id	sid	tid	token	lemma	pos
hjic-91	1	1	hungarian	hungarian	ADJ
hjic-91	1	2	journal	journal	NOUN
hjic-91	1	3	of	of	ADP
hjic-91	1	4	industrial	industrial	ADJ
hjic-91	1	5	chemistry	chemistry	NOUN
hjic-91	1	6	veszprém	veszprém	NOUN
hjic-91	1	7	vol	vol	NOUN
hjic-91	1	8	.	.	PUNCT
hjic-91	2	1	33(1	33(1	NUM
hjic-91	2	2	-	-	SYM
hjic-91	2	3	2	2	NUM
hjic-91	2	4	)	)	PUNCT
hjic-91	2	5	.	.	PUNCT
hjic-91	3	1	pp	pp	X
hjic-91	3	2	.	.	PUNCT
hjic-91	4	1	11	11	NUM
hjic-91	4	2	-	-	SYM
hjic-91	4	3	21	21	NUM
hjic-91	4	4	.	.	PUNCT
hjic-91	5	1	(	(	PUNCT
hjic-91	5	2	2005	2005	NUM
hjic-91	5	3	)	)	PUNCT
hjic-91	5	4	numerical	numerical	ADJ
hjic-91	5	5	method	method	NOUN
hjic-91	5	6	-	-	PUNCT
hjic-91	5	7	independent	independent	ADJ
hjic-91	5	8	structural	structural	ADJ
hjic-91	5	9	solvability	solvability	NOUN
hjic-91	5	10	analysis	analysis	NOUN
hjic-91	5	11	of	of	ADP
hjic-91	5	12	dae	dae	NOUN
hjic-91	5	13	models	model	NOUN
hjic-91	5	14	*	*	PUNCT
hjic-91	5	15	a.	a.	NOUN
hjic-91	5	16	leitold1	leitold1	NOUN
hjic-91	5	17	and	and	CCONJ
hjic-91	5	18	k.	k.	PROPN
hjic-91	5	19	m.	m.	NOUN
hjic-91	5	20	hangos2	hangos2	PROPN
hjic-91	5	21	1department	1department	NUM
hjic-91	5	22	of	of	ADP
hjic-91	5	23	mathematics	mathematic	NOUN
hjic-91	5	24	,	,	PUNCT
hjic-91	5	25	university	university	NOUN
hjic-91	5	26	of	of	ADP
hjic-91	5	27	veszprém	veszprém	NOUN
hjic-91	5	28	h-8201	h-8201	NUM
hjic-91	5	29	veszprém	veszprém	NOUN
hjic-91	5	30	,	,	PUNCT
hjic-91	5	31	p.o.box	p.o.box	PROPN
hjic-91	5	32	158	158	NUM
hjic-91	5	33	,	,	PUNCT
hjic-91	5	34	hungary	hungary	NOUN
hjic-91	5	35	2systems	2systems	NUM
hjic-91	5	36	and	and	CCONJ
hjic-91	5	37	control	control	PROPN
hjic-91	5	38	research	research	NOUN
hjic-91	5	39	laboratory	laboratory	NOUN
hjic-91	5	40	,	,	PUNCT
hjic-91	5	41	computer	computer	NOUN
hjic-91	5	42	and	and	CCONJ
hjic-91	5	43	automation	automation	NOUN
hjic-91	5	44	institute	institute	NOUN
hjic-91	5	45	,	,	PUNCT
hjic-91	5	46	has	have	VERB
hjic-91	5	47	h-1518	h-1518	PROPN
hjic-91	5	48	,	,	PUNCT
hjic-91	5	49	budapest	budapest	NOUN
hjic-91	5	50	,	,	PUNCT
hjic-91	5	51	p.o.box	p.o.box	PROPN
hjic-91	5	52	63	63	NUM
hjic-91	5	53	,	,	PUNCT
hjic-91	5	54	hungary	hungary	VERB
hjic-91	5	55	a	a	DET
hjic-91	5	56	graph	graph	NOUN
hjic-91	5	57	-	-	PUNCT
hjic-91	5	58	theoretical	theoretical	ADJ
hjic-91	5	59	method	method	NOUN
hjic-91	5	60	[	[	X
hjic-91	5	61	1,2	1,2	NUM
hjic-91	5	62	]	]	PUNCT
hjic-91	5	63	for	for	ADP
hjic-91	5	64	the	the	DET
hjic-91	5	65	structural	structural	ADJ
hjic-91	5	66	analysis	analysis	NOUN
hjic-91	5	67	of	of	ADP
hjic-91	5	68	dynamic	dynamic	ADJ
hjic-91	5	69	lumped	lump	VERB
hjic-91	5	70	process	process	NOUN
hjic-91	5	71	models	model	NOUN
hjic-91	5	72	described	describe	VERB
hjic-91	5	73	by	by	ADP
hjic-91	5	74	differential	differential	ADJ
hjic-91	5	75	and	and	CCONJ
hjic-91	5	76	algebraic	algebraic	ADJ
hjic-91	5	77	equations	equation	NOUN
hjic-91	5	78	(	(	PUNCT
hjic-91	5	79	daes	daes	PROPN
hjic-91	5	80	)	)	PUNCT
hjic-91	5	81	is	be	AUX
hjic-91	5	82	applied	apply	VERB
hjic-91	5	83	in	in	ADP
hjic-91	5	84	this	this	DET
hjic-91	5	85	paper	paper	NOUN
hjic-91	5	86	in	in	ADP
hjic-91	5	87	order	order	NOUN
hjic-91	5	88	to	to	PART
hjic-91	5	89	determine	determine	VERB
hjic-91	5	90	the	the	DET
hjic-91	5	91	most	most	ADV
hjic-91	5	92	important	important	ADJ
hjic-91	5	93	solvability	solvability	NOUN
hjic-91	5	94	properties	property	NOUN
hjic-91	5	95	of	of	ADP
hjic-91	5	96	these	these	DET
hjic-91	5	97	models	model	NOUN
hjic-91	5	98	by	by	ADP
hjic-91	5	99	using	use	VERB
hjic-91	5	100	the	the	DET
hjic-91	5	101	so	so	ADV
hjic-91	5	102	-	-	PUNCT
hjic-91	5	103	called	call	VERB
hjic-91	5	104	dynamic	dynamic	ADJ
hjic-91	5	105	representation	representation	NOUN
hjic-91	5	106	graph	graph	NOUN
hjic-91	5	107	.	.	PUNCT
hjic-91	6	1	the	the	DET
hjic-91	6	2	construction	construction	NOUN
hjic-91	6	3	of	of	ADP
hjic-91	6	4	the	the	DET
hjic-91	6	5	dynamic	dynamic	ADJ
hjic-91	6	6	representation	representation	NOUN
hjic-91	6	7	graphs	graph	NOUN
hjic-91	6	8	that	that	PRON
hjic-91	6	9	was	be	AUX
hjic-91	6	10	originally	originally	ADV
hjic-91	6	11	proposed	propose	VERB
hjic-91	6	12	[	[	X
hjic-91	6	13	2	2	NUM
hjic-91	6	14	]	]	PUNCT
hjic-91	6	15	for	for	ADP
hjic-91	6	16	the	the	DET
hjic-91	6	17	most	most	ADV
hjic-91	6	18	simple	simple	ADJ
hjic-91	6	19	,	,	PUNCT
hjic-91	6	20	single	single	ADJ
hjic-91	6	21	-	-	PUNCT
hjic-91	6	22	step	step	NOUN
hjic-91	6	23	,	,	PUNCT
hjic-91	6	24	explicit	explicit	ADJ
hjic-91	6	25	numerical	numerical	ADJ
hjic-91	6	26	methods	method	NOUN
hjic-91	6	27	,	,	PUNCT
hjic-91	6	28	has	have	AUX
hjic-91	6	29	been	be	AUX
hjic-91	6	30	extended	extend	VERB
hjic-91	6	31	in	in	ADP
hjic-91	6	32	this	this	DET
hjic-91	6	33	paper	paper	NOUN
hjic-91	6	34	to	to	ADP
hjic-91	6	35	higher	high	ADJ
hjic-91	6	36	order	order	NOUN
hjic-91	6	37	explicit	explicit	ADJ
hjic-91	6	38	and	and	CCONJ
hjic-91	6	39	implicit	implicit	ADJ
hjic-91	6	40	solution	solution	NOUN
hjic-91	6	41	methods	method	NOUN
hjic-91	6	42	,	,	PUNCT
hjic-91	6	43	that	that	PRON
hjic-91	6	44	are	be	AUX
hjic-91	6	45	used	use	VERB
hjic-91	6	46	more	more	ADV
hjic-91	6	47	frequently	frequently	ADV
hjic-91	6	48	and	and	CCONJ
hjic-91	6	49	efficiently	efficiently	ADV
hjic-91	6	50	for	for	ADP
hjic-91	6	51	numerical	numerical	ADJ
hjic-91	6	52	solution	solution	NOUN
hjic-91	6	53	of	of	ADP
hjic-91	6	54	dae	dae	NOUN
hjic-91	6	55	-	-	PUNCT
hjic-91	6	56	systems	system	NOUN
hjic-91	6	57	.	.	PUNCT
hjic-91	7	1	it	it	PRON
hjic-91	7	2	is	be	AUX
hjic-91	7	3	shown	show	VERB
hjic-91	7	4	here	here	ADV
hjic-91	7	5	that	that	SCONJ
hjic-91	7	6	the	the	DET
hjic-91	7	7	representation	representation	NOUN
hjic-91	7	8	graph	graph	NOUN
hjic-91	7	9	for	for	ADP
hjic-91	7	10	both	both	CCONJ
hjic-91	7	11	higher	high	ADJ
hjic-91	7	12	order	order	NOUN
hjic-91	7	13	explicit	explicit	ADJ
hjic-91	7	14	and	and	CCONJ
hjic-91	7	15	implicit	implicit	ADJ
hjic-91	7	16	solution	solution	NOUN
hjic-91	7	17	methods	method	NOUN
hjic-91	7	18	has	have	VERB
hjic-91	7	19	similar	similar	ADJ
hjic-91	7	20	properties	property	NOUN
hjic-91	7	21	to	to	ADP
hjic-91	7	22	the	the	DET
hjic-91	7	23	case	case	NOUN
hjic-91	7	24	of	of	ADP
hjic-91	7	25	explicit	explicit	ADJ
hjic-91	7	26	numerical	numerical	ADJ
hjic-91	7	27	solution	solution	NOUN
hjic-91	7	28	procedures	procedure	NOUN
hjic-91	7	29	both	both	PRON
hjic-91	7	30	for	for	ADP
hjic-91	7	31	index	index	NOUN
hjic-91	7	32	one	one	NUM
hjic-91	7	33	and	and	CCONJ
hjic-91	7	34	higher	high	ADJ
hjic-91	7	35	index	index	NOUN
hjic-91	7	36	models	model	NOUN
hjic-91	7	37	.	.	PUNCT
hjic-91	8	1	thus	thus	ADV
hjic-91	8	2	it	it	PRON
hjic-91	8	3	is	be	AUX
hjic-91	8	4	proven	prove	VERB
hjic-91	8	5	that	that	SCONJ
hjic-91	8	6	the	the	DET
hjic-91	8	7	important	important	ADJ
hjic-91	8	8	properties	property	NOUN
hjic-91	8	9	of	of	ADP
hjic-91	8	10	the	the	DET
hjic-91	8	11	representation	representation	NOUN
hjic-91	8	12	graph	graph	NOUN
hjic-91	8	13	including	include	VERB
hjic-91	8	14	the	the	DET
hjic-91	8	15	differential	differential	ADJ
hjic-91	8	16	index	index	NOUN
hjic-91	8	17	of	of	ADP
hjic-91	8	18	the	the	DET
hjic-91	8	19	models	model	NOUN
hjic-91	8	20	are	be	AUX
hjic-91	8	21	independent	independent	ADJ
hjic-91	8	22	of	of	ADP
hjic-91	8	23	the	the	DET
hjic-91	8	24	assumption	assumption	NOUN
hjic-91	8	25	whether	whether	SCONJ
hjic-91	8	26	a	a	DET
hjic-91	8	27	single	single	ADJ
hjic-91	8	28	-	-	PUNCT
hjic-91	8	29	step	step	NOUN
hjic-91	8	30	,	,	PUNCT
hjic-91	8	31	explicit	explicit	ADJ
hjic-91	8	32	or	or	CCONJ
hjic-91	8	33	implicit	implicit	ADJ
hjic-91	8	34	numerical	numerical	ADJ
hjic-91	8	35	method	method	NOUN
hjic-91	8	36	is	be	AUX
hjic-91	8	37	used	use	VERB
hjic-91	8	38	for	for	ADP
hjic-91	8	39	the	the	DET
hjic-91	8	40	solution	solution	NOUN
hjic-91	8	41	of	of	ADP
hjic-91	8	42	the	the	DET
hjic-91	8	43	differential	differential	ADJ
hjic-91	8	44	equations	equation	NOUN
hjic-91	8	45	.	.	PUNCT
hjic-91	9	1	keywords	keyword	NOUN
hjic-91	9	2	:	:	PUNCT
hjic-91	9	3	process	process	NOUN
hjic-91	9	4	models	model	NOUN
hjic-91	9	5	,	,	PUNCT
hjic-91	9	6	dae	dae	NOUN
hjic-91	9	7	-	-	PUNCT
hjic-91	9	8	models	model	NOUN
hjic-91	9	9	,	,	PUNCT
hjic-91	9	10	differential	differential	ADJ
hjic-91	9	11	index	index	NOUN
hjic-91	9	12	,	,	PUNCT
hjic-91	9	13	solvability	solvability	NOUN
hjic-91	9	14	,	,	PUNCT
hjic-91	9	15	structural	structural	ADJ
hjic-91	9	16	analysis	analysis	NOUN
hjic-91	9	17	*	*	PUNCT
hjic-91	9	18	an	an	DET
hjic-91	9	19	extended	extended	ADJ
hjic-91	9	20	version	version	NOUN
hjic-91	9	21	of	of	ADP
hjic-91	9	22	the	the	DET
hjic-91	9	23	lecture	lecture	NOUN
hjic-91	9	24	presented	present	VERB
hjic-91	9	25	in	in	ADP
hjic-91	9	26	4th	4th	ADJ
hjic-91	9	27	mathmod	mathmod	NOUN
hjic-91	9	28	symposium	symposium	NOUN
hjic-91	9	29	,	,	PUNCT
hjic-91	9	30	vienna	vienna	PROPN
hjic-91	9	31	,	,	PUNCT
hjic-91	9	32	austria	austria	PROPN
hjic-91	9	33	,	,	PUNCT
hjic-91	9	34	february	february	PROPN
hjic-91	9	35	5	5	NUM
hjic-91	9	36	-	-	SYM
hjic-91	9	37	7	7	NUM
hjic-91	9	38	,	,	PUNCT
hjic-91	9	39	2003	2003	NUM
hjic-91	9	40	introduction	introduction	NOUN
hjic-91	9	41	the	the	DET
hjic-91	9	42	structural	structural	ADJ
hjic-91	9	43	analysis	analysis	NOUN
hjic-91	9	44	of	of	ADP
hjic-91	9	45	dynamic	dynamic	ADJ
hjic-91	9	46	lumped	lump	VERB
hjic-91	9	47	process	process	NOUN
hjic-91	9	48	models	model	NOUN
hjic-91	9	49	forms	form	VERB
hjic-91	9	50	an	an	DET
hjic-91	9	51	important	important	ADJ
hjic-91	9	52	step	step	NOUN
hjic-91	9	53	in	in	ADP
hjic-91	9	54	the	the	DET
hjic-91	9	55	model	model	NOUN
hjic-91	9	56	building	building	NOUN
hjic-91	9	57	procedure	procedure	NOUN
hjic-91	9	58	[	[	X
hjic-91	9	59	3	3	X
hjic-91	9	60	]	]	PUNCT
hjic-91	9	61	and	and	CCONJ
hjic-91	9	62	it	it	PRON
hjic-91	9	63	is	be	AUX
hjic-91	9	64	used	use	VERB
hjic-91	9	65	for	for	ADP
hjic-91	9	66	the	the	DET
hjic-91	9	67	determination	determination	NOUN
hjic-91	9	68	of	of	ADP
hjic-91	9	69	the	the	DET
hjic-91	9	70	solvability	solvability	NOUN
hjic-91	9	71	properties	property	NOUN
hjic-91	9	72	of	of	ADP
hjic-91	9	73	the	the	DET
hjic-91	9	74	model	model	NOUN
hjic-91	9	75	,	,	PUNCT
hjic-91	9	76	too	too	ADV
hjic-91	9	77	.	.	PUNCT
hjic-91	10	1	this	this	DET
hjic-91	10	2	analysis	analysis	NOUN
hjic-91	10	3	includes	include	VERB
hjic-91	10	4	the	the	DET
hjic-91	10	5	determination	determination	NOUN
hjic-91	10	6	of	of	ADP
hjic-91	10	7	the	the	DET
hjic-91	10	8	degree	degree	NOUN
hjic-91	10	9	of	of	ADP
hjic-91	10	10	freedom	freedom	NOUN
hjic-91	10	11	,	,	PUNCT
hjic-91	10	12	structural	structural	ADJ
hjic-91	10	13	solvability	solvability	NOUN
hjic-91	10	14	,	,	PUNCT
hjic-91	10	15	differential	differential	ADJ
hjic-91	10	16	index	index	NOUN
hjic-91	10	17	and	and	CCONJ
hjic-91	10	18	the	the	DET
hjic-91	10	19	dynamic	dynamic	ADJ
hjic-91	10	20	degrees	degree	NOUN
hjic-91	10	21	of	of	ADP
hjic-91	10	22	freedom	freedom	NOUN
hjic-91	10	23	.	.	PUNCT
hjic-91	11	1	as	as	ADP
hjic-91	11	2	a	a	DET
hjic-91	11	3	result	result	NOUN
hjic-91	11	4	of	of	ADP
hjic-91	11	5	the	the	DET
hjic-91	11	6	analysis	analysis	NOUN
hjic-91	11	7	,	,	PUNCT
hjic-91	11	8	the	the	DET
hjic-91	11	9	decomposition	decomposition	NOUN
hjic-91	11	10	of	of	ADP
hjic-91	11	11	the	the	DET
hjic-91	11	12	model	model	NOUN
hjic-91	11	13	is	be	AUX
hjic-91	11	14	obtained	obtain	VERB
hjic-91	11	15	and	and	CCONJ
hjic-91	11	16	the	the	DET
hjic-91	11	17	calculation	calculation	NOUN
hjic-91	11	18	path	path	NOUN
hjic-91	11	19	can	can	AUX
hjic-91	11	20	be	be	AUX
hjic-91	11	21	determined	determine	VERB
hjic-91	11	22	.	.	PUNCT
hjic-91	12	1	this	this	DET
hjic-91	12	2	way	way	NOUN
hjic-91	12	3	the	the	DET
hjic-91	12	4	appropriate	appropriate	ADJ
hjic-91	12	5	numerical	numerical	ADJ
hjic-91	12	6	method	method	NOUN
hjic-91	12	7	for	for	ADP
hjic-91	12	8	solving	solve	VERB
hjic-91	12	9	the	the	DET
hjic-91	12	10	model	model	NOUN
hjic-91	12	11	can	can	AUX
hjic-91	12	12	be	be	AUX
hjic-91	12	13	chosen	choose	VERB
hjic-91	12	14	efficiently	efficiently	ADV
hjic-91	12	15	.	.	PUNCT
hjic-91	13	1	moreover	moreover	ADV
hjic-91	13	2	,	,	PUNCT
hjic-91	13	3	advice	advice	NOUN
hjic-91	13	4	on	on	ADP
hjic-91	13	5	how	how	SCONJ
hjic-91	13	6	to	to	PART
hjic-91	13	7	improve	improve	VERB
hjic-91	13	8	the	the	DET
hjic-91	13	9	computational	computational	ADJ
hjic-91	13	10	properties	property	NOUN
hjic-91	13	11	of	of	ADP
hjic-91	13	12	the	the	DET
hjic-91	13	13	model	model	NOUN
hjic-91	13	14	by	by	ADP
hjic-91	13	15	modifying	modify	VERB
hjic-91	13	16	its	its	PRON
hjic-91	13	17	form	form	NOUN
hjic-91	13	18	or	or	CCONJ
hjic-91	13	19	its	its	PRON
hjic-91	13	20	specification	specification	NOUN
hjic-91	13	21	can	can	AUX
hjic-91	13	22	also	also	ADV
hjic-91	13	23	be	be	AUX
hjic-91	13	24	given	give	VERB
hjic-91	13	25	.	.	PUNCT
hjic-91	14	1	effective	effective	ADJ
hjic-91	14	2	graph	graph	NOUN
hjic-91	14	3	-	-	PUNCT
hjic-91	14	4	theoretical	theoretical	ADJ
hjic-91	14	5	methods	method	NOUN
hjic-91	14	6	have	have	AUX
hjic-91	14	7	been	be	AUX
hjic-91	14	8	proposed	propose	VERB
hjic-91	14	9	in	in	ADP
hjic-91	14	10	the	the	DET
hjic-91	14	11	literature	literature	NOUN
hjic-91	15	1	[	[	X
hjic-91	15	2	2,4	2,4	NUM
hjic-91	15	3	]	]	PUNCT
hjic-91	15	4	based	base	VERB
hjic-91	15	5	on	on	ADP
hjic-91	15	6	the	the	DET
hjic-91	15	7	analysis	analysis	NOUN
hjic-91	15	8	tools	tool	NOUN
hjic-91	15	9	developed	develop	VERB
hjic-91	15	10	by	by	ADP
hjic-91	15	11	murota	murota	NOUN
hjic-91	15	12	,	,	PUNCT
hjic-91	15	13	et	et	NOUN
hjic-91	15	14	al	al	PROPN
hjic-91	16	1	[	[	X
hjic-91	16	2	1	1	NUM
hjic-91	16	3	]	]	PUNCT
hjic-91	16	4	,	,	PUNCT
hjic-91	16	5	for	for	ADP
hjic-91	16	6	the	the	DET
hjic-91	16	7	determination	determination	NOUN
hjic-91	16	8	of	of	ADP
hjic-91	16	9	the	the	DET
hjic-91	16	10	most	most	ADV
hjic-91	16	11	important	important	ADJ
hjic-91	16	12	solvability	solvability	NOUN
hjic-91	16	13	property	property	NOUN
hjic-91	16	14	of	of	ADP
hjic-91	16	15	lumped	lump	VERB
hjic-91	16	16	dynamic	dynamic	ADJ
hjic-91	16	17	models	model	NOUN
hjic-91	16	18	:	:	PUNCT
hjic-91	16	19	the	the	DET
hjic-91	16	20	differential	differential	ADJ
hjic-91	16	21	index	index	NOUN
hjic-91	16	22	.	.	PUNCT
hjic-91	17	1	the	the	DET
hjic-91	17	2	properties	property	NOUN
hjic-91	17	3	of	of	ADP
hjic-91	17	4	the	the	DET
hjic-91	17	5	dynamic	dynamic	ADJ
hjic-91	17	6	representation	representation	NOUN
hjic-91	17	7	graph	graph	NOUN
hjic-91	17	8	of	of	ADP
hjic-91	17	9	process	process	NOUN
hjic-91	17	10	models	model	NOUN
hjic-91	17	11	described	describe	VERB
hjic-91	17	12	by	by	ADP
hjic-91	17	13	semi	semi	ADJ
hjic-91	17	14	-	-	ADJ
hjic-91	17	15	explicit	explicit	ADJ
hjic-91	17	16	dae	dae	NOUN
hjic-91	17	17	-	-	PUNCT
hjic-91	17	18	systems	system	NOUN
hjic-91	17	19	have	have	AUX
hjic-91	17	20	also	also	ADV
hjic-91	17	21	been	be	AUX
hjic-91	17	22	analysed	analyse	VERB
hjic-91	17	23	there	there	ADV
hjic-91	17	24	in	in	ADP
hjic-91	17	25	case	case	NOUN
hjic-91	17	26	of	of	ADP
hjic-91	17	27	index	index	NOUN
hjic-91	17	28	1	1	NUM
hjic-91	17	29	and	and	CCONJ
hjic-91	17	30	higher	high	ADJ
hjic-91	17	31	index	index	NOUN
hjic-91	17	32	models	model	NOUN
hjic-91	17	33	.	.	PUNCT
hjic-91	18	1	besides	besides	SCONJ
hjic-91	18	2	of	of	ADP
hjic-91	18	3	the	the	DET
hjic-91	18	4	algorithm	algorithm	NOUN
hjic-91	18	5	of	of	ADP
hjic-91	18	6	determining	determine	VERB
hjic-91	18	7	the	the	DET
hjic-91	18	8	differential	differential	ADJ
hjic-91	18	9	index	index	NOUN
hjic-91	18	10	by	by	ADP
hjic-91	18	11	using	use	VERB
hjic-91	18	12	the	the	DET
hjic-91	18	13	representation	representation	NOUN
hjic-91	18	14	graph	graph	NOUN
hjic-91	18	15	,	,	PUNCT
hjic-91	18	16	a	a	DET
hjic-91	18	17	model	model	NOUN
hjic-91	18	18	modification	modification	NOUN
hjic-91	18	19	method	method	NOUN
hjic-91	18	20	has	have	AUX
hjic-91	18	21	also	also	ADV
hjic-91	18	22	been	be	AUX
hjic-91	18	23	proposed	propose	VERB
hjic-91	18	24	in	in	ADP
hjic-91	18	25	the	the	DET
hjic-91	18	26	literature	literature	NOUN
hjic-91	18	27	,	,	PUNCT
hjic-91	18	28	which	which	PRON
hjic-91	18	29	results	result	VERB
hjic-91	18	30	in	in	ADP
hjic-91	18	31	a	a	DET
hjic-91	18	32	structurally	structurally	ADV
hjic-91	18	33	solvable	solvable	ADJ
hjic-91	18	34	model	model	NOUN
hjic-91	18	35	even	even	ADV
hjic-91	18	36	in	in	ADP
hjic-91	18	37	the	the	DET
hjic-91	18	38	case	case	NOUN
hjic-91	18	39	of	of	ADP
hjic-91	18	40	higher	high	ADJ
hjic-91	18	41	index	index	NOUN
hjic-91	18	42	models	model	NOUN
hjic-91	18	43	[	[	X
hjic-91	18	44	5,2	5,2	NUM
hjic-91	18	45	]	]	PUNCT
hjic-91	18	46	.	.	PUNCT
hjic-91	19	1	12	12	NUM
hjic-91	19	2	basic	basic	ADJ
hjic-91	19	3	notions	notion	NOUN
hjic-91	19	4	structural	structural	ADJ
hjic-91	19	5	solvability	solvability	NOUN
hjic-91	19	6	as	as	ADP
hjic-91	19	7	a	a	DET
hjic-91	19	8	first	first	ADJ
hjic-91	19	9	step	step	NOUN
hjic-91	19	10	,	,	PUNCT
hjic-91	19	11	we	we	PRON
hjic-91	19	12	consider	consider	VERB
hjic-91	19	13	a	a	DET
hjic-91	19	14	system	system	NOUN
hjic-91	19	15	of	of	ADP
hjic-91	19	16	linear	linear	ADJ
hjic-91	19	17	or	or	CCONJ
hjic-91	19	18	non	non	ADJ
hjic-91	19	19	-	-	ADJ
hjic-91	19	20	linear	linear	ADJ
hjic-91	19	21	algebraic	algebraic	ADJ
hjic-91	19	22	equations	equation	NOUN
hjic-91	19	23	in	in	ADP
hjic-91	19	24	its	its	PRON
hjic-91	19	25	so	so	ADV
hjic-91	19	26	called	call	VERB
hjic-91	19	27	standard	standard	ADJ
hjic-91	19	28	form	form	NOUN
hjic-91	19	29	[	[	X
hjic-91	19	30	1	1	NUM
hjic-91	19	31	]	]	PUNCT
hjic-91	19	32	:	:	PUNCT
hjic-91	19	33	yi	yi	X
hjic-91	19	34	=	=	SYM
hjic-91	19	35	fi	fi	NOUN
hjic-91	19	36	(	(	PUNCT
hjic-91	19	37	x	x	NOUN
hjic-91	19	38	,	,	PUNCT
hjic-91	19	39	u	u	NOUN
hjic-91	19	40	)	)	PUNCT
hjic-91	19	41	,	,	PUNCT
hjic-91	19	42	i	i	PRON
hjic-91	19	43	=	=	NOUN
hjic-91	19	44	1	1	NUM
hjic-91	19	45	,	,	PUNCT
hjic-91	19	46	…	…	PUNCT
hjic-91	19	47	,	,	PUNCT
hjic-91	19	48	m	m	VERB
hjic-91	19	49	uk	uk	PROPN
hjic-91	19	50	=	=	SYM
hjic-91	19	51	gk	gk	PROPN
hjic-91	19	52	(	(	PUNCT
hjic-91	19	53	x	x	NOUN
hjic-91	19	54	,	,	PUNCT
hjic-91	19	55	u	u	NOUN
hjic-91	19	56	)	)	PUNCT
hjic-91	19	57	,	,	PUNCT
hjic-91	19	58	k	k	X
hjic-91	19	59	=	=	SYM
hjic-91	19	60	1	1	NUM
hjic-91	19	61	,	,	PUNCT
hjic-91	19	62	…	…	PUNCT
hjic-91	19	63	,	,	PUNCT
hjic-91	19	64	k	k	PROPN
hjic-91	19	65	where	where	SCONJ
hjic-91	19	66	xj	xj	PROPN
hjic-91	19	67	(	(	PUNCT
hjic-91	19	68	j	j	PROPN
hjic-91	19	69	=	=	SYM
hjic-91	19	70	1	1	NUM
hjic-91	19	71	,	,	PUNCT
hjic-91	19	72	…	…	PUNCT
hjic-91	19	73	,	,	PUNCT
hjic-91	19	74	n	n	CCONJ
hjic-91	19	75	)	)	PUNCT
hjic-91	19	76	and	and	CCONJ
hjic-91	19	77	uk	uk	PROPN
hjic-91	19	78	(	(	PUNCT
hjic-91	19	79	k	k	NOUN
hjic-91	19	80	=	=	SYM
hjic-91	19	81	1,	1,	NUM
hjic-91	19	82	…	…	SYM
hjic-91	19	83	,k	,k	PUNCT
hjic-91	19	84	)	)	PUNCT
hjic-91	19	85	are	be	AUX
hjic-91	19	86	unknowns	unknown	NOUN
hjic-91	19	87	,	,	PUNCT
hjic-91	19	88	yi	yi	PROPN
hjic-91	19	89	(	(	PUNCT
hjic-91	19	90	i	i	NOUN
hjic-91	19	91	=	=	NOUN
hjic-91	19	92	1,	1,	NUM
hjic-91	19	93	…	…	SYM
hjic-91	19	94	,m	,m	X
hjic-91	19	95	)	)	PUNCT
hjic-91	19	96	are	be	AUX
hjic-91	19	97	known	know	VERB
hjic-91	19	98	parameters	parameter	NOUN
hjic-91	19	99	,	,	PUNCT
hjic-91	19	100	fi	fi	INTJ
hjic-91	19	101	(	(	PUNCT
hjic-91	19	102	i	i	NOUN
hjic-91	19	103	=	=	NOUN
hjic-91	19	104	1,	1,	NUM
hjic-91	19	105	…	…	SYM
hjic-91	19	106	,m	,m	PUNCT
hjic-91	19	107	)	)	PUNCT
hjic-91	19	108	and	and	CCONJ
hjic-91	19	109	gk	gk	INTJ
hjic-91	19	110	(	(	PUNCT
hjic-91	19	111	k	k	NOUN
hjic-91	19	112	=	=	SYM
hjic-91	19	113	1,	1,	NUM
hjic-91	19	114	…	…	SYM
hjic-91	19	115	,k	,k	PUNCT
hjic-91	19	116	)	)	PUNCT
hjic-91	19	117	are	be	AUX
hjic-91	19	118	assumed	assume	VERB
hjic-91	19	119	to	to	PART
hjic-91	19	120	be	be	AUX
hjic-91	19	121	sufficiently	sufficiently	ADV
hjic-91	19	122	smooth	smooth	ADJ
hjic-91	19	123	real	real	ADV
hjic-91	19	124	-	-	PUNCT
hjic-91	19	125	valued	value	VERB
hjic-91	19	126	functions	function	NOUN
hjic-91	19	127	.	.	PUNCT
hjic-91	20	1	the	the	DET
hjic-91	20	2	system	system	NOUN
hjic-91	20	3	of	of	ADP
hjic-91	20	4	equations	equation	NOUN
hjic-91	20	5	above	above	ADV
hjic-91	20	6	is	be	AUX
hjic-91	20	7	structurally	structurally	ADV
hjic-91	20	8	solvable	solvable	ADJ
hjic-91	20	9	,	,	PUNCT
hjic-91	20	10	if	if	SCONJ
hjic-91	20	11	the	the	DET
hjic-91	20	12	jacobian	jacobian	ADJ
hjic-91	20	13	matrix	matrix	NOUN
hjic-91	20	14	j(x	j(x	PROPN
hjic-91	20	15	,	,	PUNCT
hjic-91	20	16	u	u	NOUN
hjic-91	20	17	)	)	PUNCT
hjic-91	20	18	referring	refer	VERB
hjic-91	20	19	to	to	ADP
hjic-91	20	20	the	the	DET
hjic-91	20	21	above	above	ADJ
hjic-91	20	22	model	model	NOUN
hjic-91	20	23	is	be	AUX
hjic-91	20	24	non	non	ADJ
hjic-91	20	25	-	-	ADJ
hjic-91	20	26	singular	singular	ADJ
hjic-91	20	27	.	.	PUNCT
hjic-91	21	1	consider	consider	VERB
hjic-91	21	2	a	a	DET
hjic-91	21	3	system	system	NOUN
hjic-91	21	4	of	of	ADP
hjic-91	21	5	equations	equation	NOUN
hjic-91	21	6	in	in	ADP
hjic-91	21	7	standard	standard	ADJ
hjic-91	21	8	form	form	NOUN
hjic-91	21	9	.	.	PUNCT
hjic-91	22	1	we	we	PRON
hjic-91	22	2	construct	construct	VERB
hjic-91	22	3	a	a	DET
hjic-91	22	4	directed	direct	VERB
hjic-91	22	5	graph	graph	NOUN
hjic-91	22	6	to	to	PART
hjic-91	22	7	represent	represent	VERB
hjic-91	22	8	the	the	DET
hjic-91	22	9	structure	structure	NOUN
hjic-91	22	10	of	of	ADP
hjic-91	22	11	the	the	DET
hjic-91	22	12	set	set	NOUN
hjic-91	22	13	of	of	ADP
hjic-91	22	14	equations	equation	NOUN
hjic-91	22	15	in	in	ADP
hjic-91	22	16	the	the	DET
hjic-91	22	17	following	following	ADJ
hjic-91	22	18	way	way	NOUN
hjic-91	22	19	.	.	PUNCT
hjic-91	23	1	the	the	DET
hjic-91	23	2	vertex	vertex	NOUN
hjic-91	23	3	-	-	PUNCT
hjic-91	23	4	set	set	NOUN
hjic-91	23	5	corresponding	corresponding	NOUN
hjic-91	23	6	to	to	ADP
hjic-91	23	7	unknowns	unknown	NOUN
hjic-91	23	8	and	and	CCONJ
hjic-91	23	9	parameters	parameter	NOUN
hjic-91	23	10	is	be	AUX
hjic-91	23	11	partitioned	partition	VERB
hjic-91	23	12	as	as	ADP
hjic-91	23	13	x∪u∪y	x∪u∪y	NOUN
hjic-91	23	14	,	,	PUNCT
hjic-91	23	15	where	where	SCONJ
hjic-91	23	16	x	x	X
hjic-91	23	17	=	=	PRON
hjic-91	23	18	{	{	PUNCT
hjic-91	23	19	x1	x1	PROPN
hjic-91	23	20	,	,	PUNCT
hjic-91	23	21	…	…	PUNCT
hjic-91	23	22	,	,	PUNCT
hjic-91	23	23	xn	xn	NUM
hjic-91	23	24	}	}	PUNCT
hjic-91	23	25	,	,	PUNCT
hjic-91	23	26	u	u	NOUN
hjic-91	23	27	=	=	NOUN
hjic-91	23	28	{	{	PUNCT
hjic-91	23	29	u1	u1	NOUN
hjic-91	23	30	,	,	PUNCT
hjic-91	23	31	…	…	PUNCT
hjic-91	23	32	,	,	PUNCT
hjic-91	23	33	uk	uk	PROPN
hjic-91	23	34	}	}	PUNCT
hjic-91	23	35	and	and	CCONJ
hjic-91	23	36	y	y	PROPN
hjic-91	23	37	=	=	SYM
hjic-91	23	38	{	{	PUNCT
hjic-91	23	39	y1	y1	PROPN
hjic-91	23	40	,	,	PUNCT
hjic-91	23	41	…	…	PUNCT
hjic-91	23	42	,	,	PUNCT
hjic-91	23	43	ym	ym	PROPN
hjic-91	23	44	}	}	PUNCT
hjic-91	23	45	.	.	PUNCT
hjic-91	24	1	the	the	DET
hjic-91	24	2	functional	functional	ADJ
hjic-91	24	3	dependence	dependence	NOUN
hjic-91	24	4	described	describe	VERB
hjic-91	24	5	by	by	ADP
hjic-91	24	6	an	an	DET
hjic-91	24	7	equation	equation	NOUN
hjic-91	24	8	is	be	AUX
hjic-91	24	9	expressed	express	VERB
hjic-91	24	10	by	by	ADP
hjic-91	24	11	arcs	arc	NOUN
hjic-91	24	12	coming	come	VERB
hjic-91	24	13	into	into	ADP
hjic-91	24	14	yi	yi	NOUN
hjic-91	24	15	or	or	CCONJ
hjic-91	24	16	uk	uk	PROPN
hjic-91	24	17	respectively	respectively	ADV
hjic-91	24	18	from	from	ADP
hjic-91	24	19	those	those	DET
hjic-91	24	20	xj	xj	PROPN
hjic-91	24	21	and	and	CCONJ
hjic-91	24	22	ul	ul	INTJ
hjic-91	24	23	,	,	PUNCT
hjic-91	24	24	which	which	PRON
hjic-91	24	25	appear	appear	VERB
hjic-91	24	26	on	on	ADP
hjic-91	24	27	its	its	PRON
hjic-91	24	28	right	right	ADJ
hjic-91	24	29	-	-	PUNCT
hjic-91	24	30	hand	hand	NOUN
hjic-91	24	31	side	side	NOUN
hjic-91	24	32	.	.	PUNCT
hjic-91	25	1	this	this	DET
hjic-91	25	2	graph	graph	NOUN
hjic-91	25	3	is	be	AUX
hjic-91	25	4	called	call	VERB
hjic-91	25	5	the	the	DET
hjic-91	25	6	representation	representation	NOUN
hjic-91	25	7	graph	graph	NOUN
hjic-91	25	8	of	of	ADP
hjic-91	25	9	the	the	DET
hjic-91	25	10	system	system	NOUN
hjic-91	25	11	of	of	ADP
hjic-91	25	12	equations	equation	NOUN
hjic-91	25	13	.	.	PUNCT
hjic-91	26	1	a	a	DET
hjic-91	26	2	menger	menger	NOUN
hjic-91	26	3	-	-	PUNCT
hjic-91	26	4	type	type	NOUN
hjic-91	26	5	linking	link	VERB
hjic-91	26	6	from	from	ADP
hjic-91	26	7	x	x	PUNCT
hjic-91	26	8	to	to	ADP
hjic-91	26	9	y	y	PROPN
hjic-91	26	10	is	be	AUX
hjic-91	26	11	a	a	DET
hjic-91	26	12	set	set	NOUN
hjic-91	26	13	of	of	ADP
hjic-91	26	14	pair	pair	NOUN
hjic-91	26	15	-	-	PUNCT
hjic-91	26	16	wise	wise	ADJ
hjic-91	26	17	vertex	vertex	NOUN
hjic-91	26	18	-	-	PUNCT
hjic-91	26	19	disjoint	disjoint	NOUN
hjic-91	26	20	directed	direct	VERB
hjic-91	26	21	paths	path	NOUN
hjic-91	26	22	from	from	ADP
hjic-91	26	23	a	a	DET
hjic-91	26	24	vertex	vertex	NOUN
hjic-91	26	25	in	in	ADP
hjic-91	26	26	x	x	PUNCT
hjic-91	26	27	to	to	ADP
hjic-91	26	28	a	a	DET
hjic-91	26	29	vertex	vertex	NOUN
hjic-91	26	30	in	in	ADP
hjic-91	26	31	y.	y.	NOUN
hjic-91	26	32	the	the	DET
hjic-91	26	33	size	size	NOUN
hjic-91	26	34	of	of	ADP
hjic-91	26	35	a	a	DET
hjic-91	26	36	linking	linking	NOUN
hjic-91	26	37	is	be	AUX
hjic-91	26	38	the	the	DET
hjic-91	26	39	number	number	NOUN
hjic-91	26	40	of	of	ADP
hjic-91	26	41	directed	direct	VERB
hjic-91	26	42	paths	path	NOUN
hjic-91	26	43	from	from	ADP
hjic-91	26	44	x	x	PUNCT
hjic-91	26	45	to	to	ADP
hjic-91	26	46	y	y	PROPN
hjic-91	26	47	contained	contain	VERB
hjic-91	26	48	in	in	ADP
hjic-91	26	49	the	the	DET
hjic-91	26	50	linking	linking	NOUN
hjic-91	26	51	.	.	PUNCT
hjic-91	27	1	in	in	ADP
hjic-91	27	2	case	case	NOUN
hjic-91	27	3	⏐	⏐	VERB
hjic-91	27	4	x	x	SYM
hjic-91	27	5	⏐	⏐	NOUN
hjic-91	27	6	=	=	SYM
hjic-91	27	7	⏐	⏐	NOUN
hjic-91	27	8	y	y	PROPN
hjic-91	27	9	⏐	⏐	PROPN
hjic-91	27	10	,	,	PUNCT
hjic-91	27	11	(	(	PUNCT
hjic-91	27	12	m	m	NOUN
hjic-91	27	13	=	=	SYM
hjic-91	27	14	n	n	CCONJ
hjic-91	27	15	)	)	PUNCT
hjic-91	27	16	,	,	PUNCT
hjic-91	27	17	a	a	DET
hjic-91	27	18	linking	linking	NOUN
hjic-91	27	19	of	of	ADP
hjic-91	27	20	size	size	NOUN
hjic-91	27	21	⏐	⏐	NOUN
hjic-91	27	22	x	x	SYM
hjic-91	27	23	⏐	⏐	PROPN
hjic-91	27	24	is	be	AUX
hjic-91	27	25	called	call	VERB
hjic-91	27	26	a	a	DET
hjic-91	27	27	complete	complete	ADJ
hjic-91	27	28	linking	linking	NOUN
hjic-91	27	29	.	.	PUNCT
hjic-91	28	1	the	the	DET
hjic-91	28	2	graphical	graphical	ADJ
hjic-91	28	3	condition	condition	NOUN
hjic-91	28	4	of	of	ADP
hjic-91	28	5	the	the	DET
hjic-91	28	6	structural	structural	ADJ
hjic-91	28	7	solvability	solvability	NOUN
hjic-91	28	8	is	be	AUX
hjic-91	28	9	then	then	ADV
hjic-91	28	10	the	the	DET
hjic-91	28	11	following	follow	VERB
hjic-91	28	12	[	[	X
hjic-91	28	13	1	1	NUM
hjic-91	28	14	]	]	PUNCT
hjic-91	28	15	:	:	PUNCT
hjic-91	28	16	linkage	linkage	NOUN
hjic-91	28	17	theorem	theorem	VERB
hjic-91	28	18	:	:	PUNCT
hjic-91	28	19	assume	assume	VERB
hjic-91	28	20	that	that	SCONJ
hjic-91	28	21	the	the	DET
hjic-91	28	22	nonvanishing	nonvanishe	VERB
hjic-91	28	23	elements	element	NOUN
hjic-91	28	24	of	of	ADP
hjic-91	28	25	partial	partial	ADJ
hjic-91	28	26	derivatives	derivative	NOUN
hjic-91	28	27	fi	fi	NOUN
hjic-91	28	28	and	and	CCONJ
hjic-91	28	29	gk	gk	NOUN
hjic-91	28	30	in	in	ADP
hjic-91	28	31	the	the	DET
hjic-91	28	32	standard	standard	ADJ
hjic-91	28	33	form	form	NOUN
hjic-91	28	34	model	model	NOUN
hjic-91	28	35	are	be	AUX
hjic-91	28	36	algebraically	algebraically	ADV
hjic-91	28	37	independent	independent	ADJ
hjic-91	28	38	over	over	ADP
hjic-91	28	39	the	the	DET
hjic-91	28	40	rational	rational	ADJ
hjic-91	28	41	number	number	NOUN
hjic-91	28	42	field	field	NOUN
hjic-91	28	43	q.	q.	NOUN
hjic-91	28	44	then	then	ADV
hjic-91	28	45	the	the	DET
hjic-91	28	46	model	model	NOUN
hjic-91	28	47	is	be	AUX
hjic-91	28	48	structurally	structurally	ADV
hjic-91	28	49	solvable	solvable	ADJ
hjic-91	28	50	if	if	SCONJ
hjic-91	28	51	and	and	CCONJ
hjic-91	28	52	only	only	ADV
hjic-91	28	53	if	if	SCONJ
hjic-91	28	54	there	there	PRON
hjic-91	28	55	exists	exist	VERB
hjic-91	28	56	a	a	DET
hjic-91	28	57	menger	menger	NOUN
hjic-91	28	58	-	-	PUNCT
hjic-91	28	59	type	type	NOUN
hjic-91	28	60	complete	complete	ADJ
hjic-91	28	61	linking	linking	NOUN
hjic-91	28	62	from	from	ADP
hjic-91	28	63	x	x	PUNCT
hjic-91	28	64	to	to	ADP
hjic-91	28	65	y	y	PROPN
hjic-91	28	66	on	on	ADP
hjic-91	28	67	the	the	DET
hjic-91	28	68	representation	representation	NOUN
hjic-91	28	69	graph	graph	NOUN
hjic-91	28	70	.	.	PUNCT
hjic-91	29	1	we	we	PRON
hjic-91	29	2	can	can	AUX
hjic-91	29	3	adapt	adapt	VERB
hjic-91	29	4	the	the	DET
hjic-91	29	5	graphical	graphical	ADJ
hjic-91	29	6	techniques	technique	NOUN
hjic-91	29	7	to	to	PART
hjic-91	29	8	daesystems	daesystem	NOUN
hjic-91	29	9	,	,	PUNCT
hjic-91	29	10	as	as	ADV
hjic-91	29	11	well	well	ADV
hjic-91	29	12	.	.	PUNCT
hjic-91	30	1	an	an	DET
hjic-91	30	2	ordinary	ordinary	ADJ
hjic-91	30	3	differential	differential	ADJ
hjic-91	30	4	equation	equation	NOUN
hjic-91	30	5	of	of	ADP
hjic-91	30	6	a	a	DET
hjic-91	30	7	dae	dae	NOUN
hjic-91	30	8	-	-	PUNCT
hjic-91	30	9	system	system	NOUN
hjic-91	30	10	can	can	AUX
hjic-91	30	11	be	be	AUX
hjic-91	30	12	described	describe	VERB
hjic-91	30	13	by	by	ADP
hjic-91	30	14	the	the	DET
hjic-91	30	15	following	follow	VERB
hjic-91	30	16	equation	equation	NOUN
hjic-91	30	17	:	:	PUNCT
hjic-91	30	18	x	x	X
hjic-91	30	19	’	'	PUNCT
hjic-91	30	20	=	=	SYM
hjic-91	30	21	f(x1	f(x1	NOUN
hjic-91	30	22	,	,	PUNCT
hjic-91	30	23	…	…	PUNCT
hjic-91	30	24	,	,	PUNCT
hjic-91	30	25	xn	xn	PUNCT
hjic-91	30	26	)	)	PUNCT
hjic-91	30	27	here	here	ADV
hjic-91	30	28	x	x	PUNCT
hjic-91	30	29	denotes	denote	VERB
hjic-91	30	30	an	an	DET
hjic-91	30	31	arbitrary	arbitrary	ADJ
hjic-91	30	32	variable	variable	NOUN
hjic-91	30	33	depending	depend	VERB
hjic-91	30	34	on	on	ADP
hjic-91	30	35	time	time	NOUN
hjic-91	30	36	,	,	PUNCT
hjic-91	30	37	x	x	PRON
hjic-91	30	38	’	'	PUNCT
hjic-91	30	39	denotes	denote	VERB
hjic-91	30	40	the	the	DET
hjic-91	30	41	derivative	derivative	NOUN
hjic-91	30	42	of	of	ADP
hjic-91	30	43	x	x	PUNCT
hjic-91	30	44	with	with	ADP
hjic-91	30	45	respect	respect	NOUN
hjic-91	30	46	to	to	ADP
hjic-91	30	47	time	time	NOUN
hjic-91	30	48	and	and	CCONJ
hjic-91	30	49	x1	x1	NUM
hjic-91	30	50	,	,	PUNCT
hjic-91	30	51	…	…	PUNCT
hjic-91	30	52	,	,	PUNCT
hjic-91	30	53	xn	xn	PROPN
hjic-91	30	54	are	be	AUX
hjic-91	30	55	those	those	DET
hjic-91	30	56	variables	variable	NOUN
hjic-91	30	57	which	which	PRON
hjic-91	30	58	have	have	VERB
hjic-91	30	59	effect	effect	NOUN
hjic-91	30	60	on	on	ADP
hjic-91	30	61	variable	variable	ADJ
hjic-91	30	62	x	x	NOUN
hjic-91	30	63	’	'	PUNCT
hjic-91	30	64	according	accord	VERB
hjic-91	30	65	to	to	ADP
hjic-91	30	66	the	the	DET
hjic-91	30	67	differential	differential	ADJ
hjic-91	30	68	equation	equation	NOUN
hjic-91	30	69	.	.	PUNCT
hjic-91	31	1	in	in	ADP
hjic-91	31	2	dae	dae	NOUN
hjic-91	31	3	-	-	PUNCT
hjic-91	31	4	systems	system	NOUN
hjic-91	31	5	there	there	PRON
hjic-91	31	6	are	be	VERB
hjic-91	31	7	two	two	NUM
hjic-91	31	8	types	type	NOUN
hjic-91	31	9	of	of	ADP
hjic-91	31	10	variables	variable	NOUN
hjic-91	31	11	.	.	PUNCT
hjic-91	32	1	differential	differential	ADJ
hjic-91	32	2	variables	variable	NOUN
hjic-91	32	3	are	be	AUX
hjic-91	32	4	the	the	DET
hjic-91	32	5	variables	variable	NOUN
hjic-91	32	6	with	with	ADP
hjic-91	32	7	their	their	PRON
hjic-91	32	8	time	time	NOUN
hjic-91	32	9	derivative	derivative	ADJ
hjic-91	32	10	present	present	NOUN
hjic-91	32	11	in	in	ADP
hjic-91	32	12	the	the	DET
hjic-91	32	13	model	model	NOUN
hjic-91	32	14	.	.	PUNCT
hjic-91	33	1	variables	variable	NOUN
hjic-91	33	2	,	,	PUNCT
hjic-91	33	3	which	which	PRON
hjic-91	33	4	do	do	AUX
hjic-91	33	5	not	not	PART
hjic-91	33	6	have	have	VERB
hjic-91	33	7	their	their	PRON
hjic-91	33	8	time	time	NOUN
hjic-91	33	9	derivative	derivative	ADJ
hjic-91	33	10	present	present	NOUN
hjic-91	33	11	,	,	PUNCT
hjic-91	33	12	are	be	AUX
hjic-91	33	13	called	call	VERB
hjic-91	33	14	algebraic	algebraic	ADJ
hjic-91	33	15	variables	variable	NOUN
hjic-91	33	16	.	.	PUNCT
hjic-91	34	1	the	the	DET
hjic-91	34	2	derivative	derivative	ADJ
hjic-91	34	3	x	x	NOUN
hjic-91	34	4	’	'	PUNCT
hjic-91	34	5	is	be	AUX
hjic-91	34	6	called	call	VERB
hjic-91	34	7	derivative	derivative	ADJ
hjic-91	34	8	(	(	PUNCT
hjic-91	34	9	velocity	velocity	NOUN
hjic-91	34	10	)	)	PUNCT
hjic-91	34	11	variable	variable	NOUN
hjic-91	34	12	.	.	PUNCT
hjic-91	35	1	dynamic	dynamic	ADJ
hjic-91	35	2	representation	representation	NOUN
hjic-91	35	3	graph	graph	NOUN
hjic-91	35	4	the	the	DET
hjic-91	35	5	value	value	NOUN
hjic-91	35	6	of	of	ADP
hjic-91	35	7	differential	differential	ADJ
hjic-91	35	8	variables	variable	NOUN
hjic-91	35	9	is	be	AUX
hjic-91	35	10	usually	usually	ADV
hjic-91	35	11	computed	compute	VERB
hjic-91	35	12	by	by	ADP
hjic-91	35	13	using	use	VERB
hjic-91	35	14	a	a	DET
hjic-91	35	15	numerical	numerical	ADJ
hjic-91	35	16	integration	integration	NOUN
hjic-91	35	17	method	method	NOUN
hjic-91	35	18	.	.	PUNCT
hjic-91	36	1	so	so	ADV
hjic-91	36	2	a	a	DET
hjic-91	36	3	system	system	NOUN
hjic-91	36	4	of	of	ADP
hjic-91	36	5	equations	equation	NOUN
hjic-91	36	6	including	include	VERB
hjic-91	36	7	also	also	ADV
hjic-91	36	8	differential	differential	ADJ
hjic-91	36	9	equations	equation	NOUN
hjic-91	36	10	,	,	PUNCT
hjic-91	36	11	can	can	AUX
hjic-91	36	12	be	be	AUX
hjic-91	36	13	represented	represent	VERB
hjic-91	36	14	by	by	ADP
hjic-91	36	15	a	a	DET
hjic-91	36	16	dynamic	dynamic	ADJ
hjic-91	36	17	graph	graph	NOUN
hjic-91	36	18	.	.	PUNCT
hjic-91	37	1	a	a	DET
hjic-91	37	2	dynamic	dynamic	ADJ
hjic-91	37	3	graph	graph	NOUN
hjic-91	37	4	is	be	AUX
hjic-91	37	5	a	a	DET
hjic-91	37	6	sequence	sequence	NOUN
hjic-91	37	7	of	of	ADP
hjic-91	37	8	static	static	ADJ
hjic-91	37	9	graphs	graph	NOUN
hjic-91	37	10	corresponding	correspond	VERB
hjic-91	37	11	to	to	ADP
hjic-91	37	12	each	each	DET
hjic-91	37	13	time	time	NOUN
hjic-91	37	14	step	step	NOUN
hjic-91	37	15	of	of	ADP
hjic-91	37	16	integration	integration	NOUN
hjic-91	37	17	.	.	PUNCT
hjic-91	38	1	on	on	ADP
hjic-91	38	2	a	a	DET
hjic-91	38	3	dynamic	dynamic	ADJ
hjic-91	38	4	graph	graph	NOUN
hjic-91	38	5	there	there	PRON
hjic-91	38	6	are	be	VERB
hjic-91	38	7	directed	direct	VERB
hjic-91	38	8	arcs	arc	NOUN
hjic-91	38	9	attached	attach	VERB
hjic-91	38	10	from	from	ADP
hjic-91	38	11	the	the	DET
hjic-91	38	12	previous	previous	ADJ
hjic-91	38	13	static	static	ADJ
hjic-91	38	14	graph	graph	NOUN
hjic-91	38	15	to	to	ADP
hjic-91	38	16	the	the	DET
hjic-91	38	17	succeeding	succeed	VERB
hjic-91	38	18	static	static	ADJ
hjic-91	38	19	graph	graph	NOUN
hjic-91	38	20	that	that	PRON
hjic-91	38	21	are	be	AUX
hjic-91	38	22	determined	determine	VERB
hjic-91	38	23	by	by	ADP
hjic-91	38	24	the	the	DET
hjic-91	38	25	method	method	NOUN
hjic-91	38	26	applied	apply	VERB
hjic-91	38	27	for	for	ADP
hjic-91	38	28	solving	solve	VERB
hjic-91	38	29	the	the	DET
hjic-91	38	30	ordinary	ordinary	ADJ
hjic-91	38	31	differential	differential	ADJ
hjic-91	38	32	equations	equation	NOUN
hjic-91	38	33	.	.	PUNCT
hjic-91	39	1	in	in	ADP
hjic-91	39	2	case	case	NOUN
hjic-91	39	3	of	of	ADP
hjic-91	39	4	a	a	DET
hjic-91	39	5	single	single	ADJ
hjic-91	39	6	step	step	NOUN
hjic-91	39	7	explicit	explicit	ADJ
hjic-91	39	8	method	method	NOUN
hjic-91	39	9	,	,	PUNCT
hjic-91	39	10	the	the	DET
hjic-91	39	11	value	value	NOUN
hjic-91	39	12	of	of	ADP
hjic-91	39	13	a	a	DET
hjic-91	39	14	differential	differential	ADJ
hjic-91	39	15	variable	variable	NOUN
hjic-91	39	16	at	at	ADP
hjic-91	39	17	time	time	NOUN
hjic-91	39	18	t+h	t+h	NUM
hjic-91	39	19	is	be	AUX
hjic-91	39	20	computed	compute	VERB
hjic-91	39	21	using	use	VERB
hjic-91	39	22	the	the	DET
hjic-91	39	23	corresponding	corresponding	ADJ
hjic-91	39	24	differential	differential	NOUN
hjic-91	39	25	value	value	NOUN
hjic-91	39	26	and	and	CCONJ
hjic-91	39	27	its	its	PRON
hjic-91	39	28	value	value	NOUN
hjic-91	39	29	at	at	ADP
hjic-91	39	30	a	a	DET
hjic-91	39	31	previous	previous	ADJ
hjic-91	39	32	time	time	NOUN
hjic-91	39	33	t.	t.	PROPN
hjic-91	39	34	for	for	ADP
hjic-91	39	35	example	example	NOUN
hjic-91	39	36	,	,	PUNCT
hjic-91	39	37	when	when	SCONJ
hjic-91	39	38	the	the	DET
hjic-91	39	39	explicit	explicit	ADJ
hjic-91	39	40	euler	euler	NOUN
hjic-91	39	41	method	method	NOUN
hjic-91	39	42	is	be	AUX
hjic-91	39	43	used	use	VERB
hjic-91	39	44	:	:	PUNCT
hjic-91	39	45	x(t+h	x(t+h	PUNCT
hjic-91	39	46	)	)	PUNCT
hjic-91	39	47	=	=	SYM
hjic-91	39	48	x(t	x(t	PROPN
hjic-91	39	49	)	)	PUNCT
hjic-91	39	50	+	+	NUM
hjic-91	39	51	h⋅x’(t	h⋅x’(t	NOUN
hjic-91	39	52	)	)	PUNCT
hjic-91	39	53	where	where	SCONJ
hjic-91	39	54	h	h	NOUN
hjic-91	39	55	denotes	denote	VERB
hjic-91	39	56	the	the	DET
hjic-91	39	57	step	step	NOUN
hjic-91	39	58	length	length	NOUN
hjic-91	39	59	during	during	ADP
hjic-91	39	60	the	the	DET
hjic-91	39	61	numerical	numerical	ADJ
hjic-91	39	62	integration	integration	NOUN
hjic-91	39	63	.	.	PUNCT
hjic-91	40	1	the	the	DET
hjic-91	40	2	structure	structure	NOUN
hjic-91	40	3	of	of	ADP
hjic-91	40	4	a	a	DET
hjic-91	40	5	dynamic	dynamic	ADJ
hjic-91	40	6	graph	graph	NOUN
hjic-91	40	7	assuming	assume	VERB
hjic-91	40	8	explicit	explicit	ADJ
hjic-91	40	9	euler	euler	NOUN
hjic-91	40	10	method	method	NOUN
hjic-91	40	11	for	for	ADP
hjic-91	40	12	solving	solve	VERB
hjic-91	40	13	differential	differential	ADJ
hjic-91	40	14	equations	equation	NOUN
hjic-91	40	15	can	can	AUX
hjic-91	40	16	be	be	AUX
hjic-91	40	17	seen	see	VERB
hjic-91	40	18	in	in	ADP
hjic-91	40	19	fig	fig	NOUN
hjic-91	40	20	.	.	PUNCT
hjic-91	41	1	1	1	X
hjic-91	41	2	.	.	PUNCT
hjic-91	41	3	the	the	DET
hjic-91	41	4	structural	structural	ADJ
hjic-91	41	5	analysis	analysis	NOUN
hjic-91	41	6	based	base	VERB
hjic-91	41	7	on	on	ADP
hjic-91	41	8	graph	graph	NOUN
hjic-91	41	9	theoretical	theoretical	ADJ
hjic-91	41	10	technique	technique	NOUN
hjic-91	41	11	is	be	AUX
hjic-91	41	12	carried	carry	VERB
hjic-91	41	13	out	out	ADP
hjic-91	41	14	in	in	ADP
hjic-91	41	15	steps	step	NOUN
hjic-91	41	16	performed	perform	VERB
hjic-91	41	17	sequentially	sequentially	ADV
hjic-91	41	18	.	.	PUNCT
hjic-91	42	1	the	the	DET
hjic-91	42	2	first	first	ADJ
hjic-91	42	3	step	step	NOUN
hjic-91	42	4	is	be	AUX
hjic-91	42	5	to	to	PART
hjic-91	42	6	rewrite	rewrite	VERB
hjic-91	42	7	the	the	DET
hjic-91	42	8	model	model	NOUN
hjic-91	42	9	into	into	ADP
hjic-91	42	10	its	its	PRON
hjic-91	42	11	standard	standard	ADJ
hjic-91	42	12	form	form	NOUN
hjic-91	42	13	.	.	PUNCT
hjic-91	43	1	the	the	DET
hjic-91	43	2	second	second	ADJ
hjic-91	43	3	step	step	NOUN
hjic-91	43	4	is	be	AUX
hjic-91	43	5	the	the	DET
hjic-91	43	6	assignment	assignment	NOUN
hjic-91	43	7	of	of	ADP
hjic-91	43	8	types	type	NOUN
hjic-91	43	9	to	to	PART
hjic-91	43	10	vertices	vertex	NOUN
hjic-91	43	11	in	in	ADP
hjic-91	43	12	the	the	DET
hjic-91	43	13	representation	representation	NOUN
hjic-91	43	14	graph	graph	NOUN
hjic-91	43	15	.	.	PUNCT
hjic-91	44	1	the	the	DET
hjic-91	44	2	important	important	ADJ
hjic-91	44	3	types	type	NOUN
hjic-91	44	4	of	of	ADP
hjic-91	44	5	vertices	vertex	NOUN
hjic-91	44	6	determined	determine	VERB
hjic-91	44	7	by	by	ADP
hjic-91	44	8	the	the	DET
hjic-91	44	9	model	model	NOUN
hjic-91	44	10	specification	specification	NOUN
hjic-91	44	11	are	be	AUX
hjic-91	44	12	the	the	DET
hjic-91	44	13	following	follow	VERB
hjic-91	44	14	[	[	X
hjic-91	44	15	6,2	6,2	NUM
hjic-91	44	16	]	]	PUNCT
hjic-91	44	17	:	:	PUNCT
hjic-91	44	18	•	•	ADP
hjic-91	44	19	<	<	X
hjic-91	44	20	s>(set)-type	s>(set)-type	NOUN
hjic-91	44	21	variables	variable	NOUN
hjic-91	44	22	:	:	PUNCT
hjic-91	44	23	these	these	PRON
hjic-91	44	24	represent	represent	VERB
hjic-91	44	25	variables	variable	NOUN
hjic-91	44	26	,	,	PUNCT
hjic-91	44	27	which	which	PRON
hjic-91	44	28	are	be	AUX
hjic-91	44	29	assigned	assign	VERB
hjic-91	44	30	to	to	ADP
hjic-91	44	31	the	the	DET
hjic-91	44	32	specified	specify	VERB
hjic-91	44	33	given	give	VERB
hjic-91	44	34	values	value	NOUN
hjic-91	44	35	.	.	PUNCT
hjic-91	45	1	in	in	ADP
hjic-91	45	2	the	the	DET
hjic-91	45	3	case	case	NOUN
hjic-91	45	4	of	of	ADP
hjic-91	45	5	a	a	DET
hjic-91	45	6	dynamic	dynamic	ADJ
hjic-91	45	7	representation	representation	NOUN
hjic-91	45	8	graph	graph	NOUN
hjic-91	45	9	assuming	assume	VERB
hjic-91	45	10	explicit	explicit	ADJ
hjic-91	45	11	method	method	NOUN
hjic-91	45	12	for	for	ADP
hjic-91	45	13	solving	solve	VERB
hjic-91	45	14	the	the	DET
hjic-91	45	15	differential	differential	ADJ
hjic-91	45	16	equations	equation	NOUN
hjic-91	45	17	,	,	PUNCT
hjic-91	45	18	the	the	DET
hjic-91	45	19	differential	differential	ADJ
hjic-91	45	20	variables	variable	NOUN
hjic-91	45	21	will	will	AUX
hjic-91	45	22	be	be	AUX
hjic-91	45	23	labelled	label	VERB
hjic-91	45	24	by	by	ADP
hjic-91	45	25	type	type	NOUN
hjic-91	45	26	<	<	X
hjic-91	45	27	s	s	NOUN
hjic-91	45	28	*	*	X
hjic-91	45	29	>	>	X
hjic-91	45	30	because	because	SCONJ
hjic-91	45	31	their	their	PRON
hjic-91	45	32	initial	initial	ADJ
hjic-91	45	33	value	value	NOUN
hjic-91	45	34	can	can	AUX
hjic-91	45	35	be	be	AUX
hjic-91	45	36	obtained	obtain	VERB
hjic-91	45	37	from	from	ADP
hjic-91	45	38	the	the	DET
hjic-91	45	39	initial	initial	ADJ
hjic-91	45	40	values	value	NOUN
hjic-91	45	41	,	,	PUNCT
hjic-91	45	42	and	and	CCONJ
hjic-91	45	43	then	then	ADV
hjic-91	45	44	their	their	PRON
hjic-91	45	45	values	value	NOUN
hjic-91	45	46	can	can	AUX
hjic-91	45	47	be	be	AUX
hjic-91	45	48	calculated	calculate	VERB
hjic-91	45	49	step	step	NOUN
hjic-91	45	50	by	by	ADP
hjic-91	45	51	step	step	NOUN
hjic-91	45	52	by	by	ADP
hjic-91	45	53	numerical	numerical	ADJ
hjic-91	45	54	integration	integration	NOUN
hjic-91	45	55	.	.	PUNCT
hjic-91	46	1	labels	label	NOUN
hjic-91	46	2	<	<	X
hjic-91	46	3	s	s	X
hjic-91	46	4	>	>	X
hjic-91	46	5	and	and	CCONJ
hjic-91	46	6	<	<	X
hjic-91	46	7	s	s	X
hjic-91	46	8	*	*	NOUN
hjic-91	46	9	>	>	X
hjic-91	46	10	are	be	AUX
hjic-91	46	11	treated	treat	VERB
hjic-91	46	12	the	the	DET
hjic-91	46	13	same	same	ADJ
hjic-91	46	14	way	way	NOUN
hjic-91	46	15	during	during	ADP
hjic-91	46	16	the	the	DET
hjic-91	46	17	analysis	analysis	NOUN
hjic-91	46	18	.	.	PUNCT
hjic-91	47	1	•	•	NUM
hjic-91	47	2	<	<	X
hjic-91	47	3	g>(given)-type	g>(given)-type	NOUN
hjic-91	47	4	variables	variable	NOUN
hjic-91	47	5	:	:	PUNCT
hjic-91	47	6	a	a	DET
hjic-91	47	7	variable	variable	NOUN
hjic-91	47	8	assigned	assign	VERB
hjic-91	47	9	to	to	ADP
hjic-91	47	10	a	a	DET
hjic-91	47	11	specific	specific	ADJ
hjic-91	47	12	value	value	NOUN
hjic-91	47	13	of	of	ADP
hjic-91	47	14	a	a	DET
hjic-91	47	15	left	left	ADJ
hjic-91	47	16	hand	hand	NOUN
hjic-91	47	17	side	side	NOUN
hjic-91	47	18	is	be	AUX
hjic-91	47	19	a	a	DET
hjic-91	47	20	<	<	X
hjic-91	47	21	g	g	NOUN
hjic-91	47	22	>	>	NOUN
hjic-91	47	23	type	type	NOUN
hjic-91	47	24	variable	variable	NOUN
hjic-91	47	25	.	.	PUNCT
hjic-91	48	1	unlike	unlike	ADP
hjic-91	48	2	the	the	DET
hjic-91	48	3	<	<	NOUN
hjic-91	48	4	s>-type	s>-type	NOUN
hjic-91	48	5	variables	variable	NOUN
hjic-91	48	6	,	,	PUNCT
hjic-91	48	7	the	the	DET
hjic-91	48	8	values	value	NOUN
hjic-91	48	9	of	of	ADP
hjic-91	48	10	the	the	DET
hjic-91	48	11	right	right	ADJ
hjic-91	48	12	hand	hand	NOUN
hjic-91	48	13	side	side	NOUN
hjic-91	48	14	variables	variable	NOUN
hjic-91	48	15	will	will	AUX
hjic-91	48	16	be	be	AUX
hjic-91	48	17	suitably	suitably	ADV
hjic-91	48	18	adjusted	adjust	VERB
hjic-91	48	19	so	so	SCONJ
hjic-91	48	20	as	as	SCONJ
hjic-91	48	21	to	to	PART
hjic-91	48	22	preserve	preserve	VERB
hjic-91	48	23	the	the	DET
hjic-91	48	24	equality	equality	NOUN
hjic-91	48	25	of	of	ADP
hjic-91	48	26	the	the	DET
hjic-91	48	27	two	two	NUM
hjic-91	48	28	sides	side	NOUN
hjic-91	48	29	.	.	PUNCT
hjic-91	49	1	13	13	NUM
hjic-91	49	2	x	x	SYM
hjic-91	49	3	x1	x1	NUM
hjic-91	50	1	x2	x2	NOUN
hjic-91	50	2	xn	xn	PUNCT
hjic-91	51	1	x	x	X
hjic-91	51	2	'	'	X
hjic-91	51	3	t	t	NOUN
hjic-91	51	4	x	x	PUNCT
hjic-91	51	5	x1	x1	PROPN
hjic-91	52	1	x2	x2	NOUN
hjic-91	52	2	xn	xn	PUNCT
hjic-91	52	3	x	x	X
hjic-91	52	4	'	'	PUNCT
hjic-91	52	5	t+h	t+h	NUM
hjic-91	52	6	fig.1	fig.1	ADJ
hjic-91	52	7	dynamic	dynamic	ADJ
hjic-91	52	8	representation	representation	NOUN
hjic-91	52	9	graph	graph	NOUN
hjic-91	52	10	assuming	assume	VERB
hjic-91	52	11	first	first	ADJ
hjic-91	52	12	order	order	NOUN
hjic-91	52	13	explicit	explicit	ADJ
hjic-91	52	14	solution	solution	NOUN
hjic-91	52	15	method	method	NOUN
hjic-91	52	16	according	accord	VERB
hjic-91	52	17	to	to	ADP
hjic-91	52	18	the	the	DET
hjic-91	52	19	representation	representation	NOUN
hjic-91	52	20	graph	graph	NOUN
hjic-91	52	21	,	,	PUNCT
hjic-91	52	22	the	the	DET
hjic-91	52	23	value	value	NOUN
hjic-91	52	24	of	of	ADP
hjic-91	52	25	every	every	DET
hjic-91	52	26	variable	variable	NOUN
hjic-91	52	27	which	which	PRON
hjic-91	52	28	has	have	VERB
hjic-91	52	29	incoming	incoming	ADJ
hjic-91	52	30	arcs	arc	NOUN
hjic-91	52	31	only	only	ADV
hjic-91	52	32	from	from	ADP
hjic-91	52	33	vertices	vertex	NOUN
hjic-91	52	34	labelled	label	VERB
hjic-91	52	35	by	by	ADP
hjic-91	52	36	type	type	NOUN
hjic-91	52	37	<	<	X
hjic-91	52	38	s	s	X
hjic-91	52	39	>	>	X
hjic-91	52	40	can	can	AUX
hjic-91	52	41	be	be	AUX
hjic-91	52	42	calculated	calculate	VERB
hjic-91	52	43	by	by	ADP
hjic-91	52	44	simple	simple	ADJ
hjic-91	52	45	substitution	substitution	NOUN
hjic-91	52	46	into	into	ADP
hjic-91	52	47	the	the	DET
hjic-91	52	48	corresponding	correspond	VERB
hjic-91	52	49	equation	equation	NOUN
hjic-91	52	50	.	.	PUNCT
hjic-91	53	1	these	these	DET
hjic-91	53	2	variables	variable	NOUN
hjic-91	53	3	become	become	AUX
hjic-91	53	4	secondarily	secondarily	ADV
hjic-91	53	5	labelled	label	VERB
hjic-91	53	6	by	by	ADP
hjic-91	53	7	type	type	NOUN
hjic-91	53	8	<	<	X
hjic-91	53	9	s	s	X
hjic-91	53	10	>	>	X
hjic-91	53	11	,	,	PUNCT
hjic-91	53	12	and	and	CCONJ
hjic-91	53	13	this	this	DET
hjic-91	53	14	process	process	NOUN
hjic-91	53	15	can	can	AUX
hjic-91	53	16	be	be	AUX
hjic-91	53	17	repeated	repeat	VERB
hjic-91	53	18	if	if	SCONJ
hjic-91	53	19	necessary	necessary	ADJ
hjic-91	53	20	.	.	PUNCT
hjic-91	54	1	omitting	omit	VERB
hjic-91	54	2	all	all	DET
hjic-91	54	3	vertices	vertex	NOUN
hjic-91	54	4	labelled	label	VERB
hjic-91	54	5	primarily	primarily	ADV
hjic-91	54	6	,	,	PUNCT
hjic-91	54	7	secondarily	secondarily	ADV
hjic-91	54	8	,	,	PUNCT
hjic-91	54	9	etc	etc	X
hjic-91	54	10	.	.	X
hjic-91	54	11	by	by	ADP
hjic-91	54	12	type	type	NOUN
hjic-91	54	13	<	<	X
hjic-91	54	14	s	s	X
hjic-91	54	15	>	>	X
hjic-91	54	16	and	and	CCONJ
hjic-91	54	17	all	all	DET
hjic-91	54	18	arcs	arc	NOUN
hjic-91	54	19	starting	start	VERB
hjic-91	54	20	from	from	ADP
hjic-91	54	21	them	they	PRON
hjic-91	54	22	from	from	ADP
hjic-91	54	23	the	the	DET
hjic-91	54	24	representation	representation	NOUN
hjic-91	54	25	graph	graph	NOUN
hjic-91	54	26	we	we	PRON
hjic-91	54	27	obtain	obtain	VERB
hjic-91	54	28	the	the	DET
hjic-91	54	29	reduced	reduce	VERB
hjic-91	54	30	graph	graph	NOUN
hjic-91	54	31	.	.	PUNCT
hjic-91	55	1	the	the	DET
hjic-91	55	2	classification	classification	NOUN
hjic-91	55	3	of	of	ADP
hjic-91	55	4	vertices	vertex	NOUN
hjic-91	55	5	of	of	ADP
hjic-91	55	6	a	a	DET
hjic-91	55	7	reduced	reduce	VERB
hjic-91	55	8	graph	graph	NOUN
hjic-91	55	9	is	be	AUX
hjic-91	55	10	as	as	SCONJ
hjic-91	55	11	follows	follow	VERB
hjic-91	55	12	:	:	PUNCT
hjic-91	55	13	•	•	NOUN
hjic-91	55	14	all	all	DET
hjic-91	55	15	initial	initial	ADJ
hjic-91	55	16	vertices	vertex	NOUN
hjic-91	55	17	form	form	VERB
hjic-91	55	18	the	the	DET
hjic-91	55	19	unknown	unknown	ADJ
hjic-91	55	20	variable	variable	NOUN
hjic-91	55	21	set	set	NOUN
hjic-91	55	22	x	x	SYM
hjic-91	55	23	,	,	PUNCT
hjic-91	55	24	•	•	PRON
hjic-91	55	25	all	all	DET
hjic-91	55	26	terminal	terminal	ADJ
hjic-91	55	27	vertices	vertex	NOUN
hjic-91	55	28	labelled	label	VERB
hjic-91	55	29	by	by	ADP
hjic-91	55	30	type	type	NOUN
hjic-91	55	31	<	<	X
hjic-91	55	32	g	g	X
hjic-91	55	33	>	>	X
hjic-91	55	34	constitute	constitute	VERB
hjic-91	55	35	the	the	DET
hjic-91	55	36	known	know	VERB
hjic-91	55	37	variable	variable	NOUN
hjic-91	55	38	(	(	PUNCT
hjic-91	55	39	parameter	parameter	NOUN
hjic-91	55	40	)	)	PUNCT
hjic-91	55	41	set	set	VERB
hjic-91	55	42	y	y	PROPN
hjic-91	55	43	,	,	PUNCT
hjic-91	55	44	•	•	VERB
hjic-91	55	45	all	all	DET
hjic-91	55	46	other	other	ADJ
hjic-91	55	47	vertices	vertex	NOUN
hjic-91	55	48	constitute	constitute	VERB
hjic-91	55	49	the	the	DET
hjic-91	55	50	unknown	unknown	ADJ
hjic-91	55	51	variable	variable	NOUN
hjic-91	55	52	set	set	VERB
hjic-91	55	53	u.	u.	NOUN
hjic-91	55	54	the	the	DET
hjic-91	55	55	algebraic	algebraic	ADJ
hjic-91	55	56	subgraph	subgraph	NOUN
hjic-91	55	57	belonging	belong	VERB
hjic-91	55	58	to	to	ADP
hjic-91	55	59	any	any	DET
hjic-91	55	60	static	static	ADJ
hjic-91	55	61	graph	graph	NOUN
hjic-91	55	62	in	in	ADP
hjic-91	55	63	the	the	DET
hjic-91	55	64	dynamic	dynamic	ADJ
hjic-91	55	65	representation	representation	NOUN
hjic-91	55	66	graph	graph	NOUN
hjic-91	55	67	can	can	AUX
hjic-91	55	68	be	be	AUX
hjic-91	55	69	obtained	obtain	VERB
hjic-91	55	70	by	by	ADP
hjic-91	55	71	considering	consider	VERB
hjic-91	55	72	the	the	DET
hjic-91	55	73	algebraic	algebraic	ADJ
hjic-91	55	74	part	part	NOUN
hjic-91	55	75	of	of	ADP
hjic-91	55	76	the	the	DET
hjic-91	55	77	model	model	NOUN
hjic-91	55	78	and	and	CCONJ
hjic-91	55	79	taking	take	VERB
hjic-91	55	80	its	its	PRON
hjic-91	55	81	induced	induced	ADJ
hjic-91	55	82	subgraph	subgraph	NOUN
hjic-91	55	83	.	.	PUNCT
hjic-91	56	1	the	the	DET
hjic-91	56	2	vertex	vertex	NOUN
hjic-91	56	3	set	set	NOUN
hjic-91	56	4	of	of	ADP
hjic-91	56	5	the	the	DET
hjic-91	56	6	algebraic	algebraic	ADJ
hjic-91	56	7	subgraph	subgraph	NOUN
hjic-91	56	8	contains	contain	VERB
hjic-91	56	9	the	the	DET
hjic-91	56	10	variables	variable	NOUN
hjic-91	56	11	that	that	PRON
hjic-91	56	12	appear	appear	VERB
hjic-91	56	13	in	in	ADP
hjic-91	56	14	the	the	DET
hjic-91	56	15	algebraic	algebraic	ADJ
hjic-91	56	16	equations	equation	NOUN
hjic-91	56	17	and	and	CCONJ
hjic-91	56	18	the	the	DET
hjic-91	56	19	arc	arc	NOUN
hjic-91	56	20	set	set	VERB
hjic-91	56	21	that	that	PRON
hjic-91	56	22	corresponds	correspond	VERB
hjic-91	56	23	to	to	ADP
hjic-91	56	24	the	the	DET
hjic-91	56	25	algebraic	algebraic	ADJ
hjic-91	56	26	equations	equation	NOUN
hjic-91	56	27	.	.	PUNCT
hjic-91	57	1	differential	differential	ADJ
hjic-91	57	2	index	index	NOUN
hjic-91	57	3	dynamic	dynamic	ADJ
hjic-91	57	4	process	process	NOUN
hjic-91	57	5	models	model	NOUN
hjic-91	57	6	can	can	AUX
hjic-91	57	7	be	be	AUX
hjic-91	57	8	described	describe	VERB
hjic-91	57	9	by	by	ADP
hjic-91	57	10	semiexplicit	semiexplicit	ADJ
hjic-91	57	11	daes	daes	PROPN
hjic-91	57	12	as	as	SCONJ
hjic-91	57	13	follows	follow	VERB
hjic-91	57	14	:	:	PUNCT
hjic-91	57	15	z1	z1	NOUN
hjic-91	57	16	‘	'	PUNCT
hjic-91	57	17	’	'	PUNCT
hjic-91	57	18	=	=	SYM
hjic-91	57	19	f(z1	f(z1	ADJ
hjic-91	57	20	,	,	PUNCT
hjic-91	57	21	z2	z2	PROPN
hjic-91	57	22	,	,	PUNCT
hjic-91	57	23	t	t	PROPN
hjic-91	57	24	)	)	PUNCT
hjic-91	57	25	,	,	PUNCT
hjic-91	57	26	z1(t0	z1(t0	NOUN
hjic-91	57	27	)	)	PUNCT
hjic-91	57	28	=	=	SYM
hjic-91	57	29	z10	z10	NOUN
hjic-91	57	30	0	0	NUM
hjic-91	57	31	=	=	SYM
hjic-91	57	32	g(z1	g(z1	NOUN
hjic-91	57	33	,	,	PUNCT
hjic-91	57	34	z2	z2	PROPN
hjic-91	57	35	,	,	PUNCT
hjic-91	57	36	t	t	PROPN
hjic-91	57	37	)	)	PUNCT
hjic-91	57	38	the	the	DET
hjic-91	57	39	most	most	ADV
hjic-91	57	40	important	important	ADJ
hjic-91	57	41	structural	structural	ADJ
hjic-91	57	42	computational	computational	ADJ
hjic-91	57	43	property	property	NOUN
hjic-91	57	44	of	of	ADP
hjic-91	57	45	dae	dae	NOUN
hjic-91	57	46	models	model	NOUN
hjic-91	57	47	is	be	AUX
hjic-91	57	48	the	the	DET
hjic-91	57	49	differential	differential	ADJ
hjic-91	57	50	index	index	NOUN
hjic-91	57	51	.	.	PUNCT
hjic-91	58	1	by	by	ADP
hjic-91	58	2	definition	definition	NOUN
hjic-91	58	3	[	[	X
hjic-91	58	4	7	7	NUM
hjic-91	58	5	]	]	PUNCT
hjic-91	58	6	,	,	PUNCT
hjic-91	58	7	the	the	DET
hjic-91	58	8	differential	differential	ADJ
hjic-91	58	9	index	index	NOUN
hjic-91	58	10	of	of	ADP
hjic-91	58	11	the	the	DET
hjic-91	58	12	above	above	ADJ
hjic-91	58	13	semi	semi	ADJ
hjic-91	58	14	-	-	ADJ
hjic-91	58	15	explicit	explicit	ADJ
hjic-91	58	16	dae	dae	NOUN
hjic-91	58	17	is	be	AUX
hjic-91	58	18	one	one	NUM
hjic-91	58	19	if	if	SCONJ
hjic-91	58	20	one	one	NUM
hjic-91	58	21	differentiation	differentiation	NOUN
hjic-91	58	22	is	be	AUX
hjic-91	58	23	sufficient	sufficient	ADJ
hjic-91	58	24	to	to	PART
hjic-91	58	25	express	express	VERB
hjic-91	58	26	z2	z2	NOUN
hjic-91	58	27	‘	'	PUNCT
hjic-91	58	28	’	'	PUNCT
hjic-91	58	29	as	as	ADP
hjic-91	58	30	a	a	DET
hjic-91	58	31	continuous	continuous	ADJ
hjic-91	58	32	function	function	NOUN
hjic-91	58	33	of	of	ADP
hjic-91	58	34	z1	z1	PROPN
hjic-91	58	35	,	,	PUNCT
hjic-91	58	36	z2	z2	PROPN
hjic-91	58	37	and	and	CCONJ
hjic-91	58	38	t.	t.	NOUN
hjic-91	58	39	one	one	NUM
hjic-91	58	40	differentiation	differentiation	NOUN
hjic-91	58	41	is	be	AUX
hjic-91	58	42	sufficient	sufficient	ADJ
hjic-91	58	43	if	if	SCONJ
hjic-91	58	44	and	and	CCONJ
hjic-91	58	45	only	only	ADV
hjic-91	58	46	if	if	SCONJ
hjic-91	58	47	the	the	DET
hjic-91	58	48	jacobian	jacobian	ADJ
hjic-91	58	49	matrix	matrix	NOUN
hjic-91	58	50	gz2	gz2	NOUN
hjic-91	58	51	is	be	AUX
hjic-91	58	52	non	non	ADJ
hjic-91	58	53	-	-	ADJ
hjic-91	58	54	singular	singular	ADJ
hjic-91	58	55	.	.	PUNCT
hjic-91	59	1	in	in	ADP
hjic-91	59	2	our	our	PRON
hjic-91	59	3	earlier	early	ADJ
hjic-91	59	4	work	work	NOUN
hjic-91	59	5	we	we	PRON
hjic-91	59	6	have	have	AUX
hjic-91	59	7	proved	prove	VERB
hjic-91	59	8	that	that	SCONJ
hjic-91	59	9	the	the	DET
hjic-91	59	10	differential	differential	ADJ
hjic-91	59	11	index	index	NOUN
hjic-91	59	12	of	of	ADP
hjic-91	59	13	the	the	DET
hjic-91	59	14	models	model	NOUN
hjic-91	59	15	investigated	investigate	VERB
hjic-91	59	16	in	in	ADP
hjic-91	59	17	[	[	X
hjic-91	59	18	5,2	5,2	NUM
hjic-91	59	19	]	]	PUNCT
hjic-91	59	20	is	be	AUX
hjic-91	59	21	equal	equal	ADJ
hjic-91	59	22	to	to	ADP
hjic-91	59	23	1	1	NUM
hjic-91	59	24	if	if	SCONJ
hjic-91	59	25	and	and	CCONJ
hjic-91	59	26	only	only	ADV
hjic-91	59	27	if	if	SCONJ
hjic-91	59	28	there	there	PRON
hjic-91	59	29	exists	exist	VERB
hjic-91	59	30	a	a	DET
hjic-91	59	31	menger	menger	NOUN
hjic-91	59	32	-	-	PUNCT
hjic-91	59	33	type	type	NOUN
hjic-91	59	34	complete	complete	ADJ
hjic-91	59	35	linking	linking	NOUN
hjic-91	59	36	on	on	ADP
hjic-91	59	37	the	the	DET
hjic-91	59	38	reduced	reduce	VERB
hjic-91	59	39	graph	graph	NOUN
hjic-91	59	40	at	at	ADP
hjic-91	59	41	any	any	DET
hjic-91	59	42	time	time	NOUN
hjic-91	59	43	step	step	NOUN
hjic-91	59	44	t.	t.	NOUN
hjic-91	59	45	an	an	DET
hjic-91	59	46	equivalent	equivalent	ADJ
hjic-91	59	47	condition	condition	NOUN
hjic-91	60	1	[	[	X
hjic-91	60	2	5	5	NUM
hjic-91	60	3	]	]	PUNCT
hjic-91	60	4	of	of	ADP
hjic-91	60	5	the	the	DET
hjic-91	60	6	above	above	ADJ
hjic-91	60	7	is	be	AUX
hjic-91	60	8	that	that	SCONJ
hjic-91	60	9	the	the	DET
hjic-91	60	10	differential	differential	ADJ
hjic-91	60	11	index	index	NOUN
hjic-91	60	12	of	of	ADP
hjic-91	60	13	a	a	DET
hjic-91	60	14	semi	semi	ADJ
hjic-91	60	15	-	-	ADJ
hjic-91	60	16	explicit	explicit	ADJ
hjic-91	60	17	dae	dae	NOUN
hjic-91	60	18	model	model	NOUN
hjic-91	60	19	m	m	NOUN
hjic-91	60	20	is	be	AUX
hjic-91	60	21	equal	equal	ADJ
hjic-91	60	22	to	to	ADP
hjic-91	60	23	one	one	NUM
hjic-91	60	24	if	if	SCONJ
hjic-91	60	25	and	and	CCONJ
hjic-91	60	26	only	only	ADV
hjic-91	60	27	if	if	SCONJ
hjic-91	60	28	there	there	PRON
hjic-91	60	29	exists	exist	VERB
hjic-91	60	30	a	a	DET
hjic-91	60	31	menger	menger	NOUN
hjic-91	60	32	-	-	PUNCT
hjic-91	60	33	type	type	NOUN
hjic-91	60	34	complete	complete	ADJ
hjic-91	60	35	linking	linking	NOUN
hjic-91	60	36	on	on	ADP
hjic-91	60	37	the	the	DET
hjic-91	60	38	reduced	reduce	VERB
hjic-91	60	39	graph	graph	NOUN
hjic-91	60	40	of	of	ADP
hjic-91	60	41	the	the	DET
hjic-91	60	42	algebraic	algebraic	ADJ
hjic-91	60	43	subgraph	subgraph	NOUN
hjic-91	60	44	belonging	belong	VERB
hjic-91	60	45	to	to	ADP
hjic-91	60	46	model	model	NOUN
hjic-91	60	47	m.	m.	NOUN
hjic-91	60	48	we	we	PRON
hjic-91	60	49	have	have	AUX
hjic-91	60	50	also	also	ADV
hjic-91	60	51	proposed	propose	VERB
hjic-91	60	52	an	an	DET
hjic-91	60	53	algorithm	algorithm	NOUN
hjic-91	60	54	using	use	VERB
hjic-91	60	55	the	the	DET
hjic-91	60	56	structure	structure	NOUN
hjic-91	60	57	of	of	ADP
hjic-91	60	58	the	the	DET
hjic-91	60	59	representation	representation	NOUN
hjic-91	60	60	graph	graph	NOUN
hjic-91	60	61	for	for	ADP
hjic-91	60	62	determination	determination	NOUN
hjic-91	60	63	of	of	ADP
hjic-91	60	64	the	the	DET
hjic-91	60	65	differential	differential	ADJ
hjic-91	60	66	index	index	NOUN
hjic-91	60	67	of	of	ADP
hjic-91	60	68	the	the	DET
hjic-91	60	69	underlying	underlie	VERB
hjic-91	60	70	model	model	NOUN
hjic-91	60	71	.	.	PUNCT
hjic-91	61	1	the	the	DET
hjic-91	61	2	following	follow	VERB
hjic-91	61	3	two	two	NUM
hjic-91	61	4	examples	example	NOUN
hjic-91	61	5	described	describe	VERB
hjic-91	61	6	in	in	ADP
hjic-91	61	7	details	detail	NOUN
hjic-91	61	8	in	in	ADP
hjic-91	61	9	[	[	PRON
hjic-91	61	10	5,2	5,2	NUM
hjic-91	61	11	]	]	PUNCT
hjic-91	61	12	are	be	AUX
hjic-91	61	13	used	use	VERB
hjic-91	61	14	throughout	throughout	ADP
hjic-91	61	15	the	the	DET
hjic-91	61	16	paper	paper	NOUN
hjic-91	61	17	to	to	PART
hjic-91	61	18	illustrate	illustrate	VERB
hjic-91	61	19	the	the	DET
hjic-91	61	20	notions	notion	NOUN
hjic-91	61	21	and	and	CCONJ
hjic-91	61	22	algorithms	algorithm	NOUN
hjic-91	61	23	.	.	PUNCT
hjic-91	62	1	example	example	NOUN
hjic-91	62	2	1	1	NUM
hjic-91	62	3	:	:	PUNCT
hjic-91	62	4	consider	consider	VERB
hjic-91	62	5	a	a	DET
hjic-91	62	6	liquid	liquid	ADJ
hjic-91	62	7	tank	tank	NOUN
hjic-91	62	8	system	system	NOUN
hjic-91	62	9	with	with	ADP
hjic-91	62	10	one	one	NUM
hjic-91	62	11	inlet	inlet	NOUN
hjic-91	62	12	stream	stream	NOUN
hjic-91	62	13	f	f	PROPN
hjic-91	62	14	and	and	CCONJ
hjic-91	62	15	one	one	NUM
hjic-91	62	16	exit	exit	NOUN
hjic-91	62	17	stream	stream	NOUN
hjic-91	62	18	l.	l.	PROPN
hjic-91	62	19	let	let	VERB
hjic-91	62	20	the	the	DET
hjic-91	62	21	vessel	vessel	NOUN
hjic-91	62	22	be	be	AUX
hjic-91	62	23	perfectly	perfectly	ADV
hjic-91	62	24	stirred	stir	VERB
hjic-91	62	25	.	.	PUNCT
hjic-91	63	1	heat	heat	NOUN
hjic-91	63	2	is	be	AUX
hjic-91	63	3	transferred	transfer	VERB
hjic-91	63	4	to	to	ADP
hjic-91	63	5	the	the	DET
hjic-91	63	6	liquid	liquid	NOUN
hjic-91	63	7	using	use	VERB
hjic-91	63	8	a	a	DET
hjic-91	63	9	heater	heater	NOUN
hjic-91	63	10	.	.	PUNCT
hjic-91	64	1	the	the	DET
hjic-91	64	2	standard	standard	ADJ
hjic-91	64	3	form	form	NOUN
hjic-91	64	4	of	of	ADP
hjic-91	64	5	the	the	DET
hjic-91	64	6	model	model	NOUN
hjic-91	64	7	of	of	ADP
hjic-91	64	8	the	the	DET
hjic-91	64	9	liquid	liquid	ADJ
hjic-91	64	10	tank	tank	NOUN
hjic-91	64	11	system	system	NOUN
hjic-91	64	12	(	(	PUNCT
hjic-91	64	13	m1	m1	NOUN
hjic-91	64	14	)	)	PUNCT
hjic-91	64	15	is	be	AUX
hjic-91	64	16	the	the	DET
hjic-91	64	17	following	following	NOUN
hjic-91	64	18	:	:	PUNCT
hjic-91	64	19	m	m	AUX
hjic-91	64	20	=	=	SYM
hjic-91	64	21	∫	∫	PROPN
hjic-91	64	22	m	m	NOUN
hjic-91	64	23	’	'	PUNCT
hjic-91	64	24	u	u	NOUN
hjic-91	64	25	=	=	SYM
hjic-91	64	26	∫	∫	PROPN
hjic-91	64	27	u	u	NOUN
hjic-91	64	28	’	'	PUNCT
hjic-91	64	29	m	m	PROPN
hjic-91	64	30	’	'	PUNCT
hjic-91	64	31	=	=	SYM
hjic-91	64	32	–	–	PUNCT
hjic-91	64	33	l	l	NOUN
hjic-91	64	34	+	+	CCONJ
hjic-91	64	35	f	f	PROPN
hjic-91	64	36	u	u	NOUN
hjic-91	64	37	’	'	PUNCT
hjic-91	64	38	=	=	NOUN
hjic-91	64	39	–	–	PUNCT
hjic-91	64	40	l⋅hl	l⋅hl	NOUN
hjic-91	64	41	+	+	PUNCT
hjic-91	64	42	f⋅hf	f⋅hf	NOUN
hjic-91	65	1	+	+	CCONJ
hjic-91	65	2	q	q	NOUN
hjic-91	65	3	hl	hl	NOUN
hjic-91	65	4	=	=	PUNCT
hjic-91	65	5	u	u	PROPN
hjic-91	66	1	⁄	⁄	PROPN
hjic-91	66	2	m	m	NOUN
hjic-91	66	3	hl	hl	NOUN
hjic-91	66	4	*	*	PUNCT
hjic-91	66	5	=	=	SYM
hjic-91	66	6	f1(tl	f1(tl	PROPN
hjic-91	66	7	,	,	PUNCT
hjic-91	66	8	p	p	NOUN
hjic-91	66	9	)	)	PUNCT
hjic-91	66	10	hf	hf	NOUN
hjic-91	66	11	=	=	SYM
hjic-91	66	12	f2(tf	f2(tf	PROPN
hjic-91	66	13	,	,	PUNCT
hjic-91	66	14	pf	pf	NOUN
hjic-91	66	15	)	)	PUNCT
hjic-91	66	16	s	s	PART
hjic-91	66	17	=	=	NOUN
hjic-91	66	18	hl	hl	PROPN
hjic-91	66	19	–	–	PUNCT
hjic-91	66	20	h	h	NOUN
hjic-91	66	21	l	l	NOUN
hjic-91	66	22	*	*	NOUN
hjic-91	66	23	,	,	PUNCT
hjic-91	66	24	s	s	PART
hjic-91	66	25	=	=	SYM
hjic-91	66	26	0	0	NUM
hjic-91	66	27	l	l	NOUN
hjic-91	66	28	=	=	SYM
hjic-91	66	29	f3(m	f3(m	PROPN
hjic-91	66	30	)	)	PUNCT
hjic-91	66	31	here	here	ADV
hjic-91	66	32	m	m	VERB
hjic-91	66	33	denotes	denote	VERB
hjic-91	66	34	the	the	DET
hjic-91	66	35	mass	mass	NOUN
hjic-91	66	36	,	,	PUNCT
hjic-91	66	37	u	u	NOUN
hjic-91	66	38	the	the	DET
hjic-91	66	39	internal	internal	ADJ
hjic-91	66	40	energy	energy	NOUN
hjic-91	66	41	,	,	PUNCT
hjic-91	66	42	q	q	PUNCT
hjic-91	66	43	the	the	DET
hjic-91	66	44	heat	heat	NOUN
hjic-91	66	45	transfer	transfer	NOUN
hjic-91	66	46	rate	rate	NOUN
hjic-91	66	47	,	,	PUNCT
hjic-91	66	48	hl	hl	NOUN
hjic-91	66	49	and	and	CCONJ
hjic-91	66	50	hl	hl	VERB
hjic-91	66	51	the	the	DET
hjic-91	66	52	specific	specific	ADJ
hjic-91	66	53	internal	internal	ADJ
hjic-91	66	54	enthalpy	enthalpy	NOUN
hjic-91	66	55	of	of	ADP
hjic-91	66	56	inlet	inlet	NOUN
hjic-91	66	57	and	and	CCONJ
hjic-91	66	58	outlet	outlet	NOUN
hjic-91	66	59	flow	flow	NOUN
hjic-91	66	60	,	,	PUNCT
hjic-91	66	61	respectively	respectively	ADV
hjic-91	66	62	,	,	PUNCT
hjic-91	66	63	tf	tf	PROPN
hjic-91	66	64	the	the	DET
hjic-91	66	65	temperature	temperature	NOUN
hjic-91	66	66	of	of	ADP
hjic-91	66	67	inlet	inlet	ADJ
hjic-91	66	68	flow	flow	NOUN
hjic-91	66	69	,	,	PUNCT
hjic-91	66	70	pf	pf	ADP
hjic-91	66	71	the	the	DET
hjic-91	66	72	pressure	pressure	NOUN
hjic-91	66	73	of	of	ADP
hjic-91	66	74	inlet	inlet	ADJ
hjic-91	66	75	flow	flow	NOUN
hjic-91	66	76	,	,	PUNCT
hjic-91	66	77	tl	tl	PROPN
hjic-91	66	78	the	the	DET
hjic-91	66	79	temperature	temperature	NOUN
hjic-91	66	80	in	in	ADP
hjic-91	66	81	the	the	DET
hjic-91	66	82	vessel	vessel	NOUN
hjic-91	66	83	,	,	PUNCT
hjic-91	66	84	p	p	X
hjic-91	66	85	the	the	DET
hjic-91	66	86	atmospheric	atmospheric	ADJ
hjic-91	66	87	pressure	pressure	NOUN
hjic-91	66	88	and	and	CCONJ
hjic-91	66	89	f1	f1	NOUN
hjic-91	66	90	and	and	CCONJ
hjic-91	66	91	f2	f2	PROPN
hjic-91	66	92	are	be	AUX
hjic-91	66	93	given	give	VERB
hjic-91	66	94	functions	function	NOUN
hjic-91	66	95	.	.	PUNCT
hjic-91	67	1	14	14	NUM
hjic-91	67	2	let	let	VERB
hjic-91	67	3	us	we	PRON
hjic-91	67	4	consider	consider	VERB
hjic-91	67	5	the	the	DET
hjic-91	67	6	following	follow	VERB
hjic-91	67	7	two	two	NUM
hjic-91	67	8	model	model	NOUN
hjic-91	67	9	specifications	specification	NOUN
hjic-91	67	10	.	.	PUNCT
hjic-91	68	1	specification	specification	NOUN
hjic-91	68	2	1	1	NUM
hjic-91	68	3	.	.	PUNCT
hjic-91	68	4	:	:	PUNCT
hjic-91	69	1	the	the	DET
hjic-91	69	2	variables	variable	NOUN
hjic-91	69	3	f	f	PROPN
hjic-91	69	4	,	,	PUNCT
hjic-91	69	5	tf	tf	INTJ
hjic-91	69	6	,	,	PUNCT
hjic-91	69	7	pf	pf	PROPN
hjic-91	69	8	and	and	CCONJ
hjic-91	69	9	q	q	NOUN
hjic-91	69	10	are	be	AUX
hjic-91	69	11	given	give	VERB
hjic-91	69	12	as	as	ADP
hjic-91	69	13	functions	function	NOUN
hjic-91	69	14	of	of	ADP
hjic-91	69	15	time	time	NOUN
hjic-91	69	16	,	,	PUNCT
hjic-91	69	17	the	the	DET
hjic-91	69	18	initial	initial	ADJ
hjic-91	69	19	values	value	NOUN
hjic-91	69	20	m0	m0	NOUN
hjic-91	69	21	,	,	PUNCT
hjic-91	69	22	u0	u0	ADJ
hjic-91	69	23	and	and	CCONJ
hjic-91	69	24	the	the	DET
hjic-91	69	25	pressure	pressure	NOUN
hjic-91	69	26	p	p	NOUN
hjic-91	69	27	are	be	AUX
hjic-91	69	28	constants	constant	NOUN
hjic-91	69	29	.	.	PUNCT
hjic-91	70	1	the	the	DET
hjic-91	70	2	variables	variable	NOUN
hjic-91	70	3	m	m	PROPN
hjic-91	70	4	,	,	PUNCT
hjic-91	70	5	u	u	PROPN
hjic-91	70	6	,	,	PUNCT
hjic-91	70	7	tl	tl	PROPN
hjic-91	70	8	,	,	PUNCT
hjic-91	70	9	and	and	CCONJ
hjic-91	70	10	l	l	NOUN
hjic-91	70	11	are	be	AUX
hjic-91	70	12	to	to	PART
hjic-91	70	13	be	be	AUX
hjic-91	70	14	calculated	calculate	VERB
hjic-91	70	15	as	as	ADP
hjic-91	70	16	functions	function	NOUN
hjic-91	70	17	of	of	ADP
hjic-91	70	18	time	time	NOUN
hjic-91	70	19	.	.	PUNCT
hjic-91	71	1	m	m	PROPN
hjic-91	71	2	t	t	NOUN
hjic-91	71	3	t+h	t+h	X
hjic-91	71	4	f	f	X
hjic-91	71	5	u	u	NOUN
hjic-91	71	6	tl	tl	PROPN
hjic-91	71	7	p	p	X
hjic-91	71	8	tf	tf	X
hjic-91	71	9	<	<	X
hjic-91	71	10	s	s	X
hjic-91	71	11	>	>	X
hjic-91	71	12	pf	pf	X
hjic-91	71	13	<	<	X
hjic-91	71	14	s	s	X
hjic-91	71	15	>	>	X
hjic-91	71	16	q	q	X
hjic-91	71	17	<	<	X
hjic-91	71	18	s	s	PROPN
hjic-91	71	19	*	*	X
hjic-91	71	20	>	>	X
hjic-91	71	21	<	<	X
hjic-91	71	22	s	s	X
hjic-91	71	23	>	>	X
hjic-91	71	24	l	l	NOUN
hjic-91	71	25	hl	hl	NOUN
hjic-91	71	26	hl	hl	PROPN
hjic-91	71	27	*	*	PUNCT
hjic-91	72	1	hf	hf	PROPN
hjic-91	72	2	u	u	NOUN
hjic-91	72	3	'	'	PART
hjic-91	72	4	m	m	VERB
hjic-91	72	5	'	'	PUNCT
hjic-91	72	6	s	s	PART
hjic-91	72	7	<	<	X
hjic-91	72	8	g	g	X
hjic-91	72	9	>	>	X
hjic-91	72	10	<	<	X
hjic-91	72	11	s	s	X
hjic-91	72	12	>	>	X
hjic-91	72	13	<	<	X
hjic-91	72	14	s	s	PROPN
hjic-91	72	15	*	*	X
hjic-91	72	16	>	>	X
hjic-91	72	17	<	<	X
hjic-91	72	18	s	s	X
hjic-91	72	19	>	>	X
hjic-91	72	20	m	m	PROPN
hjic-91	72	21	f	f	NOUN
hjic-91	72	22	u	u	NOUN
hjic-91	72	23	tl	tl	PROPN
hjic-91	72	24	p	p	X
hjic-91	72	25	tf	tf	X
hjic-91	72	26	<	<	X
hjic-91	72	27	s	s	X
hjic-91	72	28	>	>	X
hjic-91	72	29	pf	pf	X
hjic-91	72	30	<	<	X
hjic-91	72	31	s	s	X
hjic-91	72	32	>	>	X
hjic-91	72	33	q	q	X
hjic-91	72	34	<	<	X
hjic-91	72	35	s	s	PROPN
hjic-91	72	36	*	*	X
hjic-91	72	37	>	>	X
hjic-91	72	38	<	<	X
hjic-91	72	39	s	s	X
hjic-91	72	40	>	>	X
hjic-91	72	41	l	l	NOUN
hjic-91	72	42	hl	hl	NOUN
hjic-91	72	43	hl	hl	PROPN
hjic-91	72	44	*	*	PUNCT
hjic-91	72	45	hf	hf	PROPN
hjic-91	72	46	u	u	NOUN
hjic-91	72	47	'	'	PART
hjic-91	72	48	m	m	VERB
hjic-91	72	49	'	'	PUNCT
hjic-91	72	50	s	s	PART
hjic-91	72	51	<	<	X
hjic-91	72	52	g	g	X
hjic-91	72	53	>	>	X
hjic-91	72	54	<	<	X
hjic-91	72	55	s	s	X
hjic-91	72	56	>	>	X
hjic-91	72	57	<	<	X
hjic-91	72	58	s	s	PROPN
hjic-91	72	59	*	*	X
hjic-91	72	60	>	>	X
hjic-91	72	61	<	<	X
hjic-91	72	62	s	s	X
hjic-91	72	63	>	>	X
hjic-91	72	64	fig.2	fig.2	PROPN
hjic-91	72	65	representation	representation	NOUN
hjic-91	72	66	graph	graph	NOUN
hjic-91	72	67	of	of	ADP
hjic-91	72	68	model	model	NOUN
hjic-91	72	69	m1	m1	PROPN
hjic-91	72	70	with	with	ADP
hjic-91	72	71	specification	specification	NOUN
hjic-91	72	72	1	1	NUM
hjic-91	72	73	assuming	assume	VERB
hjic-91	72	74	first	first	ADJ
hjic-91	72	75	order	order	NOUN
hjic-91	72	76	explicit	explicit	ADJ
hjic-91	72	77	method	method	NOUN
hjic-91	72	78	the	the	DET
hjic-91	72	79	representation	representation	NOUN
hjic-91	72	80	graph	graph	NOUN
hjic-91	72	81	of	of	ADP
hjic-91	72	82	the	the	DET
hjic-91	72	83	liquid	liquid	ADJ
hjic-91	72	84	tank	tank	NOUN
hjic-91	72	85	system	system	NOUN
hjic-91	72	86	and	and	CCONJ
hjic-91	72	87	the	the	DET
hjic-91	72	88	assignment	assignment	NOUN
hjic-91	72	89	types	type	NOUN
hjic-91	72	90	of	of	ADP
hjic-91	72	91	variables	variable	NOUN
hjic-91	72	92	corresponding	correspond	VERB
hjic-91	72	93	to	to	ADP
hjic-91	72	94	the	the	DET
hjic-91	72	95	above	above	ADJ
hjic-91	72	96	specification	specification	NOUN
hjic-91	72	97	are	be	AUX
hjic-91	72	98	shown	show	VERB
hjic-91	72	99	in	in	ADP
hjic-91	72	100	fig.2	fig.2	PROPN
hjic-91	72	101	,	,	PUNCT
hjic-91	72	102	while	while	SCONJ
hjic-91	72	103	the	the	DET
hjic-91	72	104	reduced	reduce	VERB
hjic-91	72	105	graph	graph	NOUN
hjic-91	72	106	can	can	AUX
hjic-91	72	107	be	be	AUX
hjic-91	72	108	seen	see	VERB
hjic-91	72	109	in	in	ADP
hjic-91	72	110	fig.3	fig.3	PROPN
hjic-91	72	111	.	.	PUNCT
hjic-91	73	1	it	it	PRON
hjic-91	73	2	can	can	AUX
hjic-91	73	3	be	be	AUX
hjic-91	73	4	seen	see	VERB
hjic-91	73	5	,	,	PUNCT
hjic-91	73	6	that	that	SCONJ
hjic-91	73	7	there	there	PRON
hjic-91	73	8	exists	exist	VERB
hjic-91	73	9	a	a	DET
hjic-91	73	10	mengertype	mengertype	ADJ
hjic-91	73	11	complete	complete	ADJ
hjic-91	73	12	linking	linking	NOUN
hjic-91	73	13	on	on	ADP
hjic-91	73	14	the	the	DET
hjic-91	73	15	reduced	reduce	VERB
hjic-91	73	16	graph	graph	NOUN
hjic-91	73	17	,	,	PUNCT
hjic-91	73	18	which	which	PRON
hjic-91	73	19	indicates	indicate	VERB
hjic-91	73	20	that	that	SCONJ
hjic-91	73	21	the	the	DET
hjic-91	73	22	differential	differential	ADJ
hjic-91	73	23	index	index	NOUN
hjic-91	73	24	of	of	ADP
hjic-91	73	25	the	the	DET
hjic-91	73	26	above	above	ADJ
hjic-91	73	27	model	model	NOUN
hjic-91	73	28	is	be	AUX
hjic-91	73	29	equal	equal	ADJ
hjic-91	73	30	to	to	ADP
hjic-91	73	31	one	one	NUM
hjic-91	73	32	.	.	PUNCT
hjic-91	74	1	tl	tl	PROPN
hjic-91	74	2	s	s	PART
hjic-91	74	3	<	<	X
hjic-91	74	4	g	g	X
hjic-91	74	5	>	>	X
hjic-91	74	6	hl	hl	NOUN
hjic-91	74	7	*	*	PUNCT
hjic-91	74	8	fig.3	fig.3	ADJ
hjic-91	74	9	reduced	reduce	VERB
hjic-91	74	10	graph	graph	NOUN
hjic-91	74	11	of	of	ADP
hjic-91	74	12	model	model	NOUN
hjic-91	74	13	m1	m1	PROPN
hjic-91	74	14	with	with	ADP
hjic-91	74	15	specification	specification	NOUN
hjic-91	74	16	1	1	NUM
hjic-91	74	17	next	next	ADV
hjic-91	74	18	let	let	VERB
hjic-91	74	19	us	we	PRON
hjic-91	74	20	consider	consider	VERB
hjic-91	74	21	the	the	DET
hjic-91	74	22	following	follow	VERB
hjic-91	74	23	specification	specification	NOUN
hjic-91	74	24	.	.	PUNCT
hjic-91	75	1	specification	specification	NOUN
hjic-91	75	2	2	2	NUM
hjic-91	75	3	.	.	PUNCT
hjic-91	75	4	:	:	PUNCT
hjic-91	76	1	the	the	DET
hjic-91	76	2	variables	variable	NOUN
hjic-91	76	3	f	f	PROPN
hjic-91	76	4	,	,	PUNCT
hjic-91	76	5	tf	tf	INTJ
hjic-91	76	6	,	,	PUNCT
hjic-91	76	7	pf	pf	PROPN
hjic-91	76	8	and	and	CCONJ
hjic-91	76	9	tl	tl	PROPN
hjic-91	76	10	,	,	PUNCT
hjic-91	76	11	are	be	AUX
hjic-91	76	12	given	give	VERB
hjic-91	76	13	as	as	ADP
hjic-91	76	14	functions	function	NOUN
hjic-91	76	15	of	of	ADP
hjic-91	76	16	time	time	NOUN
hjic-91	76	17	,	,	PUNCT
hjic-91	76	18	the	the	DET
hjic-91	76	19	initial	initial	ADJ
hjic-91	76	20	values	value	NOUN
hjic-91	76	21	m0	m0	NOUN
hjic-91	76	22	,	,	PUNCT
hjic-91	76	23	u0	u0	ADJ
hjic-91	76	24	and	and	CCONJ
hjic-91	76	25	the	the	DET
hjic-91	76	26	pressure	pressure	NOUN
hjic-91	76	27	p	p	NOUN
hjic-91	76	28	are	be	AUX
hjic-91	76	29	constants	constant	NOUN
hjic-91	76	30	.	.	PUNCT
hjic-91	77	1	the	the	DET
hjic-91	77	2	variables	variable	NOUN
hjic-91	77	3	m	m	PROPN
hjic-91	77	4	,	,	PUNCT
hjic-91	77	5	u	u	NOUN
hjic-91	77	6	,	,	PUNCT
hjic-91	77	7	q	q	PUNCT
hjic-91	77	8	and	and	CCONJ
hjic-91	77	9	l	l	NOUN
hjic-91	77	10	are	be	AUX
hjic-91	77	11	to	to	PART
hjic-91	77	12	be	be	AUX
hjic-91	77	13	calculated	calculate	VERB
hjic-91	77	14	as	as	ADP
hjic-91	77	15	functions	function	NOUN
hjic-91	77	16	of	of	ADP
hjic-91	77	17	time	time	NOUN
hjic-91	77	18	.	.	PUNCT
hjic-91	78	1	representation	representation	NOUN
hjic-91	78	2	graph	graph	NOUN
hjic-91	78	3	of	of	ADP
hjic-91	78	4	model	model	NOUN
hjic-91	78	5	m1	m1	PROPN
hjic-91	78	6	with	with	ADP
hjic-91	78	7	the	the	DET
hjic-91	78	8	assignment	assignment	NOUN
hjic-91	78	9	of	of	ADP
hjic-91	78	10	vertices	vertex	NOUN
hjic-91	78	11	corresponding	correspond	VERB
hjic-91	78	12	to	to	ADP
hjic-91	78	13	specification	specification	NOUN
hjic-91	78	14	2	2	NUM
hjic-91	78	15	are	be	AUX
hjic-91	78	16	shown	show	VERB
hjic-91	78	17	in	in	ADP
hjic-91	78	18	fig.4	fig.4	PROPN
hjic-91	78	19	.	.	PUNCT
hjic-91	79	1	it	it	PRON
hjic-91	79	2	can	can	AUX
hjic-91	79	3	be	be	AUX
hjic-91	79	4	seen	see	VERB
hjic-91	79	5	that	that	SCONJ
hjic-91	79	6	there	there	PRON
hjic-91	79	7	is	be	VERB
hjic-91	79	8	no	no	DET
hjic-91	79	9	menger	menger	NOUN
hjic-91	79	10	-	-	PUNCT
hjic-91	79	11	type	type	NOUN
hjic-91	79	12	complete	complete	ADJ
hjic-91	79	13	linking	linking	NOUN
hjic-91	79	14	on	on	ADP
hjic-91	79	15	the	the	DET
hjic-91	79	16	graph	graph	NOUN
hjic-91	79	17	,	,	PUNCT
hjic-91	79	18	hence	hence	ADV
hjic-91	79	19	the	the	DET
hjic-91	79	20	standard	standard	ADJ
hjic-91	79	21	form	form	NOUN
hjic-91	79	22	model	model	NOUN
hjic-91	79	23	is	be	AUX
hjic-91	79	24	not	not	PART
hjic-91	79	25	structurally	structurally	ADV
hjic-91	79	26	solvable	solvable	ADJ
hjic-91	79	27	.	.	PUNCT
hjic-91	80	1	there	there	PRON
hjic-91	80	2	is	be	VERB
hjic-91	80	3	an	an	DET
hjic-91	80	4	overspecified	overspecified	ADJ
hjic-91	80	5	part	part	NOUN
hjic-91	80	6	on	on	ADP
hjic-91	80	7	the	the	DET
hjic-91	80	8	graph	graph	NOUN
hjic-91	80	9	,	,	PUNCT
hjic-91	80	10	which	which	PRON
hjic-91	80	11	indicates	indicate	VERB
hjic-91	80	12	the	the	DET
hjic-91	80	13	fact	fact	NOUN
hjic-91	80	14	that	that	SCONJ
hjic-91	80	15	the	the	DET
hjic-91	80	16	initial	initial	ADJ
hjic-91	80	17	values	value	NOUN
hjic-91	80	18	of	of	ADP
hjic-91	80	19	the	the	DET
hjic-91	80	20	model	model	NOUN
hjic-91	80	21	can	can	AUX
hjic-91	80	22	not	not	PART
hjic-91	80	23	be	be	AUX
hjic-91	80	24	chosen	choose	VERB
hjic-91	80	25	independently	independently	ADV
hjic-91	80	26	.	.	PUNCT
hjic-91	81	1	the	the	DET
hjic-91	81	2	underspecified	underspecified	ADJ
hjic-91	81	3	part	part	NOUN
hjic-91	81	4	q	q	PUNCT
hjic-91	81	5	→u	→u	PUNCT
hjic-91	81	6	indicates	indicate	VERB
hjic-91	81	7	that	that	SCONJ
hjic-91	81	8	q	q	NOUN
hjic-91	81	9	can	can	AUX
hjic-91	81	10	not	not	PART
hjic-91	81	11	be	be	AUX
hjic-91	81	12	calculated	calculate	VERB
hjic-91	81	13	from	from	ADP
hjic-91	81	14	the	the	DET
hjic-91	81	15	algebraic	algebraic	ADJ
hjic-91	81	16	equations	equation	NOUN
hjic-91	81	17	.	.	PUNCT
hjic-91	82	1	this	this	DET
hjic-91	82	2	structure	structure	NOUN
hjic-91	82	3	of	of	ADP
hjic-91	82	4	the	the	DET
hjic-91	82	5	representation	representation	NOUN
hjic-91	82	6	graph	graph	NOUN
hjic-91	82	7	shows	show	VERB
hjic-91	82	8	that	that	SCONJ
hjic-91	82	9	the	the	DET
hjic-91	82	10	differential	differential	ADJ
hjic-91	82	11	index	index	NOUN
hjic-91	82	12	of	of	ADP
hjic-91	82	13	the	the	DET
hjic-91	82	14	model	model	NOUN
hjic-91	82	15	m1	m1	PROPN
hjic-91	82	16	with	with	ADP
hjic-91	82	17	specification	specification	NOUN
hjic-91	82	18	2	2	NUM
hjic-91	82	19	is	be	AUX
hjic-91	82	20	greater	great	ADJ
hjic-91	82	21	than	than	ADP
hjic-91	82	22	1	1	NUM
hjic-91	82	23	.	.	PUNCT
hjic-91	83	1	in	in	ADP
hjic-91	83	2	our	our	PRON
hjic-91	83	3	earlier	early	ADJ
hjic-91	83	4	work	work	NOUN
hjic-91	83	5	[	[	X
hjic-91	83	6	2	2	X
hjic-91	83	7	]	]	PUNCT
hjic-91	83	8	we	we	PRON
hjic-91	83	9	suggested	suggest	VERB
hjic-91	83	10	an	an	DET
hjic-91	83	11	algorithm	algorithm	NOUN
hjic-91	83	12	,	,	PUNCT
hjic-91	83	13	which	which	PRON
hjic-91	83	14	determines	determine	VERB
hjic-91	83	15	the	the	DET
hjic-91	83	16	differential	differential	ADJ
hjic-91	83	17	index	index	NOUN
hjic-91	83	18	of	of	ADP
hjic-91	83	19	the	the	DET
hjic-91	83	20	model	model	NOUN
hjic-91	83	21	using	use	VERB
hjic-91	83	22	the	the	DET
hjic-91	83	23	structure	structure	NOUN
hjic-91	83	24	of	of	ADP
hjic-91	83	25	the	the	DET
hjic-91	83	26	representation	representation	NOUN
hjic-91	83	27	graph	graph	NOUN
hjic-91	83	28	and	and	CCONJ
hjic-91	83	29	transform	transform	VERB
hjic-91	83	30	the	the	DET
hjic-91	83	31	model	model	NOUN
hjic-91	83	32	into	into	ADP
hjic-91	83	33	a	a	DET
hjic-91	83	34	structurally	structurally	ADV
hjic-91	83	35	solvable	solvable	ADJ
hjic-91	83	36	modified	modified	ADJ
hjic-91	83	37	form	form	NOUN
hjic-91	83	38	.	.	PUNCT
hjic-91	84	1	15	15	NUM
hjic-91	84	2	m	m	NOUN
hjic-91	84	3	t	t	NOUN
hjic-91	84	4	t	t	NOUN
hjic-91	85	1	+	+	CCONJ
hjic-91	85	2	h	h	NOUN
hjic-91	85	3	f	f	NOUN
hjic-91	85	4	u	u	NOUN
hjic-91	85	5	tl	tl	PROPN
hjic-91	85	6	p	p	X
hjic-91	85	7	<	<	X
hjic-91	85	8	s	s	X
hjic-91	85	9	>	>	X
hjic-91	85	10	tf	tf	X
hjic-91	85	11	<	<	X
hjic-91	85	12	s	s	X
hjic-91	85	13	>	>	X
hjic-91	85	14	pf	pf	X
hjic-91	85	15	<	<	X
hjic-91	85	16	s	s	X
hjic-91	85	17	>	>	X
hjic-91	85	18	q	q	X
hjic-91	85	19	<	<	X
hjic-91	85	20	s	s	PROPN
hjic-91	85	21	*	*	X
hjic-91	85	22	>	>	X
hjic-91	85	23	<	<	X
hjic-91	85	24	s	s	X
hjic-91	85	25	>	>	X
hjic-91	85	26	<	<	X
hjic-91	85	27	s	s	PROPN
hjic-91	85	28	*	*	PROPN
hjic-91	85	29	>	>	X
hjic-91	85	30	l	l	NOUN
hjic-91	85	31	hl	hl	NOUN
hjic-91	85	32	hl	hl	PROPN
hjic-91	85	33	*	*	PUNCT
hjic-91	85	34	hf	hf	PROPN
hjic-91	85	35	u	u	NOUN
hjic-91	85	36	'	'	PART
hjic-91	85	37	m	m	VERB
hjic-91	85	38	'	'	PUNCT
hjic-91	85	39	s	s	PART
hjic-91	85	40	<	<	X
hjic-91	85	41	g	g	X
hjic-91	85	42	>	>	X
hjic-91	85	43	<	<	X
hjic-91	85	44	s	s	X
hjic-91	85	45	>	>	X
hjic-91	85	46	underspecified	underspecifie	VERB
hjic-91	85	47	overspecified	overspecifie	VERB
hjic-91	85	48	m	m	NOUN
hjic-91	85	49	f	f	NOUN
hjic-91	85	50	u	u	NOUN
hjic-91	85	51	tl	tl	PROPN
hjic-91	85	52	p	p	X
hjic-91	85	53	<	<	X
hjic-91	85	54	s	s	X
hjic-91	85	55	>	>	X
hjic-91	85	56	tf	tf	X
hjic-91	85	57	<	<	X
hjic-91	85	58	s	s	X
hjic-91	85	59	>	>	X
hjic-91	85	60	pf	pf	X
hjic-91	85	61	<	<	X
hjic-91	85	62	s	s	X
hjic-91	85	63	>	>	X
hjic-91	85	64	q	q	X
hjic-91	85	65	<	<	X
hjic-91	85	66	s	s	PROPN
hjic-91	85	67	*	*	X
hjic-91	85	68	>	>	X
hjic-91	85	69	<	<	X
hjic-91	85	70	s	s	X
hjic-91	85	71	>	>	X
hjic-91	85	72	<	<	X
hjic-91	85	73	s	s	PROPN
hjic-91	85	74	*	*	PROPN
hjic-91	85	75	>	>	X
hjic-91	85	76	l	l	NOUN
hjic-91	85	77	hl	hl	NOUN
hjic-91	85	78	hl	hl	PROPN
hjic-91	85	79	*	*	PUNCT
hjic-91	85	80	hf	hf	PROPN
hjic-91	85	81	u	u	NOUN
hjic-91	85	82	'	'	PART
hjic-91	85	83	m	m	VERB
hjic-91	85	84	'	'	PUNCT
hjic-91	85	85	s	s	PART
hjic-91	85	86	<	<	X
hjic-91	85	87	g	g	X
hjic-91	85	88	>	>	X
hjic-91	85	89	<	<	X
hjic-91	85	90	s	s	X
hjic-91	85	91	>	>	X
hjic-91	85	92	overspecified	overspecified	ADJ
hjic-91	85	93	underspecified	underspecified	ADJ
hjic-91	85	94	fig.4	fig.4	ADJ
hjic-91	85	95	representation	representation	NOUN
hjic-91	85	96	graph	graph	NOUN
hjic-91	85	97	of	of	ADP
hjic-91	85	98	model	model	NOUN
hjic-91	85	99	m1	m1	PROPN
hjic-91	85	100	with	with	ADP
hjic-91	85	101	specification	specification	NOUN
hjic-91	85	102	2	2	NUM
hjic-91	85	103	assuming	assume	VERB
hjic-91	85	104	first	first	ADJ
hjic-91	85	105	order	order	NOUN
hjic-91	85	106	explicit	explicit	ADJ
hjic-91	85	107	solution	solution	NOUN
hjic-91	85	108	method	method	NOUN
hjic-91	85	109	example	example	NOUN
hjic-91	85	110	2	2	NUM
hjic-91	85	111	:	:	PUNCT
hjic-91	85	112	consider	consider	VERB
hjic-91	85	113	a	a	DET
hjic-91	85	114	simple	simple	ADJ
hjic-91	85	115	tank	tank	NOUN
hjic-91	85	116	system	system	NOUN
hjic-91	85	117	shown	show	VERB
hjic-91	85	118	in	in	ADP
hjic-91	85	119	fig.5	fig.5	PROPN
hjic-91	85	120	.	.	PUNCT
hjic-91	86	1	the	the	DET
hjic-91	86	2	model	model	NOUN
hjic-91	86	3	(	(	PUNCT
hjic-91	86	4	m2	m2	PROPN
hjic-91	86	5	)	)	PUNCT
hjic-91	86	6	describing	describe	VERB
hjic-91	86	7	change	change	NOUN
hjic-91	86	8	of	of	ADP
hjic-91	86	9	the	the	DET
hjic-91	86	10	level	level	NOUN
hjic-91	86	11	of	of	ADP
hjic-91	86	12	liquid	liquid	NOUN
hjic-91	86	13	in	in	ADP
hjic-91	86	14	the	the	DET
hjic-91	86	15	tank	tank	NOUN
hjic-91	86	16	in	in	ADP
hjic-91	86	17	standard	standard	ADJ
hjic-91	86	18	form	form	NOUN
hjic-91	86	19	is	be	AUX
hjic-91	86	20	the	the	DET
hjic-91	86	21	following	following	NOUN
hjic-91	86	22	[	[	X
hjic-91	86	23	5	5	NUM
hjic-91	86	24	]	]	PUNCT
hjic-91	86	25	:	:	PUNCT
hjic-91	86	26	l	l	X
hjic-91	86	27	=	=	SYM
hjic-91	86	28	∫	∫	PROPN
hjic-91	86	29	l	l	NOUN
hjic-91	86	30	’	'	PUNCT
hjic-91	86	31	l	l	NOUN
hjic-91	86	32	’	'	PUNCT
hjic-91	86	33	=	=	SYM
hjic-91	86	34	1	1	NUM
hjic-91	86	35	/	/	SYM
hjic-91	86	36	a•(f1f2	a•(f1f2	ADJ
hjic-91	86	37	)	)	PUNCT
hjic-91	86	38	f1	f1	NOUN
hjic-91	86	39	=	=	SYM
hjic-91	86	40	cv•	cv•	PROPN
hjic-91	86	41	(	(	PUNCT
hjic-91	86	42	p1p2)1/2	p1p2)1/2	PROPN
hjic-91	86	43	f2	f2	PROPN
hjic-91	86	44	=	=	SYM
hjic-91	86	45	cv•	cv•	PROPN
hjic-91	86	46	(	(	PUNCT
hjic-91	86	47	p2	p2	PROPN
hjic-91	86	48	p3	p3	PROPN
hjic-91	86	49	)	)	PUNCT
hjic-91	86	50	1/2	1/2	NUM
hjic-91	86	51	s	s	PART
hjic-91	86	52	=	=	NOUN
hjic-91	86	53	p2	p2	PROPN
hjic-91	86	54	p0	p0	NOUN
hjic-91	86	55	ρ	ρ	NOUN
hjic-91	86	56	g	g	PROPN
hjic-91	86	57	l	l	NOUN
hjic-91	86	58	,	,	PUNCT
hjic-91	86	59	s	s	AUX
hjic-91	86	60	=	=	NOUN
hjic-91	86	61	0	0	NUM
hjic-91	86	62	here	here	ADV
hjic-91	86	63	l	l	PROPN
hjic-91	86	64	denotes	denote	VERB
hjic-91	86	65	the	the	DET
hjic-91	86	66	level	level	NOUN
hjic-91	86	67	of	of	ADP
hjic-91	86	68	the	the	DET
hjic-91	86	69	liquid	liquid	NOUN
hjic-91	86	70	in	in	ADP
hjic-91	86	71	the	the	DET
hjic-91	86	72	tank	tank	NOUN
hjic-91	86	73	,	,	PUNCT
hjic-91	86	74	f1	f1	NOUN
hjic-91	86	75	and	and	CCONJ
hjic-91	86	76	f2	f2	PRON
hjic-91	86	77	the	the	DET
hjic-91	86	78	inlet	inlet	NOUN
hjic-91	86	79	and	and	CCONJ
hjic-91	86	80	outlet	outlet	NOUN
hjic-91	86	81	flow	flow	NOUN
hjic-91	86	82	rate	rate	NOUN
hjic-91	86	83	respectively	respectively	ADV
hjic-91	86	84	.	.	PUNCT
hjic-91	87	1	p0	p0	NOUN
hjic-91	87	2	,	,	PUNCT
hjic-91	87	3	p1	p1	NOUN
hjic-91	87	4	,	,	PUNCT
hjic-91	87	5	p2	p2	PROPN
hjic-91	87	6	and	and	CCONJ
hjic-91	87	7	p3	p3	PROPN
hjic-91	87	8	are	be	AUX
hjic-91	87	9	pressures	pressure	NOUN
hjic-91	87	10	corresponding	correspond	VERB
hjic-91	87	11	to	to	ADP
hjic-91	87	12	fig.5	fig.5	PROPN
hjic-91	87	13	.	.	PUNCT
hjic-91	88	1	the	the	DET
hjic-91	88	2	cross	cross	NOUN
hjic-91	88	3	-	-	NOUN
hjic-91	88	4	section	section	NOUN
hjic-91	88	5	of	of	ADP
hjic-91	88	6	the	the	DET
hjic-91	88	7	tank	tank	NOUN
hjic-91	88	8	a	a	PRON
hjic-91	88	9	,	,	PUNCT
hjic-91	88	10	the	the	DET
hjic-91	88	11	valve	valve	NOUN
hjic-91	88	12	parameter	parameter	NOUN
hjic-91	88	13	cv	cv	PROPN
hjic-91	88	14	,	,	PUNCT
hjic-91	88	15	the	the	DET
hjic-91	88	16	density	density	NOUN
hjic-91	88	17	of	of	ADP
hjic-91	88	18	the	the	DET
hjic-91	88	19	liquid	liquid	ADJ
hjic-91	88	20	ρ	ρ	NOUN
hjic-91	88	21	and	and	CCONJ
hjic-91	88	22	the	the	DET
hjic-91	88	23	gravitational	gravitational	ADJ
hjic-91	88	24	constant	constant	ADJ
hjic-91	88	25	g	g	NOUN
hjic-91	88	26	are	be	AUX
hjic-91	88	27	constant	constant	ADJ
hjic-91	88	28	parameters	parameter	NOUN
hjic-91	88	29	.	.	PUNCT
hjic-91	89	1	p1	p1	NOUN
hjic-91	89	2	f1	f1	PROPN
hjic-91	89	3	p2	p2	PROPN
hjic-91	89	4	p0	p0	NOUN
hjic-91	89	5	p3	p3	PROPN
hjic-91	89	6	f2	f2	PROPN
hjic-91	89	7	l	l	NOUN
hjic-91	89	8	fig.5	fig.5	VERB
hjic-91	89	9	a	a	DET
hjic-91	89	10	simple	simple	ADJ
hjic-91	89	11	tank	tank	NOUN
hjic-91	89	12	system	system	NOUN
hjic-91	89	13	the	the	DET
hjic-91	89	14	variables	variable	NOUN
hjic-91	89	15	p0	p0	NOUN
hjic-91	89	16	,	,	PUNCT
hjic-91	89	17	p1	p1	NOUN
hjic-91	89	18	,	,	PUNCT
hjic-91	89	19	and	and	CCONJ
hjic-91	89	20	p3	p3	PROPN
hjic-91	89	21	are	be	AUX
hjic-91	89	22	given	give	VERB
hjic-91	89	23	as	as	ADP
hjic-91	89	24	functions	function	NOUN
hjic-91	89	25	of	of	ADP
hjic-91	89	26	time	time	NOUN
hjic-91	89	27	,	,	PUNCT
hjic-91	89	28	the	the	DET
hjic-91	89	29	initial	initial	ADJ
hjic-91	89	30	value	value	NOUN
hjic-91	89	31	l0	l0	PROPN
hjic-91	89	32	is	be	AUX
hjic-91	89	33	constant	constant	ADJ
hjic-91	89	34	.	.	PUNCT
hjic-91	90	1	the	the	DET
hjic-91	90	2	variables	variable	NOUN
hjic-91	90	3	p2	p2	NOUN
hjic-91	90	4	,	,	PUNCT
hjic-91	90	5	f1	f1	NOUN
hjic-91	90	6	,	,	PUNCT
hjic-91	90	7	f2	f2	PROPN
hjic-91	90	8	and	and	CCONJ
hjic-91	90	9	l	l	NOUN
hjic-91	90	10	are	be	AUX
hjic-91	90	11	to	to	PART
hjic-91	90	12	be	be	AUX
hjic-91	90	13	calculated	calculate	VERB
hjic-91	90	14	as	as	ADP
hjic-91	90	15	functions	function	NOUN
hjic-91	90	16	of	of	ADP
hjic-91	90	17	time	time	NOUN
hjic-91	90	18	.	.	PUNCT
hjic-91	91	1	the	the	DET
hjic-91	91	2	representation	representation	NOUN
hjic-91	91	3	graph	graph	NOUN
hjic-91	91	4	corresponding	correspond	VERB
hjic-91	91	5	to	to	ADP
hjic-91	91	6	above	above	ADP
hjic-91	91	7	model	model	NOUN
hjic-91	91	8	and	and	CCONJ
hjic-91	91	9	the	the	DET
hjic-91	91	10	variable	variable	ADJ
hjic-91	91	11	type	type	NOUN
hjic-91	91	12	specifications	specification	NOUN
hjic-91	91	13	are	be	AUX
hjic-91	91	14	shown	show	VERB
hjic-91	91	15	in	in	ADP
hjic-91	91	16	fig.6	fig.6	PROPN
hjic-91	91	17	,	,	PUNCT
hjic-91	91	18	while	while	SCONJ
hjic-91	91	19	the	the	DET
hjic-91	91	20	reduced	reduce	VERB
hjic-91	91	21	graph	graph	NOUN
hjic-91	91	22	is	be	AUX
hjic-91	91	23	shown	show	VERB
hjic-91	91	24	in	in	ADP
hjic-91	91	25	fig.7	fig.7	ADJ
hjic-91	91	26	.	.	PUNCT
hjic-91	92	1	it	it	PRON
hjic-91	92	2	can	can	AUX
hjic-91	92	3	be	be	AUX
hjic-91	92	4	seen	see	VERB
hjic-91	92	5	that	that	SCONJ
hjic-91	92	6	there	there	PRON
hjic-91	92	7	exists	exist	VERB
hjic-91	92	8	a	a	DET
hjic-91	92	9	menger	menger	NOUN
hjic-91	92	10	-	-	PUNCT
hjic-91	92	11	type	type	NOUN
hjic-91	92	12	complete	complete	ADJ
hjic-91	92	13	linking	linking	NOUN
hjic-91	92	14	on	on	ADP
hjic-91	92	15	the	the	DET
hjic-91	92	16	reduced	reduce	VERB
hjic-91	92	17	graph	graph	NOUN
hjic-91	92	18	,	,	PUNCT
hjic-91	92	19	which	which	PRON
hjic-91	92	20	indicates	indicate	VERB
hjic-91	92	21	that	that	SCONJ
hjic-91	92	22	the	the	DET
hjic-91	92	23	differential	differential	ADJ
hjic-91	92	24	index	index	NOUN
hjic-91	92	25	of	of	ADP
hjic-91	92	26	the	the	DET
hjic-91	92	27	model	model	NOUN
hjic-91	92	28	is	be	AUX
hjic-91	92	29	equal	equal	ADJ
hjic-91	92	30	to	to	ADP
hjic-91	92	31	one	one	NUM
hjic-91	92	32	.	.	PUNCT
hjic-91	93	1	representation	representation	NOUN
hjic-91	93	2	of	of	ADP
hjic-91	93	3	dae	dae	NOUN
hjic-91	93	4	-	-	PUNCT
hjic-91	93	5	s	s	NOUN
hjic-91	93	6	assuming	assume	VERB
hjic-91	93	7	a	a	DET
hjic-91	93	8	higher	high	ADJ
hjic-91	93	9	-	-	PUNCT
hjic-91	93	10	order	order	NOUN
hjic-91	93	11	explicit	explicit	ADJ
hjic-91	93	12	solution	solution	NOUN
hjic-91	93	13	method	method	NOUN
hjic-91	93	14	higher	high	ADJ
hjic-91	93	15	order	order	NOUN
hjic-91	93	16	explicit	explicit	ADJ
hjic-91	93	17	solution	solution	NOUN
hjic-91	93	18	methods	method	NOUN
hjic-91	93	19	,	,	PUNCT
hjic-91	93	20	such	such	ADJ
hjic-91	93	21	as	as	ADP
hjic-91	93	22	runge	runge	NOUN
hjic-91	93	23	-	-	PUNCT
hjic-91	93	24	kutta	kutta	NOUN
hjic-91	93	25	methods	method	NOUN
hjic-91	93	26	,	,	PUNCT
hjic-91	93	27	are	be	AUX
hjic-91	93	28	widely	widely	ADV
hjic-91	93	29	used	use	VERB
hjic-91	93	30	for	for	ADP
hjic-91	93	31	numerical	numerical	ADJ
hjic-91	93	32	solution	solution	NOUN
hjic-91	93	33	of	of	ADP
hjic-91	93	34	ordinary	ordinary	ADJ
hjic-91	93	35	differential	differential	ADJ
hjic-91	93	36	equations	equation	NOUN
hjic-91	93	37	.	.	PUNCT
hjic-91	94	1	as	as	ADP
hjic-91	94	2	a	a	DET
hjic-91	94	3	characteristic	characteristic	ADJ
hjic-91	94	4	example	example	NOUN
hjic-91	94	5	of	of	ADP
hjic-91	94	6	such	such	ADJ
hjic-91	94	7	methods	method	NOUN
hjic-91	94	8	,	,	PUNCT
hjic-91	94	9	let	let	VERB
hjic-91	94	10	us	we	PRON
hjic-91	94	11	consider	consider	VERB
hjic-91	94	12	a	a	DET
hjic-91	94	13	fourth	fourth	ADJ
hjic-91	94	14	order	order	NOUN
hjic-91	94	15	explicit	explicit	ADJ
hjic-91	94	16	runge	runge	NOUN
hjic-91	94	17	-	-	PUNCT
hjic-91	94	18	kutta	kutta	NOUN
hjic-91	94	19	method	method	NOUN
hjic-91	94	20	,	,	PUNCT
hjic-91	94	21	where	where	SCONJ
hjic-91	94	22	the	the	DET
hjic-91	94	23	value	value	NOUN
hjic-91	94	24	of	of	ADP
hjic-91	94	25	the	the	DET
hjic-91	94	26	differential	differential	ADJ
hjic-91	94	27	variable	variable	NOUN
hjic-91	94	28	x	x	PUNCT
hjic-91	94	29	at	at	ADP
hjic-91	94	30	time	time	NOUN
hjic-91	94	31	t+h	t+h	NUM
hjic-91	94	32	is	be	AUX
hjic-91	94	33	computed	compute	VERB
hjic-91	94	34	as	as	ADP
hjic-91	94	35	k1	k1	NOUN
hjic-91	94	36	=	=	SYM
hjic-91	94	37	f	f	PROPN
hjic-91	94	38	(	(	PUNCT
hjic-91	94	39	t	t	PROPN
hjic-91	94	40	,	,	PUNCT
hjic-91	94	41	x(t	x(t	PROPN
hjic-91	94	42	)	)	PUNCT
hjic-91	94	43	)	)	PUNCT
hjic-91	95	1	k2	k2	NOUN
hjic-91	95	2	=	=	SYM
hjic-91	95	3	f	f	PROPN
hjic-91	95	4	(	(	PUNCT
hjic-91	95	5	t	t	PROPN
hjic-91	95	6	+	+	CCONJ
hjic-91	95	7	h/2	h/2	NUM
hjic-91	95	8	,	,	PUNCT
hjic-91	95	9	x(t)+h/2•	x(t)+h/2•	PROPN
hjic-91	95	10	k1	k1	NOUN
hjic-91	95	11	)	)	PUNCT
hjic-91	95	12	k3	k3	PROPN
hjic-91	95	13	=	=	SYM
hjic-91	95	14	f	f	PROPN
hjic-91	95	15	(	(	PUNCT
hjic-91	95	16	t	t	PROPN
hjic-91	95	17	+	+	CCONJ
hjic-91	95	18	h/2	h/2	NUM
hjic-91	95	19	,	,	PUNCT
hjic-91	95	20	x(t)+h/2•	x(t)+h/2•	PROPN
hjic-91	95	21	k2	k2	ADJ
hjic-91	95	22	)	)	PUNCT
hjic-91	95	23	k4	k4	NOUN
hjic-91	95	24	=	=	SYM
hjic-91	95	25	f	f	PROPN
hjic-91	95	26	(	(	PUNCT
hjic-91	95	27	t	t	PROPN
hjic-91	95	28	+	+	CCONJ
hjic-91	95	29	h	h	NOUN
hjic-91	95	30	,	,	PUNCT
hjic-91	95	31	x(t	x(t	PROPN
hjic-91	95	32	)	)	PUNCT
hjic-91	96	1	+	+	NUM
hjic-91	96	2	h•	h•	NOUN
hjic-91	96	3	k3	k3	PROPN
hjic-91	96	4	)	)	PUNCT
hjic-91	97	1	x(t	x(t	PROPN
hjic-91	97	2	+	+	CCONJ
hjic-91	97	3	h	h	X
hjic-91	97	4	)	)	PUNCT
hjic-91	97	5	=	=	SYM
hjic-91	97	6	x(t	x(t	PROPN
hjic-91	97	7	)	)	PUNCT
hjic-91	98	1	+	+	CCONJ
hjic-91	98	2	h/6•	h/6•	X
hjic-91	98	3	(	(	PUNCT
hjic-91	98	4	k1	k1	X
hjic-91	98	5	+	+	PROPN
hjic-91	98	6	2	2	NUM
hjic-91	98	7	k2	k2	NOUN
hjic-91	98	8	+2	+2	PRON
hjic-91	98	9	k3	k3	VERB
hjic-91	98	10	+	+	CCONJ
hjic-91	98	11	k4	k4	NOUN
hjic-91	98	12	)	)	PUNCT
hjic-91	98	13	from	from	ADP
hjic-91	98	14	the	the	DET
hjic-91	98	15	known	know	VERB
hjic-91	98	16	value	value	NOUN
hjic-91	98	17	x(t	x(t	PROPN
hjic-91	98	18	)	)	PUNCT
hjic-91	98	19	at	at	ADP
hjic-91	98	20	time	time	NOUN
hjic-91	98	21	t	t	PROPN
hjic-91	98	22	and	and	CCONJ
hjic-91	98	23	from	from	ADP
hjic-91	98	24	the	the	DET
hjic-91	98	25	right	right	ADJ
hjic-91	98	26	-	-	PUNCT
hjic-91	98	27	hand	hand	NOUN
hjic-91	98	28	side	side	NOUN
hjic-91	98	29	function	function	NOUN
hjic-91	98	30	f.	f.	PROPN
hjic-91	98	31	16	16	NUM
hjic-91	98	32	p3	p3	PROPN
hjic-91	98	33	p2	p2	PROPN
hjic-91	98	34	p1	p1	NOUN
hjic-91	98	35	p0	p0	NOUN
hjic-91	98	36	<	<	X
hjic-91	98	37	s	s	X
hjic-91	98	38	>	>	X
hjic-91	98	39	l	l	NOUN
hjic-91	98	40	<	<	X
hjic-91	98	41	s	s	X
hjic-91	98	42	>	>	X
hjic-91	98	43	l	l	NOUN
hjic-91	98	44	'	'	PUNCT
hjic-91	98	45	f2	f2	PROPN
hjic-91	98	46	s	s	VERB
hjic-91	98	47	<	<	X
hjic-91	98	48	g	g	X
hjic-91	98	49	>	>	X
hjic-91	98	50	<	<	X
hjic-91	98	51	s	s	PROPN
hjic-91	98	52	*	*	X
hjic-91	98	53	>	>	X
hjic-91	98	54	<	<	X
hjic-91	98	55	s	s	X
hjic-91	98	56	>	>	X
hjic-91	98	57	f1	f1	PROPN
hjic-91	98	58	p3	p3	PROPN
hjic-91	98	59	p2	p2	PROPN
hjic-91	98	60	p1	p1	NOUN
hjic-91	98	61	p0	p0	NOUN
hjic-91	98	62	<	<	X
hjic-91	98	63	s	s	X
hjic-91	98	64	>	>	X
hjic-91	98	65	l	l	NOUN
hjic-91	99	1	<	<	X
hjic-91	99	2	s	s	X
hjic-91	99	3	>	>	X
hjic-91	99	4	l	l	NOUN
hjic-91	99	5	'	'	PUNCT
hjic-91	99	6	f2	f2	PROPN
hjic-91	99	7	s	s	VERB
hjic-91	99	8	<	<	X
hjic-91	99	9	g	g	X
hjic-91	99	10	>	>	X
hjic-91	99	11	<	<	X
hjic-91	99	12	s	s	PROPN
hjic-91	99	13	*	*	X
hjic-91	99	14	>	>	X
hjic-91	99	15	<	<	X
hjic-91	99	16	s	s	X
hjic-91	99	17	>	>	X
hjic-91	99	18	f1	f1	NOUN
hjic-91	99	19	fig.6	fig.6	PROPN
hjic-91	99	20	representation	representation	NOUN
hjic-91	99	21	graph	graph	NOUN
hjic-91	99	22	of	of	ADP
hjic-91	99	23	model	model	NOUN
hjic-91	99	24	m2	m2	PROPN
hjic-91	99	25	assuming	assume	VERB
hjic-91	99	26	first	first	ADJ
hjic-91	99	27	order	order	NOUN
hjic-91	99	28	explicit	explicit	ADJ
hjic-91	99	29	solution	solution	NOUN
hjic-91	99	30	method	method	NOUN
hjic-91	99	31	p2	p2	PROPN
hjic-91	99	32	l	l	NOUN
hjic-91	99	33	'	'	PUNCT
hjic-91	99	34	s	s	X
hjic-91	99	35	<	<	X
hjic-91	99	36	g	g	X
hjic-91	99	37	>	>	X
hjic-91	99	38	f2	f2	PROPN
hjic-91	99	39	f1	f1	PROPN
hjic-91	99	40	fig.7	fig.7	ADV
hjic-91	99	41	reduced	reduce	VERB
hjic-91	99	42	graph	graph	NOUN
hjic-91	99	43	of	of	ADP
hjic-91	99	44	model	model	NOUN
hjic-91	99	45	m2	m2	PROPN
hjic-91	99	46	in	in	ADP
hjic-91	99	47	order	order	NOUN
hjic-91	99	48	to	to	PART
hjic-91	99	49	construct	construct	VERB
hjic-91	99	50	the	the	DET
hjic-91	99	51	dynamic	dynamic	ADJ
hjic-91	99	52	representation	representation	NOUN
hjic-91	99	53	graph	graph	NOUN
hjic-91	99	54	for	for	ADP
hjic-91	99	55	this	this	DET
hjic-91	99	56	case	case	NOUN
hjic-91	99	57	,	,	PUNCT
hjic-91	99	58	we	we	PRON
hjic-91	99	59	construct	construct	VERB
hjic-91	99	60	three	three	NUM
hjic-91	99	61	additional	additional	ADJ
hjic-91	99	62	auxiliary	auxiliary	ADJ
hjic-91	99	63	graphs	graph	NOUN
hjic-91	99	64	in	in	ADP
hjic-91	99	65	between	between	ADP
hjic-91	99	66	a	a	DET
hjic-91	99	67	pair	pair	NOUN
hjic-91	99	68	of	of	ADP
hjic-91	99	69	static	static	ADJ
hjic-91	99	70	graphs	graph	NOUN
hjic-91	99	71	(	(	PUNCT
hjic-91	99	72	main	main	ADJ
hjic-91	99	73	graphs	graph	NOUN
hjic-91	99	74	)	)	PUNCT
hjic-91	99	75	corresponding	correspond	VERB
hjic-91	99	76	to	to	ADP
hjic-91	99	77	an	an	DET
hjic-91	99	78	integration	integration	NOUN
hjic-91	99	79	step	step	NOUN
hjic-91	99	80	from	from	ADP
hjic-91	99	81	t	t	PROPN
hjic-91	99	82	to	to	ADP
hjic-91	99	83	t+h	t+h	PROPN
hjic-91	99	84	.	.	PUNCT
hjic-91	100	1	the	the	DET
hjic-91	100	2	internal	internal	ADJ
hjic-91	100	3	structure	structure	NOUN
hjic-91	100	4	of	of	ADP
hjic-91	100	5	the	the	DET
hjic-91	100	6	auxiliary	auxiliary	ADJ
hjic-91	100	7	graphs	graph	NOUN
hjic-91	100	8	is	be	AUX
hjic-91	100	9	similar	similar	ADJ
hjic-91	100	10	to	to	ADP
hjic-91	100	11	that	that	PRON
hjic-91	100	12	of	of	ADP
hjic-91	100	13	the	the	DET
hjic-91	100	14	main	main	ADJ
hjic-91	100	15	graphs	graph	NOUN
hjic-91	100	16	with	with	ADP
hjic-91	100	17	the	the	DET
hjic-91	100	18	exception	exception	NOUN
hjic-91	100	19	,	,	PUNCT
hjic-91	100	20	that	that	SCONJ
hjic-91	100	21	they	they	PRON
hjic-91	100	22	do	do	AUX
hjic-91	100	23	not	not	PART
hjic-91	100	24	contain	contain	VERB
hjic-91	100	25	the	the	DET
hjic-91	100	26	vertices	vertex	NOUN
hjic-91	100	27	associated	associate	VERB
hjic-91	100	28	to	to	ADP
hjic-91	100	29	the	the	DET
hjic-91	100	30	differential	differential	ADJ
hjic-91	100	31	variables	variable	NOUN
hjic-91	100	32	and	and	CCONJ
hjic-91	100	33	the	the	DET
hjic-91	100	34	arcs	arcs	NOUN
hjic-91	100	35	originating	originating	NOUN
hjic-91	100	36	therefrom	therefrom	NOUN
hjic-91	100	37	.	.	PUNCT
hjic-91	101	1	the	the	DET
hjic-91	101	2	arcs	arcs	NOUN
hjic-91	101	3	between	between	ADP
hjic-91	101	4	the	the	DET
hjic-91	101	5	main	main	ADJ
hjic-91	101	6	and	and	CCONJ
hjic-91	101	7	auxiliary	auxiliary	ADJ
hjic-91	101	8	graphs	graph	NOUN
hjic-91	101	9	are	be	AUX
hjic-91	101	10	determined	determine	VERB
hjic-91	101	11	by	by	ADP
hjic-91	101	12	the	the	DET
hjic-91	101	13	numerical	numerical	ADJ
hjic-91	101	14	solution	solution	NOUN
hjic-91	101	15	method	method	NOUN
hjic-91	101	16	,	,	PUNCT
hjic-91	101	17	in	in	ADP
hjic-91	101	18	the	the	DET
hjic-91	101	19	above	above	ADJ
hjic-91	101	20	fourth	fourth	ADJ
hjic-91	101	21	order	order	NOUN
hjic-91	101	22	runge	runge	NOUN
hjic-91	101	23	-	-	PUNCT
hjic-91	101	24	kutta	kutta	NOUN
hjic-91	101	25	method	method	NOUN
hjic-91	101	26	case	case	NOUN
hjic-91	101	27	the	the	DET
hjic-91	101	28	above	above	ADJ
hjic-91	101	29	set	set	NOUN
hjic-91	101	30	of	of	ADP
hjic-91	101	31	equation	equation	NOUN
hjic-91	101	32	generates	generate	VERB
hjic-91	101	33	the	the	DET
hjic-91	101	34	arcs	arc	NOUN
hjic-91	101	35	shown	show	VERB
hjic-91	101	36	in	in	ADP
hjic-91	101	37	fig.8	fig.8	PROPN
hjic-91	101	38	.	.	PUNCT
hjic-91	102	1	if	if	SCONJ
hjic-91	102	2	there	there	PRON
hjic-91	102	3	is	be	VERB
hjic-91	102	4	an	an	DET
hjic-91	102	5	arc	arc	NOUN
hjic-91	102	6	from	from	ADP
hjic-91	102	7	the	the	DET
hjic-91	102	8	vertex	vertex	NOUN
hjic-91	102	9	of	of	ADP
hjic-91	102	10	the	the	DET
hjic-91	102	11	differential	differential	ADJ
hjic-91	102	12	variable	variable	NOUN
hjic-91	102	13	x	x	X
hjic-91	102	14	to	to	ADP
hjic-91	102	15	another	another	DET
hjic-91	102	16	vertex	vertex	NOUN
hjic-91	102	17	of	of	ADP
hjic-91	102	18	another	another	DET
hjic-91	102	19	variable	variable	ADJ
hjic-91	102	20	xk	xk	PROPN
hjic-91	102	21	on	on	ADP
hjic-91	102	22	the	the	DET
hjic-91	102	23	main	main	ADJ
hjic-91	102	24	graph	graph	NOUN
hjic-91	102	25	corresponding	correspond	VERB
hjic-91	102	26	to	to	ADP
hjic-91	102	27	time	time	NOUN
hjic-91	102	28	t	t	PROPN
hjic-91	102	29	,	,	PUNCT
hjic-91	102	30	then	then	ADV
hjic-91	102	31	we	we	PRON
hjic-91	102	32	direct	direct	VERB
hjic-91	102	33	further	further	ADJ
hjic-91	102	34	arcs	arc	NOUN
hjic-91	102	35	from	from	ADP
hjic-91	102	36	vertex	vertex	NOUN
hjic-91	102	37	x	x	PUNCT
hjic-91	102	38	towards	towards	ADP
hjic-91	102	39	every	every	DET
hjic-91	102	40	auxiliary	auxiliary	ADJ
hjic-91	102	41	graph	graph	NOUN
hjic-91	102	42	ending	end	VERB
hjic-91	102	43	at	at	ADP
hjic-91	102	44	their	their	PRON
hjic-91	102	45	vertex	vertex	NOUN
hjic-91	102	46	xk	xk	PROPN
hjic-91	102	47	.	.	PUNCT
hjic-91	103	1	the	the	DET
hjic-91	103	2	type	type	NOUN
hjic-91	103	3	labels	label	NOUN
hjic-91	103	4	of	of	ADP
hjic-91	103	5	the	the	DET
hjic-91	103	6	vertices	vertex	NOUN
hjic-91	103	7	on	on	ADP
hjic-91	103	8	the	the	DET
hjic-91	103	9	auxiliary	auxiliary	ADJ
hjic-91	103	10	graphs	graph	NOUN
hjic-91	103	11	should	should	AUX
hjic-91	103	12	be	be	AUX
hjic-91	103	13	identical	identical	ADJ
hjic-91	103	14	to	to	ADP
hjic-91	103	15	that	that	PRON
hjic-91	103	16	of	of	ADP
hjic-91	103	17	the	the	DET
hjic-91	103	18	corresponding	corresponding	ADJ
hjic-91	103	19	vertex	vertex	NOUN
hjic-91	103	20	on	on	ADP
hjic-91	103	21	the	the	DET
hjic-91	103	22	main	main	ADJ
hjic-91	103	23	graphs	graph	NOUN
hjic-91	103	24	.	.	PUNCT
hjic-91	104	1	futrhermore	futrhermore	NOUN
hjic-91	104	2	,	,	PUNCT
hjic-91	104	3	we	we	PRON
hjic-91	104	4	associate	associate	VERB
hjic-91	104	5	type	type	NOUN
hjic-91	104	6	<	<	X
hjic-91	104	7	s	s	NOUN
hjic-91	104	8	*	*	NOUN
hjic-91	104	9	>	>	X
hjic-91	104	10	labels	label	NOUN
hjic-91	104	11	to	to	ADP
hjic-91	104	12	the	the	DET
hjic-91	104	13	vertices	vertex	NOUN
hjic-91	104	14	which	which	PRON
hjic-91	104	15	have	have	VERB
hjic-91	104	16	incoming	incoming	ADJ
hjic-91	104	17	arcs	arc	NOUN
hjic-91	104	18	from	from	ADP
hjic-91	104	19	only	only	ADV
hjic-91	104	20	main	main	ADJ
hjic-91	104	21	or	or	CCONJ
hjic-91	104	22	auxiliary	auxiliary	ADJ
hjic-91	104	23	graphs	graph	NOUN
hjic-91	104	24	corresponding	correspond	VERB
hjic-91	104	25	to	to	ADP
hjic-91	104	26	previous	previous	ADJ
hjic-91	104	27	time	time	NOUN
hjic-91	104	28	instances	instance	NOUN
hjic-91	104	29	.	.	PUNCT
hjic-91	105	1	as	as	ADP
hjic-91	105	2	an	an	DET
hjic-91	105	3	example	example	NOUN
hjic-91	105	4	,	,	PUNCT
hjic-91	105	5	fig.9	fig.9	PROPN
hjic-91	105	6	shows	show	VERB
hjic-91	105	7	the	the	DET
hjic-91	105	8	representation	representation	NOUN
hjic-91	105	9	graph	graph	NOUN
hjic-91	105	10	of	of	ADP
hjic-91	105	11	model	model	NOUN
hjic-91	105	12	m2	m2	PROPN
hjic-91	105	13	assuming	assume	VERB
hjic-91	105	14	a	a	DET
hjic-91	105	15	fourth	fourth	ADJ
hjic-91	105	16	order	order	NOUN
hjic-91	105	17	explicit	explicit	ADJ
hjic-91	105	18	runge	runge	NOUN
hjic-91	105	19	-	-	PUNCT
hjic-91	105	20	kutta	kutta	NOUN
hjic-91	105	21	method	method	NOUN
hjic-91	105	22	as	as	ADP
hjic-91	105	23	its	its	PRON
hjic-91	105	24	solution	solution	NOUN
hjic-91	105	25	procedure	procedure	NOUN
hjic-91	105	26	.	.	PUNCT
hjic-91	106	1	because	because	SCONJ
hjic-91	106	2	of	of	ADP
hjic-91	106	3	the	the	DET
hjic-91	106	4	way	way	NOUN
hjic-91	106	5	of	of	ADP
hjic-91	106	6	the	the	DET
hjic-91	106	7	representation	representation	NOUN
hjic-91	106	8	,	,	PUNCT
hjic-91	106	9	the	the	DET
hjic-91	106	10	main	main	ADJ
hjic-91	106	11	graphs	graph	NOUN
hjic-91	106	12	of	of	ADP
hjic-91	106	13	a	a	DET
hjic-91	106	14	representation	representation	NOUN
hjic-91	106	15	graph	graph	NOUN
hjic-91	106	16	with	with	ADP
hjic-91	106	17	higher	high	ADJ
hjic-91	106	18	order	order	NOUN
hjic-91	106	19	explicit	explicit	ADJ
hjic-91	106	20	solution	solution	NOUN
hjic-91	106	21	method	method	NOUN
hjic-91	106	22	are	be	AUX
hjic-91	106	23	identical	identical	ADJ
hjic-91	106	24	with	with	ADP
hjic-91	106	25	the	the	DET
hjic-91	106	26	static	static	ADJ
hjic-91	106	27	graphs	graph	NOUN
hjic-91	106	28	of	of	ADP
hjic-91	106	29	the	the	DET
hjic-91	106	30	earlier	early	ADJ
hjic-91	106	31	dynamic	dynamic	ADJ
hjic-91	106	32	representation	representation	NOUN
hjic-91	106	33	graph	graph	NOUN
hjic-91	106	34	belonging	belong	VERB
hjic-91	106	35	to	to	ADP
hjic-91	106	36	the	the	DET
hjic-91	106	37	euler	euler	NOUN
hjic-91	106	38	method	method	NOUN
hjic-91	106	39	.	.	PUNCT
hjic-91	107	1	only	only	ADV
hjic-91	107	2	the	the	DET
hjic-91	107	3	connecting	connect	VERB
hjic-91	107	4	arcs	arc	NOUN
hjic-91	107	5	between	between	ADP
hjic-91	107	6	the	the	DET
hjic-91	107	7	main	main	ADJ
hjic-91	107	8	and	and	CCONJ
hjic-91	107	9	the	the	DET
hjic-91	107	10	auxiliary	auxiliary	ADJ
hjic-91	107	11	graphs	graph	NOUN
hjic-91	107	12	become	become	VERB
hjic-91	107	13	more	more	ADV
hjic-91	107	14	complicated	complicated	ADJ
hjic-91	107	15	as	as	ADP
hjic-91	107	16	a	a	DET
hjic-91	107	17	consequence	consequence	NOUN
hjic-91	107	18	of	of	ADP
hjic-91	107	19	the	the	DET
hjic-91	107	20	more	more	ADV
hjic-91	107	21	complex	complex	ADJ
hjic-91	107	22	numerical	numerical	ADJ
hjic-91	107	23	solution	solution	NOUN
hjic-91	107	24	method	method	NOUN
hjic-91	107	25	.	.	PUNCT
hjic-91	108	1	at	at	ADP
hjic-91	108	2	the	the	DET
hjic-91	108	3	same	same	ADJ
hjic-91	108	4	time	time	NOUN
hjic-91	108	5	,	,	PUNCT
hjic-91	108	6	the	the	DET
hjic-91	108	7	algebraic	algebraic	ADJ
hjic-91	108	8	subgraphs	subgraph	NOUN
hjic-91	108	9	of	of	ADP
hjic-91	108	10	the	the	DET
hjic-91	108	11	main	main	ADJ
hjic-91	108	12	and	and	CCONJ
hjic-91	108	13	auxiliary	auxiliary	ADJ
hjic-91	108	14	graphs	graph	NOUN
hjic-91	108	15	are	be	AUX
hjic-91	108	16	identical	identical	ADJ
hjic-91	108	17	to	to	ADP
hjic-91	108	18	the	the	DET
hjic-91	108	19	earlier	early	ADJ
hjic-91	108	20	algebraic	algebraic	ADJ
hjic-91	108	21	subgraphs	subgraph	NOUN
hjic-91	108	22	belonging	belong	VERB
hjic-91	108	23	to	to	ADP
hjic-91	108	24	the	the	DET
hjic-91	108	25	euler	euler	NOUN
hjic-91	108	26	method	method	NOUN
hjic-91	108	27	.	.	PUNCT
hjic-91	109	1	therefore	therefore	ADV
hjic-91	109	2	we	we	PRON
hjic-91	109	3	can	can	AUX
hjic-91	109	4	state	state	VERB
hjic-91	109	5	the	the	DET
hjic-91	109	6	following	follow	VERB
hjic-91	109	7	propositions	proposition	NOUN
hjic-91	109	8	.	.	PUNCT
hjic-91	110	1	proposition	proposition	NOUN
hjic-91	110	2	1	1	NUM
hjic-91	110	3	.	.	PUNCT
hjic-91	111	1	the	the	DET
hjic-91	111	2	differential	differential	ADJ
hjic-91	111	3	index	index	NOUN
hjic-91	111	4	of	of	ADP
hjic-91	111	5	a	a	DET
hjic-91	111	6	semiexplicit	semiexplicit	ADJ
hjic-91	111	7	dae	dae	NOUN
hjic-91	111	8	model	model	NOUN
hjic-91	111	9	m	m	NOUN
hjic-91	111	10	is	be	AUX
hjic-91	111	11	equal	equal	ADJ
hjic-91	111	12	to	to	ADP
hjic-91	111	13	one	one	NUM
hjic-91	111	14	if	if	SCONJ
hjic-91	111	15	and	and	CCONJ
hjic-91	111	16	only	only	ADV
hjic-91	111	17	if	if	SCONJ
hjic-91	111	18	there	there	PRON
hjic-91	111	19	exists	exist	VERB
hjic-91	111	20	a	a	DET
hjic-91	111	21	menger	menger	NOUN
hjic-91	111	22	-	-	PUNCT
hjic-91	111	23	type	type	NOUN
hjic-91	111	24	complete	complete	ADJ
hjic-91	111	25	linking	linking	NOUN
hjic-91	111	26	on	on	ADP
hjic-91	111	27	the	the	DET
hjic-91	111	28	reduced	reduced	ADJ
hjic-91	111	29	algebraic	algebraic	ADJ
hjic-91	111	30	subgraph	subgraph	NOUN
hjic-91	111	31	of	of	ADP
hjic-91	111	32	its	its	PRON
hjic-91	111	33	dynamic	dynamic	ADJ
hjic-91	111	34	representation	representation	NOUN
hjic-91	111	35	graph	graph	NOUN
hjic-91	111	36	independently	independently	ADV
hjic-91	111	37	of	of	ADP
hjic-91	111	38	the	the	DET
hjic-91	111	39	fact	fact	NOUN
hjic-91	111	40	if	if	SCONJ
hjic-91	111	41	a	a	DET
hjic-91	111	42	first	first	ADJ
hjic-91	111	43	or	or	CCONJ
hjic-91	111	44	higher	high	ADJ
hjic-91	111	45	order	order	NOUN
hjic-91	111	46	one	one	NUM
hjic-91	111	47	-	-	PUNCT
hjic-91	111	48	step	step	NOUN
hjic-91	111	49	explicit	explicit	ADJ
hjic-91	111	50	method	method	NOUN
hjic-91	111	51	is	be	AUX
hjic-91	111	52	applied	apply	VERB
hjic-91	111	53	for	for	ADP
hjic-91	111	54	the	the	DET
hjic-91	111	55	numerical	numerical	ADJ
hjic-91	111	56	solution	solution	NOUN
hjic-91	111	57	.	.	PUNCT
hjic-91	112	1	the	the	DET
hjic-91	112	2	reduction	reduction	NOUN
hjic-91	112	3	of	of	ADP
hjic-91	112	4	the	the	DET
hjic-91	112	5	main	main	ADJ
hjic-91	112	6	and	and	CCONJ
hjic-91	112	7	auxiliary	auxiliary	ADJ
hjic-91	112	8	graphs	graph	NOUN
hjic-91	112	9	can	can	AUX
hjic-91	112	10	be	be	AUX
hjic-91	112	11	performed	perform	VERB
hjic-91	112	12	following	follow	VERB
hjic-91	112	13	the	the	DET
hjic-91	112	14	same	same	ADJ
hjic-91	112	15	rules	rule	NOUN
hjic-91	112	16	as	as	SCONJ
hjic-91	112	17	we	we	PRON
hjic-91	112	18	have	have	AUX
hjic-91	112	19	seen	see	VERB
hjic-91	112	20	earlier	early	ADV
hjic-91	112	21	in	in	ADP
hjic-91	112	22	the	the	DET
hjic-91	112	23	case	case	NOUN
hjic-91	112	24	of	of	ADP
hjic-91	112	25	applying	apply	VERB
hjic-91	112	26	the	the	DET
hjic-91	112	27	explicit	explicit	ADJ
hjic-91	112	28	euler	euler	NOUN
hjic-91	112	29	method	method	NOUN
hjic-91	112	30	for	for	ADP
hjic-91	112	31	the	the	DET
hjic-91	112	32	numerical	numerical	ADJ
hjic-91	112	33	solution	solution	NOUN
hjic-91	112	34	.	.	PUNCT
hjic-91	113	1	then	then	ADV
hjic-91	113	2	the	the	DET
hjic-91	113	3	following	follow	VERB
hjic-91	113	4	statement	statement	NOUN
hjic-91	113	5	is	be	AUX
hjic-91	113	6	valid	valid	ADJ
hjic-91	113	7	.	.	PUNCT
hjic-91	114	1	17	17	NUM
hjic-91	114	2	x	x	SYM
hjic-91	114	3	x1	x1	NUM
hjic-91	114	4	xn	xn	PUNCT
hjic-91	114	5	x	x	X
hjic-91	114	6	'	'	PUNCT
hjic-91	114	7	=	=	SYM
hjic-91	114	8	k1	k1	PROPN
hjic-91	114	9	t	t	NOUN
hjic-91	114	10	x	x	SYM
hjic-91	115	1	x1	x1	PROPN
hjic-91	115	2	xn	xn	PUNCT
hjic-91	115	3	x	x	X
hjic-91	115	4	'	'	PUNCT
hjic-91	115	5	=	=	SYM
hjic-91	115	6	k1	k1	PROPN
hjic-91	115	7	t	t	PROPN
hjic-91	115	8	+	+	CCONJ
hjic-91	115	9	h	h	NOUN
hjic-91	116	1	x1	x1	NOUN
hjic-91	116	2	xn	xn	PUNCT
hjic-91	116	3	x	x	X
hjic-91	116	4	'	'	PUNCT
hjic-91	116	5	=	=	SYM
hjic-91	116	6	k2	k2	PROPN
hjic-91	116	7	t	t	PROPN
hjic-91	116	8	+	+	CCONJ
hjic-91	116	9	h/2	h/2	X
hjic-91	116	10	x1	x1	PROPN
hjic-91	116	11	xn	xn	PUNCT
hjic-91	116	12	x	x	X
hjic-91	116	13	'	'	PUNCT
hjic-91	116	14	=	=	PUNCT
hjic-91	116	15	k3	k3	VERB
hjic-91	116	16	t	t	PROPN
hjic-91	116	17	+	+	CCONJ
hjic-91	116	18	h/2	h/2	X
hjic-91	116	19	x1	x1	PROPN
hjic-91	116	20	xn	xn	PUNCT
hjic-91	116	21	x	x	X
hjic-91	116	22	'	'	PUNCT
hjic-91	116	23	=	=	SYM
hjic-91	116	24	k4	k4	PROPN
hjic-91	116	25	t	t	PROPN
hjic-91	116	26	+	+	CCONJ
hjic-91	116	27	h	h	NOUN
hjic-91	116	28	main	main	ADJ
hjic-91	116	29	graphs	graph	NOUN
hjic-91	116	30	auxiliary	auxiliary	ADJ
hjic-91	116	31	graphs	graph	NOUN
hjic-91	116	32	fig.8	fig.8	PROPN
hjic-91	116	33	dynamic	dynamic	ADJ
hjic-91	116	34	representation	representation	NOUN
hjic-91	116	35	graph	graph	NOUN
hjic-91	116	36	assuming	assume	VERB
hjic-91	116	37	fourth	fourth	ADJ
hjic-91	116	38	order	order	NOUN
hjic-91	116	39	explicit	explicit	ADJ
hjic-91	116	40	runge	runge	NOUN
hjic-91	116	41	-	-	PUNCT
hjic-91	116	42	kutta	kutta	NOUN
hjic-91	116	43	method	method	NOUN
hjic-91	116	44	proposition	proposition	NOUN
hjic-91	116	45	2	2	NUM
hjic-91	116	46	.	.	PUNCT
hjic-91	117	1	by	by	ADP
hjic-91	117	2	performing	perform	VERB
hjic-91	117	3	the	the	DET
hjic-91	117	4	reduction	reduction	NOUN
hjic-91	117	5	of	of	ADP
hjic-91	117	6	any	any	PRON
hjic-91	117	7	of	of	ADP
hjic-91	117	8	the	the	DET
hjic-91	117	9	main	main	ADJ
hjic-91	117	10	or	or	CCONJ
hjic-91	117	11	auxiliary	auxiliary	ADJ
hjic-91	117	12	graphs	graph	NOUN
hjic-91	117	13	,	,	PUNCT
hjic-91	117	14	the	the	DET
hjic-91	117	15	same	same	ADJ
hjic-91	117	16	reduced	reduce	VERB
hjic-91	117	17	graph	graph	NOUN
hjic-91	117	18	is	be	AUX
hjic-91	117	19	obtained	obtain	VERB
hjic-91	117	20	,	,	PUNCT
hjic-91	117	21	and	and	CCONJ
hjic-91	117	22	it	it	PRON
hjic-91	117	23	is	be	AUX
hjic-91	117	24	identical	identical	ADJ
hjic-91	117	25	to	to	ADP
hjic-91	117	26	the	the	DET
hjic-91	117	27	reduced	reduce	VERB
hjic-91	117	28	graph	graph	NOUN
hjic-91	117	29	of	of	ADP
hjic-91	117	30	the	the	DET
hjic-91	117	31	model	model	NOUN
hjic-91	117	32	when	when	SCONJ
hjic-91	117	33	assuming	assume	VERB
hjic-91	117	34	the	the	DET
hjic-91	117	35	explicit	explicit	ADJ
hjic-91	117	36	euler	euler	NOUN
hjic-91	117	37	method	method	NOUN
hjic-91	117	38	as	as	ADP
hjic-91	117	39	a	a	DET
hjic-91	117	40	numerical	numerical	ADJ
hjic-91	117	41	solution	solution	NOUN
hjic-91	117	42	procedure	procedure	NOUN
hjic-91	117	43	.	.	PUNCT
hjic-91	118	1	proof	proof	NOUN
hjic-91	118	2	.	.	PUNCT
hjic-91	119	1	the	the	DET
hjic-91	119	2	statement	statement	NOUN
hjic-91	119	3	follows	follow	VERB
hjic-91	119	4	from	from	ADP
hjic-91	119	5	the	the	DET
hjic-91	119	6	structure	structure	NOUN
hjic-91	119	7	of	of	ADP
hjic-91	119	8	the	the	DET
hjic-91	119	9	dynamic	dynamic	ADJ
hjic-91	119	10	representation	representation	NOUN
hjic-91	119	11	graph	graph	NOUN
hjic-91	119	12	and	and	CCONJ
hjic-91	119	13	from	from	ADP
hjic-91	119	14	the	the	DET
hjic-91	119	15	way	way	NOUN
hjic-91	119	16	the	the	DET
hjic-91	119	17	type	type	NOUN
hjic-91	119	18	-	-	PUNCT
hjic-91	119	19	labels	label	NOUN
hjic-91	119	20	are	be	AUX
hjic-91	119	21	associated	associate	VERB
hjic-91	119	22	to	to	ADP
hjic-91	119	23	the	the	DET
hjic-91	119	24	vertices	vertex	NOUN
hjic-91	119	25	on	on	ADP
hjic-91	119	26	the	the	DET
hjic-91	119	27	main	main	ADJ
hjic-91	119	28	and	and	CCONJ
hjic-91	119	29	auxiliary	auxiliary	ADJ
hjic-91	119	30	graphs	graph	NOUN
hjic-91	119	31	.	.	PUNCT
hjic-91	120	1	in	in	ADP
hjic-91	120	2	agreement	agreement	NOUN
hjic-91	120	3	of	of	ADP
hjic-91	120	4	the	the	DET
hjic-91	120	5	above	above	ADJ
hjic-91	120	6	proposition	proposition	NOUN
hjic-91	120	7	,	,	PUNCT
hjic-91	120	8	the	the	DET
hjic-91	120	9	reduced	reduce	VERB
hjic-91	120	10	graphs	graph	NOUN
hjic-91	120	11	of	of	ADP
hjic-91	120	12	the	the	DET
hjic-91	120	13	main	main	ADJ
hjic-91	120	14	and	and	CCONJ
hjic-91	120	15	auxiliary	auxiliary	ADJ
hjic-91	120	16	graphs	graph	NOUN
hjic-91	120	17	of	of	ADP
hjic-91	120	18	model	model	NOUN
hjic-91	120	19	m2	m2	PROPN
hjic-91	120	20	shown	show	VERB
hjic-91	120	21	in	in	ADP
hjic-91	120	22	fig.9	fig.9	PROPN
hjic-91	120	23	are	be	AUX
hjic-91	120	24	identical	identical	ADJ
hjic-91	120	25	to	to	ADP
hjic-91	120	26	the	the	DET
hjic-91	120	27	reduced	reduce	VERB
hjic-91	120	28	graph	graph	NOUN
hjic-91	120	29	seen	see	VERB
hjic-91	120	30	in	in	ADP
hjic-91	120	31	fig.7	fig.7	ADJ
hjic-91	120	32	.	.	PUNCT
hjic-91	121	1	it	it	PRON
hjic-91	121	2	is	be	AUX
hjic-91	121	3	important	important	ADJ
hjic-91	121	4	to	to	PART
hjic-91	121	5	note	note	VERB
hjic-91	121	6	that	that	SCONJ
hjic-91	121	7	there	there	PRON
hjic-91	121	8	will	will	AUX
hjic-91	121	9	be	be	AUX
hjic-91	121	10	overspecified	overspecifie	VERB
hjic-91	121	11	and	and	CCONJ
hjic-91	121	12	underspecified	underspecified	ADJ
hjic-91	121	13	subgraphs	subgraph	NOUN
hjic-91	121	14	on	on	ADP
hjic-91	121	15	each	each	PRON
hjic-91	121	16	of	of	ADP
hjic-91	121	17	the	the	DET
hjic-91	121	18	main	main	ADJ
hjic-91	121	19	and	and	CCONJ
hjic-91	121	20	auxiliary	auxiliary	ADJ
hjic-91	121	21	graphs	graph	NOUN
hjic-91	121	22	in	in	ADP
hjic-91	121	23	the	the	DET
hjic-91	121	24	case	case	NOUN
hjic-91	121	25	of	of	ADP
hjic-91	121	26	higher	high	ADJ
hjic-91	121	27	index	index	NOUN
hjic-91	121	28	models	model	NOUN
hjic-91	121	29	assuming	assume	VERB
hjic-91	121	30	higher	high	ADJ
hjic-91	121	31	order	order	NOUN
hjic-91	121	32	explicit	explicit	ADJ
hjic-91	121	33	numerical	numerical	ADJ
hjic-91	121	34	solution	solution	NOUN
hjic-91	121	35	methods	method	NOUN
hjic-91	121	36	,	,	PUNCT
hjic-91	121	37	similarly	similarly	ADV
hjic-91	121	38	to	to	ADP
hjic-91	121	39	the	the	DET
hjic-91	121	40	case	case	NOUN
hjic-91	121	41	when	when	SCONJ
hjic-91	121	42	the	the	DET
hjic-91	121	43	simple	simple	ADJ
hjic-91	121	44	explicit	explicit	ADJ
hjic-91	121	45	euler	euler	NOUN
hjic-91	121	46	method	method	NOUN
hjic-91	121	47	was	be	AUX
hjic-91	121	48	assumed	assume	VERB
hjic-91	121	49	.	.	PUNCT
hjic-91	122	1	representation	representation	NOUN
hjic-91	122	2	of	of	ADP
hjic-91	122	3	dae	dae	NOUN
hjic-91	122	4	-	-	PUNCT
hjic-91	122	5	s	s	NOUN
hjic-91	122	6	assuming	assume	VERB
hjic-91	122	7	an	an	DET
hjic-91	122	8	implicit	implicit	ADJ
hjic-91	122	9	solution	solution	NOUN
hjic-91	122	10	method	method	NOUN
hjic-91	122	11	if	if	SCONJ
hjic-91	122	12	we	we	PRON
hjic-91	122	13	consider	consider	VERB
hjic-91	122	14	a	a	DET
hjic-91	122	15	single	single	ADJ
hjic-91	122	16	-	-	PUNCT
hjic-91	122	17	step	step	NOUN
hjic-91	122	18	implicit	implicit	ADJ
hjic-91	122	19	solution	solution	NOUN
hjic-91	122	20	method	method	NOUN
hjic-91	122	21	(	(	PUNCT
hjic-91	122	22	for	for	ADP
hjic-91	122	23	example	example	NOUN
hjic-91	122	24	the	the	DET
hjic-91	122	25	implicit	implicit	ADJ
hjic-91	122	26	euler	euler	NOUN
hjic-91	122	27	method	method	NOUN
hjic-91	122	28	)	)	PUNCT
hjic-91	122	29	for	for	ADP
hjic-91	122	30	the	the	DET
hjic-91	122	31	numerical	numerical	ADJ
hjic-91	122	32	solution	solution	NOUN
hjic-91	122	33	procedure	procedure	NOUN
hjic-91	122	34	of	of	ADP
hjic-91	122	35	the	the	DET
hjic-91	122	36	differential	differential	ADJ
hjic-91	122	37	equations	equation	NOUN
hjic-91	122	38	,	,	PUNCT
hjic-91	122	39	then	then	ADV
hjic-91	122	40	the	the	DET
hjic-91	122	41	value	value	NOUN
hjic-91	122	42	of	of	ADP
hjic-91	122	43	differential	differential	ADJ
hjic-91	122	44	variable	variable	NOUN
hjic-91	122	45	x	x	PUNCT
hjic-91	122	46	at	at	ADP
hjic-91	122	47	time	time	NOUN
hjic-91	122	48	t+h	t+h	NUM
hjic-91	122	49	is	be	AUX
hjic-91	122	50	calculated	calculate	VERB
hjic-91	122	51	as	as	SCONJ
hjic-91	122	52	follows	follow	VERB
hjic-91	122	53	:	:	PUNCT
hjic-91	122	54	x(t+h	x(t+h	PUNCT
hjic-91	122	55	)	)	PUNCT
hjic-91	122	56	=	=	SYM
hjic-91	122	57	x(t	x(t	PROPN
hjic-91	122	58	)	)	PUNCT
hjic-91	122	59	+	+	CCONJ
hjic-91	122	60	h⋅x’(t+h	h⋅x’(t+h	NOUN
hjic-91	122	61	)	)	PUNCT
hjic-91	122	62	where	where	SCONJ
hjic-91	122	63	h	h	NOUN
hjic-91	122	64	is	be	AUX
hjic-91	122	65	the	the	DET
hjic-91	122	66	step	step	NOUN
hjic-91	122	67	length	length	NOUN
hjic-91	122	68	.	.	PUNCT
hjic-91	123	1	in	in	ADP
hjic-91	123	2	this	this	DET
hjic-91	123	3	case	case	NOUN
hjic-91	123	4	the	the	DET
hjic-91	123	5	modified	modified	ADJ
hjic-91	123	6	structure	structure	NOUN
hjic-91	123	7	of	of	ADP
hjic-91	123	8	the	the	DET
hjic-91	123	9	dynamic	dynamic	ADJ
hjic-91	123	10	representation	representation	NOUN
hjic-91	123	11	graph	graph	NOUN
hjic-91	123	12	is	be	AUX
hjic-91	123	13	depicted	depict	VERB
hjic-91	123	14	in	in	ADP
hjic-91	123	15	fig.10	fig.10	PRON
hjic-91	123	16	.	.	PUNCT
hjic-91	124	1	it	it	PRON
hjic-91	124	2	can	can	AUX
hjic-91	124	3	be	be	AUX
hjic-91	124	4	seen	see	VERB
hjic-91	124	5	that	that	SCONJ
hjic-91	124	6	the	the	DET
hjic-91	124	7	algebraic	algebraic	ADJ
hjic-91	124	8	part	part	NOUN
hjic-91	124	9	of	of	ADP
hjic-91	124	10	the	the	DET
hjic-91	124	11	representation	representation	NOUN
hjic-91	124	12	graph	graph	NOUN
hjic-91	124	13	does	do	AUX
hjic-91	124	14	not	not	PART
hjic-91	124	15	change	change	VERB
hjic-91	124	16	compared	compare	VERB
hjic-91	124	17	to	to	ADP
hjic-91	124	18	the	the	DET
hjic-91	124	19	case	case	NOUN
hjic-91	124	20	when	when	SCONJ
hjic-91	124	21	an	an	DET
hjic-91	124	22	explicit	explicit	ADJ
hjic-91	124	23	solution	solution	NOUN
hjic-91	124	24	method	method	NOUN
hjic-91	124	25	was	be	AUX
hjic-91	124	26	assumed	assume	VERB
hjic-91	124	27	,	,	PUNCT
hjic-91	124	28	hence	hence	ADV
hjic-91	124	29	the	the	DET
hjic-91	124	30	following	follow	VERB
hjic-91	124	31	proposition	proposition	NOUN
hjic-91	124	32	holds	hold	VERB
hjic-91	124	33	.	.	PUNCT
hjic-91	125	1	proposition	proposition	NOUN
hjic-91	125	2	3	3	NUM
hjic-91	125	3	:	:	PUNCT
hjic-91	125	4	the	the	DET
hjic-91	125	5	differential	differential	ADJ
hjic-91	125	6	index	index	NOUN
hjic-91	125	7	of	of	ADP
hjic-91	125	8	model	model	NOUN
hjic-91	125	9	m	m	NOUN
hjic-91	125	10	is	be	AUX
hjic-91	125	11	equal	equal	ADJ
hjic-91	125	12	to	to	ADP
hjic-91	125	13	1	1	NUM
hjic-91	125	14	if	if	SCONJ
hjic-91	125	15	and	and	CCONJ
hjic-91	125	16	only	only	ADV
hjic-91	125	17	if	if	SCONJ
hjic-91	125	18	,	,	PUNCT
hjic-91	125	19	there	there	PRON
hjic-91	125	20	is	be	VERB
hjic-91	125	21	a	a	DET
hjic-91	125	22	mengertype	mengertype	ADJ
hjic-91	125	23	complete	complete	ADJ
hjic-91	125	24	linking	linking	NOUN
hjic-91	125	25	on	on	ADP
hjic-91	125	26	the	the	DET
hjic-91	125	27	reduced	reduce	VERB
hjic-91	125	28	graph	graph	NOUN
hjic-91	125	29	of	of	ADP
hjic-91	125	30	the	the	DET
hjic-91	125	31	algebraic	algebraic	ADJ
hjic-91	125	32	part	part	NOUN
hjic-91	125	33	of	of	ADP
hjic-91	125	34	the	the	DET
hjic-91	125	35	dynamic	dynamic	ADJ
hjic-91	125	36	representation	representation	NOUN
hjic-91	125	37	graph	graph	NOUN
hjic-91	125	38	belonging	belong	VERB
hjic-91	125	39	to	to	ADP
hjic-91	125	40	model	model	NOUN
hjic-91	125	41	m	m	PROPN
hjic-91	125	42	,	,	PUNCT
hjic-91	125	43	independently	independently	ADV
hjic-91	125	44	of	of	ADP
hjic-91	125	45	either	either	CCONJ
hjic-91	125	46	an	an	DET
hjic-91	125	47	explicit	explicit	ADJ
hjic-91	125	48	or	or	CCONJ
hjic-91	125	49	an	an	DET
hjic-91	125	50	implicit	implicit	ADJ
hjic-91	125	51	single	single	ADJ
hjic-91	125	52	step	step	NOUN
hjic-91	125	53	numerical	numerical	ADJ
hjic-91	125	54	solution	solution	NOUN
hjic-91	125	55	procedure	procedure	NOUN
hjic-91	125	56	is	be	AUX
hjic-91	125	57	applied	apply	VERB
hjic-91	125	58	for	for	ADP
hjic-91	125	59	the	the	DET
hjic-91	125	60	solution	solution	NOUN
hjic-91	125	61	of	of	ADP
hjic-91	125	62	the	the	DET
hjic-91	125	63	differential	differential	ADJ
hjic-91	125	64	equations	equation	NOUN
hjic-91	125	65	.	.	PUNCT
hjic-91	126	1	assume	assume	VERB
hjic-91	126	2	that	that	SCONJ
hjic-91	126	3	the	the	DET
hjic-91	126	4	values	value	NOUN
hjic-91	126	5	of	of	ADP
hjic-91	126	6	all	all	DET
hjic-91	126	7	derivative	derivative	ADJ
hjic-91	126	8	variables	variable	NOUN
hjic-91	126	9	x	x	NOUN
hjic-91	126	10	’	'	PUNCT
hjic-91	126	11	directly	directly	ADV
hjic-91	126	12	or	or	CCONJ
hjic-91	126	13	indirectly	indirectly	ADV
hjic-91	126	14	depend	depend	VERB
hjic-91	126	15	on	on	ADP
hjic-91	126	16	the	the	DET
hjic-91	126	17	corresponding	corresponding	ADJ
hjic-91	126	18	differential	differential	ADJ
hjic-91	126	19	variable	variable	NOUN
hjic-91	126	20	x	x	PROPN
hjic-91	126	21	in	in	ADP
hjic-91	126	22	the	the	DET
hjic-91	126	23	model	model	NOUN
hjic-91	126	24	.	.	PUNCT
hjic-91	127	1	this	this	DET
hjic-91	127	2	assumption	assumption	NOUN
hjic-91	127	3	holds	hold	VERB
hjic-91	127	4	for	for	ADP
hjic-91	127	5	stable	stable	ADJ
hjic-91	127	6	models	model	NOUN
hjic-91	127	7	.	.	PUNCT
hjic-91	128	1	as	as	ADP
hjic-91	128	2	a	a	DET
hjic-91	128	3	result	result	NOUN
hjic-91	128	4	of	of	ADP
hjic-91	128	5	this	this	DET
hjic-91	128	6	assumption	assumption	NOUN
hjic-91	128	7	a	a	DET
hjic-91	128	8	so	so	ADV
hjic-91	128	9	called	call	VERB
hjic-91	128	10	circle	circle	NOUN
hjic-91	128	11	of	of	ADP
hjic-91	128	12	calculation	calculation	NOUN
hjic-91	128	13	is	be	AUX
hjic-91	128	14	obtained	obtain	VERB
hjic-91	128	15	in	in	ADP
hjic-91	128	16	the	the	DET
hjic-91	128	17	representation	representation	NOUN
hjic-91	128	18	graph	graph	NOUN
hjic-91	128	19	belonging	belong	VERB
hjic-91	128	20	to	to	ADP
hjic-91	128	21	the	the	DET
hjic-91	128	22	differential	differential	ADJ
hjic-91	128	23	variables	variable	NOUN
hjic-91	128	24	according	accord	VERB
hjic-91	128	25	to	to	ADP
hjic-91	128	26	the	the	DET
hjic-91	128	27	following	follow	VERB
hjic-91	128	28	definition	definition	NOUN
hjic-91	128	29	.	.	PUNCT
hjic-91	129	1	18	18	NUM
hjic-91	129	2	p3	p3	PROPN
hjic-91	129	3	p2	p2	PROPN
hjic-91	129	4	p1	p1	NOUN
hjic-91	129	5	p0	p0	NOUN
hjic-91	129	6	<	<	X
hjic-91	129	7	s	s	X
hjic-91	129	8	>	>	X
hjic-91	129	9	l	l	NOUN
hjic-91	129	10	<	<	X
hjic-91	129	11	s	s	X
hjic-91	129	12	>	>	X
hjic-91	129	13	l	l	NOUN
hjic-91	129	14	'	'	PUNCT
hjic-91	129	15	=	=	SYM
hjic-91	129	16	k1	k1	PROPN
hjic-91	129	17	f2	f2	PROPN
hjic-91	129	18	s	s	X
hjic-91	129	19	<	<	X
hjic-91	129	20	g	g	X
hjic-91	129	21	>	>	X
hjic-91	129	22	<	<	X
hjic-91	129	23	s	s	PROPN
hjic-91	129	24	*	*	X
hjic-91	129	25	>	>	X
hjic-91	129	26	<	<	X
hjic-91	129	27	s	s	X
hjic-91	129	28	>	>	X
hjic-91	129	29	f1	f1	PROPN
hjic-91	129	30	p3	p3	PROPN
hjic-91	129	31	p2	p2	PROPN
hjic-91	129	32	p1	p1	NOUN
hjic-91	129	33	p0	p0	NOUN
hjic-91	129	34	<	<	X
hjic-91	129	35	s	s	X
hjic-91	129	36	>	>	X
hjic-91	129	37	l	l	NOUN
hjic-91	129	38	<	<	X
hjic-91	129	39	s	s	X
hjic-91	129	40	>	>	X
hjic-91	129	41	l	l	NOUN
hjic-91	129	42	'	'	PUNCT
hjic-91	129	43	f2	f2	PROPN
hjic-91	129	44	s	s	VERB
hjic-91	129	45	<	<	X
hjic-91	129	46	g	g	X
hjic-91	129	47	>	>	X
hjic-91	129	48	<	<	X
hjic-91	129	49	s	s	PROPN
hjic-91	129	50	*	*	X
hjic-91	129	51	>	>	X
hjic-91	129	52	<	<	X
hjic-91	129	53	s	s	X
hjic-91	129	54	>	>	X
hjic-91	129	55	f1	f1	PROPN
hjic-91	129	56	p3	p3	PROPN
hjic-91	129	57	p2	p2	PROPN
hjic-91	129	58	p1	p1	NOUN
hjic-91	129	59	p0	p0	NOUN
hjic-91	129	60	<	<	X
hjic-91	129	61	s	s	X
hjic-91	129	62	>	>	X
hjic-91	129	63	<	<	X
hjic-91	129	64	s	s	X
hjic-91	129	65	>	>	X
hjic-91	129	66	l	l	NOUN
hjic-91	129	67	'	'	PUNCT
hjic-91	129	68	=	=	SYM
hjic-91	129	69	k2	k2	PROPN
hjic-91	129	70	f2	f2	PROPN
hjic-91	129	71	s	s	VERB
hjic-91	129	72	<	<	X
hjic-91	129	73	g	g	X
hjic-91	129	74	>	>	X
hjic-91	129	75	<	<	X
hjic-91	129	76	s	s	X
hjic-91	129	77	>	>	X
hjic-91	129	78	f1	f1	PROPN
hjic-91	129	79	p3	p3	PROPN
hjic-91	129	80	p2	p2	PROPN
hjic-91	129	81	p1	p1	NOUN
hjic-91	129	82	p0	p0	NOUN
hjic-91	129	83	<	<	X
hjic-91	129	84	s	s	X
hjic-91	129	85	>	>	X
hjic-91	129	86	<	<	X
hjic-91	129	87	s	s	X
hjic-91	129	88	>	>	X
hjic-91	129	89	l	l	NOUN
hjic-91	129	90	'	'	PUNCT
hjic-91	129	91	=	=	PRON
hjic-91	130	1	k3	k3	VERB
hjic-91	130	2	f2	f2	PROPN
hjic-91	130	3	s	s	PART
hjic-91	130	4	<	<	X
hjic-91	130	5	g	g	X
hjic-91	130	6	>	>	X
hjic-91	130	7	<	<	X
hjic-91	130	8	s	s	X
hjic-91	130	9	>	>	X
hjic-91	130	10	f1	f1	PROPN
hjic-91	130	11	p3	p3	PROPN
hjic-91	130	12	p2	p2	PROPN
hjic-91	130	13	p1	p1	NOUN
hjic-91	130	14	p0	p0	NOUN
hjic-91	130	15	<	<	X
hjic-91	130	16	s	s	X
hjic-91	130	17	>	>	X
hjic-91	130	18	<	<	X
hjic-91	130	19	s	s	X
hjic-91	130	20	>	>	X
hjic-91	130	21	l	l	NOUN
hjic-91	130	22	'	'	PUNCT
hjic-91	130	23	=	=	NOUN
hjic-91	130	24	k4	k4	NOUN
hjic-91	130	25	f2	f2	PROPN
hjic-91	130	26	s	s	PART
hjic-91	130	27	<	<	X
hjic-91	130	28	g	g	X
hjic-91	130	29	>	>	X
hjic-91	130	30	<	<	X
hjic-91	130	31	s	s	X
hjic-91	130	32	>	>	X
hjic-91	130	33	f1	f1	PROPN
hjic-91	130	34	t	t	PROPN
hjic-91	130	35	+	+	CCONJ
hjic-91	130	36	h/2	h/2	X
hjic-91	130	37	t	t	NOUN
hjic-91	130	38	+	+	CCONJ
hjic-91	130	39	h/2	h/2	X
hjic-91	130	40	t	t	NOUN
hjic-91	130	41	+	+	CCONJ
hjic-91	130	42	h	h	NOUN
hjic-91	130	43	t	t	NOUN
hjic-91	131	1	+	+	CCONJ
hjic-91	131	2	ht	ht	PROPN
hjic-91	131	3	fig.9	fig.9	PROPN
hjic-91	131	4	representation	representation	NOUN
hjic-91	131	5	graph	graph	NOUN
hjic-91	131	6	of	of	ADP
hjic-91	131	7	model	model	NOUN
hjic-91	131	8	m2	m2	PROPN
hjic-91	131	9	assuming	assume	VERB
hjic-91	131	10	fourth	fourth	ADJ
hjic-91	131	11	order	order	NOUN
hjic-91	131	12	explicit	explicit	ADJ
hjic-91	131	13	runge	runge	NOUN
hjic-91	131	14	-	-	PUNCT
hjic-91	131	15	kutta	kutta	NOUN
hjic-91	131	16	method	method	NOUN
hjic-91	131	17	definition	definition	NOUN
hjic-91	131	18	:	:	PUNCT
hjic-91	131	19	the	the	DET
hjic-91	131	20	circle	circle	NOUN
hjic-91	131	21	of	of	ADP
hjic-91	131	22	calculation	calculation	NOUN
hjic-91	131	23	belonging	belong	VERB
hjic-91	131	24	to	to	ADP
hjic-91	131	25	the	the	DET
hjic-91	131	26	differential	differential	ADJ
hjic-91	131	27	variable	variable	NOUN
hjic-91	131	28	x	x	VERB
hjic-91	131	29	is	be	AUX
hjic-91	131	30	a	a	DET
hjic-91	131	31	directed	direct	VERB
hjic-91	131	32	circle	circle	NOUN
hjic-91	131	33	path	path	NOUN
hjic-91	131	34	,	,	PUNCT
hjic-91	131	35	which	which	PRON
hjic-91	131	36	contains	contain	VERB
hjic-91	131	37	the	the	DET
hjic-91	131	38	vertices	vertex	NOUN
hjic-91	131	39	x	x	PUNCT
hjic-91	131	40	and	and	CCONJ
hjic-91	131	41	x	x	NOUN
hjic-91	131	42	’	'	PUNCT
hjic-91	131	43	and	and	CCONJ
hjic-91	131	44	this	this	DET
hjic-91	131	45	directed	direct	VERB
hjic-91	131	46	circle	circle	NOUN
hjic-91	131	47	is	be	AUX
hjic-91	131	48	either	either	DET
hjic-91	131	49	1	1	NUM
hjic-91	131	50	.	.	PUNCT
hjic-91	131	51	present	present	ADJ
hjic-91	131	52	on	on	ADP
hjic-91	131	53	the	the	DET
hjic-91	131	54	representation	representation	NOUN
hjic-91	131	55	graph	graph	NOUN
hjic-91	131	56	(	(	PUNCT
hjic-91	131	57	type	type	NOUN
hjic-91	131	58	1	1	NUM
hjic-91	131	59	circle	circle	NOUN
hjic-91	131	60	of	of	ADP
hjic-91	131	61	calculation	calculation	NOUN
hjic-91	131	62	)	)	PUNCT
hjic-91	131	63	,	,	PUNCT
hjic-91	131	64	or	or	CCONJ
hjic-91	132	1	2	2	NUM
hjic-91	132	2	.	.	PUNCT
hjic-91	133	1	if	if	SCONJ
hjic-91	133	2	it	it	PRON
hjic-91	133	3	is	be	AUX
hjic-91	133	4	absent	absent	ADJ
hjic-91	133	5	,	,	PUNCT
hjic-91	133	6	then	then	ADV
hjic-91	133	7	the	the	DET
hjic-91	133	8	basic	basic	ADJ
hjic-91	133	9	undirected	undirected	ADJ
hjic-91	133	10	circle	circle	NOUN
hjic-91	133	11	(	(	PUNCT
hjic-91	133	12	when	when	SCONJ
hjic-91	133	13	directions	direction	NOUN
hjic-91	133	14	of	of	ADP
hjic-91	133	15	arcs	arc	NOUN
hjic-91	133	16	are	be	AUX
hjic-91	133	17	not	not	PART
hjic-91	133	18	to	to	PART
hjic-91	133	19	be	be	AUX
hjic-91	133	20	considered	consider	VERB
hjic-91	133	21	)	)	PUNCT
hjic-91	133	22	can	can	AUX
hjic-91	133	23	be	be	AUX
hjic-91	133	24	found	find	VERB
hjic-91	133	25	on	on	ADP
hjic-91	133	26	the	the	DET
hjic-91	133	27	representation	representation	NOUN
hjic-91	133	28	graph	graph	NOUN
hjic-91	133	29	and	and	CCONJ
hjic-91	133	30	the	the	DET
hjic-91	133	31	circle	circle	NOUN
hjic-91	133	32	of	of	ADP
hjic-91	133	33	calculation	calculation	NOUN
hjic-91	133	34	can	can	AUX
hjic-91	133	35	be	be	AUX
hjic-91	133	36	obtained	obtain	VERB
hjic-91	133	37	by	by	ADP
hjic-91	133	38	changing	change	VERB
hjic-91	133	39	the	the	DET
hjic-91	133	40	direction	direction	NOUN
hjic-91	133	41	of	of	ADP
hjic-91	133	42	some	some	DET
hjic-91	133	43	arcs	arc	NOUN
hjic-91	133	44	(	(	PUNCT
hjic-91	133	45	type	type	NOUN
hjic-91	133	46	2	2	NUM
hjic-91	133	47	circle	circle	NOUN
hjic-91	133	48	of	of	ADP
hjic-91	133	49	calculation	calculation	NOUN
hjic-91	133	50	)	)	PUNCT
hjic-91	133	51	.	.	PUNCT
hjic-91	134	1	the	the	DET
hjic-91	134	2	direction	direction	NOUN
hjic-91	134	3	of	of	ADP
hjic-91	134	4	arc	arc	NOUN
hjic-91	134	5	x1→x2	x1→x2	PROPN
hjic-91	134	6	can	can	AUX
hjic-91	134	7	be	be	AUX
hjic-91	134	8	changed	change	VERB
hjic-91	134	9	,	,	PUNCT
hjic-91	134	10	if	if	SCONJ
hjic-91	134	11	there	there	PRON
hjic-91	134	12	exists	exist	VERB
hjic-91	134	13	a	a	DET
hjic-91	134	14	menger	menger	NOUN
hjic-91	134	15	type	type	NOUN
hjic-91	134	16	complete	complete	ADJ
hjic-91	134	17	linking	linking	NOUN
hjic-91	134	18	on	on	ADP
hjic-91	134	19	the	the	DET
hjic-91	134	20	reduced	reduced	ADJ
hjic-91	134	21	algebraic	algebraic	ADJ
hjic-91	134	22	subgraph	subgraph	NOUN
hjic-91	134	23	,	,	PUNCT
hjic-91	134	24	which	which	PRON
hjic-91	134	25	contains	contain	VERB
hjic-91	134	26	it	it	PRON
hjic-91	134	27	.	.	PUNCT
hjic-91	135	1	x	x	X
hjic-91	136	1	x1	x1	NUM
hjic-91	136	2	xn	xn	PUNCT
hjic-91	136	3	x	x	X
hjic-91	136	4	'	'	X
hjic-91	136	5	t	t	NOUN
hjic-91	136	6	x	x	SYM
hjic-91	137	1	x1	x1	PROPN
hjic-91	137	2	xn	xn	PUNCT
hjic-91	137	3	x	x	X
hjic-91	137	4	'	'	PUNCT
hjic-91	137	5	t+h	t+h	NUM
hjic-91	137	6	fig.10	fig.10	DET
hjic-91	137	7	dynamic	dynamic	ADJ
hjic-91	137	8	representation	representation	NOUN
hjic-91	137	9	graph	graph	NOUN
hjic-91	137	10	assuming	assume	VERB
hjic-91	137	11	single	single	ADJ
hjic-91	137	12	implicit	implicit	ADJ
hjic-91	137	13	solution	solution	NOUN
hjic-91	137	14	method	method	NOUN
hjic-91	137	15	19	19	NUM
hjic-91	137	16	m	m	NOUN
hjic-91	137	17	t	t	NOUN
hjic-91	137	18	t+h	t+h	X
hjic-91	137	19	f	f	X
hjic-91	137	20	u	u	NOUN
hjic-91	137	21	tl	tl	PROPN
hjic-91	137	22	p	p	X
hjic-91	137	23	tf	tf	X
hjic-91	137	24	<	<	X
hjic-91	137	25	s	s	X
hjic-91	137	26	>	>	X
hjic-91	137	27	pf	pf	X
hjic-91	137	28	<	<	X
hjic-91	137	29	s	s	X
hjic-91	137	30	>	>	X
hjic-91	137	31	q	q	X
hjic-91	137	32	<	<	X
hjic-91	137	33	c	c	X
hjic-91	137	34	>	>	X
hjic-91	137	35	<	<	X
hjic-91	137	36	s	s	X
hjic-91	137	37	>	>	X
hjic-91	137	38	l	l	NOUN
hjic-91	137	39	hl	hl	NOUN
hjic-91	137	40	hl	hl	PROPN
hjic-91	137	41	*	*	PUNCT
hjic-91	137	42	hf	hf	PROPN
hjic-91	137	43	u	u	NOUN
hjic-91	137	44	'	'	PART
hjic-91	137	45	m	m	VERB
hjic-91	137	46	'	'	PUNCT
hjic-91	137	47	s	s	PART
hjic-91	137	48	<	<	X
hjic-91	137	49	g	g	X
hjic-91	137	50	>	>	X
hjic-91	137	51	<	<	X
hjic-91	137	52	s	s	X
hjic-91	137	53	>	>	X
hjic-91	137	54	<	<	X
hjic-91	137	55	c	c	X
hjic-91	137	56	>	>	X
hjic-91	137	57	<	<	X
hjic-91	137	58	s	s	X
hjic-91	137	59	>	>	X
hjic-91	137	60	m	m	PROPN
hjic-91	137	61	f	f	NOUN
hjic-91	137	62	u	u	NOUN
hjic-91	137	63	tl	tl	PROPN
hjic-91	137	64	p	p	X
hjic-91	137	65	tf	tf	X
hjic-91	137	66	<	<	X
hjic-91	137	67	s	s	X
hjic-91	137	68	>	>	X
hjic-91	137	69	pf	pf	X
hjic-91	137	70	<	<	X
hjic-91	137	71	s	s	X
hjic-91	137	72	>	>	X
hjic-91	137	73	q	q	X
hjic-91	137	74	<	<	X
hjic-91	137	75	s	s	PROPN
hjic-91	137	76	*	*	X
hjic-91	137	77	>	>	X
hjic-91	137	78	<	<	X
hjic-91	137	79	s	s	X
hjic-91	137	80	>	>	X
hjic-91	137	81	l	l	NOUN
hjic-91	137	82	hl	hl	PROPN
hjic-91	137	83	hf	hf	PROPN
hjic-91	137	84	u	u	PROPN
hjic-91	137	85	'	'	PART
hjic-91	137	86	m	m	VERB
hjic-91	137	87	'	'	PUNCT
hjic-91	137	88	s	s	PART
hjic-91	137	89	<	<	X
hjic-91	137	90	g	g	X
hjic-91	137	91	>	>	X
hjic-91	137	92	<	<	X
hjic-91	137	93	s	s	X
hjic-91	137	94	>	>	X
hjic-91	137	95	<	<	X
hjic-91	137	96	c	c	X
hjic-91	137	97	>	>	X
hjic-91	137	98	<	<	X
hjic-91	137	99	s	s	X
hjic-91	137	100	>	>	X
hjic-91	137	101	hl	hl	NOUN
hjic-91	137	102	*	*	PUNCT
hjic-91	137	103	fig.11	fig.11	NOUN
hjic-91	137	104	representation	representation	NOUN
hjic-91	137	105	graph	graph	NOUN
hjic-91	137	106	of	of	ADP
hjic-91	137	107	model	model	NOUN
hjic-91	137	108	m1	m1	PROPN
hjic-91	137	109	with	with	ADP
hjic-91	137	110	specification	specification	NOUN
hjic-91	137	111	1	1	NUM
hjic-91	137	112	assuming	assume	VERB
hjic-91	137	113	an	an	DET
hjic-91	137	114	implicit	implicit	ADJ
hjic-91	137	115	solution	solution	NOUN
hjic-91	137	116	method	method	NOUN
hjic-91	137	117	(	(	PUNCT
hjic-91	137	118	circle	circle	NOUN
hjic-91	137	119	of	of	ADP
hjic-91	137	120	calculation	calculation	NOUN
hjic-91	137	121	)	)	PUNCT
hjic-91	137	122	the	the	DET
hjic-91	137	123	representation	representation	NOUN
hjic-91	137	124	graphs	graph	NOUN
hjic-91	137	125	of	of	ADP
hjic-91	137	126	models	model	NOUN
hjic-91	137	127	in	in	ADP
hjic-91	137	128	examples	example	NOUN
hjic-91	137	129	1	1	NUM
hjic-91	137	130	.	.	PUNCT
hjic-91	137	131	and	and	CCONJ
hjic-91	137	132	2	2	X
hjic-91	137	133	.	.	X
hjic-91	137	134	assuming	assume	VERB
hjic-91	137	135	implicit	implicit	ADJ
hjic-91	137	136	method	method	NOUN
hjic-91	137	137	for	for	ADP
hjic-91	137	138	the	the	DET
hjic-91	137	139	numerical	numerical	ADJ
hjic-91	137	140	solution	solution	NOUN
hjic-91	137	141	of	of	ADP
hjic-91	137	142	differential	differential	ADJ
hjic-91	137	143	equations	equation	NOUN
hjic-91	137	144	can	can	AUX
hjic-91	137	145	be	be	AUX
hjic-91	137	146	seen	see	VERB
hjic-91	137	147	in	in	ADP
hjic-91	137	148	figs.11	figs.11	ADJ
hjic-91	137	149	and	and	CCONJ
hjic-91	137	150	12	12	NUM
hjic-91	137	151	.	.	PUNCT
hjic-91	138	1	type	type	NOUN
hjic-91	138	2	1	1	NUM
hjic-91	138	3	circles	circle	NOUN
hjic-91	138	4	of	of	ADP
hjic-91	138	5	calculation	calculation	NOUN
hjic-91	138	6	can	can	AUX
hjic-91	138	7	be	be	AUX
hjic-91	138	8	seen	see	VERB
hjic-91	138	9	in	in	ADP
hjic-91	138	10	fig.11	fig.11	NOUN
hjic-91	138	11	,	,	PUNCT
hjic-91	138	12	where	where	SCONJ
hjic-91	138	13	the	the	DET
hjic-91	138	14	directed	direct	VERB
hjic-91	138	15	circles	circle	NOUN
hjic-91	138	16	containing	contain	VERB
hjic-91	138	17	m	m	PROPN
hjic-91	138	18	and	and	CCONJ
hjic-91	138	19	m	m	NOUN
hjic-91	138	20	’	'	PUNCT
hjic-91	138	21	or	or	CCONJ
hjic-91	138	22	u	u	PROPN
hjic-91	138	23	and	and	CCONJ
hjic-91	138	24	u	u	NOUN
hjic-91	138	25	’	'	PUNCT
hjic-91	138	26	are	be	AUX
hjic-91	138	27	present	present	ADJ
hjic-91	138	28	in	in	ADP
hjic-91	138	29	the	the	DET
hjic-91	138	30	representation	representation	NOUN
hjic-91	138	31	graph	graph	NOUN
hjic-91	138	32	.	.	PUNCT
hjic-91	139	1	a	a	DET
hjic-91	139	2	type	type	NOUN
hjic-91	139	3	2	2	NUM
hjic-91	139	4	circle	circle	NOUN
hjic-91	139	5	of	of	ADP
hjic-91	139	6	calculation	calculation	NOUN
hjic-91	139	7	can	can	AUX
hjic-91	139	8	be	be	AUX
hjic-91	139	9	found	find	VERB
hjic-91	139	10	in	in	ADP
hjic-91	139	11	fig.12	fig.12	NOUN
hjic-91	139	12	,	,	PUNCT
hjic-91	139	13	where	where	SCONJ
hjic-91	139	14	the	the	DET
hjic-91	139	15	directed	direct	VERB
hjic-91	139	16	circle	circle	NOUN
hjic-91	139	17	belonging	belong	VERB
hjic-91	139	18	to	to	ADP
hjic-91	139	19	variable	variable	ADJ
hjic-91	139	20	l	l	NOUN
hjic-91	139	21	can	can	AUX
hjic-91	139	22	be	be	AUX
hjic-91	139	23	obtained	obtain	VERB
hjic-91	139	24	by	by	ADP
hjic-91	139	25	changing	change	VERB
hjic-91	139	26	the	the	DET
hjic-91	139	27	direction	direction	NOUN
hjic-91	139	28	of	of	ADP
hjic-91	139	29	arc	arc	NOUN
hjic-91	139	30	p2→s	p2→s	PUNCT
hjic-91	139	31	.	.	PUNCT
hjic-91	140	1	according	accord	VERB
hjic-91	140	2	to	to	ADP
hjic-91	140	3	the	the	DET
hjic-91	140	4	directed	direct	VERB
hjic-91	140	5	circle	circle	NOUN
hjic-91	140	6	of	of	ADP
hjic-91	140	7	calculation	calculation	NOUN
hjic-91	140	8	the	the	DET
hjic-91	140	9	values	value	NOUN
hjic-91	140	10	of	of	ADP
hjic-91	140	11	some	some	DET
hjic-91	140	12	variables	variable	NOUN
hjic-91	140	13	(	(	PUNCT
hjic-91	140	14	for	for	ADP
hjic-91	140	15	example	example	NOUN
hjic-91	140	16	x	x	PUNCT
hjic-91	140	17	and	and	CCONJ
hjic-91	140	18	x	x	NOUN
hjic-91	140	19	’	'	PUNCT
hjic-91	140	20	)	)	PUNCT
hjic-91	140	21	can	can	AUX
hjic-91	140	22	be	be	AUX
hjic-91	140	23	calculated	calculate	VERB
hjic-91	140	24	at	at	ADP
hjic-91	140	25	any	any	DET
hjic-91	140	26	time	time	NOUN
hjic-91	140	27	t	t	NOUN
hjic-91	140	28	by	by	ADP
hjic-91	140	29	iteration	iteration	NOUN
hjic-91	140	30	.	.	PUNCT
hjic-91	141	1	therefore	therefore	ADV
hjic-91	141	2	we	we	PRON
hjic-91	141	3	propose	propose	VERB
hjic-91	141	4	a	a	DET
hjic-91	141	5	new	new	ADJ
hjic-91	141	6	type	type	NOUN
hjic-91	141	7	of	of	ADP
hjic-91	141	8	assignment	assignment	NOUN
hjic-91	141	9	for	for	ADP
hjic-91	141	10	all	all	DET
hjic-91	141	11	differential	differential	ADJ
hjic-91	141	12	variables	variable	NOUN
hjic-91	141	13	:	:	PUNCT
hjic-91	141	14	p3	p3	NOUN
hjic-91	141	15	p2	p2	PROPN
hjic-91	141	16	p1	p1	NOUN
hjic-91	141	17	p0	p0	NOUN
hjic-91	141	18	<	<	X
hjic-91	141	19	s	s	X
hjic-91	141	20	>	>	X
hjic-91	141	21	l	l	NOUN
hjic-91	142	1	<	<	X
hjic-91	142	2	s	s	X
hjic-91	142	3	>	>	X
hjic-91	142	4	l	l	NOUN
hjic-91	142	5	'	'	PUNCT
hjic-91	142	6	f2	f2	PROPN
hjic-91	142	7	s	s	VERB
hjic-91	142	8	<	<	X
hjic-91	142	9	g	g	X
hjic-91	142	10	>	>	X
hjic-91	142	11	<	<	X
hjic-91	142	12	c	c	X
hjic-91	142	13	>	>	X
hjic-91	142	14	<	<	X
hjic-91	142	15	s	s	X
hjic-91	142	16	>	>	X
hjic-91	142	17	f1	f1	PROPN
hjic-91	142	18	p3	p3	PROPN
hjic-91	142	19	p2	p2	PROPN
hjic-91	142	20	p1	p1	NOUN
hjic-91	142	21	p0	p0	NOUN
hjic-91	142	22	<	<	X
hjic-91	142	23	s	s	X
hjic-91	142	24	>	>	X
hjic-91	142	25	l	l	NOUN
hjic-91	142	26	<	<	X
hjic-91	142	27	s	s	X
hjic-91	142	28	>	>	X
hjic-91	142	29	l	l	NOUN
hjic-91	142	30	'	'	PUNCT
hjic-91	142	31	f2	f2	PROPN
hjic-91	142	32	s	s	VERB
hjic-91	142	33	<	<	X
hjic-91	142	34	g	g	X
hjic-91	142	35	>	>	X
hjic-91	142	36	<	<	X
hjic-91	142	37	c	c	X
hjic-91	142	38	>	>	X
hjic-91	142	39	<	<	X
hjic-91	142	40	s	s	X
hjic-91	142	41	>	>	X
hjic-91	142	42	f1	f1	PROPN
hjic-91	142	43	t	t	PROPN
hjic-91	142	44	t+h	t+h	NUM
hjic-91	142	45	fig.12	fig.12	NOUN
hjic-91	142	46	representation	representation	NOUN
hjic-91	142	47	graph	graph	NOUN
hjic-91	142	48	of	of	ADP
hjic-91	142	49	model	model	NOUN
hjic-91	142	50	m2	m2	PROPN
hjic-91	142	51	assuming	assume	VERB
hjic-91	142	52	an	an	DET
hjic-91	142	53	implicit	implicit	ADJ
hjic-91	142	54	solution	solution	NOUN
hjic-91	142	55	method	method	NOUN
hjic-91	142	56	•	•	ADP
hjic-91	142	57	<	<	X
hjic-91	142	58	c	c	X
hjic-91	142	59	>	>	X
hjic-91	142	60	circle	circle	NOUN
hjic-91	142	61	-	-	PUNCT
hjic-91	142	62	type	type	NOUN
hjic-91	142	63	variables	variable	NOUN
hjic-91	142	64	:	:	PUNCT
hjic-91	142	65	let	let	VERB
hjic-91	142	66	<	<	X
hjic-91	142	67	c	c	X
hjic-91	142	68	>	>	X
hjic-91	142	69	be	be	AUX
hjic-91	142	70	the	the	DET
hjic-91	142	71	label	label	NOUN
hjic-91	142	72	of	of	ADP
hjic-91	142	73	all	all	DET
hjic-91	142	74	differential	differential	ADJ
hjic-91	142	75	variables	variable	NOUN
hjic-91	142	76	in	in	ADP
hjic-91	142	77	the	the	DET
hjic-91	142	78	representation	representation	NOUN
hjic-91	142	79	graph	graph	NOUN
hjic-91	142	80	,	,	PUNCT
hjic-91	142	81	which	which	PRON
hjic-91	142	82	indicates	indicate	VERB
hjic-91	142	83	that	that	SCONJ
hjic-91	142	84	the	the	DET
hjic-91	142	85	values	value	NOUN
hjic-91	142	86	of	of	ADP
hjic-91	142	87	these	these	DET
hjic-91	142	88	variables	variable	NOUN
hjic-91	142	89	can	can	AUX
hjic-91	142	90	be	be	AUX
hjic-91	142	91	calculated	calculate	VERB
hjic-91	142	92	by	by	ADP
hjic-91	142	93	iteration	iteration	NOUN
hjic-91	142	94	only	only	ADV
hjic-91	142	95	.	.	PUNCT
hjic-91	143	1	these	these	DET
hjic-91	143	2	labels	label	NOUN
hjic-91	143	3	can	can	AUX
hjic-91	143	4	be	be	AUX
hjic-91	143	5	seen	see	VERB
hjic-91	143	6	in	in	ADP
hjic-91	143	7	figs.11	figs.11	ADJ
hjic-91	143	8	and	and	CCONJ
hjic-91	143	9	12	12	NUM
hjic-91	143	10	.	.	NOUN
hjic-91	143	11	20	20	NUM
hjic-91	143	12	reduction	reduction	NOUN
hjic-91	143	13	of	of	ADP
hjic-91	143	14	representation	representation	NOUN
hjic-91	143	15	graphs	graph	NOUN
hjic-91	143	16	assuming	assume	VERB
hjic-91	143	17	an	an	DET
hjic-91	143	18	implicit	implicit	ADJ
hjic-91	143	19	solution	solution	NOUN
hjic-91	143	20	method	method	VERB
hjic-91	143	21	the	the	DET
hjic-91	143	22	reduction	reduction	NOUN
hjic-91	143	23	of	of	ADP
hjic-91	143	24	representation	representation	NOUN
hjic-91	143	25	graphs	graph	NOUN
hjic-91	143	26	can	can	AUX
hjic-91	143	27	be	be	AUX
hjic-91	143	28	performed	perform	VERB
hjic-91	143	29	in	in	ADP
hjic-91	143	30	this	this	DET
hjic-91	143	31	case	case	NOUN
hjic-91	143	32	in	in	ADP
hjic-91	143	33	two	two	NUM
hjic-91	143	34	steps	step	NOUN
hjic-91	143	35	:	:	PUNCT
hjic-91	143	36	the	the	DET
hjic-91	143	37	primary	primary	ADJ
hjic-91	143	38	reduction	reduction	NOUN
hjic-91	143	39	is	be	AUX
hjic-91	143	40	the	the	DET
hjic-91	143	41	same	same	ADJ
hjic-91	143	42	as	as	ADP
hjic-91	143	43	in	in	ADP
hjic-91	143	44	the	the	DET
hjic-91	143	45	case	case	NOUN
hjic-91	143	46	of	of	ADP
hjic-91	143	47	explicit	explicit	ADJ
hjic-91	143	48	solution	solution	NOUN
hjic-91	143	49	methods	method	NOUN
hjic-91	143	50	:	:	PUNCT
hjic-91	143	51	the	the	DET
hjic-91	143	52	primary	primary	ADJ
hjic-91	143	53	reduced	reduce	VERB
hjic-91	143	54	graph	graph	NOUN
hjic-91	143	55	can	can	AUX
hjic-91	143	56	be	be	AUX
hjic-91	143	57	obtained	obtain	VERB
hjic-91	143	58	by	by	ADP
hjic-91	143	59	omitting	omit	VERB
hjic-91	143	60	all	all	DET
hjic-91	143	61	vertices	vertex	NOUN
hjic-91	143	62	labelled	label	VERB
hjic-91	143	63	primarily	primarily	ADV
hjic-91	143	64	,	,	PUNCT
hjic-91	143	65	secondarily	secondarily	ADV
hjic-91	143	66	,	,	PUNCT
hjic-91	143	67	etc	etc	X
hjic-91	143	68	.	.	X
hjic-91	143	69	,	,	PUNCT
hjic-91	143	70	by	by	ADP
hjic-91	143	71	type	type	NOUN
hjic-91	143	72	<	<	X
hjic-91	143	73	s	s	X
hjic-91	143	74	>	>	X
hjic-91	143	75	and	and	CCONJ
hjic-91	143	76	all	all	DET
hjic-91	143	77	arcs	arc	NOUN
hjic-91	143	78	starting	start	VERB
hjic-91	143	79	from	from	ADP
hjic-91	143	80	them	they	PRON
hjic-91	143	81	.	.	PUNCT
hjic-91	144	1	the	the	DET
hjic-91	144	2	primary	primary	ADJ
hjic-91	144	3	reduced	reduce	VERB
hjic-91	144	4	graphs	graph	NOUN
hjic-91	144	5	of	of	ADP
hjic-91	144	6	the	the	DET
hjic-91	144	7	investigated	investigate	VERB
hjic-91	144	8	models	model	NOUN
hjic-91	144	9	can	can	AUX
hjic-91	144	10	be	be	AUX
hjic-91	144	11	seen	see	VERB
hjic-91	144	12	in	in	ADP
hjic-91	144	13	figs.13	figs.13	NOUN
hjic-91	144	14	and	and	CCONJ
hjic-91	144	15	14	14	NUM
hjic-91	144	16	.	.	PUNCT
hjic-91	145	1	the	the	DET
hjic-91	145	2	primary	primary	ADJ
hjic-91	145	3	reduction	reduction	NOUN
hjic-91	145	4	is	be	AUX
hjic-91	145	5	directed	direct	VERB
hjic-91	145	6	both	both	PRON
hjic-91	145	7	to	to	ADP
hjic-91	145	8	the	the	DET
hjic-91	145	9	implicit	implicit	ADJ
hjic-91	145	10	part	part	NOUN
hjic-91	145	11	of	of	ADP
hjic-91	145	12	the	the	DET
hjic-91	145	13	model	model	NOUN
hjic-91	145	14	and	and	CCONJ
hjic-91	145	15	to	to	ADP
hjic-91	145	16	the	the	DET
hjic-91	145	17	iterations	iteration	NOUN
hjic-91	145	18	belonging	belong	VERB
hjic-91	145	19	to	to	ADP
hjic-91	145	20	the	the	DET
hjic-91	145	21	differential	differential	ADJ
hjic-91	145	22	variables	variable	NOUN
hjic-91	145	23	.	.	PUNCT
hjic-91	146	1	in	in	ADP
hjic-91	146	2	the	the	DET
hjic-91	146	3	first	first	ADJ
hjic-91	146	4	case	case	NOUN
hjic-91	146	5	(	(	PUNCT
hjic-91	146	6	fig.13	fig.13	NOUN
hjic-91	146	7	)	)	PUNCT
hjic-91	146	8	iterations	iteration	NOUN
hjic-91	146	9	can	can	AUX
hjic-91	146	10	be	be	AUX
hjic-91	146	11	calculated	calculate	VERB
hjic-91	146	12	independently	independently	ADV
hjic-91	146	13	of	of	ADP
hjic-91	146	14	the	the	DET
hjic-91	146	15	implicit	implicit	ADJ
hjic-91	146	16	calculation	calculation	NOUN
hjic-91	146	17	and	and	CCONJ
hjic-91	146	18	the	the	DET
hjic-91	146	19	sequence	sequence	NOUN
hjic-91	146	20	of	of	ADP
hjic-91	146	21	the	the	DET
hjic-91	146	22	calculation	calculation	NOUN
hjic-91	146	23	steps	step	NOUN
hjic-91	146	24	can	can	AUX
hjic-91	146	25	be	be	AUX
hjic-91	146	26	seen	see	VERB
hjic-91	146	27	,	,	PUNCT
hjic-91	146	28	too	too	ADV
hjic-91	146	29	.	.	PUNCT
hjic-91	147	1	in	in	ADP
hjic-91	147	2	the	the	DET
hjic-91	147	3	second	second	ADJ
hjic-91	147	4	case	case	NOUN
hjic-91	147	5	(	(	PUNCT
hjic-91	147	6	fig.14	fig.14	NOUN
hjic-91	147	7	)	)	PUNCT
hjic-91	147	8	the	the	DET
hjic-91	147	9	implicit	implicit	ADJ
hjic-91	147	10	calculation	calculation	NOUN
hjic-91	147	11	of	of	ADP
hjic-91	147	12	the	the	DET
hjic-91	147	13	algebraic	algebraic	ADJ
hjic-91	147	14	variable	variable	ADJ
hjic-91	147	15	p2	p2	NOUN
hjic-91	147	16	is	be	AUX
hjic-91	147	17	a	a	DET
hjic-91	147	18	part	part	NOUN
hjic-91	147	19	of	of	ADP
hjic-91	147	20	the	the	DET
hjic-91	147	21	iteration	iteration	NOUN
hjic-91	147	22	,	,	PUNCT
hjic-91	147	23	hence	hence	ADV
hjic-91	147	24	the	the	DET
hjic-91	147	25	value	value	NOUN
hjic-91	147	26	of	of	ADP
hjic-91	147	27	p2	p2	PROPN
hjic-91	147	28	can	can	AUX
hjic-91	147	29	be	be	AUX
hjic-91	147	30	obtained	obtain	VERB
hjic-91	147	31	iteratively	iteratively	ADV
hjic-91	147	32	,	,	PUNCT
hjic-91	147	33	too	too	ADV
hjic-91	147	34	.	.	PUNCT
hjic-91	148	1	l	l	NOUN
hjic-91	148	2	m	m	NOUN
hjic-91	148	3	'	'	PART
hjic-91	148	4	hl	hl	NOUN
hjic-91	148	5	u	u	NOUN
hjic-91	148	6	'	'	PUNCT
hjic-91	148	7	tl	tl	PROPN
hjic-91	148	8	hl	hl	NOUN
hjic-91	148	9	*	*	PUNCT
hjic-91	148	10	s	s	X
hjic-91	148	11	<	<	X
hjic-91	148	12	g	g	X
hjic-91	148	13	>	>	X
hjic-91	148	14	m	m	VERB
hjic-91	148	15	<	<	X
hjic-91	148	16	c	c	X
hjic-91	148	17	>	>	X
hjic-91	148	18	u	u	NOUN
hjic-91	148	19	<	<	X
hjic-91	148	20	c	c	X
hjic-91	148	21	>	>	X
hjic-91	148	22	fig.13	fig.13	PROPN
hjic-91	148	23	primary	primary	ADJ
hjic-91	148	24	reduced	reduce	VERB
hjic-91	148	25	graph	graph	NOUN
hjic-91	148	26	of	of	ADP
hjic-91	148	27	model	model	NOUN
hjic-91	148	28	m1	m1	PROPN
hjic-91	148	29	with	with	ADP
hjic-91	148	30	specification	specification	NOUN
hjic-91	148	31	1	1	NUM
hjic-91	148	32	the	the	DET
hjic-91	148	33	iterations	iteration	NOUN
hjic-91	148	34	belonging	belong	VERB
hjic-91	148	35	to	to	ADP
hjic-91	148	36	differential	differential	ADJ
hjic-91	148	37	variables	variable	NOUN
hjic-91	148	38	come	come	VERB
hjic-91	148	39	from	from	ADP
hjic-91	148	40	the	the	DET
hjic-91	148	41	implicit	implicit	ADJ
hjic-91	148	42	numerical	numerical	ADJ
hjic-91	148	43	solution	solution	NOUN
hjic-91	148	44	method	method	NOUN
hjic-91	148	45	and	and	CCONJ
hjic-91	148	46	not	not	PART
hjic-91	148	47	from	from	ADP
hjic-91	148	48	the	the	DET
hjic-91	148	49	structure	structure	NOUN
hjic-91	148	50	of	of	ADP
hjic-91	148	51	the	the	DET
hjic-91	148	52	models	model	NOUN
hjic-91	148	53	.	.	PUNCT
hjic-91	149	1	if	if	SCONJ
hjic-91	149	2	we	we	PRON
hjic-91	149	3	do	do	AUX
hjic-91	149	4	not	not	PART
hjic-91	149	5	want	want	VERB
hjic-91	149	6	to	to	PART
hjic-91	149	7	consider	consider	VERB
hjic-91	149	8	these	these	DET
hjic-91	149	9	iterations	iteration	NOUN
hjic-91	149	10	,	,	PUNCT
hjic-91	149	11	a	a	DET
hjic-91	149	12	secondary	secondary	ADJ
hjic-91	149	13	reduction	reduction	NOUN
hjic-91	149	14	can	can	AUX
hjic-91	149	15	be	be	AUX
hjic-91	149	16	constructed	construct	VERB
hjic-91	149	17	:	:	PUNCT
hjic-91	149	18	the	the	DET
hjic-91	149	19	secondary	secondary	ADJ
hjic-91	149	20	reduced	reduce	VERB
hjic-91	149	21	graph	graph	NOUN
hjic-91	149	22	can	can	AUX
hjic-91	149	23	be	be	AUX
hjic-91	149	24	obtained	obtain	VERB
hjic-91	149	25	if	if	SCONJ
hjic-91	149	26	we	we	PRON
hjic-91	149	27	omit	omit	VERB
hjic-91	149	28	the	the	DET
hjic-91	149	29	arcs	arcs	NOUN
hjic-91	149	30	x’→x	x’→x	PROPN
hjic-91	149	31	belonging	belong	VERB
hjic-91	149	32	to	to	ADP
hjic-91	149	33	all	all	DET
hjic-91	149	34	differential	differential	ADJ
hjic-91	149	35	variables	variable	NOUN
hjic-91	149	36	and	and	CCONJ
hjic-91	149	37	the	the	DET
hjic-91	149	38	labels	label	NOUN
hjic-91	149	39	<	<	X
hjic-91	149	40	c	c	X
hjic-91	149	41	>	>	X
hjic-91	149	42	are	be	AUX
hjic-91	149	43	treated	treat	VERB
hjic-91	149	44	similarly	similarly	ADV
hjic-91	149	45	to	to	ADP
hjic-91	149	46	the	the	DET
hjic-91	149	47	labels	label	NOUN
hjic-91	149	48	<	<	X
hjic-91	149	49	s	s	X
hjic-91	149	50	>	>	X
hjic-91	149	51	during	during	ADP
hjic-91	149	52	the	the	DET
hjic-91	149	53	reduction	reduction	NOUN
hjic-91	149	54	.	.	PUNCT
hjic-91	150	1	the	the	DET
hjic-91	150	2	secondary	secondary	ADJ
hjic-91	150	3	reduction	reduction	NOUN
hjic-91	150	4	is	be	AUX
hjic-91	150	5	directed	direct	VERB
hjic-91	150	6	to	to	ADP
hjic-91	150	7	the	the	DET
hjic-91	150	8	implicit	implicit	ADJ
hjic-91	150	9	part	part	NOUN
hjic-91	150	10	of	of	ADP
hjic-91	150	11	the	the	DET
hjic-91	150	12	model	model	NOUN
hjic-91	150	13	,	,	PUNCT
hjic-91	150	14	only	only	ADV
hjic-91	150	15	.	.	PUNCT
hjic-91	151	1	l	l	X
hjic-91	151	2	'	'	PUNCT
hjic-91	151	3	s	s	VERB
hjic-91	151	4	<	<	X
hjic-91	151	5	g	g	X
hjic-91	151	6	>	>	X
hjic-91	151	7	l	l	NOUN
hjic-91	151	8	<	<	X
hjic-91	151	9	c	c	X
hjic-91	151	10	>	>	X
hjic-91	151	11	f2	f2	PROPN
hjic-91	151	12	f1p2	f1p2	PROPN
hjic-91	151	13	fig.14	fig.14	ADP
hjic-91	151	14	primary	primary	ADJ
hjic-91	151	15	reduced	reduce	VERB
hjic-91	151	16	graph	graph	NOUN
hjic-91	151	17	of	of	ADP
hjic-91	151	18	model	model	NOUN
hjic-91	151	19	m2	m2	PROPN
hjic-91	151	20	proposition	proposition	NOUN
hjic-91	151	21	4	4	NUM
hjic-91	151	22	:	:	PUNCT
hjic-91	151	23	the	the	DET
hjic-91	151	24	secondary	secondary	ADJ
hjic-91	151	25	reduction	reduction	NOUN
hjic-91	151	26	yields	yield	VERB
hjic-91	151	27	the	the	DET
hjic-91	151	28	same	same	ADJ
hjic-91	151	29	reduced	reduce	VERB
hjic-91	151	30	graph	graph	NOUN
hjic-91	151	31	as	as	SCONJ
hjic-91	151	32	it	it	PRON
hjic-91	151	33	can	can	AUX
hjic-91	151	34	be	be	AUX
hjic-91	151	35	obtained	obtain	VERB
hjic-91	151	36	by	by	ADP
hjic-91	151	37	assuming	assume	VERB
hjic-91	151	38	a	a	DET
hjic-91	151	39	single	single	ADJ
hjic-91	151	40	step	step	NOUN
hjic-91	151	41	explicit	explicit	ADJ
hjic-91	151	42	numerical	numerical	ADJ
hjic-91	151	43	solution	solution	NOUN
hjic-91	151	44	procedure	procedure	NOUN
hjic-91	151	45	.	.	PUNCT
hjic-91	152	1	proof	proof	NOUN
hjic-91	152	2	:	:	PUNCT
hjic-91	152	3	it	it	PRON
hjic-91	152	4	follows	follow	VERB
hjic-91	152	5	directly	directly	ADV
hjic-91	152	6	from	from	ADP
hjic-91	152	7	the	the	DET
hjic-91	152	8	structure	structure	NOUN
hjic-91	152	9	of	of	ADP
hjic-91	152	10	dynamic	dynamic	ADJ
hjic-91	152	11	representation	representation	NOUN
hjic-91	152	12	graphs	graph	NOUN
hjic-91	152	13	and	and	CCONJ
hjic-91	152	14	from	from	ADP
hjic-91	152	15	the	the	DET
hjic-91	152	16	procedure	procedure	NOUN
hjic-91	152	17	of	of	ADP
hjic-91	152	18	reduction	reduction	NOUN
hjic-91	152	19	.	.	PUNCT
hjic-91	153	1	in	in	ADP
hjic-91	153	2	the	the	DET
hjic-91	153	3	case	case	NOUN
hjic-91	153	4	of	of	ADP
hjic-91	153	5	higher	high	ADJ
hjic-91	153	6	index	index	NOUN
hjic-91	153	7	models	model	NOUN
hjic-91	153	8	with	with	ADP
hjic-91	153	9	a	a	DET
hjic-91	153	10	single	single	ADJ
hjic-91	153	11	step	step	NOUN
hjic-91	153	12	implicit	implicit	ADJ
hjic-91	153	13	solution	solution	NOUN
hjic-91	153	14	method	method	NOUN
hjic-91	153	15	,	,	PUNCT
hjic-91	153	16	the	the	DET
hjic-91	153	17	representation	representation	NOUN
hjic-91	153	18	graph	graph	NOUN
hjic-91	153	19	contains	contain	VERB
hjic-91	153	20	an	an	DET
hjic-91	153	21	overspecified	overspecified	ADJ
hjic-91	153	22	and	and	CCONJ
hjic-91	153	23	underspecified	underspecified	ADJ
hjic-91	153	24	subgraph	subgraph	NOUN
hjic-91	153	25	,	,	PUNCT
hjic-91	153	26	in	in	ADP
hjic-91	153	27	the	the	DET
hjic-91	153	28	same	same	ADJ
hjic-91	153	29	way	way	NOUN
hjic-91	153	30	,	,	PUNCT
hjic-91	153	31	as	as	ADP
hjic-91	153	32	in	in	ADP
hjic-91	153	33	the	the	DET
hjic-91	153	34	case	case	NOUN
hjic-91	153	35	of	of	ADP
hjic-91	153	36	explicit	explicit	ADJ
hjic-91	153	37	solution	solution	NOUN
hjic-91	153	38	methods	method	NOUN
hjic-91	153	39	.	.	PUNCT
hjic-91	154	1	the	the	DET
hjic-91	154	2	algorithm	algorithm	NOUN
hjic-91	154	3	for	for	ADP
hjic-91	154	4	determination	determination	NOUN
hjic-91	154	5	of	of	ADP
hjic-91	154	6	the	the	DET
hjic-91	154	7	differential	differential	ADJ
hjic-91	154	8	index	index	NOUN
hjic-91	154	9	can	can	AUX
hjic-91	154	10	be	be	AUX
hjic-91	154	11	performed	perform	VERB
hjic-91	154	12	similarly	similarly	ADV
hjic-91	154	13	,	,	PUNCT
hjic-91	154	14	too	too	ADV
hjic-91	154	15	.	.	PUNCT
hjic-91	155	1	conclusion	conclusion	VERB
hjic-91	155	2	the	the	DET
hjic-91	155	3	effect	effect	NOUN
hjic-91	155	4	of	of	ADP
hjic-91	155	5	the	the	DET
hjic-91	155	6	numerical	numerical	ADJ
hjic-91	155	7	solution	solution	NOUN
hjic-91	155	8	procedure	procedure	NOUN
hjic-91	155	9	on	on	ADP
hjic-91	155	10	the	the	DET
hjic-91	155	11	structural	structural	ADJ
hjic-91	155	12	analysis	analysis	NOUN
hjic-91	155	13	of	of	ADP
hjic-91	155	14	dynamic	dynamic	ADJ
hjic-91	155	15	lumped	lump	VERB
hjic-91	155	16	models	model	NOUN
hjic-91	155	17	described	describe	VERB
hjic-91	155	18	by	by	ADP
hjic-91	155	19	semi	semi	ADJ
hjic-91	155	20	-	-	ADJ
hjic-91	155	21	explicit	explicit	ADJ
hjic-91	155	22	differential	differential	NOUN
hjic-91	155	23	and	and	CCONJ
hjic-91	155	24	algebraic	algebraic	ADJ
hjic-91	155	25	equations	equation	NOUN
hjic-91	155	26	was	be	AUX
hjic-91	155	27	investigated	investigate	VERB
hjic-91	155	28	in	in	ADP
hjic-91	155	29	this	this	DET
hjic-91	155	30	paper	paper	NOUN
hjic-91	155	31	.	.	PUNCT
hjic-91	156	1	the	the	DET
hjic-91	156	2	most	most	ADV
hjic-91	156	3	important	important	ADJ
hjic-91	156	4	solvability	solvability	NOUN
hjic-91	156	5	properties	property	NOUN
hjic-91	156	6	of	of	ADP
hjic-91	156	7	models	model	NOUN
hjic-91	156	8	were	be	AUX
hjic-91	156	9	determined	determine	VERB
hjic-91	156	10	by	by	ADP
hjic-91	156	11	graph	graph	NOUN
hjic-91	156	12	-	-	PUNCT
hjic-91	156	13	theoretical	theoretical	ADJ
hjic-91	156	14	methods	method	NOUN
hjic-91	156	15	using	use	VERB
hjic-91	156	16	the	the	DET
hjic-91	156	17	dynamic	dynamic	ADJ
hjic-91	156	18	representation	representation	NOUN
hjic-91	156	19	graph	graph	NOUN
hjic-91	156	20	of	of	ADP
hjic-91	156	21	the	the	DET
hjic-91	156	22	models	model	NOUN
hjic-91	156	23	.	.	PUNCT
hjic-91	157	1	we	we	PRON
hjic-91	157	2	compared	compare	VERB
hjic-91	157	3	the	the	DET
hjic-91	157	4	structure	structure	NOUN
hjic-91	157	5	of	of	ADP
hjic-91	157	6	dynamic	dynamic	ADJ
hjic-91	157	7	representation	representation	NOUN
hjic-91	157	8	graphs	graph	NOUN
hjic-91	157	9	in	in	ADP
hjic-91	157	10	the	the	DET
hjic-91	157	11	case	case	NOUN
hjic-91	157	12	of	of	ADP
hjic-91	157	13	explicit	explicit	ADJ
hjic-91	157	14	and	and	CCONJ
hjic-91	157	15	implicit	implicit	ADJ
hjic-91	157	16	solution	solution	NOUN
hjic-91	157	17	methods	method	NOUN
hjic-91	157	18	for	for	ADP
hjic-91	157	19	solving	solve	VERB
hjic-91	157	20	the	the	DET
hjic-91	157	21	differential	differential	ADJ
hjic-91	157	22	equations	equation	NOUN
hjic-91	157	23	.	.	PUNCT
hjic-91	158	1	it	it	PRON
hjic-91	158	2	was	be	AUX
hjic-91	158	3	shown	show	VERB
hjic-91	158	4	that	that	SCONJ
hjic-91	158	5	the	the	DET
hjic-91	158	6	representation	representation	NOUN
hjic-91	158	7	graph	graph	NOUN
hjic-91	158	8	with	with	ADP
hjic-91	158	9	both	both	CCONJ
hjic-91	158	10	higher	high	ADJ
hjic-91	158	11	order	order	NOUN
hjic-91	158	12	explicit	explicit	ADJ
hjic-91	158	13	and	and	CCONJ
hjic-91	158	14	implicit	implicit	ADJ
hjic-91	158	15	solution	solution	NOUN
hjic-91	158	16	methods	method	NOUN
hjic-91	158	17	has	have	VERB
hjic-91	158	18	similar	similar	ADJ
hjic-91	158	19	properties	property	NOUN
hjic-91	158	20	both	both	CCONJ
hjic-91	158	21	in	in	ADP
hjic-91	158	22	case	case	NOUN
hjic-91	158	23	of	of	ADP
hjic-91	158	24	index	index	NOUN
hjic-91	158	25	1	1	NUM
hjic-91	158	26	and	and	CCONJ
hjic-91	158	27	higher	high	ADJ
hjic-91	158	28	index	index	NOUN
hjic-91	158	29	models	model	NOUN
hjic-91	158	30	as	as	SCONJ
hjic-91	158	31	compared	compare	VERB
hjic-91	158	32	to	to	ADP
hjic-91	158	33	first	first	ADJ
hjic-91	158	34	order	order	NOUN
hjic-91	158	35	explicit	explicit	ADJ
hjic-91	158	36	single	single	ADJ
hjic-91	158	37	-	-	PUNCT
hjic-91	158	38	step	step	NOUN
hjic-91	158	39	numerical	numerical	ADJ
hjic-91	158	40	solution	solution	NOUN
hjic-91	158	41	procedures	procedure	NOUN
hjic-91	158	42	.	.	PUNCT
hjic-91	159	1	hence	hence	ADV
hjic-91	159	2	the	the	DET
hjic-91	159	3	properties	property	NOUN
hjic-91	159	4	of	of	ADP
hjic-91	159	5	representation	representation	NOUN
hjic-91	159	6	graph	graph	NOUN
hjic-91	159	7	including	include	VERB
hjic-91	159	8	the	the	DET
hjic-91	159	9	differential	differential	ADJ
hjic-91	159	10	index	index	NOUN
hjic-91	159	11	of	of	ADP
hjic-91	159	12	the	the	DET
hjic-91	159	13	models	model	NOUN
hjic-91	159	14	are	be	AUX
hjic-91	159	15	independent	independent	ADJ
hjic-91	159	16	of	of	ADP
hjic-91	159	17	the	the	DET
hjic-91	159	18	assumption	assumption	NOUN
hjic-91	159	19	whether	whether	SCONJ
hjic-91	159	20	a	a	DET
hjic-91	159	21	singlestep	singlestep	NOUN
hjic-91	159	22	,	,	PUNCT
hjic-91	159	23	explicit	explicit	ADJ
hjic-91	159	24	or	or	CCONJ
hjic-91	159	25	implicit	implicit	ADJ
hjic-91	159	26	numerical	numerical	ADJ
hjic-91	159	27	method	method	NOUN
hjic-91	159	28	is	be	AUX
hjic-91	159	29	used	use	VERB
hjic-91	159	30	for	for	ADP
hjic-91	159	31	the	the	DET
hjic-91	159	32	solution	solution	NOUN
hjic-91	159	33	of	of	ADP
hjic-91	159	34	the	the	DET
hjic-91	159	35	differential	differential	ADJ
hjic-91	159	36	equations	equation	NOUN
hjic-91	159	37	.	.	PUNCT
hjic-91	160	1	21	21	NUM
hjic-91	160	2	references	reference	NOUN
hjic-91	160	3	1	1	NUM
hjic-91	160	4	.	.	PUNCT
hjic-91	160	5	murota	murota	NOUN
hjic-91	160	6	k.	k.	NOUN
hjic-91	160	7	:	:	PUNCT
hjic-91	160	8	systems	system	NOUN
hjic-91	160	9	analysis	analysis	NOUN
hjic-91	160	10	by	by	ADP
hjic-91	160	11	graphs	graph	NOUN
hjic-91	160	12	and	and	CCONJ
hjic-91	160	13	matroids	matroid	NOUN
hjic-91	160	14	,	,	PUNCT
hjic-91	160	15	springer	springer	NOUN
hjic-91	160	16	-	-	PUNCT
hjic-91	160	17	verlag	verlag	PROPN
hjic-91	160	18	,	,	PUNCT
hjic-91	160	19	berlin	berlin	PROPN
hjic-91	160	20	,	,	PUNCT
hjic-91	160	21	1987	1987	NUM
hjic-91	160	22	2	2	NUM
hjic-91	160	23	.	.	PUNCT
hjic-91	160	24	leitold	leitold	ADJ
hjic-91	160	25	a.	a.	NOUN
hjic-91	160	26	and	and	CCONJ
hjic-91	160	27	hangos	hangos	PROPN
hjic-91	160	28	k.m	k.m	PROPN
hjic-91	160	29	.	.	PROPN
hjic-91	160	30	:	:	PUNCT
hjic-91	160	31	computers	computer	NOUN
hjic-91	160	32	and	and	CCONJ
hjic-91	160	33	chemical	chemical	NOUN
hjic-91	160	34	engineering	engineering	NOUN
hjic-91	160	35	,	,	PUNCT
hjic-91	160	36	2001	2001	NUM
hjic-91	160	37	,	,	PUNCT
hjic-91	160	38	25	25	NUM
hjic-91	160	39	,	,	PUNCT
hjic-91	160	40	16331646	16331646	NUM
hjic-91	160	41	3	3	NUM
hjic-91	160	42	.	.	X
hjic-91	160	43	hangos	hangos	PROPN
hjic-91	160	44	k.m	k.m	PROPN
hjic-91	160	45	.	.	PROPN
hjic-91	160	46	and	and	CCONJ
hjic-91	160	47	cameron	cameron	PROPN
hjic-91	160	48	i.t	i.t	PROPN
hjic-91	160	49	.	.	PROPN
hjic-91	160	50	:	:	PUNCT
hjic-91	160	51	process	process	NOUN
hjic-91	160	52	modelling	modelling	NOUN
hjic-91	160	53	and	and	CCONJ
hjic-91	160	54	model	model	NOUN
hjic-91	160	55	analysis	analysis	NOUN
hjic-91	160	56	,	,	PUNCT
hjic-91	160	57	academic	academic	ADJ
hjic-91	160	58	press	press	NOUN
hjic-91	160	59	,	,	PUNCT
hjic-91	160	60	new	new	PROPN
hjic-91	160	61	york	york	PROPN
hjic-91	160	62	,	,	PUNCT
hjic-91	160	63	london	london	PROPN
hjic-91	160	64	2001	2001	NUM
hjic-91	160	65	4	4	X
hjic-91	160	66	.	.	PUNCT
hjic-91	160	67	leitold	leitold	ADJ
hjic-91	160	68	a.	a.	NOUN
hjic-91	160	69	and	and	CCONJ
hjic-91	160	70	hangos	hangos	PROPN
hjic-91	160	71	k.m	k.m	PROPN
hjic-91	160	72	.	.	PROPN
hjic-91	160	73	:	:	PUNCT
hjic-91	160	74	hungarian	hungarian	ADJ
hjic-91	160	75	journal	journal	NOUN
hjic-91	160	76	of	of	ADP
hjic-91	160	77	industrial	industrial	ADJ
hjic-91	160	78	chemistry	chemistry	NOUN
hjic-91	160	79	,	,	PUNCT
hjic-91	160	80	2002	2002	NUM
hjic-91	160	81	,	,	PUNCT
hjic-91	160	82	30(1	30(1	NUM
hjic-91	160	83	)	)	PUNCT
hjic-91	160	84	,	,	PUNCT
hjic-91	160	85	61	61	NUM
hjic-91	160	86	-	-	SYM
hjic-91	160	87	71	71	NUM
hjic-91	160	88	5	5	NUM
hjic-91	160	89	.	.	PUNCT
hjic-91	161	1	leitold	leitold	PROPN
hjic-91	161	2	a.	a.	NOUN
hjic-91	161	3	:	:	PUNCT
hjic-91	161	4	analysis	analysis	NOUN
hjic-91	161	5	of	of	ADP
hjic-91	161	6	dynamic	dynamic	ADJ
hjic-91	161	7	process	process	NOUN
hjic-91	161	8	models	model	NOUN
hjic-91	161	9	using	use	VERB
hjic-91	161	10	computer	computer	NOUN
hjic-91	161	11	science	science	NOUN
hjic-91	161	12	methods	method	NOUN
hjic-91	161	13	,	,	PUNCT
hjic-91	161	14	phd	phd	NOUN
hjic-91	161	15	dissertation	dissertation	NOUN
hjic-91	161	16	,	,	PUNCT
hjic-91	161	17	university	university	NOUN
hjic-91	161	18	of	of	ADP
hjic-91	161	19	eötvös	eötvös	PROPN
hjic-91	161	20	lóránd	lóránd	ADJ
hjic-91	161	21	,	,	PUNCT
hjic-91	161	22	budapest	budapest	PROPN
hjic-91	161	23	,	,	PUNCT
hjic-91	161	24	2002	2002	NUM
hjic-91	161	25	6	6	NUM
hjic-91	161	26	.	.	PUNCT
hjic-91	161	27	iri	iri	PROPN
hjic-91	161	28	m.	m.	NOUN
hjic-91	161	29	,	,	PUNCT
hjic-91	161	30	tsunekawa	tsunekawa	PROPN
hjic-91	161	31	j.	j.	PROPN
hjic-91	161	32	and	and	CCONJ
hjic-91	161	33	yajima	yajima	PROPN
hjic-91	161	34	k.	k.	PROPN
hjic-91	161	35	:	:	PUNCT
hjic-91	161	36	information	information	NOUN
hjic-91	161	37	processing	processing	NOUN
hjic-91	161	38	,	,	PUNCT
hjic-91	161	39	1972	1972	NUM
hjic-91	161	40	,	,	PUNCT
hjic-91	161	41	71	71	NUM
hjic-91	161	42	.	.	PUNCT
hjic-91	162	1	vol	vol	NOUN
hjic-91	162	2	.	.	PROPN
hjic-91	163	1	2	2	NUM
hjic-91	163	2	.	.	NOUN
hjic-91	163	3	1150	1150	NUM
hjic-91	163	4	-	-	SYM
hjic-91	163	5	1155	1155	NUM
hjic-91	163	6	7	7	NUM
hjic-91	163	7	.	.	PUNCT
hjic-91	163	8	brenan	brenan	PROPN
hjic-91	163	9	k.e	k.e	PROPN
hjic-91	163	10	.	.	PROPN
hjic-91	163	11	,	,	PUNCT
hjic-91	164	1	campbell	campbell	PROPN
hjic-91	164	2	s.l	s.l	PROPN
hjic-91	164	3	.	.	PROPN
hjic-91	164	4	and	and	CCONJ
hjic-91	164	5	petzold	petzold	PROPN
hjic-91	164	6	l.r	l.r	PROPN
hjic-91	164	7	.	.	PROPN
hjic-91	164	8	:	:	PUNCT
hjic-91	165	1	numerical	numerical	ADJ
hjic-91	165	2	solution	solution	NOUN
hjic-91	165	3	of	of	ADP
hjic-91	165	4	initial	initial	ADJ
hjic-91	165	5	value	value	NOUN
hjic-91	165	6	problems	problem	NOUN
hjic-91	165	7	in	in	ADP
hjic-91	165	8	differential	differential	ADJ
hjic-91	165	9	–	–	PUNCT
hjic-91	165	10	algebraic	algebraic	ADJ
hjic-91	165	11	equations	equation	NOUN
hjic-91	165	12	,	,	PUNCT
hjic-91	165	13	north	north	NOUN
hjic-91	165	14	-	-	PUNCT
hjic-91	165	15	holland	holland	PROPN
hjic-91	165	16	,	,	PUNCT
hjic-91	165	17	new	new	PROPN
hjic-91	165	18	york	york	PROPN
hjic-91	165	19	,	,	PUNCT
hjic-91	165	20	1989	1989	NUM