id	sid	tid	token	lemma	pos
hjic-242	1	1	microsoft	microsoft	PROPN
hjic-242	1	2	word	word	NOUN
hjic-242	1	3	toc_r.doc	toc_r.doc	ADJ
hjic-242	1	4	hungarian	hungarian	ADJ
hjic-242	1	5	journal	journal	NOUN
hjic-242	1	6	of	of	ADP
hjic-242	1	7	industrial	industrial	ADJ
hjic-242	1	8	chemistry	chemistry	NOUN
hjic-242	1	9	veszprém	veszprém	NOUN
hjic-242	1	10	vol	vol	NOUN
hjic-242	1	11	.	.	PUNCT
hjic-242	2	1	37(2	37(2	PRON
hjic-242	2	2	)	)	PUNCT
hjic-242	3	1	pp	pp	ADP
hjic-242	3	2	.	.	PUNCT
hjic-242	4	1	145	145	NUM
hjic-242	4	2	-	-	SYM
hjic-242	4	3	151	151	NUM
hjic-242	4	4	(	(	PUNCT
hjic-242	4	5	2009	2009	NUM
hjic-242	4	6	)	)	PUNCT
hjic-242	4	7	structural	structural	ADJ
hjic-242	4	8	analysis	analysis	NOUN
hjic-242	4	9	of	of	ADP
hjic-242	4	10	process	process	NOUN
hjic-242	4	11	models	model	NOUN
hjic-242	4	12	using	use	VERB
hjic-242	4	13	their	their	PRON
hjic-242	4	14	representation	representation	NOUN
hjic-242	4	15	graph	graph	NOUN
hjic-242	4	16	a.	a.	NOUN
hjic-242	4	17	leitold1	leitold1	NOUN
hjic-242	4	18	,	,	PUNCT
hjic-242	4	19	m.	m.	NOUN
hjic-242	4	20	gerzson2	gerzson2	PROPN
hjic-242	4	21	university	university	PROPN
hjic-242	4	22	of	of	ADP
hjic-242	4	23	pannonia	pannonia	PROPN
hjic-242	4	24	,	,	PUNCT
hjic-242	4	25	department	department	NOUN
hjic-242	4	26	of	of	ADP
hjic-242	4	27	mathematics	mathematic	NOUN
hjic-242	4	28	,	,	PUNCT
hjic-242	4	29	p.o.b	p.o.b	NOUN
hjic-242	4	30	.	.	PUNCT
hjic-242	5	1	158	158	NUM
hjic-242	5	2	,	,	PUNCT
hjic-242	5	3	veszprém	veszprém	NOUN
hjic-242	5	4	,	,	PUNCT
hjic-242	5	5	h-8201	h-8201	PROPN
hjic-242	5	6	,	,	PUNCT
hjic-242	5	7	hungary	hungary	PROPN
hjic-242	5	8	e	e	NOUN
hjic-242	5	9	-	-	NOUN
hjic-242	5	10	mail	mail	NOUN
hjic-242	5	11	:	:	PUNCT
hjic-242	5	12	leitolda@almos.vein.hu	leitolda@almos.vein.hu	PROPN
hjic-242	5	13	university	university	PROPN
hjic-242	5	14	of	of	ADP
hjic-242	5	15	pannonia	pannonia	PROPN
hjic-242	5	16	,	,	PUNCT
hjic-242	5	17	department	department	NOUN
hjic-242	5	18	of	of	ADP
hjic-242	5	19	electrical	electrical	ADJ
hjic-242	5	20	engineering	engineering	NOUN
hjic-242	5	21	and	and	CCONJ
hjic-242	5	22	information	information	NOUN
hjic-242	5	23	systems	system	NOUN
hjic-242	5	24	,	,	PUNCT
hjic-242	5	25	p.o.b	p.o.b	NOUN
hjic-242	5	26	.	.	PUNCT
hjic-242	6	1	158	158	NUM
hjic-242	6	2	,	,	PUNCT
hjic-242	6	3	veszprém	veszprém	NOUN
hjic-242	6	4	,	,	PUNCT
hjic-242	6	5	h-8201	h-8201	PROPN
hjic-242	6	6	,	,	PUNCT
hjic-242	6	7	hungary	hungary	VERB
hjic-242	6	8	a	a	DET
hjic-242	6	9	graph	graph	NOUN
hjic-242	6	10	-	-	PUNCT
hjic-242	6	11	theoretical	theoretical	ADJ
hjic-242	6	12	method	method	NOUN
hjic-242	6	13	for	for	ADP
hjic-242	6	14	the	the	DET
hjic-242	6	15	structural	structural	ADJ
hjic-242	6	16	analysis	analysis	NOUN
hjic-242	6	17	of	of	ADP
hjic-242	6	18	dynamic	dynamic	ADJ
hjic-242	6	19	lumped	lump	VERB
hjic-242	6	20	process	process	NOUN
hjic-242	6	21	models	model	NOUN
hjic-242	6	22	described	describe	VERB
hjic-242	6	23	by	by	ADP
hjic-242	6	24	differential	differential	ADJ
hjic-242	6	25	and	and	CCONJ
hjic-242	6	26	algebraic	algebraic	ADJ
hjic-242	6	27	equations	equation	NOUN
hjic-242	6	28	(	(	PUNCT
hjic-242	6	29	daes	daes	PROPN
hjic-242	6	30	)	)	PUNCT
hjic-242	6	31	is	be	AUX
hjic-242	6	32	applied	apply	VERB
hjic-242	6	33	in	in	ADP
hjic-242	6	34	this	this	DET
hjic-242	6	35	paper	paper	NOUN
hjic-242	6	36	in	in	ADP
hjic-242	6	37	order	order	NOUN
hjic-242	6	38	to	to	PART
hjic-242	6	39	determine	determine	VERB
hjic-242	6	40	the	the	DET
hjic-242	6	41	most	most	ADV
hjic-242	6	42	important	important	ADJ
hjic-242	6	43	solvability	solvability	NOUN
hjic-242	6	44	properties	property	NOUN
hjic-242	6	45	(	(	PUNCT
hjic-242	6	46	degree	degree	NOUN
hjic-242	6	47	of	of	ADP
hjic-242	6	48	freedom	freedom	NOUN
hjic-242	6	49	,	,	PUNCT
hjic-242	6	50	structural	structural	ADJ
hjic-242	6	51	solvability	solvability	NOUN
hjic-242	6	52	,	,	PUNCT
hjic-242	6	53	model	model	NOUN
hjic-242	6	54	decomposition	decomposition	NOUN
hjic-242	6	55	,	,	PUNCT
hjic-242	6	56	dynamic	dynamic	ADJ
hjic-242	6	57	degree	degree	NOUN
hjic-242	6	58	of	of	ADP
hjic-242	6	59	freedom	freedom	NOUN
hjic-242	6	60	,	,	PUNCT
hjic-242	6	61	differential	differential	ADJ
hjic-242	6	62	index	index	NOUN
hjic-242	6	63	,	,	PUNCT
hjic-242	6	64	e.g.	e.g.	ADV
hjic-242	6	65	)	)	PUNCT
hjic-242	6	66	of	of	ADP
hjic-242	6	67	these	these	DET
hjic-242	6	68	models	model	NOUN
hjic-242	6	69	by	by	ADP
hjic-242	6	70	using	use	VERB
hjic-242	6	71	the	the	DET
hjic-242	6	72	so	so	ADV
hjic-242	6	73	-	-	PUNCT
hjic-242	6	74	called	call	VERB
hjic-242	6	75	dynamic	dynamic	ADJ
hjic-242	6	76	representation	representation	NOUN
hjic-242	6	77	graph	graph	NOUN
hjic-242	6	78	.	.	PUNCT
hjic-242	7	1	the	the	DET
hjic-242	7	2	structure	structure	NOUN
hjic-242	7	3	of	of	ADP
hjic-242	7	4	the	the	DET
hjic-242	7	5	dynamic	dynamic	ADJ
hjic-242	7	6	representation	representation	NOUN
hjic-242	7	7	graph	graph	NOUN
hjic-242	7	8	is	be	AUX
hjic-242	7	9	suitable	suitable	ADJ
hjic-242	7	10	for	for	ADP
hjic-242	7	11	the	the	DET
hjic-242	7	12	determination	determination	NOUN
hjic-242	7	13	of	of	ADP
hjic-242	7	14	the	the	DET
hjic-242	7	15	mentioned	mention	VERB
hjic-242	7	16	solvability	solvability	NOUN
hjic-242	7	17	properties	property	NOUN
hjic-242	7	18	.	.	PUNCT
hjic-242	8	1	the	the	DET
hjic-242	8	2	most	most	ADV
hjic-242	8	3	common	common	ADJ
hjic-242	8	4	methods	method	NOUN
hjic-242	8	5	in	in	ADP
hjic-242	8	6	the	the	DET
hjic-242	8	7	modelling	modelling	NOUN
hjic-242	8	8	practice	practice	NOUN
hjic-242	8	9	for	for	ADP
hjic-242	8	10	the	the	DET
hjic-242	8	11	construction	construction	NOUN
hjic-242	8	12	of	of	ADP
hjic-242	8	13	models	model	NOUN
hjic-242	8	14	of	of	ADP
hjic-242	8	15	complex	complex	ADJ
hjic-242	8	16	systems	system	NOUN
hjic-242	8	17	are	be	AUX
hjic-242	8	18	the	the	DET
hjic-242	8	19	union	union	NOUN
hjic-242	8	20	of	of	ADP
hjic-242	8	21	submodels	submodel	NOUN
hjic-242	8	22	and	and	CCONJ
hjic-242	8	23	hierarchical	hierarchical	ADJ
hjic-242	8	24	modelling	modelling	NOUN
hjic-242	8	25	.	.	PUNCT
hjic-242	9	1	our	our	PRON
hjic-242	9	2	goal	goal	NOUN
hjic-242	9	3	is	be	AUX
hjic-242	9	4	to	to	PART
hjic-242	9	5	investigate	investigate	VERB
hjic-242	9	6	the	the	DET
hjic-242	9	7	effect	effect	NOUN
hjic-242	9	8	of	of	ADP
hjic-242	9	9	the	the	DET
hjic-242	9	10	model	model	PROPN
hjic-242	9	11	union	union	PROPN
hjic-242	9	12	to	to	ADP
hjic-242	9	13	the	the	DET
hjic-242	9	14	solvability	solvability	NOUN
hjic-242	9	15	properties	property	NOUN
hjic-242	9	16	,	,	PUNCT
hjic-242	9	17	especially	especially	ADV
hjic-242	9	18	to	to	ADP
hjic-242	9	19	the	the	DET
hjic-242	9	20	differential	differential	ADJ
hjic-242	9	21	index	index	NOUN
hjic-242	9	22	.	.	PUNCT
hjic-242	10	1	we	we	PRON
hjic-242	10	2	show	show	VERB
hjic-242	10	3	how	how	SCONJ
hjic-242	10	4	the	the	DET
hjic-242	10	5	representation	representation	NOUN
hjic-242	10	6	graph	graph	NOUN
hjic-242	10	7	of	of	ADP
hjic-242	10	8	a	a	DET
hjic-242	10	9	complex	complex	ADJ
hjic-242	10	10	model	model	NOUN
hjic-242	10	11	can	can	AUX
hjic-242	10	12	be	be	AUX
hjic-242	10	13	built	build	VERB
hjic-242	10	14	up	up	ADP
hjic-242	10	15	from	from	ADP
hjic-242	10	16	the	the	DET
hjic-242	10	17	representation	representation	NOUN
hjic-242	10	18	graphs	graph	NOUN
hjic-242	10	19	of	of	ADP
hjic-242	10	20	submodels	submodel	NOUN
hjic-242	10	21	.	.	PUNCT
hjic-242	11	1	the	the	DET
hjic-242	11	2	effect	effect	NOUN
hjic-242	11	3	of	of	ADP
hjic-242	11	4	the	the	DET
hjic-242	11	5	structure	structure	NOUN
hjic-242	11	6	of	of	ADP
hjic-242	11	7	submodels	submodel	NOUN
hjic-242	11	8	and	and	CCONJ
hjic-242	11	9	their	their	PRON
hjic-242	11	10	joining	join	VERB
hjic-242	11	11	points	point	NOUN
hjic-242	11	12	to	to	ADP
hjic-242	11	13	the	the	DET
hjic-242	11	14	structure	structure	NOUN
hjic-242	11	15	of	of	ADP
hjic-242	11	16	the	the	DET
hjic-242	11	17	complex	complex	ADJ
hjic-242	11	18	graph	graph	NOUN
hjic-242	11	19	and	and	CCONJ
hjic-242	11	20	the	the	DET
hjic-242	11	21	conclusions	conclusion	NOUN
hjic-242	11	22	drawn	draw	VERB
hjic-242	11	23	from	from	ADP
hjic-242	11	24	the	the	DET
hjic-242	11	25	complex	complex	ADJ
hjic-242	11	26	graph	graph	NOUN
hjic-242	11	27	structure	structure	NOUN
hjic-242	11	28	to	to	ADP
hjic-242	11	29	the	the	DET
hjic-242	11	30	solvability	solvability	NOUN
hjic-242	11	31	properties	property	NOUN
hjic-242	11	32	are	be	AUX
hjic-242	11	33	also	also	ADV
hjic-242	11	34	investigated	investigate	VERB
hjic-242	11	35	.	.	PUNCT
hjic-242	12	1	the	the	DET
hjic-242	12	2	representation	representation	NOUN
hjic-242	12	3	graph	graph	NOUN
hjic-242	12	4	of	of	ADP
hjic-242	12	5	the	the	DET
hjic-242	12	6	complex	complex	ADJ
hjic-242	12	7	model	model	NOUN
hjic-242	12	8	can	can	AUX
hjic-242	12	9	be	be	AUX
hjic-242	12	10	easily	easily	ADV
hjic-242	12	11	built	build	VERB
hjic-242	12	12	up	up	ADP
hjic-242	12	13	from	from	ADP
hjic-242	12	14	the	the	DET
hjic-242	12	15	representation	representation	NOUN
hjic-242	12	16	graphs	graph	NOUN
hjic-242	12	17	of	of	ADP
hjic-242	12	18	the	the	DET
hjic-242	12	19	simple	simple	ADJ
hjic-242	12	20	models	model	NOUN
hjic-242	12	21	according	accord	VERB
hjic-242	12	22	to	to	ADP
hjic-242	12	23	the	the	DET
hjic-242	12	24	linking	linking	NOUN
hjic-242	12	25	of	of	ADP
hjic-242	12	26	the	the	DET
hjic-242	12	27	technological	technological	ADJ
hjic-242	12	28	subsystems	subsystem	NOUN
hjic-242	12	29	.	.	PUNCT
hjic-242	13	1	if	if	SCONJ
hjic-242	13	2	one	one	NUM
hjic-242	13	3	of	of	ADP
hjic-242	13	4	the	the	DET
hjic-242	13	5	submodels	submodel	NOUN
hjic-242	13	6	has	have	VERB
hjic-242	13	7	greater	great	ADJ
hjic-242	13	8	than	than	ADP
hjic-242	13	9	one	one	NUM
hjic-242	13	10	differential	differential	ADJ
hjic-242	13	11	index	index	NOUN
hjic-242	13	12	then	then	ADV
hjic-242	13	13	the	the	DET
hjic-242	13	14	under	under	ADJ
hjic-242	13	15	and	and	CCONJ
hjic-242	13	16	overspecified	overspecified	ADJ
hjic-242	13	17	subgraphs	subgraph	NOUN
hjic-242	13	18	referring	refer	VERB
hjic-242	13	19	to	to	ADP
hjic-242	13	20	this	this	DET
hjic-242	13	21	higher	high	ADJ
hjic-242	13	22	index	index	NOUN
hjic-242	13	23	can	can	AUX
hjic-242	13	24	be	be	AUX
hjic-242	13	25	found	find	VERB
hjic-242	13	26	in	in	ADP
hjic-242	13	27	the	the	DET
hjic-242	13	28	representation	representation	NOUN
hjic-242	13	29	graph	graph	NOUN
hjic-242	13	30	of	of	ADP
hjic-242	13	31	the	the	DET
hjic-242	13	32	complex	complex	ADJ
hjic-242	13	33	model	model	NOUN
hjic-242	13	34	,	,	PUNCT
hjic-242	13	35	too	too	ADV
hjic-242	13	36	.	.	PUNCT
hjic-242	14	1	the	the	DET
hjic-242	14	2	change	change	NOUN
hjic-242	14	3	in	in	ADP
hjic-242	14	4	the	the	DET
hjic-242	14	5	relative	relative	ADJ
hjic-242	14	6	position	position	NOUN
hjic-242	14	7	of	of	ADP
hjic-242	14	8	the	the	DET
hjic-242	14	9	underspecified	underspecified	ADJ
hjic-242	14	10	and	and	CCONJ
hjic-242	14	11	the	the	DET
hjic-242	14	12	overspecified	overspecified	ADJ
hjic-242	14	13	subgraphs	subgraph	NOUN
hjic-242	14	14	has	have	VERB
hjic-242	14	15	an	an	DET
hjic-242	14	16	effect	effect	NOUN
hjic-242	14	17	to	to	ADP
hjic-242	14	18	the	the	DET
hjic-242	14	19	value	value	NOUN
hjic-242	14	20	of	of	ADP
hjic-242	14	21	differential	differential	ADJ
hjic-242	14	22	index	index	NOUN
hjic-242	14	23	.	.	PUNCT
hjic-242	15	1	if	if	SCONJ
hjic-242	15	2	these	these	DET
hjic-242	15	3	subgraphs	subgraph	NOUN
hjic-242	15	4	move	move	VERB
hjic-242	15	5	further	far	ADV
hjic-242	15	6	from	from	ADP
hjic-242	15	7	their	their	PRON
hjic-242	15	8	original	original	ADJ
hjic-242	15	9	positions	position	NOUN
hjic-242	15	10	the	the	DET
hjic-242	15	11	value	value	NOUN
hjic-242	15	12	of	of	ADP
hjic-242	15	13	the	the	DET
hjic-242	15	14	differential	differential	ADJ
hjic-242	15	15	index	index	NOUN
hjic-242	15	16	increases	increase	NOUN
hjic-242	15	17	.	.	PUNCT
hjic-242	16	1	if	if	SCONJ
hjic-242	16	2	their	their	PRON
hjic-242	16	3	relative	relative	ADJ
hjic-242	16	4	positions	position	NOUN
hjic-242	16	5	do	do	AUX
hjic-242	16	6	not	not	PART
hjic-242	16	7	change	change	VERB
hjic-242	16	8	during	during	ADP
hjic-242	16	9	the	the	DET
hjic-242	16	10	built	build	VERB
hjic-242	16	11	up	up	ADP
hjic-242	16	12	process	process	NOUN
hjic-242	16	13	then	then	ADV
hjic-242	16	14	the	the	DET
hjic-242	16	15	value	value	NOUN
hjic-242	16	16	of	of	ADP
hjic-242	16	17	the	the	DET
hjic-242	16	18	differential	differential	ADJ
hjic-242	16	19	index	index	NOUN
hjic-242	16	20	of	of	ADP
hjic-242	16	21	the	the	DET
hjic-242	16	22	complex	complex	ADJ
hjic-242	16	23	system	system	NOUN
hjic-242	16	24	is	be	AUX
hjic-242	16	25	equal	equal	ADJ
hjic-242	16	26	to	to	ADP
hjic-242	16	27	the	the	DET
hjic-242	16	28	value	value	NOUN
hjic-242	16	29	of	of	ADP
hjic-242	16	30	the	the	DET
hjic-242	16	31	differential	differential	ADJ
hjic-242	16	32	index	index	NOUN
hjic-242	16	33	of	of	ADP
hjic-242	16	34	the	the	DET
hjic-242	16	35	subsystem	subsystem	NOUN
hjic-242	16	36	having	have	VERB
hjic-242	16	37	the	the	DET
hjic-242	16	38	higher	high	ADJ
hjic-242	16	39	value	value	NOUN
hjic-242	16	40	.	.	PUNCT
hjic-242	17	1	keywords	keyword	NOUN
hjic-242	17	2	:	:	PUNCT
hjic-242	17	3	process	process	NOUN
hjic-242	17	4	models	model	NOUN
hjic-242	17	5	,	,	PUNCT
hjic-242	17	6	model	model	NOUN
hjic-242	17	7	composition	composition	NOUN
hjic-242	17	8	,	,	PUNCT
hjic-242	17	9	dae	dae	NOUN
hjic-242	17	10	-	-	PUNCT
hjic-242	17	11	models	model	NOUN
hjic-242	17	12	,	,	PUNCT
hjic-242	17	13	differential	differential	ADJ
hjic-242	17	14	index	index	NOUN
hjic-242	17	15	,	,	PUNCT
hjic-242	17	16	solvability	solvability	NOUN
hjic-242	17	17	,	,	PUNCT
hjic-242	17	18	structural	structural	ADJ
hjic-242	17	19	analysis	analysis	NOUN
hjic-242	17	20	introduction	introduction	NOUN
hjic-242	17	21	the	the	DET
hjic-242	17	22	structural	structural	ADJ
hjic-242	17	23	analysis	analysis	NOUN
hjic-242	17	24	of	of	ADP
hjic-242	17	25	dynamic	dynamic	ADJ
hjic-242	17	26	lumped	lump	VERB
hjic-242	17	27	process	process	NOUN
hjic-242	17	28	models	model	NOUN
hjic-242	17	29	forms	form	VERB
hjic-242	17	30	an	an	DET
hjic-242	17	31	important	important	ADJ
hjic-242	17	32	step	step	NOUN
hjic-242	17	33	in	in	ADP
hjic-242	17	34	the	the	DET
hjic-242	17	35	model	model	NOUN
hjic-242	17	36	building	building	NOUN
hjic-242	17	37	procedure	procedure	NOUN
hjic-242	17	38	[	[	X
hjic-242	17	39	1	1	X
hjic-242	17	40	]	]	PUNCT
hjic-242	17	41	and	and	CCONJ
hjic-242	17	42	it	it	PRON
hjic-242	17	43	is	be	AUX
hjic-242	17	44	used	use	VERB
hjic-242	17	45	for	for	ADP
hjic-242	17	46	the	the	DET
hjic-242	17	47	determination	determination	NOUN
hjic-242	17	48	of	of	ADP
hjic-242	17	49	the	the	DET
hjic-242	17	50	solvability	solvability	NOUN
hjic-242	17	51	properties	property	NOUN
hjic-242	17	52	of	of	ADP
hjic-242	17	53	the	the	DET
hjic-242	17	54	model	model	NOUN
hjic-242	17	55	,	,	PUNCT
hjic-242	17	56	too	too	ADV
hjic-242	17	57	.	.	PUNCT
hjic-242	18	1	this	this	DET
hjic-242	18	2	analysis	analysis	NOUN
hjic-242	18	3	includes	include	VERB
hjic-242	18	4	the	the	DET
hjic-242	18	5	determination	determination	NOUN
hjic-242	18	6	of	of	ADP
hjic-242	18	7	the	the	DET
hjic-242	18	8	degree	degree	NOUN
hjic-242	18	9	of	of	ADP
hjic-242	18	10	freedom	freedom	NOUN
hjic-242	18	11	,	,	PUNCT
hjic-242	18	12	structural	structural	ADJ
hjic-242	18	13	solvability	solvability	NOUN
hjic-242	18	14	,	,	PUNCT
hjic-242	18	15	differential	differential	ADJ
hjic-242	18	16	index	index	NOUN
hjic-242	18	17	and	and	CCONJ
hjic-242	18	18	the	the	DET
hjic-242	18	19	dynamic	dynamic	ADJ
hjic-242	18	20	degrees	degree	NOUN
hjic-242	18	21	of	of	ADP
hjic-242	18	22	freedom	freedom	NOUN
hjic-242	18	23	.	.	PUNCT
hjic-242	19	1	as	as	ADP
hjic-242	19	2	a	a	DET
hjic-242	19	3	result	result	NOUN
hjic-242	19	4	of	of	ADP
hjic-242	19	5	the	the	DET
hjic-242	19	6	analysis	analysis	NOUN
hjic-242	19	7	,	,	PUNCT
hjic-242	19	8	the	the	DET
hjic-242	19	9	decomposition	decomposition	NOUN
hjic-242	19	10	of	of	ADP
hjic-242	19	11	the	the	DET
hjic-242	19	12	model	model	NOUN
hjic-242	19	13	is	be	AUX
hjic-242	19	14	obtained	obtain	VERB
hjic-242	19	15	and	and	CCONJ
hjic-242	19	16	the	the	DET
hjic-242	19	17	calculation	calculation	NOUN
hjic-242	19	18	path	path	NOUN
hjic-242	19	19	can	can	AUX
hjic-242	19	20	be	be	AUX
hjic-242	19	21	determined	determine	VERB
hjic-242	19	22	.	.	PUNCT
hjic-242	20	1	this	this	DET
hjic-242	20	2	way	way	NOUN
hjic-242	20	3	the	the	DET
hjic-242	20	4	appropriate	appropriate	ADJ
hjic-242	20	5	numerical	numerical	ADJ
hjic-242	20	6	method	method	NOUN
hjic-242	20	7	for	for	ADP
hjic-242	20	8	solving	solve	VERB
hjic-242	20	9	the	the	DET
hjic-242	20	10	model	model	NOUN
hjic-242	20	11	can	can	AUX
hjic-242	20	12	be	be	AUX
hjic-242	20	13	chosen	choose	VERB
hjic-242	20	14	efficiently	efficiently	ADV
hjic-242	20	15	.	.	PUNCT
hjic-242	21	1	moreover	moreover	ADV
hjic-242	21	2	,	,	PUNCT
hjic-242	21	3	advice	advice	NOUN
hjic-242	21	4	on	on	ADP
hjic-242	21	5	how	how	SCONJ
hjic-242	21	6	to	to	PART
hjic-242	21	7	improve	improve	VERB
hjic-242	21	8	the	the	DET
hjic-242	21	9	computational	computational	ADJ
hjic-242	21	10	properties	property	NOUN
hjic-242	21	11	of	of	ADP
hjic-242	21	12	the	the	DET
hjic-242	21	13	model	model	NOUN
hjic-242	21	14	by	by	ADP
hjic-242	21	15	modifying	modify	VERB
hjic-242	21	16	its	its	PRON
hjic-242	21	17	form	form	NOUN
hjic-242	21	18	or	or	CCONJ
hjic-242	21	19	its	its	PRON
hjic-242	21	20	specification	specification	NOUN
hjic-242	21	21	can	can	AUX
hjic-242	21	22	also	also	ADV
hjic-242	21	23	be	be	AUX
hjic-242	21	24	given	give	VERB
hjic-242	21	25	.	.	PUNCT
hjic-242	22	1	effective	effective	ADJ
hjic-242	22	2	graph	graph	NOUN
hjic-242	22	3	-	-	PUNCT
hjic-242	22	4	theoretical	theoretical	ADJ
hjic-242	22	5	methods	method	NOUN
hjic-242	22	6	have	have	AUX
hjic-242	22	7	been	be	AUX
hjic-242	22	8	proposed	propose	VERB
hjic-242	22	9	in	in	ADP
hjic-242	22	10	the	the	DET
hjic-242	22	11	literature	literature	NOUN
hjic-242	22	12	[	[	X
hjic-242	22	13	2	2	NUM
hjic-242	22	14	,	,	PUNCT
hjic-242	22	15	3	3	NUM
hjic-242	22	16	]	]	PUNCT
hjic-242	22	17	based	base	VERB
hjic-242	22	18	on	on	ADP
hjic-242	22	19	the	the	DET
hjic-242	22	20	analysis	analysis	NOUN
hjic-242	22	21	tools	tool	NOUN
hjic-242	22	22	developed	develop	VERB
hjic-242	22	23	by	by	ADP
hjic-242	22	24	[	[	X
hjic-242	22	25	4	4	NUM
hjic-242	22	26	]	]	PUNCT
hjic-242	22	27	,	,	PUNCT
hjic-242	22	28	for	for	ADP
hjic-242	22	29	the	the	DET
hjic-242	22	30	determination	determination	NOUN
hjic-242	22	31	of	of	ADP
hjic-242	22	32	the	the	DET
hjic-242	22	33	most	most	ADV
hjic-242	22	34	important	important	ADJ
hjic-242	22	35	solvability	solvability	NOUN
hjic-242	22	36	property	property	NOUN
hjic-242	22	37	of	of	ADP
hjic-242	22	38	lumped	lump	VERB
hjic-242	22	39	dynamic	dynamic	ADJ
hjic-242	22	40	models	model	NOUN
hjic-242	22	41	:	:	PUNCT
hjic-242	22	42	the	the	DET
hjic-242	22	43	differential	differential	ADJ
hjic-242	22	44	index	index	NOUN
hjic-242	22	45	.	.	PUNCT
hjic-242	23	1	the	the	DET
hjic-242	23	2	properties	property	NOUN
hjic-242	23	3	of	of	ADP
hjic-242	23	4	the	the	DET
hjic-242	23	5	dynamic	dynamic	ADJ
hjic-242	23	6	representation	representation	NOUN
hjic-242	23	7	graph	graph	NOUN
hjic-242	23	8	of	of	ADP
hjic-242	23	9	process	process	NOUN
hjic-242	23	10	models	model	NOUN
hjic-242	23	11	described	describe	VERB
hjic-242	23	12	by	by	ADP
hjic-242	23	13	semi	semi	ADJ
hjic-242	23	14	-	-	ADJ
hjic-242	23	15	explicit	explicit	ADJ
hjic-242	23	16	dae	dae	NOUN
hjic-242	23	17	-	-	PUNCT
hjic-242	23	18	systems	system	NOUN
hjic-242	23	19	have	have	AUX
hjic-242	23	20	also	also	ADV
hjic-242	23	21	been	be	AUX
hjic-242	23	22	analysed	analyse	VERB
hjic-242	23	23	there	there	ADV
hjic-242	23	24	in	in	ADP
hjic-242	23	25	case	case	NOUN
hjic-242	23	26	of	of	ADP
hjic-242	23	27	index	index	NOUN
hjic-242	23	28	1	1	NUM
hjic-242	23	29	and	and	CCONJ
hjic-242	23	30	higher	high	ADJ
hjic-242	23	31	index	index	NOUN
hjic-242	23	32	models	model	NOUN
hjic-242	23	33	.	.	PUNCT
hjic-242	24	1	beside	beside	ADP
hjic-242	24	2	the	the	DET
hjic-242	24	3	algorithm	algorithm	NOUN
hjic-242	24	4	of	of	ADP
hjic-242	24	5	determining	determine	VERB
hjic-242	24	6	the	the	DET
hjic-242	24	7	differential	differential	ADJ
hjic-242	24	8	index	index	NOUN
hjic-242	24	9	by	by	ADP
hjic-242	24	10	using	use	VERB
hjic-242	24	11	the	the	DET
hjic-242	24	12	representation	representation	NOUN
hjic-242	24	13	graph	graph	NOUN
hjic-242	24	14	,	,	PUNCT
hjic-242	24	15	a	a	DET
hjic-242	24	16	model	model	NOUN
hjic-242	24	17	modification	modification	NOUN
hjic-242	24	18	method	method	NOUN
hjic-242	24	19	has	have	AUX
hjic-242	24	20	also	also	ADV
hjic-242	24	21	been	be	AUX
hjic-242	24	22	proposed	propose	VERB
hjic-242	24	23	in	in	ADP
hjic-242	24	24	the	the	DET
hjic-242	24	25	literature	literature	NOUN
hjic-242	24	26	,	,	PUNCT
hjic-242	24	27	which	which	PRON
hjic-242	24	28	results	result	VERB
hjic-242	24	29	in	in	ADP
hjic-242	24	30	a	a	DET
hjic-242	24	31	structurally	structurally	ADV
hjic-242	24	32	solvable	solvable	ADJ
hjic-242	24	33	model	model	NOUN
hjic-242	24	34	even	even	ADV
hjic-242	24	35	in	in	ADP
hjic-242	24	36	the	the	DET
hjic-242	24	37	case	case	NOUN
hjic-242	24	38	of	of	ADP
hjic-242	24	39	higher	high	ADJ
hjic-242	24	40	index	index	NOUN
hjic-242	24	41	models	model	NOUN
hjic-242	24	42	[	[	X
hjic-242	24	43	2	2	NUM
hjic-242	24	44	]	]	PUNCT
hjic-242	24	45	.	.	PUNCT
hjic-242	25	1	basic	basic	ADJ
hjic-242	25	2	notions	notion	NOUN
hjic-242	25	3	structural	structural	ADJ
hjic-242	25	4	solvability	solvability	NOUN
hjic-242	25	5	as	as	ADP
hjic-242	25	6	a	a	DET
hjic-242	25	7	first	first	ADJ
hjic-242	25	8	step	step	NOUN
hjic-242	25	9	,	,	PUNCT
hjic-242	25	10	we	we	PRON
hjic-242	25	11	consider	consider	VERB
hjic-242	25	12	a	a	DET
hjic-242	25	13	system	system	NOUN
hjic-242	25	14	of	of	ADP
hjic-242	25	15	linear	linear	PROPN
hjic-242	25	16	or	or	CCONJ
hjic-242	25	17	nonlinear	nonlinear	ADJ
hjic-242	25	18	algebraic	algebraic	ADJ
hjic-242	25	19	equations	equation	NOUN
hjic-242	25	20	in	in	ADP
hjic-242	25	21	its	its	PRON
hjic-242	25	22	so	so	ADV
hjic-242	25	23	called	call	VERB
hjic-242	25	24	standard	standard	ADJ
hjic-242	25	25	form	form	NOUN
hjic-242	25	26	[	[	X
hjic-242	25	27	4	4	NUM
hjic-242	25	28	]	]	PUNCT
hjic-242	25	29	:	:	PUNCT
hjic-242	25	30	yi	yi	PROPN
hjic-242	25	31	=	=	SYM
hjic-242	25	32	fi	fi	NOUN
hjic-242	25	33	(	(	PUNCT
hjic-242	25	34	x	x	NOUN
hjic-242	25	35	,	,	PUNCT
hjic-242	25	36	u	u	NOUN
hjic-242	25	37	)	)	PUNCT
hjic-242	25	38	,	,	PUNCT
hjic-242	25	39	i	i	PRON
hjic-242	25	40	=	=	NOUN
hjic-242	25	41	1	1	NUM
hjic-242	25	42	,	,	PUNCT
hjic-242	25	43	…	…	PUNCT
hjic-242	25	44	,	,	PUNCT
hjic-242	25	45	m	m	VERB
hjic-242	25	46	uk	uk	PROPN
hjic-242	25	47	=	=	SYM
hjic-242	25	48	gk	gk	PROPN
hjic-242	25	49	(	(	PUNCT
hjic-242	25	50	x	x	NOUN
hjic-242	25	51	,	,	PUNCT
hjic-242	25	52	u	u	NOUN
hjic-242	25	53	)	)	PUNCT
hjic-242	25	54	,	,	PUNCT
hjic-242	25	55	k	k	X
hjic-242	25	56	=	=	SYM
hjic-242	25	57	1	1	NUM
hjic-242	25	58	,	,	PUNCT
hjic-242	25	59	…	…	PUNCT
hjic-242	25	60	,	,	PUNCT
hjic-242	25	61	k	k	PROPN
hjic-242	25	62	where	where	SCONJ
hjic-242	25	63	xj	xj	PROPN
hjic-242	25	64	(	(	PUNCT
hjic-242	25	65	j	j	PROPN
hjic-242	25	66	=	=	SYM
hjic-242	25	67	1	1	NUM
hjic-242	25	68	,	,	PUNCT
hjic-242	25	69	…	…	PUNCT
hjic-242	25	70	,	,	PUNCT
hjic-242	25	71	n	n	CCONJ
hjic-242	25	72	)	)	PUNCT
hjic-242	25	73	and	and	CCONJ
hjic-242	25	74	uk	uk	PROPN
hjic-242	25	75	(	(	PUNCT
hjic-242	25	76	k	k	NOUN
hjic-242	25	77	=	=	SYM
hjic-242	25	78	1	1	NUM
hjic-242	25	79	,	,	PUNCT
hjic-242	25	80	…	…	PUNCT
hjic-242	25	81	,	,	PUNCT
hjic-242	25	82	k	k	NOUN
hjic-242	25	83	)	)	PUNCT
hjic-242	25	84	are	be	AUX
hjic-242	25	85	unknowns	unknown	NOUN
hjic-242	25	86	,	,	PUNCT
hjic-242	25	87	yi	yi	PROPN
hjic-242	25	88	(	(	PUNCT
hjic-242	25	89	i	i	NOUN
hjic-242	25	90	=	=	NOUN
hjic-242	25	91	1	1	NUM
hjic-242	25	92	,	,	PUNCT
hjic-242	25	93	…	…	PUNCT
hjic-242	25	94	,	,	PUNCT
hjic-242	25	95	m	m	VERB
hjic-242	25	96	)	)	PUNCT
hjic-242	25	97	are	be	AUX
hjic-242	25	98	known	know	VERB
hjic-242	25	99	parameters	parameter	NOUN
hjic-242	25	100	,	,	PUNCT
hjic-242	25	101	fi	fi	INTJ
hjic-242	25	102	(	(	PUNCT
hjic-242	25	103	i	i	NOUN
hjic-242	25	104	=	=	NOUN
hjic-242	25	105	1	1	NUM
hjic-242	25	106	,	,	PUNCT
hjic-242	25	107	…	…	PUNCT
hjic-242	25	108	,	,	PUNCT
hjic-242	25	109	m	m	NOUN
hjic-242	25	110	)	)	PUNCT
hjic-242	25	111	and	and	CCONJ
hjic-242	25	112	gk	gk	PROPN
hjic-242	25	113	(	(	PUNCT
hjic-242	25	114	k	k	NOUN
hjic-242	25	115	=	=	SYM
hjic-242	25	116	1	1	NUM
hjic-242	25	117	,	,	PUNCT
hjic-242	25	118	…	…	PUNCT
hjic-242	25	119	,	,	PUNCT
hjic-242	25	120	k	k	NOUN
hjic-242	25	121	)	)	PUNCT
hjic-242	25	122	are	be	AUX
hjic-242	25	123	assumed	assume	VERB
hjic-242	25	124	to	to	PART
hjic-242	25	125	be	be	AUX
hjic-242	25	126	sufficiently	sufficiently	ADV
hjic-242	25	127	smooth	smooth	ADJ
hjic-242	25	128	real	real	ADV
hjic-242	25	129	-	-	PUNCT
hjic-242	25	130	valued	value	VERB
hjic-242	25	131	functions	function	NOUN
hjic-242	25	132	.	.	PUNCT
hjic-242	26	1	the	the	DET
hjic-242	26	2	system	system	NOUN
hjic-242	26	3	of	of	ADP
hjic-242	26	4	equations	equation	NOUN
hjic-242	26	5	146	146	NUM
hjic-242	26	6	above	above	ADV
hjic-242	26	7	is	be	AUX
hjic-242	26	8	structurally	structurally	ADV
hjic-242	26	9	solvable	solvable	ADJ
hjic-242	26	10	,	,	PUNCT
hjic-242	26	11	if	if	SCONJ
hjic-242	26	12	the	the	DET
hjic-242	26	13	jacobian	jacobian	ADJ
hjic-242	26	14	matrix	matrix	NOUN
hjic-242	26	15	j(x	j(x	PROPN
hjic-242	26	16	,	,	PUNCT
hjic-242	26	17	u	u	NOUN
hjic-242	26	18	)	)	PUNCT
hjic-242	26	19	referring	refer	VERB
hjic-242	26	20	to	to	ADP
hjic-242	26	21	the	the	DET
hjic-242	26	22	above	above	ADJ
hjic-242	26	23	model	model	NOUN
hjic-242	26	24	is	be	AUX
hjic-242	26	25	non	non	ADJ
hjic-242	26	26	-	-	ADJ
hjic-242	26	27	singular	singular	ADJ
hjic-242	26	28	.	.	PUNCT
hjic-242	27	1	consider	consider	VERB
hjic-242	27	2	a	a	DET
hjic-242	27	3	system	system	NOUN
hjic-242	27	4	of	of	ADP
hjic-242	27	5	equations	equation	NOUN
hjic-242	27	6	in	in	ADP
hjic-242	27	7	standard	standard	ADJ
hjic-242	27	8	form	form	NOUN
hjic-242	27	9	.	.	PUNCT
hjic-242	28	1	we	we	PRON
hjic-242	28	2	construct	construct	VERB
hjic-242	28	3	a	a	DET
hjic-242	28	4	directed	direct	VERB
hjic-242	28	5	graph	graph	NOUN
hjic-242	28	6	to	to	PART
hjic-242	28	7	represent	represent	VERB
hjic-242	28	8	the	the	DET
hjic-242	28	9	structure	structure	NOUN
hjic-242	28	10	of	of	ADP
hjic-242	28	11	the	the	DET
hjic-242	28	12	set	set	NOUN
hjic-242	28	13	of	of	ADP
hjic-242	28	14	equations	equation	NOUN
hjic-242	28	15	in	in	ADP
hjic-242	28	16	the	the	DET
hjic-242	28	17	following	following	ADJ
hjic-242	28	18	way	way	NOUN
hjic-242	28	19	.	.	PUNCT
hjic-242	29	1	the	the	DET
hjic-242	29	2	vertex	vertex	NOUN
hjic-242	29	3	-	-	PUNCT
hjic-242	29	4	set	set	NOUN
hjic-242	29	5	corresponding	corresponding	NOUN
hjic-242	29	6	to	to	ADP
hjic-242	29	7	unknowns	unknown	NOUN
hjic-242	29	8	and	and	CCONJ
hjic-242	29	9	parameters	parameter	NOUN
hjic-242	29	10	is	be	AUX
hjic-242	29	11	partitioned	partition	VERB
hjic-242	29	12	as	as	ADP
hjic-242	29	13	x	x	X
hjic-242	29	14	∪	∪	ADP
hjic-242	29	15	u	u	PROPN
hjic-242	29	16	∪	∪	PROPN
hjic-242	29	17	y	y	PROPN
hjic-242	29	18	,	,	PUNCT
hjic-242	29	19	where	where	SCONJ
hjic-242	29	20	x	x	ADP
hjic-242	29	21	=	=	PRON
hjic-242	29	22	{	{	PUNCT
hjic-242	29	23	x1	x1	PROPN
hjic-242	29	24	,	,	PUNCT
hjic-242	29	25	…	…	PUNCT
hjic-242	29	26	,	,	PUNCT
hjic-242	29	27	xn	xn	NUM
hjic-242	29	28	}	}	PUNCT
hjic-242	29	29	,	,	PUNCT
hjic-242	29	30	u	u	NOUN
hjic-242	29	31	=	=	NOUN
hjic-242	29	32	{	{	PUNCT
hjic-242	29	33	u1	u1	NOUN
hjic-242	29	34	,	,	PUNCT
hjic-242	29	35	…	…	PUNCT
hjic-242	29	36	,	,	PUNCT
hjic-242	29	37	uk	uk	PROPN
hjic-242	29	38	}	}	PUNCT
hjic-242	29	39	and	and	CCONJ
hjic-242	29	40	y	y	PROPN
hjic-242	29	41	=	=	SYM
hjic-242	29	42	{	{	PUNCT
hjic-242	29	43	y1	y1	PROPN
hjic-242	29	44	,	,	PUNCT
hjic-242	29	45	…	…	PUNCT
hjic-242	29	46	,	,	PUNCT
hjic-242	29	47	ym	ym	PROPN
hjic-242	29	48	}	}	PUNCT
hjic-242	29	49	.	.	PUNCT
hjic-242	30	1	the	the	DET
hjic-242	30	2	functional	functional	ADJ
hjic-242	30	3	dependence	dependence	NOUN
hjic-242	30	4	described	describe	VERB
hjic-242	30	5	by	by	ADP
hjic-242	30	6	an	an	DET
hjic-242	30	7	equation	equation	NOUN
hjic-242	30	8	is	be	AUX
hjic-242	30	9	expressed	express	VERB
hjic-242	30	10	by	by	ADP
hjic-242	30	11	arcs	arc	NOUN
hjic-242	30	12	coming	come	VERB
hjic-242	30	13	into	into	ADP
hjic-242	30	14	yi	yi	NOUN
hjic-242	30	15	or	or	CCONJ
hjic-242	30	16	uk	uk	PROPN
hjic-242	30	17	respectively	respectively	ADV
hjic-242	30	18	from	from	ADP
hjic-242	30	19	those	those	DET
hjic-242	30	20	xj	xj	PROPN
hjic-242	30	21	and	and	CCONJ
hjic-242	30	22	ul	ul	INTJ
hjic-242	30	23	,	,	PUNCT
hjic-242	30	24	which	which	PRON
hjic-242	30	25	appear	appear	VERB
hjic-242	30	26	on	on	ADP
hjic-242	30	27	its	its	PRON
hjic-242	30	28	right	right	ADJ
hjic-242	30	29	-	-	PUNCT
hjic-242	30	30	hand	hand	NOUN
hjic-242	30	31	side	side	NOUN
hjic-242	30	32	.	.	PUNCT
hjic-242	31	1	this	this	DET
hjic-242	31	2	graph	graph	NOUN
hjic-242	31	3	is	be	AUX
hjic-242	31	4	called	call	VERB
hjic-242	31	5	the	the	DET
hjic-242	31	6	representation	representation	NOUN
hjic-242	31	7	graph	graph	NOUN
hjic-242	31	8	of	of	ADP
hjic-242	31	9	the	the	DET
hjic-242	31	10	system	system	NOUN
hjic-242	31	11	of	of	ADP
hjic-242	31	12	equations	equation	NOUN
hjic-242	31	13	.	.	PUNCT
hjic-242	32	1	a	a	DET
hjic-242	32	2	menger	menger	NOUN
hjic-242	32	3	-	-	PUNCT
hjic-242	32	4	type	type	NOUN
hjic-242	32	5	linking	link	VERB
hjic-242	32	6	from	from	ADP
hjic-242	32	7	x	x	PUNCT
hjic-242	32	8	to	to	ADP
hjic-242	32	9	y	y	PROPN
hjic-242	32	10	is	be	AUX
hjic-242	32	11	a	a	DET
hjic-242	32	12	set	set	NOUN
hjic-242	32	13	of	of	ADP
hjic-242	32	14	pairwise	pairwise	NOUN
hjic-242	32	15	vertex	vertex	NOUN
hjic-242	32	16	-	-	PUNCT
hjic-242	32	17	disjoint	disjoint	NOUN
hjic-242	32	18	directed	direct	VERB
hjic-242	32	19	paths	path	NOUN
hjic-242	32	20	from	from	ADP
hjic-242	32	21	a	a	DET
hjic-242	32	22	vertex	vertex	NOUN
hjic-242	32	23	in	in	ADP
hjic-242	32	24	x	x	PUNCT
hjic-242	32	25	to	to	ADP
hjic-242	32	26	a	a	DET
hjic-242	32	27	vertex	vertex	NOUN
hjic-242	32	28	in	in	ADP
hjic-242	32	29	y.	y.	NOUN
hjic-242	32	30	the	the	DET
hjic-242	32	31	size	size	NOUN
hjic-242	32	32	of	of	ADP
hjic-242	32	33	a	a	DET
hjic-242	32	34	linking	linking	NOUN
hjic-242	32	35	is	be	AUX
hjic-242	32	36	the	the	DET
hjic-242	32	37	number	number	NOUN
hjic-242	32	38	of	of	ADP
hjic-242	32	39	directed	direct	VERB
hjic-242	32	40	paths	path	NOUN
hjic-242	32	41	from	from	ADP
hjic-242	32	42	x	x	PUNCT
hjic-242	32	43	to	to	ADP
hjic-242	32	44	y	y	PROPN
hjic-242	32	45	contained	contain	VERB
hjic-242	32	46	in	in	ADP
hjic-242	32	47	the	the	DET
hjic-242	32	48	linking	linking	NOUN
hjic-242	32	49	.	.	PUNCT
hjic-242	33	1	in	in	ADP
hjic-242	33	2	case	case	NOUN
hjic-242	33	3	⏐	⏐	VERB
hjic-242	33	4	x	x	SYM
hjic-242	33	5	⏐	⏐	NOUN
hjic-242	33	6	=	=	SYM
hjic-242	33	7	⏐	⏐	NOUN
hjic-242	33	8	y	y	PROPN
hjic-242	33	9	⏐	⏐	PROPN
hjic-242	33	10	,	,	PUNCT
hjic-242	33	11	(	(	PUNCT
hjic-242	33	12	m	m	NOUN
hjic-242	33	13	=	=	SYM
hjic-242	33	14	n	n	CCONJ
hjic-242	33	15	)	)	PUNCT
hjic-242	33	16	,	,	PUNCT
hjic-242	33	17	a	a	DET
hjic-242	33	18	linking	linking	NOUN
hjic-242	33	19	of	of	ADP
hjic-242	33	20	size	size	NOUN
hjic-242	33	21	⏐	⏐	NOUN
hjic-242	33	22	x	x	SYM
hjic-242	33	23	⏐	⏐	PROPN
hjic-242	33	24	is	be	AUX
hjic-242	33	25	called	call	VERB
hjic-242	33	26	a	a	DET
hjic-242	33	27	complete	complete	ADJ
hjic-242	33	28	linking	linking	NOUN
hjic-242	33	29	.	.	PUNCT
hjic-242	34	1	the	the	DET
hjic-242	34	2	graphical	graphical	ADJ
hjic-242	34	3	condition	condition	NOUN
hjic-242	34	4	of	of	ADP
hjic-242	34	5	the	the	DET
hjic-242	34	6	structural	structural	ADJ
hjic-242	34	7	solvability	solvability	NOUN
hjic-242	34	8	is	be	AUX
hjic-242	34	9	then	then	ADV
hjic-242	34	10	the	the	DET
hjic-242	34	11	following	follow	VERB
hjic-242	34	12	[	[	X
hjic-242	34	13	4	4	NUM
hjic-242	34	14	]	]	PUNCT
hjic-242	34	15	:	:	PUNCT
hjic-242	34	16	linkage	linkage	NOUN
hjic-242	34	17	theorem	theorem	VERB
hjic-242	34	18	:	:	PUNCT
hjic-242	34	19	assume	assume	VERB
hjic-242	34	20	that	that	SCONJ
hjic-242	34	21	the	the	DET
hjic-242	34	22	non	non	ADJ
hjic-242	34	23	-	-	ADJ
hjic-242	34	24	vanishing	vanishing	ADJ
hjic-242	34	25	elements	element	NOUN
hjic-242	34	26	of	of	ADP
hjic-242	34	27	partial	partial	ADJ
hjic-242	34	28	derivatives	derivative	NOUN
hjic-242	34	29	fi	fi	NOUN
hjic-242	34	30	and	and	CCONJ
hjic-242	34	31	gk	gk	NOUN
hjic-242	34	32	in	in	ADP
hjic-242	34	33	the	the	DET
hjic-242	34	34	standard	standard	ADJ
hjic-242	34	35	form	form	NOUN
hjic-242	34	36	model	model	NOUN
hjic-242	34	37	are	be	AUX
hjic-242	34	38	algebraically	algebraically	ADV
hjic-242	34	39	independent	independent	ADJ
hjic-242	34	40	over	over	ADP
hjic-242	34	41	the	the	DET
hjic-242	34	42	rational	rational	ADJ
hjic-242	34	43	number	number	NOUN
hjic-242	34	44	field	field	NOUN
hjic-242	34	45	q.	q.	NOUN
hjic-242	34	46	then	then	ADV
hjic-242	34	47	the	the	DET
hjic-242	34	48	model	model	NOUN
hjic-242	34	49	is	be	AUX
hjic-242	34	50	structurally	structurally	ADV
hjic-242	34	51	solvable	solvable	ADJ
hjic-242	34	52	if	if	SCONJ
hjic-242	34	53	and	and	CCONJ
hjic-242	34	54	only	only	ADV
hjic-242	34	55	if	if	SCONJ
hjic-242	34	56	there	there	PRON
hjic-242	34	57	exists	exist	VERB
hjic-242	34	58	a	a	DET
hjic-242	34	59	menger	menger	NOUN
hjic-242	34	60	-	-	PUNCT
hjic-242	34	61	type	type	NOUN
hjic-242	34	62	complete	complete	ADJ
hjic-242	34	63	linking	linking	NOUN
hjic-242	34	64	from	from	ADP
hjic-242	34	65	x	x	PUNCT
hjic-242	34	66	to	to	ADP
hjic-242	34	67	y	y	PROPN
hjic-242	34	68	on	on	ADP
hjic-242	34	69	the	the	DET
hjic-242	34	70	representation	representation	NOUN
hjic-242	34	71	graph	graph	NOUN
hjic-242	34	72	.	.	PUNCT
hjic-242	35	1	we	we	PRON
hjic-242	35	2	can	can	AUX
hjic-242	35	3	adapt	adapt	VERB
hjic-242	35	4	the	the	DET
hjic-242	35	5	graphical	graphical	ADJ
hjic-242	35	6	techniques	technique	NOUN
hjic-242	35	7	to	to	PART
hjic-242	35	8	daesystems	daesystem	NOUN
hjic-242	35	9	,	,	PUNCT
hjic-242	35	10	as	as	ADV
hjic-242	35	11	well	well	ADV
hjic-242	35	12	.	.	PUNCT
hjic-242	36	1	an	an	DET
hjic-242	36	2	ordinary	ordinary	ADJ
hjic-242	36	3	differential	differential	ADJ
hjic-242	36	4	equation	equation	NOUN
hjic-242	36	5	of	of	ADP
hjic-242	36	6	a	a	DET
hjic-242	36	7	dae	dae	NOUN
hjic-242	36	8	-	-	PUNCT
hjic-242	36	9	system	system	NOUN
hjic-242	36	10	can	can	AUX
hjic-242	36	11	be	be	AUX
hjic-242	36	12	described	describe	VERB
hjic-242	36	13	by	by	ADP
hjic-242	36	14	the	the	DET
hjic-242	36	15	following	follow	VERB
hjic-242	36	16	equation	equation	NOUN
hjic-242	36	17	:	:	PUNCT
hjic-242	36	18	x	x	X
hjic-242	36	19	’	'	PUNCT
hjic-242	36	20	=	=	SYM
hjic-242	36	21	f(x1	f(x1	NOUN
hjic-242	36	22	,	,	PUNCT
hjic-242	36	23	…	…	PUNCT
hjic-242	36	24	,	,	PUNCT
hjic-242	36	25	xn	xn	PUNCT
hjic-242	36	26	)	)	PUNCT
hjic-242	36	27	here	here	ADV
hjic-242	36	28	x	x	PUNCT
hjic-242	36	29	denotes	denote	VERB
hjic-242	36	30	an	an	DET
hjic-242	36	31	arbitrary	arbitrary	ADJ
hjic-242	36	32	variable	variable	NOUN
hjic-242	36	33	depending	depend	VERB
hjic-242	36	34	on	on	ADP
hjic-242	36	35	time	time	NOUN
hjic-242	36	36	,	,	PUNCT
hjic-242	36	37	x	x	PRON
hjic-242	36	38	’	'	PUNCT
hjic-242	36	39	denotes	denote	VERB
hjic-242	36	40	the	the	DET
hjic-242	36	41	derivative	derivative	NOUN
hjic-242	36	42	of	of	ADP
hjic-242	36	43	x	x	PUNCT
hjic-242	36	44	with	with	ADP
hjic-242	36	45	respect	respect	NOUN
hjic-242	36	46	to	to	ADP
hjic-242	36	47	time	time	NOUN
hjic-242	36	48	and	and	CCONJ
hjic-242	36	49	x1	x1	NUM
hjic-242	36	50	,	,	PUNCT
hjic-242	36	51	…	…	PUNCT
hjic-242	36	52	,	,	PUNCT
hjic-242	36	53	xn	xn	PROPN
hjic-242	36	54	are	be	AUX
hjic-242	36	55	those	those	DET
hjic-242	36	56	variables	variable	NOUN
hjic-242	36	57	which	which	PRON
hjic-242	36	58	have	have	VERB
hjic-242	36	59	effect	effect	NOUN
hjic-242	36	60	on	on	ADP
hjic-242	36	61	variable	variable	ADJ
hjic-242	36	62	x	x	NOUN
hjic-242	36	63	’	'	PUNCT
hjic-242	36	64	according	accord	VERB
hjic-242	36	65	to	to	ADP
hjic-242	36	66	the	the	DET
hjic-242	36	67	differential	differential	ADJ
hjic-242	36	68	equation	equation	NOUN
hjic-242	36	69	.	.	PUNCT
hjic-242	37	1	in	in	ADP
hjic-242	37	2	dae	dae	NOUN
hjic-242	37	3	-	-	PUNCT
hjic-242	37	4	systems	system	NOUN
hjic-242	37	5	there	there	PRON
hjic-242	37	6	are	be	VERB
hjic-242	37	7	two	two	NUM
hjic-242	37	8	types	type	NOUN
hjic-242	37	9	of	of	ADP
hjic-242	37	10	variables	variable	NOUN
hjic-242	37	11	.	.	PUNCT
hjic-242	38	1	differential	differential	ADJ
hjic-242	38	2	variables	variable	NOUN
hjic-242	38	3	are	be	AUX
hjic-242	38	4	the	the	DET
hjic-242	38	5	variables	variable	NOUN
hjic-242	38	6	with	with	ADP
hjic-242	38	7	their	their	PRON
hjic-242	38	8	time	time	NOUN
hjic-242	38	9	derivative	derivative	ADJ
hjic-242	38	10	present	present	NOUN
hjic-242	38	11	in	in	ADP
hjic-242	38	12	the	the	DET
hjic-242	38	13	model	model	NOUN
hjic-242	38	14	.	.	PUNCT
hjic-242	39	1	variables	variable	NOUN
hjic-242	39	2	,	,	PUNCT
hjic-242	39	3	which	which	PRON
hjic-242	39	4	do	do	AUX
hjic-242	39	5	not	not	PART
hjic-242	39	6	have	have	VERB
hjic-242	39	7	their	their	PRON
hjic-242	39	8	time	time	NOUN
hjic-242	39	9	derivative	derivative	ADJ
hjic-242	39	10	present	present	NOUN
hjic-242	39	11	,	,	PUNCT
hjic-242	39	12	are	be	AUX
hjic-242	39	13	called	call	VERB
hjic-242	39	14	algebraic	algebraic	ADJ
hjic-242	39	15	variables	variable	NOUN
hjic-242	39	16	.	.	PUNCT
hjic-242	40	1	the	the	DET
hjic-242	40	2	derivative	derivative	ADJ
hjic-242	40	3	x	x	NOUN
hjic-242	40	4	’	'	PUNCT
hjic-242	40	5	is	be	AUX
hjic-242	40	6	called	call	VERB
hjic-242	40	7	derivative	derivative	ADJ
hjic-242	40	8	(	(	PUNCT
hjic-242	40	9	velocity	velocity	NOUN
hjic-242	40	10	)	)	PUNCT
hjic-242	40	11	variable	variable	NOUN
hjic-242	40	12	.	.	PUNCT
hjic-242	41	1	dynamic	dynamic	ADJ
hjic-242	41	2	representation	representation	NOUN
hjic-242	41	3	graph	graph	NOUN
hjic-242	41	4	the	the	DET
hjic-242	41	5	value	value	NOUN
hjic-242	41	6	of	of	ADP
hjic-242	41	7	differential	differential	ADJ
hjic-242	41	8	variables	variable	NOUN
hjic-242	41	9	is	be	AUX
hjic-242	41	10	usually	usually	ADV
hjic-242	41	11	computed	compute	VERB
hjic-242	41	12	by	by	ADP
hjic-242	41	13	using	use	VERB
hjic-242	41	14	a	a	DET
hjic-242	41	15	numerical	numerical	ADJ
hjic-242	41	16	integration	integration	NOUN
hjic-242	41	17	method	method	NOUN
hjic-242	41	18	.	.	PUNCT
hjic-242	42	1	therefore	therefore	ADV
hjic-242	42	2	a	a	DET
hjic-242	42	3	system	system	NOUN
hjic-242	42	4	of	of	ADP
hjic-242	42	5	equations	equation	NOUN
hjic-242	42	6	including	include	VERB
hjic-242	42	7	also	also	ADV
hjic-242	42	8	differential	differential	ADJ
hjic-242	42	9	equations	equation	NOUN
hjic-242	42	10	can	can	AUX
hjic-242	42	11	be	be	AUX
hjic-242	42	12	represented	represent	VERB
hjic-242	42	13	by	by	ADP
hjic-242	42	14	a	a	DET
hjic-242	42	15	dynamic	dynamic	ADJ
hjic-242	42	16	graph	graph	NOUN
hjic-242	42	17	.	.	PUNCT
hjic-242	43	1	a	a	DET
hjic-242	43	2	dynamic	dynamic	ADJ
hjic-242	43	3	graph	graph	NOUN
hjic-242	43	4	is	be	AUX
hjic-242	43	5	a	a	DET
hjic-242	43	6	sequence	sequence	NOUN
hjic-242	43	7	of	of	ADP
hjic-242	43	8	static	static	ADJ
hjic-242	43	9	graphs	graph	NOUN
hjic-242	43	10	corresponding	correspond	VERB
hjic-242	43	11	to	to	ADP
hjic-242	43	12	each	each	DET
hjic-242	43	13	time	time	NOUN
hjic-242	43	14	step	step	NOUN
hjic-242	43	15	of	of	ADP
hjic-242	43	16	the	the	DET
hjic-242	43	17	integration	integration	NOUN
hjic-242	43	18	.	.	PUNCT
hjic-242	44	1	on	on	ADP
hjic-242	44	2	a	a	DET
hjic-242	44	3	dynamic	dynamic	ADJ
hjic-242	44	4	graph	graph	NOUN
hjic-242	44	5	there	there	PRON
hjic-242	44	6	are	be	VERB
hjic-242	44	7	directed	direct	VERB
hjic-242	44	8	arcs	arc	NOUN
hjic-242	44	9	attached	attach	VERB
hjic-242	44	10	from	from	ADP
hjic-242	44	11	the	the	DET
hjic-242	44	12	previous	previous	ADJ
hjic-242	44	13	static	static	ADJ
hjic-242	44	14	graph	graph	NOUN
hjic-242	44	15	to	to	ADP
hjic-242	44	16	the	the	DET
hjic-242	44	17	succeeding	succeed	VERB
hjic-242	44	18	static	static	ADJ
hjic-242	44	19	graph	graph	NOUN
hjic-242	44	20	that	that	PRON
hjic-242	44	21	are	be	AUX
hjic-242	44	22	determined	determine	VERB
hjic-242	44	23	by	by	ADP
hjic-242	44	24	the	the	DET
hjic-242	44	25	method	method	NOUN
hjic-242	44	26	applied	apply	VERB
hjic-242	44	27	for	for	ADP
hjic-242	44	28	solving	solve	VERB
hjic-242	44	29	the	the	DET
hjic-242	44	30	ordinary	ordinary	ADJ
hjic-242	44	31	differential	differential	ADJ
hjic-242	44	32	equations	equation	NOUN
hjic-242	44	33	.	.	PUNCT
hjic-242	45	1	in	in	ADP
hjic-242	45	2	case	case	NOUN
hjic-242	45	3	of	of	ADP
hjic-242	45	4	a	a	DET
hjic-242	45	5	single	single	ADJ
hjic-242	45	6	step	step	NOUN
hjic-242	45	7	explicit	explicit	ADJ
hjic-242	45	8	method	method	NOUN
hjic-242	45	9	,	,	PUNCT
hjic-242	45	10	the	the	DET
hjic-242	45	11	value	value	NOUN
hjic-242	45	12	of	of	ADP
hjic-242	45	13	a	a	DET
hjic-242	45	14	differential	differential	ADJ
hjic-242	45	15	variable	variable	NOUN
hjic-242	45	16	at	at	ADP
hjic-242	45	17	time	time	NOUN
hjic-242	45	18	t+h	t+h	NUM
hjic-242	45	19	is	be	AUX
hjic-242	45	20	computed	compute	VERB
hjic-242	45	21	using	use	VERB
hjic-242	45	22	the	the	DET
hjic-242	45	23	corresponding	corresponding	ADJ
hjic-242	45	24	differential	differential	NOUN
hjic-242	45	25	value	value	NOUN
hjic-242	45	26	and	and	CCONJ
hjic-242	45	27	its	its	PRON
hjic-242	45	28	value	value	NOUN
hjic-242	45	29	at	at	ADP
hjic-242	45	30	a	a	DET
hjic-242	45	31	previous	previous	ADJ
hjic-242	45	32	time	time	NOUN
hjic-242	45	33	t.	t.	PROPN
hjic-242	45	34	for	for	ADP
hjic-242	45	35	example	example	NOUN
hjic-242	45	36	,	,	PUNCT
hjic-242	45	37	when	when	SCONJ
hjic-242	45	38	the	the	DET
hjic-242	45	39	explicit	explicit	ADJ
hjic-242	45	40	euler	euler	NOUN
hjic-242	45	41	method	method	NOUN
hjic-242	45	42	is	be	AUX
hjic-242	45	43	used	use	VERB
hjic-242	45	44	:	:	PUNCT
hjic-242	45	45	x(t+h	x(t+h	PUNCT
hjic-242	45	46	)	)	PUNCT
hjic-242	45	47	=	=	SYM
hjic-242	45	48	x(t	x(t	PROPN
hjic-242	45	49	)	)	PUNCT
hjic-242	45	50	+	+	NUM
hjic-242	45	51	h⋅x’(t	h⋅x’(t	NOUN
hjic-242	45	52	)	)	PUNCT
hjic-242	45	53	where	where	SCONJ
hjic-242	45	54	h	h	NOUN
hjic-242	45	55	denotes	denote	VERB
hjic-242	45	56	the	the	DET
hjic-242	45	57	step	step	NOUN
hjic-242	45	58	length	length	NOUN
hjic-242	45	59	during	during	ADP
hjic-242	45	60	the	the	DET
hjic-242	45	61	numerical	numerical	ADJ
hjic-242	45	62	integration	integration	NOUN
hjic-242	45	63	.	.	PUNCT
hjic-242	46	1	the	the	DET
hjic-242	46	2	structure	structure	NOUN
hjic-242	46	3	of	of	ADP
hjic-242	46	4	a	a	DET
hjic-242	46	5	dynamic	dynamic	ADJ
hjic-242	46	6	graph	graph	NOUN
hjic-242	46	7	assuming	assume	VERB
hjic-242	46	8	explicit	explicit	ADJ
hjic-242	46	9	euler	euler	NOUN
hjic-242	46	10	method	method	NOUN
hjic-242	46	11	for	for	ADP
hjic-242	46	12	solving	solve	VERB
hjic-242	46	13	differential	differential	ADJ
hjic-242	46	14	equations	equation	NOUN
hjic-242	46	15	is	be	AUX
hjic-242	46	16	shown	show	VERB
hjic-242	46	17	in	in	ADP
hjic-242	46	18	fig	fig	NOUN
hjic-242	46	19	.	.	PUNCT
hjic-242	47	1	1	1	X
hjic-242	47	2	.	.	X
hjic-242	47	3	figure	figure	NOUN
hjic-242	47	4	1	1	NUM
hjic-242	47	5	:	:	PUNCT
hjic-242	47	6	dynamic	dynamic	ADJ
hjic-242	47	7	representation	representation	NOUN
hjic-242	47	8	graph	graph	NOUN
hjic-242	47	9	assuming	assume	VERB
hjic-242	47	10	first	first	ADJ
hjic-242	47	11	order	order	NOUN
hjic-242	47	12	explicit	explicit	ADJ
hjic-242	47	13	solution	solution	NOUN
hjic-242	47	14	method	method	VERB
hjic-242	47	15	the	the	DET
hjic-242	47	16	structural	structural	ADJ
hjic-242	47	17	analysis	analysis	NOUN
hjic-242	47	18	based	base	VERB
hjic-242	47	19	on	on	ADP
hjic-242	47	20	graph	graph	NOUN
hjic-242	47	21	theoretical	theoretical	ADJ
hjic-242	47	22	technique	technique	NOUN
hjic-242	47	23	is	be	AUX
hjic-242	47	24	carried	carry	VERB
hjic-242	47	25	out	out	ADP
hjic-242	47	26	in	in	ADP
hjic-242	47	27	steps	step	NOUN
hjic-242	47	28	performed	perform	VERB
hjic-242	47	29	sequentially	sequentially	ADV
hjic-242	47	30	.	.	PUNCT
hjic-242	48	1	the	the	DET
hjic-242	48	2	first	first	ADJ
hjic-242	48	3	step	step	NOUN
hjic-242	48	4	is	be	AUX
hjic-242	48	5	to	to	PART
hjic-242	48	6	rewrite	rewrite	VERB
hjic-242	48	7	the	the	DET
hjic-242	48	8	model	model	NOUN
hjic-242	48	9	into	into	ADP
hjic-242	48	10	its	its	PRON
hjic-242	48	11	standard	standard	ADJ
hjic-242	48	12	form	form	NOUN
hjic-242	48	13	.	.	PUNCT
hjic-242	49	1	the	the	DET
hjic-242	49	2	second	second	ADJ
hjic-242	49	3	step	step	NOUN
hjic-242	49	4	is	be	AUX
hjic-242	49	5	the	the	DET
hjic-242	49	6	assignment	assignment	NOUN
hjic-242	49	7	of	of	ADP
hjic-242	49	8	types	type	NOUN
hjic-242	49	9	to	to	PART
hjic-242	49	10	vertices	vertex	NOUN
hjic-242	49	11	in	in	ADP
hjic-242	49	12	the	the	DET
hjic-242	49	13	representation	representation	NOUN
hjic-242	49	14	graph	graph	NOUN
hjic-242	49	15	.	.	PUNCT
hjic-242	50	1	the	the	DET
hjic-242	50	2	important	important	ADJ
hjic-242	50	3	types	type	NOUN
hjic-242	50	4	of	of	ADP
hjic-242	50	5	vertices	vertex	NOUN
hjic-242	50	6	determined	determine	VERB
hjic-242	50	7	by	by	ADP
hjic-242	50	8	the	the	DET
hjic-242	50	9	model	model	NOUN
hjic-242	50	10	specification	specification	NOUN
hjic-242	50	11	are	be	AUX
hjic-242	50	12	the	the	DET
hjic-242	50	13	following	follow	VERB
hjic-242	50	14	[	[	X
hjic-242	50	15	2	2	NUM
hjic-242	50	16	,	,	PUNCT
hjic-242	50	17	5	5	NUM
hjic-242	50	18	]	]	PUNCT
hjic-242	50	19	:	:	PUNCT
hjic-242	50	20	•	•	NUM
hjic-242	50	21	<	<	X
hjic-242	50	22	s>(set)-type	s>(set)-type	NOUN
hjic-242	50	23	variables	variable	NOUN
hjic-242	50	24	:	:	PUNCT
hjic-242	50	25	these	these	PRON
hjic-242	50	26	represent	represent	VERB
hjic-242	50	27	variables	variable	NOUN
hjic-242	50	28	,	,	PUNCT
hjic-242	50	29	which	which	PRON
hjic-242	50	30	are	be	AUX
hjic-242	50	31	assigned	assign	VERB
hjic-242	50	32	to	to	ADP
hjic-242	50	33	the	the	DET
hjic-242	50	34	specified	specify	VERB
hjic-242	50	35	given	give	VERB
hjic-242	50	36	values	value	NOUN
hjic-242	50	37	.	.	PUNCT
hjic-242	51	1	in	in	ADP
hjic-242	51	2	the	the	DET
hjic-242	51	3	case	case	NOUN
hjic-242	51	4	of	of	ADP
hjic-242	51	5	a	a	DET
hjic-242	51	6	dynamic	dynamic	ADJ
hjic-242	51	7	representation	representation	NOUN
hjic-242	51	8	graph	graph	NOUN
hjic-242	51	9	assuming	assume	VERB
hjic-242	51	10	explicit	explicit	ADJ
hjic-242	51	11	method	method	NOUN
hjic-242	51	12	for	for	ADP
hjic-242	51	13	solving	solve	VERB
hjic-242	51	14	the	the	DET
hjic-242	51	15	differential	differential	ADJ
hjic-242	51	16	equations	equation	NOUN
hjic-242	51	17	,	,	PUNCT
hjic-242	51	18	the	the	DET
hjic-242	51	19	differential	differential	ADJ
hjic-242	51	20	variables	variable	NOUN
hjic-242	51	21	will	will	AUX
hjic-242	51	22	be	be	AUX
hjic-242	51	23	labelled	label	VERB
hjic-242	51	24	by	by	ADP
hjic-242	51	25	type	type	NOUN
hjic-242	51	26	<	<	X
hjic-242	51	27	s	s	NOUN
hjic-242	51	28	*	*	X
hjic-242	51	29	>	>	X
hjic-242	51	30	because	because	SCONJ
hjic-242	51	31	their	their	PRON
hjic-242	51	32	initial	initial	ADJ
hjic-242	51	33	value	value	NOUN
hjic-242	51	34	can	can	AUX
hjic-242	51	35	be	be	AUX
hjic-242	51	36	obtained	obtain	VERB
hjic-242	51	37	from	from	ADP
hjic-242	51	38	the	the	DET
hjic-242	51	39	initial	initial	ADJ
hjic-242	51	40	values	value	NOUN
hjic-242	51	41	,	,	PUNCT
hjic-242	51	42	and	and	CCONJ
hjic-242	51	43	then	then	ADV
hjic-242	51	44	their	their	PRON
hjic-242	51	45	values	value	NOUN
hjic-242	51	46	can	can	AUX
hjic-242	51	47	be	be	AUX
hjic-242	51	48	calculated	calculate	VERB
hjic-242	51	49	step	step	NOUN
hjic-242	51	50	by	by	ADP
hjic-242	51	51	step	step	NOUN
hjic-242	51	52	by	by	ADP
hjic-242	51	53	numerical	numerical	ADJ
hjic-242	51	54	integration	integration	NOUN
hjic-242	51	55	.	.	PUNCT
hjic-242	52	1	labels	label	NOUN
hjic-242	52	2	<	<	X
hjic-242	52	3	s	s	X
hjic-242	52	4	>	>	X
hjic-242	52	5	and	and	CCONJ
hjic-242	52	6	<	<	X
hjic-242	52	7	s	s	X
hjic-242	52	8	*	*	NOUN
hjic-242	52	9	>	>	X
hjic-242	52	10	are	be	AUX
hjic-242	52	11	treated	treat	VERB
hjic-242	52	12	the	the	DET
hjic-242	52	13	same	same	ADJ
hjic-242	52	14	way	way	NOUN
hjic-242	52	15	during	during	ADP
hjic-242	52	16	the	the	DET
hjic-242	52	17	analysis	analysis	NOUN
hjic-242	52	18	.	.	PUNCT
hjic-242	53	1	•	•	NUM
hjic-242	53	2	<	<	X
hjic-242	53	3	g>(given)-type	g>(given)-type	NOUN
hjic-242	53	4	variables	variable	NOUN
hjic-242	53	5	:	:	PUNCT
hjic-242	53	6	a	a	DET
hjic-242	53	7	variable	variable	NOUN
hjic-242	53	8	assigned	assign	VERB
hjic-242	53	9	to	to	ADP
hjic-242	53	10	a	a	DET
hjic-242	53	11	specific	specific	ADJ
hjic-242	53	12	value	value	NOUN
hjic-242	53	13	of	of	ADP
hjic-242	53	14	a	a	DET
hjic-242	53	15	left	left	ADJ
hjic-242	53	16	hand	hand	NOUN
hjic-242	53	17	side	side	NOUN
hjic-242	53	18	is	be	AUX
hjic-242	53	19	a	a	DET
hjic-242	53	20	<	<	X
hjic-242	53	21	g>-type	g>-type	NOUN
hjic-242	53	22	variable	variable	ADJ
hjic-242	53	23	.	.	PUNCT
hjic-242	54	1	unlike	unlike	ADP
hjic-242	54	2	the	the	DET
hjic-242	54	3	<	<	NOUN
hjic-242	54	4	s>-type	s>-type	NOUN
hjic-242	54	5	variables	variable	NOUN
hjic-242	54	6	,	,	PUNCT
hjic-242	54	7	the	the	DET
hjic-242	54	8	values	value	NOUN
hjic-242	54	9	of	of	ADP
hjic-242	54	10	the	the	DET
hjic-242	54	11	right	right	ADJ
hjic-242	54	12	hand	hand	NOUN
hjic-242	54	13	side	side	NOUN
hjic-242	54	14	variables	variable	NOUN
hjic-242	54	15	will	will	AUX
hjic-242	54	16	be	be	AUX
hjic-242	54	17	suitably	suitably	ADV
hjic-242	54	18	adjusted	adjust	VERB
hjic-242	54	19	so	so	SCONJ
hjic-242	54	20	as	as	SCONJ
hjic-242	54	21	to	to	PART
hjic-242	54	22	preserve	preserve	VERB
hjic-242	54	23	the	the	DET
hjic-242	54	24	equality	equality	NOUN
hjic-242	54	25	of	of	ADP
hjic-242	54	26	the	the	DET
hjic-242	54	27	two	two	NUM
hjic-242	54	28	sides	side	NOUN
hjic-242	54	29	.	.	PUNCT
hjic-242	55	1	according	accord	VERB
hjic-242	55	2	to	to	ADP
hjic-242	55	3	the	the	DET
hjic-242	55	4	representation	representation	NOUN
hjic-242	55	5	graph	graph	NOUN
hjic-242	55	6	,	,	PUNCT
hjic-242	55	7	the	the	DET
hjic-242	55	8	value	value	NOUN
hjic-242	55	9	of	of	ADP
hjic-242	55	10	every	every	DET
hjic-242	55	11	variable	variable	NOUN
hjic-242	55	12	which	which	PRON
hjic-242	55	13	has	have	VERB
hjic-242	55	14	incoming	incoming	ADJ
hjic-242	55	15	arcs	arc	NOUN
hjic-242	55	16	only	only	ADV
hjic-242	55	17	from	from	ADP
hjic-242	55	18	vertices	vertex	NOUN
hjic-242	55	19	labelled	label	VERB
hjic-242	55	20	by	by	ADP
hjic-242	55	21	type	type	NOUN
hjic-242	55	22	<	<	X
hjic-242	55	23	s	s	X
hjic-242	55	24	>	>	X
hjic-242	55	25	can	can	AUX
hjic-242	55	26	be	be	AUX
hjic-242	55	27	calculated	calculate	VERB
hjic-242	55	28	by	by	ADP
hjic-242	55	29	simple	simple	ADJ
hjic-242	55	30	substitution	substitution	NOUN
hjic-242	55	31	into	into	ADP
hjic-242	55	32	the	the	DET
hjic-242	55	33	corresponding	correspond	VERB
hjic-242	55	34	equation	equation	NOUN
hjic-242	55	35	.	.	PUNCT
hjic-242	56	1	these	these	DET
hjic-242	56	2	variables	variable	NOUN
hjic-242	56	3	become	become	AUX
hjic-242	56	4	secondarily	secondarily	ADV
hjic-242	56	5	labelled	label	VERB
hjic-242	56	6	by	by	ADP
hjic-242	56	7	type	type	NOUN
hjic-242	56	8	<	<	X
hjic-242	56	9	s	s	X
hjic-242	56	10	>	>	X
hjic-242	56	11	,	,	PUNCT
hjic-242	56	12	and	and	CCONJ
hjic-242	56	13	this	this	DET
hjic-242	56	14	process	process	NOUN
hjic-242	56	15	can	can	AUX
hjic-242	56	16	be	be	AUX
hjic-242	56	17	repeated	repeat	VERB
hjic-242	56	18	if	if	SCONJ
hjic-242	56	19	necessary	necessary	ADJ
hjic-242	56	20	.	.	PUNCT
hjic-242	57	1	omitting	omit	VERB
hjic-242	57	2	all	all	DET
hjic-242	57	3	vertices	vertex	NOUN
hjic-242	57	4	labelled	label	VERB
hjic-242	57	5	primarily	primarily	ADV
hjic-242	57	6	,	,	PUNCT
hjic-242	57	7	secondarily	secondarily	ADV
hjic-242	57	8	,	,	PUNCT
hjic-242	57	9	etc	etc	X
hjic-242	57	10	.	.	X
hjic-242	57	11	by	by	ADP
hjic-242	57	12	type	type	NOUN
hjic-242	57	13	<	<	X
hjic-242	57	14	s	s	X
hjic-242	57	15	>	>	X
hjic-242	57	16	and	and	CCONJ
hjic-242	57	17	all	all	DET
hjic-242	57	18	arcs	arc	NOUN
hjic-242	57	19	starting	start	VERB
hjic-242	57	20	from	from	ADP
hjic-242	57	21	them	they	PRON
hjic-242	57	22	from	from	ADP
hjic-242	57	23	the	the	DET
hjic-242	57	24	representation	representation	NOUN
hjic-242	57	25	graph	graph	NOUN
hjic-242	57	26	we	we	PRON
hjic-242	57	27	obtain	obtain	VERB
hjic-242	57	28	the	the	DET
hjic-242	57	29	reduced	reduce	VERB
hjic-242	57	30	graph	graph	NOUN
hjic-242	57	31	.	.	PUNCT
hjic-242	58	1	the	the	DET
hjic-242	58	2	classification	classification	NOUN
hjic-242	58	3	of	of	ADP
hjic-242	58	4	vertices	vertex	NOUN
hjic-242	58	5	of	of	ADP
hjic-242	58	6	a	a	DET
hjic-242	58	7	reduced	reduce	VERB
hjic-242	58	8	graph	graph	NOUN
hjic-242	58	9	is	be	AUX
hjic-242	58	10	as	as	SCONJ
hjic-242	58	11	follows	follow	VERB
hjic-242	58	12	:	:	PUNCT
hjic-242	58	13	•	•	NOUN
hjic-242	58	14	all	all	DET
hjic-242	58	15	initial	initial	ADJ
hjic-242	58	16	vertices	vertex	NOUN
hjic-242	58	17	form	form	VERB
hjic-242	58	18	the	the	DET
hjic-242	58	19	unknown	unknown	ADJ
hjic-242	58	20	variable	variable	NOUN
hjic-242	58	21	set	set	NOUN
hjic-242	58	22	x	x	SYM
hjic-242	58	23	,	,	PUNCT
hjic-242	58	24	•	•	PRON
hjic-242	58	25	all	all	DET
hjic-242	58	26	terminal	terminal	ADJ
hjic-242	58	27	vertices	vertex	NOUN
hjic-242	58	28	labelled	label	VERB
hjic-242	58	29	by	by	ADP
hjic-242	58	30	type	type	NOUN
hjic-242	58	31	<	<	X
hjic-242	58	32	g	g	X
hjic-242	58	33	>	>	X
hjic-242	58	34	constitute	constitute	VERB
hjic-242	58	35	the	the	DET
hjic-242	58	36	known	know	VERB
hjic-242	58	37	variable	variable	NOUN
hjic-242	58	38	(	(	PUNCT
hjic-242	58	39	parameter	parameter	NOUN
hjic-242	58	40	)	)	PUNCT
hjic-242	58	41	set	set	VERB
hjic-242	58	42	y	y	PROPN
hjic-242	58	43	,	,	PUNCT
hjic-242	58	44	•	•	VERB
hjic-242	58	45	all	all	DET
hjic-242	58	46	other	other	ADJ
hjic-242	58	47	vertices	vertex	NOUN
hjic-242	58	48	constitute	constitute	VERB
hjic-242	58	49	the	the	DET
hjic-242	58	50	unkown	unkown	ADJ
hjic-242	58	51	variable	variable	NOUN
hjic-242	58	52	set	set	VERB
hjic-242	58	53	u.	u.	PROPN
hjic-242	58	54	147	147	NUM
hjic-242	58	55	differential	differential	ADJ
hjic-242	58	56	index	index	NOUN
hjic-242	58	57	dynamic	dynamic	ADJ
hjic-242	58	58	process	process	NOUN
hjic-242	58	59	models	model	NOUN
hjic-242	58	60	can	can	AUX
hjic-242	58	61	be	be	AUX
hjic-242	58	62	described	describe	VERB
hjic-242	58	63	by	by	ADP
hjic-242	58	64	semiexplicit	semiexplicit	ADJ
hjic-242	58	65	daes	daes	PROPN
hjic-242	58	66	as	as	SCONJ
hjic-242	58	67	follows	follow	VERB
hjic-242	58	68	:	:	PUNCT
hjic-242	58	69	z1	z1	NOUN
hjic-242	58	70	‘	'	PUNCT
hjic-242	58	71	’	'	PUNCT
hjic-242	58	72	=	=	SYM
hjic-242	58	73	f(z1	f(z1	ADJ
hjic-242	58	74	,	,	PUNCT
hjic-242	58	75	z2	z2	PROPN
hjic-242	58	76	,	,	PUNCT
hjic-242	58	77	t	t	PROPN
hjic-242	58	78	)	)	PUNCT
hjic-242	58	79	,	,	PUNCT
hjic-242	58	80	z1(t0	z1(t0	NOUN
hjic-242	58	81	)	)	PUNCT
hjic-242	58	82	=	=	SYM
hjic-242	58	83	z10	z10	NOUN
hjic-242	58	84	(	(	PUNCT
hjic-242	58	85	1	1	NUM
hjic-242	58	86	)	)	PUNCT
hjic-242	58	87	0	0	NUM
hjic-242	59	1	=	=	SYM
hjic-242	59	2	g(z1	g(z1	NOUN
hjic-242	59	3	,	,	PUNCT
hjic-242	59	4	z2	z2	PROPN
hjic-242	59	5	,	,	PUNCT
hjic-242	59	6	t	t	PROPN
hjic-242	59	7	)	)	PUNCT
hjic-242	59	8	(	(	PUNCT
hjic-242	59	9	2	2	X
hjic-242	59	10	)	)	PUNCT
hjic-242	59	11	the	the	DET
hjic-242	59	12	most	most	ADV
hjic-242	59	13	important	important	ADJ
hjic-242	59	14	structural	structural	ADJ
hjic-242	59	15	computational	computational	ADJ
hjic-242	59	16	property	property	NOUN
hjic-242	59	17	of	of	ADP
hjic-242	59	18	dae	dae	NOUN
hjic-242	59	19	models	model	NOUN
hjic-242	59	20	is	be	AUX
hjic-242	59	21	the	the	DET
hjic-242	59	22	differential	differential	ADJ
hjic-242	59	23	index	index	NOUN
hjic-242	59	24	[	[	X
hjic-242	59	25	6	6	NUM
hjic-242	59	26	]	]	PUNCT
hjic-242	59	27	.	.	PUNCT
hjic-242	60	1	by	by	ADP
hjic-242	60	2	definition	definition	NOUN
hjic-242	60	3	[	[	X
hjic-242	60	4	7	7	X
hjic-242	60	5	]	]	X
hjic-242	60	6	the	the	DET
hjic-242	60	7	differential	differential	ADJ
hjic-242	60	8	index	index	NOUN
hjic-242	60	9	of	of	ADP
hjic-242	60	10	the	the	DET
hjic-242	60	11	semi	semi	ADJ
hjic-242	60	12	-	-	ADJ
hjic-242	60	13	explicit	explicit	ADJ
hjic-242	60	14	dae	dae	NOUN
hjic-242	60	15	(	(	PUNCT
hjic-242	60	16	equations	equation	NOUN
hjic-242	60	17	(	(	PUNCT
hjic-242	60	18	1)-(2	1)-(2	NUM
hjic-242	60	19	)	)	PUNCT
hjic-242	60	20	)	)	PUNCT
hjic-242	60	21	is	be	AUX
hjic-242	60	22	one	one	NUM
hjic-242	60	23	if	if	SCONJ
hjic-242	60	24	one	one	NUM
hjic-242	60	25	differentiation	differentiation	NOUN
hjic-242	60	26	is	be	AUX
hjic-242	60	27	sufficient	sufficient	ADJ
hjic-242	60	28	to	to	PART
hjic-242	60	29	express	express	VERB
hjic-242	60	30	z2	z2	NOUN
hjic-242	60	31	‘	'	PUNCT
hjic-242	60	32	’	'	PUNCT
hjic-242	60	33	as	as	SCONJ
hjic-242	60	34	a	a	DET
hjic-242	60	35	continuous	continuous	ADJ
hjic-242	60	36	function	function	NOUN
hjic-242	60	37	of	of	ADP
hjic-242	60	38	z1	z1	PROPN
hjic-242	60	39	,	,	PUNCT
hjic-242	60	40	z2	z2	PROPN
hjic-242	60	41	and	and	CCONJ
hjic-242	60	42	t.	t.	NOUN
hjic-242	60	43	one	one	NUM
hjic-242	60	44	differentiation	differentiation	NOUN
hjic-242	60	45	is	be	AUX
hjic-242	60	46	sufficient	sufficient	ADJ
hjic-242	60	47	if	if	SCONJ
hjic-242	60	48	and	and	CCONJ
hjic-242	60	49	only	only	ADV
hjic-242	60	50	if	if	SCONJ
hjic-242	60	51	the	the	DET
hjic-242	60	52	jacobian	jacobian	ADJ
hjic-242	60	53	matrix	matrix	NOUN
hjic-242	60	54	gz2	gz2	NOUN
hjic-242	60	55	is	be	AUX
hjic-242	60	56	non	non	ADJ
hjic-242	60	57	-	-	ADJ
hjic-242	60	58	singular	singular	ADJ
hjic-242	60	59	.	.	PUNCT
hjic-242	61	1	in	in	ADP
hjic-242	61	2	our	our	PRON
hjic-242	61	3	earlier	early	ADJ
hjic-242	61	4	work	work	NOUN
hjic-242	61	5	we	we	PRON
hjic-242	61	6	have	have	AUX
hjic-242	61	7	proved	prove	VERB
hjic-242	61	8	that	that	SCONJ
hjic-242	61	9	the	the	DET
hjic-242	61	10	differential	differential	ADJ
hjic-242	61	11	index	index	NOUN
hjic-242	61	12	of	of	ADP
hjic-242	61	13	the	the	DET
hjic-242	61	14	models	model	NOUN
hjic-242	61	15	investigated	investigate	VERB
hjic-242	61	16	in	in	ADP
hjic-242	61	17	[	[	X
hjic-242	61	18	2	2	NUM
hjic-242	61	19	]	]	PUNCT
hjic-242	61	20	is	be	AUX
hjic-242	61	21	equal	equal	ADJ
hjic-242	61	22	to	to	ADP
hjic-242	61	23	1	1	NUM
hjic-242	61	24	if	if	SCONJ
hjic-242	61	25	and	and	CCONJ
hjic-242	61	26	only	only	ADV
hjic-242	61	27	if	if	SCONJ
hjic-242	61	28	there	there	PRON
hjic-242	61	29	exists	exist	VERB
hjic-242	61	30	a	a	DET
hjic-242	61	31	menger	menger	NOUN
hjic-242	61	32	-	-	PUNCT
hjic-242	61	33	type	type	NOUN
hjic-242	61	34	complete	complete	ADJ
hjic-242	61	35	linking	linking	NOUN
hjic-242	61	36	on	on	ADP
hjic-242	61	37	the	the	DET
hjic-242	61	38	reduced	reduce	VERB
hjic-242	61	39	graph	graph	NOUN
hjic-242	61	40	at	at	ADP
hjic-242	61	41	any	any	DET
hjic-242	61	42	time	time	NOUN
hjic-242	61	43	step	step	NOUN
hjic-242	61	44	t.	t.	NOUN
hjic-242	61	45	if	if	SCONJ
hjic-242	61	46	the	the	DET
hjic-242	61	47	differential	differential	ADJ
hjic-242	61	48	index	index	NOUN
hjic-242	61	49	of	of	ADP
hjic-242	61	50	the	the	DET
hjic-242	61	51	investigated	investigate	VERB
hjic-242	61	52	model	model	NOUN
hjic-242	61	53	is	be	AUX
hjic-242	61	54	greater	great	ADJ
hjic-242	61	55	than	than	ADP
hjic-242	61	56	1	1	NUM
hjic-242	61	57	then	then	ADV
hjic-242	61	58	there	there	PRON
hjic-242	61	59	is	be	VERB
hjic-242	61	60	no	no	DET
hjic-242	61	61	menger	menger	NOUN
hjic-242	61	62	-	-	PUNCT
hjic-242	61	63	type	type	NOUN
hjic-242	61	64	complete	complete	ADJ
hjic-242	61	65	linking	linking	NOUN
hjic-242	61	66	on	on	ADP
hjic-242	61	67	the	the	DET
hjic-242	61	68	static	static	ADJ
hjic-242	61	69	graph	graph	NOUN
hjic-242	61	70	at	at	ADP
hjic-242	61	71	any	any	DET
hjic-242	61	72	time	time	NOUN
hjic-242	61	73	step	step	NOUN
hjic-242	61	74	t.	t.	NOUN
hjic-242	61	75	the	the	DET
hjic-242	61	76	properties	property	NOUN
hjic-242	61	77	of	of	ADP
hjic-242	61	78	a	a	DET
hjic-242	61	79	static	static	ADJ
hjic-242	61	80	graph	graph	NOUN
hjic-242	61	81	of	of	ADP
hjic-242	61	82	a	a	DET
hjic-242	61	83	dynamic	dynamic	ADJ
hjic-242	61	84	model	model	NOUN
hjic-242	61	85	,	,	PUNCT
hjic-242	61	86	which	which	PRON
hjic-242	61	87	has	have	VERB
hjic-242	61	88	differential	differential	ADJ
hjic-242	61	89	index	index	NOUN
hjic-242	61	90	>	>	NOUN
hjic-242	61	91	1	1	NUM
hjic-242	61	92	are	be	AUX
hjic-242	61	93	as	as	SCONJ
hjic-242	61	94	follows	follow	VERB
hjic-242	61	95	.	.	PUNCT
hjic-242	62	1	1	1	X
hjic-242	62	2	.	.	X
hjic-242	63	1	the	the	DET
hjic-242	63	2	fact	fact	NOUN
hjic-242	63	3	that	that	SCONJ
hjic-242	63	4	the	the	DET
hjic-242	63	5	initial	initial	ADJ
hjic-242	63	6	values	value	NOUN
hjic-242	63	7	of	of	ADP
hjic-242	63	8	differential	differential	ADJ
hjic-242	63	9	variables	variable	NOUN
hjic-242	63	10	can	can	AUX
hjic-242	63	11	not	not	PART
hjic-242	63	12	be	be	AUX
hjic-242	63	13	chosen	choose	VERB
hjic-242	63	14	independently	independently	ADV
hjic-242	63	15	results	result	NOUN
hjic-242	63	16	in	in	ADP
hjic-242	63	17	an	an	DET
hjic-242	63	18	overspecified	overspecified	ADJ
hjic-242	63	19	part	part	NOUN
hjic-242	63	20	on	on	ADP
hjic-242	63	21	the	the	DET
hjic-242	63	22	graph	graph	NOUN
hjic-242	63	23	.	.	PUNCT
hjic-242	64	1	this	this	DET
hjic-242	64	2	situation	situation	NOUN
hjic-242	64	3	can	can	AUX
hjic-242	64	4	be	be	AUX
hjic-242	64	5	easy	easy	ADV
hjic-242	64	6	shown	show	VERB
hjic-242	64	7	by	by	ADP
hjic-242	64	8	assignment	assignment	NOUN
hjic-242	64	9	of	of	ADP
hjic-242	64	10	types	type	NOUN
hjic-242	64	11	to	to	PART
hjic-242	64	12	vertices	vertice	VERB
hjic-242	64	13	corresponding	correspond	VERB
hjic-242	64	14	to	to	ADP
hjic-242	64	15	the	the	DET
hjic-242	64	16	model	model	NOUN
hjic-242	64	17	specification	specification	NOUN
hjic-242	64	18	.	.	PUNCT
hjic-242	65	1	there	there	PRON
hjic-242	65	2	is	be	VERB
hjic-242	65	3	an	an	DET
hjic-242	65	4	overspecified	overspecified	ADJ
hjic-242	65	5	part	part	NOUN
hjic-242	65	6	on	on	ADP
hjic-242	65	7	the	the	DET
hjic-242	65	8	graph	graph	NOUN
hjic-242	65	9	if	if	SCONJ
hjic-242	65	10	a	a	DET
hjic-242	65	11	vertex	vertex	NOUN
hjic-242	65	12	labelled	label	VERB
hjic-242	65	13	by	by	ADP
hjic-242	65	14	type	type	NOUN
hjic-242	65	15	<	<	X
hjic-242	65	16	s	s	NOUN
hjic-242	65	17	*	*	NOUN
hjic-242	65	18	>	>	X
hjic-242	65	19	or	or	CCONJ
hjic-242	65	20	<	<	X
hjic-242	65	21	g	g	X
hjic-242	65	22	>	>	X
hjic-242	65	23	can	can	AUX
hjic-242	65	24	also	also	ADV
hjic-242	65	25	be	be	AUX
hjic-242	65	26	labelled	label	VERB
hjic-242	65	27	preliminary	preliminary	ADJ
hjic-242	65	28	,	,	PUNCT
hjic-242	65	29	secondarily	secondarily	ADV
hjic-242	65	30	,	,	PUNCT
hjic-242	65	31	tertiarily	tertiarily	ADV
hjic-242	65	32	or	or	CCONJ
hjic-242	65	33	etc	etc	X
hjic-242	65	34	.	.	X
hjic-242	66	1	by	by	ADP
hjic-242	66	2	type	type	NOUN
hjic-242	66	3	<	<	X
hjic-242	66	4	s	s	NOUN
hjic-242	66	5	>	>	X
hjic-242	66	6	.	.	PROPN
hjic-242	66	7	2	2	X
hjic-242	66	8	.	.	X
hjic-242	66	9	non	non	ADJ
hjic-242	66	10	-	-	NOUN
hjic-242	66	11	singularity	singularity	NOUN
hjic-242	66	12	of	of	ADP
hjic-242	66	13	gz2	gz2	NOUN
hjic-242	66	14	results	result	NOUN
hjic-242	66	15	in	in	ADP
hjic-242	66	16	an	an	DET
hjic-242	66	17	underspecified	underspecified	ADJ
hjic-242	66	18	part	part	NOUN
hjic-242	66	19	on	on	ADP
hjic-242	66	20	the	the	DET
hjic-242	66	21	graph	graph	NOUN
hjic-242	66	22	.	.	PUNCT
hjic-242	67	1	in	in	ADP
hjic-242	67	2	this	this	DET
hjic-242	67	3	part	part	NOUN
hjic-242	67	4	those	those	DET
hjic-242	67	5	algebraic	algebraic	PROPN
hjic-242	67	6	variables	variable	NOUN
hjic-242	67	7	appear	appear	VERB
hjic-242	67	8	,	,	PUNCT
hjic-242	67	9	which	which	PRON
hjic-242	67	10	can	can	AUX
hjic-242	67	11	not	not	PART
hjic-242	67	12	be	be	AUX
hjic-242	67	13	calculated	calculate	VERB
hjic-242	67	14	from	from	ADP
hjic-242	67	15	algebraic	algebraic	ADJ
hjic-242	67	16	equations	equation	NOUN
hjic-242	67	17	and	and	CCONJ
hjic-242	67	18	those	those	DET
hjic-242	67	19	derivative	derivative	ADJ
hjic-242	67	20	variables	variable	NOUN
hjic-242	67	21	,	,	PUNCT
hjic-242	67	22	which	which	PRON
hjic-242	67	23	we	we	PRON
hjic-242	67	24	want	want	VERB
hjic-242	67	25	to	to	PART
hjic-242	67	26	calculate	calculate	VERB
hjic-242	67	27	from	from	ADP
hjic-242	67	28	them	they	PRON
hjic-242	67	29	.	.	PUNCT
hjic-242	68	1	we	we	PRON
hjic-242	68	2	have	have	AUX
hjic-242	68	3	also	also	ADV
hjic-242	68	4	proposed	propose	VERB
hjic-242	68	5	an	an	DET
hjic-242	68	6	algorithm	algorithm	NOUN
hjic-242	68	7	using	use	VERB
hjic-242	68	8	the	the	DET
hjic-242	68	9	structure	structure	NOUN
hjic-242	68	10	of	of	ADP
hjic-242	68	11	the	the	DET
hjic-242	68	12	representation	representation	NOUN
hjic-242	68	13	graph	graph	NOUN
hjic-242	68	14	for	for	ADP
hjic-242	68	15	determination	determination	NOUN
hjic-242	68	16	of	of	ADP
hjic-242	68	17	the	the	DET
hjic-242	68	18	differential	differential	ADJ
hjic-242	68	19	index	index	NOUN
hjic-242	68	20	of	of	ADP
hjic-242	68	21	the	the	DET
hjic-242	68	22	underlying	underlie	VERB
hjic-242	68	23	model	model	NOUN
hjic-242	68	24	.	.	PUNCT
hjic-242	69	1	the	the	DET
hjic-242	69	2	main	main	ADJ
hjic-242	69	3	steps	step	NOUN
hjic-242	69	4	of	of	ADP
hjic-242	69	5	this	this	DET
hjic-242	69	6	algorithm	algorithm	NOUN
hjic-242	69	7	are	be	AUX
hjic-242	69	8	the	the	DET
hjic-242	69	9	following	following	NOUN
hjic-242	69	10	:	:	PUNCT
hjic-242	69	11	1	1	X
hjic-242	69	12	.	.	X
hjic-242	69	13	let	let	VERB
hjic-242	69	14	us	we	PRON
hjic-242	69	15	form	form	VERB
hjic-242	69	16	the	the	DET
hjic-242	69	17	following	follow	VERB
hjic-242	69	18	variable	variable	ADJ
hjic-242	69	19	sets	set	NOUN
hjic-242	69	20	.	.	PUNCT
hjic-242	70	1	i0	i0	PROPN
hjic-242	70	2	is	be	AUX
hjic-242	70	3	the	the	DET
hjic-242	70	4	set	set	NOUN
hjic-242	70	5	of	of	ADP
hjic-242	70	6	the	the	DET
hjic-242	70	7	differential	differential	ADJ
hjic-242	70	8	variables	variable	NOUN
hjic-242	70	9	belonging	belong	VERB
hjic-242	70	10	to	to	ADP
hjic-242	70	11	the	the	DET
hjic-242	70	12	overspecified	overspecified	ADJ
hjic-242	70	13	subgraph	subgraph	NOUN
hjic-242	70	14	,	,	PUNCT
hjic-242	70	15	d0	d0	PROPN
hjic-242	70	16	is	be	AUX
hjic-242	70	17	the	the	DET
hjic-242	70	18	set	set	NOUN
hjic-242	70	19	of	of	ADP
hjic-242	70	20	the	the	DET
hjic-242	70	21	derivative	derivative	ADJ
hjic-242	70	22	variables	variable	NOUN
hjic-242	70	23	referring	refer	VERB
hjic-242	70	24	to	to	ADP
hjic-242	70	25	the	the	DET
hjic-242	70	26	differential	differential	ADJ
hjic-242	70	27	variables	variable	NOUN
hjic-242	70	28	of	of	ADP
hjic-242	70	29	set	set	NOUN
hjic-242	70	30	i0	i0	PROPN
hjic-242	70	31	,	,	PUNCT
hjic-242	70	32	i1	i1	PROPN
hjic-242	70	33	is	be	AUX
hjic-242	70	34	the	the	DET
hjic-242	70	35	set	set	NOUN
hjic-242	70	36	of	of	ADP
hjic-242	70	37	differential	differential	ADJ
hjic-242	70	38	variables	variable	NOUN
hjic-242	70	39	from	from	ADP
hjic-242	70	40	which	which	PRON
hjic-242	70	41	directed	direct	VERB
hjic-242	70	42	paths	path	NOUN
hjic-242	70	43	lead	lead	VERB
hjic-242	70	44	to	to	ADP
hjic-242	70	45	the	the	DET
hjic-242	70	46	derivative	derivative	ADJ
hjic-242	70	47	variables	variable	NOUN
hjic-242	70	48	in	in	ADP
hjic-242	70	49	the	the	DET
hjic-242	70	50	set	set	NOUN
hjic-242	70	51	d0	d0	NOUN
hjic-242	70	52	,	,	PUNCT
hjic-242	70	53	d1	d1	PROPN
hjic-242	70	54	is	be	AUX
hjic-242	70	55	the	the	DET
hjic-242	70	56	set	set	NOUN
hjic-242	70	57	of	of	ADP
hjic-242	70	58	derivative	derivative	ADJ
hjic-242	70	59	variables	variable	NOUN
hjic-242	70	60	referring	refer	VERB
hjic-242	70	61	to	to	ADP
hjic-242	70	62	the	the	DET
hjic-242	70	63	differential	differential	ADJ
hjic-242	70	64	variables	variable	NOUN
hjic-242	70	65	of	of	ADP
hjic-242	70	66	set	set	PROPN
hjic-242	70	67	i1	i1	PROPN
hjic-242	70	68	,	,	PUNCT
hjic-242	70	69	…	…	PUNCT
hjic-242	70	70	,	,	PUNCT
hjic-242	70	71	ik	ik	PROPN
hjic-242	70	72	is	be	AUX
hjic-242	70	73	the	the	DET
hjic-242	70	74	set	set	NOUN
hjic-242	70	75	of	of	ADP
hjic-242	70	76	differential	differential	ADJ
hjic-242	70	77	variables	variable	NOUN
hjic-242	70	78	from	from	ADP
hjic-242	70	79	which	which	PRON
hjic-242	70	80	directed	direct	VERB
hjic-242	70	81	paths	path	NOUN
hjic-242	70	82	lead	lead	VERB
hjic-242	70	83	to	to	ADP
hjic-242	70	84	the	the	DET
hjic-242	70	85	derivative	derivative	ADJ
hjic-242	70	86	variables	variable	NOUN
hjic-242	70	87	in	in	ADP
hjic-242	70	88	the	the	DET
hjic-242	70	89	set	set	NOUN
hjic-242	70	90	dk-1	dk-1	NOUN
hjic-242	70	91	,	,	PUNCT
hjic-242	70	92	dk	dk	PROPN
hjic-242	70	93	is	be	AUX
hjic-242	70	94	the	the	DET
hjic-242	70	95	set	set	NOUN
hjic-242	70	96	of	of	ADP
hjic-242	70	97	derivative	derivative	ADJ
hjic-242	70	98	variables	variable	NOUN
hjic-242	70	99	referring	refer	VERB
hjic-242	70	100	to	to	ADP
hjic-242	70	101	the	the	DET
hjic-242	70	102	differential	differential	ADJ
hjic-242	70	103	variables	variable	NOUN
hjic-242	70	104	of	of	ADP
hjic-242	70	105	set	set	NOUN
hjic-242	70	106	ik	ik	PROPN
hjic-242	70	107	,	,	PUNCT
hjic-242	70	108	…	…	PUNCT
hjic-242	70	109	2	2	X
hjic-242	70	110	.	.	X
hjic-242	71	1	let	let	VERB
hjic-242	71	2	n	n	PRON
hjic-242	71	3	be	be	AUX
hjic-242	71	4	the	the	DET
hjic-242	71	5	smallest	small	ADJ
hjic-242	71	6	natural	natural	ADJ
hjic-242	71	7	number	number	NOUN
hjic-242	71	8	for	for	ADP
hjic-242	71	9	which	which	PRON
hjic-242	71	10	the	the	DET
hjic-242	71	11	set	set	NOUN
hjic-242	71	12	dn	dn	NOUN
hjic-242	71	13	contains	contain	VERB
hjic-242	71	14	some	some	DET
hjic-242	71	15	derivative	derivative	ADJ
hjic-242	71	16	variables	variable	NOUN
hjic-242	71	17	of	of	ADP
hjic-242	71	18	the	the	DET
hjic-242	71	19	underspecified	underspecified	ADJ
hjic-242	71	20	subgraph	subgraph	NOUN
hjic-242	71	21	.	.	PUNCT
hjic-242	72	1	then	then	ADV
hjic-242	72	2	the	the	DET
hjic-242	72	3	differential	differential	ADJ
hjic-242	72	4	index	index	NOUN
hjic-242	72	5	of	of	ADP
hjic-242	72	6	the	the	DET
hjic-242	72	7	model	model	NOUN
hjic-242	72	8	is	be	AUX
hjic-242	72	9	νd	νd	NOUN
hjic-242	72	10	=	=	SYM
hjic-242	72	11	n+2	n+2	PRON
hjic-242	72	12	if	if	SCONJ
hjic-242	72	13	there	there	PRON
hjic-242	72	14	is	be	VERB
hjic-242	72	15	no	no	DET
hjic-242	72	16	such	such	ADJ
hjic-242	72	17	number	number	NOUN
hjic-242	72	18	n	n	NOUN
hjic-242	72	19	then	then	ADV
hjic-242	72	20	the	the	DET
hjic-242	72	21	model	model	NOUN
hjic-242	72	22	is	be	AUX
hjic-242	72	23	not	not	PART
hjic-242	72	24	structurally	structurally	ADV
hjic-242	72	25	solvable	solvable	ADJ
hjic-242	72	26	.	.	PUNCT
hjic-242	73	1	in	in	ADP
hjic-242	73	2	our	our	PRON
hjic-242	73	3	earlier	early	ADJ
hjic-242	73	4	work	work	NOUN
hjic-242	73	5	we	we	PRON
hjic-242	73	6	have	have	AUX
hjic-242	73	7	shown	show	VERB
hjic-242	73	8	that	that	SCONJ
hjic-242	73	9	the	the	DET
hjic-242	73	10	important	important	ADJ
hjic-242	73	11	properties	property	NOUN
hjic-242	73	12	of	of	ADP
hjic-242	73	13	the	the	DET
hjic-242	73	14	representation	representation	NOUN
hjic-242	73	15	graph	graph	NOUN
hjic-242	73	16	including	include	VERB
hjic-242	73	17	the	the	DET
hjic-242	73	18	differential	differential	ADJ
hjic-242	73	19	index	index	NOUN
hjic-242	73	20	of	of	ADP
hjic-242	73	21	the	the	DET
hjic-242	73	22	models	model	NOUN
hjic-242	73	23	are	be	AUX
hjic-242	73	24	independent	independent	ADJ
hjic-242	73	25	of	of	ADP
hjic-242	73	26	the	the	DET
hjic-242	73	27	assumption	assumption	NOUN
hjic-242	73	28	whether	whether	SCONJ
hjic-242	73	29	a	a	DET
hjic-242	73	30	single	single	ADJ
hjic-242	73	31	-	-	PUNCT
hjic-242	73	32	step	step	NOUN
hjic-242	73	33	,	,	PUNCT
hjic-242	73	34	explicit	explicit	ADJ
hjic-242	73	35	or	or	CCONJ
hjic-242	73	36	implicit	implicit	ADJ
hjic-242	73	37	numerical	numerical	ADJ
hjic-242	73	38	method	method	NOUN
hjic-242	73	39	is	be	AUX
hjic-242	73	40	used	use	VERB
hjic-242	73	41	for	for	ADP
hjic-242	73	42	the	the	DET
hjic-242	73	43	solution	solution	NOUN
hjic-242	73	44	of	of	ADP
hjic-242	73	45	the	the	DET
hjic-242	73	46	differential	differential	ADJ
hjic-242	73	47	equations	equation	NOUN
hjic-242	73	48	[	[	X
hjic-242	73	49	8	8	NUM
hjic-242	73	50	]	]	PUNCT
hjic-242	73	51	.	.	PUNCT
hjic-242	74	1	structural	structural	ADJ
hjic-242	74	2	analysis	analysis	NOUN
hjic-242	74	3	of	of	ADP
hjic-242	74	4	simple	simple	ADJ
hjic-242	74	5	models	model	NOUN
hjic-242	74	6	using	use	VERB
hjic-242	74	7	their	their	PRON
hjic-242	74	8	representation	representation	NOUN
hjic-242	74	9	graphs	graph	NOUN
hjic-242	74	10	in	in	ADP
hjic-242	74	11	this	this	DET
hjic-242	74	12	section	section	NOUN
hjic-242	74	13	,	,	PUNCT
hjic-242	74	14	simple	simple	ADJ
hjic-242	74	15	,	,	PUNCT
hjic-242	74	16	small	small	ADJ
hjic-242	74	17	sized	sized	ADJ
hjic-242	74	18	,	,	PUNCT
hjic-242	74	19	dynamic	dynamic	ADJ
hjic-242	74	20	models	model	NOUN
hjic-242	74	21	are	be	AUX
hjic-242	74	22	investigated	investigate	VERB
hjic-242	74	23	using	use	VERB
hjic-242	74	24	their	their	PRON
hjic-242	74	25	representation	representation	NOUN
hjic-242	74	26	graphs	graph	NOUN
hjic-242	74	27	.	.	PUNCT
hjic-242	75	1	we	we	PRON
hjic-242	75	2	show	show	VERB
hjic-242	75	3	the	the	DET
hjic-242	75	4	influence	influence	NOUN
hjic-242	75	5	of	of	ADP
hjic-242	75	6	the	the	DET
hjic-242	75	7	change	change	NOUN
hjic-242	75	8	of	of	ADP
hjic-242	75	9	the	the	DET
hjic-242	75	10	modelling	model	VERB
hjic-242	75	11	goal	goal	NOUN
hjic-242	75	12	(	(	PUNCT
hjic-242	75	13	and	and	CCONJ
hjic-242	75	14	so	so	ADV
hjic-242	75	15	the	the	DET
hjic-242	75	16	model	model	NOUN
hjic-242	75	17	specification	specification	NOUN
hjic-242	75	18	)	)	PUNCT
hjic-242	75	19	and	and	CCONJ
hjic-242	75	20	the	the	DET
hjic-242	75	21	modelling	modelling	NOUN
hjic-242	75	22	conditions	condition	NOUN
hjic-242	75	23	to	to	ADP
hjic-242	75	24	the	the	DET
hjic-242	75	25	differential	differential	ADJ
hjic-242	75	26	index	index	NOUN
hjic-242	75	27	.	.	PUNCT
hjic-242	76	1	the	the	DET
hjic-242	76	2	examples	example	NOUN
hjic-242	76	3	used	use	VERB
hjic-242	76	4	in	in	ADP
hjic-242	76	5	this	this	PRON
hjic-242	76	6	and	and	CCONJ
hjic-242	76	7	next	next	ADJ
hjic-242	76	8	sections	section	NOUN
hjic-242	76	9	are	be	AUX
hjic-242	76	10	based	base	VERB
hjic-242	76	11	on	on	ADP
hjic-242	76	12	examples	example	NOUN
hjic-242	76	13	of	of	ADP
hjic-242	76	14	[	[	X
hjic-242	76	15	9	9	NUM
hjic-242	76	16	]	]	PUNCT
hjic-242	76	17	.	.	PUNCT
hjic-242	77	1	example	example	NOUN
hjic-242	77	2	1	1	NUM
hjic-242	77	3	–	–	PUNCT
hjic-242	77	4	perfectly	perfectly	ADV
hjic-242	77	5	stirred	stir	VERB
hjic-242	77	6	tank	tank	NOUN
hjic-242	77	7	reactor	reactor	NOUN
hjic-242	77	8	suppose	suppose	VERB
hjic-242	77	9	a	a	DET
hjic-242	77	10	perfectly	perfectly	ADV
hjic-242	77	11	stirred	stir	VERB
hjic-242	77	12	tank	tank	NOUN
hjic-242	77	13	reactor	reactor	NOUN
hjic-242	77	14	and	and	CCONJ
hjic-242	77	15	let	let	VERB
hjic-242	77	16	the	the	DET
hjic-242	77	17	concentration	concentration	NOUN
hjic-242	77	18	of	of	ADP
hjic-242	77	19	its	its	PRON
hjic-242	77	20	inlet	inlet	NOUN
hjic-242	77	21	flow	flow	NOUN
hjic-242	77	22	be	be	AUX
hjic-242	77	23	denoted	denote	VERB
hjic-242	77	24	by	by	ADP
hjic-242	77	25	c0	c0	PROPN
hjic-242	77	26	.	.	PUNCT
hjic-242	78	1	the	the	DET
hjic-242	78	2	change	change	NOUN
hjic-242	78	3	of	of	ADP
hjic-242	78	4	concentration	concentration	NOUN
hjic-242	78	5	in	in	ADP
hjic-242	78	6	the	the	DET
hjic-242	78	7	tank	tank	NOUN
hjic-242	78	8	can	can	AUX
hjic-242	78	9	be	be	AUX
hjic-242	78	10	described	describe	VERB
hjic-242	78	11	by	by	ADP
hjic-242	78	12	the	the	DET
hjic-242	78	13	following	follow	VERB
hjic-242	78	14	equation	equation	NOUN
hjic-242	78	15	:	:	PUNCT
hjic-242	78	16	(	(	PUNCT
hjic-242	78	17	)	)	PUNCT
hjic-242	78	18	cc	cc	PROPN
hjic-242	78	19	v	v	PROPN
hjic-242	78	20	qc	qc	PROPN
hjic-242	78	21	−=′	−=′	PROPN
hjic-242	78	22	0	0	NUM
hjic-242	79	1	(	(	PUNCT
hjic-242	79	2	3	3	NUM
hjic-242	79	3	)	)	PUNCT
hjic-242	79	4	where	where	SCONJ
hjic-242	79	5	c	c	NOUN
hjic-242	79	6	is	be	AUX
hjic-242	79	7	the	the	DET
hjic-242	79	8	concentration	concentration	NOUN
hjic-242	79	9	in	in	ADP
hjic-242	79	10	the	the	DET
hjic-242	79	11	tank	tank	NOUN
hjic-242	79	12	,	,	PUNCT
hjic-242	79	13	q	q	PROPN
hjic-242	79	14	is	be	AUX
hjic-242	79	15	the	the	DET
hjic-242	79	16	outlet	outlet	NOUN
hjic-242	79	17	flow	flow	NOUN
hjic-242	79	18	rate	rate	NOUN
hjic-242	79	19	and	and	CCONJ
hjic-242	79	20	v	v	NOUN
hjic-242	79	21	is	be	AUX
hjic-242	79	22	the	the	DET
hjic-242	79	23	volume	volume	NOUN
hjic-242	79	24	of	of	ADP
hjic-242	79	25	the	the	DET
hjic-242	79	26	tank	tank	NOUN
hjic-242	79	27	.	.	PUNCT
hjic-242	80	1	case	case	NOUN
hjic-242	80	2	a	a	X
hjic-242	80	3	)	)	PUNCT
hjic-242	80	4	let	let	VERB
hjic-242	80	5	us	we	PRON
hjic-242	80	6	assume	assume	VERB
hjic-242	80	7	that	that	SCONJ
hjic-242	80	8	we	we	PRON
hjic-242	80	9	know	know	VERB
hjic-242	80	10	the	the	DET
hjic-242	80	11	concentration	concentration	NOUN
hjic-242	80	12	of	of	ADP
hjic-242	80	13	the	the	DET
hjic-242	80	14	inlet	inlet	NOUN
hjic-242	80	15	flow	flow	NOUN
hjic-242	80	16	in	in	ADP
hjic-242	80	17	the	the	DET
hjic-242	80	18	function	function	NOUN
hjic-242	80	19	of	of	ADP
hjic-242	80	20	time	time	NOUN
hjic-242	80	21	:	:	PUNCT
hjic-242	80	22	c0	c0	NOUN
hjic-242	80	23	=	=	SYM
hjic-242	80	24	c(t	c(t	PROPN
hjic-242	80	25	)	)	PUNCT
hjic-242	80	26	,	,	PUNCT
hjic-242	80	27	and	and	CCONJ
hjic-242	80	28	we	we	PRON
hjic-242	80	29	want	want	VERB
hjic-242	80	30	to	to	PART
hjic-242	80	31	determine	determine	VERB
hjic-242	80	32	the	the	DET
hjic-242	80	33	concentration	concentration	NOUN
hjic-242	80	34	of	of	ADP
hjic-242	80	35	the	the	DET
hjic-242	80	36	outlet	outlet	NOUN
hjic-242	80	37	flow	flow	NOUN
hjic-242	80	38	.	.	PUNCT
hjic-242	81	1	the	the	DET
hjic-242	81	2	standard	standard	ADJ
hjic-242	81	3	form	form	NOUN
hjic-242	81	4	model	model	NOUN
hjic-242	81	5	consists	consist	VERB
hjic-242	81	6	of	of	ADP
hjic-242	81	7	the	the	DET
hjic-242	81	8	following	follow	VERB
hjic-242	81	9	equations	equation	NOUN
hjic-242	81	10	:	:	PUNCT
hjic-242	81	11	c	c	X
hjic-242	81	12	=	=	SYM
hjic-242	81	13	∫	∫	PROPN
hjic-242	81	14	c	c	X
hjic-242	81	15	’	'	PUNCT
hjic-242	81	16	(	(	PUNCT
hjic-242	81	17	)	)	PUNCT
hjic-242	81	18	cc	cc	PROPN
hjic-242	81	19	v	v	PROPN
hjic-242	81	20	qc	qc	PROPN
hjic-242	81	21	−=′	−=′	PROPN
hjic-242	81	22	0	0	NUM
hjic-242	82	1	c0	c0	PROPN
hjic-242	82	2	=	=	SYM
hjic-242	82	3	c0(t	c0(t	NOUN
hjic-242	82	4	)	)	PUNCT
hjic-242	82	5	given	give	VERB
hjic-242	82	6	:	:	PUNCT
hjic-242	82	7	c(t0	c(t0	NOUN
hjic-242	82	8	)	)	PUNCT
hjic-242	82	9	,	,	PUNCT
hjic-242	82	10	c0(t	c0(t	NOUN
hjic-242	82	11	)	)	PUNCT
hjic-242	82	12	;	;	PUNCT
hjic-242	82	13	constant	constant	ADJ
hjic-242	82	14	:	:	PUNCT
hjic-242	82	15	q	q	ADJ
hjic-242	82	16	,	,	PUNCT
hjic-242	82	17	v	v	ADJ
hjic-242	82	18	;	;	PUNCT
hjic-242	82	19	to	to	PART
hjic-242	82	20	be	be	AUX
hjic-242	82	21	calculated	calculate	VERB
hjic-242	82	22	:	:	PUNCT
hjic-242	82	23	c	c	X
hjic-242	82	24	as	as	ADP
hjic-242	82	25	a	a	DET
hjic-242	82	26	function	function	NOUN
hjic-242	82	27	of	of	ADP
hjic-242	82	28	time	time	NOUN
hjic-242	82	29	.	.	PUNCT
hjic-242	83	1	since	since	SCONJ
hjic-242	83	2	the	the	DET
hjic-242	83	3	structural	structural	ADJ
hjic-242	83	4	properties	property	NOUN
hjic-242	83	5	of	of	ADP
hjic-242	83	6	the	the	DET
hjic-242	83	7	model	model	NOUN
hjic-242	83	8	described	describe	VERB
hjic-242	83	9	by	by	ADP
hjic-242	83	10	representation	representation	NOUN
hjic-242	83	11	graph	graph	NOUN
hjic-242	83	12	can	can	AUX
hjic-242	83	13	be	be	AUX
hjic-242	83	14	investigated	investigate	VERB
hjic-242	83	15	based	base	VERB
hjic-242	83	16	on	on	ADP
hjic-242	83	17	the	the	DET
hjic-242	83	18	structure	structure	NOUN
hjic-242	83	19	of	of	ADP
hjic-242	83	20	the	the	DET
hjic-242	83	21	static	static	ADJ
hjic-242	83	22	graphs	graph	NOUN
hjic-242	83	23	,	,	PUNCT
hjic-242	83	24	and	and	CCONJ
hjic-242	83	25	these	these	DET
hjic-242	83	26	properties	property	NOUN
hjic-242	83	27	are	be	AUX
hjic-242	83	28	independent	independent	ADJ
hjic-242	83	29	from	from	ADP
hjic-242	83	30	the	the	DET
hjic-242	83	31	arcs	arcs	NOUN
hjic-242	83	32	connecting	connect	VERB
hjic-242	83	33	individual	individual	ADJ
hjic-242	83	34	static	static	ADJ
hjic-242	83	35	graphs	graph	NOUN
hjic-242	83	36	to	to	ADP
hjic-242	83	37	each	each	DET
hjic-242	83	38	other	other	ADJ
hjic-242	83	39	,	,	PUNCT
hjic-242	83	40	we	we	PRON
hjic-242	83	41	illustrate	illustrate	VERB
hjic-242	83	42	only	only	ADV
hjic-242	83	43	one	one	NUM
hjic-242	83	44	static	static	ADJ
hjic-242	83	45	graph	graph	NOUN
hjic-242	83	46	as	as	ADP
hjic-242	83	47	a	a	DET
hjic-242	83	48	representation	representation	NOUN
hjic-242	83	49	graph	graph	NOUN
hjic-242	83	50	of	of	ADP
hjic-242	83	51	models	model	NOUN
hjic-242	83	52	for	for	ADP
hjic-242	83	53	the	the	DET
hjic-242	83	54	sake	sake	NOUN
hjic-242	83	55	of	of	ADP
hjic-242	83	56	simplicity	simplicity	NOUN
hjic-242	83	57	.	.	PUNCT
hjic-242	84	1	the	the	DET
hjic-242	84	2	representation	representation	NOUN
hjic-242	84	3	graph	graph	NOUN
hjic-242	84	4	of	of	ADP
hjic-242	84	5	this	this	DET
hjic-242	84	6	simple	simple	ADJ
hjic-242	84	7	model	model	NOUN
hjic-242	84	8	is	be	AUX
hjic-242	84	9	shown	show	VERB
hjic-242	84	10	in	in	ADP
hjic-242	84	11	fig	fig	NOUN
hjic-242	84	12	.	.	PUNCT
hjic-242	85	1	2a	2a	NUM
hjic-242	85	2	.	.	PUNCT
hjic-242	86	1	the	the	DET
hjic-242	86	2	reduced	reduce	VERB
hjic-242	86	3	graph	graph	NOUN
hjic-242	86	4	is	be	AUX
hjic-242	86	5	an	an	DET
hjic-242	86	6	empty	empty	ADJ
hjic-242	86	7	graph	graph	NOUN
hjic-242	86	8	in	in	ADP
hjic-242	86	9	this	this	DET
hjic-242	86	10	case	case	NOUN
hjic-242	86	11	indicating	indicate	VERB
hjic-242	86	12	the	the	DET
hjic-242	86	13	differential	differential	ADJ
hjic-242	86	14	index	index	NOUN
hjic-242	86	15	is	be	AUX
hjic-242	86	16	equal	equal	ADJ
hjic-242	86	17	to	to	ADP
hjic-242	86	18	1	1	NUM
hjic-242	86	19	.	.	PUNCT
hjic-242	87	1	we	we	PRON
hjic-242	87	2	remark	remark	VERB
hjic-242	87	3	that	that	SCONJ
hjic-242	87	4	the	the	DET
hjic-242	87	5	substitution	substitution	NOUN
hjic-242	87	6	of	of	ADP
hjic-242	87	7	the	the	DET
hjic-242	87	8	condition	condition	NOUN
hjic-242	87	9	c0	c0	NOUN
hjic-242	87	10	=	=	SYM
hjic-242	87	11	c0(t	c0(t	PROPN
hjic-242	87	12	)	)	PUNCT
hjic-242	87	13	into	into	ADP
hjic-242	87	14	the	the	DET
hjic-242	87	15	equation	equation	NOUN
hjic-242	87	16	(	(	PUNCT
hjic-242	87	17	3	3	X
hjic-242	87	18	)	)	PUNCT
hjic-242	87	19	results	result	NOUN
hjic-242	87	20	in	in	ADP
hjic-242	87	21	a	a	DET
hjic-242	87	22	model	model	NOUN
hjic-242	87	23	of	of	ADP
hjic-242	87	24	148	148	NUM
hjic-242	87	25	technological	technological	ADJ
hjic-242	87	26	system	system	NOUN
hjic-242	87	27	with	with	ADP
hjic-242	87	28	only	only	ADV
hjic-242	87	29	one	one	NUM
hjic-242	87	30	differential	differential	ADJ
hjic-242	87	31	equation	equation	NOUN
hjic-242	87	32	,	,	PUNCT
hjic-242	87	33	so	so	CCONJ
hjic-242	87	34	the	the	DET
hjic-242	87	35	differential	differential	ADJ
hjic-242	87	36	index	index	NOUN
hjic-242	87	37	would	would	AUX
hjic-242	87	38	be	be	AUX
hjic-242	87	39	equal	equal	ADJ
hjic-242	87	40	to	to	ADP
hjic-242	87	41	0	0	NUM
hjic-242	87	42	.	.	PUNCT
hjic-242	88	1	case	case	NOUN
hjic-242	88	2	b	b	X
hjic-242	88	3	)	)	PUNCT
hjic-242	88	4	let	let	VERB
hjic-242	88	5	us	we	PRON
hjic-242	88	6	assume	assume	VERB
hjic-242	88	7	now	now	ADV
hjic-242	88	8	that	that	SCONJ
hjic-242	88	9	the	the	DET
hjic-242	88	10	modelling	modelling	ADJ
hjic-242	88	11	goal	goal	NOUN
hjic-242	88	12	is	be	AUX
hjic-242	88	13	the	the	DET
hjic-242	88	14	dynamic	dynamic	ADJ
hjic-242	88	15	design	design	NOUN
hjic-242	88	16	of	of	ADP
hjic-242	88	17	the	the	DET
hjic-242	88	18	same	same	ADJ
hjic-242	88	19	system	system	NOUN
hjic-242	88	20	,	,	PUNCT
hjic-242	88	21	i.e.	i.e.	X
hjic-242	88	22	the	the	DET
hjic-242	88	23	determination	determination	NOUN
hjic-242	88	24	of	of	ADP
hjic-242	88	25	the	the	DET
hjic-242	88	26	necessary	necessary	ADJ
hjic-242	88	27	inlet	inlet	NOUN
hjic-242	88	28	flow	flow	NOUN
hjic-242	88	29	concentration	concentration	NOUN
hjic-242	88	30	in	in	ADP
hjic-242	88	31	order	order	NOUN
hjic-242	88	32	to	to	PART
hjic-242	88	33	ensure	ensure	VERB
hjic-242	88	34	the	the	DET
hjic-242	88	35	required	require	VERB
hjic-242	88	36	outlet	outlet	NOUN
hjic-242	88	37	concentration	concentration	NOUN
hjic-242	88	38	c	c	NOUN
hjic-242	88	39	=	=	SYM
hjic-242	88	40	c(t	c(t	PROPN
hjic-242	88	41	)	)	PUNCT
hjic-242	88	42	.	.	PUNCT
hjic-242	89	1	the	the	DET
hjic-242	89	2	standard	standard	ADJ
hjic-242	89	3	form	form	NOUN
hjic-242	89	4	model	model	NOUN
hjic-242	89	5	is	be	AUX
hjic-242	89	6	the	the	DET
hjic-242	89	7	following	following	NOUN
hjic-242	89	8	:	:	PUNCT
hjic-242	89	9	a	a	X
hjic-242	89	10	)	)	PUNCT
hjic-242	89	11	b	b	NOUN
hjic-242	89	12	)	)	PUNCT
hjic-242	89	13	figure	figure	NOUN
hjic-242	89	14	2	2	NUM
hjic-242	89	15	:	:	PUNCT
hjic-242	89	16	the	the	DET
hjic-242	89	17	representation	representation	NOUN
hjic-242	89	18	graphs	graph	NOUN
hjic-242	89	19	of	of	ADP
hjic-242	89	20	the	the	DET
hjic-242	89	21	example	example	NOUN
hjic-242	89	22	1	1	NUM
hjic-242	89	23	c	c	NOUN
hjic-242	89	24	=	=	SYM
hjic-242	89	25	∫	∫	PROPN
hjic-242	89	26	c	c	X
hjic-242	89	27	’	'	PUNCT
hjic-242	89	28	(	(	PUNCT
hjic-242	89	29	)	)	PUNCT
hjic-242	89	30	cc	cc	PROPN
hjic-242	89	31	v	v	PROPN
hjic-242	89	32	qc	qc	PROPN
hjic-242	89	33	−=′	−=′	PROPN
hjic-242	89	34	0	0	PUNCT
hjic-242	90	1	c	c	NOUN
hjic-242	90	2	=	=	SYM
hjic-242	90	3	c(t	c(t	PROPN
hjic-242	90	4	)	)	PUNCT
hjic-242	90	5	given	give	VERB
hjic-242	90	6	:	:	PUNCT
hjic-242	90	7	c(t0	c(t0	NOUN
hjic-242	90	8	)	)	PUNCT
hjic-242	90	9	,	,	PUNCT
hjic-242	90	10	c(t	c(t	PROPN
hjic-242	90	11	)	)	PUNCT
hjic-242	90	12	;	;	PUNCT
hjic-242	90	13	constant	constant	ADJ
hjic-242	90	14	:	:	PUNCT
hjic-242	90	15	q	q	ADJ
hjic-242	90	16	,	,	PUNCT
hjic-242	90	17	v	v	ADJ
hjic-242	90	18	;	;	PUNCT
hjic-242	90	19	to	to	PART
hjic-242	90	20	be	be	AUX
hjic-242	90	21	calculated	calculate	VERB
hjic-242	90	22	:	:	PUNCT
hjic-242	90	23	c0	c0	NOUN
hjic-242	90	24	as	as	ADP
hjic-242	90	25	a	a	DET
hjic-242	90	26	function	function	NOUN
hjic-242	90	27	of	of	ADP
hjic-242	90	28	time	time	NOUN
hjic-242	90	29	.	.	PUNCT
hjic-242	91	1	in	in	ADP
hjic-242	91	2	this	this	DET
hjic-242	91	3	case	case	NOUN
hjic-242	91	4	,	,	PUNCT
hjic-242	91	5	there	there	PRON
hjic-242	91	6	are	be	VERB
hjic-242	91	7	an	an	DET
hjic-242	91	8	underspecified	underspecified	ADJ
hjic-242	91	9	and	and	CCONJ
hjic-242	91	10	an	an	DET
hjic-242	91	11	overspecified	overspecified	ADJ
hjic-242	91	12	subgraphs	subgraphs	NOUN
hjic-242	91	13	on	on	ADP
hjic-242	91	14	the	the	DET
hjic-242	91	15	representation	representation	NOUN
hjic-242	91	16	graph	graph	NOUN
hjic-242	91	17	(	(	PUNCT
hjic-242	91	18	see	see	VERB
hjic-242	91	19	fig	fig	NOUN
hjic-242	91	20	.	.	PUNCT
hjic-242	91	21	2b	2b	NOUN
hjic-242	91	22	)	)	PUNCT
hjic-242	91	23	referring	refer	VERB
hjic-242	91	24	to	to	ADP
hjic-242	91	25	the	the	DET
hjic-242	91	26	differential	differential	ADJ
hjic-242	91	27	index	index	NOUN
hjic-242	91	28	greater	great	ADJ
hjic-242	91	29	than	than	ADP
hjic-242	91	30	1	1	NUM
hjic-242	91	31	value	value	NOUN
hjic-242	91	32	.	.	PUNCT
hjic-242	92	1	the	the	DET
hjic-242	92	2	differential	differential	ADJ
hjic-242	92	3	index	index	NOUN
hjic-242	92	4	can	can	AUX
hjic-242	92	5	be	be	AUX
hjic-242	92	6	calculated	calculate	VERB
hjic-242	92	7	based	base	VERB
hjic-242	92	8	on	on	ADP
hjic-242	92	9	the	the	DET
hjic-242	92	10	structure	structure	NOUN
hjic-242	92	11	of	of	ADP
hjic-242	92	12	the	the	DET
hjic-242	92	13	representation	representation	NOUN
hjic-242	92	14	graph	graph	NOUN
hjic-242	92	15	:	:	PUNCT
hjic-242	92	16	i0	i0	PROPN
hjic-242	92	17	=	=	PUNCT
hjic-242	92	18	{	{	PUNCT
hjic-242	92	19	c	c	NOUN
hjic-242	92	20	}	}	PUNCT
hjic-242	92	21	d0	d0	NOUN
hjic-242	92	22	=	=	SYM
hjic-242	92	23	{	{	PUNCT
hjic-242	92	24	c	c	NOUN
hjic-242	92	25	’	'	PUNCT
hjic-242	92	26	}	}	PUNCT
hjic-242	92	27	since	since	SCONJ
hjic-242	92	28	the	the	DET
hjic-242	92	29	vertex	vertex	NOUN
hjic-242	92	30	referring	refer	VERB
hjic-242	92	31	to	to	ADP
hjic-242	92	32	the	the	DET
hjic-242	92	33	derivative	derivative	ADJ
hjic-242	92	34	variable	variable	NOUN
hjic-242	92	35	c	c	NOUN
hjic-242	92	36	’	'	PUNCT
hjic-242	92	37	can	can	AUX
hjic-242	92	38	be	be	AUX
hjic-242	92	39	found	find	VERB
hjic-242	92	40	in	in	ADP
hjic-242	92	41	the	the	DET
hjic-242	92	42	underspecified	underspecified	ADJ
hjic-242	92	43	subgraph	subgraph	NOUN
hjic-242	92	44	,	,	PUNCT
hjic-242	92	45	therefore	therefore	ADV
hjic-242	92	46	n	n	CCONJ
hjic-242	92	47	=	=	SYM
hjic-242	92	48	0	0	NUM
hjic-242	92	49	and	and	CCONJ
hjic-242	92	50	νd	νd	NOUN
hjic-242	92	51	=	=	SYM
hjic-242	92	52	n	n	PROPN
hjic-242	92	53	+	+	CCONJ
hjic-242	92	54	2	2	NUM
hjic-242	92	55	=	=	SYM
hjic-242	92	56	2	2	NUM
hjic-242	92	57	.	.	NOUN
hjic-242	92	58	example	example	NOUN
hjic-242	92	59	2a	2a	NUM
hjic-242	92	60	–	–	PUNCT
hjic-242	92	61	liquid	liquid	ADJ
hjic-242	92	62	mixer	mixer	NOUN
hjic-242	92	63	model	model	NOUN
hjic-242	92	64	suppose	suppose	VERB
hjic-242	92	65	a	a	DET
hjic-242	92	66	liquid	liquid	ADJ
hjic-242	92	67	mixer	mixer	NOUN
hjic-242	92	68	tank	tank	NOUN
hjic-242	92	69	having	have	VERB
hjic-242	92	70	one	one	NUM
hjic-242	92	71	inlet	inlet	NOUN
hjic-242	92	72	and	and	CCONJ
hjic-242	92	73	one	one	NUM
hjic-242	92	74	outlet	outlet	NOUN
hjic-242	92	75	flow	flow	NOUN
hjic-242	92	76	(	(	PUNCT
hjic-242	92	77	see	see	VERB
hjic-242	92	78	fig	fig	NOUN
hjic-242	92	79	.	.	PUNCT
hjic-242	93	1	3	3	X
hjic-242	93	2	)	)	PUNCT
hjic-242	93	3	the	the	DET
hjic-242	93	4	inlet	inlet	NOUN
hjic-242	93	5	flow	flow	NOUN
hjic-242	93	6	consists	consist	VERB
hjic-242	93	7	of	of	ADP
hjic-242	93	8	two	two	NUM
hjic-242	93	9	components	component	NOUN
hjic-242	93	10	a	a	PRON
hjic-242	93	11	and	and	CCONJ
hjic-242	93	12	b.	b.	X
hjic-242	94	1	the	the	DET
hjic-242	94	2	two	two	NUM
hjic-242	94	3	components	component	NOUN
hjic-242	94	4	have	have	VERB
hjic-242	94	5	different	different	ADJ
hjic-242	94	6	density	density	NOUN
hjic-242	94	7	.	.	PUNCT
hjic-242	95	1	there	there	PRON
hjic-242	95	2	is	be	VERB
hjic-242	95	3	a	a	DET
hjic-242	95	4	certain	certain	ADJ
hjic-242	95	5	amount	amount	NOUN
hjic-242	95	6	of	of	ADP
hjic-242	95	7	liquid	liquid	NOUN
hjic-242	95	8	in	in	ADP
hjic-242	95	9	tank	tank	NOUN
hjic-242	95	10	at	at	ADP
hjic-242	95	11	t	t	PROPN
hjic-242	95	12	=	=	SYM
hjic-242	95	13	t0	t0	PROPN
hjic-242	95	14	.	.	PUNCT
hjic-242	96	1	the	the	DET
hjic-242	96	2	feed	feed	NOUN
hjic-242	96	3	is	be	AUX
hjic-242	96	4	perfectly	perfectly	ADV
hjic-242	96	5	mixed	mixed	ADJ
hjic-242	96	6	with	with	ADP
hjic-242	96	7	the	the	DET
hjic-242	96	8	tank	tank	NOUN
hjic-242	96	9	liquid	liquid	NOUN
hjic-242	96	10	.	.	PUNCT
hjic-242	97	1	the	the	DET
hjic-242	97	2	density	density	NOUN
hjic-242	97	3	of	of	ADP
hjic-242	97	4	the	the	DET
hjic-242	97	5	liquid	liquid	NOUN
hjic-242	97	6	in	in	ADP
hjic-242	97	7	tank	tank	NOUN
hjic-242	97	8	,	,	PUNCT
hjic-242	97	9	the	the	DET
hjic-242	97	10	flow	flow	NOUN
hjic-242	97	11	rates	rate	NOUN
hjic-242	97	12	and	and	CCONJ
hjic-242	97	13	the	the	DET
hjic-242	97	14	mol	mol	NOUN
hjic-242	97	15	fractions	fraction	NOUN
hjic-242	97	16	of	of	ADP
hjic-242	97	17	the	the	DET
hjic-242	97	18	components	component	NOUN
hjic-242	97	19	are	be	AUX
hjic-242	97	20	functions	function	NOUN
hjic-242	97	21	of	of	ADP
hjic-242	97	22	time	time	NOUN
hjic-242	97	23	.	.	PUNCT
hjic-242	98	1	the	the	DET
hjic-242	98	2	number	number	NOUN
hjic-242	98	3	of	of	ADP
hjic-242	98	4	moles	mole	NOUN
hjic-242	98	5	(	(	PUNCT
hjic-242	98	6	ni	ni	NOUN
hjic-242	98	7	)	)	PUNCT
hjic-242	98	8	of	of	ADP
hjic-242	98	9	components	component	NOUN
hjic-242	98	10	a	a	PRON
hjic-242	98	11	and	and	CCONJ
hjic-242	98	12	b	b	NOUN
hjic-242	98	13	can	can	AUX
hjic-242	98	14	be	be	AUX
hjic-242	98	15	described	describe	VERB
hjic-242	98	16	by	by	ADP
hjic-242	98	17	the	the	DET
hjic-242	98	18	following	follow	VERB
hjic-242	98	19	equation	equation	NOUN
hjic-242	98	20	:	:	PUNCT
hjic-242	98	21	ni	ni	NOUN
hjic-242	98	22	’	'	PUNCT
hjic-242	98	23	=	=	SYM
hjic-242	98	24	f0xi0	f0xi0	X
hjic-242	98	25	–	–	PUNCT
hjic-242	98	26	fxi	fxi	NOUN
hjic-242	98	27	where	where	SCONJ
hjic-242	98	28	i	i	PRON
hjic-242	98	29	=	=	X
hjic-242	98	30	{	{	PUNCT
hjic-242	98	31	a	a	DET
hjic-242	98	32	,	,	PUNCT
hjic-242	98	33	b	b	NOUN
hjic-242	98	34	}	}	PUNCT
hjic-242	98	35	where	where	SCONJ
hjic-242	98	36	f0	f0	PROPN
hjic-242	98	37	and	and	CCONJ
hjic-242	98	38	f	f	PROPN
hjic-242	98	39	are	be	AUX
hjic-242	98	40	the	the	DET
hjic-242	98	41	inlet	inlet	NOUN
hjic-242	98	42	and	and	CCONJ
hjic-242	98	43	outlet	outlet	NOUN
hjic-242	98	44	flow	flow	NOUN
hjic-242	98	45	rate	rate	NOUN
hjic-242	98	46	,	,	PUNCT
hjic-242	98	47	and	and	CCONJ
hjic-242	98	48	xi0	xi0	PROPN
hjic-242	98	49	and	and	CCONJ
hjic-242	98	50	xi	xi	PROPN
hjic-242	98	51	are	be	AUX
hjic-242	98	52	the	the	DET
hjic-242	98	53	mol	mol	ADP
hjic-242	98	54	fraction	fraction	NOUN
hjic-242	98	55	of	of	ADP
hjic-242	98	56	the	the	DET
hjic-242	98	57	component	component	NOUN
hjic-242	98	58	i	i	PRON
hjic-242	98	59	in	in	ADP
hjic-242	98	60	the	the	DET
hjic-242	98	61	inlet	inlet	NOUN
hjic-242	98	62	and	and	CCONJ
hjic-242	98	63	outlet	outlet	NOUN
hjic-242	98	64	flows	flow	NOUN
hjic-242	98	65	,	,	PUNCT
hjic-242	98	66	resp	resp	NOUN
hjic-242	98	67	.	.	PUNCT
hjic-242	99	1	let	let	VERB
hjic-242	99	2	pl	pl	PART
hjic-242	99	3	denote	denote	VERB
hjic-242	99	4	the	the	DET
hjic-242	99	5	pressure	pressure	NOUN
hjic-242	99	6	of	of	ADP
hjic-242	99	7	the	the	DET
hjic-242	99	8	liquid	liquid	NOUN
hjic-242	99	9	at	at	ADP
hjic-242	99	10	the	the	DET
hjic-242	99	11	bottom	bottom	NOUN
hjic-242	99	12	of	of	ADP
hjic-242	99	13	the	the	DET
hjic-242	99	14	tank	tank	NOUN
hjic-242	99	15	,	,	PUNCT
hjic-242	99	16	a	a	DET
hjic-242	99	17	the	the	DET
hjic-242	99	18	area	area	NOUN
hjic-242	99	19	of	of	ADP
hjic-242	99	20	the	the	DET
hjic-242	99	21	tank	tank	NOUN
hjic-242	99	22	and	and	CCONJ
hjic-242	99	23	mwi	mwi	PROPN
hjic-242	99	24	the	the	DET
hjic-242	99	25	molar	molar	ADJ
hjic-242	99	26	weight	weight	NOUN
hjic-242	99	27	of	of	ADP
hjic-242	99	28	the	the	DET
hjic-242	99	29	component	component	NOUN
hjic-242	99	30	i.	i.	PROPN
hjic-242	99	31	the	the	DET
hjic-242	99	32	outlet	outlet	NOUN
hjic-242	99	33	flow	flow	NOUN
hjic-242	99	34	rate	rate	NOUN
hjic-242	99	35	depends	depend	VERB
hjic-242	99	36	on	on	ADP
hjic-242	99	37	the	the	DET
hjic-242	99	38	liquid	liquid	ADJ
hjic-242	99	39	pressure	pressure	NOUN
hjic-242	99	40	(	(	PUNCT
hjic-242	99	41	pl	pl	NOUN
hjic-242	99	42	)	)	PUNCT
hjic-242	99	43	and	and	CCONJ
hjic-242	99	44	the	the	DET
hjic-242	99	45	valve	valve	NOUN
hjic-242	99	46	constant	constant	ADJ
hjic-242	99	47	(	(	PUNCT
hjic-242	99	48	k	k	NOUN
hjic-242	99	49	)	)	PUNCT
hjic-242	99	50	.	.	PUNCT
hjic-242	100	1	figure	figure	VERB
hjic-242	100	2	3	3	NUM
hjic-242	100	3	:	:	PUNCT
hjic-242	100	4	liquid	liquid	ADJ
hjic-242	100	5	mixer	mixer	NOUN
hjic-242	100	6	tank	tank	NOUN
hjic-242	100	7	with	with	ADP
hjic-242	100	8	variable	variable	ADJ
hjic-242	100	9	volume	volume	NOUN
hjic-242	100	10	the	the	DET
hjic-242	100	11	modelling	model	VERB
hjic-242	100	12	goal	goal	NOUN
hjic-242	100	13	is	be	AUX
hjic-242	100	14	to	to	PART
hjic-242	100	15	calculate	calculate	VERB
hjic-242	100	16	the	the	DET
hjic-242	100	17	liquid	liquid	ADJ
hjic-242	100	18	composition	composition	NOUN
hjic-242	100	19	in	in	ADP
hjic-242	100	20	the	the	DET
hjic-242	100	21	tank	tank	NOUN
hjic-242	100	22	.	.	PUNCT
hjic-242	101	1	the	the	DET
hjic-242	101	2	standard	standard	ADJ
hjic-242	101	3	form	form	NOUN
hjic-242	101	4	model	model	NOUN
hjic-242	101	5	consists	consist	VERB
hjic-242	101	6	of	of	ADP
hjic-242	101	7	the	the	DET
hjic-242	101	8	following	follow	VERB
hjic-242	101	9	equations	equation	NOUN
hjic-242	101	10	:	:	PUNCT
hjic-242	101	11	na	na	ADP
hjic-242	101	12	=	=	SYM
hjic-242	101	13	∫	∫	PROPN
hjic-242	101	14	na	na	NOUN
hjic-242	101	15	’	'	PUNCT
hjic-242	101	16	nb	nb	PROPN
hjic-242	101	17	=	=	SYM
hjic-242	101	18	∫	∫	PROPN
hjic-242	101	19	nb	nb	INTJ
hjic-242	101	20	’	'	PUNCT
hjic-242	101	21	na	na	NOUN
hjic-242	101	22	’	'	PUNCT
hjic-242	102	1	=	=	SYM
hjic-242	102	2	f0xa0	f0xa0	ADJ
hjic-242	102	3	–	–	PUNCT
hjic-242	102	4	fxa	fxa	NOUN
hjic-242	102	5	nb	nb	NOUN
hjic-242	102	6	’	'	PUNCT
hjic-242	102	7	=	=	NOUN
hjic-242	102	8	f0xb0	f0xb0	NOUN
hjic-242	102	9	–	–	PUNCT
hjic-242	102	10	fxb	fxb	NOUN
hjic-242	102	11	n	n	NOUN
hjic-242	102	12	=	=	SYM
hjic-242	102	13	na	na	PROPN
hjic-242	103	1	+	+	NOUN
hjic-242	103	2	nb	nb	INTJ
hjic-242	103	3	xa	xa	PROPN
hjic-242	103	4	=	=	PUNCT
hjic-242	103	5	na	na	PROPN
hjic-242	103	6	/	/	SYM
hjic-242	103	7	n	n	NOUN
hjic-242	103	8	xb	xb	NOUN
hjic-242	103	9	=	=	PUNCT
hjic-242	103	10	nb	nb	PROPN
hjic-242	103	11	/	/	SYM
hjic-242	103	12	n	n	CCONJ
hjic-242	103	13	mw	mw	NOUN
hjic-242	103	14	=	=	NOUN
hjic-242	103	15	mwaxa	mwaxa	PROPN
hjic-242	103	16	+	+	CCONJ
hjic-242	103	17	mwbxb	mwbxb	VERB
hjic-242	103	18	pl	pl	X
hjic-242	103	19	=	=	NOUN
hjic-242	103	20	p0	p0	NOUN
hjic-242	103	21	+	+	PROPN
hjic-242	103	22	(	(	PUNCT
hjic-242	103	23	mw	mw	X
hjic-242	103	24	⋅	⋅	PROPN
hjic-242	103	25	n)/a	n)/a	PROPN
hjic-242	103	26	f	f	PROPN
hjic-242	103	27	=	=	SYM
hjic-242	103	28	k⋅(pl	k⋅(pl	PROPN
hjic-242	103	29	–	–	PUNCT
hjic-242	103	30	p0)1/2	p0)1/2	NOUN
hjic-242	103	31	given	give	VERB
hjic-242	103	32	:	:	PUNCT
hjic-242	103	33	na(t0	na(t0	NUM
hjic-242	103	34	)	)	PUNCT
hjic-242	103	35	,	,	PUNCT
hjic-242	103	36	nb(t0	nb(t0	NOUN
hjic-242	103	37	)	)	PUNCT
hjic-242	103	38	,	,	PUNCT
hjic-242	103	39	xa0	xa0	PROPN
hjic-242	103	40	,	,	PUNCT
hjic-242	103	41	xb0	xb0	PROPN
hjic-242	103	42	,	,	PUNCT
hjic-242	103	43	f0	f0	PROPN
hjic-242	103	44	;	;	PUNCT
hjic-242	103	45	constant	constant	ADJ
hjic-242	103	46	:	:	PUNCT
hjic-242	103	47	mwa	mwa	PROPN
hjic-242	103	48	,	,	PUNCT
hjic-242	103	49	mwb	mwb	PROPN
hjic-242	103	50	,	,	PUNCT
hjic-242	103	51	a	a	PRON
hjic-242	103	52	,	,	PUNCT
hjic-242	103	53	k	k	NOUN
hjic-242	103	54	,	,	PUNCT
hjic-242	103	55	p0	p0	NOUN
hjic-242	103	56	;	;	PUNCT
hjic-242	103	57	to	to	PART
hjic-242	103	58	be	be	AUX
hjic-242	103	59	calculated	calculate	VERB
hjic-242	103	60	:	:	PUNCT
hjic-242	103	61	na	na	PART
hjic-242	103	62	,	,	PUNCT
hjic-242	103	63	nb	nb	PROPN
hjic-242	103	64	,	,	PUNCT
hjic-242	103	65	f	f	PROPN
hjic-242	103	66	as	as	ADP
hjic-242	103	67	functions	function	NOUN
hjic-242	103	68	of	of	ADP
hjic-242	103	69	time	time	NOUN
hjic-242	103	70	.	.	PUNCT
hjic-242	104	1	the	the	DET
hjic-242	104	2	representation	representation	NOUN
hjic-242	104	3	graph	graph	NOUN
hjic-242	104	4	of	of	ADP
hjic-242	104	5	the	the	DET
hjic-242	104	6	model	model	NOUN
hjic-242	104	7	is	be	AUX
hjic-242	104	8	shown	show	VERB
hjic-242	104	9	in	in	ADP
hjic-242	104	10	fig	fig	NOUN
hjic-242	104	11	.	.	PUNCT
hjic-242	105	1	4	4	X
hjic-242	105	2	.	.	X
hjic-242	105	3	the	the	DET
hjic-242	105	4	reduced	reduce	VERB
hjic-242	105	5	graph	graph	NOUN
hjic-242	105	6	is	be	AUX
hjic-242	105	7	an	an	DET
hjic-242	105	8	empty	empty	ADJ
hjic-242	105	9	graph	graph	NOUN
hjic-242	105	10	because	because	SCONJ
hjic-242	105	11	there	there	PRON
hjic-242	105	12	is	be	VERB
hjic-242	105	13	no	no	DET
hjic-242	105	14	implicit	implicit	ADJ
hjic-242	105	15	equation	equation	NOUN
hjic-242	105	16	in	in	ADP
hjic-242	105	17	the	the	DET
hjic-242	105	18	model	model	NOUN
hjic-242	105	19	,	,	PUNCT
hjic-242	105	20	therefore	therefore	ADV
hjic-242	105	21	the	the	DET
hjic-242	105	22	differential	differential	ADJ
hjic-242	105	23	index	index	NOUN
hjic-242	105	24	(	(	PUNCT
hjic-242	105	25	νd	νd	NOUN
hjic-242	105	26	)	)	PUNCT
hjic-242	105	27	is	be	AUX
hjic-242	105	28	equal	equal	ADJ
hjic-242	105	29	to	to	ADP
hjic-242	105	30	1	1	NUM
hjic-242	105	31	.	.	PUNCT
hjic-242	105	32	figure	figure	VERB
hjic-242	105	33	4	4	NUM
hjic-242	105	34	:	:	PUNCT
hjic-242	105	35	the	the	DET
hjic-242	105	36	representation	representation	NOUN
hjic-242	105	37	graph	graph	NOUN
hjic-242	105	38	of	of	ADP
hjic-242	105	39	the	the	DET
hjic-242	105	40	example	example	NOUN
hjic-242	105	41	2a	2a	NUM
hjic-242	105	42	example	example	NOUN
hjic-242	105	43	2b	2b	NOUN
hjic-242	105	44	–	–	PUNCT
hjic-242	105	45	liquid	liquid	ADJ
hjic-242	105	46	mixer	mixer	NOUN
hjic-242	105	47	model	model	NOUN
hjic-242	105	48	with	with	ADP
hjic-242	105	49	constant	constant	ADJ
hjic-242	105	50	tank	tank	NOUN
hjic-242	105	51	volume	volume	NOUN
hjic-242	105	52	suppose	suppose	VERB
hjic-242	105	53	a	a	DET
hjic-242	105	54	liquid	liquid	ADJ
hjic-242	105	55	mixer	mixer	NOUN
hjic-242	105	56	tank	tank	NOUN
hjic-242	105	57	as	as	ADP
hjic-242	105	58	in	in	ADP
hjic-242	105	59	example	example	NOUN
hjic-242	105	60	2a	2a	NUM
hjic-242	105	61	but	but	CCONJ
hjic-242	105	62	let	let	VERB
hjic-242	105	63	the	the	DET
hjic-242	105	64	volume	volume	NOUN
hjic-242	105	65	of	of	ADP
hjic-242	105	66	the	the	DET
hjic-242	105	67	liquid	liquid	NOUN
hjic-242	105	68	in	in	ADP
hjic-242	105	69	the	the	DET
hjic-242	105	70	tank	tank	NOUN
hjic-242	105	71	v	v	NOUN
hjic-242	105	72	be	be	AUX
hjic-242	105	73	constant	constant	ADJ
hjic-242	105	74	in	in	ADP
hjic-242	105	75	this	this	DET
hjic-242	105	76	case	case	NOUN
hjic-242	105	77	(	(	PUNCT
hjic-242	105	78	fig	fig	NOUN
hjic-242	105	79	.	.	PUNCT
hjic-242	105	80	5	5	NUM
hjic-242	105	81	)	)	PUNCT
hjic-242	105	82	.	.	PUNCT
hjic-242	106	1	let	let	VERB
hjic-242	106	2	va	va	NOUN
hjic-242	106	3	and	and	CCONJ
hjic-242	106	4	vb	vb	NOUN
hjic-242	106	5	be	be	AUX
hjic-242	106	6	the	the	DET
hjic-242	106	7	molar	molar	ADJ
hjic-242	106	8	specific	specific	ADJ
hjic-242	106	9	volumes	volume	NOUN
hjic-242	106	10	of	of	ADP
hjic-242	106	11	components	component	NOUN
hjic-242	106	12	a	a	PRON
hjic-242	106	13	and	and	CCONJ
hjic-242	106	14	b	b	NOUN
hjic-242	106	15	,	,	PUNCT
hjic-242	106	16	resp	resp	NOUN
hjic-242	106	17	.	.	PUNCT
hjic-242	107	1	the	the	DET
hjic-242	107	2	other	other	ADJ
hjic-242	107	3	assumptions	assumption	NOUN
hjic-242	107	4	are	be	AUX
hjic-242	107	5	the	the	DET
hjic-242	107	6	same	same	ADJ
hjic-242	107	7	as	as	ADP
hjic-242	107	8	in	in	ADP
hjic-242	107	9	example	example	NOUN
hjic-242	107	10	2a	2a	NUM
hjic-242	107	11	.	.	PUNCT
hjic-242	108	1	the	the	DET
hjic-242	108	2	modelling	modelling	ADJ
hjic-242	108	3	goal	goal	NOUN
hjic-242	108	4	is	be	AUX
hjic-242	108	5	to	to	PART
hjic-242	108	6	calculate	calculate	VERB
hjic-242	108	7	the	the	DET
hjic-242	108	8	liquid	liquid	ADJ
hjic-242	108	9	composition	composition	NOUN
hjic-242	108	10	in	in	ADP
hjic-242	108	11	the	the	DET
hjic-242	108	12	tank	tank	NOUN
hjic-242	108	13	,	,	PUNCT
hjic-242	108	14	again	again	ADV
hjic-242	108	15	,	,	PUNCT
hjic-242	108	16	but	but	CCONJ
hjic-242	108	17	the	the	DET
hjic-242	108	18	modified	modify	VERB
hjic-242	108	19	volume	volume	NOUN
hjic-242	108	20	condition	condition	NOUN
hjic-242	108	21	must	must	AUX
hjic-242	108	22	be	be	AUX
hjic-242	108	23	taken	take	VERB
hjic-242	108	24	into	into	ADP
hjic-242	108	25	account	account	NOUN
hjic-242	108	26	.	.	PUNCT
hjic-242	109	1	the	the	DET
hjic-242	109	2	standard	standard	ADJ
hjic-242	109	3	form	form	NOUN
hjic-242	109	4	model	model	NOUN
hjic-242	109	5	consists	consist	VERB
hjic-242	109	6	of	of	ADP
hjic-242	109	7	the	the	DET
hjic-242	109	8	following	follow	VERB
hjic-242	109	9	equations	equation	NOUN
hjic-242	109	10	:	:	PUNCT
hjic-242	109	11	na	na	ADP
hjic-242	109	12	=	=	SYM
hjic-242	109	13	∫	∫	PROPN
hjic-242	109	14	na	na	NOUN
hjic-242	109	15	’	'	PUNCT
hjic-242	109	16	nb	nb	PROPN
hjic-242	109	17	=	=	SYM
hjic-242	109	18	∫	∫	PROPN
hjic-242	109	19	nb	nb	INTJ
hjic-242	109	20	’	'	PUNCT
hjic-242	109	21	na	na	NOUN
hjic-242	109	22	’	'	PUNCT
hjic-242	109	23	=	=	NOUN
hjic-242	109	24	f0xa0	f0xa0	ADJ
hjic-242	109	25	–	–	PUNCT
hjic-242	109	26	fxa	fxa	NOUN
hjic-242	109	27	nb	nb	NOUN
hjic-242	109	28	’	'	PUNCT
hjic-242	109	29	=	=	NOUN
hjic-242	109	30	f0xb0	f0xb0	NOUN
hjic-242	109	31	–	–	PUNCT
hjic-242	109	32	fxb	fxb	VERB
hjic-242	109	33	149	149	NUM
hjic-242	109	34	n	n	NOUN
hjic-242	109	35	=	=	SYM
hjic-242	109	36	na	na	PROPN
hjic-242	110	1	+	+	NOUN
hjic-242	110	2	nb	nb	INTJ
hjic-242	110	3	xa	xa	PROPN
hjic-242	110	4	=	=	PUNCT
hjic-242	110	5	na	na	PROPN
hjic-242	110	6	/	/	SYM
hjic-242	110	7	n	n	NOUN
hjic-242	110	8	xb	xb	NOUN
hjic-242	110	9	=	=	PUNCT
hjic-242	110	10	nb	nb	PROPN
hjic-242	110	11	/	/	SYM
hjic-242	110	12	n	n	PROPN
hjic-242	110	13	v	v	NOUN
hjic-242	110	14	=	=	NOUN
hjic-242	110	15	vaxa	vaxa	NOUN
hjic-242	110	16	+	+	CCONJ
hjic-242	110	17	vbxb	vbxb	PROPN
hjic-242	110	18	v	v	NOUN
hjic-242	110	19	=	=	SYM
hjic-242	110	20	n⋅v	n⋅v	PROPN
hjic-242	110	21	given	give	VERB
hjic-242	110	22	:	:	PUNCT
hjic-242	110	23	na(t0	na(t0	NUM
hjic-242	110	24	)	)	PUNCT
hjic-242	110	25	,	,	PUNCT
hjic-242	110	26	nb(t0	nb(t0	NOUN
hjic-242	110	27	)	)	PUNCT
hjic-242	110	28	,	,	PUNCT
hjic-242	110	29	xa0	xa0	PROPN
hjic-242	110	30	,	,	PUNCT
hjic-242	110	31	xb0	xb0	PROPN
hjic-242	110	32	,	,	PUNCT
hjic-242	110	33	f0	f0	PROPN
hjic-242	110	34	,	,	PUNCT
hjic-242	110	35	v	v	NOUN
hjic-242	110	36	;	;	PUNCT
hjic-242	110	37	constant	constant	ADJ
hjic-242	110	38	:	:	PUNCT
hjic-242	110	39	va	va	NOUN
hjic-242	110	40	,	,	PUNCT
hjic-242	110	41	vb	vb	NOUN
hjic-242	110	42	;	;	PUNCT
hjic-242	110	43	to	to	PART
hjic-242	110	44	be	be	AUX
hjic-242	110	45	calculated	calculate	VERB
hjic-242	110	46	:	:	PUNCT
hjic-242	110	47	na	na	PART
hjic-242	110	48	,	,	PUNCT
hjic-242	110	49	nb	nb	PROPN
hjic-242	110	50	,	,	PUNCT
hjic-242	110	51	f	f	PROPN
hjic-242	110	52	as	as	ADP
hjic-242	110	53	functions	function	NOUN
hjic-242	110	54	of	of	ADP
hjic-242	110	55	time	time	NOUN
hjic-242	110	56	.	.	PUNCT
hjic-242	111	1	figure	figure	VERB
hjic-242	111	2	5	5	NUM
hjic-242	111	3	:	:	PUNCT
hjic-242	111	4	liquid	liquid	ADJ
hjic-242	111	5	mixer	mixer	NOUN
hjic-242	111	6	tank	tank	NOUN
hjic-242	111	7	with	with	ADP
hjic-242	111	8	constant	constant	ADJ
hjic-242	111	9	volume	volume	NOUN
hjic-242	111	10	an	an	DET
hjic-242	111	11	overspecified	overspecified	ADJ
hjic-242	111	12	and	and	CCONJ
hjic-242	111	13	an	an	DET
hjic-242	111	14	underspecified	underspecified	ADJ
hjic-242	111	15	subgraph	subgraph	NOUN
hjic-242	111	16	can	can	AUX
hjic-242	111	17	be	be	AUX
hjic-242	111	18	found	find	VERB
hjic-242	111	19	on	on	ADP
hjic-242	111	20	the	the	DET
hjic-242	111	21	representation	representation	NOUN
hjic-242	111	22	graph	graph	NOUN
hjic-242	111	23	(	(	PUNCT
hjic-242	111	24	see	see	VERB
hjic-242	111	25	fig	fig	NOUN
hjic-242	111	26	.	.	PUNCT
hjic-242	112	1	6	6	NUM
hjic-242	112	2	)	)	PUNCT
hjic-242	112	3	and	and	CCONJ
hjic-242	112	4	the	the	DET
hjic-242	112	5	differential	differential	ADJ
hjic-242	112	6	index	index	NOUN
hjic-242	112	7	can	can	AUX
hjic-242	112	8	be	be	AUX
hjic-242	112	9	determined	determine	VERB
hjic-242	112	10	based	base	VERB
hjic-242	112	11	on	on	ADP
hjic-242	112	12	their	their	PRON
hjic-242	112	13	structures	structure	NOUN
hjic-242	112	14	:	:	PUNCT
hjic-242	112	15	i0	i0	PROPN
hjic-242	112	16	=	=	PUNCT
hjic-242	112	17	{	{	PUNCT
hjic-242	112	18	na	na	NOUN
hjic-242	112	19	,	,	PUNCT
hjic-242	112	20	nb	nb	INTJ
hjic-242	112	21	}	}	PUNCT
hjic-242	112	22	d0	d0	NOUN
hjic-242	112	23	=	=	SYM
hjic-242	112	24	{	{	PUNCT
hjic-242	112	25	na	na	NOUN
hjic-242	112	26	’	'	PUNCT
hjic-242	112	27	,	,	PUNCT
hjic-242	112	28	nb	nb	INTJ
hjic-242	112	29	’	'	PUNCT
hjic-242	112	30	}	}	PUNCT
hjic-242	112	31	since	since	SCONJ
hjic-242	112	32	the	the	DET
hjic-242	112	33	vertices	vertex	NOUN
hjic-242	112	34	referring	refer	VERB
hjic-242	112	35	to	to	ADP
hjic-242	112	36	derivative	derivative	ADJ
hjic-242	112	37	variables	variable	NOUN
hjic-242	112	38	na	na	ADP
hjic-242	112	39	’	'	PUNCT
hjic-242	112	40	,	,	PUNCT
hjic-242	112	41	nb	nb	INTJ
hjic-242	112	42	’	'	PUNCT
hjic-242	112	43	can	can	AUX
hjic-242	112	44	be	be	AUX
hjic-242	112	45	found	find	VERB
hjic-242	112	46	in	in	ADP
hjic-242	112	47	the	the	DET
hjic-242	112	48	underspecified	underspecified	ADJ
hjic-242	112	49	subgraph	subgraph	NOUN
hjic-242	112	50	,	,	PUNCT
hjic-242	112	51	n	n	NOUN
hjic-242	112	52	=	=	SYM
hjic-242	112	53	0	0	NUM
hjic-242	112	54	and	and	CCONJ
hjic-242	112	55	νd	νd	NOUN
hjic-242	112	56	=	=	SYM
hjic-242	112	57	n	n	PROPN
hjic-242	112	58	+	+	CCONJ
hjic-242	112	59	2	2	NUM
hjic-242	112	60	=	=	SYM
hjic-242	112	61	2	2	NUM
hjic-242	112	62	.	.	X
hjic-242	112	63	figure	figure	NOUN
hjic-242	112	64	6	6	NUM
hjic-242	112	65	:	:	PUNCT
hjic-242	112	66	the	the	DET
hjic-242	112	67	representation	representation	NOUN
hjic-242	112	68	graph	graph	NOUN
hjic-242	112	69	of	of	ADP
hjic-242	112	70	the	the	DET
hjic-242	112	71	example	example	NOUN
hjic-242	112	72	2b	2b	NUM
hjic-242	112	73	structural	structural	ADJ
hjic-242	112	74	analysis	analysis	NOUN
hjic-242	112	75	of	of	ADP
hjic-242	112	76	composite	composite	ADJ
hjic-242	112	77	models	model	NOUN
hjic-242	112	78	in	in	ADP
hjic-242	112	79	this	this	DET
hjic-242	112	80	section	section	NOUN
hjic-242	112	81	,	,	PUNCT
hjic-242	112	82	more	more	ADV
hjic-242	112	83	complex	complex	ADJ
hjic-242	112	84	composite	composite	ADJ
hjic-242	112	85	models	model	NOUN
hjic-242	112	86	are	be	AUX
hjic-242	112	87	built	build	VERB
hjic-242	112	88	from	from	ADP
hjic-242	112	89	the	the	DET
hjic-242	112	90	simple	simple	ADJ
hjic-242	112	91	dynamic	dynamic	ADJ
hjic-242	112	92	models	model	NOUN
hjic-242	112	93	of	of	ADP
hjic-242	112	94	the	the	DET
hjic-242	112	95	previous	previous	ADJ
hjic-242	112	96	section	section	NOUN
hjic-242	112	97	.	.	PUNCT
hjic-242	113	1	the	the	DET
hjic-242	113	2	goal	goal	NOUN
hjic-242	113	3	is	be	AUX
hjic-242	113	4	to	to	PART
hjic-242	113	5	investigate	investigate	VERB
hjic-242	113	6	the	the	DET
hjic-242	113	7	effect	effect	NOUN
hjic-242	113	8	of	of	ADP
hjic-242	113	9	this	this	DET
hjic-242	113	10	“	"	PUNCT
hjic-242	113	11	build	build	VERB
hjic-242	113	12	up	up	ADP
hjic-242	113	13	process	process	NOUN
hjic-242	113	14	”	"	PUNCT
hjic-242	113	15	of	of	ADP
hjic-242	113	16	simple	simple	ADJ
hjic-242	113	17	,	,	PUNCT
hjic-242	113	18	small	small	ADJ
hjic-242	113	19	sized	sized	ADJ
hjic-242	113	20	models	model	NOUN
hjic-242	113	21	,	,	PUNCT
hjic-242	113	22	i.e	i.e	PRON
hjic-242	113	23	the	the	DET
hjic-242	113	24	effect	effect	NOUN
hjic-242	113	25	of	of	ADP
hjic-242	113	26	the	the	DET
hjic-242	113	27	model	model	NOUN
hjic-242	113	28	composition	composition	NOUN
hjic-242	113	29	to	to	ADP
hjic-242	113	30	the	the	DET
hjic-242	113	31	structural	structural	ADJ
hjic-242	113	32	properties	property	NOUN
hjic-242	113	33	of	of	ADP
hjic-242	113	34	the	the	DET
hjic-242	113	35	composite	composite	ADJ
hjic-242	113	36	models	model	NOUN
hjic-242	113	37	.	.	PUNCT
hjic-242	114	1	example	example	NOUN
hjic-242	114	2	3	3	NUM
hjic-242	114	3	–	–	PUNCT
hjic-242	114	4	cascade	cascade	NOUN
hjic-242	114	5	of	of	ADP
hjic-242	114	6	perfectly	perfectly	ADV
hjic-242	114	7	stirred	stir	VERB
hjic-242	114	8	tank	tank	NOUN
hjic-242	114	9	reactors	reactor	NOUN
hjic-242	114	10	suppose	suppose	VERB
hjic-242	114	11	a	a	DET
hjic-242	114	12	system	system	NOUN
hjic-242	114	13	consists	consist	VERB
hjic-242	114	14	of	of	ADP
hjic-242	114	15	k	k	PROPN
hjic-242	114	16	perfectly	perfectly	ADV
hjic-242	114	17	stirred	stir	VERB
hjic-242	114	18	tank	tank	NOUN
hjic-242	114	19	reactors	reactor	NOUN
hjic-242	114	20	.	.	PUNCT
hjic-242	115	1	a	a	DET
hjic-242	115	2	feed	feed	NOUN
hjic-242	115	3	of	of	ADP
hjic-242	115	4	concentration	concentration	NOUN
hjic-242	115	5	c0	c0	NOUN
hjic-242	115	6	is	be	AUX
hjic-242	115	7	fed	feed	VERB
hjic-242	115	8	into	into	ADP
hjic-242	115	9	the	the	DET
hjic-242	115	10	first	first	ADJ
hjic-242	115	11	tank	tank	NOUN
hjic-242	115	12	.	.	PUNCT
hjic-242	116	1	the	the	DET
hjic-242	116	2	concentrations	concentration	NOUN
hjic-242	116	3	in	in	ADP
hjic-242	116	4	the	the	DET
hjic-242	116	5	tanks	tank	NOUN
hjic-242	116	6	are	be	AUX
hjic-242	116	7	described	describe	VERB
hjic-242	116	8	by	by	ADP
hjic-242	116	9	the	the	DET
hjic-242	116	10	following	follow	VERB
hjic-242	116	11	equation	equation	NOUN
hjic-242	116	12	:	:	PUNCT
hjic-242	116	13	(	(	PUNCT
hjic-242	116	14	)	)	PUNCT
hjic-242	116	15	k,,,icc	k,,,icc	NOUN
hjic-242	116	16	v	v	PROPN
hjic-242	116	17	qc	qc	PROPN
hjic-242	116	18	ii	ii	PROPN
hjic-242	117	1	i	i	PRON
hjic-242	117	2	i	i	PRON
hjic-242	117	3	k211	k211	PROPN
hjic-242	118	1	=	=	PRON
hjic-242	118	2	−=′	−=′	NOUN
hjic-242	118	3	−	−	PROPN
hjic-242	118	4	where	where	SCONJ
hjic-242	118	5	ci	ci	PROPN
hjic-242	118	6	is	be	AUX
hjic-242	118	7	the	the	DET
hjic-242	118	8	concentration	concentration	NOUN
hjic-242	118	9	in	in	ADP
hjic-242	118	10	the	the	DET
hjic-242	118	11	tank	tank	NOUN
hjic-242	118	12	i	i	PRON
hjic-242	118	13	,	,	PUNCT
hjic-242	118	14	q	q	X
hjic-242	118	15	is	be	AUX
hjic-242	118	16	the	the	DET
hjic-242	118	17	flow	flow	NOUN
hjic-242	118	18	rates	rate	NOUN
hjic-242	118	19	from	from	ADP
hjic-242	118	20	tank	tank	NOUN
hjic-242	118	21	to	to	PART
hjic-242	118	22	tank	tank	VERB
hjic-242	118	23	and	and	CCONJ
hjic-242	118	24	vi	vi	PROPN
hjic-242	118	25	is	be	AUX
hjic-242	118	26	the	the	DET
hjic-242	118	27	volume	volume	NOUN
hjic-242	118	28	of	of	ADP
hjic-242	118	29	the	the	DET
hjic-242	118	30	tank	tank	NOUN
hjic-242	118	31	i.	i.	NOUN
hjic-242	118	32	two	two	NUM
hjic-242	118	33	different	different	ADJ
hjic-242	118	34	specifications	specification	NOUN
hjic-242	118	35	can	can	AUX
hjic-242	118	36	be	be	AUX
hjic-242	118	37	added	add	VERB
hjic-242	118	38	to	to	ADP
hjic-242	118	39	these	these	DET
hjic-242	118	40	equations	equation	NOUN
hjic-242	118	41	according	accord	VERB
hjic-242	118	42	to	to	ADP
hjic-242	118	43	modelling	model	VERB
hjic-242	118	44	goal	goal	NOUN
hjic-242	118	45	:	:	PUNCT
hjic-242	118	46	a	a	X
hjic-242	118	47	)	)	PUNCT
hjic-242	118	48	in	in	ADP
hjic-242	118	49	dynamic	dynamic	ADJ
hjic-242	118	50	simulation	simulation	NOUN
hjic-242	118	51	studies	study	NOUN
hjic-242	118	52	the	the	DET
hjic-242	118	53	feed	feed	NOUN
hjic-242	118	54	concentration	concentration	NOUN
hjic-242	118	55	c0	c0	NOUN
hjic-242	118	56	is	be	AUX
hjic-242	118	57	given	give	VERB
hjic-242	118	58	by	by	ADP
hjic-242	118	59	c0	c0	PROPN
hjic-242	118	60	=	=	SYM
hjic-242	118	61	c0(t	c0(t	PROPN
hjic-242	118	62	)	)	PUNCT
hjic-242	118	63	;	;	PUNCT
hjic-242	118	64	b	b	X
hjic-242	118	65	)	)	PUNCT
hjic-242	118	66	in	in	ADP
hjic-242	118	67	dynamic	dynamic	ADJ
hjic-242	118	68	design	design	NOUN
hjic-242	118	69	the	the	DET
hjic-242	118	70	product	product	NOUN
hjic-242	118	71	concentration	concentration	NOUN
hjic-242	118	72	ck	ck	ADJ
hjic-242	118	73	is	be	AUX
hjic-242	118	74	given	give	VERB
hjic-242	118	75	by	by	ADP
hjic-242	118	76	ck	ck	NOUN
hjic-242	118	77	=	=	SYM
hjic-242	118	78	ck(t	ck(t	NOUN
hjic-242	118	79	)	)	PUNCT
hjic-242	118	80	.	.	PUNCT
hjic-242	119	1	the	the	DET
hjic-242	119	2	representation	representation	NOUN
hjic-242	119	3	graphs	graph	NOUN
hjic-242	119	4	referring	refer	VERB
hjic-242	119	5	to	to	ADP
hjic-242	119	6	these	these	DET
hjic-242	119	7	specifications	specification	NOUN
hjic-242	119	8	can	can	AUX
hjic-242	119	9	be	be	AUX
hjic-242	119	10	seen	see	VERB
hjic-242	119	11	in	in	ADP
hjic-242	119	12	figs	fig	NOUN
hjic-242	119	13	7a	7a	NOUN
hjic-242	119	14	and	and	CCONJ
hjic-242	119	15	b.	b.	NOUN
hjic-242	120	1	these	these	DET
hjic-242	120	2	graphs	graph	NOUN
hjic-242	120	3	can	can	AUX
hjic-242	120	4	be	be	AUX
hjic-242	120	5	considered	consider	VERB
hjic-242	120	6	as	as	ADP
hjic-242	120	7	multiplications	multiplication	NOUN
hjic-242	120	8	of	of	ADP
hjic-242	120	9	the	the	DET
hjic-242	120	10	representation	representation	NOUN
hjic-242	120	11	graphs	graph	NOUN
hjic-242	120	12	in	in	ADP
hjic-242	120	13	figs	fig	NOUN
hjic-242	120	14	2a	2a	PROPN
hjic-242	120	15	and	and	CCONJ
hjic-242	120	16	b.	b.	PROPN
hjic-242	120	17	in	in	ADP
hjic-242	120	18	the	the	DET
hjic-242	120	19	first	first	ADJ
hjic-242	120	20	case	case	NOUN
hjic-242	120	21	,	,	PUNCT
hjic-242	120	22	the	the	DET
hjic-242	120	23	reduced	reduce	VERB
hjic-242	120	24	graph	graph	NOUN
hjic-242	120	25	is	be	AUX
hjic-242	120	26	an	an	DET
hjic-242	120	27	empty	empty	ADJ
hjic-242	120	28	graph	graph	NOUN
hjic-242	120	29	,	,	PUNCT
hjic-242	120	30	therefore	therefore	ADV
hjic-242	120	31	the	the	DET
hjic-242	120	32	differential	differential	ADJ
hjic-242	120	33	index	index	NOUN
hjic-242	120	34	is	be	AUX
hjic-242	120	35	equal	equal	ADJ
hjic-242	120	36	to	to	ADP
hjic-242	120	37	1	1	NUM
hjic-242	120	38	.	.	PUNCT
hjic-242	121	1	in	in	ADP
hjic-242	121	2	the	the	DET
hjic-242	121	3	second	second	ADJ
hjic-242	121	4	case	case	NOUN
hjic-242	121	5	,	,	PUNCT
hjic-242	121	6	there	there	PRON
hjic-242	121	7	are	be	VERB
hjic-242	121	8	under	under	ADP
hjic-242	121	9	and	and	CCONJ
hjic-242	121	10	overspecified	overspecified	ADJ
hjic-242	121	11	subgraphs	subgraph	NOUN
hjic-242	121	12	on	on	ADP
hjic-242	121	13	the	the	DET
hjic-242	121	14	representation	representation	NOUN
hjic-242	121	15	graph	graph	NOUN
hjic-242	121	16	and	and	CCONJ
hjic-242	121	17	based	base	VERB
hjic-242	121	18	on	on	ADP
hjic-242	121	19	their	their	PRON
hjic-242	121	20	structures	structure	NOUN
hjic-242	121	21	:	:	PUNCT
hjic-242	121	22	i0	i0	PROPN
hjic-242	121	23	=	=	PUNCT
hjic-242	121	24	{	{	PUNCT
hjic-242	121	25	ck	ck	NOUN
hjic-242	121	26	}	}	PUNCT
hjic-242	121	27	d0	d0	NOUN
hjic-242	121	28	=	=	SYM
hjic-242	121	29	{	{	PUNCT
hjic-242	121	30	ck	ck	NOUN
hjic-242	121	31	’	'	PUNCT
hjic-242	121	32	}	}	PUNCT
hjic-242	121	33	i1	i1	PROPN
hjic-242	121	34	=	=	PUNCT
hjic-242	121	35	{	{	PUNCT
hjic-242	121	36	ck-1	ck-1	PRON
hjic-242	121	37	}	}	PUNCT
hjic-242	121	38	d1	d1	NOUN
hjic-242	121	39	=	=	SYM
hjic-242	121	40	{	{	PUNCT
hjic-242	121	41	c’k-1	c’k-1	PROPN
hjic-242	121	42	}	}	PUNCT
hjic-242	121	43	�	�	X
hjic-242	121	44	ik-1	ik-1	ADP
hjic-242	121	45	=	=	SYM
hjic-242	121	46	{	{	PUNCT
hjic-242	121	47	c1	c1	NOUN
hjic-242	121	48	}	}	PUNCT
hjic-242	121	49	dk-1	dk-1	X
hjic-242	121	50	=	=	SYM
hjic-242	121	51	{	{	PUNCT
hjic-242	121	52	c1	c1	NOUN
hjic-242	121	53	’	'	PUNCT
hjic-242	121	54	}	}	PUNCT
hjic-242	121	55	since	since	SCONJ
hjic-242	121	56	the	the	DET
hjic-242	121	57	vertex	vertex	NOUN
hjic-242	121	58	referring	refer	VERB
hjic-242	121	59	to	to	ADP
hjic-242	121	60	the	the	DET
hjic-242	121	61	derivative	derivative	ADJ
hjic-242	121	62	variable	variable	ADJ
hjic-242	121	63	c1	c1	NOUN
hjic-242	121	64	’	'	PUNCT
hjic-242	121	65	can	can	AUX
hjic-242	121	66	be	be	AUX
hjic-242	121	67	found	find	VERB
hjic-242	121	68	in	in	ADP
hjic-242	121	69	the	the	DET
hjic-242	121	70	underspecified	underspecified	ADJ
hjic-242	121	71	subgraph	subgraph	NOUN
hjic-242	121	72	,	,	PUNCT
hjic-242	121	73	n	n	NOUN
hjic-242	121	74	=	=	SYM
hjic-242	121	75	k	k	X
hjic-242	121	76	–	–	PUNCT
hjic-242	121	77	1	1	NUM
hjic-242	121	78	and	and	CCONJ
hjic-242	121	79	νd	νd	NOUN
hjic-242	121	80	=	=	SYM
hjic-242	121	81	n	n	PROPN
hjic-242	121	82	+	+	CCONJ
hjic-242	121	83	2	2	NUM
hjic-242	121	84	=	=	SYM
hjic-242	121	85	k	k	NOUN
hjic-242	122	1	+	+	NOUN
hjic-242	122	2	1	1	X
hjic-242	122	3	.	.	X
hjic-242	122	4	a	a	DET
hjic-242	122	5	)	)	PUNCT
hjic-242	122	6	b	b	NOUN
hjic-242	122	7	)	)	PUNCT
hjic-242	122	8	figure	figure	NOUN
hjic-242	122	9	7	7	NUM
hjic-242	122	10	:	:	PUNCT
hjic-242	122	11	the	the	DET
hjic-242	122	12	representation	representation	NOUN
hjic-242	122	13	graphs	graph	NOUN
hjic-242	122	14	of	of	ADP
hjic-242	122	15	the	the	DET
hjic-242	122	16	example	example	NOUN
hjic-242	122	17	3	3	NUM
hjic-242	122	18	the	the	DET
hjic-242	122	19	effect	effect	NOUN
hjic-242	122	20	of	of	ADP
hjic-242	122	21	the	the	DET
hjic-242	122	22	increasing	increase	VERB
hjic-242	122	23	differential	differential	ADJ
hjic-242	122	24	index	index	NOUN
hjic-242	122	25	of	of	ADP
hjic-242	122	26	the	the	DET
hjic-242	122	27	cascade	cascade	NOUN
hjic-242	122	28	model	model	NOUN
hjic-242	122	29	can	can	AUX
hjic-242	122	30	be	be	AUX
hjic-242	122	31	followed	follow	VERB
hjic-242	122	32	on	on	ADP
hjic-242	122	33	the	the	DET
hjic-242	122	34	representation	representation	NOUN
hjic-242	122	35	graph	graph	NOUN
hjic-242	122	36	:	:	PUNCT
hjic-242	122	37	the	the	DET
hjic-242	122	38	underspecified	underspecified	ADJ
hjic-242	122	39	and	and	CCONJ
hjic-242	122	40	the	the	DET
hjic-242	122	41	overspecified	overspecified	ADJ
hjic-242	122	42	subgraphs	subgraphs	NOUN
hjic-242	122	43	move	move	VERB
hjic-242	122	44	increasingly	increasingly	ADV
hjic-242	122	45	further	far	ADV
hjic-242	122	46	from	from	ADP
hjic-242	122	47	each	each	DET
hjic-242	122	48	other	other	ADJ
hjic-242	122	49	as	as	SCONJ
hjic-242	122	50	the	the	DET
hjic-242	122	51	cascade	cascade	NOUN
hjic-242	122	52	elements	element	NOUN
hjic-242	122	53	are	be	AUX
hjic-242	122	54	inserted	insert	VERB
hjic-242	122	55	.	.	PUNCT
hjic-242	123	1	the	the	DET
hjic-242	123	2	path	path	NOUN
hjic-242	123	3	between	between	ADP
hjic-242	123	4	the	the	DET
hjic-242	123	5	derivative	derivative	ADJ
hjic-242	123	6	variable	variable	ADJ
hjic-242	123	7	c1	c1	NOUN
hjic-242	123	8	’	'	PUNCT
hjic-242	123	9	of	of	ADP
hjic-242	123	10	the	the	DET
hjic-242	123	11	underspecified	underspecified	ADJ
hjic-242	123	12	subgraph	subgraph	NOUN
hjic-242	123	13	and	and	CCONJ
hjic-242	123	14	the	the	DET
hjic-242	123	15	differential	differential	ADJ
hjic-242	123	16	variable	variable	NOUN
hjic-242	123	17	ck	ck	INTJ
hjic-242	123	18	of	of	ADP
hjic-242	123	19	the	the	DET
hjic-242	123	20	overspecified	overspecified	ADJ
hjic-242	123	21	subgraph	subgraph	NOUN
hjic-242	123	22	is	be	AUX
hjic-242	123	23	increasingly	increasingly	ADV
hjic-242	123	24	longer	long	ADV
hjic-242	123	25	(	(	PUNCT
hjic-242	123	26	the	the	DET
hjic-242	123	27	direction	direction	NOUN
hjic-242	123	28	is	be	AUX
hjic-242	123	29	not	not	PART
hjic-242	123	30	taken	take	VERB
hjic-242	123	31	into	into	ADP
hjic-242	123	32	account	account	NOUN
hjic-242	123	33	)	)	PUNCT
hjic-242	123	34	and	and	CCONJ
hjic-242	123	35	along	along	ADP
hjic-242	123	36	this	this	DET
hjic-242	123	37	path	path	NOUN
hjic-242	123	38	the	the	DET
hjic-242	123	39	differential	differential	NOUN
hjic-242	123	40	and	and	CCONJ
hjic-242	123	41	derivative	derivative	ADJ
hjic-242	123	42	variables	variable	NOUN
hjic-242	123	43	are	be	AUX
hjic-242	123	44	located	locate	VERB
hjic-242	123	45	alternately	alternately	ADV
hjic-242	123	46	.	.	PUNCT
hjic-242	124	1	150	150	NUM
hjic-242	124	2	example	example	NOUN
hjic-242	124	3	4	4	NUM
hjic-242	124	4	–	–	PUNCT
hjic-242	124	5	sequence	sequence	NOUN
hjic-242	124	6	of	of	ADP
hjic-242	124	7	mixing	mix	VERB
hjic-242	124	8	tanks	tank	NOUN
hjic-242	124	9	suppose	suppose	VERB
hjic-242	124	10	that	that	SCONJ
hjic-242	124	11	a	a	DET
hjic-242	124	12	system	system	NOUN
hjic-242	124	13	consist	consist	VERB
hjic-242	124	14	of	of	ADP
hjic-242	124	15	a	a	DET
hjic-242	124	16	sequence	sequence	NOUN
hjic-242	124	17	of	of	ADP
hjic-242	124	18	k	k	PROPN
hjic-242	124	19	mixer	mixer	PROPN
hjic-242	124	20	tanks	tank	NOUN
hjic-242	124	21	(	(	PUNCT
hjic-242	124	22	see	see	VERB
hjic-242	124	23	fig	fig	NOUN
hjic-242	124	24	.	.	PUNCT
hjic-242	125	1	8)	8)	X
hjic-242	125	2	.	.	PUNCT
hjic-242	126	1	let	let	VERB
hjic-242	126	2	the	the	DET
hjic-242	126	3	volume	volume	NOUN
hjic-242	126	4	of	of	ADP
hjic-242	126	5	liquid	liquid	NOUN
hjic-242	126	6	in	in	ADP
hjic-242	126	7	the	the	DET
hjic-242	126	8	tank	tank	NOUN
hjic-242	126	9	j	j	PROPN
hjic-242	126	10	be	be	AUX
hjic-242	126	11	constant	constant	ADJ
hjic-242	126	12	while	while	SCONJ
hjic-242	126	13	in	in	ADP
hjic-242	126	14	the	the	DET
hjic-242	126	15	other	other	ADJ
hjic-242	126	16	tanks	tank	NOUN
hjic-242	126	17	the	the	DET
hjic-242	126	18	liquid	liquid	ADJ
hjic-242	126	19	volumes	volume	NOUN
hjic-242	126	20	are	be	AUX
hjic-242	126	21	variables	variable	NOUN
hjic-242	126	22	.	.	PUNCT
hjic-242	127	1	the	the	DET
hjic-242	127	2	model	model	NOUN
hjic-242	127	3	of	of	ADP
hjic-242	127	4	the	the	DET
hjic-242	127	5	constant	constant	ADJ
hjic-242	127	6	volume	volume	NOUN
hjic-242	127	7	tank	tank	NOUN
hjic-242	127	8	is	be	AUX
hjic-242	127	9	described	describe	VERB
hjic-242	127	10	in	in	ADP
hjic-242	127	11	example	example	NOUN
hjic-242	127	12	2b	2b	NOUN
hjic-242	127	13	,	,	PUNCT
hjic-242	127	14	while	while	SCONJ
hjic-242	127	15	the	the	DET
hjic-242	127	16	models	model	NOUN
hjic-242	127	17	of	of	ADP
hjic-242	127	18	the	the	DET
hjic-242	127	19	other	other	ADJ
hjic-242	127	20	tanks	tank	NOUN
hjic-242	127	21	are	be	AUX
hjic-242	127	22	the	the	DET
hjic-242	127	23	same	same	ADJ
hjic-242	127	24	as	as	ADP
hjic-242	127	25	the	the	DET
hjic-242	127	26	model	model	NOUN
hjic-242	127	27	in	in	ADP
hjic-242	127	28	example	example	NOUN
hjic-242	127	29	2a	2a	NUM
hjic-242	127	30	.	.	PUNCT
hjic-242	128	1	the	the	DET
hjic-242	128	2	following	follow	VERB
hjic-242	128	3	assumptions	assumption	NOUN
hjic-242	128	4	are	be	AUX
hjic-242	128	5	held	hold	VERB
hjic-242	128	6	:	:	PUNCT
hjic-242	128	7	a	a	DET
hjic-242	128	8	liquid	liquid	ADJ
hjic-242	128	9	feed	feed	NOUN
hjic-242	128	10	stream	stream	NOUN
hjic-242	128	11	is	be	AUX
hjic-242	128	12	fed	feed	VERB
hjic-242	128	13	into	into	ADP
hjic-242	128	14	the	the	DET
hjic-242	128	15	first	first	ADJ
hjic-242	128	16	tank	tank	NOUN
hjic-242	128	17	.	.	PUNCT
hjic-242	129	1	the	the	DET
hjic-242	129	2	feed	feed	NOUN
hjic-242	129	3	consists	consist	VERB
hjic-242	129	4	of	of	ADP
hjic-242	129	5	two	two	NUM
hjic-242	129	6	components	component	NOUN
hjic-242	129	7	a	a	PRON
hjic-242	129	8	and	and	CCONJ
hjic-242	129	9	b.	b.	X
hjic-242	129	10	the	the	DET
hjic-242	129	11	liquid	liquid	NOUN
hjic-242	129	12	flows	flow	VERB
hjic-242	129	13	from	from	ADP
hjic-242	129	14	the	the	DET
hjic-242	129	15	first	first	ADJ
hjic-242	129	16	tank	tank	NOUN
hjic-242	129	17	through	through	ADP
hjic-242	129	18	the	the	DET
hjic-242	129	19	system	system	NOUN
hjic-242	129	20	.	.	PUNCT
hjic-242	130	1	the	the	DET
hjic-242	130	2	other	other	ADJ
hjic-242	130	3	assumptions	assumption	NOUN
hjic-242	130	4	are	be	AUX
hjic-242	130	5	the	the	DET
hjic-242	130	6	same	same	ADJ
hjic-242	130	7	as	as	ADP
hjic-242	130	8	in	in	ADP
hjic-242	130	9	example	example	NOUN
hjic-242	130	10	2a	2a	NUM
hjic-242	130	11	and	and	CCONJ
hjic-242	130	12	2b	2b	NOUN
hjic-242	130	13	.	.	PUNCT
hjic-242	131	1	the	the	DET
hjic-242	131	2	model	model	NOUN
hjic-242	131	3	of	of	ADP
hjic-242	131	4	this	this	DET
hjic-242	131	5	cascade	cascade	NOUN
hjic-242	131	6	system	system	NOUN
hjic-242	131	7	using	use	VERB
hjic-242	131	8	the	the	DET
hjic-242	131	9	models	model	NOUN
hjic-242	131	10	of	of	ADP
hjic-242	131	11	example	example	NOUN
hjic-242	131	12	2	2	NUM
hjic-242	131	13	.	.	PUNCT
hjic-242	131	14	is	be	AUX
hjic-242	131	15	the	the	DET
hjic-242	131	16	following	follow	VERB
hjic-242	131	17	:	:	PUNCT
hjic-242	131	18	nai	nai	X
hjic-242	131	19	=	=	SYM
hjic-242	131	20	∫	∫	PROPN
hjic-242	131	21	nai	nai	NOUN
hjic-242	131	22	’	'	PUNCT
hjic-242	131	23	nbi	nbi	PROPN
hjic-242	131	24	=	=	SYM
hjic-242	131	25	∫	∫	PROPN
hjic-242	131	26	nbi	nbi	PROPN
hjic-242	131	27	’	'	PUNCT
hjic-242	131	28	nai	nai	NOUN
hjic-242	131	29	’	'	PUNCT
hjic-242	131	30	=	=	SYM
hjic-242	131	31	fi-1xai-1	fi-1xai-1	ADJ
hjic-242	131	32	–	–	PUNCT
hjic-242	131	33	fixai	fixai	NOUN
hjic-242	131	34	nbi	nbi	NOUN
hjic-242	131	35	’	'	PUNCT
hjic-242	131	36	=	=	ADJ
hjic-242	131	37	fi-1xbi-1	fi-1xbi-1	PROPN
hjic-242	131	38	–	–	PUNCT
hjic-242	131	39	fixbi	fixbi	PROPN
hjic-242	131	40	ni	ni	PROPN
hjic-242	131	41	=	=	PROPN
hjic-242	131	42	nai	nai	PROPN
hjic-242	132	1	+	+	X
hjic-242	132	2	nbi	nbi	NOUN
hjic-242	133	1	where	where	SCONJ
hjic-242	133	2	i	i	PRON
hjic-242	133	3	=	=	NOUN
hjic-242	133	4	1	1	NUM
hjic-242	133	5	,	,	PUNCT
hjic-242	133	6	…	…	PUNCT
hjic-242	133	7	,	,	PUNCT
hjic-242	133	8	k	k	PROPN
hjic-242	133	9	xai	xai	PROPN
hjic-242	133	10	=	=	PROPN
hjic-242	133	11	nai	nai	PROPN
hjic-242	133	12	/	/	SYM
hjic-242	133	13	ni	ni	PROPN
hjic-242	133	14	xbi	xbi	PROPN
hjic-242	133	15	=	=	SYM
hjic-242	133	16	nbi	nbi	PROPN
hjic-242	133	17	/	/	SYM
hjic-242	133	18	ni	ni	PROPN
hjic-242	133	19	mwi	mwi	PROPN
hjic-242	133	20	=	=	NOUN
hjic-242	133	21	mwaxai	mwaxai	NOUN
hjic-242	133	22	+	+	SYM
hjic-242	133	23	mwbxbi	mwbxbi	NOUN
hjic-242	133	24	pli	pli	PROPN
hjic-242	133	25	=	=	PROPN
hjic-242	133	26	p0	p0	NOUN
hjic-242	133	27	+	+	NOUN
hjic-242	133	28	(	(	PUNCT
hjic-242	133	29	mwi	mwi	PROPN
hjic-242	133	30	⋅	⋅	PROPN
hjic-242	133	31	n)/a	n)/a	PROPN
hjic-242	133	32	fi	fi	NOUN
hjic-242	134	1	=	=	SYM
hjic-242	134	2	k	k	PROPN
hjic-242	134	3	(	(	PUNCT
hjic-242	134	4	pli	pli	PROPN
hjic-242	134	5	–	–	PUNCT
hjic-242	134	6	p0)1/2	p0)1/2	NOUN
hjic-242	134	7	where	where	SCONJ
hjic-242	134	8	i	i	PRON
hjic-242	134	9	=	=	NOUN
hjic-242	134	10	1	1	NUM
hjic-242	134	11	,	,	PUNCT
hjic-242	134	12	…	…	PUNCT
hjic-242	134	13	,	,	PUNCT
hjic-242	134	14	k	k	X
hjic-242	134	15	,	,	PUNCT
hjic-242	134	16	i	i	PRON
hjic-242	134	17	≠	≠	PROPN
hjic-242	134	18	j	j	PROPN
hjic-242	134	19	figure	figure	NOUN
hjic-242	134	20	8	8	NUM
hjic-242	134	21	:	:	PUNCT
hjic-242	134	22	sequence	sequence	NOUN
hjic-242	134	23	of	of	ADP
hjic-242	134	24	liquid	liquid	ADJ
hjic-242	134	25	tanks	tank	NOUN
hjic-242	134	26	vj	vj	INTJ
hjic-242	134	27	=	=	PUNCT
hjic-242	134	28	vaxaj	vaxaj	PROPN
hjic-242	134	29	+	+	CCONJ
hjic-242	134	30	vbxbj	vbxbj	ADJ
hjic-242	134	31	vj	vj	X
hjic-242	134	32	=	=	SYM
hjic-242	134	33	nj⋅vj	nj⋅vj	PROPN
hjic-242	134	34	given	give	VERB
hjic-242	134	35	:	:	PUNCT
hjic-242	134	36	nai(t0	nai(t0	ADJ
hjic-242	134	37	)	)	PUNCT
hjic-242	134	38	,	,	PUNCT
hjic-242	134	39	nbi	nbi	NOUN
hjic-242	134	40	(	(	PUNCT
hjic-242	134	41	t0	t0	PROPN
hjic-242	134	42	)	)	PUNCT
hjic-242	134	43	,	,	PUNCT
hjic-242	134	44	i	i	PRON
hjic-242	134	45	=	=	NOUN
hjic-242	134	46	1	1	NUM
hjic-242	134	47	,	,	PUNCT
hjic-242	134	48	…	…	PUNCT
hjic-242	134	49	,	,	PUNCT
hjic-242	134	50	k	k	PROPN
hjic-242	134	51	xa0	xa0	PROPN
hjic-242	134	52	,	,	PUNCT
hjic-242	134	53	xb0	xb0	PROPN
hjic-242	134	54	,	,	PUNCT
hjic-242	134	55	f0	f0	PROPN
hjic-242	134	56	,	,	PUNCT
hjic-242	134	57	vj	vj	INTJ
hjic-242	134	58	;	;	PUNCT
hjic-242	135	1	constant	constant	ADJ
hjic-242	135	2	:	:	PUNCT
hjic-242	135	3	mwa	mwa	PROPN
hjic-242	135	4	,	,	PUNCT
hjic-242	135	5	mwb	mwb	PROPN
hjic-242	135	6	,	,	PUNCT
hjic-242	135	7	a	a	PRON
hjic-242	135	8	,	,	PUNCT
hjic-242	135	9	k	k	NOUN
hjic-242	135	10	,	,	PUNCT
hjic-242	135	11	p0	p0	NOUN
hjic-242	135	12	,	,	PUNCT
hjic-242	135	13	va	va	NOUN
hjic-242	135	14	,	,	PUNCT
hjic-242	135	15	vb	vb	NOUN
hjic-242	135	16	;	;	PUNCT
hjic-242	135	17	to	to	PART
hjic-242	135	18	be	be	AUX
hjic-242	135	19	calculated	calculate	VERB
hjic-242	135	20	:	:	PUNCT
hjic-242	135	21	nai	nai	X
hjic-242	135	22	,	,	PUNCT
hjic-242	135	23	nbi	nbi	PROPN
hjic-242	135	24	,	,	PUNCT
hjic-242	135	25	fk	fk	INTJ
hjic-242	135	26	as	as	ADP
hjic-242	135	27	functions	function	NOUN
hjic-242	135	28	of	of	ADP
hjic-242	135	29	time	time	NOUN
hjic-242	135	30	.	.	PUNCT
hjic-242	136	1	this	this	DET
hjic-242	136	2	model	model	NOUN
hjic-242	136	3	is	be	AUX
hjic-242	136	4	built	build	VERB
hjic-242	136	5	up	up	ADP
hjic-242	136	6	from	from	ADP
hjic-242	136	7	k–1	k–1	PROPN
hjic-242	136	8	differential	differential	PROPN
hjic-242	136	9	index	index	NOUN
hjic-242	136	10	1	1	NUM
hjic-242	136	11	models	model	NOUN
hjic-242	136	12	and	and	CCONJ
hjic-242	136	13	one	one	NUM
hjic-242	136	14	differential	differential	ADJ
hjic-242	136	15	index	index	NOUN
hjic-242	136	16	2	2	NUM
hjic-242	136	17	model	model	NOUN
hjic-242	136	18	according	accord	VERB
hjic-242	136	19	to	to	ADP
hjic-242	136	20	the	the	DET
hjic-242	136	21	liquid	liquid	ADJ
hjic-242	136	22	mixing	mixing	NOUN
hjic-242	136	23	system	system	NOUN
hjic-242	136	24	.	.	PUNCT
hjic-242	137	1	the	the	DET
hjic-242	137	2	representation	representation	NOUN
hjic-242	137	3	graph	graph	NOUN
hjic-242	137	4	of	of	ADP
hjic-242	137	5	the	the	DET
hjic-242	137	6	whole	whole	ADJ
hjic-242	137	7	system	system	NOUN
hjic-242	137	8	can	can	AUX
hjic-242	137	9	be	be	AUX
hjic-242	137	10	constructed	construct	VERB
hjic-242	137	11	easily	easily	ADV
hjic-242	137	12	from	from	ADP
hjic-242	137	13	the	the	DET
hjic-242	137	14	representation	representation	NOUN
hjic-242	137	15	graphs	graph	NOUN
hjic-242	137	16	of	of	ADP
hjic-242	137	17	the	the	DET
hjic-242	137	18	simple	simple	ADJ
hjic-242	137	19	models	model	NOUN
hjic-242	137	20	(	(	PUNCT
hjic-242	137	21	see	see	VERB
hjic-242	137	22	figs	fig	NOUN
hjic-242	137	23	4	4	NUM
hjic-242	137	24	and	and	CCONJ
hjic-242	137	25	6	6	NUM
hjic-242	137	26	)	)	PUNCT
hjic-242	137	27	.	.	PUNCT
hjic-242	138	1	the	the	DET
hjic-242	138	2	resulted	result	VERB
hjic-242	138	3	graph	graph	NOUN
hjic-242	138	4	can	can	AUX
hjic-242	138	5	be	be	AUX
hjic-242	138	6	seen	see	VERB
hjic-242	138	7	in	in	ADP
hjic-242	138	8	fig	fig	NOUN
hjic-242	138	9	.	.	PUNCT
hjic-242	139	1	9	9	X
hjic-242	139	2	.	.	X
hjic-242	139	3	an	an	DET
hjic-242	139	4	overspecified	overspecified	ADJ
hjic-242	139	5	and	and	CCONJ
hjic-242	139	6	an	an	DET
hjic-242	139	7	underspecified	underspecified	ADJ
hjic-242	139	8	subgraph	subgraph	NOUN
hjic-242	139	9	can	can	AUX
hjic-242	139	10	be	be	AUX
hjic-242	139	11	found	find	VERB
hjic-242	139	12	on	on	ADP
hjic-242	139	13	the	the	DET
hjic-242	139	14	representation	representation	NOUN
hjic-242	139	15	graph	graph	NOUN
hjic-242	139	16	and	and	CCONJ
hjic-242	139	17	the	the	DET
hjic-242	139	18	differential	differential	ADJ
hjic-242	139	19	index	index	NOUN
hjic-242	139	20	can	can	AUX
hjic-242	139	21	be	be	AUX
hjic-242	139	22	determined	determine	VERB
hjic-242	139	23	based	base	VERB
hjic-242	139	24	on	on	ADP
hjic-242	139	25	their	their	PRON
hjic-242	139	26	structures	structure	NOUN
hjic-242	139	27	:	:	PUNCT
hjic-242	139	28	figure	figure	VERB
hjic-242	139	29	9	9	NUM
hjic-242	139	30	:	:	PUNCT
hjic-242	139	31	the	the	DET
hjic-242	139	32	representation	representation	NOUN
hjic-242	139	33	graph	graph	NOUN
hjic-242	139	34	of	of	ADP
hjic-242	139	35	the	the	DET
hjic-242	139	36	example	example	NOUN
hjic-242	139	37	4	4	NUM
hjic-242	139	38	i0	i0	PROPN
hjic-242	139	39	=	=	SYM
hjic-242	139	40	{	{	PUNCT
hjic-242	139	41	naj	naj	PROPN
hjic-242	139	42	,	,	PUNCT
hjic-242	139	43	nbj	nbj	ADJ
hjic-242	139	44	}	}	PUNCT
hjic-242	139	45	d0	d0	NOUN
hjic-242	139	46	=	=	SYM
hjic-242	139	47	{	{	PUNCT
hjic-242	139	48	naj	naj	NOUN
hjic-242	139	49	’	'	PUNCT
hjic-242	139	50	,	,	PUNCT
hjic-242	139	51	nbj	nbj	ADJ
hjic-242	139	52	’	'	PUNCT
hjic-242	139	53	}	}	PUNCT
hjic-242	139	54	since	since	SCONJ
hjic-242	139	55	the	the	DET
hjic-242	139	56	vertices	vertex	NOUN
hjic-242	139	57	referring	refer	VERB
hjic-242	139	58	to	to	ADP
hjic-242	139	59	differential	differential	ADJ
hjic-242	139	60	variables	variable	NOUN
hjic-242	139	61	naj	naj	NOUN
hjic-242	139	62	’	'	PUNCT
hjic-242	139	63	,	,	PUNCT
hjic-242	139	64	nbj	nbj	NUM
hjic-242	139	65	’	'	PUNCT
hjic-242	139	66	can	can	AUX
hjic-242	139	67	be	be	AUX
hjic-242	139	68	found	find	VERB
hjic-242	139	69	in	in	ADP
hjic-242	139	70	the	the	DET
hjic-242	139	71	underspecified	underspecified	ADJ
hjic-242	139	72	subgraph	subgraph	NOUN
hjic-242	139	73	,	,	PUNCT
hjic-242	139	74	n	n	NOUN
hjic-242	139	75	=	=	SYM
hjic-242	139	76	0	0	NUM
hjic-242	139	77	and	and	CCONJ
hjic-242	139	78	νd	νd	NOUN
hjic-242	139	79	=	=	SYM
hjic-242	139	80	n	n	PROPN
hjic-242	139	81	+	+	CCONJ
hjic-242	139	82	2	2	NUM
hjic-242	139	83	=	=	SYM
hjic-242	139	84	2	2	NUM
hjic-242	139	85	.	.	PUNCT
hjic-242	140	1	in	in	ADP
hjic-242	140	2	this	this	DET
hjic-242	140	3	example	example	NOUN
hjic-242	140	4	the	the	DET
hjic-242	140	5	union	union	NOUN
hjic-242	140	6	of	of	ADP
hjic-242	140	7	the	the	DET
hjic-242	140	8	representation	representation	NOUN
hjic-242	140	9	graphs	graph	NOUN
hjic-242	140	10	of	of	ADP
hjic-242	140	11	submodels	submodel	NOUN
hjic-242	140	12	has	have	AUX
hjic-242	140	13	been	be	AUX
hjic-242	140	14	created	create	VERB
hjic-242	140	15	in	in	ADP
hjic-242	140	16	such	such	DET
hjic-242	140	17	a	a	DET
hjic-242	140	18	way	way	NOUN
hjic-242	140	19	that	that	PRON
hjic-242	140	20	the	the	DET
hjic-242	140	21	position	position	NOUN
hjic-242	140	22	of	of	ADP
hjic-242	140	23	the	the	DET
hjic-242	140	24	underspecified	underspecified	ADJ
hjic-242	140	25	and	and	CCONJ
hjic-242	140	26	overspecified	overspecified	ADJ
hjic-242	140	27	subgraphs	subgraph	NOUN
hjic-242	140	28	referring	refer	VERB
hjic-242	140	29	to	to	ADP
hjic-242	140	30	the	the	DET
hjic-242	140	31	higher	high	ADJ
hjic-242	140	32	differential	differential	ADJ
hjic-242	140	33	index	index	NOUN
hjic-242	140	34	in	in	ADP
hjic-242	140	35	the	the	DET
hjic-242	140	36	extended	extended	ADJ
hjic-242	140	37	graph	graph	NOUN
hjic-242	140	38	is	be	AUX
hjic-242	140	39	unvaried	unvaried	ADJ
hjic-242	140	40	to	to	ADP
hjic-242	140	41	their	their	PRON
hjic-242	140	42	original	original	ADJ
hjic-242	140	43	position	position	NOUN
hjic-242	140	44	,	,	PUNCT
hjic-242	140	45	therefore	therefore	ADV
hjic-242	140	46	the	the	DET
hjic-242	140	47	differential	differential	ADJ
hjic-242	140	48	index	index	NOUN
hjic-242	140	49	of	of	ADP
hjic-242	140	50	the	the	DET
hjic-242	140	51	complex	complex	ADJ
hjic-242	140	52	model	model	NOUN
hjic-242	140	53	is	be	AUX
hjic-242	140	54	the	the	DET
hjic-242	140	55	same	same	ADJ
hjic-242	140	56	as	as	ADP
hjic-242	140	57	of	of	ADP
hjic-242	140	58	the	the	DET
hjic-242	140	59	model	model	NOUN
hjic-242	140	60	of	of	ADP
hjic-242	140	61	example	example	NOUN
hjic-242	140	62	3b	3b	NUM
hjic-242	140	63	.	.	PUNCT
hjic-242	141	1	conclusion	conclusion	NOUN
hjic-242	141	2	in	in	ADP
hjic-242	141	3	this	this	DET
hjic-242	141	4	paper	paper	NOUN
hjic-242	141	5	we	we	PRON
hjic-242	141	6	investigated	investigate	VERB
hjic-242	141	7	the	the	DET
hjic-242	141	8	solvability	solvability	NOUN
hjic-242	141	9	properties	property	NOUN
hjic-242	141	10	of	of	ADP
hjic-242	141	11	complex	complex	ADJ
hjic-242	141	12	dynamic	dynamic	ADJ
hjic-242	141	13	systems	system	NOUN
hjic-242	141	14	when	when	SCONJ
hjic-242	141	15	they	they	PRON
hjic-242	141	16	are	be	AUX
hjic-242	141	17	built	build	VERB
hjic-242	141	18	up	up	ADP
hjic-242	141	19	from	from	ADP
hjic-242	141	20	simple	simple	ADJ
hjic-242	141	21	models	model	NOUN
hjic-242	141	22	.	.	PUNCT
hjic-242	142	1	we	we	PRON
hjic-242	142	2	have	have	AUX
hjic-242	142	3	shown	show	VERB
hjic-242	142	4	that	that	SCONJ
hjic-242	142	5	the	the	DET
hjic-242	142	6	representation	representation	NOUN
hjic-242	142	7	graph	graph	NOUN
hjic-242	142	8	can	can	AUX
hjic-242	142	9	be	be	AUX
hjic-242	142	10	used	use	VERB
hjic-242	142	11	efficiently	efficiently	ADV
hjic-242	142	12	for	for	ADP
hjic-242	142	13	the	the	DET
hjic-242	142	14	investigation	investigation	NOUN
hjic-242	142	15	of	of	ADP
hjic-242	142	16	the	the	DET
hjic-242	142	17	differential	differential	ADJ
hjic-242	142	18	index	index	NOUN
hjic-242	142	19	during	during	ADP
hjic-242	142	20	the	the	DET
hjic-242	142	21	model	model	NOUN
hjic-242	142	22	composition	composition	NOUN
hjic-242	142	23	process	process	NOUN
hjic-242	142	24	,	,	PUNCT
hjic-242	142	25	151	151	NUM
hjic-242	142	26	too	too	ADV
hjic-242	142	27	.	.	PUNCT
hjic-242	143	1	the	the	DET
hjic-242	143	2	representation	representation	NOUN
hjic-242	143	3	graph	graph	NOUN
hjic-242	143	4	of	of	ADP
hjic-242	143	5	the	the	DET
hjic-242	143	6	complex	complex	ADJ
hjic-242	143	7	model	model	NOUN
hjic-242	143	8	can	can	AUX
hjic-242	143	9	be	be	AUX
hjic-242	143	10	easily	easily	ADV
hjic-242	143	11	built	build	VERB
hjic-242	143	12	up	up	ADP
hjic-242	143	13	from	from	ADP
hjic-242	143	14	the	the	DET
hjic-242	143	15	representation	representation	NOUN
hjic-242	143	16	graphs	graph	NOUN
hjic-242	143	17	of	of	ADP
hjic-242	143	18	the	the	DET
hjic-242	143	19	simple	simple	ADJ
hjic-242	143	20	models	model	NOUN
hjic-242	143	21	according	accord	VERB
hjic-242	143	22	to	to	ADP
hjic-242	143	23	the	the	DET
hjic-242	143	24	linking	linking	NOUN
hjic-242	143	25	of	of	ADP
hjic-242	143	26	the	the	DET
hjic-242	143	27	technological	technological	ADJ
hjic-242	143	28	subsystems	subsystem	NOUN
hjic-242	143	29	.	.	PUNCT
hjic-242	144	1	if	if	SCONJ
hjic-242	144	2	one	one	NUM
hjic-242	144	3	of	of	ADP
hjic-242	144	4	the	the	DET
hjic-242	144	5	submodels	submodel	NOUN
hjic-242	144	6	has	have	VERB
hjic-242	144	7	greater	great	ADJ
hjic-242	144	8	than	than	ADP
hjic-242	144	9	one	one	NUM
hjic-242	144	10	differential	differential	ADJ
hjic-242	144	11	index	index	NOUN
hjic-242	144	12	then	then	ADV
hjic-242	144	13	the	the	DET
hjic-242	144	14	under	under	ADJ
hjic-242	144	15	and	and	CCONJ
hjic-242	144	16	overspecified	overspecified	ADJ
hjic-242	144	17	subgraphs	subgraph	NOUN
hjic-242	144	18	referring	refer	VERB
hjic-242	144	19	to	to	ADP
hjic-242	144	20	this	this	DET
hjic-242	144	21	higher	high	ADJ
hjic-242	144	22	index	index	NOUN
hjic-242	144	23	can	can	AUX
hjic-242	144	24	be	be	AUX
hjic-242	144	25	found	find	VERB
hjic-242	144	26	in	in	ADP
hjic-242	144	27	the	the	DET
hjic-242	144	28	representation	representation	NOUN
hjic-242	144	29	graph	graph	NOUN
hjic-242	144	30	of	of	ADP
hjic-242	144	31	the	the	DET
hjic-242	144	32	complex	complex	ADJ
hjic-242	144	33	model	model	NOUN
hjic-242	144	34	,	,	PUNCT
hjic-242	144	35	too	too	ADV
hjic-242	144	36	.	.	PUNCT
hjic-242	145	1	the	the	DET
hjic-242	145	2	change	change	NOUN
hjic-242	145	3	in	in	ADP
hjic-242	145	4	the	the	DET
hjic-242	145	5	relative	relative	ADJ
hjic-242	145	6	position	position	NOUN
hjic-242	145	7	of	of	ADP
hjic-242	145	8	the	the	DET
hjic-242	145	9	underspecified	underspecified	ADJ
hjic-242	145	10	and	and	CCONJ
hjic-242	145	11	the	the	DET
hjic-242	145	12	overspecified	overspecified	ADJ
hjic-242	145	13	subgraphs	subgraph	NOUN
hjic-242	145	14	has	have	VERB
hjic-242	145	15	an	an	DET
hjic-242	145	16	effect	effect	NOUN
hjic-242	145	17	to	to	ADP
hjic-242	145	18	the	the	DET
hjic-242	145	19	value	value	NOUN
hjic-242	145	20	of	of	ADP
hjic-242	145	21	differential	differential	ADJ
hjic-242	145	22	index	index	NOUN
hjic-242	145	23	.	.	PUNCT
hjic-242	146	1	references	reference	NOUN
hjic-242	146	2	1	1	NUM
hjic-242	146	3	.	.	PUNCT
hjic-242	146	4	hangos	hangos	PROPN
hjic-242	146	5	k.	k.	PROPN
hjic-242	146	6	m.	m.	PROPN
hjic-242	146	7	,	,	PUNCT
hjic-242	146	8	cameron	cameron	PROPN
hjic-242	146	9	i.	i.	PROPN
hjic-242	146	10	t.	t.	PROPN
hjic-242	146	11	:	:	PUNCT
hjic-242	146	12	process	process	NOUN
hjic-242	146	13	modelling	modelling	NOUN
hjic-242	146	14	and	and	CCONJ
hjic-242	146	15	model	model	NOUN
hjic-242	146	16	analysis	analysis	NOUN
hjic-242	146	17	.	.	PUNCT
hjic-242	147	1	academic	academic	ADJ
hjic-242	147	2	press	press	NOUN
hjic-242	147	3	,	,	PUNCT
hjic-242	147	4	london	london	PROPN
hjic-242	147	5	(	(	PUNCT
hjic-242	147	6	2001	2001	NUM
hjic-242	147	7	)	)	PUNCT
hjic-242	147	8	2	2	NUM
hjic-242	147	9	.	.	PUNCT
hjic-242	148	1	leitold	leitold	PROPN
hjic-242	148	2	a.	a.	PROPN
hjic-242	148	3	,	,	PUNCT
hjic-242	148	4	hangos	hangos	PROPN
hjic-242	148	5	k.	k.	PROPN
hjic-242	148	6	m.	m.	PROPN
hjic-242	148	7	:	:	PUNCT
hjic-242	148	8	structural	structural	ADJ
hjic-242	148	9	solvability	solvability	NOUN
hjic-242	148	10	analysis	analysis	NOUN
hjic-242	148	11	of	of	ADP
hjic-242	148	12	dynamic	dynamic	ADJ
hjic-242	148	13	process	process	NOUN
hjic-242	148	14	models	model	NOUN
hjic-242	148	15	,	,	PUNCT
hjic-242	148	16	computers	computer	NOUN
hjic-242	148	17	chem	chem	NOUN
hjic-242	148	18	.	.	PUNCT
hjic-242	149	1	engng	engng	PROPN
hjic-242	149	2	25	25	NUM
hjic-242	149	3	,	,	PUNCT
hjic-242	149	4	(	(	PUNCT
hjic-242	149	5	2001	2001	NUM
hjic-242	149	6	)	)	PUNCT
hjic-242	149	7	,	,	PUNCT
hjic-242	149	8	1633–1646	1633–1646	NUM
hjic-242	149	9	3	3	NUM
hjic-242	149	10	.	.	PUNCT
hjic-242	150	1	leitold	leitold	PROPN
hjic-242	150	2	a.	a.	PROPN
hjic-242	150	3	,	,	PUNCT
hjic-242	150	4	hangos	hangos	PROPN
hjic-242	150	5	k.	k.	PROPN
hjic-242	150	6	m.	m.	PROPN
hjic-242	150	7	:	:	PUNCT
hjic-242	150	8	effect	effect	NOUN
hjic-242	150	9	of	of	ADP
hjic-242	150	10	steady	steady	ADJ
hjic-242	150	11	state	state	NOUN
hjic-242	150	12	assumption	assumption	NOUN
hjic-242	150	13	on	on	ADP
hjic-242	150	14	the	the	DET
hjic-242	150	15	structural	structural	ADJ
hjic-242	150	16	solvability	solvability	NOUN
hjic-242	150	17	of	of	ADP
hjic-242	150	18	dynamic	dynamic	ADJ
hjic-242	150	19	process	process	NOUN
hjic-242	150	20	models	model	NOUN
hjic-242	150	21	,	,	PUNCT
hjic-242	150	22	hung	hung	PROPN
hjic-242	150	23	.	.	PUNCT
hjic-242	151	1	j.	j.	PROPN
hjic-242	151	2	of	of	ADP
hjic-242	151	3	ind	ind	PROPN
hjic-242	151	4	.	.	PUNCT
hjic-242	152	1	chem	chem	PROPN
hjic-242	152	2	.	.	PUNCT
hjic-242	153	1	30	30	NUM
hjic-242	153	2	1	1	NUM
hjic-242	153	3	(	(	PUNCT
hjic-242	153	4	2002	2002	NUM
hjic-242	153	5	)	)	PUNCT
hjic-242	153	6	,	,	PUNCT
hjic-242	153	7	61–71	61–71	NOUN
hjic-242	153	8	4	4	NUM
hjic-242	153	9	.	.	PUNCT
hjic-242	154	1	murota	murota	NOUN
hjic-242	154	2	k.	k.	NOUN
hjic-242	154	3	:	:	PUNCT
hjic-242	155	1	systems	system	NOUN
hjic-242	155	2	analysis	analysis	NOUN
hjic-242	155	3	by	by	ADP
hjic-242	155	4	graphs	graph	NOUN
hjic-242	155	5	and	and	CCONJ
hjic-242	155	6	matroids	matroid	NOUN
hjic-242	155	7	.	.	PUNCT
hjic-242	156	1	springer	springer	PROPN
hjic-242	156	2	verlag	verlag	PROPN
hjic-242	156	3	,	,	PUNCT
hjic-242	156	4	berlin	berlin	PROPN
hjic-242	156	5	(	(	PUNCT
hjic-242	156	6	1987	1987	NUM
hjic-242	156	7	)	)	PUNCT
hjic-242	156	8	5	5	NUM
hjic-242	156	9	.	.	PUNCT
hjic-242	156	10	iri	iri	PROPN
hjic-242	156	11	m.	m.	NOUN
hjic-242	156	12	,	,	PUNCT
hjic-242	156	13	tsunekawa	tsunekawa	PROPN
hjic-242	156	14	j.	j.	PROPN
hjic-242	156	15	,	,	PUNCT
hjic-242	156	16	yajima	yajima	PROPN
hjic-242	156	17	k.	k.	PROPN
hjic-242	156	18	:	:	PUNCT
hjic-242	157	1	the	the	DET
hjic-242	157	2	graphical	graphical	ADJ
hjic-242	157	3	techniques	technique	NOUN
hjic-242	157	4	used	use	VERB
hjic-242	157	5	for	for	ADP
hjic-242	157	6	a	a	DET
hjic-242	157	7	chemical	chemical	NOUN
hjic-242	157	8	process	process	NOUN
hjic-242	157	9	simulator	simulator	NOUN
hjic-242	157	10	‘	'	PUNCT
hjic-242	157	11	juse	juse	PROPN
hjic-242	157	12	gifs	gifs	PROPN
hjic-242	157	13	’	'	PUNCT
hjic-242	157	14	,	,	PUNCT
hjic-242	157	15	information	information	NOUN
hjic-242	157	16	processing	processing	NOUN
hjic-242	157	17	,	,	PUNCT
hjic-242	157	18	71	71	NUM
hjic-242	157	19	.	.	PUNCT
hjic-242	157	20	(	(	PUNCT
hjic-242	157	21	1972	1972	NUM
hjic-242	157	22	)	)	PUNCT
hjic-242	157	23	vol	vol	NOUN
hjic-242	157	24	.	.	PROPN
hjic-242	157	25	2	2	NUM
hjic-242	157	26	,	,	PUNCT
hjic-242	157	27	1150–1155	1150–1155	NUM
hjic-242	157	28	6	6	NUM
hjic-242	157	29	.	.	PUNCT
hjic-242	157	30	gear	gear	PROPN
hjic-242	157	31	c.	c.	PROPN
hjic-242	157	32	w.	w.	PROPN
hjic-242	157	33	,	,	PUNCT
hjic-242	157	34	petzold	petzold	PROPN
hjic-242	157	35	l.	l.	PROPN
hjic-242	157	36	r.	r.	PROPN
hjic-242	157	37	:	:	PUNCT
hjic-242	157	38	ode	ode	ADJ
hjic-242	157	39	methods	method	NOUN
hjic-242	157	40	for	for	ADP
hjic-242	157	41	the	the	DET
hjic-242	157	42	solution	solution	NOUN
hjic-242	157	43	of	of	ADP
hjic-242	157	44	differential	differential	ADJ
hjic-242	157	45	/	/	SYM
hjic-242	157	46	algebraic	algebraic	ADJ
hjic-242	157	47	systems	system	NOUN
hjic-242	157	48	,	,	PUNCT
hjic-242	157	49	siam	siam	PROPN
hjic-242	157	50	j.	j.	PROPN
hjic-242	157	51	numer	numer	PROPN
hjic-242	157	52	.	.	PROPN
hjic-242	158	1	anal	anal	PROPN
hjic-242	158	2	.	.	PUNCT
hjic-242	159	1	(	(	PUNCT
hjic-242	159	2	1984	1984	NUM
hjic-242	159	3	)	)	PUNCT
hjic-242	159	4	vol	vol	NOUN
hjic-242	159	5	.	.	PROPN
hjic-242	160	1	21	21	NUM
hjic-242	160	2	,	,	PUNCT
hjic-242	160	3	no	no	INTJ
hjic-242	160	4	.	.	NOUN
hjic-242	160	5	4	4	NUM
hjic-242	160	6	,	,	PUNCT
hjic-242	160	7	716–728	716–728	NUM
hjic-242	160	8	7	7	NUM
hjic-242	160	9	.	.	PUNCT
hjic-242	161	1	brenan	brenan	PROPN
hjic-242	161	2	k.	k.	PROPN
hjic-242	161	3	e.	e.	PROPN
hjic-242	161	4	,	,	PUNCT
hjic-242	161	5	campbell	campbell	PROPN
hjic-242	161	6	s.	s.	PROPN
hjic-242	161	7	l.	l.	PROPN
hjic-242	161	8	,	,	PUNCT
hjic-242	161	9	petzold	petzold	PROPN
hjic-242	161	10	l.	l.	PROPN
hjic-242	161	11	r.	r.	PROPN
hjic-242	161	12	:	:	PUNCT
hjic-242	161	13	numerical	numerical	ADJ
hjic-242	161	14	solution	solution	NOUN
hjic-242	161	15	of	of	ADP
hjic-242	161	16	initial	initial	ADJ
hjic-242	161	17	value	value	NOUN
hjic-242	161	18	problems	problem	NOUN
hjic-242	161	19	in	in	ADP
hjic-242	161	20	differential	differential	ADJ
hjic-242	161	21	–	–	PUNCT
hjic-242	161	22	algebraic	algebraic	ADJ
hjic-242	161	23	equations	equation	NOUN
hjic-242	161	24	.	.	PUNCT
hjic-242	162	1	north	north	NOUN
hjic-242	162	2	-	-	PUNCT
hjic-242	162	3	holland	holland	PROPN
hjic-242	162	4	,	,	PUNCT
hjic-242	162	5	new	new	PROPN
hjic-242	162	6	york	york	PROPN
hjic-242	162	7	(	(	PUNCT
hjic-242	162	8	1989	1989	NUM
hjic-242	162	9	)	)	PUNCT
hjic-242	162	10	8	8	NUM
hjic-242	162	11	.	.	PUNCT
hjic-242	163	1	leitold	leitold	PROPN
hjic-242	163	2	a.	a.	PROPN
hjic-242	163	3	,	,	PUNCT
hjic-242	163	4	hangos	hangos	PROPN
hjic-242	163	5	k.	k.	PROPN
hjic-242	163	6	m.	m.	PROPN
hjic-242	163	7	:	:	PUNCT
hjic-242	163	8	numerical	numerical	PROPN
hjic-242	163	9	methodindependent	methodindependent	PROPN
hjic-242	163	10	structural	structural	ADJ
hjic-242	163	11	solvability	solvability	NOUN
hjic-242	163	12	analysis	analysis	NOUN
hjic-242	163	13	of	of	ADP
hjic-242	163	14	dae	dae	NOUN
hjic-242	163	15	models	model	NOUN
hjic-242	163	16	,	,	PUNCT
hjic-242	163	17	hung	hung	PROPN
hjic-242	163	18	.	.	PUNCT
hjic-242	164	1	j.	j.	PROPN
hjic-242	164	2	of	of	ADP
hjic-242	164	3	ind	ind	PROPN
hjic-242	164	4	.	.	PUNCT
hjic-242	165	1	chem	chem	PROPN
hjic-242	165	2	.	.	PUNCT
hjic-242	166	1	33	33	NUM
hjic-242	166	2	(	(	PUNCT
hjic-242	166	3	2005	2005	NUM
hjic-242	166	4	)	)	PUNCT
hjic-242	166	5	1	1	NUM
hjic-242	166	6	-	-	SYM
hjic-242	166	7	2	2	NUM
hjic-242	166	8	,	,	PUNCT
hjic-242	166	9	11–21	11–21	NUM
hjic-242	166	10	9	9	NUM
hjic-242	166	11	.	.	PUNCT
hjic-242	166	12	moe	moe	PROPN
hjic-242	166	13	h.	h.	PROPN
hjic-242	166	14	i.	i.	PROPN
hjic-242	166	15	:	:	PUNCT
hjic-242	166	16	dynamic	dynamic	ADJ
hjic-242	166	17	process	process	NOUN
hjic-242	166	18	simulation	simulation	NOUN
hjic-242	166	19	.	.	PUNCT
hjic-242	167	1	phd	phd	NOUN
hjic-242	167	2	thesis	thesis	PROPN
hjic-242	167	3	university	university	PROPN
hjic-242	167	4	of	of	ADP
hjic-242	167	5	trondheim	trondheim	PROPN
hjic-242	167	6	,	,	PUNCT
hjic-242	167	7	dept	dept	PROPN
hjic-242	167	8	.	.	PROPN
hjic-242	167	9	of	of	ADP
hjic-242	167	10	chemical	chemical	PROPN
hjic-242	167	11	eng	eng	PROPN
hjic-242	167	12	.	.	PUNCT
hjic-242	168	1	(	(	PUNCT
hjic-242	168	2	1995	1995	NUM
hjic-242	168	3	)	)	PUNCT