id	sid	tid	token	lemma	pos
ejpam-115	1	1	european	european	PROPN
ejpam-115	1	2	journal	journal	PROPN
ejpam-115	1	3	of	of	ADP
ejpam-115	1	4	pure	pure	ADJ
ejpam-115	1	5	and	and	CCONJ
ejpam-115	1	6	applied	apply	VERB
ejpam-115	1	7	mathematics	mathematic	NOUN
ejpam-115	1	8	vol	vol	NOUN
ejpam-115	1	9	.	.	PROPN
ejpam-115	2	1	1	1	NUM
ejpam-115	2	2	,	,	PUNCT
ejpam-115	2	3	no	no	INTJ
ejpam-115	2	4	.	.	NOUN
ejpam-115	2	5	2	2	NUM
ejpam-115	2	6	,	,	PUNCT
ejpam-115	2	7	2008	2008	NUM
ejpam-115	2	8	,	,	PUNCT
ejpam-115	2	9	(	(	PUNCT
ejpam-115	2	10	51	51	NUM
ejpam-115	2	11	-	-	SYM
ejpam-115	2	12	60	60	NUM
ejpam-115	2	13	)	)	PUNCT
ejpam-115	2	14	issn	issn	PROPN
ejpam-115	2	15	1307	1307	NUM
ejpam-115	2	16	-	-	SYM
ejpam-115	2	17	5543	5543	NUM
ejpam-115	2	18	–	–	PUNCT
ejpam-115	2	19	www.ejpam.com	www.ejpam.com	X
ejpam-115	2	20	on	on	ADP
ejpam-115	2	21	the	the	DET
ejpam-115	2	22	basisness	basisness	NOUN
ejpam-115	2	23	inl2(0	inl2(0	PROPN
ejpam-115	2	24	,	,	PUNCT
ejpam-115	2	25	1	1	NUM
ejpam-115	2	26	)	)	PUNCT
ejpam-115	2	27	of	of	ADP
ejpam-115	2	28	the	the	DET
ejpam-115	2	29	root	root	NOUN
ejpam-115	2	30	functions	function	NOUN
ejpam-115	2	31	in	in	ADP
ejpam-115	2	32	not	not	PART
ejpam-115	2	33	strongly	strongly	ADV
ejpam-115	2	34	regular	regular	ADJ
ejpam-115	2	35	boundary	boundary	ADJ
ejpam-115	2	36	value	value	NOUN
ejpam-115	2	37	problems	problem	NOUN
ejpam-115	2	38	khanlar	khanlar	PROPN
ejpam-115	2	39	r.	r.	PROPN
ejpam-115	2	40	mamedov∗	mamedov∗	PROPN
ejpam-115	2	41	,	,	PUNCT
ejpam-115	2	42	hamza	hamza	PROPN
ejpam-115	2	43	menken	menken	PROPN
ejpam-115	2	44	mathematics	mathematics	PROPN
ejpam-115	2	45	department	department	PROPN
ejpam-115	2	46	,	,	PUNCT
ejpam-115	2	47	science	science	NOUN
ejpam-115	2	48	and	and	CCONJ
ejpam-115	2	49	arts	art	NOUN
ejpam-115	2	50	faculty	faculty	PROPN
ejpam-115	2	51	,	,	PUNCT
ejpam-115	2	52	mersin	mersin	PROPN
ejpam-115	2	53	university	university	PROPN
ejpam-115	2	54	3343	3343	NUM
ejpam-115	2	55	,	,	PUNCT
ejpam-115	2	56	ciftlikkoy	ciftlikkoy	PROPN
ejpam-115	2	57	campus	campus	PROPN
ejpam-115	2	58	,	,	PUNCT
ejpam-115	2	59	mersin	mersin	PROPN
ejpam-115	2	60	,	,	PUNCT
ejpam-115	2	61	turkey	turkey	NOUN
ejpam-115	2	62	abstract	abstract	NOUN
ejpam-115	2	63	.	.	PUNCT
ejpam-115	3	1	in	in	ADP
ejpam-115	3	2	the	the	DET
ejpam-115	3	3	present	present	ADJ
ejpam-115	3	4	article	article	NOUN
ejpam-115	3	5	we	we	PRON
ejpam-115	3	6	consider	consider	VERB
ejpam-115	3	7	the	the	DET
ejpam-115	3	8	non	non	ADJ
ejpam-115	3	9	-	-	ADJ
ejpam-115	3	10	self	self	ADJ
ejpam-115	3	11	adjoint	adjoint	NOUN
ejpam-115	3	12	sturm	sturm	PROPN
ejpam-115	3	13	-	-	PUNCT
ejpam-115	3	14	liouville	liouville	NOUN
ejpam-115	3	15	operators	operator	NOUN
ejpam-115	3	16	with	with	ADP
ejpam-115	3	17	periodic	periodic	ADJ
ejpam-115	3	18	and	and	CCONJ
ejpam-115	3	19	anti	anti	ADJ
ejpam-115	3	20	-	-	ADJ
ejpam-115	3	21	periodic	periodic	ADJ
ejpam-115	3	22	boundary	boundary	ADJ
ejpam-115	3	23	conditions	condition	NOUN
ejpam-115	3	24	which	which	PRON
ejpam-115	3	25	are	be	AUX
ejpam-115	3	26	not	not	PART
ejpam-115	3	27	strongly	strongly	ADV
ejpam-115	3	28	regular	regular	ADJ
ejpam-115	3	29	.	.	PUNCT
ejpam-115	4	1	we	we	PRON
ejpam-115	4	2	obtain	obtain	VERB
ejpam-115	4	3	the	the	DET
ejpam-115	4	4	asymptotic	asymptotic	ADJ
ejpam-115	4	5	formulas	formula	NOUN
ejpam-115	4	6	for	for	ADP
ejpam-115	4	7	eigenvalues	eigenvalue	NOUN
ejpam-115	4	8	and	and	CCONJ
ejpam-115	4	9	eigenfunctions	eigenfunction	NOUN
ejpam-115	4	10	of	of	ADP
ejpam-115	4	11	these	these	DET
ejpam-115	4	12	boundary	boundary	ADJ
ejpam-115	4	13	value	value	NOUN
ejpam-115	4	14	problems	problem	NOUN
ejpam-115	4	15	,	,	PUNCT
ejpam-115	4	16	when	when	SCONJ
ejpam-115	4	17	the	the	DET
ejpam-115	4	18	potentialq(x	potentialq(x	NOUN
ejpam-115	4	19	)	)	PUNCT
ejpam-115	4	20	is	be	AUX
ejpam-115	4	21	a	a	DET
ejpam-115	4	22	complexvalued	complexvalued	ADJ
ejpam-115	4	23	function	function	NOUN
ejpam-115	4	24	.	.	PUNCT
ejpam-115	5	1	then	then	ADV
ejpam-115	5	2	using	use	VERB
ejpam-115	5	3	these	these	DET
ejpam-115	5	4	asymptotic	asymptotic	ADJ
ejpam-115	5	5	formulas	formula	NOUN
ejpam-115	5	6	,	,	PUNCT
ejpam-115	5	7	the	the	DET
ejpam-115	5	8	riesz	riesz	NOUN
ejpam-115	5	9	basisness	basisness	NOUN
ejpam-115	5	10	inl2(0	inl2(0	PROPN
ejpam-115	5	11	,	,	PUNCT
ejpam-115	5	12	1	1	NUM
ejpam-115	5	13	)	)	PUNCT
ejpam-115	5	14	of	of	ADP
ejpam-115	5	15	the	the	DET
ejpam-115	5	16	root	root	NOUN
ejpam-115	5	17	functions	function	NOUN
ejpam-115	5	18	are	be	AUX
ejpam-115	5	19	proved	prove	VERB
ejpam-115	5	20	.	.	PUNCT
ejpam-115	6	1	ams	am	NOUN
ejpam-115	6	2	subject	subject	ADJ
ejpam-115	6	3	classifications	classification	NOUN
ejpam-115	6	4	:	:	PUNCT
ejpam-115	6	5	34l10	34l10	NUM
ejpam-115	6	6	,	,	PUNCT
ejpam-115	6	7	34b24	34b24	NUM
ejpam-115	6	8	,	,	PUNCT
ejpam-115	6	9	47e05	47e05	NUM
ejpam-115	6	10	key	key	ADJ
ejpam-115	6	11	words	word	NOUN
ejpam-115	6	12	:	:	PUNCT
ejpam-115	6	13	riesz	riesz	VERB
ejpam-115	6	14	basis	basis	NOUN
ejpam-115	6	15	,	,	PUNCT
ejpam-115	6	16	periodic	periodic	ADJ
ejpam-115	6	17	and	and	CCONJ
ejpam-115	6	18	anti	anti	ADJ
ejpam-115	6	19	-	-	ADJ
ejpam-115	6	20	periodic	periodic	ADJ
ejpam-115	6	21	boundary	boundary	ADJ
ejpam-115	6	22	conditions	condition	NOUN
ejpam-115	6	23	,	,	PUNCT
ejpam-115	6	24	not	not	PART
ejpam-115	6	25	strongly	strongly	ADV
ejpam-115	6	26	regular	regular	ADJ
ejpam-115	6	27	boundary	boundary	ADJ
ejpam-115	6	28	conditions	condition	NOUN
ejpam-115	6	29	,	,	PUNCT
ejpam-115	6	30	eigenvalue	eigenvalue	NOUN
ejpam-115	6	31	,	,	PUNCT
ejpam-115	6	32	eigenfunction	eigenfunction	NOUN
ejpam-115	6	33	,	,	PUNCT
ejpam-115	6	34	non	non	ADJ
ejpam-115	6	35	-	-	ADJ
ejpam-115	6	36	self	self	ADJ
ejpam-115	6	37	adjoint	adjoint	NOUN
ejpam-115	6	38	sturm	sturm	PROPN
ejpam-115	6	39	-	-	PUNCT
ejpam-115	6	40	liouville	liouville	NOUN
ejpam-115	6	41	operator	operator	NOUN
ejpam-115	6	42	,	,	PUNCT
ejpam-115	6	43	bari	bari	NOUN
ejpam-115	6	44	’s	’s	PART
ejpam-115	6	45	theorem	theorem	ADJ
ejpam-115	6	46	.	.	PROPN
ejpam-115	7	1	1	1	X
ejpam-115	7	2	.	.	X
ejpam-115	7	3	introduction	introduction	NOUN
ejpam-115	7	4	it	it	PRON
ejpam-115	7	5	is	be	AUX
ejpam-115	7	6	well	well	ADV
ejpam-115	7	7	known	know	VERB
ejpam-115	7	8	that	that	SCONJ
ejpam-115	7	9	the	the	DET
ejpam-115	7	10	basisness	basisness	NOUN
ejpam-115	7	11	of	of	ADP
ejpam-115	7	12	the	the	DET
ejpam-115	7	13	root	root	NOUN
ejpam-115	7	14	functions	function	NOUN
ejpam-115	7	15	of	of	ADP
ejpam-115	7	16	a	a	DET
ejpam-115	7	17	differential	differential	ADJ
ejpam-115	7	18	operator	operator	NOUN
ejpam-115	7	19	depends	depend	VERB
ejpam-115	7	20	on	on	ADP
ejpam-115	7	21	regularity	regularity	NOUN
ejpam-115	7	22	of	of	ADP
ejpam-115	7	23	boundary	boundary	ADJ
ejpam-115	7	24	conditions	condition	NOUN
ejpam-115	7	25	generating	generate	VERB
ejpam-115	7	26	the	the	DET
ejpam-115	7	27	given	give	VERB
ejpam-115	7	28	differential	differential	ADJ
ejpam-115	7	29	operator	operator	NOUN
ejpam-115	7	30	.	.	PUNCT
ejpam-115	8	1	the	the	DET
ejpam-115	8	2	basisness	basisness	NOUN
ejpam-115	8	3	in	in	ADP
ejpam-115	8	4	the	the	DET
ejpam-115	8	5	spacel2(0	spacel2(0	PROPN
ejpam-115	8	6	,	,	PUNCT
ejpam-115	8	7	1	1	NUM
ejpam-115	8	8	)	)	PUNCT
ejpam-115	8	9	of	of	ADP
ejpam-115	8	10	the	the	DET
ejpam-115	8	11	root	root	NOUN
ejpam-115	8	12	functions	function	NOUN
ejpam-115	8	13	of	of	ADP
ejpam-115	8	14	a	a	DET
ejpam-115	8	15	linear	linear	ADJ
ejpam-115	8	16	differential	differential	NOUN
ejpam-115	8	17	operator	operator	NOUN
ejpam-115	8	18	of	of	ADP
ejpam-115	8	19	ordern	ordern	ADJ
ejpam-115	8	20	with	with	ADP
ejpam-115	8	21	regular	regular	ADJ
ejpam-115	8	22	(	(	PUNCT
ejpam-115	8	23	strongly	strongly	ADV
ejpam-115	8	24	regular	regular	ADJ
ejpam-115	8	25	,	,	PUNCT
ejpam-115	8	26	see	see	VERB
ejpam-115	8	27	.	.	PUNCT
ejpam-115	9	1	[	[	X
ejpam-115	9	2	1	1	NUM
ejpam-115	9	3	]	]	PUNCT
ejpam-115	9	4	,	,	PUNCT
ejpam-115	9	5	p.71	p.71	PROPN
ejpam-115	9	6	)	)	PUNCT
ejpam-115	9	7	boundary	boundary	ADJ
ejpam-115	9	8	conditions	condition	NOUN
ejpam-115	9	9	is	be	AUX
ejpam-115	9	10	shown	show	VERB
ejpam-115	9	11	in	in	ADP
ejpam-115	9	12	[	[	X
ejpam-115	9	13	2	2	NUM
ejpam-115	9	14	,	,	PUNCT
ejpam-115	9	15	3	3	NUM
ejpam-115	9	16	]	]	PUNCT
ejpam-115	9	17	.	.	PUNCT
ejpam-115	10	1	in	in	ADP
ejpam-115	10	2	[	[	X
ejpam-115	10	3	2	2	NUM
ejpam-115	10	4	,	,	PUNCT
ejpam-115	10	5	4	4	NUM
ejpam-115	10	6	,	,	PUNCT
ejpam-115	10	7	5	5	NUM
ejpam-115	10	8	]	]	PUNCT
ejpam-115	10	9	it	it	PRON
ejpam-115	10	10	is	be	AUX
ejpam-115	10	11	shown	show	VERB
ejpam-115	10	12	that	that	SCONJ
ejpam-115	10	13	the	the	DET
ejpam-115	10	14	root	root	NOUN
ejpam-115	10	15	functions	function	NOUN
ejpam-115	10	16	of	of	ADP
ejpam-115	10	17	a	a	DET
ejpam-115	10	18	boundary	boundary	ADJ
ejpam-115	10	19	problem	problem	NOUN
ejpam-115	10	20	which	which	PRON
ejpam-115	10	21	is	be	AUX
ejpam-115	10	22	generated	generate	VERB
ejpam-115	10	23	by	by	ADP
ejpam-115	10	24	not	not	PART
ejpam-115	10	25	strongly	strongly	ADV
ejpam-115	10	26	regular	regular	ADJ
ejpam-115	10	27	boundary	boundary	ADJ
ejpam-115	10	28	conditions	condition	NOUN
ejpam-115	10	29	may	may	AUX
ejpam-115	10	30	not	not	PART
ejpam-115	10	31	be	be	AUX
ejpam-115	10	32	form	form	NOUN
ejpam-115	10	33	a	a	DET
ejpam-115	10	34	basis	basis	NOUN
ejpam-115	10	35	inl2(0	inl2(0	NOUN
ejpam-115	10	36	,	,	PUNCT
ejpam-115	10	37	1	1	NUM
ejpam-115	10	38	)	)	PUNCT
ejpam-115	10	39	.	.	PUNCT
ejpam-115	11	1	in	in	ADP
ejpam-115	11	2	[	[	X
ejpam-115	11	3	6	6	NUM
ejpam-115	11	4	]	]	PUNCT
ejpam-115	11	5	,	,	PUNCT
ejpam-115	11	6	one	one	NUM
ejpam-115	11	7	non	non	ADJ
ejpam-115	11	8	-	-	ADJ
ejpam-115	11	9	classical	classical	ADJ
ejpam-115	11	10	heat	heat	NOUN
ejpam-115	11	11	conduction	conduction	NOUN
ejpam-115	11	12	problem	problem	NOUN
ejpam-115	11	13	in	in	ADP
ejpam-115	11	14	homogeneous	homogeneous	ADJ
ejpam-115	11	15	rod	rod	NOUN
ejpam-115	11	16	has	have	AUX
ejpam-115	11	17	been	be	AUX
ejpam-115	11	18	studied	study	VERB
ejpam-115	11	19	.	.	PUNCT
ejpam-115	12	1	this	this	DET
ejpam-115	12	2	problem	problem	NOUN
ejpam-115	12	3	is	be	AUX
ejpam-115	12	4	reduced	reduce	VERB
ejpam-115	12	5	to	to	ADP
ejpam-115	12	6	the	the	DET
ejpam-115	12	7	following	follow	VERB
ejpam-115	12	8	boundary	boundary	ADJ
ejpam-115	12	9	value	value	NOUN
ejpam-115	12	10	problem	problem	NOUN
ejpam-115	12	11	−y′′(x	−y′′(x	NOUN
ejpam-115	12	12	)	)	PUNCT
ejpam-115	12	13	=	=	PUNCT
ejpam-115	12	14	λy(x	λy(x	NOUN
ejpam-115	12	15	)	)	PUNCT
ejpam-115	12	16	,	,	PUNCT
ejpam-115	12	17	0	0	PUNCT
ejpam-115	12	18	<	<	X
ejpam-115	12	19	x	x	X
ejpam-115	12	20	<	<	X
ejpam-115	12	21	1	1	NUM
ejpam-115	12	22	,	,	PUNCT
ejpam-115	12	23	y(0	y(0	PROPN
ejpam-115	12	24	)	)	PUNCT
ejpam-115	12	25	=	=	SYM
ejpam-115	12	26	0	0	NUM
ejpam-115	12	27	,	,	PUNCT
ejpam-115	12	28	y′(0	y′(0	NOUN
ejpam-115	12	29	)	)	PUNCT
ejpam-115	12	30	=	=	SYM
ejpam-115	12	31	y′(1	y′(1	PROPN
ejpam-115	12	32	)	)	PUNCT
ejpam-115	12	33	whose	whose	DET
ejpam-115	12	34	boundary	boundary	ADJ
ejpam-115	12	35	conditions	condition	NOUN
ejpam-115	12	36	are	be	AUX
ejpam-115	12	37	regular	regular	ADJ
ejpam-115	12	38	,	,	PUNCT
ejpam-115	12	39	but	but	CCONJ
ejpam-115	12	40	not	not	PART
ejpam-115	12	41	strongly	strongly	ADV
ejpam-115	12	42	regular	regular	ADJ
ejpam-115	12	43	.	.	PUNCT
ejpam-115	13	1	all	all	DET
ejpam-115	13	2	the	the	DET
ejpam-115	13	3	eigenvalues	eigenvalue	NOUN
ejpam-115	13	4	of	of	ADP
ejpam-115	13	5	this	this	DET
ejpam-115	13	6	problem	problem	NOUN
ejpam-115	13	7	starting	start	VERB
ejpam-115	13	8	with	with	ADP
ejpam-115	13	9	the	the	DET
ejpam-115	13	10	second	second	ADJ
ejpam-115	13	11	one	one	NOUN
ejpam-115	13	12	are	be	AUX
ejpam-115	13	13	double	double	ADJ
ejpam-115	13	14	,	,	PUNCT
ejpam-115	13	15	the	the	DET
ejpam-115	13	16	total	total	ADJ
ejpam-115	13	17	number	number	NOUN
ejpam-115	13	18	of	of	ADP
ejpam-115	13	19	associated	associated	ADJ
ejpam-115	13	20	functions	function	NOUN
ejpam-115	13	21	is	be	AUX
ejpam-115	13	22	infinite	infinite	ADJ
ejpam-115	13	23	.	.	PUNCT
ejpam-115	14	1	nevertheless	nevertheless	ADV
ejpam-115	14	2	,	,	PUNCT
ejpam-115	14	3	in	in	ADP
ejpam-115	14	4	the	the	DET
ejpam-115	14	5	paper	paper	NOUN
ejpam-115	14	6	it	it	PRON
ejpam-115	14	7	was	be	AUX
ejpam-115	14	8	established	establish	VERB
ejpam-115	14	9	that	that	SCONJ
ejpam-115	14	10	the	the	DET
ejpam-115	14	11	chosen	choose	VERB
ejpam-115	14	12	specially	specially	ADJ
ejpam-115	14	13	system	system	NOUN
ejpam-115	14	14	of	of	ADP
ejpam-115	14	15	the	the	DET
ejpam-115	14	16	root	root	NOUN
ejpam-115	14	17	functions	function	NOUN
ejpam-115	14	18	forms	form	VERB
ejpam-115	14	19	an	an	DET
ejpam-115	14	20	unconditional	unconditional	ADJ
ejpam-115	14	21	basis	basis	NOUN
ejpam-115	14	22	inl2(0	inl2(0	PROPN
ejpam-115	14	23	,	,	PUNCT
ejpam-115	14	24	1	1	NUM
ejpam-115	14	25	)	)	PUNCT
ejpam-115	14	26	.	.	PUNCT
ejpam-115	15	1	∗corresponding	∗corresponde	VERB
ejpam-115	15	2	author.email	author.email	ADJ
ejpam-115	15	3	addresses:hanlar@mersin.edu.tr	addresses:hanlar@mersin.edu.tr	NOUN
ejpam-115	15	4	(	(	PUNCT
ejpam-115	15	5	kh	kh	PROPN
ejpam-115	15	6	.	.	PUNCT
ejpam-115	15	7	r.	r.	PROPN
ejpam-115	15	8	mamedov	mamedov	PROPN
ejpam-115	15	9	)	)	PUNCT
ejpam-115	15	10	,	,	PUNCT
ejpam-115	15	11	hmenken@mersin.edu.tr	hmenken@mersin.edu.tr	NOUN
ejpam-115	15	12	(	(	PUNCT
ejpam-115	15	13	h.	h.	PROPN
ejpam-115	15	14	menken	menken	PROPN
ejpam-115	15	15	)	)	PUNCT
ejpam-115	15	16	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-115	16	1	51	51	NUM
ejpam-115	17	1	c	c	X
ejpam-115	17	2	©	©	PROPN
ejpam-115	17	3	2007	2007	NUM
ejpam-115	17	4	ejpam	ejpam	NOUN
ejpam-115	17	5	all	all	DET
ejpam-115	17	6	rights	right	NOUN
ejpam-115	17	7	reserved	reserve	VERB
ejpam-115	17	8	.	.	PUNCT
ejpam-115	18	1	khanlar	khanlar	PROPN
ejpam-115	18	2	r.	r.	PROPN
ejpam-115	18	3	mamedov	mamedov	PROPN
ejpam-115	18	4	,	,	PUNCT
ejpam-115	18	5	hamza	hamza	PROPN
ejpam-115	18	6	menken	menken	PROPN
ejpam-115	18	7	/	/	SYM
ejpam-115	18	8	eur	eur	PROPN
ejpam-115	18	9	.	.	PUNCT
ejpam-115	19	1	j.	j.	PROPN
ejpam-115	19	2	pure	pure	PROPN
ejpam-115	19	3	appl	appl	PROPN
ejpam-115	19	4	.	.	PUNCT
ejpam-115	20	1	math,1	math,1	PROPN
ejpam-115	20	2	(	(	PUNCT
ejpam-115	20	3	2008	2008	NUM
ejpam-115	20	4	)	)	PUNCT
ejpam-115	20	5	,	,	PUNCT
ejpam-115	20	6	(	(	PUNCT
ejpam-115	20	7	51	51	NUM
ejpam-115	20	8	-	-	SYM
ejpam-115	20	9	60	60	NUM
ejpam-115	20	10	)	)	PUNCT
ejpam-115	20	11	52	52	NUM
ejpam-115	20	12	after	after	ADP
ejpam-115	20	13	this	this	DET
ejpam-115	20	14	work	work	NOUN
ejpam-115	20	15	,	,	PUNCT
ejpam-115	20	16	in	in	ADP
ejpam-115	20	17	[	[	PUNCT
ejpam-115	20	18	7	7	NUM
ejpam-115	20	19	]	]	PUNCT
ejpam-115	20	20	,	,	PUNCT
ejpam-115	20	21	the	the	DET
ejpam-115	20	22	boundary	boundary	ADJ
ejpam-115	20	23	-	-	PUNCT
ejpam-115	20	24	value	value	NOUN
ejpam-115	20	25	problem	problem	NOUN
ejpam-115	20	26	generated	generate	VERB
ejpam-115	20	27	by	by	ADP
ejpam-115	20	28	the	the	DET
ejpam-115	20	29	differential	differential	ADJ
ejpam-115	20	30	equation	equation	NOUN
ejpam-115	20	31	y′′	y′′	PROPN
ejpam-115	20	32	+	+	CCONJ
ejpam-115	20	33	q(x)y	q(x)y	PROPN
ejpam-115	20	34	=	=	PUNCT
ejpam-115	20	35	λy	λy	PROPN
ejpam-115	20	36	(	(	PUNCT
ejpam-115	20	37	1.1	1.1	NUM
ejpam-115	20	38	)	)	PUNCT
ejpam-115	20	39	and	and	CCONJ
ejpam-115	20	40	not	not	PART
ejpam-115	20	41	strongly	strongly	ADV
ejpam-115	20	42	regular	regular	ADJ
ejpam-115	20	43	boundary	boundary	ADJ
ejpam-115	20	44	conditions	condition	NOUN
ejpam-115	20	45	y(0)−	y(0)−	PROPN
ejpam-115	20	46	y(1	y(1	PROPN
ejpam-115	20	47	)	)	PUNCT
ejpam-115	21	1	=	=	SYM
ejpam-115	21	2	0	0	NUM
ejpam-115	21	3	,	,	PUNCT
ejpam-115	21	4	y′(0)−	y′(0)−	NOUN
ejpam-115	21	5	y′(1	y′(1	PROPN
ejpam-115	21	6	)	)	PUNCT
ejpam-115	21	7	=	=	SYM
ejpam-115	21	8	0	0	NUM
ejpam-115	21	9	(	(	PUNCT
ejpam-115	21	10	1.2	1.2	NUM
ejpam-115	21	11	)	)	PUNCT
ejpam-115	21	12	or	or	CCONJ
ejpam-115	21	13	y(0	y(0	PROPN
ejpam-115	21	14	)	)	PUNCT
ejpam-115	21	15	+	+	PROPN
ejpam-115	21	16	y(1	y(1	PROPN
ejpam-115	21	17	)	)	PUNCT
ejpam-115	21	18	=	=	SYM
ejpam-115	21	19	0	0	NUM
ejpam-115	21	20	,	,	PUNCT
ejpam-115	21	21	y′(0	y′(0	NOUN
ejpam-115	21	22	)	)	PUNCT
ejpam-115	21	23	+	+	SYM
ejpam-115	21	24	y′(1	y′(1	NOUN
ejpam-115	21	25	)	)	PUNCT
ejpam-115	21	26	=	=	SYM
ejpam-115	21	27	0	0	NUM
ejpam-115	21	28	(	(	PUNCT
ejpam-115	21	29	1.3	1.3	NUM
ejpam-115	21	30	)	)	PUNCT
ejpam-115	21	31	was	be	AUX
ejpam-115	21	32	considered	consider	VERB
ejpam-115	21	33	.	.	PUNCT
ejpam-115	22	1	here	here	ADV
ejpam-115	22	2	,	,	PUNCT
ejpam-115	22	3	q(x	q(x	PROPN
ejpam-115	22	4	)	)	PUNCT
ejpam-115	22	5	∈	∈	PROPN
ejpam-115	22	6	c(4)[0	c(4)[0	NOUN
ejpam-115	22	7	,	,	PUNCT
ejpam-115	22	8	1	1	NUM
ejpam-115	22	9	]	]	PUNCT
ejpam-115	22	10	was	be	AUX
ejpam-115	22	11	a	a	DET
ejpam-115	22	12	complex	complex	ADJ
ejpam-115	22	13	valued	value	VERB
ejpam-115	22	14	function	function	NOUN
ejpam-115	22	15	satisfying	satisfy	VERB
ejpam-115	22	16	the	the	DET
ejpam-115	22	17	condition	condition	NOUN
ejpam-115	22	18	q(0	q(0	PROPN
ejpam-115	22	19	)	)	PUNCT
ejpam-115	22	20	6=	6=	PROPN
ejpam-115	23	1	q(1	q(1	NOUN
ejpam-115	23	2	)	)	PUNCT
ejpam-115	23	3	.	.	PUNCT
ejpam-115	24	1	in	in	ADP
ejpam-115	24	2	this	this	DET
ejpam-115	24	3	paper	paper	NOUN
ejpam-115	24	4	,	,	PUNCT
ejpam-115	24	5	it	it	PRON
ejpam-115	24	6	was	be	AUX
ejpam-115	24	7	shown	show	VERB
ejpam-115	24	8	that	that	SCONJ
ejpam-115	24	9	the	the	DET
ejpam-115	24	10	root	root	NOUN
ejpam-115	24	11	functions	function	NOUN
ejpam-115	24	12	of	of	ADP
ejpam-115	24	13	the	the	DET
ejpam-115	24	14	boundary	boundary	ADJ
ejpam-115	24	15	problems	problem	NOUN
ejpam-115	24	16	(	(	PUNCT
ejpam-115	24	17	1.1	1.1	NUM
ejpam-115	24	18	)	)	PUNCT
ejpam-115	24	19	,	,	PUNCT
ejpam-115	24	20	(	(	PUNCT
ejpam-115	24	21	1.2	1.2	NUM
ejpam-115	24	22	)	)	PUNCT
ejpam-115	24	23	and	and	CCONJ
ejpam-115	24	24	(	(	PUNCT
ejpam-115	24	25	1.1	1.1	NUM
ejpam-115	24	26	)	)	PUNCT
ejpam-115	24	27	,	,	PUNCT
ejpam-115	24	28	(	(	PUNCT
ejpam-115	24	29	1.3	1.3	NUM
ejpam-115	24	30	)	)	PUNCT
ejpam-115	24	31	formed	form	VERB
ejpam-115	24	32	riesz	riesz	PROPN
ejpam-115	24	33	basis	basis	NOUN
ejpam-115	24	34	inl2(0	inl2(0	PROPN
ejpam-115	24	35	,	,	PUNCT
ejpam-115	24	36	1	1	NUM
ejpam-115	24	37	)	)	PUNCT
ejpam-115	24	38	.	.	PUNCT
ejpam-115	25	1	let	let	VERB
ejpam-115	25	2	us	we	PRON
ejpam-115	25	3	present	present	VERB
ejpam-115	25	4	briefly	briefly	ADV
ejpam-115	25	5	the	the	DET
ejpam-115	25	6	main	main	ADJ
ejpam-115	25	7	definitions	definition	NOUN
ejpam-115	25	8	and	and	CCONJ
ejpam-115	25	9	fact	fact	NOUN
ejpam-115	25	10	which	which	PRON
ejpam-115	25	11	will	will	AUX
ejpam-115	25	12	be	be	AUX
ejpam-115	25	13	used	use	VERB
ejpam-115	25	14	in	in	ADP
ejpam-115	25	15	what	what	PRON
ejpam-115	25	16	follows	follow	VERB
ejpam-115	25	17	.	.	PUNCT
ejpam-115	26	1	definition	definition	NOUN
ejpam-115	26	2	1.1	1.1	NUM
ejpam-115	26	3	.	.	PUNCT
ejpam-115	27	1	a	a	DET
ejpam-115	27	2	system{ϕn}∞n=1	system{ϕn}∞n=1	PROPN
ejpam-115	27	3	forms	form	VERB
ejpam-115	27	4	a	a	DET
ejpam-115	27	5	basis	basis	NOUN
ejpam-115	27	6	in	in	ADP
ejpam-115	27	7	a	a	DET
ejpam-115	27	8	banach	banach	NOUN
ejpam-115	27	9	spacex	spacex	NOUN
ejpam-115	27	10	if	if	SCONJ
ejpam-115	27	11	for	for	ADP
ejpam-115	27	12	any	any	DET
ejpam-115	27	13	elementf	elementf	VERB
ejpam-115	27	14	∈	∈	PROPN
ejpam-115	27	15	x	x	PUNCT
ejpam-115	27	16	there	there	PRON
ejpam-115	27	17	exists	exist	VERB
ejpam-115	27	18	a	a	DET
ejpam-115	27	19	unique	unique	ADJ
ejpam-115	27	20	expansion	expansion	NOUN
ejpam-115	27	21	of	of	ADP
ejpam-115	27	22	it	it	PRON
ejpam-115	27	23	in	in	ADP
ejpam-115	27	24	the	the	DET
ejpam-115	27	25	elements	element	NOUN
ejpam-115	27	26	of	of	ADP
ejpam-115	27	27	the	the	DET
ejpam-115	27	28	system	system	NOUN
ejpam-115	27	29	,	,	PUNCT
ejpam-115	27	30	i.e.	i.e.	X
ejpam-115	27	31	the	the	DET
ejpam-115	27	32	series	series	NOUN
ejpam-115	27	33	∞∑	∞∑	NUM
ejpam-115	27	34	j=1	j=1	PROPN
ejpam-115	27	35	cjϕj	cjϕj	NOUN
ejpam-115	27	36	convergent	convergent	NOUN
ejpam-115	27	37	to	to	ADP
ejpam-115	27	38	f	f	PROPN
ejpam-115	27	39	in	in	ADP
ejpam-115	27	40	the	the	DET
ejpam-115	27	41	norm	norm	NOUN
ejpam-115	27	42	of	of	ADP
ejpam-115	27	43	the	the	DET
ejpam-115	27	44	spacex	spacex	PROPN
ejpam-115	27	45	.	.	PUNCT
ejpam-115	28	1	definition	definition	NOUN
ejpam-115	28	2	1.2	1.2	NUM
ejpam-115	28	3	.	.	PUNCT
ejpam-115	29	1	[	[	X
ejpam-115	29	2	8,9	8,9	NUM
ejpam-115	29	3	]	]	X
ejpam-115	29	4	a	a	DET
ejpam-115	29	5	system{ϕn}∞n=1	system{ϕn}∞n=1	PROPN
ejpam-115	29	6	is	be	AUX
ejpam-115	29	7	called	call	VERB
ejpam-115	29	8	a	a	DET
ejpam-115	29	9	riesz	riesz	ADJ
ejpam-115	29	10	basis	basis	NOUN
ejpam-115	29	11	of	of	ADP
ejpam-115	29	12	the	the	DET
ejpam-115	29	13	hilbert	hilbert	PROPN
ejpam-115	29	14	spaceh	spaceh	NOUN
ejpam-115	29	15	if	if	SCONJ
ejpam-115	29	16	there	there	PRON
ejpam-115	29	17	exists	exist	VERB
ejpam-115	29	18	a	a	DET
ejpam-115	29	19	bounded	bounded	ADJ
ejpam-115	29	20	linear	linear	PROPN
ejpam-115	29	21	invertible	invertible	ADJ
ejpam-115	29	22	operatora	operatora	NOUN
ejpam-115	29	23	such	such	ADJ
ejpam-115	29	24	that	that	SCONJ
ejpam-115	29	25	the	the	DET
ejpam-115	29	26	system{aϕn}∞n=1	system{aϕn}∞n=1	NOUN
ejpam-115	29	27	forms	form	VERB
ejpam-115	29	28	an	an	DET
ejpam-115	29	29	orthonormal	orthonormal	ADJ
ejpam-115	29	30	basis	basis	NOUN
ejpam-115	29	31	inh	inh	NOUN
ejpam-115	29	32	.	.	PUNCT
ejpam-115	30	1	theorem	theorem	VERB
ejpam-115	30	2	1.1	1.1	NUM
ejpam-115	30	3	.	.	PUNCT
ejpam-115	31	1	[	[	X
ejpam-115	31	2	8,9	8,9	X
ejpam-115	31	3	]	]	X
ejpam-115	31	4	if	if	SCONJ
ejpam-115	31	5	the	the	DET
ejpam-115	31	6	sequence{ϕj}∞j=1	sequence{ϕj}∞j=1	PROPN
ejpam-115	31	7	is	be	AUX
ejpam-115	31	8	complete	complete	ADJ
ejpam-115	31	9	in	in	ADP
ejpam-115	31	10	the	the	DET
ejpam-115	31	11	hilbert	hilbert	PROPN
ejpam-115	31	12	spaceh	spaceh	NOUN
ejpam-115	31	13	,	,	PUNCT
ejpam-115	31	14	there	there	PRON
ejpam-115	31	15	corresponds	correspond	VERB
ejpam-115	31	16	to	to	ADP
ejpam-115	31	17	it	it	PRON
ejpam-115	31	18	a	a	DET
ejpam-115	31	19	complete	complete	ADJ
ejpam-115	31	20	biorthogonal	biorthogonal	ADJ
ejpam-115	31	21	sequence{ψj}∞j=1	sequence{ψj}∞j=1	NOUN
ejpam-115	31	22	,	,	PUNCT
ejpam-115	31	23	and	and	CCONJ
ejpam-115	31	24	for	for	ADP
ejpam-115	31	25	anyf	anyf	NOUN
ejpam-115	31	26	∈	∈	PROPN
ejpam-115	31	27	h	h	NOUN
ejpam-115	31	28	one	one	NOUN
ejpam-115	31	29	has	have	VERB
ejpam-115	31	30	∞∑	∞∑	NUM
ejpam-115	31	31	j=1	j=1	ADJ
ejpam-115	31	32	|(f	|(f	PROPN
ejpam-115	31	33	,	,	PUNCT
ejpam-115	31	34	ϕj)|	ϕj)|	NOUN
ejpam-115	31	35	<	<	X
ejpam-115	31	36	∞	∞	PROPN
ejpam-115	31	37	,	,	PUNCT
ejpam-115	31	38	∞∑	∞∑	NUM
ejpam-115	31	39	j=1	j=1	ADJ
ejpam-115	31	40	|(f	|(f	PROPN
ejpam-115	31	41	,	,	PUNCT
ejpam-115	31	42	ψj)|2	ψj)|2	PROPN
ejpam-115	31	43	<	<	X
ejpam-115	31	44	∞	∞	PROPN
ejpam-115	31	45	,	,	PUNCT
ejpam-115	31	46	then	then	ADV
ejpam-115	31	47	the	the	DET
ejpam-115	31	48	sequence{ψj}∞j=1	sequence{ψj}∞j=1	PROPN
ejpam-115	31	49	forms	form	VERB
ejpam-115	31	50	a	a	DET
ejpam-115	31	51	riesz	riesz	PROPN
ejpam-115	31	52	basis	basis	NOUN
ejpam-115	31	53	inh	inh	NOUN
ejpam-115	31	54	.	.	PUNCT
ejpam-115	32	1	we	we	PRON
ejpam-115	32	2	consider	consider	VERB
ejpam-115	32	3	the	the	DET
ejpam-115	32	4	boundary	boundary	ADJ
ejpam-115	32	5	-	-	PUNCT
ejpam-115	32	6	value	value	NOUN
ejpam-115	32	7	problems	problem	NOUN
ejpam-115	32	8	(	(	PUNCT
ejpam-115	32	9	1.1	1.1	NUM
ejpam-115	32	10	)	)	PUNCT
ejpam-115	32	11	,	,	PUNCT
ejpam-115	32	12	(	(	PUNCT
ejpam-115	32	13	1.2	1.2	NUM
ejpam-115	32	14	)	)	PUNCT
ejpam-115	32	15	and	and	CCONJ
ejpam-115	32	16	(	(	PUNCT
ejpam-115	32	17	1.1	1.1	NUM
ejpam-115	32	18	)	)	PUNCT
ejpam-115	32	19	,	,	PUNCT
ejpam-115	32	20	(	(	PUNCT
ejpam-115	32	21	1.3	1.3	NUM
ejpam-115	32	22	)	)	PUNCT
ejpam-115	32	23	,	,	PUNCT
ejpam-115	32	24	whereq(x	whereq(x	INTJ
ejpam-115	32	25	)	)	PUNCT
ejpam-115	32	26	∈	∈	PROPN
ejpam-115	32	27	c(4)[0	c(4)[0	NOUN
ejpam-115	32	28	,	,	PUNCT
ejpam-115	32	29	1	1	NUM
ejpam-115	32	30	]	]	PUNCT
ejpam-115	32	31	is	be	AUX
ejpam-115	32	32	a	a	DET
ejpam-115	32	33	complex	complex	ADV
ejpam-115	32	34	-	-	PUNCT
ejpam-115	32	35	valued	value	VERB
ejpam-115	32	36	function	function	NOUN
ejpam-115	32	37	.	.	PUNCT
ejpam-115	33	1	without	without	ADP
ejpam-115	33	2	loss	loss	NOUN
ejpam-115	33	3	of	of	ADP
ejpam-115	33	4	generality	generality	NOUN
ejpam-115	33	5	,	,	PUNCT
ejpam-115	33	6	we	we	PRON
ejpam-115	33	7	can	can	AUX
ejpam-115	33	8	assume	assume	VERB
ejpam-115	33	9	that	that	SCONJ
ejpam-115	33	10	1∫	1∫	NUM
ejpam-115	33	11	0	0	NUM
ejpam-115	33	12	q(x)dx	q(x)dx	PROPN
ejpam-115	33	13	=	=	NOUN
ejpam-115	33	14	0	0	NUM
ejpam-115	33	15	.	.	PUNCT
ejpam-115	34	1	in	in	ADP
ejpam-115	34	2	the	the	DET
ejpam-115	34	3	present	present	ADJ
ejpam-115	34	4	paper	paper	NOUN
ejpam-115	34	5	,	,	PUNCT
ejpam-115	34	6	in	in	ADP
ejpam-115	34	7	section	section	NOUN
ejpam-115	34	8	2	2	NUM
ejpam-115	34	9	we	we	PRON
ejpam-115	34	10	obtain	obtain	VERB
ejpam-115	34	11	the	the	DET
ejpam-115	34	12	asymptotic	asymptotic	ADJ
ejpam-115	34	13	formulas	formula	NOUN
ejpam-115	34	14	of	of	ADP
ejpam-115	34	15	eigenvalues	eigenvalue	NOUN
ejpam-115	34	16	and	and	CCONJ
ejpam-115	34	17	eigenfunctions	eigenfunction	NOUN
ejpam-115	34	18	of	of	ADP
ejpam-115	34	19	the	the	DET
ejpam-115	34	20	boundary	boundary	ADJ
ejpam-115	34	21	problems	problem	NOUN
ejpam-115	34	22	(	(	PUNCT
ejpam-115	34	23	1.1	1.1	NUM
ejpam-115	34	24	)	)	PUNCT
ejpam-115	34	25	,	,	PUNCT
ejpam-115	34	26	(	(	PUNCT
ejpam-115	34	27	1.2	1.2	NUM
ejpam-115	34	28	)	)	PUNCT
ejpam-115	34	29	.	.	PUNCT
ejpam-115	35	1	in	in	ADP
ejpam-115	35	2	section	section	NOUN
ejpam-115	35	3	3	3	NUM
ejpam-115	35	4	,	,	PUNCT
ejpam-115	35	5	using	use	VERB
ejpam-115	35	6	these	these	DET
ejpam-115	35	7	asymptotic	asymptotic	ADJ
ejpam-115	35	8	formulas	formula	NOUN
ejpam-115	35	9	and	and	CCONJ
ejpam-115	35	10	theorem	theorem	VERB
ejpam-115	35	11	1.1	1.1	NUM
ejpam-115	35	12	,	,	PUNCT
ejpam-115	35	13	we	we	PRON
ejpam-115	35	14	prove	prove	VERB
ejpam-115	35	15	the	the	DET
ejpam-115	35	16	basisness	basisness	NOUN
ejpam-115	35	17	inl2(0	inl2(0	PROPN
ejpam-115	35	18	,	,	PUNCT
ejpam-115	35	19	1	1	NUM
ejpam-115	35	20	)	)	PUNCT
ejpam-115	35	21	of	of	ADP
ejpam-115	35	22	the	the	DET
ejpam-115	35	23	root	root	NOUN
ejpam-115	35	24	functions	function	NOUN
ejpam-115	35	25	of	of	ADP
ejpam-115	35	26	the	the	DET
ejpam-115	35	27	boundary	boundary	ADJ
ejpam-115	35	28	problem	problem	NOUN
ejpam-115	35	29	(	(	PUNCT
ejpam-115	35	30	1.1	1.1	NUM
ejpam-115	35	31	)	)	PUNCT
ejpam-115	35	32	,	,	PUNCT
ejpam-115	35	33	(	(	PUNCT
ejpam-115	35	34	1.2	1.2	NUM
ejpam-115	35	35	)	)	PUNCT
ejpam-115	35	36	.	.	PUNCT
ejpam-115	36	1	in	in	ADP
ejpam-115	36	2	section	section	NOUN
ejpam-115	36	3	4	4	NUM
ejpam-115	36	4	,	,	PUNCT
ejpam-115	36	5	similar	similar	ADJ
ejpam-115	36	6	results	result	NOUN
ejpam-115	36	7	are	be	AUX
ejpam-115	36	8	obtained	obtain	VERB
ejpam-115	36	9	for	for	ADP
ejpam-115	36	10	the	the	DET
ejpam-115	36	11	boundary	boundary	ADJ
ejpam-115	36	12	problem	problem	NOUN
ejpam-115	36	13	(	(	PUNCT
ejpam-115	36	14	1.1	1.1	NUM
ejpam-115	36	15	)	)	PUNCT
ejpam-115	36	16	,	,	PUNCT
ejpam-115	36	17	(	(	PUNCT
ejpam-115	36	18	1.3	1.3	NUM
ejpam-115	36	19	)	)	PUNCT
ejpam-115	36	20	.	.	PUNCT
ejpam-115	37	1	2	2	X
ejpam-115	37	2	.	.	X
ejpam-115	37	3	the	the	DET
ejpam-115	37	4	asymptotic	asymptotic	ADJ
ejpam-115	37	5	formulas	formula	NOUN
ejpam-115	37	6	for	for	ADP
ejpam-115	37	7	eigenvalues	eigenvalue	NOUN
ejpam-115	37	8	and	and	CCONJ
ejpam-115	37	9	eigenfunctions	eigenfunction	NOUN
ejpam-115	37	10	of	of	ADP
ejpam-115	37	11	the	the	DET
ejpam-115	37	12	periodic	periodic	ADJ
ejpam-115	37	13	problem	problem	NOUN
ejpam-115	37	14	first	first	ADV
ejpam-115	37	15	we	we	PRON
ejpam-115	37	16	shall	shall	AUX
ejpam-115	37	17	prove	prove	VERB
ejpam-115	37	18	the	the	DET
ejpam-115	37	19	following	follow	VERB
ejpam-115	37	20	lemma	lemma	PROPN
ejpam-115	37	21	.	.	PUNCT
ejpam-115	38	1	khanlar	khanlar	PROPN
ejpam-115	38	2	r.	r.	PROPN
ejpam-115	38	3	mamedov	mamedov	PROPN
ejpam-115	38	4	,	,	PUNCT
ejpam-115	38	5	hamza	hamza	PROPN
ejpam-115	38	6	menken	menken	PROPN
ejpam-115	38	7	/	/	SYM
ejpam-115	38	8	eur	eur	PROPN
ejpam-115	38	9	.	.	PUNCT
ejpam-115	39	1	j.	j.	PROPN
ejpam-115	39	2	pure	pure	PROPN
ejpam-115	39	3	appl	appl	PROPN
ejpam-115	39	4	.	.	PUNCT
ejpam-115	40	1	math,1	math,1	PROPN
ejpam-115	40	2	(	(	PUNCT
ejpam-115	40	3	2008	2008	NUM
ejpam-115	40	4	)	)	PUNCT
ejpam-115	40	5	,	,	PUNCT
ejpam-115	40	6	(	(	PUNCT
ejpam-115	40	7	51	51	NUM
ejpam-115	40	8	-	-	SYM
ejpam-115	40	9	60	60	NUM
ejpam-115	40	10	)	)	PUNCT
ejpam-115	40	11	53	53	NUM
ejpam-115	40	12	lemma	lemma	PROPN
ejpam-115	40	13	2.1	2.1	NUM
ejpam-115	40	14	.	.	PUNCT
ejpam-115	41	1	all	all	DET
ejpam-115	41	2	eigenvalues	eigenvalue	NOUN
ejpam-115	41	3	of	of	ADP
ejpam-115	41	4	the	the	DET
ejpam-115	41	5	boundary	boundary	ADJ
ejpam-115	41	6	-	-	PUNCT
ejpam-115	41	7	value	value	NOUN
ejpam-115	41	8	problem	problem	NOUN
ejpam-115	41	9	(	(	PUNCT
ejpam-115	41	10	1.1	1.1	NUM
ejpam-115	41	11	)	)	PUNCT
ejpam-115	41	12	,	,	PUNCT
ejpam-115	41	13	(	(	PUNCT
ejpam-115	41	14	1.2	1.2	NUM
ejpam-115	41	15	)	)	PUNCT
ejpam-115	41	16	,	,	PUNCT
ejpam-115	41	17	starting	start	VERB
ejpam-115	41	18	from	from	ADP
ejpam-115	41	19	some	some	DET
ejpam-115	41	20	number	number	NOUN
ejpam-115	41	21	,	,	PUNCT
ejpam-115	41	22	are	be	AUX
ejpam-115	41	23	simple	simple	ADJ
ejpam-115	41	24	and	and	CCONJ
ejpam-115	41	25	form	form	VERB
ejpam-115	41	26	two	two	NUM
ejpam-115	41	27	infinite	infinite	ADJ
ejpam-115	41	28	sequencesλk,1	sequencesλk,1	NOUN
ejpam-115	41	29	,	,	PUNCT
ejpam-115	41	30	λk,2	λk,2	PROPN
ejpam-115	41	31	,	,	PUNCT
ejpam-115	41	32	k	k	NOUN
ejpam-115	41	33	=	=	SYM
ejpam-115	41	34	n	n	CCONJ
ejpam-115	41	35	,	,	PUNCT
ejpam-115	41	36	n+1	n+1	PROPN
ejpam-115	41	37	,	,	PUNCT
ejpam-115	41	38	·	·	PUNCT
ejpam-115	41	39	·	·	PUNCT
ejpam-115	41	40	·	·	PUNCT
ejpam-115	41	41	,	,	PUNCT
ejpam-115	41	42	wheren	wheren	PROPN
ejpam-115	41	43	is	be	AUX
ejpam-115	41	44	a	a	DET
ejpam-115	41	45	positive	positive	ADJ
ejpam-115	41	46	integer	integer	NOUN
ejpam-115	41	47	and	and	CCONJ
ejpam-115	41	48	λk,1	λk,1	PROPN
ejpam-115	41	49	=	=	PUNCT
ejpam-115	41	50	−(2kπ)2	−(2kπ)2	PROPN
ejpam-115	41	51	−	−	PROPN
ejpam-115	41	52	q′(1)−	q′(1)−	NOUN
ejpam-115	41	53	q′(0	q′(0	PROPN
ejpam-115	41	54	)	)	PUNCT
ejpam-115	42	1	+	+	CCONJ
ejpam-115	42	2	1∫	1∫	NUM
ejpam-115	42	3	0	0	NUM
ejpam-115	42	4	q2(t)dt	q2(t)dt	NOUN
ejpam-115	42	5	(	(	PUNCT
ejpam-115	42	6	4kπ)2	4kπ)2	NUM
ejpam-115	42	7	+	+	NOUN
ejpam-115	42	8	o	o	X
ejpam-115	42	9	(	(	PUNCT
ejpam-115	42	10	1	1	NUM
ejpam-115	42	11	k3	k3	ADJ
ejpam-115	42	12	)	)	PUNCT
ejpam-115	42	13	,	,	PUNCT
ejpam-115	42	14	(	(	PUNCT
ejpam-115	42	15	2.1	2.1	NUM
ejpam-115	42	16	)	)	PUNCT
ejpam-115	42	17	λk,2	λk,2	NOUN
ejpam-115	42	18	=	=	PUNCT
ejpam-115	43	1	−(2kπ)2	−(2kπ)2	PROPN
ejpam-115	44	1	+	+	CCONJ
ejpam-115	44	2	q′(1)−	q′(1)−	ADJ
ejpam-115	44	3	q′(0)−	q′(0)−	NOUN
ejpam-115	44	4	1∫	1∫	NUM
ejpam-115	44	5	0	0	NUM
ejpam-115	44	6	q2(t)dt	q2(t)dt	NOUN
ejpam-115	44	7	(	(	PUNCT
ejpam-115	44	8	4kπ)2	4kπ)2	NUM
ejpam-115	45	1	+	+	NOUN
ejpam-115	45	2	o	o	X
ejpam-115	45	3	(	(	PUNCT
ejpam-115	45	4	1	1	NUM
ejpam-115	45	5	k3	k3	ADJ
ejpam-115	45	6	)	)	PUNCT
ejpam-115	45	7	,	,	PUNCT
ejpam-115	45	8	(	(	PUNCT
ejpam-115	45	9	2.2	2.2	NUM
ejpam-115	45	10	)	)	PUNCT
ejpam-115	45	11	and	and	CCONJ
ejpam-115	45	12	the	the	DET
ejpam-115	45	13	corresponding	corresponding	ADJ
ejpam-115	45	14	eigenfunctions	eigenfunction	NOUN
ejpam-115	45	15	are	be	AUX
ejpam-115	45	16	of	of	ADP
ejpam-115	45	17	the	the	DET
ejpam-115	45	18	form	form	NOUN
ejpam-115	45	19	yk,1(x	yk,1(x	NOUN
ejpam-115	45	20	)	)	PUNCT
ejpam-115	46	1	=	=	PUNCT
ejpam-115	46	2	sin	sin	NOUN
ejpam-115	46	3	2kπx+o	2kπx+o	NUM
ejpam-115	46	4	(	(	PUNCT
ejpam-115	46	5	1	1	NUM
ejpam-115	46	6	k	k	NOUN
ejpam-115	46	7	)	)	PUNCT
ejpam-115	46	8	,	,	PUNCT
ejpam-115	46	9	(	(	PUNCT
ejpam-115	46	10	2.3	2.3	NUM
ejpam-115	46	11	)	)	PUNCT
ejpam-115	46	12	yk,2(x	yk,2(x	NOUN
ejpam-115	46	13	)	)	PUNCT
ejpam-115	47	1	=	=	SYM
ejpam-115	47	2	cos	cos	PROPN
ejpam-115	47	3	2kπx+o	2kπx+o	PROPN
ejpam-115	47	4	(	(	PUNCT
ejpam-115	47	5	1	1	NUM
ejpam-115	47	6	k	k	NOUN
ejpam-115	47	7	)	)	PUNCT
ejpam-115	47	8	.	.	PUNCT
ejpam-115	48	1	(	(	PUNCT
ejpam-115	48	2	2.4	2.4	NUM
ejpam-115	48	3	)	)	PUNCT
ejpam-115	48	4	proof	proof	NOUN
ejpam-115	48	5	.	.	PUNCT
ejpam-115	49	1	we	we	PRON
ejpam-115	49	2	assume	assume	VERB
ejpam-115	49	3	thatq(0	thatq(0	NOUN
ejpam-115	49	4	)	)	PUNCT
ejpam-115	50	1	=	=	SYM
ejpam-115	50	2	q(1	q(1	PROPN
ejpam-115	50	3	)	)	PUNCT
ejpam-115	50	4	.	.	PUNCT
ejpam-115	51	1	the	the	DET
ejpam-115	51	2	caseq(0	caseq(0	PROPN
ejpam-115	51	3	)	)	PUNCT
ejpam-115	51	4	6=	6=	PUNCT
ejpam-115	52	1	q(1	q(1	PROPN
ejpam-115	52	2	)	)	PUNCT
ejpam-115	52	3	was	be	AUX
ejpam-115	52	4	investigated	investigate	VERB
ejpam-115	52	5	in	in	ADP
ejpam-115	52	6	[	[	X
ejpam-115	52	7	7	7	NUM
ejpam-115	52	8	]	]	PUNCT
ejpam-115	52	9	.	.	PUNCT
ejpam-115	53	1	consider	consider	VERB
ejpam-115	53	2	the	the	DET
ejpam-115	53	3	equation	equation	NOUN
ejpam-115	53	4	(	(	PUNCT
ejpam-115	53	5	1.3	1.3	NUM
ejpam-115	53	6	)	)	PUNCT
ejpam-115	53	7	or	or	CCONJ
ejpam-115	53	8	y′′	y′′	PROPN
ejpam-115	53	9	+	+	CCONJ
ejpam-115	53	10	q(x)y	q(x)y	PROPN
ejpam-115	53	11	+	+	CCONJ
ejpam-115	53	12	µ2y	µ2y	NOUN
ejpam-115	53	13	=	=	SYM
ejpam-115	53	14	0	0	NUM
ejpam-115	53	15	,	,	PUNCT
ejpam-115	53	16	(	(	PUNCT
ejpam-115	53	17	2.5	2.5	NUM
ejpam-115	53	18	)	)	PUNCT
ejpam-115	53	19	whereµ	whereµ	NOUN
ejpam-115	53	20	=	=	SYM
ejpam-115	53	21	√	√	PROPN
ejpam-115	53	22	−λ	−λ	NOUN
ejpam-115	53	23	and	and	CCONJ
ejpam-115	53	24	√	√	ADJ
ejpam-115	53	25	reiϕ/2	reiϕ/2	NUM
ejpam-115	53	26	for−π	for−π	PROPN
ejpam-115	53	27	<	<	X
ejpam-115	53	28	ϕ	ϕ	X
ejpam-115	53	29	≤	≤	NUM
ejpam-115	53	30	π	π	PROPN
ejpam-115	53	31	.	.	PUNCT
ejpam-115	54	1	from	from	ADP
ejpam-115	54	2	[	[	X
ejpam-115	54	3	1,10	1,10	NUM
ejpam-115	54	4	]	]	PUNCT
ejpam-115	54	5	,	,	PUNCT
ejpam-115	54	6	it	it	PRON
ejpam-115	54	7	is	be	AUX
ejpam-115	54	8	well	well	ADV
ejpam-115	54	9	known	know	VERB
ejpam-115	54	10	that	that	SCONJ
ejpam-115	54	11	the	the	DET
ejpam-115	54	12	eigenvalues	eigenvalue	NOUN
ejpam-115	54	13	of	of	ADP
ejpam-115	54	14	the	the	DET
ejpam-115	54	15	boundary	boundary	ADJ
ejpam-115	54	16	problem	problem	NOUN
ejpam-115	54	17	(	(	PUNCT
ejpam-115	54	18	1.1	1.1	NUM
ejpam-115	54	19	)	)	PUNCT
ejpam-115	54	20	,	,	PUNCT
ejpam-115	54	21	(	(	PUNCT
ejpam-115	54	22	1.2	1.2	NUM
ejpam-115	54	23	)	)	PUNCT
ejpam-115	54	24	are	be	AUX
ejpam-115	54	25	asymptotically	asymptotically	ADV
ejpam-115	54	26	located	locate	VERB
ejpam-115	54	27	in	in	ADP
ejpam-115	54	28	pairs	pair	NOUN
ejpam-115	54	29	,	,	PUNCT
ejpam-115	54	30	i.e.	i.e.	X
ejpam-115	54	31	λk,1	λk,1	NOUN
ejpam-115	54	32	=	=	PUNCT
ejpam-115	54	33	λk,2	λk,2	PROPN
ejpam-115	54	34	+	+	NOUN
ejpam-115	54	35	o(k1/2	o(k1/2	NUM
ejpam-115	54	36	)	)	PUNCT
ejpam-115	55	1	=	=	SYM
ejpam-115	55	2	−(2kπ)2	−(2kπ)2	ADJ
ejpam-115	55	3	{	{	PUNCT
ejpam-115	55	4	1	1	NUM
ejpam-115	55	5	+	+	NUM
ejpam-115	55	6	ξ0	ξ0	PROPN
ejpam-115	55	7	k	k	PROPN
ejpam-115	56	1	+	+	PROPN
ejpam-115	56	2	o	o	X
ejpam-115	56	3	(	(	PUNCT
ejpam-115	56	4	1	1	NUM
ejpam-115	56	5	k3/2	k3/2	NOUN
ejpam-115	56	6	)	)	PUNCT
ejpam-115	56	7	}	}	PUNCT
ejpam-115	56	8	,	,	PUNCT
ejpam-115	56	9	(	(	PUNCT
ejpam-115	56	10	k	k	NOUN
ejpam-115	56	11	=	=	PUNCT
ejpam-115	56	12	n	n	CCONJ
ejpam-115	56	13	,	,	PUNCT
ejpam-115	56	14	n	n	PROPN
ejpam-115	56	15	+	+	NUM
ejpam-115	56	16	1	1	NUM
ejpam-115	56	17	,	,	PUNCT
ejpam-115	56	18	·	·	PUNCT
ejpam-115	56	19	·	·	PUNCT
ejpam-115	56	20	·	·	PUNCT
ejpam-115	56	21	)	)	PUNCT
ejpam-115	56	22	.	.	PUNCT
ejpam-115	57	1	it	it	PRON
ejpam-115	57	2	follows	follow	VERB
ejpam-115	57	3	from	from	ADP
ejpam-115	57	4	the	the	DET
ejpam-115	57	5	last	last	ADJ
ejpam-115	57	6	relation	relation	NOUN
ejpam-115	57	7	that	that	SCONJ
ejpam-115	57	8	µk,1	µk,1	NOUN
ejpam-115	57	9	=	=	PUNCT
ejpam-115	57	10	√	√	ADP
ejpam-115	57	11	−λk,1	−λk,1	NOUN
ejpam-115	57	12	=	=	PUNCT
ejpam-115	57	13	2kπ	2kπ	NOUN
ejpam-115	57	14	{	{	PUNCT
ejpam-115	57	15	1	1	NUM
ejpam-115	57	16	+	+	NUM
ejpam-115	57	17	ξ0	ξ0	ADJ
ejpam-115	57	18	2k	2k	NOUN
ejpam-115	57	19	+	+	PROPN
ejpam-115	57	20	o	o	PROPN
ejpam-115	57	21	(	(	PUNCT
ejpam-115	57	22	1	1	NUM
ejpam-115	57	23	k3/2	k3/2	NOUN
ejpam-115	57	24	)	)	PUNCT
ejpam-115	57	25	}	}	PUNCT
ejpam-115	57	26	,	,	PUNCT
ejpam-115	57	27	(	(	PUNCT
ejpam-115	58	1	k	k	NOUN
ejpam-115	58	2	=	=	PUNCT
ejpam-115	58	3	n	n	CCONJ
ejpam-115	58	4	,	,	PUNCT
ejpam-115	58	5	n	n	PROPN
ejpam-115	58	6	+	+	NUM
ejpam-115	58	7	1	1	NUM
ejpam-115	58	8	,	,	PUNCT
ejpam-115	58	9	·	·	PUNCT
ejpam-115	58	10	·	·	PUNCT
ejpam-115	58	11	·	·	PUNCT
ejpam-115	58	12	)	)	PUNCT
ejpam-115	58	13	µk,2	µk,2	NOUN
ejpam-115	58	14	=	=	NOUN
ejpam-115	58	15	√	√	NOUN
ejpam-115	58	16	−λk,2	−λk,2	NOUN
ejpam-115	58	17	=	=	SYM
ejpam-115	58	18	2kπ	2kπ	NOUN
ejpam-115	58	19	{	{	PUNCT
ejpam-115	58	20	1	1	NUM
ejpam-115	58	21	+	+	NUM
ejpam-115	58	22	ξ0	ξ0	ADJ
ejpam-115	58	23	2k	2k	NOUN
ejpam-115	58	24	+	+	PROPN
ejpam-115	58	25	o	o	PROPN
ejpam-115	58	26	(	(	PUNCT
ejpam-115	58	27	1	1	NUM
ejpam-115	58	28	k3/2	k3/2	NOUN
ejpam-115	58	29	)	)	PUNCT
ejpam-115	58	30	}	}	PUNCT
ejpam-115	58	31	,	,	PUNCT
ejpam-115	58	32	(	(	PUNCT
ejpam-115	58	33	k	k	NOUN
ejpam-115	58	34	=	=	PUNCT
ejpam-115	58	35	n	n	CCONJ
ejpam-115	58	36	,	,	PUNCT
ejpam-115	58	37	n	n	PROPN
ejpam-115	58	38	+	+	NUM
ejpam-115	58	39	1	1	NUM
ejpam-115	58	40	,	,	PUNCT
ejpam-115	58	41	·	·	PUNCT
ejpam-115	58	42	·	·	PUNCT
ejpam-115	58	43	·	·	PUNCT
ejpam-115	58	44	)	)	PUNCT
ejpam-115	58	45	.	.	PUNCT
ejpam-115	59	1	hence	hence	ADV
ejpam-115	59	2	,	,	PUNCT
ejpam-115	59	3	there	there	PRON
ejpam-115	59	4	exists	exist	VERB
ejpam-115	59	5	a	a	DET
ejpam-115	59	6	positive	positive	ADJ
ejpam-115	59	7	numberco	numberco	NOUN
ejpam-115	59	8	such	such	ADJ
ejpam-115	59	9	that|=(µk,1)|	that|=(µk,1)|	ADJ
ejpam-115	59	10	≤	≤	NUM
ejpam-115	59	11	co	co	NOUN
ejpam-115	59	12	and|=(µk,2)|	and|=(µk,2)|	PROPN
ejpam-115	59	13	≤	≤	PROPN
ejpam-115	59	14	co.	co.	PROPN
ejpam-115	59	15	thus	thus	ADV
ejpam-115	59	16	,	,	PUNCT
ejpam-115	59	17	the	the	DET
ejpam-115	59	18	relation	relation	NOUN
ejpam-115	59	19	µk,1	µk,1	NOUN
ejpam-115	59	20	,	,	PUNCT
ejpam-115	59	21	µk,2	µk,2	PROPN
ejpam-115	59	22	∈	∈	NOUN
ejpam-115	59	23	q	q	NOUN
ejpam-115	59	24	=	=	PUNCT
ejpam-115	59	25	{	{	PUNCT
ejpam-115	59	26	µ	µ	NOUN
ejpam-115	59	27	:	:	PUNCT
ejpam-115	59	28	<	<	X
ejpam-115	59	29	(	(	PUNCT
ejpam-115	59	30	µ	µ	NOUN
ejpam-115	59	31	)	)	PUNCT
ejpam-115	59	32	≥	≥	NOUN
ejpam-115	59	33	0	0	NUM
ejpam-115	59	34	,	,	PUNCT
ejpam-115	59	35	|=(µ)|	|=(µ)|	PROPN
ejpam-115	59	36	≤	≤	PUNCT
ejpam-115	59	37	co	co	VERB
ejpam-115	59	38	}	}	PUNCT
ejpam-115	59	39	holds	hold	VERB
ejpam-115	59	40	for	for	ADP
ejpam-115	59	41	allk	allk	NOUN
ejpam-115	59	42	=	=	SYM
ejpam-115	59	43	n	n	CCONJ
ejpam-115	59	44	,	,	PUNCT
ejpam-115	59	45	n	n	PROPN
ejpam-115	59	46	+	+	NUM
ejpam-115	59	47	1	1	NUM
ejpam-115	59	48	,	,	PUNCT
ejpam-115	59	49	·	·	PUNCT
ejpam-115	59	50	·	·	PUNCT
ejpam-115	59	51	·	·	PUNCT
ejpam-115	59	52	.	.	PUNCT
ejpam-115	60	1	it	it	PRON
ejpam-115	60	2	is	be	AUX
ejpam-115	60	3	easy	easy	ADJ
ejpam-115	60	4	to	to	PART
ejpam-115	60	5	verify	verify	VERB
ejpam-115	60	6	thatq	thatq	ADJ
ejpam-115	60	7	⊂	⊂	PROPN
ejpam-115	60	8	s0	s0	PROPN
ejpam-115	60	9	−	−	PROPN
ejpam-115	60	10	ico	ico	PROPN
ejpam-115	60	11	≡	≡	PROPN
ejpam-115	60	12	t	t	PROPN
ejpam-115	60	13	,	,	PUNCT
ejpam-115	60	14	wheres0	wheres0	NOUN
ejpam-115	61	1	=	=	NOUN
ejpam-115	61	2	{	{	PUNCT
ejpam-115	61	3	µ	µ	X
ejpam-115	61	4	:	:	PUNCT
ejpam-115	61	5	0	0	NUM
ejpam-115	61	6	≤	≤	NUM
ejpam-115	61	7	argµ	argµ	NOUN
ejpam-115	61	8	≤	≤	PROPN
ejpam-115	61	9	π	π	PROPN
ejpam-115	61	10	2	2	NUM
ejpam-115	61	11	}	}	PUNCT
ejpam-115	61	12	.	.	PUNCT
ejpam-115	62	1	from	from	ADP
ejpam-115	62	2	[	[	X
ejpam-115	62	3	1,10	1,10	NUM
ejpam-115	62	4	]	]	PUNCT
ejpam-115	62	5	,	,	PUNCT
ejpam-115	62	6	it	it	PRON
ejpam-115	62	7	is	be	AUX
ejpam-115	62	8	well	well	ADV
ejpam-115	62	9	known	know	VERB
ejpam-115	62	10	that	that	SCONJ
ejpam-115	62	11	in	in	ADP
ejpam-115	62	12	a	a	DET
ejpam-115	62	13	regiont	regiont	NOUN
ejpam-115	62	14	of	of	ADP
ejpam-115	62	15	the	the	DET
ejpam-115	62	16	complex	complex	ADJ
ejpam-115	62	17	planeµ	planeµ	NOUN
ejpam-115	62	18	the	the	DET
ejpam-115	62	19	equation	equation	NOUN
ejpam-115	62	20	(	(	PUNCT
ejpam-115	62	21	2.5	2.5	NUM
ejpam-115	62	22	)	)	PUNCT
ejpam-115	62	23	has	have	VERB
ejpam-115	62	24	two	two	NUM
ejpam-115	62	25	linear	linear	ADJ
ejpam-115	62	26	independent	independent	ADJ
ejpam-115	62	27	solutionsϕ1(x	solutionsϕ1(x	NOUN
ejpam-115	62	28	,	,	PUNCT
ejpam-115	62	29	µ	µ	NOUN
ejpam-115	62	30	)	)	PUNCT
ejpam-115	62	31	,	,	PUNCT
ejpam-115	62	32	ϕ2(x	ϕ2(x	PROPN
ejpam-115	62	33	,	,	PUNCT
ejpam-115	62	34	µ	µ	NOUN
ejpam-115	62	35	)	)	PUNCT
ejpam-115	62	36	satisfying	satisfy	VERB
ejpam-115	62	37	the	the	DET
ejpam-115	62	38	relations	relation	NOUN
ejpam-115	62	39	ϕj(x	ϕj(x	NOUN
ejpam-115	62	40	,	,	PUNCT
ejpam-115	62	41	µ	µ	NOUN
ejpam-115	62	42	)	)	PUNCT
ejpam-115	63	1	=	=	SYM
ejpam-115	63	2	eµωjx	eµωjx	ADJ
ejpam-115	63	3	{	{	PUNCT
ejpam-115	63	4	6∑	6∑	NUM
ejpam-115	63	5	m=0	m=0	PROPN
ejpam-115	63	6	um(x	um(x	PROPN
ejpam-115	63	7	)	)	PUNCT
ejpam-115	63	8	(	(	PUNCT
ejpam-115	63	9	2ωjµ)m	2ωjµ)m	NUM
ejpam-115	64	1	+	+	NOUN
ejpam-115	64	2	o	o	PROPN
ejpam-115	64	3	(	(	PUNCT
ejpam-115	64	4	1	1	NUM
ejpam-115	64	5	µ7	µ7	ADJ
ejpam-115	64	6	)	)	PUNCT
ejpam-115	64	7	}	}	PUNCT
ejpam-115	64	8	,	,	PUNCT
ejpam-115	64	9	(	(	PUNCT
ejpam-115	64	10	j	j	NOUN
ejpam-115	64	11	=	=	SYM
ejpam-115	64	12	1	1	NUM
ejpam-115	64	13	,	,	PUNCT
ejpam-115	64	14	2	2	NUM
ejpam-115	64	15	)	)	PUNCT
ejpam-115	64	16	,	,	PUNCT
ejpam-115	64	17	khanlar	khanlar	PROPN
ejpam-115	64	18	r.	r.	PROPN
ejpam-115	64	19	mamedov	mamedov	PROPN
ejpam-115	64	20	,	,	PUNCT
ejpam-115	64	21	hamza	hamza	PROPN
ejpam-115	64	22	menken	menken	PROPN
ejpam-115	64	23	/	/	SYM
ejpam-115	64	24	eur	eur	PROPN
ejpam-115	64	25	.	.	PUNCT
ejpam-115	65	1	j.	j.	PROPN
ejpam-115	65	2	pure	pure	PROPN
ejpam-115	65	3	appl	appl	PROPN
ejpam-115	65	4	.	.	PUNCT
ejpam-115	66	1	math,1	math,1	PROPN
ejpam-115	66	2	(	(	PUNCT
ejpam-115	66	3	2008	2008	NUM
ejpam-115	66	4	)	)	PUNCT
ejpam-115	66	5	,	,	PUNCT
ejpam-115	66	6	(	(	PUNCT
ejpam-115	66	7	51	51	NUM
ejpam-115	66	8	-	-	SYM
ejpam-115	66	9	60	60	NUM
ejpam-115	66	10	)	)	PUNCT
ejpam-115	66	11	54	54	NUM
ejpam-115	66	12	ϕ′j(x	ϕ′j(x	PROPN
ejpam-115	66	13	,	,	PUNCT
ejpam-115	66	14	µ	µ	NOUN
ejpam-115	66	15	)	)	PUNCT
ejpam-115	66	16	=	=	SYM
ejpam-115	66	17	µωje	µωje	PROPN
ejpam-115	66	18	µωjx	µωjx	PROPN
ejpam-115	66	19	{	{	PUNCT
ejpam-115	66	20	u0(x	u0(x	NOUN
ejpam-115	66	21	)	)	PUNCT
ejpam-115	66	22	+	+	NUM
ejpam-115	66	23	6∑	6∑	NUM
ejpam-115	66	24	m=1	m=1	X
ejpam-115	66	25	um(x	um(x	PUNCT
ejpam-115	66	26	)	)	PUNCT
ejpam-115	66	27	+	+	CCONJ
ejpam-115	66	28	2u′m−1(x	2u′m−1(x	NUM
ejpam-115	66	29	)	)	PUNCT
ejpam-115	66	30	(	(	PUNCT
ejpam-115	66	31	2ωjµ)m	2ωjµ)m	NUM
ejpam-115	66	32	+	+	NOUN
ejpam-115	66	33	o	o	PROPN
ejpam-115	66	34	(	(	PUNCT
ejpam-115	66	35	1	1	NUM
ejpam-115	66	36	µ7	µ7	ADJ
ejpam-115	66	37	)	)	PUNCT
ejpam-115	66	38	}	}	PUNCT
ejpam-115	66	39	,	,	PUNCT
ejpam-115	66	40	(	(	PUNCT
ejpam-115	66	41	j	j	NOUN
ejpam-115	66	42	=	=	SYM
ejpam-115	66	43	1	1	NUM
ejpam-115	66	44	,	,	PUNCT
ejpam-115	66	45	2	2	NUM
ejpam-115	66	46	)	)	PUNCT
ejpam-115	66	47	,	,	PUNCT
ejpam-115	66	48	where	where	SCONJ
ejpam-115	66	49	ω1	ω1	PROPN
ejpam-115	66	50	=	=	PUNCT
ejpam-115	67	1	−ω2	−ω2	ADP
ejpam-115	67	2	=	=	VERB
ejpam-115	67	3	i	i	PROPN
ejpam-115	67	4	,	,	PUNCT
ejpam-115	67	5	u0(x	u0(x	PROPN
ejpam-115	67	6	)	)	PUNCT
ejpam-115	67	7	≡	≡	PROPN
ejpam-115	67	8	1	1	NUM
ejpam-115	67	9	,	,	PUNCT
ejpam-115	67	10	um(x	um(x	PUNCT
ejpam-115	67	11	)	)	PUNCT
ejpam-115	67	12	=	=	SYM
ejpam-115	68	1	−	−	PROPN
ejpam-115	69	1	x∫	x∫	ADJ
ejpam-115	69	2	0	0	NUM
ejpam-115	70	1	l	l	NOUN
ejpam-115	70	2	(	(	PUNCT
ejpam-115	70	3	um−1(t	um−1(t	ADJ
ejpam-115	70	4	)	)	PUNCT
ejpam-115	70	5	)	)	PUNCT
ejpam-115	71	1	dt	dt	PROPN
ejpam-115	71	2	,	,	PUNCT
ejpam-115	71	3	m	m	VERB
ejpam-115	71	4	=	=	NOUN
ejpam-115	71	5	1	1	NUM
ejpam-115	71	6	,	,	PUNCT
ejpam-115	71	7	2	2	NUM
ejpam-115	71	8	,	,	PUNCT
ejpam-115	71	9	3	3	NUM
ejpam-115	71	10	,	,	PUNCT
ejpam-115	71	11	4	4	NUM
ejpam-115	71	12	,	,	PUNCT
ejpam-115	71	13	5	5	NUM
ejpam-115	71	14	,	,	PUNCT
ejpam-115	71	15	6	6	NUM
ejpam-115	71	16	.	.	PUNCT
ejpam-115	72	1	it	it	PRON
ejpam-115	72	2	follows	follow	VERB
ejpam-115	72	3	that	that	SCONJ
ejpam-115	72	4	ϕj(0	ϕj(0	PROPN
ejpam-115	72	5	,	,	PUNCT
ejpam-115	72	6	µ	µ	NOUN
ejpam-115	72	7	)	)	PUNCT
ejpam-115	72	8	=	=	SYM
ejpam-115	73	1	1	1	NUM
ejpam-115	73	2	+	+	NOUN
ejpam-115	73	3	o	o	NOUN
ejpam-115	73	4	(	(	PUNCT
ejpam-115	73	5	1	1	NUM
ejpam-115	73	6	µ7	µ7	ADJ
ejpam-115	73	7	)	)	PUNCT
ejpam-115	73	8	,	,	PUNCT
ejpam-115	73	9	ϕj(1	ϕj(1	PROPN
ejpam-115	73	10	,	,	PUNCT
ejpam-115	73	11	µ	µ	NOUN
ejpam-115	73	12	)	)	PUNCT
ejpam-115	73	13	=	=	VERB
ejpam-115	73	14	eµωj	eµωj	PROPN
ejpam-115	73	15	1−	1−	NUM
ejpam-115	73	16	1	1	NUM
ejpam-115	73	17	(	(	PUNCT
ejpam-115	73	18	2ωjµ)3	2ωjµ)3	NUM
ejpam-115	74	1	[	[	X
ejpam-115	74	2	q′(1)−	q′(1)−	NOUN
ejpam-115	74	3	q′(0	q′(0	PROPN
ejpam-115	74	4	)	)	PUNCT
ejpam-115	74	5	+	+	CCONJ
ejpam-115	75	1	1∫	1∫	NUM
ejpam-115	75	2	0	0	NUM
ejpam-115	75	3	q2(t)dt	q2(t)dt	NOUN
ejpam-115	75	4	]	]	X
ejpam-115	75	5	+	+	CCONJ
ejpam-115	75	6	1	1	NUM
ejpam-115	75	7	(	(	PUNCT
ejpam-115	75	8	2ωjµ)4	2ωjµ)4	NUM
ejpam-115	76	1	[	[	X
ejpam-115	76	2	q′′(1)−	q′′(1)−	ADJ
ejpam-115	76	3	q′′(0	q′′(0	X
ejpam-115	76	4	)	)	PUNCT
ejpam-115	77	1	+	+	CCONJ
ejpam-115	77	2	5	5	NUM
ejpam-115	77	3	2	2	NUM
ejpam-115	77	4	q2(1)−	q2(1)−	NOUN
ejpam-115	77	5	3	3	NUM
ejpam-115	77	6	2	2	NUM
ejpam-115	77	7	q2(0)−	q2(0)−	NOUN
ejpam-115	77	8	q(0)q(1)]−	q(0)q(1)]−	NOUN
ejpam-115	77	9	1	1	NUM
ejpam-115	77	10	(	(	PUNCT
ejpam-115	77	11	2ωjµ)5	2ωjµ)5	NUM
ejpam-115	77	12	[	[	X
ejpam-115	77	13	q′′′(1)−	q′′′(1)−	NOUN
ejpam-115	77	14	q′′′(0	q′′′(0	ADP
ejpam-115	77	15	)	)	PUNCT
ejpam-115	78	1	+	+	NUM
ejpam-115	78	2	7q(1)q′(1	7q(1)q′(1	X
ejpam-115	78	3	)	)	PUNCT
ejpam-115	78	4	−5q(0)q′(0)−	−5q(0)q′(0)−	PROPN
ejpam-115	78	5	q(0)q′(1)−	q(0)q′(1)−	NUM
ejpam-115	78	6	q(1)q′(0	q(1)q′(0	NOUN
ejpam-115	78	7	)	)	PUNCT
ejpam-115	78	8	+	+	CCONJ
ejpam-115	78	9	(	(	PUNCT
ejpam-115	78	10	q(1)−	q(1)−	PROPN
ejpam-115	78	11	q(0	q(0	PROPN
ejpam-115	78	12	)	)	PUNCT
ejpam-115	78	13	)	)	PUNCT
ejpam-115	79	1	1∫	1∫	NUM
ejpam-115	79	2	0	0	NUM
ejpam-115	79	3	q2(t)dt	q2(t)dt	NOUN
ejpam-115	79	4	+2	+2	PROPN
ejpam-115	79	5	1∫	1∫	NUM
ejpam-115	79	6	0	0	NUM
ejpam-115	80	1	q3(t)dt−	q3(t)dt−	PROPN
ejpam-115	80	2	1∫	1∫	NUM
ejpam-115	80	3	0	0	NUM
ejpam-115	80	4	q′	q′	NOUN
ejpam-115	80	5	2	2	NUM
ejpam-115	80	6	(	(	PUNCT
ejpam-115	80	7	t)dt	t)dt	PROPN
ejpam-115	80	8	]	]	X
ejpam-115	80	9	+	+	CCONJ
ejpam-115	80	10	1	1	NUM
ejpam-115	80	11	(	(	PUNCT
ejpam-115	80	12	2ωjµ)6	2ωjµ)6	NUM
ejpam-115	81	1	[	[	X
ejpam-115	81	2	q(4)(1)−	q(4)(1)−	NOUN
ejpam-115	81	3	q(4)(0	q(4)(0	NUM
ejpam-115	81	4	)	)	PUNCT
ejpam-115	81	5	+	+	NUM
ejpam-115	81	6	9q(1)q′′(1	9q(1)q′′(1	NUM
ejpam-115	81	7	)	)	PUNCT
ejpam-115	81	8	−7q(0)q′′(0)−	−7q(0)q′′(0)−	NOUN
ejpam-115	81	9	q(0)q′′(1)−	q(0)q′′(1)−	PROPN
ejpam-115	81	10	q(1)q′′(0	q(1)q′′(0	PROPN
ejpam-115	81	11	)	)	PUNCT
ejpam-115	81	12	+	+	CCONJ
ejpam-115	81	13	11	11	NUM
ejpam-115	81	14	2	2	NUM
ejpam-115	81	15	q′2(1)−	q′2(1)−	NOUN
ejpam-115	81	16	9	9	NUM
ejpam-115	81	17	2	2	NUM
ejpam-115	81	18	q′2(0)−	q′2(0)−	NOUN
ejpam-115	81	19	q′(0)q′(1	q′(0)q′(1	PROPN
ejpam-115	81	20	)	)	PUNCT
ejpam-115	81	21	+	+	CCONJ
ejpam-115	81	22	15	15	NUM
ejpam-115	81	23	2	2	NUM
ejpam-115	81	24	q3(1)−	q3(1)−	NOUN
ejpam-115	81	25	7	7	NUM
ejpam-115	81	26	2	2	NUM
ejpam-115	81	27	q3(0)−	q3(0)−	NOUN
ejpam-115	81	28	5	5	NUM
ejpam-115	81	29	2	2	NUM
ejpam-115	81	30	q(0)q2(1)−	q(0)q2(1)−	NOUN
ejpam-115	81	31	3	3	NUM
ejpam-115	81	32	2	2	NUM
ejpam-115	81	33	q(1)q2(0	q(1)q2(0	NOUN
ejpam-115	81	34	)	)	PUNCT
ejpam-115	82	1	+	+	ADJ
ejpam-115	82	2	(	(	PUNCT
ejpam-115	82	3	q′(1)−	q′(1)−	NOUN
ejpam-115	82	4	q′(0	q′(0	PROPN
ejpam-115	82	5	)	)	PUNCT
ejpam-115	82	6	)	)	PUNCT
ejpam-115	83	1	1∫	1∫	NUM
ejpam-115	83	2	0	0	NUM
ejpam-115	83	3	q2(t)dt+	q2(t)dt+	ADP
ejpam-115	83	4	1	1	NUM
ejpam-115	83	5	2	2	NUM
ejpam-115	83	6	(	(	PUNCT
ejpam-115	83	7	1∫	1∫	NUM
ejpam-115	83	8	0	0	NUM
ejpam-115	83	9	q2(t)dt)2	q2(t)dt)2	NOUN
ejpam-115	83	10	]	]	PUNCT
ejpam-115	84	1	+	+	NOUN
ejpam-115	84	2	o	o	X
ejpam-115	84	3	(	(	PUNCT
ejpam-115	84	4	1	1	NUM
ejpam-115	84	5	µ7	µ7	ADJ
ejpam-115	84	6	)	)	PUNCT
ejpam-115	84	7			NOUN
ejpam-115	84	8	,	,	PUNCT
ejpam-115	84	9	ϕ′j(0	ϕ′j(0	PROPN
ejpam-115	84	10	,	,	PUNCT
ejpam-115	84	11	µ	µ	NOUN
ejpam-115	84	12	)	)	PUNCT
ejpam-115	84	13	=	=	SYM
ejpam-115	84	14	µωj	µωj	ADJ
ejpam-115	84	15	{	{	PUNCT
ejpam-115	84	16	1−	1−	NUM
ejpam-115	84	17	2q(0	2q(0	NUM
ejpam-115	84	18	)	)	PUNCT
ejpam-115	84	19	(	(	PUNCT
ejpam-115	84	20	2ωjµ)2	2ωjµ)2	NUM
ejpam-115	84	21	+	+	CCONJ
ejpam-115	84	22	2q′(0	2q′(0	NOUN
ejpam-115	84	23	)	)	PUNCT
ejpam-115	84	24	(	(	PUNCT
ejpam-115	84	25	2ωjµ)3	2ωjµ)3	NUM
ejpam-115	84	26	−	−	NUM
ejpam-115	84	27	1	1	NUM
ejpam-115	84	28	(	(	PUNCT
ejpam-115	84	29	2ωjµ)4	2ωjµ)4	NUM
ejpam-115	85	1	[	[	X
ejpam-115	85	2	2q′′(0	2q′′(0	NUM
ejpam-115	85	3	)	)	PUNCT
ejpam-115	86	1	+	+	NOUN
ejpam-115	86	2	2q2(0	2q2(0	NUM
ejpam-115	86	3	)	)	PUNCT
ejpam-115	86	4	]	]	PUNCT
ejpam-115	87	1	+	+	CCONJ
ejpam-115	87	2	1	1	NUM
ejpam-115	87	3	(	(	PUNCT
ejpam-115	87	4	2ωjµ)5	2ωjµ)5	NUM
ejpam-115	87	5	[	[	X
ejpam-115	87	6	2q	2q	NUM
ejpam-115	87	7	′′′	′′′	PROPN
ejpam-115	87	8	(	(	PUNCT
ejpam-115	87	9	0	0	NUM
ejpam-115	87	10	)	)	PUNCT
ejpam-115	87	11	+	+	CCONJ
ejpam-115	87	12	8q(0)q′(0)]−	8q(0)q′(0)]−	NUM
ejpam-115	87	13	1	1	NUM
ejpam-115	87	14	(	(	PUNCT
ejpam-115	87	15	2ωjµ)6	2ωjµ)6	NUM
ejpam-115	88	1	[	[	X
ejpam-115	88	2	2q(4)(0	2q(4)(0	NUM
ejpam-115	88	3	)	)	PUNCT
ejpam-115	88	4	+10q′2(0	+10q′2(0	NOUN
ejpam-115	88	5	)	)	PUNCT
ejpam-115	89	1	+	+	CCONJ
ejpam-115	89	2	12q(0)q′′(0	12q(0)q′′(0	NUM
ejpam-115	89	3	)	)	PUNCT
ejpam-115	89	4	+	+	NUM
ejpam-115	89	5	4q3(0	4q3(0	NUM
ejpam-115	89	6	)	)	PUNCT
ejpam-115	89	7	]	]	PUNCT
ejpam-115	90	1	+	+	PUNCT
ejpam-115	90	2	o	o	X
ejpam-115	90	3	(	(	PUNCT
ejpam-115	90	4	1	1	NUM
ejpam-115	90	5	µ7	µ7	ADJ
ejpam-115	90	6	)	)	PUNCT
ejpam-115	90	7	}	}	PUNCT
ejpam-115	90	8	,	,	PUNCT
ejpam-115	90	9	ϕ′j(1	ϕ′j(1	NUM
ejpam-115	90	10	,	,	PUNCT
ejpam-115	90	11	µ	µ	NOUN
ejpam-115	90	12	)	)	PUNCT
ejpam-115	90	13	=	=	SYM
ejpam-115	90	14	µωje	µωje	PROPN
ejpam-115	90	15	µωj	µωj	PROPN
ejpam-115	90	16	1−	1−	PROPN
ejpam-115	90	17	q(0	q(0	PROPN
ejpam-115	90	18	)	)	PUNCT
ejpam-115	90	19	+	+	PUNCT
ejpam-115	90	20	q(1	q(1	NOUN
ejpam-115	90	21	)	)	PUNCT
ejpam-115	90	22	(	(	PUNCT
ejpam-115	90	23	2ωjµ)2	2ωjµ)2	NUM
ejpam-115	90	24	+	+	CCONJ
ejpam-115	90	25	1	1	NUM
ejpam-115	90	26	(	(	PUNCT
ejpam-115	90	27	2ωjµ)3	2ωjµ)3	NUM
ejpam-115	91	1	[	[	X
ejpam-115	91	2	q′(1	q′(1	X
ejpam-115	91	3	)	)	PUNCT
ejpam-115	91	4	+	+	NUM
ejpam-115	91	5	q′(0)−	q′(0)−	X
ejpam-115	91	6	1∫	1∫	NUM
ejpam-115	91	7	0	0	NUM
ejpam-115	91	8	q2(t)dt	q2(t)dt	NOUN
ejpam-115	91	9	]	]	X
ejpam-115	91	10	−	−	PROPN
ejpam-115	91	11	1	1	NUM
ejpam-115	91	12	(	(	PUNCT
ejpam-115	91	13	2ωjµ)4	2ωjµ)4	NUM
ejpam-115	91	14	[	[	X
ejpam-115	91	15	q′′(1	q′′(1	NOUN
ejpam-115	91	16	)	)	PUNCT
ejpam-115	91	17	+	+	NUM
ejpam-115	92	1	q′′(0	q′′(0	NOUN
ejpam-115	92	2	)	)	PUNCT
ejpam-115	93	1	+	+	CCONJ
ejpam-115	93	2	3	3	NUM
ejpam-115	93	3	2	2	NUM
ejpam-115	93	4	q2(1	q2(1	NOUN
ejpam-115	93	5	)	)	PUNCT
ejpam-115	94	1	+	+	CCONJ
ejpam-115	94	2	3	3	NUM
ejpam-115	94	3	2	2	NUM
ejpam-115	94	4	q2(0)−	q2(0)−	NOUN
ejpam-115	94	5	q(0)q(1	q(0)q(1	NOUN
ejpam-115	94	6	)	)	PUNCT
ejpam-115	94	7	]	]	PUNCT
ejpam-115	95	1	khanlar	khanlar	PROPN
ejpam-115	95	2	r.	r.	PROPN
ejpam-115	95	3	mamedov	mamedov	PROPN
ejpam-115	95	4	,	,	PUNCT
ejpam-115	95	5	hamza	hamza	PROPN
ejpam-115	95	6	menken	menken	PROPN
ejpam-115	95	7	/	/	SYM
ejpam-115	95	8	eur	eur	PROPN
ejpam-115	95	9	.	.	PUNCT
ejpam-115	96	1	j.	j.	PROPN
ejpam-115	96	2	pure	pure	PROPN
ejpam-115	96	3	appl	appl	PROPN
ejpam-115	96	4	.	.	PUNCT
ejpam-115	97	1	math,1	math,1	PROPN
ejpam-115	97	2	(	(	PUNCT
ejpam-115	97	3	2008	2008	NUM
ejpam-115	97	4	)	)	PUNCT
ejpam-115	97	5	,	,	PUNCT
ejpam-115	97	6	(	(	PUNCT
ejpam-115	97	7	51	51	NUM
ejpam-115	97	8	-	-	SYM
ejpam-115	97	9	60	60	NUM
ejpam-115	97	10	)	)	PUNCT
ejpam-115	97	11	55	55	NUM
ejpam-115	98	1	+	+	CCONJ
ejpam-115	98	2	1	1	NUM
ejpam-115	98	3	(	(	PUNCT
ejpam-115	98	4	2ωjµ)5	2ωjµ)5	NUM
ejpam-115	98	5	[	[	X
ejpam-115	98	6	q′′′(1	q′′′(1	NUM
ejpam-115	98	7	)	)	PUNCT
ejpam-115	98	8	+	+	NUM
ejpam-115	98	9	q′′′(0	q′′′(0	X
ejpam-115	98	10	)	)	PUNCT
ejpam-115	99	1	+	+	NUM
ejpam-115	99	2	5q(1)q′(1	5q(1)q′(1	ADJ
ejpam-115	99	3	)	)	PUNCT
ejpam-115	100	1	+	+	CCONJ
ejpam-115	100	2	5q(0)q′(0)−	5q(0)q′(0)−	NUM
ejpam-115	100	3	q(0)q′(1	q(0)q′(1	PROPN
ejpam-115	100	4	)	)	PUNCT
ejpam-115	100	5	−q(1)q′(0	−q(1)q′(0	NOUN
ejpam-115	100	6	)	)	PUNCT
ejpam-115	101	1	+	+	CCONJ
ejpam-115	101	2	(	(	PUNCT
ejpam-115	101	3	q(1	q(1	NOUN
ejpam-115	101	4	)	)	PUNCT
ejpam-115	101	5	+	+	CCONJ
ejpam-115	101	6	q(0	q(0	NOUN
ejpam-115	101	7	)	)	PUNCT
ejpam-115	101	8	)	)	PUNCT
ejpam-115	102	1	1∫	1∫	NUM
ejpam-115	102	2	0	0	NUM
ejpam-115	103	1	q2(t)dt−	q2(t)dt−	PROPN
ejpam-115	103	2	2	2	NUM
ejpam-115	103	3	1∫	1∫	NUM
ejpam-115	103	4	0	0	NUM
ejpam-115	103	5	q3(t)dt+	q3(t)dt+	NOUN
ejpam-115	104	1	1∫	1∫	NUM
ejpam-115	104	2	0	0	NUM
ejpam-115	104	3	q′2(t)dt	q′2(t)dt	NOUN
ejpam-115	104	4	]	]	PUNCT
ejpam-115	104	5	−	−	PROPN
ejpam-115	104	6	1	1	NUM
ejpam-115	104	7	(	(	PUNCT
ejpam-115	104	8	2ωjµ)6	2ωjµ)6	NUM
ejpam-115	105	1	[	[	X
ejpam-115	105	2	q(4)(1	q(4)(1	NUM
ejpam-115	105	3	)	)	PUNCT
ejpam-115	105	4	+	+	PUNCT
ejpam-115	105	5	q(4)(0	q(4)(0	X
ejpam-115	105	6	)	)	PUNCT
ejpam-115	105	7	+	+	CCONJ
ejpam-115	105	8	13	13	NUM
ejpam-115	105	9	2	2	NUM
ejpam-115	105	10	q′2(1	q′2(1	PROPN
ejpam-115	105	11	)	)	PUNCT
ejpam-115	105	12	+	+	CCONJ
ejpam-115	105	13	9	9	NUM
ejpam-115	105	14	2	2	NUM
ejpam-115	105	15	q′2(0)−	q′2(0)−	NOUN
ejpam-115	105	16	q′(0)q′(1	q′(0)q′(1	PROPN
ejpam-115	105	17	)	)	PUNCT
ejpam-115	106	1	+7q(1)q′′(1	+7q(1)q′′(1	PROPN
ejpam-115	106	2	)	)	PUNCT
ejpam-115	107	1	+	+	CCONJ
ejpam-115	107	2	7q(0)q′′(0)−	7q(0)q′′(0)−	PROPN
ejpam-115	107	3	q(0)q′′(1)−	q(0)q′′(1)−	ADJ
ejpam-115	107	4	q(1)q′′(0	q(1)q′′(0	NOUN
ejpam-115	107	5	)	)	PUNCT
ejpam-115	107	6	+	+	CCONJ
ejpam-115	107	7	7	7	NUM
ejpam-115	107	8	2	2	NUM
ejpam-115	107	9	q3(1	q3(1	PROPN
ejpam-115	107	10	)	)	PUNCT
ejpam-115	108	1	+	+	CCONJ
ejpam-115	108	2	7	7	NUM
ejpam-115	108	3	2	2	NUM
ejpam-115	108	4	q3(0)−	q3(0)−	NOUN
ejpam-115	108	5	3	3	NUM
ejpam-115	108	6	2	2	NUM
ejpam-115	108	7	q(0)q2(1)−	q(0)q2(1)−	NOUN
ejpam-115	108	8	3	3	NUM
ejpam-115	108	9	2	2	NUM
ejpam-115	108	10	q(1)q2(0	q(1)q2(0	NOUN
ejpam-115	108	11	)	)	PUNCT
ejpam-115	108	12	+	+	CCONJ
ejpam-115	108	13	(	(	PUNCT
ejpam-115	108	14	q′(1	q′(1	ADJ
ejpam-115	108	15	)	)	PUNCT
ejpam-115	108	16	+	+	NUM
ejpam-115	109	1	q′(0	q′(0	NOUN
ejpam-115	109	2	)	)	PUNCT
ejpam-115	109	3	)	)	PUNCT
ejpam-115	110	1	1∫	1∫	NUM
ejpam-115	110	2	0	0	NUM
ejpam-115	110	3	q2(t)dt	q2(t)dt	VERB
ejpam-115	110	4	−1	−1	NOUN
ejpam-115	110	5	2	2	NUM
ejpam-115	110	6	(	(	PUNCT
ejpam-115	110	7	1∫	1∫	NUM
ejpam-115	110	8	0	0	NUM
ejpam-115	110	9	q2(t)dt)2	q2(t)dt)2	NOUN
ejpam-115	110	10	]	]	PUNCT
ejpam-115	111	1	+	+	NOUN
ejpam-115	111	2	o	o	X
ejpam-115	111	3	(	(	PUNCT
ejpam-115	111	4	1	1	NUM
ejpam-115	111	5	µ7	µ7	ADJ
ejpam-115	111	6	)	)	PUNCT
ejpam-115	111	7			NOUN
ejpam-115	111	8	.	.	PUNCT
ejpam-115	112	1	let	let	VERB
ejpam-115	112	2	us	we	PRON
ejpam-115	112	3	substitute	substitute	VERB
ejpam-115	112	4	all	all	DET
ejpam-115	112	5	these	these	DET
ejpam-115	112	6	expressions	expression	NOUN
ejpam-115	112	7	into	into	ADP
ejpam-115	112	8	the	the	DET
ejpam-115	112	9	characteristic	characteristic	ADJ
ejpam-115	112	10	determinant	determinant	ADJ
ejpam-115	112	11	∆(µ	∆(µ	NOUN
ejpam-115	112	12	)	)	PUNCT
ejpam-115	112	13	=	=	SYM
ejpam-115	112	14	∣∣∣∣	∣∣∣∣	NOUN
ejpam-115	112	15	u1(ϕ1	u1(ϕ1	ADJ
ejpam-115	112	16	)	)	PUNCT
ejpam-115	112	17	u1(ϕ2	u1(ϕ2	NOUN
ejpam-115	112	18	)	)	PUNCT
ejpam-115	112	19	u2(ϕ1	u2(ϕ1	NOUN
ejpam-115	112	20	)	)	PUNCT
ejpam-115	112	21	u2(ϕ2	u2(ϕ2	NUM
ejpam-115	112	22	)	)	PUNCT
ejpam-115	112	23	∣∣∣∣	∣∣∣∣	NOUN
ejpam-115	112	24	,	,	PUNCT
ejpam-115	112	25	whereu1(y	whereu1(y	PROPN
ejpam-115	112	26	)	)	PUNCT
ejpam-115	113	1	=	=	SYM
ejpam-115	113	2	y(1)−	y(1)−	PROPN
ejpam-115	113	3	y(0	y(0	PROPN
ejpam-115	113	4	)	)	PUNCT
ejpam-115	113	5	,	,	PUNCT
ejpam-115	113	6	u2(y	u2(y	X
ejpam-115	113	7	)	)	PUNCT
ejpam-115	113	8	=	=	SYM
ejpam-115	113	9	y′(1)−	y′(1)−	NOUN
ejpam-115	113	10	y′(0	y′(0	PROPN
ejpam-115	113	11	)	)	PUNCT
ejpam-115	113	12	.	.	PUNCT
ejpam-115	114	1	by	by	ADP
ejpam-115	114	2	elementary	elementary	ADJ
ejpam-115	114	3	transformations	transformation	NOUN
ejpam-115	114	4	,	,	PUNCT
ejpam-115	114	5	we	we	PRON
ejpam-115	114	6	obtain	obtain	VERB
ejpam-115	114	7	the	the	DET
ejpam-115	114	8	relation	relation	NOUN
ejpam-115	114	9	(	(	PUNCT
ejpam-115	114	10	iµ)−1∆(µ	iµ)−1∆(µ	NOUN
ejpam-115	114	11	)	)	PUNCT
ejpam-115	114	12	=	=	SYM
ejpam-115	114	13	e2iµ	e2iµ	X
ejpam-115	114	14	1−	1−	NUM
ejpam-115	114	15	2q(0	2q(0	NUM
ejpam-115	114	16	)	)	PUNCT
ejpam-115	114	17	(	(	PUNCT
ejpam-115	114	18	2iµ)2	2iµ)2	NUM
ejpam-115	114	19	−	−	NOUN
ejpam-115	114	20	1	1	NUM
ejpam-115	114	21	(	(	PUNCT
ejpam-115	114	22	2iµ)3	2iµ)3	PROPN
ejpam-115	114	23	1∫	1∫	NUM
ejpam-115	114	24	0	0	NUM
ejpam-115	115	1	q2(t)dt−	q2(t)dt−	ADJ
ejpam-115	115	2	1	1	NUM
ejpam-115	115	3	(	(	PUNCT
ejpam-115	115	4	2iµ)4	2iµ)4	NUM
ejpam-115	115	5	[	[	X
ejpam-115	115	6	2q′′(0)−	2q′′(0)−	NUM
ejpam-115	115	7	1	1	NUM
ejpam-115	115	8	2	2	NUM
ejpam-115	115	9	q2(1	q2(1	NOUN
ejpam-115	115	10	)	)	PUNCT
ejpam-115	115	11	+	+	CCONJ
ejpam-115	115	12	3	3	NUM
ejpam-115	115	13	2	2	NUM
ejpam-115	115	14	q2(0	q2(0	NOUN
ejpam-115	115	15	)	)	PUNCT
ejpam-115	115	16	+	+	CCONJ
ejpam-115	116	1	q(0)q(1)]−	q(0)q(1)]−	PROPN
ejpam-115	116	2	1	1	NUM
ejpam-115	116	3	(	(	PUNCT
ejpam-115	116	4	2iµ)5	2iµ)5	NUM
ejpam-115	117	1	[	[	X
ejpam-115	117	2	q(1)q′(1)−	q(1)q′(1)−	NUM
ejpam-115	117	3	q(0)q′(1)−	q(0)q′(1)−	VERB
ejpam-115	117	4	q(0)q′(0	q(0)q′(0	NOUN
ejpam-115	117	5	)	)	PUNCT
ejpam-115	118	1	+	+	NOUN
ejpam-115	118	2	q(1)q′(0)−	q(1)q′(0)−	NOUN
ejpam-115	118	3	2q(0	2q(0	NUM
ejpam-115	118	4	)	)	PUNCT
ejpam-115	119	1	1∫	1∫	NUM
ejpam-115	119	2	0	0	NUM
ejpam-115	119	3	q2(t)dt+	q2(t)dt+	ADP
ejpam-115	119	4	2	2	NUM
ejpam-115	119	5	1∫	1∫	NUM
ejpam-115	119	6	0	0	NUM
ejpam-115	120	1	q3(t)dt−	q3(t)dt−	PROPN
ejpam-115	120	2	1∫	1∫	NUM
ejpam-115	120	3	0	0	NUM
ejpam-115	120	4	q′2(t)dt	q′2(t)dt	NOUN
ejpam-115	120	5	]	]	PUNCT
ejpam-115	120	6	−	−	PROPN
ejpam-115	120	7	1	1	NUM
ejpam-115	120	8	(	(	PUNCT
ejpam-115	120	9	2iµ)6	2iµ)6	PROPN
ejpam-115	121	1	[	[	X
ejpam-115	121	2	2q(4)(0	2q(4)(0	NUM
ejpam-115	121	3	)	)	PUNCT
ejpam-115	121	4	+	+	CCONJ
ejpam-115	121	5	1	1	NUM
ejpam-115	121	6	2	2	NUM
ejpam-115	121	7	q′2(1	q′2(1	PROPN
ejpam-115	121	8	)	)	PUNCT
ejpam-115	122	1	+	+	CCONJ
ejpam-115	122	2	21	21	NUM
ejpam-115	122	3	2	2	NUM
ejpam-115	122	4	q′2(0)−	q′2(0)−	NOUN
ejpam-115	122	5	q′(0)q′(1)−	q′(0)q′(1)−	ADJ
ejpam-115	122	6	q(1)q′′(1	q(1)q′′(1	PROPN
ejpam-115	122	7	)	)	PUNCT
ejpam-115	122	8	+11q(0)q′′(0	+11q(0)q′′(0	NOUN
ejpam-115	122	9	)	)	PUNCT
ejpam-115	123	1	+	+	CCONJ
ejpam-115	123	2	q(0)q′′(1	q(0)q′′(1	NOUN
ejpam-115	123	3	)	)	PUNCT
ejpam-115	124	1	+	+	CCONJ
ejpam-115	125	1	q(1)q′′(0)−	q(1)q′′(0)−	PROPN
ejpam-115	125	2	2q3(1	2q3(1	NUM
ejpam-115	125	3	)	)	PUNCT
ejpam-115	125	4	+	+	CCONJ
ejpam-115	125	5	3q3(0	3q3(0	NUM
ejpam-115	125	6	)	)	PUNCT
ejpam-115	126	1	+3q(0)q2(1)−	+3q(0)q2(1)−	PROPN
ejpam-115	126	2	(	(	PUNCT
ejpam-115	126	3	1∫	1∫	NUM
ejpam-115	126	4	0	0	NUM
ejpam-115	126	5	q2(t)dt)2	q2(t)dt)2	NOUN
ejpam-115	126	6	]	]	PUNCT
ejpam-115	127	1	+	+	NOUN
ejpam-115	127	2	o	o	X
ejpam-115	127	3	(	(	PUNCT
ejpam-115	127	4	1	1	NUM
ejpam-115	127	5	µ7	µ7	ADJ
ejpam-115	127	6	)	)	PUNCT
ejpam-115	128	1			ADP
ejpam-115	128	2	khanlar	khanlar	PROPN
ejpam-115	128	3	r.	r.	PROPN
ejpam-115	128	4	mamedov	mamedov	PROPN
ejpam-115	128	5	,	,	PUNCT
ejpam-115	128	6	hamza	hamza	PROPN
ejpam-115	128	7	menken	menken	PROPN
ejpam-115	128	8	/	/	SYM
ejpam-115	128	9	eur	eur	PROPN
ejpam-115	128	10	.	.	PUNCT
ejpam-115	129	1	j.	j.	PROPN
ejpam-115	129	2	pure	pure	PROPN
ejpam-115	129	3	appl	appl	PROPN
ejpam-115	129	4	.	.	PUNCT
ejpam-115	130	1	math,1	math,1	PROPN
ejpam-115	130	2	(	(	PUNCT
ejpam-115	130	3	2008	2008	NUM
ejpam-115	130	4	)	)	PUNCT
ejpam-115	130	5	,	,	PUNCT
ejpam-115	130	6	(	(	PUNCT
ejpam-115	130	7	51	51	NUM
ejpam-115	130	8	-	-	SYM
ejpam-115	130	9	60	60	NUM
ejpam-115	130	10	)	)	PUNCT
ejpam-115	130	11	56	56	NUM
ejpam-115	130	12	−2eiµ	−2eiµ	NUM
ejpam-115	130	13	{	{	PUNCT
ejpam-115	130	14	1−	1−	NUM
ejpam-115	130	15	2q(0	2q(0	NUM
ejpam-115	130	16	)	)	PUNCT
ejpam-115	130	17	(	(	PUNCT
ejpam-115	130	18	2iµ)2	2iµ)2	NUM
ejpam-115	130	19	−	−	NOUN
ejpam-115	130	20	1	1	NUM
ejpam-115	130	21	(	(	PUNCT
ejpam-115	130	22	2iµ)4	2iµ)4	NUM
ejpam-115	130	23	[	[	X
ejpam-115	130	24	2q′′(0	2q′′(0	NUM
ejpam-115	130	25	)	)	PUNCT
ejpam-115	130	26	+	+	CCONJ
ejpam-115	130	27	2q2(0)]−	2q2(0)]−	NUM
ejpam-115	130	28	1	1	NUM
ejpam-115	130	29	(	(	PUNCT
ejpam-115	130	30	2iµ)6	2iµ)6	PROPN
ejpam-115	130	31	[	[	X
ejpam-115	130	32	2q(4)(0	2q(4)(0	NUM
ejpam-115	130	33	)	)	PUNCT
ejpam-115	130	34	+12q(0)q′′(0	+12q(0)q′′(0	NOUN
ejpam-115	130	35	)	)	PUNCT
ejpam-115	131	1	+	+	NUM
ejpam-115	131	2	10q′2(0	10q′2(0	NUM
ejpam-115	131	3	)	)	PUNCT
ejpam-115	132	1	+	+	CCONJ
ejpam-115	132	2	4q3(0	4q3(0	NUM
ejpam-115	132	3	)	)	PUNCT
ejpam-115	132	4	]	]	PUNCT
ejpam-115	133	1	+	+	PUNCT
ejpam-115	133	2	o	o	X
ejpam-115	133	3	(	(	PUNCT
ejpam-115	133	4	1	1	NUM
ejpam-115	133	5	µ7	µ7	ADJ
ejpam-115	133	6	)	)	PUNCT
ejpam-115	133	7	}	}	PUNCT
ejpam-115	133	8	+	+	CCONJ
ejpam-115	133	9	1−	1−	NUM
ejpam-115	133	10	2q(0	2q(0	NUM
ejpam-115	133	11	)	)	PUNCT
ejpam-115	133	12	(	(	PUNCT
ejpam-115	133	13	2iµ)2	2iµ)2	NUM
ejpam-115	133	14	+	+	SYM
ejpam-115	133	15	1	1	NUM
ejpam-115	133	16	(	(	PUNCT
ejpam-115	133	17	2iµ)3	2iµ)3	PROPN
ejpam-115	133	18	1∫	1∫	NUM
ejpam-115	133	19	0	0	NUM
ejpam-115	134	1	q2(t)dt−	q2(t)dt−	ADJ
ejpam-115	134	2	1	1	NUM
ejpam-115	134	3	(	(	PUNCT
ejpam-115	134	4	2iµ)4	2iµ)4	NUM
ejpam-115	134	5	[	[	X
ejpam-115	134	6	2q′′(0)−	2q′′(0)−	NUM
ejpam-115	134	7	1	1	NUM
ejpam-115	134	8	2	2	NUM
ejpam-115	134	9	q2(1	q2(1	NOUN
ejpam-115	134	10	)	)	PUNCT
ejpam-115	134	11	+	+	CCONJ
ejpam-115	134	12	3	3	NUM
ejpam-115	134	13	2	2	NUM
ejpam-115	134	14	q2(0	q2(0	NOUN
ejpam-115	134	15	)	)	PUNCT
ejpam-115	134	16	+	+	SYM
ejpam-115	134	17	q(0)q(1	q(0)q(1	NOUN
ejpam-115	134	18	)	)	PUNCT
ejpam-115	134	19	]	]	PUNCT
ejpam-115	135	1	+	+	CCONJ
ejpam-115	135	2	1	1	NUM
ejpam-115	135	3	(	(	PUNCT
ejpam-115	135	4	2iµ)5	2iµ)5	NUM
ejpam-115	135	5	[	[	X
ejpam-115	135	6	q(1)q′(1)−	q(1)q′(1)−	NUM
ejpam-115	135	7	q(0)q′(0)−	q(0)q′(0)−	X
ejpam-115	135	8	q(0)q′(1	q(0)q′(1	PROPN
ejpam-115	135	9	)	)	PUNCT
ejpam-115	136	1	+	+	NOUN
ejpam-115	136	2	q(1)q′(0)−	q(1)q′(0)−	NOUN
ejpam-115	136	3	2q(0	2q(0	NUM
ejpam-115	136	4	)	)	PUNCT
ejpam-115	137	1	1∫	1∫	NUM
ejpam-115	137	2	0	0	NUM
ejpam-115	137	3	q2(t)d+	q2(t)d+	NOUN
ejpam-115	137	4	2	2	NUM
ejpam-115	137	5	1∫	1∫	NUM
ejpam-115	137	6	0	0	NUM
ejpam-115	138	1	q3(t)dt−	q3(t)dt−	PROPN
ejpam-115	138	2	1∫	1∫	NUM
ejpam-115	138	3	0	0	NUM
ejpam-115	138	4	q′2(t)dt	q′2(t)dt	NOUN
ejpam-115	138	5	]	]	PUNCT
ejpam-115	138	6	−	−	PROPN
ejpam-115	138	7	1	1	NUM
ejpam-115	138	8	(	(	PUNCT
ejpam-115	138	9	2iµ)6	2iµ)6	PROPN
ejpam-115	139	1	[	[	X
ejpam-115	139	2	2q(4)(0	2q(4)(0	NUM
ejpam-115	139	3	)	)	PUNCT
ejpam-115	139	4	+	+	CCONJ
ejpam-115	139	5	1	1	NUM
ejpam-115	139	6	2	2	NUM
ejpam-115	139	7	q′2(1	q′2(1	PROPN
ejpam-115	139	8	)	)	PUNCT
ejpam-115	140	1	+	+	CCONJ
ejpam-115	140	2	21	21	NUM
ejpam-115	140	3	2	2	NUM
ejpam-115	140	4	q′2(0)−	q′2(0)−	NOUN
ejpam-115	140	5	q′(0)q′(1)−	q′(0)q′(1)−	ADJ
ejpam-115	140	6	q(1)q′′(1	q(1)q′′(1	PROPN
ejpam-115	140	7	)	)	PUNCT
ejpam-115	140	8	+11q(0)q′′(0	+11q(0)q′′(0	NOUN
ejpam-115	140	9	)	)	PUNCT
ejpam-115	141	1	+	+	CCONJ
ejpam-115	141	2	q(0)q′′(1	q(0)q′′(1	NOUN
ejpam-115	141	3	)	)	PUNCT
ejpam-115	142	1	+	+	CCONJ
ejpam-115	143	1	q(1)q′′(0)−	q(1)q′′(0)−	PROPN
ejpam-115	143	2	2q3(1	2q3(1	NUM
ejpam-115	143	3	)	)	PUNCT
ejpam-115	143	4	+	+	CCONJ
ejpam-115	143	5	3q3(0	3q3(0	NUM
ejpam-115	143	6	)	)	PUNCT
ejpam-115	144	1	+3q(0)q2(1)−	+3q(0)q2(1)−	PROPN
ejpam-115	144	2	(	(	PUNCT
ejpam-115	144	3	1∫	1∫	NUM
ejpam-115	144	4	0	0	NUM
ejpam-115	144	5	q2(t)dt)2	q2(t)dt)2	NOUN
ejpam-115	144	6	]	]	PUNCT
ejpam-115	145	1	+	+	NOUN
ejpam-115	145	2	o	o	X
ejpam-115	145	3	(	(	PUNCT
ejpam-115	145	4	1	1	NUM
ejpam-115	145	5	µ7	µ7	ADJ
ejpam-115	145	6	)	)	PUNCT
ejpam-115	145	7			NOUN
ejpam-115	145	8	,	,	PUNCT
ejpam-115	145	9	(	(	PUNCT
ejpam-115	145	10	2.6	2.6	NUM
ejpam-115	145	11	)	)	PUNCT
ejpam-115	145	12	for	for	ADP
ejpam-115	145	13	µ	µ	PRON
ejpam-115	145	14	∈	∈	NOUN
ejpam-115	145	15	t	t	NOUN
ejpam-115	145	16	sufficiently	sufficiently	ADV
ejpam-115	145	17	large	large	ADJ
ejpam-115	145	18	in	in	ADP
ejpam-115	145	19	absolute	absolute	ADJ
ejpam-115	145	20	value	value	NOUN
ejpam-115	145	21	.	.	PUNCT
ejpam-115	146	1	let	let	VERB
ejpam-115	146	2	b(µ	b(µ	NOUN
ejpam-115	146	3	)	)	PUNCT
ejpam-115	146	4	be	be	VERB
ejpam-115	146	5	the	the	DET
ejpam-115	146	6	coefficient	coefficient	NOUN
ejpam-115	146	7	ofe2iµ	ofe2iµ	PROPN
ejpam-115	146	8	in	in	ADP
ejpam-115	146	9	(	(	PUNCT
ejpam-115	146	10	2.6	2.6	NUM
ejpam-115	146	11	)	)	PUNCT
ejpam-115	146	12	.	.	PUNCT
ejpam-115	147	1	using	use	VERB
ejpam-115	147	2	the	the	DET
ejpam-115	147	3	expansion	expansion	NOUN
ejpam-115	147	4	1	1	NUM
ejpam-115	147	5	1−	1−	NUM
ejpam-115	147	6	x	x	SYM
ejpam-115	147	7	=	=	SYM
ejpam-115	147	8	1	1	NUM
ejpam-115	147	9	+	+	CCONJ
ejpam-115	148	1	x+	x+	ADJ
ejpam-115	148	2	x2	x2	PROPN
ejpam-115	148	3	+	+	CCONJ
ejpam-115	148	4	x3	x3	ADJ
ejpam-115	148	5	+	+	NOUN
ejpam-115	148	6	o(x4	o(x4	ADJ
ejpam-115	148	7	)	)	PUNCT
ejpam-115	148	8	,	,	PUNCT
ejpam-115	148	9	x→	x→	PROPN
ejpam-115	148	10	0	0	NUM
ejpam-115	148	11	,	,	PUNCT
ejpam-115	148	12	it	it	PRON
ejpam-115	148	13	can	can	AUX
ejpam-115	148	14	be	be	AUX
ejpam-115	148	15	easily	easily	ADV
ejpam-115	148	16	seen	see	VERB
ejpam-115	148	17	that	that	SCONJ
ejpam-115	148	18	the	the	DET
ejpam-115	148	19	relation	relation	NOUN
ejpam-115	148	20	b−1(µ	b−1(µ	NOUN
ejpam-115	148	21	)	)	PUNCT
ejpam-115	148	22	=	=	SYM
ejpam-115	149	1	1	1	NUM
ejpam-115	149	2	+	+	NUM
ejpam-115	149	3	2q(0	2q(0	NUM
ejpam-115	149	4	)	)	PUNCT
ejpam-115	149	5	(	(	PUNCT
ejpam-115	149	6	2iµ)2	2iµ)2	NUM
ejpam-115	149	7	+	+	SYM
ejpam-115	149	8	1	1	NUM
ejpam-115	149	9	(	(	PUNCT
ejpam-115	149	10	2iµ)3	2iµ)3	PROPN
ejpam-115	149	11	1∫	1∫	NUM
ejpam-115	149	12	0	0	NUM
ejpam-115	149	13	q2(t)dt+	q2(t)dt+	ADP
ejpam-115	149	14	1	1	NUM
ejpam-115	149	15	(	(	PUNCT
ejpam-115	149	16	2ωjµ)4	2ωjµ)4	NUM
ejpam-115	150	1	[	[	X
ejpam-115	150	2	2q′′(0)−	2q′′(0)−	NUM
ejpam-115	150	3	1	1	NUM
ejpam-115	150	4	2	2	NUM
ejpam-115	150	5	q2(1	q2(1	NOUN
ejpam-115	150	6	)	)	PUNCT
ejpam-115	151	1	+	+	CCONJ
ejpam-115	151	2	11	11	NUM
ejpam-115	151	3	2	2	NUM
ejpam-115	151	4	q2(0	q2(0	PROPN
ejpam-115	151	5	)	)	PUNCT
ejpam-115	151	6	+	+	NOUN
ejpam-115	151	7	q(0)q(1	q(0)q(1	NOUN
ejpam-115	151	8	)	)	PUNCT
ejpam-115	151	9	]	]	PUNCT
ejpam-115	152	1	+	+	CCONJ
ejpam-115	152	2	1	1	NUM
ejpam-115	152	3	(	(	PUNCT
ejpam-115	152	4	2iµ)5	2iµ)5	NUM
ejpam-115	152	5	[	[	X
ejpam-115	152	6	q(1)q′(1)−	q(1)q′(1)−	NUM
ejpam-115	152	7	q(0)q′(0)−	q(0)q′(0)−	X
ejpam-115	152	8	q(0)q′(1	q(0)q′(1	PROPN
ejpam-115	152	9	)	)	PUNCT
ejpam-115	152	10	+	+	NUM
ejpam-115	152	11	q(1)q′(0	q(1)q′(0	NOUN
ejpam-115	152	12	)	)	PUNCT
ejpam-115	152	13	+2q(0	+2q(0	NOUN
ejpam-115	152	14	)	)	PUNCT
ejpam-115	153	1	1∫	1∫	NUM
ejpam-115	153	2	0	0	NUM
ejpam-115	153	3	q2(t)dt+	q2(t)dt+	ADP
ejpam-115	153	4	2	2	NUM
ejpam-115	153	5	1∫	1∫	NUM
ejpam-115	153	6	0	0	NUM
ejpam-115	154	1	q3(t)dt−	q3(t)dt−	PROPN
ejpam-115	154	2	1∫	1∫	NUM
ejpam-115	154	3	0	0	NUM
ejpam-115	154	4	q′2(t)dt	q′2(t)dt	NOUN
ejpam-115	154	5	]	]	X
ejpam-115	155	1	+	+	CCONJ
ejpam-115	155	2	1	1	NUM
ejpam-115	155	3	(	(	PUNCT
ejpam-115	155	4	2iµ)6	2iµ)6	NUM
ejpam-115	155	5	[	[	X
ejpam-115	155	6	2q(4)(0	2q(4)(0	NUM
ejpam-115	155	7	)	)	PUNCT
ejpam-115	155	8	+	+	CCONJ
ejpam-115	155	9	1	1	NUM
ejpam-115	155	10	2	2	NUM
ejpam-115	155	11	q′2(1	q′2(1	PROPN
ejpam-115	155	12	)	)	PUNCT
ejpam-115	156	1	+	+	CCONJ
ejpam-115	156	2	21	21	NUM
ejpam-115	156	3	2	2	NUM
ejpam-115	156	4	q′2(0)−	q′2(0)−	NOUN
ejpam-115	156	5	q′(0)q′(1)−	q′(0)q′(1)−	PROPN
ejpam-115	156	6	q(1)q′′(1	q(1)q′′(1	PROPN
ejpam-115	156	7	)	)	PUNCT
ejpam-115	157	1	+	+	NUM
ejpam-115	157	2	19q(0)q′′(0	19q(0)q′′(0	NOUN
ejpam-115	157	3	)	)	PUNCT
ejpam-115	158	1	+	+	NOUN
ejpam-115	158	2	q(0)q′′(1	q(0)q′′(1	NOUN
ejpam-115	158	3	)	)	PUNCT
ejpam-115	159	1	+	+	CCONJ
ejpam-115	160	1	q(1)q′′(0)−	q(1)q′′(0)−	PROPN
ejpam-115	160	2	2q3(1	2q3(1	NUM
ejpam-115	160	3	)	)	PUNCT
ejpam-115	160	4	+	+	NUM
ejpam-115	160	5	17q3(0	17q3(0	NUM
ejpam-115	160	6	)	)	PUNCT
ejpam-115	160	7	+	+	NUM
ejpam-115	160	8	q(0)q2(1	q(0)q2(1	NOUN
ejpam-115	160	9	)	)	PUNCT
ejpam-115	160	10	+4q(1)q2(0	+4q(1)q2(0	NUM
ejpam-115	160	11	)	)	PUNCT
ejpam-115	160	12	+	+	CCONJ
ejpam-115	160	13	1	1	NUM
ejpam-115	160	14	2	2	NUM
ejpam-115	160	15	(	(	PUNCT
ejpam-115	160	16	1∫	1∫	NUM
ejpam-115	160	17	0	0	NUM
ejpam-115	160	18	q2(t)dt)2	q2(t)dt)2	NOUN
ejpam-115	160	19	]	]	PUNCT
ejpam-115	161	1	+	+	NOUN
ejpam-115	161	2	o	o	X
ejpam-115	161	3	(	(	PUNCT
ejpam-115	161	4	1	1	NUM
ejpam-115	161	5	µ7	µ7	ADJ
ejpam-115	161	6	)	)	PUNCT
ejpam-115	161	7			NOUN
ejpam-115	161	8	(	(	PUNCT
ejpam-115	161	9	2.7	2.7	NUM
ejpam-115	161	10	)	)	PUNCT
ejpam-115	161	11	khanlar	khanlar	PROPN
ejpam-115	161	12	r.	r.	PROPN
ejpam-115	161	13	mamedov	mamedov	PROPN
ejpam-115	161	14	,	,	PUNCT
ejpam-115	161	15	hamza	hamza	PROPN
ejpam-115	161	16	menken	menken	PROPN
ejpam-115	161	17	/	/	SYM
ejpam-115	161	18	eur	eur	PROPN
ejpam-115	161	19	.	.	PUNCT
ejpam-115	162	1	j.	j.	PROPN
ejpam-115	162	2	pure	pure	PROPN
ejpam-115	162	3	appl	appl	PROPN
ejpam-115	162	4	.	.	PUNCT
ejpam-115	163	1	math,1	math,1	PROPN
ejpam-115	163	2	(	(	PUNCT
ejpam-115	163	3	2008	2008	NUM
ejpam-115	163	4	)	)	PUNCT
ejpam-115	163	5	,	,	PUNCT
ejpam-115	163	6	(	(	PUNCT
ejpam-115	163	7	51	51	NUM
ejpam-115	163	8	-	-	SYM
ejpam-115	163	9	60	60	NUM
ejpam-115	163	10	)	)	PUNCT
ejpam-115	163	11	57	57	NUM
ejpam-115	163	12	holds	hold	VERB
ejpam-115	163	13	forµ	forµ	ADJ
ejpam-115	163	14	∈	∈	PROPN
ejpam-115	163	15	t	t	NOUN
ejpam-115	163	16	sufficiently	sufficiently	ADV
ejpam-115	163	17	large	large	ADJ
ejpam-115	163	18	in	in	ADP
ejpam-115	163	19	absolute	absolute	ADJ
ejpam-115	163	20	value	value	NOUN
ejpam-115	163	21	.	.	PUNCT
ejpam-115	164	1	thus	thus	ADV
ejpam-115	164	2	,	,	PUNCT
ejpam-115	164	3	forµ	forµ	PROPN
ejpam-115	164	4	∈	∈	PROPN
ejpam-115	164	5	t	t	PUNCT
ejpam-115	164	6	sufficiently	sufficiently	ADV
ejpam-115	164	7	large	large	ADJ
ejpam-115	164	8	in	in	ADP
ejpam-115	164	9	absolute	absolute	ADJ
ejpam-115	164	10	value	value	NOUN
ejpam-115	164	11	,	,	PUNCT
ejpam-115	164	12	the	the	DET
ejpam-115	164	13	equation∆(µ	equation∆(µ	NOUN
ejpam-115	164	14	)	)	PUNCT
ejpam-115	165	1	=	=	SYM
ejpam-115	165	2	0	0	PUNCT
ejpam-115	165	3	is	be	AUX
ejpam-115	165	4	equivalent	equivalent	ADJ
ejpam-115	165	5	to	to	ADP
ejpam-115	165	6	the	the	DET
ejpam-115	165	7	equation	equation	NOUN
ejpam-115	165	8	(	(	PUNCT
ejpam-115	165	9	iµ)−1b−1(µ)∆(µ)eiµ	iµ)−1b−1(µ)∆(µ)eiµ	NOUN
ejpam-115	165	10	=	=	PUNCT
ejpam-115	165	11	0	0	X
ejpam-115	165	12	.	.	PUNCT
ejpam-115	166	1	(	(	PUNCT
ejpam-115	166	2	2.8	2.8	NUM
ejpam-115	166	3	)	)	PUNCT
ejpam-115	166	4	using	use	VERB
ejpam-115	166	5	(	(	PUNCT
ejpam-115	166	6	2.6	2.6	NUM
ejpam-115	166	7	)	)	PUNCT
ejpam-115	166	8	,	,	PUNCT
ejpam-115	166	9	(	(	PUNCT
ejpam-115	166	10	2.7	2.7	NUM
ejpam-115	166	11	)	)	PUNCT
ejpam-115	166	12	and	and	CCONJ
ejpam-115	166	13	the	the	DET
ejpam-115	166	14	relationsq(1	relationsq(1	NOUN
ejpam-115	166	15	)	)	PUNCT
ejpam-115	166	16	=	=	SYM
ejpam-115	166	17	q(0	q(0	PROPN
ejpam-115	166	18	)	)	PUNCT
ejpam-115	166	19	andq′(1	andq′(1	NOUN
ejpam-115	166	20	)	)	PUNCT
ejpam-115	166	21	6=	6=	PUNCT
ejpam-115	167	1	q′(0	q′(0	NOUN
ejpam-115	167	2	)	)	PUNCT
ejpam-115	167	3	,	,	PUNCT
ejpam-115	167	4	from	from	ADP
ejpam-115	167	5	the	the	DET
ejpam-115	167	6	equation	equation	NOUN
ejpam-115	167	7	(	(	PUNCT
ejpam-115	167	8	2.8	2.8	NUM
ejpam-115	167	9	)	)	PUNCT
ejpam-115	167	10	,	,	PUNCT
ejpam-115	167	11	we	we	PRON
ejpam-115	167	12	obtain	obtain	VERB
ejpam-115	167	13	two	two	NUM
ejpam-115	167	14	equations	equation	NOUN
ejpam-115	167	15	µk,1	µk,1	NOUN
ejpam-115	167	16	=	=	SYM
ejpam-115	167	17	2kπ	2kπ	NOUN
ejpam-115	168	1	+	+	CCONJ
ejpam-115	168	2	q′(1)−	q′(1)−	PROPN
ejpam-115	168	3	q′(0	q′(0	PROPN
ejpam-115	168	4	)	)	PUNCT
ejpam-115	169	1	+	+	CCONJ
ejpam-115	170	1	1∫	1∫	NUM
ejpam-115	170	2	0	0	NUM
ejpam-115	170	3	q2(t)dt	q2(t)dt	NOUN
ejpam-115	170	4	(	(	PUNCT
ejpam-115	170	5	4kπ)3	4kπ)3	NUM
ejpam-115	170	6	+	+	NOUN
ejpam-115	170	7	o	o	NOUN
ejpam-115	170	8	(	(	PUNCT
ejpam-115	170	9	1	1	NUM
ejpam-115	170	10	k4	k4	NOUN
ejpam-115	170	11	)	)	PUNCT
ejpam-115	170	12	,	,	PUNCT
ejpam-115	170	13	(	(	PUNCT
ejpam-115	170	14	2.9	2.9	NUM
ejpam-115	170	15	)	)	PUNCT
ejpam-115	170	16	µk,2	µk,2	NOUN
ejpam-115	170	17	=	=	PROPN
ejpam-115	170	18	2kπ	2kπ	NOUN
ejpam-115	170	19	−	−	NOUN
ejpam-115	170	20	q′(1)−	q′(1)−	NOUN
ejpam-115	170	21	q′(0)−	q′(0)−	NOUN
ejpam-115	170	22	1∫	1∫	NUM
ejpam-115	170	23	0	0	NUM
ejpam-115	170	24	q2(t)dt	q2(t)dt	NOUN
ejpam-115	170	25	(	(	PUNCT
ejpam-115	170	26	4kπ)3	4kπ)3	NUM
ejpam-115	171	1	+	+	NOUN
ejpam-115	171	2	o	o	NOUN
ejpam-115	171	3	(	(	PUNCT
ejpam-115	171	4	1	1	NUM
ejpam-115	171	5	k4	k4	NOUN
ejpam-115	171	6	)	)	PUNCT
ejpam-115	171	7	.	.	PUNCT
ejpam-115	172	1	(	(	PUNCT
ejpam-115	172	2	2.10	2.10	NUM
ejpam-115	172	3	)	)	PUNCT
ejpam-115	172	4	by	by	ADP
ejpam-115	172	5	rouche	rouche	PROPN
ejpam-115	172	6	’s	’s	PART
ejpam-115	172	7	theorem	theorem	PROPN
ejpam-115	172	8	,	,	PUNCT
ejpam-115	172	9	we	we	PRON
ejpam-115	172	10	have	have	VERB
ejpam-115	172	11	asymptotic	asymptotic	ADJ
ejpam-115	172	12	expressions	expression	NOUN
ejpam-115	172	13	for	for	ADP
ejpam-115	172	14	the	the	DET
ejpam-115	172	15	rootsµk,1	rootsµk,1	ADJ
ejpam-115	172	16	andµk,2	andµk,2	NOUN
ejpam-115	172	17	,	,	PUNCT
ejpam-115	172	18	k	k	NOUN
ejpam-115	172	19	=	=	PUNCT
ejpam-115	172	20	n	n	CCONJ
ejpam-115	172	21	,	,	PUNCT
ejpam-115	172	22	n+	n+	ADP
ejpam-115	172	23	1	1	NUM
ejpam-115	172	24	,	,	PUNCT
ejpam-115	172	25	·	·	PUNCT
ejpam-115	172	26	·	·	PUNCT
ejpam-115	172	27	·	·	PUNCT
ejpam-115	172	28	,	,	PUNCT
ejpam-115	172	29	of	of	ADP
ejpam-115	172	30	the	the	DET
ejpam-115	172	31	equations	equation	NOUN
ejpam-115	172	32	(	(	PUNCT
ejpam-115	172	33	2.9	2.9	NUM
ejpam-115	172	34	)	)	PUNCT
ejpam-115	172	35	and	and	CCONJ
ejpam-115	172	36	(	(	PUNCT
ejpam-115	172	37	2.10	2.10	NUM
ejpam-115	172	38	)	)	PUNCT
ejpam-115	172	39	,	,	PUNCT
ejpam-115	172	40	respectively	respectively	ADV
ejpam-115	172	41	,	,	PUNCT
ejpam-115	172	42	wheren	wheren	PROPN
ejpam-115	172	43	is	be	AUX
ejpam-115	172	44	a	a	DET
ejpam-115	172	45	positive	positive	ADJ
ejpam-115	172	46	integer	integer	NOUN
ejpam-115	172	47	µk,1	µk,1	NOUN
ejpam-115	172	48	=	=	SYM
ejpam-115	172	49	2kπ	2kπ	NOUN
ejpam-115	173	1	+	+	CCONJ
ejpam-115	173	2	q′(1)−	q′(1)−	PROPN
ejpam-115	173	3	q′(0	q′(0	PROPN
ejpam-115	173	4	)	)	PUNCT
ejpam-115	173	5	(	(	PUNCT
ejpam-115	173	6	4kπ)3	4kπ)3	NUM
ejpam-115	174	1	+	+	NOUN
ejpam-115	174	2	o	o	NOUN
ejpam-115	174	3	(	(	PUNCT
ejpam-115	174	4	1	1	NUM
ejpam-115	174	5	k4	k4	NOUN
ejpam-115	174	6	)	)	PUNCT
ejpam-115	174	7	,	,	PUNCT
ejpam-115	174	8	(	(	PUNCT
ejpam-115	174	9	2.11	2.11	NUM
ejpam-115	174	10	)	)	PUNCT
ejpam-115	174	11	µk,2	µk,2	NOUN
ejpam-115	174	12	=	=	PROPN
ejpam-115	174	13	2kπ	2kπ	NOUN
ejpam-115	174	14	−	−	PROPN
ejpam-115	174	15	q′(1)−	q′(1)−	NOUN
ejpam-115	174	16	q′(0	q′(0	PROPN
ejpam-115	174	17	)	)	PUNCT
ejpam-115	174	18	(	(	PUNCT
ejpam-115	174	19	4kπ)3	4kπ)3	NUM
ejpam-115	175	1	+	+	NOUN
ejpam-115	175	2	o	o	NOUN
ejpam-115	175	3	(	(	PUNCT
ejpam-115	175	4	1	1	NUM
ejpam-115	175	5	k4	k4	NOUN
ejpam-115	175	6	)	)	PUNCT
ejpam-115	175	7	.	.	PUNCT
ejpam-115	176	1	(	(	PUNCT
ejpam-115	176	2	2.12	2.12	NUM
ejpam-115	176	3	)	)	PUNCT
ejpam-115	176	4	note	note	VERB
ejpam-115	176	5	thatµk,1	thatµk,1	ADJ
ejpam-115	176	6	andµk,2	andµk,2	NOUN
ejpam-115	176	7	are	be	AUX
ejpam-115	176	8	simple	simple	ADJ
ejpam-115	176	9	roots	root	NOUN
ejpam-115	176	10	of	of	ADP
ejpam-115	176	11	the	the	DET
ejpam-115	176	12	equations	equation	NOUN
ejpam-115	176	13	(	(	PUNCT
ejpam-115	176	14	2.9	2.9	NUM
ejpam-115	176	15	)	)	PUNCT
ejpam-115	176	16	and	and	CCONJ
ejpam-115	176	17	(	(	PUNCT
ejpam-115	176	18	2.10	2.10	NUM
ejpam-115	176	19	)	)	PUNCT
ejpam-115	176	20	,	,	PUNCT
ejpam-115	176	21	respectively	respectively	ADV
ejpam-115	176	22	.	.	PUNCT
ejpam-115	177	1	from	from	ADP
ejpam-115	177	2	the	the	DET
ejpam-115	177	3	relations	relation	NOUN
ejpam-115	177	4	(	(	PUNCT
ejpam-115	177	5	2.11	2.11	NUM
ejpam-115	177	6	)	)	PUNCT
ejpam-115	177	7	,	,	PUNCT
ejpam-115	177	8	(	(	PUNCT
ejpam-115	177	9	2.12	2.12	NUM
ejpam-115	177	10	)	)	PUNCT
ejpam-115	177	11	and	and	CCONJ
ejpam-115	177	12	the	the	DET
ejpam-115	177	13	relationsλk,1	relationsλk,1	NOUN
ejpam-115	177	14	=	=	SYM
ejpam-115	177	15	−	−	PROPN
ejpam-115	177	16	µ2	µ2	PROPN
ejpam-115	177	17	k,1	k,1	PROPN
ejpam-115	177	18	,	,	PUNCT
ejpam-115	177	19	λk,2	λk,2	NOUN
ejpam-115	177	20	=	=	PUNCT
ejpam-115	177	21	−	−	PROPN
ejpam-115	177	22	µ2	µ2	PROPN
ejpam-115	177	23	k,2	k,2	PROPN
ejpam-115	177	24	,	,	PUNCT
ejpam-115	177	25	we	we	PRON
ejpam-115	177	26	obtain	obtain	VERB
ejpam-115	177	27	the	the	DET
ejpam-115	177	28	formula	formula	NOUN
ejpam-115	177	29	(	(	PUNCT
ejpam-115	177	30	2.1	2.1	NUM
ejpam-115	177	31	)	)	PUNCT
ejpam-115	177	32	and	and	CCONJ
ejpam-115	177	33	observe	observe	VERB
ejpam-115	177	34	that	that	SCONJ
ejpam-115	177	35	these	these	DET
ejpam-115	177	36	eigenvalues	eigenvalue	NOUN
ejpam-115	177	37	are	be	AUX
ejpam-115	177	38	simple	simple	ADJ
ejpam-115	177	39	.	.	PUNCT
ejpam-115	178	1	let	let	VERB
ejpam-115	178	2	us	we	PRON
ejpam-115	178	3	calculateu2(ϕ1(x	calculateu2(ϕ1(x	VERB
ejpam-115	178	4	,	,	PUNCT
ejpam-115	178	5	µk,1	µk,1	NOUN
ejpam-115	178	6	)	)	PUNCT
ejpam-115	178	7	)	)	PUNCT
ejpam-115	179	1	andu2(ϕ2(x	andu2(ϕ2(x	NOUN
ejpam-115	179	2	,	,	PUNCT
ejpam-115	179	3	µk,1	µk,1	PROPN
ejpam-115	179	4	)	)	PUNCT
ejpam-115	179	5	)	)	PUNCT
ejpam-115	179	6	.	.	PUNCT
ejpam-115	180	1	since	since	SCONJ
ejpam-115	180	2	eiµk,1	eiµk,1	NOUN
ejpam-115	180	3	−	−	PROPN
ejpam-115	180	4	1	1	NUM
ejpam-115	180	5	=	=	NUM
ejpam-115	180	6	q′(1)−	q′(1)−	NOUN
ejpam-115	180	7	q′(0	q′(0	PROPN
ejpam-115	180	8	)	)	PUNCT
ejpam-115	181	1	+	+	CCONJ
ejpam-115	182	1	1∫	1∫	NUM
ejpam-115	182	2	0	0	NUM
ejpam-115	182	3	q2(t)dt	q2(t)dt	NOUN
ejpam-115	182	4	(	(	PUNCT
ejpam-115	182	5	2iµk,1)3	2iµk,1)3	NOUN
ejpam-115	182	6	+	+	NOUN
ejpam-115	182	7	o	o	X
ejpam-115	182	8	(	(	PUNCT
ejpam-115	182	9	1	1	NUM
ejpam-115	182	10	µ4	µ4	PROPN
ejpam-115	182	11	k,1	k,1	PROPN
ejpam-115	182	12	)	)	PUNCT
ejpam-115	182	13	,	,	PUNCT
ejpam-115	182	14	we	we	PRON
ejpam-115	182	15	have	have	VERB
ejpam-115	182	16	u2(ϕ1(x	u2(ϕ1(x	NUM
ejpam-115	182	17	,	,	PUNCT
ejpam-115	182	18	µk,1	µk,1	NOUN
ejpam-115	182	19	)	)	PUNCT
ejpam-115	182	20	)	)	PUNCT
ejpam-115	183	1	=	=	SYM
ejpam-115	183	2	ϕ′1(1	ϕ′1(1	PROPN
ejpam-115	183	3	,	,	PUNCT
ejpam-115	183	4	µk,1)−	µk,1)−	PROPN
ejpam-115	183	5	ϕ′1(0	ϕ′1(0	PROPN
ejpam-115	183	6	,	,	PUNCT
ejpam-115	183	7	µk,1	µk,1	PROPN
ejpam-115	183	8	)	)	PUNCT
ejpam-115	183	9	=	=	PUNCT
ejpam-115	184	1	iµk,1e	iµk,1e	ADJ
ejpam-115	184	2	iµk,1	iµk,1	NOUN
ejpam-115	184	3	[	[	X
ejpam-115	184	4	1−	1−	NUM
ejpam-115	184	5	q(1	q(1	PROPN
ejpam-115	184	6	)	)	PUNCT
ejpam-115	185	1	+	+	CCONJ
ejpam-115	185	2	q(0	q(0	NOUN
ejpam-115	185	3	)	)	PUNCT
ejpam-115	185	4	(	(	PUNCT
ejpam-115	185	5	2iµk,1)2	2iµk,1)2	NUM
ejpam-115	185	6	+	+	CCONJ
ejpam-115	185	7	q′(1	q′(1	ADJ
ejpam-115	185	8	)	)	PUNCT
ejpam-115	186	1	+	+	NUM
ejpam-115	186	2	q′(0)−	q′(0)−	NOUN
ejpam-115	186	3	1∫	1∫	NUM
ejpam-115	186	4	0	0	NUM
ejpam-115	186	5	q2(t)dt	q2(t)dt	NOUN
ejpam-115	186	6	(	(	PUNCT
ejpam-115	186	7	2iµk,1)3	2iµk,1)3	NOUN
ejpam-115	187	1	+	+	NOUN
ejpam-115	187	2	o	o	X
ejpam-115	187	3	(	(	PUNCT
ejpam-115	187	4	1	1	NUM
ejpam-115	187	5	µ4	µ4	PROPN
ejpam-115	187	6	k,1	k,1	PROPN
ejpam-115	187	7	)	)	PUNCT
ejpam-115	187	8	]	]	PUNCT
ejpam-115	187	9	−iµk,1[1−	−iµk,1[1−	PROPN
ejpam-115	187	10	2q(0	2q(0	NUM
ejpam-115	187	11	)	)	PUNCT
ejpam-115	187	12	(	(	PUNCT
ejpam-115	187	13	2iµk,1)2	2iµk,1)2	NUM
ejpam-115	187	14	+	+	CCONJ
ejpam-115	187	15	2q′(0	2q′(0	NOUN
ejpam-115	187	16	)	)	PUNCT
ejpam-115	187	17	(	(	PUNCT
ejpam-115	187	18	2iµk,1)3	2iµk,1)3	NOUN
ejpam-115	187	19	+	+	NOUN
ejpam-115	187	20	o	o	X
ejpam-115	187	21	(	(	PUNCT
ejpam-115	187	22	1	1	NUM
ejpam-115	187	23	µ4	µ4	PROPN
ejpam-115	187	24	k,1	k,1	PROPN
ejpam-115	187	25	)	)	PUNCT
ejpam-115	187	26	]	]	PUNCT
ejpam-115	188	1	=	=	PUNCT
ejpam-115	188	2	q′(1)−	q′(1)−	NOUN
ejpam-115	188	3	q′(0	q′(0	PROPN
ejpam-115	188	4	)	)	PUNCT
ejpam-115	188	5	(	(	PUNCT
ejpam-115	188	6	2iµk,1)2	2iµk,1)2	NUM
ejpam-115	189	1	+	+	NOUN
ejpam-115	189	2	o	o	NOUN
ejpam-115	189	3	(	(	PUNCT
ejpam-115	189	4	1	1	NUM
ejpam-115	189	5	µ3	µ3	NOUN
ejpam-115	189	6	k,1	k,1	PROPN
ejpam-115	189	7	)	)	PUNCT
ejpam-115	189	8	.	.	PUNCT
ejpam-115	190	1	(	(	PUNCT
ejpam-115	190	2	2.13	2.13	NUM
ejpam-115	190	3	)	)	PUNCT
ejpam-115	190	4	khanlar	khanlar	PROPN
ejpam-115	190	5	r.	r.	PROPN
ejpam-115	190	6	mamedov	mamedov	PROPN
ejpam-115	190	7	,	,	PUNCT
ejpam-115	190	8	hamza	hamza	PROPN
ejpam-115	190	9	menken	menken	PROPN
ejpam-115	190	10	/	/	SYM
ejpam-115	190	11	eur	eur	PROPN
ejpam-115	190	12	.	.	PUNCT
ejpam-115	191	1	j.	j.	PROPN
ejpam-115	191	2	pure	pure	PROPN
ejpam-115	191	3	appl	appl	PROPN
ejpam-115	191	4	.	.	PUNCT
ejpam-115	192	1	math,1	math,1	PROPN
ejpam-115	192	2	(	(	PUNCT
ejpam-115	192	3	2008	2008	NUM
ejpam-115	192	4	)	)	PUNCT
ejpam-115	192	5	,	,	PUNCT
ejpam-115	192	6	(	(	PUNCT
ejpam-115	192	7	51	51	NUM
ejpam-115	192	8	-	-	SYM
ejpam-115	192	9	60	60	NUM
ejpam-115	192	10	)	)	PUNCT
ejpam-115	192	11	58	58	NUM
ejpam-115	192	12	in	in	ADP
ejpam-115	192	13	a	a	DET
ejpam-115	192	14	similar	similar	ADJ
ejpam-115	192	15	way	way	NOUN
ejpam-115	192	16	,	,	PUNCT
ejpam-115	192	17	we	we	PRON
ejpam-115	192	18	obtain	obtain	VERB
ejpam-115	192	19	u2(ϕ2(x	u2(ϕ2(x	NOUN
ejpam-115	192	20	,	,	PUNCT
ejpam-115	192	21	µk,1	µk,1	NOUN
ejpam-115	192	22	)	)	PUNCT
ejpam-115	192	23	)	)	PUNCT
ejpam-115	193	1	=	=	SYM
ejpam-115	193	2	q′(1)−	q′(1)−	NOUN
ejpam-115	193	3	q′(0	q′(0	PROPN
ejpam-115	193	4	)	)	PUNCT
ejpam-115	193	5	(	(	PUNCT
ejpam-115	193	6	2iµk,1)2	2iµk,1)2	NUM
ejpam-115	194	1	+	+	NOUN
ejpam-115	194	2	o	o	NOUN
ejpam-115	194	3	(	(	PUNCT
ejpam-115	194	4	1	1	NUM
ejpam-115	194	5	µ3	µ3	NOUN
ejpam-115	194	6	k,1	k,1	PROPN
ejpam-115	194	7	)	)	PUNCT
ejpam-115	194	8	.	.	PUNCT
ejpam-115	195	1	without	without	ADP
ejpam-115	195	2	loss	loss	NOUN
ejpam-115	195	3	of	of	ADP
ejpam-115	195	4	generality	generality	NOUN
ejpam-115	195	5	,	,	PUNCT
ejpam-115	195	6	we	we	PRON
ejpam-115	195	7	can	can	AUX
ejpam-115	195	8	assume	assume	VERB
ejpam-115	195	9	thatq′(1)−	thatq′(1)−	ADJ
ejpam-115	195	10	q′(0	q′(0	NOUN
ejpam-115	195	11	)	)	PUNCT
ejpam-115	195	12	6=	6=	ADP
ejpam-115	195	13	0	0	NUM
ejpam-115	195	14	.	.	PUNCT
ejpam-115	196	1	sinceu2(ϕj(x	sinceu2(ϕj(x	X
ejpam-115	196	2	,	,	PUNCT
ejpam-115	196	3	µk,1	µk,1	NOUN
ejpam-115	196	4	)	)	PUNCT
ejpam-115	196	5	)	)	PUNCT
ejpam-115	197	1	6=	6=	ADP
ejpam-115	197	2	0	0	NUM
ejpam-115	197	3	,	,	PUNCT
ejpam-115	197	4	j	j	PROPN
ejpam-115	197	5	=	=	SYM
ejpam-115	197	6	1	1	NUM
ejpam-115	197	7	,	,	PUNCT
ejpam-115	197	8	2	2	NUM
ejpam-115	197	9	,	,	PUNCT
ejpam-115	197	10	andq′(1)−q′(0	andq′(1)−q′(0	NOUN
ejpam-115	197	11	)	)	PUNCT
ejpam-115	197	12	6=	6=	ADP
ejpam-115	197	13	0	0	NUM
ejpam-115	197	14	,	,	PUNCT
ejpam-115	197	15	we	we	PRON
ejpam-115	197	16	seek	seek	VERB
ejpam-115	197	17	the	the	DET
ejpam-115	197	18	eigenfunctionyk,1(x	eigenfunctionyk,1(x	NOUN
ejpam-115	197	19	)	)	PUNCT
ejpam-115	197	20	corresponding	correspond	VERB
ejpam-115	197	21	to	to	ADP
ejpam-115	197	22	the	the	DET
ejpam-115	197	23	eigenvalue	eigenvalue	PROPN
ejpam-115	197	24	λk,1	λk,1	PROPN
ejpam-115	197	25	in	in	ADP
ejpam-115	197	26	the	the	DET
ejpam-115	197	27	form	form	NOUN
ejpam-115	197	28	yk,1(x	yk,1(x	NOUN
ejpam-115	197	29	)	)	PUNCT
ejpam-115	198	1	=	=	PUNCT
ejpam-115	198	2	(	(	PUNCT
ejpam-115	198	3	2iµk,1)2	2iµk,1)2	NUM
ejpam-115	198	4	2i	2i	NOUN
ejpam-115	199	1	[	[	X
ejpam-115	199	2	q′(1)−	q′(1)−	NOUN
ejpam-115	199	3	q′(0	q′(0	PROPN
ejpam-115	199	4	)	)	PUNCT
ejpam-115	199	5	]	]	PUNCT
ejpam-115	199	6	∣∣∣∣	∣∣∣∣	PROPN
ejpam-115	199	7	ϕ1(x	ϕ1(x	PROPN
ejpam-115	199	8	,	,	PUNCT
ejpam-115	199	9	µk,1	µk,1	NOUN
ejpam-115	199	10	)	)	PUNCT
ejpam-115	199	11	ϕ2(x	ϕ2(x	PROPN
ejpam-115	199	12	,	,	PUNCT
ejpam-115	199	13	µk,1	µk,1	NOUN
ejpam-115	199	14	)	)	PUNCT
ejpam-115	199	15	u2(ϕ1(x	u2(ϕ1(x	PROPN
ejpam-115	199	16	,	,	PUNCT
ejpam-115	199	17	µk,1	µk,1	NOUN
ejpam-115	199	18	)	)	PUNCT
ejpam-115	199	19	)	)	PUNCT
ejpam-115	199	20	u2(ϕ2(x	u2(ϕ2(x	PROPN
ejpam-115	199	21	,	,	PUNCT
ejpam-115	199	22	µk,1	µk,1	NOUN
ejpam-115	199	23	)	)	PUNCT
ejpam-115	199	24	)	)	PUNCT
ejpam-115	199	25	∣∣∣∣	∣∣∣∣	PROPN
ejpam-115	199	26	.	.	PUNCT
ejpam-115	200	1	(	(	PUNCT
ejpam-115	200	2	2.14	2.14	NUM
ejpam-115	200	3	)	)	PUNCT
ejpam-115	200	4	from	from	ADP
ejpam-115	200	5	the	the	DET
ejpam-115	200	6	equalities	equality	NOUN
ejpam-115	200	7	ϕj(x	ϕj(x	NOUN
ejpam-115	200	8	,	,	PUNCT
ejpam-115	200	9	µk,1	µk,1	NOUN
ejpam-115	200	10	)	)	PUNCT
ejpam-115	200	11	=	=	PUNCT
ejpam-115	201	1	eµk,1ωjx	eµk,1ωjx	ADJ
ejpam-115	201	2	[	[	PUNCT
ejpam-115	201	3	1	1	NUM
ejpam-115	201	4	+	+	CCONJ
ejpam-115	201	5	u1(x	u1(x	NUM
ejpam-115	201	6	)	)	PUNCT
ejpam-115	201	7	(	(	PUNCT
ejpam-115	201	8	2wjµk,1	2wjµk,1	NOUN
ejpam-115	201	9	)	)	PUNCT
ejpam-115	201	10	+	+	PUNCT
ejpam-115	201	11	u2(x	u2(x	X
ejpam-115	201	12	)	)	PUNCT
ejpam-115	201	13	(	(	PUNCT
ejpam-115	201	14	2wjµk,1)2	2wjµk,1)2	NUM
ejpam-115	201	15	+	+	ADJ
ejpam-115	201	16	o	o	NOUN
ejpam-115	201	17	(	(	PUNCT
ejpam-115	201	18	1	1	NUM
ejpam-115	201	19	µ3	µ3	NOUN
ejpam-115	201	20	k,1	k,1	PROPN
ejpam-115	201	21	)	)	PUNCT
ejpam-115	201	22	]	]	PUNCT
ejpam-115	201	23	,	,	PUNCT
ejpam-115	201	24	j	j	PROPN
ejpam-115	201	25	=	=	SYM
ejpam-115	201	26	1	1	NUM
ejpam-115	201	27	,	,	PUNCT
ejpam-115	201	28	2	2	NUM
ejpam-115	201	29	and	and	CCONJ
ejpam-115	201	30	the	the	DET
ejpam-115	201	31	formulas	formula	NOUN
ejpam-115	201	32	(	(	PUNCT
ejpam-115	201	33	2.13	2.13	NUM
ejpam-115	201	34	)	)	PUNCT
ejpam-115	201	35	,	,	PUNCT
ejpam-115	201	36	(	(	PUNCT
ejpam-115	201	37	2.14	2.14	NUM
ejpam-115	201	38	)	)	PUNCT
ejpam-115	201	39	we	we	PRON
ejpam-115	201	40	obtain	obtain	VERB
ejpam-115	201	41	yk,1(x	yk,1(x	NOUN
ejpam-115	201	42	)	)	PUNCT
ejpam-115	201	43	=	=	SYM
ejpam-115	201	44	sinµk,1x+o	sinµk,1x+o	PROPN
ejpam-115	201	45	(	(	PUNCT
ejpam-115	201	46	1	1	NUM
ejpam-115	201	47	µk,1	µk,1	PROPN
ejpam-115	201	48	)	)	PUNCT
ejpam-115	201	49	.	.	PUNCT
ejpam-115	202	1	therefore	therefore	ADV
ejpam-115	202	2	,	,	PUNCT
ejpam-115	202	3	the	the	DET
ejpam-115	202	4	eigenfunctionyk,1(x	eigenfunctionyk,1(x	NOUN
ejpam-115	202	5	)	)	PUNCT
ejpam-115	202	6	satisfies	satisfy	VERB
ejpam-115	202	7	the	the	DET
ejpam-115	202	8	asymptotic	asymptotic	ADJ
ejpam-115	202	9	formula	formula	NOUN
ejpam-115	202	10	(	(	PUNCT
ejpam-115	202	11	2.5	2.5	NUM
ejpam-115	202	12	)	)	PUNCT
ejpam-115	202	13	.	.	PUNCT
ejpam-115	203	1	in	in	ADP
ejpam-115	203	2	a	a	DET
ejpam-115	203	3	similar	similar	ADJ
ejpam-115	203	4	way	way	NOUN
ejpam-115	203	5	,	,	PUNCT
ejpam-115	203	6	sinceu1(ϕj(x	sinceu1(ϕj(x	NUM
ejpam-115	203	7	,	,	PUNCT
ejpam-115	203	8	µk,1	µk,1	NOUN
ejpam-115	203	9	)	)	PUNCT
ejpam-115	203	10	)	)	PUNCT
ejpam-115	203	11	6=	6=	ADP
ejpam-115	203	12	0	0	NUM
ejpam-115	203	13	,	,	PUNCT
ejpam-115	203	14	j	j	PROPN
ejpam-115	203	15	=	=	SYM
ejpam-115	203	16	1	1	NUM
ejpam-115	203	17	,	,	PUNCT
ejpam-115	203	18	2	2	NUM
ejpam-115	203	19	,	,	PUNCT
ejpam-115	203	20	andq′(1)−	andq′(1)−	VERB
ejpam-115	203	21	q′(0	q′(0	NOUN
ejpam-115	203	22	)	)	PUNCT
ejpam-115	203	23	6=	6=	ADP
ejpam-115	203	24	0	0	NUM
ejpam-115	203	25	,	,	PUNCT
ejpam-115	203	26	we	we	PRON
ejpam-115	203	27	can	can	AUX
ejpam-115	203	28	seek	seek	VERB
ejpam-115	203	29	the	the	DET
ejpam-115	203	30	eigenfunctionsyk,2(x	eigenfunctionsyk,2(x	NOUN
ejpam-115	203	31	)	)	PUNCT
ejpam-115	203	32	corresponding	correspond	VERB
ejpam-115	203	33	to	to	ADP
ejpam-115	203	34	the	the	DET
ejpam-115	203	35	eigenvaluesλk,2	eigenvaluesλk,2	NOUN
ejpam-115	203	36	in	in	ADP
ejpam-115	203	37	the	the	DET
ejpam-115	203	38	form	form	NOUN
ejpam-115	203	39	yk,2(x	yk,2(x	NOUN
ejpam-115	203	40	)	)	PUNCT
ejpam-115	204	1	=	=	SYM
ejpam-115	205	1	−	−	PROPN
ejpam-115	205	2	(	(	PUNCT
ejpam-115	205	3	2iµk,2)3	2iµk,2)3	NUM
ejpam-115	205	4	4	4	NUM
ejpam-115	206	1	[	[	X
ejpam-115	206	2	q′(1)−	q′(1)−	NOUN
ejpam-115	206	3	q′(0	q′(0	PROPN
ejpam-115	206	4	)	)	PUNCT
ejpam-115	206	5	]	]	PUNCT
ejpam-115	206	6	∣∣∣∣	∣∣∣∣	PROPN
ejpam-115	206	7	ϕ1(x	ϕ1(x	PROPN
ejpam-115	206	8	,	,	PUNCT
ejpam-115	206	9	µk,2	µk,2	PROPN
ejpam-115	206	10	)	)	PUNCT
ejpam-115	206	11	ϕ2(x	ϕ2(x	PROPN
ejpam-115	206	12	,	,	PUNCT
ejpam-115	206	13	µk,2	µk,2	PROPN
ejpam-115	206	14	)	)	PUNCT
ejpam-115	206	15	u1(ϕ1(x	u1(ϕ1(x	NOUN
ejpam-115	206	16	,	,	PUNCT
ejpam-115	206	17	µk,2	µk,2	PROPN
ejpam-115	206	18	)	)	PUNCT
ejpam-115	206	19	)	)	PUNCT
ejpam-115	206	20	u1(ϕ2(x	u1(ϕ2(x	NOUN
ejpam-115	206	21	,	,	PUNCT
ejpam-115	206	22	µk,2	µk,2	PROPN
ejpam-115	206	23	)	)	PUNCT
ejpam-115	206	24	)	)	PUNCT
ejpam-115	206	25	∣∣∣∣	∣∣∣∣	PROPN
ejpam-115	206	26	.	.	PUNCT
ejpam-115	207	1	thus	thus	ADV
ejpam-115	207	2	,	,	PUNCT
ejpam-115	207	3	we	we	PRON
ejpam-115	207	4	obtain	obtain	VERB
ejpam-115	207	5	yk,2(x	yk,2(x	NOUN
ejpam-115	207	6	)	)	PUNCT
ejpam-115	208	1	=	=	PUNCT
ejpam-115	208	2	cosµk,2x+o	cosµk,2x+o	PROPN
ejpam-115	208	3	(	(	PUNCT
ejpam-115	208	4	1	1	NUM
ejpam-115	208	5	µk,2	µk,2	PROPN
ejpam-115	208	6	)	)	PUNCT
ejpam-115	208	7	.	.	PUNCT
ejpam-115	209	1	this	this	PRON
ejpam-115	209	2	completes	complete	VERB
ejpam-115	209	3	the	the	DET
ejpam-115	209	4	proof	proof	NOUN
ejpam-115	209	5	of	of	ADP
ejpam-115	209	6	the	the	DET
ejpam-115	209	7	lemma	lemma	PROPN
ejpam-115	209	8	.	.	PROPN
ejpam-115	210	1	3	3	X
ejpam-115	210	2	.	.	X
ejpam-115	211	1	the	the	DET
ejpam-115	211	2	riesz	riesz	PROPN
ejpam-115	211	3	basisness	basisness	NOUN
ejpam-115	211	4	inl2(0	inl2(0	PROPN
ejpam-115	211	5	,	,	PUNCT
ejpam-115	211	6	1	1	NUM
ejpam-115	211	7	)	)	PUNCT
ejpam-115	211	8	of	of	ADP
ejpam-115	211	9	the	the	DET
ejpam-115	211	10	root	root	NOUN
ejpam-115	211	11	functions	function	NOUN
ejpam-115	211	12	for	for	ADP
ejpam-115	211	13	the	the	DET
ejpam-115	211	14	periodic	periodic	ADJ
ejpam-115	211	15	problem	problem	NOUN
ejpam-115	211	16	theorem	theorem	VERB
ejpam-115	211	17	3.1	3.1	NUM
ejpam-115	211	18	.	.	PUNCT
ejpam-115	212	1	the	the	DET
ejpam-115	212	2	root	root	NOUN
ejpam-115	212	3	functions	function	NOUN
ejpam-115	212	4	of	of	ADP
ejpam-115	212	5	the	the	DET
ejpam-115	212	6	boundary	boundary	ADJ
ejpam-115	212	7	problem	problem	NOUN
ejpam-115	212	8	(	(	PUNCT
ejpam-115	212	9	1.1	1.1	NUM
ejpam-115	212	10	)	)	PUNCT
ejpam-115	212	11	,	,	PUNCT
ejpam-115	212	12	(	(	PUNCT
ejpam-115	212	13	1.2	1.2	NUM
ejpam-115	212	14	)	)	PUNCT
ejpam-115	212	15	form	form	NOUN
ejpam-115	212	16	a	a	DET
ejpam-115	212	17	riesz	riesz	NOUN
ejpam-115	212	18	basis	basis	NOUN
ejpam-115	212	19	in	in	ADP
ejpam-115	212	20	l2(0	l2(0	NOUN
ejpam-115	212	21	,	,	PUNCT
ejpam-115	212	22	1	1	NUM
ejpam-115	212	23	)	)	PUNCT
ejpam-115	212	24	.	.	PUNCT
ejpam-115	213	1	proof	proof	NOUN
ejpam-115	213	2	.	.	PUNCT
ejpam-115	214	1	the	the	DET
ejpam-115	214	2	system	system	NOUN
ejpam-115	214	3	of	of	ADP
ejpam-115	214	4	the	the	DET
ejpam-115	214	5	root	root	NOUN
ejpam-115	214	6	functions	function	NOUN
ejpam-115	214	7	of	of	ADP
ejpam-115	214	8	the	the	DET
ejpam-115	214	9	boundary	boundary	ADJ
ejpam-115	214	10	problem	problem	NOUN
ejpam-115	214	11	(	(	PUNCT
ejpam-115	214	12	1.1	1.1	NUM
ejpam-115	214	13	)	)	PUNCT
ejpam-115	214	14	,	,	PUNCT
ejpam-115	214	15	(	(	PUNCT
ejpam-115	214	16	1.2	1.2	NUM
ejpam-115	214	17	)	)	PUNCT
ejpam-115	214	18	is	be	AUX
ejpam-115	214	19	complete	complete	ADJ
ejpam-115	214	20	and	and	CCONJ
ejpam-115	214	21	minimal	minimal	ADJ
ejpam-115	214	22	inl2(0	inl2(0	PROPN
ejpam-115	214	23	,	,	PUNCT
ejpam-115	214	24	1	1	NUM
ejpam-115	214	25	)	)	PUNCT
ejpam-115	214	26	.	.	PUNCT
ejpam-115	215	1	the	the	DET
ejpam-115	215	2	minimality	minimality	NOUN
ejpam-115	215	3	of	of	ADP
ejpam-115	215	4	this	this	DET
ejpam-115	215	5	system	system	NOUN
ejpam-115	215	6	follows	follow	VERB
ejpam-115	215	7	from	from	ADP
ejpam-115	215	8	the	the	DET
ejpam-115	215	9	fact	fact	NOUN
ejpam-115	215	10	that	that	SCONJ
ejpam-115	215	11	this	this	DET
ejpam-115	215	12	system	system	NOUN
ejpam-115	215	13	has	have	AUX
ejpam-115	215	14	a	a	DET
ejpam-115	215	15	biorthogonal	biorthogonal	ADJ
ejpam-115	215	16	system	system	NOUN
ejpam-115	215	17	consisting	consist	VERB
ejpam-115	215	18	of	of	ADP
ejpam-115	215	19	the	the	DET
ejpam-115	215	20	root	root	NOUN
ejpam-115	215	21	functions	function	NOUN
ejpam-115	215	22	of	of	ADP
ejpam-115	215	23	the	the	DET
ejpam-115	215	24	adjoint	adjoint	NOUN
ejpam-115	215	25	operator	operator	NOUN
ejpam-115	215	26	l∗(v	l∗(v	PROPN
ejpam-115	215	27	)	)	PUNCT
ejpam-115	216	1	=	=	SYM
ejpam-115	216	2	v′′	v′′	NOUN
ejpam-115	216	3	+	+	CCONJ
ejpam-115	216	4	q(x)v	q(x)v	PROPN
ejpam-115	216	5	,	,	PUNCT
ejpam-115	216	6	v(1	v(1	PROPN
ejpam-115	216	7	)	)	PUNCT
ejpam-115	216	8	=	=	SYM
ejpam-115	216	9	v(0	v(0	NOUN
ejpam-115	216	10	)	)	PUNCT
ejpam-115	216	11	,	,	PUNCT
ejpam-115	216	12	v′(1	v′(1	PROPN
ejpam-115	216	13	)	)	PUNCT
ejpam-115	216	14	=	=	SYM
ejpam-115	216	15	v′(0	v′(0	NOUN
ejpam-115	216	16	)	)	PUNCT
ejpam-115	216	17	.	.	PUNCT
ejpam-115	217	1	khanlar	khanlar	PROPN
ejpam-115	217	2	r.	r.	PROPN
ejpam-115	217	3	mamedov	mamedov	PROPN
ejpam-115	217	4	,	,	PUNCT
ejpam-115	217	5	hamza	hamza	PROPN
ejpam-115	217	6	menken	menken	PROPN
ejpam-115	217	7	/	/	SYM
ejpam-115	217	8	eur	eur	PROPN
ejpam-115	217	9	.	.	PUNCT
ejpam-115	218	1	j.	j.	PROPN
ejpam-115	218	2	pure	pure	PROPN
ejpam-115	218	3	appl	appl	PROPN
ejpam-115	218	4	.	.	PUNCT
ejpam-115	219	1	math,1	math,1	PROPN
ejpam-115	219	2	(	(	PUNCT
ejpam-115	219	3	2008	2008	NUM
ejpam-115	219	4	)	)	PUNCT
ejpam-115	219	5	,	,	PUNCT
ejpam-115	219	6	(	(	PUNCT
ejpam-115	219	7	51	51	NUM
ejpam-115	219	8	-	-	SYM
ejpam-115	219	9	60	60	NUM
ejpam-115	219	10	)	)	PUNCT
ejpam-115	219	11	59	59	NUM
ejpam-115	219	12	for	for	ADP
ejpam-115	219	13	anyf	anyf	NOUN
ejpam-115	219	14	∈	∈	PROPN
ejpam-115	219	15	l2(0	l2(0	NOUN
ejpam-115	219	16	,	,	PUNCT
ejpam-115	219	17	1	1	NUM
ejpam-115	219	18	)	)	PUNCT
ejpam-115	219	19	,	,	PUNCT
ejpam-115	219	20	with	with	ADP
ejpam-115	219	21	a	a	DET
ejpam-115	219	22	direct	direct	ADJ
ejpam-115	219	23	computation	computation	NOUN
ejpam-115	219	24	we	we	PRON
ejpam-115	219	25	have	have	VERB
ejpam-115	219	26	that	that	SCONJ
ejpam-115	219	27	∞∑	∞∑	NUM
ejpam-115	219	28	n	n	CCONJ
ejpam-115	219	29	=	=	NOUN
ejpam-115	219	30	n	n	PRON
ejpam-115	219	31	|(f	|(f	PROPN
ejpam-115	219	32	,	,	PUNCT
ejpam-115	219	33	yk,1)|2	yk,1)|2	X
ejpam-115	219	34	<	<	X
ejpam-115	219	35	∞	∞	PROPN
ejpam-115	219	36	,	,	PUNCT
ejpam-115	219	37	∞∑	∞∑	NUM
ejpam-115	219	38	n	n	CCONJ
ejpam-115	219	39	=	=	NOUN
ejpam-115	219	40	n	n	PRON
ejpam-115	219	41	|(f	|(f	PROPN
ejpam-115	219	42	,	,	PUNCT
ejpam-115	219	43	yk,2)|2	yk,2)|2	NOUN
ejpam-115	219	44	<	<	X
ejpam-115	219	45	∞.	∞.	PROPN
ejpam-115	219	46	on	on	ADP
ejpam-115	219	47	the	the	DET
ejpam-115	219	48	other	other	ADJ
ejpam-115	219	49	hand	hand	NOUN
ejpam-115	219	50	,	,	PUNCT
ejpam-115	219	51	the	the	DET
ejpam-115	219	52	eigenfunctions	eigenfunction	NOUN
ejpam-115	219	53	of	of	ADP
ejpam-115	219	54	the	the	DET
ejpam-115	219	55	adjoint	adjoint	NOUN
ejpam-115	219	56	operator	operator	NOUN
ejpam-115	219	57	have	have	AUX
ejpam-115	219	58	of	of	ADP
ejpam-115	219	59	the	the	DET
ejpam-115	219	60	form	form	NOUN
ejpam-115	219	61	υk,1(x	υk,1(x	PROPN
ejpam-115	219	62	)	)	PUNCT
ejpam-115	219	63	=	=	SYM
ejpam-115	219	64	2	2	NUM
ejpam-115	219	65	sin	sin	NOUN
ejpam-115	219	66	2kπx+o	2kπx+o	NUM
ejpam-115	219	67	(	(	PUNCT
ejpam-115	219	68	1	1	NUM
ejpam-115	219	69	k	k	NOUN
ejpam-115	219	70	)	)	PUNCT
ejpam-115	219	71	,	,	PUNCT
ejpam-115	219	72	(	(	PUNCT
ejpam-115	219	73	3.1	3.1	NUM
ejpam-115	219	74	)	)	PUNCT
ejpam-115	219	75	υk,2(x	υk,2(x	PROPN
ejpam-115	219	76	)	)	PUNCT
ejpam-115	219	77	=	=	SYM
ejpam-115	219	78	2	2	NUM
ejpam-115	219	79	cos	cos	PROPN
ejpam-115	219	80	2kπx+o	2kπx+o	PROPN
ejpam-115	219	81	(	(	PUNCT
ejpam-115	219	82	1	1	NUM
ejpam-115	219	83	k	k	NOUN
ejpam-115	219	84	)	)	PUNCT
ejpam-115	219	85	,	,	PUNCT
ejpam-115	219	86	(	(	PUNCT
ejpam-115	219	87	3.2	3.2	NUM
ejpam-115	219	88	)	)	PUNCT
ejpam-115	219	89	and	and	CCONJ
ejpam-115	219	90	the	the	DET
ejpam-115	219	91	inequalities	inequality	NOUN
ejpam-115	219	92	∞∑	∞∑	NUM
ejpam-115	219	93	n	n	CCONJ
ejpam-115	219	94	=	=	NOUN
ejpam-115	219	95	n	n	PRON
ejpam-115	219	96	|(f	|(f	PROPN
ejpam-115	219	97	,	,	PUNCT
ejpam-115	219	98	υk,1)|2	υk,1)|2	VERB
ejpam-115	219	99	<	<	X
ejpam-115	219	100	∞	∞	NUM
ejpam-115	219	101	and	and	CCONJ
ejpam-115	219	102	∞∑	∞∑	PROPN
ejpam-115	219	103	n	n	CCONJ
ejpam-115	219	104	=	=	NOUN
ejpam-115	219	105	n	n	PRON
ejpam-115	219	106	|(f	|(f	PROPN
ejpam-115	219	107	,	,	PUNCT
ejpam-115	219	108	υk,2)|2	υk,2)|2	NOUN
ejpam-115	219	109	<	<	X
ejpam-115	219	110	∞	∞	NUM
ejpam-115	219	111	hold	hold	NOUN
ejpam-115	219	112	.	.	PUNCT
ejpam-115	220	1	according	accord	VERB
ejpam-115	220	2	to	to	ADP
ejpam-115	220	3	theorem	theorem	ADJ
ejpam-115	220	4	1.1	1.1	NUM
ejpam-115	220	5	,	,	PUNCT
ejpam-115	220	6	the	the	DET
ejpam-115	220	7	root	root	NOUN
ejpam-115	220	8	functions	function	NOUN
ejpam-115	220	9	of	of	ADP
ejpam-115	220	10	the	the	DET
ejpam-115	220	11	boundary	boundary	ADJ
ejpam-115	220	12	problem	problem	NOUN
ejpam-115	220	13	(	(	PUNCT
ejpam-115	220	14	1.1	1.1	NUM
ejpam-115	220	15	)	)	PUNCT
ejpam-115	220	16	,	,	PUNCT
ejpam-115	220	17	(	(	PUNCT
ejpam-115	220	18	1.2	1.2	NUM
ejpam-115	220	19	)	)	PUNCT
ejpam-115	220	20	form	form	NOUN
ejpam-115	220	21	a	a	DET
ejpam-115	220	22	riesz	riesz	NOUN
ejpam-115	220	23	basis	basis	NOUN
ejpam-115	220	24	inl2(0	inl2(0	PROPN
ejpam-115	220	25	,	,	PUNCT
ejpam-115	220	26	1	1	NUM
ejpam-115	220	27	)	)	PUNCT
ejpam-115	220	28	.	.	PUNCT
ejpam-115	221	1	this	this	PRON
ejpam-115	221	2	completes	complete	VERB
ejpam-115	221	3	the	the	DET
ejpam-115	221	4	proof	proof	NOUN
ejpam-115	221	5	.	.	PUNCT
ejpam-115	222	1	4	4	X
ejpam-115	222	2	.	.	X
ejpam-115	222	3	the	the	DET
ejpam-115	222	4	basisness	basisness	NOUN
ejpam-115	222	5	inl2(0	inl2(0	PROPN
ejpam-115	222	6	,	,	PUNCT
ejpam-115	222	7	1	1	NUM
ejpam-115	222	8	)	)	PUNCT
ejpam-115	222	9	of	of	ADP
ejpam-115	222	10	the	the	DET
ejpam-115	222	11	root	root	NOUN
ejpam-115	222	12	functions	function	NOUN
ejpam-115	222	13	for	for	ADP
ejpam-115	222	14	the	the	DET
ejpam-115	222	15	anti	anti	ADJ
ejpam-115	222	16	-	-	ADJ
ejpam-115	222	17	periodic	periodic	ADJ
ejpam-115	222	18	boundary	boundary	ADJ
ejpam-115	222	19	-	-	PUNCT
ejpam-115	222	20	value	value	NOUN
ejpam-115	222	21	problem	problem	NOUN
ejpam-115	222	22	similarly	similarly	ADV
ejpam-115	222	23	,	,	PUNCT
ejpam-115	222	24	the	the	DET
ejpam-115	222	25	following	follow	VERB
ejpam-115	222	26	results	result	NOUN
ejpam-115	222	27	are	be	AUX
ejpam-115	222	28	obtained	obtain	VERB
ejpam-115	222	29	for	for	ADP
ejpam-115	222	30	the	the	DET
ejpam-115	222	31	boundary	boundary	ADJ
ejpam-115	222	32	problem	problem	NOUN
ejpam-115	222	33	(	(	PUNCT
ejpam-115	222	34	1.1	1.1	NUM
ejpam-115	222	35	)	)	PUNCT
ejpam-115	222	36	,	,	PUNCT
ejpam-115	222	37	(	(	PUNCT
ejpam-115	222	38	1.3	1.3	NUM
ejpam-115	222	39	)	)	PUNCT
ejpam-115	222	40	.	.	PUNCT
ejpam-115	223	1	lemma	lemma	PROPN
ejpam-115	223	2	4.1	4.1	NUM
ejpam-115	223	3	.	.	PUNCT
ejpam-115	224	1	all	all	DET
ejpam-115	224	2	eigenvalues	eigenvalue	NOUN
ejpam-115	224	3	of	of	ADP
ejpam-115	224	4	the	the	DET
ejpam-115	224	5	boundary	boundary	ADJ
ejpam-115	224	6	value	value	NOUN
ejpam-115	224	7	problem	problem	NOUN
ejpam-115	224	8	(	(	PUNCT
ejpam-115	224	9	1.1	1.1	NUM
ejpam-115	224	10	)	)	PUNCT
ejpam-115	224	11	,	,	PUNCT
ejpam-115	224	12	(	(	PUNCT
ejpam-115	224	13	1.3	1.3	NUM
ejpam-115	224	14	)	)	PUNCT
ejpam-115	224	15	,	,	PUNCT
ejpam-115	224	16	starting	start	VERB
ejpam-115	224	17	from	from	ADP
ejpam-115	224	18	some	some	DET
ejpam-115	224	19	number	number	NOUN
ejpam-115	224	20	,	,	PUNCT
ejpam-115	224	21	are	be	AUX
ejpam-115	224	22	simple	simple	ADJ
ejpam-115	224	23	and	and	CCONJ
ejpam-115	224	24	form	form	VERB
ejpam-115	224	25	two	two	NUM
ejpam-115	224	26	infinite	infinite	ADJ
ejpam-115	224	27	sequenceλk,1	sequenceλk,1	NOUN
ejpam-115	224	28	,	,	PUNCT
ejpam-115	224	29	λk,2	λk,2	PROPN
ejpam-115	224	30	,	,	PUNCT
ejpam-115	224	31	k	k	NOUN
ejpam-115	224	32	=	=	SYM
ejpam-115	224	33	n	n	CCONJ
ejpam-115	224	34	,	,	PUNCT
ejpam-115	224	35	n+1	n+1	PROPN
ejpam-115	224	36	,	,	PUNCT
ejpam-115	224	37	·	·	PUNCT
ejpam-115	224	38	·	·	PUNCT
ejpam-115	224	39	·	·	PUNCT
ejpam-115	224	40	,	,	PUNCT
ejpam-115	224	41	wheren	wheren	NOUN
ejpam-115	224	42	is	be	AUX
ejpam-115	224	43	a	a	DET
ejpam-115	224	44	positive	positive	ADJ
ejpam-115	224	45	integer	integer	NOUN
ejpam-115	224	46	and	and	CCONJ
ejpam-115	224	47	λk,1	λk,1	NOUN
ejpam-115	224	48	=	=	PUNCT
ejpam-115	225	1	−	−	PROPN
ejpam-115	226	1	[	[	X
ejpam-115	226	2	(	(	PUNCT
ejpam-115	226	3	2k	2k	NUM
ejpam-115	226	4	+	+	CCONJ
ejpam-115	226	5	1)π]2	1)π]2	NUM
ejpam-115	226	6	+	+	CCONJ
ejpam-115	226	7	q′(1)−	q′(1)−	ADJ
ejpam-115	226	8	q′(0)−	q′(0)−	NOUN
ejpam-115	226	9	1∫	1∫	NUM
ejpam-115	226	10	0	0	NUM
ejpam-115	226	11	q2(x)dx	q2(x)dx	NOUN
ejpam-115	227	1	[	[	X
ejpam-115	227	2	2(2k	2(2k	NUM
ejpam-115	227	3	+	+	NUM
ejpam-115	227	4	1)π]2	1)π]2	NUM
ejpam-115	227	5	+	+	NOUN
ejpam-115	227	6	o	o	NOUN
ejpam-115	227	7	(	(	PUNCT
ejpam-115	227	8	1	1	NUM
ejpam-115	227	9	k3	k3	ADJ
ejpam-115	227	10	)	)	PUNCT
ejpam-115	227	11	,	,	PUNCT
ejpam-115	227	12	(	(	PUNCT
ejpam-115	227	13	4.1	4.1	NUM
ejpam-115	227	14	)	)	PUNCT
ejpam-115	227	15	λk,2	λk,2	NOUN
ejpam-115	227	16	=	=	PUNCT
ejpam-115	228	1	−	−	PROPN
ejpam-115	229	1	[	[	X
ejpam-115	229	2	(	(	PUNCT
ejpam-115	229	3	2k	2k	NUM
ejpam-115	229	4	+	+	CCONJ
ejpam-115	229	5	1)π]2	1)π]2	NUM
ejpam-115	229	6	−	−	PROPN
ejpam-115	229	7	q′(1)−	q′(1)−	NOUN
ejpam-115	229	8	q′(0	q′(0	PROPN
ejpam-115	229	9	)	)	PUNCT
ejpam-115	229	10	+	+	CCONJ
ejpam-115	230	1	1∫	1∫	NUM
ejpam-115	230	2	0	0	NUM
ejpam-115	230	3	q2(x)dx	q2(x)dx	NOUN
ejpam-115	231	1	[	[	X
ejpam-115	231	2	2(2k	2(2k	NUM
ejpam-115	231	3	+	+	NUM
ejpam-115	231	4	1)π]2	1)π]2	NUM
ejpam-115	231	5	+	+	NOUN
ejpam-115	231	6	o	o	NOUN
ejpam-115	231	7	(	(	PUNCT
ejpam-115	231	8	1	1	NUM
ejpam-115	231	9	k3	k3	ADJ
ejpam-115	231	10	)	)	PUNCT
ejpam-115	231	11	,	,	PUNCT
ejpam-115	231	12	(	(	PUNCT
ejpam-115	231	13	4.2	4.2	NUM
ejpam-115	231	14	)	)	PUNCT
ejpam-115	231	15	and	and	CCONJ
ejpam-115	231	16	the	the	DET
ejpam-115	231	17	corresponding	corresponding	ADJ
ejpam-115	231	18	eigenfunctions	eigenfunction	NOUN
ejpam-115	231	19	are	be	AUX
ejpam-115	231	20	of	of	ADP
ejpam-115	231	21	the	the	DET
ejpam-115	231	22	form	form	NOUN
ejpam-115	231	23	yk,1(x	yk,1(x	NOUN
ejpam-115	231	24	)	)	PUNCT
ejpam-115	232	1	=	=	SYM
ejpam-115	232	2	sin(2k	sin(2k	NOUN
ejpam-115	232	3	+	+	CCONJ
ejpam-115	232	4	1)πx+o	1)πx+o	NUM
ejpam-115	232	5	(	(	PUNCT
ejpam-115	232	6	1	1	NUM
ejpam-115	232	7	k	k	NOUN
ejpam-115	232	8	)	)	PUNCT
ejpam-115	232	9	,	,	PUNCT
ejpam-115	232	10	(	(	PUNCT
ejpam-115	232	11	4.3	4.3	NUM
ejpam-115	232	12	)	)	PUNCT
ejpam-115	232	13	yk,2(x	yk,2(x	NOUN
ejpam-115	232	14	)	)	PUNCT
ejpam-115	232	15	=	=	SYM
ejpam-115	233	1	cos(2k	cos(2k	NOUN
ejpam-115	233	2	+	+	CCONJ
ejpam-115	233	3	1)πx+o	1)πx+o	NUM
ejpam-115	233	4	(	(	PUNCT
ejpam-115	233	5	1	1	NUM
ejpam-115	233	6	k	k	NOUN
ejpam-115	233	7	)	)	PUNCT
ejpam-115	233	8	.	.	PUNCT
ejpam-115	234	1	(	(	PUNCT
ejpam-115	234	2	4.4	4.4	NUM
ejpam-115	234	3	)	)	PUNCT
ejpam-115	234	4	proof	proof	NOUN
ejpam-115	234	5	.	.	PUNCT
ejpam-115	235	1	in	in	ADP
ejpam-115	235	2	the	the	DET
ejpam-115	235	3	anti	anti	ADJ
ejpam-115	235	4	-	-	ADJ
ejpam-115	235	5	periodic	periodic	ADJ
ejpam-115	235	6	case	case	NOUN
ejpam-115	235	7	,	,	PUNCT
ejpam-115	235	8	in	in	ADP
ejpam-115	235	9	a	a	DET
ejpam-115	235	10	similar	similar	ADJ
ejpam-115	235	11	way	way	NOUN
ejpam-115	235	12	to	to	ADP
ejpam-115	235	13	the	the	DET
ejpam-115	235	14	proof	proof	NOUN
ejpam-115	235	15	lemma	lemma	PROPN
ejpam-115	235	16	2.1	2.1	NUM
ejpam-115	235	17	,	,	PUNCT
ejpam-115	235	18	we	we	PRON
ejpam-115	235	19	have	have	VERB
ejpam-115	235	20	the	the	DET
ejpam-115	235	21	relations	relation	NOUN
ejpam-115	235	22	eiµ	eiµ	VERB
ejpam-115	236	1	+	+	CCONJ
ejpam-115	236	2	1	1	X
ejpam-115	236	3	=	=	NUM
ejpam-115	236	4	q′(1)−	q′(1)−	NOUN
ejpam-115	236	5	q′(0)−	q′(0)−	NOUN
ejpam-115	237	1	1∫	1∫	NUM
ejpam-115	237	2	0	0	NUM
ejpam-115	237	3	q2(x)dx	q2(x)dx	NOUN
ejpam-115	237	4	(	(	PUNCT
ejpam-115	237	5	2iµ)3	2iµ)3	NUM
ejpam-115	237	6	+	+	NOUN
ejpam-115	237	7	o	o	PROPN
ejpam-115	237	8	(	(	PUNCT
ejpam-115	237	9	1	1	NUM
ejpam-115	237	10	µ4	µ4	PROPN
ejpam-115	237	11	)	)	PUNCT
ejpam-115	237	12	,	,	PUNCT
ejpam-115	237	13	eiµ	eiµ	VERB
ejpam-115	237	14	+	+	CCONJ
ejpam-115	237	15	1	1	NUM
ejpam-115	237	16	=	=	SYM
ejpam-115	237	17	−	−	NOUN
ejpam-115	237	18	q′(1)−	q′(1)−	INTJ
ejpam-115	237	19	q′(0)−	q′(0)−	NOUN
ejpam-115	238	1	1∫	1∫	NUM
ejpam-115	238	2	0	0	NUM
ejpam-115	238	3	q2(x)dx	q2(x)dx	NOUN
ejpam-115	238	4	(	(	PUNCT
ejpam-115	238	5	2iµ)3	2iµ)3	NUM
ejpam-115	238	6	+	+	NOUN
ejpam-115	238	7	o	o	PROPN
ejpam-115	238	8	(	(	PUNCT
ejpam-115	238	9	1	1	NUM
ejpam-115	238	10	µ4	µ4	PROPN
ejpam-115	238	11	)	)	PUNCT
ejpam-115	238	12	.	.	PUNCT
ejpam-115	239	1	references	reference	NOUN
ejpam-115	239	2	60	60	NUM
ejpam-115	239	3	from	from	ADP
ejpam-115	239	4	these	these	DET
ejpam-115	239	5	relations	relation	NOUN
ejpam-115	239	6	we	we	PRON
ejpam-115	239	7	can	can	AUX
ejpam-115	239	8	obtain	obtain	VERB
ejpam-115	239	9	(	(	PUNCT
ejpam-115	239	10	4.1	4.1	NUM
ejpam-115	239	11	)	)	PUNCT
ejpam-115	239	12	and	and	CCONJ
ejpam-115	239	13	(	(	PUNCT
ejpam-115	239	14	4.2	4.2	NUM
ejpam-115	239	15	)	)	PUNCT
ejpam-115	239	16	.	.	PUNCT
ejpam-115	240	1	again	again	ADV
ejpam-115	240	2	in	in	ADP
ejpam-115	240	3	a	a	DET
ejpam-115	240	4	similar	similar	ADJ
ejpam-115	240	5	way	way	NOUN
ejpam-115	240	6	to	to	ADP
ejpam-115	240	7	the	the	DET
ejpam-115	240	8	proof	proof	NOUN
ejpam-115	240	9	lemma	lemma	PROPN
ejpam-115	240	10	2.1	2.1	NUM
ejpam-115	240	11	,	,	PUNCT
ejpam-115	240	12	we	we	PRON
ejpam-115	240	13	obtain	obtain	VERB
ejpam-115	240	14	u1(ϕ1(x	u1(ϕ1(x	NOUN
ejpam-115	240	15	,	,	PUNCT
ejpam-115	240	16	µk,1	µk,1	NOUN
ejpam-115	240	17	)	)	PUNCT
ejpam-115	240	18	)	)	PUNCT
ejpam-115	241	1	=	=	SYM
ejpam-115	241	2	ϕ1(1	ϕ1(1	PROPN
ejpam-115	241	3	,	,	PUNCT
ejpam-115	241	4	µk,1	µk,1	NOUN
ejpam-115	241	5	)	)	PUNCT
ejpam-115	242	1	+	+	CCONJ
ejpam-115	242	2	ϕ1(0	ϕ1(0	PROPN
ejpam-115	242	3	,	,	PUNCT
ejpam-115	242	4	µk,1	µk,1	NOUN
ejpam-115	242	5	)	)	PUNCT
ejpam-115	243	1	=	=	PUNCT
ejpam-115	244	1	2[q′(1)−	2[q′(1)−	NUM
ejpam-115	244	2	q′(0	q′(0	ADJ
ejpam-115	244	3	)	)	PUNCT
ejpam-115	244	4	]	]	PUNCT
ejpam-115	244	5	(	(	PUNCT
ejpam-115	244	6	2iµk,1)3	2iµk,1)3	NOUN
ejpam-115	245	1	+	+	NOUN
ejpam-115	245	2	o	o	X
ejpam-115	245	3	(	(	PUNCT
ejpam-115	245	4	1	1	NUM
ejpam-115	245	5	µ4	µ4	PROPN
ejpam-115	245	6	k,1	k,1	PROPN
ejpam-115	245	7	)	)	PUNCT
ejpam-115	245	8	,	,	PUNCT
ejpam-115	245	9	u1(ϕ2(x	u1(ϕ2(x	PROPN
ejpam-115	245	10	,	,	PUNCT
ejpam-115	245	11	µk,1	µk,1	NOUN
ejpam-115	245	12	)	)	PUNCT
ejpam-115	245	13	)	)	PUNCT
ejpam-115	245	14	=	=	SYM
ejpam-115	245	15	ϕ2(1	ϕ2(1	PROPN
ejpam-115	245	16	,	,	PUNCT
ejpam-115	245	17	µk,1	µk,1	NOUN
ejpam-115	245	18	)	)	PUNCT
ejpam-115	245	19	+	+	CCONJ
ejpam-115	245	20	ϕ2(0	ϕ2(0	NOUN
ejpam-115	245	21	,	,	PUNCT
ejpam-115	245	22	µk,1	µk,1	NOUN
ejpam-115	245	23	)	)	PUNCT
ejpam-115	245	24	=	=	SYM
ejpam-115	246	1	−2[q′(1)−	−2[q′(1)−	NUM
ejpam-115	246	2	q′(0	q′(0	PROPN
ejpam-115	246	3	)	)	PUNCT
ejpam-115	246	4	]	]	PUNCT
ejpam-115	247	1	(	(	PUNCT
ejpam-115	247	2	2iµk,1)3	2iµk,1)3	NOUN
ejpam-115	247	3	+	+	NOUN
ejpam-115	247	4	o	o	X
ejpam-115	247	5	(	(	PUNCT
ejpam-115	247	6	1	1	NUM
ejpam-115	247	7	µ4	µ4	PROPN
ejpam-115	247	8	k,1	k,1	PROPN
ejpam-115	247	9	)	)	PUNCT
ejpam-115	247	10	.	.	PUNCT
ejpam-115	248	1	sinceu1(ϕj(x	sinceu1(ϕj(x	NUM
ejpam-115	248	2	,	,	PUNCT
ejpam-115	248	3	µk,1	µk,1	NOUN
ejpam-115	248	4	)	)	PUNCT
ejpam-115	248	5	)	)	PUNCT
ejpam-115	249	1	6=	6=	NUM
ejpam-115	250	1	0,j	0,j	NOUN
ejpam-115	250	2	=	=	SYM
ejpam-115	250	3	1	1	NUM
ejpam-115	250	4	,	,	PUNCT
ejpam-115	250	5	2	2	NUM
ejpam-115	250	6	,	,	PUNCT
ejpam-115	250	7	we	we	PRON
ejpam-115	250	8	can	can	AUX
ejpam-115	250	9	seek	seek	VERB
ejpam-115	250	10	the	the	DET
ejpam-115	250	11	eigenfunctionyk,1(x	eigenfunctionyk,1(x	NOUN
ejpam-115	250	12	)	)	PUNCT
ejpam-115	250	13	corresponding	correspond	VERB
ejpam-115	250	14	to	to	ADP
ejpam-115	250	15	the	the	DET
ejpam-115	250	16	eigenvalueλk,1	eigenvalueλk,1	NOUN
ejpam-115	250	17	in	in	ADP
ejpam-115	250	18	the	the	DET
ejpam-115	250	19	form	form	NOUN
ejpam-115	250	20	yk,1(x	yk,1(x	NOUN
ejpam-115	250	21	)	)	PUNCT
ejpam-115	251	1	=	=	SYM
ejpam-115	252	1	−	−	PROPN
ejpam-115	252	2	(	(	PUNCT
ejpam-115	252	3	2iµk,1)3	2iµk,1)3	NOUN
ejpam-115	253	1	[	[	X
ejpam-115	253	2	q′(1)−	q′(1)−	NOUN
ejpam-115	253	3	q′(0	q′(0	PROPN
ejpam-115	253	4	)	)	PUNCT
ejpam-115	253	5	]	]	PUNCT
ejpam-115	254	1	∣∣∣∣	∣∣∣∣	PROPN
ejpam-115	254	2	ϕ1(x	ϕ1(x	PROPN
ejpam-115	254	3	,	,	PUNCT
ejpam-115	254	4	µk,1	µk,1	NOUN
ejpam-115	254	5	)	)	PUNCT
ejpam-115	254	6	ϕ2(x	ϕ2(x	PROPN
ejpam-115	254	7	,	,	PUNCT
ejpam-115	254	8	µk,1	µk,1	NOUN
ejpam-115	254	9	)	)	PUNCT
ejpam-115	254	10	u1(ϕ1(x	u1(ϕ1(x	NOUN
ejpam-115	254	11	,	,	PUNCT
ejpam-115	254	12	µk,1	µk,1	NOUN
ejpam-115	254	13	)	)	PUNCT
ejpam-115	254	14	)	)	PUNCT
ejpam-115	254	15	u1(ϕ2(x	u1(ϕ2(x	PROPN
ejpam-115	254	16	,	,	PUNCT
ejpam-115	254	17	µk,1	µk,1	NOUN
ejpam-115	254	18	)	)	PUNCT
ejpam-115	254	19	)	)	PUNCT
ejpam-115	255	1	∣∣∣∣	∣∣∣∣	PROPN
ejpam-115	255	2	.	.	PUNCT
ejpam-115	256	1	hence	hence	ADV
ejpam-115	256	2	,	,	PUNCT
ejpam-115	256	3	we	we	PRON
ejpam-115	256	4	have	have	VERB
ejpam-115	256	5	yk,1(x	yk,1(x	NOUN
ejpam-115	256	6	)	)	PUNCT
ejpam-115	257	1	=	=	SYM
ejpam-115	257	2	sin(2k	sin(2k	NOUN
ejpam-115	257	3	+	+	CCONJ
ejpam-115	257	4	1)πx+o	1)πx+o	NUM
ejpam-115	257	5	(	(	PUNCT
ejpam-115	257	6	1	1	NUM
ejpam-115	257	7	k	k	NOUN
ejpam-115	257	8	)	)	PUNCT
ejpam-115	257	9	,	,	PUNCT
ejpam-115	257	10	i.e.	i.e.	X
ejpam-115	257	11	,	,	PUNCT
ejpam-115	257	12	the	the	DET
ejpam-115	257	13	formula	formula	NOUN
ejpam-115	257	14	(	(	PUNCT
ejpam-115	257	15	4.3	4.3	NUM
ejpam-115	257	16	)	)	PUNCT
ejpam-115	257	17	satisfies	satisfie	NOUN
ejpam-115	257	18	.	.	PUNCT
ejpam-115	258	1	in	in	ADP
ejpam-115	258	2	similar	similar	ADJ
ejpam-115	258	3	way	way	NOUN
ejpam-115	258	4	we	we	PRON
ejpam-115	258	5	can	can	AUX
ejpam-115	258	6	obtain	obtain	VERB
ejpam-115	258	7	the	the	DET
ejpam-115	258	8	formula	formula	NOUN
ejpam-115	258	9	(	(	PUNCT
ejpam-115	258	10	4.4	4.4	NUM
ejpam-115	258	11	)	)	PUNCT
ejpam-115	258	12	.	.	PUNCT
ejpam-115	259	1	theorem	theorem	VERB
ejpam-115	259	2	4.1	4.1	NUM
ejpam-115	259	3	.	.	PUNCT
ejpam-115	260	1	the	the	DET
ejpam-115	260	2	root	root	NOUN
ejpam-115	260	3	functions	function	NOUN
ejpam-115	260	4	of	of	ADP
ejpam-115	260	5	the	the	DET
ejpam-115	260	6	boundary	boundary	ADJ
ejpam-115	260	7	problem	problem	NOUN
ejpam-115	260	8	(	(	PUNCT
ejpam-115	260	9	1.1	1.1	NUM
ejpam-115	260	10	)	)	PUNCT
ejpam-115	260	11	,	,	PUNCT
ejpam-115	260	12	(	(	PUNCT
ejpam-115	260	13	1.3	1.3	NUM
ejpam-115	260	14	)	)	PUNCT
ejpam-115	260	15	form	form	NOUN
ejpam-115	260	16	a	a	DET
ejpam-115	260	17	riesz	riesz	NOUN
ejpam-115	260	18	basis	basis	NOUN
ejpam-115	260	19	in	in	ADP
ejpam-115	260	20	l2(0	l2(0	NOUN
ejpam-115	260	21	,	,	PUNCT
ejpam-115	260	22	1	1	NUM
ejpam-115	260	23	)	)	PUNCT
ejpam-115	260	24	.	.	PUNCT
ejpam-115	261	1	references	reference	NOUN
ejpam-115	261	2	[	[	X
ejpam-115	261	3	1	1	NUM
ejpam-115	261	4	]	]	PUNCT
ejpam-115	261	5	m.	m.	NOUN
ejpam-115	261	6	a.	a.	PROPN
ejpam-115	261	7	naimark	naimark	PROPN
ejpam-115	261	8	,	,	PUNCT
ejpam-115	261	9	linear	linear	PROPN
ejpam-115	261	10	differential	differential	NOUN
ejpam-115	261	11	operators	operator	NOUN
ejpam-115	261	12	,	,	PUNCT
ejpam-115	261	13	part	part	NOUN
ejpam-115	261	14	i	i	PROPN
ejpam-115	261	15	,	,	PUNCT
ejpam-115	261	16	frederick	frederick	PROPN
ejpam-115	261	17	ungar	ungar	PROPN
ejpam-115	261	18	pub	pub	PROPN
ejpam-115	261	19	.	.	PUNCT
ejpam-115	262	1	co.	co.	PROPN
ejpam-115	262	2	,	,	PUNCT
ejpam-115	262	3	new	new	PROPN
ejpam-115	262	4	york	york	PROPN
ejpam-115	262	5	,	,	PUNCT
ejpam-115	262	6	1967	1967	NUM
ejpam-115	262	7	.	.	PUNCT
ejpam-115	263	1	[	[	X
ejpam-115	263	2	2	2	X
ejpam-115	263	3	]	]	X
ejpam-115	263	4	g.	g.	PROPN
ejpam-115	263	5	m.	m.	PROPN
ejpam-115	263	6	kesel’man	kesel’man	PROPN
ejpam-115	263	7	,	,	PUNCT
ejpam-115	263	8	on	on	ADP
ejpam-115	263	9	the	the	DET
ejpam-115	263	10	unconditional	unconditional	ADJ
ejpam-115	263	11	convergence	convergence	NOUN
ejpam-115	263	12	of	of	ADP
ejpam-115	263	13	expansions	expansion	NOUN
ejpam-115	263	14	in	in	ADP
ejpam-115	263	15	the	the	DET
ejpam-115	263	16	eigenfunctions	eigenfunction	NOUN
ejpam-115	263	17	of	of	ADP
ejpam-115	263	18	some	some	DET
ejpam-115	263	19	differential	differential	ADJ
ejpam-115	263	20	operators	operator	NOUN
ejpam-115	263	21	,	,	PUNCT
ejpam-115	263	22	izv	izv	PROPN
ejpam-115	263	23	.	.	PROPN
ejpam-115	263	24	vyssh	vyssh	PROPN
ejpam-115	263	25	.	.	PUNCT
ejpam-115	264	1	uchebn	uchebn	NOUN
ejpam-115	264	2	.	.	PUNCT
ejpam-115	265	1	zaved	zave	VERB
ejpam-115	265	2	.	.	PUNCT
ejpam-115	266	1	mat	mat	NOUN
ejpam-115	266	2	.	.	PUNCT
ejpam-115	267	1	[	[	X
ejpam-115	267	2	soviet	soviet	ADJ
ejpam-115	267	3	math	math	NOUN
ejpam-115	267	4	.	.	PUNCT
ejpam-115	268	1	(	(	PUNCT
ejpam-115	268	2	iz	iz	INTJ
ejpam-115	268	3	.	.	PUNCT
ejpam-115	268	4	vuz	vuz	PROPN
ejpam-115	268	5	)	)	PUNCT
ejpam-115	268	6	]	]	PUNCT
ejpam-115	268	7	,	,	PUNCT
ejpam-115	268	8	n.2	n.2	NOUN
ejpam-115	268	9	:	:	PUNCT
ejpam-115	268	10	82	82	NUM
ejpam-115	268	11	-	-	SYM
ejpam-115	268	12	93	93	NUM
ejpam-115	268	13	(	(	PUNCT
ejpam-115	268	14	1964	1964	NUM
ejpam-115	268	15	)	)	PUNCT
ejpam-115	268	16	.	.	PUNCT
ejpam-115	269	1	[	[	X
ejpam-115	269	2	3	3	X
ejpam-115	269	3	]	]	PUNCT
ejpam-115	269	4	v.	v.	ADP
ejpam-115	269	5	p.	p.	PROPN
ejpam-115	269	6	mikhailov	mikhailov	PROPN
ejpam-115	269	7	,	,	PUNCT
ejpam-115	269	8	on	on	ADP
ejpam-115	269	9	the	the	DET
ejpam-115	269	10	bases	basis	NOUN
ejpam-115	269	11	inl2(0	inl2(0	PROPN
ejpam-115	269	12	,	,	PUNCT
ejpam-115	269	13	1	1	NUM
ejpam-115	269	14	)	)	PUNCT
ejpam-115	269	15	,	,	PUNCT
ejpam-115	269	16	dokl	dokl	NOUN
ejpam-115	269	17	.	.	PUNCT
ejpam-115	269	18	akad	akad	PROPN
ejpam-115	269	19	.	.	PUNCT
ejpam-115	270	1	nauk	nauk	NOUN
ejpam-115	270	2	sssr	sssr	NOUN
ejpam-115	271	1	[	[	X
ejpam-115	271	2	soviet	soviet	ADJ
ejpam-115	271	3	math	math	NOUN
ejpam-115	271	4	.	.	PUNCT
ejpam-115	272	1	dokl	dokl	NOUN
ejpam-115	272	2	.	.	PUNCT
ejpam-115	273	1	]	]	X
ejpam-115	273	2	,	,	PUNCT
ejpam-115	273	3	144	144	NUM
ejpam-115	273	4	,	,	PUNCT
ejpam-115	273	5	n.5	n.5	SYM
ejpam-115	273	6	:	:	PUNCT
ejpam-115	273	7	981	981	NUM
ejpam-115	273	8	-	-	SYM
ejpam-115	273	9	984	984	NUM
ejpam-115	273	10	(	(	PUNCT
ejpam-115	273	11	1962	1962	NUM
ejpam-115	273	12	)	)	PUNCT
ejpam-115	273	13	.	.	PUNCT
ejpam-115	274	1	[	[	X
ejpam-115	274	2	4	4	NUM
ejpam-115	274	3	]	]	X
ejpam-115	274	4	n.	n.	PROPN
ejpam-115	274	5	dunford	dunford	PROPN
ejpam-115	274	6	,	,	PUNCT
ejpam-115	274	7	j.	j.	PROPN
ejpam-115	274	8	t.	t.	PROPN
ejpam-115	274	9	schwartz	schwartz	PROPN
ejpam-115	274	10	,	,	PUNCT
ejpam-115	274	11	linear	linear	PROPN
ejpam-115	274	12	operators	operator	NOUN
ejpam-115	274	13	,	,	PUNCT
ejpam-115	274	14	prt.3	prt.3	PROPN
ejpam-115	274	15	spectral	spectral	ADJ
ejpam-115	274	16	operators	operator	NOUN
ejpam-115	274	17	,	,	PUNCT
ejpam-115	274	18	wiley	wiley	PROPN
ejpam-115	274	19	,	,	PUNCT
ejpam-115	274	20	new	new	PROPN
ejpam-115	274	21	york	york	PROPN
ejpam-115	274	22	,	,	PUNCT
ejpam-115	274	23	1970	1970	NUM
ejpam-115	274	24	.	.	PUNCT
ejpam-115	275	1	[	[	X
ejpam-115	275	2	5	5	X
ejpam-115	275	3	]	]	PUNCT
ejpam-115	275	4	p.	p.	PROPN
ejpam-115	275	5	w.	w.	PROPN
ejpam-115	275	6	walker	walker	PROPN
ejpam-115	275	7	,	,	PUNCT
ejpam-115	275	8	a	a	DET
ejpam-115	275	9	nonspectral	nonspectral	ADJ
ejpam-115	275	10	birkhoff	birkhoff	NOUN
ejpam-115	275	11	-	-	PUNCT
ejpam-115	275	12	regular	regular	ADJ
ejpam-115	275	13	differential	differential	ADJ
ejpam-115	275	14	operators	operator	NOUN
ejpam-115	275	15	,	,	PUNCT
ejpam-115	275	16	proc	proc	NOUN
ejpam-115	275	17	.	.	PROPN
ejpam-115	275	18	of	of	ADP
ejpam-115	275	19	american	american	PROPN
ejpam-115	275	20	math	math	PROPN
ejpam-115	275	21	.	.	PUNCT
ejpam-115	276	1	soc.v	soc.v	X
ejpam-115	276	2	.	.	PROPN
ejpam-115	276	3	66	66	NUM
ejpam-115	276	4	,	,	PUNCT
ejpam-115	276	5	n.1	n.1	NUM
ejpam-115	276	6	:	:	PUNCT
ejpam-115	276	7	187	187	NUM
ejpam-115	276	8	-	-	SYM
ejpam-115	276	9	188	188	NUM
ejpam-115	276	10	(	(	PUNCT
ejpam-115	276	11	1977	1977	NUM
ejpam-115	276	12	)	)	PUNCT
ejpam-115	276	13	.	.	PUNCT
ejpam-115	277	1	[	[	X
ejpam-115	277	2	6	6	NUM
ejpam-115	277	3	]	]	X
ejpam-115	277	4	n.i	n.i	PROPN
ejpam-115	277	5	.	.	PROPN
ejpam-115	277	6	ionkin	ionkin	PROPN
ejpam-115	277	7	,	,	PUNCT
ejpam-115	277	8	the	the	DET
ejpam-115	277	9	solution	solution	NOUN
ejpam-115	277	10	of	of	ADP
ejpam-115	277	11	a	a	DET
ejpam-115	277	12	boundary	boundary	ADJ
ejpam-115	277	13	-	-	PUNCT
ejpam-115	277	14	value	value	NOUN
ejpam-115	277	15	problem	problem	NOUN
ejpam-115	277	16	in	in	ADP
ejpam-115	277	17	heat	heat	NOUN
ejpam-115	277	18	conduction	conduction	NOUN
ejpam-115	277	19	with	with	ADP
ejpam-115	277	20	a	a	DET
ejpam-115	277	21	nonclassical	nonclassical	ADJ
ejpam-115	277	22	boundary	boundary	ADJ
ejpam-115	277	23	condition	condition	NOUN
ejpam-115	277	24	,	,	PUNCT
ejpam-115	277	25	differ	differ	VERB
ejpam-115	277	26	.	.	PUNCT
ejpam-115	278	1	equations	equation	NOUN
ejpam-115	278	2	,	,	PUNCT
ejpam-115	278	3	v.13	v.13	PRON
ejpam-115	278	4	,	,	PUNCT
ejpam-115	278	5	n.	n.	NOUN
ejpam-115	278	6	2	2	NUM
ejpam-115	278	7	:	:	PUNCT
ejpam-115	278	8	294	294	NUM
ejpam-115	278	9	-	-	SYM
ejpam-115	278	10	304	304	NUM
ejpam-115	278	11	(	(	PUNCT
ejpam-115	278	12	1977	1977	NUM
ejpam-115	278	13	)	)	PUNCT
ejpam-115	278	14	.	.	PUNCT
ejpam-115	279	1	[	[	X
ejpam-115	279	2	7	7	X
ejpam-115	279	3	]	]	X
ejpam-115	279	4	n.	n.	PROPN
ejpam-115	279	5	b.	b.	PROPN
ejpam-115	279	6	kerimov	kerimov	PROPN
ejpam-115	279	7	,	,	PUNCT
ejpam-115	279	8	kh	kh	PROPN
ejpam-115	279	9	.	.	PUNCT
ejpam-115	279	10	r.	r.	PROPN
ejpam-115	279	11	mamedov	mamedov	PROPN
ejpam-115	279	12	,	,	PUNCT
ejpam-115	279	13	on	on	ADP
ejpam-115	279	14	the	the	DET
ejpam-115	279	15	riesz	riesz	PROPN
ejpam-115	279	16	basis	basis	NOUN
ejpam-115	279	17	property	property	NOUN
ejpam-115	279	18	of	of	ADP
ejpam-115	279	19	the	the	DET
ejpam-115	279	20	root	root	NOUN
ejpam-115	279	21	functions	function	NOUN
ejpam-115	279	22	in	in	ADP
ejpam-115	279	23	certain	certain	ADJ
ejpam-115	279	24	regular	regular	ADJ
ejpam-115	279	25	boundary	boundary	ADJ
ejpam-115	279	26	value	value	NOUN
ejpam-115	279	27	problems	problem	NOUN
ejpam-115	279	28	,	,	PUNCT
ejpam-115	279	29	math	math	NOUN
ejpam-115	279	30	.	.	PUNCT
ejpam-115	280	1	notes	note	NOUN
ejpam-115	280	2	,	,	PUNCT
ejpam-115	280	3	v.	v.	ADP
ejpam-115	280	4	64	64	NUM
ejpam-115	280	5	,	,	PUNCT
ejpam-115	280	6	n.4	n.4	NUM
ejpam-115	280	7	:	:	PUNCT
ejpam-115	280	8	483	483	NUM
ejpam-115	280	9	-	-	PUNCT
ejpam-115	280	10	487(1998	487(1998	NUM
ejpam-115	280	11	)	)	PUNCT
ejpam-115	280	12	.	.	PUNCT
ejpam-115	281	1	[	[	X
ejpam-115	281	2	8	8	NUM
ejpam-115	281	3	]	]	X
ejpam-115	281	4	n.	n.	PROPN
ejpam-115	281	5	k.	k.	PROPN
ejpam-115	281	6	bari	bari	PROPN
ejpam-115	281	7	,	,	PUNCT
ejpam-115	281	8	biorthogonal	biorthogonal	ADJ
ejpam-115	281	9	systems	system	NOUN
ejpam-115	281	10	and	and	CCONJ
ejpam-115	281	11	bases	basis	NOUN
ejpam-115	281	12	in	in	ADP
ejpam-115	281	13	hilbert	hilbert	PROPN
ejpam-115	281	14	spaces	space	NOUN
ejpam-115	281	15	,	,	PUNCT
ejpam-115	281	16	uchen	uchen	NOUN
ejpam-115	281	17	.	.	PUNCT
ejpam-115	281	18	zap	zap	PROPN
ejpam-115	281	19	.	.	PUNCT
ejpam-115	281	20	moskov	moskov	PROPN
ejpam-115	281	21	.	.	PUNCT
ejpam-115	282	1	gos	gos	PROPN
ejpam-115	282	2	.	.	PUNCT
ejpam-115	283	1	univ.148	univ.148	PROPN
ejpam-115	283	2	,	,	PUNCT
ejpam-115	283	3	4:68	4:68	NUM
ejpam-115	283	4	-	-	SYM
ejpam-115	283	5	107	107	NUM
ejpam-115	283	6	(	(	PUNCT
ejpam-115	283	7	1951	1951	NUM
ejpam-115	283	8	)	)	PUNCT
ejpam-115	283	9	(	(	PUNCT
ejpam-115	283	10	russian	russian	NOUN
ejpam-115	283	11	)	)	PUNCT
ejpam-115	283	12	.	.	PUNCT
ejpam-115	284	1	[	[	X
ejpam-115	284	2	9	9	NUM
ejpam-115	284	3	]	]	SYM
ejpam-115	284	4	i.	i.	PROPN
ejpam-115	284	5	c.	c.	PROPN
ejpam-115	284	6	gohberg	gohberg	PROPN
ejpam-115	284	7	,	,	PUNCT
ejpam-115	284	8	m.	m.	NOUN
ejpam-115	284	9	g.	g.	PROPN
ejpam-115	284	10	krein	krein	PROPN
ejpam-115	284	11	,	,	PUNCT
ejpam-115	284	12	introduction	introduction	NOUN
ejpam-115	284	13	to	to	ADP
ejpam-115	284	14	the	the	DET
ejpam-115	284	15	theory	theory	NOUN
ejpam-115	284	16	of	of	ADP
ejpam-115	284	17	linear	linear	PROPN
ejpam-115	284	18	nonselfadjoint	nonselfadjoint	NOUN
ejpam-115	284	19	operators	operator	NOUN
ejpam-115	284	20	,	,	PUNCT
ejpam-115	284	21	american	american	ADJ
ejpam-115	284	22	math	math	PROPN
ejpam-115	284	23	.	.	PUNCT
ejpam-115	285	1	soc	soc	PROPN
ejpam-115	285	2	.	.	PUNCT
ejpam-115	285	3	,	,	PUNCT
ejpam-115	285	4	providence	providence	NOUN
ejpam-115	285	5	,	,	PUNCT
ejpam-115	285	6	rhode	rhode	NOUN
ejpam-115	285	7	island	island	NOUN
ejpam-115	285	8	,	,	PUNCT
ejpam-115	285	9	1969	1969	NUM
ejpam-115	285	10	.	.	PUNCT
ejpam-115	286	1	[	[	X
ejpam-115	286	2	10	10	NUM
ejpam-115	286	3	]	]	X
ejpam-115	286	4	v.	v.	ADP
ejpam-115	286	5	a	a	DET
ejpam-115	286	6	marchenko	marchenko	NOUN
ejpam-115	286	7	,	,	PUNCT
ejpam-115	286	8	sturm	sturm	NOUN
ejpam-115	286	9	-	-	PUNCT
ejpam-115	286	10	liouville	liouville	NOUN
ejpam-115	286	11	operators	operator	NOUN
ejpam-115	286	12	and	and	CCONJ
ejpam-115	286	13	applications	application	NOUN
ejpam-115	286	14	,	,	PUNCT
ejpam-115	286	15	birkhauser	birkhaus	ADJ
ejpam-115	286	16	verlag	verlag	NOUN
ejpam-115	286	17	,	,	PUNCT
ejpam-115	286	18	1986	1986	NUM
ejpam-115	286	19	.	.	PUNCT