id	sid	tid	token	lemma	pos
ap-5063	1	1	acta	acta	PROPN
ap-5063	1	2	polytechnica	polytechnica	PROPN
ap-5063	1	3	doi:10.14311	doi:10.14311	PROPN
ap-5063	1	4	/	/	SYM
ap-5063	1	5	ap.2018.58.0402	ap.2018.58.0402	PROPN
ap-5063	1	6	acta	acta	PROPN
ap-5063	1	7	polytechnica	polytechnica	PROPN
ap-5063	1	8	58(6):402–413	58(6):402–413	PROPN
ap-5063	1	9	,	,	PUNCT
ap-5063	1	10	2018	2018	NUM
ap-5063	1	11	©	©	PROPN
ap-5063	1	12	czech	czech	PROPN
ap-5063	1	13	technical	technical	PROPN
ap-5063	1	14	university	university	PROPN
ap-5063	1	15	in	in	ADP
ap-5063	1	16	prague	prague	PROPN
ap-5063	1	17	,	,	PUNCT
ap-5063	1	18	2018	2018	NUM
ap-5063	1	19	available	available	ADJ
ap-5063	1	20	online	online	ADV
ap-5063	1	21	at	at	ADP
ap-5063	1	22	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-5063	1	23	multidimensional	multidimensional	ADJ
ap-5063	1	24	hybrid	hybrid	ADJ
ap-5063	1	25	boundary	boundary	ADJ
ap-5063	1	26	value	value	NOUN
ap-5063	1	27	problem	problem	NOUN
ap-5063	1	28	marzena	marzena	ADP
ap-5063	1	29	szajewskaa,∗	szajewskaa,∗	PROPN
ap-5063	1	30	,	,	PUNCT
ap-5063	1	31	agnieszka	agnieszka	PROPN
ap-5063	1	32	tereszkiewiczb	tereszkiewiczb	PROPN
ap-5063	1	33	a	a	DET
ap-5063	1	34	institute	institute	NOUN
ap-5063	1	35	of	of	ADP
ap-5063	1	36	mathematics	mathematics	PROPN
ap-5063	1	37	,	,	PUNCT
ap-5063	1	38	university	university	NOUN
ap-5063	1	39	of	of	ADP
ap-5063	1	40	bialystok	bialystok	ADJ
ap-5063	1	41	,	,	PUNCT
ap-5063	1	42	1	1	NUM
ap-5063	1	43	m	m	NOUN
ap-5063	1	44	ciolkowskiego	ciolkowskiego	NOUN
ap-5063	1	45	,	,	PUNCT
ap-5063	1	46	pl-15	pl-15	NOUN
ap-5063	1	47	-	-	PUNCT
ap-5063	1	48	245	245	NUM
ap-5063	1	49	bialystok	bialystok	ADJ
ap-5063	1	50	,	,	PUNCT
ap-5063	1	51	poland	poland	PROPN
ap-5063	1	52	b	b	PROPN
ap-5063	1	53	bialystok	bialystok	PROPN
ap-5063	1	54	university	university	NOUN
ap-5063	1	55	of	of	ADP
ap-5063	1	56	technology	technology	NOUN
ap-5063	1	57	,	,	PUNCT
ap-5063	1	58	faculty	faculty	NOUN
ap-5063	1	59	of	of	ADP
ap-5063	1	60	civil	civil	ADJ
ap-5063	1	61	and	and	CCONJ
ap-5063	1	62	environmental	environmental	ADJ
ap-5063	1	63	engineering	engineering	NOUN
ap-5063	1	64	,	,	PUNCT
ap-5063	1	65	45	45	NUM
ap-5063	1	66	e	e	NOUN
ap-5063	1	67	wiejska	wiejska	NOUN
ap-5063	1	68	,	,	PUNCT
ap-5063	1	69	pl-15	pl-15	NOUN
ap-5063	1	70	-	-	PUNCT
ap-5063	1	71	351	351	NUM
ap-5063	1	72	bialystok	bialystok	ADJ
ap-5063	1	73	,	,	PUNCT
ap-5063	1	74	poland	poland	PROPN
ap-5063	1	75	∗	∗	NOUN
ap-5063	1	76	corresponding	correspond	VERB
ap-5063	1	77	author	author	NOUN
ap-5063	1	78	:	:	PUNCT
ap-5063	1	79	m.szajewska@math.uwb.edu.pl	m.szajewska@math.uwb.edu.pl	NUM
ap-5063	1	80	abstract	abstract	NOUN
ap-5063	1	81	.	.	PUNCT
ap-5063	2	1	the	the	DET
ap-5063	2	2	purpose	purpose	NOUN
ap-5063	2	3	of	of	ADP
ap-5063	2	4	this	this	DET
ap-5063	2	5	paper	paper	NOUN
ap-5063	2	6	is	be	AUX
ap-5063	2	7	to	to	PART
ap-5063	2	8	discuss	discuss	VERB
ap-5063	2	9	three	three	NUM
ap-5063	2	10	types	type	NOUN
ap-5063	2	11	of	of	ADP
ap-5063	2	12	boundary	boundary	ADJ
ap-5063	2	13	conditions	condition	NOUN
ap-5063	2	14	for	for	ADP
ap-5063	2	15	few	few	ADJ
ap-5063	2	16	families	family	NOUN
ap-5063	2	17	of	of	ADP
ap-5063	2	18	special	special	ADJ
ap-5063	2	19	functions	function	NOUN
ap-5063	2	20	orthogonal	orthogonal	ADJ
ap-5063	2	21	on	on	ADP
ap-5063	2	22	the	the	DET
ap-5063	2	23	fundamental	fundamental	ADJ
ap-5063	2	24	region	region	NOUN
ap-5063	2	25	.	.	PUNCT
ap-5063	3	1	boundary	boundary	ADJ
ap-5063	3	2	value	value	NOUN
ap-5063	3	3	problems	problem	NOUN
ap-5063	3	4	are	be	AUX
ap-5063	3	5	considered	consider	VERB
ap-5063	3	6	on	on	ADP
ap-5063	3	7	a	a	DET
ap-5063	3	8	simplex	simplex	NOUN
ap-5063	3	9	f	f	PROPN
ap-5063	3	10	in	in	ADP
ap-5063	3	11	the	the	DET
ap-5063	3	12	real	real	ADJ
ap-5063	3	13	euclidean	euclidean	ADJ
ap-5063	3	14	space	space	NOUN
ap-5063	3	15	rn	rn	PROPN
ap-5063	3	16	of	of	ADP
ap-5063	3	17	dimension	dimension	PROPN
ap-5063	3	18	n	n	CCONJ
ap-5063	3	19	>	>	X
ap-5063	3	20	2	2	X
ap-5063	3	21	.	.	PUNCT
ap-5063	4	1	keywords	keyword	NOUN
ap-5063	4	2	:	:	PUNCT
ap-5063	4	3	hybrid	hybrid	ADJ
ap-5063	4	4	functions	function	NOUN
ap-5063	4	5	,	,	PUNCT
ap-5063	4	6	dirichlet	dirichlet	PROPN
ap-5063	4	7	boundary	boundary	PROPN
ap-5063	4	8	value	value	NOUN
ap-5063	4	9	problem	problem	NOUN
ap-5063	4	10	,	,	PUNCT
ap-5063	4	11	neumann	neumann	PROPN
ap-5063	4	12	boundary	boundary	PROPN
ap-5063	4	13	value	value	NOUN
ap-5063	4	14	problem	problem	NOUN
ap-5063	4	15	,	,	PUNCT
ap-5063	4	16	mixed	mixed	ADJ
ap-5063	4	17	boundary	boundary	ADJ
ap-5063	4	18	value	value	NOUN
ap-5063	4	19	problem	problem	NOUN
ap-5063	4	20	.	.	PUNCT
ap-5063	5	1	1	1	X
ap-5063	5	2	.	.	X
ap-5063	5	3	introduction	introduction	NOUN
ap-5063	5	4	the	the	DET
ap-5063	5	5	boundary	boundary	ADJ
ap-5063	5	6	value	value	NOUN
ap-5063	5	7	problems	problem	NOUN
ap-5063	5	8	,	,	PUNCT
ap-5063	5	9	considered	consider	VERB
ap-5063	5	10	in	in	ADP
ap-5063	5	11	the	the	DET
ap-5063	5	12	paper	paper	NOUN
ap-5063	5	13	,	,	PUNCT
ap-5063	5	14	is	be	AUX
ap-5063	5	15	a	a	DET
ap-5063	5	16	generalization	generalization	NOUN
ap-5063	5	17	of	of	ADP
ap-5063	5	18	[	[	X
ap-5063	5	19	24	24	NUM
ap-5063	5	20	]	]	PUNCT
ap-5063	5	21	in	in	ADP
ap-5063	5	22	which	which	PRON
ap-5063	5	23	the	the	DET
ap-5063	5	24	authors	author	NOUN
ap-5063	5	25	presented	present	VERB
ap-5063	5	26	two	two	NUM
ap-5063	5	27	-	-	PUNCT
ap-5063	5	28	dimensional	dimensional	ADJ
ap-5063	5	29	hybrids	hybrid	NOUN
ap-5063	5	30	with	with	ADP
ap-5063	5	31	mixed	mixed	ADJ
ap-5063	5	32	boundary	boundary	ADJ
ap-5063	5	33	value	value	NOUN
ap-5063	5	34	problems	problem	NOUN
ap-5063	5	35	.	.	PUNCT
ap-5063	6	1	here	here	ADV
ap-5063	6	2	we	we	PRON
ap-5063	6	3	take	take	VERB
ap-5063	6	4	a	a	DET
ap-5063	6	5	real	real	ADJ
ap-5063	6	6	euclidean	euclidean	ADJ
ap-5063	6	7	space	space	NOUN
ap-5063	6	8	rn	rn	PROPN
ap-5063	6	9	of	of	ADP
ap-5063	6	10	dimension	dimension	NOUN
ap-5063	6	11	n	n	CCONJ
ap-5063	6	12	on	on	ADP
ap-5063	6	13	finite	finite	ADJ
ap-5063	6	14	regions	region	NOUN
ap-5063	6	15	f	f	PROPN
ap-5063	6	16	⊂	⊂	PROPN
ap-5063	6	17	rn	rn	PROPN
ap-5063	6	18	that	that	PRON
ap-5063	6	19	are	be	AUX
ap-5063	6	20	polyhedral	polyhedral	ADJ
ap-5063	6	21	domains	domain	NOUN
ap-5063	6	22	.	.	PUNCT
ap-5063	7	1	the	the	DET
ap-5063	7	2	aim	aim	NOUN
ap-5063	7	3	of	of	ADP
ap-5063	7	4	this	this	DET
ap-5063	7	5	paper	paper	NOUN
ap-5063	7	6	is	be	AUX
ap-5063	7	7	to	to	PART
ap-5063	7	8	seek	seek	VERB
ap-5063	7	9	solutions	solution	NOUN
ap-5063	7	10	of	of	ADP
ap-5063	7	11	the	the	DET
ap-5063	7	12	helmholtz	helmholtz	NOUN
ap-5063	7	13	equation	equation	NOUN
ap-5063	7	14	with	with	ADP
ap-5063	7	15	mixed	mixed	ADJ
ap-5063	7	16	boundary	boundary	ADJ
ap-5063	7	17	condition	condition	NOUN
ap-5063	7	18	by	by	ADP
ap-5063	7	19	analogy	analogy	NOUN
ap-5063	7	20	to	to	ADP
ap-5063	7	21	two	two	NUM
ap-5063	7	22	-	-	PUNCT
ap-5063	7	23	dimensional	dimensional	ADJ
ap-5063	7	24	cases	case	NOUN
ap-5063	7	25	.	.	PUNCT
ap-5063	8	1	the	the	DET
ap-5063	8	2	solutions	solution	NOUN
ap-5063	8	3	are	be	AUX
ap-5063	8	4	presented	present	VERB
ap-5063	8	5	as	as	ADP
ap-5063	8	6	expansions	expansion	NOUN
ap-5063	8	7	into	into	ADP
ap-5063	8	8	a	a	DET
ap-5063	8	9	series	series	NOUN
ap-5063	8	10	of	of	ADP
ap-5063	8	11	special	special	ADJ
ap-5063	8	12	functions	function	NOUN
ap-5063	8	13	that	that	PRON
ap-5063	8	14	satisfy	satisfy	VERB
ap-5063	8	15	required	require	VERB
ap-5063	8	16	conditions	condition	NOUN
ap-5063	8	17	at	at	ADP
ap-5063	8	18	the	the	DET
ap-5063	8	19	(	(	PUNCT
ap-5063	8	20	n−	n−	NOUN
ap-5063	8	21	1)-dimensional	1)-dimensional	ADJ
ap-5063	8	22	boundaries	boundary	NOUN
ap-5063	8	23	of	of	ADP
ap-5063	8	24	f	f	PROPN
ap-5063	8	25	.	.	PUNCT
ap-5063	9	1	the	the	DET
ap-5063	9	2	recent	recent	ADJ
ap-5063	9	3	discovery	discovery	NOUN
ap-5063	9	4	of	of	ADP
ap-5063	9	5	special	special	ADJ
ap-5063	9	6	functions	function	NOUN
ap-5063	9	7	[	[	X
ap-5063	9	8	5	5	NUM
ap-5063	9	9	,	,	PUNCT
ap-5063	9	10	10	10	NUM
ap-5063	9	11	,	,	PUNCT
ap-5063	9	12	11	11	NUM
ap-5063	9	13	,	,	PUNCT
ap-5063	9	14	16	16	NUM
ap-5063	9	15	,	,	PUNCT
ap-5063	9	16	19	19	NUM
ap-5063	9	17	,	,	PUNCT
ap-5063	9	18	23	23	NUM
ap-5063	9	19	]	]	PUNCT
ap-5063	9	20	makes	make	VERB
ap-5063	9	21	realization	realization	NOUN
ap-5063	9	22	of	of	ADP
ap-5063	9	23	this	this	DET
ap-5063	9	24	idea	idea	NOUN
ap-5063	9	25	easy	easy	ADJ
ap-5063	9	26	and	and	CCONJ
ap-5063	9	27	straightforward	straightforward	ADJ
ap-5063	9	28	in	in	ADP
ap-5063	9	29	any	any	DET
ap-5063	9	30	dimension	dimension	NOUN
ap-5063	9	31	.	.	PUNCT
ap-5063	10	1	the	the	DET
ap-5063	10	2	new	new	ADJ
ap-5063	10	3	functions	function	NOUN
ap-5063	10	4	,	,	PUNCT
ap-5063	10	5	called	call	VERB
ap-5063	10	6	’	'	PUNCT
ap-5063	10	7	multidimensional	multidimensional	ADJ
ap-5063	10	8	hybrids	hybrid	NOUN
ap-5063	10	9	’	'	PUNCT
ap-5063	10	10	,	,	PUNCT
ap-5063	10	11	satisfy	satisfy	VERB
ap-5063	10	12	the	the	DET
ap-5063	10	13	dirichlet	dirichlet	PROPN
ap-5063	10	14	boundary	boundary	ADJ
ap-5063	10	15	condition	condition	NOUN
ap-5063	10	16	on	on	ADP
ap-5063	10	17	some	some	DET
ap-5063	10	18	parts	part	NOUN
ap-5063	10	19	of	of	ADP
ap-5063	10	20	the	the	DET
ap-5063	10	21	boundary	boundary	ADJ
ap-5063	10	22	f	f	PROPN
ap-5063	10	23	and	and	CCONJ
ap-5063	10	24	neumann	neumann	PROPN
ap-5063	10	25	on	on	ADP
ap-5063	10	26	the	the	DET
ap-5063	10	27	remaining	remain	VERB
ap-5063	10	28	ones	one	NOUN
ap-5063	10	29	.	.	PUNCT
ap-5063	11	1	the	the	DET
ap-5063	11	2	methods	method	NOUN
ap-5063	11	3	used	use	VERB
ap-5063	11	4	in	in	ADP
ap-5063	11	5	the	the	DET
ap-5063	11	6	paper	paper	NOUN
ap-5063	11	7	are	be	AUX
ap-5063	11	8	the	the	DET
ap-5063	11	9	standard	standard	ADJ
ap-5063	11	10	methods	method	NOUN
ap-5063	11	11	of	of	ADP
ap-5063	11	12	separation	separation	NOUN
ap-5063	11	13	of	of	ADP
ap-5063	11	14	variables	variable	NOUN
ap-5063	11	15	for	for	ADP
ap-5063	11	16	differential	differential	ADJ
ap-5063	11	17	equations	equation	NOUN
ap-5063	11	18	(	(	PUNCT
ap-5063	11	19	see	see	VERB
ap-5063	11	20	for	for	ADP
ap-5063	11	21	example	example	NOUN
ap-5063	11	22	[	[	X
ap-5063	11	23	15	15	NUM
ap-5063	11	24	,	,	PUNCT
ap-5063	11	25	18	18	NUM
ap-5063	11	26	]	]	PUNCT
ap-5063	11	27	)	)	PUNCT
ap-5063	11	28	and	and	CCONJ
ap-5063	11	29	the	the	DET
ap-5063	11	30	branching	branch	VERB
ap-5063	11	31	rule	rule	NOUN
ap-5063	11	32	method	method	NOUN
ap-5063	11	33	for	for	ADP
ap-5063	11	34	orbits	orbit	NOUN
ap-5063	11	35	of	of	ADP
ap-5063	11	36	reflection	reflection	NOUN
ap-5063	11	37	groups	group	NOUN
ap-5063	11	38	(	(	PUNCT
ap-5063	11	39	see	see	VERB
ap-5063	11	40	for	for	ADP
ap-5063	11	41	example	example	NOUN
ap-5063	11	42	[	[	X
ap-5063	11	43	19	19	NUM
ap-5063	11	44	,	,	PUNCT
ap-5063	11	45	24	24	NUM
ap-5063	11	46	,	,	PUNCT
ap-5063	11	47	28	28	NUM
ap-5063	11	48	]	]	PUNCT
ap-5063	11	49	)	)	PUNCT
ap-5063	11	50	.	.	PUNCT
ap-5063	12	1	the	the	DET
ap-5063	12	2	boundary	boundary	ADJ
ap-5063	12	3	value	value	NOUN
ap-5063	12	4	conditions	condition	NOUN
ap-5063	12	5	play	play	VERB
ap-5063	12	6	an	an	DET
ap-5063	12	7	important	important	ADJ
ap-5063	12	8	role	role	NOUN
ap-5063	12	9	in	in	ADP
ap-5063	12	10	mathematics	mathematic	NOUN
ap-5063	12	11	and	and	CCONJ
ap-5063	12	12	physics	physics	NOUN
ap-5063	12	13	.	.	PUNCT
ap-5063	13	1	they	they	PRON
ap-5063	13	2	are	be	AUX
ap-5063	13	3	used	use	VERB
ap-5063	13	4	,	,	PUNCT
ap-5063	13	5	for	for	ADP
ap-5063	13	6	example	example	NOUN
ap-5063	13	7	,	,	PUNCT
ap-5063	13	8	in	in	ADP
ap-5063	13	9	the	the	DET
ap-5063	13	10	theory	theory	NOUN
ap-5063	13	11	of	of	ADP
ap-5063	13	12	elasticity	elasticity	NOUN
ap-5063	13	13	,	,	PUNCT
ap-5063	13	14	electrostatics	electrostatic	NOUN
ap-5063	13	15	and	and	CCONJ
ap-5063	13	16	fluid	fluid	ADJ
ap-5063	13	17	mechanics	mechanic	NOUN
ap-5063	13	18	[	[	X
ap-5063	13	19	4	4	NUM
ap-5063	13	20	,	,	PUNCT
ap-5063	13	21	9	9	NUM
ap-5063	13	22	,	,	PUNCT
ap-5063	13	23	26	26	NUM
ap-5063	13	24	]	]	PUNCT
ap-5063	13	25	.	.	PUNCT
ap-5063	14	1	in	in	ADP
ap-5063	14	2	§	§	PROPN
ap-5063	14	3	2	2	NUM
ap-5063	14	4	,	,	PUNCT
ap-5063	14	5	we	we	PRON
ap-5063	14	6	present	present	VERB
ap-5063	14	7	the	the	DET
ap-5063	14	8	well	well	ADV
ap-5063	14	9	known	know	VERB
ap-5063	14	10	helmholtz	helmholtz	NOUN
ap-5063	14	11	equation	equation	NOUN
ap-5063	14	12	and	and	CCONJ
ap-5063	14	13	three	three	NUM
ap-5063	14	14	types	type	NOUN
ap-5063	14	15	of	of	ADP
ap-5063	14	16	boundary	boundary	ADJ
ap-5063	14	17	conditions	condition	NOUN
ap-5063	14	18	.	.	PUNCT
ap-5063	15	1	in	in	ADP
ap-5063	15	2	§	§	PROPN
ap-5063	15	3	3	3	NUM
ap-5063	15	4	,	,	PUNCT
ap-5063	15	5	we	we	PRON
ap-5063	15	6	recall	recall	VERB
ap-5063	15	7	some	some	DET
ap-5063	15	8	facts	fact	NOUN
ap-5063	15	9	about	about	ADP
ap-5063	15	10	finite	finite	ADJ
ap-5063	15	11	reflection	reflection	NOUN
ap-5063	15	12	groups	group	NOUN
ap-5063	15	13	.	.	PUNCT
ap-5063	16	1	the	the	DET
ap-5063	16	2	next	next	ADJ
ap-5063	16	3	section	section	NOUN
ap-5063	16	4	is	be	AUX
ap-5063	16	5	devoted	devote	VERB
ap-5063	16	6	to	to	ADP
ap-5063	16	7	special	special	ADJ
ap-5063	16	8	functions	function	NOUN
ap-5063	16	9	,	,	PUNCT
ap-5063	16	10	projection	projection	NOUN
ap-5063	16	11	matrices	matrix	NOUN
ap-5063	16	12	and	and	CCONJ
ap-5063	16	13	branching	branch	VERB
ap-5063	16	14	rules	rule	NOUN
ap-5063	16	15	.	.	PUNCT
ap-5063	17	1	in	in	ADP
ap-5063	17	2	§	§	PROPN
ap-5063	17	3	5	5	NUM
ap-5063	17	4	we	we	PRON
ap-5063	17	5	present	present	VERB
ap-5063	17	6	3d	3d	NUM
ap-5063	17	7	cases	case	NOUN
ap-5063	17	8	in	in	ADP
ap-5063	17	9	details	detail	NOUN
ap-5063	17	10	,	,	PUNCT
ap-5063	17	11	namely	namely	ADV
ap-5063	17	12	b3	b3	PROPN
ap-5063	17	13	,	,	PUNCT
ap-5063	17	14	c3	c3	PROPN
ap-5063	17	15	,	,	PUNCT
ap-5063	17	16	c2×a1	c2×a1	PROPN
ap-5063	17	17	,	,	PUNCT
ap-5063	17	18	g2×a1	g2×a1	PROPN
ap-5063	17	19	,	,	PUNCT
ap-5063	17	20	a1×	a1×	PROPN
ap-5063	17	21	a1×a1	a1×a1	PROPN
ap-5063	17	22	.	.	PUNCT
ap-5063	18	1	in	in	ADP
ap-5063	18	2	the	the	DET
ap-5063	18	3	appendix	appendix	NOUN
ap-5063	18	4	we	we	PRON
ap-5063	18	5	list	list	VERB
ap-5063	18	6	tables	table	NOUN
ap-5063	18	7	containing	contain	VERB
ap-5063	18	8	the	the	DET
ap-5063	18	9	values	value	NOUN
ap-5063	18	10	of	of	ADP
ap-5063	18	11	functions	function	NOUN
ap-5063	18	12	on	on	ADP
ap-5063	18	13	the	the	DET
ap-5063	18	14	boundaries	boundary	NOUN
ap-5063	18	15	of	of	ADP
ap-5063	18	16	fundamental	fundamental	ADJ
ap-5063	18	17	region	region	NOUN
ap-5063	18	18	.	.	PUNCT
ap-5063	19	1	2	2	X
ap-5063	19	2	.	.	X
ap-5063	19	3	helmholtz	helmholtz	NOUN
ap-5063	19	4	equation	equation	NOUN
ap-5063	19	5	and	and	CCONJ
ap-5063	19	6	boundary	boundary	ADJ
ap-5063	19	7	conditions	condition	NOUN
ap-5063	19	8	in	in	ADP
ap-5063	19	9	this	this	DET
ap-5063	19	10	paper	paper	NOUN
ap-5063	19	11	we	we	PRON
ap-5063	19	12	consider	consider	VERB
ap-5063	19	13	the	the	DET
ap-5063	19	14	partial	partial	ADJ
ap-5063	19	15	differential	differential	NOUN
ap-5063	19	16	equation	equation	NOUN
ap-5063	19	17	called	call	VERB
ap-5063	19	18	the	the	DET
ap-5063	19	19	homogeneous	homogeneous	ADJ
ap-5063	19	20	helmholtz	helmholtz	NOUN
ap-5063	19	21	equation	equation	NOUN
ap-5063	19	22	[	[	X
ap-5063	19	23	15	15	NUM
ap-5063	19	24	,	,	PUNCT
ap-5063	19	25	18	18	NUM
ap-5063	19	26	,	,	PUNCT
ap-5063	19	27	25	25	NUM
ap-5063	19	28	,	,	PUNCT
ap-5063	19	29	and	and	CCONJ
ap-5063	19	30	references	reference	NOUN
ap-5063	19	31	therein	therein	ADV
ap-5063	19	32	]	]	X
ap-5063	19	33	:	:	PUNCT
ap-5063	19	34	∆ψ(x	∆ψ(x	NOUN
ap-5063	19	35	)	)	PUNCT
ap-5063	19	36	=	=	SYM
ap-5063	20	1	−w2ψ(x	−w2ψ(x	NOUN
ap-5063	20	2	)	)	PUNCT
ap-5063	20	3	,	,	PUNCT
ap-5063	20	4	(	(	PUNCT
ap-5063	20	5	1	1	X
ap-5063	20	6	)	)	PUNCT
ap-5063	20	7	where	where	SCONJ
ap-5063	20	8	w	w	NOUN
ap-5063	20	9	-	-	ADJ
ap-5063	20	10	positive	positive	ADJ
ap-5063	20	11	real	real	ADJ
ap-5063	20	12	constant	constant	ADJ
ap-5063	20	13	,	,	PUNCT
ap-5063	20	14	x	x	SYM
ap-5063	20	15	=	=	SYM
ap-5063	20	16	(	(	PUNCT
ap-5063	20	17	y1	y1	INTJ
ap-5063	20	18	,	,	PUNCT
ap-5063	20	19	.	.	PUNCT
ap-5063	20	20	.	.	PUNCT
ap-5063	20	21	.	.	PUNCT
ap-5063	21	1	,	,	PUNCT
ap-5063	21	2	yn	yn	PROPN
ap-5063	21	3	)	)	PUNCT
ap-5063	21	4	is	be	AUX
ap-5063	21	5	given	give	VERB
ap-5063	21	6	in	in	ADP
ap-5063	21	7	cartesian	cartesian	ADJ
ap-5063	21	8	coordinates	coordinate	NOUN
ap-5063	21	9	and	and	CCONJ
ap-5063	21	10	∆	∆	PROPN
ap-5063	21	11	=	=	SYM
ap-5063	22	1	n∑	n∑	PROPN
ap-5063	22	2	i=1	i=1	PROPN
ap-5063	23	1	∂2	∂2	PROPN
ap-5063	23	2	∂y2	∂y2	NOUN
ap-5063	23	3	i	i	PRON
ap-5063	23	4	.	.	PUNCT
ap-5063	24	1	using	use	VERB
ap-5063	24	2	a	a	DET
ap-5063	24	3	standard	standard	ADJ
ap-5063	24	4	method	method	NOUN
ap-5063	24	5	of	of	ADP
ap-5063	24	6	separation	separation	NOUN
ap-5063	24	7	of	of	ADP
ap-5063	24	8	variables	variable	NOUN
ap-5063	24	9	for	for	ADP
ap-5063	24	10	(	(	PUNCT
ap-5063	24	11	1	1	NUM
ap-5063	24	12	)	)	PUNCT
ap-5063	24	13	(	(	PUNCT
ap-5063	24	14	see	see	VERB
ap-5063	24	15	for	for	ADP
ap-5063	24	16	example	example	NOUN
ap-5063	24	17	[	[	X
ap-5063	24	18	15	15	NUM
ap-5063	24	19	]	]	PUNCT
ap-5063	24	20	)	)	PUNCT
ap-5063	24	21	and	and	CCONJ
ap-5063	24	22	searching	search	VERB
ap-5063	24	23	for	for	ADP
ap-5063	24	24	the	the	DET
ap-5063	24	25	solutions	solution	NOUN
ap-5063	24	26	in	in	ADP
ap-5063	24	27	the	the	DET
ap-5063	24	28	form	form	NOUN
ap-5063	24	29	ψ(x	ψ(x	NOUN
ap-5063	24	30	)	)	PUNCT
ap-5063	24	31	=	=	SYM
ap-5063	24	32	x1(y1	x1(y1	X
ap-5063	24	33	)	)	PUNCT
ap-5063	24	34	·	·	PUNCT
ap-5063	24	35	·	·	PUNCT
ap-5063	24	36	·	·	PUNCT
ap-5063	24	37	xn(yn	xn(yn	ADJ
ap-5063	24	38	)	)	PUNCT
ap-5063	24	39	,	,	PUNCT
ap-5063	24	40	we	we	PRON
ap-5063	24	41	have	have	VERB
ap-5063	24	42	the	the	DET
ap-5063	24	43	following	follow	VERB
ap-5063	24	44	differential	differential	ADJ
ap-5063	24	45	equation	equation	NOUN
ap-5063	24	46	x	x	X
ap-5063	24	47	′′1x2	′′1x2	X
ap-5063	24	48	·	·	PUNCT
ap-5063	24	49	·	·	PUNCT
ap-5063	24	50	·	·	PUNCT
ap-5063	24	51	xn	xn	PUNCT
ap-5063	25	1	+	+	ADJ
ap-5063	25	2	x1x	x1x	PROPN
ap-5063	25	3	′′	′′	PROPN
ap-5063	25	4	2	2	NUM
ap-5063	25	5	·	·	PUNCT
ap-5063	25	6	·	·	PUNCT
ap-5063	25	7	·	·	PUNCT
ap-5063	25	8	xn	xn	PUNCT
ap-5063	26	1	+	+	NUM
ap-5063	26	2	·	·	PUNCT
ap-5063	26	3	·	·	PUNCT
ap-5063	26	4	·	·	PUNCT
ap-5063	26	5	+	+	ADJ
ap-5063	26	6	x1x2	x1x2	X
ap-5063	26	7	·	·	PUNCT
ap-5063	26	8	·	·	PUNCT
ap-5063	26	9	·	·	PUNCT
ap-5063	26	10	x	x	X
ap-5063	26	11	′′n	′′n	NOUN
ap-5063	26	12	+	+	CCONJ
ap-5063	26	13	w2x1x2	w2x1x2	X
ap-5063	26	14	·	·	PUNCT
ap-5063	26	15	·	·	PUNCT
ap-5063	26	16	·	·	PUNCT
ap-5063	26	17	xn	xn	PUNCT
ap-5063	27	1	=	=	SYM
ap-5063	27	2	0	0	PROPN
ap-5063	27	3	.	.	PUNCT
ap-5063	28	1	(	(	PUNCT
ap-5063	28	2	2	2	NUM
ap-5063	28	3	)	)	PUNCT
ap-5063	28	4	by	by	ADP
ap-5063	28	5	introducing	introduce	VERB
ap-5063	28	6	−k2	−k2	PROPN
ap-5063	28	7	1	1	NUM
ap-5063	28	8	,	,	PUNCT
ap-5063	28	9	.	.	PUNCT
ap-5063	28	10	.	.	PUNCT
ap-5063	28	11	.	.	PUNCT
ap-5063	29	1	,	,	PUNCT
ap-5063	29	2	−k2	−k2	PROPN
ap-5063	29	3	n	n	CCONJ
ap-5063	29	4	so	so	ADV
ap-5063	29	5	-	-	PUNCT
ap-5063	29	6	called	call	VERB
ap-5063	29	7	separation	separation	NOUN
ap-5063	29	8	constants	constant	NOUN
ap-5063	29	9	,	,	PUNCT
ap-5063	29	10	we	we	PRON
ap-5063	29	11	get	get	VERB
ap-5063	29	12	the	the	DET
ap-5063	29	13	solution	solution	NOUN
ap-5063	29	14	of	of	ADP
ap-5063	29	15	(	(	PUNCT
ap-5063	29	16	2	2	NUM
ap-5063	29	17	)	)	PUNCT
ap-5063	29	18	in	in	ADP
ap-5063	29	19	the	the	DET
ap-5063	29	20	form	form	NOUN
ap-5063	29	21	x1	x1	PROPN
ap-5063	29	22	1	1	NUM
ap-5063	29	23	(	(	PUNCT
ap-5063	29	24	y1	y1	NOUN
ap-5063	29	25	)	)	PUNCT
ap-5063	29	26	=	=	PUNCT
ap-5063	29	27	cos(k1	cos(k1	PROPN
ap-5063	29	28	y1	y1	PROPN
ap-5063	29	29	)	)	PUNCT
ap-5063	29	30	,	,	PUNCT
ap-5063	29	31	...	...	PUNCT
ap-5063	30	1	x1	x1	NUM
ap-5063	30	2	n−1(yn−1	n−1(yn−1	NOUN
ap-5063	30	3	)	)	PUNCT
ap-5063	30	4	=	=	PUNCT
ap-5063	31	1	cos(kn−1	cos(kn−1	PROPN
ap-5063	31	2	yn−1	yn−1	PROPN
ap-5063	31	3	)	)	PUNCT
ap-5063	31	4	,	,	PUNCT
ap-5063	31	5	x1	x1	PROPN
ap-5063	31	6	n(yn	n(yn	ADV
ap-5063	31	7	)	)	PUNCT
ap-5063	31	8	=	=	PUNCT
ap-5063	31	9	cos(kn	cos(kn	X
ap-5063	31	10	yn	yn	PROPN
ap-5063	31	11	)	)	PUNCT
ap-5063	31	12	,	,	PUNCT
ap-5063	31	13	x2	x2	PROPN
ap-5063	31	14	1	1	NUM
ap-5063	31	15	(	(	PUNCT
ap-5063	31	16	y1	y1	NOUN
ap-5063	31	17	)	)	PUNCT
ap-5063	31	18	=	=	SYM
ap-5063	31	19	sin(k1	sin(k1	PROPN
ap-5063	31	20	y1	y1	PROPN
ap-5063	31	21	)	)	PUNCT
ap-5063	31	22	,	,	PUNCT
ap-5063	31	23	...	...	PUNCT
ap-5063	32	1	x2	x2	PROPN
ap-5063	32	2	n−1(yn−1	n−1(yn−1	ADJ
ap-5063	32	3	)	)	PUNCT
ap-5063	32	4	=	=	PUNCT
ap-5063	33	1	sin(kn−1	sin(kn−1	PROPN
ap-5063	33	2	yn−1	yn−1	PROPN
ap-5063	33	3	)	)	PUNCT
ap-5063	33	4	,	,	PUNCT
ap-5063	33	5	x2	x2	PROPN
ap-5063	33	6	n(yn	n(yn	ADV
ap-5063	33	7	)	)	PUNCT
ap-5063	34	1	=	=	SYM
ap-5063	34	2	sin(kn	sin(kn	NUM
ap-5063	34	3	yn	yn	PROPN
ap-5063	34	4	)	)	PUNCT
ap-5063	34	5	,	,	PUNCT
ap-5063	34	6	(	(	PUNCT
ap-5063	34	7	3	3	X
ap-5063	34	8	)	)	PUNCT
ap-5063	35	1	where	where	SCONJ
ap-5063	35	2	kn	kn	NOUN
ap-5063	35	3	:	:	PUNCT
ap-5063	35	4	=	=	SYM
ap-5063	35	5	√	√	PROPN
ap-5063	35	6	w2	w2	NOUN
ap-5063	35	7	−	−	PROPN
ap-5063	35	8	∑n−1	∑n−1	ADP
ap-5063	35	9	i=1	i=1	PROPN
ap-5063	35	10	ki2	ki2	PROPN
ap-5063	35	11	,	,	PUNCT
ap-5063	35	12	ki	ki	PROPN
ap-5063	35	13	6=	6=	ADP
ap-5063	35	14	0	0	NUM
ap-5063	35	15	for	for	ADP
ap-5063	35	16	i	i	PRON
ap-5063	35	17	=	=	NOUN
ap-5063	35	18	1	1	NUM
ap-5063	35	19	,	,	PUNCT
ap-5063	35	20	.	.	PUNCT
ap-5063	35	21	.	.	PUNCT
ap-5063	35	22	.	.	PUNCT
ap-5063	36	1	,	,	PUNCT
ap-5063	36	2	n.	n.	VERB
ap-5063	36	3	the	the	DET
ap-5063	36	4	way	way	NOUN
ap-5063	36	5	of	of	ADP
ap-5063	36	6	choosing	choose	VERB
ap-5063	36	7	separation	separation	NOUN
ap-5063	36	8	constants	constant	NOUN
ap-5063	36	9	is	be	AUX
ap-5063	36	10	not	not	PART
ap-5063	36	11	unique	unique	ADJ
ap-5063	36	12	.	.	PUNCT
ap-5063	37	1	in	in	ADP
ap-5063	37	2	this	this	DET
ap-5063	37	3	paper	paper	NOUN
ap-5063	37	4	ki	ki	PROPN
ap-5063	37	5	,	,	PUNCT
ap-5063	37	6	i	i	NOUN
ap-5063	37	7	=	=	NOUN
ap-5063	37	8	1	1	NUM
ap-5063	37	9	,	,	PUNCT
ap-5063	37	10	.	.	PUNCT
ap-5063	37	11	.	.	PUNCT
ap-5063	37	12	.	.	PUNCT
ap-5063	38	1	,	,	PUNCT
ap-5063	38	2	n−1	n−1	PROPN
ap-5063	38	3	are	be	AUX
ap-5063	38	4	selected	select	VERB
ap-5063	38	5	according	accord	VERB
ap-5063	38	6	to	to	ADP
ap-5063	38	7	a	a	DET
ap-5063	38	8	branching	branch	VERB
ap-5063	38	9	rule	rule	NOUN
ap-5063	38	10	method	method	NOUN
ap-5063	38	11	[	[	X
ap-5063	38	12	19	19	NUM
ap-5063	38	13	,	,	PUNCT
ap-5063	38	14	24	24	NUM
ap-5063	38	15	,	,	PUNCT
ap-5063	38	16	28	28	NUM
ap-5063	38	17	]	]	PUNCT
ap-5063	38	18	,	,	PUNCT
ap-5063	38	19	see	see	VERB
ap-5063	38	20	next	next	ADJ
ap-5063	38	21	sections	section	NOUN
ap-5063	38	22	.	.	PUNCT
ap-5063	39	1	three	three	NUM
ap-5063	39	2	types	type	NOUN
ap-5063	39	3	of	of	ADP
ap-5063	39	4	boundary	boundary	ADJ
ap-5063	39	5	conditions	condition	NOUN
ap-5063	39	6	.	.	PUNCT
ap-5063	40	1	d	d	X
ap-5063	40	2	:	:	PUNCT
ap-5063	40	3	a	a	DET
ap-5063	40	4	dirichlet	dirichlet	PROPN
ap-5063	40	5	boundary	boundary	ADJ
ap-5063	40	6	condition	condition	NOUN
ap-5063	40	7	defines	define	VERB
ap-5063	40	8	the	the	DET
ap-5063	40	9	value	value	NOUN
ap-5063	40	10	of	of	ADP
ap-5063	40	11	the	the	DET
ap-5063	40	12	function	function	NOUN
ap-5063	40	13	itself	itself	PRON
ap-5063	40	14	ψ(x	ψ(x	NOUN
ap-5063	40	15	)	)	PUNCT
ap-5063	41	1	=	=	SYM
ap-5063	41	2	f(x	f(x	PROPN
ap-5063	41	3	)	)	PUNCT
ap-5063	41	4	,	,	PUNCT
ap-5063	41	5	for	for	ADP
ap-5063	41	6	x	x	PROPN
ap-5063	41	7	∈	∈	PROPN
ap-5063	41	8	∂f	∂f	PROPN
ap-5063	41	9	,	,	PUNCT
ap-5063	41	10	402	402	NUM
ap-5063	41	11	http://dx.doi.org/10.14311/ap.2018.58.0402	http://dx.doi.org/10.14311/ap.2018.58.0402	DET
ap-5063	41	12	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-5063	41	13	vol	vol	NOUN
ap-5063	41	14	.	.	PUNCT
ap-5063	42	1	58	58	NUM
ap-5063	42	2	no	no	INTJ
ap-5063	42	3	.	.	PUNCT
ap-5063	43	1	6/2018	6/2018	NUM
ap-5063	43	2	multidimensional	multidimensional	ADJ
ap-5063	43	3	hybrid	hybrid	ADJ
ap-5063	43	4	boundary	boundary	ADJ
ap-5063	43	5	value	value	NOUN
ap-5063	43	6	problem	problem	NOUN
ap-5063	43	7	where	where	SCONJ
ap-5063	43	8	f(x	f(x	PROPN
ap-5063	43	9	)	)	PUNCT
ap-5063	43	10	is	be	AUX
ap-5063	43	11	a	a	DET
ap-5063	43	12	given	give	VERB
ap-5063	43	13	function	function	NOUN
ap-5063	43	14	defined	define	VERB
ap-5063	43	15	on	on	ADP
ap-5063	43	16	the	the	DET
ap-5063	43	17	boundary	boundary	NOUN
ap-5063	43	18	.	.	PUNCT
ap-5063	44	1	n	n	CCONJ
ap-5063	44	2	:	:	PUNCT
ap-5063	44	3	a	a	DET
ap-5063	44	4	neumann	neumann	PROPN
ap-5063	44	5	boundary	boundary	ADJ
ap-5063	44	6	condition	condition	NOUN
ap-5063	44	7	defines	define	VERB
ap-5063	44	8	the	the	DET
ap-5063	44	9	value	value	NOUN
ap-5063	44	10	of	of	ADP
ap-5063	44	11	the	the	DET
ap-5063	44	12	normal	normal	ADJ
ap-5063	44	13	derivative	derivative	NOUN
ap-5063	44	14	of	of	ADP
ap-5063	44	15	the	the	DET
ap-5063	44	16	function	function	NOUN
ap-5063	44	17	∂ψ	∂ψ	PROPN
ap-5063	45	1	∂n	∂n	PROPN
ap-5063	45	2	(	(	PUNCT
ap-5063	45	3	x	x	X
ap-5063	45	4	)	)	PUNCT
ap-5063	45	5	=	=	SYM
ap-5063	45	6	f(x	f(x	PROPN
ap-5063	45	7	)	)	PUNCT
ap-5063	45	8	,	,	PUNCT
ap-5063	45	9	for	for	ADP
ap-5063	45	10	x	x	PROPN
ap-5063	45	11	∈	∈	PROPN
ap-5063	45	12	∂f	∂f	PROPN
ap-5063	45	13	,	,	PUNCT
ap-5063	45	14	where	where	SCONJ
ap-5063	45	15	n	n	PRON
ap-5063	45	16	denotes	denote	VERB
ap-5063	45	17	normal	normal	ADJ
ap-5063	45	18	vector	vector	NOUN
ap-5063	45	19	to	to	ADP
ap-5063	45	20	the	the	DET
ap-5063	45	21	boundary	boundary	ADJ
ap-5063	45	22	∂f	∂f	PROPN
ap-5063	45	23	.	.	PUNCT
ap-5063	46	1	m	m	VERB
ap-5063	46	2	:	:	PUNCT
ap-5063	46	3	a	a	DET
ap-5063	46	4	mixed	mixed	ADJ
ap-5063	46	5	boundary	boundary	ADJ
ap-5063	46	6	condition	condition	NOUN
ap-5063	46	7	defines	define	VERB
ap-5063	46	8	the	the	DET
ap-5063	46	9	value	value	NOUN
ap-5063	46	10	of	of	ADP
ap-5063	46	11	the	the	DET
ap-5063	46	12	function	function	NOUN
ap-5063	46	13	itself	itself	PRON
ap-5063	46	14	on	on	ADP
ap-5063	46	15	one	one	NUM
ap-5063	46	16	part	part	NOUN
ap-5063	46	17	of	of	ADP
ap-5063	46	18	the	the	DET
ap-5063	46	19	boundary	boundary	NOUN
ap-5063	46	20	and	and	CCONJ
ap-5063	46	21	the	the	DET
ap-5063	46	22	value	value	NOUN
ap-5063	46	23	of	of	ADP
ap-5063	46	24	the	the	DET
ap-5063	46	25	normal	normal	ADJ
ap-5063	46	26	derivative	derivative	NOUN
ap-5063	46	27	of	of	ADP
ap-5063	46	28	the	the	DET
ap-5063	46	29	function	function	NOUN
ap-5063	46	30	on	on	ADP
ap-5063	46	31	the	the	DET
ap-5063	46	32	other	other	ADJ
ap-5063	46	33	part	part	NOUN
ap-5063	46	34	of	of	ADP
ap-5063	46	35	the	the	DET
ap-5063	46	36	boundary	boundary	ADJ
ap-5063	46	37	d	d	NOUN
ap-5063	46	38	:	:	PUNCT
ap-5063	46	39	ψ|∂f0	ψ|∂f0	X
ap-5063	46	40	=	=	SYM
ap-5063	46	41	f0	f0	PROPN
ap-5063	46	42	,	,	PUNCT
ap-5063	46	43	n	n	CCONJ
ap-5063	46	44	:	:	PUNCT
ap-5063	47	1	∂ψ	∂ψ	VERB
ap-5063	47	2	∂n	∂n	PROPN
ap-5063	47	3	∣∣∣	∣∣∣	NOUN
ap-5063	47	4	∂f1	∂f1	PROPN
ap-5063	47	5	=	=	SYM
ap-5063	47	6	f1	f1	NOUN
ap-5063	47	7	,	,	PUNCT
ap-5063	47	8	where	where	SCONJ
ap-5063	47	9	∂f	∂f	PROPN
ap-5063	47	10	=	=	SYM
ap-5063	47	11	∂f0∪∂f1	∂f0∪∂f1	PROPN
ap-5063	47	12	and	and	CCONJ
ap-5063	47	13	f0	f0	PROPN
ap-5063	47	14	,	,	PUNCT
ap-5063	47	15	f1	f1	NOUN
ap-5063	47	16	are	be	AUX
ap-5063	47	17	given	give	VERB
ap-5063	47	18	functions	function	NOUN
ap-5063	47	19	,	,	PUNCT
ap-5063	47	20	defined	define	VERB
ap-5063	47	21	on	on	ADP
ap-5063	47	22	the	the	DET
ap-5063	47	23	appropriate	appropriate	ADJ
ap-5063	47	24	boundary	boundary	NOUN
ap-5063	47	25	.	.	PUNCT
ap-5063	48	1	3	3	X
ap-5063	48	2	.	.	X
ap-5063	48	3	finite	finite	PROPN
ap-5063	48	4	reflection	reflection	NOUN
ap-5063	48	5	groups	group	NOUN
ap-5063	48	6	our	our	PRON
ap-5063	48	7	method	method	NOUN
ap-5063	48	8	is	be	AUX
ap-5063	48	9	general	general	ADJ
ap-5063	48	10	and	and	CCONJ
ap-5063	48	11	can	can	AUX
ap-5063	48	12	be	be	AUX
ap-5063	48	13	presented	present	VERB
ap-5063	48	14	for	for	ADP
ap-5063	48	15	any	any	DET
ap-5063	48	16	crystallographic	crystallographic	ADJ
ap-5063	48	17	finite	finite	ADJ
ap-5063	48	18	reflection	reflection	NOUN
ap-5063	48	19	groups	group	NOUN
ap-5063	48	20	g	g	ADP
ap-5063	48	21	of	of	ADP
ap-5063	48	22	any	any	DET
ap-5063	48	23	rank	rank	NOUN
ap-5063	48	24	and	and	CCONJ
ap-5063	48	25	any	any	DET
ap-5063	48	26	dimension	dimension	NOUN
ap-5063	48	27	which	which	PRON
ap-5063	48	28	are	be	AUX
ap-5063	48	29	associated	associate	VERB
ap-5063	48	30	with	with	ADP
ap-5063	48	31	simple	simple	ADJ
ap-5063	48	32	and	and	CCONJ
ap-5063	48	33	semisimple	semisimple	NOUN
ap-5063	48	34	lie	lie	VERB
ap-5063	48	35	algebras	algebra	NOUN
ap-5063	48	36	/	/	SYM
ap-5063	48	37	groups	group	NOUN
ap-5063	48	38	[	[	X
ap-5063	48	39	1	1	NUM
ap-5063	48	40	,	,	PUNCT
ap-5063	48	41	7	7	NUM
ap-5063	48	42	,	,	PUNCT
ap-5063	48	43	10	10	NUM
ap-5063	48	44	,	,	PUNCT
ap-5063	48	45	27	27	NUM
ap-5063	48	46	]	]	PUNCT
ap-5063	48	47	.	.	PUNCT
ap-5063	49	1	there	there	PRON
ap-5063	49	2	is	be	VERB
ap-5063	49	3	a	a	DET
ap-5063	49	4	complete	complete	ADJ
ap-5063	49	5	classification	classification	NOUN
ap-5063	49	6	of	of	ADP
ap-5063	49	7	finite	finite	ADJ
ap-5063	49	8	reflection	reflection	NOUN
ap-5063	49	9	groups	group	NOUN
ap-5063	49	10	given	give	VERB
ap-5063	49	11	by	by	ADP
ap-5063	49	12	dynkin	dynkin	ADJ
ap-5063	49	13	diagrams	diagram	NOUN
ap-5063	49	14	[	[	X
ap-5063	49	15	2	2	NUM
ap-5063	49	16	,	,	PUNCT
ap-5063	49	17	3	3	NUM
ap-5063	49	18	,	,	PUNCT
ap-5063	49	19	10	10	NUM
ap-5063	49	20	]	]	PUNCT
ap-5063	49	21	.	.	PUNCT
ap-5063	50	1	these	these	DET
ap-5063	50	2	graphs	graph	NOUN
ap-5063	50	3	provide	provide	VERB
ap-5063	50	4	the	the	DET
ap-5063	50	5	relative	relative	ADJ
ap-5063	50	6	angles	angle	NOUN
ap-5063	50	7	and	and	CCONJ
ap-5063	50	8	relative	relative	ADJ
ap-5063	50	9	length	length	NOUN
ap-5063	50	10	of	of	ADP
ap-5063	50	11	the	the	DET
ap-5063	50	12	vectors	vector	NOUN
ap-5063	50	13	of	of	ADP
ap-5063	50	14	a	a	DET
ap-5063	50	15	set	set	NOUN
ap-5063	50	16	of	of	ADP
ap-5063	50	17	simple	simple	ADJ
ap-5063	50	18	roots	root	NOUN
ap-5063	50	19	of	of	ADP
ap-5063	50	20	the	the	DET
ap-5063	50	21	root	root	NOUN
ap-5063	50	22	systems	system	NOUN
ap-5063	50	23	.	.	PUNCT
ap-5063	51	1	there	there	PRON
ap-5063	51	2	are	be	VERB
ap-5063	51	3	two	two	NUM
ap-5063	51	4	kinds	kind	NOUN
ap-5063	51	5	of	of	ADP
ap-5063	51	6	root	root	NOUN
ap-5063	51	7	systems	system	NOUN
ap-5063	51	8	according	accord	VERB
ap-5063	51	9	to	to	ADP
ap-5063	51	10	the	the	DET
ap-5063	51	11	number	number	NOUN
ap-5063	51	12	of	of	ADP
ap-5063	51	13	roots	root	NOUN
ap-5063	51	14	with	with	ADP
ap-5063	51	15	different	different	ADJ
ap-5063	51	16	lengths	length	NOUN
ap-5063	51	17	:	:	PUNCT
ap-5063	51	18	systems	system	NOUN
ap-5063	51	19	with	with	ADP
ap-5063	51	20	one	one	NUM
ap-5063	51	21	root	root	NOUN
ap-5063	51	22	length	length	NOUN
ap-5063	51	23	,	,	PUNCT
ap-5063	51	24	and	and	CCONJ
ap-5063	51	25	systems	system	NOUN
ap-5063	51	26	with	with	ADP
ap-5063	51	27	two	two	NUM
ap-5063	51	28	root	root	NOUN
ap-5063	51	29	lengths	length	NOUN
ap-5063	51	30	.	.	PUNCT
ap-5063	52	1	a	a	DET
ap-5063	52	2	reflection	reflection	NOUN
ap-5063	52	3	r	r	NOUN
ap-5063	52	4	in	in	ADP
ap-5063	52	5	a	a	DET
ap-5063	52	6	hyperplane	hyperplane	NOUN
ap-5063	52	7	orthogonal	orthogonal	NOUN
ap-5063	52	8	to	to	ADP
ap-5063	52	9	the	the	DET
ap-5063	52	10	long	long	ADJ
ap-5063	52	11	/	/	SYM
ap-5063	52	12	short	short	ADJ
ap-5063	52	13	root	root	NOUN
ap-5063	52	14	and	and	CCONJ
ap-5063	52	15	passing	pass	VERB
ap-5063	52	16	through	through	ADP
ap-5063	52	17	the	the	DET
ap-5063	52	18	origin	origin	NOUN
ap-5063	52	19	of	of	ADP
ap-5063	52	20	rn	rn	PROPN
ap-5063	52	21	be	be	AUX
ap-5063	52	22	denoted	denote	VERB
ap-5063	52	23	by	by	ADP
ap-5063	52	24	rl	rl	NOUN
ap-5063	52	25	/	/	SYM
ap-5063	52	26	rs	rs	NOUN
ap-5063	52	27	respectively	respectively	ADV
ap-5063	52	28	.	.	PUNCT
ap-5063	53	1	working	work	VERB
ap-5063	53	2	with	with	ADP
ap-5063	53	3	finite	finite	ADJ
ap-5063	53	4	reflection	reflection	NOUN
ap-5063	53	5	groups	group	NOUN
ap-5063	53	6	,	,	PUNCT
ap-5063	53	7	it	it	PRON
ap-5063	53	8	is	be	AUX
ap-5063	53	9	convenient	convenient	ADJ
ap-5063	53	10	to	to	PART
ap-5063	53	11	use	use	VERB
ap-5063	53	12	four	four	NUM
ap-5063	53	13	bases	basis	NOUN
ap-5063	53	14	in	in	ADP
ap-5063	53	15	rn	rn	PROPN
ap-5063	53	16	,	,	PUNCT
ap-5063	53	17	namely	namely	ADV
ap-5063	53	18	natural	natural	ADJ
ap-5063	53	19	e-	e-	PROPN
ap-5063	53	20	,	,	PUNCT
ap-5063	53	21	the	the	DET
ap-5063	53	22	simple	simple	ADJ
ap-5063	53	23	root	root	NOUN
ap-5063	53	24	α-	α-	X
ap-5063	53	25	,	,	PUNCT
ap-5063	53	26	co	co	ADJ
ap-5063	53	27	-	-	NOUN
ap-5063	53	28	root	root	NOUN
ap-5063	53	29	α̌and	α̌and	NUM
ap-5063	53	30	weight	weight	NOUN
ap-5063	53	31	ω	ω	NOUN
ap-5063	53	32	-	-	PUNCT
ap-5063	53	33	bases	basis	NOUN
ap-5063	53	34	[	[	X
ap-5063	53	35	2	2	NUM
ap-5063	53	36	,	,	PUNCT
ap-5063	53	37	7	7	NUM
ap-5063	53	38	,	,	PUNCT
ap-5063	53	39	10	10	NUM
ap-5063	53	40	]	]	PUNCT
ap-5063	53	41	.	.	PUNCT
ap-5063	54	1	the	the	DET
ap-5063	54	2	co	co	NOUN
ap-5063	54	3	-	-	NOUN
ap-5063	54	4	root	root	ADJ
ap-5063	54	5	basis	basis	NOUN
ap-5063	54	6	α̌	α̌	PUNCT
ap-5063	54	7	is	be	AUX
ap-5063	54	8	defined	define	VERB
ap-5063	54	9	by	by	ADP
ap-5063	54	10	the	the	DET
ap-5063	54	11	formula	formula	NOUN
ap-5063	55	1	α̌i	α̌i	ADJ
ap-5063	55	2	=	=	SYM
ap-5063	55	3	2αi	2αi	ADJ
ap-5063	55	4	〈	〈	PROPN
ap-5063	55	5	αi|αi	αi|αi	PROPN
ap-5063	55	6	〉	〉	NOUN
ap-5063	55	7	.	.	PUNCT
ap-5063	56	1	the	the	DET
ap-5063	56	2	ω	ω	NOUN
ap-5063	56	3	-	-	PUNCT
ap-5063	56	4	basis	basis	NOUN
ap-5063	56	5	is	be	AUX
ap-5063	56	6	dual	dual	ADJ
ap-5063	56	7	to	to	ADP
ap-5063	56	8	simple	simple	ADJ
ap-5063	56	9	root	root	NOUN
ap-5063	56	10	basis	basis	NOUN
ap-5063	56	11	.	.	PUNCT
ap-5063	57	1	the	the	DET
ap-5063	57	2	relationship	relationship	NOUN
ap-5063	57	3	between	between	ADP
ap-5063	57	4	considered	consider	VERB
ap-5063	57	5	bases	basis	NOUN
ap-5063	57	6	is	be	AUX
ap-5063	57	7	standard	standard	ADJ
ap-5063	57	8	for	for	ADP
ap-5063	57	9	group	group	NOUN
ap-5063	57	10	theory	theory	NOUN
ap-5063	57	11	and	and	CCONJ
ap-5063	57	12	is	be	AUX
ap-5063	57	13	expressed	express	VERB
ap-5063	57	14	by	by	ADP
ap-5063	57	15	〈	〈	PROPN
ap-5063	57	16	α̌i|ωj	α̌i|ωj	PROPN
ap-5063	57	17	〉	〉	NOUN
ap-5063	57	18	=	=	SYM
ap-5063	57	19	δij	δij	NOUN
ap-5063	57	20	.	.	PUNCT
ap-5063	58	1	there	there	PRON
ap-5063	58	2	are	be	VERB
ap-5063	58	3	two	two	NUM
ap-5063	58	4	types	type	NOUN
ap-5063	58	5	of	of	ADP
ap-5063	58	6	fundamental	fundamental	ADJ
ap-5063	58	7	region	region	NOUN
ap-5063	58	8	either	either	CCONJ
ap-5063	58	9	simplex	simplex	NOUN
ap-5063	58	10	for	for	ADP
ap-5063	58	11	simple	simple	ADJ
ap-5063	58	12	lie	lie	NOUN
ap-5063	58	13	group	group	NOUN
ap-5063	58	14	g	g	NOUN
ap-5063	58	15	or	or	CCONJ
ap-5063	58	16	prism	prism	NOUN
ap-5063	58	17	for	for	ADP
ap-5063	58	18	semisimple	semisimple	NOUN
ap-5063	58	19	one	one	NUM
ap-5063	58	20	.	.	PUNCT
ap-5063	59	1	the	the	DET
ap-5063	59	2	simplex	simplex	NOUN
ap-5063	59	3	with	with	ADP
ap-5063	59	4	n+	n+	ADP
ap-5063	59	5	1	1	NUM
ap-5063	59	6	vertices	vertex	NOUN
ap-5063	59	7	has	have	VERB
ap-5063	59	8	the	the	DET
ap-5063	59	9	following	follow	VERB
ap-5063	59	10	coordinates	coordinate	NOUN
ap-5063	59	11	f	f	PROPN
ap-5063	59	12	=	=	PRON
ap-5063	59	13	{	{	PUNCT
ap-5063	59	14	0	0	NUM
ap-5063	59	15	,	,	PUNCT
ap-5063	59	16	ω1	ω1	PROPN
ap-5063	59	17	q1	q1	PROPN
ap-5063	59	18	,	,	PUNCT
ap-5063	59	19	.	.	PUNCT
ap-5063	59	20	.	.	PUNCT
ap-5063	60	1	.	.	PUNCT
ap-5063	61	1	,	,	PUNCT
ap-5063	62	1	ωn	ωn	PRON
ap-5063	62	2	qn	qn	PROPN
ap-5063	62	3	}	}	PUNCT
ap-5063	62	4	,	,	PUNCT
ap-5063	62	5	where	where	SCONJ
ap-5063	62	6	qi	qi	PROPN
ap-5063	62	7	,	,	PUNCT
ap-5063	62	8	i	i	NOUN
ap-5063	62	9	=	=	NOUN
ap-5063	62	10	1	1	NUM
ap-5063	62	11	,	,	PUNCT
ap-5063	62	12	.	.	PUNCT
ap-5063	62	13	.	.	PUNCT
ap-5063	62	14	.	.	PUNCT
ap-5063	62	15	,	,	PUNCT
ap-5063	62	16	n	n	CCONJ
ap-5063	62	17	,	,	PUNCT
ap-5063	62	18	called	call	VERB
ap-5063	62	19	co	co	NOUN
ap-5063	62	20	-	-	NOUN
ap-5063	62	21	marks	mark	NOUN
ap-5063	62	22	,	,	PUNCT
ap-5063	62	23	can	can	AUX
ap-5063	62	24	be	be	AUX
ap-5063	62	25	found	find	VERB
ap-5063	62	26	in	in	ADP
ap-5063	62	27	[	[	X
ap-5063	62	28	6	6	NUM
ap-5063	62	29	,	,	PUNCT
ap-5063	62	30	10	10	NUM
ap-5063	62	31	]	]	PUNCT
ap-5063	62	32	for	for	ADP
ap-5063	62	33	any	any	DET
ap-5063	62	34	simple	simple	ADJ
ap-5063	62	35	lie	lie	NOUN
ap-5063	62	36	group	group	NOUN
ap-5063	62	37	g	g	PROPN
ap-5063	62	38	of	of	ADP
ap-5063	62	39	any	any	DET
ap-5063	62	40	rank	rank	NOUN
ap-5063	62	41	and	and	CCONJ
ap-5063	62	42	any	any	DET
ap-5063	62	43	dimension	dimension	NOUN
ap-5063	62	44	.	.	PUNCT
ap-5063	63	1	the	the	DET
ap-5063	63	2	fundamental	fundamental	ADJ
ap-5063	63	3	region	region	NOUN
ap-5063	63	4	for	for	ADP
ap-5063	63	5	prisms	prism	NOUN
ap-5063	63	6	can	can	AUX
ap-5063	63	7	be	be	AUX
ap-5063	63	8	given	give	VERB
ap-5063	63	9	in	in	ADP
ap-5063	63	10	the	the	DET
ap-5063	63	11	following	follow	VERB
ap-5063	63	12	sense	sense	NOUN
ap-5063	63	13	.	.	PUNCT
ap-5063	64	1	let	let	VERB
ap-5063	64	2	g	g	PROPN
ap-5063	64	3	=	=	VERB
ap-5063	64	4	g1	g1	PROPN
ap-5063	64	5	×	×	PROPN
ap-5063	64	6	g2	g2	PROPN
ap-5063	64	7	,	,	PUNCT
ap-5063	64	8	where	where	SCONJ
ap-5063	64	9	g1	g1	PROPN
ap-5063	64	10	,	,	PUNCT
ap-5063	64	11	g2	g2	PROPN
ap-5063	64	12	are	be	AUX
ap-5063	64	13	finite	finite	ADJ
ap-5063	64	14	reflection	reflection	NOUN
ap-5063	64	15	groups	group	NOUN
ap-5063	64	16	.	.	PUNCT
ap-5063	65	1	let	let	VERB
ap-5063	65	2	ω1	ω1	PROPN
ap-5063	65	3	,	,	PUNCT
ap-5063	65	4	.	.	PUNCT
ap-5063	65	5	.	.	PUNCT
ap-5063	66	1	.	.	PUNCT
ap-5063	67	1	,	,	PUNCT
ap-5063	67	2	ωk	ωk	ADP
ap-5063	67	3	be	be	AUX
ap-5063	67	4	a	a	DET
ap-5063	67	5	set	set	NOUN
ap-5063	67	6	of	of	ADP
ap-5063	67	7	generating	generate	VERB
ap-5063	67	8	elements	element	NOUN
ap-5063	67	9	of	of	ADP
ap-5063	67	10	g1	g1	NOUN
ap-5063	67	11	and	and	CCONJ
ap-5063	67	12	ωk+1	ωk+1	VERB
ap-5063	67	13	,	,	PUNCT
ap-5063	67	14	.	.	PUNCT
ap-5063	67	15	.	.	PUNCT
ap-5063	68	1	.	.	PUNCT
ap-5063	69	1	,	,	PUNCT
ap-5063	69	2	ωn	ωn	PROPN
ap-5063	69	3	of	of	ADP
ap-5063	69	4	g2	g2	PROPN
ap-5063	69	5	.	.	PUNCT
ap-5063	70	1	then	then	ADV
ap-5063	70	2	the	the	DET
ap-5063	70	3	prism	prism	NOUN
ap-5063	70	4	can	can	AUX
ap-5063	70	5	be	be	AUX
ap-5063	70	6	written	write	VERB
ap-5063	70	7	as	as	SCONJ
ap-5063	70	8	follows	follow	VERB
ap-5063	70	9	f	f	PROPN
ap-5063	70	10	=	=	PUNCT
ap-5063	70	11	{	{	PUNCT
ap-5063	70	12	0	0	NUM
ap-5063	70	13	,	,	PUNCT
ap-5063	70	14	ωi	ωi	X
ap-5063	70	15	qi	qi	NOUN
ap-5063	70	16	,	,	PUNCT
ap-5063	70	17	ωj	ωj	ADP
ap-5063	70	18	qj	qj	PROPN
ap-5063	70	19	,	,	PUNCT
ap-5063	70	20	ωi	ωi	X
ap-5063	70	21	qi	qi	PROPN
ap-5063	70	22	+	+	CCONJ
ap-5063	70	23	ωj	ωj	ADP
ap-5063	70	24	qj	qj	PROPN
ap-5063	70	25	}	}	PUNCT
ap-5063	70	26	,	,	PUNCT
ap-5063	70	27	where	where	SCONJ
ap-5063	70	28	i	i	PRON
ap-5063	70	29	=	=	NOUN
ap-5063	70	30	1	1	NUM
ap-5063	70	31	,	,	PUNCT
ap-5063	70	32	.	.	PUNCT
ap-5063	70	33	.	.	PUNCT
ap-5063	70	34	.	.	PUNCT
ap-5063	71	1	,	,	PUNCT
ap-5063	71	2	k	k	PROPN
ap-5063	71	3	and	and	CCONJ
ap-5063	71	4	j	j	PROPN
ap-5063	71	5	=	=	SYM
ap-5063	71	6	k	k	PROPN
ap-5063	72	1	+	+	PROPN
ap-5063	72	2	1	1	NUM
ap-5063	72	3	,	,	PUNCT
ap-5063	72	4	.	.	PUNCT
ap-5063	72	5	.	.	PUNCT
ap-5063	73	1	.	.	PUNCT
ap-5063	74	1	,	,	PUNCT
ap-5063	74	2	n	n	PROPN
ap-5063	74	3	and	and	CCONJ
ap-5063	74	4	qi	qi	PROPN
ap-5063	74	5	,	,	PUNCT
ap-5063	74	6	qj	qj	PROPN
ap-5063	74	7	are	be	AUX
ap-5063	74	8	co	co	NOUN
ap-5063	74	9	-	-	NOUN
ap-5063	74	10	marks	mark	NOUN
ap-5063	74	11	[	[	X
ap-5063	74	12	6	6	NUM
ap-5063	74	13	,	,	PUNCT
ap-5063	74	14	10	10	NUM
ap-5063	74	15	]	]	PUNCT
ap-5063	74	16	.	.	PUNCT
ap-5063	75	1	let	let	VERB
ap-5063	75	2	∂fi	∂fi	PROPN
ap-5063	75	3	be	be	AUX
ap-5063	75	4	contained	contain	VERB
ap-5063	75	5	in	in	ADP
ap-5063	75	6	the	the	DET
ap-5063	75	7	hyperplane	hyperplane	NOUN
ap-5063	75	8	generated	generate	VERB
ap-5063	75	9	by	by	ADP
ap-5063	75	10	a	a	DET
ap-5063	75	11	set	set	NOUN
ap-5063	75	12	of	of	ADP
ap-5063	75	13	orthogonal	orthogonal	ADJ
ap-5063	75	14	reflections	reflection	NOUN
ap-5063	75	15	r0	r0	NOUN
ap-5063	75	16	,	,	PUNCT
ap-5063	75	17	r1	r1	NOUN
ap-5063	75	18	,	,	PUNCT
ap-5063	75	19	.	.	PUNCT
ap-5063	75	20	.	.	PUNCT
ap-5063	76	1	.	.	PUNCT
ap-5063	77	1	,	,	PUNCT
ap-5063	77	2	ri−1	ri−1	PROPN
ap-5063	77	3	,	,	PUNCT
ap-5063	77	4	ri+1	ri+1	PROPN
ap-5063	77	5	,	,	PUNCT
ap-5063	77	6	.	.	PUNCT
ap-5063	77	7	.	.	PUNCT
ap-5063	78	1	.	.	PUNCT
ap-5063	79	1	,	,	PUNCT
ap-5063	79	2	rn	rn	PROPN
ap-5063	79	3	,	,	PUNCT
ap-5063	79	4	i	i	PRON
ap-5063	79	5	=	=	PUNCT
ap-5063	79	6	{	{	PUNCT
ap-5063	79	7	0	0	NUM
ap-5063	79	8	,	,	PUNCT
ap-5063	79	9	.	.	PUNCT
ap-5063	79	10	.	.	PUNCT
ap-5063	79	11	.	.	PUNCT
ap-5063	79	12	,	,	PUNCT
ap-5063	79	13	n	n	CCONJ
ap-5063	79	14	}	}	PUNCT
ap-5063	79	15	,	,	PUNCT
ap-5063	79	16	where	where	SCONJ
ap-5063	79	17	r0	r0	NOUN
ap-5063	79	18	is	be	AUX
ap-5063	79	19	an	an	DET
ap-5063	79	20	affine	affine	ADJ
ap-5063	79	21	reflection	reflection	NOUN
ap-5063	79	22	(	(	PUNCT
ap-5063	79	23	it	it	PRON
ap-5063	79	24	corresponds	correspond	VERB
ap-5063	79	25	to	to	ADP
ap-5063	79	26	long	long	ADJ
ap-5063	79	27	reflection	reflection	NOUN
ap-5063	79	28	)	)	PUNCT
ap-5063	79	29	.	.	PUNCT
ap-5063	80	1	if	if	SCONJ
ap-5063	80	2	ri	ri	PROPN
ap-5063	80	3	corresponds	correspond	VERB
ap-5063	80	4	to	to	ADP
ap-5063	80	5	the	the	DET
ap-5063	80	6	reflection	reflection	NOUN
ap-5063	80	7	orthogonal	orthogonal	NOUN
ap-5063	80	8	to	to	ADP
ap-5063	80	9	the	the	DET
ap-5063	80	10	short	short	ADJ
ap-5063	80	11	/	/	SYM
ap-5063	80	12	long	long	ADJ
ap-5063	80	13	root	root	NOUN
ap-5063	80	14	then	then	ADV
ap-5063	80	15	we	we	PRON
ap-5063	80	16	denote	denote	VERB
ap-5063	80	17	a	a	DET
ap-5063	80	18	part	part	NOUN
ap-5063	80	19	of	of	ADP
ap-5063	80	20	the	the	DET
ap-5063	80	21	boundary	boundary	NOUN
ap-5063	80	22	by	by	ADP
ap-5063	80	23	∂fs	∂fs	PROPN
ap-5063	80	24	or	or	CCONJ
ap-5063	80	25	∂fl	∂fl	PROPN
ap-5063	80	26	respectively	respectively	ADV
ap-5063	80	27	.	.	PUNCT
ap-5063	81	1	in	in	ADP
ap-5063	81	2	other	other	ADJ
ap-5063	81	3	words	word	NOUN
ap-5063	81	4	we	we	PRON
ap-5063	81	5	can	can	AUX
ap-5063	81	6	say	say	VERB
ap-5063	81	7	that	that	SCONJ
ap-5063	81	8	the	the	DET
ap-5063	81	9	boundary	boundary	ADJ
ap-5063	81	10	∂f	∂f	PROPN
ap-5063	81	11	of	of	ADP
ap-5063	81	12	the	the	DET
ap-5063	81	13	fundamental	fundamental	ADJ
ap-5063	81	14	region	region	NOUN
ap-5063	81	15	f	f	PROPN
ap-5063	81	16	will	will	AUX
ap-5063	81	17	be	be	AUX
ap-5063	81	18	denoted	denote	VERB
ap-5063	81	19	by	by	ADP
ap-5063	81	20	∂fl/∂fs	∂fl/∂fs	PROPN
ap-5063	81	21	if	if	SCONJ
ap-5063	81	22	its	its	PRON
ap-5063	81	23	normal	normal	ADJ
ap-5063	81	24	vector	vector	NOUN
ap-5063	81	25	is	be	AUX
ap-5063	81	26	perpendicular	perpendicular	ADJ
ap-5063	81	27	to	to	ADP
ap-5063	81	28	the	the	DET
ap-5063	81	29	long	long	ADJ
ap-5063	81	30	/	/	SYM
ap-5063	81	31	short	short	ADJ
ap-5063	81	32	root	root	NOUN
ap-5063	81	33	α	α	NOUN
ap-5063	81	34	respectively	respectively	ADV
ap-5063	81	35	.	.	PUNCT
ap-5063	82	1	4	4	X
ap-5063	82	2	.	.	NOUN
ap-5063	82	3	special	special	ADJ
ap-5063	82	4	functions	function	NOUN
ap-5063	82	5	as	as	ADP
ap-5063	82	6	a	a	DET
ap-5063	82	7	solution	solution	NOUN
ap-5063	82	8	of	of	ADP
ap-5063	82	9	helmholtz	helmholtz	NOUN
ap-5063	82	10	equation	equation	NOUN
ap-5063	82	11	there	there	PRON
ap-5063	82	12	are	be	VERB
ap-5063	82	13	four	four	NUM
ap-5063	82	14	kinds	kind	NOUN
ap-5063	82	15	of	of	ADP
ap-5063	82	16	special	special	ADJ
ap-5063	82	17	functions	function	NOUN
ap-5063	82	18	of	of	ADP
ap-5063	82	19	interest	interest	NOUN
ap-5063	82	20	to	to	ADP
ap-5063	82	21	us	we	PRON
ap-5063	82	22	whose	whose	DET
ap-5063	82	23	orthogonality	orthogonality	NOUN
ap-5063	82	24	on	on	ADP
ap-5063	82	25	lattice	lattice	PROPN
ap-5063	82	26	fragment	fragment	NOUN
ap-5063	82	27	f	f	PROPN
ap-5063	82	28	is	be	AUX
ap-5063	82	29	known	know	VERB
ap-5063	82	30	for	for	ADP
ap-5063	82	31	any	any	DET
ap-5063	82	32	simple	simple	ADJ
ap-5063	82	33	lie	lie	NOUN
ap-5063	82	34	group	group	NOUN
ap-5063	83	1	[	[	X
ap-5063	83	2	5	5	NUM
ap-5063	83	3	,	,	PUNCT
ap-5063	83	4	6	6	NUM
ap-5063	83	5	,	,	PUNCT
ap-5063	83	6	10	10	NUM
ap-5063	83	7	,	,	PUNCT
ap-5063	83	8	16	16	NUM
ap-5063	83	9	,	,	PUNCT
ap-5063	83	10	17	17	NUM
ap-5063	83	11	,	,	PUNCT
ap-5063	83	12	19	19	NUM
ap-5063	83	13	,	,	PUNCT
ap-5063	83	14	20	20	NUM
ap-5063	83	15	,	,	PUNCT
ap-5063	83	16	23	23	NUM
ap-5063	83	17	,	,	PUNCT
ap-5063	83	18	and	and	CCONJ
ap-5063	83	19	references	reference	NOUN
ap-5063	83	20	therein	therein	ADV
ap-5063	83	21	]	]	PUNCT
ap-5063	83	22	.	.	PUNCT
ap-5063	84	1	the	the	DET
ap-5063	84	2	general	general	ADJ
ap-5063	84	3	formula	formula	NOUN
ap-5063	84	4	for	for	ADP
ap-5063	84	5	special	special	ADJ
ap-5063	84	6	functions	function	NOUN
ap-5063	84	7	(	(	PUNCT
ap-5063	84	8	called	call	VERB
ap-5063	84	9	orbit	orbit	NOUN
ap-5063	84	10	functions	function	NOUN
ap-5063	84	11	)	)	PUNCT
ap-5063	85	1	[	[	X
ap-5063	85	2	10	10	NUM
ap-5063	85	3	,	,	PUNCT
ap-5063	85	4	11	11	NUM
ap-5063	85	5	]	]	PUNCT
ap-5063	85	6	corresponding	correspond	VERB
ap-5063	85	7	to	to	ADP
ap-5063	85	8	the	the	DET
ap-5063	85	9	finite	finite	PROPN
ap-5063	85	10	reflection	reflection	NOUN
ap-5063	85	11	group	group	PROPN
ap-5063	85	12	g	g	PROPN
ap-5063	85	13	is	be	AUX
ap-5063	85	14	given	give	VERB
ap-5063	85	15	by	by	ADP
ap-5063	85	16	∑	∑	ADV
ap-5063	85	17	w∈g	w∈g	NOUN
ap-5063	85	18	σ(w)e2πi〈wλ|x	σ(w)e2πi〈wλ|x	PROPN
ap-5063	85	19	〉	〉	PROPN
ap-5063	85	20	,	,	PUNCT
ap-5063	85	21	λ	λ	PROPN
ap-5063	85	22	∈	∈	PROPN
ap-5063	85	23	p+	p+	NOUN
ap-5063	85	24	,	,	PUNCT
ap-5063	85	25	x	x	SYM
ap-5063	85	26	∈	∈	PROPN
ap-5063	85	27	f	f	X
ap-5063	85	28	(	(	PUNCT
ap-5063	85	29	4	4	NUM
ap-5063	85	30	)	)	PUNCT
ap-5063	85	31	where	where	SCONJ
ap-5063	85	32	the	the	DET
ap-5063	85	33	summation	summation	NOUN
ap-5063	85	34	extends	extend	VERB
ap-5063	85	35	over	over	ADP
ap-5063	85	36	the	the	DET
ap-5063	85	37	whole	whole	ADJ
ap-5063	85	38	group	group	NOUN
ap-5063	85	39	g	g	PROPN
ap-5063	85	40	,	,	PUNCT
ap-5063	85	41	p+	p+	NOUN
ap-5063	85	42	denotes	denote	NOUN
ap-5063	85	43	the	the	DET
ap-5063	85	44	set	set	NOUN
ap-5063	85	45	of	of	ADP
ap-5063	85	46	dominant	dominant	ADJ
ap-5063	85	47	weights	weight	NOUN
ap-5063	85	48	[	[	X
ap-5063	85	49	10	10	NUM
ap-5063	85	50	]	]	PUNCT
ap-5063	85	51	and	and	CCONJ
ap-5063	85	52	σ(w	σ(w	NUM
ap-5063	85	53	)	)	PUNCT
ap-5063	86	1	=	=	PRON
ap-5063	86	2	±1	±1	VERB
ap-5063	86	3	depends	depend	VERB
ap-5063	86	4	on	on	ADP
ap-5063	86	5	the	the	DET
ap-5063	86	6	type	type	NOUN
ap-5063	86	7	of	of	ADP
ap-5063	86	8	the	the	DET
ap-5063	86	9	orbit	orbit	NOUN
ap-5063	86	10	function	function	NOUN
ap-5063	86	11	.	.	PUNCT
ap-5063	87	1	the	the	DET
ap-5063	87	2	homomorphism	homomorphism	PROPN
ap-5063	87	3	σ	σ	X
ap-5063	87	4	:	:	PUNCT
ap-5063	87	5	g	g	NOUN
ap-5063	87	6	→	→	PUNCT
ap-5063	87	7	{	{	PUNCT
ap-5063	87	8	±1	±1	NOUN
ap-5063	87	9	}	}	PUNCT
ap-5063	87	10	is	be	AUX
ap-5063	87	11	a	a	DET
ap-5063	87	12	product	product	NOUN
ap-5063	87	13	of	of	ADP
ap-5063	87	14	σ(rl	σ(rl	PROPN
ap-5063	87	15	)	)	PUNCT
ap-5063	87	16	,	,	PUNCT
ap-5063	87	17	σ(rs	σ(r	NOUN
ap-5063	87	18	)	)	PUNCT
ap-5063	87	19	∈	∈	PROPN
ap-5063	87	20	{	{	PUNCT
ap-5063	87	21	±1	±1	NOUN
ap-5063	87	22	}	}	PUNCT
ap-5063	87	23	.	.	PUNCT
ap-5063	88	1	there	there	PRON
ap-5063	88	2	are	be	VERB
ap-5063	88	3	four	four	NUM
ap-5063	88	4	types	type	NOUN
ap-5063	88	5	of	of	ADP
ap-5063	88	6	maps	map	NOUN
ap-5063	88	7	σ	σ	PROPN
ap-5063	89	1	[	[	X
ap-5063	89	2	16	16	NUM
ap-5063	89	3	,	,	PUNCT
ap-5063	89	4	17	17	NUM
ap-5063	89	5	]	]	PUNCT
ap-5063	89	6	:	:	PUNCT
ap-5063	89	7	σ(rl	σ(rl	NUM
ap-5063	89	8	)	)	PUNCT
ap-5063	89	9	=	=	SYM
ap-5063	89	10	σ(rs	σ(r	NOUN
ap-5063	89	11	)	)	PUNCT
ap-5063	89	12	=	=	SYM
ap-5063	90	1	1	1	NUM
ap-5063	90	2	=	=	NOUN
ap-5063	90	3	⇒	⇒	NOUN
ap-5063	90	4	c	c	NOUN
ap-5063	90	5	,	,	PUNCT
ap-5063	90	6	σ(rl	σ(rl	NUM
ap-5063	90	7	)	)	PUNCT
ap-5063	90	8	=	=	SYM
ap-5063	90	9	σ(rs	σ(r	NOUN
ap-5063	90	10	)	)	PUNCT
ap-5063	90	11	=	=	SYM
ap-5063	90	12	−1	−1	NOUN
ap-5063	90	13	=	=	VERB
ap-5063	90	14	⇒	⇒	NOUN
ap-5063	90	15	s	s	PART
ap-5063	90	16	,	,	PUNCT
ap-5063	90	17	σ(rl	σ(rl	NUM
ap-5063	90	18	)	)	PUNCT
ap-5063	90	19	=	=	SYM
ap-5063	90	20	−1	−1	NOUN
ap-5063	90	21	,	,	PUNCT
ap-5063	90	22	σ(rs	σ(r	NOUN
ap-5063	90	23	)	)	PUNCT
ap-5063	90	24	=	=	SYM
ap-5063	91	1	1	1	NUM
ap-5063	91	2	=	=	NOUN
ap-5063	91	3	⇒	⇒	NOUN
ap-5063	91	4	sl	sl	NUM
ap-5063	91	5	,	,	PUNCT
ap-5063	91	6	σ(rl	σ(rl	NUM
ap-5063	91	7	)	)	PUNCT
ap-5063	91	8	=	=	SYM
ap-5063	91	9	1	1	NUM
ap-5063	91	10	,	,	PUNCT
ap-5063	91	11	σ(rs	σ(r	NOUN
ap-5063	91	12	)	)	PUNCT
ap-5063	91	13	=	=	SYM
ap-5063	91	14	−1	−1	NOUN
ap-5063	91	15	=	=	VERB
ap-5063	91	16	⇒	⇒	X
ap-5063	91	17	ss	ss	NOUN
ap-5063	91	18	.	.	PUNCT
ap-5063	91	19	(	(	PUNCT
ap-5063	91	20	5	5	X
ap-5063	91	21	)	)	PUNCT
ap-5063	91	22	all	all	DET
ap-5063	91	23	four	four	NUM
ap-5063	91	24	families	family	NOUN
ap-5063	91	25	of	of	ADP
ap-5063	91	26	functions	function	NOUN
ap-5063	91	27	defined	define	VERB
ap-5063	91	28	above	above	ADV
ap-5063	91	29	are	be	AUX
ap-5063	91	30	formed	form	VERB
ap-5063	91	31	as	as	ADP
ap-5063	91	32	finite	finite	ADJ
ap-5063	91	33	sums	sum	NOUN
ap-5063	91	34	of	of	ADP
ap-5063	91	35	exponential	exponential	ADJ
ap-5063	91	36	terms	term	NOUN
ap-5063	91	37	.	.	PUNCT
ap-5063	92	1	the	the	DET
ap-5063	92	2	first	first	ADJ
ap-5063	92	3	two	two	NUM
ap-5063	92	4	families	family	NOUN
ap-5063	92	5	,	,	PUNCT
ap-5063	92	6	namely	namely	ADV
ap-5063	92	7	cand	cand	PROPN
ap-5063	92	8	s	s	NOUN
ap-5063	92	9	-	-	PUNCT
ap-5063	92	10	functions	function	NOUN
ap-5063	92	11	are	be	AUX
ap-5063	92	12	generalized	generalized	ADJ
ap-5063	92	13	cosine	cosine	NOUN
ap-5063	92	14	and	and	CCONJ
ap-5063	92	15	sine	sine	ADJ
ap-5063	92	16	functions	function	NOUN
ap-5063	92	17	.	.	PUNCT
ap-5063	93	1	they	they	PRON
ap-5063	93	2	are	be	AUX
ap-5063	93	3	symmetric	symmetric	ADJ
ap-5063	93	4	and	and	CCONJ
ap-5063	93	5	skew	skew	NOUN
ap-5063	93	6	-	-	PUNCT
ap-5063	93	7	symmetric	symmetric	ADJ
ap-5063	93	8	with	with	ADP
ap-5063	93	9	respect	respect	NOUN
ap-5063	93	10	to	to	ADP
ap-5063	93	11	the	the	DET
ap-5063	93	12	finite	finite	ADJ
ap-5063	93	13	reflection	reflection	NOUN
ap-5063	93	14	group	group	NOUN
ap-5063	93	15	[	[	X
ap-5063	93	16	6	6	NUM
ap-5063	93	17	,	,	PUNCT
ap-5063	93	18	10	10	NUM
ap-5063	93	19	,	,	PUNCT
ap-5063	93	20	16	16	NUM
ap-5063	93	21	,	,	PUNCT
ap-5063	93	22	19–21	19–21	NUM
ap-5063	93	23	,	,	PUNCT
ap-5063	93	24	23	23	NUM
ap-5063	93	25	]	]	PUNCT
ap-5063	93	26	.	.	PUNCT
ap-5063	94	1	the	the	DET
ap-5063	94	2	other	other	ADJ
ap-5063	94	3	two	two	NUM
ap-5063	94	4	,	,	PUNCT
ap-5063	94	5	ssand	ssand	NOUN
ap-5063	94	6	sl	sl	NOUN
ap-5063	94	7	-	-	PUNCT
ap-5063	94	8	functions	function	NOUN
ap-5063	94	9	[	[	X
ap-5063	94	10	11	11	NUM
ap-5063	94	11	,	,	PUNCT
ap-5063	94	12	12	12	NUM
ap-5063	94	13	,	,	PUNCT
ap-5063	94	14	16	16	NUM
ap-5063	94	15	,	,	PUNCT
ap-5063	94	16	17	17	NUM
ap-5063	94	17	,	,	PUNCT
ap-5063	94	18	23	23	NUM
ap-5063	94	19	]	]	PUNCT
ap-5063	94	20	have	have	VERB
ap-5063	94	21	analogous	analogous	ADJ
ap-5063	94	22	properties	property	NOUN
ap-5063	94	23	as	as	ADP
ap-5063	94	24	cand	cand	NOUN
ap-5063	94	25	s	s	PROPN
ap-5063	94	26	-	-	PUNCT
ap-5063	94	27	functions	function	NOUN
ap-5063	94	28	.	.	PUNCT
ap-5063	95	1	the	the	DET
ap-5063	95	2	main	main	ADJ
ap-5063	95	3	difference	difference	NOUN
ap-5063	95	4	between	between	ADP
ap-5063	95	5	them	they	PRON
ap-5063	95	6	is	be	AUX
ap-5063	95	7	their	their	PRON
ap-5063	95	8	behaviour	behaviour	NOUN
ap-5063	95	9	at	at	ADP
ap-5063	95	10	the	the	DET
ap-5063	95	11	boundary	boundary	NOUN
ap-5063	95	12	of	of	ADP
ap-5063	95	13	their	their	PRON
ap-5063	95	14	domain	domain	NOUN
ap-5063	95	15	of	of	ADP
ap-5063	95	16	orthogonality	orthogonality	NOUN
ap-5063	95	17	in	in	ADP
ap-5063	95	18	rn	rn	PROPN
ap-5063	95	19	.	.	PUNCT
ap-5063	96	1	every	every	DET
ap-5063	96	2	finite	finite	PROPN
ap-5063	96	3	group	group	NOUN
ap-5063	96	4	g	g	PROPN
ap-5063	96	5	generated	generate	VERB
ap-5063	96	6	by	by	ADP
ap-5063	96	7	reflections	reflection	NOUN
ap-5063	96	8	can	can	AUX
ap-5063	96	9	be	be	AUX
ap-5063	96	10	reduced	reduce	VERB
ap-5063	96	11	to	to	ADP
ap-5063	96	12	a	a	DET
ap-5063	96	13	subgroup	subgroup	NOUN
ap-5063	96	14	a1×	a1×	NOUN
ap-5063	96	15	·	·	PUNCT
ap-5063	96	16	·	·	PUNCT
ap-5063	96	17	·	·	PUNCT
ap-5063	96	18	×a1	×a1	ADP
ap-5063	96	19	using	use	VERB
ap-5063	96	20	a	a	DET
ap-5063	96	21	branching	branch	VERB
ap-5063	96	22	403	403	NUM
ap-5063	96	23	marzena	marzena	ADJ
ap-5063	96	24	szajewska	szajewska	NOUN
ap-5063	96	25	,	,	PUNCT
ap-5063	96	26	agnieszka	agnieszka	PROPN
ap-5063	96	27	tereszkiewicz	tereszkiewicz	PROPN
ap-5063	96	28	acta	acta	PROPN
ap-5063	96	29	polytechnica	polytechnica	PROPN
ap-5063	96	30	rule	rule	NOUN
ap-5063	96	31	method	method	NOUN
ap-5063	96	32	described	describe	VERB
ap-5063	96	33	in	in	ADP
ap-5063	96	34	[	[	X
ap-5063	96	35	13	13	NUM
ap-5063	96	36	,	,	PUNCT
ap-5063	96	37	14	14	NUM
ap-5063	96	38	,	,	PUNCT
ap-5063	96	39	19	19	NUM
ap-5063	96	40	,	,	PUNCT
ap-5063	96	41	22	22	NUM
ap-5063	96	42	,	,	PUNCT
ap-5063	96	43	24	24	NUM
ap-5063	96	44	,	,	PUNCT
ap-5063	96	45	28	28	NUM
ap-5063	96	46	]	]	PUNCT
ap-5063	96	47	.	.	PUNCT
ap-5063	97	1	this	this	DET
ap-5063	97	2	method	method	NOUN
ap-5063	97	3	allows	allow	VERB
ap-5063	97	4	us	we	PRON
ap-5063	97	5	to	to	PART
ap-5063	97	6	do	do	VERB
ap-5063	97	7	the	the	DET
ap-5063	97	8	separation	separation	NOUN
ap-5063	97	9	of	of	ADP
ap-5063	97	10	variables	variable	NOUN
ap-5063	97	11	for	for	ADP
ap-5063	97	12	special	special	ADJ
ap-5063	97	13	functions	function	NOUN
ap-5063	97	14	(	(	PUNCT
ap-5063	97	15	5	5	X
ap-5063	97	16	)	)	PUNCT
ap-5063	97	17	corresponding	correspond	VERB
ap-5063	97	18	to	to	ADP
ap-5063	97	19	group	group	NOUN
ap-5063	97	20	g.	g.	PROPN
ap-5063	97	21	as	as	ADP
ap-5063	97	22	a	a	DET
ap-5063	97	23	result	result	NOUN
ap-5063	97	24	,	,	PUNCT
ap-5063	97	25	we	we	PRON
ap-5063	97	26	have	have	VERB
ap-5063	97	27	all	all	DET
ap-5063	97	28	the	the	DET
ap-5063	97	29	functions	function	NOUN
ap-5063	97	30	written	write	VERB
ap-5063	97	31	as	as	ADP
ap-5063	97	32	a	a	DET
ap-5063	97	33	product	product	NOUN
ap-5063	97	34	of	of	ADP
ap-5063	97	35	sine	sine	NOUN
ap-5063	97	36	and	and	CCONJ
ap-5063	97	37	cosine	cosine	NOUN
ap-5063	97	38	functions	function	NOUN
ap-5063	97	39	.	.	PUNCT
ap-5063	98	1	remark	remark	PROPN
ap-5063	98	2	1	1	NUM
ap-5063	98	3	.	.	PUNCT
ap-5063	99	1	all	all	DET
ap-5063	99	2	four	four	NUM
ap-5063	99	3	families	family	NOUN
ap-5063	99	4	of	of	ADP
ap-5063	99	5	functions	function	NOUN
ap-5063	99	6	(	(	PUNCT
ap-5063	99	7	5	5	NUM
ap-5063	99	8	)	)	PUNCT
ap-5063	99	9	presented	present	VERB
ap-5063	99	10	above	above	ADV
ap-5063	99	11	are	be	AUX
ap-5063	99	12	solutions	solution	NOUN
ap-5063	99	13	of	of	ADP
ap-5063	99	14	the	the	DET
ap-5063	99	15	helmholtz	helmholtz	NOUN
ap-5063	99	16	equation	equation	NOUN
ap-5063	99	17	(	(	PUNCT
ap-5063	99	18	1	1	X
ap-5063	99	19	)	)	PUNCT
ap-5063	99	20	where	where	SCONJ
ap-5063	99	21	w2	w2	NOUN
ap-5063	99	22	=	=	PROPN
ap-5063	99	23	4π2〈λ|λ	4π2〈λ|λ	NUM
ap-5063	99	24	〉	〉	NOUN
ap-5063	99	25	with	with	ADP
ap-5063	99	26	one	one	NUM
ap-5063	99	27	of	of	ADP
ap-5063	99	28	the	the	DET
ap-5063	99	29	three	three	NUM
ap-5063	99	30	types	type	NOUN
ap-5063	99	31	of	of	ADP
ap-5063	99	32	boundary	boundary	ADJ
ap-5063	99	33	conditions	condition	NOUN
ap-5063	99	34	described	describe	VERB
ap-5063	99	35	in	in	ADP
ap-5063	99	36	§	§	PROPN
ap-5063	99	37	2	2	NUM
ap-5063	99	38	.	.	PUNCT
ap-5063	99	39	projection	projection	NOUN
ap-5063	99	40	matrix	matrix	NOUN
ap-5063	99	41	reduces	reduce	VERB
ap-5063	99	42	any	any	DET
ap-5063	99	43	n	n	ADV
ap-5063	99	44	-	-	PUNCT
ap-5063	99	45	dimensional	dimensional	ADJ
ap-5063	99	46	group	group	NOUN
ap-5063	99	47	g	g	NOUN
ap-5063	99	48	to	to	ADP
ap-5063	99	49	a	a	DET
ap-5063	99	50	subgroup	subgroup	NOUN
ap-5063	99	51	a1×	a1×	NOUN
ap-5063	99	52	.	.	PUNCT
ap-5063	99	53	.	.	PUNCT
ap-5063	100	1	.×a1	.×a1	PUNCT
ap-5063	101	1	[	[	X
ap-5063	101	2	13	13	NUM
ap-5063	101	3	,	,	PUNCT
ap-5063	101	4	19	19	NUM
ap-5063	101	5	]	]	PUNCT
ap-5063	101	6	.	.	PUNCT
ap-5063	102	1	the	the	DET
ap-5063	102	2	branching	branch	VERB
ap-5063	102	3	rule	rule	NOUN
ap-5063	102	4	allows	allow	VERB
ap-5063	102	5	one	one	PRON
ap-5063	102	6	to	to	PART
ap-5063	102	7	divide	divide	VERB
ap-5063	102	8	any	any	DET
ap-5063	102	9	orbit	orbit	NOUN
ap-5063	102	10	of	of	ADP
ap-5063	102	11	group	group	NOUN
ap-5063	102	12	g	g	PROPN
ap-5063	102	13	into	into	ADP
ap-5063	102	14	a	a	DET
ap-5063	102	15	union	union	NOUN
ap-5063	102	16	of	of	ADP
ap-5063	102	17	orbits	orbit	NOUN
ap-5063	102	18	of	of	ADP
ap-5063	102	19	group	group	NOUN
ap-5063	102	20	a1	a1	PROPN
ap-5063	102	21	.	.	PUNCT
ap-5063	103	1	as	as	ADP
ap-5063	103	2	an	an	DET
ap-5063	103	3	example	example	NOUN
ap-5063	103	4	see	see	VERB
ap-5063	103	5	3d	3d	NUM
ap-5063	103	6	cases	case	NOUN
ap-5063	103	7	described	describe	VERB
ap-5063	103	8	in	in	ADP
ap-5063	103	9	§	§	PROPN
ap-5063	103	10	5	5	NUM
ap-5063	103	11	.	.	PUNCT
ap-5063	103	12	remark	remark	NOUN
ap-5063	103	13	2	2	NUM
ap-5063	103	14	.	.	PUNCT
ap-5063	104	1	the	the	DET
ap-5063	104	2	union	union	NOUN
ap-5063	104	3	of	of	ADP
ap-5063	104	4	orbits	orbit	NOUN
ap-5063	104	5	which	which	PRON
ap-5063	104	6	we	we	PRON
ap-5063	104	7	get	get	VERB
ap-5063	104	8	after	after	ADP
ap-5063	104	9	reduction	reduction	NOUN
ap-5063	104	10	determine	determine	VERB
ap-5063	104	11	our	our	PRON
ap-5063	104	12	choice	choice	NOUN
ap-5063	104	13	of	of	ADP
ap-5063	104	14	separating	separate	VERB
ap-5063	104	15	constants	constant	NOUN
ap-5063	104	16	used	use	VERB
ap-5063	104	17	in	in	ADP
ap-5063	104	18	solution	solution	NOUN
ap-5063	104	19	of	of	ADP
ap-5063	104	20	helmholtz	helmholtz	NOUN
ap-5063	104	21	equation	equation	NOUN
ap-5063	104	22	(	(	PUNCT
ap-5063	104	23	1	1	NUM
ap-5063	104	24	)	)	PUNCT
ap-5063	104	25	.	.	PUNCT
ap-5063	105	1	the	the	DET
ap-5063	105	2	behaviour	behaviour	NOUN
ap-5063	105	3	of	of	ADP
ap-5063	105	4	the	the	DET
ap-5063	105	5	functions	function	NOUN
ap-5063	105	6	c	c	X
ap-5063	105	7	,	,	PUNCT
ap-5063	105	8	s	s	X
ap-5063	105	9	,	,	PUNCT
ap-5063	105	10	ss	ss	NOUN
ap-5063	105	11	and	and	CCONJ
ap-5063	105	12	sl	sl	VERB
ap-5063	105	13	on	on	ADP
ap-5063	105	14	the	the	DET
ap-5063	105	15	boundary	boundary	ADJ
ap-5063	105	16	∂f	∂f	PROPN
ap-5063	105	17	can	can	AUX
ap-5063	105	18	be	be	AUX
ap-5063	105	19	summarize	summarize	VERB
ap-5063	105	20	in	in	ADP
ap-5063	105	21	the	the	DET
ap-5063	105	22	tab	tab	NOUN
ap-5063	105	23	.	.	PUNCT
ap-5063	106	1	1	1	NUM
ap-5063	106	2	.	.	X
ap-5063	107	1	d	d	NOUN
ap-5063	107	2	n	n	PRON
ap-5063	107	3	∂fs	∂fs	PROPN
ap-5063	107	4	∂fl	∂fl	PROPN
ap-5063	107	5	∂fs	∂fs	PROPN
ap-5063	107	6	∂fl	∂fl	PROPN
ap-5063	107	7	cλ(x	cλ(x	PROPN
ap-5063	107	8	)	)	PUNCT
ap-5063	107	9	∗	∗	NOUN
ap-5063	107	10	∗	∗	X
ap-5063	107	11	0	0	NUM
ap-5063	107	12	0	0	NUM
ap-5063	107	13	sλ(x	sλ(x	PROPN
ap-5063	107	14	)	)	PUNCT
ap-5063	107	15	0	0	NUM
ap-5063	107	16	0	0	NUM
ap-5063	107	17	∗	∗	NOUN
ap-5063	107	18	∗	∗	X
ap-5063	107	19	ssλ(x	ssλ(x	PROPN
ap-5063	107	20	)	)	PUNCT
ap-5063	107	21	0	0	NUM
ap-5063	108	1	∗	∗	NOUN
ap-5063	108	2	∗	∗	NOUN
ap-5063	108	3	0	0	PUNCT
ap-5063	109	1	slλ(x	slλ(x	NOUN
ap-5063	109	2	)	)	PUNCT
ap-5063	109	3	∗	∗	NOUN
ap-5063	109	4	0	0	NUM
ap-5063	109	5	0	0	NUM
ap-5063	109	6	∗	∗	NOUN
ap-5063	109	7	table	table	NOUN
ap-5063	109	8	1	1	NUM
ap-5063	109	9	.	.	PUNCT
ap-5063	110	1	behaviour	behaviour	NOUN
ap-5063	110	2	of	of	ADP
ap-5063	110	3	the	the	DET
ap-5063	110	4	functions	function	NOUN
ap-5063	110	5	c	c	X
ap-5063	110	6	,	,	PUNCT
ap-5063	110	7	s	s	X
ap-5063	110	8	,	,	PUNCT
ap-5063	110	9	ss	ss	NOUN
ap-5063	110	10	and	and	CCONJ
ap-5063	110	11	sl	sl	VERB
ap-5063	110	12	on	on	ADP
ap-5063	110	13	the	the	DET
ap-5063	110	14	boundary	boundary	ADJ
ap-5063	110	15	∂f	∂f	PROPN
ap-5063	110	16	for	for	ADP
ap-5063	110	17	any	any	DET
ap-5063	110	18	finite	finite	ADJ
ap-5063	110	19	refleciton	refleciton	PROPN
ap-5063	110	20	group	group	PROPN
ap-5063	110	21	g	g	PROPN
ap-5063	110	22	where	where	SCONJ
ap-5063	110	23	∗	∗	NOUN
ap-5063	110	24	denotes	denote	VERB
ap-5063	110	25	any	any	DET
ap-5063	110	26	function	function	NOUN
ap-5063	110	27	non	non	ADJ
ap-5063	110	28	-	-	ADJ
ap-5063	110	29	equivalent	equivalent	ADJ
ap-5063	110	30	to	to	ADP
ap-5063	110	31	0	0	NUM
ap-5063	110	32	.	.	PUNCT
ap-5063	111	1	for	for	ADP
ap-5063	111	2	any	any	DET
ap-5063	111	3	group	group	NOUN
ap-5063	111	4	g	g	PROPN
ap-5063	111	5	considered	consider	VERB
ap-5063	111	6	in	in	ADP
ap-5063	111	7	the	the	DET
ap-5063	111	8	paper	paper	NOUN
ap-5063	111	9	cfunctions	cfunction	NOUN
ap-5063	111	10	fulfil	fulfil	VERB
ap-5063	111	11	the	the	DET
ap-5063	111	12	dirichlet	dirichlet	PROPN
ap-5063	111	13	condition	condition	NOUN
ap-5063	111	14	with	with	ADP
ap-5063	111	15	value	value	NOUN
ap-5063	111	16	nonequivalent	nonequivalent	VERB
ap-5063	111	17	to	to	ADP
ap-5063	111	18	0	0	NUM
ap-5063	111	19	and	and	CCONJ
ap-5063	111	20	the	the	DET
ap-5063	111	21	neumann	neumann	PROPN
ap-5063	111	22	condition	condition	NOUN
ap-5063	111	23	with	with	ADP
ap-5063	111	24	0	0	NUM
ap-5063	111	25	value	value	NOUN
ap-5063	111	26	on	on	ADP
ap-5063	111	27	the	the	DET
ap-5063	111	28	whole	whole	ADJ
ap-5063	111	29	boundary	boundary	NOUN
ap-5063	111	30	.	.	PUNCT
ap-5063	112	1	the	the	DET
ap-5063	112	2	s	s	NOUN
ap-5063	112	3	-	-	PUNCT
ap-5063	112	4	functions	function	NOUN
ap-5063	112	5	behave	behave	VERB
ap-5063	112	6	inversely	inversely	ADV
ap-5063	112	7	.	.	PUNCT
ap-5063	113	1	the	the	DET
ap-5063	113	2	ss	ss	NOUN
ap-5063	113	3	-	-	PUNCT
ap-5063	113	4	functions	function	NOUN
ap-5063	113	5	fulfil	fulfil	VERB
ap-5063	113	6	the	the	DET
ap-5063	113	7	dirichlet	dirichlet	PROPN
ap-5063	113	8	condition	condition	NOUN
ap-5063	113	9	with	with	ADP
ap-5063	113	10	a	a	DET
ap-5063	113	11	value	value	NOUN
ap-5063	113	12	non	non	ADJ
ap-5063	113	13	-	-	ADJ
ap-5063	113	14	equivalent	equivalent	ADJ
ap-5063	113	15	to	to	ADP
ap-5063	113	16	0	0	NUM
ap-5063	113	17	on	on	ADP
ap-5063	113	18	the	the	DET
ap-5063	113	19	part	part	NOUN
ap-5063	113	20	of	of	ADP
ap-5063	113	21	boundary	boundary	NOUN
ap-5063	113	22	denoted	denote	VERB
ap-5063	113	23	by	by	ADP
ap-5063	113	24	∂fl	∂fl	PROPN
ap-5063	113	25	and	and	CCONJ
ap-5063	113	26	the	the	DET
ap-5063	113	27	neumann	neumann	PROPN
ap-5063	113	28	condition	condition	NOUN
ap-5063	113	29	with	with	ADP
ap-5063	113	30	a	a	DET
ap-5063	113	31	value	value	NOUN
ap-5063	113	32	non	non	ADJ
ap-5063	113	33	-	-	ADJ
ap-5063	113	34	equivalent	equivalent	ADJ
ap-5063	113	35	to	to	ADP
ap-5063	113	36	0	0	NUM
ap-5063	113	37	on	on	ADP
ap-5063	113	38	the	the	DET
ap-5063	113	39	part	part	NOUN
ap-5063	113	40	of	of	ADP
ap-5063	113	41	the	the	DET
ap-5063	113	42	boundary	boundary	NOUN
ap-5063	113	43	denoted	denote	VERB
ap-5063	113	44	by	by	ADP
ap-5063	113	45	∂fs	∂fs	PROPN
ap-5063	113	46	.	.	PUNCT
ap-5063	114	1	the	the	DET
ap-5063	114	2	sl	sl	PROPN
ap-5063	114	3	functions	function	NOUN
ap-5063	114	4	behave	behave	VERB
ap-5063	114	5	inversely	inversely	ADV
ap-5063	114	6	.	.	PUNCT
ap-5063	115	1	in	in	ADP
ap-5063	115	2	the	the	DET
ap-5063	115	3	case	case	NOUN
ap-5063	115	4	of	of	ADP
ap-5063	115	5	c	c	NOUN
ap-5063	115	6	-	-	PUNCT
ap-5063	115	7	functions	function	NOUN
ap-5063	115	8	we	we	PRON
ap-5063	115	9	talk	talk	VERB
ap-5063	115	10	about	about	ADP
ap-5063	115	11	dirichlet	dirichlet	PROPN
ap-5063	115	12	boundary	boundary	ADJ
ap-5063	115	13	condition	condition	NOUN
ap-5063	115	14	and	and	CCONJ
ap-5063	115	15	s	s	NOUN
ap-5063	115	16	-	-	PUNCT
ap-5063	115	17	functions	function	NOUN
ap-5063	115	18	neumann	neumann	PROPN
ap-5063	115	19	boundary	boundary	ADJ
ap-5063	115	20	condition	condition	NOUN
ap-5063	115	21	.	.	PUNCT
ap-5063	116	1	for	for	ADP
ap-5063	116	2	ssand	ssand	NOUN
ap-5063	116	3	sl	sl	NOUN
ap-5063	116	4	-	-	PUNCT
ap-5063	116	5	functions	function	NOUN
ap-5063	116	6	we	we	PRON
ap-5063	116	7	talk	talk	VERB
ap-5063	116	8	about	about	ADP
ap-5063	116	9	mixed	mixed	ADJ
ap-5063	116	10	boundary	boundary	ADJ
ap-5063	116	11	condition	condition	NOUN
ap-5063	116	12	.	.	PUNCT
ap-5063	117	1	in	in	ADP
ap-5063	117	2	the	the	DET
ap-5063	117	3	next	next	ADJ
ap-5063	117	4	section	section	NOUN
ap-5063	117	5	we	we	PRON
ap-5063	117	6	present	present	VERB
ap-5063	117	7	3d	3d	NUM
ap-5063	117	8	cases	case	NOUN
ap-5063	117	9	in	in	ADP
ap-5063	117	10	details	detail	NOUN
ap-5063	117	11	.	.	PUNCT
ap-5063	118	1	5	5	X
ap-5063	118	2	.	.	X
ap-5063	118	3	3d	3d	NUM
ap-5063	118	4	finite	finite	PROPN
ap-5063	118	5	reflection	reflection	NOUN
ap-5063	118	6	groups	group	NOUN
ap-5063	118	7	the	the	DET
ap-5063	118	8	3	3	NUM
ap-5063	118	9	dimensional	dimensional	ADJ
ap-5063	118	10	groups	group	NOUN
ap-5063	118	11	which	which	PRON
ap-5063	118	12	we	we	PRON
ap-5063	118	13	considered	consider	VERB
ap-5063	118	14	here	here	ADV
ap-5063	118	15	are	be	AUX
ap-5063	118	16	b3	b3	NOUN
ap-5063	118	17	,	,	PUNCT
ap-5063	118	18	c3	c3	PROPN
ap-5063	118	19	,	,	PUNCT
ap-5063	118	20	c2×a1	c2×a1	PROPN
ap-5063	118	21	,	,	PUNCT
ap-5063	118	22	g2×a1	g2×a1	PROPN
ap-5063	118	23	,	,	PUNCT
ap-5063	118	24	a1×a1×a1	a1×a1×a1	ADP
ap-5063	119	1	[	[	X
ap-5063	119	2	2	2	NUM
ap-5063	119	3	,	,	PUNCT
ap-5063	119	4	7	7	NUM
ap-5063	119	5	,	,	PUNCT
ap-5063	119	6	8	8	NUM
ap-5063	119	7	,	,	PUNCT
ap-5063	119	8	10	10	NUM
ap-5063	119	9	]	]	PUNCT
ap-5063	119	10	.	.	PUNCT
ap-5063	120	1	we	we	PRON
ap-5063	120	2	use	use	VERB
ap-5063	120	3	the	the	DET
ap-5063	120	4	following	following	ADJ
ap-5063	120	5	notation	notation	NOUN
ap-5063	120	6	for	for	ADP
ap-5063	120	7	coordinates	coordinate	NOUN
ap-5063	120	8	:	:	PUNCT
ap-5063	120	9	r3	r3	PROPN
ap-5063	120	10	3	3	NUM
ap-5063	120	11	λ	λ	NOUN
ap-5063	120	12	=	=	SYM
ap-5063	120	13	(	(	PUNCT
ap-5063	120	14	a	a	DET
ap-5063	120	15	,	,	PUNCT
ap-5063	120	16	b	b	NOUN
ap-5063	120	17	,	,	PUNCT
ap-5063	120	18	c)ω	c)ω	NOUN
ap-5063	120	19	=	=	SYM
ap-5063	121	1	aω1	aω1	ADV
ap-5063	122	1	+	+	NUM
ap-5063	122	2	bω2	bω2	NOUN
ap-5063	122	3	+	+	X
ap-5063	122	4	cω3	cω3	X
ap-5063	122	5	,	,	PUNCT
ap-5063	122	6	r3	r3	PROPN
ap-5063	122	7	3	3	NUM
ap-5063	122	8	x	x	SYM
ap-5063	122	9	=	=	SYM
ap-5063	122	10	(	(	PUNCT
ap-5063	122	11	x1	x1	PROPN
ap-5063	122	12	,	,	PUNCT
ap-5063	122	13	x2	x2	PROPN
ap-5063	122	14	,	,	PUNCT
ap-5063	122	15	x3)α̌	x3)α̌	PUNCT
ap-5063	123	1	=	=	PRON
ap-5063	123	2	(	(	PUNCT
ap-5063	123	3	y1	y1	PROPN
ap-5063	123	4	,	,	PUNCT
ap-5063	123	5	y2	y2	PROPN
ap-5063	123	6	,	,	PUNCT
ap-5063	123	7	y3)e	y3)e	VERB
ap-5063	123	8	,	,	PUNCT
ap-5063	123	9	where	where	SCONJ
ap-5063	123	10	indexes	index	NOUN
ap-5063	123	11	e	e	NOUN
ap-5063	123	12	,	,	PUNCT
ap-5063	123	13	ω	ω	PROPN
ap-5063	123	14	,	,	PUNCT
ap-5063	123	15	and	and	CCONJ
ap-5063	123	16	α̌	α̌	NUM
ap-5063	123	17	denote	denote	NOUN
ap-5063	123	18	natural-	natural-	PROPN
ap-5063	123	19	,	,	PUNCT
ap-5063	123	20	ω-	ω-	NUM
ap-5063	123	21	,	,	PUNCT
ap-5063	123	22	and	and	CCONJ
ap-5063	123	23	α̌basis	α̌basis	NOUN
ap-5063	123	24	,	,	PUNCT
ap-5063	123	25	respectively	respectively	ADV
ap-5063	123	26	.	.	PUNCT
ap-5063	124	1	the	the	DET
ap-5063	124	2	action	action	NOUN
ap-5063	124	3	of	of	ADP
ap-5063	124	4	the	the	DET
ap-5063	124	5	laplace	laplace	NOUN
ap-5063	124	6	operator	operator	NOUN
ap-5063	124	7	∇	∇	X
ap-5063	124	8	on	on	ADP
ap-5063	124	9	the	the	DET
ap-5063	124	10	functions	function	NOUN
ap-5063	124	11	given	give	VERB
ap-5063	124	12	in	in	ADP
ap-5063	124	13	different	different	ADJ
ap-5063	124	14	bases	basis	NOUN
ap-5063	124	15	can	can	AUX
ap-5063	124	16	be	be	AUX
ap-5063	124	17	found	find	VERB
ap-5063	124	18	in	in	ADP
ap-5063	124	19	[	[	X
ap-5063	124	20	10	10	NUM
ap-5063	124	21	]	]	PUNCT
ap-5063	124	22	.	.	PUNCT
ap-5063	125	1	in	in	ADP
ap-5063	125	2	the	the	DET
ap-5063	125	3	next	next	ADJ
ap-5063	125	4	subsections	subsection	NOUN
ap-5063	125	5	we	we	PRON
ap-5063	125	6	describe	describe	VERB
ap-5063	125	7	each	each	DET
ap-5063	125	8	case	case	NOUN
ap-5063	125	9	in	in	ADP
ap-5063	125	10	details	detail	NOUN
ap-5063	125	11	.	.	PUNCT
ap-5063	126	1	for	for	ADP
ap-5063	126	2	each	each	DET
ap-5063	126	3	case	case	NOUN
ap-5063	126	4	we	we	PRON
ap-5063	126	5	present	present	VERB
ap-5063	126	6	functions	function	NOUN
ap-5063	126	7	which	which	PRON
ap-5063	126	8	are	be	AUX
ap-5063	126	9	the	the	DET
ap-5063	126	10	solutions	solution	NOUN
ap-5063	126	11	of	of	ADP
ap-5063	126	12	helmholtz	helmholtz	NOUN
ap-5063	126	13	equation	equation	NOUN
ap-5063	126	14	(	(	PUNCT
ap-5063	126	15	1	1	NUM
ap-5063	126	16	)	)	PUNCT
ap-5063	126	17	.	.	PUNCT
ap-5063	127	1	we	we	PRON
ap-5063	127	2	give	give	VERB
ap-5063	127	3	the	the	DET
ap-5063	127	4	exact	exact	ADJ
ap-5063	127	5	forms	form	NOUN
ap-5063	127	6	of	of	ADP
ap-5063	127	7	the	the	DET
ap-5063	127	8	projection	projection	NOUN
ap-5063	127	9	matrices	matrix	NOUN
ap-5063	127	10	and	and	CCONJ
ap-5063	127	11	branching	branch	VERB
ap-5063	127	12	rules	rule	NOUN
ap-5063	127	13	which	which	PRON
ap-5063	127	14	allow	allow	VERB
ap-5063	127	15	us	we	PRON
ap-5063	127	16	to	to	PART
ap-5063	127	17	choose	choose	VERB
ap-5063	127	18	the	the	DET
ap-5063	127	19	separation	separation	NOUN
ap-5063	127	20	constants	constant	NOUN
ap-5063	127	21	used	use	VERB
ap-5063	127	22	in	in	ADP
ap-5063	127	23	(	(	PUNCT
ap-5063	127	24	3	3	NUM
ap-5063	127	25	)	)	PUNCT
ap-5063	127	26	.	.	PUNCT
ap-5063	128	1	all	all	DET
ap-5063	128	2	functions	function	NOUN
ap-5063	128	3	described	describe	VERB
ap-5063	128	4	below	below	ADP
ap-5063	128	5	fulfil	fulfil	NOUN
ap-5063	128	6	one	one	NUM
ap-5063	128	7	of	of	ADP
ap-5063	128	8	the	the	DET
ap-5063	128	9	three	three	NUM
ap-5063	128	10	types	type	NOUN
ap-5063	128	11	of	of	ADP
ap-5063	128	12	boundary	boundary	ADJ
ap-5063	128	13	conditions	condition	NOUN
ap-5063	128	14	described	describe	VERB
ap-5063	128	15	in	in	ADP
ap-5063	128	16	§	§	PROPN
ap-5063	128	17	,	,	PUNCT
ap-5063	128	18	2	2	NUM
ap-5063	128	19	.	.	NOUN
ap-5063	128	20	5.1	5.1	NUM
ap-5063	128	21	.	.	PUNCT
ap-5063	129	1	b3	b3	PROPN
ap-5063	129	2	and	and	CCONJ
ap-5063	129	3	c3	c3	PROPN
ap-5063	129	4	groups	group	NOUN
ap-5063	129	5	the	the	DET
ap-5063	129	6	α	α	NUM
ap-5063	129	7	-	-	PUNCT
ap-5063	129	8	basis	basis	NOUN
ap-5063	129	9	vectors	vector	NOUN
ap-5063	129	10	in	in	ADP
ap-5063	129	11	cartesian	cartesian	ADJ
ap-5063	129	12	coordinates	coordinate	NOUN
ap-5063	129	13	are	be	AUX
ap-5063	129	14	b3	b3	NOUN
ap-5063	129	15	:	:	PUNCT
ap-5063	129	16	c3	c3	PROPN
ap-5063	129	17	:	:	PUNCT
ap-5063	129	18	α1	α1	PROPN
ap-5063	129	19	:	:	PUNCT
ap-5063	129	20	=	=	SYM
ap-5063	129	21	(	(	PUNCT
ap-5063	129	22	1,−1	1,−1	NUM
ap-5063	129	23	,	,	PUNCT
ap-5063	129	24	0)e	0)e	NOUN
ap-5063	129	25	,	,	PUNCT
ap-5063	129	26	α1	α1	PROPN
ap-5063	129	27	:	:	PUNCT
ap-5063	129	28	=	=	SYM
ap-5063	129	29	1√	1√	NUM
ap-5063	129	30	2	2	NUM
ap-5063	129	31	(	(	PUNCT
ap-5063	129	32	1,−1	1,−1	NUM
ap-5063	129	33	,	,	PUNCT
ap-5063	129	34	0)e	0)e	NOUN
ap-5063	129	35	,	,	PUNCT
ap-5063	129	36	α2	α2	ADJ
ap-5063	129	37	:	:	PUNCT
ap-5063	129	38	=	=	SYM
ap-5063	129	39	(	(	PUNCT
ap-5063	129	40	0	0	NUM
ap-5063	129	41	,	,	PUNCT
ap-5063	129	42	1,−1)e	1,−1)e	NUM
ap-5063	129	43	,	,	PUNCT
ap-5063	129	44	α2	α2	PROPN
ap-5063	129	45	:	:	PUNCT
ap-5063	129	46	=	=	SYM
ap-5063	129	47	1√	1√	NUM
ap-5063	129	48	2	2	NUM
ap-5063	129	49	(	(	PUNCT
ap-5063	129	50	0	0	NUM
ap-5063	129	51	,	,	PUNCT
ap-5063	129	52	1,−1)e	1,−1)e	NUM
ap-5063	129	53	,	,	PUNCT
ap-5063	129	54	α3	α3	PROPN
ap-5063	129	55	:	:	PUNCT
ap-5063	129	56	=	=	SYM
ap-5063	129	57	(	(	PUNCT
ap-5063	129	58	0	0	NUM
ap-5063	129	59	,	,	PUNCT
ap-5063	129	60	0	0	NUM
ap-5063	129	61	,	,	PUNCT
ap-5063	129	62	1)e	1)e	NUM
ap-5063	129	63	,	,	PUNCT
ap-5063	129	64	α3	α3	NOUN
ap-5063	129	65	:	:	PUNCT
ap-5063	129	66	=	=	SYM
ap-5063	129	67	1√	1√	NUM
ap-5063	129	68	2	2	NUM
ap-5063	129	69	(	(	PUNCT
ap-5063	129	70	0	0	NUM
ap-5063	129	71	,	,	PUNCT
ap-5063	129	72	0	0	NUM
ap-5063	129	73	,	,	PUNCT
ap-5063	129	74	2)e	2)e	NUM
ap-5063	129	75	.	.	PUNCT
ap-5063	130	1	as	as	SCONJ
ap-5063	130	2	one	one	PRON
ap-5063	130	3	can	can	AUX
ap-5063	130	4	easily	easily	ADV
ap-5063	130	5	notice	notice	VERB
ap-5063	130	6	the	the	DET
ap-5063	130	7	short	short	ADJ
ap-5063	130	8	root	root	NOUN
ap-5063	130	9	for	for	ADP
ap-5063	130	10	b3	b3	PROPN
ap-5063	130	11	is	be	AUX
ap-5063	130	12	α3	α3	ADJ
ap-5063	130	13	and	and	CCONJ
ap-5063	130	14	for	for	ADP
ap-5063	130	15	c3	c3	PROPN
ap-5063	130	16	are	be	AUX
ap-5063	130	17	α1	α1	PROPN
ap-5063	130	18	,	,	PUNCT
ap-5063	130	19	α2	α2	ADJ
ap-5063	130	20	.	.	PUNCT
ap-5063	131	1	the	the	DET
ap-5063	131	2	fundamental	fundamental	ADJ
ap-5063	131	3	regions	region	NOUN
ap-5063	131	4	f	f	PROPN
ap-5063	131	5	for	for	ADP
ap-5063	131	6	b3	b3	PROPN
ap-5063	131	7	and	and	CCONJ
ap-5063	131	8	c3	c3	PROPN
ap-5063	131	9	groups	group	NOUN
ap-5063	131	10	,	,	PUNCT
ap-5063	131	11	written	write	VERB
ap-5063	131	12	in	in	ADP
ap-5063	131	13	ω	ω	NOUN
ap-5063	131	14	-	-	NOUN
ap-5063	131	15	basis	basis	NOUN
ap-5063	131	16	,	,	PUNCT
ap-5063	131	17	have	have	VERB
ap-5063	131	18	the	the	DET
ap-5063	131	19	vertices	vertex	NOUN
ap-5063	131	20	:	:	PUNCT
ap-5063	131	21	fb3	fb3	X
ap-5063	131	22	=	=	SYM
ap-5063	131	23	{	{	PUNCT
ap-5063	131	24	0	0	NUM
ap-5063	131	25	,	,	PUNCT
ap-5063	131	26	ω1	ω1	PROPN
ap-5063	131	27	,	,	PUNCT
ap-5063	131	28	1	1	NUM
ap-5063	131	29	2ω2	2ω2	NUM
ap-5063	131	30	,	,	PUNCT
ap-5063	131	31	ω3	ω3	PROPN
ap-5063	131	32	}	}	PUNCT
ap-5063	131	33	,	,	PUNCT
ap-5063	131	34	fc3	fc3	PROPN
ap-5063	131	35	=	=	PUNCT
ap-5063	131	36	{	{	PUNCT
ap-5063	131	37	0	0	NUM
ap-5063	131	38	,	,	PUNCT
ap-5063	131	39	ω1	ω1	PROPN
ap-5063	131	40	,	,	PUNCT
ap-5063	131	41	ω2	ω2	ADJ
ap-5063	131	42	,	,	PUNCT
ap-5063	131	43	ω3	ω3	NOUN
ap-5063	131	44	}	}	PUNCT
ap-5063	131	45	,	,	PUNCT
ap-5063	131	46	and	and	CCONJ
ap-5063	131	47	are	be	AUX
ap-5063	131	48	shown	show	VERB
ap-5063	131	49	in	in	ADP
ap-5063	131	50	fig	fig	NOUN
ap-5063	131	51	.	.	PUNCT
ap-5063	132	1	1	1	X
ap-5063	132	2	.	.	X
ap-5063	132	3	figure	figure	NOUN
ap-5063	132	4	1	1	NUM
ap-5063	132	5	.	.	PUNCT
ap-5063	133	1	the	the	DET
ap-5063	133	2	fundamental	fundamental	ADJ
ap-5063	133	3	region	region	NOUN
ap-5063	133	4	f	f	PROPN
ap-5063	133	5	for	for	ADP
ap-5063	133	6	b3	b3	PROPN
ap-5063	133	7	and	and	CCONJ
ap-5063	133	8	c3	c3	PROPN
ap-5063	133	9	group	group	NOUN
ap-5063	133	10	.	.	PUNCT
ap-5063	134	1	the	the	DET
ap-5063	134	2	reduction	reduction	NOUN
ap-5063	134	3	of	of	ADP
ap-5063	134	4	b3	b3	PROPN
ap-5063	134	5	and	and	CCONJ
ap-5063	134	6	c3	c3	PROPN
ap-5063	134	7	to	to	ADP
ap-5063	134	8	a	a	DET
ap-5063	134	9	subgroup	subgroup	NOUN
ap-5063	134	10	a1	a1	NOUN
ap-5063	134	11	×	×	NOUN
ap-5063	134	12	a1	a1	NOUN
ap-5063	134	13	×a1	×a1	PROPN
ap-5063	134	14	is	be	AUX
ap-5063	134	15	given	give	VERB
ap-5063	134	16	by	by	ADP
ap-5063	134	17	the	the	DET
ap-5063	134	18	projection	projection	NOUN
ap-5063	134	19	matrices	matrix	NOUN
ap-5063	134	20	pb3	pb3	NOUN
ap-5063	135	1	=	=	PUNCT
ap-5063	135	2	1	1	PROPN
ap-5063	135	3	1	1	NUM
ap-5063	135	4	0	0	NUM
ap-5063	135	5	1	1	NUM
ap-5063	135	6	1	1	NUM
ap-5063	135	7	1	1	NUM
ap-5063	135	8	0	0	NUM
ap-5063	135	9	2	2	NUM
ap-5063	135	10	1	1	NUM
ap-5063	135	11			PROPN
ap-5063	135	12	,	,	PUNCT
ap-5063	135	13	pc3	pc3	PROPN
ap-5063	135	14	=	=	SYM
ap-5063	135	15	1	1	PROPN
ap-5063	135	16	1	1	NUM
ap-5063	135	17	1	1	NUM
ap-5063	135	18	0	0	NUM
ap-5063	135	19	1	1	NUM
ap-5063	135	20	1	1	NUM
ap-5063	135	21	0	0	NUM
ap-5063	135	22	0	0	NUM
ap-5063	135	23	1	1	NUM
ap-5063	135	24			PROPN
ap-5063	135	25	.	.	PUNCT
ap-5063	136	1	then	then	ADV
ap-5063	136	2	the	the	DET
ap-5063	136	3	branching	branch	VERB
ap-5063	136	4	rule	rule	NOUN
ap-5063	136	5	is	be	AUX
ap-5063	136	6	the	the	DET
ap-5063	136	7	following	following	NOUN
ap-5063	136	8	:	:	PUNCT
ap-5063	136	9	o(a	o(a	NUM
ap-5063	136	10	,	,	PUNCT
ap-5063	136	11	b	b	NOUN
ap-5063	136	12	,	,	PUNCT
ap-5063	136	13	c	c	NOUN
ap-5063	136	14	)	)	PUNCT
ap-5063	136	15	pb3−−→	pb3−−→	NOUN
ap-5063	136	16	o(2a+2b+c)o(2b+c)o(c	o(2a+2b+c)o(2b+c)o(c	PROPN
ap-5063	136	17	)	)	PUNCT
ap-5063	136	18	∪o(2b+c)o(2a+2b+c)o(c	∪o(2b+c)o(2a+2b+c)o(c	NOUN
ap-5063	136	19	)	)	PUNCT
ap-5063	136	20	∪o(2a+2b+c)o(c)o(2b+c	∪o(2a+2b+c)o(c)o(2b+c	ADJ
ap-5063	136	21	)	)	PUNCT
ap-5063	136	22	∪o(c)o(2a+2b+c)o(2b+c	∪o(c)o(2a+2b+c)o(2b+c	NOUN
ap-5063	136	23	)	)	PUNCT
ap-5063	136	24	∪o(2b+c)o(c)o(2a+2b+c	∪o(2b+c)o(c)o(2a+2b+c	PROPN
ap-5063	136	25	)	)	PUNCT
ap-5063	136	26	∪o(c)o(2b+c)o(2a+2b+c	∪o(c)o(2b+c)o(2a+2b+c	PROPN
ap-5063	136	27	)	)	PUNCT
ap-5063	136	28	,	,	PUNCT
ap-5063	136	29	404	404	NUM
ap-5063	136	30	vol	vol	NOUN
ap-5063	136	31	.	.	PUNCT
ap-5063	137	1	58	58	NUM
ap-5063	137	2	no	no	INTJ
ap-5063	137	3	.	.	PUNCT
ap-5063	138	1	6/2018	6/2018	NUM
ap-5063	138	2	multidimensional	multidimensional	ADJ
ap-5063	138	3	hybrid	hybrid	ADJ
ap-5063	138	4	boundary	boundary	ADJ
ap-5063	138	5	value	value	NOUN
ap-5063	138	6	problem	problem	NOUN
ap-5063	138	7	o(a	o(a	PROPN
ap-5063	138	8	,	,	PUNCT
ap-5063	138	9	b	b	NOUN
ap-5063	138	10	,	,	PUNCT
ap-5063	138	11	c	c	NOUN
ap-5063	138	12	)	)	PUNCT
ap-5063	138	13	pc3−−→	pc3−−→	NOUN
ap-5063	138	14	o(a+b+c)o(b+c)o(c	o(a+b+c)o(b+c)o(c	ADJ
ap-5063	138	15	)	)	PUNCT
ap-5063	138	16	∪o(b+c)o(a+b+c)o(c	∪o(b+c)o(a+b+c)o(c	NOUN
ap-5063	138	17	)	)	PUNCT
ap-5063	139	1	∪o(a+b+c)o(c)o(b+c	∪o(a+b+c)o(c)o(b+c	NOUN
ap-5063	139	2	)	)	PUNCT
ap-5063	139	3	∪o(b+c)o(c)o(a+b+c	∪o(b+c)o(c)o(a+b+c	NUM
ap-5063	139	4	)	)	PUNCT
ap-5063	139	5	∪o(c)o(a+b+c)o(b+c	∪o(c)o(a+b+c)o(b+c	NUM
ap-5063	139	6	)	)	PUNCT
ap-5063	140	1	∪o(c)o(b+c)o(a+b+c	∪o(c)o(b+c)o(a+b+c	PROPN
ap-5063	140	2	)	)	PUNCT
ap-5063	140	3	.	.	PUNCT
ap-5063	141	1	according	accord	VERB
ap-5063	141	2	to	to	ADP
ap-5063	141	3	remarks	remark	NOUN
ap-5063	141	4	1	1	NUM
ap-5063	141	5	and	and	CCONJ
ap-5063	141	6	2	2	NUM
ap-5063	141	7	the	the	DET
ap-5063	141	8	separation	separation	NOUN
ap-5063	141	9	constants	constant	NOUN
ap-5063	141	10	for	for	ADP
ap-5063	141	11	b3	b3	PROPN
ap-5063	141	12	and	and	CCONJ
ap-5063	141	13	c3	c3	PROPN
ap-5063	141	14	group	group	NOUN
ap-5063	141	15	we	we	PRON
ap-5063	141	16	can	can	AUX
ap-5063	141	17	choose	choose	VERB
ap-5063	141	18	as	as	ADP
ap-5063	141	19	−k2	−k2	PROPN
ap-5063	141	20	1	1	NUM
ap-5063	141	21	=	=	SYM
ap-5063	141	22	−π2(2a+	−π2(2a+	ADJ
ap-5063	141	23	2b+	2b+	NUM
ap-5063	141	24	c)2	c)2	NOUN
ap-5063	141	25	,	,	PUNCT
ap-5063	141	26	−k2	−k2	PROPN
ap-5063	141	27	2	2	NUM
ap-5063	141	28	=	=	SYM
ap-5063	141	29	−π2(2b+	−π2(2b+	PROPN
ap-5063	141	30	c)2	c)2	NOUN
ap-5063	141	31	,	,	PUNCT
ap-5063	141	32	−k2	−k2	PROPN
ap-5063	141	33	3	3	NUM
ap-5063	141	34	=	=	SYM
ap-5063	141	35	−π2c2	−π2c2	PROPN
ap-5063	141	36	,	,	PUNCT
ap-5063	141	37	(	(	PUNCT
ap-5063	141	38	6	6	NUM
ap-5063	141	39	)	)	PUNCT
ap-5063	141	40	where	where	SCONJ
ap-5063	141	41	w2	w2	NOUN
ap-5063	141	42	=	=	PROPN
ap-5063	141	43	4π2(a2	4π2(a2	NUM
ap-5063	142	1	+	+	CCONJ
ap-5063	142	2	2ab+	2ab+	NUM
ap-5063	142	3	2b2	2b2	NUM
ap-5063	142	4	+	+	NUM
ap-5063	142	5	ac+	ac+	NOUN
ap-5063	142	6	2bc+	2bc+	NUM
ap-5063	142	7	3	3	NUM
ap-5063	142	8	4c	4c	NOUN
ap-5063	142	9	2	2	NUM
ap-5063	142	10	)	)	PUNCT
ap-5063	142	11	.	.	PUNCT
ap-5063	143	1	the	the	DET
ap-5063	143	2	separation	separation	NOUN
ap-5063	143	3	constants	constant	VERB
ap-5063	143	4	for	for	ADP
ap-5063	143	5	c3	c3	PROPN
ap-5063	143	6	group	group	NOUN
ap-5063	143	7	are	be	AUX
ap-5063	143	8	−k2	−k2	PROPN
ap-5063	143	9	1	1	NUM
ap-5063	143	10	=	=	SYM
ap-5063	143	11	−π2(a+	−π2(a+	NOUN
ap-5063	143	12	b+	b+	X
ap-5063	143	13	c)2	c)2	PROPN
ap-5063	143	14	,	,	PUNCT
ap-5063	143	15	−k2	−k2	PROPN
ap-5063	143	16	2	2	NUM
ap-5063	143	17	=	=	SYM
ap-5063	143	18	−π2(b+	−π2(b+	X
ap-5063	143	19	c)2	c)2	NOUN
ap-5063	143	20	,	,	PUNCT
ap-5063	143	21	−k2	−k2	PROPN
ap-5063	143	22	3	3	NUM
ap-5063	143	23	=	=	SYM
ap-5063	143	24	−π2c2	−π2c2	PROPN
ap-5063	143	25	,	,	PUNCT
ap-5063	143	26	(	(	PUNCT
ap-5063	143	27	7	7	X
ap-5063	143	28	)	)	PUNCT
ap-5063	143	29	where	where	SCONJ
ap-5063	143	30	w2	w2	NOUN
ap-5063	143	31	=	=	PROPN
ap-5063	143	32	4π2	4π2	PROPN
ap-5063	143	33	(	(	PUNCT
ap-5063	143	34	1	1	NUM
ap-5063	143	35	2a	2a	NUM
ap-5063	143	36	2	2	NUM
ap-5063	143	37	+	+	CCONJ
ap-5063	143	38	ab+	ab+	NOUN
ap-5063	143	39	b2	b2	NOUN
ap-5063	143	40	+	+	CCONJ
ap-5063	143	41	ac+	ac+	NOUN
ap-5063	143	42	2bc+	2bc+	NUM
ap-5063	143	43	3	3	NUM
ap-5063	143	44	2c	2c	NUM
ap-5063	143	45	2	2	NUM
ap-5063	143	46	)	)	PUNCT
ap-5063	143	47	.	.	PUNCT
ap-5063	144	1	the	the	DET
ap-5063	144	2	explicit	explicit	ADJ
ap-5063	144	3	forms	form	NOUN
ap-5063	144	4	of	of	ADP
ap-5063	144	5	orbit	orbit	NOUN
ap-5063	144	6	functions	function	NOUN
ap-5063	144	7	for	for	ADP
ap-5063	144	8	b3	b3	PROPN
ap-5063	144	9	and	and	CCONJ
ap-5063	144	10	c3	c3	PROPN
ap-5063	144	11	group	group	NOUN
ap-5063	144	12	have	have	VERB
ap-5063	144	13	form	form	NOUN
ap-5063	144	14	b3	b3	NOUN
ap-5063	144	15	:	:	PUNCT
ap-5063	144	16	ca	ca	NOUN
ap-5063	144	17	,	,	PUNCT
ap-5063	144	18	b	b	NOUN
ap-5063	144	19	,	,	PUNCT
ap-5063	144	20	c(x	c(x	NOUN
ap-5063	144	21	)	)	PUNCT
ap-5063	144	22	=	=	SYM
ap-5063	144	23	c2a+2b+c(x1)c2b+c(x2)cc(x3	c2a+2b+c(x1)c2b+c(x2)cc(x3	NUM
ap-5063	144	24	)	)	PUNCT
ap-5063	145	1	+	+	CCONJ
ap-5063	145	2	c2b+c(x1)c2a+2b+c(x2)cc(x3	c2b+c(x1)c2a+2b+c(x2)cc(x3	NOUN
ap-5063	145	3	)	)	PUNCT
ap-5063	146	1	+	+	CCONJ
ap-5063	146	2	c2a+2b+c(x1)cc(x2)c2b+c(x3	c2a+2b+c(x1)cc(x2)c2b+c(x3	NUM
ap-5063	146	3	)	)	PUNCT
ap-5063	146	4	+	+	PUNCT
ap-5063	146	5	cc(x1)c2a+2b+c(x2)c2b+c(x3	cc(x1)c2a+2b+c(x2)c2b+c(x3	NUM
ap-5063	146	6	)	)	PUNCT
ap-5063	146	7	+	+	NUM
ap-5063	146	8	c2b+c(x1)cc(x2)c2a+2b+c(x3	c2b+c(x1)cc(x2)c2a+2b+c(x3	PUNCT
ap-5063	146	9	)	)	PUNCT
ap-5063	147	1	+	+	PUNCT
ap-5063	147	2	cc(x1)c2b+c(x2)c2a+2b+c(x3	cc(x1)c2b+c(x2)c2a+2b+c(x3	X
ap-5063	147	3	)	)	PUNCT
ap-5063	147	4	,	,	PUNCT
ap-5063	147	5	sla	sla	PROPN
ap-5063	147	6	,	,	PUNCT
ap-5063	147	7	b	b	NOUN
ap-5063	147	8	,	,	PUNCT
ap-5063	147	9	c(x	c(x	NOUN
ap-5063	147	10	)	)	PUNCT
ap-5063	147	11	=	=	SYM
ap-5063	147	12	c2a+2b+c(x1)c2b+c(x2)cc(x3	c2a+2b+c(x1)c2b+c(x2)cc(x3	NUM
ap-5063	147	13	)	)	PUNCT
ap-5063	148	1	−	−	PROPN
ap-5063	148	2	c2b+c(x1)c2a+2b+c(x2)cc(x3	c2b+c(x1)c2a+2b+c(x2)cc(x3	NOUN
ap-5063	148	3	)	)	PUNCT
ap-5063	148	4	−	−	ADP
ap-5063	148	5	c2a+2b+c(x1)cc(x2)c2b+c(x3	c2a+2b+c(x1)cc(x2)c2b+c(x3	NUM
ap-5063	148	6	)	)	PUNCT
ap-5063	148	7	+	+	PUNCT
ap-5063	148	8	cc(x1)c2a+2b+c(x2)c2b+c(x3	cc(x1)c2a+2b+c(x2)c2b+c(x3	NUM
ap-5063	148	9	)	)	PUNCT
ap-5063	148	10	+	+	NUM
ap-5063	148	11	c2b+c(x1)cc(x2)c2a+2b+c(x3	c2b+c(x1)cc(x2)c2a+2b+c(x3	X
ap-5063	148	12	)	)	PUNCT
ap-5063	148	13	−	−	PROPN
ap-5063	149	1	cc(x1)c2b+c(x2)c2a+2b+c(x3	cc(x1)c2b+c(x2)c2a+2b+c(x3	NUM
ap-5063	149	2	)	)	PUNCT
ap-5063	149	3	,	,	PUNCT
ap-5063	149	4	sa	sa	PROPN
ap-5063	149	5	,	,	PUNCT
ap-5063	149	6	b	b	NOUN
ap-5063	149	7	,	,	PUNCT
ap-5063	149	8	c(x	c(x	NOUN
ap-5063	149	9	)	)	PUNCT
ap-5063	149	10	=	=	SYM
ap-5063	149	11	s2a+2b+c(x1)s2b+c(x2)sc(x3	s2a+2b+c(x1)s2b+c(x2)sc(x3	NUM
ap-5063	149	12	)	)	PUNCT
ap-5063	149	13	−	−	PROPN
ap-5063	149	14	s2b+c(x1)s2a+2b+c(x2)sc(x3	s2b+c(x1)s2a+2b+c(x2)sc(x3	NOUN
ap-5063	149	15	)	)	PUNCT
ap-5063	149	16	−	−	PROPN
ap-5063	150	1	s2a+2b+c(x1)sc(x2)s2b+c(x3	s2a+2b+c(x1)sc(x2)s2b+c(x3	X
ap-5063	150	2	)	)	PUNCT
ap-5063	151	1	+	+	CCONJ
ap-5063	151	2	sc(x1)s2a+2b+c(x2)s2b+c(x3	sc(x1)s2a+2b+c(x2)s2b+c(x3	NUM
ap-5063	151	3	)	)	PUNCT
ap-5063	151	4	+	+	NUM
ap-5063	151	5	s2b+c(x1)sc(x2)s2a+2b+c(x3	s2b+c(x1)sc(x2)s2a+2b+c(x3	NOUN
ap-5063	151	6	)	)	PUNCT
ap-5063	151	7	−	−	PROPN
ap-5063	151	8	sc(x1)s2b+c(x2)s2a+2b+c(x3	sc(x1)s2b+c(x2)s2a+2b+c(x3	PROPN
ap-5063	151	9	)	)	PUNCT
ap-5063	151	10	,	,	PUNCT
ap-5063	151	11	ssa	ssa	NOUN
ap-5063	151	12	,	,	PUNCT
ap-5063	151	13	b	b	NOUN
ap-5063	151	14	,	,	PUNCT
ap-5063	151	15	c(x	c(x	NOUN
ap-5063	151	16	)	)	PUNCT
ap-5063	151	17	=	=	SYM
ap-5063	151	18	s2a+2b+c(x1)s2b+c(x2)sc(x3	s2a+2b+c(x1)s2b+c(x2)sc(x3	NUM
ap-5063	151	19	)	)	PUNCT
ap-5063	152	1	+	+	CCONJ
ap-5063	152	2	s2b+c(x1)s2a+2b+c(x2)sc(x3	s2b+c(x1)s2a+2b+c(x2)sc(x3	NOUN
ap-5063	152	3	)	)	PUNCT
ap-5063	153	1	+	+	CCONJ
ap-5063	153	2	s2a+2b+c(x1)sc(x2)s2b+c(x3	s2a+2b+c(x1)sc(x2)s2b+c(x3	X
ap-5063	153	3	)	)	PUNCT
ap-5063	153	4	+	+	CCONJ
ap-5063	153	5	sc(x1)s2a+2b+c(x2)s2b+c(x3	sc(x1)s2a+2b+c(x2)s2b+c(x3	NUM
ap-5063	153	6	)	)	PUNCT
ap-5063	153	7	+	+	NUM
ap-5063	153	8	s2b+c(x1)sc(x2)s2a+2b+c(x3	s2b+c(x1)sc(x2)s2a+2b+c(x3	NOUN
ap-5063	153	9	)	)	PUNCT
ap-5063	153	10	+	+	CCONJ
ap-5063	153	11	sc(x1)s2b+c(x2)s2a+2b+c(x3	sc(x1)s2b+c(x2)s2a+2b+c(x3	NUM
ap-5063	153	12	)	)	PUNCT
ap-5063	153	13	;	;	PUNCT
ap-5063	153	14	c3	c3	PROPN
ap-5063	153	15	:	:	PUNCT
ap-5063	153	16	ca	ca	PROPN
ap-5063	153	17	,	,	PUNCT
ap-5063	153	18	b	b	NOUN
ap-5063	153	19	,	,	PUNCT
ap-5063	153	20	c(x	c(x	NOUN
ap-5063	153	21	)	)	PUNCT
ap-5063	153	22	=	=	PUNCT
ap-5063	153	23	ca+b+c(x1)cb+c(x2)cc(x3	ca+b+c(x1)cb+c(x2)cc(x3	NOUN
ap-5063	153	24	)	)	PUNCT
ap-5063	153	25	+	+	CCONJ
ap-5063	153	26	cb+c(x1)ca+b+c(x2)cc(x3	cb+c(x1)ca+b+c(x2)cc(x3	PRON
ap-5063	153	27	)	)	PUNCT
ap-5063	153	28	+	+	NUM
ap-5063	153	29	ca+b+c(x1)cc(x2)cb+c(x3	ca+b+c(x1)cc(x2)cb+c(x3	NUM
ap-5063	153	30	)	)	PUNCT
ap-5063	154	1	+	+	CCONJ
ap-5063	154	2	cc(x1)ca+b+c(x2)cb+c(x3	cc(x1)ca+b+c(x2)cb+c(x3	NOUN
ap-5063	154	3	)	)	PUNCT
ap-5063	155	1	+	+	PUNCT
ap-5063	155	2	cb+c(x1)cc(x2)ca+b+c(x3	cb+c(x1)cc(x2)ca+b+c(x3	NOUN
ap-5063	155	3	)	)	PUNCT
ap-5063	156	1	+	+	CCONJ
ap-5063	156	2	cc(x1)cb+c(x2)ca+b+c(x3	cc(x1)cb+c(x2)ca+b+c(x3	PROPN
ap-5063	156	3	)	)	PUNCT
ap-5063	156	4	,	,	PUNCT
ap-5063	156	5	ssa	ssa	NOUN
ap-5063	156	6	,	,	PUNCT
ap-5063	156	7	b	b	NOUN
ap-5063	156	8	,	,	PUNCT
ap-5063	156	9	c(x	c(x	NOUN
ap-5063	156	10	)	)	PUNCT
ap-5063	156	11	=	=	SYM
ap-5063	157	1	ca+b+c(x1)cb+c(x2)cc(x3	ca+b+c(x1)cb+c(x2)cc(x3	NOUN
ap-5063	157	2	)	)	PUNCT
ap-5063	157	3	−	−	PROPN
ap-5063	157	4	cb+c(x1)ca+b+c(x2)cc(x3	cb+c(x1)ca+b+c(x2)cc(x3	SYM
ap-5063	157	5	)	)	PUNCT
ap-5063	158	1	−	−	PROPN
ap-5063	158	2	ca+b+c(x1)cc(x2)cb+c(x3	ca+b+c(x1)cc(x2)cb+c(x3	NOUN
ap-5063	158	3	)	)	PUNCT
ap-5063	159	1	+	+	CCONJ
ap-5063	159	2	cc(x1)ca+b+c(x2)cb+c(x3	cc(x1)ca+b+c(x2)cb+c(x3	NOUN
ap-5063	159	3	)	)	PUNCT
ap-5063	160	1	+	+	SYM
ap-5063	160	2	cb+c(x1)cc(x2)ca+b+c(x3	cb+c(x1)cc(x2)ca+b+c(x3	NOUN
ap-5063	160	3	)	)	PUNCT
ap-5063	160	4	−	−	PROPN
ap-5063	161	1	cc(x1)cb+c(x2)ca+b+c(x3	cc(x1)cb+c(x2)ca+b+c(x3	PROPN
ap-5063	161	2	)	)	PUNCT
ap-5063	161	3	,	,	PUNCT
ap-5063	161	4	sa	sa	PROPN
ap-5063	161	5	,	,	PUNCT
ap-5063	161	6	b	b	NOUN
ap-5063	161	7	,	,	PUNCT
ap-5063	161	8	c(x	c(x	NOUN
ap-5063	161	9	)	)	PUNCT
ap-5063	161	10	=	=	PUNCT
ap-5063	161	11	sa+b+c(x1)sb+c(x2)sc(x3	sa+b+c(x1)sb+c(x2)sc(x3	NOUN
ap-5063	161	12	)	)	PUNCT
ap-5063	161	13	−	−	PROPN
ap-5063	161	14	sb+c(x1)sa+b+c(x2)sc(x3	sb+c(x1)sa+b+c(x2)sc(x3	NUM
ap-5063	161	15	)	)	PUNCT
ap-5063	161	16	−	−	PROPN
ap-5063	161	17	sa+b+c(x1)sc(x2)sb+c(x3	sa+b+c(x1)sc(x2)sb+c(x3	NOUN
ap-5063	161	18	)	)	PUNCT
ap-5063	161	19	+	+	CCONJ
ap-5063	161	20	sc(x1)sa+b+c(x2)sb+c(x3	sc(x1)sa+b+c(x2)sb+c(x3	ADJ
ap-5063	161	21	)	)	PUNCT
ap-5063	161	22	+	+	NUM
ap-5063	161	23	sb+c(x1)sc(x2)sa+b+c(x3	sb+c(x1)sc(x2)sa+b+c(x3	X
ap-5063	161	24	)	)	PUNCT
ap-5063	161	25	−	−	PROPN
ap-5063	161	26	sc(x1)sb+c(x2)sa+b+c(x3	sc(x1)sb+c(x2)sa+b+c(x3	PROPN
ap-5063	161	27	)	)	PUNCT
ap-5063	161	28	sla	sla	PROPN
ap-5063	161	29	,	,	PUNCT
ap-5063	161	30	b	b	NOUN
ap-5063	161	31	,	,	PUNCT
ap-5063	161	32	c(x	c(x	NOUN
ap-5063	161	33	)	)	PUNCT
ap-5063	161	34	=	=	PUNCT
ap-5063	161	35	sa+b+c(x1)sb+c(x2)sc(x3	sa+b+c(x1)sb+c(x2)sc(x3	NOUN
ap-5063	161	36	)	)	PUNCT
ap-5063	161	37	+	+	PUNCT
ap-5063	161	38	sb+c(x1)sa+b+c(x2)sc(x3	sb+c(x1)sa+b+c(x2)sc(x3	X
ap-5063	161	39	)	)	PUNCT
ap-5063	162	1	+	+	CCONJ
ap-5063	162	2	sa+b+c(x1)sc(x2)sb+c(x3	sa+b+c(x1)sc(x2)sb+c(x3	NOUN
ap-5063	162	3	)	)	PUNCT
ap-5063	163	1	+	+	CCONJ
ap-5063	163	2	sc(x1)sa+b+c(x2)sb+c(x3	sc(x1)sa+b+c(x2)sb+c(x3	ADJ
ap-5063	163	3	)	)	PUNCT
ap-5063	163	4	+	+	NUM
ap-5063	163	5	sb+c(x1)sc(x2)sa+b+c(x3	sb+c(x1)sc(x2)sa+b+c(x3	X
ap-5063	163	6	)	)	PUNCT
ap-5063	164	1	+	+	CCONJ
ap-5063	164	2	sc(x1)sb+c(x2)sa+b+c(x3	sc(x1)sb+c(x2)sa+b+c(x3	PROPN
ap-5063	164	3	)	)	PUNCT
ap-5063	164	4	.	.	PUNCT
ap-5063	165	1	the	the	DET
ap-5063	165	2	functions	function	NOUN
ap-5063	165	3	on	on	ADP
ap-5063	165	4	the	the	DET
ap-5063	165	5	right	right	ADJ
ap-5063	165	6	side	side	NOUN
ap-5063	165	7	of	of	ADP
ap-5063	165	8	the	the	DET
ap-5063	165	9	above	above	ADJ
ap-5063	165	10	equations	equation	NOUN
ap-5063	165	11	are	be	AUX
ap-5063	165	12	special	special	ADJ
ap-5063	165	13	functions	function	NOUN
ap-5063	165	14	corresponding	correspond	VERB
ap-5063	165	15	to	to	ADP
ap-5063	165	16	group	group	NOUN
ap-5063	165	17	a1	a1	NOUN
ap-5063	165	18	cµ(xi	cµ(xi	PROPN
ap-5063	165	19	)	)	PUNCT
ap-5063	166	1	=	=	PUNCT
ap-5063	166	2	∑	∑	PROPN
ap-5063	166	3	µ∈a1	µ∈a1	PROPN
ap-5063	166	4	e2πi〈µ|xi	e2πi〈µ|xi	PROPN
ap-5063	166	5	〉	〉	PROPN
ap-5063	166	6	=	=	SYM
ap-5063	166	7	2	2	NUM
ap-5063	166	8	cos(2πµxi	cos(2πµxi	NOUN
ap-5063	166	9	)	)	PUNCT
ap-5063	166	10	,	,	PUNCT
ap-5063	166	11	sµ(xi	sµ(xi	PROPN
ap-5063	166	12	)	)	PUNCT
ap-5063	167	1	=	=	PUNCT
ap-5063	168	1	∑	∑	PUNCT
ap-5063	168	2	µ∈a1	µ∈a1	NOUN
ap-5063	168	3	σ(µ)e2πi〈µ|xi	σ(µ)e2πi〈µ|xi	PROPN
ap-5063	168	4	〉	〉	PROPN
ap-5063	168	5	=	=	SYM
ap-5063	168	6	2i	2i	PROPN
ap-5063	168	7	sin(2πµxi	sin(2πµxi	PROPN
ap-5063	168	8	)	)	PUNCT
ap-5063	168	9	,	,	PUNCT
ap-5063	168	10	where	where	SCONJ
ap-5063	168	11	µ	µ	PROPN
ap-5063	168	12	∈	∈	PROPN
ap-5063	168	13	p+	p+	NOUN
ap-5063	168	14	a1	a1	NOUN
ap-5063	168	15	,	,	PUNCT
ap-5063	168	16	xi	xi	PROPN
ap-5063	168	17	∈	∈	PROPN
ap-5063	168	18	fa1	fa1	NOUN
ap-5063	168	19	,	,	PUNCT
ap-5063	168	20	i	i	PRON
ap-5063	168	21	=	=	NOUN
ap-5063	168	22	1	1	NUM
ap-5063	168	23	,	,	PUNCT
ap-5063	168	24	2	2	NUM
ap-5063	168	25	,	,	PUNCT
ap-5063	168	26	3	3	NUM
ap-5063	168	27	.	.	PUNCT
ap-5063	169	1	the	the	DET
ap-5063	169	2	coordinate	coordinate	NOUN
ap-5063	169	3	xi	xi	AUX
ap-5063	169	4	respond	respond	VERB
ap-5063	169	5	to	to	ADP
ap-5063	169	6	the	the	DET
ap-5063	169	7	i	i	PROPN
ap-5063	169	8	-	-	PUNCT
ap-5063	169	9	th	th	X
ap-5063	169	10	coordinate	coordinate	NOUN
ap-5063	169	11	in	in	ADP
ap-5063	169	12	a1	a1	NOUN
ap-5063	169	13	×	×	NOUN
ap-5063	169	14	a1	a1	NOUN
ap-5063	169	15	×	×	NOUN
ap-5063	169	16	a1	a1	NOUN
ap-5063	169	17	.	.	PUNCT
ap-5063	170	1	the	the	DET
ap-5063	170	2	functions	function	NOUN
ap-5063	170	3	cµ(xi	cµ(xi	PROPN
ap-5063	170	4	)	)	PUNCT
ap-5063	170	5	and	and	CCONJ
ap-5063	170	6	sµ(xi	sµ(xi	PROPN
ap-5063	170	7	)	)	PUNCT
ap-5063	170	8	are	be	AUX
ap-5063	170	9	the	the	DET
ap-5063	170	10	solutions	solution	NOUN
ap-5063	170	11	of	of	ADP
ap-5063	170	12	helmholtz	helmholtz	NOUN
ap-5063	170	13	equation	equation	NOUN
ap-5063	170	14	(	(	PUNCT
ap-5063	170	15	1	1	X
ap-5063	170	16	)	)	PUNCT
ap-5063	170	17	in	in	ADP
ap-5063	170	18	the	the	DET
ap-5063	170	19	form	form	NOUN
ap-5063	170	20	(	(	PUNCT
ap-5063	170	21	3	3	NUM
ap-5063	170	22	)	)	PUNCT
ap-5063	170	23	in	in	ADP
ap-5063	170	24	1d	1d	NUM
ap-5063	170	25	case	case	NOUN
ap-5063	170	26	.	.	PUNCT
ap-5063	171	1	for	for	ADP
ap-5063	171	2	group	group	NOUN
ap-5063	171	3	b3	b3	PROPN
ap-5063	171	4	the	the	DET
ap-5063	171	5	functions	function	NOUN
ap-5063	171	6	cand	cand	PROPN
ap-5063	171	7	slare	slare	VERB
ap-5063	171	8	real	real	ADV
ap-5063	171	9	valued	value	VERB
ap-5063	171	10	and	and	CCONJ
ap-5063	171	11	sand	sand	NOUN
ap-5063	171	12	ss	ss	NOUN
ap-5063	171	13	are	be	AUX
ap-5063	171	14	purely	purely	ADV
ap-5063	171	15	imaginary	imaginary	ADJ
ap-5063	171	16	.	.	PUNCT
ap-5063	172	1	in	in	ADP
ap-5063	172	2	the	the	DET
ap-5063	172	3	case	case	NOUN
ap-5063	172	4	of	of	ADP
ap-5063	172	5	c3	c3	PROPN
ap-5063	172	6	,	,	PUNCT
ap-5063	172	7	the	the	DET
ap-5063	172	8	functions	function	NOUN
ap-5063	172	9	cand	cand	PROPN
ap-5063	172	10	ssare	ssare	VERB
ap-5063	172	11	real	real	ADV
ap-5063	172	12	valued	value	VERB
ap-5063	172	13	and	and	CCONJ
ap-5063	172	14	sand	sand	NOUN
ap-5063	172	15	sl	sl	NOUN
ap-5063	172	16	are	be	AUX
ap-5063	172	17	purely	purely	ADV
ap-5063	172	18	imaginary	imaginary	ADJ
ap-5063	172	19	.	.	PUNCT
ap-5063	173	1	the	the	DET
ap-5063	173	2	normal	normal	ADJ
ap-5063	173	3	vectors	vector	NOUN
ap-5063	173	4	shown	show	VERB
ap-5063	173	5	on	on	ADP
ap-5063	173	6	fig	fig	NOUN
ap-5063	173	7	.	.	PUNCT
ap-5063	173	8	2	2	NUM
ap-5063	173	9	are	be	AUX
ap-5063	173	10	b3	b3	NOUN
ap-5063	173	11	:	:	PUNCT
ap-5063	173	12	c3	c3	NOUN
ap-5063	173	13	:	:	PUNCT
ap-5063	173	14	n1	n1	PROPN
ap-5063	173	15	=	=	SYM
ap-5063	173	16	{	{	PUNCT
ap-5063	173	17	−	−	PROPN
ap-5063	173	18	1√	1√	PROPN
ap-5063	173	19	2	2	NUM
ap-5063	173	20	,	,	PUNCT
ap-5063	173	21	1√	1√	PROPN
ap-5063	173	22	2	2	NUM
ap-5063	173	23	,	,	PUNCT
ap-5063	173	24	0	0	NUM
ap-5063	173	25	}	}	PUNCT
ap-5063	173	26	,	,	PUNCT
ap-5063	173	27	n1	n1	PROPN
ap-5063	173	28	=	=	SYM
ap-5063	173	29	{	{	PUNCT
ap-5063	173	30	0	0	NUM
ap-5063	173	31	,	,	PUNCT
ap-5063	173	32	0	0	NUM
ap-5063	173	33	,	,	PUNCT
ap-5063	173	34	1	1	NUM
ap-5063	173	35	}	}	PUNCT
ap-5063	173	36	,	,	PUNCT
ap-5063	173	37	n2	n2	NOUN
ap-5063	173	38	=	=	PUNCT
ap-5063	173	39	{	{	PUNCT
ap-5063	173	40	0,−	0,−	NUM
ap-5063	173	41	1√	1√	PROPN
ap-5063	173	42	2	2	NUM
ap-5063	173	43	,	,	PUNCT
ap-5063	173	44	1√	1√	NOUN
ap-5063	173	45	2	2	NUM
ap-5063	173	46	}	}	PUNCT
ap-5063	173	47	,	,	PUNCT
ap-5063	173	48	n2	n2	NOUN
ap-5063	173	49	=	=	PUNCT
ap-5063	173	50	{	{	PUNCT
ap-5063	173	51	0	0	NUM
ap-5063	173	52	,	,	PUNCT
ap-5063	173	53	1√	1√	PROPN
ap-5063	173	54	2	2	NUM
ap-5063	173	55	,	,	PUNCT
ap-5063	173	56	−	−	PROPN
ap-5063	173	57	1√	1√	PROPN
ap-5063	173	58	2	2	NUM
ap-5063	173	59	}	}	PUNCT
ap-5063	173	60	,	,	PUNCT
ap-5063	173	61	n3	n3	NOUN
ap-5063	173	62	=	=	SYM
ap-5063	173	63	{	{	PUNCT
ap-5063	173	64	0	0	NUM
ap-5063	173	65	,	,	PUNCT
ap-5063	173	66	0,−1	0,−1	PRON
ap-5063	173	67	}	}	PUNCT
ap-5063	173	68	,	,	PUNCT
ap-5063	173	69	n3	n3	NOUN
ap-5063	173	70	=	=	SYM
ap-5063	173	71	{	{	PUNCT
ap-5063	173	72	1√	1√	PROPN
ap-5063	173	73	2	2	NUM
ap-5063	173	74	,	,	PUNCT
ap-5063	173	75	−	−	PROPN
ap-5063	173	76	1√	1√	PROPN
ap-5063	173	77	2	2	NUM
ap-5063	173	78	,	,	PUNCT
ap-5063	173	79	0	0	NUM
ap-5063	173	80	}	}	PUNCT
ap-5063	173	81	,	,	PUNCT
ap-5063	173	82	n4	n4	PROPN
ap-5063	173	83	=	=	PUNCT
ap-5063	173	84	{	{	PUNCT
ap-5063	173	85	1√	1√	PROPN
ap-5063	173	86	2	2	NUM
ap-5063	173	87	,	,	PUNCT
ap-5063	173	88	1√	1√	PROPN
ap-5063	173	89	2	2	NUM
ap-5063	173	90	,	,	PUNCT
ap-5063	173	91	0	0	NUM
ap-5063	173	92	}	}	PUNCT
ap-5063	173	93	,	,	PUNCT
ap-5063	173	94	n4	n4	PROPN
ap-5063	173	95	=	=	PUNCT
ap-5063	173	96	{	{	PUNCT
ap-5063	173	97	1	1	NUM
ap-5063	173	98	,	,	PUNCT
ap-5063	173	99	0	0	NUM
ap-5063	173	100	,	,	PUNCT
ap-5063	173	101	0	0	NUM
ap-5063	173	102	}	}	PUNCT
ap-5063	173	103	.	.	PUNCT
ap-5063	174	1	405	405	NUM
ap-5063	174	2	marzena	marzena	PROPN
ap-5063	174	3	szajewska	szajewska	NOUN
ap-5063	174	4	,	,	PUNCT
ap-5063	174	5	agnieszka	agnieszka	PROPN
ap-5063	174	6	tereszkiewicz	tereszkiewicz	PROPN
ap-5063	174	7	acta	acta	PROPN
ap-5063	174	8	polytechnica	polytechnica	PROPN
ap-5063	174	9	figure	figure	NOUN
ap-5063	174	10	2	2	NUM
ap-5063	174	11	.	.	X
ap-5063	174	12	normal	normal	ADJ
ap-5063	174	13	vectors	vector	NOUN
ap-5063	174	14	for	for	ADP
ap-5063	174	15	b3	b3	PROPN
ap-5063	174	16	and	and	CCONJ
ap-5063	174	17	c3	c3	PROPN
ap-5063	174	18	.	.	PUNCT
ap-5063	175	1	in	in	ADP
ap-5063	175	2	the	the	DET
ap-5063	175	3	case	case	NOUN
ap-5063	175	4	of	of	ADP
ap-5063	175	5	b3	b3	PROPN
ap-5063	175	6	group	group	NOUN
ap-5063	175	7	normal	normal	ADJ
ap-5063	175	8	vector	vector	NOUN
ap-5063	175	9	n4	n4	PROPN
ap-5063	175	10	is	be	AUX
ap-5063	175	11	perpendicular	perpendicular	ADJ
ap-5063	175	12	to	to	ADP
ap-5063	175	13	the	the	DET
ap-5063	175	14	short	short	ADJ
ap-5063	175	15	simple	simple	ADJ
ap-5063	175	16	root	root	NOUN
ap-5063	175	17	.	.	PUNCT
ap-5063	176	1	the	the	DET
ap-5063	176	2	rest	rest	NOUN
ap-5063	176	3	of	of	ADP
ap-5063	176	4	them	they	PRON
ap-5063	176	5	,	,	PUNCT
ap-5063	176	6	namely	namely	ADV
ap-5063	176	7	n1	n1	NOUN
ap-5063	176	8	,	,	PUNCT
ap-5063	176	9	n2	n2	NOUN
ap-5063	176	10	,	,	PUNCT
ap-5063	176	11	n3	n3	NOUN
ap-5063	176	12	are	be	AUX
ap-5063	176	13	perpendicular	perpendicular	ADJ
ap-5063	176	14	to	to	ADP
ap-5063	176	15	the	the	DET
ap-5063	176	16	long	long	ADJ
ap-5063	176	17	simple	simple	ADJ
ap-5063	176	18	roots	root	NOUN
ap-5063	176	19	.	.	PUNCT
ap-5063	177	1	so	so	ADV
ap-5063	177	2	the	the	DET
ap-5063	177	3	boundaries	boundary	NOUN
ap-5063	177	4	that	that	PRON
ap-5063	177	5	correspond	correspond	VERB
ap-5063	177	6	to	to	ADP
ap-5063	177	7	normal	normal	ADJ
ap-5063	177	8	vectors	vector	NOUN
ap-5063	177	9	are	be	AUX
ap-5063	177	10	∂fs	∂fs	PROPN
ap-5063	177	11	for	for	ADP
ap-5063	177	12	n1	n1	NOUN
ap-5063	177	13	and	and	CCONJ
ap-5063	177	14	∂fl	∂fl	VERB
ap-5063	177	15	for	for	ADP
ap-5063	177	16	the	the	DET
ap-5063	177	17	others	other	NOUN
ap-5063	177	18	.	.	PUNCT
ap-5063	178	1	the	the	DET
ap-5063	178	2	values	value	NOUN
ap-5063	178	3	of	of	ADP
ap-5063	178	4	the	the	DET
ap-5063	178	5	functions	function	NOUN
ap-5063	178	6	on	on	ADP
ap-5063	178	7	the	the	DET
ap-5063	178	8	boundaries	boundary	NOUN
ap-5063	178	9	are	be	AUX
ap-5063	178	10	summarized	summarize	VERB
ap-5063	178	11	in	in	ADP
ap-5063	178	12	the	the	DET
ap-5063	178	13	appendix	appendix	NOUN
ap-5063	178	14	in	in	ADP
ap-5063	178	15	tab	tab	NOUN
ap-5063	178	16	.	.	PUNCT
ap-5063	179	1	2	2	X
ap-5063	179	2	.	.	X
ap-5063	179	3	in	in	ADP
ap-5063	179	4	the	the	DET
ap-5063	179	5	case	case	NOUN
ap-5063	179	6	of	of	ADP
ap-5063	179	7	c3	c3	PROPN
ap-5063	179	8	it	it	PRON
ap-5063	179	9	is	be	AUX
ap-5063	179	10	a	a	DET
ap-5063	179	11	little	little	ADJ
ap-5063	179	12	bit	bit	NOUN
ap-5063	179	13	different	different	ADJ
ap-5063	179	14	,	,	PUNCT
ap-5063	179	15	the	the	DET
ap-5063	179	16	normal	normal	ADJ
ap-5063	179	17	vectors	vector	NOUN
ap-5063	179	18	n2	n2	ADJ
ap-5063	179	19	,	,	PUNCT
ap-5063	179	20	n3	n3	PROPN
ap-5063	179	21	are	be	AUX
ap-5063	179	22	perpendicular	perpendicular	ADJ
ap-5063	179	23	to	to	ADP
ap-5063	179	24	the	the	DET
ap-5063	179	25	short	short	ADJ
ap-5063	179	26	simple	simple	ADJ
ap-5063	179	27	roots	root	NOUN
ap-5063	179	28	and	and	CCONJ
ap-5063	179	29	n1	n1	NOUN
ap-5063	179	30	,	,	PUNCT
ap-5063	179	31	n4	n4	PROPN
ap-5063	179	32	to	to	ADP
ap-5063	179	33	the	the	DET
ap-5063	179	34	long	long	ADJ
ap-5063	179	35	simple	simple	ADJ
ap-5063	179	36	roots	root	NOUN
ap-5063	179	37	.	.	PUNCT
ap-5063	180	1	the	the	DET
ap-5063	180	2	values	value	NOUN
ap-5063	180	3	of	of	ADP
ap-5063	180	4	the	the	DET
ap-5063	180	5	functions	function	NOUN
ap-5063	180	6	on	on	ADP
ap-5063	180	7	the	the	DET
ap-5063	180	8	boundaries	boundary	NOUN
ap-5063	180	9	are	be	AUX
ap-5063	180	10	given	give	VERB
ap-5063	180	11	in	in	ADP
ap-5063	180	12	the	the	DET
ap-5063	180	13	appendix	appendix	NOUN
ap-5063	180	14	in	in	ADP
ap-5063	180	15	tab	tab	NOUN
ap-5063	180	16	.	.	PUNCT
ap-5063	181	1	3	3	NUM
ap-5063	181	2	.	.	X
ap-5063	181	3	5.2	5.2	NUM
ap-5063	181	4	.	.	PUNCT
ap-5063	182	1	c2	c2	PROPN
ap-5063	182	2	×	×	PROPN
ap-5063	182	3	a1	a1	NOUN
ap-5063	182	4	and	and	CCONJ
ap-5063	182	5	g2	g2	PROPN
ap-5063	182	6	×	×	NOUN
ap-5063	182	7	a1	a1	NOUN
ap-5063	182	8	groups	group	NOUN
ap-5063	182	9	the	the	DET
ap-5063	182	10	α	α	NUM
ap-5063	182	11	-	-	PUNCT
ap-5063	182	12	basis	basis	NOUN
ap-5063	182	13	vectors	vector	NOUN
ap-5063	182	14	in	in	ADP
ap-5063	182	15	cartesian	cartesian	ADJ
ap-5063	182	16	coordinates	coordinate	NOUN
ap-5063	182	17	have	have	VERB
ap-5063	182	18	the	the	DET
ap-5063	182	19	form	form	NOUN
ap-5063	182	20	c2	c2	PROPN
ap-5063	182	21	×a1	×a1	PROPN
ap-5063	182	22	:	:	PUNCT
ap-5063	182	23	g2	g2	PROPN
ap-5063	182	24	×a1	×a1	PROPN
ap-5063	182	25	:	:	PUNCT
ap-5063	182	26	α1	α1	NOUN
ap-5063	182	27	:	:	PUNCT
ap-5063	182	28	=	=	SYM
ap-5063	182	29	1√	1√	NUM
ap-5063	182	30	2	2	NUM
ap-5063	182	31	(	(	PUNCT
ap-5063	182	32	1,−1	1,−1	NUM
ap-5063	182	33	,	,	PUNCT
ap-5063	182	34	0)e	0)e	NOUN
ap-5063	182	35	,	,	PUNCT
ap-5063	182	36	α1	α1	PROPN
ap-5063	182	37	:	:	PUNCT
ap-5063	182	38	=	=	SYM
ap-5063	182	39	(	(	PUNCT
ap-5063	182	40	√	√	NUM
ap-5063	182	41	2	2	NUM
ap-5063	182	42	,	,	PUNCT
ap-5063	182	43	0	0	NUM
ap-5063	182	44	,	,	PUNCT
ap-5063	182	45	0)e	0)e	NOUN
ap-5063	182	46	,	,	PUNCT
ap-5063	182	47	α2	α2	ADJ
ap-5063	182	48	:	:	PUNCT
ap-5063	182	49	=	=	SYM
ap-5063	182	50	2√	2√	NUM
ap-5063	182	51	2	2	NUM
ap-5063	182	52	(	(	PUNCT
ap-5063	182	53	0	0	NUM
ap-5063	182	54	,	,	PUNCT
ap-5063	182	55	2	2	NUM
ap-5063	182	56	,	,	PUNCT
ap-5063	182	57	0)e	0)e	NOUN
ap-5063	182	58	,	,	PUNCT
ap-5063	182	59	α2	α2	ADJ
ap-5063	182	60	:	:	PUNCT
ap-5063	182	61	=	=	SYM
ap-5063	182	62	(	(	PUNCT
ap-5063	182	63	−	−	PROPN
ap-5063	182	64	1√	1√	PROPN
ap-5063	182	65	2	2	NUM
ap-5063	182	66	,	,	PUNCT
ap-5063	182	67	1√	1√	PROPN
ap-5063	182	68	6	6	NUM
ap-5063	182	69	,	,	PUNCT
ap-5063	182	70	0	0	NUM
ap-5063	182	71	)	)	PUNCT
ap-5063	183	1	e	e	NOUN
ap-5063	183	2	,	,	PUNCT
ap-5063	183	3	α3	α3	INTJ
ap-5063	183	4	:	:	PUNCT
ap-5063	183	5	=	=	SYM
ap-5063	183	6	1√	1√	NUM
ap-5063	183	7	2	2	NUM
ap-5063	183	8	(	(	PUNCT
ap-5063	183	9	0	0	NUM
ap-5063	183	10	,	,	PUNCT
ap-5063	183	11	0	0	NUM
ap-5063	183	12	,	,	PUNCT
ap-5063	183	13	2)e	2)e	NUM
ap-5063	183	14	,	,	PUNCT
ap-5063	183	15	α3	α3	NOUN
ap-5063	183	16	:	:	PUNCT
ap-5063	183	17	=	=	SYM
ap-5063	183	18	1√	1√	NUM
ap-5063	183	19	2	2	NUM
ap-5063	183	20	(	(	PUNCT
ap-5063	183	21	0	0	NUM
ap-5063	183	22	,	,	PUNCT
ap-5063	183	23	0	0	NUM
ap-5063	183	24	,	,	PUNCT
ap-5063	183	25	2)e	2)e	NUM
ap-5063	183	26	.	.	PUNCT
ap-5063	184	1	the	the	DET
ap-5063	184	2	vertices	vertex	NOUN
ap-5063	184	3	of	of	ADP
ap-5063	184	4	the	the	DET
ap-5063	184	5	fundamental	fundamental	ADJ
ap-5063	184	6	regions	region	NOUN
ap-5063	184	7	f	f	PROPN
ap-5063	184	8	for	for	ADP
ap-5063	184	9	c2	c2	PROPN
ap-5063	184	10	×	×	PROPN
ap-5063	184	11	a1	a1	PROPN
ap-5063	184	12	,	,	PUNCT
ap-5063	184	13	g2×a1	g2×a1	NOUN
ap-5063	184	14	groups	group	NOUN
ap-5063	184	15	,	,	PUNCT
ap-5063	184	16	shown	show	VERB
ap-5063	184	17	in	in	ADP
ap-5063	184	18	fig	fig	NOUN
ap-5063	184	19	.	.	PUNCT
ap-5063	185	1	3	3	NUM
ap-5063	185	2	,	,	PUNCT
ap-5063	185	3	written	write	VERB
ap-5063	185	4	in	in	ADP
ap-5063	185	5	ω	ω	VERB
ap-5063	185	6	-	-	PUNCT
ap-5063	185	7	basis	basis	NOUN
ap-5063	185	8	are	be	AUX
ap-5063	186	1	fc2×a1	fc2×a1	ADV
ap-5063	186	2	=	=	PUNCT
ap-5063	186	3	{	{	PUNCT
ap-5063	186	4	0	0	NUM
ap-5063	186	5	,	,	PUNCT
ap-5063	186	6	ω1	ω1	PROPN
ap-5063	186	7	,	,	PUNCT
ap-5063	186	8	ω2	ω2	ADJ
ap-5063	186	9	,	,	PUNCT
ap-5063	186	10	ω3	ω3	NOUN
ap-5063	186	11	,	,	PUNCT
ap-5063	186	12	ω1	ω1	PROPN
ap-5063	186	13	+	+	CCONJ
ap-5063	186	14	ω3	ω3	PROPN
ap-5063	186	15	,	,	PUNCT
ap-5063	186	16	ω2	ω2	ADJ
ap-5063	186	17	+	+	CCONJ
ap-5063	186	18	ω3	ω3	NOUN
ap-5063	186	19	}	}	PUNCT
ap-5063	186	20	,	,	PUNCT
ap-5063	186	21	fg2×a1	fg2×a1	PROPN
ap-5063	186	22	=	=	PUNCT
ap-5063	186	23	{	{	PUNCT
ap-5063	186	24	0	0	NUM
ap-5063	186	25	,	,	PUNCT
ap-5063	186	26	1	1	NUM
ap-5063	186	27	2ω1	2ω1	NUM
ap-5063	186	28	,	,	PUNCT
ap-5063	186	29	ω2	ω2	ADJ
ap-5063	186	30	,	,	PUNCT
ap-5063	186	31	ω3	ω3	NOUN
ap-5063	186	32	,	,	PUNCT
ap-5063	186	33	1	1	NUM
ap-5063	186	34	2ω1	2ω1	NUM
ap-5063	186	35	+	+	CCONJ
ap-5063	186	36	ω3	ω3	ADJ
ap-5063	186	37	,	,	PUNCT
ap-5063	186	38	ω2	ω2	ADJ
ap-5063	186	39	+	+	CCONJ
ap-5063	186	40	ω3	ω3	NOUN
ap-5063	186	41	}	}	PUNCT
ap-5063	186	42	.	.	PUNCT
ap-5063	187	1	figure	figure	VERB
ap-5063	187	2	3	3	NUM
ap-5063	187	3	.	.	PUNCT
ap-5063	188	1	the	the	DET
ap-5063	188	2	fundamental	fundamental	ADJ
ap-5063	188	3	region	region	NOUN
ap-5063	188	4	f	f	PROPN
ap-5063	188	5	for	for	ADP
ap-5063	188	6	c2	c2	PROPN
ap-5063	188	7	×a1	×a1	PROPN
ap-5063	188	8	and	and	CCONJ
ap-5063	188	9	g2	g2	PROPN
ap-5063	188	10	×	×	PROPN
ap-5063	188	11	a1	a1	NOUN
ap-5063	188	12	group	group	NOUN
ap-5063	188	13	.	.	PUNCT
ap-5063	189	1	the	the	DET
ap-5063	189	2	groups	group	NOUN
ap-5063	189	3	c2	c2	PROPN
ap-5063	189	4	×a1	×a1	PROPN
ap-5063	189	5	,	,	PUNCT
ap-5063	189	6	g2	g2	PROPN
ap-5063	189	7	×a1	×a1	PROPN
ap-5063	189	8	can	can	AUX
ap-5063	189	9	be	be	AUX
ap-5063	189	10	reduced	reduce	VERB
ap-5063	189	11	to	to	ADP
ap-5063	189	12	a	a	DET
ap-5063	189	13	subgroup	subgroup	NOUN
ap-5063	189	14	a1×a1×a1	a1×a1×a1	NOUN
ap-5063	189	15	using	use	VERB
ap-5063	189	16	a	a	DET
ap-5063	189	17	branching	branch	VERB
ap-5063	189	18	rule	rule	NOUN
ap-5063	189	19	method	method	NOUN
ap-5063	189	20	described	describe	VERB
ap-5063	189	21	in	in	ADP
ap-5063	189	22	[	[	X
ap-5063	189	23	19	19	NUM
ap-5063	189	24	,	,	PUNCT
ap-5063	189	25	24	24	NUM
ap-5063	189	26	]	]	PUNCT
ap-5063	189	27	.	.	PUNCT
ap-5063	190	1	the	the	DET
ap-5063	190	2	projection	projection	NOUN
ap-5063	190	3	matrices	matrix	NOUN
ap-5063	190	4	and	and	CCONJ
ap-5063	190	5	the	the	DET
ap-5063	190	6	branching	branch	VERB
ap-5063	190	7	rules	rule	NOUN
ap-5063	190	8	are	be	AUX
ap-5063	190	9	pc2×a1	pc2×a1	ADJ
ap-5063	190	10	=	=	PUNCT
ap-5063	190	11	1	1	PROPN
ap-5063	190	12	1	1	NUM
ap-5063	190	13	0	0	NUM
ap-5063	190	14	0	0	NUM
ap-5063	190	15	1	1	NUM
ap-5063	190	16	0	0	NUM
ap-5063	190	17	0	0	NUM
ap-5063	190	18	0	0	NUM
ap-5063	190	19	1	1	NUM
ap-5063	190	20			PROPN
ap-5063	190	21	,	,	PUNCT
ap-5063	190	22	pg2×a1	pg2×a1	PROPN
ap-5063	190	23	=	=	PUNCT
ap-5063	190	24	1	1	PROPN
ap-5063	190	25	1	1	NUM
ap-5063	190	26	0	0	NUM
ap-5063	190	27	3	3	NUM
ap-5063	190	28	1	1	NUM
ap-5063	190	29	0	0	NUM
ap-5063	190	30	0	0	NUM
ap-5063	190	31	0	0	NUM
ap-5063	190	32	1	1	NUM
ap-5063	190	33			PROPN
ap-5063	190	34	,	,	PUNCT
ap-5063	190	35	o(a	o(a	PROPN
ap-5063	190	36	,	,	PUNCT
ap-5063	190	37	b)o(c	b)o(c	NOUN
ap-5063	190	38	)	)	PUNCT
ap-5063	190	39	pc2×a1−−−−−→	pc2×a1−−−−−→	NOUN
ap-5063	190	40	o(a+b)o(b)o(c	o(a+b)o(b)o(c	VERB
ap-5063	190	41	)	)	PUNCT
ap-5063	190	42	∪o(b)o(a+b)o(c	∪o(b)o(a+b)o(c	NOUN
ap-5063	190	43	)	)	PUNCT
ap-5063	190	44	,	,	PUNCT
ap-5063	190	45	o(a	o(a	PROPN
ap-5063	190	46	,	,	PUNCT
ap-5063	190	47	b)o(c	b)o(c	ADV
ap-5063	190	48	)	)	PUNCT
ap-5063	190	49	pg2×a1−−−−−→	pg2×a1−−−−−→	NOUN
ap-5063	190	50	o(a+b)o(3a+b)o(c	o(a+b)o(3a+b)o(c	ADV
ap-5063	190	51	)	)	PUNCT
ap-5063	190	52	∪o(2a+b)o(b)o(c	∪o(2a+b)o(b)o(c	PROPN
ap-5063	190	53	)	)	PUNCT
ap-5063	190	54	∪o(a)o(3a+2b)o(c	∪o(a)o(3a+2b)o(c	NUM
ap-5063	190	55	)	)	PUNCT
ap-5063	190	56	.	.	PUNCT
ap-5063	191	1	the	the	DET
ap-5063	191	2	separation	separation	NOUN
ap-5063	191	3	constants	constant	NOUN
ap-5063	191	4	for	for	ADP
ap-5063	191	5	c2	c2	PROPN
ap-5063	191	6	×a1	×a1	PROPN
ap-5063	191	7	are	be	AUX
ap-5063	191	8	−k2	−k2	PROPN
ap-5063	191	9	1	1	NUM
ap-5063	191	10	=	=	SYM
ap-5063	191	11	−π2(a+b)2	−π2(a+b)2	NUM
ap-5063	191	12	,	,	PUNCT
ap-5063	191	13	−k2	−k2	PROPN
ap-5063	191	14	2	2	NUM
ap-5063	191	15	=	=	SYM
ap-5063	191	16	−π2b2	−π2b2	NOUN
ap-5063	191	17	,	,	PUNCT
ap-5063	191	18	−k2	−k2	PROPN
ap-5063	191	19	3	3	NUM
ap-5063	191	20	=	=	SYM
ap-5063	191	21	−π2c2	−π2c2	PROPN
ap-5063	191	22	,	,	PUNCT
ap-5063	191	23	(	(	PUNCT
ap-5063	191	24	8)	8)	NUM
ap-5063	191	25	where	where	SCONJ
ap-5063	191	26	w2	w2	NOUN
ap-5063	191	27	=	=	PROPN
ap-5063	191	28	4π2(a2	4π2(a2	PROPN
ap-5063	191	29	+	+	NUM
ap-5063	191	30	ab+	ab+	NOUN
ap-5063	191	31	b2	b2	NOUN
ap-5063	191	32	+	+	CCONJ
ap-5063	191	33	1	1	NUM
ap-5063	191	34	2c	2c	NUM
ap-5063	191	35	2	2	NUM
ap-5063	191	36	)	)	PUNCT
ap-5063	191	37	and	and	CCONJ
ap-5063	191	38	for	for	ADP
ap-5063	191	39	g2	g2	PROPN
ap-5063	191	40	×a1	×a1	ADP
ap-5063	191	41	equal	equal	ADJ
ap-5063	191	42	−k2	−k2	ADJ
ap-5063	191	43	1	1	NUM
ap-5063	191	44	=	=	SYM
ap-5063	191	45	−2π2(2a+	−2π2(2a+	NOUN
ap-5063	191	46	b)2	b)2	ADJ
ap-5063	191	47	,	,	PUNCT
ap-5063	191	48	−l21	−l21	PRON
ap-5063	191	49	=	=	PUNCT
ap-5063	191	50	−2π2(a+	−2π2(a+	PROPN
ap-5063	191	51	b)2	b)2	ADJ
ap-5063	191	52	,	,	PUNCT
ap-5063	191	53	−k2	−k2	PROPN
ap-5063	191	54	2	2	NUM
ap-5063	191	55	=	=	SYM
ap-5063	191	56	−	−	PROPN
ap-5063	191	57	2	2	NUM
ap-5063	191	58	3π	3π	NOUN
ap-5063	191	59	2b2	2b2	NUM
ap-5063	191	60	,	,	PUNCT
ap-5063	191	61	−l22	−l22	X
ap-5063	191	62	=	=	SYM
ap-5063	191	63	−	−	PROPN
ap-5063	191	64	2	2	NUM
ap-5063	191	65	3π	3π	NOUN
ap-5063	191	66	2(3a+	2(3a+	NUM
ap-5063	191	67	b)2	b)2	ADJ
ap-5063	191	68	,	,	PUNCT
ap-5063	191	69	−k2	−k2	PROPN
ap-5063	191	70	3	3	NUM
ap-5063	191	71	=	=	SYM
ap-5063	191	72	−2π2c2	−2π2c2	PROPN
ap-5063	191	73	,	,	PUNCT
ap-5063	191	74	−l23	−l23	NOUN
ap-5063	191	75	=	=	SYM
ap-5063	191	76	−2π2c2	−2π2c2	PROPN
ap-5063	191	77	,	,	PUNCT
ap-5063	191	78	−m2	−m2	NOUN
ap-5063	191	79	1	1	NUM
ap-5063	191	80	=	=	SYM
ap-5063	191	81	−2π2a2	−2π2a2	PROPN
ap-5063	191	82	,	,	PUNCT
ap-5063	191	83	−m2	−m2	NOUN
ap-5063	191	84	2	2	NUM
ap-5063	191	85	=	=	SYM
ap-5063	191	86	−	−	PROPN
ap-5063	191	87	2	2	NUM
ap-5063	191	88	3π	3π	NOUN
ap-5063	191	89	2(3a+	2(3a+	NUM
ap-5063	191	90	2b)2	2b)2	NUM
ap-5063	191	91	,	,	PUNCT
ap-5063	191	92	−m2	−m2	NOUN
ap-5063	191	93	3	3	NUM
ap-5063	191	94	=	=	SYM
ap-5063	191	95	−2π2c2	−2π2c2	PROPN
ap-5063	191	96	,	,	PUNCT
ap-5063	191	97	(	(	PUNCT
ap-5063	191	98	9	9	X
ap-5063	191	99	)	)	PUNCT
ap-5063	191	100	where	where	SCONJ
ap-5063	191	101	w2	w2	NOUN
ap-5063	191	102	=	=	PROPN
ap-5063	191	103	4π2(2a2	4π2(2a2	PROPN
ap-5063	192	1	+	+	CCONJ
ap-5063	192	2	2ab+	2ab+	NUM
ap-5063	192	3	2	2	NUM
ap-5063	192	4	3b	3b	NOUN
ap-5063	192	5	2	2	NUM
ap-5063	192	6	+	+	CCONJ
ap-5063	192	7	1	1	NUM
ap-5063	192	8	2c	2c	NUM
ap-5063	192	9	2	2	NUM
ap-5063	192	10	)	)	PUNCT
ap-5063	192	11	.	.	PUNCT
ap-5063	193	1	the	the	DET
ap-5063	193	2	explicit	explicit	ADJ
ap-5063	193	3	forms	form	NOUN
ap-5063	193	4	of	of	ADP
ap-5063	193	5	orbit	orbit	NOUN
ap-5063	193	6	functions	function	NOUN
ap-5063	193	7	are	be	AUX
ap-5063	193	8	c2	c2	PROPN
ap-5063	193	9	×a1	×a1	PROPN
ap-5063	193	10	:	:	PUNCT
ap-5063	193	11	ca	ca	PROPN
ap-5063	193	12	,	,	PUNCT
ap-5063	193	13	b	b	NOUN
ap-5063	193	14	,	,	PUNCT
ap-5063	193	15	c(x	c(x	NOUN
ap-5063	193	16	)	)	PUNCT
ap-5063	193	17	=	=	PUNCT
ap-5063	193	18	ca+b(x1)cb(x2)cc(x3	ca+b(x1)cb(x2)cc(x3	X
ap-5063	193	19	)	)	PUNCT
ap-5063	194	1	+	+	CCONJ
ap-5063	194	2	cb(x1)ca+b(x2)cc(x3	cb(x1)ca+b(x2)cc(x3	NUM
ap-5063	194	3	)	)	PUNCT
ap-5063	194	4	,	,	PUNCT
ap-5063	194	5	ssa	ssa	NOUN
ap-5063	194	6	,	,	PUNCT
ap-5063	194	7	b	b	NOUN
ap-5063	194	8	,	,	PUNCT
ap-5063	194	9	c(x	c(x	NOUN
ap-5063	194	10	)	)	PUNCT
ap-5063	194	11	=	=	PUNCT
ap-5063	194	12	ca+b(x1)cb(x2)cc(x3	ca+b(x1)cb(x2)cc(x3	X
ap-5063	194	13	)	)	PUNCT
ap-5063	194	14	−	−	PROPN
ap-5063	195	1	cb(x1)ca+b(x2)cc(x3	cb(x1)ca+b(x2)cc(x3	NUM
ap-5063	195	2	)	)	PUNCT
ap-5063	195	3	,	,	PUNCT
ap-5063	195	4	sa	sa	PROPN
ap-5063	195	5	,	,	PUNCT
ap-5063	195	6	b	b	NOUN
ap-5063	195	7	,	,	PUNCT
ap-5063	195	8	c(x	c(x	NOUN
ap-5063	195	9	)	)	PUNCT
ap-5063	195	10	=	=	SYM
ap-5063	195	11	sa+b(x1)sb(x2)sc(x3	sa+b(x1)sb(x2)sc(x3	NOUN
ap-5063	195	12	)	)	PUNCT
ap-5063	196	1	−	−	PROPN
ap-5063	196	2	sb(x1)sa+b(x2)sc(x3	sb(x1)sa+b(x2)sc(x3	PROPN
ap-5063	196	3	)	)	PUNCT
ap-5063	196	4	,	,	PUNCT
ap-5063	196	5	sla	sla	PROPN
ap-5063	196	6	,	,	PUNCT
ap-5063	196	7	b	b	NOUN
ap-5063	196	8	,	,	PUNCT
ap-5063	196	9	c(x	c(x	NOUN
ap-5063	196	10	)	)	PUNCT
ap-5063	196	11	=	=	SYM
ap-5063	196	12	sa+b(x1)sb(x2)sc(x3	sa+b(x1)sb(x2)sc(x3	NOUN
ap-5063	196	13	)	)	PUNCT
ap-5063	197	1	+	+	CCONJ
ap-5063	197	2	sb(x1)sa+b(x2)sc(x3	sb(x1)sa+b(x2)sc(x3	NOUN
ap-5063	197	3	)	)	PUNCT
ap-5063	197	4	;	;	PUNCT
ap-5063	197	5	g2	g2	PROPN
ap-5063	197	6	×a1	×a1	PROPN
ap-5063	197	7	:	:	PUNCT
ap-5063	197	8	ca	ca	PROPN
ap-5063	197	9	,	,	PUNCT
ap-5063	197	10	b	b	NOUN
ap-5063	197	11	,	,	PUNCT
ap-5063	197	12	c(x	c(x	NOUN
ap-5063	197	13	)	)	PUNCT
ap-5063	197	14	=	=	SYM
ap-5063	197	15	ca(x1)c3a+2b(x2)cc(x3	ca(x1)c3a+2b(x2)cc(x3	PROPN
ap-5063	197	16	)	)	PUNCT
ap-5063	197	17	+	+	X
ap-5063	197	18	ca+b(x1)c3a+b(x2)cc(x3	ca+b(x1)c3a+b(x2)cc(x3	ADJ
ap-5063	197	19	)	)	PUNCT
ap-5063	197	20	+	+	CCONJ
ap-5063	197	21	c2a+b(x1)cb(x2)cc(x3	c2a+b(x1)cb(x2)cc(x3	NUM
ap-5063	197	22	)	)	PUNCT
ap-5063	197	23	,	,	PUNCT
ap-5063	197	24	sla	sla	PROPN
ap-5063	197	25	,	,	PUNCT
ap-5063	197	26	b	b	NOUN
ap-5063	197	27	,	,	PUNCT
ap-5063	197	28	c(x	c(x	NOUN
ap-5063	197	29	)	)	PUNCT
ap-5063	197	30	=	=	SYM
ap-5063	197	31	sa(x1)c3a+2b(x2)sc(x3	sa(x1)c3a+2b(x2)sc(x3	PROPN
ap-5063	197	32	)	)	PUNCT
ap-5063	197	33	−	−	PROPN
ap-5063	197	34	sa+b(x1)c3a+b(x2)sc(x3	sa+b(x1)c3a+b(x2)sc(x3	NOUN
ap-5063	197	35	)	)	PUNCT
ap-5063	197	36	+	+	CCONJ
ap-5063	197	37	s2a+b(x1)cb(x2)sc(x3	s2a+b(x1)cb(x2)sc(x3	NUM
ap-5063	197	38	)	)	PUNCT
ap-5063	197	39	,	,	PUNCT
ap-5063	197	40	sa	sa	PROPN
ap-5063	197	41	,	,	PUNCT
ap-5063	197	42	b	b	NOUN
ap-5063	197	43	,	,	PUNCT
ap-5063	197	44	c(x	c(x	NOUN
ap-5063	197	45	)	)	PUNCT
ap-5063	197	46	=	=	SYM
ap-5063	198	1	sa(x1)s3a+2b(x2)sc(x3	sa(x1)s3a+2b(x2)sc(x3	NOUN
ap-5063	198	2	)	)	PUNCT
ap-5063	198	3	−	−	PROPN
ap-5063	199	1	sa+b(x1)s3a+b(x2)sc(x3	sa+b(x1)s3a+b(x2)sc(x3	ADJ
ap-5063	199	2	)	)	PUNCT
ap-5063	200	1	+	+	CCONJ
ap-5063	200	2	s2a+b(x1)sb(x2)sc(x3	s2a+b(x1)sb(x2)sc(x3	NUM
ap-5063	200	3	)	)	PUNCT
ap-5063	200	4	,	,	PUNCT
ap-5063	200	5	406	406	NUM
ap-5063	200	6	vol	vol	NOUN
ap-5063	200	7	.	.	PUNCT
ap-5063	201	1	58	58	NUM
ap-5063	201	2	no	no	INTJ
ap-5063	201	3	.	.	PUNCT
ap-5063	202	1	6/2018	6/2018	NUM
ap-5063	202	2	multidimensional	multidimensional	ADJ
ap-5063	202	3	hybrid	hybrid	ADJ
ap-5063	202	4	boundary	boundary	ADJ
ap-5063	202	5	value	value	NOUN
ap-5063	202	6	problem	problem	NOUN
ap-5063	202	7	ssa	ssa	PROPN
ap-5063	202	8	,	,	PUNCT
ap-5063	202	9	b	b	NOUN
ap-5063	202	10	,	,	PUNCT
ap-5063	202	11	c(x	c(x	NOUN
ap-5063	202	12	)	)	PUNCT
ap-5063	202	13	=	=	SYM
ap-5063	202	14	ca(x1)s3a+2b(x2)cc(x3	ca(x1)s3a+2b(x2)cc(x3	PROPN
ap-5063	202	15	)	)	PUNCT
ap-5063	202	16	−	−	PROPN
ap-5063	203	1	ca+b(x1)s3a+b(x2)cc(x3	ca+b(x1)s3a+b(x2)cc(x3	ADJ
ap-5063	203	2	)	)	PUNCT
ap-5063	204	1	−	−	ADP
ap-5063	205	1	c2a+b(x1)sb(x2)cc(x3	c2a+b(x1)sb(x2)cc(x3	NUM
ap-5063	205	2	)	)	PUNCT
ap-5063	205	3	,	,	PUNCT
ap-5063	205	4	where	where	SCONJ
ap-5063	205	5	cµ(xi	cµ(xi	PROPN
ap-5063	205	6	)	)	PUNCT
ap-5063	205	7	,	,	PUNCT
ap-5063	205	8	sµ(xi	sµ(xi	PROPN
ap-5063	205	9	)	)	PUNCT
ap-5063	205	10	for	for	ADP
ap-5063	205	11	i	i	PROPN
ap-5063	205	12	=	=	SYM
ap-5063	205	13	1	1	NUM
ap-5063	205	14	,	,	PUNCT
ap-5063	205	15	2	2	NUM
ap-5063	205	16	,	,	PUNCT
ap-5063	205	17	3	3	NUM
ap-5063	205	18	are	be	AUX
ap-5063	205	19	the	the	DET
ap-5063	205	20	same	same	ADJ
ap-5063	205	21	as	as	ADP
ap-5063	205	22	in	in	ADP
ap-5063	205	23	the	the	DET
ap-5063	205	24	previous	previous	ADJ
ap-5063	205	25	cases	case	NOUN
ap-5063	205	26	.	.	PUNCT
ap-5063	206	1	for	for	SCONJ
ap-5063	206	2	group	group	NOUN
ap-5063	206	3	c2	c2	PROPN
ap-5063	206	4	×	×	PROPN
ap-5063	206	5	a1	a1	NOUN
ap-5063	206	6	the	the	DET
ap-5063	206	7	functions	function	NOUN
ap-5063	206	8	cand	cand	NOUN
ap-5063	206	9	ssare	ssare	VERB
ap-5063	206	10	real	real	ADV
ap-5063	206	11	valued	value	VERB
ap-5063	206	12	and	and	CCONJ
ap-5063	206	13	sand	sand	NOUN
ap-5063	206	14	sl	sl	NOUN
ap-5063	206	15	are	be	AUX
ap-5063	206	16	purely	purely	ADV
ap-5063	206	17	imaginary	imaginary	ADJ
ap-5063	206	18	.	.	PUNCT
ap-5063	207	1	in	in	ADP
ap-5063	207	2	the	the	DET
ap-5063	207	3	case	case	NOUN
ap-5063	207	4	of	of	ADP
ap-5063	207	5	g2×a1	g2×a1	PROPN
ap-5063	207	6	,	,	PUNCT
ap-5063	207	7	the	the	DET
ap-5063	207	8	functions	function	NOUN
ap-5063	207	9	cand	cand	NOUN
ap-5063	207	10	slare	slare	VERB
ap-5063	207	11	real	real	ADV
ap-5063	207	12	valued	value	VERB
ap-5063	207	13	and	and	CCONJ
ap-5063	207	14	sand	sand	NOUN
ap-5063	207	15	ss	ss	NOUN
ap-5063	207	16	are	be	AUX
ap-5063	207	17	purely	purely	ADV
ap-5063	207	18	imaginary	imaginary	ADJ
ap-5063	207	19	.	.	PUNCT
ap-5063	208	1	figure	figure	NOUN
ap-5063	208	2	4	4	NUM
ap-5063	208	3	.	.	X
ap-5063	208	4	normal	normal	ADJ
ap-5063	208	5	vectors	vector	NOUN
ap-5063	208	6	of	of	ADP
ap-5063	208	7	f	f	PROPN
ap-5063	208	8	for	for	ADP
ap-5063	208	9	c2	c2	PROPN
ap-5063	208	10	×	×	PROPN
ap-5063	208	11	a1	a1	NOUN
ap-5063	208	12	,	,	PUNCT
ap-5063	208	13	g2	g2	PROPN
ap-5063	208	14	×	×	NOUN
ap-5063	208	15	a1	a1	NOUN
ap-5063	208	16	groups	group	NOUN
ap-5063	208	17	.	.	PUNCT
ap-5063	209	1	the	the	DET
ap-5063	209	2	normal	normal	ADJ
ap-5063	209	3	vectors	vector	NOUN
ap-5063	209	4	shown	show	VERB
ap-5063	209	5	in	in	ADP
ap-5063	209	6	fig	fig	NOUN
ap-5063	209	7	.	.	PUNCT
ap-5063	209	8	4	4	NUM
ap-5063	209	9	are	be	AUX
ap-5063	209	10	c2	c2	PROPN
ap-5063	209	11	×a1	×a1	PROPN
ap-5063	209	12	:	:	PUNCT
ap-5063	209	13	g2	g2	PROPN
ap-5063	209	14	×a1	×a1	PROPN
ap-5063	209	15	:	:	PUNCT
ap-5063	209	16	n1	n1	PROPN
ap-5063	209	17	=	=	SYM
ap-5063	209	18	{	{	PUNCT
ap-5063	209	19	0	0	NUM
ap-5063	209	20	,	,	PUNCT
ap-5063	209	21	0,−1	0,−1	PRON
ap-5063	209	22	}	}	PUNCT
ap-5063	209	23	,	,	PUNCT
ap-5063	209	24	n1	n1	PROPN
ap-5063	209	25	=	=	SYM
ap-5063	209	26	{	{	PUNCT
ap-5063	209	27	0	0	NUM
ap-5063	209	28	,	,	PUNCT
ap-5063	209	29	0,−1	0,−1	PRON
ap-5063	209	30	}	}	PUNCT
ap-5063	209	31	,	,	PUNCT
ap-5063	209	32	n2	n2	NOUN
ap-5063	209	33	=	=	PUNCT
ap-5063	209	34	{	{	PUNCT
ap-5063	209	35	0,−1	0,−1	PROPN
ap-5063	209	36	,	,	PUNCT
ap-5063	209	37	0	0	NUM
ap-5063	209	38	}	}	PUNCT
ap-5063	209	39	,	,	PUNCT
ap-5063	209	40	n2	n2	NOUN
ap-5063	209	41	=	=	PUNCT
ap-5063	209	42	{	{	PUNCT
ap-5063	209	43	√	√	NUM
ap-5063	209	44	3	3	NUM
ap-5063	209	45	2	2	NUM
ap-5063	209	46	,	,	PUNCT
ap-5063	209	47	−	−	PROPN
ap-5063	209	48	1	1	NUM
ap-5063	209	49	2	2	NUM
ap-5063	209	50	,	,	PUNCT
ap-5063	209	51	0	0	NUM
ap-5063	209	52	}	}	PUNCT
ap-5063	209	53	,	,	PUNCT
ap-5063	209	54	n3	n3	NOUN
ap-5063	209	55	=	=	SYM
ap-5063	209	56	{	{	PUNCT
ap-5063	209	57	−	−	PROPN
ap-5063	209	58	1√	1√	PROPN
ap-5063	209	59	2	2	NUM
ap-5063	209	60	,	,	PUNCT
ap-5063	209	61	1√	1√	PROPN
ap-5063	209	62	2	2	NUM
ap-5063	209	63	,	,	PUNCT
ap-5063	209	64	0	0	NUM
ap-5063	209	65	}	}	PUNCT
ap-5063	209	66	,	,	PUNCT
ap-5063	209	67	n3	n3	NOUN
ap-5063	209	68	=	=	SYM
ap-5063	209	69	{	{	PUNCT
ap-5063	209	70	−1	−1	NOUN
ap-5063	209	71	,	,	PUNCT
ap-5063	209	72	0	0	NUM
ap-5063	209	73	,	,	PUNCT
ap-5063	209	74	0	0	NUM
ap-5063	209	75	}	}	PUNCT
ap-5063	209	76	,	,	PUNCT
ap-5063	209	77	n4	n4	PROPN
ap-5063	209	78	=	=	PUNCT
ap-5063	209	79	{	{	PUNCT
ap-5063	209	80	1	1	NUM
ap-5063	209	81	,	,	PUNCT
ap-5063	209	82	0	0	NUM
ap-5063	209	83	,	,	PUNCT
ap-5063	209	84	0	0	NUM
ap-5063	209	85	}	}	PUNCT
ap-5063	209	86	,	,	PUNCT
ap-5063	209	87	n4	n4	PROPN
ap-5063	209	88	=	=	PUNCT
ap-5063	209	89	{	{	PUNCT
ap-5063	209	90	1	1	NUM
ap-5063	209	91	2	2	NUM
ap-5063	209	92	,	,	PUNCT
ap-5063	209	93	√	√	NUM
ap-5063	209	94	3	3	NUM
ap-5063	209	95	2	2	NUM
ap-5063	209	96	,	,	PUNCT
ap-5063	209	97	0	0	NUM
ap-5063	209	98	}	}	PUNCT
ap-5063	209	99	,	,	PUNCT
ap-5063	209	100	n5	n5	PROPN
ap-5063	209	101	=	=	PUNCT
ap-5063	209	102	{	{	PUNCT
ap-5063	209	103	0	0	NUM
ap-5063	209	104	,	,	PUNCT
ap-5063	209	105	0	0	NUM
ap-5063	209	106	,	,	PUNCT
ap-5063	209	107	1	1	NUM
ap-5063	209	108	}	}	PUNCT
ap-5063	209	109	,	,	PUNCT
ap-5063	209	110	n5	n5	PROPN
ap-5063	209	111	=	=	PUNCT
ap-5063	209	112	{	{	PUNCT
ap-5063	209	113	0	0	NUM
ap-5063	209	114	,	,	PUNCT
ap-5063	209	115	0	0	NUM
ap-5063	209	116	,	,	PUNCT
ap-5063	209	117	1	1	NUM
ap-5063	209	118	}	}	PUNCT
ap-5063	209	119	.	.	PUNCT
ap-5063	210	1	in	in	ADP
ap-5063	210	2	the	the	DET
ap-5063	210	3	case	case	NOUN
ap-5063	210	4	of	of	ADP
ap-5063	210	5	c2	c2	PROPN
ap-5063	210	6	×a1	×a1	VERB
ap-5063	210	7	the	the	DET
ap-5063	210	8	group	group	NOUN
ap-5063	210	9	normal	normal	ADJ
ap-5063	210	10	vector	vector	NOUN
ap-5063	210	11	n3	n3	NOUN
ap-5063	210	12	is	be	AUX
ap-5063	210	13	perpendicular	perpendicular	ADJ
ap-5063	210	14	to	to	ADP
ap-5063	210	15	the	the	DET
ap-5063	210	16	short	short	ADJ
ap-5063	210	17	simple	simple	ADJ
ap-5063	210	18	root	root	NOUN
ap-5063	210	19	.	.	PUNCT
ap-5063	211	1	the	the	DET
ap-5063	211	2	rest	rest	NOUN
ap-5063	211	3	of	of	ADP
ap-5063	211	4	them	they	PRON
ap-5063	211	5	,	,	PUNCT
ap-5063	211	6	namely	namely	ADV
ap-5063	211	7	n1	n1	NOUN
ap-5063	211	8	,	,	PUNCT
ap-5063	211	9	n2	n2	NOUN
ap-5063	211	10	,	,	PUNCT
ap-5063	211	11	n4	n4	PROPN
ap-5063	211	12	,	,	PUNCT
ap-5063	211	13	n5	n5	PROPN
ap-5063	211	14	are	be	AUX
ap-5063	211	15	perpendicular	perpendicular	ADJ
ap-5063	211	16	to	to	ADP
ap-5063	211	17	the	the	DET
ap-5063	211	18	long	long	ADJ
ap-5063	211	19	simple	simple	ADJ
ap-5063	211	20	roots	root	NOUN
ap-5063	211	21	.	.	PUNCT
ap-5063	212	1	so	so	ADV
ap-5063	212	2	the	the	DET
ap-5063	212	3	boundaries	boundary	NOUN
ap-5063	212	4	that	that	PRON
ap-5063	212	5	correspond	correspond	VERB
ap-5063	212	6	to	to	ADP
ap-5063	212	7	normal	normal	ADJ
ap-5063	212	8	vectors	vector	NOUN
ap-5063	212	9	are	be	AUX
ap-5063	212	10	∂fs	∂fs	PROPN
ap-5063	212	11	for	for	ADP
ap-5063	212	12	n3	n3	NOUN
ap-5063	212	13	and	and	CCONJ
ap-5063	212	14	∂fl	∂fl	PROPN
ap-5063	212	15	for	for	ADP
ap-5063	212	16	the	the	DET
ap-5063	212	17	others	other	NOUN
ap-5063	212	18	.	.	PUNCT
ap-5063	213	1	the	the	DET
ap-5063	213	2	values	value	NOUN
ap-5063	213	3	of	of	ADP
ap-5063	213	4	the	the	DET
ap-5063	213	5	functions	function	NOUN
ap-5063	213	6	on	on	ADP
ap-5063	213	7	the	the	DET
ap-5063	213	8	boundaries	boundary	NOUN
ap-5063	213	9	are	be	AUX
ap-5063	213	10	summarized	summarize	VERB
ap-5063	213	11	in	in	ADP
ap-5063	213	12	appendix	appendix	NOUN
ap-5063	213	13	in	in	ADP
ap-5063	213	14	tab	tab	NOUN
ap-5063	213	15	.	.	PUNCT
ap-5063	214	1	4	4	X
ap-5063	214	2	.	.	X
ap-5063	214	3	in	in	ADP
ap-5063	214	4	the	the	DET
ap-5063	214	5	case	case	NOUN
ap-5063	214	6	of	of	ADP
ap-5063	214	7	g2	g2	PROPN
ap-5063	214	8	×a1	×a1	PROPN
ap-5063	214	9	,	,	PUNCT
ap-5063	214	10	the	the	DET
ap-5063	214	11	normal	normal	ADJ
ap-5063	214	12	vector	vector	NOUN
ap-5063	214	13	n2	n2	NOUN
ap-5063	214	14	corresponds	correspond	VERB
ap-5063	214	15	to	to	ADP
ap-5063	214	16	the	the	DET
ap-5063	214	17	short	short	ADJ
ap-5063	214	18	simple	simple	ADJ
ap-5063	214	19	root	root	NOUN
ap-5063	214	20	so	so	SCONJ
ap-5063	214	21	to	to	ADP
ap-5063	214	22	the	the	DET
ap-5063	214	23	boundary	boundary	ADJ
ap-5063	214	24	∂fs	∂fs	PROPN
ap-5063	214	25	and	and	CCONJ
ap-5063	214	26	the	the	DET
ap-5063	214	27	rest	rest	NOUN
ap-5063	214	28	of	of	ADP
ap-5063	214	29	normal	normal	ADJ
ap-5063	214	30	vectors	vector	NOUN
ap-5063	214	31	to	to	ADP
ap-5063	214	32	the	the	DET
ap-5063	214	33	long	long	ADJ
ap-5063	214	34	simple	simple	ADJ
ap-5063	214	35	roots	root	NOUN
ap-5063	214	36	i.e.	i.e.	X
ap-5063	214	37	to	to	ADP
ap-5063	214	38	the	the	DET
ap-5063	214	39	boundaries	boundary	NOUN
ap-5063	214	40	∂fl	∂fl	ADJ
ap-5063	214	41	.	.	PUNCT
ap-5063	215	1	the	the	DET
ap-5063	215	2	values	value	NOUN
ap-5063	215	3	of	of	ADP
ap-5063	215	4	the	the	DET
ap-5063	215	5	functions	function	NOUN
ap-5063	215	6	on	on	ADP
ap-5063	215	7	the	the	DET
ap-5063	215	8	boundaries	boundary	NOUN
ap-5063	215	9	are	be	AUX
ap-5063	215	10	given	give	VERB
ap-5063	215	11	in	in	ADP
ap-5063	215	12	appendix	appendix	NOUN
ap-5063	215	13	in	in	ADP
ap-5063	215	14	tab	tab	NOUN
ap-5063	215	15	.	.	PUNCT
ap-5063	216	1	5	5	NUM
ap-5063	216	2	.	.	X
ap-5063	216	3	5.3	5.3	NUM
ap-5063	216	4	.	.	PUNCT
ap-5063	217	1	a1	a1	NOUN
ap-5063	217	2	×	×	NOUN
ap-5063	217	3	a1	a1	NOUN
ap-5063	217	4	×	×	NOUN
ap-5063	217	5	a1	a1	NOUN
ap-5063	217	6	group	group	NOUN
ap-5063	217	7	although	although	SCONJ
ap-5063	217	8	the	the	DET
ap-5063	217	9	root	root	NOUN
ap-5063	217	10	system	system	NOUN
ap-5063	217	11	of	of	ADP
ap-5063	217	12	a1×a1×a1	a1×a1×a1	NOUN
ap-5063	217	13	does	do	AUX
ap-5063	217	14	not	not	PART
ap-5063	217	15	have	have	VERB
ap-5063	217	16	two	two	NUM
ap-5063	217	17	different	different	ADJ
ap-5063	217	18	lengths	length	NOUN
ap-5063	217	19	of	of	ADP
ap-5063	217	20	roots	root	NOUN
ap-5063	217	21	,	,	PUNCT
ap-5063	217	22	it	it	PRON
ap-5063	217	23	is	be	AUX
ap-5063	217	24	still	still	ADV
ap-5063	217	25	an	an	DET
ap-5063	217	26	interesting	interesting	ADJ
ap-5063	217	27	case	case	NOUN
ap-5063	217	28	for	for	ADP
ap-5063	217	29	us	we	PRON
ap-5063	217	30	.	.	PUNCT
ap-5063	218	1	the	the	DET
ap-5063	218	2	α	α	NUM
ap-5063	218	3	-	-	PUNCT
ap-5063	218	4	basis	basis	NOUN
ap-5063	218	5	vectors	vector	NOUN
ap-5063	218	6	in	in	ADP
ap-5063	218	7	cartesian	cartesian	ADJ
ap-5063	218	8	coordinates	coordinate	NOUN
ap-5063	218	9	have	have	VERB
ap-5063	218	10	the	the	DET
ap-5063	218	11	form	form	NOUN
ap-5063	218	12	α1	α1	PROPN
ap-5063	218	13	:	:	PUNCT
ap-5063	218	14	=	=	SYM
ap-5063	218	15	(	(	PUNCT
ap-5063	218	16	√	√	NUM
ap-5063	218	17	2	2	NUM
ap-5063	218	18	,	,	PUNCT
ap-5063	218	19	0	0	NUM
ap-5063	218	20	,	,	PUNCT
ap-5063	218	21	0)e	0)e	NOUN
ap-5063	218	22	,	,	PUNCT
ap-5063	218	23	α2	α2	ADJ
ap-5063	218	24	:	:	PUNCT
ap-5063	218	25	=	=	SYM
ap-5063	218	26	(	(	PUNCT
ap-5063	218	27	0	0	NUM
ap-5063	218	28	,	,	PUNCT
ap-5063	218	29	√	√	NOUN
ap-5063	218	30	2	2	NUM
ap-5063	218	31	,	,	PUNCT
ap-5063	218	32	0)e	0)e	NOUN
ap-5063	218	33	,	,	PUNCT
ap-5063	218	34	α3	α3	NOUN
ap-5063	218	35	:	:	PUNCT
ap-5063	218	36	=	=	SYM
ap-5063	218	37	(	(	PUNCT
ap-5063	218	38	0	0	NUM
ap-5063	218	39	,	,	PUNCT
ap-5063	218	40	0	0	NUM
ap-5063	218	41	,	,	PUNCT
ap-5063	218	42	√	√	NUM
ap-5063	218	43	2)e	2)e	NUM
ap-5063	218	44	.	.	PUNCT
ap-5063	219	1	according	accord	VERB
ap-5063	219	2	to	to	ADP
ap-5063	219	3	(	(	PUNCT
ap-5063	219	4	4	4	NUM
ap-5063	219	5	)	)	PUNCT
ap-5063	219	6	and	and	CCONJ
ap-5063	219	7	(	(	PUNCT
ap-5063	219	8	5	5	X
ap-5063	219	9	)	)	PUNCT
ap-5063	219	10	there	there	PRON
ap-5063	219	11	are	be	VERB
ap-5063	219	12	two	two	NUM
ap-5063	219	13	families	family	NOUN
ap-5063	219	14	of	of	ADP
ap-5063	219	15	special	special	ADJ
ap-5063	219	16	functions	function	NOUN
ap-5063	219	17	c	c	PROPN
ap-5063	219	18	and	and	CCONJ
ap-5063	219	19	s.	s.	PROPN
ap-5063	219	20	by	by	ADP
ap-5063	219	21	the	the	DET
ap-5063	219	22	analogy	analogy	NOUN
ap-5063	219	23	to	to	ADP
ap-5063	219	24	homomorphism	homomorphism	PROPN
ap-5063	219	25	(	(	PUNCT
ap-5063	219	26	5	5	NUM
ap-5063	219	27	)	)	PUNCT
ap-5063	219	28	we	we	PRON
ap-5063	219	29	can	can	AUX
ap-5063	219	30	define	define	VERB
ap-5063	219	31	new	new	ADJ
ap-5063	219	32	families	family	NOUN
ap-5063	219	33	of	of	ADP
ap-5063	219	34	functions	function	NOUN
ap-5063	219	35	.	.	PUNCT
ap-5063	220	1	σ(r1	σ(r1	NOUN
ap-5063	220	2	)	)	PUNCT
ap-5063	220	3	=	=	SYM
ap-5063	220	4	σ(r2	σ(r2	NOUN
ap-5063	220	5	)	)	PUNCT
ap-5063	220	6	=	=	SYM
ap-5063	220	7	σ(r3	σ(r3	NOUN
ap-5063	220	8	)	)	PUNCT
ap-5063	220	9	=	=	SYM
ap-5063	220	10	1	1	NUM
ap-5063	220	11	=	=	NOUN
ap-5063	220	12	⇒	⇒	X
ap-5063	220	13	ccc	ccc	NOUN
ap-5063	220	14	,	,	PUNCT
ap-5063	220	15	σ(r1	σ(r1	NOUN
ap-5063	220	16	)	)	PUNCT
ap-5063	220	17	=	=	SYM
ap-5063	220	18	σ(r2	σ(r2	NOUN
ap-5063	220	19	)	)	PUNCT
ap-5063	220	20	=	=	SYM
ap-5063	220	21	σ(r3	σ(r3	NOUN
ap-5063	220	22	)	)	PUNCT
ap-5063	220	23	=	=	SYM
ap-5063	220	24	−1	−1	NOUN
ap-5063	220	25	=	=	VERB
ap-5063	220	26	⇒	⇒	NOUN
ap-5063	220	27	sss	sss	NOUN
ap-5063	220	28	,	,	PUNCT
ap-5063	220	29	σ(r1	σ(r1	NOUN
ap-5063	220	30	)	)	PUNCT
ap-5063	220	31	=	=	SYM
ap-5063	220	32	σ(r2	σ(r2	NOUN
ap-5063	220	33	)	)	PUNCT
ap-5063	220	34	=	=	SYM
ap-5063	220	35	1	1	NUM
ap-5063	220	36	,	,	PUNCT
ap-5063	220	37	σ(r3	σ(r3	NOUN
ap-5063	220	38	)	)	PUNCT
ap-5063	220	39	=	=	SYM
ap-5063	220	40	−1	−1	NOUN
ap-5063	220	41	=	=	NOUN
ap-5063	220	42	⇒	⇒	PROPN
ap-5063	220	43	ccs	ccs	PROPN
ap-5063	220	44	,	,	PUNCT
ap-5063	220	45	σ(r1	σ(r1	PROPN
ap-5063	220	46	)	)	PUNCT
ap-5063	220	47	=	=	SYM
ap-5063	220	48	σ(r2	σ(r2	NOUN
ap-5063	220	49	)	)	PUNCT
ap-5063	220	50	=	=	SYM
ap-5063	220	51	−1	−1	NOUN
ap-5063	220	52	,	,	PUNCT
ap-5063	220	53	σ(r3	σ(r3	NOUN
ap-5063	220	54	)	)	PUNCT
ap-5063	220	55	=	=	SYM
ap-5063	220	56	1	1	NUM
ap-5063	220	57	=	=	NOUN
ap-5063	220	58	⇒	⇒	X
ap-5063	220	59	ssc	ssc	PROPN
ap-5063	220	60	,	,	PUNCT
ap-5063	220	61	σ(r1	σ(r1	NOUN
ap-5063	220	62	)	)	PUNCT
ap-5063	220	63	=	=	SYM
ap-5063	220	64	σ(r3	σ(r3	NOUN
ap-5063	220	65	)	)	PUNCT
ap-5063	220	66	=	=	SYM
ap-5063	220	67	1	1	NUM
ap-5063	220	68	,	,	PUNCT
ap-5063	220	69	σ(r2	σ(r2	NOUN
ap-5063	220	70	)	)	PUNCT
ap-5063	220	71	=	=	SYM
ap-5063	220	72	−1	−1	NOUN
ap-5063	220	73	=	=	VERB
ap-5063	220	74	⇒	⇒	X
ap-5063	220	75	csc	csc	PROPN
ap-5063	220	76	,	,	PUNCT
ap-5063	220	77	σ(r1	σ(r1	NOUN
ap-5063	220	78	)	)	PUNCT
ap-5063	220	79	=	=	SYM
ap-5063	220	80	−1	−1	NOUN
ap-5063	220	81	,	,	PUNCT
ap-5063	220	82	σ(r2	σ(r2	NOUN
ap-5063	220	83	)	)	PUNCT
ap-5063	220	84	=	=	SYM
ap-5063	220	85	σ(r3	σ(r3	NOUN
ap-5063	220	86	)	)	PUNCT
ap-5063	220	87	=	=	SYM
ap-5063	221	1	1	1	NUM
ap-5063	221	2	=	=	NOUN
ap-5063	221	3	⇒	⇒	X
ap-5063	221	4	scc	scc	NOUN
ap-5063	221	5	,	,	PUNCT
ap-5063	221	6	σ(r1	σ(r1	NOUN
ap-5063	221	7	)	)	PUNCT
ap-5063	221	8	=	=	SYM
ap-5063	221	9	1	1	NUM
ap-5063	221	10	,	,	PUNCT
ap-5063	221	11	σ(r2	σ(r2	NOUN
ap-5063	221	12	)	)	PUNCT
ap-5063	221	13	=	=	SYM
ap-5063	221	14	σ(r3	σ(r3	NOUN
ap-5063	221	15	)	)	PUNCT
ap-5063	221	16	=	=	SYM
ap-5063	221	17	−1	−1	NOUN
ap-5063	221	18	=	=	NOUN
ap-5063	221	19	⇒	⇒	X
ap-5063	221	20	css	css	PROPN
ap-5063	221	21	,	,	PUNCT
ap-5063	221	22	σ(r2	σ(r2	NOUN
ap-5063	221	23	)	)	PUNCT
ap-5063	221	24	=	=	SYM
ap-5063	221	25	−1	−1	NOUN
ap-5063	221	26	,	,	PUNCT
ap-5063	221	27	σ(r1	σ(r1	NOUN
ap-5063	221	28	)	)	PUNCT
ap-5063	221	29	=	=	SYM
ap-5063	221	30	σ(r3	σ(r3	NOUN
ap-5063	221	31	)	)	PUNCT
ap-5063	221	32	=	=	SYM
ap-5063	221	33	1	1	NUM
ap-5063	221	34	=	=	NOUN
ap-5063	221	35	⇒	⇒	NOUN
ap-5063	221	36	scs	scs	NOUN
ap-5063	221	37	,	,	PUNCT
ap-5063	221	38	where	where	SCONJ
ap-5063	221	39	ccc	ccc	PROPN
ap-5063	221	40	,	,	PUNCT
ap-5063	221	41	sss	sss	VERB
ap-5063	221	42	correspond	correspond	VERB
ap-5063	221	43	to	to	ADP
ap-5063	221	44	c	c	PROPN
ap-5063	221	45	and	and	CCONJ
ap-5063	221	46	s	s	NOUN
ap-5063	221	47	-	-	NOUN
ap-5063	221	48	functions	function	NOUN
ap-5063	221	49	,	,	PUNCT
ap-5063	221	50	respectively	respectively	ADV
ap-5063	221	51	and	and	CCONJ
ap-5063	221	52	the	the	DET
ap-5063	221	53	rest	rest	NOUN
ap-5063	221	54	of	of	ADP
ap-5063	221	55	them	they	PRON
ap-5063	221	56	to	to	PART
ap-5063	221	57	sland	sland	VERB
ap-5063	221	58	ss	ss	NOUN
ap-5063	221	59	-	-	PUNCT
ap-5063	221	60	functions	function	NOUN
ap-5063	221	61	.	.	PUNCT
ap-5063	222	1	all	all	DET
ap-5063	222	2	families	family	NOUN
ap-5063	222	3	of	of	ADP
ap-5063	222	4	functions	function	NOUN
ap-5063	222	5	defined	define	VERB
ap-5063	222	6	on	on	ADP
ap-5063	222	7	the	the	DET
ap-5063	222	8	fundamental	fundamental	ADJ
ap-5063	222	9	region	region	NOUN
ap-5063	222	10	fa1×a1×a1	fa1×a1×a1	NOUN
ap-5063	222	11	=	=	SYM
ap-5063	222	12	{	{	PUNCT
ap-5063	222	13	0	0	NUM
ap-5063	222	14	,	,	PUNCT
ap-5063	222	15	ω1	ω1	PROPN
ap-5063	222	16	,	,	PUNCT
ap-5063	222	17	ω2	ω2	ADJ
ap-5063	222	18	,	,	PUNCT
ap-5063	222	19	ω3	ω3	NOUN
ap-5063	222	20	,	,	PUNCT
ap-5063	222	21	ω1	ω1	PROPN
ap-5063	222	22	+	+	CCONJ
ap-5063	222	23	ω2	ω2	ADJ
ap-5063	222	24	,	,	PUNCT
ap-5063	222	25	ω1	ω1	PROPN
ap-5063	222	26	+	+	CCONJ
ap-5063	222	27	ω3	ω3	PROPN
ap-5063	222	28	,	,	PUNCT
ap-5063	222	29	ω2	ω2	PROPN
ap-5063	222	30	+	+	CCONJ
ap-5063	222	31	ω3	ω3	PROPN
ap-5063	222	32	,	,	PUNCT
ap-5063	222	33	ω1	ω1	PROPN
ap-5063	222	34	+	+	CCONJ
ap-5063	222	35	ω2	ω2	ADJ
ap-5063	222	36	+	+	CCONJ
ap-5063	222	37	ω3	ω3	NOUN
ap-5063	222	38	}	}	PUNCT
ap-5063	222	39	.	.	PUNCT
ap-5063	223	1	fulfill	fulfill	NOUN
ap-5063	223	2	mixed	mix	VERB
ap-5063	223	3	boundary	boundary	ADJ
ap-5063	223	4	condition	condition	NOUN
ap-5063	223	5	(	(	PUNCT
ap-5063	223	6	see	see	VERB
ap-5063	223	7	tab	tab	NOUN
ap-5063	223	8	.	.	PROPN
ap-5063	223	9	6	6	NUM
ap-5063	223	10	)	)	PUNCT
ap-5063	223	11	.	.	PUNCT
ap-5063	224	1	figure	figure	NOUN
ap-5063	224	2	5	5	NUM
ap-5063	224	3	.	.	PUNCT
ap-5063	225	1	the	the	DET
ap-5063	225	2	fundamental	fundamental	ADJ
ap-5063	225	3	region	region	NOUN
ap-5063	225	4	f	f	PROPN
ap-5063	225	5	with	with	ADP
ap-5063	225	6	normal	normal	ADJ
ap-5063	225	7	vectors	vector	NOUN
ap-5063	225	8	of	of	ADP
ap-5063	225	9	a1	a1	NOUN
ap-5063	225	10	×	×	NOUN
ap-5063	225	11	a1	a1	NOUN
ap-5063	225	12	×	×	NOUN
ap-5063	225	13	a1	a1	NOUN
ap-5063	225	14	group	group	NOUN
ap-5063	225	15	.	.	PUNCT
ap-5063	226	1	the	the	DET
ap-5063	226	2	projection	projection	NOUN
ap-5063	226	3	matrix	matrix	NOUN
ap-5063	226	4	is	be	AUX
ap-5063	226	5	the	the	DET
ap-5063	226	6	identity	identity	NOUN
ap-5063	226	7	matrix	matrix	NOUN
ap-5063	226	8	and	and	CCONJ
ap-5063	226	9	then	then	ADV
ap-5063	226	10	the	the	DET
ap-5063	226	11	choice	choice	NOUN
ap-5063	226	12	of	of	ADP
ap-5063	226	13	separation	separation	NOUN
ap-5063	226	14	constants	constant	NOUN
ap-5063	226	15	is	be	AUX
ap-5063	226	16	trivial	trivial	ADJ
ap-5063	226	17	:	:	PUNCT
ap-5063	226	18	−	−	PROPN
ap-5063	226	19	k2	k2	ADJ
ap-5063	226	20	1	1	NUM
ap-5063	226	21	=	=	SYM
ap-5063	226	22	−π2a2	−π2a2	PROPN
ap-5063	226	23	,	,	PUNCT
ap-5063	226	24	−k2	−k2	PROPN
ap-5063	226	25	2	2	NUM
ap-5063	226	26	=	=	SYM
ap-5063	226	27	−π2b2	−π2b2	NOUN
ap-5063	226	28	,	,	PUNCT
ap-5063	226	29	−k2	−k2	PROPN
ap-5063	226	30	3	3	NUM
ap-5063	226	31	=	=	SYM
ap-5063	226	32	−π2c2	−π2c2	PROPN
ap-5063	226	33	.	.	PUNCT
ap-5063	227	1	(	(	PUNCT
ap-5063	227	2	10	10	NUM
ap-5063	227	3	)	)	PUNCT
ap-5063	227	4	according	accord	VERB
ap-5063	227	5	to	to	ADP
ap-5063	227	6	the	the	DET
ap-5063	227	7	branching	branch	VERB
ap-5063	227	8	rule	rule	NOUN
ap-5063	227	9	o(a	o(a	NOUN
ap-5063	227	10	,	,	PUNCT
ap-5063	227	11	b	b	NOUN
ap-5063	227	12	,	,	PUNCT
ap-5063	227	13	c	c	NOUN
ap-5063	227	14	)	)	PUNCT
ap-5063	227	15	pa1×a1×a1−−−−−−−−→	pa1×a1×a1−−−−−−−−→	NOUN
ap-5063	227	16	o(a)o(b)o(c	o(a)o(b)o(c	NUM
ap-5063	227	17	)	)	PUNCT
ap-5063	227	18	we	we	PRON
ap-5063	227	19	have	have	AUX
ap-5063	227	20	ccca	ccca	VERB
ap-5063	227	21	,	,	PUNCT
ap-5063	227	22	b	b	NOUN
ap-5063	227	23	,	,	PUNCT
ap-5063	227	24	c(x	c(x	NOUN
ap-5063	227	25	)	)	PUNCT
ap-5063	227	26	:	:	PUNCT
ap-5063	228	1	=	=	SYM
ap-5063	228	2	ca(x1)cb(x2)cc(x3	ca(x1)cb(x2)cc(x3	PROPN
ap-5063	228	3	)	)	PUNCT
ap-5063	228	4	,	,	PUNCT
ap-5063	228	5	scsa	scsa	VERB
ap-5063	228	6	,	,	PUNCT
ap-5063	228	7	b	b	NOUN
ap-5063	228	8	,	,	PUNCT
ap-5063	228	9	c(x	c(x	NOUN
ap-5063	228	10	)	)	PUNCT
ap-5063	228	11	:	:	PUNCT
ap-5063	228	12	=	=	SYM
ap-5063	228	13	sa(x1)cb(x2)sc(x3	sa(x1)cb(x2)sc(x3	X
ap-5063	228	14	)	)	PUNCT
ap-5063	228	15	,	,	PUNCT
ap-5063	228	16	cssa	cssa	NOUN
ap-5063	228	17	,	,	PUNCT
ap-5063	228	18	b	b	NOUN
ap-5063	228	19	,	,	PUNCT
ap-5063	228	20	c(x	c(x	NOUN
ap-5063	228	21	)	)	PUNCT
ap-5063	228	22	:	:	PUNCT
ap-5063	229	1	=	=	SYM
ap-5063	229	2	ca(x1)sb(x2)sc(x3	ca(x1)sb(x2)sc(x3	PROPN
ap-5063	229	3	)	)	PUNCT
ap-5063	229	4	,	,	PUNCT
ap-5063	229	5	ssca	ssca	NOUN
ap-5063	229	6	,	,	PUNCT
ap-5063	229	7	b	b	NOUN
ap-5063	229	8	,	,	PUNCT
ap-5063	229	9	c(x	c(x	NOUN
ap-5063	229	10	)	)	PUNCT
ap-5063	229	11	:	:	PUNCT
ap-5063	229	12	=	=	SYM
ap-5063	229	13	sa(x1)sb(x2)cc(x3	sa(x1)sb(x2)cc(x3	PROPN
ap-5063	229	14	)	)	PUNCT
ap-5063	229	15	,	,	PUNCT
ap-5063	229	16	sssa	sssa	PROPN
ap-5063	229	17	,	,	PUNCT
ap-5063	229	18	b	b	NOUN
ap-5063	229	19	,	,	PUNCT
ap-5063	229	20	c(x	c(x	NOUN
ap-5063	229	21	)	)	PUNCT
ap-5063	229	22	:	:	PUNCT
ap-5063	229	23	=	=	PUNCT
ap-5063	229	24	sa(x1)sb(x2)sc(x3	sa(x1)sb(x2)sc(x3	PROPN
ap-5063	229	25	)	)	PUNCT
ap-5063	229	26	,	,	PUNCT
ap-5063	229	27	csca	csca	NOUN
ap-5063	229	28	,	,	PUNCT
ap-5063	229	29	b	b	NOUN
ap-5063	229	30	,	,	PUNCT
ap-5063	229	31	c(x	c(x	NOUN
ap-5063	229	32	)	)	PUNCT
ap-5063	229	33	:	:	PUNCT
ap-5063	229	34	=	=	PUNCT
ap-5063	229	35	ca(x1)sb(x2)cc(x3	ca(x1)sb(x2)cc(x3	PROPN
ap-5063	229	36	)	)	PUNCT
ap-5063	229	37	,	,	PUNCT
ap-5063	229	38	ccsa	ccsa	PROPN
ap-5063	229	39	,	,	PUNCT
ap-5063	229	40	b	b	NOUN
ap-5063	229	41	,	,	PUNCT
ap-5063	229	42	c(x	c(x	NOUN
ap-5063	229	43	)	)	PUNCT
ap-5063	229	44	:	:	PUNCT
ap-5063	229	45	=	=	PUNCT
ap-5063	229	46	ca(x1)cb(x2)sc(x3	ca(x1)cb(x2)sc(x3	NOUN
ap-5063	229	47	)	)	PUNCT
ap-5063	229	48	,	,	PUNCT
ap-5063	229	49	scca	scca	PROPN
ap-5063	229	50	,	,	PUNCT
ap-5063	229	51	b	b	NOUN
ap-5063	229	52	,	,	PUNCT
ap-5063	229	53	c(x	c(x	NOUN
ap-5063	229	54	)	)	PUNCT
ap-5063	229	55	:	:	PUNCT
ap-5063	229	56	=	=	PUNCT
ap-5063	229	57	sa(x1)cb(x2)cc(x3	sa(x1)cb(x2)cc(x3	PROPN
ap-5063	229	58	)	)	PUNCT
ap-5063	229	59	,	,	PUNCT
ap-5063	229	60	407	407	NUM
ap-5063	229	61	marzena	marzena	ADJ
ap-5063	229	62	szajewska	szajewska	NOUN
ap-5063	229	63	,	,	PUNCT
ap-5063	229	64	agnieszka	agnieszka	PROPN
ap-5063	229	65	tereszkiewicz	tereszkiewicz	PROPN
ap-5063	229	66	acta	acta	PROPN
ap-5063	229	67	polytechnica	polytechnica	PROPN
ap-5063	229	68	where	where	SCONJ
ap-5063	229	69	cµ(xi	cµ(xi	PROPN
ap-5063	229	70	)	)	PUNCT
ap-5063	229	71	,	,	PUNCT
ap-5063	229	72	sµ(xi	sµ(xi	PROPN
ap-5063	229	73	)	)	PUNCT
ap-5063	229	74	for	for	ADP
ap-5063	229	75	i	i	PROPN
ap-5063	229	76	=	=	SYM
ap-5063	229	77	1	1	NUM
ap-5063	229	78	,	,	PUNCT
ap-5063	229	79	2	2	NUM
ap-5063	229	80	,	,	PUNCT
ap-5063	229	81	3	3	NUM
ap-5063	229	82	are	be	AUX
ap-5063	229	83	the	the	DET
ap-5063	229	84	same	same	ADJ
ap-5063	229	85	as	as	ADP
ap-5063	229	86	in	in	ADP
ap-5063	229	87	the	the	DET
ap-5063	229	88	previous	previous	ADJ
ap-5063	229	89	cases	case	NOUN
ap-5063	229	90	.	.	PUNCT
ap-5063	230	1	the	the	DET
ap-5063	230	2	first	first	ADJ
ap-5063	230	3	four	four	NUM
ap-5063	230	4	families	family	NOUN
ap-5063	230	5	of	of	ADP
ap-5063	230	6	functions	function	NOUN
ap-5063	230	7	are	be	AUX
ap-5063	230	8	real	real	ADV
ap-5063	230	9	valued	value	VERB
ap-5063	230	10	and	and	CCONJ
ap-5063	230	11	the	the	DET
ap-5063	230	12	rest	rest	NOUN
ap-5063	230	13	of	of	ADP
ap-5063	230	14	them	they	PRON
ap-5063	230	15	are	be	AUX
ap-5063	230	16	pure	pure	ADJ
ap-5063	230	17	imaginary	imaginary	ADJ
ap-5063	230	18	.	.	PUNCT
ap-5063	231	1	normal	normal	ADJ
ap-5063	231	2	vectors	vector	NOUN
ap-5063	231	3	shown	show	VERB
ap-5063	231	4	on	on	ADP
ap-5063	231	5	fig	fig	NOUN
ap-5063	231	6	.	.	PUNCT
ap-5063	232	1	5	5	NUM
ap-5063	232	2	are	be	AUX
ap-5063	232	3	n1	n1	NOUN
ap-5063	232	4	=	=	SYM
ap-5063	232	5	{	{	PUNCT
ap-5063	232	6	0	0	NUM
ap-5063	232	7	,	,	PUNCT
ap-5063	232	8	0,−1	0,−1	PRON
ap-5063	232	9	}	}	PUNCT
ap-5063	232	10	,	,	PUNCT
ap-5063	232	11	n2	n2	NOUN
ap-5063	232	12	=	=	PUNCT
ap-5063	232	13	{	{	PUNCT
ap-5063	232	14	0,−1	0,−1	PROPN
ap-5063	232	15	,	,	PUNCT
ap-5063	232	16	0	0	NUM
ap-5063	232	17	}	}	PUNCT
ap-5063	232	18	,	,	PUNCT
ap-5063	232	19	n3	n3	NOUN
ap-5063	232	20	=	=	SYM
ap-5063	232	21	{	{	PUNCT
ap-5063	232	22	−1	−1	NOUN
ap-5063	232	23	,	,	PUNCT
ap-5063	232	24	0	0	NUM
ap-5063	232	25	,	,	PUNCT
ap-5063	232	26	0	0	NUM
ap-5063	232	27	}	}	PUNCT
ap-5063	232	28	,	,	PUNCT
ap-5063	232	29	n4	n4	PROPN
ap-5063	232	30	=	=	PUNCT
ap-5063	232	31	{	{	PUNCT
ap-5063	232	32	0	0	NUM
ap-5063	232	33	,	,	PUNCT
ap-5063	232	34	1	1	NUM
ap-5063	232	35	,	,	PUNCT
ap-5063	232	36	0	0	NUM
ap-5063	232	37	}	}	PUNCT
ap-5063	232	38	,	,	PUNCT
ap-5063	232	39	n5	n5	PROPN
ap-5063	232	40	=	=	PUNCT
ap-5063	232	41	{	{	PUNCT
ap-5063	232	42	1	1	NUM
ap-5063	232	43	,	,	PUNCT
ap-5063	232	44	0	0	NUM
ap-5063	232	45	,	,	PUNCT
ap-5063	232	46	0	0	NUM
ap-5063	232	47	}	}	PUNCT
ap-5063	232	48	,	,	PUNCT
ap-5063	232	49	n6	n6	PROPN
ap-5063	232	50	=	=	PUNCT
ap-5063	232	51	{	{	PUNCT
ap-5063	232	52	0	0	NUM
ap-5063	232	53	,	,	PUNCT
ap-5063	232	54	0	0	NUM
ap-5063	232	55	,	,	PUNCT
ap-5063	232	56	1	1	NUM
ap-5063	232	57	}	}	PUNCT
ap-5063	232	58	.	.	PUNCT
ap-5063	233	1	the	the	DET
ap-5063	233	2	values	value	NOUN
ap-5063	233	3	of	of	ADP
ap-5063	233	4	the	the	DET
ap-5063	233	5	functions	function	NOUN
ap-5063	233	6	on	on	ADP
ap-5063	233	7	the	the	DET
ap-5063	233	8	boundaries	boundary	NOUN
ap-5063	233	9	are	be	AUX
ap-5063	233	10	shown	show	VERB
ap-5063	233	11	in	in	ADP
ap-5063	233	12	appendix	appendix	NOUN
ap-5063	233	13	in	in	ADP
ap-5063	233	14	tab	tab	NOUN
ap-5063	233	15	.	.	PUNCT
ap-5063	234	1	6	6	NUM
ap-5063	234	2	.	.	NOUN
ap-5063	234	3	6	6	NUM
ap-5063	234	4	.	.	X
ap-5063	234	5	appendix	appendix	NOUN
ap-5063	234	6	in	in	ADP
ap-5063	234	7	tables	table	NOUN
ap-5063	234	8	2–6	2–6	NUM
ap-5063	235	1	we	we	PRON
ap-5063	235	2	collect	collect	VERB
ap-5063	235	3	the	the	DET
ap-5063	235	4	values	value	NOUN
ap-5063	235	5	of	of	ADP
ap-5063	235	6	special	special	ADJ
ap-5063	235	7	functions	function	NOUN
ap-5063	235	8	on	on	ADP
ap-5063	235	9	the	the	DET
ap-5063	235	10	boundaries	boundary	NOUN
ap-5063	235	11	of	of	ADP
ap-5063	235	12	the	the	DET
ap-5063	235	13	fundamental	fundamental	ADJ
ap-5063	235	14	region	region	NOUN
ap-5063	235	15	f	f	PROPN
ap-5063	235	16	for	for	ADP
ap-5063	235	17	each	each	PRON
ap-5063	235	18	of	of	ADP
ap-5063	235	19	3d	3d	NUM
ap-5063	235	20	finite	finite	PROPN
ap-5063	235	21	reflection	reflection	NOUN
ap-5063	235	22	groups	group	NOUN
ap-5063	235	23	presented	present	VERB
ap-5063	235	24	in	in	ADP
ap-5063	235	25	the	the	DET
ap-5063	235	26	paper	paper	NOUN
ap-5063	235	27	.	.	PUNCT
ap-5063	236	1	references	reference	NOUN
ap-5063	236	2	[	[	X
ap-5063	236	3	1	1	NUM
ap-5063	236	4	]	]	PUNCT
ap-5063	236	5	borel	borel	PROPN
ap-5063	236	6	,	,	PUNCT
ap-5063	236	7	a.	a.	NOUN
ap-5063	236	8	,	,	PUNCT
ap-5063	236	9	and	and	CCONJ
ap-5063	236	10	j.	j.	PROPN
ap-5063	236	11	de	de	PROPN
ap-5063	236	12	siebental	siebental	PROPN
ap-5063	236	13	,	,	PUNCT
ap-5063	236	14	“	"	PUNCT
ap-5063	236	15	les	les	X
ap-5063	236	16	sous	sous	ADJ
ap-5063	236	17	-	-	PUNCT
ap-5063	236	18	groupes	groupes	PROPN
ap-5063	236	19	fermés	fermés	PROPN
ap-5063	236	20	de	de	PROPN
ap-5063	236	21	rang	ring	VERB
ap-5063	236	22	maximum	maximum	PROPN
ap-5063	236	23	de	de	X
ap-5063	236	24	groupes	groupes	X
ap-5063	236	25	de	de	X
ap-5063	236	26	lie	lie	NOUN
ap-5063	236	27	clos	clo	NOUN
ap-5063	236	28	.	.	PUNCT
ap-5063	236	29	”	"	PUNCT
ap-5063	237	1	comment	comment	NOUN
ap-5063	237	2	.	.	PUNCT
ap-5063	238	1	math	math	NOUN
ap-5063	238	2	.	.	PUNCT
ap-5063	239	1	helv	helv	PROPN
ap-5063	239	2	.	.	PROPN
ap-5063	240	1	23	23	NUM
ap-5063	240	2	,	,	PUNCT
ap-5063	240	3	(	(	PUNCT
ap-5063	240	4	1949	1949	NUM
ap-5063	240	5	):	):	PUNCT
ap-5063	241	1	200–221	200–221	NUM
ap-5063	241	2	.	.	PUNCT
ap-5063	242	1	[	[	X
ap-5063	242	2	2	2	NUM
ap-5063	242	3	]	]	X
ap-5063	242	4	bourbaki	bourbaki	NOUN
ap-5063	242	5	,	,	PUNCT
ap-5063	242	6	n.	n.	PROPN
ap-5063	242	7	groupes	groupe	NOUN
ap-5063	242	8	et	et	PROPN
ap-5063	242	9	algèbres	algèbre	NOUN
ap-5063	242	10	de	de	ADP
ap-5063	242	11	lie	lie	NOUN
ap-5063	242	12	,	,	PUNCT
ap-5063	242	13	chapters	chapter	NOUN
ap-5063	242	14	iv	iv	NUM
ap-5063	242	15	,	,	PUNCT
ap-5063	242	16	v	v	NOUN
ap-5063	242	17	,	,	PUNCT
ap-5063	242	18	vi	vi	PROPN
ap-5063	242	19	,	,	PUNCT
ap-5063	242	20	hermann	hermann	PROPN
ap-5063	242	21	,	,	PUNCT
ap-5063	242	22	paris	paris	PROPN
ap-5063	242	23	,	,	PUNCT
ap-5063	242	24	1968	1968	NUM
ap-5063	242	25	.	.	PUNCT
ap-5063	243	1	[	[	X
ap-5063	243	2	3	3	NUM
ap-5063	243	3	]	]	X
ap-5063	243	4	dynkin	dynkin	ADJ
ap-5063	243	5	,	,	PUNCT
ap-5063	243	6	e.b	e.b	NOUN
ap-5063	243	7	.	.	PUNCT
ap-5063	244	1	“	"	PUNCT
ap-5063	244	2	semisimple	semisimple	NOUN
ap-5063	244	3	subalgebras	subalgebra	NOUN
ap-5063	244	4	of	of	ADP
ap-5063	244	5	semisimple	semisimple	PROPN
ap-5063	244	6	lie	lie	NOUN
ap-5063	244	7	algebras	algebra	NOUN
ap-5063	244	8	.	.	PUNCT
ap-5063	244	9	”	"	PUNCT
ap-5063	245	1	ams	am	NOUN
ap-5063	245	2	trnanslations	trnanslation	NOUN
ap-5063	245	3	,	,	PUNCT
ap-5063	245	4	series	series	NOUN
ap-5063	245	5	2	2	NUM
ap-5063	245	6	,	,	PUNCT
ap-5063	245	7	vol	vol	NOUN
ap-5063	245	8	.	.	PROPN
ap-5063	245	9	6	6	NUM
ap-5063	245	10	,	,	PUNCT
ap-5063	245	11	(	(	PUNCT
ap-5063	245	12	1957	1957	NUM
ap-5063	245	13	):	):	PUNCT
ap-5063	245	14	111–244	111–244	NUM
ap-5063	245	15	.	.	PUNCT
ap-5063	246	1	[	[	X
ap-5063	246	2	4	4	NUM
ap-5063	246	3	]	]	X
ap-5063	246	4	griffiths	griffiths	PROPN
ap-5063	246	5	,	,	PUNCT
ap-5063	246	6	d.j	d.j	PROPN
ap-5063	246	7	.	.	PROPN
ap-5063	246	8	,	,	PUNCT
ap-5063	246	9	and	and	CCONJ
ap-5063	246	10	r.	r.	PROPN
ap-5063	246	11	college	college	PROPN
ap-5063	246	12	,	,	PUNCT
ap-5063	246	13	introduction	introduction	NOUN
ap-5063	246	14	to	to	ADP
ap-5063	246	15	electrodynamics	electrodynamic	NOUN
ap-5063	246	16	,	,	PUNCT
ap-5063	246	17	prentice	prentice	NOUN
ap-5063	246	18	hall	hall	PROPN
ap-5063	246	19	,	,	PUNCT
ap-5063	246	20	new	new	PROPN
ap-5063	246	21	jersey	jersey	PROPN
ap-5063	246	22	,	,	PUNCT
ap-5063	246	23	1999	1999	NUM
ap-5063	246	24	.	.	PUNCT
ap-5063	247	1	[	[	X
ap-5063	247	2	5	5	NUM
ap-5063	247	3	]	]	PUNCT
ap-5063	247	4	hakova	hakova	PROPN
ap-5063	247	5	,	,	PUNCT
ap-5063	247	6	l.	l.	PROPN
ap-5063	247	7	,	,	PUNCT
ap-5063	247	8	hrivnak	hrivnak	PROPN
ap-5063	247	9	,	,	PUNCT
ap-5063	247	10	j.	j.	PROPN
ap-5063	247	11	,	,	PUNCT
ap-5063	247	12	and	and	CCONJ
ap-5063	247	13	j.	j.	PROPN
ap-5063	247	14	patera	patera	PROPN
ap-5063	247	15	,	,	PUNCT
ap-5063	247	16	“	"	PUNCT
ap-5063	247	17	four	four	NUM
ap-5063	247	18	families	family	NOUN
ap-5063	247	19	of	of	ADP
ap-5063	247	20	weyl	weyl	PROPN
ap-5063	247	21	group	group	NOUN
ap-5063	247	22	orbit	orbit	NOUN
ap-5063	247	23	functions	function	NOUN
ap-5063	247	24	of	of	ADP
ap-5063	247	25	b3	b3	PROPN
ap-5063	247	26	and	and	CCONJ
ap-5063	247	27	c3	c3	PROPN
ap-5063	247	28	.	.	PUNCT
ap-5063	247	29	”	"	PUNCT
ap-5063	248	1	j.	j.	PROPN
ap-5063	248	2	math	math	PROPN
ap-5063	248	3	.	.	PUNCT
ap-5063	249	1	phys	phy	NOUN
ap-5063	249	2	.	.	PUNCT
ap-5063	250	1	54	54	NUM
ap-5063	250	2	,	,	PUNCT
ap-5063	250	3	083501	083501	NUM
ap-5063	250	4	(	(	PUNCT
ap-5063	250	5	2013	2013	NUM
ap-5063	250	6	)	)	PUNCT
ap-5063	250	7	.	.	PUNCT
ap-5063	251	1	[	[	X
ap-5063	251	2	6	6	NUM
ap-5063	251	3	]	]	PUNCT
ap-5063	251	4	hrivnak	hrivnak	NOUN
ap-5063	251	5	,	,	PUNCT
ap-5063	251	6	j.	j.	PROPN
ap-5063	251	7	,	,	PUNCT
ap-5063	251	8	and	and	CCONJ
ap-5063	251	9	j.	j.	PROPN
ap-5063	251	10	patera	patera	PROPN
ap-5063	251	11	,	,	PUNCT
ap-5063	251	12	“	"	PUNCT
ap-5063	251	13	on	on	ADP
ap-5063	251	14	discretization	discretization	NOUN
ap-5063	251	15	of	of	ADP
ap-5063	251	16	tori	tori	NOUN
ap-5063	251	17	of	of	ADP
ap-5063	251	18	compact	compact	ADJ
ap-5063	251	19	simple	simple	ADJ
ap-5063	251	20	lie	lie	NOUN
ap-5063	251	21	groups	group	NOUN
ap-5063	251	22	.	.	PUNCT
ap-5063	251	23	”	"	PUNCT
ap-5063	252	1	j.	j.	PROPN
ap-5063	252	2	phys	phys	PROPN
ap-5063	252	3	.	.	PUNCT
ap-5063	253	1	a	a	DET
ap-5063	253	2	:	:	PUNCT
ap-5063	253	3	math	math	NOUN
ap-5063	253	4	.	.	PUNCT
ap-5063	254	1	theor	theor	PROPN
ap-5063	254	2	.	.	PROPN
ap-5063	255	1	,	,	PUNCT
ap-5063	255	2	42	42	NUM
ap-5063	255	3	(	(	PUNCT
ap-5063	255	4	2009	2009	NUM
ap-5063	255	5	)	)	PUNCT
ap-5063	255	6	385208	385208	NUM
ap-5063	255	7	;	;	PUNCT
ap-5063	255	8	arxiv:0905.2395	arxiv:0905.2395	PROPN
ap-5063	255	9	.	.	PUNCT
ap-5063	256	1	[	[	X
ap-5063	256	2	7	7	NUM
ap-5063	256	3	]	]	X
ap-5063	256	4	humphreys	humphreys	PROPN
ap-5063	256	5	,	,	PUNCT
ap-5063	256	6	j.e	j.e	PROPN
ap-5063	256	7	.	.	PROPN
ap-5063	256	8	introduction	introduction	NOUN
ap-5063	256	9	to	to	PART
ap-5063	256	10	lie	lie	VERB
ap-5063	256	11	algebras	algebra	NOUN
ap-5063	256	12	and	and	CCONJ
ap-5063	256	13	representation	representation	NOUN
ap-5063	256	14	theory	theory	NOUN
ap-5063	256	15	,	,	PUNCT
ap-5063	256	16	new	new	PROPN
ap-5063	256	17	york	york	PROPN
ap-5063	256	18	,	,	PUNCT
ap-5063	256	19	springer	springer	NOUN
ap-5063	256	20	,	,	PUNCT
ap-5063	256	21	1972	1972	NUM
ap-5063	256	22	.	.	PUNCT
ap-5063	257	1	[	[	X
ap-5063	257	2	8	8	NUM
ap-5063	257	3	]	]	X
ap-5063	257	4	humphreys	humphreys	PROPN
ap-5063	257	5	,	,	PUNCT
ap-5063	257	6	j.e	j.e	PROPN
ap-5063	257	7	.	.	PROPN
ap-5063	257	8	reflection	reflection	NOUN
ap-5063	257	9	groups	group	NOUN
ap-5063	257	10	and	and	CCONJ
ap-5063	257	11	coxeter	coxet	ADJ
ap-5063	257	12	groups	group	NOUN
ap-5063	257	13	,	,	PUNCT
ap-5063	257	14	cambridge	cambridge	PROPN
ap-5063	257	15	univ	univ	PROPN
ap-5063	257	16	.	.	PUNCT
ap-5063	258	1	press	press	PROPN
ap-5063	258	2	,	,	PUNCT
ap-5063	258	3	cambridge	cambridge	PROPN
ap-5063	258	4	,	,	PUNCT
ap-5063	258	5	1990	1990	NUM
ap-5063	258	6	.	.	PUNCT
ap-5063	259	1	[	[	X
ap-5063	259	2	9	9	NUM
ap-5063	259	3	]	]	PUNCT
ap-5063	259	4	jung:1980	jung:1980	NOUN
ap-5063	259	5	,	,	PUNCT
ap-5063	259	6	c.	c.	NOUN
ap-5063	259	7	“	"	PUNCT
ap-5063	259	8	an	an	DET
ap-5063	259	9	exactly	exactly	ADV
ap-5063	259	10	soluble	soluble	ADJ
ap-5063	259	11	three	three	NUM
ap-5063	259	12	-	-	PUNCT
ap-5063	259	13	body	body	NOUN
ap-5063	259	14	problem	problem	NOUN
ap-5063	259	15	in	in	ADP
ap-5063	259	16	one	one	NUM
ap-5063	259	17	-	-	PUNCT
ap-5063	259	18	dimension	dimension	NOUN
ap-5063	259	19	.	.	PUNCT
ap-5063	259	20	”	"	PUNCT
ap-5063	259	21	can	can	AUX
ap-5063	259	22	.	.	PUNCT
ap-5063	260	1	j.	j.	PROPN
ap-5063	260	2	phys	phys	PROPN
ap-5063	260	3	.	.	PUNCT
ap-5063	260	4	,	,	PUNCT
ap-5063	260	5	58	58	NUM
ap-5063	260	6	,	,	PUNCT
ap-5063	260	7	(	(	PUNCT
ap-5063	260	8	1980	1980	NUM
ap-5063	260	9	)	)	PUNCT
ap-5063	260	10	,	,	PUNCT
ap-5063	260	11	719–728	719–728	NUM
ap-5063	260	12	.	.	PUNCT
ap-5063	261	1	[	[	X
ap-5063	261	2	10	10	NUM
ap-5063	261	3	]	]	X
ap-5063	261	4	klimyk	klimyk	NOUN
ap-5063	261	5	,	,	PUNCT
ap-5063	261	6	a.	a.	NOUN
ap-5063	261	7	,	,	PUNCT
ap-5063	261	8	and	and	CCONJ
ap-5063	261	9	j.	j.	PROPN
ap-5063	261	10	patera	patera	PROPN
ap-5063	261	11	,	,	PUNCT
ap-5063	261	12	“	"	PUNCT
ap-5063	261	13	orbit	orbit	NOUN
ap-5063	261	14	functions	function	NOUN
ap-5063	261	15	.	.	PUNCT
ap-5063	261	16	”	"	PUNCT
ap-5063	262	1	sigma	sigma	PROPN
ap-5063	262	2	(	(	PUNCT
ap-5063	262	3	symmetry	symmetry	NOUN
ap-5063	262	4	,	,	PUNCT
ap-5063	262	5	integrability	integrability	NOUN
ap-5063	262	6	and	and	CCONJ
ap-5063	262	7	geometry	geometry	NOUN
ap-5063	262	8	:	:	PUNCT
ap-5063	262	9	methods	method	NOUN
ap-5063	262	10	and	and	CCONJ
ap-5063	262	11	applications	application	NOUN
ap-5063	262	12	)	)	PUNCT
ap-5063	262	13	,	,	PUNCT
ap-5063	262	14	2	2	NUM
ap-5063	262	15	(	(	PUNCT
ap-5063	262	16	2006	2006	NUM
ap-5063	262	17	)	)	PUNCT
ap-5063	262	18	,	,	PUNCT
ap-5063	262	19	006	006	NUM
ap-5063	262	20	,	,	PUNCT
ap-5063	262	21	60	60	NUM
ap-5063	262	22	pages	page	NOUN
ap-5063	262	23	,	,	PUNCT
ap-5063	262	24	math	math	NOUN
ap-5063	262	25	-	-	PUNCT
ap-5063	262	26	ph/0601037	ph/0601037	NOUN
ap-5063	262	27	.	.	PUNCT
ap-5063	263	1	[	[	X
ap-5063	263	2	11	11	NUM
ap-5063	263	3	]	]	X
ap-5063	263	4	klimyk	klimyk	NOUN
ap-5063	263	5	a.	a.	PROPN
ap-5063	263	6	,	,	PUNCT
ap-5063	263	7	and	and	CCONJ
ap-5063	263	8	j.	j.	PROPN
ap-5063	263	9	patera	patera	PROPN
ap-5063	263	10	“	"	PUNCT
ap-5063	263	11	antisymmetric	antisymmetric	PROPN
ap-5063	263	12	orbit	orbit	NOUN
ap-5063	263	13	functions	function	NOUN
ap-5063	263	14	.	.	PUNCT
ap-5063	263	15	”	"	PUNCT
ap-5063	264	1	sigma	sigma	PROPN
ap-5063	264	2	,	,	PUNCT
ap-5063	264	3	3	3	NUM
ap-5063	264	4	(	(	PUNCT
ap-5063	264	5	2007	2007	NUM
ap-5063	264	6	)	)	PUNCT
ap-5063	264	7	paper	paper	NOUN
ap-5063	264	8	023	023	NUM
ap-5063	264	9	,	,	PUNCT
ap-5063	264	10	83	83	NUM
ap-5063	264	11	pages	page	NOUN
ap-5063	264	12	,	,	PUNCT
ap-5063	264	13	math	math	NOUN
ap-5063	264	14	-	-	PUNCT
ap-5063	264	15	ph/0702040v1	ph/0702040v1	NOUN
ap-5063	264	16	.	.	PUNCT
ap-5063	265	1	[	[	X
ap-5063	265	2	12	12	NUM
ap-5063	265	3	]	]	X
ap-5063	265	4	lemire	lemire	PROPN
ap-5063	265	5	,	,	PUNCT
ap-5063	265	6	f.w	f.w	PROPN
ap-5063	265	7	.	.	PROPN
ap-5063	265	8	,	,	PUNCT
ap-5063	265	9	patera	patera	NOUN
ap-5063	265	10	,	,	PUNCT
ap-5063	265	11	j.	j.	PROPN
ap-5063	265	12	,	,	PUNCT
ap-5063	265	13	and	and	CCONJ
ap-5063	265	14	m.	m.	NOUN
ap-5063	265	15	szajewska	szajewska	NOUN
ap-5063	265	16	,	,	PUNCT
ap-5063	265	17	“	"	PUNCT
ap-5063	265	18	dominant	dominant	ADJ
ap-5063	265	19	weight	weight	NOUN
ap-5063	265	20	multiplicities	multiplicity	NOUN
ap-5063	265	21	in	in	ADP
ap-5063	265	22	hybrid	hybrid	ADJ
ap-5063	265	23	characters	character	NOUN
ap-5063	265	24	of	of	ADP
ap-5063	265	25	bn	bn	NOUN
ap-5063	265	26	,	,	PUNCT
ap-5063	265	27	cn	cn	PROPN
ap-5063	265	28	,	,	PUNCT
ap-5063	265	29	f4	f4	PROPN
ap-5063	265	30	,	,	PUNCT
ap-5063	265	31	g2	g2	PROPN
ap-5063	265	32	.	.	PUNCT
ap-5063	265	33	”	"	PUNCT
ap-5063	265	34	internat	internat	PROPN
ap-5063	265	35	.	.	PUNCT
ap-5063	266	1	j.	j.	PROPN
ap-5063	266	2	theoret	theoret	PROPN
ap-5063	266	3	.	.	PUNCT
ap-5063	267	1	phys	phy	NOUN
ap-5063	267	2	.	.	PUNCT
ap-5063	267	3	,	,	PUNCT
ap-5063	267	4	vol	vol	NOUN
ap-5063	267	5	.	.	PROPN
ap-5063	267	6	54	54	NUM
ap-5063	267	7	(	(	PUNCT
ap-5063	267	8	11	11	NUM
ap-5063	267	9	)	)	PUNCT
ap-5063	267	10	,	,	PUNCT
ap-5063	267	11	(	(	PUNCT
ap-5063	267	12	2015	2015	NUM
ap-5063	267	13	)	)	PUNCT
ap-5063	267	14	,	,	PUNCT
ap-5063	267	15	4011–4026	4011–4026	NUM
ap-5063	267	16	.	.	PUNCT
ap-5063	268	1	[	[	X
ap-5063	268	2	13	13	NUM
ap-5063	268	3	]	]	X
ap-5063	268	4	mckay	mckay	PROPN
ap-5063	268	5	,	,	PUNCT
ap-5063	268	6	w.g	w.g	PROPN
ap-5063	268	7	.	.	PROPN
ap-5063	268	8	,	,	PUNCT
ap-5063	268	9	and	and	CCONJ
ap-5063	268	10	j.	j.	PROPN
ap-5063	268	11	patera	patera	PROPN
ap-5063	268	12	,	,	PUNCT
ap-5063	268	13	tables	table	NOUN
ap-5063	268	14	of	of	ADP
ap-5063	268	15	dimensions	dimension	NOUN
ap-5063	268	16	,	,	PUNCT
ap-5063	268	17	indices	index	NOUN
ap-5063	268	18	,	,	PUNCT
ap-5063	268	19	and	and	CCONJ
ap-5063	268	20	branching	branch	VERB
ap-5063	268	21	rules	rule	NOUN
ap-5063	268	22	for	for	ADP
ap-5063	268	23	representations	representation	NOUN
ap-5063	268	24	of	of	ADP
ap-5063	268	25	simple	simple	ADJ
ap-5063	268	26	lie	lie	NOUN
ap-5063	268	27	algebras	algebra	NOUN
ap-5063	268	28	,	,	PUNCT
ap-5063	268	29	marcel	marcel	PROPN
ap-5063	268	30	dekker	dekker	PROPN
ap-5063	268	31	,	,	PUNCT
ap-5063	268	32	new	new	PROPN
ap-5063	268	33	york	york	PROPN
ap-5063	268	34	,	,	PUNCT
ap-5063	268	35	1981	1981	NUM
ap-5063	268	36	.	.	PUNCT
ap-5063	269	1	[	[	X
ap-5063	269	2	14	14	NUM
ap-5063	269	3	]	]	X
ap-5063	269	4	mckay	mckay	PROPN
ap-5063	269	5	,	,	PUNCT
ap-5063	269	6	w.g	w.g	PROPN
ap-5063	269	7	.	.	PROPN
ap-5063	269	8	,	,	PUNCT
ap-5063	269	9	patera	patera	NOUN
ap-5063	269	10	,	,	PUNCT
ap-5063	269	11	j.	j.	PROPN
ap-5063	269	12	,	,	PUNCT
ap-5063	269	13	and	and	CCONJ
ap-5063	269	14	d.	d.	PROPN
ap-5063	269	15	sankoff	sankoff	PROPN
ap-5063	269	16	,	,	PUNCT
ap-5063	269	17	“	"	PUNCT
ap-5063	269	18	the	the	DET
ap-5063	269	19	computation	computation	NOUN
ap-5063	269	20	of	of	ADP
ap-5063	269	21	branching	branch	VERB
ap-5063	269	22	rules	rule	NOUN
ap-5063	269	23	for	for	ADP
ap-5063	269	24	representations	representation	NOUN
ap-5063	269	25	of	of	ADP
ap-5063	269	26	semisimple	semisimple	ADJ
ap-5063	269	27	lie	lie	NOUN
ap-5063	269	28	algebras	algebra	NOUN
ap-5063	269	29	.	.	PUNCT
ap-5063	269	30	”	"	PUNCT
ap-5063	270	1	computers	computer	NOUN
ap-5063	270	2	in	in	ADP
ap-5063	270	3	nonassociative	nonassociative	ADJ
ap-5063	270	4	rings	ring	NOUN
ap-5063	270	5	and	and	CCONJ
ap-5063	270	6	algebras	algebra	NOUN
ap-5063	270	7	,	,	PUNCT
ap-5063	270	8	ed	ed	PROPN
ap-5063	270	9	.	.	PUNCT
ap-5063	271	1	j.	j.	PROPN
ap-5063	271	2	beck	beck	PROPN
ap-5063	271	3	and	and	CCONJ
ap-5063	271	4	b.	b.	PROPN
ap-5063	271	5	kolman	kolman	PROPN
ap-5063	271	6	,	,	PUNCT
ap-5063	271	7	academic	academic	ADJ
ap-5063	271	8	press	press	NOUN
ap-5063	271	9	,	,	PUNCT
ap-5063	271	10	new	new	PROPN
ap-5063	271	11	york	york	PROPN
ap-5063	271	12	,	,	PUNCT
ap-5063	271	13	1977	1977	NUM
ap-5063	271	14	.	.	PUNCT
ap-5063	272	1	[	[	X
ap-5063	272	2	15	15	NUM
ap-5063	272	3	]	]	X
ap-5063	272	4	miller	miller	PROPN
ap-5063	272	5	,	,	PUNCT
ap-5063	272	6	w.	w.	PROPN
ap-5063	272	7	symmetry	symmetry	PROPN
ap-5063	272	8	and	and	CCONJ
ap-5063	272	9	separation	separation	NOUN
ap-5063	272	10	of	of	ADP
ap-5063	272	11	variables	variable	NOUN
ap-5063	272	12	,	,	PUNCT
ap-5063	272	13	with	with	ADP
ap-5063	272	14	a	a	DET
ap-5063	272	15	foreword	foreword	NOUN
ap-5063	272	16	by	by	ADP
ap-5063	272	17	richard	richard	PROPN
ap-5063	272	18	askey	askey	PROPN
ap-5063	272	19	,	,	PUNCT
ap-5063	272	20	encyclopedia	encyclopedia	NOUN
ap-5063	272	21	of	of	ADP
ap-5063	272	22	mathematics	mathematic	NOUN
ap-5063	272	23	and	and	CCONJ
ap-5063	272	24	its	its	PRON
ap-5063	272	25	applications	application	NOUN
ap-5063	272	26	4	4	NUM
ap-5063	272	27	,	,	PUNCT
ap-5063	272	28	addison	addison	PROPN
ap-5063	272	29	-	-	PUNCT
ap-5063	272	30	wesley	wesley	PROPN
ap-5063	272	31	publishing	publishing	PROPN
ap-5063	272	32	co.	co.	PROPN
ap-5063	272	33	,	,	PUNCT
ap-5063	272	34	reading	reading	NOUN
ap-5063	272	35	,	,	PUNCT
ap-5063	272	36	mass.-london	mass.-london	PROPN
ap-5063	272	37	-	-	ADJ
ap-5063	272	38	amsterdam	amsterdam	ADJ
ap-5063	272	39	,	,	PUNCT
ap-5063	272	40	1977	1977	NUM
ap-5063	272	41	.	.	PUNCT
ap-5063	273	1	[	[	X
ap-5063	273	2	16	16	NUM
ap-5063	273	3	]	]	X
ap-5063	273	4	moody	moody	PROPN
ap-5063	273	5	,	,	PUNCT
ap-5063	273	6	r.v	r.v	PROPN
ap-5063	273	7	.	.	PROPN
ap-5063	273	8	,	,	PUNCT
ap-5063	273	9	motlochova	motlochova	PROPN
ap-5063	273	10	,	,	PUNCT
ap-5063	273	11	l.	l.	PROPN
ap-5063	273	12	,	,	PUNCT
ap-5063	273	13	and	and	CCONJ
ap-5063	273	14	j.	j.	PROPN
ap-5063	273	15	patera	patera	PROPN
ap-5063	273	16	,	,	PUNCT
ap-5063	273	17	“	"	PUNCT
ap-5063	273	18	gaussian	gaussian	ADJ
ap-5063	273	19	cubature	cubature	NOUN
ap-5063	273	20	arising	arise	VERB
ap-5063	273	21	from	from	ADP
ap-5063	273	22	hybrid	hybrid	ADJ
ap-5063	273	23	characters	character	NOUN
ap-5063	273	24	of	of	ADP
ap-5063	273	25	simple	simple	ADJ
ap-5063	273	26	lie	lie	NOUN
ap-5063	273	27	groups	group	NOUN
ap-5063	273	28	.	.	PUNCT
ap-5063	273	29	”	"	PUNCT
ap-5063	274	1	j.	j.	PROPN
ap-5063	274	2	fourier	fourier	PROPN
ap-5063	274	3	analysis	analysis	NOUN
ap-5063	274	4	and	and	CCONJ
ap-5063	274	5	its	its	PRON
ap-5063	274	6	applications	application	NOUN
ap-5063	274	7	,	,	PUNCT
ap-5063	274	8	online	online	PROPN
ap-5063	274	9	issn	issn	PROPN
ap-5063	274	10	1531	1531	NUM
ap-5063	274	11	-	-	SYM
ap-5063	274	12	5851	5851	NUM
ap-5063	274	13	(	(	PUNCT
ap-5063	274	14	2014	2014	NUM
ap-5063	274	15	)	)	PUNCT
ap-5063	274	16	,	,	PUNCT
ap-5063	274	17	23	23	NUM
ap-5063	274	18	pp	pp	NOUN
ap-5063	274	19	.	.	PUNCT
ap-5063	274	20	,	,	PUNCT
ap-5063	274	21	arxiv:1202.4415	arxiv:1202.4415	NOUN
ap-5063	274	22	,	,	PUNCT
ap-5063	274	23	doi:10.1007	doi:10.1007	NOUN
ap-5063	274	24	/	/	SYM
ap-5063	274	25	s00041	s00041	NOUN
ap-5063	274	26	-	-	PUNCT
ap-5063	274	27	014	014	NUM
ap-5063	274	28	-	-	PUNCT
ap-5063	274	29	9355	9355	NUM
ap-5063	274	30	-	-	SYM
ap-5063	274	31	0	0	NUM
ap-5063	275	1	[	[	X
ap-5063	275	2	17	17	NUM
ap-5063	275	3	]	]	X
ap-5063	275	4	moody	moody	PROPN
ap-5063	275	5	,	,	PUNCT
ap-5063	275	6	r.v	r.v	PROPN
ap-5063	275	7	.	.	PROPN
ap-5063	275	8	,	,	PUNCT
ap-5063	275	9	and	and	CCONJ
ap-5063	275	10	j.	j.	PROPN
ap-5063	275	11	patera	patera	PROPN
ap-5063	275	12	,	,	PUNCT
ap-5063	275	13	“	"	PUNCT
ap-5063	275	14	characters	character	NOUN
ap-5063	275	15	of	of	ADP
ap-5063	275	16	elements	element	NOUN
ap-5063	275	17	of	of	ADP
ap-5063	275	18	finite	finite	ADJ
ap-5063	275	19	order	order	NOUN
ap-5063	275	20	in	in	ADP
ap-5063	275	21	simple	simple	ADJ
ap-5063	275	22	lie	lie	NOUN
ap-5063	275	23	groups	group	NOUN
ap-5063	275	24	.	.	PUNCT
ap-5063	275	25	”	"	PUNCT
ap-5063	276	1	siam	siam	PROPN
ap-5063	276	2	j.	j.	PROPN
ap-5063	276	3	on	on	ADP
ap-5063	276	4	algebraic	algebraic	ADJ
ap-5063	276	5	and	and	CCONJ
ap-5063	276	6	discrete	discrete	ADJ
ap-5063	276	7	methods	method	NOUN
ap-5063	276	8	,	,	PUNCT
ap-5063	276	9	5	5	NUM
ap-5063	276	10	(	(	PUNCT
ap-5063	276	11	1984	1984	NUM
ap-5063	276	12	)	)	PUNCT
ap-5063	276	13	,	,	PUNCT
ap-5063	276	14	359–383	359–383	NUM
ap-5063	276	15	.	.	PUNCT
ap-5063	277	1	[	[	X
ap-5063	277	2	18	18	NUM
ap-5063	277	3	]	]	SYM
ap-5063	277	4	moon	moon	NOUN
ap-5063	277	5	,	,	PUNCT
ap-5063	277	6	p.	p.	NOUN
ap-5063	277	7	,	,	PUNCT
ap-5063	277	8	and	and	CCONJ
ap-5063	277	9	d.e	d.e	PROPN
ap-5063	277	10	.	.	PROPN
ap-5063	277	11	spencer	spencer	PROPN
ap-5063	277	12	,	,	PUNCT
ap-5063	277	13	field	field	NOUN
ap-5063	277	14	theory	theory	NOUN
ap-5063	277	15	handbook	handbook	NOUN
ap-5063	277	16	,	,	PUNCT
ap-5063	277	17	including	include	VERB
ap-5063	277	18	coordinate	coordinate	NOUN
ap-5063	277	19	systems	system	NOUN
ap-5063	277	20	,	,	PUNCT
ap-5063	277	21	differential	differential	ADJ
ap-5063	277	22	equations	equation	NOUN
ap-5063	277	23	,	,	PUNCT
ap-5063	277	24	and	and	CCONJ
ap-5063	277	25	their	their	PRON
ap-5063	277	26	solutions	solution	NOUN
ap-5063	277	27	,	,	PUNCT
ap-5063	277	28	2nd	2nd	ADJ
ap-5063	277	29	ed	ed	NOUN
ap-5063	277	30	.	.	PUNCT
ap-5063	277	31	new	new	PROPN
ap-5063	277	32	york	york	PROPN
ap-5063	277	33	:	:	PUNCT
ap-5063	277	34	springer	springer	NOUN
ap-5063	277	35	-	-	PUNCT
ap-5063	277	36	verlag	verlag	PROPN
ap-5063	277	37	,	,	PUNCT
ap-5063	277	38	1988	1988	NUM
ap-5063	277	39	.	.	PUNCT
ap-5063	278	1	[	[	X
ap-5063	278	2	19	19	NUM
ap-5063	278	3	]	]	X
ap-5063	278	4	nesterenko	nesterenko	PROPN
ap-5063	278	5	,	,	PUNCT
ap-5063	278	6	m.	m.	NOUN
ap-5063	278	7	,	,	PUNCT
ap-5063	278	8	patera	patera	NOUN
ap-5063	278	9	,	,	PUNCT
ap-5063	278	10	j.	j.	PROPN
ap-5063	278	11	,	,	PUNCT
ap-5063	278	12	szajewska	szajewska	NOUN
ap-5063	278	13	,	,	PUNCT
ap-5063	278	14	m.	m.	NOUN
ap-5063	278	15	,	,	PUNCT
ap-5063	278	16	and	and	CCONJ
ap-5063	278	17	a.	a.	NOUN
ap-5063	278	18	tereszkiewicz	tereszkiewicz	PROPN
ap-5063	278	19	,	,	PUNCT
ap-5063	278	20	“	"	PUNCT
ap-5063	278	21	orthogonal	orthogonal	ADJ
ap-5063	278	22	polynomials	polynomial	NOUN
ap-5063	278	23	of	of	ADP
ap-5063	278	24	compact	compact	ADJ
ap-5063	278	25	simple	simple	ADJ
ap-5063	278	26	lie	lie	NOUN
ap-5063	278	27	groups	group	NOUN
ap-5063	278	28	:	:	PUNCT
ap-5063	278	29	branching	branch	VERB
ap-5063	278	30	rules	rule	NOUN
ap-5063	278	31	for	for	ADP
ap-5063	278	32	polynomials	polynomial	NOUN
ap-5063	278	33	.	.	PUNCT
ap-5063	278	34	”	"	PUNCT
ap-5063	279	1	j.	j.	PROPN
ap-5063	279	2	phys	phys	PROPN
ap-5063	279	3	.	.	PUNCT
ap-5063	280	1	a	a	DET
ap-5063	280	2	math	math	NOUN
ap-5063	280	3	.	.	PUNCT
ap-5063	281	1	theor	theor	PROPN
ap-5063	281	2	.	.	PUNCT
ap-5063	282	1	43	43	NUM
ap-5063	282	2	(	(	PUNCT
ap-5063	282	3	2010	2010	NUM
ap-5063	282	4	)	)	PUNCT
ap-5063	282	5	,	,	PUNCT
ap-5063	283	1	no	no	INTJ
ap-5063	283	2	.	.	NOUN
ap-5063	283	3	495207	495207	NUM
ap-5063	283	4	,	,	PUNCT
ap-5063	283	5	1–27	1–27	NOUN
ap-5063	283	6	.	.	PUNCT
ap-5063	284	1	[	[	X
ap-5063	284	2	20	20	NUM
ap-5063	284	3	]	]	X
ap-5063	284	4	nesterenko	nesterenko	PROPN
ap-5063	284	5	,	,	PUNCT
ap-5063	284	6	m.	m.	NOUN
ap-5063	284	7	,	,	PUNCT
ap-5063	284	8	patera	patera	NOUN
ap-5063	284	9	,	,	PUNCT
ap-5063	284	10	j.	j.	PROPN
ap-5063	284	11	,	,	PUNCT
ap-5063	284	12	and	and	CCONJ
ap-5063	284	13	a.	a.	NOUN
ap-5063	284	14	tereszkiewicz	tereszkiewicz	NOUN
ap-5063	284	15	“	"	PUNCT
ap-5063	284	16	orthogonal	orthogonal	ADJ
ap-5063	284	17	polynomials	polynomial	NOUN
ap-5063	284	18	of	of	ADP
ap-5063	284	19	compact	compact	ADJ
ap-5063	284	20	simple	simple	ADJ
ap-5063	284	21	lie	lie	NOUN
ap-5063	284	22	groups	group	NOUN
ap-5063	284	23	.	.	PUNCT
ap-5063	284	24	”	"	PUNCT
ap-5063	285	1	int	int	NOUN
ap-5063	285	2	.	.	PUNCT
ap-5063	286	1	j.	j.	PROPN
ap-5063	286	2	math	math	PROPN
ap-5063	286	3	.	.	PUNCT
ap-5063	287	1	math	math	NOUN
ap-5063	287	2	.	.	PUNCT
ap-5063	288	1	sci	sci	PROPN
ap-5063	288	2	.	.	PROPN
ap-5063	288	3	,	,	PUNCT
ap-5063	288	4	(	(	PUNCT
ap-5063	288	5	2011	2011	NUM
ap-5063	288	6	)	)	PUNCT
ap-5063	288	7	,	,	PUNCT
ap-5063	288	8	no	no	INTJ
ap-5063	288	9	.	.	NOUN
ap-5063	288	10	969424	969424	NUM
ap-5063	288	11	,	,	PUNCT
ap-5063	288	12	1	1	NUM
ap-5063	288	13	-	-	SYM
ap-5063	288	14	23	23	NUM
ap-5063	288	15	.	.	PUNCT
ap-5063	289	1	[	[	X
ap-5063	289	2	21	21	NUM
ap-5063	289	3	]	]	PUNCT
ap-5063	289	4	patera	patera	NOUN
ap-5063	289	5	,	,	PUNCT
ap-5063	289	6	j.	j.	PROPN
ap-5063	289	7	“compact	“compact	PROPN
ap-5063	289	8	simple	simple	ADJ
ap-5063	289	9	lie	lie	NOUN
ap-5063	289	10	groups	group	NOUN
ap-5063	289	11	and	and	CCONJ
ap-5063	289	12	theirs	theirs	PRON
ap-5063	289	13	c-	c-	X
ap-5063	289	14	,	,	PUNCT
ap-5063	289	15	s-	s-	X
ap-5063	289	16	,	,	PUNCT
ap-5063	289	17	and	and	CCONJ
ap-5063	289	18	e	e	X
ap-5063	289	19	-	-	NOUN
ap-5063	289	20	transforms	transform	VERB
ap-5063	289	21	.	.	PUNCT
ap-5063	289	22	”	"	PUNCT
ap-5063	289	23	sigma	sigma	PROPN
ap-5063	289	24	,	,	PUNCT
ap-5063	289	25	1	1	NUM
ap-5063	289	26	(	(	PUNCT
ap-5063	289	27	2005	2005	NUM
ap-5063	289	28	)	)	PUNCT
ap-5063	289	29	,	,	PUNCT
ap-5063	289	30	025	025	NUM
ap-5063	289	31	,	,	PUNCT
ap-5063	289	32	6	6	NUM
ap-5063	289	33	pages	page	NOUN
ap-5063	289	34	,	,	PUNCT
ap-5063	289	35	math	math	NOUN
ap-5063	289	36	-	-	PUNCT
ap-5063	289	37	ph/0512029	ph/0512029	NOUN
ap-5063	289	38	.	.	PUNCT
ap-5063	290	1	[	[	X
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ap-5063	299	7	)	)	PUNCT
ap-5063	299	8	,	,	PUNCT
ap-5063	299	9	245–253	245–253	NUM
ap-5063	299	10	.	.	PUNCT
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ap-5063	300	2	25	25	NUM
ap-5063	300	3	]	]	PUNCT
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ap-5063	300	5	,	,	PUNCT
ap-5063	300	6	a.n	a.n	PROPN
ap-5063	300	7	.	.	PROPN
ap-5063	300	8	,	,	PUNCT
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ap-5063	300	19	dover	dover	PROPN
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ap-5063	300	21	.	.	PUNCT
ap-5063	300	22	,	,	PUNCT
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ap-5063	300	25	,	,	PUNCT
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ap-5063	301	2	26	26	NUM
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ap-5063	301	10	.	.	PROPN
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ap-5063	301	16	,	,	PUNCT
ap-5063	301	17	mcgraw	mcgraw	PROPN
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ap-5063	301	30	.	.	PUNCT
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ap-5063	302	11	.	.	PROPN
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ap-5063	302	18	,	,	PUNCT
ap-5063	302	19	springer	springer	NOUN
ap-5063	302	20	,	,	PUNCT
ap-5063	302	21	new	new	PROPN
ap-5063	302	22	york	york	PROPN
ap-5063	302	23	,	,	PUNCT
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ap-5063	304	9	”	"	PUNCT
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ap-5063	409	8	+	+	CCONJ
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ap-5063	409	11	1	1	NUM
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ap-5063	409	14	)	)	PUNCT
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ap-5063	409	16	2a	2a	NUM
ap-5063	409	17	+	+	CCONJ
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ap-5063	409	69	x	x	NOUN
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ap-5063	409	85	)	)	PUNCT
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ap-5063	409	87	2a	2a	NUM
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ap-5063	409	92	(	(	PUNCT
ap-5063	409	93	z	z	NOUN
ap-5063	409	94	)	)	PUNCT
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ap-5063	409	96	2	2	NUM
ap-5063	409	97	.	.	PUNCT
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ap-5063	410	4	c-	c-	X
ap-5063	410	5	,	,	PUNCT
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ap-5063	410	7	,	,	PUNCT
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ap-5063	410	9	ss	ss	NOUN
ap-5063	410	10	-	-	PUNCT
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ap-5063	410	12	on	on	ADP
ap-5063	410	13	the	the	DET
ap-5063	410	14	boundaries	boundary	NOUN
ap-5063	410	15	of	of	ADP
ap-5063	410	16	fundamental	fundamental	ADJ
ap-5063	410	17	region	region	NOUN
ap-5063	410	18	f	f	PROPN
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ap-5063	410	20	b3	b3	PROPN
ap-5063	410	21	.	.	PUNCT
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ap-5063	411	2	separation	separation	NOUN
ap-5063	411	3	constants	constant	VERB
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ap-5063	411	5	,	,	PUNCT
ap-5063	411	6	i	i	PRON
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ap-5063	411	9	,	,	PUNCT
ap-5063	411	10	2	2	NUM
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ap-5063	411	12	3	3	NUM
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ap-5063	411	14	given	give	VERB
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ap-5063	411	16	(	(	PUNCT
ap-5063	411	17	6	6	NUM
ap-5063	411	18	)	)	PUNCT
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ap-5063	411	21	5.1	5.1	NUM
ap-5063	411	22	.	.	PUNCT
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ap-5063	411	25	szajewska	szajewska	NOUN
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ap-5063	411	28	tereszkiewicz	tereszkiewicz	PROPN
ap-5063	411	29	acta	acta	PROPN
ap-5063	411	30	polytechnica	polytechnica	PROPN
ap-5063	411	31	c3	c3	PROPN
ap-5063	411	32	c	c	PROPN
ap-5063	411	33	s	s	PROPN
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ap-5063	411	44	)	)	PUNCT
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ap-5063	415	2	)	)	PUNCT
ap-5063	415	3	)	)	PUNCT
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ap-5063	416	5	0	0	NUM
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ap-5063	421	3	1√	1√	PROPN
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ap-5063	421	8	1√	1√	PROPN
ap-5063	421	9	2	2	NUM
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ap-5063	424	5	2	2	NUM
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ap-5063	428	3	)	)	PUNCT
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ap-5063	429	4	0+sc(y)sb+c(y)sa+b+c(z	0+sc(y)sb+c(y)sa+b+c(z	NUM
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ap-5063	432	4	1√	1√	PROPN
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ap-5063	432	13	)	)	PUNCT
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ap-5063	432	22	1√	1√	PROPN
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ap-5063	432	26	)	)	PUNCT
ap-5063	432	27	)	)	PUNCT
ap-5063	433	1	c3	c3	X
ap-5063	433	2	ss	ss	PROPN
ap-5063	434	1	d	d	PROPN
ap-5063	434	2	n	n	PROPN
ap-5063	434	3	f1	f1	PROPN
ap-5063	434	4	−2(cb+c(x)ca+b+c(y)−cc(y)ca+b+c(x	−2(cb+c(x)ca+b+c(y)−cc(y)ca+b+c(x	PROPN
ap-5063	434	5	)	)	PUNCT
ap-5063	434	6	0+cb+c(y)ca+b+c(x)+cc(x)ca+b+c(y	0+cb+c(y)ca+b+c(x)+cc(x)ca+b+c(y	NUM
ap-5063	434	7	)	)	PUNCT
ap-5063	434	8	+	+	NOUN
ap-5063	434	9	cc(y)cb+c(x)−cc(x)cb+c(y	cc(y)cb+c(x)−cc(x)cb+c(y	PROPN
ap-5063	434	10	)	)	PUNCT
ap-5063	434	11	)	)	PUNCT
ap-5063	435	1	f2	f2	INTJ
ap-5063	435	2	0	0	PUNCT
ap-5063	436	1	i	i	PRON
ap-5063	436	2	√	√	VERB
ap-5063	436	3	2(k1cc(z)cb+c(x)sa+b+c(z)−k1cc(x)cb+c(z)sa+b+c(z	2(k1cc(z)cb+c(x)sa+b+c(z)−k1cc(x)cb+c(z)sa+b+c(z	NUM
ap-5063	436	4	)	)	PUNCT
ap-5063	436	5	−k2cc(z)sb+c(z)ca+b+c(x)+k2cc(x)sb+c(z)ca+b+c(z	−k2cc(z)sb+c(z)ca+b+c(x)+k2cc(x)sb+c(z)ca+b+c(z	NUM
ap-5063	436	6	)	)	PUNCT
ap-5063	437	1	+	+	NOUN
ap-5063	437	2	k3sc(z)cb+c(z)ca+b+c(x)−k3sc(z)cb+c(x)ca+b+c(z	k3sc(z)cb+c(z)ca+b+c(x)−k3sc(z)cb+c(x)ca+b+c(z	NOUN
ap-5063	437	3	)	)	PUNCT
ap-5063	437	4	)	)	PUNCT
ap-5063	437	5	f3	f3	NOUN
ap-5063	437	6	0	0	NUM
ap-5063	438	1	−i	−i	ADJ
ap-5063	438	2	√	√	NUM
ap-5063	438	3	2(k1cc(z)cb+c(y)sa+b+c(y)−k1cc(y)cb+c(z)sa+b+c(y	2(k1cc(z)cb+c(y)sa+b+c(y)−k1cc(y)cb+c(z)sa+b+c(y	NUM
ap-5063	438	4	)	)	PUNCT
ap-5063	438	5	−k2cc(z)sb+c(y)ca+b+c(y)+k2cc(y)sb+c(y)ca+b+c(z	−k2cc(z)sb+c(y)ca+b+c(y)+k2cc(y)sb+c(y)ca+b+c(z	NOUN
ap-5063	438	6	)	)	PUNCT
ap-5063	439	1	+	+	ADJ
ap-5063	439	2	k3sc(y)cb+c(z)ca+b+c(y)−k3sc(y)cb+c(y)ca+b+c(z	k3sc(y)cb+c(z)ca+b+c(y)−k3sc(y)cb+c(y)ca+b+c(z	NOUN
ap-5063	439	3	)	)	PUNCT
ap-5063	439	4	)	)	PUNCT
ap-5063	440	1	f4	f4	ADP
ap-5063	440	2	cc(z)ca+b+c	cc(z)ca+b+c	PROPN
ap-5063	440	3	(	(	PUNCT
ap-5063	440	4	1√	1√	PROPN
ap-5063	440	5	2	2	NUM
ap-5063	440	6	)	)	PUNCT
ap-5063	440	7	cb+c(y)−cc(y)ca+b+c	cb+c(y)−cc(y)ca+b+c	PROPN
ap-5063	440	8	(	(	PUNCT
ap-5063	440	9	1√	1√	NOUN
ap-5063	440	10	2	2	NUM
ap-5063	440	11	)	)	PUNCT
ap-5063	440	12	cb+c(z	cb+c(z	PROPN
ap-5063	440	13	)	)	PUNCT
ap-5063	440	14	0−cb+c	0−cb+c	NOUN
ap-5063	440	15	(	(	PUNCT
ap-5063	440	16	1√	1√	PROPN
ap-5063	440	17	2	2	NUM
ap-5063	440	18	)	)	PUNCT
ap-5063	440	19	cc(z)ca+b+c(y)+cc	cc(z)ca+b+c(y)+cc	PROPN
ap-5063	440	20	(	(	PUNCT
ap-5063	440	21	1√	1√	PROPN
ap-5063	440	22	2	2	NUM
ap-5063	440	23	)	)	PUNCT
ap-5063	440	24	cb+c(z)ca+b+c(y	cb+c(z)ca+b+c(y	X
ap-5063	440	25	)	)	PUNCT
ap-5063	440	26	+	+	NOUN
ap-5063	440	27	cb+c	cb+c	PROPN
ap-5063	440	28	(	(	PUNCT
ap-5063	440	29	1√	1√	PROPN
ap-5063	440	30	2	2	NUM
ap-5063	440	31	)	)	PUNCT
ap-5063	440	32	cc(y)ca+b+c(z)−cc	cc(y)ca+b+c(z)−cc	PROPN
ap-5063	440	33	(	(	PUNCT
ap-5063	440	34	1√	1√	PROPN
ap-5063	440	35	2	2	NUM
ap-5063	440	36	)	)	PUNCT
ap-5063	440	37	cb+c(y)ca+b+c(z	cb+c(y)ca+b+c(z	NUM
ap-5063	440	38	)	)	PUNCT
ap-5063	440	39	table	table	NOUN
ap-5063	440	40	3	3	NUM
ap-5063	440	41	.	.	PUNCT
ap-5063	441	1	the	the	DET
ap-5063	441	2	values	value	NOUN
ap-5063	441	3	of	of	ADP
ap-5063	441	4	c-	c-	X
ap-5063	441	5	,	,	PUNCT
ap-5063	441	6	s-	s-	X
ap-5063	441	7	,	,	PUNCT
ap-5063	441	8	sland	sland	NOUN
ap-5063	441	9	ss	ss	NOUN
ap-5063	441	10	-	-	PUNCT
ap-5063	441	11	functions	function	NOUN
ap-5063	441	12	on	on	ADP
ap-5063	441	13	the	the	DET
ap-5063	441	14	boundaries	boundary	NOUN
ap-5063	441	15	of	of	ADP
ap-5063	441	16	fundamental	fundamental	ADJ
ap-5063	441	17	region	region	NOUN
ap-5063	441	18	f	f	PROPN
ap-5063	441	19	of	of	ADP
ap-5063	441	20	c3	c3	PROPN
ap-5063	441	21	.	.	PUNCT
ap-5063	442	1	the	the	DET
ap-5063	442	2	separation	separation	NOUN
ap-5063	442	3	constants	constant	VERB
ap-5063	442	4	ki	ki	PROPN
ap-5063	442	5	,	,	PUNCT
ap-5063	442	6	i	i	PRON
ap-5063	442	7	=	=	NOUN
ap-5063	442	8	1	1	NUM
ap-5063	442	9	,	,	PUNCT
ap-5063	442	10	2	2	NUM
ap-5063	442	11	,	,	PUNCT
ap-5063	442	12	3	3	NUM
ap-5063	442	13	are	be	AUX
ap-5063	442	14	given	give	VERB
ap-5063	442	15	by	by	ADP
ap-5063	442	16	(	(	PUNCT
ap-5063	442	17	7	7	NUM
ap-5063	442	18	)	)	PUNCT
ap-5063	442	19	in	in	ADP
ap-5063	442	20	§	§	PROPN
ap-5063	442	21	5.1	5.1	NUM
ap-5063	442	22	.	.	PUNCT
ap-5063	442	23	410	410	NUM
ap-5063	442	24	vol	vol	NOUN
ap-5063	442	25	.	.	PUNCT
ap-5063	443	1	58	58	NUM
ap-5063	443	2	no	no	INTJ
ap-5063	443	3	.	.	PUNCT
ap-5063	444	1	6/2018	6/2018	NUM
ap-5063	444	2	multidimensional	multidimensional	ADJ
ap-5063	444	3	hybrid	hybrid	ADJ
ap-5063	444	4	boundary	boundary	ADJ
ap-5063	444	5	value	value	NOUN
ap-5063	444	6	problem	problem	NOUN
ap-5063	445	1	c2×a1	c2×a1	PROPN
ap-5063	445	2	c	c	PROPN
ap-5063	445	3	s	s	PROPN
ap-5063	445	4	d	d	PROPN
ap-5063	445	5	n	n	PROPN
ap-5063	445	6	d	d	PROPN
ap-5063	445	7	n	n	PRON
ap-5063	445	8	f1	f1	NOUN
ap-5063	445	9	2(ca+b(x)cb(y)+cb(x)ca+b(y	2(ca+b(x)cb(y)+cb(x)ca+b(y	NUM
ap-5063	445	10	)	)	PUNCT
ap-5063	445	11	)	)	PUNCT
ap-5063	445	12	0	0	NUM
ap-5063	445	13	0	0	NUM
ap-5063	445	14	−2ik3(sa+b(x)sb(y)−sb(x)sa+b(y	−2ik3(sa+b(x)sb(y)−sb(x)sa+b(y	NUM
ap-5063	445	15	)	)	PUNCT
ap-5063	445	16	)	)	PUNCT
ap-5063	446	1	f2	f2	PROPN
ap-5063	446	2	2(ca+b(x)cc(z)+cb(x)cc(z	2(ca+b(x)cc(z)+cb(x)cc(z	NUM
ap-5063	446	3	)	)	PUNCT
ap-5063	446	4	)	)	PUNCT
ap-5063	446	5	0	0	NUM
ap-5063	446	6	0	0	NUM
ap-5063	446	7	−2ik2sa+b(x)sc(z)+ik1sb(x)sc(z	−2ik2sa+b(x)sc(z)+ik1sb(x)sc(z	NOUN
ap-5063	446	8	)	)	PUNCT
ap-5063	446	9	f3	f3	NOUN
ap-5063	446	10	2ca+b(y)cb(y)cc(z	2ca+b(y)cb(y)cc(z	NUM
ap-5063	446	11	)	)	PUNCT
ap-5063	446	12	0	0	NUM
ap-5063	446	13	0	0	NUM
ap-5063	446	14	−i	−i	ADJ
ap-5063	446	15	√	√	NUM
ap-5063	446	16	2(k1ca+b(y)sb(y)sc(z)−k2cb(y)sa+b(y)sc(z	2(k1ca+b(y)sb(y)sc(z)−k2cb(y)sa+b(y)sc(z	NUM
ap-5063	446	17	)	)	PUNCT
ap-5063	446	18	)	)	PUNCT
ap-5063	447	1	f4	f4	PRON
ap-5063	447	2	ca+b	ca+b	PROPN
ap-5063	447	3	(	(	PUNCT
ap-5063	447	4	√	√	ADV
ap-5063	447	5	2	2	NUM
ap-5063	447	6	2	2	NUM
ap-5063	447	7	)	)	PUNCT
ap-5063	447	8	cb(y)cc(z)+cb	cb(y)cc(z)+cb	NOUN
ap-5063	447	9	(	(	PUNCT
ap-5063	447	10	√	√	ADV
ap-5063	447	11	2	2	NUM
ap-5063	447	12	2	2	NUM
ap-5063	447	13	)	)	PUNCT
ap-5063	447	14	ca+b(y)cc(z	ca+b(y)cc(z	PROPN
ap-5063	447	15	)	)	PUNCT
ap-5063	447	16	0	0	NUM
ap-5063	447	17	0	0	NUM
ap-5063	447	18	ik1ca+b	ik1ca+b	NOUN
ap-5063	447	19	(	(	PUNCT
ap-5063	447	20	√	√	ADV
ap-5063	447	21	2	2	NUM
ap-5063	447	22	2	2	NUM
ap-5063	447	23	)	)	PUNCT
ap-5063	447	24	sb(y)sc(z)−ik2cb	sb(y)sc(z)−ik2cb	NOUN
ap-5063	447	25	(	(	PUNCT
ap-5063	447	26	√	√	NUM
ap-5063	447	27	2	2	NUM
ap-5063	447	28	2	2	NUM
ap-5063	447	29	)	)	PUNCT
ap-5063	447	30	sa+b(y)sc(z	sa+b(y)sc(z	NOUN
ap-5063	447	31	)	)	PUNCT
ap-5063	447	32	f5	f5	PROPN
ap-5063	447	33	ca+b(x)cb(y)cc	ca+b(x)cb(y)cc	PROPN
ap-5063	447	34	(	(	PUNCT
ap-5063	447	35	√	√	ADV
ap-5063	447	36	2	2	NUM
ap-5063	447	37	2	2	NUM
ap-5063	447	38	)	)	PUNCT
ap-5063	447	39	+	+	PUNCT
ap-5063	447	40	cb(x)ca+b(y)cc	cb(x)ca+b(y)cc	X
ap-5063	447	41	(	(	PUNCT
ap-5063	447	42	√	√	ADV
ap-5063	447	43	2	2	NUM
ap-5063	447	44	2	2	NUM
ap-5063	447	45	)	)	PUNCT
ap-5063	447	46	0	0	NUM
ap-5063	447	47	0	0	NUM
ap-5063	448	1	ik3(sa+b(x)sb(y)cc	ik3(sa+b(x)sb(y)cc	NOUN
ap-5063	448	2	(	(	PUNCT
ap-5063	448	3	√	√	ADV
ap-5063	448	4	2	2	NUM
ap-5063	448	5	2	2	NUM
ap-5063	448	6	)	)	PUNCT
ap-5063	448	7	−sb(x)sa+b(y)cc	−sb(x)sa+b(y)cc	NOUN
ap-5063	448	8	(	(	PUNCT
ap-5063	448	9	√	√	ADV
ap-5063	448	10	2	2	NUM
ap-5063	448	11	2	2	NUM
ap-5063	448	12	)	)	PUNCT
ap-5063	448	13	)	)	PUNCT
ap-5063	449	1	c2×a1	c2×a1	PROPN
ap-5063	450	1	sl	sl	INTJ
ap-5063	450	2	d	d	PROPN
ap-5063	450	3	n	n	PROPN
ap-5063	450	4	f1	f1	NOUN
ap-5063	450	5	0	0	PUNCT
ap-5063	451	1	−2ik3(sa+b(x)sb(y)+sb(x)sa+b(y	−2ik3(sa+b(x)sb(y)+sb(x)sa+b(y	ADJ
ap-5063	451	2	)	)	PUNCT
ap-5063	451	3	)	)	PUNCT
ap-5063	452	1	f2	f2	CCONJ
ap-5063	452	2	0	0	NUM
ap-5063	452	3	−2i(k2sa+b(x)sc(z)+k1sb(x)sc(z	−2i(k2sa+b(x)sc(z)+k1sb(x)sc(z	NOUN
ap-5063	452	4	)	)	PUNCT
ap-5063	452	5	)	)	PUNCT
ap-5063	452	6	f3	f3	PROPN
ap-5063	452	7	2sa+b(y)sb(y)sc(z	2sa+b(y)sb(y)sc(z	NUM
ap-5063	452	8	)	)	PUNCT
ap-5063	452	9	0	0	PUNCT
ap-5063	453	1	f4	f4	NOUN
ap-5063	453	2	0	0	NUM
ap-5063	453	3	i(k1ca+b	i(k1ca+b	NOUN
ap-5063	453	4	(	(	PUNCT
ap-5063	453	5	√	√	ADV
ap-5063	453	6	2	2	NUM
ap-5063	453	7	2	2	NUM
ap-5063	453	8	)	)	PUNCT
ap-5063	453	9	sb(y)sc(z)+k2cb	sb(y)sc(z)+k2cb	PROPN
ap-5063	453	10	(	(	PUNCT
ap-5063	453	11	√	√	NUM
ap-5063	453	12	2	2	NUM
ap-5063	453	13	2	2	NUM
ap-5063	453	14	)	)	PUNCT
ap-5063	453	15	sa+b(y)sc(z	sa+b(y)sc(z	NOUN
ap-5063	453	16	)	)	PUNCT
ap-5063	453	17	)	)	PUNCT
ap-5063	453	18	f5	f5	VERB
ap-5063	453	19	0	0	NUM
ap-5063	453	20	ik3(sa+b(x)sb(y)cc	ik3(sa+b(x)sb(y)cc	NOUN
ap-5063	453	21	(	(	PUNCT
ap-5063	453	22	√	√	ADV
ap-5063	453	23	2	2	NUM
ap-5063	453	24	2	2	NUM
ap-5063	453	25	)	)	PUNCT
ap-5063	453	26	+	+	X
ap-5063	453	27	sb(x)sa+b(y)cc	sb(x)sa+b(y)cc	PROPN
ap-5063	453	28	(	(	PUNCT
ap-5063	453	29	√	√	ADV
ap-5063	453	30	2	2	NUM
ap-5063	453	31	2	2	NUM
ap-5063	453	32	)	)	PUNCT
ap-5063	453	33	)	)	PUNCT
ap-5063	454	1	c2×a1	c2×a1	ADP
ap-5063	454	2	ss	ss	PROPN
ap-5063	454	3	d	d	PROPN
ap-5063	454	4	n	n	PRON
ap-5063	454	5	f1	f1	NOUN
ap-5063	454	6	2(ca+b(x)cb(y)−cb(x)ca+b(y	2(ca+b(x)cb(y)−cb(x)ca+b(y	NUM
ap-5063	454	7	)	)	PUNCT
ap-5063	454	8	)	)	PUNCT
ap-5063	454	9	0	0	PUNCT
ap-5063	455	1	f2	f2	PROPN
ap-5063	455	2	2(ca+b(x)cc(z)−cb(x)cc(z	2(ca+b(x)cc(z)−cb(x)cc(z	NUM
ap-5063	455	3	)	)	PUNCT
ap-5063	455	4	)	)	PUNCT
ap-5063	455	5	0	0	NUM
ap-5063	456	1	f3	f3	NOUN
ap-5063	456	2	0	0	NUM
ap-5063	457	1	−i	−i	ADJ
ap-5063	458	1	√	√	ADP
ap-5063	458	2	2(k1sa+b(y)cb(y)cc(z)−k2sb(y)ca+b(y)cc(z	2(k1sa+b(y)cb(y)cc(z)−k2sb(y)ca+b(y)cc(z	NUM
ap-5063	458	3	)	)	PUNCT
ap-5063	458	4	)	)	PUNCT
ap-5063	459	1	f4	f4	PRON
ap-5063	459	2	ca+b	ca+b	PROPN
ap-5063	459	3	(	(	PUNCT
ap-5063	459	4	√	√	ADV
ap-5063	459	5	2	2	NUM
ap-5063	459	6	2	2	NUM
ap-5063	459	7	)	)	PUNCT
ap-5063	459	8	cb(y)cc(z)−cb	cb(y)cc(z)−cb	PROPN
ap-5063	459	9	(	(	PUNCT
ap-5063	459	10	√	√	NUM
ap-5063	459	11	2	2	NUM
ap-5063	459	12	2	2	NUM
ap-5063	459	13	)	)	PUNCT
ap-5063	459	14	ca+b(y)cc(z	ca+b(y)cc(z	PROPN
ap-5063	459	15	)	)	PUNCT
ap-5063	459	16	0	0	NUM
ap-5063	459	17	f5	f5	PROPN
ap-5063	459	18	ca+b(x)cb(y)cc	ca+b(x)cb(y)cc	PROPN
ap-5063	459	19	(	(	PUNCT
ap-5063	459	20	√	√	ADV
ap-5063	459	21	2	2	NUM
ap-5063	459	22	2	2	NUM
ap-5063	459	23	)	)	PUNCT
ap-5063	459	24	−cb(x)ca+b(y)cc	−cb(x)ca+b(y)cc	NOUN
ap-5063	459	25	(	(	PUNCT
ap-5063	459	26	√	√	ADV
ap-5063	459	27	2	2	NUM
ap-5063	459	28	2	2	NUM
ap-5063	459	29	)	)	PUNCT
ap-5063	459	30	0	0	NUM
ap-5063	459	31	table	table	NOUN
ap-5063	459	32	4	4	NUM
ap-5063	459	33	.	.	PUNCT
ap-5063	460	1	the	the	DET
ap-5063	460	2	values	value	NOUN
ap-5063	460	3	of	of	ADP
ap-5063	460	4	c-	c-	X
ap-5063	460	5	,	,	PUNCT
ap-5063	460	6	s-	s-	X
ap-5063	460	7	,	,	PUNCT
ap-5063	460	8	sland	sland	NOUN
ap-5063	460	9	ss	ss	NOUN
ap-5063	460	10	-	-	PUNCT
ap-5063	460	11	functions	function	NOUN
ap-5063	460	12	on	on	ADP
ap-5063	460	13	the	the	DET
ap-5063	460	14	boundaries	boundary	NOUN
ap-5063	460	15	of	of	ADP
ap-5063	460	16	fundamental	fundamental	ADJ
ap-5063	460	17	region	region	NOUN
ap-5063	460	18	f	f	PROPN
ap-5063	460	19	of	of	ADP
ap-5063	460	20	c2	c2	PROPN
ap-5063	460	21	×	×	PROPN
ap-5063	460	22	a1	a1	NOUN
ap-5063	460	23	.	.	PUNCT
ap-5063	461	1	the	the	DET
ap-5063	461	2	separation	separation	NOUN
ap-5063	461	3	constants	constant	VERB
ap-5063	461	4	ki	ki	PROPN
ap-5063	461	5	,	,	PUNCT
ap-5063	461	6	i	i	PRON
ap-5063	461	7	=	=	NOUN
ap-5063	461	8	1	1	NUM
ap-5063	461	9	,	,	PUNCT
ap-5063	461	10	2	2	NUM
ap-5063	461	11	,	,	PUNCT
ap-5063	461	12	3	3	NUM
ap-5063	461	13	are	be	AUX
ap-5063	461	14	given	give	VERB
ap-5063	461	15	by	by	ADP
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ap-5063	461	17	8)	8)	NUM
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ap-5063	506	15	(	(	PUNCT
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ap-5063	507	12	(	(	PUNCT
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ap-5063	509	9	2	2	NUM
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ap-5063	509	13	s	s	NOUN
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ap-5063	509	20	(	(	PUNCT
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ap-5063	509	23	(	(	PUNCT
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ap-5063	509	30	(	(	PUNCT
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ap-5063	509	33	−	−	PROPN
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ap-5063	510	2	a	a	DET
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ap-5063	510	5	(	(	PUNCT
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ap-5063	510	9	3a	3a	NUM
ap-5063	510	10	+	+	SYM
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ap-5063	510	12	(	(	PUNCT
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ap-5063	511	5	(	(	PUNCT
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ap-5063	511	10	(	(	PUNCT
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ap-5063	512	26	−	−	PUNCT
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ap-5063	525	22	−	−	PROPN
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ap-5063	526	5	(	(	PUNCT
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ap-5063	526	10	+	+	SYM
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ap-5063	527	8	−	−	PROPN
ap-5063	527	9	c	c	NOUN
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ap-5063	527	11	+	+	CCONJ
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ap-5063	527	13	(	(	PUNCT
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ap-5063	527	18	(	(	PUNCT
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ap-5063	527	20	)	)	PUNCT
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ap-5063	529	20	(	(	PUNCT
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ap-5063	531	1	58	58	NUM
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ap-5063	531	3	.	.	PUNCT
ap-5063	532	1	6/2018	6/2018	NUM
ap-5063	532	2	multidimensional	multidimensional	ADJ
ap-5063	532	3	hybrid	hybrid	ADJ
ap-5063	532	4	boundary	boundary	ADJ
ap-5063	532	5	value	value	NOUN
ap-5063	532	6	problem	problem	NOUN
ap-5063	532	7	a1×a1×a1	a1×a1×a1	PROPN
ap-5063	532	8	ccc	ccc	PROPN
ap-5063	532	9	sss	sss	VERB
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ap-5063	532	11	n	n	PROPN
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ap-5063	532	13	n	n	PRON
ap-5063	532	14	f1	f1	NOUN
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ap-5063	532	18	0	0	NUM
ap-5063	533	1	−	−	NOUN
ap-5063	534	1	√	√	NOUN
ap-5063	534	2	2πik3sa(x)sb(y)cc(0	2πik3sa(x)sb(y)cc(0	NUM
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ap-5063	534	4	f2	f2	PROPN
ap-5063	534	5	ca(x)cb(0)cc(z	ca(x)cb(0)cc(z	NOUN
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ap-5063	534	8	0	0	NUM
ap-5063	535	1	−	−	NUM
ap-5063	535	2	√	√	NUM
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ap-5063	535	5	f3	f3	PROPN
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ap-5063	535	9	0	0	NUM
ap-5063	536	1	−	−	NOUN
ap-5063	536	2	√	√	NUM
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ap-5063	536	5	f4	f4	NOUN
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ap-5063	536	8	1√	1√	PROPN
ap-5063	536	9	2	2	NUM
ap-5063	536	10	)	)	PUNCT
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ap-5063	536	14	0	0	NUM
ap-5063	536	15	√	√	NUM
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ap-5063	536	17	(	(	PUNCT
ap-5063	536	18	1√	1√	PROPN
ap-5063	536	19	2	2	NUM
ap-5063	536	20	)	)	PUNCT
ap-5063	536	21	sc(z	sc(z	NOUN
ap-5063	536	22	)	)	PUNCT
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ap-5063	536	24	ca	ca	NOUN
ap-5063	536	25	(	(	PUNCT
ap-5063	536	26	1√	1√	PROPN
ap-5063	536	27	2	2	NUM
ap-5063	536	28	)	)	PUNCT
ap-5063	536	29	cb(y)cc(z	cb(y)cc(z	NOUN
ap-5063	536	30	)	)	PUNCT
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ap-5063	536	32	0	0	NUM
ap-5063	537	1	√	√	NUM
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ap-5063	537	3	(	(	PUNCT
ap-5063	537	4	1√	1√	PROPN
ap-5063	537	5	2	2	NUM
ap-5063	537	6	)	)	PUNCT
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ap-5063	537	10	ca(x)cb(y)cc	ca(x)cb(y)cc	PROPN
ap-5063	537	11	(	(	PUNCT
ap-5063	537	12	1√	1√	PROPN
ap-5063	537	13	2	2	NUM
ap-5063	537	14	)	)	PUNCT
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ap-5063	537	16	0	0	NUM
ap-5063	537	17	√	√	NUM
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ap-5063	537	19	(	(	PUNCT
ap-5063	537	20	1√	1√	PROPN
ap-5063	537	21	2	2	NUM
ap-5063	537	22	)	)	PUNCT
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ap-5063	537	25	ssc	ssc	PROPN
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ap-5063	537	27	n	n	PROPN
ap-5063	537	28	d	d	PROPN
ap-5063	537	29	n	n	CCONJ
ap-5063	537	30	f1	f1	NOUN
ap-5063	537	31	0	0	NUM
ap-5063	537	32	−	−	PROPN
ap-5063	538	1	√	√	NUM
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ap-5063	538	3	)	)	PUNCT
ap-5063	538	4	sa(x)sb(y)cc(0	sa(x)sb(y)cc(0	NUM
ap-5063	538	5	)	)	PUNCT
ap-5063	538	6	0	0	NUM
ap-5063	538	7	f2	f2	PROPN
ap-5063	538	8	ca(x)cb(0)sc(z	ca(x)cb(0)sc(z	PROPN
ap-5063	538	9	)	)	PUNCT
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ap-5063	538	11	0	0	NUM
ap-5063	538	12	−	−	NOUN
ap-5063	538	13	√	√	NUM
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ap-5063	538	15	)	)	PUNCT
ap-5063	538	16	f3	f3	PROPN
ap-5063	538	17	ca(0)cb(y)sc(z	ca(0)cb(y)sc(z	PROPN
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ap-5063	538	19	0	0	NUM
ap-5063	538	20	0	0	NUM
ap-5063	539	1	−	−	NOUN
ap-5063	540	1	√	√	NUM
ap-5063	540	2	2πik1ca(0)sb(y)cc(z	2πik1ca(0)sb(y)cc(z	NUM
ap-5063	540	3	)	)	PUNCT
ap-5063	540	4	f4	f4	NOUN
ap-5063	540	5	ca(x)cb	ca(x)cb	NOUN
ap-5063	540	6	(	(	PUNCT
ap-5063	540	7	1√	1√	PROPN
ap-5063	540	8	2	2	NUM
ap-5063	540	9	)	)	PUNCT
ap-5063	540	10	sc(z	sc(z	NOUN
ap-5063	540	11	)	)	PUNCT
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ap-5063	540	13	0	0	NUM
ap-5063	540	14	√	√	NUM
ap-5063	540	15	2πik2sa(x)cb	2πik2sa(x)cb	NUM
ap-5063	540	16	(	(	PUNCT
ap-5063	540	17	1√	1√	PROPN
ap-5063	540	18	2	2	NUM
ap-5063	540	19	)	)	PUNCT
ap-5063	540	20	cc(z	cc(z	X
ap-5063	540	21	)	)	PUNCT
ap-5063	541	1	f5	f5	PROPN
ap-5063	541	2	ca	ca	NOUN
ap-5063	541	3	(	(	PUNCT
ap-5063	541	4	1√	1√	PROPN
ap-5063	541	5	2	2	NUM
ap-5063	541	6	)	)	PUNCT
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ap-5063	541	10	0	0	NUM
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ap-5063	541	13	(	(	PUNCT
ap-5063	541	14	1√	1√	PROPN
ap-5063	541	15	2	2	NUM
ap-5063	541	16	)	)	PUNCT
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ap-5063	541	21	√	√	NUM
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ap-5063	541	23	(	(	PUNCT
ap-5063	541	24	1√	1√	PROPN
ap-5063	541	25	2	2	NUM
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ap-5063	541	28	(	(	PUNCT
ap-5063	541	29	1√	1√	PROPN
ap-5063	541	30	2	2	NUM
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ap-5063	542	12	0	0	NUM
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ap-5063	543	7	−	−	NOUN
ap-5063	543	8	√	√	NUM
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ap-5063	543	11	sa(x)cb(0)sc(z	sa(x)cb(0)sc(z	NOUN
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ap-5063	544	2	√	√	NUM
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ap-5063	545	2	0	0	NUM
ap-5063	545	3	√	√	NUM
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ap-5063	545	6	1√	1√	PROPN
ap-5063	545	7	2	2	NUM
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ap-5063	545	12	(	(	PUNCT
ap-5063	545	13	1√	1√	PROPN
ap-5063	545	14	2	2	NUM
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ap-5063	546	5	2	2	NUM
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ap-5063	546	21	(	(	PUNCT
ap-5063	546	22	1√	1√	PROPN
ap-5063	546	23	2	2	NUM
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ap-5063	546	35	css	css	PROPN
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ap-5063	550	6	0	0	NUM
ap-5063	551	1	−	−	NOUN
ap-5063	551	2	√	√	NUM
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ap-5063	552	3	(	(	PUNCT
ap-5063	552	4	1√	1√	PROPN
ap-5063	552	5	2	2	NUM
ap-5063	552	6	)	)	PUNCT
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ap-5063	552	10	0	0	NUM
ap-5063	552	11	√	√	NUM
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ap-5063	552	13	(	(	PUNCT
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ap-5063	552	21	√	√	NOUN
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ap-5063	552	24	1√	1√	PROPN
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ap-5063	552	28	)	)	PUNCT
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ap-5063	553	2	(	(	PUNCT
ap-5063	553	3	1√	1√	PROPN
ap-5063	553	4	2	2	NUM
ap-5063	553	5	)	)	PUNCT
ap-5063	553	6	sb(y)sc(z	sb(y)sc(z	NOUN
ap-5063	553	7	)	)	PUNCT
ap-5063	553	8	0	0	NUM
ap-5063	554	1	f6	f6	PROPN
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ap-5063	554	3	(	(	PUNCT
ap-5063	554	4	1√	1√	NOUN
ap-5063	554	5	2	2	NUM
ap-5063	554	6	)	)	PUNCT
ap-5063	554	7	0	0	NUM
ap-5063	554	8	0	0	NUM
ap-5063	554	9	√	√	NUM
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ap-5063	554	11	(	(	PUNCT
ap-5063	554	12	1√	1√	PROPN
ap-5063	554	13	2	2	NUM
ap-5063	554	14	)	)	PUNCT
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ap-5063	555	2	values	value	NOUN
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ap-5063	555	4	six	six	NUM
ap-5063	555	5	families	family	NOUN
ap-5063	555	6	of	of	ADP
ap-5063	555	7	functions	function	NOUN
ap-5063	555	8	on	on	ADP
ap-5063	555	9	the	the	DET
ap-5063	555	10	boundaries	boundary	NOUN
ap-5063	555	11	of	of	ADP
ap-5063	555	12	fundamental	fundamental	ADJ
ap-5063	555	13	region	region	NOUN
ap-5063	555	14	f	f	PROPN
ap-5063	555	15	of	of	ADP
ap-5063	555	16	a1	a1	PROPN
ap-5063	555	17	×	×	NOUN
ap-5063	555	18	a1	a1	NOUN
ap-5063	555	19	×	×	NOUN
ap-5063	555	20	a1	a1	NOUN
ap-5063	555	21	.	.	PUNCT
ap-5063	556	1	the	the	DET
ap-5063	556	2	separation	separation	NOUN
ap-5063	556	3	constants	constant	VERB
ap-5063	556	4	ki	ki	PROPN
ap-5063	556	5	,	,	PUNCT
ap-5063	556	6	i	i	PRON
ap-5063	556	7	=	=	NOUN
ap-5063	556	8	1	1	NUM
ap-5063	556	9	,	,	PUNCT
ap-5063	556	10	2	2	NUM
ap-5063	556	11	,	,	PUNCT
ap-5063	556	12	3	3	NUM
ap-5063	556	13	are	be	AUX
ap-5063	556	14	given	give	VERB
ap-5063	556	15	by	by	ADP
ap-5063	556	16	(	(	PUNCT
ap-5063	556	17	10	10	NUM
ap-5063	556	18	)	)	PUNCT
ap-5063	556	19	in	in	ADP
ap-5063	556	20	§	§	PROPN
ap-5063	556	21	5.3	5.3	NUM
ap-5063	556	22	.	.	PUNCT
ap-5063	556	23	413	413	NUM
ap-5063	556	24	acta	acta	PROPN
ap-5063	556	25	polytechnica	polytechnica	PROPN
ap-5063	556	26	58(6):402–413	58(6):402–413	PROPN
ap-5063	556	27	,	,	PUNCT
ap-5063	556	28	2018	2018	NUM
ap-5063	556	29	1	1	NUM
ap-5063	556	30	introduction	introduction	NOUN
ap-5063	556	31	2	2	NUM
ap-5063	556	32	helmholtz	helmholtz	NOUN
ap-5063	556	33	equation	equation	NOUN
ap-5063	556	34	and	and	CCONJ
ap-5063	556	35	boundary	boundary	ADJ
ap-5063	556	36	conditions	condition	NOUN
ap-5063	556	37	3	3	NUM
ap-5063	556	38	finite	finite	ADJ
ap-5063	556	39	reflection	reflection	NOUN
ap-5063	556	40	groups	group	NOUN
ap-5063	556	41	4	4	NUM
ap-5063	556	42	special	special	ADJ
ap-5063	556	43	functions	function	NOUN
ap-5063	556	44	as	as	ADP
ap-5063	556	45	a	a	DET
ap-5063	556	46	solution	solution	NOUN
ap-5063	556	47	of	of	ADP
ap-5063	556	48	helmholtz	helmholtz	NOUN
ap-5063	556	49	equation	equation	NOUN
ap-5063	556	50	5	5	NUM
ap-5063	556	51	3d	3d	NUM
ap-5063	556	52	finite	finite	PROPN
ap-5063	556	53	reflection	reflection	NOUN
ap-5063	556	54	groups	group	NOUN
ap-5063	556	55	5.1	5.1	NUM
ap-5063	556	56	b3	b3	PROPN
ap-5063	556	57	and	and	CCONJ
ap-5063	556	58	c3	c3	NOUN
ap-5063	556	59	groups	group	NOUN
ap-5063	556	60	5.2	5.2	NUM
ap-5063	556	61	c2a1	c2a1	NOUN
ap-5063	556	62	and	and	CCONJ
ap-5063	556	63	g2a1	g2a1	NOUN
ap-5063	556	64	groups	group	NOUN
ap-5063	556	65	5.3	5.3	NUM
ap-5063	556	66	a1	a1	NOUN
ap-5063	556	67	a1	a1	NOUN
ap-5063	556	68	a1	a1	NOUN
ap-5063	556	69	group	group	NOUN
ap-5063	556	70	6	6	NUM
ap-5063	556	71	appendix	appendix	ADJ
ap-5063	556	72	references	reference	NOUN