id	sid	tid	token	lemma	pos
cet-14439	1	1	doi	doi	NOUN
cet-14439	1	2	:	:	PUNCT
cet-14439	1	3	10.3303	10.3303	NUM
cet-14439	1	4	/	/	SYM
cet-14439	1	5	cet24109016	cet24109016	PROPN
cet-14439	1	6	paper	paper	PROPN
cet-14439	1	7	received	receive	VERB
cet-14439	1	8	:	:	PUNCT
cet-14439	1	9	26	26	NUM
cet-14439	1	10	november	november	PROPN
cet-14439	1	11	2023	2023	NUM
cet-14439	1	12	;	;	PUNCT
cet-14439	1	13	revised	revise	VERB
cet-14439	1	14	:	:	PUNCT
cet-14439	1	15	4	4	NUM
cet-14439	1	16	february	february	NOUN
cet-14439	1	17	2024	2024	NUM
cet-14439	1	18	;	;	PUNCT
cet-14439	1	19	accepted	accept	VERB
cet-14439	1	20	:	:	PUNCT
cet-14439	1	21	14	14	NUM
cet-14439	1	22	april	april	PROPN
cet-14439	1	23	2024	2024	NUM
cet-14439	1	24	please	please	INTJ
cet-14439	1	25	cite	cite	VERB
cet-14439	1	26	this	this	DET
cet-14439	1	27	article	article	NOUN
cet-14439	1	28	as	as	ADP
cet-14439	1	29	:	:	PUNCT
cet-14439	1	30	trindade	trindade	VERB
cet-14439	1	31	júnior	júnior	PROPN
cet-14439	1	32	v.n	v.n	PROPN
cet-14439	1	33	.	.	PROPN
cet-14439	1	34	,	,	PUNCT
cet-14439	1	35	guirardello	guirardello	PROPN
cet-14439	1	36	r.	r.	PROPN
cet-14439	1	37	,	,	PUNCT
cet-14439	1	38	2024	2024	NUM
cet-14439	1	39	,	,	PUNCT
cet-14439	1	40	numerical	numerical	ADJ
cet-14439	1	41	simulation	simulation	NOUN
cet-14439	1	42	of	of	ADP
cet-14439	1	43	gamma	gamma	NOUN
cet-14439	1	44	-	-	PUNCT
cet-14439	1	45	valerolactone	valerolactone	NOUN
cet-14439	1	46	adsorption	adsorption	NOUN
cet-14439	1	47	into	into	ADP
cet-14439	1	48	porous	porous	ADJ
cet-14439	1	49	spheres	sphere	NOUN
cet-14439	1	50	in	in	ADP
cet-14439	1	51	a	a	DET
cet-14439	1	52	batch	batch	NOUN
cet-14439	1	53	process	process	NOUN
cet-14439	1	54	,	,	PUNCT
cet-14439	1	55	chemical	chemical	ADJ
cet-14439	1	56	engineering	engineering	NOUN
cet-14439	1	57	transactions	transaction	NOUN
cet-14439	1	58	,	,	PUNCT
cet-14439	1	59	109	109	NUM
cet-14439	1	60	,	,	PUNCT
cet-14439	1	61	91	91	NUM
cet-14439	1	62	-	-	SYM
cet-14439	1	63	96	96	NUM
cet-14439	1	64	doi:10.3303	doi:10.3303	NOUN
cet-14439	1	65	/	/	SYM
cet-14439	1	66	cet24109016	cet24109016	PROPN
cet-14439	1	67	chemical	chemical	PROPN
cet-14439	1	68	engineering	engineering	PROPN
cet-14439	1	69	transactions	transaction	NOUN
cet-14439	1	70	vol	vol	NOUN
cet-14439	1	71	.	.	PROPN
cet-14439	2	1	109	109	NUM
cet-14439	2	2	,	,	PUNCT
cet-14439	2	3	2024	2024	NUM
cet-14439	2	4	a	a	DET
cet-14439	2	5	publication	publication	NOUN
cet-14439	2	6	of	of	ADP
cet-14439	2	7	the	the	DET
cet-14439	2	8	italian	italian	ADJ
cet-14439	2	9	association	association	NOUN
cet-14439	2	10	of	of	ADP
cet-14439	2	11	chemical	chemical	PROPN
cet-14439	2	12	engineering	engineering	NOUN
cet-14439	2	13	online	online	ADV
cet-14439	2	14	at	at	ADP
cet-14439	2	15	www.cetjournal.it	www.cetjournal.it	PROPN
cet-14439	2	16	guest	guest	NOUN
cet-14439	2	17	editors	editor	NOUN
cet-14439	2	18	:	:	PUNCT
cet-14439	2	19	leonardo	leonardo	PROPN
cet-14439	2	20	tognotti	tognotti	PROPN
cet-14439	2	21	,	,	PUNCT
cet-14439	2	22	rubens	rubens	PROPN
cet-14439	2	23	maciel	maciel	PROPN
cet-14439	2	24	filho	filho	PROPN
cet-14439	2	25	,	,	PUNCT
cet-14439	2	26	viatcheslav	viatcheslav	PROPN
cet-14439	2	27	kafarov	kafarov	PROPN
cet-14439	2	28	copyright	copyright	NOUN
cet-14439	2	29	©	©	PROPN
cet-14439	2	30	2024	2024	NUM
cet-14439	2	31	,	,	PUNCT
cet-14439	2	32	aidic	aidic	ADJ
cet-14439	2	33	servizi	servizi	PROPN
cet-14439	2	34	s.r.l	s.r.l	NOUN
cet-14439	2	35	.	.	PUNCT
cet-14439	3	1	isbn	isbn	PROPN
cet-14439	3	2	979	979	NUM
cet-14439	3	3	-	-	SYM
cet-14439	3	4	12	12	NUM
cet-14439	3	5	-	-	PUNCT
cet-14439	3	6	81206	81206	NUM
cet-14439	3	7	-	-	PUNCT
cet-14439	3	8	09	09	NUM
cet-14439	3	9	-	-	PUNCT
cet-14439	3	10	0	0	NUM
cet-14439	3	11	;	;	PUNCT
cet-14439	3	12	issn	issn	PROPN
cet-14439	3	13	2283	2283	NUM
cet-14439	3	14	-	-	SYM
cet-14439	3	15	9216	9216	NUM
cet-14439	3	16	numerical	numerical	ADJ
cet-14439	3	17	simulation	simulation	NOUN
cet-14439	3	18	of	of	ADP
cet-14439	3	19	-valerolactone	-valerolactone	NUM
cet-14439	3	20	adsorption	adsorption	NOUN
cet-14439	3	21	into	into	ADP
cet-14439	3	22	porous	porous	ADJ
cet-14439	3	23	spheres	sphere	NOUN
cet-14439	3	24	in	in	ADP
cet-14439	3	25	a	a	DET
cet-14439	3	26	batch	batch	NOUN
cet-14439	3	27	process	process	NOUN
cet-14439	3	28	valter	valter	NOUN
cet-14439	3	29	nunes	nunes	PROPN
cet-14439	3	30	trindade	trindade	VERB
cet-14439	3	31	júnior	júnior	PROPN
cet-14439	3	32	,	,	PUNCT
cet-14439	3	33	reginaldo	reginaldo	PROPN
cet-14439	3	34	guirardello	guirardello	PROPN
cet-14439	3	35	school	school	NOUN
cet-14439	3	36	of	of	ADP
cet-14439	3	37	chemical	chemical	PROPN
cet-14439	3	38	engineering	engineering	NOUN
cet-14439	3	39	,	,	PUNCT
cet-14439	3	40	university	university	PROPN
cet-14439	3	41	of	of	ADP
cet-14439	3	42	campinas	campinas	PROPN
cet-14439	3	43	,	,	PUNCT
cet-14439	3	44	av	av	PROPN
cet-14439	3	45	.	.	PUNCT
cet-14439	4	1	albert	albert	PROPN
cet-14439	4	2	einstein	einstein	PROPN
cet-14439	4	3	500	500	NUM
cet-14439	4	4	,	,	PUNCT
cet-14439	4	5	13083	13083	NUM
cet-14439	4	6	-	-	SYM
cet-14439	4	7	852	852	NUM
cet-14439	4	8	,	,	PUNCT
cet-14439	4	9	campinas	campinas	PROPN
cet-14439	4	10	-	-	PUNCT
cet-14439	4	11	sp	sp	PROPN
cet-14439	4	12	,	,	PUNCT
cet-14439	4	13	brazil	brazil	PROPN
cet-14439	4	14	guira@unicamp.br	guira@unicamp.br	VERB
cet-14439	4	15	the	the	DET
cet-14439	4	16	production	production	NOUN
cet-14439	4	17	of	of	ADP
cet-14439	4	18	ethanol	ethanol	NOUN
cet-14439	4	19	from	from	ADP
cet-14439	4	20	lignocellulosic	lignocellulosic	ADJ
cet-14439	4	21	biomass	biomass	NOUN
cet-14439	4	22	is	be	AUX
cet-14439	4	23	more	more	ADV
cet-14439	4	24	complex	complex	ADJ
cet-14439	4	25	in	in	ADP
cet-14439	4	26	relation	relation	NOUN
cet-14439	4	27	to	to	PART
cet-14439	4	28	ethanol	ethanol	NOUN
cet-14439	4	29	produced	produce	VERB
cet-14439	4	30	from	from	ADP
cet-14439	4	31	feedstock	feedstock	NOUN
cet-14439	4	32	containing	contain	VERB
cet-14439	4	33	sugars	sugar	NOUN
cet-14439	4	34	or	or	CCONJ
cet-14439	4	35	starch	starch	NOUN
cet-14439	4	36	,	,	PUNCT
cet-14439	4	37	since	since	SCONJ
cet-14439	4	38	it	it	PRON
cet-14439	4	39	requires	require	VERB
cet-14439	4	40	the	the	DET
cet-14439	4	41	conversion	conversion	NOUN
cet-14439	4	42	of	of	ADP
cet-14439	4	43	polysaccharides	polysaccharide	NOUN
cet-14439	4	44	,	,	PUNCT
cet-14439	4	45	cellulose	cellulose	NOUN
cet-14439	4	46	or	or	CCONJ
cet-14439	4	47	hemicellulose	hemicellulose	NOUN
cet-14439	4	48	,	,	PUNCT
cet-14439	4	49	into	into	ADP
cet-14439	4	50	fermentable	fermentable	ADJ
cet-14439	4	51	sugars	sugar	NOUN
cet-14439	4	52	.	.	PUNCT
cet-14439	5	1	an	an	DET
cet-14439	5	2	alternative	alternative	NOUN
cet-14439	5	3	to	to	PART
cet-14439	5	4	improve	improve	VERB
cet-14439	5	5	this	this	DET
cet-14439	5	6	conversion	conversion	NOUN
cet-14439	5	7	of	of	ADP
cet-14439	5	8	biomass	biomass	NOUN
cet-14439	5	9	polysaccharides	polysaccharide	NOUN
cet-14439	5	10	into	into	ADP
cet-14439	5	11	sugars	sugar	NOUN
cet-14439	5	12	is	be	AUX
cet-14439	5	13	the	the	DET
cet-14439	5	14	use	use	NOUN
cet-14439	5	15	of	of	ADP
cet-14439	5	16	-valerolactone	-valerolactone	NUM
cet-14439	5	17	(	(	PUNCT
cet-14439	5	18	gvl	gvl	PROPN
cet-14439	5	19	)	)	PUNCT
cet-14439	5	20	as	as	ADP
cet-14439	5	21	a	a	DET
cet-14439	5	22	solvent	solvent	NOUN
cet-14439	5	23	.	.	PUNCT
cet-14439	6	1	however	however	ADV
cet-14439	6	2	,	,	PUNCT
cet-14439	6	3	the	the	DET
cet-14439	6	4	gvl	gvl	PROPN
cet-14439	6	5	must	must	AUX
cet-14439	6	6	be	be	AUX
cet-14439	6	7	removed	remove	VERB
cet-14439	6	8	before	before	ADP
cet-14439	6	9	the	the	DET
cet-14439	6	10	fermentation	fermentation	NOUN
cet-14439	6	11	,	,	PUNCT
cet-14439	6	12	since	since	SCONJ
cet-14439	6	13	its	its	PRON
cet-14439	6	14	presence	presence	NOUN
cet-14439	6	15	is	be	AUX
cet-14439	6	16	harmful	harmful	ADJ
cet-14439	6	17	to	to	ADP
cet-14439	6	18	the	the	DET
cet-14439	6	19	microorganisms	microorganism	NOUN
cet-14439	6	20	that	that	PRON
cet-14439	6	21	metabolize	metabolize	VERB
cet-14439	6	22	glucose	glucose	NOUN
cet-14439	6	23	to	to	PART
cet-14439	6	24	produce	produce	VERB
cet-14439	6	25	ethanol	ethanol	NOUN
cet-14439	6	26	.	.	PUNCT
cet-14439	7	1	one	one	NUM
cet-14439	7	2	extraction	extraction	NOUN
cet-14439	7	3	technique	technique	NOUN
cet-14439	7	4	is	be	AUX
cet-14439	7	5	the	the	DET
cet-14439	7	6	use	use	NOUN
cet-14439	7	7	of	of	ADP
cet-14439	7	8	subcritical	subcritical	ADJ
cet-14439	7	9	co2	co2	NOUN
cet-14439	7	10	,	,	PUNCT
cet-14439	7	11	which	which	PRON
cet-14439	7	12	is	be	AUX
cet-14439	7	13	able	able	ADJ
cet-14439	7	14	to	to	PART
cet-14439	7	15	separate	separate	VERB
cet-14439	7	16	large	large	ADJ
cet-14439	7	17	amounts	amount	NOUN
cet-14439	7	18	of	of	ADP
cet-14439	7	19	gvl	gvl	PROPN
cet-14439	7	20	,	,	PUNCT
cet-14439	7	21	but	but	CCONJ
cet-14439	7	22	a	a	DET
cet-14439	7	23	complementary	complementary	ADJ
cet-14439	7	24	method	method	NOUN
cet-14439	7	25	is	be	AUX
cet-14439	7	26	still	still	ADV
cet-14439	7	27	required	require	VERB
cet-14439	7	28	to	to	PART
cet-14439	7	29	separate	separate	VERB
cet-14439	7	30	small	small	ADJ
cet-14439	7	31	quantities	quantity	NOUN
cet-14439	7	32	of	of	ADP
cet-14439	7	33	gvl	gvl	PROPN
cet-14439	7	34	remaining	remain	VERB
cet-14439	7	35	in	in	ADP
cet-14439	7	36	the	the	DET
cet-14439	7	37	sugar	sugar	NOUN
cet-14439	7	38	solution	solution	NOUN
cet-14439	7	39	,	,	PUNCT
cet-14439	7	40	which	which	PRON
cet-14439	7	41	can	can	AUX
cet-14439	7	42	be	be	AUX
cet-14439	7	43	done	do	VERB
cet-14439	7	44	efficiently	efficiently	ADV
cet-14439	7	45	with	with	ADP
cet-14439	7	46	adsorption	adsorption	NOUN
cet-14439	7	47	.	.	PUNCT
cet-14439	8	1	in	in	ADP
cet-14439	8	2	this	this	DET
cet-14439	8	3	work	work	NOUN
cet-14439	8	4	,	,	PUNCT
cet-14439	8	5	the	the	DET
cet-14439	8	6	adsorption	adsorption	NOUN
cet-14439	8	7	of	of	ADP
cet-14439	8	8	-valerolactone	-valerolactone	NUM
cet-14439	8	9	by	by	ADP
cet-14439	8	10	porous	porous	ADJ
cet-14439	8	11	spheres	sphere	NOUN
cet-14439	8	12	made	make	VERB
cet-14439	8	13	of	of	ADP
cet-14439	8	14	a	a	DET
cet-14439	8	15	resin	resin	NOUN
cet-14439	8	16	in	in	ADP
cet-14439	8	17	batch	batch	NOUN
cet-14439	8	18	mode	mode	NOUN
cet-14439	8	19	is	be	AUX
cet-14439	8	20	studied	study	VERB
cet-14439	8	21	to	to	PART
cet-14439	8	22	remove	remove	VERB
cet-14439	8	23	the	the	DET
cet-14439	8	24	gvl	gvl	NOUN
cet-14439	8	25	from	from	ADP
cet-14439	8	26	the	the	DET
cet-14439	8	27	sugar	sugar	NOUN
cet-14439	8	28	solution	solution	NOUN
cet-14439	8	29	containing	contain	VERB
cet-14439	8	30	glucose	glucose	NOUN
cet-14439	8	31	.	.	PUNCT
cet-14439	9	1	this	this	DET
cet-14439	9	2	work	work	NOUN
cet-14439	9	3	is	be	AUX
cet-14439	9	4	computational	computational	ADJ
cet-14439	9	5	and	and	CCONJ
cet-14439	9	6	the	the	DET
cet-14439	9	7	modelling	modelling	NOUN
cet-14439	9	8	considers	consider	VERB
cet-14439	9	9	the	the	DET
cet-14439	9	10	mass	mass	NOUN
cet-14439	9	11	transfer	transfer	NOUN
cet-14439	9	12	from	from	ADP
cet-14439	9	13	the	the	DET
cet-14439	9	14	solution	solution	NOUN
cet-14439	9	15	to	to	ADP
cet-14439	9	16	the	the	DET
cet-14439	9	17	surface	surface	NOUN
cet-14439	9	18	of	of	ADP
cet-14439	9	19	the	the	DET
cet-14439	9	20	spheres	sphere	NOUN
cet-14439	9	21	,	,	PUNCT
cet-14439	9	22	the	the	DET
cet-14439	9	23	diffusion	diffusion	NOUN
cet-14439	9	24	inside	inside	ADP
cet-14439	9	25	the	the	DET
cet-14439	9	26	pores	pore	NOUN
cet-14439	9	27	of	of	ADP
cet-14439	9	28	the	the	DET
cet-14439	9	29	spheres	sphere	NOUN
cet-14439	9	30	,	,	PUNCT
cet-14439	9	31	and	and	CCONJ
cet-14439	9	32	then	then	ADV
cet-14439	9	33	the	the	DET
cet-14439	9	34	adsorption	adsorption	NOUN
cet-14439	9	35	of	of	ADP
cet-14439	9	36	gvl	gvl	PROPN
cet-14439	9	37	.	.	PUNCT
cet-14439	10	1	the	the	DET
cet-14439	10	2	numerical	numerical	ADJ
cet-14439	10	3	resolution	resolution	NOUN
cet-14439	10	4	is	be	AUX
cet-14439	10	5	done	do	VERB
cet-14439	10	6	using	use	VERB
cet-14439	10	7	two	two	NUM
cet-14439	10	8	numerical	numerical	ADJ
cet-14439	10	9	methods	method	NOUN
cet-14439	10	10	,	,	PUNCT
cet-14439	10	11	the	the	DET
cet-14439	10	12	finite	finite	NOUN
cet-14439	10	13	differences	difference	NOUN
cet-14439	10	14	and	and	CCONJ
cet-14439	10	15	the	the	DET
cet-14439	10	16	variational	variational	ADJ
cet-14439	10	17	method	method	NOUN
cet-14439	10	18	.	.	PUNCT
cet-14439	11	1	the	the	DET
cet-14439	11	2	results	result	NOUN
cet-14439	11	3	are	be	AUX
cet-14439	11	4	compared	compare	VERB
cet-14439	11	5	using	use	VERB
cet-14439	11	6	different	different	ADJ
cet-14439	11	7	numbers	number	NOUN
cet-14439	11	8	of	of	ADP
cet-14439	11	9	radial	radial	ADJ
cet-14439	11	10	intervals	interval	NOUN
cet-14439	11	11	in	in	ADP
cet-14439	11	12	the	the	DET
cet-14439	11	13	spherical	spherical	ADJ
cet-14439	11	14	particles	particle	NOUN
cet-14439	11	15	.	.	PUNCT
cet-14439	12	1	keywords	keyword	NOUN
cet-14439	12	2	:	:	PUNCT
cet-14439	12	3	biomass	biomass	NOUN
cet-14439	12	4	,	,	PUNCT
cet-14439	12	5	ethanol	ethanol	NOUN
cet-14439	12	6	,	,	PUNCT
cet-14439	12	7	glucose	glucose	NOUN
cet-14439	12	8	,	,	PUNCT
cet-14439	12	9	-valerolactone	-valerolactone	NUM
cet-14439	12	10	,	,	PUNCT
cet-14439	12	11	adsorption	adsorption	NOUN
cet-14439	12	12	,	,	PUNCT
cet-14439	12	13	finite	finite	VERB
cet-14439	12	14	differences	difference	NOUN
cet-14439	12	15	,	,	PUNCT
cet-14439	12	16	variational	variational	ADJ
cet-14439	12	17	formulation	formulation	NOUN
cet-14439	12	18	.	.	PUNCT
cet-14439	13	1	1	1	X
cet-14439	13	2	.	.	X
cet-14439	13	3	introduction	introduction	NOUN
cet-14439	13	4	ethanol	ethanol	NOUN
cet-14439	13	5	can	can	AUX
cet-14439	13	6	be	be	AUX
cet-14439	13	7	produced	produce	VERB
cet-14439	13	8	from	from	ADP
cet-14439	13	9	lignocellulosic	lignocellulosic	ADJ
cet-14439	13	10	biomass	biomass	NOUN
cet-14439	13	11	by	by	ADP
cet-14439	13	12	the	the	DET
cet-14439	13	13	hydrolysis	hydrolysis	NOUN
cet-14439	13	14	of	of	ADP
cet-14439	13	15	cellulose	cellulose	NOUN
cet-14439	13	16	and	and	CCONJ
cet-14439	13	17	hemicellulose	hemicellulose	NOUN
cet-14439	13	18	into	into	ADP
cet-14439	13	19	monosaccharides	monosaccharide	NOUN
cet-14439	13	20	(	(	PUNCT
cet-14439	13	21	sugars	sugar	NOUN
cet-14439	13	22	)	)	PUNCT
cet-14439	13	23	.	.	PUNCT
cet-14439	14	1	lignocellulosic	lignocellulosic	PROPN
cet-14439	14	2	sources	source	NOUN
cet-14439	14	3	available	available	ADJ
cet-14439	14	4	at	at	ADP
cet-14439	14	5	industrial	industrial	ADJ
cet-14439	14	6	scale	scale	NOUN
cet-14439	14	7	are	be	AUX
cet-14439	14	8	corn	corn	NOUN
cet-14439	14	9	crop	crop	NOUN
cet-14439	14	10	residues	residue	NOUN
cet-14439	14	11	and	and	CCONJ
cet-14439	14	12	sugarcane	sugarcane	NOUN
cet-14439	14	13	bagasse	bagasse	NOUN
cet-14439	14	14	,	,	PUNCT
cet-14439	14	15	for	for	ADP
cet-14439	14	16	example	example	NOUN
cet-14439	14	17	,	,	PUNCT
cet-14439	14	18	but	but	CCONJ
cet-14439	14	19	there	there	PRON
cet-14439	14	20	are	be	VERB
cet-14439	14	21	many	many	ADJ
cet-14439	14	22	others	other	NOUN
cet-14439	14	23	.	.	PUNCT
cet-14439	15	1	however	however	ADV
cet-14439	15	2	,	,	PUNCT
cet-14439	15	3	the	the	DET
cet-14439	15	4	hydrolysis	hydrolysis	NOUN
cet-14439	15	5	process	process	NOUN
cet-14439	15	6	of	of	ADP
cet-14439	15	7	these	these	DET
cet-14439	15	8	materials	material	NOUN
cet-14439	15	9	is	be	AUX
cet-14439	15	10	complex	complex	ADJ
cet-14439	15	11	and	and	CCONJ
cet-14439	15	12	expensive	expensive	ADJ
cet-14439	15	13	,	,	PUNCT
cet-14439	15	14	so	so	SCONJ
cet-14439	15	15	improvements	improvement	NOUN
cet-14439	15	16	are	be	AUX
cet-14439	15	17	required	require	VERB
cet-14439	15	18	to	to	PART
cet-14439	15	19	make	make	VERB
cet-14439	15	20	this	this	DET
cet-14439	15	21	process	process	NOUN
cet-14439	15	22	economically	economically	ADV
cet-14439	15	23	viable	viable	ADJ
cet-14439	15	24	.	.	PUNCT
cet-14439	16	1	it	it	PRON
cet-14439	16	2	has	have	AUX
cet-14439	16	3	been	be	AUX
cet-14439	16	4	shown	show	VERB
cet-14439	16	5	that	that	SCONJ
cet-14439	16	6	-valerolactone	-valerolactone	NUM
cet-14439	16	7	(	(	PUNCT
cet-14439	16	8	gvl	gvl	PROPN
cet-14439	16	9	)	)	PUNCT
cet-14439	16	10	as	as	SCONJ
cet-14439	16	11	solvent	solvent	ADJ
cet-14439	16	12	in	in	ADP
cet-14439	16	13	the	the	DET
cet-14439	16	14	conversion	conversion	NOUN
cet-14439	16	15	of	of	ADP
cet-14439	16	16	the	the	DET
cet-14439	16	17	lignocellulosic	lignocellulosic	ADJ
cet-14439	16	18	biomass	biomass	NOUN
cet-14439	16	19	into	into	ADP
cet-14439	16	20	sugars	sugar	NOUN
cet-14439	16	21	,	,	PUNCT
cet-14439	16	22	in	in	ADP
cet-14439	16	23	the	the	DET
cet-14439	16	24	presence	presence	NOUN
cet-14439	16	25	of	of	ADP
cet-14439	16	26	low	low	ADJ
cet-14439	16	27	concentration	concentration	NOUN
cet-14439	16	28	acid	acid	NOUN
cet-14439	16	29	,	,	PUNCT
cet-14439	16	30	has	have	VERB
cet-14439	16	31	advantages	advantage	NOUN
cet-14439	16	32	over	over	ADP
cet-14439	16	33	water	water	NOUN
cet-14439	16	34	alone	alone	ADV
cet-14439	16	35	(	(	PUNCT
cet-14439	16	36	mellmer	mellmer	NOUN
cet-14439	16	37	et	et	PROPN
cet-14439	16	38	al	al	PROPN
cet-14439	16	39	.	.	PROPN
cet-14439	16	40	,	,	PUNCT
cet-14439	16	41	2014	2014	NUM
cet-14439	16	42	)	)	PUNCT
cet-14439	16	43	,	,	PUNCT
cet-14439	16	44	with	with	ADP
cet-14439	16	45	increased	increase	VERB
cet-14439	16	46	catalytic	catalytic	ADJ
cet-14439	16	47	activity	activity	NOUN
cet-14439	16	48	(	(	PUNCT
cet-14439	16	49	alonso	alonso	NOUN
cet-14439	16	50	et	et	NOUN
cet-14439	16	51	al	al	PROPN
cet-14439	16	52	.	.	PROPN
cet-14439	16	53	,	,	PUNCT
cet-14439	16	54	2013	2013	NUM
cet-14439	16	55	)	)	PUNCT
cet-14439	16	56	,	,	PUNCT
cet-14439	16	57	and	and	CCONJ
cet-14439	16	58	higher	high	ADJ
cet-14439	16	59	selectivity	selectivity	NOUN
cet-14439	16	60	and	and	CCONJ
cet-14439	16	61	efficiency	efficiency	NOUN
cet-14439	16	62	of	of	ADP
cet-14439	16	63	the	the	DET
cet-14439	16	64	hydrolysis	hydrolysis	NOUN
cet-14439	16	65	reaction	reaction	NOUN
cet-14439	16	66	,	,	PUNCT
cet-14439	16	67	minimizing	minimize	VERB
cet-14439	16	68	sugar	sugar	NOUN
cet-14439	16	69	degradation	degradation	NOUN
cet-14439	16	70	(	(	PUNCT
cet-14439	16	71	luterbacher	luterbacher	VERB
cet-14439	16	72	et	et	PROPN
cet-14439	16	73	al	al	PROPN
cet-14439	16	74	.	.	PROPN
cet-14439	16	75	,	,	PUNCT
cet-14439	16	76	2014	2014	NUM
cet-14439	16	77	)	)	PUNCT
cet-14439	16	78	.	.	PUNCT
cet-14439	17	1	after	after	ADP
cet-14439	17	2	the	the	DET
cet-14439	17	3	hydrolysis	hydrolysis	NOUN
cet-14439	17	4	,	,	PUNCT
cet-14439	17	5	gvl	gvl	PROPN
cet-14439	17	6	must	must	AUX
cet-14439	17	7	be	be	AUX
cet-14439	17	8	separated	separate	VERB
cet-14439	17	9	from	from	ADP
cet-14439	17	10	the	the	DET
cet-14439	17	11	sugar	sugar	NOUN
cet-14439	17	12	solution	solution	NOUN
cet-14439	17	13	,	,	PUNCT
cet-14439	17	14	because	because	SCONJ
cet-14439	17	15	a	a	DET
cet-14439	17	16	high	high	ADJ
cet-14439	17	17	concentration	concentration	NOUN
cet-14439	17	18	of	of	ADP
cet-14439	17	19	this	this	DET
cet-14439	17	20	solvent	solvent	NOUN
cet-14439	17	21	is	be	AUX
cet-14439	17	22	harmful	harmful	ADJ
cet-14439	17	23	in	in	ADP
cet-14439	17	24	the	the	DET
cet-14439	17	25	fermentation	fermentation	NOUN
cet-14439	17	26	stage	stage	NOUN
cet-14439	17	27	,	,	PUNCT
cet-14439	17	28	due	due	ADP
cet-14439	17	29	to	to	ADP
cet-14439	17	30	its	its	PRON
cet-14439	17	31	toxicity	toxicity	NOUN
cet-14439	17	32	to	to	ADP
cet-14439	17	33	the	the	DET
cet-14439	17	34	microorganisms	microorganism	NOUN
cet-14439	17	35	that	that	PRON
cet-14439	17	36	metabolize	metabolize	VERB
cet-14439	17	37	glucose	glucose	NOUN
cet-14439	17	38	to	to	PART
cet-14439	17	39	produce	produce	VERB
cet-14439	17	40	ethanol	ethanol	NOUN
cet-14439	17	41	.	.	PUNCT
cet-14439	18	1	it	it	PRON
cet-14439	18	2	was	be	AUX
cet-14439	18	3	found	find	VERB
cet-14439	18	4	that	that	SCONJ
cet-14439	18	5	an	an	DET
cet-14439	18	6	extraction	extraction	NOUN
cet-14439	18	7	with	with	ADP
cet-14439	18	8	subcritical	subcritical	ADJ
cet-14439	18	9	co2	co2	NOUN
cet-14439	18	10	was	be	AUX
cet-14439	18	11	able	able	ADJ
cet-14439	18	12	to	to	PART
cet-14439	18	13	decrease	decrease	VERB
cet-14439	18	14	the	the	DET
cet-14439	18	15	concentration	concentration	NOUN
cet-14439	18	16	of	of	ADP
cet-14439	18	17	gvl	gvl	PROPN
cet-14439	18	18	,	,	PUNCT
cet-14439	18	19	but	but	CCONJ
cet-14439	18	20	a	a	DET
cet-14439	18	21	further	further	ADJ
cet-14439	18	22	separation	separation	NOUN
cet-14439	18	23	was	be	AUX
cet-14439	18	24	still	still	ADV
cet-14439	18	25	required	require	VERB
cet-14439	18	26	in	in	ADP
cet-14439	18	27	order	order	NOUN
cet-14439	18	28	to	to	PART
cet-14439	18	29	reduce	reduce	VERB
cet-14439	18	30	the	the	DET
cet-14439	18	31	gvl	gvl	NOUN
cet-14439	18	32	to	to	ADP
cet-14439	18	33	acceptable	acceptable	ADJ
cet-14439	18	34	levels	level	NOUN
cet-14439	18	35	(	(	PUNCT
cet-14439	18	36	luterbacher	luterbacher	VERB
cet-14439	18	37	et	et	PROPN
cet-14439	18	38	al	al	PROPN
cet-14439	18	39	.	.	PROPN
cet-14439	18	40	2014	2014	NUM
cet-14439	18	41	)	)	PUNCT
cet-14439	18	42	.	.	PUNCT
cet-14439	19	1	adsorption	adsorption	NOUN
cet-14439	19	2	has	have	AUX
cet-14439	19	3	been	be	AUX
cet-14439	19	4	found	find	VERB
cet-14439	19	5	to	to	PART
cet-14439	19	6	have	have	VERB
cet-14439	19	7	high	high	ADJ
cet-14439	19	8	efficiency	efficiency	NOUN
cet-14439	19	9	as	as	ADP
cet-14439	19	10	a	a	DET
cet-14439	19	11	complementary	complementary	ADJ
cet-14439	19	12	separation	separation	NOUN
cet-14439	19	13	step	step	NOUN
cet-14439	19	14	to	to	PART
cet-14439	19	15	selectively	selectively	ADV
cet-14439	19	16	remove	remove	VERB
cet-14439	19	17	gvl	gvl	PROPN
cet-14439	19	18	from	from	ADP
cet-14439	19	19	the	the	DET
cet-14439	19	20	solution	solution	NOUN
cet-14439	19	21	(	(	PUNCT
cet-14439	19	22	trindade	trindade	ADJ
cet-14439	19	23	,	,	PUNCT
cet-14439	19	24	2015a	2015a	NUM
cet-14439	19	25	;	;	PUNCT
cet-14439	19	26	trindade	trindade	VERB
cet-14439	19	27	et	et	PROPN
cet-14439	19	28	al	al	PROPN
cet-14439	19	29	,	,	PUNCT
cet-14439	19	30	2015b	2015b	NUM
cet-14439	19	31	)	)	PUNCT
cet-14439	19	32	.	.	PUNCT
cet-14439	20	1	trindade	trindade	VERB
cet-14439	20	2	(	(	PUNCT
cet-14439	20	3	2015a	2015a	NUM
cet-14439	20	4	)	)	PUNCT
cet-14439	20	5	evaluated	evaluate	VERB
cet-14439	20	6	the	the	DET
cet-14439	20	7	use	use	NOUN
cet-14439	20	8	of	of	ADP
cet-14439	20	9	four	four	NUM
cet-14439	20	10	adsorbents	adsorbent	NOUN
cet-14439	20	11	in	in	ADP
cet-14439	20	12	the	the	DET
cet-14439	20	13	removal	removal	NOUN
cet-14439	20	14	of	of	ADP
cet-14439	20	15	gvl	gvl	PROPN
cet-14439	20	16	from	from	ADP
cet-14439	20	17	the	the	DET
cet-14439	20	18	glucose	glucose	NOUN
cet-14439	20	19	solution	solution	NOUN
cet-14439	20	20	,	,	PUNCT
cet-14439	20	21	and	and	CCONJ
cet-14439	20	22	found	find	VERB
cet-14439	20	23	that	that	SCONJ
cet-14439	20	24	the	the	DET
cet-14439	20	25	resin	resin	NOUN
cet-14439	20	26	sepabeads	sepabead	VERB
cet-14439	20	27	sp850	sp850	PROPN
cet-14439	20	28	,	,	PUNCT
cet-14439	20	29	which	which	PRON
cet-14439	20	30	is	be	AUX
cet-14439	20	31	a	a	DET
cet-14439	20	32	highly	highly	ADV
cet-14439	20	33	porous	porous	ADJ
cet-14439	20	34	styrenic	styrenic	ADJ
cet-14439	20	35	adsorbent	adsorbent	NOUN
cet-14439	20	36	,	,	PUNCT
cet-14439	20	37	was	be	AUX
cet-14439	20	38	the	the	DET
cet-14439	20	39	most	most	ADV
cet-14439	20	40	selective	selective	ADJ
cet-14439	20	41	to	to	PART
cet-14439	20	42	adsorb	adsorb	VERB
cet-14439	20	43	gvl	gvl	PROPN
cet-14439	20	44	compared	compare	VERB
cet-14439	20	45	to	to	ADP
cet-14439	20	46	glucose	glucose	NOUN
cet-14439	20	47	.	.	PUNCT
cet-14439	21	1	the	the	DET
cet-14439	21	2	objective	objective	NOUN
cet-14439	21	3	of	of	ADP
cet-14439	21	4	this	this	DET
cet-14439	21	5	work	work	NOUN
cet-14439	21	6	was	be	AUX
cet-14439	21	7	to	to	PART
cet-14439	21	8	model	model	VERB
cet-14439	21	9	the	the	DET
cet-14439	21	10	adsorption	adsorption	NOUN
cet-14439	21	11	of	of	ADP
cet-14439	21	12	gvl	gvl	PROPN
cet-14439	21	13	into	into	ADP
cet-14439	21	14	spheres	sphere	NOUN
cet-14439	21	15	of	of	ADP
cet-14439	21	16	sp850	sp850	PROPN
cet-14439	21	17	in	in	ADP
cet-14439	21	18	a	a	DET
cet-14439	21	19	batch	batch	NOUN
cet-14439	21	20	process	process	NOUN
cet-14439	21	21	,	,	PUNCT
cet-14439	21	22	in	in	ADP
cet-14439	21	23	order	order	NOUN
cet-14439	21	24	to	to	PART
cet-14439	21	25	reproduce	reproduce	VERB
cet-14439	21	26	the	the	DET
cet-14439	21	27	batch	batch	NOUN
cet-14439	21	28	experimental	experimental	ADJ
cet-14439	21	29	results	result	NOUN
cet-14439	21	30	obtained	obtain	VERB
cet-14439	21	31	by	by	ADP
cet-14439	21	32	trindade	trindade	PROPN
cet-14439	21	33	(	(	PUNCT
cet-14439	21	34	2015a	2015a	NUM
cet-14439	21	35	)	)	PUNCT
cet-14439	21	36	,	,	PUNCT
cet-14439	21	37	and	and	CCONJ
cet-14439	21	38	thus	thus	ADV
cet-14439	21	39	help	help	VERB
cet-14439	21	40	improve	improve	VERB
cet-14439	21	41	this	this	DET
cet-14439	21	42	separation	separation	NOUN
cet-14439	21	43	step	step	NOUN
cet-14439	21	44	.	.	PUNCT
cet-14439	22	1	the	the	DET
cet-14439	22	2	model	model	NOUN
cet-14439	22	3	considers	consider	VERB
cet-14439	22	4	both	both	CCONJ
cet-14439	22	5	external	external	ADJ
cet-14439	22	6	and	and	CCONJ
cet-14439	22	7	internal	internal	ADJ
cet-14439	22	8	mass	mass	NOUN
cet-14439	22	9	transfer	transfer	NOUN
cet-14439	22	10	,	,	PUNCT
cet-14439	22	11	using	use	VERB
cet-14439	22	12	a	a	DET
cet-14439	22	13	langmuir	langmuir	PROPN
cet-14439	22	14	type	type	NOUN
cet-14439	22	15	isotherm	isotherm	NOUN
cet-14439	22	16	for	for	ADP
cet-14439	22	17	adsorption	adsorption	NOUN
cet-14439	22	18	in	in	ADP
cet-14439	22	19	the	the	DET
cet-14439	22	20	spheres	sphere	NOUN
cet-14439	22	21	,	,	PUNCT
cet-14439	22	22	and	and	CCONJ
cet-14439	22	23	was	be	AUX
cet-14439	22	24	solved	solve	VERB
cet-14439	22	25	with	with	ADP
cet-14439	22	26	two	two	NUM
cet-14439	22	27	numerical	numerical	ADJ
cet-14439	22	28	methods	method	NOUN
cet-14439	22	29	,	,	PUNCT
cet-14439	22	30	finite	finite	VERB
cet-14439	22	31	differences	difference	NOUN
cet-14439	22	32	and	and	CCONJ
cet-14439	22	33	variational	variational	ADJ
cet-14439	22	34	method	method	NOUN
cet-14439	22	35	.	.	PUNCT
cet-14439	23	1	the	the	DET
cet-14439	23	2	results	result	NOUN
cet-14439	23	3	were	be	AUX
cet-14439	23	4	then	then	ADV
cet-14439	23	5	compared	compare	VERB
cet-14439	23	6	with	with	ADP
cet-14439	23	7	the	the	DET
cet-14439	23	8	experimental	experimental	ADJ
cet-14439	23	9	data	datum	NOUN
cet-14439	23	10	available	available	ADJ
cet-14439	23	11	.	.	PUNCT
cet-14439	24	1	91	91	NUM
cet-14439	24	2	2	2	NUM
cet-14439	24	3	.	.	PUNCT
cet-14439	24	4	mathematical	mathematical	ADJ
cet-14439	24	5	model	model	NOUN
cet-14439	24	6	adsorption	adsorption	NOUN
cet-14439	24	7	in	in	ADP
cet-14439	24	8	a	a	DET
cet-14439	24	9	porous	porous	ADJ
cet-14439	24	10	medium	medium	NOUN
cet-14439	24	11	is	be	AUX
cet-14439	24	12	a	a	DET
cet-14439	24	13	very	very	ADV
cet-14439	24	14	important	important	ADJ
cet-14439	24	15	separation	separation	NOUN
cet-14439	24	16	process	process	NOUN
cet-14439	24	17	,	,	PUNCT
cet-14439	24	18	for	for	ADP
cet-14439	24	19	a	a	DET
cet-14439	24	20	variety	variety	NOUN
cet-14439	24	21	of	of	ADP
cet-14439	24	22	substances	substance	NOUN
cet-14439	24	23	.	.	PUNCT
cet-14439	25	1	for	for	ADP
cet-14439	25	2	a	a	DET
cet-14439	25	3	batch	batch	NOUN
cet-14439	25	4	system	system	NOUN
cet-14439	25	5	containing	contain	VERB
cet-14439	25	6	a	a	DET
cet-14439	25	7	volume	volume	NOUN
cet-14439	25	8	of	of	ADP
cet-14439	25	9	solution	solution	NOUN
cet-14439	25	10	(	(	PUNCT
cet-14439	25	11	𝑉	𝑉	PROPN
cet-14439	25	12	)	)	PUNCT
cet-14439	25	13	and	and	CCONJ
cet-14439	25	14	a	a	DET
cet-14439	25	15	volume	volume	NOUN
cet-14439	25	16	of	of	ADP
cet-14439	25	17	porous	porous	ADJ
cet-14439	25	18	spheres	sphere	NOUN
cet-14439	25	19	(	(	PUNCT
cet-14439	25	20	𝑣	𝑣	NOUN
cet-14439	25	21	)	)	PUNCT
cet-14439	25	22	,	,	PUNCT
cet-14439	25	23	the	the	DET
cet-14439	25	24	modeling	modeling	NOUN
cet-14439	25	25	of	of	ADP
cet-14439	25	26	the	the	DET
cet-14439	25	27	solute	solute	ADJ
cet-14439	25	28	concentration	concentration	NOUN
cet-14439	25	29	in	in	ADP
cet-14439	25	30	the	the	DET
cet-14439	25	31	solution	solution	NOUN
cet-14439	25	32	,	,	PUNCT
cet-14439	25	33	𝐶(𝑡	𝐶(𝑡	NOUN
cet-14439	25	34	)	)	PUNCT
cet-14439	25	35	,	,	PUNCT
cet-14439	25	36	and	and	CCONJ
cet-14439	25	37	in	in	ADP
cet-14439	25	38	the	the	DET
cet-14439	25	39	spheres	sphere	NOUN
cet-14439	25	40	,	,	PUNCT
cet-14439	25	41	𝑐(𝑟	𝑐(𝑟	NOUN
cet-14439	25	42	,	,	PUNCT
cet-14439	25	43	𝑡	𝑡	NOUN
cet-14439	25	44	)	)	PUNCT
cet-14439	25	45	,	,	PUNCT
cet-14439	25	46	can	can	AUX
cet-14439	25	47	be	be	AUX
cet-14439	25	48	written	write	VERB
cet-14439	25	49	as	as	ADP
cet-14439	25	50	a	a	DET
cet-14439	25	51	set	set	NOUN
cet-14439	25	52	of	of	ADP
cet-14439	25	53	differential	differential	ADJ
cet-14439	25	54	equations	equation	NOUN
cet-14439	25	55	(	(	PUNCT
cet-14439	25	56	horstmann	horstmann	PROPN
cet-14439	25	57	and	and	CCONJ
cet-14439	25	58	chase	chase	NOUN
cet-14439	25	59	,	,	PUNCT
cet-14439	25	60	1989	1989	NUM
cet-14439	25	61	)	)	PUNCT
cet-14439	25	62	.	.	PUNCT
cet-14439	26	1	in	in	ADP
cet-14439	26	2	this	this	DET
cet-14439	26	3	work	work	NOUN
cet-14439	26	4	,	,	PUNCT
cet-14439	26	5	a	a	DET
cet-14439	26	6	langmuir	langmuir	PROPN
cet-14439	26	7	type	type	NOUN
cet-14439	26	8	isotherm	isotherm	NOUN
cet-14439	26	9	is	be	AUX
cet-14439	26	10	considered	consider	VERB
cet-14439	26	11	,	,	PUNCT
cet-14439	26	12	given	give	VERB
cet-14439	26	13	as	as	ADP
cet-14439	26	14	:	:	PUNCT
cet-14439	26	15	𝑞	𝑞	X
cet-14439	26	16	=	=	X
cet-14439	26	17	𝑞𝑚	𝑞𝑚	ADP
cet-14439	26	18	∙	∙	PROPN
cet-14439	26	19	𝑏	𝑏	PROPN
cet-14439	26	20	∙	∙	PROPN
cet-14439	26	21	𝑐	𝑐	PROPN
cet-14439	26	22	(	(	PUNCT
cet-14439	26	23	1	1	NUM
cet-14439	26	24	+	+	CCONJ
cet-14439	26	25	𝑏	𝑏	PROPN
cet-14439	26	26	∙	∙	PROPN
cet-14439	26	27	𝑐	𝑐	NOUN
cet-14439	26	28	)	)	PUNCT
cet-14439	26	29	(	(	PUNCT
cet-14439	26	30	1	1	X
cet-14439	26	31	)	)	PUNCT
cet-14439	26	32	where	where	SCONJ
cet-14439	26	33	𝑞	𝑞	PROPN
cet-14439	26	34	is	be	AUX
cet-14439	26	35	the	the	DET
cet-14439	26	36	amount	amount	NOUN
cet-14439	26	37	of	of	ADP
cet-14439	26	38	solute	solute	NOUN
cet-14439	26	39	adsorbed	adsorb	VERB
cet-14439	26	40	in	in	ADP
cet-14439	26	41	the	the	DET
cet-14439	26	42	spheres	sphere	NOUN
cet-14439	26	43	,	,	PUNCT
cet-14439	26	44	and	and	CCONJ
cet-14439	26	45	𝑞𝑚	𝑞𝑚	NOUN
cet-14439	26	46	is	be	AUX
cet-14439	26	47	the	the	DET
cet-14439	26	48	maximum	maximum	ADJ
cet-14439	26	49	amount	amount	NOUN
cet-14439	26	50	of	of	ADP
cet-14439	26	51	solute	solute	NOUN
cet-14439	26	52	that	that	PRON
cet-14439	26	53	can	can	AUX
cet-14439	26	54	be	be	AUX
cet-14439	26	55	adsorbed	adsorb	VERB
cet-14439	26	56	by	by	ADP
cet-14439	26	57	the	the	DET
cet-14439	26	58	spheres	sphere	NOUN
cet-14439	26	59	.	.	PUNCT
cet-14439	27	1	the	the	DET
cet-14439	27	2	model	model	NOUN
cet-14439	27	3	can	can	AUX
cet-14439	27	4	then	then	ADV
cet-14439	27	5	be	be	AUX
cet-14439	27	6	made	make	VERB
cet-14439	27	7	dimensionless	dimensionless	NOUN
cet-14439	27	8	by	by	ADP
cet-14439	27	9	defining	define	VERB
cet-14439	27	10	𝑢	𝑢	PROPN
cet-14439	27	11	=	=	PROPN
cet-14439	27	12	𝑐	𝑐	PROPN
cet-14439	27	13	𝐶0⁄	𝐶0⁄	PROPN
cet-14439	27	14	and	and	CCONJ
cet-14439	27	15	𝑤	𝑤	X
cet-14439	27	16	=	=	SYM
cet-14439	27	17	𝐶	𝐶	PROPN
cet-14439	27	18	𝐶0⁄	𝐶0⁄	PROPN
cet-14439	27	19	(	(	PUNCT
cet-14439	27	20	guirardello	guirardello	PROPN
cet-14439	27	21	,	,	PUNCT
cet-14439	27	22	2013	2013	NUM
cet-14439	27	23	)	)	PUNCT
cet-14439	27	24	,	,	PUNCT
cet-14439	27	25	so	so	SCONJ
cet-14439	27	26	that	that	SCONJ
cet-14439	27	27	:	:	PUNCT
cet-14439	27	28	𝑓′(𝑢	𝑓′(𝑢	X
cet-14439	27	29	)	)	PUNCT
cet-14439	27	30	∙	∙	PROPN
cet-14439	27	31	𝜕𝑢	𝜕𝑢	NOUN
cet-14439	27	32	𝜕𝜏	𝜕𝜏	NOUN
cet-14439	27	33	=	=	SYM
cet-14439	27	34	1	1	NUM
cet-14439	27	35	𝑥2	𝑥2	NOUN
cet-14439	27	36	∙	∙	PROPN
cet-14439	27	37	𝜕	𝜕	NOUN
cet-14439	27	38	𝜕𝑥	𝜕𝑥	X
cet-14439	28	1	[	[	X
cet-14439	28	2	𝑥2	𝑥2	NOUN
cet-14439	28	3	∙	∙	PROPN
cet-14439	28	4	𝜕𝑢	𝜕𝑢	NOUN
cet-14439	28	5	𝜕𝑥	𝜕𝑥	NOUN
cet-14439	28	6	]	]	PUNCT
cet-14439	28	7	(	(	PUNCT
cet-14439	28	8	2	2	X
cet-14439	28	9	)	)	PUNCT
cet-14439	28	10	𝑑𝑤	𝑑𝑤	PROPN
cet-14439	28	11	𝑑𝜏	𝑑𝜏	NOUN
cet-14439	28	12	=	=	SYM
cet-14439	28	13	−𝛼	−𝛼	PROPN
cet-14439	28	14	∙	∙	PUNCT
cet-14439	29	1	[	[	X
cet-14439	29	2	𝑤	𝑤	ADP
cet-14439	29	3	−	−	NOUN
cet-14439	29	4	𝑢(1	𝑢(1	NOUN
cet-14439	29	5	,	,	PUNCT
cet-14439	29	6	𝜏	𝜏	NOUN
cet-14439	29	7	)	)	PUNCT
cet-14439	29	8	]	]	PUNCT
cet-14439	29	9	(	(	PUNCT
cet-14439	29	10	3	3	X
cet-14439	29	11	)	)	PUNCT
cet-14439	29	12	with	with	ADP
cet-14439	29	13	boundary	boundary	ADJ
cet-14439	29	14	and	and	CCONJ
cet-14439	29	15	initial	initial	ADJ
cet-14439	29	16	conditions	condition	NOUN
cet-14439	29	17	given	give	VERB
cet-14439	29	18	by	by	ADP
cet-14439	29	19	:	:	PUNCT
cet-14439	29	20	𝜕𝑢	𝜕𝑢	NOUN
cet-14439	29	21	𝜕𝑥	𝜕𝑥	NOUN
cet-14439	30	1	=	=	PUNCT
cet-14439	30	2	𝛽	𝛽	NOUN
cet-14439	30	3	∙	∙	PROPN
cet-14439	30	4	(	(	PUNCT
cet-14439	30	5	𝑤	𝑤	ADP
cet-14439	30	6	−	−	NOUN
cet-14439	30	7	𝑢	𝑢	NOUN
cet-14439	30	8	)	)	PUNCT
cet-14439	30	9	at	at	ADP
cet-14439	30	10	𝑥	𝑥	NOUN
cet-14439	30	11	=	=	SYM
cet-14439	30	12	1	1	NUM
cet-14439	30	13	𝜏	𝜏	X
cet-14439	30	14	>	>	X
cet-14439	30	15	0	0	PUNCT
cet-14439	31	1	(	(	PUNCT
cet-14439	31	2	4	4	NUM
cet-14439	31	3	)	)	PUNCT
cet-14439	31	4	𝜕𝑢	𝜕𝑢	NOUN
cet-14439	31	5	𝜕𝑥	𝜕𝑥	X
cet-14439	32	1	=	=	SYM
cet-14439	32	2	0	0	PUNCT
cet-14439	33	1	at	at	ADP
cet-14439	33	2	𝑥	𝑥	NOUN
cet-14439	33	3	=	=	SYM
cet-14439	33	4	0	0	NUM
cet-14439	33	5	𝜏	𝜏	X
cet-14439	33	6	>	>	X
cet-14439	33	7	0	0	PUNCT
cet-14439	34	1	(	(	PUNCT
cet-14439	34	2	5	5	NUM
cet-14439	34	3	)	)	PUNCT
cet-14439	34	4	𝑢	𝑢	NOUN
cet-14439	34	5	=	=	NOUN
cet-14439	34	6	0	0	NUM
cet-14439	34	7	at	at	ADP
cet-14439	34	8	𝜏	𝜏	NOUN
cet-14439	34	9	=	=	SYM
cet-14439	34	10	0	0	NUM
cet-14439	34	11	0	0	NUM
cet-14439	34	12	≤	≤	NUM
cet-14439	34	13	𝑥	𝑥	PUNCT
cet-14439	34	14	≤	≤	NUM
cet-14439	34	15	1	1	NUM
cet-14439	34	16	(	(	PUNCT
cet-14439	34	17	6	6	NUM
cet-14439	34	18	)	)	PUNCT
cet-14439	34	19	𝑤	𝑤	NOUN
cet-14439	34	20	=	=	SYM
cet-14439	34	21	1	1	NUM
cet-14439	34	22	at	at	ADP
cet-14439	34	23	𝜏	𝜏	NOUN
cet-14439	34	24	=	=	SYM
cet-14439	34	25	0	0	NUM
cet-14439	34	26	(	(	PUNCT
cet-14439	34	27	7	7	NUM
cet-14439	34	28	)	)	PUNCT
cet-14439	35	1	where	where	SCONJ
cet-14439	35	2	𝑥	𝑥	NOUN
cet-14439	35	3	=	=	SYM
cet-14439	35	4	𝑟	𝑟	X
cet-14439	35	5	𝑅⁄	𝑅⁄	PROPN
cet-14439	35	6	,	,	PUNCT
cet-14439	35	7	𝜏	𝜏	X
cet-14439	35	8	=	=	SYM
cet-14439	35	9	𝑡	𝑡	PROPN
cet-14439	35	10	∙	∙	PROPN
cet-14439	35	11	𝐷	𝐷	PROPN
cet-14439	35	12	𝑅2⁄	𝑅2⁄	ADV
cet-14439	35	13	,	,	PUNCT
cet-14439	35	14	and	and	CCONJ
cet-14439	35	15	:	:	PUNCT
cet-14439	35	16	𝛼	𝛼	X
cet-14439	35	17	=	=	VERB
cet-14439	35	18	3	3	NUM
cet-14439	35	19	∙	∙	PROPN
cet-14439	35	20	𝑣	𝑣	ADP
cet-14439	35	21	𝑉	𝑉	PROPN
cet-14439	35	22	∙	∙	PROPN
cet-14439	35	23	(	(	PUNCT
cet-14439	35	24	𝑅	𝑅	PROPN
cet-14439	35	25	∙	∙	PROPN
cet-14439	35	26	𝑘𝑓	𝑘𝑓	PROPN
cet-14439	35	27	𝐷	𝐷	PROPN
cet-14439	35	28	)	)	PUNCT
cet-14439	35	29	(	(	PUNCT
cet-14439	35	30	8)	8)	NUM
cet-14439	35	31	𝛽	𝛽	NOUN
cet-14439	35	32	=	=	SYM
cet-14439	35	33	(	(	PUNCT
cet-14439	35	34	𝑅	𝑅	PROPN
cet-14439	35	35	∙	∙	PROPN
cet-14439	35	36	𝑘𝑓	𝑘𝑓	ADP
cet-14439	35	37	𝜀	𝜀	ADP
cet-14439	35	38	∙	∙	PROPN
cet-14439	35	39	𝐷	𝐷	PROPN
cet-14439	35	40	)	)	PUNCT
cet-14439	35	41	(	(	PUNCT
cet-14439	35	42	9	9	X
cet-14439	35	43	)	)	PUNCT
cet-14439	35	44	𝑓′(𝑢	𝑓′(𝑢	PROPN
cet-14439	35	45	)	)	PUNCT
cet-14439	35	46	=	=	SYM
cet-14439	35	47	1	1	NUM
cet-14439	35	48	+	+	CCONJ
cet-14439	35	49	(	(	PUNCT
cet-14439	35	50	1	1	NUM
cet-14439	35	51	−	−	NUM
cet-14439	35	52	𝜀	𝜀	NOUN
cet-14439	35	53	)	)	PUNCT
cet-14439	35	54	𝜀	𝜀	ADP
cet-14439	35	55	∙	∙	PROPN
cet-14439	35	56	𝑞𝑚	𝑞𝑚	NOUN
cet-14439	35	57	∙	∙	PROPN
cet-14439	35	58	𝑏	𝑏	PROPN
cet-14439	35	59	(	(	PUNCT
cet-14439	35	60	1	1	NUM
cet-14439	35	61	+	+	NUM
cet-14439	35	62	𝑏	𝑏	NOUN
cet-14439	35	63	∙	∙	PROPN
cet-14439	35	64	𝐶0	𝐶0	PROPN
cet-14439	35	65	∙	∙	PROPN
cet-14439	35	66	𝑢)2	𝑢)2	PROPN
cet-14439	35	67	(	(	PUNCT
cet-14439	35	68	10	10	NUM
cet-14439	35	69	)	)	SYM
cet-14439	35	70	3	3	NUM
cet-14439	35	71	.	.	X
cet-14439	35	72	methodology	methodology	NOUN
cet-14439	35	73	two	two	NUM
cet-14439	35	74	numerical	numerical	ADJ
cet-14439	35	75	approaches	approach	NOUN
cet-14439	35	76	were	be	AUX
cet-14439	35	77	used	use	VERB
cet-14439	35	78	in	in	ADP
cet-14439	35	79	this	this	DET
cet-14439	35	80	work	work	NOUN
cet-14439	35	81	to	to	PART
cet-14439	35	82	make	make	VERB
cet-14439	35	83	the	the	DET
cet-14439	35	84	discretization	discretization	NOUN
cet-14439	35	85	in	in	ADP
cet-14439	35	86	the	the	DET
cet-14439	35	87	𝑥	𝑥	PROPN
cet-14439	35	88	variable	variable	NOUN
cet-14439	35	89	:	:	PUNCT
cet-14439	35	90	finite	finite	VERB
cet-14439	35	91	differences	difference	NOUN
cet-14439	35	92	and	and	CCONJ
cet-14439	35	93	variational	variational	ADJ
cet-14439	35	94	calculus	calculus	NOUN
cet-14439	35	95	.	.	PUNCT
cet-14439	36	1	both	both	DET
cet-14439	36	2	approaches	approach	NOUN
cet-14439	36	3	are	be	AUX
cet-14439	36	4	detailed	detail	VERB
cet-14439	36	5	here	here	ADV
cet-14439	36	6	.	.	PUNCT
cet-14439	37	1	3.1	3.1	NUM
cet-14439	37	2	finite	finite	NOUN
cet-14439	37	3	differences	difference	NOUN
cet-14439	37	4	the	the	DET
cet-14439	37	5	finite	finite	PROPN
cet-14439	37	6	differences	difference	NOUN
cet-14439	37	7	method	method	NOUN
cet-14439	37	8	is	be	AUX
cet-14439	37	9	well	well	ADV
cet-14439	37	10	known	know	VERB
cet-14439	37	11	and	and	CCONJ
cet-14439	37	12	is	be	AUX
cet-14439	37	13	based	base	VERB
cet-14439	37	14	on	on	ADP
cet-14439	37	15	the	the	DET
cet-14439	37	16	substitution	substitution	NOUN
cet-14439	37	17	of	of	ADP
cet-14439	37	18	the	the	DET
cet-14439	37	19	exact	exact	ADJ
cet-14439	37	20	derivatives	derivative	NOUN
cet-14439	37	21	by	by	ADP
cet-14439	37	22	numerical	numerical	ADJ
cet-14439	37	23	ones	one	NOUN
cet-14439	37	24	.	.	PUNCT
cet-14439	38	1	however	however	ADV
cet-14439	38	2	,	,	PUNCT
cet-14439	38	3	here	here	ADV
cet-14439	38	4	it	it	PRON
cet-14439	38	5	is	be	AUX
cet-14439	38	6	used	use	VERB
cet-14439	38	7	appropriate	appropriate	ADJ
cet-14439	38	8	expressions	expression	NOUN
cet-14439	38	9	for	for	ADP
cet-14439	38	10	the	the	DET
cet-14439	38	11	boundary	boundary	ADJ
cet-14439	38	12	points	point	NOUN
cet-14439	38	13	(	(	PUNCT
cet-14439	38	14	𝑥	𝑥	NOUN
cet-14439	38	15	=	=	SYM
cet-14439	38	16	0	0	NUM
cet-14439	38	17	and	and	CCONJ
cet-14439	38	18	𝑥	𝑥	NOUN
cet-14439	38	19	=	=	SYM
cet-14439	38	20	1	1	NUM
cet-14439	38	21	)	)	PUNCT
cet-14439	38	22	,	,	PUNCT
cet-14439	38	23	so	so	SCONJ
cet-14439	38	24	that	that	SCONJ
cet-14439	38	25	the	the	DET
cet-14439	38	26	boundary	boundary	ADJ
cet-14439	38	27	conditions	condition	NOUN
cet-14439	38	28	are	be	AUX
cet-14439	38	29	naturally	naturally	ADV
cet-14439	38	30	inserted	insert	VERB
cet-14439	38	31	in	in	ADP
cet-14439	38	32	the	the	DET
cet-14439	38	33	numerical	numerical	ADJ
cet-14439	38	34	resolution	resolution	NOUN
cet-14439	38	35	of	of	ADP
cet-14439	38	36	the	the	DET
cet-14439	38	37	pde	pde	NOUN
cet-14439	38	38	:	:	PUNCT
cet-14439	38	39	(	(	PUNCT
cet-14439	38	40	𝜕2𝑢	𝜕2𝑢	PROPN
cet-14439	39	1	𝜕𝑥2)|	𝜕𝑥2)|	NUM
cet-14439	39	2	𝑖	𝑖	NOUN
cet-14439	39	3	=	=	NOUN
cet-14439	39	4	𝑢𝑖	𝑢𝑖	PROPN
cet-14439	39	5	′′	′′	PROPN
cet-14439	39	6	≅	≅	PROPN
cet-14439	39	7	−7	−7	PROPN
cet-14439	39	8	∙	∙	VERB
cet-14439	39	9	𝑢𝑖	𝑢𝑖	PRON
cet-14439	39	10	+	+	NOUN
cet-14439	39	11	8	8	NUM
cet-14439	39	12	∙	∙	PROPN
cet-14439	39	13	𝑢𝑖+1	𝑢𝑖+1	X
cet-14439	39	14	−	−	PROPN
cet-14439	39	15	𝑢𝑖+2	𝑢𝑖+2	NUM
cet-14439	39	16	−	−	NOUN
cet-14439	39	17	6	6	NUM
cet-14439	39	18	∙	∙	PROPN
cet-14439	39	19	∆𝑥	∆𝑥	PROPN
cet-14439	40	1	∙	∙	NOUN
cet-14439	40	2	𝑢𝑖	𝑢𝑖	ADP
cet-14439	40	3	′	′	NOUN
cet-14439	40	4	2	2	NUM
cet-14439	40	5	∙	∙	X
cet-14439	40	6	∆𝑥2	∆𝑥2	NOUN
cet-14439	40	7	𝑖	𝑖	NOUN
cet-14439	40	8	=	=	PUNCT
cet-14439	40	9	0	0	NUM
cet-14439	40	10	or	or	CCONJ
cet-14439	40	11	𝑥	𝑥	X
cet-14439	40	12	=	=	SYM
cet-14439	40	13	0	0	NUM
cet-14439	41	1	(	(	PUNCT
cet-14439	41	2	11	11	NUM
cet-14439	41	3	)	)	PUNCT
cet-14439	41	4	(	(	PUNCT
cet-14439	41	5	𝜕2𝑢	𝜕2𝑢	NUM
cet-14439	41	6	𝜕𝑥2	𝜕𝑥2	NOUN
cet-14439	41	7	)	)	PUNCT
cet-14439	42	1	|	|	ADV
cet-14439	42	2	𝑖	𝑖	SYM
cet-14439	42	3	=	=	NOUN
cet-14439	42	4	𝑢𝑖	𝑢𝑖	PROPN
cet-14439	42	5	′′	′′	PROPN
cet-14439	42	6	≅	≅	PROPN
cet-14439	42	7	−7	−7	PROPN
cet-14439	42	8	∙	∙	VERB
cet-14439	42	9	𝑢𝑖	𝑢𝑖	PRON
cet-14439	42	10	+	+	CCONJ
cet-14439	42	11	8	8	NUM
cet-14439	42	12	∙	∙	PROPN
cet-14439	42	13	𝑢𝑖−1	𝑢𝑖−1	NOUN
cet-14439	42	14	−	−	PROPN
cet-14439	42	15	𝑢𝑖−2	𝑢𝑖−2	ADJ
cet-14439	42	16	+	+	CCONJ
cet-14439	42	17	6	6	NUM
cet-14439	42	18	∙	∙	NOUN
cet-14439	42	19	∆𝑥	∆𝑥	PROPN
cet-14439	43	1	∙	∙	NOUN
cet-14439	43	2	𝑢𝑖	𝑢𝑖	ADP
cet-14439	43	3	′	′	NOUN
cet-14439	43	4	2	2	NUM
cet-14439	43	5	∙	∙	X
cet-14439	43	6	∆𝑥2	∆𝑥2	NOUN
cet-14439	43	7	𝑖	𝑖	NOUN
cet-14439	44	1	=	=	PUNCT
cet-14439	44	2	𝑁	𝑁	PROPN
cet-14439	44	3	or	or	CCONJ
cet-14439	44	4	𝑥	𝑥	NOUN
cet-14439	44	5	=	=	SYM
cet-14439	44	6	1	1	NUM
cet-14439	44	7	(	(	PUNCT
cet-14439	44	8	12	12	NUM
cet-14439	44	9	)	)	PUNCT
cet-14439	44	10	both	both	DET
cet-14439	44	11	expressions	expression	NOUN
cet-14439	44	12	are	be	AUX
cet-14439	44	13	second	second	ADJ
cet-14439	44	14	order	order	NOUN
cet-14439	44	15	in	in	ADP
cet-14439	44	16	the	the	DET
cet-14439	44	17	interval	interval	NOUN
cet-14439	44	18	(	(	PUNCT
cet-14439	44	19	error	error	NOUN
cet-14439	44	20	~	~	PUNCT
cet-14439	44	21	∆𝑥2	∆𝑥2	NOUN
cet-14439	44	22	)	)	PUNCT
cet-14439	44	23	and	and	CCONJ
cet-14439	44	24	make	make	VERB
cet-14439	44	25	use	use	NOUN
cet-14439	44	26	of	of	ADP
cet-14439	44	27	the	the	DET
cet-14439	44	28	known	know	VERB
cet-14439	44	29	first	first	ADJ
cet-14439	44	30	derivative	derivative	NOUN
cet-14439	44	31	,	,	PUNCT
cet-14439	44	32	so	so	SCONJ
cet-14439	44	33	that	that	SCONJ
cet-14439	44	34	the	the	DET
cet-14439	44	35	boundary	boundary	ADJ
cet-14439	44	36	conditions	condition	NOUN
cet-14439	44	37	can	can	AUX
cet-14439	44	38	be	be	AUX
cet-14439	44	39	inserted	insert	VERB
cet-14439	44	40	directly	directly	ADV
cet-14439	44	41	.	.	PUNCT
cet-14439	45	1	there	there	PRON
cet-14439	45	2	is	be	VERB
cet-14439	45	3	no	no	DET
cet-14439	45	4	need	need	NOUN
cet-14439	45	5	for	for	ADP
cet-14439	45	6	similar	similar	ADJ
cet-14439	45	7	expressions	expression	NOUN
cet-14439	45	8	for	for	ADP
cet-14439	45	9	the	the	DET
cet-14439	45	10	first	first	ADJ
cet-14439	45	11	derivatives	derivative	NOUN
cet-14439	45	12	,	,	PUNCT
cet-14439	45	13	since	since	SCONJ
cet-14439	45	14	they	they	PRON
cet-14439	45	15	are	be	AUX
cet-14439	45	16	given	give	VERB
cet-14439	45	17	by	by	ADP
cet-14439	45	18	the	the	DET
cet-14439	45	19	boundary	boundary	ADJ
cet-14439	45	20	conditions	condition	NOUN
cet-14439	45	21	at	at	ADP
cet-14439	45	22	these	these	DET
cet-14439	45	23	two	two	NUM
cet-14439	45	24	points	point	NOUN
cet-14439	45	25	:	:	PUNCT
cet-14439	45	26	92	92	NUM
cet-14439	45	27	(	(	PUNCT
cet-14439	45	28	𝜕𝑢	𝜕𝑢	NOUN
cet-14439	45	29	𝜕𝑥	𝜕𝑥	NOUN
cet-14439	45	30	)	)	PUNCT
cet-14439	46	1	|	|	ADV
cet-14439	46	2	𝑖	𝑖	SYM
cet-14439	46	3	=	=	NOUN
cet-14439	46	4	𝑢𝑖	𝑢𝑖	NOUN
cet-14439	46	5	′	′	NUM
cet-14439	46	6	=	=	SYM
cet-14439	46	7	0	0	PUNCT
cet-14439	47	1	𝑖	𝑖	SYM
cet-14439	47	2	=	=	NOUN
cet-14439	47	3	0	0	NUM
cet-14439	47	4	or	or	CCONJ
cet-14439	47	5	𝑥	𝑥	X
cet-14439	47	6	=	=	SYM
cet-14439	47	7	0	0	NUM
cet-14439	47	8	(	(	PUNCT
cet-14439	47	9	13	13	NUM
cet-14439	47	10	)	)	PUNCT
cet-14439	47	11	(	(	PUNCT
cet-14439	47	12	𝜕𝑢	𝜕𝑢	NOUN
cet-14439	47	13	𝜕𝑥	𝜕𝑥	NOUN
cet-14439	47	14	)	)	PUNCT
cet-14439	48	1	|	|	ADV
cet-14439	48	2	𝑖	𝑖	SYM
cet-14439	48	3	=	=	NOUN
cet-14439	48	4	𝑢𝑖	𝑢𝑖	NOUN
cet-14439	48	5	′	′	NOUN
cet-14439	48	6	=	=	PUNCT
cet-14439	48	7	𝛽	𝛽	NOUN
cet-14439	48	8	∙	∙	PROPN
cet-14439	48	9	(	(	PUNCT
cet-14439	48	10	𝑤	𝑤	ADP
cet-14439	48	11	−	−	NOUN
cet-14439	48	12	𝑢𝑖	𝑢𝑖	NOUN
cet-14439	48	13	)	)	PUNCT
cet-14439	48	14	𝑖	𝑖	NOUN
cet-14439	49	1	=	=	PUNCT
cet-14439	49	2	𝑁	𝑁	PROPN
cet-14439	49	3	or	or	CCONJ
cet-14439	49	4	𝑥	𝑥	NOUN
cet-14439	49	5	=	=	SYM
cet-14439	49	6	1	1	NUM
cet-14439	49	7	(	(	PUNCT
cet-14439	49	8	14	14	NUM
cet-14439	49	9	)	)	PUNCT
cet-14439	49	10	however	however	ADV
cet-14439	49	11	,	,	PUNCT
cet-14439	49	12	at	at	ADP
cet-14439	49	13	𝑥	𝑥	NOUN
cet-14439	49	14	=	=	SYM
cet-14439	49	15	0	0	NUM
cet-14439	49	16	the	the	DET
cet-14439	49	17	l'hospital	l'hospital	ADJ
cet-14439	49	18	theorem	theorem	NOUN
cet-14439	49	19	must	must	AUX
cet-14439	49	20	be	be	AUX
cet-14439	49	21	applied	apply	VERB
cet-14439	49	22	in	in	ADP
cet-14439	49	23	eq	eq	NOUN
cet-14439	49	24	(	(	PUNCT
cet-14439	49	25	2	2	NUM
cet-14439	49	26	)	)	PUNCT
cet-14439	49	27	in	in	ADP
cet-14439	49	28	order	order	NOUN
cet-14439	49	29	to	to	PART
cet-14439	49	30	avoid	avoid	VERB
cet-14439	49	31	getting	get	VERB
cet-14439	49	32	0	0	NUM
cet-14439	49	33	0⁄	0⁄	NOUN
cet-14439	49	34	,	,	PUNCT
cet-14439	49	35	since	since	SCONJ
cet-14439	49	36	the	the	DET
cet-14439	49	37	first	first	ADJ
cet-14439	49	38	derivative	derivative	NOUN
cet-14439	49	39	is	be	AUX
cet-14439	49	40	divided	divide	VERB
cet-14439	49	41	by	by	ADP
cet-14439	49	42	𝑥	𝑥	PROPN
cet-14439	49	43	after	after	ADP
cet-14439	49	44	rearrangement	rearrangement	NOUN
cet-14439	49	45	of	of	ADP
cet-14439	49	46	the	the	DET
cet-14439	49	47	right	right	ADJ
cet-14439	49	48	hand	hand	NOUN
cet-14439	49	49	side	side	NOUN
cet-14439	49	50	of	of	ADP
cet-14439	49	51	that	that	DET
cet-14439	49	52	equation	equation	NOUN
cet-14439	49	53	.	.	PUNCT
cet-14439	50	1	for	for	ADP
cet-14439	50	2	the	the	DET
cet-14439	50	3	interior	interior	ADJ
cet-14439	50	4	points	point	NOUN
cet-14439	50	5	(	(	PUNCT
cet-14439	50	6	𝑥𝑖	𝑥𝑖	PROPN
cet-14439	50	7	,	,	PUNCT
cet-14439	50	8	𝑖	𝑖	NOUN
cet-14439	50	9	=	=	SYM
cet-14439	50	10	1	1	NUM
cet-14439	50	11	,	,	PUNCT
cet-14439	50	12	⋯	⋯	VERB
cet-14439	50	13	,	,	PUNCT
cet-14439	50	14	𝑁	𝑁	PROPN
cet-14439	50	15	−	−	PROPN
cet-14439	50	16	1	1	NUM
cet-14439	50	17	)	)	PUNCT
cet-14439	50	18	,	,	PUNCT
cet-14439	50	19	the	the	DET
cet-14439	50	20	usual	usual	ADJ
cet-14439	50	21	second	second	ADJ
cet-14439	50	22	order	order	NOUN
cet-14439	50	23	expressions	expression	NOUN
cet-14439	50	24	(	(	PUNCT
cet-14439	50	25	error	error	NOUN
cet-14439	50	26	~	~	PUNCT
cet-14439	50	27	∆𝑥2	∆𝑥2	NOUN
cet-14439	50	28	)	)	PUNCT
cet-14439	50	29	are	be	AUX
cet-14439	50	30	used	use	VERB
cet-14439	50	31	:	:	PUNCT
cet-14439	50	32	(	(	PUNCT
cet-14439	50	33	𝜕2𝑢	𝜕2𝑢	PROPN
cet-14439	50	34	𝜕𝑥2)|	𝜕𝑥2)|	NUM
cet-14439	50	35	𝑖	𝑖	NOUN
cet-14439	50	36	=	=	NOUN
cet-14439	50	37	𝑢𝑖	𝑢𝑖	PROPN
cet-14439	51	1	′′	′′	PROPN
cet-14439	51	2	≅	≅	PROPN
cet-14439	51	3	𝑢𝑖+1	𝑢𝑖+1	PROPN
cet-14439	51	4	−	−	PROPN
cet-14439	51	5	2	2	NUM
cet-14439	51	6	∙	∙	NOUN
cet-14439	51	7	𝑢𝑖	𝑢𝑖	NOUN
cet-14439	51	8	+	+	CCONJ
cet-14439	51	9	𝑢𝑖−1	𝑢𝑖−1	PROPN
cet-14439	51	10	∆𝑥2	∆𝑥2	PROPN
cet-14439	51	11	(	(	PUNCT
cet-14439	51	12	15	15	NUM
cet-14439	51	13	)	)	PUNCT
cet-14439	51	14	(	(	PUNCT
cet-14439	51	15	𝜕𝑢	𝜕𝑢	NOUN
cet-14439	51	16	𝜕𝑥	𝜕𝑥	NOUN
cet-14439	51	17	)	)	PUNCT
cet-14439	51	18	|	|	ADV
cet-14439	51	19	𝑖	𝑖	SYM
cet-14439	51	20	=	=	NOUN
cet-14439	51	21	𝑢𝑖	𝑢𝑖	NOUN
cet-14439	51	22	′	′	NUM
cet-14439	51	23	≅	≅	NUM
cet-14439	51	24	𝑢𝑖+1	𝑢𝑖+1	PROPN
cet-14439	51	25	−	−	PROPN
cet-14439	51	26	𝑢𝑖−1	𝑢𝑖−1	NOUN
cet-14439	51	27	2	2	NUM
cet-14439	51	28	∙	∙	PROPN
cet-14439	51	29	∆𝑥	∆𝑥	NOUN
cet-14439	51	30	(	(	PUNCT
cet-14439	51	31	16	16	NUM
cet-14439	51	32	)	)	PUNCT
cet-14439	51	33	3.2	3.2	NUM
cet-14439	51	34	variational	variational	ADJ
cet-14439	51	35	formulation	formulation	NOUN
cet-14439	51	36	it	it	PRON
cet-14439	51	37	is	be	AUX
cet-14439	51	38	not	not	PART
cet-14439	51	39	possible	possible	ADJ
cet-14439	51	40	to	to	PART
cet-14439	51	41	arrive	arrive	VERB
cet-14439	51	42	directly	directly	ADV
cet-14439	51	43	at	at	ADP
cet-14439	51	44	the	the	DET
cet-14439	51	45	diffusion	diffusion	NOUN
cet-14439	51	46	equation	equation	NOUN
cet-14439	51	47	using	use	VERB
cet-14439	51	48	a	a	DET
cet-14439	51	49	variational	variational	ADJ
cet-14439	51	50	formulation	formulation	NOUN
cet-14439	51	51	,	,	PUNCT
cet-14439	51	52	since	since	SCONJ
cet-14439	51	53	the	the	DET
cet-14439	51	54	first	first	ADJ
cet-14439	51	55	derivative	derivative	NOUN
cet-14439	51	56	vanishes	vanish	VERB
cet-14439	51	57	when	when	SCONJ
cet-14439	51	58	the	the	DET
cet-14439	51	59	euler	euler	ADJ
cet-14439	51	60	-	-	PUNCT
cet-14439	51	61	lagrange	lagrange	NOUN
cet-14439	51	62	equation	equation	NOUN
cet-14439	51	63	is	be	AUX
cet-14439	51	64	applied	apply	VERB
cet-14439	51	65	to	to	ADP
cet-14439	51	66	the	the	DET
cet-14439	51	67	functional	functional	ADJ
cet-14439	51	68	.	.	PUNCT
cet-14439	52	1	however	however	ADV
cet-14439	52	2	,	,	PUNCT
cet-14439	52	3	it	it	PRON
cet-14439	52	4	is	be	AUX
cet-14439	52	5	possible	possible	ADJ
cet-14439	52	6	to	to	PART
cet-14439	52	7	asymptotically	asymptotically	ADV
cet-14439	52	8	arrive	arrive	VERB
cet-14439	52	9	to	to	ADP
cet-14439	52	10	the	the	DET
cet-14439	52	11	diffusion	diffusion	NOUN
cet-14439	52	12	equation	equation	NOUN
cet-14439	52	13	by	by	ADP
cet-14439	52	14	using	use	VERB
cet-14439	52	15	a	a	DET
cet-14439	52	16	procedure	procedure	NOUN
cet-14439	52	17	starting	start	VERB
cet-14439	52	18	with	with	ADP
cet-14439	52	19	a	a	DET
cet-14439	52	20	similar	similar	ADJ
cet-14439	52	21	equation	equation	NOUN
cet-14439	52	22	and	and	CCONJ
cet-14439	52	23	then	then	ADV
cet-14439	52	24	making	make	VERB
cet-14439	52	25	a	a	DET
cet-14439	52	26	quantity	quantity	NOUN
cet-14439	52	27	going	go	VERB
cet-14439	52	28	to	to	PART
cet-14439	52	29	infinity	infinity	VERB
cet-14439	52	30	.	.	PUNCT
cet-14439	53	1	the	the	DET
cet-14439	53	2	following	follow	VERB
cet-14439	53	3	functional	functional	NOUN
cet-14439	53	4	is	be	AUX
cet-14439	53	5	then	then	ADV
cet-14439	53	6	proposed	propose	VERB
cet-14439	53	7	:	:	PUNCT
cet-14439	53	8	𝐼	𝐼	PROPN
cet-14439	53	9	=	=	SYM
cet-14439	53	10	∫	∫	PROPN
cet-14439	54	1	[	[	X
cet-14439	54	2	∫	∫	X
cet-14439	54	3	𝑒−𝜆∙𝜏	𝑒−𝜆∙𝜏	X
cet-14439	54	4	∙	∙	PROPN
cet-14439	54	5	(	(	PUNCT
cet-14439	54	6	λ∙	λ∙	NOUN
cet-14439	54	7	𝑓′(𝑢	𝑓′(𝑢	PROPN
cet-14439	54	8	)	)	PUNCT
cet-14439	54	9	∙	∙	NOUN
cet-14439	54	10	𝑢𝜏	𝑢𝜏	ADP
cet-14439	54	11	2	2	NUM
cet-14439	54	12	+	+	NUM
cet-14439	54	13	𝜆2	𝜆2	NOUN
cet-14439	54	14	∙	∙	NOUN
cet-14439	54	15	𝑢𝑥	𝑢𝑥	ADP
cet-14439	54	16	2	2	NUM
cet-14439	54	17	)	)	PUNCT
cet-14439	54	18	∙	∙	PROPN
cet-14439	54	19	𝑑𝜏	𝑑𝜏	PROPN
cet-14439	55	1	−	−	PROPN
cet-14439	55	2	𝜆	𝜆	ADP
cet-14439	55	3	∙	∙	PROPN
cet-14439	55	4	𝑢𝑥	𝑢𝑥	ADP
cet-14439	55	5	2(𝑥	2(𝑥	NUM
cet-14439	55	6	,	,	PUNCT
cet-14439	55	7	0	0	NUM
cet-14439	55	8	)	)	PUNCT
cet-14439	55	9	∞	∞	NOUN
cet-14439	55	10	0	0	NUM
cet-14439	55	11	]	]	PUNCT
cet-14439	56	1	∙	∙	PROPN
cet-14439	56	2	𝑥2	𝑥2	NOUN
cet-14439	56	3	∙	∙	PROPN
cet-14439	56	4	𝑑𝑥	𝑑𝑥	VERB
cet-14439	56	5	1	1	NUM
cet-14439	56	6	0	0	NUM
cet-14439	56	7	+	+	NUM
cet-14439	56	8	∫	∫	X
cet-14439	56	9	𝛽	𝛽	X
cet-14439	56	10	∙	∙	PROPN
cet-14439	56	11	𝑒−𝜆∙𝜏	𝑒−𝜆∙𝜏	PUNCT
cet-14439	57	1	∙	∙	PROPN
cet-14439	58	1	[	[	X
cet-14439	58	2	𝜆2	𝜆2	X
cet-14439	58	3	∙	∙	PROPN
cet-14439	58	4	(	(	PUNCT
cet-14439	58	5	𝑤	𝑤	ADP
cet-14439	58	6	−	−	PROPN
cet-14439	58	7	𝑢(1	𝑢(1	NOUN
cet-14439	58	8	,	,	PUNCT
cet-14439	58	9	𝜏	𝜏	NOUN
cet-14439	58	10	)	)	PUNCT
cet-14439	58	11	)	)	PUNCT
cet-14439	58	12	2	2	NUM
cet-14439	59	1	+	+	CCONJ
cet-14439	59	2	𝜆	𝜆	X
cet-14439	59	3	∙	∙	PROPN
cet-14439	59	4	1	1	NUM
cet-14439	59	5	𝛼	𝛼	NOUN
cet-14439	59	6	∙	∙	PROPN
cet-14439	59	7	𝑤𝜏	𝑤𝜏	ADP
cet-14439	59	8	2	2	X
cet-14439	59	9	]	]	PUNCT
cet-14439	59	10	∙	∙	PROPN
cet-14439	59	11	𝑑𝜏	𝑑𝜏	PROPN
cet-14439	59	12	∞	∞	PROPN
cet-14439	59	13	0	0	NUM
cet-14439	59	14	(	(	PUNCT
cet-14439	59	15	17	17	NUM
cet-14439	59	16	)	)	PUNCT
cet-14439	59	17	where	where	SCONJ
cet-14439	59	18	𝑢𝑥	𝑢𝑥	ADP
cet-14439	59	19	is	be	AUX
cet-14439	59	20	the	the	DET
cet-14439	59	21	first	first	ADJ
cet-14439	59	22	derivative	derivative	NOUN
cet-14439	59	23	of	of	ADP
cet-14439	59	24	𝑢	𝑢	NOUN
cet-14439	59	25	with	with	ADP
cet-14439	59	26	respect	respect	NOUN
cet-14439	59	27	to	to	ADP
cet-14439	59	28	𝑥	𝑥	PRON
cet-14439	59	29	,	,	PUNCT
cet-14439	59	30	𝑢𝜏	𝑢𝜏	NOUN
cet-14439	59	31	is	be	AUX
cet-14439	59	32	the	the	DET
cet-14439	59	33	first	first	ADJ
cet-14439	59	34	derivative	derivative	NOUN
cet-14439	59	35	of	of	ADP
cet-14439	59	36	𝑢	𝑢	NOUN
cet-14439	59	37	with	with	ADP
cet-14439	59	38	respect	respect	NOUN
cet-14439	59	39	to	to	ADP
cet-14439	59	40	𝜏	𝜏	NUM
cet-14439	59	41	,	,	PUNCT
cet-14439	59	42	and	and	CCONJ
cet-14439	59	43	𝑤𝜏	𝑤𝜏	VERB
cet-14439	59	44	is	be	AUX
cet-14439	59	45	the	the	DET
cet-14439	59	46	first	first	ADJ
cet-14439	59	47	derivative	derivative	NOUN
cet-14439	59	48	of	of	ADP
cet-14439	59	49	𝑤	𝑤	ADP
cet-14439	59	50	with	with	ADP
cet-14439	59	51	respect	respect	NOUN
cet-14439	59	52	to	to	PART
cet-14439	59	53	𝜏.	𝜏.	VERB
cet-14439	59	54	some	some	DET
cet-14439	59	55	asymptotic	asymptotic	ADJ
cet-14439	59	56	relations	relation	NOUN
cet-14439	59	57	can	can	AUX
cet-14439	59	58	be	be	AUX
cet-14439	59	59	obtained	obtain	VERB
cet-14439	59	60	for	for	ADP
cet-14439	59	61	large	large	ADJ
cet-14439	59	62	values	value	NOUN
cet-14439	59	63	of	of	ADP
cet-14439	59	64	𝜆.	𝜆.	NOUN
cet-14439	59	65	from	from	ADP
cet-14439	59	66	the	the	DET
cet-14439	59	67	theory	theory	NOUN
cet-14439	59	68	of	of	ADP
cet-14439	59	69	laplace	laplace	NOUN
cet-14439	59	70	transforms	transform	VERB
cet-14439	59	71	,	,	PUNCT
cet-14439	59	72	the	the	DET
cet-14439	59	73	following	follow	VERB
cet-14439	59	74	equation	equation	NOUN
cet-14439	59	75	is	be	AUX
cet-14439	59	76	valid	valid	ADJ
cet-14439	59	77	(	(	PUNCT
cet-14439	59	78	spiegel	spiegel	PROPN
cet-14439	59	79	,	,	PUNCT
cet-14439	59	80	1965	1965	NUM
cet-14439	59	81	):	):	PUNCT
cet-14439	59	82	∫	∫	PROPN
cet-14439	59	83	𝑒−𝜆∙𝜏	𝑒−𝜆∙𝜏	NUM
cet-14439	59	84	∙	∙	PROPN
cet-14439	59	85	𝑓(𝜏	𝑓(𝜏	PROPN
cet-14439	59	86	)	)	PUNCT
cet-14439	59	87	∙	∙	PROPN
cet-14439	59	88	𝑑𝜏	𝑑𝜏	X
cet-14439	60	1	=	=	PUNCT
cet-14439	60	2	∑	∑	PROPN
cet-14439	60	3	1	1	NUM
cet-14439	60	4	𝜆𝑘+1	𝜆𝑘+1	NUM
cet-14439	60	5	∞	∞	PROPN
cet-14439	60	6	𝑘=0	𝑘=0	PROPN
cet-14439	60	7	∞	∞	NOUN
cet-14439	60	8	0	0	NUM
cet-14439	60	9	∙	∙	PROPN
cet-14439	60	10	𝑓(𝑘)(0	𝑓(𝑘)(0	PROPN
cet-14439	60	11	)	)	PUNCT
cet-14439	60	12	(	(	PUNCT
cet-14439	60	13	18	18	NUM
cet-14439	60	14	)	)	PUNCT
cet-14439	60	15	so	so	SCONJ
cet-14439	60	16	that	that	SCONJ
cet-14439	60	17	eq	eq	NOUN
cet-14439	60	18	(	(	PUNCT
cet-14439	60	19	17	17	NUM
cet-14439	60	20	)	)	PUNCT
cet-14439	60	21	converges	converge	VERB
cet-14439	60	22	to	to	ADP
cet-14439	60	23	a	a	DET
cet-14439	60	24	finite	finite	ADJ
cet-14439	60	25	value	value	NOUN
cet-14439	60	26	when	when	SCONJ
cet-14439	60	27	𝜆	𝜆	X
cet-14439	60	28	→	→	SYM
cet-14439	60	29	∞.	∞.	PROPN
cet-14439	60	30	the	the	DET
cet-14439	60	31	stationary	stationary	ADJ
cet-14439	60	32	condition	condition	NOUN
cet-14439	60	33	of	of	ADP
cet-14439	60	34	a	a	DET
cet-14439	60	35	functional	functional	ADJ
cet-14439	60	36	is	be	AUX
cet-14439	60	37	given	give	VERB
cet-14439	60	38	by	by	ADP
cet-14439	60	39	the	the	DET
cet-14439	60	40	euler	euler	PROPN
cet-14439	60	41	-	-	PUNCT
cet-14439	60	42	lagrange	lagrange	NOUN
cet-14439	60	43	equation	equation	NOUN
cet-14439	60	44	.	.	PUNCT
cet-14439	61	1	for	for	ADP
cet-14439	61	2	an	an	DET
cet-14439	61	3	integrand	integrand	NOUN
cet-14439	61	4	(	(	PUNCT
cet-14439	61	5	𝐹	𝐹	PROPN
cet-14439	61	6	)	)	PUNCT
cet-14439	61	7	that	that	PRON
cet-14439	61	8	depends	depend	VERB
cet-14439	61	9	only	only	ADV
cet-14439	61	10	on	on	ADP
cet-14439	61	11	𝑢	𝑢	NOUN
cet-14439	61	12	,	,	PUNCT
cet-14439	61	13	𝑢𝑥	𝑢𝑥	ADP
cet-14439	61	14	,	,	PUNCT
cet-14439	61	15	𝑢𝜏	𝑢𝜏	NOUN
cet-14439	61	16	,	,	PUNCT
cet-14439	61	17	the	the	DET
cet-14439	61	18	stationary	stationary	ADJ
cet-14439	61	19	condition	condition	NOUN
cet-14439	61	20	is	be	AUX
cet-14439	61	21	:	:	PUNCT
cet-14439	61	22	−	−	PUNCT
cet-14439	61	23	𝜕𝐹	𝜕𝐹	NOUN
cet-14439	61	24	𝜕𝑢	𝜕𝑢	ADJ
cet-14439	61	25	+	+	CCONJ
cet-14439	61	26	𝜕	𝜕	NOUN
cet-14439	61	27	𝜕𝜏	𝜕𝜏	NOUN
cet-14439	61	28	(	(	PUNCT
cet-14439	61	29	𝜕𝐹	𝜕𝐹	NOUN
cet-14439	61	30	𝜕𝑢𝜏	𝜕𝑢𝜏	PUNCT
cet-14439	61	31	)	)	PUNCT
cet-14439	62	1	+	+	CCONJ
cet-14439	62	2	𝜕	𝜕	NOUN
cet-14439	62	3	𝜕𝑥	𝜕𝑥	X
cet-14439	62	4	(	(	PUNCT
cet-14439	62	5	𝜕𝐹	𝜕𝐹	NOUN
cet-14439	62	6	𝜕𝑢𝑥	𝜕𝑢𝑥	PUNCT
cet-14439	62	7	)	)	PUNCT
cet-14439	62	8	=	=	SYM
cet-14439	62	9	0	0	NUM
cet-14439	62	10	(	(	PUNCT
cet-14439	62	11	19	19	NUM
cet-14439	62	12	)	)	PUNCT
cet-14439	62	13	applying	apply	VERB
cet-14439	62	14	this	this	DET
cet-14439	62	15	stationary	stationary	ADJ
cet-14439	62	16	condition	condition	NOUN
cet-14439	62	17	to	to	ADP
cet-14439	62	18	the	the	DET
cet-14439	62	19	proposed	propose	VERB
cet-14439	62	20	functional	functional	ADJ
cet-14439	62	21	with	with	ADP
cet-14439	62	22	respect	respect	NOUN
cet-14439	62	23	to	to	ADP
cet-14439	62	24	the	the	DET
cet-14439	62	25	profile	profile	NOUN
cet-14439	62	26	𝑢(𝑥	𝑢(𝑥	PROPN
cet-14439	62	27	,	,	PUNCT
cet-14439	62	28	𝜏	𝜏	NOUN
cet-14439	62	29	)	)	PUNCT
cet-14439	62	30	,	,	PUNCT
cet-14439	62	31	after	after	ADP
cet-14439	62	32	some	some	DET
cet-14439	62	33	rearrangements	rearrangement	NOUN
cet-14439	62	34	,	,	PUNCT
cet-14439	62	35	the	the	DET
cet-14439	62	36	results	result	NOUN
cet-14439	62	37	is	be	AUX
cet-14439	62	38	:	:	PUNCT
cet-14439	62	39	[	[	X
cet-14439	62	40	−𝑓′(𝑢	−𝑓′(𝑢	INTJ
cet-14439	62	41	)	)	PUNCT
cet-14439	62	42	∙	∙	NOUN
cet-14439	62	43	𝑢𝜏	𝑢𝜏	ADP
cet-14439	62	44	+	+	CCONJ
cet-14439	62	45	1	1	NUM
cet-14439	62	46	𝑥2	𝑥2	NOUN
cet-14439	62	47	∙	∙	PROPN
cet-14439	62	48	𝜕	𝜕	PROPN
cet-14439	62	49	𝜕𝑥	𝜕𝑥	NOUN
cet-14439	62	50	(	(	PUNCT
cet-14439	62	51	𝑥2	𝑥2	NOUN
cet-14439	62	52	∙	∙	PROPN
cet-14439	62	53	𝑢𝑥	𝑢𝑥	ADP
cet-14439	62	54	)	)	PUNCT
cet-14439	62	55	]	]	PUNCT
cet-14439	63	1	+	+	CCONJ
cet-14439	63	2	1	1	NUM
cet-14439	63	3	2	2	NUM
cet-14439	63	4	∙	∙	PROPN
cet-14439	63	5	𝜆	𝜆	X
cet-14439	63	6	∙	∙	PROPN
cet-14439	63	7	[	[	X
cet-14439	63	8	𝑓′′(𝑢	𝑓′′(𝑢	X
cet-14439	63	9	)	)	PUNCT
cet-14439	63	10	∙	∙	NOUN
cet-14439	63	11	𝑢𝜏	𝑢𝜏	ADP
cet-14439	63	12	2	2	NUM
cet-14439	63	13	+	+	CCONJ
cet-14439	63	14	2	2	NUM
cet-14439	63	15	∙	∙	PROPN
cet-14439	63	16	𝑓′(𝑢	𝑓′(𝑢	PROPN
cet-14439	63	17	)	)	PUNCT
cet-14439	63	18	∙	∙	PROPN
cet-14439	63	19	𝑢𝜏𝜏	𝑢𝜏𝜏	NOUN
cet-14439	63	20	]	]	X
cet-14439	63	21	=	=	SYM
cet-14439	63	22	0	0	NUM
cet-14439	63	23	(	(	PUNCT
cet-14439	63	24	20	20	NUM
cet-14439	63	25	)	)	PUNCT
cet-14439	63	26	this	this	PRON
cet-14439	63	27	is	be	AUX
cet-14439	63	28	not	not	PART
cet-14439	63	29	eq	eq	ADJ
cet-14439	63	30	(	(	PUNCT
cet-14439	63	31	2	2	NUM
cet-14439	63	32	)	)	PUNCT
cet-14439	63	33	,	,	PUNCT
cet-14439	63	34	but	but	CCONJ
cet-14439	63	35	as	as	ADP
cet-14439	63	36	𝜆	𝜆	PRON
cet-14439	63	37	→	→	SYM
cet-14439	63	38	∞	∞	NOUN
cet-14439	63	39	this	this	DET
cet-14439	63	40	equation	equation	NOUN
cet-14439	63	41	asymptotically	asymptotically	ADV
cet-14439	63	42	tends	tend	VERB
cet-14439	63	43	to	to	ADP
cet-14439	63	44	eq	eq	NOUN
cet-14439	63	45	(	(	PUNCT
cet-14439	63	46	2	2	NUM
cet-14439	63	47	)	)	PUNCT
cet-14439	63	48	.	.	PUNCT
cet-14439	64	1	boundary	boundary	ADJ
cet-14439	64	2	condition	condition	NOUN
cet-14439	64	3	eq	eq	ADP
cet-14439	64	4	(	(	PUNCT
cet-14439	64	5	5	5	NUM
cet-14439	64	6	)	)	PUNCT
cet-14439	64	7	is	be	AUX
cet-14439	64	8	naturally	naturally	ADV
cet-14439	64	9	satisfied	satisfied	ADJ
cet-14439	64	10	,	,	PUNCT
cet-14439	64	11	while	while	SCONJ
cet-14439	64	12	boundary	boundary	ADJ
cet-14439	64	13	condition	condition	NOUN
cet-14439	64	14	eq	eq	ADP
cet-14439	64	15	(	(	PUNCT
cet-14439	64	16	4	4	X
cet-14439	64	17	)	)	PUNCT
cet-14439	64	18	comes	come	VERB
cet-14439	64	19	from	from	ADP
cet-14439	64	20	the	the	DET
cet-14439	64	21	stationary	stationary	ADJ
cet-14439	64	22	condition	condition	NOUN
cet-14439	64	23	for	for	ADP
cet-14439	64	24	the	the	DET
cet-14439	64	25	term	term	NOUN
cet-14439	64	26	𝑢(1	𝑢(1	PROPN
cet-14439	64	27	,	,	PUNCT
cet-14439	64	28	𝜏	𝜏	NOUN
cet-14439	64	29	)	)	PUNCT
cet-14439	64	30	.	.	PUNCT
cet-14439	65	1	initial	initial	ADJ
cet-14439	65	2	condition	condition	NOUN
cet-14439	65	3	eq	eq	ADP
cet-14439	65	4	(	(	PUNCT
cet-14439	65	5	6	6	NUM
cet-14439	65	6	)	)	PUNCT
cet-14439	65	7	is	be	AUX
cet-14439	65	8	given	give	VERB
cet-14439	65	9	.	.	PUNCT
cet-14439	66	1	the	the	DET
cet-14439	66	2	stationary	stationary	ADJ
cet-14439	66	3	condition	condition	NOUN
cet-14439	66	4	for	for	ADP
cet-14439	66	5	the	the	DET
cet-14439	66	6	profile	profile	NOUN
cet-14439	66	7	𝑤(𝜏	𝑤(𝜏	PROPN
cet-14439	66	8	)	)	PUNCT
cet-14439	66	9	is	be	AUX
cet-14439	66	10	given	give	VERB
cet-14439	66	11	by	by	ADP
cet-14439	66	12	:	:	PUNCT
cet-14439	66	13	−	−	PROPN
cet-14439	66	14	𝜕𝐹	𝜕𝐹	PRON
cet-14439	66	15	𝜕𝑤	𝜕𝑤	VERB
cet-14439	66	16	+	+	CCONJ
cet-14439	66	17	𝑑	𝑑	PROPN
cet-14439	66	18	𝑑𝜏	𝑑𝜏	X
cet-14439	66	19	(	(	PUNCT
cet-14439	66	20	𝜕𝐹	𝜕𝐹	NOUN
cet-14439	66	21	𝜕𝑤𝜏	𝜕𝑤𝜏	PUNCT
cet-14439	66	22	)	)	PUNCT
cet-14439	67	1	=	=	SYM
cet-14439	67	2	0	0	PUNCT
cet-14439	67	3	(	(	PUNCT
cet-14439	67	4	21	21	NUM
cet-14439	67	5	)	)	PUNCT
cet-14439	67	6	which	which	PRON
cet-14439	67	7	,	,	PUNCT
cet-14439	67	8	after	after	ADP
cet-14439	67	9	rearrangements	rearrangement	NOUN
cet-14439	67	10	,	,	PUNCT
cet-14439	67	11	leads	lead	VERB
cet-14439	67	12	to	to	ADP
cet-14439	67	13	:	:	PUNCT
cet-14439	67	14	93	93	NUM
cet-14439	68	1	[	[	X
cet-14439	68	2	𝑤	𝑤	ADP
cet-14439	68	3	−	−	NOUN
cet-14439	68	4	𝑢(1	𝑢(1	NOUN
cet-14439	68	5	,	,	PUNCT
cet-14439	68	6	𝜏	𝜏	NOUN
cet-14439	68	7	)	)	PUNCT
cet-14439	68	8	]	]	PUNCT
cet-14439	69	1	+	+	CCONJ
cet-14439	69	2	1	1	NUM
cet-14439	69	3	𝛼	𝛼	X
cet-14439	69	4	∙	∙	PROPN
cet-14439	69	5	𝑤𝜏	𝑤𝜏	ADP
cet-14439	69	6	−	−	PROPN
cet-14439	69	7	1	1	NUM
cet-14439	69	8	𝜆	𝜆	ADP
cet-14439	69	9	∙	∙	PROPN
cet-14439	69	10	1	1	NUM
cet-14439	69	11	𝛼	𝛼	NOUN
cet-14439	69	12	∙	∙	PROPN
cet-14439	69	13	𝑤𝜏𝜏	𝑤𝜏𝜏	NOUN
cet-14439	69	14	=	=	SYM
cet-14439	69	15	0	0	NUM
cet-14439	69	16	(	(	PUNCT
cet-14439	69	17	22	22	NUM
cet-14439	69	18	)	)	PUNCT
cet-14439	69	19	this	this	PRON
cet-14439	69	20	is	be	AUX
cet-14439	69	21	not	not	PART
cet-14439	69	22	eq	eq	NOUN
cet-14439	69	23	(	(	PUNCT
cet-14439	69	24	3	3	NUM
cet-14439	69	25	)	)	PUNCT
cet-14439	69	26	,	,	PUNCT
cet-14439	69	27	but	but	CCONJ
cet-14439	69	28	as	as	ADP
cet-14439	69	29	𝜆	𝜆	PRON
cet-14439	69	30	→	→	SYM
cet-14439	69	31	∞	∞	NOUN
cet-14439	69	32	this	this	DET
cet-14439	69	33	equation	equation	NOUN
cet-14439	69	34	asymptotically	asymptotically	ADV
cet-14439	69	35	tends	tend	VERB
cet-14439	69	36	to	to	ADP
cet-14439	69	37	eq	eq	NOUN
cet-14439	69	38	(	(	PUNCT
cet-14439	69	39	3	3	NUM
cet-14439	69	40	)	)	PUNCT
cet-14439	69	41	.	.	PUNCT
cet-14439	70	1	initial	initial	ADJ
cet-14439	70	2	condition	condition	NOUN
cet-14439	70	3	eq	eq	ADP
cet-14439	70	4	(	(	PUNCT
cet-14439	70	5	7	7	X
cet-14439	70	6	)	)	PUNCT
cet-14439	70	7	is	be	AUX
cet-14439	70	8	given	give	VERB
cet-14439	70	9	.	.	PUNCT
cet-14439	71	1	3.2.1	3.2.1	NUM
cet-14439	71	2	the	the	DET
cet-14439	71	3	ritz	ritz	PROPN
cet-14439	71	4	method	method	NOUN
cet-14439	71	5	solution	solution	NOUN
cet-14439	71	6	with	with	ADP
cet-14439	71	7	an	an	DET
cet-14439	71	8	interpolating	interpolate	VERB
cet-14439	71	9	polynomial	polynomial	ADJ
cet-14439	71	10	one	one	NUM
cet-14439	71	11	particular	particular	ADJ
cet-14439	71	12	application	application	NOUN
cet-14439	71	13	of	of	ADP
cet-14439	71	14	the	the	DET
cet-14439	71	15	variational	variational	ADJ
cet-14439	71	16	method	method	NOUN
cet-14439	71	17	is	be	AUX
cet-14439	71	18	finding	find	VERB
cet-14439	71	19	approximated	approximate	VERB
cet-14439	71	20	solutions	solution	NOUN
cet-14439	71	21	to	to	PART
cet-14439	71	22	differential	differential	ADJ
cet-14439	71	23	equations	equation	NOUN
cet-14439	71	24	,	,	PUNCT
cet-14439	71	25	also	also	ADV
cet-14439	71	26	known	know	VERB
cet-14439	71	27	as	as	ADP
cet-14439	71	28	the	the	DET
cet-14439	71	29	ritz	ritz	PROPN
cet-14439	71	30	method	method	NOUN
cet-14439	71	31	.	.	PUNCT
cet-14439	72	1	it	it	PRON
cet-14439	72	2	consists	consist	VERB
cet-14439	72	3	in	in	ADP
cet-14439	72	4	finding	find	VERB
cet-14439	72	5	a	a	DET
cet-14439	72	6	corresponding	corresponding	ADJ
cet-14439	72	7	functional	functional	NOUN
cet-14439	72	8	that	that	PRON
cet-14439	72	9	results	result	VERB
cet-14439	72	10	in	in	ADP
cet-14439	72	11	the	the	DET
cet-14439	72	12	differential	differential	ADJ
cet-14439	72	13	equation	equation	NOUN
cet-14439	72	14	,	,	PUNCT
cet-14439	72	15	then	then	ADV
cet-14439	72	16	using	use	VERB
cet-14439	72	17	trial	trial	NOUN
cet-14439	72	18	functions	function	NOUN
cet-14439	72	19	in	in	ADP
cet-14439	72	20	the	the	DET
cet-14439	72	21	functional	functional	ADJ
cet-14439	72	22	,	,	PUNCT
cet-14439	72	23	and	and	CCONJ
cet-14439	72	24	then	then	ADV
cet-14439	72	25	applying	apply	VERB
cet-14439	72	26	the	the	DET
cet-14439	72	27	stationary	stationary	ADJ
cet-14439	72	28	conditions	condition	NOUN
cet-14439	72	29	with	with	ADP
cet-14439	72	30	respect	respect	NOUN
cet-14439	72	31	to	to	ADP
cet-14439	72	32	the	the	DET
cet-14439	72	33	parameters	parameter	NOUN
cet-14439	72	34	in	in	ADP
cet-14439	72	35	the	the	DET
cet-14439	72	36	trial	trial	NOUN
cet-14439	72	37	functions	function	NOUN
cet-14439	72	38	.	.	PUNCT
cet-14439	73	1	using	use	VERB
cet-14439	73	2	lagrangian	lagrangian	ADJ
cet-14439	73	3	interpolation	interpolation	NOUN
cet-14439	73	4	,	,	PUNCT
cet-14439	73	5	the	the	DET
cet-14439	73	6	following	follow	VERB
cet-14439	73	7	trial	trial	NOUN
cet-14439	73	8	function	function	NOUN
cet-14439	73	9	is	be	AUX
cet-14439	73	10	considered	consider	VERB
cet-14439	73	11	:	:	PUNCT
cet-14439	73	12	𝑢(𝑥	𝑢(𝑥	NUM
cet-14439	73	13	,	,	PUNCT
cet-14439	73	14	𝜏	𝜏	NOUN
cet-14439	73	15	)	)	PUNCT
cet-14439	73	16	=	=	SYM
cet-14439	73	17	∑	∑	NOUN
cet-14439	73	18	𝑙𝑗(𝑥	𝑙𝑗(𝑥	X
cet-14439	73	19	)	)	PUNCT
cet-14439	73	20	∙	∙	PROPN
cet-14439	73	21	𝑢(𝑥𝑗	𝑢(𝑥𝑗	PROPN
cet-14439	73	22	,	,	PUNCT
cet-14439	73	23	𝜏	𝜏	NOUN
cet-14439	73	24	)	)	PUNCT
cet-14439	73	25	𝑀	𝑀	PROPN
cet-14439	73	26	𝑗=1	𝑗=1	PROPN
cet-14439	73	27	(	(	PUNCT
cet-14439	73	28	23	23	NUM
cet-14439	73	29	)	)	PUNCT
cet-14439	73	30	where	where	SCONJ
cet-14439	73	31	𝑙𝑗(𝑥	𝑙𝑗(𝑥	NOUN
cet-14439	73	32	)	)	PUNCT
cet-14439	73	33	are	be	AUX
cet-14439	73	34	the	the	DET
cet-14439	73	35	lagrangian	lagrangian	ADJ
cet-14439	73	36	polynomials	polynomial	NOUN
cet-14439	73	37	at	at	ADP
cet-14439	73	38	some	some	DET
cet-14439	73	39	given	give	VERB
cet-14439	73	40	points	point	NOUN
cet-14439	73	41	𝑥1	𝑥1	PROPN
cet-14439	73	42	,	,	PUNCT
cet-14439	73	43	⋯	⋯	PROPN
cet-14439	73	44	,	,	PUNCT
cet-14439	73	45	𝑥𝑀	𝑥𝑀	NOUN
cet-14439	73	46	,	,	PUNCT
cet-14439	73	47	so	so	SCONJ
cet-14439	73	48	that	that	SCONJ
cet-14439	73	49	𝑙𝑗(𝑥𝑘	𝑙𝑗(𝑥𝑘	ADJ
cet-14439	73	50	)	)	PUNCT
cet-14439	74	1	=	=	SYM
cet-14439	74	2	0	0	NUM
cet-14439	75	1	for	for	ADP
cet-14439	75	2	𝑘	𝑘	DET
cet-14439	75	3	≠	≠	PROPN
cet-14439	75	4	𝑗	𝑗	NOUN
cet-14439	75	5	and	and	CCONJ
cet-14439	75	6	1	1	NUM
cet-14439	75	7	otherwise	otherwise	ADV
cet-14439	75	8	.	.	PUNCT
cet-14439	76	1	the	the	DET
cet-14439	76	2	trial	trial	NOUN
cet-14439	76	3	function	function	NOUN
cet-14439	76	4	is	be	AUX
cet-14439	76	5	then	then	ADV
cet-14439	76	6	substituted	substitute	VERB
cet-14439	76	7	into	into	ADP
cet-14439	76	8	eq	eq	PROPN
cet-14439	76	9	(	(	PUNCT
cet-14439	76	10	17	17	NUM
cet-14439	76	11	)	)	PUNCT
cet-14439	76	12	.	.	PUNCT
cet-14439	77	1	a	a	DET
cet-14439	77	2	gaussian	gaussian	ADJ
cet-14439	77	3	quadrature	quadrature	NOUN
cet-14439	77	4	is	be	AUX
cet-14439	77	5	applied	apply	VERB
cet-14439	77	6	,	,	PUNCT
cet-14439	77	7	and	and	CCONJ
cet-14439	77	8	since	since	SCONJ
cet-14439	77	9	the	the	DET
cet-14439	77	10	integration	integration	NOUN
cet-14439	77	11	is	be	AUX
cet-14439	77	12	from	from	ADP
cet-14439	77	13	𝑥	𝑥	NOUN
cet-14439	77	14	=	=	SYM
cet-14439	77	15	0	0	NUM
cet-14439	77	16	to	to	ADP
cet-14439	77	17	𝑥	𝑥	NOUN
cet-14439	77	18	=	=	SYM
cet-14439	77	19	1	1	NUM
cet-14439	77	20	,	,	PUNCT
cet-14439	77	21	with	with	ADP
cet-14439	77	22	weight	weight	NOUN
cet-14439	77	23	function	function	NOUN
cet-14439	77	24	𝑥2	𝑥2	NOUN
cet-14439	77	25	,	,	PUNCT
cet-14439	77	26	the	the	DET
cet-14439	77	27	gaussian	gaussian	ADJ
cet-14439	77	28	integration	integration	NOUN
cet-14439	77	29	of	of	ADP
cet-14439	77	30	moments	moment	NOUN
cet-14439	77	31	with	with	ADP
cet-14439	77	32	𝑘	𝑘	NOUN
cet-14439	77	33	=	=	SYM
cet-14439	77	34	2	2	NUM
cet-14439	77	35	is	be	AUX
cet-14439	77	36	used	use	VERB
cet-14439	77	37	(	(	PUNCT
cet-14439	77	38	abramowitz	abramowitz	NOUN
cet-14439	77	39	and	and	CCONJ
cet-14439	77	40	stegun	stegun	NOUN
cet-14439	77	41	,	,	PUNCT
cet-14439	77	42	1972	1972	NUM
cet-14439	77	43	)	)	PUNCT
cet-14439	77	44	.	.	PUNCT
cet-14439	78	1	the	the	DET
cet-14439	78	2	following	follow	VERB
cet-14439	78	3	results	result	NOUN
cet-14439	78	4	will	will	AUX
cet-14439	78	5	then	then	ADV
cet-14439	78	6	be	be	AUX
cet-14439	78	7	used	use	VERB
cet-14439	78	8	:	:	PUNCT
cet-14439	78	9	∫	∫	PROPN
cet-14439	78	10	𝑓′(𝑢	𝑓′(𝑢	PROPN
cet-14439	78	11	)	)	PUNCT
cet-14439	78	12	∙	∙	NOUN
cet-14439	78	13	𝑢𝜏	𝑢𝜏	ADP
cet-14439	78	14	2	2	NUM
cet-14439	78	15	∙	∙	PROPN
cet-14439	78	16	𝑥2	𝑥2	NOUN
cet-14439	78	17	∙	∙	PROPN
cet-14439	78	18	𝑑𝑥	𝑑𝑥	VERB
cet-14439	78	19	1	1	NUM
cet-14439	78	20	0	0	NUM
cet-14439	78	21	=	=	SYM
cet-14439	78	22	∑	∑	PUNCT
cet-14439	79	1	[	[	X
cet-14439	79	2	𝑊𝑗	𝑊𝑗	PROPN
cet-14439	79	3	∙	∙	PROPN
cet-14439	79	4	𝑓′(𝑢𝑗	𝑓′(𝑢𝑗	NOUN
cet-14439	79	5	)	)	PUNCT
cet-14439	79	6	∙	∙	PROPN
cet-14439	79	7	(	(	PUNCT
cet-14439	79	8	𝑑𝑢𝑗	𝑑𝑢𝑗	X
cet-14439	79	9	𝑑𝜏	𝑑𝜏	NOUN
cet-14439	79	10	)	)	PUNCT
cet-14439	79	11	2	2	NUM
cet-14439	79	12	]	]	PUNCT
cet-14439	79	13	𝑀	𝑀	PROPN
cet-14439	79	14	𝑗=1	𝑗=1	PROPN
cet-14439	79	15	(	(	PUNCT
cet-14439	79	16	24	24	NUM
cet-14439	79	17	)	)	PUNCT
cet-14439	79	18	∫	∫	NOUN
cet-14439	79	19	𝑢𝑥	𝑢𝑥	ADP
cet-14439	79	20	2	2	NUM
cet-14439	79	21	∙	∙	PROPN
cet-14439	79	22	𝑥2	𝑥2	NOUN
cet-14439	79	23	∙	∙	PROPN
cet-14439	79	24	𝑑𝑥	𝑑𝑥	VERB
cet-14439	79	25	1	1	NUM
cet-14439	79	26	0	0	NUM
cet-14439	79	27	=	=	SYM
cet-14439	79	28	∑	∑	PUNCT
cet-14439	80	1	[	[	X
cet-14439	80	2	𝑊𝑗	𝑊𝑗	PROPN
cet-14439	80	3	∙	∙	PROPN
cet-14439	80	4	(	(	PUNCT
cet-14439	80	5	∑	∑	PUNCT
cet-14439	80	6	𝑙𝑘	𝑙𝑘	INTJ
cet-14439	80	7	′	′	NOUN
cet-14439	80	8	(	(	PUNCT
cet-14439	80	9	𝑥𝑗	𝑥𝑗	PROPN
cet-14439	80	10	)	)	PUNCT
cet-14439	80	11	∙	∙	PROPN
cet-14439	80	12	𝑢(𝑥𝑘	𝑢(𝑥𝑘	PROPN
cet-14439	80	13	,	,	PUNCT
cet-14439	80	14	𝜏	𝜏	NOUN
cet-14439	80	15	)	)	PUNCT
cet-14439	80	16	𝑀	𝑀	PROPN
cet-14439	80	17	𝑘=1	𝑘=1	PROPN
cet-14439	80	18	)	)	PUNCT
cet-14439	80	19	2	2	NUM
cet-14439	80	20	]	]	PUNCT
cet-14439	80	21	𝑀	𝑀	PROPN
cet-14439	80	22	𝑗=1	𝑗=1	PROPN
cet-14439	80	23	(	(	PUNCT
cet-14439	80	24	25	25	NUM
cet-14439	80	25	)	)	PUNCT
cet-14439	80	26	where	where	SCONJ
cet-14439	80	27	𝑢𝑗	𝑢𝑗	X
cet-14439	80	28	=	=	SYM
cet-14439	80	29	𝑢(𝑥𝑗	𝑢(𝑥𝑗	NOUN
cet-14439	80	30	,	,	PUNCT
cet-14439	80	31	𝜏	𝜏	NOUN
cet-14439	80	32	)	)	PUNCT
cet-14439	80	33	is	be	AUX
cet-14439	80	34	a	a	DET
cet-14439	80	35	function	function	NOUN
cet-14439	80	36	of	of	ADP
cet-14439	80	37	𝜏	𝜏	PRON
cet-14439	80	38	at	at	ADP
cet-14439	80	39	each	each	DET
cet-14439	80	40	given	give	VERB
cet-14439	80	41	point	point	NOUN
cet-14439	80	42	𝑥𝑗	𝑥𝑗	PROPN
cet-14439	80	43	,	,	PUNCT
cet-14439	80	44	and	and	CCONJ
cet-14439	80	45	where	where	SCONJ
cet-14439	80	46	the	the	DET
cet-14439	80	47	points	point	NOUN
cet-14439	80	48	𝑥𝑗	𝑥𝑗	VERB
cet-14439	80	49	and	and	CCONJ
cet-14439	80	50	the	the	DET
cet-14439	80	51	weights	weight	NOUN
cet-14439	80	52	𝑊𝑗	𝑊𝑗	PROPN
cet-14439	80	53	can	can	AUX
cet-14439	80	54	be	be	AUX
cet-14439	80	55	found	find	VERB
cet-14439	80	56	in	in	ADP
cet-14439	80	57	abramowitz	abramowitz	NOUN
cet-14439	80	58	and	and	CCONJ
cet-14439	80	59	stegun	stegun	NOUN
cet-14439	80	60	(	(	PUNCT
cet-14439	80	61	1972	1972	NUM
cet-14439	80	62	)	)	PUNCT
cet-14439	80	63	for	for	ADP
cet-14439	80	64	gaussian	gaussian	ADJ
cet-14439	80	65	integration	integration	NOUN
cet-14439	80	66	of	of	ADP
cet-14439	80	67	moments	moment	NOUN
cet-14439	80	68	with	with	ADP
cet-14439	80	69	𝑘	𝑘	PROPN
cet-14439	80	70	=	=	SYM
cet-14439	80	71	2	2	NUM
cet-14439	80	72	(	(	PUNCT
cet-14439	80	73	the	the	DET
cet-14439	80	74	weight	weight	NOUN
cet-14439	80	75	function	function	NOUN
cet-14439	80	76	𝑥2	𝑥2	NOUN
cet-14439	80	77	is	be	AUX
cet-14439	80	78	already	already	ADV
cet-14439	80	79	included	include	VERB
cet-14439	80	80	in	in	ADP
cet-14439	80	81	the	the	DET
cet-14439	80	82	weights	weight	NOUN
cet-14439	80	83	𝑊𝑗	𝑊𝑗	PROPN
cet-14439	80	84	)	)	PUNCT
cet-14439	80	85	.	.	PUNCT
cet-14439	81	1	the	the	DET
cet-14439	81	2	functional	functional	ADJ
cet-14439	81	3	𝐼	𝐼	PROPN
cet-14439	81	4	is	be	AUX
cet-14439	81	5	then	then	ADV
cet-14439	81	6	given	give	VERB
cet-14439	81	7	by	by	ADP
cet-14439	81	8	eq	eq	ADJ
cet-14439	81	9	(	(	PUNCT
cet-14439	81	10	26	26	NUM
cet-14439	81	11	)	)	PUNCT
cet-14439	81	12	,	,	PUNCT
cet-14439	81	13	where	where	SCONJ
cet-14439	81	14	𝑢𝑗	𝑢𝑗	X
cet-14439	81	15	=	=	SYM
cet-14439	81	16	𝑢(𝑥𝑗	𝑢(𝑥𝑗	NOUN
cet-14439	81	17	,	,	PUNCT
cet-14439	81	18	𝜏	𝜏	NOUN
cet-14439	81	19	)	)	PUNCT
cet-14439	81	20	and	and	CCONJ
cet-14439	81	21	𝑢𝑗,𝜏	𝑢𝑗,𝜏	PUNCT
cet-14439	81	22	=	=	SYM
cet-14439	82	1	𝑑𝑢𝑗	𝑑𝑢𝑗	PRON
cet-14439	82	2	𝑑𝜏⁄	𝑑𝜏⁄	NOUN
cet-14439	82	3	:	:	PUNCT
cet-14439	82	4	𝐼	𝐼	PROPN
cet-14439	82	5	=	=	SYM
cet-14439	82	6	∫	∫	PROPN
cet-14439	82	7	𝑒−𝜆∙𝜏	𝑒−𝜆∙𝜏	NOUN
cet-14439	83	1	∙	∙	PROPN
cet-14439	83	2	∞	∞	PUNCT
cet-14439	83	3	0	0	PUNCT
cet-14439	84	1	[	[	X
cet-14439	84	2	𝜆	𝜆	X
cet-14439	84	3	∙	∙	PROPN
cet-14439	84	4	∑	∑	PUNCT
cet-14439	84	5	𝑊𝑗	𝑊𝑗	PROPN
cet-14439	84	6	∙	∙	PROPN
cet-14439	84	7	𝑓′(𝑢𝑗	𝑓′(𝑢𝑗	NOUN
cet-14439	84	8	)	)	PUNCT
cet-14439	84	9	∙	∙	PROPN
cet-14439	84	10	(	(	PUNCT
cet-14439	84	11	𝑑𝑢𝑗	𝑑𝑢𝑗	X
cet-14439	84	12	𝑑𝜏	𝑑𝜏	NOUN
cet-14439	84	13	)	)	PUNCT
cet-14439	84	14	2	2	NUM
cet-14439	84	15	+	+	NUM
cet-14439	84	16	𝜆2	𝜆2	NOUN
cet-14439	84	17	∙	∙	NOUN
cet-14439	84	18	∑	∑	PUNCT
cet-14439	85	1	𝑊𝑗	𝑊𝑗	PROPN
cet-14439	85	2	∙	∙	PROPN
cet-14439	85	3	(	(	PUNCT
cet-14439	85	4	∑	∑	PUNCT
cet-14439	85	5	𝑙𝑘	𝑙𝑘	INTJ
cet-14439	85	6	′	′	NOUN
cet-14439	85	7	(	(	PUNCT
cet-14439	85	8	𝑥𝑗	𝑥𝑗	PROPN
cet-14439	85	9	)	)	PUNCT
cet-14439	85	10	∙	∙	PROPN
cet-14439	85	11	𝑢(𝑥𝑘	𝑢(𝑥𝑘	PROPN
cet-14439	85	12	,	,	PUNCT
cet-14439	85	13	𝜏	𝜏	NOUN
cet-14439	85	14	)	)	PUNCT
cet-14439	85	15	𝑀	𝑀	PROPN
cet-14439	85	16	𝑘=1	𝑘=1	PROPN
cet-14439	85	17	)	)	PUNCT
cet-14439	85	18	2𝑀	2𝑀	INTJ
cet-14439	85	19	𝑗=1	𝑗=1	PROPN
cet-14439	85	20	𝑀	𝑀	PROPN
cet-14439	85	21	𝑗=1	𝑗=1	PROPN
cet-14439	85	22	]	]	PUNCT
cet-14439	86	1	∙	∙	PROPN
cet-14439	86	2	𝑑𝜏	𝑑𝜏	PROPN
cet-14439	86	3	−𝜆	−𝜆	NOUN
cet-14439	86	4	∙	∙	PROPN
cet-14439	86	5	∑	∑	PUNCT
cet-14439	86	6	𝑊𝑗	𝑊𝑗	PROPN
cet-14439	86	7	∙	∙	PROPN
cet-14439	86	8	(	(	PUNCT
cet-14439	86	9	∑	∑	PUNCT
cet-14439	86	10	𝑙𝑘	𝑙𝑘	INTJ
cet-14439	86	11	′	′	NOUN
cet-14439	86	12	(	(	PUNCT
cet-14439	86	13	𝑥𝑗	𝑥𝑗	PROPN
cet-14439	86	14	)	)	PUNCT
cet-14439	86	15	∙	∙	PROPN
cet-14439	86	16	𝑢(𝑥𝑘	𝑢(𝑥𝑘	PROPN
cet-14439	86	17	,	,	PUNCT
cet-14439	86	18	0	0	NUM
cet-14439	86	19	)	)	PUNCT
cet-14439	86	20	𝑀	𝑀	PROPN
cet-14439	86	21	𝑘=1	𝑘=1	PROPN
cet-14439	86	22	)	)	PUNCT
cet-14439	86	23	2𝑀	2𝑀	INTJ
cet-14439	86	24	𝑗=1	𝑗=1	PROPN
cet-14439	87	1	+	+	CCONJ
cet-14439	87	2	∫	∫	X
cet-14439	87	3	𝛽	𝛽	X
cet-14439	87	4	∙	∙	PROPN
cet-14439	87	5	𝑒−𝜆∙𝜏	𝑒−𝜆∙𝜏	PUNCT
cet-14439	88	1	∙	∙	PROPN
cet-14439	89	1	[	[	X
cet-14439	89	2	𝜆2	𝜆2	X
cet-14439	89	3	∙	∙	PROPN
cet-14439	89	4	(	(	PUNCT
cet-14439	89	5	𝑤	𝑤	ADP
cet-14439	89	6	−	−	PROPN
cet-14439	89	7	𝑢(1	𝑢(1	NOUN
cet-14439	89	8	,	,	PUNCT
cet-14439	89	9	𝜏	𝜏	NOUN
cet-14439	89	10	)	)	PUNCT
cet-14439	89	11	)	)	PUNCT
cet-14439	89	12	2	2	NUM
cet-14439	90	1	+	+	CCONJ
cet-14439	90	2	𝜆	𝜆	X
cet-14439	90	3	∙	∙	PROPN
cet-14439	90	4	1	1	NUM
cet-14439	90	5	𝛼	𝛼	NOUN
cet-14439	90	6	∙	∙	PROPN
cet-14439	90	7	𝑤𝜏	𝑤𝜏	ADP
cet-14439	90	8	2	2	X
cet-14439	90	9	]	]	PUNCT
cet-14439	90	10	∙	∙	PROPN
cet-14439	90	11	𝑑𝜏	𝑑𝜏	PROPN
cet-14439	90	12	∞	∞	PROPN
cet-14439	90	13	0	0	NUM
cet-14439	90	14	(	(	PUNCT
cet-14439	90	15	26	26	NUM
cet-14439	90	16	)	)	PUNCT
cet-14439	90	17	where	where	SCONJ
cet-14439	90	18	the	the	DET
cet-14439	90	19	value	value	NOUN
cet-14439	90	20	of	of	ADP
cet-14439	90	21	𝑢(1	𝑢(1	PROPN
cet-14439	90	22	,	,	PUNCT
cet-14439	90	23	𝜏	𝜏	NOUN
cet-14439	90	24	)	)	PUNCT
cet-14439	90	25	is	be	AUX
cet-14439	90	26	calculated	calculate	VERB
cet-14439	90	27	by	by	ADP
cet-14439	90	28	substituting	substitute	VERB
cet-14439	90	29	𝑥	𝑥	NOUN
cet-14439	90	30	=	=	SYM
cet-14439	90	31	1	1	NUM
cet-14439	90	32	in	in	ADP
cet-14439	90	33	eq	eq	NOUN
cet-14439	90	34	(	(	PUNCT
cet-14439	90	35	23	23	NUM
cet-14439	90	36	)	)	PUNCT
cet-14439	90	37	,	,	PUNCT
cet-14439	90	38	since	since	SCONJ
cet-14439	90	39	all	all	DET
cet-14439	90	40	𝑥𝑗	𝑥𝑗	PROPN
cet-14439	90	41	≠	≠	PROPN
cet-14439	90	42	1	1	NUM
cet-14439	90	43	.	.	PUNCT
cet-14439	90	44	also	also	ADV
cet-14439	90	45	,	,	PUNCT
cet-14439	90	46	using	use	VERB
cet-14439	90	47	the	the	DET
cet-14439	90	48	initial	initial	ADJ
cet-14439	90	49	conditions	condition	NOUN
cet-14439	90	50	,	,	PUNCT
cet-14439	90	51	all	all	DET
cet-14439	90	52	𝑢(𝑥𝑘	𝑢(𝑥𝑘	PROPN
cet-14439	90	53	,	,	PUNCT
cet-14439	90	54	0	0	NUM
cet-14439	90	55	)	)	PUNCT
cet-14439	90	56	=	=	SYM
cet-14439	90	57	0	0	NUM
cet-14439	90	58	,	,	PUNCT
cet-14439	90	59	so	so	SCONJ
cet-14439	90	60	that	that	SCONJ
cet-14439	90	61	the	the	DET
cet-14439	90	62	corresponding	corresponding	ADJ
cet-14439	90	63	term	term	NOUN
cet-14439	90	64	is	be	AUX
cet-14439	90	65	zero	zero	NUM
cet-14439	90	66	.	.	PUNCT
cet-14439	91	1	the	the	DET
cet-14439	91	2	stationary	stationary	ADJ
cet-14439	91	3	condition	condition	NOUN
cet-14439	91	4	for	for	ADP
cet-14439	91	5	𝐼	𝐼	PROPN
cet-14439	91	6	with	with	ADP
cet-14439	91	7	respect	respect	NOUN
cet-14439	91	8	to	to	ADP
cet-14439	91	9	the	the	DET
cet-14439	91	10	profiles	profile	NOUN
cet-14439	91	11	𝑢(𝑥𝑗	𝑢(𝑥𝑗	NOUN
cet-14439	91	12	,	,	PUNCT
cet-14439	91	13	𝜏	𝜏	NOUN
cet-14439	91	14	)	)	PUNCT
cet-14439	91	15	,	,	PUNCT
cet-14439	91	16	for	for	ADP
cet-14439	91	17	𝑗	𝑗	NOUN
cet-14439	91	18	=	=	SYM
cet-14439	91	19	1	1	NUM
cet-14439	91	20	,	,	PUNCT
cet-14439	91	21	⋯	⋯	PROPN
cet-14439	91	22	,	,	PUNCT
cet-14439	91	23	𝑀	𝑀	PROPN
cet-14439	91	24	,	,	PUNCT
cet-14439	91	25	is	be	AUX
cet-14439	91	26	given	give	VERB
cet-14439	91	27	by	by	ADP
cet-14439	91	28	:	:	PUNCT
cet-14439	91	29	−	−	PROPN
cet-14439	91	30	𝜕𝐹	𝜕𝐹	NOUN
cet-14439	91	31	𝜕𝑢𝑗	𝜕𝑢𝑗	PUNCT
cet-14439	92	1	+	+	CCONJ
cet-14439	92	2	𝑑	𝑑	PROPN
cet-14439	92	3	𝑑𝜏	𝑑𝜏	X
cet-14439	92	4	(	(	PUNCT
cet-14439	92	5	𝜕𝐹	𝜕𝐹	NOUN
cet-14439	92	6	𝜕𝑢𝑗,𝜏	𝜕𝑢𝑗,𝜏	ADJ
cet-14439	92	7	)	)	PUNCT
cet-14439	93	1	=	=	SYM
cet-14439	93	2	0	0	NUM
cet-14439	93	3	(	(	PUNCT
cet-14439	93	4	27	27	NUM
cet-14439	93	5	)	)	PUNCT
cet-14439	93	6	applying	apply	VERB
cet-14439	93	7	this	this	DET
cet-14439	93	8	stationary	stationary	ADJ
cet-14439	93	9	condition	condition	NOUN
cet-14439	93	10	for	for	ADP
cet-14439	93	11	𝐼	𝐼	PROPN
cet-14439	93	12	,	,	PUNCT
cet-14439	93	13	for	for	ADP
cet-14439	93	14	all	all	DET
cet-14439	93	15	𝑗	𝑗	ADJ
cet-14439	93	16	,	,	PUNCT
cet-14439	93	17	and	and	CCONJ
cet-14439	93	18	then	then	ADV
cet-14439	93	19	making	make	VERB
cet-14439	93	20	the	the	DET
cet-14439	93	21	limit	limit	NOUN
cet-14439	93	22	𝜆	𝜆	ADP
cet-14439	93	23	→	→	SYM
cet-14439	93	24	∞	∞	PROPN
cet-14439	93	25	,	,	PUNCT
cet-14439	93	26	the	the	DET
cet-14439	93	27	following	follow	VERB
cet-14439	93	28	equation	equation	NOUN
cet-14439	93	29	is	be	AUX
cet-14439	93	30	obtained	obtain	VERB
cet-14439	93	31	,	,	PUNCT
cet-14439	93	32	after	after	ADP
cet-14439	93	33	rearrangement	rearrangement	NOUN
cet-14439	93	34	:	:	PUNCT
cet-14439	93	35	𝑊𝑗	𝑊𝑗	PROPN
cet-14439	93	36	∙	∙	PROPN
cet-14439	93	37	𝑓′(𝑢(𝑥𝑗	𝑓′(𝑢(𝑥𝑗	PROPN
cet-14439	93	38	,	,	PUNCT
cet-14439	93	39	𝜏	𝜏	NOUN
cet-14439	93	40	)	)	PUNCT
cet-14439	93	41	)	)	PUNCT
cet-14439	94	1	∙	∙	PROPN
cet-14439	94	2	𝑑𝑢	𝑑𝑢	X
cet-14439	94	3	𝑑𝜏	𝑑𝜏	PROPN
cet-14439	94	4	(	(	PUNCT
cet-14439	94	5	𝑥𝑗	𝑥𝑗	PROPN
cet-14439	94	6	,	,	PUNCT
cet-14439	94	7	𝜏	𝜏	PROPN
cet-14439	94	8	)	)	PUNCT
cet-14439	94	9	=	=	SYM
cet-14439	94	10	−	−	PROPN
cet-14439	94	11	∑	∑	PUNCT
cet-14439	94	12	𝐴𝑗𝑘	𝐴𝑗𝑘	PROPN
cet-14439	94	13	∙	∙	PROPN
cet-14439	94	14	𝑢(𝑥𝑘	𝑢(𝑥𝑘	PROPN
cet-14439	94	15	,	,	PUNCT
cet-14439	94	16	𝜏	𝜏	NOUN
cet-14439	94	17	)	)	PUNCT
cet-14439	94	18	𝑀	𝑀	NOUN
cet-14439	94	19	𝑘=1	𝑘=1	NOUN
cet-14439	95	1	+	+	PUNCT
cet-14439	95	2	𝛽	𝛽	NOUN
cet-14439	95	3	∙	∙	PROPN
cet-14439	95	4	(	(	PUNCT
cet-14439	95	5	𝑤	𝑤	ADP
cet-14439	95	6	−	−	PROPN
cet-14439	95	7	𝑢(1	𝑢(1	NOUN
cet-14439	95	8	,	,	PUNCT
cet-14439	95	9	𝜏	𝜏	NOUN
cet-14439	95	10	)	)	PUNCT
cet-14439	95	11	)	)	PUNCT
cet-14439	96	1	∙	∙	PROPN
cet-14439	96	2	𝑙𝑗(1	𝑙𝑗(1	PROPN
cet-14439	96	3	)	)	PUNCT
cet-14439	96	4	(	(	PUNCT
cet-14439	96	5	28	28	NUM
cet-14439	96	6	)	)	PUNCT
cet-14439	96	7	this	this	DET
cet-14439	96	8	same	same	ADJ
cet-14439	96	9	equation	equation	NOUN
cet-14439	96	10	was	be	AUX
cet-14439	96	11	obtained	obtain	VERB
cet-14439	96	12	by	by	ADP
cet-14439	96	13	guirardello	guirardello	PROPN
cet-14439	96	14	(	(	PUNCT
cet-14439	96	15	2013	2013	NUM
cet-14439	96	16	)	)	PUNCT
cet-14439	96	17	,	,	PUNCT
cet-14439	96	18	using	use	VERB
cet-14439	96	19	a	a	DET
cet-14439	96	20	different	different	ADJ
cet-14439	96	21	approach	approach	NOUN
cet-14439	96	22	,	,	PUNCT
cet-14439	96	23	where	where	SCONJ
cet-14439	96	24	𝐴𝑗𝑘	𝐴𝑗𝑘	PROPN
cet-14439	96	25	is	be	AUX
cet-14439	96	26	given	give	VERB
cet-14439	96	27	by	by	ADP
cet-14439	96	28	:	:	PUNCT
cet-14439	96	29	𝐴𝑗𝑘	𝐴𝑗𝑘	PROPN
cet-14439	96	30	=	=	PUNCT
cet-14439	96	31	∑	∑	PUNCT
cet-14439	97	1	𝑊𝑖	𝑊𝑖	PROPN
cet-14439	97	2	∙	∙	PROPN
cet-14439	97	3	𝑀	𝑀	PROPN
cet-14439	97	4	𝑖=1	𝑖=1	PUNCT
cet-14439	97	5	𝑙𝑗	𝑙𝑗	PROPN
cet-14439	97	6	′(𝑥𝑖	′(𝑥𝑖	ADJ
cet-14439	97	7	)	)	PUNCT
cet-14439	98	1	∙	∙	NOUN
cet-14439	98	2	𝑙𝑘	𝑙𝑘	INTJ
cet-14439	99	1	′	′	NUM
cet-14439	99	2	(	(	PUNCT
cet-14439	99	3	𝑥𝑖	𝑥𝑖	NOUN
cet-14439	99	4	)	)	PUNCT
cet-14439	99	5	(	(	PUNCT
cet-14439	99	6	29	29	NUM
cet-14439	99	7	)	)	SYM
cet-14439	99	8	94	94	NUM
cet-14439	99	9	repeating	repeat	VERB
cet-14439	99	10	the	the	DET
cet-14439	99	11	same	same	ADJ
cet-14439	99	12	procedure	procedure	NOUN
cet-14439	99	13	for	for	ADP
cet-14439	99	14	𝑤	𝑤	ADP
cet-14439	99	15	results	result	NOUN
cet-14439	99	16	in	in	ADP
cet-14439	99	17	eq	eq	NOUN
cet-14439	99	18	(	(	PUNCT
cet-14439	99	19	3	3	NUM
cet-14439	99	20	)	)	PUNCT
cet-14439	99	21	.	.	PUNCT
cet-14439	100	1	finally	finally	ADV
cet-14439	100	2	,	,	PUNCT
cet-14439	100	3	the	the	DET
cet-14439	100	4	set	set	NOUN
cet-14439	100	5	of	of	ADP
cet-14439	100	6	ordinary	ordinary	ADJ
cet-14439	100	7	differential	differential	ADJ
cet-14439	100	8	equations	equation	NOUN
cet-14439	100	9	(	(	PUNCT
cet-14439	100	10	ode	ode	PROPN
cet-14439	100	11	)	)	PUNCT
cet-14439	100	12	,	,	PUNCT
cet-14439	100	13	given	give	VERB
cet-14439	100	14	by	by	ADP
cet-14439	100	15	eq	eq	ADJ
cet-14439	100	16	(	(	PUNCT
cet-14439	100	17	3	3	NUM
cet-14439	100	18	)	)	PUNCT
cet-14439	100	19	and	and	CCONJ
cet-14439	100	20	eq	eq	NOUN
cet-14439	100	21	(	(	PUNCT
cet-14439	100	22	28	28	NUM
cet-14439	100	23	)	)	PUNCT
cet-14439	100	24	,	,	PUNCT
cet-14439	100	25	is	be	AUX
cet-14439	100	26	solved	solve	VERB
cet-14439	100	27	,	,	PUNCT
cet-14439	100	28	using	use	VERB
cet-14439	100	29	the	the	DET
cet-14439	100	30	initial	initial	ADJ
cet-14439	100	31	conditions	condition	NOUN
cet-14439	100	32	𝑢(𝑥𝑗	𝑢(𝑥𝑗	NOUN
cet-14439	100	33	,	,	PUNCT
cet-14439	100	34	0	0	NUM
cet-14439	100	35	)	)	PUNCT
cet-14439	100	36	=	=	SYM
cet-14439	100	37	0	0	NUM
cet-14439	100	38	and	and	CCONJ
cet-14439	100	39	𝑤(0	𝑤(0	NOUN
cet-14439	100	40	)	)	PUNCT
cet-14439	100	41	=	=	SYM
cet-14439	101	1	1	1	NUM
cet-14439	101	2	.	.	NOUN
cet-14439	101	3	4	4	NUM
cet-14439	101	4	.	.	X
cet-14439	101	5	experimental	experimental	ADJ
cet-14439	101	6	data	datum	NOUN
cet-14439	101	7	the	the	DET
cet-14439	101	8	experimental	experimental	ADJ
cet-14439	101	9	values	value	NOUN
cet-14439	101	10	used	use	VERB
cet-14439	101	11	in	in	ADP
cet-14439	101	12	this	this	DET
cet-14439	101	13	work	work	NOUN
cet-14439	101	14	were	be	AUX
cet-14439	101	15	taken	take	VERB
cet-14439	101	16	from	from	ADP
cet-14439	101	17	trindade	trindade	PROPN
cet-14439	101	18	(	(	PUNCT
cet-14439	101	19	2015a	2015a	NUM
cet-14439	101	20	)	)	PUNCT
cet-14439	101	21	,	,	PUNCT
cet-14439	101	22	who	who	PRON
cet-14439	101	23	conducted	conduct	VERB
cet-14439	101	24	batch	batch	NOUN
cet-14439	101	25	experiments	experiment	NOUN
cet-14439	101	26	with	with	ADP
cet-14439	101	27	several	several	ADJ
cet-14439	101	28	adsorbents	adsorbent	NOUN
cet-14439	101	29	,	,	PUNCT
cet-14439	101	30	one	one	NUM
cet-14439	101	31	of	of	ADP
cet-14439	101	32	them	they	PRON
cet-14439	101	33	the	the	DET
cet-14439	101	34	synthetic	synthetic	ADJ
cet-14439	101	35	resin	resin	NOUN
cet-14439	101	36	sepabeadstm	sepabeadstm	PROPN
cet-14439	101	37	sp850	sp850	PROPN
cet-14439	101	38	.	.	PUNCT
cet-14439	102	1	this	this	PRON
cet-14439	102	2	is	be	AUX
cet-14439	102	3	a	a	DET
cet-14439	102	4	hydrophobic	hydrophobic	NOUN
cet-14439	102	5	resin	resin	NOUN
cet-14439	102	6	which	which	PRON
cet-14439	102	7	showed	show	VERB
cet-14439	102	8	a	a	DET
cet-14439	102	9	high	high	ADJ
cet-14439	102	10	selectivity	selectivity	NOUN
cet-14439	102	11	for	for	ADP
cet-14439	102	12	-valerolactone	-valerolactone	NUM
cet-14439	102	13	,	,	PUNCT
cet-14439	102	14	while	while	SCONJ
cet-14439	102	15	adsorbing	adsorb	VERB
cet-14439	102	16	very	very	ADV
cet-14439	102	17	little	little	ADJ
cet-14439	102	18	glucose	glucose	NOUN
cet-14439	102	19	.	.	PUNCT
cet-14439	103	1	it	it	PRON
cet-14439	103	2	is	be	AUX
cet-14439	103	3	also	also	ADV
cet-14439	103	4	very	very	ADV
cet-14439	103	5	porous	porous	ADJ
cet-14439	103	6	,	,	PUNCT
cet-14439	103	7	so	so	SCONJ
cet-14439	103	8	that	that	SCONJ
cet-14439	103	9	the	the	DET
cet-14439	103	10	aqueous	aqueous	ADJ
cet-14439	103	11	solution	solution	NOUN
cet-14439	103	12	can	can	AUX
cet-14439	103	13	enter	enter	VERB
cet-14439	103	14	the	the	DET
cet-14439	103	15	macro	macro	NOUN
cet-14439	103	16	-	-	NOUN
cet-14439	103	17	porous	porous	ADJ
cet-14439	103	18	,	,	PUNCT
cet-14439	103	19	but	but	CCONJ
cet-14439	103	20	without	without	ADP
cet-14439	103	21	the	the	DET
cet-14439	103	22	resin	resin	NOUN
cet-14439	103	23	adsorbing	adsorb	VERB
cet-14439	103	24	the	the	DET
cet-14439	103	25	water	water	NOUN
cet-14439	103	26	.	.	PUNCT
cet-14439	104	1	therefore	therefore	ADV
cet-14439	104	2	,	,	PUNCT
cet-14439	104	3	this	this	DET
cet-14439	104	4	resin	resin	NOUN
cet-14439	104	5	was	be	AUX
cet-14439	104	6	found	find	VERB
cet-14439	104	7	suitable	suitable	ADJ
cet-14439	104	8	for	for	ADP
cet-14439	104	9	the	the	DET
cet-14439	104	10	separation	separation	NOUN
cet-14439	104	11	of	of	ADP
cet-14439	104	12	-valerolactone	-valerolactone	NUM
cet-14439	104	13	from	from	ADP
cet-14439	104	14	the	the	DET
cet-14439	104	15	glucose	glucose	NOUN
cet-14439	104	16	solution	solution	NOUN
cet-14439	104	17	.	.	PUNCT
cet-14439	105	1	the	the	DET
cet-14439	105	2	results	result	NOUN
cet-14439	105	3	are	be	AUX
cet-14439	105	4	presented	present	VERB
cet-14439	105	5	in	in	ADP
cet-14439	105	6	tables	table	NOUN
cet-14439	105	7	1	1	NUM
cet-14439	105	8	and	and	CCONJ
cet-14439	105	9	2	2	NUM
cet-14439	105	10	.	.	X
cet-14439	106	1	these	these	DET
cet-14439	106	2	batch	batch	NOUN
cet-14439	106	3	tests	test	NOUN
cet-14439	106	4	were	be	AUX
cet-14439	106	5	conducted	conduct	VERB
cet-14439	106	6	at	at	ADP
cet-14439	106	7	25	25	NUM
cet-14439	106	8	ºc	ºc	NOUN
cet-14439	106	9	,	,	PUNCT
cet-14439	106	10	with	with	ADP
cet-14439	106	11	an	an	DET
cet-14439	106	12	acid	acid	ADJ
cet-14439	106	13	ph	ph	NOUN
cet-14439	106	14	.	.	PROPN
cet-14439	106	15	in	in	ADP
cet-14439	106	16	the	the	DET
cet-14439	106	17	tests	test	NOUN
cet-14439	106	18	,	,	PUNCT
cet-14439	106	19	the	the	DET
cet-14439	106	20	diameter	diameter	NOUN
cet-14439	106	21	of	of	ADP
cet-14439	106	22	the	the	DET
cet-14439	106	23	particles	particle	NOUN
cet-14439	106	24	was	be	AUX
cet-14439	106	25	500	500	NUM
cet-14439	106	26	m	m	PROPN
cet-14439	106	27	,	,	PUNCT
cet-14439	106	28	and	and	CCONJ
cet-14439	106	29	they	they	PRON
cet-14439	106	30	were	be	AUX
cet-14439	106	31	carried	carry	VERB
cet-14439	106	32	out	out	ADP
cet-14439	106	33	by	by	ADP
cet-14439	106	34	mixing	mix	VERB
cet-14439	106	35	the	the	DET
cet-14439	106	36	dry	dry	ADJ
cet-14439	106	37	resin	resin	NOUN
cet-14439	106	38	with	with	ADP
cet-14439	106	39	the	the	DET
cet-14439	106	40	solution	solution	NOUN
cet-14439	106	41	in	in	ADP
cet-14439	106	42	the	the	DET
cet-14439	106	43	proportion	proportion	NOUN
cet-14439	106	44	of	of	ADP
cet-14439	106	45	𝑚res	𝑚re	NOUN
cet-14439	106	46	𝑉⁄	𝑉⁄	PROPN
cet-14439	106	47	=	=	SYM
cet-14439	106	48	0.01	0.01	NUM
cet-14439	106	49	g	g	NOUN
cet-14439	106	50	/	/	SYM
cet-14439	106	51	ml	ml	NOUN
cet-14439	106	52	.	.	NOUN
cet-14439	106	53	table	table	NOUN
cet-14439	106	54	1	1	NUM
cet-14439	106	55	presents	present	VERB
cet-14439	106	56	the	the	DET
cet-14439	106	57	results	result	NOUN
cet-14439	106	58	for	for	ADP
cet-14439	106	59	selectivity	selectivity	NOUN
cet-14439	106	60	in	in	ADP
cet-14439	106	61	the	the	DET
cet-14439	106	62	adsorption	adsorption	NOUN
cet-14439	106	63	,	,	PUNCT
cet-14439	106	64	for	for	ADP
cet-14439	106	65	initial	initial	ADJ
cet-14439	106	66	concentrations	concentration	NOUN
cet-14439	106	67	of	of	ADP
cet-14439	106	68	27.2015	27.2015	NUM
cet-14439	106	69	g	g	NOUN
cet-14439	106	70	l⁄	l⁄	VERB
cet-14439	106	71	for	for	ADP
cet-14439	106	72	-valerolactone	-valerolactone	NUM
cet-14439	106	73	(	(	PUNCT
cet-14439	106	74	gvl	gvl	PROPN
cet-14439	106	75	)	)	PUNCT
cet-14439	106	76	and	and	CCONJ
cet-14439	106	77	66.4235	66.4235	NUM
cet-14439	106	78	g	g	NOUN
cet-14439	106	79	l⁄	l⁄	NOUN
cet-14439	106	80	for	for	ADP
cet-14439	106	81	glucose	glucose	NOUN
cet-14439	106	82	(	(	PUNCT
cet-14439	106	83	gl	gl	NOUN
cet-14439	106	84	)	)	PUNCT
cet-14439	106	85	.	.	PUNCT
cet-14439	107	1	it	it	PRON
cet-14439	107	2	can	can	AUX
cet-14439	107	3	be	be	AUX
cet-14439	107	4	seen	see	VERB
cet-14439	107	5	from	from	ADP
cet-14439	107	6	table	table	NOUN
cet-14439	107	7	1	1	NUM
cet-14439	107	8	that	that	DET
cet-14439	107	9	adsorption	adsorption	NOUN
cet-14439	107	10	of	of	ADP
cet-14439	107	11	glucose	glucose	NOUN
cet-14439	107	12	and	and	CCONJ
cet-14439	107	13	-valerolactone	-valerolactone	NUM
cet-14439	107	14	are	be	AUX
cet-14439	107	15	not	not	PART
cet-14439	107	16	competitive	competitive	ADJ
cet-14439	107	17	for	for	ADP
cet-14439	107	18	this	this	DET
cet-14439	107	19	resin	resin	NOUN
cet-14439	107	20	.	.	PUNCT
cet-14439	108	1	table	table	NOUN
cet-14439	108	2	2	2	NUM
cet-14439	108	3	presents	present	VERB
cet-14439	108	4	the	the	DET
cet-14439	108	5	concentration	concentration	NOUN
cet-14439	108	6	in	in	ADP
cet-14439	108	7	the	the	DET
cet-14439	108	8	solution	solution	NOUN
cet-14439	108	9	.	.	PUNCT
cet-14439	109	1	from	from	ADP
cet-14439	109	2	other	other	ADJ
cet-14439	109	3	tests	test	NOUN
cet-14439	109	4	,	,	PUNCT
cet-14439	109	5	it	it	PRON
cet-14439	109	6	was	be	AUX
cet-14439	109	7	found	find	VERB
cet-14439	109	8	that	that	SCONJ
cet-14439	109	9	for	for	ADP
cet-14439	109	10	-valerolactone	-valerolactone	NUM
cet-14439	109	11	the	the	DET
cet-14439	109	12	fitted	fit	VERB
cet-14439	109	13	parameters	parameter	NOUN
cet-14439	109	14	for	for	ADP
cet-14439	109	15	a	a	DET
cet-14439	109	16	langmuir	langmuir	PROPN
cet-14439	109	17	type	type	NOUN
cet-14439	109	18	isotherm	isotherm	NOUN
cet-14439	109	19	were	be	AUX
cet-14439	109	20	𝑞𝑚	𝑞𝑚	NOUN
cet-14439	109	21	=	=	SYM
cet-14439	109	22	2.6366	2.6366	NUM
cet-14439	109	23	ggvl	ggvl	NOUN
cet-14439	109	24	gres⁄	gres⁄	INTJ
cet-14439	109	25	and	and	CCONJ
cet-14439	109	26	𝑏	𝑏	NOUN
cet-14439	109	27	=	=	SYM
cet-14439	109	28	0.0044	0.0044	NUM
cet-14439	109	29	l	l	NOUN
cet-14439	109	30	/	/	SYM
cet-14439	109	31	g	g	PROPN
cet-14439	109	32	(	(	PUNCT
cet-14439	109	33	trindade	trindade	PROPN
cet-14439	109	34	,	,	PUNCT
cet-14439	109	35	2015a	2015a	NUM
cet-14439	109	36	)	)	PUNCT
cet-14439	109	37	.	.	PUNCT
cet-14439	110	1	however	however	ADV
cet-14439	110	2	,	,	PUNCT
cet-14439	110	3	in	in	ADP
cet-14439	110	4	the	the	DET
cet-14439	110	5	model	model	NOUN
cet-14439	110	6	𝑞𝑚	𝑞𝑚	NOUN
cet-14439	110	7	has	have	VERB
cet-14439	110	8	units	unit	NOUN
cet-14439	110	9	of	of	ADP
cet-14439	110	10	[	[	X
cet-14439	110	11	mass	mass	ADJ
cet-14439	110	12	solute	solute	NOUN
cet-14439	110	13	volume	volume	NOUN
cet-14439	110	14	resin⁄	resin⁄	PROPN
cet-14439	110	15	]	]	X
cet-14439	110	16	,	,	PUNCT
cet-14439	110	17	so	so	CCONJ
cet-14439	110	18	it	it	PRON
cet-14439	110	19	is	be	AUX
cet-14439	110	20	necessary	necessary	ADJ
cet-14439	110	21	to	to	PART
cet-14439	110	22	convert	convert	VERB
cet-14439	110	23	it	it	PRON
cet-14439	110	24	using	use	VERB
cet-14439	110	25	the	the	DET
cet-14439	110	26	density	density	NOUN
cet-14439	110	27	of	of	ADP
cet-14439	110	28	the	the	DET
cet-14439	110	29	resin	resin	NOUN
cet-14439	110	30	.	.	PUNCT
cet-14439	111	1	table	table	NOUN
cet-14439	111	2	1	1	NUM
cet-14439	111	3	:	:	PUNCT
cet-14439	111	4	adsorbed	adsorb	VERB
cet-14439	111	5	quantities	quantity	NOUN
cet-14439	111	6	for	for	ADP
cet-14439	111	7	glucose	glucose	NOUN
cet-14439	111	8	and	and	CCONJ
cet-14439	111	9	-valerolactone	-valerolactone	NUM
cet-14439	111	10	by	by	ADP
cet-14439	111	11	sp850	sp850	PROPN
cet-14439	111	12	.	.	PUNCT
cet-14439	111	13	time	time	NOUN
cet-14439	111	14	ggl	ggl	PROPN
cet-14439	111	15	gres⁄	gres⁄	PROPN
cet-14439	111	16	ggvl	ggvl	PROPN
cet-14439	111	17	gres⁄	gres⁄	PROPN
cet-14439	111	18	15	15	NUM
cet-14439	111	19	min	min	NOUN
cet-14439	111	20	−	−	PROPN
cet-14439	111	21	0.2056	0.2056	NUM
cet-14439	111	22	48	48	NUM
cet-14439	111	23	h	h	NOUN
cet-14439	111	24	0.0060	0.0060	NUM
cet-14439	111	25	0.2528	0.2528	NUM
cet-14439	111	26	'	'	PUNCT
cet-14439	111	27	−	−	NOUN
cet-14439	111	28	'	'	PUNCT
cet-14439	111	29	means	mean	VERB
cet-14439	111	30	too	too	ADV
cet-14439	111	31	low	low	ADJ
cet-14439	111	32	to	to	PART
cet-14439	111	33	measure	measure	VERB
cet-14439	111	34	by	by	ADP
cet-14439	111	35	hplc	hplc	NOUN
cet-14439	111	36	table	table	NOUN
cet-14439	111	37	2	2	NUM
cet-14439	111	38	:	:	PUNCT
cet-14439	111	39	batch	batch	VERB
cet-14439	111	40	trials	trial	NOUN
cet-14439	111	41	for	for	ADP
cet-14439	111	42	-valerolactone	-valerolactone	NUM
cet-14439	111	43	adsorption	adsorption	NOUN
cet-14439	111	44	by	by	ADP
cet-14439	111	45	sp850	sp850	PROPN
cet-14439	111	46	.	.	PUNCT
cet-14439	111	47	time	time	NOUN
cet-14439	112	1	𝐶	𝐶	PROPN
cet-14439	112	2	𝐶0⁄	𝐶0⁄	PROPN
cet-14439	112	3	0	0	NUM
cet-14439	112	4	1.0000	1.0000	NUM
cet-14439	112	5	15	15	NUM
cet-14439	112	6	min	min	NOUN
cet-14439	112	7	0.9168	0.9168	NUM
cet-14439	112	8	48	48	NUM
cet-14439	112	9	h	h	NOUN
cet-14439	112	10	0.9069	0.9069	NUM
cet-14439	112	11	5	5	NUM
cet-14439	112	12	.	.	PUNCT
cet-14439	112	13	results	result	NOUN
cet-14439	112	14	and	and	CCONJ
cet-14439	112	15	discussion	discussion	NOUN
cet-14439	112	16	5.1	5.1	NUM
cet-14439	112	17	case	case	NOUN
cet-14439	112	18	study	study	VERB
cet-14439	112	19	the	the	DET
cet-14439	112	20	model	model	NOUN
cet-14439	112	21	was	be	AUX
cet-14439	112	22	solved	solve	VERB
cet-14439	112	23	for	for	ADP
cet-14439	112	24	a	a	DET
cet-14439	112	25	case	case	NOUN
cet-14439	112	26	study	study	NOUN
cet-14439	112	27	considering	consider	VERB
cet-14439	112	28	porous	porous	ADJ
cet-14439	112	29	particles	particle	NOUN
cet-14439	112	30	of	of	ADP
cet-14439	112	31	sp850	sp850	PROPN
cet-14439	112	32	with	with	ADP
cet-14439	112	33	the	the	DET
cet-14439	112	34	following	follow	VERB
cet-14439	112	35	adsorption	adsorption	NOUN
cet-14439	112	36	parameters	parameter	NOUN
cet-14439	112	37	:	:	PUNCT
cet-14439	112	38	𝑞𝑚	𝑞𝑚	VERB
cet-14439	112	39	=	=	VERB
cet-14439	112	40	2663.0	2663.0	NUM
cet-14439	112	41	g	g	NOUN
cet-14439	112	42	/	/	SYM
cet-14439	112	43	lres	lre	NOUN
cet-14439	112	44	and	and	CCONJ
cet-14439	112	45	𝑏	𝑏	NOUN
cet-14439	112	46	=	=	SYM
cet-14439	112	47	0.0044	0.0044	NUM
cet-14439	112	48	l	l	NOUN
cet-14439	112	49	/	/	SYM
cet-14439	112	50	g.	g.	NOUN
cet-14439	112	51	the	the	DET
cet-14439	112	52	conditions	condition	NOUN
cet-14439	112	53	for	for	ADP
cet-14439	112	54	the	the	DET
cet-14439	112	55	solution	solution	NOUN
cet-14439	112	56	and	and	CCONJ
cet-14439	112	57	resin	resin	NOUN
cet-14439	112	58	in	in	ADP
cet-14439	112	59	the	the	DET
cet-14439	112	60	stirred	stir	VERB
cet-14439	112	61	tank	tank	NOUN
cet-14439	112	62	were	be	AUX
cet-14439	112	63	:	:	PUNCT
cet-14439	112	64	𝑉	𝑉	PROPN
cet-14439	112	65	=	=	PROPN
cet-14439	112	66	10	10	NUM
cet-14439	112	67	ml	ml	NOUN
cet-14439	112	68	,	,	PUNCT
cet-14439	112	69	𝑣	𝑣	X
cet-14439	112	70	=	=	PUNCT
cet-14439	112	71	0.209	0.209	NUM
cet-14439	112	72	ml	ml	NOUN
cet-14439	112	73	,	,	PUNCT
cet-14439	112	74	and	and	CCONJ
cet-14439	112	75	𝐶0	𝐶0	NOUN
cet-14439	112	76	=	=	SYM
cet-14439	112	77	27.2015	27.2015	NUM
cet-14439	112	78	g	g	NOUN
cet-14439	112	79	/	/	SYM
cet-14439	112	80	l.	l.	NOUN
cet-14439	112	81	the	the	DET
cet-14439	112	82	porosity	porosity	NOUN
cet-14439	112	83	of	of	ADP
cet-14439	112	84	the	the	DET
cet-14439	112	85	particles	particle	NOUN
cet-14439	112	86	was	be	AUX
cet-14439	112	87	𝜀	𝜀	NOUN
cet-14439	112	88	=	=	SYM
cet-14439	112	89	0.526	0.526	NUM
cet-14439	112	90	.	.	PUNCT
cet-14439	113	1	also	also	ADV
cet-14439	113	2	,	,	PUNCT
cet-14439	113	3	the	the	DET
cet-14439	113	4	spheres	sphere	NOUN
cet-14439	113	5	radius	radius	NOUN
cet-14439	113	6	was	be	AUX
cet-14439	113	7	𝑅	𝑅	PROPN
cet-14439	113	8	=	=	PROPN
cet-14439	113	9	250	250	NUM
cet-14439	113	10	μm	μm	NOUN
cet-14439	113	11	(	(	PUNCT
cet-14439	113	12	𝑑𝑝	𝑑𝑝	NOUN
cet-14439	113	13	=	=	SYM
cet-14439	113	14	500	500	NUM
cet-14439	113	15	μm	μm	NUM
cet-14439	113	16	)	)	PUNCT
cet-14439	113	17	.	.	PUNCT
cet-14439	114	1	these	these	DET
cet-14439	114	2	values	value	NOUN
cet-14439	114	3	were	be	AUX
cet-14439	114	4	used	use	VERB
cet-14439	114	5	to	to	PART
cet-14439	114	6	reproduce	reproduce	VERB
cet-14439	114	7	the	the	DET
cet-14439	114	8	conditions	condition	NOUN
cet-14439	114	9	of	of	ADP
cet-14439	114	10	the	the	DET
cet-14439	114	11	experimental	experimental	ADJ
cet-14439	114	12	tests	test	NOUN
cet-14439	114	13	(	(	PUNCT
cet-14439	114	14	𝑚res	𝑚re	NOUN
cet-14439	114	15	=	=	PRON
cet-14439	114	16	𝜌res	𝜌re	VERB
cet-14439	114	17	∙	∙	PROPN
cet-14439	114	18	𝑣	𝑣	ADP
cet-14439	114	19	∙	∙	PROPN
cet-14439	114	20	(	(	PUNCT
cet-14439	114	21	1	1	NUM
cet-14439	114	22	−	−	NUM
cet-14439	114	23	𝜀	𝜀	NOUN
cet-14439	114	24	)	)	PUNCT
cet-14439	114	25	=	=	SYM
cet-14439	114	26	0.1	0.1	NUM
cet-14439	114	27	g	g	NOUN
cet-14439	114	28	and	and	CCONJ
cet-14439	114	29	𝑞𝑚[by	𝑞𝑚[by	NOUN
cet-14439	114	30	volume	volume	NOUN
cet-14439	114	31	resin	resin	NOUN
cet-14439	114	32	]	]	PUNCT
cet-14439	114	33	=	=	SYM
cet-14439	114	34	𝜌res	𝜌re	VERB
cet-14439	114	35	∙	∙	PROPN
cet-14439	114	36	𝑞𝑚[by	𝑞𝑚[by	PROPN
cet-14439	114	37	mass	mass	NOUN
cet-14439	114	38	resin	resin	NOUN
cet-14439	114	39	]	]	PUNCT
cet-14439	114	40	)	)	PUNCT
cet-14439	114	41	.	.	PUNCT
cet-14439	115	1	the	the	DET
cet-14439	115	2	value	value	NOUN
cet-14439	115	3	of	of	ADP
cet-14439	115	4	𝑘𝑓	𝑘𝑓	PROPN
cet-14439	115	5	=	=	SYM
cet-14439	115	6	1.7	1.7	NUM
cet-14439	115	7	∙	∙	PROPN
cet-14439	115	8	10−5	10−5	NUM
cet-14439	115	9	m	m	NOUN
cet-14439	115	10	s⁄	s⁄	PROPN
cet-14439	115	11	was	be	AUX
cet-14439	115	12	estimated	estimate	VERB
cet-14439	115	13	from	from	ADP
cet-14439	115	14	the	the	DET
cet-14439	115	15	correlation	correlation	NOUN
cet-14439	115	16	of	of	ADP
cet-14439	115	17	geankoplis	geankopli	NOUN
cet-14439	115	18	for	for	ADP
cet-14439	115	19	particles	particle	NOUN
cet-14439	115	20	in	in	ADP
cet-14439	115	21	stirred	stir	VERB
cet-14439	115	22	tanks	tank	NOUN
cet-14439	115	23	(	(	PUNCT
cet-14439	115	24	geankoplis	geankoplis	PROPN
cet-14439	115	25	,	,	PUNCT
cet-14439	115	26	1983	1983	NUM
cet-14439	115	27	,	,	PUNCT
cet-14439	115	28	apud	apud	PROPN
cet-14439	115	29	skidmore	skidmore	PROPN
cet-14439	115	30	et	et	PROPN
cet-14439	115	31	al	al	PROPN
cet-14439	115	32	,	,	PUNCT
cet-14439	115	33	1990	1990	NUM
cet-14439	115	34	)	)	PUNCT
cet-14439	115	35	,	,	PUNCT
cet-14439	115	36	using	use	VERB
cet-14439	115	37	the	the	DET
cet-14439	115	38	molecular	molecular	ADJ
cet-14439	115	39	diffusion	diffusion	NOUN
cet-14439	115	40	coefficient	coefficient	NOUN
cet-14439	115	41	of	of	ADP
cet-14439	115	42	gvl	gvl	PROPN
cet-14439	115	43	in	in	ADP
cet-14439	115	44	water	water	NOUN
cet-14439	115	45	which	which	PRON
cet-14439	115	46	was	be	AUX
cet-14439	115	47	estimated	estimate	VERB
cet-14439	115	48	as	as	ADP
cet-14439	115	49	𝐷𝐴𝐵	𝐷𝐴𝐵	NOUN
cet-14439	115	50	=	=	SYM
cet-14439	115	51	1.03	1.03	NUM
cet-14439	115	52	∙	∙	PROPN
cet-14439	115	53	10−9	10−9	NUM
cet-14439	115	54	m2	m2	PROPN
cet-14439	115	55	s⁄	s⁄	PROPN
cet-14439	115	56	with	with	ADP
cet-14439	115	57	the	the	DET
cet-14439	115	58	correlation	correlation	NOUN
cet-14439	115	59	of	of	ADP
cet-14439	115	60	othmer	othmer	NOUN
cet-14439	115	61	and	and	CCONJ
cet-14439	115	62	thakar	thakar	NOUN
cet-14439	115	63	for	for	ADP
cet-14439	115	64	dilute	dilute	VERB
cet-14439	115	65	aqueous	aqueous	ADJ
cet-14439	115	66	systems	system	NOUN
cet-14439	115	67	(	(	PUNCT
cet-14439	115	68	sherwood	sherwood	PROPN
cet-14439	115	69	et	et	PROPN
cet-14439	115	70	al	al	PROPN
cet-14439	115	71	,	,	PUNCT
cet-14439	115	72	1975	1975	NUM
cet-14439	115	73	)	)	PUNCT
cet-14439	115	74	.	.	PUNCT
cet-14439	116	1	5.2	5.2	NUM
cet-14439	116	2	results	result	VERB
cet-14439	116	3	the	the	DET
cet-14439	116	4	variational	variational	ADJ
cet-14439	116	5	method	method	NOUN
cet-14439	116	6	was	be	AUX
cet-14439	116	7	solved	solve	VERB
cet-14439	116	8	for	for	ADP
cet-14439	116	9	m=3	m=3	PROPN
cet-14439	116	10	and	and	CCONJ
cet-14439	116	11	m=5	m=5	ADJ
cet-14439	116	12	(	(	PUNCT
cet-14439	116	13	3	3	NUM
cet-14439	116	14	and	and	CCONJ
cet-14439	116	15	5	5	NUM
cet-14439	116	16	points	point	NOUN
cet-14439	116	17	,	,	PUNCT
cet-14439	116	18	respectively	respectively	ADV
cet-14439	116	19	)	)	PUNCT
cet-14439	116	20	,	,	PUNCT
cet-14439	116	21	and	and	CCONJ
cet-14439	116	22	the	the	DET
cet-14439	116	23	resulting	result	VERB
cet-14439	116	24	ode	ode	ADJ
cet-14439	116	25	system	system	NOUN
cet-14439	116	26	was	be	AUX
cet-14439	116	27	solved	solve	VERB
cet-14439	116	28	with	with	ADP
cet-14439	116	29	a	a	DET
cet-14439	116	30	4th	4th	ADJ
cet-14439	116	31	order	order	NOUN
cet-14439	116	32	runge	runge	NOUN
cet-14439	116	33	-	-	PUNCT
cet-14439	116	34	kutta	kutta	NOUN
cet-14439	116	35	method	method	NOUN
cet-14439	116	36	,	,	PUNCT
cet-14439	116	37	with	with	ADP
cet-14439	116	38	∆𝑡	∆𝑡	PROPN
cet-14439	116	39	=	=	SYM
cet-14439	116	40	0.01	0.01	NUM
cet-14439	116	41	min	min	NOUN
cet-14439	116	42	.	.	PUNCT
cet-14439	117	1	the	the	DET
cet-14439	117	2	finite	finite	ADJ
cet-14439	117	3	difference	difference	NOUN
cet-14439	117	4	method	method	NOUN
cet-14439	117	5	was	be	AUX
cet-14439	117	6	solved	solve	VERB
cet-14439	117	7	with	with	ADP
cet-14439	117	8	5	5	NUM
cet-14439	117	9	and	and	CCONJ
cet-14439	117	10	10	10	NUM
cet-14439	117	11	intervals	interval	NOUN
cet-14439	117	12	(	(	PUNCT
cet-14439	117	13	6	6	NUM
cet-14439	117	14	and	and	CCONJ
cet-14439	117	15	11	11	NUM
cet-14439	117	16	points	point	NOUN
cet-14439	117	17	,	,	PUNCT
cet-14439	117	18	respectively	respectively	ADV
cet-14439	117	19	)	)	PUNCT
cet-14439	117	20	,	,	PUNCT
cet-14439	117	21	and	and	CCONJ
cet-14439	117	22	the	the	DET
cet-14439	117	23	resulting	result	VERB
cet-14439	117	24	ode	ode	ADJ
cet-14439	117	25	system	system	NOUN
cet-14439	117	26	was	be	AUX
cet-14439	117	27	also	also	ADV
cet-14439	117	28	solved	solve	VERB
cet-14439	117	29	with	with	ADP
cet-14439	117	30	a	a	DET
cet-14439	117	31	4th	4th	ADJ
cet-14439	117	32	order	order	NOUN
cet-14439	117	33	runge	runge	NOUN
cet-14439	117	34	-	-	PUNCT
cet-14439	117	35	kutta	kutta	NOUN
cet-14439	117	36	method	method	NOUN
cet-14439	117	37	,	,	PUNCT
cet-14439	117	38	with	with	ADP
cet-14439	117	39	∆𝑡	∆𝑡	PROPN
cet-14439	117	40	=	=	SYM
cet-14439	117	41	0.01	0.01	NUM
cet-14439	117	42	min	min	NOUN
cet-14439	117	43	.	.	PUNCT
cet-14439	118	1	the	the	DET
cet-14439	118	2	results	result	NOUN
cet-14439	118	3	for	for	ADP
cet-14439	118	4	the	the	DET
cet-14439	118	5	dimensionless	dimensionless	NOUN
cet-14439	118	6	concentration	concentration	NOUN
cet-14439	118	7	in	in	ADP
cet-14439	118	8	the	the	DET
cet-14439	118	9	solution	solution	NOUN
cet-14439	118	10	(	(	PUNCT
cet-14439	118	11	𝑤	𝑤	X
cet-14439	118	12	)	)	PUNCT
cet-14439	118	13	are	be	AUX
cet-14439	118	14	presented	present	VERB
cet-14439	118	15	in	in	ADP
cet-14439	118	16	table	table	NOUN
cet-14439	118	17	3	3	NUM
cet-14439	118	18	,	,	PUNCT
cet-14439	118	19	where	where	SCONJ
cet-14439	118	20	it	it	PRON
cet-14439	118	21	can	can	AUX
cet-14439	118	22	be	be	AUX
cet-14439	118	23	seen	see	VERB
cet-14439	118	24	a	a	DET
cet-14439	118	25	good	good	ADJ
cet-14439	118	26	agreement	agreement	NOUN
cet-14439	118	27	between	between	ADP
cet-14439	118	28	the	the	DET
cet-14439	118	29	two	two	NUM
cet-14439	118	30	methods	method	NOUN
cet-14439	118	31	.	.	PUNCT
cet-14439	119	1	it	it	PRON
cet-14439	119	2	is	be	AUX
cet-14439	119	3	important	important	ADJ
cet-14439	119	4	to	to	PART
cet-14439	119	5	point	point	VERB
cet-14439	119	6	out	out	ADP
cet-14439	119	7	that	that	SCONJ
cet-14439	119	8	some	some	DET
cet-14439	119	9	care	care	NOUN
cet-14439	119	10	must	must	AUX
cet-14439	119	11	be	be	AUX
cet-14439	119	12	taken	take	VERB
cet-14439	119	13	with	with	ADP
cet-14439	119	14	respect	respect	NOUN
cet-14439	119	15	to	to	ADP
cet-14439	119	16	the	the	DET
cet-14439	119	17	time	time	NOUN
cet-14439	119	18	interval	interval	NOUN
cet-14439	119	19	∆𝑡.	∆𝑡.	NOUN
cet-14439	119	20	parabolic	parabolic	ADJ
cet-14439	119	21	pdes	pde	NOUN
cet-14439	119	22	as	as	ADP
cet-14439	119	23	eq	eq	NOUN
cet-14439	119	24	(	(	PUNCT
cet-14439	119	25	2	2	NUM
cet-14439	119	26	)	)	PUNCT
cet-14439	119	27	may	may	AUX
cet-14439	119	28	result	result	VERB
cet-14439	119	29	in	in	ADP
cet-14439	119	30	a	a	DET
cet-14439	119	31	stiff	stiff	ADJ
cet-14439	119	32	ode	ode	NOUN
cet-14439	119	33	system	system	NOUN
cet-14439	119	34	when	when	SCONJ
cet-14439	119	35	a	a	DET
cet-14439	119	36	discretization	discretization	NOUN
cet-14439	119	37	is	be	AUX
cet-14439	119	38	applied	apply	VERB
cet-14439	119	39	in	in	ADP
cet-14439	119	40	the	the	DET
cet-14439	119	41	𝑥	𝑥	PROPN
cet-14439	119	42	domain	domain	NOUN
cet-14439	119	43	.	.	PUNCT
cet-14439	120	1	95	95	NUM
cet-14439	120	2	table	table	NOUN
cet-14439	120	3	3	3	NUM
cet-14439	120	4	:	:	PUNCT
cet-14439	120	5	results	result	NOUN
cet-14439	120	6	for	for	ADP
cet-14439	120	7	the	the	DET
cet-14439	120	8	dimensionless	dimensionless	NOUN
cet-14439	120	9	concentration	concentration	NOUN
cet-14439	120	10	in	in	ADP
cet-14439	120	11	the	the	DET
cet-14439	120	12	solution	solution	NOUN
cet-14439	120	13	(	(	PUNCT
cet-14439	120	14	𝑤	𝑤	X
cet-14439	120	15	)	)	PUNCT
cet-14439	120	16	for	for	ADP
cet-14439	120	17	the	the	DET
cet-14439	120	18	case	case	NOUN
cet-14439	120	19	study	study	NOUN
cet-14439	120	20	.	.	PUNCT
cet-14439	121	1	time	time	NOUN
cet-14439	121	2	(	(	PUNCT
cet-14439	121	3	min	min	NOUN
cet-14439	121	4	)	)	PUNCT
cet-14439	121	5			NOUN
cet-14439	121	6	variational	variational	ADJ
cet-14439	121	7	(	(	PUNCT
cet-14439	121	8	m=3	m=3	ADJ
cet-14439	121	9	)	)	PUNCT
cet-14439	121	10	variational	variational	ADJ
cet-14439	121	11	(	(	PUNCT
cet-14439	121	12	m=5	m=5	NOUN
cet-14439	121	13	)	)	PUNCT
cet-14439	121	14	finite	finite	PROPN
cet-14439	121	15	diff	diff	PROPN
cet-14439	121	16	.	.	PUNCT
cet-14439	122	1	(	(	PUNCT
cet-14439	122	2	∆𝑥	∆𝑥	NOUN
cet-14439	122	3	=	=	SYM
cet-14439	122	4	0.2	0.2	NUM
cet-14439	122	5	)	)	PUNCT
cet-14439	122	6	finite	finite	PROPN
cet-14439	122	7	diff	diff	PROPN
cet-14439	122	8	.	.	PUNCT
cet-14439	123	1	(	(	PUNCT
cet-14439	123	2	∆𝑥	∆𝑥	NOUN
cet-14439	123	3	=	=	SYM
cet-14439	123	4	0.1	0.1	NUM
cet-14439	123	5	)	)	PUNCT
cet-14439	123	6	0.00	0.00	NUM
cet-14439	123	7	0.0000	0.0000	NUM
cet-14439	123	8	1.0000	1.0000	NUM
cet-14439	123	9	1.0000	1.0000	NUM
cet-14439	123	10	1.0000	1.0000	NUM
cet-14439	123	11	1.0000	1.0000	NUM
cet-14439	123	12	5.00	5.00	NUM
cet-14439	123	13	0.3600	0.3600	NUM
cet-14439	123	14	0.9446	0.9446	NUM
cet-14439	123	15	0.9434	0.9434	NUM
cet-14439	123	16	0.9451	0.9451	NUM
cet-14439	123	17	0.9439	0.9439	NUM
cet-14439	123	18	10.00	10.00	NUM
cet-14439	123	19	0.7200	0.7200	NUM
cet-14439	123	20	0.9274	0.9274	NUM
cet-14439	123	21	0.9268	0.9268	NUM
cet-14439	123	22	0.9280	0.9280	NUM
cet-14439	123	23	0.9271	0.9271	NUM
cet-14439	123	24	15.00	15.00	NUM
cet-14439	123	25	1.0800	1.0800	NUM
cet-14439	123	26	0.9172	0.9172	NUM
cet-14439	123	27	0.9169	0.9169	NUM
cet-14439	123	28	0.9178	0.9178	NUM
cet-14439	123	29	0.9171	0.9171	NUM
cet-14439	123	30	20.00	20.00	NUM
cet-14439	123	31	1.4400	1.4400	NUM
cet-14439	123	32	0.9105	0.9105	NUM
cet-14439	123	33	0.9104	0.9104	NUM
cet-14439	124	1	0.9111	0.9111	NUM
cet-14439	124	2	0.9105	0.9105	NUM
cet-14439	124	3	25.00	25.00	NUM
cet-14439	124	4	1.8000	1.8000	NUM
cet-14439	124	5	0.9059	0.9059	NUM
cet-14439	124	6	0.9059	0.9059	NUM
cet-14439	125	1	0.9065	0.9065	NUM
cet-14439	125	2	0.9060	0.9060	NUM
cet-14439	125	3	30.00	30.00	NUM
cet-14439	125	4	2.1600	2.1600	NUM
cet-14439	125	5	0.9028	0.9028	NUM
cet-14439	125	6	0.9028	0.9028	NUM
cet-14439	125	7	0.9033	0.9033	NUM
cet-14439	125	8	0.9030	0.9030	NUM
cet-14439	125	9			NOUN
cet-14439	125	10			VERB
cet-14439	125	11	0.8962	0.8962	NUM
cet-14439	125	12	0.8962	0.8962	NUM
cet-14439	125	13	0.8962	0.8962	NUM
cet-14439	125	14	0.8962	0.8962	NUM
cet-14439	126	1	the	the	DET
cet-14439	126	2	value	value	NOUN
cet-14439	126	3	of	of	ADP
cet-14439	126	4	𝐷	𝐷	NOUN
cet-14439	126	5	=	=	NOUN
cet-14439	126	6	7.5	7.5	NUM
cet-14439	126	7	∙	∙	PROPN
cet-14439	126	8	10−11	10−11	NUM
cet-14439	126	9	m2	m2	PROPN
cet-14439	126	10	s⁄	s⁄	PROPN
cet-14439	126	11	was	be	AUX
cet-14439	126	12	fitted	fit	VERB
cet-14439	126	13	to	to	PART
cet-14439	126	14	reproduce	reproduce	VERB
cet-14439	126	15	the	the	DET
cet-14439	126	16	experimental	experimental	ADJ
cet-14439	126	17	values	value	NOUN
cet-14439	126	18	in	in	ADP
cet-14439	126	19	table	table	NOUN
cet-14439	126	20	2	2	NUM
cet-14439	126	21	.	.	PUNCT
cet-14439	127	1	however	however	ADV
cet-14439	127	2	,	,	PUNCT
cet-14439	127	3	there	there	PRON
cet-14439	127	4	is	be	VERB
cet-14439	127	5	a	a	DET
cet-14439	127	6	difference	difference	NOUN
cet-14439	127	7	at	at	ADP
cet-14439	127	8	equilibrium	equilibrium	NOUN
cet-14439	127	9	,	,	PUNCT
cet-14439	127	10	𝑤∞	𝑤∞	X
cet-14439	127	11	=	=	SYM
cet-14439	127	12	0.8962	0.8962	NUM
cet-14439	127	13	,	,	PUNCT
cet-14439	127	14	which	which	PRON
cet-14439	127	15	is	be	AUX
cet-14439	127	16	due	due	ADJ
cet-14439	127	17	to	to	ADP
cet-14439	127	18	the	the	DET
cet-14439	127	19	experiments	experiment	NOUN
cet-14439	127	20	had	have	AUX
cet-14439	127	21	used	use	VERB
cet-14439	127	22	dry	dry	ADJ
cet-14439	127	23	resin	resin	NOUN
cet-14439	127	24	at	at	ADP
cet-14439	127	25	𝑡	𝑡	X
cet-14439	127	26	=	=	SYM
cet-14439	127	27	0	0	NUM
cet-14439	127	28	,	,	PUNCT
cet-14439	127	29	while	while	SCONJ
cet-14439	127	30	the	the	DET
cet-14439	127	31	model	model	NOUN
cet-14439	127	32	implicitly	implicitly	ADV
cet-14439	127	33	assumes	assume	VERB
cet-14439	127	34	a	a	DET
cet-14439	127	35	wet	wet	ADJ
cet-14439	127	36	resin	resin	NOUN
cet-14439	127	37	at	at	ADP
cet-14439	127	38	𝑡	𝑡	X
cet-14439	127	39	=	=	SYM
cet-14439	127	40	0	0	PUNCT
cet-14439	127	41	(	(	PUNCT
cet-14439	127	42	𝑐	𝑐	NOUN
cet-14439	127	43	=	=	SYM
cet-14439	127	44	0	0	NUM
cet-14439	127	45	means	mean	VERB
cet-14439	127	46	no	no	DET
cet-14439	127	47	solute	solute	NOUN
cet-14439	127	48	,	,	PUNCT
cet-14439	127	49	but	but	CCONJ
cet-14439	127	50	the	the	DET
cet-14439	127	51	solvent	solvent	NOUN
cet-14439	127	52	is	be	AUX
cet-14439	127	53	inside	inside	ADP
cet-14439	127	54	the	the	DET
cet-14439	127	55	pores	pore	NOUN
cet-14439	127	56	in	in	ADP
cet-14439	127	57	the	the	DET
cet-14439	127	58	model	model	NOUN
cet-14439	127	59	)	)	PUNCT
cet-14439	127	60	.	.	PUNCT
cet-14439	128	1	this	this	PRON
cet-14439	128	2	affects	affect	VERB
cet-14439	128	3	the	the	DET
cet-14439	128	4	mass	mass	NOUN
cet-14439	128	5	balance	balance	NOUN
cet-14439	128	6	.	.	PUNCT
cet-14439	129	1	the	the	DET
cet-14439	129	2	calculated	calculate	VERB
cet-14439	129	3	value	value	NOUN
cet-14439	129	4	at	at	ADP
cet-14439	129	5	equilibrium	equilibrium	NOUN
cet-14439	129	6	,	,	PUNCT
cet-14439	129	7	considering	consider	VERB
cet-14439	129	8	dry	dry	ADJ
cet-14439	129	9	resin	resin	NOUN
cet-14439	129	10	at	at	ADP
cet-14439	129	11	𝑡	𝑡	PROPN
cet-14439	129	12	=	=	SYM
cet-14439	129	13	0	0	NUM
cet-14439	129	14	,	,	PUNCT
cet-14439	129	15	is	be	AUX
cet-14439	129	16	𝑤∞	𝑤∞	X
cet-14439	129	17	=	=	SYM
cet-14439	129	18	0.9052	0.9052	NUM
cet-14439	129	19	,	,	PUNCT
cet-14439	129	20	which	which	PRON
cet-14439	129	21	is	be	AUX
cet-14439	129	22	closer	close	ADJ
cet-14439	129	23	to	to	ADP
cet-14439	129	24	the	the	DET
cet-14439	129	25	experimental	experimental	ADJ
cet-14439	129	26	value	value	NOUN
cet-14439	129	27	in	in	ADP
cet-14439	129	28	table	table	NOUN
cet-14439	129	29	2	2	NUM
cet-14439	129	30	.	.	NOUN
cet-14439	129	31	one	one	NUM
cet-14439	129	32	way	way	NOUN
cet-14439	129	33	to	to	PART
cet-14439	129	34	solve	solve	VERB
cet-14439	129	35	this	this	PRON
cet-14439	129	36	is	be	AUX
cet-14439	129	37	to	to	PART
cet-14439	129	38	use	use	VERB
cet-14439	129	39	𝑉∗	𝑉∗	NOUN
cet-14439	129	40	,	,	PUNCT
cet-14439	129	41	such	such	ADJ
cet-14439	129	42	that	that	DET
cet-14439	129	43	𝑉∗	𝑉∗	NOUN
cet-14439	129	44	=	=	SYM
cet-14439	129	45	𝑉	𝑉	PROPN
cet-14439	130	1	−	−	NOUN
cet-14439	130	2	𝑣	𝑣	ADP
cet-14439	130	3	∙	∙	PROPN
cet-14439	130	4	𝜀	𝜀	PROPN
cet-14439	130	5	,	,	PUNCT
cet-14439	130	6	and	and	CCONJ
cet-14439	130	7	𝑐	𝑐	ADP
cet-14439	130	8	≠	≠	PROPN
cet-14439	130	9	0	0	NUM
cet-14439	130	10	at	at	ADP
cet-14439	130	11	𝑡	𝑡	NOUN
cet-14439	130	12	=	=	SYM
cet-14439	130	13	0	0	PUNCT
cet-14439	130	14	(	(	PUNCT
cet-14439	130	15	but	but	CCONJ
cet-14439	130	16	𝑐0	𝑐0	VERB
cet-14439	130	17	≠	≠	PROPN
cet-14439	130	18	𝐶0	𝐶0	NOUN
cet-14439	130	19	,	,	PUNCT
cet-14439	130	20	due	due	ADJ
cet-14439	130	21	to	to	ADP
cet-14439	130	22	𝑞0	𝑞0	NOUN
cet-14439	130	23	)	)	PUNCT
cet-14439	130	24	,	,	PUNCT
cet-14439	130	25	to	to	PART
cet-14439	130	26	compare	compare	VERB
cet-14439	130	27	experimental	experimental	ADJ
cet-14439	130	28	and	and	CCONJ
cet-14439	130	29	simulated	simulated	ADJ
cet-14439	130	30	values	value	NOUN
cet-14439	130	31	.	.	PUNCT
cet-14439	131	1	6	6	X
cet-14439	131	2	.	.	X
cet-14439	131	3	conclusions	conclusion	NOUN
cet-14439	131	4	the	the	DET
cet-14439	131	5	numerical	numerical	ADJ
cet-14439	131	6	methods	method	NOUN
cet-14439	131	7	used	use	VERB
cet-14439	131	8	were	be	AUX
cet-14439	131	9	able	able	ADJ
cet-14439	131	10	to	to	PART
cet-14439	131	11	give	give	VERB
cet-14439	131	12	reliable	reliable	ADJ
cet-14439	131	13	results	result	NOUN
cet-14439	131	14	to	to	PART
cet-14439	131	15	represent	represent	VERB
cet-14439	131	16	the	the	DET
cet-14439	131	17	adsorption	adsorption	NOUN
cet-14439	131	18	of	of	ADP
cet-14439	131	19	gvl	gvl	PROPN
cet-14439	131	20	into	into	ADP
cet-14439	131	21	spheres	sphere	NOUN
cet-14439	131	22	of	of	ADP
cet-14439	131	23	sp850	sp850	PROPN
cet-14439	131	24	resin	resin	NOUN
cet-14439	131	25	.	.	PUNCT
cet-14439	132	1	this	this	DET
cet-14439	132	2	resin	resin	NOUN
cet-14439	132	3	is	be	AUX
cet-14439	132	4	very	very	ADV
cet-14439	132	5	selective	selective	ADJ
cet-14439	132	6	to	to	PART
cet-14439	132	7	separate	separate	VERB
cet-14439	132	8	gvl	gvl	PROPN
cet-14439	132	9	from	from	ADP
cet-14439	132	10	a	a	DET
cet-14439	132	11	solution	solution	NOUN
cet-14439	132	12	of	of	ADP
cet-14439	132	13	glucose	glucose	NOUN
cet-14439	132	14	.	.	PUNCT
cet-14439	133	1	therefore	therefore	ADV
cet-14439	133	2	,	,	PUNCT
cet-14439	133	3	the	the	DET
cet-14439	133	4	model	model	NOUN
cet-14439	133	5	and	and	CCONJ
cet-14439	133	6	the	the	DET
cet-14439	133	7	numerical	numerical	ADJ
cet-14439	133	8	methods	method	NOUN
cet-14439	133	9	studied	study	VERB
cet-14439	133	10	here	here	ADV
cet-14439	133	11	can	can	AUX
cet-14439	133	12	be	be	AUX
cet-14439	133	13	used	use	VERB
cet-14439	133	14	to	to	PART
cet-14439	133	15	design	design	VERB
cet-14439	133	16	a	a	DET
cet-14439	133	17	better	well	ADJ
cet-14439	133	18	separation	separation	NOUN
cet-14439	133	19	process	process	NOUN
cet-14439	133	20	using	use	VERB
cet-14439	133	21	adsorption	adsorption	NOUN
cet-14439	133	22	.	.	PUNCT
cet-14439	134	1	the	the	DET
cet-14439	134	2	fitted	fit	VERB
cet-14439	134	3	diffusion	diffusion	NOUN
cet-14439	134	4	coefficient	coefficient	NOUN
cet-14439	134	5	inside	inside	ADP
cet-14439	134	6	the	the	DET
cet-14439	134	7	particles	particle	NOUN
cet-14439	134	8	,	,	PUNCT
cet-14439	134	9	𝐷	𝐷	NOUN
cet-14439	134	10	,	,	PUNCT
cet-14439	134	11	lead	lead	VERB
cet-14439	134	12	to	to	ADP
cet-14439	134	13	the	the	DET
cet-14439	134	14	dimensionless	dimensionless	NOUN
cet-14439	134	15	number	number	NOUN
cet-14439	134	16	𝑘𝑓	𝑘𝑓	ADP
cet-14439	134	17	∙	∙	PROPN
cet-14439	134	18	𝑅	𝑅	PROPN
cet-14439	134	19	𝐷⁄	𝐷⁄	PROPN
cet-14439	134	20	=	=	SYM
cet-14439	134	21	56.67	56.67	NUM
cet-14439	134	22	,	,	PUNCT
cet-14439	134	23	indicating	indicate	VERB
cet-14439	134	24	that	that	SCONJ
cet-14439	134	25	for	for	ADP
cet-14439	134	26	this	this	DET
cet-14439	134	27	case	case	NOUN
cet-14439	134	28	study	study	VERB
cet-14439	134	29	the	the	DET
cet-14439	134	30	internal	internal	ADJ
cet-14439	134	31	resistance	resistance	NOUN
cet-14439	134	32	for	for	ADP
cet-14439	134	33	mass	mass	ADJ
cet-14439	134	34	transfer	transfer	NOUN
cet-14439	134	35	is	be	AUX
cet-14439	134	36	much	much	ADV
cet-14439	134	37	higher	high	ADJ
cet-14439	134	38	than	than	ADP
cet-14439	134	39	the	the	DET
cet-14439	134	40	external	external	ADJ
cet-14439	134	41	resistance	resistance	NOUN
cet-14439	134	42	.	.	PUNCT
cet-14439	135	1	the	the	DET
cet-14439	135	2	value	value	NOUN
cet-14439	135	3	of	of	ADP
cet-14439	135	4	𝐷	𝐷	NOUN
cet-14439	135	5	can	can	AUX
cet-14439	135	6	then	then	ADV
cet-14439	135	7	be	be	AUX
cet-14439	135	8	used	use	VERB
cet-14439	135	9	in	in	ADP
cet-14439	135	10	other	other	ADJ
cet-14439	135	11	systems	system	NOUN
cet-14439	135	12	,	,	PUNCT
cet-14439	135	13	since	since	SCONJ
cet-14439	135	14	it	it	PRON
cet-14439	135	15	is	be	AUX
cet-14439	135	16	a	a	DET
cet-14439	135	17	parameter	parameter	NOUN
cet-14439	135	18	inside	inside	ADP
cet-14439	135	19	the	the	DET
cet-14439	135	20	particles	particle	NOUN
cet-14439	135	21	,	,	PUNCT
cet-14439	135	22	for	for	ADP
cet-14439	135	23	example	example	NOUN
cet-14439	135	24	a	a	DET
cet-14439	135	25	fixed	fix	VERB
cet-14439	135	26	bed	bed	NOUN
cet-14439	135	27	column	column	NOUN
cet-14439	135	28	,	,	PUNCT
cet-14439	135	29	but	but	CCONJ
cet-14439	135	30	then	then	ADV
cet-14439	135	31	the	the	DET
cet-14439	135	32	value	value	NOUN
cet-14439	135	33	of	of	ADP
cet-14439	135	34	𝑘𝑓	𝑘𝑓	PRON
cet-14439	135	35	may	may	AUX
cet-14439	135	36	be	be	AUX
cet-14439	135	37	different	different	ADJ
cet-14439	135	38	from	from	ADP
cet-14439	135	39	the	the	DET
cet-14439	135	40	one	one	NOUN
cet-14439	135	41	in	in	ADP
cet-14439	135	42	a	a	DET
cet-14439	135	43	stirred	stir	VERB
cet-14439	135	44	tank	tank	NOUN
cet-14439	135	45	.	.	PUNCT
cet-14439	136	1	references	reference	NOUN
cet-14439	136	2	abramowitz	abramowitz	PROPN
cet-14439	136	3	m.	m.	PROPN
cet-14439	136	4	,	,	PUNCT
cet-14439	136	5	stegun	stegun	NOUN
cet-14439	136	6	i.a	i.a	PROPN
cet-14439	136	7	.	.	PROPN
cet-14439	136	8	,	,	PUNCT
cet-14439	136	9	1972	1972	NUM
cet-14439	136	10	,	,	PUNCT
cet-14439	136	11	handbook	handbook	NOUN
cet-14439	136	12	of	of	ADP
cet-14439	136	13	mathematical	mathematical	ADJ
cet-14439	136	14	functions	function	NOUN
cet-14439	136	15	,	,	PUNCT
cet-14439	136	16	national	national	ADJ
cet-14439	136	17	bureau	bureau	PROPN
cet-14439	136	18	of	of	ADP
cet-14439	136	19	standards	standard	NOUN
cet-14439	136	20	,	,	PUNCT
cet-14439	136	21	applied	apply	VERB
cet-14439	136	22	mathematics	mathematic	NOUN
cet-14439	136	23	series	series	NOUN
cet-14439	136	24	55	55	NUM
cet-14439	136	25	,	,	PUNCT
cet-14439	136	26	tenth	tenth	ADJ
cet-14439	136	27	printing	printing	NOUN
cet-14439	136	28	.	.	PUNCT
cet-14439	137	1	alonso	alonso	PROPN
cet-14439	137	2	d.m	d.m	PROPN
cet-14439	137	3	.	.	PROPN
cet-14439	137	4	,	,	PUNCT
cet-14439	137	5	gallo	gallo	PROPN
cet-14439	137	6	j.m.r	j.m.r	VERB
cet-14439	137	7	.	.	PROPN
cet-14439	137	8	,	,	PUNCT
cet-14439	138	1	mellmer	mellmer	PROPN
cet-14439	138	2	m.a	m.a	PROPN
cet-14439	138	3	.	.	PROPN
cet-14439	138	4	,	,	PUNCT
cet-14439	138	5	wettsteinab	wettsteinab	PROPN
cet-14439	138	6	s.g	s.g	PROPN
cet-14439	138	7	.	.	PROPN
cet-14439	138	8	,	,	PUNCT
cet-14439	138	9	dumesic	dumesic	PROPN
cet-14439	138	10	j.a	j.a	PROPN
cet-14439	138	11	.	.	PROPN
cet-14439	138	12	,	,	PUNCT
cet-14439	138	13	2013	2013	NUM
cet-14439	138	14	,	,	PUNCT
cet-14439	138	15	direct	direct	ADJ
cet-14439	138	16	conversion	conversion	NOUN
cet-14439	138	17	of	of	ADP
cet-14439	138	18	cellulose	cellulose	NOUN
cet-14439	138	19	to	to	ADP
cet-14439	138	20	levulinic	levulinic	NOUN
cet-14439	138	21	acid	acid	PROPN
cet-14439	138	22	and	and	CCONJ
cet-14439	138	23	gamma	gamma	NOUN
cet-14439	138	24	-	-	PUNCT
cet-14439	138	25	valerolactone	valerolactone	NOUN
cet-14439	138	26	using	use	VERB
cet-14439	138	27	solid	solid	ADJ
cet-14439	138	28	acid	acid	NOUN
cet-14439	138	29	catalysts	catalyst	NOUN
cet-14439	138	30	,	,	PUNCT
cet-14439	138	31	catalysis	catalysis	NOUN
cet-14439	138	32	science	science	NOUN
cet-14439	138	33	&	&	CCONJ
cet-14439	138	34	technology	technology	PROPN
cet-14439	138	35	,	,	PUNCT
cet-14439	138	36	3	3	NUM
cet-14439	138	37	,	,	PUNCT
cet-14439	138	38	927	927	NUM
cet-14439	138	39	-	-	SYM
cet-14439	138	40	931	931	NUM
cet-14439	138	41	.	.	PUNCT
cet-14439	139	1	geankoplis	geankoplis	PROPN
cet-14439	139	2	c.j	c.j	PROPN
cet-14439	139	3	.	.	PROPN
cet-14439	139	4	,	,	PUNCT
cet-14439	139	5	1983	1983	NUM
cet-14439	139	6	,	,	PUNCT
cet-14439	139	7	transport	transport	NOUN
cet-14439	139	8	processes	process	NOUN
cet-14439	139	9	and	and	CCONJ
cet-14439	139	10	unit	unit	NOUN
cet-14439	139	11	operations	operation	NOUN
cet-14439	139	12	,	,	PUNCT
cet-14439	139	13	allyn	allyn	NOUN
cet-14439	139	14	and	and	CCONJ
cet-14439	139	15	bacon	bacon	NOUN
cet-14439	139	16	,	,	PUNCT
cet-14439	139	17	boston	boston	PROPN
cet-14439	139	18	,	,	PUNCT
cet-14439	139	19	ma	ma	PROPN
cet-14439	139	20	,	,	PUNCT
cet-14439	139	21	2nd	2nd	ADJ
cet-14439	139	22	ed	ed	NOUN
cet-14439	139	23	.	.	PUNCT
cet-14439	140	1	guirardello	guirardello	PROPN
cet-14439	140	2	r.	r.	PROPN
cet-14439	140	3	,	,	PUNCT
cet-14439	140	4	2013	2013	NUM
cet-14439	140	5	,	,	PUNCT
cet-14439	140	6	numerical	numerical	ADJ
cet-14439	140	7	solution	solution	NOUN
cet-14439	140	8	for	for	ADP
cet-14439	140	9	adsorption	adsorption	NOUN
cet-14439	140	10	in	in	ADP
cet-14439	140	11	porous	porous	ADJ
cet-14439	140	12	spheres	sphere	NOUN
cet-14439	140	13	using	use	VERB
cet-14439	140	14	a	a	DET
cet-14439	140	15	variational	variational	ADJ
cet-14439	140	16	formulation	formulation	NOUN
cet-14439	140	17	,	,	PUNCT
cet-14439	140	18	11th	11th	ADJ
cet-14439	140	19	international	international	ADJ
cet-14439	140	20	conference	conference	NOUN
cet-14439	140	21	of	of	ADP
cet-14439	140	22	numerical	numerical	ADJ
cet-14439	140	23	analysis	analysis	NOUN
cet-14439	140	24	and	and	CCONJ
cet-14439	140	25	applied	apply	VERB
cet-14439	140	26	mathematics	mathematic	NOUN
cet-14439	140	27	2013	2013	NUM
cet-14439	140	28	icnaam	icnaam	NOUN
cet-14439	140	29	2013	2013	NUM
cet-14439	140	30	,	,	PUNCT
cet-14439	140	31	rhodes	rhode	NOUN
cet-14439	140	32	,	,	PUNCT
cet-14439	140	33	v.	v.	ADP
cet-14439	140	34	1558	1558	NUM
cet-14439	140	35	.	.	PUNCT
cet-14439	141	1	p.	p.	NOUN
cet-14439	141	2	2018	2018	NUM
cet-14439	141	3	-	-	SYM
cet-14439	141	4	2021	2021	NUM
cet-14439	141	5	.	.	PUNCT
cet-14439	142	1	horstmann	horstmann	PROPN
cet-14439	142	2	b.j	b.j	AUX
cet-14439	142	3	.	.	PROPN
cet-14439	142	4	,	,	PUNCT
cet-14439	142	5	chase	chase	PROPN
cet-14439	142	6	h.a	h.a	PROPN
cet-14439	142	7	.	.	PROPN
cet-14439	142	8	,	,	PUNCT
cet-14439	142	9	1989	1989	NUM
cet-14439	142	10	,	,	PUNCT
cet-14439	142	11	modelling	model	VERB
cet-14439	142	12	the	the	DET
cet-14439	142	13	affinity	affinity	NOUN
cet-14439	142	14	adsorption	adsorption	NOUN
cet-14439	142	15	of	of	ADP
cet-14439	142	16	immunoglobulin	immunoglobulin	NOUN
cet-14439	142	17	g	g	NOUN
cet-14439	142	18	to	to	ADP
cet-14439	142	19	protein	protein	NOUN
cet-14439	142	20	a	a	DET
cet-14439	142	21	immobilised	immobilise	VERB
cet-14439	142	22	to	to	ADP
cet-14439	142	23	agarose	agarose	NOUN
cet-14439	142	24	matrices	matrix	NOUN
cet-14439	142	25	,	,	PUNCT
cet-14439	142	26	chemical	chemical	NOUN
cet-14439	142	27	engineering	engineering	NOUN
cet-14439	142	28	research	research	NOUN
cet-14439	142	29	and	and	CCONJ
cet-14439	142	30	design	design	NOUN
cet-14439	142	31	67	67	NUM
cet-14439	142	32	,	,	PUNCT
cet-14439	142	33	pp	pp	ADJ
cet-14439	142	34	.	.	PUNCT
cet-14439	143	1	243	243	NUM
cet-14439	143	2	-	-	SYM
cet-14439	143	3	254	254	NUM
cet-14439	143	4	.	.	PUNCT
cet-14439	144	1	luterbacher	luterbacher	PROPN
cet-14439	144	2	j.s	j.s	PROPN
cet-14439	144	3	.	.	PROPN
cet-14439	144	4	,	,	PUNCT
cet-14439	144	5	rand	rand	NOUN
cet-14439	144	6	j.m	j.m	PROPN
cet-14439	144	7	.	.	PROPN
cet-14439	144	8	,	,	PUNCT
cet-14439	144	9	alonso	alonso	PROPN
cet-14439	144	10	m.d	m.d	PROPN
cet-14439	144	11	.	.	PROPN
cet-14439	144	12	,	,	PUNCT
cet-14439	144	13	han	han	PROPN
cet-14439	144	14	j.	j.	PROPN
cet-14439	144	15	,	,	PUNCT
cet-14439	144	16	youngquist	youngquist	PROPN
cet-14439	144	17	j.t	j.t	PROPN
cet-14439	144	18	.	.	PROPN
cet-14439	144	19	,	,	PUNCT
cet-14439	144	20	maravelias	maravelias	PROPN
cet-14439	144	21	c.t	c.t	PROPN
cet-14439	144	22	.	.	PROPN
cet-14439	144	23	,	,	PUNCT
cet-14439	144	24	pfleger	pfleger	PROPN
cet-14439	144	25	b.f	b.f	PROPN
cet-14439	144	26	.	.	PROPN
cet-14439	144	27	,	,	PUNCT
cet-14439	144	28	dumesic	dumesic	PROPN
cet-14439	144	29	j.a	j.a	PROPN
cet-14439	144	30	.	.	PROPN
cet-14439	144	31	,	,	PUNCT
cet-14439	144	32	2014	2014	NUM
cet-14439	144	33	,	,	PUNCT
cet-14439	144	34	nonenzymatic	nonenzymatic	ADJ
cet-14439	144	35	sugar	sugar	NOUN
cet-14439	144	36	production	production	NOUN
cet-14439	144	37	from	from	ADP
cet-14439	144	38	biomass	biomass	NOUN
cet-14439	144	39	using	use	VERB
cet-14439	144	40	biomass	biomass	NOUN
cet-14439	144	41	-	-	PUNCT
cet-14439	144	42	derived	derive	VERB
cet-14439	144	43	γ	γ	NOUN
cet-14439	144	44	-	-	NOUN
cet-14439	144	45	valerolactone	valerolactone	NOUN
cet-14439	144	46	.	.	PUNCT
cet-14439	145	1	science	science	NOUN
cet-14439	145	2	,	,	PUNCT
cet-14439	145	3	american	american	PROPN
cet-14439	145	4	association	association	PROPN
cet-14439	145	5	for	for	ADP
cet-14439	145	6	the	the	DET
cet-14439	145	7	advancement	advancement	NOUN
cet-14439	145	8	of	of	ADP
cet-14439	145	9	science	science	NOUN
cet-14439	145	10	,	,	PUNCT
cet-14439	145	11	343	343	NUM
cet-14439	145	12	,	,	PUNCT
cet-14439	145	13	277	277	NUM
cet-14439	145	14	-	-	SYM
cet-14439	145	15	280	280	NUM
cet-14439	145	16	.	.	PUNCT
cet-14439	146	1	mellmer	mellmer	PROPN
cet-14439	146	2	m.a	m.a	PROPN
cet-14439	146	3	.	.	PROPN
cet-14439	146	4	,	,	PUNCT
cet-14439	146	5	alonso	alonso	PROPN
cet-14439	146	6	d.m	d.m	PROPN
cet-14439	146	7	.	.	PROPN
cet-14439	146	8	,	,	PUNCT
cet-14439	146	9	luterbacher	luterbacher	PROPN
cet-14439	146	10	j.s	j.s	PROPN
cet-14439	146	11	.	.	PROPN
cet-14439	146	12	,	,	PUNCT
cet-14439	146	13	gallo	gallo	PROPN
cet-14439	146	14	j.m	j.m	PROPN
cet-14439	146	15	.	.	PROPN
cet-14439	146	16	,	,	PUNCT
cet-14439	146	17	dumesic	dumesic	PROPN
cet-14439	146	18	j.a	j.a	PROPN
cet-14439	146	19	.	.	PROPN
cet-14439	146	20	,	,	PUNCT
cet-14439	146	21	2014	2014	NUM
cet-14439	146	22	,	,	PUNCT
cet-14439	146	23	effects	effect	NOUN
cet-14439	146	24	of	of	ADP
cet-14439	146	25	γ	γ	NOUN
cet-14439	146	26	-	-	NOUN
cet-14439	146	27	valerolactone	valerolactone	NOUN
cet-14439	146	28	in	in	ADP
cet-14439	146	29	hydrolysis	hydrolysis	NOUN
cet-14439	146	30	of	of	ADP
cet-14439	146	31	lignocellulosic	lignocellulosic	ADJ
cet-14439	146	32	biomass	biomass	NOUN
cet-14439	146	33	to	to	ADP
cet-14439	146	34	monosaccharides	monosaccharide	NOUN
cet-14439	146	35	,	,	PUNCT
cet-14439	146	36	green	green	ADJ
cet-14439	146	37	chemistry	chemistry	NOUN
cet-14439	146	38	,	,	PUNCT
cet-14439	146	39	royal	royal	ADJ
cet-14439	146	40	society	society	NOUN
cet-14439	146	41	of	of	ADP
cet-14439	146	42	chemistry	chemistry	NOUN
cet-14439	146	43	,	,	PUNCT
cet-14439	146	44	16	16	NUM
cet-14439	146	45	,	,	PUNCT
cet-14439	146	46	4659	4659	NUM
cet-14439	146	47	-	-	SYM
cet-14439	146	48	4662	4662	NUM
cet-14439	146	49	.	.	PUNCT
cet-14439	147	1	sherwood	sherwood	PROPN
cet-14439	147	2	t.k	t.k	PROPN
cet-14439	147	3	.	.	PROPN
cet-14439	147	4	,	,	PUNCT
cet-14439	147	5	pigford	pigford	PROPN
cet-14439	147	6	r.l	r.l	PROPN
cet-14439	147	7	.	.	PROPN
cet-14439	147	8	,	,	PUNCT
cet-14439	147	9	wilke	wilke	PROPN
cet-14439	147	10	c.r	c.r	PROPN
cet-14439	147	11	.	.	PROPN
cet-14439	147	12	,	,	PUNCT
cet-14439	147	13	1975	1975	NUM
cet-14439	147	14	,	,	PUNCT
cet-14439	147	15	mass	mass	NOUN
cet-14439	147	16	transfer	transfer	NOUN
cet-14439	147	17	,	,	PUNCT
cet-14439	147	18	mcgraw	mcgraw	PROPN
cet-14439	147	19	hill	hill	PROPN
cet-14439	147	20	inc	inc	PROPN
cet-14439	147	21	.	.	PROPN
cet-14439	148	1	skidmore	skidmore	PROPN
cet-14439	148	2	g.l	g.l	PROPN
cet-14439	148	3	.	.	PROPN
cet-14439	148	4	,	,	PUNCT
cet-14439	148	5	horstmann	horstmann	PROPN
cet-14439	148	6	b.j	b.j	PROPN
cet-14439	148	7	.	.	PROPN
cet-14439	148	8	,	,	PUNCT
cet-14439	148	9	chase	chase	PROPN
cet-14439	148	10	h.a	h.a	PROPN
cet-14439	148	11	.	.	PROPN
cet-14439	148	12	,	,	PUNCT
cet-14439	148	13	1990	1990	NUM
cet-14439	148	14	,	,	PUNCT
cet-14439	148	15	modelling	model	VERB
cet-14439	148	16	single	single	ADJ
cet-14439	148	17	-	-	PUNCT
cet-14439	148	18	component	component	NOUN
cet-14439	148	19	protein	protein	NOUN
cet-14439	148	20	adsorption	adsorption	NOUN
cet-14439	148	21	to	to	ADP
cet-14439	148	22	the	the	DET
cet-14439	148	23	cation	cation	NOUN
cet-14439	148	24	exchanger	exchanger	NOUN
cet-14439	148	25	s	s	NOUN
cet-14439	148	26	sepharose	sepharose	NOUN
cet-14439	148	27	®	®	NOUN
cet-14439	148	28	ff	ff	NOUN
cet-14439	148	29	,	,	PUNCT
cet-14439	148	30	journal	journal	NOUN
cet-14439	148	31	of	of	ADP
cet-14439	148	32	chromatography	chromatography	NOUN
cet-14439	148	33	,	,	PUNCT
cet-14439	148	34	498	498	NUM
cet-14439	148	35	,	,	PUNCT
cet-14439	148	36	113	113	NUM
cet-14439	148	37	-	-	SYM
cet-14439	148	38	128	128	NUM
cet-14439	148	39	.	.	PUNCT
cet-14439	149	1	spiegel	spiegel	PROPN
cet-14439	149	2	m.r	m.r	PROPN
cet-14439	149	3	.	.	PROPN
cet-14439	149	4	,	,	PUNCT
cet-14439	149	5	1965	1965	NUM
cet-14439	149	6	,	,	PUNCT
cet-14439	149	7	theory	theory	NOUN
cet-14439	149	8	and	and	CCONJ
cet-14439	149	9	problems	problem	NOUN
cet-14439	149	10	of	of	ADP
cet-14439	149	11	laplace	laplace	NOUN
cet-14439	149	12	transforms	transform	VERB
cet-14439	149	13	,	,	PUNCT
cet-14439	149	14	schaum	schaum	PROPN
cet-14439	149	15	’s	’s	PART
cet-14439	149	16	outline	outline	PROPN
cet-14439	149	17	series	series	PROPN
cet-14439	149	18	in	in	ADP
cet-14439	149	19	mathematics	mathematics	PROPN
cet-14439	149	20	,	,	PUNCT
cet-14439	149	21	mcgraw	mcgraw	PROPN
cet-14439	149	22	-	-	PUNCT
cet-14439	149	23	hill	hill	NOUN
cet-14439	149	24	book	book	NOUN
cet-14439	149	25	company	company	NOUN
cet-14439	149	26	,	,	PUNCT
cet-14439	149	27	new	new	PROPN
cet-14439	149	28	york	york	PROPN
cet-14439	149	29	,	,	PUNCT
cet-14439	149	30	reprinted	reprint	VERB
cet-14439	149	31	1986	1986	NUM
cet-14439	149	32	.	.	PUNCT
cet-14439	150	1	trindade	trindade	VERB
cet-14439	150	2	junior	junior	PROPN
cet-14439	150	3	v.n	v.n	PROPN
cet-14439	150	4	.	.	PROPN
cet-14439	150	5	,	,	PUNCT
cet-14439	150	6	2015a	2015a	NUM
cet-14439	150	7	,	,	PUNCT
cet-14439	150	8	análise	análise	PROPN
cet-14439	150	9	dos	do	VERB
cet-14439	150	10	processos	processos	PROPN
cet-14439	150	11	de	de	X
cet-14439	150	12	separação	separação	VERB
cet-14439	150	13	na	na	ADP
cet-14439	150	14	produção	produção	PROPN
cet-14439	150	15	de	de	PROPN
cet-14439	150	16	etanol	etanol	PROPN
cet-14439	150	17	celulósico	celulósico	PROPN
cet-14439	150	18	a	a	DET
cet-14439	150	19	partir	partir	X
cet-14439	150	20	de	de	X
cet-14439	150	21	biomassa	biomassa	NOUN
cet-14439	150	22	por	por	NOUN
cet-14439	150	23	rota	rota	PROPN
cet-14439	150	24	não	não	PROPN
cet-14439	150	25	enzimática	enzimática	PROPN
cet-14439	150	26	,	,	PUNCT
cet-14439	150	27	doctoral	doctoral	ADJ
cet-14439	150	28	thesis	thesis	NOUN
cet-14439	150	29	,	,	PUNCT
cet-14439	150	30	university	university	NOUN
cet-14439	150	31	of	of	ADP
cet-14439	150	32	campinas	campinas	PROPN
cet-14439	150	33	,	,	PUNCT
cet-14439	150	34	brazil	brazil	PROPN
cet-14439	150	35	.	.	PUNCT
cet-14439	151	1	trindade	trindade	VERB
cet-14439	151	2	junior	junior	PROPN
cet-14439	151	3	v.n	v.n	PROPN
cet-14439	151	4	.	.	PROPN
cet-14439	151	5	,	,	PUNCT
cet-14439	151	6	luterbacher	luterbacher	PROPN
cet-14439	151	7	j.s	j.s	PROPN
cet-14439	151	8	.	.	PROPN
cet-14439	151	9	,	,	PUNCT
cet-14439	151	10	dumesic	dumesic	PROPN
cet-14439	151	11	j.a	j.a	PROPN
cet-14439	151	12	.	.	PROPN
cet-14439	151	13	,	,	PUNCT
cet-14439	151	14	silva	silva	PROPN
cet-14439	151	15	e.a	e.a	PROPN
cet-14439	151	16	.	.	PROPN
cet-14439	151	17	,	,	PUNCT
cet-14439	151	18	guirardello	guirardello	PROPN
cet-14439	151	19	r.	r.	PROPN
cet-14439	151	20	,	,	PUNCT
cet-14439	151	21	2015b	2015b	NUM
cet-14439	151	22	,	,	PUNCT
cet-14439	151	23	adsorption	adsorption	NOUN
cet-14439	151	24	of	of	ADP
cet-14439	151	25	water	water	NOUN
cet-14439	151	26	/	/	SYM
cet-14439	151	27	glucose	glucose	NOUN
cet-14439	151	28	mixture	mixture	NOUN
cet-14439	151	29	onto	onto	ADP
cet-14439	151	30	amberlite	amberlite	ADJ
cet-14439	151	31	resin	resin	NOUN
cet-14439	151	32	,	,	PUNCT
cet-14439	151	33	chemical	chemical	NOUN
cet-14439	151	34	engineering	engineering	NOUN
cet-14439	151	35	transactions	transaction	NOUN
cet-14439	151	36	,	,	PUNCT
cet-14439	151	37	43	43	NUM
cet-14439	151	38	,	,	PUNCT
cet-14439	151	39	607	607	NUM
cet-14439	151	40	-	-	PUNCT
cet-14439	151	41	612	612	NUM
cet-14439	151	42	.	.	PUNCT
cet-14439	152	1	96	96	NUM
cet-14439	152	2	7guirardello.pdf	7guirardello.pdf	NUM
cet-14439	152	3	numerical	numerical	ADJ
cet-14439	152	4	simulation	simulation	NOUN
cet-14439	152	5	of	of	ADP
cet-14439	152	6	-valerolactone	-valerolactone	NUM
cet-14439	152	7	adsorption	adsorption	NOUN
cet-14439	152	8	into	into	ADP
cet-14439	152	9	porous	porous	ADJ
cet-14439	152	10	spheres	sphere	NOUN
cet-14439	152	11	in	in	ADP
cet-14439	152	12	a	a	DET
cet-14439	152	13	batch	batch	NOUN
cet-14439	152	14	process	process	NOUN