id	sid	tid	token	lemma	pos
hjic-104	1	1	hungarian	hungarian	ADJ
hjic-104	1	2	journal	journal	NOUN
hjic-104	1	3	of	of	ADP
hjic-104	1	4	industrial	industrial	ADJ
hjic-104	1	5	chemistry	chemistry	NOUN
hjic-104	1	6	veszprém	veszprém	NOUN
hjic-104	1	7	vol	vol	NOUN
hjic-104	1	8	.	.	PUNCT
hjic-104	2	1	33(1	33(1	NUM
hjic-104	2	2	-	-	SYM
hjic-104	2	3	2	2	NUM
hjic-104	2	4	)	)	PUNCT
hjic-104	2	5	.	.	PUNCT
hjic-104	3	1	pp	pp	ADV
hjic-104	3	2	.	.	PUNCT
hjic-104	4	1	119	119	NUM
hjic-104	4	2	-	-	SYM
hjic-104	4	3	124	124	NUM
hjic-104	4	4	.	.	PUNCT
hjic-104	5	1	(	(	PUNCT
hjic-104	5	2	2005	2005	NUM
hjic-104	5	3	)	)	PUNCT
hjic-104	5	4	neumann	neumann	PROPN
hjic-104	5	5	boundary	boundary	ADJ
hjic-104	5	6	value	value	NOUN
hjic-104	5	7	problems	problem	NOUN
hjic-104	5	8	with	with	ADP
hjic-104	5	9	bem	bem	NOUN
hjic-104	5	10	and	and	CCONJ
hjic-104	5	11	collocation	collocation	NOUN
hjic-104	5	12	n.	n.	NOUN
hjic-104	5	13	herrmann1	herrmann1	PROPN
hjic-104	6	1	and	and	CCONJ
hjic-104	7	1	v.	v.	ADP
hjic-104	7	2	karnjanatawee2	karnjanatawee2	PROPN
hjic-104	8	1	1institut	1institut	NUM
hjic-104	8	2	für	für	PROPN
hjic-104	8	3	angewandte	angewandte	PROPN
hjic-104	8	4	mathematik	mathematik	PROPN
hjic-104	8	5	,	,	PUNCT
hjic-104	8	6	universität	universität	PROPN
hjic-104	8	7	hannover	hannover	PROPN
hjic-104	8	8	,	,	PUNCT
hjic-104	8	9	hannover	hannover	PROPN
hjic-104	8	10	,	,	PUNCT
hjic-104	8	11	germany	germany	PROPN
hjic-104	8	12	2dept	2dept	NUM
hjic-104	8	13	.	.	PROPN
hjic-104	8	14	of	of	ADP
hjic-104	8	15	mathematics	mathematic	NOUN
hjic-104	8	16	,	,	PUNCT
hjic-104	8	17	king	king	NOUN
hjic-104	8	18	mongkut	mongkut	PROPN
hjic-104	8	19	university	university	PROPN
hjic-104	8	20	of	of	ADP
hjic-104	8	21	technology	technology	PROPN
hjic-104	8	22	thonburi	thonburi	PROPN
hjic-104	8	23	,	,	PUNCT
hjic-104	8	24	bangkok	bangkok	PROPN
hjic-104	8	25	,	,	PUNCT
hjic-104	8	26	thailand	thailand	PROPN
hjic-104	8	27	this	this	DET
hjic-104	8	28	paper	paper	NOUN
hjic-104	8	29	is	be	AUX
hjic-104	8	30	an	an	DET
hjic-104	8	31	introduction	introduction	NOUN
hjic-104	8	32	into	into	ADP
hjic-104	8	33	the	the	DET
hjic-104	8	34	boundary	boundary	ADJ
hjic-104	8	35	element	element	NOUN
hjic-104	8	36	method	method	NOUN
hjic-104	8	37	(	(	PUNCT
hjic-104	8	38	bem	bem	PROPN
hjic-104	8	39	)	)	PUNCT
hjic-104	8	40	with	with	ADP
hjic-104	8	41	collocation	collocation	NOUN
hjic-104	8	42	to	to	PART
hjic-104	8	43	find	find	VERB
hjic-104	8	44	the	the	DET
hjic-104	8	45	numerical	numerical	ADJ
hjic-104	8	46	solution	solution	NOUN
hjic-104	8	47	of	of	ADP
hjic-104	8	48	two	two	NUM
hjic-104	8	49	different	different	ADJ
hjic-104	8	50	types	type	NOUN
hjic-104	8	51	of	of	ADP
hjic-104	8	52	neumann	neumann	PROPN
hjic-104	8	53	problems	problem	NOUN
hjic-104	8	54	.	.	PUNCT
hjic-104	9	1	at	at	ADP
hjic-104	9	2	first	first	ADV
hjic-104	9	3	we	we	PRON
hjic-104	9	4	start	start	VERB
hjic-104	9	5	with	with	ADP
hjic-104	9	6	the	the	DET
hjic-104	9	7	laplace	laplace	NOUN
hjic-104	9	8	equation	equation	NOUN
hjic-104	9	9	and	and	CCONJ
hjic-104	9	10	continue	continue	VERB
hjic-104	9	11	later	later	ADV
hjic-104	9	12	with	with	ADP
hjic-104	9	13	the	the	DET
hjic-104	9	14	heat	heat	NOUN
hjic-104	9	15	equation	equation	NOUN
hjic-104	9	16	on	on	ADP
hjic-104	9	17	a	a	DET
hjic-104	9	18	bounded	bounded	ADJ
hjic-104	9	19	convex	convex	NOUN
hjic-104	9	20	domain	domain	NOUN
hjic-104	9	21	with	with	ADP
hjic-104	9	22	smooth	smooth	ADJ
hjic-104	9	23	boundary	boundary	NOUN
hjic-104	9	24	in	in	ADP
hjic-104	9	25	two	two	NUM
hjic-104	9	26	dimensions	dimension	NOUN
hjic-104	9	27	.	.	PUNCT
hjic-104	10	1	we	we	PRON
hjic-104	10	2	will	will	AUX
hjic-104	10	3	show	show	VERB
hjic-104	10	4	how	how	SCONJ
hjic-104	10	5	to	to	PART
hjic-104	10	6	transform	transform	VERB
hjic-104	10	7	the	the	DET
hjic-104	10	8	governing	govern	VERB
hjic-104	10	9	problem	problem	NOUN
hjic-104	10	10	into	into	ADP
hjic-104	10	11	a	a	DET
hjic-104	10	12	boundary	boundary	ADJ
hjic-104	10	13	integral	integral	ADJ
hjic-104	10	14	equation	equation	NOUN
hjic-104	10	15	which	which	PRON
hjic-104	10	16	can	can	AUX
hjic-104	10	17	be	be	AUX
hjic-104	10	18	solved	solve	VERB
hjic-104	10	19	by	by	ADP
hjic-104	10	20	dividing	divide	VERB
hjic-104	10	21	the	the	DET
hjic-104	10	22	boundary	boundary	NOUN
hjic-104	10	23	into	into	ADP
hjic-104	10	24	a	a	DET
hjic-104	10	25	finite	finite	ADJ
hjic-104	10	26	number	number	NOUN
hjic-104	10	27	of	of	ADP
hjic-104	10	28	segments	segment	NOUN
hjic-104	10	29	and	and	CCONJ
hjic-104	10	30	applying	apply	VERB
hjic-104	10	31	the	the	DET
hjic-104	10	32	collocation	collocation	NOUN
hjic-104	10	33	method	method	NOUN
hjic-104	10	34	.	.	PUNCT
hjic-104	11	1	we	we	PRON
hjic-104	11	2	finish	finish	VERB
hjic-104	11	3	presenting	present	VERB
hjic-104	11	4	an	an	DET
hjic-104	11	5	example	example	NOUN
hjic-104	11	6	of	of	ADP
hjic-104	11	7	the	the	DET
hjic-104	11	8	heat	heat	NOUN
hjic-104	11	9	equation	equation	NOUN
hjic-104	11	10	.	.	PUNCT
hjic-104	12	1	keywords	keyword	NOUN
hjic-104	12	2	:	:	PUNCT
hjic-104	12	3	boundary	boundary	ADJ
hjic-104	12	4	element	element	NOUN
hjic-104	12	5	method	method	NOUN
hjic-104	12	6	,	,	PUNCT
hjic-104	12	7	laplace	laplace	NOUN
hjic-104	12	8	equation	equation	NOUN
hjic-104	12	9	,	,	PUNCT
hjic-104	12	10	heat	heat	NOUN
hjic-104	12	11	equation	equation	NOUN
hjic-104	12	12	,	,	PUNCT
hjic-104	12	13	neumann	neumann	PROPN
hjic-104	12	14	boundary	boundary	PROPN
hjic-104	12	15	value	value	NOUN
hjic-104	12	16	problem	problem	NOUN
hjic-104	12	17	,	,	PUNCT
hjic-104	12	18	collocation	collocation	NOUN
hjic-104	12	19	introduction	introduction	NOUN
hjic-104	12	20	let	let	VERB
hjic-104	12	21	ω	ω	NOUN
hjic-104	12	22	be	be	AUX
hjic-104	12	23	a	a	DET
hjic-104	12	24	convex	convex	NOUN
hjic-104	12	25	open	open	ADJ
hjic-104	12	26	domain	domain	NOUN
hjic-104	12	27	in	in	ADP
hjic-104	12	28	2r	2r	NUM
hjic-104	12	29	with	with	ADP
hjic-104	12	30	smooth	smooth	ADJ
hjic-104	12	31	boundary	boundary	NOUN
hjic-104	12	32	.	.	PUNCT
hjic-104	13	1	consider	consider	VERB
hjic-104	13	2	the	the	DET
hjic-104	13	3	laplace	laplace	NOUN
hjic-104	13	4	equation	equation	NOUN
hjic-104	13	5	:	:	PUNCT
hjic-104	13	6	ω∂	ω∂	X
hjic-104	13	7	in	in	ADP
hjic-104	13	8	ω	ω	NUM
hjic-104	13	9	,	,	PUNCT
hjic-104	13	10	(	(	PUNCT
hjic-104	13	11	)	)	PUNCT
hjic-104	13	12	0=∆	0=∆	NOUN
hjic-104	13	13	y	y	PROPN
hjic-104	13	14	,	,	PUNCT
hjic-104	13	15	xu	xu	PROPN
hjic-104	14	1	(	(	PUNCT
hjic-104	14	2	)	)	PUNCT
hjic-104	14	3	(	(	PUNCT
hjic-104	14	4	y	y	PROPN
hjic-104	14	5	,	,	PUNCT
hjic-104	14	6	xg	xg	PROPN
hjic-104	14	7	n	n	PROPN
hjic-104	14	8	y	y	PROPN
hjic-104	14	9	,	,	PUNCT
hjic-104	14	10	xu	xu	PROPN
hjic-104	14	11	=	=	SYM
hjic-104	14	12	∂	∂	NUM
hjic-104	14	13	∂	∂	NUM
hjic-104	14	14	)	)	PUNCT
hjic-104	14	15	on	on	ADP
hjic-104	14	16	ω∂	ω∂	NUM
hjic-104	14	17	,	,	PUNCT
hjic-104	14	18	where	where	SCONJ
hjic-104	14	19	2	2	NUM
hjic-104	14	20	2	2	NUM
hjic-104	14	21	2	2	NUM
hjic-104	14	22	2	2	NUM
hjic-104	14	23	yx	yx	NOUN
hjic-104	14	24	∂	∂	NUM
hjic-104	14	25	∂	∂	NUM
hjic-104	14	26	+	+	NUM
hjic-104	14	27	∂	∂	NUM
hjic-104	14	28	∂	∂	NUM
hjic-104	14	29	=	=	NOUN
hjic-104	14	30	∆	∆	PROPN
hjic-104	14	31	and	and	CCONJ
hjic-104	14	32	the	the	DET
hjic-104	14	33	heat	heat	NOUN
hjic-104	14	34	equation	equation	NOUN
hjic-104	14	35	(	(	PUNCT
hjic-104	14	36	)	)	PUNCT
hjic-104	14	37	(	(	PUNCT
hjic-104	14	38	)	)	PUNCT
hjic-104	14	39	(	(	PUNCT
hjic-104	14	40	)	)	PUNCT
hjic-104	14	41	,	,	PUNCT
hjic-104	14	42	y	y	PROPN
hjic-104	14	43	t	t	PROPN
hjic-104	14	44	,	,	PUNCT
hjic-104	14	45	y	y	PROPN
hjic-104	14	46	,	,	PUNCT
hjic-104	14	47	xu	xu	PROPN
hjic-104	14	48	x	x	SYM
hjic-104	14	49	t	t	PROPN
hjic-104	14	50	,	,	PUNCT
hjic-104	14	51	y	y	PROPN
hjic-104	14	52	,	,	PUNCT
hjic-104	14	53	xu	xu	PROPN
hjic-104	14	54	t	t	PROPN
hjic-104	14	55	t	t	PROPN
hjic-104	14	56	,	,	PUNCT
hjic-104	14	57	y	y	PROPN
hjic-104	14	58	,	,	PUNCT
hjic-104	14	59	xu	xu	PROPN
hjic-104	14	60	2	2	NUM
hjic-104	14	61	2	2	NUM
hjic-104	14	62	2	2	NUM
hjic-104	14	63	2	2	NUM
hjic-104	14	64	∂	∂	NUM
hjic-104	14	65	∂	∂	NUM
hjic-104	14	66	+	+	NUM
hjic-104	14	67	∂	∂	NUM
hjic-104	14	68	∂	∂	NUM
hjic-104	14	69	=	=	SYM
hjic-104	14	70	∂	∂	NOUN
hjic-104	14	71	∂	∂	NOUN
hjic-104	14	72	where	where	SCONJ
hjic-104	14	73	(	(	PUNCT
hjic-104	14	74	)	)	PUNCT
hjic-104	14	75	(	(	PUNCT
hjic-104	14	76	]	]	X
hjic-104	14	77	t	t	PROPN
hjic-104	14	78	,	,	PUNCT
hjic-104	14	79	t	t	PROPN
hjic-104	14	80	,	,	PUNCT
hjic-104	14	81	y	y	PROPN
hjic-104	14	82	,	,	PUNCT
hjic-104	14	83	x	x	SYM
hjic-104	14	84	0∈ω∈	0∈ω∈	PROPN
hjic-104	14	85	with	with	ADP
hjic-104	14	86	initial	initial	ADJ
hjic-104	14	87	and	and	CCONJ
hjic-104	14	88	boundary	boundary	ADJ
hjic-104	14	89	conditions	condition	NOUN
hjic-104	14	90	,	,	PUNCT
hjic-104	14	91	(	(	PUNCT
hjic-104	14	92	)	)	PUNCT
hjic-104	14	93	(	(	PUNCT
hjic-104	14	94	,	,	PUNCT
hjic-104	14	95	y	y	PROPN
hjic-104	14	96	,	,	PUNCT
hjic-104	14	97	xf	xf	PROPN
hjic-104	14	98	,	,	PUNCT
hjic-104	14	99	y	y	PROPN
hjic-104	14	100	,	,	PUNCT
hjic-104	14	101	xu	xu	PUNCT
hjic-104	15	1	=	=	NOUN
hjic-104	15	2	0	0	NUM
hjic-104	15	3	)	)	PUNCT
hjic-104	15	4	(	(	PUNCT
hjic-104	15	5	)	)	PUNCT
hjic-104	15	6	ω∈y	ω∈y	NOUN
hjic-104	15	7	,	,	PUNCT
hjic-104	15	8	x	x	X
hjic-104	15	9	(	(	PUNCT
hjic-104	15	10	)	)	PUNCT
hjic-104	15	11	(	(	PUNCT
hjic-104	15	12	)	)	PUNCT
hjic-104	15	13	(	(	PUNCT
hjic-104	15	14	)	)	PUNCT
hjic-104	15	15	(	(	PUNCT
hjic-104	15	16	]	]	X
hjic-104	15	17	t	t	PROPN
hjic-104	15	18	,	,	PUNCT
hjic-104	15	19	t	t	PROPN
hjic-104	15	20	,	,	PUNCT
hjic-104	15	21	y	y	PROPN
hjic-104	15	22	,	,	PUNCT
hjic-104	15	23	x	x	PROPN
hjic-104	15	24	,	,	PUNCT
hjic-104	15	25	t	t	PROPN
hjic-104	15	26	,	,	PUNCT
hjic-104	15	27	y	y	PROPN
hjic-104	15	28	,	,	PUNCT
hjic-104	15	29	xg	xg	PROPN
hjic-104	15	30	n	n	PROPN
hjic-104	15	31	t	t	PROPN
hjic-104	15	32	,	,	PUNCT
hjic-104	15	33	y	y	PROPN
hjic-104	15	34	,	,	PUNCT
hjic-104	15	35	xu	xu	PROPN
hjic-104	15	36	0∈ω∂∈=	0∈ω∂∈=	PROPN
hjic-104	15	37	∂	∂	NUM
hjic-104	15	38	∂	∂	NUM
hjic-104	15	39	by	by	ADP
hjic-104	15	40	using	use	VERB
hjic-104	15	41	the	the	DET
hjic-104	15	42	fundamental	fundamental	ADJ
hjic-104	15	43	solution	solution	NOUN
hjic-104	15	44	we	we	PRON
hjic-104	15	45	will	will	AUX
hjic-104	15	46	develop	develop	VERB
hjic-104	15	47	the	the	DET
hjic-104	15	48	boundary	boundary	ADJ
hjic-104	15	49	integral	integral	ADJ
hjic-104	15	50	equation	equation	NOUN
hjic-104	15	51	(	(	PUNCT
hjic-104	15	52	bie	bie	PROPN
hjic-104	15	53	)	)	PUNCT
hjic-104	15	54	from	from	ADP
hjic-104	15	55	the	the	DET
hjic-104	15	56	governing	govern	VERB
hjic-104	15	57	boundary	boundary	ADJ
hjic-104	15	58	value	value	NOUN
hjic-104	15	59	problem	problem	NOUN
hjic-104	15	60	and	and	CCONJ
hjic-104	15	61	will	will	AUX
hjic-104	15	62	create	create	VERB
hjic-104	15	63	a	a	DET
hjic-104	15	64	fredholm	fredholm	ADJ
hjic-104	15	65	integral	integral	ADJ
hjic-104	15	66	equation	equation	NOUN
hjic-104	15	67	of	of	ADP
hjic-104	15	68	the	the	DET
hjic-104	15	69	second	second	ADJ
hjic-104	15	70	kind	kind	NOUN
hjic-104	15	71	.	.	PUNCT
hjic-104	16	1	according	accord	VERB
hjic-104	16	2	to	to	ADP
hjic-104	16	3	the	the	DET
hjic-104	16	4	fact	fact	NOUN
hjic-104	16	5	that	that	SCONJ
hjic-104	16	6	the	the	DET
hjic-104	16	7	solution	solution	NOUN
hjic-104	16	8	of	of	ADP
hjic-104	16	9	a	a	DET
hjic-104	16	10	neumann	neumann	PROPN
hjic-104	16	11	value	value	NOUN
hjic-104	16	12	problem	problem	NOUN
hjic-104	16	13	is	be	AUX
hjic-104	16	14	not	not	PART
hjic-104	16	15	unique	unique	ADJ
hjic-104	16	16	the	the	DET
hjic-104	16	17	same	same	ADJ
hjic-104	16	18	is	be	AUX
hjic-104	16	19	true	true	ADJ
hjic-104	16	20	for	for	ADP
hjic-104	16	21	the	the	DET
hjic-104	16	22	approximate	approximate	ADJ
hjic-104	16	23	solution	solution	NOUN
hjic-104	16	24	which	which	PRON
hjic-104	16	25	we	we	PRON
hjic-104	16	26	get	get	VERB
hjic-104	16	27	by	by	ADP
hjic-104	16	28	using	use	VERB
hjic-104	16	29	bem	bem	PROPN
hjic-104	16	30	and	and	CCONJ
hjic-104	16	31	collocation	collocation	NOUN
hjic-104	16	32	.	.	PUNCT
hjic-104	17	1	piecewise	piecewise	NOUN
hjic-104	17	2	constant	constant	ADJ
hjic-104	17	3	and	and	CCONJ
hjic-104	17	4	piecewise	piecewise	NOUN
hjic-104	17	5	linear	linear	NOUN
hjic-104	17	6	functions	function	NOUN
hjic-104	17	7	will	will	AUX
hjic-104	17	8	be	be	AUX
hjic-104	17	9	used	use	VERB
hjic-104	17	10	to	to	PART
hjic-104	17	11	form	form	VERB
hjic-104	17	12	the	the	DET
hjic-104	17	13	ansatz	ansatz	ADJ
hjic-104	17	14	functions	function	NOUN
hjic-104	17	15	which	which	PRON
hjic-104	17	16	lead	lead	VERB
hjic-104	17	17	to	to	ADP
hjic-104	17	18	a	a	DET
hjic-104	17	19	simple	simple	ADJ
hjic-104	17	20	linear	linear	NOUN
hjic-104	17	21	system	system	NOUN
hjic-104	17	22	of	of	ADP
hjic-104	17	23	equations	equation	NOUN
hjic-104	17	24	.	.	PUNCT
hjic-104	18	1	neumann	neumann	PROPN
hjic-104	18	2	boundary	boundary	PROPN
hjic-104	18	3	value	value	NOUN
hjic-104	18	4	problem	problem	NOUN
hjic-104	18	5	for	for	ADP
hjic-104	18	6	the	the	DET
hjic-104	18	7	laplace	laplace	NOUN
hjic-104	18	8	equation	equation	NOUN
hjic-104	18	9	let	let	VERB
hjic-104	18	10	ω	ω	PRON
hjic-104	18	11	be	be	AUX
hjic-104	18	12	a	a	DET
hjic-104	18	13	convex	convex	NOUN
hjic-104	18	14	open	open	ADJ
hjic-104	18	15	domain	domain	NOUN
hjic-104	18	16	in	in	ADP
hjic-104	18	17	2r	2r	NUM
hjic-104	18	18	with	with	ADP
hjic-104	18	19	smooth	smooth	ADJ
hjic-104	18	20	boundary	boundary	ADJ
hjic-104	18	21	ω∂	ω∂	NOUN
hjic-104	18	22	.	.	PUNCT
hjic-104	19	1	consider	consider	VERB
hjic-104	19	2	the	the	DET
hjic-104	19	3	neumann	neumann	PROPN
hjic-104	19	4	boundary	boundary	PROPN
hjic-104	19	5	value	value	NOUN
hjic-104	19	6	problem	problem	NOUN
hjic-104	19	7	(	(	PUNCT
hjic-104	19	8	nbvp	nbvp	PROPN
hjic-104	19	9	)	)	PUNCT
hjic-104	19	10	:	:	PUNCT
hjic-104	19	11	(	(	PUNCT
hjic-104	19	12	)	)	PUNCT
hjic-104	19	13	0=∆	0=∆	NOUN
hjic-104	19	14	y	y	PROPN
hjic-104	19	15	,	,	PUNCT
hjic-104	19	16	xu	xu	PROPN
hjic-104	19	17	in	in	ADP
hjic-104	19	18	ω	ω	PROPN
hjic-104	19	19	,	,	PUNCT
hjic-104	19	20	(	(	PUNCT
hjic-104	19	21	1	1	NUM
hjic-104	19	22	)	)	PUNCT
hjic-104	19	23	(	(	PUNCT
hjic-104	19	24	)	)	PUNCT
hjic-104	19	25	(	(	PUNCT
hjic-104	19	26	y	y	PROPN
hjic-104	19	27	,	,	PUNCT
hjic-104	19	28	xg	xg	PROPN
hjic-104	19	29	n	n	PROPN
hjic-104	19	30	y	y	PROPN
hjic-104	19	31	,	,	PUNCT
hjic-104	19	32	xu	xu	PROPN
hjic-104	19	33	=	=	SYM
hjic-104	19	34	)	)	PUNCT
hjic-104	19	35	∂	∂	NUM
hjic-104	19	36	∂	∂	NUM
hjic-104	19	37	on	on	ADP
hjic-104	19	38	ω∂	ω∂	NUM
hjic-104	19	39	.	.	PUNCT
hjic-104	20	1	(	(	PUNCT
hjic-104	20	2	2	2	X
hjic-104	20	3	)	)	PUNCT
hjic-104	20	4	it	it	PRON
hjic-104	20	5	is	be	AUX
hjic-104	20	6	well	well	ADV
hjic-104	20	7	known	know	VERB
hjic-104	20	8	that	that	SCONJ
hjic-104	20	9	for	for	ADP
hjic-104	20	10	two	two	NUM
hjic-104	20	11	dimensions	dimension	NOUN
hjic-104	20	12	(	(	PUNCT
hjic-104	20	13	)	)	PUNCT
hjic-104	20	14	π	π	PROPN
hjic-104	20	15	ξ	ξ	X
hjic-104	20	16	ξ	ξ	SYM
hjic-104	20	17	2	2	NUM
hjic-104	20	18	−	−	NOUN
hjic-104	20	19	−=	−=	NOUN
hjic-104	20	20	xlog	xlog	PROPN
hjic-104	20	21	,	,	PUNCT
hjic-104	20	22	xe	xe	PROPN
hjic-104	20	23	(	(	PUNCT
hjic-104	20	24	3	3	NUM
hjic-104	20	25	)	)	PUNCT
hjic-104	20	26	is	be	AUX
hjic-104	20	27	the	the	DET
hjic-104	20	28	green	green	NOUN
hjic-104	20	29	's	's	PART
hjic-104	20	30	function	function	NOUN
hjic-104	20	31	or	or	CCONJ
hjic-104	20	32	the	the	DET
hjic-104	20	33	fundamental	fundamental	ADJ
hjic-104	20	34	solution	solution	NOUN
hjic-104	20	35	for	for	ADP
hjic-104	20	36	the	the	DET
hjic-104	20	37	operator	operator	NOUN
hjic-104	20	38	∆	∆	PROPN
hjic-104	20	39	,	,	PUNCT
hjic-104	20	40	that	that	PRON
hjic-104	20	41	means	mean	VERB
hjic-104	20	42	it	it	PRON
hjic-104	20	43	is	be	AUX
hjic-104	20	44	the	the	DET
hjic-104	20	45	solution	solution	NOUN
hjic-104	20	46	of	of	ADP
hjic-104	20	47	the	the	DET
hjic-104	20	48	problem	problem	NOUN
hjic-104	20	49	(	(	PUNCT
hjic-104	20	50	)	)	PUNCT
hjic-104	20	51	(	(	PUNCT
hjic-104	20	52	)	)	PUNCT
hjic-104	20	53	2r∈∀−−=∆	2r∈∀−−=∆	PROPN
hjic-104	20	54	ξξδξξ	ξξδξξ	INTJ
hjic-104	20	55	,	,	PUNCT
hjic-104	20	56	xx	xx	PROPN
hjic-104	20	57	,	,	PUNCT
hjic-104	20	58	xe	xe	PROPN
hjic-104	20	59	.	.	PUNCT
hjic-104	21	1	(	(	PUNCT
hjic-104	21	2	4	4	X
hjic-104	21	3	)	)	PUNCT
hjic-104	21	4	it	it	PRON
hjic-104	21	5	can	can	AUX
hjic-104	21	6	be	be	AUX
hjic-104	21	7	seen	see	VERB
hjic-104	21	8	that	that	SCONJ
hjic-104	21	9	e	e	NOUN
hjic-104	21	10	is	be	AUX
hjic-104	21	11	not	not	PART
hjic-104	21	12	defined	define	VERB
hjic-104	21	13	at	at	ADP
hjic-104	21	14	ξ	ξ	X
hjic-104	21	15	=	=	NOUN
hjic-104	21	16	x	x	NOUN
hjic-104	21	17	,	,	PUNCT
hjic-104	21	18	where	where	SCONJ
hjic-104	21	19	e	e	NOUN
hjic-104	21	20	is	be	AUX
hjic-104	21	21	singular	singular	ADJ
hjic-104	21	22	.	.	PUNCT
hjic-104	22	1	120	120	NUM
hjic-104	22	2	boundary	boundary	ADJ
hjic-104	22	3	integral	integral	ADJ
hjic-104	22	4	equation	equation	NOUN
hjic-104	22	5	for	for	SCONJ
hjic-104	22	6	we	we	PRON
hjic-104	22	7	follow	follow	VERB
hjic-104	22	8	the	the	DET
hjic-104	22	9	definition	definition	NOUN
hjic-104	22	10	of	of	ADP
hjic-104	22	11	the	the	DET
hjic-104	22	12	distribution	distribution	NOUN
hjic-104	22	13	ω∈x	ω∈x	NUM
hjic-104	22	14	δ	δ	PROPN
hjic-104	22	15	,	,	PUNCT
hjic-104	22	16	and	and	CCONJ
hjic-104	22	17	with	with	ADP
hjic-104	22	18	(	(	PUNCT
hjic-104	22	19	1	1	NUM
hjic-104	22	20	)	)	PUNCT
hjic-104	22	21	and	and	CCONJ
hjic-104	22	22	(	(	PUNCT
hjic-104	22	23	4	4	NUM
hjic-104	22	24	)	)	PUNCT
hjic-104	22	25	(	(	PUNCT
hjic-104	22	26	)	)	PUNCT
hjic-104	22	27	(	(	PUNCT
hjic-104	22	28	)	)	PUNCT
hjic-104	22	29	(	(	PUNCT
hjic-104	22	30	)	)	PUNCT
hjic-104	22	31	uxxu	uxxu	ADV
hjic-104	22	32	ξδ	ξδ	ADP
hjic-104	22	33	−=	−=	X
hjic-104	22	34	(	(	PUNCT
hjic-104	22	35	)	)	PUNCT
hjic-104	22	36	(	(	PUNCT
hjic-104	22	37	)	)	PUNCT
hjic-104	22	38	(	(	PUNCT
hjic-104	22	39	)	)	PUNCT
hjic-104	22	40	(	(	PUNCT
hjic-104	22	41	)	)	PUNCT
hjic-104	22	42	(	(	PUNCT
hjic-104	22	43	)	)	PUNCT
hjic-104	22	44	(	(	PUNCT
hjic-104	22	45	∫ω	∫ω	PROPN
hjic-104	22	46	∆−∆=	∆−∆=	PROPN
hjic-104	22	47	ξξξξξ	ξξξξξ	NOUN
hjic-104	22	48	ξ	ξ	PROPN
hjic-104	22	49	du	du	PROPN
hjic-104	22	50	,	,	PUNCT
hjic-104	22	51	xe	xe	PROPN
hjic-104	22	52	,	,	PUNCT
hjic-104	22	53	xeu	xeu	PROPN
hjic-104	22	54	)	)	PUNCT
hjic-104	22	55	the	the	DET
hjic-104	22	56	second	second	ADJ
hjic-104	22	57	green	green	ADJ
hjic-104	22	58	-	-	PUNCT
hjic-104	22	59	gauß	gauß	NOUN
hjic-104	22	60	formula	formula	NOUN
hjic-104	22	61	gives	give	VERB
hjic-104	22	62	(	(	PUNCT
hjic-104	22	63	)	)	PUNCT
hjic-104	22	64	(	(	PUNCT
hjic-104	22	65	)	)	PUNCT
hjic-104	22	66	(	(	PUNCT
hjic-104	22	67	)	)	PUNCT
hjic-104	22	68	(	(	PUNCT
hjic-104	22	69	)	)	PUNCT
hjic-104	22	70	(	(	PUNCT
hjic-104	22	71	)	)	PUNCT
hjic-104	22	72	ω∈∀⎟	ω∈∀⎟	ADJ
hjic-104	22	73	⎠	⎠	NOUN
hjic-104	22	74	⎞	⎞	X
hjic-104	22	75	⎜	⎜	PROPN
hjic-104	22	76	⎝	⎝	PUNCT
hjic-104	22	77	⎛	⎛	NOUN
hjic-104	22	78	∂	∂	NUM
hjic-104	22	79	∂	∂	NUM
hjic-104	22	80	−	−	PROPN
hjic-104	22	81	∂	∂	NUM
hjic-104	22	82	∂	∂	NUM
hjic-104	22	83	=	=	SYM
hjic-104	22	84	∫	∫	PROPN
hjic-104	22	85	ω∂	ω∂	PROPN
hjic-104	22	86	xdu	xdu	PROPN
hjic-104	22	87	n	n	PROPN
hjic-104	22	88	,	,	PUNCT
hjic-104	22	89	xe	xe	PROPN
hjic-104	22	90	,	,	PUNCT
hjic-104	22	91	xe	xe	PROPN
hjic-104	22	92	n	n	PROPN
hjic-104	22	93	u	u	PROPN
hjic-104	22	94	xu	xu	PROPN
hjic-104	22	95	ξσξ	ξσξ	PROPN
hjic-104	22	96	ξ	ξ	PROPN
hjic-104	22	97	ξ	ξ	PROPN
hjic-104	22	98	ξ	ξ	PROPN
hjic-104	22	99	.(5	.(5	NOUN
hjic-104	22	100	)	)	PUNCT
hjic-104	22	101	there	there	PRON
hjic-104	22	102	is	be	VERB
hjic-104	22	103	no	no	DET
hjic-104	22	104	singularity	singularity	NOUN
hjic-104	22	105	for	for	ADP
hjic-104	22	106	.	.	PUNCT
hjic-104	23	1	therefore	therefore	ADV
hjic-104	23	2	for	for	ADP
hjic-104	23	3	ω∈x	ω∈x	ADJ
hjic-104	23	4	ω∈x	ω∈x	NOUN
hjic-104	23	5	we	we	PRON
hjic-104	23	6	can	can	AUX
hjic-104	23	7	compute	compute	VERB
hjic-104	23	8	u(x	u(x	NOUN
hjic-104	23	9	)	)	PUNCT
hjic-104	23	10	by	by	ADP
hjic-104	23	11	knowing	know	VERB
hjic-104	23	12	the	the	DET
hjic-104	23	13	boundary	boundary	ADJ
hjic-104	23	14	data	datum	NOUN
hjic-104	23	15	u(x	u(x	NOUN
hjic-104	23	16	)	)	PUNCT
hjic-104	23	17	and	and	CCONJ
hjic-104	23	18	n	n	CCONJ
hjic-104	23	19	u	u	PROPN
hjic-104	23	20	∂	∂	NOUN
hjic-104	23	21	∂	∂	NUM
hjic-104	23	22	on	on	ADV
hjic-104	23	23	.	.	PUNCT
hjic-104	24	1	we	we	PRON
hjic-104	24	2	will	will	AUX
hjic-104	24	3	refer	refer	VERB
hjic-104	24	4	to	to	ADP
hjic-104	24	5	this	this	DET
hjic-104	24	6	formula	formula	NOUN
hjic-104	24	7	as	as	ADP
hjic-104	24	8	the	the	DET
hjic-104	24	9	representation	representation	NOUN
hjic-104	24	10	of	of	ADP
hjic-104	24	11	the	the	DET
hjic-104	24	12	solution	solution	NOUN
hjic-104	24	13	ω∂	ω∂	PUNCT
hjic-104	24	14	u(x	u(x	NOUN
hjic-104	24	15	)	)	PUNCT
hjic-104	24	16	for	for	ADP
hjic-104	24	17	.	.	PUNCT
hjic-104	24	18	ω∈x	ω∈x	ADJ
hjic-104	24	19	our	our	PRON
hjic-104	24	20	neumann	neumann	PROPN
hjic-104	24	21	problem	problem	NOUN
hjic-104	24	22	from	from	ADP
hjic-104	24	23	above	above	ADV
hjic-104	24	24	gives	give	VERB
hjic-104	24	25	n	n	PRON
hjic-104	24	26	u	u	PROPN
hjic-104	24	27	∂	∂	NOUN
hjic-104	24	28	∂	∂	NUM
hjic-104	24	29	on	on	ADV
hjic-104	24	30	.	.	PUNCT
hjic-104	25	1	we	we	PRON
hjic-104	25	2	have	have	VERB
hjic-104	25	3	to	to	PART
hjic-104	25	4	find	find	VERB
hjic-104	25	5	ω∂	ω∂	ADJ
hjic-104	25	6	u(x	u(x	NOUN
hjic-104	25	7	)	)	PUNCT
hjic-104	25	8	=	=	SYM
hjic-104	26	1	g(x	g(x	NOUN
hjic-104	26	2	)	)	PUNCT
hjic-104	26	3	on	on	ADP
hjic-104	26	4	.	.	PUNCT
hjic-104	26	5	ω∂	ω∂	NOUN
hjic-104	27	1	both	both	DET
hjic-104	27	2	integrals	integral	NOUN
hjic-104	27	3	in	in	ADP
hjic-104	27	4	(	(	PUNCT
hjic-104	27	5	5	5	NUM
hjic-104	27	6	)	)	PUNCT
hjic-104	27	7	(	(	PUNCT
hjic-104	27	8	)	)	PUNCT
hjic-104	27	9	(	(	PUNCT
hjic-104	27	10	)	)	PUNCT
hjic-104	27	11	(	(	PUNCT
hjic-104	27	12	)	)	PUNCT
hjic-104	27	13	(	(	PUNCT
hjic-104	27	14	)	)	PUNCT
hjic-104	27	15	∫∫	∫∫	ADV
hjic-104	27	16	ω∂ω∂	ω∂ω∂	NOUN
hjic-104	27	17	∂	∂	NUM
hjic-104	27	18	∂	∂	NUM
hjic-104	27	19	∂	∂	NUM
hjic-104	27	20	∂	∂	NUM
hjic-104	27	21	ξ	ξ	X
hjic-104	27	22	ξ	ξ	X
hjic-104	27	23	ξ	ξ	X
hjic-104	27	24	σξξσξξ	σξξσξξ	NOUN
hjic-104	27	25	du	du	X
hjic-104	27	26	n	n	X
hjic-104	27	27	,	,	PUNCT
hjic-104	27	28	xed	xed	PROPN
hjic-104	27	29	,	,	PUNCT
hjic-104	27	30	xe	xe	PROPN
hjic-104	27	31	n	n	NUM
hjic-104	27	32	u	u	PROPN
hjic-104	27	33	and	and	CCONJ
hjic-104	27	34	(	(	PUNCT
hjic-104	27	35	6	6	NUM
hjic-104	27	36	)	)	PUNCT
hjic-104	27	37	are	be	AUX
hjic-104	27	38	well	well	ADV
hjic-104	27	39	defined	define	VERB
hjic-104	27	40	for	for	ADP
hjic-104	27	41	.	.	PUNCT
hjic-104	28	1	but	but	CCONJ
hjic-104	28	2	for	for	SCONJ
hjic-104	28	3	we	we	PRON
hjic-104	28	4	have	have	VERB
hjic-104	28	5	a	a	DET
hjic-104	28	6	jump	jump	NOUN
hjic-104	28	7	of	of	ADP
hjic-104	28	8	magnitude	magnitude	NOUN
hjic-104	28	9	ω∈x	ω∈x	ADJ
hjic-104	28	10	ω∂∈x	ω∂∈x	NUM
hjic-104	28	11	(	(	PUNCT
hjic-104	28	12	)	)	PUNCT
hjic-104	28	13	2	2	NUM
hjic-104	28	14	xu	xu	INTJ
hjic-104	28	15	for	for	ADP
hjic-104	28	16	the	the	DET
hjic-104	28	17	second	second	ADJ
hjic-104	28	18	integral	integral	ADJ
hjic-104	28	19	:	:	PUNCT
hjic-104	28	20	(	(	PUNCT
hjic-104	28	21	)	)	PUNCT
hjic-104	28	22	(	(	PUNCT
hjic-104	28	23	)	)	PUNCT
hjic-104	28	24	(	(	PUNCT
hjic-104	28	25	)	)	PUNCT
hjic-104	28	26	(	(	PUNCT
hjic-104	28	27	)	)	PUNCT
hjic-104	28	28	(	(	PUNCT
hjic-104	29	1	)	)	PUNCT
hjic-104	29	2	∫∫	∫∫	ADV
hjic-104	29	3	ω∂ω∂ω∂∈→	ω∂ω∂ω∂∈→	NUM
hjic-104	29	4	∂	∂	NUM
hjic-104	29	5	∂	∂	NUM
hjic-104	29	6	+	+	NOUN
hjic-104	29	7	=	=	X
hjic-104	29	8	∂	∂	NUM
hjic-104	29	9	∂	∂	NUM
hjic-104	29	10	ξ	ξ	X
hjic-104	29	11	ξ	ξ	PROPN
hjic-104	29	12	ξ	ξ	X
hjic-104	29	13	ξ	ξ	PROPN
hjic-104	29	14	σξ	σξ	PROPN
hjic-104	29	15	ξ	ξ	PROPN
hjic-104	29	16	σξξ	σξξ	NOUN
hjic-104	29	17	du	du	PROPN
hjic-104	29	18	n	n	PROPN
hjic-104	29	19	,	,	PUNCT
hjic-104	29	20	xexu	xexu	X
hjic-104	29	21	du	du	PROPN
hjic-104	29	22	n	n	PROPN
hjic-104	29	23	,	,	PUNCT
hjic-104	29	24	xelim	xelim	PROPN
hjic-104	29	25	xx	xx	NUM
hjic-104	29	26	00	00	NUM
hjic-104	29	27	20	20	NUM
hjic-104	30	1	and	and	CCONJ
hjic-104	30	2	so	so	ADV
hjic-104	30	3	we	we	PRON
hjic-104	30	4	obtain	obtain	VERB
hjic-104	30	5	the	the	DET
hjic-104	30	6	boundary	boundary	ADJ
hjic-104	30	7	integral	integral	ADJ
hjic-104	30	8	equation	equation	NOUN
hjic-104	30	9	(	(	PUNCT
hjic-104	30	10	)	)	PUNCT
hjic-104	30	11	(	(	PUNCT
hjic-104	30	12	)	)	PUNCT
hjic-104	30	13	(	(	PUNCT
hjic-104	30	14	)	)	PUNCT
hjic-104	30	15	(	(	PUNCT
hjic-104	30	16	)	)	PUNCT
hjic-104	30	17	(	(	PUNCT
hjic-104	30	18	)	)	PUNCT
hjic-104	30	19	(	(	PUNCT
hjic-104	30	20	)	)	PUNCT
hjic-104	30	21	∫	∫	PROPN
hjic-104	30	22	ω∂	ω∂	PRON
hjic-104	31	1	⎟	⎟	X
hjic-104	31	2	⎟	⎟	X
hjic-104	31	3	⎠	⎠	PUNCT
hjic-104	31	4	⎞	⎞	PROPN
hjic-104	31	5	⎜	⎜	PROPN
hjic-104	31	6	⎜	⎜	PROPN
hjic-104	31	7	⎝	⎝	PUNCT
hjic-104	31	8	⎛	⎛	NOUN
hjic-104	31	9	∂	∂	NUM
hjic-104	31	10	∂	∂	NUM
hjic-104	31	11	−	−	NOUN
hjic-104	31	12	∂	∂	NUM
hjic-104	31	13	∂	∂	NOUN
hjic-104	31	14	+	+	ADP
hjic-104	31	15	=	=	X
hjic-104	31	16	ξ	ξ	X
hjic-104	31	17	ξ	ξ	X
hjic-104	31	18	σξ	σξ	PROPN
hjic-104	31	19	ξξ	ξξ	ADP
hjic-104	31	20	ξ	ξ	X
hjic-104	31	21	du	du	X
hjic-104	31	22	n	n	PROPN
hjic-104	31	23	,	,	PUNCT
hjic-104	31	24	xe	xe	PROPN
hjic-104	31	25	n	n	PROPN
hjic-104	31	26	u	u	PROPN
hjic-104	31	27	,	,	PUNCT
hjic-104	31	28	xe	xe	PROPN
hjic-104	31	29	xu	xu	PROPN
hjic-104	32	1	xu	xu	PROPN
hjic-104	32	2	0	0	NUM
hjic-104	33	1	0	0	NUM
hjic-104	33	2	0	0	NUM
hjic-104	33	3	0	0	NUM
hjic-104	33	4	2	2	NUM
hjic-104	33	5	(	(	PUNCT
hjic-104	33	6	7	7	NUM
hjic-104	33	7	)	)	PUNCT
hjic-104	33	8	ω∂∈∀	ω∂∈∀	PROPN
hjic-104	33	9	0x	0x	NOUN
hjic-104	33	10	then	then	ADV
hjic-104	33	11	we	we	PRON
hjic-104	33	12	get	get	VERB
hjic-104	33	13	from	from	ADP
hjic-104	33	14	(	(	PUNCT
hjic-104	33	15	7	7	NUM
hjic-104	33	16	)	)	PUNCT
hjic-104	33	17	a	a	DET
hjic-104	33	18	fredholm	fredholm	NOUN
hjic-104	33	19	integral	integral	ADJ
hjic-104	33	20	equation	equation	NOUN
hjic-104	33	21	of	of	ADP
hjic-104	33	22	the	the	DET
hjic-104	33	23	second	second	ADJ
hjic-104	33	24	kind	kind	NOUN
hjic-104	33	25	(	(	PUNCT
hjic-104	33	26	)	)	PUNCT
hjic-104	33	27	(	(	PUNCT
hjic-104	33	28	)	)	PUNCT
hjic-104	33	29	(	(	PUNCT
hjic-104	33	30	)	)	PUNCT
hjic-104	33	31	(	(	PUNCT
hjic-104	33	32	)	)	PUNCT
hjic-104	33	33	(	(	PUNCT
hjic-104	33	34	)	)	PUNCT
hjic-104	33	35	ξξ	ξξ	ADP
hjic-104	33	36	ξ	ξ	X
hjic-104	33	37	σ	σ	X
hjic-104	33	38	ξ	ξ	PROPN
hjic-104	33	39	ξσξ	ξσξ	NOUN
hjic-104	33	40	ξ	ξ	PROPN
hjic-104	33	41	d	d	PROPN
hjic-104	33	42	n	n	PRON
hjic-104	33	43	u	u	NOUN
hjic-104	33	44	,	,	PUNCT
hjic-104	33	45	xedu	xedu	PROPN
hjic-104	33	46	n	n	PRON
hjic-104	33	47	,	,	PUNCT
hjic-104	33	48	xexu	xexu	PUNCT
hjic-104	34	1	∫∫	∫∫	ADP
hjic-104	34	2	ω∂ω∂	ω∂ω∂	NOUN
hjic-104	34	3	∂	∂	NUM
hjic-104	34	4	∂	∂	NUM
hjic-104	34	5	=	=	SYM
hjic-104	34	6	∂	∂	NOUN
hjic-104	34	7	∂	∂	NOUN
hjic-104	34	8	+	+	NUM
hjic-104	34	9	2	2	NUM
hjic-104	34	10	(	(	PUNCT
hjic-104	34	11	8)	8)	NUM
hjic-104	34	12	ω∂∈∀x	ω∂∈∀x	NOUN
hjic-104	34	13	where	where	SCONJ
hjic-104	34	14	u	u	NOUN
hjic-104	34	15	on	on	ADP
hjic-104	34	16	the	the	DET
hjic-104	34	17	left	left	ADJ
hjic-104	34	18	hand	hand	NOUN
hjic-104	34	19	side	side	NOUN
hjic-104	34	20	is	be	AUX
hjic-104	34	21	unknown	unknown	ADJ
hjic-104	34	22	and	and	CCONJ
hjic-104	34	23	(	(	PUNCT
hjic-104	34	24	)	)	PUNCT
hjic-104	34	25	(	(	PUNCT
hjic-104	34	26	)	)	PUNCT
hjic-104	34	27	xg	xg	PROPN
hjic-104	35	1	n	n	PROPN
hjic-104	35	2	xu	xu	PROPN
hjic-104	36	1	=	=	SYM
hjic-104	36	2	∂	∂	NUM
hjic-104	36	3	∂	∂	NUM
hjic-104	36	4	on	on	ADP
hjic-104	36	5	is	be	AUX
hjic-104	36	6	given	give	VERB
hjic-104	36	7	.	.	PUNCT
hjic-104	37	1	ω∂	ω∂	ADJ
hjic-104	37	2	collocation	collocation	NOUN
hjic-104	37	3	method	method	VERB
hjic-104	37	4	the	the	DET
hjic-104	37	5	integral	integral	ADJ
hjic-104	37	6	equation	equation	NOUN
hjic-104	37	7	(	(	PUNCT
hjic-104	37	8	9	9	X
hjic-104	37	9	)	)	PUNCT
hjic-104	37	10	does	do	AUX
hjic-104	37	11	generally	generally	ADV
hjic-104	37	12	not	not	PART
hjic-104	37	13	admit	admit	VERB
hjic-104	37	14	a	a	DET
hjic-104	37	15	solution	solution	NOUN
hjic-104	37	16	in	in	ADP
hjic-104	37	17	closed	closed	ADJ
hjic-104	37	18	form	form	NOUN
hjic-104	37	19	.	.	PUNCT
hjic-104	38	1	we	we	PRON
hjic-104	38	2	will	will	AUX
hjic-104	38	3	show	show	VERB
hjic-104	38	4	how	how	SCONJ
hjic-104	38	5	to	to	PART
hjic-104	38	6	solve	solve	VERB
hjic-104	38	7	such	such	DET
hjic-104	38	8	a	a	DET
hjic-104	38	9	problem	problem	NOUN
hjic-104	38	10	numerically	numerically	ADV
hjic-104	38	11	using	use	VERB
hjic-104	38	12	the	the	DET
hjic-104	38	13	collocation	collocation	NOUN
hjic-104	38	14	method	method	NOUN
hjic-104	38	15	.	.	PUNCT
hjic-104	39	1	given	give	VERB
hjic-104	39	2	(	(	PUNCT
hjic-104	39	3	)	)	PUNCT
hjic-104	39	4	(	(	PUNCT
hjic-104	39	5	)	)	PUNCT
hjic-104	39	6	,	,	PUNCT
hjic-104	39	7	x	x	X
hjic-104	39	8	,	,	PUNCT
hjic-104	39	9	xg	xg	PROPN
hjic-104	39	10	n	n	PROPN
hjic-104	39	11	xu	xu	PROPN
hjic-104	39	12	ω∂∈=	ω∂∈=	PROPN
hjic-104	39	13	∂	∂	NUM
hjic-104	39	14	∂	∂	NUM
hjic-104	39	15	solve	solve	NOUN
hjic-104	39	16	for	for	ADP
hjic-104	39	17	the	the	DET
hjic-104	39	18	unknown	unknown	ADJ
hjic-104	39	19	dirichlet	dirichlet	PROPN
hjic-104	39	20	data	datum	NOUN
hjic-104	39	21	u(x	u(x	NOUN
hjic-104	39	22	)	)	PUNCT
hjic-104	39	23	,	,	PUNCT
hjic-104	39	24	ω∂∈x	ω∂∈x	NUM
hjic-104	39	25	from	from	ADP
hjic-104	39	26	(	(	PUNCT
hjic-104	39	27	)	)	PUNCT
hjic-104	39	28	(	(	PUNCT
hjic-104	39	29	)	)	PUNCT
hjic-104	39	30	(	(	PUNCT
hjic-104	39	31	)	)	PUNCT
hjic-104	39	32	(	(	PUNCT
hjic-104	39	33	)	)	PUNCT
hjic-104	39	34	(	(	PUNCT
hjic-104	39	35	)	)	PUNCT
hjic-104	39	36	,	,	PUNCT
hjic-104	39	37	dg	dg	PROPN
hjic-104	39	38	,	,	PUNCT
hjic-104	39	39	xedu	xedu	PROPN
hjic-104	39	40	n	n	PRON
hjic-104	39	41	,	,	PUNCT
hjic-104	39	42	xexu	xexu	PROPN
hjic-104	39	43	ξξ	ξξ	ADP
hjic-104	39	44	ξ	ξ	X
hjic-104	39	45	σξξσξ	σξξσξ	NOUN
hjic-104	39	46	ξ	ξ	X
hjic-104	39	47	∫∫	∫∫	PROPN
hjic-104	39	48	ω∂ω∂	ω∂ω∂	PROPN
hjic-104	39	49	=	=	SYM
hjic-104	39	50	∂	∂	NUM
hjic-104	39	51	∂	∂	NOUN
hjic-104	39	52	+	+	NUM
hjic-104	39	53	2	2	NUM
hjic-104	39	54	(	(	PUNCT
hjic-104	39	55	9	9	NUM
hjic-104	39	56	)	)	PUNCT
hjic-104	39	57	ω∂∈∀x	ω∂∈∀x	VERB
hjic-104	39	58	the	the	DET
hjic-104	39	59	solution	solution	NOUN
hjic-104	39	60	of	of	ADP
hjic-104	39	61	(	(	PUNCT
hjic-104	39	62	9	9	NUM
hjic-104	39	63	)	)	PUNCT
hjic-104	39	64	is	be	AUX
hjic-104	39	65	not	not	PART
hjic-104	39	66	unique	unique	ADJ
hjic-104	39	67	since	since	SCONJ
hjic-104	39	68	if	if	SCONJ
hjic-104	39	69	we	we	PRON
hjic-104	39	70	replace	replace	VERB
hjic-104	39	71	u(x	u(x	NOUN
hjic-104	39	72	)	)	PUNCT
hjic-104	39	73	by	by	ADP
hjic-104	39	74	(	(	PUNCT
hjic-104	39	75	)	)	PUNCT
hjic-104	39	76	(	(	PUNCT
hjic-104	39	77	)	)	PUNCT
hjic-104	39	78	cxuxu	cxuxu	NOUN
hjic-104	40	1	+	+	PROPN
hjic-104	40	2	=	=	NOUN
hjic-104	40	3	where	where	SCONJ
hjic-104	40	4	c	c	NOUN
hjic-104	40	5	is	be	AUX
hjic-104	40	6	constant	constant	ADJ
hjic-104	40	7	then	then	ADV
hjic-104	40	8	u	u	NOUN
hjic-104	40	9	is	be	AUX
hjic-104	40	10	a	a	DET
hjic-104	40	11	solution	solution	NOUN
hjic-104	40	12	,	,	PUNCT
hjic-104	40	13	too	too	ADV
hjic-104	40	14	.	.	PUNCT
hjic-104	41	1	we	we	PRON
hjic-104	41	2	need	need	VERB
hjic-104	41	3	a	a	DET
hjic-104	41	4	compatibility	compatibility	NOUN
hjic-104	41	5	condition	condition	NOUN
hjic-104	41	6	so	so	SCONJ
hjic-104	41	7	that	that	SCONJ
hjic-104	41	8	the	the	DET
hjic-104	41	9	neumann	neumann	PROPN
hjic-104	41	10	boundary	boundary	PROPN
hjic-104	41	11	value	value	NOUN
hjic-104	41	12	problem	problem	NOUN
hjic-104	41	13	is	be	AUX
hjic-104	41	14	well	well	ADV
hjic-104	41	15	posed	pose	VERB
hjic-104	41	16	:	:	PUNCT
hjic-104	41	17	g(x	g(x	NOUN
hjic-104	41	18	)	)	PUNCT
hjic-104	41	19	should	should	AUX
hjic-104	41	20	satisfy	satisfy	VERB
hjic-104	41	21	(	(	PUNCT
hjic-104	41	22	)	)	PUNCT
hjic-104	41	23	(	(	PUNCT
hjic-104	41	24	)	)	PUNCT
hjic-104	41	25	(	(	PUNCT
hjic-104	41	26	)	)	PUNCT
hjic-104	41	27	∫∫∫	∫∫∫	PROPN
hjic-104	41	28	ω∂ω∂ω	ω∂ω∂ω	X
hjic-104	41	29	=	=	SYM
hjic-104	41	30	∂	∂	NUM
hjic-104	41	31	∂	∂	NUM
hjic-104	41	32	=	=	NOUN
hjic-104	41	33	∆=	∆=	NOUN
hjic-104	41	34	σσ	σσ	ADV
hjic-104	41	35	dxgd	dxgd	ADV
hjic-104	41	36	n	n	X
hjic-104	41	37	xudxxu0	xudxxu0	NOUN
hjic-104	42	1	(	(	PUNCT
hjic-104	42	2	10	10	NUM
hjic-104	42	3	)	)	PUNCT
hjic-104	42	4	we	we	PRON
hjic-104	42	5	use	use	VERB
hjic-104	42	6	now	now	ADV
hjic-104	42	7	the	the	DET
hjic-104	42	8	collocation	collocation	NOUN
hjic-104	42	9	method	method	NOUN
hjic-104	42	10	to	to	PART
hjic-104	42	11	discretize	discretize	VERB
hjic-104	42	12	the	the	DET
hjic-104	42	13	problem	problem	NOUN
hjic-104	42	14	.	.	PUNCT
hjic-104	43	1	we	we	PRON
hjic-104	43	2	subdivide	subdivide	VERB
hjic-104	43	3	the	the	DET
hjic-104	43	4	boundary	boundary	NOUN
hjic-104	43	5	into	into	ADP
hjic-104	43	6	n	n	CCONJ
hjic-104	43	7	arcs	arc	NOUN
hjic-104	43	8	and	and	CCONJ
hjic-104	43	9	call	call	VERB
hjic-104	43	10	the	the	DET
hjic-104	43	11	midpoints	midpoint	NOUN
hjic-104	43	12	of	of	ADP
hjic-104	43	13	the	the	DET
hjic-104	43	14	arcs	arc	NOUN
hjic-104	43	15	with	with	ADP
hjic-104	43	16	.	.	PUNCT
hjic-104	44	1	we	we	PRON
hjic-104	44	2	take	take	VERB
hjic-104	44	3	the	the	DET
hjic-104	44	4	ansatz	ansatz	ADJ
hjic-104	44	5	:	:	PUNCT
hjic-104	44	6	ω∂	ω∂	NUM
hjic-104	44	7	n	n	CCONJ
hjic-104	44	8	,	,	PUNCT
hjic-104	44	9	,	,	PUNCT
hjic-104	44	10	,	,	PUNCT
hjic-104	44	11	γγγ	γγγ	PRON
hjic-104	44	12	k21	k21	NOUN
hjic-104	44	13	nx,,x	nx,,x	PROPN
hjic-104	44	14	,	,	PUNCT
hjic-104	44	15	x	x	PROPN
hjic-104	44	16	k21	k21	PROPN
hjic-104	44	17	1xxn	1xxn	NUM
hjic-104	44	18	=	=	SYM
hjic-104	44	19	(	(	PUNCT
hjic-104	44	20	11	11	NUM
hjic-104	44	21	)	)	PUNCT
hjic-104	44	22	(	(	PUNCT
hjic-104	44	23	)	)	PUNCT
hjic-104	44	24	(	(	PUNCT
hjic-104	44	25	)	)	PUNCT
hjic-104	44	26	∑	∑	PUNCT
hjic-104	44	27	=	=	SYM
hjic-104	44	28	=	=	SYM
hjic-104	45	1	n	n	PROPN
hjic-104	45	2	i	i	PRON
hjic-104	45	3	ii	ii	VERB
hjic-104	45	4	xaxu~	xaxu~	PROPN
hjic-104	45	5	1	1	NUM
hjic-104	45	6	χ	χ	X
hjic-104	45	7	where	where	SCONJ
hjic-104	45	8	(	(	PUNCT
hjic-104	45	9	)	)	PUNCT
hjic-104	45	10	xiχ	xiχ	PROPN
hjic-104	45	11	is	be	AUX
hjic-104	45	12	the	the	DET
hjic-104	45	13	characteristic	characteristic	ADJ
hjic-104	45	14	function	function	NOUN
hjic-104	45	15	on	on	ADP
hjic-104	45	16	and	and	CCONJ
hjic-104	45	17	are	be	AUX
hjic-104	45	18	unknown	unknown	ADJ
hjic-104	45	19	parameters	parameter	NOUN
hjic-104	45	20	.	.	PUNCT
hjic-104	46	1	that	that	PRON
hjic-104	46	2	means	mean	VERB
hjic-104	46	3	iγ	iγ	ADP
hjic-104	46	4	ia	ia	PROPN
hjic-104	46	5	(	(	PUNCT
hjic-104	46	6	)	)	PUNCT
hjic-104	46	7	xu~	xu~	PROPN
hjic-104	46	8	is	be	AUX
hjic-104	46	9	a	a	DET
hjic-104	46	10	piecewise	piecewise	NOUN
hjic-104	46	11	constant	constant	ADJ
hjic-104	46	12	approximation	approximation	NOUN
hjic-104	46	13	to	to	ADP
hjic-104	46	14	u(x	u(x	NOUN
hjic-104	46	15	)	)	PUNCT
hjic-104	46	16	on	on	ADP
hjic-104	46	17	.	.	PUNCT
hjic-104	47	1	as	as	ADP
hjic-104	47	2	collocation	collocation	NOUN
hjic-104	47	3	points	point	NOUN
hjic-104	47	4	we	we	PRON
hjic-104	47	5	use	use	VERB
hjic-104	47	6	the	the	DET
hjic-104	47	7	midpoints	midpoint	NOUN
hjic-104	47	8	.	.	PUNCT
hjic-104	48	1	this	this	PRON
hjic-104	48	2	leads	lead	VERB
hjic-104	48	3	to	to	ADP
hjic-104	48	4	ω∂	ω∂	NOUN
hjic-104	48	5	(	(	PUNCT
hjic-104	48	6	)	)	PUNCT
hjic-104	48	7	(	(	PUNCT
hjic-104	48	8	)	)	PUNCT
hjic-104	48	9	(	(	PUNCT
hjic-104	48	10	)	)	PUNCT
hjic-104	48	11	,	,	PUNCT
hjic-104	48	12	dg	dg	PROPN
hjic-104	48	13	,	,	PUNCT
hjic-104	48	14	xed	xed	PROPN
hjic-104	48	15	n	n	PROPN
hjic-104	48	16	,	,	PUNCT
hjic-104	48	17	xe	xe	PROPN
hjic-104	48	18	a	a	PRON
hjic-104	48	19	a	a	DET
hjic-104	48	20	j	j	PROPN
hjic-104	49	1	n	n	CCONJ
hjic-104	50	1	i	i	PRON
hjic-104	50	2	j	j	PROPN
hjic-104	51	1	i	i	PRON
hjic-104	51	2	j	j	PROPN
hjic-104	52	1	i	i	PRON
hjic-104	52	2	∫∑	∫∑	PROPN
hjic-104	52	3	∫	∫	PROPN
hjic-104	52	4	ω∂	ω∂	X
hjic-104	53	1	=	=	SYM
hjic-104	53	2	γ	γ	X
hjic-104	53	3	=	=	SYM
hjic-104	53	4	∂	∂	NUM
hjic-104	53	5	∂	∂	NOUN
hjic-104	53	6	+	+	CCONJ
hjic-104	53	7	ξξ	ξξ	PART
hjic-104	53	8	ξ	ξ	PRON
hjic-104	53	9	σξξσ	σξξσ	NOUN
hjic-104	53	10	ξ	ξ	X
hjic-104	53	11	12	12	NUM
hjic-104	53	12	(	(	PUNCT
hjic-104	53	13	12	12	NUM
hjic-104	53	14	)	)	PUNCT
hjic-104	53	15	nj	nj	PROPN
hjic-104	53	16	≤≤1	≤≤1	PUNCT
hjic-104	54	1	these	these	PRON
hjic-104	54	2	are	be	AUX
hjic-104	54	3	n	n	PRON
hjic-104	54	4	linear	linear	ADJ
hjic-104	54	5	equations	equation	NOUN
hjic-104	54	6	with	with	ADP
hjic-104	54	7	the	the	DET
hjic-104	54	8	unknowns	unknown	NOUN
hjic-104	54	9	,	,	PUNCT
hjic-104	54	10	so	so	SCONJ
hjic-104	54	11	that	that	SCONJ
hjic-104	54	12	we	we	PRON
hjic-104	54	13	have	have	VERB
hjic-104	54	14	na,,a	na,,a	PROPN
hjic-104	54	15	k1	k1	NOUN
hjic-104	55	1	n	n	CCONJ
hjic-104	55	2	×	×	NOUN
hjic-104	55	3	n	n	CCONJ
hjic-104	55	4	linear	linear	ADJ
hjic-104	55	5	system	system	NOUN
hjic-104	55	6	of	of	ADP
hjic-104	55	7	equations	equation	NOUN
hjic-104	55	8	neumann	neumann	PROPN
hjic-104	55	9	boundary	boundary	ADJ
hjic-104	55	10	value	value	NOUN
hjic-104	55	11	problem	problem	NOUN
hjic-104	55	12	for	for	ADP
hjic-104	55	13	the	the	DET
hjic-104	55	14	heat	heat	NOUN
hjic-104	55	15	equation	equation	NOUN
hjic-104	55	16	let	let	VERB
hjic-104	55	17	ω	ω	PRON
hjic-104	55	18	be	be	AUX
hjic-104	55	19	a	a	DET
hjic-104	55	20	bounded	bounded	ADJ
hjic-104	55	21	convex	convex	NOUN
hjic-104	55	22	domain	domain	NOUN
hjic-104	55	23	with	with	ADP
hjic-104	55	24	smooth	smooth	ADJ
hjic-104	55	25	boundary	boundary	ADJ
hjic-104	55	26	γ	γ	NOUN
hjic-104	55	27	=	=	NOUN
hjic-104	55	28	ω∂	ω∂	NOUN
hjic-104	55	29	in	in	ADP
hjic-104	55	30	2r	2r	NUM
hjic-104	55	31	.	.	PUNCT
hjic-104	56	1	consider	consider	VERB
hjic-104	56	2	the	the	DET
hjic-104	56	3	heat	heat	NOUN
hjic-104	56	4	equation	equation	NOUN
hjic-104	56	5	(	(	PUNCT
hjic-104	56	6	)	)	PUNCT
hjic-104	56	7	(	(	PUNCT
hjic-104	56	8	)	)	PUNCT
hjic-104	56	9	(	(	PUNCT
hjic-104	56	10	)	)	PUNCT
hjic-104	56	11	,	,	PUNCT
hjic-104	56	12	y	y	PROPN
hjic-104	56	13	t	t	PROPN
hjic-104	56	14	,	,	PUNCT
hjic-104	56	15	y	y	PROPN
hjic-104	56	16	,	,	PUNCT
hjic-104	56	17	xu	xu	PROPN
hjic-104	56	18	x	x	SYM
hjic-104	56	19	t	t	PROPN
hjic-104	56	20	,	,	PUNCT
hjic-104	56	21	y	y	PROPN
hjic-104	56	22	,	,	PUNCT
hjic-104	56	23	xu	xu	PROPN
hjic-104	56	24	t	t	PROPN
hjic-104	56	25	t	t	PROPN
hjic-104	56	26	,	,	PUNCT
hjic-104	56	27	y	y	PROPN
hjic-104	56	28	,	,	PUNCT
hjic-104	56	29	xu	xu	PROPN
hjic-104	56	30	2	2	NUM
hjic-104	56	31	2	2	NUM
hjic-104	56	32	2	2	NUM
hjic-104	56	33	2	2	NUM
hjic-104	56	34	∂	∂	NUM
hjic-104	56	35	∂	∂	NUM
hjic-104	56	36	+	+	NUM
hjic-104	56	37	∂	∂	NUM
hjic-104	56	38	∂	∂	NUM
hjic-104	56	39	=	=	SYM
hjic-104	56	40	∂	∂	NUM
hjic-104	56	41	∂	∂	NUM
hjic-104	56	42	(	(	PUNCT
hjic-104	56	43	13	13	NUM
hjic-104	56	44	)	)	PUNCT
hjic-104	56	45	(	(	PUNCT
hjic-104	56	46	)	)	PUNCT
hjic-104	56	47	(	(	PUNCT
hjic-104	56	48	]	]	X
hjic-104	56	49	t	t	PROPN
hjic-104	56	50	,	,	PUNCT
hjic-104	56	51	t	t	PROPN
hjic-104	56	52	,	,	PUNCT
hjic-104	56	53	y	y	PROPN
hjic-104	56	54	,	,	PUNCT
hjic-104	56	55	x	x	SYM
hjic-104	56	56	0∈ω∈	0∈ω∈	PROPN
hjic-104	56	57	with	with	ADP
hjic-104	56	58	initial	initial	ADJ
hjic-104	56	59	and	and	CCONJ
hjic-104	56	60	boundary	boundary	ADJ
hjic-104	56	61	conditions	condition	NOUN
hjic-104	56	62	,	,	PUNCT
hjic-104	56	63	(	(	PUNCT
hjic-104	56	64	)	)	PUNCT
hjic-104	56	65	(	(	PUNCT
hjic-104	56	66	)	)	PUNCT
hjic-104	56	67	,	,	PUNCT
hjic-104	56	68	y	y	PROPN
hjic-104	56	69	,	,	PUNCT
hjic-104	56	70	xf	xf	PROPN
hjic-104	56	71	,	,	PUNCT
hjic-104	56	72	y	y	PROPN
hjic-104	56	73	,	,	PUNCT
hjic-104	56	74	xu	xu	PUNCT
hjic-104	57	1	=	=	SYM
hjic-104	57	2	0	0	PROPN
hjic-104	57	3	(	(	PUNCT
hjic-104	57	4	)	)	PUNCT
hjic-104	57	5	ω∈y	ω∈y	NOUN
hjic-104	57	6	,	,	PUNCT
hjic-104	57	7	x	x	X
hjic-104	57	8	(	(	PUNCT
hjic-104	57	9	14	14	NUM
hjic-104	57	10	)	)	PUNCT
hjic-104	57	11	(	(	PUNCT
hjic-104	57	12	)	)	PUNCT
hjic-104	57	13	(	(	PUNCT
hjic-104	57	14	)	)	PUNCT
hjic-104	57	15	(	(	PUNCT
hjic-104	57	16	)	)	PUNCT
hjic-104	57	17	(	(	PUNCT
hjic-104	57	18	]	]	X
hjic-104	57	19	t	t	PROPN
hjic-104	57	20	,	,	PUNCT
hjic-104	57	21	t	t	PROPN
hjic-104	57	22	,	,	PUNCT
hjic-104	57	23	y	y	PROPN
hjic-104	57	24	,	,	PUNCT
hjic-104	57	25	x	x	PROPN
hjic-104	57	26	,	,	PUNCT
hjic-104	57	27	t	t	PROPN
hjic-104	57	28	,	,	PUNCT
hjic-104	57	29	y	y	PROPN
hjic-104	57	30	,	,	PUNCT
hjic-104	57	31	xg	xg	PROPN
hjic-104	57	32	n	n	PROPN
hjic-104	57	33	t	t	PROPN
hjic-104	57	34	,	,	PUNCT
hjic-104	57	35	y	y	PROPN
hjic-104	57	36	,	,	PUNCT
hjic-104	57	37	xu	xu	PROPN
hjic-104	57	38	0∈γ∈=	0∈γ∈=	PROPN
hjic-104	57	39	∂	∂	NUM
hjic-104	57	40	∂	∂	NOUN
hjic-104	57	41	.	.	PUNCT
hjic-104	58	1	(	(	PUNCT
hjic-104	58	2	15	15	NUM
hjic-104	58	3	)	)	PUNCT
hjic-104	58	4	the	the	DET
hjic-104	58	5	problem	problem	NOUN
hjic-104	58	6	will	will	AUX
hjic-104	58	7	be	be	AUX
hjic-104	58	8	transformed	transform	VERB
hjic-104	58	9	into	into	ADP
hjic-104	58	10	an	an	DET
hjic-104	58	11	integral	integral	ADJ
hjic-104	58	12	equation	equation	NOUN
hjic-104	58	13	by	by	ADP
hjic-104	58	14	using	use	VERB
hjic-104	58	15	the	the	DET
hjic-104	58	16	fundamental	fundamental	ADJ
hjic-104	58	17	solution	solution	NOUN
hjic-104	58	18	and	and	CCONJ
hjic-104	58	19	will	will	AUX
hjic-104	58	20	be	be	AUX
hjic-104	58	21	solved	solve	VERB
hjic-104	58	22	by	by	ADP
hjic-104	58	23	applying	apply	VERB
hjic-104	58	24	the	the	DET
hjic-104	58	25	collocation	collocation	NOUN
hjic-104	58	26	method	method	NOUN
hjic-104	58	27	in	in	ADP
hjic-104	58	28	the	the	DET
hjic-104	58	29	same	same	ADJ
hjic-104	58	30	manner	manner	NOUN
hjic-104	58	31	as	as	ADP
hjic-104	58	32	for	for	ADP
hjic-104	58	33	the	the	DET
hjic-104	58	34	laplace	laplace	NOUN
hjic-104	58	35	equation	equation	NOUN
hjic-104	58	36	(	(	PUNCT
hjic-104	58	37	1	1	NUM
hjic-104	58	38	)	)	PUNCT
hjic-104	58	39	and	and	CCONJ
hjic-104	58	40	(	(	PUNCT
hjic-104	58	41	2	2	NUM
hjic-104	58	42	)	)	PUNCT
hjic-104	58	43	.	.	PUNCT
hjic-104	59	1	boundary	boundary	ADJ
hjic-104	59	2	integral	integral	ADJ
hjic-104	59	3	equation	equation	NOUN
hjic-104	59	4	the	the	DET
hjic-104	59	5	well	well	ADV
hjic-104	59	6	-	-	PUNCT
hjic-104	59	7	known	know	VERB
hjic-104	59	8	green	green	NOUN
hjic-104	59	9	’s	’s	PART
hjic-104	59	10	function	function	NOUN
hjic-104	59	11	or	or	CCONJ
hjic-104	59	12	fundamental	fundamental	ADJ
hjic-104	59	13	solution	solution	NOUN
hjic-104	59	14	for	for	ADP
hjic-104	59	15	the	the	DET
hjic-104	59	16	heat	heat	NOUN
hjic-104	59	17	equation	equation	NOUN
hjic-104	59	18	121	121	NUM
hjic-104	59	19	(	(	PUNCT
hjic-104	59	20	)	)	PUNCT
hjic-104	59	21	(	(	PUNCT
hjic-104	59	22	)	)	PUNCT
hjic-104	59	23	(	(	PUNCT
hjic-104	59	24	)	)	PUNCT
hjic-104	59	25	⎪	⎪	NOUN
hjic-104	59	26	⎪	⎪	NOUN
hjic-104	59	27	⎩	⎩	NUM
hjic-104	60	1	⎪⎪	⎪⎪	PROPN
hjic-104	60	2	⎨	⎨	ADJ
hjic-104	60	3	⎧	⎧	PROPN
hjic-104	60	4	≤	≤	PROPN
hjic-104	60	5	>	>	PUNCT
hjic-104	60	6	−=	−=	PUNCT
hjic-104	60	7	−	−	PROPN
hjic-104	60	8	−−	−−	NOUN
hjic-104	60	9	τ	τ	PROPN
hjic-104	60	10	τ	τ	PROPN
hjic-104	60	11	τπτξ	τπτξ	PROPN
hjic-104	60	12	τ	τ	PROPN
hjic-104	60	13	ξ	ξ	PROPN
hjic-104	60	14	t	t	PROPN
hjic-104	60	15	te	te	PROPN
hjic-104	60	16	tt	tt	PROPN
hjic-104	60	17	,	,	PUNCT
hjic-104	60	18	x;,e	x;,e	PROPN
hjic-104	60	19	t	t	PROPN
hjic-104	60	20	x	x	AUX
hjic-104	60	21	if0	if0	VERB
hjic-104	60	22	if	if	SCONJ
hjic-104	60	23	4	4	NUM
hjic-104	60	24	1	1	NUM
hjic-104	60	25	4	4	NUM
hjic-104	60	26	2	2	NUM
hjic-104	60	27	,	,	PUNCT
hjic-104	60	28	(	(	PUNCT
hjic-104	60	29	16	16	NUM
hjic-104	60	30	)	)	PUNCT
hjic-104	60	31	is	be	AUX
hjic-104	60	32	used	use	VERB
hjic-104	60	33	as	as	ADP
hjic-104	60	34	weight	weight	NOUN
hjic-104	60	35	function	function	NOUN
hjic-104	60	36	to	to	PART
hjic-104	60	37	generate	generate	VERB
hjic-104	60	38	the	the	DET
hjic-104	60	39	integral	integral	ADJ
hjic-104	60	40	equation	equation	NOUN
hjic-104	60	41	(	(	PUNCT
hjic-104	60	42	)	)	PUNCT
hjic-104	60	43	(	(	PUNCT
hjic-104	60	44	)	)	PUNCT
hjic-104	60	45	(	(	PUNCT
hjic-104	60	46	)	)	PUNCT
hjic-104	60	47	∫	∫	PROPN
hjic-104	61	1	∫	∫	PROPN
hjic-104	61	2	ω	ω	PROPN
hjic-104	62	1	=	=	AUX
hjic-104	62	2	⎟	⎟	X
hjic-104	62	3	⎠	⎠	X
hjic-104	62	4	⎞	⎞	VERB
hjic-104	62	5	⎜	⎜	PROPN
hjic-104	62	6	⎝	⎝	PUNCT
hjic-104	62	7	⎛	⎛	NOUN
hjic-104	62	8	∂	∂	NUM
hjic-104	62	9	∂	∂	NUM
hjic-104	62	10	−∆	−∆	NOUN
hjic-104	62	11	t	t	PROPN
hjic-104	62	12	ddt,;,et	ddt,;,et	PROPN
hjic-104	62	13	,	,	PUNCT
hjic-104	62	14	u	u	NOUN
hjic-104	62	15	,	,	PUNCT
hjic-104	62	16	u	u	NOUN
hjic-104	62	17	0ττ	0ττ	NOUN
hjic-104	62	18	τ	τ	PROPN
hjic-104	62	19	τ	τ	PROPN
hjic-104	62	20	ξxξξξξ	ξxξξξξ	NOUN
hjic-104	62	21	where	where	SCONJ
hjic-104	62	22	(	(	PUNCT
hjic-104	62	23	t	t	PROPN
hjic-104	62	24	,	,	PUNCT
hjic-104	62	25	u	u	NOUN
hjic-104	62	26	x	x	PROPN
hjic-104	62	27	)	)	PUNCT
hjic-104	62	28	is	be	AUX
hjic-104	62	29	the	the	DET
hjic-104	62	30	unknown	unknown	ADJ
hjic-104	62	31	solution	solution	NOUN
hjic-104	62	32	of	of	ADP
hjic-104	62	33	the	the	DET
hjic-104	62	34	heat	heat	NOUN
hjic-104	62	35	equation	equation	NOUN
hjic-104	62	36	,	,	PUNCT
hjic-104	62	37	(	(	PUNCT
hjic-104	62	38	)	)	PUNCT
hjic-104	62	39	,	,	PUNCT
hjic-104	62	40	,	,	PUNCT
hjic-104	62	41	21	21	NUM
hjic-104	62	42	ξξ	ξξ	NOUN
hjic-104	62	43	=	=	SYM
hjic-104	62	44	ξ	ξ	X
hjic-104	62	45	(	(	PUNCT
hjic-104	62	46	)	)	PUNCT
hjic-104	62	47	,	,	PUNCT
hjic-104	62	48	y	y	PROPN
hjic-104	62	49	,	,	PUNCT
hjic-104	62	50	x	x	NOUN
hjic-104	62	51	=	=	NOUN
hjic-104	62	52	x	x	SYM
hjic-104	62	53	2	2	NUM
hjic-104	62	54	2	2	NUM
hjic-104	62	55	2	2	NUM
hjic-104	62	56	2	2	NUM
hjic-104	62	57	1	1	NUM
hjic-104	62	58	2	2	NUM
hjic-104	62	59	ξξ	ξξ	NOUN
hjic-104	62	60	∂	∂	NUM
hjic-104	62	61	∂	∂	NUM
hjic-104	62	62	+	+	NUM
hjic-104	62	63	∂	∂	NUM
hjic-104	62	64	∂	∂	NUM
hjic-104	62	65	=	=	NOUN
hjic-104	62	66	∆	∆	X
hjic-104	62	67	ξ	ξ	X
hjic-104	62	68	.	.	PUNCT
hjic-104	63	1	let	let	VERB
hjic-104	63	2	ω	ω	PRON
hjic-104	63	3	be	be	AUX
hjic-104	63	4	a	a	DET
hjic-104	63	5	bounded	bounded	ADJ
hjic-104	63	6	convex	convex	NOUN
hjic-104	63	7	domain	domain	NOUN
hjic-104	63	8	in	in	ADP
hjic-104	63	9	2r	2r	NUM
hjic-104	63	10	with	with	ADP
hjic-104	63	11	smooth	smooth	ADJ
hjic-104	63	12	boundary	boundary	ADJ
hjic-104	63	13	ω∂=γ	ω∂=γ	NOUN
hjic-104	63	14	.	.	PUNCT
hjic-104	64	1	by	by	ADP
hjic-104	64	2	using	use	VERB
hjic-104	64	3	the	the	DET
hjic-104	64	4	gauss	gauss	ADJ
hjic-104	64	5	-	-	PUNCT
hjic-104	64	6	green	green	ADJ
hjic-104	64	7	formula	formula	NOUN
hjic-104	64	8	the	the	DET
hjic-104	64	9	integral	integral	ADJ
hjic-104	64	10	becomes	become	NOUN
hjic-104	64	11	:	:	PUNCT
hjic-104	64	12	(	(	PUNCT
hjic-104	64	13	)	)	PUNCT
hjic-104	64	14	(	(	PUNCT
hjic-104	64	15	)	)	PUNCT
hjic-104	64	16	(	(	PUNCT
hjic-104	64	17	)	)	PUNCT
hjic-104	64	18	(	(	PUNCT
hjic-104	64	19	)	)	PUNCT
hjic-104	64	20	(	(	PUNCT
hjic-104	64	21	)	)	PUNCT
hjic-104	64	22	(	(	PUNCT
hjic-104	64	23	)	)	PUNCT
hjic-104	64	24	(	(	PUNCT
hjic-104	64	25	)	)	PUNCT
hjic-104	64	26	∫∫	∫∫	ADV
hjic-104	64	27	∫	∫	PROPN
hjic-104	64	28	∫	∫	PROPN
hjic-104	64	29	∫	∫	PROPN
hjic-104	64	30	ωγ	ωγ	ADP
hjic-104	64	31	γ	γ	PROPN
hjic-104	64	32	+	+	SYM
hjic-104	64	33	∂	∂	NUM
hjic-104	64	34	∂	∂	NUM
hjic-104	64	35	−	−	PROPN
hjic-104	64	36	⋅	⋅	PROPN
hjic-104	64	37	∂	∂	NUM
hjic-104	64	38	∂	∂	NOUN
hjic-104	64	39	=	=	NOUN
hjic-104	64	40	ξξξτστξτξ	ξξξτστξτξ	VERB
hjic-104	64	41	τστξτξ	τστξτξ	ADP
hjic-104	64	42	ξ	ξ	PROPN
hjic-104	64	43	ξ	ξ	X
hjic-104	64	44	ξ	ξ	X
hjic-104	64	45	ξ	ξ	X
hjic-104	64	46	dt	dt	PROPN
hjic-104	64	47	,	,	PUNCT
hjic-104	64	48	x;,efdd	x;,efdd	PROPN
hjic-104	64	49	n	n	PRON
hjic-104	64	50	t	t	PROPN
hjic-104	64	51	,	,	PUNCT
hjic-104	64	52	x;,e	x;,e	PROPN
hjic-104	64	53	,	,	PUNCT
hjic-104	64	54	u	u	PROPN
hjic-104	64	55	ddt	ddt	PROPN
hjic-104	64	56	,	,	PUNCT
hjic-104	64	57	x;,e	x;,e	PROPN
hjic-104	64	58	n	n	PROPN
hjic-104	64	59	,	,	PUNCT
hjic-104	64	60	ut	ut	PROPN
hjic-104	64	61	,	,	PUNCT
hjic-104	64	62	xu	xu	PROPN
hjic-104	65	1	t	t	PROPN
hjic-104	65	2	t	t	PROPN
hjic-104	65	3	0	0	NUM
hjic-104	65	4	0	0	NUM
hjic-104	65	5	0	0	NUM
hjic-104	65	6	for	for	ADP
hjic-104	65	7	(	(	PUNCT
hjic-104	65	8	)	)	PUNCT
hjic-104	65	9	(	(	PUNCT
hjic-104	65	10	]	]	X
hjic-104	65	11	t	t	PROPN
hjic-104	65	12	,	,	PUNCT
hjic-104	65	13	t	t	PROPN
hjic-104	65	14	,	,	PUNCT
hjic-104	65	15	x	x	PROPN
hjic-104	65	16	0×ω∈	0×ω∈	NOUN
hjic-104	65	17	the	the	DET
hjic-104	65	18	left	left	ADJ
hjic-104	65	19	hand	hand	NOUN
hjic-104	65	20	side	side	NOUN
hjic-104	65	21	of	of	ADP
hjic-104	65	22	the	the	DET
hjic-104	65	23	formula	formula	NOUN
hjic-104	65	24	has	have	VERB
hjic-104	65	25	to	to	PART
hjic-104	65	26	be	be	AUX
hjic-104	65	27	replaced	replace	VERB
hjic-104	65	28	by	by	ADP
hjic-104	65	29	the	the	DET
hjic-104	65	30	famous	famous	ADJ
hjic-104	65	31	jump	jump	NOUN
hjic-104	65	32	relation	relation	NOUN
hjic-104	65	33	if	if	SCONJ
hjic-104	65	34	x	x	PRON
hjic-104	65	35	is	be	AUX
hjic-104	65	36	on	on	ADP
hjic-104	65	37	the	the	DET
hjic-104	65	38	boundary	boundary	NOUN
hjic-104	65	39	.	.	PUNCT
hjic-104	66	1	so	so	ADV
hjic-104	66	2	we	we	PRON
hjic-104	66	3	are	be	AUX
hjic-104	66	4	led	lead	VERB
hjic-104	66	5	to	to	ADP
hjic-104	66	6	a	a	DET
hjic-104	66	7	boundary	boundary	ADJ
hjic-104	66	8	integral	integral	ADJ
hjic-104	66	9	equation	equation	NOUN
hjic-104	66	10	for	for	ADP
hjic-104	66	11	γ∈x	γ∈x	NOUN
hjic-104	66	12	and	and	CCONJ
hjic-104	66	13	.	.	PUNCT
hjic-104	67	1	tt	tt	PROPN
hjic-104	67	2	≤<0	≤<0	PROPN
hjic-104	67	3	(	(	PUNCT
hjic-104	67	4	)	)	PUNCT
hjic-104	67	5	(	(	PUNCT
hjic-104	67	6	)	)	PUNCT
hjic-104	67	7	(	(	PUNCT
hjic-104	67	8	)	)	PUNCT
hjic-104	67	9	(	(	PUNCT
hjic-104	67	10	)	)	PUNCT
hjic-104	67	11	(	(	PUNCT
hjic-104	67	12	)	)	PUNCT
hjic-104	67	13	(	(	PUNCT
hjic-104	67	14	)	)	PUNCT
hjic-104	67	15	(	(	PUNCT
hjic-104	67	16	)	)	PUNCT
hjic-104	67	17	∫	∫	PROPN
hjic-104	68	1	∫	∫	PROPN
hjic-104	68	2	∫	∫	PROPN
hjic-104	68	3	∫	∫	PROPN
hjic-104	68	4	∫	∫	PROPN
hjic-104	68	5	ω	ω	PROPN
hjic-104	68	6	γ	γ	PROPN
hjic-104	68	7	γ	γ	X
hjic-104	68	8	+	+	X
hjic-104	68	9	∂	∂	NUM
hjic-104	68	10	∂	∂	NUM
hjic-104	68	11	−	−	PROPN
hjic-104	68	12	⋅	⋅	PROPN
hjic-104	68	13	∂	∂	NUM
hjic-104	68	14	∂	∂	NOUN
hjic-104	68	15	=	=	NOUN
hjic-104	68	16	ξξξ	ξξξ	NOUN
hjic-104	68	17	τσ	τσ	PROPN
hjic-104	68	18	τξ	τξ	ADP
hjic-104	68	19	τξ	τξ	ADP
hjic-104	68	20	τστξ	τστξ	NOUN
hjic-104	68	21	τξ	τξ	ADP
hjic-104	68	22	ξ	ξ	X
hjic-104	68	23	ξ	ξ	X
hjic-104	68	24	ξ	ξ	X
hjic-104	68	25	ξ	ξ	X
hjic-104	68	26	dt	dt	PROPN
hjic-104	68	27	,	,	PUNCT
hjic-104	68	28	x;,ef	x;,ef	PROPN
hjic-104	68	29	dd	dd	PROPN
hjic-104	68	30	n	n	PROPN
hjic-104	68	31	t	t	PROPN
hjic-104	68	32	,	,	PUNCT
hjic-104	68	33	x;,e	x;,e	PROPN
hjic-104	68	34	,	,	PUNCT
hjic-104	68	35	u	u	PROPN
hjic-104	68	36	ddt	ddt	PROPN
hjic-104	68	37	,	,	PUNCT
hjic-104	68	38	x;,e	x;,e	PROPN
hjic-104	68	39	n	n	PROPN
hjic-104	68	40	,	,	PUNCT
hjic-104	68	41	ut	ut	PROPN
hjic-104	68	42	,	,	PUNCT
hjic-104	68	43	xu	xu	PROPN
hjic-104	69	1	t	t	PROPN
hjic-104	69	2	t	t	NOUN
hjic-104	69	3	0	0	NUM
hjic-104	69	4	2	2	NUM
hjic-104	69	5	1	1	NUM
hjic-104	69	6	0	0	NUM
hjic-104	69	7	0	0	NUM
hjic-104	69	8	substitute	substitute	NOUN
hjic-104	69	9	the	the	DET
hjic-104	69	10	given	give	VERB
hjic-104	69	11	boundary	boundary	ADJ
hjic-104	69	12	condition	condition	NOUN
hjic-104	69	13	into	into	ADP
hjic-104	69	14	(	(	PUNCT
hjic-104	69	15	)	)	PUNCT
hjic-104	69	16	ξ	ξ	PROPN
hjic-104	69	17	τξ	τξ	ADP
hjic-104	69	18	n	n	PROPN
hjic-104	69	19	,	,	PUNCT
hjic-104	69	20	u	u	PROPN
hjic-104	69	21	∂	∂	NOUN
hjic-104	69	22	∂	∂	NOUN
hjic-104	69	23	the	the	DET
hjic-104	69	24	boundary	boundary	ADJ
hjic-104	69	25	integral	integral	ADJ
hjic-104	69	26	equation	equation	NOUN
hjic-104	69	27	becomes	become	VERB
hjic-104	69	28	(	(	PUNCT
hjic-104	69	29	)	)	PUNCT
hjic-104	69	30	(	(	PUNCT
hjic-104	69	31	)	)	PUNCT
hjic-104	69	32	(	(	PUNCT
hjic-104	69	33	)	)	PUNCT
hjic-104	69	34	(	(	PUNCT
hjic-104	69	35	)	)	PUNCT
hjic-104	69	36	(	(	PUNCT
hjic-104	69	37	)	)	PUNCT
hjic-104	69	38	(	(	PUNCT
hjic-104	69	39	)	)	PUNCT
hjic-104	69	40	(	(	PUNCT
hjic-104	69	41	)	)	PUNCT
hjic-104	70	1	∫∫	∫∫	ADV
hjic-104	70	2	∫	∫	PROPN
hjic-104	70	3	∫	∫	PROPN
hjic-104	70	4	∫	∫	PROPN
hjic-104	70	5	ωγ	ωγ	PROPN
hjic-104	70	6	γ	γ	PROPN
hjic-104	70	7	+	+	PROPN
hjic-104	70	8	⋅=	⋅=	PROPN
hjic-104	70	9	∂	∂	NUM
hjic-104	70	10	∂	∂	NOUN
hjic-104	70	11	+	+	CCONJ
hjic-104	70	12	ξξξτστξτξ	ξξξτστξτξ	NOUN
hjic-104	70	13	τσ	τσ	ADP
hjic-104	70	14	τξ	τξ	ADP
hjic-104	70	15	τξ	τξ	ADP
hjic-104	70	16	ξ	ξ	X
hjic-104	70	17	ξ	ξ	X
hjic-104	70	18	ξ	ξ	X
hjic-104	70	19	dt	dt	PROPN
hjic-104	70	20	,	,	PUNCT
hjic-104	70	21	x;,efddt	x;,efddt	NUM
hjic-104	70	22	,	,	PUNCT
hjic-104	70	23	x;,e	x;,e	PROPN
hjic-104	70	24	,	,	PUNCT
hjic-104	70	25	g	g	PROPN
hjic-104	70	26	dd	dd	PROPN
hjic-104	70	27	n	n	PROPN
hjic-104	70	28	t	t	PROPN
hjic-104	70	29	,	,	PUNCT
hjic-104	70	30	x;,e	x;,e	PROPN
hjic-104	70	31	,	,	PUNCT
hjic-104	70	32	ut	ut	PROPN
hjic-104	70	33	,	,	PUNCT
hjic-104	70	34	xu	xu	PROPN
hjic-104	71	1	t	t	PROPN
hjic-104	71	2	t	t	NOUN
hjic-104	71	3	0	0	NUM
hjic-104	71	4	2	2	NUM
hjic-104	71	5	1	1	NUM
hjic-104	71	6	0	0	NUM
hjic-104	71	7	0	0	NUM
hjic-104	71	8	collocation	collocation	NOUN
hjic-104	71	9	method	method	NOUN
hjic-104	71	10	we	we	PRON
hjic-104	71	11	divide	divide	VERB
hjic-104	71	12	the	the	DET
hjic-104	71	13	boundary	boundary	NOUN
hjic-104	71	14	into	into	ADP
hjic-104	71	15	n	n	CCONJ
hjic-104	71	16	segments	segment	NOUN
hjic-104	71	17	as	as	SCONJ
hjic-104	71	18	shown	show	VERB
hjic-104	71	19	.	.	PUNCT
hjic-104	72	1	ω∂=γ	ω∂=γ	NOUN
hjic-104	72	2	let	let	VERB
hjic-104	72	3	.	.	PUNCT
hjic-104	73	1	γ∈=+	γ∈=+	ADV
hjic-104	73	2	1121	1121	NUM
hjic-104	73	3	xx	xx	NUM
hjic-104	73	4	,	,	PUNCT
hjic-104	73	5	x,,x	x,,x	PROPN
hjic-104	73	6	,	,	PUNCT
hjic-104	73	7	x	x	SYM
hjic-104	73	8	nnk	nnk	VERB
hjic-104	73	9	define	define	VERB
hjic-104	73	10	(	(	PUNCT
hjic-104	73	11	)	)	PUNCT
hjic-104	73	12	{	{	PUNCT
hjic-104	73	13	}	}	PUNCT
hjic-104	73	14	101	101	NUM
hjic-104	73	15	1	1	NUM
hjic-104	73	16	2	2	NUM
hjic-104	73	17	≤≤−+=∈=γ′	≤≤−+=∈=γ′	PROPN
hjic-104	73	18	+	+	CCONJ
hjic-104	73	19	λλλ	λλλ	ADJ
hjic-104	73	20	,	,	PUNCT
hjic-104	73	21	xxx	xxx	PROPN
hjic-104	73	22	:x	:x	PROPN
hjic-104	73	23	iii	iii	PUNCT
hjic-104	73	24	r	r	NOUN
hjic-104	73	25	where	where	SCONJ
hjic-104	73	26	n,,i	n,,i	PRON
hjic-104	73	27	k1=	k1=	PROPN
hjic-104	73	28	.	.	PUNCT
hjic-104	74	1	then	then	ADV
hjic-104	74	2	is	be	AUX
hjic-104	74	3	a	a	DET
hjic-104	74	4	polygon	polygon	NOUN
hjic-104	74	5	in	in	ADP
hjic-104	74	6	ω	ω	PROPN
hjic-104	74	7	since	since	SCONJ
hjic-104	74	8	ω	ω	PROPN
hjic-104	74	9	is	be	AUX
hjic-104	74	10	convex	convex	NOUN
hjic-104	74	11	.	.	PUNCT
hjic-104	75	1	nγ′γ′	nγ′γ′	NOUN
hjic-104	75	2	uku1	uku1	PROPN
hjic-104	75	3	let	let	VERB
hjic-104	75	4	jn′v	jn′v	NOUN
hjic-104	75	5	be	be	AUX
hjic-104	75	6	the	the	DET
hjic-104	75	7	outer	outer	ADJ
hjic-104	75	8	unit	unit	NOUN
hjic-104	75	9	normal	normal	ADJ
hjic-104	75	10	vector	vector	NOUN
hjic-104	75	11	on	on	ADP
hjic-104	75	12	iγ′	iγ′	NOUN
hjic-104	75	13	,	,	PUNCT
hjic-104	75	14	in,,i	in,,i	NOUN
hjic-104	75	15	maxh	maxh	X
hjic-104	75	16	γ′=	γ′=	NOUN
hjic-104	76	1	=	=	SYM
hjic-104	76	2	k0	k0	PROPN
hjic-104	76	3	be	be	AUX
hjic-104	76	4	the	the	DET
hjic-104	76	5	step	step	NOUN
hjic-104	76	6	width	width	NOUN
hjic-104	76	7	in	in	ADP
hjic-104	76	8	space	space	NOUN
hjic-104	76	9	and	and	CCONJ
hjic-104	76	10	for	for	ADP
hjic-104	76	11	n∈m	n∈m	PROPN
hjic-104	76	12	m	m	PROPN
hjic-104	76	13	tk	tk	NOUN
hjic-104	76	14	=	=	PRON
hjic-104	76	15	be	be	AUX
hjic-104	76	16	the	the	DET
hjic-104	76	17	step	step	NOUN
hjic-104	76	18	width	width	NOUN
hjic-104	76	19	in	in	ADP
hjic-104	76	20	time	time	NOUN
hjic-104	76	21	and	and	CCONJ
hjic-104	76	22	we	we	PRON
hjic-104	76	23	get	get	VERB
hjic-104	76	24	the	the	DET
hjic-104	76	25	time	time	NOUN
hjic-104	76	26	steps	step	NOUN
hjic-104	76	27	(	(	PUNCT
hjic-104	76	28	,	,	PUNCT
hjic-104	76	29	m	m	PROPN
hjic-104	76	30	)	)	PUNCT
hjic-104	76	31	.	.	PUNCT
hjic-104	77	1	jkt	jkt	PROPN
hjic-104	77	2	j	j	PROPN
hjic-104	77	3	=	=	SYM
hjic-104	77	4	k,,j	k,,j	PROPN
hjic-104	77	5	10=	10=	ADJ
hjic-104	77	6	using	use	VERB
hjic-104	77	7	collocation	collocation	NOUN
hjic-104	77	8	method	method	NOUN
hjic-104	77	9	the	the	DET
hjic-104	77	10	piecewise	piecewise	NOUN
hjic-104	77	11	linear	linear	PROPN
hjic-104	77	12	spline	spline	NOUN
hjic-104	77	13	functions	function	NOUN
hjic-104	77	14	(	(	PUNCT
hjic-104	77	15	)	)	PUNCT
hjic-104	77	16	n,,i	n,,i	NOUN
hjic-104	77	17	,	,	PUNCT
hjic-104	77	18	otherwise	otherwise	ADV
hjic-104	77	19	x	x	X
hjic-104	77	20	,	,	PUNCT
hjic-104	77	21	xx	xx	NUM
hjic-104	77	22	xx	xx	NUM
hjic-104	78	1	x	x	NOUN
hjic-104	78	2	,	,	PUNCT
hjic-104	78	3	xx	xx	NUM
hjic-104	78	4	xx	xx	NUM
hjic-104	79	1	x	x	PUNCT
hjic-104	80	1	i	i	PRON
hjic-104	80	2	ii	ii	VERB
hjic-104	81	1	i	i	PRON
hjic-104	81	2	i	i	PRON
hjic-104	81	3	ii	ii	VERB
hjic-104	82	1	i	i	PRON
hjic-104	82	2	i	i	PRON
hjic-104	82	3	k1	k1	VERB
hjic-104	82	4	0	0	NUM
hjic-104	82	5	1	1	NUM
hjic-104	82	6	1	1	NUM
hjic-104	82	7	1	1	NUM
hjic-104	82	8	1	1	NUM
hjic-104	82	9	1	1	NUM
hjic-104	82	10	=	=	SYM
hjic-104	82	11	⎪	⎪	NOUN
hjic-104	82	12	⎪	⎪	NOUN
hjic-104	82	13	⎪	⎪	NOUN
hjic-104	82	14	⎪	⎪	NOUN
hjic-104	82	15	⎩	⎩	PROPN
hjic-104	82	16	⎪	⎪	NOUN
hjic-104	82	17	⎪	⎪	NOUN
hjic-104	82	18	⎪	⎪	NOUN
hjic-104	82	19	⎪	⎪	NOUN
hjic-104	82	20	⎨	⎨	ADJ
hjic-104	82	21	⎧	⎧	PROPN
hjic-104	82	22	γ′∈′	γ′∈′	X
hjic-104	82	23	−	−	PROPN
hjic-104	82	24	′−	′−	PROPN
hjic-104	82	25	γ′∈′	γ′∈′	X
hjic-104	82	26	−	−	NOUN
hjic-104	82	27	−′	−′	NUM
hjic-104	82	28	=	=	NOUN
hjic-104	83	1	′	′	NUM
hjic-104	84	1	+	+	CCONJ
hjic-104	85	1	+	+	CCONJ
hjic-104	85	2	−	−	NOUN
hjic-104	85	3	−	−	NOUN
hjic-104	86	1	−	−	PROPN
hjic-104	86	2	ϕ	ϕ	NOUN
hjic-104	86	3	are	be	AUX
hjic-104	86	4	applied	apply	VERB
hjic-104	86	5	to	to	ADP
hjic-104	86	6	space	space	NOUN
hjic-104	86	7	and	and	CCONJ
hjic-104	86	8	the	the	DET
hjic-104	86	9	piecewise	piecewise	NOUN
hjic-104	86	10	constant	constant	ADJ
hjic-104	86	11	characteristic	characteristic	ADJ
hjic-104	86	12	functions	function	NOUN
hjic-104	86	13	(	(	PUNCT
hjic-104	86	14	)	)	PUNCT
hjic-104	86	15	(	(	PUNCT
hjic-104	86	16	]	]	PUNCT
hjic-104	86	17	(	(	PUNCT
hjic-104	86	18	]	]	X
hjic-104	86	19	m,,j	m,,j	PROPN
hjic-104	86	20	,	,	PUNCT
hjic-104	86	21	t	t	PROPN
hjic-104	86	22	,	,	PUNCT
hjic-104	86	23	tt	tt	PROPN
hjic-104	86	24	t	t	PROPN
hjic-104	86	25	,	,	PUNCT
hjic-104	86	26	tt	tt	PROPN
hjic-104	86	27	t	t	PROPN
hjic-104	86	28	jj	jj	PROPN
hjic-104	86	29	jj	jj	PROPN
hjic-104	86	30	j	j	PROPN
hjic-104	86	31	k1	k1	PROPN
hjic-104	86	32	1	1	NUM
hjic-104	86	33	0	0	NUM
hjic-104	86	34	1	1	NUM
hjic-104	86	35	1	1	NUM
hjic-104	86	36	=	=	SYM
hjic-104	86	37	⎪⎩	⎪⎩	ADJ
hjic-104	86	38	⎪	⎪	NOUN
hjic-104	86	39	⎨	⎨	ADJ
hjic-104	86	40	⎧	⎧	PROPN
hjic-104	86	41	∈	∈	PROPN
hjic-104	86	42	∉	∉	X
hjic-104	86	43	=	=	PUNCT
hjic-104	87	1	−	−	PROPN
hjic-104	87	2	−	−	NOUN
hjic-104	88	1	χ	χ	NOUN
hjic-104	88	2	are	be	AUX
hjic-104	88	3	applied	apply	VERB
hjic-104	88	4	to	to	ADP
hjic-104	88	5	time	time	NOUN
hjic-104	88	6	.	.	PUNCT
hjic-104	89	1	with	with	ADP
hjic-104	89	2	both	both	PRON
hjic-104	89	3	we	we	PRON
hjic-104	89	4	form	form	VERB
hjic-104	89	5	the	the	DET
hjic-104	89	6	ansatz	ansatz	ADJ
hjic-104	89	7	function	function	NOUN
hjic-104	89	8	(	(	PUNCT
hjic-104	89	9	)	)	PUNCT
hjic-104	89	10	(	(	PUNCT
hjic-104	89	11	)	)	PUNCT
hjic-104	89	12	(	(	PUNCT
hjic-104	89	13	∑∑	∑∑	NOUN
hjic-104	89	14	=	=	PUNCT
hjic-104	89	15	=	=	SYM
hjic-104	89	16	′=′	′=′	PROPN
hjic-104	89	17	m	m	VERB
hjic-104	89	18	j	j	PROPN
hjic-104	89	19	n	n	INTJ
hjic-104	90	1	i	i	PRON
hjic-104	90	2	ji	ji	INTJ
hjic-104	91	1	j	j	PROPN
hjic-104	91	2	i	i	PRON
hjic-104	91	3	txut	txut	VERB
hjic-104	91	4	,	,	PUNCT
hjic-104	91	5	xu~	xu~	PROPN
hjic-104	91	6	1	1	NUM
hjic-104	91	7	1	1	NUM
hjic-104	91	8	χϕ	χϕ	NOUN
hjic-104	91	9	)	)	PUNCT
hjic-104	91	10	where	where	SCONJ
hjic-104	91	11	u	u	PRON
hjic-104	91	12	are	be	AUX
hjic-104	91	13	the	the	DET
hjic-104	91	14	unknown	unknown	ADJ
hjic-104	91	15	coefficients	coefficient	NOUN
hjic-104	91	16	which	which	PRON
hjic-104	91	17	we	we	PRON
hjic-104	91	18	have	have	VERB
hjic-104	91	19	to	to	PART
hjic-104	91	20	find	find	VERB
hjic-104	91	21	.	.	PUNCT
hjic-104	92	1	j	j	PROPN
hjic-104	92	2	i	i	PRON
hjic-104	92	3	at	at	ADP
hjic-104	92	4	the	the	DET
hjic-104	92	5	time	time	NOUN
hjic-104	92	6	step	step	NOUN
hjic-104	92	7	p	p	NOUN
hjic-104	92	8	of	of	ADP
hjic-104	92	9	segment	segment	NOUN
hjic-104	92	10	i	i	PRON
hjic-104	92	11	the	the	DET
hjic-104	92	12	boundary	boundary	ADJ
hjic-104	92	13	integral	integral	ADJ
hjic-104	92	14	equation	equation	NOUN
hjic-104	92	15	becomes	become	VERB
hjic-104	92	16	xn+1	xn+1	PROPN
hjic-104	92	17	=	=	NOUN
hjic-104	92	18	x1	x1	NUM
hjic-104	93	1	x2	x2	INTJ
hjic-104	93	2	xi	xi	PROPN
hjic-104	93	3	xi+1	xi+1	PROPN
hjic-104	93	4	xn	xn	PROPN
hjic-104	93	5	γ	γ	PROPN
hjic-104	93	6	γ	γ	PROPN
hjic-104	93	7	'	'	PUNCT
hjic-104	93	8	ni	ni	PROPN
hjic-104	93	9	122	122	NUM
hjic-104	93	10	(	(	PUNCT
hjic-104	93	11	)	)	PUNCT
hjic-104	93	12	(	(	PUNCT
hjic-104	93	13	)	)	PUNCT
hjic-104	93	14	(	(	PUNCT
hjic-104	93	15	)	)	PUNCT
hjic-104	93	16	(	(	PUNCT
hjic-104	93	17	)	)	PUNCT
hjic-104	93	18	(	(	PUNCT
hjic-104	93	19	)	)	PUNCT
hjic-104	93	20	(	(	PUNCT
hjic-104	93	21	)	)	PUNCT
hjic-104	93	22	∫	∫	PROPN
hjic-104	94	1	∫	∫	PROPN
hjic-104	94	2	∫	∫	PROPN
hjic-104	94	3	∫	∫	PROPN
hjic-104	94	4	∫	∫	PROPN
hjic-104	94	5	ω′	ω′	PROPN
hjic-104	94	6	γ′	γ′	PROPN
hjic-104	94	7	′	′	NUM
hjic-104	94	8	γ′	γ′	NOUN
hjic-104	95	1	′	′	NUM
hjic-104	96	1	′	′	NUM
hjic-104	96	2	′′′+	′′′+	SYM
hjic-104	96	3	′′⋅′=	′′⋅′=	ADP
hjic-104	97	1	′	′	NUM
hjic-104	97	2	∂	∂	NOUN
hjic-104	97	3	′∂	′∂	NOUN
hjic-104	97	4	′+	′+	PUNCT
hjic-104	97	5	ξξξ	ξξξ	NOUN
hjic-104	97	6	τστξτξ	τστξτξ	NOUN
hjic-104	97	7	τσ	τσ	PROPN
hjic-104	97	8	τξ	τξ	PROPN
hjic-104	97	9	τξ	τξ	ADP
hjic-104	97	10	ξ	ξ	X
hjic-104	97	11	ξ	ξ	X
hjic-104	97	12	ξ	ξ	X
hjic-104	97	13	dt	dt	PROPN
hjic-104	97	14	,	,	PUNCT
hjic-104	97	15	x;,ef	x;,ef	PROPN
hjic-104	97	16	ddt	ddt	PROPN
hjic-104	97	17	,	,	PUNCT
hjic-104	97	18	x;,e	x;,e	PROPN
hjic-104	97	19	,	,	PUNCT
hjic-104	97	20	g	g	PROPN
hjic-104	97	21	dd	dd	PROPN
hjic-104	97	22	n	n	PROPN
hjic-104	97	23	t	t	PROPN
hjic-104	97	24	,	,	PUNCT
hjic-104	97	25	x;,e	x;,e	NOUN
hjic-104	97	26	,	,	PUNCT
hjic-104	97	27	u	u	NOUN
hjic-104	97	28	~	~	PUNCT
hjic-104	97	29	u	u	SYM
hjic-104	97	30	pi	pi	NOUN
hjic-104	97	31	t	t	PROPN
hjic-104	97	32	t	t	PROPN
hjic-104	97	33	pi	pi	PROPN
hjic-104	97	34	t	t	PROPN
hjic-104	97	35	pip	pip	NOUN
hjic-104	98	1	i	i	PRON
hjic-104	98	2	p	p	PROPN
hjic-104	98	3	p	p	X
hjic-104	98	4	0	0	NUM
hjic-104	98	5	2	2	NUM
hjic-104	98	6	1	1	NUM
hjic-104	98	7	0	0	NUM
hjic-104	98	8	0	0	NUM
hjic-104	98	9	this	this	PRON
hjic-104	98	10	is	be	AUX
hjic-104	98	11	a	a	DET
hjic-104	98	12	system	system	NOUN
hjic-104	98	13	of	of	ADP
hjic-104	98	14	linear	linear	PROPN
hjic-104	98	15	equations	equation	NOUN
hjic-104	98	16	.	.	PUNCT
hjic-104	99	1	the	the	DET
hjic-104	99	2	coefficients	coefficient	NOUN
hjic-104	99	3	can	can	AUX
hjic-104	99	4	be	be	AUX
hjic-104	99	5	written	write	VERB
hjic-104	99	6	in	in	ADP
hjic-104	99	7	short	short	ADJ
hjic-104	99	8	form	form	NOUN
hjic-104	99	9	as	as	ADP
hjic-104	99	10	(	(	PUNCT
hjic-104	99	11	)	)	PUNCT
hjic-104	99	12	(	(	PUNCT
hjic-104	99	13	)	)	PUNCT
hjic-104	99	14	∫	∫	PROPN
hjic-104	99	15	∫	∫	PROPN
hjic-104	100	1	−	−	PROPN
hjic-104	100	2	γ′	γ′	NUM
hjic-104	101	1	′	′	NUM
hjic-104	101	2	′	′	NUM
hjic-104	102	1	′	′	NUM
hjic-104	102	2	∂	∂	NOUN
hjic-104	102	3	′∂	′∂	NOUN
hjic-104	103	1	′=	′=	NOUN
hjic-104	103	2	q	q	PROPN
hjic-104	103	3	q	q	PROPN
hjic-104	103	4	t	t	PROPN
hjic-104	103	5	t	t	PROPN
hjic-104	103	6	qi	qi	PROPN
hjic-104	103	7	j	j	PROPN
hjic-104	103	8	pq	pq	INTJ
hjic-104	103	9	ij	ij	INTJ
hjic-104	103	10	dd	dd	INTJ
hjic-104	103	11	n	n	PROPN
hjic-104	103	12	t	t	PROPN
hjic-104	103	13	,	,	PUNCT
hjic-104	103	14	x;,e	x;,e	PROPN
hjic-104	103	15	b	b	PROPN
hjic-104	103	16	1	1	NUM
hjic-104	103	17	τσ	τσ	PROPN
hjic-104	103	18	τξ	τξ	ADP
hjic-104	103	19	ξϕ	ξϕ	ADP
hjic-104	103	20	ξ	ξ	PROPN
hjic-104	103	21	ξ	ξ	PROPN
hjic-104	103	22	(	(	PUNCT
hjic-104	103	23	)	)	PUNCT
hjic-104	103	24	(	(	PUNCT
hjic-104	103	25	)	)	PUNCT
hjic-104	103	26	(	(	PUNCT
hjic-104	103	27	)	)	PUNCT
hjic-104	103	28	(	(	PUNCT
hjic-104	103	29	)	)	PUNCT
hjic-104	103	30	∫	∫	PROPN
hjic-104	103	31	∫	∫	PROPN
hjic-104	103	32	∫	∫	PROPN
hjic-104	103	33	ω′	ω′	PROPN
hjic-104	103	34	γ′	γ′	PROPN
hjic-104	103	35	′	′	NUM
hjic-104	103	36	′′′+	′′′+	SYM
hjic-104	103	37	′′⋅′=	′′⋅′=	ADP
hjic-104	103	38	ξξξ	ξξξ	NOUN
hjic-104	103	39	τστξτξ	τστξτξ	ADP
hjic-104	103	40	ξ	ξ	PROPN
hjic-104	103	41	dt	dt	PROPN
hjic-104	103	42	,	,	PUNCT
hjic-104	103	43	x;,ef	x;,ef	PROPN
hjic-104	103	44	ddt	ddt	PROPN
hjic-104	103	45	,	,	PUNCT
hjic-104	103	46	x;,e	x;,e	PROPN
hjic-104	103	47	,	,	PUNCT
hjic-104	103	48	gc	gc	PROPN
hjic-104	103	49	pi	pi	PROPN
hjic-104	103	50	t	t	PROPN
hjic-104	103	51	t	t	PROPN
hjic-104	103	52	pi	pi	NOUN
hjic-104	104	1	p	p	X
hjic-104	105	1	i	i	PRON
hjic-104	105	2	p	p	NOUN
hjic-104	105	3	0	0	NUM
hjic-104	105	4	0	0	NUM
hjic-104	106	1	the	the	DET
hjic-104	106	2	boundary	boundary	ADJ
hjic-104	106	3	integral	integral	ADJ
hjic-104	106	4	equation	equation	NOUN
hjic-104	106	5	at	at	ADP
hjic-104	106	6	time	time	NOUN
hjic-104	106	7	step	step	NOUN
hjic-104	106	8	p	p	NOUN
hjic-104	106	9	of	of	ADP
hjic-104	106	10	segment	segment	NOUN
hjic-104	106	11	i	i	PRON
hjic-104	106	12	is	be	AUX
hjic-104	106	13	rewritten	rewrite	VERB
hjic-104	106	14	as	as	ADP
hjic-104	106	15	:	:	PUNCT
hjic-104	106	16	[	[	PUNCT
hjic-104	106	17	]	]	X
hjic-104	106	18	[	[	PUNCT
hjic-104	106	19	]	]	X
hjic-104	106	20	⎥	⎥	PROPN
hjic-104	106	21	⎥	⎥	PROPN
hjic-104	106	22	⎥	⎥	PROPN
hjic-104	106	23	⎦	⎦	NOUN
hjic-104	106	24	⎤	⎤	ADJ
hjic-104	106	25	⎢	⎢	NOUN
hjic-104	106	26	⎢	⎢	NOUN
hjic-104	106	27	⎢	⎢	NOUN
hjic-104	106	28	⎣	⎣	PROPN
hjic-104	106	29	⎡	⎡	NOUN
hjic-104	106	30	+	+	CCONJ
hjic-104	106	31	⎥	⎥	PROPN
hjic-104	106	32	⎥	⎥	PROPN
hjic-104	106	33	⎥	⎥	PROPN
hjic-104	107	1	⎦	⎦	NOUN
hjic-104	107	2	⎤	⎤	ADJ
hjic-104	107	3	⎢	⎢	NOUN
hjic-104	107	4	⎢	⎢	NOUN
hjic-104	107	5	⎢	⎢	NOUN
hjic-104	107	6	⎣	⎣	PROPN
hjic-104	107	7	⎡	⎡	ADJ
hjic-104	107	8	⎟⎟	⎟⎟	ADJ
hjic-104	107	9	⎠	⎠	NOUN
hjic-104	107	10	⎞	⎞	NOUN
hjic-104	107	11	⎜⎜	⎜⎜	NOUN
hjic-104	107	12	⎝	⎝	PUNCT
hjic-104	107	13	⎛	⎛	NOUN
hjic-104	107	14	−=	−=	NOUN
hjic-104	107	15	⎥	⎥	PROPN
hjic-104	107	16	⎥	⎥	PROPN
hjic-104	107	17	⎥	⎥	PROPN
hjic-104	107	18	⎦	⎦	NOUN
hjic-104	107	19	⎤	⎤	ADJ
hjic-104	107	20	⎢	⎢	NOUN
hjic-104	107	21	⎢	⎢	NOUN
hjic-104	107	22	⎢	⎢	NOUN
hjic-104	107	23	⎣	⎣	ADJ
hjic-104	107	24	⎡	⎡	NOUN
hjic-104	107	25	⎟	⎟	X
hjic-104	107	26	⎟	⎟	X
hjic-104	107	27	⎟	⎟	X
hjic-104	107	28	⎟	⎟	X
hjic-104	107	29	⎟	⎟	X
hjic-104	107	30	⎠	⎠	PUNCT
hjic-104	107	31	⎞	⎞	PROPN
hjic-104	107	32	⎜	⎜	PROPN
hjic-104	107	33	⎜	⎜	PROPN
hjic-104	107	34	⎜	⎜	PROPN
hjic-104	107	35	⎜	⎜	PROPN
hjic-104	107	36	⎜	⎜	PROPN
hjic-104	107	37	⎝	⎝	PUNCT
hjic-104	107	38	⎛	⎛	PROPN
hjic-104	108	1	+	+	CCONJ
hjic-104	108	2	⎥	⎥	PROPN
hjic-104	108	3	⎥	⎥	PROPN
hjic-104	108	4	⎥	⎥	PROPN
hjic-104	108	5	⎥	⎥	PROPN
hjic-104	108	6	⎥	⎥	PROPN
hjic-104	108	7	⎦	⎦	NOUN
hjic-104	108	8	⎤	⎤	ADJ
hjic-104	108	9	⎢	⎢	NOUN
hjic-104	108	10	⎢	⎢	NOUN
hjic-104	108	11	⎢	⎢	NOUN
hjic-104	108	12	⎢	⎢	NOUN
hjic-104	108	13	⎢	⎢	NOUN
hjic-104	108	14	⎣	⎣	PROPN
hjic-104	108	15	⎡	⎡	VERB
hjic-104	108	16	∑	∑	PUNCT
hjic-104	108	17	−	−	PROPN
hjic-104	108	18	=	=	PUNCT
hjic-104	109	1	p	p	NOUN
hjic-104	109	2	n	n	PRON
hjic-104	109	3	p	p	NOUN
hjic-104	109	4	q	q	PROPN
hjic-104	109	5	n	n	PROPN
hjic-104	109	6	q	q	PROPN
hjic-104	109	7	p	p	X
hjic-104	109	8	q	q	X
hjic-104	109	9	pq	pq	INTJ
hjic-104	109	10	ij	ij	INTJ
hjic-104	109	11	p	p	NOUN
hjic-104	109	12	n	n	PRON
hjic-104	109	13	p	p	NOUN
hjic-104	109	14	pp	pp	ADJ
hjic-104	109	15	ij	ij	INTJ
hjic-104	110	1	c	c	NOUN
hjic-104	110	2	c	c	NOUN
hjic-104	110	3	u	u	X
hjic-104	110	4	u	u	X
hjic-104	110	5	b	b	PROPN
hjic-104	110	6	u	u	X
hjic-104	110	7	u	u	PROPN
hjic-104	110	8	b	b	PROPN
hjic-104	110	9	mmmo	mmmo	ADJ
hjic-104	110	10	111	111	NUM
hjic-104	110	11	1	1	NUM
hjic-104	110	12	1	1	NUM
hjic-104	110	13	2	2	NUM
hjic-104	110	14	1	1	NUM
hjic-104	110	15	2	2	NUM
hjic-104	110	16	1	1	NUM
hjic-104	110	17	which	which	PRON
hjic-104	110	18	should	should	AUX
hjic-104	110	19	be	be	AUX
hjic-104	110	20	solved	solve	VERB
hjic-104	110	21	to	to	PART
hjic-104	110	22	get	get	VERB
hjic-104	110	23	the	the	DET
hjic-104	110	24	solution	solution	NOUN
hjic-104	110	25	.	.	PUNCT
hjic-104	111	1	example	example	NOUN
hjic-104	111	2	as	as	ADP
hjic-104	111	3	example	example	NOUN
hjic-104	111	4	we	we	PRON
hjic-104	111	5	consider	consider	VERB
hjic-104	111	6	the	the	DET
hjic-104	111	7	heat	heat	NOUN
hjic-104	111	8	equation	equation	NOUN
hjic-104	111	9	(	(	PUNCT
hjic-104	111	10	)	)	PUNCT
hjic-104	111	11	(	(	PUNCT
hjic-104	111	12	)	)	PUNCT
hjic-104	111	13	(	(	PUNCT
hjic-104	111	14	)	)	PUNCT
hjic-104	111	15	(	(	PUNCT
hjic-104	111	16	)	)	PUNCT
hjic-104	111	17	(	(	PUNCT
hjic-104	111	18	]	]	SYM
hjic-104	111	19	10	10	NUM
hjic-104	111	20	2	2	NUM
hjic-104	111	21	2	2	NUM
hjic-104	111	22	2	2	NUM
hjic-104	111	23	2	2	NUM
hjic-104	111	24	,	,	PUNCT
hjic-104	111	25	t	t	PROPN
hjic-104	111	26	,	,	PUNCT
hjic-104	111	27	y	y	PROPN
hjic-104	111	28	,	,	PUNCT
hjic-104	111	29	x	x	PROPN
hjic-104	111	30	,	,	PUNCT
hjic-104	111	31	y	y	PROPN
hjic-104	111	32	t	t	PROPN
hjic-104	111	33	,	,	PUNCT
hjic-104	111	34	y	y	PROPN
hjic-104	111	35	,	,	PUNCT
hjic-104	111	36	xu	xu	PROPN
hjic-104	111	37	x	x	SYM
hjic-104	111	38	t	t	PROPN
hjic-104	111	39	,	,	PUNCT
hjic-104	111	40	y	y	PROPN
hjic-104	111	41	,	,	PUNCT
hjic-104	111	42	xu	xu	PROPN
hjic-104	111	43	t	t	PROPN
hjic-104	111	44	t	t	PROPN
hjic-104	111	45	,	,	PUNCT
hjic-104	111	46	y	y	PROPN
hjic-104	111	47	,	,	PUNCT
hjic-104	111	48	xu	xu	PROPN
hjic-104	111	49	∈ω∈	∈ω∈	PROPN
hjic-104	111	50	∂	∂	NUM
hjic-104	111	51	∂	∂	NUM
hjic-104	111	52	+	+	NUM
hjic-104	111	53	∂	∂	NUM
hjic-104	111	54	∂	∂	NUM
hjic-104	111	55	=	=	SYM
hjic-104	111	56	∂	∂	NOUN
hjic-104	111	57	∂	∂	NOUN
hjic-104	111	58	with	with	ADP
hjic-104	111	59	the	the	DET
hjic-104	111	60	following	follow	VERB
hjic-104	111	61	initial	initial	ADJ
hjic-104	111	62	and	and	CCONJ
hjic-104	111	63	neumann	neumann	PROPN
hjic-104	111	64	boundary	boundary	ADJ
hjic-104	111	65	conditions	condition	NOUN
hjic-104	111	66	,	,	PUNCT
hjic-104	111	67	(	(	PUNCT
hjic-104	111	68	)	)	PUNCT
hjic-104	111	69	,	,	PUNCT
hjic-104	111	70	,	,	PUNCT
hjic-104	111	71	y	y	PROPN
hjic-104	111	72	,	,	PUNCT
hjic-104	111	73	xu	xu	PROPN
hjic-104	111	74	10	10	NUM
hjic-104	112	1	=	=	SYM
hjic-104	112	2	(	(	PUNCT
hjic-104	112	3	)	)	PUNCT
hjic-104	112	4	ω∈y	ω∈y	NOUN
hjic-104	112	5	,	,	PUNCT
hjic-104	112	6	x	x	X
hjic-104	112	7	(	(	PUNCT
hjic-104	112	8	17	17	NUM
hjic-104	112	9	)	)	PUNCT
hjic-104	112	10	(	(	PUNCT
hjic-104	112	11	)	)	PUNCT
hjic-104	112	12	(	(	PUNCT
hjic-104	112	13	)	)	PUNCT
hjic-104	112	14	(	(	PUNCT
hjic-104	112	15	]	]	SYM
hjic-104	112	16	100	100	NUM
hjic-104	112	17	,	,	PUNCT
hjic-104	112	18	t	t	PROPN
hjic-104	112	19	,	,	PUNCT
hjic-104	112	20	y	y	PROPN
hjic-104	112	21	,	,	PUNCT
hjic-104	112	22	x	x	NOUN
hjic-104	112	23	,	,	PUNCT
hjic-104	112	24	n	n	PROPN
hjic-104	112	25	t	t	PROPN
hjic-104	112	26	,	,	PUNCT
hjic-104	112	27	y	y	PROPN
hjic-104	112	28	,	,	PUNCT
hjic-104	112	29	xu	xu	PROPN
hjic-104	112	30	∈γ∈=	∈γ∈=	PROPN
hjic-104	112	31	∂	∂	PROPN
hjic-104	112	32	∂	∂	NUM
hjic-104	112	33	(	(	PUNCT
hjic-104	112	34	18	18	NUM
hjic-104	112	35	)	)	PUNCT
hjic-104	112	36	where	where	SCONJ
hjic-104	112	37	ω	ω	PROPN
hjic-104	112	38	is	be	AUX
hjic-104	112	39	the	the	DET
hjic-104	112	40	unit	unit	NOUN
hjic-104	112	41	circle	circle	NOUN
hjic-104	112	42	.	.	PUNCT
hjic-104	113	1	forming	form	VERB
hjic-104	113	2	the	the	DET
hjic-104	113	3	boundary	boundary	ADJ
hjic-104	113	4	integral	integral	ADJ
hjic-104	113	5	equation	equation	NOUN
hjic-104	113	6	and	and	CCONJ
hjic-104	113	7	substituting	substitute	VERB
hjic-104	113	8	the	the	DET
hjic-104	113	9	data	datum	NOUN
hjic-104	113	10	given	give	VERB
hjic-104	113	11	in	in	ADP
hjic-104	113	12	(	(	PUNCT
hjic-104	113	13	17	17	NUM
hjic-104	113	14	)	)	PUNCT
hjic-104	113	15	and	and	CCONJ
hjic-104	113	16	(	(	PUNCT
hjic-104	113	17	18	18	NUM
hjic-104	113	18	)	)	PUNCT
hjic-104	113	19	we	we	PRON
hjic-104	113	20	get	get	VERB
hjic-104	113	21	(	(	PUNCT
hjic-104	113	22	)	)	PUNCT
hjic-104	113	23	(	(	PUNCT
hjic-104	113	24	)	)	PUNCT
hjic-104	113	25	(	(	PUNCT
hjic-104	113	26	)	)	PUNCT
hjic-104	113	27	(	(	PUNCT
hjic-104	113	28	)	)	PUNCT
hjic-104	114	1	∫∫	∫∫	ADV
hjic-104	114	2	∫	∫	PROPN
hjic-104	114	3	ωγ	ωγ	ADP
hjic-104	114	4	=	=	SYM
hjic-104	114	5	∂	∂	NUM
hjic-104	114	6	∂	∂	NOUN
hjic-104	114	7	+	+	CCONJ
hjic-104	114	8	ξτσττ	ξτσττ	NOUN
hjic-104	114	9	ξ	ξ	X
hjic-104	114	10	ξ	ξ	PROPN
hjic-104	114	11	dt,;,edd	dt,;,edd	PROPN
hjic-104	114	12	n	n	PRON
hjic-104	114	13	t,;,e	t,;,e	NOUN
hjic-104	114	14	,	,	PUNCT
hjic-104	114	15	ut	ut	PROPN
hjic-104	114	16	,	,	PUNCT
hjic-104	114	17	u	u	NOUN
hjic-104	114	18	t	t	NOUN
hjic-104	114	19	xξxξξx	xξxξξx	NOUN
hjic-104	114	20	0	0	NUM
hjic-104	114	21	2	2	NUM
hjic-104	114	22	1	1	NUM
hjic-104	114	23	0	0	NUM
hjic-104	114	24	,	,	PUNCT
hjic-104	114	25	(	(	PUNCT
hjic-104	114	26	)	)	PUNCT
hjic-104	114	27	(	(	PUNCT
hjic-104	114	28	]	]	X
hjic-104	114	29	10,t	10,t	NUM
hjic-104	114	30	,	,	PUNCT
hjic-104	114	31	y	y	PROPN
hjic-104	114	32	,	,	PUNCT
hjic-104	114	33	x	x	X
hjic-104	114	34	∈γ∈=x	∈γ∈=x	VERB
hjic-104	114	35	to	to	PART
hjic-104	114	36	apply	apply	VERB
hjic-104	114	37	the	the	DET
hjic-104	114	38	collocation	collocation	NOUN
hjic-104	114	39	method	method	NOUN
hjic-104	114	40	we	we	PRON
hjic-104	114	41	divide	divide	VERB
hjic-104	114	42	the	the	DET
hjic-104	114	43	perimeter	perimeter	NOUN
hjic-104	114	44	of	of	ADP
hjic-104	114	45	the	the	DET
hjic-104	114	46	unit	unit	NOUN
hjic-104	114	47	circle	circle	NOUN
hjic-104	114	48	into	into	ADP
hjic-104	114	49	6	6	NUM
hjic-104	114	50	segments	segment	NOUN
hjic-104	114	51	and	and	CCONJ
hjic-104	114	52	discretize	discretize	VERB
hjic-104	114	53	the	the	DET
hjic-104	114	54	time	time	NOUN
hjic-104	114	55	into	into	ADP
hjic-104	114	56	10	10	NUM
hjic-104	114	57	time	time	NOUN
hjic-104	114	58	steps	step	NOUN
hjic-104	114	59	.	.	PUNCT
hjic-104	115	1	with	with	ADP
hjic-104	115	2	piecewise	piecewise	NOUN
hjic-104	115	3	linear	linear	NOUN
hjic-104	115	4	functions	function	NOUN
hjic-104	115	5	used	use	VERB
hjic-104	115	6	in	in	ADP
hjic-104	115	7	space	space	NOUN
hjic-104	115	8	and	and	CCONJ
hjic-104	115	9	piecewise	piecewise	NOUN
hjic-104	115	10	constant	constant	ADJ
hjic-104	115	11	functions	function	NOUN
hjic-104	115	12	(	(	PUNCT
hjic-104	115	13	61	61	NUM
hjic-104	115	14	,	,	PUNCT
hjic-104	115	15	,	,	PUNCT
hjic-104	115	16	i	i	PRON
hjic-104	115	17	,	,	PUNCT
hjic-104	115	18	i	i	PRON
hjic-104	115	19	k=ϕ	k=ϕ	NOUN
hjic-104	115	20	)	)	PUNCT
hjic-104	115	21	(	(	PUNCT
hjic-104	115	22	)	)	PUNCT
hjic-104	115	23	101	101	NUM
hjic-104	115	24	,	,	PUNCT
hjic-104	115	25	,	,	PUNCT
hjic-104	115	26	j	j	PROPN
hjic-104	115	27	,	,	PUNCT
hjic-104	115	28	j	j	PROPN
hjic-104	115	29	k	k	PROPN
hjic-104	115	30	=	=	NOUN
hjic-104	115	31	χ	χ	NOUN
hjic-104	115	32	used	use	VERB
hjic-104	115	33	in	in	ADP
hjic-104	115	34	time	time	NOUN
hjic-104	115	35	,	,	PUNCT
hjic-104	115	36	the	the	DET
hjic-104	115	37	ansatz	ansatz	ADJ
hjic-104	115	38	function	function	NOUN
hjic-104	115	39	is	be	AUX
hjic-104	115	40	(	(	PUNCT
hjic-104	115	41	)	)	PUNCT
hjic-104	115	42	(	(	PUNCT
hjic-104	115	43	)	)	PUNCT
hjic-104	115	44	(	(	PUNCT
hjic-104	115	45	∑∑	∑∑	NOUN
hjic-104	115	46	=	=	PUNCT
hjic-104	115	47	=	=	SYM
hjic-104	115	48	′=′	′=′	PROPN
hjic-104	115	49	10	10	NUM
hjic-104	115	50	1	1	NUM
hjic-104	115	51	6	6	NUM
hjic-104	115	52	1j	1j	NUM
hjic-104	116	1	i	i	PRON
hjic-104	116	2	ji	ji	INTJ
hjic-104	117	1	j	j	PROPN
hjic-104	117	2	i	i	PRON
hjic-104	117	3	txut	txut	VERB
hjic-104	117	4	,	,	PUNCT
hjic-104	117	5	xu~	xu~	PROPN
hjic-104	117	6	χϕ	χϕ	PROPN
hjic-104	117	7	)	)	PUNCT
hjic-104	117	8	where	where	SCONJ
hjic-104	117	9	u	u	PRON
hjic-104	117	10	are	be	AUX
hjic-104	117	11	the	the	DET
hjic-104	117	12	unknown	unknown	ADJ
hjic-104	117	13	constant	constant	ADJ
hjic-104	117	14	collocation	collocation	NOUN
hjic-104	117	15	points	point	NOUN
hjic-104	117	16	.	.	PUNCT
hjic-104	118	1	j	j	NOUN
hjic-104	119	1	i	i	PRON
hjic-104	119	2	then	then	ADV
hjic-104	119	3	the	the	DET
hjic-104	119	4	boundary	boundary	ADJ
hjic-104	119	5	integral	integral	ADJ
hjic-104	119	6	equation	equation	NOUN
hjic-104	119	7	at	at	ADP
hjic-104	119	8	time	time	NOUN
hjic-104	119	9	step	step	NOUN
hjic-104	119	10	p	p	NOUN
hjic-104	119	11	becomes	become	VERB
hjic-104	119	12	(	(	PUNCT
hjic-104	119	13	)	)	PUNCT
hjic-104	119	14	(	(	PUNCT
hjic-104	119	15	)	)	PUNCT
hjic-104	119	16	(	(	PUNCT
hjic-104	119	17	)	)	PUNCT
hjic-104	119	18	610	610	NUM
hjic-104	119	19	2	2	NUM
hjic-104	119	20	1	1	NUM
hjic-104	119	21	0	0	NUM
hjic-104	119	22	,	,	PUNCT
hjic-104	119	23	,	,	PUNCT
hjic-104	119	24	i	i	PRON
hjic-104	119	25	,	,	PUNCT
hjic-104	119	26	dt,;,e	dt,;,e	NOUN
hjic-104	119	27	dd	dd	NOUN
hjic-104	119	28	n	n	CCONJ
hjic-104	119	29	t,;,e	t,;,e	NOUN
hjic-104	119	30	,	,	PUNCT
hjic-104	119	31	u	u	NOUN
hjic-104	119	32	~	~	SYM
hjic-104	119	33	u	u	SYM
hjic-104	119	34	pi	pi	PROPN
hjic-104	119	35	t	t	PROPN
hjic-104	119	36	pip	pip	NOUN
hjic-104	120	1	i	i	PRON
hjic-104	120	2	k=′′=	k=′′=	PROPN
hjic-104	120	3	∂	∂	NUM
hjic-104	120	4	′∂	′∂	NOUN
hjic-104	120	5	′+	′+	PUNCT
hjic-104	120	6	∫	∫	PROPN
hjic-104	120	7	∫	∫	PROPN
hjic-104	120	8	∫	∫	PROPN
hjic-104	120	9	ω	ω	PROPN
hjic-104	120	10	γ′	γ′	PROPN
hjic-104	120	11	′	′	NUM
hjic-104	121	1	′	′	NUM
hjic-104	122	1	ξ	ξ	X
hjic-104	122	2	τσ	τσ	PROPN
hjic-104	122	3	τ	τ	PROPN
hjic-104	122	4	τ	τ	PROPN
hjic-104	122	5	ξ	ξ	X
hjic-104	122	6	ξ	ξ	PROPN
hjic-104	122	7	xξ	xξ	PROPN
hjic-104	122	8	xξ	xξ	PROPN
hjic-104	122	9	ξ	ξ	X
hjic-104	122	10	so	so	ADV
hjic-104	122	11	at	at	ADP
hjic-104	122	12	the	the	DET
hjic-104	122	13	first	first	ADJ
hjic-104	122	14	time	time	NOUN
hjic-104	122	15	step	step	NOUN
hjic-104	122	16	we	we	PRON
hjic-104	122	17	have	have	VERB
hjic-104	122	18	the	the	DET
hjic-104	122	19	equation	equation	NOUN
hjic-104	122	20	(	(	PUNCT
hjic-104	122	21	)	)	PUNCT
hjic-104	123	1	(	(	PUNCT
hjic-104	123	2	)	)	PUNCT
hjic-104	123	3	∫	∫	PROPN
hjic-104	124	1	∫	∫	PROPN
hjic-104	124	2	∫	∫	PROPN
hjic-104	124	3	ω	ω	PROPN
hjic-104	124	4	γ′	γ′	PROPN
hjic-104	124	5	′	′	NUM
hjic-104	124	6	′	′	NUM
hjic-104	124	7	′′=	′′=	NUM
hjic-104	124	8	∂	∂	NUM
hjic-104	124	9	∂	∂	NOUN
hjic-104	125	1	+	+	ADJ
hjic-104	125	2	+	+	ADJ
hjic-104	125	3	+	+	ADJ
hjic-104	125	4	ξξ	ξξ	NOUN
hjic-104	125	5	τσϕϕ	τσϕϕ	NOUN
hjic-104	125	6	ξ	ξ	X
hjic-104	125	7	ξ	ξ	X
hjic-104	125	8	dt	dt	PROPN
hjic-104	125	9	,	,	PUNCT
hjic-104	125	10	x,,e	x,,e	PROPN
hjic-104	125	11	dd	dd	PROPN
hjic-104	126	1	n	n	PROPN
hjic-104	126	2	e	e	NOUN
hjic-104	126	3	uuu	uuu	PROPN
hjic-104	127	1	i	i	PRON
hjic-104	127	2	t	t	VERB
hjic-104	128	1	i	i	PRON
hjic-104	128	2	i	i	VERB
hjic-104	128	3	1	1	NUM
hjic-104	128	4	0	0	NUM
hjic-104	128	5	1	1	NUM
hjic-104	128	6	6	6	NUM
hjic-104	128	7	1	1	NUM
hjic-104	128	8	61	61	NUM
hjic-104	128	9	1	1	NUM
hjic-104	128	10	1	1	NUM
hjic-104	128	11	1	1	NUM
hjic-104	128	12	0	0	NUM
hjic-104	128	13	2	2	NUM
hjic-104	128	14	1	1	NUM
hjic-104	128	15	k	k	NOUN
hjic-104	128	16	,	,	PUNCT
hjic-104	128	17	where	where	SCONJ
hjic-104	128	18	i	i	PRON
hjic-104	128	19	=	=	NOUN
hjic-104	128	20	1	1	NUM
hjic-104	128	21	,	,	PUNCT
hjic-104	128	22	…	…	PUNCT
hjic-104	128	23	,	,	PUNCT
hjic-104	128	24	6	6	NUM
hjic-104	128	25	and	and	CCONJ
hjic-104	128	26	(	(	PUNCT
hjic-104	128	27	)	)	PUNCT
hjic-104	128	28	ξξ	ξξ	ADP
hjic-104	128	29	τξ	τξ	ADP
hjic-104	129	1	′′	′′	PROPN
hjic-104	129	2	∂	∂	NOUN
hjic-104	129	3	′∂	′∂	NOUN
hjic-104	129	4	=	=	SYM
hjic-104	129	5	∂	∂	NUM
hjic-104	129	6	∂	∂	NUM
hjic-104	129	7	n	n	PRON
hjic-104	129	8	t	t	PROPN
hjic-104	129	9	,	,	PUNCT
hjic-104	129	10	x;,e	x;,e	PROPN
hjic-104	129	11	n	n	PROPN
hjic-104	129	12	e	e	NOUN
hjic-104	129	13	ii	ii	PROPN
hjic-104	129	14	1	1	NUM
hjic-104	129	15	1	1	NUM
hjic-104	129	16	.	.	PUNCT
hjic-104	130	1	this	this	PRON
hjic-104	130	2	is	be	AUX
hjic-104	130	3	a	a	DET
hjic-104	130	4	system	system	NOUN
hjic-104	130	5	of	of	ADP
hjic-104	130	6	linear	linear	PROPN
hjic-104	130	7	equations	equation	NOUN
hjic-104	130	8	⎥	⎥	PROPN
hjic-104	130	9	⎥	⎥	PROPN
hjic-104	130	10	⎥	⎥	PROPN
hjic-104	130	11	⎥	⎥	PROPN
hjic-104	130	12	⎥	⎥	PROPN
hjic-104	130	13	⎥	⎥	PROPN
hjic-104	130	14	⎥	⎥	PROPN
hjic-104	130	15	⎥	⎥	PROPN
hjic-104	130	16	⎥	⎥	PROPN
hjic-104	130	17	⎦	⎦	NOUN
hjic-104	130	18	⎤	⎤	ADJ
hjic-104	130	19	⎢	⎢	NOUN
hjic-104	130	20	⎢	⎢	NOUN
hjic-104	130	21	⎢	⎢	NOUN
hjic-104	130	22	⎢	⎢	NOUN
hjic-104	130	23	⎢	⎢	NOUN
hjic-104	130	24	⎢	⎢	NOUN
hjic-104	130	25	⎢	⎢	NOUN
hjic-104	130	26	⎢	⎢	NOUN
hjic-104	130	27	⎢	⎢	NOUN
hjic-104	130	28	⎣	⎣	PROPN
hjic-104	130	29	⎡	⎡	VERB
hjic-104	130	30	⎥	⎥	PROPN
hjic-104	130	31	⎥	⎥	PROPN
hjic-104	130	32	⎥	⎥	PROPN
hjic-104	130	33	⎥	⎥	PROPN
hjic-104	130	34	⎥	⎥	PROPN
hjic-104	130	35	⎥	⎥	PROPN
hjic-104	130	36	⎥	⎥	PROPN
hjic-104	130	37	⎥	⎥	PROPN
hjic-104	130	38	⎥	⎥	PROPN
hjic-104	131	1	⎦	⎦	NOUN
hjic-104	131	2	⎤	⎤	ADJ
hjic-104	131	3	⎢	⎢	NOUN
hjic-104	131	4	⎢	⎢	NOUN
hjic-104	131	5	⎢	⎢	NOUN
hjic-104	131	6	⎢	⎢	NOUN
hjic-104	131	7	⎢	⎢	NOUN
hjic-104	131	8	⎢	⎢	NOUN
hjic-104	131	9	⎢	⎢	NOUN
hjic-104	131	10	⎢	⎢	NOUN
hjic-104	131	11	⎢	⎢	NOUN
hjic-104	131	12	⎣	⎣	PROPN
hjic-104	131	13	⎡	⎡	NUM
hjic-104	131	14	∂	∂	NOUN
hjic-104	131	15	∂	∂	NUM
hjic-104	131	16	∂	∂	NUM
hjic-104	131	17	∂	∂	NUM
hjic-104	131	18	∂	∂	NUM
hjic-104	131	19	∂	∂	NUM
hjic-104	131	20	∂	∂	NUM
hjic-104	131	21	∂	∂	NUM
hjic-104	131	22	∂	∂	NUM
hjic-104	131	23	∂	∂	NUM
hjic-104	131	24	∂	∂	NUM
hjic-104	131	25	∂	∂	NOUN
hjic-104	131	26	+	+	CCONJ
hjic-104	131	27	⎥	⎥	PROPN
hjic-104	131	28	⎥	⎥	PROPN
hjic-104	131	29	⎥	⎥	PROPN
hjic-104	131	30	⎥	⎥	PROPN
hjic-104	131	31	⎥	⎥	PROPN
hjic-104	131	32	⎥	⎥	PROPN
hjic-104	131	33	⎥	⎥	PROPN
hjic-104	132	1	⎦	⎦	NOUN
hjic-104	132	2	⎤	⎤	ADJ
hjic-104	132	3	⎢	⎢	NOUN
hjic-104	132	4	⎢	⎢	NOUN
hjic-104	132	5	⎢	⎢	NOUN
hjic-104	132	6	⎢	⎢	NOUN
hjic-104	132	7	⎢	⎢	NOUN
hjic-104	132	8	⎢	⎢	NOUN
hjic-104	132	9	⎢	⎢	NOUN
hjic-104	132	10	⎣	⎣	PROPN
hjic-104	132	11	⎡	⎡	ADJ
hjic-104	132	12	∫	∫	NOUN
hjic-104	133	1	∫∫	∫∫	ADV
hjic-104	133	2	∫	∫	PROPN
hjic-104	133	3	∫	∫	PROPN
hjic-104	134	1	∫∫	∫∫	ADV
hjic-104	134	2	∫	∫	PROPN
hjic-104	134	3	∫	∫	PROPN
hjic-104	135	1	∫∫	∫∫	ADV
hjic-104	135	2	∫	∫	PROPN
hjic-104	135	3	γ′∪γ′	γ′∪γ′	X
hjic-104	135	4	′γ′∪γ′	′γ′∪γ′	INTJ
hjic-104	136	1	′	′	NUM
hjic-104	136	2	γ′∪γ′	γ′∪γ′	NOUN
hjic-104	137	1	′γ′∪γ′	′γ′∪γ′	INTJ
hjic-104	138	1	′	′	NUM
hjic-104	138	2	γ′∪γ′	γ′∪γ′	NOUN
hjic-104	138	3	′γ′∪γ′	′γ′∪γ′	VERB
hjic-104	138	4	′	′	NUM
hjic-104	138	5	1	1	NUM
hjic-104	138	6	6	6	NUM
hjic-104	138	7	1	1	NUM
hjic-104	138	8	2	2	NUM
hjic-104	138	9	1	1	NUM
hjic-104	138	10	1	1	NUM
hjic-104	138	11	0	0	NUM
hjic-104	138	12	2	2	NUM
hjic-104	138	13	1	1	NUM
hjic-104	138	14	6	6	NUM
hjic-104	138	15	0	0	NUM
hjic-104	138	16	1	1	NUM
hjic-104	138	17	1	1	NUM
hjic-104	138	18	6	6	NUM
hjic-104	138	19	0	0	NUM
hjic-104	138	20	2	2	NUM
hjic-104	138	21	1	1	NUM
hjic-104	138	22	2	2	NUM
hjic-104	138	23	0	0	NUM
hjic-104	138	24	1	1	NUM
hjic-104	138	25	1	1	NUM
hjic-104	138	26	2	2	NUM
hjic-104	138	27	0	0	NUM
hjic-104	138	28	6	6	NUM
hjic-104	138	29	1	1	NUM
hjic-104	138	30	1	1	NUM
hjic-104	138	31	0	0	NUM
hjic-104	138	32	1	1	NUM
hjic-104	138	33	1	1	NUM
hjic-104	138	34	1	1	NUM
hjic-104	138	35	1	1	NUM
hjic-104	138	36	21	21	NUM
hjic-104	138	37	1	1	NUM
hjic-104	138	38	16	16	NUM
hjic-104	138	39	1	1	NUM
hjic-104	138	40	21	21	NUM
hjic-104	138	41	1	1	NUM
hjic-104	138	42	16	16	NUM
hjic-104	138	43	1	1	NUM
hjic-104	138	44	65	65	NUM
hjic-104	138	45	1	1	NUM
hjic-104	138	46	16	16	NUM
hjic-104	138	47	2	2	NUM
hjic-104	138	48	100	100	NUM
hjic-104	138	49	0	0	NUM
hjic-104	138	50	2	2	NUM
hjic-104	138	51	10	10	NUM
hjic-104	138	52	00	00	NUM
hjic-104	138	53	2	2	NUM
hjic-104	138	54	1	1	NUM
hjic-104	138	55	u	u	NOUN
hjic-104	138	56	u	u	NOUN
hjic-104	138	57	u	u	NOUN
hjic-104	138	58	dd	dd	NOUN
hjic-104	138	59	n	n	CCONJ
hjic-104	138	60	edd	edd	PROPN
hjic-104	138	61	n	n	ADP
hjic-104	138	62	e	e	PROPN
hjic-104	138	63	dd	dd	PROPN
hjic-104	138	64	n	n	CCONJ
hjic-104	138	65	edd	edd	PROPN
hjic-104	138	66	n	n	ADP
hjic-104	138	67	e	e	PROPN
hjic-104	138	68	dd	dd	PROPN
hjic-104	138	69	n	n	CCONJ
hjic-104	138	70	edd	edd	PROPN
hjic-104	138	71	n	n	ADP
hjic-104	138	72	e	e	NOUN
hjic-104	138	73	tt	tt	X
hjic-104	138	74	tt	tt	PROPN
hjic-104	138	75	tt	tt	PROPN
hjic-104	138	76	m	m	VERB
hjic-104	138	77	m	m	VERB
hjic-104	138	78	l	l	NOUN
hjic-104	138	79	mm	mm	NOUN
hjic-104	138	80	l	l	NOUN
hjic-104	138	81	l	l	NOUN
hjic-104	138	82	omm	omm	PROPN
hjic-104	139	1	l	l	PROPN
hjic-104	140	1	l	l	NOUN
hjic-104	141	1	τσϕτσϕ	τσϕτσϕ	ADJ
hjic-104	141	2	τσϕτσϕ	τσϕτσϕ	ADJ
hjic-104	141	3	τσϕτσϕ	τσϕτσϕ	ADJ
hjic-104	142	1	ξξ	ξξ	ADV
hjic-104	142	2	ξξ	ξξ	ADV
hjic-104	142	3	ξξ	ξξ	ADP
hjic-104	142	4	(	(	PUNCT
hjic-104	142	5	)	)	PUNCT
hjic-104	142	6	(	(	PUNCT
hjic-104	142	7	)	)	PUNCT
hjic-104	142	8	(	(	PUNCT
hjic-104	142	9	)	)	PUNCT
hjic-104	142	10	⎥	⎥	PROPN
hjic-104	142	11	⎥	⎥	PROPN
hjic-104	142	12	⎥	⎥	PROPN
hjic-104	142	13	⎥	⎥	PROPN
hjic-104	142	14	⎥	⎥	PROPN
hjic-104	142	15	⎥	⎥	PROPN
hjic-104	143	1	⎦	⎦	NOUN
hjic-104	143	2	⎤	⎤	ADJ
hjic-104	143	3	⎢	⎢	NOUN
hjic-104	143	4	⎢	⎢	NOUN
hjic-104	143	5	⎢	⎢	NOUN
hjic-104	143	6	⎢	⎢	NOUN
hjic-104	143	7	⎢	⎢	NOUN
hjic-104	143	8	⎢	⎢	NOUN
hjic-104	143	9	⎣	⎣	ADJ
hjic-104	143	10	⎡	⎡	NOUN
hjic-104	143	11	′	′	NOUN
hjic-104	143	12	′	′	NUM
hjic-104	143	13	′	′	NUM
hjic-104	144	1	=	=	SYM
hjic-104	145	1	∫	∫	PROPN
hjic-104	145	2	∫	∫	PROPN
hjic-104	145	3	∫	∫	PROPN
hjic-104	145	4	ω′	ω′	PROPN
hjic-104	145	5	ω′	ω′	PROPN
hjic-104	145	6	ω′	ω′	PROPN
hjic-104	145	7	16	16	NUM
hjic-104	145	8	12	12	NUM
hjic-104	145	9	11	11	NUM
hjic-104	145	10	;	;	PUNCT
hjic-104	145	11	0	0	NUM
hjic-104	145	12	;	;	PUNCT
hjic-104	145	13	0	0	NUM
hjic-104	145	14	;	;	PUNCT
hjic-104	145	15	0	0	NUM
hjic-104	145	16	t,,e	t,,e	NOUN
hjic-104	145	17	t,,e	t,,e	NOUN
hjic-104	145	18	t,,e	t,,e	NOUN
hjic-104	145	19	x	x	X
hjic-104	145	20	x	x	PUNCT
hjic-104	145	21	x	x	SYM
hjic-104	145	22	ξ	ξ	X
hjic-104	145	23	ξ	ξ	X
hjic-104	145	24	ξ	ξ	PROPN
hjic-104	145	25	m	m	NOUN
hjic-104	145	26	.	.	PUNCT
hjic-104	146	1	the	the	DET
hjic-104	146	2	quantities	quantity	NOUN
hjic-104	146	3	ξ	ξ	X
hjic-104	146	4	′∂	′∂	NOUN
hjic-104	146	5	∂	∂	NUM
hjic-104	146	6	n	n	NOUN
hjic-104	146	7	ei	ei	NOUN
hjic-104	146	8	1	1	NUM
hjic-104	146	9	with	with	ADP
hjic-104	146	10	(	(	PUNCT
hjic-104	146	11	)	)	PUNCT
hjic-104	146	12	(	(	PUNCT
hjic-104	146	13	)	)	PUNCT
hjic-104	146	14	(	(	PUNCT
hjic-104	146	15	)	)	PUNCT
hjic-104	146	16	⎪	⎪	NOUN
hjic-104	146	17	⎪	⎪	NOUN
hjic-104	146	18	⎩	⎩	NUM
hjic-104	146	19	⎪⎪	⎪⎪	PROPN
hjic-104	146	20	⎨	⎨	ADJ
hjic-104	146	21	⎧	⎧	PROPN
hjic-104	146	22	≤	≤	PROPN
hjic-104	146	23	>	>	PUNCT
hjic-104	146	24	−=′	−=′	PROPN
hjic-104	147	1	−	−	PRON
hjic-104	147	2	−′−	−′−	NOUN
hjic-104	147	3	τ	τ	X
hjic-104	147	4	τ	τ	PROPN
hjic-104	147	5	τπτξ	τπτξ	PROPN
hjic-104	147	6	τ	τ	PROPN
hjic-104	147	7	ξ	ξ	PROPN
hjic-104	147	8	1	1	NUM
hjic-104	147	9	1	1	NUM
hjic-104	147	10	4	4	NUM
hjic-104	147	11	11	11	NUM
hjic-104	147	12	if0	if0	NOUN
hjic-104	147	13	if	if	SCONJ
hjic-104	147	14	4	4	NUM
hjic-104	147	15	1	1	NUM
hjic-104	147	16	1	1	NUM
hjic-104	147	17	2	2	NUM
hjic-104	147	18	t	t	NOUN
hjic-104	147	19	te	te	PROPN
hjic-104	147	20	tt	tt	PROPN
hjic-104	147	21	,	,	PUNCT
hjic-104	147	22	x	x	PROPN
hjic-104	147	23	;	;	PUNCT
hjic-104	147	24	,	,	PUNCT
hjic-104	147	25	t	t	PROPN
hjic-104	147	26	x	x	PUNCT
hjic-104	148	1	i	i	PRON
hjic-104	148	2	i	i	PRON
hjic-104	148	3	e	e	VERB
hjic-104	148	4	are	be	AUX
hjic-104	148	5	(	(	PUNCT
hjic-104	148	6	)	)	PUNCT
hjic-104	148	7	(	(	PUNCT
hjic-104	148	8	)	)	PUNCT
hjic-104	148	9	(	(	PUNCT
hjic-104	148	10	)	)	PUNCT
hjic-104	148	11	τξ	τξ	X
hjic-104	148	12	ξ	ξ	PROPN
hjic-104	148	13	ξ	ξ	PROPN
hjic-104	148	14	τπξ	τπξ	NOUN
hjic-104	148	15	−	−	PROPN
hjic-104	149	1	−′	−′	NUM
hjic-104	149	2	−′	−′	NUM
hjic-104	149	3	′	′	NUM
hjic-104	150	1	′	′	NUM
hjic-104	151	1	−	−	PROPN
hjic-104	151	2	⋅−′	⋅−′	NOUN
hjic-104	151	3	−=⋅	−=⋅	PROPN
hjic-104	151	4	′∂	′∂	NOUN
hjic-104	151	5	∂	∂	NUM
hjic-104	151	6	=	=	SYM
hjic-104	151	7	∂	∂	NUM
hjic-104	151	8	∂	∂	NUM
hjic-104	151	9	1	1	NUM
hjic-104	151	10	2	2	NUM
hjic-104	151	11	4	4	NUM
hjic-104	151	12	2	2	NUM
hjic-104	151	13	1	1	NUM
hjic-104	151	14	11	11	NUM
hjic-104	151	15	8	8	NUM
hjic-104	151	16	tiii	tiii	NOUN
hjic-104	151	17	i	i	NOUN
hjic-104	151	18	e	e	NOUN
hjic-104	151	19	t	t	X
hjic-104	151	20	e	e	X
hjic-104	151	21	n	n	X
hjic-104	151	22	e	e	X
hjic-104	151	23	xξnxξ	xξnxξ	NOUN
hjic-104	151	24	n	n	PROPN
hjic-104	151	25	.	.	PUNCT
hjic-104	152	1	the	the	DET
hjic-104	152	2	term	term	NOUN
hjic-104	152	3	(	(	PUNCT
hjic-104	152	4	)	)	PUNCT
hjic-104	152	5	ξξ	ξξ	NOUN
hjic-104	152	6	′⋅−′	′⋅−′	NOUN
hjic-104	152	7	nx	nx	NOUN
hjic-104	152	8	i	i	PRON
hjic-104	152	9	can	can	AUX
hjic-104	152	10	be	be	AUX
hjic-104	152	11	shown	show	VERB
hjic-104	152	12	in	in	ADP
hjic-104	152	13	the	the	DET
hjic-104	152	14	picture	picture	NOUN
hjic-104	152	15	below	below	ADP
hjic-104	152	16	ix	ix	ADP
hjic-104	152	17	y	y	PROPN
hjic-104	152	18	jx	jx	PROPN
hjic-104	153	1	1+jxξ′	1+jxξ′	NUM
hjic-104	153	2	ξ	ξ	PROPN
hjic-104	153	3	′n	′n	NOUN
hjic-104	153	4	123	123	NUM
hjic-104	153	5	it	it	PRON
hjic-104	153	6	is	be	AUX
hjic-104	153	7	clear	clear	ADJ
hjic-104	153	8	that	that	SCONJ
hjic-104	153	9	(	(	PUNCT
hjic-104	153	10	)	)	PUNCT
hjic-104	153	11	(	(	PUNCT
hjic-104	153	12	)	)	PUNCT
hjic-104	153	13	(	(	PUNCT
hjic-104	153	14	)	)	PUNCT
hjic-104	153	15	(	(	PUNCT
hjic-104	153	16	)	)	PUNCT
hjic-104	153	17	ξξ	ξξ	ADP
hjic-104	153	18	ξξ	ξξ	ADP
hjic-104	153	19	′′	′′	PROPN
hjic-104	153	20	⋅−′+−=⋅−′	⋅−′+−=⋅−′	PROPN
hjic-104	153	21	nn	nn	PROPN
hjic-104	153	22	yxyx	yxyx	PROPN
hjic-104	153	23	ii	ii	PROPN
hjic-104	153	24	ji	ji	PROPN
hjic-104	153	25	dxy	dxy	PROPN
hjic-104	153	26	=	=	PROPN
hjic-104	153	27	−=	−=	X
hjic-104	153	28	.	.	PUNCT
hjic-104	154	1	jd	jd	NOUN
hjic-104	154	2	are	be	AUX
hjic-104	154	3	constant	constant	ADJ
hjic-104	154	4	.	.	PUNCT
hjic-104	155	1	then	then	ADV
hjic-104	155	2	the	the	DET
hjic-104	155	3	elements	element	NOUN
hjic-104	155	4	of	of	ADP
hjic-104	155	5	the	the	DET
hjic-104	155	6	coefficient	coefficient	NOUN
hjic-104	155	7	matrix	matrix	NOUN
hjic-104	155	8	of	of	ADP
hjic-104	155	9	above	above	ADJ
hjic-104	155	10	system	system	NOUN
hjic-104	155	11	are	be	AUX
hjic-104	155	12	(	(	PUNCT
hjic-104	155	13	)	)	PUNCT
hjic-104	155	14	(	(	PUNCT
hjic-104	155	15	)	)	PUNCT
hjic-104	155	16	(	(	PUNCT
hjic-104	155	17	)	)	PUNCT
hjic-104	155	18	(	(	PUNCT
hjic-104	155	19	)	)	PUNCT
hjic-104	155	20	∫	∫	PROPN
hjic-104	156	1	∫	∫	PROPN
hjic-104	156	2	∫	∫	PROPN
hjic-104	157	1	∫∫	∫∫	ADV
hjic-104	157	2	∫	∫	PROPN
hjic-104	157	3	γ′	γ′	PROPN
hjic-104	158	1	′	′	NUM
hjic-104	158	2	−	−	PROPN
hjic-104	159	1	−′	−′	NUM
hjic-104	159	2	−	−	NOUN
hjic-104	159	3	γ′	γ′	PROPN
hjic-104	159	4	′	′	NUM
hjic-104	160	1	−	−	NOUN
hjic-104	160	2	−′	−′	NUM
hjic-104	160	3	−	−	PROPN
hjic-104	161	1	−	−	NOUN
hjic-104	161	2	γ′∪γ′	γ′∪γ′	VERB
hjic-104	161	3	′	′	NUM
hjic-104	162	1	−	−	NOUN
hjic-104	163	1	−	−	PROPN
hjic-104	163	2	−	−	PROPN
hjic-104	163	3	−=	−=	NOUN
hjic-104	163	4	∂	∂	NUM
hjic-104	163	5	∂	∂	NUM
hjic-104	163	6	−−	−−	PROPN
hjic-104	163	7	j	j	PROPN
hjic-104	164	1	i	i	PRON
hjic-104	164	2	j	j	VERB
hjic-104	165	1	i	i	PRON
hjic-104	165	2	jj	jj	PROPN
hjic-104	166	1	t	t	PROPN
hjic-104	166	2	j	j	PROPN
hjic-104	166	3	t	t	PROPN
hjic-104	166	4	x	x	PROPN
hjic-104	167	1	j	j	PROPN
hjic-104	167	2	t	t	PROPN
hjic-104	167	3	j	j	PROPN
hjic-104	168	1	t	t	PROPN
hjic-104	168	2	x	x	PROPN
hjic-104	168	3	j	j	PROPN
hjic-104	168	4	t	t	PROPN
hjic-104	168	5	j	j	PROPN
hjic-104	169	1	i	i	PRON
hjic-104	169	2	dde	dde	PROPN
hjic-104	169	3	t	t	PROPN
hjic-104	169	4	d	d	PROPN
hjic-104	169	5	dde	dde	PROPN
hjic-104	169	6	t	t	PROPN
hjic-104	169	7	d	d	X
hjic-104	169	8	dd	dd	PROPN
hjic-104	169	9	n	n	PROPN
hjic-104	169	10	e	e	NOUN
hjic-104	169	11	1	1	NUM
hjic-104	169	12	1	1	NUM
hjic-104	169	13	2	2	NUM
hjic-104	169	14	1	1	NUM
hjic-104	169	15	1	1	NUM
hjic-104	169	16	1	1	NUM
hjic-104	169	17	2	2	NUM
hjic-104	169	18	1	1	NUM
hjic-104	169	19	1	1	NUM
hjic-104	169	20	0	0	NUM
hjic-104	169	21	4	4	NUM
hjic-104	169	22	1	1	NUM
hjic-104	169	23	0	0	NUM
hjic-104	169	24	4	4	NUM
hjic-104	169	25	1	1	NUM
hjic-104	169	26	1	1	NUM
hjic-104	169	27	0	0	NUM
hjic-104	169	28	1	1	NUM
hjic-104	169	29	8	8	NUM
hjic-104	169	30	8	8	NUM
hjic-104	169	31	ξ	ξ	X
hjic-104	169	32	τ	τ	X
hjic-104	169	33	ξ	ξ	X
hjic-104	169	34	ξ	ξ	X
hjic-104	169	35	τ	τ	X
hjic-104	169	36	ξ	ξ	X
hjic-104	169	37	ξ	ξ	PROPN
hjic-104	169	38	στϕ	στϕ	NOUN
hjic-104	169	39	τπ	τπ	ADP
hjic-104	169	40	στϕ	στϕ	NOUN
hjic-104	169	41	τπ	τπ	X
hjic-104	169	42	τσϕ	τσϕ	VERB
hjic-104	169	43	.	.	PUNCT
hjic-104	170	1	we	we	PRON
hjic-104	170	2	integrate	integrate	VERB
hjic-104	170	3	analytically	analytically	ADV
hjic-104	170	4	with	with	ADP
hjic-104	170	5	respect	respect	NOUN
hjic-104	170	6	to	to	ADP
hjic-104	170	7	the	the	DET
hjic-104	170	8	time	time	NOUN
hjic-104	170	9	variable	variable	NOUN
hjic-104	170	10	and	and	CCONJ
hjic-104	170	11	get	get	VERB
hjic-104	170	12	∫	∫	PROPN
hjic-104	171	1	∫∫	∫∫	ADV
hjic-104	171	2	∫	∫	PROPN
hjic-104	171	3	γ′	γ′	PROPN
hjic-104	172	1	′	′	NUM
hjic-104	173	1	−′	−′	NUM
hjic-104	173	2	−	−	NOUN
hjic-104	173	3	γ′	γ′	PROPN
hjic-104	174	1	′	′	NUM
hjic-104	174	2	−′	−′	NUM
hjic-104	175	1	−	−	NOUN
hjic-104	176	1	−	−	NOUN
hjic-104	177	1	γ′∪γ′	γ′∪γ′	VERB
hjic-104	177	2	′	′	NUM
hjic-104	178	1	−′	−′	NUM
hjic-104	178	2	−	−	PROPN
hjic-104	178	3	−′	−′	PROPN
hjic-104	178	4	−=	−=	NOUN
hjic-104	178	5	∂	∂	NUM
hjic-104	178	6	∂	∂	NUM
hjic-104	178	7	−−	−−	PROPN
hjic-104	178	8	j	j	PROPN
hjic-104	179	1	i	i	PRON
hjic-104	179	2	j	j	PROPN
hjic-104	180	1	i	i	INTJ
hjic-104	180	2	jj	jj	PROPN
hjic-104	180	3	de	de	PROPN
hjic-104	180	4	x	x	PROPN
hjic-104	180	5	d	d	X
hjic-104	180	6	de	de	X
hjic-104	180	7	x	x	PROPN
hjic-104	180	8	d	d	X
hjic-104	180	9	dd	dd	NOUN
hjic-104	180	10	n	n	PROPN
hjic-104	180	11	e	e	X
hjic-104	180	12	j	j	PROPN
hjic-104	180	13	t	t	PROPN
hjic-104	180	14	x	x	PROPN
hjic-104	181	1	i	i	PRON
hjic-104	181	2	j	j	PROPN
hjic-104	182	1	j	j	PROPN
hjic-104	182	2	t	t	PROPN
hjic-104	182	3	x	x	PROPN
hjic-104	183	1	i	i	PRON
hjic-104	183	2	j	j	PROPN
hjic-104	184	1	t	t	PROPN
hjic-104	184	2	j	j	PROPN
hjic-104	184	3	i	i	X
hjic-104	184	4	ξ	ξ	PROPN
hjic-104	184	5	ξ	ξ	X
hjic-104	184	6	ξ	ξ	X
hjic-104	184	7	ξ	ξ	X
hjic-104	184	8	ξ	ξ	X
hjic-104	184	9	σϕ	σϕ	NOUN
hjic-104	184	10	ξπ	ξπ	NOUN
hjic-104	184	11	σϕ	σϕ	NOUN
hjic-104	184	12	ξπ	ξπ	NOUN
hjic-104	184	13	τσϕ	τσϕ	VERB
hjic-104	184	14	1	1	NUM
hjic-104	184	15	2	2	NUM
hjic-104	184	16	1	1	NUM
hjic-104	184	17	1	1	NUM
hjic-104	184	18	2	2	NUM
hjic-104	184	19	1	1	NUM
hjic-104	184	20	1	1	NUM
hjic-104	184	21	4	4	NUM
hjic-104	184	22	2	2	NUM
hjic-104	184	23	4	4	NUM
hjic-104	184	24	2	2	NUM
hjic-104	184	25	1	1	NUM
hjic-104	184	26	0	0	NUM
hjic-104	184	27	1	1	NUM
hjic-104	184	28	2	2	NUM
hjic-104	184	29	2	2	NUM
hjic-104	184	30	.	.	PUNCT
hjic-104	185	1	we	we	PRON
hjic-104	185	2	calculate	calculate	VERB
hjic-104	185	3	each	each	DET
hjic-104	185	4	term	term	NOUN
hjic-104	185	5	numerically	numerically	ADV
hjic-104	185	6	and	and	CCONJ
hjic-104	185	7	obtain	obtain	VERB
hjic-104	185	8	the	the	DET
hjic-104	185	9	system	system	NOUN
hjic-104	185	10	of	of	ADP
hjic-104	185	11	linear	linear	PROPN
hjic-104	185	12	equations	equation	NOUN
hjic-104	185	13	⎥	⎥	PROPN
hjic-104	185	14	⎥	⎥	PROPN
hjic-104	185	15	⎥	⎥	PROPN
hjic-104	185	16	⎥	⎥	PROPN
hjic-104	185	17	⎥	⎥	PROPN
hjic-104	185	18	⎥	⎥	PROPN
hjic-104	185	19	⎦	⎦	NOUN
hjic-104	185	20	⎤	⎤	ADJ
hjic-104	185	21	⎢	⎢	NOUN
hjic-104	185	22	⎢	⎢	NOUN
hjic-104	185	23	⎢	⎢	NOUN
hjic-104	185	24	⎢	⎢	NOUN
hjic-104	185	25	⎢	⎢	NOUN
hjic-104	185	26	⎢	⎢	NOUN
hjic-104	185	27	⎣	⎣	PROPN
hjic-104	185	28	⎡	⎡	NOUN
hjic-104	185	29	=	=	PROPN
hjic-104	185	30	⎥	⎥	PROPN
hjic-104	185	31	⎥	⎥	PROPN
hjic-104	185	32	⎥	⎥	PROPN
hjic-104	185	33	⎥	⎥	PROPN
hjic-104	185	34	⎥	⎥	PROPN
hjic-104	185	35	⎥	⎥	PROPN
hjic-104	185	36	⎥	⎥	PROPN
hjic-104	185	37	⎦	⎦	NOUN
hjic-104	185	38	⎤	⎤	ADJ
hjic-104	185	39	⎢	⎢	NOUN
hjic-104	185	40	⎢	⎢	NOUN
hjic-104	185	41	⎢	⎢	NOUN
hjic-104	185	42	⎢	⎢	NOUN
hjic-104	185	43	⎢	⎢	NOUN
hjic-104	185	44	⎢	⎢	NOUN
hjic-104	185	45	⎢	⎢	NOUN
hjic-104	185	46	⎣	⎣	PROPN
hjic-104	185	47	⎡	⎡	NUM
hjic-104	185	48	3282980	3282980	NUM
hjic-104	185	49	3282980	3282980	NUM
hjic-104	185	50	3282980	3282980	NUM
hjic-104	185	51	3282980	3282980	NUM
hjic-104	185	52	3282980	3282980	NUM
hjic-104	185	53	3282980	3282980	NUM
hjic-104	185	54	1	1	NUM
hjic-104	185	55	6	6	NUM
hjic-104	185	56	1	1	NUM
hjic-104	185	57	5	5	NUM
hjic-104	185	58	1	1	NUM
hjic-104	185	59	4	4	NUM
hjic-104	185	60	1	1	NUM
hjic-104	185	61	3	3	NUM
hjic-104	185	62	1	1	NUM
hjic-104	185	63	2	2	NUM
hjic-104	185	64	1	1	NUM
hjic-104	185	65	1	1	NUM
hjic-104	185	66	.	.	PUNCT
hjic-104	185	67	.	.	PUNCT
hjic-104	185	68	.	.	PUNCT
hjic-104	185	69	.	.	PUNCT
hjic-104	185	70	.	.	PUNCT
hjic-104	185	71	.	.	PUNCT
hjic-104	186	1	u	u	PRON
hjic-104	187	1	u	u	X
hjic-104	187	2	u	u	X
hjic-104	187	3	u	u	X
hjic-104	187	4	u	u	NOUN
hjic-104	187	5	u	u	NOUN
hjic-104	187	6	a	a	DET
hjic-104	187	7	⎥	⎥	PROPN
hjic-104	187	8	⎥	⎥	PROPN
hjic-104	187	9	⎥	⎥	PROPN
hjic-104	187	10	⎥	⎥	PROPN
hjic-104	187	11	⎥	⎥	PROPN
hjic-104	187	12	⎥	⎥	PROPN
hjic-104	187	13	⎦	⎦	NOUN
hjic-104	187	14	⎤	⎤	ADJ
hjic-104	187	15	⎢	⎢	NOUN
hjic-104	187	16	⎢	⎢	NOUN
hjic-104	187	17	⎢	⎢	NOUN
hjic-104	187	18	⎢	⎢	NOUN
hjic-104	187	19	⎢	⎢	NOUN
hjic-104	187	20	⎢	⎢	NOUN
hjic-104	187	21	⎣	⎣	PROPN
hjic-104	187	22	⎡	⎡	NOUN
hjic-104	187	23	=	=	PUNCT
hjic-104	187	24	0.50020200.000490000200.00049002020	0.50020200.000490000200.00049002020	NOUN
hjic-104	187	25	0020200.50020200.000490000200.00049	0020200.50020200.000490000200.00049	NUM
hjic-104	187	26	0.000490020200.50020200.00049000020	0.000490020200.50020200.00049000020	NUM
hjic-104	187	27	0000200.000490020200.50020200.00049	0000200.000490020200.50020200.00049	NUM
hjic-104	187	28	0.000490000200.0004900202050002020	0.000490000200.0004900202050002020	VERB
hjic-104	187	29	0020200.000490000200.000490020200.5	0020200.000490000200.000490020200.5	NOUN
hjic-104	187	30	...	...	PUNCT
hjic-104	187	31	...	...	PUNCT
hjic-104	187	32	...	...	PUNCT
hjic-104	187	33	...	...	PUNCT
hjic-104	188	1	....	....	PUNCT
hjic-104	188	2	...	...	PUNCT
hjic-104	189	1	a	a	DET
hjic-104	189	2	the	the	DET
hjic-104	189	3	solution	solution	NOUN
hjic-104	189	4	of	of	ADP
hjic-104	189	5	the	the	DET
hjic-104	189	6	first	first	ADJ
hjic-104	189	7	time	time	NOUN
hjic-104	189	8	step	step	NOUN
hjic-104	189	9	is	be	AUX
hjic-104	190	1	⎥	⎥	PROPN
hjic-104	190	2	⎥	⎥	PROPN
hjic-104	190	3	⎥	⎥	PROPN
hjic-104	190	4	⎥	⎥	PROPN
hjic-104	190	5	⎥	⎥	PROPN
hjic-104	190	6	⎥	⎥	PROPN
hjic-104	190	7	⎦	⎦	NOUN
hjic-104	190	8	⎤	⎤	ADJ
hjic-104	190	9	⎢	⎢	NOUN
hjic-104	190	10	⎢	⎢	NOUN
hjic-104	190	11	⎢	⎢	NOUN
hjic-104	190	12	⎢	⎢	NOUN
hjic-104	190	13	⎢	⎢	NOUN
hjic-104	190	14	⎢	⎢	NOUN
hjic-104	190	15	⎣	⎣	PROPN
hjic-104	190	16	⎡	⎡	NOUN
hjic-104	190	17	=	=	PROPN
hjic-104	190	18	⎥	⎥	PROPN
hjic-104	190	19	⎥	⎥	PROPN
hjic-104	190	20	⎥	⎥	PROPN
hjic-104	190	21	⎥	⎥	PROPN
hjic-104	190	22	⎥	⎥	PROPN
hjic-104	190	23	⎥	⎥	PROPN
hjic-104	190	24	⎥	⎥	PROPN
hjic-104	190	25	⎦	⎦	NOUN
hjic-104	190	26	⎤	⎤	ADJ
hjic-104	190	27	⎢	⎢	NOUN
hjic-104	190	28	⎢	⎢	NOUN
hjic-104	190	29	⎢	⎢	NOUN
hjic-104	190	30	⎢	⎢	NOUN
hjic-104	190	31	⎢	⎢	NOUN
hjic-104	190	32	⎢	⎢	NOUN
hjic-104	190	33	⎢	⎢	NOUN
hjic-104	190	34	⎣	⎣	PROPN
hjic-104	190	35	⎡	⎡	NUM
hjic-104	190	36	650050	650050	NUM
hjic-104	190	37	650050	650050	NUM
hjic-104	190	38	650050	650050	NUM
hjic-104	190	39	650050	650050	NUM
hjic-104	190	40	650050	650050	NUM
hjic-104	190	41	650050	650050	NUM
hjic-104	190	42	1	1	NUM
hjic-104	190	43	6	6	NUM
hjic-104	190	44	1	1	NUM
hjic-104	190	45	5	5	NUM
hjic-104	190	46	1	1	NUM
hjic-104	190	47	4	4	NUM
hjic-104	190	48	1	1	NUM
hjic-104	190	49	3	3	NUM
hjic-104	190	50	1	1	NUM
hjic-104	190	51	2	2	NUM
hjic-104	190	52	1	1	NUM
hjic-104	190	53	1	1	NUM
hjic-104	190	54	.	.	PUNCT
hjic-104	190	55	.	.	PUNCT
hjic-104	190	56	.	.	PUNCT
hjic-104	191	1	.	.	PUNCT
hjic-104	191	2	.	.	PUNCT
hjic-104	192	1	.	.	PUNCT
hjic-104	193	1	u	u	PRON
hjic-104	194	1	u	u	X
hjic-104	194	2	u	u	X
hjic-104	194	3	u	u	X
hjic-104	194	4	u	u	NOUN
hjic-104	194	5	u	u	NOUN
hjic-104	194	6	conclusions	conclusion	NOUN
hjic-104	194	7	as	as	SCONJ
hjic-104	194	8	shown	show	VERB
hjic-104	194	9	in	in	ADP
hjic-104	194	10	this	this	DET
hjic-104	194	11	paper	paper	NOUN
hjic-104	194	12	the	the	DET
hjic-104	194	13	boundary	boundary	ADJ
hjic-104	194	14	element	element	NOUN
hjic-104	194	15	method	method	NOUN
hjic-104	194	16	(	(	PUNCT
hjic-104	194	17	bem	bem	PROPN
hjic-104	194	18	)	)	PUNCT
hjic-104	194	19	can	can	AUX
hjic-104	194	20	be	be	AUX
hjic-104	194	21	applied	apply	VERB
hjic-104	194	22	to	to	ADP
hjic-104	194	23	elliptic	elliptic	ADJ
hjic-104	194	24	and	and	CCONJ
hjic-104	194	25	parabolic	parabolic	ADJ
hjic-104	194	26	differential	differential	ADJ
hjic-104	194	27	equations	equation	NOUN
hjic-104	194	28	.	.	PUNCT
hjic-104	195	1	the	the	DET
hjic-104	195	2	benefit	benefit	NOUN
hjic-104	195	3	of	of	ADP
hjic-104	195	4	the	the	DET
hjic-104	195	5	method	method	NOUN
hjic-104	195	6	compared	compare	VERB
hjic-104	195	7	to	to	ADP
hjic-104	195	8	conventional	conventional	ADJ
hjic-104	195	9	methods	method	NOUN
hjic-104	195	10	such	such	ADJ
hjic-104	195	11	as	as	ADP
hjic-104	195	12	finite	finite	ADJ
hjic-104	195	13	different	different	ADJ
hjic-104	195	14	and	and	CCONJ
hjic-104	195	15	finite	finite	ADJ
hjic-104	195	16	element	element	NOUN
hjic-104	195	17	method	method	NOUN
hjic-104	195	18	is	be	AUX
hjic-104	195	19	the	the	DET
hjic-104	195	20	reduction	reduction	NOUN
hjic-104	195	21	of	of	ADP
hjic-104	195	22	dimension	dimension	NOUN
hjic-104	195	23	of	of	ADP
hjic-104	195	24	the	the	DET
hjic-104	195	25	problem	problem	NOUN
hjic-104	195	26	by	by	ADP
hjic-104	195	27	one	one	NUM
hjic-104	195	28	since	since	SCONJ
hjic-104	195	29	the	the	DET
hjic-104	195	30	bem	bem	NOUN
hjic-104	195	31	deals	deal	VERB
hjic-104	195	32	only	only	ADV
hjic-104	195	33	with	with	ADP
hjic-104	195	34	the	the	DET
hjic-104	195	35	corresponding	corresponding	ADJ
hjic-104	195	36	boundary	boundary	ADJ
hjic-104	195	37	integral	integral	ADJ
hjic-104	195	38	equation	equation	NOUN
hjic-104	195	39	.	.	PUNCT
hjic-104	196	1	moreover	moreover	ADV
hjic-104	196	2	for	for	ADP
hjic-104	196	3	applying	apply	VERB
hjic-104	196	4	the	the	DET
hjic-104	196	5	collocation	collocation	NOUN
hjic-104	196	6	method	method	VERB
hjic-104	196	7	the	the	DET
hjic-104	196	8	unknown	unknown	ADJ
hjic-104	196	9	trial	trial	NOUN
hjic-104	196	10	or	or	CCONJ
hjic-104	196	11	ansatz	ansatz	ADJ
hjic-104	196	12	function	function	NOUN
hjic-104	196	13	can	can	AUX
hjic-104	196	14	be	be	AUX
hjic-104	196	15	formed	form	VERB
hjic-104	196	16	by	by	ADP
hjic-104	196	17	simple	simple	ADJ
hjic-104	196	18	functions	function	NOUN
hjic-104	196	19	i.e.	i.e.	X
hjic-104	196	20	piecewise	piecewise	NOUN
hjic-104	196	21	constant	constant	ADJ
hjic-104	196	22	and	and	CCONJ
hjic-104	196	23	piecewise	piecewise	NOUN
hjic-104	196	24	linear	linear	NOUN
hjic-104	196	25	functions	function	NOUN
hjic-104	196	26	.	.	PUNCT
hjic-104	197	1	however	however	ADV
hjic-104	197	2	the	the	DET
hjic-104	197	3	disadvantage	disadvantage	NOUN
hjic-104	197	4	of	of	ADP
hjic-104	197	5	the	the	DET
hjic-104	197	6	method	method	NOUN
hjic-104	197	7	is	be	AUX
hjic-104	197	8	the	the	DET
hjic-104	197	9	knowledge	knowledge	NOUN
hjic-104	197	10	of	of	ADP
hjic-104	197	11	the	the	DET
hjic-104	197	12	fundamental	fundamental	ADJ
hjic-104	197	13	solution	solution	NOUN
hjic-104	197	14	.	.	PUNCT
hjic-104	198	1	so	so	ADV
hjic-104	198	2	its	its	PRON
hjic-104	198	3	application	application	NOUN
hjic-104	198	4	is	be	AUX
hjic-104	198	5	limited	limit	VERB
hjic-104	198	6	to	to	AUX
hjic-104	198	7	linear	linear	VERB
hjic-104	198	8	differential	differential	ADJ
hjic-104	198	9	equations	equation	NOUN
hjic-104	198	10	symbols	symbol	NOUN
hjic-104	199	1	pq	pq	INTJ
hjic-104	200	1	ij	ij	INTJ
hjic-104	201	1	pq	pq	INTJ
hjic-104	202	1	ij	ij	INTJ
hjic-104	203	1	pq	pq	INTJ
hjic-104	204	1	ij	ij	INTJ
hjic-104	204	2	c	c	PROPN
hjic-104	204	3	,	,	PUNCT
hjic-104	204	4	b	b	PROPN
hjic-104	204	5	,	,	PUNCT
hjic-104	204	6	a	a	DET
hjic-104	204	7	parameters	parameter	NOUN
hjic-104	204	8	h	h	NOUN
hjic-104	204	9	space	space	NOUN
hjic-104	204	10	step	step	NOUN
hjic-104	204	11	k	k	PRON
hjic-104	204	12	time	time	NOUN
hjic-104	204	13	step	step	NOUN
hjic-104	204	14	i	i	PROPN
hjic-104	204	15	,	,	PUNCT
hjic-104	204	16	j	j	PROPN
hjic-104	204	17	index	index	NOUN
hjic-104	204	18	parameters	parameter	NOUN
hjic-104	204	19	m	m	VERB
hjic-104	204	20	number	number	NOUN
hjic-104	204	21	of	of	ADP
hjic-104	204	22	time	time	NOUN
hjic-104	204	23	intervals	interval	NOUN
hjic-104	204	24	n	n	PRON
hjic-104	204	25	number	number	NOUN
hjic-104	204	26	elements	element	NOUN
hjic-104	204	27	jnv	jnv	NOUN
hjic-104	204	28	unit	unit	NOUN
hjic-104	204	29	normal	normal	ADJ
hjic-104	204	30	vector	vector	NOUN
hjic-104	204	31	p	p	NOUN
hjic-104	204	32	,	,	PUNCT
hjic-104	204	33	q	q	ADJ
hjic-104	204	34	time	time	NOUN
hjic-104	204	35	parameters	parameter	NOUN
hjic-104	204	36	t	t	PROPN
hjic-104	204	37	time	time	NOUN
hjic-104	204	38	variable	variable	NOUN
hjic-104	204	39	(	(	PUNCT
hjic-104	204	40	)	)	PUNCT
hjic-104	204	41	t	t	PROPN
hjic-104	204	42	,	,	PUNCT
hjic-104	204	43	y	y	PROPN
hjic-104	204	44	,	,	PUNCT
hjic-104	204	45	xu	xu	PROPN
hjic-104	204	46	solution	solution	NOUN
hjic-104	204	47	n	n	CCONJ
hjic-104	204	48	iu	iu	ADP
hjic-104	204	49	collocation	collocation	NOUN
hjic-104	204	50	parameters	parameter	NOUN
hjic-104	204	51	x	x	X
hjic-104	204	52	,	,	PUNCT
hjic-104	204	53	y	y	PROPN
hjic-104	204	54	space	space	NOUN
hjic-104	204	55	variable	variable	NOUN
hjic-104	204	56	x	x	PUNCT
hjic-104	204	57	space	space	NOUN
hjic-104	204	58	vector	vector	NOUN
hjic-104	204	59	greek	greek	NOUN
hjic-104	204	60	letters	letter	NOUN
hjic-104	204	61	α	α	PRON
hjic-104	204	62	a	a	DET
hjic-104	204	63	constant	constant	ADJ
hjic-104	204	64	χ	χ	NOUN
hjic-104	204	65	,	,	PUNCT
hjic-104	204	66	ϕ	ϕ	PROPN
hjic-104	204	67	trial	trial	NOUN
hjic-104	204	68	function	function	VERB
hjic-104	204	69	γ	γ	NOUN
hjic-104	204	70	boundary	boundary	NOUN
hjic-104	204	71	of	of	ADP
hjic-104	204	72	the	the	DET
hjic-104	204	73	domain	domain	NOUN
hjic-104	204	74	γ	γ	NOUN
hjic-104	204	75	'	'	PART
hjic-104	204	76	polygonal	polygonal	ADJ
hjic-104	204	77	boundary	boundary	NOUN
hjic-104	204	78	ξ	ξ	PROPN
hjic-104	204	79	,	,	PUNCT
hjic-104	204	80	τ	τ	X
hjic-104	204	81	integral	integral	ADJ
hjic-104	204	82	variable	variable	ADJ
hjic-104	204	83	ω	ω	PROPN
hjic-104	204	84	domain	domain	NOUN
hjic-104	204	85	ω	ω	NOUN
hjic-104	204	86	'	'	PUNCT
hjic-104	204	87	polygonal	polygonal	ADJ
hjic-104	204	88	domain	domain	NOUN
hjic-104	204	89	references	reference	NOUN
hjic-104	204	90	1	1	NUM
hjic-104	204	91	.	.	PUNCT
hjic-104	204	92	brebria	brebria	PROPN
hjic-104	204	93	c.a	c.a	PROPN
hjic-104	204	94	.	.	PROPN
hjic-104	204	95	and	and	CCONJ
hjic-104	204	96	walker	walker	PROPN
hjic-104	204	97	s.	s.	PROPN
hjic-104	204	98	:	:	PUNCT
hjic-104	205	1	boundary	boundary	ADJ
hjic-104	205	2	element	element	NOUN
hjic-104	205	3	techniques	technique	NOUN
hjic-104	205	4	in	in	ADP
hjic-104	205	5	engineering	engineering	NOUN
hjic-104	205	6	,	,	PUNCT
hjic-104	205	7	newnes	newne	NOUN
hjic-104	205	8	butterworths	butterworth	NOUN
hjic-104	205	9	,	,	PUNCT
hjic-104	205	10	london	london	PROPN
hjic-104	205	11	,	,	PUNCT
hjic-104	205	12	1980	1980	NUM
hjic-104	205	13	2	2	NUM
hjic-104	205	14	.	.	PUNCT
hjic-104	205	15	costabel	costabel	ADJ
hjic-104	205	16	m.	m.	NOUN
hjic-104	205	17	:	:	PUNCT
hjic-104	205	18	boundary	boundary	ADJ
hjic-104	205	19	integral	integral	ADJ
hjic-104	205	20	operators	operator	NOUN
hjic-104	205	21	for	for	ADP
hjic-104	205	22	the	the	DET
hjic-104	205	23	heat	heat	NOUN
hjic-104	205	24	equation	equation	NOUN
hjic-104	205	25	,	,	PUNCT
hjic-104	205	26	integral	integral	ADJ
hjic-104	205	27	equations	equation	NOUN
hjic-104	205	28	operatortheory	operatortheory	NOUN
hjic-104	205	29	,	,	PUNCT
hjic-104	205	30	1990	1990	NUM
hjic-104	205	31	,	,	PUNCT
hjic-104	205	32	vol.13	vol.13	NOUN
hjic-104	205	33	,	,	PUNCT
hjic-104	205	34	498	498	NUM
hjic-104	205	35	552	552	NUM
hjic-104	205	36	3	3	NUM
hjic-104	205	37	.	.	PUNCT
hjic-104	205	38	costabel	costabel	ADJ
hjic-104	205	39	m.	m.	NOUN
hjic-104	205	40	,	,	PUNCT
hjic-104	205	41	stephan	stephan	PROPN
hjic-104	205	42	e.p	e.p	PROPN
hjic-104	205	43	.	.	PROPN
hjic-104	205	44	:	:	PUNCT
hjic-104	205	45	.	.	PUNCT
hjic-104	205	46	,	,	PUNCT
hjic-104	205	47	on	on	ADP
hjic-104	205	48	the	the	DET
hjic-104	205	49	convergence	convergence	NOUN
hjic-104	205	50	of	of	ADP
hjic-104	205	51	collocation	collocation	NOUN
hjic-104	205	52	methods	method	NOUN
hjic-104	205	53	for	for	ADP
hjic-104	205	54	boundary	boundary	ADJ
hjic-104	205	55	integral	integral	ADJ
hjic-104	205	56	equations	equation	NOUN
hjic-104	205	57	on	on	ADP
hjic-104	205	58	polygons	polygon	NOUN
hjic-104	205	59	,	,	PUNCT
hjic-104	205	60	mathematics	mathematic	NOUN
hjic-104	205	61	of	of	ADP
hjic-104	205	62	computation	computation	NOUN
hjic-104	205	63	,	,	PUNCT
hjic-104	205	64	1987	1987	NUM
hjic-104	205	65	,	,	PUNCT
hjic-104	205	66	vol.49	vol.49	NOUN
hjic-104	205	67	,	,	PUNCT
hjic-104	205	68	461	461	NUM
hjic-104	205	69	-478	-478	NOUN
hjic-104	205	70	4	4	NUM
hjic-104	205	71	.	.	PUNCT
hjic-104	205	72	costabel	costabel	ADJ
hjic-104	205	73	m.	m.	NOUN
hjic-104	205	74	,	,	PUNCT
hjic-104	205	75	onishi	onishi	PROPN
hjic-104	205	76	k.	k.	PROPN
hjic-104	205	77	,	,	PUNCT
hjic-104	205	78	wendland	wendland	PROPN
hjic-104	205	79	w.	w.	PROPN
hjic-104	205	80	l.	l.	PROPN
hjic-104	205	81	:	:	PUNCT
hjic-104	205	82	boundary	boundary	ADJ
hjic-104	205	83	element	element	NOUN
hjic-104	205	84	collocation	collocation	NOUN
hjic-104	205	85	method	method	NOUN
hjic-104	205	86	for	for	ADP
hjic-104	205	87	the	the	DET
hjic-104	205	88	neumann	neumann	PROPN
hjic-104	205	89	problem	problem	NOUN
hjic-104	205	90	of	of	ADP
hjic-104	205	91	the	the	DET
hjic-104	205	92	heat	heat	NOUN
hjic-104	205	93	equation	equation	NOUN
hjic-104	205	94	,	,	PUNCT
hjic-104	205	95	academic	academic	PROPN
hjic-104	205	96	press	press	PROPN
hjic-104	205	97	inc	inc	PROPN
hjic-104	205	98	.	.	PROPN
hjic-104	205	99	,	,	PUNCT
hjic-104	205	100	1987	1987	NUM
hjic-104	205	101	5	5	NUM
hjic-104	205	102	.	.	PUNCT
hjic-104	206	1	dyck	dyck	PROPN
hjic-104	206	2	u.	u.	NOUN
hjic-104	206	3	:	:	PUNCT
hjic-104	206	4	randelement	randelement	NOUN
hjic-104	206	5	-	-	PUNCT
hjic-104	206	6	lösungen	lösungen	NOUN
hjic-104	206	7	für	für	PROPN
hjic-104	206	8	die	die	VERB
hjic-104	206	9	wärmeleitungsgleichung	wärmeleitungsgleichung	PROPN
hjic-104	206	10	,	,	PUNCT
hjic-104	206	11	master	master	NOUN
hjic-104	206	12	thesis	thesis	NOUN
hjic-104	206	13	in	in	ADP
hjic-104	206	14	mathematics	mathematics	PROPN
hjic-104	206	15	,	,	PUNCT
hjic-104	206	16	hannover	hannover	PROPN
hjic-104	206	17	university	university	PROPN
hjic-104	206	18	,	,	PUNCT
hjic-104	206	19	germany	germany	PROPN
hjic-104	206	20	,	,	PUNCT
hjic-104	206	21	1992	1992	NUM
hjic-104	206	22	6	6	NUM
hjic-104	206	23	.	.	PUNCT
hjic-104	207	1	friedman	friedman	PROPN
hjic-104	207	2	a.	a.	PROPN
hjic-104	207	3	:	:	PUNCT
hjic-104	207	4	partial	partial	ADJ
hjic-104	207	5	differential	differential	ADJ
hjic-104	207	6	equations	equation	NOUN
hjic-104	207	7	of	of	ADP
hjic-104	207	8	parabolic	parabolic	ADJ
hjic-104	207	9	type	type	NOUN
hjic-104	207	10	,	,	PUNCT
hjic-104	207	11	prentice	prentice	NOUN
hjic-104	207	12	hall	hall	PROPN
hjic-104	207	13	.	.	PUNCT
hjic-104	208	1	inc	inc	PROPN
hjic-104	208	2	.	.	PROPN
hjic-104	208	3	,	,	PUNCT
hjic-104	208	4	1964	1964	NUM
hjic-104	208	5	7	7	NUM
hjic-104	208	6	.	.	PUNCT
hjic-104	209	1	herrmann	herrmann	PROPN
hjic-104	209	2	n.	n.	PROPN
hjic-104	209	3	:	:	PUNCT
hjic-104	209	4	bem	bem	NOUN
hjic-104	209	5	with	with	ADP
hjic-104	209	6	collocation	collocation	NOUN
hjic-104	209	7	for	for	ADP
hjic-104	209	8	the	the	DET
hjic-104	209	9	heat	heat	NOUN
hjic-104	209	10	equation	equation	NOUN
hjic-104	209	11	with	with	ADP
hjic-104	209	12	neumann	neumann	PROPN
hjic-104	209	13	and	and	CCONJ
hjic-104	209	14	mixed	mixed	ADJ
hjic-104	209	15	boundary	boundary	ADJ
hjic-104	209	16	124	124	NUM
hjic-104	209	17	values	value	NOUN
hjic-104	209	18	,	,	PUNCT
hjic-104	209	19	ams	am	NOUN
hjic-104	209	20	contemporary	contemporary	PROPN
hjic-104	209	21	mathematics	mathematics	PROPN
hjic-104	209	22	,	,	PUNCT
hjic-104	209	23	2002	2002	NUM
hjic-104	209	24	,	,	PUNCT
hjic-104	209	25	vol.295	vol.295	ADJ
hjic-104	209	26	,	,	PUNCT
hjic-104	209	27	265	265	NUM
hjic-104	209	28	277	277	NUM
hjic-104	209	29	8	8	NUM
hjic-104	209	30	.	.	PUNCT
hjic-104	210	1	herrmann	herrmann	PROPN
hjic-104	210	2	n.	n.	PROPN
hjic-104	210	3	:	:	PUNCT
hjic-104	210	4	improved	improve	VERB
hjic-104	210	5	method	method	NOUN
hjic-104	210	6	for	for	ADP
hjic-104	210	7	solving	solve	VERB
hjic-104	210	8	the	the	DET
hjic-104	210	9	heat	heat	NOUN
hjic-104	210	10	equation	equation	NOUN
hjic-104	210	11	with	with	ADP
hjic-104	210	12	bem	bem	NOUN
hjic-104	210	13	and	and	CCONJ
hjic-104	210	14	collocation	collocation	NOUN
hjic-104	210	15	,	,	PUNCT
hjic-104	210	16	ams	am	NOUN
hjic-104	210	17	contemporary	contemporary	ADJ
hjic-104	210	18	mathematics	mathematics	PROPN
hjic-104	210	19	,	,	PUNCT
hjic-104	210	20	2003	2003	NUM
hjic-104	210	21	,	,	PUNCT
hjic-104	210	22	vol.329	vol.329	NUM
hjic-104	210	23	,	,	PUNCT
hjic-104	210	24	165	165	NUM
hjic-104	210	25	174	174	NUM
hjic-104	210	26	9	9	NUM
hjic-104	210	27	.	.	PUNCT
hjic-104	211	1	herrmann	herrmann	PROPN
hjic-104	211	2	n.	n.	PROPN
hjic-104	211	3	:	:	PUNCT
hjic-104	211	4	time	time	NOUN
hjic-104	211	5	discretization	discretization	NOUN
hjic-104	211	6	of	of	ADP
hjic-104	211	7	linear	linear	ADJ
hjic-104	211	8	parabolic	parabolic	NOUN
hjic-104	211	9	problems	problem	NOUN
hjic-104	211	10	,	,	PUNCT
hjic-104	211	11	hungarian	hungarian	ADJ
hjic-104	211	12	journal	journal	NOUN
hjic-104	211	13	of	of	ADP
hjic-104	211	14	industrial	industrial	ADJ
hjic-104	211	15	chemistry	chemistry	NOUN
hjic-104	211	16	,	,	PUNCT
hjic-104	211	17	1991	1991	NUM
hjic-104	211	18	,	,	PUNCT
hjic-104	211	19	vol.19	vol.19	NOUN
hjic-104	211	20	,	,	PUNCT
hjic-104	211	21	275	275	NUM
hjic-104	211	22	281	281	NUM
hjic-104	211	23	10	10	NUM
hjic-104	211	24	.	.	PUNCT
hjic-104	212	1	herrmann	herrmann	PROPN
hjic-104	212	2	n.	n.	PROPN
hjic-104	212	3	:	:	PUNCT
hjic-104	212	4	numerical	numerical	ADJ
hjic-104	212	5	problems	problem	NOUN
hjic-104	212	6	in	in	ADP
hjic-104	212	7	determining	determine	VERB
hjic-104	212	8	pore	pore	ADJ
hjic-104	212	9	-	-	PUNCT
hjic-104	212	10	size	size	NOUN
hjic-104	212	11	distribution	distribution	NOUN
hjic-104	212	12	in	in	ADP
hjic-104	212	13	porous	porous	ADJ
hjic-104	212	14	material	material	NOUN
hjic-104	212	15	,	,	PUNCT
hjic-104	212	16	workshop	workshop	NOUN
hjic-104	212	17	at	at	ADP
hjic-104	212	18	the	the	DET
hjic-104	212	19	university	university	NOUN
hjic-104	212	20	of	of	ADP
hjic-104	212	21	budapest	budapest	PROPN
hjic-104	212	22	,	,	PUNCT
hjic-104	212	23	invited	invite	VERB
hjic-104	212	24	lecture	lecture	NOUN
hjic-104	212	25	,	,	PUNCT
hjic-104	212	26	1995	1995	NUM
hjic-104	212	27	11	11	NUM
hjic-104	212	28	.	.	PUNCT
hjic-104	213	1	herrmann	herrmann	PROPN
hjic-104	213	2	n.	n.	PROPN
hjic-104	213	3	,	,	PUNCT
hjic-104	213	4	siefer	siefer	PROPN
hjic-104	213	5	j.	j.	PROPN
hjic-104	213	6	,	,	PUNCT
hjic-104	213	7	stephan	stephan	PROPN
hjic-104	213	8	e.p	e.p	PROPN
hjic-104	213	9	.	.	PROPN
hjic-104	213	10	,	,	PUNCT
hjic-104	213	11	and	and	CCONJ
hjic-104	213	12	wagner	wagner	PROPN
hjic-104	213	13	r.	r.	PROPN
hjic-104	213	14	,	,	PUNCT
hjic-104	213	15	mathematik	mathematik	PROPN
hjic-104	213	16	und	und	PROPN
hjic-104	213	17	umwelt	umwelt	PROPN
hjic-104	213	18	,	,	PUNCT
hjic-104	213	19	edition	edition	PROPN
hjic-104	213	20	univ	univ	PROPN
hjic-104	213	21	.	.	PROPN
hjic-104	213	22	hannover	hannover	PROPN
hjic-104	213	23	,	,	PUNCT
hjic-104	213	24	theodor	theodor	PROPN
hjic-104	213	25	oppermann	oppermann	PROPN
hjic-104	213	26	verlag	verlag	PROPN
hjic-104	213	27	,	,	PUNCT
hjic-104	213	28	hannover	hannover	PROPN
hjic-104	213	29	,	,	PUNCT
hjic-104	213	30	1994	1994	NUM
hjic-104	213	31	12	12	NUM
hjic-104	213	32	.	.	PUNCT
hjic-104	214	1	herrmann	herrmann	PROPN
hjic-104	214	2	n.	n.	PROPN
hjic-104	214	3	and	and	CCONJ
hjic-104	214	4	stephan	stephan	PROPN
hjic-104	214	5	e.p	e.p	PROPN
hjic-104	214	6	.	.	PROPN
hjic-104	214	7	,	,	PUNCT
hjic-104	214	8	fem	fem	PROPN
hjic-104	214	9	und	und	PROPN
hjic-104	214	10	bem	bem	PROPN
hjic-104	214	11	einführung	einführung	PROPN
hjic-104	214	12	,	,	PUNCT
hjic-104	214	13	eigendruck	eigendruck	NOUN
hjic-104	214	14	inst	inst	NOUN
hjic-104	214	15	.	.	PUNCT
hjic-104	215	1	f.	f.	PROPN
hjic-104	215	2	angew	angew	PROPN
hjic-104	215	3	.	.	PUNCT
hjic-104	216	1	math	math	PROPN
hjic-104	216	2	.	.	PUNCT
hjic-104	216	3	,	,	PUNCT
hjic-104	217	1	univ	univ	PROPN
hjic-104	217	2	.	.	PROPN
hjic-104	217	3	hannover	hannover	PROPN
hjic-104	217	4	,	,	PUNCT
hjic-104	217	5	1991	1991	NUM
hjic-104	217	6	13	13	NUM
hjic-104	217	7	.	.	PUNCT
hjic-104	218	1	iso	iso	PROPN
hjic-104	218	2	y.	y.	PROPN
hjic-104	218	3	:	:	PUNCT
hjic-104	218	4	convergence	convergence	NOUN
hjic-104	218	5	of	of	ADP
hjic-104	218	6	boundary	boundary	ADJ
hjic-104	218	7	element	element	NOUN
hjic-104	218	8	solutions	solution	NOUN
hjic-104	218	9	for	for	ADP
hjic-104	218	10	the	the	DET
hjic-104	218	11	heat	heat	NOUN
hjic-104	218	12	equation	equation	NOUN
hjic-104	218	13	,	,	PUNCT
hjic-104	218	14	journal	journal	NOUN
hjic-104	218	15	of	of	ADP
hjic-104	218	16	computational	computational	ADJ
hjic-104	218	17	and	and	CCONJ
hjic-104	218	18	applied	applied	ADJ
hjic-104	218	19	mathematics	mathematic	NOUN
hjic-104	218	20	,	,	PUNCT
hjic-104	218	21	1991	1991	NUM
hjic-104	218	22	,	,	PUNCT
hjic-104	218	23	vol.38	vol.38	NOUN
hjic-104	218	24	,	,	PUNCT
hjic-104	218	25	201	201	NUM
hjic-104	218	26	–	–	PUNCT
hjic-104	218	27	209	209	NUM