ejpam-3949	250	2	e	e	ADP
ejpam-3949	250	3	−	−	PROPN
ejpam-3949	250	4	1−r	1−r	NUM
ejpam-3949	250	5	1−q′	1−q′	NUM
ejpam-3949	250	6	e	e	SYM
ejpam-3949	250	7	1−r	1−r	NUM
ejpam-3949	250	8	1−q′	1−q′	NUM
ejpam-3949	250	9	uu+	uu+	NOUN
ejpam-3949	250	10	1	1	NUM
ejpam-3949	250	11	1−	1−	NUM
ejpam-3949	250	12	r	r	NOUN
ejpam-3949	250	13	e	e	NOUN
ejpam-3949	250	14	−	−	PROPN
ejpam-3949	250	15	1−r	1−r	NUM
ejpam-3949	250	16	1−q′	1−q′	NUM
ejpam-3949	250	17	e	e	SYM
ejpam-3949	250	18	1−r	1−r	NUM
ejpam-3949	250	19	1−q′	1−q′	NUM
ejpam-3949	250	20	u	u	NOUN
ejpam-3949	250	21	−	−	PROPN
ejpam-3949	250	22	1	1	NUM
ejpam-3949	250	23	1−	1−	NUM
ejpam-3949	250	24	r	r	NOUN
ejpam-3949	250	25	+	+	CCONJ
ejpam-3949	250	26	α+	α+	PRON
ejpam-3949	250	27	βεi	βεi	NOUN
ejpam-3949	250	28	=	=	NOUN
ejpam-3949	250	29	0	0	PROPN
ejpam-3949	250	30	.	.	PUNCT
ejpam-3949	251	1	but	but	CCONJ
ejpam-3949	251	2	equation	equation	NOUN
ejpam-3949	251	3	(	(	PUNCT
ejpam-3949	251	4	31	31	NUM
ejpam-3949	251	5	)	)	PUNCT
ejpam-3949	251	6	can	can	AUX
ejpam-3949	251	7	be	be	AUX
ejpam-3949	251	8	written	write	VERB
ejpam-3949	251	9	as	as	ADP
ejpam-3949	251	10	lnu	lnu	NOUN
ejpam-3949	251	11	=	=	SYM
ejpam-3949	251	12	1−	1−	NUM
ejpam-3949	251	13	q′	q′	NOUN
ejpam-3949	251	14	1−	1−	NUM
ejpam-3949	252	1	q	q	NOUN
ejpam-3949	253	1	(	(	PUNCT
ejpam-3949	253	2	pq−1i	pq−1i	NOUN
ejpam-3949	253	3	−	−	NOUN
ejpam-3949	253	4	1	1	NUM
ejpam-3949	253	5	)	)	PUNCT
ejpam-3949	253	6	pq−1i	pq−1i	NOUN
ejpam-3949	253	7	=	=	NOUN
ejpam-3949	253	8	1	1	NUM
ejpam-3949	254	1	+	+	NUM
ejpam-3949	254	2	1−	1−	NUM
ejpam-3949	254	3	q	q	NOUN
ejpam-3949	254	4	1−	1−	NUM
ejpam-3949	254	5	q′	q′	NOUN
ejpam-3949	254	6	lnu	lnu	PROPN
ejpam-3949	254	7	.	.	PUNCT
ejpam-3949	255	1	hence	hence	ADV
ejpam-3949	255	2	,	,	PUNCT
ejpam-3949	255	3	−	−	PROPN
ejpam-3949	255	4	(	(	PUNCT
ejpam-3949	255	5	1	1	NUM
ejpam-3949	255	6	+	+	NUM
ejpam-3949	255	7	1−	1−	NUM
ejpam-3949	255	8	q	q	NOUN
ejpam-3949	255	9	1−	1−	NUM
ejpam-3949	255	10	q′	q′	NOUN
ejpam-3949	255	11	lnu	lnu	NOUN
ejpam-3949	255	12	)	)	PUNCT
ejpam-3949	256	1	e	e	NOUN
ejpam-3949	256	2	1−r	1−r	NUM
ejpam-3949	256	3	1−q′	1−q′	NUM
ejpam-3949	256	4	uu+	uu+	NOUN
ejpam-3949	256	5	1	1	NUM
ejpam-3949	256	6	1−	1−	NUM
ejpam-3949	256	7	r	r	NOUN
ejpam-3949	256	8	e	e	X
ejpam-3949	256	9	1−r	1−r	NUM
ejpam-3949	256	10	1−q′	1−q′	NUM
ejpam-3949	256	11	u	u	NOUN
ejpam-3949	256	12	+	+	X
ejpam-3949	256	13	(	(	PUNCT
ejpam-3949	256	14	−	−	PROPN
ejpam-3949	256	15	1	1	NUM
ejpam-3949	256	16	1−	1−	NUM
ejpam-3949	256	17	r	r	NOUN
ejpam-3949	256	18	+	+	CCONJ
ejpam-3949	256	19	α+	α+	PUNCT
ejpam-3949	256	20	βεi	βεi	NOUN
ejpam-3949	256	21	)	)	PUNCT
ejpam-3949	256	22	e	e	X
ejpam-3949	256	23	−	−	PROPN
ejpam-3949	256	24	1−r	1−r	NUM
ejpam-3949	256	25	1−q′	1−q′	NUM
ejpam-3949	256	26	=	=	SYM
ejpam-3949	256	27	0	0	NUM
ejpam-3949	256	28	e	e	NOUN
ejpam-3949	256	29	1−r	1−r	NUM
ejpam-3949	256	30	1−q′	1−q′	NUM
ejpam-3949	256	31	uu+	uu+	NOUN
ejpam-3949	256	32	1−	1−	NUM
ejpam-3949	257	1	q	q	NOUN
ejpam-3949	258	1	1−	1−	NUM
ejpam-3949	258	2	q′	q′	NOUN
ejpam-3949	258	3	u(lnu)e	u(lnu)e	PROPN
ejpam-3949	258	4	1−r	1−r	NUM
ejpam-3949	258	5	1−q′	1−q′	NUM
ejpam-3949	258	6	u	u	NOUN
ejpam-3949	258	7	−	−	PROPN
ejpam-3949	258	8	1	1	NUM
ejpam-3949	258	9	1−	1−	NUM
ejpam-3949	258	10	r	r	NOUN
ejpam-3949	258	11	e	e	NOUN
ejpam-3949	258	12	1−r	1−r	NUM
ejpam-3949	258	13	1−q′	1−q′	NUM
ejpam-3949	258	14	u	u	NOUN
ejpam-3949	258	15	=	=	PUNCT
ejpam-3949	258	16	(	(	PUNCT
ejpam-3949	258	17	−	−	PROPN
ejpam-3949	258	18	1	1	NUM
ejpam-3949	258	19	1−	1−	NUM
ejpam-3949	258	20	r	r	NOUN
ejpam-3949	258	21	+	+	CCONJ
ejpam-3949	258	22	α+	α+	PUNCT
ejpam-3949	258	23	βεi	βεi	NOUN
ejpam-3949	258	24	)	)	PUNCT
ejpam-3949	259	1	e	e	X
ejpam-3949	259	2	−	−	PROPN
ejpam-3949	259	3	1−r	1−r	NUM
ejpam-3949	259	4	1−q′	1−q′	NUM
ejpam-3949	259	5	1−	1−	NUM
ejpam-3949	260	1	r	r	NOUN
ejpam-3949	260	2	1−	1−	NUM
ejpam-3949	260	3	q′	q′	NOUN
ejpam-3949	260	4	ue	ue	PROPN
ejpam-3949	260	5	1−r	1−r	NUM
ejpam-3949	260	6	1−q′	1−q′	NUM
ejpam-3949	260	7	u	u	NOUN
ejpam-3949	260	8	+	+	NOUN
ejpam-3949	260	9	1−	1−	NUM
ejpam-3949	260	10	q	q	NOUN
ejpam-3949	260	11	1−	1−	NUM
ejpam-3949	260	12	q′	q′	NOUN
ejpam-3949	260	13	1−	1−	NUM
ejpam-3949	260	14	r	r	NOUN
ejpam-3949	260	15	1−	1−	NUM
ejpam-3949	260	16	q′	q′	NOUN
ejpam-3949	260	17	u(lnu)e	u(lnu)e	PROPN
ejpam-3949	260	18	1−r	1−r	NUM
ejpam-3949	260	19	1−q′	1−q′	NUM
ejpam-3949	260	20	u	u	NOUN
ejpam-3949	260	21	−	−	PROPN
ejpam-3949	260	22	1−	1−	NUM
ejpam-3949	260	23	r	r	NOUN
ejpam-3949	260	24	1−	1−	NUM
ejpam-3949	260	25	q′	q′	NOUN
ejpam-3949	260	26	1	1	NUM
ejpam-3949	260	27	1−	1−	NUM
ejpam-3949	260	28	r	r	NOUN
ejpam-3949	260	29	e	e	NOUN
ejpam-3949	260	30	1−r	1−r	NUM
ejpam-3949	260	31	1−q′	1−q′	NUM
ejpam-3949	260	32	u	u	NOUN
ejpam-3949	260	33	=	=	PUNCT
ejpam-3949	260	34	(	(	PUNCT
ejpam-3949	260	35	−	−	PROPN
ejpam-3949	260	36	1	1	NUM
ejpam-3949	260	37	1−	1−	NUM
ejpam-3949	260	38	r	r	NOUN
ejpam-3949	260	39	+	+	CCONJ
ejpam-3949	260	40	α+	α+	NOUN
ejpam-3949	260	41	βεi	βεi	NOUN
ejpam-3949	260	42	)	)	PUNCT
ejpam-3949	261	1	1−	1−	NUM
ejpam-3949	261	2	r	r	NOUN
ejpam-3949	261	3	1−	1−	NUM
ejpam-3949	261	4	q′	q′	NOUN
ejpam-3949	261	5	e	e	NOUN
ejpam-3949	261	6	−	−	PROPN
ejpam-3949	261	7	1−r	1−r	NUM
ejpam-3949	261	8	1−q′	1−q′	NUM
ejpam-3949	261	9	.	.	PUNCT
ejpam-3949	262	1	by	by	ADP
ejpam-3949	262	2	taking	take	VERB
ejpam-3949	262	3	y	y	PROPN
ejpam-3949	262	4	=	=	SYM
ejpam-3949	262	5	1−r	1−r	PROPN
ejpam-3949	262	6	1−q′u	1−q′u	NUM
ejpam-3949	262	7	,	,	PUNCT
ejpam-3949	262	8	we	we	PRON
ejpam-3949	262	9	obtain	obtain	VERB
ejpam-3949	262	10	yey	yey	NOUN
ejpam-3949	263	1	+	+	CCONJ
ejpam-3949	264	1	1−	1−	NUM
ejpam-3949	264	2	q	q	NOUN
ejpam-3949	264	3	1−	1−	NUM
ejpam-3949	264	4	q′	q′	NOUN
ejpam-3949	264	5	y	y	NOUN
ejpam-3949	264	6	ln	ln	ADV
ejpam-3949	264	7	(	(	PUNCT
ejpam-3949	264	8	1−	1−	NUM
ejpam-3949	264	9	q′	q′	NOUN
ejpam-3949	264	10	1−	1−	NUM
ejpam-3949	264	11	r	r	NOUN
ejpam-3949	264	12	y	y	PROPN
ejpam-3949	264	13	)	)	PUNCT
ejpam-3949	265	1	ey	ey	INTJ
ejpam-3949	265	2	−	−	NOUN
ejpam-3949	265	3	1	1	NUM
ejpam-3949	265	4	1−	1−	NUM
ejpam-3949	265	5	q′	q′	NOUN
ejpam-3949	265	6	ey	ey	PRON
ejpam-3949	265	7	=	=	NOUN
ejpam-3949	265	8	x	x	X
ejpam-3949	265	9	where	where	SCONJ
ejpam-3949	265	10	x	x	SYM
ejpam-3949	265	11	=	=	PRON
ejpam-3949	265	12	(	(	PUNCT
ejpam-3949	265	13	−	−	PROPN
ejpam-3949	265	14	1	1	NUM
ejpam-3949	265	15	1−	1−	NUM
ejpam-3949	265	16	r	r	NOUN
ejpam-3949	265	17	+	+	CCONJ
ejpam-3949	265	18	α+	α+	NOUN
ejpam-3949	265	19	βεi	βεi	NOUN
ejpam-3949	265	20	)	)	PUNCT
ejpam-3949	265	21	1−	1−	NUM
ejpam-3949	265	22	r	r	NOUN
ejpam-3949	265	23	1−	1−	NUM
ejpam-3949	265	24	q′	q′	NOUN
ejpam-3949	265	25	e	e	NOUN
ejpam-3949	265	26	−	−	PROPN
ejpam-3949	265	27	1−r	1−r	NUM
ejpam-3949	265	28	1−q′	1−q′	NUM
ejpam-3949	265	29	.	.	PUNCT
ejpam-3949	266	1	(	(	PUNCT
ejpam-3949	266	2	32	32	NUM
ejpam-3949	266	3	)	)	PUNCT
ejpam-3949	266	4	thus	thus	ADV
ejpam-3949	266	5	,	,	PUNCT
ejpam-3949	266	6	(	(	PUNCT
ejpam-3949	266	7	1−	1−	NUM
ejpam-3949	266	8	q	q	NOUN
ejpam-3949	266	9	1−	1−	NUM
ejpam-3949	266	10	q′	q′	NOUN
ejpam-3949	266	11	y	y	NOUN
ejpam-3949	266	12	ln	ln	ADV
ejpam-3949	266	13	(	(	PUNCT
ejpam-3949	266	14	1−	1−	NUM
ejpam-3949	266	15	q′	q′	NOUN
ejpam-3949	266	16	1−	1−	NUM
ejpam-3949	266	17	r	r	NOUN
ejpam-3949	266	18	y	y	PROPN
ejpam-3949	266	19	)	)	PUNCT
ejpam-3949	267	1	+	+	CCONJ
ejpam-3949	267	2	y	y	PROPN
ejpam-3949	267	3	−	−	PROPN
ejpam-3949	267	4	1	1	NUM
ejpam-3949	267	5	1−	1−	NUM
ejpam-3949	267	6	q′	q′	NOUN
ejpam-3949	267	7	)	)	PUNCT
ejpam-3949	268	1	ey	ey	PROPN
ejpam-3949	268	2	=	=	PUNCT
ejpam-3949	268	3	x.	x.	NOUN
ejpam-3949	268	4	with	with	ADP
ejpam-3949	268	5	a	a	DET
ejpam-3949	268	6	=	=	SYM
ejpam-3949	268	7	1−	1−	NUM
ejpam-3949	268	8	q	q	NOUN
ejpam-3949	268	9	1−	1−	NUM
ejpam-3949	268	10	q′	q′	NOUN
ejpam-3949	268	11	,	,	PUNCT
ejpam-3949	268	12	b	b	X
ejpam-3949	268	13	=	=	SYM
ejpam-3949	268	14	1−	1−	NUM
ejpam-3949	268	15	q′	q′	NOUN
ejpam-3949	268	16	1−	1−	NUM
ejpam-3949	268	17	r	r	NOUN
ejpam-3949	268	18	,	,	PUNCT
ejpam-3949	268	19	c	c	NOUN
ejpam-3949	268	20	=	=	SYM
ejpam-3949	269	1	−	−	PROPN
ejpam-3949	269	2	1	1	NUM
ejpam-3949	269	3	1−	1−	NUM
ejpam-3949	269	4	q′	q′	NOUN
ejpam-3949	269	5	,	,	PUNCT
ejpam-3949	269	6	(	(	PUNCT
ejpam-3949	269	7	33	33	NUM
ejpam-3949	269	8	)	)	PUNCT
ejpam-3949	269	9	c.	c.	NOUN
ejpam-3949	269	10	corcino	corcino	PROPN
ejpam-3949	269	11	,	,	PUNCT
ejpam-3949	269	12	r.	r.	PROPN
ejpam-3949	269	13	corcino	corcino	PROPN
ejpam-3949	269	14	/	/	SYM
ejpam-3949	269	15	eur	eur	PROPN
ejpam-3949	269	16	.	.	PUNCT
ejpam-3949	270	1	j.	j.	PROPN
ejpam-3949	270	2	pure	pure	PROPN
ejpam-3949	270	3	appl	appl	PROPN
ejpam-3949	270	4	.	.	PROPN
ejpam-3949	270	5	math	math	PROPN
ejpam-3949	270	6	,	,	PUNCT
ejpam-3949	270	7	14	14	NUM
ejpam-3949	270	8	(	(	PUNCT
ejpam-3949	270	9	2	2	NUM
ejpam-3949	270	10	)	)	PUNCT
ejpam-3949	270	11	(	(	PUNCT
ejpam-3949	270	12	2021	2021	NUM
ejpam-3949	270	13	)	)	PUNCT
ejpam-3949	270	14	,	,	PUNCT
ejpam-3949	270	15	506	506	NUM
ejpam-3949	270	16	-	-	SYM
ejpam-3949	270	17	520	520	NUM
ejpam-3949	270	18	518	518	NUM
ejpam-3949	270	19	it	it	PRON
ejpam-3949	270	20	follows	follow	VERB
ejpam-3949	270	21	that	that	PRON
ejpam-3949	270	22	(	(	PUNCT
ejpam-3949	270	23	ay	ay	INTJ
ejpam-3949	270	24	ln	ln	INTJ
ejpam-3949	270	25	(	(	PUNCT
ejpam-3949	270	26	by	by	ADP
ejpam-3949	270	27	)	)	PUNCT
ejpam-3949	271	1	+	+	CCONJ
ejpam-3949	271	2	y	y	PROPN
ejpam-3949	271	3	+	+	CCONJ
ejpam-3949	271	4	c	c	X
ejpam-3949	271	5	)	)	PUNCT
ejpam-3949	272	1	ey	ey	PROPN
ejpam-3949	272	2	=	=	NOUN
ejpam-3949	272	3	x.	x.	NOUN
ejpam-3949	272	4	this	this	PRON
ejpam-3949	272	5	implies	imply	VERB
ejpam-3949	272	6	that	that	SCONJ
ejpam-3949	272	7	y	y	PROPN
ejpam-3949	272	8	=	=	SYM
ejpam-3949	272	9	wlt	wlt	PROPN
ejpam-3949	272	10	(	(	PUNCT
ejpam-3949	272	11	x	x	NOUN
ejpam-3949	272	12	)	)	PUNCT
ejpam-3949	272	13	1−	1−	NUM
ejpam-3949	272	14	r	r	NOUN
ejpam-3949	272	15	1−	1−	NUM
ejpam-3949	272	16	q′	q′	NOUN
ejpam-3949	272	17	u	u	NOUN
ejpam-3949	272	18	=	=	PROPN
ejpam-3949	272	19	wlt	wlt	PROPN
ejpam-3949	272	20	(	(	PUNCT
ejpam-3949	272	21	x	x	NOUN
ejpam-3949	272	22	)	)	PUNCT
ejpam-3949	272	23	u	u	NOUN
ejpam-3949	272	24	=	=	NOUN
ejpam-3949	272	25	1−	1−	NUM
ejpam-3949	272	26	q′	q′	NOUN
ejpam-3949	272	27	1−	1−	NUM
ejpam-3949	272	28	r	r	NOUN
ejpam-3949	272	29	wlt	wlt	PROPN
ejpam-3949	272	30	(	(	PUNCT
ejpam-3949	272	31	x	x	X
ejpam-3949	272	32	)	)	PUNCT
ejpam-3949	272	33	using	use	VERB
ejpam-3949	272	34	equation	equation	NOUN
ejpam-3949	272	35	(	(	PUNCT
ejpam-3949	272	36	31	31	NUM
ejpam-3949	272	37	)	)	PUNCT
ejpam-3949	272	38	exp	exp	NOUN
ejpam-3949	272	39	(	(	PUNCT
ejpam-3949	272	40	1−	1−	NUM
ejpam-3949	272	41	q′	q′	NOUN
ejpam-3949	272	42	1−	1−	NUM
ejpam-3949	272	43	q	q	NOUN
ejpam-3949	272	44	(	(	PUNCT
ejpam-3949	272	45	pq−1i	pq−1i	NOUN
ejpam-3949	272	46	−	−	NOUN
ejpam-3949	272	47	1	1	NUM
ejpam-3949	272	48	)	)	PUNCT
ejpam-3949	272	49	)	)	PUNCT
ejpam-3949	273	1	=	=	SYM
ejpam-3949	274	1	1−	1−	NUM
ejpam-3949	274	2	q′	q′	NOUN
ejpam-3949	274	3	1−	1−	NUM
ejpam-3949	274	4	r	r	NOUN
ejpam-3949	274	5	wlt	wlt	PROPN
ejpam-3949	274	6	(	(	PUNCT
ejpam-3949	274	7	x	x	NOUN
ejpam-3949	274	8	)	)	PUNCT
ejpam-3949	274	9	1−	1−	NUM
ejpam-3949	274	10	q′	q′	NOUN
ejpam-3949	274	11	1−	1−	NUM
ejpam-3949	274	12	q	q	NOUN
ejpam-3949	274	13	(	(	PUNCT
ejpam-3949	274	14	pq−1i	pq−1i	NOUN
ejpam-3949	274	15	−	−	NOUN
ejpam-3949	274	16	1	1	NUM
ejpam-3949	274	17	)	)	PUNCT
ejpam-3949	274	18	=	=	SYM
ejpam-3949	275	1	ln	ln	ADJ
ejpam-3949	275	2	(	(	PUNCT
ejpam-3949	275	3	1−	1−	NUM
ejpam-3949	275	4	q′	q′	NOUN
ejpam-3949	275	5	1−	1−	NUM
ejpam-3949	275	6	r	r	NOUN
ejpam-3949	275	7	wlt	wlt	PROPN
ejpam-3949	275	8	(	(	PUNCT
ejpam-3949	275	9	x	x	NOUN
ejpam-3949	275	10	)	)	PUNCT
ejpam-3949	275	11	)	)	PUNCT
ejpam-3949	275	12	.	.	PUNCT
ejpam-3949	276	1	therefore	therefore	ADV
ejpam-3949	276	2	,	,	PUNCT
ejpam-3949	276	3	the	the	DET
ejpam-3949	276	4	probability	probability	NOUN
ejpam-3949	276	5	distribution	distribution	NOUN
ejpam-3949	276	6	is	be	AUX
ejpam-3949	276	7	given	give	VERB
ejpam-3949	276	8	by	by	ADP
ejpam-3949	276	9	pi	pi	NOUN
ejpam-3949	276	10	=	=	SYM
ejpam-3949	276	11	1	1	NUM
ejpam-3949	276	12	zq	zq	PROPN
ejpam-3949	276	13	,	,	PUNCT
ejpam-3949	276	14	q′,r	q′,r	PROPN
ejpam-3949	276	15	{	{	PUNCT
ejpam-3949	276	16	1−	1−	NUM
ejpam-3949	276	17	q	q	NOUN
ejpam-3949	276	18	1−	1−	NUM
ejpam-3949	276	19	q′	q′	NOUN
ejpam-3949	276	20	ln	ln	NOUN
ejpam-3949	277	1	(	(	PUNCT
ejpam-3949	277	2	1−	1−	NUM
ejpam-3949	277	3	q′	q′	NOUN
ejpam-3949	277	4	1−	1−	NUM
ejpam-3949	277	5	r	r	NOUN
ejpam-3949	277	6	wlt	wlt	PROPN
ejpam-3949	277	7	(	(	PUNCT
ejpam-3949	277	8	x	x	NOUN
ejpam-3949	277	9	)	)	PUNCT
ejpam-3949	277	10	)	)	PUNCT
ejpam-3949	278	1	+	+	CCONJ
ejpam-3949	278	2	1	1	NUM
ejpam-3949	278	3	}	}	SYM
ejpam-3949	278	4	1	1	NUM
ejpam-3949	278	5	q−1	q−1	PROPN
ejpam-3949	278	6	(	(	PUNCT
ejpam-3949	278	7	34	34	NUM
ejpam-3949	278	8	)	)	PUNCT
ejpam-3949	278	9	where	where	SCONJ
ejpam-3949	278	10	zq	zq	PROPN
ejpam-3949	278	11	,	,	PUNCT
ejpam-3949	278	12	q′,r	q′,r	PROPN
ejpam-3949	278	13	=	=	PROPN
ejpam-3949	278	14	ω∑	ω∑	PROPN
ejpam-3949	278	15	i=1	i=1	PROPN
ejpam-3949	278	16	{	{	PUNCT
ejpam-3949	278	17	1−	1−	NUM
ejpam-3949	278	18	q	q	NOUN
ejpam-3949	278	19	1−	1−	NUM
ejpam-3949	278	20	q′	q′	NOUN
ejpam-3949	278	21	ln	ln	NOUN
ejpam-3949	278	22	(	(	PUNCT
ejpam-3949	278	23	1−	1−	NUM
ejpam-3949	278	24	q′	q′	NOUN
ejpam-3949	278	25	1−	1−	NUM
ejpam-3949	278	26	r	r	NOUN
ejpam-3949	278	27	wlt	wlt	PROPN
ejpam-3949	278	28	(	(	PUNCT
ejpam-3949	278	29	x	x	NOUN
ejpam-3949	278	30	)	)	PUNCT
ejpam-3949	278	31	)	)	PUNCT
ejpam-3949	279	1	+	+	CCONJ
ejpam-3949	279	2	1	1	NUM
ejpam-3949	279	3	}	}	SYM
ejpam-3949	279	4	1	1	NUM
ejpam-3949	279	5	q−1	q−1	PROPN
ejpam-3949	279	6	.	.	PUNCT
ejpam-3949	280	1	x	x	X
ejpam-3949	280	2	=	=	PUNCT
ejpam-3949	281	1	(	(	PUNCT
ejpam-3949	281	2	1−	1−	NUM
ejpam-3949	281	3	α(1−	α(1−	PROPN
ejpam-3949	281	4	r)−	r)−	PROPN
ejpam-3949	281	5	β(1−	β(1−	PUNCT
ejpam-3949	282	1	r)εi	r)εi	NOUN
ejpam-3949	282	2	)	)	PUNCT
ejpam-3949	283	1	1	1	NUM
ejpam-3949	283	2	q′	q′	NOUN
ejpam-3949	283	3	−	−	PROPN
ejpam-3949	283	4	1	1	NUM
ejpam-3949	283	5	e	e	NOUN
ejpam-3949	283	6	−	−	PROPN
ejpam-3949	283	7	1−r	1−r	NUM
ejpam-3949	283	8	1−q′	1−q′	NUM
ejpam-3949	283	9	=	=	SYM
ejpam-3949	284	1	1	1	NUM
ejpam-3949	284	2	q′	q′	NOUN
ejpam-3949	284	3	−	−	PROPN
ejpam-3949	284	4	1	1	NUM
ejpam-3949	284	5	e	e	NOUN
ejpam-3949	284	6	−	−	PROPN
ejpam-3949	284	7	1−r	1−r	NUM
ejpam-3949	284	8	1−q′	1−q′	NUM
ejpam-3949	284	9	(	(	PUNCT
ejpam-3949	284	10	1−	1−	NUM
ejpam-3949	284	11	α(1−	α(1−	PROPN
ejpam-3949	284	12	r	r	NOUN
ejpam-3949	284	13	)	)	PUNCT
ejpam-3949	284	14	)	)	PUNCT
ejpam-3949	284	15	(	(	PUNCT
ejpam-3949	284	16	1−	1−	NUM
ejpam-3949	284	17	β(1−	β(1−	NOUN
ejpam-3949	284	18	r	r	X
ejpam-3949	284	19	)	)	PUNCT
ejpam-3949	284	20	1−	1−	NUM
ejpam-3949	284	21	α(1−	α(1−	PROPN
ejpam-3949	284	22	r	r	X
ejpam-3949	284	23	)	)	PUNCT
ejpam-3949	284	24	εi	εi	NOUN
ejpam-3949	284	25	)	)	PUNCT
ejpam-3949	284	26	=	=	SYM
ejpam-3949	284	27	1	1	NUM
ejpam-3949	284	28	q′	q′	NOUN
ejpam-3949	284	29	−	−	PROPN
ejpam-3949	284	30	1	1	NUM
ejpam-3949	284	31	e	e	NOUN
ejpam-3949	284	32	−	−	PROPN
ejpam-3949	284	33	1−r	1−r	NUM
ejpam-3949	284	34	1−q′	1−q′	NUM
ejpam-3949	284	35	(	(	PUNCT
ejpam-3949	284	36	1−	1−	NUM
ejpam-3949	284	37	α(1−	α(1−	PROPN
ejpam-3949	284	38	r	r	NOUN
ejpam-3949	284	39	)	)	PUNCT
ejpam-3949	284	40	)	)	PUNCT
ejpam-3949	285	1	(	(	PUNCT
ejpam-3949	285	2	1−	1−	NUM
ejpam-3949	285	3	βr(1−	βr(1−	PROPN
ejpam-3949	285	4	r)εi	r)εi	PROPN
ejpam-3949	285	5	)	)	PUNCT
ejpam-3949	285	6	=	=	SYM
ejpam-3949	285	7	1	1	NUM
ejpam-3949	285	8	q′	q′	NOUN
ejpam-3949	285	9	−	−	PROPN
ejpam-3949	285	10	1	1	NUM
ejpam-3949	285	11	e	e	NOUN
ejpam-3949	285	12	−	−	PROPN
ejpam-3949	285	13	1−r	1−r	NUM
ejpam-3949	285	14	1−q′	1−q′	NUM
ejpam-3949	285	15	(	(	PUNCT
ejpam-3949	285	16	1−	1−	NUM
ejpam-3949	285	17	α(1−	α(1−	PROPN
ejpam-3949	285	18	r	r	NOUN
ejpam-3949	285	19	)	)	PUNCT
ejpam-3949	285	20	)	)	PUNCT
ejpam-3949	286	1	[	[	X
ejpam-3949	286	2	expr(−βrεi	expr(−βrεi	NOUN
ejpam-3949	286	3	)	)	PUNCT
ejpam-3949	286	4	]	]	X
ejpam-3949	286	5	1−r	1−r	NUM
ejpam-3949	286	6	,	,	PUNCT
ejpam-3949	286	7	where	where	SCONJ
ejpam-3949	286	8	βr	βr	NOUN
ejpam-3949	286	9	may	may	AUX
ejpam-3949	286	10	be	be	AUX
ejpam-3949	286	11	defined	define	VERB
ejpam-3949	286	12	as	as	ADP
ejpam-3949	286	13	the	the	DET
ejpam-3949	286	14	inverse	inverse	NOUN
ejpam-3949	286	15	of	of	ADP
ejpam-3949	286	16	the	the	DET
ejpam-3949	286	17	pseudo	pseudo	NOUN
ejpam-3949	286	18	-	-	NOUN
ejpam-3949	286	19	temperature	temperature	NOUN
ejpam-3949	286	20	βr	βr	ADP
ejpam-3949	286	21	≡	≡	PROPN
ejpam-3949	286	22	1	1	NUM
ejpam-3949	286	23	krtr	krtr	NOUN
ejpam-3949	286	24	=	=	PUNCT
ejpam-3949	286	25	β	β	X
ejpam-3949	286	26	1−	1−	NUM
ejpam-3949	286	27	α(1−	α(1−	PROPN
ejpam-3949	286	28	r	r	X
ejpam-3949	286	29	)	)	PUNCT
ejpam-3949	286	30	,	,	PUNCT
ejpam-3949	286	31	pi	pi	NOUN
ejpam-3949	286	32	=	=	SYM
ejpam-3949	286	33	1	1	NUM
ejpam-3949	286	34	zq	zq	PROPN
ejpam-3949	286	35	,	,	PUNCT
ejpam-3949	286	36	q′,r	q′,r	VERB
ejpam-3949	286	37	1	1	PUNCT
ejpam-3949	286	38	+	+	CCONJ
ejpam-3949	286	39	(	(	PUNCT
ejpam-3949	286	40	1−	1−	NUM
ejpam-3949	286	41	q	q	NOUN
ejpam-3949	286	42	)	)	PUNCT
ejpam-3949	286	43	ln	ln	NOUN
ejpam-3949	286	44	(	(	PUNCT
ejpam-3949	286	45	1−	1−	NUM
ejpam-3949	286	46	q′	q′	NOUN
ejpam-3949	286	47	1−	1−	NUM
ejpam-3949	287	1	r	r	NOUN
ejpam-3949	287	2	wlt	wlt	NOUN
ejpam-3949	287	3	(	(	PUNCT
ejpam-3949	287	4	e	e	PROPN
ejpam-3949	287	5	1−r	1−r	NUM
ejpam-3949	287	6	q′−1	q′−1	PROPN
ejpam-3949	287	7	(	(	PUNCT
ejpam-3949	287	8	1−	1−	NUM
ejpam-3949	287	9	α(1−	α(1−	X
ejpam-3949	287	10	r))e−βrεi(1−r)r	r))e−βrεi(1−r)r	NOUN
ejpam-3949	287	11	q′	q′	NOUN
ejpam-3949	287	12	−	−	NOUN
ejpam-3949	287	13	1	1	NUM
ejpam-3949	287	14	)	)	PUNCT
ejpam-3949	287	15	)	)	PUNCT
ejpam-3949	288	1	1	1	NUM
ejpam-3949	288	2	1−q′	1−q′	NUM
ejpam-3949	288	3			NOUN
ejpam-3949	288	4	1	1	NUM
ejpam-3949	288	5	q−1	q−1	PROPN
ejpam-3949	288	6	references	reference	VERB
ejpam-3949	288	7	519	519	NUM
ejpam-3949	288	8	=	=	SYM
ejpam-3949	288	9	1	1	NUM
ejpam-3949	288	10	zq	zq	PROPN
ejpam-3949	288	11	,	,	PUNCT
ejpam-3949	288	12	q′,r	q′,r	PROPN
ejpam-3949	288	13	expq	expq	PROPN
ejpam-3949	288	14	ln	ln	ADP
ejpam-3949	288	15	(	(	PUNCT
ejpam-3949	288	16	1−	1−	NUM
ejpam-3949	288	17	q′	q′	NOUN
ejpam-3949	288	18	1−	1−	NUM
ejpam-3949	288	19	r	r	NOUN
ejpam-3949	288	20	wlt	wlt	NOUN
ejpam-3949	288	21	(	(	PUNCT
ejpam-3949	288	22	e	e	PROPN
ejpam-3949	288	23	1−r	1−r	NUM
ejpam-3949	288	24	q′−1	q′−1	PROPN
ejpam-3949	288	25	(	(	PUNCT
ejpam-3949	288	26	1−	1−	NUM
ejpam-3949	288	27	α(1−	α(1−	X
ejpam-3949	289	1	r))e−βrεi(1−r)r	r))e−βrεi(1−r)r	NOUN
ejpam-3949	289	2	q′	q′	NOUN
ejpam-3949	290	1	−	−	NOUN
ejpam-3949	290	2	1	1	NUM
ejpam-3949	290	3	)	)	PUNCT
ejpam-3949	290	4	)	)	PUNCT
ejpam-3949	290	5	1	1	NUM
ejpam-3949	290	6	1−q′	1−q′	NUM
ejpam-3949	290	7			NOUN
ejpam-3949	290	8	−1	−1	NOUN
ejpam-3949	290	9	.	.	PUNCT
ejpam-3949	291	1	we	we	PRON
ejpam-3949	291	2	can	can	AUX
ejpam-3949	291	3	assume	assume	VERB
ejpam-3949	291	4	the	the	DET
ejpam-3949	291	5	energy	energy	NOUN
ejpam-3949	291	6	level	level	NOUN
ejpam-3949	291	7	,	,	PUNCT
ejpam-3949	291	8	εi	εi	VERB
ejpam-3949	291	9	,	,	PUNCT
ejpam-3949	291	10	as	as	ADP
ejpam-3949	291	11	a	a	DET
ejpam-3949	291	12	quadratic	quadratic	ADJ
ejpam-3949	291	13	function	function	NOUN
ejpam-3949	291	14	of	of	ADP
ejpam-3949	291	15	the	the	DET
ejpam-3949	291	16	variable	variable	NOUN
ejpam-3949	291	17	xi	xi	PROPN
ejpam-3949	291	18	.	.	PUNCT
ejpam-3949	292	1	the	the	DET
ejpam-3949	292	2	continuous	continuous	ADJ
ejpam-3949	292	3	normalized	normalize	VERB
ejpam-3949	292	4	probability	probability	NOUN
ejpam-3949	292	5	distribution	distribution	NOUN
ejpam-3949	292	6	of	of	ADP
ejpam-3949	292	7	x	x	PUNCT
ejpam-3949	292	8	can	can	AUX
ejpam-3949	292	9	then	then	ADV
ejpam-3949	292	10	be	be	AUX
ejpam-3949	292	11	rewritten	rewrite	VERB
ejpam-3949	292	12	as	as	ADP
ejpam-3949	292	13	p(x	p(x	NOUN
ejpam-3949	292	14	)	)	PUNCT
ejpam-3949	292	15	=	=	PUNCT
ejpam-3949	293	1	1	1	PROPN
ejpam-3949	293	2	+	+	CCONJ
ejpam-3949	293	3	(	(	PUNCT
ejpam-3949	293	4	1−	1−	NUM
ejpam-3949	293	5	q	q	NOUN
ejpam-3949	293	6	)	)	PUNCT
ejpam-3949	293	7	ln	ln	NOUN
ejpam-3949	293	8	(	(	PUNCT
ejpam-3949	293	9	1−q′	1−q′	NUM
ejpam-3949	293	10	1−rwlt	1−rwlt	NUM
ejpam-3949	293	11	(	(	PUNCT
ejpam-3949	293	12	e	e	PROPN
ejpam-3949	293	13	1−r	1−r	NUM
ejpam-3949	293	14	q′−1	q′−1	NUM
ejpam-3949	293	15	(	(	PUNCT
ejpam-3949	293	16	1−α(1−r))e−βrx	1−α(1−r))e−βrx	NUM
ejpam-3949	293	17	2(1−r	2(1−r	NUM
ejpam-3949	293	18	)	)	PUNCT
ejpam-3949	293	19	r	r	NOUN
ejpam-3949	293	20	q′−1	q′−1	NUM
ejpam-3949	293	21	)	)	PUNCT
ejpam-3949	293	22	)	)	PUNCT
ejpam-3949	294	1	1	1	NUM
ejpam-3949	294	2	1−q′	1−q′	NUM
ejpam-3949	294	3			NOUN
ejpam-3949	294	4	1	1	NUM
ejpam-3949	294	5	q−1	q−1	PROPN
ejpam-3949	294	6	∫∞	∫∞	NOUN
ejpam-3949	294	7	−∞	−∞	ADP
ejpam-3949	294	8	1	1	PUNCT
ejpam-3949	294	9	+	+	CCONJ
ejpam-3949	294	10	(	(	PUNCT
ejpam-3949	294	11	1−	1−	NUM
ejpam-3949	294	12	q	q	NOUN
ejpam-3949	294	13	)	)	PUNCT
ejpam-3949	294	14	ln	ln	NOUN
ejpam-3949	295	1	(	(	PUNCT
ejpam-3949	295	2	1−q′	1−q′	NUM
ejpam-3949	295	3	1−rwlt	1−rwlt	NUM
ejpam-3949	295	4	(	(	PUNCT
ejpam-3949	295	5	e	e	PROPN
ejpam-3949	295	6	1−r	1−r	NUM
ejpam-3949	295	7	q′−1	q′−1	NUM
ejpam-3949	295	8	(	(	PUNCT
ejpam-3949	295	9	1−α(1−r))e−βrx	1−α(1−r))e−βrx	NUM
ejpam-3949	295	10	2(1−r	2(1−r	NUM
ejpam-3949	295	11	)	)	PUNCT
ejpam-3949	295	12	r	r	NOUN
ejpam-3949	295	13	q′−1	q′−1	NUM
ejpam-3949	295	14	)	)	PUNCT
ejpam-3949	295	15	)	)	PUNCT
ejpam-3949	295	16	1	1	NUM
ejpam-3949	295	17	1−q′	1−q′	NUM
ejpam-3949	296	1			NOUN
ejpam-3949	296	2	1	1	NUM
ejpam-3949	296	3	q−1	q−1	PROPN
ejpam-3949	296	4	dx	dx	PROPN
ejpam-3949	296	5	.	.	PUNCT
ejpam-3949	297	1	4	4	X
ejpam-3949	297	2	.	.	X
ejpam-3949	297	3	conclusion	conclusion	NOUN
ejpam-3949	297	4	in	in	ADP
ejpam-3949	297	5	this	this	DET
ejpam-3949	297	6	paper	paper	NOUN
ejpam-3949	297	7	,	,	PUNCT
ejpam-3949	297	8	a	a	DET
ejpam-3949	297	9	special	special	ADJ
ejpam-3949	297	10	set	set	NOUN
ejpam-3949	297	11	of	of	ADP
ejpam-3949	297	12	three	three	NUM
ejpam-3949	297	13	-	-	PUNCT
ejpam-3949	297	14	parameter	parameter	NOUN
ejpam-3949	297	15	entropies	entropy	NOUN
ejpam-3949	297	16	[	[	X
ejpam-3949	297	17	5	5	NUM
ejpam-3949	297	18	]	]	PUNCT
ejpam-3949	297	19	were	be	AUX
ejpam-3949	297	20	maximized	maximize	VERB
ejpam-3949	297	21	in	in	ADP
ejpam-3949	297	22	the	the	DET
ejpam-3949	297	23	canonical	canonical	ADJ
ejpam-3949	297	24	ensemble	ensemble	ADJ
ejpam-3949	297	25	by	by	ADP
ejpam-3949	297	26	the	the	DET
ejpam-3949	297	27	energy	energy	NOUN
ejpam-3949	297	28	constraint	constraint	NOUN
ejpam-3949	297	29	ω∑	ω∑	ADP
ejpam-3949	297	30	i=1	i=1	PROPN
ejpam-3949	297	31	piεi	piεi	PROPN
ejpam-3949	298	1	=	=	PUNCT
ejpam-3949	298	2	e.	e.	PROPN
ejpam-3949	298	3	it	it	PRON
ejpam-3949	298	4	is	be	AUX
ejpam-3949	298	5	expected	expect	VERB
ejpam-3949	298	6	that	that	SCONJ
ejpam-3949	298	7	the	the	DET
ejpam-3949	298	8	probability	probability	NOUN
ejpam-3949	298	9	distribution	distribution	NOUN
ejpam-3949	298	10	,	,	PUNCT
ejpam-3949	298	11	pi(εi	pi(εi	NOUN
ejpam-3949	298	12	)	)	PUNCT
ejpam-3949	298	13	,	,	PUNCT
ejpam-3949	298	14	can	can	AUX
ejpam-3949	298	15	be	be	AUX
ejpam-3949	298	16	expressed	express	VERB
ejpam-3949	298	17	in	in	ADP
ejpam-3949	298	18	terms	term	NOUN
ejpam-3949	298	19	of	of	ADP
ejpam-3949	298	20	the	the	DET
ejpam-3949	298	21	generalized	generalized	ADJ
ejpam-3949	298	22	three	three	NUM
ejpam-3949	298	23	-	-	PUNCT
ejpam-3949	298	24	parameter	parameter	NOUN
ejpam-3949	298	25	exponential	exponential	NOUN
ejpam-3949	298	26	defined	define	VERB
ejpam-3949	298	27	in	in	ADP
ejpam-3949	298	28	[	[	X
ejpam-3949	298	29	5	5	NUM
ejpam-3949	298	30	]	]	PUNCT
ejpam-3949	298	31	.	.	PUNCT
ejpam-3949	299	1	however	however	ADV
ejpam-3949	299	2	,	,	PUNCT
ejpam-3949	299	3	an	an	DET
ejpam-3949	299	4	interesting	interesting	ADJ
ejpam-3949	299	5	form	form	NOUN
ejpam-3949	299	6	of	of	ADP
ejpam-3949	299	7	the	the	DET
ejpam-3949	299	8	solution	solution	NOUN
ejpam-3949	299	9	of	of	ADP
ejpam-3949	299	10	the	the	DET
ejpam-3949	299	11	related	relate	VERB
ejpam-3949	299	12	equation	equation	NOUN
ejpam-3949	299	13	is	be	AUX
ejpam-3949	299	14	obtained	obtain	VERB
ejpam-3949	299	15	expressing	express	VERB
ejpam-3949	299	16	the	the	DET
ejpam-3949	299	17	solution	solution	NOUN
ejpam-3949	299	18	in	in	ADP
ejpam-3949	299	19	terms	term	NOUN
ejpam-3949	299	20	of	of	ADP
ejpam-3949	299	21	the	the	DET
ejpam-3949	299	22	translated	translate	VERB
ejpam-3949	299	23	logarithmic	logarithmic	PROPN
ejpam-3949	299	24	lambert	lambert	PROPN
ejpam-3949	299	25	function	function	NOUN
ejpam-3949	299	26	which	which	PRON
ejpam-3949	299	27	is	be	AUX
ejpam-3949	299	28	a	a	DET
ejpam-3949	299	29	generalization	generalization	NOUN
ejpam-3949	299	30	of	of	ADP
ejpam-3949	299	31	the	the	DET
ejpam-3949	299	32	classical	classical	ADJ
ejpam-3949	299	33	lambert	lambert	PROPN
ejpam-3949	299	34	w	w	PROPN
ejpam-3949	299	35	function	function	NOUN
ejpam-3949	299	36	.	.	PUNCT
ejpam-3949	300	1	acknowledgements	acknowledgement	NOUN
ejpam-3949	300	2	this	this	DET
ejpam-3949	300	3	research	research	NOUN
ejpam-3949	300	4	is	be	AUX
ejpam-3949	300	5	funded	fund	VERB
ejpam-3949	300	6	by	by	ADP
ejpam-3949	300	7	cebu	cebu	PROPN
ejpam-3949	300	8	normal	normal	ADJ
ejpam-3949	300	9	university	university	PROPN
ejpam-3949	300	10	(	(	PUNCT
ejpam-3949	300	11	cnu	cnu	PROPN
ejpam-3949	300	12	)	)	PUNCT
ejpam-3949	300	13	and	and	CCONJ
ejpam-3949	300	14	the	the	DET
ejpam-3949	300	15	commission	commission	NOUN
ejpam-3949	300	16	on	on	ADP
ejpam-3949	300	17	higher	high	ADJ
ejpam-3949	300	18	education	education	NOUN
ejpam-3949	300	19	grants	grant	NOUN
ejpam-3949	300	20	-	-	PUNCT
ejpam-3949	300	21	in	in	ADP
ejpam-3949	300	22	-	-	PUNCT
ejpam-3949	300	23	aid	aid	NOUN
ejpam-3949	300	24	(	(	PUNCT
ejpam-3949	300	25	ched	che	VERB
ejpam-3949	300	26	-	-	PUNCT
ejpam-3949	300	27	gia	gia	NOUN
ejpam-3949	300	28	)	)	PUNCT
ejpam-3949	300	29	for	for	ADP
ejpam-3949	300	30	research	research	NOUN
ejpam-3949	300	31	.	.	PUNCT
ejpam-3949	301	1	references	reference	NOUN
ejpam-3949	301	2	[	[	X
ejpam-3949	301	3	1	1	X
ejpam-3949	301	4	]	]	PUNCT
ejpam-3949	301	5	s.	s.	PROPN
ejpam-3949	301	6	asgarani	asgarani	PROPN
ejpam-3949	301	7	and	and	CCONJ
ejpam-3949	301	8	b.	b.	PROPN
ejpam-3949	301	9	mirza	mirza	PROPN
ejpam-3949	301	10	,	,	PUNCT
ejpam-3949	301	11	probability	probability	NOUN
ejpam-3949	301	12	distribution	distribution	NOUN
ejpam-3949	301	13	of	of	ADP
ejpam-3949	301	14	(	(	PUNCT
ejpam-3949	301	15	schwämmle	schwämmle	X
ejpam-3949	301	16	and	and	CCONJ
ejpam-3949	301	17	tsallis	tsallis	ADJ
ejpam-3949	301	18	)	)	PUNCT
ejpam-3949	301	19	twoparameter	twoparameter	ADJ
ejpam-3949	301	20	entropies	entropy	NOUN
ejpam-3949	301	21	and	and	CCONJ
ejpam-3949	301	22	the	the	DET
ejpam-3949	301	23	lambert	lambert	PROPN
ejpam-3949	301	24	w	w	PROPN
ejpam-3949	301	25	-	-	PUNCT
ejpam-3949	301	26	function	function	NOUN
ejpam-3949	301	27	,	,	PUNCT
ejpam-3949	301	28	phys	phy	NOUN
ejpam-3949	301	29	.	.	PUNCT
ejpam-3949	302	1	a	a	DET
ejpam-3949	302	2	2008	2008	NUM
ejpam-3949	302	3	,	,	PUNCT
ejpam-3949	302	4	387	387	NUM
ejpam-3949	302	5	,	,	PUNCT
ejpam-3949	302	6	6277–6283	6277–6283	NUM
ejpam-3949	302	7	.	.	PUNCT
ejpam-3949	303	1	[	[	X
ejpam-3949	303	2	2	2	NUM
ejpam-3949	303	3	]	]	X
ejpam-3949	303	4	c.g	c.g	PROPN
ejpam-3949	303	5	.	.	PROPN
ejpam-3949	303	6	chakrabarti	chakrabarti	PROPN
ejpam-3949	303	7	and	and	CCONJ
ejpam-3949	303	8	k.	k.	PROPN
ejpam-3949	303	9	de	de	PROPN
ejpam-3949	303	10	,	,	PUNCT
ejpam-3949	303	11	boltzmann	boltzmann	PROPN
ejpam-3949	303	12	-	-	PUNCT
ejpam-3949	303	13	gibbs	gibbs	PROPN
ejpam-3949	303	14	entropy	entropy	PROPN
ejpam-3949	303	15	:	:	PUNCT
ejpam-3949	303	16	axiomatic	axiomatic	ADJ
ejpam-3949	303	17	characterization	characterization	NOUN
ejpam-3949	303	18	and	and	CCONJ
ejpam-3949	303	19	application	application	NOUN
ejpam-3949	303	20	,	,	PUNCT
ejpam-3949	303	21	internat	internat	PROPN
ejpam-3949	303	22	.	.	PUNCT
ejpam-3949	304	1	j.	j.	PROPN
ejpam-3949	304	2	math	math	PROPN
ejpam-3949	304	3	.	.	PUNCT
ejpam-3949	304	4	&	&	CCONJ
ejpam-3949	304	5	math	math	PROPN
ejpam-3949	304	6	.	.	PUNCT
ejpam-3949	305	1	sci	sci	PROPN
ejpam-3949	305	2	.	.	PROPN
ejpam-3949	305	3	,	,	PUNCT
ejpam-3949	305	4	2000	2000	NUM
ejpam-3949	305	5	,	,	PUNCT
ejpam-3949	305	6	23	23	NUM
ejpam-3949	305	7	,	,	PUNCT
ejpam-3949	305	8	243–251	243–251	NUM
ejpam-3949	305	9	.	.	PUNCT
ejpam-3949	306	1	[	[	X
ejpam-3949	306	2	3	3	NUM
ejpam-3949	306	3	]	]	X
ejpam-3949	306	4	r.	r.	X
ejpam-3949	306	5	chandrashekar	chandrashekar	PROPN
ejpam-3949	306	6	and	and	CCONJ
ejpam-3949	306	7	j.	j.	PROPN
ejpam-3949	306	8	segar	segar	PROPN
ejpam-3949	306	9	,	,	PUNCT
ejpam-3949	306	10	adiabatic	adiabatic	ADJ
ejpam-3949	306	11	thermostatics	thermostatic	NOUN
ejpam-3949	306	12	of	of	ADP
ejpam-3949	306	13	the	the	DET
ejpam-3949	306	14	two	two	NUM
ejpam-3949	306	15	parameter	parameter	NOUN
ejpam-3949	306	16	entropy	entropy	NOUN
ejpam-3949	306	17	and	and	CCONJ
ejpam-3949	306	18	the	the	DET
ejpam-3949	306	19	role	role	NOUN
ejpam-3949	306	20	of	of	ADP
ejpam-3949	306	21	lambert	lambert	PROPN
ejpam-3949	306	22	’s	’s	PART
ejpam-3949	306	23	w	w	PROPN
ejpam-3949	306	24	function	function	NOUN
ejpam-3949	306	25	in	in	ADP
ejpam-3949	306	26	its	its	PRON
ejpam-3949	306	27	applications	application	NOUN
ejpam-3949	306	28	,	,	PUNCT
ejpam-3949	306	29	phys	phy	NOUN
ejpam-3949	306	30	.	.	PUNCT
ejpam-3949	307	1	a	a	DET
ejpam-3949	307	2	,	,	PUNCT
ejpam-3949	307	3	2013	2013	NUM
ejpam-3949	307	4	,	,	PUNCT
ejpam-3949	307	5	392	392	NUM
ejpam-3949	307	6	,	,	PUNCT
ejpam-3949	307	7	4299–4315	4299–4315	NUM
ejpam-3949	307	8	.	.	PUNCT
ejpam-3949	307	9	references	reference	NOUN
ejpam-3949	307	10	520	520	NUM
ejpam-3949	308	1	[	[	X
ejpam-3949	308	2	4	4	NUM
ejpam-3949	308	3	]	]	X
ejpam-3949	308	4	r.	r.	X
ejpam-3949	308	5	chandrashekar	chandrashekar	PROPN
ejpam-3949	308	6	and	and	CCONJ
ejpam-3949	308	7	ss	ss	PROPN
ejpam-3949	308	8	.	.	PUNCT
ejpam-3949	308	9	n.	n.	PROPN
ejpam-3949	308	10	mohammed	mohammed	PROPN
ejpam-3949	308	11	,	,	PUNCT
ejpam-3949	308	12	a	a	DET
ejpam-3949	308	13	class	class	NOUN
ejpam-3949	308	14	of	of	ADP
ejpam-3949	308	15	energy	energy	NOUN
ejpam-3949	308	16	based	base	VERB
ejpam-3949	308	17	ensembles	ensemble	NOUN
ejpam-3949	308	18	in	in	ADP
ejpam-3949	308	19	tsallis	tsallis	PROPN
ejpam-3949	308	20	statistics	statistics	PROPN
ejpam-3949	308	21	,	,	PUNCT
ejpam-3949	308	22	j.	j.	PROPN
ejpam-3949	308	23	stat	stat	PROPN
ejpam-3949	308	24	.	.	PUNCT
ejpam-3949	309	1	mech	mech	PROPN
ejpam-3949	309	2	.	.	PUNCT
ejpam-3949	310	1	theory	theory	PROPN
ejpam-3949	310	2	exp	exp	PROPN
ejpam-3949	310	3	.	.	PROPN
ejpam-3949	310	4	,	,	PUNCT
ejpam-3949	310	5	2011	2011	NUM
ejpam-3949	310	6	,	,	PUNCT
ejpam-3949	310	7	2011	2011	NUM
ejpam-3949	310	8	,	,	PUNCT
ejpam-3949	310	9	p05018	p05018	NOUN
ejpam-3949	310	10	.	.	PUNCT
ejpam-3949	311	1	[	[	X
ejpam-3949	311	2	5	5	NUM
ejpam-3949	311	3	]	]	PUNCT
ejpam-3949	311	4	c.	c.	PROPN
ejpam-3949	311	5	corcino	corcino	PROPN
ejpam-3949	311	6	and	and	CCONJ
ejpam-3949	311	7	r.	r.	PROPN
ejpam-3949	311	8	corcino	corcino	PROPN
ejpam-3949	311	9	,	,	PUNCT
ejpam-3949	311	10	three	three	NUM
ejpam-3949	311	11	-	-	PUNCT
ejpam-3949	311	12	parameter	parameter	NOUN
ejpam-3949	311	13	logarithm	logarithm	NOUN
ejpam-3949	311	14	and	and	CCONJ
ejpam-3949	311	15	entropy	entropy	PROPN
ejpam-3949	311	16	,	,	PUNCT
ejpam-3949	311	17	j.	j.	PROPN
ejpam-3949	311	18	funct	funct	PROPN
ejpam-3949	311	19	.	.	PUNCT
ejpam-3949	312	1	spaces	space	NOUN
ejpam-3949	312	2	,	,	PUNCT
ejpam-3949	312	3	2020	2020	NUM
ejpam-3949	312	4	,	,	PUNCT
ejpam-3949	312	5	2020	2020	NUM
ejpam-3949	312	6	,	,	PUNCT
ejpam-3949	312	7	article	article	NOUN
ejpam-3949	312	8	i	i	PROPN
ejpam-3949	312	9	d	d	PROPN
ejpam-3949	312	10	9791789	9791789	NUM
ejpam-3949	312	11	,	,	PUNCT
ejpam-3949	312	12	10	10	NUM
ejpam-3949	312	13	pages	page	NOUN
ejpam-3949	312	14	.	.	PUNCT
ejpam-3949	313	1	https://doi.org/10.1155/2020/9791789	https://doi.org/10.1155/2020/9791789	ADV
ejpam-3949	313	2	.	.	PUNCT
ejpam-3949	314	1	[	[	X
ejpam-3949	314	2	6	6	NUM
ejpam-3949	314	3	]	]	PUNCT
ejpam-3949	314	4	w.	w.	PROPN
ejpam-3949	314	5	gibbs	gibbs	PROPN
ejpam-3949	314	6	,	,	PUNCT
ejpam-3949	314	7	entropy	entropy	ADJ
ejpam-3949	314	8	-	-	ADJ
ejpam-3949	314	9	basic	basic	ADJ
ejpam-3949	314	10	knowledge	knowledge	NOUN
ejpam-3949	314	11	101	101	NUM
ejpam-3949	314	12	,	,	PUNCT
ejpam-3949	314	13	www.basicknowledge101.com	www.basicknowledge101.com	X
ejpam-3949	314	14	.	.	PUNCT
ejpam-3949	315	1	[	[	X
ejpam-3949	315	2	7	7	X
ejpam-3949	315	3	]	]	X
ejpam-3949	315	4	v.	v.	ADP
ejpam-3949	315	5	schwämmle	schwämmle	PUNCT
ejpam-3949	315	6	and	and	CCONJ
ejpam-3949	315	7	c.	c.	PROPN
ejpam-3949	315	8	tsallis	tsallis	PROPN
ejpam-3949	315	9	,	,	PUNCT
ejpam-3949	315	10	two	two	NUM
ejpam-3949	315	11	-	-	PUNCT
ejpam-3949	315	12	parameter	parameter	NOUN
ejpam-3949	315	13	generalization	generalization	NOUN
ejpam-3949	315	14	of	of	ADP
ejpam-3949	315	15	the	the	DET
ejpam-3949	315	16	logarithm	logarithm	NOUN
ejpam-3949	315	17	and	and	CCONJ
ejpam-3949	315	18	exponential	exponential	ADJ
ejpam-3949	315	19	functions	function	NOUN
ejpam-3949	315	20	and	and	CCONJ
ejpam-3949	315	21	boltzmann	boltzmann	PROPN
ejpam-3949	315	22	-	-	PUNCT
ejpam-3949	315	23	gibbs	gibbs	PROPN
ejpam-3949	315	24	-	-	PUNCT
ejpam-3949	315	25	shannon	shannon	PROPN
ejpam-3949	315	26	entropy	entropy	PROPN
ejpam-3949	315	27	,	,	PUNCT
ejpam-3949	315	28	j.	j.	PROPN
ejpam-3949	315	29	math	math	PROPN
ejpam-3949	315	30	.	.	PUNCT
ejpam-3949	316	1	phys	phy	NOUN
ejpam-3949	316	2	.	.	PUNCT
ejpam-3949	316	3	,	,	PUNCT
ejpam-3949	316	4	2007	2007	NUM
ejpam-3949	316	5	,	,	PUNCT
ejpam-3949	316	6	48	48	NUM
ejpam-3949	316	7	,	,	PUNCT
ejpam-3949	316	8	113301	113301	NUM
ejpam-3949	316	9	.	.	PUNCT
ejpam-3949	317	1	[	[	X
ejpam-3949	317	2	8	8	NUM
ejpam-3949	317	3	]	]	X
ejpam-3949	317	4	c.	c.	PROPN
ejpam-3949	317	5	tsallis	tsallis	PROPN
ejpam-3949	317	6	,	,	PUNCT
ejpam-3949	317	7	possible	possible	ADJ
ejpam-3949	317	8	generalizations	generalization	NOUN
ejpam-3949	317	9	of	of	ADP
ejpam-3949	317	10	boltzmann	boltzmann	PROPN
ejpam-3949	317	11	-	-	PUNCT
ejpam-3949	317	12	gibbs	gibbs	PROPN
ejpam-3949	317	13	statistics	statistics	PROPN
ejpam-3949	317	14	,	,	PUNCT
ejpam-3949	317	15	j.	j.	PROPN
ejpam-3949	317	16	stat	stat	PROPN
ejpam-3949	317	17	.	.	PUNCT
ejpam-3949	318	1	phys	phy	NOUN
ejpam-3949	318	2	.	.	PUNCT
ejpam-3949	318	3	,	,	PUNCT
ejpam-3949	318	4	1988	1988	NUM
ejpam-3949	318	5	,	,	PUNCT
ejpam-3949	318	6	52	52	NUM
ejpam-3949	318	7	,	,	PUNCT
ejpam-3949	318	8	479–487	479–487	NUM
ejpam-3949	318	9	.	.	PUNCT
ejpam-3949	319	1	[	[	X
ejpam-3949	319	2	9	9	NUM
ejpam-3949	319	3	]	]	X
ejpam-3949	319	4	m.f	m.f	PROPN
ejpam-3949	319	5	.	.	PUNCT
ejpam-3949	319	6	shlesinger	shlesinger	PROPN
ejpam-3949	319	7	,	,	PUNCT
ejpam-3949	319	8	g.m	g.m	PROPN
ejpam-3949	319	9	.	.	PROPN
ejpam-3949	319	10	zaslavsky	zaslavsky	PROPN
ejpam-3949	319	11	,	,	PUNCT
ejpam-3949	319	12	j.	j.	PROPN
ejpam-3949	319	13	klafter	klafter	PROPN
ejpam-3949	319	14	,	,	PUNCT
ejpam-3949	319	15	nature	nature	NOUN
ejpam-3949	319	16	,	,	PUNCT
ejpam-3949	319	17	1993	1993	NUM
ejpam-3949	319	18	,	,	PUNCT
ejpam-3949	319	19	363	363	NUM
ejpam-3949	319	20	,	,	PUNCT
ejpam-3949	319	21	31–37	31–37	NOUN
ejpam-3949	319	22	.	.	PUNCT
ejpam-3949	320	1	[	[	X
ejpam-3949	320	2	10	10	NUM
ejpam-3949	320	3	]	]	X
ejpam-3949	320	4	c.	c.	PROPN
ejpam-3949	320	5	beck	beck	PROPN
ejpam-3949	320	6	,	,	PUNCT
ejpam-3949	320	7	application	application	NOUN
ejpam-3949	320	8	of	of	ADP
ejpam-3949	320	9	generalized	generalized	ADJ
ejpam-3949	320	10	thermostatics	thermostatic	NOUN
ejpam-3949	320	11	to	to	ADP
ejpam-3949	320	12	fully	fully	ADV
ejpam-3949	320	13	developed	develop	VERB
ejpam-3949	320	14	turbulence	turbulence	NOUN
ejpam-3949	320	15	,	,	PUNCT
ejpam-3949	320	16	physica	physica	VERB
ejpam-3949	320	17	a	a	DET
ejpam-3949	320	18	:	:	PUNCT
ejpam-3949	320	19	statistical	statistical	ADJ
ejpam-3949	320	20	mechanics	mechanic	NOUN
ejpam-3949	320	21	and	and	CCONJ
ejpam-3949	320	22	its	its	PRON
ejpam-3949	320	23	applications	application	NOUN
ejpam-3949	320	24	,	,	PUNCT
ejpam-3949	320	25	2000	2000	NUM
ejpam-3949	320	26	,	,	PUNCT
ejpam-3949	320	27	277	277	NUM
ejpam-3949	320	28	,	,	PUNCT
ejpam-3949	320	29	115–123	115–123	NUM
ejpam-3949	320	30	.	.	PUNCT
ejpam-3949	321	1	[	[	X
ejpam-3949	321	2	11	11	NUM
ejpam-3949	321	3	]	]	PUNCT
ejpam-3949	321	4	i.	i.	NOUN
ejpam-3949	321	5	bediaga	bediaga	PROPN
ejpam-3949	321	6	,	,	PUNCT
ejpam-3949	321	7	e.m	e.m	PROPN
ejpam-3949	321	8	.	.	PROPN
ejpam-3949	321	9	curado	curado	PROPN
ejpam-3949	321	10	,	,	PUNCT
ejpam-3949	321	11	j.m	j.m	PROPN
ejpam-3949	321	12	.	.	PROPN
ejpam-3949	321	13	de	de	PROPN
ejpam-3949	321	14	miranda	miranda	PROPN
ejpam-3949	321	15	,	,	PUNCT
ejpam-3949	321	16	a	a	DET
ejpam-3949	321	17	nonextensive	nonextensive	NOUN
ejpam-3949	321	18	thermodynamical	thermodynamical	ADJ
ejpam-3949	321	19	equilibrium	equilibrium	NOUN
ejpam-3949	321	20	approach	approach	NOUN
ejpam-3949	321	21	in	in	ADP
ejpam-3949	321	22	e+e−	e+e−	PROPN
ejpam-3949	321	23	→	→	SYM
ejpam-3949	321	24	hadrons	hadron	NOUN
ejpam-3949	321	25	,	,	PUNCT
ejpam-3949	321	26	physica	physica	NOUN
ejpam-3949	321	27	a	a	DET
ejpam-3949	321	28	:	:	PUNCT
ejpam-3949	321	29	statistical	statistical	ADJ
ejpam-3949	321	30	mechanics	mechanic	NOUN
ejpam-3949	321	31	and	and	CCONJ
ejpam-3949	321	32	its	its	PRON
ejpam-3949	321	33	applications	application	NOUN
ejpam-3949	321	34	,	,	PUNCT
ejpam-3949	321	35	2000	2000	NUM
ejpam-3949	321	36	,	,	PUNCT
ejpam-3949	321	37	286	286	NUM
ejpam-3949	321	38	,	,	PUNCT
ejpam-3949	321	39	156	156	NUM
ejpam-3949	321	40	-	-	SYM
ejpam-3949	321	41	163	163	NUM
ejpam-3949	321	42	.	.	PUNCT
ejpam-3949	322	1	[	[	X
ejpam-3949	322	2	12	12	NUM
ejpam-3949	322	3	]	]	X
ejpam-3949	322	4	d.b	d.b	PROPN
ejpam-3949	322	5	.	.	PROPN
ejpam-3949	322	6	walton	walton	PROPN
ejpam-3949	322	7	,	,	PUNCT
ejpam-3949	322	8	j.	j.	PROPN
ejpam-3949	322	9	rafelski	rafelski	PROPN
ejpam-3949	322	10	,	,	PUNCT
ejpam-3949	322	11	equilibrium	equilibrium	NOUN
ejpam-3949	322	12	distribution	distribution	NOUN
ejpam-3949	322	13	of	of	ADP
ejpam-3949	322	14	heavy	heavy	ADJ
ejpam-3949	322	15	quarks	quarks	NOUN
ejpam-3949	322	16	in	in	ADP
ejpam-3949	322	17	fokker	fokker	NOUN
ejpam-3949	322	18	-	-	PUNCT
ejpam-3949	322	19	plank	plank	NOUN
ejpam-3949	322	20	dynamics	dynamic	NOUN
ejpam-3949	322	21	,	,	PUNCT
ejpam-3949	322	22	phys	phy	NOUN
ejpam-3949	322	23	.	.	PUNCT
ejpam-3949	323	1	rev	rev	PROPN
ejpam-3949	323	2	.	.	PROPN
ejpam-3949	323	3	lett	lett	PROPN
ejpam-3949	323	4	.	.	PROPN
ejpam-3949	323	5	,	,	PUNCT
ejpam-3949	323	6	2000	2000	NUM
ejpam-3949	323	7	,	,	PUNCT
ejpam-3949	323	8	84	84	NUM
ejpam-3949	323	9	,	,	PUNCT
ejpam-3949	323	10	p.	p.	NOUN
ejpam-3949	323	11	31	31	NUM
ejpam-3949	323	12	.	.	PUNCT
ejpam-3949	324	1	[	[	X
ejpam-3949	324	2	13	13	NUM
ejpam-3949	324	3	]	]	X
ejpam-3949	324	4	j.	j.	PROPN
ejpam-3949	324	5	binney	binney	PROPN
ejpam-3949	324	6	,	,	PUNCT
ejpam-3949	324	7	s.tremaine	s.tremaine	NOUN
ejpam-3949	324	8	,	,	PUNCT
ejpam-3949	324	9	glactic	glactic	ADJ
ejpam-3949	324	10	dynamics	dynamic	NOUN
ejpam-3949	324	11	,	,	PUNCT
ejpam-3949	324	12	princeton	princeton	PROPN
ejpam-3949	324	13	university	university	PROPN
ejpam-3949	324	14	press	press	PROPN
ejpam-3949	324	15	,	,	PUNCT
ejpam-3949	324	16	princeton	princeton	PROPN
ejpam-3949	324	17	,	,	PUNCT
ejpam-3949	324	18	nj	nj	PROPN
ejpam-3949	324	19	,	,	PUNCT
ejpam-3949	324	20	1987	1987	NUM
ejpam-3949	324	21	;	;	PUNCT
ejpam-3949	324	22	p.	p.	NOUN
ejpam-3949	324	23	267	267	NUM
ejpam-3949	324	24	.	.	PUNCT
ejpam-3949	325	1	[	[	X
ejpam-3949	325	2	14	14	NUM
ejpam-3949	325	3	]	]	X
ejpam-3949	325	4	d.c	d.c	PROPN
ejpam-3949	325	5	.	.	PROPN
ejpam-3949	325	6	clayton	clayton	PROPN
ejpam-3949	325	7	,	,	PUNCT
ejpam-3949	325	8	maxwellian	maxwellian	ADJ
ejpam-3949	325	9	relative	relative	ADJ
ejpam-3949	325	10	energies	energy	NOUN
ejpam-3949	325	11	and	and	CCONJ
ejpam-3949	325	12	solar	solar	ADJ
ejpam-3949	325	13	neutrinos	neutrino	NOUN
ejpam-3949	325	14	,	,	PUNCT
ejpam-3949	325	15	nature	nature	NOUN
ejpam-3949	325	16	1974	1974	NUM
ejpam-3949	325	17	,	,	PUNCT
ejpam-3949	325	18	249	249	NUM
ejpam-3949	325	19	,	,	PUNCT
ejpam-3949	325	20	p.	p.	NOUN
ejpam-3949	325	21	131	131	NUM
ejpam-3949	325	22	.	.	PUNCT
ejpam-3949	326	1	[	[	X
ejpam-3949	326	2	15	15	NUM
ejpam-3949	326	3	]	]	X
ejpam-3949	326	4	f.	f.	PROPN
ejpam-3949	326	5	reif	reif	PROPN
ejpam-3949	326	6	,	,	PUNCT
ejpam-3949	326	7	fundamentals	fundamental	NOUN
ejpam-3949	326	8	of	of	ADP
ejpam-3949	326	9	statistical	statistical	ADJ
ejpam-3949	326	10	and	and	CCONJ
ejpam-3949	326	11	thermal	thermal	ADJ
ejpam-3949	326	12	physics	physic	NOUN
ejpam-3949	326	13	,	,	PUNCT
ejpam-3949	326	14	international	international	ADJ
ejpam-3949	326	15	editions	edition	NOUN
ejpam-3949	326	16	,	,	PUNCT
ejpam-3949	326	17	mcgraw	mcgraw	PROPN
ejpam-3949	326	18	-	-	PUNCT
ejpam-3949	326	19	hill	hill	NOUN
ejpam-3949	326	20	book	book	NOUN
ejpam-3949	326	21	company	company	NOUN
ejpam-3949	326	22	,	,	PUNCT
ejpam-3949	326	23	singapore	singapore	PROPN
ejpam-3949	326	24	,	,	PUNCT
ejpam-3949	326	25	1985	1985	NUM
ejpam-3949	326	26	.	.	PUNCT