id	sid	tid	token	lemma	pos
ejpam-3328	1	1	reduction	reduction	NOUN
ejpam-3328	1	2	of	of	ADP
ejpam-3328	1	3	modern	modern	ADJ
ejpam-3328	1	4	mathematical	mathematical	ADJ
ejpam-3328	1	5	problems	problem	NOUN
ejpam-3328	1	6	to	to	ADP
ejpam-3328	1	7	the	the	DET
ejpam-3328	1	8	classical	classical	ADJ
ejpam-3328	1	9	riemann	riemann	PROPN
ejpam-3328	1	10	--	--	PUNCT
ejpam-3328	1	11	poincarunhbox	poincarunhbox	PROPN
ejpam-3328	1	12	voidb@x	voidb@x	PROPN
ejpam-3328	1	13	�	�	PROPN
ejpam-3328	1	14	group	group	PROPN
ejpam-3328	1	15	let	let	VERB
ejpam-3328	1	16	unhbox	unhbox	PROPN
ejpam-3328	1	17	voidb@x	voidb@x	VERB
ejpam-3328	1	18	setbox	setbox	PROPN
ejpam-3328	1	19	@tempboxa	@tempboxa	PROPN
ejpam-3328	1	20	hbox	hbox	NOUN
ejpam-3328	1	21	{	{	PUNCT
ejpam-3328	1	22	eglobal	eglobal	ADJ
ejpam-3328	1	23	mathchardef	mathchardef	PROPN
ejpam-3328	1	24	accent@spacefactor	accent@spacefactor	NOUN
ejpam-3328	2	1	spacefactor	spacefactor	NOUN
ejpam-3328	2	2	}	}	PUNCT
ejpam-3328	2	3	accent	accent	VERB
ejpam-3328	2	4	19	19	NUM
ejpam-3328	2	5	eegroup	eegroup	NOUN
ejpam-3328	2	6	spacefactor	spacefactor	NOUN
ejpam-3328	2	7	accent@spacefactor	accent@spacefactor	PROPN
ejpam-3328	3	1	--hilbert	--hilbert	PROPN
ejpam-3328	3	2	problem	problem	PROPN
ejpam-3328	3	3	european	european	PROPN
ejpam-3328	3	4	journal	journal	PROPN
ejpam-3328	3	5	of	of	ADP
ejpam-3328	3	6	pure	pure	ADJ
ejpam-3328	3	7	and	and	CCONJ
ejpam-3328	3	8	applied	apply	VERB
ejpam-3328	3	9	mathematics	mathematic	NOUN
ejpam-3328	3	10	vol	vol	NOUN
ejpam-3328	3	11	.	.	PUNCT
ejpam-3328	4	1	11	11	NUM
ejpam-3328	4	2	,	,	PUNCT
ejpam-3328	4	3	no	no	INTJ
ejpam-3328	4	4	.	.	NOUN
ejpam-3328	4	5	4	4	NUM
ejpam-3328	4	6	,	,	PUNCT
ejpam-3328	4	7	2018	2018	NUM
ejpam-3328	4	8	,	,	PUNCT
ejpam-3328	4	9	1143	1143	NUM
ejpam-3328	4	10	-	-	SYM
ejpam-3328	4	11	1176	1176	NUM
ejpam-3328	4	12	issn	issn	PROPN
ejpam-3328	4	13	1307	1307	NUM
ejpam-3328	4	14	-	-	SYM
ejpam-3328	4	15	5543	5543	NUM
ejpam-3328	4	16	–	–	PUNCT
ejpam-3328	4	17	www.ejpam.com	www.ejpam.com	X
ejpam-3328	4	18	published	publish	VERB
ejpam-3328	4	19	by	by	ADP
ejpam-3328	4	20	new	new	PROPN
ejpam-3328	4	21	york	york	PROPN
ejpam-3328	4	22	business	business	PROPN
ejpam-3328	4	23	global	global	ADJ
ejpam-3328	4	24	reduction	reduction	NOUN
ejpam-3328	4	25	of	of	ADP
ejpam-3328	4	26	modern	modern	ADJ
ejpam-3328	4	27	mathematical	mathematical	ADJ
ejpam-3328	4	28	problems	problem	NOUN
ejpam-3328	4	29	to	to	ADP
ejpam-3328	4	30	the	the	DET
ejpam-3328	4	31	classical	classical	ADJ
ejpam-3328	4	32	riemann	riemann	PROPN
ejpam-3328	4	33	–	–	PUNCT
ejpam-3328	4	34	poincaré–hilbert	poincaré–hilbert	PROPN
ejpam-3328	4	35	problem	problem	NOUN
ejpam-3328	4	36	asset	asset	NOUN
ejpam-3328	4	37	durmagambetov	durmagambetov	PROPN
ejpam-3328	4	38	institute	institute	PROPN
ejpam-3328	4	39	of	of	ADP
ejpam-3328	4	40	information	information	NOUN
ejpam-3328	4	41	and	and	CCONJ
ejpam-3328	4	42	computational	computational	ADJ
ejpam-3328	4	43	technologies	technology	NOUN
ejpam-3328	4	44	,	,	PUNCT
ejpam-3328	4	45	international	international	ADJ
ejpam-3328	4	46	science	science	NOUN
ejpam-3328	4	47	complex	complex	ADJ
ejpam-3328	4	48	“	"	PUNCT
ejpam-3328	4	49	astana	astana	PROPN
ejpam-3328	4	50	”	"	PUNCT
ejpam-3328	4	51	,	,	PUNCT
ejpam-3328	5	1	kazakhstan	kazakhstan	PROPN
ejpam-3328	5	2	abstract	abstract	NOUN
ejpam-3328	5	3	.	.	PUNCT
ejpam-3328	6	1	using	use	VERB
ejpam-3328	6	2	the	the	DET
ejpam-3328	6	3	example	example	NOUN
ejpam-3328	6	4	of	of	ADP
ejpam-3328	6	5	a	a	DET
ejpam-3328	6	6	complicated	complicated	ADJ
ejpam-3328	6	7	problem	problem	NOUN
ejpam-3328	6	8	such	such	ADJ
ejpam-3328	6	9	as	as	ADP
ejpam-3328	6	10	the	the	DET
ejpam-3328	6	11	cauchy	cauchy	ADJ
ejpam-3328	6	12	problem	problem	NOUN
ejpam-3328	6	13	for	for	ADP
ejpam-3328	6	14	the	the	DET
ejpam-3328	6	15	navier	navier	NOUN
ejpam-3328	6	16	–	–	PUNCT
ejpam-3328	6	17	stokes	stoke	NOUN
ejpam-3328	6	18	equation	equation	NOUN
ejpam-3328	6	19	,	,	PUNCT
ejpam-3328	6	20	we	we	PRON
ejpam-3328	6	21	show	show	VERB
ejpam-3328	6	22	how	how	SCONJ
ejpam-3328	6	23	the	the	DET
ejpam-3328	6	24	poincaré–riemann	poincaré–riemann	NOUN
ejpam-3328	6	25	–	–	PUNCT
ejpam-3328	6	26	hilbert	hilbert	NOUN
ejpam-3328	6	27	boundary	boundary	ADJ
ejpam-3328	6	28	-	-	PUNCT
ejpam-3328	6	29	value	value	NOUN
ejpam-3328	6	30	problem	problem	NOUN
ejpam-3328	6	31	enables	enable	VERB
ejpam-3328	6	32	us	we	PRON
ejpam-3328	6	33	to	to	PART
ejpam-3328	6	34	construct	construct	VERB
ejpam-3328	6	35	effective	effective	ADJ
ejpam-3328	6	36	estimates	estimate	NOUN
ejpam-3328	6	37	of	of	ADP
ejpam-3328	6	38	solutions	solution	NOUN
ejpam-3328	6	39	for	for	ADP
ejpam-3328	6	40	this	this	DET
ejpam-3328	6	41	case	case	NOUN
ejpam-3328	6	42	.	.	PUNCT
ejpam-3328	7	1	the	the	DET
ejpam-3328	7	2	apparatus	apparatus	NOUN
ejpam-3328	7	3	of	of	ADP
ejpam-3328	7	4	the	the	DET
ejpam-3328	7	5	threedimensional	threedimensional	ADJ
ejpam-3328	7	6	inverse	inverse	NOUN
ejpam-3328	7	7	problem	problem	NOUN
ejpam-3328	7	8	of	of	ADP
ejpam-3328	7	9	quantum	quantum	NOUN
ejpam-3328	7	10	scattering	scattering	NOUN
ejpam-3328	7	11	theory	theory	NOUN
ejpam-3328	7	12	is	be	AUX
ejpam-3328	7	13	developed	develop	VERB
ejpam-3328	7	14	for	for	ADP
ejpam-3328	7	15	this	this	PRON
ejpam-3328	7	16	.	.	PUNCT
ejpam-3328	8	1	it	it	PRON
ejpam-3328	8	2	is	be	AUX
ejpam-3328	8	3	shown	show	VERB
ejpam-3328	8	4	that	that	SCONJ
ejpam-3328	8	5	the	the	DET
ejpam-3328	8	6	unitary	unitary	ADJ
ejpam-3328	8	7	scattering	scatter	VERB
ejpam-3328	8	8	operator	operator	NOUN
ejpam-3328	8	9	can	can	AUX
ejpam-3328	8	10	be	be	AUX
ejpam-3328	8	11	studied	study	VERB
ejpam-3328	8	12	as	as	ADP
ejpam-3328	8	13	a	a	DET
ejpam-3328	8	14	solution	solution	NOUN
ejpam-3328	8	15	of	of	ADP
ejpam-3328	8	16	the	the	DET
ejpam-3328	8	17	poincaré–riemann	poincaré–riemann	NOUN
ejpam-3328	8	18	–	–	PUNCT
ejpam-3328	8	19	hilbert	hilbert	NOUN
ejpam-3328	8	20	boundary	boundary	ADJ
ejpam-3328	8	21	-	-	PUNCT
ejpam-3328	8	22	value	value	NOUN
ejpam-3328	8	23	problem	problem	NOUN
ejpam-3328	8	24	.	.	PUNCT
ejpam-3328	9	1	this	this	PRON
ejpam-3328	9	2	allows	allow	VERB
ejpam-3328	9	3	us	we	PRON
ejpam-3328	9	4	to	to	PART
ejpam-3328	9	5	go	go	VERB
ejpam-3328	9	6	on	on	ADP
ejpam-3328	9	7	to	to	PART
ejpam-3328	9	8	study	study	VERB
ejpam-3328	9	9	the	the	DET
ejpam-3328	9	10	potential	potential	NOUN
ejpam-3328	9	11	in	in	ADP
ejpam-3328	9	12	the	the	DET
ejpam-3328	9	13	schrödinger	schrödinger	NOUN
ejpam-3328	9	14	equation	equation	NOUN
ejpam-3328	9	15	,	,	PUNCT
ejpam-3328	9	16	which	which	PRON
ejpam-3328	9	17	we	we	PRON
ejpam-3328	9	18	consider	consider	VERB
ejpam-3328	9	19	as	as	ADP
ejpam-3328	9	20	a	a	DET
ejpam-3328	9	21	velocity	velocity	NOUN
ejpam-3328	9	22	component	component	NOUN
ejpam-3328	9	23	in	in	ADP
ejpam-3328	9	24	the	the	DET
ejpam-3328	9	25	navier	navier	NOUN
ejpam-3328	9	26	–	–	PUNCT
ejpam-3328	9	27	stokes	stoke	NOUN
ejpam-3328	9	28	equation	equation	NOUN
ejpam-3328	9	29	.	.	PUNCT
ejpam-3328	10	1	the	the	DET
ejpam-3328	10	2	same	same	ADJ
ejpam-3328	10	3	scheme	scheme	NOUN
ejpam-3328	10	4	of	of	ADP
ejpam-3328	10	5	reduction	reduction	NOUN
ejpam-3328	10	6	of	of	ADP
ejpam-3328	10	7	riemann	riemann	PROPN
ejpam-3328	10	8	integral	integral	ADJ
ejpam-3328	10	9	equations	equation	NOUN
ejpam-3328	10	10	for	for	ADP
ejpam-3328	10	11	the	the	DET
ejpam-3328	10	12	zeta	zeta	PROPN
ejpam-3328	10	13	function	function	NOUN
ejpam-3328	10	14	to	to	ADP
ejpam-3328	10	15	the	the	DET
ejpam-3328	10	16	poincaré–riemann	poincaré–riemann	NOUN
ejpam-3328	10	17	–	–	PUNCT
ejpam-3328	10	18	hilbert	hilbert	NOUN
ejpam-3328	10	19	boundary	boundary	ADJ
ejpam-3328	10	20	-	-	PUNCT
ejpam-3328	10	21	value	value	NOUN
ejpam-3328	10	22	problem	problem	NOUN
ejpam-3328	10	23	allows	allow	VERB
ejpam-3328	10	24	us	we	PRON
ejpam-3328	10	25	to	to	PART
ejpam-3328	10	26	construct	construct	VERB
ejpam-3328	10	27	effective	effective	ADJ
ejpam-3328	10	28	estimates	estimate	NOUN
ejpam-3328	10	29	that	that	PRON
ejpam-3328	10	30	describe	describe	VERB
ejpam-3328	10	31	the	the	DET
ejpam-3328	10	32	behaviour	behaviour	NOUN
ejpam-3328	10	33	of	of	ADP
ejpam-3328	10	34	the	the	DET
ejpam-3328	10	35	zeros	zero	NOUN
ejpam-3328	10	36	of	of	ADP
ejpam-3328	10	37	the	the	DET
ejpam-3328	10	38	zeta	zeta	PROPN
ejpam-3328	10	39	function	function	NOUN
ejpam-3328	10	40	very	very	ADV
ejpam-3328	10	41	well	well	ADV
ejpam-3328	10	42	.	.	PUNCT
ejpam-3328	11	1	2010	2010	NUM
ejpam-3328	11	2	mathematics	mathematic	NOUN
ejpam-3328	11	3	subject	subject	NOUN
ejpam-3328	11	4	classifications	classification	NOUN
ejpam-3328	11	5	:	:	PUNCT
ejpam-3328	11	6	11	11	NUM
ejpam-3328	11	7	key	key	ADJ
ejpam-3328	11	8	words	word	NOUN
ejpam-3328	11	9	and	and	CCONJ
ejpam-3328	11	10	phrases	phrase	NOUN
ejpam-3328	11	11	:	:	PUNCT
ejpam-3328	11	12	schrödinger	schrödinger	NOUN
ejpam-3328	11	13	’s	’s	PART
ejpam-3328	11	14	equation	equation	NOUN
ejpam-3328	11	15	,	,	PUNCT
ejpam-3328	11	16	potential	potential	NOUN
ejpam-3328	11	17	;	;	PUNCT
ejpam-3328	11	18	scattering	scatter	VERB
ejpam-3328	11	19	amplitude	amplitude	NOUN
ejpam-3328	11	20	,	,	PUNCT
ejpam-3328	11	21	cauchy	cauchy	NOUN
ejpam-3328	11	22	problem	problem	NOUN
ejpam-3328	11	23	,	,	PUNCT
ejpam-3328	11	24	navier	navier	NOUN
ejpam-3328	11	25	–	–	PUNCT
ejpam-3328	11	26	stokes	stoke	NOUN
ejpam-3328	11	27	equations	equation	NOUN
ejpam-3328	11	28	,	,	PUNCT
ejpam-3328	11	29	millennium	millennium	PROPN
ejpam-3328	11	30	prize	prize	PROPN
ejpam-3328	11	31	problems	problem	NOUN
ejpam-3328	11	32	;	;	PUNCT
ejpam-3328	11	33	dirichlet	dirichlet	PROPN
ejpam-3328	11	34	,	,	PUNCT
ejpam-3328	11	35	riemann	riemann	PROPN
ejpam-3328	11	36	,	,	PUNCT
ejpam-3328	11	37	hilbert	hilbert	PROPN
ejpam-3328	11	38	;	;	PUNCT
ejpam-3328	11	39	poincaré	poincaré	ADJ
ejpam-3328	11	40	,	,	PUNCT
ejpam-3328	11	41	riemann	riemann	PROPN
ejpam-3328	11	42	hypothesis	hypothesis	NOUN
ejpam-3328	11	43	;	;	PUNCT
ejpam-3328	11	44	zeta	zeta	PROPN
ejpam-3328	11	45	function	function	PROPN
ejpam-3328	11	46	,	,	PUNCT
ejpam-3328	11	47	hadamard	hadamard	NOUN
ejpam-3328	11	48	1	1	NUM
ejpam-3328	11	49	.	.	PUNCT
ejpam-3328	12	1	introduction	introduction	NOUN
ejpam-3328	12	2	using	use	VERB
ejpam-3328	12	3	the	the	DET
ejpam-3328	12	4	example	example	NOUN
ejpam-3328	12	5	of	of	ADP
ejpam-3328	12	6	a	a	DET
ejpam-3328	12	7	complicated	complicated	ADJ
ejpam-3328	12	8	problem	problem	NOUN
ejpam-3328	12	9	such	such	ADJ
ejpam-3328	12	10	as	as	ADP
ejpam-3328	12	11	the	the	DET
ejpam-3328	12	12	cauchy	cauchy	ADJ
ejpam-3328	12	13	problem	problem	NOUN
ejpam-3328	12	14	for	for	ADP
ejpam-3328	12	15	the	the	DET
ejpam-3328	12	16	navier	navier	NOUN
ejpam-3328	12	17	–	–	PUNCT
ejpam-3328	12	18	stokes	stoke	NOUN
ejpam-3328	12	19	equation	equation	NOUN
ejpam-3328	12	20	,	,	PUNCT
ejpam-3328	12	21	we	we	PRON
ejpam-3328	12	22	show	show	VERB
ejpam-3328	12	23	how	how	SCONJ
ejpam-3328	12	24	the	the	DET
ejpam-3328	12	25	poincaré–riemann	poincaré–riemann	NOUN
ejpam-3328	12	26	–	–	PUNCT
ejpam-3328	12	27	hilbert	hilbert	NOUN
ejpam-3328	12	28	boundary	boundary	ADJ
ejpam-3328	12	29	-	-	PUNCT
ejpam-3328	12	30	value	value	NOUN
ejpam-3328	12	31	problem	problem	NOUN
ejpam-3328	12	32	enables	enable	VERB
ejpam-3328	12	33	us	we	PRON
ejpam-3328	12	34	to	to	PART
ejpam-3328	12	35	construct	construct	VERB
ejpam-3328	12	36	effective	effective	ADJ
ejpam-3328	12	37	estimates	estimate	NOUN
ejpam-3328	12	38	of	of	ADP
ejpam-3328	12	39	solutions	solution	NOUN
ejpam-3328	12	40	for	for	ADP
ejpam-3328	12	41	this	this	DET
ejpam-3328	12	42	case	case	NOUN
ejpam-3328	12	43	.	.	PUNCT
ejpam-3328	13	1	the	the	DET
ejpam-3328	13	2	apparatus	apparatus	NOUN
ejpam-3328	13	3	of	of	ADP
ejpam-3328	13	4	the	the	DET
ejpam-3328	13	5	three	three	NUM
ejpam-3328	13	6	-	-	PUNCT
ejpam-3328	13	7	dimensional	dimensional	ADJ
ejpam-3328	13	8	inverse	inverse	NOUN
ejpam-3328	13	9	problem	problem	NOUN
ejpam-3328	13	10	of	of	ADP
ejpam-3328	13	11	quantum	quantum	NOUN
ejpam-3328	13	12	scattering	scattering	NOUN
ejpam-3328	13	13	theory	theory	NOUN
ejpam-3328	13	14	is	be	AUX
ejpam-3328	13	15	developed	develop	VERB
ejpam-3328	13	16	for	for	ADP
ejpam-3328	13	17	this	this	PRON
ejpam-3328	13	18	.	.	PUNCT
ejpam-3328	14	1	it	it	PRON
ejpam-3328	14	2	is	be	AUX
ejpam-3328	14	3	shown	show	VERB
ejpam-3328	14	4	that	that	SCONJ
ejpam-3328	14	5	the	the	DET
ejpam-3328	14	6	unitary	unitary	ADJ
ejpam-3328	14	7	scattering	scatter	VERB
ejpam-3328	14	8	operator	operator	NOUN
ejpam-3328	14	9	can	can	AUX
ejpam-3328	14	10	be	be	AUX
ejpam-3328	14	11	studied	study	VERB
ejpam-3328	14	12	as	as	ADP
ejpam-3328	14	13	a	a	DET
ejpam-3328	14	14	solution	solution	NOUN
ejpam-3328	14	15	of	of	ADP
ejpam-3328	14	16	the	the	DET
ejpam-3328	14	17	poincaré–riemann	poincaré–riemann	NOUN
ejpam-3328	14	18	–	–	PUNCT
ejpam-3328	14	19	hilbert	hilbert	NOUN
ejpam-3328	14	20	boundary	boundary	ADJ
ejpam-3328	14	21	-	-	PUNCT
ejpam-3328	14	22	value	value	NOUN
ejpam-3328	14	23	problem	problem	NOUN
ejpam-3328	14	24	.	.	PUNCT
ejpam-3328	15	1	this	this	PRON
ejpam-3328	15	2	allows	allow	VERB
ejpam-3328	15	3	us	we	PRON
ejpam-3328	15	4	to	to	PART
ejpam-3328	15	5	go	go	VERB
ejpam-3328	15	6	on	on	ADP
ejpam-3328	15	7	to	to	PART
ejpam-3328	15	8	study	study	VERB
ejpam-3328	15	9	the	the	DET
ejpam-3328	15	10	potential	potential	NOUN
ejpam-3328	15	11	in	in	ADP
ejpam-3328	15	12	the	the	DET
ejpam-3328	15	13	schrödinger	schrödinger	NOUN
ejpam-3328	15	14	equation	equation	NOUN
ejpam-3328	15	15	,	,	PUNCT
ejpam-3328	15	16	which	which	PRON
ejpam-3328	15	17	we	we	PRON
ejpam-3328	15	18	consider	consider	VERB
ejpam-3328	15	19	as	as	ADP
ejpam-3328	15	20	a	a	DET
ejpam-3328	15	21	velocity	velocity	NOUN
ejpam-3328	15	22	component	component	NOUN
ejpam-3328	15	23	in	in	ADP
ejpam-3328	15	24	the	the	DET
ejpam-3328	15	25	navier	navier	NOUN
ejpam-3328	15	26	–	–	PUNCT
ejpam-3328	15	27	stokes	stoke	NOUN
ejpam-3328	15	28	equation	equation	NOUN
ejpam-3328	15	29	.	.	PUNCT
ejpam-3328	16	1	the	the	DET
ejpam-3328	16	2	same	same	ADJ
ejpam-3328	16	3	scheme	scheme	NOUN
ejpam-3328	16	4	of	of	ADP
ejpam-3328	16	5	reduction	reduction	NOUN
ejpam-3328	16	6	of	of	ADP
ejpam-3328	16	7	riemann	riemann	PROPN
ejpam-3328	16	8	integral	integral	ADJ
ejpam-3328	16	9	equations	equation	NOUN
ejpam-3328	16	10	for	for	ADP
ejpam-3328	16	11	the	the	DET
ejpam-3328	16	12	zeta	zeta	PROPN
ejpam-3328	16	13	function	function	NOUN
ejpam-3328	16	14	to	to	ADP
ejpam-3328	16	15	the	the	DET
ejpam-3328	16	16	poincaré–riemann	poincaré–riemann	NOUN
ejpam-3328	16	17	–	–	PUNCT
ejpam-3328	16	18	hilbert	hilbert	NOUN
ejpam-3328	16	19	boundary	boundary	ADJ
ejpam-3328	16	20	-	-	PUNCT
ejpam-3328	16	21	value	value	NOUN
ejpam-3328	16	22	problem	problem	NOUN
ejpam-3328	16	23	allows	allow	VERB
ejpam-3328	16	24	us	we	PRON
ejpam-3328	16	25	to	to	PART
ejpam-3328	16	26	construct	construct	VERB
ejpam-3328	16	27	effective	effective	ADJ
ejpam-3328	16	28	estimates	estimate	NOUN
ejpam-3328	16	29	that	that	PRON
ejpam-3328	16	30	describe	describe	VERB
ejpam-3328	16	31	the	the	DET
ejpam-3328	16	32	behaviour	behaviour	NOUN
ejpam-3328	16	33	of	of	ADP
ejpam-3328	16	34	the	the	DET
ejpam-3328	16	35	zeros	zero	NOUN
ejpam-3328	16	36	of	of	ADP
ejpam-3328	16	37	the	the	DET
ejpam-3328	16	38	zeta	zeta	PROPN
ejpam-3328	16	39	function	function	NOUN
ejpam-3328	16	40	very	very	ADV
ejpam-3328	16	41	well	well	ADV
ejpam-3328	16	42	.	.	PUNCT
ejpam-3328	17	1	doi	doi	NOUN
ejpam-3328	17	2	:	:	PUNCT
ejpam-3328	17	3	https://doi.org/10.29020/nybg.ejpam.v11i4.3328	https://doi.org/10.29020/nybg.ejpam.v11i4.3328	PROPN
ejpam-3328	17	4	email	email	NOUN
ejpam-3328	17	5	addresses	address	NOUN
ejpam-3328	17	6	:	:	PUNCT
ejpam-3328	17	7	aset.durmagambet@gmail.com	aset.durmagambet@gmail.com	X
ejpam-3328	17	8	(	(	PUNCT
ejpam-3328	17	9	a.	a.	NOUN
ejpam-3328	17	10	durmagambetov	durmagambetov	PROPN
ejpam-3328	17	11	)	)	PUNCT
ejpam-3328	17	12	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3328	17	13	1143	1143	NUM
ejpam-3328	17	14	c	c	NOUN
ejpam-3328	17	15	©	©	PROPN
ejpam-3328	17	16	2018	2018	NUM
ejpam-3328	17	17	ejpam	ejpam	VERB
ejpam-3328	17	18	all	all	DET
ejpam-3328	17	19	rights	right	NOUN
ejpam-3328	17	20	reserved	reserve	VERB
ejpam-3328	17	21	.	.	PUNCT
ejpam-3328	18	1	a.	a.	NOUN
ejpam-3328	18	2	durmagambetov	durmagambetov	PROPN
ejpam-3328	18	3	/	/	SYM
ejpam-3328	18	4	eur	eur	PROPN
ejpam-3328	18	5	.	.	PUNCT
ejpam-3328	19	1	j.	j.	PROPN
ejpam-3328	19	2	pure	pure	PROPN
ejpam-3328	19	3	appl	appl	PROPN
ejpam-3328	19	4	.	.	PROPN
ejpam-3328	19	5	math	math	PROPN
ejpam-3328	19	6	,	,	PUNCT
ejpam-3328	19	7	11	11	NUM
ejpam-3328	19	8	(	(	PUNCT
ejpam-3328	19	9	4	4	NUM
ejpam-3328	19	10	)	)	PUNCT
ejpam-3328	19	11	(	(	PUNCT
ejpam-3328	19	12	2018	2018	NUM
ejpam-3328	19	13	)	)	PUNCT
ejpam-3328	19	14	,	,	PUNCT
ejpam-3328	19	15	1143	1143	NUM
ejpam-3328	19	16	-	-	SYM
ejpam-3328	19	17	1176	1176	NUM
ejpam-3328	19	18	1144	1144	NUM
ejpam-3328	19	19	2	2	NUM
ejpam-3328	19	20	.	.	PUNCT
ejpam-3328	19	21	results	result	NOUN
ejpam-3328	19	22	for	for	ADP
ejpam-3328	19	23	the	the	DET
ejpam-3328	19	24	one	one	NUM
ejpam-3328	19	25	-	-	PUNCT
ejpam-3328	19	26	dimensional	dimensional	ADJ
ejpam-3328	19	27	case	case	NOUN
ejpam-3328	19	28	let	let	VERB
ejpam-3328	19	29	us	we	PRON
ejpam-3328	19	30	consider	consider	VERB
ejpam-3328	19	31	a	a	DET
ejpam-3328	19	32	one	one	NUM
ejpam-3328	19	33	-	-	PUNCT
ejpam-3328	19	34	dimensional	dimensional	ADJ
ejpam-3328	19	35	function	function	NOUN
ejpam-3328	19	36	f	f	NOUN
ejpam-3328	19	37	and	and	CCONJ
ejpam-3328	19	38	its	its	PRON
ejpam-3328	19	39	fourier	fourier	NOUN
ejpam-3328	19	40	transformation	transformation	NOUN
ejpam-3328	19	41	f̃	f̃	PROPN
ejpam-3328	19	42	.	.	PUNCT
ejpam-3328	20	1	using	use	VERB
ejpam-3328	20	2	the	the	DET
ejpam-3328	20	3	notions	notion	NOUN
ejpam-3328	20	4	of	of	ADP
ejpam-3328	20	5	module	module	NOUN
ejpam-3328	20	6	and	and	CCONJ
ejpam-3328	20	7	phase	phase	NOUN
ejpam-3328	20	8	,	,	PUNCT
ejpam-3328	20	9	we	we	PRON
ejpam-3328	20	10	write	write	VERB
ejpam-3328	20	11	the	the	DET
ejpam-3328	20	12	fourier	fourier	ADJ
ejpam-3328	20	13	transformation	transformation	NOUN
ejpam-3328	20	14	in	in	ADP
ejpam-3328	20	15	the	the	DET
ejpam-3328	20	16	following	follow	VERB
ejpam-3328	20	17	form	form	NOUN
ejpam-3328	20	18	:	:	PUNCT
ejpam-3328	20	19	f̃	f̃	PROPN
ejpam-3328	20	20	=	=	PUNCT
ejpam-3328	20	21	|f̃	|f̃	NOUN
ejpam-3328	20	22	|	|	ADV
ejpam-3328	20	23	exp(iψ	exp(iψ	NOUN
ejpam-3328	20	24	)	)	PUNCT
ejpam-3328	20	25	,	,	PUNCT
ejpam-3328	20	26	where	where	SCONJ
ejpam-3328	20	27	ψ	ψ	NOUN
ejpam-3328	20	28	is	be	AUX
ejpam-3328	20	29	the	the	DET
ejpam-3328	20	30	phase	phase	NOUN
ejpam-3328	20	31	.	.	PUNCT
ejpam-3328	21	1	the	the	DET
ejpam-3328	21	2	plancherel	plancherel	NOUN
ejpam-3328	21	3	equality	equality	NOUN
ejpam-3328	21	4	states	state	VERB
ejpam-3328	21	5	that	that	PRON
ejpam-3328	21	6	||f	||f	VERB
ejpam-3328	21	7	||l2	||l2	NOUN
ejpam-3328	21	8	=	=	PUNCT
ejpam-3328	21	9	const||f̃	const||f̃	VERB
ejpam-3328	21	10	||l2	||l2	NOUN
ejpam-3328	21	11	.	.	PUNCT
ejpam-3328	22	1	here	here	ADV
ejpam-3328	22	2	we	we	PRON
ejpam-3328	22	3	can	can	AUX
ejpam-3328	22	4	see	see	VERB
ejpam-3328	22	5	that	that	SCONJ
ejpam-3328	22	6	the	the	DET
ejpam-3328	22	7	phase	phase	NOUN
ejpam-3328	22	8	does	do	AUX
ejpam-3328	22	9	not	not	PART
ejpam-3328	22	10	contribute	contribute	VERB
ejpam-3328	22	11	to	to	ADP
ejpam-3328	22	12	determination	determination	NOUN
ejpam-3328	22	13	of	of	ADP
ejpam-3328	22	14	the	the	DET
ejpam-3328	22	15	x	x	NOUN
ejpam-3328	22	16	norm	norm	NOUN
ejpam-3328	22	17	.	.	PUNCT
ejpam-3328	23	1	to	to	PART
ejpam-3328	23	2	estimate	estimate	VERB
ejpam-3328	23	3	the	the	DET
ejpam-3328	23	4	maximum	maximum	NOUN
ejpam-3328	23	5	we	we	PRON
ejpam-3328	23	6	make	make	VERB
ejpam-3328	23	7	a	a	DET
ejpam-3328	23	8	simple	simple	ADJ
ejpam-3328	23	9	estimate	estimate	NOUN
ejpam-3328	23	10	as	as	ADP
ejpam-3328	23	11	max|f	max|f	NOUN
ejpam-3328	23	12	|2	|2	NUM
ejpam-3328	23	13	≤	≤	NOUN
ejpam-3328	23	14	2||f	2||f	NUM
ejpam-3328	23	15	||l2	||l2	NOUN
ejpam-3328	23	16	||∇f	||∇f	PROPN
ejpam-3328	23	17	||l2	||l2	PROPN
ejpam-3328	23	18	.	.	PUNCT
ejpam-3328	24	1	now	now	ADV
ejpam-3328	24	2	we	we	PRON
ejpam-3328	24	3	have	have	VERB
ejpam-3328	24	4	an	an	DET
ejpam-3328	24	5	estimate	estimate	NOUN
ejpam-3328	24	6	of	of	ADP
ejpam-3328	24	7	the	the	DET
ejpam-3328	24	8	function	function	NOUN
ejpam-3328	24	9	maximum	maximum	NOUN
ejpam-3328	24	10	in	in	ADP
ejpam-3328	24	11	which	which	PRON
ejpam-3328	24	12	the	the	DET
ejpam-3328	24	13	phase	phase	NOUN
ejpam-3328	24	14	is	be	AUX
ejpam-3328	24	15	not	not	PART
ejpam-3328	24	16	involved	involve	VERB
ejpam-3328	24	17	.	.	PUNCT
ejpam-3328	25	1	let	let	VERB
ejpam-3328	25	2	us	we	PRON
ejpam-3328	25	3	consider	consider	VERB
ejpam-3328	25	4	the	the	DET
ejpam-3328	25	5	behaviour	behaviour	NOUN
ejpam-3328	25	6	of	of	ADP
ejpam-3328	25	7	a	a	DET
ejpam-3328	25	8	progressing	progress	VERB
ejpam-3328	25	9	wave	wave	NOUN
ejpam-3328	25	10	travelling	travel	VERB
ejpam-3328	25	11	with	with	ADP
ejpam-3328	25	12	a	a	DET
ejpam-3328	25	13	constant	constant	ADJ
ejpam-3328	25	14	velocity	velocity	NOUN
ejpam-3328	25	15	of	of	ADP
ejpam-3328	25	16	v	v	NOUN
ejpam-3328	25	17	=	=	SYM
ejpam-3328	25	18	a	a	PRON
ejpam-3328	25	19	described	describe	VERB
ejpam-3328	25	20	by	by	ADP
ejpam-3328	25	21	the	the	DET
ejpam-3328	25	22	function	function	NOUN
ejpam-3328	25	23	f	f	PROPN
ejpam-3328	25	24	(	(	PUNCT
ejpam-3328	25	25	x	x	PROPN
ejpam-3328	25	26	,	,	PUNCT
ejpam-3328	25	27	t	t	PROPN
ejpam-3328	25	28	)	)	PUNCT
ejpam-3328	25	29	=	=	PUNCT
ejpam-3328	25	30	f(x+	f(x+	NOUN
ejpam-3328	25	31	at	at	ADP
ejpam-3328	25	32	)	)	PUNCT
ejpam-3328	25	33	.	.	PUNCT
ejpam-3328	26	1	its	its	PRON
ejpam-3328	26	2	fourier	fourier	ADJ
ejpam-3328	26	3	transformation	transformation	NOUN
ejpam-3328	26	4	with	with	ADP
ejpam-3328	26	5	respect	respect	NOUN
ejpam-3328	26	6	to	to	ADP
ejpam-3328	26	7	the	the	DET
ejpam-3328	26	8	variable	variable	NOUN
ejpam-3328	26	9	x	x	PUNCT
ejpam-3328	26	10	is	be	AUX
ejpam-3328	26	11	f̃	f̃	PROPN
ejpam-3328	26	12	=	=	PUNCT
ejpam-3328	26	13	f̃exp(iatk	f̃exp(iatk	PROPN
ejpam-3328	26	14	)	)	PUNCT
ejpam-3328	26	15	.	.	PUNCT
ejpam-3328	27	1	again	again	ADV
ejpam-3328	27	2	,	,	PUNCT
ejpam-3328	27	3	in	in	ADP
ejpam-3328	27	4	this	this	DET
ejpam-3328	27	5	case	case	NOUN
ejpam-3328	27	6	,	,	PUNCT
ejpam-3328	27	7	we	we	PRON
ejpam-3328	27	8	can	can	AUX
ejpam-3328	27	9	see	see	VERB
ejpam-3328	27	10	that	that	SCONJ
ejpam-3328	27	11	when	when	SCONJ
ejpam-3328	27	12	we	we	PRON
ejpam-3328	27	13	study	study	VERB
ejpam-3328	27	14	a	a	DET
ejpam-3328	27	15	module	module	NOUN
ejpam-3328	27	16	of	of	ADP
ejpam-3328	27	17	the	the	DET
ejpam-3328	27	18	fourier	fourier	NOUN
ejpam-3328	27	19	transformation	transformation	NOUN
ejpam-3328	27	20	,	,	PUNCT
ejpam-3328	27	21	we	we	PRON
ejpam-3328	27	22	will	will	AUX
ejpam-3328	27	23	not	not	PART
ejpam-3328	27	24	obtain	obtain	VERB
ejpam-3328	27	25	major	major	ADJ
ejpam-3328	27	26	physical	physical	ADJ
ejpam-3328	27	27	information	information	NOUN
ejpam-3328	27	28	about	about	ADP
ejpam-3328	27	29	the	the	DET
ejpam-3328	27	30	wave	wave	NOUN
ejpam-3328	27	31	,	,	PUNCT
ejpam-3328	27	32	such	such	ADJ
ejpam-3328	27	33	as	as	ADP
ejpam-3328	27	34	its	its	PRON
ejpam-3328	27	35	velocity	velocity	NOUN
ejpam-3328	27	36	and	and	CCONJ
ejpam-3328	27	37	location	location	NOUN
ejpam-3328	27	38	of	of	ADP
ejpam-3328	27	39	the	the	DET
ejpam-3328	27	40	wave	wave	NOUN
ejpam-3328	27	41	crest	crest	NOUN
ejpam-3328	27	42	because	because	SCONJ
ejpam-3328	27	43	|f̃	|f̃	PROPN
ejpam-3328	27	44	|	|	ADV
ejpam-3328	27	45	=	=	PUNCT
ejpam-3328	27	46	|f̃	|f̃	PROPN
ejpam-3328	27	47	|	|	ADV
ejpam-3328	27	48	.	.	PUNCT
ejpam-3328	28	1	these	these	DET
ejpam-3328	28	2	two	two	NUM
ejpam-3328	28	3	examples	example	NOUN
ejpam-3328	28	4	show	show	VERB
ejpam-3328	28	5	the	the	DET
ejpam-3328	28	6	weaknesses	weakness	NOUN
ejpam-3328	28	7	of	of	ADP
ejpam-3328	28	8	studying	study	VERB
ejpam-3328	28	9	the	the	DET
ejpam-3328	28	10	fourier	fourier	NOUN
ejpam-3328	28	11	transformation	transformation	NOUN
ejpam-3328	28	12	.	.	PUNCT
ejpam-3328	29	1	many	many	ADJ
ejpam-3328	29	2	researchers	researcher	NOUN
ejpam-3328	29	3	focus	focus	VERB
ejpam-3328	29	4	on	on	ADP
ejpam-3328	29	5	the	the	DET
ejpam-3328	29	6	study	study	NOUN
ejpam-3328	29	7	of	of	ADP
ejpam-3328	29	8	functions	function	NOUN
ejpam-3328	29	9	using	use	VERB
ejpam-3328	29	10	the	the	DET
ejpam-3328	29	11	embedding	embed	VERB
ejpam-3328	29	12	theorem	theorem	VERB
ejpam-3328	29	13	,	,	PUNCT
ejpam-3328	29	14	in	in	ADP
ejpam-3328	29	15	which	which	PRON
ejpam-3328	29	16	the	the	DET
ejpam-3328	29	17	main	main	ADJ
ejpam-3328	29	18	object	object	NOUN
ejpam-3328	29	19	of	of	ADP
ejpam-3328	29	20	the	the	DET
ejpam-3328	29	21	study	study	NOUN
ejpam-3328	29	22	is	be	AUX
ejpam-3328	29	23	the	the	DET
ejpam-3328	29	24	module	module	NOUN
ejpam-3328	29	25	of	of	ADP
ejpam-3328	29	26	the	the	DET
ejpam-3328	29	27	function	function	NOUN
ejpam-3328	29	28	.	.	PUNCT
ejpam-3328	30	1	however	however	ADV
ejpam-3328	30	2	,	,	PUNCT
ejpam-3328	30	3	as	as	SCONJ
ejpam-3328	30	4	we	we	PRON
ejpam-3328	30	5	have	have	AUX
ejpam-3328	30	6	seen	see	VERB
ejpam-3328	30	7	in	in	ADP
ejpam-3328	30	8	the	the	DET
ejpam-3328	30	9	given	give	VERB
ejpam-3328	30	10	examples	example	NOUN
ejpam-3328	30	11	,	,	PUNCT
ejpam-3328	30	12	the	the	DET
ejpam-3328	30	13	phase	phase	NOUN
ejpam-3328	30	14	is	be	AUX
ejpam-3328	30	15	a	a	DET
ejpam-3328	30	16	principal	principal	ADJ
ejpam-3328	30	17	physical	physical	ADJ
ejpam-3328	30	18	characteristic	characteristic	NOUN
ejpam-3328	30	19	of	of	ADP
ejpam-3328	30	20	any	any	DET
ejpam-3328	30	21	process	process	NOUN
ejpam-3328	30	22	,	,	PUNCT
ejpam-3328	30	23	and	and	CCONJ
ejpam-3328	30	24	as	as	SCONJ
ejpam-3328	30	25	we	we	PRON
ejpam-3328	30	26	can	can	AUX
ejpam-3328	30	27	see	see	VERB
ejpam-3328	30	28	in	in	ADP
ejpam-3328	30	29	mathematical	mathematical	ADJ
ejpam-3328	30	30	studies	study	NOUN
ejpam-3328	30	31	that	that	PRON
ejpam-3328	30	32	use	use	VERB
ejpam-3328	30	33	the	the	DET
ejpam-3328	30	34	embedding	embed	VERB
ejpam-3328	30	35	theorem	theorem	NOUN
ejpam-3328	30	36	with	with	ADP
ejpam-3328	30	37	energy	energy	NOUN
ejpam-3328	30	38	estimates	estimate	NOUN
ejpam-3328	30	39	,	,	PUNCT
ejpam-3328	30	40	the	the	DET
ejpam-3328	30	41	phase	phase	NOUN
ejpam-3328	30	42	disappears	disappear	VERB
ejpam-3328	30	43	.	.	PUNCT
ejpam-3328	31	1	along	along	ADP
ejpam-3328	31	2	with	with	ADP
ejpam-3328	31	3	the	the	DET
ejpam-3328	31	4	phase	phase	NOUN
ejpam-3328	31	5	,	,	PUNCT
ejpam-3328	31	6	all	all	DET
ejpam-3328	31	7	reasonable	reasonable	ADJ
ejpam-3328	31	8	information	information	NOUN
ejpam-3328	31	9	about	about	ADP
ejpam-3328	31	10	the	the	DET
ejpam-3328	31	11	physical	physical	ADJ
ejpam-3328	31	12	process	process	NOUN
ejpam-3328	31	13	disappears	disappear	VERB
ejpam-3328	31	14	,	,	PUNCT
ejpam-3328	31	15	as	as	SCONJ
ejpam-3328	31	16	demonstrated	demonstrate	VERB
ejpam-3328	31	17	by	by	ADP
ejpam-3328	31	18	tao	tao	PROPN
ejpam-3328	32	1	[	[	X
ejpam-3328	32	2	1	1	NUM
ejpam-3328	32	3	]	]	PUNCT
ejpam-3328	32	4	and	and	CCONJ
ejpam-3328	32	5	other	other	ADJ
ejpam-3328	32	6	research	research	NOUN
ejpam-3328	32	7	studies	study	NOUN
ejpam-3328	32	8	.	.	PUNCT
ejpam-3328	33	1	in	in	ADP
ejpam-3328	33	2	fact	fact	NOUN
ejpam-3328	33	3	,	,	PUNCT
ejpam-3328	33	4	tao	tao	PROPN
ejpam-3328	33	5	built	build	VERB
ejpam-3328	33	6	progressing	progress	VERB
ejpam-3328	33	7	waves	wave	NOUN
ejpam-3328	33	8	that	that	PRON
ejpam-3328	33	9	are	be	AUX
ejpam-3328	33	10	not	not	PART
ejpam-3328	33	11	followed	follow	VERB
ejpam-3328	33	12	by	by	ADP
ejpam-3328	33	13	energy	energy	NOUN
ejpam-3328	33	14	estimates	estimate	NOUN
ejpam-3328	33	15	.	.	PUNCT
ejpam-3328	34	1	let	let	VERB
ejpam-3328	34	2	us	we	PRON
ejpam-3328	34	3	proceed	proceed	VERB
ejpam-3328	34	4	with	with	ADP
ejpam-3328	34	5	a	a	DET
ejpam-3328	34	6	more	more	ADV
ejpam-3328	34	7	essential	essential	ADJ
ejpam-3328	34	8	analysis	analysis	NOUN
ejpam-3328	34	9	of	of	ADP
ejpam-3328	34	10	the	the	DET
ejpam-3328	34	11	influence	influence	NOUN
ejpam-3328	34	12	of	of	ADP
ejpam-3328	34	13	the	the	DET
ejpam-3328	34	14	phase	phase	NOUN
ejpam-3328	34	15	on	on	ADP
ejpam-3328	34	16	the	the	DET
ejpam-3328	34	17	behaviour	behaviour	NOUN
ejpam-3328	34	18	of	of	ADP
ejpam-3328	34	19	functions	function	NOUN
ejpam-3328	34	20	.	.	PUNCT
ejpam-3328	35	1	theorem	theorem	NOUN
ejpam-3328	35	2	1	1	NUM
ejpam-3328	35	3	.	.	X
ejpam-3328	36	1	there	there	PRON
ejpam-3328	36	2	are	be	VERB
ejpam-3328	36	3	functions	function	NOUN
ejpam-3328	36	4	of	of	ADP
ejpam-3328	36	5	w	w	NOUN
ejpam-3328	36	6	1	1	NUM
ejpam-3328	36	7	2	2	NUM
ejpam-3328	36	8	(	(	PUNCT
ejpam-3328	36	9	r	r	NOUN
ejpam-3328	36	10	)	)	PUNCT
ejpam-3328	36	11	with	with	ADP
ejpam-3328	36	12	a	a	DET
ejpam-3328	36	13	constant	constant	ADJ
ejpam-3328	36	14	rate	rate	NOUN
ejpam-3328	36	15	of	of	ADP
ejpam-3328	36	16	the	the	DET
ejpam-3328	36	17	norm	norm	NOUN
ejpam-3328	36	18	for	for	ADP
ejpam-3328	36	19	a	a	DET
ejpam-3328	36	20	gradient	gradient	ADJ
ejpam-3328	36	21	catastrophe	catastrophe	NOUN
ejpam-3328	36	22	for	for	ADP
ejpam-3328	36	23	which	which	PRON
ejpam-3328	36	24	a	a	DET
ejpam-3328	36	25	phase	phase	NOUN
ejpam-3328	36	26	change	change	NOUN
ejpam-3328	36	27	of	of	ADP
ejpam-3328	36	28	its	its	PRON
ejpam-3328	36	29	fourier	fourier	NOUN
ejpam-3328	36	30	transformation	transformation	NOUN
ejpam-3328	36	31	is	be	AUX
ejpam-3328	36	32	sufficient	sufficient	ADJ
ejpam-3328	36	33	.	.	PUNCT
ejpam-3328	37	1	proof	proof	NOUN
ejpam-3328	37	2	:	:	PUNCT
ejpam-3328	37	3	to	to	PART
ejpam-3328	37	4	prove	prove	VERB
ejpam-3328	37	5	this	this	PRON
ejpam-3328	37	6	,	,	PUNCT
ejpam-3328	37	7	we	we	PRON
ejpam-3328	37	8	consider	consider	VERB
ejpam-3328	37	9	a	a	DET
ejpam-3328	37	10	sequence	sequence	NOUN
ejpam-3328	37	11	of	of	ADP
ejpam-3328	37	12	testing	testing	NOUN
ejpam-3328	37	13	functions	function	NOUN
ejpam-3328	37	14	f̃n	f̃n	X
ejpam-3328	38	1	=	=	SYM
ejpam-3328	38	2	∆/(1+k2	∆/(1+k2	NOUN
ejpam-3328	38	3	)	)	PUNCT
ejpam-3328	38	4	,	,	PUNCT
ejpam-3328	38	5	∆	∆	PROPN
ejpam-3328	38	6	=	=	SYM
ejpam-3328	39	1	(	(	PUNCT
ejpam-3328	39	2	i−	i−	PROPN
ejpam-3328	39	3	k)n/(i+	k)n/(i+	PROPN
ejpam-3328	39	4	k)n	k)n	PROPN
ejpam-3328	39	5	.	.	PUNCT
ejpam-3328	40	1	it	it	PRON
ejpam-3328	40	2	is	be	AUX
ejpam-3328	40	3	obvious	obvious	ADJ
ejpam-3328	40	4	that	that	SCONJ
ejpam-3328	40	5	|f̃n|	|f̃n|	NOUN
ejpam-3328	40	6	=	=	SYM
ejpam-3328	40	7	1/(1	1/(1	PROPN
ejpam-3328	40	8	+	+	SYM
ejpam-3328	40	9	k2	k2	ADJ
ejpam-3328	40	10	)	)	PUNCT
ejpam-3328	40	11	and	and	CCONJ
ejpam-3328	40	12	max|fn|2	max|fn|2	ADJ
ejpam-3328	40	13	≤	≤	NOUN
ejpam-3328	40	14	2||fn||l2	2||fn||l2	NUM
ejpam-3328	40	15	||∇fn||l2	||∇fn||l2	PROPN
ejpam-3328	40	16	≤	≤	NUM
ejpam-3328	40	17	const	const	NOUN
ejpam-3328	40	18	.	.	PUNCT
ejpam-3328	41	1	calculating	calculate	VERB
ejpam-3328	41	2	the	the	DET
ejpam-3328	41	3	fourier	fourier	ADJ
ejpam-3328	41	4	transformation	transformation	NOUN
ejpam-3328	41	5	of	of	ADP
ejpam-3328	41	6	these	these	DET
ejpam-3328	41	7	testing	testing	NOUN
ejpam-3328	41	8	functions	function	NOUN
ejpam-3328	41	9	,	,	PUNCT
ejpam-3328	41	10	we	we	PRON
ejpam-3328	41	11	obtain	obtain	VERB
ejpam-3328	41	12	fn(x	fn(x	PUNCT
ejpam-3328	41	13	)	)	PUNCT
ejpam-3328	42	1	=	=	SYM
ejpam-3328	42	2	x(−1)(n−1)2π	x(−1)(n−1)2π	PROPN
ejpam-3328	42	3	exp(−x)l1	exp(−x)l1	PROPN
ejpam-3328	42	4	(	(	PUNCT
ejpam-3328	42	5	n−1)(2x)if	n−1)(2x)if	NOUN
ejpam-3328	42	6	x	x	SYM
ejpam-3328	42	7	>	>	X
ejpam-3328	42	8	0	0	NUM
ejpam-3328	42	9	,	,	PUNCT
ejpam-3328	42	10	fn(x	fn(x	X
ejpam-3328	42	11	)	)	PUNCT
ejpam-3328	42	12	=	=	SYM
ejpam-3328	42	13	0	0	PUNCT
ejpam-3328	43	1	if	if	SCONJ
ejpam-3328	43	2	x	x	PROPN
ejpam-3328	43	3	≤	≤	NOUN
ejpam-3328	43	4	0	0	NUM
ejpam-3328	43	5	,	,	PUNCT
ejpam-3328	43	6	(	(	PUNCT
ejpam-3328	43	7	1	1	X
ejpam-3328	43	8	)	)	PUNCT
ejpam-3328	43	9	where	where	SCONJ
ejpam-3328	43	10	l1	l1	PROPN
ejpam-3328	43	11	(	(	PUNCT
ejpam-3328	43	12	n−1)(2x	n−1)(2x	PROPN
ejpam-3328	43	13	)	)	PUNCT
ejpam-3328	43	14	is	be	AUX
ejpam-3328	43	15	a	a	DET
ejpam-3328	43	16	laguerre	laguerre	NOUN
ejpam-3328	43	17	polynomial	polynomial	ADJ
ejpam-3328	43	18	.	.	PUNCT
ejpam-3328	44	1	now	now	ADV
ejpam-3328	44	2	we	we	PRON
ejpam-3328	44	3	see	see	VERB
ejpam-3328	44	4	that	that	SCONJ
ejpam-3328	44	5	the	the	DET
ejpam-3328	44	6	functions	function	NOUN
ejpam-3328	44	7	are	be	AUX
ejpam-3328	44	8	equibounded	equibounde	VERB
ejpam-3328	44	9	and	and	CCONJ
ejpam-3328	44	10	derivatives	derivative	NOUN
ejpam-3328	44	11	of	of	ADP
ejpam-3328	44	12	these	these	DET
ejpam-3328	44	13	functions	function	NOUN
ejpam-3328	44	14	will	will	AUX
ejpam-3328	44	15	grow	grow	VERB
ejpam-3328	44	16	with	with	ADP
ejpam-3328	44	17	the	the	DET
ejpam-3328	44	18	growth	growth	NOUN
ejpam-3328	44	19	of	of	ADP
ejpam-3328	44	20	n.	n.	NOUN
ejpam-3328	44	21	thus	thus	ADV
ejpam-3328	44	22	,	,	PUNCT
ejpam-3328	44	23	we	we	PRON
ejpam-3328	44	24	have	have	AUX
ejpam-3328	44	25	built	build	VERB
ejpam-3328	44	26	an	an	DET
ejpam-3328	44	27	example	example	NOUN
ejpam-3328	44	28	of	of	ADP
ejpam-3328	44	29	a	a	DET
ejpam-3328	44	30	sequence	sequence	NOUN
ejpam-3328	44	31	of	of	ADP
ejpam-3328	44	32	the	the	DET
ejpam-3328	44	33	bounded	bounded	ADJ
ejpam-3328	44	34	functions	function	NOUN
ejpam-3328	44	35	of	of	ADP
ejpam-3328	44	36	w	w	PROPN
ejpam-3328	44	37	1	1	NUM
ejpam-3328	44	38	2	2	NUM
ejpam-3328	44	39	(	(	PUNCT
ejpam-3328	44	40	r	r	NOUN
ejpam-3328	44	41	)	)	PUNCT
ejpam-3328	44	42	which	which	PRON
ejpam-3328	44	43	have	have	VERB
ejpam-3328	44	44	a	a	DET
ejpam-3328	44	45	constant	constant	ADJ
ejpam-3328	44	46	norm	norm	NOUN
ejpam-3328	44	47	w	w	PROPN
ejpam-3328	44	48	1	1	NUM
ejpam-3328	44	49	2	2	NUM
ejpam-3328	44	50	(	(	PUNCT
ejpam-3328	44	51	r	r	NOUN
ejpam-3328	44	52	)	)	PUNCT
ejpam-3328	44	53	,	,	PUNCT
ejpam-3328	44	54	and	and	CCONJ
ejpam-3328	44	55	this	this	DET
ejpam-3328	44	56	sequence	sequence	NOUN
ejpam-3328	44	57	converges	converge	VERB
ejpam-3328	44	58	to	to	ADP
ejpam-3328	44	59	a	a	DET
ejpam-3328	44	60	discontinuous	discontinuous	ADJ
ejpam-3328	44	61	function	function	NOUN
ejpam-3328	44	62	.	.	PUNCT
ejpam-3328	45	1	the	the	DET
ejpam-3328	45	2	results	result	NOUN
ejpam-3328	45	3	show	show	VERB
ejpam-3328	45	4	the	the	DET
ejpam-3328	45	5	flaws	flaw	NOUN
ejpam-3328	45	6	of	of	ADP
ejpam-3328	45	7	the	the	DET
ejpam-3328	45	8	embedding	embed	VERB
ejpam-3328	45	9	theorems	theorem	NOUN
ejpam-3328	45	10	when	when	SCONJ
ejpam-3328	45	11	analyzing	analyze	VERB
ejpam-3328	45	12	the	the	DET
ejpam-3328	45	13	behavior	behavior	NOUN
ejpam-3328	45	14	of	of	ADP
ejpam-3328	45	15	functions	function	NOUN
ejpam-3328	45	16	.	.	PUNCT
ejpam-3328	46	1	therefore	therefore	ADV
ejpam-3328	46	2	,	,	PUNCT
ejpam-3328	46	3	this	this	DET
ejpam-3328	46	4	work	work	NOUN
ejpam-3328	46	5	is	be	AUX
ejpam-3328	46	6	devoted	devote	VERB
ejpam-3328	46	7	to	to	ADP
ejpam-3328	46	8	overcoming	overcome	VERB
ejpam-3328	46	9	them	they	PRON
ejpam-3328	46	10	and	and	CCONJ
ejpam-3328	46	11	the	the	DET
ejpam-3328	46	12	basis	basis	NOUN
ejpam-3328	46	13	for	for	ADP
ejpam-3328	46	14	solving	solve	VERB
ejpam-3328	46	15	the	the	DET
ejpam-3328	46	16	formulated	formulated	ADJ
ejpam-3328	46	17	problem	problem	NOUN
ejpam-3328	46	18	is	be	AUX
ejpam-3328	46	19	the	the	DET
ejpam-3328	46	20	analytical	analytical	ADJ
ejpam-3328	46	21	properties	property	NOUN
ejpam-3328	46	22	of	of	ADP
ejpam-3328	46	23	the	the	DET
ejpam-3328	46	24	fourier	fourier	NOUN
ejpam-3328	46	25	transforms	transform	VERB
ejpam-3328	46	26	of	of	ADP
ejpam-3328	46	27	functions	function	NOUN
ejpam-3328	46	28	on	on	ADP
ejpam-3328	46	29	compact	compact	ADJ
ejpam-3328	46	30	sets	set	NOUN
ejpam-3328	46	31	.	.	PUNCT
ejpam-3328	47	1	analytical	analytical	ADJ
ejpam-3328	47	2	properties	property	NOUN
ejpam-3328	47	3	and	and	CCONJ
ejpam-3328	47	4	estimates	estimate	NOUN
ejpam-3328	47	5	of	of	ADP
ejpam-3328	47	6	the	the	DET
ejpam-3328	47	7	fourier	fourier	NOUN
ejpam-3328	47	8	transform	transform	NOUN
ejpam-3328	47	9	of	of	ADP
ejpam-3328	47	10	functions	function	NOUN
ejpam-3328	47	11	are	be	AUX
ejpam-3328	47	12	studied	study	VERB
ejpam-3328	47	13	using	use	VERB
ejpam-3328	47	14	the	the	DET
ejpam-3328	47	15	poincar	poincar	ADJ
ejpam-3328	47	16	riemann	riemann	PROPN
ejpam-3328	47	17	hilbert	hilbert	PROPN
ejpam-3328	47	18	boundary	boundary	PROPN
ejpam-3328	47	19	value	value	NOUN
ejpam-3328	47	20	problem	problem	NOUN
ejpam-3328	47	21	a.	a.	NOUN
ejpam-3328	47	22	durmagambetov	durmagambetov	PROPN
ejpam-3328	47	23	/	/	SYM
ejpam-3328	47	24	eur	eur	PROPN
ejpam-3328	47	25	.	.	PUNCT
ejpam-3328	48	1	j.	j.	PROPN
ejpam-3328	48	2	pure	pure	PROPN
ejpam-3328	48	3	appl	appl	PROPN
ejpam-3328	48	4	.	.	PROPN
ejpam-3328	48	5	math	math	PROPN
ejpam-3328	48	6	,	,	PUNCT
ejpam-3328	48	7	11	11	NUM
ejpam-3328	48	8	(	(	PUNCT
ejpam-3328	48	9	4	4	NUM
ejpam-3328	48	10	)	)	PUNCT
ejpam-3328	48	11	(	(	PUNCT
ejpam-3328	48	12	2018	2018	NUM
ejpam-3328	48	13	)	)	PUNCT
ejpam-3328	48	14	,	,	PUNCT
ejpam-3328	48	15	1143	1143	NUM
ejpam-3328	48	16	-	-	SYM
ejpam-3328	48	17	1176	1176	NUM
ejpam-3328	48	18	1145	1145	NUM
ejpam-3328	48	19	3	3	NUM
ejpam-3328	48	20	.	.	PUNCT
ejpam-3328	48	21	results	result	NOUN
ejpam-3328	48	22	for	for	ADP
ejpam-3328	48	23	the	the	DET
ejpam-3328	48	24	three	three	NUM
ejpam-3328	48	25	-	-	PUNCT
ejpam-3328	48	26	dimensional	dimensional	ADJ
ejpam-3328	48	27	case	case	NOUN
ejpam-3328	48	28	consider	consider	VERB
ejpam-3328	48	29	schrödinger	schrödinger	NOUN
ejpam-3328	48	30	’s	’s	PART
ejpam-3328	48	31	equation	equation	NOUN
ejpam-3328	48	32	:	:	PUNCT
ejpam-3328	48	33	−∆xψ	−∆xψ	NOUN
ejpam-3328	48	34	+	+	CCONJ
ejpam-3328	48	35	qψ	qψ	PROPN
ejpam-3328	48	36	=	=	PUNCT
ejpam-3328	48	37	k2ψ	k2ψ	PROPN
ejpam-3328	48	38	,	,	PUNCT
ejpam-3328	48	39	k	k	PROPN
ejpam-3328	48	40	∈	∈	PROPN
ejpam-3328	48	41	c.	c.	NOUN
ejpam-3328	48	42	(	(	PUNCT
ejpam-3328	48	43	2	2	X
ejpam-3328	48	44	)	)	PUNCT
ejpam-3328	48	45	let	let	VERB
ejpam-3328	48	46	ψ+(k	ψ+(k	NUM
ejpam-3328	48	47	,	,	PUNCT
ejpam-3328	48	48	θ	θ	NOUN
ejpam-3328	48	49	,	,	PUNCT
ejpam-3328	48	50	x	x	X
ejpam-3328	48	51	)	)	PUNCT
ejpam-3328	48	52	be	be	AUX
ejpam-3328	48	53	a	a	DET
ejpam-3328	48	54	solution	solution	NOUN
ejpam-3328	48	55	of	of	ADP
ejpam-3328	48	56	(	(	PUNCT
ejpam-3328	48	57	2	2	NUM
ejpam-3328	48	58	)	)	PUNCT
ejpam-3328	48	59	with	with	ADP
ejpam-3328	48	60	the	the	DET
ejpam-3328	48	61	following	following	ADJ
ejpam-3328	48	62	asymptotic	asymptotic	ADJ
ejpam-3328	48	63	behaviour	behaviour	NOUN
ejpam-3328	48	64	:	:	PUNCT
ejpam-3328	48	65	ψ+(k	ψ+(k	NUM
ejpam-3328	48	66	,	,	PUNCT
ejpam-3328	48	67	θ	θ	NOUN
ejpam-3328	48	68	,	,	PUNCT
ejpam-3328	48	69	x	x	NOUN
ejpam-3328	48	70	)	)	PUNCT
ejpam-3328	48	71	=	=	SYM
ejpam-3328	48	72	ψ0(k	ψ0(k	PROPN
ejpam-3328	48	73	,	,	PUNCT
ejpam-3328	48	74	θ	θ	PROPN
ejpam-3328	48	75	,	,	PUNCT
ejpam-3328	48	76	x	x	NOUN
ejpam-3328	48	77	)	)	PUNCT
ejpam-3328	49	1	+	+	CCONJ
ejpam-3328	49	2	eik|x|	eik|x|	PROPN
ejpam-3328	49	3	|x|	|x|	PROPN
ejpam-3328	49	4	a(k	a(k	PROPN
ejpam-3328	49	5	,	,	PUNCT
ejpam-3328	50	1	θ	θ	PROPN
ejpam-3328	50	2	′	′	NUM
ejpam-3328	50	3	,	,	PUNCT
ejpam-3328	50	4	θ	θ	NOUN
ejpam-3328	50	5	)	)	PUNCT
ejpam-3328	51	1	+	+	CCONJ
ejpam-3328	51	2	0	0	NUM
ejpam-3328	51	3	(	(	PUNCT
ejpam-3328	51	4	1	1	NUM
ejpam-3328	51	5	|x|	|x|	PROPN
ejpam-3328	51	6	)	)	PUNCT
ejpam-3328	51	7	,	,	PUNCT
ejpam-3328	51	8	|x|	|x|	PROPN
ejpam-3328	51	9	→	→	SYM
ejpam-3328	51	10	∞	∞	PROPN
ejpam-3328	51	11	,	,	PUNCT
ejpam-3328	51	12	(	(	PUNCT
ejpam-3328	51	13	3	3	X
ejpam-3328	51	14	)	)	PUNCT
ejpam-3328	51	15	where	where	SCONJ
ejpam-3328	51	16	a(k	a(k	PROPN
ejpam-3328	51	17	,	,	PUNCT
ejpam-3328	51	18	θ	θ	PROPN
ejpam-3328	51	19	′	′	NUM
ejpam-3328	51	20	,	,	PUNCT
ejpam-3328	51	21	θ	θ	X
ejpam-3328	51	22	)	)	PUNCT
ejpam-3328	51	23	is	be	AUX
ejpam-3328	51	24	the	the	DET
ejpam-3328	51	25	scattering	scatter	VERB
ejpam-3328	51	26	amplitude	amplitude	NOUN
ejpam-3328	51	27	and	and	CCONJ
ejpam-3328	51	28	θ	θ	NOUN
ejpam-3328	51	29	′	′	NUM
ejpam-3328	52	1	=	=	PUNCT
ejpam-3328	52	2	x	x	SYM
ejpam-3328	52	3	|x|	|x|	PROPN
ejpam-3328	52	4	,	,	PUNCT
ejpam-3328	52	5	θ	θ	PROPN
ejpam-3328	52	6	∈	∈	PROPN
ejpam-3328	52	7	s	s	PART
ejpam-3328	52	8	2	2	NUM
ejpam-3328	52	9	for	for	ADP
ejpam-3328	52	10	k	k	PROPN
ejpam-3328	52	11	∈	∈	PROPN
ejpam-3328	52	12	c̄+	c̄+	PROPN
ejpam-3328	52	13	=	=	SYM
ejpam-3328	52	14	{	{	PUNCT
ejpam-3328	52	15	imk	imk	PROPN
ejpam-3328	52	16	≥	≥	PROPN
ejpam-3328	52	17	0	0	NUM
ejpam-3328	52	18	}	}	PUNCT
ejpam-3328	52	19	ψ0(k	ψ0(k	PROPN
ejpam-3328	52	20	,	,	PUNCT
ejpam-3328	52	21	θ	θ	PROPN
ejpam-3328	52	22	,	,	PUNCT
ejpam-3328	52	23	x	x	NOUN
ejpam-3328	52	24	)	)	PUNCT
ejpam-3328	52	25	=	=	SYM
ejpam-3328	52	26	eik(θ	eik(θ	PROPN
ejpam-3328	52	27	,	,	PUNCT
ejpam-3328	52	28	x	x	NOUN
ejpam-3328	52	29	):	):	PUNCT
ejpam-3328	52	30	a(k	a(k	PROPN
ejpam-3328	52	31	,	,	PUNCT
ejpam-3328	52	32	θ	θ	PROPN
ejpam-3328	52	33	′	′	NUM
ejpam-3328	52	34	,	,	PUNCT
ejpam-3328	52	35	θ	θ	X
ejpam-3328	52	36	)	)	PUNCT
ejpam-3328	52	37	=	=	SYM
ejpam-3328	53	1	−	−	PROPN
ejpam-3328	53	2	1	1	NUM
ejpam-3328	53	3	4π	4π	NUM
ejpam-3328	53	4	∫	∫	PROPN
ejpam-3328	53	5	r3	r3	PROPN
ejpam-3328	53	6	q(x)ψ+(k	q(x)ψ+(k	PROPN
ejpam-3328	53	7	,	,	PUNCT
ejpam-3328	53	8	θ	θ	PROPN
ejpam-3328	53	9	,	,	PUNCT
ejpam-3328	53	10	x)e−ikθ	x)e−ikθ	PROPN
ejpam-3328	53	11	′	′	NUM
ejpam-3328	53	12	xdx	xdx	PROPN
ejpam-3328	53	13	.	.	PUNCT
ejpam-3328	54	1	solutions	solution	NOUN
ejpam-3328	54	2	to	to	ADP
ejpam-3328	54	3	(	(	PUNCT
ejpam-3328	54	4	2	2	NUM
ejpam-3328	54	5	)	)	PUNCT
ejpam-3328	54	6	and	and	CCONJ
ejpam-3328	54	7	(	(	PUNCT
ejpam-3328	54	8	3	3	X
ejpam-3328	54	9	)	)	PUNCT
ejpam-3328	54	10	are	be	AUX
ejpam-3328	54	11	obtained	obtain	VERB
ejpam-3328	54	12	by	by	ADP
ejpam-3328	54	13	solving	solve	VERB
ejpam-3328	54	14	the	the	DET
ejpam-3328	54	15	integral	integral	ADJ
ejpam-3328	54	16	equation	equation	NOUN
ejpam-3328	54	17	ψ+(k	ψ+(k	NOUN
ejpam-3328	54	18	,	,	PUNCT
ejpam-3328	54	19	θ	θ	NOUN
ejpam-3328	54	20	,	,	PUNCT
ejpam-3328	54	21	x	x	NOUN
ejpam-3328	54	22	)	)	PUNCT
ejpam-3328	54	23	=	=	SYM
ejpam-3328	54	24	ψ0(k	ψ0(k	PROPN
ejpam-3328	54	25	,	,	PUNCT
ejpam-3328	54	26	θ	θ	PROPN
ejpam-3328	54	27	,	,	PUNCT
ejpam-3328	54	28	x	x	NOUN
ejpam-3328	54	29	)	)	PUNCT
ejpam-3328	55	1	+	+	NUM
ejpam-3328	55	2	∫	∫	PROPN
ejpam-3328	55	3	r3	r3	PROPN
ejpam-3328	55	4	q(y	q(y	PROPN
ejpam-3328	55	5	)	)	PUNCT
ejpam-3328	55	6	e+ik|x−y|	e+ik|x−y|	NOUN
ejpam-3328	55	7	|x−	|x−	PROPN
ejpam-3328	55	8	y|	y|	PROPN
ejpam-3328	55	9	ψ+(k	ψ+(k	PROPN
ejpam-3328	55	10	,	,	PUNCT
ejpam-3328	55	11	θ	θ	NOUN
ejpam-3328	55	12	,	,	PUNCT
ejpam-3328	55	13	y)dy	y)dy	PROPN
ejpam-3328	55	14	=	=	SYM
ejpam-3328	55	15	g(qψ+	g(qψ+	PROPN
ejpam-3328	55	16	)	)	PUNCT
ejpam-3328	55	17	,	,	PUNCT
ejpam-3328	55	18	which	which	PRON
ejpam-3328	55	19	is	be	AUX
ejpam-3328	55	20	called	call	VERB
ejpam-3328	55	21	the	the	DET
ejpam-3328	55	22	lippman	lippman	NOUN
ejpam-3328	55	23	–	–	PUNCT
ejpam-3328	55	24	schwinger	schwinger	NOUN
ejpam-3328	55	25	equation	equation	NOUN
ejpam-3328	55	26	.	.	PUNCT
ejpam-3328	56	1	let	let	VERB
ejpam-3328	56	2	us	we	PRON
ejpam-3328	56	3	introduce	introduce	VERB
ejpam-3328	56	4	θ	θ	PROPN
ejpam-3328	56	5	,	,	PUNCT
ejpam-3328	56	6	θ	θ	NOUN
ejpam-3328	56	7	′	′	NOUN
ejpam-3328	56	8	∈	∈	PROPN
ejpam-3328	56	9	s2	s2	PROPN
ejpam-3328	56	10	,	,	PUNCT
ejpam-3328	56	11	df	df	PROPN
ejpam-3328	56	12	=	=	SYM
ejpam-3328	56	13	k	k	PROPN
ejpam-3328	56	14	∫	∫	PROPN
ejpam-3328	56	15	s2	s2	PROPN
ejpam-3328	56	16	a(k	a(k	PROPN
ejpam-3328	56	17	,	,	PUNCT
ejpam-3328	56	18	θ	θ	PROPN
ejpam-3328	56	19	′	′	NUM
ejpam-3328	56	20	,	,	PUNCT
ejpam-3328	56	21	θ)f(k	θ)f(k	ADJ
ejpam-3328	56	22	,	,	PUNCT
ejpam-3328	56	23	θ	θ	PROPN
ejpam-3328	56	24	′	′	NUM
ejpam-3328	56	25	)	)	PUNCT
ejpam-3328	57	1	dθ	dθ	PROPN
ejpam-3328	57	2	′	′	NUM
ejpam-3328	57	3	.	.	PUNCT
ejpam-3328	58	1	let	let	VERB
ejpam-3328	58	2	us	we	PRON
ejpam-3328	58	3	also	also	ADV
ejpam-3328	58	4	define	define	VERB
ejpam-3328	58	5	the	the	DET
ejpam-3328	58	6	solution	solution	NOUN
ejpam-3328	58	7	ψ−(k	ψ−(k	NOUN
ejpam-3328	58	8	,	,	PUNCT
ejpam-3328	58	9	θ	θ	PROPN
ejpam-3328	58	10	,	,	PUNCT
ejpam-3328	58	11	x	x	NOUN
ejpam-3328	58	12	)	)	PUNCT
ejpam-3328	58	13	for	for	ADP
ejpam-3328	58	14	k	k	PROPN
ejpam-3328	58	15	∈	∈	PROPN
ejpam-3328	58	16	c̄−	c̄−	NOUN
ejpam-3328	58	17	=	=	PUNCT
ejpam-3328	58	18	{	{	PUNCT
ejpam-3328	58	19	imk	imk	PROPN
ejpam-3328	58	20	≤	≤	PROPN
ejpam-3328	58	21	0	0	NUM
ejpam-3328	58	22	}	}	PUNCT
ejpam-3328	58	23	as	as	ADP
ejpam-3328	58	24	ψ−(k	ψ−(k	NOUN
ejpam-3328	58	25	,	,	PUNCT
ejpam-3328	58	26	θ	θ	PROPN
ejpam-3328	58	27	,	,	PUNCT
ejpam-3328	58	28	x	x	NOUN
ejpam-3328	58	29	)	)	PUNCT
ejpam-3328	58	30	=	=	SYM
ejpam-3328	58	31	ψ+(−k,−θ	ψ+(−k,−θ	X
ejpam-3328	58	32	,	,	PUNCT
ejpam-3328	58	33	x	x	NOUN
ejpam-3328	58	34	)	)	PUNCT
ejpam-3328	58	35	.	.	PUNCT
ejpam-3328	59	1	as	as	SCONJ
ejpam-3328	59	2	is	be	AUX
ejpam-3328	59	3	well	well	ADV
ejpam-3328	59	4	known	known	ADJ
ejpam-3328	59	5	[	[	X
ejpam-3328	59	6	8	8	NUM
ejpam-3328	59	7	]	]	PUNCT
ejpam-3328	59	8	,	,	PUNCT
ejpam-3328	59	9	ψ+(k	ψ+(k	X
ejpam-3328	59	10	,	,	PUNCT
ejpam-3328	59	11	θ	θ	NOUN
ejpam-3328	59	12	,	,	PUNCT
ejpam-3328	59	13	x)−ψ−(k	x)−ψ−(k	NUM
ejpam-3328	59	14	,	,	PUNCT
ejpam-3328	59	15	θ	θ	PROPN
ejpam-3328	59	16	,	,	PUNCT
ejpam-3328	59	17	x	x	NOUN
ejpam-3328	59	18	)	)	PUNCT
ejpam-3328	60	1	=	=	SYM
ejpam-3328	60	2	−	−	PROPN
ejpam-3328	61	1	k	k	PROPN
ejpam-3328	61	2	4π	4π	NUM
ejpam-3328	61	3	∫	∫	PROPN
ejpam-3328	61	4	s2	s2	PROPN
ejpam-3328	61	5	a(k	a(k	PROPN
ejpam-3328	61	6	,	,	PUNCT
ejpam-3328	61	7	θ	θ	PROPN
ejpam-3328	61	8	′	′	NOUN
ejpam-3328	61	9	,	,	PUNCT
ejpam-3328	61	10	θ)ψ−(k	θ)ψ−(k	NOUN
ejpam-3328	61	11	,	,	PUNCT
ejpam-3328	61	12	θ	θ	PROPN
ejpam-3328	61	13	′	′	NOUN
ejpam-3328	61	14	,	,	PUNCT
ejpam-3328	62	1	x)dθ	x)dθ	PROPN
ejpam-3328	62	2	′	′	NOUN
ejpam-3328	62	3	,	,	PUNCT
ejpam-3328	62	4	k	k	PROPN
ejpam-3328	62	5	∈	∈	PROPN
ejpam-3328	62	6	r.	r.	PROPN
ejpam-3328	62	7	(	(	PUNCT
ejpam-3328	62	8	4	4	X
ejpam-3328	62	9	)	)	PUNCT
ejpam-3328	62	10	this	this	DET
ejpam-3328	62	11	equation	equation	NOUN
ejpam-3328	62	12	is	be	AUX
ejpam-3328	62	13	the	the	DET
ejpam-3328	62	14	key	key	NOUN
ejpam-3328	62	15	to	to	ADP
ejpam-3328	62	16	solving	solve	VERB
ejpam-3328	62	17	the	the	DET
ejpam-3328	62	18	inverse	inverse	NOUN
ejpam-3328	62	19	scattering	scattering	NOUN
ejpam-3328	62	20	problem	problem	NOUN
ejpam-3328	62	21	and	and	CCONJ
ejpam-3328	62	22	was	be	AUX
ejpam-3328	62	23	first	first	ADV
ejpam-3328	62	24	used	use	VERB
ejpam-3328	62	25	by	by	ADP
ejpam-3328	62	26	newton	newton	PROPN
ejpam-3328	63	1	[	[	X
ejpam-3328	63	2	8,9	8,9	NUM
ejpam-3328	63	3	]	]	PUNCT
ejpam-3328	63	4	and	and	CCONJ
ejpam-3328	63	5	somersalo	somersalo	PROPN
ejpam-3328	63	6	et	et	PROPN
ejpam-3328	63	7	al	al	PROPN
ejpam-3328	63	8	.	.	PUNCT
ejpam-3328	64	1	[	[	X
ejpam-3328	64	2	10	10	NUM
ejpam-3328	64	3	]	]	PUNCT
ejpam-3328	64	4	.	.	PUNCT
ejpam-3328	65	1	definition	definition	NOUN
ejpam-3328	65	2	1	1	NUM
ejpam-3328	65	3	.	.	PUNCT
ejpam-3328	66	1	the	the	DET
ejpam-3328	66	2	set	set	NOUN
ejpam-3328	66	3	of	of	ADP
ejpam-3328	66	4	measurable	measurable	ADJ
ejpam-3328	66	5	functions	function	NOUN
ejpam-3328	66	6	r	r	NOUN
ejpam-3328	66	7	with	with	ADP
ejpam-3328	66	8	the	the	DET
ejpam-3328	66	9	norm	norm	NOUN
ejpam-3328	66	10	defined	define	VERB
ejpam-3328	66	11	by	by	ADP
ejpam-3328	66	12	||q||r	||q||r	PROPN
ejpam-3328	66	13	=	=	SYM
ejpam-3328	66	14	∫	∫	PROPN
ejpam-3328	66	15	r6	r6	PROPN
ejpam-3328	66	16	q(x)q(y	q(x)q(y	NOUN
ejpam-3328	66	17	)	)	PUNCT
ejpam-3328	66	18	|x−	|x−	PROPN
ejpam-3328	66	19	y|2	y|2	PROPN
ejpam-3328	66	20	dxdy	dxdy	PROPN
ejpam-3328	66	21	<	<	X
ejpam-3328	66	22	∞	∞	PROPN
ejpam-3328	66	23	is	be	AUX
ejpam-3328	66	24	recognised	recognise	VERB
ejpam-3328	66	25	as	as	ADP
ejpam-3328	66	26	being	be	AUX
ejpam-3328	66	27	of	of	ADP
ejpam-3328	66	28	rollnik	rollnik	NOUN
ejpam-3328	66	29	class	class	NOUN
ejpam-3328	66	30	.	.	PUNCT
ejpam-3328	67	1	a.	a.	NOUN
ejpam-3328	67	2	durmagambetov	durmagambetov	PROPN
ejpam-3328	67	3	/	/	SYM
ejpam-3328	67	4	eur	eur	PROPN
ejpam-3328	67	5	.	.	PUNCT
ejpam-3328	68	1	j.	j.	PROPN
ejpam-3328	68	2	pure	pure	PROPN
ejpam-3328	68	3	appl	appl	PROPN
ejpam-3328	68	4	.	.	PROPN
ejpam-3328	68	5	math	math	PROPN
ejpam-3328	68	6	,	,	PUNCT
ejpam-3328	68	7	11	11	NUM
ejpam-3328	68	8	(	(	PUNCT
ejpam-3328	68	9	4	4	NUM
ejpam-3328	68	10	)	)	PUNCT
ejpam-3328	68	11	(	(	PUNCT
ejpam-3328	68	12	2018	2018	NUM
ejpam-3328	68	13	)	)	PUNCT
ejpam-3328	68	14	,	,	PUNCT
ejpam-3328	68	15	1143	1143	NUM
ejpam-3328	68	16	-	-	SYM
ejpam-3328	68	17	1176	1176	NUM
ejpam-3328	68	18	1146	1146	NUM
ejpam-3328	68	19	equation	equation	NOUN
ejpam-3328	68	20	(	(	PUNCT
ejpam-3328	68	21	4	4	NUM
ejpam-3328	68	22	)	)	PUNCT
ejpam-3328	68	23	is	be	AUX
ejpam-3328	68	24	equivalent	equivalent	ADJ
ejpam-3328	68	25	to	to	ADP
ejpam-3328	68	26	the	the	DET
ejpam-3328	68	27	following	following	NOUN
ejpam-3328	68	28	:	:	PUNCT
ejpam-3328	68	29	ψ+	ψ+	ADJ
ejpam-3328	68	30	=	=	PUNCT
ejpam-3328	68	31	sψ−	sψ−	NOUN
ejpam-3328	68	32	,	,	PUNCT
ejpam-3328	68	33	where	where	SCONJ
ejpam-3328	68	34	s	s	NOUN
ejpam-3328	68	35	is	be	AUX
ejpam-3328	68	36	a	a	DET
ejpam-3328	68	37	scattering	scatter	VERB
ejpam-3328	68	38	operator	operator	NOUN
ejpam-3328	68	39	with	with	ADP
ejpam-3328	68	40	the	the	DET
ejpam-3328	68	41	kernel	kernel	NOUN
ejpam-3328	68	42	s(k	s(k	ADV
ejpam-3328	68	43	,	,	PUNCT
ejpam-3328	68	44	l	l	NOUN
ejpam-3328	68	45	)	)	PUNCT
ejpam-3328	68	46	=	=	SYM
ejpam-3328	68	47	∫	∫	PROPN
ejpam-3328	68	48	r3	r3	PROPN
ejpam-3328	68	49	ψ+(k	ψ+(k	PROPN
ejpam-3328	68	50	,	,	PUNCT
ejpam-3328	68	51	x)ψ∗−	x)ψ∗−	PROPN
ejpam-3328	68	52	(	(	PUNCT
ejpam-3328	68	53	l	l	PROPN
ejpam-3328	68	54	,	,	PUNCT
ejpam-3328	68	55	x)dx	x)dx	PROPN
ejpam-3328	68	56	.	.	PUNCT
ejpam-3328	69	1	the	the	DET
ejpam-3328	69	2	following	follow	VERB
ejpam-3328	69	3	theorem	theorem	NOUN
ejpam-3328	69	4	was	be	AUX
ejpam-3328	69	5	stated	state	VERB
ejpam-3328	69	6	in	in	ADP
ejpam-3328	69	7	[	[	X
ejpam-3328	69	8	9	9	NUM
ejpam-3328	69	9	]	]	NUM
ejpam-3328	69	10	:	:	PUNCT
ejpam-3328	69	11	theorem	theorem	NOUN
ejpam-3328	69	12	2	2	NUM
ejpam-3328	69	13	.	.	PUNCT
ejpam-3328	69	14	(	(	PUNCT
ejpam-3328	69	15	energy	energy	NOUN
ejpam-3328	69	16	and	and	CCONJ
ejpam-3328	69	17	momentum	momentum	NOUN
ejpam-3328	69	18	conservation	conservation	NOUN
ejpam-3328	69	19	laws	law	NOUN
ejpam-3328	69	20	)	)	PUNCT
ejpam-3328	69	21	let	let	VERB
ejpam-3328	69	22	q	q	PROPN
ejpam-3328	69	23	∈	∈	PROPN
ejpam-3328	69	24	r.	r.	PROPN
ejpam-3328	69	25	then	then	ADV
ejpam-3328	69	26	,	,	PUNCT
ejpam-3328	69	27	ss∗	ss∗	NOUN
ejpam-3328	69	28	=	=	PUNCT
ejpam-3328	69	29	i	i	PROPN
ejpam-3328	69	30	and	and	CCONJ
ejpam-3328	69	31	s∗s	s∗s	PUNCT
ejpam-3328	69	32	=	=	PUNCT
ejpam-3328	69	33	i	i	PROPN
ejpam-3328	69	34	,	,	PUNCT
ejpam-3328	69	35	where	where	SCONJ
ejpam-3328	69	36	i	i	PRON
ejpam-3328	69	37	is	be	AUX
ejpam-3328	69	38	a	a	DET
ejpam-3328	69	39	unitary	unitary	ADJ
ejpam-3328	69	40	operator	operator	NOUN
ejpam-3328	69	41	.	.	PUNCT
ejpam-3328	70	1	corollary	corollary	ADJ
ejpam-3328	70	2	1	1	NUM
ejpam-3328	70	3	.	.	PUNCT
ejpam-3328	70	4	ss∗	ss∗	NOUN
ejpam-3328	71	1	=	=	PUNCT
ejpam-3328	71	2	i	i	PROPN
ejpam-3328	71	3	and	and	CCONJ
ejpam-3328	71	4	s∗s	s∗s	PUNCT
ejpam-3328	71	5	=	=	PUNCT
ejpam-3328	71	6	i	i	PRON
ejpam-3328	71	7	yield	yield	VERB
ejpam-3328	71	8	a(k	a(k	PROPN
ejpam-3328	71	9	,	,	PUNCT
ejpam-3328	71	10	θ	θ	PROPN
ejpam-3328	71	11	′	′	NUM
ejpam-3328	71	12	,	,	PUNCT
ejpam-3328	71	13	θ)−a(k	θ)−a(k	PROPN
ejpam-3328	71	14	,	,	PUNCT
ejpam-3328	71	15	θ	θ	PROPN
ejpam-3328	71	16	,	,	PUNCT
ejpam-3328	71	17	θ	θ	NOUN
ejpam-3328	71	18	′	′	NUM
ejpam-3328	71	19	)	)	PUNCT
ejpam-3328	71	20	∗	∗	NOUN
ejpam-3328	71	21	=	=	SYM
ejpam-3328	71	22	ik	ik	X
ejpam-3328	71	23	2π	2π	PROPN
ejpam-3328	71	24	∫	∫	PROPN
ejpam-3328	71	25	s2	s2	PROPN
ejpam-3328	71	26	a(k	a(k	PROPN
ejpam-3328	71	27	,	,	PUNCT
ejpam-3328	71	28	θ	θ	PROPN
ejpam-3328	71	29	,	,	PUNCT
ejpam-3328	71	30	θ	θ	PROPN
ejpam-3328	71	31	′′	′′	PROPN
ejpam-3328	71	32	)	)	PUNCT
ejpam-3328	72	1	a(k	a(k	PROPN
ejpam-3328	72	2	,	,	PUNCT
ejpam-3328	72	3	θ	θ	PROPN
ejpam-3328	72	4	′	′	NUM
ejpam-3328	72	5	,	,	PUNCT
ejpam-3328	72	6	θ	θ	X
ejpam-3328	72	7	′′	′′	PROPN
ejpam-3328	72	8	)	)	PUNCT
ejpam-3328	73	1	∗dθ	∗dθ	PUNCT
ejpam-3328	73	2	′′	′′	PROPN
ejpam-3328	73	3	.	.	PUNCT
ejpam-3328	74	1	theorem	theorem	VERB
ejpam-3328	74	2	3	3	NUM
ejpam-3328	74	3	.	.	PUNCT
ejpam-3328	74	4	(	(	PUNCT
ejpam-3328	74	5	birmann	birmann	NOUN
ejpam-3328	74	6	–	–	PUNCT
ejpam-3328	74	7	schwinger	schwinger	NOUN
ejpam-3328	74	8	estimation	estimation	NOUN
ejpam-3328	74	9	)	)	PUNCT
ejpam-3328	74	10	let	let	VERB
ejpam-3328	74	11	q	q	PROPN
ejpam-3328	74	12	∈	∈	PROPN
ejpam-3328	74	13	r.	r.	PROPN
ejpam-3328	74	14	then	then	ADV
ejpam-3328	74	15	,	,	PUNCT
ejpam-3328	74	16	the	the	DET
ejpam-3328	74	17	number	number	NOUN
ejpam-3328	74	18	of	of	ADP
ejpam-3328	74	19	discrete	discrete	ADJ
ejpam-3328	74	20	eigenvalues	eigenvalue	NOUN
ejpam-3328	74	21	can	can	AUX
ejpam-3328	74	22	be	be	AUX
ejpam-3328	74	23	estimated	estimate	VERB
ejpam-3328	74	24	as	as	ADP
ejpam-3328	74	25	n(q	n(q	PROPN
ejpam-3328	74	26	)	)	PUNCT
ejpam-3328	74	27	≤	≤	NUM
ejpam-3328	74	28	1	1	NUM
ejpam-3328	74	29	(	(	PUNCT
ejpam-3328	74	30	4π)2	4π)2	NUM
ejpam-3328	74	31	∫	∫	PROPN
ejpam-3328	74	32	r3	r3	PROPN
ejpam-3328	74	33	∫	∫	PROPN
ejpam-3328	74	34	r3	r3	PROPN
ejpam-3328	74	35	q(x)q(y	q(x)q(y	PROPN
ejpam-3328	74	36	)	)	PUNCT
ejpam-3328	74	37	|x−	|x−	PROPN
ejpam-3328	74	38	y|2	y|2	PROPN
ejpam-3328	74	39	dxdy	dxdy	PROPN
ejpam-3328	74	40	.	.	PUNCT
ejpam-3328	75	1	lemma	lemma	PROPN
ejpam-3328	75	2	1	1	X
ejpam-3328	75	3	.	.	PUNCT
ejpam-3328	76	1	let	let	VERB
ejpam-3328	76	2	(	(	PUNCT
ejpam-3328	76	3	|q|l1(r3	|q|l1(r3	PROPN
ejpam-3328	76	4	)	)	PUNCT
ejpam-3328	76	5	+	+	NUM
ejpam-3328	76	6	4π|q|l2(r3	4π|q|l2(r3	NUM
ejpam-3328	76	7	)	)	PUNCT
ejpam-3328	76	8	)	)	PUNCT
ejpam-3328	77	1	<	<	X
ejpam-3328	77	2	α	α	X
ejpam-3328	77	3	<	<	X
ejpam-3328	77	4	1/2	1/2	NUM
ejpam-3328	77	5	.	.	PUNCT
ejpam-3328	78	1	then	then	ADV
ejpam-3328	78	2	,	,	PUNCT
ejpam-3328	78	3	‖ψ+‖l∞	‖ψ+‖l∞	PROPN
ejpam-3328	78	4	≤	≤	NOUN
ejpam-3328	78	5	(	(	PUNCT
ejpam-3328	78	6	|q|l1(r3	|q|l1(r3	PROPN
ejpam-3328	78	7	)	)	PUNCT
ejpam-3328	78	8	+	+	NUM
ejpam-3328	78	9	4π|q|l2(r3	4π|q|l2(r3	NUM
ejpam-3328	78	10	)	)	PUNCT
ejpam-3328	78	11	)	)	PUNCT
ejpam-3328	78	12	1−	1−	NUM
ejpam-3328	78	13	(	(	PUNCT
ejpam-3328	78	14	|q|l1(r3	|q|l1(r3	PROPN
ejpam-3328	78	15	)	)	PUNCT
ejpam-3328	78	16	+	+	NUM
ejpam-3328	78	17	4π|q|l2(r3	4π|q|l2(r3	NUM
ejpam-3328	78	18	)	)	PUNCT
ejpam-3328	78	19	)	)	PUNCT
ejpam-3328	78	20	<	<	X
ejpam-3328	79	1	α	α	X
ejpam-3328	79	2	1−	1−	NUM
ejpam-3328	79	3	α	α	NOUN
ejpam-3328	79	4	,	,	PUNCT
ejpam-3328	79	5	∥∥∥∥∂(ψ+	∥∥∥∥∂(ψ+	NOUN
ejpam-3328	79	6	−ψ0	−ψ0	PROPN
ejpam-3328	79	7	)	)	PUNCT
ejpam-3328	80	1	∂k	∂k	ADP
ejpam-3328	80	2	∥∥∥∥	∥∥∥∥	NOUN
ejpam-3328	80	3	l∞	l∞	NOUN
ejpam-3328	80	4	≤	≤	NUM
ejpam-3328	80	5	|q|l1(r3	|q|l1(r3	NOUN
ejpam-3328	80	6	)	)	PUNCT
ejpam-3328	81	1	+	+	NUM
ejpam-3328	81	2	4π|q|l2(r3	4π|q|l2(r3	NUM
ejpam-3328	81	3	)	)	PUNCT
ejpam-3328	81	4	1−	1−	NUM
ejpam-3328	81	5	(	(	PUNCT
ejpam-3328	81	6	|q|l1(r3	|q|l1(r3	PROPN
ejpam-3328	81	7	)	)	PUNCT
ejpam-3328	81	8	+	+	NUM
ejpam-3328	81	9	4π|q|l2(r3	4π|q|l2(r3	NUM
ejpam-3328	81	10	)	)	PUNCT
ejpam-3328	81	11	)	)	PUNCT
ejpam-3328	82	1	<	<	X
ejpam-3328	82	2	α	α	X
ejpam-3328	82	3	1−	1−	NUM
ejpam-3328	82	4	α	α	NOUN
ejpam-3328	82	5	.	.	PUNCT
ejpam-3328	83	1	proof	proof	NOUN
ejpam-3328	83	2	.	.	PUNCT
ejpam-3328	84	1	by	by	ADP
ejpam-3328	84	2	the	the	DET
ejpam-3328	84	3	lippman	lippman	PROPN
ejpam-3328	84	4	–	–	PUNCT
ejpam-3328	84	5	schwinger	schwinger	NOUN
ejpam-3328	84	6	equation	equation	NOUN
ejpam-3328	84	7	,	,	PUNCT
ejpam-3328	84	8	we	we	PRON
ejpam-3328	84	9	have	have	VERB
ejpam-3328	84	10	|ψ+	|ψ+	PROPN
ejpam-3328	84	11	−ψ0|	−ψ0|	VERB
ejpam-3328	84	12	≤	≤	ADJ
ejpam-3328	84	13	|gqψ+|	|gqψ+|	NOUN
ejpam-3328	84	14	,	,	PUNCT
ejpam-3328	84	15	|ψ+	|ψ+	PROPN
ejpam-3328	84	16	−ψ0|l∞	−ψ0|l∞	NOUN
ejpam-3328	84	17	≤	≤	NOUN
ejpam-3328	84	18	|ψ+	|ψ+	NUM
ejpam-3328	84	19	−ψ0|l∞	−ψ0|l∞	NOUN
ejpam-3328	84	20	|gq|+	|gq|+	NOUN
ejpam-3328	84	21	|gq|	|gq|	NOUN
ejpam-3328	84	22	,	,	PUNCT
ejpam-3328	84	23	and	and	CCONJ
ejpam-3328	84	24	,	,	PUNCT
ejpam-3328	84	25	finally	finally	ADV
ejpam-3328	84	26	,	,	PUNCT
ejpam-3328	84	27	|ψ+	|ψ+	PROPN
ejpam-3328	84	28	−ψ0|	−ψ0|	VERB
ejpam-3328	84	29	≤	≤	PROPN
ejpam-3328	84	30	(	(	PUNCT
ejpam-3328	84	31	|q|l1(r3	|q|l1(r3	PROPN
ejpam-3328	84	32	)	)	PUNCT
ejpam-3328	84	33	+	+	NUM
ejpam-3328	84	34	4π|q|l2(r3	4π|q|l2(r3	NUM
ejpam-3328	84	35	)	)	PUNCT
ejpam-3328	84	36	)	)	PUNCT
ejpam-3328	85	1	1−	1−	NUM
ejpam-3328	85	2	(	(	PUNCT
ejpam-3328	85	3	|q|l1(r3	|q|l1(r3	PROPN
ejpam-3328	85	4	)	)	PUNCT
ejpam-3328	85	5	+	+	NUM
ejpam-3328	85	6	4π|q|l2(r3	4π|q|l2(r3	NUM
ejpam-3328	85	7	)	)	PUNCT
ejpam-3328	85	8	)	)	PUNCT
ejpam-3328	85	9	.	.	PUNCT
ejpam-3328	86	1	by	by	ADP
ejpam-3328	86	2	the	the	DET
ejpam-3328	86	3	lippman	lippman	PROPN
ejpam-3328	86	4	–	–	PUNCT
ejpam-3328	86	5	schwinger	schwinger	NOUN
ejpam-3328	86	6	equation	equation	NOUN
ejpam-3328	86	7	,	,	PUNCT
ejpam-3328	86	8	we	we	PRON
ejpam-3328	86	9	also	also	ADV
ejpam-3328	86	10	have∣∣∣∣∂	have∣∣∣∣∂	VERB
ejpam-3328	86	11	(	(	PUNCT
ejpam-3328	86	12	ψ+	ψ+	PUNCT
ejpam-3328	86	13	−ψ0	−ψ0	NOUN
ejpam-3328	86	14	)	)	PUNCT
ejpam-3328	87	1	∂k	∂k	PROPN
ejpam-3328	87	2	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3328	87	3	≤	≤	PROPN
ejpam-3328	87	4	∣∣∣∣∂gq∂k	∣∣∣∣∂gq∂k	PROPN
ejpam-3328	87	5	ψ+	ψ+	VERB
ejpam-3328	87	6	∣∣∣∣+	∣∣∣∣+	PROPN
ejpam-3328	87	7	∣∣∣∣gq∂	∣∣∣∣gq∂	NOUN
ejpam-3328	87	8	(	(	PUNCT
ejpam-3328	87	9	ψ+	ψ+	X
ejpam-3328	87	10	−ψ0	−ψ0	NOUN
ejpam-3328	87	11	)	)	PUNCT
ejpam-3328	87	12	∂k	∂k	PROPN
ejpam-3328	87	13	∣∣∣∣+	∣∣∣∣+	NOUN
ejpam-3328	87	14	|gq|	|gq|	PROPN
ejpam-3328	87	15	,	,	PUNCT
ejpam-3328	87	16	a.	a.	NOUN
ejpam-3328	87	17	durmagambetov	durmagambetov	PROPN
ejpam-3328	87	18	/	/	SYM
ejpam-3328	87	19	eur	eur	PROPN
ejpam-3328	87	20	.	.	PUNCT
ejpam-3328	88	1	j.	j.	PROPN
ejpam-3328	88	2	pure	pure	PROPN
ejpam-3328	88	3	appl	appl	PROPN
ejpam-3328	88	4	.	.	PROPN
ejpam-3328	88	5	math	math	PROPN
ejpam-3328	88	6	,	,	PUNCT
ejpam-3328	88	7	11	11	NUM
ejpam-3328	88	8	(	(	PUNCT
ejpam-3328	88	9	4	4	NUM
ejpam-3328	88	10	)	)	PUNCT
ejpam-3328	88	11	(	(	PUNCT
ejpam-3328	88	12	2018	2018	NUM
ejpam-3328	88	13	)	)	PUNCT
ejpam-3328	88	14	,	,	PUNCT
ejpam-3328	88	15	1143	1143	NUM
ejpam-3328	88	16	-	-	SYM
ejpam-3328	88	17	1176	1176	NUM
ejpam-3328	88	18	1147∣∣∣∣∂(ψ+	1147∣∣∣∣∂(ψ+	NUM
ejpam-3328	88	19	−ψ0	−ψ0	NOUN
ejpam-3328	88	20	)	)	PUNCT
ejpam-3328	89	1	∂k	∂k	PROPN
ejpam-3328	89	2	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3328	89	3	≤	≤	NOUN
ejpam-3328	89	4	(	(	PUNCT
ejpam-3328	89	5	|q|l1(r3	|q|l1(r3	PROPN
ejpam-3328	89	6	)	)	PUNCT
ejpam-3328	89	7	+	+	NUM
ejpam-3328	89	8	4π|q|l2(r3	4π|q|l2(r3	NUM
ejpam-3328	89	9	)	)	PUNCT
ejpam-3328	89	10	)	)	PUNCT
ejpam-3328	89	11	,	,	PUNCT
ejpam-3328	89	12	∥∥∥∥∂(ψ+	∥∥∥∥∂(ψ+	NOUN
ejpam-3328	89	13	−ψ0	−ψ0	PROPN
ejpam-3328	89	14	)	)	PUNCT
ejpam-3328	90	1	∂k	∂k	ADP
ejpam-3328	90	2	∥∥∥∥	∥∥∥∥	NOUN
ejpam-3328	90	3	l∞	l∞	NOUN
ejpam-3328	90	4	≤	≤	NUM
ejpam-3328	90	5	|q|l1(r3	|q|l1(r3	NOUN
ejpam-3328	90	6	)	)	PUNCT
ejpam-3328	91	1	+	+	NUM
ejpam-3328	91	2	4π|q|l2(r3	4π|q|l2(r3	NUM
ejpam-3328	91	3	)	)	PUNCT
ejpam-3328	91	4	1−	1−	NUM
ejpam-3328	91	5	(	(	PUNCT
ejpam-3328	91	6	|q|l1(r3	|q|l1(r3	PROPN
ejpam-3328	91	7	)	)	PUNCT
ejpam-3328	91	8	+	+	NUM
ejpam-3328	91	9	4π|q|l2(r3	4π|q|l2(r3	NUM
ejpam-3328	91	10	)	)	PUNCT
ejpam-3328	91	11	)	)	PUNCT
ejpam-3328	91	12	,	,	PUNCT
ejpam-3328	91	13	which	which	PRON
ejpam-3328	91	14	completes	complete	VERB
ejpam-3328	91	15	the	the	DET
ejpam-3328	91	16	proof	proof	NOUN
ejpam-3328	91	17	.	.	PUNCT
ejpam-3328	92	1	let	let	VERB
ejpam-3328	92	2	us	we	PRON
ejpam-3328	92	3	introduce	introduce	VERB
ejpam-3328	92	4	the	the	DET
ejpam-3328	92	5	following	following	ADJ
ejpam-3328	92	6	notation	notation	NOUN
ejpam-3328	92	7	:	:	PUNCT
ejpam-3328	92	8	q(k	q(k	NOUN
ejpam-3328	92	9	,	,	PUNCT
ejpam-3328	92	10	θ	θ	PROPN
ejpam-3328	92	11	,	,	PUNCT
ejpam-3328	92	12	θ	θ	NOUN
ejpam-3328	92	13	′	′	NUM
ejpam-3328	92	14	)	)	PUNCT
ejpam-3328	93	1	=	=	SYM
ejpam-3328	93	2	∫	∫	PROPN
ejpam-3328	93	3	r3	r3	PROPN
ejpam-3328	93	4	q(x)eik(θ−θ′	q(x)eik(θ−θ′	PROPN
ejpam-3328	93	5	)	)	PUNCT
ejpam-3328	93	6	xdx	xdx	PROPN
ejpam-3328	93	7	,	,	PUNCT
ejpam-3328	93	8	k(s	k(s	PROPN
ejpam-3328	93	9	)	)	PUNCT
ejpam-3328	93	10	=	=	SYM
ejpam-3328	93	11	s	s	NOUN
ejpam-3328	93	12	,	,	PUNCT
ejpam-3328	93	13	x(x	x(x	PROPN
ejpam-3328	93	14	)	)	PUNCT
ejpam-3328	93	15	=	=	SYM
ejpam-3328	93	16	x	x	X
ejpam-3328	93	17	,	,	PUNCT
ejpam-3328	93	18	t+q	t+q	PROPN
ejpam-3328	93	19	=	=	SYM
ejpam-3328	93	20	∫	∫	PROPN
ejpam-3328	94	1	+	+	NUM
ejpam-3328	94	2	∞	∞	PROPN
ejpam-3328	94	3	−∞	−∞	ADP
ejpam-3328	94	4	q(s	q(s	PROPN
ejpam-3328	94	5	,	,	PUNCT
ejpam-3328	94	6	θ	θ	PROPN
ejpam-3328	94	7	,	,	PUNCT
ejpam-3328	94	8	θ	θ	NOUN
ejpam-3328	94	9	′	′	NUM
ejpam-3328	94	10	)	)	PUNCT
ejpam-3328	95	1	s−	s−	PROPN
ejpam-3328	95	2	t−	t−	PROPN
ejpam-3328	95	3	i0	i0	PROPN
ejpam-3328	95	4	ds	ds	PROPN
ejpam-3328	95	5	,	,	PUNCT
ejpam-3328	95	6	t−q	t−q	X
ejpam-3328	95	7	=	=	SYM
ejpam-3328	95	8	∫	∫	PROPN
ejpam-3328	96	1	+	+	NUM
ejpam-3328	96	2	∞	∞	PROPN
ejpam-3328	96	3	−∞	−∞	ADP
ejpam-3328	96	4	q(s	q(s	PROPN
ejpam-3328	96	5	,	,	PUNCT
ejpam-3328	96	6	θ	θ	PROPN
ejpam-3328	96	7	,	,	PUNCT
ejpam-3328	96	8	θ	θ	NOUN
ejpam-3328	96	9	′	′	NUM
ejpam-3328	96	10	)	)	PUNCT
ejpam-3328	97	1	s−	s−	PROPN
ejpam-3328	97	2	t+	t+	PUNCT
ejpam-3328	97	3	i0	i0	PROPN
ejpam-3328	97	4	ds	ds	PROPN
ejpam-3328	97	5	.	.	PUNCT
ejpam-3328	97	6	lemma	lemma	PROPN
ejpam-3328	97	7	2	2	X
ejpam-3328	97	8	.	.	PUNCT
ejpam-3328	97	9	let	let	VERB
ejpam-3328	97	10	q	q	PROPN
ejpam-3328	97	11	∈	∈	PROPN
ejpam-3328	97	12	r	r	NOUN
ejpam-3328	97	13	∩	∩	NOUN
ejpam-3328	97	14	l1(r3	l1(r3	NOUN
ejpam-3328	97	15	)	)	PUNCT
ejpam-3328	97	16	,	,	PUNCT
ejpam-3328	97	17	‖q‖l1	‖q‖l1	PROPN
ejpam-3328	97	18	+	+	NUM
ejpam-3328	97	19	4π|q|l2(r3	4π|q|l2(r3	NUM
ejpam-3328	97	20	)	)	PUNCT
ejpam-3328	97	21	<	<	X
ejpam-3328	97	22	α	α	X
ejpam-3328	97	23	<	<	X
ejpam-3328	97	24	1/2	1/2	NUM
ejpam-3328	97	25	.	.	PUNCT
ejpam-3328	98	1	then	then	ADV
ejpam-3328	98	2	,	,	PUNCT
ejpam-3328	98	3	‖a+‖l∞	‖a+‖l∞	INTJ
ejpam-3328	98	4	<	<	X
ejpam-3328	98	5	α+	α+	PUNCT
ejpam-3328	98	6	α	α	NOUN
ejpam-3328	98	7	1−	1−	NUM
ejpam-3328	98	8	α	α	NOUN
ejpam-3328	98	9	,	,	PUNCT
ejpam-3328	98	10	∥∥∥∥∂a+	∥∥∥∥∂a+	PROPN
ejpam-3328	98	11	∂k	∂k	PROPN
ejpam-3328	98	12	∥∥∥∥	∥∥∥∥	PROPN
ejpam-3328	98	13	l∞	l∞	NOUN
ejpam-3328	98	14	<	<	X
ejpam-3328	98	15	α+	α+	PUNCT
ejpam-3328	98	16	α	α	NOUN
ejpam-3328	98	17	1−	1−	NUM
ejpam-3328	98	18	α	α	NOUN
ejpam-3328	98	19	.	.	PUNCT
ejpam-3328	99	1	proof	proof	NOUN
ejpam-3328	99	2	.	.	PUNCT
ejpam-3328	100	1	multiplying	multiply	VERB
ejpam-3328	100	2	the	the	DET
ejpam-3328	100	3	lippman	lippman	NOUN
ejpam-3328	100	4	–	–	PUNCT
ejpam-3328	100	5	schwinger	schwinger	NOUN
ejpam-3328	100	6	equation	equation	NOUN
ejpam-3328	100	7	by	by	ADP
ejpam-3328	100	8	q(x)ψ0(k	q(x)ψ0(k	NOUN
ejpam-3328	100	9	,	,	PUNCT
ejpam-3328	100	10	θ	θ	PROPN
ejpam-3328	100	11	,	,	PUNCT
ejpam-3328	100	12	x	x	NOUN
ejpam-3328	100	13	)	)	PUNCT
ejpam-3328	100	14	and	and	CCONJ
ejpam-3328	100	15	then	then	ADV
ejpam-3328	100	16	integrating	integrate	VERB
ejpam-3328	100	17	,	,	PUNCT
ejpam-3328	100	18	we	we	PRON
ejpam-3328	100	19	have	have	VERB
ejpam-3328	100	20	a(k	a(k	PROPN
ejpam-3328	100	21	,	,	PUNCT
ejpam-3328	100	22	θ	θ	PROPN
ejpam-3328	100	23	,	,	PUNCT
ejpam-3328	100	24	θ	θ	NOUN
ejpam-3328	100	25	′	′	NUM
ejpam-3328	100	26	)	)	PUNCT
ejpam-3328	101	1	=	=	PUNCT
ejpam-3328	101	2	q(k	q(k	PROPN
ejpam-3328	101	3	,	,	PUNCT
ejpam-3328	101	4	θ	θ	PROPN
ejpam-3328	101	5	,	,	PUNCT
ejpam-3328	101	6	θ	θ	NOUN
ejpam-3328	101	7	′	′	NUM
ejpam-3328	101	8	)	)	PUNCT
ejpam-3328	102	1	+	+	CCONJ
ejpam-3328	102	2	∫	∫	PROPN
ejpam-3328	102	3	r3	r3	PROPN
ejpam-3328	102	4	q(x)ψ0(k	q(x)ψ0(k	PROPN
ejpam-3328	102	5	,	,	PUNCT
ejpam-3328	102	6	θ	θ	PROPN
ejpam-3328	102	7	,	,	PUNCT
ejpam-3328	102	8	x)gqψ+dx	x)gqψ+dx	NOUN
ejpam-3328	102	9	.	.	PUNCT
ejpam-3328	103	1	we	we	PRON
ejpam-3328	103	2	can	can	AUX
ejpam-3328	103	3	estimate	estimate	VERB
ejpam-3328	103	4	this	this	DET
ejpam-3328	103	5	latest	late	ADJ
ejpam-3328	103	6	equation	equation	NOUN
ejpam-3328	103	7	as	as	ADP
ejpam-3328	103	8	|a|	|a|	NOUN
ejpam-3328	103	9	≤	≤	NOUN
ejpam-3328	103	10	α+	α+	PUNCT
ejpam-3328	103	11	α	α	NOUN
ejpam-3328	103	12	(	(	PUNCT
ejpam-3328	103	13	|q|l1(r3	|q|l1(r3	PROPN
ejpam-3328	103	14	)	)	PUNCT
ejpam-3328	103	15	+	+	NUM
ejpam-3328	103	16	4π|q|l2(r3	4π|q|l2(r3	NUM
ejpam-3328	103	17	)	)	PUNCT
ejpam-3328	103	18	)	)	PUNCT
ejpam-3328	103	19	1−	1−	NUM
ejpam-3328	103	20	(	(	PUNCT
ejpam-3328	103	21	|q|l1(r3	|q|l1(r3	PROPN
ejpam-3328	103	22	)	)	PUNCT
ejpam-3328	104	1	+	+	NUM
ejpam-3328	104	2	4π|q|l2(r3	4π|q|l2(r3	NUM
ejpam-3328	104	3	)	)	PUNCT
ejpam-3328	104	4	)	)	PUNCT
ejpam-3328	104	5	.	.	PUNCT
ejpam-3328	105	1	following	follow	VERB
ejpam-3328	105	2	a	a	DET
ejpam-3328	105	3	similar	similar	ADJ
ejpam-3328	105	4	procedure	procedure	NOUN
ejpam-3328	105	5	for	for	ADP
ejpam-3328	105	6	∥∥∥∂a+	∥∥∥∂a+	NOUN
ejpam-3328	105	7	∂k	∂k	PROPN
ejpam-3328	105	8	∥∥∥	∥∥∥	PROPN
ejpam-3328	105	9	completes	complete	VERB
ejpam-3328	105	10	the	the	DET
ejpam-3328	105	11	proof	proof	NOUN
ejpam-3328	105	12	.	.	PUNCT
ejpam-3328	106	1	we	we	PRON
ejpam-3328	106	2	define	define	VERB
ejpam-3328	106	3	the	the	DET
ejpam-3328	106	4	operators	operator	NOUN
ejpam-3328	106	5	t±	t±	ADP
ejpam-3328	106	6	,	,	PUNCT
ejpam-3328	106	7	t	t	PROPN
ejpam-3328	106	8	for	for	ADP
ejpam-3328	106	9	f	f	PROPN
ejpam-3328	106	10	∈w	∈w	PROPN
ejpam-3328	106	11	1	1	NUM
ejpam-3328	106	12	2	2	NUM
ejpam-3328	106	13	(	(	PUNCT
ejpam-3328	106	14	r	r	NOUN
ejpam-3328	106	15	)	)	PUNCT
ejpam-3328	106	16	as	as	SCONJ
ejpam-3328	106	17	follows	follow	VERB
ejpam-3328	106	18	:	:	PUNCT
ejpam-3328	106	19	t+f	t+f	NUM
ejpam-3328	106	20	=	=	SYM
ejpam-3328	106	21	1	1	NUM
ejpam-3328	106	22	2πi	2πi	NOUN
ejpam-3328	106	23	lim	lim	PROPN
ejpam-3328	106	24	imz→0	imz→0	PROPN
ejpam-3328	106	25	∞∫	∞∫	PROPN
ejpam-3328	106	26	−∞	−∞	ADP
ejpam-3328	106	27	f(s	f(	NOUN
ejpam-3328	106	28	)	)	PUNCT
ejpam-3328	106	29	s−	s−	PROPN
ejpam-3328	106	30	z	z	PROPN
ejpam-3328	106	31	ds	ds	PROPN
ejpam-3328	106	32	,	,	PUNCT
ejpam-3328	106	33	i	i	PRON
ejpam-3328	106	34	m	m	VERB
ejpam-3328	106	35	z	z	NOUN
ejpam-3328	106	36	>	>	X
ejpam-3328	106	37	0	0	NUM
ejpam-3328	106	38	,	,	PUNCT
ejpam-3328	106	39	t−f	t−f	X
ejpam-3328	106	40	=	=	SYM
ejpam-3328	106	41	1	1	NUM
ejpam-3328	106	42	2πi	2πi	NOUN
ejpam-3328	106	43	lim	lim	PROPN
ejpam-3328	106	44	imz→0	imz→0	PROPN
ejpam-3328	106	45	∞∫	∞∫	PROPN
ejpam-3328	106	46	−∞	−∞	ADP
ejpam-3328	106	47	f(s	f(	NOUN
ejpam-3328	106	48	)	)	PUNCT
ejpam-3328	106	49	s−	s−	PROPN
ejpam-3328	106	50	z	z	PROPN
ejpam-3328	106	51	ds	ds	PROPN
ejpam-3328	106	52	,	,	PUNCT
ejpam-3328	106	53	i	i	PRON
ejpam-3328	106	54	m	m	VERB
ejpam-3328	106	55	z	z	NOUN
ejpam-3328	106	56	<	<	X
ejpam-3328	106	57	0	0	PROPN
ejpam-3328	106	58	,	,	PUNCT
ejpam-3328	106	59	t	t	PROPN
ejpam-3328	106	60	f	f	PROPN
ejpam-3328	106	61	=	=	SYM
ejpam-3328	106	62	1	1	NUM
ejpam-3328	106	63	2	2	NUM
ejpam-3328	106	64	(	(	PUNCT
ejpam-3328	106	65	t+	t+	NOUN
ejpam-3328	106	66	+	+	CCONJ
ejpam-3328	106	67	t−)f	t−)f	NOUN
ejpam-3328	106	68	.	.	PUNCT
ejpam-3328	107	1	consider	consider	VERB
ejpam-3328	107	2	the	the	DET
ejpam-3328	107	3	riemann	riemann	PROPN
ejpam-3328	107	4	problem	problem	NOUN
ejpam-3328	107	5	of	of	ADP
ejpam-3328	107	6	finding	find	VERB
ejpam-3328	107	7	a	a	DET
ejpam-3328	107	8	function	function	NOUN
ejpam-3328	107	9	φ	φ	NOUN
ejpam-3328	107	10	that	that	PRON
ejpam-3328	107	11	is	be	AUX
ejpam-3328	107	12	analytic	analytic	ADJ
ejpam-3328	107	13	in	in	ADP
ejpam-3328	107	14	the	the	DET
ejpam-3328	107	15	complex	complex	ADJ
ejpam-3328	107	16	plane	plane	NOUN
ejpam-3328	107	17	with	with	ADP
ejpam-3328	107	18	a	a	DET
ejpam-3328	107	19	cut	cut	NOUN
ejpam-3328	107	20	along	along	ADP
ejpam-3328	107	21	the	the	DET
ejpam-3328	107	22	real	real	ADJ
ejpam-3328	107	23	axis	axis	NOUN
ejpam-3328	107	24	.	.	PUNCT
ejpam-3328	108	1	values	value	NOUN
ejpam-3328	108	2	of	of	ADP
ejpam-3328	108	3	φ	φ	PROPN
ejpam-3328	108	4	on	on	ADP
ejpam-3328	108	5	the	the	DET
ejpam-3328	108	6	two	two	NUM
ejpam-3328	108	7	sides	side	NOUN
ejpam-3328	108	8	of	of	ADP
ejpam-3328	108	9	the	the	DET
ejpam-3328	108	10	cut	cut	NOUN
ejpam-3328	108	11	are	be	AUX
ejpam-3328	108	12	denoted	denote	VERB
ejpam-3328	108	13	as	as	ADP
ejpam-3328	108	14	φ+	φ+	NOUN
ejpam-3328	108	15	and	and	CCONJ
ejpam-3328	108	16	φ−.	φ−.	VERB
ejpam-3328	108	17	the	the	DET
ejpam-3328	108	18	following	follow	VERB
ejpam-3328	108	19	presents	present	VERB
ejpam-3328	108	20	the	the	DET
ejpam-3328	108	21	results	result	NOUN
ejpam-3328	108	22	of	of	ADP
ejpam-3328	108	23	[	[	X
ejpam-3328	108	24	12	12	NUM
ejpam-3328	108	25	]	]	X
ejpam-3328	108	26	:	:	PUNCT
ejpam-3328	108	27	a.	a.	NOUN
ejpam-3328	108	28	durmagambetov	durmagambetov	PROPN
ejpam-3328	108	29	/	/	SYM
ejpam-3328	108	30	eur	eur	PROPN
ejpam-3328	108	31	.	.	PUNCT
ejpam-3328	109	1	j.	j.	PROPN
ejpam-3328	109	2	pure	pure	PROPN
ejpam-3328	109	3	appl	appl	PROPN
ejpam-3328	109	4	.	.	PROPN
ejpam-3328	109	5	math	math	PROPN
ejpam-3328	109	6	,	,	PUNCT
ejpam-3328	109	7	11	11	NUM
ejpam-3328	109	8	(	(	PUNCT
ejpam-3328	109	9	4	4	NUM
ejpam-3328	109	10	)	)	PUNCT
ejpam-3328	109	11	(	(	PUNCT
ejpam-3328	109	12	2018	2018	NUM
ejpam-3328	109	13	)	)	PUNCT
ejpam-3328	109	14	,	,	PUNCT
ejpam-3328	109	15	1143	1143	NUM
ejpam-3328	109	16	-	-	SYM
ejpam-3328	109	17	1176	1176	NUM
ejpam-3328	109	18	1148	1148	NUM
ejpam-3328	109	19	lemma	lemma	PROPN
ejpam-3328	109	20	3	3	NUM
ejpam-3328	109	21	.	.	PUNCT
ejpam-3328	109	22	tt	tt	PROPN
ejpam-3328	110	1	=	=	NOUN
ejpam-3328	110	2	1	1	NUM
ejpam-3328	110	3	4	4	NUM
ejpam-3328	110	4	i	i	NOUN
ejpam-3328	110	5	,	,	PUNCT
ejpam-3328	110	6	tt+	tt+	NOUN
ejpam-3328	110	7	=	=	NOUN
ejpam-3328	110	8	1	1	NUM
ejpam-3328	110	9	2	2	NUM
ejpam-3328	110	10	t+	t+	VERB
ejpam-3328	110	11	,	,	PUNCT
ejpam-3328	110	12	tt−	tt−	PUNCT
ejpam-3328	110	13	=	=	SYM
ejpam-3328	110	14	−1	−1	NOUN
ejpam-3328	110	15	2	2	NUM
ejpam-3328	110	16	t−	t−	NOUN
ejpam-3328	110	17	,	,	PUNCT
ejpam-3328	110	18	t+	t+	PUNCT
ejpam-3328	110	19	=	=	SYM
ejpam-3328	110	20	t	t	PROPN
ejpam-3328	110	21	+	+	CCONJ
ejpam-3328	110	22	1	1	NUM
ejpam-3328	110	23	2	2	NUM
ejpam-3328	110	24	i	i	NOUN
ejpam-3328	110	25	,	,	PUNCT
ejpam-3328	110	26	t−	t−	PROPN
ejpam-3328	110	27	=	=	SYM
ejpam-3328	110	28	t	t	PROPN
ejpam-3328	110	29	−	−	NUM
ejpam-3328	110	30	1	1	NUM
ejpam-3328	110	31	2	2	NUM
ejpam-3328	110	32	i	i	NOUN
ejpam-3328	110	33	,	,	PUNCT
ejpam-3328	110	34	t−t−	t−t−	AUX
ejpam-3328	110	35	=	=	SYM
ejpam-3328	110	36	−t−.	−t−.	PROPN
ejpam-3328	110	37	denote	denote	VERB
ejpam-3328	110	38	φ+(k	φ+(k	PROPN
ejpam-3328	110	39	,	,	PUNCT
ejpam-3328	110	40	θ	θ	PROPN
ejpam-3328	110	41	,	,	PUNCT
ejpam-3328	110	42	x	x	NOUN
ejpam-3328	110	43	)	)	PUNCT
ejpam-3328	110	44	=	=	SYM
ejpam-3328	110	45	ψ+(k	ψ+(k	PROPN
ejpam-3328	110	46	,	,	PUNCT
ejpam-3328	110	47	θ	θ	NOUN
ejpam-3328	110	48	,	,	PUNCT
ejpam-3328	110	49	x)−ψ0(k	x)−ψ0(k	X
ejpam-3328	110	50	,	,	PUNCT
ejpam-3328	110	51	θ	θ	PROPN
ejpam-3328	110	52	,	,	PUNCT
ejpam-3328	110	53	x	x	NOUN
ejpam-3328	110	54	)	)	PUNCT
ejpam-3328	110	55	,	,	PUNCT
ejpam-3328	110	56	φ−(k	φ−(k	PROPN
ejpam-3328	110	57	,	,	PUNCT
ejpam-3328	110	58	θ	θ	PROPN
ejpam-3328	110	59	,	,	PUNCT
ejpam-3328	110	60	x	x	NOUN
ejpam-3328	110	61	)	)	PUNCT
ejpam-3328	110	62	=	=	SYM
ejpam-3328	111	1	ψ−(k,−θ	ψ−(k,−θ	NOUN
ejpam-3328	111	2	,	,	PUNCT
ejpam-3328	111	3	x)−ψ0(k	x)−ψ0(k	X
ejpam-3328	111	4	,	,	PUNCT
ejpam-3328	111	5	θ	θ	PROPN
ejpam-3328	111	6	,	,	PUNCT
ejpam-3328	111	7	x	x	NOUN
ejpam-3328	111	8	)	)	PUNCT
ejpam-3328	111	9	,	,	PUNCT
ejpam-3328	111	10	g(k	g(k	NOUN
ejpam-3328	111	11	,	,	PUNCT
ejpam-3328	111	12	θ	θ	PROPN
ejpam-3328	111	13	,	,	PUNCT
ejpam-3328	111	14	x	x	NOUN
ejpam-3328	111	15	)	)	PUNCT
ejpam-3328	111	16	=	=	SYM
ejpam-3328	111	17	φ+(k	φ+(k	NOUN
ejpam-3328	111	18	,	,	PUNCT
ejpam-3328	111	19	θ	θ	PROPN
ejpam-3328	111	20	,	,	PUNCT
ejpam-3328	111	21	x)−	x)−	PROPN
ejpam-3328	111	22	φ−(k	φ−(k	PROPN
ejpam-3328	111	23	,	,	PUNCT
ejpam-3328	111	24	θ	θ	PROPN
ejpam-3328	111	25	,	,	PUNCT
ejpam-3328	111	26	x)/	x)/	NOUN
ejpam-3328	111	27	lemma	lemma	PROPN
ejpam-3328	111	28	4	4	X
ejpam-3328	111	29	.	.	PUNCT
ejpam-3328	112	1	let	let	VERB
ejpam-3328	112	2	q	q	PROPN
ejpam-3328	112	3	∈	∈	PROPN
ejpam-3328	112	4	r	r	NOUN
ejpam-3328	112	5	,	,	PUNCT
ejpam-3328	112	6	n(q	n(q	PROPN
ejpam-3328	112	7	)	)	PUNCT
ejpam-3328	112	8	<	<	X
ejpam-3328	112	9	1	1	NUM
ejpam-3328	112	10	,	,	PUNCT
ejpam-3328	112	11	g+	g+	NOUN
ejpam-3328	112	12	=	=	SYM
ejpam-3328	112	13	g(k	g(k	PROPN
ejpam-3328	112	14	,	,	PUNCT
ejpam-3328	112	15	θ	θ	PROPN
ejpam-3328	112	16	,	,	PUNCT
ejpam-3328	112	17	x	x	NOUN
ejpam-3328	112	18	)	)	PUNCT
ejpam-3328	112	19	,	,	PUNCT
ejpam-3328	112	20	and	and	CCONJ
ejpam-3328	112	21	g−	g−	ADJ
ejpam-3328	112	22	=	=	SYM
ejpam-3328	112	23	g(k,−θ	g(k,−θ	PROPN
ejpam-3328	112	24	,	,	PUNCT
ejpam-3328	112	25	x	x	X
ejpam-3328	112	26	)	)	PUNCT
ejpam-3328	112	27	.	.	PUNCT
ejpam-3328	113	1	then	then	ADV
ejpam-3328	113	2	,	,	PUNCT
ejpam-3328	113	3	φ+(k	φ+(k	PROPN
ejpam-3328	113	4	,	,	PUNCT
ejpam-3328	113	5	θ	θ	NOUN
ejpam-3328	113	6	,	,	PUNCT
ejpam-3328	113	7	x	x	NOUN
ejpam-3328	113	8	)	)	PUNCT
ejpam-3328	113	9	=	=	PUNCT
ejpam-3328	113	10	t+g+	t+g+	NOUN
ejpam-3328	113	11	+	+	CCONJ
ejpam-3328	113	12	eikθx	eikθx	ADJ
ejpam-3328	113	13	,	,	PUNCT
ejpam-3328	113	14	φ−(k	φ−(k	PROPN
ejpam-3328	113	15	,	,	PUNCT
ejpam-3328	113	16	θ	θ	PROPN
ejpam-3328	113	17	,	,	PUNCT
ejpam-3328	113	18	x	x	NOUN
ejpam-3328	113	19	)	)	PUNCT
ejpam-3328	113	20	=	=	SYM
ejpam-3328	113	21	t−g+	t−g+	PROPN
ejpam-3328	114	1	+	+	CCONJ
ejpam-3328	114	2	eikθx	eikθx	ADJ
ejpam-3328	114	3	.	.	PUNCT
ejpam-3328	115	1	proof	proof	NOUN
ejpam-3328	115	2	.	.	PUNCT
ejpam-3328	116	1	the	the	DET
ejpam-3328	116	2	proof	proof	NOUN
ejpam-3328	116	3	of	of	ADP
ejpam-3328	116	4	the	the	DET
ejpam-3328	116	5	above	above	ADJ
ejpam-3328	116	6	follows	follow	VERB
ejpam-3328	116	7	from	from	ADP
ejpam-3328	116	8	the	the	DET
ejpam-3328	116	9	classic	classic	ADJ
ejpam-3328	116	10	results	result	NOUN
ejpam-3328	116	11	for	for	ADP
ejpam-3328	116	12	the	the	DET
ejpam-3328	116	13	riemann	riemann	PROPN
ejpam-3328	116	14	problem	problem	NOUN
ejpam-3328	116	15	.	.	PUNCT
ejpam-3328	117	1	lemma	lemma	PROPN
ejpam-3328	117	2	5	5	X
ejpam-3328	117	3	.	.	PUNCT
ejpam-3328	118	1	let	let	VERB
ejpam-3328	118	2	q	q	PROPN
ejpam-3328	118	3	∈	∈	PROPN
ejpam-3328	118	4	r	r	NOUN
ejpam-3328	118	5	,	,	PUNCT
ejpam-3328	118	6	n(q	n(q	PROPN
ejpam-3328	118	7	)	)	PUNCT
ejpam-3328	118	8	<	<	X
ejpam-3328	118	9	1	1	NUM
ejpam-3328	118	10	,	,	PUNCT
ejpam-3328	118	11	g+	g+	NOUN
ejpam-3328	118	12	=	=	SYM
ejpam-3328	118	13	g(k	g(k	PROPN
ejpam-3328	118	14	,	,	PUNCT
ejpam-3328	118	15	θ	θ	PROPN
ejpam-3328	118	16	,	,	PUNCT
ejpam-3328	118	17	x	x	NOUN
ejpam-3328	118	18	)	)	PUNCT
ejpam-3328	118	19	,	,	PUNCT
ejpam-3328	118	20	and	and	CCONJ
ejpam-3328	118	21	g−	g−	ADJ
ejpam-3328	118	22	=	=	SYM
ejpam-3328	118	23	g(k,−θ	g(k,−θ	PROPN
ejpam-3328	118	24	,	,	PUNCT
ejpam-3328	118	25	x	x	NOUN
ejpam-3328	118	26	)	)	PUNCT
ejpam-3328	118	27	,	,	PUNCT
ejpam-3328	118	28	)	)	PUNCT
ejpam-3328	118	29	.	.	PUNCT
ejpam-3328	119	1	then	then	ADV
ejpam-3328	119	2	,	,	PUNCT
ejpam-3328	119	3	ψ+(k	ψ+(k	X
ejpam-3328	119	4	,	,	PUNCT
ejpam-3328	119	5	θ	θ	NOUN
ejpam-3328	119	6	,	,	PUNCT
ejpam-3328	119	7	x	x	NOUN
ejpam-3328	119	8	)	)	PUNCT
ejpam-3328	119	9	=	=	SYM
ejpam-3328	119	10	(	(	PUNCT
ejpam-3328	119	11	t+g+	t+g+	X
ejpam-3328	119	12	+	+	X
ejpam-3328	119	13	eikθx	eikθx	ADJ
ejpam-3328	119	14	)	)	PUNCT
ejpam-3328	119	15	,	,	PUNCT
ejpam-3328	119	16	ψ−(k	ψ−(k	PROPN
ejpam-3328	119	17	,	,	PUNCT
ejpam-3328	119	18	θ	θ	PROPN
ejpam-3328	119	19	,	,	PUNCT
ejpam-3328	119	20	x	x	NOUN
ejpam-3328	119	21	)	)	PUNCT
ejpam-3328	119	22	=	=	SYM
ejpam-3328	119	23	(	(	PUNCT
ejpam-3328	119	24	t−g−	t−g−	ADP
ejpam-3328	119	25	+	+	X
ejpam-3328	119	26	e−ikθx	e−ikθx	NOUN
ejpam-3328	119	27	)	)	PUNCT
ejpam-3328	119	28	.	.	PUNCT
ejpam-3328	120	1	proof	proof	NOUN
ejpam-3328	120	2	.	.	PUNCT
ejpam-3328	121	1	the	the	DET
ejpam-3328	121	2	proof	proof	NOUN
ejpam-3328	121	3	of	of	ADP
ejpam-3328	121	4	the	the	DET
ejpam-3328	121	5	above	above	ADJ
ejpam-3328	121	6	follows	follow	VERB
ejpam-3328	121	7	from	from	ADP
ejpam-3328	121	8	the	the	DET
ejpam-3328	121	9	definitions	definition	NOUN
ejpam-3328	121	10	of	of	ADP
ejpam-3328	121	11	g	g	NOUN
ejpam-3328	121	12	,	,	PUNCT
ejpam-3328	121	13	φ±	φ±	PROPN
ejpam-3328	121	14	,	,	PUNCT
ejpam-3328	121	15	and	and	CCONJ
ejpam-3328	121	16	ψ±	ψ±	PROPN
ejpam-3328	121	17	.	.	PUNCT
ejpam-3328	122	1	lemma	lemma	PROPN
ejpam-3328	122	2	6	6	NUM
ejpam-3328	122	3	.	.	PUNCT
ejpam-3328	123	1	let	let	VERB
ejpam-3328	123	2	sup	sup	NOUN
ejpam-3328	123	3	k	k	PROPN
ejpam-3328	123	4	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-3328	123	5	∞∫	∞∫	PROPN
ejpam-3328	123	6	−∞	−∞	PUNCT
ejpam-3328	123	7	pa(p	pa(p	NOUN
ejpam-3328	123	8	,	,	PUNCT
ejpam-3328	123	9	θ	θ	PROPN
ejpam-3328	123	10	′	′	NUM
ejpam-3328	123	11	,	,	PUNCT
ejpam-3328	123	12	θ	θ	NOUN
ejpam-3328	123	13	)	)	PUNCT
ejpam-3328	123	14	4π(p−	4π(p−	NUM
ejpam-3328	124	1	k	k	PROPN
ejpam-3328	124	2	+	+	CCONJ
ejpam-3328	124	3	i0	i0	PROPN
ejpam-3328	124	4	)	)	PUNCT
ejpam-3328	124	5	dp	dp	NOUN
ejpam-3328	124	6	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-3328	124	7	<	<	X
ejpam-3328	124	8	α	α	PROPN
ejpam-3328	124	9	,	,	PUNCT
ejpam-3328	124	10	∫	∫	PROPN
ejpam-3328	124	11	s2	s2	PROPN
ejpam-3328	124	12	αdθ	αdθ	NOUN
ejpam-3328	124	13	<	<	X
ejpam-3328	124	14	1/2	1/2	NUM
ejpam-3328	124	15	.	.	PUNCT
ejpam-3328	125	1	then	then	ADV
ejpam-3328	125	2	,	,	PUNCT
ejpam-3328	125	3	∏	∏	PROPN
ejpam-3328	125	4	0≤j	0≤j	PROPN
ejpam-3328	125	5	<	<	X
ejpam-3328	125	6	n	n	NOUN
ejpam-3328	125	7	∫	∫	PROPN
ejpam-3328	125	8	s2	s2	PROPN
ejpam-3328	125	9	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-3328	125	10	∫	∫	PROPN
ejpam-3328	125	11	∞	∞	PROPN
ejpam-3328	126	1	−∞	−∞	PUNCT
ejpam-3328	126	2	kja(kj	kja(kj	NOUN
ejpam-3328	126	3	,	,	PUNCT
ejpam-3328	126	4	θ	θ	NOUN
ejpam-3328	126	5	′	′	NUM
ejpam-3328	126	6	kj	kj	PROPN
ejpam-3328	126	7	,	,	PUNCT
ejpam-3328	126	8	θkj	θkj	NOUN
ejpam-3328	126	9	)	)	PUNCT
ejpam-3328	127	1	4π(kj+1	4π(kj+1	NUM
ejpam-3328	127	2	−	−	NOUN
ejpam-3328	127	3	kj	kj	PROPN
ejpam-3328	127	4	+	+	CCONJ
ejpam-3328	127	5	i0	i0	PROPN
ejpam-3328	127	6	)	)	PUNCT
ejpam-3328	127	7	dkj	dkj	NOUN
ejpam-3328	127	8	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-3328	127	9	dθkj	dθkj	NOUN
ejpam-3328	127	10	≤	≤	NOUN
ejpam-3328	127	11	2−n	2−n	NUM
ejpam-3328	127	12	.	.	PUNCT
ejpam-3328	128	1	proof	proof	NOUN
ejpam-3328	128	2	.	.	PUNCT
ejpam-3328	129	1	denote	denote	VERB
ejpam-3328	129	2	αj	αj	X
ejpam-3328	130	1	=	=	NOUN
ejpam-3328	130	2	∣∣∣∣∣v	∣∣∣∣∣v	PROPN
ejpam-3328	131	1	p	p	X
ejpam-3328	131	2	∫	∫	PROPN
ejpam-3328	131	3	∞	∞	PROPN
ejpam-3328	131	4	−∞	−∞	PUNCT
ejpam-3328	131	5	kja(kj	kja(kj	NOUN
ejpam-3328	131	6	,	,	PUNCT
ejpam-3328	131	7	θ	θ	NOUN
ejpam-3328	131	8	′	′	NUM
ejpam-3328	132	1	kj	kj	PROPN
ejpam-3328	132	2	,	,	PUNCT
ejpam-3328	132	3	θkj	θkj	NOUN
ejpam-3328	132	4	)	)	PUNCT
ejpam-3328	133	1	4π(kj+1	4π(kj+1	NUM
ejpam-3328	133	2	−	−	NOUN
ejpam-3328	133	3	kj	kj	PROPN
ejpam-3328	133	4	+	+	CCONJ
ejpam-3328	133	5	i0	i0	PROPN
ejpam-3328	133	6	)	)	PUNCT
ejpam-3328	133	7	dkj	dkj	PROPN
ejpam-3328	133	8	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-3328	133	9	,	,	PUNCT
ejpam-3328	133	10	therefore	therefore	ADV
ejpam-3328	133	11	,	,	PUNCT
ejpam-3328	133	12	∏	∏	PROPN
ejpam-3328	133	13	0≤j	0≤j	NUM
ejpam-3328	133	14	<	<	X
ejpam-3328	133	15	n	n	NOUN
ejpam-3328	133	16	∫	∫	PROPN
ejpam-3328	133	17	s2	s2	PROPN
ejpam-3328	133	18	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-3328	133	19	∫	∫	PROPN
ejpam-3328	134	1	∞	∞	PROPN
ejpam-3328	134	2	−∞	−∞	PUNCT
ejpam-3328	134	3	kja(kj	kja(kj	NOUN
ejpam-3328	134	4	,	,	PUNCT
ejpam-3328	134	5	θ	θ	NOUN
ejpam-3328	134	6	′	′	NUM
ejpam-3328	135	1	kj	kj	PROPN
ejpam-3328	135	2	,	,	PUNCT
ejpam-3328	135	3	θkj	θkj	NOUN
ejpam-3328	135	4	)	)	PUNCT
ejpam-3328	136	1	4π(kj+1	4π(kj+1	NUM
ejpam-3328	136	2	−	−	NOUN
ejpam-3328	136	3	kj	kj	PROPN
ejpam-3328	136	4	+	+	CCONJ
ejpam-3328	136	5	i0	i0	PROPN
ejpam-3328	136	6	)	)	PUNCT
ejpam-3328	136	7	dkj	dkj	NOUN
ejpam-3328	136	8	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-3328	136	9	dθkj	dθkj	NOUN
ejpam-3328	136	10	≤	≤	PUNCT
ejpam-3328	136	11	∏	∏	NUM
ejpam-3328	136	12	0≤j	0≤j	PROPN
ejpam-3328	136	13	<	<	NOUN
ejpam-3328	136	14	n	n	NOUN
ejpam-3328	136	15	∫	∫	PROPN
ejpam-3328	136	16	s2	s2	PROPN
ejpam-3328	136	17	αjdθkj	αjdθkj	NOUN
ejpam-3328	136	18	<	<	X
ejpam-3328	136	19	2−n	2−n	NUM
ejpam-3328	136	20	.	.	PUNCT
ejpam-3328	137	1	this	this	PRON
ejpam-3328	137	2	completes	complete	VERB
ejpam-3328	137	3	the	the	DET
ejpam-3328	137	4	proof	proof	NOUN
ejpam-3328	137	5	.	.	PUNCT
ejpam-3328	138	1	a.	a.	NOUN
ejpam-3328	138	2	durmagambetov	durmagambetov	PROPN
ejpam-3328	138	3	/	/	SYM
ejpam-3328	138	4	eur	eur	PROPN
ejpam-3328	138	5	.	.	PUNCT
ejpam-3328	139	1	j.	j.	PROPN
ejpam-3328	139	2	pure	pure	PROPN
ejpam-3328	139	3	appl	appl	PROPN
ejpam-3328	139	4	.	.	PROPN
ejpam-3328	139	5	math	math	PROPN
ejpam-3328	139	6	,	,	PUNCT
ejpam-3328	139	7	11	11	NUM
ejpam-3328	139	8	(	(	PUNCT
ejpam-3328	139	9	4	4	NUM
ejpam-3328	139	10	)	)	PUNCT
ejpam-3328	139	11	(	(	PUNCT
ejpam-3328	139	12	2018	2018	NUM
ejpam-3328	139	13	)	)	PUNCT
ejpam-3328	139	14	,	,	PUNCT
ejpam-3328	139	15	1143	1143	NUM
ejpam-3328	139	16	-	-	SYM
ejpam-3328	139	17	1176	1176	NUM
ejpam-3328	139	18	1149	1149	NUM
ejpam-3328	139	19	lemma	lemma	PROPN
ejpam-3328	139	20	7	7	NUM
ejpam-3328	139	21	.	.	PUNCT
ejpam-3328	140	1	let	let	VERB
ejpam-3328	140	2	sup	sup	NOUN
ejpam-3328	140	3	k	k	PROPN
ejpam-3328	140	4	∫	∫	PROPN
ejpam-3328	140	5	s2	s2	PROPN
ejpam-3328	140	6	|t−qk|	|t−qk|	PROPN
ejpam-3328	141	1	dθ	dθ	PROPN
ejpam-3328	141	2	≤	≤	PUNCT
ejpam-3328	142	1	α	α	PRON
ejpam-3328	142	2	<	<	X
ejpam-3328	142	3	1	1	NUM
ejpam-3328	142	4	2c	2c	NUM
ejpam-3328	142	5	<	<	X
ejpam-3328	142	6	1	1	NUM
ejpam-3328	142	7	,	,	PUNCT
ejpam-3328	142	8	sup	sup	PROPN
ejpam-3328	142	9	k	k	PROPN
ejpam-3328	142	10	∫	∫	PROPN
ejpam-3328	142	11	s2	s2	PROPN
ejpam-3328	142	12	|t−q̃k|	|t−q̃k|	NOUN
ejpam-3328	142	13	dθ	dθ	VERB
ejpam-3328	142	14	≤	≤	NUM
ejpam-3328	143	1	α	α	PRON
ejpam-3328	143	2	<	<	X
ejpam-3328	143	3	1	1	NUM
ejpam-3328	143	4	2c	2c	NUM
ejpam-3328	143	5	<	<	X
ejpam-3328	143	6	1	1	NUM
ejpam-3328	143	7	,	,	PUNCT
ejpam-3328	143	8	sup	sup	PROPN
ejpam-3328	143	9	k	k	PROPN
ejpam-3328	143	10	∫	∫	PROPN
ejpam-3328	143	11	s2	s2	PROPN
ejpam-3328	143	12	∣∣t−qq̃k2	∣∣t−qq̃k2	X
ejpam-3328	143	13	∣∣	∣∣	NUM
ejpam-3328	143	14	dθ	dθ	PROPN
ejpam-3328	143	15	≤	≤	PUNCT
ejpam-3328	144	1	α	α	PRON
ejpam-3328	144	2	<	<	X
ejpam-3328	144	3	1	1	NUM
ejpam-3328	144	4	2c	2c	NUM
ejpam-3328	144	5	<	<	X
ejpam-3328	144	6	1	1	NUM
ejpam-3328	144	7	.	.	PUNCT
ejpam-3328	145	1	then	then	ADV
ejpam-3328	145	2	,	,	PUNCT
ejpam-3328	145	3	sup	sup	PROPN
ejpam-3328	145	4	k	k	PROPN
ejpam-3328	145	5	∫	∫	PROPN
ejpam-3328	145	6	s2	s2	PROPN
ejpam-3328	145	7	|t−ak|	|t−ak|	PROPN
ejpam-3328	146	1	dθ	dθ	PROPN
ejpam-3328	146	2	≤	≤	PROPN
ejpam-3328	146	3	c	c	PROPN
ejpam-3328	146	4	∫	∫	PROPN
ejpam-3328	146	5	s2	s2	PROPN
ejpam-3328	146	6	|t−qk|	|t−qk|	PROPN
ejpam-3328	147	1	dθ	dθ	PROPN
ejpam-3328	147	2	1−	1−	NUM
ejpam-3328	147	3	sup	sup	NOUN
ejpam-3328	147	4	k	k	PROPN
ejpam-3328	147	5	∫	∫	PROPN
ejpam-3328	147	6	s2	s2	PROPN
ejpam-3328	147	7	|t−aq̃k2|	|t−aq̃k2|	PUNCT
ejpam-3328	147	8	dθ	dθ	PROPN
ejpam-3328	147	9	,	,	PUNCT
ejpam-3328	147	10	sup	sup	PROPN
ejpam-3328	147	11	k	k	PROPN
ejpam-3328	147	12	∣∣∣∣∫	∣∣∣∣∫	PRON
ejpam-3328	147	13	s2	s2	NOUN
ejpam-3328	147	14	t−aq̃k	t−aq̃k	VERB
ejpam-3328	147	15	2dθ	2dθ	ADJ
ejpam-3328	147	16	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3328	147	17	≤	≤	NOUN
ejpam-3328	147	18	c	c	NOUN
ejpam-3328	147	19	∣∣t−	∣∣t−	VERB
ejpam-3328	147	20	∫s2	∫s2	NOUN
ejpam-3328	147	21	qq̃k	qq̃k	NOUN
ejpam-3328	147	22	2dθ	2dθ	NOUN
ejpam-3328	147	23	∣∣	∣∣	NUM
ejpam-3328	147	24	1−	1−	NUM
ejpam-3328	147	25	∣∣t−	∣∣t−	VERB
ejpam-3328	147	26	∫s2	∫s2	PROPN
ejpam-3328	147	27	q̃kdθ	q̃kdθ	NOUN
ejpam-3328	147	28	∣∣	∣∣	PUNCT
ejpam-3328	147	29	.	.	PUNCT
ejpam-3328	148	1	proof	proof	NOUN
ejpam-3328	148	2	.	.	PUNCT
ejpam-3328	149	1	by	by	ADP
ejpam-3328	149	2	the	the	DET
ejpam-3328	149	3	definition	definition	NOUN
ejpam-3328	149	4	of	of	ADP
ejpam-3328	149	5	the	the	DET
ejpam-3328	149	6	amplitude	amplitude	NOUN
ejpam-3328	149	7	and	and	CCONJ
ejpam-3328	149	8	lemma	lemma	PROPN
ejpam-3328	149	9	4	4	NUM
ejpam-3328	149	10	,	,	PUNCT
ejpam-3328	149	11	we	we	PRON
ejpam-3328	149	12	have	have	VERB
ejpam-3328	149	13	a(k	a(k	PROPN
ejpam-3328	149	14	,	,	PUNCT
ejpam-3328	149	15	θ	θ	PROPN
ejpam-3328	149	16	′	′	NUM
ejpam-3328	149	17	,	,	PUNCT
ejpam-3328	149	18	θ	θ	X
ejpam-3328	149	19	)	)	PUNCT
ejpam-3328	149	20	=	=	SYM
ejpam-3328	150	1	−	−	PROPN
ejpam-3328	150	2	1	1	NUM
ejpam-3328	150	3	4π	4π	NUM
ejpam-3328	150	4	∫	∫	PROPN
ejpam-3328	150	5	r3	r3	PROPN
ejpam-3328	150	6	q(x)ψ+(k	q(x)ψ+(k	PROPN
ejpam-3328	150	7	,	,	PUNCT
ejpam-3328	150	8	θ	θ	PROPN
ejpam-3328	150	9	,	,	PUNCT
ejpam-3328	150	10	x)e−ikθ	x)e−ikθ	PROPN
ejpam-3328	150	11	′	′	NUM
ejpam-3328	150	12	xdx	xdx	PROPN
ejpam-3328	150	13	=	=	PUNCT
ejpam-3328	151	1	−	−	PROPN
ejpam-3328	151	2	1	1	NUM
ejpam-3328	151	3	4π	4π	NUM
ejpam-3328	151	4	∫	∫	PROPN
ejpam-3328	151	5	r3	r3	PROPN
ejpam-3328	151	6	q(x	q(x	PROPN
ejpam-3328	151	7	)	)	PUNCT
ejpam-3328	152	1	[	[	PUNCT
ejpam-3328	152	2	eikθ	eikθ	NOUN
ejpam-3328	152	3	′	′	NUM
ejpam-3328	152	4	x	x	PUNCT
ejpam-3328	153	1	+	+	PUNCT
ejpam-3328	153	2	t+g(k	t+g(k	NUM
ejpam-3328	153	3	,	,	PUNCT
ejpam-3328	153	4	θ	θ	PROPN
ejpam-3328	153	5	,	,	PUNCT
ejpam-3328	153	6	θ	θ	NOUN
ejpam-3328	153	7	′	′	NUM
ejpam-3328	153	8	)	)	PUNCT
ejpam-3328	153	9	]	]	PUNCT
ejpam-3328	153	10	e−ikθ	e−ikθ	VERB
ejpam-3328	153	11	′	′	NUM
ejpam-3328	153	12	xdx	xdx	PROPN
ejpam-3328	153	13	.	.	PUNCT
ejpam-3328	154	1	we	we	PRON
ejpam-3328	154	2	can	can	AUX
ejpam-3328	154	3	rewrite	rewrite	VERB
ejpam-3328	154	4	this	this	PRON
ejpam-3328	154	5	as	as	ADP
ejpam-3328	154	6	a(k	a(k	PROPN
ejpam-3328	154	7	,	,	PUNCT
ejpam-3328	154	8	θ	θ	PROPN
ejpam-3328	154	9	′	′	NUM
ejpam-3328	154	10	,	,	PUNCT
ejpam-3328	154	11	θ	θ	X
ejpam-3328	154	12	)	)	PUNCT
ejpam-3328	154	13	=	=	SYM
ejpam-3328	155	1	−	−	PROPN
ejpam-3328	155	2	1	1	NUM
ejpam-3328	155	3	4π	4π	NUM
ejpam-3328	155	4	∫	∫	PROPN
ejpam-3328	155	5	r3	r3	PROPN
ejpam-3328	155	6	q(x	q(x	PROPN
ejpam-3328	155	7	)	)	PUNCT
ejpam-3328	155	8	eikθx	eikθx	NUM
ejpam-3328	156	1	+	+	CCONJ
ejpam-3328	156	2	∑	∑	ADV
ejpam-3328	156	3	n≥0	n≥0	PROPN
ejpam-3328	156	4	(	(	PUNCT
ejpam-3328	156	5	−t−d)nψ0	−t−d)nψ0	PROPN
ejpam-3328	156	6			NOUN
ejpam-3328	156	7	e−ikθ′xdx	e−ikθ′xdx	PROPN
ejpam-3328	156	8	.	.	PUNCT
ejpam-3328	157	1	(	(	PUNCT
ejpam-3328	157	2	5	5	X
ejpam-3328	157	3	)	)	PUNCT
ejpam-3328	157	4	lemma	lemma	PROPN
ejpam-3328	157	5	6	6	NUM
ejpam-3328	157	6	yields	yield	NOUN
ejpam-3328	157	7	sup	sup	PROPN
ejpam-3328	157	8	k	k	PROPN
ejpam-3328	157	9	∫	∫	PROPN
ejpam-3328	158	1	s2	s2	PROPN
ejpam-3328	158	2	|t−ak|	|t−ak|	PROPN
ejpam-3328	159	1	dθ	dθ	PROPN
ejpam-3328	159	2	≤	≤	PROPN
ejpam-3328	159	3	sup	sup	PROPN
ejpam-3328	159	4	k	k	PROPN
ejpam-3328	159	5	∫	∫	PROPN
ejpam-3328	159	6	s2	s2	PROPN
ejpam-3328	159	7	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3328	159	8	1	1	NUM
ejpam-3328	159	9	4π	4π	NUM
ejpam-3328	159	10	t−qk	t−qk	ADJ
ejpam-3328	159	11	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3328	159	12	dθ	dθ	PROPN
ejpam-3328	159	13	+	+	CCONJ
ejpam-3328	159	14	(	(	PUNCT
ejpam-3328	159	15	sup	sup	NOUN
ejpam-3328	159	16	k	k	PROPN
ejpam-3328	159	17	∫	∫	PROPN
ejpam-3328	159	18	s2	s2	PROPN
ejpam-3328	159	19	|t−ka|	|t−ka|	PROPN
ejpam-3328	160	1	dθ	dθ	PROPN
ejpam-3328	160	2	)	)	PUNCT
ejpam-3328	160	3	2	2	NUM
ejpam-3328	160	4	∫	∫	NOUN
ejpam-3328	160	5	s2	s2	PROPN
ejpam-3328	160	6	∣∣t−aq̃k2	∣∣t−aq̃k2	NOUN
ejpam-3328	160	7	∣∣	∣∣	NUM
ejpam-3328	160	8	dθ	dθ	PROPN
ejpam-3328	160	9	(	(	PUNCT
ejpam-3328	160	10	1−	1−	NUM
ejpam-3328	160	11	sup	sup	NOUN
ejpam-3328	160	12	k	k	PROPN
ejpam-3328	160	13	∫	∫	PROPN
ejpam-3328	160	14	s2	s2	PROPN
ejpam-3328	160	15	|t−ka|	|t−ka|	PROPN
ejpam-3328	160	16	dθ	dθ	PROPN
ejpam-3328	160	17	)	)	PUNCT
ejpam-3328	160	18	2	2	NUM
ejpam-3328	160	19	.	.	PUNCT
ejpam-3328	161	1	owing	owe	VERB
ejpam-3328	161	2	to	to	ADP
ejpam-3328	161	3	the	the	DET
ejpam-3328	161	4	smallness	smallness	NOUN
ejpam-3328	161	5	of	of	ADP
ejpam-3328	161	6	the	the	DET
ejpam-3328	161	7	terms	term	NOUN
ejpam-3328	161	8	on	on	ADP
ejpam-3328	161	9	the	the	DET
ejpam-3328	161	10	right	right	ADJ
ejpam-3328	161	11	-	-	PUNCT
ejpam-3328	161	12	hand	hand	NOUN
ejpam-3328	161	13	side	side	NOUN
ejpam-3328	161	14	,	,	PUNCT
ejpam-3328	161	15	the	the	DET
ejpam-3328	161	16	following	follow	VERB
ejpam-3328	161	17	estimate	estimate	NOUN
ejpam-3328	161	18	follows	follow	VERB
ejpam-3328	161	19	:	:	PUNCT
ejpam-3328	162	1	sup	sup	PROPN
ejpam-3328	162	2	k	k	PROPN
ejpam-3328	162	3	∫	∫	PROPN
ejpam-3328	162	4	s2	s2	PROPN
ejpam-3328	162	5	|t−ak|	|t−ak|	PROPN
ejpam-3328	163	1	dθ	dθ	PROPN
ejpam-3328	163	2	≤	≤	ADJ
ejpam-3328	163	3	2	2	NUM
ejpam-3328	163	4	sup	sup	NOUN
ejpam-3328	163	5	k	k	PROPN
ejpam-3328	163	6	∫	∫	PROPN
ejpam-3328	163	7	s2	s2	PROPN
ejpam-3328	163	8	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3328	163	9	1	1	NUM
ejpam-3328	163	10	4π	4π	NUM
ejpam-3328	163	11	t−qk	t−qk	PROPN
ejpam-3328	163	12	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3328	163	13	dθ	dθ	PROPN
ejpam-3328	163	14	.	.	PUNCT
ejpam-3328	164	1	similarly	similarly	ADV
ejpam-3328	164	2	,	,	PUNCT
ejpam-3328	164	3	sup	sup	PROPN
ejpam-3328	164	4	k	k	PROPN
ejpam-3328	164	5	∫	∫	PROPN
ejpam-3328	164	6	s2	s2	PROPN
ejpam-3328	164	7	∣∣t−aq̃k2	∣∣t−aq̃k2	NOUN
ejpam-3328	164	8	∣∣	∣∣	NUM
ejpam-3328	164	9	dθ	dθ	PROPN
ejpam-3328	164	10	≤	≤	PROPN
ejpam-3328	164	11	c	c	PROPN
ejpam-3328	164	12	∫	∫	PROPN
ejpam-3328	164	13	s2	s2	PROPN
ejpam-3328	164	14	∣∣t−qq̃k2	∣∣t−qq̃k2	X
ejpam-3328	164	15	∣∣	∣∣	NUM
ejpam-3328	164	16	dθ	dθ	PROPN
ejpam-3328	164	17	+	+	PROPN
ejpam-3328	164	18	∫	∫	PROPN
ejpam-3328	164	19	s2	s2	PROPN
ejpam-3328	164	20	∣∣t−aq̃k2	∣∣t−aq̃k2	NOUN
ejpam-3328	164	21	∣∣	∣∣	NUM
ejpam-3328	164	22	dθ	dθ	PROPN
ejpam-3328	164	23	∫	∫	PROPN
ejpam-3328	164	24	s2	s2	PROPN
ejpam-3328	164	25	|t−q̃k|	|t−q̃k|	PROPN
ejpam-3328	164	26	dθ	dθ	PROPN
ejpam-3328	164	27	,	,	PUNCT
ejpam-3328	164	28	sup	sup	PROPN
ejpam-3328	164	29	k	k	PROPN
ejpam-3328	164	30	∫	∫	PROPN
ejpam-3328	164	31	s2	s2	PROPN
ejpam-3328	164	32	∣∣t−aq̃k2	∣∣t−aq̃k2	NOUN
ejpam-3328	164	33	∣∣	∣∣	NUM
ejpam-3328	164	34	dθ	dθ	PROPN
ejpam-3328	164	35	≤	≤	PROPN
ejpam-3328	164	36	c	c	PROPN
ejpam-3328	164	37	∫	∫	PROPN
ejpam-3328	164	38	s2	s2	PROPN
ejpam-3328	164	39	∣∣t−qq̃k2	∣∣t−qq̃k2	X
ejpam-3328	164	40	∣∣	∣∣	NUM
ejpam-3328	164	41	dθ	dθ	PROPN
ejpam-3328	164	42	1−	1−	NUM
ejpam-3328	164	43	∫	∫	PROPN
ejpam-3328	164	44	s2	s2	PROPN
ejpam-3328	164	45	|t−q̃k|	|t−q̃k|	PROPN
ejpam-3328	164	46	dθ	dθ	PROPN
ejpam-3328	164	47	,	,	PUNCT
ejpam-3328	164	48	a.	a.	NOUN
ejpam-3328	164	49	durmagambetov	durmagambetov	PROPN
ejpam-3328	164	50	/	/	SYM
ejpam-3328	164	51	eur	eur	PROPN
ejpam-3328	164	52	.	.	PUNCT
ejpam-3328	165	1	j.	j.	PROPN
ejpam-3328	165	2	pure	pure	PROPN
ejpam-3328	165	3	appl	appl	PROPN
ejpam-3328	165	4	.	.	PROPN
ejpam-3328	165	5	math	math	PROPN
ejpam-3328	165	6	,	,	PUNCT
ejpam-3328	165	7	11	11	NUM
ejpam-3328	165	8	(	(	PUNCT
ejpam-3328	165	9	4	4	NUM
ejpam-3328	165	10	)	)	PUNCT
ejpam-3328	165	11	(	(	PUNCT
ejpam-3328	165	12	2018	2018	NUM
ejpam-3328	165	13	)	)	PUNCT
ejpam-3328	165	14	,	,	PUNCT
ejpam-3328	165	15	1143	1143	NUM
ejpam-3328	165	16	-	-	SYM
ejpam-3328	165	17	1176	1176	NUM
ejpam-3328	165	18	1150	1150	NUM
ejpam-3328	165	19	sup	sup	NOUN
ejpam-3328	165	20	k	k	PROPN
ejpam-3328	165	21	∫	∫	PROPN
ejpam-3328	165	22	s2	s2	PROPN
ejpam-3328	165	23	∣∣t−aq̃k2	∣∣t−aq̃k2	NOUN
ejpam-3328	165	24	∣∣	∣∣	NUM
ejpam-3328	165	25	dθ	dθ	PROPN
ejpam-3328	165	26	≤	≤	NUM
ejpam-3328	165	27	2	2	NUM
ejpam-3328	165	28	sup	sup	NOUN
ejpam-3328	165	29	k	k	PROPN
ejpam-3328	165	30	∫	∫	PROPN
ejpam-3328	165	31	s2	s2	PROPN
ejpam-3328	165	32	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3328	165	33	1	1	NUM
ejpam-3328	165	34	4π	4π	NUM
ejpam-3328	165	35	t−qq̃k	t−qq̃k	PUNCT
ejpam-3328	165	36	2	2	NUM
ejpam-3328	165	37	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3328	165	38	dθ	dθ	PROPN
ejpam-3328	165	39	.	.	PUNCT
ejpam-3328	166	1	this	this	PRON
ejpam-3328	166	2	completes	complete	VERB
ejpam-3328	166	3	the	the	DET
ejpam-3328	166	4	proof	proof	NOUN
ejpam-3328	166	5	.	.	PUNCT
ejpam-3328	167	1	to	to	PART
ejpam-3328	167	2	simplify	simplify	VERB
ejpam-3328	167	3	the	the	DET
ejpam-3328	167	4	writing	writing	NOUN
ejpam-3328	167	5	of	of	ADP
ejpam-3328	167	6	the	the	DET
ejpam-3328	167	7	following	follow	VERB
ejpam-3328	167	8	calculations	calculation	NOUN
ejpam-3328	167	9	,	,	PUNCT
ejpam-3328	167	10	we	we	PRON
ejpam-3328	167	11	introduce	introduce	VERB
ejpam-3328	167	12	the	the	DET
ejpam-3328	167	13	set	set	NOUN
ejpam-3328	167	14	defined	define	VERB
ejpam-3328	167	15	by	by	ADP
ejpam-3328	167	16	mε(k	mε(k	ADJ
ejpam-3328	167	17	)	)	PUNCT
ejpam-3328	168	1	=	=	PRON
ejpam-3328	168	2	(	(	PUNCT
ejpam-3328	168	3	s|ε	s|ε	X
ejpam-3328	168	4	<	<	X
ejpam-3328	169	1	|s|+	|s|+	PROPN
ejpam-3328	169	2	|k	|k	NOUN
ejpam-3328	169	3	−	−	ADP
ejpam-3328	169	4	s|	s|	VERB
ejpam-3328	169	5	<	<	X
ejpam-3328	169	6	1	1	NUM
ejpam-3328	169	7	ε	ε	PROPN
ejpam-3328	169	8	)	)	PUNCT
ejpam-3328	169	9	.	.	PUNCT
ejpam-3328	170	1	the	the	DET
ejpam-3328	170	2	heaviside	heaviside	ADJ
ejpam-3328	170	3	function	function	NOUN
ejpam-3328	170	4	is	be	AUX
ejpam-3328	170	5	given	give	VERB
ejpam-3328	170	6	by	by	ADP
ejpam-3328	170	7	θ(x	θ(x	PROPN
ejpam-3328	170	8	)	)	PUNCT
ejpam-3328	170	9	=	=	PRON
ejpam-3328	171	1	{	{	PUNCT
ejpam-3328	171	2	1	1	NUM
ejpam-3328	171	3	,	,	PUNCT
ejpam-3328	171	4	if	if	SCONJ
ejpam-3328	171	5	x	x	PROPN
ejpam-3328	171	6	>	>	X
ejpam-3328	171	7	0	0	NUM
ejpam-3328	171	8	,	,	PUNCT
ejpam-3328	171	9	−1	−1	VERB
ejpam-3328	171	10	if	if	SCONJ
ejpam-3328	171	11	x	x	X
ejpam-3328	171	12	<	<	X
ejpam-3328	171	13	0	0	NUM
ejpam-3328	171	14	}	}	PUNCT
ejpam-3328	171	15	.	.	PUNCT
ejpam-3328	172	1	lemma	lemma	PROPN
ejpam-3328	172	2	8	8	NUM
ejpam-3328	172	3	.	.	PUNCT
ejpam-3328	173	1	let	let	VERB
ejpam-3328	173	2	q,∇q	q,∇q	PROPN
ejpam-3328	173	3	∈	∈	PROPN
ejpam-3328	173	4	∩l2(r3	∩l2(r3	ADP
ejpam-3328	173	5	)	)	PUNCT
ejpam-3328	173	6	,	,	PUNCT
ejpam-3328	173	7	|a|	|a|	PROPN
ejpam-3328	173	8	>	>	X
ejpam-3328	173	9	0	0	PROPN
ejpam-3328	173	10	.	.	PUNCT
ejpam-3328	174	1	then	then	ADV
ejpam-3328	174	2	,	,	PUNCT
ejpam-3328	174	3	πi	πi	ADV
ejpam-3328	174	4	∫	∫	PROPN
ejpam-3328	174	5	r3	r3	PROPN
ejpam-3328	174	6	θ(a)eik|x|aq(x)dx	θ(a)eik|x|aq(x)dx	PROPN
ejpam-3328	174	7	=	=	SYM
ejpam-3328	174	8	lim	lim	PROPN
ejpam-3328	174	9	ε→0	ε→0	X
ejpam-3328	175	1	∫	∫	PROPN
ejpam-3328	175	2	s∈mε(k	s∈mε(k	PROPN
ejpam-3328	175	3	)	)	PUNCT
ejpam-3328	175	4	∫	∫	PROPN
ejpam-3328	175	5	r3	r3	PROPN
ejpam-3328	176	1	eis|x|a	eis|x|a	PROPN
ejpam-3328	176	2	k	k	PROPN
ejpam-3328	177	1	−	−	PROPN
ejpam-3328	177	2	s	s	PART
ejpam-3328	177	3	q(x)dxds	q(x)dxds	NOUN
ejpam-3328	177	4	,	,	PUNCT
ejpam-3328	177	5	πi	πi	ADV
ejpam-3328	177	6	∫	∫	PROPN
ejpam-3328	177	7	r3	r3	PROPN
ejpam-3328	177	8	θ(a)keik|x|aq(x)dx	θ(a)keik|x|aq(x)dx	PROPN
ejpam-3328	177	9	=	=	PROPN
ejpam-3328	177	10	lim	lim	PROPN
ejpam-3328	177	11	ε→0	ε→0	X
ejpam-3328	177	12	∫	∫	PROPN
ejpam-3328	177	13	s∈mε(k	s∈mε(k	PROPN
ejpam-3328	177	14	)	)	PUNCT
ejpam-3328	177	15	∫	∫	PROPN
ejpam-3328	178	1	r3	r3	PROPN
ejpam-3328	178	2	s	s	PROPN
ejpam-3328	179	1	eis|x|a	eis|x|a	PROPN
ejpam-3328	179	2	k	k	PROPN
ejpam-3328	179	3	−	−	PROPN
ejpam-3328	179	4	s	s	PART
ejpam-3328	179	5	q(x)dxds	q(x)dxds	NOUN
ejpam-3328	179	6	.	.	PUNCT
ejpam-3328	180	1	proof	proof	NOUN
ejpam-3328	180	2	.	.	PUNCT
ejpam-3328	181	1	the	the	DET
ejpam-3328	181	2	lemma	lemma	PROPN
ejpam-3328	181	3	can	can	AUX
ejpam-3328	181	4	be	be	AUX
ejpam-3328	181	5	proved	prove	VERB
ejpam-3328	181	6	by	by	ADP
ejpam-3328	181	7	the	the	DET
ejpam-3328	181	8	conditions	condition	NOUN
ejpam-3328	181	9	of	of	ADP
ejpam-3328	181	10	lemma	lemma	PROPN
ejpam-3328	181	11	and	and	CCONJ
ejpam-3328	181	12	the	the	DET
ejpam-3328	181	13	lemma	lemma	PROPN
ejpam-3328	181	14	of	of	ADP
ejpam-3328	181	15	jordan	jordan	PROPN
ejpam-3328	181	16	.	.	PUNCT
ejpam-3328	182	1	lemma	lemma	PROPN
ejpam-3328	182	2	9	9	NUM
ejpam-3328	182	3	.	.	PUNCT
ejpam-3328	183	1	let	let	VERB
ejpam-3328	183	2	l	l	NOUN
ejpam-3328	183	3	=	=	SYM
ejpam-3328	183	4	2	2	NUM
ejpam-3328	183	5	,	,	PUNCT
ejpam-3328	183	6	i0	i0	PROPN
ejpam-3328	183	7	=	=	SYM
ejpam-3328	183	8	ψ0(x	ψ0(x	PROPN
ejpam-3328	183	9	,	,	PUNCT
ejpam-3328	183	10	k)|r	k)|r	PART
ejpam-3328	184	1	=	=	NOUN
ejpam-3328	184	2	r0	r0	NOUN
ejpam-3328	184	3	.	.	PUNCT
ejpam-3328	185	1	then	then	ADV
ejpam-3328	185	2	∣∣∣∣∫	∣∣∣∣∫	PRON
ejpam-3328	185	3	+	+	NOUN
ejpam-3328	185	4	∞	∞	PROPN
ejpam-3328	185	5	−∞	−∞	ADP
ejpam-3328	185	6	∫	∫	PROPN
ejpam-3328	185	7	s2	s2	PROPN
ejpam-3328	185	8	∫	∫	PROPN
ejpam-3328	185	9	s2	s2	NOUN
ejpam-3328	185	10	q̃(k(θ	q̃(k(θ	NOUN
ejpam-3328	185	11	−	−	NOUN
ejpam-3328	185	12	θ′))i0k	θ′))i0k	NOUN
ejpam-3328	185	13	2dkdθdθ′	2dkdθdθ′	NUM
ejpam-3328	185	14	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3328	185	15	≤	≤	NUM
ejpam-3328	185	16	sup	sup	NOUN
ejpam-3328	185	17	x∈r3	x∈r3	NOUN
ejpam-3328	185	18	|q(x)|+	|q(x)|+	ADJ
ejpam-3328	185	19	c0	c0	NOUN
ejpam-3328	185	20	(	(	PUNCT
ejpam-3328	185	21	1	1	NUM
ejpam-3328	185	22	r0	r0	NOUN
ejpam-3328	185	23	+	+	CCONJ
ejpam-3328	185	24	r0	r0	NOUN
ejpam-3328	185	25	)	)	PUNCT
ejpam-3328	185	26	‖q‖l2(r3	‖q‖l2(r3	PUNCT
ejpam-3328	185	27	)	)	PUNCT
ejpam-3328	185	28	,	,	PUNCT
ejpam-3328	185	29	sup	sup	NOUN
ejpam-3328	185	30	θ∈s2	θ∈s2	VERB
ejpam-3328	185	31	∣∣∣∣∫	∣∣∣∣∫	NOUN
ejpam-3328	185	32	+	+	NOUN
ejpam-3328	185	33	∞	∞	PROPN
ejpam-3328	185	34	−∞	−∞	ADP
ejpam-3328	185	35	∫	∫	PROPN
ejpam-3328	185	36	s2	s2	PROPN
ejpam-3328	185	37	∫	∫	PROPN
ejpam-3328	185	38	s2	s2	PROPN
ejpam-3328	185	39	qtkqi0k	qtkqi0k	PROPN
ejpam-3328	185	40	2dθ′′dθ′dk	2dθ′′dθ′dk	NUM
ejpam-3328	185	41	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3328	185	42	≤	≤	NUM
ejpam-3328	185	43	c0	c0	NOUN
ejpam-3328	185	44	(	(	PUNCT
ejpam-3328	185	45	1	1	NUM
ejpam-3328	185	46	r0	r0	NOUN
ejpam-3328	185	47	+	+	CCONJ
ejpam-3328	185	48	r0	r0	NOUN
ejpam-3328	185	49	)	)	PUNCT
ejpam-3328	185	50	‖q‖2l2(r3	‖q‖2l2(r3	PROPN
ejpam-3328	185	51	)	)	PUNCT
ejpam-3328	185	52	.	.	PUNCT
ejpam-3328	186	1	proof	proof	NOUN
ejpam-3328	186	2	.	.	PUNCT
ejpam-3328	187	1	by	by	ADP
ejpam-3328	187	2	the	the	DET
ejpam-3328	187	3	definition	definition	NOUN
ejpam-3328	187	4	of	of	ADP
ejpam-3328	187	5	the	the	DET
ejpam-3328	187	6	fourier	fourier	NOUN
ejpam-3328	187	7	transform	transform	NOUN
ejpam-3328	187	8	,	,	PUNCT
ejpam-3328	187	9	we	we	PRON
ejpam-3328	187	10	have∫	have∫	VERB
ejpam-3328	188	1	+	+	ADJ
ejpam-3328	189	1	∞	∞	PROPN
ejpam-3328	189	2	−∞	−∞	ADP
ejpam-3328	189	3	∫	∫	PROPN
ejpam-3328	189	4	s2	s2	PROPN
ejpam-3328	189	5	∫	∫	PROPN
ejpam-3328	189	6	s2	s2	PROPN
ejpam-3328	189	7	q̃(k(θ−θ′))i0k	q̃(k(θ−θ′))i0k	NOUN
ejpam-3328	189	8	2dkdθdθ′	2dkdθdθ′	NUM
ejpam-3328	189	9	=	=	SYM
ejpam-3328	189	10	∫	∫	PROPN
ejpam-3328	190	1	+	+	NOUN
ejpam-3328	190	2	∞	∞	PROPN
ejpam-3328	191	1	−∞	−∞	ADP
ejpam-3328	191	2	∫	∫	PROPN
ejpam-3328	191	3	s2	s2	PROPN
ejpam-3328	191	4	∫	∫	PROPN
ejpam-3328	191	5	s2	s2	PROPN
ejpam-3328	191	6	∫	∫	PROPN
ejpam-3328	192	1	+	+	PROPN
ejpam-3328	192	2	∞	∞	PROPN
ejpam-3328	192	3	0	0	NUM
ejpam-3328	192	4	q(x)eikx(θ−θ′)eix0kk2dkdθdθ′drdγ	q(x)eikx(θ−θ′)eix0kk2dkdθdθ′drdγ	NOUN
ejpam-3328	192	5	,	,	PUNCT
ejpam-3328	192	6	where	where	SCONJ
ejpam-3328	192	7	x	x	ADP
ejpam-3328	192	8	=	=	PRON
ejpam-3328	192	9	rγ	rγ	VERB
ejpam-3328	192	10	the	the	DET
ejpam-3328	192	11	lemma	lemma	PROPN
ejpam-3328	192	12	of	of	ADP
ejpam-3328	192	13	jordan	jordan	PROPN
ejpam-3328	192	14	completes	complete	VERB
ejpam-3328	192	15	the	the	DET
ejpam-3328	192	16	proof	proof	NOUN
ejpam-3328	192	17	for	for	ADP
ejpam-3328	192	18	the	the	DET
ejpam-3328	192	19	first	first	ADJ
ejpam-3328	192	20	inequality	inequality	NOUN
ejpam-3328	192	21	.	.	PUNCT
ejpam-3328	193	1	the	the	DET
ejpam-3328	193	2	second	second	ADJ
ejpam-3328	193	3	inequality	inequality	NOUN
ejpam-3328	193	4	is	be	AUX
ejpam-3328	193	5	proved	prove	VERB
ejpam-3328	193	6	like	like	ADP
ejpam-3328	193	7	the	the	DET
ejpam-3328	193	8	first:∫	first:∫	NOUN
ejpam-3328	193	9	+	+	PROPN
ejpam-3328	193	10	∞	∞	PROPN
ejpam-3328	193	11	−∞	−∞	ADP
ejpam-3328	193	12	∫	∫	PROPN
ejpam-3328	193	13	s2	s2	PROPN
ejpam-3328	193	14	∫	∫	PROPN
ejpam-3328	193	15	s2	s2	PROPN
ejpam-3328	193	16	qtkqi0k	qtkqi0k	PROPN
ejpam-3328	193	17	2dθ′′dθ′dk	2dθ′′dθ′dk	NUM
ejpam-3328	193	18	=	=	SYM
ejpam-3328	194	1	∫	∫	PROPN
ejpam-3328	195	1	+	+	NUM
ejpam-3328	195	2	∞	∞	PROPN
ejpam-3328	195	3	−∞	−∞	ADP
ejpam-3328	195	4	∫	∫	PROPN
ejpam-3328	195	5	+	+	PROPN
ejpam-3328	195	6	∞	∞	PROPN
ejpam-3328	195	7	−∞	−∞	ADP
ejpam-3328	195	8	∫	∫	PROPN
ejpam-3328	195	9	s2	s2	PROPN
ejpam-3328	195	10	∫	∫	PROPN
ejpam-3328	195	11	s2	s2	PROPN
ejpam-3328	195	12	∫	∫	PROPN
ejpam-3328	195	13	s2	s2	PROPN
ejpam-3328	195	14	(	(	PUNCT
ejpam-3328	195	15	q̃(s	q̃(s	PROPN
ejpam-3328	195	16	cos(θ′)−	cos(θ′)−	PROPN
ejpam-3328	195	17	s	s	PART
ejpam-3328	195	18	cos(θ′′))q̃(k	cos(θ′′))q̃(k	X
ejpam-3328	195	19	cos(θ)−	cos(θ)−	PROPN
ejpam-3328	195	20	s	s	PART
ejpam-3328	195	21	cos(θ′′	cos(θ′′	PROPN
ejpam-3328	195	22	)	)	PUNCT
ejpam-3328	195	23	)	)	PUNCT
ejpam-3328	195	24	s	s	VERB
ejpam-3328	196	1	k	k	NOUN
ejpam-3328	196	2	−	−	PROPN
ejpam-3328	196	3	s	s	PART
ejpam-3328	196	4	i0k	i0k	NOUN
ejpam-3328	196	5	2dθ′dθ′′dθdkds	2dθ′dθ′′dθdkds	PROPN
ejpam-3328	196	6	.	.	PUNCT
ejpam-3328	196	7	a.	a.	NOUN
ejpam-3328	196	8	durmagambetov	durmagambetov	PROPN
ejpam-3328	196	9	/	/	SYM
ejpam-3328	196	10	eur	eur	PROPN
ejpam-3328	196	11	.	.	PUNCT
ejpam-3328	197	1	j.	j.	PROPN
ejpam-3328	197	2	pure	pure	PROPN
ejpam-3328	197	3	appl	appl	PROPN
ejpam-3328	197	4	.	.	PROPN
ejpam-3328	197	5	math	math	PROPN
ejpam-3328	197	6	,	,	PUNCT
ejpam-3328	197	7	11	11	NUM
ejpam-3328	197	8	(	(	PUNCT
ejpam-3328	197	9	4	4	NUM
ejpam-3328	197	10	)	)	PUNCT
ejpam-3328	197	11	(	(	PUNCT
ejpam-3328	197	12	2018	2018	NUM
ejpam-3328	197	13	)	)	PUNCT
ejpam-3328	197	14	,	,	PUNCT
ejpam-3328	197	15	1143	1143	NUM
ejpam-3328	197	16	-	-	SYM
ejpam-3328	197	17	1176	1176	NUM
ejpam-3328	197	18	1151	1151	NUM
ejpam-3328	197	19	lemma	lemma	PROPN
ejpam-3328	197	20	8	8	NUM
ejpam-3328	197	21	yields∫	yields∫	NOUN
ejpam-3328	197	22	+	+	PROPN
ejpam-3328	197	23	∞	∞	PROPN
ejpam-3328	197	24	−∞	−∞	ADP
ejpam-3328	197	25	∫	∫	PROPN
ejpam-3328	197	26	s2	s2	PROPN
ejpam-3328	197	27	∫	∫	PROPN
ejpam-3328	197	28	s2	s2	PROPN
ejpam-3328	197	29	∫	∫	PROPN
ejpam-3328	197	30	s2	s2	PROPN
ejpam-3328	197	31	(	(	PUNCT
ejpam-3328	197	32	q̃(k	q̃(k	NOUN
ejpam-3328	197	33	cos(θ′)−	cos(θ′)−	PROPN
ejpam-3328	197	34	k	k	PROPN
ejpam-3328	197	35	cos(θ))q̃(k	cos(θ))q̃(k	PROPN
ejpam-3328	197	36	cos(θ)−	cos(θ)−	PROPN
ejpam-3328	197	37	k	k	PROPN
ejpam-3328	197	38	cos(θ′′	cos(θ′′	PROPN
ejpam-3328	197	39	)	)	PUNCT
ejpam-3328	197	40	)	)	PUNCT
ejpam-3328	198	1	i0k	i0k	NOUN
ejpam-3328	198	2	3θ(cos(θ′′))dθ′dθ′′dθdk−	3θ(cos(θ′′))dθ′dθ′′dθdk−	NUM
ejpam-3328	198	3	∫	∫	PROPN
ejpam-3328	199	1	+	+	X
ejpam-3328	199	2	∞	∞	PROPN
ejpam-3328	199	3	−∞	−∞	ADP
ejpam-3328	199	4	∫	∫	PROPN
ejpam-3328	199	5	s2	s2	PROPN
ejpam-3328	199	6	∫	∫	PROPN
ejpam-3328	199	7	s2	s2	PROPN
ejpam-3328	199	8	∫	∫	PROPN
ejpam-3328	199	9	s2	s2	PROPN
ejpam-3328	199	10	(	(	PUNCT
ejpam-3328	199	11	q̃(k	q̃(k	NOUN
ejpam-3328	199	12	cos(θ′)−	cos(θ′)−	PROPN
ejpam-3328	199	13	k	k	PROPN
ejpam-3328	199	14	cos(θ))q̃(k	cos(θ))q̃(k	PROPN
ejpam-3328	199	15	cos(θ)−	cos(θ)−	PROPN
ejpam-3328	199	16	k	k	PROPN
ejpam-3328	199	17	cos(θ′′	cos(θ′′	PROPN
ejpam-3328	199	18	)	)	PUNCT
ejpam-3328	199	19	)	)	PUNCT
ejpam-3328	199	20	i0k	i0k	VERB
ejpam-3328	199	21	3θ(−	3θ(−	NUM
ejpam-3328	199	22	cos(θ′′))dθ′dθ′′dθdk	cos(θ′′))dθ′dθ′′dθdk	X
ejpam-3328	199	23	.	.	PUNCT
ejpam-3328	200	1	integrating	integrate	VERB
ejpam-3328	200	2	θ	θ	NOUN
ejpam-3328	200	3	,	,	PUNCT
ejpam-3328	200	4	θ′	θ′	NOUN
ejpam-3328	200	5	,	,	PUNCT
ejpam-3328	200	6	θ′′	θ′′	NUM
ejpam-3328	200	7	,	,	PUNCT
ejpam-3328	200	8	and	and	CCONJ
ejpam-3328	200	9	k	k	NOUN
ejpam-3328	200	10	,	,	PUNCT
ejpam-3328	200	11	we	we	PRON
ejpam-3328	200	12	obtain	obtain	VERB
ejpam-3328	200	13	the	the	DET
ejpam-3328	200	14	proof	proof	NOUN
ejpam-3328	200	15	of	of	ADP
ejpam-3328	200	16	the	the	DET
ejpam-3328	200	17	second	second	ADJ
ejpam-3328	200	18	inequality	inequality	NOUN
ejpam-3328	200	19	of	of	ADP
ejpam-3328	200	20	the	the	DET
ejpam-3328	200	21	lemma	lemma	PROPN
ejpam-3328	200	22	.	.	PUNCT
ejpam-3328	201	1	lemma	lemma	PROPN
ejpam-3328	201	2	10	10	NUM
ejpam-3328	201	3	.	.	PUNCT
ejpam-3328	202	1	let	let	VERB
ejpam-3328	202	2	sup	sup	NOUN
ejpam-3328	202	3	k	k	PROPN
ejpam-3328	202	4	|t−qk|	|t−qk|	PROPN
ejpam-3328	202	5	≤	≤	PUNCT
ejpam-3328	203	1	α	α	PRON
ejpam-3328	203	2	<	<	X
ejpam-3328	203	3	1	1	NUM
ejpam-3328	203	4	2c	2c	NUM
ejpam-3328	203	5	<	<	X
ejpam-3328	203	6	1	1	NUM
ejpam-3328	203	7	,	,	PUNCT
ejpam-3328	203	8	sup	sup	NOUN
ejpam-3328	203	9	k	k	PROPN
ejpam-3328	203	10	|t−q̃k|	|t−q̃k|	NOUN
ejpam-3328	203	11	≤	≤	PUNCT
ejpam-3328	204	1	α	α	PRON
ejpam-3328	204	2	<	<	X
ejpam-3328	204	3	1	1	NUM
ejpam-3328	204	4	2c	2c	NUM
ejpam-3328	204	5	<	<	X
ejpam-3328	204	6	1	1	NUM
ejpam-3328	204	7	,	,	PUNCT
ejpam-3328	204	8	sup	sup	PROPN
ejpam-3328	204	9	k	k	PROPN
ejpam-3328	204	10	∣∣t−qq̃k2	∣∣t−qq̃k2	X
ejpam-3328	204	11	∣∣	∣∣	NUM
ejpam-3328	204	12	≤	≤	NUM
ejpam-3328	204	13	α	α	PRON
ejpam-3328	204	14	<	<	X
ejpam-3328	204	15	1	1	NUM
ejpam-3328	204	16	2c	2c	NUM
ejpam-3328	204	17	<	<	X
ejpam-3328	204	18	1	1	NUM
ejpam-3328	204	19	,	,	PUNCT
ejpam-3328	204	20	l	l	NOUN
ejpam-3328	204	21	=	=	SYM
ejpam-3328	204	22	0	0	NUM
ejpam-3328	204	23	,	,	PUNCT
ejpam-3328	204	24	1	1	NUM
ejpam-3328	204	25	,	,	PUNCT
ejpam-3328	204	26	2	2	NUM
ejpam-3328	204	27	.	.	PUNCT
ejpam-3328	205	1	then	then	ADV
ejpam-3328	205	2	,	,	PUNCT
ejpam-3328	205	3	∣∣∣∣∫	∣∣∣∣∫	PRON
ejpam-3328	205	4	+	+	NOUN
ejpam-3328	205	5	∞	∞	PROPN
ejpam-3328	205	6	−∞	−∞	ADP
ejpam-3328	205	7	∫	∫	PROPN
ejpam-3328	205	8	s2	s2	PROPN
ejpam-3328	205	9	∫	∫	PROPN
ejpam-3328	205	10	s2	s2	PROPN
ejpam-3328	205	11	a(k	a(k	PROPN
ejpam-3328	205	12	,	,	PUNCT
ejpam-3328	205	13	θ′	θ′	NOUN
ejpam-3328	205	14	,	,	PUNCT
ejpam-3328	205	15	θ)kldkdθ′dθ	θ)kldkdθ′dθ	PROPN
ejpam-3328	205	16	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3328	205	17	≤	≤	NOUN
ejpam-3328	205	18	∣∣∣∣∫	∣∣∣∣∫	NOUN
ejpam-3328	206	1	+	+	NOUN
ejpam-3328	206	2	∞	∞	PROPN
ejpam-3328	206	3	−∞	−∞	ADP
ejpam-3328	206	4	∫	∫	PROPN
ejpam-3328	206	5	s2	s2	PROPN
ejpam-3328	206	6	∫	∫	PROPN
ejpam-3328	206	7	s2	s2	VERB
ejpam-3328	206	8	q̃(k(θ	q̃(k(θ	PRON
ejpam-3328	206	9	−	−	PROPN
ejpam-3328	206	10	θ′))kldkdθ′dθ	θ′))kldkdθ′dθ	NOUN
ejpam-3328	206	11	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3328	207	1	+	+	PROPN
ejpam-3328	207	2	c	c	PROPN
ejpam-3328	207	3	sup	sup	X
ejpam-3328	207	4	θ∈s2	θ∈s2	NOUN
ejpam-3328	207	5	∣∣∣∣∫	∣∣∣∣∫	NOUN
ejpam-3328	207	6	+	+	NOUN
ejpam-3328	207	7	∞	∞	PROPN
ejpam-3328	207	8	−∞	−∞	ADP
ejpam-3328	207	9	∫	∫	PROPN
ejpam-3328	207	10	s2	s2	PROPN
ejpam-3328	207	11	∫	∫	PROPN
ejpam-3328	207	12	s2	s2	PROPN
ejpam-3328	207	13	qtkakldθ′′dθ′dk	qtkakldθ′′dθ′dk	PRON
ejpam-3328	207	14	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3328	207	15	,	,	PUNCT
ejpam-3328	207	16	∣∣∣∣∫	∣∣∣∣∫	NOUN
ejpam-3328	207	17	+	+	NOUN
ejpam-3328	207	18	∞	∞	PROPN
ejpam-3328	207	19	−∞	−∞	ADP
ejpam-3328	207	20	∫	∫	PROPN
ejpam-3328	207	21	s2	s2	PROPN
ejpam-3328	207	22	∫	∫	PROPN
ejpam-3328	207	23	s2	s2	PROPN
ejpam-3328	207	24	a(k	a(k	PROPN
ejpam-3328	207	25	,	,	PUNCT
ejpam-3328	207	26	θ′	θ′	NOUN
ejpam-3328	207	27	,	,	PUNCT
ejpam-3328	207	28	θ)k2dkdθ′dθ	θ)k2dkdθ′dθ	PROPN
ejpam-3328	207	29	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3328	207	30	≤	≤	NUM
ejpam-3328	207	31	sup	sup	NUM
ejpam-3328	207	32	x∈r3	x∈r3	NOUN
ejpam-3328	207	33	|q|+c0	|q|+c0	X
ejpam-3328	207	34	‖q‖w	‖q‖w	PROPN
ejpam-3328	207	35	1	1	NUM
ejpam-3328	207	36	2	2	NUM
ejpam-3328	207	37	(	(	PUNCT
ejpam-3328	207	38	r3	r3	PROPN
ejpam-3328	207	39	)	)	PUNCT
ejpam-3328	207	40	‖q‖l2(r3	‖q‖l2(r3	PUNCT
ejpam-3328	207	41	)	)	PUNCT
ejpam-3328	207	42	(	(	PUNCT
ejpam-3328	207	43	∣∣∣∣∫	∣∣∣∣∫	NUM
ejpam-3328	207	44	s2	s2	NOUN
ejpam-3328	207	45	tkadθ′′	tkadθ′′	VERB
ejpam-3328	207	46	∣∣∣∣+	∣∣∣∣+	PROPN
ejpam-3328	207	47	1	1	NUM
ejpam-3328	207	48	)	)	PUNCT
ejpam-3328	207	49	.	.	PUNCT
ejpam-3328	208	1	proof	proof	NOUN
ejpam-3328	208	2	.	.	PUNCT
ejpam-3328	209	1	using	use	VERB
ejpam-3328	209	2	the	the	DET
ejpam-3328	209	3	definition	definition	NOUN
ejpam-3328	209	4	of	of	ADP
ejpam-3328	209	5	the	the	DET
ejpam-3328	209	6	amplitude	amplitude	NOUN
ejpam-3328	209	7	,	,	PUNCT
ejpam-3328	209	8	lemmas	lemma	VERB
ejpam-3328	209	9	3	3	NUM
ejpam-3328	209	10	and	and	CCONJ
ejpam-3328	209	11	4	4	NUM
ejpam-3328	209	12	,	,	PUNCT
ejpam-3328	209	13	and	and	CCONJ
ejpam-3328	209	14	the	the	DET
ejpam-3328	209	15	lemma	lemma	PROPN
ejpam-3328	209	16	of	of	ADP
ejpam-3328	209	17	jordan	jordan	PROPN
ejpam-3328	209	18	yields∫	yields∫	VERB
ejpam-3328	210	1	+	+	PROPN
ejpam-3328	210	2	∞	∞	PROPN
ejpam-3328	210	3	−∞	−∞	ADP
ejpam-3328	210	4	∫	∫	PROPN
ejpam-3328	210	5	s2	s2	PROPN
ejpam-3328	210	6	∫	∫	PROPN
ejpam-3328	210	7	s2	s2	PROPN
ejpam-3328	210	8	a(k	a(k	PROPN
ejpam-3328	210	9	,	,	PUNCT
ejpam-3328	210	10	θ	θ	PROPN
ejpam-3328	210	11	′	′	NUM
ejpam-3328	210	12	,	,	PUNCT
ejpam-3328	210	13	θ)kldkdθ′dθ	θ)kldkdθ′dθ	PROPN
ejpam-3328	210	14	=	=	SYM
ejpam-3328	210	15	−	−	PROPN
ejpam-3328	210	16	∫	∫	PROPN
ejpam-3328	211	1	+	+	NOUN
ejpam-3328	211	2	∞	∞	PROPN
ejpam-3328	211	3	−∞	−∞	ADP
ejpam-3328	211	4	1	1	NUM
ejpam-3328	211	5	4π	4π	NUM
ejpam-3328	211	6	∫	∫	PROPN
ejpam-3328	211	7	s2	s2	PROPN
ejpam-3328	211	8	∫	∫	PROPN
ejpam-3328	211	9	s2	s2	PROPN
ejpam-3328	211	10	∫	∫	PROPN
ejpam-3328	211	11	r3	r3	PROPN
ejpam-3328	211	12	q(x)ψ+(k	q(x)ψ+(k	PROPN
ejpam-3328	211	13	,	,	PUNCT
ejpam-3328	211	14	θ	θ	PROPN
ejpam-3328	211	15	,	,	PUNCT
ejpam-3328	211	16	x)e−ikθ	x)e−ikθ	PROPN
ejpam-3328	211	17	′	′	NOUN
ejpam-3328	211	18	xkldxdkdθ′	xkldxdkdθ′	PUNCT
ejpam-3328	212	1	=	=	PUNCT
ejpam-3328	213	1	−	−	PROPN
ejpam-3328	213	2	1	1	NUM
ejpam-3328	213	3	4π	4π	NUM
ejpam-3328	213	4	∫	∫	PROPN
ejpam-3328	214	1	s2	s2	PROPN
ejpam-3328	214	2	∫	∫	PROPN
ejpam-3328	214	3	s2	s2	PROPN
ejpam-3328	214	4	∫	∫	PROPN
ejpam-3328	214	5	r3	r3	PROPN
ejpam-3328	214	6	q(x	q(x	PROPN
ejpam-3328	214	7	)	)	PUNCT
ejpam-3328	214	8	eikθx	eikθx	NUM
ejpam-3328	215	1	+	+	CCONJ
ejpam-3328	215	2	∑	∑	PART
ejpam-3328	215	3	n≥1	n≥1	NOUN
ejpam-3328	215	4	(	(	PUNCT
ejpam-3328	215	5	−t−d)nψ0	−t−d)nψ0	NOUN
ejpam-3328	215	6			NOUN
ejpam-3328	215	7	e−ikθ′xkldθ′dxdk	e−ikθ′xkldθ′dxdk	ADV
ejpam-3328	215	8	=	=	SYM
ejpam-3328	215	9	∫	∫	PROPN
ejpam-3328	216	1	+	+	NUM
ejpam-3328	216	2	∞	∞	PROPN
ejpam-3328	216	3	−∞	−∞	ADP
ejpam-3328	216	4	∫	∫	PROPN
ejpam-3328	216	5	s2	s2	PROPN
ejpam-3328	216	6	∫	∫	PROPN
ejpam-3328	216	7	s2	s2	VERB
ejpam-3328	216	8	q̃(k(θ	q̃(k(θ	PRON
ejpam-3328	216	9	−	−	PROPN
ejpam-3328	216	10	θ′))kldkdθ′dθ	θ′))kldkdθ′dθ	NOUN
ejpam-3328	216	11	+	+	CCONJ
ejpam-3328	216	12	∑	∑	PUNCT
ejpam-3328	216	13	n≥1	n≥1	PROPN
ejpam-3328	216	14	wn	wn	PROPN
ejpam-3328	216	15	,	,	PUNCT
ejpam-3328	216	16	w1	w1	PROPN
ejpam-3328	216	17	=	=	SYM
ejpam-3328	216	18	∫	∫	PROPN
ejpam-3328	216	19	r3	r3	PROPN
ejpam-3328	216	20	∫	∫	PROPN
ejpam-3328	217	1	+	+	PROPN
ejpam-3328	217	2	∞	∞	PROPN
ejpam-3328	217	3	−∞	−∞	ADP
ejpam-3328	217	4	∫	∫	PROPN
ejpam-3328	217	5	s2	s2	PROPN
ejpam-3328	217	6	∫	∫	PROPN
ejpam-3328	217	7	s2	s2	PROPN
ejpam-3328	217	8	sa(s	sa(s	PROPN
ejpam-3328	217	9	,	,	PUNCT
ejpam-3328	217	10	θ	θ	PROPN
ejpam-3328	217	11	′′	′′	PROPN
ejpam-3328	217	12	,	,	PUNCT
ejpam-3328	217	13	θ)e−ikθ	θ)e−ikθ	VERB
ejpam-3328	217	14	′	′	NUM
ejpam-3328	217	15	xq(x)eisθ	xq(x)eisθ	NOUN
ejpam-3328	217	16	′′x	′′x	PROPN
ejpam-3328	218	1	k	k	PROPN
ejpam-3328	218	2	−	−	PROPN
ejpam-3328	218	3	s	s	PART
ejpam-3328	218	4	kldkdxdsdθ′dθ′′	kldkdxdsdθ′dθ′′	PROPN
ejpam-3328	218	5	,	,	PUNCT
ejpam-3328	218	6	|w1|	|w1|	NOUN
ejpam-3328	218	7	≤	≤	NUM
ejpam-3328	218	8	c	c	PROPN
ejpam-3328	218	9	sup	sup	NOUN
ejpam-3328	218	10	θ∈s2	θ∈s2	NOUN
ejpam-3328	218	11	∣∣∣∣∫	∣∣∣∣∫	NOUN
ejpam-3328	218	12	+	+	NOUN
ejpam-3328	218	13	∞	∞	PROPN
ejpam-3328	218	14	−∞	−∞	ADP
ejpam-3328	218	15	∫	∫	PROPN
ejpam-3328	218	16	s2	s2	PROPN
ejpam-3328	218	17	∫	∫	PROPN
ejpam-3328	218	18	s2	s2	PROPN
ejpam-3328	218	19	qtkakldθ′′dθ′dk	qtkakldθ′′dθ′dk	PRON
ejpam-3328	218	20	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3328	218	21	.	.	PUNCT
ejpam-3328	219	1	a.	a.	PROPN
ejpam-3328	219	2	durmagambetov	durmagambetov	PROPN
ejpam-3328	219	3	/	/	SYM
ejpam-3328	219	4	eur	eur	PROPN
ejpam-3328	219	5	.	.	PUNCT
ejpam-3328	220	1	j.	j.	PROPN
ejpam-3328	220	2	pure	pure	PROPN
ejpam-3328	220	3	appl	appl	PROPN
ejpam-3328	220	4	.	.	PROPN
ejpam-3328	220	5	math	math	PROPN
ejpam-3328	220	6	,	,	PUNCT
ejpam-3328	220	7	11	11	NUM
ejpam-3328	220	8	(	(	PUNCT
ejpam-3328	220	9	4	4	NUM
ejpam-3328	220	10	)	)	PUNCT
ejpam-3328	220	11	(	(	PUNCT
ejpam-3328	220	12	2018	2018	NUM
ejpam-3328	220	13	)	)	PUNCT
ejpam-3328	220	14	,	,	PUNCT
ejpam-3328	220	15	1143	1143	NUM
ejpam-3328	220	16	-	-	SYM
ejpam-3328	220	17	1176	1176	NUM
ejpam-3328	220	18	1152	1152	NUM
ejpam-3328	220	19	similarly	similarly	ADV
ejpam-3328	220	20	,	,	PUNCT
ejpam-3328	220	21	|wn|	|wn|	PROPN
ejpam-3328	220	22	≤	≤	NUM
ejpam-3328	220	23	c	c	PROPN
ejpam-3328	220	24	sup	sup	NOUN
ejpam-3328	220	25	θ∈s2	θ∈s2	NOUN
ejpam-3328	220	26	∣∣∣∣∫	∣∣∣∣∫	NOUN
ejpam-3328	220	27	+	+	NOUN
ejpam-3328	220	28	∞	∞	PROPN
ejpam-3328	220	29	−∞	−∞	ADP
ejpam-3328	220	30	∫	∫	PROPN
ejpam-3328	220	31	s2	s2	PROPN
ejpam-3328	220	32	∫	∫	PROPN
ejpam-3328	220	33	s2	s2	PROPN
ejpam-3328	220	34	qtkakldθ′′dθ′dk	qtkakldθ′′dθ′dk	NOUN
ejpam-3328	220	35	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3328	220	36	∣∣∣∣∫	∣∣∣∣∫	PROPN
ejpam-3328	220	37	s2	s2	NOUN
ejpam-3328	220	38	tkadθ′′	tkadθ′′	PROPN
ejpam-3328	220	39	∣∣∣∣n	∣∣∣∣n	NOUN
ejpam-3328	220	40	.	.	PUNCT
ejpam-3328	221	1	finally	finally	ADV
ejpam-3328	221	2	,	,	PUNCT
ejpam-3328	221	3	∣∣∣∣∫	∣∣∣∣∫	PRON
ejpam-3328	221	4	+	+	NOUN
ejpam-3328	221	5	∞	∞	PROPN
ejpam-3328	221	6	−∞	−∞	ADP
ejpam-3328	221	7	∫	∫	PROPN
ejpam-3328	221	8	s2	s2	PROPN
ejpam-3328	221	9	∫	∫	PROPN
ejpam-3328	221	10	s2	s2	PROPN
ejpam-3328	221	11	a(k	a(k	PROPN
ejpam-3328	221	12	,	,	PUNCT
ejpam-3328	221	13	θ′	θ′	NOUN
ejpam-3328	221	14	,	,	PUNCT
ejpam-3328	221	15	θ)dkdθ′dθ	θ)dkdθ′dθ	PROPN
ejpam-3328	221	16	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3328	221	17	≤	≤	PROPN
ejpam-3328	221	18	∣∣∣∣∫	∣∣∣∣∫	NOUN
ejpam-3328	222	1	+	+	NOUN
ejpam-3328	222	2	∞	∞	PROPN
ejpam-3328	222	3	−∞	−∞	ADP
ejpam-3328	222	4	∫	∫	PROPN
ejpam-3328	222	5	s2	s2	PROPN
ejpam-3328	222	6	∫	∫	PROPN
ejpam-3328	222	7	s2	s2	VERB
ejpam-3328	222	8	q̃(k(θ	q̃(k(θ	NOUN
ejpam-3328	222	9	−	−	X
ejpam-3328	222	10	θ′))dkdθdθ′	θ′))dkdθdθ′	X
ejpam-3328	222	11	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3328	222	12	+	+	PROPN
ejpam-3328	222	13	c0	c0	PROPN
ejpam-3328	222	14	‖q‖2l2(r3	‖q‖2l2(r3	X
ejpam-3328	222	15	)	)	PUNCT
ejpam-3328	222	16	(	(	PUNCT
ejpam-3328	222	17	∣∣∣∣∫	∣∣∣∣∫	NUM
ejpam-3328	222	18	s2	s2	NOUN
ejpam-3328	222	19	tkadθ′′	tkadθ′′	VERB
ejpam-3328	222	20	∣∣∣∣+	∣∣∣∣+	PROPN
ejpam-3328	222	21	1	1	NUM
ejpam-3328	222	22	)	)	PUNCT
ejpam-3328	222	23	,	,	PUNCT
ejpam-3328	222	24	∣∣∣∣∫	∣∣∣∣∫	PRON
ejpam-3328	223	1	+	+	NOUN
ejpam-3328	223	2	∞	∞	PROPN
ejpam-3328	223	3	−∞	−∞	ADP
ejpam-3328	223	4	∫	∫	PROPN
ejpam-3328	223	5	s2	s2	PROPN
ejpam-3328	223	6	∫	∫	PROPN
ejpam-3328	223	7	s2	s2	PROPN
ejpam-3328	223	8	a(k	a(k	PROPN
ejpam-3328	223	9	,	,	PUNCT
ejpam-3328	223	10	θ′	θ′	NOUN
ejpam-3328	223	11	,	,	PUNCT
ejpam-3328	223	12	θ)k2dkdθ′	θ)k2dkdθ′	VERB
ejpam-3328	223	13	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3328	223	14	≤	≤	PROPN
ejpam-3328	223	15	sup	sup	NOUN
ejpam-3328	223	16	x∈r3	x∈r3	PROPN
ejpam-3328	223	17	|q|+	|q|+	PROPN
ejpam-3328	223	18	c0	c0	PROPN
ejpam-3328	223	19	‖q‖2l2(r3	‖q‖2l2(r3	X
ejpam-3328	223	20	)	)	PUNCT
ejpam-3328	223	21	(	(	PUNCT
ejpam-3328	223	22	∣∣∣∣∫	∣∣∣∣∫	NUM
ejpam-3328	223	23	s2	s2	NOUN
ejpam-3328	223	24	tkadθ′′	tkadθ′′	VERB
ejpam-3328	223	25	∣∣∣∣+	∣∣∣∣+	PROPN
ejpam-3328	223	26	1	1	NUM
ejpam-3328	223	27	)	)	PUNCT
ejpam-3328	223	28	.	.	PUNCT
ejpam-3328	224	1	this	this	PRON
ejpam-3328	224	2	completes	complete	VERB
ejpam-3328	224	3	the	the	DET
ejpam-3328	224	4	proof	proof	NOUN
ejpam-3328	224	5	.	.	PUNCT
ejpam-3328	225	1	lemma	lemma	PROPN
ejpam-3328	225	2	11	11	NUM
ejpam-3328	225	3	.	.	PUNCT
ejpam-3328	226	1	let	let	VERB
ejpam-3328	226	2	sup	sup	NOUN
ejpam-3328	226	3	k	k	PROPN
ejpam-3328	226	4	∫	∫	PROPN
ejpam-3328	226	5	s2	s2	PROPN
ejpam-3328	226	6	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-3328	226	7	∞∫	∞∫	PROPN
ejpam-3328	226	8	−∞	−∞	PUNCT
ejpam-3328	226	9	pa(p	pa(p	NOUN
ejpam-3328	226	10	,	,	PUNCT
ejpam-3328	226	11	θ	θ	PROPN
ejpam-3328	226	12	′	′	NUM
ejpam-3328	226	13	,	,	PUNCT
ejpam-3328	226	14	θ	θ	NOUN
ejpam-3328	226	15	)	)	PUNCT
ejpam-3328	226	16	4π(p−	4π(p−	NUM
ejpam-3328	226	17	k	k	PROPN
ejpam-3328	226	18	+	+	CCONJ
ejpam-3328	226	19	i0	i0	PROPN
ejpam-3328	226	20	)	)	PUNCT
ejpam-3328	226	21	dp	dp	PROPN
ejpam-3328	226	22	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-3328	226	23	dθ	dθ	PROPN
ejpam-3328	226	24	<	<	X
ejpam-3328	226	25	α	α	X
ejpam-3328	226	26	<	<	X
ejpam-3328	226	27	1/2	1/2	NUM
ejpam-3328	226	28	,	,	PUNCT
ejpam-3328	226	29	sup	sup	PROPN
ejpam-3328	226	30	k	k	X
ejpam-3328	226	31	∣∣∣pa(p	∣∣∣pa(p	ADJ
ejpam-3328	226	32	,	,	PUNCT
ejpam-3328	226	33	θ	θ	PROPN
ejpam-3328	226	34	′	′	NUM
ejpam-3328	226	35	,	,	PUNCT
ejpam-3328	226	36	θ	θ	NOUN
ejpam-3328	226	37	)	)	PUNCT
ejpam-3328	226	38	∣∣∣	∣∣∣	NOUN
ejpam-3328	226	39	<	<	X
ejpam-3328	226	40	α	α	X
ejpam-3328	226	41	<	<	X
ejpam-3328	226	42	1/2	1/2	NUM
ejpam-3328	226	43	.	.	PUNCT
ejpam-3328	227	1	then	then	ADV
ejpam-3328	227	2	,	,	PUNCT
ejpam-3328	227	3	|t−dψ0|	|t−dψ0|	PROPN
ejpam-3328	227	4	<	<	X
ejpam-3328	227	5	α	α	X
ejpam-3328	227	6	1−	1−	NUM
ejpam-3328	227	7	α	α	NOUN
ejpam-3328	227	8	,	,	PUNCT
ejpam-3328	227	9	|t+dψ0|	|t+dψ0|	CCONJ
ejpam-3328	227	10	<	<	X
ejpam-3328	227	11	α	α	X
ejpam-3328	227	12	1−	1−	NUM
ejpam-3328	227	13	α	α	NOUN
ejpam-3328	227	14	,	,	PUNCT
ejpam-3328	228	1	|dψ0|	|dψ0|	ADJ
ejpam-3328	228	2	<	<	X
ejpam-3328	229	1	α	α	X
ejpam-3328	229	2	1−	1−	NUM
ejpam-3328	229	3	α	α	NOUN
ejpam-3328	229	4	,	,	PUNCT
ejpam-3328	229	5	t−g−	t−g−	X
ejpam-3328	229	6	=	=	SYM
ejpam-3328	229	7	(	(	PUNCT
ejpam-3328	229	8	i	i	PRON
ejpam-3328	229	9	−	−	VERB
ejpam-3328	229	10	t−d)−1t−dψ0	t−d)−1t−dψ0	NOUN
ejpam-3328	229	11	,	,	PUNCT
ejpam-3328	229	12	ψ−	ψ−	PUNCT
ejpam-3328	229	13	=	=	PUNCT
ejpam-3328	229	14	(	(	PUNCT
ejpam-3328	229	15	i	i	PRON
ejpam-3328	229	16	−	−	VERB
ejpam-3328	229	17	t−d)−1t−dψ0	t−d)−1t−dψ0	VERB
ejpam-3328	229	18	+	+	CCONJ
ejpam-3328	229	19	ψ0	ψ0	ADJ
ejpam-3328	229	20	,	,	PUNCT
ejpam-3328	229	21	and	and	CCONJ
ejpam-3328	229	22	q	q	NOUN
ejpam-3328	229	23	satisfies	satisfy	VERB
ejpam-3328	229	24	the	the	DET
ejpam-3328	229	25	following	follow	VERB
ejpam-3328	229	26	inequalities	inequality	NOUN
ejpam-3328	229	27	:	:	PUNCT
ejpam-3328	229	28	sup	sup	NOUN
ejpam-3328	229	29	x∈r3	x∈r3	PROPN
ejpam-3328	229	30	|q(x)|	|q(x)|	PROPN
ejpam-3328	229	31	≤	≤	PROPN
ejpam-3328	229	32	∣∣∣∣∫	∣∣∣∣∫	NUM
ejpam-3328	229	33	s2	s2	PROPN
ejpam-3328	229	34	tkqdθ	tkqdθ	NOUN
ejpam-3328	229	35	∣∣∣∣c0	∣∣∣∣c0	PROPN
ejpam-3328	229	36	(	(	PUNCT
ejpam-3328	229	37	‖q‖2l2(r3	‖q‖2l2(r3	ADP
ejpam-3328	229	38	)	)	PUNCT
ejpam-3328	230	1	+	+	CCONJ
ejpam-3328	230	2	1	1	X
ejpam-3328	230	3	)	)	PUNCT
ejpam-3328	230	4	+	+	CCONJ
ejpam-3328	230	5	c0	c0	PROPN
ejpam-3328	230	6	‖q‖l2(r3	‖q‖l2(r3	PUNCT
ejpam-3328	230	7	)	)	PUNCT
ejpam-3328	230	8	.	.	PUNCT
ejpam-3328	231	1	proof	proof	NOUN
ejpam-3328	231	2	.	.	PUNCT
ejpam-3328	232	1	using	use	VERB
ejpam-3328	232	2	the	the	DET
ejpam-3328	232	3	equation	equation	NOUN
ejpam-3328	232	4	ψ+(k	ψ+(k	NOUN
ejpam-3328	232	5	,	,	PUNCT
ejpam-3328	232	6	θ	θ	NOUN
ejpam-3328	232	7	,	,	PUNCT
ejpam-3328	232	8	x)−ψ−(k	x)−ψ−(k	NUM
ejpam-3328	232	9	,	,	PUNCT
ejpam-3328	232	10	θ	θ	PROPN
ejpam-3328	232	11	,	,	PUNCT
ejpam-3328	232	12	x	x	NOUN
ejpam-3328	232	13	)	)	PUNCT
ejpam-3328	232	14	=	=	SYM
ejpam-3328	233	1	−	−	PROPN
ejpam-3328	233	2	k	k	PROPN
ejpam-3328	233	3	4π	4π	NUM
ejpam-3328	233	4	∫	∫	PROPN
ejpam-3328	233	5	s2	s2	PROPN
ejpam-3328	233	6	a(k	a(k	PROPN
ejpam-3328	233	7	,	,	PUNCT
ejpam-3328	233	8	θ	θ	PROPN
ejpam-3328	233	9	′	′	NOUN
ejpam-3328	233	10	,	,	PUNCT
ejpam-3328	233	11	θ)ψ−(k	θ)ψ−(k	NOUN
ejpam-3328	233	12	,	,	PUNCT
ejpam-3328	233	13	θ	θ	PROPN
ejpam-3328	233	14	′	′	NOUN
ejpam-3328	233	15	,	,	PUNCT
ejpam-3328	234	1	x)dθ	x)dθ	PROPN
ejpam-3328	234	2	′	′	NOUN
ejpam-3328	234	3	,	,	PUNCT
ejpam-3328	234	4	k	k	PROPN
ejpam-3328	234	5	∈	∈	PROPN
ejpam-3328	234	6	r	r	NOUN
ejpam-3328	234	7	,	,	PUNCT
ejpam-3328	234	8	we	we	PRON
ejpam-3328	234	9	can	can	AUX
ejpam-3328	234	10	write	write	VERB
ejpam-3328	234	11	t+g+	t+g+	ADV
ejpam-3328	234	12	−	−	ADP
ejpam-3328	234	13	t−g−	t−g−	ADP
ejpam-3328	234	14	=	=	SYM
ejpam-3328	234	15	d(t−g−	d(t−g−	PROPN
ejpam-3328	234	16	+	+	CCONJ
ejpam-3328	234	17	ψ0	ψ0	ADJ
ejpam-3328	234	18	)	)	PUNCT
ejpam-3328	234	19	.	.	PUNCT
ejpam-3328	235	1	applying	apply	VERB
ejpam-3328	235	2	the	the	DET
ejpam-3328	235	3	operator	operator	NOUN
ejpam-3328	235	4	t−	t−	PROPN
ejpam-3328	235	5	to	to	ADP
ejpam-3328	235	6	the	the	DET
ejpam-3328	235	7	last	last	ADJ
ejpam-3328	235	8	equation	equation	NOUN
ejpam-3328	235	9	,	,	PUNCT
ejpam-3328	235	10	we	we	PRON
ejpam-3328	235	11	have	have	VERB
ejpam-3328	235	12	t−g−	t−g−	ADP
ejpam-3328	235	13	=	=	SYM
ejpam-3328	235	14	t−d(t−g−	t−d(t−g−	PROPN
ejpam-3328	235	15	+	+	CCONJ
ejpam-3328	235	16	ψ0	ψ0	ADJ
ejpam-3328	235	17	)	)	PUNCT
ejpam-3328	235	18	,	,	PUNCT
ejpam-3328	235	19	(	(	PUNCT
ejpam-3328	235	20	i	i	PRON
ejpam-3328	235	21	−	−	VERB
ejpam-3328	235	22	t−d)t−g−	t−d)t−g−	NOUN
ejpam-3328	235	23	=	=	SYM
ejpam-3328	235	24	t−dψ0	t−dψ0	NOUN
ejpam-3328	235	25	,	,	PUNCT
ejpam-3328	235	26	t−g−	t−g−	ADP
ejpam-3328	235	27	=	=	PUNCT
ejpam-3328	235	28	∑	∑	PUNCT
ejpam-3328	235	29	n≥0	n≥0	PROPN
ejpam-3328	235	30	(	(	PUNCT
ejpam-3328	235	31	−t−d)n	−t−d)n	NOUN
ejpam-3328	235	32	ψ0	ψ0	PROPN
ejpam-3328	235	33	.	.	PUNCT
ejpam-3328	236	1	a.	a.	PROPN
ejpam-3328	236	2	durmagambetov	durmagambetov	PROPN
ejpam-3328	236	3	/	/	SYM
ejpam-3328	236	4	eur	eur	PROPN
ejpam-3328	236	5	.	.	PUNCT
ejpam-3328	237	1	j.	j.	PROPN
ejpam-3328	237	2	pure	pure	PROPN
ejpam-3328	237	3	appl	appl	PROPN
ejpam-3328	237	4	.	.	PROPN
ejpam-3328	237	5	math	math	PROPN
ejpam-3328	237	6	,	,	PUNCT
ejpam-3328	237	7	11	11	NUM
ejpam-3328	237	8	(	(	PUNCT
ejpam-3328	237	9	4	4	NUM
ejpam-3328	237	10	)	)	PUNCT
ejpam-3328	237	11	(	(	PUNCT
ejpam-3328	237	12	2018	2018	NUM
ejpam-3328	237	13	)	)	PUNCT
ejpam-3328	237	14	,	,	PUNCT
ejpam-3328	237	15	1143	1143	NUM
ejpam-3328	237	16	-	-	SYM
ejpam-3328	237	17	1176	1176	NUM
ejpam-3328	237	18	1153	1153	NUM
ejpam-3328	237	19	estimating	estimate	VERB
ejpam-3328	237	20	the	the	DET
ejpam-3328	237	21	terms	term	NOUN
ejpam-3328	237	22	of	of	ADP
ejpam-3328	237	23	the	the	DET
ejpam-3328	237	24	series	series	NOUN
ejpam-3328	237	25	,	,	PUNCT
ejpam-3328	237	26	we	we	PRON
ejpam-3328	237	27	obtain	obtain	AUX
ejpam-3328	237	28	using	use	VERB
ejpam-3328	237	29	lemma	lemma	PROPN
ejpam-3328	237	30	4	4	NUM
ejpam-3328	237	31	|(t−d)nψ0|	|(t−d)nψ0|	NOUN
ejpam-3328	237	32	≤	≤	NOUN
ejpam-3328	237	33	∑	∑	PUNCT
ejpam-3328	237	34	n≥0	n≥0	PROPN
ejpam-3328	237	35	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-3328	237	36	∫	∫	PROPN
ejpam-3328	237	37	∞	∞	PROPN
ejpam-3328	237	38	−∞	−∞	X
ejpam-3328	237	39	·	·	PUNCT
ejpam-3328	237	40	·	·	PUNCT
ejpam-3328	237	41	·	·	PUNCT
ejpam-3328	238	1	∫	∫	PROPN
ejpam-3328	238	2	∞	∞	PROPN
ejpam-3328	238	3	−∞	−∞	ADP
ejpam-3328	238	4	ψ0	ψ0	PROPN
ejpam-3328	238	5	∏	∏	PROPN
ejpam-3328	238	6	0≤j	0≤j	NUM
ejpam-3328	238	7	<	<	NOUN
ejpam-3328	238	8	n	n	NOUN
ejpam-3328	238	9	∫	∫	NOUN
ejpam-3328	238	10	s2	s2	PROPN
ejpam-3328	238	11	kja(kj	kja(kj	NOUN
ejpam-3328	238	12	,	,	PUNCT
ejpam-3328	238	13	θ	θ	NOUN
ejpam-3328	238	14	′	′	NUM
ejpam-3328	239	1	kj	kj	PROPN
ejpam-3328	239	2	,	,	PUNCT
ejpam-3328	239	3	θkj	θkj	NOUN
ejpam-3328	239	4	)	)	PUNCT
ejpam-3328	240	1	dθ	dθ	PROPN
ejpam-3328	241	1	′	′	NUM
ejpam-3328	241	2	kj	kj	NOUN
ejpam-3328	241	3	4π(kj+1)−	4π(kj+1)−	NUM
ejpam-3328	241	4	kj	kj	PROPN
ejpam-3328	241	5	+	+	CCONJ
ejpam-3328	241	6	i0	i0	PROPN
ejpam-3328	241	7	)	)	PUNCT
ejpam-3328	241	8	dk1	dk1	NOUN
ejpam-3328	241	9	.	.	PUNCT
ejpam-3328	241	10	.	.	PUNCT
ejpam-3328	241	11	.	.	PUNCT
ejpam-3328	242	1	dkn	dkn	PROPN
ejpam-3328	242	2	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-3328	242	3	≤	≤	PROPN
ejpam-3328	242	4	∑	∑	PUNCT
ejpam-3328	242	5	n>0	n>0	DET
ejpam-3328	242	6	2nαn	2nαn	NUM
ejpam-3328	242	7	=	=	SYM
ejpam-3328	242	8	2α	2α	X
ejpam-3328	242	9	1−	1−	NUM
ejpam-3328	242	10	2α	2α	NOUN
ejpam-3328	242	11	.	.	PUNCT
ejpam-3328	243	1	denoting	denote	VERB
ejpam-3328	243	2	λ	λ	PROPN
ejpam-3328	243	3	=	=	SYM
ejpam-3328	243	4	∂	∂	PUNCT
ejpam-3328	244	1	∂k	∂k	NOUN
ejpam-3328	244	2	,	,	PUNCT
ejpam-3328	244	3	r	r	NOUN
ejpam-3328	244	4	=	=	PUNCT
ejpam-3328	245	1	√	√	NUM
ejpam-3328	245	2	x2	x2	NOUN
ejpam-3328	245	3	1	1	NUM
ejpam-3328	246	1	+	+	NUM
ejpam-3328	246	2	x2	x2	PROPN
ejpam-3328	246	3	2	2	NUM
ejpam-3328	247	1	+	+	NUM
ejpam-3328	247	2	x2	x2	PROPN
ejpam-3328	247	3	3	3	NUM
ejpam-3328	247	4	,	,	PUNCT
ejpam-3328	247	5	we	we	PRON
ejpam-3328	247	6	have	have	VERB
ejpam-3328	247	7	λ	λ	PROPN
ejpam-3328	247	8	∫	∫	PROPN
ejpam-3328	247	9	s2	s2	PROPN
ejpam-3328	247	10	ψ0dθ	ψ0dθ	PUNCT
ejpam-3328	248	1	=	=	SYM
ejpam-3328	248	2	λ	λ	NOUN
ejpam-3328	248	3	sin(kr	sin(kr	NOUN
ejpam-3328	248	4	)	)	PUNCT
ejpam-3328	248	5	ikr	ikr	NOUN
ejpam-3328	248	6	=	=	SYM
ejpam-3328	248	7	cos(kr	cos(kr	NOUN
ejpam-3328	248	8	)	)	PUNCT
ejpam-3328	248	9	ik	ik	PROPN
ejpam-3328	248	10	−	−	PROPN
ejpam-3328	248	11	sin(kr	sin(kr	NOUN
ejpam-3328	248	12	)	)	PUNCT
ejpam-3328	248	13	ik2r	ik2r	PROPN
ejpam-3328	248	14	,	,	PUNCT
ejpam-3328	248	15	λ	λ	PROPN
ejpam-3328	248	16	∫	∫	PROPN
ejpam-3328	248	17	s2	s2	PROPN
ejpam-3328	248	18	h0ψ0dθ	h0ψ0dθ	PUNCT
ejpam-3328	249	1	=	=	X
ejpam-3328	249	2	λk2	λk2	PROPN
ejpam-3328	249	3	sin(kr	sin(kr	NOUN
ejpam-3328	249	4	)	)	PUNCT
ejpam-3328	249	5	ikr	ikr	X
ejpam-3328	249	6	=	=	SYM
ejpam-3328	250	1	k	k	PROPN
ejpam-3328	250	2	cos(kr	cos(kr	PROPN
ejpam-3328	250	3	)	)	PUNCT
ejpam-3328	251	1	i	i	PRON
ejpam-3328	251	2	+	+	NUM
ejpam-3328	251	3	sin(kr	sin(kr	X
ejpam-3328	251	4	)	)	PUNCT
ejpam-3328	251	5	ik2r	ik2r	PROPN
ejpam-3328	251	6	,	,	PUNCT
ejpam-3328	251	7	∣∣∣∣λ	∣∣∣∣λ	VERB
ejpam-3328	251	8	∫	∫	PROPN
ejpam-3328	251	9	s2	s2	PROPN
ejpam-3328	251	10	ψdθ	ψdθ	ADP
ejpam-3328	251	11	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3328	251	12	=	=	PUNCT
ejpam-3328	251	13	∣∣∣∣∣∣λ	∣∣∣∣∣∣λ	NOUN
ejpam-3328	251	14	∫	∫	PROPN
ejpam-3328	251	15	s2	s2	PROPN
ejpam-3328	251	16	ψ0dθ	ψ0dθ	PUNCT
ejpam-3328	252	1	+	+	CCONJ
ejpam-3328	252	2	λ	λ	PROPN
ejpam-3328	252	3	∫	∫	PROPN
ejpam-3328	252	4	s2	s2	PROPN
ejpam-3328	252	5	∑	∑	PROPN
ejpam-3328	252	6	n≥0	n≥0	PROPN
ejpam-3328	252	7	(	(	PUNCT
ejpam-3328	252	8	−t−d)n	−t−d)n	PROPN
ejpam-3328	252	9	ψ0dθ	ψ0dθ	PUNCT
ejpam-3328	252	10	∣∣∣∣∣∣	∣∣∣∣∣∣	X
ejpam-3328	252	11	>	>	X
ejpam-3328	253	1	(	(	PUNCT
ejpam-3328	253	2	1	1	NUM
ejpam-3328	253	3	k	k	NOUN
ejpam-3328	253	4	−	−	NOUN
ejpam-3328	253	5	α	α	NOUN
ejpam-3328	253	6	1−	1−	NUM
ejpam-3328	253	7	α	α	NOUN
ejpam-3328	253	8	)	)	PUNCT
ejpam-3328	253	9	,	,	PUNCT
ejpam-3328	253	10	as	as	ADP
ejpam-3328	253	11	kr	kr	PROPN
ejpam-3328	253	12	=	=	SYM
ejpam-3328	253	13	π	π	PROPN
ejpam-3328	253	14	,	,	PUNCT
ejpam-3328	253	15	and	and	CCONJ
ejpam-3328	253	16	λ	λ	X
ejpam-3328	253	17	1	1	NUM
ejpam-3328	253	18	k	k	NOUN
ejpam-3328	253	19	−	−	PROPN
ejpam-3328	253	20	t	t	NOUN
ejpam-3328	253	21	=	=	PUNCT
ejpam-3328	254	1	−	−	PROPN
ejpam-3328	254	2	1	1	NUM
ejpam-3328	254	3	(	(	PUNCT
ejpam-3328	254	4	k	k	NOUN
ejpam-3328	254	5	−	−	PROPN
ejpam-3328	254	6	t)2	t)2	NOUN
ejpam-3328	254	7	equation	equation	NOUN
ejpam-3328	254	8	(	(	PUNCT
ejpam-3328	254	9	2	2	X
ejpam-3328	254	10	)	)	PUNCT
ejpam-3328	254	11	yields	yield	NOUN
ejpam-3328	254	12	q	q	NOUN
ejpam-3328	255	1	=	=	PUNCT
ejpam-3328	255	2	λ	λ	X
ejpam-3328	255	3	(	(	PUNCT
ejpam-3328	255	4	h0	h0	PROPN
ejpam-3328	255	5	∫	∫	PROPN
ejpam-3328	255	6	s2	s2	PROPN
ejpam-3328	255	7	ψdθ	ψdθ	ADP
ejpam-3328	255	8	+	+	CCONJ
ejpam-3328	255	9	k2	k2	ADJ
ejpam-3328	255	10	∫	∫	PROPN
ejpam-3328	255	11	s2	s2	PROPN
ejpam-3328	255	12	ψdθ	ψdθ	NOUN
ejpam-3328	255	13	)	)	PUNCT
ejpam-3328	256	1	λ	λ	PROPN
ejpam-3328	256	2	∫	∫	PROPN
ejpam-3328	256	3	s2	s2	VERB
ejpam-3328	256	4	ψdθ	ψdθ	NOUN
ejpam-3328	256	5	=	=	SYM
ejpam-3328	256	6	2k	2k	NUM
ejpam-3328	256	7	∫	∫	PROPN
ejpam-3328	256	8	s2	s2	PROPN
ejpam-3328	256	9	t−g−dθ	t−g−dθ	ADP
ejpam-3328	256	10	+	+	CCONJ
ejpam-3328	256	11	k2	k2	ADJ
ejpam-3328	256	12	∫	∫	PROPN
ejpam-3328	256	13	s2	s2	PROPN
ejpam-3328	256	14	λt−g−dθ	λt−g−dθ	X
ejpam-3328	257	1	+	+	ADJ
ejpam-3328	257	2	h0λ	h0λ	PROPN
ejpam-3328	257	3	∫	∫	PROPN
ejpam-3328	257	4	s2	s2	PROPN
ejpam-3328	257	5	t−g−dθ	t−g−dθ	ADP
ejpam-3328	257	6	λ	λ	PROPN
ejpam-3328	257	7	∫	∫	PROPN
ejpam-3328	257	8	s2	s2	VERB
ejpam-3328	257	9	ψdθ	ψdθ	NOUN
ejpam-3328	257	10	=	=	SYM
ejpam-3328	257	11	2k	2k	NUM
ejpam-3328	257	12	∫	∫	PROPN
ejpam-3328	257	13	s2	s2	PROPN
ejpam-3328	257	14	t−g−dθ	t−g−dθ	ADP
ejpam-3328	257	15	+	+	CCONJ
ejpam-3328	257	16	λ	λ	PROPN
ejpam-3328	257	17	∫	∫	PROPN
ejpam-3328	257	18	s2	s2	PROPN
ejpam-3328	257	19	∑	∑	ADV
ejpam-3328	257	20	n≥1	n≥1	PROPN
ejpam-3328	257	21	(	(	PUNCT
ejpam-3328	257	22	−t−d)n	−t−d)n	PROPN
ejpam-3328	257	23	(	(	PUNCT
ejpam-3328	257	24	k2	k2	PROPN
ejpam-3328	257	25	−	−	PROPN
ejpam-3328	257	26	k2)ψ0dθ	k2)ψ0dθ	PROPN
ejpam-3328	258	1	λ	λ	PROPN
ejpam-3328	258	2	∫	∫	PROPN
ejpam-3328	258	3	s2	s2	VERB
ejpam-3328	258	4	ψdθ	ψdθ	NOUN
ejpam-3328	258	5	=	=	SYM
ejpam-3328	258	6	w0	w0	PROPN
ejpam-3328	258	7	+	+	CCONJ
ejpam-3328	258	8	∑	∑	PROPN
ejpam-3328	258	9	n≥1	n≥1	PROPN
ejpam-3328	258	10	∫	∫	PROPN
ejpam-3328	258	11	s2	s2	PROPN
ejpam-3328	258	12	wn	wn	PROPN
ejpam-3328	258	13	λ	λ	PROPN
ejpam-3328	258	14	∫	∫	PROPN
ejpam-3328	258	15	s2	s2	PROPN
ejpam-3328	258	16	ψdθ	ψdθ	NOUN
ejpam-3328	258	17	.	.	PUNCT
ejpam-3328	259	1	denoting	denote	VERB
ejpam-3328	259	2	z(k	z(k	PROPN
ejpam-3328	259	3	,	,	PUNCT
ejpam-3328	259	4	s	s	PART
ejpam-3328	259	5	)	)	PUNCT
ejpam-3328	259	6	=	=	PUNCT
ejpam-3328	259	7	s+	s+	PUNCT
ejpam-3328	259	8	2k	2k	NUM
ejpam-3328	259	9	+	+	CCONJ
ejpam-3328	259	10	2k2	2k2	NUM
ejpam-3328	260	1	k	k	NOUN
ejpam-3328	260	2	−	−	PROPN
ejpam-3328	260	3	s	s	PART
ejpam-3328	260	4	,	,	PUNCT
ejpam-3328	260	5	we	we	PRON
ejpam-3328	260	6	then	then	ADV
ejpam-3328	260	7	have	have	VERB
ejpam-3328	260	8	|w1|	|w1|	NOUN
ejpam-3328	260	9	≤	≤	NUM
ejpam-3328	260	10	∣∣∣∣∫	∣∣∣∣∫	NOUN
ejpam-3328	260	11	+	+	NOUN
ejpam-3328	260	12	∞	∞	PROPN
ejpam-3328	260	13	−∞	−∞	ADP
ejpam-3328	260	14	∫	∫	PROPN
ejpam-3328	260	15	s2	s2	PROPN
ejpam-3328	260	16	∫	∫	PROPN
ejpam-3328	260	17	s2	s2	PROPN
ejpam-3328	260	18	a(s	a(s	PROPN
ejpam-3328	260	19	,	,	PUNCT
ejpam-3328	260	20	θ	θ	PROPN
ejpam-3328	260	21	,	,	PUNCT
ejpam-3328	260	22	θ′)s	θ′)s	AUX
ejpam-3328	260	23	s2	s2	VERB
ejpam-3328	260	24	−	−	PROPN
ejpam-3328	260	25	k2	k2	PROPN
ejpam-3328	260	26	(	(	PUNCT
ejpam-3328	260	27	k	k	PROPN
ejpam-3328	260	28	−	−	PROPN
ejpam-3328	260	29	s)2	s)2	PROPN
ejpam-3328	260	30	ψ0	ψ0	ADV
ejpam-3328	260	31	sin(θ)dsdθ	sin(θ)dsdθ	VERB
ejpam-3328	260	32	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3328	260	33	k	k	PROPN
ejpam-3328	260	34	=	=	PROPN
ejpam-3328	260	35	k0	k0	PROPN
ejpam-3328	260	36	≤	≤	PROPN
ejpam-3328	260	37	∣∣∣∣∫	∣∣∣∣∫	NOUN
ejpam-3328	261	1	+	+	NOUN
ejpam-3328	261	2	∞	∞	PROPN
ejpam-3328	261	3	−∞	−∞	ADP
ejpam-3328	261	4	∫	∫	PROPN
ejpam-3328	261	5	s2	s2	PROPN
ejpam-3328	261	6	∫	∫	PROPN
ejpam-3328	261	7	s2	s2	PROPN
ejpam-3328	261	8	z(k	z(k	PROPN
ejpam-3328	261	9	,	,	PUNCT
ejpam-3328	261	10	)	)	PUNCT
ejpam-3328	262	1	q̃(k(θ	q̃(k(θ	X
ejpam-3328	263	1	−	−	NOUN
ejpam-3328	263	2	θ′))ψ0dkdθ	θ′))ψ0dkdθ	PROPN
ejpam-3328	263	3	∣∣∣∣+	∣∣∣∣+	PROPN
ejpam-3328	263	4	c0	c0	PROPN
ejpam-3328	263	5	∣∣∣∣∫	∣∣∣∣∫	PROPN
ejpam-3328	263	6	s2	s2	PROPN
ejpam-3328	263	7	tkqdθ	tkqdθ	NOUN
ejpam-3328	263	8	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3328	263	9	.	.	PUNCT
ejpam-3328	263	10	a.	a.	PROPN
ejpam-3328	263	11	durmagambetov	durmagambetov	PROPN
ejpam-3328	263	12	/	/	SYM
ejpam-3328	263	13	eur	eur	PROPN
ejpam-3328	263	14	.	.	PUNCT
ejpam-3328	264	1	j.	j.	PROPN
ejpam-3328	264	2	pure	pure	PROPN
ejpam-3328	264	3	appl	appl	PROPN
ejpam-3328	264	4	.	.	PROPN
ejpam-3328	264	5	math	math	PROPN
ejpam-3328	264	6	,	,	PUNCT
ejpam-3328	264	7	11	11	NUM
ejpam-3328	264	8	(	(	PUNCT
ejpam-3328	264	9	4	4	NUM
ejpam-3328	264	10	)	)	PUNCT
ejpam-3328	264	11	(	(	PUNCT
ejpam-3328	264	12	2018	2018	NUM
ejpam-3328	264	13	)	)	PUNCT
ejpam-3328	264	14	,	,	PUNCT
ejpam-3328	264	15	1143	1143	NUM
ejpam-3328	264	16	-	-	SYM
ejpam-3328	264	17	1176	1176	NUM
ejpam-3328	264	18	1154	1154	NUM
ejpam-3328	264	19	for	for	ADP
ejpam-3328	264	20	calculating	calculate	VERB
ejpam-3328	264	21	wn	wn	PROPN
ejpam-3328	264	22	,	,	PUNCT
ejpam-3328	264	23	as	as	ADP
ejpam-3328	264	24	n	n	PROPN
ejpam-3328	264	25	≥	≥	NOUN
ejpam-3328	264	26	1	1	NUM
ejpam-3328	264	27	,	,	PUNCT
ejpam-3328	264	28	take	take	VERB
ejpam-3328	264	29	the	the	DET
ejpam-3328	264	30	simple	simple	ADJ
ejpam-3328	264	31	transformation	transformation	NOUN
ejpam-3328	264	32	s3	s3	PROPN
ejpam-3328	264	33	n	n	PROPN
ejpam-3328	264	34	sn	sn	NOUN
ejpam-3328	264	35	−	−	PROPN
ejpam-3328	264	36	sn−1	sn−1	PROPN
ejpam-3328	264	37	=	=	SYM
ejpam-3328	264	38	s3	s3	PROPN
ejpam-3328	264	39	n	n	CCONJ
ejpam-3328	264	40	−	−	PROPN
ejpam-3328	264	41	s2	s2	PROPN
ejpam-3328	264	42	nsn−1	nsn−1	PROPN
ejpam-3328	264	43	sn	sn	PROPN
ejpam-3328	264	44	−	−	PROPN
ejpam-3328	265	1	sn−1	sn−1	PROPN
ejpam-3328	265	2	+	+	CCONJ
ejpam-3328	265	3	s2	s2	VERB
ejpam-3328	265	4	nsn−1	nsn−1	PROPN
ejpam-3328	265	5	sn	sn	PROPN
ejpam-3328	265	6	−	−	PUNCT
ejpam-3328	265	7	sn−1	sn−1	PROPN
ejpam-3328	265	8	=	=	SYM
ejpam-3328	265	9	s2	s2	PROPN
ejpam-3328	265	10	n	n	PROPN
ejpam-3328	265	11	+	+	CCONJ
ejpam-3328	265	12	s2	s2	VERB
ejpam-3328	265	13	nsn−1	nsn−1	PROPN
ejpam-3328	265	14	sn	sn	PROPN
ejpam-3328	265	15	−	−	PUNCT
ejpam-3328	265	16	sn−1	sn−1	PROPN
ejpam-3328	265	17	=	=	SYM
ejpam-3328	265	18	s2	s2	PROPN
ejpam-3328	265	19	n	n	PROPN
ejpam-3328	265	20	+	+	CCONJ
ejpam-3328	265	21	s2	s2	VERB
ejpam-3328	265	22	nsn−1	nsn−1	PROPN
ejpam-3328	265	23	−	−	PROPN
ejpam-3328	265	24	sns2	sns2	VERB
ejpam-3328	265	25	n−1	n−1	PROPN
ejpam-3328	265	26	sn	sn	PROPN
ejpam-3328	265	27	−	−	PROPN
ejpam-3328	266	1	sn−1	sn−1	PROPN
ejpam-3328	266	2	+	+	CCONJ
ejpam-3328	266	3	sns	sns	PROPN
ejpam-3328	266	4	2	2	NUM
ejpam-3328	266	5	n−1	n−1	PROPN
ejpam-3328	266	6	sn	sn	PROPN
ejpam-3328	266	7	−	−	PROPN
ejpam-3328	266	8	sn−1	sn−1	PROPN
ejpam-3328	266	9	=	=	SYM
ejpam-3328	266	10	s2	s2	PROPN
ejpam-3328	266	11	n	n	NOUN
ejpam-3328	266	12	+	+	NUM
ejpam-3328	266	13	snsn−1	snsn−1	PROPN
ejpam-3328	266	14	+	+	CCONJ
ejpam-3328	266	15	sns	sns	PROPN
ejpam-3328	266	16	2	2	NUM
ejpam-3328	266	17	n−1	n−1	PROPN
ejpam-3328	266	18	sn	sn	PROPN
ejpam-3328	266	19	−	−	PROPN
ejpam-3328	266	20	sn−1	sn−1	PROPN
ejpam-3328	266	21	,	,	PUNCT
ejpam-3328	266	22	(	(	PUNCT
ejpam-3328	266	23	6	6	NUM
ejpam-3328	266	24	)	)	PUNCT
ejpam-3328	266	25	as3	as3	PROPN
ejpam-3328	266	26	n	n	CCONJ
ejpam-3328	266	27	sn	sn	NOUN
ejpam-3328	266	28	−	−	PROPN
ejpam-3328	266	29	sn−1	sn−1	PROPN
ejpam-3328	266	30	=	=	SYM
ejpam-3328	266	31	as2	as2	PROPN
ejpam-3328	266	32	n	n	X
ejpam-3328	266	33	+	+	ADV
ejpam-3328	266	34	asnsn−1	asnsn−1	PROPN
ejpam-3328	266	35	+	+	NUM
ejpam-3328	266	36	asns	asns	NOUN
ejpam-3328	266	37	2	2	NUM
ejpam-3328	266	38	n−1	n−1	PROPN
ejpam-3328	266	39	sn	sn	PROPN
ejpam-3328	266	40	−	−	PROPN
ejpam-3328	266	41	sn−1	sn−1	PROPN
ejpam-3328	266	42	=	=	SYM
ejpam-3328	266	43	v1	v1	PROPN
ejpam-3328	266	44	+	+	CCONJ
ejpam-3328	266	45	v2	v2	PROPN
ejpam-3328	266	46	+	+	CCONJ
ejpam-3328	266	47	v3	v3	PROPN
ejpam-3328	266	48	.	.	PUNCT
ejpam-3328	267	1	using	use	VERB
ejpam-3328	267	2	lemma	lemma	PROPN
ejpam-3328	267	3	10	10	NUM
ejpam-3328	267	4	for	for	ADP
ejpam-3328	267	5	estimating	estimate	VERB
ejpam-3328	267	6	v1	v1	NOUN
ejpam-3328	267	7	and	and	CCONJ
ejpam-3328	267	8	v2	v2	PROPN
ejpam-3328	267	9	and	and	CCONJ
ejpam-3328	267	10	,	,	PUNCT
ejpam-3328	267	11	for	for	ADP
ejpam-3328	267	12	v3	v3	PROPN
ejpam-3328	267	13	,	,	PUNCT
ejpam-3328	267	14	taking	take	VERB
ejpam-3328	267	15	again	again	ADV
ejpam-3328	267	16	the	the	DET
ejpam-3328	267	17	simple	simple	ADJ
ejpam-3328	267	18	transformation	transformation	NOUN
ejpam-3328	267	19	for	for	ADP
ejpam-3328	267	20	s3	s3	PROPN
ejpam-3328	267	21	n−1	n−1	PROPN
ejpam-3328	267	22	,	,	PUNCT
ejpam-3328	267	23	which	which	PRON
ejpam-3328	267	24	will	will	AUX
ejpam-3328	267	25	appear	appear	VERB
ejpam-3328	267	26	in	in	ADP
ejpam-3328	267	27	the	the	DET
ejpam-3328	267	28	integration	integration	NOUN
ejpam-3328	267	29	over	over	ADP
ejpam-3328	267	30	sn−1	sn−1	PROPN
ejpam-3328	267	31	,	,	PUNCT
ejpam-3328	267	32	we	we	PRON
ejpam-3328	267	33	finally	finally	ADV
ejpam-3328	267	34	get	get	VERB
ejpam-3328	267	35	|q(x)|r	|q(x)|r	PROPN
ejpam-3328	267	36	=	=	NOUN
ejpam-3328	267	37	r0	r0	NOUN
ejpam-3328	267	38	=	=	PUNCT
ejpam-3328	267	39	∣∣∣∣∣λ	∣∣∣∣∣λ	NOUN
ejpam-3328	267	40	(	(	PUNCT
ejpam-3328	267	41	h0	h0	PROPN
ejpam-3328	267	42	∫	∫	PROPN
ejpam-3328	267	43	s2	s2	PROPN
ejpam-3328	267	44	ψdθ	ψdθ	ADP
ejpam-3328	267	45	+	+	CCONJ
ejpam-3328	267	46	k2	k2	ADJ
ejpam-3328	267	47	∫	∫	PROPN
ejpam-3328	267	48	s2	s2	PROPN
ejpam-3328	267	49	ψdθ	ψdθ	NOUN
ejpam-3328	267	50	)	)	PUNCT
ejpam-3328	268	1	λ	λ	PROPN
ejpam-3328	268	2	∫	∫	PROPN
ejpam-3328	268	3	s2	s2	NOUN
ejpam-3328	268	4	ψdθ	ψdθ	NOUN
ejpam-3328	268	5	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-3328	269	1	k	k	NOUN
ejpam-3328	270	1	=	=	NOUN
ejpam-3328	270	2	k0,r=	k0,r=	X
ejpam-3328	270	3	π	π	PROPN
ejpam-3328	270	4	k0	k0	PROPN
ejpam-3328	270	5	≤	≤	PROPN
ejpam-3328	270	6	∣∣∣∫	∣∣∣∫	NOUN
ejpam-3328	270	7	+	+	NOUN
ejpam-3328	270	8	∞	∞	PROPN
ejpam-3328	270	9	−∞	−∞	ADP
ejpam-3328	270	10	∫	∫	PROPN
ejpam-3328	270	11	s2	s2	PROPN
ejpam-3328	270	12	∫	∫	PROPN
ejpam-3328	270	13	s2	s2	PROPN
ejpam-3328	270	14	z(k	z(k	PROPN
ejpam-3328	270	15	,	,	PUNCT
ejpam-3328	270	16	)	)	PUNCT
ejpam-3328	270	17	q̃(k(θ	q̃(k(θ	X
ejpam-3328	271	1	−	−	NOUN
ejpam-3328	271	2	θ′))ψ0dkdθdθ	θ′))ψ0dkdθdθ	NUM
ejpam-3328	271	3	′	′	NOUN
ejpam-3328	271	4	∣∣∣+	∣∣∣+	PROPN
ejpam-3328	271	5	c0	c0	PROPN
ejpam-3328	271	6	∣∣∫	∣∣∫	PROPN
ejpam-3328	271	7	s2	s2	PROPN
ejpam-3328	271	8	tkqdθ	tkqdθ	NOUN
ejpam-3328	271	9	∣∣	∣∣	NUM
ejpam-3328	271	10	(	(	PUNCT
ejpam-3328	271	11	1	1	NUM
ejpam-3328	271	12	k0	k0	PROPN
ejpam-3328	271	13	−	−	PROPN
ejpam-3328	271	14	α	α	PROPN
ejpam-3328	271	15	(	(	PUNCT
ejpam-3328	271	16	1−α	1−α	NUM
ejpam-3328	271	17	)	)	PUNCT
ejpam-3328	271	18	)	)	PUNCT
ejpam-3328	272	1	+	+	CCONJ
ejpam-3328	272	2	finally	finally	ADV
ejpam-3328	272	3	,	,	PUNCT
ejpam-3328	272	4	we	we	PRON
ejpam-3328	272	5	get	get	VERB
ejpam-3328	272	6	|q(x)|r	|q(x)|r	PROPN
ejpam-3328	272	7	=	=	NOUN
ejpam-3328	272	8	r0	r0	NOUN
ejpam-3328	272	9	≤	≤	NUM
ejpam-3328	272	10	sup	sup	NOUN
ejpam-3328	272	11	x∈r3	x∈r3	PROPN
ejpam-3328	272	12	|q(x)|α+	|q(x)|α+	PROPN
ejpam-3328	272	13	c0	c0	PROPN
ejpam-3328	272	14	‖q‖2l2(r3	‖q‖2l2(r3	X
ejpam-3328	272	15	)	)	PUNCT
ejpam-3328	273	1	+	+	CCONJ
ejpam-3328	273	2	c0	c0	PROPN
ejpam-3328	273	3	‖q‖l2(r3	‖q‖l2(r3	PUNCT
ejpam-3328	273	4	)	)	PUNCT
ejpam-3328	274	1	+	+	CCONJ
ejpam-3328	274	2	∣∣∣∣∫	∣∣∣∣∫	NUM
ejpam-3328	274	3	s2	s2	NOUN
ejpam-3328	274	4	tkqdθ	tkqdθ	NOUN
ejpam-3328	274	5	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3328	274	6	.	.	PUNCT
ejpam-3328	275	1	the	the	DET
ejpam-3328	275	2	invariance	invariance	NOUN
ejpam-3328	275	3	of	of	ADP
ejpam-3328	275	4	the	the	DET
ejpam-3328	275	5	schrödinger	schrödinger	NOUN
ejpam-3328	275	6	equations	equation	NOUN
ejpam-3328	275	7	with	with	ADP
ejpam-3328	275	8	respect	respect	NOUN
ejpam-3328	275	9	to	to	ADP
ejpam-3328	275	10	translations	translation	NOUN
ejpam-3328	275	11	and	and	CCONJ
ejpam-3328	275	12	the	the	DET
ejpam-3328	275	13	arbitrariness	arbitrariness	NOUN
ejpam-3328	275	14	of	of	ADP
ejpam-3328	275	15	r0	r0	NOUN
ejpam-3328	275	16	yield	yield	NOUN
ejpam-3328	275	17	sup	sup	NOUN
ejpam-3328	275	18	x∈r3	x∈r3	NOUN
ejpam-3328	275	19	|q(x)|	|q(x)|	PROPN
ejpam-3328	275	20	≤	≤	PROPN
ejpam-3328	275	21	∣∣∣∣∫	∣∣∣∣∫	NUM
ejpam-3328	275	22	s2	s2	PROPN
ejpam-3328	275	23	tkqdθ	tkqdθ	NOUN
ejpam-3328	275	24	∣∣∣∣c0	∣∣∣∣c0	PROPN
ejpam-3328	275	25	(	(	PUNCT
ejpam-3328	275	26	‖q‖2l2(r3	‖q‖2l2(r3	ADP
ejpam-3328	275	27	)	)	PUNCT
ejpam-3328	275	28	+	+	CCONJ
ejpam-3328	275	29	1	1	X
ejpam-3328	275	30	)	)	PUNCT
ejpam-3328	275	31	+	+	CCONJ
ejpam-3328	275	32	c0	c0	PROPN
ejpam-3328	275	33	‖q‖l2(r3	‖q‖l2(r3	PUNCT
ejpam-3328	275	34	)	)	PUNCT
ejpam-3328	275	35	.	.	PUNCT
ejpam-3328	276	1	4	4	X
ejpam-3328	276	2	.	.	X
ejpam-3328	276	3	discussion	discussion	NOUN
ejpam-3328	276	4	of	of	ADP
ejpam-3328	276	5	the	the	DET
ejpam-3328	276	6	three	three	NUM
ejpam-3328	276	7	-	-	PUNCT
ejpam-3328	276	8	dimensional	dimensional	ADJ
ejpam-3328	276	9	inverse	inverse	NOUN
ejpam-3328	276	10	scattering	scattering	NOUN
ejpam-3328	276	11	problem	problem	NOUN
ejpam-3328	276	12	this	this	DET
ejpam-3328	276	13	study	study	NOUN
ejpam-3328	276	14	has	have	AUX
ejpam-3328	276	15	shown	show	VERB
ejpam-3328	276	16	,	,	PUNCT
ejpam-3328	276	17	once	once	ADV
ejpam-3328	276	18	again	again	ADV
ejpam-3328	276	19	,	,	PUNCT
ejpam-3328	276	20	the	the	DET
ejpam-3328	276	21	outstanding	outstanding	ADJ
ejpam-3328	276	22	properties	property	NOUN
ejpam-3328	276	23	of	of	ADP
ejpam-3328	276	24	the	the	DET
ejpam-3328	276	25	scattering	scatter	VERB
ejpam-3328	276	26	operator	operator	NOUN
ejpam-3328	276	27	,	,	PUNCT
ejpam-3328	276	28	which	which	PRON
ejpam-3328	276	29	,	,	PUNCT
ejpam-3328	276	30	in	in	ADP
ejpam-3328	276	31	combination	combination	NOUN
ejpam-3328	276	32	with	with	ADP
ejpam-3328	276	33	the	the	DET
ejpam-3328	276	34	analytical	analytical	ADJ
ejpam-3328	276	35	properties	property	NOUN
ejpam-3328	276	36	of	of	ADP
ejpam-3328	276	37	the	the	DET
ejpam-3328	276	38	wave	wave	NOUN
ejpam-3328	276	39	function	function	NOUN
ejpam-3328	276	40	,	,	PUNCT
ejpam-3328	276	41	allows	allow	VERB
ejpam-3328	276	42	us	we	PRON
ejpam-3328	276	43	to	to	PART
ejpam-3328	276	44	obtain	obtain	VERB
ejpam-3328	276	45	almost	almost	ADV
ejpam-3328	276	46	-	-	PUNCT
ejpam-3328	276	47	explicit	explicit	ADJ
ejpam-3328	276	48	formulas	formula	NOUN
ejpam-3328	276	49	for	for	ADP
ejpam-3328	276	50	the	the	DET
ejpam-3328	276	51	potential	potential	NOUN
ejpam-3328	276	52	from	from	ADP
ejpam-3328	276	53	the	the	DET
ejpam-3328	276	54	scattering	scatter	VERB
ejpam-3328	276	55	amplitude	amplitude	NOUN
ejpam-3328	276	56	.	.	PUNCT
ejpam-3328	277	1	furthermore	furthermore	ADV
ejpam-3328	277	2	,	,	PUNCT
ejpam-3328	277	3	this	this	DET
ejpam-3328	277	4	appro	appro	ADJ
ejpam-3328	277	5	.	.	PUNCT
ejpam-3328	278	1	the	the	DET
ejpam-3328	278	2	estimations	estimation	NOUN
ejpam-3328	278	3	following	follow	VERB
ejpam-3328	278	4	from	from	ADP
ejpam-3328	278	5	this	this	DET
ejpam-3328	278	6	overcome	overcome	NOUN
ejpam-3328	278	7	the	the	DET
ejpam-3328	278	8	problem	problem	NOUN
ejpam-3328	278	9	of	of	ADP
ejpam-3328	278	10	overdetermination	overdetermination	NOUN
ejpam-3328	278	11	,	,	PUNCT
ejpam-3328	278	12	resulting	result	VERB
ejpam-3328	278	13	from	from	ADP
ejpam-3328	278	14	the	the	DET
ejpam-3328	278	15	fact	fact	NOUN
ejpam-3328	278	16	that	that	SCONJ
ejpam-3328	278	17	the	the	DET
ejpam-3328	278	18	potential	potential	NOUN
ejpam-3328	278	19	is	be	AUX
ejpam-3328	278	20	a	a	DET
ejpam-3328	278	21	function	function	NOUN
ejpam-3328	278	22	of	of	ADP
ejpam-3328	278	23	three	three	NUM
ejpam-3328	278	24	variables	variable	NOUN
ejpam-3328	278	25	,	,	PUNCT
ejpam-3328	278	26	whereas	whereas	SCONJ
ejpam-3328	278	27	the	the	DET
ejpam-3328	278	28	amplitude	amplitude	NOUN
ejpam-3328	278	29	is	be	AUX
ejpam-3328	278	30	a	a	DET
ejpam-3328	278	31	function	function	NOUN
ejpam-3328	278	32	of	of	ADP
ejpam-3328	278	33	five	five	NUM
ejpam-3328	278	34	variables	variable	NOUN
ejpam-3328	278	35	.	.	PUNCT
ejpam-3328	279	1	we	we	PRON
ejpam-3328	279	2	have	have	AUX
ejpam-3328	279	3	shown	show	VERB
ejpam-3328	279	4	that	that	SCONJ
ejpam-3328	279	5	it	it	PRON
ejpam-3328	279	6	is	be	AUX
ejpam-3328	279	7	sufficient	sufficient	ADJ
ejpam-3328	279	8	to	to	PART
ejpam-3328	279	9	average	average	VERB
ejpam-3328	279	10	the	the	DET
ejpam-3328	279	11	scattering	scatter	VERB
ejpam-3328	279	12	amplitude	amplitude	NOUN
ejpam-3328	279	13	to	to	PART
ejpam-3328	279	14	eliminate	eliminate	VERB
ejpam-3328	279	15	the	the	DET
ejpam-3328	279	16	two	two	NUM
ejpam-3328	279	17	extra	extra	ADJ
ejpam-3328	279	18	variables	variable	NOUN
ejpam-3328	279	19	.	.	PUNCT
ejpam-3328	280	1	a.	a.	NOUN
ejpam-3328	280	2	durmagambetov	durmagambetov	PROPN
ejpam-3328	280	3	/	/	SYM
ejpam-3328	280	4	eur	eur	PROPN
ejpam-3328	280	5	.	.	PUNCT
ejpam-3328	281	1	j.	j.	PROPN
ejpam-3328	281	2	pure	pure	PROPN
ejpam-3328	281	3	appl	appl	PROPN
ejpam-3328	281	4	.	.	PROPN
ejpam-3328	281	5	math	math	PROPN
ejpam-3328	281	6	,	,	PUNCT
ejpam-3328	281	7	11	11	NUM
ejpam-3328	281	8	(	(	PUNCT
ejpam-3328	281	9	4	4	NUM
ejpam-3328	281	10	)	)	PUNCT
ejpam-3328	281	11	(	(	PUNCT
ejpam-3328	281	12	2018	2018	NUM
ejpam-3328	281	13	)	)	PUNCT
ejpam-3328	281	14	,	,	PUNCT
ejpam-3328	281	15	1143	1143	NUM
ejpam-3328	281	16	-	-	SYM
ejpam-3328	281	17	1176	1176	NUM
ejpam-3328	281	18	1155	1155	NUM
ejpam-3328	281	19	5	5	NUM
ejpam-3328	281	20	.	.	PUNCT
ejpam-3328	282	1	studying	study	VERB
ejpam-3328	282	2	the	the	DET
ejpam-3328	282	3	properties	property	NOUN
ejpam-3328	282	4	of	of	ADP
ejpam-3328	282	5	solutions	solution	NOUN
ejpam-3328	282	6	of	of	ADP
ejpam-3328	282	7	the	the	DET
ejpam-3328	282	8	cauchy	cauchy	ADJ
ejpam-3328	282	9	problem	problem	NOUN
ejpam-3328	282	10	for	for	ADP
ejpam-3328	282	11	the	the	DET
ejpam-3328	282	12	navier	navier	NOUN
ejpam-3328	282	13	–	–	PUNCT
ejpam-3328	282	14	stokes	stoke	NOUN
ejpam-3328	282	15	equations	equation	NOUN
ejpam-3328	282	16	using	use	VERB
ejpam-3328	282	17	analytic	analytic	ADJ
ejpam-3328	282	18	functions	function	NOUN
ejpam-3328	282	19	generated	generate	VERB
ejpam-3328	282	20	by	by	ADP
ejpam-3328	282	21	the	the	DET
ejpam-3328	282	22	schrödinger	schrödinger	NOUN
ejpam-3328	282	23	equations	equation	NOUN
ejpam-3328	282	24	and	and	CCONJ
ejpam-3328	282	25	related	relate	VERB
ejpam-3328	282	26	to	to	ADP
ejpam-3328	282	27	the	the	DET
ejpam-3328	282	28	poincaré--riemann	poincaré--riemann	PROPN
ejpam-3328	282	29	-	-	PUNCT
ejpam-3328	282	30	hilbert	hilbert	PROPN
ejpam-3328	282	31	problem	problem	NOUN
ejpam-3328	282	32	numerous	numerous	ADJ
ejpam-3328	282	33	studies	study	NOUN
ejpam-3328	282	34	of	of	ADP
ejpam-3328	282	35	the	the	DET
ejpam-3328	282	36	navier	navier	NOUN
ejpam-3328	282	37	–	–	PUNCT
ejpam-3328	282	38	stokes	stoke	NOUN
ejpam-3328	282	39	equations	equation	NOUN
ejpam-3328	282	40	have	have	AUX
ejpam-3328	282	41	been	be	AUX
ejpam-3328	282	42	devoted	devote	VERB
ejpam-3328	282	43	to	to	ADP
ejpam-3328	282	44	the	the	DET
ejpam-3328	282	45	problem	problem	NOUN
ejpam-3328	282	46	of	of	ADP
ejpam-3328	282	47	the	the	DET
ejpam-3328	282	48	smoothness	smoothness	NOUN
ejpam-3328	282	49	of	of	ADP
ejpam-3328	282	50	its	its	PRON
ejpam-3328	282	51	solutions	solution	NOUN
ejpam-3328	282	52	.	.	PUNCT
ejpam-3328	283	1	a	a	DET
ejpam-3328	283	2	good	good	ADJ
ejpam-3328	283	3	overview	overview	NOUN
ejpam-3328	283	4	of	of	ADP
ejpam-3328	283	5	these	these	DET
ejpam-3328	283	6	studies	study	NOUN
ejpam-3328	283	7	is	be	AUX
ejpam-3328	283	8	given	give	VERB
ejpam-3328	283	9	in	in	ADP
ejpam-3328	283	10	refs	ref	NOUN
ejpam-3328	283	11	.	.	PUNCT
ejpam-3328	284	1	[	[	X
ejpam-3328	284	2	13–17	13–17	NUM
ejpam-3328	284	3	]	]	PUNCT
ejpam-3328	284	4	.	.	PUNCT
ejpam-3328	285	1	the	the	DET
ejpam-3328	285	2	spatial	spatial	ADJ
ejpam-3328	285	3	differentiability	differentiability	NOUN
ejpam-3328	285	4	of	of	ADP
ejpam-3328	285	5	the	the	DET
ejpam-3328	285	6	solutions	solution	NOUN
ejpam-3328	285	7	is	be	AUX
ejpam-3328	285	8	an	an	DET
ejpam-3328	285	9	important	important	ADJ
ejpam-3328	285	10	factor	factor	NOUN
ejpam-3328	285	11	,	,	PUNCT
ejpam-3328	285	12	as	as	SCONJ
ejpam-3328	285	13	it	it	PRON
ejpam-3328	285	14	controls	control	VERB
ejpam-3328	285	15	their	their	PRON
ejpam-3328	285	16	evolution	evolution	NOUN
ejpam-3328	285	17	.	.	PUNCT
ejpam-3328	286	1	obviously	obviously	ADV
ejpam-3328	286	2	,	,	PUNCT
ejpam-3328	286	3	differentiable	differentiable	ADJ
ejpam-3328	286	4	solutions	solution	NOUN
ejpam-3328	286	5	do	do	AUX
ejpam-3328	286	6	not	not	PART
ejpam-3328	286	7	provide	provide	VERB
ejpam-3328	286	8	an	an	DET
ejpam-3328	286	9	effective	effective	ADJ
ejpam-3328	286	10	description	description	NOUN
ejpam-3328	286	11	of	of	ADP
ejpam-3328	286	12	turbulence	turbulence	NOUN
ejpam-3328	286	13	.	.	PUNCT
ejpam-3328	287	1	nevertheless	nevertheless	ADV
ejpam-3328	287	2	,	,	PUNCT
ejpam-3328	287	3	the	the	DET
ejpam-3328	287	4	global	global	ADJ
ejpam-3328	287	5	solvability	solvability	NOUN
ejpam-3328	287	6	and	and	CCONJ
ejpam-3328	287	7	differentiability	differentiability	NOUN
ejpam-3328	287	8	of	of	ADP
ejpam-3328	287	9	the	the	DET
ejpam-3328	287	10	solutions	solution	NOUN
ejpam-3328	287	11	have	have	AUX
ejpam-3328	287	12	not	not	PART
ejpam-3328	287	13	been	be	AUX
ejpam-3328	287	14	proven	prove	VERB
ejpam-3328	287	15	,	,	PUNCT
ejpam-3328	287	16	and	and	CCONJ
ejpam-3328	287	17	therefore	therefore	ADV
ejpam-3328	287	18	the	the	DET
ejpam-3328	287	19	problem	problem	NOUN
ejpam-3328	287	20	of	of	ADP
ejpam-3328	287	21	describing	describe	VERB
ejpam-3328	287	22	turbulence	turbulence	NOUN
ejpam-3328	287	23	remains	remain	VERB
ejpam-3328	287	24	open	open	ADJ
ejpam-3328	287	25	.	.	PUNCT
ejpam-3328	288	1	it	it	PRON
ejpam-3328	288	2	is	be	AUX
ejpam-3328	288	3	interesting	interesting	ADJ
ejpam-3328	288	4	to	to	PART
ejpam-3328	288	5	study	study	VERB
ejpam-3328	288	6	the	the	DET
ejpam-3328	288	7	properties	property	NOUN
ejpam-3328	288	8	of	of	ADP
ejpam-3328	288	9	the	the	DET
ejpam-3328	288	10	fourier	fourier	NOUN
ejpam-3328	288	11	transform	transform	NOUN
ejpam-3328	288	12	of	of	ADP
ejpam-3328	288	13	solutions	solution	NOUN
ejpam-3328	288	14	of	of	ADP
ejpam-3328	288	15	the	the	DET
ejpam-3328	288	16	navier	navier	NOUN
ejpam-3328	288	17	–	–	PUNCT
ejpam-3328	288	18	stokes	stokes	PROPN
ejpam-3328	288	19	equations	equation	NOUN
ejpam-3328	288	20	.	.	PUNCT
ejpam-3328	289	1	of	of	ADP
ejpam-3328	289	2	particular	particular	ADJ
ejpam-3328	289	3	interest	interest	NOUN
ejpam-3328	289	4	is	be	AUX
ejpam-3328	289	5	how	how	SCONJ
ejpam-3328	289	6	they	they	PRON
ejpam-3328	289	7	can	can	AUX
ejpam-3328	289	8	be	be	AUX
ejpam-3328	289	9	used	use	VERB
ejpam-3328	289	10	in	in	ADP
ejpam-3328	289	11	the	the	DET
ejpam-3328	289	12	description	description	NOUN
ejpam-3328	289	13	of	of	ADP
ejpam-3328	289	14	turbulence	turbulence	NOUN
ejpam-3328	289	15	and	and	CCONJ
ejpam-3328	289	16	whether	whether	SCONJ
ejpam-3328	289	17	they	they	PRON
ejpam-3328	289	18	are	be	AUX
ejpam-3328	289	19	differentiable	differentiable	ADJ
ejpam-3328	289	20	.	.	PUNCT
ejpam-3328	290	1	the	the	DET
ejpam-3328	290	2	differentiability	differentiability	NOUN
ejpam-3328	290	3	of	of	ADP
ejpam-3328	290	4	such	such	ADJ
ejpam-3328	290	5	fourier	fourier	NOUN
ejpam-3328	290	6	transforms	transform	VERB
ejpam-3328	290	7	appears	appear	VERB
ejpam-3328	290	8	to	to	PART
ejpam-3328	290	9	be	be	AUX
ejpam-3328	290	10	related	relate	VERB
ejpam-3328	290	11	to	to	ADP
ejpam-3328	290	12	the	the	DET
ejpam-3328	290	13	appearance	appearance	NOUN
ejpam-3328	290	14	or	or	CCONJ
ejpam-3328	290	15	disappearance	disappearance	NOUN
ejpam-3328	290	16	of	of	ADP
ejpam-3328	290	17	resonance	resonance	NOUN
ejpam-3328	290	18	,	,	PUNCT
ejpam-3328	290	19	as	as	SCONJ
ejpam-3328	290	20	this	this	PRON
ejpam-3328	290	21	implies	imply	VERB
ejpam-3328	290	22	the	the	DET
ejpam-3328	290	23	absence	absence	NOUN
ejpam-3328	290	24	of	of	ADP
ejpam-3328	290	25	large	large	ADJ
ejpam-3328	290	26	energy	energy	NOUN
ejpam-3328	290	27	flows	flow	NOUN
ejpam-3328	290	28	from	from	ADP
ejpam-3328	290	29	small	small	ADJ
ejpam-3328	290	30	to	to	ADP
ejpam-3328	290	31	large	large	ADJ
ejpam-3328	290	32	harmonics	harmonic	NOUN
ejpam-3328	290	33	,	,	PUNCT
ejpam-3328	290	34	which	which	PRON
ejpam-3328	290	35	in	in	ADP
ejpam-3328	290	36	turn	turn	NOUN
ejpam-3328	290	37	precludes	preclude	VERB
ejpam-3328	290	38	the	the	DET
ejpam-3328	290	39	appearance	appearance	NOUN
ejpam-3328	290	40	of	of	ADP
ejpam-3328	290	41	turbulence	turbulence	NOUN
ejpam-3328	290	42	.	.	PUNCT
ejpam-3328	291	1	therefore	therefore	ADV
ejpam-3328	291	2	,	,	PUNCT
ejpam-3328	291	3	obtaining	obtain	VERB
ejpam-3328	291	4	uniform	uniform	ADJ
ejpam-3328	291	5	global	global	ADJ
ejpam-3328	291	6	estimations	estimation	NOUN
ejpam-3328	291	7	of	of	ADP
ejpam-3328	291	8	the	the	DET
ejpam-3328	291	9	fourier	fourier	NOUN
ejpam-3328	291	10	transform	transform	NOUN
ejpam-3328	291	11	of	of	ADP
ejpam-3328	291	12	solutions	solution	NOUN
ejpam-3328	291	13	of	of	ADP
ejpam-3328	291	14	the	the	DET
ejpam-3328	291	15	navier	navier	NOUN
ejpam-3328	291	16	–	–	PUNCT
ejpam-3328	291	17	stokes	stokes	PROPN
ejpam-3328	291	18	equations	equation	NOUN
ejpam-3328	291	19	means	mean	VERB
ejpam-3328	291	20	that	that	SCONJ
ejpam-3328	291	21	the	the	DET
ejpam-3328	291	22	principle	principle	NOUN
ejpam-3328	291	23	modelling	modelling	NOUN
ejpam-3328	291	24	of	of	ADP
ejpam-3328	291	25	complex	complex	ADJ
ejpam-3328	291	26	flows	flow	NOUN
ejpam-3328	291	27	and	and	CCONJ
ejpam-3328	291	28	related	related	ADJ
ejpam-3328	291	29	calculations	calculation	NOUN
ejpam-3328	291	30	will	will	AUX
ejpam-3328	291	31	be	be	AUX
ejpam-3328	291	32	based	base	VERB
ejpam-3328	291	33	on	on	ADP
ejpam-3328	291	34	the	the	DET
ejpam-3328	291	35	fourier	fourier	NOUN
ejpam-3328	291	36	transform	transform	NOUN
ejpam-3328	291	37	method	method	NOUN
ejpam-3328	291	38	.	.	PUNCT
ejpam-3328	292	1	we	we	PRON
ejpam-3328	292	2	are	be	AUX
ejpam-3328	292	3	continuing	continue	VERB
ejpam-3328	292	4	to	to	PART
ejpam-3328	292	5	research	research	VERB
ejpam-3328	292	6	these	these	DET
ejpam-3328	292	7	issues	issue	NOUN
ejpam-3328	292	8	in	in	ADP
ejpam-3328	292	9	relation	relation	NOUN
ejpam-3328	292	10	to	to	ADP
ejpam-3328	292	11	a	a	DET
ejpam-3328	292	12	numerical	numerical	ADJ
ejpam-3328	292	13	weather	weather	PROPN
ejpam-3328	292	14	prediction	prediction	NOUN
ejpam-3328	292	15	model	model	NOUN
ejpam-3328	292	16	;	;	PUNCT
ejpam-3328	292	17	this	this	DET
ejpam-3328	292	18	paper	paper	NOUN
ejpam-3328	292	19	provides	provide	VERB
ejpam-3328	292	20	a	a	DET
ejpam-3328	292	21	theoretical	theoretical	ADJ
ejpam-3328	292	22	justification	justification	NOUN
ejpam-3328	292	23	for	for	ADP
ejpam-3328	292	24	this	this	DET
ejpam-3328	292	25	approach	approach	NOUN
ejpam-3328	292	26	.	.	PUNCT
ejpam-3328	293	1	consider	consider	VERB
ejpam-3328	293	2	the	the	DET
ejpam-3328	293	3	cauchy	cauchy	ADJ
ejpam-3328	293	4	problem	problem	NOUN
ejpam-3328	293	5	for	for	ADP
ejpam-3328	293	6	the	the	DET
ejpam-3328	293	7	navier	navier	NOUN
ejpam-3328	293	8	–	–	PUNCT
ejpam-3328	293	9	stokes	stokes	PROPN
ejpam-3328	293	10	equations	equation	NOUN
ejpam-3328	293	11	:	:	PUNCT
ejpam-3328	294	1	∂~v	∂~v	PROPN
ejpam-3328	294	2	∂t	∂t	PROPN
ejpam-3328	294	3	−	−	PROPN
ejpam-3328	294	4	ν∆~v	ν∆~v	PROPN
ejpam-3328	294	5	+	+	CCONJ
ejpam-3328	294	6	(	(	PUNCT
ejpam-3328	294	7	~v,∇~v	~v,∇~v	NUM
ejpam-3328	294	8	)	)	PUNCT
ejpam-3328	294	9	=	=	SYM
ejpam-3328	294	10	−∇p+	−∇p+	NUM
ejpam-3328	294	11	~f(x	~f(x	NOUN
ejpam-3328	294	12	,	,	PUNCT
ejpam-3328	294	13	t	t	PROPN
ejpam-3328	294	14	)	)	PUNCT
ejpam-3328	294	15	,	,	PUNCT
ejpam-3328	294	16	div	div	X
ejpam-3328	294	17	~v	~v	PUNCT
ejpam-3328	294	18	=	=	SYM
ejpam-3328	294	19	0	0	NUM
ejpam-3328	294	20	,	,	PUNCT
ejpam-3328	294	21	(	(	PUNCT
ejpam-3328	294	22	7	7	NUM
ejpam-3328	294	23	)	)	PUNCT
ejpam-3328	294	24	~v|t=0	~v|t=0	NUM
ejpam-3328	294	25	=	=	SYM
ejpam-3328	294	26	~v0(x	~v0(x	NOUN
ejpam-3328	294	27	)	)	PUNCT
ejpam-3328	294	28	(	(	PUNCT
ejpam-3328	294	29	8)	8)	NUM
ejpam-3328	294	30	in	in	ADP
ejpam-3328	294	31	the	the	DET
ejpam-3328	294	32	domain	domain	NOUN
ejpam-3328	294	33	qt	qt	NOUN
ejpam-3328	294	34	=	=	SYM
ejpam-3328	294	35	r3	r3	PROPN
ejpam-3328	294	36	×	×	NOUN
ejpam-3328	294	37	(	(	PUNCT
ejpam-3328	294	38	0	0	NUM
ejpam-3328	294	39	,	,	PUNCT
ejpam-3328	294	40	t	t	PROPN
ejpam-3328	294	41	)	)	PUNCT
ejpam-3328	294	42	,	,	PUNCT
ejpam-3328	294	43	where	where	SCONJ
ejpam-3328	294	44	div	div	X
ejpam-3328	294	45	~v0	~v0	PUNCT
ejpam-3328	294	46	=	=	SYM
ejpam-3328	294	47	0	0	X
ejpam-3328	294	48	.	.	PUNCT
ejpam-3328	295	1	(	(	PUNCT
ejpam-3328	295	2	9	9	X
ejpam-3328	295	3	)	)	PUNCT
ejpam-3328	295	4	the	the	DET
ejpam-3328	295	5	problem	problem	NOUN
ejpam-3328	295	6	defined	define	VERB
ejpam-3328	295	7	by	by	ADP
ejpam-3328	295	8	(	(	PUNCT
ejpam-3328	295	9	7)–(9	7)–(9	NOUN
ejpam-3328	295	10	)	)	PUNCT
ejpam-3328	295	11	has	have	VERB
ejpam-3328	295	12	at	at	ADV
ejpam-3328	295	13	least	least	ADV
ejpam-3328	295	14	one	one	NUM
ejpam-3328	295	15	weak	weak	ADJ
ejpam-3328	295	16	solution	solution	NOUN
ejpam-3328	295	17	(	(	PUNCT
ejpam-3328	295	18	~v	~v	X
ejpam-3328	295	19	,	,	PUNCT
ejpam-3328	295	20	p	p	NOUN
ejpam-3328	295	21	)	)	PUNCT
ejpam-3328	295	22	in	in	ADP
ejpam-3328	295	23	the	the	DET
ejpam-3328	295	24	so	so	ADV
ejpam-3328	295	25	-	-	PUNCT
ejpam-3328	295	26	called	call	VERB
ejpam-3328	295	27	leray	leray	ADJ
ejpam-3328	295	28	–	–	PUNCT
ejpam-3328	295	29	hopf	hopf	ADJ
ejpam-3328	295	30	class	class	NOUN
ejpam-3328	296	1	[	[	X
ejpam-3328	296	2	16	16	NUM
ejpam-3328	296	3	]	]	PUNCT
ejpam-3328	296	4	.	.	PUNCT
ejpam-3328	297	1	the	the	DET
ejpam-3328	297	2	following	follow	VERB
ejpam-3328	297	3	results	result	NOUN
ejpam-3328	297	4	have	have	AUX
ejpam-3328	297	5	been	be	AUX
ejpam-3328	297	6	proved	prove	VERB
ejpam-3328	297	7	[	[	X
ejpam-3328	297	8	15	15	NUM
ejpam-3328	297	9	]	]	NOUN
ejpam-3328	297	10	:	:	PUNCT
ejpam-3328	297	11	theorem	theorem	NOUN
ejpam-3328	297	12	4	4	NUM
ejpam-3328	297	13	.	.	PUNCT
ejpam-3328	298	1	if	if	SCONJ
ejpam-3328	298	2	~v0	~v0	PUNCT
ejpam-3328	298	3	∈w	∈w	VERB
ejpam-3328	298	4	1	1	NUM
ejpam-3328	298	5	2	2	NUM
ejpam-3328	298	6	(	(	PUNCT
ejpam-3328	298	7	r3	r3	PROPN
ejpam-3328	298	8	)	)	PUNCT
ejpam-3328	298	9	,	,	PUNCT
ejpam-3328	298	10	~f(x	~f(x	NOUN
ejpam-3328	298	11	,	,	PUNCT
ejpam-3328	298	12	t	t	PROPN
ejpam-3328	298	13	)	)	PUNCT
ejpam-3328	298	14	∈	∈	PROPN
ejpam-3328	298	15	l2(qt	l2(qt	PROPN
ejpam-3328	298	16	)	)	PUNCT
ejpam-3328	298	17	,	,	PUNCT
ejpam-3328	298	18	there	there	PRON
ejpam-3328	298	19	is	be	VERB
ejpam-3328	298	20	a	a	DET
ejpam-3328	298	21	single	single	ADJ
ejpam-3328	298	22	generalised	generalise	VERB
ejpam-3328	298	23	solution	solution	NOUN
ejpam-3328	298	24	of	of	ADP
ejpam-3328	298	25	(	(	PUNCT
ejpam-3328	298	26	7)–(9	7)–(9	NOUN
ejpam-3328	298	27	)	)	PUNCT
ejpam-3328	298	28	in	in	ADP
ejpam-3328	298	29	the	the	DET
ejpam-3328	298	30	domain	domain	NOUN
ejpam-3328	298	31	qt1	qt1	PROPN
ejpam-3328	298	32	,	,	PUNCT
ejpam-3328	298	33	t1	t1	NOUN
ejpam-3328	298	34	∈	∈	PROPN
ejpam-3328	299	1	[	[	X
ejpam-3328	299	2	0	0	NUM
ejpam-3328	299	3	,	,	PUNCT
ejpam-3328	299	4	t	t	X
ejpam-3328	299	5	]	]	PUNCT
ejpam-3328	299	6	,	,	PUNCT
ejpam-3328	299	7	satisfying	satisfy	VERB
ejpam-3328	299	8	the	the	DET
ejpam-3328	299	9	following	follow	VERB
ejpam-3328	299	10	conditions	condition	NOUN
ejpam-3328	299	11	:	:	PUNCT
ejpam-3328	299	12	~v,∇2	~v,∇2	NUM
ejpam-3328	299	13	~	~	SYM
ejpam-3328	299	14	v	v	NOUN
ejpam-3328	299	15	,	,	PUNCT
ejpam-3328	299	16	∇p	∇p	PROPN
ejpam-3328	299	17	∈	∈	PROPN
ejpam-3328	299	18	l2(qt	l2(qt	PROPN
ejpam-3328	299	19	)	)	PUNCT
ejpam-3328	299	20	.	.	PUNCT
ejpam-3328	300	1	note	note	VERB
ejpam-3328	300	2	that	that	SCONJ
ejpam-3328	300	3	t1	t1	NOUN
ejpam-3328	300	4	depends	depend	VERB
ejpam-3328	300	5	on	on	ADP
ejpam-3328	300	6	~v0	~v0	PUNCT
ejpam-3328	300	7	and	and	CCONJ
ejpam-3328	300	8	~f(x	~f(x	NOUN
ejpam-3328	300	9	,	,	PUNCT
ejpam-3328	300	10	t	t	PROPN
ejpam-3328	300	11	)	)	PUNCT
ejpam-3328	300	12	.	.	PUNCT
ejpam-3328	301	1	a.	a.	NOUN
ejpam-3328	301	2	durmagambetov	durmagambetov	PROPN
ejpam-3328	301	3	/	/	SYM
ejpam-3328	301	4	eur	eur	PROPN
ejpam-3328	301	5	.	.	PUNCT
ejpam-3328	302	1	j.	j.	PROPN
ejpam-3328	302	2	pure	pure	PROPN
ejpam-3328	302	3	appl	appl	PROPN
ejpam-3328	302	4	.	.	PROPN
ejpam-3328	302	5	math	math	PROPN
ejpam-3328	302	6	,	,	PUNCT
ejpam-3328	302	7	11	11	NUM
ejpam-3328	302	8	(	(	PUNCT
ejpam-3328	302	9	4	4	NUM
ejpam-3328	302	10	)	)	PUNCT
ejpam-3328	302	11	(	(	PUNCT
ejpam-3328	302	12	2018	2018	NUM
ejpam-3328	302	13	)	)	PUNCT
ejpam-3328	302	14	,	,	PUNCT
ejpam-3328	302	15	1143	1143	NUM
ejpam-3328	302	16	-	-	SYM
ejpam-3328	302	17	1176	1176	NUM
ejpam-3328	302	18	1156	1156	NUM
ejpam-3328	302	19	lemma	lemma	PROPN
ejpam-3328	302	20	12	12	NUM
ejpam-3328	302	21	.	.	PUNCT
ejpam-3328	303	1	if	if	SCONJ
ejpam-3328	303	2	we	we	PRON
ejpam-3328	303	3	let	let	VERB
ejpam-3328	303	4	~v0	~v0	PUNCT
ejpam-3328	303	5	∈w	∈w	VERB
ejpam-3328	303	6	2	2	NUM
ejpam-3328	303	7	2	2	NUM
ejpam-3328	303	8	(	(	PUNCT
ejpam-3328	303	9	r3	r3	PROPN
ejpam-3328	303	10	)	)	PUNCT
ejpam-3328	303	11	,	,	PUNCT
ejpam-3328	303	12	~f	~f	PUNCT
ejpam-3328	303	13	∈	∈	PROPN
ejpam-3328	303	14	l2(qt	l2(qt	PROPN
ejpam-3328	303	15	)	)	PUNCT
ejpam-3328	303	16	,	,	PUNCT
ejpam-3328	303	17	then	then	ADV
ejpam-3328	303	18	the	the	DET
ejpam-3328	303	19	solution	solution	NOUN
ejpam-3328	303	20	of	of	ADP
ejpam-3328	303	21	(	(	PUNCT
ejpam-3328	303	22	7)–(9	7)–(9	NOUN
ejpam-3328	303	23	)	)	PUNCT
ejpam-3328	303	24	satisfies	satisfy	VERB
ejpam-3328	303	25	the	the	DET
ejpam-3328	303	26	following	follow	VERB
ejpam-3328	303	27	inequalities	inequality	NOUN
ejpam-3328	303	28	:	:	PUNCT
ejpam-3328	303	29	sup	sup	NOUN
ejpam-3328	303	30	0≤t≤t	0≤t≤t	NUM
ejpam-3328	303	31	||~v||2l2(r3	||~v||2l2(r3	NUM
ejpam-3328	303	32	)	)	PUNCT
ejpam-3328	304	1	+	+	CCONJ
ejpam-3328	304	2	ν	ν	X
ejpam-3328	304	3	t∫	t∫	NUM
ejpam-3328	304	4	0	0	NUM
ejpam-3328	304	5	||∇~v||2l2(r3)dτ	||∇~v||2l2(r3)dτ	NOUN
ejpam-3328	304	6	≤	≤	NOUN
ejpam-3328	304	7	||~v0||2l2(r3	||~v0||2l2(r3	NOUN
ejpam-3328	304	8	)	)	PUNCT
ejpam-3328	305	1	+	+	CCONJ
ejpam-3328	305	2	||~f	||~f	NOUN
ejpam-3328	305	3	||l2(qt	||l2(qt	NOUN
ejpam-3328	305	4	)	)	PUNCT
ejpam-3328	305	5	,	,	PUNCT
ejpam-3328	305	6	sup	sup	NOUN
ejpam-3328	305	7	0≤t≤t	0≤t≤t	NUM
ejpam-3328	305	8	||	||	NOUN
ejpam-3328	305	9	~∇v||2l2(r3	~∇v||2l2(r3	NUM
ejpam-3328	305	10	)	)	PUNCT
ejpam-3328	306	1	+	+	CCONJ
ejpam-3328	306	2	ν	ν	X
ejpam-3328	306	3	t∫	t∫	NUM
ejpam-3328	306	4	0	0	NUM
ejpam-3328	306	5	||h0	||h0	PROPN
ejpam-3328	306	6	~	~	X
ejpam-3328	306	7	v||2l2(r3)dτ	v||2l2(r3)dτ	NOUN
ejpam-3328	306	8	≤	≤	NUM
ejpam-3328	306	9	||∇~v0||2l2(r3	||∇~v0||2l2(r3	NOUN
ejpam-3328	306	10	)	)	PUNCT
ejpam-3328	307	1	+	+	CCONJ
ejpam-3328	307	2	||~f	||~f	NOUN
ejpam-3328	307	3	||l2(qt	||l2(qt	NOUN
ejpam-3328	307	4	)	)	PUNCT
ejpam-3328	308	1	+	+	CCONJ
ejpam-3328	308	2	∫	∫	PROPN
ejpam-3328	308	3	t	t	PROPN
ejpam-3328	308	4	0	0	NUM
ejpam-3328	308	5	||(~v,∇~v)||l2(r3)||h0	||(~v,∇~v)||l2(r3)||h0	NUM
ejpam-3328	308	6	~	~	SYM
ejpam-3328	308	7	v||l2(r3	v||l2(r3	NOUN
ejpam-3328	308	8	)	)	PUNCT
ejpam-3328	308	9	,	,	PUNCT
ejpam-3328	308	10	ν	ν	X
ejpam-3328	308	11	t∫	t∫	PROPN
ejpam-3328	308	12	0	0	NUM
ejpam-3328	308	13	||h0	||h0	PROPN
ejpam-3328	308	14	~	~	X
ejpam-3328	308	15	v||2l2(r3)dτ	v||2l2(r3)dτ	NOUN
ejpam-3328	308	16	≤	≤	PUNCT
ejpam-3328	308	17	c	c	NOUN
ejpam-3328	308	18	+	+	NOUN
ejpam-3328	308	19	1	1	NUM
ejpam-3328	308	20	ν	ν	NOUN
ejpam-3328	308	21	∫	∫	PROPN
ejpam-3328	308	22	t	t	PROPN
ejpam-3328	308	23	0	0	NUM
ejpam-3328	308	24	||(~v,∇~v)||2l2(r3)dt	||(~v,∇~v)||2l2(r3)dt	PROPN
ejpam-3328	308	25	.	.	PUNCT
ejpam-3328	309	1	lemma	lemma	PROPN
ejpam-3328	309	2	13	13	NUM
ejpam-3328	309	3	.	.	PUNCT
ejpam-3328	310	1	let	let	VERB
ejpam-3328	310	2	~v0	~v0	PUNCT
ejpam-3328	310	3	∈	∈	PROPN
ejpam-3328	310	4	w	w	NOUN
ejpam-3328	310	5	2	2	NUM
ejpam-3328	310	6	2	2	NUM
ejpam-3328	310	7	(	(	PUNCT
ejpam-3328	310	8	r3	r3	PROPN
ejpam-3328	310	9	)	)	PUNCT
ejpam-3328	310	10	,	,	PUNCT
ejpam-3328	310	11	~̃v0	~̃v0	NOUN
ejpam-3328	310	12	∈	∈	PROPN
ejpam-3328	311	1	w	w	PROPN
ejpam-3328	311	2	2	2	NUM
ejpam-3328	311	3	2	2	NUM
ejpam-3328	311	4	(	(	PUNCT
ejpam-3328	311	5	r3	r3	PROPN
ejpam-3328	311	6	)	)	PUNCT
ejpam-3328	311	7	,	,	PUNCT
ejpam-3328	311	8	and	and	CCONJ
ejpam-3328	311	9	~f	~f	PUNCT
ejpam-3328	311	10	∈	∈	PROPN
ejpam-3328	311	11	l2(qt	l2(qt	PROPN
ejpam-3328	311	12	)	)	PUNCT
ejpam-3328	311	13	.	.	PUNCT
ejpam-3328	312	1	then	then	ADV
ejpam-3328	312	2	,	,	PUNCT
ejpam-3328	312	3	the	the	DET
ejpam-3328	312	4	solution	solution	NOUN
ejpam-3328	312	5	of	of	ADP
ejpam-3328	312	6	(	(	PUNCT
ejpam-3328	312	7	7)–(9	7)–(9	NOUN
ejpam-3328	312	8	)	)	PUNCT
ejpam-3328	312	9	satisfies	satisfy	VERB
ejpam-3328	312	10	the	the	DET
ejpam-3328	312	11	following	following	NOUN
ejpam-3328	312	12	:	:	PUNCT
ejpam-3328	312	13	~̃v	~̃v	NUM
ejpam-3328	312	14	=	=	SYM
ejpam-3328	312	15	~̃v0	~̃v0	NOUN
ejpam-3328	312	16	+	+	CCONJ
ejpam-3328	312	17	t∫	t∫	PRON
ejpam-3328	312	18	0	0	NUM
ejpam-3328	312	19	e−νk	e−νk	PROPN
ejpam-3328	312	20	2|(t−τ	2|(t−τ	NUM
ejpam-3328	312	21	)	)	PUNCT
ejpam-3328	312	22	(	(	PUNCT
ejpam-3328	312	23	˜[(~v,∇)~v	˜[(~v,∇)~v	X
ejpam-3328	312	24	]	]	X
ejpam-3328	312	25	+	+	NUM
ejpam-3328	312	26	~̃f	~̃f	NUM
ejpam-3328	312	27	)	)	PUNCT
ejpam-3328	312	28	dτ	dτ	NOUN
ejpam-3328	312	29	,	,	PUNCT
ejpam-3328	312	30	where	where	SCONJ
ejpam-3328	312	31	~f	~f	PUNCT
ejpam-3328	312	32	=	=	PUNCT
ejpam-3328	312	33	−∇p+	−∇p+	PROPN
ejpam-3328	312	34	~f	~f	PUNCT
ejpam-3328	312	35	.	.	PUNCT
ejpam-3328	313	1	proof	proof	NOUN
ejpam-3328	313	2	.	.	PUNCT
ejpam-3328	314	1	this	this	PRON
ejpam-3328	314	2	follows	follow	VERB
ejpam-3328	314	3	from	from	ADP
ejpam-3328	314	4	the	the	DET
ejpam-3328	314	5	definition	definition	NOUN
ejpam-3328	314	6	of	of	ADP
ejpam-3328	314	7	the	the	DET
ejpam-3328	314	8	fourier	fourier	NOUN
ejpam-3328	314	9	transform	transform	NOUN
ejpam-3328	314	10	and	and	CCONJ
ejpam-3328	314	11	the	the	DET
ejpam-3328	314	12	theory	theory	NOUN
ejpam-3328	314	13	of	of	ADP
ejpam-3328	314	14	linear	linear	PROPN
ejpam-3328	314	15	differential	differential	ADJ
ejpam-3328	314	16	equations	equation	NOUN
ejpam-3328	314	17	.	.	PUNCT
ejpam-3328	315	1	let	let	VERB
ejpam-3328	315	2	us	we	PRON
ejpam-3328	315	3	introduce	introduce	VERB
ejpam-3328	315	4	the	the	DET
ejpam-3328	315	5	operators	operator	NOUN
ejpam-3328	315	6	fk	fk	INTJ
ejpam-3328	315	7	and	and	CCONJ
ejpam-3328	315	8	fkk′	fkk′	NUM
ejpam-3328	315	9	as	as	SCONJ
ejpam-3328	315	10	fkf	fkf	PRON
ejpam-3328	315	11	=	=	SYM
ejpam-3328	315	12	∫	∫	PROPN
ejpam-3328	315	13	r3	r3	PROPN
ejpam-3328	315	14	ei(k	ei(k	PROPN
ejpam-3328	315	15	,	,	PUNCT
ejpam-3328	315	16	x)f(x)dx	x)f(x)dx	ADJ
ejpam-3328	315	17	,	,	PUNCT
ejpam-3328	315	18	fkk′f	fkk′f	ADV
ejpam-3328	315	19	=	=	SYM
ejpam-3328	315	20	∫	∫	PROPN
ejpam-3328	315	21	r3	r3	PROPN
ejpam-3328	315	22	ei(k	ei(k	PROPN
ejpam-3328	315	23	,	,	PUNCT
ejpam-3328	315	24	x)−i(x	x)−i(x	PROPN
ejpam-3328	315	25	,	,	PUNCT
ejpam-3328	315	26	k′)f(x)dx	k′)f(x)dx	X
ejpam-3328	315	27	,	,	PUNCT
ejpam-3328	315	28	~̃v(k	~̃v(k	NOUN
ejpam-3328	315	29	)	)	PUNCT
ejpam-3328	315	30	=	=	PUNCT
ejpam-3328	316	1	fk	fk	PROPN
ejpam-3328	316	2	~	~	PROPN
ejpam-3328	316	3	v	v	NOUN
ejpam-3328	316	4	,	,	PUNCT
ejpam-3328	316	5	~v	~v	NUM
ejpam-3328	316	6	(	(	PUNCT
ejpam-3328	316	7	k	k	X
ejpam-3328	316	8	,	,	PUNCT
ejpam-3328	316	9	k′	k′	PROPN
ejpam-3328	316	10	)	)	PUNCT
ejpam-3328	317	1	=	=	SYM
ejpam-3328	317	2	fkk′~v	fkk′~v	NOUN
ejpam-3328	317	3	=	=	SYM
ejpam-3328	317	4	∫	∫	PROPN
ejpam-3328	317	5	r3	r3	PROPN
ejpam-3328	317	6	ei(k	ei(k	PROPN
ejpam-3328	317	7	,	,	PUNCT
ejpam-3328	317	8	x)−i(x	x)−i(x	PROPN
ejpam-3328	317	9	,	,	PUNCT
ejpam-3328	317	10	k′)~vdx	k′)~vdx	PROPN
ejpam-3328	317	11	.	.	PUNCT
ejpam-3328	318	1	lemma	lemma	PROPN
ejpam-3328	318	2	14	14	NUM
ejpam-3328	318	3	.	.	PUNCT
ejpam-3328	319	1	let	let	VERB
ejpam-3328	319	2	~v0	~v0	PUNCT
ejpam-3328	319	3	∈	∈	PROPN
ejpam-3328	319	4	w	w	NOUN
ejpam-3328	319	5	2	2	NUM
ejpam-3328	319	6	2	2	NUM
ejpam-3328	319	7	(	(	PUNCT
ejpam-3328	319	8	r3	r3	PROPN
ejpam-3328	319	9	)	)	PUNCT
ejpam-3328	319	10	,	,	PUNCT
ejpam-3328	319	11	~f	~f	PUNCT
ejpam-3328	319	12	∈	∈	PROPN
ejpam-3328	319	13	l2(qt	l2(qt	PROPN
ejpam-3328	319	14	)	)	PUNCT
ejpam-3328	319	15	,	,	PUNCT
ejpam-3328	319	16	and	and	CCONJ
ejpam-3328	319	17	|tkv0|	|tkv0|	PRON
ejpam-3328	319	18	+	+	NUM
ejpam-3328	319	19	|tkv0|	|tkv0|	PRON
ejpam-3328	319	20	+	+	CCONJ
ejpam-3328	319	21	∣∣∣tk2v0	∣∣∣tk2v0	ADJ
ejpam-3328	319	22	~̃v0	~̃v0	NOUN
ejpam-3328	319	23	∣∣∣	∣∣∣	NOUN
ejpam-3328	319	24	<	<	X
ejpam-3328	319	25	c.	c.	PROPN
ejpam-3328	319	26	then	then	ADV
ejpam-3328	319	27	,	,	PUNCT
ejpam-3328	319	28	the	the	DET
ejpam-3328	319	29	solution	solution	NOUN
ejpam-3328	319	30	of	of	ADP
ejpam-3328	319	31	(	(	PUNCT
ejpam-3328	319	32	7)–(9	7)–(9	NOUN
ejpam-3328	319	33	)	)	PUNCT
ejpam-3328	319	34	in	in	ADP
ejpam-3328	319	35	theorem	theorem	ADJ
ejpam-3328	319	36	4	4	NUM
ejpam-3328	319	37	satisfies	satisfie	NOUN
ejpam-3328	319	38	the	the	DET
ejpam-3328	319	39	following	follow	VERB
ejpam-3328	319	40	inequalities	inequality	NOUN
ejpam-3328	319	41	:	:	PUNCT
ejpam-3328	319	42	|ṽ(k)|	|ṽ(k)|	NOUN
ejpam-3328	319	43	<	<	X
ejpam-3328	319	44	c	c	PROPN
ejpam-3328	319	45	,	,	PUNCT
ejpam-3328	319	46	|tkṽ(k)|	|tkṽ(k)|	NOUN
ejpam-3328	319	47	<	<	X
ejpam-3328	319	48	c0||v||l2(r3	c0||v||l2(r3	NUM
ejpam-3328	319	49	)	)	PUNCT
ejpam-3328	320	1	+	+	CCONJ
ejpam-3328	320	2	c0t√	c0t√	VERB
ejpam-3328	320	3	ν	ν	NOUN
ejpam-3328	320	4	||∇v||l2(r3)||v||l2(r3	||∇v||l2(r3)||v||l2(r3	NOUN
ejpam-3328	320	5	)	)	PUNCT
ejpam-3328	320	6	.	.	PUNCT
ejpam-3328	321	1	a.	a.	NOUN
ejpam-3328	321	2	durmagambetov	durmagambetov	PROPN
ejpam-3328	321	3	/	/	SYM
ejpam-3328	321	4	eur	eur	PROPN
ejpam-3328	321	5	.	.	PUNCT
ejpam-3328	322	1	j.	j.	PROPN
ejpam-3328	322	2	pure	pure	PROPN
ejpam-3328	322	3	appl	appl	PROPN
ejpam-3328	322	4	.	.	PROPN
ejpam-3328	322	5	math	math	PROPN
ejpam-3328	322	6	,	,	PUNCT
ejpam-3328	322	7	11	11	NUM
ejpam-3328	322	8	(	(	PUNCT
ejpam-3328	322	9	4	4	NUM
ejpam-3328	322	10	)	)	PUNCT
ejpam-3328	322	11	(	(	PUNCT
ejpam-3328	322	12	2018	2018	NUM
ejpam-3328	322	13	)	)	PUNCT
ejpam-3328	322	14	,	,	PUNCT
ejpam-3328	322	15	1143	1143	NUM
ejpam-3328	322	16	-	-	SYM
ejpam-3328	322	17	1176	1176	NUM
ejpam-3328	322	18	1157	1157	NUM
ejpam-3328	322	19	proof	proof	NOUN
ejpam-3328	322	20	.	.	PUNCT
ejpam-3328	323	1	this	this	PRON
ejpam-3328	323	2	follows	follow	VERB
ejpam-3328	323	3	from	from	ADP
ejpam-3328	323	4	~̇v	~̇v	PROPN
ejpam-3328	323	5	=	=	SYM
ejpam-3328	324	1	−(~v∇)~v	−(~v∇)~v	PROPN
ejpam-3328	324	2	+	+	CCONJ
ejpam-3328	324	3	(	(	PUNCT
ejpam-3328	324	4	ν	ν	X
ejpam-3328	324	5	~	~	PUNCT
ejpam-3328	324	6	v	v	ADP
ejpam-3328	324	7	+	+	NOUN
ejpam-3328	324	8	∇p	∇p	ADV
ejpam-3328	324	9	)	)	PUNCT
ejpam-3328	325	1	+	+	NUM
ejpam-3328	325	2	f	f	X
ejpam-3328	325	3	,	,	PUNCT
ejpam-3328	325	4	~̃v	~̃v	VERB
ejpam-3328	325	5	=	=	SYM
ejpam-3328	325	6	~̃v0	~̃v0	NOUN
ejpam-3328	325	7	+	+	CCONJ
ejpam-3328	325	8	∫	∫	PROPN
ejpam-3328	325	9	t	t	PROPN
ejpam-3328	325	10	0	0	NUM
ejpam-3328	325	11	e−νk	e−νk	PROPN
ejpam-3328	325	12	2(t−τ)fk	2(t−τ)fk	NUM
ejpam-3328	325	13	(	(	PUNCT
ejpam-3328	325	14	−	−	PROPN
ejpam-3328	325	15	(	(	PUNCT
ejpam-3328	325	16	~v,∇)~v	~v,∇)~v	NOUN
ejpam-3328	325	17	)	)	PUNCT
ejpam-3328	325	18	+	+	NOUN
ejpam-3328	325	19	∇p+	∇p+	PROPN
ejpam-3328	325	20	f	f	PROPN
ejpam-3328	325	21	)	)	PUNCT
ejpam-3328	325	22	dτ	dτ	PROPN
ejpam-3328	325	23	.	.	PROPN
ejpam-3328	326	1	from	from	ADP
ejpam-3328	326	2	the	the	DET
ejpam-3328	326	3	last	last	ADJ
ejpam-3328	326	4	equation	equation	NOUN
ejpam-3328	326	5	we	we	PRON
ejpam-3328	326	6	have	have	VERB
ejpam-3328	326	7	|~v|	|~v|	VERB
ejpam-3328	326	8	≤	≤	NUM
ejpam-3328	326	9	|~v0|+	|~v0|+	NOUN
ejpam-3328	327	1	ct	ct	PROPN
ejpam-3328	327	2	.	.	PUNCT
ejpam-3328	328	1	denote	denote	VERB
ejpam-3328	328	2	β	β	X
ejpam-3328	328	3	=	=	PUNCT
ejpam-3328	328	4	√	√	NUM
ejpam-3328	328	5	ν(t−	ν(t−	PROPN
ejpam-3328	328	6	τ	τ	PROPN
ejpam-3328	328	7	)	)	PUNCT
ejpam-3328	328	8	,	,	PUNCT
ejpam-3328	328	9	a	a	DET
ejpam-3328	328	10	=	=	NOUN
ejpam-3328	328	11	θx	θx	PART
ejpam-3328	328	12	formula	formula	NOUN
ejpam-3328	328	13	121	121	NUM
ejpam-3328	328	14	(	(	PUNCT
ejpam-3328	328	15	23	23	NUM
ejpam-3328	328	16	)	)	PUNCT
ejpam-3328	328	17	from	from	ADP
ejpam-3328	328	18	[	[	X
ejpam-3328	328	19	11	11	NUM
ejpam-3328	328	20	]	]	PUNCT
ejpam-3328	328	21	as	as	ADP
ejpam-3328	328	22	n	n	NOUN
ejpam-3328	328	23	=	=	SYM
ejpam-3328	328	24	0	0	NUM
ejpam-3328	328	25	:	:	PUNCT
ejpam-3328	328	26	yield	yield	VERB
ejpam-3328	328	27	|tk	|tk	NUM
ejpam-3328	328	28	~	~	NOUN
ejpam-3328	328	29	v|	v|	X
ejpam-3328	328	30	<	<	X
ejpam-3328	328	31	∣∣∣ke−β2k2	∣∣∣ke−β2k2	PROPN
ejpam-3328	328	32	∣∣∣+	∣∣∣+	PROPN
ejpam-3328	328	33	√	√	PROPN
ejpam-3328	329	1	πβ−1e	πβ−1e	CCONJ
ejpam-3328	329	2	−	−	PROPN
ejpam-3328	329	3	a2	a2	PROPN
ejpam-3328	329	4	8β2d0	8β2d0	NUM
ejpam-3328	329	5	(	(	PUNCT
ejpam-3328	329	6	a√	a√	PROPN
ejpam-3328	329	7	2β	2β	NOUN
ejpam-3328	329	8	)	)	PUNCT
ejpam-3328	329	9	,	,	PUNCT
ejpam-3328	329	10	|tk	|tk	ADP
ejpam-3328	329	11	~	~	PUNCT
ejpam-3328	329	12	v|	v|	NOUN
ejpam-3328	329	13	≤	≤	NUM
ejpam-3328	329	14	|tk	|tk	NOUN
ejpam-3328	329	15	~	~	NOUN
ejpam-3328	329	16	v0|	v0|	NOUN
ejpam-3328	329	17	+	+	CCONJ
ejpam-3328	329	18	∣∣∣∣tk	∣∣∣∣tk	PROPN
ejpam-3328	329	19	∫	∫	PROPN
ejpam-3328	329	20	t	t	NOUN
ejpam-3328	329	21	0	0	NUM
ejpam-3328	329	22	e−νk	e−νk	PROPN
ejpam-3328	329	23	2(t−τ)fk	2(t−τ)fk	NUM
ejpam-3328	329	24	(	(	PUNCT
ejpam-3328	329	25	−(~v,∇)~v	−(~v,∇)~v	X
ejpam-3328	329	26	]	]	X
ejpam-3328	329	27	+	+	NOUN
ejpam-3328	329	28	∇p+	∇p+	NOUN
ejpam-3328	329	29	f	f	X
ejpam-3328	329	30	)	)	PUNCT
ejpam-3328	330	1	dk	dk	PROPN
ejpam-3328	330	2	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3328	330	3	≤	≤	PROPN
ejpam-3328	330	4	|tk	|tk	ADP
ejpam-3328	330	5	~	~	SYM
ejpam-3328	330	6	v0|+	v0|+	PROPN
ejpam-3328	330	7	∫	∫	PROPN
ejpam-3328	330	8	t	t	PROPN
ejpam-3328	330	9	0	0	NUM
ejpam-3328	330	10	∣∣∣ke−β2k2	∣∣∣ke−β2k2	PROPN
ejpam-3328	330	11	∣∣∣+	∣∣∣+	PROPN
ejpam-3328	330	12	∣∣∣∣√πβ−1e	∣∣∣∣√πβ−1e	PROPN
ejpam-3328	330	13	−	−	PROPN
ejpam-3328	330	14	a2	a2	PROPN
ejpam-3328	330	15	8β2d0	8β2d0	NUM
ejpam-3328	330	16	(	(	PUNCT
ejpam-3328	330	17	a√	a√	PROPN
ejpam-3328	330	18	2β	2β	NOUN
ejpam-3328	330	19	)	)	PUNCT
ejpam-3328	330	20	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3328	330	21	||∇~v||l2(r3)dt	||∇~v||l2(r3)dt	PROPN
ejpam-3328	330	22	≤	≤	NOUN
ejpam-3328	330	23	c0||v||l2(r3	c0||v||l2(r3	NUM
ejpam-3328	330	24	)	)	PUNCT
ejpam-3328	331	1	+	+	CCONJ
ejpam-3328	331	2	c0t√	c0t√	VERB
ejpam-3328	331	3	ν	ν	NOUN
ejpam-3328	331	4	||∇v||l2(r3)||v||l2(r3	||∇v||l2(r3)||v||l2(r3	NOUN
ejpam-3328	331	5	)	)	PUNCT
ejpam-3328	331	6	.	.	PUNCT
ejpam-3328	332	1	lemma	lemma	PROPN
ejpam-3328	332	2	15	15	NUM
ejpam-3328	332	3	.	.	PUNCT
ejpam-3328	333	1	let	let	VERB
ejpam-3328	333	2	~v0	~v0	PUNCT
ejpam-3328	333	3	∈	∈	PROPN
ejpam-3328	333	4	w	w	NOUN
ejpam-3328	333	5	2	2	NUM
ejpam-3328	333	6	2	2	NUM
ejpam-3328	333	7	(	(	PUNCT
ejpam-3328	333	8	r3	r3	PROPN
ejpam-3328	333	9	)	)	PUNCT
ejpam-3328	333	10	,	,	PUNCT
ejpam-3328	333	11	~f	~f	PUNCT
ejpam-3328	333	12	∈	∈	PROPN
ejpam-3328	333	13	l2(qt	l2(qt	PROPN
ejpam-3328	333	14	)	)	PUNCT
ejpam-3328	333	15	,	,	PUNCT
ejpam-3328	333	16	and	and	CCONJ
ejpam-3328	333	17	|tkv0|	|tkv0|	PRON
ejpam-3328	333	18	+	+	NUM
ejpam-3328	333	19	|tkv0|	|tkv0|	PRON
ejpam-3328	333	20	+	+	CCONJ
ejpam-3328	333	21	∣∣∣tk2v0	∣∣∣tk2v0	ADJ
ejpam-3328	333	22	~̃v0	~̃v0	NOUN
ejpam-3328	333	23	∣∣∣	∣∣∣	NOUN
ejpam-3328	333	24	.	.	PUNCT
ejpam-3328	334	1	then	then	ADV
ejpam-3328	334	2	,	,	PUNCT
ejpam-3328	334	3	the	the	DET
ejpam-3328	334	4	solution	solution	NOUN
ejpam-3328	334	5	of	of	ADP
ejpam-3328	334	6	(	(	PUNCT
ejpam-3328	334	7	7)–(9	7)–(9	NOUN
ejpam-3328	334	8	)	)	PUNCT
ejpam-3328	334	9	in	in	ADP
ejpam-3328	334	10	theorem	theorem	ADJ
ejpam-3328	334	11	4	4	NUM
ejpam-3328	334	12	satisfies	satisfie	NOUN
ejpam-3328	334	13	the	the	DET
ejpam-3328	334	14	following	follow	VERB
ejpam-3328	334	15	inequalities	inequality	NOUN
ejpam-3328	334	16	:	:	PUNCT
ejpam-3328	334	17	|~v	|~v	PROPN
ejpam-3328	334	18	(	(	PUNCT
ejpam-3328	334	19	k	k	X
ejpam-3328	334	20	,	,	PUNCT
ejpam-3328	334	21	k′)|	k′)|	X
ejpam-3328	334	22	<	<	X
ejpam-3328	334	23	c	c	X
ejpam-3328	334	24	,	,	PUNCT
ejpam-3328	334	25	k|~v	k|~v	PROPN
ejpam-3328	334	26	(	(	PUNCT
ejpam-3328	334	27	k	k	X
ejpam-3328	334	28	,	,	PUNCT
ejpam-3328	334	29	k′)|	k′)|	X
ejpam-3328	334	30	<	<	X
ejpam-3328	334	31	c√	c√	PROPN
ejpam-3328	334	32	(	(	PUNCT
ejpam-3328	334	33	1−	1−	NUM
ejpam-3328	334	34	cos(θ	cos(θ	NOUN
ejpam-3328	334	35	)	)	PUNCT
ejpam-3328	334	36	)	)	PUNCT
ejpam-3328	334	37	,	,	PUNCT
ejpam-3328	334	38	|t	|t	PROPN
ejpam-3328	334	39	~v	~v	PUNCT
ejpam-3328	334	40	k|	k|	X
ejpam-3328	334	41	<	<	X
ejpam-3328	334	42	c0||v||l2(r3	c0||v||l2(r3	NUM
ejpam-3328	334	43	)	)	PUNCT
ejpam-3328	335	1	+	+	NUM
ejpam-3328	335	2	c0t√	c0t√	NOUN
ejpam-3328	335	3	ν(1−	ν(1−	NOUN
ejpam-3328	335	4	cos(θ	cos(θ	X
ejpam-3328	335	5	)	)	PUNCT
ejpam-3328	335	6	)	)	PUNCT
ejpam-3328	335	7	||∇v||l2(r3)||v||l2(r3	||∇v||l2(r3)||v||l2(r3	PROPN
ejpam-3328	335	8	)	)	PUNCT
ejpam-3328	335	9	.	.	PUNCT
ejpam-3328	336	1	proof	proof	NOUN
ejpam-3328	336	2	.	.	PUNCT
ejpam-3328	337	1	this	this	PRON
ejpam-3328	337	2	follows	follow	VERB
ejpam-3328	337	3	from	from	ADP
ejpam-3328	337	4	~̇v	~̇v	PROPN
ejpam-3328	337	5	=	=	SYM
ejpam-3328	337	6	−fkk′[(~v,∇)~v	−fkk′[(~v,∇)~v	NOUN
ejpam-3328	337	7	]	]	X
ejpam-3328	337	8	+	+	CCONJ
ejpam-3328	337	9	fkk′(ν∆~v	fkk′(ν∆~v	NOUN
ejpam-3328	337	10	+	+	NOUN
ejpam-3328	337	11	∇p	∇p	ADV
ejpam-3328	337	12	)	)	PUNCT
ejpam-3328	338	1	+	+	NUM
ejpam-3328	339	1	fkk′f	fkk′f	NOUN
ejpam-3328	339	2	.	.	PUNCT
ejpam-3328	340	1	after	after	ADP
ejpam-3328	340	2	the	the	DET
ejpam-3328	340	3	transformations	transformation	NOUN
ejpam-3328	340	4	,	,	PUNCT
ejpam-3328	340	5	we	we	PRON
ejpam-3328	340	6	obtain	obtain	VERB
ejpam-3328	340	7	~̇v	~̇v	NOUN
ejpam-3328	340	8	=	=	SYM
ejpam-3328	341	1	−fkk′[(~v∇)~v	−fkk′[(~v∇)~v	PROPN
ejpam-3328	341	2	]	]	X
ejpam-3328	341	3	+	+	CCONJ
ejpam-3328	341	4	(	(	PUNCT
ejpam-3328	341	5	νkfkk′~v	νkfkk′~v	PROPN
ejpam-3328	341	6	+	+	CCONJ
ejpam-3328	341	7	fkk′∇p	fkk′∇p	PROPN
ejpam-3328	341	8	)	)	PUNCT
ejpam-3328	342	1	+	+	NUM
ejpam-3328	342	2	fkk′f	fkk′f	ADV
ejpam-3328	342	3	,	,	PUNCT
ejpam-3328	342	4	~v	~v	PUNCT
ejpam-3328	342	5	=	=	SYM
ejpam-3328	342	6	~v0	~v0	PUNCT
ejpam-3328	342	7	+	+	CCONJ
ejpam-3328	342	8	∫	∫	PROPN
ejpam-3328	342	9	t	t	PROPN
ejpam-3328	342	10	0	0	NUM
ejpam-3328	342	11	e−νk	e−νk	PROPN
ejpam-3328	342	12	2(1−cos(θ))(t−τ	2(1−cos(θ))(t−τ	NUM
ejpam-3328	342	13	)	)	PUNCT
ejpam-3328	342	14	(	(	PUNCT
ejpam-3328	342	15	−fkk′[(~v,∇)~v	−fkk′[(~v,∇)~v	NOUN
ejpam-3328	342	16	]	]	X
ejpam-3328	342	17	+	+	CCONJ
ejpam-3328	342	18	fkk′∇p+	fkk′∇p+	NOUN
ejpam-3328	342	19	fkk′f	fkk′f	ADV
ejpam-3328	342	20	)	)	PUNCT
ejpam-3328	342	21	.	.	PUNCT
ejpam-3328	343	1	a.	a.	NOUN
ejpam-3328	343	2	durmagambetov	durmagambetov	PROPN
ejpam-3328	343	3	/	/	SYM
ejpam-3328	343	4	eur	eur	PROPN
ejpam-3328	343	5	.	.	PUNCT
ejpam-3328	344	1	j.	j.	PROPN
ejpam-3328	344	2	pure	pure	PROPN
ejpam-3328	344	3	appl	appl	PROPN
ejpam-3328	344	4	.	.	PROPN
ejpam-3328	344	5	math	math	PROPN
ejpam-3328	344	6	,	,	PUNCT
ejpam-3328	344	7	11	11	NUM
ejpam-3328	344	8	(	(	PUNCT
ejpam-3328	344	9	4	4	NUM
ejpam-3328	344	10	)	)	PUNCT
ejpam-3328	344	11	(	(	PUNCT
ejpam-3328	344	12	2018	2018	NUM
ejpam-3328	344	13	)	)	PUNCT
ejpam-3328	344	14	,	,	PUNCT
ejpam-3328	344	15	1143	1143	NUM
ejpam-3328	344	16	-	-	SYM
ejpam-3328	344	17	1176	1176	NUM
ejpam-3328	344	18	1158	1158	NUM
ejpam-3328	344	19	from	from	ADP
ejpam-3328	344	20	the	the	DET
ejpam-3328	344	21	last	last	ADJ
ejpam-3328	344	22	equation	equation	NOUN
ejpam-3328	344	23	,	,	PUNCT
ejpam-3328	344	24	we	we	PRON
ejpam-3328	344	25	have	have	AUX
ejpam-3328	344	26	|~v	|~v	PROPN
ejpam-3328	344	27	|	|	ADV
ejpam-3328	344	28	≤	≤	NUM
ejpam-3328	344	29	|~v0|+	|~v0|+	NOUN
ejpam-3328	345	1	c0	c0	PROPN
ejpam-3328	345	2	∫	∫	PROPN
ejpam-3328	345	3	t	t	PROPN
ejpam-3328	345	4	0	0	NUM
ejpam-3328	345	5	||∇v||l2(r3)||v||l2(r3)dτ	||∇v||l2(r3)||v||l2(r3)dτ	NOUN
ejpam-3328	345	6	.	.	PUNCT
ejpam-3328	346	1	denote	denote	VERB
ejpam-3328	346	2	β	β	X
ejpam-3328	346	3	=	=	PUNCT
ejpam-3328	346	4	√	√	PROPN
ejpam-3328	346	5	(	(	PUNCT
ejpam-3328	346	6	1−	1−	NUM
ejpam-3328	346	7	cos(θ))(t−	cos(θ))(t−	PROPN
ejpam-3328	346	8	τ)ν	τ)ν	PROPN
ejpam-3328	346	9	,	,	PUNCT
ejpam-3328	346	10	a	a	PRON
ejpam-3328	346	11	=	=	X
ejpam-3328	346	12	(	(	PUNCT
ejpam-3328	346	13	θ	θ	PROPN
ejpam-3328	346	14	−	−	PROPN
ejpam-3328	347	1	θ′)x	θ′)x	PROPN
ejpam-3328	347	2	formula	formula	NOUN
ejpam-3328	347	3	121	121	NUM
ejpam-3328	347	4	(	(	PUNCT
ejpam-3328	347	5	23	23	NUM
ejpam-3328	347	6	)	)	PUNCT
ejpam-3328	347	7	from	from	ADP
ejpam-3328	347	8	[	[	X
ejpam-3328	347	9	11	11	NUM
ejpam-3328	347	10	]	]	PUNCT
ejpam-3328	347	11	as	as	ADP
ejpam-3328	347	12	n	n	NOUN
ejpam-3328	347	13	=	=	SYM
ejpam-3328	347	14	0	0	NUM
ejpam-3328	347	15	:	:	PUNCT
ejpam-3328	347	16	yield	yield	VERB
ejpam-3328	347	17	∣∣∣tk	∣∣∣tk	NOUN
ejpam-3328	347	18	~	~	NOUN
ejpam-3328	347	19	v	v	NOUN
ejpam-3328	347	20	∣∣∣	∣∣∣	NOUN
ejpam-3328	347	21	<	<	X
ejpam-3328	347	22	∣∣∣ke−β2k2	∣∣∣ke−β2k2	PROPN
ejpam-3328	347	23	∣∣∣+	∣∣∣+	PROPN
ejpam-3328	347	24	√	√	PROPN
ejpam-3328	348	1	πβ−1e	πβ−1e	CCONJ
ejpam-3328	349	1	−	−	PROPN
ejpam-3328	350	1	a2	a2	PROPN
ejpam-3328	350	2	8β2d0	8β2d0	NUM
ejpam-3328	350	3	(	(	PUNCT
ejpam-3328	350	4	a√	a√	PROPN
ejpam-3328	350	5	2β	2β	NOUN
ejpam-3328	350	6	)	)	PUNCT
ejpam-3328	350	7	,	,	PUNCT
ejpam-3328	350	8	∣∣∣tk	∣∣∣tk	NUM
ejpam-3328	350	9	~	~	NOUN
ejpam-3328	350	10	v	v	X
ejpam-3328	350	11	∣∣∣	∣∣∣	ADJ
ejpam-3328	350	12	≤	≤	NUM
ejpam-3328	350	13	∣∣∣tk	∣∣∣tk	NUM
ejpam-3328	350	14	~	~	NOUN
ejpam-3328	350	15	v0	v0	NOUN
ejpam-3328	350	16	∣∣∣	∣∣∣	NOUN
ejpam-3328	351	1	+	+	CCONJ
ejpam-3328	351	2	∣∣∣∣tk	∣∣∣∣tk	PROPN
ejpam-3328	351	3	∫	∫	PROPN
ejpam-3328	351	4	t	t	NOUN
ejpam-3328	351	5	0	0	NUM
ejpam-3328	351	6	e−νk	e−νk	PROPN
ejpam-3328	351	7	2(1−cos(θ))(t−τ	2(1−cos(θ))(t−τ	NUM
ejpam-3328	351	8	)	)	PUNCT
ejpam-3328	351	9	(	(	PUNCT
ejpam-3328	351	10	−fkk′(~v,∇)~v	−fkk′(~v,∇)~v	X
ejpam-3328	351	11	]	]	X
ejpam-3328	351	12	+	+	CCONJ
ejpam-3328	351	13	fkk′∇p+	fkk′∇p+	NOUN
ejpam-3328	351	14	fkk′f	fkk′f	ADV
ejpam-3328	351	15	)	)	PUNCT
ejpam-3328	352	1	dk	dk	PROPN
ejpam-3328	352	2	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3328	352	3	≤	≤	PROPN
ejpam-3328	352	4	∣∣∣tk	∣∣∣tk	NUM
ejpam-3328	352	5	~	~	NOUN
ejpam-3328	352	6	v0	v0	NOUN
ejpam-3328	352	7	∣∣∣+	∣∣∣+	NUM
ejpam-3328	352	8	∫	∫	PROPN
ejpam-3328	352	9	t	t	PROPN
ejpam-3328	352	10	0	0	NUM
ejpam-3328	352	11	∣∣∣ke−β2k2	∣∣∣ke−β2k2	PROPN
ejpam-3328	352	12	∣∣∣+	∣∣∣+	PROPN
ejpam-3328	352	13	∣∣∣∣√πβ−1e	∣∣∣∣√πβ−1e	PROPN
ejpam-3328	352	14	−	−	PROPN
ejpam-3328	352	15	a2	a2	PROPN
ejpam-3328	352	16	8β2d0	8β2d0	NUM
ejpam-3328	352	17	(	(	PUNCT
ejpam-3328	352	18	a√	a√	PROPN
ejpam-3328	352	19	2β	2β	NOUN
ejpam-3328	352	20	)	)	PUNCT
ejpam-3328	352	21	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3328	352	22	||∇~v||l2(r3)||~v||l2(r3)dt	||∇~v||l2(r3)||~v||l2(r3)dt	NOUN
ejpam-3328	352	23	<	<	X
ejpam-3328	352	24	c0||v||l2(r3	c0||v||l2(r3	PROPN
ejpam-3328	352	25	)	)	PUNCT
ejpam-3328	352	26	+	+	NUM
ejpam-3328	352	27	c0t√	c0t√	NOUN
ejpam-3328	352	28	ν(1−	ν(1−	NOUN
ejpam-3328	352	29	cos(θ	cos(θ	X
ejpam-3328	352	30	)	)	PUNCT
ejpam-3328	352	31	)	)	PUNCT
ejpam-3328	352	32	||∇v||l2(r3)||v||l2(r3	||∇v||l2(r3)||v||l2(r3	PROPN
ejpam-3328	352	33	)	)	PUNCT
ejpam-3328	352	34	.	.	PUNCT
ejpam-3328	353	1	theorem	theorem	NOUN
ejpam-3328	353	2	5	5	NUM
ejpam-3328	353	3	.	.	PUNCT
ejpam-3328	354	1	let	let	VERB
ejpam-3328	354	2	~v0	~v0	PUNCT
ejpam-3328	354	3	∈	∈	PROPN
ejpam-3328	354	4	w	w	NOUN
ejpam-3328	354	5	2	2	NUM
ejpam-3328	354	6	2	2	NUM
ejpam-3328	354	7	(	(	PUNCT
ejpam-3328	354	8	r3	r3	PROPN
ejpam-3328	354	9	)	)	PUNCT
ejpam-3328	354	10	,	,	PUNCT
ejpam-3328	354	11	~f	~f	PUNCT
ejpam-3328	354	12	∈	∈	PROPN
ejpam-3328	354	13	l2(qt	l2(qt	PROPN
ejpam-3328	354	14	)	)	PUNCT
ejpam-3328	354	15	,	,	PUNCT
ejpam-3328	355	1	~̃	~̃	PROPN
ejpam-3328	355	2	f	f	PROPN
ejpam-3328	355	3	∈	∈	PROPN
ejpam-3328	355	4	w	w	PROPN
ejpam-3328	355	5	2,1	2,1	NUM
ejpam-3328	355	6	2	2	NUM
ejpam-3328	355	7	(	(	PUNCT
ejpam-3328	355	8	qt	qt	NOUN
ejpam-3328	355	9	)	)	PUNCT
ejpam-3328	355	10	,	,	PUNCT
ejpam-3328	355	11	|tkv0|	|tkv0|	PROPN
ejpam-3328	355	12	+	+	PUNCT
ejpam-3328	355	13	|tkv0|	|tkv0|	PRON
ejpam-3328	355	14	+	+	ADJ
ejpam-3328	355	15	∣∣∣tk2v0	∣∣∣tk2v0	PROPN
ejpam-3328	355	16	~̃v0	~̃v0	NOUN
ejpam-3328	355	17	∣∣∣	∣∣∣	NOUN
ejpam-3328	355	18	<	<	X
ejpam-3328	355	19	c	c	NOUN
ejpam-3328	355	20	,	,	PUNCT
ejpam-3328	355	21	and	and	CCONJ
ejpam-3328	355	22	∫∞	∫∞	NOUN
ejpam-3328	355	23	0	0	PUNCT
ejpam-3328	355	24	||h0	||h0	PROPN
ejpam-3328	355	25	~f	~f	PUNCT
ejpam-3328	355	26	||l2(r3)dt	||l2(r3)dt	PROPN
ejpam-3328	355	27	<	<	X
ejpam-3328	355	28	c.	c.	PROPN
ejpam-3328	355	29	then	then	ADV
ejpam-3328	355	30	,	,	PUNCT
ejpam-3328	355	31	the	the	DET
ejpam-3328	355	32	solution	solution	NOUN
ejpam-3328	355	33	of	of	ADP
ejpam-3328	355	34	(	(	PUNCT
ejpam-3328	355	35	7)–(9	7)–(9	NOUN
ejpam-3328	355	36	)	)	PUNCT
ejpam-3328	355	37	in	in	ADP
ejpam-3328	355	38	theorem	theorem	ADJ
ejpam-3328	355	39	4	4	NUM
ejpam-3328	355	40	satisfies	satisfie	NOUN
ejpam-3328	355	41	the	the	DET
ejpam-3328	355	42	following	follow	VERB
ejpam-3328	355	43	inequalities	inequality	NOUN
ejpam-3328	355	44	:	:	PUNCT
ejpam-3328	355	45	sup	sup	NOUN
ejpam-3328	355	46	x∈r3	x∈r3	PROPN
ejpam-3328	355	47	||~v(x)||	||~v(x)||	X
ejpam-3328	356	1	<	<	X
ejpam-3328	356	2	c	c	X
ejpam-3328	356	3	,	,	PUNCT
ejpam-3328	356	4	||∇~v||l2(r3	||∇~v||l2(r3	NOUN
ejpam-3328	356	5	)	)	PUNCT
ejpam-3328	356	6	+	+	CCONJ
ejpam-3328	356	7	ν	ν	X
ejpam-3328	356	8	t∫	t∫	NUM
ejpam-3328	356	9	0	0	NUM
ejpam-3328	356	10	∫	∫	PROPN
ejpam-3328	356	11	r3	r3	PROPN
ejpam-3328	356	12	|h0	|h0	NOUN
ejpam-3328	356	13	~	~	SYM
ejpam-3328	356	14	v|2dxdτ	v|2dxdτ	X
ejpam-3328	356	15	≤	≤	NUM
ejpam-3328	356	16	const	const	NOUN
ejpam-3328	356	17	.	.	PUNCT
ejpam-3328	357	1	proof	proof	NOUN
ejpam-3328	357	2	.	.	PUNCT
ejpam-3328	358	1	consider	consider	VERB
ejpam-3328	358	2	the	the	DET
ejpam-3328	358	3	cauchy	cauchy	ADJ
ejpam-3328	358	4	problem	problem	NOUN
ejpam-3328	358	5	for	for	ADP
ejpam-3328	358	6	the	the	DET
ejpam-3328	358	7	navier	navier	NOUN
ejpam-3328	358	8	–	–	PUNCT
ejpam-3328	358	9	stokes	stokes	PROPN
ejpam-3328	358	10	equations	equation	NOUN
ejpam-3328	358	11	:	:	PUNCT
ejpam-3328	359	1	∂~v	∂~v	PROPN
ejpam-3328	359	2	∂t	∂t	PROPN
ejpam-3328	359	3	−	−	PROPN
ejpam-3328	359	4	ν∆~v	ν∆~v	PROPN
ejpam-3328	359	5	+	+	CCONJ
ejpam-3328	359	6	(	(	PUNCT
ejpam-3328	359	7	~v,∇~v	~v,∇~v	NUM
ejpam-3328	359	8	)	)	PUNCT
ejpam-3328	359	9	=	=	SYM
ejpam-3328	359	10	−∇p+	−∇p+	NUM
ejpam-3328	359	11	~f(x	~f(x	NOUN
ejpam-3328	359	12	,	,	PUNCT
ejpam-3328	359	13	t	t	PROPN
ejpam-3328	359	14	)	)	PUNCT
ejpam-3328	359	15	,	,	PUNCT
ejpam-3328	359	16	div	div	X
ejpam-3328	359	17	~v	~v	PUNCT
ejpam-3328	359	18	=	=	SYM
ejpam-3328	359	19	0	0	NUM
ejpam-3328	359	20	,	,	PUNCT
ejpam-3328	359	21	(	(	PUNCT
ejpam-3328	359	22	10	10	NUM
ejpam-3328	359	23	)	)	PUNCT
ejpam-3328	359	24	~v|t=0	~v|t=0	NUM
ejpam-3328	359	25	=	=	SYM
ejpam-3328	359	26	~v0(x	~v0(x	NOUN
ejpam-3328	359	27	)	)	PUNCT
ejpam-3328	359	28	(	(	PUNCT
ejpam-3328	359	29	11	11	NUM
ejpam-3328	359	30	)	)	PUNCT
ejpam-3328	359	31	in	in	ADP
ejpam-3328	359	32	the	the	DET
ejpam-3328	359	33	domain	domain	NOUN
ejpam-3328	359	34	qt	qt	NOUN
ejpam-3328	359	35	=	=	SYM
ejpam-3328	359	36	r3	r3	PROPN
ejpam-3328	359	37	×	×	NOUN
ejpam-3328	359	38	(	(	PUNCT
ejpam-3328	359	39	0	0	NUM
ejpam-3328	359	40	,	,	PUNCT
ejpam-3328	359	41	t	t	PROPN
ejpam-3328	359	42	)	)	PUNCT
ejpam-3328	359	43	,	,	PUNCT
ejpam-3328	359	44	where	where	SCONJ
ejpam-3328	359	45	div	div	X
ejpam-3328	359	46	~v0	~v0	PUNCT
ejpam-3328	359	47	=	=	SYM
ejpam-3328	359	48	0	0	X
ejpam-3328	359	49	.	.	PUNCT
ejpam-3328	360	1	(	(	PUNCT
ejpam-3328	360	2	12	12	NUM
ejpam-3328	360	3	)	)	PUNCT
ejpam-3328	360	4	we	we	PRON
ejpam-3328	360	5	perform	perform	VERB
ejpam-3328	360	6	the	the	DET
ejpam-3328	360	7	following	follow	VERB
ejpam-3328	360	8	transformations	transformation	NOUN
ejpam-3328	360	9	:	:	PUNCT
ejpam-3328	360	10	~uε	~uε	PROPN
ejpam-3328	360	11	=	=	SYM
ejpam-3328	360	12	ε	ε	PROPN
ejpam-3328	360	13	~	~	PROPN
ejpam-3328	360	14	v	v	NOUN
ejpam-3328	360	15	,	,	PUNCT
ejpam-3328	360	16	pε	pε	NOUN
ejpam-3328	360	17	=	=	SYM
ejpam-3328	360	18	pε	pε	PROPN
ejpam-3328	360	19	,	,	PUNCT
ejpam-3328	360	20	fε	fε	NOUN
ejpam-3328	360	21	=	=	SYM
ejpam-3328	360	22	fε2	fε2	PROPN
ejpam-3328	360	23	,	,	PUNCT
ejpam-3328	360	24	νε	νε	NOUN
ejpam-3328	360	25	=	=	PUNCT
ejpam-3328	360	26	εν	εν	PROPN
ejpam-3328	360	27	,	,	PUNCT
ejpam-3328	360	28	s	s	PART
ejpam-3328	360	29	=	=	X
ejpam-3328	360	30	t	t	X
ejpam-3328	360	31	ε	ε	PROPN
ejpam-3328	360	32	.	.	PUNCT
ejpam-3328	361	1	a.	a.	PROPN
ejpam-3328	361	2	durmagambetov	durmagambetov	PROPN
ejpam-3328	361	3	/	/	SYM
ejpam-3328	361	4	eur	eur	PROPN
ejpam-3328	361	5	.	.	PUNCT
ejpam-3328	362	1	j.	j.	PROPN
ejpam-3328	362	2	pure	pure	PROPN
ejpam-3328	362	3	appl	appl	PROPN
ejpam-3328	362	4	.	.	PROPN
ejpam-3328	362	5	math	math	PROPN
ejpam-3328	362	6	,	,	PUNCT
ejpam-3328	362	7	11	11	NUM
ejpam-3328	362	8	(	(	PUNCT
ejpam-3328	362	9	4	4	NUM
ejpam-3328	362	10	)	)	PUNCT
ejpam-3328	362	11	(	(	PUNCT
ejpam-3328	362	12	2018	2018	NUM
ejpam-3328	362	13	)	)	PUNCT
ejpam-3328	362	14	,	,	PUNCT
ejpam-3328	362	15	1143	1143	NUM
ejpam-3328	362	16	-	-	SYM
ejpam-3328	362	17	1176	1176	NUM
ejpam-3328	362	18	1159	1159	NUM
ejpam-3328	362	19	then	then	ADV
ejpam-3328	362	20	,	,	PUNCT
ejpam-3328	362	21	∂	∂	X
ejpam-3328	362	22	~uε	~uε	PROPN
ejpam-3328	362	23	∂s	∂s	PROPN
ejpam-3328	362	24	−	−	PROPN
ejpam-3328	362	25	νε∆~uε	νε∆~uε	NOUN
ejpam-3328	363	1	+	+	CCONJ
ejpam-3328	363	2	(	(	PUNCT
ejpam-3328	363	3	~uε,∇~uε	~uε,∇~uε	NOUN
ejpam-3328	363	4	)	)	PUNCT
ejpam-3328	363	5	=	=	SYM
ejpam-3328	364	1	−∇εpε	−∇εpε	ADJ
ejpam-3328	365	1	+	+	CCONJ
ejpam-3328	365	2	~fε(x	~fε(x	ADP
ejpam-3328	365	3	,	,	PUNCT
ejpam-3328	365	4	t	t	PROPN
ejpam-3328	365	5	)	)	PUNCT
ejpam-3328	365	6	,	,	PUNCT
ejpam-3328	365	7	div	div	X
ejpam-3328	365	8	~uε	~uε	PROPN
ejpam-3328	365	9	=	=	SYM
ejpam-3328	365	10	0	0	NUM
ejpam-3328	365	11	,	,	PUNCT
ejpam-3328	365	12	(	(	PUNCT
ejpam-3328	365	13	13	13	NUM
ejpam-3328	365	14	)	)	PUNCT
ejpam-3328	365	15	~uε|t=0	~uε|t=0	PRON
ejpam-3328	365	16	=	=	SYM
ejpam-3328	365	17	~uε0(x	~uε0(x	NOUN
ejpam-3328	365	18	)	)	PUNCT
ejpam-3328	365	19	(	(	PUNCT
ejpam-3328	365	20	14	14	NUM
ejpam-3328	365	21	)	)	PUNCT
ejpam-3328	365	22	in	in	ADP
ejpam-3328	365	23	the	the	DET
ejpam-3328	365	24	domain	domain	NOUN
ejpam-3328	365	25	qt	qt	NOUN
ejpam-3328	365	26	=	=	SYM
ejpam-3328	365	27	r3	r3	PROPN
ejpam-3328	365	28	×	×	NOUN
ejpam-3328	365	29	(	(	PUNCT
ejpam-3328	365	30	0	0	NUM
ejpam-3328	365	31	,	,	PUNCT
ejpam-3328	365	32	tε	tε	NOUN
ejpam-3328	365	33	)	)	PUNCT
ejpam-3328	365	34	,	,	PUNCT
ejpam-3328	365	35	where	where	SCONJ
ejpam-3328	365	36	div	div	X
ejpam-3328	365	37	~uε|t=0	~uε|t=0	NOUN
ejpam-3328	365	38	=	=	NOUN
ejpam-3328	365	39	0	0	X
ejpam-3328	365	40	.	.	PUNCT
ejpam-3328	366	1	(	(	PUNCT
ejpam-3328	366	2	15	15	X
ejpam-3328	366	3	)	)	PUNCT
ejpam-3328	366	4	let	let	VERB
ejpam-3328	366	5	us	we	PRON
ejpam-3328	366	6	return	return	VERB
ejpam-3328	366	7	for	for	ADP
ejpam-3328	366	8	convenience	convenience	NOUN
ejpam-3328	366	9	to	to	ADP
ejpam-3328	366	10	the	the	DET
ejpam-3328	366	11	notation	notation	NOUN
ejpam-3328	366	12	vi	vi	NOUN
ejpam-3328	366	13	=	=	SYM
ejpam-3328	366	14	uεi	uεi	NOUN
ejpam-3328	366	15	,	,	PUNCT
ejpam-3328	366	16	using	use	VERB
ejpam-3328	366	17	the	the	DET
ejpam-3328	366	18	equation	equation	NOUN
ejpam-3328	366	19	for	for	ADP
ejpam-3328	366	20	each	each	DET
ejpam-3328	366	21	vi	vi	NOUN
ejpam-3328	366	22	=	=	NOUN
ejpam-3328	366	23	uεi	uεi	NOUN
ejpam-3328	366	24	.	.	PUNCT
ejpam-3328	367	1	this	this	PRON
ejpam-3328	367	2	gives	give	VERB
ejpam-3328	367	3	us	we	PRON
ejpam-3328	367	4	−∆xψ	−∆xψ	NOUN
ejpam-3328	367	5	+	+	CCONJ
ejpam-3328	367	6	viψ	viψ	NOUN
ejpam-3328	367	7	=	=	SYM
ejpam-3328	367	8	k2ψ	k2ψ	NOUN
ejpam-3328	367	9	,	,	PUNCT
ejpam-3328	367	10	k	k	PROPN
ejpam-3328	367	11	∈	∈	PROPN
ejpam-3328	367	12	c.	c.	NOUN
ejpam-3328	367	13	using	use	VERB
ejpam-3328	367	14	lemmas	lemmas	PROPN
ejpam-3328	367	15	12	12	NUM
ejpam-3328	367	16	-	-	SYM
ejpam-3328	367	17	15	15	NUM
ejpam-3328	367	18	,	,	PUNCT
ejpam-3328	367	19	we	we	PRON
ejpam-3328	367	20	get	get	VERB
ejpam-3328	367	21	estimates	estimate	NOUN
ejpam-3328	367	22	for	for	ADP
ejpam-3328	367	23	ai	ai	PROPN
ejpam-3328	367	24	,	,	PUNCT
ejpam-3328	367	25	~vi	~vi	PROPN
ejpam-3328	367	26	,	,	PUNCT
ejpam-3328	367	27	tai	tai	PROPN
ejpam-3328	367	28	,	,	PUNCT
ejpam-3328	367	29	t	t	PROPN
ejpam-3328	367	30	~vi	~vi	PROPN
ejpam-3328	367	31	,	,	PUNCT
ejpam-3328	367	32	kai	kai	PROPN
ejpam-3328	367	33	,	,	PUNCT
ejpam-3328	367	34	k	k	PROPN
ejpam-3328	367	35	~	~	SYM
ejpam-3328	367	36	vi	vi	PROPN
ejpam-3328	367	37	,	,	PUNCT
ejpam-3328	367	38	tkai	tkai	NOUN
ejpam-3328	367	39	,	,	PUNCT
ejpam-3328	367	40	tk	tk	PROPN
ejpam-3328	367	41	~	~	PROPN
ejpam-3328	367	42	vi	vi	PROPN
ejpam-3328	367	43	,	,	PUNCT
ejpam-3328	367	44	tkṽi	tkṽi	PROPN
ejpam-3328	367	45	,	,	PUNCT
ejpam-3328	367	46	tk	tk	PROPN
ejpam-3328	367	47	2v	2v	PROPN
ejpam-3328	367	48	ṽi	ṽi	PROPN
ejpam-3328	367	49	.	.	PUNCT
ejpam-3328	368	1	the	the	DET
ejpam-3328	368	2	last	last	ADJ
ejpam-3328	368	3	estimations	estimation	NOUN
ejpam-3328	368	4	yield	yield	VERB
ejpam-3328	368	5	the	the	DET
ejpam-3328	368	6	representation	representation	NOUN
ejpam-3328	368	7	q	q	NOUN
ejpam-3328	368	8	=	=	SYM
ejpam-3328	368	9	λ	λ	X
ejpam-3328	368	10	(	(	PUNCT
ejpam-3328	368	11	h0	h0	PROPN
ejpam-3328	368	12	∫	∫	PROPN
ejpam-3328	368	13	s2	s2	PROPN
ejpam-3328	368	14	ψdθ	ψdθ	ADP
ejpam-3328	368	15	+	+	CCONJ
ejpam-3328	368	16	k2	k2	ADJ
ejpam-3328	368	17	∫	∫	PROPN
ejpam-3328	368	18	s2	s2	PROPN
ejpam-3328	368	19	ψdθ	ψdθ	NOUN
ejpam-3328	368	20	)	)	PUNCT
ejpam-3328	369	1	λ	λ	PROPN
ejpam-3328	369	2	∫	∫	PROPN
ejpam-3328	369	3	s2	s2	NOUN
ejpam-3328	369	4	ψdθ	ψdθ	NOUN
ejpam-3328	369	5	|r=	|r=	VERB
ejpam-3328	369	6	π	π	PROPN
ejpam-3328	369	7	k0	k0	PROPN
ejpam-3328	369	8	,	,	PUNCT
ejpam-3328	369	9	k	k	PROPN
ejpam-3328	369	10	=	=	PROPN
ejpam-3328	369	11	k0	k0	PROPN
ejpam-3328	369	12	,	,	PUNCT
ejpam-3328	369	13	and	and	CCONJ
ejpam-3328	369	14	lemma	lemma	PROPN
ejpam-3328	369	15	11	11	NUM
ejpam-3328	369	16	implies	imply	VERB
ejpam-3328	369	17	||∇~v||2l2(r3	||∇~v||2l2(r3	NOUN
ejpam-3328	369	18	)	)	PUNCT
ejpam-3328	370	1	+	+	CCONJ
ejpam-3328	371	1	νε	νε	NOUN
ejpam-3328	371	2	t∫	t∫	DET
ejpam-3328	371	3	0	0	NUM
ejpam-3328	371	4	||h0	||h0	PROPN
ejpam-3328	371	5	~	~	X
ejpam-3328	371	6	v||2l2(r3)dτ	v||2l2(r3)dτ	NOUN
ejpam-3328	371	7	≤	≤	NUM
ejpam-3328	371	8	∫	∫	PROPN
ejpam-3328	371	9	∞	∞	NUM
ejpam-3328	371	10	0	0	NUM
ejpam-3328	372	1	||(~v)||l2(r3)||||h0	||(~v)||l2(r3)||||h0	NUM
ejpam-3328	372	2	~f	~f	PUNCT
ejpam-3328	372	3	||l2(r3)dτ+	||l2(r3)dτ+	NUM
ejpam-3328	372	4	||∇~v0||2l2(r3	||∇~v0||2l2(r3	PUNCT
ejpam-3328	372	5	)	)	PUNCT
ejpam-3328	373	1	+	+	CCONJ
ejpam-3328	373	2	c0	c0	PROPN
ejpam-3328	373	3	νε	νε	PROPN
ejpam-3328	373	4	∫	∫	PROPN
ejpam-3328	373	5	t	t	PROPN
ejpam-3328	373	6	0	0	PROPN
ejpam-3328	374	1	(	(	PUNCT
ejpam-3328	374	2	c1	c1	PROPN
ejpam-3328	374	3	νε	νε	PROPN
ejpam-3328	374	4	||(∇~v)||2l2(r3)||(~v)||2l2(r3	||(∇~v)||2l2(r3)||(~v)||2l2(r3	PROPN
ejpam-3328	374	5	)	)	PUNCT
ejpam-3328	374	6	+	+	NUM
ejpam-3328	374	7	||~v||2l2(r3	||~v||2l2(r3	NUM
ejpam-3328	374	8	)	)	PUNCT
ejpam-3328	374	9	)	)	PUNCT
ejpam-3328	375	1	||(∇~v)||2l2(r3)dτ	||(∇~v)||2l2(r3)dτ	PROPN
ejpam-3328	375	2	.	.	PUNCT
ejpam-3328	376	1	denote	denote	PROPN
ejpam-3328	376	2	α(s	α(s	PROPN
ejpam-3328	376	3	)	)	PUNCT
ejpam-3328	377	1	=	=	SYM
ejpam-3328	377	2	c0	c0	PROPN
ejpam-3328	377	3	νε	νε	PROPN
ejpam-3328	377	4	(	(	PUNCT
ejpam-3328	377	5	c1	c1	PROPN
ejpam-3328	377	6	νε	νε	PROPN
ejpam-3328	377	7	||(∇~v)||2l2(r3)||(~v)||2l2(r3	||(∇~v)||2l2(r3)||(~v)||2l2(r3	PROPN
ejpam-3328	377	8	)	)	PUNCT
ejpam-3328	377	9	+	+	NUM
ejpam-3328	377	10	||~v||2l2(r3	||~v||2l2(r3	NUM
ejpam-3328	377	11	)	)	PUNCT
ejpam-3328	377	12	)	)	PUNCT
ejpam-3328	377	13	,	,	PUNCT
ejpam-3328	377	14	∫	∫	PROPN
ejpam-3328	377	15	t	t	PROPN
ejpam-3328	377	16	tεν	tεν	PROPN
ejpam-3328	377	17	0	0	NUM
ejpam-3328	377	18	α(s)ds	α(s)ds	NUM
ejpam-3328	377	19	≤	≤	NUM
ejpam-3328	377	20	∫	∫	NOUN
ejpam-3328	377	21	1	1	NUM
ejpam-3328	377	22	νε	νε	NOUN
ejpam-3328	377	23	0	0	NUM
ejpam-3328	377	24	c0	c0	PROPN
ejpam-3328	377	25	νε	νε	PROPN
ejpam-3328	377	26	(	(	PUNCT
ejpam-3328	377	27	c1	c1	PROPN
ejpam-3328	377	28	νε	νε	PROPN
ejpam-3328	377	29	||(∇~v)||2l2(r3)||(~v)||2l2(r3	||(∇~v)||2l2(r3)||(~v)||2l2(r3	PROPN
ejpam-3328	377	30	)	)	PUNCT
ejpam-3328	377	31	+	+	NUM
ejpam-3328	377	32	||~v||2l2(r3	||~v||2l2(r3	NUM
ejpam-3328	377	33	)	)	PUNCT
ejpam-3328	377	34	)	)	PUNCT
ejpam-3328	378	1	ds	ds	ADJ
ejpam-3328	378	2	≤	≤	NOUN
ejpam-3328	378	3	c0c1	c0c1	PUNCT
ejpam-3328	378	4	ν3	ν3	NOUN
ejpam-3328	378	5	ε	ε	PROPN
ejpam-3328	378	6	sup	sup	NOUN
ejpam-3328	378	7	t	t	PROPN
ejpam-3328	378	8	||(~v)||2l2(r3	||(~v)||2l2(r3	PROPN
ejpam-3328	378	9	)	)	PUNCT
ejpam-3328	378	10	∫	∫	PROPN
ejpam-3328	379	1	∞	∞	PROPN
ejpam-3328	379	2	0	0	NUM
ejpam-3328	380	1	νε||(∇~v)||2l2(r3)||ds+	νε||(∇~v)||2l2(r3)||ds+	PROPN
ejpam-3328	380	2	c0	c0	PROPN
ejpam-3328	380	3	νε	νε	PROPN
ejpam-3328	380	4	sup	sup	PROPN
ejpam-3328	380	5	t	t	PROPN
ejpam-3328	380	6	||(~v)||2l2(r3	||(~v)||2l2(r3	PROPN
ejpam-3328	380	7	)	)	PUNCT
ejpam-3328	380	8	≤	≤	NOUN
ejpam-3328	380	9	c0ε	c0ε	ADP
ejpam-3328	380	10	4	4	NUM
ejpam-3328	380	11	εν3	εν3	NOUN
ejpam-3328	380	12	ε	ε	NOUN
ejpam-3328	380	13	+	+	CCONJ
ejpam-3328	380	14	c0ε	c0ε	PROPN
ejpam-3328	380	15	2	2	NUM
ejpam-3328	380	16	ν	ν	NOUN
ejpam-3328	380	17	ε	ε	PROPN
ejpam-3328	380	18	νε	νε	NOUN
ejpam-3328	380	19	≤	≤	NUM
ejpam-3328	380	20	2c0	2c0	NUM
ejpam-3328	380	21	.	.	PUNCT
ejpam-3328	381	1	as	as	ADP
ejpam-3328	381	2	ε	ε	PROPN
ejpam-3328	381	3	=	=	SYM
ejpam-3328	381	4	νε0	νε0	PROPN
ejpam-3328	381	5	,	,	PUNCT
ejpam-3328	381	6	the	the	DET
ejpam-3328	381	7	gronwall	gronwall	ADJ
ejpam-3328	381	8	–	–	PUNCT
ejpam-3328	381	9	bellman	bellman	NOUN
ejpam-3328	381	10	lemma	lemma	PROPN
ejpam-3328	381	11	yields	yields	PROPN
ejpam-3328	381	12	||∇~v||2l2(r3	||∇~v||2l2(r3	PROPN
ejpam-3328	381	13	)	)	PUNCT
ejpam-3328	382	1	+	+	CCONJ
ejpam-3328	382	2	νε	νε	NOUN
ejpam-3328	382	3	t∫	t∫	PRON
ejpam-3328	382	4	0	0	NUM
ejpam-3328	382	5	∫	∫	PROPN
ejpam-3328	382	6	r3	r3	PROPN
ejpam-3328	382	7	|h0	|h0	NOUN
ejpam-3328	382	8	~	~	SYM
ejpam-3328	382	9	v|2dxdτ	v|2dxdτ	NOUN
ejpam-3328	382	10	≤	≤	NUM
ejpam-3328	382	11	||∇~v0||2l2(r3	||∇~v0||2l2(r3	NOUN
ejpam-3328	382	12	)	)	PUNCT
ejpam-3328	383	1	e	e	NOUN
ejpam-3328	383	2	2c0	2c0	NUM
ejpam-3328	383	3	+	+	NOUN
ejpam-3328	383	4	e2c0	e2c0	NOUN
ejpam-3328	383	5	∫	∫	PROPN
ejpam-3328	383	6	∞	∞	NUM
ejpam-3328	383	7	0	0	NUM
ejpam-3328	384	1	||(~v)||l2(r3)||||h0	||(~v)||l2(r3)||||h0	NUM
ejpam-3328	384	2	~f	~f	PUNCT
ejpam-3328	384	3	||l2(r3)dτ	||l2(r3)dτ	PROPN
ejpam-3328	384	4	.	.	PUNCT
ejpam-3328	384	5	theorem	theorem	NOUN
ejpam-3328	384	6	5	5	NUM
ejpam-3328	384	7	asserts	assert	VERB
ejpam-3328	384	8	the	the	DET
ejpam-3328	384	9	global	global	ADJ
ejpam-3328	384	10	solvability	solvability	NOUN
ejpam-3328	384	11	and	and	CCONJ
ejpam-3328	384	12	uniqueness	uniqueness	NOUN
ejpam-3328	384	13	of	of	ADP
ejpam-3328	384	14	the	the	DET
ejpam-3328	384	15	cauchy	cauchy	ADJ
ejpam-3328	384	16	problem	problem	NOUN
ejpam-3328	384	17	for	for	ADP
ejpam-3328	384	18	the	the	DET
ejpam-3328	384	19	navier	navier	NOUN
ejpam-3328	384	20	–	–	PUNCT
ejpam-3328	384	21	stokes	stokes	PROPN
ejpam-3328	384	22	equations	equation	NOUN
ejpam-3328	384	23	.	.	PUNCT
ejpam-3328	385	1	a.	a.	NOUN
ejpam-3328	385	2	durmagambetov	durmagambetov	PROPN
ejpam-3328	385	3	/	/	SYM
ejpam-3328	385	4	eur	eur	PROPN
ejpam-3328	385	5	.	.	PUNCT
ejpam-3328	386	1	j.	j.	PROPN
ejpam-3328	386	2	pure	pure	PROPN
ejpam-3328	386	3	appl	appl	PROPN
ejpam-3328	386	4	.	.	PROPN
ejpam-3328	386	5	math	math	PROPN
ejpam-3328	386	6	,	,	PUNCT
ejpam-3328	386	7	11	11	NUM
ejpam-3328	386	8	(	(	PUNCT
ejpam-3328	386	9	4	4	NUM
ejpam-3328	386	10	)	)	PUNCT
ejpam-3328	386	11	(	(	PUNCT
ejpam-3328	386	12	2018	2018	NUM
ejpam-3328	386	13	)	)	PUNCT
ejpam-3328	386	14	,	,	PUNCT
ejpam-3328	386	15	1143	1143	NUM
ejpam-3328	386	16	-	-	SYM
ejpam-3328	386	17	1176	1176	NUM
ejpam-3328	386	18	1160	1160	NUM
ejpam-3328	386	19	6	6	NUM
ejpam-3328	386	20	.	.	PUNCT
ejpam-3328	386	21	discussion	discussion	NOUN
ejpam-3328	386	22	as	as	SCONJ
ejpam-3328	386	23	noted	note	VERB
ejpam-3328	386	24	in	in	ADP
ejpam-3328	386	25	the	the	DET
ejpam-3328	386	26	introduction	introduction	NOUN
ejpam-3328	386	27	,	,	PUNCT
ejpam-3328	386	28	the	the	DET
ejpam-3328	386	29	key	key	ADJ
ejpam-3328	386	30	method	method	NOUN
ejpam-3328	386	31	of	of	ADP
ejpam-3328	386	32	investigating	investigate	VERB
ejpam-3328	386	33	the	the	DET
ejpam-3328	386	34	cauchy	cauchy	ADJ
ejpam-3328	386	35	problem	problem	NOUN
ejpam-3328	386	36	for	for	ADP
ejpam-3328	386	37	the	the	DET
ejpam-3328	386	38	navier	navier	NOUN
ejpam-3328	386	39	–	–	PUNCT
ejpam-3328	386	40	stokes	stokes	PROPN
ejpam-3328	386	41	equations	equation	NOUN
ejpam-3328	386	42	is	be	AUX
ejpam-3328	386	43	its	its	PRON
ejpam-3328	386	44	reduction	reduction	NOUN
ejpam-3328	386	45	to	to	ADP
ejpam-3328	386	46	the	the	DET
ejpam-3328	386	47	poincaré–riemann	poincaré–riemann	NOUN
ejpam-3328	386	48	–	–	PUNCT
ejpam-3328	386	49	hilbert	hilbert	NOUN
ejpam-3328	386	50	problem	problem	NOUN
ejpam-3328	386	51	.	.	PUNCT
ejpam-3328	387	1	by	by	ADP
ejpam-3328	387	2	studying	study	VERB
ejpam-3328	387	3	the	the	DET
ejpam-3328	387	4	wave	wave	NOUN
ejpam-3328	387	5	functions	function	NOUN
ejpam-3328	387	6	for	for	ADP
ejpam-3328	387	7	the	the	DET
ejpam-3328	387	8	schrd̈inger	schrd̈inger	NOUN
ejpam-3328	387	9	equation	equation	NOUN
ejpam-3328	387	10	of	of	ADP
ejpam-3328	387	11	the	the	DET
ejpam-3328	387	12	generated	generate	VERB
ejpam-3328	387	13	velocity	velocity	NOUN
ejpam-3328	387	14	components	component	NOUN
ejpam-3328	387	15	,	,	PUNCT
ejpam-3328	387	16	we	we	PRON
ejpam-3328	387	17	obtain	obtain	VERB
ejpam-3328	387	18	unique	unique	ADJ
ejpam-3328	387	19	estimates	estimate	NOUN
ejpam-3328	387	20	for	for	ADP
ejpam-3328	387	21	the	the	DET
ejpam-3328	387	22	maximum	maximum	ADJ
ejpam-3328	387	23	velocity	velocity	NOUN
ejpam-3328	387	24	.	.	PUNCT
ejpam-3328	388	1	uniform	uniform	ADJ
ejpam-3328	388	2	global	global	ADJ
ejpam-3328	388	3	estimations	estimation	NOUN
ejpam-3328	388	4	of	of	ADP
ejpam-3328	388	5	the	the	DET
ejpam-3328	388	6	fourier	fourier	NOUN
ejpam-3328	388	7	transform	transform	NOUN
ejpam-3328	388	8	of	of	ADP
ejpam-3328	388	9	solutions	solution	NOUN
ejpam-3328	388	10	of	of	ADP
ejpam-3328	388	11	the	the	DET
ejpam-3328	388	12	navier	navier	NOUN
ejpam-3328	388	13	–	–	PUNCT
ejpam-3328	388	14	stokes	stokes	PROPN
ejpam-3328	388	15	equations	equation	NOUN
ejpam-3328	388	16	indicate	indicate	VERB
ejpam-3328	388	17	that	that	SCONJ
ejpam-3328	388	18	the	the	DET
ejpam-3328	388	19	principle	principle	NOUN
ejpam-3328	388	20	modelling	modelling	NOUN
ejpam-3328	388	21	of	of	ADP
ejpam-3328	388	22	complex	complex	ADJ
ejpam-3328	388	23	flows	flow	NOUN
ejpam-3328	388	24	and	and	CCONJ
ejpam-3328	388	25	related	related	ADJ
ejpam-3328	388	26	calculations	calculation	NOUN
ejpam-3328	388	27	can	can	AUX
ejpam-3328	388	28	be	be	AUX
ejpam-3328	388	29	based	base	VERB
ejpam-3328	388	30	on	on	ADP
ejpam-3328	388	31	the	the	DET
ejpam-3328	388	32	fourier	fourier	NOUN
ejpam-3328	388	33	transform	transform	NOUN
ejpam-3328	388	34	method	method	NOUN
ejpam-3328	388	35	.	.	PUNCT
ejpam-3328	389	1	in	in	ADP
ejpam-3328	389	2	terms	term	NOUN
ejpam-3328	389	3	of	of	ADP
ejpam-3328	389	4	the	the	DET
ejpam-3328	389	5	fourier	fourier	NOUN
ejpam-3328	389	6	transform	transform	NOUN
ejpam-3328	389	7	,	,	PUNCT
ejpam-3328	389	8	under	under	ADP
ejpam-3328	389	9	both	both	DET
ejpam-3328	389	10	smooth	smooth	ADJ
ejpam-3328	389	11	initial	initial	ADJ
ejpam-3328	389	12	conditions	condition	NOUN
ejpam-3328	389	13	and	and	CCONJ
ejpam-3328	389	14	right	right	ADJ
ejpam-3328	389	15	-	-	PUNCT
ejpam-3328	389	16	hand	hand	NOUN
ejpam-3328	389	17	sides	side	NOUN
ejpam-3328	389	18	,	,	PUNCT
ejpam-3328	389	19	no	no	DET
ejpam-3328	389	20	exacerbations	exacerbation	NOUN
ejpam-3328	389	21	appear	appear	VERB
ejpam-3328	389	22	in	in	ADP
ejpam-3328	389	23	the	the	DET
ejpam-3328	389	24	speed	speed	NOUN
ejpam-3328	389	25	and	and	CCONJ
ejpam-3328	389	26	pressure	pressure	NOUN
ejpam-3328	389	27	modes	mode	NOUN
ejpam-3328	389	28	.	.	PUNCT
ejpam-3328	390	1	a	a	DET
ejpam-3328	390	2	loss	loss	NOUN
ejpam-3328	390	3	of	of	ADP
ejpam-3328	390	4	smoothness	smoothness	NOUN
ejpam-3328	390	5	in	in	ADP
ejpam-3328	390	6	terms	term	NOUN
ejpam-3328	390	7	of	of	ADP
ejpam-3328	390	8	the	the	DET
ejpam-3328	390	9	fourier	fourier	NOUN
ejpam-3328	390	10	transform	transform	NOUN
ejpam-3328	390	11	can	can	AUX
ejpam-3328	390	12	only	only	ADV
ejpam-3328	390	13	be	be	AUX
ejpam-3328	390	14	expected	expect	VERB
ejpam-3328	390	15	in	in	ADP
ejpam-3328	390	16	the	the	DET
ejpam-3328	390	17	case	case	NOUN
ejpam-3328	390	18	of	of	ADP
ejpam-3328	390	19	singular	singular	ADJ
ejpam-3328	390	20	initial	initial	ADJ
ejpam-3328	390	21	conditions	condition	NOUN
ejpam-3328	390	22	or	or	CCONJ
ejpam-3328	390	23	of	of	ADP
ejpam-3328	390	24	unlimited	unlimited	ADJ
ejpam-3328	390	25	forces	force	NOUN
ejpam-3328	390	26	in	in	ADP
ejpam-3328	390	27	l2(qt	l2(qt	PROPN
ejpam-3328	390	28	)	)	PUNCT
ejpam-3328	390	29	.	.	PUNCT
ejpam-3328	391	1	the	the	DET
ejpam-3328	391	2	theory	theory	NOUN
ejpam-3328	391	3	developed	develop	VERB
ejpam-3328	391	4	by	by	ADP
ejpam-3328	391	5	us	we	PRON
ejpam-3328	391	6	is	be	AUX
ejpam-3328	391	7	supported	support	VERB
ejpam-3328	391	8	by	by	ADP
ejpam-3328	391	9	numerical	numerical	ADJ
ejpam-3328	391	10	calculations	calculation	NOUN
ejpam-3328	391	11	performed	perform	VERB
ejpam-3328	391	12	in	in	ADP
ejpam-3328	391	13	refs	ref	NOUN
ejpam-3328	391	14	.	.	PUNCT
ejpam-3328	392	1	[	[	X
ejpam-3328	392	2	18–20	18–20	NUM
ejpam-3328	392	3	]	]	PUNCT
ejpam-3328	392	4	,	,	PUNCT
ejpam-3328	392	5	where	where	SCONJ
ejpam-3328	392	6	the	the	DET
ejpam-3328	392	7	dependence	dependence	NOUN
ejpam-3328	392	8	of	of	ADP
ejpam-3328	392	9	the	the	DET
ejpam-3328	392	10	smoothness	smoothness	NOUN
ejpam-3328	392	11	of	of	ADP
ejpam-3328	392	12	the	the	DET
ejpam-3328	392	13	solution	solution	NOUN
ejpam-3328	392	14	on	on	ADP
ejpam-3328	392	15	the	the	DET
ejpam-3328	392	16	oscillations	oscillation	NOUN
ejpam-3328	392	17	of	of	ADP
ejpam-3328	392	18	the	the	DET
ejpam-3328	392	19	system	system	NOUN
ejpam-3328	392	20	is	be	AUX
ejpam-3328	392	21	clearly	clearly	ADV
ejpam-3328	392	22	deduced	deduce	VERB
ejpam-3328	392	23	.	.	PUNCT
ejpam-3328	393	1	7	7	X
ejpam-3328	393	2	.	.	X
ejpam-3328	393	3	reduction	reduction	NOUN
ejpam-3328	393	4	of	of	ADP
ejpam-3328	393	5	the	the	DET
ejpam-3328	393	6	riemann	riemann	PROPN
ejpam-3328	393	7	hypothesis	hypothesis	NOUN
ejpam-3328	393	8	to	to	ADP
ejpam-3328	393	9	the	the	DET
ejpam-3328	393	10	poincaré–riemann	poincaré–riemann	NOUN
ejpam-3328	393	11	–	–	PUNCT
ejpam-3328	393	12	hilbert	hilbert	NOUN
ejpam-3328	393	13	problem	problem	NOUN
ejpam-3328	393	14	this	this	DET
ejpam-3328	393	15	study	study	NOUN
ejpam-3328	393	16	is	be	AUX
ejpam-3328	393	17	concerned	concern	VERB
ejpam-3328	393	18	with	with	ADP
ejpam-3328	393	19	the	the	DET
ejpam-3328	393	20	properties	property	NOUN
ejpam-3328	393	21	of	of	ADP
ejpam-3328	393	22	modified	modify	VERB
ejpam-3328	393	23	zeta	zeta	NOUN
ejpam-3328	393	24	functions	function	NOUN
ejpam-3328	393	25	.	.	PUNCT
ejpam-3328	394	1	riemann	riemann	PROPN
ejpam-3328	394	2	’s	’s	PART
ejpam-3328	394	3	zeta	zeta	PROPN
ejpam-3328	394	4	function	function	NOUN
ejpam-3328	394	5	is	be	AUX
ejpam-3328	394	6	defined	define	VERB
ejpam-3328	394	7	by	by	ADP
ejpam-3328	394	8	the	the	DET
ejpam-3328	394	9	dirichlet	dirichlet	PROPN
ejpam-3328	394	10	series	series	PROPN
ejpam-3328	394	11	ζ(s	ζ(s	PROPN
ejpam-3328	394	12	)	)	PUNCT
ejpam-3328	394	13	=	=	SYM
ejpam-3328	395	1	∞∑	∞∑	NUM
ejpam-3328	395	2	n=1	n=1	NUM
ejpam-3328	395	3	1	1	NUM
ejpam-3328	395	4	ns	ns	NOUN
ejpam-3328	395	5	,	,	PUNCT
ejpam-3328	395	6	s	s	PART
ejpam-3328	395	7	=	=	SYM
ejpam-3328	395	8	σ	σ	PROPN
ejpam-3328	395	9	+	+	CCONJ
ejpam-3328	395	10	it	it	PRON
ejpam-3328	395	11	,	,	PUNCT
ejpam-3328	395	12	(	(	PUNCT
ejpam-3328	395	13	16	16	NUM
ejpam-3328	395	14	)	)	PUNCT
ejpam-3328	395	15	which	which	PRON
ejpam-3328	395	16	is	be	AUX
ejpam-3328	395	17	absolutely	absolutely	ADV
ejpam-3328	395	18	and	and	CCONJ
ejpam-3328	395	19	uniformly	uniformly	ADV
ejpam-3328	395	20	convergent	convergent	NOUN
ejpam-3328	395	21	in	in	ADP
ejpam-3328	395	22	any	any	DET
ejpam-3328	395	23	finite	finite	ADJ
ejpam-3328	395	24	region	region	NOUN
ejpam-3328	395	25	of	of	ADP
ejpam-3328	395	26	the	the	DET
ejpam-3328	395	27	complex	complex	NOUN
ejpam-3328	395	28	s	s	X
ejpam-3328	395	29	plane	plane	NOUN
ejpam-3328	395	30	for	for	ADP
ejpam-3328	395	31	which	which	PRON
ejpam-3328	395	32	σ	σ	PROPN
ejpam-3328	395	33	≥	≥	NUM
ejpam-3328	395	34	1	1	NUM
ejpam-3328	395	35	+	+	CCONJ
ejpam-3328	395	36	ε	ε	PROPN
ejpam-3328	395	37	,	,	PUNCT
ejpam-3328	395	38	ε	ε	PROPN
ejpam-3328	395	39	>	>	X
ejpam-3328	395	40	0	0	PROPN
ejpam-3328	395	41	.	.	PUNCT
ejpam-3328	396	1	if	if	SCONJ
ejpam-3328	396	2	σ	σ	PROPN
ejpam-3328	396	3	>	>	X
ejpam-3328	396	4	1	1	NUM
ejpam-3328	396	5	,	,	PUNCT
ejpam-3328	396	6	then	then	ADV
ejpam-3328	396	7	ζ	ζ	NOUN
ejpam-3328	396	8	is	be	AUX
ejpam-3328	396	9	represented	represent	VERB
ejpam-3328	396	10	by	by	ADP
ejpam-3328	396	11	the	the	DET
ejpam-3328	396	12	following	follow	VERB
ejpam-3328	396	13	euler	euler	NOUN
ejpam-3328	396	14	product	product	NOUN
ejpam-3328	396	15	formula	formula	NOUN
ejpam-3328	396	16	:	:	PUNCT
ejpam-3328	396	17	ζ(s	ζ(s	X
ejpam-3328	396	18	)	)	PUNCT
ejpam-3328	396	19	=	=	SYM
ejpam-3328	397	1	∏	∏	PROPN
ejpam-3328	397	2	p	p	X
ejpam-3328	397	3	[	[	PUNCT
ejpam-3328	397	4	1−	1−	NUM
ejpam-3328	397	5	1	1	NUM
ejpam-3328	397	6	ps	ps	NOUN
ejpam-3328	397	7	]	]	X
ejpam-3328	397	8	−1	−1	NOUN
ejpam-3328	397	9	,	,	PUNCT
ejpam-3328	397	10	(	(	PUNCT
ejpam-3328	397	11	17	17	NUM
ejpam-3328	397	12	)	)	PUNCT
ejpam-3328	397	13	where	where	SCONJ
ejpam-3328	397	14	p	p	NOUN
ejpam-3328	397	15	runs	run	VERB
ejpam-3328	397	16	over	over	ADP
ejpam-3328	397	17	all	all	DET
ejpam-3328	397	18	prime	prime	ADJ
ejpam-3328	397	19	numbers	number	NOUN
ejpam-3328	397	20	.	.	PUNCT
ejpam-3328	398	1	ζ(s	ζ(s	PROPN
ejpam-3328	398	2	)	)	PUNCT
ejpam-3328	398	3	was	be	AUX
ejpam-3328	398	4	first	first	ADV
ejpam-3328	398	5	introduced	introduce	VERB
ejpam-3328	398	6	in	in	ADP
ejpam-3328	398	7	1737	1737	NUM
ejpam-3328	398	8	by	by	ADP
ejpam-3328	398	9	euler	euler	NOUN
ejpam-3328	399	1	[	[	X
ejpam-3328	399	2	21	21	NUM
ejpam-3328	399	3	]	]	X
ejpam-3328	399	4	,	,	PUNCT
ejpam-3328	399	5	who	who	PRON
ejpam-3328	399	6	also	also	ADV
ejpam-3328	399	7	obtained	obtain	VERB
ejpam-3328	399	8	formula	formula	NOUN
ejpam-3328	399	9	(	(	PUNCT
ejpam-3328	399	10	22	22	NUM
ejpam-3328	399	11	)	)	PUNCT
ejpam-3328	399	12	.	.	PUNCT
ejpam-3328	400	1	dirichlet	dirichlet	PROPN
ejpam-3328	400	2	and	and	CCONJ
ejpam-3328	400	3	chebyshev	chebyshev	PROPN
ejpam-3328	400	4	considered	consider	VERB
ejpam-3328	400	5	this	this	DET
ejpam-3328	400	6	function	function	NOUN
ejpam-3328	400	7	in	in	ADP
ejpam-3328	400	8	their	their	PRON
ejpam-3328	400	9	study	study	NOUN
ejpam-3328	400	10	on	on	ADP
ejpam-3328	400	11	the	the	DET
ejpam-3328	400	12	distribution	distribution	NOUN
ejpam-3328	400	13	of	of	ADP
ejpam-3328	400	14	prime	prime	ADJ
ejpam-3328	400	15	numbers	number	NOUN
ejpam-3328	400	16	[	[	X
ejpam-3328	400	17	22	22	NUM
ejpam-3328	400	18	]	]	PUNCT
ejpam-3328	400	19	.	.	PUNCT
ejpam-3328	401	1	however	however	ADV
ejpam-3328	401	2	,	,	PUNCT
ejpam-3328	401	3	the	the	DET
ejpam-3328	401	4	most	most	ADV
ejpam-3328	401	5	profound	profound	ADJ
ejpam-3328	401	6	properties	property	NOUN
ejpam-3328	401	7	of	of	ADP
ejpam-3328	401	8	ζ(z	ζ(z	NOUN
ejpam-3328	401	9	)	)	PUNCT
ejpam-3328	401	10	were	be	AUX
ejpam-3328	401	11	only	only	ADV
ejpam-3328	401	12	discovered	discover	VERB
ejpam-3328	401	13	later	later	ADV
ejpam-3328	401	14	,	,	PUNCT
ejpam-3328	401	15	when	when	SCONJ
ejpam-3328	401	16	it	it	PRON
ejpam-3328	401	17	was	be	AUX
ejpam-3328	401	18	extended	extend	VERB
ejpam-3328	401	19	to	to	ADP
ejpam-3328	401	20	the	the	DET
ejpam-3328	401	21	complex	complex	ADJ
ejpam-3328	401	22	plane	plane	NOUN
ejpam-3328	401	23	.	.	PUNCT
ejpam-3328	402	1	in	in	ADP
ejpam-3328	402	2	1876	1876	NUM
ejpam-3328	402	3	,	,	PUNCT
ejpam-3328	402	4	riemann	riemann	PROPN
ejpam-3328	402	5	[	[	X
ejpam-3328	402	6	23	23	NUM
ejpam-3328	402	7	]	]	PUNCT
ejpam-3328	402	8	proved	prove	VERB
ejpam-3328	402	9	that	that	SCONJ
ejpam-3328	402	10	ζ(s	ζ(s	NOUN
ejpam-3328	402	11	)	)	PUNCT
ejpam-3328	402	12	allows	allow	VERB
ejpam-3328	402	13	analytical	analytical	ADJ
ejpam-3328	402	14	continuation	continuation	NOUN
ejpam-3328	402	15	to	to	ADP
ejpam-3328	402	16	the	the	DET
ejpam-3328	402	17	entire	entire	ADJ
ejpam-3328	402	18	z	z	NOUN
ejpam-3328	402	19	plane	plane	NOUN
ejpam-3328	402	20	as	as	SCONJ
ejpam-3328	402	21	follows	follow	VERB
ejpam-3328	402	22	:	:	PUNCT
ejpam-3328	402	23	π−s/2γ(s/2)ζ(s	π−s/2γ(s/2)ζ(s	NOUN
ejpam-3328	402	24	)	)	PUNCT
ejpam-3328	402	25	=	=	PUNCT
ejpam-3328	403	1	1/(s(s−	1/(s(s−	NUM
ejpam-3328	403	2	1	1	NUM
ejpam-3328	403	3	)	)	PUNCT
ejpam-3328	403	4	)	)	PUNCT
ejpam-3328	404	1	+	+	PUNCT
ejpam-3328	404	2	+	+	X
ejpam-3328	404	3	∞∫	∞∫	NOUN
ejpam-3328	404	4	1	1	NUM
ejpam-3328	404	5	(	(	PUNCT
ejpam-3328	404	6	xs/2−1	xs/2−1	NOUN
ejpam-3328	404	7	+	+	CCONJ
ejpam-3328	404	8	x−(1+s)/2)θ(x)dx	x−(1+s)/2)θ(x)dx	PROPN
ejpam-3328	404	9	,	,	PUNCT
ejpam-3328	404	10	(	(	PUNCT
ejpam-3328	404	11	18	18	NUM
ejpam-3328	404	12	)	)	PUNCT
ejpam-3328	404	13	where	where	SCONJ
ejpam-3328	404	14	γ(z	γ(z	NOUN
ejpam-3328	404	15	)	)	PUNCT
ejpam-3328	404	16	is	be	AUX
ejpam-3328	404	17	the	the	DET
ejpam-3328	404	18	gamma	gamma	NOUN
ejpam-3328	404	19	function	function	NOUN
ejpam-3328	404	20	and	and	CCONJ
ejpam-3328	404	21	θ(x	θ(x	PROPN
ejpam-3328	404	22	)	)	PUNCT
ejpam-3328	404	23	=	=	PUNCT
ejpam-3328	404	24	∞∑	∞∑	NUM
ejpam-3328	404	25	n=1	n=1	PROPN
ejpam-3328	404	26	exp(−πn2x	exp(−πn2x	NOUN
ejpam-3328	404	27	)	)	PUNCT
ejpam-3328	404	28	.	.	PUNCT
ejpam-3328	405	1	a.	a.	NOUN
ejpam-3328	405	2	durmagambetov	durmagambetov	PROPN
ejpam-3328	405	3	/	/	SYM
ejpam-3328	405	4	eur	eur	PROPN
ejpam-3328	405	5	.	.	PUNCT
ejpam-3328	406	1	j.	j.	PROPN
ejpam-3328	406	2	pure	pure	PROPN
ejpam-3328	406	3	appl	appl	PROPN
ejpam-3328	406	4	.	.	PROPN
ejpam-3328	406	5	math	math	PROPN
ejpam-3328	406	6	,	,	PUNCT
ejpam-3328	406	7	11	11	NUM
ejpam-3328	406	8	(	(	PUNCT
ejpam-3328	406	9	4	4	NUM
ejpam-3328	406	10	)	)	PUNCT
ejpam-3328	406	11	(	(	PUNCT
ejpam-3328	406	12	2018	2018	NUM
ejpam-3328	406	13	)	)	PUNCT
ejpam-3328	406	14	,	,	PUNCT
ejpam-3328	406	15	1143	1143	NUM
ejpam-3328	406	16	-	-	SYM
ejpam-3328	406	17	1176	1176	NUM
ejpam-3328	406	18	1161	1161	NUM
ejpam-3328	406	19	ζ(s	ζ(s	NOUN
ejpam-3328	406	20	)	)	PUNCT
ejpam-3328	406	21	is	be	AUX
ejpam-3328	406	22	a	a	DET
ejpam-3328	406	23	regular	regular	ADJ
ejpam-3328	406	24	function	function	NOUN
ejpam-3328	406	25	for	for	ADP
ejpam-3328	406	26	all	all	DET
ejpam-3328	406	27	values	value	NOUN
ejpam-3328	406	28	of	of	ADP
ejpam-3328	406	29	s	s	NOUN
ejpam-3328	406	30	,	,	PUNCT
ejpam-3328	406	31	except	except	SCONJ
ejpam-3328	406	32	s	s	NOUN
ejpam-3328	406	33	=	=	SYM
ejpam-3328	406	34	1	1	NUM
ejpam-3328	406	35	,	,	PUNCT
ejpam-3328	406	36	where	where	SCONJ
ejpam-3328	406	37	it	it	PRON
ejpam-3328	406	38	has	have	VERB
ejpam-3328	406	39	a	a	DET
ejpam-3328	406	40	simple	simple	ADJ
ejpam-3328	406	41	pole	pole	NOUN
ejpam-3328	406	42	with	with	ADP
ejpam-3328	406	43	residue	residue	NOUN
ejpam-3328	406	44	1	1	NUM
ejpam-3328	406	45	;	;	PUNCT
ejpam-3328	406	46	moreover	moreover	ADV
ejpam-3328	406	47	,	,	PUNCT
ejpam-3328	406	48	it	it	PRON
ejpam-3328	406	49	satisfies	satisfy	VERB
ejpam-3328	406	50	the	the	DET
ejpam-3328	406	51	following	follow	VERB
ejpam-3328	406	52	functional	functional	ADJ
ejpam-3328	406	53	equation	equation	NOUN
ejpam-3328	406	54	:	:	PUNCT
ejpam-3328	406	55	π−s/2γ(s/2)ζ(s	π−s/2γ(s/2)ζ(s	NOUN
ejpam-3328	406	56	)	)	PUNCT
ejpam-3328	406	57	=	=	PUNCT
ejpam-3328	407	1	π−(1−s)/2γ((1−	π−(1−s)/2γ((1−	PROPN
ejpam-3328	407	2	s)/2)ζ(1−	s)/2)ζ(1−	PROPN
ejpam-3328	407	3	s	s	PART
ejpam-3328	407	4	)	)	PUNCT
ejpam-3328	407	5	.	.	PUNCT
ejpam-3328	408	1	(	(	PUNCT
ejpam-3328	408	2	19	19	NUM
ejpam-3328	408	3	)	)	PUNCT
ejpam-3328	408	4	this	this	DET
ejpam-3328	408	5	equation	equation	NOUN
ejpam-3328	408	6	is	be	AUX
ejpam-3328	408	7	called	call	VERB
ejpam-3328	408	8	riemann	riemann	PROPN
ejpam-3328	408	9	’s	’s	PART
ejpam-3328	408	10	functional	functional	ADJ
ejpam-3328	408	11	equation	equation	NOUN
ejpam-3328	408	12	.	.	PUNCT
ejpam-3328	409	1	riemann	riemann	PROPN
ejpam-3328	409	2	’s	’s	PART
ejpam-3328	409	3	zeta	zeta	PROPN
ejpam-3328	409	4	function	function	NOUN
ejpam-3328	409	5	is	be	AUX
ejpam-3328	409	6	an	an	DET
ejpam-3328	409	7	important	important	ADJ
ejpam-3328	409	8	subject	subject	NOUN
ejpam-3328	409	9	of	of	ADP
ejpam-3328	409	10	study	study	NOUN
ejpam-3328	409	11	and	and	CCONJ
ejpam-3328	409	12	has	have	VERB
ejpam-3328	409	13	numerous	numerous	ADJ
ejpam-3328	409	14	interesting	interesting	ADJ
ejpam-3328	409	15	generalisations	generalisation	NOUN
ejpam-3328	409	16	.	.	PUNCT
ejpam-3328	410	1	the	the	DET
ejpam-3328	410	2	role	role	NOUN
ejpam-3328	410	3	of	of	ADP
ejpam-3328	410	4	the	the	DET
ejpam-3328	410	5	zeta	zeta	NOUN
ejpam-3328	410	6	function	function	NOUN
ejpam-3328	410	7	is	be	AUX
ejpam-3328	410	8	highly	highly	ADV
ejpam-3328	410	9	significant	significant	ADJ
ejpam-3328	410	10	in	in	ADP
ejpam-3328	410	11	number	number	NOUN
ejpam-3328	410	12	theory	theory	NOUN
ejpam-3328	410	13	,	,	PUNCT
ejpam-3328	410	14	where	where	SCONJ
ejpam-3328	410	15	it	it	PRON
ejpam-3328	410	16	is	be	AUX
ejpam-3328	410	17	connected	connect	VERB
ejpam-3328	410	18	with	with	ADP
ejpam-3328	410	19	various	various	ADJ
ejpam-3328	410	20	fundamental	fundamental	ADJ
ejpam-3328	410	21	functions	function	NOUN
ejpam-3328	410	22	,	,	PUNCT
ejpam-3328	410	23	such	such	ADJ
ejpam-3328	410	24	as	as	ADP
ejpam-3328	410	25	the	the	DET
ejpam-3328	410	26	möbius	möbius	PROPN
ejpam-3328	410	27	function	function	NOUN
ejpam-3328	410	28	,	,	PUNCT
ejpam-3328	410	29	the	the	DET
ejpam-3328	410	30	liouville	liouville	NOUN
ejpam-3328	410	31	function	function	NOUN
ejpam-3328	410	32	,	,	PUNCT
ejpam-3328	410	33	the	the	DET
ejpam-3328	410	34	number	number	NOUN
ejpam-3328	410	35	of	of	ADP
ejpam-3328	410	36	divisors	divisor	NOUN
ejpam-3328	410	37	,	,	PUNCT
ejpam-3328	410	38	and	and	CCONJ
ejpam-3328	410	39	the	the	DET
ejpam-3328	410	40	number	number	NOUN
ejpam-3328	410	41	of	of	ADP
ejpam-3328	410	42	prime	prime	ADJ
ejpam-3328	410	43	divisors	divisor	NOUN
ejpam-3328	410	44	.	.	PUNCT
ejpam-3328	411	1	the	the	DET
ejpam-3328	411	2	detailed	detailed	ADJ
ejpam-3328	411	3	theory	theory	NOUN
ejpam-3328	411	4	of	of	ADP
ejpam-3328	411	5	zeta	zeta	NOUN
ejpam-3328	411	6	functions	function	NOUN
ejpam-3328	411	7	is	be	AUX
ejpam-3328	411	8	presented	present	VERB
ejpam-3328	411	9	in	in	ADP
ejpam-3328	411	10	ref	ref	NOUN
ejpam-3328	411	11	.	.	PUNCT
ejpam-3328	412	1	[	[	X
ejpam-3328	412	2	24	24	NUM
ejpam-3328	412	3	]	]	PUNCT
ejpam-3328	412	4	.	.	PUNCT
ejpam-3328	413	1	the	the	DET
ejpam-3328	413	2	zeta	zeta	PROPN
ejpam-3328	413	3	function	function	NOUN
ejpam-3328	413	4	has	have	AUX
ejpam-3328	413	5	found	find	VERB
ejpam-3328	413	6	application	application	NOUN
ejpam-3328	413	7	in	in	ADP
ejpam-3328	413	8	various	various	ADJ
ejpam-3328	413	9	other	other	ADJ
ejpam-3328	413	10	fields	field	NOUN
ejpam-3328	413	11	,	,	PUNCT
ejpam-3328	413	12	notably	notably	ADV
ejpam-3328	413	13	in	in	ADP
ejpam-3328	413	14	quantum	quantum	ADJ
ejpam-3328	413	15	statistical	statistical	ADJ
ejpam-3328	413	16	mechanics	mechanic	NOUN
ejpam-3328	413	17	and	and	CCONJ
ejpam-3328	413	18	quantum	quantum	NOUN
ejpam-3328	413	19	field	field	NOUN
ejpam-3328	413	20	theory	theory	NOUN
ejpam-3328	413	21	[	[	X
ejpam-3328	413	22	25–27	25–27	NUM
ejpam-3328	413	23	]	]	X
ejpam-3328	413	24	.	.	PUNCT
ejpam-3328	414	1	riemann	riemann	PROPN
ejpam-3328	414	2	’s	’s	PART
ejpam-3328	414	3	zeta	zeta	PROPN
ejpam-3328	414	4	function	function	NOUN
ejpam-3328	414	5	is	be	AUX
ejpam-3328	414	6	often	often	ADV
ejpam-3328	414	7	introduced	introduce	VERB
ejpam-3328	414	8	in	in	ADP
ejpam-3328	414	9	quantum	quantum	ADJ
ejpam-3328	414	10	statistics	statistic	NOUN
ejpam-3328	414	11	formulas	formula	NOUN
ejpam-3328	414	12	.	.	PUNCT
ejpam-3328	415	1	a	a	DET
ejpam-3328	415	2	well	well	ADV
ejpam-3328	415	3	-	-	PUNCT
ejpam-3328	415	4	known	know	VERB
ejpam-3328	415	5	example	example	NOUN
ejpam-3328	415	6	is	be	AUX
ejpam-3328	415	7	the	the	DET
ejpam-3328	415	8	stefan	stefan	PROPN
ejpam-3328	415	9	–	–	PUNCT
ejpam-3328	415	10	boltzman	boltzman	NOUN
ejpam-3328	415	11	law	law	NOUN
ejpam-3328	415	12	for	for	ADP
ejpam-3328	415	13	blackbody	blackbody	ADJ
ejpam-3328	415	14	radiation	radiation	NOUN
ejpam-3328	415	15	.	.	PUNCT
ejpam-3328	416	1	its	its	PRON
ejpam-3328	416	2	ubiquitous	ubiquitous	ADJ
ejpam-3328	416	3	use	use	NOUN
ejpam-3328	416	4	in	in	ADP
ejpam-3328	416	5	seemingly	seemingly	ADV
ejpam-3328	416	6	unrelated	unrelated	ADJ
ejpam-3328	416	7	areas	area	NOUN
ejpam-3328	416	8	demonstrates	demonstrate	VERB
ejpam-3328	416	9	the	the	DET
ejpam-3328	416	10	necessity	necessity	NOUN
ejpam-3328	416	11	for	for	ADP
ejpam-3328	416	12	further	further	ADJ
ejpam-3328	416	13	investigation	investigation	NOUN
ejpam-3328	416	14	.	.	PUNCT
ejpam-3328	417	1	the	the	DET
ejpam-3328	417	2	present	present	ADJ
ejpam-3328	417	3	study	study	NOUN
ejpam-3328	417	4	is	be	AUX
ejpam-3328	417	5	concerned	concern	VERB
ejpam-3328	417	6	with	with	ADP
ejpam-3328	417	7	the	the	DET
ejpam-3328	417	8	analytical	analytical	ADJ
ejpam-3328	417	9	properties	property	NOUN
ejpam-3328	417	10	of	of	ADP
ejpam-3328	417	11	the	the	DET
ejpam-3328	417	12	following	follow	VERB
ejpam-3328	417	13	generalised	generalise	VERB
ejpam-3328	417	14	zeta	zeta	NOUN
ejpam-3328	417	15	functions	function	NOUN
ejpam-3328	417	16	:	:	PUNCT
ejpam-3328	417	17	p	p	X
ejpam-3328	417	18	(	(	PUNCT
ejpam-3328	417	19	s	s	NOUN
ejpam-3328	417	20	)	)	PUNCT
ejpam-3328	417	21	=	=	SYM
ejpam-3328	417	22	∑	∑	PUNCT
ejpam-3328	417	23	j≥1	j≥1	PROPN
ejpam-3328	417	24	1	1	NUM
ejpam-3328	417	25	psj	psj	NOUN
ejpam-3328	417	26	,	,	PUNCT
ejpam-3328	417	27	re(s	re(s	ADJ
ejpam-3328	417	28	)	)	PUNCT
ejpam-3328	417	29	>	>	X
ejpam-3328	418	1	1	1	NUM
ejpam-3328	418	2	+	+	CCONJ
ejpam-3328	418	3	δ	δ	PROPN
ejpam-3328	418	4	,	,	PUNCT
ejpam-3328	418	5	δ	δ	PROPN
ejpam-3328	418	6	>	>	X
ejpam-3328	418	7	0	0	PROPN
ejpam-3328	418	8	,	,	PUNCT
ejpam-3328	418	9	where	where	SCONJ
ejpam-3328	418	10	{	{	PUNCT
ejpam-3328	418	11	pj	pj	NOUN
ejpam-3328	418	12	:	:	PUNCT
ejpam-3328	418	13	j	j	PROPN
ejpam-3328	418	14	≥	≥	NUM
ejpam-3328	418	15	1	1	NUM
ejpam-3328	418	16	}	}	PUNCT
ejpam-3328	418	17	is	be	AUX
ejpam-3328	418	18	an	an	DET
ejpam-3328	418	19	increasing	increase	VERB
ejpam-3328	418	20	enumeration	enumeration	NOUN
ejpam-3328	418	21	of	of	ADP
ejpam-3328	418	22	all	all	DET
ejpam-3328	418	23	prime	prime	ADJ
ejpam-3328	418	24	numbers	number	NOUN
ejpam-3328	418	25	.	.	PUNCT
ejpam-3328	419	1	the	the	DET
ejpam-3328	419	2	form	form	NOUN
ejpam-3328	419	3	of	of	ADP
ejpam-3328	419	4	p	p	PROPN
ejpam-3328	419	5	(	(	PUNCT
ejpam-3328	419	6	s	s	NOUN
ejpam-3328	419	7	)	)	PUNCT
ejpam-3328	419	8	suggests	suggest	VERB
ejpam-3328	419	9	that	that	SCONJ
ejpam-3328	419	10	it	it	PRON
ejpam-3328	419	11	possesses	possess	VERB
ejpam-3328	419	12	the	the	DET
ejpam-3328	419	13	same	same	ADJ
ejpam-3328	419	14	properties	property	NOUN
ejpam-3328	419	15	as	as	ADP
ejpam-3328	419	16	the	the	DET
ejpam-3328	419	17	zeta	zeta	NOUN
ejpam-3328	419	18	function	function	NOUN
ejpam-3328	419	19	;	;	PUNCT
ejpam-3328	419	20	however	however	ADV
ejpam-3328	419	21	,	,	PUNCT
ejpam-3328	419	22	this	this	PRON
ejpam-3328	419	23	is	be	AUX
ejpam-3328	419	24	not	not	PART
ejpam-3328	419	25	quite	quite	ADV
ejpam-3328	419	26	obvious	obvious	ADJ
ejpam-3328	419	27	and	and	CCONJ
ejpam-3328	419	28	can	can	AUX
ejpam-3328	419	29	be	be	AUX
ejpam-3328	419	30	seen	see	VERB
ejpam-3328	419	31	by	by	ADP
ejpam-3328	419	32	considering	consider	VERB
ejpam-3328	419	33	ln(ζ(s	ln(ζ(	NOUN
ejpam-3328	419	34	)	)	PUNCT
ejpam-3328	419	35	)	)	PUNCT
ejpam-3328	420	1	=	=	PUNCT
ejpam-3328	421	1	∞∑	∞∑	NUM
ejpam-3328	421	2	n=1	n=1	ADP
ejpam-3328	421	3	p	p	X
ejpam-3328	421	4	(	(	PUNCT
ejpam-3328	421	5	ns)/n	ns)/n	PROPN
ejpam-3328	421	6	,	,	PUNCT
ejpam-3328	421	7	f(s	f(s	ADV
ejpam-3328	421	8	)	)	PUNCT
ejpam-3328	421	9	=	=	PUNCT
ejpam-3328	422	1	ln(ζ(s))−	ln(ζ(s))−	NOUN
ejpam-3328	422	2	p	p	NOUN
ejpam-3328	422	3	(	(	PUNCT
ejpam-3328	422	4	s	s	NOUN
ejpam-3328	422	5	)	)	PUNCT
ejpam-3328	422	6	,	,	PUNCT
ejpam-3328	422	7	re(s	re(s	ADJ
ejpam-3328	422	8	)	)	PUNCT
ejpam-3328	422	9	>	>	X
ejpam-3328	422	10	1	1	NUM
ejpam-3328	422	11	+	+	CCONJ
ejpam-3328	422	12	δ	δ	PROPN
ejpam-3328	422	13	,	,	PUNCT
ejpam-3328	422	14	δ	δ	PROPN
ejpam-3328	422	15	>	>	X
ejpam-3328	422	16	0	0	PROPN
ejpam-3328	422	17	.	.	PUNCT
ejpam-3328	423	1	(	(	PUNCT
ejpam-3328	423	2	20	20	NUM
ejpam-3328	423	3	)	)	PUNCT
ejpam-3328	423	4	hadamard	hadamard	NOUN
ejpam-3328	423	5	was	be	AUX
ejpam-3328	423	6	the	the	DET
ejpam-3328	423	7	first	first	ADJ
ejpam-3328	423	8	to	to	PART
ejpam-3328	423	9	apply	apply	VERB
ejpam-3328	423	10	p	p	NOUN
ejpam-3328	423	11	(	(	PUNCT
ejpam-3328	423	12	s	s	NOUN
ejpam-3328	423	13	)	)	PUNCT
ejpam-3328	423	14	in	in	ADP
ejpam-3328	423	15	the	the	DET
ejpam-3328	423	16	study	study	NOUN
ejpam-3328	423	17	of	of	ADP
ejpam-3328	423	18	the	the	DET
ejpam-3328	423	19	zeta	zeta	PROPN
ejpam-3328	423	20	function	function	NOUN
ejpam-3328	423	21	[	[	X
ejpam-3328	423	22	28	28	NUM
ejpam-3328	423	23	]	]	PUNCT
ejpam-3328	423	24	.	.	PUNCT
ejpam-3328	424	1	chernoff	chernoff	PROPN
ejpam-3328	424	2	made	make	VERB
ejpam-3328	424	3	significant	significant	ADJ
ejpam-3328	424	4	progress	progress	NOUN
ejpam-3328	424	5	in	in	ADP
ejpam-3328	424	6	the	the	DET
ejpam-3328	424	7	riemann	riemann	PROPN
ejpam-3328	424	8	hypothesis	hypothesis	NOUN
ejpam-3328	424	9	using	use	VERB
ejpam-3328	424	10	p	p	X
ejpam-3328	424	11	(	(	PUNCT
ejpam-3328	424	12	s	s	NOUN
ejpam-3328	424	13	)	)	PUNCT
ejpam-3328	425	1	[	[	X
ejpam-3328	425	2	29	29	NUM
ejpam-3328	425	3	]	]	PUNCT
ejpam-3328	425	4	.	.	PUNCT
ejpam-3328	426	1	in	in	ADP
ejpam-3328	426	2	the	the	DET
ejpam-3328	426	3	present	present	ADJ
ejpam-3328	426	4	study	study	NOUN
ejpam-3328	426	5	,	,	PUNCT
ejpam-3328	426	6	modifications	modification	NOUN
ejpam-3328	426	7	of	of	ADP
ejpam-3328	426	8	chernoff	chernoff	NOUN
ejpam-3328	426	9	’s	’s	PART
ejpam-3328	426	10	results	result	NOUN
ejpam-3328	426	11	are	be	AUX
ejpam-3328	426	12	obtained	obtain	VERB
ejpam-3328	426	13	.	.	PUNCT
ejpam-3328	427	1	specifically	specifically	ADV
ejpam-3328	427	2	,	,	PUNCT
ejpam-3328	427	3	his	his	PRON
ejpam-3328	427	4	study	study	NOUN
ejpam-3328	427	5	on	on	ADP
ejpam-3328	427	6	the	the	DET
ejpam-3328	427	7	pseudo	pseudo	NOUN
ejpam-3328	427	8	zeta	zeta	NOUN
ejpam-3328	427	9	function	function	NOUN
ejpam-3328	427	10	is	be	AUX
ejpam-3328	427	11	completed	complete	VERB
ejpam-3328	427	12	.	.	PUNCT
ejpam-3328	428	1	chernoff	chernoff	PROPN
ejpam-3328	428	2	obtained	obtain	VERB
ejpam-3328	428	3	an	an	DET
ejpam-3328	428	4	equivalent	equivalent	ADJ
ejpam-3328	428	5	formulation	formulation	NOUN
ejpam-3328	428	6	of	of	ADP
ejpam-3328	428	7	the	the	DET
ejpam-3328	428	8	riemann	riemann	PROPN
ejpam-3328	428	9	hypothesis	hypothesis	NOUN
ejpam-3328	428	10	in	in	ADP
ejpam-3328	428	11	terms	term	NOUN
ejpam-3328	428	12	of	of	ADP
ejpam-3328	428	13	a	a	DET
ejpam-3328	428	14	pseudo	pseudo	NOUN
ejpam-3328	428	15	zeta	zeta	NOUN
ejpam-3328	428	16	function	function	NOUN
ejpam-3328	428	17	as	as	SCONJ
ejpam-3328	428	18	follows	follow	VERB
ejpam-3328	428	19	.	.	PUNCT
ejpam-3328	429	1	theorem	theorem	VERB
ejpam-3328	429	2	.	.	PUNCT
ejpam-3328	430	1	(	(	PUNCT
ejpam-3328	430	2	chernoff	chernoff	NOUN
ejpam-3328	430	3	)	)	PUNCT
ejpam-3328	430	4	let	let	VERB
ejpam-3328	430	5	c(s	c(	NOUN
ejpam-3328	430	6	)	)	PUNCT
ejpam-3328	430	7	=	=	SYM
ejpam-3328	430	8	∏	∏	PROPN
ejpam-3328	430	9	n>1	n>1	PROPN
ejpam-3328	430	10	[	[	PUNCT
ejpam-3328	430	11	1−	1−	NUM
ejpam-3328	430	12	1	1	NUM
ejpam-3328	430	13	(	(	PUNCT
ejpam-3328	430	14	n	n	NOUN
ejpam-3328	430	15	ln(n))s	ln(n))s	PUNCT
ejpam-3328	430	16	]	]	X
ejpam-3328	430	17	−1	−1	NOUN
ejpam-3328	430	18	.	.	PUNCT
ejpam-3328	431	1	then	then	ADV
ejpam-3328	431	2	,	,	PUNCT
ejpam-3328	431	3	c(s	c(s	X
ejpam-3328	431	4	)	)	PUNCT
ejpam-3328	431	5	continues	continue	VERB
ejpam-3328	431	6	analytically	analytically	ADV
ejpam-3328	431	7	into	into	ADP
ejpam-3328	431	8	the	the	DET
ejpam-3328	431	9	critical	critical	ADJ
ejpam-3328	431	10	strip	strip	NOUN
ejpam-3328	431	11	and	and	CCONJ
ejpam-3328	431	12	has	have	VERB
ejpam-3328	431	13	no	no	DET
ejpam-3328	431	14	zeros	zero	NOUN
ejpam-3328	431	15	there	there	ADV
ejpam-3328	431	16	.	.	PUNCT
ejpam-3328	432	1	the	the	DET
ejpam-3328	432	2	significance	significance	NOUN
ejpam-3328	432	3	of	of	ADP
ejpam-3328	432	4	this	this	DET
ejpam-3328	432	5	theorem	theorem	NOUN
ejpam-3328	432	6	is	be	AUX
ejpam-3328	432	7	that	that	SCONJ
ejpam-3328	432	8	,	,	PUNCT
ejpam-3328	432	9	if	if	SCONJ
ejpam-3328	432	10	the	the	DET
ejpam-3328	432	11	primes	prime	NOUN
ejpam-3328	432	12	were	be	AUX
ejpam-3328	432	13	distributed	distribute	VERB
ejpam-3328	432	14	more	more	ADV
ejpam-3328	432	15	regularly	regularly	ADV
ejpam-3328	432	16	(	(	PUNCT
ejpam-3328	432	17	i.e.	i.e.	X
ejpam-3328	432	18	,	,	PUNCT
ejpam-3328	432	19	if	if	SCONJ
ejpam-3328	432	20	pn	pn	PROPN
ejpam-3328	432	21	≡	≡	PROPN
ejpam-3328	432	22	n	n	CCONJ
ejpam-3328	432	23	log	log	VERB
ejpam-3328	432	24	n	n	CCONJ
ejpam-3328	432	25	)	)	PUNCT
ejpam-3328	432	26	,	,	PUNCT
ejpam-3328	432	27	then	then	ADV
ejpam-3328	432	28	the	the	DET
ejpam-3328	432	29	riemann	riemann	PROPN
ejpam-3328	432	30	hypothesis	hypothesis	NOUN
ejpam-3328	432	31	would	would	AUX
ejpam-3328	432	32	be	be	AUX
ejpam-3328	432	33	trivially	trivially	ADV
ejpam-3328	432	34	true	true	ADJ
ejpam-3328	432	35	.	.	PUNCT
ejpam-3328	433	1	in	in	ADP
ejpam-3328	433	2	an	an	DET
ejpam-3328	433	3	effort	effort	NOUN
ejpam-3328	433	4	to	to	PART
ejpam-3328	433	5	further	far	ADV
ejpam-3328	433	6	develop	develop	VERB
ejpam-3328	433	7	the	the	DET
ejpam-3328	433	8	work	work	NOUN
ejpam-3328	433	9	of	of	ADP
ejpam-3328	433	10	chernoff	chernoff	NOUN
ejpam-3328	433	11	and	and	CCONJ
ejpam-3328	433	12	hadamard	hadamard	NOUN
ejpam-3328	433	13	,	,	PUNCT
ejpam-3328	433	14	the	the	DET
ejpam-3328	433	15	following	following	ADJ
ejpam-3328	433	16	question	question	NOUN
ejpam-3328	433	17	naturally	naturally	ADV
ejpam-3328	433	18	arises	arise	VERB
ejpam-3328	433	19	:	:	PUNCT
ejpam-3328	433	20	does	do	AUX
ejpam-3328	433	21	the	the	DET
ejpam-3328	433	22	pseudo	pseudo	NOUN
ejpam-3328	433	23	zeta	zeta	NOUN
ejpam-3328	433	24	function	function	NOUN
ejpam-3328	433	25	p	p	PROPN
ejpam-3328	433	26	(	(	PUNCT
ejpam-3328	433	27	s	s	X
ejpam-3328	433	28	)	)	PUNCT
ejpam-3328	433	29	continue	continue	VERB
ejpam-3328	433	30	analytically	analytically	ADV
ejpam-3328	433	31	into	into	ADP
ejpam-3328	433	32	the	the	DET
ejpam-3328	433	33	critical	critical	ADJ
ejpam-3328	433	34	strip	strip	NOUN
ejpam-3328	433	35	?	?	PUNCT
ejpam-3328	434	1	it	it	PRON
ejpam-3328	434	2	should	should	AUX
ejpam-3328	434	3	be	be	AUX
ejpam-3328	434	4	noted	note	VERB
ejpam-3328	434	5	that	that	SCONJ
ejpam-3328	434	6	analytic	analytic	ADJ
ejpam-3328	434	7	extensions	extension	NOUN
ejpam-3328	434	8	of	of	ADP
ejpam-3328	434	9	p	p	NOUN
ejpam-3328	434	10	(	(	PUNCT
ejpam-3328	434	11	s	s	X
ejpam-3328	434	12	)	)	PUNCT
ejpam-3328	434	13	were	be	AUX
ejpam-3328	434	14	first	first	ADV
ejpam-3328	434	15	studied	study	VERB
ejpam-3328	434	16	by	by	ADP
ejpam-3328	434	17	landau	landau	NOUN
ejpam-3328	434	18	and	and	CCONJ
ejpam-3328	434	19	walvis	walvis	VERB
ejpam-3328	434	20	a.	a.	PROPN
ejpam-3328	434	21	durmagambetov	durmagambetov	PROPN
ejpam-3328	434	22	/	/	SYM
ejpam-3328	434	23	eur	eur	PROPN
ejpam-3328	434	24	.	.	PUNCT
ejpam-3328	435	1	j.	j.	PROPN
ejpam-3328	435	2	pure	pure	PROPN
ejpam-3328	435	3	appl	appl	PROPN
ejpam-3328	435	4	.	.	PROPN
ejpam-3328	435	5	math	math	PROPN
ejpam-3328	435	6	,	,	PUNCT
ejpam-3328	435	7	11	11	NUM
ejpam-3328	435	8	(	(	PUNCT
ejpam-3328	435	9	4	4	NUM
ejpam-3328	435	10	)	)	PUNCT
ejpam-3328	435	11	(	(	PUNCT
ejpam-3328	435	12	2018	2018	NUM
ejpam-3328	435	13	)	)	PUNCT
ejpam-3328	435	14	,	,	PUNCT
ejpam-3328	435	15	1143	1143	NUM
ejpam-3328	435	16	-	-	SYM
ejpam-3328	435	17	1176	1176	NUM
ejpam-3328	435	18	1162	1162	NUM
ejpam-3328	436	1	[	[	X
ejpam-3328	436	2	30	30	NUM
ejpam-3328	436	3	]	]	PUNCT
ejpam-3328	436	4	and	and	CCONJ
ejpam-3328	436	5	estarmann	estarmann	NOUN
ejpam-3328	437	1	[	[	X
ejpam-3328	437	2	31	31	NUM
ejpam-3328	437	3	,	,	PUNCT
ejpam-3328	437	4	32	32	NUM
ejpam-3328	437	5	]	]	PUNCT
ejpam-3328	437	6	;	;	PUNCT
ejpam-3328	437	7	however	however	ADV
ejpam-3328	437	8	,	,	PUNCT
ejpam-3328	437	9	no	no	DET
ejpam-3328	437	10	satisfactory	satisfactory	ADJ
ejpam-3328	437	11	estimates	estimate	NOUN
ejpam-3328	437	12	for	for	ADP
ejpam-3328	437	13	p	p	PROPN
ejpam-3328	437	14	(	(	PUNCT
ejpam-3328	437	15	s	s	X
ejpam-3328	437	16	)	)	PUNCT
ejpam-3328	437	17	were	be	AUX
ejpam-3328	437	18	obtained	obtain	VERB
ejpam-3328	437	19	,	,	PUNCT
ejpam-3328	437	20	and	and	CCONJ
ejpam-3328	437	21	the	the	DET
ejpam-3328	437	22	present	present	ADJ
ejpam-3328	437	23	study	study	NOUN
ejpam-3328	437	24	is	be	AUX
ejpam-3328	437	25	concerned	concern	VERB
ejpam-3328	437	26	with	with	ADP
ejpam-3328	437	27	this	this	DET
ejpam-3328	437	28	question	question	NOUN
ejpam-3328	437	29	.	.	PUNCT
ejpam-3328	438	1	theorem	theorem	VERB
ejpam-3328	438	2	.	.	PUNCT
ejpam-3328	439	1	(	(	PUNCT
ejpam-3328	439	2	landau	landau	NOUN
ejpam-3328	439	3	,	,	PUNCT
ejpam-3328	439	4	walvis	walvis	ADJ
ejpam-3328	439	5	,	,	PUNCT
ejpam-3328	439	6	and	and	CCONJ
ejpam-3328	439	7	estarmann	estarmann	NOUN
ejpam-3328	439	8	)	)	PUNCT
ejpam-3328	439	9	let	let	AUX
ejpam-3328	439	10	µ(n	µ(n	VERB
ejpam-3328	439	11	)	)	PUNCT
ejpam-3328	439	12	be	be	AUX
ejpam-3328	439	13	a	a	DET
ejpam-3328	439	14	möbius	möbius	PROPN
ejpam-3328	439	15	function	function	NOUN
ejpam-3328	439	16	.	.	PUNCT
ejpam-3328	440	1	then	then	ADV
ejpam-3328	440	2	,	,	PUNCT
ejpam-3328	440	3	p	p	X
ejpam-3328	440	4	(	(	PUNCT
ejpam-3328	440	5	s	s	NOUN
ejpam-3328	440	6	)	)	PUNCT
ejpam-3328	440	7	=	=	SYM
ejpam-3328	440	8	∑	∑	PUNCT
ejpam-3328	440	9	n≥1	n≥1	PROPN
ejpam-3328	440	10	µ(n	µ(n	PROPN
ejpam-3328	440	11	)	)	PUNCT
ejpam-3328	440	12	ln	ln	ADJ
ejpam-3328	440	13	ζ(ns	ζ(ns	NOUN
ejpam-3328	440	14	)	)	PUNCT
ejpam-3328	440	15	n	n	ADV
ejpam-3328	440	16	as	as	ADV
ejpam-3328	440	17	re(s	re(s	ADJ
ejpam-3328	440	18	)	)	PUNCT
ejpam-3328	440	19	>	>	X
ejpam-3328	440	20	1	1	NUM
ejpam-3328	440	21	+	+	CCONJ
ejpam-3328	440	22	δ	δ	PROPN
ejpam-3328	440	23	,	,	PUNCT
ejpam-3328	440	24	δ	δ	PROPN
ejpam-3328	440	25	>	>	X
ejpam-3328	440	26	0	0	PROPN
ejpam-3328	440	27	,	,	PUNCT
ejpam-3328	440	28	∑	∑	ADV
ejpam-3328	440	29	n≥1	n≥1	NOUN
ejpam-3328	440	30	µ(n	µ(n	PROPN
ejpam-3328	440	31	)	)	PUNCT
ejpam-3328	440	32	ln	ln	ADJ
ejpam-3328	440	33	ζ(ns	ζ(ns	NOUN
ejpam-3328	440	34	)	)	PUNCT
ejpam-3328	440	35	n	n	PRON
ejpam-3328	440	36	is	be	AUX
ejpam-3328	440	37	a	a	DET
ejpam-3328	440	38	meromorphic	meromorphic	ADJ
ejpam-3328	440	39	function	function	NOUN
ejpam-3328	440	40	as	as	ADP
ejpam-3328	440	41	re(s	re(s	ADJ
ejpam-3328	440	42	)	)	PUNCT
ejpam-3328	440	43	>	>	X
ejpam-3328	441	1	δ	δ	PROPN
ejpam-3328	441	2	,	,	PUNCT
ejpam-3328	441	3	δ	δ	PROPN
ejpam-3328	441	4	>	>	X
ejpam-3328	441	5	0	0	X
ejpam-3328	441	6	.	.	PUNCT
ejpam-3328	442	1	the	the	DET
ejpam-3328	442	2	section	section	NOUN
ejpam-3328	442	3	is	be	AUX
ejpam-3328	442	4	organised	organise	VERB
ejpam-3328	442	5	as	as	SCONJ
ejpam-3328	442	6	follows	follow	VERB
ejpam-3328	442	7	.	.	PUNCT
ejpam-3328	443	1	intermediate	intermediate	ADJ
ejpam-3328	443	2	estimates	estimate	NOUN
ejpam-3328	443	3	are	be	AUX
ejpam-3328	443	4	first	first	ADV
ejpam-3328	443	5	obtained	obtain	VERB
ejpam-3328	443	6	for	for	ADP
ejpam-3328	443	7	ln	ln	ADJ
ejpam-3328	443	8	ζ(s	ζ(s	PROPN
ejpam-3328	443	9	)	)	PUNCT
ejpam-3328	443	10	.	.	PUNCT
ejpam-3328	444	1	subsequently	subsequently	ADV
ejpam-3328	444	2	,	,	PUNCT
ejpam-3328	444	3	the	the	DET
ejpam-3328	444	4	sets	set	NOUN
ejpam-3328	444	5	where	where	SCONJ
ejpam-3328	444	6	the	the	DET
ejpam-3328	444	7	logarithm	logarithm	NOUN
ejpam-3328	444	8	of	of	ADP
ejpam-3328	444	9	the	the	DET
ejpam-3328	444	10	zeta	zeta	NOUN
ejpam-3328	444	11	function	function	NOUN
ejpam-3328	444	12	is	be	AUX
ejpam-3328	444	13	uniquely	uniquely	ADV
ejpam-3328	444	14	determined	determine	VERB
ejpam-3328	444	15	are	be	AUX
ejpam-3328	444	16	defined	define	VERB
ejpam-3328	444	17	.	.	PUNCT
ejpam-3328	445	1	these	these	DET
ejpam-3328	445	2	sets	set	NOUN
ejpam-3328	445	3	are	be	AUX
ejpam-3328	445	4	composed	compose	VERB
ejpam-3328	445	5	of	of	ADP
ejpam-3328	445	6	rectangles	rectangle	NOUN
ejpam-3328	445	7	in	in	ADP
ejpam-3328	445	8	which	which	PRON
ejpam-3328	445	9	the	the	DET
ejpam-3328	445	10	zeta	zeta	NOUN
ejpam-3328	445	11	function	function	NOUN
ejpam-3328	445	12	has	have	VERB
ejpam-3328	445	13	no	no	DET
ejpam-3328	445	14	roots	root	NOUN
ejpam-3328	445	15	,	,	PUNCT
ejpam-3328	445	16	and	and	CCONJ
ejpam-3328	445	17	they	they	PRON
ejpam-3328	445	18	cover	cover	VERB
ejpam-3328	445	19	the	the	DET
ejpam-3328	445	20	entire	entire	ADJ
ejpam-3328	445	21	critical	critical	ADJ
ejpam-3328	445	22	strip	strip	NOUN
ejpam-3328	445	23	except	except	SCONJ
ejpam-3328	445	24	for	for	ADP
ejpam-3328	445	25	the	the	DET
ejpam-3328	445	26	rectangular	rectangular	ADJ
ejpam-3328	445	27	regions	region	NOUN
ejpam-3328	445	28	in	in	ADP
ejpam-3328	445	29	which	which	PRON
ejpam-3328	445	30	the	the	DET
ejpam-3328	445	31	zeros	zero	NOUN
ejpam-3328	445	32	of	of	ADP
ejpam-3328	445	33	the	the	DET
ejpam-3328	445	34	zeta	zeta	PROPN
ejpam-3328	445	35	functions	function	NOUN
ejpam-3328	445	36	are	be	AUX
ejpam-3328	445	37	located	locate	VERB
ejpam-3328	445	38	.	.	PUNCT
ejpam-3328	446	1	in	in	ADP
ejpam-3328	446	2	the	the	DET
ejpam-3328	446	3	rectangles	rectangle	NOUN
ejpam-3328	446	4	in	in	ADP
ejpam-3328	446	5	which	which	PRON
ejpam-3328	446	6	there	there	PRON
ejpam-3328	446	7	are	be	VERB
ejpam-3328	446	8	no	no	DET
ejpam-3328	446	9	zeros	zero	NOUN
ejpam-3328	446	10	of	of	ADP
ejpam-3328	446	11	the	the	DET
ejpam-3328	446	12	zeta	zeta	PROPN
ejpam-3328	446	13	function	function	NOUN
ejpam-3328	446	14	,	,	PUNCT
ejpam-3328	446	15	the	the	DET
ejpam-3328	446	16	real	real	ADJ
ejpam-3328	446	17	value	value	NOUN
ejpam-3328	446	18	of	of	ADP
ejpam-3328	446	19	its	its	PRON
ejpam-3328	446	20	logarithm	logarithm	NOUN
ejpam-3328	446	21	can	can	AUX
ejpam-3328	446	22	be	be	AUX
ejpam-3328	446	23	defined	define	VERB
ejpam-3328	446	24	,	,	PUNCT
ejpam-3328	446	25	and	and	CCONJ
ejpam-3328	446	26	in	in	ADP
ejpam-3328	446	27	these	these	DET
ejpam-3328	446	28	sets	set	NOUN
ejpam-3328	446	29	,	,	PUNCT
ejpam-3328	446	30	the	the	DET
ejpam-3328	446	31	mirrorsymmetric	mirrorsymmetric	ADJ
ejpam-3328	446	32	equation	equation	NOUN
ejpam-3328	446	33	that	that	PRON
ejpam-3328	446	34	arises	arise	VERB
ejpam-3328	446	35	by	by	ADP
ejpam-3328	446	36	taking	take	VERB
ejpam-3328	446	37	the	the	DET
ejpam-3328	446	38	logarithm	logarithm	NOUN
ejpam-3328	446	39	on	on	ADP
ejpam-3328	446	40	both	both	DET
ejpam-3328	446	41	sides	side	NOUN
ejpam-3328	446	42	of	of	ADP
ejpam-3328	446	43	the	the	DET
ejpam-3328	446	44	riemann	riemann	PROPN
ejpam-3328	446	45	functional	functional	ADJ
ejpam-3328	446	46	equation	equation	NOUN
ejpam-3328	446	47	is	be	AUX
ejpam-3328	446	48	investigated	investigate	VERB
ejpam-3328	446	49	.	.	PUNCT
ejpam-3328	447	1	then	then	ADV
ejpam-3328	447	2	,	,	PUNCT
ejpam-3328	447	3	the	the	DET
ejpam-3328	447	4	fourier	fourier	NOUN
ejpam-3328	447	5	transform	transform	NOUN
ejpam-3328	447	6	is	be	AUX
ejpam-3328	447	7	applied	apply	VERB
ejpam-3328	447	8	to	to	ADP
ejpam-3328	447	9	it	it	PRON
ejpam-3328	447	10	,	,	PUNCT
ejpam-3328	447	11	and	and	CCONJ
ejpam-3328	447	12	it	it	PRON
ejpam-3328	447	13	is	be	AUX
ejpam-3328	447	14	multiplied	multiply	VERB
ejpam-3328	447	15	by	by	ADP
ejpam-3328	447	16	a	a	DET
ejpam-3328	447	17	regulating	regulate	VERB
ejpam-3328	447	18	factor	factor	NOUN
ejpam-3328	447	19	.	.	PUNCT
ejpam-3328	448	1	in	in	ADP
ejpam-3328	448	2	this	this	DET
ejpam-3328	448	3	manner	manner	NOUN
ejpam-3328	448	4	,	,	PUNCT
ejpam-3328	448	5	a	a	DET
ejpam-3328	448	6	riemann	riemann	PROPN
ejpam-3328	448	7	–	–	PUNCT
ejpam-3328	448	8	hilbert	hilbert	NOUN
ejpam-3328	448	9	boundary	boundary	ADJ
ejpam-3328	448	10	-	-	PUNCT
ejpam-3328	448	11	value	value	NOUN
ejpam-3328	448	12	problem	problem	NOUN
ejpam-3328	448	13	is	be	AUX
ejpam-3328	448	14	obtained	obtain	VERB
ejpam-3328	448	15	for	for	ADP
ejpam-3328	448	16	ln	ln	ADJ
ejpam-3328	448	17	ζ(s	ζ(s	PROPN
ejpam-3328	448	18	)	)	PUNCT
ejpam-3328	448	19	the	the	DET
ejpam-3328	448	20	properties	property	NOUN
ejpam-3328	448	21	of	of	ADP
ejpam-3328	448	22	the	the	DET
ejpam-3328	448	23	solution	solution	NOUN
ejpam-3328	448	24	to	to	ADP
ejpam-3328	448	25	the	the	DET
ejpam-3328	448	26	riemann	riemann	PROPN
ejpam-3328	448	27	–	–	PUNCT
ejpam-3328	448	28	hilbert	hilbert	PROPN
ejpam-3328	448	29	boundary	boundary	ADJ
ejpam-3328	448	30	-	-	PUNCT
ejpam-3328	448	31	value	value	NOUN
ejpam-3328	448	32	problem	problem	NOUN
ejpam-3328	448	33	are	be	AUX
ejpam-3328	448	34	expressed	express	VERB
ejpam-3328	448	35	in	in	ADP
ejpam-3328	448	36	terms	term	NOUN
ejpam-3328	448	37	of	of	ADP
ejpam-3328	448	38	the	the	DET
ejpam-3328	448	39	hilbert	hilbert	NOUN
ejpam-3328	448	40	integral	integral	ADJ
ejpam-3328	448	41	transform	transform	NOUN
ejpam-3328	448	42	.	.	PUNCT
ejpam-3328	449	1	in	in	ADP
ejpam-3328	449	2	the	the	DET
ejpam-3328	449	3	rectangles	rectangle	NOUN
ejpam-3328	449	4	in	in	ADP
ejpam-3328	449	5	which	which	PRON
ejpam-3328	449	6	the	the	DET
ejpam-3328	449	7	zeta	zeta	NOUN
ejpam-3328	449	8	function	function	NOUN
ejpam-3328	449	9	has	have	VERB
ejpam-3328	449	10	no	no	DET
ejpam-3328	449	11	roots	root	NOUN
ejpam-3328	449	12	,	,	PUNCT
ejpam-3328	449	13	the	the	DET
ejpam-3328	449	14	hilbert	hilbert	NOUN
ejpam-3328	449	15	transform	transform	NOUN
ejpam-3328	449	16	can	can	AUX
ejpam-3328	449	17	be	be	AUX
ejpam-3328	449	18	used	use	VERB
ejpam-3328	449	19	to	to	PART
ejpam-3328	449	20	obtain	obtain	VERB
ejpam-3328	449	21	exact	exact	ADJ
ejpam-3328	449	22	lower	low	ADJ
ejpam-3328	449	23	bounds	bound	NOUN
ejpam-3328	449	24	for	for	ADP
ejpam-3328	449	25	the	the	DET
ejpam-3328	449	26	zeta	zeta	PROPN
ejpam-3328	449	27	function	function	NOUN
ejpam-3328	449	28	in	in	ADP
ejpam-3328	449	29	the	the	DET
ejpam-3328	449	30	critical	critical	ADJ
ejpam-3328	449	31	strip	strip	NOUN
ejpam-3328	449	32	.	.	PUNCT
ejpam-3328	450	1	8	8	X
ejpam-3328	450	2	.	.	X
ejpam-3328	450	3	results	result	NOUN
ejpam-3328	450	4	as	as	SCONJ
ejpam-3328	450	5	mentioned	mention	VERB
ejpam-3328	450	6	in	in	ADP
ejpam-3328	450	7	the	the	DET
ejpam-3328	450	8	introduction	introduction	NOUN
ejpam-3328	450	9	,	,	PUNCT
ejpam-3328	450	10	certain	certain	ADJ
ejpam-3328	450	11	simple	simple	ADJ
ejpam-3328	450	12	intermediate	intermediate	ADJ
ejpam-3328	450	13	estimates	estimate	NOUN
ejpam-3328	450	14	are	be	AUX
ejpam-3328	450	15	first	first	ADV
ejpam-3328	450	16	obtained	obtain	VERB
ejpam-3328	450	17	.	.	PUNCT
ejpam-3328	451	1	the	the	DET
ejpam-3328	451	2	rectangles	rectangle	NOUN
ejpam-3328	451	3	in	in	ADP
ejpam-3328	451	4	which	which	PRON
ejpam-3328	451	5	the	the	DET
ejpam-3328	451	6	zeta	zeta	NOUN
ejpam-3328	451	7	function	function	NOUN
ejpam-3328	451	8	has	have	AUX
ejpam-3328	451	9	n’t	not	PART
ejpam-3328	451	10	zeros	zero	NOUN
ejpam-3328	451	11	are	be	AUX
ejpam-3328	451	12	first	first	ADV
ejpam-3328	451	13	introduced	introduce	VERB
ejpam-3328	451	14	as	as	SCONJ
ejpam-3328	451	15	follows	follow	VERB
ejpam-3328	451	16	:	:	PUNCT
ejpam-3328	451	17	d(n	d(n	NOUN
ejpam-3328	451	18	)	)	PUNCT
ejpam-3328	451	19	=	=	PUNCT
ejpam-3328	452	1	(	(	PUNCT
ejpam-3328	452	2	s|0.1	s|0.1	NOUN
ejpam-3328	452	3	<	<	X
ejpam-3328	452	4	re(s	re(s	PROPN
ejpam-3328	452	5	)	)	PUNCT
ejpam-3328	452	6	<	<	X
ejpam-3328	452	7	0.9	0.9	NUM
ejpam-3328	452	8	,	,	PUNCT
ejpam-3328	452	9	im(s	im(s	PROPN
ejpam-3328	452	10	)	)	PUNCT
ejpam-3328	452	11	6=	6=	NUM
ejpam-3328	452	12	im(sn	im(sn	PROPN
ejpam-3328	452	13	)	)	PUNCT
ejpam-3328	452	14	,	,	PUNCT
ejpam-3328	452	15	im(sn)−	im(sn)−	PROPN
ejpam-3328	452	16	dn	dn	PROPN
ejpam-3328	452	17	≤	≤	PROPN
ejpam-3328	452	18	im(s	im(	NOUN
ejpam-3328	452	19	)	)	PUNCT
ejpam-3328	452	20	≤	≤	NUM
ejpam-3328	452	21	im(sn	im(sn	PROPN
ejpam-3328	452	22	)	)	PUNCT
ejpam-3328	452	23	+	+	CCONJ
ejpam-3328	452	24	dn	dn	PROPN
ejpam-3328	452	25	,	,	PUNCT
ejpam-3328	452	26	d(n	d(n	NOUN
ejpam-3328	452	27	)	)	PUNCT
ejpam-3328	452	28	=	=	PUNCT
ejpam-3328	453	1	(	(	PUNCT
ejpam-3328	453	2	s|0.1	s|0.1	NOUN
ejpam-3328	453	3	<	<	X
ejpam-3328	453	4	re(s	re(s	PROPN
ejpam-3328	453	5	)	)	PUNCT
ejpam-3328	453	6	<	<	X
ejpam-3328	453	7	0.9	0.9	NUM
ejpam-3328	453	8	,	,	PUNCT
ejpam-3328	453	9	im(−s	im(−	NOUN
ejpam-3328	453	10	)	)	PUNCT
ejpam-3328	453	11	6=	6=	NUM
ejpam-3328	453	12	im(−sn	im(−sn	NOUN
ejpam-3328	453	13	)	)	PUNCT
ejpam-3328	453	14	,	,	PUNCT
ejpam-3328	453	15	−im(sn)−dn	−im(sn)−dn	PROPN
ejpam-3328	453	16	≤	≤	PUNCT
ejpam-3328	453	17	im(s	im(s	PROPN
ejpam-3328	453	18	)	)	PUNCT
ejpam-3328	453	19	≤	≤	NOUN
ejpam-3328	454	1	−im(sn)+dn	−im(sn)+dn	PROPN
ejpam-3328	454	2	,	,	PUNCT
ejpam-3328	454	3	,	,	PUNCT
ejpam-3328	454	4	where	where	SCONJ
ejpam-3328	454	5	ζ(sn+1	ζ(sn+1	ADJ
ejpam-3328	454	6	)	)	PUNCT
ejpam-3328	454	7	=	=	SYM
ejpam-3328	454	8	0	0	NUM
ejpam-3328	454	9	,	,	PUNCT
ejpam-3328	454	10	ζ(sn	ζ(sn	NUM
ejpam-3328	454	11	)	)	PUNCT
ejpam-3328	454	12	=	=	SYM
ejpam-3328	454	13	0	0	NUM
ejpam-3328	454	14	,	,	PUNCT
ejpam-3328	454	15	ζ(1−	ζ(1−	PROPN
ejpam-3328	454	16	sn	sn	PROPN
ejpam-3328	454	17	)	)	PUNCT
ejpam-3328	454	18	=	=	SYM
ejpam-3328	454	19	0	0	NUM
ejpam-3328	454	20	,	,	PUNCT
ejpam-3328	454	21	ζ(1−	ζ(1−	PROPN
ejpam-3328	454	22	sn+1	sn+1	X
ejpam-3328	454	23	)	)	PUNCT
ejpam-3328	454	24	=	=	SYM
ejpam-3328	454	25	0	0	NUM
ejpam-3328	454	26	,	,	PUNCT
ejpam-3328	454	27	ζ(1−	ζ(1−	PROPN
ejpam-3328	454	28	sn	sn	PROPN
ejpam-3328	454	29	)	)	PUNCT
ejpam-3328	454	30	=	=	SYM
ejpam-3328	455	1	0	0	NUM
ejpam-3328	455	2	,	,	PUNCT
ejpam-3328	455	3	dn	dn	NOUN
ejpam-3328	455	4	=	=	PUNCT
ejpam-3328	455	5	(	(	PUNCT
ejpam-3328	455	6	im(sn+1)−	im(sn+1)−	PROPN
ejpam-3328	455	7	im(sn))/2	im(sn))/2	ADJ
ejpam-3328	455	8	.	.	PUNCT
ejpam-3328	456	1	the	the	DET
ejpam-3328	456	2	sets	set	NOUN
ejpam-3328	456	3	of	of	ADP
ejpam-3328	456	4	d(n	d(n	NOUN
ejpam-3328	456	5	)	)	PUNCT
ejpam-3328	456	6	,	,	PUNCT
ejpam-3328	456	7	are	be	AUX
ejpam-3328	456	8	shown	show	VERB
ejpam-3328	456	9	in	in	ADP
ejpam-3328	456	10	the	the	DET
ejpam-3328	456	11	figure	figure	NOUN
ejpam-3328	456	12	1	1	NUM
ejpam-3328	456	13	below	below	ADV
ejpam-3328	456	14	.	.	PUNCT
ejpam-3328	457	1	a.	a.	NOUN
ejpam-3328	457	2	durmagambetov	durmagambetov	PROPN
ejpam-3328	457	3	/	/	SYM
ejpam-3328	457	4	eur	eur	PROPN
ejpam-3328	457	5	.	.	PUNCT
ejpam-3328	458	1	j.	j.	PROPN
ejpam-3328	458	2	pure	pure	PROPN
ejpam-3328	458	3	appl	appl	PROPN
ejpam-3328	458	4	.	.	PROPN
ejpam-3328	458	5	math	math	PROPN
ejpam-3328	458	6	,	,	PUNCT
ejpam-3328	458	7	11	11	NUM
ejpam-3328	458	8	(	(	PUNCT
ejpam-3328	458	9	4	4	NUM
ejpam-3328	458	10	)	)	PUNCT
ejpam-3328	458	11	(	(	PUNCT
ejpam-3328	458	12	2018	2018	NUM
ejpam-3328	458	13	)	)	PUNCT
ejpam-3328	458	14	,	,	PUNCT
ejpam-3328	458	15	1143	1143	NUM
ejpam-3328	458	16	-	-	SYM
ejpam-3328	458	17	1176	1176	NUM
ejpam-3328	458	18	1163	1163	NUM
ejpam-3328	458	19	figure	figure	NOUN
ejpam-3328	458	20	1	1	NUM
ejpam-3328	458	21	:	:	PUNCT
ejpam-3328	458	22	re(s	re(s	ADJ
ejpam-3328	458	23	)	)	PUNCT
ejpam-3328	458	24	im(s	im(s	PROPN
ejpam-3328	458	25	)	)	PUNCT
ejpam-3328	458	26	0	0	NUM
ejpam-3328	459	1	1/2+ε1/2−ε	1/2+ε1/2−ε	NUM
ejpam-3328	459	2	1	1	NUM
ejpam-3328	459	3	−ε	−ε	PROPN
ejpam-3328	459	4	d(n	d(n	PROPN
ejpam-3328	459	5	)	)	PUNCT
ejpam-3328	459	6	d(n	d(n	PROPN
ejpam-3328	459	7	)	)	PUNCT
ejpam-3328	459	8	theorem	theorem	VERB
ejpam-3328	459	9	6	6	NUM
ejpam-3328	459	10	.	.	PUNCT
ejpam-3328	460	1	let	let	VERB
ejpam-3328	460	2	s	s	PRON
ejpam-3328	460	3	∈	∈	PROPN
ejpam-3328	460	4	dn	dn	NOUN
ejpam-3328	460	5	∪d(n	∪d(n	NOUN
ejpam-3328	460	6	)	)	PUNCT
ejpam-3328	460	7	and	and	CCONJ
ejpam-3328	460	8	f	f	PROPN
ejpam-3328	460	9	(	(	PUNCT
ejpam-3328	460	10	s	s	X
ejpam-3328	460	11	)	)	PUNCT
ejpam-3328	460	12	=	=	SYM
ejpam-3328	460	13	s	s	PART
ejpam-3328	460	14	2	2	NUM
ejpam-3328	460	15	ln(π)−	ln(π)−	NOUN
ejpam-3328	460	16	ln(γ(s/2))−	ln(γ(s/2))−	NOUN
ejpam-3328	460	17	1−s	1−s	NUM
ejpam-3328	460	18	2	2	NUM
ejpam-3328	460	19	ln(π	ln(π	PUNCT
ejpam-3328	460	20	)	)	PUNCT
ejpam-3328	461	1	+	+	CCONJ
ejpam-3328	461	2	ln(γ(1−	ln(γ(1−	PROPN
ejpam-3328	461	3	s)/2	s)/2	PROPN
ejpam-3328	461	4	)	)	PUNCT
ejpam-3328	461	5	)	)	PUNCT
ejpam-3328	461	6	.	.	PUNCT
ejpam-3328	462	1	then	then	ADV
ejpam-3328	462	2	,	,	PUNCT
ejpam-3328	462	3	sup	sup	NOUN
ejpam-3328	462	4	s∈dn∪d(n	s∈dn∪d(n	NOUN
ejpam-3328	462	5	)	)	PUNCT
ejpam-3328	462	6	|f	|f	PROPN
ejpam-3328	463	1	(	(	PUNCT
ejpam-3328	463	2	τ	τ	PROPN
ejpam-3328	463	3	+	+	PROPN
ejpam-3328	463	4	iα)|+	iα)|+	PROPN
ejpam-3328	463	5	sup	sup	NOUN
ejpam-3328	463	6	s∈dn∪d(n	s∈dn∪d(n	NOUN
ejpam-3328	463	7	)	)	PUNCT
ejpam-3328	463	8	|df	|df	PROPN
ejpam-3328	463	9	(	(	PUNCT
ejpam-3328	463	10	τ	τ	X
ejpam-3328	463	11	+	+	NUM
ejpam-3328	463	12	iα	iα	NOUN
ejpam-3328	463	13	)	)	PUNCT
ejpam-3328	463	14	dτ	dτ	NOUN
ejpam-3328	464	1	|	|	ADV
ejpam-3328	464	2	<	<	X
ejpam-3328	464	3	ccn	ccn	PROPN
ejpam-3328	464	4	.	.	PUNCT
ejpam-3328	465	1	proof	proof	NOUN
ejpam-3328	465	2	.	.	PUNCT
ejpam-3328	466	1	as	as	ADP
ejpam-3328	466	2	s	s	PROPN
ejpam-3328	466	3	∈	∈	PROPN
ejpam-3328	466	4	dn	dn	NOUN
ejpam-3328	466	5	∪	∪	ADJ
ejpam-3328	466	6	d(n	d(n	NOUN
ejpam-3328	466	7	)	)	PUNCT
ejpam-3328	466	8	,	,	PUNCT
ejpam-3328	466	9	this	this	PRON
ejpam-3328	466	10	implies	imply	VERB
ejpam-3328	466	11	that	that	SCONJ
ejpam-3328	466	12	f	f	PROPN
ejpam-3328	466	13	is	be	AUX
ejpam-3328	466	14	holomorphic	holomorphic	ADJ
ejpam-3328	466	15	,	,	PUNCT
ejpam-3328	466	16	which	which	PRON
ejpam-3328	466	17	completes	complete	VERB
ejpam-3328	466	18	the	the	DET
ejpam-3328	466	19	proof	proof	NOUN
ejpam-3328	466	20	.	.	PUNCT
ejpam-3328	467	1	as	as	SCONJ
ejpam-3328	467	2	mentioned	mention	VERB
ejpam-3328	467	3	in	in	ADP
ejpam-3328	467	4	the	the	DET
ejpam-3328	467	5	introduction	introduction	NOUN
ejpam-3328	467	6	,	,	PUNCT
ejpam-3328	467	7	a	a	DET
ejpam-3328	467	8	riemann	riemann	PROPN
ejpam-3328	467	9	–	–	PUNCT
ejpam-3328	467	10	hilbert	hilbert	NOUN
ejpam-3328	467	11	boundary	boundary	ADJ
ejpam-3328	467	12	-	-	PUNCT
ejpam-3328	467	13	value	value	NOUN
ejpam-3328	467	14	problem	problem	NOUN
ejpam-3328	467	15	should	should	AUX
ejpam-3328	467	16	be	be	AUX
ejpam-3328	467	17	obtained	obtain	VERB
ejpam-3328	467	18	.	.	PUNCT
ejpam-3328	468	1	to	to	ADP
ejpam-3328	468	2	this	this	DET
ejpam-3328	468	3	end	end	NOUN
ejpam-3328	468	4	,	,	PUNCT
ejpam-3328	468	5	an	an	DET
ejpam-3328	468	6	equation	equation	NOUN
ejpam-3328	468	7	should	should	AUX
ejpam-3328	468	8	be	be	AUX
ejpam-3328	468	9	derived	derive	VERB
ejpam-3328	468	10	that	that	PRON
ejpam-3328	468	11	determines	determine	VERB
ejpam-3328	468	12	the	the	DET
ejpam-3328	468	13	difference	difference	NOUN
ejpam-3328	468	14	between	between	ADP
ejpam-3328	468	15	the	the	DET
ejpam-3328	468	16	boundary	boundary	ADJ
ejpam-3328	468	17	values	value	NOUN
ejpam-3328	468	18	of	of	ADP
ejpam-3328	468	19	the	the	DET
ejpam-3328	468	20	analytic	analytic	ADJ
ejpam-3328	468	21	functions	function	NOUN
ejpam-3328	468	22	in	in	ADP
ejpam-3328	468	23	the	the	DET
ejpam-3328	468	24	upper	upper	ADJ
ejpam-3328	468	25	plane	plane	NOUN
ejpam-3328	468	26	and	and	CCONJ
ejpam-3328	468	27	the	the	DET
ejpam-3328	468	28	lower	low	ADJ
ejpam-3328	468	29	plane	plane	NOUN
ejpam-3328	468	30	.	.	PUNCT
ejpam-3328	469	1	denote	denote	VERB
ejpam-3328	469	2	q(s	q(s	NOUN
ejpam-3328	469	3	)	)	PUNCT
ejpam-3328	469	4	=	=	SYM
ejpam-3328	469	5	re(ln(ζ(s	re(ln(ζ(s	NOUN
ejpam-3328	469	6	)	)	PUNCT
ejpam-3328	469	7	)	)	PUNCT
ejpam-3328	469	8	)	)	PUNCT
ejpam-3328	470	1	=	=	SYM
ejpam-3328	470	2	ln(|ζ(s)|	ln(|ζ(s)|	PROPN
ejpam-3328	470	3	)	)	PUNCT
ejpam-3328	470	4	.	.	PUNCT
ejpam-3328	471	1	theorem	theorem	ADJ
ejpam-3328	471	2	7	7	NUM
ejpam-3328	471	3	.	.	PUNCT
ejpam-3328	472	1	let	let	VERB
ejpam-3328	472	2	s	s	PRON
ejpam-3328	472	3	∈	∈	PROPN
ejpam-3328	472	4	d(n	d(n	PROPN
ejpam-3328	472	5	)	)	PUNCT
ejpam-3328	472	6	or	or	CCONJ
ejpam-3328	472	7	s	s	PROPN
ejpam-3328	472	8	∈	∈	PROPN
ejpam-3328	472	9	d(n	d(n	PROPN
ejpam-3328	472	10	)	)	PUNCT
ejpam-3328	472	11	and	and	CCONJ
ejpam-3328	472	12	f	f	PROPN
ejpam-3328	472	13	(	(	PUNCT
ejpam-3328	472	14	s	s	X
ejpam-3328	472	15	)	)	PUNCT
ejpam-3328	472	16	=	=	SYM
ejpam-3328	472	17	s	s	PART
ejpam-3328	472	18	2	2	NUM
ejpam-3328	472	19	ln(π)−	ln(π)−	NOUN
ejpam-3328	472	20	ln(γ(s/2))−	ln(γ(s/2))−	NOUN
ejpam-3328	472	21	1−	1−	NUM
ejpam-3328	472	22	s	s	NOUN
ejpam-3328	472	23	2	2	NUM
ejpam-3328	472	24	ln(π	ln(π	PUNCT
ejpam-3328	472	25	)	)	PUNCT
ejpam-3328	473	1	+	+	CCONJ
ejpam-3328	473	2	ln(γ(1−	ln(γ(1−	PROPN
ejpam-3328	473	3	s)/2	s)/2	PROPN
ejpam-3328	473	4	)	)	PUNCT
ejpam-3328	473	5	)	)	PUNCT
ejpam-3328	473	6	.	.	PUNCT
ejpam-3328	474	1	then	then	ADV
ejpam-3328	474	2	,	,	PUNCT
ejpam-3328	474	3	q(s	q(s	PROPN
ejpam-3328	474	4	)	)	PUNCT
ejpam-3328	474	5	=	=	PUNCT
ejpam-3328	475	1	q(1−	q(1−	NOUN
ejpam-3328	475	2	s	s	PART
ejpam-3328	475	3	)	)	PUNCT
ejpam-3328	476	1	+	+	CCONJ
ejpam-3328	476	2	re(f	re(f	X
ejpam-3328	476	3	(	(	PUNCT
ejpam-3328	476	4	s	s	NOUN
ejpam-3328	476	5	)	)	PUNCT
ejpam-3328	476	6	)	)	PUNCT
ejpam-3328	476	7	.	.	PUNCT
ejpam-3328	477	1	proof	proof	NOUN
ejpam-3328	477	2	.	.	PUNCT
ejpam-3328	478	1	can	can	AUX
ejpam-3328	478	2	be	be	AUX
ejpam-3328	478	3	taking	take	VERB
ejpam-3328	478	4	the	the	DET
ejpam-3328	478	5	logarithm	logarithm	NOUN
ejpam-3328	478	6	of	of	ADP
ejpam-3328	478	7	eq	eq	PROPN
ejpam-3328	478	8	.	.	PUNCT
ejpam-3328	479	1	(	(	PUNCT
ejpam-3328	479	2	19)for	19)for	NUM
ejpam-3328	479	3	s	s	NOUN
ejpam-3328	479	4	∈	∈	PROPN
ejpam-3328	479	5	d(n	d(n	PROPN
ejpam-3328	479	6	)	)	PUNCT
ejpam-3328	479	7	or	or	CCONJ
ejpam-3328	479	8	s	s	PROPN
ejpam-3328	479	9	∈	∈	PROPN
ejpam-3328	479	10	d(n	d(n	PROPN
ejpam-3328	479	11	)	)	PUNCT
ejpam-3328	479	12	,	,	PUNCT
ejpam-3328	479	13	and	and	CCONJ
ejpam-3328	479	14	an	an	DET
ejpam-3328	479	15	equation	equation	NOUN
ejpam-3328	479	16	for	for	ADP
ejpam-3328	479	17	q(s	q(s	NOUN
ejpam-3328	479	18	)	)	PUNCT
ejpam-3328	479	19	may	may	AUX
ejpam-3328	479	20	be	be	AUX
ejpam-3328	479	21	obtained	obtain	VERB
ejpam-3328	479	22	as	as	ADP
ejpam-3328	479	23	an	an	DET
ejpam-3328	479	24	equation	equation	NOUN
ejpam-3328	479	25	for	for	ADP
ejpam-3328	479	26	the	the	DET
ejpam-3328	479	27	real	real	ADJ
ejpam-3328	479	28	part	part	NOUN
ejpam-3328	479	29	.	.	PUNCT
ejpam-3328	480	1	a.	a.	NOUN
ejpam-3328	480	2	durmagambetov	durmagambetov	PROPN
ejpam-3328	480	3	/	/	SYM
ejpam-3328	480	4	eur	eur	PROPN
ejpam-3328	480	5	.	.	PUNCT
ejpam-3328	481	1	j.	j.	PROPN
ejpam-3328	481	2	pure	pure	PROPN
ejpam-3328	481	3	appl	appl	PROPN
ejpam-3328	481	4	.	.	PROPN
ejpam-3328	481	5	math	math	PROPN
ejpam-3328	481	6	,	,	PUNCT
ejpam-3328	481	7	11	11	NUM
ejpam-3328	481	8	(	(	PUNCT
ejpam-3328	481	9	4	4	NUM
ejpam-3328	481	10	)	)	PUNCT
ejpam-3328	481	11	(	(	PUNCT
ejpam-3328	481	12	2018	2018	NUM
ejpam-3328	481	13	)	)	PUNCT
ejpam-3328	481	14	,	,	PUNCT
ejpam-3328	481	15	1143	1143	NUM
ejpam-3328	481	16	-	-	SYM
ejpam-3328	481	17	1176	1176	NUM
ejpam-3328	481	18	1164	1164	NUM
ejpam-3328	481	19	consequently	consequently	ADV
ejpam-3328	481	20	,	,	PUNCT
ejpam-3328	481	21	the	the	DET
ejpam-3328	481	22	following	follow	VERB
ejpam-3328	481	23	functions	function	NOUN
ejpam-3328	481	24	are	be	AUX
ejpam-3328	481	25	introduced:	introduced:	NOUN
ejpam-3328	481	26	νε(s	νε(s	NOUN
ejpam-3328	481	27	)	)	PUNCT
ejpam-3328	481	28	=	=	SYM
ejpam-3328	481	29	0	0	NUM
ejpam-3328	481	30	,	,	PUNCT
ejpam-3328	481	31	re(s	re(s	PUNCT
ejpam-3328	481	32	)	)	PUNCT
ejpam-3328	481	33	<	<	X
ejpam-3328	481	34	2ε	2ε	NUM
ejpam-3328	481	35	;	;	PUNCT
ejpam-3328	481	36	νε(s	νε(s	X
ejpam-3328	481	37	)	)	PUNCT
ejpam-3328	481	38	=	=	SYM
ejpam-3328	482	1	1	1	NUM
ejpam-3328	482	2	,	,	PUNCT
ejpam-3328	482	3	ε	ε	PROPN
ejpam-3328	482	4	<	<	X
ejpam-3328	482	5	re(s	re(s	PROPN
ejpam-3328	482	6	)	)	PUNCT
ejpam-3328	482	7	<	<	X
ejpam-3328	482	8	1/2−	1/2−	NUM
ejpam-3328	482	9	2ε	2ε	NUM
ejpam-3328	482	10	;	;	PUNCT
ejpam-3328	482	11	νε(s	νε(s	X
ejpam-3328	482	12	)	)	PUNCT
ejpam-3328	482	13	=	=	SYM
ejpam-3328	483	1	0	0	NUM
ejpam-3328	483	2	,	,	PUNCT
ejpam-3328	483	3	1/2−	1/2−	NUM
ejpam-3328	483	4	2ε	2ε	NOUN
ejpam-3328	483	5	<	<	X
ejpam-3328	483	6	re(s	re(s	PROPN
ejpam-3328	483	7	)	)	PUNCT
ejpam-3328	483	8	<	<	X
ejpam-3328	484	1	1/2	1/2	NUM
ejpam-3328	484	2	+	+	NUM
ejpam-3328	484	3	2ε	2ε	NUM
ejpam-3328	484	4	;	;	PUNCT
ejpam-3328	484	5	νε(s	νε(s	X
ejpam-3328	484	6	)	)	PUNCT
ejpam-3328	484	7	=	=	SYM
ejpam-3328	485	1	1	1	NUM
ejpam-3328	485	2	,	,	PUNCT
ejpam-3328	485	3	1/2	1/2	NUM
ejpam-3328	485	4	+	+	NUM
ejpam-3328	485	5	2ε	2ε	NOUN
ejpam-3328	485	6	<	<	X
ejpam-3328	485	7	re(s	re(s	PROPN
ejpam-3328	485	8	)	)	PUNCT
ejpam-3328	485	9	<	<	X
ejpam-3328	485	10	1−	1−	NUM
ejpam-3328	485	11	2ε	2ε	NUM
ejpam-3328	485	12	;	;	PUNCT
ejpam-3328	485	13	νε(s	νε(s	X
ejpam-3328	485	14	)	)	PUNCT
ejpam-3328	485	15	=	=	SYM
ejpam-3328	485	16	0	0	NUM
ejpam-3328	485	17	,	,	PUNCT
ejpam-3328	485	18	re(s	re(s	ADJ
ejpam-3328	485	19	)	)	PUNCT
ejpam-3328	485	20	>	>	X
ejpam-3328	485	21	1−	1−	NUM
ejpam-3328	485	22	2ε	2ε	NUM
ejpam-3328	485	23	;	;	PUNCT
ejpam-3328	485	24	ψ(t	ψ(t	PROPN
ejpam-3328	485	25	)	)	PUNCT
ejpam-3328	485	26	=	=	PRON
ejpam-3328	485	27	σe	σe	VERB
ejpam-3328	485	28	1	1	NUM
ejpam-3328	485	29	t2−1	t2−1	NOUN
ejpam-3328	485	30	,	,	PUNCT
ejpam-3328	485	31	t2	t2	NOUN
ejpam-3328	485	32	<	<	X
ejpam-3328	485	33	1	1	NUM
ejpam-3328	485	34	,	,	PUNCT
ejpam-3328	485	35	1	1	NUM
ejpam-3328	485	36	σ	σ	NOUN
ejpam-3328	485	37	=	=	SYM
ejpam-3328	485	38	1∫	1∫	NUM
ejpam-3328	485	39	−1	−1	NOUN
ejpam-3328	485	40	e	e	NOUN
ejpam-3328	485	41	1	1	NUM
ejpam-3328	485	42	t2−1dt	t2−1dt	NOUN
ejpam-3328	485	43	;	;	PUNCT
ejpam-3328	485	44	ψ(t	ψ(t	PROPN
ejpam-3328	485	45	)	)	PUNCT
ejpam-3328	485	46	=	=	SYM
ejpam-3328	485	47	0	0	NUM
ejpam-3328	485	48	,	,	PUNCT
ejpam-3328	485	49	t2	t2	NOUN
ejpam-3328	485	50	≥	≥	NUM
ejpam-3328	485	51	1	1	NUM
ejpam-3328	485	52	;	;	PUNCT
ejpam-3328	485	53	µε(x	µε(x	PUNCT
ejpam-3328	485	54	)	)	PUNCT
ejpam-3328	485	55	=	=	SYM
ejpam-3328	485	56	∫	∫	PROPN
ejpam-3328	486	1	ψ(s	ψ(s	PROPN
ejpam-3328	486	2	/	/	SYM
ejpam-3328	486	3	ε)νε(x−	ε)νε(x−	PUNCT
ejpam-3328	486	4	t)dt	t)dt	PROPN
ejpam-3328	486	5	/	/	SYM
ejpam-3328	486	6	ε	ε	PROPN
ejpam-3328	486	7	=	=	SYM
ejpam-3328	486	8	∫	∫	PROPN
ejpam-3328	486	9	ψ(x−	ψ(x−	PROPN
ejpam-3328	486	10	t	t	PROPN
ejpam-3328	486	11	/	/	SYM
ejpam-3328	486	12	ε)νε(t)dt	ε)νε(t)dt	PROPN
ejpam-3328	486	13	/	/	SYM
ejpam-3328	486	14	ε	ε	PROPN
ejpam-3328	486	15	.	.	PUNCT
ejpam-3328	487	1	lemma	lemma	PROPN
ejpam-3328	487	2	16	16	NUM
ejpam-3328	487	3	.	.	PUNCT
ejpam-3328	488	1	for	for	ADP
ejpam-3328	488	2	νε	νε	NOUN
ejpam-3328	488	3	and	and	CCONJ
ejpam-3328	488	4	µε	µε	NOUN
ejpam-3328	488	5	,	,	PUNCT
ejpam-3328	488	6	we	we	PRON
ejpam-3328	488	7	have	have	VERB
ejpam-3328	488	8	νε(x	νε(x	NOUN
ejpam-3328	488	9	)	)	PUNCT
ejpam-3328	488	10	=	=	PUNCT
ejpam-3328	489	1	νε(1−	νε(1−	PROPN
ejpam-3328	489	2	x	x	X
ejpam-3328	489	3	)	)	PUNCT
ejpam-3328	489	4	and	and	CCONJ
ejpam-3328	489	5	µε(x	µε(x	NOUN
ejpam-3328	489	6	)	)	PUNCT
ejpam-3328	489	7	=	=	PUNCT
ejpam-3328	490	1	µε(1−	µε(1−	PROPN
ejpam-3328	490	2	x	x	X
ejpam-3328	490	3	)	)	PUNCT
ejpam-3328	490	4	.	.	PUNCT
ejpam-3328	491	1	proof	proof	NOUN
ejpam-3328	491	2	.	.	PUNCT
ejpam-3328	492	1	we	we	PRON
ejpam-3328	492	2	have	have	VERB
ejpam-3328	492	3	νε(x	νε(x	NOUN
ejpam-3328	492	4	)	)	PUNCT
ejpam-3328	492	5	=	=	PUNCT
ejpam-3328	493	1	νε(1−	νε(1−	PROPN
ejpam-3328	493	2	x	x	X
ejpam-3328	493	3	)	)	PUNCT
ejpam-3328	493	4	by	by	ADP
ejpam-3328	493	5	definition	definition	NOUN
ejpam-3328	493	6	.	.	PUNCT
ejpam-3328	494	1	moreover	moreover	ADV
ejpam-3328	494	2	,	,	PUNCT
ejpam-3328	494	3	µε(x	µε(x	PUNCT
ejpam-3328	494	4	)	)	PUNCT
ejpam-3328	494	5	=	=	SYM
ejpam-3328	495	1	∫	∫	PROPN
ejpam-3328	496	1	ψ(s	ψ(s	PROPN
ejpam-3328	496	2	/	/	SYM
ejpam-3328	496	3	ε)νε(x−	ε)νε(x−	PROPN
ejpam-3328	496	4	s)ds	s)ds	PROPN
ejpam-3328	496	5	/	/	SYM
ejpam-3328	496	6	ε	ε	PROPN
ejpam-3328	496	7	=	=	SYM
ejpam-3328	496	8	∫	∫	PROPN
ejpam-3328	497	1	ψ(s	ψ(s	PROPN
ejpam-3328	497	2	/	/	SYM
ejpam-3328	497	3	ε)νε(1−	ε)νε(1−	ADJ
ejpam-3328	497	4	x+	x+	PROPN
ejpam-3328	497	5	s)ds	s)ds	PROPN
ejpam-3328	497	6	/	/	SYM
ejpam-3328	497	7	ε	ε	PROPN
ejpam-3328	497	8	=	=	PUNCT
ejpam-3328	497	9	µε(1−	µε(1−	PROPN
ejpam-3328	497	10	x	x	X
ejpam-3328	497	11	)	)	PUNCT
ejpam-3328	497	12	.	.	PUNCT
ejpam-3328	498	1	lemma	lemma	PROPN
ejpam-3328	498	2	17	17	NUM
ejpam-3328	498	3	.	.	PUNCT
ejpam-3328	499	1	let	let	VERB
ejpam-3328	499	2	1/2	1/2	NUM
ejpam-3328	500	1	+	+	NUM
ejpam-3328	500	2	3ε	3ε	NUM
ejpam-3328	500	3	<	<	X
ejpam-3328	500	4	x	x	X
ejpam-3328	500	5	<	<	X
ejpam-3328	500	6	1−	1−	NUM
ejpam-3328	500	7	3ε	3ε	NUM
ejpam-3328	500	8	.	.	PUNCT
ejpam-3328	501	1	then	then	ADV
ejpam-3328	501	2	,	,	PUNCT
ejpam-3328	501	3	µε(x	µε(x	PUNCT
ejpam-3328	501	4	)	)	PUNCT
ejpam-3328	501	5	=	=	SYM
ejpam-3328	501	6	1	1	X
ejpam-3328	501	7	.	.	PUNCT
ejpam-3328	501	8	proof	proof	NOUN
ejpam-3328	501	9	.	.	PUNCT
ejpam-3328	501	10	µε(x	µε(x	PUNCT
ejpam-3328	501	11	)	)	PUNCT
ejpam-3328	502	1	=	=	SYM
ejpam-3328	502	2	∫	∫	PROPN
ejpam-3328	503	1	ψ(s	ψ(s	PROPN
ejpam-3328	503	2	/	/	SYM
ejpam-3328	503	3	ε)νε(x−	ε)νε(x−	PROPN
ejpam-3328	503	4	s)ds	s)ds	PROPN
ejpam-3328	503	5	/	/	SYM
ejpam-3328	503	6	ε	ε	PROPN
ejpam-3328	503	7	=	=	SYM
ejpam-3328	503	8	∫	∫	PROPN
ejpam-3328	503	9	ε	ε	PROPN
ejpam-3328	503	10	−ε	−ε	PROPN
ejpam-3328	504	1	ψ(s	ψ(s	PROPN
ejpam-3328	504	2	/	/	SYM
ejpam-3328	504	3	ε)νε(x−	ε)νε(x−	PROPN
ejpam-3328	504	4	s)ds	s)ds	PROPN
ejpam-3328	504	5	/	/	SYM
ejpam-3328	504	6	ε	ε	PROPN
ejpam-3328	504	7	=	=	SYM
ejpam-3328	504	8	∫	∫	PROPN
ejpam-3328	504	9	ε	ε	PROPN
ejpam-3328	504	10	−ε	−ε	PROPN
ejpam-3328	505	1	ψ(s	ψ(s	PROPN
ejpam-3328	505	2	/	/	SYM
ejpam-3328	505	3	ε)ds	ε)ds	PROPN
ejpam-3328	505	4	/	/	SYM
ejpam-3328	505	5	ε	ε	PROPN
ejpam-3328	505	6	=	=	SYM
ejpam-3328	505	7	1	1	X
ejpam-3328	505	8	.	.	PUNCT
ejpam-3328	505	9	to	to	PART
ejpam-3328	505	10	compute	compute	VERB
ejpam-3328	505	11	the	the	DET
ejpam-3328	505	12	fourier	fourier	NOUN
ejpam-3328	505	13	transform	transform	NOUN
ejpam-3328	505	14	of	of	ADP
ejpam-3328	505	15	the	the	DET
ejpam-3328	505	16	equation	equation	NOUN
ejpam-3328	505	17	for	for	ADP
ejpam-3328	505	18	q	q	NOUN
ejpam-3328	505	19	,	,	PUNCT
ejpam-3328	505	20	the	the	DET
ejpam-3328	505	21	functions	function	NOUN
ejpam-3328	505	22	r(k	r(k	PROPN
ejpam-3328	505	23	)	)	PUNCT
ejpam-3328	505	24	,	,	PUNCT
ejpam-3328	505	25	qε(s	qε(s	NOUN
ejpam-3328	505	26	)	)	PUNCT
ejpam-3328	505	27	,	,	PUNCT
ejpam-3328	505	28	qε(1−s	qε(1−s	NOUN
ejpam-3328	505	29	)	)	PUNCT
ejpam-3328	505	30	,	,	PUNCT
ejpam-3328	505	31	and	and	CCONJ
ejpam-3328	505	32	re(fε(s	re(fε(s	NOUN
ejpam-3328	505	33	)	)	PUNCT
ejpam-3328	505	34	)	)	PUNCT
ejpam-3328	505	35	,	,	PUNCT
ejpam-3328	505	36	the	the	DET
ejpam-3328	505	37	fourier	fourier	NOUN
ejpam-3328	505	38	transform	transform	NOUN
ejpam-3328	505	39	of	of	ADP
ejpam-3328	505	40	qε(s	qε(s	NOUN
ejpam-3328	505	41	)	)	PUNCT
ejpam-3328	505	42	,	,	PUNCT
ejpam-3328	505	43	the	the	DET
ejpam-3328	505	44	fourier	fourier	NOUN
ejpam-3328	505	45	transform	transform	NOUN
ejpam-3328	505	46	of	of	ADP
ejpam-3328	505	47	qε(1−s	qε(1−s	NOUN
ejpam-3328	505	48	)	)	PUNCT
ejpam-3328	505	49	,	,	PUNCT
ejpam-3328	505	50	and	and	CCONJ
ejpam-3328	505	51	the	the	DET
ejpam-3328	505	52	fourier	fourier	NOUN
ejpam-3328	505	53	transform	transform	NOUN
ejpam-3328	505	54	of	of	ADP
ejpam-3328	505	55	fε(s	fε(s	NOUN
ejpam-3328	505	56	)	)	PUNCT
ejpam-3328	505	57	are	be	AUX
ejpam-3328	505	58	introduced	introduce	VERB
ejpam-3328	505	59	as	as	SCONJ
ejpam-3328	505	60	follows	follow	VERB
ejpam-3328	505	61	:	:	PUNCT
ejpam-3328	505	62	qε(s	qε(s	X
ejpam-3328	505	63	)	)	PUNCT
ejpam-3328	505	64	=	=	SYM
ejpam-3328	505	65	q(s)µε(re(s	q(s)µε(re(s	NOUN
ejpam-3328	505	66	)	)	PUNCT
ejpam-3328	505	67	)	)	PUNCT
ejpam-3328	505	68	,	,	PUNCT
ejpam-3328	505	69	qε(1−	qε(1−	PROPN
ejpam-3328	505	70	s	s	PART
ejpam-3328	505	71	)	)	PUNCT
ejpam-3328	505	72	=	=	SYM
ejpam-3328	506	1	q(1−	q(1−	NOUN
ejpam-3328	506	2	s)µε(1−	s)µε(1−	ADJ
ejpam-3328	506	3	re(s	re(s	ADJ
ejpam-3328	506	4	)	)	PUNCT
ejpam-3328	506	5	)	)	PUNCT
ejpam-3328	507	1	,	,	PUNCT
ejpam-3328	507	2	r(k	r(k	PROPN
ejpam-3328	507	3	)	)	PUNCT
ejpam-3328	507	4	=	=	SYM
ejpam-3328	508	1	e−ik	e−ik	NOUN
ejpam-3328	508	2	k	k	CCONJ
ejpam-3328	508	3	−	−	PROPN
ejpam-3328	508	4	ia	ia	PROPN
ejpam-3328	508	5	+	+	CCONJ
ejpam-3328	508	6	1	1	NUM
ejpam-3328	508	7	,	,	PUNCT
ejpam-3328	508	8	fε(s	fε(s	NUM
ejpam-3328	508	9	)	)	PUNCT
ejpam-3328	508	10	=	=	SYM
ejpam-3328	508	11	re(f	re(f	X
ejpam-3328	508	12	(	(	PUNCT
ejpam-3328	508	13	s))µε(re(s	s))µε(re(s	ADJ
ejpam-3328	508	14	)	)	PUNCT
ejpam-3328	508	15	)	)	PUNCT
ejpam-3328	508	16	,	,	PUNCT
ejpam-3328	508	17	1√	1√	PROPN
ejpam-3328	508	18	2π	2π	NUM
ejpam-3328	508	19	∫	∫	NOUN
ejpam-3328	508	20	1−ε	1−ε	NUM
ejpam-3328	508	21	ε	ε	PROPN
ejpam-3328	508	22	qε(1−	qε(1−	PROPN
ejpam-3328	508	23	τ	τ	X
ejpam-3328	508	24	−	−	NOUN
ejpam-3328	508	25	iα)e−ikτdτ	iα)e−ikτdτ	NOUN
ejpam-3328	508	26	=	=	SYM
ejpam-3328	508	27	e−ik√	e−ik√	PROPN
ejpam-3328	508	28	2π	2π	PROPN
ejpam-3328	508	29	∫	∫	PROPN
ejpam-3328	508	30	1−ε	1−ε	X
ejpam-3328	508	31	ε	ε	PROPN
ejpam-3328	508	32	µε(1−	µε(1−	ADJ
ejpam-3328	508	33	re(s))qε(τ	re(s))qε(τ	PROPN
ejpam-3328	508	34	−	−	PROPN
ejpam-3328	508	35	iα)eikτdτ	iα)eikτdτ	NOUN
ejpam-3328	508	36	,	,	PUNCT
ejpam-3328	508	37	q̃ε(k	q̃ε(k	VERB
ejpam-3328	508	38	,	,	PUNCT
ejpam-3328	508	39	α	α	NOUN
ejpam-3328	508	40	)	)	PUNCT
ejpam-3328	508	41	=	=	SYM
ejpam-3328	508	42	1√	1√	NUM
ejpam-3328	508	43	2π	2π	NUM
ejpam-3328	508	44	∫	∫	PROPN
ejpam-3328	508	45	1−ε	1−ε	NUM
ejpam-3328	508	46	ε	ε	PROPN
ejpam-3328	508	47	qε(τ	qε(τ	X
ejpam-3328	508	48	+	+	CCONJ
ejpam-3328	508	49	iα)e−ikτdτ	iα)e−ikτdτ	NOUN
ejpam-3328	508	50	,	,	PUNCT
ejpam-3328	508	51	f̃ε(k	f̃ε(k	PROPN
ejpam-3328	508	52	,	,	PUNCT
ejpam-3328	508	53	α	α	NOUN
ejpam-3328	508	54	)	)	PUNCT
ejpam-3328	508	55	=	=	SYM
ejpam-3328	508	56	1√	1√	NUM
ejpam-3328	508	57	2π	2π	NUM
ejpam-3328	508	58	∫	∫	NOUN
ejpam-3328	508	59	0.9	0.9	NUM
ejpam-3328	508	60	0.1	0.1	NUM
ejpam-3328	508	61	re(fε(τ	re(fε(τ	VERB
ejpam-3328	508	62	+	+	NOUN
ejpam-3328	508	63	iα)e−ikτ	iα)e−ikτ	NOUN
ejpam-3328	508	64	)	)	PUNCT
ejpam-3328	508	65	ds	ds	ADJ
ejpam-3328	508	66	,	,	PUNCT
ejpam-3328	508	67	jε(k	jε(k	PROPN
ejpam-3328	508	68	,	,	PUNCT
ejpam-3328	508	69	α	α	NOUN
ejpam-3328	508	70	)	)	PUNCT
ejpam-3328	508	71	=	=	SYM
ejpam-3328	508	72	1√	1√	NUM
ejpam-3328	508	73	2π	2π	NUM
ejpam-3328	508	74	∫	∫	PROPN
ejpam-3328	508	75	1−ε	1−ε	NUM
ejpam-3328	508	76	ε	ε	PROPN
ejpam-3328	508	77	qε(τ	qε(τ	ADP
ejpam-3328	508	78	−	−	PROPN
ejpam-3328	508	79	iα)eikτdτ	iα)eikτdτ	NOUN
ejpam-3328	508	80	,	,	PUNCT
ejpam-3328	508	81	iε(k	iε(k	PROPN
ejpam-3328	508	82	,	,	PUNCT
ejpam-3328	508	83	α	α	X
ejpam-3328	508	84	)	)	PUNCT
ejpam-3328	508	85	=	=	SYM
ejpam-3328	508	86	1√	1√	NUM
ejpam-3328	508	87	2π	2π	NUM
ejpam-3328	508	88	∫	∫	PROPN
ejpam-3328	508	89	1−ε	1−ε	NUM
ejpam-3328	508	90	ε	ε	PROPN
ejpam-3328	508	91	qε(τ	qε(τ	X
ejpam-3328	508	92	+	+	CCONJ
ejpam-3328	508	93	iα)e−ikτdτ	iα)e−ikτdτ	NOUN
ejpam-3328	508	94	.	.	PUNCT
ejpam-3328	509	1	(	(	PUNCT
ejpam-3328	509	2	21	21	NUM
ejpam-3328	509	3	)	)	PUNCT
ejpam-3328	509	4	to	to	PART
ejpam-3328	509	5	obtain	obtain	VERB
ejpam-3328	509	6	the	the	DET
ejpam-3328	509	7	riemann	riemann	PROPN
ejpam-3328	509	8	–	–	PUNCT
ejpam-3328	509	9	hilbert	hilbert	PROPN
ejpam-3328	509	10	boundary	boundary	ADJ
ejpam-3328	509	11	-	-	PUNCT
ejpam-3328	509	12	value	value	NOUN
ejpam-3328	509	13	problem	problem	NOUN
ejpam-3328	509	14	,	,	PUNCT
ejpam-3328	509	15	the	the	DET
ejpam-3328	509	16	following	follow	VERB
ejpam-3328	509	17	lemma	lemma	PROPN
ejpam-3328	509	18	is	be	AUX
ejpam-3328	509	19	required	require	VERB
ejpam-3328	509	20	.	.	PUNCT
ejpam-3328	510	1	a.	a.	NOUN
ejpam-3328	510	2	durmagambetov	durmagambetov	PROPN
ejpam-3328	510	3	/	/	SYM
ejpam-3328	510	4	eur	eur	PROPN
ejpam-3328	510	5	.	.	PUNCT
ejpam-3328	511	1	j.	j.	PROPN
ejpam-3328	511	2	pure	pure	PROPN
ejpam-3328	511	3	appl	appl	PROPN
ejpam-3328	511	4	.	.	PROPN
ejpam-3328	511	5	math	math	PROPN
ejpam-3328	511	6	,	,	PUNCT
ejpam-3328	511	7	11	11	NUM
ejpam-3328	511	8	(	(	PUNCT
ejpam-3328	511	9	4	4	NUM
ejpam-3328	511	10	)	)	PUNCT
ejpam-3328	511	11	(	(	PUNCT
ejpam-3328	511	12	2018	2018	NUM
ejpam-3328	511	13	)	)	PUNCT
ejpam-3328	511	14	,	,	PUNCT
ejpam-3328	511	15	1143	1143	NUM
ejpam-3328	511	16	-	-	SYM
ejpam-3328	511	17	1176	1176	NUM
ejpam-3328	511	18	1165	1165	NUM
ejpam-3328	511	19	lemma	lemma	PROPN
ejpam-3328	511	20	18	18	NUM
ejpam-3328	511	21	.	.	PUNCT
ejpam-3328	512	1	let	let	VERB
ejpam-3328	512	2	a	a	DET
ejpam-3328	512	3	>	>	X
ejpam-3328	512	4	2	2	NUM
ejpam-3328	512	5	.	.	PUNCT
ejpam-3328	513	1	then	then	ADV
ejpam-3328	513	2	,	,	PUNCT
ejpam-3328	513	3	ind(r	ind(r	PROPN
ejpam-3328	513	4	)	)	PUNCT
ejpam-3328	513	5	=	=	SYM
ejpam-3328	513	6	0	0	X
ejpam-3328	513	7	.	.	PUNCT
ejpam-3328	514	1	proof	proof	NOUN
ejpam-3328	514	2	.	.	PUNCT
ejpam-3328	515	1	by	by	ADP
ejpam-3328	515	2	definition	definition	NOUN
ejpam-3328	515	3	,	,	PUNCT
ejpam-3328	515	4	ind(r	ind(r	NOUN
ejpam-3328	515	5	)	)	PUNCT
ejpam-3328	515	6	=	=	SYM
ejpam-3328	515	7	1	1	NUM
ejpam-3328	515	8	2πi	2πi	NOUN
ejpam-3328	515	9	∫	∫	PROPN
ejpam-3328	516	1	+	+	NUM
ejpam-3328	516	2	∞	∞	PROPN
ejpam-3328	516	3	−∞	−∞	ADP
ejpam-3328	516	4	r(k)′	r(k)′	PROPN
ejpam-3328	516	5	r(k	r(k	PROPN
ejpam-3328	516	6	)	)	PUNCT
ejpam-3328	516	7	dk	dk	NOUN
ejpam-3328	516	8	as	as	ADP
ejpam-3328	516	9	im(k	im(k	NOUN
ejpam-3328	516	10	)	)	PUNCT
ejpam-3328	516	11	<	<	X
ejpam-3328	516	12	0	0	NUM
ejpam-3328	516	13	,	,	PUNCT
ejpam-3328	516	14	|e−ik|	|e−ik|	VERB
ejpam-3328	516	15	<	<	X
ejpam-3328	516	16	1	1	NUM
ejpam-3328	516	17	and	and	CCONJ
ejpam-3328	516	18	|k	|k	NOUN
ejpam-3328	516	19	−	−	PROPN
ejpam-3328	516	20	ia|	ia|	NOUN
ejpam-3328	516	21	>	>	SYM
ejpam-3328	516	22	2	2	NUM
ejpam-3328	516	23	yield	yield	NOUN
ejpam-3328	516	24	r(k)′	r(k)′	PROPN
ejpam-3328	516	25	r(k	r(k	PROPN
ejpam-3328	516	26	)	)	PUNCT
ejpam-3328	516	27	have	have	VERB
ejpam-3328	516	28	no	no	DET
ejpam-3328	516	29	pole	pole	NOUN
ejpam-3328	516	30	.	.	PUNCT
ejpam-3328	517	1	this	this	DET
ejpam-3328	517	2	latest	late	ADJ
ejpam-3328	517	3	statement	statement	NOUN
ejpam-3328	517	4	and	and	CCONJ
ejpam-3328	517	5	lemma	lemma	PROPN
ejpam-3328	517	6	of	of	ADP
ejpam-3328	517	7	jordan	jordan	PROPN
ejpam-3328	517	8	yield	yield	VERB
ejpam-3328	517	9	ind	ind	NOUN
ejpam-3328	517	10	=	=	NOUN
ejpam-3328	517	11	0	0	X
ejpam-3328	517	12	.	.	PUNCT
ejpam-3328	517	13	to	to	PART
ejpam-3328	517	14	obtain	obtain	VERB
ejpam-3328	517	15	the	the	DET
ejpam-3328	517	16	necessary	necessary	ADJ
ejpam-3328	517	17	asymptotics	asymptotic	NOUN
ejpam-3328	517	18	,	,	PUNCT
ejpam-3328	517	19	the	the	DET
ejpam-3328	517	20	following	follow	VERB
ejpam-3328	517	21	lemma	lemma	PROPN
ejpam-3328	517	22	is	be	AUX
ejpam-3328	517	23	required	require	VERB
ejpam-3328	517	24	.	.	PUNCT
ejpam-3328	518	1	lemma	lemma	PROPN
ejpam-3328	518	2	19	19	NUM
ejpam-3328	518	3	.	.	PUNCT
ejpam-3328	519	1	let	let	VERB
ejpam-3328	519	2	a	a	DET
ejpam-3328	519	3	>	>	X
ejpam-3328	519	4	2	2	NUM
ejpam-3328	519	5	.	.	PUNCT
ejpam-3328	520	1	then	then	ADV
ejpam-3328	520	2	,	,	PUNCT
ejpam-3328	520	3	ln(r(k	ln(r(k	X
ejpam-3328	520	4	)	)	PUNCT
ejpam-3328	520	5	)	)	PUNCT
ejpam-3328	520	6	is	be	AUX
ejpam-3328	520	7	a	a	DET
ejpam-3328	520	8	single	single	ADV
ejpam-3328	520	9	-	-	PUNCT
ejpam-3328	520	10	valued	value	VERB
ejpam-3328	520	11	analytical	analytical	ADJ
ejpam-3328	520	12	function	function	NOUN
ejpam-3328	520	13	in	in	ADP
ejpam-3328	520	14	the	the	DET
ejpam-3328	520	15	lower	low	ADJ
ejpam-3328	520	16	half	half	NOUN
ejpam-3328	520	17	plane	plane	NOUN
ejpam-3328	520	18	.	.	PUNCT
ejpam-3328	521	1	proof	proof	NOUN
ejpam-3328	521	2	.	.	PUNCT
ejpam-3328	522	1	im(k	im(k	X
ejpam-3328	522	2	)	)	PUNCT
ejpam-3328	522	3	≤	≤	NOUN
ejpam-3328	522	4	0	0	NUM
ejpam-3328	522	5	yields	yield	NOUN
ejpam-3328	522	6	re(r(k	re(r(k	NOUN
ejpam-3328	522	7	)	)	PUNCT
ejpam-3328	522	8	)	)	PUNCT
ejpam-3328	523	1	=	=	SYM
ejpam-3328	523	2	1	1	NUM
ejpam-3328	523	3	+	+	CCONJ
ejpam-3328	523	4	re	re	ADP
ejpam-3328	523	5	[	[	PUNCT
ejpam-3328	523	6	eik	eik	PROPN
ejpam-3328	523	7	k	k	PROPN
ejpam-3328	523	8	−	−	PROPN
ejpam-3328	523	9	ia	ia	PROPN
ejpam-3328	523	10	]	]	PUNCT
ejpam-3328	523	11	>	>	X
ejpam-3328	523	12	0	0	PROPN
ejpam-3328	523	13	,	,	PUNCT
ejpam-3328	523	14	which	which	PRON
ejpam-3328	523	15	completes	complete	VERB
ejpam-3328	523	16	proof	proof	NOUN
ejpam-3328	523	17	.	.	PUNCT
ejpam-3328	524	1	denote	denote	VERB
ejpam-3328	524	2	ω(s	ω(s	NOUN
ejpam-3328	524	3	)	)	PUNCT
ejpam-3328	524	4	=	=	SYM
ejpam-3328	524	5	re(s−	re(s−	X
ejpam-3328	524	6	sn	sn	NOUN
ejpam-3328	524	7	)	)	PUNCT
ejpam-3328	524	8	and	and	CCONJ
ejpam-3328	524	9	ω(s	ω(s	NOUN
ejpam-3328	524	10	)	)	PUNCT
ejpam-3328	524	11	=	=	PUNCT
ejpam-3328	524	12	(	(	PUNCT
ejpam-3328	524	13	s−sn)ρ(sn)(s−1+sn)ρ(sn	s−sn)ρ(sn)(s−1+sn)ρ(sn	PROPN
ejpam-3328	524	14	)	)	PUNCT
ejpam-3328	524	15	.	.	PUNCT
ejpam-3328	525	1	(	(	PUNCT
ejpam-3328	525	2	1−s	1−s	NUM
ejpam-3328	525	3	)	)	PUNCT
ejpam-3328	525	4	ρ(sn	ρ(sn	NUM
ejpam-3328	525	5	)	)	PUNCT
ejpam-3328	525	6	is	be	AUX
ejpam-3328	525	7	multiplicity	multiplicity	NOUN
ejpam-3328	525	8	root	root	NOUN
ejpam-3328	525	9	of	of	ADP
ejpam-3328	525	10	ζ(s	ζ(s	PROPN
ejpam-3328	525	11	)	)	PUNCT
ejpam-3328	525	12	as	as	SCONJ
ejpam-3328	525	13	s	s	NOUN
ejpam-3328	525	14	=	=	VERB
ejpam-3328	525	15	sn	sn	PROPN
ejpam-3328	525	16	the	the	DET
ejpam-3328	525	17	following	follow	VERB
ejpam-3328	525	18	presents	present	VERB
ejpam-3328	525	19	results	result	NOUN
ejpam-3328	525	20	of	of	ADP
ejpam-3328	525	21	[	[	X
ejpam-3328	525	22	34	34	NUM
ejpam-3328	525	23	]	]	X
ejpam-3328	525	24	theorem	theorem	NOUN
ejpam-3328	525	25	of	of	ADP
ejpam-3328	525	26	backlund	backlund	PROPN
ejpam-3328	525	27	r.	r.	PROPN
ejpam-3328	525	28	let	let	VERB
ejpam-3328	525	29	ζ(sn	ζ(sn	ADJ
ejpam-3328	525	30	)	)	PUNCT
ejpam-3328	526	1	=	=	SYM
ejpam-3328	526	2	0	0	NUM
ejpam-3328	526	3	then	then	ADV
ejpam-3328	526	4	ρ(sn	ρ(sn	NUM
ejpam-3328	526	5	)	)	PUNCT
ejpam-3328	526	6	<	<	X
ejpam-3328	526	7	c0ln|sn|	c0ln|sn|	PROPN
ejpam-3328	526	8	.	.	PUNCT
ejpam-3328	527	1	to	to	PART
ejpam-3328	527	2	obtain	obtain	VERB
ejpam-3328	527	3	the	the	DET
ejpam-3328	527	4	necessary	necessary	ADJ
ejpam-3328	527	5	asymptotics	asymptotic	NOUN
ejpam-3328	527	6	,	,	PUNCT
ejpam-3328	527	7	the	the	DET
ejpam-3328	527	8	following	follow	VERB
ejpam-3328	527	9	lemma	lemma	PROPN
ejpam-3328	527	10	is	be	AUX
ejpam-3328	527	11	required	require	VERB
ejpam-3328	527	12	.	.	PUNCT
ejpam-3328	528	1	lemma	lemma	PROPN
ejpam-3328	528	2	20	20	NUM
ejpam-3328	528	3	.	.	PUNCT
ejpam-3328	529	1	let	let	VERB
ejpam-3328	529	2	γn	γn	NOUN
ejpam-3328	529	3	=	=	NOUN
ejpam-3328	529	4	1	1	NUM
ejpam-3328	529	5	4ρ(sn	4ρ(sn	NUM
ejpam-3328	529	6	)	)	PUNCT
ejpam-3328	529	7	,	,	PUNCT
ejpam-3328	529	8	|ω(1/2)|	|ω(1/2)|	X
ejpam-3328	530	1	=	=	PRON
ejpam-3328	530	2	εn	εn	ADJ
ejpam-3328	530	3	>	>	X
ejpam-3328	530	4	0	0	NUM
ejpam-3328	530	5	,	,	PUNCT
ejpam-3328	530	6	and	and	CCONJ
ejpam-3328	530	7	dn	dn	NOUN
ejpam-3328	530	8	=	=	SYM
ejpam-3328	530	9	(	(	PUNCT
ejpam-3328	530	10	im(sn+1)−	im(sn+1)−	PROPN
ejpam-3328	530	11	im(sn))/2	im(sn))/2	NOUN
ejpam-3328	530	12	.	.	PUNCT
ejpam-3328	531	1	then	then	ADV
ejpam-3328	531	2	,	,	PUNCT
ejpam-3328	531	3	we	we	PRON
ejpam-3328	531	4	have	have	VERB
ejpam-3328	531	5	the	the	DET
ejpam-3328	531	6	following	follow	VERB
ejpam-3328	531	7	estimate	estimate	NOUN
ejpam-3328	531	8	as	as	ADP
ejpam-3328	531	9	ε	ε	PROPN
ejpam-3328	531	10	=	=	PUNCT
ejpam-3328	531	11	0.01ε2n	0.01ε2n	PROPN
ejpam-3328	531	12	:	:	PUNCT
ejpam-3328	531	13	sup	sup	NUM
ejpam-3328	531	14	imsn−dn≤α≤imsn+dn	imsn−dn≤α≤imsn+dn	NOUN
ejpam-3328	531	15	∫	∫	PROPN
ejpam-3328	531	16	1−ε	1−ε	PROPN
ejpam-3328	531	17	ε	ε	PROPN
ejpam-3328	531	18	|qε(τ	|qε(τ	NOUN
ejpam-3328	532	1	+	+	CCONJ
ejpam-3328	532	2	iα)|2	iα)|2	NOUN
ejpam-3328	532	3	+	+	CCONJ
ejpam-3328	532	4	|qε(τ	|qε(τ	X
ejpam-3328	532	5	+	+	CCONJ
ejpam-3328	532	6	iα)|	iα)|	PRON
ejpam-3328	532	7	dτ	dτ	NOUN
ejpam-3328	532	8	<	<	X
ejpam-3328	532	9	cncεncγ	cncεncγ	X
ejpam-3328	532	10	,	,	PUNCT
ejpam-3328	532	11	sup	sup	PROPN
ejpam-3328	532	12	−imsn−dn≤α≤−imsn+dn	−imsn−dn≤α≤−imsn+dn	SYM
ejpam-3328	532	13	∫	∫	PROPN
ejpam-3328	532	14	1−ε	1−ε	PROPN
ejpam-3328	532	15	ε	ε	PROPN
ejpam-3328	533	1	|qε(τ	|qε(τ	NOUN
ejpam-3328	533	2	−	−	PROPN
ejpam-3328	533	3	iα)|2	iα)|2	NOUN
ejpam-3328	533	4	+	+	CCONJ
ejpam-3328	533	5	|qε(τ	|qε(τ	ADP
ejpam-3328	533	6	−	−	ADP
ejpam-3328	533	7	iα)|	iα)|	PUNCT
ejpam-3328	533	8	dτ	dτ	INTJ
ejpam-3328	533	9	<	<	X
ejpam-3328	533	10	cncεncγ	cncεncγ	X
ejpam-3328	533	11	,	,	PUNCT
ejpam-3328	533	12	sup	sup	PROPN
ejpam-3328	533	13	imsn−dn≤α≤imsn+dn	imsn−dn≤α≤imsn+dn	PROPN
ejpam-3328	533	14	∫	∫	PROPN
ejpam-3328	533	15	1−ε	1−ε	PROPN
ejpam-3328	533	16	ε	ε	VERB
ejpam-3328	533	17	|fε(τ	|fε(τ	ADP
ejpam-3328	533	18	+	+	CCONJ
ejpam-3328	533	19	iα)|2	iα)|2	NOUN
ejpam-3328	533	20	+	+	CCONJ
ejpam-3328	533	21	|fε(τ	|fε(τ	X
ejpam-3328	533	22	+	+	CCONJ
ejpam-3328	533	23	iα)|	iα)|	PRON
ejpam-3328	533	24	dτ	dτ	NOUN
ejpam-3328	533	25	<	<	X
ejpam-3328	533	26	cncεncγ	cncεncγ	X
ejpam-3328	533	27	,	,	PUNCT
ejpam-3328	533	28	sup	sup	PROPN
ejpam-3328	533	29	−imsn−dn≤α≤−imsn+dn	−imsn−dn≤α≤−imsn+dn	SYM
ejpam-3328	533	30	∫	∫	PROPN
ejpam-3328	533	31	1−ε	1−ε	PROPN
ejpam-3328	533	32	ε	ε	VERB
ejpam-3328	533	33	|fε(τ	|fε(τ	ADP
ejpam-3328	533	34	−	−	PROPN
ejpam-3328	533	35	iα)|2	iα)|2	NOUN
ejpam-3328	533	36	+	+	CCONJ
ejpam-3328	533	37	|fε(τ	|fε(τ	ADP
ejpam-3328	533	38	−	−	PROPN
ejpam-3328	533	39	iα)|	iα)|	ADJ
ejpam-3328	533	40	dτ	dτ	NOUN
ejpam-3328	533	41	<	<	X
ejpam-3328	533	42	cncεncγ	cncεncγ	PROPN
ejpam-3328	533	43	.	.	PUNCT
ejpam-3328	534	1	a.	a.	NOUN
ejpam-3328	534	2	durmagambetov	durmagambetov	PROPN
ejpam-3328	534	3	/	/	SYM
ejpam-3328	534	4	eur	eur	PROPN
ejpam-3328	534	5	.	.	PUNCT
ejpam-3328	535	1	j.	j.	PROPN
ejpam-3328	535	2	pure	pure	PROPN
ejpam-3328	535	3	appl	appl	PROPN
ejpam-3328	535	4	.	.	PROPN
ejpam-3328	535	5	math	math	PROPN
ejpam-3328	535	6	,	,	PUNCT
ejpam-3328	535	7	11	11	NUM
ejpam-3328	535	8	(	(	PUNCT
ejpam-3328	535	9	4	4	NUM
ejpam-3328	535	10	)	)	PUNCT
ejpam-3328	535	11	(	(	PUNCT
ejpam-3328	535	12	2018	2018	NUM
ejpam-3328	535	13	)	)	PUNCT
ejpam-3328	535	14	,	,	PUNCT
ejpam-3328	535	15	1143	1143	NUM
ejpam-3328	535	16	-	-	SYM
ejpam-3328	535	17	1176	1176	NUM
ejpam-3328	535	18	1166	1166	NUM
ejpam-3328	535	19	proof	proof	NOUN
ejpam-3328	535	20	.	.	PUNCT
ejpam-3328	536	1	by	by	ADP
ejpam-3328	536	2	the	the	DET
ejpam-3328	536	3	definition	definition	NOUN
ejpam-3328	536	4	of	of	ADP
ejpam-3328	536	5	qε(s	qε(s	NOUN
ejpam-3328	536	6	)	)	PUNCT
ejpam-3328	536	7	,	,	PUNCT
ejpam-3328	536	8	we	we	PRON
ejpam-3328	536	9	have	have	AUX
ejpam-3328	536	10	iq	iq	VERB
ejpam-3328	536	11	=	=	SYM
ejpam-3328	536	12	∫	∫	PROPN
ejpam-3328	536	13	1−ε	1−ε	PROPN
ejpam-3328	536	14	ε	ε	PROPN
ejpam-3328	536	15	|qε(τ	|qε(τ	NOUN
ejpam-3328	537	1	+	+	CCONJ
ejpam-3328	537	2	iα)|2	iα)|2	NOUN
ejpam-3328	537	3	+	+	CCONJ
ejpam-3328	537	4	|qε(τ	|qε(τ	X
ejpam-3328	537	5	+	+	CCONJ
ejpam-3328	537	6	iα)|	iα)|	PRON
ejpam-3328	537	7	dτ	dτ	NOUN
ejpam-3328	537	8	=	=	SYM
ejpam-3328	537	9	∫	∫	PROPN
ejpam-3328	537	10	1−ε	1−ε	PROPN
ejpam-3328	537	11	ε	ε	PROPN
ejpam-3328	537	12	|ln	|ln	PUNCT
ejpam-3328	537	13	|ζ(τ	|ζ(τ	PROPN
ejpam-3328	537	14	+	+	CCONJ
ejpam-3328	537	15	iα)||2	iα)||2	PROPN
ejpam-3328	537	16	+	+	CCONJ
ejpam-3328	537	17	|ln	|ln	X
ejpam-3328	537	18	|ζ(τ	|ζ(τ	PROPN
ejpam-3328	537	19	+	+	CCONJ
ejpam-3328	537	20	iα)||	iα)||	PROPN
ejpam-3328	537	21	dτ	dτ	NOUN
ejpam-3328	537	22	≤	≤	NUM
ejpam-3328	537	23	∫	∫	PROPN
ejpam-3328	537	24	1−ε	1−ε	PROPN
ejpam-3328	537	25	ε	ε	PROPN
ejpam-3328	537	26	∣∣∣∣ln	∣∣∣∣ln	PROPN
ejpam-3328	537	27	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3328	537	28	ζ(τ	ζ(τ	PROPN
ejpam-3328	537	29	+	+	CCONJ
ejpam-3328	537	30	iα	iα	ADJ
ejpam-3328	537	31	)	)	PUNCT
ejpam-3328	537	32	ω(τ	ω(τ	PROPN
ejpam-3328	537	33	+	+	CCONJ
ejpam-3328	537	34	iα	iα	NOUN
ejpam-3328	537	35	)	)	PUNCT
ejpam-3328	537	36	∣∣∣∣∣∣∣∣2	∣∣∣∣∣∣∣∣2	NOUN
ejpam-3328	537	37	+	+	CCONJ
ejpam-3328	537	38	∣∣∣∣ln	∣∣∣∣ln	NOUN
ejpam-3328	537	39	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3328	537	40	1	1	NUM
ejpam-3328	537	41	ω(τ	ω(τ	PROPN
ejpam-3328	537	42	+	+	CCONJ
ejpam-3328	537	43	iα	iα	NOUN
ejpam-3328	537	44	)	)	PUNCT
ejpam-3328	537	45	∣∣∣∣∣∣∣∣2	∣∣∣∣∣∣∣∣2	NOUN
ejpam-3328	537	46	+	+	CCONJ
ejpam-3328	537	47	∣∣∣∣ln	∣∣∣∣ln	NOUN
ejpam-3328	537	48	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3328	537	49	ζ(τ	ζ(τ	PROPN
ejpam-3328	537	50	+	+	CCONJ
ejpam-3328	537	51	iα	iα	ADJ
ejpam-3328	537	52	)	)	PUNCT
ejpam-3328	537	53	ω(τ	ω(τ	PROPN
ejpam-3328	537	54	+	+	CCONJ
ejpam-3328	537	55	iα	iα	NOUN
ejpam-3328	537	56	)	)	PUNCT
ejpam-3328	537	57	∣∣∣∣∣∣∣∣+	∣∣∣∣∣∣∣∣+	PROPN
ejpam-3328	537	58	∣∣∣∣ln	∣∣∣∣ln	PROPN
ejpam-3328	537	59	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3328	537	60	1	1	NUM
ejpam-3328	537	61	ω(τ	ω(τ	PROPN
ejpam-3328	537	62	+	+	CCONJ
ejpam-3328	537	63	iα	iα	ADJ
ejpam-3328	537	64	)	)	PUNCT
ejpam-3328	537	65	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	ADP
ejpam-3328	537	66	dτ	dτ	PROPN
ejpam-3328	537	67	.	.	PROPN
ejpam-3328	537	68	denote	denote	PROPN
ejpam-3328	537	69	lmax	lmax	NOUN
ejpam-3328	537	70	=	=	PUNCT
ejpam-3328	537	71	max	max	PROPN
ejpam-3328	537	72	s∈d(n)∪d(n	s∈d(n)∪d(n	PROPN
ejpam-3328	537	73	)	)	PUNCT
ejpam-3328	537	74	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3328	537	75	ζ(s	ζ(s	NOUN
ejpam-3328	537	76	)	)	PUNCT
ejpam-3328	537	77	ω(s	ω(s	NOUN
ejpam-3328	537	78	)	)	PUNCT
ejpam-3328	537	79	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3328	537	80	,	,	PUNCT
ejpam-3328	537	81	lmin	lmin	NOUN
ejpam-3328	537	82	=	=	SYM
ejpam-3328	537	83	min	min	NOUN
ejpam-3328	537	84	s∈d(n)∪d(n	s∈d(n)∪d(n	PROPN
ejpam-3328	537	85	)	)	PUNCT
ejpam-3328	537	86	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3328	537	87	ζ(s	ζ(s	NOUN
ejpam-3328	537	88	)	)	PUNCT
ejpam-3328	537	89	ω(s	ω(s	NOUN
ejpam-3328	537	90	)	)	PUNCT
ejpam-3328	537	91	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3328	537	92	.	.	PUNCT
ejpam-3328	538	1	then	then	ADV
ejpam-3328	538	2	,	,	PUNCT
ejpam-3328	538	3	iq	iq	PROPN
ejpam-3328	538	4	≤	≤	PUNCT
ejpam-3328	538	5	∣∣∣∣ln	∣∣∣∣ln	AUX
ejpam-3328	538	6	∣∣∣∣lmax	∣∣∣∣lmax	VERB
ejpam-3328	538	7	+	+	CCONJ
ejpam-3328	538	8	1	1	NUM
ejpam-3328	538	9	lmin	lmin	NOUN
ejpam-3328	538	10	∣∣∣∣∣∣∣∣+∣∣∣∣ln	∣∣∣∣∣∣∣∣+∣∣∣∣ln	X
ejpam-3328	538	11	∣∣∣∣lmax	∣∣∣∣lmax	NOUN
ejpam-3328	538	12	+	+	CCONJ
ejpam-3328	538	13	1	1	NUM
ejpam-3328	538	14	lmin	lmin	NOUN
ejpam-3328	538	15	∣∣∣∣∣∣∣∣2	∣∣∣∣∣∣∣∣2	NOUN
ejpam-3328	538	16	+	+	PROPN
ejpam-3328	538	17	cγ	cγ	ADJ
ejpam-3328	538	18	∫	∫	PROPN
ejpam-3328	538	19	1−ε	1−ε	PROPN
ejpam-3328	538	20	ε	ε	PROPN
ejpam-3328	538	21	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3328	538	22	1	1	NUM
ejpam-3328	538	23	ω(τ	ω(τ	PROPN
ejpam-3328	538	24	+	+	CCONJ
ejpam-3328	538	25	iα	iα	NOUN
ejpam-3328	538	26	)	)	PUNCT
ejpam-3328	538	27	∣∣∣∣2γ+	∣∣∣∣2γ+	ADJ
ejpam-3328	538	28	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3328	538	29	1	1	NUM
ejpam-3328	538	30	ω(τ	ω(τ	PROPN
ejpam-3328	538	31	+	+	CCONJ
ejpam-3328	538	32	iα	iα	NOUN
ejpam-3328	538	33	)	)	PUNCT
ejpam-3328	538	34	∣∣∣∣γ	∣∣∣∣γ	PROPN
ejpam-3328	538	35	dτ	dτ	PROPN
ejpam-3328	538	36	,	,	PUNCT
ejpam-3328	538	37	which	which	PRON
ejpam-3328	538	38	completes	complete	VERB
ejpam-3328	538	39	the	the	DET
ejpam-3328	538	40	proof	proof	NOUN
ejpam-3328	538	41	.	.	PUNCT
ejpam-3328	539	1	the	the	DET
ejpam-3328	539	2	previous	previous	ADJ
ejpam-3328	539	3	constructions	construction	NOUN
ejpam-3328	539	4	allow	allow	VERB
ejpam-3328	539	5	the	the	DET
ejpam-3328	539	6	calculation	calculation	NOUN
ejpam-3328	539	7	of	of	ADP
ejpam-3328	539	8	the	the	DET
ejpam-3328	539	9	asymptotics	asymptotic	NOUN
ejpam-3328	539	10	as	as	SCONJ
ejpam-3328	539	11	follows	follow	VERB
ejpam-3328	539	12	.	.	PUNCT
ejpam-3328	540	1	lemma	lemma	PROPN
ejpam-3328	540	2	21	21	NUM
ejpam-3328	540	3	.	.	PUNCT
ejpam-3328	541	1	let	let	VERB
ejpam-3328	541	2	(	(	PUNCT
ejpam-3328	541	3	3/4	3/4	NUM
ejpam-3328	541	4	+	+	CCONJ
ejpam-3328	541	5	iα	iα	NOUN
ejpam-3328	541	6	)	)	PUNCT
ejpam-3328	541	7	∈	∈	PROPN
ejpam-3328	541	8	d(n	d(n	PROPN
ejpam-3328	541	9	)	)	PUNCT
ejpam-3328	541	10	.	.	PUNCT
ejpam-3328	542	1	then	then	ADV
ejpam-3328	542	2	,	,	PUNCT
ejpam-3328	542	3	lim	lim	PROPN
ejpam-3328	542	4	im(k)→−∞	im(k)→−∞	PROPN
ejpam-3328	542	5	iε(k	iε(k	PROPN
ejpam-3328	542	6	,	,	PUNCT
ejpam-3328	542	7	α	α	X
ejpam-3328	542	8	)	)	PUNCT
ejpam-3328	542	9	=	=	SYM
ejpam-3328	542	10	0	0	PROPN
ejpam-3328	542	11	,	,	PUNCT
ejpam-3328	542	12	lim	lim	PROPN
ejpam-3328	542	13	im(k)→∞	im(k)→∞	PROPN
ejpam-3328	542	14	jε(k	jε(k	PROPN
ejpam-3328	542	15	,	,	PUNCT
ejpam-3328	542	16	α	α	NOUN
ejpam-3328	542	17	)	)	PUNCT
ejpam-3328	542	18	=	=	SYM
ejpam-3328	542	19	0	0	NUM
ejpam-3328	542	20	,	,	PUNCT
ejpam-3328	542	21	(	(	PUNCT
ejpam-3328	542	22	22	22	NUM
ejpam-3328	542	23	)	)	PUNCT
ejpam-3328	542	24	and	and	CCONJ
ejpam-3328	542	25	,	,	PUNCT
ejpam-3328	542	26	as	as	ADP
ejpam-3328	542	27	im(k	im(k	NUM
ejpam-3328	542	28	)	)	PUNCT
ejpam-3328	542	29	=	=	SYM
ejpam-3328	542	30	0	0	PROPN
ejpam-3328	542	31	,	,	PUNCT
ejpam-3328	542	32	lim	lim	PROPN
ejpam-3328	542	33	re(k)→∞	re(k)→∞	PROPN
ejpam-3328	542	34	iε(k	iε(k	PROPN
ejpam-3328	542	35	,	,	PUNCT
ejpam-3328	542	36	α	α	X
ejpam-3328	542	37	)	)	PUNCT
ejpam-3328	542	38	=	=	SYM
ejpam-3328	542	39	0	0	PROPN
ejpam-3328	542	40	,	,	PUNCT
ejpam-3328	542	41	lim	lim	PROPN
ejpam-3328	542	42	re(k)→∞	re(k)→∞	PROPN
ejpam-3328	542	43	jε(k	jε(k	PROPN
ejpam-3328	542	44	,	,	PUNCT
ejpam-3328	542	45	α	α	X
ejpam-3328	542	46	)	)	PUNCT
ejpam-3328	542	47	=	=	SYM
ejpam-3328	543	1	0	0	X
ejpam-3328	543	2	.	.	PUNCT
ejpam-3328	544	1	(	(	PUNCT
ejpam-3328	544	2	23	23	X
ejpam-3328	544	3	)	)	PUNCT
ejpam-3328	544	4	proof	proof	NOUN
ejpam-3328	544	5	.	.	PUNCT
ejpam-3328	545	1	lemma	lemma	PROPN
ejpam-3328	545	2	20	20	NUM
ejpam-3328	545	3	yields	yield	NOUN
ejpam-3328	545	4	|iε(k	|iε(k	NUM
ejpam-3328	545	5	,	,	PUNCT
ejpam-3328	545	6	α)|	α)|	VERB
ejpam-3328	545	7	=	=	SYM
ejpam-3328	545	8	∣∣∣∣∫	∣∣∣∣∫	PRON
ejpam-3328	545	9	1−ε	1−ε	NUM
ejpam-3328	546	1	ε	ε	PROPN
ejpam-3328	546	2	qε(τ	qε(τ	X
ejpam-3328	546	3	+	+	CCONJ
ejpam-3328	546	4	iα)e−ikτdτ	iα)e−ikτdτ	NOUN
ejpam-3328	546	5	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3328	546	6	≤	≤	NUM
ejpam-3328	546	7	∫	∫	PROPN
ejpam-3328	546	8	1−ε	1−ε	PROPN
ejpam-3328	546	9	ε	ε	PROPN
ejpam-3328	546	10	(	(	PUNCT
ejpam-3328	546	11	|qε(τ	|qε(τ	X
ejpam-3328	546	12	+	+	CCONJ
ejpam-3328	546	13	iα)|2	iα)|2	NOUN
ejpam-3328	546	14	dτ	dτ	NOUN
ejpam-3328	546	15	)	)	PUNCT
ejpam-3328	546	16	1/2	1/2	NUM
ejpam-3328	546	17	1	1	NUM
ejpam-3328	546	18	|im(k)|1/2	|im(k)|1/2	ADJ
ejpam-3328	546	19	.	.	PUNCT
ejpam-3328	547	1	a	a	DET
ejpam-3328	547	2	similar	similar	ADJ
ejpam-3328	547	3	argument	argument	NOUN
ejpam-3328	547	4	is	be	AUX
ejpam-3328	547	5	used	use	VERB
ejpam-3328	547	6	for	for	ADP
ejpam-3328	547	7	the	the	DET
ejpam-3328	547	8	function	function	NOUN
ejpam-3328	547	9	jε(k	jε(k	NOUN
ejpam-3328	547	10	,	,	PUNCT
ejpam-3328	547	11	α	α	NOUN
ejpam-3328	547	12	)	)	PUNCT
ejpam-3328	548	1	=	=	SYM
ejpam-3328	548	2	1√	1√	NUM
ejpam-3328	548	3	2π	2π	NUM
ejpam-3328	548	4	∫	∫	PROPN
ejpam-3328	548	5	1−ε	1−ε	NUM
ejpam-3328	548	6	ε	ε	PROPN
ejpam-3328	548	7	qε(τ	qε(τ	VERB
ejpam-3328	548	8	−	−	PROPN
ejpam-3328	548	9	iα)eikτdτ	iα)eikτdτ	NOUN
ejpam-3328	548	10	.	.	PUNCT
ejpam-3328	549	1	as	as	ADP
ejpam-3328	549	2	im(k	im(k	NUM
ejpam-3328	549	3	)	)	PUNCT
ejpam-3328	549	4	>	>	X
ejpam-3328	549	5	0	0	NUM
ejpam-3328	549	6	,	,	PUNCT
ejpam-3328	549	7	jε(k	jε(k	PROPN
ejpam-3328	549	8	,	,	PUNCT
ejpam-3328	549	9	α	α	X
ejpam-3328	549	10	)	)	PUNCT
ejpam-3328	549	11	can	can	AUX
ejpam-3328	549	12	be	be	AUX
ejpam-3328	549	13	estimated	estimate	VERB
ejpam-3328	549	14	using	use	VERB
ejpam-3328	549	15	the	the	DET
ejpam-3328	549	16	last	last	ADJ
ejpam-3328	549	17	expression	expression	NOUN
ejpam-3328	549	18	and	and	CCONJ
ejpam-3328	549	19	lemma	lemma	PROPN
ejpam-3328	549	20	5	5	NUM
ejpam-3328	549	21	as	as	SCONJ
ejpam-3328	549	22	follows	follow	VERB
ejpam-3328	549	23	:	:	PUNCT
ejpam-3328	549	24	|jε(k	|jε(k	NUM
ejpam-3328	549	25	,	,	PUNCT
ejpam-3328	549	26	α)|	α)|	VERB
ejpam-3328	549	27	<	<	X
ejpam-3328	549	28	∫	∫	PROPN
ejpam-3328	549	29	1−ε	1−ε	PROPN
ejpam-3328	549	30	ε	ε	PROPN
ejpam-3328	549	31	(	(	PUNCT
ejpam-3328	549	32	|qε(τ	|qε(τ	ADP
ejpam-3328	549	33	−	−	PRON
ejpam-3328	549	34	iα)|2	iα)|2	NOUN
ejpam-3328	549	35	dτ	dτ	PROPN
ejpam-3328	549	36	)	)	PUNCT
ejpam-3328	549	37	1/2	1/2	NUM
ejpam-3328	549	38	1	1	NUM
ejpam-3328	549	39	|im(k)|1/2	|im(k)|1/2	ADJ
ejpam-3328	549	40	.	.	PUNCT
ejpam-3328	550	1	as	as	ADP
ejpam-3328	550	2	im(k	im(k	NUM
ejpam-3328	550	3	)	)	PUNCT
ejpam-3328	550	4	=	=	SYM
ejpam-3328	550	5	0	0	NUM
ejpam-3328	550	6	,	,	PUNCT
ejpam-3328	550	7	by	by	ADP
ejpam-3328	550	8	the	the	DET
ejpam-3328	550	9	riemann	riemann	PROPN
ejpam-3328	550	10	–	–	PUNCT
ejpam-3328	550	11	lebesgue	lebesgue	PROPN
ejpam-3328	550	12	lemma	lemma	PROPN
ejpam-3328	550	13	,	,	PUNCT
ejpam-3328	550	14	we	we	PRON
ejpam-3328	550	15	have	have	VERB
ejpam-3328	550	16	lim	lim	PROPN
ejpam-3328	550	17	re(k)→∞	re(k)→∞	PROPN
ejpam-3328	550	18	iε(k	iε(k	PROPN
ejpam-3328	550	19	,	,	PUNCT
ejpam-3328	550	20	α	α	X
ejpam-3328	550	21	)	)	PUNCT
ejpam-3328	550	22	=	=	SYM
ejpam-3328	550	23	0	0	PROPN
ejpam-3328	550	24	,	,	PUNCT
ejpam-3328	550	25	lim	lim	PROPN
ejpam-3328	550	26	re(k)→∞	re(k)→∞	PROPN
ejpam-3328	550	27	jε(k	jε(k	PROPN
ejpam-3328	550	28	,	,	PUNCT
ejpam-3328	550	29	α	α	X
ejpam-3328	550	30	)	)	PUNCT
ejpam-3328	551	1	=	=	SYM
ejpam-3328	551	2	0	0	NUM
ejpam-3328	551	3	,	,	PUNCT
ejpam-3328	551	4	(	(	PUNCT
ejpam-3328	551	5	24	24	NUM
ejpam-3328	551	6	)	)	PUNCT
ejpam-3328	551	7	a.	a.	NOUN
ejpam-3328	551	8	durmagambetov	durmagambetov	PROPN
ejpam-3328	551	9	/	/	SYM
ejpam-3328	551	10	eur	eur	PROPN
ejpam-3328	551	11	.	.	PUNCT
ejpam-3328	552	1	j.	j.	PROPN
ejpam-3328	552	2	pure	pure	PROPN
ejpam-3328	552	3	appl	appl	PROPN
ejpam-3328	552	4	.	.	PROPN
ejpam-3328	552	5	math	math	PROPN
ejpam-3328	552	6	,	,	PUNCT
ejpam-3328	552	7	11	11	NUM
ejpam-3328	552	8	(	(	PUNCT
ejpam-3328	552	9	4	4	NUM
ejpam-3328	552	10	)	)	PUNCT
ejpam-3328	552	11	(	(	PUNCT
ejpam-3328	552	12	2018	2018	NUM
ejpam-3328	552	13	)	)	PUNCT
ejpam-3328	552	14	,	,	PUNCT
ejpam-3328	552	15	1143	1143	NUM
ejpam-3328	552	16	-	-	SYM
ejpam-3328	552	17	1176	1176	NUM
ejpam-3328	552	18	1167	1167	NUM
ejpam-3328	552	19	which	which	PRON
ejpam-3328	552	20	completes	complete	VERB
ejpam-3328	552	21	the	the	DET
ejpam-3328	552	22	proof	proof	NOUN
ejpam-3328	552	23	.	.	PUNCT
ejpam-3328	553	1	for	for	ADP
ejpam-3328	553	2	f	f	PROPN
ejpam-3328	553	3	∈	∈	PROPN
ejpam-3328	553	4	w	w	PROPN
ejpam-3328	553	5	1	1	NUM
ejpam-3328	553	6	2	2	NUM
ejpam-3328	553	7	(	(	PUNCT
ejpam-3328	553	8	r	r	NOUN
ejpam-3328	553	9	)	)	PUNCT
ejpam-3328	553	10	=	=	SYM
ejpam-3328	553	11	{	{	PUNCT
ejpam-3328	553	12	f	f	PROPN
ejpam-3328	553	13	∈	∈	PROPN
ejpam-3328	553	14	l2(r	l2(r	PROPN
ejpam-3328	553	15	)	)	PUNCT
ejpam-3328	553	16	:	:	PUNCT
ejpam-3328	553	17	(	(	PUNCT
ejpam-3328	553	18	1	1	NUM
ejpam-3328	553	19	+	+	NUM
ejpam-3328	553	20	|ω|2)1/2f̂(ω	|ω|2)1/2f̂(ω	NUM
ejpam-3328	553	21	)	)	PUNCT
ejpam-3328	553	22	∈	∈	NOUN
ejpam-3328	553	23	l2	l2	NOUN
ejpam-3328	553	24	)	)	PUNCT
ejpam-3328	553	25	}	}	PUNCT
ejpam-3328	553	26	,	,	PUNCT
ejpam-3328	553	27	the	the	DET
ejpam-3328	553	28	operators	operator	NOUN
ejpam-3328	553	29	t±	t±	X
ejpam-3328	553	30	and	and	CCONJ
ejpam-3328	553	31	t	t	PROPN
ejpam-3328	553	32	are	be	AUX
ejpam-3328	553	33	defined	define	VERB
ejpam-3328	553	34	as	as	SCONJ
ejpam-3328	553	35	follows	follow	VERB
ejpam-3328	553	36	:	:	PUNCT
ejpam-3328	554	1	t+f	t+f	NUM
ejpam-3328	554	2	=	=	SYM
ejpam-3328	554	3	1	1	NUM
ejpam-3328	554	4	2πi	2πi	NOUN
ejpam-3328	554	5	lim	lim	PROPN
ejpam-3328	554	6	imz→0	imz→0	PROPN
ejpam-3328	554	7	∞∫	∞∫	PROPN
ejpam-3328	554	8	−∞	−∞	ADP
ejpam-3328	554	9	f(s	f(	NOUN
ejpam-3328	554	10	)	)	PUNCT
ejpam-3328	554	11	s−	s−	PROPN
ejpam-3328	554	12	z	z	PROPN
ejpam-3328	554	13	ds	ds	PROPN
ejpam-3328	554	14	,	,	PUNCT
ejpam-3328	554	15	i	i	PRON
ejpam-3328	554	16	m	m	VERB
ejpam-3328	554	17	z	z	NOUN
ejpam-3328	554	18	>	>	X
ejpam-3328	554	19	0	0	NUM
ejpam-3328	554	20	,	,	PUNCT
ejpam-3328	554	21	t−f	t−f	X
ejpam-3328	554	22	=	=	SYM
ejpam-3328	554	23	1	1	NUM
ejpam-3328	554	24	2πi	2πi	NOUN
ejpam-3328	554	25	lim	lim	PROPN
ejpam-3328	554	26	imz→0	imz→0	PROPN
ejpam-3328	554	27	∞∫	∞∫	PROPN
ejpam-3328	554	28	−∞	−∞	ADP
ejpam-3328	554	29	f(s	f(	NOUN
ejpam-3328	554	30	)	)	PUNCT
ejpam-3328	554	31	s−	s−	PROPN
ejpam-3328	554	32	z	z	PROPN
ejpam-3328	554	33	ds	ds	PROPN
ejpam-3328	554	34	,	,	PUNCT
ejpam-3328	554	35	i	i	PRON
ejpam-3328	554	36	m	m	VERB
ejpam-3328	554	37	z	z	NOUN
ejpam-3328	554	38	<	<	X
ejpam-3328	554	39	0	0	PROPN
ejpam-3328	554	40	,	,	PUNCT
ejpam-3328	554	41	t	t	PROPN
ejpam-3328	554	42	f	f	PROPN
ejpam-3328	554	43	=	=	SYM
ejpam-3328	554	44	1	1	NUM
ejpam-3328	554	45	2	2	NUM
ejpam-3328	554	46	(	(	PUNCT
ejpam-3328	554	47	t+	t+	NOUN
ejpam-3328	554	48	+	+	CCONJ
ejpam-3328	554	49	t−)f	t−)f	NOUN
ejpam-3328	554	50	.	.	PUNCT
ejpam-3328	555	1	these	these	DET
ejpam-3328	555	2	operators	operator	NOUN
ejpam-3328	555	3	are	be	AUX
ejpam-3328	555	4	closely	closely	ADV
ejpam-3328	555	5	related	relate	VERB
ejpam-3328	555	6	to	to	ADP
ejpam-3328	555	7	the	the	DET
ejpam-3328	555	8	hilbert	hilbert	NOUN
ejpam-3328	555	9	transform	transform	NOUN
ejpam-3328	555	10	,	,	PUNCT
ejpam-3328	555	11	whose	whose	DET
ejpam-3328	555	12	isometric	isometric	ADJ
ejpam-3328	555	13	properties	property	NOUN
ejpam-3328	555	14	were	be	AUX
ejpam-3328	555	15	studied	study	VERB
ejpam-3328	555	16	by	by	ADP
ejpam-3328	555	17	poincaré.	poincaré.	PROPN
ejpam-3328	555	18	the	the	DET
ejpam-3328	555	19	following	follow	VERB
ejpam-3328	555	20	result	result	NOUN
ejpam-3328	555	21	is	be	AUX
ejpam-3328	555	22	from	from	ADP
ejpam-3328	555	23	[	[	X
ejpam-3328	555	24	33	33	NUM
ejpam-3328	555	25	]	]	PUNCT
ejpam-3328	555	26	.	.	PUNCT
ejpam-3328	556	1	lemma	lemma	PROPN
ejpam-3328	556	2	22	22	NUM
ejpam-3328	556	3	.	.	PUNCT
ejpam-3328	557	1	tt	tt	X
ejpam-3328	557	2	=	=	NOUN
ejpam-3328	558	1	1	1	NUM
ejpam-3328	558	2	4	4	NUM
ejpam-3328	558	3	i	i	NOUN
ejpam-3328	558	4	,	,	PUNCT
ejpam-3328	558	5	tt+	tt+	NOUN
ejpam-3328	558	6	=	=	NOUN
ejpam-3328	558	7	1	1	NUM
ejpam-3328	558	8	2	2	NUM
ejpam-3328	558	9	t+	t+	VERB
ejpam-3328	558	10	,	,	PUNCT
ejpam-3328	558	11	tt−	tt−	PUNCT
ejpam-3328	558	12	=	=	SYM
ejpam-3328	558	13	−1	−1	NOUN
ejpam-3328	558	14	2	2	NUM
ejpam-3328	558	15	t−	t−	NOUN
ejpam-3328	558	16	,	,	PUNCT
ejpam-3328	558	17	t+	t+	PUNCT
ejpam-3328	558	18	=	=	SYM
ejpam-3328	558	19	t	t	PROPN
ejpam-3328	558	20	+	+	CCONJ
ejpam-3328	558	21	1	1	NUM
ejpam-3328	558	22	2	2	NUM
ejpam-3328	558	23	i	i	NOUN
ejpam-3328	558	24	,	,	PUNCT
ejpam-3328	558	25	t−	t−	PROPN
ejpam-3328	558	26	=	=	SYM
ejpam-3328	558	27	t	t	PROPN
ejpam-3328	559	1	−	−	NUM
ejpam-3328	559	2	1	1	NUM
ejpam-3328	559	3	2	2	NUM
ejpam-3328	559	4	i	i	NOUN
ejpam-3328	559	5	,	,	PUNCT
ejpam-3328	559	6	where	where	SCONJ
ejpam-3328	559	7	i	i	PRON
ejpam-3328	559	8	is	be	AUX
ejpam-3328	559	9	the	the	DET
ejpam-3328	559	10	identity	identity	NOUN
ejpam-3328	559	11	operator	operator	NOUN
ejpam-3328	559	12	(	(	PUNCT
ejpam-3328	559	13	if	if	SCONJ
ejpam-3328	559	14	=	=	SYM
ejpam-3328	559	15	f	f	X
ejpam-3328	559	16	)	)	PUNCT
ejpam-3328	559	17	.	.	PUNCT
ejpam-3328	560	1	the	the	DET
ejpam-3328	560	2	reduction	reduction	NOUN
ejpam-3328	560	3	to	to	ADP
ejpam-3328	560	4	a	a	DET
ejpam-3328	560	5	riemann	riemann	PROPN
ejpam-3328	560	6	–	–	PUNCT
ejpam-3328	560	7	hilbert	hilbert	NOUN
ejpam-3328	560	8	boundary	boundary	ADJ
ejpam-3328	560	9	-	-	PUNCT
ejpam-3328	560	10	value	value	NOUN
ejpam-3328	560	11	problem	problem	NOUN
ejpam-3328	560	12	can	can	AUX
ejpam-3328	560	13	now	now	ADV
ejpam-3328	560	14	be	be	AUX
ejpam-3328	560	15	formulated	formulate	VERB
ejpam-3328	560	16	as	as	SCONJ
ejpam-3328	560	17	follows	follow	NOUN
ejpam-3328	560	18	.	.	PUNCT
ejpam-3328	561	1	theorem	theorem	ADJ
ejpam-3328	561	2	8	8	NUM
ejpam-3328	561	3	.	.	PUNCT
ejpam-3328	562	1	let	let	VERB
ejpam-3328	562	2	(	(	PUNCT
ejpam-3328	562	3	3/4	3/4	NUM
ejpam-3328	562	4	+	+	CCONJ
ejpam-3328	562	5	iα	iα	NOUN
ejpam-3328	562	6	)	)	PUNCT
ejpam-3328	562	7	∈	∈	PROPN
ejpam-3328	562	8	d(n	d(n	PROPN
ejpam-3328	562	9	)	)	PUNCT
ejpam-3328	562	10	,	,	PUNCT
ejpam-3328	562	11	a	a	DET
ejpam-3328	562	12	>	>	X
ejpam-3328	562	13	2	2	NUM
ejpam-3328	562	14	,	,	PUNCT
ejpam-3328	562	15	(	(	PUNCT
ejpam-3328	562	16	25	25	NUM
ejpam-3328	562	17	)	)	PUNCT
ejpam-3328	562	18	γ+(k	γ+(k	NUM
ejpam-3328	562	19	)	)	PUNCT
ejpam-3328	563	1	=	=	SYM
ejpam-3328	563	2	−	−	PROPN
ejpam-3328	563	3	1	1	NUM
ejpam-3328	563	4	2πi	2πi	NOUN
ejpam-3328	563	5	∫	∫	PROPN
ejpam-3328	563	6	∞	∞	PROPN
ejpam-3328	564	1	−∞	−∞	ADP
ejpam-3328	564	2	ln(r(t))dt	ln(r(t))dt	NOUN
ejpam-3328	565	1	t−	t−	PROPN
ejpam-3328	565	2	k	k	PROPN
ejpam-3328	566	1	−	−	PROPN
ejpam-3328	566	2	i0	i0	PROPN
ejpam-3328	566	3	,	,	PUNCT
ejpam-3328	566	4	(	(	PUNCT
ejpam-3328	566	5	26	26	NUM
ejpam-3328	566	6	)	)	PUNCT
ejpam-3328	566	7	γ−(k	γ−(k	NOUN
ejpam-3328	566	8	)	)	PUNCT
ejpam-3328	566	9	=	=	SYM
ejpam-3328	567	1	−	−	PROPN
ejpam-3328	567	2	1	1	NUM
ejpam-3328	567	3	2πi	2πi	NOUN
ejpam-3328	567	4	∫	∫	PROPN
ejpam-3328	567	5	∞	∞	PROPN
ejpam-3328	568	1	−∞	−∞	ADP
ejpam-3328	568	2	ln(r(t))dt	ln(r(t))dt	NOUN
ejpam-3328	568	3	t−	t−	PROPN
ejpam-3328	568	4	k	k	PROPN
ejpam-3328	569	1	+	+	CCONJ
ejpam-3328	569	2	i0	i0	PROPN
ejpam-3328	569	3	,	,	PUNCT
ejpam-3328	569	4	(	(	PUNCT
ejpam-3328	569	5	27	27	NUM
ejpam-3328	569	6	)	)	PUNCT
ejpam-3328	569	7	x+(k	x+(k	PROPN
ejpam-3328	569	8	)	)	PUNCT
ejpam-3328	569	9	=	=	SYM
ejpam-3328	569	10	eγ+(k	eγ+(k	NOUN
ejpam-3328	569	11	)	)	PUNCT
ejpam-3328	569	12	,	,	PUNCT
ejpam-3328	569	13	x−(k	x−(k	PROPN
ejpam-3328	569	14	)	)	PUNCT
ejpam-3328	569	15	=	=	SYM
ejpam-3328	570	1	eγ−(k	eγ−(k	PROPN
ejpam-3328	570	2	)	)	PUNCT
ejpam-3328	570	3	,	,	PUNCT
ejpam-3328	570	4	r(k	r(k	PROPN
ejpam-3328	570	5	)	)	PUNCT
ejpam-3328	570	6	=	=	SYM
ejpam-3328	570	7	x−(k	x−(k	PROPN
ejpam-3328	570	8	)	)	PUNCT
ejpam-3328	570	9	x+(k	x+(k	PROPN
ejpam-3328	570	10	)	)	PUNCT
ejpam-3328	570	11	,	,	PUNCT
ejpam-3328	570	12	gε(k	gε(k	NOUN
ejpam-3328	570	13	,	,	PUNCT
ejpam-3328	570	14	α	α	NOUN
ejpam-3328	570	15	)	)	PUNCT
ejpam-3328	570	16	=	=	SYM
ejpam-3328	571	1	jε(k	jε(k	PROPN
ejpam-3328	571	2	,	,	PUNCT
ejpam-3328	571	3	α	α	NOUN
ejpam-3328	571	4	)	)	PUNCT
ejpam-3328	571	5	.	.	PUNCT
ejpam-3328	572	1	(	(	PUNCT
ejpam-3328	572	2	28	28	NUM
ejpam-3328	572	3	)	)	PUNCT
ejpam-3328	572	4	then	then	ADV
ejpam-3328	572	5	,	,	PUNCT
ejpam-3328	572	6	jε(k	jε(k	PROPN
ejpam-3328	572	7	,	,	PUNCT
ejpam-3328	572	8	α	α	NOUN
ejpam-3328	572	9	)	)	PUNCT
ejpam-3328	572	10	=	=	SYM
ejpam-3328	572	11	−x+(k	−x+(k	NOUN
ejpam-3328	572	12	)	)	PUNCT
ejpam-3328	572	13	2πi	2πi	NOUN
ejpam-3328	572	14	∫	∫	PROPN
ejpam-3328	572	15	∞	∞	PROPN
ejpam-3328	572	16	−∞	−∞	X
ejpam-3328	572	17	gε(t	gε(t	PROPN
ejpam-3328	572	18	,	,	PUNCT
ejpam-3328	572	19	α	α	NOUN
ejpam-3328	572	20	)	)	PUNCT
ejpam-3328	572	21	x−(t	x−(t	PROPN
ejpam-3328	572	22	)	)	PUNCT
ejpam-3328	572	23	dt	dt	PROPN
ejpam-3328	573	1	t−	t−	PROPN
ejpam-3328	573	2	k	k	PROPN
ejpam-3328	573	3	−	−	PROPN
ejpam-3328	574	1	i0	i0	PROPN
ejpam-3328	574	2	=	=	PUNCT
ejpam-3328	574	3	x+(k)t+	x+(k)t+	PROPN
ejpam-3328	574	4	gε	gε	PROPN
ejpam-3328	574	5	x−	x−	PROPN
ejpam-3328	574	6	,	,	PUNCT
ejpam-3328	574	7	iε(k	iε(k	NUM
ejpam-3328	574	8	,	,	PUNCT
ejpam-3328	574	9	α	α	X
ejpam-3328	574	10	)	)	PUNCT
ejpam-3328	574	11	k	k	PROPN
ejpam-3328	574	12	−	−	PROPN
ejpam-3328	574	13	ia	ia	PROPN
ejpam-3328	574	14	−	−	PROPN
ejpam-3328	574	15	f̃ε(k	f̃ε(k	PROPN
ejpam-3328	574	16	,	,	PUNCT
ejpam-3328	574	17	α	α	NOUN
ejpam-3328	574	18	)	)	PUNCT
ejpam-3328	575	1	k	k	PROPN
ejpam-3328	575	2	−	−	PROPN
ejpam-3328	575	3	ia	ia	PROPN
ejpam-3328	575	4	=	=	SYM
ejpam-3328	575	5	−x−(k	−x−(k	PROPN
ejpam-3328	575	6	)	)	PUNCT
ejpam-3328	575	7	2πi	2πi	NOUN
ejpam-3328	575	8	∫	∫	PROPN
ejpam-3328	575	9	∞	∞	PROPN
ejpam-3328	575	10	−∞	−∞	X
ejpam-3328	575	11	gε(t	gε(t	PROPN
ejpam-3328	575	12	,	,	PUNCT
ejpam-3328	575	13	α	α	NOUN
ejpam-3328	575	14	)	)	PUNCT
ejpam-3328	575	15	x−(t	x−(t	PROPN
ejpam-3328	575	16	)	)	PUNCT
ejpam-3328	576	1	dt	dt	PROPN
ejpam-3328	576	2	t−	t−	PROPN
ejpam-3328	576	3	k	k	PROPN
ejpam-3328	577	1	+	+	CCONJ
ejpam-3328	577	2	i0	i0	PROPN
ejpam-3328	577	3	dt	dt	PROPN
ejpam-3328	578	1	=	=	PUNCT
ejpam-3328	578	2	x−(k)t−	x−(k)t−	PROPN
ejpam-3328	578	3	gε	gε	PROPN
ejpam-3328	578	4	x−	x−	PROPN
ejpam-3328	578	5	.	.	PUNCT
ejpam-3328	579	1	proof	proof	NOUN
ejpam-3328	579	2	.	.	PUNCT
ejpam-3328	580	1	by	by	ADP
ejpam-3328	580	2	theorem	theorem	NOUN
ejpam-3328	580	3	7	7	NUM
ejpam-3328	580	4	and	and	CCONJ
ejpam-3328	580	5	lemma	lemma	PROPN
ejpam-3328	580	6	16	16	NUM
ejpam-3328	580	7	we	we	PRON
ejpam-3328	580	8	have	have	VERB
ejpam-3328	580	9	qε(s	qε(	NOUN
ejpam-3328	580	10	)	)	PUNCT
ejpam-3328	580	11	=	=	PUNCT
ejpam-3328	581	1	qε(1−	qε(1−	PROPN
ejpam-3328	581	2	s	s	X
ejpam-3328	581	3	)	)	PUNCT
ejpam-3328	581	4	+	+	NUM
ejpam-3328	581	5	fε(s	fε(	NOUN
ejpam-3328	581	6	)	)	PUNCT
ejpam-3328	581	7	.	.	PUNCT
ejpam-3328	582	1	(	(	PUNCT
ejpam-3328	582	2	29	29	NUM
ejpam-3328	582	3	)	)	PUNCT
ejpam-3328	582	4	using	use	VERB
ejpam-3328	582	5	the	the	DET
ejpam-3328	582	6	fourier	fourier	NOUN
ejpam-3328	582	7	transform	transform	NOUN
ejpam-3328	582	8	,	,	PUNCT
ejpam-3328	582	9	we	we	PRON
ejpam-3328	582	10	obtain	obtain	VERB
ejpam-3328	582	11	iε(k	iε(k	NUM
ejpam-3328	582	12	,	,	PUNCT
ejpam-3328	582	13	α	α	NOUN
ejpam-3328	582	14	)	)	PUNCT
ejpam-3328	583	1	=	=	SYM
ejpam-3328	583	2	e−ikjε(k	e−ikjε(k	PROPN
ejpam-3328	583	3	,	,	PUNCT
ejpam-3328	583	4	α	α	NOUN
ejpam-3328	583	5	)	)	PUNCT
ejpam-3328	583	6	+	+	CCONJ
ejpam-3328	583	7	f̃ε(k	f̃ε(k	PROPN
ejpam-3328	583	8	,	,	PUNCT
ejpam-3328	583	9	α	α	NOUN
ejpam-3328	583	10	)	)	PUNCT
ejpam-3328	583	11	.	.	PUNCT
ejpam-3328	584	1	(	(	PUNCT
ejpam-3328	584	2	30	30	NUM
ejpam-3328	584	3	)	)	PUNCT
ejpam-3328	584	4	a.	a.	NOUN
ejpam-3328	584	5	durmagambetov	durmagambetov	PROPN
ejpam-3328	584	6	/	/	SYM
ejpam-3328	584	7	eur	eur	PROPN
ejpam-3328	584	8	.	.	PUNCT
ejpam-3328	585	1	j.	j.	PROPN
ejpam-3328	585	2	pure	pure	PROPN
ejpam-3328	585	3	appl	appl	PROPN
ejpam-3328	585	4	.	.	PROPN
ejpam-3328	585	5	math	math	PROPN
ejpam-3328	585	6	,	,	PUNCT
ejpam-3328	585	7	11	11	NUM
ejpam-3328	585	8	(	(	PUNCT
ejpam-3328	585	9	4	4	NUM
ejpam-3328	585	10	)	)	PUNCT
ejpam-3328	585	11	(	(	PUNCT
ejpam-3328	585	12	2018	2018	NUM
ejpam-3328	585	13	)	)	PUNCT
ejpam-3328	585	14	,	,	PUNCT
ejpam-3328	585	15	1143	1143	NUM
ejpam-3328	585	16	-	-	SYM
ejpam-3328	585	17	1176	1176	NUM
ejpam-3328	585	18	1168	1168	NUM
ejpam-3328	585	19	multiplying	multiply	VERB
ejpam-3328	585	20	this	this	DET
ejpam-3328	585	21	equation	equation	NOUN
ejpam-3328	585	22	by	by	ADP
ejpam-3328	585	23	1	1	NUM
ejpam-3328	585	24	k−ia	k−ia	NOUN
ejpam-3328	585	25	,	,	PUNCT
ejpam-3328	585	26	we	we	PRON
ejpam-3328	585	27	get	get	VERB
ejpam-3328	585	28	iε(k	iε(k	NUM
ejpam-3328	585	29	,	,	PUNCT
ejpam-3328	585	30	α	α	X
ejpam-3328	585	31	)	)	PUNCT
ejpam-3328	585	32	k	k	PROPN
ejpam-3328	585	33	−	−	PROPN
ejpam-3328	585	34	ia	ia	PROPN
ejpam-3328	585	35	=	=	PROPN
ejpam-3328	585	36	e−ikjε(k	e−ikjε(k	PROPN
ejpam-3328	585	37	,	,	PUNCT
ejpam-3328	585	38	α	α	X
ejpam-3328	585	39	)	)	PUNCT
ejpam-3328	586	1	k	k	PROPN
ejpam-3328	586	2	−	−	PROPN
ejpam-3328	586	3	ia	ia	PROPN
ejpam-3328	586	4	+	+	CCONJ
ejpam-3328	586	5	f̃ε(k	f̃ε(k	PROPN
ejpam-3328	586	6	,	,	PUNCT
ejpam-3328	586	7	α	α	NOUN
ejpam-3328	586	8	)	)	PUNCT
ejpam-3328	586	9	k	k	PROPN
ejpam-3328	587	1	−	−	PROPN
ejpam-3328	587	2	ia	ia	PROPN
ejpam-3328	587	3	.	.	PUNCT
ejpam-3328	588	1	(	(	PUNCT
ejpam-3328	588	2	31	31	NUM
ejpam-3328	588	3	)	)	PUNCT
ejpam-3328	588	4	we	we	PRON
ejpam-3328	588	5	can	can	AUX
ejpam-3328	588	6	rewrite	rewrite	VERB
ejpam-3328	588	7	the	the	DET
ejpam-3328	588	8	last	last	ADJ
ejpam-3328	588	9	equation	equation	NOUN
ejpam-3328	588	10	as	as	ADP
ejpam-3328	588	11	iε(k	iε(k	NUM
ejpam-3328	588	12	,	,	PUNCT
ejpam-3328	588	13	α	α	NOUN
ejpam-3328	588	14	)	)	PUNCT
ejpam-3328	588	15	k	k	PROPN
ejpam-3328	588	16	−	−	PROPN
ejpam-3328	588	17	ia	ia	PROPN
ejpam-3328	589	1	−	−	PROPN
ejpam-3328	590	1	f̃ε(k	f̃ε(k	PROPN
ejpam-3328	590	2	,	,	PUNCT
ejpam-3328	590	3	α	α	NOUN
ejpam-3328	590	4	)	)	PUNCT
ejpam-3328	590	5	k	k	PROPN
ejpam-3328	590	6	−	−	PROPN
ejpam-3328	590	7	ia	ia	PROPN
ejpam-3328	590	8	=	=	SYM
ejpam-3328	590	9	r(k)jε(k	r(k)jε(k	PROPN
ejpam-3328	590	10	,	,	PUNCT
ejpam-3328	590	11	α	α	NOUN
ejpam-3328	590	12	)	)	PUNCT
ejpam-3328	590	13	+	+	CCONJ
ejpam-3328	590	14	jε(k	jε(k	ADJ
ejpam-3328	590	15	,	,	PUNCT
ejpam-3328	590	16	α	α	NOUN
ejpam-3328	590	17	)	)	PUNCT
ejpam-3328	590	18	.	.	PUNCT
ejpam-3328	591	1	(	(	PUNCT
ejpam-3328	591	2	32	32	NUM
ejpam-3328	591	3	)	)	PUNCT
ejpam-3328	591	4	then	then	ADV
ejpam-3328	591	5	,	,	PUNCT
ejpam-3328	591	6	ψ−(k	ψ−(k	PROPN
ejpam-3328	591	7	,	,	PUNCT
ejpam-3328	591	8	α	α	NOUN
ejpam-3328	591	9	)	)	PUNCT
ejpam-3328	591	10	=	=	SYM
ejpam-3328	591	11	iε(k	iε(k	PROPN
ejpam-3328	591	12	,	,	PUNCT
ejpam-3328	591	13	α	α	NOUN
ejpam-3328	591	14	)	)	PUNCT
ejpam-3328	591	15	k	k	PROPN
ejpam-3328	591	16	−	−	PROPN
ejpam-3328	591	17	ia	ia	PROPN
ejpam-3328	591	18	−	−	PROPN
ejpam-3328	591	19	f̃ε(k	f̃ε(k	PROPN
ejpam-3328	591	20	,	,	PUNCT
ejpam-3328	591	21	α	α	NOUN
ejpam-3328	591	22	)	)	PUNCT
ejpam-3328	591	23	k	k	PROPN
ejpam-3328	591	24	−	−	PROPN
ejpam-3328	591	25	ia	ia	PROPN
ejpam-3328	591	26	,	,	PUNCT
ejpam-3328	591	27	(	(	PUNCT
ejpam-3328	591	28	33	33	NUM
ejpam-3328	591	29	)	)	PUNCT
ejpam-3328	591	30	ψ+(k	ψ+(k	PROPN
ejpam-3328	591	31	,	,	PUNCT
ejpam-3328	591	32	α	α	X
ejpam-3328	591	33	)	)	PUNCT
ejpam-3328	591	34	=	=	SYM
ejpam-3328	591	35	jε(k	jε(k	PROPN
ejpam-3328	591	36	,	,	PUNCT
ejpam-3328	591	37	α	α	NOUN
ejpam-3328	591	38	)	)	PUNCT
ejpam-3328	591	39	,	,	PUNCT
ejpam-3328	591	40	(	(	PUNCT
ejpam-3328	591	41	34	34	NUM
ejpam-3328	591	42	)	)	PUNCT
ejpam-3328	591	43	gε(t	gε(t	NOUN
ejpam-3328	591	44	,	,	PUNCT
ejpam-3328	591	45	α	α	NOUN
ejpam-3328	591	46	)	)	PUNCT
ejpam-3328	591	47	=	=	SYM
ejpam-3328	591	48	jε(k	jε(k	PROPN
ejpam-3328	591	49	,	,	PUNCT
ejpam-3328	591	50	α	α	NOUN
ejpam-3328	591	51	)	)	PUNCT
ejpam-3328	591	52	.	.	PUNCT
ejpam-3328	592	1	(	(	PUNCT
ejpam-3328	592	2	35	35	NUM
ejpam-3328	592	3	)	)	PUNCT
ejpam-3328	592	4	by	by	ADP
ejpam-3328	592	5	using	use	VERB
ejpam-3328	592	6	lemma	lemma	PROPN
ejpam-3328	592	7	21	21	NUM
ejpam-3328	592	8	,	,	PUNCT
ejpam-3328	592	9	the	the	DET
ejpam-3328	592	10	following	follow	VERB
ejpam-3328	592	11	riemann	riemann	PROPN
ejpam-3328	592	12	–	–	PUNCT
ejpam-3328	592	13	hilbert	hilbert	NOUN
ejpam-3328	592	14	boundary	boundary	ADJ
ejpam-3328	592	15	-	-	PUNCT
ejpam-3328	592	16	value	value	NOUN
ejpam-3328	592	17	problem	problem	NOUN
ejpam-3328	592	18	is	be	AUX
ejpam-3328	592	19	obtained	obtain	VERB
ejpam-3328	592	20	regarding	regard	VERB
ejpam-3328	592	21	the	the	DET
ejpam-3328	592	22	definition	definition	NOUN
ejpam-3328	592	23	of	of	ADP
ejpam-3328	592	24	an	an	DET
ejpam-3328	592	25	analytic	analytic	ADJ
ejpam-3328	592	26	function	function	NOUN
ejpam-3328	592	27	from	from	ADP
ejpam-3328	592	28	its	its	PRON
ejpam-3328	592	29	boundary	boundary	ADJ
ejpam-3328	592	30	values	value	NOUN
ejpam-3328	592	31	on	on	ADP
ejpam-3328	592	32	the	the	DET
ejpam-3328	592	33	real	real	ADJ
ejpam-3328	592	34	line	line	NOUN
ejpam-3328	592	35	:	:	PUNCT
ejpam-3328	592	36	ψ−(k	ψ−(k	NOUN
ejpam-3328	592	37	,	,	PUNCT
ejpam-3328	592	38	α	α	X
ejpam-3328	592	39	)	)	PUNCT
ejpam-3328	592	40	=	=	PUNCT
ejpam-3328	592	41	r(k)ψ+(k	r(k)ψ+(k	PROPN
ejpam-3328	592	42	,	,	PUNCT
ejpam-3328	592	43	α	α	X
ejpam-3328	592	44	)	)	PUNCT
ejpam-3328	593	1	+	+	NOUN
ejpam-3328	593	2	gε(k	gε(k	NOUN
ejpam-3328	593	3	,	,	PUNCT
ejpam-3328	593	4	α	α	NOUN
ejpam-3328	593	5	)	)	PUNCT
ejpam-3328	593	6	,	,	PUNCT
ejpam-3328	593	7	(	(	PUNCT
ejpam-3328	593	8	36	36	X
ejpam-3328	593	9	)	)	PUNCT
ejpam-3328	593	10	lim	lim	PROPN
ejpam-3328	593	11	im(k)→∞	im(k)→∞	PROPN
ejpam-3328	593	12	ψ+(k	ψ+(k	PROPN
ejpam-3328	593	13	,	,	PUNCT
ejpam-3328	593	14	α	α	X
ejpam-3328	593	15	)	)	PUNCT
ejpam-3328	593	16	=	=	SYM
ejpam-3328	593	17	0	0	PROPN
ejpam-3328	593	18	,	,	PUNCT
ejpam-3328	593	19	lim	lim	PROPN
ejpam-3328	593	20	im(k)→−∞	im(k)→−∞	PROPN
ejpam-3328	593	21	ψ−(k	ψ−(k	PROPN
ejpam-3328	593	22	,	,	PUNCT
ejpam-3328	593	23	α	α	X
ejpam-3328	593	24	)	)	PUNCT
ejpam-3328	593	25	=	=	SYM
ejpam-3328	594	1	0	0	X
ejpam-3328	594	2	.	.	PUNCT
ejpam-3328	595	1	(	(	PUNCT
ejpam-3328	595	2	37	37	NUM
ejpam-3328	595	3	)	)	PUNCT
ejpam-3328	595	4	hilbert	hilbert	PROPN
ejpam-3328	595	5	’s	’s	PART
ejpam-3328	595	6	formula	formula	NOUN
ejpam-3328	595	7	and	and	CCONJ
ejpam-3328	595	8	lemmas	lemma	NOUN
ejpam-3328	595	9	20	20	NUM
ejpam-3328	595	10	and	and	CCONJ
ejpam-3328	595	11	21	21	NUM
ejpam-3328	595	12	give	give	VERB
ejpam-3328	595	13	the	the	DET
ejpam-3328	595	14	solution	solution	NOUN
ejpam-3328	595	15	to	to	ADP
ejpam-3328	595	16	this	this	DET
ejpam-3328	595	17	riemann	riemann	PROPN
ejpam-3328	595	18	–	–	PUNCT
ejpam-3328	595	19	hilbert	hilbert	PROPN
ejpam-3328	595	20	boundary	boundary	ADJ
ejpam-3328	595	21	value	value	NOUN
ejpam-3328	595	22	problem	problem	NOUN
ejpam-3328	595	23	as	as	ADP
ejpam-3328	595	24	ψ+(k	ψ+(k	PROPN
ejpam-3328	595	25	,	,	PUNCT
ejpam-3328	595	26	α	α	X
ejpam-3328	595	27	)	)	PUNCT
ejpam-3328	595	28	=	=	SYM
ejpam-3328	595	29	−x+(k	−x+(k	NOUN
ejpam-3328	595	30	)	)	PUNCT
ejpam-3328	595	31	2πi	2πi	NOUN
ejpam-3328	595	32	∫	∫	PROPN
ejpam-3328	595	33	∞	∞	PROPN
ejpam-3328	595	34	−∞	−∞	X
ejpam-3328	595	35	gε(t	gε(t	PROPN
ejpam-3328	595	36	,	,	PUNCT
ejpam-3328	595	37	α	α	NOUN
ejpam-3328	595	38	)	)	PUNCT
ejpam-3328	595	39	x−(t	x−(t	PROPN
ejpam-3328	595	40	)	)	PUNCT
ejpam-3328	595	41	dt	dt	PROPN
ejpam-3328	596	1	t−	t−	PROPN
ejpam-3328	596	2	k	k	PROPN
ejpam-3328	597	1	−	−	PROPN
ejpam-3328	597	2	i0	i0	PROPN
ejpam-3328	597	3	,	,	PUNCT
ejpam-3328	597	4	(	(	PUNCT
ejpam-3328	597	5	38	38	NUM
ejpam-3328	597	6	)	)	PUNCT
ejpam-3328	597	7	ψ−(k	ψ−(k	NOUN
ejpam-3328	597	8	,	,	PUNCT
ejpam-3328	597	9	α	α	NOUN
ejpam-3328	597	10	)	)	PUNCT
ejpam-3328	597	11	=	=	SYM
ejpam-3328	597	12	−x−(k	−x−(k	PROPN
ejpam-3328	597	13	)	)	PUNCT
ejpam-3328	598	1	2πi	2πi	NOUN
ejpam-3328	598	2	∫	∫	PROPN
ejpam-3328	598	3	∞	∞	PROPN
ejpam-3328	598	4	−∞	−∞	X
ejpam-3328	598	5	gε(t	gε(t	PROPN
ejpam-3328	598	6	,	,	PUNCT
ejpam-3328	598	7	α	α	NOUN
ejpam-3328	598	8	)	)	PUNCT
ejpam-3328	598	9	x−(t	x−(t	PROPN
ejpam-3328	598	10	)	)	PUNCT
ejpam-3328	599	1	dt	dt	PROPN
ejpam-3328	599	2	t−	t−	PROPN
ejpam-3328	599	3	k	k	PROPN
ejpam-3328	600	1	+	+	CCONJ
ejpam-3328	600	2	i0	i0	PROPN
ejpam-3328	600	3	.	.	PUNCT
ejpam-3328	601	1	(	(	PUNCT
ejpam-3328	601	2	39	39	NUM
ejpam-3328	601	3	)	)	PUNCT
ejpam-3328	601	4	denote	denote	NOUN
ejpam-3328	601	5	φ+(k	φ+(k	PROPN
ejpam-3328	601	6	,	,	PUNCT
ejpam-3328	601	7	α	α	NOUN
ejpam-3328	601	8	)	)	PUNCT
ejpam-3328	601	9	=	=	SYM
ejpam-3328	602	1	ψ+(k	ψ+(k	PROPN
ejpam-3328	602	2	,	,	PUNCT
ejpam-3328	602	3	α)−	α)−	VERB
ejpam-3328	602	4	jε(k	jε(k	NOUN
ejpam-3328	602	5	,	,	PUNCT
ejpam-3328	602	6	α)r(k	α)r(k	PROPN
ejpam-3328	602	7	)	)	PUNCT
ejpam-3328	602	8	x−(k	x−(k	PROPN
ejpam-3328	602	9	)	)	PUNCT
ejpam-3328	602	10	,	,	PUNCT
ejpam-3328	602	11	(	(	PUNCT
ejpam-3328	602	12	40	40	NUM
ejpam-3328	602	13	)	)	PUNCT
ejpam-3328	602	14	φ−(k	φ−(k	PROPN
ejpam-3328	602	15	,	,	PUNCT
ejpam-3328	602	16	α	α	NOUN
ejpam-3328	602	17	)	)	PUNCT
ejpam-3328	602	18	=	=	SYM
ejpam-3328	602	19	ψ−(k	ψ−(k	NOUN
ejpam-3328	602	20	,	,	PUNCT
ejpam-3328	602	21	α	α	NOUN
ejpam-3328	602	22	)	)	PUNCT
ejpam-3328	602	23	x−(k	x−(k	PROPN
ejpam-3328	602	24	)	)	PUNCT
ejpam-3328	602	25	−	−	PROPN
ejpam-3328	602	26	iε(k	iε(k	ADP
ejpam-3328	602	27	,	,	PUNCT
ejpam-3328	602	28	α)−	α)−	PROPN
ejpam-3328	602	29	f̃ε(k	f̃ε(k	PROPN
ejpam-3328	602	30	,	,	PUNCT
ejpam-3328	602	31	α	α	X
ejpam-3328	602	32	)	)	PUNCT
ejpam-3328	602	33	x−(k)(k	x−(k)(k	PROPN
ejpam-3328	602	34	−	−	PROPN
ejpam-3328	602	35	ia	ia	PROPN
ejpam-3328	602	36	)	)	PUNCT
ejpam-3328	602	37	.	.	PUNCT
ejpam-3328	603	1	(	(	PUNCT
ejpam-3328	603	2	41	41	NUM
ejpam-3328	603	3	)	)	PUNCT
ejpam-3328	603	4	for	for	ADP
ejpam-3328	603	5	φ+(k	φ+(k	PROPN
ejpam-3328	603	6	,	,	PUNCT
ejpam-3328	603	7	α	α	NOUN
ejpam-3328	603	8	)	)	PUNCT
ejpam-3328	603	9	and	and	CCONJ
ejpam-3328	603	10	φ−(k	φ−(k	PROPN
ejpam-3328	603	11	,	,	PUNCT
ejpam-3328	603	12	α	α	X
ejpam-3328	603	13	)	)	PUNCT
ejpam-3328	603	14	we	we	PRON
ejpam-3328	603	15	have	have	VERB
ejpam-3328	603	16	a	a	DET
ejpam-3328	603	17	new	new	ADJ
ejpam-3328	603	18	riemann	riemann	PROPN
ejpam-3328	603	19	–	–	PUNCT
ejpam-3328	603	20	hilbert	hilbert	PROPN
ejpam-3328	603	21	boundary	boundary	ADJ
ejpam-3328	603	22	-	-	PUNCT
ejpam-3328	603	23	value	value	NOUN
ejpam-3328	603	24	problem	problem	NOUN
ejpam-3328	603	25	:	:	PUNCT
ejpam-3328	603	26	φ−(k	φ−(k	PROPN
ejpam-3328	603	27	,	,	PUNCT
ejpam-3328	603	28	α	α	X
ejpam-3328	603	29	)	)	PUNCT
ejpam-3328	603	30	=	=	SYM
ejpam-3328	603	31	φ+(k	φ+(k	PROPN
ejpam-3328	603	32	,	,	PUNCT
ejpam-3328	603	33	α	α	NOUN
ejpam-3328	603	34	)	)	PUNCT
ejpam-3328	603	35	,	,	PUNCT
ejpam-3328	603	36	(	(	PUNCT
ejpam-3328	603	37	42	42	X
ejpam-3328	603	38	)	)	PUNCT
ejpam-3328	603	39	a.	a.	NOUN
ejpam-3328	603	40	durmagambetov	durmagambetov	PROPN
ejpam-3328	603	41	/	/	SYM
ejpam-3328	603	42	eur	eur	PROPN
ejpam-3328	603	43	.	.	PUNCT
ejpam-3328	604	1	j.	j.	PROPN
ejpam-3328	604	2	pure	pure	PROPN
ejpam-3328	604	3	appl	appl	PROPN
ejpam-3328	604	4	.	.	PROPN
ejpam-3328	604	5	math	math	PROPN
ejpam-3328	604	6	,	,	PUNCT
ejpam-3328	604	7	11	11	NUM
ejpam-3328	604	8	(	(	PUNCT
ejpam-3328	604	9	4	4	NUM
ejpam-3328	604	10	)	)	PUNCT
ejpam-3328	604	11	(	(	PUNCT
ejpam-3328	604	12	2018	2018	NUM
ejpam-3328	604	13	)	)	PUNCT
ejpam-3328	604	14	,	,	PUNCT
ejpam-3328	604	15	1143	1143	NUM
ejpam-3328	604	16	-	-	SYM
ejpam-3328	604	17	1176	1176	NUM
ejpam-3328	604	18	1169	1169	NUM
ejpam-3328	604	19	lim	lim	PROPN
ejpam-3328	604	20	im(k)→∞	im(k)→∞	PROPN
ejpam-3328	604	21	φ+(k	φ+(k	PROPN
ejpam-3328	604	22	,	,	PUNCT
ejpam-3328	604	23	α	α	X
ejpam-3328	604	24	)	)	PUNCT
ejpam-3328	604	25	=	=	SYM
ejpam-3328	604	26	0	0	PROPN
ejpam-3328	604	27	,	,	PUNCT
ejpam-3328	604	28	lim	lim	PROPN
ejpam-3328	604	29	im(k)→−∞	im(k)→−∞	PROPN
ejpam-3328	604	30	φ−(k	φ−(k	PROPN
ejpam-3328	604	31	,	,	PUNCT
ejpam-3328	604	32	α	α	X
ejpam-3328	604	33	)	)	PUNCT
ejpam-3328	604	34	=	=	SYM
ejpam-3328	604	35	0	0	X
ejpam-3328	604	36	.	.	PUNCT
ejpam-3328	605	1	(	(	PUNCT
ejpam-3328	605	2	43	43	NUM
ejpam-3328	605	3	)	)	PUNCT
ejpam-3328	605	4	liouville	liouville	PROPN
ejpam-3328	605	5	’s	’s	PART
ejpam-3328	605	6	theorem	theorem	NOUN
ejpam-3328	605	7	implies	imply	VERB
ejpam-3328	605	8	that	that	SCONJ
ejpam-3328	605	9	φ−(k	φ−(k	PROPN
ejpam-3328	605	10	,	,	PUNCT
ejpam-3328	605	11	α	α	X
ejpam-3328	605	12	)	)	PUNCT
ejpam-3328	605	13	=	=	SYM
ejpam-3328	605	14	0,φ+(k	0,φ+(k	PROPN
ejpam-3328	605	15	,	,	PUNCT
ejpam-3328	605	16	α	α	X
ejpam-3328	605	17	)	)	PUNCT
ejpam-3328	605	18	=	=	SYM
ejpam-3328	605	19	0	0	NUM
ejpam-3328	605	20	,	,	PUNCT
ejpam-3328	605	21	(	(	PUNCT
ejpam-3328	605	22	44	44	NUM
ejpam-3328	605	23	)	)	PUNCT
ejpam-3328	605	24	which	which	PRON
ejpam-3328	605	25	completes	complete	VERB
ejpam-3328	605	26	the	the	DET
ejpam-3328	605	27	proof	proof	NOUN
ejpam-3328	605	28	.	.	PUNCT
ejpam-3328	606	1	9	9	X
ejpam-3328	606	2	.	.	X
ejpam-3328	606	3	discussion	discussion	NOUN
ejpam-3328	606	4	our	our	PRON
ejpam-3328	606	5	computations	computation	NOUN
ejpam-3328	606	6	led	lead	VERB
ejpam-3328	606	7	to	to	ADP
ejpam-3328	606	8	a	a	DET
ejpam-3328	606	9	new	new	ADJ
ejpam-3328	606	10	definition	definition	NOUN
ejpam-3328	606	11	of	of	ADP
ejpam-3328	606	12	the	the	DET
ejpam-3328	606	13	functions	function	NOUN
ejpam-3328	606	14	iε(k	iε(k	NUM
ejpam-3328	606	15	)	)	PUNCT
ejpam-3328	606	16	and	and	CCONJ
ejpam-3328	606	17	jε(k	jε(k	PROPN
ejpam-3328	606	18	)	)	PUNCT
ejpam-3328	606	19	,	,	PUNCT
ejpam-3328	606	20	which	which	PRON
ejpam-3328	606	21	we	we	PRON
ejpam-3328	606	22	obtained	obtain	VERB
ejpam-3328	606	23	from	from	ADP
ejpam-3328	606	24	the	the	DET
ejpam-3328	606	25	riemann	riemann	PROPN
ejpam-3328	606	26	–	–	PUNCT
ejpam-3328	606	27	hilbert	hilbert	PROPN
ejpam-3328	606	28	boundary	boundary	ADJ
ejpam-3328	606	29	-	-	PUNCT
ejpam-3328	606	30	value	value	NOUN
ejpam-3328	606	31	problem	problem	NOUN
ejpam-3328	606	32	.	.	PUNCT
ejpam-3328	607	1	from	from	ADP
ejpam-3328	607	2	the	the	DET
ejpam-3328	607	3	uniqueness	uniqueness	NOUN
ejpam-3328	607	4	of	of	ADP
ejpam-3328	607	5	the	the	DET
ejpam-3328	607	6	solution	solution	NOUN
ejpam-3328	607	7	of	of	ADP
ejpam-3328	607	8	the	the	DET
ejpam-3328	607	9	riemann	riemann	PROPN
ejpam-3328	607	10	–	–	PUNCT
ejpam-3328	607	11	hilbert	hilbert	PROPN
ejpam-3328	607	12	boundary	boundary	ADJ
ejpam-3328	607	13	-	-	PUNCT
ejpam-3328	607	14	value	value	NOUN
ejpam-3328	607	15	problem	problem	NOUN
ejpam-3328	607	16	functions	function	NOUN
ejpam-3328	607	17	iε(k	iε(k	NUM
ejpam-3328	607	18	)	)	PUNCT
ejpam-3328	607	19	and	and	CCONJ
ejpam-3328	607	20	jε(k	jε(k	PROPN
ejpam-3328	607	21	)	)	PUNCT
ejpam-3328	607	22	,	,	PUNCT
ejpam-3328	607	23	defined	define	VERB
ejpam-3328	607	24	earlier	early	ADV
ejpam-3328	607	25	in	in	ADP
ejpam-3328	607	26	(	(	PUNCT
ejpam-3328	607	27	21	21	NUM
ejpam-3328	607	28	)	)	PUNCT
ejpam-3328	607	29	and	and	CCONJ
ejpam-3328	607	30	obtained	obtain	VERB
ejpam-3328	607	31	from	from	ADP
ejpam-3328	607	32	the	the	DET
ejpam-3328	607	33	hilbert	hilbert	NOUN
ejpam-3328	607	34	formula	formula	NOUN
ejpam-3328	607	35	are	be	AUX
ejpam-3328	607	36	equal	equal	ADJ
ejpam-3328	607	37	!	!	PUNCT
ejpam-3328	608	1	to	to	PART
ejpam-3328	608	2	obtain	obtain	VERB
ejpam-3328	608	3	the	the	DET
ejpam-3328	608	4	final	final	ADJ
ejpam-3328	608	5	estimates	estimate	NOUN
ejpam-3328	608	6	for	for	ADP
ejpam-3328	608	7	the	the	DET
ejpam-3328	608	8	zeta	zeta	PROPN
ejpam-3328	608	9	function	function	NOUN
ejpam-3328	608	10	,	,	PUNCT
ejpam-3328	608	11	the	the	DET
ejpam-3328	608	12	isometric	isometric	ADJ
ejpam-3328	608	13	properties	property	NOUN
ejpam-3328	608	14	of	of	ADP
ejpam-3328	608	15	the	the	DET
ejpam-3328	608	16	integral	integral	ADJ
ejpam-3328	608	17	hilbert	hilbert	NOUN
ejpam-3328	608	18	transform	transform	NOUN
ejpam-3328	608	19	will	will	AUX
ejpam-3328	608	20	be	be	AUX
ejpam-3328	608	21	used	use	VERB
ejpam-3328	608	22	.	.	PUNCT
ejpam-3328	609	1	theorem	theorem	ADJ
ejpam-3328	609	2	9	9	NUM
ejpam-3328	609	3	.	.	PUNCT
ejpam-3328	610	1	let	let	VERB
ejpam-3328	610	2	(	(	PUNCT
ejpam-3328	610	3	3/4	3/4	NUM
ejpam-3328	610	4	+	+	CCONJ
ejpam-3328	610	5	iα	iα	NOUN
ejpam-3328	610	6	)	)	PUNCT
ejpam-3328	610	7	∈	∈	PROPN
ejpam-3328	610	8	d(n	d(n	PROPN
ejpam-3328	610	9	)	)	PUNCT
ejpam-3328	610	10	and	and	CCONJ
ejpam-3328	610	11	a	a	DET
ejpam-3328	610	12	>	>	X
ejpam-3328	610	13	2	2	NUM
ejpam-3328	610	14	.	.	PUNCT
ejpam-3328	611	1	then	then	ADV
ejpam-3328	611	2	,	,	PUNCT
ejpam-3328	611	3	c−1	c−1	PROPN
ejpam-3328	611	4	<	<	X
ejpam-3328	611	5	|x−(t)|	|x−(t)|	ADJ
ejpam-3328	611	6	<	<	X
ejpam-3328	611	7	c	c	X
ejpam-3328	611	8	,	,	PUNCT
ejpam-3328	611	9	c−1	c−1	PROPN
ejpam-3328	611	10	<	<	X
ejpam-3328	611	11	|x+(t)|	|x+(t)|	PUNCT
ejpam-3328	611	12	<	<	X
ejpam-3328	611	13	c	c	X
ejpam-3328	611	14	,	,	PUNCT
ejpam-3328	611	15	||ψ+||l2	||ψ+||l2	PROPN
ejpam-3328	611	16	≤	≤	PROPN
ejpam-3328	611	17	cε	cε	VERB
ejpam-3328	611	18	,	,	PUNCT
ejpam-3328	611	19	||ψ−||l2	||ψ−||l2	PROPN
ejpam-3328	611	20	≤	≤	NUM
ejpam-3328	611	21	cε	cε	VERB
ejpam-3328	611	22	.	.	PUNCT
ejpam-3328	611	23	proof	proof	NOUN
ejpam-3328	611	24	.	.	PUNCT
ejpam-3328	612	1	by	by	ADP
ejpam-3328	612	2	lemmas	lemmas	PROPN
ejpam-3328	612	3	18	18	NUM
ejpam-3328	612	4	,	,	PUNCT
ejpam-3328	612	5	19	19	NUM
ejpam-3328	612	6	,	,	PUNCT
ejpam-3328	612	7	and	and	CCONJ
ejpam-3328	612	8	22	22	NUM
ejpam-3328	612	9	,	,	PUNCT
ejpam-3328	612	10	we	we	PRON
ejpam-3328	612	11	get	get	VERB
ejpam-3328	612	12	γ−(k	γ−(k	ADP
ejpam-3328	612	13	)	)	PUNCT
ejpam-3328	612	14	=	=	SYM
ejpam-3328	612	15	1	1	NUM
ejpam-3328	612	16	2πi	2πi	NOUN
ejpam-3328	612	17	∫	∫	PROPN
ejpam-3328	612	18	∞	∞	PROPN
ejpam-3328	613	1	−∞	−∞	ADP
ejpam-3328	613	2	ln(r(t))dt	ln(r(t))dt	NOUN
ejpam-3328	613	3	t−	t−	PROPN
ejpam-3328	613	4	k	k	PROPN
ejpam-3328	614	1	+	+	CCONJ
ejpam-3328	614	2	i0	i0	PROPN
ejpam-3328	614	3	=	=	PUNCT
ejpam-3328	614	4	t−	t−	X
ejpam-3328	614	5	ln(r	ln(r	NOUN
ejpam-3328	614	6	)	)	PUNCT
ejpam-3328	614	7	=	=	SYM
ejpam-3328	614	8	ln(r	ln(r	NOUN
ejpam-3328	614	9	)	)	PUNCT
ejpam-3328	614	10	,	,	PUNCT
ejpam-3328	614	11	x−(t	x−(t	PROPN
ejpam-3328	614	12	)	)	PUNCT
ejpam-3328	614	13	=	=	SYM
ejpam-3328	614	14	r(t	r(t	NOUN
ejpam-3328	614	15	)	)	PUNCT
ejpam-3328	614	16	,	,	PUNCT
ejpam-3328	614	17	x+(t	x+(t	PROPN
ejpam-3328	614	18	)	)	PUNCT
ejpam-3328	614	19	=	=	SYM
ejpam-3328	615	1	1	1	X
ejpam-3328	615	2	.	.	PUNCT
ejpam-3328	615	3	the	the	DET
ejpam-3328	615	4	last	last	ADJ
ejpam-3328	615	5	estimate	estimate	NOUN
ejpam-3328	615	6	implies	imply	VERB
ejpam-3328	615	7	c−1	c−1	PROPN
ejpam-3328	615	8	<	<	X
ejpam-3328	615	9	|x−(t)|	|x−(t)|	ADJ
ejpam-3328	615	10	<	<	X
ejpam-3328	615	11	c	c	X
ejpam-3328	615	12	,	,	PUNCT
ejpam-3328	615	13	|x+(t)|	|x+(t)|	PUNCT
ejpam-3328	615	14	=	=	NOUN
ejpam-3328	615	15	1	1	X
ejpam-3328	615	16	.	.	X
ejpam-3328	615	17	using	use	VERB
ejpam-3328	615	18	theorem	theorem	NOUN
ejpam-3328	615	19	9	9	NUM
ejpam-3328	615	20	,	,	PUNCT
ejpam-3328	615	21	we	we	PRON
ejpam-3328	615	22	obtain	obtain	VERB
ejpam-3328	615	23	||ψ−||2l2	||ψ−||2l2	PROPN
ejpam-3328	615	24	+	+	CCONJ
ejpam-3328	615	25	||ψ+||2l2	||ψ+||2l2	PUNCT
ejpam-3328	616	1	=	=	SYM
ejpam-3328	616	2	∫	∫	PROPN
ejpam-3328	617	1	+	+	NUM
ejpam-3328	617	2	∞	∞	PROPN
ejpam-3328	617	3	−∞	−∞	X
ejpam-3328	617	4	∣∣∣∣∣iε(k	∣∣∣∣∣iε(k	PROPN
ejpam-3328	617	5	,	,	PUNCT
ejpam-3328	617	6	α	α	NOUN
ejpam-3328	617	7	)	)	PUNCT
ejpam-3328	617	8	k	k	PROPN
ejpam-3328	617	9	−	−	PROPN
ejpam-3328	617	10	ia	ia	PROPN
ejpam-3328	617	11	−	−	PROPN
ejpam-3328	617	12	f̃ε(k	f̃ε(k	PROPN
ejpam-3328	617	13	,	,	PUNCT
ejpam-3328	617	14	α	α	NOUN
ejpam-3328	617	15	)	)	PUNCT
ejpam-3328	617	16	k	k	PROPN
ejpam-3328	617	17	−	−	PROPN
ejpam-3328	617	18	ia	ia	PROPN
ejpam-3328	617	19	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-3328	617	20	2	2	NUM
ejpam-3328	617	21	dk	dk	NOUN
ejpam-3328	617	22	+	+	CCONJ
ejpam-3328	617	23	∫	∫	PROPN
ejpam-3328	618	1	+	+	NUM
ejpam-3328	618	2	∞	∞	PROPN
ejpam-3328	618	3	−∞	−∞	ADP
ejpam-3328	618	4	|jε(k	|jε(k	PROPN
ejpam-3328	618	5	,	,	PUNCT
ejpam-3328	618	6	α)|2	α)|2	NOUN
ejpam-3328	618	7	dk	dk	PROPN
ejpam-3328	618	8	≤	≤	PROPN
ejpam-3328	618	9	cncε	cncε	PROPN
ejpam-3328	618	10	.	.	PUNCT
ejpam-3328	619	1	a.	a.	PROPN
ejpam-3328	619	2	durmagambetov	durmagambetov	PROPN
ejpam-3328	619	3	/	/	SYM
ejpam-3328	619	4	eur	eur	PROPN
ejpam-3328	619	5	.	.	PUNCT
ejpam-3328	620	1	j.	j.	PROPN
ejpam-3328	620	2	pure	pure	PROPN
ejpam-3328	620	3	appl	appl	PROPN
ejpam-3328	620	4	.	.	PROPN
ejpam-3328	620	5	math	math	PROPN
ejpam-3328	620	6	,	,	PUNCT
ejpam-3328	620	7	11	11	NUM
ejpam-3328	620	8	(	(	PUNCT
ejpam-3328	620	9	4	4	NUM
ejpam-3328	620	10	)	)	PUNCT
ejpam-3328	620	11	(	(	PUNCT
ejpam-3328	620	12	2018	2018	NUM
ejpam-3328	620	13	)	)	PUNCT
ejpam-3328	620	14	,	,	PUNCT
ejpam-3328	620	15	1143	1143	NUM
ejpam-3328	620	16	-	-	SYM
ejpam-3328	620	17	1176	1176	NUM
ejpam-3328	620	18	1170	1170	NUM
ejpam-3328	620	19	lemma	lemma	PROPN
ejpam-3328	620	20	23	23	NUM
ejpam-3328	620	21	.	.	PUNCT
ejpam-3328	621	1	let	let	VERB
ejpam-3328	621	2	βn	βn	VERB
ejpam-3328	621	3	and	and	CCONJ
ejpam-3328	621	4	φn	φn	ADP
ejpam-3328	621	5	satisfy	satisfy	VERB
ejpam-3328	621	6	the	the	DET
ejpam-3328	621	7	equations	equation	NOUN
ejpam-3328	621	8	eβ	eβ	ADP
ejpam-3328	621	9	=	=	PUNCT
ejpam-3328	621	10	√	√	PROPN
ejpam-3328	621	11	(	(	PUNCT
ejpam-3328	621	12	2πn+	2πn+	NUM
ejpam-3328	621	13	φ)2	φ)2	PROPN
ejpam-3328	621	14	+	+	CCONJ
ejpam-3328	621	15	(	(	PUNCT
ejpam-3328	621	16	β	β	X
ejpam-3328	621	17	−	−	PROPN
ejpam-3328	621	18	a)2	a)2	PROPN
ejpam-3328	621	19	,	,	PUNCT
ejpam-3328	621	20	φ	φ	NOUN
ejpam-3328	621	21	=	=	SYM
ejpam-3328	622	1	π	π	X
ejpam-3328	622	2	−	−	NOUN
ejpam-3328	622	3	arg	arg	NOUN
ejpam-3328	622	4	(	(	PUNCT
ejpam-3328	622	5	2πn+	2πn+	ADJ
ejpam-3328	622	6	φ+	φ+	X
ejpam-3328	622	7	i(−a+	i(−a+	X
ejpam-3328	622	8	β	β	NOUN
ejpam-3328	622	9	)	)	PUNCT
ejpam-3328	622	10	)	)	PUNCT
ejpam-3328	622	11	.	.	PUNCT
ejpam-3328	623	1	then	then	ADV
ejpam-3328	623	2	,	,	PUNCT
ejpam-3328	623	3	tn	tn	PROPN
ejpam-3328	623	4	=	=	SYM
ejpam-3328	623	5	2πn+	2πn+	NUM
ejpam-3328	623	6	π	π	NOUN
ejpam-3328	623	7	+	+	CCONJ
ejpam-3328	623	8	iβn	iβn	NOUN
ejpam-3328	623	9	+	+	CCONJ
ejpam-3328	623	10	φn	φn	PROPN
ejpam-3328	623	11	,	,	PUNCT
ejpam-3328	623	12	n	n	PRON
ejpam-3328	623	13	≥	≥	NOUN
ejpam-3328	623	14	.0	.0	NUM
ejpam-3328	623	15	the	the	DET
ejpam-3328	623	16	root	root	NOUN
ejpam-3328	623	17	of	of	ADP
ejpam-3328	623	18	equation	equation	NOUN
ejpam-3328	623	19	is	be	AUX
ejpam-3328	623	20	r(k	r(k	PROPN
ejpam-3328	623	21	)	)	PUNCT
ejpam-3328	623	22	=	=	SYM
ejpam-3328	623	23	0	0	NUM
ejpam-3328	623	24	and	and	CCONJ
ejpam-3328	623	25	βn	βn	ADJ
ejpam-3328	623	26	=	=	ADJ
ejpam-3328	623	27	ln(2πn	ln(2πn	NOUN
ejpam-3328	623	28	)	)	PUNCT
ejpam-3328	623	29	+	+	NUM
ejpam-3328	623	30	o(1	o(1	NOUN
ejpam-3328	623	31	)	)	PUNCT
ejpam-3328	623	32	,	,	PUNCT
ejpam-3328	623	33	φn	φn	ADP
ejpam-3328	624	1	=	=	PUNCT
ejpam-3328	624	2	π	π	X
ejpam-3328	625	1	+	+	PROPN
ejpam-3328	625	2	o(ln(n)/n	o(ln(n)/n	PROPN
ejpam-3328	625	3	)	)	PUNCT
ejpam-3328	625	4	,	,	PUNCT
ejpam-3328	625	5	n	n	PRON
ejpam-3328	625	6	≥	≥	NOUN
ejpam-3328	625	7	1	1	NUM
ejpam-3328	625	8	.	.	PUNCT
ejpam-3328	625	9	proof	proof	NOUN
ejpam-3328	625	10	.	.	PUNCT
ejpam-3328	626	1	r(tn	r(tn	NOUN
ejpam-3328	626	2	)	)	PUNCT
ejpam-3328	627	1	=	=	PRON
ejpam-3328	627	2	e−itn	e−itn	VERB
ejpam-3328	627	3	tn	tn	PROPN
ejpam-3328	627	4	−	−	PROPN
ejpam-3328	627	5	ia	ia	PROPN
ejpam-3328	627	6	+	+	CCONJ
ejpam-3328	627	7	1	1	NUM
ejpam-3328	627	8	=	=	NOUN
ejpam-3328	627	9	e−i2πn+β−iφ	e−i2πn+β−iφ	NOUN
ejpam-3328	627	10	2πn+	2πn+	NUM
ejpam-3328	627	11	φ+	φ+	NOUN
ejpam-3328	627	12	i(βn	i(βn	ADP
ejpam-3328	627	13	−	−	PROPN
ejpam-3328	627	14	a	a	X
ejpam-3328	627	15	)	)	PUNCT
ejpam-3328	627	16	+	+	NOUN
ejpam-3328	627	17	1	1	NUM
ejpam-3328	627	18	=	=	SYM
ejpam-3328	627	19	e−i2πn+βn−iφ	e−i2πn+βn−iφ	NOUN
ejpam-3328	627	20	ei	ei	NOUN
ejpam-3328	627	21	arg(2πn+φ+i(−a+βn	arg(2πn+φ+i(−a+βn	NOUN
ejpam-3328	627	22	)	)	PUNCT
ejpam-3328	627	23	)	)	PUNCT
ejpam-3328	628	1	√	√	PROPN
ejpam-3328	628	2	(	(	PUNCT
ejpam-3328	628	3	2πn+	2πn+	NUM
ejpam-3328	628	4	φ)2	φ)2	PROPN
ejpam-3328	628	5	+	+	CCONJ
ejpam-3328	628	6	(	(	PUNCT
ejpam-3328	628	7	βn	βn	INTJ
ejpam-3328	628	8	−	−	PROPN
ejpam-3328	628	9	a)2	a)2	NOUN
ejpam-3328	628	10	+	+	CCONJ
ejpam-3328	628	11	1	1	NUM
ejpam-3328	628	12	=	=	SYM
ejpam-3328	628	13	−eβn√	−eβn√	NOUN
ejpam-3328	628	14	(	(	PUNCT
ejpam-3328	628	15	2πn+	2πn+	ADJ
ejpam-3328	628	16	φn)2	φn)2	NOUN
ejpam-3328	628	17	+	+	CCONJ
ejpam-3328	628	18	(	(	PUNCT
ejpam-3328	628	19	βn	βn	INTJ
ejpam-3328	628	20	−	−	PROPN
ejpam-3328	628	21	a)2	a)2	NOUN
ejpam-3328	628	22	+	+	CCONJ
ejpam-3328	628	23	1	1	NUM
ejpam-3328	628	24	=	=	SYM
ejpam-3328	628	25	−1	−1	NOUN
ejpam-3328	628	26	+	+	NOUN
ejpam-3328	628	27	1	1	NUM
ejpam-3328	628	28	=	=	SYM
ejpam-3328	628	29	0	0	X
ejpam-3328	628	30	.	.	PUNCT
ejpam-3328	629	1	take	take	VERB
ejpam-3328	629	2	β	β	NOUN
ejpam-3328	629	3	=	=	SYM
ejpam-3328	629	4	ln(2πn	ln(2πn	NOUN
ejpam-3328	629	5	)	)	PUNCT
ejpam-3328	630	1	+	+	NUM
ejpam-3328	630	2	γn	γn	NUM
ejpam-3328	630	3	.	.	PUNCT
ejpam-3328	631	1	then	then	ADV
ejpam-3328	631	2	,	,	PUNCT
ejpam-3328	631	3	eγn	eγn	NOUN
ejpam-3328	631	4	=	=	SYM
ejpam-3328	631	5	√	√	ADP
ejpam-3328	631	6	1	1	NUM
ejpam-3328	631	7	+	+	CCONJ
ejpam-3328	631	8	(	(	PUNCT
ejpam-3328	631	9	ln(nπ	ln(nπ	PROPN
ejpam-3328	631	10	)	)	PUNCT
ejpam-3328	631	11	+	+	SYM
ejpam-3328	631	12	γn	γn	ADP
ejpam-3328	631	13	−	−	NOUN
ejpam-3328	631	14	a)2	a)2	PROPN
ejpam-3328	631	15	(	(	PUNCT
ejpam-3328	631	16	2πn+	2πn+	NUM
ejpam-3328	631	17	φ)2	φ)2	PROPN
ejpam-3328	631	18	.	.	PUNCT
ejpam-3328	632	1	for	for	ADP
ejpam-3328	632	2	φ	φ	NUM
ejpam-3328	632	3	,	,	PUNCT
ejpam-3328	632	4	we	we	PRON
ejpam-3328	632	5	have	have	VERB
ejpam-3328	632	6	φn	φn	ADP
ejpam-3328	632	7	=	=	SYM
ejpam-3328	632	8	π	π	PROPN
ejpam-3328	632	9	−	−	PROPN
ejpam-3328	632	10	arctan	arctan	PROPN
ejpam-3328	632	11	(	(	PUNCT
ejpam-3328	632	12	(	(	PUNCT
ejpam-3328	632	13	−a+	−a+	X
ejpam-3328	632	14	β	β	X
ejpam-3328	632	15	)	)	PUNCT
ejpam-3328	632	16	2πn+	2πn+	NUM
ejpam-3328	632	17	φn	φn	ADP
ejpam-3328	632	18	)	)	PUNCT
ejpam-3328	632	19	,	,	PUNCT
ejpam-3328	632	20	and	and	CCONJ
ejpam-3328	632	21	we	we	PRON
ejpam-3328	632	22	get	get	VERB
ejpam-3328	632	23	φn	φn	ADP
ejpam-3328	632	24	=	=	PUNCT
ejpam-3328	632	25	π	π	X
ejpam-3328	633	1	+	+	PROPN
ejpam-3328	633	2	o(ln(n)/n	o(ln(n)/n	PROPN
ejpam-3328	633	3	)	)	PUNCT
ejpam-3328	633	4	,	,	PUNCT
ejpam-3328	633	5	which	which	PRON
ejpam-3328	633	6	completes	complete	VERB
ejpam-3328	633	7	the	the	DET
ejpam-3328	633	8	proof	proof	NOUN
ejpam-3328	633	9	.	.	PUNCT
ejpam-3328	634	1	theorem	theorem	ADJ
ejpam-3328	634	2	10	10	NUM
ejpam-3328	634	3	.	.	PUNCT
ejpam-3328	635	1	let	let	VERB
ejpam-3328	635	2	s	s	PRON
ejpam-3328	635	3	∈	∈	PROPN
ejpam-3328	635	4	d(m	d(m	PROPN
ejpam-3328	635	5	)	)	PUNCT
ejpam-3328	635	6	∪d(m	∪d(m	PROPN
ejpam-3328	635	7	)	)	PUNCT
ejpam-3328	635	8	and	and	CCONJ
ejpam-3328	635	9	a	a	DET
ejpam-3328	635	10	>	>	X
ejpam-3328	635	11	2	2	NUM
ejpam-3328	635	12	,	,	PUNCT
ejpam-3328	635	13	with	with	ADP
ejpam-3328	635	14	1/2	1/2	NUM
ejpam-3328	635	15	+	+	NUM
ejpam-3328	635	16	3ε	3ε	NUM
ejpam-3328	635	17	<	<	X
ejpam-3328	635	18	re(s	re(s	PROPN
ejpam-3328	635	19	)	)	PUNCT
ejpam-3328	635	20	<	<	X
ejpam-3328	635	21	1−	1−	NUM
ejpam-3328	635	22	3ε	3ε	NUM
ejpam-3328	635	23	.	.	PUNCT
ejpam-3328	636	1	then	then	ADV
ejpam-3328	636	2	,	,	PUNCT
ejpam-3328	636	3	|q(s)|	|q(s)|	PROPN
ejpam-3328	636	4	<	<	X
ejpam-3328	636	5	cmcε	cmcε	PROPN
ejpam-3328	636	6	.	.	PUNCT
ejpam-3328	636	7	proof	proof	NOUN
ejpam-3328	636	8	.	.	PUNCT
ejpam-3328	637	1	by	by	ADP
ejpam-3328	637	2	theorem	theorem	NOUN
ejpam-3328	637	3	9	9	NUM
ejpam-3328	637	4	,	,	PUNCT
ejpam-3328	637	5	ψ−(k	ψ−(k	NOUN
ejpam-3328	637	6	,	,	PUNCT
ejpam-3328	637	7	α	α	NOUN
ejpam-3328	637	8	)	)	PUNCT
ejpam-3328	637	9	=	=	SYM
ejpam-3328	637	10	iε(k	iε(k	PROPN
ejpam-3328	637	11	,	,	PUNCT
ejpam-3328	637	12	α	α	NOUN
ejpam-3328	637	13	)	)	PUNCT
ejpam-3328	637	14	k	k	PROPN
ejpam-3328	637	15	−	−	PROPN
ejpam-3328	637	16	ia	ia	PROPN
ejpam-3328	637	17	−	−	PROPN
ejpam-3328	637	18	f̃ε(k	f̃ε(k	PROPN
ejpam-3328	637	19	,	,	PUNCT
ejpam-3328	637	20	α	α	NOUN
ejpam-3328	637	21	)	)	PUNCT
ejpam-3328	638	1	k	k	PROPN
ejpam-3328	638	2	−	−	PROPN
ejpam-3328	638	3	ia	ia	PROPN
ejpam-3328	638	4	=	=	SYM
ejpam-3328	638	5	−x−(k	−x−(k	PROPN
ejpam-3328	638	6	)	)	PUNCT
ejpam-3328	638	7	2πi	2πi	NOUN
ejpam-3328	638	8	∫	∫	PROPN
ejpam-3328	638	9	∞	∞	PROPN
ejpam-3328	638	10	−∞	−∞	X
ejpam-3328	638	11	gε(t	gε(t	PROPN
ejpam-3328	638	12	,	,	PUNCT
ejpam-3328	638	13	α	α	NOUN
ejpam-3328	638	14	)	)	PUNCT
ejpam-3328	638	15	x−(t	x−(t	PROPN
ejpam-3328	638	16	)	)	PUNCT
ejpam-3328	639	1	dt	dt	PROPN
ejpam-3328	639	2	t−	t−	PROPN
ejpam-3328	639	3	k	k	PROPN
ejpam-3328	640	1	+	+	CCONJ
ejpam-3328	640	2	i0	i0	PROPN
ejpam-3328	640	3	.	.	PUNCT
ejpam-3328	641	1	a.	a.	NOUN
ejpam-3328	641	2	durmagambetov	durmagambetov	PROPN
ejpam-3328	641	3	/	/	SYM
ejpam-3328	641	4	eur	eur	PROPN
ejpam-3328	641	5	.	.	PUNCT
ejpam-3328	642	1	j.	j.	PROPN
ejpam-3328	642	2	pure	pure	PROPN
ejpam-3328	642	3	appl	appl	PROPN
ejpam-3328	642	4	.	.	PROPN
ejpam-3328	642	5	math	math	PROPN
ejpam-3328	642	6	,	,	PUNCT
ejpam-3328	642	7	11	11	NUM
ejpam-3328	642	8	(	(	PUNCT
ejpam-3328	642	9	4	4	NUM
ejpam-3328	642	10	)	)	PUNCT
ejpam-3328	642	11	(	(	PUNCT
ejpam-3328	642	12	2018	2018	NUM
ejpam-3328	642	13	)	)	PUNCT
ejpam-3328	642	14	,	,	PUNCT
ejpam-3328	642	15	1143	1143	NUM
ejpam-3328	642	16	-	-	SYM
ejpam-3328	642	17	1176	1176	NUM
ejpam-3328	642	18	1171	1171	NUM
ejpam-3328	642	19	denote	denote	NOUN
ejpam-3328	642	20	i1	i1	PROPN
ejpam-3328	642	21	=	=	PUNCT
ejpam-3328	643	1	∫	∫	PROPN
ejpam-3328	643	2	∞	∞	PROPN
ejpam-3328	643	3	−∞	−∞	X
ejpam-3328	643	4	gε(t	gε(t	PROPN
ejpam-3328	643	5	,	,	PUNCT
ejpam-3328	643	6	α	α	NOUN
ejpam-3328	643	7	)	)	PUNCT
ejpam-3328	643	8	x−(t)(t−	x−(t)(t−	PROPN
ejpam-3328	644	1	k	k	PROPN
ejpam-3328	644	2	+	+	CCONJ
ejpam-3328	644	3	i0	i0	PROPN
ejpam-3328	644	4	)	)	PUNCT
ejpam-3328	644	5	dt	dt	PROPN
ejpam-3328	644	6	,	,	PUNCT
ejpam-3328	644	7	i2	i2	PROPN
ejpam-3328	644	8	=	=	SYM
ejpam-3328	644	9	(	(	PUNCT
ejpam-3328	644	10	k	k	X
ejpam-3328	644	11	−	−	PROPN
ejpam-3328	644	12	ia)i1	ia)i1	PROPN
ejpam-3328	644	13	.	.	PUNCT
ejpam-3328	645	1	lemma	lemma	PROPN
ejpam-3328	645	2	22	22	NUM
ejpam-3328	645	3	and	and	CCONJ
ejpam-3328	645	4	lemma	lemma	PROPN
ejpam-3328	645	5	of	of	ADP
ejpam-3328	645	6	jordan	jordan	PROPN
ejpam-3328	645	7	yield	yield	PROPN
ejpam-3328	645	8	i1	i1	PROPN
ejpam-3328	645	9	=	=	PUNCT
ejpam-3328	646	1	∫	∫	PROPN
ejpam-3328	646	2	∞	∞	PROPN
ejpam-3328	646	3	−∞	−∞	X
ejpam-3328	646	4	gε(t	gε(t	PROPN
ejpam-3328	646	5	,	,	PUNCT
ejpam-3328	646	6	α	α	NOUN
ejpam-3328	646	7	)	)	PUNCT
ejpam-3328	646	8	x−(t)(t−	x−(t)(t−	PROPN
ejpam-3328	647	1	k	k	PROPN
ejpam-3328	647	2	+	+	CCONJ
ejpam-3328	647	3	i0	i0	PROPN
ejpam-3328	647	4	)	)	PUNCT
ejpam-3328	647	5	dt	dt	X
ejpam-3328	648	1	=	=	PUNCT
ejpam-3328	648	2	∞∑	∞∑	NUM
ejpam-3328	648	3	0	0	NUM
ejpam-3328	648	4	gε(tn	gε(tn	NOUN
ejpam-3328	648	5	,	,	PUNCT
ejpam-3328	648	6	α	α	NOUN
ejpam-3328	648	7	)	)	PUNCT
ejpam-3328	648	8	x	x	SYM
ejpam-3328	648	9	′−(tn)(tn	′−(tn)(tn	PROPN
ejpam-3328	648	10	−	−	PROPN
ejpam-3328	648	11	k	k	PROPN
ejpam-3328	648	12	+	+	CCONJ
ejpam-3328	648	13	i0	i0	PROPN
ejpam-3328	648	14	)	)	PUNCT
ejpam-3328	648	15	,	,	PUNCT
ejpam-3328	648	16	iε(k	iε(k	NUM
ejpam-3328	648	17	,	,	PUNCT
ejpam-3328	648	18	α	α	X
ejpam-3328	648	19	)	)	PUNCT
ejpam-3328	648	20	=	=	SYM
ejpam-3328	648	21	fε(k	fε(k	PROPN
ejpam-3328	648	22	,	,	PUNCT
ejpam-3328	648	23	α	α	X
ejpam-3328	648	24	)	)	PUNCT
ejpam-3328	649	1	+	+	NOUN
ejpam-3328	649	2	x−(k)(k	x−(k)(k	NOUN
ejpam-3328	649	3	−	−	PROPN
ejpam-3328	649	4	ia	ia	PROPN
ejpam-3328	649	5	)	)	PUNCT
ejpam-3328	649	6	∞∑	∞∑	PROPN
ejpam-3328	649	7	0	0	NUM
ejpam-3328	649	8	gε(tn	gε(tn	NOUN
ejpam-3328	649	9	,	,	PUNCT
ejpam-3328	649	10	α	α	NOUN
ejpam-3328	649	11	)	)	PUNCT
ejpam-3328	649	12	x	x	SYM
ejpam-3328	649	13	′−(tn)(tn	′−(tn)(tn	PROPN
ejpam-3328	649	14	−	−	PROPN
ejpam-3328	649	15	k	k	PROPN
ejpam-3328	649	16	+	+	CCONJ
ejpam-3328	649	17	i0	i0	PROPN
ejpam-3328	649	18	)	)	PUNCT
ejpam-3328	649	19	.	.	PUNCT
ejpam-3328	650	1	as	as	SCONJ
ejpam-3328	650	2	k	k	PROPN
ejpam-3328	650	3	∈	∈	PROPN
ejpam-3328	650	4	(	(	PUNCT
ejpam-3328	650	5	−n	−n	NOUN
ejpam-3328	650	6	,	,	PUNCT
ejpam-3328	650	7	n	n	CCONJ
ejpam-3328	650	8	)	)	PUNCT
ejpam-3328	650	9	is	be	AUX
ejpam-3328	650	10	a	a	DET
ejpam-3328	650	11	uniformly	uniformly	ADV
ejpam-3328	650	12	convergent	convergent	NOUN
ejpam-3328	650	13	series	series	NOUN
ejpam-3328	650	14	,	,	PUNCT
ejpam-3328	650	15	we	we	PRON
ejpam-3328	650	16	have∫	have∫	VERB
ejpam-3328	650	17	+	+	ADV
ejpam-3328	650	18	n	n	PRON
ejpam-3328	650	19	−n	−n	ADV
ejpam-3328	650	20	eitk	eitk	VERB
ejpam-3328	650	21	d2	d2	PROPN
ejpam-3328	650	22	dk2	dk2	PROPN
ejpam-3328	650	23	(	(	PUNCT
ejpam-3328	650	24	iε(k	iε(k	PROPN
ejpam-3328	650	25	,	,	PUNCT
ejpam-3328	650	26	α	α	NOUN
ejpam-3328	650	27	)	)	PUNCT
ejpam-3328	650	28	x−(k	x−(k	PROPN
ejpam-3328	650	29	)	)	PUNCT
ejpam-3328	650	30	)	)	PUNCT
ejpam-3328	651	1	dk	dk	X
ejpam-3328	651	2	=	=	PUNCT
ejpam-3328	651	3	∫	∫	PROPN
ejpam-3328	652	1	+	+	CCONJ
ejpam-3328	652	2	n	n	PROPN
ejpam-3328	652	3	−n	−n	ADV
ejpam-3328	652	4	eitk	eitk	VERB
ejpam-3328	652	5	d2	d2	PROPN
ejpam-3328	652	6	dk2	dk2	PROPN
ejpam-3328	652	7	(	(	PUNCT
ejpam-3328	652	8	fε(k	fε(k	PROPN
ejpam-3328	652	9	,	,	PUNCT
ejpam-3328	652	10	α	α	NOUN
ejpam-3328	652	11	)	)	PUNCT
ejpam-3328	652	12	x−(k	x−(k	PROPN
ejpam-3328	652	13	)	)	PUNCT
ejpam-3328	652	14	)	)	PUNCT
ejpam-3328	653	1	dk+	dk+	PROPN
ejpam-3328	653	2	∫	∫	PROPN
ejpam-3328	654	1	+	+	CCONJ
ejpam-3328	654	2	n	n	PROPN
ejpam-3328	654	3	−n	−n	ADV
ejpam-3328	654	4	eitk	eitk	VERB
ejpam-3328	654	5	d2	d2	PROPN
ejpam-3328	654	6	dk2	dk2	PROPN
ejpam-3328	654	7	(	(	PUNCT
ejpam-3328	654	8	(	(	PUNCT
ejpam-3328	654	9	k	k	X
ejpam-3328	654	10	−	−	PROPN
ejpam-3328	654	11	ia)i1	ia)i1	PROPN
ejpam-3328	654	12	)	)	PUNCT
ejpam-3328	655	1	dk	dk	PROPN
ejpam-3328	655	2	.	.	PUNCT
ejpam-3328	656	1	by	by	ADP
ejpam-3328	656	2	the	the	DET
ejpam-3328	656	3	definition	definition	NOUN
ejpam-3328	656	4	i1	i1	NOUN
ejpam-3328	656	5	,	,	PUNCT
ejpam-3328	656	6	we	we	PRON
ejpam-3328	656	7	have∫	have∫	VERB
ejpam-3328	656	8	+	+	ADV
ejpam-3328	656	9	n	n	PRON
ejpam-3328	656	10	−n	−n	ADV
ejpam-3328	656	11	eitk	eitk	VERB
ejpam-3328	656	12	d2	d2	PROPN
ejpam-3328	656	13	dk2	dk2	PROPN
ejpam-3328	656	14	(	(	PUNCT
ejpam-3328	656	15	(	(	PUNCT
ejpam-3328	656	16	k	k	X
ejpam-3328	656	17	−	−	PROPN
ejpam-3328	656	18	ia)i1	ia)i1	NOUN
ejpam-3328	656	19	)	)	PUNCT
ejpam-3328	657	1	dk	dk	PROPN
ejpam-3328	657	2	=	=	PUNCT
ejpam-3328	657	3	∫	∫	PROPN
ejpam-3328	658	1	+	+	SYM
ejpam-3328	658	2	n	n	PROPN
ejpam-3328	658	3	−n	−n	ADJ
ejpam-3328	658	4	n∑	n∑	NOUN
ejpam-3328	658	5	1	1	NUM
ejpam-3328	658	6	eitk	eitk	VERB
ejpam-3328	658	7	d2	d2	PROPN
ejpam-3328	658	8	dk2	dk2	PROPN
ejpam-3328	658	9	(	(	PUNCT
ejpam-3328	658	10	(	(	PUNCT
ejpam-3328	658	11	k	k	INTJ
ejpam-3328	658	12	−	−	PROPN
ejpam-3328	658	13	ia)gε(tn	ia)gε(tn	ADP
ejpam-3328	658	14	,	,	PUNCT
ejpam-3328	658	15	α	α	NOUN
ejpam-3328	658	16	)	)	PUNCT
ejpam-3328	658	17	x	x	SYM
ejpam-3328	658	18	′−(tn)(tn	′−(tn)(tn	PROPN
ejpam-3328	658	19	−	−	PROPN
ejpam-3328	659	1	k	k	PROPN
ejpam-3328	659	2	+	+	CCONJ
ejpam-3328	659	3	i0	i0	PROPN
ejpam-3328	659	4	)	)	PUNCT
ejpam-3328	659	5	)	)	PUNCT
ejpam-3328	660	1	dk	dk	PROPN
ejpam-3328	660	2	+	+	NUM
ejpam-3328	660	3	∫	∫	PROPN
ejpam-3328	661	1	+	+	CCONJ
ejpam-3328	661	2	n	n	PROPN
ejpam-3328	661	3	−n	−n	ADJ
ejpam-3328	661	4	∞∑	∞∑	PROPN
ejpam-3328	661	5	n	n	X
ejpam-3328	661	6	d2	d2	PROPN
ejpam-3328	661	7	dk2	dk2	PROPN
ejpam-3328	661	8	(	(	PUNCT
ejpam-3328	661	9	(	(	PUNCT
ejpam-3328	661	10	k	k	INTJ
ejpam-3328	661	11	−	−	PROPN
ejpam-3328	661	12	ia)gε(tn	ia)gε(tn	ADP
ejpam-3328	661	13	,	,	PUNCT
ejpam-3328	661	14	α	α	NOUN
ejpam-3328	661	15	)	)	PUNCT
ejpam-3328	661	16	x	x	SYM
ejpam-3328	661	17	′−(tn)(tn	′−(tn)(tn	PROPN
ejpam-3328	661	18	−	−	PROPN
ejpam-3328	661	19	k	k	PROPN
ejpam-3328	661	20	+	+	CCONJ
ejpam-3328	661	21	i0	i0	PROPN
ejpam-3328	661	22	)	)	PUNCT
ejpam-3328	661	23	)	)	PUNCT
ejpam-3328	662	1	eitkdk	eitkdk	NOUN
ejpam-3328	662	2	=	=	PUNCT
ejpam-3328	662	3	w1	w1	PROPN
ejpam-3328	662	4	+	+	PROPN
ejpam-3328	662	5	w2	w2	NOUN
ejpam-3328	662	6	,	,	PUNCT
ejpam-3328	662	7	w1	w1	NOUN
ejpam-3328	662	8	=	=	SYM
ejpam-3328	662	9	∫	∫	PROPN
ejpam-3328	663	1	+	+	SYM
ejpam-3328	663	2	n	n	PROPN
ejpam-3328	663	3	−n	−n	ADJ
ejpam-3328	663	4	n∑	n∑	NOUN
ejpam-3328	663	5	1	1	NUM
ejpam-3328	663	6	2	2	NUM
ejpam-3328	663	7	(	(	PUNCT
ejpam-3328	663	8	gε(tn	gε(tn	PROPN
ejpam-3328	663	9	,	,	PUNCT
ejpam-3328	663	10	α	α	NOUN
ejpam-3328	663	11	)	)	PUNCT
ejpam-3328	663	12	x	x	SYM
ejpam-3328	663	13	′−(tn)(tn	′−(tn)(tn	PROPN
ejpam-3328	663	14	−	−	PROPN
ejpam-3328	664	1	k	k	PROPN
ejpam-3328	665	1	+	+	X
ejpam-3328	665	2	i0)2	i0)2	X
ejpam-3328	665	3	+	+	CCONJ
ejpam-3328	665	4	(	(	PUNCT
ejpam-3328	665	5	k	k	X
ejpam-3328	665	6	−	−	PROPN
ejpam-3328	665	7	ia)gε(tn	ia)gε(tn	ADP
ejpam-3328	665	8	,	,	PUNCT
ejpam-3328	665	9	α	α	NOUN
ejpam-3328	665	10	)	)	PUNCT
ejpam-3328	665	11	x	x	SYM
ejpam-3328	665	12	′−(tn)(tn	′−(tn)(tn	PROPN
ejpam-3328	665	13	−	−	PROPN
ejpam-3328	666	1	k	k	NOUN
ejpam-3328	666	2	+	+	CCONJ
ejpam-3328	666	3	i0)3	i0)3	CCONJ
ejpam-3328	666	4	)	)	PUNCT
ejpam-3328	666	5	eitkdk	eitkdk	ADJ
ejpam-3328	666	6	,	,	PUNCT
ejpam-3328	666	7	w2	w2	NOUN
ejpam-3328	666	8	=	=	SYM
ejpam-3328	666	9	∫	∫	PROPN
ejpam-3328	667	1	+	+	CCONJ
ejpam-3328	667	2	n	n	PROPN
ejpam-3328	667	3	−n	−n	ADV
ejpam-3328	667	4	∞∑	∞∑	PROPN
ejpam-3328	667	5	n+1	n+1	NUM
ejpam-3328	667	6	2	2	NUM
ejpam-3328	667	7	(	(	PUNCT
ejpam-3328	667	8	gε(tn	gε(tn	PROPN
ejpam-3328	667	9	,	,	PUNCT
ejpam-3328	667	10	α	α	NOUN
ejpam-3328	667	11	)	)	PUNCT
ejpam-3328	667	12	x	x	SYM
ejpam-3328	667	13	′−(tn)(tn	′−(tn)(tn	PROPN
ejpam-3328	667	14	−	−	PROPN
ejpam-3328	667	15	k	k	PROPN
ejpam-3328	668	1	+	+	X
ejpam-3328	668	2	i0)2	i0)2	X
ejpam-3328	668	3	+	+	CCONJ
ejpam-3328	668	4	(	(	PUNCT
ejpam-3328	668	5	k	k	X
ejpam-3328	668	6	−	−	PROPN
ejpam-3328	668	7	ia)gε(tn	ia)gε(tn	ADP
ejpam-3328	668	8	,	,	PUNCT
ejpam-3328	668	9	α	α	NOUN
ejpam-3328	668	10	)	)	PUNCT
ejpam-3328	668	11	x	x	SYM
ejpam-3328	668	12	′−(tn)(tn	′−(tn)(tn	PROPN
ejpam-3328	668	13	−	−	PROPN
ejpam-3328	669	1	k	k	NOUN
ejpam-3328	669	2	+	+	CCONJ
ejpam-3328	669	3	i0)3	i0)3	CCONJ
ejpam-3328	669	4	)	)	PUNCT
ejpam-3328	669	5	eitkdk	eitkdk	ADJ
ejpam-3328	669	6	.	.	PUNCT
ejpam-3328	670	1	denote	denote	VERB
ejpam-3328	670	2	w	w	PROPN
ejpam-3328	670	3	0	0	NUM
ejpam-3328	670	4	1	1	NUM
ejpam-3328	670	5	(	(	PUNCT
ejpam-3328	670	6	k	k	NOUN
ejpam-3328	670	7	)	)	PUNCT
ejpam-3328	671	1	=	=	SYM
ejpam-3328	671	2	n∑	n∑	NOUN
ejpam-3328	671	3	1	1	NUM
ejpam-3328	671	4	2	2	NUM
ejpam-3328	671	5	(	(	PUNCT
ejpam-3328	671	6	gε(tn	gε(tn	PROPN
ejpam-3328	671	7	,	,	PUNCT
ejpam-3328	671	8	α	α	NOUN
ejpam-3328	671	9	)	)	PUNCT
ejpam-3328	671	10	x	x	SYM
ejpam-3328	671	11	′−(tn)(tn	′−(tn)(tn	PROPN
ejpam-3328	671	12	−	−	PROPN
ejpam-3328	672	1	k	k	PROPN
ejpam-3328	673	1	+	+	X
ejpam-3328	673	2	i0)2	i0)2	X
ejpam-3328	673	3	+	+	CCONJ
ejpam-3328	673	4	(	(	PUNCT
ejpam-3328	673	5	k	k	X
ejpam-3328	673	6	−	−	PROPN
ejpam-3328	673	7	ia)gε(tn	ia)gε(tn	ADP
ejpam-3328	673	8	,	,	PUNCT
ejpam-3328	673	9	α	α	NOUN
ejpam-3328	673	10	)	)	PUNCT
ejpam-3328	673	11	x	x	SYM
ejpam-3328	673	12	′−(tn)(tn	′−(tn)(tn	PROPN
ejpam-3328	673	13	−	−	PROPN
ejpam-3328	674	1	k	k	NOUN
ejpam-3328	675	1	+	+	CCONJ
ejpam-3328	675	2	i0)3	i0)3	CCONJ
ejpam-3328	675	3	)	)	PUNCT
ejpam-3328	675	4	eitk	eitk	VERB
ejpam-3328	675	5	and	and	CCONJ
ejpam-3328	675	6	w	w	NOUN
ejpam-3328	675	7	0	0	NUM
ejpam-3328	675	8	2	2	NUM
ejpam-3328	675	9	(	(	PUNCT
ejpam-3328	675	10	k	k	NOUN
ejpam-3328	675	11	)	)	PUNCT
ejpam-3328	675	12	=	=	PUNCT
ejpam-3328	676	1	∞∑	∞∑	NUM
ejpam-3328	676	2	n+1	n+1	NUM
ejpam-3328	676	3	2	2	NUM
ejpam-3328	676	4	(	(	PUNCT
ejpam-3328	676	5	gε(tn	gε(tn	PROPN
ejpam-3328	676	6	,	,	PUNCT
ejpam-3328	676	7	α	α	NOUN
ejpam-3328	676	8	)	)	PUNCT
ejpam-3328	676	9	x	x	SYM
ejpam-3328	676	10	′−(tn)(tn	′−(tn)(tn	PROPN
ejpam-3328	676	11	−	−	PROPN
ejpam-3328	676	12	k	k	PROPN
ejpam-3328	677	1	+	+	X
ejpam-3328	677	2	i0)2	i0)2	X
ejpam-3328	677	3	+	+	CCONJ
ejpam-3328	677	4	(	(	PUNCT
ejpam-3328	677	5	k	k	X
ejpam-3328	677	6	−	−	PROPN
ejpam-3328	677	7	ia)gε(tn	ia)gε(tn	ADP
ejpam-3328	677	8	,	,	PUNCT
ejpam-3328	677	9	α	α	NOUN
ejpam-3328	677	10	)	)	PUNCT
ejpam-3328	677	11	x	x	SYM
ejpam-3328	677	12	′−(tn)(tn	′−(tn)(tn	PROPN
ejpam-3328	677	13	−	−	PROPN
ejpam-3328	678	1	k	k	NOUN
ejpam-3328	678	2	+	+	CCONJ
ejpam-3328	678	3	i0)3	i0)3	CCONJ
ejpam-3328	678	4	)	)	PUNCT
ejpam-3328	678	5	eitk	eitk	PROPN
ejpam-3328	678	6	.	.	PUNCT
ejpam-3328	679	1	consider	consider	VERB
ejpam-3328	679	2	the	the	DET
ejpam-3328	679	3	integration	integration	NOUN
ejpam-3328	679	4	of	of	ADP
ejpam-3328	679	5	the	the	DET
ejpam-3328	679	6	functions	function	NOUN
ejpam-3328	679	7	w	w	NOUN
ejpam-3328	679	8	0	0	NUM
ejpam-3328	679	9	1	1	NUM
ejpam-3328	679	10	and	and	CCONJ
ejpam-3328	679	11	w	w	NOUN
ejpam-3328	679	12	0	0	NUM
ejpam-3328	679	13	2	2	NUM
ejpam-3328	679	14	around	around	ADP
ejpam-3328	679	15	the	the	DET
ejpam-3328	679	16	square	square	ADJ
ejpam-3328	679	17	contour	contour	NOUN
ejpam-3328	679	18	s	s	NOUN
ejpam-3328	679	19	with	with	ADP
ejpam-3328	679	20	vertices	vertex	NOUN
ejpam-3328	679	21	±n	±n	PROPN
ejpam-3328	679	22	and	and	CCONJ
ejpam-3328	679	23	±n	±n	ADJ
ejpam-3328	679	24	−	−	PROPN
ejpam-3328	679	25	in	in	ADP
ejpam-3328	679	26	and	and	CCONJ
ejpam-3328	679	27	oriented	orient	VERB
ejpam-3328	679	28	positively	positively	ADV
ejpam-3328	679	29	.	.	PUNCT
ejpam-3328	680	1	analyticity	analyticity	NOUN
ejpam-3328	680	2	of	of	ADP
ejpam-3328	680	3	the	the	DET
ejpam-3328	680	4	functions	function	NOUN
ejpam-3328	680	5	w	w	NOUN
ejpam-3328	680	6	0	0	NUM
ejpam-3328	680	7	1	1	NUM
ejpam-3328	680	8	and	and	CCONJ
ejpam-3328	680	9	w	w	PROPN
ejpam-3328	680	10	0	0	NUM
ejpam-3328	680	11	2	2	NUM
ejpam-3328	680	12	yields	yield	NOUN
ejpam-3328	680	13	∫	∫	PROPN
ejpam-3328	680	14	s	s	PROPN
ejpam-3328	680	15	w	w	PROPN
ejpam-3328	680	16	0	0	NUM
ejpam-3328	680	17	1	1	NUM
ejpam-3328	680	18	ds	ds	NOUN
ejpam-3328	680	19	=	=	SYM
ejpam-3328	680	20	0	0	NUM
ejpam-3328	680	21	,	,	PUNCT
ejpam-3328	680	22	∫	∫	PROPN
ejpam-3328	680	23	s	s	PROPN
ejpam-3328	680	24	w	w	PROPN
ejpam-3328	680	25	0	0	NUM
ejpam-3328	680	26	2	2	NUM
ejpam-3328	680	27	ds	ds	NOUN
ejpam-3328	680	28	=	=	SYM
ejpam-3328	680	29	0	0	NUM
ejpam-3328	680	30	a.	a.	NOUN
ejpam-3328	680	31	durmagambetov	durmagambetov	PROPN
ejpam-3328	680	32	/	/	SYM
ejpam-3328	680	33	eur	eur	PROPN
ejpam-3328	680	34	.	.	PUNCT
ejpam-3328	681	1	j.	j.	PROPN
ejpam-3328	681	2	pure	pure	PROPN
ejpam-3328	681	3	appl	appl	PROPN
ejpam-3328	681	4	.	.	PROPN
ejpam-3328	681	5	math	math	PROPN
ejpam-3328	681	6	,	,	PUNCT
ejpam-3328	681	7	11	11	NUM
ejpam-3328	681	8	(	(	PUNCT
ejpam-3328	681	9	4	4	NUM
ejpam-3328	681	10	)	)	PUNCT
ejpam-3328	681	11	(	(	PUNCT
ejpam-3328	681	12	2018	2018	NUM
ejpam-3328	681	13	)	)	PUNCT
ejpam-3328	681	14	,	,	PUNCT
ejpam-3328	681	15	1143	1143	NUM
ejpam-3328	681	16	-	-	SYM
ejpam-3328	681	17	1176	1176	NUM
ejpam-3328	681	18	1172	1172	NUM
ejpam-3328	681	19	and	and	CCONJ
ejpam-3328	681	20	w1	w1	NOUN
ejpam-3328	681	21	=	=	SYM
ejpam-3328	681	22	∫	∫	PROPN
ejpam-3328	682	1	−in	−in	PROPN
ejpam-3328	682	2	0	0	PROPN
ejpam-3328	683	1	w	w	NOUN
ejpam-3328	683	2	0	0	NUM
ejpam-3328	683	3	1	1	NUM
ejpam-3328	683	4	(	(	PUNCT
ejpam-3328	683	5	−n	−n	NOUN
ejpam-3328	683	6	+	+	NUM
ejpam-3328	683	7	iτ)idτ	iτ)idτ	X
ejpam-3328	683	8	+	+	CCONJ
ejpam-3328	683	9	∫	∫	PROPN
ejpam-3328	683	10	0	0	NUM
ejpam-3328	684	1	−in	−in	PROPN
ejpam-3328	684	2	w	w	NOUN
ejpam-3328	684	3	0	0	NUM
ejpam-3328	684	4	1	1	NUM
ejpam-3328	684	5	(	(	PUNCT
ejpam-3328	684	6	n	n	X
ejpam-3328	684	7	+	+	NUM
ejpam-3328	684	8	iτ)idτ	iτ)idτ	PRON
ejpam-3328	684	9	+	+	CCONJ
ejpam-3328	684	10	∫	∫	PROPN
ejpam-3328	684	11	−n	−n	PROPN
ejpam-3328	684	12	n	n	PROPN
ejpam-3328	684	13	w	w	PROPN
ejpam-3328	684	14	0	0	NUM
ejpam-3328	684	15	1	1	NUM
ejpam-3328	684	16	(	(	PUNCT
ejpam-3328	684	17	−in	−in	PROPN
ejpam-3328	684	18	+	+	SYM
ejpam-3328	684	19	τ)dτ	τ)dτ	PROPN
ejpam-3328	684	20	,	,	PUNCT
ejpam-3328	684	21	w2	w2	NOUN
ejpam-3328	684	22	=	=	SYM
ejpam-3328	684	23	∫	∫	PROPN
ejpam-3328	685	1	−in	−in	PROPN
ejpam-3328	685	2	0	0	PROPN
ejpam-3328	685	3	w	w	NOUN
ejpam-3328	685	4	0	0	NUM
ejpam-3328	685	5	2	2	NUM
ejpam-3328	685	6	(	(	PUNCT
ejpam-3328	685	7	−n	−n	NOUN
ejpam-3328	685	8	+	+	NUM
ejpam-3328	685	9	iτ)idτ	iτ)idτ	X
ejpam-3328	686	1	+	+	CCONJ
ejpam-3328	686	2	∫	∫	PROPN
ejpam-3328	686	3	0	0	NUM
ejpam-3328	687	1	−in	−in	PROPN
ejpam-3328	687	2	w	w	NOUN
ejpam-3328	687	3	0	0	NUM
ejpam-3328	687	4	2	2	NUM
ejpam-3328	687	5	(	(	PUNCT
ejpam-3328	687	6	n	n	X
ejpam-3328	687	7	+	+	NUM
ejpam-3328	687	8	iτ)idτ	iτ)idτ	PRON
ejpam-3328	687	9	+	+	CCONJ
ejpam-3328	687	10	∫	∫	PROPN
ejpam-3328	687	11	−n	−n	PROPN
ejpam-3328	687	12	n	n	PROPN
ejpam-3328	687	13	w	w	PROPN
ejpam-3328	687	14	0	0	NUM
ejpam-3328	687	15	2	2	NUM
ejpam-3328	687	16	(	(	PUNCT
ejpam-3328	687	17	−in	−in	NOUN
ejpam-3328	687	18	+	+	PUNCT
ejpam-3328	687	19	τ)dτ	τ)dτ	PROPN
ejpam-3328	687	20	.	.	PUNCT
ejpam-3328	688	1	the	the	DET
ejpam-3328	688	2	last	last	ADJ
ejpam-3328	688	3	integrals	integral	NOUN
ejpam-3328	688	4	yield	yield	VERB
ejpam-3328	688	5	|w1|	|w1|	NOUN
ejpam-3328	688	6	≤	≤	NUM
ejpam-3328	688	7	∣∣∣∣∫	∣∣∣∣∫	NUM
ejpam-3328	688	8	−in	−in	NOUN
ejpam-3328	688	9	0	0	NUM
ejpam-3328	689	1	w	w	NOUN
ejpam-3328	689	2	0	0	NUM
ejpam-3328	689	3	1	1	NUM
ejpam-3328	689	4	(	(	PUNCT
ejpam-3328	689	5	−n	−n	NOUN
ejpam-3328	689	6	+	+	NUM
ejpam-3328	689	7	iτ)idτ	iτ)idτ	PROPN
ejpam-3328	689	8	∣∣∣∣+	∣∣∣∣+	PROPN
ejpam-3328	689	9	∣∣∣∣∫	∣∣∣∣∫	NUM
ejpam-3328	689	10	0	0	NUM
ejpam-3328	690	1	−in	−in	PROPN
ejpam-3328	690	2	w	w	NOUN
ejpam-3328	690	3	0	0	NUM
ejpam-3328	690	4	1	1	NUM
ejpam-3328	690	5	(	(	PUNCT
ejpam-3328	690	6	n	n	X
ejpam-3328	690	7	+	+	NUM
ejpam-3328	690	8	iτ)idτ	iτ)idτ	PROPN
ejpam-3328	690	9	∣∣∣∣+	∣∣∣∣+	PROPN
ejpam-3328	690	10	∣∣∣∣∫	∣∣∣∣∫	NUM
ejpam-3328	690	11	−n	−n	PROPN
ejpam-3328	690	12	n	n	PROPN
ejpam-3328	690	13	w	w	NOUN
ejpam-3328	690	14	0	0	NUM
ejpam-3328	690	15	1	1	NUM
ejpam-3328	690	16	(	(	PUNCT
ejpam-3328	690	17	−in	−in	PROPN
ejpam-3328	690	18	+	+	CCONJ
ejpam-3328	690	19	τ)dτ	τ)dτ	ADJ
ejpam-3328	690	20	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3328	690	21	=	=	NOUN
ejpam-3328	690	22	r11	r11	NOUN
ejpam-3328	690	23	+	+	NOUN
ejpam-3328	690	24	r12	r12	ADJ
ejpam-3328	690	25	+	+	NOUN
ejpam-3328	690	26	r13	r13	NOUN
ejpam-3328	690	27	.	.	PUNCT
ejpam-3328	691	1	it	it	PRON
ejpam-3328	691	2	is	be	AUX
ejpam-3328	691	3	enough	enough	ADJ
ejpam-3328	691	4	to	to	PART
ejpam-3328	691	5	calculate	calculate	VERB
ejpam-3328	691	6	r11	r11	NOUN
ejpam-3328	691	7	,	,	PUNCT
ejpam-3328	691	8	as	as	SCONJ
ejpam-3328	691	9	the	the	DET
ejpam-3328	691	10	remaining	remain	VERB
ejpam-3328	691	11	calculations	calculation	NOUN
ejpam-3328	691	12	are	be	AUX
ejpam-3328	691	13	done	do	VERB
ejpam-3328	691	14	in	in	ADP
ejpam-3328	691	15	the	the	DET
ejpam-3328	691	16	same	same	ADJ
ejpam-3328	691	17	way	way	NOUN
ejpam-3328	691	18	.	.	PUNCT
ejpam-3328	692	1	therefore	therefore	ADV
ejpam-3328	692	2	,	,	PUNCT
ejpam-3328	692	3	r11	r11	NOUN
ejpam-3328	692	4	≤	≤	NOUN
ejpam-3328	692	5	n∑	n∑	NOUN
ejpam-3328	692	6	1	1	NUM
ejpam-3328	692	7	1	1	NUM
ejpam-3328	692	8	nε	nε	PROPN
ejpam-3328	692	9	∫	∫	PROPN
ejpam-3328	692	10	n	n	CCONJ
ejpam-3328	692	11	0	0	NUM
ejpam-3328	693	1	cε	cε	X
ejpam-3328	693	2	(	(	PUNCT
ejpam-3328	693	3	2πn+	2πn+	NUM
ejpam-3328	693	4	φ−n)2	φ−n)2	NUM
ejpam-3328	693	5	+	+	CCONJ
ejpam-3328	693	6	(	(	PUNCT
ejpam-3328	693	7	bn	bn	INTJ
ejpam-3328	693	8	−	−	PROPN
ejpam-3328	693	9	τ)2	τ)2	PROPN
ejpam-3328	693	10	dτ	dτ	NOUN
ejpam-3328	693	11	≤	≤	PROPN
ejpam-3328	693	12	cε	cε	VERB
ejpam-3328	693	13	n	n	X
ejpam-3328	693	14	ε	ε	X
ejpam-3328	693	15	.	.	PUNCT
ejpam-3328	694	1	performing	perform	VERB
ejpam-3328	694	2	the	the	DET
ejpam-3328	694	3	same	same	ADJ
ejpam-3328	694	4	calculations	calculation	NOUN
ejpam-3328	694	5	for	for	ADP
ejpam-3328	694	6	w2	w2	NOUN
ejpam-3328	694	7	yields	yield	NOUN
ejpam-3328	694	8	|w2|	|w2|	NOUN
ejpam-3328	694	9	≤	≤	PROPN
ejpam-3328	694	10	∣∣∣∣∫	∣∣∣∣∫	NUM
ejpam-3328	694	11	−in	−in	NOUN
ejpam-3328	694	12	0	0	NUM
ejpam-3328	695	1	w	w	NOUN
ejpam-3328	695	2	0	0	NUM
ejpam-3328	695	3	2	2	NUM
ejpam-3328	695	4	(	(	PUNCT
ejpam-3328	695	5	−n	−n	NOUN
ejpam-3328	695	6	+	+	NUM
ejpam-3328	695	7	iτ)idτ	iτ)idτ	PROPN
ejpam-3328	695	8	∣∣∣∣+	∣∣∣∣+	PROPN
ejpam-3328	695	9	∣∣∣∣∫	∣∣∣∣∫	NUM
ejpam-3328	695	10	0	0	NUM
ejpam-3328	696	1	−in	−in	PROPN
ejpam-3328	696	2	w	w	NOUN
ejpam-3328	696	3	0	0	NUM
ejpam-3328	696	4	2	2	NUM
ejpam-3328	696	5	(	(	PUNCT
ejpam-3328	696	6	n	n	X
ejpam-3328	696	7	+	+	NUM
ejpam-3328	696	8	iτ)idτ	iτ)idτ	PROPN
ejpam-3328	696	9	∣∣∣∣+	∣∣∣∣+	PROPN
ejpam-3328	696	10	∣∣∣∣∫	∣∣∣∣∫	NUM
ejpam-3328	696	11	−n	−n	PROPN
ejpam-3328	696	12	n	n	PROPN
ejpam-3328	696	13	w	w	NOUN
ejpam-3328	696	14	0	0	NUM
ejpam-3328	696	15	2	2	NUM
ejpam-3328	696	16	(	(	PUNCT
ejpam-3328	696	17	−in	−in	NOUN
ejpam-3328	696	18	+	+	CCONJ
ejpam-3328	696	19	τ)dτ	τ)dτ	ADJ
ejpam-3328	696	20	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3328	696	21	=	=	SYM
ejpam-3328	696	22	r21	r21	NOUN
ejpam-3328	696	23	+	+	NOUN
ejpam-3328	696	24	r22	r22	NOUN
ejpam-3328	696	25	+	+	NOUN
ejpam-3328	696	26	r23	r23	NOUN
ejpam-3328	696	27	.	.	PUNCT
ejpam-3328	697	1	it	it	PRON
ejpam-3328	697	2	is	be	AUX
ejpam-3328	697	3	also	also	ADV
ejpam-3328	697	4	enough	enough	ADJ
ejpam-3328	697	5	to	to	PART
ejpam-3328	697	6	calculate	calculate	VERB
ejpam-3328	697	7	r21	r21	NOUN
ejpam-3328	697	8	.	.	PUNCT
ejpam-3328	698	1	the	the	DET
ejpam-3328	698	2	result	result	NOUN
ejpam-3328	698	3	is	be	AUX
ejpam-3328	698	4	r21	r21	NOUN
ejpam-3328	698	5	≤	≤	NOUN
ejpam-3328	698	6	∞∑	∞∑	NUM
ejpam-3328	698	7	n+1	n+1	NUM
ejpam-3328	698	8	1	1	NUM
ejpam-3328	698	9	nε	nε	PROPN
ejpam-3328	698	10	∫	∫	PROPN
ejpam-3328	698	11	n	n	CCONJ
ejpam-3328	698	12	0	0	NUM
ejpam-3328	699	1	cε	cε	X
ejpam-3328	699	2	(	(	PUNCT
ejpam-3328	699	3	2πn+	2πn+	NUM
ejpam-3328	699	4	φ−n)2	φ−n)2	NUM
ejpam-3328	699	5	+	+	CCONJ
ejpam-3328	699	6	(	(	PUNCT
ejpam-3328	699	7	bn	bn	INTJ
ejpam-3328	699	8	−	−	PROPN
ejpam-3328	699	9	τ)2	τ)2	PROPN
ejpam-3328	699	10	dτ	dτ	NOUN
ejpam-3328	699	11	≤	≤	PROPN
ejpam-3328	699	12	cε	cε	VERB
ejpam-3328	699	13	n	n	X
ejpam-3328	699	14	ε	ε	PROPN
ejpam-3328	699	15	.	.	PUNCT
ejpam-3328	700	1	we	we	PRON
ejpam-3328	700	2	perform	perform	VERB
ejpam-3328	700	3	simple	simple	ADJ
ejpam-3328	700	4	calculations	calculation	NOUN
ejpam-3328	700	5	to	to	PART
ejpam-3328	700	6	form	form	VERB
ejpam-3328	700	7	a	a	DET
ejpam-3328	700	8	final	final	ADJ
ejpam-3328	700	9	estimate:∫	estimate:∫	NOUN
ejpam-3328	701	1	+	+	ADV
ejpam-3328	701	2	n	n	PRON
ejpam-3328	701	3	−n	−n	ADV
ejpam-3328	701	4	eitk	eitk	VERB
ejpam-3328	701	5	d2	d2	PROPN
ejpam-3328	701	6	dk2	dk2	PROPN
ejpam-3328	701	7	iε(k	iε(k	PROPN
ejpam-3328	701	8	,	,	PUNCT
ejpam-3328	701	9	α)dk	α)dk	PROPN
ejpam-3328	701	10	=	=	SYM
ejpam-3328	701	11	∫	∫	PROPN
ejpam-3328	702	1	+	+	CCONJ
ejpam-3328	702	2	n	n	PROPN
ejpam-3328	702	3	−n	−n	ADV
ejpam-3328	702	4	eitk	eitk	VERB
ejpam-3328	702	5	d2	d2	PROPN
ejpam-3328	702	6	dk2	dk2	PROPN
ejpam-3328	702	7	(	(	PUNCT
ejpam-3328	702	8	iε(k	iε(k	PROPN
ejpam-3328	702	9	,	,	PUNCT
ejpam-3328	702	10	α	α	NOUN
ejpam-3328	702	11	)	)	PUNCT
ejpam-3328	702	12	x−(k	x−(k	PROPN
ejpam-3328	702	13	)	)	PUNCT
ejpam-3328	702	14	)	)	PUNCT
ejpam-3328	703	1	dk−2	dk−2	VERB
ejpam-3328	703	2	∫	∫	PROPN
ejpam-3328	704	1	+	+	CCONJ
ejpam-3328	704	2	n	n	ADP
ejpam-3328	704	3	−n	−n	ADV
ejpam-3328	704	4	eitk	eitk	VERB
ejpam-3328	704	5	d	d	X
ejpam-3328	704	6	dk	dk	PROPN
ejpam-3328	704	7	(	(	PUNCT
ejpam-3328	704	8	iε(k	iε(k	PROPN
ejpam-3328	704	9	,	,	PUNCT
ejpam-3328	704	10	α	α	NOUN
ejpam-3328	704	11	)	)	PUNCT
ejpam-3328	704	12	)	)	PUNCT
ejpam-3328	705	1	d	d	X
ejpam-3328	705	2	dk	dk	X
ejpam-3328	705	3	(	(	PUNCT
ejpam-3328	705	4	1	1	NUM
ejpam-3328	705	5	x−(k	x−(k	NOUN
ejpam-3328	705	6	)	)	PUNCT
ejpam-3328	705	7	)	)	PUNCT
ejpam-3328	705	8	dk	dk	PROPN
ejpam-3328	705	9	−	−	NUM
ejpam-3328	705	10	∫	∫	PROPN
ejpam-3328	706	1	+	+	CCONJ
ejpam-3328	706	2	n	n	PROPN
ejpam-3328	706	3	−n	−n	ADV
ejpam-3328	706	4	eitkiε(k	eitkiε(k	PROPN
ejpam-3328	706	5	,	,	PUNCT
ejpam-3328	706	6	α	α	NOUN
ejpam-3328	706	7	)	)	PUNCT
ejpam-3328	706	8	d2	d2	PROPN
ejpam-3328	706	9	dk2	dk2	PROPN
ejpam-3328	706	10	(	(	PUNCT
ejpam-3328	706	11	1	1	NUM
ejpam-3328	706	12	x−(k	x−(k	NOUN
ejpam-3328	706	13	)	)	PUNCT
ejpam-3328	706	14	)	)	PUNCT
ejpam-3328	707	1	dk+	dk+	PROPN
ejpam-3328	707	2	∫	∫	PROPN
ejpam-3328	708	1	+	+	CCONJ
ejpam-3328	708	2	n	n	PROPN
ejpam-3328	708	3	−n	−n	ADV
ejpam-3328	708	4	eitk	eitk	VERB
ejpam-3328	708	5	d2	d2	PROPN
ejpam-3328	708	6	dk2	dk2	PROPN
ejpam-3328	708	7	iεdk−	iεdk−	PROPN
ejpam-3328	708	8	∫	∫	PROPN
ejpam-3328	709	1	+	+	CCONJ
ejpam-3328	709	2	n	n	PRON
ejpam-3328	709	3	−n	−n	ADV
ejpam-3328	709	4	eitk	eitk	VERB
ejpam-3328	709	5	d2	d2	PROPN
ejpam-3328	709	6	dk2	dk2	PROPN
ejpam-3328	709	7	(	(	PUNCT
ejpam-3328	709	8	iε(k	iε(k	PROPN
ejpam-3328	709	9	,	,	PUNCT
ejpam-3328	709	10	α	α	NOUN
ejpam-3328	709	11	)	)	PUNCT
ejpam-3328	709	12	)	)	PUNCT
ejpam-3328	709	13	1	1	NUM
ejpam-3328	709	14	x−(k	x−(k	SYM
ejpam-3328	709	15	)	)	PUNCT
ejpam-3328	710	1	dk	dk	PROPN
ejpam-3328	710	2	.	.	PROPN
ejpam-3328	710	3	theorem	theorem	VERB
ejpam-3328	710	4	9	9	NUM
ejpam-3328	710	5	and	and	CCONJ
ejpam-3328	710	6	the	the	DET
ejpam-3328	710	7	estimates	estimate	NOUN
ejpam-3328	710	8	of	of	ADP
ejpam-3328	710	9	w1	w1	NOUN
ejpam-3328	710	10	,	,	PUNCT
ejpam-3328	710	11	w2	w2	NOUN
ejpam-3328	710	12	,	,	PUNCT
ejpam-3328	710	13	(	(	PUNCT
ejpam-3328	710	14	x−	x−	PROPN
ejpam-3328	710	15	−	−	PROPN
ejpam-3328	710	16	1),dx−dk	1),dx−dk	NUM
ejpam-3328	710	17	,	,	PUNCT
ejpam-3328	710	18	d2x−	d2x−	VERB
ejpam-3328	711	1	dk2	dk2	PROPN
ejpam-3328	711	2	yield∣∣∣∣∫	yield∣∣∣∣∫	PROPN
ejpam-3328	711	3	+	+	PROPN
ejpam-3328	711	4	n	n	PROPN
ejpam-3328	711	5	−n	−n	ADV
ejpam-3328	711	6	eitk	eitk	VERB
ejpam-3328	711	7	d2	d2	PROPN
ejpam-3328	711	8	dk2	dk2	PROPN
ejpam-3328	711	9	iεdk	iεdk	PROPN
ejpam-3328	711	10	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3328	711	11	≤	≤	NUM
ejpam-3328	711	12	cεcm	cεcm	NOUN
ejpam-3328	711	13	.	.	PUNCT
ejpam-3328	712	1	by	by	ADP
ejpam-3328	712	2	lemma	lemma	PROPN
ejpam-3328	712	3	17	17	NUM
ejpam-3328	712	4	,	,	PUNCT
ejpam-3328	712	5	as	as	ADP
ejpam-3328	712	6	1/2	1/2	NUM
ejpam-3328	712	7	+	+	NUM
ejpam-3328	712	8	3ε	3ε	NUM
ejpam-3328	712	9	<	<	X
ejpam-3328	712	10	re(s	re(s	PROPN
ejpam-3328	712	11	)	)	PUNCT
ejpam-3328	712	12	<	<	X
ejpam-3328	712	13	1−	1−	NUM
ejpam-3328	712	14	3ε	3ε	NUM
ejpam-3328	712	15	,	,	PUNCT
ejpam-3328	712	16	the	the	DET
ejpam-3328	712	17	last	last	ADJ
ejpam-3328	712	18	estimate	estimate	NOUN
ejpam-3328	712	19	yields	yield	VERB
ejpam-3328	712	20	|q(s)|	|q(s)|	PROPN
ejpam-3328	712	21	<	<	X
ejpam-3328	712	22	cmcε	cmcε	PROPN
ejpam-3328	712	23	,	,	PUNCT
ejpam-3328	712	24	which	which	PRON
ejpam-3328	712	25	completes	complete	VERB
ejpam-3328	712	26	the	the	DET
ejpam-3328	712	27	proof	proof	NOUN
ejpam-3328	712	28	,	,	PUNCT
ejpam-3328	712	29	as	as	SCONJ
ejpam-3328	712	30	mentioned	mention	VERB
ejpam-3328	712	31	in	in	ADP
ejpam-3328	712	32	the	the	DET
ejpam-3328	712	33	introduction	introduction	NOUN
ejpam-3328	712	34	,	,	PUNCT
ejpam-3328	712	35	the	the	DET
ejpam-3328	712	36	values	value	NOUN
ejpam-3328	712	37	of	of	ADP
ejpam-3328	712	38	the	the	DET
ejpam-3328	712	39	zeta	zeta	NOUN
ejpam-3328	712	40	function	function	NOUN
ejpam-3328	712	41	in	in	ADP
ejpam-3328	712	42	adjacent	adjacent	ADJ
ejpam-3328	712	43	rectangles	rectangle	NOUN
ejpam-3328	712	44	should	should	AUX
ejpam-3328	712	45	be	be	AUX
ejpam-3328	712	46	compared	compare	VERB
ejpam-3328	712	47	.	.	PUNCT
ejpam-3328	713	1	this	this	PRON
ejpam-3328	713	2	will	will	AUX
ejpam-3328	713	3	be	be	AUX
ejpam-3328	713	4	done	do	VERB
ejpam-3328	713	5	in	in	ADP
ejpam-3328	713	6	the	the	DET
ejpam-3328	713	7	following	follow	VERB
ejpam-3328	713	8	theorem	theorem	PROPN
ejpam-3328	713	9	.	.	PUNCT
ejpam-3328	713	10	a.	a.	PROPN
ejpam-3328	713	11	durmagambetov	durmagambetov	PROPN
ejpam-3328	713	12	/	/	SYM
ejpam-3328	713	13	eur	eur	PROPN
ejpam-3328	713	14	.	.	PUNCT
ejpam-3328	714	1	j.	j.	PROPN
ejpam-3328	714	2	pure	pure	PROPN
ejpam-3328	714	3	appl	appl	PROPN
ejpam-3328	714	4	.	.	PROPN
ejpam-3328	714	5	math	math	PROPN
ejpam-3328	714	6	,	,	PUNCT
ejpam-3328	714	7	11	11	NUM
ejpam-3328	714	8	(	(	PUNCT
ejpam-3328	714	9	4	4	NUM
ejpam-3328	714	10	)	)	PUNCT
ejpam-3328	714	11	(	(	PUNCT
ejpam-3328	714	12	2018	2018	NUM
ejpam-3328	714	13	)	)	PUNCT
ejpam-3328	714	14	,	,	PUNCT
ejpam-3328	714	15	1143	1143	NUM
ejpam-3328	714	16	-	-	SYM
ejpam-3328	714	17	1176	1176	NUM
ejpam-3328	714	18	1173	1173	NUM
ejpam-3328	714	19	theorem	theorem	NOUN
ejpam-3328	714	20	11	11	NUM
ejpam-3328	714	21	.	.	PUNCT
ejpam-3328	715	1	riemann	riemann	PROPN
ejpam-3328	715	2	’s	’s	PART
ejpam-3328	715	3	function	function	NOUN
ejpam-3328	715	4	has	have	VERB
ejpam-3328	715	5	nontrivial	nontrivial	ADJ
ejpam-3328	715	6	zeros	zero	NOUN
ejpam-3328	715	7	only	only	ADV
ejpam-3328	715	8	on	on	ADP
ejpam-3328	715	9	the	the	DET
ejpam-3328	715	10	line	line	NOUN
ejpam-3328	715	11	re(s	re(s	PUNCT
ejpam-3328	715	12	)	)	PUNCT
ejpam-3328	715	13	=	=	SYM
ejpam-3328	715	14	1/2	1/2	NUM
ejpam-3328	715	15	.	.	PUNCT
ejpam-3328	716	1	proof	proof	NOUN
ejpam-3328	716	2	.	.	PUNCT
ejpam-3328	717	1	let	let	VERB
ejpam-3328	717	2	it	it	PRON
ejpam-3328	717	3	be	be	AUX
ejpam-3328	717	4	assumed	assume	VERB
ejpam-3328	717	5	that	that	SCONJ
ejpam-3328	717	6	there	there	PRON
ejpam-3328	717	7	is	be	VERB
ejpam-3328	717	8	a	a	DET
ejpam-3328	717	9	root	root	NOUN
ejpam-3328	717	10	of	of	ADP
ejpam-3328	717	11	the	the	DET
ejpam-3328	717	12	zeta	zeta	NOUN
ejpam-3328	717	13	function	function	NOUN
ejpam-3328	717	14	with	with	ADP
ejpam-3328	717	15	sn	sn	PROPN
ejpam-3328	717	16	=	=	PROPN
ejpam-3328	717	17	1/2	1/2	NUM
ejpam-3328	717	18	+	+	NUM
ejpam-3328	717	19	δn	δn	NOUN
ejpam-3328	718	1	+	+	CCONJ
ejpam-3328	718	2	i	i	PRON
ejpam-3328	718	3	∗	∗	NOUN
ejpam-3328	718	4	αn	αn	NOUN
ejpam-3328	718	5	,	,	PUNCT
ejpam-3328	718	6	where	where	SCONJ
ejpam-3328	718	7	δn	δn	ADV
ejpam-3328	718	8	>	>	X
ejpam-3328	718	9	0	0	X
ejpam-3328	718	10	.	.	PUNCT
ejpam-3328	719	1	let	let	VERB
ejpam-3328	719	2	sn−1	sn−1	PROPN
ejpam-3328	719	3	=	=	PROPN
ejpam-3328	719	4	1/2	1/2	NUM
ejpam-3328	719	5	+	+	CCONJ
ejpam-3328	719	6	δn−1	δn−1	PROPN
ejpam-3328	719	7	+	+	CCONJ
ejpam-3328	719	8	iαn−1	iαn−1	PROPN
ejpam-3328	719	9	,	,	PUNCT
ejpam-3328	719	10	where	where	SCONJ
ejpam-3328	719	11	δn−1	δn−1	PROPN
ejpam-3328	719	12	>	>	X
ejpam-3328	719	13	0	0	NUM
ejpam-3328	719	14	is	be	AUX
ejpam-3328	719	15	another	another	DET
ejpam-3328	719	16	root	root	NOUN
ejpam-3328	719	17	nearest	near	ADJ
ejpam-3328	719	18	to	to	ADP
ejpam-3328	719	19	it	it	PRON
ejpam-3328	719	20	.	.	PUNCT
ejpam-3328	720	1	then	then	ADV
ejpam-3328	720	2	,	,	PUNCT
ejpam-3328	720	3	the	the	DET
ejpam-3328	720	4	following	follow	VERB
ejpam-3328	720	5	sets	set	NOUN
ejpam-3328	720	6	corresponding	correspond	VERB
ejpam-3328	720	7	to	to	ADP
ejpam-3328	720	8	sn	sn	PROPN
ejpam-3328	720	9	are	be	AUX
ejpam-3328	720	10	constructed	construct	VERB
ejpam-3328	720	11	:	:	PUNCT
ejpam-3328	720	12	d(n	d(n	NOUN
ejpam-3328	720	13	)	)	PUNCT
ejpam-3328	720	14	=	=	SYM
ejpam-3328	720	15	(	(	PUNCT
ejpam-3328	720	16	s|ε	s|ε	X
ejpam-3328	720	17	<	<	X
ejpam-3328	720	18	re(s	re(s	PROPN
ejpam-3328	720	19	)	)	PUNCT
ejpam-3328	720	20	<	<	X
ejpam-3328	720	21	1−	1−	NUM
ejpam-3328	720	22	ε	ε	PROPN
ejpam-3328	720	23	,	,	PUNCT
ejpam-3328	720	24	im(s	im(s	PROPN
ejpam-3328	720	25	)	)	PUNCT
ejpam-3328	720	26	6=	6=	NUM
ejpam-3328	720	27	im(sn	im(sn	PROPN
ejpam-3328	720	28	)	)	PUNCT
ejpam-3328	720	29	,	,	PUNCT
ejpam-3328	720	30	im(sn)−	im(sn)−	PROPN
ejpam-3328	720	31	dn	dn	PROPN
ejpam-3328	720	32	≤	≤	PROPN
ejpam-3328	720	33	im(s	im(	NOUN
ejpam-3328	720	34	)	)	PUNCT
ejpam-3328	720	35	≤	≤	NUM
ejpam-3328	720	36	im(sn	im(sn	PROPN
ejpam-3328	720	37	)	)	PUNCT
ejpam-3328	720	38	+	+	CCONJ
ejpam-3328	720	39	dn	dn	PROPN
ejpam-3328	720	40	,	,	PUNCT
ejpam-3328	720	41	d(n	d(n	NOUN
ejpam-3328	720	42	)	)	PUNCT
ejpam-3328	720	43	=	=	SYM
ejpam-3328	720	44	(	(	PUNCT
ejpam-3328	720	45	s|ε	s|ε	X
ejpam-3328	720	46	<	<	X
ejpam-3328	720	47	re(s	re(s	PROPN
ejpam-3328	720	48	)	)	PUNCT
ejpam-3328	720	49	<	<	X
ejpam-3328	720	50	1−	1−	NUM
ejpam-3328	720	51	ε	ε	PROPN
ejpam-3328	720	52	,	,	PUNCT
ejpam-3328	720	53	im(−s	im(−	NOUN
ejpam-3328	720	54	)	)	PUNCT
ejpam-3328	720	55	6=	6=	NUM
ejpam-3328	720	56	im(−sn	im(−sn	NOUN
ejpam-3328	720	57	)	)	PUNCT
ejpam-3328	720	58	,	,	PUNCT
ejpam-3328	720	59	−im(sn)−dn	−im(sn)−dn	PROPN
ejpam-3328	720	60	≤	≤	PUNCT
ejpam-3328	720	61	im(s	im(s	PROPN
ejpam-3328	720	62	)	)	PUNCT
ejpam-3328	720	63	≤	≤	NUM
ejpam-3328	720	64	−im(sn	−im(sn	NUM
ejpam-3328	720	65	)	)	PUNCT
ejpam-3328	721	1	+	+	ADP
ejpam-3328	721	2	dn	dn	PROPN
ejpam-3328	721	3	,	,	PUNCT
ejpam-3328	721	4	where	where	SCONJ
ejpam-3328	721	5	ζ(sn+1	ζ(sn+1	ADJ
ejpam-3328	721	6	)	)	PUNCT
ejpam-3328	721	7	=	=	SYM
ejpam-3328	721	8	0	0	NUM
ejpam-3328	721	9	,	,	PUNCT
ejpam-3328	721	10	ζ(sn	ζ(sn	NUM
ejpam-3328	721	11	)	)	PUNCT
ejpam-3328	721	12	=	=	SYM
ejpam-3328	721	13	0	0	NUM
ejpam-3328	721	14	,	,	PUNCT
ejpam-3328	721	15	ζ(1−	ζ(1−	PROPN
ejpam-3328	721	16	sn	sn	PROPN
ejpam-3328	721	17	)	)	PUNCT
ejpam-3328	721	18	=	=	SYM
ejpam-3328	721	19	0	0	NUM
ejpam-3328	721	20	,	,	PUNCT
ejpam-3328	721	21	ζ(1−	ζ(1−	PROPN
ejpam-3328	721	22	sn+1	sn+1	X
ejpam-3328	721	23	)	)	PUNCT
ejpam-3328	721	24	=	=	SYM
ejpam-3328	721	25	0	0	NUM
ejpam-3328	721	26	,	,	PUNCT
ejpam-3328	721	27	ζ(1−	ζ(1−	PROPN
ejpam-3328	721	28	sn	sn	PROPN
ejpam-3328	721	29	)	)	PUNCT
ejpam-3328	721	30	=	=	SYM
ejpam-3328	722	1	0	0	NUM
ejpam-3328	722	2	,	,	PUNCT
ejpam-3328	722	3	dn	dn	NOUN
ejpam-3328	722	4	=	=	PUNCT
ejpam-3328	722	5	(	(	PUNCT
ejpam-3328	722	6	im(sn+1)−	im(sn+1)−	PROPN
ejpam-3328	722	7	im(sn))/2	im(sn))/2	NOUN
ejpam-3328	722	8	,	,	PUNCT
ejpam-3328	722	9	where	where	SCONJ
ejpam-3328	722	10	ε	ε	PROPN
ejpam-3328	722	11	=	=	SYM
ejpam-3328	722	12	0.01δ2	0.01δ2	NOUN
ejpam-3328	722	13	n.	n.	NOUN
ejpam-3328	722	14	as	as	ADP
ejpam-3328	722	15	1/2	1/2	NUM
ejpam-3328	722	16	<	<	X
ejpam-3328	722	17	re(s	re(s	PROPN
ejpam-3328	722	18	)	)	PUNCT
ejpam-3328	722	19	<	<	X
ejpam-3328	722	20	1	1	NUM
ejpam-3328	722	21	and	and	CCONJ
ejpam-3328	722	22	s	s	PROPN
ejpam-3328	722	23	∈	∈	PROPN
ejpam-3328	722	24	d(n	d(n	PROPN
ejpam-3328	722	25	)	)	PUNCT
ejpam-3328	722	26	∪d(n	∪d(n	NOUN
ejpam-3328	722	27	)	)	PUNCT
ejpam-3328	723	1	,	,	PUNCT
ejpam-3328	723	2	then	then	ADV
ejpam-3328	723	3	we	we	PRON
ejpam-3328	723	4	have	have	VERB
ejpam-3328	723	5	the	the	DET
ejpam-3328	723	6	equation	equation	NOUN
ejpam-3328	723	7	for	for	ADP
ejpam-3328	723	8	q.	q.	NOUN
ejpam-3328	723	9	theorem	theorem	VERB
ejpam-3328	723	10	11	11	NUM
ejpam-3328	723	11	now	now	ADV
ejpam-3328	723	12	yields	yield	NOUN
ejpam-3328	723	13	|	|	ADV
ejpam-3328	723	14	ln(|ζ(1/2	ln(|ζ(1/2	VERB
ejpam-3328	723	15	+	+	CCONJ
ejpam-3328	723	16	δn	δn	NOUN
ejpam-3328	723	17	+	+	CCONJ
ejpam-3328	723	18	iαn	iαn	PROPN
ejpam-3328	723	19	−	−	PROPN
ejpam-3328	723	20	iδ)|	iδ)|	PROPN
ejpam-3328	723	21	)	)	PUNCT
ejpam-3328	723	22	=	=	PUNCT
ejpam-3328	723	23	|q(1/2	|q(1/2	NOUN
ejpam-3328	723	24	+	+	NUM
ejpam-3328	723	25	δn	δn	PROPN
ejpam-3328	723	26	−	−	PROPN
ejpam-3328	723	27	iαn	iαn	NOUN
ejpam-3328	723	28	−	−	PROPN
ejpam-3328	723	29	iδ)|	iδ)|	PROPN
ejpam-3328	723	30	<	<	X
ejpam-3328	723	31	2cncε	2cncε	PROPN
ejpam-3328	723	32	.	.	PUNCT
ejpam-3328	724	1	furthermore	furthermore	ADV
ejpam-3328	724	2	,	,	PUNCT
ejpam-3328	724	3	lim	lim	PROPN
ejpam-3328	724	4	δ→0	δ→0	PUNCT
ejpam-3328	724	5	|	|	ADV
ejpam-3328	724	6	ln(|ζ(1/2	ln(|ζ(1/2	ADJ
ejpam-3328	724	7	+	+	CCONJ
ejpam-3328	724	8	δn	δn	NOUN
ejpam-3328	724	9	+	+	X
ejpam-3328	724	10	iαn	iαn	ADJ
ejpam-3328	724	11	−	−	PROPN
ejpam-3328	724	12	iδ)|)|	iδ)|)|	PROPN
ejpam-3328	724	13	=	=	NUM
ejpam-3328	724	14	∞.	∞.	PROPN
ejpam-3328	724	15	these	these	DET
ejpam-3328	724	16	estimates	estimate	NOUN
ejpam-3328	724	17	for	for	ADP
ejpam-3328	724	18	|q(s)|	|q(s)|	PROPN
ejpam-3328	724	19	and	and	CCONJ
ejpam-3328	724	20	|f(s)|	|f(s)|	PROPN
ejpam-3328	724	21	imply	imply	VERB
ejpam-3328	724	22	that	that	SCONJ
ejpam-3328	724	23	the	the	DET
ejpam-3328	724	24	function	function	NOUN
ejpam-3328	724	25	does	do	AUX
ejpam-3328	724	26	not	not	PART
ejpam-3328	724	27	have	have	VERB
ejpam-3328	724	28	zeros	zero	NOUN
ejpam-3328	724	29	on	on	ADP
ejpam-3328	724	30	the	the	DET
ejpam-3328	724	31	half	half	ADJ
ejpam-3328	724	32	plane	plane	NOUN
ejpam-3328	724	33	re(s	re(s	ADJ
ejpam-3328	724	34	)	)	PUNCT
ejpam-3328	724	35	>	>	PUNCT
ejpam-3328	724	36	1/2	1/2	NUM
ejpam-3328	724	37	.	.	PUNCT
ejpam-3328	725	1	by	by	ADP
ejpam-3328	725	2	the	the	DET
ejpam-3328	725	3	integral	integral	ADJ
ejpam-3328	725	4	representation	representation	NOUN
ejpam-3328	725	5	(	(	PUNCT
ejpam-3328	725	6	3	3	NUM
ejpam-3328	725	7	)	)	PUNCT
ejpam-3328	725	8	,	,	PUNCT
ejpam-3328	725	9	these	these	DET
ejpam-3328	725	10	results	result	NOUN
ejpam-3328	725	11	are	be	AUX
ejpam-3328	725	12	extended	extend	VERB
ejpam-3328	725	13	to	to	ADP
ejpam-3328	725	14	the	the	DET
ejpam-3328	725	15	half	half	ADJ
ejpam-3328	725	16	plane	plane	NOUN
ejpam-3328	725	17	re(s	re(s	PUNCT
ejpam-3328	725	18	)	)	PUNCT
ejpam-3328	726	1	<	<	X
ejpam-3328	726	2	1/2	1/2	NUM
ejpam-3328	726	3	.	.	PUNCT
ejpam-3328	727	1	therefore	therefore	ADV
ejpam-3328	727	2	,	,	PUNCT
ejpam-3328	727	3	riemann	riemann	PROPN
ejpam-3328	727	4	’s	’s	PART
ejpam-3328	727	5	hypothesis	hypothesis	NOUN
ejpam-3328	727	6	has	have	AUX
ejpam-3328	727	7	been	be	AUX
ejpam-3328	727	8	proved	prove	VERB
ejpam-3328	727	9	.	.	PUNCT
ejpam-3328	728	1	10	10	NUM
ejpam-3328	728	2	.	.	PUNCT
ejpam-3328	728	3	conclusions	conclusion	NOUN
ejpam-3328	728	4	as	as	SCONJ
ejpam-3328	728	5	can	can	AUX
ejpam-3328	728	6	be	be	AUX
ejpam-3328	728	7	seen	see	VERB
ejpam-3328	728	8	from	from	ADP
ejpam-3328	728	9	the	the	DET
ejpam-3328	728	10	results	result	NOUN
ejpam-3328	728	11	obtained	obtain	VERB
ejpam-3328	728	12	,	,	PUNCT
ejpam-3328	728	13	the	the	DET
ejpam-3328	728	14	genius	genius	NOUN
ejpam-3328	728	15	of	of	ADP
ejpam-3328	728	16	poincaré	poincaré	ADJ
ejpam-3328	728	17	scholars	scholar	NOUN
ejpam-3328	728	18	such	such	ADJ
ejpam-3328	728	19	as	as	ADP
ejpam-3328	728	20	riemann	riemann	PROPN
ejpam-3328	728	21	and	and	CCONJ
ejpam-3328	728	22	hilbert	hilbert	PROPN
ejpam-3328	728	23	still	still	ADV
ejpam-3328	728	24	illuminates	illuminate	VERB
ejpam-3328	728	25	the	the	DET
ejpam-3328	728	26	path	path	NOUN
ejpam-3328	728	27	of	of	ADP
ejpam-3328	728	28	modern	modern	ADJ
ejpam-3328	728	29	scholars	scholar	NOUN
ejpam-3328	728	30	.	.	PUNCT
ejpam-3328	729	1	an	an	DET
ejpam-3328	729	2	example	example	NOUN
ejpam-3328	729	3	of	of	ADP
ejpam-3328	729	4	a	a	DET
ejpam-3328	729	5	complicated	complicated	ADJ
ejpam-3328	729	6	problem	problem	NOUN
ejpam-3328	729	7	such	such	ADJ
ejpam-3328	729	8	as	as	ADP
ejpam-3328	729	9	the	the	DET
ejpam-3328	729	10	cauchy	cauchy	ADJ
ejpam-3328	729	11	problem	problem	NOUN
ejpam-3328	729	12	for	for	ADP
ejpam-3328	729	13	the	the	DET
ejpam-3328	729	14	navier	navier	NOUN
ejpam-3328	729	15	–	–	PUNCT
ejpam-3328	729	16	stokes	stoke	NOUN
ejpam-3328	729	17	equation	equation	NOUN
ejpam-3328	729	18	shows	show	VERB
ejpam-3328	729	19	how	how	SCONJ
ejpam-3328	729	20	the	the	DET
ejpam-3328	729	21	poincaré–riemann	poincaré–riemann	NOUN
ejpam-3328	729	22	–	–	PUNCT
ejpam-3328	729	23	hilbert	hilbert	NOUN
ejpam-3328	729	24	boundary	boundary	ADJ
ejpam-3328	729	25	-	-	PUNCT
ejpam-3328	729	26	value	value	NOUN
ejpam-3328	729	27	problem	problem	NOUN
ejpam-3328	729	28	allows	allow	VERB
ejpam-3328	729	29	us	we	PRON
ejpam-3328	729	30	to	to	PART
ejpam-3328	729	31	construct	construct	VERB
ejpam-3328	729	32	effective	effective	ADJ
ejpam-3328	729	33	estimates	estimate	NOUN
ejpam-3328	729	34	of	of	ADP
ejpam-3328	729	35	solutions	solution	NOUN
ejpam-3328	729	36	for	for	ADP
ejpam-3328	729	37	this	this	DET
ejpam-3328	729	38	case	case	NOUN
ejpam-3328	729	39	.	.	PUNCT
ejpam-3328	730	1	for	for	ADP
ejpam-3328	730	2	this	this	PRON
ejpam-3328	730	3	,	,	PUNCT
ejpam-3328	730	4	the	the	DET
ejpam-3328	730	5	apparatus	apparatus	NOUN
ejpam-3328	730	6	of	of	ADP
ejpam-3328	730	7	the	the	DET
ejpam-3328	730	8	three	three	NUM
ejpam-3328	730	9	-	-	PUNCT
ejpam-3328	730	10	dimensional	dimensional	ADJ
ejpam-3328	730	11	inverse	inverse	NOUN
ejpam-3328	730	12	problem	problem	NOUN
ejpam-3328	730	13	of	of	ADP
ejpam-3328	730	14	the	the	DET
ejpam-3328	730	15	theory	theory	NOUN
ejpam-3328	730	16	of	of	ADP
ejpam-3328	730	17	quantum	quantum	NOUN
ejpam-3328	730	18	scattering	scattering	NOUN
ejpam-3328	730	19	is	be	AUX
ejpam-3328	730	20	developed	develop	VERB
ejpam-3328	730	21	.	.	PUNCT
ejpam-3328	731	1	it	it	PRON
ejpam-3328	731	2	is	be	AUX
ejpam-3328	731	3	shown	show	VERB
ejpam-3328	731	4	that	that	SCONJ
ejpam-3328	731	5	the	the	DET
ejpam-3328	731	6	unitary	unitary	ADJ
ejpam-3328	731	7	scattering	scatter	VERB
ejpam-3328	731	8	operator	operator	NOUN
ejpam-3328	731	9	can	can	AUX
ejpam-3328	731	10	be	be	AUX
ejpam-3328	731	11	investigated	investigate	VERB
ejpam-3328	731	12	as	as	ADP
ejpam-3328	731	13	a	a	DET
ejpam-3328	731	14	solution	solution	NOUN
ejpam-3328	731	15	of	of	ADP
ejpam-3328	731	16	the	the	DET
ejpam-3328	731	17	poincaré–riemann	poincaré–riemann	NOUN
ejpam-3328	731	18	–	–	PUNCT
ejpam-3328	731	19	hilbert	hilbert	NOUN
ejpam-3328	731	20	boundary	boundary	ADJ
ejpam-3328	731	21	-	-	PUNCT
ejpam-3328	731	22	value	value	NOUN
ejpam-3328	731	23	problem	problem	NOUN
ejpam-3328	731	24	.	.	PUNCT
ejpam-3328	732	1	this	this	PRON
ejpam-3328	732	2	allows	allow	VERB
ejpam-3328	732	3	us	we	PRON
ejpam-3328	732	4	to	to	PART
ejpam-3328	732	5	continue	continue	VERB
ejpam-3328	732	6	studying	study	VERB
ejpam-3328	732	7	the	the	DET
ejpam-3328	732	8	potential	potential	NOUN
ejpam-3328	732	9	in	in	ADP
ejpam-3328	732	10	the	the	DET
ejpam-3328	732	11	schrödinger	schrödinger	NOUN
ejpam-3328	732	12	equation	equation	NOUN
ejpam-3328	732	13	,	,	PUNCT
ejpam-3328	732	14	which	which	PRON
ejpam-3328	732	15	we	we	PRON
ejpam-3328	732	16	consider	consider	VERB
ejpam-3328	732	17	as	as	ADP
ejpam-3328	732	18	a	a	DET
ejpam-3328	732	19	velocity	velocity	NOUN
ejpam-3328	732	20	component	component	NOUN
ejpam-3328	732	21	in	in	ADP
ejpam-3328	732	22	the	the	DET
ejpam-3328	732	23	navier	navier	NOUN
ejpam-3328	732	24	–	–	PUNCT
ejpam-3328	732	25	stokes	stoke	NOUN
ejpam-3328	732	26	equation	equation	NOUN
ejpam-3328	732	27	.	.	PUNCT
ejpam-3328	733	1	the	the	DET
ejpam-3328	733	2	same	same	ADJ
ejpam-3328	733	3	scheme	scheme	NOUN
ejpam-3328	733	4	of	of	ADP
ejpam-3328	733	5	reduction	reduction	NOUN
ejpam-3328	733	6	of	of	ADP
ejpam-3328	733	7	riemann	riemann	PROPN
ejpam-3328	733	8	integral	integral	ADJ
ejpam-3328	733	9	equations	equation	NOUN
ejpam-3328	733	10	for	for	ADP
ejpam-3328	733	11	the	the	DET
ejpam-3328	733	12	zeta	zeta	PROPN
ejpam-3328	733	13	function	function	NOUN
ejpam-3328	733	14	to	to	ADP
ejpam-3328	733	15	the	the	DET
ejpam-3328	733	16	poincaré–riemann	poincaré–riemann	NOUN
ejpam-3328	733	17	–	–	PUNCT
ejpam-3328	733	18	hilbert	hilbert	NOUN
ejpam-3328	733	19	boundary	boundary	ADJ
ejpam-3328	733	20	-	-	PUNCT
ejpam-3328	733	21	value	value	NOUN
ejpam-3328	733	22	problem	problem	NOUN
ejpam-3328	733	23	enables	enable	VERB
ejpam-3328	733	24	us	we	PRON
ejpam-3328	733	25	to	to	PART
ejpam-3328	733	26	construct	construct	VERB
ejpam-3328	733	27	effective	effective	ADJ
ejpam-3328	733	28	estimates	estimate	NOUN
ejpam-3328	733	29	that	that	PRON
ejpam-3328	733	30	describe	describe	VERB
ejpam-3328	733	31	the	the	DET
ejpam-3328	733	32	behaviour	behaviour	NOUN
ejpam-3328	733	33	of	of	ADP
ejpam-3328	733	34	the	the	DET
ejpam-3328	733	35	zeros	zero	NOUN
ejpam-3328	733	36	of	of	ADP
ejpam-3328	733	37	the	the	DET
ejpam-3328	733	38	zeta	zeta	PROPN
ejpam-3328	733	39	function	function	NOUN
ejpam-3328	733	40	well	well	ADV
ejpam-3328	733	41	.	.	PUNCT
ejpam-3328	734	1	in	in	ADP
ejpam-3328	734	2	summary	summary	NOUN
ejpam-3328	734	3	,	,	PUNCT
ejpam-3328	734	4	it	it	PRON
ejpam-3328	734	5	is	be	AUX
ejpam-3328	734	6	possible	possible	ADJ
ejpam-3328	734	7	to	to	PART
ejpam-3328	734	8	tell	tell	VERB
ejpam-3328	734	9	these	these	DET
ejpam-3328	734	10	outstanding	outstanding	ADJ
ejpam-3328	734	11	scientists	scientist	NOUN
ejpam-3328	734	12	the	the	DET
ejpam-3328	734	13	problems	problem	NOUN
ejpam-3328	734	14	have	have	AUX
ejpam-3328	734	15	been	be	AUX
ejpam-3328	734	16	formulated	formulate	VERB
ejpam-3328	734	17	and	and	CCONJ
ejpam-3328	734	18	all	all	DET
ejpam-3328	734	19	modern	modern	ADJ
ejpam-3328	734	20	methods	method	NOUN
ejpam-3328	734	21	of	of	ADP
ejpam-3328	734	22	their	their	PRON
ejpam-3328	734	23	decision	decision	NOUN
ejpam-3328	734	24	are	be	AUX
ejpam-3328	734	25	put	put	VERB
ejpam-3328	734	26	in	in	ADP
ejpam-3328	734	27	pawn	pawn	NOUN
ejpam-3328	734	28	.	.	PUNCT
ejpam-3328	735	1	references	reference	NOUN
ejpam-3328	735	2	1174	1174	NUM
ejpam-3328	735	3	acknowledgements	acknowledgement	VERB
ejpam-3328	735	4	the	the	DET
ejpam-3328	735	5	author	author	NOUN
ejpam-3328	735	6	thanks	thank	NOUN
ejpam-3328	735	7	the	the	DET
ejpam-3328	735	8	nas	nas	NOUN
ejpam-3328	735	9	rk	rk	NOUN
ejpam-3328	735	10	,	,	PUNCT
ejpam-3328	735	11	in	in	ADP
ejpam-3328	735	12	particular	particular	ADJ
ejpam-3328	735	13	,	,	PUNCT
ejpam-3328	735	14	academician	academician	PROPN
ejpam-3328	735	15	nas	nas	PROPN
ejpam-3328	735	16	rk	rk	PROPN
ejpam-3328	735	17	b.	b.	PROPN
ejpam-3328	735	18	zhumagulov	zhumagulov	PROPN
ejpam-3328	735	19	for	for	ADP
ejpam-3328	735	20	constant	constant	ADJ
ejpam-3328	735	21	attention	attention	NOUN
ejpam-3328	735	22	and	and	CCONJ
ejpam-3328	735	23	support	support	NOUN
ejpam-3328	735	24	.	.	PUNCT
ejpam-3328	736	1	moreover	moreover	ADV
ejpam-3328	736	2	,	,	PUNCT
ejpam-3328	736	3	the	the	DET
ejpam-3328	736	4	author	author	NOUN
ejpam-3328	736	5	is	be	AUX
ejpam-3328	736	6	grateful	grateful	ADJ
ejpam-3328	736	7	for	for	ADP
ejpam-3328	736	8	the	the	DET
ejpam-3328	736	9	mathematics	mathematic	NOUN
ejpam-3328	736	10	seminar	seminar	NOUN
ejpam-3328	736	11	at	at	ADP
ejpam-3328	736	12	the	the	DET
ejpam-3328	736	13	kazakhstan	kazakhstan	PROPN
ejpam-3328	736	14	branch	branch	PROPN
ejpam-3328	736	15	of	of	ADP
ejpam-3328	736	16	moscow	moscow	PROPN
ejpam-3328	736	17	state	state	PROPN
ejpam-3328	736	18	university	university	PROPN
ejpam-3328	736	19	,	,	PUNCT
ejpam-3328	736	20	at	at	ADP
ejpam-3328	736	21	which	which	PRON
ejpam-3328	736	22	valuable	valuable	ADJ
ejpam-3328	736	23	comments	comment	NOUN
ejpam-3328	736	24	were	be	AUX
ejpam-3328	736	25	made	make	VERB
ejpam-3328	736	26	,	,	PUNCT
ejpam-3328	736	27	and	and	CCONJ
ejpam-3328	736	28	thanks	thanks	PROPN
ejpam-3328	736	29	professors	professors	PROPN
ejpam-3328	736	30	b.	b.	PROPN
ejpam-3328	736	31	kanguzhin	kanguzhin	PROPN
ejpam-3328	736	32	and	and	CCONJ
ejpam-3328	736	33	m.	m.	NOUN
ejpam-3328	736	34	otelbaev	otelbaev	PROPN
ejpam-3328	736	35	and	and	CCONJ
ejpam-3328	736	36	the	the	DET
ejpam-3328	736	37	organisers	organiser	NOUN
ejpam-3328	736	38	of	of	ADP
ejpam-3328	736	39	automorphicformsworkshop.org/afw2018	automorphicformsworkshop.org/afw2018	PROPN
ejpam-3328	736	40	for	for	ADP
ejpam-3328	736	41	their	their	PRON
ejpam-3328	736	42	detailed	detailed	ADJ
ejpam-3328	736	43	review	review	NOUN
ejpam-3328	736	44	and	and	CCONJ
ejpam-3328	736	45	valuable	valuable	ADJ
ejpam-3328	736	46	comments	comment	NOUN
ejpam-3328	736	47	.	.	PUNCT
ejpam-3328	737	1	the	the	DET
ejpam-3328	737	2	author	author	NOUN
ejpam-3328	737	3	is	be	AUX
ejpam-3328	737	4	especially	especially	ADV
ejpam-3328	737	5	grateful	grateful	ADJ
ejpam-3328	737	6	to	to	ADP
ejpam-3328	737	7	professors	professors	PROPN
ejpam-3328	737	8	steven	steven	PROPN
ejpam-3328	737	9	miller	miller	PROPN
ejpam-3328	737	10	,	,	PUNCT
ejpam-3328	737	11	p	p	NOUN
ejpam-3328	737	12	plotnikov	plotnikov	NOUN
ejpam-3328	737	13	,	,	PUNCT
ejpam-3328	737	14	and	and	CCONJ
ejpam-3328	737	15	a	a	DET
ejpam-3328	737	16	mednykh	mednykh	NOUN
ejpam-3328	737	17	for	for	ADP
ejpam-3328	737	18	their	their	PRON
ejpam-3328	737	19	thorough	thorough	ADJ
ejpam-3328	737	20	analysis	analysis	NOUN
ejpam-3328	737	21	of	of	ADP
ejpam-3328	737	22	the	the	DET
ejpam-3328	737	23	work	work	NOUN
ejpam-3328	737	24	and	and	CCONJ
ejpam-3328	737	25	detailed	detailed	ADJ
ejpam-3328	737	26	recommendations	recommendation	NOUN
ejpam-3328	737	27	that	that	PRON
ejpam-3328	737	28	have	have	AUX
ejpam-3328	737	29	significantly	significantly	ADV
ejpam-3328	737	30	improved	improve	VERB
ejpam-3328	737	31	the	the	DET
ejpam-3328	737	32	paper	paper	NOUN
ejpam-3328	737	33	.	.	PUNCT
ejpam-3328	738	1	the	the	DET
ejpam-3328	738	2	author	author	NOUN
ejpam-3328	738	3	thanks	thank	VERB
ejpam-3328	738	4	financial	financial	ADJ
ejpam-3328	738	5	support	support	NOUN
ejpam-3328	738	6	of	of	ADP
ejpam-3328	738	7	the	the	DET
ejpam-3328	738	8	science	science	NOUN
ejpam-3328	738	9	fund	fund	NOUN
ejpam-3328	738	10	of	of	ADP
ejpam-3328	738	11	the	the	DET
ejpam-3328	738	12	ministry	ministry	PROPN
ejpam-3328	738	13	of	of	ADP
ejpam-3328	738	14	education	education	PROPN
ejpam-3328	738	15	and	and	CCONJ
ejpam-3328	738	16	science	science	NOUN
ejpam-3328	738	17	of	of	ADP
ejpam-3328	738	18	the	the	DET
ejpam-3328	738	19	republic	republic	NOUN
ejpam-3328	738	20	of	of	ADP
ejpam-3328	738	21	kazakhstan	kazakhstan	PROPN
ejpam-3328	738	22	according	accord	VERB
ejpam-3328	738	23	to	to	ADP
ejpam-3328	738	24	grant	grant	VERB
ejpam-3328	738	25	ap05132573	ap05132573	NOUN
ejpam-3328	738	26	-	-	PUNCT
ejpam-3328	738	27	ot-18	ot-18	NOUN
ejpam-3328	738	28	references	reference	NOUN
ejpam-3328	738	29	[	[	X
ejpam-3328	738	30	1	1	NUM
ejpam-3328	738	31	]	]	X
ejpam-3328	738	32	terence	terence	NOUN
ejpam-3328	738	33	tao	tao	PROPN
ejpam-3328	738	34	,	,	PUNCT
ejpam-3328	738	35	finite	finite	ADJ
ejpam-3328	738	36	time	time	NOUN
ejpam-3328	738	37	blowup	blowup	ADJ
ejpam-3328	738	38	for	for	ADP
ejpam-3328	738	39	an	an	DET
ejpam-3328	738	40	averaged	average	VERB
ejpam-3328	738	41	three	three	NUM
ejpam-3328	738	42	-	-	PUNCT
ejpam-3328	738	43	dimensional	dimensional	ADJ
ejpam-3328	738	44	navier	navier	NOUN
ejpam-3328	738	45	-	-	PUNCT
ejpam-3328	738	46	stokes	stoke	NOUN
ejpam-3328	738	47	equation	equation	NOUN
ejpam-3328	738	48	,	,	PUNCT
ejpam-3328	738	49	-arxiv:1402.0290	-arxiv:1402.0290	PUNCT
ejpam-3328	739	1	[	[	X
ejpam-3328	739	2	math.ap	math.ap	X
ejpam-3328	739	3	]	]	X
ejpam-3328	739	4	[	[	X
ejpam-3328	739	5	2	2	NUM
ejpam-3328	739	6	]	]	PUNCT
ejpam-3328	739	7	l.	l.	PROPN
ejpam-3328	739	8	d.	d.	PROPN
ejpam-3328	739	9	faddeev	faddeev	PROPN
ejpam-3328	739	10	,	,	PUNCT
ejpam-3328	739	11	the	the	DET
ejpam-3328	739	12	inverse	inverse	NOUN
ejpam-3328	739	13	problem	problem	NOUN
ejpam-3328	739	14	in	in	ADP
ejpam-3328	739	15	the	the	DET
ejpam-3328	739	16	quantum	quantum	ADJ
ejpam-3328	739	17	theory	theory	NOUN
ejpam-3328	739	18	of	of	ADP
ejpam-3328	739	19	scattering	scattering	NOUN
ejpam-3328	739	20	.	.	PUNCT
ejpam-3328	740	1	ii	ii	PROPN
ejpam-3328	740	2	,	,	PUNCT
ejpam-3328	740	3	itogi	itogi	PROPN
ejpam-3328	740	4	nauki	nauki	PROPN
ejpam-3328	741	1	i	i	PRON
ejpam-3328	741	2	tekhniki	tekhniki	PROPN
ejpam-3328	741	3	.	.	PUNCT
ejpam-3328	742	1	ser	ser	PROPN
ejpam-3328	742	2	.	.	PUNCT
ejpam-3328	743	1	sovrem	sovrem	PROPN
ejpam-3328	743	2	.	.	PUNCT
ejpam-3328	744	1	probl	probl	PROPN
ejpam-3328	744	2	.	.	PUNCT
ejpam-3328	745	1	mat	mat	PROPN
ejpam-3328	745	2	.	.	PROPN
ejpam-3328	745	3	,	,	PUNCT
ejpam-3328	745	4	3	3	X
ejpam-3328	745	5	,	,	PUNCT
ejpam-3328	745	6	viniti	viniti	PROPN
ejpam-3328	745	7	,	,	PUNCT
ejpam-3328	745	8	moscow	moscow	PROPN
ejpam-3328	745	9	,	,	PUNCT
ejpam-3328	745	10	1974	1974	NUM
ejpam-3328	745	11	,	,	PUNCT
ejpam-3328	745	12	93180	93180	NUM
ejpam-3328	746	1	[	[	X
ejpam-3328	746	2	3	3	X
ejpam-3328	746	3	]	]	X
ejpam-3328	746	4	charles	charles	PROPN
ejpam-3328	746	5	l.	l.	PROPN
ejpam-3328	746	6	fefferman	fefferman	PROPN
ejpam-3328	746	7	existence	existence	NOUN
ejpam-3328	746	8	and	and	CCONJ
ejpam-3328	746	9	smoothness	smoothness	NOUN
ejpam-3328	746	10	of	of	ADP
ejpam-3328	746	11	the	the	DET
ejpam-3328	746	12	navier	navier	NOUN
ejpam-3328	746	13	-	-	PUNCT
ejpam-3328	746	14	stokes	stoke	NOUN
ejpam-3328	746	15	equation	equation	NOUN
ejpam-3328	746	16	.	.	PUNCT
ejpam-3328	747	1	the	the	DET
ejpam-3328	747	2	millennium	millennium	PROPN
ejpam-3328	747	3	prize	prize	PROPN
ejpam-3328	747	4	problems	problem	NOUN
ejpam-3328	747	5	,	,	PUNCT
ejpam-3328	747	6	5767	5767	NUM
ejpam-3328	747	7	,	,	PUNCT
ejpam-3328	747	8	clay	clay	NOUN
ejpam-3328	747	9	math	math	NOUN
ejpam-3328	747	10	.	.	PUNCT
ejpam-3328	748	1	inst	inst	PROPN
ejpam-3328	748	2	.	.	PROPN
ejpam-3328	748	3	,	,	PUNCT
ejpam-3328	748	4	cambridge	cambridge	PROPN
ejpam-3328	748	5	,	,	PUNCT
ejpam-3328	748	6	ma	ma	PROPN
ejpam-3328	748	7	,	,	PUNCT
ejpam-3328	748	8	2006	2006	NUM
ejpam-3328	748	9	.	.	PUNCT
ejpam-3328	749	1	[	[	X
ejpam-3328	749	2	4	4	NUM
ejpam-3328	749	3	]	]	X
ejpam-3328	749	4	j.s.russell	j.s.russell	ADJ
ejpam-3328	749	5	report	report	NOUN
ejpam-3328	749	6	on	on	ADP
ejpam-3328	749	7	waves	wave	NOUN
ejpam-3328	749	8	:	:	PUNCT
ejpam-3328	749	9	(	(	PUNCT
ejpam-3328	749	10	report	report	NOUN
ejpam-3328	749	11	of	of	ADP
ejpam-3328	749	12	the	the	DET
ejpam-3328	749	13	fourteenth	fourteenth	ADJ
ejpam-3328	749	14	meeting	meeting	NOUN
ejpam-3328	749	15	of	of	ADP
ejpam-3328	749	16	the	the	DET
ejpam-3328	749	17	british	british	PROPN
ejpam-3328	749	18	association	association	PROPN
ejpam-3328	749	19	for	for	ADP
ejpam-3328	749	20	the	the	DET
ejpam-3328	749	21	advancement	advancement	NOUN
ejpam-3328	749	22	of	of	ADP
ejpam-3328	749	23	science	science	PROPN
ejpam-3328	749	24	,	,	PUNCT
ejpam-3328	749	25	york	york	PROPN
ejpam-3328	749	26	,	,	PUNCT
ejpam-3328	749	27	september	september	PROPN
ejpam-3328	749	28	1844	1844	NUM
ejpam-3328	749	29	(	(	PUNCT
ejpam-3328	749	30	london	london	PROPN
ejpam-3328	749	31	1845	1845	NUM
ejpam-3328	749	32	)	)	PUNCT
ejpam-3328	749	33	,	,	PUNCT
ejpam-3328	749	34	pp	pp	PROPN
ejpam-3328	749	35	311390	311390	NUM
ejpam-3328	749	36	,	,	PUNCT
ejpam-3328	749	37	plates	plate	NOUN
ejpam-3328	749	38	xlvii	xlvii	PROPN
ejpam-3328	749	39	-	-	PUNCT
ejpam-3328	749	40	lvii	lvii	ADJ
ejpam-3328	749	41	)	)	PUNCT
ejpam-3328	750	1	[	[	X
ejpam-3328	750	2	5	5	NUM
ejpam-3328	750	3	]	]	X
ejpam-3328	750	4	j.s.russell	j.s.russell	NOUN
ejpam-3328	750	5	(	(	PUNCT
ejpam-3328	750	6	1838	1838	NUM
ejpam-3328	750	7	)	)	PUNCT
ejpam-3328	750	8	,	,	PUNCT
ejpam-3328	750	9	report	report	NOUN
ejpam-3328	750	10	of	of	ADP
ejpam-3328	750	11	the	the	DET
ejpam-3328	750	12	committee	committee	NOUN
ejpam-3328	750	13	on	on	ADP
ejpam-3328	750	14	waves	wave	NOUN
ejpam-3328	750	15	,	,	PUNCT
ejpam-3328	750	16	report	report	NOUN
ejpam-3328	750	17	of	of	ADP
ejpam-3328	750	18	the	the	DET
ejpam-3328	750	19	7th	7th	ADJ
ejpam-3328	750	20	meeting	meeting	NOUN
ejpam-3328	750	21	of	of	ADP
ejpam-3328	750	22	british	british	PROPN
ejpam-3328	750	23	association	association	PROPN
ejpam-3328	750	24	for	for	ADP
ejpam-3328	750	25	the	the	DET
ejpam-3328	750	26	advancement	advancement	NOUN
ejpam-3328	750	27	of	of	ADP
ejpam-3328	750	28	science	science	NOUN
ejpam-3328	750	29	,	,	PUNCT
ejpam-3328	750	30	john	john	PROPN
ejpam-3328	750	31	murray	murray	PROPN
ejpam-3328	750	32	,	,	PUNCT
ejpam-3328	750	33	london	london	PROPN
ejpam-3328	750	34	,	,	PUNCT
ejpam-3328	750	35	pp.417	pp.417	PROPN
ejpam-3328	750	36	-	-	PUNCT
ejpam-3328	750	37	496	496	NUM
ejpam-3328	750	38	.	.	PUNCT
ejpam-3328	751	1	[	[	X
ejpam-3328	751	2	6	6	NUM
ejpam-3328	751	3	]	]	PUNCT
ejpam-3328	751	4	mark	mark	PROPN
ejpam-3328	751	5	j.	j.	PROPN
ejpam-3328	751	6	ablowitz	ablowitz	PROPN
ejpam-3328	751	7	,	,	PUNCT
ejpam-3328	751	8	harvey	harvey	PROPN
ejpam-3328	751	9	segur	segur	PROPN
ejpam-3328	751	10	solitons	solitons	PROPN
ejpam-3328	751	11	and	and	CCONJ
ejpam-3328	751	12	the	the	DET
ejpam-3328	751	13	inverse	inverse	NOUN
ejpam-3328	751	14	scattering	scattering	NOUN
ejpam-3328	751	15	transform	transform	NOUN
ejpam-3328	751	16	siam	siam	NOUN
ejpam-3328	751	17	,	,	PUNCT
ejpam-3328	751	18	1981p	1981p	NUM
ejpam-3328	751	19	.	.	PUNCT
ejpam-3328	752	1	435	435	NUM
ejpam-3328	752	2	.	.	PUNCT
ejpam-3328	753	1	[	[	X
ejpam-3328	753	2	7	7	NUM
ejpam-3328	753	3	]	]	SYM
ejpam-3328	753	4	n.j.zabusky	n.j.zabusky	NOUN
ejpam-3328	753	5	and	and	CCONJ
ejpam-3328	753	6	m.d.kruskal	m.d.kruskal	NOUN
ejpam-3328	753	7	(	(	PUNCT
ejpam-3328	753	8	1965	1965	NUM
ejpam-3328	753	9	)	)	PUNCT
ejpam-3328	753	10	,	,	PUNCT
ejpam-3328	753	11	interaction	interaction	NOUN
ejpam-3328	753	12	of	of	ADP
ejpam-3328	753	13	solitons	soliton	NOUN
ejpam-3328	753	14	in	in	ADP
ejpam-3328	753	15	a	a	DET
ejpam-3328	753	16	collisionless	collisionless	ADJ
ejpam-3328	753	17	plasma	plasma	NOUN
ejpam-3328	753	18	and	and	CCONJ
ejpam-3328	753	19	the	the	DET
ejpam-3328	753	20	recurrence	recurrence	NOUN
ejpam-3328	753	21	of	of	ADP
ejpam-3328	753	22	initial	initial	ADJ
ejpam-3328	753	23	states	state	NOUN
ejpam-3328	753	24	,	,	PUNCT
ejpam-3328	753	25	phys.rev.lett	phys.rev.lett	PROPN
ejpam-3328	753	26	.	.	PUNCT
ejpam-3328	753	27	,	,	PUNCT
ejpam-3328	753	28	15	15	NUM
ejpam-3328	753	29	pp	pp	NOUN
ejpam-3328	753	30	.	.	PUNCT
ejpam-3328	754	1	240243	240243	NUM
ejpam-3328	754	2	.	.	PUNCT
ejpam-3328	755	1	[	[	X
ejpam-3328	755	2	8	8	NUM
ejpam-3328	755	3	]	]	X
ejpam-3328	755	4	r.g	r.g	PROPN
ejpam-3328	755	5	newton	newton	PROPN
ejpam-3328	755	6	,	,	PUNCT
ejpam-3328	755	7	new	new	ADJ
ejpam-3328	755	8	result	result	NOUN
ejpam-3328	755	9	on	on	ADP
ejpam-3328	755	10	the	the	DET
ejpam-3328	755	11	inverse	inverse	NOUN
ejpam-3328	755	12	scattering	scattering	NOUN
ejpam-3328	755	13	problem	problem	NOUN
ejpam-3328	755	14	in	in	ADP
ejpam-3328	755	15	three	three	NUM
ejpam-3328	755	16	dimentions	dimention	NOUN
ejpam-3328	755	17	,	,	PUNCT
ejpam-3328	755	18	phys	phy	NOUN
ejpam-3328	755	19	.	.	PUNCT
ejpam-3328	756	1	rev	rev	PROPN
ejpam-3328	756	2	.	.	PROPN
ejpam-3328	756	3	lett	lett	PROPN
ejpam-3328	756	4	.	.	PUNCT
ejpam-3328	757	1	v43	v43	PROPN
ejpam-3328	757	2	,	,	PUNCT
ejpam-3328	757	3	8,pp.541	8,pp.541	NUM
ejpam-3328	757	4	-	-	SYM
ejpam-3328	757	5	542,1979	542,1979	NUM
ejpam-3328	758	1	[	[	X
ejpam-3328	758	2	9	9	NUM
ejpam-3328	758	3	]	]	X
ejpam-3328	758	4	r.g	r.g	PROPN
ejpam-3328	758	5	newton	newton	PROPN
ejpam-3328	758	6	,	,	PUNCT
ejpam-3328	758	7	inverse	inverse	NOUN
ejpam-3328	758	8	scattering	scatter	VERB
ejpam-3328	758	9	three	three	NUM
ejpam-3328	758	10	dimensions	dimension	NOUN
ejpam-3328	758	11	,	,	PUNCT
ejpam-3328	758	12	jour	jour	PROPN
ejpam-3328	758	13	.	.	PUNCT
ejpam-3328	758	14	math	math	NOUN
ejpam-3328	758	15	.	.	PUNCT
ejpam-3328	759	1	phys	phy	NOUN
ejpam-3328	759	2	.	.	PUNCT
ejpam-3328	760	1	21	21	NUM
ejpam-3328	760	2	,	,	PUNCT
ejpam-3328	760	3	pp.16981715,1980	pp.16981715,1980	NOUN
ejpam-3328	760	4	[	[	X
ejpam-3328	760	5	10	10	NUM
ejpam-3328	760	6	]	]	X
ejpam-3328	760	7	somersalo	somersalo	PROPN
ejpam-3328	760	8	e.	e.	PROPN
ejpam-3328	760	9	et	et	PROPN
ejpam-3328	760	10	al	al	PROPN
ejpam-3328	760	11	.	.	PROPN
ejpam-3328	760	12	inverse	inverse	ADJ
ejpam-3328	760	13	scattering	scattering	NOUN
ejpam-3328	760	14	problem	problem	NOUN
ejpam-3328	760	15	for	for	ADP
ejpam-3328	760	16	the	the	DET
ejpam-3328	760	17	schrodinger	schrodinger	NOUN
ejpam-3328	760	18	’s	’s	PART
ejpam-3328	760	19	equation	equation	NOUN
ejpam-3328	760	20	in	in	ADP
ejpam-3328	760	21	three	three	NUM
ejpam-3328	760	22	dimensions	dimension	NOUN
ejpam-3328	760	23	:	:	PUNCT
ejpam-3328	760	24	connections	connection	NOUN
ejpam-3328	760	25	between	between	ADP
ejpam-3328	760	26	exact	exact	ADJ
ejpam-3328	760	27	and	and	CCONJ
ejpam-3328	760	28	approximate	approximate	ADJ
ejpam-3328	760	29	methods	method	NOUN
ejpam-3328	760	30	.	.	PUNCT
ejpam-3328	761	1	1988	1988	NUM
ejpam-3328	761	2	.	.	PUNCT
ejpam-3328	762	1	[	[	X
ejpam-3328	762	2	11	11	NUM
ejpam-3328	762	3	]	]	SYM
ejpam-3328	762	4	tables	table	NOUN
ejpam-3328	762	5	of	of	ADP
ejpam-3328	762	6	integral	integral	ADJ
ejpam-3328	762	7	transforms	transform	NOUN
ejpam-3328	762	8	.	.	PUNCT
ejpam-3328	763	1	v.i	v.i	PROPN
ejpam-3328	763	2	mcgraw	mcgraw	PROPN
ejpam-3328	763	3	-	-	PUNCT
ejpam-3328	763	4	hill	hill	NOUN
ejpam-3328	763	5	book	book	NOUN
ejpam-3328	763	6	company	company	NOUN
ejpam-3328	763	7	,	,	PUNCT
ejpam-3328	763	8	inc.1954	inc.1954	PRON
ejpam-3328	763	9	references	reference	NOUN
ejpam-3328	763	10	1175	1175	NUM
ejpam-3328	764	1	[	[	X
ejpam-3328	764	2	12	12	NUM
ejpam-3328	764	3	]	]	X
ejpam-3328	764	4	poincar	poincar	PROPN
ejpam-3328	764	5	h.	h.	PROPN
ejpam-3328	764	6	,	,	PUNCT
ejpam-3328	764	7	lecons	lecon	NOUN
ejpam-3328	764	8	de	de	PROPN
ejpam-3328	764	9	mecanique	mecanique	PROPN
ejpam-3328	764	10	celeste	celeste	PROPN
ejpam-3328	764	11	,	,	PUNCT
ejpam-3328	764	12	t.	t.	NOUN
ejpam-3328	764	13	3	3	NUM
ejpam-3328	764	14	,	,	PUNCT
ejpam-3328	764	15	p.	p.	NOUN
ejpam-3328	764	16	,	,	PUNCT
ejpam-3328	764	17	1910	1910	NUM
ejpam-3328	764	18	.	.	PUNCT
ejpam-3328	765	1	[	[	X
ejpam-3328	765	2	13	13	NUM
ejpam-3328	765	3	]	]	X
ejpam-3328	765	4	leray	leray	ADV
ejpam-3328	765	5	,	,	PUNCT
ejpam-3328	765	6	j.	j.	PROPN
ejpam-3328	765	7	(	(	PUNCT
ejpam-3328	765	8	1934	1934	NUM
ejpam-3328	765	9	)	)	PUNCT
ejpam-3328	765	10	.	.	PUNCT
ejpam-3328	765	11	”	"	PUNCT
ejpam-3328	765	12	sur	sur	PROPN
ejpam-3328	765	13	le	le	X
ejpam-3328	765	14	mouvement	mouvement	PROPN
ejpam-3328	765	15	d’un	d’un	PROPN
ejpam-3328	765	16	liquide	liquide	PROPN
ejpam-3328	765	17	visqueux	visqueux	PROPN
ejpam-3328	765	18	emplissant	emplissant	PROPN
ejpam-3328	765	19	l’espace	l’espace	PROPN
ejpam-3328	765	20	”	"	PUNCT
ejpam-3328	765	21	.	.	PUNCT
ejpam-3328	766	1	acta	acta	PROPN
ejpam-3328	766	2	mathematica	mathematica	PROPN
ejpam-3328	766	3	63	63	NUM
ejpam-3328	766	4	:	:	SYM
ejpam-3328	766	5	193248	193248	NUM
ejpam-3328	766	6	.	.	PUNCT
ejpam-3328	767	1	doi:10.1007	doi:10.1007	NOUN
ejpam-3328	767	2	/	/	SYM
ejpam-3328	767	3	bf02547354	bf02547354	PROPN
ejpam-3328	767	4	.	.	PUNCT
ejpam-3328	768	1	[	[	X
ejpam-3328	768	2	14	14	NUM
ejpam-3328	768	3	]	]	X
ejpam-3328	768	4	o.a	o.a	PROPN
ejpam-3328	768	5	.	.	PROPN
ejpam-3328	768	6	ladyzhenskaya	ladyzhenskaya	PROPN
ejpam-3328	768	7	,	,	PUNCT
ejpam-3328	768	8	mathematic	mathematic	ADJ
ejpam-3328	768	9	problems	problem	NOUN
ejpam-3328	768	10	of	of	ADP
ejpam-3328	768	11	viscous	viscous	ADJ
ejpam-3328	768	12	incondensable	incondensable	ADJ
ejpam-3328	768	13	liquid	liquid	ADJ
ejpam-3328	768	14	dynamics	dynamic	NOUN
ejpam-3328	768	15	.	.	PUNCT
ejpam-3328	769	1	m.	m.	NOUN
ejpam-3328	769	2	:	:	PUNCT
ejpam-3328	769	3	science	science	NOUN
ejpam-3328	769	4	,	,	PUNCT
ejpam-3328	769	5	1970	1970	NUM
ejpam-3328	769	6	.	.	PUNCT
ejpam-3328	770	1	p.	p.	NOUN
ejpam-3328	770	2	288	288	NUM
ejpam-3328	771	1	[	[	X
ejpam-3328	771	2	15	15	NUM
ejpam-3328	771	3	]	]	X
ejpam-3328	771	4	solonnikov	solonnikov	PROPN
ejpam-3328	771	5	v.a	v.a	PROPN
ejpam-3328	771	6	.	.	PROPN
ejpam-3328	771	7	estimates	estimate	NOUN
ejpam-3328	771	8	solving	solve	VERB
ejpam-3328	771	9	nonstationary	nonstationary	ADJ
ejpam-3328	771	10	linearized	linearize	VERB
ejpam-3328	771	11	systems	system	NOUN
ejpam-3328	771	12	of	of	ADP
ejpam-3328	771	13	navier	navier	NOUN
ejpam-3328	771	14	-	-	PUNCT
ejpam-3328	771	15	stokes	stoke	NOUN
ejpam-3328	771	16	’	'	PUNCT
ejpam-3328	771	17	equations	equation	NOUN
ejpam-3328	771	18	.	.	PUNCT
ejpam-3328	772	1	transactions	transaction	NOUN
ejpam-3328	772	2	academy	academy	PROPN
ejpam-3328	772	3	of	of	ADP
ejpam-3328	772	4	sciences	sciences	PROPN
ejpam-3328	772	5	ussr	ussr	ADJ
ejpam-3328	772	6	vol	vol	NOUN
ejpam-3328	772	7	.	.	PROPN
ejpam-3328	772	8	70	70	NUM
ejpam-3328	772	9	,	,	PUNCT
ejpam-3328	772	10	1964	1964	NUM
ejpam-3328	772	11	.	.	PUNCT
ejpam-3328	773	1	p.	p.	NOUN
ejpam-3328	773	2	213	213	NUM
ejpam-3328	773	3	–	–	PUNCT
ejpam-3328	773	4	317	317	NUM
ejpam-3328	773	5	.	.	PUNCT
ejpam-3328	774	1	[	[	X
ejpam-3328	774	2	16	16	NUM
ejpam-3328	774	3	]	]	PUNCT
ejpam-3328	774	4	on	on	ADP
ejpam-3328	774	5	global	global	ADJ
ejpam-3328	774	6	weak	weak	ADJ
ejpam-3328	774	7	solutions	solution	NOUN
ejpam-3328	774	8	to	to	ADP
ejpam-3328	774	9	the	the	DET
ejpam-3328	774	10	cauchy	cauchy	ADJ
ejpam-3328	774	11	problem	problem	NOUN
ejpam-3328	774	12	for	for	ADP
ejpam-3328	774	13	the	the	DET
ejpam-3328	774	14	navier	navier	NOUN
ejpam-3328	774	15	-	-	PUNCT
ejpam-3328	774	16	stokes	stoke	NOUN
ejpam-3328	774	17	equations	equation	NOUN
ejpam-3328	774	18	with	with	ADP
ejpam-3328	774	19	large	large	ADJ
ejpam-3328	774	20	l-3	l-3	PROPN
ejpam-3328	774	21	-	-	PUNCT
ejpam-3328	774	22	initial	initial	ADJ
ejpam-3328	774	23	data	datum	NOUN
ejpam-3328	774	24	seregin	seregin	NOUN
ejpam-3328	774	25	,	,	PUNCT
ejpam-3328	774	26	g	g	NOUN
ejpam-3328	774	27	;	;	PUNCT
ejpam-3328	774	28	sverak	sverak	NOUN
ejpam-3328	774	29	,	,	PUNCT
ejpam-3328	774	30	v	v	NOUN
ejpam-3328	774	31	;	;	PUNCT
ejpam-3328	774	32	nonlinear	nonlinear	ADJ
ejpam-3328	774	33	analysis	analysis	NOUN
ejpam-3328	774	34	-	-	PUNCT
ejpam-3328	774	35	theory	theory	NOUN
ejpam-3328	774	36	methods	method	NOUN
ejpam-3328	774	37	and	and	CCONJ
ejpam-3328	774	38	applications	application	NOUN
ejpam-3328	774	39	volume	volume	NOUN
ejpam-3328	774	40	154	154	NUM
ejpam-3328	774	41	page	page	NOUN
ejpam-3328	774	42	269	269	NUM
ejpam-3328	774	43	-	-	SYM
ejpam-3328	774	44	296	296	NUM
ejpam-3328	774	45	(	(	PUNCT
ejpam-3328	774	46	may	may	PROPN
ejpam-3328	774	47	2017	2017	NUM
ejpam-3328	774	48	)	)	PUNCT
ejpam-3328	774	49	estimates	estimate	NOUN
ejpam-3328	774	50	of	of	ADP
ejpam-3328	774	51	solutions	solution	NOUN
ejpam-3328	774	52	to	to	ADP
ejpam-3328	774	53	the	the	DET
ejpam-3328	774	54	perturbed	perturb	VERB
ejpam-3328	774	55	stokes	stoke	NOUN
ejpam-3328	774	56	system	system	NOUN
ejpam-3328	774	57	[	[	X
ejpam-3328	774	58	17	17	NUM
ejpam-3328	774	59	]	]	X
ejpam-3328	774	60	v.	v.	PROPN
ejpam-3328	774	61	vialov	vialov	PROPN
ejpam-3328	774	62	,	,	PUNCT
ejpam-3328	774	63	t.	t.	PROPN
ejpam-3328	774	64	shilkin	shilkin	PROPN
ejpam-3328	774	65	notes	note	NOUN
ejpam-3328	774	66	of	of	ADP
ejpam-3328	774	67	the	the	DET
ejpam-3328	774	68	scientific	scientific	ADJ
ejpam-3328	774	69	seminars	seminar	NOUN
ejpam-3328	774	70	of	of	ADP
ejpam-3328	774	71	pomi	pomi	NOUN
ejpam-3328	774	72	,	,	PUNCT
ejpam-3328	774	73	410	410	NUM
ejpam-3328	774	74	(	(	PUNCT
ejpam-3328	774	75	2013	2013	NUM
ejpam-3328	774	76	)	)	PUNCT
ejpam-3328	774	77	,	,	PUNCT
ejpam-3328	774	78	524	524	NUM
ejpam-3328	774	79	[	[	X
ejpam-3328	774	80	18	18	NUM
ejpam-3328	774	81	]	]	X
ejpam-3328	774	82	f.	f.	PROPN
ejpam-3328	774	83	mebarek	mebarek	PROPN
ejpam-3328	774	84	-	-	PUNCT
ejpam-3328	774	85	oudina	oudina	PROPN
ejpam-3328	774	86	r.	r.	PROPN
ejpam-3328	774	87	bessah	bessah	PROPN
ejpam-3328	774	88	,	,	PUNCT
ejpam-3328	774	89	magnetohydrodynamic	magnetohydrodynamic	ADJ
ejpam-3328	774	90	stability	stability	NOUN
ejpam-3328	774	91	of	of	ADP
ejpam-3328	774	92	natural	natural	ADJ
ejpam-3328	774	93	convection	convection	NOUN
ejpam-3328	774	94	flows	flow	NOUN
ejpam-3328	774	95	in	in	ADP
ejpam-3328	774	96	czochralski	czochralski	NOUN
ejpam-3328	774	97	crystal	crystal	NOUN
ejpam-3328	774	98	growth	growth	NOUN
ejpam-3328	774	99	.	.	PUNCT
ejpam-3328	775	1	world	world	PROPN
ejpam-3328	775	2	journal	journal	PROPN
ejpam-3328	775	3	of	of	ADP
ejpam-3328	775	4	engineering	engineering	NOUN
ejpam-3328	775	5	,	,	PUNCT
ejpam-3328	775	6	vol	vol	NOUN
ejpam-3328	775	7	.	.	PROPN
ejpam-3328	775	8	4	4	NUM
ejpam-3328	775	9	no.4	no.4	PROPN
ejpam-3328	775	10	,	,	PUNCT
ejpam-3328	775	11	pp	pp	X
ejpam-3328	775	12	.	.	PUNCT
ejpam-3328	775	13	1522	1522	NUM
ejpam-3328	775	14	,	,	PUNCT
ejpam-3328	775	15	2007	2007	NUM
ejpam-3328	775	16	.	.	PUNCT
ejpam-3328	776	1	[	[	X
ejpam-3328	776	2	19	19	NUM
ejpam-3328	776	3	]	]	PUNCT
ejpam-3328	776	4	f.	f.	PROPN
ejpam-3328	776	5	mebarek	mebarek	PROPN
ejpam-3328	776	6	-	-	PUNCT
ejpam-3328	776	7	oudina	oudina	PROPN
ejpam-3328	776	8	and	and	CCONJ
ejpam-3328	776	9	r.	r.	PROPN
ejpam-3328	776	10	bessah	bessah	PROPN
ejpam-3328	776	11	,	,	PUNCT
ejpam-3328	776	12	oscillatory	oscillatory	ADJ
ejpam-3328	776	13	mixed	mixed	ADJ
ejpam-3328	776	14	convection	convection	NOUN
ejpam-3328	776	15	flow	flow	NOUN
ejpam-3328	776	16	in	in	ADP
ejpam-3328	776	17	a	a	DET
ejpam-3328	776	18	cylindrical	cylindrical	ADJ
ejpam-3328	776	19	container	container	NOUN
ejpam-3328	776	20	with	with	ADP
ejpam-3328	776	21	rotating	rotate	VERB
ejpam-3328	776	22	disk	disk	NOUN
ejpam-3328	776	23	under	under	ADP
ejpam-3328	776	24	axial	axial	ADJ
ejpam-3328	776	25	magnetic	magnetic	ADJ
ejpam-3328	776	26	field	field	NOUN
ejpam-3328	776	27	and	and	CCONJ
ejpam-3328	776	28	various	various	ADJ
ejpam-3328	776	29	electric	electric	ADJ
ejpam-3328	776	30	conductivity	conductivity	NOUN
ejpam-3328	776	31	walls	wall	NOUN
ejpam-3328	776	32	,	,	PUNCT
ejpam-3328	776	33	i.	i.	PROPN
ejpam-3328	776	34	review	review	PROPN
ejpam-3328	776	35	of	of	ADP
ejpam-3328	776	36	physics	physics	PROPN
ejpam-3328	776	37	,	,	PUNCT
ejpam-3328	776	38	4(1	4(1	NOUN
ejpam-3328	776	39	)	)	PUNCT
ejpam-3328	776	40	45	45	NUM
ejpam-3328	776	41	-	-	SYM
ejpam-3328	776	42	51	51	NUM
ejpam-3328	776	43	,	,	PUNCT
ejpam-3328	776	44	2010	2010	NUM
ejpam-3328	776	45	.	.	PUNCT
ejpam-3328	776	46	.	.	PUNCT
ejpam-3328	777	1	[	[	X
ejpam-3328	777	2	20	20	NUM
ejpam-3328	777	3	]	]	PUNCT
ejpam-3328	777	4	f.	f.	PROPN
ejpam-3328	777	5	mebarek	mebarek	PROPN
ejpam-3328	777	6	-	-	PUNCT
ejpam-3328	777	7	oudina	oudina	PROPN
ejpam-3328	777	8	,	,	PUNCT
ejpam-3328	777	9	numerical	numerical	ADJ
ejpam-3328	777	10	modeling	modeling	NOUN
ejpam-3328	777	11	of	of	ADP
ejpam-3328	777	12	the	the	DET
ejpam-3328	777	13	hydrodynamic	hydrodynamic	ADJ
ejpam-3328	777	14	stability	stability	NOUN
ejpam-3328	777	15	in	in	ADP
ejpam-3328	777	16	vertical	vertical	ADJ
ejpam-3328	777	17	annulus	annulus	NOUN
ejpam-3328	777	18	with	with	ADP
ejpam-3328	777	19	heat	heat	NOUN
ejpam-3328	777	20	source	source	NOUN
ejpam-3328	777	21	of	of	ADP
ejpam-3328	777	22	different	different	ADJ
ejpam-3328	777	23	lengths	length	NOUN
ejpam-3328	777	24	,	,	PUNCT
ejpam-3328	777	25	engineering	engineering	NOUN
ejpam-3328	777	26	science	science	NOUN
ejpam-3328	777	27	and	and	CCONJ
ejpam-3328	777	28	technolgy	technolgy	NOUN
ejpam-3328	777	29	,	,	PUNCT
ejpam-3328	777	30	an	an	DET
ejpam-3328	777	31	international	international	ADJ
ejpam-3328	777	32	journal	journal	NOUN
ejpam-3328	777	33	,	,	PUNCT
ejpam-3328	777	34	20	20	NUM
ejpam-3328	777	35	,	,	PUNCT
ejpam-3328	777	36	1324	1324	NUM
ejpam-3328	777	37	-	-	SYM
ejpam-3328	777	38	1333	1333	NUM
ejpam-3328	777	39	[	[	X
ejpam-3328	777	40	21	21	NUM
ejpam-3328	777	41	]	]	X
ejpam-3328	777	42	leonhard	leonhard	PROPN
ejpam-3328	777	43	euler	euler	PROPN
ejpam-3328	777	44	.	.	PUNCT
ejpam-3328	777	45	introduction	introduction	NOUN
ejpam-3328	777	46	to	to	ADP
ejpam-3328	777	47	analysis	analysis	NOUN
ejpam-3328	777	48	of	of	ADP
ejpam-3328	777	49	the	the	DET
ejpam-3328	777	50	infinite	infinite	NOUN
ejpam-3328	777	51	by	by	ADP
ejpam-3328	777	52	john	john	PROPN
ejpam-3328	777	53	blanton	blanton	PROPN
ejpam-3328	777	54	(	(	PUNCT
ejpam-3328	777	55	book	book	NOUN
ejpam-3328	777	56	i	i	PROPN
ejpam-3328	777	57	,	,	PUNCT
ejpam-3328	777	58	isbn	isbn	PROPN
ejpam-3328	777	59	0	0	NUM
ejpam-3328	777	60	-	-	SYM
ejpam-3328	777	61	387	387	NUM
ejpam-3328	777	62	-	-	PUNCT
ejpam-3328	777	63	96824	96824	NUM
ejpam-3328	777	64	-	-	PUNCT
ejpam-3328	777	65	5	5	NUM
ejpam-3328	777	66	,	,	PUNCT
ejpam-3328	777	67	springer	springer	NOUN
ejpam-3328	777	68	-	-	PUNCT
ejpam-3328	777	69	verlag	verlag	PROPN
ejpam-3328	777	70	1988	1988	NUM
ejpam-3328	777	71	;)	;)	PUNCT
ejpam-3328	778	1	[	[	X
ejpam-3328	778	2	22	22	NUM
ejpam-3328	778	3	]	]	PUNCT
ejpam-3328	778	4	chebyshev	chebyshev	PROPN
ejpam-3328	778	5	p.l	p.l	PROPN
ejpam-3328	778	6	.	.	PROPN
ejpam-3328	778	7	fav	fav	PROPN
ejpam-3328	778	8	.	.	PROPN
ejpam-3328	778	9	mathematical	mathematical	PROPN
ejpam-3328	778	10	works	work	NOUN
ejpam-3328	778	11	,	,	PUNCT
ejpam-3328	778	12	.-l	.-l	PROPN
ejpam-3328	778	13	.	.	PUNCT
ejpam-3328	778	14	,	,	PUNCT
ejpam-3328	778	15	1946	1946	NUM
ejpam-3328	778	16	;	;	PUNCT
ejpam-3328	778	17	[	[	X
ejpam-3328	778	18	23	23	NUM
ejpam-3328	778	19	]	]	X
ejpam-3328	778	20	riemann	riemann	PROPN
ejpam-3328	778	21	,	,	PUNCT
ejpam-3328	778	22	g.	g.	PROPN
ejpam-3328	778	23	f.	f.	PROPN
ejpam-3328	778	24	b.	b.	PROPN
ejpam-3328	778	25	on	on	ADP
ejpam-3328	778	26	the	the	DET
ejpam-3328	778	27	number	number	NOUN
ejpam-3328	778	28	of	of	ADP
ejpam-3328	778	29	prime	prime	ADJ
ejpam-3328	778	30	numbers	number	NOUN
ejpam-3328	778	31	less	less	ADJ
ejpam-3328	778	32	than	than	ADP
ejpam-3328	778	33	a	a	DET
ejpam-3328	778	34	given	give	VERB
ejpam-3328	778	35	quantity	quantity	NOUN
ejpam-3328	778	36	new	new	PROPN
ejpam-3328	778	37	york	york	PROPN
ejpam-3328	778	38	:	:	PUNCT
ejpam-3328	778	39	chelsea	chelsea	PROPN
ejpam-3328	778	40	,	,	PUNCT
ejpam-3328	778	41	1972	1972	NUM
ejpam-3328	778	42	.	.	PUNCT
ejpam-3328	779	1	[	[	X
ejpam-3328	779	2	24	24	NUM
ejpam-3328	779	3	]	]	X
ejpam-3328	779	4	e.	e.	PROPN
ejpam-3328	779	5	c.	c.	PROPN
ejpam-3328	779	6	titchmarsh	titchmarsh	PROPN
ejpam-3328	779	7	(	(	PUNCT
ejpam-3328	779	8	1986	1986	NUM
ejpam-3328	779	9	)	)	PUNCT
ejpam-3328	779	10	.	.	PUNCT
ejpam-3328	780	1	the	the	DET
ejpam-3328	780	2	theory	theory	NOUN
ejpam-3328	780	3	of	of	ADP
ejpam-3328	780	4	the	the	DET
ejpam-3328	780	5	riemann	riemann	PROPN
ejpam-3328	780	6	zeta	zeta	PROPN
ejpam-3328	780	7	function	function	PROPN
ejpam-3328	780	8	,	,	PUNCT
ejpam-3328	780	9	second	second	ADV
ejpam-3328	780	10	revised	revise	VERB
ejpam-3328	780	11	(	(	PUNCT
ejpam-3328	780	12	heath	heath	NOUN
ejpam-3328	780	13	-	-	PUNCT
ejpam-3328	780	14	brown	brown	ADJ
ejpam-3328	780	15	)	)	PUNCT
ejpam-3328	780	16	edition	edition	NOUN
ejpam-3328	780	17	.	.	PUNCT
ejpam-3328	781	1	oxford	oxford	PROPN
ejpam-3328	781	2	university	university	PROPN
ejpam-3328	781	3	press	press	NOUN
ejpam-3328	781	4	.	.	PUNCT
ejpam-3328	782	1	[	[	X
ejpam-3328	782	2	25	25	NUM
ejpam-3328	782	3	]	]	PUNCT
ejpam-3328	782	4	ray	ray	PROPN
ejpam-3328	782	5	d.	d.	PROPN
ejpam-3328	782	6	,	,	PUNCT
ejpam-3328	782	7	singer	singer	NOUN
ejpam-3328	782	8	i.	i.	PROPN
ejpam-3328	782	9	m.	m.	PROPN
ejpam-3328	782	10	r	r	NOUN
ejpam-3328	782	11	-	-	PUNCT
ejpam-3328	782	12	torsion	torsion	NOUN
ejpam-3328	782	13	and	and	CCONJ
ejpam-3328	782	14	the	the	DET
ejpam-3328	782	15	laplacian	laplacian	NOUN
ejpam-3328	782	16	on	on	ADP
ejpam-3328	782	17	riemannian	riemannian	ADJ
ejpam-3328	782	18	manifolds	manifold	NOUN
ejpam-3328	782	19	.	.	PUNCT
ejpam-3328	783	1	adv	adv	PROPN
ejpam-3328	783	2	.	.	PUNCT
ejpam-3328	784	1	in	in	ADP
ejpam-3328	784	2	math	math	NOUN
ejpam-3328	784	3	.	.	PUNCT
ejpam-3328	784	4	,	,	PUNCT
ejpam-3328	784	5	1971	1971	NUM
ejpam-3328	784	6	,	,	PUNCT
ejpam-3328	784	7	vol	vol	NOUN
ejpam-3328	784	8	.	.	PROPN
ejpam-3328	784	9	7	7	NUM
ejpam-3328	784	10	,	,	PUNCT
ejpam-3328	784	11	p.	p.	NOUN
ejpam-3328	784	12	145210	145210	NUM
ejpam-3328	784	13	.	.	PUNCT
ejpam-3328	785	1	[	[	X
ejpam-3328	785	2	26	26	NUM
ejpam-3328	785	3	]	]	PUNCT
ejpam-3328	785	4	bost	bost	PROPN
ejpam-3328	785	5	j.-b	j.-b	PROPN
ejpam-3328	785	6	.	.	PUNCT
ejpam-3328	786	1	fibres	fibre	NOUN
ejpam-3328	786	2	determinants	determinant	NOUN
ejpam-3328	786	3	,	,	PUNCT
ejpam-3328	786	4	determinants	determinant	NOUN
ejpam-3328	786	5	regularises	regularise	NOUN
ejpam-3328	786	6	et	et	NOUN
ejpam-3328	786	7	measures	measure	NOUN
ejpam-3328	786	8	sur	sur	PROPN
ejpam-3328	786	9	les	les	X
ejpam-3328	786	10	espaces	espaces	X
ejpam-3328	786	11	de	de	X
ejpam-3328	786	12	modules	module	NOUN
ejpam-3328	786	13	des	des	NOUN
ejpam-3328	786	14	courbes	courbe	NOUN
ejpam-3328	786	15	complexes	complex	NOUN
ejpam-3328	786	16	,	,	PUNCT
ejpam-3328	786	17	sem	sem	PROPN
ejpam-3328	786	18	.	.	PROPN
ejpam-3328	786	19	bourbaki	bourbaki	PROPN
ejpam-3328	786	20	,	,	PUNCT
ejpam-3328	786	21	39	39	NUM
ejpam-3328	786	22	eme	eme	NOUN
ejpam-3328	786	23	annee1986	annee1986	PROPN
ejpam-3328	786	24	-	-	PUNCT
ejpam-3328	786	25	1987	1987	NUM
ejpam-3328	786	26	,	,	PUNCT
ejpam-3328	787	1	[	[	X
ejpam-3328	787	2	27	27	NUM
ejpam-3328	787	3	]	]	PUNCT
ejpam-3328	787	4	kawagoe	kawagoe	PROPN
ejpam-3328	787	5	k.	k.	PROPN
ejpam-3328	787	6	,	,	PUNCT
ejpam-3328	787	7	wakayama	wakayama	NOUN
ejpam-3328	787	8	m.	m.	NOUN
ejpam-3328	787	9	,yamasaki	,yamasaki	PUNCT
ejpam-3328	787	10	y.	y.	PROPN
ejpam-3328	787	11	the	the	DET
ejpam-3328	787	12	q	q	NOUN
ejpam-3328	787	13	-	-	PUNCT
ejpam-3328	787	14	analogues	analogue	NOUN
ejpam-3328	787	15	of	of	ADP
ejpam-3328	787	16	the	the	DET
ejpam-3328	787	17	riemann	riemann	PROPN
ejpam-3328	787	18	zeta	zeta	PROPN
ejpam-3328	787	19	,	,	PUNCT
ejpam-3328	787	20	dirichlet	dirichlet	PROPN
ejpam-3328	787	21	l	l	PROPN
ejpam-3328	787	22	-	-	NOUN
ejpam-3328	787	23	functions	function	NOUN
ejpam-3328	787	24	,	,	PUNCT
ejpam-3328	787	25	and	and	CCONJ
ejpam-3328	787	26	a	a	DET
ejpam-3328	787	27	crystal	crystal	NOUN
ejpam-3328	787	28	zeta	zeta	NOUN
ejpam-3328	787	29	-	-	PUNCT
ejpam-3328	787	30	function	function	NOUN
ejpam-3328	787	31	.	.	PUNCT
ejpam-3328	788	1	forum	forum	PROPN
ejpam-3328	788	2	math	math	PROPN
ejpam-3328	788	3	,	,	PUNCT
ejpam-3328	788	4	2008	2008	NUM
ejpam-3328	788	5	,	,	PUNCT
ejpam-3328	788	6	vol	vol	NOUN
ejpam-3328	788	7	.	.	PROPN
ejpam-3328	788	8	1	1	NUM
ejpam-3328	788	9	,	,	PUNCT
ejpam-3328	788	10	p.	p.	NOUN
ejpam-3328	788	11	126	126	NUM
ejpam-3328	788	12	.	.	PUNCT
ejpam-3328	789	1	references	reference	NOUN
ejpam-3328	789	2	1176	1176	NUM
ejpam-3328	789	3	[	[	X
ejpam-3328	789	4	28	28	NUM
ejpam-3328	789	5	]	]	X
ejpam-3328	789	6	hadamard	hadamard	PROPN
ejpam-3328	789	7	j.	j.	PROPN
ejpam-3328	789	8	une	une	PROPN
ejpam-3328	789	9	application	application	PROPN
ejpam-3328	789	10	d’une	d’une	NOUN
ejpam-3328	789	11	formule	formule	NOUN
ejpam-3328	789	12	inteorale	inteorale	NOUN
ejpam-3328	789	13	relative	relative	PROPN
ejpam-3328	789	14	aux	aux	PROPN
ejpam-3328	789	15	series	series	PROPN
ejpam-3328	789	16	de	de	PROPN
ejpam-3328	789	17	dirichlet	dirichlet	PROPN
ejpam-3328	789	18	,	,	PUNCT
ejpam-3328	789	19	bull	bull	NOUN
ejpam-3328	789	20	.	.	PUNCT
ejpam-3328	790	1	soc	soc	PROPN
ejpam-3328	790	2	.	.	PUNCT
ejpam-3328	791	1	math	math	PROPN
ejpam-3328	791	2	,	,	PUNCT
ejpam-3328	791	3	de	de	PROPN
ejpam-3328	791	4	france	france	PROPN
ejpam-3328	791	5	,	,	PUNCT
ejpam-3328	791	6	56	56	NUM
ejpam-3328	791	7	a927	a927	NUM
ejpam-3328	791	8	)	)	PUNCT
ejpam-3328	791	9	,	,	PUNCT
ejpam-3328	791	10	4344	4344	NUM
ejpam-3328	791	11	.	.	PUNCT
ejpam-3328	792	1	[	[	X
ejpam-3328	792	2	29	29	NUM
ejpam-3328	792	3	]	]	X
ejpam-3328	792	4	paul	paul	PROPN
ejpam-3328	792	5	r.	r.	PROPN
ejpam-3328	792	6	chernoff	chernoff	PROPN
ejpam-3328	792	7	a	a	DET
ejpam-3328	792	8	pseudo	pseudo	NOUN
ejpam-3328	792	9	zeta	zeta	NOUN
ejpam-3328	792	10	function	function	NOUN
ejpam-3328	792	11	and	and	CCONJ
ejpam-3328	792	12	the	the	DET
ejpam-3328	792	13	distribution	distribution	NOUN
ejpam-3328	792	14	of	of	ADP
ejpam-3328	792	15	primes	prime	NOUN
ejpam-3328	792	16	pnas	pnas	PROPN
ejpam-3328	792	17	2000	2000	NUM
ejpam-3328	792	18	97	97	NUM
ejpam-3328	792	19	(	(	PUNCT
ejpam-3328	792	20	14	14	NUM
ejpam-3328	792	21	)	)	PUNCT
ejpam-3328	792	22	7697	7697	NUM
ejpam-3328	792	23	-	-	SYM
ejpam-3328	792	24	7699	7699	NUM
ejpam-3328	792	25	;	;	PUNCT
ejpam-3328	792	26	doi:10.1073	doi:10.1073	NOUN
ejpam-3328	792	27	/	/	SYM
ejpam-3328	792	28	pnas.97.14.7697	pnas.97.14.7697	NOUN
ejpam-3328	792	29	a933	a933	PROPN
ejpam-3328	792	30	)	)	PUNCT
ejpam-3328	792	31	,	,	PUNCT
ejpam-3328	793	1	[	[	X
ejpam-3328	793	2	30	30	NUM
ejpam-3328	793	3	]	]	PUNCT
ejpam-3328	793	4	landau	landau	PROPN
ejpam-3328	793	5	e.	e.	PROPN
ejpam-3328	793	6	,	,	PUNCT
ejpam-3328	793	7	walfisz	walfisz	PROPN
ejpam-3328	793	8	a.	a.	NOUN
ejpam-3328	793	9	ober	ober	PROPN
ejpam-3328	793	10	die	die	VERB
ejpam-3328	793	11	nichtfortsetzbarkeit	nichtfortsetzbarkeit	PROPN
ejpam-3328	793	12	einiger	einiger	PROPN
ejpam-3328	793	13	durch	durch	PROPN
ejpam-3328	793	14	dirichletsrhe	dirichletsrhe	PROPN
ejpam-3328	793	15	reihen	reihen	PROPN
ejpam-3328	793	16	definierter	definierter	PROPN
ejpam-3328	793	17	funktionen	funktionen	PROPN
ejpam-3328	793	18	,	,	PUNCT
ejpam-3328	793	19	rend	rend	VERB
ejpam-3328	793	20	,	,	PUNCT
ejpam-3328	793	21	di	di	NOUN
ejpam-3328	793	22	palermo	palermo	NOUN
ejpam-3328	793	23	,	,	PUNCT
ejpam-3328	793	24	44	44	NUM
ejpam-3328	793	25	a919	a919	NUM
ejpam-3328	793	26	)	)	PUNCT
ejpam-3328	793	27	,	,	PUNCT
ejpam-3328	793	28	8286	8286	NUM
ejpam-3328	793	29	.	.	PUNCT
ejpam-3328	794	1	congress	congress	PROPN
ejpam-3328	794	2	cambridge	cambridge	PROPN
ejpam-3328	794	3	1912	1912	NUM
ejpam-3328	794	4	,	,	PUNCT
ejpam-3328	794	5	1	1	NUM
ejpam-3328	794	6	,	,	PUNCT
ejpam-3328	794	7	[	[	X
ejpam-3328	794	8	31	31	NUM
ejpam-3328	794	9	]	]	PUNCT
ejpam-3328	794	10	estarmann	estarmann	PROPN
ejpam-3328	795	1	t.	t.	PROPN
ejpam-3328	795	2	on	on	ADP
ejpam-3328	795	3	certain	certain	ADJ
ejpam-3328	795	4	functions	function	NOUN
ejpam-3328	795	5	represented	represent	VERB
ejpam-3328	795	6	by	by	ADP
ejpam-3328	795	7	dirichlet	dirichlet	PROPN
ejpam-3328	795	8	series	series	PROPN
ejpam-3328	795	9	,	,	PUNCT
ejpam-3328	795	10	proc	proc	PROPN
ejpam-3328	795	11	.	.	PUNCT
ejpam-3328	796	1	lond	lond	PROPN
ejpam-3328	796	2	.	.	PUNCT
ejpam-3328	797	1	math	math	NOUN
ejpam-3328	797	2	.	.	PUNCT
ejpam-3328	798	1	soc	soc	PROPN
ejpam-3328	798	2	.	.	PUNCT
ejpam-3328	799	1	(	(	PUNCT
ejpam-3328	799	2	2	2	NUM
ejpam-3328	799	3	)	)	PUNCT
ejpam-3328	799	4	,	,	PUNCT
ejpam-3328	799	5	27	27	NUM
ejpam-3328	799	6	1928	1928	NUM
ejpam-3328	799	7	,	,	PUNCT
ejpam-3328	799	8	435448	435448	NUM
ejpam-3328	799	9	.	.	PUNCT
ejpam-3328	800	1	[	[	X
ejpam-3328	800	2	32	32	NUM
ejpam-3328	800	3	]	]	PUNCT
ejpam-3328	800	4	estarmann	estarmann	NOUN
ejpam-3328	800	5	t.	t.	PROPN
ejpam-3328	800	6	on	on	ADP
ejpam-3328	800	7	a	a	DET
ejpam-3328	800	8	problem	problem	NOUN
ejpam-3328	800	9	of	of	ADP
ejpam-3328	800	10	analytic	analytic	ADJ
ejpam-3328	800	11	continuation	continuation	NOUN
ejpam-3328	800	12	,	,	PUNCT
ejpam-3328	800	13	proc	proc	NOUN
ejpam-3328	800	14	.	.	PUNCT
ejpam-3328	801	1	lond	lond	PROPN
ejpam-3328	801	2	.	.	PUNCT
ejpam-3328	802	1	math	math	NOUN
ejpam-3328	802	2	.	.	PUNCT
ejpam-3328	803	1	soc	soc	PROPN
ejpam-3328	803	2	,	,	PUNCT
ejpam-3328	803	3	27	27	NUM
ejpam-3328	803	4	1928	1928	NUM
ejpam-3328	803	5	,	,	PUNCT
ejpam-3328	803	6	471482	471482	NUM
ejpam-3328	803	7	.	.	PUNCT
ejpam-3328	804	1	[	[	X
ejpam-3328	804	2	33	33	NUM
ejpam-3328	804	3	]	]	PUNCT
ejpam-3328	804	4	poincaré	poincaré	ADJ
ejpam-3328	804	5	h.	h.	PROPN
ejpam-3328	804	6	,	,	PUNCT
ejpam-3328	804	7	lecons	lecon	NOUN
ejpam-3328	804	8	de	de	PROPN
ejpam-3328	804	9	mecanique	mecanique	PROPN
ejpam-3328	804	10	celeste	celeste	PROPN
ejpam-3328	804	11	,	,	PUNCT
ejpam-3328	804	12	t.	t.	NOUN
ejpam-3328	804	13	3	3	NUM
ejpam-3328	804	14	,	,	PUNCT
ejpam-3328	804	15	p.	p.	NOUN
ejpam-3328	804	16	,	,	PUNCT
ejpam-3328	804	17	1910	1910	NUM
ejpam-3328	804	18	.	.	PUNCT
ejpam-3328	805	1	[	[	X
ejpam-3328	805	2	34	34	NUM
ejpam-3328	805	3	]	]	X
ejpam-3328	805	4	backlund	backlund	PROPN
ejpam-3328	805	5	r.	r.	PROPN
ejpam-3328	805	6	,	,	PUNCT
ejpam-3328	805	7	sur	sur	PROPN
ejpam-3328	805	8	les	les	X
ejpam-3328	805	9	zeros	zeros	X
ejpam-3328	805	10	de	de	X
ejpam-3328	805	11	la	la	X
ejpam-3328	805	12	function	function	PROPN
ejpam-3328	805	13	ζ(s	ζ(s	PROPN
ejpam-3328	805	14	)	)	PUNCT
ejpam-3328	805	15	de	de	X
ejpam-3328	805	16	riemann	riemann	PROPN
ejpam-3328	805	17	,	,	PUNCT
ejpam-3328	805	18	c.r	c.r	PROPN
ejpam-3328	805	19	.	.	PROPN
ejpam-3328	805	20	acad.sci	acad.sci	NOUN
ejpam-3328	805	21	.	.	PUNCT
ejpam-3328	805	22	,(1914	,(1914	PUNCT
ejpam-3328	805	23	)	)	PUNCT
ejpam-3328	805	24	1979	1979	NUM
ejpam-3328	805	25	-	-	SYM
ejpam-3328	805	26	1981	1981	NUM
ejpam-3328	805	27	n3	n3	NOUN