id	sid	tid	token	lemma	pos
ap-3509	1	1	acta	acta	PROPN
ap-3509	1	2	polytechnica	polytechnica	PROPN
ap-3509	1	3	doi:10.14311	doi:10.14311	PROPN
ap-3509	1	4	/	/	SYM
ap-3509	1	5	ap.2016.56.0245	ap.2016.56.0245	PROPN
ap-3509	1	6	acta	acta	PROPN
ap-3509	1	7	polytechnica	polytechnica	PROPN
ap-3509	1	8	56(3):245–253	56(3):245–253	PROPN
ap-3509	1	9	,	,	PUNCT
ap-3509	1	10	2016	2016	NUM
ap-3509	1	11	©	©	PROPN
ap-3509	1	12	czech	czech	PROPN
ap-3509	1	13	technical	technical	PROPN
ap-3509	1	14	university	university	PROPN
ap-3509	1	15	in	in	ADP
ap-3509	1	16	prague	prague	PROPN
ap-3509	1	17	,	,	PUNCT
ap-3509	1	18	2016	2016	NUM
ap-3509	1	19	available	available	ADJ
ap-3509	1	20	online	online	ADV
ap-3509	1	21	at	at	ADP
ap-3509	1	22	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-3509	1	23	two	two	NUM
ap-3509	1	24	-	-	PUNCT
ap-3509	1	25	dimensional	dimensional	ADJ
ap-3509	1	26	hybrids	hybrid	NOUN
ap-3509	1	27	with	with	ADP
ap-3509	1	28	mixed	mixed	ADJ
ap-3509	1	29	boundary	boundary	ADJ
ap-3509	1	30	value	value	NOUN
ap-3509	1	31	problems	problem	NOUN
ap-3509	1	32	marzena	marzena	PROPN
ap-3509	1	33	szajewska	szajewska	PROPN
ap-3509	1	34	,	,	PUNCT
ap-3509	1	35	agnieszka	agnieszka	PROPN
ap-3509	1	36	tereszkiewicz∗	tereszkiewicz∗	PROPN
ap-3509	1	37	institute	institute	PROPN
ap-3509	1	38	of	of	ADP
ap-3509	1	39	mathematics	mathematics	PROPN
ap-3509	1	40	,	,	PUNCT
ap-3509	1	41	university	university	NOUN
ap-3509	1	42	of	of	ADP
ap-3509	1	43	bialystok	bialystok	ADJ
ap-3509	1	44	,	,	PUNCT
ap-3509	1	45	1	1	NUM
ap-3509	1	46	m	m	NOUN
ap-3509	1	47	ciolkowskiego	ciolkowskiego	NOUN
ap-3509	1	48	,	,	PUNCT
ap-3509	1	49	pl-15	pl-15	NOUN
ap-3509	1	50	-	-	PUNCT
ap-3509	1	51	245	245	NUM
ap-3509	1	52	bialystok	bialystok	ADJ
ap-3509	1	53	,	,	PUNCT
ap-3509	1	54	poland	poland	PROPN
ap-3509	1	55	∗	∗	NOUN
ap-3509	1	56	corresponding	correspond	VERB
ap-3509	1	57	author	author	NOUN
ap-3509	1	58	:	:	PUNCT
ap-3509	1	59	a.tereszkiewicz@uwb.edu.pl	a.tereszkiewicz@uwb.edu.pl	VERB
ap-3509	1	60	abstract	abstract	ADJ
ap-3509	1	61	.	.	PUNCT
ap-3509	2	1	boundary	boundary	ADJ
ap-3509	2	2	value	value	NOUN
ap-3509	2	3	problems	problem	NOUN
ap-3509	2	4	are	be	AUX
ap-3509	2	5	considered	consider	VERB
ap-3509	2	6	on	on	ADP
ap-3509	2	7	a	a	DET
ap-3509	2	8	simplex	simplex	NOUN
ap-3509	2	9	f	f	PROPN
ap-3509	2	10	in	in	ADP
ap-3509	2	11	the	the	DET
ap-3509	2	12	real	real	ADJ
ap-3509	2	13	euclidean	euclidean	ADJ
ap-3509	2	14	space	space	NOUN
ap-3509	2	15	r2	r2	NOUN
ap-3509	2	16	.	.	PUNCT
ap-3509	3	1	the	the	DET
ap-3509	3	2	recent	recent	ADJ
ap-3509	3	3	discovery	discovery	NOUN
ap-3509	3	4	of	of	ADP
ap-3509	3	5	new	new	ADJ
ap-3509	3	6	families	family	NOUN
ap-3509	3	7	of	of	ADP
ap-3509	3	8	special	special	ADJ
ap-3509	3	9	functions	function	NOUN
ap-3509	3	10	,	,	PUNCT
ap-3509	3	11	orthogonal	orthogonal	ADJ
ap-3509	3	12	on	on	ADP
ap-3509	3	13	f	f	PROPN
ap-3509	3	14	,	,	PUNCT
ap-3509	3	15	makes	make	VERB
ap-3509	3	16	it	it	PRON
ap-3509	3	17	possible	possible	ADJ
ap-3509	3	18	to	to	PART
ap-3509	3	19	consider	consider	VERB
ap-3509	3	20	not	not	PART
ap-3509	3	21	only	only	ADV
ap-3509	3	22	the	the	DET
ap-3509	3	23	dirichlet	dirichlet	PROPN
ap-3509	3	24	or	or	CCONJ
ap-3509	3	25	neumann	neumann	PROPN
ap-3509	3	26	boundary	boundary	ADJ
ap-3509	3	27	value	value	NOUN
ap-3509	3	28	problems	problem	NOUN
ap-3509	3	29	on	on	ADP
ap-3509	3	30	f	f	PROPN
ap-3509	3	31	,	,	PUNCT
ap-3509	3	32	but	but	CCONJ
ap-3509	3	33	also	also	ADV
ap-3509	3	34	the	the	DET
ap-3509	3	35	mixed	mixed	ADJ
ap-3509	3	36	boundary	boundary	ADJ
ap-3509	3	37	value	value	NOUN
ap-3509	3	38	problem	problem	NOUN
ap-3509	3	39	which	which	PRON
ap-3509	3	40	is	be	AUX
ap-3509	3	41	a	a	DET
ap-3509	3	42	mixture	mixture	NOUN
ap-3509	3	43	of	of	ADP
ap-3509	3	44	dirichlet	dirichlet	PROPN
ap-3509	3	45	and	and	CCONJ
ap-3509	3	46	neumann	neumann	PROPN
ap-3509	3	47	type	type	PROPN
ap-3509	3	48	,	,	PUNCT
ap-3509	3	49	ie	ie	X
ap-3509	3	50	.	.	PUNCT
ap-3509	4	1	on	on	ADP
ap-3509	4	2	some	some	DET
ap-3509	4	3	parts	part	NOUN
ap-3509	4	4	of	of	ADP
ap-3509	4	5	the	the	DET
ap-3509	4	6	boundary	boundary	NOUN
ap-3509	4	7	of	of	ADP
ap-3509	4	8	f	f	PROPN
ap-3509	4	9	a	a	DET
ap-3509	4	10	dirichlet	dirichlet	PROPN
ap-3509	4	11	condition	condition	NOUN
ap-3509	4	12	is	be	AUX
ap-3509	4	13	fulfilled	fulfil	VERB
ap-3509	4	14	and	and	CCONJ
ap-3509	4	15	on	on	ADP
ap-3509	4	16	the	the	DET
ap-3509	4	17	other	other	ADJ
ap-3509	4	18	neumann	neumann	PROPN
ap-3509	4	19	’s	’s	PART
ap-3509	4	20	works	work	NOUN
ap-3509	4	21	.	.	PUNCT
ap-3509	5	1	keywords	keyword	NOUN
ap-3509	5	2	:	:	PUNCT
ap-3509	5	3	hybrid	hybrid	ADJ
ap-3509	5	4	functions	function	NOUN
ap-3509	5	5	,	,	PUNCT
ap-3509	5	6	dirichlet	dirichlet	PROPN
ap-3509	5	7	boundary	boundary	PROPN
ap-3509	5	8	value	value	NOUN
ap-3509	5	9	problem	problem	NOUN
ap-3509	5	10	,	,	PUNCT
ap-3509	5	11	neumann	neumann	PROPN
ap-3509	5	12	boundary	boundary	PROPN
ap-3509	5	13	value	value	NOUN
ap-3509	5	14	problem	problem	NOUN
ap-3509	5	15	,	,	PUNCT
ap-3509	5	16	mixed	mixed	ADJ
ap-3509	5	17	boundary	boundary	ADJ
ap-3509	5	18	value	value	NOUN
ap-3509	5	19	problem	problem	NOUN
ap-3509	5	20	.	.	PUNCT
ap-3509	6	1	1	1	X
ap-3509	6	2	.	.	X
ap-3509	6	3	introduction	introduction	NOUN
ap-3509	6	4	the	the	DET
ap-3509	6	5	boundary	boundary	ADJ
ap-3509	6	6	value	value	NOUN
ap-3509	6	7	problems	problem	NOUN
ap-3509	6	8	,	,	PUNCT
ap-3509	6	9	considered	consider	VERB
ap-3509	6	10	in	in	ADP
ap-3509	6	11	this	this	DET
ap-3509	6	12	paper	paper	NOUN
ap-3509	6	13	,	,	PUNCT
ap-3509	6	14	occurring	occur	VERB
ap-3509	6	15	in	in	ADP
ap-3509	6	16	a	a	DET
ap-3509	6	17	real	real	ADJ
ap-3509	6	18	euclidean	euclidean	ADJ
ap-3509	6	19	space	space	NOUN
ap-3509	6	20	r2	r2	PROPN
ap-3509	6	21	on	on	ADP
ap-3509	6	22	finite	finite	PROPN
ap-3509	6	23	region	region	NOUN
ap-3509	6	24	f	f	PROPN
ap-3509	6	25	⊂	⊂	PROPN
ap-3509	6	26	r2	r2	PROPN
ap-3509	6	27	that	that	PRON
ap-3509	6	28	is	be	AUX
ap-3509	6	29	half	half	NOUN
ap-3509	6	30	of	of	ADP
ap-3509	6	31	a	a	DET
ap-3509	6	32	square	square	ADJ
ap-3509	6	33	or	or	CCONJ
ap-3509	6	34	half	half	NOUN
ap-3509	6	35	of	of	ADP
ap-3509	6	36	an	an	DET
ap-3509	6	37	equilateral	equilateral	ADJ
ap-3509	6	38	triangle	triangle	NOUN
ap-3509	6	39	.	.	PUNCT
ap-3509	7	1	the	the	DET
ap-3509	7	2	main	main	ADJ
ap-3509	7	3	idea	idea	NOUN
ap-3509	7	4	of	of	ADP
ap-3509	7	5	this	this	DET
ap-3509	7	6	paper	paper	NOUN
ap-3509	7	7	is	be	AUX
ap-3509	7	8	to	to	PART
ap-3509	7	9	study	study	VERB
ap-3509	7	10	the	the	DET
ap-3509	7	11	solutions	solution	NOUN
ap-3509	7	12	of	of	ADP
ap-3509	7	13	helmholtz	helmholtz	NOUN
ap-3509	7	14	equation	equation	NOUN
ap-3509	7	15	with	with	ADP
ap-3509	7	16	the	the	DET
ap-3509	7	17	mixed	mixed	ADJ
ap-3509	7	18	boundary	boundary	ADJ
ap-3509	7	19	value	value	NOUN
ap-3509	7	20	problems	problem	NOUN
ap-3509	7	21	.	.	PUNCT
ap-3509	8	1	a	a	DET
ap-3509	8	2	surprising	surprising	ADJ
ap-3509	8	3	variety	variety	NOUN
ap-3509	8	4	of	of	ADP
ap-3509	8	5	recently	recently	ADV
ap-3509	8	6	emerged	emerge	VERB
ap-3509	8	7	suitable	suitable	ADJ
ap-3509	8	8	new	new	ADJ
ap-3509	8	9	families	family	NOUN
ap-3509	8	10	of	of	ADP
ap-3509	8	11	special	special	ADJ
ap-3509	8	12	functions	function	NOUN
ap-3509	8	13	makes	make	VERB
ap-3509	8	14	that	that	SCONJ
ap-3509	8	15	the	the	DET
ap-3509	8	16	realization	realization	NOUN
ap-3509	8	17	of	of	ADP
ap-3509	8	18	this	this	DET
ap-3509	8	19	idea	idea	NOUN
ap-3509	8	20	is	be	AUX
ap-3509	8	21	relatively	relatively	ADV
ap-3509	8	22	simple	simple	ADJ
ap-3509	8	23	and	and	CCONJ
ap-3509	8	24	straightforward	straightforward	ADJ
ap-3509	8	25	in	in	ADP
ap-3509	8	26	any	any	DET
ap-3509	8	27	dimension	dimension	NOUN
ap-3509	8	28	.	.	PUNCT
ap-3509	9	1	in	in	ADP
ap-3509	9	2	addition	addition	NOUN
ap-3509	9	3	to	to	ADP
ap-3509	9	4	the	the	DET
ap-3509	9	5	classical	classical	ADJ
ap-3509	9	6	boundary	boundary	ADJ
ap-3509	9	7	value	value	NOUN
ap-3509	9	8	problems	problem	NOUN
ap-3509	9	9	of	of	ADP
ap-3509	9	10	dirichlet	dirichlet	PROPN
ap-3509	9	11	and	and	CCONJ
ap-3509	9	12	neumann	neumann	PROPN
ap-3509	9	13	type	type	PROPN
ap-3509	9	14	,	,	PUNCT
ap-3509	9	15	the	the	DET
ap-3509	9	16	new	new	ADJ
ap-3509	9	17	functions	function	NOUN
ap-3509	9	18	,	,	PUNCT
ap-3509	9	19	called	call	VERB
ap-3509	9	20	‘	'	PUNCT
ap-3509	9	21	hybrids	hybrid	NOUN
ap-3509	9	22	’	'	PUNCT
ap-3509	10	1	[	[	X
ap-3509	10	2	6	6	NUM
ap-3509	10	3	,	,	PUNCT
ap-3509	10	4	10	10	NUM
ap-3509	10	5	]	]	PUNCT
ap-3509	10	6	,	,	PUNCT
ap-3509	10	7	display	display	NOUN
ap-3509	10	8	properties	property	NOUN
ap-3509	10	9	at	at	ADP
ap-3509	10	10	the	the	DET
ap-3509	10	11	boundary	boundary	NOUN
ap-3509	10	12	of	of	ADP
ap-3509	10	13	f	f	PROPN
ap-3509	10	14	,	,	PUNCT
ap-3509	10	15	on	on	ADP
ap-3509	10	16	some	some	DET
ap-3509	10	17	parts	part	NOUN
ap-3509	10	18	of	of	ADP
ap-3509	10	19	the	the	DET
ap-3509	10	20	boundary	boundary	ADJ
ap-3509	10	21	being	be	AUX
ap-3509	10	22	dirichlet	dirichlet	PROPN
ap-3509	10	23	’s	’s	ADV
ap-3509	10	24	,	,	PUNCT
ap-3509	10	25	while	while	SCONJ
ap-3509	10	26	on	on	ADP
ap-3509	10	27	the	the	DET
ap-3509	10	28	remaining	remain	VERB
ap-3509	10	29	ones	one	NOUN
ap-3509	10	30	neumann	neumann	PROPN
ap-3509	10	31	’s	’s	PART
ap-3509	10	32	.	.	PUNCT
ap-3509	11	1	the	the	DET
ap-3509	11	2	boundary	boundary	ADJ
ap-3509	11	3	value	value	NOUN
ap-3509	11	4	conditions	condition	NOUN
ap-3509	11	5	play	play	VERB
ap-3509	11	6	an	an	DET
ap-3509	11	7	important	important	ADJ
ap-3509	11	8	role	role	NOUN
ap-3509	11	9	in	in	ADP
ap-3509	11	10	describing	describe	VERB
ap-3509	11	11	the	the	DET
ap-3509	11	12	physical	physical	ADJ
ap-3509	11	13	phenomena	phenomenon	NOUN
ap-3509	11	14	.	.	PUNCT
ap-3509	12	1	they	they	PRON
ap-3509	12	2	are	be	AUX
ap-3509	12	3	used	use	VERB
ap-3509	12	4	,	,	PUNCT
ap-3509	12	5	inter	inter	ADJ
ap-3509	12	6	alia	alia	NOUN
ap-3509	12	7	,	,	PUNCT
ap-3509	12	8	in	in	ADP
ap-3509	12	9	the	the	DET
ap-3509	12	10	theory	theory	NOUN
ap-3509	12	11	of	of	ADP
ap-3509	12	12	elasticity	elasticity	NOUN
ap-3509	12	13	,	,	PUNCT
ap-3509	12	14	electrostatics	electrostatic	NOUN
ap-3509	12	15	and	and	CCONJ
ap-3509	12	16	fluid	fluid	ADJ
ap-3509	12	17	mechanics	mechanic	NOUN
ap-3509	12	18	[	[	X
ap-3509	12	19	2	2	NUM
ap-3509	12	20	,	,	PUNCT
ap-3509	12	21	4	4	NUM
ap-3509	12	22	,	,	PUNCT
ap-3509	12	23	16	16	NUM
ap-3509	12	24	]	]	PUNCT
ap-3509	12	25	.	.	PUNCT
ap-3509	13	1	in	in	ADP
ap-3509	13	2	section	section	NOUN
ap-3509	13	3	2	2	NUM
ap-3509	13	4	we	we	PRON
ap-3509	13	5	introduce	introduce	VERB
ap-3509	13	6	some	some	DET
ap-3509	13	7	facts	fact	NOUN
ap-3509	13	8	about	about	ADP
ap-3509	13	9	weyl	weyl	VERB
ap-3509	13	10	groups	group	NOUN
ap-3509	13	11	c2	c2	PROPN
ap-3509	13	12	and	and	CCONJ
ap-3509	13	13	g2	g2	PROPN
ap-3509	13	14	.	.	PUNCT
ap-3509	14	1	in	in	ADP
ap-3509	14	2	section	section	NOUN
ap-3509	14	3	3	3	NUM
ap-3509	14	4	we	we	PRON
ap-3509	14	5	show	show	VERB
ap-3509	14	6	the	the	DET
ap-3509	14	7	exact	exact	ADJ
ap-3509	14	8	formulas	formula	NOUN
ap-3509	14	9	for	for	ADP
ap-3509	14	10	four	four	NUM
ap-3509	14	11	families	family	NOUN
ap-3509	14	12	of	of	ADP
ap-3509	14	13	special	special	ADJ
ap-3509	14	14	functions	function	NOUN
ap-3509	14	15	for	for	ADP
ap-3509	14	16	each	each	PRON
ap-3509	14	17	of	of	ADP
ap-3509	14	18	the	the	DET
ap-3509	14	19	group	group	NOUN
ap-3509	14	20	c2	c2	PROPN
ap-3509	14	21	and	and	CCONJ
ap-3509	14	22	g2	g2	PROPN
ap-3509	14	23	.	.	PUNCT
ap-3509	15	1	the	the	DET
ap-3509	15	2	branching	branch	VERB
ap-3509	15	3	rules	rule	NOUN
ap-3509	15	4	used	use	VERB
ap-3509	15	5	to	to	PART
ap-3509	15	6	separate	separate	VERB
ap-3509	15	7	variables	variable	NOUN
ap-3509	15	8	in	in	ADP
ap-3509	15	9	section	section	NOUN
ap-3509	15	10	4	4	NUM
ap-3509	15	11	are	be	AUX
ap-3509	15	12	described	describe	VERB
ap-3509	15	13	in	in	ADP
ap-3509	15	14	details	detail	NOUN
ap-3509	15	15	for	for	ADP
ap-3509	15	16	example	example	NOUN
ap-3509	15	17	in	in	ADP
ap-3509	15	18	the	the	DET
ap-3509	15	19	following	follow	VERB
ap-3509	15	20	papers	paper	NOUN
ap-3509	15	21	[	[	X
ap-3509	15	22	9	9	NUM
ap-3509	15	23	,	,	PUNCT
ap-3509	15	24	11	11	NUM
ap-3509	15	25	,	,	PUNCT
ap-3509	15	26	14	14	NUM
ap-3509	15	27	]	]	PUNCT
ap-3509	15	28	.	.	PUNCT
ap-3509	16	1	in	in	ADP
ap-3509	16	2	section	section	NOUN
ap-3509	16	3	5	5	NUM
ap-3509	16	4	three	three	NUM
ap-3509	16	5	types	type	NOUN
ap-3509	16	6	of	of	ADP
ap-3509	16	7	boundary	boundary	ADJ
ap-3509	16	8	value	value	NOUN
ap-3509	16	9	problems	problem	NOUN
ap-3509	16	10	are	be	AUX
ap-3509	16	11	considered	consider	VERB
ap-3509	16	12	for	for	ADP
ap-3509	16	13	four	four	NUM
ap-3509	16	14	families	family	NOUN
ap-3509	16	15	of	of	ADP
ap-3509	16	16	special	special	ADJ
ap-3509	16	17	functions	function	NOUN
ap-3509	16	18	described	describe	VERB
ap-3509	16	19	in	in	ADP
ap-3509	16	20	section	section	NOUN
ap-3509	16	21	3	3	NUM
ap-3509	16	22	.	.	PUNCT
ap-3509	17	1	although	although	SCONJ
ap-3509	17	2	for	for	ADP
ap-3509	17	3	the	the	DET
ap-3509	17	4	case	case	NOUN
ap-3509	17	5	a1×a1	a1×a1	PROPN
ap-3509	17	6	,	,	PUNCT
ap-3509	17	7	there	there	PRON
ap-3509	17	8	is	be	VERB
ap-3509	17	9	no	no	DET
ap-3509	17	10	hybrid	hybrid	ADJ
ap-3509	17	11	functions	function	NOUN
ap-3509	17	12	,	,	PUNCT
ap-3509	17	13	the	the	DET
ap-3509	17	14	mixed	mixed	ADJ
ap-3509	17	15	boundary	boundary	ADJ
ap-3509	17	16	value	value	NOUN
ap-3509	17	17	problem	problem	NOUN
ap-3509	17	18	occurs	occur	VERB
ap-3509	17	19	.	.	PUNCT
ap-3509	18	1	we	we	PRON
ap-3509	18	2	present	present	VERB
ap-3509	18	3	this	this	DET
ap-3509	18	4	case	case	NOUN
ap-3509	18	5	in	in	ADP
ap-3509	18	6	details	detail	NOUN
ap-3509	18	7	in	in	ADP
ap-3509	18	8	appendix	appendix	NOUN
ap-3509	18	9	.	.	PUNCT
ap-3509	19	1	2	2	X
ap-3509	19	2	.	.	X
ap-3509	19	3	weyl	weyl	PROPN
ap-3509	19	4	group	group	PROPN
ap-3509	19	5	c2	c2	PROPN
ap-3509	19	6	and	and	CCONJ
ap-3509	19	7	g2	g2	PROPN
ap-3509	19	8	in	in	ADP
ap-3509	19	9	this	this	DET
ap-3509	19	10	section	section	NOUN
ap-3509	19	11	we	we	PRON
ap-3509	19	12	recall	recall	VERB
ap-3509	19	13	certain	certain	ADJ
ap-3509	19	14	facts	fact	NOUN
ap-3509	19	15	about	about	ADP
ap-3509	19	16	weyl	weyl	VERB
ap-3509	19	17	groups	group	NOUN
ap-3509	19	18	c2	c2	PROPN
ap-3509	19	19	and	and	CCONJ
ap-3509	19	20	g2	g2	PROPN
ap-3509	20	1	[	[	X
ap-3509	20	2	1	1	NUM
ap-3509	20	3	,	,	PUNCT
ap-3509	20	4	3	3	NUM
ap-3509	20	5	,	,	PUNCT
ap-3509	20	6	5	5	NUM
ap-3509	20	7	]	]	PUNCT
ap-3509	20	8	.	.	PUNCT
ap-3509	21	1	we	we	PRON
ap-3509	21	2	use	use	VERB
ap-3509	21	3	four	four	NUM
ap-3509	21	4	bases	basis	NOUN
ap-3509	21	5	in	in	ADP
ap-3509	21	6	r2	r2	PROPN
ap-3509	21	7	,	,	PUNCT
ap-3509	21	8	namely	namely	ADV
ap-3509	21	9	e-	e-	X
ap-3509	21	10	,	,	PUNCT
ap-3509	21	11	α-	α-	X
ap-3509	21	12	,	,	PUNCT
ap-3509	21	13	α̌and	α̌and	NUM
ap-3509	21	14	ωbasis	ωbasis	NOUN
ap-3509	21	15	.	.	PUNCT
ap-3509	22	1	the	the	DET
ap-3509	22	2	first	first	ADJ
ap-3509	22	3	one	one	NUM
ap-3509	22	4	,	,	PUNCT
ap-3509	22	5	e	e	NOUN
ap-3509	22	6	-	-	NOUN
ap-3509	22	7	basis	basis	NOUN
ap-3509	22	8	,	,	PUNCT
ap-3509	22	9	is	be	AUX
ap-3509	22	10	a	a	DET
ap-3509	22	11	natural	natural	ADJ
ap-3509	22	12	basis	basis	NOUN
ap-3509	22	13	for	for	ADP
ap-3509	22	14	an	an	DET
ap-3509	22	15	euclidean	euclidean	ADJ
ap-3509	22	16	space	space	NOUN
ap-3509	22	17	.	.	PUNCT
ap-3509	23	1	the	the	DET
ap-3509	23	2	simple	simple	ADJ
ap-3509	23	3	root	root	NOUN
ap-3509	23	4	basis	basis	NOUN
ap-3509	23	5	,	,	PUNCT
ap-3509	23	6	α	α	NOUN
ap-3509	23	7	-	-	NOUN
ap-3509	23	8	basis	basis	NOUN
ap-3509	23	9	,	,	PUNCT
ap-3509	23	10	exists	exist	VERB
ap-3509	23	11	for	for	SCONJ
ap-3509	23	12	every	every	DET
ap-3509	23	13	finite	finite	ADJ
ap-3509	23	14	group	group	NOUN
ap-3509	23	15	figure	figure	NOUN
ap-3509	23	16	1	1	NUM
ap-3509	23	17	.	.	PUNCT
ap-3509	23	18	shaded	shade	VERB
ap-3509	23	19	triangles	triangle	NOUN
ap-3509	23	20	represent	represent	VERB
ap-3509	23	21	the	the	DET
ap-3509	23	22	fundamental	fundamental	ADJ
ap-3509	23	23	regions	region	NOUN
ap-3509	23	24	f	f	PROPN
ap-3509	23	25	for	for	ADP
ap-3509	23	26	c2	c2	PROPN
ap-3509	23	27	and	and	CCONJ
ap-3509	23	28	g2	g2	PROPN
ap-3509	23	29	group	group	NOUN
ap-3509	23	30	.	.	PUNCT
ap-3509	24	1	generated	generate	VERB
ap-3509	24	2	by	by	ADP
ap-3509	24	3	reflections	reflection	NOUN
ap-3509	24	4	.	.	PUNCT
ap-3509	25	1	the	the	DET
ap-3509	25	2	co	co	NOUN
ap-3509	25	3	-	-	NOUN
ap-3509	25	4	root	root	ADJ
ap-3509	25	5	basis	basis	NOUN
ap-3509	25	6	α̌	α̌	PUNCT
ap-3509	25	7	is	be	AUX
ap-3509	25	8	defined	define	VERB
ap-3509	25	9	by	by	ADP
ap-3509	25	10	the	the	DET
ap-3509	25	11	formula	formula	NOUN
ap-3509	25	12	:	:	PUNCT
ap-3509	26	1	α̌i	α̌i	PROPN
ap-3509	26	2	=	=	SYM
ap-3509	26	3	2αi	2αi	ADJ
ap-3509	26	4	〈	〈	PROPN
ap-3509	26	5	αi|αi	αi|αi	PROPN
ap-3509	26	6	〉	〉	NOUN
ap-3509	26	7	.	.	PUNCT
ap-3509	27	1	the	the	DET
ap-3509	27	2	ω	ω	NOUN
ap-3509	27	3	-	-	PUNCT
ap-3509	27	4	basis	basis	NOUN
ap-3509	27	5	is	be	AUX
ap-3509	27	6	dual	dual	ADJ
ap-3509	27	7	to	to	ADP
ap-3509	27	8	simple	simple	ADJ
ap-3509	27	9	root	root	NOUN
ap-3509	27	10	basis	basis	NOUN
ap-3509	27	11	.	.	PUNCT
ap-3509	28	1	the	the	DET
ap-3509	28	2	relationship	relationship	NOUN
ap-3509	28	3	between	between	ADP
ap-3509	28	4	considered	consider	VERB
ap-3509	28	5	bases	basis	NOUN
ap-3509	28	6	is	be	AUX
ap-3509	28	7	standard	standard	ADJ
ap-3509	28	8	for	for	ADP
ap-3509	28	9	group	group	NOUN
ap-3509	28	10	theory	theory	NOUN
ap-3509	28	11	and	and	CCONJ
ap-3509	28	12	is	be	AUX
ap-3509	28	13	expressed	express	VERB
ap-3509	28	14	by	by	ADP
ap-3509	28	15	:	:	PUNCT
ap-3509	28	16	〈	〈	PROPN
ap-3509	28	17	α̌i|ωj	α̌i|ωj	NOUN
ap-3509	28	18	〉	〉	NOUN
ap-3509	28	19	=	=	SYM
ap-3509	28	20	δij	δij	NOUN
ap-3509	28	21	.	.	PUNCT
ap-3509	29	1	below	below	ADP
ap-3509	29	2	we	we	PRON
ap-3509	29	3	present	present	VERB
ap-3509	29	4	the	the	DET
ap-3509	29	5	α	α	NUM
ap-3509	29	6	-	-	PUNCT
ap-3509	29	7	basis	basis	NOUN
ap-3509	29	8	vectors	vector	NOUN
ap-3509	29	9	in	in	ADP
ap-3509	29	10	cartesian	cartesian	ADJ
ap-3509	29	11	coordinates	coordinate	NOUN
ap-3509	29	12	for	for	ADP
ap-3509	29	13	each	each	PRON
ap-3509	29	14	of	of	ADP
ap-3509	29	15	considered	consider	VERB
ap-3509	29	16	groups	group	NOUN
ap-3509	29	17	:	:	PUNCT
ap-3509	29	18	c2	c2	PROPN
ap-3509	29	19	:	:	PUNCT
ap-3509	29	20	α1	α1	PROPN
ap-3509	29	21	:	:	PUNCT
ap-3509	29	22	=	=	SYM
ap-3509	29	23	1√	1√	NUM
ap-3509	29	24	2	2	NUM
ap-3509	29	25	(	(	PUNCT
ap-3509	29	26	1,−1)e	1,−1)e	NUM
ap-3509	29	27	,	,	PUNCT
ap-3509	29	28	α2	α2	PROPN
ap-3509	29	29	:	:	PUNCT
ap-3509	29	30	=	=	SYM
ap-3509	29	31	2√	2√	NUM
ap-3509	29	32	2	2	NUM
ap-3509	29	33	(	(	PUNCT
ap-3509	29	34	0	0	NUM
ap-3509	29	35	,	,	PUNCT
ap-3509	29	36	1)e	1)e	NUM
ap-3509	29	37	,	,	PUNCT
ap-3509	29	38	g2	g2	PROPN
ap-3509	29	39	:	:	PUNCT
ap-3509	29	40	α1	α1	PROPN
ap-3509	29	41	:	:	PUNCT
ap-3509	29	42	=	=	SYM
ap-3509	29	43	(	(	PUNCT
ap-3509	29	44	√	√	NUM
ap-3509	29	45	2	2	NUM
ap-3509	29	46	,	,	PUNCT
ap-3509	29	47	0)e	0)e	NOUN
ap-3509	29	48	,	,	PUNCT
ap-3509	29	49	α2	α2	ADJ
ap-3509	29	50	:	:	PUNCT
ap-3509	29	51	=	=	SYM
ap-3509	29	52	(	(	PUNCT
ap-3509	29	53	−	−	PROPN
ap-3509	29	54	1√	1√	PROPN
ap-3509	29	55	2	2	NUM
ap-3509	29	56	,	,	PUNCT
ap-3509	29	57	1√	1√	NOUN
ap-3509	29	58	6	6	NUM
ap-3509	29	59	)	)	PUNCT
ap-3509	29	60	e	e	NOUN
ap-3509	29	61	.	.	PUNCT
ap-3509	30	1	the	the	DET
ap-3509	30	2	following	follow	VERB
ap-3509	30	3	notation	notation	NOUN
ap-3509	30	4	for	for	ADP
ap-3509	30	5	coordinates	coordinate	NOUN
ap-3509	30	6	is	be	AUX
ap-3509	30	7	used	use	VERB
ap-3509	30	8	:	:	PUNCT
ap-3509	30	9	r2	r2	PROPN
ap-3509	30	10	3	3	NUM
ap-3509	30	11	λ	λ	NOUN
ap-3509	30	12	=	=	SYM
ap-3509	30	13	(	(	PUNCT
ap-3509	30	14	a	a	PRON
ap-3509	30	15	,	,	PUNCT
ap-3509	30	16	b)ω	b)ω	PUNCT
ap-3509	31	1	=	=	PUNCT
ap-3509	32	1	aω1	aω1	ADV
ap-3509	33	1	+	+	CCONJ
ap-3509	33	2	bω2	bω2	ADV
ap-3509	33	3	.	.	PUNCT
ap-3509	34	1	r2	r2	PROPN
ap-3509	34	2	3	3	NUM
ap-3509	34	3	x	x	SYM
ap-3509	34	4	=	=	SYM
ap-3509	34	5	(	(	PUNCT
ap-3509	34	6	x1	x1	PROPN
ap-3509	34	7	,	,	PUNCT
ap-3509	34	8	x2)α̌	x2)α̌	PROPN
ap-3509	34	9	=	=	PUNCT
ap-3509	34	10	(	(	PUNCT
ap-3509	34	11	y1	y1	INTJ
ap-3509	34	12	,	,	PUNCT
ap-3509	34	13	y2)e	y2)e	PROPN
ap-3509	34	14	,	,	PUNCT
ap-3509	34	15	where	where	SCONJ
ap-3509	34	16	indexes	index	NOUN
ap-3509	34	17	ω	ω	PROPN
ap-3509	34	18	,	,	PUNCT
ap-3509	34	19	e	e	NOUN
ap-3509	34	20	,	,	PUNCT
ap-3509	34	21	and	and	CCONJ
ap-3509	34	22	α̌	α̌	NUM
ap-3509	34	23	denote	denote	NOUN
ap-3509	34	24	ω-	ω-	X
ap-3509	34	25	,	,	PUNCT
ap-3509	34	26	natural-	natural-	NOUN
ap-3509	34	27	,	,	PUNCT
ap-3509	34	28	and	and	CCONJ
ap-3509	34	29	α̌-basis	α̌-basis	PROPN
ap-3509	34	30	,	,	PUNCT
ap-3509	34	31	respectively	respectively	ADV
ap-3509	34	32	.	.	PUNCT
ap-3509	35	1	245	245	NUM
ap-3509	35	2	http://dx.doi.org/10.14311/ap.2016.56.0245	http://dx.doi.org/10.14311/ap.2016.56.0245	VERB
ap-3509	35	3	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-3509	35	4	marzena	marzena	ADJ
ap-3509	35	5	szajewska	szajewska	NOUN
ap-3509	35	6	,	,	PUNCT
ap-3509	35	7	agnieszka	agnieszka	PROPN
ap-3509	35	8	tereszkiewicz	tereszkiewicz	PROPN
ap-3509	35	9	acta	acta	PROPN
ap-3509	35	10	polytechnica	polytechnica	PROPN
ap-3509	35	11	the	the	DET
ap-3509	35	12	fundamental	fundamental	ADJ
ap-3509	35	13	regions	region	NOUN
ap-3509	35	14	f	f	PROPN
ap-3509	35	15	for	for	ADP
ap-3509	35	16	c2	c2	PROPN
ap-3509	35	17	and	and	CCONJ
ap-3509	35	18	g2	g2	PROPN
ap-3509	35	19	group	group	NOUN
ap-3509	35	20	,	,	PUNCT
ap-3509	35	21	written	write	VERB
ap-3509	35	22	in	in	ADP
ap-3509	35	23	ω	ω	NOUN
ap-3509	35	24	-	-	NOUN
ap-3509	35	25	basis	basis	NOUN
ap-3509	35	26	,	,	PUNCT
ap-3509	35	27	have	have	VERB
ap-3509	35	28	the	the	DET
ap-3509	35	29	vertices	vertex	NOUN
ap-3509	35	30	fc2	fc2	PROPN
ap-3509	35	31	=	=	X
ap-3509	35	32	{	{	PUNCT
ap-3509	35	33	0	0	NUM
ap-3509	35	34	,	,	PUNCT
ap-3509	35	35	ω1	ω1	PROPN
ap-3509	35	36	,	,	PUNCT
ap-3509	35	37	ω2	ω2	ADJ
ap-3509	35	38	}	}	PUNCT
ap-3509	35	39	,	,	PUNCT
ap-3509	35	40	fg2	fg2	ADV
ap-3509	35	41	=	=	SYM
ap-3509	35	42	{	{	PUNCT
ap-3509	35	43	0	0	NUM
ap-3509	35	44	,	,	PUNCT
ap-3509	35	45	ω1	ω1	PROPN
ap-3509	35	46	2	2	NUM
ap-3509	35	47	,	,	PUNCT
ap-3509	35	48	ω2	ω2	ADJ
ap-3509	35	49	}	}	PUNCT
ap-3509	35	50	and	and	CCONJ
ap-3509	35	51	are	be	AUX
ap-3509	35	52	shown	show	VERB
ap-3509	35	53	in	in	ADP
ap-3509	35	54	figure	figure	NOUN
ap-3509	35	55	1	1	NUM
ap-3509	35	56	.	.	PUNCT
ap-3509	36	1	the	the	DET
ap-3509	36	2	groups	group	NOUN
ap-3509	36	3	c2	c2	PROPN
ap-3509	36	4	and	and	CCONJ
ap-3509	36	5	g2	g2	PROPN
ap-3509	36	6	can	can	AUX
ap-3509	36	7	be	be	AUX
ap-3509	36	8	reduced	reduce	VERB
ap-3509	36	9	to	to	ADP
ap-3509	36	10	a	a	DET
ap-3509	36	11	subgroup	subgroup	NOUN
ap-3509	36	12	a1	a1	NOUN
ap-3509	36	13	×a1	×a1	ADP
ap-3509	36	14	using	use	VERB
ap-3509	36	15	a	a	DET
ap-3509	36	16	branching	branch	VERB
ap-3509	36	17	rule	rule	NOUN
ap-3509	36	18	method	method	NOUN
ap-3509	36	19	described	describe	VERB
ap-3509	36	20	in	in	ADP
ap-3509	36	21	[	[	X
ap-3509	36	22	11	11	NUM
ap-3509	36	23	,	,	PUNCT
ap-3509	36	24	14	14	NUM
ap-3509	36	25	]	]	PUNCT
ap-3509	36	26	.	.	PUNCT
ap-3509	37	1	for	for	ADP
ap-3509	37	2	c2	c2	PROPN
ap-3509	37	3	case	case	NOUN
ap-3509	37	4	it	it	PRON
ap-3509	37	5	is	be	AUX
ap-3509	37	6	done	do	VERB
ap-3509	37	7	by	by	ADP
ap-3509	37	8	the	the	DET
ap-3509	37	9	projection	projection	NOUN
ap-3509	37	10	matrix	matrix	NOUN
ap-3509	37	11	pc2	pc2	NOUN
ap-3509	37	12	=	=	SYM
ap-3509	37	13	(	(	PUNCT
ap-3509	37	14	1	1	NUM
ap-3509	37	15	1	1	NUM
ap-3509	37	16	0	0	NUM
ap-3509	37	17	1	1	NUM
ap-3509	37	18	)	)	PUNCT
ap-3509	37	19	(	(	PUNCT
ap-3509	37	20	1	1	X
ap-3509	37	21	)	)	PUNCT
ap-3509	37	22	acting	act	VERB
ap-3509	37	23	on	on	ADP
ap-3509	37	24	the	the	DET
ap-3509	37	25	whole	whole	ADJ
ap-3509	37	26	orbit	orbit	NOUN
ap-3509	37	27	of	of	ADP
ap-3509	37	28	a	a	DET
ap-3509	37	29	group	group	NOUN
ap-3509	37	30	.	.	PUNCT
ap-3509	38	1	the	the	DET
ap-3509	38	2	branching	branch	VERB
ap-3509	38	3	rule	rule	NOUN
ap-3509	38	4	is	be	AUX
ap-3509	38	5	the	the	DET
ap-3509	38	6	following	following	NOUN
ap-3509	38	7	:	:	PUNCT
ap-3509	38	8	o(a	o(a	NUM
ap-3509	38	9	,	,	PUNCT
ap-3509	38	10	b	b	X
ap-3509	38	11	)	)	PUNCT
ap-3509	38	12	pc2−→	pc2−→	PROPN
ap-3509	38	13	o(a+	o(a+	ADJ
ap-3509	38	14	b)o(b	b)o(b	NOUN
ap-3509	38	15	)	)	PUNCT
ap-3509	38	16	∪o(b)o(a+	∪o(b)o(a+	NOUN
ap-3509	38	17	b	b	NOUN
ap-3509	38	18	)	)	PUNCT
ap-3509	38	19	.	.	PUNCT
ap-3509	39	1	(	(	PUNCT
ap-3509	39	2	2	2	X
ap-3509	39	3	)	)	PUNCT
ap-3509	39	4	the	the	DET
ap-3509	39	5	reduction	reduction	NOUN
ap-3509	39	6	from	from	ADP
ap-3509	39	7	g2	g2	PROPN
ap-3509	39	8	to	to	PART
ap-3509	39	9	a1	a1	VERB
ap-3509	39	10	×	×	NOUN
ap-3509	39	11	a1	a1	NOUN
ap-3509	39	12	is	be	AUX
ap-3509	39	13	given	give	VERB
ap-3509	39	14	by	by	ADP
ap-3509	39	15	the	the	DET
ap-3509	39	16	matrix	matrix	NOUN
ap-3509	39	17	pg2	pg2	NOUN
ap-3509	39	18	=	=	SYM
ap-3509	39	19	(	(	PUNCT
ap-3509	39	20	1	1	NUM
ap-3509	39	21	1	1	NUM
ap-3509	39	22	3	3	NUM
ap-3509	39	23	1	1	NUM
ap-3509	39	24	)	)	PUNCT
ap-3509	39	25	.	.	PUNCT
ap-3509	40	1	(	(	PUNCT
ap-3509	40	2	3	3	X
ap-3509	40	3	)	)	PUNCT
ap-3509	40	4	the	the	DET
ap-3509	40	5	branching	branch	VERB
ap-3509	40	6	rule	rule	NOUN
ap-3509	40	7	,	,	PUNCT
ap-3509	40	8	in	in	ADP
ap-3509	40	9	this	this	DET
ap-3509	40	10	case	case	NOUN
ap-3509	40	11	,	,	PUNCT
ap-3509	40	12	has	have	VERB
ap-3509	40	13	a	a	DET
ap-3509	40	14	form	form	NOUN
ap-3509	40	15	:	:	PUNCT
ap-3509	40	16	o(a	o(a	NUM
ap-3509	40	17	,	,	PUNCT
ap-3509	40	18	b	b	X
ap-3509	40	19	)	)	PUNCT
ap-3509	40	20	pg2−−−→	pg2−−−→	NOUN
ap-3509	40	21	o(a+	o(a+	ADJ
ap-3509	40	22	b)o(3a+	b)o(3a+	NUM
ap-3509	40	23	b	b	NOUN
ap-3509	40	24	)	)	PUNCT
ap-3509	40	25	∪o(2a+	∪o(2a+	PUNCT
ap-3509	41	1	b)o(b	b)o(b	NOUN
ap-3509	41	2	)	)	PUNCT
ap-3509	41	3	∪o(a)o(3a+	∪o(a)o(3a+	NOUN
ap-3509	41	4	2b	2b	NOUN
ap-3509	41	5	)	)	PUNCT
ap-3509	41	6	.	.	PUNCT
ap-3509	42	1	(	(	PUNCT
ap-3509	42	2	4	4	X
ap-3509	42	3	)	)	PUNCT
ap-3509	42	4	for	for	ADP
ap-3509	42	5	group	group	NOUN
ap-3509	42	6	a1	a1	NOUN
ap-3509	42	7	×a1	×a1	ADV
ap-3509	42	8	we	we	PRON
ap-3509	42	9	use	use	VERB
ap-3509	42	10	the	the	DET
ap-3509	42	11	following	follow	VERB
ap-3509	42	12	notation	notation	NOUN
ap-3509	42	13	for	for	ADP
ap-3509	42	14	coordinates	coordinate	NOUN
ap-3509	42	15	r2	r2	PROPN
ap-3509	42	16	3	3	NUM
ap-3509	42	17	x	x	SYM
ap-3509	42	18	=	=	SYM
ap-3509	42	19	(	(	PUNCT
ap-3509	42	20	x	x	X
ap-3509	42	21	,	,	PUNCT
ap-3509	42	22	y)e	y)e	PUNCT
ap-3509	43	1	∈	∈	PROPN
ap-3509	43	2	a1	a1	NOUN
ap-3509	43	3	×a1	×a1	PROPN
ap-3509	43	4	.	.	PUNCT
ap-3509	44	1	3	3	X
ap-3509	44	2	.	.	X
ap-3509	44	3	c-	c-	X
ap-3509	44	4	,	,	PUNCT
ap-3509	44	5	s-	s-	X
ap-3509	44	6	,	,	PUNCT
ap-3509	44	7	ss-	ss-	X
ap-3509	44	8	,	,	PUNCT
ap-3509	44	9	and	and	CCONJ
ap-3509	44	10	sl	sl	NOUN
ap-3509	44	11	-	-	PUNCT
ap-3509	44	12	functions	function	NOUN
ap-3509	44	13	of	of	ADP
ap-3509	44	14	g	g	NOUN
ap-3509	44	15	=	=	PROPN
ap-3509	44	16	c2	c2	PROPN
ap-3509	44	17	or	or	CCONJ
ap-3509	44	18	g2	g2	PROPN
ap-3509	44	19	the	the	DET
ap-3509	44	20	general	general	ADJ
ap-3509	44	21	formula	formula	NOUN
ap-3509	44	22	for	for	ADP
ap-3509	44	23	special	special	ADJ
ap-3509	44	24	functions	function	NOUN
ap-3509	44	25	corresponding	correspond	VERB
ap-3509	44	26	to	to	ADP
ap-3509	44	27	the	the	DET
ap-3509	44	28	weyl	weyl	VERB
ap-3509	44	29	group	group	NOUN
ap-3509	44	30	[	[	X
ap-3509	44	31	5	5	NUM
ap-3509	44	32	]	]	PUNCT
ap-3509	44	33	is	be	AUX
ap-3509	44	34	given	give	VERB
ap-3509	44	35	by∑	by∑	ADJ
ap-3509	44	36	w∈g	w∈g	NOUN
ap-3509	44	37	σ(w)e2πi〈wλ|x	σ(w)e2πi〈wλ|x	PROPN
ap-3509	44	38	〉	〉	PROPN
ap-3509	44	39	,	,	PUNCT
ap-3509	44	40	where	where	SCONJ
ap-3509	44	41	the	the	DET
ap-3509	44	42	coordinates	coordinate	NOUN
ap-3509	44	43	x	x	PUNCT
ap-3509	44	44	=	=	SYM
ap-3509	44	45	(	(	PUNCT
ap-3509	44	46	x1	x1	PROPN
ap-3509	44	47	,	,	PUNCT
ap-3509	44	48	x2)α̌	x2)α̌	PROPN
ap-3509	44	49	∈	∈	PROPN
ap-3509	44	50	r2	r2	NOUN
ap-3509	44	51	and	and	CCONJ
ap-3509	44	52	weight	weight	NOUN
ap-3509	44	53	λ	λ	PROPN
ap-3509	44	54	=	=	PRON
ap-3509	44	55	(	(	PUNCT
ap-3509	44	56	a	a	DET
ap-3509	44	57	,	,	PUNCT
ap-3509	44	58	b)ω	b)ω	X
ap-3509	44	59	are	be	AUX
ap-3509	44	60	given	give	VERB
ap-3509	44	61	in	in	ADP
ap-3509	44	62	α̌and	α̌and	NUM
ap-3509	44	63	ω	ω	NUM
ap-3509	44	64	-	-	NOUN
ap-3509	44	65	basis	basis	NOUN
ap-3509	44	66	,	,	PUNCT
ap-3509	44	67	respectively	respectively	ADV
ap-3509	44	68	.	.	PUNCT
ap-3509	45	1	the	the	DET
ap-3509	45	2	homomorphism	homomorphism	PROPN
ap-3509	45	3	σ	σ	X
ap-3509	45	4	:	:	PUNCT
ap-3509	45	5	g	g	NOUN
ap-3509	45	6	→	→	SYM
ap-3509	45	7	{	{	PUNCT
ap-3509	45	8	±1	±1	NOUN
ap-3509	45	9	}	}	PUNCT
ap-3509	45	10	(	(	PUNCT
ap-3509	45	11	by	by	ADP
ap-3509	45	12	g	g	PROPN
ap-3509	45	13	we	we	PRON
ap-3509	45	14	denote	denote	VERB
ap-3509	45	15	the	the	DET
ap-3509	45	16	group	group	NOUN
ap-3509	45	17	c2	c2	PROPN
ap-3509	45	18	or	or	CCONJ
ap-3509	45	19	g2	g2	PROPN
ap-3509	45	20	)	)	PUNCT
ap-3509	45	21	determine	determine	VERB
ap-3509	45	22	the	the	DET
ap-3509	45	23	four	four	NUM
ap-3509	45	24	families	family	NOUN
ap-3509	45	25	of	of	ADP
ap-3509	45	26	special	special	ADJ
ap-3509	45	27	functions	function	NOUN
ap-3509	46	1	[	[	X
ap-3509	46	2	9	9	NUM
ap-3509	46	3	]	]	PUNCT
ap-3509	46	4	,	,	PUNCT
ap-3509	46	5	that	that	PRON
ap-3509	46	6	are	be	AUX
ap-3509	46	7	of	of	ADP
ap-3509	46	8	interest	interest	NOUN
ap-3509	46	9	to	to	ADP
ap-3509	46	10	us	we	PRON
ap-3509	46	11	.	.	PUNCT
ap-3509	47	1	the	the	DET
ap-3509	47	2	map	map	NOUN
ap-3509	47	3	σ(w	σ(w	PROPN
ap-3509	47	4	)	)	PUNCT
ap-3509	47	5	is	be	AUX
ap-3509	47	6	a	a	DET
ap-3509	47	7	product	product	NOUN
ap-3509	47	8	of	of	ADP
ap-3509	47	9	σ(rl	σ(rl	PROPN
ap-3509	47	10	)	)	PUNCT
ap-3509	47	11	,	,	PUNCT
ap-3509	47	12	σ(rs	σ(r	NOUN
ap-3509	47	13	)	)	PUNCT
ap-3509	47	14	∈	∈	PROPN
ap-3509	47	15	{	{	PUNCT
ap-3509	47	16	±1	±1	NOUN
ap-3509	47	17	}	}	PUNCT
ap-3509	47	18	,	,	PUNCT
ap-3509	47	19	where	where	SCONJ
ap-3509	47	20	rl	rl	X
ap-3509	47	21	,	,	PUNCT
ap-3509	47	22	rs	rs	X
ap-3509	47	23	denote	denote	NOUN
ap-3509	47	24	long	long	ADJ
ap-3509	47	25	and	and	CCONJ
ap-3509	47	26	short	short	ADJ
ap-3509	47	27	reflections	reflection	NOUN
ap-3509	47	28	in	in	ADP
ap-3509	47	29	w	w	NOUN
ap-3509	47	30	,	,	PUNCT
ap-3509	47	31	respectively	respectively	ADV
ap-3509	47	32	.	.	PUNCT
ap-3509	48	1	consequently	consequently	ADV
ap-3509	48	2	,	,	PUNCT
ap-3509	48	3	there	there	PRON
ap-3509	48	4	are	be	VERB
ap-3509	48	5	four	four	NUM
ap-3509	48	6	types	type	NOUN
ap-3509	48	7	of	of	ADP
ap-3509	48	8	homomorphisms	homomorphisms	PROPN
ap-3509	48	9	σ	σ	NOUN
ap-3509	48	10	:	:	PUNCT
ap-3509	48	11	c	c	NOUN
ap-3509	48	12	:	:	PUNCT
ap-3509	48	13	σ(rl	σ(rl	NUM
ap-3509	48	14	)	)	PUNCT
ap-3509	48	15	=	=	SYM
ap-3509	48	16	σ(rs	σ(r	NOUN
ap-3509	48	17	)	)	PUNCT
ap-3509	48	18	=	=	SYM
ap-3509	48	19	1	1	NUM
ap-3509	48	20	,	,	PUNCT
ap-3509	48	21	s	s	PART
ap-3509	48	22	:	:	PUNCT
ap-3509	48	23	σ(rl	σ(rl	NUM
ap-3509	48	24	)	)	PUNCT
ap-3509	48	25	=	=	SYM
ap-3509	48	26	σ(rs	σ(r	NOUN
ap-3509	48	27	)	)	PUNCT
ap-3509	48	28	=	=	SYM
ap-3509	48	29	−1	−1	NOUN
ap-3509	48	30	,	,	PUNCT
ap-3509	48	31	sl	sl	INTJ
ap-3509	48	32	:	:	PUNCT
ap-3509	48	33	σ(rl	σ(rl	NUM
ap-3509	48	34	)	)	PUNCT
ap-3509	48	35	=	=	SYM
ap-3509	48	36	−1	−1	NOUN
ap-3509	48	37	,	,	PUNCT
ap-3509	48	38	σ(rs	σ(r	NOUN
ap-3509	48	39	)	)	PUNCT
ap-3509	48	40	=	=	SYM
ap-3509	48	41	1	1	NUM
ap-3509	48	42	,	,	PUNCT
ap-3509	48	43	ss	ss	INTJ
ap-3509	48	44	:	:	PUNCT
ap-3509	48	45	σ(rl	σ(rl	NUM
ap-3509	48	46	)	)	PUNCT
ap-3509	48	47	=	=	SYM
ap-3509	48	48	1	1	NUM
ap-3509	48	49	,	,	PUNCT
ap-3509	48	50	σ(rs	σ(r	NOUN
ap-3509	48	51	)	)	PUNCT
ap-3509	48	52	=	=	SYM
ap-3509	48	53	−1	−1	NOUN
ap-3509	48	54	.	.	PUNCT
ap-3509	49	1	3.1	3.1	NUM
ap-3509	49	2	.	.	PUNCT
ap-3509	50	1	explicit	explicit	ADJ
ap-3509	50	2	forms	form	NOUN
ap-3509	50	3	of	of	ADP
ap-3509	50	4	cand	cand	NOUN
ap-3509	50	5	s	s	NOUN
ap-3509	50	6	-	-	PUNCT
ap-3509	50	7	functions	function	NOUN
ap-3509	50	8	in	in	ADP
ap-3509	50	9	this	this	DET
ap-3509	50	10	subsection	subsection	NOUN
ap-3509	50	11	we	we	PRON
ap-3509	50	12	provide	provide	VERB
ap-3509	50	13	an	an	DET
ap-3509	50	14	exact	exact	ADJ
ap-3509	50	15	formulas	formula	NOUN
ap-3509	50	16	for	for	ADP
ap-3509	50	17	the	the	DET
ap-3509	50	18	two	two	NUM
ap-3509	50	19	types	type	NOUN
ap-3509	50	20	of	of	ADP
ap-3509	50	21	special	special	ADJ
ap-3509	50	22	functions	function	NOUN
ap-3509	50	23	,	,	PUNCT
ap-3509	50	24	namely	namely	ADV
ap-3509	50	25	,	,	PUNCT
ap-3509	50	26	cand	cand	PROPN
ap-3509	50	27	s	s	NOUN
ap-3509	50	28	-	-	PUNCT
ap-3509	50	29	functions	function	NOUN
ap-3509	50	30	for	for	ADP
ap-3509	50	31	c2	c2	PROPN
ap-3509	50	32	and	and	CCONJ
ap-3509	50	33	g2	g2	PROPN
ap-3509	50	34	group	group	NOUN
ap-3509	50	35	.	.	PUNCT
ap-3509	51	1	the	the	DET
ap-3509	51	2	upper	upper	ADJ
ap-3509	51	3	signs	sign	NOUN
ap-3509	51	4	in	in	ADP
ap-3509	51	5	the	the	DET
ap-3509	51	6	formulas	formula	NOUN
ap-3509	51	7	correspond	correspond	VERB
ap-3509	51	8	to	to	ADP
ap-3509	51	9	c(a	c(a	PROPN
ap-3509	51	10	,	,	PUNCT
ap-3509	51	11	b)(x	b)(x	PROPN
ap-3509	51	12	)	)	PUNCT
ap-3509	51	13	functions	function	NOUN
ap-3509	51	14	and	and	CCONJ
ap-3509	51	15	the	the	DET
ap-3509	51	16	lower	low	ADJ
ap-3509	51	17	ones	one	NOUN
ap-3509	51	18	match	match	VERB
ap-3509	51	19	up	up	ADP
ap-3509	51	20	to	to	ADP
ap-3509	51	21	s(a	s(a	PROPN
ap-3509	51	22	,	,	PUNCT
ap-3509	51	23	b)(x	b)(x	PROPN
ap-3509	51	24	)	)	PUNCT
ap-3509	51	25	functions	function	NOUN
ap-3509	52	1	[	[	X
ap-3509	52	2	9	9	NUM
ap-3509	52	3	,	,	PUNCT
ap-3509	52	4	13	13	NUM
ap-3509	52	5	]	]	PUNCT
ap-3509	52	6	:	:	PUNCT
ap-3509	52	7	c2	c2	PROPN
ap-3509	52	8	:	:	PUNCT
ap-3509	52	9	±2	±2	PROPN
ap-3509	52	10	[	[	PUNCT
ap-3509	52	11	cos(2π((a+	cos(2π((a+	NOUN
ap-3509	52	12	2b)x1	2b)x1	NUM
ap-3509	52	13	+	+	CCONJ
ap-3509	52	14	(	(	PUNCT
ap-3509	52	15	−a−	−a−	PROPN
ap-3509	52	16	b)x2	b)x2	PROPN
ap-3509	52	17	)	)	PUNCT
ap-3509	52	18	)	)	PUNCT
ap-3509	52	19	±	±	PROPN
ap-3509	52	20	cos(2π((a+	cos(2π((a+	NOUN
ap-3509	52	21	2b)x1	2b)x1	NUM
ap-3509	52	22	−	−	PROPN
ap-3509	52	23	bx2	bx2	PROPN
ap-3509	52	24	)	)	PUNCT
ap-3509	52	25	)	)	PUNCT
ap-3509	53	1	+	+	CCONJ
ap-3509	53	2	cos(2π(−ax1	cos(2π(−ax1	NOUN
ap-3509	53	3	+	+	CCONJ
ap-3509	53	4	(	(	PUNCT
ap-3509	53	5	a+	a+	PRON
ap-3509	53	6	b)x2	b)x2	NOUN
ap-3509	53	7	)	)	PUNCT
ap-3509	53	8	)	)	PUNCT
ap-3509	54	1	+	+	CCONJ
ap-3509	54	2	cos(2π(ax1	cos(2π(ax1	NOUN
ap-3509	54	3	+	+	CCONJ
ap-3509	54	4	bx2	bx2	PROPN
ap-3509	54	5	)	)	PUNCT
ap-3509	54	6	]	]	PUNCT
ap-3509	54	7	,	,	PUNCT
ap-3509	54	8	g2	g2	PROPN
ap-3509	54	9	:	:	PUNCT
ap-3509	54	10	2	2	NUM
ap-3509	54	11	[	[	PUNCT
ap-3509	54	12	cos(2π((2a+	cos(2π((2a+	NOUN
ap-3509	54	13	b)x1	b)x1	NOUN
ap-3509	54	14	−	−	PROPN
ap-3509	55	1	(	(	PUNCT
ap-3509	55	2	3a+	3a+	NUM
ap-3509	55	3	2b)x2	2b)x2	NUM
ap-3509	55	4	)	)	PUNCT
ap-3509	56	1	+	+	NUM
ap-3509	56	2	cos(2π(ax1	cos(2π(ax1	NOUN
ap-3509	56	3	+	+	CCONJ
ap-3509	56	4	bx2	bx2	PROPN
ap-3509	56	5	)	)	PUNCT
ap-3509	56	6	±	±	NOUN
ap-3509	56	7	cos(2π(a+	cos(2π(a+	PROPN
ap-3509	56	8	b)x1	b)x1	NOUN
ap-3509	56	9	−	−	PROPN
ap-3509	56	10	bx2	bx2	PROPN
ap-3509	56	11	)	)	PUNCT
ap-3509	56	12	±	±	PROPN
ap-3509	56	13	cos(2π(ax1	cos(2π(ax1	NOUN
ap-3509	56	14	−	−	PROPN
ap-3509	57	1	(	(	PUNCT
ap-3509	57	2	3a+	3a+	NUM
ap-3509	57	3	b)x2	b)x2	PROPN
ap-3509	57	4	)	)	PUNCT
ap-3509	57	5	±	±	NUM
ap-3509	57	6	cos(2π((2a+	cos(2π((2a+	NOUN
ap-3509	57	7	b)x1	b)x1	NOUN
ap-3509	57	8	−	−	PROPN
ap-3509	58	1	(	(	PUNCT
ap-3509	58	2	3a+	3a+	NUM
ap-3509	58	3	b)x2	b)x2	PROPN
ap-3509	58	4	)	)	PUNCT
ap-3509	59	1	+	+	NUM
ap-3509	59	2	cos(2π(a+	cos(2π(a+	PROPN
ap-3509	59	3	b)x1	b)x1	NOUN
ap-3509	59	4	−	−	PROPN
ap-3509	60	1	(	(	PUNCT
ap-3509	60	2	3a+	3a+	NUM
ap-3509	60	3	2b)x2	2b)x2	NUM
ap-3509	60	4	)	)	PUNCT
ap-3509	60	5	]	]	PUNCT
ap-3509	60	6	.	.	PUNCT
ap-3509	61	1	3.2	3.2	NUM
ap-3509	61	2	.	.	PUNCT
ap-3509	61	3	explicit	explicit	ADJ
ap-3509	61	4	form	form	NOUN
ap-3509	61	5	of	of	ADP
ap-3509	61	6	ss	ss	NOUN
ap-3509	61	7	and	and	CCONJ
ap-3509	61	8	sl	sl	NOUN
ap-3509	61	9	-	-	PUNCT
ap-3509	61	10	functions	function	NOUN
ap-3509	61	11	similarly	similarly	ADV
ap-3509	61	12	,	,	PUNCT
ap-3509	61	13	as	as	ADP
ap-3509	61	14	in	in	ADP
ap-3509	61	15	the	the	DET
ap-3509	61	16	previous	previous	ADJ
ap-3509	61	17	subsection	subsection	NOUN
ap-3509	61	18	,	,	PUNCT
ap-3509	61	19	we	we	PRON
ap-3509	61	20	present	present	VERB
ap-3509	61	21	exact	exact	ADJ
ap-3509	61	22	formulas	formula	NOUN
ap-3509	61	23	for	for	ADP
ap-3509	61	24	sland	sland	NOUN
ap-3509	61	25	ssfunctions	ssfunction	NOUN
ap-3509	61	26	.	.	PUNCT
ap-3509	62	1	again	again	ADV
ap-3509	62	2	,	,	PUNCT
ap-3509	62	3	the	the	DET
ap-3509	62	4	upper	upper	ADJ
ap-3509	62	5	signs	sign	NOUN
ap-3509	62	6	correspond	correspond	VERB
ap-3509	62	7	to	to	ADP
ap-3509	62	8	ss(a	ss(a	NUM
ap-3509	62	9	,	,	PUNCT
ap-3509	62	10	b)(x	b)(x	NOUN
ap-3509	62	11	)	)	PUNCT
ap-3509	62	12	function	function	NOUN
ap-3509	62	13	and	and	CCONJ
ap-3509	62	14	the	the	DET
ap-3509	62	15	lower	low	ADJ
ap-3509	62	16	ones	one	NOUN
ap-3509	62	17	belong	belong	VERB
ap-3509	62	18	to	to	ADP
ap-3509	62	19	sl(a	sl(a	PROPN
ap-3509	62	20	,	,	PUNCT
ap-3509	62	21	b)(x	b)(x	NOUN
ap-3509	62	22	)	)	PUNCT
ap-3509	62	23	function	function	NOUN
ap-3509	63	1	[	[	X
ap-3509	63	2	9	9	NUM
ap-3509	63	3	,	,	PUNCT
ap-3509	63	4	13	13	NUM
ap-3509	63	5	]	]	PUNCT
ap-3509	63	6	:	:	PUNCT
ap-3509	63	7	c2	c2	PROPN
ap-3509	63	8	:	:	PUNCT
ap-3509	63	9	2	2	NUM
ap-3509	63	10	[	[	PUNCT
ap-3509	63	11	∓	∓	NOUN
ap-3509	63	12	cos(2π((a+	cos(2π((a+	NOUN
ap-3509	63	13	2b)x1	2b)x1	NUM
ap-3509	63	14	−	−	PROPN
ap-3509	63	15	(	(	PUNCT
ap-3509	63	16	a+	a+	PUNCT
ap-3509	63	17	b)x2	b)x2	PROPN
ap-3509	63	18	)	)	PUNCT
ap-3509	63	19	)	)	PUNCT
ap-3509	63	20	±	±	PROPN
ap-3509	63	21	cos(2π((a+	cos(2π((a+	NOUN
ap-3509	63	22	2b)x1	2b)x1	NUM
ap-3509	63	23	−	−	PROPN
ap-3509	63	24	bx2	bx2	PROPN
ap-3509	63	25	)	)	PUNCT
ap-3509	63	26	)	)	PUNCT
ap-3509	64	1	−	−	PROPN
ap-3509	65	1	cos(2π(−ax1	cos(2π(−ax1	NOUN
ap-3509	65	2	+	+	CCONJ
ap-3509	65	3	(	(	PUNCT
ap-3509	65	4	a+	a+	PRON
ap-3509	65	5	b)x2	b)x2	NOUN
ap-3509	65	6	)	)	PUNCT
ap-3509	65	7	)	)	PUNCT
ap-3509	66	1	+	+	CCONJ
ap-3509	66	2	cos(2π(ax1	cos(2π(ax1	NOUN
ap-3509	66	3	+	+	CCONJ
ap-3509	66	4	bx2	bx2	PROPN
ap-3509	66	5	)	)	PUNCT
ap-3509	66	6	]	]	PUNCT
ap-3509	66	7	,	,	PUNCT
ap-3509	66	8	g2	g2	PROPN
ap-3509	66	9	:	:	PUNCT
ap-3509	66	10	2i	2i	NUM
ap-3509	66	11	[	[	PUNCT
ap-3509	66	12	sin(2π((a+	sin(2π((a+	NOUN
ap-3509	66	13	b)x1	b)x1	NOUN
ap-3509	66	14	−	−	PROPN
ap-3509	67	1	(	(	PUNCT
ap-3509	67	2	3a+	3a+	NUM
ap-3509	67	3	2b)x2	2b)x2	NUM
ap-3509	67	4	)	)	PUNCT
ap-3509	67	5	)	)	PUNCT
ap-3509	68	1	+	+	CCONJ
ap-3509	68	2	sin(2π(ax1	sin(2π(ax1	NOUN
ap-3509	68	3	+	+	CCONJ
ap-3509	68	4	bx2	bx2	NOUN
ap-3509	68	5	)	)	PUNCT
ap-3509	68	6	)	)	PUNCT
ap-3509	68	7	±	±	NUM
ap-3509	68	8	sin(2π((2a+	sin(2π((2a+	NOUN
ap-3509	68	9	b)x1	b)x1	NOUN
ap-3509	68	10	−	−	PROPN
ap-3509	68	11	(	(	PUNCT
ap-3509	68	12	3a+	3a+	NUM
ap-3509	68	13	2b)x2	2b)x2	NUM
ap-3509	68	14	)	)	PUNCT
ap-3509	68	15	)	)	PUNCT
ap-3509	69	1	∓	∓	NOUN
ap-3509	69	2	sin(2π(ax1	sin(2π(ax1	INTJ
ap-3509	70	1	−	−	PROPN
ap-3509	70	2	(	(	PUNCT
ap-3509	70	3	3a+	3a+	NUM
ap-3509	70	4	b)x2	b)x2	NOUN
ap-3509	70	5	)	)	PUNCT
ap-3509	70	6	)	)	PUNCT
ap-3509	71	1	−	−	ADP
ap-3509	72	1	sin(2π((2a+	sin(2π((2a+	VERB
ap-3509	72	2	b)x1	b)x1	NOUN
ap-3509	72	3	−	−	PROPN
ap-3509	73	1	(	(	PUNCT
ap-3509	73	2	3a+	3a+	NUM
ap-3509	73	3	b)x2	b)x2	NOUN
ap-3509	73	4	)	)	PUNCT
ap-3509	73	5	)	)	PUNCT
ap-3509	74	1	∓	∓	NOUN
ap-3509	74	2	sin(2π((a+	sin(2π((a+	NOUN
ap-3509	74	3	b)x1	b)x1	PROPN
ap-3509	74	4	−	−	PROPN
ap-3509	74	5	bx2	bx2	PROPN
ap-3509	74	6	)	)	PUNCT
ap-3509	74	7	)	)	PUNCT
ap-3509	74	8	]	]	PUNCT
ap-3509	74	9	.	.	PUNCT
ap-3509	75	1	remark	remark	PROPN
ap-3509	75	2	1	1	NUM
ap-3509	75	3	.	.	PUNCT
ap-3509	76	1	the	the	DET
ap-3509	76	2	weight	weight	NOUN
ap-3509	76	3	coordinates	coordinate	NOUN
ap-3509	76	4	(	(	PUNCT
ap-3509	76	5	a	a	PRON
ap-3509	76	6	,	,	PUNCT
ap-3509	76	7	b)ω	b)ω	NOUN
ap-3509	76	8	for	for	ADP
ap-3509	76	9	the	the	DET
ap-3509	76	10	four	four	NUM
ap-3509	76	11	families	family	NOUN
ap-3509	76	12	of	of	ADP
ap-3509	76	13	special	special	ADJ
ap-3509	76	14	functions	function	NOUN
ap-3509	76	15	are	be	AUX
ap-3509	76	16	different	different	ADJ
ap-3509	76	17	,	,	PUNCT
ap-3509	76	18	namely	namely	ADV
ap-3509	76	19	c(a	c(a	PROPN
ap-3509	76	20	,	,	PUNCT
ap-3509	76	21	b)(x	b)(x	PROPN
ap-3509	76	22	)	)	PUNCT
ap-3509	76	23	:	:	PUNCT
ap-3509	76	24	a	a	X
ap-3509	76	25	,	,	PUNCT
ap-3509	76	26	b	b	PROPN
ap-3509	76	27	∈	∈	PROPN
ap-3509	76	28	z≥0	z≥0	NOUN
ap-3509	76	29	,	,	PUNCT
ap-3509	76	30	s(a	s(a	PROPN
ap-3509	76	31	,	,	PUNCT
ap-3509	76	32	b)(x	b)(x	PROPN
ap-3509	76	33	)	)	PUNCT
ap-3509	76	34	:	:	PUNCT
ap-3509	76	35	a	a	X
ap-3509	76	36	,	,	PUNCT
ap-3509	76	37	b	b	X
ap-3509	76	38	∈	∈	PROPN
ap-3509	76	39	z>0	z>0	NOUN
ap-3509	76	40	,	,	PUNCT
ap-3509	76	41	ss(a	ss(a	NOUN
ap-3509	76	42	,	,	PUNCT
ap-3509	76	43	b)(x	b)(x	PROPN
ap-3509	76	44	)	)	PUNCT
ap-3509	76	45	:	:	PUNCT
ap-3509	76	46	{	{	PUNCT
ap-3509	76	47	a	a	DET
ap-3509	76	48	∈	∈	PROPN
ap-3509	76	49	z>0	z>0	NOUN
ap-3509	76	50	,	,	PUNCT
ap-3509	76	51	b	b	PROPN
ap-3509	76	52	∈	∈	PROPN
ap-3509	76	53	z≥0	z≥0	PROPN
ap-3509	76	54	for	for	ADP
ap-3509	76	55	c2	c2	PROPN
ap-3509	76	56	,	,	PUNCT
ap-3509	76	57	a	a	DET
ap-3509	76	58	∈	∈	PROPN
ap-3509	76	59	z≥0	z≥0	NOUN
ap-3509	76	60	,	,	PUNCT
ap-3509	76	61	b	b	X
ap-3509	76	62	∈	∈	NOUN
ap-3509	76	63	z>0	z>0	NOUN
ap-3509	76	64	for	for	ADP
ap-3509	76	65	g2	g2	PROPN
ap-3509	76	66	,	,	PUNCT
ap-3509	76	67	sl(a	sl(a	X
ap-3509	76	68	,	,	PUNCT
ap-3509	76	69	b)(x	b)(x	PROPN
ap-3509	76	70	)	)	PUNCT
ap-3509	76	71	:	:	PUNCT
ap-3509	76	72	{	{	PUNCT
ap-3509	76	73	a	a	DET
ap-3509	76	74	∈	∈	PROPN
ap-3509	76	75	z≥0	z≥0	NOUN
ap-3509	76	76	,	,	PUNCT
ap-3509	76	77	b	b	X
ap-3509	76	78	∈	∈	NOUN
ap-3509	76	79	z>0	z>0	NOUN
ap-3509	76	80	for	for	ADP
ap-3509	76	81	c2	c2	PROPN
ap-3509	76	82	,	,	PUNCT
ap-3509	76	83	a	a	DET
ap-3509	76	84	∈	∈	PROPN
ap-3509	76	85	z>0	z>0	NOUN
ap-3509	76	86	,	,	PUNCT
ap-3509	76	87	b	b	PROPN
ap-3509	76	88	∈	∈	PROPN
ap-3509	76	89	z≥0	z≥0	PROPN
ap-3509	76	90	for	for	ADP
ap-3509	76	91	g2	g2	PROPN
ap-3509	76	92	,	,	PUNCT
ap-3509	76	93	the	the	DET
ap-3509	76	94	next	next	ADJ
ap-3509	76	95	remark	remark	NOUN
ap-3509	76	96	is	be	AUX
ap-3509	76	97	a	a	DET
ap-3509	76	98	consequence	consequence	NOUN
ap-3509	76	99	of	of	ADP
ap-3509	76	100	explicit	explicit	ADJ
ap-3509	76	101	forms	form	NOUN
ap-3509	76	102	of	of	ADP
ap-3509	76	103	functions	function	NOUN
ap-3509	76	104	written	write	VERB
ap-3509	76	105	in	in	ADP
ap-3509	76	106	subsections	subsection	NOUN
ap-3509	76	107	3.1	3.1	NUM
ap-3509	76	108	,	,	PUNCT
ap-3509	76	109	3.2	3.2	NUM
ap-3509	76	110	.	.	PUNCT
ap-3509	77	1	remark	remark	NOUN
ap-3509	77	2	2	2	NUM
ap-3509	77	3	.	.	NOUN
ap-3509	77	4	four	four	NUM
ap-3509	77	5	families	family	NOUN
ap-3509	77	6	of	of	ADP
ap-3509	77	7	special	special	ADJ
ap-3509	77	8	functions	function	NOUN
ap-3509	77	9	are	be	AUX
ap-3509	77	10	real	real	ADJ
ap-3509	77	11	in	in	ADP
ap-3509	77	12	case	case	NOUN
ap-3509	77	13	of	of	ADP
ap-3509	77	14	c2	c2	PROPN
ap-3509	77	15	group	group	NOUN
ap-3509	77	16	.	.	PUNCT
ap-3509	78	1	the	the	DET
ap-3509	78	2	functions	function	NOUN
ap-3509	78	3	c-	c-	X
ap-3509	78	4	,	,	PUNCT
ap-3509	78	5	sare	sare	PROPN
ap-3509	78	6	real	real	ADJ
ap-3509	78	7	,	,	PUNCT
ap-3509	78	8	and	and	CCONJ
ap-3509	78	9	sl-	sl-	X
ap-3509	78	10	,	,	PUNCT
ap-3509	78	11	ssare	ssare	VERB
ap-3509	78	12	pure	pure	ADJ
ap-3509	78	13	imaginary	imaginary	ADJ
ap-3509	78	14	in	in	ADP
ap-3509	78	15	case	case	NOUN
ap-3509	78	16	of	of	ADP
ap-3509	78	17	g2	g2	PROPN
ap-3509	78	18	group	group	NOUN
ap-3509	78	19	.	.	PUNCT
ap-3509	79	1	246	246	NUM
ap-3509	79	2	vol	vol	NOUN
ap-3509	79	3	.	.	PUNCT
ap-3509	80	1	56	56	NUM
ap-3509	80	2	no	no	NOUN
ap-3509	80	3	.	.	PUNCT
ap-3509	81	1	3/2016	3/2016	NUM
ap-3509	81	2	two	two	NUM
ap-3509	81	3	-	-	PUNCT
ap-3509	81	4	dimensional	dimensional	ADJ
ap-3509	81	5	hybrids	hybrid	NOUN
ap-3509	81	6	with	with	ADP
ap-3509	81	7	mixed	mixed	ADJ
ap-3509	81	8	boundary	boundary	ADJ
ap-3509	81	9	value	value	NOUN
ap-3509	81	10	problems	problem	NOUN
ap-3509	81	11	4	4	NUM
ap-3509	81	12	.	.	PUNCT
ap-3509	81	13	helmholtz	helmholtz	NOUN
ap-3509	81	14	differential	differential	ADJ
ap-3509	81	15	equation	equation	NOUN
ap-3509	81	16	in	in	ADP
ap-3509	81	17	this	this	DET
ap-3509	81	18	section	section	NOUN
ap-3509	81	19	we	we	PRON
ap-3509	81	20	consider	consider	VERB
ap-3509	81	21	the	the	DET
ap-3509	81	22	well	well	ADV
ap-3509	81	23	-	-	PUNCT
ap-3509	81	24	known	know	VERB
ap-3509	81	25	partial	partial	ADJ
ap-3509	81	26	differential	differential	NOUN
ap-3509	81	27	equation	equation	NOUN
ap-3509	81	28	∆ψ(x	∆ψ(x	NOUN
ap-3509	81	29	)	)	PUNCT
ap-3509	82	1	=	=	SYM
ap-3509	82	2	−w2ψ(x	−w2ψ(x	NOUN
ap-3509	82	3	)	)	PUNCT
ap-3509	82	4	,	,	PUNCT
ap-3509	83	1	w	w	NOUN
ap-3509	83	2	−	−	PROPN
ap-3509	83	3	positive	positive	ADJ
ap-3509	83	4	real	real	ADJ
ap-3509	83	5	constant	constant	NOUN
ap-3509	83	6	called	call	VERB
ap-3509	83	7	homogeneous	homogeneous	ADJ
ap-3509	83	8	helmholtz	helmholtz	NOUN
ap-3509	83	9	equation	equation	NOUN
ap-3509	83	10	(	(	PUNCT
ap-3509	83	11	see	see	VERB
ap-3509	83	12	for	for	ADP
ap-3509	83	13	example	example	NOUN
ap-3509	83	14	[	[	X
ap-3509	83	15	7	7	NUM
ap-3509	83	16	,	,	PUNCT
ap-3509	83	17	8	8	NUM
ap-3509	83	18	,	,	PUNCT
ap-3509	83	19	15	15	NUM
ap-3509	83	20	]	]	PUNCT
ap-3509	83	21	and	and	CCONJ
ap-3509	83	22	references	reference	NOUN
ap-3509	83	23	therein	therein	ADV
ap-3509	83	24	)	)	PUNCT
ap-3509	83	25	,	,	PUNCT
ap-3509	84	1	where	where	SCONJ
ap-3509	84	2	x	x	X
ap-3509	84	3	=	=	PRON
ap-3509	84	4	(	(	PUNCT
ap-3509	84	5	y1	y1	PROPN
ap-3509	84	6	,	,	PUNCT
ap-3509	84	7	y2)e	y2)e	ADJ
ap-3509	84	8	and	and	CCONJ
ap-3509	84	9	∆	∆	PROPN
ap-3509	84	10	=	=	SYM
ap-3509	84	11	∂2	∂2	PROPN
ap-3509	84	12	∂y2	∂y2	NOUN
ap-3509	84	13	1	1	NUM
ap-3509	84	14	+	+	CCONJ
ap-3509	84	15	∂2	∂2	NOUN
ap-3509	84	16	∂y2	∂y2	NOUN
ap-3509	84	17	2	2	NUM
ap-3509	84	18	.	.	PUNCT
ap-3509	85	1	remark	remark	VERB
ap-3509	85	2	3	3	NUM
ap-3509	86	1	[	[	X
ap-3509	86	2	5	5	NUM
ap-3509	86	3	]	]	PUNCT
ap-3509	86	4	.	.	PUNCT
ap-3509	87	1	the	the	DET
ap-3509	87	2	special	special	ADJ
ap-3509	87	3	functions	function	NOUN
ap-3509	87	4	described	describe	VERB
ap-3509	87	5	in	in	ADP
ap-3509	87	6	the	the	DET
ap-3509	87	7	previous	previous	ADJ
ap-3509	87	8	section	section	NOUN
ap-3509	87	9	are	be	AUX
ap-3509	87	10	eigenfunctions	eigenfunction	NOUN
ap-3509	87	11	of	of	ADP
ap-3509	87	12	the	the	DET
ap-3509	87	13	laplace	laplace	NOUN
ap-3509	87	14	operator	operator	NOUN
ap-3509	87	15	.	.	PUNCT
ap-3509	88	1	the	the	DET
ap-3509	88	2	explicit	explicit	ADJ
ap-3509	88	3	form	form	NOUN
ap-3509	88	4	of	of	ADP
ap-3509	88	5	the	the	DET
ap-3509	88	6	laplace	laplace	NOUN
ap-3509	88	7	operator	operator	NOUN
ap-3509	88	8	in	in	ADP
ap-3509	88	9	coordinates	coordinate	NOUN
ap-3509	88	10	relative	relative	ADJ
ap-3509	88	11	to	to	ADP
ap-3509	88	12	the	the	DET
ap-3509	88	13	ω	ω	NOUN
ap-3509	88	14	-	-	PUNCT
ap-3509	88	15	basis	basis	NOUN
ap-3509	88	16	and	and	CCONJ
ap-3509	88	17	α̌-basis	α̌-basis	NOUN
ap-3509	88	18	is	be	AUX
ap-3509	88	19	the	the	DET
ap-3509	88	20	following	follow	VERB
ap-3509	88	21	c2	c2	PROPN
ap-3509	88	22	:	:	PUNCT
ap-3509	89	1	∆ω	∆ω	PROPN
ap-3509	89	2	=	=	SYM
ap-3509	90	1	2∂2	2∂2	NUM
ap-3509	90	2	1	1	NUM
ap-3509	90	3	−	−	NOUN
ap-3509	90	4	2∂1∂2	2∂1∂2	NOUN
ap-3509	90	5	+	+	CCONJ
ap-3509	90	6	∂2	∂2	PROPN
ap-3509	90	7	2	2	NUM
ap-3509	90	8	,	,	PUNCT
ap-3509	90	9	∆α̌	∆α̌	X
ap-3509	90	10	=	=	SYM
ap-3509	90	11	1	1	NUM
ap-3509	90	12	2∂	2∂	NUM
ap-3509	90	13	2	2	NUM
ap-3509	90	14	1	1	NUM
ap-3509	90	15	+	+	CCONJ
ap-3509	90	16	∂1∂2	∂1∂2	NOUN
ap-3509	90	17	+	+	CCONJ
ap-3509	90	18	∂2	∂2	NUM
ap-3509	90	19	2	2	NUM
ap-3509	90	20	,	,	PUNCT
ap-3509	90	21	g2	g2	PROPN
ap-3509	90	22	:	:	PUNCT
ap-3509	90	23	∆ω	∆ω	PROPN
ap-3509	90	24	=	=	SYM
ap-3509	90	25	∂2	∂2	PROPN
ap-3509	90	26	1	1	NUM
ap-3509	90	27	−	−	NOUN
ap-3509	90	28	3∂1∂2	3∂1∂2	NUM
ap-3509	91	1	+	+	CCONJ
ap-3509	91	2	3∂2	3∂2	NUM
ap-3509	91	3	2	2	NUM
ap-3509	91	4	,	,	PUNCT
ap-3509	91	5	∆α̌	∆α̌	X
ap-3509	91	6	=	=	SYM
ap-3509	91	7	2∂2	2∂2	NUM
ap-3509	91	8	1	1	NUM
ap-3509	92	1	+	+	CCONJ
ap-3509	92	2	2∂1∂2	2∂1∂2	PRON
ap-3509	92	3	+	+	CCONJ
ap-3509	92	4	2	2	NUM
ap-3509	92	5	3∂	3∂	NUM
ap-3509	92	6	2	2	NUM
ap-3509	92	7	2	2	NUM
ap-3509	92	8	.	.	PUNCT
ap-3509	93	1	since	since	SCONJ
ap-3509	93	2	∆e2πi〈λ|x	∆e2πi〈λ|x	PROPN
ap-3509	93	3	〉	〉	PROPN
ap-3509	93	4	=	=	SYM
ap-3509	93	5	−4π2〈λ|λ〉e2πi〈λ|x	−4π2〈λ|λ〉e2πi〈λ|x	NOUN
ap-3509	93	6	〉	〉	NOUN
ap-3509	93	7	then	then	ADV
ap-3509	93	8	we	we	PRON
ap-3509	93	9	have	have	VERB
ap-3509	93	10	∆ψλ(x	∆ψλ(x	NOUN
ap-3509	93	11	)	)	PUNCT
ap-3509	94	1	=	=	SYM
ap-3509	94	2	−4π2〈λ|λ〉ψλ(x	−4π2〈λ|λ〉ψλ(x	NOUN
ap-3509	94	3	)	)	PUNCT
ap-3509	94	4	,	,	PUNCT
ap-3509	94	5	where	where	SCONJ
ap-3509	94	6	ψλ(x	ψλ(x	NUM
ap-3509	94	7	)	)	PUNCT
ap-3509	94	8	is	be	AUX
ap-3509	94	9	one	one	NUM
ap-3509	94	10	of	of	ADP
ap-3509	94	11	the	the	DET
ap-3509	94	12	functions	function	NOUN
ap-3509	94	13	c	c	X
ap-3509	94	14	,	,	PUNCT
ap-3509	94	15	s	s	X
ap-3509	94	16	,	,	PUNCT
ap-3509	94	17	ss	ss	NOUN
ap-3509	94	18	or	or	CCONJ
ap-3509	94	19	sl	sl	INTJ
ap-3509	94	20	.	.	PUNCT
ap-3509	95	1	the	the	DET
ap-3509	95	2	inner	inner	ADJ
ap-3509	95	3	product	product	NOUN
ap-3509	95	4	of	of	ADP
ap-3509	95	5	λs	λs	PROPN
ap-3509	95	6	is	be	AUX
ap-3509	95	7	equal	equal	ADJ
ap-3509	95	8	c2	c2	PROPN
ap-3509	95	9	:	:	PUNCT
ap-3509	96	1	〈	〈	PROPN
ap-3509	96	2	λ|λ	λ|λ	PROPN
ap-3509	96	3	〉	〉	NOUN
ap-3509	96	4	=	=	SYM
ap-3509	96	5	1	1	NUM
ap-3509	96	6	2a	2a	NUM
ap-3509	96	7	2	2	NUM
ap-3509	96	8	+	+	CCONJ
ap-3509	96	9	ab+	ab+	NOUN
ap-3509	96	10	b2	b2	NOUN
ap-3509	96	11	,	,	PUNCT
ap-3509	96	12	g2	g2	PROPN
ap-3509	96	13	:	:	PUNCT
ap-3509	97	1	〈	〈	PROPN
ap-3509	97	2	λ|λ	λ|λ	PROPN
ap-3509	97	3	〉	〉	PROPN
ap-3509	97	4	=	=	SYM
ap-3509	97	5	2a2	2a2	NUM
ap-3509	98	1	+	+	CCONJ
ap-3509	98	2	2ab+	2ab+	NUM
ap-3509	98	3	2	2	NUM
ap-3509	98	4	3b	3b	NOUN
ap-3509	98	5	2	2	NUM
ap-3509	98	6	.	.	SYM
ap-3509	98	7	4.1	4.1	NUM
ap-3509	98	8	.	.	PUNCT
ap-3509	99	1	separation	separation	NOUN
ap-3509	99	2	of	of	ADP
ap-3509	99	3	variables	variable	NOUN
ap-3509	99	4	for	for	ADP
ap-3509	99	5	the	the	DET
ap-3509	99	6	helmholtz	helmholtz	NOUN
ap-3509	99	7	equation	equation	NOUN
ap-3509	99	8	using	use	VERB
ap-3509	99	9	a	a	DET
ap-3509	99	10	standard	standard	ADJ
ap-3509	99	11	method	method	NOUN
ap-3509	99	12	of	of	ADP
ap-3509	99	13	separation	separation	NOUN
ap-3509	99	14	of	of	ADP
ap-3509	99	15	variables	variable	NOUN
ap-3509	99	16	for	for	ADP
ap-3509	99	17	the	the	DET
ap-3509	99	18	helmholtz	helmholtz	NOUN
ap-3509	99	19	equation	equation	NOUN
ap-3509	99	20	[	[	X
ap-3509	99	21	7	7	NUM
ap-3509	99	22	]	]	SYM
ap-3509	99	23	∆ψ(x	∆ψ(x	NOUN
ap-3509	99	24	)	)	PUNCT
ap-3509	99	25	=	=	SYM
ap-3509	99	26	−w2ψ(x	−w2ψ(x	NOUN
ap-3509	99	27	)	)	PUNCT
ap-3509	99	28	,	,	PUNCT
ap-3509	99	29	x	x	X
ap-3509	99	30	=	=	PUNCT
ap-3509	99	31	(	(	PUNCT
ap-3509	99	32	y1	y1	PROPN
ap-3509	99	33	,	,	PUNCT
ap-3509	99	34	y2)e	y2)e	ADJ
ap-3509	99	35	,	,	PUNCT
ap-3509	99	36	and	and	CCONJ
ap-3509	99	37	searching	search	VERB
ap-3509	99	38	for	for	ADP
ap-3509	99	39	the	the	DET
ap-3509	99	40	solutions	solution	NOUN
ap-3509	99	41	in	in	ADP
ap-3509	99	42	the	the	DET
ap-3509	99	43	form	form	NOUN
ap-3509	99	44	ψ(x	ψ(x	NOUN
ap-3509	99	45	)	)	PUNCT
ap-3509	100	1	=	=	PUNCT
ap-3509	100	2	x(y1)y	x(y1)y	PROPN
ap-3509	100	3	(	(	PUNCT
ap-3509	100	4	y2	y2	PROPN
ap-3509	100	5	)	)	PUNCT
ap-3509	100	6	,	,	PUNCT
ap-3509	100	7	we	we	PRON
ap-3509	100	8	have	have	VERB
ap-3509	100	9	the	the	DET
ap-3509	100	10	following	follow	VERB
ap-3509	100	11	differential	differential	ADJ
ap-3509	100	12	equation	equation	NOUN
ap-3509	100	13	x	x	PRON
ap-3509	100	14	′′y	′′y	VERB
ap-3509	101	1	+	+	NOUN
ap-3509	101	2	xy	xy	X
ap-3509	101	3	′′	′′	NOUN
ap-3509	101	4	+	+	CCONJ
ap-3509	101	5	w2xy	w2xy	PROPN
ap-3509	101	6	=	=	SYM
ap-3509	101	7	0	0	X
ap-3509	101	8	.	.	X
ap-3509	101	9	introducing	introduce	VERB
ap-3509	101	10	−k2	−k2	NOUN
ap-3509	101	11	-	-	PUNCT
ap-3509	101	12	separation	separation	NOUN
ap-3509	101	13	constant	constant	NOUN
ap-3509	101	14	,	,	PUNCT
ap-3509	101	15	we	we	PRON
ap-3509	101	16	get	get	VERB
ap-3509	101	17	a	a	DET
ap-3509	101	18	pair	pair	NOUN
ap-3509	101	19	of	of	ADP
ap-3509	101	20	the	the	DET
ap-3509	101	21	ordinary	ordinary	ADJ
ap-3509	101	22	differential	differential	ADJ
ap-3509	101	23	equations	equation	NOUN
ap-3509	101	24	easy	easy	ADJ
ap-3509	101	25	to	to	PART
ap-3509	101	26	solve	solve	VERB
ap-3509	101	27	:	:	PUNCT
ap-3509	101	28	x	x	SYM
ap-3509	101	29	′′	′′	NOUN
ap-3509	101	30	+	+	CCONJ
ap-3509	101	31	k2x	k2x	X
ap-3509	101	32	=	=	SYM
ap-3509	101	33	0	0	NUM
ap-3509	101	34	,	,	PUNCT
ap-3509	101	35	y	y	PROPN
ap-3509	101	36	′′	′′	PROPN
ap-3509	101	37	+	+	CCONJ
ap-3509	101	38	(	(	PUNCT
ap-3509	101	39	w2	w2	NOUN
ap-3509	101	40	−	−	PROPN
ap-3509	101	41	k2)y	k2)y	PROPN
ap-3509	101	42	=	=	NOUN
ap-3509	102	1	0	0	X
ap-3509	102	2	.	.	PUNCT
ap-3509	103	1	(	(	PUNCT
ap-3509	103	2	5	5	X
ap-3509	103	3	)	)	PUNCT
ap-3509	103	4	a	a	DET
ap-3509	103	5	basic	basic	ADJ
ap-3509	103	6	solution	solution	NOUN
ap-3509	103	7	of	of	ADP
ap-3509	103	8	(	(	PUNCT
ap-3509	103	9	5	5	X
ap-3509	103	10	)	)	PUNCT
ap-3509	103	11	we	we	PRON
ap-3509	103	12	can	can	AUX
ap-3509	103	13	write	write	VERB
ap-3509	103	14	in	in	ADP
ap-3509	103	15	the	the	DET
ap-3509	103	16	form	form	NOUN
ap-3509	103	17	x1(y1	x1(y1	NUM
ap-3509	103	18	)	)	PUNCT
ap-3509	103	19	=	=	SYM
ap-3509	103	20	cos	cos	PROPN
ap-3509	103	21	ky1	ky1	PROPN
ap-3509	103	22	,	,	PUNCT
ap-3509	103	23	y1(y2	y1(y2	NUM
ap-3509	103	24	)	)	PUNCT
ap-3509	103	25	=	=	SYM
ap-3509	103	26	cos	cos	PROPN
ap-3509	103	27	√	√	PROPN
ap-3509	103	28	w2	w2	NOUN
ap-3509	103	29	−	−	PROPN
ap-3509	103	30	k2y2	k2y2	PROPN
ap-3509	103	31	,	,	PUNCT
ap-3509	103	32	x2(y1	x2(y1	NUM
ap-3509	103	33	)	)	PUNCT
ap-3509	103	34	=	=	VERB
ap-3509	103	35	sin	sin	NOUN
ap-3509	103	36	ky1	ky1	PROPN
ap-3509	103	37	,	,	PUNCT
ap-3509	103	38	y2(y2	y2(y2	NOUN
ap-3509	103	39	)	)	PUNCT
ap-3509	103	40	=	=	PUNCT
ap-3509	103	41	sin	sin	NOUN
ap-3509	103	42	√	√	NOUN
ap-3509	103	43	w2	w2	NOUN
ap-3509	104	1	−	−	PROPN
ap-3509	104	2	k2y2	k2y2	PROPN
ap-3509	104	3	,	,	PUNCT
ap-3509	104	4	where	where	SCONJ
ap-3509	104	5	k	k	PROPN
ap-3509	104	6	6=	6=	ADP
ap-3509	104	7	0	0	NUM
ap-3509	104	8	and	and	CCONJ
ap-3509	104	9	w2	w2	PROPN
ap-3509	104	10	−	−	PROPN
ap-3509	104	11	k2	k2	PROPN
ap-3509	104	12	6=	6=	PROPN
ap-3509	104	13	0	0	NUM
ap-3509	104	14	.	.	PUNCT
ap-3509	105	1	according	accord	VERB
ap-3509	105	2	to	to	ADP
ap-3509	105	3	the	the	DET
ap-3509	105	4	assumptions	assumption	NOUN
ap-3509	105	5	that	that	PRON
ap-3509	105	6	k	k	PROPN
ap-3509	105	7	6=	6=	ADP
ap-3509	105	8	0	0	NUM
ap-3509	105	9	and	and	CCONJ
ap-3509	105	10	w2	w2	PROPN
ap-3509	105	11	6=	6=	PROPN
ap-3509	105	12	k2	k2	PROPN
ap-3509	105	13	we	we	PRON
ap-3509	105	14	consider	consider	VERB
ap-3509	105	15	c-	c-	PRON
ap-3509	105	16	,	,	PUNCT
ap-3509	105	17	s-	s-	X
ap-3509	105	18	,	,	PUNCT
ap-3509	105	19	ss-	ss-	X
ap-3509	105	20	,	,	PUNCT
ap-3509	105	21	and	and	CCONJ
ap-3509	105	22	sl	sl	NOUN
ap-3509	105	23	-	-	PUNCT
ap-3509	105	24	functions	function	NOUN
ap-3509	105	25	only	only	ADV
ap-3509	105	26	with	with	ADP
ap-3509	105	27	positive	positive	ADJ
ap-3509	105	28	weights	weight	NOUN
ap-3509	105	29	.	.	PUNCT
ap-3509	106	1	4.2	4.2	NUM
ap-3509	106	2	.	.	PUNCT
ap-3509	107	1	c2	c2	PROPN
ap-3509	107	2	case	case	NOUN
ap-3509	107	3	from	from	ADP
ap-3509	107	4	the	the	DET
ap-3509	107	5	projection	projection	NOUN
ap-3509	107	6	matrix	matrix	NOUN
ap-3509	107	7	pc2	pc2	NOUN
ap-3509	107	8	(	(	PUNCT
ap-3509	107	9	1	1	NUM
ap-3509	107	10	)	)	PUNCT
ap-3509	107	11	and	and	CCONJ
ap-3509	107	12	the	the	DET
ap-3509	107	13	branching	branch	VERB
ap-3509	107	14	rule	rule	NOUN
ap-3509	107	15	(	(	PUNCT
ap-3509	107	16	2	2	X
ap-3509	107	17	)	)	PUNCT
ap-3509	107	18	we	we	PRON
ap-3509	107	19	find	find	VERB
ap-3509	107	20	two	two	NUM
ap-3509	107	21	separation	separation	NOUN
ap-3509	107	22	constants	constant	NOUN
ap-3509	107	23	−k2	−k2	PROPN
ap-3509	107	24	1	1	NUM
ap-3509	107	25	and	and	CCONJ
ap-3509	107	26	−k2	−k2	PROPN
ap-3509	107	27	2	2	NUM
ap-3509	107	28	,	,	PUNCT
ap-3509	107	29	which	which	PRON
ap-3509	107	30	have	have	VERB
ap-3509	107	31	a	a	DET
ap-3509	107	32	form	form	NOUN
ap-3509	107	33	−k2	−k2	ADJ
ap-3509	107	34	1	1	NUM
ap-3509	107	35	=	=	SYM
ap-3509	107	36	−2(a+	−2(a+	NOUN
ap-3509	107	37	b)2π2	b)2π2	PROPN
ap-3509	107	38	,	,	PUNCT
ap-3509	107	39	w2	w2	NOUN
ap-3509	107	40	−	−	PROPN
ap-3509	107	41	k2	k2	PROPN
ap-3509	107	42	1	1	NUM
ap-3509	107	43	=	=	SYM
ap-3509	107	44	2b2π2	2b2π2	NUM
ap-3509	107	45	,	,	PUNCT
ap-3509	107	46	−k2	−k2	PROPN
ap-3509	107	47	2	2	NUM
ap-3509	107	48	=	=	SYM
ap-3509	107	49	−2b2π2	−2b2π2	PROPN
ap-3509	107	50	,	,	PUNCT
ap-3509	107	51	w2	w2	NOUN
ap-3509	107	52	−	−	PROPN
ap-3509	107	53	k2	k2	PROPN
ap-3509	107	54	2	2	NUM
ap-3509	107	55	=	=	SYM
ap-3509	107	56	2(a+	2(a+	NUM
ap-3509	107	57	b)2π2	b)2π2	NOUN
ap-3509	107	58	.	.	PUNCT
ap-3509	108	1	noting	note	VERB
ap-3509	108	2	that	that	SCONJ
ap-3509	108	3	k2	k2	PROPN
ap-3509	108	4	1	1	NUM
ap-3509	108	5	=	=	NOUN
ap-3509	108	6	w2	w2	NOUN
ap-3509	108	7	−	−	PROPN
ap-3509	108	8	k2	k2	PROPN
ap-3509	108	9	2	2	NUM
ap-3509	108	10	,	,	PUNCT
ap-3509	108	11	as	as	SCONJ
ap-3509	108	12	a	a	DET
ap-3509	108	13	separation	separation	NOUN
ap-3509	108	14	constant	constant	ADJ
ap-3509	108	15	we	we	PRON
ap-3509	108	16	take	take	VERB
ap-3509	108	17	−k2	−k2	PROPN
ap-3509	108	18	=	=	SYM
ap-3509	108	19	−2(a+	−2(a+	NOUN
ap-3509	108	20	b)2π2	b)2π2	PROPN
ap-3509	108	21	,	,	PUNCT
ap-3509	108	22	w2	w2	NOUN
ap-3509	108	23	−	−	PROPN
ap-3509	108	24	k2	k2	PROPN
ap-3509	108	25	=	=	PROPN
ap-3509	108	26	2b2π2	2b2π2	PROPN
ap-3509	108	27	.	.	PUNCT
ap-3509	109	1	using	use	VERB
ap-3509	109	2	the	the	DET
ap-3509	109	3	branching	branch	VERB
ap-3509	109	4	rule	rule	NOUN
ap-3509	109	5	(	(	PUNCT
ap-3509	109	6	2	2	NUM
ap-3509	109	7	)	)	PUNCT
ap-3509	109	8	from	from	ADP
ap-3509	109	9	section	section	NOUN
ap-3509	109	10	2	2	NUM
ap-3509	109	11	for	for	ADP
ap-3509	109	12	special	special	ADJ
ap-3509	109	13	functions	function	NOUN
ap-3509	109	14	c	c	X
ap-3509	109	15	,	,	PUNCT
ap-3509	109	16	s	s	PROPN
ap-3509	109	17	,	,	PUNCT
ap-3509	109	18	ss	ss	PROPN
ap-3509	109	19	,	,	PUNCT
ap-3509	109	20	sl	sl	VERB
ap-3509	109	21	we	we	PRON
ap-3509	109	22	can	can	AUX
ap-3509	109	23	rewrite	rewrite	VERB
ap-3509	109	24	those	those	DET
ap-3509	109	25	functions	function	NOUN
ap-3509	109	26	in	in	ADP
ap-3509	109	27	the	the	DET
ap-3509	109	28	form	form	NOUN
ap-3509	109	29	:	:	PUNCT
ap-3509	109	30	ca	ca	NOUN
ap-3509	109	31	,	,	PUNCT
ap-3509	109	32	b(x	b(x	NOUN
ap-3509	109	33	)	)	PUNCT
ap-3509	109	34	=	=	SYM
ap-3509	109	35	4	4	NUM
ap-3509	109	36	[	[	PUNCT
ap-3509	109	37	cos(ky1	cos(ky1	NOUN
ap-3509	109	38	)	)	PUNCT
ap-3509	109	39	cos	cos	PROPN
ap-3509	109	40	(	(	PUNCT
ap-3509	109	41	√	√	PROPN
ap-3509	109	42	w2	w2	NOUN
ap-3509	109	43	−	−	PROPN
ap-3509	109	44	k2y2	k2y2	PROPN
ap-3509	109	45	)	)	PUNCT
ap-3509	110	1	+	+	CCONJ
ap-3509	110	2	cos	cos	PROPN
ap-3509	110	3	(	(	PUNCT
ap-3509	110	4	√	√	PROPN
ap-3509	110	5	w2	w2	NOUN
ap-3509	110	6	−	−	PROPN
ap-3509	110	7	k2y1	k2y1	PROPN
ap-3509	110	8	)	)	PUNCT
ap-3509	110	9	cos(ky2	cos(ky2	PROPN
ap-3509	110	10	)	)	PUNCT
ap-3509	110	11	]	]	PUNCT
ap-3509	110	12	,	,	PUNCT
ap-3509	110	13	sa	sa	NOUN
ap-3509	110	14	,	,	PUNCT
ap-3509	110	15	b(x	b(x	NOUN
ap-3509	110	16	)	)	PUNCT
ap-3509	110	17	=	=	SYM
ap-3509	110	18	4	4	NUM
ap-3509	110	19	[	[	PUNCT
ap-3509	110	20	sin	sin	NOUN
ap-3509	110	21	(	(	PUNCT
ap-3509	110	22	√	√	NOUN
ap-3509	110	23	w2	w2	NOUN
ap-3509	110	24	−	−	PROPN
ap-3509	110	25	k2y1	k2y1	PROPN
ap-3509	110	26	)	)	PUNCT
ap-3509	110	27	sin(ky2	sin(ky2	PROPN
ap-3509	110	28	)	)	PUNCT
ap-3509	110	29	−	−	PROPN
ap-3509	111	1	sin(ky1	sin(ky1	ADJ
ap-3509	111	2	)	)	PUNCT
ap-3509	111	3	sin	sin	NOUN
ap-3509	111	4	(	(	PUNCT
ap-3509	111	5	√	√	NOUN
ap-3509	111	6	w2	w2	NOUN
ap-3509	111	7	−	−	PROPN
ap-3509	111	8	k2y2	k2y2	PROPN
ap-3509	111	9	)	)	PUNCT
ap-3509	111	10	]	]	PUNCT
ap-3509	111	11	,	,	PUNCT
ap-3509	111	12	ssa	ssa	NOUN
ap-3509	111	13	,	,	PUNCT
ap-3509	111	14	b(x	b(x	NOUN
ap-3509	111	15	)	)	PUNCT
ap-3509	111	16	=	=	SYM
ap-3509	111	17	4	4	NUM
ap-3509	111	18	[	[	PUNCT
ap-3509	111	19	cos(ky1	cos(ky1	NOUN
ap-3509	111	20	)	)	PUNCT
ap-3509	111	21	cos	cos	PROPN
ap-3509	111	22	(	(	PUNCT
ap-3509	111	23	√	√	PROPN
ap-3509	111	24	w2	w2	NOUN
ap-3509	111	25	−	−	PROPN
ap-3509	111	26	k2y2	k2y2	PROPN
ap-3509	111	27	)	)	PUNCT
ap-3509	111	28	−	−	PROPN
ap-3509	111	29	cos	cos	PROPN
ap-3509	111	30	(	(	PUNCT
ap-3509	111	31	√	√	PROPN
ap-3509	111	32	w2	w2	NOUN
ap-3509	111	33	−	−	PROPN
ap-3509	111	34	k2y1	k2y1	PROPN
ap-3509	111	35	)	)	PUNCT
ap-3509	111	36	cos(ky2	cos(ky2	PROPN
ap-3509	111	37	)	)	PUNCT
ap-3509	111	38	]	]	PUNCT
ap-3509	111	39	,	,	PUNCT
ap-3509	111	40	sla	sla	PROPN
ap-3509	111	41	,	,	PUNCT
ap-3509	111	42	b(x	b(x	NOUN
ap-3509	111	43	)	)	PUNCT
ap-3509	111	44	=	=	SYM
ap-3509	111	45	−4	−4	X
ap-3509	111	46	[	[	PUNCT
ap-3509	111	47	sin	sin	NOUN
ap-3509	111	48	(	(	PUNCT
ap-3509	111	49	√	√	NOUN
ap-3509	111	50	w2	w2	NOUN
ap-3509	111	51	−	−	PROPN
ap-3509	111	52	k2y1	k2y1	PROPN
ap-3509	111	53	)	)	PUNCT
ap-3509	111	54	sin(ky2	sin(ky2	PROPN
ap-3509	111	55	)	)	PUNCT
ap-3509	112	1	+	+	CCONJ
ap-3509	112	2	sin(ky1	sin(ky1	ADJ
ap-3509	112	3	)	)	PUNCT
ap-3509	112	4	sin	sin	NOUN
ap-3509	112	5	(	(	PUNCT
ap-3509	112	6	√	√	NOUN
ap-3509	112	7	w2	w2	NOUN
ap-3509	112	8	−	−	PROPN
ap-3509	112	9	k2y2	k2y2	PROPN
ap-3509	112	10	)	)	PUNCT
ap-3509	112	11	]	]	PUNCT
ap-3509	112	12	.	.	PUNCT
ap-3509	113	1	by	by	ADP
ap-3509	113	2	changing	change	VERB
ap-3509	113	3	the	the	DET
ap-3509	113	4	variables	variable	NOUN
ap-3509	113	5	by	by	ADP
ap-3509	113	6	y1	y1	NOUN
ap-3509	113	7	=	=	PUNCT
ap-3509	113	8	√	√	NUM
ap-3509	113	9	2x	2x	NUM
ap-3509	113	10	,	,	PUNCT
ap-3509	113	11	y2	y2	PROPN
ap-3509	113	12	=	=	SYM
ap-3509	113	13	√	√	ADP
ap-3509	113	14	2	2	NUM
ap-3509	113	15	we	we	PRON
ap-3509	113	16	get	get	VERB
ap-3509	113	17	the	the	DET
ap-3509	113	18	reduction	reduction	NOUN
ap-3509	113	19	to	to	PART
ap-3509	113	20	a1	a1	VERB
ap-3509	113	21	×a1	×a1	PROPN
ap-3509	113	22	subgroup	subgroup	NOUN
ap-3509	113	23	ca	ca	NOUN
ap-3509	113	24	,	,	PUNCT
ap-3509	113	25	b(x	b(x	NOUN
ap-3509	113	26	)	)	PUNCT
ap-3509	113	27	=	=	SYM
ap-3509	113	28	ca+b(x)cb(y	ca+b(x)cb(y	NOUN
ap-3509	113	29	)	)	PUNCT
ap-3509	114	1	+	+	CCONJ
ap-3509	115	1	cb(x)ca+b(y	cb(x)ca+b(y	ADJ
ap-3509	115	2	)	)	PUNCT
ap-3509	115	3	,	,	PUNCT
ap-3509	115	4	sa	sa	PROPN
ap-3509	115	5	,	,	PUNCT
ap-3509	115	6	b(x	b(x	NOUN
ap-3509	115	7	)	)	PUNCT
ap-3509	115	8	=	=	PRON
ap-3509	116	1	sa+b(x)sb(y)−	sa+b(x)sb(y)−	PROPN
ap-3509	116	2	sb(x)sa+b(y	sb(x)sa+b(y	PROPN
ap-3509	116	3	)	)	PUNCT
ap-3509	116	4	,	,	PUNCT
ap-3509	116	5	ssa	ssa	NOUN
ap-3509	116	6	,	,	PUNCT
ap-3509	116	7	b(x	b(x	NOUN
ap-3509	116	8	)	)	PUNCT
ap-3509	116	9	=	=	SYM
ap-3509	116	10	sa+b(x)sb(y	sa+b(x)sb(y	X
ap-3509	116	11	)	)	PUNCT
ap-3509	117	1	+	+	CCONJ
ap-3509	118	1	sb(x)sa+b(y	sb(x)sa+b(y	PROPN
ap-3509	118	2	)	)	PUNCT
ap-3509	118	3	,	,	PUNCT
ap-3509	118	4	sla	sla	PROPN
ap-3509	118	5	,	,	PUNCT
ap-3509	118	6	b(x	b(x	NOUN
ap-3509	118	7	)	)	PUNCT
ap-3509	118	8	=	=	NOUN
ap-3509	118	9	ca+b(x)cb(y)−	ca+b(x)cb(y)−	ADP
ap-3509	118	10	cb(x)ca+b(y	cb(x)ca+b(y	PROPN
ap-3509	118	11	)	)	PUNCT
ap-3509	118	12	,	,	PUNCT
ap-3509	118	13	(	(	PUNCT
ap-3509	118	14	6	6	X
ap-3509	118	15	)	)	PUNCT
ap-3509	118	16	the	the	DET
ap-3509	118	17	functions	function	NOUN
ap-3509	118	18	cµ(x	cµ(x	ADJ
ap-3509	118	19	)	)	PUNCT
ap-3509	118	20	,	,	PUNCT
ap-3509	118	21	and	and	CCONJ
ap-3509	118	22	sµ(x	sµ(x	NUM
ap-3509	118	23	)	)	PUNCT
ap-3509	118	24	,	,	PUNCT
ap-3509	118	25	on	on	ADP
ap-3509	118	26	the	the	DET
ap-3509	118	27	right	right	ADJ
ap-3509	118	28	side	side	NOUN
ap-3509	118	29	of	of	ADP
ap-3509	118	30	(	(	PUNCT
ap-3509	118	31	6	6	NUM
ap-3509	118	32	)	)	PUNCT
ap-3509	118	33	,	,	PUNCT
ap-3509	118	34	are	be	AUX
ap-3509	118	35	defined	define	VERB
ap-3509	118	36	in	in	ADP
ap-3509	118	37	appendix	appendix	NOUN
ap-3509	118	38	.	.	PUNCT
ap-3509	119	1	the	the	DET
ap-3509	119	2	coordinates	coordinate	NOUN
ap-3509	119	3	(	(	PUNCT
ap-3509	119	4	x	x	X
ap-3509	119	5	,	,	PUNCT
ap-3509	119	6	y	y	NOUN
ap-3509	119	7	)	)	PUNCT
ap-3509	119	8	∈	∈	NOUN
ap-3509	119	9	a1	a1	NOUN
ap-3509	119	10	×a1	×a1	PROPN
ap-3509	119	11	are	be	AUX
ap-3509	119	12	written	write	VERB
ap-3509	119	13	in	in	ADP
ap-3509	119	14	α	α	NOUN
ap-3509	119	15	-	-	NOUN
ap-3509	119	16	basis	basis	NOUN
ap-3509	119	17	.	.	PUNCT
ap-3509	120	1	4.3	4.3	NUM
ap-3509	120	2	.	.	PUNCT
ap-3509	121	1	g2	g2	PROPN
ap-3509	121	2	case	case	NOUN
ap-3509	121	3	from	from	ADP
ap-3509	121	4	the	the	DET
ap-3509	121	5	projection	projection	NOUN
ap-3509	121	6	matrix	matrix	NOUN
ap-3509	121	7	pg2	pg2	NOUN
ap-3509	121	8	(	(	PUNCT
ap-3509	121	9	3	3	NUM
ap-3509	121	10	)	)	PUNCT
ap-3509	121	11	and	and	CCONJ
ap-3509	121	12	the	the	DET
ap-3509	121	13	branching	branch	VERB
ap-3509	121	14	rule	rule	NOUN
ap-3509	121	15	(	(	PUNCT
ap-3509	121	16	4	4	X
ap-3509	121	17	)	)	PUNCT
ap-3509	121	18	we	we	PRON
ap-3509	121	19	find	find	VERB
ap-3509	121	20	three	three	NUM
ap-3509	121	21	separation	separation	NOUN
ap-3509	121	22	constants	constant	NOUN
ap-3509	121	23	−k2	−k2	PROPN
ap-3509	121	24	1	1	NUM
ap-3509	121	25	,	,	PUNCT
ap-3509	121	26	−k2	−k2	PROPN
ap-3509	121	27	2	2	NUM
ap-3509	121	28	,	,	PUNCT
ap-3509	121	29	and	and	CCONJ
ap-3509	121	30	−k2	−k2	PROPN
ap-3509	121	31	3	3	NUM
ap-3509	121	32	,	,	PUNCT
ap-3509	121	33	which	which	PRON
ap-3509	121	34	have	have	VERB
ap-3509	121	35	a	a	DET
ap-3509	121	36	form	form	NOUN
ap-3509	121	37	−	−	PROPN
ap-3509	121	38	k2	k2	ADJ
ap-3509	121	39	1	1	NUM
ap-3509	121	40	=	=	SYM
ap-3509	121	41	−2(2a+	−2(2a+	NOUN
ap-3509	121	42	b)2π2	b)2π2	NOUN
ap-3509	121	43	,	,	PUNCT
ap-3509	121	44	w2	w2	NOUN
ap-3509	121	45	−	−	PROPN
ap-3509	121	46	k2	k2	PROPN
ap-3509	121	47	1	1	NUM
ap-3509	121	48	=	=	SYM
ap-3509	121	49	2	2	NUM
ap-3509	121	50	3b	3b	NOUN
ap-3509	121	51	2π2	2π2	NUM
ap-3509	121	52	,	,	PUNCT
ap-3509	121	53	(	(	PUNCT
ap-3509	121	54	7	7	X
ap-3509	121	55	)	)	PUNCT
ap-3509	121	56	−	−	PROPN
ap-3509	121	57	k2	k2	ADJ
ap-3509	121	58	2	2	NUM
ap-3509	121	59	=	=	SYM
ap-3509	121	60	−2(a+	−2(a+	NOUN
ap-3509	121	61	b)2π2	b)2π2	PROPN
ap-3509	121	62	,	,	PUNCT
ap-3509	121	63	w2	w2	NOUN
ap-3509	121	64	−	−	PROPN
ap-3509	121	65	k2	k2	PROPN
ap-3509	121	66	2	2	NUM
ap-3509	121	67	=	=	SYM
ap-3509	121	68	2	2	NUM
ap-3509	121	69	3	3	NUM
ap-3509	121	70	(	(	PUNCT
ap-3509	121	71	3a+	3a+	NUM
ap-3509	121	72	b)2π2	b)2π2	NOUN
ap-3509	121	73	,	,	PUNCT
ap-3509	121	74	−	−	PROPN
ap-3509	121	75	k2	k2	ADJ
ap-3509	121	76	3	3	NUM
ap-3509	121	77	=	=	SYM
ap-3509	121	78	−2a2π2	−2a2π2	PROPN
ap-3509	121	79	,	,	PUNCT
ap-3509	121	80	w2	w2	NOUN
ap-3509	121	81	−	−	PROPN
ap-3509	121	82	k2	k2	PROPN
ap-3509	121	83	3	3	NUM
ap-3509	121	84	=	=	SYM
ap-3509	121	85	2	2	NUM
ap-3509	121	86	3	3	NUM
ap-3509	121	87	(	(	PUNCT
ap-3509	121	88	3a+	3a+	NUM
ap-3509	121	89	2b)2π2	2b)2π2	NUM
ap-3509	121	90	.	.	PUNCT
ap-3509	122	1	using	use	VERB
ap-3509	122	2	the	the	DET
ap-3509	122	3	branching	branch	VERB
ap-3509	122	4	rule	rule	NOUN
ap-3509	122	5	(	(	PUNCT
ap-3509	122	6	4	4	NUM
ap-3509	122	7	)	)	PUNCT
ap-3509	122	8	from	from	ADP
ap-3509	122	9	section	section	NOUN
ap-3509	122	10	2	2	NUM
ap-3509	122	11	for	for	ADP
ap-3509	122	12	special	special	ADJ
ap-3509	122	13	functions	function	NOUN
ap-3509	122	14	c	c	X
ap-3509	122	15	,	,	PUNCT
ap-3509	122	16	s	s	PROPN
ap-3509	122	17	,	,	PUNCT
ap-3509	122	18	ss	ss	PROPN
ap-3509	122	19	,	,	PUNCT
ap-3509	122	20	sl	sl	VERB
ap-3509	122	21	we	we	PRON
ap-3509	122	22	can	can	AUX
ap-3509	122	23	rewrite	rewrite	VERB
ap-3509	122	24	those	those	DET
ap-3509	122	25	functions	function	NOUN
ap-3509	122	26	247	247	NUM
ap-3509	122	27	marzena	marzena	ADJ
ap-3509	122	28	szajewska	szajewska	NOUN
ap-3509	122	29	,	,	PUNCT
ap-3509	122	30	agnieszka	agnieszka	PROPN
ap-3509	122	31	tereszkiewicz	tereszkiewicz	PROPN
ap-3509	122	32	acta	acta	PROPN
ap-3509	122	33	polytechnica	polytechnica	PROPN
ap-3509	122	34	figure	figure	NOUN
ap-3509	122	35	2	2	NUM
ap-3509	122	36	.	.	PUNCT
ap-3509	122	37	fundamental	fundamental	ADJ
ap-3509	122	38	regions	region	NOUN
ap-3509	122	39	of	of	ADP
ap-3509	122	40	c2	c2	PROPN
ap-3509	122	41	and	and	CCONJ
ap-3509	122	42	g2	g2	PROPN
ap-3509	122	43	groups	group	NOUN
ap-3509	122	44	.	.	PUNCT
ap-3509	123	1	sides	side	NOUN
ap-3509	123	2	are	be	AUX
ap-3509	123	3	marked	mark	VERB
ap-3509	123	4	by	by	ADP
ap-3509	123	5	s	s	NOUN
ap-3509	123	6	and	and	CCONJ
ap-3509	123	7	l	l	NOUN
ap-3509	123	8	symbols	symbol	NOUN
ap-3509	123	9	which	which	PRON
ap-3509	123	10	correspond	correspond	VERB
ap-3509	123	11	to	to	ADP
ap-3509	123	12	the	the	DET
ap-3509	123	13	reflection	reflection	NOUN
ap-3509	123	14	orthogonal	orthogonal	NOUN
ap-3509	123	15	to	to	ADP
ap-3509	123	16	the	the	DET
ap-3509	123	17	short	short	ADJ
ap-3509	123	18	and	and	CCONJ
ap-3509	123	19	long	long	ADJ
ap-3509	123	20	root	root	NOUN
ap-3509	123	21	,	,	PUNCT
ap-3509	123	22	respectively	respectively	ADV
ap-3509	123	23	.	.	PUNCT
ap-3509	124	1	figure	figure	NOUN
ap-3509	124	2	3	3	NUM
ap-3509	124	3	.	.	PUNCT
ap-3509	125	1	the	the	DET
ap-3509	125	2	normal	normal	ADJ
ap-3509	125	3	vectors	vector	NOUN
ap-3509	125	4	and	and	CCONJ
ap-3509	125	5	boundaries	boundary	NOUN
ap-3509	125	6	are	be	AUX
ap-3509	125	7	indicated	indicate	VERB
ap-3509	125	8	for	for	ADP
ap-3509	125	9	the	the	DET
ap-3509	125	10	weyl	weyl	PROPN
ap-3509	125	11	group	group	NOUN
ap-3509	125	12	c2	c2	PROPN
ap-3509	125	13	.	.	PUNCT
ap-3509	126	1	in	in	ADP
ap-3509	126	2	the	the	DET
ap-3509	126	3	form	form	NOUN
ap-3509	126	4	:	:	PUNCT
ap-3509	126	5	ca	ca	AUX
ap-3509	126	6	,	,	PUNCT
ap-3509	126	7	b(x	b(x	NOUN
ap-3509	126	8	)	)	PUNCT
ap-3509	126	9	=	=	SYM
ap-3509	126	10	4	4	NUM
ap-3509	126	11	[	[	PUNCT
ap-3509	126	12	cos(k1y1	cos(k1y1	NOUN
ap-3509	126	13	)	)	PUNCT
ap-3509	127	1	cos	cos	PROPN
ap-3509	127	2	(	(	PUNCT
ap-3509	127	3	√	√	PROPN
ap-3509	127	4	w2	w2	NOUN
ap-3509	127	5	−	−	PROPN
ap-3509	127	6	k2	k2	PROPN
ap-3509	127	7	1y2	1y2	NUM
ap-3509	127	8	)	)	PUNCT
ap-3509	127	9	+	+	CCONJ
ap-3509	127	10	cos(k2y1	cos(k2y1	NOUN
ap-3509	127	11	)	)	PUNCT
ap-3509	127	12	cos	cos	PROPN
ap-3509	127	13	(	(	PUNCT
ap-3509	127	14	√	√	PROPN
ap-3509	127	15	w2	w2	NOUN
ap-3509	127	16	−	−	PROPN
ap-3509	127	17	k2	k2	PROPN
ap-3509	127	18	2y2	2y2	NUM
ap-3509	127	19	)	)	PUNCT
ap-3509	127	20	+	+	CCONJ
ap-3509	127	21	cos(k3y1	cos(k3y1	ADJ
ap-3509	127	22	)	)	PUNCT
ap-3509	127	23	cos	cos	PROPN
ap-3509	127	24	(	(	PUNCT
ap-3509	127	25	√	√	PROPN
ap-3509	127	26	w2	w2	NOUN
ap-3509	127	27	−	−	PROPN
ap-3509	127	28	k2	k2	PROPN
ap-3509	127	29	3y2	3y2	NOUN
ap-3509	127	30	)	)	PUNCT
ap-3509	127	31	]	]	PUNCT
ap-3509	127	32	,	,	PUNCT
ap-3509	127	33	sa	sa	NOUN
ap-3509	127	34	,	,	PUNCT
ap-3509	127	35	b(x	b(x	NOUN
ap-3509	127	36	)	)	PUNCT
ap-3509	127	37	=	=	SYM
ap-3509	127	38	4	4	NUM
ap-3509	127	39	[	[	PUNCT
ap-3509	127	40	−	−	NUM
ap-3509	127	41	sin(k1y1	sin(k1y1	NOUN
ap-3509	127	42	)	)	PUNCT
ap-3509	127	43	sin	sin	NOUN
ap-3509	127	44	(	(	PUNCT
ap-3509	127	45	√	√	PROPN
ap-3509	127	46	w2	w2	NOUN
ap-3509	127	47	−	−	PROPN
ap-3509	127	48	k2	k2	PROPN
ap-3509	127	49	1y2	1y2	NUM
ap-3509	127	50	)	)	PUNCT
ap-3509	127	51	+	+	CCONJ
ap-3509	127	52	sin(k2y1	sin(k2y1	NOUN
ap-3509	127	53	)	)	PUNCT
ap-3509	127	54	sin	sin	NOUN
ap-3509	127	55	(	(	PUNCT
ap-3509	127	56	√	√	PROPN
ap-3509	127	57	w2	w2	NOUN
ap-3509	127	58	−	−	PROPN
ap-3509	127	59	k2	k2	PROPN
ap-3509	127	60	2y2	2y2	NUM
ap-3509	127	61	)	)	PUNCT
ap-3509	127	62	−	−	PROPN
ap-3509	127	63	sin(k3y2	sin(k3y2	ADJ
ap-3509	127	64	)	)	PUNCT
ap-3509	127	65	sin	sin	NOUN
ap-3509	127	66	(	(	PUNCT
ap-3509	127	67	√	√	PROPN
ap-3509	127	68	w2	w2	NOUN
ap-3509	127	69	−	−	PROPN
ap-3509	127	70	k2	k2	PROPN
ap-3509	127	71	3y2	3y2	NOUN
ap-3509	127	72	)	)	PUNCT
ap-3509	127	73	]	]	PUNCT
ap-3509	127	74	,	,	PUNCT
ap-3509	127	75	ssa	ssa	NOUN
ap-3509	127	76	,	,	PUNCT
ap-3509	127	77	b(x	b(x	NOUN
ap-3509	127	78	)	)	PUNCT
ap-3509	127	79	=	=	SYM
ap-3509	127	80	4i	4i	NOUN
ap-3509	127	81	[	[	PUNCT
ap-3509	127	82	−	−	PROPN
ap-3509	127	83	cos(k1y1	cos(k1y1	NOUN
ap-3509	127	84	)	)	PUNCT
ap-3509	127	85	sin	sin	NOUN
ap-3509	127	86	(	(	PUNCT
ap-3509	127	87	√	√	PROPN
ap-3509	127	88	w2	w2	NOUN
ap-3509	127	89	−	−	PROPN
ap-3509	127	90	k2	k2	PROPN
ap-3509	127	91	1y2	1y2	NUM
ap-3509	127	92	)	)	PUNCT
ap-3509	127	93	−	−	ADP
ap-3509	127	94	cos(k2y1	cos(k2y1	NOUN
ap-3509	127	95	)	)	PUNCT
ap-3509	127	96	sin	sin	NOUN
ap-3509	127	97	(	(	PUNCT
ap-3509	127	98	√	√	PROPN
ap-3509	127	99	w2	w2	NOUN
ap-3509	127	100	−	−	PROPN
ap-3509	127	101	k2	k2	PROPN
ap-3509	127	102	2y2	2y2	NUM
ap-3509	127	103	)	)	PUNCT
ap-3509	127	104	+	+	CCONJ
ap-3509	127	105	cos(k3y1	cos(k3y1	ADJ
ap-3509	127	106	)	)	PUNCT
ap-3509	127	107	sin	sin	NOUN
ap-3509	127	108	(	(	PUNCT
ap-3509	127	109	√	√	PROPN
ap-3509	127	110	w2	w2	NOUN
ap-3509	127	111	−	−	PROPN
ap-3509	127	112	k2	k2	PROPN
ap-3509	127	113	3y2	3y2	NOUN
ap-3509	127	114	)	)	PUNCT
ap-3509	127	115	]	]	PUNCT
ap-3509	127	116	,	,	PUNCT
ap-3509	127	117	sla	sla	PROPN
ap-3509	127	118	,	,	PUNCT
ap-3509	127	119	b(x	b(x	NOUN
ap-3509	127	120	)	)	PUNCT
ap-3509	127	121	=	=	SYM
ap-3509	127	122	4i	4i	NOUN
ap-3509	127	123	[	[	PUNCT
ap-3509	127	124	−	−	NUM
ap-3509	127	125	sin(k1y1	sin(k1y1	NOUN
ap-3509	127	126	)	)	PUNCT
ap-3509	127	127	cos	cos	PROPN
ap-3509	127	128	(	(	PUNCT
ap-3509	127	129	√	√	PROPN
ap-3509	127	130	w2	w2	NOUN
ap-3509	127	131	−	−	PROPN
ap-3509	127	132	k2	k2	PROPN
ap-3509	127	133	1y2	1y2	NUM
ap-3509	127	134	)	)	PUNCT
ap-3509	127	135	+	+	CCONJ
ap-3509	127	136	sin(k2y1	sin(k2y1	NOUN
ap-3509	127	137	)	)	PUNCT
ap-3509	127	138	cos	cos	PROPN
ap-3509	127	139	(	(	PUNCT
ap-3509	127	140	√	√	PROPN
ap-3509	127	141	w2	w2	NOUN
ap-3509	127	142	−	−	PROPN
ap-3509	127	143	k2	k2	PROPN
ap-3509	127	144	2y2	2y2	NUM
ap-3509	127	145	)	)	PUNCT
ap-3509	127	146	+	+	X
ap-3509	127	147	sin(k3y1	sin(k3y1	ADJ
ap-3509	127	148	)	)	PUNCT
ap-3509	127	149	cos	cos	PROPN
ap-3509	127	150	(	(	PUNCT
ap-3509	127	151	√	√	PROPN
ap-3509	127	152	w2	w2	NOUN
ap-3509	127	153	−	−	PROPN
ap-3509	127	154	k2	k2	PROPN
ap-3509	127	155	3y2	3y2	NOUN
ap-3509	127	156	)	)	PUNCT
ap-3509	127	157	]	]	PUNCT
ap-3509	127	158	.	.	PUNCT
ap-3509	128	1	by	by	ADP
ap-3509	128	2	changing	change	VERB
ap-3509	128	3	the	the	DET
ap-3509	128	4	variables	variable	NOUN
ap-3509	128	5	by	by	ADP
ap-3509	128	6	y1	y1	NOUN
ap-3509	128	7	=	=	PUNCT
ap-3509	128	8	√	√	NUM
ap-3509	128	9	2x	2x	NUM
ap-3509	128	10	,	,	PUNCT
ap-3509	128	11	y2	y2	PROPN
ap-3509	128	12	=	=	SYM
ap-3509	128	13	√	√	ADP
ap-3509	128	14	6	6	NUM
ap-3509	128	15	we	we	PRON
ap-3509	128	16	get	get	VERB
ap-3509	128	17	the	the	DET
ap-3509	128	18	reduction	reduction	NOUN
ap-3509	128	19	to	to	PART
ap-3509	128	20	a1	a1	VERB
ap-3509	128	21	×a1	×a1	PROPN
ap-3509	128	22	subgroup	subgroup	NOUN
ap-3509	128	23	ca	ca	NOUN
ap-3509	128	24	,	,	PUNCT
ap-3509	128	25	b(x	b(x	NOUN
ap-3509	128	26	)	)	PUNCT
ap-3509	128	27	=	=	SYM
ap-3509	128	28	ca(x)c3a+2b(y	ca(x)c3a+2b(y	X
ap-3509	128	29	)	)	PUNCT
ap-3509	129	1	+	+	CCONJ
ap-3509	130	1	ca+b(x)c3a+b(y	ca+b(x)c3a+b(y	ADJ
ap-3509	130	2	)	)	PUNCT
ap-3509	131	1	+	+	CCONJ
ap-3509	132	1	c2a+b(x)cb(y	c2a+b(x)cb(y	PROPN
ap-3509	132	2	)	)	PUNCT
ap-3509	132	3	,	,	PUNCT
ap-3509	132	4	sa	sa	PROPN
ap-3509	132	5	,	,	PUNCT
ap-3509	132	6	b(x	b(x	NOUN
ap-3509	132	7	)	)	PUNCT
ap-3509	132	8	=	=	SYM
ap-3509	132	9	sa(x)s3a+2b(y	sa(x)s3a+2b(y	X
ap-3509	132	10	)	)	PUNCT
ap-3509	132	11	−	−	PROPN
ap-3509	133	1	sa+b(x)s3a+b(y	sa+b(x)s3a+b(y	ADJ
ap-3509	133	2	)	)	PUNCT
ap-3509	134	1	+	+	CCONJ
ap-3509	135	1	s2a+b(x)sb(y	s2a+b(x)sb(y	ADJ
ap-3509	135	2	)	)	PUNCT
ap-3509	135	3	,	,	PUNCT
ap-3509	135	4	ssa	ssa	NOUN
ap-3509	135	5	,	,	PUNCT
ap-3509	135	6	b(x	b(x	NOUN
ap-3509	135	7	)	)	PUNCT
ap-3509	135	8	=	=	SYM
ap-3509	135	9	ca(x)s3a+2b(y	ca(x)s3a+2b(y	X
ap-3509	135	10	)	)	PUNCT
ap-3509	135	11	−	−	PROPN
ap-3509	135	12	ca+b(x)s3a+b(y)−	ca+b(x)s3a+b(y)−	NOUN
ap-3509	135	13	c2a+b(x)sb(y	c2a+b(x)sb(y	PROPN
ap-3509	135	14	)	)	PUNCT
ap-3509	135	15	,	,	PUNCT
ap-3509	135	16	sla	sla	PROPN
ap-3509	135	17	,	,	PUNCT
ap-3509	135	18	b(x	b(x	NOUN
ap-3509	135	19	)	)	PUNCT
ap-3509	135	20	=	=	PUNCT
ap-3509	135	21	sa(x)c3a+2b(y	sa(x)c3a+2b(y	ADJ
ap-3509	135	22	)	)	PUNCT
ap-3509	135	23	−	−	PROPN
ap-3509	136	1	sa+b(x)c3a+b(y	sa+b(x)c3a+b(y	PROPN
ap-3509	136	2	)	)	PUNCT
ap-3509	137	1	+	+	SYM
ap-3509	137	2	s2a+b(x)cb(y	s2a+b(x)cb(y	ADJ
ap-3509	137	3	)	)	PUNCT
ap-3509	137	4	.	.	PUNCT
ap-3509	138	1	(	(	PUNCT
ap-3509	138	2	8)	8)	NUM
ap-3509	138	3	(	(	PUNCT
ap-3509	138	4	d	d	NOUN
ap-3509	138	5	)	)	PUNCT
ap-3509	138	6	(	(	PUNCT
ap-3509	138	7	n	n	CCONJ
ap-3509	138	8	)	)	PUNCT
ap-3509	138	9	c2	c2	PROPN
ap-3509	138	10	,	,	PUNCT
ap-3509	138	11	g2	g2	PROPN
ap-3509	138	12	s	s	PART
ap-3509	138	13	l	l	NOUN
ap-3509	138	14	s	s	PART
ap-3509	138	15	l	l	NOUN
ap-3509	138	16	ca	ca	NOUN
ap-3509	138	17	,	,	PUNCT
ap-3509	138	18	b(x	b(x	NOUN
ap-3509	138	19	)	)	PUNCT
ap-3509	138	20	∗	∗	NOUN
ap-3509	138	21	∗	∗	NOUN
ap-3509	138	22	0	0	NUM
ap-3509	138	23	0	0	NUM
ap-3509	138	24	sa	sa	NOUN
ap-3509	138	25	,	,	PUNCT
ap-3509	138	26	b(x	b(x	NOUN
ap-3509	138	27	)	)	PUNCT
ap-3509	138	28	0	0	NUM
ap-3509	138	29	0	0	NUM
ap-3509	138	30	∗	∗	NOUN
ap-3509	138	31	∗	∗	NOUN
ap-3509	138	32	(	(	PUNCT
ap-3509	138	33	m	m	NOUN
ap-3509	138	34	)	)	PUNCT
ap-3509	138	35	(	(	PUNCT
ap-3509	138	36	d	d	X
ap-3509	138	37	)	)	PUNCT
ap-3509	138	38	(	(	PUNCT
ap-3509	138	39	n	n	CCONJ
ap-3509	138	40	)	)	PUNCT
ap-3509	138	41	c2	c2	PROPN
ap-3509	138	42	,	,	PUNCT
ap-3509	138	43	g2	g2	PROPN
ap-3509	138	44	s	s	PART
ap-3509	138	45	l	l	NOUN
ap-3509	138	46	s	s	PART
ap-3509	138	47	l	l	NOUN
ap-3509	138	48	ssa	ssa	NOUN
ap-3509	138	49	,	,	PUNCT
ap-3509	138	50	b(x	b(x	NOUN
ap-3509	138	51	)	)	PUNCT
ap-3509	138	52	0	0	NUM
ap-3509	138	53	∗	∗	NOUN
ap-3509	138	54	∗	∗	NOUN
ap-3509	138	55	0	0	NUM
ap-3509	138	56	sla	sla	PROPN
ap-3509	138	57	,	,	PUNCT
ap-3509	138	58	b(x	b(x	NOUN
ap-3509	138	59	)	)	PUNCT
ap-3509	138	60	∗	∗	NOUN
ap-3509	138	61	0	0	NUM
ap-3509	138	62	0	0	NUM
ap-3509	138	63	∗	∗	NOUN
ap-3509	138	64	table	table	NOUN
ap-3509	138	65	1	1	NUM
ap-3509	138	66	.	.	PUNCT
ap-3509	139	1	behaviour	behaviour	NOUN
ap-3509	139	2	of	of	ADP
ap-3509	139	3	the	the	DET
ap-3509	139	4	functions	function	NOUN
ap-3509	139	5	c	c	X
ap-3509	139	6	,	,	PUNCT
ap-3509	139	7	s	s	X
ap-3509	139	8	,	,	PUNCT
ap-3509	139	9	ss	ss	NOUN
ap-3509	139	10	and	and	CCONJ
ap-3509	139	11	sl	sl	VERB
ap-3509	139	12	on	on	ADP
ap-3509	139	13	the	the	DET
ap-3509	139	14	boundary	boundary	ADJ
ap-3509	139	15	∂f	∂f	PROPN
ap-3509	139	16	for	for	ADP
ap-3509	139	17	c2	c2	PROPN
ap-3509	139	18	and	and	CCONJ
ap-3509	139	19	g2	g2	PROPN
ap-3509	139	20	group	group	NOUN
ap-3509	139	21	where	where	SCONJ
ap-3509	139	22	∗	∗	NOUN
ap-3509	139	23	denotes	denote	VERB
ap-3509	139	24	any	any	DET
ap-3509	139	25	function	function	NOUN
ap-3509	139	26	non	non	ADJ
ap-3509	139	27	-	-	ADJ
ap-3509	139	28	equivalent	equivalent	ADJ
ap-3509	139	29	to	to	ADP
ap-3509	139	30	0	0	NUM
ap-3509	139	31	.	.	PUNCT
ap-3509	140	1	the	the	DET
ap-3509	140	2	functions	function	NOUN
ap-3509	140	3	cµ(x	cµ(x	ADJ
ap-3509	140	4	)	)	PUNCT
ap-3509	140	5	,	,	PUNCT
ap-3509	140	6	and	and	CCONJ
ap-3509	140	7	sµ(x	sµ(x	NUM
ap-3509	140	8	)	)	PUNCT
ap-3509	140	9	,	,	PUNCT
ap-3509	140	10	on	on	ADP
ap-3509	140	11	the	the	DET
ap-3509	140	12	right	right	ADJ
ap-3509	140	13	side	side	NOUN
ap-3509	140	14	of	of	ADP
ap-3509	140	15	(	(	PUNCT
ap-3509	140	16	8)	8)	NUM
ap-3509	140	17	,	,	PUNCT
ap-3509	140	18	are	be	AUX
ap-3509	140	19	defined	define	VERB
ap-3509	140	20	in	in	ADP
ap-3509	140	21	appendix	appendix	NOUN
ap-3509	140	22	.	.	PUNCT
ap-3509	141	1	the	the	DET
ap-3509	141	2	coordinates	coordinate	NOUN
ap-3509	141	3	(	(	PUNCT
ap-3509	141	4	x	x	X
ap-3509	141	5	,	,	PUNCT
ap-3509	141	6	y	y	NOUN
ap-3509	141	7	)	)	PUNCT
ap-3509	141	8	∈	∈	NOUN
ap-3509	141	9	a1	a1	NOUN
ap-3509	141	10	×a1	×a1	PROPN
ap-3509	141	11	are	be	AUX
ap-3509	141	12	written	write	VERB
ap-3509	141	13	in	in	ADP
ap-3509	141	14	α	α	NOUN
ap-3509	141	15	-	-	NOUN
ap-3509	141	16	basis	basis	NOUN
ap-3509	141	17	.	.	PUNCT
ap-3509	142	1	proposition	proposition	NOUN
ap-3509	142	2	1	1	NUM
ap-3509	142	3	.	.	PUNCT
ap-3509	142	4	cµ(x	cµ(x	PUNCT
ap-3509	142	5	)	)	PUNCT
ap-3509	142	6	,	,	PUNCT
ap-3509	142	7	and	and	CCONJ
ap-3509	142	8	sµ(x	sµ(x	NUM
ap-3509	142	9	)	)	PUNCT
ap-3509	142	10	functions	function	NOUN
ap-3509	142	11	presented	present	VERB
ap-3509	142	12	in	in	ADP
ap-3509	142	13	(	(	PUNCT
ap-3509	142	14	8)	8)	NUM
ap-3509	142	15	fulfill	fulfill	NOUN
ap-3509	142	16	the	the	DET
ap-3509	142	17	following	follow	VERB
ap-3509	142	18	relationships	relationship	NOUN
ap-3509	142	19	−	−	NOUN
ap-3509	142	20	k3s3a+2b(x)ca(x	k3s3a+2b(x)ca(x	ADP
ap-3509	142	21	)	)	PUNCT
ap-3509	143	1	+	+	CCONJ
ap-3509	143	2	k2s3a+b(x)ca+b(x)−	k2s3a+b(x)ca+b(x)−	PROPN
ap-3509	143	3	k1sb(x)c2a+b(x	k1sb(x)c2a+b(x	PROPN
ap-3509	143	4	)	)	PUNCT
ap-3509	143	5	=	=	PUNCT
ap-3509	144	1	√	√	NUM
ap-3509	144	2	3	3	NUM
ap-3509	144	3	(	(	PUNCT
ap-3509	144	4	√	√	PROPN
ap-3509	144	5	w2	w2	NOUN
ap-3509	144	6	−	−	PROPN
ap-3509	144	7	k2	k2	PROPN
ap-3509	144	8	3c3a+2b(x)sa(x	3c3a+2b(x)sa(x	PROPN
ap-3509	144	9	)	)	PUNCT
ap-3509	144	10	−	−	PROPN
ap-3509	144	11	√	√	PROPN
ap-3509	144	12	w2	w2	PROPN
ap-3509	144	13	−	−	PROPN
ap-3509	144	14	k2	k2	PROPN
ap-3509	144	15	2c3a+b(x)sa+b(x	2c3a+b(x)sa+b(x	NUM
ap-3509	144	16	)	)	PUNCT
ap-3509	144	17	−	−	PROPN
ap-3509	144	18	√	√	PROPN
ap-3509	144	19	w2	w2	PROPN
ap-3509	144	20	−	−	PROPN
ap-3509	144	21	k2	k2	PROPN
ap-3509	144	22	1cb(x)s2a+b(x	1cb(x)s2a+b(x	NUM
ap-3509	144	23	)	)	PUNCT
ap-3509	144	24	)	)	PUNCT
ap-3509	144	25	,	,	PUNCT
ap-3509	144	26	−	−	PROPN
ap-3509	144	27	k3s3a+2b(x)sa(x	k3s3a+2b(x)sa(x	NOUN
ap-3509	144	28	)	)	PUNCT
ap-3509	144	29	+	+	CCONJ
ap-3509	144	30	k2s3a+b(x)sa+b(x	k2s3a+b(x)sa+b(x	VERB
ap-3509	144	31	)	)	PUNCT
ap-3509	145	1	+	+	CCONJ
ap-3509	145	2	k1sb(x)s2a+b(x	k1sb(x)s2a+b(x	PROPN
ap-3509	145	3	)	)	PUNCT
ap-3509	145	4	=	=	PUNCT
ap-3509	146	1	√	√	NUM
ap-3509	146	2	3	3	NUM
ap-3509	146	3	(	(	PUNCT
ap-3509	146	4	√	√	PROPN
ap-3509	146	5	w2	w2	NOUN
ap-3509	146	6	−	−	PROPN
ap-3509	146	7	k2	k2	PROPN
ap-3509	146	8	3c3a+2b(x)ca(x	3c3a+2b(x)ca(x	PROPN
ap-3509	146	9	)	)	PUNCT
ap-3509	146	10	−	−	NOUN
ap-3509	146	11	√	√	PROPN
ap-3509	146	12	w2	w2	PROPN
ap-3509	146	13	−	−	PROPN
ap-3509	146	14	k2	k2	PROPN
ap-3509	146	15	2c3a+b(x)ca+b(x	2c3a+b(x)ca+b(x	NUM
ap-3509	146	16	)	)	PUNCT
ap-3509	146	17	−	−	NOUN
ap-3509	146	18	√	√	PROPN
ap-3509	146	19	w2	w2	NOUN
ap-3509	146	20	−	−	PROPN
ap-3509	146	21	k2	k2	PROPN
ap-3509	146	22	1cb(x)c2a+b(x	1cb(x)c2a+b(x	NUM
ap-3509	146	23	)	)	PUNCT
ap-3509	146	24	)	)	PUNCT
ap-3509	146	25	,	,	PUNCT
ap-3509	146	26	where	where	SCONJ
ap-3509	146	27	ki	ki	PROPN
ap-3509	146	28	,	,	PUNCT
ap-3509	146	29	√	√	PROPN
ap-3509	146	30	w2	w2	NOUN
ap-3509	146	31	−	−	PROPN
ap-3509	146	32	ki	ki	PROPN
ap-3509	146	33	,	,	PUNCT
ap-3509	146	34	i	i	PRON
ap-3509	146	35	=	=	NOUN
ap-3509	146	36	1	1	NUM
ap-3509	146	37	,	,	PUNCT
ap-3509	146	38	2	2	NUM
ap-3509	146	39	,	,	PUNCT
ap-3509	146	40	3	3	NUM
ap-3509	146	41	are	be	AUX
ap-3509	146	42	defined	define	VERB
ap-3509	146	43	by	by	ADP
ap-3509	146	44	(	(	PUNCT
ap-3509	146	45	7	7	NUM
ap-3509	146	46	)	)	PUNCT
ap-3509	146	47	.	.	PUNCT
ap-3509	147	1	5	5	X
ap-3509	147	2	.	.	NUM
ap-3509	147	3	types	type	NOUN
ap-3509	147	4	of	of	ADP
ap-3509	147	5	boundary	boundary	ADJ
ap-3509	147	6	conditions	condition	NOUN
ap-3509	147	7	in	in	ADP
ap-3509	147	8	this	this	DET
ap-3509	147	9	paper	paper	NOUN
ap-3509	147	10	we	we	PRON
ap-3509	147	11	consider	consider	VERB
ap-3509	147	12	three	three	NUM
ap-3509	147	13	types	type	NOUN
ap-3509	147	14	of	of	ADP
ap-3509	147	15	boundary	boundary	ADJ
ap-3509	147	16	conditions	condition	NOUN
ap-3509	147	17	.	.	PUNCT
ap-3509	148	1	(	(	PUNCT
ap-3509	148	2	1	1	NUM
ap-3509	148	3	.	.	PUNCT
ap-3509	148	4	)	)	PUNCT
ap-3509	149	1	the	the	DET
ap-3509	149	2	first	first	ADJ
ap-3509	149	3	type	type	NOUN
ap-3509	149	4	,	,	PUNCT
ap-3509	149	5	called	call	VERB
ap-3509	149	6	a	a	DET
ap-3509	149	7	dirichlet	dirichlet	PROPN
ap-3509	149	8	boundary	boundary	ADJ
ap-3509	149	9	condition	condition	NOUN
ap-3509	149	10	,	,	PUNCT
ap-3509	149	11	defines	define	VERB
ap-3509	149	12	the	the	DET
ap-3509	149	13	value	value	NOUN
ap-3509	149	14	of	of	ADP
ap-3509	149	15	the	the	DET
ap-3509	149	16	function	function	NOUN
ap-3509	149	17	itself	itself	PRON
ap-3509	149	18	:	:	PUNCT
ap-3509	149	19	ψ(x	ψ(x	NUM
ap-3509	149	20	)	)	PUNCT
ap-3509	149	21	=	=	SYM
ap-3509	149	22	f(x	f(x	PROPN
ap-3509	149	23	)	)	PUNCT
ap-3509	149	24	,	,	PUNCT
ap-3509	149	25	for	for	ADP
ap-3509	149	26	x	x	PROPN
ap-3509	149	27	∈	∈	PROPN
ap-3509	149	28	∂f	∂f	PROPN
ap-3509	149	29	,	,	PUNCT
ap-3509	149	30	(	(	PUNCT
ap-3509	149	31	d	d	NOUN
ap-3509	149	32	)	)	PUNCT
ap-3509	149	33	where	where	SCONJ
ap-3509	149	34	f(x	f(x	PROPN
ap-3509	149	35	)	)	PUNCT
ap-3509	149	36	is	be	AUX
ap-3509	149	37	a	a	DET
ap-3509	149	38	given	give	VERB
ap-3509	149	39	function	function	NOUN
ap-3509	149	40	defined	define	VERB
ap-3509	149	41	on	on	ADP
ap-3509	149	42	the	the	DET
ap-3509	149	43	boundary	boundary	NOUN
ap-3509	149	44	.	.	PUNCT
ap-3509	150	1	(	(	PUNCT
ap-3509	150	2	2	2	NUM
ap-3509	150	3	.	.	PUNCT
ap-3509	150	4	)	)	PUNCT
ap-3509	151	1	the	the	DET
ap-3509	151	2	second	second	ADJ
ap-3509	151	3	type	type	NOUN
ap-3509	151	4	,	,	PUNCT
ap-3509	151	5	called	call	VERB
ap-3509	151	6	a	a	DET
ap-3509	151	7	neumann	neumann	PROPN
ap-3509	151	8	boundary	boundary	ADJ
ap-3509	151	9	condition	condition	NOUN
ap-3509	151	10	,	,	PUNCT
ap-3509	151	11	defines	define	VERB
ap-3509	151	12	the	the	DET
ap-3509	151	13	value	value	NOUN
ap-3509	151	14	of	of	ADP
ap-3509	151	15	the	the	DET
ap-3509	151	16	normal	normal	ADJ
ap-3509	151	17	derivative	derivative	NOUN
ap-3509	151	18	of	of	ADP
ap-3509	151	19	the	the	DET
ap-3509	151	20	function	function	NOUN
ap-3509	151	21	:	:	PUNCT
ap-3509	152	1	∂ψ	∂ψ	PROPN
ap-3509	152	2	∂n	∂n	PROPN
ap-3509	152	3	(	(	PUNCT
ap-3509	152	4	x	x	X
ap-3509	152	5	)	)	PUNCT
ap-3509	152	6	=	=	SYM
ap-3509	152	7	f(x	f(x	PROPN
ap-3509	152	8	)	)	PUNCT
ap-3509	152	9	,	,	PUNCT
ap-3509	152	10	for	for	ADP
ap-3509	152	11	x	x	PROPN
ap-3509	152	12	∈	∈	PROPN
ap-3509	152	13	∂f	∂f	PROPN
ap-3509	152	14	,	,	PUNCT
ap-3509	152	15	(	(	PUNCT
ap-3509	152	16	n	n	CCONJ
ap-3509	152	17	)	)	PUNCT
ap-3509	152	18	where	where	SCONJ
ap-3509	152	19	n	n	PRON
ap-3509	152	20	denotes	denote	VERB
ap-3509	152	21	normal	normal	ADJ
ap-3509	152	22	to	to	ADP
ap-3509	152	23	the	the	DET
ap-3509	152	24	boundary	boundary	ADJ
ap-3509	152	25	∂f	∂f	PROPN
ap-3509	152	26	.	.	PUNCT
ap-3509	153	1	248	248	NUM
ap-3509	153	2	vol	vol	NOUN
ap-3509	153	3	.	.	PUNCT
ap-3509	154	1	56	56	NUM
ap-3509	154	2	no	no	NOUN
ap-3509	154	3	.	.	PUNCT
ap-3509	155	1	3/2016	3/2016	NUM
ap-3509	155	2	two	two	NUM
ap-3509	155	3	-	-	PUNCT
ap-3509	155	4	dimensional	dimensional	ADJ
ap-3509	155	5	hybrids	hybrid	NOUN
ap-3509	155	6	with	with	ADP
ap-3509	155	7	mixed	mixed	ADJ
ap-3509	155	8	boundary	boundary	ADJ
ap-3509	155	9	value	value	NOUN
ap-3509	155	10	problems	problem	NOUN
ap-3509	155	11	c1,3(x	c1,3(x	PROPN
ap-3509	155	12	)	)	PUNCT
ap-3509	155	13	s1,3(x	s1,3(x	PROPN
ap-3509	155	14	)	)	PUNCT
ap-3509	155	15	figure	figure	NOUN
ap-3509	155	16	4	4	NUM
ap-3509	155	17	.	.	PUNCT
ap-3509	156	1	the	the	DET
ap-3509	156	2	contour	contour	NOUN
ap-3509	156	3	plot	plot	NOUN
ap-3509	156	4	of	of	ADP
ap-3509	156	5	c1,3(x	c1,3(x	PROPN
ap-3509	156	6	)	)	PUNCT
ap-3509	156	7	,	,	PUNCT
ap-3509	156	8	s1,3(x	s1,3(x	PROPN
ap-3509	156	9	)	)	PUNCT
ap-3509	156	10	.	.	PUNCT
ap-3509	157	1	the	the	DET
ap-3509	157	2	triangle	triangle	NOUN
ap-3509	157	3	denotes	denote	VERB
ap-3509	157	4	the	the	DET
ap-3509	157	5	fundamental	fundamental	ADJ
ap-3509	157	6	domain	domain	NOUN
ap-3509	157	7	f	f	PROPN
ap-3509	157	8	of	of	ADP
ap-3509	157	9	the	the	DET
ap-3509	157	10	affine	affine	NOUN
ap-3509	157	11	weyl	weyl	PROPN
ap-3509	157	12	group	group	PROPN
ap-3509	157	13	c2	c2	PROPN
ap-3509	157	14	.	.	PUNCT
ap-3509	158	1	sl1,3(x	sl1,3(x	PROPN
ap-3509	158	2	)	)	PUNCT
ap-3509	158	3	ss1,3(x	ss1,3(x	PROPN
ap-3509	158	4	)	)	PUNCT
ap-3509	158	5	figure	figure	NOUN
ap-3509	158	6	5	5	NUM
ap-3509	158	7	.	.	PUNCT
ap-3509	159	1	the	the	DET
ap-3509	159	2	contour	contour	NOUN
ap-3509	159	3	plot	plot	NOUN
ap-3509	159	4	of	of	ADP
ap-3509	159	5	sl	sl	PROPN
ap-3509	159	6	1,3(x	1,3(x	PROPN
ap-3509	159	7	)	)	PUNCT
ap-3509	159	8	,	,	PUNCT
ap-3509	159	9	ss	ss	PROPN
ap-3509	159	10	1,3(x	1,3(x	NUM
ap-3509	159	11	)	)	PUNCT
ap-3509	159	12	.	.	PUNCT
ap-3509	160	1	the	the	DET
ap-3509	160	2	triangle	triangle	NOUN
ap-3509	160	3	denotes	denote	VERB
ap-3509	160	4	the	the	DET
ap-3509	160	5	fundamental	fundamental	ADJ
ap-3509	160	6	domain	domain	NOUN
ap-3509	160	7	f	f	PROPN
ap-3509	160	8	of	of	ADP
ap-3509	160	9	the	the	DET
ap-3509	160	10	affine	affine	NOUN
ap-3509	160	11	weyl	weyl	PROPN
ap-3509	160	12	group	group	PROPN
ap-3509	160	13	c2	c2	PROPN
ap-3509	160	14	.	.	PUNCT
ap-3509	161	1	figure	figure	VERB
ap-3509	161	2	6	6	NUM
ap-3509	161	3	.	.	PUNCT
ap-3509	162	1	the	the	DET
ap-3509	162	2	normal	normal	ADJ
ap-3509	162	3	vectors	vector	NOUN
ap-3509	162	4	and	and	CCONJ
ap-3509	162	5	boundaries	boundary	NOUN
ap-3509	162	6	are	be	AUX
ap-3509	162	7	indicated	indicate	VERB
ap-3509	162	8	for	for	ADP
ap-3509	162	9	the	the	DET
ap-3509	162	10	weyl	weyl	PROPN
ap-3509	162	11	group	group	NOUN
ap-3509	162	12	g2	g2	PROPN
ap-3509	162	13	(	(	PUNCT
ap-3509	162	14	3	3	NUM
ap-3509	162	15	.	.	PUNCT
ap-3509	162	16	)	)	PUNCT
ap-3509	163	1	the	the	DET
ap-3509	163	2	third	third	ADJ
ap-3509	163	3	type	type	NOUN
ap-3509	163	4	,	,	PUNCT
ap-3509	163	5	called	call	VERB
ap-3509	163	6	a	a	DET
ap-3509	163	7	mixed	mixed	ADJ
ap-3509	163	8	boundary	boundary	ADJ
ap-3509	163	9	condition	condition	NOUN
ap-3509	163	10	,	,	PUNCT
ap-3509	163	11	defines	define	VERB
ap-3509	163	12	the	the	DET
ap-3509	163	13	value	value	NOUN
ap-3509	163	14	of	of	ADP
ap-3509	163	15	the	the	DET
ap-3509	163	16	function	function	NOUN
ap-3509	163	17	itself	itself	PRON
ap-3509	163	18	on	on	ADP
ap-3509	163	19	one	one	NUM
ap-3509	163	20	part	part	NOUN
ap-3509	163	21	of	of	ADP
ap-3509	163	22	the	the	DET
ap-3509	163	23	boundary	boundary	NOUN
ap-3509	163	24	and	and	CCONJ
ap-3509	163	25	the	the	DET
ap-3509	163	26	value	value	NOUN
ap-3509	163	27	of	of	ADP
ap-3509	163	28	the	the	DET
ap-3509	163	29	normal	normal	ADJ
ap-3509	163	30	derivative	derivative	NOUN
ap-3509	163	31	of	of	ADP
ap-3509	163	32	the	the	DET
ap-3509	163	33	function	function	NOUN
ap-3509	163	34	on	on	ADP
ap-3509	163	35	the	the	DET
ap-3509	163	36	other	other	ADJ
ap-3509	163	37	part	part	NOUN
ap-3509	163	38	of	of	ADP
ap-3509	163	39	the	the	DET
ap-3509	163	40	boundary	boundary	NOUN
ap-3509	163	41	:	:	PUNCT
ap-3509	163	42	{	{	PUNCT
ap-3509	163	43	ψ(x	ψ(x	NOUN
ap-3509	163	44	)	)	PUNCT
ap-3509	164	1	=	=	SYM
ap-3509	164	2	f0(x	f0(x	NOUN
ap-3509	164	3	)	)	PUNCT
ap-3509	164	4	for	for	ADP
ap-3509	164	5	x	x	PROPN
ap-3509	164	6	∈	∈	PROPN
ap-3509	164	7	∂f0	∂f0	PROPN
ap-3509	164	8	,	,	PUNCT
ap-3509	164	9	∂ψ	∂ψ	PROPN
ap-3509	164	10	∂n	∂n	PROPN
ap-3509	164	11	(	(	PUNCT
ap-3509	164	12	x	x	X
ap-3509	164	13	)	)	PUNCT
ap-3509	164	14	=	=	SYM
ap-3509	164	15	f1(x	f1(x	PROPN
ap-3509	164	16	)	)	PUNCT
ap-3509	164	17	for	for	ADP
ap-3509	164	18	x	x	PROPN
ap-3509	164	19	∈	∈	PROPN
ap-3509	164	20	∂f1	∂f1	PROPN
ap-3509	164	21	,	,	PUNCT
ap-3509	164	22	(	(	PUNCT
ap-3509	164	23	m	m	NOUN
ap-3509	164	24	)	)	PUNCT
ap-3509	164	25	where	where	SCONJ
ap-3509	164	26	∂f	∂f	PROPN
ap-3509	164	27	=	=	SYM
ap-3509	164	28	∂f0	∂f0	ADV
ap-3509	164	29	∪	∪	VERB
ap-3509	164	30	∂f1	∂f1	PROPN
ap-3509	164	31	and	and	CCONJ
ap-3509	164	32	f0(x	f0(x	NOUN
ap-3509	164	33	)	)	PUNCT
ap-3509	164	34	,	,	PUNCT
ap-3509	164	35	f1(x	f1(x	CCONJ
ap-3509	164	36	)	)	PUNCT
ap-3509	164	37	are	be	AUX
ap-3509	164	38	given	give	VERB
ap-3509	164	39	functions	function	NOUN
ap-3509	164	40	,	,	PUNCT
ap-3509	164	41	defined	define	VERB
ap-3509	164	42	on	on	ADP
ap-3509	164	43	the	the	DET
ap-3509	164	44	appropriate	appropriate	ADJ
ap-3509	164	45	boundary	boundary	NOUN
ap-3509	164	46	.	.	PUNCT
ap-3509	165	1	remark	remark	NOUN
ap-3509	165	2	4	4	NUM
ap-3509	166	1	[	[	X
ap-3509	166	2	12	12	NUM
ap-3509	166	3	]	]	PUNCT
ap-3509	166	4	.	.	PUNCT
ap-3509	167	1	for	for	ADP
ap-3509	167	2	the	the	DET
ap-3509	167	3	dirichlet	dirichlet	PROPN
ap-3509	167	4	boundary	boundary	PROPN
ap-3509	167	5	conditions	condition	NOUN
ap-3509	167	6	all	all	DET
ap-3509	167	7	eigenvalues	eigenvalue	NOUN
ap-3509	167	8	are	be	AUX
ap-3509	167	9	positive	positive	ADJ
ap-3509	167	10	.	.	PUNCT
ap-3509	168	1	for	for	ADP
ap-3509	168	2	the	the	DET
ap-3509	168	3	neumann	neumann	PROPN
ap-3509	168	4	boundary	boundary	ADJ
ap-3509	168	5	condition	condition	NOUN
ap-3509	168	6	all	all	DET
ap-3509	168	7	eigenvalues	eigenvalue	NOUN
ap-3509	168	8	are	be	AUX
ap-3509	168	9	non	non	ADJ
ap-3509	168	10	-	-	ADJ
ap-3509	168	11	negative	negative	ADJ
ap-3509	168	12	.	.	PUNCT
ap-3509	169	1	in	in	ADP
ap-3509	169	2	table	table	NOUN
ap-3509	169	3	1	1	NUM
ap-3509	169	4	we	we	PRON
ap-3509	169	5	present	present	VERB
ap-3509	169	6	how	how	SCONJ
ap-3509	169	7	the	the	DET
ap-3509	169	8	four	four	NUM
ap-3509	169	9	types	type	NOUN
ap-3509	169	10	of	of	ADP
ap-3509	169	11	functions	function	NOUN
ap-3509	169	12	,	,	PUNCT
ap-3509	169	13	defined	define	VERB
ap-3509	169	14	in	in	ADP
ap-3509	169	15	section	section	NOUN
ap-3509	169	16	3	3	NUM
ap-3509	169	17	,	,	PUNCT
ap-3509	169	18	behave	behave	VERB
ap-3509	169	19	on	on	ADP
ap-3509	169	20	the	the	DET
ap-3509	169	21	boundary	boundary	ADJ
ap-3509	169	22	∂f	∂f	PROPN
ap-3509	169	23	of	of	ADP
ap-3509	169	24	the	the	DET
ap-3509	169	25	fundamental	fundamental	ADJ
ap-3509	169	26	region	region	NOUN
ap-3509	169	27	f	f	PROPN
ap-3509	169	28	.	.	PUNCT
ap-3509	170	1	the	the	DET
ap-3509	170	2	fundamental	fundamental	ADJ
ap-3509	170	3	region	region	NOUN
ap-3509	170	4	f	f	PROPN
ap-3509	170	5	for	for	ADP
ap-3509	170	6	c2	c2	PROPN
ap-3509	170	7	and	and	CCONJ
ap-3509	170	8	g2	g2	PROPN
ap-3509	170	9	groups	group	NOUN
ap-3509	170	10	is	be	AUX
ap-3509	170	11	presented	present	VERB
ap-3509	170	12	in	in	ADP
ap-3509	170	13	figure	figure	NOUN
ap-3509	170	14	2	2	NUM
ap-3509	170	15	.	.	PUNCT
ap-3509	171	1	symbol	symbol	NOUN
ap-3509	171	2	s	s	NOUN
ap-3509	171	3	corresponds	correspond	NOUN
ap-3509	171	4	to	to	ADP
ap-3509	171	5	the	the	DET
ap-3509	171	6	reflection	reflection	NOUN
ap-3509	171	7	orthogonal	orthogonal	NOUN
ap-3509	171	8	to	to	ADP
ap-3509	171	9	the	the	DET
ap-3509	171	10	short	short	ADJ
ap-3509	171	11	root	root	NOUN
ap-3509	171	12	and	and	CCONJ
ap-3509	171	13	l	l	NOUN
ap-3509	171	14	corresponds	correspond	NOUN
ap-3509	171	15	to	to	ADP
ap-3509	171	16	the	the	DET
ap-3509	171	17	reflection	reflection	NOUN
ap-3509	171	18	orthogonal	orthogonal	NOUN
ap-3509	171	19	to	to	ADP
ap-3509	171	20	the	the	DET
ap-3509	171	21	long	long	ADJ
ap-3509	171	22	root	root	NOUN
ap-3509	171	23	.	.	PUNCT
ap-3509	172	1	5.1	5.1	NUM
ap-3509	172	2	.	.	PUNCT
ap-3509	173	1	c2	c2	PROPN
ap-3509	173	2	case	case	NOUN
ap-3509	173	3	the	the	DET
ap-3509	173	4	normal	normal	ADJ
ap-3509	173	5	vectors	vector	NOUN
ap-3509	173	6	to	to	ADP
ap-3509	173	7	the	the	DET
ap-3509	173	8	fundamental	fundamental	ADJ
ap-3509	173	9	region	region	NOUN
ap-3509	173	10	f	f	PROPN
ap-3509	173	11	of	of	ADP
ap-3509	173	12	the	the	DET
ap-3509	173	13	weyl	weyl	PROPN
ap-3509	173	14	group	group	NOUN
ap-3509	173	15	c2	c2	PROPN
ap-3509	173	16	are	be	AUX
ap-3509	173	17	the	the	DET
ap-3509	173	18	following	follow	VERB
ap-3509	173	19	:	:	PUNCT
ap-3509	173	20	n1	n1	PROPN
ap-3509	173	21	=	=	SYM
ap-3509	173	22	(	(	PUNCT
ap-3509	173	23	0,−1)e	0,−1)e	NUM
ap-3509	173	24	,	,	PUNCT
ap-3509	173	25	n2	n2	NOUN
ap-3509	173	26	=	=	PUNCT
ap-3509	173	27	(	(	PUNCT
ap-3509	173	28	−	−	PROPN
ap-3509	173	29	1√	1√	PROPN
ap-3509	173	30	2	2	NUM
ap-3509	173	31	,	,	PUNCT
ap-3509	173	32	1√	1√	PROPN
ap-3509	173	33	2	2	NUM
ap-3509	173	34	)	)	PUNCT
ap-3509	173	35	e	e	NOUN
ap-3509	173	36	,	,	PUNCT
ap-3509	173	37	n3	n3	NOUN
ap-3509	173	38	=	=	SYM
ap-3509	173	39	(	(	PUNCT
ap-3509	173	40	1	1	NUM
ap-3509	173	41	,	,	PUNCT
ap-3509	173	42	0)e	0)e	NOUN
ap-3509	173	43	.	.	PUNCT
ap-3509	174	1	in	in	ADP
ap-3509	174	2	figure	figure	NOUN
ap-3509	174	3	3	3	NUM
ap-3509	174	4	we	we	PRON
ap-3509	174	5	present	present	VERB
ap-3509	174	6	the	the	DET
ap-3509	174	7	fundamental	fundamental	ADJ
ap-3509	174	8	region	region	NOUN
ap-3509	174	9	f	f	PROPN
ap-3509	174	10	with	with	ADP
ap-3509	174	11	indicated	indicate	VERB
ap-3509	174	12	boundaries	boundary	NOUN
ap-3509	174	13	and	and	CCONJ
ap-3509	174	14	corresponding	correspond	VERB
ap-3509	174	15	normal	normal	ADJ
ap-3509	174	16	vectors	vector	NOUN
ap-3509	174	17	.	.	PUNCT
ap-3509	175	1	the	the	DET
ap-3509	175	2	values	value	NOUN
ap-3509	175	3	of	of	ADP
ap-3509	175	4	the	the	DET
ap-3509	175	5	four	four	NUM
ap-3509	175	6	families	family	NOUN
ap-3509	175	7	of	of	ADP
ap-3509	175	8	special	special	ADJ
ap-3509	175	9	functions	function	NOUN
ap-3509	175	10	c	c	X
ap-3509	175	11	,	,	PUNCT
ap-3509	175	12	s	s	X
ap-3509	175	13	,	,	PUNCT
ap-3509	175	14	ss	ss	PROPN
ap-3509	175	15	and	and	CCONJ
ap-3509	175	16	sl	sl	AUX
ap-3509	175	17	satisfying	satisfy	VERB
ap-3509	175	18	the	the	DET
ap-3509	175	19	dirichlet	dirichlet	PROPN
ap-3509	175	20	boundary	boundary	ADJ
ap-3509	175	21	condition	condition	NOUN
ap-3509	175	22	(	(	PUNCT
ap-3509	175	23	d	d	NOUN
ap-3509	175	24	)	)	PUNCT
ap-3509	175	25	on	on	ADP
ap-3509	175	26	the	the	DET
ap-3509	175	27	boundary	boundary	ADJ
ap-3509	175	28	∂f	∂f	PROPN
ap-3509	175	29	of	of	ADP
ap-3509	175	30	the	the	DET
ap-3509	175	31	fundamental	fundamental	ADJ
ap-3509	175	32	figure	figure	NOUN
ap-3509	175	33	7	7	NUM
ap-3509	175	34	.	.	PUNCT
ap-3509	176	1	a	a	DET
ap-3509	176	2	shaded	shade	VERB
ap-3509	176	3	square	square	NOUN
ap-3509	176	4	represents	represent	VERB
ap-3509	176	5	the	the	DET
ap-3509	176	6	fundamental	fundamental	ADJ
ap-3509	176	7	region	region	NOUN
ap-3509	176	8	f	f	PROPN
ap-3509	176	9	of	of	ADP
ap-3509	176	10	a1	a1	PROPN
ap-3509	176	11	×	×	PROPN
ap-3509	176	12	a1	a1	NOUN
ap-3509	176	13	.	.	PUNCT
ap-3509	176	14	figure	figure	NOUN
ap-3509	176	15	8	8	NUM
ap-3509	176	16	.	.	PUNCT
ap-3509	177	1	the	the	DET
ap-3509	177	2	boundaries	boundary	NOUN
ap-3509	177	3	of	of	ADP
ap-3509	177	4	the	the	DET
ap-3509	177	5	fundamental	fundamental	ADJ
ap-3509	177	6	region	region	NOUN
ap-3509	177	7	f	f	PROPN
ap-3509	177	8	of	of	ADP
ap-3509	177	9	a1	a1	PROPN
ap-3509	177	10	×	×	NOUN
ap-3509	177	11	a1	a1	NOUN
ap-3509	177	12	are	be	AUX
ap-3509	177	13	indicated	indicate	VERB
ap-3509	177	14	.	.	PUNCT
ap-3509	178	1	region	region	NOUN
ap-3509	178	2	f	f	PROPN
ap-3509	178	3	are	be	AUX
ap-3509	178	4	presented	present	VERB
ap-3509	178	5	in	in	ADP
ap-3509	178	6	tables	table	NOUN
ap-3509	178	7	2	2	NUM
ap-3509	178	8	,	,	PUNCT
ap-3509	178	9	4	4	NUM
ap-3509	178	10	,	,	PUNCT
ap-3509	178	11	and	and	CCONJ
ap-3509	178	12	5	5	NUM
ap-3509	178	13	.	.	X
ap-3509	178	14	tables	table	NOUN
ap-3509	178	15	3	3	NUM
ap-3509	178	16	–	–	SYM
ap-3509	178	17	5	5	NUM
ap-3509	178	18	present	present	VERB
ap-3509	178	19	the	the	DET
ap-3509	178	20	values	value	NOUN
ap-3509	178	21	of	of	ADP
ap-3509	178	22	the	the	DET
ap-3509	178	23	functions	function	NOUN
ap-3509	178	24	satisfying	satisfy	VERB
ap-3509	178	25	the	the	DET
ap-3509	178	26	neumann	neumann	PROPN
ap-3509	178	27	boundary	boundary	ADJ
ap-3509	178	28	condition	condition	NOUN
ap-3509	178	29	(	(	PUNCT
ap-3509	178	30	n	n	CCONJ
ap-3509	178	31	)	)	PUNCT
ap-3509	178	32	.	.	PUNCT
ap-3509	179	1	the	the	DET
ap-3509	179	2	examples	example	NOUN
ap-3509	179	3	of	of	ADP
ap-3509	179	4	functions	function	NOUN
ap-3509	179	5	and	and	CCONJ
ap-3509	179	6	their	their	PRON
ap-3509	179	7	behaviours	behaviour	NOUN
ap-3509	179	8	on	on	ADP
ap-3509	179	9	the	the	DET
ap-3509	179	10	boundary	boundary	ADJ
ap-3509	179	11	∂f	∂f	PROPN
ap-3509	179	12	is	be	AUX
ap-3509	179	13	presented	present	VERB
ap-3509	179	14	in	in	ADP
ap-3509	179	15	figures	figure	NOUN
ap-3509	179	16	4	4	NUM
ap-3509	179	17	and	and	CCONJ
ap-3509	179	18	5	5	NUM
ap-3509	179	19	.	.	X
ap-3509	179	20	5.2	5.2	NUM
ap-3509	179	21	.	.	PUNCT
ap-3509	180	1	g2	g2	PROPN
ap-3509	180	2	case	case	NOUN
ap-3509	180	3	the	the	DET
ap-3509	180	4	normal	normal	ADJ
ap-3509	180	5	vectors	vector	NOUN
ap-3509	180	6	to	to	ADP
ap-3509	180	7	the	the	DET
ap-3509	180	8	fundamental	fundamental	ADJ
ap-3509	180	9	region	region	NOUN
ap-3509	180	10	f	f	PROPN
ap-3509	180	11	of	of	ADP
ap-3509	180	12	the	the	DET
ap-3509	180	13	weyl	weyl	PROPN
ap-3509	180	14	group	group	NOUN
ap-3509	180	15	g2	g2	PROPN
ap-3509	180	16	are	be	AUX
ap-3509	180	17	the	the	DET
ap-3509	180	18	following	follow	VERB
ap-3509	180	19	:	:	PUNCT
ap-3509	180	20	n1	n1	PROPN
ap-3509	180	21	=	=	SYM
ap-3509	180	22	(	(	PUNCT
ap-3509	180	23	−1	−1	NOUN
ap-3509	180	24	,	,	PUNCT
ap-3509	180	25	0)e	0)e	NOUN
ap-3509	180	26	,	,	PUNCT
ap-3509	180	27	n2	n2	NOUN
ap-3509	180	28	=	=	PUNCT
ap-3509	180	29	(	(	PUNCT
ap-3509	180	30	√3	√3	PROPN
ap-3509	180	31	2	2	NUM
ap-3509	180	32	,	,	PUNCT
ap-3509	180	33	−	−	PROPN
ap-3509	180	34	1	1	NUM
ap-3509	180	35	2	2	NUM
ap-3509	180	36	)	)	PUNCT
ap-3509	180	37	e	e	NOUN
ap-3509	180	38	,	,	PUNCT
ap-3509	180	39	n3	n3	NOUN
ap-3509	180	40	=	=	SYM
ap-3509	180	41	(	(	PUNCT
ap-3509	180	42	1	1	NUM
ap-3509	180	43	2	2	NUM
ap-3509	180	44	,	,	PUNCT
ap-3509	180	45	√	√	NUM
ap-3509	180	46	3	3	NUM
ap-3509	180	47	2	2	NUM
ap-3509	180	48	)	)	PUNCT
ap-3509	180	49	e	e	NOUN
ap-3509	180	50	in	in	ADP
ap-3509	180	51	figure	figure	NOUN
ap-3509	180	52	6	6	NUM
ap-3509	180	53	we	we	PRON
ap-3509	180	54	present	present	VERB
ap-3509	180	55	the	the	DET
ap-3509	180	56	fundamental	fundamental	ADJ
ap-3509	180	57	region	region	NOUN
ap-3509	180	58	f	f	PROPN
ap-3509	180	59	with	with	ADP
ap-3509	180	60	indicated	indicate	VERB
ap-3509	180	61	boundaries	boundary	NOUN
ap-3509	180	62	and	and	CCONJ
ap-3509	180	63	corresponding	correspond	VERB
ap-3509	180	64	normal	normal	ADJ
ap-3509	180	65	vectors	vector	NOUN
ap-3509	180	66	.	.	PUNCT
ap-3509	181	1	the	the	DET
ap-3509	181	2	values	value	NOUN
ap-3509	181	3	of	of	ADP
ap-3509	181	4	the	the	DET
ap-3509	181	5	functions	function	NOUN
ap-3509	181	6	for	for	ADP
ap-3509	181	7	group	group	NOUN
ap-3509	181	8	g2	g2	PROPN
ap-3509	181	9	fulfilling	fulfil	VERB
ap-3509	181	10	the	the	DET
ap-3509	181	11	dirichlet	dirichlet	PROPN
ap-3509	181	12	boundary	boundary	ADJ
ap-3509	181	13	condition	condition	NOUN
ap-3509	181	14	(	(	PUNCT
ap-3509	181	15	d	d	NOUN
ap-3509	181	16	)	)	PUNCT
ap-3509	181	17	on	on	ADP
ap-3509	181	18	the	the	DET
ap-3509	181	19	boundary	boundary	NOUN
ap-3509	181	20	of	of	ADP
ap-3509	181	21	the	the	DET
ap-3509	181	22	fundamental	fundamental	ADJ
ap-3509	181	23	region	region	NOUN
ap-3509	181	24	f	f	PROPN
ap-3509	181	25	are	be	AUX
ap-3509	181	26	presented	present	VERB
ap-3509	181	27	in	in	ADP
ap-3509	181	28	tables	table	NOUN
ap-3509	181	29	6	6	NUM
ap-3509	181	30	,	,	PUNCT
ap-3509	181	31	8	8	NUM
ap-3509	181	32	,	,	PUNCT
ap-3509	181	33	and	and	CCONJ
ap-3509	181	34	9	9	X
ap-3509	181	35	.	.	PUNCT
ap-3509	182	1	the	the	DET
ap-3509	182	2	values	value	NOUN
ap-3509	182	3	of	of	ADP
ap-3509	182	4	the	the	DET
ap-3509	182	5	functions	function	NOUN
ap-3509	182	6	satisfying	satisfy	VERB
ap-3509	182	7	the	the	DET
ap-3509	182	8	neumann	neumann	PROPN
ap-3509	182	9	boundary	boundary	ADJ
ap-3509	182	10	condition	condition	NOUN
ap-3509	182	11	(	(	PUNCT
ap-3509	182	12	n	n	CCONJ
ap-3509	182	13	)	)	PUNCT
ap-3509	182	14	are	be	AUX
ap-3509	182	15	given	give	VERB
ap-3509	182	16	in	in	ADP
ap-3509	182	17	tables	table	NOUN
ap-3509	182	18	7–9	7–9	NUM
ap-3509	182	19	.	.	PUNCT
ap-3509	183	1	the	the	DET
ap-3509	183	2	examples	example	NOUN
ap-3509	183	3	of	of	ADP
ap-3509	183	4	functions	function	NOUN
ap-3509	183	5	and	and	CCONJ
ap-3509	183	6	their	their	PRON
ap-3509	183	7	behaviours	behaviour	NOUN
ap-3509	183	8	on	on	ADP
ap-3509	183	9	the	the	DET
ap-3509	183	10	boundary	boundary	ADJ
ap-3509	183	11	∂f	∂f	PROPN
ap-3509	183	12	is	be	AUX
ap-3509	183	13	presented	present	VERB
ap-3509	183	14	in	in	ADP
ap-3509	183	15	figures	figure	NOUN
ap-3509	183	16	9	9	NUM
ap-3509	183	17	and	and	CCONJ
ap-3509	183	18	10	10	NUM
ap-3509	183	19	.	.	PUNCT
ap-3509	184	1	249	249	NUM
ap-3509	184	2	marzena	marzena	PROPN
ap-3509	184	3	szajewska	szajewska	NOUN
ap-3509	184	4	,	,	PUNCT
ap-3509	184	5	agnieszka	agnieszka	PROPN
ap-3509	184	6	tereszkiewicz	tereszkiewicz	PROPN
ap-3509	184	7	acta	acta	PROPN
ap-3509	184	8	polytechnica	polytechnica	PROPN
ap-3509	184	9	ca	ca	PROPN
ap-3509	184	10	,	,	PUNCT
ap-3509	184	11	b(x	b(x	NOUN
ap-3509	184	12	)	)	PUNCT
ap-3509	184	13	dirichlet	dirichlet	NOUN
ap-3509	184	14	condition	condition	NOUN
ap-3509	184	15	f1	f1	PROPN
ap-3509	184	16	2ca+b(x	2ca+b(x	NUM
ap-3509	184	17	)	)	PUNCT
ap-3509	184	18	+	+	SYM
ap-3509	184	19	2cb(x	2cb(x	X
ap-3509	184	20	)	)	PUNCT
ap-3509	184	21	f2	f2	PROPN
ap-3509	184	22	2ca+b(x)cb(x	2ca+b(x)cb(x	NUM
ap-3509	184	23	)	)	PUNCT
ap-3509	184	24	f3	f3	NOUN
ap-3509	184	25	ca+b(1)cb(y	ca+b(1)cb(y	NUM
ap-3509	184	26	)	)	PUNCT
ap-3509	185	1	+	+	CCONJ
ap-3509	185	2	cb(1)ca+b(y	cb(1)ca+b(y	ADJ
ap-3509	185	3	)	)	PUNCT
ap-3509	185	4	table	table	NOUN
ap-3509	185	5	2	2	NUM
ap-3509	185	6	.	.	PUNCT
ap-3509	185	7	values	value	NOUN
ap-3509	185	8	of	of	ADP
ap-3509	185	9	ca	ca	NOUN
ap-3509	185	10	,	,	PUNCT
ap-3509	185	11	b(x	b(x	NOUN
ap-3509	185	12	)	)	PUNCT
ap-3509	185	13	function	function	NOUN
ap-3509	185	14	at	at	ADP
ap-3509	185	15	the	the	DET
ap-3509	185	16	boundary	boundary	NOUN
ap-3509	185	17	of	of	ADP
ap-3509	185	18	the	the	DET
ap-3509	185	19	fundamental	fundamental	ADJ
ap-3509	185	20	region	region	NOUN
ap-3509	185	21	f	f	PROPN
ap-3509	185	22	in	in	ADP
ap-3509	185	23	c2	c2	PROPN
ap-3509	185	24	case	case	NOUN
ap-3509	185	25	.	.	PUNCT
ap-3509	186	1	sa	sa	NOUN
ap-3509	186	2	,	,	PUNCT
ap-3509	186	3	b(x	b(x	NOUN
ap-3509	186	4	)	)	PUNCT
ap-3509	186	5	neumann	neumann	PROPN
ap-3509	186	6	condition	condition	NOUN
ap-3509	186	7	f1	f1	PROPN
ap-3509	186	8	2i	2i	NOUN
ap-3509	186	9	(	(	PUNCT
ap-3509	186	10	ksb(x)−	ksb(x)−	PROPN
ap-3509	186	11	√	√	PROPN
ap-3509	186	12	w2	w2	NOUN
ap-3509	186	13	−	−	PROPN
ap-3509	186	14	k2sa+b(x	k2sa+b(x	PROPN
ap-3509	186	15	)	)	PUNCT
ap-3509	186	16	)	)	PUNCT
ap-3509	187	1	f2	f2	PROPN
ap-3509	187	2	2i	2i	NOUN
ap-3509	187	3	(	(	PUNCT
ap-3509	187	4	√	√	PROPN
ap-3509	187	5	w2	w2	NOUN
ap-3509	187	6	−	−	PROPN
ap-3509	187	7	k2sa+b(x)cb(x)−	k2sa+b(x)cb(x)−	PROPN
ap-3509	187	8	ksb(x)ca+b(x	ksb(x)ca+b(x	PROPN
ap-3509	187	9	)	)	PUNCT
ap-3509	187	10	)	)	PUNCT
ap-3509	188	1	f3	f3	PROPN
ap-3509	188	2	i	i	PRON
ap-3509	188	3	(	(	PUNCT
ap-3509	188	4	√	√	PROPN
ap-3509	188	5	w2	w2	NOUN
ap-3509	188	6	−	−	PROPN
ap-3509	188	7	k2ca+b(1)sb(y)−	k2ca+b(1)sb(y)−	PROPN
ap-3509	188	8	kcb(1)sa+b(y	kcb(1)sa+b(y	ADV
ap-3509	188	9	)	)	PUNCT
ap-3509	188	10	)	)	PUNCT
ap-3509	188	11	table	table	NOUN
ap-3509	188	12	3	3	NUM
ap-3509	188	13	.	.	PUNCT
ap-3509	188	14	values	value	NOUN
ap-3509	188	15	of	of	ADP
ap-3509	188	16	sa	sa	NOUN
ap-3509	188	17	,	,	PUNCT
ap-3509	188	18	b(x	b(x	NOUN
ap-3509	188	19	)	)	PUNCT
ap-3509	188	20	function	function	NOUN
ap-3509	188	21	at	at	ADP
ap-3509	188	22	the	the	DET
ap-3509	188	23	boundary	boundary	NOUN
ap-3509	188	24	of	of	ADP
ap-3509	188	25	the	the	DET
ap-3509	188	26	fundamental	fundamental	ADJ
ap-3509	188	27	region	region	NOUN
ap-3509	188	28	f	f	PROPN
ap-3509	188	29	in	in	ADP
ap-3509	188	30	c2	c2	PROPN
ap-3509	188	31	case	case	NOUN
ap-3509	188	32	.	.	PUNCT
ap-3509	189	1	mixed	mixed	ADJ
ap-3509	189	2	condition	condition	NOUN
ap-3509	189	3	ssa	ssa	NOUN
ap-3509	189	4	,	,	PUNCT
ap-3509	189	5	b(x	b(x	NOUN
ap-3509	189	6	)	)	PUNCT
ap-3509	189	7	dirichlet	dirichlet	NOUN
ap-3509	189	8	condition	condition	NOUN
ap-3509	189	9	neumann	neumann	PROPN
ap-3509	189	10	condition	condition	PROPN
ap-3509	189	11	f1	f1	PROPN
ap-3509	189	12	2(ca+b(x)−	2(ca+b(x)−	PROPN
ap-3509	189	13	cb(x	cb(x	NUM
ap-3509	189	14	)	)	PUNCT
ap-3509	189	15	)	)	PUNCT
ap-3509	189	16	0	0	PUNCT
ap-3509	190	1	f2	f2	ADJ
ap-3509	190	2	0	0	NUM
ap-3509	190	3	2i	2i	NUM
ap-3509	190	4	(	(	PUNCT
ap-3509	190	5	−	−	PROPN
ap-3509	190	6	√	√	PROPN
ap-3509	190	7	w2	w2	NOUN
ap-3509	190	8	−	−	PROPN
ap-3509	190	9	k2sa+b(x)cb(x	k2sa+b(x)cb(x	PROPN
ap-3509	190	10	)	)	PUNCT
ap-3509	190	11	+	+	CCONJ
ap-3509	190	12	ksb(x)ca+b(x	ksb(x)ca+b(x	NOUN
ap-3509	190	13	)	)	PUNCT
ap-3509	190	14	)	)	PUNCT
ap-3509	190	15	f3	f3	PROPN
ap-3509	190	16	c(a+b)(1)cb(y)−	c(a+b)(1)cb(y)−	PROPN
ap-3509	190	17	cb(1)ca+b(y	cb(1)ca+b(y	PROPN
ap-3509	190	18	)	)	PUNCT
ap-3509	190	19	0	0	NUM
ap-3509	190	20	table	table	NOUN
ap-3509	190	21	4	4	NUM
ap-3509	190	22	.	.	PUNCT
ap-3509	190	23	values	value	NOUN
ap-3509	190	24	of	of	ADP
ap-3509	190	25	ss	ss	PRON
ap-3509	190	26	a	a	PRON
ap-3509	190	27	,	,	PUNCT
ap-3509	190	28	b(x	b(x	NOUN
ap-3509	190	29	)	)	PUNCT
ap-3509	190	30	function	function	NOUN
ap-3509	190	31	at	at	ADP
ap-3509	190	32	the	the	DET
ap-3509	190	33	boundary	boundary	NOUN
ap-3509	190	34	of	of	ADP
ap-3509	190	35	the	the	DET
ap-3509	190	36	fundamental	fundamental	ADJ
ap-3509	190	37	region	region	NOUN
ap-3509	190	38	f	f	PROPN
ap-3509	190	39	in	in	ADP
ap-3509	190	40	c2	c2	PROPN
ap-3509	190	41	case	case	NOUN
ap-3509	190	42	.	.	PUNCT
ap-3509	191	1	mixed	mixed	ADJ
ap-3509	191	2	condition	condition	NOUN
ap-3509	191	3	sla	sla	NOUN
ap-3509	191	4	,	,	PUNCT
ap-3509	191	5	b(x	b(x	NOUN
ap-3509	191	6	)	)	PUNCT
ap-3509	191	7	dirichlet	dirichlet	NOUN
ap-3509	191	8	condition	condition	NOUN
ap-3509	191	9	neumann	neumann	PROPN
ap-3509	191	10	condition	condition	PROPN
ap-3509	191	11	f1	f1	PROPN
ap-3509	191	12	0	0	NUM
ap-3509	191	13	2i	2i	NUM
ap-3509	191	14	(	(	PUNCT
ap-3509	191	15	−	−	PROPN
ap-3509	191	16	√	√	PROPN
ap-3509	191	17	w2	w2	NOUN
ap-3509	191	18	−	−	PROPN
ap-3509	191	19	k2sb(x)−	k2sb(x)−	PROPN
ap-3509	191	20	ksa+b(x	ksa+b(x	PROPN
ap-3509	191	21	)	)	PUNCT
ap-3509	191	22	)	)	PUNCT
ap-3509	192	1	f2	f2	PROPN
ap-3509	192	2	2sa+b(x)sb(x	2sa+b(x)sb(x	NUM
ap-3509	192	3	)	)	PUNCT
ap-3509	192	4	0	0	NUM
ap-3509	193	1	f3	f3	NOUN
ap-3509	193	2	0	0	NUM
ap-3509	194	1	i	i	PRON
ap-3509	194	2	(	(	PUNCT
ap-3509	194	3	√	√	PROPN
ap-3509	194	4	w2	w2	NOUN
ap-3509	194	5	−	−	PROPN
ap-3509	194	6	k2ca+b(1)sb(y	k2ca+b(1)sb(y	PROPN
ap-3509	194	7	)	)	PUNCT
ap-3509	194	8	+	+	CCONJ
ap-3509	194	9	kcb(1)sa+b(y	kcb(1)sa+b(y	ADJ
ap-3509	194	10	)	)	PUNCT
ap-3509	194	11	)	)	PUNCT
ap-3509	194	12	table	table	NOUN
ap-3509	194	13	5	5	NUM
ap-3509	194	14	.	.	PUNCT
ap-3509	195	1	values	value	NOUN
ap-3509	195	2	of	of	ADP
ap-3509	195	3	sl	sl	INTJ
ap-3509	195	4	a	a	DET
ap-3509	195	5	,	,	PUNCT
ap-3509	195	6	b(x	b(x	NOUN
ap-3509	195	7	)	)	PUNCT
ap-3509	195	8	function	function	NOUN
ap-3509	195	9	at	at	ADP
ap-3509	195	10	the	the	DET
ap-3509	195	11	boundary	boundary	NOUN
ap-3509	195	12	of	of	ADP
ap-3509	195	13	the	the	DET
ap-3509	195	14	fundamental	fundamental	ADJ
ap-3509	195	15	region	region	NOUN
ap-3509	195	16	f	f	PROPN
ap-3509	195	17	in	in	ADP
ap-3509	195	18	c2	c2	PROPN
ap-3509	195	19	case	case	NOUN
ap-3509	195	20	.	.	PUNCT
ap-3509	196	1	ca	can	AUX
ap-3509	196	2	,	,	PUNCT
ap-3509	196	3	b(x	b(x	NOUN
ap-3509	196	4	)	)	PUNCT
ap-3509	196	5	dirichlet	dirichlet	NOUN
ap-3509	196	6	condition	condition	NOUN
ap-3509	196	7	f1	f1	PROPN
ap-3509	196	8	2(cb(y	2(cb(y	PROPN
ap-3509	196	9	)	)	PUNCT
ap-3509	197	1	+	+	CCONJ
ap-3509	197	2	c3a+b(y	c3a+b(y	PROPN
ap-3509	197	3	)	)	PUNCT
ap-3509	198	1	+	+	NUM
ap-3509	198	2	c3a+2b(y	c3a+2b(y	NOUN
ap-3509	198	3	)	)	PUNCT
ap-3509	198	4	)	)	PUNCT
ap-3509	199	1	f2	f2	PROPN
ap-3509	199	2	c2a+b(x)cb(x	c2a+b(x)cb(x	PROPN
ap-3509	199	3	)	)	PUNCT
ap-3509	199	4	+	+	CCONJ
ap-3509	199	5	ca+b(x)c3a+b(x	ca+b(x)c3a+b(x	ADJ
ap-3509	199	6	)	)	PUNCT
ap-3509	199	7	+	+	CCONJ
ap-3509	199	8	ca(x)c3a+2b(x	ca(x)c3a+2b(x	ADJ
ap-3509	199	9	)	)	PUNCT
ap-3509	199	10	f3	f3	PROPN
ap-3509	199	11	c2a+b(x)cb(x−	c2a+b(x)cb(x−	PROPN
ap-3509	199	12	1	1	NUM
ap-3509	199	13	)	)	PUNCT
ap-3509	199	14	+	+	NUM
ap-3509	199	15	ca+b(x)c3a+b(x−	ca+b(x)c3a+b(x−	NOUN
ap-3509	199	16	1	1	X
ap-3509	199	17	)	)	PUNCT
ap-3509	199	18	+	+	CCONJ
ap-3509	199	19	ca(x)c3a+2b(x−	ca(x)c3a+2b(x−	PROPN
ap-3509	199	20	1	1	NUM
ap-3509	199	21	)	)	PUNCT
ap-3509	199	22	table	table	NOUN
ap-3509	199	23	6	6	NUM
ap-3509	199	24	.	.	PUNCT
ap-3509	199	25	values	value	NOUN
ap-3509	199	26	of	of	ADP
ap-3509	199	27	ca	ca	NOUN
ap-3509	199	28	,	,	PUNCT
ap-3509	199	29	b(x	b(x	NOUN
ap-3509	199	30	)	)	PUNCT
ap-3509	199	31	function	function	NOUN
ap-3509	199	32	at	at	ADP
ap-3509	199	33	the	the	DET
ap-3509	199	34	boundary	boundary	NOUN
ap-3509	199	35	of	of	ADP
ap-3509	199	36	the	the	DET
ap-3509	199	37	fundamental	fundamental	ADJ
ap-3509	199	38	region	region	NOUN
ap-3509	199	39	f	f	PROPN
ap-3509	199	40	in	in	ADP
ap-3509	199	41	g2	g2	PROPN
ap-3509	199	42	case	case	NOUN
ap-3509	199	43	.	.	PUNCT
ap-3509	200	1	sa	sa	NOUN
ap-3509	200	2	,	,	PUNCT
ap-3509	200	3	b(x	b(x	NOUN
ap-3509	200	4	)	)	PUNCT
ap-3509	200	5	neumann	neumann	PROPN
ap-3509	200	6	condition	condition	PROPN
ap-3509	200	7	f1	f1	PROPN
ap-3509	200	8	2i(−k3s3a+2b(y	2i(−k3s3a+2b(y	PROPN
ap-3509	200	9	)	)	PUNCT
ap-3509	201	1	+	+	CCONJ
ap-3509	201	2	k2s3a+b(y)−	k2s3a+b(y)−	X
ap-3509	201	3	k1sb(y	k1sb(y	PROPN
ap-3509	201	4	)	)	PUNCT
ap-3509	201	5	)	)	PUNCT
ap-3509	202	1	f2	f2	PROPN
ap-3509	202	2	−2i	−2i	PROPN
ap-3509	202	3	(	(	PUNCT
ap-3509	202	4	√	√	PROPN
ap-3509	202	5	w2	w2	NOUN
ap-3509	202	6	−	−	PROPN
ap-3509	202	7	k2	k2	PROPN
ap-3509	202	8	3	3	NUM
ap-3509	202	9	c3a+2b(x)sa(x)−	c3a+2b(x)sa(x)−	PROPN
ap-3509	202	10	√	√	PROPN
ap-3509	202	11	w2	w2	PROPN
ap-3509	202	12	−	−	PROPN
ap-3509	202	13	k2	k2	PROPN
ap-3509	202	14	2	2	NUM
ap-3509	202	15	c3a+b(x)sa+b(x	c3a+b(x)sa+b(x	NOUN
ap-3509	202	16	)	)	PUNCT
ap-3509	203	1	+	+	CCONJ
ap-3509	203	2	√	√	PROPN
ap-3509	203	3	w2	w2	NOUN
ap-3509	203	4	−	−	PROPN
ap-3509	203	5	k2	k2	PROPN
ap-3509	203	6	1	1	NUM
ap-3509	203	7	cb(x)s2a+b(x	cb(x)s2a+b(x	ADJ
ap-3509	203	8	)	)	PUNCT
ap-3509	203	9	)	)	PUNCT
ap-3509	204	1	f3	f3	PROPN
ap-3509	204	2	2i(k3s3a+2b(x−	2i(k3s3a+2b(x−	PROPN
ap-3509	204	3	1)ca(x)−	1)ca(x)−	PROPN
ap-3509	204	4	k2s3a+b(x−	k2s3a+b(x−	NOUN
ap-3509	204	5	1)ca+b(x	1)ca+b(x	NUM
ap-3509	204	6	)	)	PUNCT
ap-3509	205	1	+	+	CCONJ
ap-3509	205	2	k1sb(x−	k1sb(x−	PROPN
ap-3509	205	3	1)c2a+b(x	1)c2a+b(x	NUM
ap-3509	205	4	)	)	PUNCT
ap-3509	205	5	)	)	PUNCT
ap-3509	205	6	table	table	NOUN
ap-3509	205	7	7	7	NUM
ap-3509	205	8	.	.	PUNCT
ap-3509	206	1	values	value	NOUN
ap-3509	206	2	of	of	ADP
ap-3509	206	3	sa	sa	NOUN
ap-3509	206	4	,	,	PUNCT
ap-3509	206	5	b(x	b(x	NOUN
ap-3509	206	6	)	)	PUNCT
ap-3509	206	7	function	function	NOUN
ap-3509	206	8	at	at	ADP
ap-3509	206	9	the	the	DET
ap-3509	206	10	boundary	boundary	NOUN
ap-3509	206	11	of	of	ADP
ap-3509	206	12	the	the	DET
ap-3509	206	13	fundamental	fundamental	ADJ
ap-3509	206	14	region	region	NOUN
ap-3509	206	15	f	f	PROPN
ap-3509	206	16	in	in	ADP
ap-3509	206	17	g2	g2	PROPN
ap-3509	206	18	case	case	NOUN
ap-3509	206	19	.	.	PUNCT
ap-3509	207	1	250	250	NUM
ap-3509	207	2	vol	vol	NOUN
ap-3509	207	3	.	.	PUNCT
ap-3509	208	1	56	56	NUM
ap-3509	208	2	no	no	NOUN
ap-3509	208	3	.	.	PUNCT
ap-3509	209	1	3/2016	3/2016	NUM
ap-3509	209	2	two	two	NUM
ap-3509	209	3	-	-	PUNCT
ap-3509	209	4	dimensional	dimensional	ADJ
ap-3509	209	5	hybrids	hybrid	NOUN
ap-3509	209	6	with	with	ADP
ap-3509	209	7	mixed	mixed	ADJ
ap-3509	209	8	boundary	boundary	ADJ
ap-3509	209	9	value	value	NOUN
ap-3509	209	10	problems	problem	NOUN
ap-3509	209	11	mixed	mixed	ADJ
ap-3509	209	12	condition	condition	NOUN
ap-3509	209	13	ssa	ssa	NOUN
ap-3509	209	14	,	,	PUNCT
ap-3509	209	15	b(x	b(x	NOUN
ap-3509	209	16	)	)	PUNCT
ap-3509	209	17	dirichlet	dirichlet	NOUN
ap-3509	209	18	condition	condition	NOUN
ap-3509	209	19	neumann	neumann	PROPN
ap-3509	209	20	condition	condition	PROPN
ap-3509	209	21	f1	f1	PROPN
ap-3509	209	22	2(−sb(x)−	2(−sb(x)−	PROPN
ap-3509	209	23	s3a+b(x	s3a+b(x	PROPN
ap-3509	209	24	)	)	PUNCT
ap-3509	209	25	+	+	CCONJ
ap-3509	209	26	s3a+2b(x	s3a+2b(x	X
ap-3509	209	27	)	)	PUNCT
ap-3509	209	28	)	)	PUNCT
ap-3509	209	29	0	0	PUNCT
ap-3509	210	1	f2	f2	ADJ
ap-3509	210	2	0	0	NUM
ap-3509	210	3	2i	2i	NUM
ap-3509	210	4	(	(	PUNCT
ap-3509	210	5	√	√	PROPN
ap-3509	210	6	w2	w2	NOUN
ap-3509	210	7	−	−	PROPN
ap-3509	210	8	k2	k2	PROPN
ap-3509	210	9	3c3a+2b(x)ca(x	3c3a+2b(x)ca(x	PROPN
ap-3509	210	10	)	)	PUNCT
ap-3509	210	11	+	+	CCONJ
ap-3509	210	12	√	√	VERB
ap-3509	210	13	w2	w2	NOUN
ap-3509	210	14	−	−	PROPN
ap-3509	210	15	k2	k2	PROPN
ap-3509	210	16	2c3a+b(x)ca+b(x	2c3a+b(x)ca+b(x	NUM
ap-3509	210	17	)	)	PUNCT
ap-3509	210	18	+	+	CCONJ
ap-3509	210	19	√	√	PROPN
ap-3509	210	20	w2	w2	NOUN
ap-3509	210	21	−	−	PROPN
ap-3509	210	22	k2	k2	PROPN
ap-3509	210	23	1cb(x)c2a+b(x	1cb(x)c2a+b(x	NUM
ap-3509	210	24	)	)	PUNCT
ap-3509	210	25	)	)	PUNCT
ap-3509	211	1	f3	f3	PROPN
ap-3509	211	2	−c2a+b(x)sb(x−	−c2a+b(x)sb(x−	PROPN
ap-3509	211	3	1)−	1)−	PROPN
ap-3509	211	4	ca+b(x)s3a+b(x−	ca+b(x)s3a+b(x−	NOUN
ap-3509	211	5	1	1	NUM
ap-3509	211	6	)	)	PUNCT
ap-3509	211	7	+	+	CCONJ
ap-3509	211	8	ca(x)s3a+2b(x−	ca(x)s3a+2b(x−	NUM
ap-3509	211	9	1	1	NUM
ap-3509	211	10	)	)	PUNCT
ap-3509	211	11	table	table	NOUN
ap-3509	211	12	8	8	NUM
ap-3509	211	13	.	.	PUNCT
ap-3509	212	1	values	value	NOUN
ap-3509	212	2	of	of	ADP
ap-3509	212	3	ss	ss	PRON
ap-3509	212	4	a	a	PRON
ap-3509	212	5	,	,	PUNCT
ap-3509	212	6	b(x	b(x	NOUN
ap-3509	212	7	)	)	PUNCT
ap-3509	212	8	function	function	NOUN
ap-3509	212	9	at	at	ADP
ap-3509	212	10	the	the	DET
ap-3509	212	11	boundary	boundary	NOUN
ap-3509	212	12	of	of	ADP
ap-3509	212	13	the	the	DET
ap-3509	212	14	fundamental	fundamental	ADJ
ap-3509	212	15	region	region	NOUN
ap-3509	212	16	f	f	PROPN
ap-3509	212	17	in	in	ADP
ap-3509	212	18	g2	g2	PROPN
ap-3509	212	19	case	case	NOUN
ap-3509	212	20	.	.	PUNCT
ap-3509	213	1	mixed	mixed	ADJ
ap-3509	213	2	condition	condition	NOUN
ap-3509	213	3	sla	sla	NOUN
ap-3509	213	4	,	,	PUNCT
ap-3509	213	5	b(x	b(x	NOUN
ap-3509	213	6	)	)	PUNCT
ap-3509	213	7	dirichlet	dirichlet	NOUN
ap-3509	213	8	condition	condition	NOUN
ap-3509	213	9	neumann	neumann	PROPN
ap-3509	213	10	condition	condition	PROPN
ap-3509	213	11	f1	f1	PROPN
ap-3509	213	12	0	0	NUM
ap-3509	213	13	2i(−k3c3a+2b(y)−	2i(−k3c3a+2b(y)−	NUM
ap-3509	213	14	k2c3a+b(y	k2c3a+b(y	PROPN
ap-3509	213	15	)	)	PUNCT
ap-3509	214	1	+	+	CCONJ
ap-3509	215	1	k1cb(y	k1cb(y	NOUN
ap-3509	215	2	)	)	PUNCT
ap-3509	215	3	)	)	PUNCT
ap-3509	216	1	f2	f2	PROPN
ap-3509	216	2	−s2a+b(x)cb(x	−s2a+b(x)cb(x	NUM
ap-3509	216	3	)	)	PUNCT
ap-3509	217	1	+	+	CCONJ
ap-3509	217	2	sa+b(x)c3a+b(x	sa+b(x)c3a+b(x	PROPN
ap-3509	217	3	)	)	PUNCT
ap-3509	217	4	+	+	CCONJ
ap-3509	217	5	sa(x)c3a+2b(x	sa(x)c3a+2b(x	ADJ
ap-3509	217	6	)	)	PUNCT
ap-3509	217	7	0	0	NUM
ap-3509	218	1	f3	f3	NOUN
ap-3509	218	2	0	0	NUM
ap-3509	218	3	2i(k3c3a+2b(x−	2i(k3c3a+2b(x−	NUM
ap-3509	218	4	1)ca(x	1)ca(x	NUM
ap-3509	218	5	)	)	PUNCT
ap-3509	218	6	+	+	NUM
ap-3509	218	7	k2c3a+b(x−	k2c3a+b(x−	NOUN
ap-3509	218	8	1)ca+b(x	1)ca+b(x	NUM
ap-3509	218	9	)	)	PUNCT
ap-3509	219	1	−	−	PROPN
ap-3509	219	2	k1cb(x−	k1cb(x−	PROPN
ap-3509	219	3	1)c2a+b(x	1)c2a+b(x	PROPN
ap-3509	219	4	)	)	PUNCT
ap-3509	219	5	)	)	PUNCT
ap-3509	219	6	table	table	NOUN
ap-3509	219	7	9	9	NUM
ap-3509	219	8	.	.	PUNCT
ap-3509	220	1	values	value	NOUN
ap-3509	220	2	of	of	ADP
ap-3509	220	3	sl	sl	INTJ
ap-3509	220	4	a	a	DET
ap-3509	220	5	,	,	PUNCT
ap-3509	220	6	b(x	b(x	NOUN
ap-3509	220	7	)	)	PUNCT
ap-3509	220	8	function	function	NOUN
ap-3509	220	9	at	at	ADP
ap-3509	220	10	the	the	DET
ap-3509	220	11	boundary	boundary	NOUN
ap-3509	220	12	of	of	ADP
ap-3509	220	13	the	the	DET
ap-3509	220	14	fundamental	fundamental	ADJ
ap-3509	220	15	region	region	NOUN
ap-3509	220	16	f	f	PROPN
ap-3509	220	17	in	in	ADP
ap-3509	220	18	g2	g2	PROPN
ap-3509	220	19	case	case	NOUN
ap-3509	220	20	.	.	PUNCT
ap-3509	221	1	<	<	X
ap-3509	221	2	c1,3(x	c1,3(x	PROPN
ap-3509	221	3	)	)	PUNCT
ap-3509	221	4	<	<	X
ap-3509	221	5	s1,3(x	s1,3(x	PROPN
ap-3509	221	6	)	)	PUNCT
ap-3509	221	7	figure	figure	NOUN
ap-3509	221	8	9	9	NUM
ap-3509	221	9	.	.	PUNCT
ap-3509	222	1	the	the	DET
ap-3509	222	2	contour	contour	NOUN
ap-3509	222	3	plot	plot	NOUN
ap-3509	222	4	of	of	ADP
ap-3509	222	5	real	real	ADJ
ap-3509	222	6	part	part	NOUN
ap-3509	222	7	of	of	ADP
ap-3509	222	8	c1,3(x	c1,3(x	PROPN
ap-3509	222	9	)	)	PUNCT
ap-3509	222	10	,	,	PUNCT
ap-3509	222	11	s1,3(x	s1,3(x	PROPN
ap-3509	222	12	)	)	PUNCT
ap-3509	222	13	functions	function	NOUN
ap-3509	222	14	.	.	PUNCT
ap-3509	223	1	the	the	DET
ap-3509	223	2	triangle	triangle	NOUN
ap-3509	223	3	denotes	denote	VERB
ap-3509	223	4	the	the	DET
ap-3509	223	5	fundamental	fundamental	ADJ
ap-3509	223	6	domain	domain	NOUN
ap-3509	223	7	f	f	PROPN
ap-3509	223	8	of	of	ADP
ap-3509	223	9	the	the	DET
ap-3509	223	10	affine	affine	NOUN
ap-3509	223	11	weyl	weyl	PROPN
ap-3509	223	12	group	group	PROPN
ap-3509	223	13	g2	g2	PROPN
ap-3509	223	14	.	.	PUNCT
ap-3509	224	1	=	=	PUNCT
ap-3509	224	2	sl1,3(x	sl1,3(x	PROPN
ap-3509	224	3	)	)	PUNCT
ap-3509	224	4	=	=	SYM
ap-3509	224	5	ss1,3(x	ss1,3(x	PROPN
ap-3509	224	6	)	)	PUNCT
ap-3509	224	7	figure	figure	NOUN
ap-3509	224	8	10	10	NUM
ap-3509	224	9	.	.	PUNCT
ap-3509	225	1	the	the	DET
ap-3509	225	2	contour	contour	NOUN
ap-3509	225	3	plot	plot	NOUN
ap-3509	225	4	of	of	ADP
ap-3509	225	5	imaginary	imaginary	ADJ
ap-3509	225	6	part	part	NOUN
ap-3509	225	7	of	of	ADP
ap-3509	225	8	sl	sl	PROPN
ap-3509	225	9	1,3(x	1,3(x	PROPN
ap-3509	225	10	)	)	PUNCT
ap-3509	225	11	,	,	PUNCT
ap-3509	225	12	ss	ss	PROPN
ap-3509	225	13	1,3(x	1,3(x	NUM
ap-3509	225	14	)	)	PUNCT
ap-3509	225	15	functions	function	NOUN
ap-3509	225	16	.	.	PUNCT
ap-3509	226	1	the	the	DET
ap-3509	226	2	triangle	triangle	NOUN
ap-3509	226	3	denotes	denote	VERB
ap-3509	226	4	the	the	DET
ap-3509	226	5	fundamental	fundamental	ADJ
ap-3509	226	6	domain	domain	NOUN
ap-3509	226	7	f	f	PROPN
ap-3509	226	8	of	of	ADP
ap-3509	226	9	the	the	DET
ap-3509	226	10	affine	affine	NOUN
ap-3509	226	11	weyl	weyl	PROPN
ap-3509	226	12	group	group	PROPN
ap-3509	226	13	g2	g2	PROPN
ap-3509	226	14	.	.	PUNCT
ap-3509	227	1	<	<	X
ap-3509	227	2	c1,3(x	c1,3(x	PROPN
ap-3509	227	3	)	)	PUNCT
ap-3509	227	4	<	<	X
ap-3509	227	5	s1,3(x	s1,3(x	PROPN
ap-3509	227	6	)	)	PUNCT
ap-3509	227	7	figure	figure	NOUN
ap-3509	227	8	11	11	NUM
ap-3509	227	9	.	.	PUNCT
ap-3509	228	1	the	the	DET
ap-3509	228	2	contour	contour	NOUN
ap-3509	228	3	plot	plot	NOUN
ap-3509	228	4	of	of	ADP
ap-3509	228	5	real	real	ADJ
ap-3509	228	6	part	part	NOUN
ap-3509	228	7	of	of	ADP
ap-3509	228	8	c1,3(x	c1,3(x	PROPN
ap-3509	228	9	)	)	PUNCT
ap-3509	228	10	,	,	PUNCT
ap-3509	228	11	and	and	CCONJ
ap-3509	228	12	s1,3(x	s1,3(x	PROPN
ap-3509	228	13	)	)	PUNCT
ap-3509	228	14	functions	function	NOUN
ap-3509	228	15	.	.	PUNCT
ap-3509	229	1	the	the	DET
ap-3509	229	2	square	square	ADJ
ap-3509	229	3	denotes	denote	VERB
ap-3509	229	4	the	the	DET
ap-3509	229	5	fundamental	fundamental	ADJ
ap-3509	229	6	domain	domain	NOUN
ap-3509	229	7	f	f	PROPN
ap-3509	229	8	of	of	ADP
ap-3509	229	9	a1	a1	PROPN
ap-3509	229	10	×	×	PROPN
ap-3509	229	11	a1	a1	NOUN
ap-3509	229	12	.	.	PUNCT
ap-3509	230	1	=	=	PUNCT
ap-3509	230	2	cs1,3(x	cs1,3(x	PROPN
ap-3509	230	3	)	)	PUNCT
ap-3509	230	4	=	=	SYM
ap-3509	230	5	sc1,3(x	sc1,3(x	PROPN
ap-3509	230	6	)	)	PUNCT
ap-3509	230	7	figure	figure	NOUN
ap-3509	230	8	12	12	NUM
ap-3509	230	9	.	.	PUNCT
ap-3509	231	1	the	the	DET
ap-3509	231	2	contour	contour	NOUN
ap-3509	231	3	plot	plot	NOUN
ap-3509	231	4	of	of	ADP
ap-3509	231	5	imaginary	imaginary	ADJ
ap-3509	231	6	part	part	NOUN
ap-3509	231	7	of	of	ADP
ap-3509	231	8	cs1,3(x	cs1,3(x	PROPN
ap-3509	231	9	)	)	PUNCT
ap-3509	231	10	,	,	PUNCT
ap-3509	231	11	and	and	CCONJ
ap-3509	231	12	sc1,3(x	sc1,3(x	PROPN
ap-3509	231	13	)	)	PUNCT
ap-3509	231	14	functions	function	NOUN
ap-3509	231	15	.	.	PUNCT
ap-3509	232	1	the	the	DET
ap-3509	232	2	square	square	ADJ
ap-3509	232	3	denotes	denote	VERB
ap-3509	232	4	the	the	DET
ap-3509	232	5	fundamental	fundamental	ADJ
ap-3509	232	6	domain	domain	NOUN
ap-3509	232	7	f	f	PROPN
ap-3509	232	8	of	of	ADP
ap-3509	232	9	a1	a1	PROPN
ap-3509	232	10	×	×	PROPN
ap-3509	232	11	a1	a1	NOUN
ap-3509	232	12	.	.	NOUN
ap-3509	232	13	251	251	NUM
ap-3509	232	14	marzena	marzena	PROPN
ap-3509	232	15	szajewska	szajewska	NOUN
ap-3509	232	16	,	,	PUNCT
ap-3509	232	17	agnieszka	agnieszka	PROPN
ap-3509	232	18	tereszkiewicz	tereszkiewicz	PROPN
ap-3509	232	19	acta	acta	PROPN
ap-3509	232	20	polytechnica	polytechnica	PROPN
ap-3509	232	21	ca	ca	PROPN
ap-3509	232	22	,	,	PUNCT
ap-3509	232	23	b(x	b(x	NOUN
ap-3509	232	24	)	)	PUNCT
ap-3509	232	25	dirichlet	dirichlet	NOUN
ap-3509	232	26	condition	condition	NOUN
ap-3509	232	27	f1	f1	PROPN
ap-3509	232	28	2cb(y	2cb(y	NUM
ap-3509	232	29	)	)	PUNCT
ap-3509	232	30	f2	f2	PROPN
ap-3509	232	31	2ca(x	2ca(x	NOUN
ap-3509	232	32	)	)	PUNCT
ap-3509	232	33	f3	f3	PROPN
ap-3509	232	34	ca(1)cb(y	ca(1)cb(y	X
ap-3509	232	35	)	)	PUNCT
ap-3509	233	1	f4	f4	PROPN
ap-3509	233	2	ca(x)cb(1	ca(x)cb(1	NOUN
ap-3509	233	3	)	)	PUNCT
ap-3509	233	4	table	table	NOUN
ap-3509	233	5	10	10	NUM
ap-3509	233	6	.	.	PUNCT
ap-3509	234	1	values	value	NOUN
ap-3509	234	2	of	of	ADP
ap-3509	234	3	ca	ca	NOUN
ap-3509	234	4	,	,	PUNCT
ap-3509	234	5	b(x	b(x	NOUN
ap-3509	234	6	)	)	PUNCT
ap-3509	234	7	function	function	NOUN
ap-3509	234	8	at	at	ADP
ap-3509	234	9	the	the	DET
ap-3509	234	10	boundary	boundary	ADJ
ap-3509	234	11	∂f	∂f	PROPN
ap-3509	234	12	of	of	ADP
ap-3509	234	13	the	the	DET
ap-3509	234	14	fundamental	fundamental	ADJ
ap-3509	234	15	region	region	NOUN
ap-3509	234	16	f	f	PROPN
ap-3509	234	17	.	.	PUNCT
ap-3509	235	1	sa	sa	PROPN
ap-3509	235	2	,	,	PUNCT
ap-3509	235	3	b(x	b(x	NOUN
ap-3509	235	4	)	)	PUNCT
ap-3509	235	5	neumann	neumann	PROPN
ap-3509	235	6	condition	condition	NOUN
ap-3509	235	7	f1	f1	PROPN
ap-3509	235	8	−2i	−2i	PROPN
ap-3509	235	9	ksb(y	ksb(y	PROPN
ap-3509	235	10	)	)	PUNCT
ap-3509	235	11	f2	f2	PROPN
ap-3509	235	12	−2i	−2i	PROPN
ap-3509	235	13	√	√	PROPN
ap-3509	235	14	w2	w2	NOUN
ap-3509	235	15	−	−	PROPN
ap-3509	235	16	k2sa(x	k2sa(x	PROPN
ap-3509	235	17	)	)	PUNCT
ap-3509	235	18	f3	f3	PROPN
ap-3509	235	19	i	i	PRON
ap-3509	235	20	kca(1)sb(y	kca(1)sb(y	PROPN
ap-3509	235	21	)	)	PUNCT
ap-3509	236	1	f4	f4	PROPN
ap-3509	236	2	i	i	PROPN
ap-3509	236	3	√	√	PROPN
ap-3509	236	4	w2	w2	NOUN
ap-3509	236	5	−	−	PROPN
ap-3509	236	6	k2sa(x)cb(1	k2sa(x)cb(1	NUM
ap-3509	236	7	)	)	PUNCT
ap-3509	236	8	table	table	NOUN
ap-3509	236	9	11	11	NUM
ap-3509	236	10	.	.	PUNCT
ap-3509	237	1	values	value	NOUN
ap-3509	237	2	of	of	ADP
ap-3509	237	3	sa	sa	NOUN
ap-3509	237	4	,	,	PUNCT
ap-3509	237	5	b(x	b(x	NOUN
ap-3509	237	6	)	)	PUNCT
ap-3509	237	7	function	function	NOUN
ap-3509	237	8	at	at	ADP
ap-3509	237	9	the	the	DET
ap-3509	237	10	boundary	boundary	ADJ
ap-3509	237	11	∂f	∂f	PROPN
ap-3509	237	12	of	of	ADP
ap-3509	237	13	the	the	DET
ap-3509	237	14	fundamental	fundamental	ADJ
ap-3509	237	15	region	region	NOUN
ap-3509	237	16	f	f	PROPN
ap-3509	237	17	.	.	PUNCT
ap-3509	238	1	mixed	mixed	ADJ
ap-3509	238	2	condition	condition	NOUN
ap-3509	238	3	csa	csa	PROPN
ap-3509	238	4	,	,	PUNCT
ap-3509	238	5	b(x	b(x	NOUN
ap-3509	238	6	)	)	PUNCT
ap-3509	238	7	dirichlet	dirichlet	PROPN
ap-3509	238	8	neumann	neumann	PROPN
ap-3509	238	9	f1	f1	PROPN
ap-3509	238	10	2sb(y	2sb(y	NUM
ap-3509	238	11	)	)	PUNCT
ap-3509	238	12	0	0	PUNCT
ap-3509	239	1	f2	f2	ADJ
ap-3509	239	2	0	0	NUM
ap-3509	239	3	−2i	−2i	NOUN
ap-3509	239	4	√	√	PROPN
ap-3509	239	5	w2	w2	NOUN
ap-3509	239	6	−	−	PROPN
ap-3509	239	7	k2ca(x	k2ca(x	PROPN
ap-3509	239	8	)	)	PUNCT
ap-3509	239	9	f3	f3	NOUN
ap-3509	239	10	ca(1)sb(y	ca(1)sb(y	VERB
ap-3509	239	11	)	)	PUNCT
ap-3509	239	12	0	0	PUNCT
ap-3509	240	1	f4	f4	NOUN
ap-3509	240	2	0	0	NUM
ap-3509	241	1	i	i	PRON
ap-3509	241	2	√	√	VERB
ap-3509	241	3	w2	w2	NOUN
ap-3509	241	4	−	−	PROPN
ap-3509	241	5	k2ca(x)cb(1	k2ca(x)cb(1	NUM
ap-3509	241	6	)	)	PUNCT
ap-3509	241	7	table	table	NOUN
ap-3509	241	8	12	12	NUM
ap-3509	241	9	.	.	PUNCT
ap-3509	242	1	values	value	NOUN
ap-3509	242	2	of	of	ADP
ap-3509	242	3	csa	csa	PROPN
ap-3509	242	4	,	,	PUNCT
ap-3509	242	5	b(x	b(x	NOUN
ap-3509	242	6	)	)	PUNCT
ap-3509	242	7	function	function	NOUN
ap-3509	242	8	at	at	ADP
ap-3509	242	9	the	the	DET
ap-3509	242	10	boundary	boundary	ADJ
ap-3509	242	11	∂f	∂f	PROPN
ap-3509	242	12	of	of	ADP
ap-3509	242	13	the	the	DET
ap-3509	242	14	fundamental	fundamental	ADJ
ap-3509	242	15	region	region	NOUN
ap-3509	242	16	f	f	PROPN
ap-3509	242	17	.	.	PUNCT
ap-3509	243	1	mixed	mixed	ADJ
ap-3509	243	2	condition	condition	NOUN
ap-3509	243	3	sca	sca	NOUN
ap-3509	243	4	,	,	PUNCT
ap-3509	243	5	b(x	b(x	NOUN
ap-3509	243	6	)	)	PUNCT
ap-3509	243	7	dirichlet	dirichlet	PROPN
ap-3509	243	8	neumann	neumann	PROPN
ap-3509	243	9	f1	f1	PROPN
ap-3509	243	10	0	0	PROPN
ap-3509	243	11	−2i	−2i	PROPN
ap-3509	243	12	kcb(y	kcb(y	PROPN
ap-3509	243	13	)	)	PUNCT
ap-3509	243	14	f2	f2	PROPN
ap-3509	243	15	2sa(x	2sa(x	NUM
ap-3509	243	16	)	)	PUNCT
ap-3509	243	17	0	0	NUM
ap-3509	244	1	f3	f3	NOUN
ap-3509	244	2	0	0	NUM
ap-3509	245	1	i	i	PRON
ap-3509	245	2	kca(1)cb(y	kca(1)cb(y	VERB
ap-3509	245	3	)	)	PUNCT
ap-3509	246	1	f4	f4	NUM
ap-3509	246	2	sa(x)cb(1	sa(x)cb(1	NOUN
ap-3509	246	3	)	)	PUNCT
ap-3509	246	4	0	0	NUM
ap-3509	246	5	table	table	NOUN
ap-3509	246	6	13	13	NUM
ap-3509	246	7	.	.	PUNCT
ap-3509	247	1	values	value	NOUN
ap-3509	247	2	of	of	ADP
ap-3509	247	3	sca	sca	PROPN
ap-3509	247	4	,	,	PUNCT
ap-3509	247	5	b(x	b(x	NOUN
ap-3509	247	6	)	)	PUNCT
ap-3509	247	7	function	function	NOUN
ap-3509	247	8	at	at	ADP
ap-3509	247	9	the	the	DET
ap-3509	247	10	boundary	boundary	ADJ
ap-3509	247	11	∂f	∂f	PROPN
ap-3509	247	12	of	of	ADP
ap-3509	247	13	the	the	DET
ap-3509	247	14	fundamental	fundamental	ADJ
ap-3509	247	15	region	region	NOUN
ap-3509	247	16	f	f	PROPN
ap-3509	247	17	.	.	PUNCT
ap-3509	248	1	6	6	X
ap-3509	248	2	.	.	X
ap-3509	248	3	appendix	appendix	NOUN
ap-3509	248	4	in	in	ADP
ap-3509	248	5	this	this	DET
ap-3509	248	6	section	section	NOUN
ap-3509	248	7	we	we	PRON
ap-3509	248	8	present	present	VERB
ap-3509	248	9	the	the	DET
ap-3509	248	10	simplest	simple	ADJ
ap-3509	248	11	case	case	NOUN
ap-3509	248	12	,	,	PUNCT
ap-3509	248	13	namely	namely	ADV
ap-3509	248	14	a1	a1	NOUN
ap-3509	248	15	×	×	NOUN
ap-3509	248	16	a1	a1	NOUN
ap-3509	248	17	.	.	PUNCT
ap-3509	249	1	the	the	DET
ap-3509	249	2	fundamental	fundamental	ADJ
ap-3509	249	3	region	region	NOUN
ap-3509	249	4	f	f	PROPN
ap-3509	249	5	(	(	PUNCT
ap-3509	249	6	shown	show	VERB
ap-3509	249	7	in	in	ADP
ap-3509	249	8	figure	figure	NOUN
ap-3509	249	9	7	7	NUM
ap-3509	249	10	)	)	PUNCT
ap-3509	249	11	is	be	AUX
ap-3509	249	12	a	a	DET
ap-3509	249	13	square	square	NOUN
ap-3509	249	14	with	with	ADP
ap-3509	249	15	vertices	vertex	NOUN
ap-3509	249	16	{	{	PUNCT
ap-3509	249	17	0	0	NUM
ap-3509	249	18	,	,	PUNCT
ap-3509	249	19	ω1	ω1	PROPN
ap-3509	249	20	,	,	PUNCT
ap-3509	249	21	ω2	ω2	NUM
ap-3509	249	22	,	,	PUNCT
ap-3509	249	23	ω1	ω1	PROPN
ap-3509	249	24	+	+	CCONJ
ap-3509	249	25	ω2	ω2	ADJ
ap-3509	249	26	}	}	PUNCT
ap-3509	249	27	in	in	ADP
ap-3509	249	28	the	the	DET
ap-3509	249	29	ω	ω	NOUN
ap-3509	249	30	-	-	NOUN
ap-3509	249	31	basis	basis	NOUN
ap-3509	249	32	.	.	PUNCT
ap-3509	250	1	the	the	DET
ap-3509	250	2	bases	basis	NOUN
ap-3509	250	3	written	write	VERB
ap-3509	250	4	in	in	ADP
ap-3509	250	5	the	the	DET
ap-3509	250	6	orthonormal	orthonormal	ADJ
ap-3509	250	7	basis	basis	NOUN
ap-3509	250	8	{	{	PUNCT
ap-3509	250	9	e1	e1	NOUN
ap-3509	250	10	,	,	PUNCT
ap-3509	250	11	e2	e2	PROPN
ap-3509	250	12	}	}	PUNCT
ap-3509	250	13	have	have	VERB
ap-3509	250	14	the	the	DET
ap-3509	250	15	form	form	NOUN
ap-3509	250	16	αi	αi	NOUN
ap-3509	250	17	=	=	SYM
ap-3509	250	18	√	√	ADP
ap-3509	250	19	2ei	2ei	NOUN
ap-3509	250	20	,	,	PUNCT
ap-3509	250	21	ωi	ωi	NOUN
ap-3509	250	22	=	=	SYM
ap-3509	250	23	1√	1√	NUM
ap-3509	250	24	2ei	2ei	NOUN
ap-3509	251	1	i	i	NOUN
ap-3509	251	2	=	=	NOUN
ap-3509	251	3	1	1	NUM
ap-3509	251	4	,	,	PUNCT
ap-3509	251	5	2	2	NUM
ap-3509	251	6	.	.	X
ap-3509	251	7	there	there	PRON
ap-3509	251	8	are	be	VERB
ap-3509	251	9	four	four	NUM
ap-3509	251	10	families	family	NOUN
ap-3509	251	11	of	of	ADP
ap-3509	251	12	special	special	ADJ
ap-3509	251	13	functions	function	NOUN
ap-3509	251	14	,	,	PUNCT
ap-3509	251	15	namely	namely	ADV
ap-3509	251	16	c-	c-	X
ap-3509	251	17	,	,	PUNCT
ap-3509	251	18	s-	s-	X
ap-3509	251	19	,	,	PUNCT
ap-3509	251	20	csand	csand	PROPN
ap-3509	251	21	sc	sc	PROPN
ap-3509	251	22	-	-	PUNCT
ap-3509	251	23	functions	function	NOUN
ap-3509	251	24	.	.	PUNCT
ap-3509	252	1	their	their	PRON
ap-3509	252	2	forms	form	NOUN
ap-3509	252	3	are	be	AUX
ap-3509	252	4	the	the	DET
ap-3509	252	5	following	following	NOUN
ap-3509	252	6	:	:	PUNCT
ap-3509	252	7	ca	ca	NOUN
ap-3509	252	8	,	,	PUNCT
ap-3509	252	9	b(x	b(x	NOUN
ap-3509	252	10	)	)	PUNCT
ap-3509	252	11	=	=	SYM
ap-3509	252	12	ca(x)cb(y	ca(x)cb(y	PROPN
ap-3509	252	13	)	)	PUNCT
ap-3509	252	14	=	=	SYM
ap-3509	252	15	4	4	NUM
ap-3509	252	16	cos(2πax	cos(2πax	NUM
ap-3509	252	17	)	)	PUNCT
ap-3509	252	18	cos(2πby	cos(2πby	NOUN
ap-3509	252	19	)	)	PUNCT
ap-3509	252	20	,	,	PUNCT
ap-3509	252	21	sa	sa	PROPN
ap-3509	252	22	,	,	PUNCT
ap-3509	252	23	b(x	b(x	NOUN
ap-3509	252	24	)	)	PUNCT
ap-3509	252	25	=	=	SYM
ap-3509	252	26	sa(x)sb(y	sa(x)sb(y	ADJ
ap-3509	252	27	)	)	PUNCT
ap-3509	252	28	=	=	SYM
ap-3509	252	29	−4	−4	X
ap-3509	252	30	sin(2πax	sin(2πax	ADV
ap-3509	252	31	)	)	PUNCT
ap-3509	252	32	sin(2πby	sin(2πby	PROPN
ap-3509	252	33	)	)	PUNCT
ap-3509	252	34	,	,	PUNCT
ap-3509	252	35	csa	csa	PROPN
ap-3509	252	36	,	,	PUNCT
ap-3509	252	37	b(x	b(x	NOUN
ap-3509	252	38	)	)	PUNCT
ap-3509	252	39	=	=	SYM
ap-3509	252	40	ca(x)sb(y	ca(x)sb(y	NOUN
ap-3509	252	41	)	)	PUNCT
ap-3509	253	1	=	=	SYM
ap-3509	253	2	4i	4i	NUM
ap-3509	253	3	cos(2πax	cos(2πax	PROPN
ap-3509	253	4	)	)	PUNCT
ap-3509	253	5	sin(2πby	sin(2πby	PROPN
ap-3509	253	6	)	)	PUNCT
ap-3509	253	7	,	,	PUNCT
ap-3509	253	8	sca	sca	NOUN
ap-3509	253	9	,	,	PUNCT
ap-3509	253	10	b(x	b(x	NOUN
ap-3509	253	11	)	)	PUNCT
ap-3509	253	12	=	=	SYM
ap-3509	253	13	sa(x)cb(y	sa(x)cb(y	ADJ
ap-3509	253	14	)	)	PUNCT
ap-3509	254	1	=	=	SYM
ap-3509	254	2	4i	4i	NUM
ap-3509	254	3	sin(2πax	sin(2πax	ADJ
ap-3509	254	4	)	)	PUNCT
ap-3509	254	5	cos(2πby	cos(2πby	NOUN
ap-3509	254	6	)	)	PUNCT
ap-3509	254	7	,	,	PUNCT
ap-3509	254	8	where	where	SCONJ
ap-3509	254	9	cµ(x	cµ(x	VERB
ap-3509	254	10	)	)	PUNCT
ap-3509	254	11	=	=	SYM
ap-3509	254	12	e2πiµx	e2πiµx	PROPN
ap-3509	254	13	+	+	CCONJ
ap-3509	254	14	e−2πiµx	e−2πiµx	ADJ
ap-3509	254	15	,	,	PUNCT
ap-3509	254	16	sµ(x	sµ(x	NUM
ap-3509	254	17	)	)	PUNCT
ap-3509	255	1	=	=	PUNCT
ap-3509	255	2	e2πiµx	e2πiµx	PROPN
ap-3509	255	3	−	−	PROPN
ap-3509	255	4	e−2πiµx	e−2πiµx	NOUN
ap-3509	255	5	.	.	PUNCT
ap-3509	256	1	the	the	DET
ap-3509	256	2	behaviour	behaviour	NOUN
ap-3509	256	3	of	of	ADP
ap-3509	256	4	c-	c-	X
ap-3509	256	5	,	,	PUNCT
ap-3509	256	6	s-	s-	X
ap-3509	256	7	,	,	PUNCT
ap-3509	256	8	cs-	cs-	ADJ
ap-3509	256	9	,	,	PUNCT
ap-3509	256	10	and	and	CCONJ
ap-3509	256	11	sc	sc	NOUN
ap-3509	256	12	-	-	PUNCT
ap-3509	256	13	functions	function	NOUN
ap-3509	256	14	on	on	ADP
ap-3509	256	15	the	the	DET
ap-3509	256	16	boundary	boundary	ADJ
ap-3509	256	17	∂f	∂f	PROPN
ap-3509	256	18	of	of	ADP
ap-3509	256	19	the	the	DET
ap-3509	256	20	fundamental	fundamental	ADJ
ap-3509	256	21	region	region	NOUN
ap-3509	256	22	f	f	PROPN
ap-3509	256	23	described	describe	VERB
ap-3509	256	24	in	in	ADP
ap-3509	256	25	figure	figure	NOUN
ap-3509	256	26	8	8	NUM
ap-3509	256	27	is	be	AUX
ap-3509	256	28	gathered	gather	VERB
ap-3509	256	29	in	in	ADP
ap-3509	256	30	tables	table	NOUN
ap-3509	256	31	10	10	NUM
ap-3509	256	32	-	-	SYM
ap-3509	256	33	13	13	NUM
ap-3509	256	34	.	.	PUNCT
ap-3509	257	1	the	the	DET
ap-3509	257	2	values	value	NOUN
ap-3509	257	3	if	if	SCONJ
ap-3509	257	4	the	the	DET
ap-3509	257	5	functions	function	NOUN
ap-3509	257	6	we	we	PRON
ap-3509	257	7	write	write	VERB
ap-3509	257	8	using	use	VERB
ap-3509	257	9	a	a	DET
ap-3509	257	10	separation	separation	NOUN
ap-3509	257	11	constant	constant	ADJ
ap-3509	257	12	−k2	−k2	PROPN
ap-3509	257	13	:	:	PUNCT
ap-3509	257	14	−k2	−k2	PROPN
ap-3509	257	15	=	=	PUNCT
ap-3509	257	16	−2a2π2	−2a2π2	PROPN
ap-3509	257	17	,	,	PUNCT
ap-3509	257	18	w2	w2	NOUN
ap-3509	257	19	−	−	PROPN
ap-3509	257	20	k2	k2	PROPN
ap-3509	257	21	=	=	PROPN
ap-3509	257	22	2b2π2	2b2π2	PROPN
ap-3509	257	23	.	.	PUNCT
ap-3509	258	1	in	in	ADP
ap-3509	258	2	figures	figure	NOUN
ap-3509	258	3	11	11	NUM
ap-3509	258	4	and	and	CCONJ
ap-3509	258	5	12	12	NUM
ap-3509	258	6	plots	plot	NOUN
ap-3509	258	7	of	of	ADP
ap-3509	258	8	real	real	ADJ
ap-3509	258	9	and	and	CCONJ
ap-3509	258	10	imaginary	imaginary	ADJ
ap-3509	258	11	part	part	NOUN
ap-3509	258	12	of	of	ADP
ap-3509	258	13	functions	function	NOUN
ap-3509	258	14	with	with	ADP
ap-3509	258	15	weight	weight	NOUN
ap-3509	258	16	λ	λ	NOUN
ap-3509	258	17	=	=	SYM
ap-3509	258	18	(	(	PUNCT
ap-3509	258	19	1	1	NUM
ap-3509	258	20	,	,	PUNCT
ap-3509	258	21	3	3	NUM
ap-3509	258	22	)	)	PUNCT
ap-3509	258	23	are	be	AUX
ap-3509	258	24	shown	show	VERB
ap-3509	258	25	.	.	PUNCT
ap-3509	259	1	acknowledgements	acknowledgement	NOUN
ap-3509	259	2	the	the	DET
ap-3509	259	3	authors	author	NOUN
ap-3509	259	4	would	would	AUX
ap-3509	259	5	like	like	VERB
ap-3509	259	6	to	to	PART
ap-3509	259	7	thank	thank	VERB
ap-3509	259	8	dr	dr	PROPN
ap-3509	259	9	.	.	PROPN
ap-3509	259	10	j.	j.	PROPN
ap-3509	259	11	patera	patera	PROPN
ap-3509	259	12	for	for	ADP
ap-3509	259	13	stimulating	stimulate	VERB
ap-3509	259	14	discussions	discussion	NOUN
ap-3509	259	15	and	and	CCONJ
ap-3509	259	16	comments	comment	NOUN
ap-3509	259	17	.	.	PUNCT
ap-3509	260	1	references	reference	NOUN
ap-3509	260	2	[	[	X
ap-3509	260	3	1	1	NUM
ap-3509	260	4	]	]	X
ap-3509	260	5	n.	n.	NOUN
ap-3509	260	6	bourbaki	bourbaki	PROPN
ap-3509	260	7	,	,	PUNCT
ap-3509	260	8	groupes	groupe	NOUN
ap-3509	260	9	et	et	NOUN
ap-3509	260	10	algèbres	algèbre	NOUN
ap-3509	260	11	de	de	ADP
ap-3509	260	12	lie	lie	NOUN
ap-3509	260	13	,	,	PUNCT
ap-3509	260	14	chapters	chapter	NOUN
ap-3509	260	15	iv	iv	NUM
ap-3509	260	16	,	,	PUNCT
ap-3509	260	17	v	v	NOUN
ap-3509	260	18	,	,	PUNCT
ap-3509	260	19	vi	vi	PROPN
ap-3509	260	20	,	,	PUNCT
ap-3509	260	21	hermann	hermann	PROPN
ap-3509	260	22	,	,	PUNCT
ap-3509	260	23	paris	paris	PROPN
ap-3509	260	24	1968	1968	NUM
ap-3509	260	25	.	.	PUNCT
ap-3509	261	1	[	[	X
ap-3509	261	2	2	2	NUM
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ap-3509	261	17	,	,	PUNCT
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ap-3509	261	21	1999	1999	NUM
ap-3509	261	22	.	.	PUNCT
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ap-3509	262	2	3	3	X
ap-3509	262	3	]	]	X
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ap-3509	263	20	,	,	PUNCT
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ap-3509	263	22	.	.	PUNCT
ap-3509	264	1	j.	j.	PROPN
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ap-3509	264	8	)	)	PUNCT
ap-3509	264	9	,	,	PUNCT
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ap-3509	264	11	-	-	SYM
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ap-3509	264	13	.	.	PUNCT
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ap-3509	265	2	5	5	NUM
ap-3509	265	3	]	]	PUNCT
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ap-3509	265	9	,	,	PUNCT
ap-3509	265	10	orbit	orbit	NOUN
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ap-3509	265	12	,	,	PUNCT
ap-3509	265	13	sigma	sigma	PROPN
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ap-3509	265	15	symmetry	symmetry	NOUN
ap-3509	265	16	,	,	PUNCT
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ap-3509	265	19	geometry	geometry	NOUN
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ap-3509	265	22	and	and	CCONJ
ap-3509	265	23	applications	application	NOUN
ap-3509	265	24	)	)	PUNCT
ap-3509	265	25	2	2	NUM
ap-3509	265	26	(	(	PUNCT
ap-3509	265	27	2006	2006	NUM
ap-3509	265	28	)	)	PUNCT
ap-3509	265	29	,	,	PUNCT
ap-3509	265	30	006	006	NUM
ap-3509	265	31	,	,	PUNCT
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ap-3509	265	34	,	,	PUNCT
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ap-3509	265	36	-	-	PUNCT
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ap-3509	265	38	.	.	PUNCT
ap-3509	266	1	[	[	X
ap-3509	266	2	6	6	NUM
ap-3509	266	3	]	]	X
ap-3509	266	4	f.w	f.w	PROPN
ap-3509	266	5	.	.	PROPN
ap-3509	266	6	lemire	lemire	PROPN
ap-3509	266	7	,	,	PUNCT
ap-3509	266	8	j.	j.	PROPN
ap-3509	266	9	patera	patera	PROPN
ap-3509	266	10	,	,	PUNCT
ap-3509	266	11	m.	m.	NOUN
ap-3509	266	12	szajewska	szajewska	NOUN
ap-3509	266	13	,	,	PUNCT
ap-3509	266	14	dominant	dominant	ADJ
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ap-3509	266	17	in	in	ADP
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ap-3509	266	22	,	,	PUNCT
ap-3509	266	23	cn	cn	PROPN
ap-3509	266	24	,	,	PUNCT
ap-3509	266	25	f4	f4	PROPN
ap-3509	266	26	,	,	PUNCT
ap-3509	266	27	g2	g2	PROPN
ap-3509	266	28	,	,	PUNCT
ap-3509	266	29	internat	internat	PROPN
ap-3509	266	30	.	.	PUNCT
ap-3509	267	1	j.	j.	PROPN
ap-3509	267	2	theoret	theoret	PROPN
ap-3509	267	3	.	.	PUNCT
ap-3509	268	1	phys	phy	NOUN
ap-3509	268	2	.	.	PUNCT
ap-3509	268	3	,	,	PUNCT
ap-3509	268	4	vol	vol	NOUN
ap-3509	268	5	.	.	PROPN
ap-3509	268	6	54	54	NUM
ap-3509	268	7	(	(	PUNCT
ap-3509	268	8	11	11	NUM
ap-3509	268	9	)	)	PUNCT
ap-3509	268	10	(	(	PUNCT
ap-3509	268	11	2015	2015	NUM
ap-3509	268	12	)	)	PUNCT
ap-3509	268	13	,	,	PUNCT
ap-3509	268	14	4011	4011	NUM
ap-3509	268	15	-	-	SYM
ap-3509	268	16	4026	4026	NUM
ap-3509	268	17	.	.	PUNCT
ap-3509	269	1	[	[	X
ap-3509	269	2	7	7	X
ap-3509	269	3	]	]	X
ap-3509	269	4	w.	w.	PROPN
ap-3509	269	5	miller	miller	PROPN
ap-3509	269	6	,	,	PUNCT
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ap-3509	269	8	and	and	CCONJ
ap-3509	269	9	separation	separation	NOUN
ap-3509	269	10	of	of	ADP
ap-3509	269	11	variables	variable	NOUN
ap-3509	269	12	,	,	PUNCT
ap-3509	269	13	with	with	ADP
ap-3509	269	14	a	a	DET
ap-3509	269	15	foreword	foreword	NOUN
ap-3509	269	16	by	by	ADP
ap-3509	269	17	richard	richard	PROPN
ap-3509	269	18	askey	askey	PROPN
ap-3509	269	19	,	,	PUNCT
ap-3509	269	20	encyclopedia	encyclopedia	NOUN
ap-3509	269	21	of	of	ADP
ap-3509	269	22	mathematics	mathematic	NOUN
ap-3509	269	23	and	and	CCONJ
ap-3509	269	24	its	its	PRON
ap-3509	269	25	applications	application	NOUN
ap-3509	269	26	4	4	NUM
ap-3509	269	27	,	,	PUNCT
ap-3509	269	28	addison	addison	PROPN
ap-3509	269	29	-	-	PUNCT
ap-3509	269	30	wesley	wesley	PROPN
ap-3509	269	31	publishing	publishing	PROPN
ap-3509	269	32	co.	co.	PROPN
ap-3509	269	33	,	,	PUNCT
ap-3509	269	34	reading	reading	NOUN
ap-3509	269	35	,	,	PUNCT
ap-3509	269	36	mass.-london	mass.-london	PROPN
ap-3509	269	37	-	-	ADJ
ap-3509	269	38	amsterdam	amsterdam	ADJ
ap-3509	269	39	,	,	PUNCT
ap-3509	269	40	1977	1977	NUM
ap-3509	269	41	.	.	PUNCT
ap-3509	270	1	[	[	X
ap-3509	270	2	8	8	NUM
ap-3509	270	3	]	]	X
ap-3509	270	4	p.	p.	NOUN
ap-3509	270	5	moon	moon	PROPN
ap-3509	270	6	,	,	PUNCT
ap-3509	270	7	d.e	d.e	PROPN
ap-3509	270	8	.	.	PROPN
ap-3509	270	9	spencer	spencer	PROPN
ap-3509	270	10	,	,	PUNCT
ap-3509	270	11	field	field	NOUN
ap-3509	270	12	theory	theory	NOUN
ap-3509	270	13	handbook	handbook	NOUN
ap-3509	270	14	,	,	PUNCT
ap-3509	270	15	including	include	VERB
ap-3509	270	16	coordinate	coordinate	NOUN
ap-3509	270	17	systems	system	NOUN
ap-3509	270	18	,	,	PUNCT
ap-3509	270	19	differential	differential	ADJ
ap-3509	270	20	equations	equation	NOUN
ap-3509	270	21	,	,	PUNCT
ap-3509	270	22	and	and	CCONJ
ap-3509	270	23	their	their	PRON
ap-3509	270	24	solutions	solution	NOUN
ap-3509	270	25	,	,	PUNCT
ap-3509	270	26	2nd	2nd	ADJ
ap-3509	270	27	ed	ed	NOUN
ap-3509	270	28	.	.	PUNCT
ap-3509	271	1	new	new	PROPN
ap-3509	271	2	york	york	PROPN
ap-3509	271	3	:	:	PUNCT
ap-3509	271	4	springer	springer	NOUN
ap-3509	271	5	-	-	PUNCT
ap-3509	271	6	verlag	verlag	PROPN
ap-3509	271	7	,	,	PUNCT
ap-3509	271	8	1988	1988	NUM
ap-3509	271	9	.	.	PUNCT
ap-3509	272	1	[	[	X
ap-3509	272	2	9	9	NUM
ap-3509	272	3	]	]	PUNCT
ap-3509	272	4	l.	l.	PROPN
ap-3509	272	5	motlochova	motlochova	PROPN
ap-3509	272	6	,	,	PUNCT
ap-3509	272	7	j.	j.	PROPN
ap-3509	272	8	patera	patera	PROPN
ap-3509	272	9	,	,	PUNCT
ap-3509	272	10	four	four	NUM
ap-3509	272	11	families	family	NOUN
ap-3509	272	12	of	of	ADP
ap-3509	272	13	orthogonal	orthogonal	ADJ
ap-3509	272	14	polynomials	polynomial	NOUN
ap-3509	272	15	of	of	ADP
ap-3509	272	16	c2	c2	PROPN
ap-3509	272	17	and	and	CCONJ
ap-3509	272	18	symmetric	symmetric	ADJ
ap-3509	272	19	and	and	CCONJ
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ap-3509	272	22	of	of	ADP
ap-3509	272	23	sine	sine	NOUN
ap-3509	272	24	and	and	CCONJ
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ap-3509	272	26	functions	function	NOUN
ap-3509	272	27	,	,	PUNCT
ap-3509	272	28	eprint	eprint	NOUN
ap-3509	272	29	arxiv:1101.3597	arxiv:1101.3597	PROPN
ap-3509	272	30	.	.	PUNCT
ap-3509	273	1	[	[	X
ap-3509	273	2	10	10	NUM
ap-3509	273	3	]	]	X
ap-3509	273	4	r.v	r.v	PROPN
ap-3509	273	5	.	.	PROPN
ap-3509	273	6	moody	moody	PROPN
ap-3509	273	7	,	,	PUNCT
ap-3509	273	8	l.	l.	PROPN
ap-3509	273	9	motlochova	motlochova	PROPN
ap-3509	273	10	,	,	PUNCT
ap-3509	273	11	j.	j.	PROPN
ap-3509	273	12	patera	patera	PROPN
ap-3509	273	13	,	,	PUNCT
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ap-3509	273	17	from	from	ADP
ap-3509	273	18	hybrid	hybrid	ADJ
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ap-3509	273	20	of	of	ADP
ap-3509	273	21	simple	simple	ADJ
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ap-3509	273	24	,	,	PUNCT
ap-3509	273	25	j.	j.	PROPN
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ap-3509	273	28	and	and	CCONJ
ap-3509	273	29	its	its	PRON
ap-3509	273	30	applications	application	NOUN
ap-3509	273	31	,	,	PUNCT
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ap-3509	273	33	issn	issn	PROPN
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ap-3509	273	35	-	-	SYM
ap-3509	273	36	5851	5851	NUM
ap-3509	273	37	(	(	PUNCT
ap-3509	273	38	2014	2014	NUM
ap-3509	273	39	)	)	PUNCT
ap-3509	273	40	,	,	PUNCT
ap-3509	273	41	doi	doi	X
ap-3509	273	42	10.1007	10.1007	NUM
ap-3509	273	43	/	/	SYM
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ap-3509	273	45	-	-	PUNCT
ap-3509	273	46	014	014	NUM
ap-3509	273	47	-	-	PUNCT
ap-3509	273	48	9355	9355	NUM
ap-3509	273	49	-	-	SYM
ap-3509	273	50	0	0	NUM
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ap-3509	275	3	.	.	PUNCT
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ap-3509	276	3	-	-	PUNCT
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ap-3509	276	27	polynomials	polynomial	NOUN
ap-3509	276	28	of	of	ADP
ap-3509	276	29	compact	compact	ADJ
ap-3509	276	30	simple	simple	ADJ
ap-3509	276	31	lie	lie	NOUN
ap-3509	276	32	groups	group	NOUN
ap-3509	276	33	:	:	PUNCT
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ap-3509	276	35	rules	rule	NOUN
ap-3509	276	36	for	for	ADP
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ap-3509	276	38	,	,	PUNCT
ap-3509	276	39	j.	j.	PROPN
ap-3509	276	40	phys	phys	PROPN
ap-3509	276	41	.	.	PUNCT
ap-3509	277	1	a	a	DET
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ap-3509	277	3	.	.	PUNCT
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ap-3509	279	1	43	43	NUM
ap-3509	279	2	(	(	PUNCT
ap-3509	279	3	2010	2010	NUM
ap-3509	279	4	)	)	PUNCT
ap-3509	279	5	,	,	PUNCT
ap-3509	280	1	no	no	INTJ
ap-3509	280	2	.	.	NOUN
ap-3509	280	3	495207	495207	NUM
ap-3509	280	4	,	,	PUNCT
ap-3509	280	5	1–27	1–27	NOUN
ap-3509	280	6	.	.	PUNCT
ap-3509	281	1	[	[	X
ap-3509	281	2	12	12	NUM
ap-3509	281	3	]	]	PUNCT
ap-3509	281	4	p.	p.	NOUN
ap-3509	281	5	olver	olver	NOUN
ap-3509	281	6	,	,	PUNCT
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ap-3509	281	8	to	to	ADP
ap-3509	281	9	partial	partial	ADJ
ap-3509	281	10	differential	differential	NOUN
ap-3509	281	11	equations	equation	NOUN
ap-3509	281	12	,	,	PUNCT
ap-3509	281	13	springer	springer	NOUN
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ap-3509	281	15	publishing	publishing	NOUN
ap-3509	281	16	,	,	PUNCT
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ap-3509	282	2	13	13	NUM
ap-3509	282	3	]	]	PUNCT
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ap-3509	282	8	types	type	NOUN
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ap-3509	282	11	functions	function	NOUN
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ap-3509	282	15	their	their	PRON
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ap-3509	282	17	,	,	PUNCT
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ap-3509	282	19	transform	transform	NOUN
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ap-3509	283	1	spec	spec	PROPN
ap-3509	283	2	.	.	PUNCT
ap-3509	284	1	funct	funct	PROPN
ap-3509	284	2	.	.	PUNCT
ap-3509	285	1	vol	vol	NOUN
ap-3509	285	2	.	.	PUNCT
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ap-3509	286	2	(	(	PUNCT
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ap-3509	286	4	)	)	PUNCT
ap-3509	286	5	(	(	PUNCT
ap-3509	286	6	2012	2012	NUM
ap-3509	286	7	)	)	PUNCT
ap-3509	286	8	,	,	PUNCT
ap-3509	287	1	455–472	455–472	NUM
ap-3509	287	2	.	.	PUNCT
ap-3509	288	1	[	[	X
ap-3509	288	2	14	14	NUM
ap-3509	288	3	]	]	PUNCT
ap-3509	288	4	m.	m.	NOUN
ap-3509	288	5	szajewska	szajewska	NOUN
ap-3509	288	6	,	,	PUNCT
ap-3509	288	7	special	special	ADJ
ap-3509	288	8	functions	function	NOUN
ap-3509	288	9	and	and	CCONJ
ap-3509	288	10	orthogonal	orthogonal	ADJ
ap-3509	288	11	polynomials	polynomial	NOUN
ap-3509	288	12	of	of	ADP
ap-3509	288	13	compact	compact	ADJ
ap-3509	288	14	simple	simple	ADJ
ap-3509	288	15	lie	lie	NOUN
ap-3509	288	16	groups	group	NOUN
ap-3509	288	17	and	and	CCONJ
ap-3509	288	18	some	some	PRON
ap-3509	288	19	of	of	ADP
ap-3509	288	20	their	their	PRON
ap-3509	288	21	applications	application	NOUN
ap-3509	288	22	,	,	PUNCT
ap-3509	288	23	warsaw	warsaw	PROPN
ap-3509	288	24	university	university	PROPN
ap-3509	288	25	of	of	ADP
ap-3509	288	26	technology	technology	NOUN
ap-3509	288	27	,	,	PUNCT
ap-3509	288	28	faculty	faculty	NOUN
ap-3509	288	29	of	of	ADP
ap-3509	288	30	mathematics	mathematic	NOUN
ap-3509	288	31	and	and	CCONJ
ap-3509	288	32	information	information	NOUN
ap-3509	288	33	science	science	NOUN
ap-3509	288	34	,	,	PUNCT
ap-3509	288	35	2011	2011	NUM
ap-3509	288	36	.	.	PUNCT
ap-3509	289	1	[	[	X
ap-3509	289	2	15	15	NUM
ap-3509	289	3	]	]	X
ap-3509	289	4	a.n	a.n	PROPN
ap-3509	289	5	.	.	PROPN
ap-3509	289	6	tikhonov	tikhonov	PROPN
ap-3509	289	7	,	,	PUNCT
ap-3509	289	8	a.a	a.a	PROPN
ap-3509	289	9	.	.	PROPN
ap-3509	289	10	samarskii	samarskii	PROPN
ap-3509	289	11	,	,	PUNCT
ap-3509	289	12	equations	equation	NOUN
ap-3509	289	13	of	of	ADP
ap-3509	289	14	mathematical	mathematical	ADJ
ap-3509	289	15	physics	physics	PROPN
ap-3509	289	16	,	,	PUNCT
ap-3509	289	17	dover	dover	PROPN
ap-3509	289	18	publ	publ	PROPN
ap-3509	289	19	.	.	PUNCT
ap-3509	289	20	,	,	PUNCT
ap-3509	289	21	new	new	PROPN
ap-3509	289	22	york	york	PROPN
ap-3509	289	23	,	,	PUNCT
ap-3509	289	24	1990	1990	NUM
ap-3509	289	25	.	.	PUNCT
ap-3509	290	1	[	[	X
ap-3509	290	2	16	16	NUM
ap-3509	290	3	]	]	PUNCT
ap-3509	290	4	s.	s.	PROPN
ap-3509	290	5	timoshenko	timoshenko	PROPN
ap-3509	290	6	,	,	PUNCT
ap-3509	290	7	j.n	j.n	PROPN
ap-3509	290	8	.	.	PROPN
ap-3509	290	9	goodier	goodier	NOUN
ap-3509	290	10	,	,	PUNCT
ap-3509	290	11	theory	theory	NOUN
ap-3509	290	12	of	of	ADP
ap-3509	290	13	elasticity	elasticity	NOUN
ap-3509	290	14	,	,	PUNCT
ap-3509	290	15	mcgraw	mcgraw	PROPN
ap-3509	290	16	-	-	PUNCT
ap-3509	290	17	hill	hill	NOUN
ap-3509	290	18	book	book	NOUN
ap-3509	290	19	company	company	PROPN
ap-3509	290	20	,	,	PUNCT
ap-3509	290	21	inc	inc	PROPN
ap-3509	290	22	.	.	PROPN
ap-3509	290	23	,	,	PUNCT
ap-3509	290	24	new	new	PROPN
ap-3509	290	25	york	york	PROPN
ap-3509	290	26	,	,	PUNCT
ap-3509	290	27	1961	1961	NUM
ap-3509	290	28	.	.	PUNCT
ap-3509	291	1	253	253	NUM
ap-3509	291	2	acta	acta	PROPN
ap-3509	291	3	polytechnica	polytechnica	PROPN
ap-3509	291	4	56(3):245–253	56(3):245–253	PROPN
ap-3509	291	5	,	,	PUNCT
ap-3509	291	6	2016	2016	NUM
ap-3509	291	7	1	1	NUM
ap-3509	291	8	introduction	introduction	NOUN
ap-3509	291	9	2	2	NUM
ap-3509	291	10	weyl	weyl	NOUN
ap-3509	291	11	group	group	NOUN
ap-3509	291	12	c2	c2	PROPN
ap-3509	291	13	and	and	CCONJ
ap-3509	291	14	g2	g2	PROPN
ap-3509	291	15	3	3	NUM
ap-3509	291	16	c-	c-	NOUN
ap-3509	291	17	,	,	PUNCT
ap-3509	291	18	s-	s-	X
ap-3509	291	19	,	,	PUNCT
ap-3509	291	20	ss-	ss-	X
ap-3509	291	21	,	,	PUNCT
ap-3509	291	22	and	and	CCONJ
ap-3509	291	23	sl	sl	NOUN
ap-3509	291	24	-	-	PUNCT
ap-3509	291	25	functions	function	NOUN
ap-3509	291	26	of	of	ADP
ap-3509	291	27	g	g	NOUN
ap-3509	291	28	=	=	NOUN
ap-3509	291	29	c2	c2	PROPN
ap-3509	291	30	or	or	CCONJ
ap-3509	291	31	g2	g2	PROPN
ap-3509	291	32	3.1	3.1	NUM
ap-3509	291	33	explicit	explicit	ADJ
ap-3509	291	34	forms	form	NOUN
ap-3509	291	35	of	of	ADP
ap-3509	291	36	cand	cand	NOUN
ap-3509	291	37	s	s	NOUN
ap-3509	291	38	-	-	PUNCT
ap-3509	291	39	functions	function	NOUN
ap-3509	291	40	3.2	3.2	NUM
ap-3509	291	41	explicit	explicit	ADJ
ap-3509	291	42	form	form	NOUN
ap-3509	291	43	of	of	ADP
ap-3509	291	44	ss	ss	NOUN
ap-3509	291	45	and	and	CCONJ
ap-3509	291	46	sl	sl	NOUN
ap-3509	291	47	-	-	PUNCT
ap-3509	291	48	functions	function	NOUN
ap-3509	291	49	4	4	NUM
ap-3509	291	50	helmholtz	helmholtz	NOUN
ap-3509	291	51	differential	differential	ADJ
ap-3509	291	52	equation	equation	NOUN
ap-3509	291	53	4.1	4.1	NUM
ap-3509	291	54	separation	separation	NOUN
ap-3509	291	55	of	of	ADP
ap-3509	291	56	variables	variable	NOUN
ap-3509	291	57	for	for	ADP
ap-3509	291	58	the	the	DET
ap-3509	291	59	helmholtz	helmholtz	NOUN
ap-3509	291	60	equation	equation	NOUN
ap-3509	291	61	4.2	4.2	NUM
ap-3509	291	62	c2	c2	PROPN
ap-3509	291	63	case	case	NOUN
ap-3509	291	64	4.3	4.3	NUM
ap-3509	291	65	g2	g2	PROPN
ap-3509	291	66	case	case	NOUN
ap-3509	291	67	5	5	NUM
ap-3509	291	68	types	type	NOUN
ap-3509	291	69	of	of	ADP
ap-3509	291	70	boundary	boundary	ADJ
ap-3509	291	71	conditions	condition	NOUN
ap-3509	291	72	5.1	5.1	NUM
ap-3509	291	73	c2	c2	PROPN
ap-3509	291	74	case	case	NOUN
ap-3509	291	75	5.2	5.2	NUM
ap-3509	291	76	g2	g2	PROPN
ap-3509	291	77	case	case	NOUN
ap-3509	291	78	6	6	NUM
ap-3509	291	79	appendix	appendix	ADJ
ap-3509	291	80	acknowledgements	acknowledgement	NOUN
ap-3509	291	81	references	reference	NOUN