id	sid	tid	token	lemma	pos
ejpam-3007	1	1	european	european	PROPN
ejpam-3007	1	2	journal	journal	PROPN
ejpam-3007	1	3	of	of	ADP
ejpam-3007	1	4	pure	pure	ADJ
ejpam-3007	1	5	and	and	CCONJ
ejpam-3007	1	6	applied	apply	VERB
ejpam-3007	1	7	mathematics	mathematic	NOUN
ejpam-3007	1	8	vol	vol	NOUN
ejpam-3007	1	9	.	.	PROPN
ejpam-3007	2	1	10	10	NUM
ejpam-3007	2	2	,	,	PUNCT
ejpam-3007	2	3	no	no	INTJ
ejpam-3007	2	4	.	.	NOUN
ejpam-3007	2	5	4	4	NUM
ejpam-3007	2	6	,	,	PUNCT
ejpam-3007	2	7	2017	2017	NUM
ejpam-3007	2	8	,	,	PUNCT
ejpam-3007	2	9	763	763	NUM
ejpam-3007	2	10	-	-	SYM
ejpam-3007	2	11	785	785	NUM
ejpam-3007	2	12	issn	issn	PROPN
ejpam-3007	2	13	1307	1307	NUM
ejpam-3007	2	14	-	-	SYM
ejpam-3007	2	15	5543	5543	NUM
ejpam-3007	2	16	–	–	PUNCT
ejpam-3007	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3007	2	18	published	publish	VERB
ejpam-3007	2	19	by	by	ADP
ejpam-3007	2	20	new	new	PROPN
ejpam-3007	2	21	york	york	PROPN
ejpam-3007	2	22	business	business	PROPN
ejpam-3007	2	23	global	global	PROPN
ejpam-3007	2	24	global	global	ADJ
ejpam-3007	2	25	estimation	estimation	NOUN
ejpam-3007	2	26	of	of	ADP
ejpam-3007	2	27	the	the	DET
ejpam-3007	2	28	cauchy	cauchy	PROPN
ejpam-3007	2	29	problem	problem	NOUN
ejpam-3007	2	30	solution	solution	NOUN
ejpam-3007	2	31	’	'	PUNCT
ejpam-3007	2	32	and	and	CCONJ
ejpam-3007	2	33	blow	blow	VERB
ejpam-3007	2	34	up	up	ADP
ejpam-3007	2	35	the	the	DET
ejpam-3007	2	36	navier	navier	NOUN
ejpam-3007	2	37	-	-	PUNCT
ejpam-3007	2	38	stokes	stokes	PROPN
ejpam-3007	2	39	equation	equation	NOUN
ejpam-3007	2	40	asset	asset	NOUN
ejpam-3007	2	41	durmagambetov1	durmagambetov1	NOUN
ejpam-3007	2	42	1	1	NUM
ejpam-3007	2	43	faculty	faculty	NOUN
ejpam-3007	2	44	of	of	ADP
ejpam-3007	2	45	mathematiks	mathematiks	PROPN
ejpam-3007	2	46	,	,	PUNCT
ejpam-3007	2	47	l.n.gumilyov	l.n.gumilyov	PROPN
ejpam-3007	2	48	eurasian	eurasian	PROPN
ejpam-3007	2	49	national	national	PROPN
ejpam-3007	2	50	university	university	PROPN
ejpam-3007	2	51	,	,	PUNCT
ejpam-3007	2	52	kazakhstan	kazakhstan	PROPN
ejpam-3007	2	53	abstract	abstract	NOUN
ejpam-3007	2	54	.	.	PUNCT
ejpam-3007	3	1	the	the	DET
ejpam-3007	3	2	paper	paper	NOUN
ejpam-3007	3	3	presents	present	VERB
ejpam-3007	3	4	results	result	NOUN
ejpam-3007	3	5	of	of	ADP
ejpam-3007	3	6	the	the	DET
ejpam-3007	3	7	research	research	NOUN
ejpam-3007	3	8	of	of	ADP
ejpam-3007	3	9	gradient	gradient	ADJ
ejpam-3007	3	10	catastrophe	catastrophe	NOUN
ejpam-3007	3	11	development	development	NOUN
ejpam-3007	3	12	during	during	ADP
ejpam-3007	3	13	phase	phase	NOUN
ejpam-3007	3	14	change	change	NOUN
ejpam-3007	3	15	.	.	PUNCT
ejpam-3007	4	1	it	it	PRON
ejpam-3007	4	2	shows	show	VERB
ejpam-3007	4	3	that	that	SCONJ
ejpam-3007	4	4	classical	classical	ADJ
ejpam-3007	4	5	methods	method	NOUN
ejpam-3007	4	6	of	of	ADP
ejpam-3007	4	7	the	the	DET
ejpam-3007	4	8	function	function	NOUN
ejpam-3007	4	9	estimation	estimation	NOUN
ejpam-3007	4	10	theory	theory	NOUN
ejpam-3007	4	11	do	do	AUX
ejpam-3007	4	12	not	not	PART
ejpam-3007	4	13	fit	fit	VERB
ejpam-3007	4	14	well	well	ADV
ejpam-3007	4	15	to	to	PART
ejpam-3007	4	16	study	study	VERB
ejpam-3007	4	17	gradient	gradient	NOUN
ejpam-3007	4	18	catastrophe	catastrophe	NOUN
ejpam-3007	4	19	problem	problem	NOUN
ejpam-3007	4	20	.	.	PUNCT
ejpam-3007	5	1	the	the	DET
ejpam-3007	5	2	paper	paper	NOUN
ejpam-3007	5	3	presents	present	VERB
ejpam-3007	5	4	results	result	NOUN
ejpam-3007	5	5	,	,	PUNCT
ejpam-3007	5	6	indicating	indicate	VERB
ejpam-3007	5	7	that	that	SCONJ
ejpam-3007	5	8	embedding	embed	VERB
ejpam-3007	5	9	theorems	theorem	NOUN
ejpam-3007	5	10	do	do	AUX
ejpam-3007	5	11	not	not	PART
ejpam-3007	5	12	allow	allow	VERB
ejpam-3007	5	13	to	to	PART
ejpam-3007	5	14	study	study	VERB
ejpam-3007	5	15	a	a	DET
ejpam-3007	5	16	process	process	NOUN
ejpam-3007	5	17	of	of	ADP
ejpam-3007	5	18	a	a	DET
ejpam-3007	5	19	catastrophe	catastrophe	NOUN
ejpam-3007	5	20	formation	formation	NOUN
ejpam-3007	5	21	.	.	PUNCT
ejpam-3007	6	1	in	in	ADP
ejpam-3007	6	2	fact	fact	NOUN
ejpam-3007	6	3	,	,	PUNCT
ejpam-3007	6	4	the	the	DET
ejpam-3007	6	5	paper	paper	NOUN
ejpam-3007	6	6	justifies	justify	VERB
ejpam-3007	6	7	terence	terence	PROPN
ejpam-3007	6	8	tao	tao	PROPN
ejpam-3007	6	9	’s	’s	PART
ejpam-3007	6	10	pessimism	pessimism	NOUN
ejpam-3007	6	11	about	about	ADP
ejpam-3007	6	12	a	a	DET
ejpam-3007	6	13	failure	failure	NOUN
ejpam-3007	6	14	of	of	ADP
ejpam-3007	6	15	modern	modern	ADJ
ejpam-3007	6	16	mathematics	mathematic	NOUN
ejpam-3007	6	17	to	to	PART
ejpam-3007	6	18	solve	solve	VERB
ejpam-3007	6	19	the	the	DET
ejpam-3007	6	20	navier	navier	NOUN
ejpam-3007	6	21	-	-	PUNCT
ejpam-3007	6	22	stokes	stoke	NOUN
ejpam-3007	6	23	problem	problem	NOUN
ejpam-3007	6	24	.	.	PUNCT
ejpam-3007	7	1	an	an	DET
ejpam-3007	7	2	alternative	alternative	ADJ
ejpam-3007	7	3	method	method	NOUN
ejpam-3007	7	4	is	be	AUX
ejpam-3007	7	5	proposed	propose	VERB
ejpam-3007	7	6	for	for	ADP
ejpam-3007	7	7	dealing	deal	VERB
ejpam-3007	7	8	with	with	ADP
ejpam-3007	7	9	the	the	DET
ejpam-3007	7	10	gradient	gradient	NOUN
ejpam-3007	7	11	catastrophe	catastrophe	NOUN
ejpam-3007	7	12	by	by	ADP
ejpam-3007	7	13	studying	study	VERB
ejpam-3007	7	14	fourier	fourier	ADJ
ejpam-3007	7	15	transformation	transformation	NOUN
ejpam-3007	7	16	for	for	ADP
ejpam-3007	7	17	a	a	DET
ejpam-3007	7	18	function	function	NOUN
ejpam-3007	7	19	and	and	CCONJ
ejpam-3007	7	20	selecting	select	VERB
ejpam-3007	7	21	a	a	DET
ejpam-3007	7	22	function	function	NOUN
ejpam-3007	7	23	singularity	singularity	NOUN
ejpam-3007	7	24	through	through	ADP
ejpam-3007	7	25	phase	phase	NOUN
ejpam-3007	7	26	singularities	singularity	NOUN
ejpam-3007	7	27	of	of	ADP
ejpam-3007	7	28	fourier	fouri	ADJ
ejpam-3007	7	29	transformation	transformation	NOUN
ejpam-3007	7	30	for	for	ADP
ejpam-3007	7	31	a	a	DET
ejpam-3007	7	32	given	give	VERB
ejpam-3007	7	33	function	function	NOUN
ejpam-3007	7	34	.	.	PUNCT
ejpam-3007	8	1	the	the	DET
ejpam-3007	8	2	analytic	analytic	ADJ
ejpam-3007	8	3	properties	property	NOUN
ejpam-3007	8	4	of	of	ADP
ejpam-3007	8	5	the	the	DET
ejpam-3007	8	6	scattering	scatter	VERB
ejpam-3007	8	7	amplitude	amplitude	NOUN
ejpam-3007	8	8	are	be	AUX
ejpam-3007	8	9	discussed	discuss	VERB
ejpam-3007	8	10	in	in	ADP
ejpam-3007	8	11	r3	r3	PROPN
ejpam-3007	8	12	,	,	PUNCT
ejpam-3007	8	13	and	and	CCONJ
ejpam-3007	8	14	a	a	DET
ejpam-3007	8	15	representation	representation	NOUN
ejpam-3007	8	16	of	of	ADP
ejpam-3007	8	17	the	the	DET
ejpam-3007	8	18	potential	potential	NOUN
ejpam-3007	8	19	is	be	AUX
ejpam-3007	8	20	obtained	obtain	VERB
ejpam-3007	8	21	using	use	VERB
ejpam-3007	8	22	the	the	DET
ejpam-3007	8	23	scattering	scatter	VERB
ejpam-3007	8	24	amplitude	amplitude	NOUN
ejpam-3007	8	25	.	.	PUNCT
ejpam-3007	9	1	a	a	DET
ejpam-3007	9	2	uniform	uniform	ADJ
ejpam-3007	9	3	time	time	NOUN
ejpam-3007	9	4	estimation	estimation	NOUN
ejpam-3007	9	5	of	of	ADP
ejpam-3007	9	6	the	the	DET
ejpam-3007	9	7	cauchy	cauchy	PROPN
ejpam-3007	9	8	problem	problem	NOUN
ejpam-3007	9	9	solution	solution	NOUN
ejpam-3007	9	10	for	for	ADP
ejpam-3007	9	11	the	the	DET
ejpam-3007	9	12	navier	navier	NOUN
ejpam-3007	9	13	-	-	PUNCT
ejpam-3007	9	14	stokes	stoke	NOUN
ejpam-3007	9	15	equations	equation	NOUN
ejpam-3007	9	16	is	be	AUX
ejpam-3007	9	17	provided.describes	provided.describes	PROPN
ejpam-3007	9	18	the	the	DET
ejpam-3007	9	19	loss	loss	NOUN
ejpam-3007	9	20	of	of	ADP
ejpam-3007	9	21	smoothness	smoothness	NOUN
ejpam-3007	9	22	of	of	ADP
ejpam-3007	9	23	classical	classical	ADJ
ejpam-3007	9	24	solutions	solution	NOUN
ejpam-3007	9	25	for	for	ADP
ejpam-3007	9	26	the	the	DET
ejpam-3007	9	27	navier	navier	NOUN
ejpam-3007	9	28	-	-	PUNCT
ejpam-3007	9	29	stokes	stokes	PROPN
ejpam-3007	9	30	equations	equations	PROPN
ejpam-3007	9	31	-millennium	-millennium	PROPN
ejpam-3007	9	32	prize	prize	NOUN
ejpam-3007	9	33	problems	problem	NOUN
ejpam-3007	9	34	.	.	PUNCT
ejpam-3007	10	1	key	key	ADJ
ejpam-3007	10	2	words	word	NOUN
ejpam-3007	10	3	and	and	CCONJ
ejpam-3007	10	4	phrases	phrase	NOUN
ejpam-3007	10	5	:	:	PUNCT
ejpam-3007	10	6	schrödinger	schrödinger	NOUN
ejpam-3007	10	7	’s	’s	PART
ejpam-3007	10	8	equation	equation	NOUN
ejpam-3007	10	9	;	;	PUNCT
ejpam-3007	10	10	potential	potential	ADJ
ejpam-3007	10	11	,	,	PUNCT
ejpam-3007	10	12	scattering	scatter	VERB
ejpam-3007	10	13	amplitude	amplitude	NOUN
ejpam-3007	10	14	,	,	PUNCT
ejpam-3007	10	15	cauchy	cauchy	NOUN
ejpam-3007	10	16	problem	problem	NOUN
ejpam-3007	10	17	,	,	PUNCT
ejpam-3007	10	18	navier	navier	NOUN
ejpam-3007	10	19	–	–	PUNCT
ejpam-3007	10	20	stokes	stoke	NOUN
ejpam-3007	10	21	equations	equation	NOUN
ejpam-3007	10	22	,	,	PUNCT
ejpam-3007	10	23	fourier	fourier	NOUN
ejpam-3007	10	24	transform	transform	NOUN
ejpam-3007	10	25	,	,	PUNCT
ejpam-3007	10	26	the	the	DET
ejpam-3007	10	27	global	global	ADJ
ejpam-3007	10	28	solvability	solvability	NOUN
ejpam-3007	10	29	and	and	CCONJ
ejpam-3007	10	30	uniqueness	uniqueness	NOUN
ejpam-3007	10	31	of	of	ADP
ejpam-3007	10	32	the	the	DET
ejpam-3007	10	33	cauchy	cauchy	PROPN
ejpam-3007	10	34	problem	problem	NOUN
ejpam-3007	10	35	,	,	PUNCT
ejpam-3007	10	36	the	the	DET
ejpam-3007	10	37	loss	loss	NOUN
ejpam-3007	10	38	of	of	ADP
ejpam-3007	10	39	smoothness	smoothness	NOUN
ejpam-3007	10	40	,	,	PUNCT
ejpam-3007	10	41	the	the	DET
ejpam-3007	10	42	millennium	millennium	NOUN
ejpam-3007	10	43	prize	prize	PROPN
ejpam-3007	10	44	problems	problem	VERB
ejpam-3007	10	45	1	1	NUM
ejpam-3007	10	46	.	.	PUNCT
ejpam-3007	11	1	introduction	introduction	NOUN
ejpam-3007	11	2	the	the	DET
ejpam-3007	11	3	research	research	NOUN
ejpam-3007	11	4	presents	present	VERB
ejpam-3007	11	5	a	a	DET
ejpam-3007	11	6	process	process	NOUN
ejpam-3007	11	7	of	of	ADP
ejpam-3007	11	8	gradient	gradient	ADJ
ejpam-3007	11	9	catastrophe	catastrophe	NOUN
ejpam-3007	11	10	formation	formation	NOUN
ejpam-3007	11	11	under	under	ADP
ejpam-3007	11	12	conditions	condition	NOUN
ejpam-3007	11	13	of	of	ADP
ejpam-3007	11	14	phase	phase	NOUN
ejpam-3007	11	15	change	change	NOUN
ejpam-3007	11	16	.	.	PUNCT
ejpam-3007	12	1	the	the	DET
ejpam-3007	12	2	paper	paper	NOUN
ejpam-3007	12	3	shows	show	VERB
ejpam-3007	12	4	that	that	SCONJ
ejpam-3007	12	5	classical	classical	ADJ
ejpam-3007	12	6	methods	method	NOUN
ejpam-3007	12	7	of	of	ADP
ejpam-3007	12	8	the	the	DET
ejpam-3007	12	9	function	function	NOUN
ejpam-3007	12	10	estimation	estimation	NOUN
ejpam-3007	12	11	theory	theory	NOUN
ejpam-3007	12	12	in	in	ADP
ejpam-3007	12	13	context	context	NOUN
ejpam-3007	12	14	of	of	ADP
ejpam-3007	12	15	sobolevschwartz	sobolevschwartz	PROPN
ejpam-3007	12	16	space	space	NOUN
ejpam-3007	12	17	theory	theory	NOUN
ejpam-3007	12	18	are	be	AUX
ejpam-3007	12	19	not	not	PART
ejpam-3007	12	20	suitable	suitable	ADJ
ejpam-3007	12	21	for	for	ADP
ejpam-3007	12	22	studying	study	VERB
ejpam-3007	12	23	gradient	gradient	ADJ
ejpam-3007	12	24	catastrophe	catastrophe	NOUN
ejpam-3007	12	25	problem	problem	NOUN
ejpam-3007	12	26	.	.	PUNCT
ejpam-3007	13	1	results	result	NOUN
ejpam-3007	13	2	which	which	PRON
ejpam-3007	13	3	are	be	AUX
ejpam-3007	13	4	presented	present	VERB
ejpam-3007	13	5	here	here	ADV
ejpam-3007	13	6	show	show	VERB
ejpam-3007	13	7	that	that	SCONJ
ejpam-3007	13	8	the	the	DET
ejpam-3007	13	9	embedding	embed	VERB
ejpam-3007	13	10	theorems	theorem	NOUN
ejpam-3007	13	11	do	do	AUX
ejpam-3007	13	12	not	not	PART
ejpam-3007	13	13	allow	allow	VERB
ejpam-3007	13	14	to	to	PART
ejpam-3007	13	15	study	study	VERB
ejpam-3007	13	16	a	a	DET
ejpam-3007	13	17	process	process	NOUN
ejpam-3007	13	18	of	of	ADP
ejpam-3007	13	19	a	a	DET
ejpam-3007	13	20	catastrophe	catastrophe	NOUN
ejpam-3007	13	21	formation	formation	NOUN
ejpam-3007	13	22	.	.	PUNCT
ejpam-3007	14	1	actually	actually	ADV
ejpam-3007	14	2	,	,	PUNCT
ejpam-3007	14	3	the	the	DET
ejpam-3007	14	4	paper	paper	NOUN
ejpam-3007	14	5	justifies	justify	VERB
ejpam-3007	14	6	terence	terence	PROPN
ejpam-3007	14	7	taos	taos	PROPN
ejpam-3007	14	8	pessimism	pessimism	NOUN
ejpam-3007	14	9	about	about	ADP
ejpam-3007	14	10	a	a	DET
ejpam-3007	14	11	failure	failure	NOUN
ejpam-3007	14	12	of	of	ADP
ejpam-3007	14	13	using	use	VERB
ejpam-3007	14	14	present	present	ADJ
ejpam-3007	14	15	mathematical	mathematical	ADJ
ejpam-3007	14	16	methods	method	NOUN
ejpam-3007	14	17	for	for	ADP
ejpam-3007	14	18	solving	solve	VERB
ejpam-3007	14	19	the	the	DET
ejpam-3007	14	20	navier	navier	NOUN
ejpam-3007	14	21	-	-	PUNCT
ejpam-3007	14	22	stokes	stoke	NOUN
ejpam-3007	14	23	problem	problem	NOUN
ejpam-3007	14	24	.	.	PUNCT
ejpam-3007	15	1	an	an	DET
ejpam-3007	15	2	alternative	alternative	ADJ
ejpam-3007	15	3	method	method	NOUN
ejpam-3007	15	4	is	be	AUX
ejpam-3007	15	5	proposed	propose	VERB
ejpam-3007	15	6	for	for	ADP
ejpam-3007	15	7	studying	study	VERB
ejpam-3007	15	8	gradient	gradient	ADJ
ejpam-3007	15	9	catastrophe	catastrophe	NOUN
ejpam-3007	15	10	by	by	ADP
ejpam-3007	15	11	applying	apply	VERB
ejpam-3007	15	12	fourier	fourier	NOUN
ejpam-3007	15	13	transformation	transformation	NOUN
ejpam-3007	15	14	to	to	ADP
ejpam-3007	15	15	a	a	DET
ejpam-3007	15	16	function	function	NOUN
ejpam-3007	15	17	and	and	CCONJ
ejpam-3007	15	18	selecting	select	VERB
ejpam-3007	15	19	function	function	NOUN
ejpam-3007	15	20	singularity	singularity	NOUN
ejpam-3007	15	21	through	through	ADP
ejpam-3007	15	22	phase	phase	NOUN
ejpam-3007	15	23	singularities	singularity	NOUN
ejpam-3007	15	24	of	of	ADP
ejpam-3007	15	25	fourier	fouri	ADJ
ejpam-3007	15	26	transformation	transformation	NOUN
ejpam-3007	15	27	for	for	ADP
ejpam-3007	15	28	a	a	DET
ejpam-3007	15	29	given	give	VERB
ejpam-3007	15	30	function	function	NOUN
ejpam-3007	15	31	.	.	PUNCT
ejpam-3007	16	1	we	we	PRON
ejpam-3007	16	2	know	know	VERB
ejpam-3007	16	3	a	a	DET
ejpam-3007	16	4	general	general	ADJ
ejpam-3007	16	5	definition	definition	NOUN
ejpam-3007	16	6	of	of	ADP
ejpam-3007	16	7	a	a	DET
ejpam-3007	16	8	gradient	gradient	ADJ
ejpam-3007	16	9	catastrophe	catastrophe	NOUN
ejpam-3007	16	10	an	an	DET
ejpam-3007	16	11	unbounded	unbounded	ADJ
ejpam-3007	16	12	increase	increase	NOUN
ejpam-3007	16	13	of	of	ADP
ejpam-3007	16	14	a	a	DET
ejpam-3007	16	15	function	function	NOUN
ejpam-3007	16	16	derivative	derivative	NOUN
ejpam-3007	16	17	upon	upon	SCONJ
ejpam-3007	16	18	conditions	condition	NOUN
ejpam-3007	16	19	of	of	ADP
ejpam-3007	16	20	boundedness	boundedness	NOUN
ejpam-3007	16	21	of	of	ADP
ejpam-3007	16	22	the	the	DET
ejpam-3007	16	23	function	function	NOUN
ejpam-3007	16	24	itself	itself	PRON
ejpam-3007	16	25	.	.	PUNCT
ejpam-3007	17	1	this	this	DET
ejpam-3007	17	2	phenomenon	phenomenon	NOUN
ejpam-3007	17	3	occurs	occur	VERB
ejpam-3007	17	4	email	email	NOUN
ejpam-3007	17	5	address	address	NOUN
ejpam-3007	17	6	:	:	PUNCT
ejpam-3007	17	7	aset.durmagambet@gmail.com	aset.durmagambet@gmail.com	X
ejpam-3007	17	8	(	(	PUNCT
ejpam-3007	17	9	a.	a.	NOUN
ejpam-3007	17	10	durmagambetov	durmagambetov	PROPN
ejpam-3007	17	11	)	)	PUNCT
ejpam-3007	17	12	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3007	18	1	763	763	NUM
ejpam-3007	19	1	c	c	X
ejpam-3007	19	2	©	©	PROPN
ejpam-3007	19	3	2017	2017	NUM
ejpam-3007	19	4	ejpam	ejpam	VERB
ejpam-3007	19	5	all	all	DET
ejpam-3007	19	6	rights	right	NOUN
ejpam-3007	19	7	reserved	reserve	VERB
ejpam-3007	19	8	.	.	PUNCT
ejpam-3007	20	1	a.	a.	NOUN
ejpam-3007	20	2	durmagambetov	durmagambetov	PROPN
ejpam-3007	20	3	/	/	SYM
ejpam-3007	20	4	eur	eur	PROPN
ejpam-3007	20	5	.	.	PUNCT
ejpam-3007	21	1	j.	j.	PROPN
ejpam-3007	21	2	pure	pure	PROPN
ejpam-3007	21	3	appl	appl	PROPN
ejpam-3007	21	4	.	.	PROPN
ejpam-3007	21	5	math	math	PROPN
ejpam-3007	21	6	,	,	PUNCT
ejpam-3007	21	7	10	10	NUM
ejpam-3007	21	8	(	(	PUNCT
ejpam-3007	21	9	4	4	NUM
ejpam-3007	21	10	)	)	PUNCT
ejpam-3007	21	11	(	(	PUNCT
ejpam-3007	21	12	2017	2017	NUM
ejpam-3007	21	13	)	)	PUNCT
ejpam-3007	21	14	,	,	PUNCT
ejpam-3007	21	15	763	763	NUM
ejpam-3007	21	16	-	-	SYM
ejpam-3007	21	17	785	785	NUM
ejpam-3007	21	18	764	764	NUM
ejpam-3007	21	19	in	in	ADP
ejpam-3007	21	20	various	various	ADJ
ejpam-3007	21	21	problems	problem	NOUN
ejpam-3007	21	22	of	of	ADP
ejpam-3007	21	23	hydrodynamics	hydrodynamic	NOUN
ejpam-3007	21	24	,	,	PUNCT
ejpam-3007	21	25	such	such	ADJ
ejpam-3007	21	26	as	as	ADP
ejpam-3007	21	27	a	a	DET
ejpam-3007	21	28	formation	formation	NOUN
ejpam-3007	21	29	of	of	ADP
ejpam-3007	21	30	shock	shock	NOUN
ejpam-3007	21	31	waves	wave	NOUN
ejpam-3007	21	32	,	,	PUNCT
ejpam-3007	21	33	weather	weather	NOUN
ejpam-3007	21	34	fronts	front	NOUN
ejpam-3007	21	35	,	,	PUNCT
ejpam-3007	21	36	hydraulic	hydraulic	ADJ
ejpam-3007	21	37	and	and	CCONJ
ejpam-3007	21	38	seismic	seismic	ADJ
ejpam-3007	21	39	fracturing	fracturing	NOUN
ejpam-3007	21	40	,	,	PUNCT
ejpam-3007	21	41	and	and	CCONJ
ejpam-3007	21	42	others	other	NOUN
ejpam-3007	21	43	.	.	PUNCT
ejpam-3007	22	1	in	in	ADP
ejpam-3007	22	2	modern	modern	ADJ
ejpam-3007	22	3	physics	physic	NOUN
ejpam-3007	22	4	and	and	CCONJ
ejpam-3007	22	5	mathematics	mathematic	NOUN
ejpam-3007	22	6	,	,	PUNCT
ejpam-3007	22	7	as	as	ADV
ejpam-3007	22	8	well	well	ADV
ejpam-3007	22	9	as	as	ADP
ejpam-3007	22	10	in	in	ADP
ejpam-3007	22	11	many	many	ADJ
ejpam-3007	22	12	other	other	ADJ
ejpam-3007	22	13	areas	area	NOUN
ejpam-3007	22	14	of	of	ADP
ejpam-3007	22	15	science	science	NOUN
ejpam-3007	22	16	and	and	CCONJ
ejpam-3007	22	17	technology	technology	NOUN
ejpam-3007	22	18	,	,	PUNCT
ejpam-3007	22	19	this	this	DET
ejpam-3007	22	20	phenomenon	phenomenon	NOUN
ejpam-3007	22	21	is	be	AUX
ejpam-3007	22	22	considered	consider	VERB
ejpam-3007	22	23	as	as	ADP
ejpam-3007	22	24	a	a	DET
ejpam-3007	22	25	very	very	ADV
ejpam-3007	22	26	difficult	difficult	ADJ
ejpam-3007	22	27	problem	problem	NOUN
ejpam-3007	22	28	,	,	PUNCT
ejpam-3007	22	29	both	both	CCONJ
ejpam-3007	22	30	from	from	ADP
ejpam-3007	22	31	a	a	DET
ejpam-3007	22	32	theoretical	theoretical	ADJ
ejpam-3007	22	33	and	and	CCONJ
ejpam-3007	22	34	applied	apply	VERB
ejpam-3007	22	35	perspective	perspective	NOUN
ejpam-3007	22	36	.	.	PUNCT
ejpam-3007	23	1	from	from	ADP
ejpam-3007	23	2	a	a	DET
ejpam-3007	23	3	theoretical	theoretical	ADJ
ejpam-3007	23	4	point	point	NOUN
ejpam-3007	23	5	of	of	ADP
ejpam-3007	23	6	view	view	NOUN
ejpam-3007	23	7	this	this	PRON
ejpam-3007	23	8	is	be	AUX
ejpam-3007	23	9	important	important	ADJ
ejpam-3007	23	10	as	as	SCONJ
ejpam-3007	23	11	we	we	PRON
ejpam-3007	23	12	have	have	VERB
ejpam-3007	23	13	to	to	PART
ejpam-3007	23	14	know	know	VERB
ejpam-3007	23	15	how	how	SCONJ
ejpam-3007	23	16	to	to	PART
ejpam-3007	23	17	describe	describe	VERB
ejpam-3007	23	18	qualitative	qualitative	ADJ
ejpam-3007	23	19	changes	change	NOUN
ejpam-3007	23	20	in	in	ADP
ejpam-3007	23	21	processes	process	NOUN
ejpam-3007	23	22	,	,	PUNCT
ejpam-3007	23	23	which	which	PRON
ejpam-3007	23	24	are	be	AUX
ejpam-3007	23	25	manifested	manifest	VERB
ejpam-3007	23	26	in	in	ADP
ejpam-3007	23	27	appearance	appearance	NOUN
ejpam-3007	23	28	of	of	ADP
ejpam-3007	23	29	new	new	ADJ
ejpam-3007	23	30	quality	quality	NOUN
ejpam-3007	23	31	objects	object	NOUN
ejpam-3007	23	32	during	during	ADP
ejpam-3007	23	33	a	a	DET
ejpam-3007	23	34	process	process	NOUN
ejpam-3007	23	35	of	of	ADP
ejpam-3007	23	36	description	description	NOUN
ejpam-3007	23	37	model	model	NOUN
ejpam-3007	23	38	evolution	evolution	NOUN
ejpam-3007	23	39	,	,	PUNCT
ejpam-3007	23	40	and	and	CCONJ
ejpam-3007	23	41	in	in	ADP
ejpam-3007	23	42	the	the	DET
ejpam-3007	23	43	context	context	NOUN
ejpam-3007	23	44	of	of	ADP
ejpam-3007	23	45	applied	apply	VERB
ejpam-3007	23	46	research	research	NOUN
ejpam-3007	23	47	,	,	PUNCT
ejpam-3007	23	48	the	the	DET
ejpam-3007	23	49	problem	problem	NOUN
ejpam-3007	23	50	is	be	AUX
ejpam-3007	23	51	facing	face	VERB
ejpam-3007	23	52	numerical	numerical	ADJ
ejpam-3007	23	53	instability	instability	NOUN
ejpam-3007	23	54	in	in	ADP
ejpam-3007	23	55	the	the	DET
ejpam-3007	23	56	event	event	NOUN
ejpam-3007	23	57	of	of	ADP
ejpam-3007	23	58	a	a	DET
ejpam-3007	23	59	gradient	gradient	ADJ
ejpam-3007	23	60	catastrophe	catastrophe	NOUN
ejpam-3007	23	61	formation	formation	NOUN
ejpam-3007	23	62	.	.	PUNCT
ejpam-3007	24	1	thus	thus	ADV
ejpam-3007	24	2	,	,	PUNCT
ejpam-3007	24	3	we	we	PRON
ejpam-3007	24	4	approach	approach	VERB
ejpam-3007	24	5	an	an	DET
ejpam-3007	24	6	important	important	ADJ
ejpam-3007	24	7	obstacle	obstacle	NOUN
ejpam-3007	24	8	while	while	SCONJ
ejpam-3007	24	9	using	use	VERB
ejpam-3007	24	10	modeling	model	VERB
ejpam-3007	24	11	a	a	DET
ejpam-3007	24	12	barrier	barrier	NOUN
ejpam-3007	24	13	created	create	VERB
ejpam-3007	24	14	by	by	ADP
ejpam-3007	24	15	the	the	DET
ejpam-3007	24	16	gradient	gradient	NOUN
ejpam-3007	24	17	catastrophe	catastrophe	NOUN
ejpam-3007	24	18	.	.	PUNCT
ejpam-3007	25	1	since	since	SCONJ
ejpam-3007	25	2	,	,	PUNCT
ejpam-3007	25	3	on	on	ADP
ejpam-3007	25	4	the	the	DET
ejpam-3007	25	5	one	one	NUM
ejpam-3007	25	6	hand	hand	NOUN
ejpam-3007	25	7	,	,	PUNCT
ejpam-3007	25	8	the	the	DET
ejpam-3007	25	9	gradient	gradient	NOUN
ejpam-3007	25	10	catastrophe	catastrophe	NOUN
ejpam-3007	25	11	is	be	AUX
ejpam-3007	25	12	still	still	ADV
ejpam-3007	25	13	unknown	unknown	ADJ
ejpam-3007	25	14	phenomenon	phenomenon	NOUN
ejpam-3007	25	15	,	,	PUNCT
ejpam-3007	25	16	it	it	PRON
ejpam-3007	25	17	is	be	AUX
ejpam-3007	25	18	very	very	ADV
ejpam-3007	25	19	important	important	ADJ
ejpam-3007	25	20	from	from	ADP
ejpam-3007	25	21	a	a	DET
ejpam-3007	25	22	practical	practical	ADJ
ejpam-3007	25	23	point	point	NOUN
ejpam-3007	25	24	of	of	ADP
ejpam-3007	25	25	view	view	NOUN
ejpam-3007	25	26	,	,	PUNCT
ejpam-3007	25	27	because	because	SCONJ
ejpam-3007	25	28	the	the	DET
ejpam-3007	25	29	phenomenon	phenomenon	NOUN
ejpam-3007	25	30	is	be	AUX
ejpam-3007	25	31	connected	connect	VERB
ejpam-3007	25	32	with	with	ADP
ejpam-3007	25	33	the	the	DET
ejpam-3007	25	34	most	most	ADV
ejpam-3007	25	35	interesting	interesting	ADJ
ejpam-3007	25	36	and	and	CCONJ
ejpam-3007	25	37	important	important	ADJ
ejpam-3007	25	38	aspects	aspect	NOUN
ejpam-3007	25	39	of	of	ADP
ejpam-3007	25	40	reality	reality	NOUN
ejpam-3007	25	41	.	.	PUNCT
ejpam-3007	26	1	terence	terence	PROPN
ejpam-3007	26	2	tao	tao	PROPN
ejpam-3007	26	3	formulated	formulate	VERB
ejpam-3007	26	4	and	and	CCONJ
ejpam-3007	26	5	illustrated	illustrate	VERB
ejpam-3007	26	6	this	this	PRON
ejpam-3007	26	7	in	in	ADP
ejpam-3007	26	8	[	[	X
ejpam-3007	26	9	1	1	NUM
ejpam-3007	26	10	]	]	PUNCT
ejpam-3007	26	11	based	base	VERB
ejpam-3007	26	12	on	on	ADP
ejpam-3007	26	13	the	the	DET
ejpam-3007	26	14	millennium	millennium	NOUN
ejpam-3007	26	15	problem	problem	NOUN
ejpam-3007	26	16	stated	state	VERB
ejpam-3007	26	17	by	by	ADP
ejpam-3007	26	18	clay	clay	NOUN
ejpam-3007	26	19	institute	institute	NOUN
ejpam-3007	26	20	for	for	ADP
ejpam-3007	26	21	the	the	DET
ejpam-3007	26	22	navier	navier	NOUN
ejpam-3007	26	23	-	-	PUNCT
ejpam-3007	26	24	stokes	stoke	NOUN
ejpam-3007	26	25	equations	equation	NOUN
ejpam-3007	26	26	.	.	PUNCT
ejpam-3007	27	1	our	our	PRON
ejpam-3007	27	2	point	point	NOUN
ejpam-3007	27	3	of	of	ADP
ejpam-3007	27	4	view	view	NOUN
ejpam-3007	27	5	on	on	ADP
ejpam-3007	27	6	these	these	DET
ejpam-3007	27	7	issues	issue	NOUN
ejpam-3007	27	8	agrees	agree	VERB
ejpam-3007	27	9	with	with	ADP
ejpam-3007	27	10	one	one	NUM
ejpam-3007	27	11	,	,	PUNCT
ejpam-3007	27	12	stated	state	VERB
ejpam-3007	27	13	in	in	ADP
ejpam-3007	27	14	article	article	NOUN
ejpam-3007	27	15	[	[	X
ejpam-3007	27	16	1],[5],[6	1],[5],[6	X
ejpam-3007	27	17	]	]	PUNCT
ejpam-3007	27	18	but	but	CCONJ
ejpam-3007	27	19	in	in	ADP
ejpam-3007	27	20	our	our	PRON
ejpam-3007	27	21	research	research	NOUN
ejpam-3007	27	22	we	we	PRON
ejpam-3007	27	23	propose	propose	VERB
ejpam-3007	27	24	a	a	DET
ejpam-3007	27	25	way	way	NOUN
ejpam-3007	27	26	for	for	ADP
ejpam-3007	27	27	solving	solve	VERB
ejpam-3007	27	28	these	these	DET
ejpam-3007	27	29	problems	problem	NOUN
ejpam-3007	27	30	.	.	PUNCT
ejpam-3007	28	1	our	our	PRON
ejpam-3007	28	2	point	point	NOUN
ejpam-3007	28	3	of	of	ADP
ejpam-3007	28	4	view	view	NOUN
ejpam-3007	28	5	is	be	AUX
ejpam-3007	28	6	that	that	SCONJ
ejpam-3007	28	7	the	the	DET
ejpam-3007	28	8	modern	modern	ADJ
ejpam-3007	28	9	mathematical	mathematical	ADJ
ejpam-3007	28	10	methods	method	NOUN
ejpam-3007	28	11	of	of	ADP
ejpam-3007	28	12	the	the	DET
ejpam-3007	28	13	theory	theory	NOUN
ejpam-3007	28	14	of	of	ADP
ejpam-3007	28	15	functions	function	NOUN
ejpam-3007	28	16	dedicated	dedicate	VERB
ejpam-3007	28	17	to	to	ADP
ejpam-3007	28	18	the	the	DET
ejpam-3007	28	19	function	function	NOUN
ejpam-3007	28	20	estimation	estimation	NOUN
ejpam-3007	28	21	have	have	AUX
ejpam-3007	28	22	ignored	ignore	VERB
ejpam-3007	28	23	such	such	DET
ejpam-3007	28	24	an	an	DET
ejpam-3007	28	25	important	important	ADJ
ejpam-3007	28	26	component	component	NOUN
ejpam-3007	28	27	of	of	ADP
ejpam-3007	28	28	the	the	DET
ejpam-3007	28	29	fourier	fourier	ADJ
ejpam-3007	28	30	transformation	transformation	NOUN
ejpam-3007	28	31	as	as	ADP
ejpam-3007	28	32	its	its	PRON
ejpam-3007	28	33	phase	phase	NOUN
ejpam-3007	28	34	.	.	PUNCT
ejpam-3007	29	1	our	our	PRON
ejpam-3007	29	2	research	research	NOUN
ejpam-3007	29	3	is	be	AUX
ejpam-3007	29	4	outlined	outline	VERB
ejpam-3007	29	5	as	as	SCONJ
ejpam-3007	29	6	follows	follow	VERB
ejpam-3007	29	7	:	:	PUNCT
ejpam-3007	29	8	first	first	ADV
ejpam-3007	29	9	,	,	PUNCT
ejpam-3007	29	10	we	we	PRON
ejpam-3007	29	11	give	give	VERB
ejpam-3007	29	12	examples	example	NOUN
ejpam-3007	29	13	of	of	ADP
ejpam-3007	29	14	the	the	DET
ejpam-3007	29	15	gradient	gradient	NOUN
ejpam-3007	29	16	catastrophe	catastrophe	NOUN
ejpam-3007	29	17	caused	cause	VERB
ejpam-3007	29	18	by	by	ADP
ejpam-3007	29	19	the	the	DET
ejpam-3007	29	20	phase	phase	NOUN
ejpam-3007	29	21	change	change	NOUN
ejpam-3007	29	22	,	,	PUNCT
ejpam-3007	29	23	and	and	CCONJ
ejpam-3007	29	24	then	then	ADV
ejpam-3007	29	25	proceed	proceed	VERB
ejpam-3007	29	26	to	to	ADP
ejpam-3007	29	27	an	an	DET
ejpam-3007	29	28	expansion	expansion	NOUN
ejpam-3007	29	29	of	of	ADP
ejpam-3007	29	30	classes	class	NOUN
ejpam-3007	29	31	of	of	ADP
ejpam-3007	29	32	functions	function	NOUN
ejpam-3007	29	33	subjected	subject	VERB
ejpam-3007	29	34	to	to	ADP
ejpam-3007	29	35	the	the	DET
ejpam-3007	29	36	gradient	gradient	NOUN
ejpam-3007	29	37	catastrophe	catastrophe	NOUN
ejpam-3007	29	38	.	.	PUNCT
ejpam-3007	30	1	our	our	PRON
ejpam-3007	30	2	final	final	ADJ
ejpam-3007	30	3	results	result	NOUN
ejpam-3007	30	4	lie	lie	VERB
ejpam-3007	30	5	in	in	ADP
ejpam-3007	30	6	the	the	DET
ejpam-3007	30	7	nonlinear	nonlinear	ADJ
ejpam-3007	30	8	representation	representation	NOUN
ejpam-3007	30	9	of	of	ADP
ejpam-3007	30	10	functions	function	NOUN
ejpam-3007	30	11	showing	show	VERB
ejpam-3007	30	12	some	some	DET
ejpam-3007	30	13	new	new	ADJ
ejpam-3007	30	14	classification	classification	NOUN
ejpam-3007	30	15	of	of	ADP
ejpam-3007	30	16	functions	function	NOUN
ejpam-3007	30	17	through	through	ADP
ejpam-3007	30	18	a	a	DET
ejpam-3007	30	19	phase	phase	NOUN
ejpam-3007	30	20	classification	classification	NOUN
ejpam-3007	30	21	.	.	PUNCT
ejpam-3007	31	1	in	in	ADP
ejpam-3007	31	2	addition	addition	NOUN
ejpam-3007	31	3	,	,	PUNCT
ejpam-3007	31	4	the	the	DET
ejpam-3007	31	5	notions	notion	NOUN
ejpam-3007	31	6	of	of	ADP
ejpam-3007	31	7	discreteness	discreteness	NOUN
ejpam-3007	31	8	and	and	CCONJ
ejpam-3007	31	9	continuity	continuity	NOUN
ejpam-3007	31	10	of	of	ADP
ejpam-3007	31	11	functions	function	NOUN
ejpam-3007	31	12	are	be	AUX
ejpam-3007	31	13	naturally	naturally	ADV
ejpam-3007	31	14	merged	merge	VERB
ejpam-3007	31	15	.	.	PUNCT
ejpam-3007	32	1	and	and	CCONJ
ejpam-3007	32	2	,	,	PUNCT
ejpam-3007	32	3	in	in	ADP
ejpam-3007	32	4	our	our	PRON
ejpam-3007	32	5	opinon	opinon	NOUN
ejpam-3007	32	6	,	,	PUNCT
ejpam-3007	32	7	this	this	PRON
ejpam-3007	32	8	leads	lead	VERB
ejpam-3007	32	9	to	to	ADP
ejpam-3007	32	10	understanding	understanding	NOUN
ejpam-3007	32	11	of	of	ADP
ejpam-3007	32	12	how	how	SCONJ
ejpam-3007	32	13	discrete	discrete	ADJ
ejpam-3007	32	14	objects	object	NOUN
ejpam-3007	32	15	are	be	AUX
ejpam-3007	32	16	born	bear	VERB
ejpam-3007	32	17	under	under	ADP
ejpam-3007	32	18	a	a	DET
ejpam-3007	32	19	continuous	continuous	ADJ
ejpam-3007	32	20	change	change	NOUN
ejpam-3007	32	21	of	of	ADP
ejpam-3007	32	22	the	the	DET
ejpam-3007	32	23	world	world	NOUN
ejpam-3007	32	24	.	.	PUNCT
ejpam-3007	33	1	discrete	discrete	ADJ
ejpam-3007	33	2	objects	object	NOUN
ejpam-3007	33	3	are	be	AUX
ejpam-3007	33	4	associated	associate	VERB
ejpam-3007	33	5	with	with	ADP
ejpam-3007	33	6	discrete	discrete	ADJ
ejpam-3007	33	7	spectrum	spectrum	NOUN
ejpam-3007	33	8	of	of	ADP
ejpam-3007	33	9	the	the	DET
ejpam-3007	33	10	liouvilleschrdinger	liouvilleschrdinger	ADJ
ejpam-3007	33	11	equations	equation	NOUN
ejpam-3007	33	12	.	.	PUNCT
ejpam-3007	34	1	and	and	CCONJ
ejpam-3007	34	2	they	they	PRON
ejpam-3007	34	3	,	,	PUNCT
ejpam-3007	34	4	as	as	SCONJ
ejpam-3007	34	5	it	it	PRON
ejpam-3007	34	6	is	be	AUX
ejpam-3007	34	7	known	know	VERB
ejpam-3007	34	8	,	,	PUNCT
ejpam-3007	34	9	reflect	reflect	VERB
ejpam-3007	34	10	the	the	DET
ejpam-3007	34	11	wave	wave	NOUN
ejpam-3007	34	12	nature	nature	NOUN
ejpam-3007	34	13	of	of	ADP
ejpam-3007	34	14	things	thing	NOUN
ejpam-3007	34	15	.	.	PUNCT
ejpam-3007	35	1	but	but	CCONJ
ejpam-3007	35	2	here	here	ADV
ejpam-3007	35	3	,	,	PUNCT
ejpam-3007	35	4	we	we	PRON
ejpam-3007	35	5	abstract	abstract	VERB
ejpam-3007	35	6	away	away	ADV
ejpam-3007	35	7	from	from	ADP
ejpam-3007	35	8	the	the	DET
ejpam-3007	35	9	quantum	quantum	ADJ
ejpam-3007	35	10	formalism	formalism	NOUN
ejpam-3007	35	11	,	,	PUNCT
ejpam-3007	35	12	because	because	SCONJ
ejpam-3007	35	13	our	our	PRON
ejpam-3007	35	14	goal	goal	NOUN
ejpam-3007	35	15	lies	lie	VERB
ejpam-3007	35	16	in	in	ADP
ejpam-3007	35	17	a	a	DET
ejpam-3007	35	18	purely	purely	ADV
ejpam-3007	35	19	mathematical	mathematical	ADJ
ejpam-3007	35	20	approach	approach	NOUN
ejpam-3007	35	21	to	to	ADP
ejpam-3007	35	22	the	the	DET
ejpam-3007	35	23	analysis	analysis	NOUN
ejpam-3007	35	24	of	of	ADP
ejpam-3007	35	25	the	the	DET
ejpam-3007	35	26	arbitrary	arbitrary	ADJ
ejpam-3007	35	27	functions	function	NOUN
ejpam-3007	35	28	.	.	PUNCT
ejpam-3007	36	1	for	for	ADP
ejpam-3007	36	2	the	the	DET
ejpam-3007	36	3	analysis	analysis	NOUN
ejpam-3007	36	4	of	of	ADP
ejpam-3007	36	5	which	which	PRON
ejpam-3007	36	6	,	,	PUNCT
ejpam-3007	36	7	we	we	PRON
ejpam-3007	36	8	formally	formally	ADV
ejpam-3007	36	9	consider	consider	VERB
ejpam-3007	36	10	a	a	DET
ejpam-3007	36	11	function	function	NOUN
ejpam-3007	36	12	as	as	ADP
ejpam-3007	36	13	a	a	DET
ejpam-3007	36	14	potential	potential	NOUN
ejpam-3007	36	15	of	of	ADP
ejpam-3007	36	16	the	the	DET
ejpam-3007	36	17	schrdinger	schrdinger	ADJ
ejpam-3007	36	18	equation	equation	NOUN
ejpam-3007	36	19	.	.	PUNCT
ejpam-3007	37	1	at	at	ADP
ejpam-3007	37	2	the	the	DET
ejpam-3007	37	3	same	same	ADJ
ejpam-3007	37	4	time	time	NOUN
ejpam-3007	37	5	we	we	PRON
ejpam-3007	37	6	come	come	VERB
ejpam-3007	37	7	across	across	ADP
ejpam-3007	37	8	the	the	DET
ejpam-3007	37	9	concepts	concept	NOUN
ejpam-3007	37	10	that	that	PRON
ejpam-3007	37	11	generated	generate	VERB
ejpam-3007	37	12	by	by	ADP
ejpam-3007	37	13	the	the	DET
ejpam-3007	37	14	liouvilleschrdinger	liouvilleschrdinger	ADJ
ejpam-3007	37	15	equations	equation	NOUN
ejpam-3007	37	16	.	.	PUNCT
ejpam-3007	38	1	these	these	DET
ejpam-3007	38	2	concepts	concept	NOUN
ejpam-3007	38	3	allow	allow	VERB
ejpam-3007	38	4	to	to	PART
ejpam-3007	38	5	classify	classify	VERB
ejpam-3007	38	6	and	and	CCONJ
ejpam-3007	38	7	estimate	estimate	VERB
ejpam-3007	38	8	functions	function	NOUN
ejpam-3007	38	9	by	by	ADP
ejpam-3007	38	10	a	a	DET
ejpam-3007	38	11	phase	phase	NOUN
ejpam-3007	38	12	generated	generate	VERB
ejpam-3007	38	13	by	by	ADP
ejpam-3007	38	14	discrete	discrete	ADJ
ejpam-3007	38	15	spectrum	spectrum	NOUN
ejpam-3007	38	16	of	of	ADP
ejpam-3007	38	17	the	the	DET
ejpam-3007	38	18	liouville	liouville	NOUN
ejpam-3007	38	19	equation	equation	NOUN
ejpam-3007	38	20	.	.	PUNCT
ejpam-3007	39	1	2	2	X
ejpam-3007	39	2	.	.	X
ejpam-3007	39	3	results	result	NOUN
ejpam-3007	39	4	for	for	ADP
ejpam-3007	39	5	the	the	DET
ejpam-3007	39	6	one	one	NUM
ejpam-3007	39	7	-	-	PUNCT
ejpam-3007	39	8	dimensional	dimensional	ADJ
ejpam-3007	39	9	case	case	NOUN
ejpam-3007	39	10	let	let	VERB
ejpam-3007	39	11	us	we	PRON
ejpam-3007	39	12	consider	consider	VERB
ejpam-3007	39	13	one	one	NUM
ejpam-3007	39	14	-	-	PUNCT
ejpam-3007	39	15	dimensional	dimensional	ADJ
ejpam-3007	39	16	function	function	NOUN
ejpam-3007	39	17	f	f	NOUN
ejpam-3007	39	18	and	and	CCONJ
ejpam-3007	39	19	its	its	PRON
ejpam-3007	39	20	fourier	fourier	NOUN
ejpam-3007	39	21	transformation	transformation	NOUN
ejpam-3007	39	22	f̃	f̃	PROPN
ejpam-3007	39	23	.	.	PUNCT
ejpam-3007	40	1	using	use	VERB
ejpam-3007	40	2	notions	notion	NOUN
ejpam-3007	40	3	of	of	ADP
ejpam-3007	40	4	module	module	NOUN
ejpam-3007	40	5	and	and	CCONJ
ejpam-3007	40	6	phase	phase	NOUN
ejpam-3007	40	7	,	,	PUNCT
ejpam-3007	40	8	we	we	PRON
ejpam-3007	40	9	write	write	VERB
ejpam-3007	40	10	fourier	fourier	ADJ
ejpam-3007	40	11	transformation	transformation	NOUN
ejpam-3007	40	12	in	in	ADP
ejpam-3007	40	13	the	the	DET
ejpam-3007	40	14	following	follow	VERB
ejpam-3007	40	15	form	form	NOUN
ejpam-3007	40	16	f̃	f̃	PROPN
ejpam-3007	40	17	=	=	PUNCT
ejpam-3007	40	18	|f̃	|f̃	PROPN
ejpam-3007	40	19	|	|	ADV
ejpam-3007	40	20	exp(iφ	exp(iφ	PRON
ejpam-3007	40	21	)	)	PUNCT
ejpam-3007	40	22	,	,	PUNCT
ejpam-3007	40	23	where	where	SCONJ
ejpam-3007	40	24	φ	φ	PROPN
ejpam-3007	40	25	is	be	AUX
ejpam-3007	40	26	phase	phase	NOUN
ejpam-3007	40	27	.	.	PUNCT
ejpam-3007	41	1	to	to	PART
ejpam-3007	41	2	cite	cite	VERB
ejpam-3007	41	3	plancherel	plancherel	NOUN
ejpam-3007	41	4	equality	equality	NOUN
ejpam-3007	41	5	:	:	PUNCT
ejpam-3007	41	6	||f	||f	NOUN
ejpam-3007	41	7	||l2	||l2	NOUN
ejpam-3007	41	8	=	=	PUNCT
ejpam-3007	41	9	const||f̃	const||f̃	VERB
ejpam-3007	41	10	||l2	||l2	NOUN
ejpam-3007	41	11	.	.	PUNCT
ejpam-3007	42	1	here	here	ADV
ejpam-3007	42	2	we	we	PRON
ejpam-3007	42	3	can	can	AUX
ejpam-3007	42	4	see	see	VERB
ejpam-3007	42	5	that	that	SCONJ
ejpam-3007	42	6	a	a	DET
ejpam-3007	42	7	phase	phase	NOUN
ejpam-3007	42	8	is	be	AUX
ejpam-3007	42	9	not	not	PART
ejpam-3007	42	10	contributed	contribute	VERB
ejpam-3007	42	11	to	to	ADP
ejpam-3007	42	12	determination	determination	NOUN
ejpam-3007	42	13	of	of	ADP
ejpam-3007	42	14	x	x	PUNCT
ejpam-3007	42	15	norm	norm	NOUN
ejpam-3007	42	16	.	.	PUNCT
ejpam-3007	43	1	to	to	PART
ejpam-3007	43	2	estimate	estimate	VERB
ejpam-3007	43	3	a	a	DET
ejpam-3007	43	4	maximum	maximum	NOUN
ejpam-3007	43	5	we	we	PRON
ejpam-3007	43	6	have	have	VERB
ejpam-3007	43	7	a	a	DET
ejpam-3007	43	8	simple	simple	ADJ
ejpam-3007	43	9	estimate	estimate	NOUN
ejpam-3007	43	10	as	as	ADP
ejpam-3007	43	11	max|f	max|f	NOUN
ejpam-3007	43	12	|2	|2	NUM
ejpam-3007	43	13	≤	≤	NOUN
ejpam-3007	43	14	2||f	2||f	NUM
ejpam-3007	43	15	||l2	||l2	NOUN
ejpam-3007	43	16	||∇f	||∇f	PROPN
ejpam-3007	43	17	||l2	||l2	PROPN
ejpam-3007	43	18	.now	.now	PUNCT
ejpam-3007	44	1	we	we	PRON
ejpam-3007	44	2	have	have	VERB
ejpam-3007	44	3	an	an	DET
ejpam-3007	44	4	estimate	estimate	NOUN
ejpam-3007	44	5	of	of	ADP
ejpam-3007	44	6	the	the	DET
ejpam-3007	44	7	function	function	NOUN
ejpam-3007	44	8	maximum	maximum	NOUN
ejpam-3007	44	9	in	in	ADP
ejpam-3007	44	10	which	which	PRON
ejpam-3007	44	11	a	a	DET
ejpam-3007	44	12	phase	phase	NOUN
ejpam-3007	44	13	is	be	AUX
ejpam-3007	44	14	not	not	PART
ejpam-3007	44	15	involved	involve	VERB
ejpam-3007	44	16	.	.	PUNCT
ejpam-3007	45	1	let	let	VERB
ejpam-3007	45	2	us	we	PRON
ejpam-3007	45	3	consider	consider	VERB
ejpam-3007	45	4	a	a	DET
ejpam-3007	45	5	behavior	behavior	NOUN
ejpam-3007	45	6	of	of	ADP
ejpam-3007	45	7	a	a	DET
ejpam-3007	45	8	progressing	progressing	ADJ
ejpam-3007	45	9	wave	wave	NOUN
ejpam-3007	45	10	running	run	VERB
ejpam-3007	45	11	with	with	ADP
ejpam-3007	45	12	a	a	DET
ejpam-3007	45	13	constant	constant	ADJ
ejpam-3007	45	14	velocity	velocity	NOUN
ejpam-3007	45	15	of	of	ADP
ejpam-3007	45	16	v	v	NOUN
ejpam-3007	45	17	=	=	SYM
ejpam-3007	45	18	a	a	PRON
ejpam-3007	45	19	described	describe	VERB
ejpam-3007	45	20	by	by	ADP
ejpam-3007	45	21	function	function	NOUN
ejpam-3007	45	22	f	f	PROPN
ejpam-3007	45	23	(	(	PUNCT
ejpam-3007	45	24	x	x	PROPN
ejpam-3007	45	25	,	,	PUNCT
ejpam-3007	45	26	t	t	PROPN
ejpam-3007	45	27	)	)	PUNCT
ejpam-3007	45	28	=	=	PUNCT
ejpam-3007	45	29	f(x+	f(x+	NOUN
ejpam-3007	45	30	at	at	ADP
ejpam-3007	45	31	)	)	PUNCT
ejpam-3007	45	32	.	.	PUNCT
ejpam-3007	46	1	for	for	ADP
ejpam-3007	46	2	its	its	PRON
ejpam-3007	46	3	fourier	fourier	ADJ
ejpam-3007	46	4	transformation	transformation	NOUN
ejpam-3007	46	5	along	along	ADP
ejpam-3007	46	6	x	x	PUNCT
ejpam-3007	46	7	variable	variable	NOUN
ejpam-3007	46	8	we	we	PRON
ejpam-3007	46	9	have	have	VERB
ejpam-3007	46	10	f̃	f̃	PROPN
ejpam-3007	46	11	=	=	SYM
ejpam-3007	46	12	f̃	f̃	PROPN
ejpam-3007	46	13	exp(iatk	exp(iatk	NOUN
ejpam-3007	46	14	)	)	PUNCT
ejpam-3007	46	15	.	.	PUNCT
ejpam-3007	47	1	again	again	ADV
ejpam-3007	47	2	in	in	ADP
ejpam-3007	47	3	this	this	DET
ejpam-3007	47	4	case	case	NOUN
ejpam-3007	47	5	we	we	PRON
ejpam-3007	47	6	can	can	AUX
ejpam-3007	47	7	see	see	VERB
ejpam-3007	47	8	that	that	SCONJ
ejpam-3007	47	9	when	when	SCONJ
ejpam-3007	47	10	we	we	PRON
ejpam-3007	47	11	will	will	AUX
ejpam-3007	47	12	be	be	AUX
ejpam-3007	47	13	studying	study	VERB
ejpam-3007	47	14	a	a	DET
ejpam-3007	47	15	module	module	NOUN
ejpam-3007	47	16	a.	a.	NOUN
ejpam-3007	47	17	durmagambetov	durmagambetov	PROPN
ejpam-3007	47	18	/	/	SYM
ejpam-3007	47	19	eur	eur	PROPN
ejpam-3007	47	20	.	.	PUNCT
ejpam-3007	48	1	j.	j.	PROPN
ejpam-3007	48	2	pure	pure	PROPN
ejpam-3007	48	3	appl	appl	PROPN
ejpam-3007	48	4	.	.	PROPN
ejpam-3007	48	5	math	math	PROPN
ejpam-3007	48	6	,	,	PUNCT
ejpam-3007	48	7	10	10	NUM
ejpam-3007	48	8	(	(	PUNCT
ejpam-3007	48	9	4	4	NUM
ejpam-3007	48	10	)	)	PUNCT
ejpam-3007	48	11	(	(	PUNCT
ejpam-3007	48	12	2017	2017	NUM
ejpam-3007	48	13	)	)	PUNCT
ejpam-3007	48	14	,	,	PUNCT
ejpam-3007	48	15	763	763	NUM
ejpam-3007	48	16	-	-	SYM
ejpam-3007	48	17	785	785	NUM
ejpam-3007	48	18	765	765	NUM
ejpam-3007	48	19	of	of	ADP
ejpam-3007	48	20	the	the	DET
ejpam-3007	48	21	fourier	fourier	NOUN
ejpam-3007	48	22	transformation	transformation	NOUN
ejpam-3007	48	23	,	,	PUNCT
ejpam-3007	48	24	we	we	PRON
ejpam-3007	48	25	will	will	AUX
ejpam-3007	48	26	not	not	PART
ejpam-3007	48	27	obtain	obtain	VERB
ejpam-3007	48	28	major	major	ADJ
ejpam-3007	48	29	physical	physical	ADJ
ejpam-3007	48	30	information	information	NOUN
ejpam-3007	48	31	about	about	ADP
ejpam-3007	48	32	the	the	DET
ejpam-3007	48	33	wave	wave	NOUN
ejpam-3007	48	34	,	,	PUNCT
ejpam-3007	48	35	such	such	ADJ
ejpam-3007	48	36	as	as	ADP
ejpam-3007	48	37	its	its	PRON
ejpam-3007	48	38	velocity	velocity	NOUN
ejpam-3007	48	39	and	and	CCONJ
ejpam-3007	48	40	location	location	NOUN
ejpam-3007	48	41	of	of	ADP
ejpam-3007	48	42	the	the	DET
ejpam-3007	48	43	wave	wave	NOUN
ejpam-3007	48	44	crest	crest	NOUN
ejpam-3007	48	45	because	because	SCONJ
ejpam-3007	48	46	of	of	ADP
ejpam-3007	48	47	|f̃	|f̃	PROPN
ejpam-3007	48	48	|	|	ADV
ejpam-3007	48	49	=	=	PUNCT
ejpam-3007	48	50	|f̃	|f̃	PROPN
ejpam-3007	48	51	|	|	ADV
ejpam-3007	48	52	.	.	PUNCT
ejpam-3007	49	1	these	these	DET
ejpam-3007	49	2	two	two	NUM
ejpam-3007	49	3	examples	example	NOUN
ejpam-3007	49	4	show	show	VERB
ejpam-3007	49	5	w	w	NOUN
ejpam-3007	49	6	eaknesses	eaknesse	NOUN
ejpam-3007	49	7	of	of	ADP
ejpam-3007	49	8	studying	study	VERB
ejpam-3007	49	9	fourier	fourier	ADJ
ejpam-3007	49	10	transformation	transformation	NOUN
ejpam-3007	49	11	.	.	PUNCT
ejpam-3007	50	1	on	on	ADP
ejpam-3007	50	2	the	the	DET
ejpam-3007	50	3	other	other	ADJ
ejpam-3007	50	4	hand	hand	NOUN
ejpam-3007	50	5	,	,	PUNCT
ejpam-3007	50	6	many	many	ADJ
ejpam-3007	50	7	researchers	researcher	NOUN
ejpam-3007	50	8	focus	focus	VERB
ejpam-3007	50	9	on	on	ADP
ejpam-3007	50	10	the	the	DET
ejpam-3007	50	11	study	study	NOUN
ejpam-3007	50	12	of	of	ADP
ejpam-3007	50	13	functions	function	NOUN
ejpam-3007	50	14	using	use	VERB
ejpam-3007	50	15	embedding	embed	VERB
ejpam-3007	50	16	theorem	theorem	VERB
ejpam-3007	50	17	,	,	PUNCT
ejpam-3007	50	18	but	but	CCONJ
ejpam-3007	50	19	in	in	ADP
ejpam-3007	50	20	the	the	DET
ejpam-3007	50	21	embedding	embed	VERB
ejpam-3007	50	22	theorems	theorem	NOUN
ejpam-3007	50	23	main	main	ADJ
ejpam-3007	50	24	object	object	NOUN
ejpam-3007	50	25	of	of	ADP
ejpam-3007	50	26	the	the	DET
ejpam-3007	50	27	study	study	NOUN
ejpam-3007	50	28	is	be	AUX
ejpam-3007	50	29	module	module	NOUN
ejpam-3007	50	30	of	of	ADP
ejpam-3007	50	31	function	function	NOUN
ejpam-3007	50	32	.	.	PUNCT
ejpam-3007	51	1	but	but	CCONJ
ejpam-3007	51	2	as	as	SCONJ
ejpam-3007	51	3	we	we	PRON
ejpam-3007	51	4	have	have	AUX
ejpam-3007	51	5	seen	see	VERB
ejpam-3007	51	6	in	in	ADP
ejpam-3007	51	7	given	give	VERB
ejpam-3007	51	8	examples	example	NOUN
ejpam-3007	51	9	,	,	PUNCT
ejpam-3007	51	10	a	a	DET
ejpam-3007	51	11	phase	phase	NOUN
ejpam-3007	51	12	is	be	AUX
ejpam-3007	51	13	a	a	DET
ejpam-3007	51	14	main	main	ADJ
ejpam-3007	51	15	physical	physical	ADJ
ejpam-3007	51	16	characteristic	characteristic	NOUN
ejpam-3007	51	17	of	of	ADP
ejpam-3007	51	18	a	a	DET
ejpam-3007	51	19	process	process	NOUN
ejpam-3007	51	20	,	,	PUNCT
ejpam-3007	51	21	and	and	CCONJ
ejpam-3007	51	22	as	as	SCONJ
ejpam-3007	51	23	we	we	PRON
ejpam-3007	51	24	can	can	AUX
ejpam-3007	51	25	see	see	VERB
ejpam-3007	51	26	in	in	ADP
ejpam-3007	51	27	the	the	DET
ejpam-3007	51	28	mathematical	mathematical	ADJ
ejpam-3007	51	29	studies	study	NOUN
ejpam-3007	51	30	,	,	PUNCT
ejpam-3007	51	31	which	which	PRON
ejpam-3007	51	32	use	use	VERB
ejpam-3007	51	33	embedding	embed	VERB
ejpam-3007	51	34	theorems	theorem	NOUN
ejpam-3007	51	35	with	with	ADP
ejpam-3007	51	36	energy	energy	NOUN
ejpam-3007	51	37	estimates	estimate	NOUN
ejpam-3007	51	38	,	,	PUNCT
ejpam-3007	51	39	the	the	DET
ejpam-3007	51	40	phase	phase	NOUN
ejpam-3007	51	41	disappears	disappear	VERB
ejpam-3007	51	42	.	.	PUNCT
ejpam-3007	52	1	along	along	ADP
ejpam-3007	52	2	with	with	ADP
ejpam-3007	52	3	phase	phase	NOUN
ejpam-3007	52	4	,	,	PUNCT
ejpam-3007	52	5	all	all	DET
ejpam-3007	52	6	reasonable	reasonable	ADJ
ejpam-3007	52	7	information	information	NOUN
ejpam-3007	52	8	about	about	ADP
ejpam-3007	52	9	physical	physical	ADJ
ejpam-3007	52	10	process	process	NOUN
ejpam-3007	52	11	disappears	disappear	VERB
ejpam-3007	52	12	,	,	PUNCT
ejpam-3007	52	13	as	as	SCONJ
ejpam-3007	52	14	demonstrated	demonstrate	VERB
ejpam-3007	52	15	by	by	ADP
ejpam-3007	52	16	terence	terence	PROPN
ejpam-3007	52	17	tao	tao	PROPN
ejpam-3007	53	1	[	[	X
ejpam-3007	53	2	1	1	X
ejpam-3007	53	3	]	]	PUNCT
ejpam-3007	53	4	and	and	CCONJ
ejpam-3007	53	5	other	other	ADJ
ejpam-3007	53	6	research	research	NOUN
ejpam-3007	53	7	considerations	consideration	NOUN
ejpam-3007	53	8	.	.	PUNCT
ejpam-3007	54	1	in	in	ADP
ejpam-3007	54	2	fact	fact	NOUN
ejpam-3007	54	3	,	,	PUNCT
ejpam-3007	54	4	he	he	PRON
ejpam-3007	54	5	built	build	VERB
ejpam-3007	54	6	progressing	progress	VERB
ejpam-3007	54	7	waves	wave	NOUN
ejpam-3007	54	8	that	that	PRON
ejpam-3007	54	9	are	be	AUX
ejpam-3007	54	10	not	not	PART
ejpam-3007	54	11	followed	follow	VERB
ejpam-3007	54	12	energy	energy	NOUN
ejpam-3007	54	13	estimates	estimate	NOUN
ejpam-3007	54	14	.	.	PUNCT
ejpam-3007	55	1	let	let	VERB
ejpam-3007	55	2	us	we	PRON
ejpam-3007	55	3	proceed	proceed	VERB
ejpam-3007	55	4	with	with	ADP
ejpam-3007	55	5	more	more	ADV
ejpam-3007	55	6	essential	essential	ADJ
ejpam-3007	55	7	analysis	analysis	NOUN
ejpam-3007	55	8	of	of	ADP
ejpam-3007	55	9	influence	influence	NOUN
ejpam-3007	55	10	of	of	ADP
ejpam-3007	55	11	the	the	DET
ejpam-3007	55	12	phase	phase	NOUN
ejpam-3007	55	13	on	on	ADP
ejpam-3007	55	14	behavior	behavior	NOUN
ejpam-3007	55	15	of	of	ADP
ejpam-3007	55	16	functions	function	NOUN
ejpam-3007	55	17	.	.	PUNCT
ejpam-3007	56	1	theorem	theorem	NOUN
ejpam-3007	56	2	1	1	NUM
ejpam-3007	56	3	.	.	X
ejpam-3007	57	1	there	there	PRON
ejpam-3007	57	2	are	be	VERB
ejpam-3007	57	3	functions	function	NOUN
ejpam-3007	57	4	of	of	ADP
ejpam-3007	57	5	w	w	NOUN
ejpam-3007	57	6	1	1	NUM
ejpam-3007	57	7	2	2	NUM
ejpam-3007	57	8	(	(	PUNCT
ejpam-3007	57	9	r	r	NOUN
ejpam-3007	57	10	)	)	PUNCT
ejpam-3007	57	11	with	with	ADP
ejpam-3007	57	12	a	a	DET
ejpam-3007	57	13	constant	constant	ADJ
ejpam-3007	57	14	rate	rate	NOUN
ejpam-3007	57	15	of	of	ADP
ejpam-3007	57	16	the	the	DET
ejpam-3007	57	17	norm	norm	NOUN
ejpam-3007	57	18	for	for	ADP
ejpam-3007	57	19	a	a	DET
ejpam-3007	57	20	gradient	gradient	ADJ
ejpam-3007	57	21	catastrophe	catastrophe	NOUN
ejpam-3007	57	22	of	of	ADP
ejpam-3007	57	23	which	which	PRON
ejpam-3007	57	24	a	a	DET
ejpam-3007	57	25	phase	phase	NOUN
ejpam-3007	57	26	change	change	NOUN
ejpam-3007	57	27	of	of	ADP
ejpam-3007	57	28	its	its	PRON
ejpam-3007	57	29	fourier	fourier	NOUN
ejpam-3007	57	30	transformation	transformation	NOUN
ejpam-3007	57	31	is	be	AUX
ejpam-3007	57	32	sufficient	sufficient	ADJ
ejpam-3007	57	33	.	.	PUNCT
ejpam-3007	58	1	proof	proof	NOUN
ejpam-3007	58	2	.	.	PUNCT
ejpam-3007	59	1	to	to	PART
ejpam-3007	59	2	prove	prove	VERB
ejpam-3007	59	3	this	this	PRON
ejpam-3007	59	4	,	,	PUNCT
ejpam-3007	59	5	we	we	PRON
ejpam-3007	59	6	consider	consider	VERB
ejpam-3007	59	7	a	a	DET
ejpam-3007	59	8	sequence	sequence	NOUN
ejpam-3007	59	9	of	of	ADP
ejpam-3007	59	10	testing	testing	NOUN
ejpam-3007	59	11	functions	function	NOUN
ejpam-3007	59	12	f̃n	f̃n	AUX
ejpam-3007	59	13	=	=	PUNCT
ejpam-3007	59	14	∆/(1+k2),∆	∆/(1+k2),∆	X
ejpam-3007	59	15	=	=	SYM
ejpam-3007	59	16	(	(	PUNCT
ejpam-3007	59	17	i	i	PRON
ejpam-3007	59	18	−	−	VERB
ejpam-3007	59	19	k)n/(i	k)n/(i	NOUN
ejpam-3007	59	20	+	+	CCONJ
ejpam-3007	59	21	k)n	k)n	ADJ
ejpam-3007	59	22	.	.	PUNCT
ejpam-3007	60	1	it	it	PRON
ejpam-3007	60	2	is	be	AUX
ejpam-3007	60	3	obvious	obvious	ADJ
ejpam-3007	60	4	that	that	SCONJ
ejpam-3007	60	5	|f̃n|	|f̃n|	NOUN
ejpam-3007	60	6	=	=	SYM
ejpam-3007	60	7	1/(1	1/(1	PROPN
ejpam-3007	60	8	+	+	CCONJ
ejpam-3007	60	9	k2	k2	ADJ
ejpam-3007	60	10	)	)	PUNCT
ejpam-3007	60	11	.	.	PUNCT
ejpam-3007	61	1	max|fn|2	max|fn|2	ADJ
ejpam-3007	61	2	≤	≤	NOUN
ejpam-3007	61	3	2||fn||l2	2||fn||l2	NUM
ejpam-3007	61	4	||∇fn||l2	||∇fn||l2	PROPN
ejpam-3007	61	5	≤	≤	NUM
ejpam-3007	61	6	const	const	NOUN
ejpam-3007	61	7	..	..	PUNCT
ejpam-3007	61	8	calculating	calculate	VERB
ejpam-3007	61	9	the	the	DET
ejpam-3007	61	10	fourier	fourier	ADJ
ejpam-3007	61	11	transformation	transformation	NOUN
ejpam-3007	61	12	of	of	ADP
ejpam-3007	61	13	these	these	DET
ejpam-3007	61	14	testing	testing	NOUN
ejpam-3007	61	15	functions	function	NOUN
ejpam-3007	61	16	,	,	PUNCT
ejpam-3007	61	17	we	we	PRON
ejpam-3007	61	18	obtain	obtain	VERB
ejpam-3007	61	19	:	:	PUNCT
ejpam-3007	61	20	fn	fn	NOUN
ejpam-3007	61	21	=	=	SYM
ejpam-3007	61	22	x(−1)(n−1)2π	x(−1)(n−1)2π	PROPN
ejpam-3007	61	23	exp(−x)l1	exp(−x)l1	PROPN
ejpam-3007	61	24	(	(	PUNCT
ejpam-3007	61	25	n−1)(2x	n−1)(2x	PROPN
ejpam-3007	61	26	)	)	PUNCT
ejpam-3007	61	27	where	where	SCONJ
ejpam-3007	61	28	l1	l1	PROPN
ejpam-3007	61	29	(	(	PUNCT
ejpam-3007	61	30	n−1)(2x	n−1)(2x	PROPN
ejpam-3007	61	31	)	)	PUNCT
ejpam-3007	61	32	is	be	AUX
ejpam-3007	61	33	a	a	DET
ejpam-3007	61	34	laguerre	laguerre	NOUN
ejpam-3007	61	35	polynomial	polynomial	ADJ
ejpam-3007	61	36	.	.	PUNCT
ejpam-3007	62	1	now	now	ADV
ejpam-3007	62	2	we	we	PRON
ejpam-3007	62	3	see	see	VERB
ejpam-3007	62	4	that	that	SCONJ
ejpam-3007	62	5	the	the	DET
ejpam-3007	62	6	functions	function	NOUN
ejpam-3007	62	7	are	be	AUX
ejpam-3007	62	8	equibounded	equibounde	VERB
ejpam-3007	62	9	and	and	CCONJ
ejpam-3007	62	10	derivatives	derivative	NOUN
ejpam-3007	62	11	of	of	ADP
ejpam-3007	62	12	these	these	DET
ejpam-3007	62	13	functions	function	NOUN
ejpam-3007	62	14	will	will	AUX
ejpam-3007	62	15	grow	grow	VERB
ejpam-3007	62	16	with	with	ADP
ejpam-3007	62	17	the	the	DET
ejpam-3007	62	18	growth	growth	NOUN
ejpam-3007	62	19	of	of	ADP
ejpam-3007	62	20	n.	n.	NOUN
ejpam-3007	62	21	thus	thus	ADV
ejpam-3007	62	22	,	,	PUNCT
ejpam-3007	62	23	we	we	PRON
ejpam-3007	62	24	have	have	AUX
ejpam-3007	62	25	built	build	VERB
ejpam-3007	62	26	an	an	DET
ejpam-3007	62	27	example	example	NOUN
ejpam-3007	62	28	of	of	ADP
ejpam-3007	62	29	a	a	DET
ejpam-3007	62	30	sequence	sequence	NOUN
ejpam-3007	62	31	of	of	ADP
ejpam-3007	62	32	the	the	DET
ejpam-3007	62	33	bounded	bounded	ADJ
ejpam-3007	62	34	functions	function	NOUN
ejpam-3007	62	35	of	of	ADP
ejpam-3007	62	36	w	w	PROPN
ejpam-3007	62	37	1	1	NUM
ejpam-3007	62	38	2	2	NUM
ejpam-3007	62	39	(	(	PUNCT
ejpam-3007	62	40	r	r	NOUN
ejpam-3007	62	41	)	)	PUNCT
ejpam-3007	62	42	which	which	PRON
ejpam-3007	62	43	have	have	VERB
ejpam-3007	62	44	a	a	DET
ejpam-3007	62	45	constant	constant	ADJ
ejpam-3007	62	46	norm	norm	NOUN
ejpam-3007	62	47	w	w	PROPN
ejpam-3007	62	48	1	1	NUM
ejpam-3007	62	49	2	2	NUM
ejpam-3007	62	50	(	(	PUNCT
ejpam-3007	62	51	r	r	NOUN
ejpam-3007	62	52	)	)	PUNCT
ejpam-3007	62	53	and	and	CCONJ
ejpam-3007	62	54	this	this	DET
ejpam-3007	62	55	sequence	sequence	NOUN
ejpam-3007	62	56	converges	converge	VERB
ejpam-3007	62	57	to	to	ADP
ejpam-3007	62	58	a	a	DET
ejpam-3007	62	59	discontinuous	discontinuous	ADJ
ejpam-3007	62	60	function	function	NOUN
ejpam-3007	62	61	.	.	PUNCT
ejpam-3007	63	1	thus	thus	ADV
ejpam-3007	63	2	,	,	PUNCT
ejpam-3007	63	3	we	we	PRON
ejpam-3007	63	4	have	have	AUX
ejpam-3007	63	5	demonstrated	demonstrate	VERB
ejpam-3007	63	6	an	an	DET
ejpam-3007	63	7	importance	importance	NOUN
ejpam-3007	63	8	of	of	ADP
ejpam-3007	63	9	the	the	DET
ejpam-3007	63	10	phase	phase	NOUN
ejpam-3007	63	11	and	and	CCONJ
ejpam-3007	63	12	that	that	SCONJ
ejpam-3007	63	13	the	the	DET
ejpam-3007	63	14	phase	phase	NOUN
ejpam-3007	63	15	is	be	AUX
ejpam-3007	63	16	not	not	PART
ejpam-3007	63	17	involved	involve	VERB
ejpam-3007	63	18	into	into	ADP
ejpam-3007	63	19	energy	energy	NOUN
ejpam-3007	63	20	norms	norm	NOUN
ejpam-3007	63	21	that	that	PRON
ejpam-3007	63	22	are	be	AUX
ejpam-3007	63	23	inherent	inherent	ADJ
ejpam-3007	63	24	to	to	ADP
ejpam-3007	63	25	the	the	DET
ejpam-3007	63	26	mathematical	mathematical	ADJ
ejpam-3007	63	27	arguments	argument	NOUN
ejpam-3007	63	28	used	use	VERB
ejpam-3007	63	29	in	in	ADP
ejpam-3007	63	30	physical	physical	ADJ
ejpam-3007	63	31	processes	process	NOUN
ejpam-3007	63	32	analysis	analysis	NOUN
ejpam-3007	63	33	.	.	PUNCT
ejpam-3007	64	1	our	our	PRON
ejpam-3007	64	2	next	next	ADJ
ejpam-3007	64	3	goal	goal	NOUN
ejpam-3007	64	4	is	be	AUX
ejpam-3007	64	5	to	to	PART
ejpam-3007	64	6	maximally	maximally	ADV
ejpam-3007	64	7	expand	expand	VERB
ejpam-3007	64	8	this	this	DET
ejpam-3007	64	9	class	class	NOUN
ejpam-3007	64	10	of	of	ADP
ejpam-3007	64	11	functions	function	NOUN
ejpam-3007	64	12	in	in	ADP
ejpam-3007	64	13	which	which	PRON
ejpam-3007	64	14	a	a	DET
ejpam-3007	64	15	phase	phase	NOUN
ejpam-3007	64	16	is	be	AUX
ejpam-3007	64	17	important	important	ADJ
ejpam-3007	64	18	.	.	PUNCT
ejpam-3007	65	1	our	our	PRON
ejpam-3007	65	2	goal	goal	NOUN
ejpam-3007	65	3	is	be	AUX
ejpam-3007	65	4	also	also	ADV
ejpam-3007	65	5	to	to	PART
ejpam-3007	65	6	use	use	VERB
ejpam-3007	65	7	a	a	DET
ejpam-3007	65	8	phase	phase	NOUN
ejpam-3007	65	9	,	,	PUNCT
ejpam-3007	65	10	which	which	PRON
ejpam-3007	65	11	appears	appear	VERB
ejpam-3007	65	12	in	in	ADP
ejpam-3007	65	13	the	the	DET
ejpam-3007	65	14	inverse	inverse	NOUN
ejpam-3007	65	15	scattering	scattering	NOUN
ejpam-3007	65	16	problem	problem	NOUN
ejpam-3007	65	17	;	;	PUNCT
ejpam-3007	65	18	moreover	moreover	ADV
ejpam-3007	65	19	we	we	PRON
ejpam-3007	65	20	will	will	AUX
ejpam-3007	65	21	be	be	AUX
ejpam-3007	65	22	interested	interested	ADJ
ejpam-3007	65	23	mainly	mainly	ADV
ejpam-3007	65	24	in	in	ADP
ejpam-3007	65	25	a	a	DET
ejpam-3007	65	26	phase	phase	NOUN
ejpam-3007	65	27	generated	generate	VERB
ejpam-3007	65	28	by	by	ADP
ejpam-3007	65	29	a	a	DET
ejpam-3007	65	30	discrete	discrete	ADJ
ejpam-3007	65	31	spectrum	spectrum	NOUN
ejpam-3007	65	32	of	of	ADP
ejpam-3007	65	33	the	the	DET
ejpam-3007	65	34	liouville	liouville	NOUN
ejpam-3007	65	35	equation	equation	NOUN
ejpam-3007	65	36	.	.	PUNCT
ejpam-3007	66	1	thereby	thereby	ADV
ejpam-3007	66	2	,	,	PUNCT
ejpam-3007	66	3	we	we	PRON
ejpam-3007	66	4	come	come	VERB
ejpam-3007	66	5	now	now	ADV
ejpam-3007	66	6	to	to	ADP
ejpam-3007	66	7	an	an	DET
ejpam-3007	66	8	important	important	ADJ
ejpam-3007	66	9	subject	subject	NOUN
ejpam-3007	66	10	of	of	ADP
ejpam-3007	66	11	our	our	PRON
ejpam-3007	66	12	research	research	NOUN
ejpam-3007	66	13	,	,	PUNCT
ejpam-3007	66	14	such	such	ADJ
ejpam-3007	66	15	as	as	ADP
ejpam-3007	66	16	an	an	DET
ejpam-3007	66	17	occurrence	occurrence	NOUN
ejpam-3007	66	18	of	of	ADP
ejpam-3007	66	19	discontinuities	discontinuity	NOUN
ejpam-3007	66	20	,	,	PUNCT
ejpam-3007	66	21	fronts	front	NOUN
ejpam-3007	66	22	and	and	CCONJ
ejpam-3007	66	23	other	other	ADJ
ejpam-3007	66	24	instable	instable	ADJ
ejpam-3007	66	25	states	state	NOUN
ejpam-3007	66	26	in	in	ADP
ejpam-3007	66	27	numerical	numerical	ADJ
ejpam-3007	66	28	modeling	modeling	NOUN
ejpam-3007	66	29	and	and	CCONJ
ejpam-3007	66	30	which	which	PRON
ejpam-3007	66	31	are	be	AUX
ejpam-3007	66	32	at	at	ADP
ejpam-3007	66	33	the	the	DET
ejpam-3007	66	34	same	same	ADJ
ejpam-3007	66	35	very	very	ADV
ejpam-3007	66	36	stable	stable	ADJ
ejpam-3007	66	37	physical	physical	ADJ
ejpam-3007	66	38	objects	object	NOUN
ejpam-3007	66	39	.	.	PUNCT
ejpam-3007	67	1	theorem	theorem	NOUN
ejpam-3007	67	2	2	2	NUM
ejpam-3007	67	3	.	.	X
ejpam-3007	68	1	there	there	PRON
ejpam-3007	68	2	are	be	VERB
ejpam-3007	68	3	functions	function	NOUN
ejpam-3007	68	4	of	of	ADP
ejpam-3007	68	5	w	w	NOUN
ejpam-3007	68	6	1	1	NUM
ejpam-3007	68	7	2	2	NUM
ejpam-3007	68	8	(	(	PUNCT
ejpam-3007	68	9	r	r	NOUN
ejpam-3007	68	10	)	)	PUNCT
ejpam-3007	68	11	with	with	ADP
ejpam-3007	68	12	a	a	DET
ejpam-3007	68	13	constant	constant	ADJ
ejpam-3007	68	14	rate	rate	NOUN
ejpam-3007	68	15	of	of	ADP
ejpam-3007	68	16	the	the	DET
ejpam-3007	68	17	norm	norm	NOUN
ejpam-3007	68	18	for	for	ADP
ejpam-3007	68	19	a	a	DET
ejpam-3007	68	20	gradient	gradient	ADJ
ejpam-3007	68	21	catastrophe	catastrophe	NOUN
ejpam-3007	68	22	of	of	ADP
ejpam-3007	68	23	which	which	PRON
ejpam-3007	68	24	a	a	DET
ejpam-3007	68	25	phase	phase	NOUN
ejpam-3007	68	26	change	change	NOUN
ejpam-3007	68	27	of	of	ADP
ejpam-3007	68	28	its	its	PRON
ejpam-3007	68	29	fourier	fourier	NOUN
ejpam-3007	68	30	transformation	transformation	NOUN
ejpam-3007	68	31	is	be	AUX
ejpam-3007	68	32	sufficient	sufficient	ADJ
ejpam-3007	68	33	.	.	PUNCT
ejpam-3007	69	1	proof	proof	NOUN
ejpam-3007	69	2	.	.	PUNCT
ejpam-3007	70	1	to	to	PART
ejpam-3007	70	2	prove	prove	VERB
ejpam-3007	70	3	this	this	PRON
ejpam-3007	70	4	,	,	PUNCT
ejpam-3007	70	5	we	we	PRON
ejpam-3007	70	6	consider	consider	VERB
ejpam-3007	70	7	a	a	DET
ejpam-3007	70	8	sequence	sequence	NOUN
ejpam-3007	70	9	of	of	ADP
ejpam-3007	70	10	testing	testing	NOUN
ejpam-3007	70	11	functions	function	NOUN
ejpam-3007	70	12	f̃n	f̃n	AUX
ejpam-3007	70	13	=	=	PUNCT
ejpam-3007	70	14	∆/(1+k2),∆	∆/(1+k2),∆	X
ejpam-3007	70	15	=	=	SYM
ejpam-3007	70	16	(	(	PUNCT
ejpam-3007	70	17	i	i	PRON
ejpam-3007	70	18	−	−	VERB
ejpam-3007	70	19	k)n/(i	k)n/(i	NOUN
ejpam-3007	70	20	+	+	CCONJ
ejpam-3007	70	21	k)n	k)n	ADJ
ejpam-3007	70	22	.	.	PUNCT
ejpam-3007	71	1	it	it	PRON
ejpam-3007	71	2	is	be	AUX
ejpam-3007	71	3	obvious	obvious	ADJ
ejpam-3007	71	4	that	that	SCONJ
ejpam-3007	71	5	|f̃n|	|f̃n|	NOUN
ejpam-3007	71	6	=	=	SYM
ejpam-3007	71	7	1/(1	1/(1	PROPN
ejpam-3007	71	8	+	+	CCONJ
ejpam-3007	71	9	k2	k2	ADJ
ejpam-3007	71	10	)	)	PUNCT
ejpam-3007	71	11	.	.	PUNCT
ejpam-3007	72	1	max|fn|2	max|fn|2	ADJ
ejpam-3007	72	2	≤	≤	NOUN
ejpam-3007	72	3	2||fn||l2	2||fn||l2	NUM
ejpam-3007	72	4	||∇fn||l2	||∇fn||l2	PROPN
ejpam-3007	72	5	≤	≤	NUM
ejpam-3007	72	6	const	const	NOUN
ejpam-3007	72	7	..	..	PUNCT
ejpam-3007	72	8	calculating	calculate	VERB
ejpam-3007	72	9	the	the	DET
ejpam-3007	72	10	fourier	fourier	ADJ
ejpam-3007	72	11	transformation	transformation	NOUN
ejpam-3007	72	12	of	of	ADP
ejpam-3007	72	13	these	these	DET
ejpam-3007	72	14	testing	testing	NOUN
ejpam-3007	72	15	functions	function	NOUN
ejpam-3007	72	16	,	,	PUNCT
ejpam-3007	72	17	we	we	PRON
ejpam-3007	72	18	obtain	obtain	VERB
ejpam-3007	72	19	:	:	PUNCT
ejpam-3007	72	20	fn	fn	NOUN
ejpam-3007	72	21	=	=	SYM
ejpam-3007	72	22	x(−1)(n−1)2π	x(−1)(n−1)2π	PROPN
ejpam-3007	72	23	exp(−x)l1	exp(−x)l1	PROPN
ejpam-3007	72	24	(	(	PUNCT
ejpam-3007	72	25	n−1)(2x	n−1)(2x	PROPN
ejpam-3007	72	26	)	)	PUNCT
ejpam-3007	72	27	where	where	SCONJ
ejpam-3007	72	28	l1	l1	PROPN
ejpam-3007	72	29	(	(	PUNCT
ejpam-3007	72	30	n−1)(2x	n−1)(2x	PROPN
ejpam-3007	72	31	)	)	PUNCT
ejpam-3007	72	32	is	be	AUX
ejpam-3007	72	33	a	a	DET
ejpam-3007	72	34	laguerre	laguerre	NOUN
ejpam-3007	72	35	polynomial	polynomial	ADJ
ejpam-3007	72	36	.	.	PUNCT
ejpam-3007	73	1	now	now	ADV
ejpam-3007	73	2	we	we	PRON
ejpam-3007	73	3	see	see	VERB
ejpam-3007	73	4	that	that	SCONJ
ejpam-3007	73	5	the	the	DET
ejpam-3007	73	6	functions	function	NOUN
ejpam-3007	73	7	are	be	AUX
ejpam-3007	73	8	equibounded	equibounde	VERB
ejpam-3007	73	9	and	and	CCONJ
ejpam-3007	73	10	derivatives	derivative	NOUN
ejpam-3007	73	11	of	of	ADP
ejpam-3007	73	12	these	these	DET
ejpam-3007	73	13	functions	function	NOUN
ejpam-3007	73	14	will	will	AUX
ejpam-3007	73	15	grow	grow	VERB
ejpam-3007	73	16	with	with	ADP
ejpam-3007	73	17	the	the	DET
ejpam-3007	73	18	growth	growth	NOUN
ejpam-3007	73	19	of	of	ADP
ejpam-3007	73	20	n.	n.	NOUN
ejpam-3007	73	21	thus	thus	ADV
ejpam-3007	73	22	,	,	PUNCT
ejpam-3007	73	23	we	we	PRON
ejpam-3007	73	24	have	have	AUX
ejpam-3007	73	25	built	build	VERB
ejpam-3007	73	26	an	an	DET
ejpam-3007	73	27	example	example	NOUN
ejpam-3007	73	28	of	of	ADP
ejpam-3007	73	29	a	a	DET
ejpam-3007	73	30	sequence	sequence	NOUN
ejpam-3007	73	31	of	of	ADP
ejpam-3007	73	32	the	the	DET
ejpam-3007	73	33	bounded	bounded	ADJ
ejpam-3007	73	34	functions	function	NOUN
ejpam-3007	73	35	of	of	ADP
ejpam-3007	73	36	w	w	PROPN
ejpam-3007	73	37	1	1	NUM
ejpam-3007	73	38	2	2	NUM
ejpam-3007	73	39	(	(	PUNCT
ejpam-3007	73	40	r	r	NOUN
ejpam-3007	73	41	)	)	PUNCT
ejpam-3007	73	42	which	which	PRON
ejpam-3007	73	43	have	have	VERB
ejpam-3007	73	44	a	a	DET
ejpam-3007	73	45	constant	constant	ADJ
ejpam-3007	73	46	norm	norm	NOUN
ejpam-3007	73	47	w	w	PROPN
ejpam-3007	73	48	1	1	NUM
ejpam-3007	73	49	2	2	NUM
ejpam-3007	73	50	(	(	PUNCT
ejpam-3007	73	51	r	r	NOUN
ejpam-3007	73	52	)	)	PUNCT
ejpam-3007	73	53	and	and	CCONJ
ejpam-3007	73	54	this	this	DET
ejpam-3007	73	55	sequence	sequence	NOUN
ejpam-3007	73	56	converges	converge	VERB
ejpam-3007	73	57	to	to	ADP
ejpam-3007	73	58	a	a	DET
ejpam-3007	73	59	discontinuous	discontinuous	ADJ
ejpam-3007	73	60	function	function	NOUN
ejpam-3007	73	61	.	.	PUNCT
ejpam-3007	74	1	a.	a.	NOUN
ejpam-3007	74	2	durmagambetov	durmagambetov	PROPN
ejpam-3007	74	3	/	/	SYM
ejpam-3007	74	4	eur	eur	PROPN
ejpam-3007	74	5	.	.	PUNCT
ejpam-3007	75	1	j.	j.	PROPN
ejpam-3007	75	2	pure	pure	PROPN
ejpam-3007	75	3	appl	appl	PROPN
ejpam-3007	75	4	.	.	PROPN
ejpam-3007	75	5	math	math	PROPN
ejpam-3007	75	6	,	,	PUNCT
ejpam-3007	75	7	10	10	NUM
ejpam-3007	75	8	(	(	PUNCT
ejpam-3007	75	9	4	4	NUM
ejpam-3007	75	10	)	)	PUNCT
ejpam-3007	75	11	(	(	PUNCT
ejpam-3007	75	12	2017	2017	NUM
ejpam-3007	75	13	)	)	PUNCT
ejpam-3007	75	14	,	,	PUNCT
ejpam-3007	75	15	763	763	NUM
ejpam-3007	75	16	-	-	SYM
ejpam-3007	75	17	785	785	NUM
ejpam-3007	75	18	766	766	NUM
ejpam-3007	75	19	thus	thus	ADV
ejpam-3007	76	1	,	,	PUNCT
ejpam-3007	76	2	we	we	PRON
ejpam-3007	76	3	have	have	AUX
ejpam-3007	76	4	demonstrated	demonstrate	VERB
ejpam-3007	76	5	an	an	DET
ejpam-3007	76	6	importance	importance	NOUN
ejpam-3007	76	7	of	of	ADP
ejpam-3007	76	8	the	the	DET
ejpam-3007	76	9	phase	phase	NOUN
ejpam-3007	76	10	and	and	CCONJ
ejpam-3007	76	11	that	that	SCONJ
ejpam-3007	76	12	the	the	DET
ejpam-3007	76	13	phase	phase	NOUN
ejpam-3007	76	14	is	be	AUX
ejpam-3007	76	15	not	not	PART
ejpam-3007	76	16	involved	involve	VERB
ejpam-3007	76	17	into	into	ADP
ejpam-3007	76	18	energy	energy	NOUN
ejpam-3007	76	19	norms	norm	NOUN
ejpam-3007	76	20	that	that	PRON
ejpam-3007	76	21	are	be	AUX
ejpam-3007	76	22	inherent	inherent	ADJ
ejpam-3007	76	23	to	to	ADP
ejpam-3007	76	24	the	the	DET
ejpam-3007	76	25	mathematical	mathematical	ADJ
ejpam-3007	76	26	arguments	argument	NOUN
ejpam-3007	76	27	used	use	VERB
ejpam-3007	76	28	in	in	ADP
ejpam-3007	76	29	physical	physical	ADJ
ejpam-3007	76	30	processes	process	NOUN
ejpam-3007	76	31	analysis	analysis	NOUN
ejpam-3007	76	32	.	.	PUNCT
ejpam-3007	77	1	our	our	PRON
ejpam-3007	77	2	next	next	ADJ
ejpam-3007	77	3	goal	goal	NOUN
ejpam-3007	77	4	is	be	AUX
ejpam-3007	77	5	to	to	PART
ejpam-3007	77	6	maximally	maximally	ADV
ejpam-3007	77	7	expand	expand	VERB
ejpam-3007	77	8	this	this	DET
ejpam-3007	77	9	class	class	NOUN
ejpam-3007	77	10	of	of	ADP
ejpam-3007	77	11	functions	function	NOUN
ejpam-3007	77	12	in	in	ADP
ejpam-3007	77	13	which	which	PRON
ejpam-3007	77	14	a	a	DET
ejpam-3007	77	15	phase	phase	NOUN
ejpam-3007	77	16	is	be	AUX
ejpam-3007	77	17	important	important	ADJ
ejpam-3007	77	18	.	.	PUNCT
ejpam-3007	78	1	our	our	PRON
ejpam-3007	78	2	goal	goal	NOUN
ejpam-3007	78	3	is	be	AUX
ejpam-3007	78	4	also	also	ADV
ejpam-3007	78	5	to	to	PART
ejpam-3007	78	6	use	use	VERB
ejpam-3007	78	7	a	a	DET
ejpam-3007	78	8	phase	phase	NOUN
ejpam-3007	78	9	,	,	PUNCT
ejpam-3007	78	10	which	which	PRON
ejpam-3007	78	11	appears	appear	VERB
ejpam-3007	78	12	in	in	ADP
ejpam-3007	78	13	the	the	DET
ejpam-3007	78	14	inverse	inverse	NOUN
ejpam-3007	78	15	scattering	scattering	NOUN
ejpam-3007	78	16	problem	problem	NOUN
ejpam-3007	78	17	;	;	PUNCT
ejpam-3007	78	18	moreover	moreover	ADV
ejpam-3007	78	19	we	we	PRON
ejpam-3007	78	20	will	will	AUX
ejpam-3007	78	21	be	be	AUX
ejpam-3007	78	22	interested	interested	ADJ
ejpam-3007	78	23	mainly	mainly	ADV
ejpam-3007	78	24	in	in	ADP
ejpam-3007	78	25	a	a	DET
ejpam-3007	78	26	phase	phase	NOUN
ejpam-3007	78	27	generated	generate	VERB
ejpam-3007	78	28	by	by	ADP
ejpam-3007	78	29	a	a	DET
ejpam-3007	78	30	discrete	discrete	ADJ
ejpam-3007	78	31	spectrum	spectrum	NOUN
ejpam-3007	78	32	of	of	ADP
ejpam-3007	78	33	the	the	DET
ejpam-3007	78	34	liouville	liouville	NOUN
ejpam-3007	78	35	equation	equation	NOUN
ejpam-3007	78	36	.	.	PUNCT
ejpam-3007	79	1	thereby	thereby	ADV
ejpam-3007	79	2	,	,	PUNCT
ejpam-3007	79	3	we	we	PRON
ejpam-3007	79	4	come	come	VERB
ejpam-3007	79	5	now	now	ADV
ejpam-3007	79	6	to	to	ADP
ejpam-3007	79	7	an	an	DET
ejpam-3007	79	8	important	important	ADJ
ejpam-3007	79	9	subject	subject	NOUN
ejpam-3007	79	10	of	of	ADP
ejpam-3007	79	11	our	our	PRON
ejpam-3007	79	12	research	research	NOUN
ejpam-3007	79	13	,	,	PUNCT
ejpam-3007	79	14	such	such	ADJ
ejpam-3007	79	15	as	as	ADP
ejpam-3007	79	16	an	an	DET
ejpam-3007	79	17	occurrence	occurrence	NOUN
ejpam-3007	79	18	of	of	ADP
ejpam-3007	79	19	discontinuities	discontinuity	NOUN
ejpam-3007	79	20	,	,	PUNCT
ejpam-3007	79	21	fronts	front	NOUN
ejpam-3007	79	22	and	and	CCONJ
ejpam-3007	79	23	other	other	ADJ
ejpam-3007	79	24	instable	instable	ADJ
ejpam-3007	79	25	states	state	NOUN
ejpam-3007	79	26	in	in	ADP
ejpam-3007	79	27	numerical	numerical	ADJ
ejpam-3007	79	28	modeling	modeling	NOUN
ejpam-3007	79	29	and	and	CCONJ
ejpam-3007	79	30	which	which	PRON
ejpam-3007	79	31	are	be	AUX
ejpam-3007	79	32	at	at	ADP
ejpam-3007	79	33	the	the	DET
ejpam-3007	79	34	same	same	ADJ
ejpam-3007	79	35	very	very	ADV
ejpam-3007	79	36	stable	stable	ADJ
ejpam-3007	79	37	physical	physical	ADJ
ejpam-3007	79	38	objects	object	NOUN
ejpam-3007	79	39	.	.	PUNCT
ejpam-3007	80	1	as	as	SCONJ
ejpam-3007	80	2	we	we	PRON
ejpam-3007	80	3	think	think	VERB
ejpam-3007	80	4	,	,	PUNCT
ejpam-3007	80	5	our	our	PRON
ejpam-3007	80	6	arguments	argument	NOUN
ejpam-3007	80	7	are	be	AUX
ejpam-3007	80	8	very	very	ADV
ejpam-3007	80	9	important	important	ADJ
ejpam-3007	80	10	in	in	ADP
ejpam-3007	80	11	issues	issue	NOUN
ejpam-3007	80	12	of	of	ADP
ejpam-3007	80	13	plasma	plasma	NOUN
ejpam-3007	80	14	stability	stability	NOUN
ejpam-3007	80	15	in	in	ADP
ejpam-3007	80	16	nuclear	nuclear	ADJ
ejpam-3007	80	17	fusion	fusion	NOUN
ejpam-3007	80	18	technology	technology	NOUN
ejpam-3007	80	19	,	,	PUNCT
ejpam-3007	80	20	since	since	SCONJ
ejpam-3007	80	21	the	the	DET
ejpam-3007	80	22	gradient	gradient	NOUN
ejpam-3007	80	23	catastrophe	catastrophe	NOUN
ejpam-3007	80	24	formation	formation	NOUN
ejpam-3007	80	25	serves	serve	VERB
ejpam-3007	80	26	as	as	ADP
ejpam-3007	80	27	a	a	DET
ejpam-3007	80	28	preamble	preamble	NOUN
ejpam-3007	80	29	to	to	ADP
ejpam-3007	80	30	a	a	DET
ejpam-3007	80	31	process	process	NOUN
ejpam-3007	80	32	of	of	ADP
ejpam-3007	80	33	nuclear	nuclear	ADJ
ejpam-3007	80	34	fusion	fusion	NOUN
ejpam-3007	80	35	stop	stop	NOUN
ejpam-3007	80	36	.	.	PUNCT
ejpam-3007	81	1	to	to	PART
ejpam-3007	81	2	build	build	VERB
ejpam-3007	81	3	more	more	ADJ
ejpam-3007	81	4	in	in	ADP
ejpam-3007	81	5	-	-	PUNCT
ejpam-3007	81	6	depth	depth	NOUN
ejpam-3007	81	7	analysis	analysis	NOUN
ejpam-3007	81	8	we	we	PRON
ejpam-3007	81	9	apply	apply	VERB
ejpam-3007	81	10	results	result	NOUN
ejpam-3007	81	11	of	of	ADP
ejpam-3007	81	12	scattering	scatter	VERB
ejpam-3007	81	13	theory	theory	NOUN
ejpam-3007	81	14	to	to	ADP
ejpam-3007	81	15	our	our	PRON
ejpam-3007	81	16	problem	problem	NOUN
ejpam-3007	81	17	.	.	PUNCT
ejpam-3007	82	1	for	for	ADP
ejpam-3007	82	2	this	this	PRON
ejpam-3007	82	3	,	,	PUNCT
ejpam-3007	82	4	we	we	PRON
ejpam-3007	82	5	consider	consider	VERB
ejpam-3007	82	6	a	a	DET
ejpam-3007	82	7	spectral	spectral	ADJ
ejpam-3007	82	8	problem	problem	NOUN
ejpam-3007	82	9	for	for	ADP
ejpam-3007	82	10	the	the	DET
ejpam-3007	82	11	liouville	liouville	NOUN
ejpam-3007	82	12	equations	equation	NOUN
ejpam-3007	82	13	with	with	ADP
ejpam-3007	82	14	a	a	DET
ejpam-3007	82	15	potential	potential	ADJ
ejpam-3007	82	16	q	q	NOUN
ejpam-3007	82	17	that	that	SCONJ
ejpam-3007	82	18	satisfies	satisfie	NOUN
ejpam-3007	82	19	and	and	CCONJ
ejpam-3007	82	20	belongs	belong	VERB
ejpam-3007	82	21	to	to	ADP
ejpam-3007	82	22	m	m	PROPN
ejpam-3007	82	23	space	space	NOUN
ejpam-3007	82	24	of	of	ADP
ejpam-3007	82	25	functions	function	NOUN
ejpam-3007	82	26	with	with	ADP
ejpam-3007	82	27	the	the	DET
ejpam-3007	82	28	following	follow	VERB
ejpam-3007	82	29	norm	norm	NOUN
ejpam-3007	82	30	||q||m	||q||m	PROPN
ejpam-3007	82	31	=	=	SYM
ejpam-3007	82	32	+	+	PROPN
ejpam-3007	82	33	∞∫	∞∫	PROPN
ejpam-3007	82	34	−∞	−∞	ADP
ejpam-3007	82	35	|q(x)|(1	|q(x)|(1	NOUN
ejpam-3007	82	36	+	+	X
ejpam-3007	82	37	|x|)dx	|x|)dx	NOUN
ejpam-3007	82	38	as	as	SCONJ
ejpam-3007	82	39	it	it	PRON
ejpam-3007	82	40	is	be	AUX
ejpam-3007	82	41	known	know	VERB
ejpam-3007	82	42	from	from	ADP
ejpam-3007	82	43	−ψ	−ψ	NOUN
ejpam-3007	82	44	”	"	PUNCT
ejpam-3007	82	45	+	+	CCONJ
ejpam-3007	82	46	qψ	qψ	X
ejpam-3007	82	47	=	=	SYM
ejpam-3007	82	48	|k|2ψ	|k|2ψ	X
ejpam-3007	82	49	,	,	PUNCT
ejpam-3007	82	50	k	k	PROPN
ejpam-3007	82	51	∈	∈	PROPN
ejpam-3007	82	52	c	c	X
ejpam-3007	82	53	(	(	PUNCT
ejpam-3007	82	54	1	1	NUM
ejpam-3007	82	55	)	)	PUNCT
ejpam-3007	82	56	with	with	ADP
ejpam-3007	82	57	the	the	DET
ejpam-3007	82	58	following	follow	VERB
ejpam-3007	82	59	asymptotics	asymptotic	NOUN
ejpam-3007	82	60	:	:	PUNCT
ejpam-3007	82	61	lim	lim	PROPN
ejpam-3007	82	62	x→−∞	x→−∞	PROPN
ejpam-3007	82	63	ψ1(k	ψ1(k	PROPN
ejpam-3007	82	64	,	,	PUNCT
ejpam-3007	82	65	x	x	NOUN
ejpam-3007	82	66	)	)	PUNCT
ejpam-3007	82	67	=	=	SYM
ejpam-3007	82	68	eikx	eikx	PROPN
ejpam-3007	82	69	+	+	CCONJ
ejpam-3007	82	70	s12(k)e−ikx	s12(k)e−ikx	PROPN
ejpam-3007	82	71	,	,	PUNCT
ejpam-3007	82	72	lim	lim	PROPN
ejpam-3007	82	73	x→+∞	x→+∞	PROPN
ejpam-3007	82	74	ψ1(k	ψ1(k	PROPN
ejpam-3007	82	75	,	,	PUNCT
ejpam-3007	82	76	x	x	NOUN
ejpam-3007	82	77	)	)	PUNCT
ejpam-3007	82	78	=	=	SYM
ejpam-3007	82	79	s11(k)e−ikx	s11(k)e−ikx	PROPN
ejpam-3007	82	80	(	(	PUNCT
ejpam-3007	82	81	2	2	X
ejpam-3007	82	82	)	)	PUNCT
ejpam-3007	82	83	lim	lim	NOUN
ejpam-3007	83	1	x→−∞	x→−∞	PROPN
ejpam-3007	83	2	ψ2(k	ψ2(k	PROPN
ejpam-3007	83	3	,	,	PUNCT
ejpam-3007	83	4	x	x	NOUN
ejpam-3007	83	5	)	)	PUNCT
ejpam-3007	83	6	=	=	SYM
ejpam-3007	83	7	s22(k)e−ikx	s22(k)e−ikx	PROPN
ejpam-3007	83	8	,	,	PUNCT
ejpam-3007	83	9	lim	lim	PROPN
ejpam-3007	83	10	x→+∞	x→+∞	PROPN
ejpam-3007	83	11	ψ2(k	ψ2(k	PROPN
ejpam-3007	83	12	,	,	PUNCT
ejpam-3007	83	13	x	x	NOUN
ejpam-3007	83	14	)	)	PUNCT
ejpam-3007	83	15	=	=	SYM
ejpam-3007	84	1	e−ikx	e−ikx	NOUN
ejpam-3007	84	2	+	+	X
ejpam-3007	84	3	s11(k)eikx	s11(k)eikx	PROPN
ejpam-3007	84	4	(	(	PUNCT
ejpam-3007	84	5	3	3	X
ejpam-3007	84	6	)	)	PUNCT
ejpam-3007	84	7	it	it	PRON
ejpam-3007	84	8	is	be	AUX
ejpam-3007	84	9	also	also	ADV
ejpam-3007	84	10	known	know	VERB
ejpam-3007	84	11	from	from	ADP
ejpam-3007	84	12	the	the	DET
ejpam-3007	84	13	theory	theory	NOUN
ejpam-3007	84	14	of	of	ADP
ejpam-3007	84	15	equations	equation	NOUN
ejpam-3007	84	16	[	[	X
ejpam-3007	84	17	2	2	NUM
ejpam-3007	84	18	]	]	PUNCT
ejpam-3007	84	19	,	,	PUNCT
ejpam-3007	84	20	that	that	SCONJ
ejpam-3007	84	21	any	any	DET
ejpam-3007	84	22	solution	solution	NOUN
ejpam-3007	84	23	is	be	AUX
ejpam-3007	84	24	a	a	DET
ejpam-3007	84	25	combination	combination	NOUN
ejpam-3007	84	26	of	of	ADP
ejpam-3007	84	27	some	some	DET
ejpam-3007	84	28	fundamental	fundamental	ADJ
ejpam-3007	84	29	solutions	solution	NOUN
ejpam-3007	84	30	satisfying	satisfy	VERB
ejpam-3007	84	31	certain	certain	ADJ
ejpam-3007	84	32	boundary	boundary	ADJ
ejpam-3007	84	33	conditions	condition	NOUN
ejpam-3007	84	34	.	.	PUNCT
ejpam-3007	85	1	lim	lim	PROPN
ejpam-3007	85	2	x→∞	x→∞	NUM
ejpam-3007	85	3	f1(k	f1(k	PROPN
ejpam-3007	85	4	,	,	PUNCT
ejpam-3007	85	5	x)e−ikx	x)e−ikx	PROPN
ejpam-3007	85	6	=	=	SYM
ejpam-3007	85	7	1	1	PROPN
ejpam-3007	85	8	,	,	PUNCT
ejpam-3007	85	9	lim	lim	PROPN
ejpam-3007	85	10	x→−∞	x→−∞	PROPN
ejpam-3007	85	11	f2(k	f2(k	PROPN
ejpam-3007	85	12	,	,	PUNCT
ejpam-3007	85	13	x)eikx	x)eikx	PUNCT
ejpam-3007	85	14	=	=	PUNCT
ejpam-3007	86	1	1	1	X
ejpam-3007	86	2	.	.	PUNCT
ejpam-3007	86	3	(	(	PUNCT
ejpam-3007	86	4	4	4	X
ejpam-3007	86	5	)	)	PUNCT
ejpam-3007	86	6	it	it	PRON
ejpam-3007	86	7	is	be	AUX
ejpam-3007	86	8	known	know	VERB
ejpam-3007	86	9	[	[	PUNCT
ejpam-3007	86	10	2	2	NUM
ejpam-3007	86	11	]	]	PUNCT
ejpam-3007	86	12	,	,	PUNCT
ejpam-3007	86	13	that	that	SCONJ
ejpam-3007	86	14	they	they	PRON
ejpam-3007	86	15	satisfy	satisfy	VERB
ejpam-3007	86	16	the	the	DET
ejpam-3007	86	17	following	follow	VERB
ejpam-3007	86	18	equations	equation	NOUN
ejpam-3007	86	19	:	:	PUNCT
ejpam-3007	86	20	f1(k	f1(k	PROPN
ejpam-3007	86	21	,	,	PUNCT
ejpam-3007	86	22	x	x	NOUN
ejpam-3007	86	23	)	)	PUNCT
ejpam-3007	86	24	=	=	PUNCT
ejpam-3007	86	25	eikx	eikx	VERB
ejpam-3007	86	26	−	−	PROPN
ejpam-3007	87	1	+	+	PROPN
ejpam-3007	87	2	∞∫	∞∫	PROPN
ejpam-3007	87	3	−∞	−∞	ADP
ejpam-3007	87	4	g1(k	g1(k	PROPN
ejpam-3007	87	5	,	,	PUNCT
ejpam-3007	87	6	x	x	NOUN
ejpam-3007	87	7	,	,	PUNCT
ejpam-3007	87	8	t)q(t)f1(k	t)q(t)f1(k	NOUN
ejpam-3007	87	9	,	,	PUNCT
ejpam-3007	87	10	t)dt	t)dt	PROPN
ejpam-3007	87	11	,	,	PUNCT
ejpam-3007	87	12	(	(	PUNCT
ejpam-3007	87	13	5	5	X
ejpam-3007	87	14	)	)	PUNCT
ejpam-3007	87	15	f2(k	f2(k	PROPN
ejpam-3007	87	16	,	,	PUNCT
ejpam-3007	87	17	x	x	NOUN
ejpam-3007	87	18	)	)	PUNCT
ejpam-3007	88	1	=	=	VERB
ejpam-3007	88	2	e−ikx	e−ikx	NOUN
ejpam-3007	88	3	+	+	PUNCT
ejpam-3007	89	1	+	+	ADJ
ejpam-3007	89	2	∞∫	∞∫	PROPN
ejpam-3007	89	3	−∞	−∞	ADP
ejpam-3007	89	4	g2(k	g2(k	PROPN
ejpam-3007	89	5	,	,	PUNCT
ejpam-3007	89	6	x	x	NOUN
ejpam-3007	89	7	,	,	PUNCT
ejpam-3007	89	8	t)q(t)f1(k	t)q(t)f1(k	NOUN
ejpam-3007	89	9	,	,	PUNCT
ejpam-3007	89	10	t)dt	t)dt	PROPN
ejpam-3007	89	11	,	,	PUNCT
ejpam-3007	89	12	(	(	PUNCT
ejpam-3007	89	13	6	6	NUM
ejpam-3007	89	14	)	)	PUNCT
ejpam-3007	89	15	(	(	PUNCT
ejpam-3007	89	16	7	7	X
ejpam-3007	89	17	)	)	PUNCT
ejpam-3007	89	18	e+(k	e+(k	NUM
ejpam-3007	89	19	,	,	PUNCT
ejpam-3007	89	20	x	x	X
ejpam-3007	89	21	)	)	PUNCT
ejpam-3007	89	22	=	=	SYM
ejpam-3007	89	23	eikx	eikx	PROPN
ejpam-3007	89	24	e−(k	e−(k	PROPN
ejpam-3007	89	25	,	,	PUNCT
ejpam-3007	89	26	x	x	NOUN
ejpam-3007	89	27	)	)	PUNCT
ejpam-3007	89	28	=	=	VERB
ejpam-3007	89	29	e−ikx	e−ikx	ADJ
ejpam-3007	89	30	,	,	PUNCT
ejpam-3007	89	31	(	(	PUNCT
ejpam-3007	89	32	8)	8)	NUM
ejpam-3007	89	33	g1(k	g1(k	NOUN
ejpam-3007	89	34	,	,	PUNCT
ejpam-3007	89	35	x	x	PROPN
ejpam-3007	89	36	,	,	PUNCT
ejpam-3007	89	37	t	t	PROPN
ejpam-3007	89	38	)	)	PUNCT
ejpam-3007	89	39	=	=	SYM
ejpam-3007	89	40	−θ(x−	−θ(x−	ADP
ejpam-3007	89	41	t)sin(k(x−	t)sin(k(x−	NUM
ejpam-3007	89	42	t	t	PROPN
ejpam-3007	89	43	)	)	PUNCT
ejpam-3007	89	44	)	)	PUNCT
ejpam-3007	90	1	k	k	PROPN
ejpam-3007	90	2	,	,	PUNCT
ejpam-3007	90	3	g2(k	g2(k	PROPN
ejpam-3007	90	4	,	,	PUNCT
ejpam-3007	90	5	x	x	PROPN
ejpam-3007	90	6	,	,	PUNCT
ejpam-3007	90	7	t	t	PROPN
ejpam-3007	90	8	)	)	PUNCT
ejpam-3007	90	9	=	=	SYM
ejpam-3007	90	10	θ(x−	θ(x−	PROPN
ejpam-3007	90	11	t)sin(k(x−	t)sin(k(x−	NUM
ejpam-3007	90	12	t	t	PROPN
ejpam-3007	90	13	)	)	PUNCT
ejpam-3007	90	14	)	)	PUNCT
ejpam-3007	91	1	k	k	NOUN
ejpam-3007	91	2	,	,	PUNCT
ejpam-3007	91	3	(	(	PUNCT
ejpam-3007	91	4	9	9	X
ejpam-3007	91	5	)	)	PUNCT
ejpam-3007	91	6	f1	f1	NOUN
ejpam-3007	91	7	=	=	PUNCT
ejpam-3007	91	8	e+	e+	PUNCT
ejpam-3007	91	9	−	−	PROPN
ejpam-3007	91	10	∞∑	∞∑	NUM
ejpam-3007	91	11	j=1	j=1	ADJ
ejpam-3007	91	12	gj1e+	gj1e+	PROPN
ejpam-3007	91	13	,	,	PUNCT
ejpam-3007	91	14	f2	f2	PROPN
ejpam-3007	91	15	=	=	PUNCT
ejpam-3007	91	16	e−	e−	X
ejpam-3007	91	17	+	+	CCONJ
ejpam-3007	91	18	∞∑	∞∑	NUM
ejpam-3007	91	19	j=1	j=1	ADJ
ejpam-3007	91	20	gj2e−	gj2e−	NOUN
ejpam-3007	91	21	,	,	PUNCT
ejpam-3007	91	22	(	(	PUNCT
ejpam-3007	91	23	10	10	NUM
ejpam-3007	91	24	)	)	PUNCT
ejpam-3007	91	25	a.	a.	NOUN
ejpam-3007	91	26	durmagambetov	durmagambetov	PROPN
ejpam-3007	91	27	/	/	SYM
ejpam-3007	91	28	eur	eur	PROPN
ejpam-3007	91	29	.	.	PUNCT
ejpam-3007	92	1	j.	j.	PROPN
ejpam-3007	92	2	pure	pure	PROPN
ejpam-3007	92	3	appl	appl	PROPN
ejpam-3007	92	4	.	.	PROPN
ejpam-3007	92	5	math	math	PROPN
ejpam-3007	92	6	,	,	PUNCT
ejpam-3007	92	7	10	10	NUM
ejpam-3007	92	8	(	(	PUNCT
ejpam-3007	92	9	4	4	NUM
ejpam-3007	92	10	)	)	PUNCT
ejpam-3007	92	11	(	(	PUNCT
ejpam-3007	92	12	2017	2017	NUM
ejpam-3007	92	13	)	)	PUNCT
ejpam-3007	92	14	,	,	PUNCT
ejpam-3007	92	15	763	763	NUM
ejpam-3007	92	16	-	-	SYM
ejpam-3007	92	17	785	785	NUM
ejpam-3007	92	18	767	767	NUM
ejpam-3007	92	19	let	let	VERB
ejpam-3007	92	20	us	we	PRON
ejpam-3007	92	21	also	also	ADV
ejpam-3007	92	22	provide	provide	VERB
ejpam-3007	92	23	known	know	VERB
ejpam-3007	92	24	results	result	NOUN
ejpam-3007	92	25	for	for	ADP
ejpam-3007	92	26	the	the	DET
ejpam-3007	92	27	scattering	scatter	VERB
ejpam-3007	92	28	coefficients	coefficient	NOUN
ejpam-3007	92	29	and	and	CCONJ
ejpam-3007	92	30	fundamental	fundamental	ADJ
ejpam-3007	92	31	solutions	solution	NOUN
ejpam-3007	92	32	outlined	outline	VERB
ejpam-3007	92	33	in	in	ADP
ejpam-3007	92	34	[	[	X
ejpam-3007	92	35	2	2	NUM
ejpam-3007	92	36	]	]	PUNCT
ejpam-3007	92	37	.	.	PUNCT
ejpam-3007	93	1	u+	u+	PROPN
ejpam-3007	93	2	1	1	NUM
ejpam-3007	93	3	(	(	PUNCT
ejpam-3007	93	4	k	k	NOUN
ejpam-3007	93	5	,	,	PUNCT
ejpam-3007	93	6	x	x	NOUN
ejpam-3007	93	7	)	)	PUNCT
ejpam-3007	93	8	=	=	SYM
ejpam-3007	93	9	s12f2(k	s12f2(k	NOUN
ejpam-3007	93	10	,	,	PUNCT
ejpam-3007	93	11	x	x	NOUN
ejpam-3007	93	12	)	)	PUNCT
ejpam-3007	93	13	,	,	PUNCT
ejpam-3007	93	14	u+	u+	NUM
ejpam-3007	93	15	2	2	NUM
ejpam-3007	93	16	(	(	PUNCT
ejpam-3007	93	17	k	k	NOUN
ejpam-3007	93	18	,	,	PUNCT
ejpam-3007	93	19	x	x	NOUN
ejpam-3007	93	20	)	)	PUNCT
ejpam-3007	93	21	=	=	SYM
ejpam-3007	93	22	s11f1(k	s11f1(k	PROPN
ejpam-3007	93	23	,	,	PUNCT
ejpam-3007	93	24	x	x	NOUN
ejpam-3007	93	25	)	)	PUNCT
ejpam-3007	93	26	,	,	PUNCT
ejpam-3007	93	27	u−1	u−1	PROPN
ejpam-3007	93	28	(	(	PUNCT
ejpam-3007	93	29	k	k	NOUN
ejpam-3007	93	30	,	,	PUNCT
ejpam-3007	93	31	x	x	NOUN
ejpam-3007	93	32	)	)	PUNCT
ejpam-3007	93	33	=	=	SYM
ejpam-3007	93	34	u+	u+	NUM
ejpam-3007	93	35	1	1	NUM
ejpam-3007	93	36	(	(	PUNCT
ejpam-3007	93	37	k	k	NOUN
ejpam-3007	93	38	,	,	PUNCT
ejpam-3007	93	39	x	x	NOUN
ejpam-3007	93	40	)	)	PUNCT
ejpam-3007	93	41	,	,	PUNCT
ejpam-3007	93	42	u+	u+	NUM
ejpam-3007	93	43	2	2	NUM
ejpam-3007	93	44	(	(	PUNCT
ejpam-3007	93	45	k	k	NOUN
ejpam-3007	93	46	,	,	PUNCT
ejpam-3007	93	47	x	x	NOUN
ejpam-3007	93	48	)	)	PUNCT
ejpam-3007	93	49	=	=	SYM
ejpam-3007	93	50	u+	u+	NUM
ejpam-3007	93	51	2	2	NUM
ejpam-3007	93	52	(	(	PUNCT
ejpam-3007	93	53	k	k	NOUN
ejpam-3007	93	54	,	,	PUNCT
ejpam-3007	93	55	x	x	NOUN
ejpam-3007	93	56	)	)	PUNCT
ejpam-3007	93	57	,	,	PUNCT
ejpam-3007	93	58	(	(	PUNCT
ejpam-3007	93	59	11	11	X
ejpam-3007	93	60	)	)	PUNCT
ejpam-3007	93	61	s11s	s11s	NOUN
ejpam-3007	93	62	∗	∗	NOUN
ejpam-3007	93	63	12	12	NUM
ejpam-3007	93	64	+	+	CCONJ
ejpam-3007	93	65	s12	s12	NOUN
ejpam-3007	93	66	,	,	PUNCT
ejpam-3007	93	67	s	s	NOUN
ejpam-3007	93	68	∗	∗	NOUN
ejpam-3007	93	69	22	22	NUM
ejpam-3007	93	70	=	=	SYM
ejpam-3007	93	71	0	0	NUM
ejpam-3007	93	72	,	,	PUNCT
ejpam-3007	93	73	s2	s2	VERB
ejpam-3007	93	74	11	11	NUM
ejpam-3007	93	75	+	+	CCONJ
ejpam-3007	93	76	s2	s2	VERB
ejpam-3007	93	77	12	12	NUM
ejpam-3007	93	78	=	=	SYM
ejpam-3007	93	79	s2	s2	NOUN
ejpam-3007	93	80	22	22	NUM
ejpam-3007	93	81	+	+	CCONJ
ejpam-3007	93	82	s2	s2	VERB
ejpam-3007	93	83	21	21	NUM
ejpam-3007	93	84	=	=	SYM
ejpam-3007	93	85	1	1	NUM
ejpam-3007	93	86	,	,	PUNCT
ejpam-3007	93	87	si	si	NOUN
ejpam-3007	93	88	,	,	PUNCT
ejpam-3007	93	89	j(−k	j(−k	NOUN
ejpam-3007	93	90	)	)	PUNCT
ejpam-3007	93	91	=	=	PUNCT
ejpam-3007	93	92	s∗i	s∗i	NOUN
ejpam-3007	93	93	,	,	PUNCT
ejpam-3007	93	94	j(k	j(k	NOUN
ejpam-3007	93	95	)	)	PUNCT
ejpam-3007	93	96	,	,	PUNCT
ejpam-3007	93	97	(	(	PUNCT
ejpam-3007	93	98	12	12	X
ejpam-3007	93	99	)	)	PUNCT
ejpam-3007	93	100	lim	lim	PROPN
ejpam-3007	93	101	|k|→∞	|k|→∞	PROPN
ejpam-3007	93	102	s12	s12	NOUN
ejpam-3007	93	103	=	=	SYM
ejpam-3007	93	104	s21	s21	NOUN
ejpam-3007	93	105	=	=	SYM
ejpam-3007	93	106	1	1	NUM
ejpam-3007	93	107	+	+	NOUN
ejpam-3007	93	108	o(1/|k|	o(1/|k|	NUM
ejpam-3007	93	109	)	)	PUNCT
ejpam-3007	93	110	,	,	PUNCT
ejpam-3007	93	111	,	,	PUNCT
ejpam-3007	93	112	lim	lim	PROPN
ejpam-3007	93	113	|k|→∞	|k|→∞	PROPN
ejpam-3007	93	114	s11	s11	NOUN
ejpam-3007	93	115	=	=	SYM
ejpam-3007	93	116	s22	s22	NOUN
ejpam-3007	93	117	=	=	PUNCT
ejpam-3007	93	118	o(1/|k|	o(1/|k|	NUM
ejpam-3007	93	119	)	)	PUNCT
ejpam-3007	93	120	,	,	PUNCT
ejpam-3007	93	121	(	(	PUNCT
ejpam-3007	93	122	13	13	X
ejpam-3007	93	123	)	)	PUNCT
ejpam-3007	93	124	s11	s11	NOUN
ejpam-3007	93	125	=	=	PUNCT
ejpam-3007	93	126	exp	exp	NOUN
ejpam-3007	93	127	(	(	PUNCT
ejpam-3007	93	128	1	1	NUM
ejpam-3007	93	129	2πi	2πi	NOUN
ejpam-3007	93	130	+	+	NOUN
ejpam-3007	93	131	∞∫	∞∫	PROPN
ejpam-3007	93	132	−∞	−∞	ADP
ejpam-3007	93	133	ln(1−	ln(1−	PROPN
ejpam-3007	93	134	|s12|	|s12|	PROPN
ejpam-3007	93	135	)	)	PUNCT
ejpam-3007	93	136	k′	k′	PROPN
ejpam-3007	93	137	−	−	PROPN
ejpam-3007	94	1	k	k	NOUN
ejpam-3007	94	2	dk	dk	PROPN
ejpam-3007	94	3	′	′	PROPN
ejpam-3007	94	4	n∏	n∏	PROPN
ejpam-3007	94	5	j=1	j=1	NOUN
ejpam-3007	94	6	(	(	PUNCT
ejpam-3007	94	7	iej	iej	X
ejpam-3007	95	1	+	+	X
ejpam-3007	95	2	k	k	PROPN
ejpam-3007	95	3	k	k	PROPN
ejpam-3007	96	1	−	−	PROPN
ejpam-3007	96	2	iej	iej	NOUN
ejpam-3007	96	3	)	)	PUNCT
ejpam-3007	97	1	dk	dk	PROPN
ejpam-3007	97	2	′	′	NOUN
ejpam-3007	97	3	,	,	PUNCT
ejpam-3007	97	4	(	(	PUNCT
ejpam-3007	97	5	14	14	NUM
ejpam-3007	97	6	)	)	PUNCT
ejpam-3007	97	7	s11(k	s11(k	NOUN
ejpam-3007	97	8	)	)	PUNCT
ejpam-3007	98	1	=	=	SYM
ejpam-3007	98	2	lim	lim	NOUN
ejpam-3007	98	3	ε→0	ε→0	NOUN
ejpam-3007	98	4	=	=	SYM
ejpam-3007	98	5	s11(k	s11(k	PUNCT
ejpam-3007	98	6	+	+	X
ejpam-3007	98	7	iε	iε	NOUN
ejpam-3007	98	8	)	)	PUNCT
ejpam-3007	98	9	,	,	PUNCT
ejpam-3007	98	10	s21(k	s21(k	NUM
ejpam-3007	98	11	)	)	PUNCT
ejpam-3007	98	12	=	=	SYM
ejpam-3007	98	13	−s12(−k)s11(k	−s12(−k)s11(k	NOUN
ejpam-3007	98	14	)	)	PUNCT
ejpam-3007	98	15	s11(−k	s11(−k	NOUN
ejpam-3007	98	16	)	)	PUNCT
ejpam-3007	98	17	(	(	PUNCT
ejpam-3007	98	18	15	15	NUM
ejpam-3007	98	19	)	)	PUNCT
ejpam-3007	98	20	s21(k	s21(k	NOUN
ejpam-3007	98	21	)	)	PUNCT
ejpam-3007	98	22	=	=	SYM
ejpam-3007	98	23	1	1	NUM
ejpam-3007	98	24	2ki	2ki	NOUN
ejpam-3007	98	25	+	+	NOUN
ejpam-3007	98	26	∞∫	∞∫	PROPN
ejpam-3007	98	27	−∞	−∞	ADP
ejpam-3007	98	28	exp(ikt)q(t)f2(k	exp(ikt)q(t)f2(k	PROPN
ejpam-3007	98	29	,	,	PUNCT
ejpam-3007	98	30	t)dt	t)dt	PROPN
ejpam-3007	98	31	1−	1−	NUM
ejpam-3007	98	32	1	1	NUM
ejpam-3007	98	33	2ki	2ki	NOUN
ejpam-3007	98	34	+	+	NOUN
ejpam-3007	98	35	∞∫	∞∫	PROPN
ejpam-3007	98	36	−∞	−∞	ADP
ejpam-3007	98	37	exp(ikt)q(t)f2(k	exp(ikt)q(t)f2(k	PROPN
ejpam-3007	98	38	,	,	PUNCT
ejpam-3007	98	39	t)dt	t)dt	PROPN
ejpam-3007	98	40	,	,	PUNCT
ejpam-3007	98	41	s12(k	s12(k	PROPN
ejpam-3007	98	42	)	)	PUNCT
ejpam-3007	98	43	=	=	SYM
ejpam-3007	98	44	1	1	NUM
ejpam-3007	98	45	2ki	2ki	NOUN
ejpam-3007	98	46	+	+	NOUN
ejpam-3007	98	47	∞∫	∞∫	NOUN
ejpam-3007	98	48	−∞	−∞	ADP
ejpam-3007	98	49	exp(−ikt)q(t)f1(k	exp(−ikt)q(t)f1(k	NOUN
ejpam-3007	98	50	,	,	PUNCT
ejpam-3007	98	51	t)dt	t)dt	PROPN
ejpam-3007	98	52	1−	1−	NUM
ejpam-3007	98	53	1	1	NUM
ejpam-3007	98	54	2ki	2ki	NOUN
ejpam-3007	98	55	+	+	NOUN
ejpam-3007	98	56	∞∫	∞∫	PROPN
ejpam-3007	98	57	−∞	−∞	ADP
ejpam-3007	98	58	exp(ikt)q(t)f1(k	exp(ikt)q(t)f1(k	PROPN
ejpam-3007	98	59	,	,	PUNCT
ejpam-3007	98	60	t)dt	t)dt	PROPN
ejpam-3007	98	61	,	,	PUNCT
ejpam-3007	98	62	(	(	PUNCT
ejpam-3007	98	63	16	16	NUM
ejpam-3007	98	64	)	)	PUNCT
ejpam-3007	98	65	b(k	b(k	PROPN
ejpam-3007	98	66	)	)	PUNCT
ejpam-3007	98	67	=	=	SYM
ejpam-3007	98	68	1	1	NUM
ejpam-3007	98	69	2ki	2ki	NOUN
ejpam-3007	98	70	+	+	NOUN
ejpam-3007	98	71	∞∫	∞∫	NOUN
ejpam-3007	98	72	−∞	−∞	ADP
ejpam-3007	98	73	exp(−ikt)q(t)f1(k	exp(−ikt)q(t)f1(k	PROPN
ejpam-3007	98	74	,	,	PUNCT
ejpam-3007	98	75	t)dt	t)dt	PROPN
ejpam-3007	98	76	,	,	PUNCT
ejpam-3007	98	77	a(k	a(k	NUM
ejpam-3007	98	78	)	)	PUNCT
ejpam-3007	98	79	=	=	SYM
ejpam-3007	99	1	1−	1−	NUM
ejpam-3007	99	2	1	1	NUM
ejpam-3007	99	3	2ki	2ki	NOUN
ejpam-3007	99	4	+	+	NOUN
ejpam-3007	99	5	∞∫	∞∫	PROPN
ejpam-3007	99	6	−∞	−∞	ADP
ejpam-3007	99	7	exp(ikt)q(t)f1(k	exp(ikt)q(t)f1(k	PROPN
ejpam-3007	99	8	,	,	PUNCT
ejpam-3007	99	9	t)dt	t)dt	PROPN
ejpam-3007	99	10	.	.	PROPN
ejpam-3007	99	11	(	(	PUNCT
ejpam-3007	99	12	17	17	NUM
ejpam-3007	99	13	)	)	PUNCT
ejpam-3007	99	14	now	now	ADV
ejpam-3007	99	15	we	we	PRON
ejpam-3007	99	16	are	be	AUX
ejpam-3007	99	17	able	able	ADJ
ejpam-3007	99	18	to	to	PART
ejpam-3007	99	19	return	return	VERB
ejpam-3007	99	20	to	to	ADP
ejpam-3007	99	21	our	our	PRON
ejpam-3007	99	22	question	question	NOUN
ejpam-3007	99	23	of	of	ADP
ejpam-3007	99	24	the	the	DET
ejpam-3007	99	25	gradient	gradient	NOUN
ejpam-3007	99	26	catastrophe	catastrophe	NOUN
ejpam-3007	99	27	for	for	ADP
ejpam-3007	99	28	more	more	ADJ
ejpam-3007	99	29	general	general	ADJ
ejpam-3007	99	30	class	class	NOUN
ejpam-3007	99	31	of	of	ADP
ejpam-3007	99	32	functions	function	NOUN
ejpam-3007	99	33	.	.	PUNCT
ejpam-3007	100	1	for	for	ADP
ejpam-3007	100	2	this	this	PRON
ejpam-3007	100	3	we	we	PRON
ejpam-3007	100	4	consider	consider	VERB
ejpam-3007	100	5	liouville	liouville	NOUN
ejpam-3007	100	6	equation	equation	NOUN
ejpam-3007	100	7	and	and	CCONJ
ejpam-3007	100	8	a	a	DET
ejpam-3007	100	9	sequence	sequence	NOUN
ejpam-3007	100	10	of	of	ADP
ejpam-3007	100	11	inverse	inverse	NOUN
ejpam-3007	100	12	scattering	scattering	NOUN
ejpam-3007	100	13	problems	problem	NOUN
ejpam-3007	100	14	with	with	ADP
ejpam-3007	100	15	constant	constant	ADJ
ejpam-3007	100	16	in	in	ADP
ejpam-3007	100	17	module	module	NOUN
ejpam-3007	100	18	scattering	scatter	VERB
ejpam-3007	100	19	coefficients	coefficient	NOUN
ejpam-3007	100	20	si	si	PROPN
ejpam-3007	100	21	,	,	PUNCT
ejpam-3007	100	22	j	j	PROPN
ejpam-3007	100	23	,	,	PUNCT
ejpam-3007	100	24	where	where	SCONJ
ejpam-3007	100	25	discrete	discrete	ADJ
ejpam-3007	100	26	eigenvalues	eigenvalue	VERB
ejpam-3007	100	27	ei	ei	NOUN
ejpam-3007	100	28	,	,	PUNCT
ejpam-3007	100	29	0	0	PUNCT
ejpam-3007	100	30	<	<	X
ejpam-3007	101	1	i	i	X
ejpam-3007	101	2	<	<	X
ejpam-3007	101	3	n+	n+	X
ejpam-3007	101	4	1	1	NUM
ejpam-3007	101	5	such	such	ADJ
ejpam-3007	101	6	that	that	SCONJ
ejpam-3007	101	7	lim	lim	PROPN
ejpam-3007	101	8	n→∞	n→∞	X
ejpam-3007	101	9	=	=	SYM
ejpam-3007	101	10	e∞	e∞	X
ejpam-3007	101	11	theorem	theorem	VERB
ejpam-3007	101	12	3	3	X
ejpam-3007	101	13	.	.	X
ejpam-3007	102	1	there	there	PRON
ejpam-3007	102	2	are	be	VERB
ejpam-3007	102	3	potentials	potential	NOUN
ejpam-3007	102	4	from	from	ADP
ejpam-3007	102	5	w	w	PROPN
ejpam-3007	102	6	1	1	NUM
ejpam-3007	102	7	2	2	NUM
ejpam-3007	102	8	(	(	PUNCT
ejpam-3007	102	9	r)m	r)m	NOUN
ejpam-3007	102	10	with	with	ADP
ejpam-3007	102	11	the	the	DET
ejpam-3007	102	12	constant	constant	ADJ
ejpam-3007	102	13	norm	norm	NOUN
ejpam-3007	102	14	of	of	ADP
ejpam-3007	102	15	w	w	PROPN
ejpam-3007	102	16	1	1	NUM
ejpam-3007	102	17	2	2	NUM
ejpam-3007	102	18	(	(	PUNCT
ejpam-3007	102	19	r)m	r)m	NOUN
ejpam-3007	102	20	for	for	ADP
ejpam-3007	102	21	the	the	DET
ejpam-3007	102	22	gradient	gradient	NOUN
ejpam-3007	102	23	catastrophe	catastrophe	NOUN
ejpam-3007	102	24	for	for	ADP
ejpam-3007	102	25	which	which	DET
ejpam-3007	102	26	existence	existence	NOUN
ejpam-3007	102	27	of	of	ADP
ejpam-3007	102	28	limit	limit	NOUN
ejpam-3007	102	29	point	point	NOUN
ejpam-3007	102	30	for	for	ADP
ejpam-3007	102	31	the	the	DET
ejpam-3007	102	32	discrete	discrete	ADJ
ejpam-3007	102	33	spectrum	spectrum	NOUN
ejpam-3007	102	34	with	with	ADP
ejpam-3007	102	35	given	give	VERB
ejpam-3007	102	36	potential	potential	NOUN
ejpam-3007	102	37	in	in	ADP
ejpam-3007	102	38	the	the	DET
ejpam-3007	102	39	liouville	liouville	NOUN
ejpam-3007	102	40	equation	equation	NOUN
ejpam-3007	102	41	is	be	AUX
ejpam-3007	102	42	sufficient	sufficient	ADJ
ejpam-3007	102	43	.	.	PUNCT
ejpam-3007	103	1	proof	proof	NOUN
ejpam-3007	103	2	.	.	PUNCT
ejpam-3007	104	1	following	follow	VERB
ejpam-3007	104	2	notations	notation	NOUN
ejpam-3007	104	3	[	[	X
ejpam-3007	104	4	2	2	NUM
ejpam-3007	104	5	]	]	PUNCT
ejpam-3007	104	6	,	,	PUNCT
ejpam-3007	104	7	we	we	PRON
ejpam-3007	104	8	introduce	introduce	VERB
ejpam-3007	104	9	functions	function	NOUN
ejpam-3007	104	10	a+	a+	ADP
ejpam-3007	104	11	,	,	PUNCT
ejpam-3007	104	12	b+,ω+	b+,ω+	X
ejpam-3007	104	13	according	accord	VERB
ejpam-3007	104	14	to	to	ADP
ejpam-3007	104	15	the	the	DET
ejpam-3007	104	16	formulas	formula	NOUN
ejpam-3007	104	17	:	:	PUNCT
ejpam-3007	104	18	s21(k	s21(k	NOUN
ejpam-3007	104	19	)	)	PUNCT
ejpam-3007	104	20	=	=	PUNCT
ejpam-3007	105	1	+	+	NOUN
ejpam-3007	105	2	∞∫	∞∫	PROPN
ejpam-3007	105	3	−∞	−∞	ADP
ejpam-3007	105	4	a+(t	a+(t	PROPN
ejpam-3007	105	5	)	)	PUNCT
ejpam-3007	105	6	exp(2ikt)dt	exp(2ikt)dt	PROPN
ejpam-3007	105	7	,	,	PUNCT
ejpam-3007	105	8	ω+(t	ω+(t	NUM
ejpam-3007	105	9	)	)	PUNCT
ejpam-3007	106	1	=	=	SYM
ejpam-3007	107	1	n∑	n∑	PROPN
ejpam-3007	107	2	i=1	i=1	PROPN
ejpam-3007	108	1	m1	m1	PROPN
ejpam-3007	108	2	j	j	PROPN
ejpam-3007	108	3	exp(−ejt	exp(−ejt	PROPN
ejpam-3007	108	4	)	)	PUNCT
ejpam-3007	108	5	+	+	NOUN
ejpam-3007	108	6	a+(t	a+(t	NOUN
ejpam-3007	108	7	)	)	PUNCT
ejpam-3007	108	8	(	(	PUNCT
ejpam-3007	108	9	18	18	NUM
ejpam-3007	108	10	)	)	PUNCT
ejpam-3007	108	11	b+(x	b+(x	PROPN
ejpam-3007	108	12	,	,	PUNCT
ejpam-3007	108	13	y	y	NOUN
ejpam-3007	108	14	)	)	PUNCT
ejpam-3007	108	15	+	+	PUNCT
ejpam-3007	109	1	+	+	ADJ
ejpam-3007	109	2	∞∫	∞∫	NOUN
ejpam-3007	109	3	0	0	NUM
ejpam-3007	110	1	b+(x+	b+(x+	VERB
ejpam-3007	110	2	y	y	PROPN
ejpam-3007	111	1	+	+	CCONJ
ejpam-3007	111	2	t)ω+(x+	t)ω+(x+	ADV
ejpam-3007	111	3	y	y	PROPN
ejpam-3007	111	4	+	+	CCONJ
ejpam-3007	111	5	t)dt+	t)dt+	NOUN
ejpam-3007	111	6	ω+(x+	ω+(x+	ADJ
ejpam-3007	111	7	y	y	X
ejpam-3007	111	8	)	)	PUNCT
ejpam-3007	111	9	=	=	SYM
ejpam-3007	111	10	0	0	NUM
ejpam-3007	111	11	(	(	PUNCT
ejpam-3007	111	12	19	19	NUM
ejpam-3007	111	13	)	)	PUNCT
ejpam-3007	111	14	where	where	SCONJ
ejpam-3007	111	15	m1	m1	PROPN
ejpam-3007	111	16	j	j	PROPN
ejpam-3007	111	17	are	be	AUX
ejpam-3007	111	18	normalized	normalize	VERB
ejpam-3007	111	19	numbers	number	NOUN
ejpam-3007	111	20	.	.	PUNCT
ejpam-3007	112	1	in	in	ADP
ejpam-3007	112	2	other	other	ADJ
ejpam-3007	112	3	words	word	NOUN
ejpam-3007	112	4	,	,	PUNCT
ejpam-3007	112	5	we	we	PRON
ejpam-3007	112	6	will	will	AUX
ejpam-3007	112	7	consider	consider	VERB
ejpam-3007	112	8	inverse	inverse	NOUN
ejpam-3007	112	9	problems	problem	NOUN
ejpam-3007	112	10	of	of	ADP
ejpam-3007	112	11	the	the	DET
ejpam-3007	112	12	potential	potential	ADJ
ejpam-3007	112	13	recovery	recovery	NOUN
ejpam-3007	112	14	,	,	PUNCT
ejpam-3007	112	15	and	and	CCONJ
ejpam-3007	112	16	for	for	ADP
ejpam-3007	112	17	the	the	DET
ejpam-3007	112	18	n	n	ADV
ejpam-3007	112	19	-	-	PUNCT
ejpam-3007	112	20	th	th	VERB
ejpam-3007	112	21	potential	potential	NOUN
ejpam-3007	112	22	we	we	PRON
ejpam-3007	112	23	will	will	AUX
ejpam-3007	112	24	consider	consider	VERB
ejpam-3007	112	25	a	a	DET
ejpam-3007	112	26	case	case	NOUN
ejpam-3007	112	27	with	with	ADP
ejpam-3007	112	28	an	an	DET
ejpam-3007	112	29	accuracy	accuracy	NOUN
ejpam-3007	112	30	a.	a.	NOUN
ejpam-3007	112	31	durmagambetov	durmagambetov	PROPN
ejpam-3007	112	32	/	/	SYM
ejpam-3007	112	33	eur	eur	PROPN
ejpam-3007	112	34	.	.	PUNCT
ejpam-3007	113	1	j.	j.	PROPN
ejpam-3007	113	2	pure	pure	PROPN
ejpam-3007	113	3	appl	appl	PROPN
ejpam-3007	113	4	.	.	PROPN
ejpam-3007	113	5	math	math	PROPN
ejpam-3007	113	6	,	,	PUNCT
ejpam-3007	113	7	10	10	NUM
ejpam-3007	113	8	(	(	PUNCT
ejpam-3007	113	9	4	4	NUM
ejpam-3007	113	10	)	)	PUNCT
ejpam-3007	113	11	(	(	PUNCT
ejpam-3007	113	12	2017	2017	NUM
ejpam-3007	113	13	)	)	PUNCT
ejpam-3007	113	14	,	,	PUNCT
ejpam-3007	113	15	763	763	NUM
ejpam-3007	113	16	-	-	SYM
ejpam-3007	113	17	785	785	NUM
ejpam-3007	113	18	768	768	NUM
ejpam-3007	113	19	up	up	ADP
ejpam-3007	113	20	to	to	ADP
ejpam-3007	113	21	n	n	CCONJ
ejpam-3007	113	22	discrete	discrete	ADJ
ejpam-3007	113	23	eigenvalues	eigenvalue	NOUN
ejpam-3007	113	24	.	.	PUNCT
ejpam-3007	114	1	it	it	PRON
ejpam-3007	114	2	is	be	AUX
ejpam-3007	114	3	sufficient	sufficient	ADJ
ejpam-3007	114	4	to	to	PART
ejpam-3007	114	5	consider	consider	VERB
ejpam-3007	114	6	a	a	DET
ejpam-3007	114	7	first	first	ADJ
ejpam-3007	114	8	approximation	approximation	NOUN
ejpam-3007	114	9	of	of	ADP
ejpam-3007	114	10	these	these	DET
ejpam-3007	114	11	equations	equation	NOUN
ejpam-3007	114	12	.	.	PUNCT
ejpam-3007	115	1	in	in	ADP
ejpam-3007	115	2	a	a	DET
ejpam-3007	115	3	first	first	ADJ
ejpam-3007	115	4	approximation	approximation	NOUN
ejpam-3007	115	5	,	,	PUNCT
ejpam-3007	115	6	the	the	DET
ejpam-3007	115	7	n	n	CCONJ
ejpam-3007	115	8	-	-	PUNCT
ejpam-3007	115	9	th	th	VERB
ejpam-3007	115	10	potential	potential	NOUN
ejpam-3007	115	11	is	be	AUX
ejpam-3007	115	12	recovered	recover	VERB
ejpam-3007	115	13	by	by	ADP
ejpam-3007	115	14	the	the	DET
ejpam-3007	115	15	equation	equation	NOUN
ejpam-3007	115	16	for	for	ADP
ejpam-3007	115	17	b+(x	b+(x	PROPN
ejpam-3007	115	18	,	,	PUNCT
ejpam-3007	115	19	y	y	PROPN
ejpam-3007	115	20	)	)	PUNCT
ejpam-3007	115	21	and	and	CCONJ
ejpam-3007	115	22	also	also	ADV
ejpam-3007	115	23	in	in	ADP
ejpam-3007	115	24	a	a	DET
ejpam-3007	115	25	first	first	ADJ
ejpam-3007	115	26	approximation	approximation	NOUN
ejpam-3007	115	27	.	.	PUNCT
ejpam-3007	116	1	we	we	PRON
ejpam-3007	116	2	have	have	VERB
ejpam-3007	116	3	the	the	DET
ejpam-3007	116	4	following	follow	VERB
ejpam-3007	116	5	arguments	argument	NOUN
ejpam-3007	116	6	for	for	ADP
ejpam-3007	116	7	the	the	DET
ejpam-3007	116	8	first	first	ADJ
ejpam-3007	116	9	approximation	approximation	NOUN
ejpam-3007	116	10	d	d	X
ejpam-3007	116	11	dx	dx	PROPN
ejpam-3007	116	12	b+(x	b+(x	PROPN
ejpam-3007	116	13	,	,	PUNCT
ejpam-3007	116	14	x	x	X
ejpam-3007	116	15	)	)	PUNCT
ejpam-3007	116	16	=	=	SYM
ejpam-3007	117	1	−	−	PROPN
ejpam-3007	117	2	d	d	X
ejpam-3007	117	3	dx	dx	PROPN
ejpam-3007	117	4	ω+(2x	ω+(2x	PROPN
ejpam-3007	117	5	)	)	PUNCT
ejpam-3007	117	6	.	.	PUNCT
ejpam-3007	118	1	(	(	PUNCT
ejpam-3007	118	2	20	20	NUM
ejpam-3007	118	3	)	)	PUNCT
ejpam-3007	118	4	d	d	PROPN
ejpam-3007	118	5	dx	dx	PROPN
ejpam-3007	118	6	ω+(2x	ω+(2x	PROPN
ejpam-3007	118	7	)	)	PUNCT
ejpam-3007	119	1	=	=	PUNCT
ejpam-3007	119	2	n∑	n∑	NOUN
ejpam-3007	119	3	i=1	i=1	PRON
ejpam-3007	119	4	−ejm1	−ejm1	PROPN
ejpam-3007	119	5	j	j	PROPN
ejpam-3007	119	6	exp(−ejt	exp(−ejt	PROPN
ejpam-3007	119	7	)	)	PUNCT
ejpam-3007	120	1	+	+	CCONJ
ejpam-3007	120	2	d	d	NUM
ejpam-3007	120	3	dx	dx	PROPN
ejpam-3007	120	4	a+(x	a+(x	PROPN
ejpam-3007	120	5	)	)	PUNCT
ejpam-3007	120	6	(	(	PUNCT
ejpam-3007	120	7	21	21	NUM
ejpam-3007	120	8	)	)	PUNCT
ejpam-3007	120	9	for	for	ADP
ejpam-3007	120	10	the	the	DET
ejpam-3007	120	11	last	last	ADJ
ejpam-3007	120	12	term	term	NOUN
ejpam-3007	120	13	,	,	PUNCT
ejpam-3007	120	14	we	we	PRON
ejpam-3007	120	15	also	also	ADV
ejpam-3007	120	16	consider	consider	VERB
ejpam-3007	120	17	a	a	DET
ejpam-3007	120	18	first	first	ADJ
ejpam-3007	120	19	approximation	approximation	NOUN
ejpam-3007	121	1	d	d	X
ejpam-3007	121	2	dx	dx	PROPN
ejpam-3007	121	3	a+(x	a+(x	PROPN
ejpam-3007	121	4	)	)	PUNCT
ejpam-3007	122	1	=	=	PUNCT
ejpam-3007	123	1	+	+	NOUN
ejpam-3007	123	2	∞∫	∞∫	PROPN
ejpam-3007	123	3	−∞	−∞	ADP
ejpam-3007	123	4	q̃+(2	q̃+(2	PROPN
ejpam-3007	123	5	t	t	PROPN
ejpam-3007	123	6	)	)	PUNCT
ejpam-3007	123	7	exp(2ixt)δ(k)2dt	exp(2ixt)δ(k)2dt	PROPN
ejpam-3007	123	8	,	,	PUNCT
ejpam-3007	123	9	(	(	PUNCT
ejpam-3007	123	10	22	22	NUM
ejpam-3007	123	11	)	)	PUNCT
ejpam-3007	123	12	δ(k	δ(k	NOUN
ejpam-3007	123	13	)	)	PUNCT
ejpam-3007	123	14	=	=	PUNCT
ejpam-3007	123	15	n∏	n∏	NOUN
ejpam-3007	123	16	j=1	j=1	NOUN
ejpam-3007	123	17	(	(	PUNCT
ejpam-3007	123	18	iej	iej	X
ejpam-3007	123	19	+	+	X
ejpam-3007	123	20	k	k	PROPN
ejpam-3007	123	21	k	k	PROPN
ejpam-3007	123	22	−	−	PROPN
ejpam-3007	123	23	iej	iej	NOUN
ejpam-3007	123	24	)	)	PUNCT
ejpam-3007	123	25	∗	∗	NOUN
ejpam-3007	123	26	exp	exp	NOUN
ejpam-3007	123	27	(	(	PUNCT
ejpam-3007	123	28	1	1	NUM
ejpam-3007	123	29	2πi	2πi	NOUN
ejpam-3007	123	30	v	v	ADP
ejpam-3007	123	31	p	p	PROPN
ejpam-3007	123	32	+	+	PROPN
ejpam-3007	123	33	∞∫	∞∫	PROPN
ejpam-3007	123	34	−∞	−∞	ADP
ejpam-3007	123	35	ln(1−	ln(1−	PROPN
ejpam-3007	123	36	|s12|	|s12|	PROPN
ejpam-3007	123	37	)	)	PUNCT
ejpam-3007	123	38	)	)	PUNCT
ejpam-3007	123	39	k′	k′	PROPN
ejpam-3007	124	1	−	−	PROPN
ejpam-3007	125	1	k	k	NOUN
ejpam-3007	125	2	dk	dk	PROPN
ejpam-3007	125	3	′	′	NOUN
ejpam-3007	125	4	)	)	PUNCT
ejpam-3007	125	5	(	(	PUNCT
ejpam-3007	125	6	23	23	NUM
ejpam-3007	125	7	)	)	PUNCT
ejpam-3007	125	8	to	to	PART
ejpam-3007	125	9	prove	prove	VERB
ejpam-3007	125	10	this	this	PRON
ejpam-3007	125	11	,	,	PUNCT
ejpam-3007	125	12	let	let	VERB
ejpam-3007	125	13	us	we	PRON
ejpam-3007	125	14	consider	consider	VERB
ejpam-3007	125	15	a	a	DET
ejpam-3007	125	16	sequence	sequence	NOUN
ejpam-3007	125	17	of	of	ADP
ejpam-3007	125	18	d	d	PROPN
ejpam-3007	125	19	dxa+(x)with	dxa+(x)with	ADP
ejpam-3007	125	20	n	n	CCONJ
ejpam-3007	125	21	going	go	VERB
ejpam-3007	125	22	to	to	PART
ejpam-3007	125	23	infinity	infinity	VERB
ejpam-3007	125	24	and	and	CCONJ
ejpam-3007	125	25	under	under	ADP
ejpam-3007	125	26	a	a	DET
ejpam-3007	125	27	proper	proper	ADJ
ejpam-3007	125	28	selection	selection	NOUN
ejpam-3007	125	29	of	of	ADP
ejpam-3007	125	30	scattering	scatter	VERB
ejpam-3007	125	31	coefficients	coefficient	NOUN
ejpam-3007	125	32	,	,	PUNCT
ejpam-3007	125	33	we	we	PRON
ejpam-3007	125	34	fall	fall	VERB
ejpam-3007	125	35	into	into	ADP
ejpam-3007	125	36	conditions	condition	NOUN
ejpam-3007	125	37	of	of	ADP
ejpam-3007	125	38	the	the	DET
ejpam-3007	125	39	theorem	theorem	NOUN
ejpam-3007	125	40	1	1	X
ejpam-3007	125	41	.	.	PUNCT
ejpam-3007	126	1	let	let	VERB
ejpam-3007	126	2	us	we	PRON
ejpam-3007	126	3	come	come	VERB
ejpam-3007	126	4	down	down	ADP
ejpam-3007	126	5	from	from	ADP
ejpam-3007	126	6	specific	specific	ADJ
ejpam-3007	126	7	obvious	obvious	ADJ
ejpam-3007	126	8	examples	example	NOUN
ejpam-3007	126	9	to	to	ADP
ejpam-3007	126	10	more	more	ADV
ejpam-3007	126	11	systematic	systematic	ADJ
ejpam-3007	126	12	analysis	analysis	NOUN
ejpam-3007	126	13	of	of	ADP
ejpam-3007	126	14	the	the	DET
ejpam-3007	126	15	gradient	gradient	NOUN
ejpam-3007	126	16	catastrophe	catastrophe	NOUN
ejpam-3007	126	17	.	.	PUNCT
ejpam-3007	127	1	in	in	ADP
ejpam-3007	127	2	given	give	VERB
ejpam-3007	127	3	below	below	ADP
ejpam-3007	127	4	all	all	DET
ejpam-3007	127	5	our	our	PRON
ejpam-3007	127	6	arguments	argument	NOUN
ejpam-3007	127	7	will	will	AUX
ejpam-3007	127	8	be	be	AUX
ejpam-3007	127	9	based	base	VERB
ejpam-3007	127	10	on	on	ADP
ejpam-3007	127	11	well	well	ADV
ejpam-3007	127	12	-	-	PUNCT
ejpam-3007	127	13	known	know	VERB
ejpam-3007	127	14	equation	equation	NOUN
ejpam-3007	127	15	:	:	PUNCT
ejpam-3007	127	16	s21(k	s21(k	NOUN
ejpam-3007	127	17	)	)	PUNCT
ejpam-3007	127	18	=	=	SYM
ejpam-3007	127	19	−s12(−k)s11(k)/s11(−k	−s12(−k)s11(k)/s11(−k	NOUN
ejpam-3007	127	20	)	)	PUNCT
ejpam-3007	127	21	let	let	VERB
ejpam-3007	127	22	us	we	PRON
ejpam-3007	127	23	consider	consider	VERB
ejpam-3007	127	24	s21	s21	NOUN
ejpam-3007	127	25	,	,	PUNCT
ejpam-3007	127	26	s12	s12	NOUN
ejpam-3007	127	27	in	in	ADP
ejpam-3007	127	28	the	the	DET
ejpam-3007	127	29	following	follow	VERB
ejpam-3007	127	30	form	form	NOUN
ejpam-3007	127	31	:	:	PUNCT
ejpam-3007	127	32	2iks12(k	2iks12(k	NUM
ejpam-3007	127	33	)	)	PUNCT
ejpam-3007	127	34	=	=	SYM
ejpam-3007	127	35	q̃(2k	q̃(2k	X
ejpam-3007	127	36	)	)	PUNCT
ejpam-3007	127	37	+	+	NUM
ejpam-3007	127	38	i1(k	i1(k	NOUN
ejpam-3007	127	39	)	)	PUNCT
ejpam-3007	127	40	,	,	PUNCT
ejpam-3007	127	41	2iks21(k	2iks21(k	X
ejpam-3007	127	42	)	)	PUNCT
ejpam-3007	127	43	=	=	SYM
ejpam-3007	127	44	q̃(−2k	q̃(−2k	X
ejpam-3007	127	45	)	)	PUNCT
ejpam-3007	127	46	+	+	PUNCT
ejpam-3007	127	47	i2(k	i2(k	NOUN
ejpam-3007	127	48	)	)	PUNCT
ejpam-3007	127	49	.	.	PUNCT
ejpam-3007	128	1	(	(	PUNCT
ejpam-3007	128	2	24	24	NUM
ejpam-3007	128	3	)	)	PUNCT
ejpam-3007	128	4	let	let	VERB
ejpam-3007	128	5	us	we	PRON
ejpam-3007	128	6	conceive	conceive	VERB
ejpam-3007	128	7	q̃(2k	q̃(2k	NOUN
ejpam-3007	128	8	)	)	PUNCT
ejpam-3007	128	9	=	=	SYM
ejpam-3007	128	10	u(k	u(k	PROPN
ejpam-3007	128	11	)	)	PUNCT
ejpam-3007	128	12	+	+	NUM
ejpam-3007	128	13	iv(k	iv(k	NOUN
ejpam-3007	128	14	)	)	PUNCT
ejpam-3007	128	15	.	.	PUNCT
ejpam-3007	129	1	then	then	ADV
ejpam-3007	129	2	we	we	PRON
ejpam-3007	129	3	will	will	AUX
ejpam-3007	129	4	have	have	VERB
ejpam-3007	129	5	the	the	DET
ejpam-3007	129	6	following	follow	VERB
ejpam-3007	129	7	equation	equation	NOUN
ejpam-3007	129	8	for	for	ADP
ejpam-3007	129	9	u	u	NOUN
ejpam-3007	129	10	,	,	PUNCT
ejpam-3007	129	11	v	v	NOUN
ejpam-3007	129	12	u(k	u(k	PROPN
ejpam-3007	129	13	)	)	PUNCT
ejpam-3007	129	14	+	+	PUNCT
ejpam-3007	129	15	iv(k	iv(k	NOUN
ejpam-3007	129	16	)	)	PUNCT
ejpam-3007	129	17	=	=	SYM
ejpam-3007	129	18	2iks12(k)−	2iks12(k)−	NUM
ejpam-3007	129	19	i1(k	i1(k	NOUN
ejpam-3007	129	20	)	)	PUNCT
ejpam-3007	129	21	,	,	PUNCT
ejpam-3007	129	22	u(k)−	u(k)−	PROPN
ejpam-3007	129	23	iv(k	iv(k	PRON
ejpam-3007	129	24	)	)	PUNCT
ejpam-3007	129	25	=	=	PUNCT
ejpam-3007	130	1	2iks21(k)−	2iks21(k)−	NUM
ejpam-3007	130	2	i2(k	i2(k	NOUN
ejpam-3007	130	3	)	)	PUNCT
ejpam-3007	130	4	,	,	PUNCT
ejpam-3007	130	5	(	(	PUNCT
ejpam-3007	130	6	25	25	NUM
ejpam-3007	130	7	)	)	PUNCT
ejpam-3007	130	8	s11(k	s11(k	NOUN
ejpam-3007	130	9	)	)	PUNCT
ejpam-3007	130	10	s11(−k	s11(−k	NOUN
ejpam-3007	130	11	)	)	PUNCT
ejpam-3007	130	12	=	=	SYM
ejpam-3007	130	13	exp(2iδ(k	exp(2iδ(k	NOUN
ejpam-3007	130	14	)	)	PUNCT
ejpam-3007	130	15	)	)	PUNCT
ejpam-3007	130	16	,	,	PUNCT
ejpam-3007	130	17	δ(k	δ(k	NOUN
ejpam-3007	130	18	)	)	PUNCT
ejpam-3007	130	19	=	=	SYM
ejpam-3007	130	20	arg(s11(k	arg(s11(k	PROPN
ejpam-3007	130	21	)	)	PUNCT
ejpam-3007	130	22	)	)	PUNCT
ejpam-3007	130	23	.	.	PUNCT
ejpam-3007	131	1	(	(	PUNCT
ejpam-3007	131	2	26	26	NUM
ejpam-3007	131	3	)	)	PUNCT
ejpam-3007	131	4	now	now	ADV
ejpam-3007	131	5	we	we	PRON
ejpam-3007	131	6	can	can	AUX
ejpam-3007	131	7	formulate	formulate	VERB
ejpam-3007	131	8	the	the	DET
ejpam-3007	131	9	following	follow	VERB
ejpam-3007	131	10	theorem	theorem	NOUN
ejpam-3007	131	11	.	.	PUNCT
ejpam-3007	131	12	theorem	theorem	NOUN
ejpam-3007	131	13	4	4	NUM
ejpam-3007	131	14	.	.	PUNCT
ejpam-3007	132	1	the	the	DET
ejpam-3007	132	2	following	follow	VERB
ejpam-3007	132	3	equations	equation	NOUN
ejpam-3007	132	4	are	be	AUX
ejpam-3007	132	5	true	true	ADJ
ejpam-3007	132	6	u(k	u(k	PROPN
ejpam-3007	132	7	)	)	PUNCT
ejpam-3007	132	8	=	=	PUNCT
ejpam-3007	133	1	(	(	PUNCT
ejpam-3007	133	2	1	1	NUM
ejpam-3007	133	3	+	+	NUM
ejpam-3007	133	4	cos(2δ(k)))r1	cos(2δ(k)))r1	NOUN
ejpam-3007	133	5	+	+	CCONJ
ejpam-3007	133	6	sin(2δ(k))r2	sin(2δ(k))r2	ADJ
ejpam-3007	133	7	sin(2δ(k	sin(2δ(k	NOUN
ejpam-3007	133	8	)	)	PUNCT
ejpam-3007	133	9	)	)	PUNCT
ejpam-3007	133	10	,	,	PUNCT
ejpam-3007	133	11	v	v	X
ejpam-3007	133	12	=	=	SYM
ejpam-3007	133	13	(	(	PUNCT
ejpam-3007	133	14	−1	−1	NOUN
ejpam-3007	133	15	+	+	NUM
ejpam-3007	133	16	sin(2δ(k)))r1	sin(2δ(k)))r1	NOUN
ejpam-3007	134	1	+	+	CCONJ
ejpam-3007	134	2	(	(	PUNCT
ejpam-3007	134	3	1−	1−	NUM
ejpam-3007	134	4	cos(2δ(k)))r2	cos(2δ(k)))r2	NOUN
ejpam-3007	134	5	sin(2δ(k	sin(2δ(k	NOUN
ejpam-3007	134	6	)	)	PUNCT
ejpam-3007	134	7	)	)	PUNCT
ejpam-3007	135	1	(	(	PUNCT
ejpam-3007	135	2	27	27	NUM
ejpam-3007	135	3	)	)	PUNCT
ejpam-3007	135	4	a.	a.	NOUN
ejpam-3007	135	5	durmagambetov	durmagambetov	PROPN
ejpam-3007	135	6	/	/	SYM
ejpam-3007	135	7	eur	eur	PROPN
ejpam-3007	135	8	.	.	PUNCT
ejpam-3007	136	1	j.	j.	PROPN
ejpam-3007	136	2	pure	pure	PROPN
ejpam-3007	136	3	appl	appl	PROPN
ejpam-3007	136	4	.	.	PROPN
ejpam-3007	136	5	math	math	PROPN
ejpam-3007	136	6	,	,	PUNCT
ejpam-3007	136	7	10	10	NUM
ejpam-3007	136	8	(	(	PUNCT
ejpam-3007	136	9	4	4	NUM
ejpam-3007	136	10	)	)	PUNCT
ejpam-3007	136	11	(	(	PUNCT
ejpam-3007	136	12	2017	2017	NUM
ejpam-3007	136	13	)	)	PUNCT
ejpam-3007	136	14	,	,	PUNCT
ejpam-3007	136	15	763	763	NUM
ejpam-3007	136	16	-	-	SYM
ejpam-3007	136	17	785	785	NUM
ejpam-3007	136	18	769	769	NUM
ejpam-3007	136	19	proof	proof	NOUN
ejpam-3007	136	20	.	.	PUNCT
ejpam-3007	137	1	using	use	VERB
ejpam-3007	137	2	equation	equation	NOUN
ejpam-3007	137	3	(	(	PUNCT
ejpam-3007	137	4	26	26	NUM
ejpam-3007	137	5	)	)	PUNCT
ejpam-3007	137	6	and	and	CCONJ
ejpam-3007	137	7	representation	representation	NOUN
ejpam-3007	137	8	for	for	ADP
ejpam-3007	137	9	fourier	fourier	ADJ
ejpam-3007	137	10	transformation	transformation	NOUN
ejpam-3007	137	11	we	we	PRON
ejpam-3007	137	12	obtain	obtain	VERB
ejpam-3007	137	13	whence	whence	NOUN
ejpam-3007	137	14	,	,	PUNCT
ejpam-3007	137	15	solving	solve	VERB
ejpam-3007	137	16	the	the	DET
ejpam-3007	137	17	equation	equation	NOUN
ejpam-3007	137	18	for	for	ADP
ejpam-3007	137	19	u	u	NOUN
ejpam-3007	137	20	and	and	CCONJ
ejpam-3007	137	21	v	v	NOUN
ejpam-3007	137	22	,	,	PUNCT
ejpam-3007	137	23	we	we	PRON
ejpam-3007	137	24	obtain	obtain	VERB
ejpam-3007	137	25	u(k	u(k	PROPN
ejpam-3007	137	26	)	)	PUNCT
ejpam-3007	138	1	+	+	PUNCT
ejpam-3007	138	2	iv(k	iv(k	NOUN
ejpam-3007	138	3	)	)	PUNCT
ejpam-3007	139	1	+	+	PUNCT
ejpam-3007	139	2	i1(k	i1(k	X
ejpam-3007	139	3	)	)	PUNCT
ejpam-3007	139	4	=	=	NOUN
ejpam-3007	139	5	(	(	PUNCT
ejpam-3007	139	6	u(k)−	u(k)−	PROPN
ejpam-3007	139	7	iv(k	iv(k	PUNCT
ejpam-3007	139	8	)	)	PUNCT
ejpam-3007	139	9	+	+	CCONJ
ejpam-3007	139	10	i2(k))(cos(2δ(k	i2(k))(cos(2δ(k	NOUN
ejpam-3007	139	11	)	)	PUNCT
ejpam-3007	139	12	)	)	PUNCT
ejpam-3007	140	1	+	+	CCONJ
ejpam-3007	140	2	i	i	PRON
ejpam-3007	140	3	sin(2δ(k	sin(2δ(k	NOUN
ejpam-3007	140	4	)	)	PUNCT
ejpam-3007	140	5	)	)	PUNCT
ejpam-3007	140	6	)	)	PUNCT
ejpam-3007	140	7	,	,	PUNCT
ejpam-3007	140	8	(	(	PUNCT
ejpam-3007	140	9	28	28	NUM
ejpam-3007	140	10	)	)	PUNCT
ejpam-3007	140	11	from	from	ADP
ejpam-3007	140	12	last	last	ADJ
ejpam-3007	140	13	equation	equation	NOUN
ejpam-3007	140	14	we	we	PRON
ejpam-3007	140	15	have	have	VERB
ejpam-3007	140	16	u(k)(1−	u(k)(1−	PROPN
ejpam-3007	140	17	cos(2δ(k	cos(2δ(k	NOUN
ejpam-3007	140	18	)	)	PUNCT
ejpam-3007	140	19	)	)	PUNCT
ejpam-3007	140	20	)	)	PUNCT
ejpam-3007	140	21	)	)	PUNCT
ejpam-3007	141	1	+	+	CCONJ
ejpam-3007	141	2	v(k)(1−	v(k)(1−	X
ejpam-3007	141	3	sin(2δ(k	sin(2δ(k	NOUN
ejpam-3007	141	4	)	)	PUNCT
ejpam-3007	141	5	)	)	PUNCT
ejpam-3007	141	6	)	)	PUNCT
ejpam-3007	142	1	=	=	SYM
ejpam-3007	142	2	r1	r1	PROPN
ejpam-3007	142	3	,	,	PUNCT
ejpam-3007	142	4	(	(	PUNCT
ejpam-3007	142	5	29	29	NUM
ejpam-3007	142	6	)	)	PUNCT
ejpam-3007	142	7	−u(k	−u(k	ADJ
ejpam-3007	142	8	)	)	PUNCT
ejpam-3007	142	9	sin(2δ(k	sin(2δ(k	NOUN
ejpam-3007	142	10	)	)	PUNCT
ejpam-3007	142	11	)	)	PUNCT
ejpam-3007	143	1	+	+	CCONJ
ejpam-3007	143	2	v(k)(1	v(k)(1	PROPN
ejpam-3007	143	3	+	+	CCONJ
ejpam-3007	143	4	cos(2δ(k	cos(2δ(k	PROPN
ejpam-3007	143	5	)	)	PUNCT
ejpam-3007	143	6	)	)	PUNCT
ejpam-3007	143	7	)	)	PUNCT
ejpam-3007	144	1	=	=	SYM
ejpam-3007	144	2	r2	r2	PROPN
ejpam-3007	144	3	(	(	PUNCT
ejpam-3007	144	4	30	30	NUM
ejpam-3007	144	5	)	)	PUNCT
ejpam-3007	144	6	where	where	SCONJ
ejpam-3007	144	7	r1	r1	PROPN
ejpam-3007	144	8	=	=	SYM
ejpam-3007	144	9	real(−i1	real(−i1	PROPN
ejpam-3007	144	10	+	+	CCONJ
ejpam-3007	144	11	i2	i2	PROPN
ejpam-3007	144	12	cos(2δ(k	cos(2δ(k	PROPN
ejpam-3007	144	13	)	)	PUNCT
ejpam-3007	144	14	)	)	PUNCT
ejpam-3007	144	15	+	+	CCONJ
ejpam-3007	144	16	i(i1	i(i1	NOUN
ejpam-3007	144	17	sin(2δ(k	sin(2δ(k	PROPN
ejpam-3007	144	18	)	)	PUNCT
ejpam-3007	144	19	)	)	PUNCT
ejpam-3007	144	20	)	)	PUNCT
ejpam-3007	144	21	)	)	PUNCT
ejpam-3007	144	22	,	,	PUNCT
ejpam-3007	144	23	(	(	PUNCT
ejpam-3007	144	24	31	31	NUM
ejpam-3007	144	25	)	)	PUNCT
ejpam-3007	144	26	r2	r2	NOUN
ejpam-3007	144	27	=	=	SYM
ejpam-3007	144	28	im(−i1	im(−i1	PROPN
ejpam-3007	144	29	+	+	PROPN
ejpam-3007	144	30	i2	i2	PROPN
ejpam-3007	144	31	cos(2δ(k	cos(2δ(k	PROPN
ejpam-3007	144	32	)	)	PUNCT
ejpam-3007	144	33	)	)	PUNCT
ejpam-3007	145	1	+	+	CCONJ
ejpam-3007	145	2	i(i1	i(i1	NOUN
ejpam-3007	145	3	sin(2δ(k	sin(2δ(k	PROPN
ejpam-3007	145	4	)	)	PUNCT
ejpam-3007	145	5	)	)	PUNCT
ejpam-3007	145	6	.	.	PUNCT
ejpam-3007	146	1	(	(	PUNCT
ejpam-3007	146	2	32	32	NUM
ejpam-3007	146	3	)	)	PUNCT
ejpam-3007	146	4	theorem	theorem	NOUN
ejpam-3007	146	5	5	5	NUM
ejpam-3007	146	6	.	.	PUNCT
ejpam-3007	147	1	if	if	SCONJ
ejpam-3007	147	2	δ(k)(k	δ(k)(k	NOUN
ejpam-3007	147	3	)	)	PUNCT
ejpam-3007	148	1	=	=	SYM
ejpam-3007	148	2	0	0	NUM
ejpam-3007	148	3	,	,	PUNCT
ejpam-3007	148	4	|q̃(k)|	|q̃(k)|	VERB
ejpam-3007	148	5	<	<	X
ejpam-3007	148	6	c	c	X
ejpam-3007	148	7	<	<	X
ejpam-3007	148	8	∞	∞	NUM
ejpam-3007	148	9	then	then	ADV
ejpam-3007	148	10	r1(k	r1(k	NOUN
ejpam-3007	148	11	)	)	PUNCT
ejpam-3007	148	12	=	=	SYM
ejpam-3007	148	13	0	0	X
ejpam-3007	148	14	.	.	PUNCT
ejpam-3007	149	1	proof	proof	NOUN
ejpam-3007	149	2	.	.	PUNCT
ejpam-3007	150	1	using	use	VERB
ejpam-3007	150	2	equation	equation	NOUN
ejpam-3007	150	3	(	(	PUNCT
ejpam-3007	150	4	30	30	NUM
ejpam-3007	150	5	-	-	SYM
ejpam-3007	150	6	31	31	NUM
ejpam-3007	150	7	)	)	PUNCT
ejpam-3007	150	8	and	and	CCONJ
ejpam-3007	150	9	conditional	conditional	ADJ
ejpam-3007	150	10	theorem	theorem	NOUN
ejpam-3007	150	11	we	we	PRON
ejpam-3007	150	12	obtain	obtain	VERB
ejpam-3007	150	13	proof	proof	NOUN
ejpam-3007	150	14	.	.	PUNCT
ejpam-3007	151	1	theorem	theorem	VERB
ejpam-3007	151	2	6	6	NUM
ejpam-3007	151	3	.	.	PUNCT
ejpam-3007	152	1	the	the	DET
ejpam-3007	152	2	following	follow	VERB
ejpam-3007	152	3	estimates	estimate	NOUN
ejpam-3007	152	4	are	be	AUX
ejpam-3007	152	5	true	true	ADJ
ejpam-3007	152	6	for	for	ADP
ejpam-3007	152	7	fourier	fouri	ADJ
ejpam-3007	152	8	transformation	transformation	NOUN
ejpam-3007	152	9	|u|	|u|	ADP
ejpam-3007	152	10	<	<	X
ejpam-3007	152	11	c(|r1|+	c(|r1|+	PROPN
ejpam-3007	152	12	|r2|+	|r2|+	PROPN
ejpam-3007	152	13	|∇r1|	|∇r1|	PROPN
ejpam-3007	152	14	)	)	PUNCT
ejpam-3007	152	15	,	,	PUNCT
ejpam-3007	152	16	(	(	PUNCT
ejpam-3007	152	17	33	33	NUM
ejpam-3007	152	18	)	)	PUNCT
ejpam-3007	152	19	|v|	|v|	PROPN
ejpam-3007	152	20	<	<	X
ejpam-3007	152	21	c(|r1|+	c(|r1|+	PROPN
ejpam-3007	152	22	|r2|+	|r2|+	PROPN
ejpam-3007	152	23	|∇r1|	|∇r1|	PROPN
ejpam-3007	152	24	)	)	PUNCT
ejpam-3007	152	25	,	,	PUNCT
ejpam-3007	152	26	(	(	PUNCT
ejpam-3007	152	27	34	34	NUM
ejpam-3007	152	28	)	)	PUNCT
ejpam-3007	152	29	|̃q|	|̃q|	NOUN
ejpam-3007	152	30	<	<	X
ejpam-3007	152	31	c(|r1|+	c(|r1|+	PROPN
ejpam-3007	152	32	|r2|+	|r2|+	PROPN
ejpam-3007	152	33	|∇r1|	|∇r1|	PROPN
ejpam-3007	152	34	)	)	PUNCT
ejpam-3007	152	35	.	.	PUNCT
ejpam-3007	153	1	(	(	PUNCT
ejpam-3007	153	2	35	35	NUM
ejpam-3007	153	3	)	)	PUNCT
ejpam-3007	153	4	proof	proof	NOUN
ejpam-3007	153	5	.	.	PUNCT
ejpam-3007	154	1	follows	follow	VERB
ejpam-3007	154	2	from	from	ADP
ejpam-3007	154	3	the	the	DET
ejpam-3007	154	4	representation	representation	NOUN
ejpam-3007	154	5	of	of	ADP
ejpam-3007	154	6	u	u	PROPN
ejpam-3007	154	7	,	,	PUNCT
ejpam-3007	154	8	v.	v.	CCONJ
ejpam-3007	154	9	here	here	ADV
ejpam-3007	154	10	,	,	PUNCT
ejpam-3007	154	11	we	we	PRON
ejpam-3007	154	12	just	just	ADV
ejpam-3007	154	13	point	point	VERB
ejpam-3007	154	14	out	out	ADP
ejpam-3007	154	15	this	this	PRON
ejpam-3007	154	16	as	as	ADP
ejpam-3007	154	17	a	a	DET
ejpam-3007	154	18	separate	separate	ADJ
ejpam-3007	154	19	theorem	theorem	NOUN
ejpam-3007	154	20	in	in	ADP
ejpam-3007	154	21	order	order	NOUN
ejpam-3007	154	22	to	to	PART
ejpam-3007	154	23	emphasize	emphasize	VERB
ejpam-3007	154	24	the	the	DET
ejpam-3007	154	25	significance	significance	NOUN
ejpam-3007	154	26	of	of	ADP
ejpam-3007	154	27	this	this	DET
ejpam-3007	154	28	result	result	NOUN
ejpam-3007	154	29	.	.	PUNCT
ejpam-3007	155	1	we	we	PRON
ejpam-3007	155	2	note	note	VERB
ejpam-3007	155	3	separately	separately	ADV
ejpam-3007	155	4	the	the	DET
ejpam-3007	155	5	terms	term	NOUN
ejpam-3007	155	6	with	with	ADP
ejpam-3007	155	7	a	a	DET
ejpam-3007	155	8	derivative	derivative	ADJ
ejpam-3007	155	9	∇r1	∇r1	NOUN
ejpam-3007	155	10	.	.	PUNCT
ejpam-3007	156	1	obviously	obviously	ADV
ejpam-3007	156	2	,	,	PUNCT
ejpam-3007	156	3	these	these	DET
ejpam-3007	156	4	terms	term	NOUN
ejpam-3007	156	5	are	be	AUX
ejpam-3007	156	6	appeared	appear	VERB
ejpam-3007	156	7	due	due	ADJ
ejpam-3007	156	8	to	to	ADP
ejpam-3007	156	9	points	point	NOUN
ejpam-3007	156	10	of	of	ADP
ejpam-3007	156	11	the	the	DET
ejpam-3007	156	12	phase	phase	NOUN
ejpam-3007	156	13	nulling	nulling	NOUN
ejpam-3007	156	14	.	.	PUNCT
ejpam-3007	157	1	theorem	theorem	VERB
ejpam-3007	157	2	7	7	NUM
ejpam-3007	157	3	.	.	X
ejpam-3007	157	4	for	for	ADP
ejpam-3007	157	5	estimation	estimation	NOUN
ejpam-3007	157	6	of	of	ADP
ejpam-3007	157	7	a	a	DET
ejpam-3007	157	8	maximum	maximum	NOUN
ejpam-3007	157	9	of	of	ADP
ejpam-3007	157	10	the	the	DET
ejpam-3007	157	11	potential	potential	NOUN
ejpam-3007	157	12	the	the	DET
ejpam-3007	157	13	following	follow	VERB
ejpam-3007	157	14	estimates	estimate	NOUN
ejpam-3007	157	15	are	be	AUX
ejpam-3007	157	16	true	true	ADJ
ejpam-3007	157	17	|q|	|q|	VERB
ejpam-3007	157	18	<	<	X
ejpam-3007	157	19	c	c	PROPN
ejpam-3007	157	20	+	+	PROPN
ejpam-3007	157	21	∞∫	∞∫	PROPN
ejpam-3007	157	22	−∞	−∞	ADP
ejpam-3007	157	23	(	(	PUNCT
ejpam-3007	157	24	c(|i1|+	c(|i1|+	X
ejpam-3007	157	25	|i2|+	|i2|+	X
ejpam-3007	157	26	|∇i1|+	|∇i1|+	PROPN
ejpam-3007	157	27	|∇i2|))dk	|∇i2|))dk	X
ejpam-3007	157	28	(	(	PUNCT
ejpam-3007	157	29	36	36	NUM
ejpam-3007	157	30	)	)	PUNCT
ejpam-3007	157	31	proof	proof	NOUN
ejpam-3007	157	32	.	.	PUNCT
ejpam-3007	158	1	follows	follow	VERB
ejpam-3007	158	2	from	from	ADP
ejpam-3007	158	3	the	the	DET
ejpam-3007	158	4	estimation	estimation	NOUN
ejpam-3007	158	5	of	of	ADP
ejpam-3007	158	6	u	u	PROPN
ejpam-3007	158	7	,	,	PUNCT
ejpam-3007	158	8	v	v	NOUN
ejpam-3007	158	9	and	and	CCONJ
ejpam-3007	158	10	use	use	VERB
ejpam-3007	158	11	ofr1	ofr1	PROPN
ejpam-3007	158	12	,	,	PUNCT
ejpam-3007	158	13	r2	r2	NOUN
ejpam-3007	158	14	which	which	PRON
ejpam-3007	158	15	are	be	AUX
ejpam-3007	158	16	simple	simple	ADJ
ejpam-3007	158	17	arguments	argument	NOUN
ejpam-3007	158	18	.	.	PUNCT
ejpam-3007	159	1	here	here	ADV
ejpam-3007	159	2	we	we	PRON
ejpam-3007	159	3	outline	outline	VERB
ejpam-3007	159	4	the	the	DET
ejpam-3007	159	5	theorem	theorem	NOUN
ejpam-3007	159	6	in	in	ADP
ejpam-3007	159	7	order	order	NOUN
ejpam-3007	159	8	to	to	PART
ejpam-3007	159	9	emphasize	emphasize	VERB
ejpam-3007	159	10	importance	importance	NOUN
ejpam-3007	159	11	of	of	ADP
ejpam-3007	159	12	this	this	DET
ejpam-3007	159	13	result	result	NOUN
ejpam-3007	159	14	for	for	ADP
ejpam-3007	159	15	3dimentional	3dimentional	PROPN
ejpam-3007	159	16	case	case	NOUN
ejpam-3007	159	17	.	.	PUNCT
ejpam-3007	160	1	analyzing	analyze	VERB
ejpam-3007	160	2	the	the	DET
ejpam-3007	160	3	last	last	ADJ
ejpam-3007	160	4	formula	formula	NOUN
ejpam-3007	160	5	,	,	PUNCT
ejpam-3007	160	6	we	we	PRON
ejpam-3007	160	7	see	see	VERB
ejpam-3007	160	8	again	again	ADV
ejpam-3007	160	9	an	an	DET
ejpam-3007	160	10	effect	effect	NOUN
ejpam-3007	160	11	of	of	ADP
ejpam-3007	160	12	the	the	DET
ejpam-3007	160	13	phase	phase	NOUN
ejpam-3007	160	14	on	on	ADP
ejpam-3007	160	15	the	the	DET
ejpam-3007	160	16	function	function	NOUN
ejpam-3007	160	17	behavior	behavior	NOUN
ejpam-3007	160	18	.	.	PUNCT
ejpam-3007	161	1	in	in	ADP
ejpam-3007	161	2	addition	addition	NOUN
ejpam-3007	161	3	,	,	PUNCT
ejpam-3007	161	4	a	a	DET
ejpam-3007	161	5	finiteness	finiteness	NOUN
ejpam-3007	161	6	of	of	ADP
ejpam-3007	161	7	the	the	DET
ejpam-3007	161	8	discrete	discrete	ADJ
ejpam-3007	161	9	spectrum	spectrum	NOUN
ejpam-3007	161	10	is	be	AUX
ejpam-3007	161	11	the	the	DET
ejpam-3007	161	12	main	main	ADJ
ejpam-3007	161	13	requirement	requirement	NOUN
ejpam-3007	161	14	of	of	ADP
ejpam-3007	161	15	the	the	DET
ejpam-3007	161	16	gradient	gradient	NOUN
ejpam-3007	161	17	catastrophe	catastrophe	NOUN
ejpam-3007	161	18	nonoccurrence	nonoccurrence	NOUN
ejpam-3007	161	19	.	.	PUNCT
ejpam-3007	162	1	and	and	CCONJ
ejpam-3007	162	2	from	from	ADP
ejpam-3007	162	3	other	other	ADJ
ejpam-3007	162	4	hand	hand	NOUN
ejpam-3007	162	5	,	,	PUNCT
ejpam-3007	162	6	in	in	ADP
ejpam-3007	162	7	case	case	NOUN
ejpam-3007	162	8	of	of	ADP
ejpam-3007	162	9	a.	a.	NOUN
ejpam-3007	162	10	durmagambetov	durmagambetov	PROPN
ejpam-3007	162	11	/	/	SYM
ejpam-3007	162	12	eur	eur	PROPN
ejpam-3007	162	13	.	.	PUNCT
ejpam-3007	163	1	j.	j.	PROPN
ejpam-3007	163	2	pure	pure	PROPN
ejpam-3007	163	3	appl	appl	PROPN
ejpam-3007	163	4	.	.	PROPN
ejpam-3007	163	5	math	math	PROPN
ejpam-3007	163	6	,	,	PUNCT
ejpam-3007	163	7	10	10	NUM
ejpam-3007	163	8	(	(	PUNCT
ejpam-3007	163	9	4	4	NUM
ejpam-3007	163	10	)	)	PUNCT
ejpam-3007	163	11	(	(	PUNCT
ejpam-3007	163	12	2017	2017	NUM
ejpam-3007	163	13	)	)	PUNCT
ejpam-3007	163	14	,	,	PUNCT
ejpam-3007	163	15	763	763	NUM
ejpam-3007	163	16	-	-	SYM
ejpam-3007	163	17	785	785	NUM
ejpam-3007	163	18	770	770	NUM
ejpam-3007	163	19	unconstrained	unconstrained	ADJ
ejpam-3007	163	20	growth	growth	NOUN
ejpam-3007	163	21	of	of	ADP
ejpam-3007	163	22	points	point	NOUN
ejpam-3007	163	23	in	in	ADP
ejpam-3007	163	24	discrete	discrete	ADJ
ejpam-3007	163	25	spectrum	spectrum	NOUN
ejpam-3007	163	26	,	,	PUNCT
ejpam-3007	163	27	we	we	PRON
ejpam-3007	163	28	fall	fall	VERB
ejpam-3007	163	29	into	into	ADP
ejpam-3007	163	30	the	the	DET
ejpam-3007	163	31	terms	term	NOUN
ejpam-3007	163	32	of	of	ADP
ejpam-3007	163	33	theorems	theorem	NOUN
ejpam-3007	163	34	1	1	NUM
ejpam-3007	163	35	and	and	CCONJ
ejpam-3007	163	36	2	2	NUM
ejpam-3007	163	37	.	.	X
ejpam-3007	164	1	the	the	DET
ejpam-3007	164	2	last	last	ADJ
ejpam-3007	164	3	theorem	theorem	NOUN
ejpam-3007	164	4	expands	expand	VERB
ejpam-3007	164	5	a	a	DET
ejpam-3007	164	6	class	class	NOUN
ejpam-3007	164	7	of	of	ADP
ejpam-3007	164	8	functions	function	NOUN
ejpam-3007	164	9	described	describe	VERB
ejpam-3007	164	10	in	in	ADP
ejpam-3007	164	11	in	in	ADP
ejpam-3007	164	12	theorem	theorem	NOUN
ejpam-3007	164	13	1	1	NUM
ejpam-3007	164	14	,	,	PUNCT
ejpam-3007	164	15	as	as	SCONJ
ejpam-3007	164	16	we	we	PRON
ejpam-3007	164	17	planned	plan	VERB
ejpam-3007	164	18	at	at	ADP
ejpam-3007	164	19	the	the	DET
ejpam-3007	164	20	beginning	beginning	NOUN
ejpam-3007	164	21	.	.	PUNCT
ejpam-3007	165	1	now	now	ADV
ejpam-3007	165	2	,	,	PUNCT
ejpam-3007	165	3	studying	study	VERB
ejpam-3007	165	4	the	the	DET
ejpam-3007	165	5	behavior	behavior	NOUN
ejpam-3007	165	6	of	of	ADP
ejpam-3007	165	7	a	a	DET
ejpam-3007	165	8	gradient	gradient	NOUN
ejpam-3007	165	9	depending	depend	VERB
ejpam-3007	165	10	on	on	ADP
ejpam-3007	165	11	q	q	NOUN
ejpam-3007	165	12	we	we	PRON
ejpam-3007	165	13	come	come	VERB
ejpam-3007	165	14	to	to	ADP
ejpam-3007	165	15	the	the	DET
ejpam-3007	165	16	conclusion	conclusion	NOUN
ejpam-3007	165	17	that	that	SCONJ
ejpam-3007	165	18	its	its	PRON
ejpam-3007	165	19	unconstrained	unconstrained	ADJ
ejpam-3007	165	20	growth	growth	NOUN
ejpam-3007	165	21	will	will	AUX
ejpam-3007	165	22	be	be	AUX
ejpam-3007	165	23	dictated	dictate	VERB
ejpam-3007	165	24	by	by	ADP
ejpam-3007	165	25	the	the	DET
ejpam-3007	165	26	phase	phase	NOUN
ejpam-3007	165	27	cluster	cluster	NOUN
ejpam-3007	165	28	point	point	NOUN
ejpam-3007	165	29	,	,	PUNCT
ejpam-3007	165	30	which	which	PRON
ejpam-3007	165	31	,	,	PUNCT
ejpam-3007	165	32	in	in	ADP
ejpam-3007	165	33	its	its	PRON
ejpam-3007	165	34	turn	turn	NOUN
ejpam-3007	165	35	,	,	PUNCT
ejpam-3007	165	36	is	be	AUX
ejpam-3007	165	37	due	due	ADJ
ejpam-3007	165	38	to	to	PART
ejpam-3007	165	39	discrete	discrete	VERB
ejpam-3007	165	40	spectrum	spectrum	NOUN
ejpam-3007	165	41	acquisition	acquisition	NOUN
ejpam-3007	165	42	.	.	PUNCT
ejpam-3007	166	1	hence	hence	ADV
ejpam-3007	166	2	we	we	PRON
ejpam-3007	166	3	get	get	VERB
ejpam-3007	166	4	the	the	DET
ejpam-3007	166	5	most	most	ADV
ejpam-3007	166	6	important	important	ADJ
ejpam-3007	166	7	conclusion	conclusion	NOUN
ejpam-3007	166	8	we	we	PRON
ejpam-3007	166	9	get	get	VERB
ejpam-3007	166	10	information	information	NOUN
ejpam-3007	166	11	about	about	ADP
ejpam-3007	166	12	the	the	DET
ejpam-3007	166	13	catastrophe	catastrophe	NOUN
ejpam-3007	166	14	with	with	ADP
ejpam-3007	166	15	discrete	discrete	ADJ
ejpam-3007	166	16	jumps	jump	NOUN
ejpam-3007	166	17	!	!	PUNCT
ejpam-3007	167	1	theorem	theorem	VERB
ejpam-3007	167	2	8	8	NUM
ejpam-3007	167	3	.	.	PUNCT
ejpam-3007	168	1	for	for	ADP
ejpam-3007	168	2	a	a	DET
ejpam-3007	168	3	potential	potential	NOUN
ejpam-3007	168	4	the	the	DET
ejpam-3007	168	5	following	follow	VERB
ejpam-3007	168	6	representation	representation	NOUN
ejpam-3007	168	7	is	be	AUX
ejpam-3007	168	8	true	true	ADJ
ejpam-3007	168	9	q	q	NOUN
ejpam-3007	168	10	=	=	SYM
ejpam-3007	168	11	q(q	q(q	PROPN
ejpam-3007	168	12	,	,	PUNCT
ejpam-3007	168	13	e1	e1	PROPN
ejpam-3007	168	14	,	,	PUNCT
ejpam-3007	168	15	...	...	PUNCT
ejpam-3007	168	16	en	en	X
ejpam-3007	168	17	)	)	PUNCT
ejpam-3007	168	18	;	;	PUNCT
ejpam-3007	168	19	(	(	PUNCT
ejpam-3007	168	20	37	37	X
ejpam-3007	168	21	)	)	PUNCT
ejpam-3007	168	22	proof	proof	NOUN
ejpam-3007	168	23	.	.	PUNCT
ejpam-3007	169	1	just	just	ADV
ejpam-3007	169	2	consists	consist	VERB
ejpam-3007	169	3	in	in	ADP
ejpam-3007	169	4	calculating	calculate	VERB
ejpam-3007	169	5	i1(k	i1(k	NOUN
ejpam-3007	169	6	)	)	PUNCT
ejpam-3007	169	7	,	,	PUNCT
ejpam-3007	169	8	i2(k	i2(k	PROPN
ejpam-3007	169	9	)	)	PUNCT
ejpam-3007	169	10	in	in	ADP
ejpam-3007	169	11	a	a	DET
ejpam-3007	169	12	form	form	NOUN
ejpam-3007	169	13	of	of	ADP
ejpam-3007	169	14	series	series	NOUN
ejpam-3007	169	15	of	of	ADP
ejpam-3007	169	16	q	q	NOUN
ejpam-3007	169	17	and	and	CCONJ
ejpam-3007	169	18	substitution	substitution	NOUN
ejpam-3007	169	19	of	of	ADP
ejpam-3007	169	20	a	a	DET
ejpam-3007	169	21	result	result	NOUN
ejpam-3007	169	22	of	of	ADP
ejpam-3007	169	23	the	the	DET
ejpam-3007	169	24	calculation	calculation	NOUN
ejpam-3007	169	25	into	into	ADP
ejpam-3007	169	26	the	the	DET
ejpam-3007	169	27	formula	formula	NOUN
ejpam-3007	169	28	for	for	ADP
ejpam-3007	169	29	u	u	NOUN
ejpam-3007	169	30	,	,	PUNCT
ejpam-3007	169	31	v	v	ADP
ejpam-3007	169	32	moreover	moreover	ADV
ejpam-3007	169	33	a	a	DET
ejpam-3007	169	34	right	right	ADJ
ejpam-3007	169	35	side	side	NOUN
ejpam-3007	169	36	of	of	ADP
ejpam-3007	169	37	the	the	DET
ejpam-3007	169	38	obtained	obtain	VERB
ejpam-3007	169	39	formula	formula	NOUN
ejpam-3007	169	40	contains	contain	VERB
ejpam-3007	169	41	second	second	ADJ
ejpam-3007	169	42	-	-	PUNCT
ejpam-3007	169	43	order	order	NOUN
ejpam-3007	169	44	terms	term	NOUN
ejpam-3007	169	45	only	only	ADV
ejpam-3007	169	46	.	.	PUNCT
ejpam-3007	170	1	this	this	DET
ejpam-3007	170	2	representation	representation	NOUN
ejpam-3007	170	3	,	,	PUNCT
ejpam-3007	170	4	in	in	ADP
ejpam-3007	170	5	contrast	contrast	NOUN
ejpam-3007	170	6	to	to	ADP
ejpam-3007	170	7	the	the	DET
ejpam-3007	170	8	classical	classical	ADJ
ejpam-3007	170	9	inverse	inverse	NOUN
ejpam-3007	170	10	problems	problem	NOUN
ejpam-3007	170	11	,	,	PUNCT
ejpam-3007	170	12	allows	allow	VERB
ejpam-3007	170	13	using	use	VERB
ejpam-3007	170	14	arbitrary	arbitrary	ADJ
ejpam-3007	170	15	information	information	NOUN
ejpam-3007	170	16	on	on	ADP
ejpam-3007	170	17	the	the	DET
ejpam-3007	170	18	potential	potential	NOUN
ejpam-3007	170	19	for	for	ADP
ejpam-3007	170	20	closure	closure	NOUN
ejpam-3007	170	21	of	of	ADP
ejpam-3007	170	22	these	these	DET
ejpam-3007	170	23	equations	equation	NOUN
ejpam-3007	170	24	,	,	PUNCT
ejpam-3007	170	25	because	because	SCONJ
ejpam-3007	170	26	a	a	DET
ejpam-3007	170	27	skeleton	skeleton	NOUN
ejpam-3007	170	28	of	of	ADP
ejpam-3007	170	29	this	this	DET
ejpam-3007	170	30	integral	integral	ADJ
ejpam-3007	170	31	equation	equation	NOUN
ejpam-3007	170	32	is	be	AUX
ejpam-3007	170	33	represented	represent	VERB
ejpam-3007	170	34	by	by	ADP
ejpam-3007	170	35	sets	set	NOUN
ejpam-3007	170	36	of	of	ADP
ejpam-3007	170	37	constants	constant	NOUN
ejpam-3007	170	38	in	in	ADP
ejpam-3007	170	39	the	the	DET
ejpam-3007	170	40	form	form	NOUN
ejpam-3007	170	41	of	of	ADP
ejpam-3007	170	42	eigenvalues	eigenvalue	NOUN
ejpam-3007	170	43	.	.	PUNCT
ejpam-3007	171	1	one	one	NUM
ejpam-3007	171	2	of	of	ADP
ejpam-3007	171	3	the	the	DET
ejpam-3007	171	4	surprising	surprising	ADJ
ejpam-3007	171	5	properties	property	NOUN
ejpam-3007	171	6	of	of	ADP
ejpam-3007	171	7	this	this	DET
ejpam-3007	171	8	representation	representation	NOUN
ejpam-3007	171	9	and	and	CCONJ
ejpam-3007	171	10	all	all	DET
ejpam-3007	171	11	this	this	DET
ejpam-3007	171	12	research	research	NOUN
ejpam-3007	171	13	is	be	AUX
ejpam-3007	171	14	discreteness	discreteness	NOUN
ejpam-3007	171	15	in	in	ADP
ejpam-3007	171	16	continuity	continuity	NOUN
ejpam-3007	171	17	.	.	PUNCT
ejpam-3007	172	1	since	since	SCONJ
ejpam-3007	172	2	a	a	DET
ejpam-3007	172	3	value	value	NOUN
ejpam-3007	172	4	of	of	ADP
ejpam-3007	172	5	the	the	DET
ejpam-3007	172	6	phase	phase	NOUN
ejpam-3007	172	7	,	,	PUNCT
ejpam-3007	172	8	as	as	SCONJ
ejpam-3007	172	9	we	we	PRON
ejpam-3007	172	10	can	can	AUX
ejpam-3007	172	11	see	see	VERB
ejpam-3007	172	12	,	,	PUNCT
ejpam-3007	172	13	changes	change	NOUN
ejpam-3007	172	14	discontinuously	discontinuously	ADV
ejpam-3007	172	15	,	,	PUNCT
ejpam-3007	172	16	while	while	SCONJ
ejpam-3007	172	17	a	a	DET
ejpam-3007	172	18	potential	potential	ADJ
ejpam-3007	172	19	-	-	PUNCT
ejpam-3007	172	20	function	function	NOUN
ejpam-3007	172	21	itself	itself	PRON
ejpam-3007	172	22	may	may	AUX
ejpam-3007	172	23	vary	vary	VERB
ejpam-3007	172	24	continuously	continuously	ADV
ejpam-3007	172	25	.	.	PUNCT
ejpam-3007	173	1	this	this	PRON
ejpam-3007	173	2	implies	imply	VERB
ejpam-3007	173	3	an	an	DET
ejpam-3007	173	4	important	important	ADJ
ejpam-3007	173	5	conclusion	conclusion	NOUN
ejpam-3007	173	6	about	about	ADP
ejpam-3007	173	7	the	the	DET
ejpam-3007	173	8	instability	instability	NOUN
ejpam-3007	173	9	in	in	ADP
ejpam-3007	173	10	numerical	numerical	ADJ
ejpam-3007	173	11	methods	method	NOUN
ejpam-3007	173	12	,	,	PUNCT
ejpam-3007	173	13	i.e.	i.e.	X
ejpam-3007	173	14	it	it	PRON
ejpam-3007	173	15	is	be	AUX
ejpam-3007	173	16	necessary	necessary	ADJ
ejpam-3007	173	17	to	to	PART
ejpam-3007	173	18	control	control	NOUN
ejpam-3007	173	19	phase	phase	NOUN
ejpam-3007	173	20	jumps	jump	VERB
ejpam-3007	173	21	in	in	ADP
ejpam-3007	173	22	numerical	numerical	ADJ
ejpam-3007	173	23	modeling	modeling	NOUN
ejpam-3007	173	24	to	to	PART
ejpam-3007	173	25	avoid	avoid	VERB
ejpam-3007	173	26	falling	fall	VERB
ejpam-3007	173	27	into	into	ADP
ejpam-3007	173	28	a	a	DET
ejpam-3007	173	29	state	state	NOUN
ejpam-3007	173	30	of	of	ADP
ejpam-3007	173	31	instability	instability	NOUN
ejpam-3007	173	32	.	.	PUNCT
ejpam-3007	174	1	a	a	DET
ejpam-3007	174	2	conclusion	conclusion	NOUN
ejpam-3007	174	3	of	of	ADP
ejpam-3007	174	4	nonscalability	nonscalability	NOUN
ejpam-3007	174	5	of	of	ADP
ejpam-3007	174	6	such	such	ADJ
ejpam-3007	174	7	models	model	NOUN
ejpam-3007	174	8	is	be	AUX
ejpam-3007	174	9	critically	critically	ADV
ejpam-3007	174	10	important	important	ADJ
ejpam-3007	174	11	since	since	SCONJ
ejpam-3007	174	12	eigenvalues	eigenvalue	NOUN
ejpam-3007	174	13	may	may	AUX
ejpam-3007	174	14	appear	appear	VERB
ejpam-3007	174	15	or	or	CCONJ
ejpam-3007	174	16	may	may	AUX
ejpam-3007	174	17	disappear	disappear	VERB
ejpam-3007	174	18	under	under	ADP
ejpam-3007	174	19	changes	change	NOUN
ejpam-3007	174	20	in	in	ADP
ejpam-3007	174	21	the	the	DET
ejpam-3007	174	22	potential	potential	ADJ
ejpam-3007	174	23	scale	scale	NOUN
ejpam-3007	174	24	,	,	PUNCT
ejpam-3007	174	25	whereupon	whereupon	ADV
ejpam-3007	174	26	a	a	DET
ejpam-3007	174	27	model	model	NOUN
ejpam-3007	174	28	will	will	AUX
ejpam-3007	174	29	be	be	AUX
ejpam-3007	174	30	changed	change	VERB
ejpam-3007	174	31	significantly	significantly	ADV
ejpam-3007	174	32	.	.	PUNCT
ejpam-3007	175	1	this	this	DET
ejpam-3007	175	2	theorem	theorem	NOUN
ejpam-3007	175	3	shows	show	VERB
ejpam-3007	175	4	that	that	SCONJ
ejpam-3007	175	5	we	we	PRON
ejpam-3007	175	6	have	have	AUX
ejpam-3007	175	7	obtained	obtain	VERB
ejpam-3007	175	8	fundamentally	fundamentally	ADV
ejpam-3007	175	9	new	new	ADJ
ejpam-3007	175	10	nonlinear	nonlinear	ADJ
ejpam-3007	175	11	integral	integral	ADJ
ejpam-3007	175	12	relations	relation	NOUN
ejpam-3007	175	13	that	that	PRON
ejpam-3007	175	14	allow	allow	VERB
ejpam-3007	175	15	taking	take	VERB
ejpam-3007	175	16	a	a	DET
ejpam-3007	175	17	fundamentally	fundamentally	ADV
ejpam-3007	175	18	fresh	fresh	ADJ
ejpam-3007	175	19	look	look	NOUN
ejpam-3007	175	20	at	at	ADP
ejpam-3007	175	21	the	the	DET
ejpam-3007	175	22	problem	problem	NOUN
ejpam-3007	175	23	of	of	ADP
ejpam-3007	175	24	estimating	estimate	VERB
ejpam-3007	175	25	functions	function	NOUN
ejpam-3007	175	26	.	.	PUNCT
ejpam-3007	176	1	now	now	ADV
ejpam-3007	176	2	,	,	PUNCT
ejpam-3007	176	3	instead	instead	ADV
ejpam-3007	176	4	of	of	ADP
ejpam-3007	176	5	integral	integral	ADJ
ejpam-3007	176	6	representations	representation	NOUN
ejpam-3007	176	7	,	,	PUNCT
ejpam-3007	176	8	that	that	PRON
ejpam-3007	176	9	generate	generate	VERB
ejpam-3007	176	10	embedding	embed	VERB
ejpam-3007	176	11	theorem	theorem	NOUN
ejpam-3007	176	12	in	in	ADP
ejpam-3007	176	13	the	the	DET
ejpam-3007	176	14	sobolev	sobolev	NOUN
ejpam-3007	176	15	spaces	space	NOUN
ejpam-3007	176	16	and	and	CCONJ
ejpam-3007	176	17	by	by	ADP
ejpam-3007	176	18	which	which	PRON
ejpam-3007	176	19	numerous	numerous	ADJ
ejpam-3007	176	20	outstanding	outstanding	ADJ
ejpam-3007	176	21	achievements	achievement	NOUN
ejpam-3007	176	22	in	in	ADP
ejpam-3007	176	23	modern	modern	ADJ
ejpam-3007	176	24	mathematics	mathematic	NOUN
ejpam-3007	176	25	have	have	AUX
ejpam-3007	176	26	been	be	AUX
ejpam-3007	176	27	gained	gain	VERB
ejpam-3007	176	28	,	,	PUNCT
ejpam-3007	176	29	we	we	PRON
ejpam-3007	176	30	turn	turn	VERB
ejpam-3007	176	31	to	to	ADP
ejpam-3007	176	32	the	the	DET
ejpam-3007	176	33	newest	new	ADJ
ejpam-3007	176	34	non	non	ADJ
ejpam-3007	176	35	-	-	ADJ
ejpam-3007	176	36	linear	linear	ADJ
ejpam-3007	176	37	integral	integral	ADJ
ejpam-3007	176	38	relations	relation	NOUN
ejpam-3007	176	39	and	and	CCONJ
ejpam-3007	176	40	hope	hope	NOUN
ejpam-3007	176	41	thereby	thereby	ADV
ejpam-3007	176	42	opening	open	VERB
ejpam-3007	176	43	up	up	ADP
ejpam-3007	176	44	new	new	ADJ
ejpam-3007	176	45	pages	page	NOUN
ejpam-3007	176	46	of	of	ADP
ejpam-3007	176	47	mathematics	mathematic	NOUN
ejpam-3007	176	48	that	that	PRON
ejpam-3007	176	49	will	will	AUX
ejpam-3007	176	50	take	take	VERB
ejpam-3007	176	51	us	we	PRON
ejpam-3007	176	52	further	far	ADV
ejpam-3007	176	53	into	into	ADP
ejpam-3007	176	54	the	the	DET
ejpam-3007	176	55	wonderful	wonderful	ADJ
ejpam-3007	176	56	world	world	NOUN
ejpam-3007	176	57	of	of	ADP
ejpam-3007	176	58	mathematics	mathematic	NOUN
ejpam-3007	176	59	.	.	PUNCT
ejpam-3007	177	1	3	3	X
ejpam-3007	177	2	.	.	X
ejpam-3007	177	3	introduction	introduction	NOUN
ejpam-3007	177	4	for	for	ADP
ejpam-3007	177	5	the	the	DET
ejpam-3007	177	6	three	three	NUM
ejpam-3007	177	7	-	-	PUNCT
ejpam-3007	177	8	dimensional	dimensional	ADJ
ejpam-3007	177	9	case	case	NOUN
ejpam-3007	177	10	in	in	ADP
ejpam-3007	177	11	this	this	DET
ejpam-3007	177	12	work	work	NOUN
ejpam-3007	177	13	we	we	PRON
ejpam-3007	177	14	present	present	VERB
ejpam-3007	177	15	final	final	ADJ
ejpam-3007	177	16	solving	solving	NOUN
ejpam-3007	177	17	millennium	millennium	NOUN
ejpam-3007	177	18	prize	prize	NOUN
ejpam-3007	177	19	problems	problem	NOUN
ejpam-3007	177	20	formulated	formulate	VERB
ejpam-3007	177	21	clay	clay	NOUN
ejpam-3007	177	22	math	math	NOUN
ejpam-3007	177	23	.	.	PUNCT
ejpam-3007	178	1	inst	inst	PROPN
ejpam-3007	178	2	.	.	PROPN
ejpam-3007	178	3	,	,	PUNCT
ejpam-3007	178	4	cambridge	cambridge	NOUN
ejpam-3007	178	5	in	in	ADP
ejpam-3007	178	6	[	[	X
ejpam-3007	178	7	3	3	NUM
ejpam-3007	178	8	]	]	PUNCT
ejpam-3007	178	9	before	before	ADP
ejpam-3007	178	10	this	this	DET
ejpam-3007	178	11	work	work	NOUN
ejpam-3007	178	12	we	we	PRON
ejpam-3007	178	13	already	already	ADV
ejpam-3007	178	14	had	have	VERB
ejpam-3007	178	15	first	first	ADJ
ejpam-3007	178	16	results	result	NOUN
ejpam-3007	178	17	in	in	ADP
ejpam-3007	178	18	[	[	X
ejpam-3007	178	19	4]-[6	4]-[6	X
ejpam-3007	178	20	]	]	X
ejpam-3007	178	21	.	.	PUNCT
ejpam-3007	179	1	the	the	DET
ejpam-3007	179	2	navierstokes	navierstoke	NOUN
ejpam-3007	179	3	existence	existence	NOUN
ejpam-3007	179	4	and	and	CCONJ
ejpam-3007	179	5	smoothness	smoothness	ADJ
ejpam-3007	179	6	problem	problem	NOUN
ejpam-3007	179	7	concerns	concern	VERB
ejpam-3007	179	8	the	the	DET
ejpam-3007	179	9	mathematical	mathematical	ADJ
ejpam-3007	179	10	properties	property	NOUN
ejpam-3007	179	11	of	of	ADP
ejpam-3007	179	12	solutions	solution	NOUN
ejpam-3007	179	13	to	to	ADP
ejpam-3007	179	14	the	the	DET
ejpam-3007	179	15	navierstokes	navierstoke	NOUN
ejpam-3007	179	16	equations	equation	NOUN
ejpam-3007	179	17	.	.	PUNCT
ejpam-3007	180	1	these	these	DET
ejpam-3007	180	2	equations	equation	NOUN
ejpam-3007	180	3	describe	describe	VERB
ejpam-3007	180	4	the	the	DET
ejpam-3007	180	5	motion	motion	NOUN
ejpam-3007	180	6	of	of	ADP
ejpam-3007	180	7	a	a	DET
ejpam-3007	180	8	fluid	fluid	NOUN
ejpam-3007	180	9	in	in	ADP
ejpam-3007	180	10	space	space	NOUN
ejpam-3007	180	11	.	.	PUNCT
ejpam-3007	181	1	solutions	solution	NOUN
ejpam-3007	181	2	to	to	ADP
ejpam-3007	181	3	the	the	DET
ejpam-3007	181	4	navierstokes	navierstoke	NOUN
ejpam-3007	181	5	equations	equation	NOUN
ejpam-3007	181	6	are	be	AUX
ejpam-3007	181	7	used	use	VERB
ejpam-3007	181	8	in	in	ADP
ejpam-3007	181	9	many	many	ADJ
ejpam-3007	181	10	practical	practical	ADJ
ejpam-3007	181	11	applications	application	NOUN
ejpam-3007	181	12	.	.	PUNCT
ejpam-3007	182	1	however	however	ADV
ejpam-3007	182	2	,	,	PUNCT
ejpam-3007	182	3	theoretical	theoretical	ADJ
ejpam-3007	182	4	understanding	understanding	NOUN
ejpam-3007	182	5	of	of	ADP
ejpam-3007	182	6	the	the	DET
ejpam-3007	182	7	solutions	solution	NOUN
ejpam-3007	182	8	to	to	ADP
ejpam-3007	182	9	these	these	DET
ejpam-3007	182	10	equations	equation	NOUN
ejpam-3007	182	11	is	be	AUX
ejpam-3007	182	12	incomplete	incomplete	ADJ
ejpam-3007	182	13	.	.	PUNCT
ejpam-3007	183	1	in	in	ADP
ejpam-3007	183	2	particular	particular	ADJ
ejpam-3007	183	3	,	,	PUNCT
ejpam-3007	183	4	solutions	solution	NOUN
ejpam-3007	183	5	of	of	ADP
ejpam-3007	183	6	the	the	DET
ejpam-3007	183	7	navierstokes	navierstoke	NOUN
ejpam-3007	183	8	equations	equation	NOUN
ejpam-3007	183	9	often	often	ADV
ejpam-3007	183	10	include	include	VERB
ejpam-3007	183	11	turbulence	turbulence	NOUN
ejpam-3007	183	12	,	,	PUNCT
ejpam-3007	183	13	which	which	PRON
ejpam-3007	183	14	remains	remain	VERB
ejpam-3007	183	15	one	one	NUM
ejpam-3007	183	16	of	of	ADP
ejpam-3007	183	17	the	the	DET
ejpam-3007	183	18	greatest	great	ADJ
ejpam-3007	183	19	unsolved	unsolved	ADJ
ejpam-3007	183	20	problems	problem	NOUN
ejpam-3007	183	21	in	in	ADP
ejpam-3007	183	22	physics	physics	NOUN
ejpam-3007	183	23	.	.	PUNCT
ejpam-3007	184	1	even	even	ADV
ejpam-3007	184	2	much	much	ADV
ejpam-3007	184	3	more	more	ADJ
ejpam-3007	184	4	basic	basic	ADJ
ejpam-3007	184	5	properties	property	NOUN
ejpam-3007	184	6	of	of	ADP
ejpam-3007	184	7	the	the	DET
ejpam-3007	184	8	solutions	solution	NOUN
ejpam-3007	184	9	to	to	ADP
ejpam-3007	184	10	navierstokes	navierstoke	NOUN
ejpam-3007	184	11	have	have	AUX
ejpam-3007	184	12	never	never	ADV
ejpam-3007	184	13	been	be	AUX
ejpam-3007	184	14	proven	prove	VERB
ejpam-3007	184	15	.	.	PUNCT
ejpam-3007	185	1	for	for	ADP
ejpam-3007	185	2	the	the	DET
ejpam-3007	185	3	three	three	NUM
ejpam-3007	185	4	-	-	PUNCT
ejpam-3007	185	5	dimensional	dimensional	ADJ
ejpam-3007	185	6	system	system	NOUN
ejpam-3007	185	7	of	of	ADP
ejpam-3007	185	8	equations	equation	NOUN
ejpam-3007	185	9	,	,	PUNCT
ejpam-3007	185	10	and	and	CCONJ
ejpam-3007	185	11	given	give	VERB
ejpam-3007	185	12	some	some	DET
ejpam-3007	185	13	initial	initial	ADJ
ejpam-3007	185	14	conditions	condition	NOUN
ejpam-3007	185	15	,	,	PUNCT
ejpam-3007	185	16	mathematicians	mathematician	NOUN
ejpam-3007	185	17	have	have	AUX
ejpam-3007	185	18	not	not	PART
ejpam-3007	185	19	yet	yet	ADV
ejpam-3007	185	20	proved	prove	VERB
ejpam-3007	185	21	that	that	SCONJ
ejpam-3007	185	22	a.	a.	NOUN
ejpam-3007	185	23	durmagambetov	durmagambetov	PROPN
ejpam-3007	185	24	/	/	SYM
ejpam-3007	185	25	eur	eur	PROPN
ejpam-3007	185	26	.	.	PUNCT
ejpam-3007	186	1	j.	j.	PROPN
ejpam-3007	186	2	pure	pure	PROPN
ejpam-3007	186	3	appl	appl	PROPN
ejpam-3007	186	4	.	.	PROPN
ejpam-3007	186	5	math	math	PROPN
ejpam-3007	186	6	,	,	PUNCT
ejpam-3007	186	7	10	10	NUM
ejpam-3007	186	8	(	(	PUNCT
ejpam-3007	186	9	4	4	NUM
ejpam-3007	186	10	)	)	PUNCT
ejpam-3007	186	11	(	(	PUNCT
ejpam-3007	186	12	2017	2017	NUM
ejpam-3007	186	13	)	)	PUNCT
ejpam-3007	186	14	,	,	PUNCT
ejpam-3007	186	15	763	763	NUM
ejpam-3007	186	16	-	-	SYM
ejpam-3007	186	17	785	785	NUM
ejpam-3007	186	18	771	771	NUM
ejpam-3007	186	19	smooth	smooth	ADJ
ejpam-3007	186	20	solutions	solution	NOUN
ejpam-3007	186	21	always	always	ADV
ejpam-3007	186	22	exist	exist	VERB
ejpam-3007	186	23	,	,	PUNCT
ejpam-3007	186	24	or	or	CCONJ
ejpam-3007	186	25	that	that	SCONJ
ejpam-3007	186	26	if	if	SCONJ
ejpam-3007	186	27	they	they	PRON
ejpam-3007	186	28	do	do	AUX
ejpam-3007	186	29	exist	exist	VERB
ejpam-3007	186	30	,	,	PUNCT
ejpam-3007	186	31	they	they	PRON
ejpam-3007	186	32	have	have	AUX
ejpam-3007	186	33	bounded	bound	VERB
ejpam-3007	186	34	energy	energy	NOUN
ejpam-3007	186	35	per	per	ADP
ejpam-3007	186	36	unit	unit	NOUN
ejpam-3007	186	37	mass	mass	PROPN
ejpam-3007	186	38	.	.	PUNCT
ejpam-3007	187	1	this	this	PRON
ejpam-3007	187	2	is	be	AUX
ejpam-3007	187	3	called	call	VERB
ejpam-3007	187	4	the	the	DET
ejpam-3007	187	5	navierstokes	navierstoke	NOUN
ejpam-3007	187	6	existence	existence	NOUN
ejpam-3007	187	7	and	and	CCONJ
ejpam-3007	187	8	smoothness	smoothness	ADJ
ejpam-3007	187	9	problem	problem	NOUN
ejpam-3007	187	10	.	.	PUNCT
ejpam-3007	188	1	since	since	SCONJ
ejpam-3007	188	2	understanding	understand	VERB
ejpam-3007	188	3	the	the	DET
ejpam-3007	188	4	navierstokes	navierstoke	NOUN
ejpam-3007	188	5	equations	equation	NOUN
ejpam-3007	188	6	is	be	AUX
ejpam-3007	188	7	considered	consider	VERB
ejpam-3007	188	8	to	to	PART
ejpam-3007	188	9	be	be	AUX
ejpam-3007	188	10	the	the	DET
ejpam-3007	188	11	first	first	ADJ
ejpam-3007	188	12	step	step	NOUN
ejpam-3007	188	13	to	to	ADP
ejpam-3007	188	14	understanding	understand	VERB
ejpam-3007	188	15	the	the	DET
ejpam-3007	188	16	elusive	elusive	ADJ
ejpam-3007	188	17	phenomenon	phenomenon	NOUN
ejpam-3007	188	18	of	of	ADP
ejpam-3007	188	19	turbulence	turbulence	NOUN
ejpam-3007	188	20	,	,	PUNCT
ejpam-3007	188	21	the	the	DET
ejpam-3007	188	22	clay	clay	NOUN
ejpam-3007	188	23	mathematics	mathematics	PROPN
ejpam-3007	188	24	institute	institute	PROPN
ejpam-3007	188	25	in	in	ADP
ejpam-3007	188	26	may	may	PROPN
ejpam-3007	188	27	2000	2000	NUM
ejpam-3007	188	28	made	make	VERB
ejpam-3007	188	29	this	this	DET
ejpam-3007	188	30	problem	problem	NOUN
ejpam-3007	188	31	one	one	NUM
ejpam-3007	188	32	of	of	ADP
ejpam-3007	188	33	its	its	PRON
ejpam-3007	188	34	seven	seven	NUM
ejpam-3007	188	35	millennium	millennium	NOUN
ejpam-3007	188	36	prize	prize	NOUN
ejpam-3007	188	37	problems	problem	NOUN
ejpam-3007	188	38	in	in	ADP
ejpam-3007	188	39	mathematics	mathematic	NOUN
ejpam-3007	188	40	.	.	PUNCT
ejpam-3007	189	1	in	in	ADP
ejpam-3007	189	2	this	this	DET
ejpam-3007	189	3	paper	paper	NOUN
ejpam-3007	189	4	,	,	PUNCT
ejpam-3007	189	5	we	we	PRON
ejpam-3007	189	6	introduce	introduce	VERB
ejpam-3007	189	7	important	important	ADJ
ejpam-3007	189	8	explanations	explanation	NOUN
ejpam-3007	189	9	results	result	NOUN
ejpam-3007	189	10	presented	present	VERB
ejpam-3007	189	11	in	in	ADP
ejpam-3007	189	12	the	the	DET
ejpam-3007	189	13	previous	previous	ADJ
ejpam-3007	189	14	studies	study	NOUN
ejpam-3007	189	15	in	in	ADP
ejpam-3007	189	16	[	[	X
ejpam-3007	189	17	4]-[6	4]-[6	X
ejpam-3007	189	18	]	]	PUNCT
ejpam-3007	189	19	.	.	PUNCT
ejpam-3007	190	1	we	we	PRON
ejpam-3007	190	2	therefore	therefore	ADV
ejpam-3007	190	3	reiterate	reiterate	VERB
ejpam-3007	190	4	the	the	DET
ejpam-3007	190	5	basic	basic	ADJ
ejpam-3007	190	6	provisions	provision	NOUN
ejpam-3007	190	7	of	of	ADP
ejpam-3007	190	8	the	the	DET
ejpam-3007	190	9	preceding	precede	VERB
ejpam-3007	190	10	articles	article	NOUN
ejpam-3007	190	11	to	to	PART
ejpam-3007	190	12	clarify	clarify	VERB
ejpam-3007	190	13	understanding	understand	VERB
ejpam-3007	190	14	them	they	PRON
ejpam-3007	190	15	.	.	PUNCT
ejpam-3007	191	1	first	first	ADV
ejpam-3007	191	2	,	,	PUNCT
ejpam-3007	191	3	we	we	PRON
ejpam-3007	191	4	consider	consider	VERB
ejpam-3007	191	5	some	some	DET
ejpam-3007	191	6	ideas	idea	NOUN
ejpam-3007	191	7	for	for	ADP
ejpam-3007	191	8	the	the	DET
ejpam-3007	191	9	potential	potential	NOUN
ejpam-3007	191	10	in	in	ADP
ejpam-3007	191	11	the	the	DET
ejpam-3007	191	12	inverse	inverse	NOUN
ejpam-3007	191	13	scattering	scattering	NOUN
ejpam-3007	191	14	problem	problem	NOUN
ejpam-3007	191	15	,	,	PUNCT
ejpam-3007	191	16	and	and	CCONJ
ejpam-3007	191	17	this	this	PRON
ejpam-3007	191	18	is	be	AUX
ejpam-3007	191	19	then	then	ADV
ejpam-3007	191	20	used	use	VERB
ejpam-3007	191	21	to	to	PART
ejpam-3007	191	22	estimate	estimate	VERB
ejpam-3007	191	23	of	of	ADP
ejpam-3007	191	24	solutions	solution	NOUN
ejpam-3007	191	25	of	of	ADP
ejpam-3007	191	26	the	the	DET
ejpam-3007	191	27	cauchy	cauchy	ADJ
ejpam-3007	191	28	problem	problem	NOUN
ejpam-3007	191	29	for	for	ADP
ejpam-3007	191	30	the	the	DET
ejpam-3007	191	31	navier	navier	NOUN
ejpam-3007	191	32	-	-	PUNCT
ejpam-3007	191	33	stokes	stoke	NOUN
ejpam-3007	191	34	equations	equation	NOUN
ejpam-3007	191	35	.	.	PUNCT
ejpam-3007	192	1	a	a	DET
ejpam-3007	192	2	similar	similar	ADJ
ejpam-3007	192	3	approach	approach	NOUN
ejpam-3007	192	4	has	have	AUX
ejpam-3007	192	5	been	be	AUX
ejpam-3007	192	6	developed	develop	VERB
ejpam-3007	192	7	for	for	ADP
ejpam-3007	192	8	one	one	NUM
ejpam-3007	192	9	-	-	PUNCT
ejpam-3007	192	10	dimensional	dimensional	ADJ
ejpam-3007	192	11	nonlinear	nonlinear	ADJ
ejpam-3007	192	12	equations	equation	NOUN
ejpam-3007	192	13	[	[	X
ejpam-3007	192	14	7,8,9,10	7,8,9,10	X
ejpam-3007	192	15	]	]	PUNCT
ejpam-3007	192	16	,	,	PUNCT
ejpam-3007	192	17	but	but	CCONJ
ejpam-3007	192	18	to	to	ADP
ejpam-3007	192	19	date	date	NOUN
ejpam-3007	192	20	,	,	PUNCT
ejpam-3007	192	21	there	there	PRON
ejpam-3007	192	22	have	have	AUX
ejpam-3007	192	23	been	be	AUX
ejpam-3007	192	24	no	no	DET
ejpam-3007	192	25	results	result	NOUN
ejpam-3007	192	26	for	for	ADP
ejpam-3007	192	27	the	the	DET
ejpam-3007	192	28	inverse	inverse	NOUN
ejpam-3007	192	29	scattering	scattering	NOUN
ejpam-3007	192	30	problem	problem	NOUN
ejpam-3007	192	31	for	for	ADP
ejpam-3007	192	32	three	three	NUM
ejpam-3007	192	33	-	-	PUNCT
ejpam-3007	192	34	dimensional	dimensional	ADJ
ejpam-3007	192	35	nonlinear	nonlinear	ADJ
ejpam-3007	192	36	equations	equation	NOUN
ejpam-3007	192	37	.	.	PUNCT
ejpam-3007	193	1	this	this	PRON
ejpam-3007	193	2	is	be	AUX
ejpam-3007	193	3	primarily	primarily	ADV
ejpam-3007	193	4	due	due	ADJ
ejpam-3007	193	5	to	to	ADP
ejpam-3007	193	6	difficulties	difficulty	NOUN
ejpam-3007	193	7	in	in	ADP
ejpam-3007	193	8	solving	solve	VERB
ejpam-3007	193	9	the	the	DET
ejpam-3007	193	10	three	three	NUM
ejpam-3007	193	11	-	-	PUNCT
ejpam-3007	193	12	dimensional	dimensional	ADJ
ejpam-3007	193	13	inverse	inverse	NOUN
ejpam-3007	193	14	scattering	scattering	NOUN
ejpam-3007	193	15	problem	problem	NOUN
ejpam-3007	193	16	.	.	PUNCT
ejpam-3007	194	1	this	this	DET
ejpam-3007	194	2	paper	paper	NOUN
ejpam-3007	194	3	is	be	AUX
ejpam-3007	194	4	organized	organize	VERB
ejpam-3007	194	5	as	as	SCONJ
ejpam-3007	194	6	follows	follow	VERB
ejpam-3007	194	7	:	:	PUNCT
ejpam-3007	194	8	first	first	ADV
ejpam-3007	194	9	,	,	PUNCT
ejpam-3007	194	10	we	we	PRON
ejpam-3007	194	11	study	study	VERB
ejpam-3007	194	12	the	the	DET
ejpam-3007	194	13	inverse	inverse	NOUN
ejpam-3007	194	14	scattering	scattering	NOUN
ejpam-3007	194	15	problem	problem	NOUN
ejpam-3007	194	16	,	,	PUNCT
ejpam-3007	194	17	resulting	result	VERB
ejpam-3007	194	18	in	in	ADP
ejpam-3007	194	19	a	a	DET
ejpam-3007	194	20	formula	formula	NOUN
ejpam-3007	194	21	for	for	ADP
ejpam-3007	194	22	the	the	DET
ejpam-3007	194	23	scattering	scatter	VERB
ejpam-3007	194	24	potential	potential	NOUN
ejpam-3007	194	25	.	.	PUNCT
ejpam-3007	195	1	furthermore	furthermore	ADV
ejpam-3007	195	2	,	,	PUNCT
ejpam-3007	195	3	with	with	ADP
ejpam-3007	195	4	the	the	DET
ejpam-3007	195	5	use	use	NOUN
ejpam-3007	195	6	of	of	ADP
ejpam-3007	195	7	this	this	DET
ejpam-3007	195	8	potential	potential	NOUN
ejpam-3007	195	9	,	,	PUNCT
ejpam-3007	195	10	we	we	PRON
ejpam-3007	195	11	obtain	obtain	VERB
ejpam-3007	195	12	uniform	uniform	ADJ
ejpam-3007	195	13	time	time	NOUN
ejpam-3007	195	14	estimates	estimate	NOUN
ejpam-3007	195	15	in	in	ADP
ejpam-3007	195	16	time	time	NOUN
ejpam-3007	195	17	of	of	ADP
ejpam-3007	195	18	solutions	solution	NOUN
ejpam-3007	195	19	of	of	ADP
ejpam-3007	195	20	the	the	DET
ejpam-3007	195	21	navier	navier	NOUN
ejpam-3007	195	22	–	–	PUNCT
ejpam-3007	195	23	stokes	stoke	NOUN
ejpam-3007	195	24	equations	equation	NOUN
ejpam-3007	195	25	,	,	PUNCT
ejpam-3007	195	26	which	which	PRON
ejpam-3007	195	27	suggest	suggest	VERB
ejpam-3007	195	28	the	the	DET
ejpam-3007	195	29	global	global	ADJ
ejpam-3007	195	30	solvability	solvability	NOUN
ejpam-3007	195	31	of	of	ADP
ejpam-3007	195	32	the	the	DET
ejpam-3007	195	33	cauchy	cauchy	ADJ
ejpam-3007	195	34	problem	problem	NOUN
ejpam-3007	195	35	for	for	ADP
ejpam-3007	195	36	the	the	DET
ejpam-3007	195	37	navier	navier	NOUN
ejpam-3007	195	38	–	–	PUNCT
ejpam-3007	195	39	stokes	stokes	PROPN
ejpam-3007	195	40	equations	equation	NOUN
ejpam-3007	195	41	.	.	PUNCT
ejpam-3007	196	1	essentially	essentially	ADV
ejpam-3007	196	2	,	,	PUNCT
ejpam-3007	196	3	the	the	DET
ejpam-3007	196	4	present	present	ADJ
ejpam-3007	196	5	study	study	NOUN
ejpam-3007	196	6	expands	expand	VERB
ejpam-3007	196	7	the	the	DET
ejpam-3007	196	8	results	result	NOUN
ejpam-3007	196	9	for	for	ADP
ejpam-3007	196	10	one	one	NUM
ejpam-3007	196	11	-	-	PUNCT
ejpam-3007	196	12	dimensional	dimensional	ADJ
ejpam-3007	196	13	nonlinear	nonlinear	ADJ
ejpam-3007	196	14	equations	equation	NOUN
ejpam-3007	196	15	with	with	ADP
ejpam-3007	196	16	inverse	inverse	NOUN
ejpam-3007	196	17	scattering	scatter	VERB
ejpam-3007	196	18	methods	method	NOUN
ejpam-3007	196	19	to	to	PART
ejpam-3007	196	20	multi	multi	ADJ
ejpam-3007	196	21	-	-	ADJ
ejpam-3007	196	22	dimensional	dimensional	ADJ
ejpam-3007	196	23	cases	case	NOUN
ejpam-3007	196	24	.	.	PUNCT
ejpam-3007	197	1	in	in	ADP
ejpam-3007	197	2	our	our	PRON
ejpam-3007	197	3	opinion	opinion	NOUN
ejpam-3007	197	4	,	,	PUNCT
ejpam-3007	197	5	the	the	DET
ejpam-3007	197	6	main	main	ADJ
ejpam-3007	197	7	achievement	achievement	NOUN
ejpam-3007	197	8	is	be	AUX
ejpam-3007	197	9	a	a	DET
ejpam-3007	197	10	relatively	relatively	ADV
ejpam-3007	197	11	unchanged	unchanged	ADJ
ejpam-3007	197	12	projection	projection	NOUN
ejpam-3007	197	13	onto	onto	ADP
ejpam-3007	197	14	the	the	DET
ejpam-3007	197	15	space	space	NOUN
ejpam-3007	197	16	of	of	ADP
ejpam-3007	197	17	the	the	DET
ejpam-3007	197	18	continuous	continuous	ADJ
ejpam-3007	197	19	spectrum	spectrum	NOUN
ejpam-3007	197	20	for	for	ADP
ejpam-3007	197	21	the	the	DET
ejpam-3007	197	22	solution	solution	NOUN
ejpam-3007	197	23	of	of	ADP
ejpam-3007	197	24	nonlinear	nonlinear	ADJ
ejpam-3007	197	25	equations	equation	NOUN
ejpam-3007	197	26	,	,	PUNCT
ejpam-3007	197	27	that	that	PRON
ejpam-3007	197	28	allows	allow	VERB
ejpam-3007	197	29	to	to	PART
ejpam-3007	197	30	focus	focus	VERB
ejpam-3007	197	31	only	only	ADV
ejpam-3007	197	32	on	on	ADP
ejpam-3007	197	33	the	the	DET
ejpam-3007	197	34	behavior	behavior	NOUN
ejpam-3007	197	35	associated	associate	VERB
ejpam-3007	197	36	with	with	ADP
ejpam-3007	197	37	the	the	DET
ejpam-3007	197	38	decomposition	decomposition	NOUN
ejpam-3007	197	39	of	of	ADP
ejpam-3007	197	40	the	the	DET
ejpam-3007	197	41	solutions	solution	NOUN
ejpam-3007	197	42	to	to	ADP
ejpam-3007	197	43	the	the	DET
ejpam-3007	197	44	discrete	discrete	ADJ
ejpam-3007	197	45	spectrum	spectrum	NOUN
ejpam-3007	197	46	.	.	PUNCT
ejpam-3007	198	1	in	in	ADP
ejpam-3007	198	2	the	the	DET
ejpam-3007	198	3	absence	absence	NOUN
ejpam-3007	198	4	of	of	ADP
ejpam-3007	198	5	a	a	DET
ejpam-3007	198	6	discrete	discrete	ADJ
ejpam-3007	198	7	spectrum	spectrum	NOUN
ejpam-3007	198	8	,	,	PUNCT
ejpam-3007	198	9	we	we	PRON
ejpam-3007	198	10	obtain	obtain	VERB
ejpam-3007	198	11	estimations	estimation	NOUN
ejpam-3007	198	12	for	for	ADP
ejpam-3007	198	13	the	the	DET
ejpam-3007	198	14	maximum	maximum	ADJ
ejpam-3007	198	15	potential	potential	NOUN
ejpam-3007	198	16	in	in	ADP
ejpam-3007	198	17	the	the	DET
ejpam-3007	198	18	weaker	weak	ADJ
ejpam-3007	198	19	norms	norm	NOUN
ejpam-3007	198	20	,	,	PUNCT
ejpam-3007	198	21	compared	compare	VERB
ejpam-3007	198	22	with	with	ADP
ejpam-3007	198	23	the	the	DET
ejpam-3007	198	24	norms	norm	NOUN
ejpam-3007	198	25	for	for	ADP
ejpam-3007	198	26	sobolev	sobolev	NOUN
ejpam-3007	198	27	’	'	PUNCT
ejpam-3007	198	28	spaces	space	NOUN
ejpam-3007	198	29	.	.	PUNCT
ejpam-3007	199	1	consider	consider	VERB
ejpam-3007	199	2	the	the	DET
ejpam-3007	199	3	operators	operator	NOUN
ejpam-3007	199	4	h	h	NOUN
ejpam-3007	200	1	=	=	PROPN
ejpam-3007	200	2	−∆x+	−∆x+	PROPN
ejpam-3007	200	3	q(x	q(x	PROPN
ejpam-3007	200	4	)	)	PUNCT
ejpam-3007	200	5	,	,	PUNCT
ejpam-3007	200	6	h0	h0	NOUN
ejpam-3007	200	7	=	=	PROPN
ejpam-3007	200	8	−∆x	−∆x	ADV
ejpam-3007	200	9	defined	define	VERB
ejpam-3007	200	10	in	in	ADP
ejpam-3007	200	11	the	the	DET
ejpam-3007	200	12	dense	dense	ADJ
ejpam-3007	200	13	set	set	NOUN
ejpam-3007	200	14	w	w	PROPN
ejpam-3007	200	15	2	2	NUM
ejpam-3007	200	16	2	2	NUM
ejpam-3007	200	17	(	(	PUNCT
ejpam-3007	200	18	r3	r3	PROPN
ejpam-3007	200	19	)	)	PUNCT
ejpam-3007	200	20	in	in	ADP
ejpam-3007	200	21	the	the	DET
ejpam-3007	200	22	space	space	NOUN
ejpam-3007	200	23	l2(r3	l2(r3	NOUN
ejpam-3007	200	24	)	)	PUNCT
ejpam-3007	200	25	,	,	PUNCT
ejpam-3007	200	26	and	and	CCONJ
ejpam-3007	200	27	let	let	VERB
ejpam-3007	200	28	q	q	PART
ejpam-3007	200	29	be	be	AUX
ejpam-3007	200	30	a	a	DET
ejpam-3007	200	31	bounded	bounded	ADJ
ejpam-3007	200	32	fast	fast	ADV
ejpam-3007	200	33	-	-	PUNCT
ejpam-3007	200	34	decreasing	decrease	VERB
ejpam-3007	200	35	function	function	NOUN
ejpam-3007	200	36	.	.	PUNCT
ejpam-3007	201	1	the	the	DET
ejpam-3007	201	2	operator	operator	NOUN
ejpam-3007	201	3	h	h	NOUN
ejpam-3007	201	4	is	be	AUX
ejpam-3007	201	5	called	call	VERB
ejpam-3007	201	6	schrödinger	schrödinger	NOUN
ejpam-3007	201	7	’s	’s	PART
ejpam-3007	201	8	operator	operator	NOUN
ejpam-3007	201	9	.	.	PUNCT
ejpam-3007	202	1	we	we	PRON
ejpam-3007	202	2	consider	consider	VERB
ejpam-3007	202	3	the	the	DET
ejpam-3007	202	4	three	three	NUM
ejpam-3007	202	5	-	-	PUNCT
ejpam-3007	202	6	dimensional	dimensional	ADJ
ejpam-3007	202	7	inverse	inverse	NOUN
ejpam-3007	202	8	scattering	scattering	NOUN
ejpam-3007	202	9	problem	problem	NOUN
ejpam-3007	202	10	for	for	ADP
ejpam-3007	202	11	schrödinger	schrödinger	NOUN
ejpam-3007	202	12	’s	’s	PART
ejpam-3007	202	13	operator	operator	NOUN
ejpam-3007	202	14	:	:	PUNCT
ejpam-3007	202	15	the	the	DET
ejpam-3007	202	16	scattering	scatter	VERB
ejpam-3007	202	17	potential	potential	NOUN
ejpam-3007	202	18	must	must	AUX
ejpam-3007	202	19	be	be	AUX
ejpam-3007	202	20	reconstructed	reconstruct	VERB
ejpam-3007	202	21	from	from	ADP
ejpam-3007	202	22	the	the	DET
ejpam-3007	202	23	scattering	scatter	VERB
ejpam-3007	202	24	amplitude	amplitude	NOUN
ejpam-3007	202	25	.	.	PUNCT
ejpam-3007	203	1	this	this	DET
ejpam-3007	203	2	problem	problem	NOUN
ejpam-3007	203	3	has	have	AUX
ejpam-3007	203	4	been	be	AUX
ejpam-3007	203	5	studied	study	VERB
ejpam-3007	203	6	by	by	ADP
ejpam-3007	203	7	a	a	DET
ejpam-3007	203	8	number	number	NOUN
ejpam-3007	203	9	of	of	ADP
ejpam-3007	203	10	researchers	researcher	NOUN
ejpam-3007	203	11	[	[	PUNCT
ejpam-3007	203	12	9,11,12	9,11,12	NUM
ejpam-3007	203	13	]	]	PUNCT
ejpam-3007	203	14	and	and	CCONJ
ejpam-3007	203	15	references	reference	NOUN
ejpam-3007	203	16	therein	therein	ADV
ejpam-3007	203	17	]	]	X
ejpam-3007	203	18	4	4	X
ejpam-3007	203	19	.	.	X
ejpam-3007	203	20	results	result	NOUN
ejpam-3007	203	21	for	for	ADP
ejpam-3007	203	22	the	the	DET
ejpam-3007	203	23	three	three	NUM
ejpam-3007	203	24	-	-	PUNCT
ejpam-3007	203	25	dimensional	dimensional	ADJ
ejpam-3007	203	26	case	case	NOUN
ejpam-3007	203	27	consider	consider	VERB
ejpam-3007	203	28	schrödinger	schrödinger	NOUN
ejpam-3007	203	29	’s	’s	PART
ejpam-3007	203	30	equation	equation	NOUN
ejpam-3007	203	31	:	:	PUNCT
ejpam-3007	203	32	−∆xψ	−∆xψ	NOUN
ejpam-3007	203	33	+	+	CCONJ
ejpam-3007	203	34	qψ	qψ	PROPN
ejpam-3007	203	35	=	=	SYM
ejpam-3007	203	36	|k|2ψ	|k|2ψ	X
ejpam-3007	203	37	,	,	PUNCT
ejpam-3007	204	1	k	k	PROPN
ejpam-3007	204	2	∈	∈	PROPN
ejpam-3007	204	3	c	c	PROPN
ejpam-3007	204	4	(	(	PUNCT
ejpam-3007	204	5	38	38	NUM
ejpam-3007	204	6	)	)	PUNCT
ejpam-3007	204	7	let	let	VERB
ejpam-3007	204	8	ψ+(k	ψ+(k	NUM
ejpam-3007	204	9	,	,	PUNCT
ejpam-3007	204	10	θ	θ	NOUN
ejpam-3007	204	11	,	,	PUNCT
ejpam-3007	204	12	x	x	X
ejpam-3007	204	13	)	)	PUNCT
ejpam-3007	204	14	be	be	AUX
ejpam-3007	204	15	a	a	DET
ejpam-3007	204	16	solution	solution	NOUN
ejpam-3007	204	17	of	of	ADP
ejpam-3007	204	18	(	(	PUNCT
ejpam-3007	204	19	38	38	NUM
ejpam-3007	204	20	)	)	PUNCT
ejpam-3007	204	21	with	with	ADP
ejpam-3007	204	22	the	the	DET
ejpam-3007	204	23	following	following	ADJ
ejpam-3007	204	24	asympotic	asympotic	ADJ
ejpam-3007	204	25	behavior	behavior	NOUN
ejpam-3007	204	26	:	:	PUNCT
ejpam-3007	204	27	ψ+(k	ψ+(k	NUM
ejpam-3007	204	28	,	,	PUNCT
ejpam-3007	204	29	θ	θ	NOUN
ejpam-3007	204	30	,	,	PUNCT
ejpam-3007	204	31	x	x	NOUN
ejpam-3007	204	32	)	)	PUNCT
ejpam-3007	204	33	=	=	SYM
ejpam-3007	205	1	φ0(θ	φ0(θ	PROPN
ejpam-3007	205	2	,	,	PUNCT
ejpam-3007	205	3	x	x	PRON
ejpam-3007	205	4	)	)	PUNCT
ejpam-3007	206	1	+	+	NUM
ejpam-3007	206	2	ei|k||x|	ei|k||x|	PROPN
ejpam-3007	206	3	|x|	|x|	PROPN
ejpam-3007	206	4	a(k	a(k	PROPN
ejpam-3007	206	5	,	,	PUNCT
ejpam-3007	206	6	θ	θ	PROPN
ejpam-3007	206	7	′	′	NUM
ejpam-3007	206	8	,	,	PUNCT
ejpam-3007	206	9	θ	θ	NOUN
ejpam-3007	206	10	)	)	PUNCT
ejpam-3007	207	1	+	+	CCONJ
ejpam-3007	207	2	0	0	NUM
ejpam-3007	207	3	(	(	PUNCT
ejpam-3007	207	4	1	1	NUM
ejpam-3007	207	5	|x|	|x|	PROPN
ejpam-3007	207	6	)	)	PUNCT
ejpam-3007	207	7	,	,	PUNCT
ejpam-3007	207	8	|x|	|x|	PROPN
ejpam-3007	207	9	→	→	SYM
ejpam-3007	207	10	∞	∞	PROPN
ejpam-3007	207	11	,	,	PUNCT
ejpam-3007	207	12	(	(	PUNCT
ejpam-3007	207	13	39	39	NUM
ejpam-3007	207	14	)	)	PUNCT
ejpam-3007	207	15	a.	a.	NOUN
ejpam-3007	207	16	durmagambetov	durmagambetov	PROPN
ejpam-3007	207	17	/	/	SYM
ejpam-3007	207	18	eur	eur	PROPN
ejpam-3007	207	19	.	.	PUNCT
ejpam-3007	208	1	j.	j.	PROPN
ejpam-3007	208	2	pure	pure	PROPN
ejpam-3007	208	3	appl	appl	PROPN
ejpam-3007	208	4	.	.	PROPN
ejpam-3007	208	5	math	math	PROPN
ejpam-3007	208	6	,	,	PUNCT
ejpam-3007	208	7	10	10	NUM
ejpam-3007	208	8	(	(	PUNCT
ejpam-3007	208	9	4	4	NUM
ejpam-3007	208	10	)	)	PUNCT
ejpam-3007	208	11	(	(	PUNCT
ejpam-3007	208	12	2017	2017	NUM
ejpam-3007	208	13	)	)	PUNCT
ejpam-3007	208	14	,	,	PUNCT
ejpam-3007	208	15	763	763	NUM
ejpam-3007	208	16	-	-	SYM
ejpam-3007	208	17	785	785	NUM
ejpam-3007	208	18	772	772	NUM
ejpam-3007	208	19	where	where	SCONJ
ejpam-3007	208	20	a(k	a(k	PROPN
ejpam-3007	208	21	,	,	PUNCT
ejpam-3007	208	22	θ	θ	PROPN
ejpam-3007	208	23	′	′	NUM
ejpam-3007	208	24	,	,	PUNCT
ejpam-3007	208	25	θ	θ	X
ejpam-3007	208	26	)	)	PUNCT
ejpam-3007	208	27	is	be	AUX
ejpam-3007	208	28	the	the	DET
ejpam-3007	208	29	scattering	scatter	VERB
ejpam-3007	208	30	amplitude	amplitude	NOUN
ejpam-3007	208	31	and	and	CCONJ
ejpam-3007	208	32	θ	θ	NOUN
ejpam-3007	208	33	′	′	NUM
ejpam-3007	209	1	=	=	PUNCT
ejpam-3007	209	2	x	x	SYM
ejpam-3007	209	3	|x|	|x|	PROPN
ejpam-3007	209	4	,	,	PUNCT
ejpam-3007	209	5	θ	θ	PROPN
ejpam-3007	209	6	∈	∈	PROPN
ejpam-3007	209	7	s	s	PART
ejpam-3007	209	8	2	2	NUM
ejpam-3007	209	9	for	for	ADP
ejpam-3007	209	10	k	k	PROPN
ejpam-3007	209	11	∈	∈	PROPN
ejpam-3007	209	12	c̄+	c̄+	PROPN
ejpam-3007	209	13	=	=	SYM
ejpam-3007	209	14	{	{	PUNCT
ejpam-3007	209	15	imk	imk	PROPN
ejpam-3007	209	16	≥	≥	PROPN
ejpam-3007	209	17	0	0	NUM
ejpam-3007	209	18	}	}	PUNCT
ejpam-3007	209	19	φ0(θ	φ0(θ	PROPN
ejpam-3007	209	20	,	,	PUNCT
ejpam-3007	209	21	x	x	NOUN
ejpam-3007	209	22	)	)	PUNCT
ejpam-3007	209	23	=	=	VERB
ejpam-3007	209	24	eikθx	eikθx	VERB
ejpam-3007	209	25	a(k	a(k	PROPN
ejpam-3007	209	26	,	,	PUNCT
ejpam-3007	209	27	θ	θ	PROPN
ejpam-3007	209	28	′	′	NUM
ejpam-3007	209	29	,	,	PUNCT
ejpam-3007	209	30	θ	θ	X
ejpam-3007	209	31	)	)	PUNCT
ejpam-3007	209	32	=	=	SYM
ejpam-3007	210	1	−	−	PROPN
ejpam-3007	210	2	1	1	NUM
ejpam-3007	210	3	4π	4π	NUM
ejpam-3007	210	4	∫	∫	PROPN
ejpam-3007	210	5	r3	r3	PROPN
ejpam-3007	210	6	q(x)ψ+(k	q(x)ψ+(k	PROPN
ejpam-3007	210	7	,	,	PUNCT
ejpam-3007	210	8	θ	θ	PROPN
ejpam-3007	210	9	,	,	PUNCT
ejpam-3007	210	10	x)e−ikθ	x)e−ikθ	PROPN
ejpam-3007	210	11	′	′	NUM
ejpam-3007	210	12	xdx	xdx	PROPN
ejpam-3007	210	13	.	.	PUNCT
ejpam-3007	211	1	(	(	PUNCT
ejpam-3007	211	2	40	40	NUM
ejpam-3007	211	3	)	)	PUNCT
ejpam-3007	211	4	let	let	VERB
ejpam-3007	211	5	us	we	PRON
ejpam-3007	211	6	also	also	ADV
ejpam-3007	211	7	define	define	VERB
ejpam-3007	211	8	the	the	DET
ejpam-3007	211	9	solution	solution	NOUN
ejpam-3007	211	10	ψ−(k	ψ−(k	NOUN
ejpam-3007	211	11	,	,	PUNCT
ejpam-3007	211	12	θ	θ	PROPN
ejpam-3007	211	13	,	,	PUNCT
ejpam-3007	211	14	x	x	NOUN
ejpam-3007	211	15	)	)	PUNCT
ejpam-3007	211	16	for	for	ADP
ejpam-3007	211	17	k	k	PROPN
ejpam-3007	211	18	∈	∈	PROPN
ejpam-3007	211	19	c̄−	c̄−	NOUN
ejpam-3007	211	20	=	=	PUNCT
ejpam-3007	211	21	{	{	PUNCT
ejpam-3007	211	22	imk	imk	PROPN
ejpam-3007	211	23	≤	≤	PROPN
ejpam-3007	211	24	0	0	NUM
ejpam-3007	211	25	}	}	PUNCT
ejpam-3007	211	26	as	as	ADP
ejpam-3007	211	27	ψ−(k	ψ−(k	NOUN
ejpam-3007	211	28	,	,	PUNCT
ejpam-3007	211	29	θ	θ	PROPN
ejpam-3007	211	30	,	,	PUNCT
ejpam-3007	211	31	x	x	NOUN
ejpam-3007	211	32	)	)	PUNCT
ejpam-3007	211	33	=	=	SYM
ejpam-3007	211	34	ψ+(−k,−θ	ψ+(−k,−θ	X
ejpam-3007	211	35	,	,	PUNCT
ejpam-3007	211	36	x	x	NOUN
ejpam-3007	211	37	)	)	PUNCT
ejpam-3007	211	38	.	.	PUNCT
ejpam-3007	212	1	as	as	SCONJ
ejpam-3007	212	2	is	be	AUX
ejpam-3007	212	3	well	well	ADJ
ejpam-3007	212	4	known[9	known[9	ADV
ejpam-3007	212	5	]	]	X
ejpam-3007	212	6	:	:	PUNCT
ejpam-3007	212	7	ψ+(k	ψ+(k	NUM
ejpam-3007	212	8	,	,	PUNCT
ejpam-3007	212	9	θ	θ	NOUN
ejpam-3007	212	10	,	,	PUNCT
ejpam-3007	212	11	x	x	NOUN
ejpam-3007	212	12	)	)	PUNCT
ejpam-3007	212	13	−	−	PROPN
ejpam-3007	212	14	ψ−(k	ψ−(k	PROPN
ejpam-3007	212	15	,	,	PUNCT
ejpam-3007	212	16	θ	θ	PROPN
ejpam-3007	212	17	,	,	PUNCT
ejpam-3007	212	18	x	x	NOUN
ejpam-3007	212	19	)	)	PUNCT
ejpam-3007	213	1	=	=	SYM
ejpam-3007	213	2	−	−	PROPN
ejpam-3007	214	1	k	k	PROPN
ejpam-3007	214	2	4π	4π	NUM
ejpam-3007	214	3	∫	∫	PROPN
ejpam-3007	214	4	s2	s2	PROPN
ejpam-3007	214	5	a(k	a(k	PROPN
ejpam-3007	214	6	,	,	PUNCT
ejpam-3007	214	7	θ	θ	PROPN
ejpam-3007	214	8	′	′	NOUN
ejpam-3007	214	9	,	,	PUNCT
ejpam-3007	214	10	θ)ψ−(k	θ)ψ−(k	NOUN
ejpam-3007	214	11	,	,	PUNCT
ejpam-3007	214	12	θ	θ	PROPN
ejpam-3007	214	13	′	′	NOUN
ejpam-3007	214	14	,	,	PUNCT
ejpam-3007	215	1	x)dθ	x)dθ	PROPN
ejpam-3007	215	2	′	′	NOUN
ejpam-3007	215	3	,	,	PUNCT
ejpam-3007	215	4	k	k	PROPN
ejpam-3007	215	5	∈	∈	PROPN
ejpam-3007	215	6	r.	r.	PROPN
ejpam-3007	215	7	(	(	PUNCT
ejpam-3007	215	8	41	41	NUM
ejpam-3007	215	9	)	)	PUNCT
ejpam-3007	215	10	this	this	DET
ejpam-3007	215	11	equation	equation	NOUN
ejpam-3007	215	12	is	be	AUX
ejpam-3007	215	13	the	the	DET
ejpam-3007	215	14	key	key	NOUN
ejpam-3007	215	15	to	to	ADP
ejpam-3007	215	16	solving	solve	VERB
ejpam-3007	215	17	the	the	DET
ejpam-3007	215	18	inverse	inverse	NOUN
ejpam-3007	215	19	scattering	scattering	NOUN
ejpam-3007	215	20	problem	problem	NOUN
ejpam-3007	215	21	,	,	PUNCT
ejpam-3007	215	22	and	and	CCONJ
ejpam-3007	215	23	was	be	AUX
ejpam-3007	215	24	first	first	ADV
ejpam-3007	215	25	used	use	VERB
ejpam-3007	215	26	by	by	ADP
ejpam-3007	215	27	newton	newton	PROPN
ejpam-3007	216	1	[	[	X
ejpam-3007	216	2	11,12	11,12	NUM
ejpam-3007	216	3	]	]	PUNCT
ejpam-3007	216	4	and	and	CCONJ
ejpam-3007	216	5	somersalo	somersalo	PROPN
ejpam-3007	216	6	et	et	PROPN
ejpam-3007	216	7	al	al	PROPN
ejpam-3007	216	8	.	.	PUNCT
ejpam-3007	217	1	[	[	X
ejpam-3007	217	2	13	13	NUM
ejpam-3007	217	3	]	]	PUNCT
ejpam-3007	217	4	.	.	PUNCT
ejpam-3007	218	1	equation	equation	NOUN
ejpam-3007	218	2	(	(	PUNCT
ejpam-3007	218	3	41	41	NUM
ejpam-3007	218	4	)	)	PUNCT
ejpam-3007	218	5	is	be	AUX
ejpam-3007	218	6	equivalent	equivalent	ADJ
ejpam-3007	218	7	to	to	ADP
ejpam-3007	218	8	the	the	DET
ejpam-3007	218	9	following	following	NOUN
ejpam-3007	218	10	:	:	PUNCT
ejpam-3007	218	11	ψ+	ψ+	ADJ
ejpam-3007	218	12	=	=	SYM
ejpam-3007	218	13	sψ−	sψ−	NOUN
ejpam-3007	218	14	,	,	PUNCT
ejpam-3007	218	15	(	(	PUNCT
ejpam-3007	218	16	42	42	NUM
ejpam-3007	218	17	)	)	PUNCT
ejpam-3007	218	18	where	where	SCONJ
ejpam-3007	218	19	s	s	NOUN
ejpam-3007	218	20	is	be	AUX
ejpam-3007	218	21	a	a	DET
ejpam-3007	218	22	scattering	scatter	VERB
ejpam-3007	218	23	operator	operator	NOUN
ejpam-3007	218	24	with	with	ADP
ejpam-3007	218	25	the	the	DET
ejpam-3007	218	26	kernel	kernel	NOUN
ejpam-3007	218	27	s(k	s(k	ADV
ejpam-3007	218	28	,	,	PUNCT
ejpam-3007	218	29	l	l	NOUN
ejpam-3007	218	30	)	)	PUNCT
ejpam-3007	218	31	,	,	PUNCT
ejpam-3007	218	32	s(k	s(k	ADV
ejpam-3007	218	33	,	,	PUNCT
ejpam-3007	218	34	l	l	NOUN
ejpam-3007	218	35	)	)	PUNCT
ejpam-3007	218	36	=	=	SYM
ejpam-3007	218	37	∫	∫	PROPN
ejpam-3007	218	38	r3	r3	PROPN
ejpam-3007	218	39	ψ+(k	ψ+(k	PROPN
ejpam-3007	218	40	,	,	PUNCT
ejpam-3007	218	41	x)ψ∗−	x)ψ∗−	PROPN
ejpam-3007	218	42	(	(	PUNCT
ejpam-3007	218	43	l	l	PROPN
ejpam-3007	218	44	,	,	PUNCT
ejpam-3007	218	45	x)dx	x)dx	PROPN
ejpam-3007	218	46	.	.	PUNCT
ejpam-3007	219	1	the	the	DET
ejpam-3007	219	2	following	follow	VERB
ejpam-3007	219	3	theorem	theorem	NOUN
ejpam-3007	219	4	was	be	AUX
ejpam-3007	219	5	stated	state	VERB
ejpam-3007	219	6	in	in	ADP
ejpam-3007	219	7	[	[	X
ejpam-3007	219	8	2	2	NUM
ejpam-3007	219	9	]	]	PUNCT
ejpam-3007	219	10	:	:	PUNCT
ejpam-3007	219	11	theorem	theorem	NOUN
ejpam-3007	219	12	9	9	NUM
ejpam-3007	219	13	.	.	PUNCT
ejpam-3007	220	1	(	(	PUNCT
ejpam-3007	220	2	the	the	DET
ejpam-3007	220	3	energy	energy	NOUN
ejpam-3007	220	4	and	and	CCONJ
ejpam-3007	220	5	momentum	momentum	NOUN
ejpam-3007	220	6	conservation	conservation	NOUN
ejpam-3007	220	7	laws	law	NOUN
ejpam-3007	220	8	)	)	PUNCT
ejpam-3007	220	9	let	let	VERB
ejpam-3007	220	10	q	q	PROPN
ejpam-3007	220	11	∈	∈	PROPN
ejpam-3007	220	12	r.	r.	PROPN
ejpam-3007	220	13	then	then	ADV
ejpam-3007	220	14	,	,	PUNCT
ejpam-3007	221	1	ss∗	ss∗	NOUN
ejpam-3007	221	2	=	=	PUNCT
ejpam-3007	221	3	i	i	PROPN
ejpam-3007	221	4	,	,	PUNCT
ejpam-3007	221	5	s∗s	s∗s	X
ejpam-3007	221	6	=	=	SYM
ejpam-3007	221	7	i	i	PROPN
ejpam-3007	221	8	,	,	PUNCT
ejpam-3007	221	9	where	where	SCONJ
ejpam-3007	221	10	i	i	PRON
ejpam-3007	221	11	is	be	AUX
ejpam-3007	221	12	a	a	DET
ejpam-3007	221	13	unitary	unitary	ADJ
ejpam-3007	221	14	operator	operator	NOUN
ejpam-3007	221	15	.	.	PUNCT
ejpam-3007	222	1	definition	definition	NOUN
ejpam-3007	222	2	1	1	NUM
ejpam-3007	222	3	.	.	PUNCT
ejpam-3007	223	1	the	the	DET
ejpam-3007	223	2	set	set	NOUN
ejpam-3007	223	3	of	of	ADP
ejpam-3007	223	4	measurable	measurable	ADJ
ejpam-3007	223	5	functions	function	NOUN
ejpam-3007	223	6	r	r	NOUN
ejpam-3007	223	7	with	with	ADP
ejpam-3007	223	8	the	the	DET
ejpam-3007	223	9	norm	norm	NOUN
ejpam-3007	223	10	,	,	PUNCT
ejpam-3007	223	11	defined	define	VERB
ejpam-3007	223	12	by	by	ADP
ejpam-3007	223	13	||q||r	||q||r	PROPN
ejpam-3007	223	14	=	=	SYM
ejpam-3007	223	15	∫	∫	PROPN
ejpam-3007	223	16	r6	r6	PROPN
ejpam-3007	223	17	q(x)q(y	q(x)q(y	X
ejpam-3007	223	18	)	)	PUNCT
ejpam-3007	223	19	|x−y|2	|x−y|2	ADJ
ejpam-3007	223	20	dxdy	dxdy	NOUN
ejpam-3007	223	21	<	<	X
ejpam-3007	223	22	∞	∞	PROPN
ejpam-3007	223	23	is	be	AUX
ejpam-3007	223	24	recognized	recognize	VERB
ejpam-3007	223	25	as	as	ADP
ejpam-3007	223	26	being	be	AUX
ejpam-3007	223	27	of	of	ADP
ejpam-3007	223	28	rollnik	rollnik	NOUN
ejpam-3007	223	29	class	class	NOUN
ejpam-3007	223	30	.	.	PUNCT
ejpam-3007	224	1	let	let	VERB
ejpam-3007	224	2	us	we	PRON
ejpam-3007	224	3	take	take	VERB
ejpam-3007	224	4	into	into	ADP
ejpam-3007	224	5	consideration	consideration	NOUN
ejpam-3007	224	6	a	a	DET
ejpam-3007	224	7	series	series	NOUN
ejpam-3007	224	8	for	for	ADP
ejpam-3007	224	9	a	a	DET
ejpam-3007	224	10	:	:	PUNCT
ejpam-3007	224	11	a(k	a(k	NUM
ejpam-3007	224	12	,	,	PUNCT
ejpam-3007	224	13	k′	k′	NUM
ejpam-3007	224	14	)	)	PUNCT
ejpam-3007	224	15	=	=	PUNCT
ejpam-3007	225	1	∞∑	∞∑	PRON
ejpam-3007	225	2	n=0	n=0	NUM
ejpam-3007	225	3	an(k	an(k	NOUN
ejpam-3007	225	4	,	,	PUNCT
ejpam-3007	225	5	k′	k′	PROPN
ejpam-3007	225	6	)	)	PUNCT
ejpam-3007	225	7	,	,	PUNCT
ejpam-3007	225	8	a0(k	a0(k	PROPN
ejpam-3007	225	9	,	,	PUNCT
ejpam-3007	225	10	k′	k′	NUM
ejpam-3007	225	11	)	)	PUNCT
ejpam-3007	225	12	=	=	SYM
ejpam-3007	225	13	1	1	NUM
ejpam-3007	225	14	(	(	PUNCT
ejpam-3007	225	15	2π)3	2π)3	NUM
ejpam-3007	225	16	∫	∫	PROPN
ejpam-3007	225	17	r3	r3	PROPN
ejpam-3007	225	18	ei(k−k	ei(k−k	PROPN
ejpam-3007	225	19	′,x)q(x)dx	′,x)q(x)dx	PROPN
ejpam-3007	225	20	,	,	PUNCT
ejpam-3007	225	21	(	(	PUNCT
ejpam-3007	225	22	43	43	NUM
ejpam-3007	225	23	)	)	PUNCT
ejpam-3007	225	24	an(k	an(k	NOUN
ejpam-3007	225	25	,	,	PUNCT
ejpam-3007	225	26	k′	k′	NUM
ejpam-3007	225	27	)	)	PUNCT
ejpam-3007	225	28	=	=	SYM
ejpam-3007	225	29	1	1	NUM
ejpam-3007	225	30	(	(	PUNCT
ejpam-3007	225	31	2π)3	2π)3	NUM
ejpam-3007	225	32	(	(	PUNCT
ejpam-3007	225	33	−1)n	−1)n	X
ejpam-3007	225	34	(	(	PUNCT
ejpam-3007	225	35	4π)n	4π)n	NUM
ejpam-3007	225	36	∫	∫	PROPN
ejpam-3007	225	37	r3(n+1	r3(n+1	PROPN
ejpam-3007	225	38	)	)	PUNCT
ejpam-3007	225	39	ei(k	ei(k	NOUN
ejpam-3007	225	40	,	,	PUNCT
ejpam-3007	225	41	x0)q(x0	x0)q(x0	PROPN
ejpam-3007	225	42	)	)	PUNCT
ejpam-3007	225	43	ei|k||x0−x1|	ei|k||x0−x1|	PROPN
ejpam-3007	225	44	|x0	|x0	NOUN
ejpam-3007	225	45	−	−	PROPN
ejpam-3007	226	1	x1|	x1|	PROPN
ejpam-3007	226	2	q(x1)×	q(x1)×	PROPN
ejpam-3007	226	3	...	...	PUNCT
ejpam-3007	226	4	×	×	PROPN
ejpam-3007	226	5	×	×	NOUN
ejpam-3007	226	6	...	...	PUNCT
ejpam-3007	226	7	×	×	NOUN
ejpam-3007	226	8	q(xn−1	q(xn−1	NOUN
ejpam-3007	226	9	)	)	PUNCT
ejpam-3007	226	10	ei|k||xn−1−xn|	ei|k||xn−1−xn|	NOUN
ejpam-3007	226	11	|xn−1	|xn−1	PROPN
ejpam-3007	226	12	−	−	PROPN
ejpam-3007	226	13	xn|	xn|	PROPN
ejpam-3007	227	1	q(xn)e−i(k	q(xn)e−i(k	PROPN
ejpam-3007	227	2	′,xn)dx0	′,xn)dx0	NOUN
ejpam-3007	227	3	...	...	PUNCT
ejpam-3007	227	4	dxn	dxn	PROPN
ejpam-3007	227	5	.	.	PUNCT
ejpam-3007	228	1	as	as	ADV
ejpam-3007	228	2	well	well	ADV
ejpam-3007	228	3	as	as	ADP
ejpam-3007	228	4	in	in	ADP
ejpam-3007	228	5	[	[	NOUN
ejpam-3007	228	6	8	8	NUM
ejpam-3007	228	7	]	]	PUNCT
ejpam-3007	228	8	,	,	PUNCT
ejpam-3007	228	9	p.120	p.120	ADJ
ejpam-3007	228	10	we	we	PRON
ejpam-3007	228	11	formulate	formulate	VERB
ejpam-3007	228	12	.	.	PUNCT
ejpam-3007	229	1	definition	definition	NOUN
ejpam-3007	229	2	2	2	NUM
ejpam-3007	229	3	.	.	PUNCT
ejpam-3007	229	4	series	series	NOUN
ejpam-3007	229	5	(	(	PUNCT
ejpam-3007	229	6	43	43	NUM
ejpam-3007	229	7	)	)	PUNCT
ejpam-3007	229	8	is	be	AUX
ejpam-3007	229	9	called	call	VERB
ejpam-3007	229	10	born	bear	VERB
ejpam-3007	229	11	’s	’s	PART
ejpam-3007	229	12	series	series	NOUN
ejpam-3007	229	13	.	.	PUNCT
ejpam-3007	230	1	theorem	theorem	VERB
ejpam-3007	230	2	10	10	NUM
ejpam-3007	230	3	.	.	PUNCT
ejpam-3007	231	1	let	let	VERB
ejpam-3007	231	2	q	q	PROPN
ejpam-3007	231	3	∈	∈	PROPN
ejpam-3007	231	4	l1(r3	l1(r3	NOUN
ejpam-3007	231	5	)	)	PUNCT
ejpam-3007	231	6	∩	∩	ADJ
ejpam-3007	231	7	r	r	NOUN
ejpam-3007	231	8	.	.	PUNCT
ejpam-3007	232	1	if	if	SCONJ
ejpam-3007	232	2	‖q‖2r	‖q‖2r	PROPN
ejpam-3007	232	3	≤	≤	NOUN
ejpam-3007	232	4	4π	4π	NUM
ejpam-3007	232	5	,	,	PUNCT
ejpam-3007	232	6	then	then	ADV
ejpam-3007	232	7	born	bear	VERB
ejpam-3007	232	8	’s	’s	PART
ejpam-3007	232	9	series	series	NOUN
ejpam-3007	232	10	for	for	ADP
ejpam-3007	232	11	a(k	a(k	PROPN
ejpam-3007	232	12	,	,	PUNCT
ejpam-3007	232	13	k′	k′	PROPN
ejpam-3007	232	14	)	)	PUNCT
ejpam-3007	232	15	converges	converge	NOUN
ejpam-3007	232	16	as	as	ADP
ejpam-3007	232	17	k	k	PROPN
ejpam-3007	232	18	,	,	PUNCT
ejpam-3007	232	19	k′	k′	PROPN
ejpam-3007	232	20	∈	∈	PROPN
ejpam-3007	232	21	r3	r3	PROPN
ejpam-3007	232	22	.	.	PUNCT
ejpam-3007	233	1	a.	a.	PROPN
ejpam-3007	233	2	durmagambetov	durmagambetov	PROPN
ejpam-3007	233	3	/	/	SYM
ejpam-3007	233	4	eur	eur	PROPN
ejpam-3007	233	5	.	.	PUNCT
ejpam-3007	234	1	j.	j.	PROPN
ejpam-3007	234	2	pure	pure	PROPN
ejpam-3007	234	3	appl	appl	PROPN
ejpam-3007	234	4	.	.	PROPN
ejpam-3007	234	5	math	math	PROPN
ejpam-3007	234	6	,	,	PUNCT
ejpam-3007	234	7	10	10	NUM
ejpam-3007	234	8	(	(	PUNCT
ejpam-3007	234	9	4	4	NUM
ejpam-3007	234	10	)	)	PUNCT
ejpam-3007	234	11	(	(	PUNCT
ejpam-3007	234	12	2017	2017	NUM
ejpam-3007	234	13	)	)	PUNCT
ejpam-3007	234	14	,	,	PUNCT
ejpam-3007	234	15	763	763	NUM
ejpam-3007	234	16	-	-	SYM
ejpam-3007	234	17	785	785	NUM
ejpam-3007	234	18	773	773	NUM
ejpam-3007	234	19	proof	proof	NOUN
ejpam-3007	234	20	.	.	PUNCT
ejpam-3007	235	1	is	be	AUX
ejpam-3007	235	2	in	in	ADP
ejpam-3007	235	3	[	[	X
ejpam-3007	235	4	8	8	NUM
ejpam-3007	235	5	]	]	PUNCT
ejpam-3007	235	6	,	,	PUNCT
ejpam-3007	235	7	121	121	NUM
ejpam-3007	235	8	.	.	PUNCT
ejpam-3007	236	1	let	let	VERB
ejpam-3007	236	2	us	we	PRON
ejpam-3007	236	3	introduce	introduce	VERB
ejpam-3007	236	4	the	the	DET
ejpam-3007	236	5	following	following	ADJ
ejpam-3007	236	6	notation	notation	NOUN
ejpam-3007	236	7	:	:	PUNCT
ejpam-3007	236	8	qf	qf	PROPN
ejpam-3007	236	9	=	=	PUNCT
ejpam-3007	236	10	∫	∫	PROPN
ejpam-3007	236	11	s2	s2	PROPN
ejpam-3007	236	12	q(k	q(k	PROPN
ejpam-3007	236	13	,	,	PUNCT
ejpam-3007	236	14	θ	θ	PROPN
ejpam-3007	236	15	′	′	NUM
ejpam-3007	236	16	,	,	PUNCT
ejpam-3007	236	17	θ)f(k	θ)f(k	ADJ
ejpam-3007	236	18	,	,	PUNCT
ejpam-3007	236	19	θ	θ	PROPN
ejpam-3007	236	20	′	′	NUM
ejpam-3007	236	21	)	)	PUNCT
ejpam-3007	237	1	dθ	dθ	PROPN
ejpam-3007	237	2	′	′	NUM
ejpam-3007	237	3	,	,	PUNCT
ejpam-3007	237	4	t+	t+	PUNCT
ejpam-3007	237	5	q	q	PROPN
ejpam-3007	237	6	f	f	X
ejpam-3007	237	7	=	=	SYM
ejpam-3007	237	8	∫	∫	PROPN
ejpam-3007	237	9	∞	∞	PROPN
ejpam-3007	237	10	0	0	NUM
ejpam-3007	237	11	∫	∫	PROPN
ejpam-3007	237	12	s2	s2	PROPN
ejpam-3007	237	13	q(k	q(k	PROPN
ejpam-3007	237	14	,	,	PUNCT
ejpam-3007	237	15	θ	θ	PROPN
ejpam-3007	237	16	′	′	NUM
ejpam-3007	237	17	,	,	PUNCT
ejpam-3007	237	18	θ)f(k	θ)f(k	ADJ
ejpam-3007	237	19	,	,	PUNCT
ejpam-3007	237	20	θ	θ	PROPN
ejpam-3007	237	21	′	′	NUM
ejpam-3007	237	22	)	)	PUNCT
ejpam-3007	238	1	dθ	dθ	NOUN
ejpam-3007	238	2	′	′	NUM
ejpam-3007	238	3	|k|2	|k|2	PROPN
ejpam-3007	238	4	−	−	PROPN
ejpam-3007	238	5	s2	s2	NOUN
ejpam-3007	238	6	−	−	PROPN
ejpam-3007	238	7	i0	i0	PROPN
ejpam-3007	238	8	s2ds	s2ds	PROPN
ejpam-3007	238	9	,	,	PUNCT
ejpam-3007	238	10	f	f	PROPN
ejpam-3007	238	11	=	=	PUNCT
ejpam-3007	238	12	f(k	f(k	PROPN
ejpam-3007	238	13	,	,	PUNCT
ejpam-3007	238	14	θ	θ	PROPN
ejpam-3007	238	15	′	′	NUM
ejpam-3007	238	16	)	)	PUNCT
ejpam-3007	238	17	,	,	PUNCT
ejpam-3007	238	18	q(k	q(k	PROPN
ejpam-3007	238	19	,	,	PUNCT
ejpam-3007	238	20	θ	θ	PROPN
ejpam-3007	238	21	′	′	NUM
ejpam-3007	238	22	,	,	PUNCT
ejpam-3007	238	23	θ	θ	X
ejpam-3007	238	24	)	)	PUNCT
ejpam-3007	238	25	=	=	SYM
ejpam-3007	239	1	˜q(k	˜q(k	PROPN
ejpam-3007	239	2	−	−	PROPN
ejpam-3007	239	3	k′	k′	PROPN
ejpam-3007	239	4	)	)	PUNCT
ejpam-3007	239	5	,	,	PUNCT
ejpam-3007	239	6	θ′	θ′	NOUN
ejpam-3007	239	7	=	=	SYM
ejpam-3007	239	8	k	k	NOUN
ejpam-3007	239	9	′	′	NUM
ejpam-3007	239	10	|k′	|k′	NOUN
ejpam-3007	239	11	|	|	ADV
ejpam-3007	239	12	,	,	PUNCT
ejpam-3007	239	13	θ	θ	PROPN
ejpam-3007	239	14	=	=	SYM
ejpam-3007	240	1	k	k	X
ejpam-3007	240	2	|k|	|k|	PROPN
ejpam-3007	240	3	,	,	PUNCT
ejpam-3007	240	4	θ	θ	PROPN
ejpam-3007	240	5	,	,	PUNCT
ejpam-3007	240	6	θ	θ	NOUN
ejpam-3007	240	7	′	′	NOUN
ejpam-3007	240	8	∈	∈	PROPN
ejpam-3007	240	9	s2	s2	PROPN
ejpam-3007	240	10	,	,	PUNCT
ejpam-3007	240	11	sφx0f	sφx0f	X
ejpam-3007	240	12	=	=	SYM
ejpam-3007	240	13	∫	∫	PROPN
ejpam-3007	240	14	s2	s2	PROPN
ejpam-3007	240	15	f(k	f(k	PROPN
ejpam-3007	240	16	,	,	PUNCT
ejpam-3007	240	17	θ)ei(x0,k)dθ	θ)ei(x0,k)dθ	NOUN
ejpam-3007	240	18	,	,	PUNCT
ejpam-3007	240	19	for	for	ADP
ejpam-3007	240	20	f	f	PROPN
ejpam-3007	240	21	=	=	PUNCT
ejpam-3007	240	22	f(k	f(k	PROPN
ejpam-3007	240	23	,	,	PUNCT
ejpam-3007	240	24	θ	θ	PROPN
ejpam-3007	240	25	′	′	NUM
ejpam-3007	240	26	,	,	PUNCT
ejpam-3007	240	27	x	x	X
ejpam-3007	240	28	)	)	PUNCT
ejpam-3007	240	29	,	,	PUNCT
ejpam-3007	240	30	df	df	PROPN
ejpam-3007	240	31	=	=	SYM
ejpam-3007	240	32	k	k	PROPN
ejpam-3007	240	33	∫	∫	PROPN
ejpam-3007	240	34	s2	s2	PROPN
ejpam-3007	240	35	a(k	a(k	PROPN
ejpam-3007	240	36	,	,	PUNCT
ejpam-3007	240	37	θ	θ	PROPN
ejpam-3007	240	38	′	′	NUM
ejpam-3007	240	39	,	,	PUNCT
ejpam-3007	240	40	θ)f(k	θ)f(k	ADJ
ejpam-3007	240	41	,	,	PUNCT
ejpam-3007	240	42	θ	θ	PROPN
ejpam-3007	240	43	′	′	NOUN
ejpam-3007	240	44	,	,	PUNCT
ejpam-3007	241	1	x)dθ	x)dθ	PROPN
ejpam-3007	241	2	′	′	NUM
ejpam-3007	241	3	,	,	PUNCT
ejpam-3007	241	4	(	(	PUNCT
ejpam-3007	241	5	44	44	NUM
ejpam-3007	241	6	)	)	PUNCT
ejpam-3007	241	7	lemma	lemma	PROPN
ejpam-3007	241	8	11	11	NUM
ejpam-3007	241	9	.	.	PUNCT
ejpam-3007	241	10	suppose	suppose	VERB
ejpam-3007	241	11	that	that	SCONJ
ejpam-3007	241	12	q	q	PROPN
ejpam-3007	241	13	∈	∈	PROPN
ejpam-3007	241	14	r	r	NOUN
ejpam-3007	241	15	,	,	PUNCT
ejpam-3007	241	16	maxk	maxk	NOUN
ejpam-3007	241	17	,	,	PUNCT
ejpam-3007	241	18	k′	k′	PROPN
ejpam-3007	241	19	|t+	|t+	PROPN
ejpam-3007	241	20	q	q	PUNCT
ejpam-3007	241	21	(	(	PUNCT
ejpam-3007	241	22	k	k	X
ejpam-3007	241	23	,	,	PUNCT
ejpam-3007	241	24	k′|	k′|	VERB
ejpam-3007	241	25	<	<	X
ejpam-3007	241	26	1	1	NUM
ejpam-3007	241	27	/	/	SYM
ejpam-3007	241	28	c0	c0	NOUN
ejpam-3007	241	29	,	,	PUNCT
ejpam-3007	241	30	csupek	csupek	PROPN
ejpam-3007	241	31	,	,	PUNCT
ejpam-3007	241	32	ek′	ek′	INTJ
ejpam-3007	241	33	,	,	PUNCT
ejpam-3007	241	34	k|q(k	k|q(k	PROPN
ejpam-3007	241	35	,	,	PUNCT
ejpam-3007	241	36	k′)|	k′)|	X
ejpam-3007	241	37	<	<	X
ejpam-3007	241	38	1	1	NUM
ejpam-3007	241	39	,	,	PUNCT
ejpam-3007	241	40	then	then	ADV
ejpam-3007	241	41	a(k	a(k	NUM
ejpam-3007	241	42	,	,	PUNCT
ejpam-3007	241	43	k′	k′	NUM
ejpam-3007	241	44	)	)	PUNCT
ejpam-3007	241	45	=	=	SYM
ejpam-3007	241	46	c0q̃(k	c0q̃(k	PROPN
ejpam-3007	241	47	−	−	PROPN
ejpam-3007	241	48	k′	k′	PROPN
ejpam-3007	241	49	)	)	PUNCT
ejpam-3007	242	1	+	+	CCONJ
ejpam-3007	242	2	c2	c2	PROPN
ejpam-3007	242	3	0	0	NUM
ejpam-3007	242	4	∫	∫	PROPN
ejpam-3007	242	5	r3	r3	PROPN
ejpam-3007	242	6	∫	∫	PROPN
ejpam-3007	242	7	r3	r3	PROPN
ejpam-3007	242	8	q̃(k	q̃(k	PROPN
ejpam-3007	242	9	+	+	NUM
ejpam-3007	242	10	p)q̃(p−	p)q̃(p−	NOUN
ejpam-3007	242	11	k′	k′	NUM
ejpam-3007	242	12	)	)	PUNCT
ejpam-3007	242	13	(	(	PUNCT
ejpam-3007	242	14	|p|2	|p|2	PROPN
ejpam-3007	242	15	−	−	PUNCT
ejpam-3007	242	16	|k|2	|k|2	PROPN
ejpam-3007	242	17	−	−	PROPN
ejpam-3007	242	18	i0	i0	PROPN
ejpam-3007	242	19	)	)	PUNCT
ejpam-3007	243	1	dk	dk	PROPN
ejpam-3007	243	2	+	+	CCONJ
ejpam-3007	243	3	....	....	PUNCT
ejpam-3007	244	1	a(k	a(k	ADJ
ejpam-3007	244	2	,	,	PUNCT
ejpam-3007	244	3	k′	k′	PROPN
ejpam-3007	244	4	)	)	PUNCT
ejpam-3007	244	5	=	=	SYM
ejpam-3007	244	6	c0q(k	c0q(k	PROPN
ejpam-3007	244	7	,	,	PUNCT
ejpam-3007	244	8	k′	k′	PROPN
ejpam-3007	244	9	)	)	PUNCT
ejpam-3007	245	1	+	+	CCONJ
ejpam-3007	245	2	c2	c2	PROPN
ejpam-3007	245	3	0	0	NUM
ejpam-3007	245	4	t	t	NOUN
ejpam-3007	245	5	+	+	CCONJ
ejpam-3007	245	6	qq+	qq+	PROPN
ejpam-3007	245	7	c2	c2	PROPN
ejpam-3007	245	8	0	0	NUM
ejpam-3007	245	9	t	t	NOUN
ejpam-3007	245	10	+	+	CCONJ
ejpam-3007	245	11	q	q	PROPN
ejpam-3007	245	12	t	t	PROPN
ejpam-3007	246	1	+	+	CCONJ
ejpam-3007	246	2	qq	qq	X
ejpam-3007	246	3	...	...	PUNCT
ejpam-3007	247	1	supek	supek	ADJ
ejpam-3007	247	2	,	,	PUNCT
ejpam-3007	247	3	ek′	ek′	INTJ
ejpam-3007	247	4	,	,	PUNCT
ejpam-3007	247	5	k|a(k	k|a(k	PROPN
ejpam-3007	247	6	,	,	PUNCT
ejpam-3007	247	7	k′)|	k′)|	X
ejpam-3007	247	8	<	<	X
ejpam-3007	247	9	csupek	csupek	PROPN
ejpam-3007	247	10	,	,	PUNCT
ejpam-3007	247	11	ek′	ek′	INTJ
ejpam-3007	247	12	,	,	PUNCT
ejpam-3007	247	13	k|q(k	k|q(k	PROPN
ejpam-3007	247	14	,	,	PUNCT
ejpam-3007	247	15	k′)|+	k′)|+	PROPN
ejpam-3007	247	16	csupek	csupek	PROPN
ejpam-3007	247	17	,	,	PUNCT
ejpam-3007	247	18	ek′	ek′	INTJ
ejpam-3007	247	19	,	,	PUNCT
ejpam-3007	247	20	k|tq(k	k|tq(k	ADJ
ejpam-3007	247	21	,	,	PUNCT
ejpam-3007	247	22	k′)|	k′)|	PROPN
ejpam-3007	247	23	,	,	PUNCT
ejpam-3007	247	24	supek	supek	ADJ
ejpam-3007	247	25	,	,	PUNCT
ejpam-3007	247	26	ek′	ek′	ADJ
ejpam-3007	247	27	,	,	PUNCT
ejpam-3007	247	28	k|ta(k	k|ta(k	NOUN
ejpam-3007	247	29	,	,	PUNCT
ejpam-3007	247	30	k′)|	k′)|	X
ejpam-3007	247	31	<	<	X
ejpam-3007	247	32	csupek	csupek	PROPN
ejpam-3007	247	33	,	,	PUNCT
ejpam-3007	247	34	ek′	ek′	INTJ
ejpam-3007	247	35	,	,	PUNCT
ejpam-3007	247	36	k|tq(k	k|tq(k	ADJ
ejpam-3007	247	37	,	,	PUNCT
ejpam-3007	247	38	k′)|+	k′)|+	PROPN
ejpam-3007	247	39	csupek	csupek	PROPN
ejpam-3007	247	40	,	,	PUNCT
ejpam-3007	247	41	ek′	ek′	INTJ
ejpam-3007	247	42	,	,	PUNCT
ejpam-3007	247	43	k|q(k	k|q(k	PROPN
ejpam-3007	247	44	,	,	PUNCT
ejpam-3007	247	45	k′)|	k′)|	PROPN
ejpam-3007	247	46	proof	proof	NOUN
ejpam-3007	247	47	.	.	PUNCT
ejpam-3007	248	1	folows	folow	NOUN
ejpam-3007	248	2	from	from	ADP
ejpam-3007	248	3	the	the	DET
ejpam-3007	248	4	definition	definition	NOUN
ejpam-3007	248	5	a(k	a(k	PROPN
ejpam-3007	248	6	,	,	PUNCT
ejpam-3007	248	7	k′	k′	PROPN
ejpam-3007	248	8	)	)	PUNCT
ejpam-3007	248	9	,	,	PUNCT
ejpam-3007	248	10	t+	t+	PRON
ejpam-3007	248	11	q	q	PROPN
ejpam-3007	248	12	f	f	PROPN
ejpam-3007	248	13	and	and	CCONJ
ejpam-3007	248	14	the	the	DET
ejpam-3007	248	15	formula	formula	NOUN
ejpam-3007	248	16	for	for	ADP
ejpam-3007	248	17	a	a	DET
ejpam-3007	248	18	geometric	geometric	ADJ
ejpam-3007	248	19	progression	progression	NOUN
ejpam-3007	248	20	as	as	SCONJ
ejpam-3007	248	21	shown	show	VERB
ejpam-3007	248	22	in	in	ADP
ejpam-3007	248	23	[	[	X
ejpam-3007	248	24	14	14	NUM
ejpam-3007	248	25	]	]	PUNCT
ejpam-3007	248	26	,	,	PUNCT
ejpam-3007	248	27	ψ±(k	ψ±(k	PROPN
ejpam-3007	248	28	,	,	PUNCT
ejpam-3007	248	29	x	x	X
ejpam-3007	248	30	)	)	PUNCT
ejpam-3007	248	31	is	be	AUX
ejpam-3007	248	32	an	an	DET
ejpam-3007	248	33	orthonormal	orthonormal	ADJ
ejpam-3007	248	34	system	system	NOUN
ejpam-3007	248	35	of	of	ADP
ejpam-3007	248	36	h	h	NOUN
ejpam-3007	248	37	eigenfunctions	eigenfunction	NOUN
ejpam-3007	248	38	for	for	ADP
ejpam-3007	248	39	the	the	DET
ejpam-3007	248	40	continuous	continuous	ADJ
ejpam-3007	248	41	spectrum	spectrum	NOUN
ejpam-3007	248	42	.	.	PUNCT
ejpam-3007	249	1	in	in	ADP
ejpam-3007	249	2	addition	addition	NOUN
ejpam-3007	249	3	to	to	ADP
ejpam-3007	249	4	the	the	DET
ejpam-3007	249	5	continuous	continuous	ADJ
ejpam-3007	249	6	spectrum	spectrum	NOUN
ejpam-3007	249	7	there	there	PRON
ejpam-3007	249	8	are	be	VERB
ejpam-3007	249	9	a	a	DET
ejpam-3007	249	10	finite	finite	ADJ
ejpam-3007	249	11	number	number	NOUN
ejpam-3007	249	12	n	n	PROPN
ejpam-3007	249	13	of	of	ADP
ejpam-3007	249	14	h	h	PRON
ejpam-3007	249	15	negative	negative	ADJ
ejpam-3007	249	16	eigenvalues	eigenvalue	NOUN
ejpam-3007	249	17	,	,	PUNCT
ejpam-3007	249	18	designated	designate	VERB
ejpam-3007	249	19	as	as	ADP
ejpam-3007	249	20	−e2	−e2	PROPN
ejpam-3007	249	21	j	j	PROPN
ejpam-3007	249	22	with	with	ADP
ejpam-3007	249	23	corresponding	correspond	VERB
ejpam-3007	249	24	normalized	normalize	VERB
ejpam-3007	249	25	eigenfunctions	eigenfunction	NOUN
ejpam-3007	250	1	ψj(x,−e2	ψj(x,−e2	PROPN
ejpam-3007	250	2	j	j	PROPN
ejpam-3007	250	3	)	)	PUNCT
ejpam-3007	250	4	(	(	PUNCT
ejpam-3007	250	5	j	j	NOUN
ejpam-3007	250	6	=	=	SYM
ejpam-3007	250	7	1	1	NUM
ejpam-3007	250	8	,	,	PUNCT
ejpam-3007	250	9	n	n	CCONJ
ejpam-3007	250	10	)	)	PUNCT
ejpam-3007	250	11	,	,	PUNCT
ejpam-3007	250	12	where	where	SCONJ
ejpam-3007	250	13	ψj(x,−e2	ψj(x,−e2	PROPN
ejpam-3007	250	14	j	j	PROPN
ejpam-3007	250	15	)	)	PUNCT
ejpam-3007	250	16	∈	∈	PROPN
ejpam-3007	250	17	l2(r3	l2(r3	NOUN
ejpam-3007	250	18	)	)	PUNCT
ejpam-3007	250	19	.	.	PUNCT
ejpam-3007	251	1	we	we	PRON
ejpam-3007	251	2	present	present	VERB
ejpam-3007	251	3	povzner	povzner	NOUN
ejpam-3007	251	4	’s	’s	PART
ejpam-3007	251	5	results	result	NOUN
ejpam-3007	251	6	[	[	X
ejpam-3007	251	7	14	14	NUM
ejpam-3007	251	8	]	]	PUNCT
ejpam-3007	251	9	below	below	ADV
ejpam-3007	251	10	:	:	PUNCT
ejpam-3007	251	11	theorem	theorem	NOUN
ejpam-3007	251	12	12	12	NUM
ejpam-3007	251	13	.	.	PUNCT
ejpam-3007	252	1	(	(	PUNCT
ejpam-3007	252	2	completeness	completeness	NOUN
ejpam-3007	252	3	)	)	PUNCT
ejpam-3007	252	4	for	for	ADP
ejpam-3007	252	5	both	both	CCONJ
ejpam-3007	252	6	an	an	DET
ejpam-3007	252	7	arbitrary	arbitrary	ADJ
ejpam-3007	252	8	f	f	PROPN
ejpam-3007	252	9	∈	∈	PROPN
ejpam-3007	252	10	l2(r3	l2(r3	PROPN
ejpam-3007	252	11	)	)	PUNCT
ejpam-3007	252	12	and	and	CCONJ
ejpam-3007	252	13	for	for	ADP
ejpam-3007	252	14	h	h	NOUN
ejpam-3007	252	15	eigenfunctions	eigenfunction	NOUN
ejpam-3007	252	16	,	,	PUNCT
ejpam-3007	252	17	parseval	parseval	NOUN
ejpam-3007	252	18	’s	’s	PART
ejpam-3007	252	19	identity	identity	NOUN
ejpam-3007	252	20	is	be	AUX
ejpam-3007	252	21	valid	valid	ADJ
ejpam-3007	252	22	.	.	PUNCT
ejpam-3007	253	1	|f	|f	PROPN
ejpam-3007	254	1	|2l2	|2l2	INTJ
ejpam-3007	254	2	=	=	SYM
ejpam-3007	254	3	(	(	PUNCT
ejpam-3007	254	4	pdf	pdf	NOUN
ejpam-3007	254	5	,	,	PUNCT
ejpam-3007	254	6	pdf	pdf	NOUN
ejpam-3007	254	7	)	)	PUNCT
ejpam-3007	254	8	+	+	CCONJ
ejpam-3007	254	9	(	(	PUNCT
ejpam-3007	254	10	pacf	pacf	NOUN
ejpam-3007	254	11	,	,	PUNCT
ejpam-3007	254	12	pacf	pacf	NOUN
ejpam-3007	254	13	)	)	PUNCT
ejpam-3007	254	14	.	.	PUNCT
ejpam-3007	255	1	pdf	pdf	NOUN
ejpam-3007	255	2	=	=	PUNCT
ejpam-3007	256	1	n∑	n∑	NOUN
ejpam-3007	256	2	j=1	j=1	ADJ
ejpam-3007	256	3	fjψj(x,−ej	fjψj(x,−ej	NOUN
ejpam-3007	256	4	)	)	PUNCT
ejpam-3007	256	5	.	.	PUNCT
ejpam-3007	257	1	pacf	pacf	NOUN
ejpam-3007	258	1	=	=	SYM
ejpam-3007	258	2	∫	∫	PROPN
ejpam-3007	258	3	∞	∞	PROPN
ejpam-3007	258	4	0	0	NUM
ejpam-3007	258	5	∫	∫	PROPN
ejpam-3007	258	6	s2	s2	PROPN
ejpam-3007	258	7	s2f̄(s)ψ+(s	s2f̄(s)ψ+(s	PROPN
ejpam-3007	258	8	,	,	PUNCT
ejpam-3007	258	9	θ	θ	PROPN
ejpam-3007	258	10	,	,	PUNCT
ejpam-3007	258	11	x)dθds	x)dθds	PROPN
ejpam-3007	258	12	,	,	PUNCT
ejpam-3007	258	13	(	(	PUNCT
ejpam-3007	258	14	45	45	NUM
ejpam-3007	258	15	)	)	PUNCT
ejpam-3007	258	16	where	where	SCONJ
ejpam-3007	258	17	f̄	f̄	PROPN
ejpam-3007	258	18	and	and	CCONJ
ejpam-3007	258	19	fj	fj	PROPN
ejpam-3007	258	20	are	be	AUX
ejpam-3007	258	21	fourier	fourier	ADJ
ejpam-3007	258	22	coefficients	coefficient	NOUN
ejpam-3007	258	23	for	for	ADP
ejpam-3007	258	24	the	the	DET
ejpam-3007	258	25	continuous	continuous	ADJ
ejpam-3007	258	26	and	and	CCONJ
ejpam-3007	258	27	discrete	discrete	ADJ
ejpam-3007	258	28	cases	case	NOUN
ejpam-3007	258	29	.	.	PUNCT
ejpam-3007	259	1	theorem	theorem	VERB
ejpam-3007	259	2	13	13	NUM
ejpam-3007	259	3	.	.	PUNCT
ejpam-3007	260	1	(	(	PUNCT
ejpam-3007	260	2	birmann	birmann	NOUN
ejpam-3007	260	3	–	–	PUNCT
ejpam-3007	260	4	schwinger	schwinger	NOUN
ejpam-3007	260	5	estimation	estimation	NOUN
ejpam-3007	260	6	)	)	PUNCT
ejpam-3007	260	7	.	.	PUNCT
ejpam-3007	261	1	let	let	VERB
ejpam-3007	261	2	q	q	PROPN
ejpam-3007	261	3	∈	∈	PROPN
ejpam-3007	261	4	r.	r.	PROPN
ejpam-3007	261	5	then	then	ADV
ejpam-3007	261	6	,	,	PUNCT
ejpam-3007	261	7	the	the	DET
ejpam-3007	261	8	number	number	NOUN
ejpam-3007	261	9	of	of	ADP
ejpam-3007	261	10	discrete	discrete	ADJ
ejpam-3007	261	11	eigenvalues	eigenvalue	NOUN
ejpam-3007	261	12	can	can	AUX
ejpam-3007	261	13	be	be	AUX
ejpam-3007	261	14	estimated	estimate	VERB
ejpam-3007	261	15	as	as	ADP
ejpam-3007	261	16	:	:	PUNCT
ejpam-3007	261	17	n(q	n(q	PROPN
ejpam-3007	261	18	)	)	PUNCT
ejpam-3007	261	19	≤	≤	NUM
ejpam-3007	261	20	1	1	NUM
ejpam-3007	261	21	(	(	PUNCT
ejpam-3007	261	22	4π)2	4π)2	NUM
ejpam-3007	261	23	∫	∫	PROPN
ejpam-3007	261	24	r3	r3	PROPN
ejpam-3007	261	25	∫	∫	PROPN
ejpam-3007	261	26	r3	r3	PROPN
ejpam-3007	261	27	q(x)q(y	q(x)q(y	PROPN
ejpam-3007	261	28	)	)	PUNCT
ejpam-3007	261	29	|x−	|x−	PROPN
ejpam-3007	261	30	y|2	y|2	PROPN
ejpam-3007	261	31	dxdy	dxdy	PROPN
ejpam-3007	261	32	.	.	PUNCT
ejpam-3007	262	1	(	(	PUNCT
ejpam-3007	262	2	46	46	NUM
ejpam-3007	262	3	)	)	PUNCT
ejpam-3007	262	4	a.	a.	NOUN
ejpam-3007	262	5	durmagambetov	durmagambetov	PROPN
ejpam-3007	262	6	/	/	SYM
ejpam-3007	262	7	eur	eur	PROPN
ejpam-3007	262	8	.	.	PUNCT
ejpam-3007	263	1	j.	j.	PROPN
ejpam-3007	263	2	pure	pure	PROPN
ejpam-3007	263	3	appl	appl	PROPN
ejpam-3007	263	4	.	.	PROPN
ejpam-3007	263	5	math	math	PROPN
ejpam-3007	263	6	,	,	PUNCT
ejpam-3007	263	7	10	10	NUM
ejpam-3007	263	8	(	(	PUNCT
ejpam-3007	263	9	4	4	NUM
ejpam-3007	263	10	)	)	PUNCT
ejpam-3007	263	11	(	(	PUNCT
ejpam-3007	263	12	2017	2017	NUM
ejpam-3007	263	13	)	)	PUNCT
ejpam-3007	263	14	,	,	PUNCT
ejpam-3007	263	15	763	763	NUM
ejpam-3007	263	16	-	-	SYM
ejpam-3007	263	17	785	785	NUM
ejpam-3007	263	18	774	774	NUM
ejpam-3007	263	19	this	this	DET
ejpam-3007	263	20	theorem	theorem	NOUN
ejpam-3007	263	21	was	be	AUX
ejpam-3007	263	22	proved	prove	VERB
ejpam-3007	263	23	in	in	ADP
ejpam-3007	263	24	[	[	X
ejpam-3007	263	25	14	14	NUM
ejpam-3007	263	26	]	]	PUNCT
ejpam-3007	263	27	.	.	PUNCT
ejpam-3007	264	1	we	we	PRON
ejpam-3007	264	2	define	define	VERB
ejpam-3007	264	3	the	the	DET
ejpam-3007	264	4	operators	operator	NOUN
ejpam-3007	264	5	t±	t±	ADP
ejpam-3007	264	6	,	,	PUNCT
ejpam-3007	264	7	t	t	PROPN
ejpam-3007	264	8	for	for	ADP
ejpam-3007	264	9	f	f	PROPN
ejpam-3007	264	10	∈	∈	PROPN
ejpam-3007	264	11	w	w	PROPN
ejpam-3007	264	12	1	1	NUM
ejpam-3007	264	13	2	2	NUM
ejpam-3007	264	14	(	(	PUNCT
ejpam-3007	264	15	r	r	NOUN
ejpam-3007	264	16	)	)	PUNCT
ejpam-3007	264	17	as	as	SCONJ
ejpam-3007	264	18	follows	follow	VERB
ejpam-3007	264	19	:	:	PUNCT
ejpam-3007	264	20	t+f	t+f	NUM
ejpam-3007	264	21	=	=	SYM
ejpam-3007	264	22	1	1	NUM
ejpam-3007	264	23	2πi	2πi	NOUN
ejpam-3007	264	24	lim	lim	PROPN
ejpam-3007	264	25	imz→0	imz→0	PROPN
ejpam-3007	264	26	∞∫	∞∫	PROPN
ejpam-3007	264	27	−∞	−∞	ADP
ejpam-3007	264	28	f(s	f(	NOUN
ejpam-3007	264	29	)	)	PUNCT
ejpam-3007	264	30	s−	s−	PROPN
ejpam-3007	264	31	z	z	PROPN
ejpam-3007	264	32	ds	ds	PROPN
ejpam-3007	264	33	,	,	PUNCT
ejpam-3007	264	34	i	i	PRON
ejpam-3007	264	35	m	m	VERB
ejpam-3007	264	36	z	z	NOUN
ejpam-3007	264	37	>	>	X
ejpam-3007	264	38	0	0	NUM
ejpam-3007	264	39	,	,	PUNCT
ejpam-3007	264	40	t−f	t−f	X
ejpam-3007	264	41	=	=	SYM
ejpam-3007	264	42	1	1	NUM
ejpam-3007	264	43	2πi	2πi	NOUN
ejpam-3007	264	44	lim	lim	PROPN
ejpam-3007	264	45	imz→0	imz→0	PROPN
ejpam-3007	264	46	∞∫	∞∫	PROPN
ejpam-3007	264	47	−∞	−∞	ADP
ejpam-3007	264	48	f(s	f(	NOUN
ejpam-3007	264	49	)	)	PUNCT
ejpam-3007	264	50	s−	s−	PROPN
ejpam-3007	264	51	z	z	PROPN
ejpam-3007	264	52	ds	ds	PROPN
ejpam-3007	264	53	,	,	PUNCT
ejpam-3007	264	54	i	i	PRON
ejpam-3007	264	55	m	m	VERB
ejpam-3007	264	56	z	z	NOUN
ejpam-3007	264	57	<	<	X
ejpam-3007	264	58	0	0	NUM
ejpam-3007	264	59	,	,	PUNCT
ejpam-3007	264	60	(	(	PUNCT
ejpam-3007	264	61	47	47	NUM
ejpam-3007	264	62	)	)	PUNCT
ejpam-3007	264	63	tf	tf	NOUN
ejpam-3007	265	1	=	=	SYM
ejpam-3007	265	2	1	1	NUM
ejpam-3007	265	3	2	2	NUM
ejpam-3007	265	4	(	(	PUNCT
ejpam-3007	265	5	t+	t+	NOUN
ejpam-3007	265	6	+	+	CCONJ
ejpam-3007	265	7	t−)f	t−)f	NOUN
ejpam-3007	265	8	.	.	PUNCT
ejpam-3007	266	1	(	(	PUNCT
ejpam-3007	266	2	48	48	NUM
ejpam-3007	266	3	)	)	PUNCT
ejpam-3007	266	4	consider	consider	VERB
ejpam-3007	266	5	the	the	DET
ejpam-3007	266	6	riemann	riemann	PROPN
ejpam-3007	266	7	problem	problem	NOUN
ejpam-3007	266	8	of	of	ADP
ejpam-3007	266	9	finding	find	VERB
ejpam-3007	266	10	a	a	DET
ejpam-3007	266	11	function	function	NOUN
ejpam-3007	266	12	φ	φ	NOUN
ejpam-3007	266	13	,	,	PUNCT
ejpam-3007	266	14	that	that	PRON
ejpam-3007	266	15	is	be	AUX
ejpam-3007	266	16	analytic	analytic	ADJ
ejpam-3007	266	17	in	in	ADP
ejpam-3007	266	18	the	the	DET
ejpam-3007	266	19	complex	complex	ADJ
ejpam-3007	266	20	plane	plane	NOUN
ejpam-3007	266	21	with	with	ADP
ejpam-3007	266	22	a	a	DET
ejpam-3007	266	23	cut	cut	NOUN
ejpam-3007	266	24	along	along	ADP
ejpam-3007	266	25	the	the	DET
ejpam-3007	266	26	real	real	ADJ
ejpam-3007	266	27	axis.values	axis.value	NOUN
ejpam-3007	266	28	of	of	ADP
ejpam-3007	266	29	φ	φ	PROPN
ejpam-3007	266	30	on	on	ADP
ejpam-3007	266	31	the	the	DET
ejpam-3007	266	32	sides	side	NOUN
ejpam-3007	266	33	of	of	ADP
ejpam-3007	266	34	the	the	DET
ejpam-3007	266	35	cut	cut	NOUN
ejpam-3007	266	36	are	be	AUX
ejpam-3007	266	37	denoted	denote	VERB
ejpam-3007	266	38	as	as	ADP
ejpam-3007	266	39	φ+	φ+	NOUN
ejpam-3007	266	40	,	,	PUNCT
ejpam-3007	266	41	φ−.the	φ−.the	NOUN
ejpam-3007	266	42	following	following	NOUN
ejpam-3007	266	43	presents	present	VERB
ejpam-3007	266	44	the	the	DET
ejpam-3007	266	45	results	result	NOUN
ejpam-3007	266	46	of	of	ADP
ejpam-3007	266	47	[	[	X
ejpam-3007	266	48	16	16	NUM
ejpam-3007	266	49	]	]	X
ejpam-3007	266	50	:	:	PUNCT
ejpam-3007	266	51	lemma	lemma	PROPN
ejpam-3007	266	52	14	14	NUM
ejpam-3007	266	53	.	.	PUNCT
ejpam-3007	267	1	tt	tt	X
ejpam-3007	267	2	=	=	NOUN
ejpam-3007	268	1	1	1	NUM
ejpam-3007	268	2	4	4	NUM
ejpam-3007	268	3	i	i	NOUN
ejpam-3007	268	4	,	,	PUNCT
ejpam-3007	268	5	tt+	tt+	NOUN
ejpam-3007	268	6	=	=	NOUN
ejpam-3007	268	7	1	1	NUM
ejpam-3007	268	8	2	2	NUM
ejpam-3007	268	9	t+	t+	VERB
ejpam-3007	268	10	,	,	PUNCT
ejpam-3007	268	11	tt−	tt−	PUNCT
ejpam-3007	268	12	=	=	SYM
ejpam-3007	268	13	−1	−1	NOUN
ejpam-3007	268	14	2	2	NUM
ejpam-3007	268	15	t−	t−	NOUN
ejpam-3007	268	16	,	,	PUNCT
ejpam-3007	268	17	t+	t+	PUNCT
ejpam-3007	268	18	=	=	SYM
ejpam-3007	268	19	t	t	PROPN
ejpam-3007	268	20	+	+	CCONJ
ejpam-3007	268	21	1	1	NUM
ejpam-3007	268	22	2	2	NUM
ejpam-3007	268	23	i	i	NOUN
ejpam-3007	268	24	,	,	PUNCT
ejpam-3007	268	25	t−	t−	PROPN
ejpam-3007	268	26	=	=	SYM
ejpam-3007	268	27	t	t	PROPN
ejpam-3007	269	1	−	−	NUM
ejpam-3007	269	2	1	1	NUM
ejpam-3007	269	3	2	2	NUM
ejpam-3007	269	4	i	i	NOUN
ejpam-3007	269	5	,	,	PUNCT
ejpam-3007	269	6	t−t−	t−t−	ADP
ejpam-3007	269	7	=	=	SYM
ejpam-3007	269	8	−t−	−t−	X
ejpam-3007	269	9	(	(	PUNCT
ejpam-3007	269	10	49	49	NUM
ejpam-3007	269	11	)	)	PUNCT
ejpam-3007	269	12	theorem	theorem	NOUN
ejpam-3007	269	13	15	15	NUM
ejpam-3007	269	14	.	.	PUNCT
ejpam-3007	270	1	let	let	VERB
ejpam-3007	270	2	q	q	PROPN
ejpam-3007	270	3	∈	∈	PROPN
ejpam-3007	270	4	r	r	NOUN
ejpam-3007	270	5	,	,	PUNCT
ejpam-3007	270	6	n(q	n(q	PROPN
ejpam-3007	270	7	)	)	PUNCT
ejpam-3007	270	8	<	<	X
ejpam-3007	270	9	1	1	NUM
ejpam-3007	270	10	,	,	PUNCT
ejpam-3007	270	11	g	g	NOUN
ejpam-3007	270	12	=	=	PUNCT
ejpam-3007	270	13	(	(	PUNCT
ejpam-3007	270	14	φ+	φ+	X
ejpam-3007	270	15	−	−	PROPN
ejpam-3007	270	16	φ−	φ−	PROPN
ejpam-3007	270	17	)	)	PUNCT
ejpam-3007	270	18	.	.	PUNCT
ejpam-3007	271	1	then	then	ADV
ejpam-3007	271	2	,	,	PUNCT
ejpam-3007	271	3	φ±	φ±	PROPN
ejpam-3007	271	4	=	=	SYM
ejpam-3007	271	5	t±g	t±g	PROPN
ejpam-3007	271	6	.	.	PUNCT
ejpam-3007	272	1	(	(	PUNCT
ejpam-3007	272	2	50	50	NUM
ejpam-3007	272	3	)	)	PUNCT
ejpam-3007	272	4	proof	proof	NOUN
ejpam-3007	272	5	.	.	PUNCT
ejpam-3007	273	1	the	the	DET
ejpam-3007	273	2	proof	proof	NOUN
ejpam-3007	273	3	of	of	ADP
ejpam-3007	273	4	the	the	DET
ejpam-3007	273	5	above	above	ADJ
ejpam-3007	273	6	follows	follow	VERB
ejpam-3007	273	7	from	from	ADP
ejpam-3007	273	8	the	the	DET
ejpam-3007	273	9	classic	classic	ADJ
ejpam-3007	273	10	results	result	NOUN
ejpam-3007	273	11	for	for	ADP
ejpam-3007	273	12	the	the	DET
ejpam-3007	273	13	riemann	riemann	PROPN
ejpam-3007	273	14	problem	problem	NOUN
ejpam-3007	273	15	.	.	PUNCT
ejpam-3007	274	1	lemma	lemma	PROPN
ejpam-3007	274	2	16	16	NUM
ejpam-3007	274	3	.	.	PUNCT
ejpam-3007	275	1	let	let	VERB
ejpam-3007	275	2	q	q	PROPN
ejpam-3007	275	3	∈	∈	PROPN
ejpam-3007	275	4	r	r	NOUN
ejpam-3007	275	5	,	,	PUNCT
ejpam-3007	275	6	n(q	n(q	PROPN
ejpam-3007	275	7	)	)	PUNCT
ejpam-3007	275	8	<	<	X
ejpam-3007	275	9	1	1	NUM
ejpam-3007	275	10	g+	g+	NOUN
ejpam-3007	275	11	=	=	SYM
ejpam-3007	275	12	g(k	g(k	PROPN
ejpam-3007	275	13	,	,	PUNCT
ejpam-3007	275	14	θ	θ	PROPN
ejpam-3007	275	15	,	,	PUNCT
ejpam-3007	275	16	x	x	NOUN
ejpam-3007	275	17	)	)	PUNCT
ejpam-3007	275	18	,	,	PUNCT
ejpam-3007	275	19	g−	g−	PROPN
ejpam-3007	275	20	=	=	SYM
ejpam-3007	275	21	g(k,−θ	g(k,−θ	PROPN
ejpam-3007	275	22	,	,	PUNCT
ejpam-3007	275	23	x	x	NOUN
ejpam-3007	275	24	)	)	PUNCT
ejpam-3007	275	25	,	,	PUNCT
ejpam-3007	275	26	)	)	PUNCT
ejpam-3007	275	27	.	.	PUNCT
ejpam-3007	276	1	then	then	ADV
ejpam-3007	276	2	,	,	PUNCT
ejpam-3007	276	3	ψ+(k	ψ+(k	X
ejpam-3007	276	4	,	,	PUNCT
ejpam-3007	276	5	θ	θ	NOUN
ejpam-3007	276	6	,	,	PUNCT
ejpam-3007	276	7	x	x	NOUN
ejpam-3007	276	8	)	)	PUNCT
ejpam-3007	276	9	=	=	SYM
ejpam-3007	276	10	(	(	PUNCT
ejpam-3007	276	11	t+g+	t+g+	X
ejpam-3007	276	12	+	+	X
ejpam-3007	276	13	eikθx	eikθx	ADJ
ejpam-3007	276	14	)	)	PUNCT
ejpam-3007	276	15	,	,	PUNCT
ejpam-3007	276	16	ψ−(k	ψ−(k	PROPN
ejpam-3007	276	17	,	,	PUNCT
ejpam-3007	276	18	θ	θ	PROPN
ejpam-3007	276	19	,	,	PUNCT
ejpam-3007	276	20	x	x	NOUN
ejpam-3007	276	21	)	)	PUNCT
ejpam-3007	276	22	=	=	SYM
ejpam-3007	276	23	(	(	PUNCT
ejpam-3007	276	24	t−g−	t−g−	ADP
ejpam-3007	276	25	+	+	X
ejpam-3007	276	26	e−ikθx	e−ikθx	NOUN
ejpam-3007	276	27	)	)	PUNCT
ejpam-3007	276	28	.	.	PUNCT
ejpam-3007	277	1	(	(	PUNCT
ejpam-3007	277	2	51	51	NUM
ejpam-3007	277	3	)	)	PUNCT
ejpam-3007	277	4	proof	proof	NOUN
ejpam-3007	277	5	.	.	PUNCT
ejpam-3007	278	1	the	the	DET
ejpam-3007	278	2	proof	proof	NOUN
ejpam-3007	278	3	of	of	ADP
ejpam-3007	278	4	the	the	DET
ejpam-3007	278	5	above	above	ADJ
ejpam-3007	278	6	follows	follow	VERB
ejpam-3007	278	7	from	from	ADP
ejpam-3007	278	8	the	the	DET
ejpam-3007	278	9	definitions	definition	NOUN
ejpam-3007	278	10	of	of	ADP
ejpam-3007	278	11	g	g	NOUN
ejpam-3007	278	12	,	,	PUNCT
ejpam-3007	278	13	φ±,ψ±	φ±,ψ±	PROPN
ejpam-3007	278	14	.	.	PUNCT
ejpam-3007	279	1	lemma	lemma	PROPN
ejpam-3007	279	2	17	17	NUM
ejpam-3007	279	3	.	.	PUNCT
ejpam-3007	280	1	let	let	VERB
ejpam-3007	280	2	,	,	PUNCT
ejpam-3007	280	3	n(q	n(q	PROPN
ejpam-3007	280	4	)	)	PUNCT
ejpam-3007	280	5	<	<	X
ejpam-3007	280	6	1	1	NUM
ejpam-3007	280	7	,	,	PUNCT
ejpam-3007	280	8	sup	sup	PROPN
ejpam-3007	280	9	k	k	PROPN
ejpam-3007	280	10	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-3007	280	11	∞∫	∞∫	PROPN
ejpam-3007	280	12	−∞	−∞	ADP
ejpam-3007	280	13	∫	∫	PROPN
ejpam-3007	280	14	s2	s2	PROPN
ejpam-3007	280	15	pa(p	pa(p	VERB
ejpam-3007	280	16	,	,	PUNCT
ejpam-3007	280	17	θ	θ	NOUN
ejpam-3007	280	18	′	′	NOUN
ejpam-3007	280	19	,	,	PUNCT
ejpam-3007	281	1	θ)dθ	θ)dθ	PROPN
ejpam-3007	281	2	′	′	NOUN
ejpam-3007	281	3	4π(p−	4π(p−	NUM
ejpam-3007	281	4	k	k	PROPN
ejpam-3007	281	5	+	+	CCONJ
ejpam-3007	281	6	i0	i0	PROPN
ejpam-3007	281	7	)	)	PUNCT
ejpam-3007	281	8	dp	dp	NOUN
ejpam-3007	281	9	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-3007	281	10	<	<	X
ejpam-3007	281	11	α	α	X
ejpam-3007	281	12	<	<	X
ejpam-3007	281	13	1	1	NUM
ejpam-3007	281	14	sup	sup	NOUN
ejpam-3007	281	15	k	k	X
ejpam-3007	281	16	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-3007	281	17	∞∫	∞∫	PROPN
ejpam-3007	281	18	−∞	−∞	ADP
ejpam-3007	281	19	∫	∫	PROPN
ejpam-3007	281	20	s2	s2	PROPN
ejpam-3007	281	21	pa(p	pa(p	VERB
ejpam-3007	281	22	,	,	PUNCT
ejpam-3007	281	23	θ	θ	PROPN
ejpam-3007	281	24	′	′	NOUN
ejpam-3007	281	25	,	,	PUNCT
ejpam-3007	281	26	θ)φ0dθ	θ)φ0dθ	NOUN
ejpam-3007	281	27	′	′	PROPN
ejpam-3007	281	28	4π(p−	4π(p−	NUM
ejpam-3007	281	29	k	k	PROPN
ejpam-3007	281	30	+	+	CCONJ
ejpam-3007	281	31	i0	i0	PROPN
ejpam-3007	281	32	)	)	PUNCT
ejpam-3007	281	33	dp	dp	NOUN
ejpam-3007	282	1	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-3007	282	2	<	<	X
ejpam-3007	282	3	α	α	X
ejpam-3007	282	4	<	<	X
ejpam-3007	282	5	1	1	NUM
ejpam-3007	282	6	then	then	ADV
ejpam-3007	282	7	t−g−	t−g−	ADP
ejpam-3007	282	8	=	=	SYM
ejpam-3007	282	9	(	(	PUNCT
ejpam-3007	282	10	i	i	PRON
ejpam-3007	282	11	−	−	PROPN
ejpam-3007	282	12	t−d)−1t−dφ0	t−d)−1t−dφ0	PROPN
ejpam-3007	282	13	,	,	PUNCT
ejpam-3007	282	14	ψ−	ψ−	PUNCT
ejpam-3007	282	15	=	=	PUNCT
ejpam-3007	282	16	(	(	PUNCT
ejpam-3007	282	17	i	i	PRON
ejpam-3007	282	18	−	−	PROPN
ejpam-3007	283	1	t−d)−1t−dφ0	t−d)−1t−dφ0	PROPN
ejpam-3007	283	2	+	+	CCONJ
ejpam-3007	283	3	φ0	φ0	PROPN
ejpam-3007	283	4	,	,	PUNCT
ejpam-3007	283	5	|t−dφ0|	|t−dφ0|	PROPN
ejpam-3007	283	6	<	<	X
ejpam-3007	283	7	α	α	PROPN
ejpam-3007	283	8	1−	1−	NUM
ejpam-3007	283	9	α	α	NOUN
ejpam-3007	283	10	(	(	PUNCT
ejpam-3007	283	11	52	52	NUM
ejpam-3007	283	12	)	)	PUNCT
ejpam-3007	283	13	proof	proof	NOUN
ejpam-3007	283	14	.	.	PUNCT
ejpam-3007	284	1	using	use	VERB
ejpam-3007	284	2	equation	equation	NOUN
ejpam-3007	284	3	ψ+(k	ψ+(k	NOUN
ejpam-3007	284	4	,	,	PUNCT
ejpam-3007	284	5	θ	θ	NOUN
ejpam-3007	284	6	,	,	PUNCT
ejpam-3007	284	7	x	x	NOUN
ejpam-3007	284	8	)	)	PUNCT
ejpam-3007	284	9	−	−	PROPN
ejpam-3007	284	10	ψ−(k	ψ−(k	PROPN
ejpam-3007	284	11	,	,	PUNCT
ejpam-3007	284	12	θ	θ	PROPN
ejpam-3007	284	13	,	,	PUNCT
ejpam-3007	284	14	x	x	NOUN
ejpam-3007	284	15	)	)	PUNCT
ejpam-3007	284	16	=	=	SYM
ejpam-3007	285	1	−	−	PROPN
ejpam-3007	285	2	k	k	PROPN
ejpam-3007	285	3	4π	4π	NUM
ejpam-3007	285	4	∫	∫	PROPN
ejpam-3007	285	5	s2	s2	PROPN
ejpam-3007	285	6	a(k	a(k	PROPN
ejpam-3007	285	7	,	,	PUNCT
ejpam-3007	285	8	θ	θ	PROPN
ejpam-3007	285	9	′	′	NOUN
ejpam-3007	285	10	,	,	PUNCT
ejpam-3007	285	11	θ)ψ−(k	θ)ψ−(k	NOUN
ejpam-3007	285	12	,	,	PUNCT
ejpam-3007	285	13	θ	θ	PROPN
ejpam-3007	285	14	′	′	NOUN
ejpam-3007	285	15	,	,	PUNCT
ejpam-3007	286	1	x)dθ	x)dθ	PROPN
ejpam-3007	286	2	′	′	NOUN
ejpam-3007	286	3	,	,	PUNCT
ejpam-3007	286	4	k	k	PROPN
ejpam-3007	286	5	∈	∈	PROPN
ejpam-3007	286	6	r.	r.	PROPN
ejpam-3007	286	7	(	(	PUNCT
ejpam-3007	286	8	53	53	NUM
ejpam-3007	286	9	)	)	PUNCT
ejpam-3007	286	10	we	we	PRON
ejpam-3007	286	11	can	can	AUX
ejpam-3007	286	12	rewrite	rewrite	VERB
ejpam-3007	286	13	t+g+	t+g+	ADV
ejpam-3007	286	14	−	−	NOUN
ejpam-3007	286	15	t−g−	t−g−	ADP
ejpam-3007	286	16	=	=	SYM
ejpam-3007	286	17	d(t−g−	d(t−g−	PROPN
ejpam-3007	286	18	+	+	CCONJ
ejpam-3007	286	19	φ0	φ0	ADJ
ejpam-3007	286	20	)	)	PUNCT
ejpam-3007	286	21	a.	a.	NOUN
ejpam-3007	286	22	durmagambetov	durmagambetov	PROPN
ejpam-3007	286	23	/	/	SYM
ejpam-3007	286	24	eur	eur	PROPN
ejpam-3007	286	25	.	.	PUNCT
ejpam-3007	287	1	j.	j.	PROPN
ejpam-3007	287	2	pure	pure	PROPN
ejpam-3007	287	3	appl	appl	PROPN
ejpam-3007	287	4	.	.	PROPN
ejpam-3007	287	5	math	math	PROPN
ejpam-3007	287	6	,	,	PUNCT
ejpam-3007	287	7	10	10	NUM
ejpam-3007	287	8	(	(	PUNCT
ejpam-3007	287	9	4	4	NUM
ejpam-3007	287	10	)	)	PUNCT
ejpam-3007	287	11	(	(	PUNCT
ejpam-3007	287	12	2017	2017	NUM
ejpam-3007	287	13	)	)	PUNCT
ejpam-3007	287	14	,	,	PUNCT
ejpam-3007	287	15	763	763	NUM
ejpam-3007	287	16	-	-	SYM
ejpam-3007	287	17	785	785	NUM
ejpam-3007	287	18	775	775	NUM
ejpam-3007	287	19	applying	apply	VERB
ejpam-3007	287	20	the	the	DET
ejpam-3007	287	21	operator	operator	NOUN
ejpam-3007	287	22	t−	t−	DET
ejpam-3007	287	23	last	last	ADJ
ejpam-3007	287	24	equation	equation	NOUN
ejpam-3007	287	25	we	we	PRON
ejpam-3007	287	26	have	have	VERB
ejpam-3007	287	27	t−g−	t−g−	ADP
ejpam-3007	287	28	=	=	SYM
ejpam-3007	287	29	t−d(t−g−	t−d(t−g−	PROPN
ejpam-3007	287	30	+	+	CCONJ
ejpam-3007	287	31	φ0	φ0	PROPN
ejpam-3007	287	32	)	)	PUNCT
ejpam-3007	287	33	(	(	PUNCT
ejpam-3007	287	34	i	i	PRON
ejpam-3007	287	35	−	−	PROPN
ejpam-3007	287	36	t−d)t−g−	t−d)t−g−	NOUN
ejpam-3007	287	37	=	=	SYM
ejpam-3007	287	38	t−dφ0	t−dφ0	INTJ
ejpam-3007	287	39	,	,	PUNCT
ejpam-3007	287	40	t−g−	t−g−	ADP
ejpam-3007	287	41	=	=	PUNCT
ejpam-3007	287	42	∑	∑	PUNCT
ejpam-3007	287	43	n≥0	n≥0	PROPN
ejpam-3007	287	44	(	(	PUNCT
ejpam-3007	287	45	−t−d)n	−t−d)n	PROPN
ejpam-3007	287	46	φ0	φ0	PROPN
ejpam-3007	287	47	estimating	estimate	VERB
ejpam-3007	287	48	the	the	DET
ejpam-3007	287	49	terms	term	NOUN
ejpam-3007	287	50	of	of	ADP
ejpam-3007	287	51	the	the	DET
ejpam-3007	287	52	series	series	NOUN
ejpam-3007	287	53	,	,	PUNCT
ejpam-3007	287	54	we	we	PRON
ejpam-3007	287	55	obtain	obtain	VERB
ejpam-3007	287	56	|t−g−|	|t−g−|	NOUN
ejpam-3007	287	57	≤	≤	NOUN
ejpam-3007	287	58	∑	∑	PUNCT
ejpam-3007	287	59	n≥0	n≥0	ADJ
ejpam-3007	287	60	|t−dnφ0|	|t−dnφ0|	NOUN
ejpam-3007	287	61	≤	≤	NOUN
ejpam-3007	287	62	∑	∑	PUNCT
ejpam-3007	287	63	n≥0	n≥0	PROPN
ejpam-3007	287	64	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-3007	287	65	∫	∫	PROPN
ejpam-3007	287	66	∞	∞	PROPN
ejpam-3007	287	67	−∞	−∞	PROPN
ejpam-3007	287	68	....	....	PUNCT
ejpam-3007	287	69	∫	∫	PROPN
ejpam-3007	287	70	∞	∞	PROPN
ejpam-3007	288	1	−∞	−∞	PUNCT
ejpam-3007	288	2	φ0	φ0	PROPN
ejpam-3007	288	3	∏	∏	PROPN
ejpam-3007	288	4	∫	∫	NOUN
ejpam-3007	288	5	s2	s2	PROPN
ejpam-3007	288	6	kja(kj	kja(kj	NOUN
ejpam-3007	288	7	,	,	PUNCT
ejpam-3007	288	8	θ	θ	NOUN
ejpam-3007	288	9	′	′	NUM
ejpam-3007	288	10	kj	kj	PROPN
ejpam-3007	288	11	,	,	PUNCT
ejpam-3007	288	12	θkj	θkj	NOUN
ejpam-3007	288	13	)	)	PUNCT
ejpam-3007	289	1	dθ	dθ	PROPN
ejpam-3007	290	1	′	′	NUM
ejpam-3007	290	2	kj	kj	NOUN
ejpam-3007	290	3	4π(kj+1)−	4π(kj+1)−	NUM
ejpam-3007	290	4	kj	kj	PROPN
ejpam-3007	290	5	+	+	CCONJ
ejpam-3007	290	6	i0	i0	PROPN
ejpam-3007	290	7	)	)	PUNCT
ejpam-3007	290	8	dk1	dk1	PROPN
ejpam-3007	290	9	...	...	PUNCT
ejpam-3007	290	10	dkn	dkn	NOUN
ejpam-3007	291	1	∣∣∣∣∣	∣∣∣∣∣	NOUN
ejpam-3007	291	2	≤	≤	ADJ
ejpam-3007	291	3	≤	≤	NOUN
ejpam-3007	291	4	∑	∑	PUNCT
ejpam-3007	291	5	n≥0	n≥0	PROPN
ejpam-3007	291	6	sup	sup	PROPN
ejpam-3007	291	7	k	k	X
ejpam-3007	291	8	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-3007	291	9	∞∫	∞∫	PROPN
ejpam-3007	291	10	−∞	−∞	ADP
ejpam-3007	291	11	∫	∫	PROPN
ejpam-3007	291	12	s2	s2	PROPN
ejpam-3007	291	13	pa(p	pa(p	VERB
ejpam-3007	291	14	,	,	PUNCT
ejpam-3007	291	15	θ	θ	PROPN
ejpam-3007	291	16	′	′	NUM
ejpam-3007	291	17	,	,	PUNCT
ejpam-3007	291	18	θ)φ−∞dθ	θ)φ−∞dθ	NOUN
ejpam-3007	291	19	′	′	NOUN
ejpam-3007	291	20	4π(p−	4π(p−	NUM
ejpam-3007	292	1	k	k	PROPN
ejpam-3007	292	2	+	+	CCONJ
ejpam-3007	292	3	i0	i0	PROPN
ejpam-3007	292	4	)	)	PUNCT
ejpam-3007	292	5	dp	dp	NOUN
ejpam-3007	292	6	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-3007	292	7	∏	∏	PROPN
ejpam-3007	292	8	0≤j	0≤j	PROPN
ejpam-3007	292	9	<	<	NOUN
ejpam-3007	292	10	n	n	NUM
ejpam-3007	292	11	sup	sup	NOUN
ejpam-3007	292	12	kj	kj	PROPN
ejpam-3007	293	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-3007	293	2	∫	∫	PROPN
ejpam-3007	294	1	∞	∞	PROPN
ejpam-3007	294	2	−∞	−∞	ADP
ejpam-3007	294	3	∫	∫	PROPN
ejpam-3007	294	4	s2	s2	PROPN
ejpam-3007	294	5	kja(kj	kja(kj	NOUN
ejpam-3007	294	6	,	,	PUNCT
ejpam-3007	294	7	θ	θ	NOUN
ejpam-3007	294	8	′	′	NUM
ejpam-3007	294	9	kj	kj	PROPN
ejpam-3007	294	10	,	,	PUNCT
ejpam-3007	294	11	θkj	θkj	NOUN
ejpam-3007	294	12	)	)	PUNCT
ejpam-3007	294	13	dθ	dθ	PROPN
ejpam-3007	295	1	′	′	NUM
ejpam-3007	295	2	kj	kj	NOUN
ejpam-3007	295	3	4π(kj+1)−	4π(kj+1)−	NUM
ejpam-3007	295	4	kj	kj	PROPN
ejpam-3007	295	5	+	+	CCONJ
ejpam-3007	295	6	i0	i0	PROPN
ejpam-3007	295	7	)	)	PUNCT
ejpam-3007	295	8	dkj	dkj	NOUN
ejpam-3007	295	9	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-3007	295	10	≤	≤	PROPN
ejpam-3007	295	11	∑	∑	PUNCT
ejpam-3007	296	1	n>0	n>0	PROPN
ejpam-3007	296	2	αn	αn	NOUN
ejpam-3007	296	3	=	=	SYM
ejpam-3007	296	4	α	α	PROPN
ejpam-3007	296	5	1−	1−	NUM
ejpam-3007	296	6	α	α	NOUN
ejpam-3007	296	7	using	use	VERB
ejpam-3007	296	8	operator	operator	NOUN
ejpam-3007	296	9	λ	λ	NOUN
ejpam-3007	296	10	=	=	PUNCT
ejpam-3007	296	11	∆k	∆k	X
ejpam-3007	297	1	=	=	SYM
ejpam-3007	297	2	3∑	3∑	NUM
ejpam-3007	297	3	i=1	i=1	PRON
ejpam-3007	297	4	∂2	∂2	NOUN
ejpam-3007	298	1	∂k2i	∂k2i	CCONJ
ejpam-3007	298	2	we	we	PRON
ejpam-3007	298	3	can	can	AUX
ejpam-3007	298	4	formulate	formulate	VERB
ejpam-3007	298	5	folows	folow	NOUN
ejpam-3007	298	6	results	result	NOUN
ejpam-3007	298	7	:	:	PUNCT
ejpam-3007	298	8	lemma	lemma	PROPN
ejpam-3007	298	9	18	18	NUM
ejpam-3007	298	10	.	.	PUNCT
ejpam-3007	299	1	let	let	VERB
ejpam-3007	299	2	q	q	PROPN
ejpam-3007	299	3	∈	∈	PROPN
ejpam-3007	299	4	r	r	NOUN
ejpam-3007	299	5	,	,	PUNCT
ejpam-3007	299	6	n(q	n(q	PROPN
ejpam-3007	299	7	)	)	PUNCT
ejpam-3007	299	8	<	<	X
ejpam-3007	299	9	1	1	NUM
ejpam-3007	299	10	,	,	PUNCT
ejpam-3007	299	11	and	and	CCONJ
ejpam-3007	299	12	assume	assume	VERB
ejpam-3007	299	13	that	that	SCONJ
ejpam-3007	299	14	(	(	PUNCT
ejpam-3007	299	15	i	i	PRON
ejpam-3007	299	16	−	−	PROPN
ejpam-3007	299	17	t−d)−1	t−d)−1	NOUN
ejpam-3007	299	18	exists	exist	VERB
ejpam-3007	299	19	.	.	PUNCT
ejpam-3007	300	1	then	then	ADV
ejpam-3007	300	2	,	,	PUNCT
ejpam-3007	300	3	t−dt−λg−	t−dt−λg−	PROPN
ejpam-3007	300	4	=	=	SYM
ejpam-3007	300	5	t−λg−	t−λg−	PROPN
ejpam-3007	300	6	+	+	NOUN
ejpam-3007	300	7	t−(∇d,∇t−g	t−(∇d,∇t−g	NOUN
ejpam-3007	300	8	)	)	PUNCT
ejpam-3007	301	1	+	+	NUM
ejpam-3007	301	2	t−λdφ0	t−λdφ0	NOUN
ejpam-3007	301	3	t−λg−	t−λg−	PROPN
ejpam-3007	302	1	=	=	PRON
ejpam-3007	302	2	(	(	PUNCT
ejpam-3007	302	3	i	i	PRON
ejpam-3007	302	4	−	−	PROPN
ejpam-3007	302	5	t−d)−1	t−d)−1	NOUN
ejpam-3007	302	6	(	(	PUNCT
ejpam-3007	302	7	t−(∇d,∇t−g)−	t−(∇d,∇t−g)−	PROPN
ejpam-3007	302	8	t−λdφ0	t−λdφ0	PROPN
ejpam-3007	302	9	)	)	PUNCT
ejpam-3007	302	10	(	(	PUNCT
ejpam-3007	302	11	54	54	NUM
ejpam-3007	302	12	)	)	PUNCT
ejpam-3007	302	13	proof	proof	NOUN
ejpam-3007	302	14	.	.	PUNCT
ejpam-3007	303	1	the	the	DET
ejpam-3007	303	2	proof	proof	NOUN
ejpam-3007	303	3	of	of	ADP
ejpam-3007	303	4	the	the	DET
ejpam-3007	303	5	above	above	ADJ
ejpam-3007	303	6	follows	follow	VERB
ejpam-3007	303	7	from	from	ADP
ejpam-3007	303	8	the	the	DET
ejpam-3007	303	9	definitions	definition	NOUN
ejpam-3007	303	10	of	of	ADP
ejpam-3007	303	11	g	g	NOUN
ejpam-3007	303	12	,	,	PUNCT
ejpam-3007	303	13	φ±,ψ−	φ±,ψ−	PROPN
ejpam-3007	303	14	and	and	CCONJ
ejpam-3007	303	15	equation	equation	NOUN
ejpam-3007	303	16	(	(	PUNCT
ejpam-3007	303	17	41	41	NUM
ejpam-3007	303	18	)	)	PUNCT
ejpam-3007	303	19	lemma	lemma	PROPN
ejpam-3007	303	20	19	19	NUM
ejpam-3007	303	21	.	.	PUNCT
ejpam-3007	304	1	let	let	VERB
ejpam-3007	304	2	q	q	PROPN
ejpam-3007	304	3	∈	∈	PROPN
ejpam-3007	304	4	r	r	NOUN
ejpam-3007	304	5	,	,	PUNCT
ejpam-3007	304	6	n(q	n(q	PROPN
ejpam-3007	304	7	)	)	PUNCT
ejpam-3007	304	8	<	<	X
ejpam-3007	305	1	1	1	X
ejpam-3007	305	2	.	.	PUNCT
ejpam-3007	305	3	then	then	ADV
ejpam-3007	305	4	,	,	PUNCT
ejpam-3007	305	5	q	q	PROPN
ejpam-3007	305	6	=	=	PROPN
ejpam-3007	305	7	lim	lim	PROPN
ejpam-3007	305	8	z→0	z→0	PROPN
ejpam-3007	305	9	h0ψ−/ψ−	h0ψ−/ψ−	PROPN
ejpam-3007	305	10	,	,	PUNCT
ejpam-3007	305	11	(	(	PUNCT
ejpam-3007	305	12	55	55	NUM
ejpam-3007	305	13	)	)	PUNCT
ejpam-3007	305	14	q	q	NOUN
ejpam-3007	306	1	=	=	SYM
ejpam-3007	306	2	lim	lim	PROPN
ejpam-3007	306	3	z→0	z→0	X
ejpam-3007	306	4	λh0ψ−/λψ−	λh0ψ−/λψ−	PROPN
ejpam-3007	306	5	(	(	PUNCT
ejpam-3007	306	6	56	56	NUM
ejpam-3007	306	7	)	)	PUNCT
ejpam-3007	306	8	proof	proof	NOUN
ejpam-3007	306	9	.	.	PUNCT
ejpam-3007	307	1	the	the	DET
ejpam-3007	307	2	lemma	lemma	PROPN
ejpam-3007	307	3	can	can	AUX
ejpam-3007	307	4	be	be	AUX
ejpam-3007	307	5	proved	prove	VERB
ejpam-3007	307	6	by	by	ADP
ejpam-3007	307	7	substituting	substitute	VERB
ejpam-3007	307	8	ψ−	ψ−	VERB
ejpam-3007	307	9	into	into	ADP
ejpam-3007	307	10	equation	equation	NOUN
ejpam-3007	307	11	(	(	PUNCT
ejpam-3007	307	12	38	38	NUM
ejpam-3007	307	13	)	)	PUNCT
ejpam-3007	307	14	.	.	PUNCT
ejpam-3007	308	1	5	5	X
ejpam-3007	308	2	.	.	X
ejpam-3007	308	3	conclusions	conclusion	NOUN
ejpam-3007	308	4	for	for	ADP
ejpam-3007	308	5	the	the	DET
ejpam-3007	308	6	three	three	NUM
ejpam-3007	308	7	-	-	PUNCT
ejpam-3007	308	8	dimensional	dimensional	ADJ
ejpam-3007	308	9	inverse	inverse	NOUN
ejpam-3007	308	10	scattering	scattering	NOUN
ejpam-3007	308	11	problem	problem	NOUN
ejpam-3007	308	12	this	this	DET
ejpam-3007	308	13	study	study	NOUN
ejpam-3007	308	14	has	have	AUX
ejpam-3007	308	15	shown	show	VERB
ejpam-3007	308	16	once	once	ADV
ejpam-3007	308	17	again	again	ADV
ejpam-3007	308	18	the	the	DET
ejpam-3007	308	19	outstanding	outstanding	ADJ
ejpam-3007	308	20	properties	property	NOUN
ejpam-3007	308	21	of	of	ADP
ejpam-3007	308	22	the	the	DET
ejpam-3007	308	23	scattering	scatter	VERB
ejpam-3007	308	24	operator	operator	NOUN
ejpam-3007	308	25	,	,	PUNCT
ejpam-3007	308	26	which	which	PRON
ejpam-3007	308	27	,	,	PUNCT
ejpam-3007	308	28	in	in	ADP
ejpam-3007	308	29	combination	combination	NOUN
ejpam-3007	308	30	with	with	ADP
ejpam-3007	308	31	the	the	DET
ejpam-3007	308	32	analytical	analytical	ADJ
ejpam-3007	308	33	properties	property	NOUN
ejpam-3007	308	34	of	of	ADP
ejpam-3007	308	35	the	the	DET
ejpam-3007	308	36	wave	wave	NOUN
ejpam-3007	308	37	function	function	NOUN
ejpam-3007	308	38	,	,	PUNCT
ejpam-3007	308	39	allow	allow	VERB
ejpam-3007	308	40	to	to	PART
ejpam-3007	308	41	obtain	obtain	VERB
ejpam-3007	308	42	an	an	DET
ejpam-3007	308	43	almostexplicit	almostexplicit	ADJ
ejpam-3007	308	44	formulas	formula	NOUN
ejpam-3007	308	45	for	for	ADP
ejpam-3007	308	46	the	the	DET
ejpam-3007	308	47	potential	potential	NOUN
ejpam-3007	308	48	to	to	PART
ejpam-3007	308	49	be	be	AUX
ejpam-3007	308	50	obtained	obtain	VERB
ejpam-3007	308	51	from	from	ADP
ejpam-3007	308	52	the	the	DET
ejpam-3007	308	53	scattering	scatter	VERB
ejpam-3007	308	54	amplitude	amplitude	NOUN
ejpam-3007	308	55	.	.	PUNCT
ejpam-3007	309	1	furthermore	furthermore	ADV
ejpam-3007	309	2	,	,	PUNCT
ejpam-3007	309	3	this	this	DET
ejpam-3007	309	4	appro	appro	ADJ
ejpam-3007	309	5	.	.	PUNCT
ejpam-3007	310	1	the	the	DET
ejpam-3007	310	2	estimations	estimation	NOUN
ejpam-3007	310	3	follow	follow	VERB
ejpam-3007	310	4	from	from	ADP
ejpam-3007	310	5	this	this	DET
ejpam-3007	310	6	reach	reach	NOUN
ejpam-3007	310	7	overcomes	overcome	VERB
ejpam-3007	310	8	the	the	DET
ejpam-3007	310	9	problem	problem	NOUN
ejpam-3007	310	10	of	of	ADP
ejpam-3007	310	11	over	over	ADP
ejpam-3007	310	12	-	-	PUNCT
ejpam-3007	310	13	determination	determination	NOUN
ejpam-3007	310	14	,	,	PUNCT
ejpam-3007	310	15	resulting	result	VERB
ejpam-3007	310	16	from	from	ADP
ejpam-3007	310	17	the	the	DET
ejpam-3007	310	18	fact	fact	NOUN
ejpam-3007	310	19	that	that	SCONJ
ejpam-3007	310	20	the	the	DET
ejpam-3007	310	21	potential	potential	NOUN
ejpam-3007	310	22	is	be	AUX
ejpam-3007	310	23	a	a	DET
ejpam-3007	310	24	function	function	NOUN
ejpam-3007	310	25	of	of	ADP
ejpam-3007	310	26	three	three	NUM
ejpam-3007	310	27	variables	variable	NOUN
ejpam-3007	310	28	,	,	PUNCT
ejpam-3007	310	29	whereas	whereas	SCONJ
ejpam-3007	310	30	the	the	DET
ejpam-3007	310	31	amplitude	amplitude	NOUN
ejpam-3007	310	32	is	be	AUX
ejpam-3007	310	33	a	a	DET
ejpam-3007	310	34	function	function	NOUN
ejpam-3007	310	35	of	of	ADP
ejpam-3007	310	36	five	five	NUM
ejpam-3007	310	37	variables	variable	NOUN
ejpam-3007	310	38	.	.	PUNCT
ejpam-3007	311	1	we	we	PRON
ejpam-3007	311	2	have	have	AUX
ejpam-3007	311	3	shown	show	VERB
ejpam-3007	311	4	that	that	SCONJ
ejpam-3007	311	5	it	it	PRON
ejpam-3007	311	6	is	be	AUX
ejpam-3007	311	7	sufficient	sufficient	ADJ
ejpam-3007	311	8	to	to	PART
ejpam-3007	311	9	average	average	VERB
ejpam-3007	311	10	the	the	DET
ejpam-3007	311	11	scattering	scatter	VERB
ejpam-3007	311	12	amplitude	amplitude	NOUN
ejpam-3007	311	13	to	to	PART
ejpam-3007	311	14	eliminate	eliminate	VERB
ejpam-3007	311	15	the	the	DET
ejpam-3007	311	16	two	two	NUM
ejpam-3007	311	17	extra	extra	ADJ
ejpam-3007	311	18	variables	variable	NOUN
ejpam-3007	311	19	.	.	PUNCT
ejpam-3007	312	1	a.	a.	NOUN
ejpam-3007	312	2	durmagambetov	durmagambetov	PROPN
ejpam-3007	312	3	/	/	SYM
ejpam-3007	312	4	eur	eur	PROPN
ejpam-3007	312	5	.	.	PUNCT
ejpam-3007	313	1	j.	j.	PROPN
ejpam-3007	313	2	pure	pure	PROPN
ejpam-3007	313	3	appl	appl	PROPN
ejpam-3007	313	4	.	.	PROPN
ejpam-3007	313	5	math	math	PROPN
ejpam-3007	313	6	,	,	PUNCT
ejpam-3007	313	7	10	10	NUM
ejpam-3007	313	8	(	(	PUNCT
ejpam-3007	313	9	4	4	NUM
ejpam-3007	313	10	)	)	PUNCT
ejpam-3007	313	11	(	(	PUNCT
ejpam-3007	313	12	2017	2017	NUM
ejpam-3007	313	13	)	)	PUNCT
ejpam-3007	313	14	,	,	PUNCT
ejpam-3007	313	15	763	763	NUM
ejpam-3007	313	16	-	-	SYM
ejpam-3007	313	17	785	785	NUM
ejpam-3007	313	18	776	776	NUM
ejpam-3007	313	19	6	6	NUM
ejpam-3007	313	20	.	.	PUNCT
ejpam-3007	314	1	cauchy	cauchy	ADJ
ejpam-3007	314	2	problem	problem	NOUN
ejpam-3007	314	3	for	for	ADP
ejpam-3007	314	4	the	the	DET
ejpam-3007	314	5	navier	navier	NOUN
ejpam-3007	314	6	–	–	PUNCT
ejpam-3007	314	7	stokes	stoke	VERB
ejpam-3007	314	8	equation	equation	NOUN
ejpam-3007	314	9	numerous	numerous	ADJ
ejpam-3007	314	10	studies	study	NOUN
ejpam-3007	314	11	of	of	ADP
ejpam-3007	314	12	the	the	DET
ejpam-3007	314	13	navier	navier	NOUN
ejpam-3007	314	14	-	-	PUNCT
ejpam-3007	314	15	stokes	stoke	NOUN
ejpam-3007	314	16	equations	equation	NOUN
ejpam-3007	314	17	have	have	AUX
ejpam-3007	314	18	been	be	AUX
ejpam-3007	314	19	devoted	devote	VERB
ejpam-3007	314	20	to	to	ADP
ejpam-3007	314	21	the	the	DET
ejpam-3007	314	22	problem	problem	NOUN
ejpam-3007	314	23	of	of	ADP
ejpam-3007	314	24	the	the	DET
ejpam-3007	314	25	smoothness	smoothness	NOUN
ejpam-3007	314	26	of	of	ADP
ejpam-3007	314	27	its	its	PRON
ejpam-3007	314	28	solutions	solution	NOUN
ejpam-3007	314	29	.	.	PUNCT
ejpam-3007	315	1	a	a	DET
ejpam-3007	315	2	good	good	ADJ
ejpam-3007	315	3	overview	overview	NOUN
ejpam-3007	315	4	of	of	ADP
ejpam-3007	315	5	these	these	DET
ejpam-3007	315	6	studies	study	NOUN
ejpam-3007	315	7	is	be	AUX
ejpam-3007	315	8	given	give	VERB
ejpam-3007	315	9	in	in	ADP
ejpam-3007	315	10	[	[	X
ejpam-3007	315	11	17]-[20	17]-[20	NUM
ejpam-3007	315	12	]	]	PUNCT
ejpam-3007	315	13	.	.	PUNCT
ejpam-3007	316	1	the	the	DET
ejpam-3007	316	2	spatial	spatial	ADJ
ejpam-3007	316	3	differentiability	differentiability	NOUN
ejpam-3007	316	4	of	of	ADP
ejpam-3007	316	5	the	the	DET
ejpam-3007	316	6	solutions	solution	NOUN
ejpam-3007	316	7	is	be	AUX
ejpam-3007	316	8	an	an	DET
ejpam-3007	316	9	important	important	ADJ
ejpam-3007	316	10	factor	factor	NOUN
ejpam-3007	316	11	,	,	PUNCT
ejpam-3007	316	12	this	this	PRON
ejpam-3007	316	13	controls	control	VERB
ejpam-3007	316	14	their	their	PRON
ejpam-3007	316	15	evolution	evolution	NOUN
ejpam-3007	316	16	.	.	PUNCT
ejpam-3007	317	1	obviously	obviously	ADV
ejpam-3007	317	2	,	,	PUNCT
ejpam-3007	317	3	differentiable	differentiable	ADJ
ejpam-3007	317	4	solutions	solution	NOUN
ejpam-3007	317	5	do	do	AUX
ejpam-3007	317	6	not	not	PART
ejpam-3007	317	7	provide	provide	VERB
ejpam-3007	317	8	an	an	DET
ejpam-3007	317	9	effective	effective	ADJ
ejpam-3007	317	10	description	description	NOUN
ejpam-3007	317	11	of	of	ADP
ejpam-3007	317	12	turbulence	turbulence	NOUN
ejpam-3007	317	13	.	.	PUNCT
ejpam-3007	318	1	nevertheless	nevertheless	ADV
ejpam-3007	318	2	,	,	PUNCT
ejpam-3007	318	3	the	the	DET
ejpam-3007	318	4	global	global	ADJ
ejpam-3007	318	5	solvability	solvability	NOUN
ejpam-3007	318	6	and	and	CCONJ
ejpam-3007	318	7	differentiability	differentiability	NOUN
ejpam-3007	318	8	of	of	ADP
ejpam-3007	318	9	the	the	DET
ejpam-3007	318	10	solutions	solution	NOUN
ejpam-3007	318	11	has	have	AUX
ejpam-3007	318	12	not	not	PART
ejpam-3007	318	13	been	be	AUX
ejpam-3007	318	14	proven	prove	VERB
ejpam-3007	318	15	,	,	PUNCT
ejpam-3007	318	16	and	and	CCONJ
ejpam-3007	318	17	therefore	therefore	ADV
ejpam-3007	318	18	the	the	DET
ejpam-3007	318	19	problem	problem	NOUN
ejpam-3007	318	20	of	of	ADP
ejpam-3007	318	21	describing	describe	VERB
ejpam-3007	318	22	turbulence	turbulence	NOUN
ejpam-3007	318	23	remains	remain	VERB
ejpam-3007	318	24	open	open	ADJ
ejpam-3007	318	25	.	.	PUNCT
ejpam-3007	319	1	it	it	PRON
ejpam-3007	319	2	is	be	AUX
ejpam-3007	319	3	interesting	interesting	ADJ
ejpam-3007	319	4	to	to	PART
ejpam-3007	319	5	study	study	VERB
ejpam-3007	319	6	the	the	DET
ejpam-3007	319	7	properties	property	NOUN
ejpam-3007	319	8	of	of	ADP
ejpam-3007	319	9	the	the	DET
ejpam-3007	319	10	fourier	fourier	NOUN
ejpam-3007	319	11	transform	transform	NOUN
ejpam-3007	319	12	of	of	ADP
ejpam-3007	319	13	solutions	solution	NOUN
ejpam-3007	319	14	of	of	ADP
ejpam-3007	319	15	the	the	DET
ejpam-3007	319	16	navier	navier	NOUN
ejpam-3007	319	17	-	-	PUNCT
ejpam-3007	319	18	stokes	stokes	PROPN
ejpam-3007	319	19	equations	equation	NOUN
ejpam-3007	319	20	.	.	PUNCT
ejpam-3007	320	1	of	of	ADP
ejpam-3007	320	2	particular	particular	ADJ
ejpam-3007	320	3	interest	interest	NOUN
ejpam-3007	320	4	is	be	AUX
ejpam-3007	320	5	how	how	SCONJ
ejpam-3007	320	6	they	they	PRON
ejpam-3007	320	7	can	can	AUX
ejpam-3007	320	8	be	be	AUX
ejpam-3007	320	9	used	use	VERB
ejpam-3007	320	10	in	in	ADP
ejpam-3007	320	11	the	the	DET
ejpam-3007	320	12	description	description	NOUN
ejpam-3007	320	13	of	of	ADP
ejpam-3007	320	14	turbulence	turbulence	NOUN
ejpam-3007	320	15	,	,	PUNCT
ejpam-3007	320	16	and	and	CCONJ
ejpam-3007	320	17	whether	whether	SCONJ
ejpam-3007	320	18	they	they	PRON
ejpam-3007	320	19	are	be	AUX
ejpam-3007	320	20	differentiable	differentiable	ADJ
ejpam-3007	320	21	.	.	PUNCT
ejpam-3007	321	1	the	the	DET
ejpam-3007	321	2	differentiability	differentiability	NOUN
ejpam-3007	321	3	of	of	ADP
ejpam-3007	321	4	such	such	ADJ
ejpam-3007	321	5	fourier	fourier	NOUN
ejpam-3007	321	6	transforms	transform	VERB
ejpam-3007	321	7	appears	appear	VERB
ejpam-3007	321	8	to	to	PART
ejpam-3007	321	9	be	be	AUX
ejpam-3007	321	10	related	relate	VERB
ejpam-3007	321	11	to	to	ADP
ejpam-3007	321	12	the	the	DET
ejpam-3007	321	13	appearance	appearance	NOUN
ejpam-3007	321	14	or	or	CCONJ
ejpam-3007	321	15	disappearance	disappearance	NOUN
ejpam-3007	321	16	of	of	ADP
ejpam-3007	321	17	resonance	resonance	NOUN
ejpam-3007	321	18	,	,	PUNCT
ejpam-3007	321	19	as	as	SCONJ
ejpam-3007	321	20	this	this	PRON
ejpam-3007	321	21	implies	imply	VERB
ejpam-3007	321	22	the	the	DET
ejpam-3007	321	23	absence	absence	NOUN
ejpam-3007	321	24	of	of	ADP
ejpam-3007	321	25	large	large	ADJ
ejpam-3007	321	26	energy	energy	NOUN
ejpam-3007	321	27	flows	flow	NOUN
ejpam-3007	321	28	from	from	ADP
ejpam-3007	321	29	small	small	ADJ
ejpam-3007	321	30	to	to	ADP
ejpam-3007	321	31	large	large	ADJ
ejpam-3007	321	32	harmonics	harmonic	NOUN
ejpam-3007	321	33	,	,	PUNCT
ejpam-3007	321	34	which	which	PRON
ejpam-3007	321	35	in	in	ADP
ejpam-3007	321	36	turn	turn	NOUN
ejpam-3007	321	37	precludes	preclude	VERB
ejpam-3007	321	38	the	the	DET
ejpam-3007	321	39	appearance	appearance	NOUN
ejpam-3007	321	40	of	of	ADP
ejpam-3007	321	41	turbulence	turbulence	NOUN
ejpam-3007	321	42	.	.	PUNCT
ejpam-3007	322	1	thus	thus	ADV
ejpam-3007	322	2	,	,	PUNCT
ejpam-3007	322	3	obtaining	obtain	VERB
ejpam-3007	322	4	uniform	uniform	ADJ
ejpam-3007	322	5	global	global	ADJ
ejpam-3007	322	6	estimations	estimation	NOUN
ejpam-3007	322	7	of	of	ADP
ejpam-3007	322	8	the	the	DET
ejpam-3007	322	9	fourier	fourier	NOUN
ejpam-3007	322	10	transform	transform	NOUN
ejpam-3007	322	11	of	of	ADP
ejpam-3007	322	12	solutions	solution	NOUN
ejpam-3007	322	13	of	of	ADP
ejpam-3007	322	14	the	the	DET
ejpam-3007	322	15	navier	navier	NOUN
ejpam-3007	322	16	-	-	PUNCT
ejpam-3007	322	17	stokes	stoke	NOUN
ejpam-3007	322	18	equations	equation	NOUN
ejpam-3007	322	19	means	mean	VERB
ejpam-3007	322	20	that	that	SCONJ
ejpam-3007	322	21	the	the	DET
ejpam-3007	322	22	principle	principle	NOUN
ejpam-3007	322	23	modeling	modeling	NOUN
ejpam-3007	322	24	of	of	ADP
ejpam-3007	322	25	complex	complex	ADJ
ejpam-3007	322	26	flows	flow	NOUN
ejpam-3007	322	27	and	and	CCONJ
ejpam-3007	322	28	related	related	ADJ
ejpam-3007	322	29	calculations	calculation	NOUN
ejpam-3007	322	30	will	will	AUX
ejpam-3007	322	31	be	be	AUX
ejpam-3007	322	32	based	base	VERB
ejpam-3007	322	33	on	on	ADP
ejpam-3007	322	34	the	the	DET
ejpam-3007	322	35	fourier	fourier	NOUN
ejpam-3007	322	36	transform	transform	NOUN
ejpam-3007	322	37	method	method	NOUN
ejpam-3007	322	38	.	.	PUNCT
ejpam-3007	323	1	the	the	DET
ejpam-3007	323	2	authors	author	NOUN
ejpam-3007	323	3	are	be	AUX
ejpam-3007	323	4	continuing	continue	VERB
ejpam-3007	323	5	to	to	PART
ejpam-3007	323	6	research	research	VERB
ejpam-3007	323	7	these	these	DET
ejpam-3007	323	8	issues	issue	NOUN
ejpam-3007	323	9	in	in	ADP
ejpam-3007	323	10	relation	relation	NOUN
ejpam-3007	323	11	to	to	ADP
ejpam-3007	323	12	a	a	DET
ejpam-3007	323	13	numerical	numerical	ADJ
ejpam-3007	323	14	weather	weather	PROPN
ejpam-3007	323	15	prediction	prediction	NOUN
ejpam-3007	323	16	model	model	NOUN
ejpam-3007	323	17	;	;	PUNCT
ejpam-3007	323	18	this	this	DET
ejpam-3007	323	19	paper	paper	NOUN
ejpam-3007	323	20	provides	provide	VERB
ejpam-3007	323	21	a	a	DET
ejpam-3007	323	22	theoretical	theoretical	ADJ
ejpam-3007	323	23	justification	justification	NOUN
ejpam-3007	323	24	for	for	ADP
ejpam-3007	323	25	this	this	DET
ejpam-3007	323	26	approach	approach	NOUN
ejpam-3007	323	27	.	.	PUNCT
ejpam-3007	324	1	consider	consider	VERB
ejpam-3007	324	2	the	the	DET
ejpam-3007	324	3	cauchy	cauchy	ADJ
ejpam-3007	324	4	problem	problem	NOUN
ejpam-3007	324	5	for	for	ADP
ejpam-3007	324	6	the	the	DET
ejpam-3007	324	7	navier	navier	NOUN
ejpam-3007	324	8	-	-	PUNCT
ejpam-3007	324	9	stokes	stoke	NOUN
ejpam-3007	324	10	equations	equation	NOUN
ejpam-3007	324	11	:	:	PUNCT
ejpam-3007	324	12	qt	qt	NOUN
ejpam-3007	324	13	−	−	PROPN
ejpam-3007	324	14	ν∆q	ν∆q	NOUN
ejpam-3007	324	15	+	+	CCONJ
ejpam-3007	324	16	(	(	PUNCT
ejpam-3007	324	17	q,∇q	q,∇q	NUM
ejpam-3007	324	18	)	)	PUNCT
ejpam-3007	324	19	=	=	SYM
ejpam-3007	325	1	−∇p+	−∇p+	PROPN
ejpam-3007	325	2	f(x	f(x	PROPN
ejpam-3007	325	3	,	,	PUNCT
ejpam-3007	325	4	t	t	PROPN
ejpam-3007	325	5	)	)	PUNCT
ejpam-3007	325	6	,	,	PUNCT
ejpam-3007	325	7	div	div	X
ejpam-3007	325	8	q	q	NOUN
ejpam-3007	325	9	=	=	SYM
ejpam-3007	325	10	0	0	NUM
ejpam-3007	325	11	,	,	PUNCT
ejpam-3007	325	12	(	(	PUNCT
ejpam-3007	325	13	57	57	NUM
ejpam-3007	325	14	)	)	PUNCT
ejpam-3007	325	15	q|t=0	q|t=0	PROPN
ejpam-3007	325	16	=	=	SYM
ejpam-3007	325	17	q0(x	q0(x	PROPN
ejpam-3007	325	18	)	)	PUNCT
ejpam-3007	325	19	(	(	PUNCT
ejpam-3007	325	20	58	58	NUM
ejpam-3007	325	21	)	)	PUNCT
ejpam-3007	325	22	in	in	ADP
ejpam-3007	325	23	the	the	DET
ejpam-3007	325	24	domain	domain	NOUN
ejpam-3007	325	25	qt	qt	NOUN
ejpam-3007	325	26	=	=	SYM
ejpam-3007	325	27	r3	r3	PROPN
ejpam-3007	325	28	×	×	NOUN
ejpam-3007	325	29	(	(	PUNCT
ejpam-3007	325	30	0	0	NUM
ejpam-3007	325	31	,	,	PUNCT
ejpam-3007	325	32	t	t	NOUN
ejpam-3007	325	33	)	)	PUNCT
ejpam-3007	325	34	,	,	PUNCT
ejpam-3007	325	35	where	where	SCONJ
ejpam-3007	325	36	:	:	PUNCT
ejpam-3007	325	37	div	div	PROPN
ejpam-3007	325	38	q0	q0	NOUN
ejpam-3007	325	39	=	=	X
ejpam-3007	325	40	0	0	PROPN
ejpam-3007	325	41	.	.	PUNCT
ejpam-3007	326	1	(	(	PUNCT
ejpam-3007	326	2	59	59	NUM
ejpam-3007	326	3	)	)	PUNCT
ejpam-3007	326	4	the	the	DET
ejpam-3007	326	5	problem	problem	NOUN
ejpam-3007	326	6	defined	define	VERB
ejpam-3007	326	7	by	by	ADP
ejpam-3007	326	8	(	(	PUNCT
ejpam-3007	326	9	57	57	NUM
ejpam-3007	326	10	)	)	PUNCT
ejpam-3007	326	11	,	,	PUNCT
ejpam-3007	326	12	(	(	PUNCT
ejpam-3007	326	13	58	58	NUM
ejpam-3007	326	14	)	)	PUNCT
ejpam-3007	326	15	,	,	PUNCT
ejpam-3007	326	16	(	(	PUNCT
ejpam-3007	326	17	59	59	NUM
ejpam-3007	326	18	)	)	PUNCT
ejpam-3007	326	19	has	have	VERB
ejpam-3007	326	20	at	at	ADV
ejpam-3007	326	21	least	least	ADV
ejpam-3007	326	22	one	one	NUM
ejpam-3007	326	23	weak	weak	ADJ
ejpam-3007	326	24	solution	solution	NOUN
ejpam-3007	326	25	(	(	PUNCT
ejpam-3007	326	26	q	q	X
ejpam-3007	326	27	,	,	PUNCT
ejpam-3007	326	28	p	p	NOUN
ejpam-3007	326	29	)	)	PUNCT
ejpam-3007	326	30	in	in	ADP
ejpam-3007	326	31	the	the	DET
ejpam-3007	326	32	so	so	ADV
ejpam-3007	326	33	-	-	PUNCT
ejpam-3007	326	34	called	call	VERB
ejpam-3007	326	35	leray	leray	ADJ
ejpam-3007	326	36	–	–	PUNCT
ejpam-3007	326	37	hopf	hopf	ADJ
ejpam-3007	326	38	class	class	NOUN
ejpam-3007	327	1	[	[	X
ejpam-3007	327	2	16	16	NUM
ejpam-3007	327	3	]	]	PUNCT
ejpam-3007	327	4	.	.	PUNCT
ejpam-3007	328	1	the	the	DET
ejpam-3007	328	2	following	follow	VERB
ejpam-3007	328	3	results	result	NOUN
ejpam-3007	328	4	have	have	AUX
ejpam-3007	328	5	been	be	AUX
ejpam-3007	328	6	proved	prove	VERB
ejpam-3007	328	7	[	[	X
ejpam-3007	328	8	17	17	NUM
ejpam-3007	328	9	]	]	X
ejpam-3007	328	10	:	:	PUNCT
ejpam-3007	328	11	theorem	theorem	NOUN
ejpam-3007	328	12	20	20	NUM
ejpam-3007	328	13	.	.	PUNCT
ejpam-3007	329	1	if	if	SCONJ
ejpam-3007	329	2	q0	q0	PROPN
ejpam-3007	329	3	∈w	∈w	VERB
ejpam-3007	329	4	1	1	NUM
ejpam-3007	329	5	2	2	NUM
ejpam-3007	329	6	(	(	PUNCT
ejpam-3007	329	7	r3	r3	PROPN
ejpam-3007	329	8	)	)	PUNCT
ejpam-3007	329	9	,	,	PUNCT
ejpam-3007	329	10	f	f	PROPN
ejpam-3007	329	11	∈	∈	PROPN
ejpam-3007	329	12	l2(qt	l2(qt	PROPN
ejpam-3007	329	13	)	)	PUNCT
ejpam-3007	329	14	,	,	PUNCT
ejpam-3007	329	15	(	(	PUNCT
ejpam-3007	329	16	60	60	NUM
ejpam-3007	329	17	)	)	PUNCT
ejpam-3007	329	18	there	there	PRON
ejpam-3007	329	19	is	be	VERB
ejpam-3007	329	20	a	a	DET
ejpam-3007	329	21	single	single	ADJ
ejpam-3007	329	22	generalized	generalized	ADJ
ejpam-3007	329	23	solution	solution	NOUN
ejpam-3007	329	24	of	of	ADP
ejpam-3007	329	25	(	(	PUNCT
ejpam-3007	329	26	57	57	NUM
ejpam-3007	329	27	)	)	PUNCT
ejpam-3007	329	28	,	,	PUNCT
ejpam-3007	329	29	(	(	PUNCT
ejpam-3007	329	30	58	58	NUM
ejpam-3007	329	31	)	)	PUNCT
ejpam-3007	329	32	,	,	PUNCT
ejpam-3007	329	33	(	(	PUNCT
ejpam-3007	329	34	59	59	NUM
ejpam-3007	329	35	)	)	PUNCT
ejpam-3007	329	36	in	in	ADP
ejpam-3007	329	37	the	the	DET
ejpam-3007	329	38	domain	domain	NOUN
ejpam-3007	329	39	qt1	qt1	PROPN
ejpam-3007	329	40	,	,	PUNCT
ejpam-3007	329	41	t1	t1	NOUN
ejpam-3007	329	42	∈	∈	PROPN
ejpam-3007	330	1	[	[	X
ejpam-3007	330	2	0	0	NUM
ejpam-3007	330	3	,	,	PUNCT
ejpam-3007	330	4	t	t	X
ejpam-3007	330	5	]	]	PUNCT
ejpam-3007	330	6	,	,	PUNCT
ejpam-3007	330	7	satisfying	satisfy	VERB
ejpam-3007	330	8	the	the	DET
ejpam-3007	330	9	following	follow	VERB
ejpam-3007	330	10	conditions	condition	NOUN
ejpam-3007	330	11	:	:	PUNCT
ejpam-3007	330	12	qt,∇2q	qt,∇2q	NOUN
ejpam-3007	330	13	,	,	PUNCT
ejpam-3007	330	14	∇p	∇p	PROPN
ejpam-3007	330	15	∈	∈	PROPN
ejpam-3007	330	16	l2(qt	l2(qt	PROPN
ejpam-3007	330	17	)	)	PUNCT
ejpam-3007	330	18	.	.	PUNCT
ejpam-3007	331	1	(	(	PUNCT
ejpam-3007	331	2	61	61	NUM
ejpam-3007	331	3	)	)	PUNCT
ejpam-3007	331	4	note	note	NOUN
ejpam-3007	331	5	that	that	SCONJ
ejpam-3007	331	6	t1	t1	NOUN
ejpam-3007	331	7	depends	depend	VERB
ejpam-3007	331	8	on	on	ADP
ejpam-3007	331	9	q0	q0	PROPN
ejpam-3007	331	10	and	and	CCONJ
ejpam-3007	331	11	f	f	PROPN
ejpam-3007	331	12	.	.	PUNCT
ejpam-3007	332	1	lemma	lemma	PROPN
ejpam-3007	332	2	21	21	NUM
ejpam-3007	332	3	.	.	PUNCT
ejpam-3007	333	1	let	let	VERB
ejpam-3007	333	2	q0	q0	PROPN
ejpam-3007	333	3	∈w	∈w	PROPN
ejpam-3007	333	4	1	1	NUM
ejpam-3007	333	5	2	2	NUM
ejpam-3007	333	6	(	(	PUNCT
ejpam-3007	333	7	r3	r3	PROPN
ejpam-3007	333	8	)	)	PUNCT
ejpam-3007	333	9	,	,	PUNCT
ejpam-3007	333	10	f	f	PROPN
ejpam-3007	333	11	∈	∈	PROPN
ejpam-3007	333	12	l2(qt	l2(qt	PROPN
ejpam-3007	333	13	)	)	PUNCT
ejpam-3007	333	14	.then	.then	ADP
ejpam-3007	333	15	,	,	PUNCT
ejpam-3007	333	16	sup	sup	NOUN
ejpam-3007	333	17	0≤t≤t	0≤t≤t	NUM
ejpam-3007	333	18	||q||2l2(r3	||q||2l2(r3	NUM
ejpam-3007	333	19	)	)	PUNCT
ejpam-3007	334	1	+	+	CCONJ
ejpam-3007	334	2	t∫	t∫	ADJ
ejpam-3007	334	3	0	0	NUM
ejpam-3007	334	4	||∇q||2l2(r3)dτ	||∇q||2l2(r3)dτ	PROPN
ejpam-3007	334	5	≤	≤	NOUN
ejpam-3007	334	6	||q0||2l2(r3	||q0||2l2(r3	ADV
ejpam-3007	334	7	)	)	PUNCT
ejpam-3007	335	1	+	+	NUM
ejpam-3007	335	2	||f	||f	NOUN
ejpam-3007	335	3	||l2(qt	||l2(qt	NOUN
ejpam-3007	335	4	)	)	PUNCT
ejpam-3007	335	5	.	.	PUNCT
ejpam-3007	336	1	(	(	PUNCT
ejpam-3007	336	2	62	62	NUM
ejpam-3007	336	3	)	)	PUNCT
ejpam-3007	336	4	a.	a.	NOUN
ejpam-3007	336	5	durmagambetov	durmagambetov	PROPN
ejpam-3007	336	6	/	/	SYM
ejpam-3007	336	7	eur	eur	PROPN
ejpam-3007	336	8	.	.	PUNCT
ejpam-3007	337	1	j.	j.	PROPN
ejpam-3007	337	2	pure	pure	PROPN
ejpam-3007	337	3	appl	appl	PROPN
ejpam-3007	337	4	.	.	PROPN
ejpam-3007	337	5	math	math	PROPN
ejpam-3007	337	6	,	,	PUNCT
ejpam-3007	337	7	10	10	NUM
ejpam-3007	337	8	(	(	PUNCT
ejpam-3007	337	9	4	4	NUM
ejpam-3007	337	10	)	)	PUNCT
ejpam-3007	337	11	(	(	PUNCT
ejpam-3007	337	12	2017	2017	NUM
ejpam-3007	337	13	)	)	PUNCT
ejpam-3007	337	14	,	,	PUNCT
ejpam-3007	337	15	763	763	NUM
ejpam-3007	337	16	-	-	SYM
ejpam-3007	337	17	785	785	NUM
ejpam-3007	337	18	777	777	NUM
ejpam-3007	337	19	our	our	PRON
ejpam-3007	337	20	goal	goal	NOUN
ejpam-3007	337	21	is	be	AUX
ejpam-3007	337	22	to	to	PART
ejpam-3007	337	23	provide	provide	VERB
ejpam-3007	337	24	global	global	ADJ
ejpam-3007	337	25	estimations	estimation	NOUN
ejpam-3007	337	26	for	for	ADP
ejpam-3007	337	27	the	the	DET
ejpam-3007	337	28	fourier	fourier	NOUN
ejpam-3007	337	29	transforms	transform	VERB
ejpam-3007	337	30	of	of	ADP
ejpam-3007	337	31	derivatives	derivative	NOUN
ejpam-3007	337	32	of	of	ADP
ejpam-3007	337	33	the	the	DET
ejpam-3007	337	34	navier	navier	NOUN
ejpam-3007	337	35	–	–	PUNCT
ejpam-3007	337	36	stokes	stokes	PROPN
ejpam-3007	337	37	equations	equation	NOUN
ejpam-3007	337	38	’	'	PUNCT
ejpam-3007	337	39	solutions	solution	NOUN
ejpam-3007	337	40	(	(	PUNCT
ejpam-3007	337	41	57	57	NUM
ejpam-3007	337	42	)	)	PUNCT
ejpam-3007	337	43	,	,	PUNCT
ejpam-3007	337	44	(	(	PUNCT
ejpam-3007	337	45	58	58	NUM
ejpam-3007	337	46	)	)	PUNCT
ejpam-3007	337	47	,	,	PUNCT
ejpam-3007	337	48	(	(	PUNCT
ejpam-3007	337	49	59	59	NUM
ejpam-3007	337	50	)	)	PUNCT
ejpam-3007	337	51	without	without	ADP
ejpam-3007	337	52	the	the	DET
ejpam-3007	337	53	that	that	SCONJ
ejpam-3007	337	54	the	the	DET
ejpam-3007	337	55	smallness	smallness	NOUN
ejpam-3007	337	56	of	of	ADP
ejpam-3007	337	57	the	the	DET
ejpam-3007	337	58	initial	initial	ADJ
ejpam-3007	337	59	velocity	velocity	NOUN
ejpam-3007	337	60	and	and	CCONJ
ejpam-3007	337	61	force	force	NOUN
ejpam-3007	337	62	are	be	AUX
ejpam-3007	337	63	small	small	ADJ
ejpam-3007	337	64	.	.	PUNCT
ejpam-3007	338	1	we	we	PRON
ejpam-3007	338	2	obtain	obtain	VERB
ejpam-3007	338	3	the	the	DET
ejpam-3007	338	4	following	following	ADJ
ejpam-3007	338	5	uniform	uniform	ADJ
ejpam-3007	338	6	time	time	PROPN
ejpam-3007	338	7	estimation	estimation	NOUN
ejpam-3007	338	8	.	.	PUNCT
ejpam-3007	339	1	lemma	lemma	PROPN
ejpam-3007	339	2	22	22	NUM
ejpam-3007	339	3	.	.	PUNCT
ejpam-3007	340	1	the	the	DET
ejpam-3007	340	2	solution	solution	NOUN
ejpam-3007	340	3	of	of	ADP
ejpam-3007	340	4	(	(	PUNCT
ejpam-3007	340	5	57	57	NUM
ejpam-3007	340	6	)	)	PUNCT
ejpam-3007	340	7	,	,	PUNCT
ejpam-3007	340	8	(	(	PUNCT
ejpam-3007	340	9	58	58	NUM
ejpam-3007	340	10	)	)	PUNCT
ejpam-3007	340	11	,	,	PUNCT
ejpam-3007	340	12	(	(	PUNCT
ejpam-3007	340	13	59	59	NUM
ejpam-3007	340	14	)	)	PUNCT
ejpam-3007	340	15	according	accord	VERB
ejpam-3007	340	16	to	to	ADP
ejpam-3007	340	17	theorem	theorem	ADJ
ejpam-3007	340	18	20	20	NUM
ejpam-3007	340	19	satisfies	satisfie	NOUN
ejpam-3007	340	20	:	:	PUNCT
ejpam-3007	340	21	q̃	q̃	PROPN
ejpam-3007	340	22	=	=	SYM
ejpam-3007	340	23	q̃0	q̃0	PROPN
ejpam-3007	340	24	+	+	CCONJ
ejpam-3007	340	25	t∫	t∫	ADJ
ejpam-3007	340	26	0	0	NUM
ejpam-3007	340	27	e−ν|k|	e−ν|k|	PROPN
ejpam-3007	340	28	2|(t−τ	2|(t−τ	NUM
ejpam-3007	340	29	)	)	PUNCT
ejpam-3007	340	30	(	(	PUNCT
ejpam-3007	340	31	˜[(q,∇)q	˜[(q,∇)q	X
ejpam-3007	340	32	]	]	X
ejpam-3007	340	33	+	+	CCONJ
ejpam-3007	340	34	f̃	f̃	PROPN
ejpam-3007	340	35	)	)	PUNCT
ejpam-3007	340	36	dτ	dτ	PROPN
ejpam-3007	340	37	,	,	PUNCT
ejpam-3007	340	38	(	(	PUNCT
ejpam-3007	340	39	63	63	NUM
ejpam-3007	340	40	)	)	PUNCT
ejpam-3007	340	41	where	where	SCONJ
ejpam-3007	340	42	f	f	NOUN
ejpam-3007	340	43	=	=	PUNCT
ejpam-3007	340	44	−∇p+	−∇p+	PROPN
ejpam-3007	340	45	f	f	PROPN
ejpam-3007	340	46	.	.	PUNCT
ejpam-3007	341	1	proof	proof	NOUN
ejpam-3007	341	2	.	.	PUNCT
ejpam-3007	342	1	this	this	PRON
ejpam-3007	342	2	follows	follow	VERB
ejpam-3007	342	3	from	from	ADP
ejpam-3007	342	4	the	the	DET
ejpam-3007	342	5	definition	definition	NOUN
ejpam-3007	342	6	of	of	ADP
ejpam-3007	342	7	the	the	DET
ejpam-3007	342	8	fourier	fourier	NOUN
ejpam-3007	342	9	transform	transform	NOUN
ejpam-3007	342	10	and	and	CCONJ
ejpam-3007	342	11	the	the	DET
ejpam-3007	342	12	theory	theory	NOUN
ejpam-3007	342	13	of	of	ADP
ejpam-3007	342	14	linear	linear	PROPN
ejpam-3007	342	15	differential	differential	ADJ
ejpam-3007	342	16	equations	equation	NOUN
ejpam-3007	342	17	.	.	PUNCT
ejpam-3007	343	1	lemma	lemma	PROPN
ejpam-3007	343	2	23	23	NUM
ejpam-3007	343	3	.	.	PUNCT
ejpam-3007	344	1	the	the	DET
ejpam-3007	344	2	solution	solution	NOUN
ejpam-3007	344	3	of	of	ADP
ejpam-3007	344	4	(	(	PUNCT
ejpam-3007	344	5	57	57	NUM
ejpam-3007	344	6	)	)	PUNCT
ejpam-3007	344	7	,	,	PUNCT
ejpam-3007	344	8	(	(	PUNCT
ejpam-3007	344	9	58	58	NUM
ejpam-3007	344	10	)	)	PUNCT
ejpam-3007	344	11	,	,	PUNCT
ejpam-3007	344	12	(	(	PUNCT
ejpam-3007	344	13	59	59	NUM
ejpam-3007	344	14	)	)	PUNCT
ejpam-3007	344	15	satisfies	satisfie	NOUN
ejpam-3007	344	16	:	:	PUNCT
ejpam-3007	344	17	p̃	p̃	PROPN
ejpam-3007	344	18	=	=	SYM
ejpam-3007	344	19	∑	∑	PUNCT
ejpam-3007	344	20	i	i	PROPN
ejpam-3007	344	21	,	,	PUNCT
ejpam-3007	344	22	j	j	PROPN
ejpam-3007	344	23	kikj	kikj	PROPN
ejpam-3007	344	24	|k|2	|k|2	PROPN
ejpam-3007	344	25	q̃iqj	q̃iqj	NOUN
ejpam-3007	344	26	+	+	X
ejpam-3007	345	1	i	i	PRON
ejpam-3007	345	2	∑	∑	VERB
ejpam-3007	345	3	i	i	PRON
ejpam-3007	345	4	ki	ki	PROPN
ejpam-3007	345	5	|k|2	|k|2	PROPN
ejpam-3007	345	6	f̃i	f̃i	NOUN
ejpam-3007	345	7	(	(	PUNCT
ejpam-3007	345	8	64	64	NUM
ejpam-3007	345	9	)	)	PUNCT
ejpam-3007	345	10	and	and	CCONJ
ejpam-3007	345	11	the	the	DET
ejpam-3007	345	12	following	follow	VERB
ejpam-3007	345	13	estimations	estimation	NOUN
ejpam-3007	345	14	:	:	PUNCT
ejpam-3007	345	15	||p||l2(r3	||p||l2(r3	NUM
ejpam-3007	345	16	)	)	PUNCT
ejpam-3007	345	17	≤	≤	NOUN
ejpam-3007	346	1	3||∇q||	3||∇q||	NUM
ejpam-3007	346	2	3	3	NUM
ejpam-3007	346	3	2	2	NUM
ejpam-3007	346	4	l2(r3	l2(r3	NUM
ejpam-3007	346	5	)	)	PUNCT
ejpam-3007	346	6	||q||	||q||	NOUN
ejpam-3007	346	7	1	1	NUM
ejpam-3007	346	8	2	2	NUM
ejpam-3007	346	9	l2(r3	l2(r3	NUM
ejpam-3007	346	10	)	)	PUNCT
ejpam-3007	346	11	,	,	PUNCT
ejpam-3007	346	12	(	(	PUNCT
ejpam-3007	346	13	65	65	NUM
ejpam-3007	346	14	)	)	PUNCT
ejpam-3007	346	15	|∇p̃|	|∇p̃|	ADJ
ejpam-3007	346	16	≤	≤	NUM
ejpam-3007	346	17	|q̃	|q̃	NOUN
ejpam-3007	346	18	2|	2|	NUM
ejpam-3007	346	19	|k|	|k|	PROPN
ejpam-3007	346	20	+	+	CCONJ
ejpam-3007	346	21	|f̃	|f̃	VERB
ejpam-3007	346	22	|	|	ADV
ejpam-3007	346	23	|k|2	|k|2	NOUN
ejpam-3007	346	24	+	+	NOUN
ejpam-3007	346	25	1	1	NUM
ejpam-3007	346	26	|k|	|k|	PROPN
ejpam-3007	346	27	∣∣∣∇f̃	∣∣∣∇f̃	PROPN
ejpam-3007	346	28	∣∣∣+	∣∣∣+	PROPN
ejpam-3007	346	29	3	3	NUM
ejpam-3007	346	30	∣∣∇q̃2	∣∣∇q̃2	NUM
ejpam-3007	346	31	∣∣	∣∣	PROPN
ejpam-3007	346	32	.	.	PUNCT
ejpam-3007	347	1	(	(	PUNCT
ejpam-3007	347	2	66	66	NUM
ejpam-3007	347	3	)	)	PUNCT
ejpam-3007	347	4	proof	proof	NOUN
ejpam-3007	347	5	.	.	PUNCT
ejpam-3007	348	1	this	this	DET
ejpam-3007	348	2	expression	expression	NOUN
ejpam-3007	348	3	for	for	ADP
ejpam-3007	348	4	p	p	NOUN
ejpam-3007	348	5	is	be	AUX
ejpam-3007	348	6	obtained	obtain	VERB
ejpam-3007	348	7	using	use	VERB
ejpam-3007	348	8	div	div	PROPN
ejpam-3007	348	9	and	and	CCONJ
ejpam-3007	348	10	the	the	DET
ejpam-3007	348	11	fourier	fourier	NOUN
ejpam-3007	348	12	transform	transform	NOUN
ejpam-3007	348	13	presentation	presentation	NOUN
ejpam-3007	348	14	.	.	PUNCT
ejpam-3007	349	1	lemma	lemma	PROPN
ejpam-3007	349	2	24	24	NUM
ejpam-3007	349	3	.	.	PUNCT
ejpam-3007	350	1	the	the	DET
ejpam-3007	350	2	solution	solution	NOUN
ejpam-3007	350	3	of	of	ADP
ejpam-3007	350	4	(	(	PUNCT
ejpam-3007	350	5	57	57	NUM
ejpam-3007	350	6	)	)	PUNCT
ejpam-3007	350	7	,	,	PUNCT
ejpam-3007	350	8	(	(	PUNCT
ejpam-3007	350	9	58	58	NUM
ejpam-3007	350	10	)	)	PUNCT
ejpam-3007	350	11	,	,	PUNCT
ejpam-3007	350	12	(	(	PUNCT
ejpam-3007	350	13	59	59	NUM
ejpam-3007	350	14	)	)	PUNCT
ejpam-3007	350	15	in	in	ADP
ejpam-3007	350	16	theorem	theorem	ADJ
ejpam-3007	350	17	20	20	NUM
ejpam-3007	350	18	satisfies	satisfie	NOUN
ejpam-3007	350	19	the	the	DET
ejpam-3007	350	20	following	follow	VERB
ejpam-3007	350	21	inequalities	inequality	NOUN
ejpam-3007	350	22	:	:	PUNCT
ejpam-3007	350	23	∫	∫	PROPN
ejpam-3007	350	24	r3	r3	PROPN
ejpam-3007	350	25	|x|2|q|2dx+	|x|2|q|2dx+	NOUN
ejpam-3007	350	26	t∫	t∫	ADJ
ejpam-3007	350	27	0	0	NUM
ejpam-3007	350	28	∫	∫	PROPN
ejpam-3007	350	29	r3	r3	PROPN
ejpam-3007	350	30	|x|2|∇q|2dxdτ	|x|2|∇q|2dxdτ	NOUN
ejpam-3007	350	31	≤	≤	NUM
ejpam-3007	350	32	const	const	NOUN
ejpam-3007	350	33	,	,	PUNCT
ejpam-3007	350	34	∫	∫	PROPN
ejpam-3007	350	35	r3	r3	PROPN
ejpam-3007	350	36	|x|4|q|2dx+	|x|4|q|2dx+	NOUN
ejpam-3007	350	37	t∫	t∫	ADJ
ejpam-3007	350	38	0	0	NUM
ejpam-3007	350	39	∫	∫	PROPN
ejpam-3007	350	40	r3	r3	PROPN
ejpam-3007	350	41	|x|4|∇q|2dxdτ	|x|4|∇q|2dxdτ	PROPN
ejpam-3007	350	42	≤	≤	NUM
ejpam-3007	350	43	const	const	NOUN
ejpam-3007	350	44	,	,	PUNCT
ejpam-3007	350	45	(	(	PUNCT
ejpam-3007	350	46	67	67	NUM
ejpam-3007	350	47	)	)	PUNCT
ejpam-3007	350	48	or	or	CCONJ
ejpam-3007	350	49	||∇q̃||l2(r3	||∇q̃||l2(r3	NUM
ejpam-3007	350	50	)	)	PUNCT
ejpam-3007	351	1	+	+	CCONJ
ejpam-3007	351	2	t∫	t∫	PRON
ejpam-3007	351	3	0	0	NUM
ejpam-3007	351	4	∫	∫	PROPN
ejpam-3007	351	5	r3	r3	PROPN
ejpam-3007	351	6	|k|2|∇̃q|2dkdτ	|k|2|∇̃q|2dkdτ	PROPN
ejpam-3007	351	7	≤	≤	PROPN
ejpam-3007	351	8	const	const	NOUN
ejpam-3007	351	9	,	,	PUNCT
ejpam-3007	351	10	∣∣∣∣∇2q̃	∣∣∣∣∇2q̃	PROPN
ejpam-3007	351	11	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3007	351	12	l2(r3	l2(r3	NOUN
ejpam-3007	351	13	)	)	PUNCT
ejpam-3007	351	14	+	+	CCONJ
ejpam-3007	351	15	t∫	t∫	PRON
ejpam-3007	351	16	0	0	NUM
ejpam-3007	351	17	∫	∫	PROPN
ejpam-3007	351	18	r3	r3	PROPN
ejpam-3007	351	19	|k|2|∇̃2q|2dkdτ	|k|2|∇̃2q|2dkdτ	PROPN
ejpam-3007	351	20	≤	≤	NUM
ejpam-3007	351	21	const	const	NOUN
ejpam-3007	351	22	.	.	PUNCT
ejpam-3007	352	1	(	(	PUNCT
ejpam-3007	352	2	68	68	NUM
ejpam-3007	352	3	)	)	PUNCT
ejpam-3007	352	4	this	this	PRON
ejpam-3007	352	5	follows	follow	VERB
ejpam-3007	352	6	from	from	ADP
ejpam-3007	352	7	the	the	DET
ejpam-3007	352	8	a	a	DET
ejpam-3007	352	9	priori	priori	ADJ
ejpam-3007	352	10	estimation	estimation	NOUN
ejpam-3007	352	11	of	of	ADP
ejpam-3007	352	12	lemma	lemma	PROPN
ejpam-3007	352	13	21	21	NUM
ejpam-3007	352	14	,	,	PUNCT
ejpam-3007	352	15	conditions	condition	NOUN
ejpam-3007	352	16	of	of	ADP
ejpam-3007	352	17	lemma	lemma	PROPN
ejpam-3007	352	18	24,the	24,the	DET
ejpam-3007	352	19	navier	navier	NOUN
ejpam-3007	352	20	–	–	PUNCT
ejpam-3007	352	21	stokes	stokes	PROPN
ejpam-3007	352	22	equations	equation	NOUN
ejpam-3007	352	23	.	.	PUNCT
ejpam-3007	353	1	a.	a.	NOUN
ejpam-3007	353	2	durmagambetov	durmagambetov	PROPN
ejpam-3007	353	3	/	/	SYM
ejpam-3007	353	4	eur	eur	PROPN
ejpam-3007	353	5	.	.	PUNCT
ejpam-3007	354	1	j.	j.	PROPN
ejpam-3007	354	2	pure	pure	PROPN
ejpam-3007	354	3	appl	appl	PROPN
ejpam-3007	354	4	.	.	PROPN
ejpam-3007	354	5	math	math	PROPN
ejpam-3007	354	6	,	,	PUNCT
ejpam-3007	354	7	10	10	NUM
ejpam-3007	354	8	(	(	PUNCT
ejpam-3007	354	9	4	4	NUM
ejpam-3007	354	10	)	)	PUNCT
ejpam-3007	354	11	(	(	PUNCT
ejpam-3007	354	12	2017	2017	NUM
ejpam-3007	354	13	)	)	PUNCT
ejpam-3007	354	14	,	,	PUNCT
ejpam-3007	354	15	763	763	NUM
ejpam-3007	354	16	-	-	SYM
ejpam-3007	354	17	785	785	NUM
ejpam-3007	354	18	778	778	NUM
ejpam-3007	354	19	lemma	lemma	PROPN
ejpam-3007	354	20	25	25	NUM
ejpam-3007	354	21	.	.	PUNCT
ejpam-3007	355	1	the	the	DET
ejpam-3007	355	2	solution	solution	NOUN
ejpam-3007	355	3	of	of	ADP
ejpam-3007	355	4	(	(	PUNCT
ejpam-3007	355	5	57	57	NUM
ejpam-3007	355	6	)	)	PUNCT
ejpam-3007	355	7	,	,	PUNCT
ejpam-3007	355	8	(	(	PUNCT
ejpam-3007	355	9	58	58	NUM
ejpam-3007	355	10	)	)	PUNCT
ejpam-3007	355	11	,	,	PUNCT
ejpam-3007	355	12	(	(	PUNCT
ejpam-3007	355	13	59	59	NUM
ejpam-3007	355	14	)	)	PUNCT
ejpam-3007	355	15	satisfies	satisfy	VERB
ejpam-3007	355	16	the	the	DET
ejpam-3007	355	17	following	follow	VERB
ejpam-3007	355	18	inequalities	inequality	NOUN
ejpam-3007	355	19	:	:	PUNCT
ejpam-3007	356	1	max	max	PROPN
ejpam-3007	356	2	k	k	PROPN
ejpam-3007	357	1	|q̃|	|q̃|	PROPN
ejpam-3007	357	2	≤	≤	PROPN
ejpam-3007	357	3	max	max	PROPN
ejpam-3007	357	4	k	k	PROPN
ejpam-3007	357	5	|q̃0|	|q̃0|	PROPN
ejpam-3007	358	1	+	+	CCONJ
ejpam-3007	358	2	t	t	PROPN
ejpam-3007	358	3	2	2	NUM
ejpam-3007	358	4	sup	sup	NOUN
ejpam-3007	358	5	0≤t≤t	0≤t≤t	NUM
ejpam-3007	358	6	||q||2l2(r3	||q||2l2(r3	NUM
ejpam-3007	358	7	)	)	PUNCT
ejpam-3007	359	1	+	+	CCONJ
ejpam-3007	359	2	t∫	t∫	PRON
ejpam-3007	359	3	0	0	NUM
ejpam-3007	359	4	||∇q||2l2(r3)dτ	||∇q||2l2(r3)dτ	PROPN
ejpam-3007	359	5	,	,	PUNCT
ejpam-3007	359	6	(	(	PUNCT
ejpam-3007	359	7	69	69	NUM
ejpam-3007	359	8	)	)	PUNCT
ejpam-3007	359	9	max	max	PROPN
ejpam-3007	360	1	k	k	PROPN
ejpam-3007	360	2	|∇q̃|	|∇q̃|	PROPN
ejpam-3007	360	3	≤	≤	PROPN
ejpam-3007	360	4	max	max	PROPN
ejpam-3007	360	5	k	k	PROPN
ejpam-3007	360	6	|∇q̃0|	|∇q̃0|	PROPN
ejpam-3007	360	7	+	+	PROPN
ejpam-3007	360	8	t	t	PROPN
ejpam-3007	360	9	2	2	NUM
ejpam-3007	360	10	sup	sup	NOUN
ejpam-3007	360	11	0≤t≤t	0≤t≤t	NUM
ejpam-3007	360	12	||∇q̃||l2(r3	||∇q̃||l2(r3	NOUN
ejpam-3007	360	13	)	)	PUNCT
ejpam-3007	361	1	+	+	CCONJ
ejpam-3007	361	2	t∫	t∫	DET
ejpam-3007	361	3	0	0	NUM
ejpam-3007	361	4	∫	∫	PROPN
ejpam-3007	361	5	r3	r3	PROPN
ejpam-3007	361	6	|k|2|∇̃q|2dkdτ	|k|2|∇̃q|2dkdτ	PROPN
ejpam-3007	361	7	,	,	PUNCT
ejpam-3007	361	8	(	(	PUNCT
ejpam-3007	361	9	70	70	NUM
ejpam-3007	361	10	)	)	PUNCT
ejpam-3007	362	1	max	max	PROPN
ejpam-3007	363	1	k	k	PROPN
ejpam-3007	363	2	∣∣∇2q̃	∣∣∇2q̃	PROPN
ejpam-3007	363	3	∣∣	∣∣	NUM
ejpam-3007	363	4	≤	≤	NUM
ejpam-3007	363	5	max	max	PROPN
ejpam-3007	363	6	k	k	PROPN
ejpam-3007	363	7	∣∣∇2q̃0	∣∣∇2q̃0	NOUN
ejpam-3007	363	8	∣∣	∣∣	X
ejpam-3007	363	9	+	+	CCONJ
ejpam-3007	363	10	t	t	PROPN
ejpam-3007	363	11	2	2	NUM
ejpam-3007	363	12	sup	sup	NOUN
ejpam-3007	363	13	0≤t≤t	0≤t≤t	NUM
ejpam-3007	363	14	∣∣∣∣∇2q̃	∣∣∣∣∇2q̃	NOUN
ejpam-3007	363	15	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3007	363	16	l2(r3	l2(r3	NOUN
ejpam-3007	363	17	)	)	PUNCT
ejpam-3007	363	18	+	+	CCONJ
ejpam-3007	363	19	t∫	t∫	PRON
ejpam-3007	363	20	0	0	NUM
ejpam-3007	363	21	∫	∫	PROPN
ejpam-3007	363	22	r3	r3	PROPN
ejpam-3007	363	23	|k|2|∇2q̃|2dkdτ	|k|2|∇2q̃|2dkdτ	PROPN
ejpam-3007	363	24	.	.	PUNCT
ejpam-3007	364	1	(	(	PUNCT
ejpam-3007	364	2	71	71	NUM
ejpam-3007	364	3	)	)	PUNCT
ejpam-3007	364	4	proof	proof	NOUN
ejpam-3007	364	5	.	.	PUNCT
ejpam-3007	365	1	this	this	PRON
ejpam-3007	365	2	follows	follow	VERB
ejpam-3007	365	3	from	from	ADP
ejpam-3007	365	4	the	the	DET
ejpam-3007	365	5	a	a	DET
ejpam-3007	365	6	priori	priori	ADJ
ejpam-3007	365	7	estimation	estimation	NOUN
ejpam-3007	365	8	of	of	ADP
ejpam-3007	365	9	lemma	lemma	PROPN
ejpam-3007	365	10	21	21	NUM
ejpam-3007	365	11	,	,	PUNCT
ejpam-3007	365	12	conditions	condition	NOUN
ejpam-3007	365	13	of	of	ADP
ejpam-3007	365	14	lemma	lemma	PROPN
ejpam-3007	365	15	25,the	25,the	PRON
ejpam-3007	365	16	navier	navier	NOUN
ejpam-3007	365	17	–	–	PUNCT
ejpam-3007	365	18	stokes	stokes	PROPN
ejpam-3007	365	19	equations	equation	NOUN
ejpam-3007	365	20	.	.	PUNCT
ejpam-3007	366	1	lemma	lemma	PROPN
ejpam-3007	366	2	26	26	NUM
ejpam-3007	366	3	.	.	PUNCT
ejpam-3007	367	1	the	the	DET
ejpam-3007	367	2	solution	solution	NOUN
ejpam-3007	367	3	of	of	ADP
ejpam-3007	367	4	(	(	PUNCT
ejpam-3007	367	5	57	57	NUM
ejpam-3007	367	6	)	)	PUNCT
ejpam-3007	367	7	,	,	PUNCT
ejpam-3007	367	8	(	(	PUNCT
ejpam-3007	367	9	58	58	NUM
ejpam-3007	367	10	)	)	PUNCT
ejpam-3007	367	11	,	,	PUNCT
ejpam-3007	367	12	(	(	PUNCT
ejpam-3007	367	13	59	59	NUM
ejpam-3007	367	14	)	)	PUNCT
ejpam-3007	367	15	according	accord	VERB
ejpam-3007	367	16	to	to	ADP
ejpam-3007	367	17	theorem	theorem	ADJ
ejpam-3007	367	18	20	20	NUM
ejpam-3007	367	19	satisfies	satisfie	NOUN
ejpam-3007	367	20	ci	ci	PROPN
ejpam-3007	367	21	≤	≤	NUM
ejpam-3007	367	22	const	const	NOUN
ejpam-3007	367	23	,	,	PUNCT
ejpam-3007	367	24	(	(	PUNCT
ejpam-3007	367	25	i	i	NOUN
ejpam-3007	367	26	=	=	NOUN
ejpam-3007	367	27	0	0	NUM
ejpam-3007	367	28	,	,	PUNCT
ejpam-3007	367	29	2	2	NUM
ejpam-3007	367	30	,	,	PUNCT
ejpam-3007	367	31	4	4	NUM
ejpam-3007	367	32	)	)	PUNCT
ejpam-3007	367	33	,	,	PUNCT
ejpam-3007	367	34	where	where	SCONJ
ejpam-3007	367	35	:	:	PUNCT
ejpam-3007	367	36	c0	c0	PROPN
ejpam-3007	367	37	=	=	SYM
ejpam-3007	367	38	t∫	t∫	PROPN
ejpam-3007	367	39	0	0	NUM
ejpam-3007	367	40	|f̃1|2dτ	|f̃1|2dτ	NOUN
ejpam-3007	367	41	,	,	PUNCT
ejpam-3007	367	42	f1	f1	NOUN
ejpam-3007	367	43	=	=	PUNCT
ejpam-3007	367	44	(	(	PUNCT
ejpam-3007	367	45	q,∇)q	q,∇)q	NOUN
ejpam-3007	367	46	+	+	NOUN
ejpam-3007	367	47	f	f	X
ejpam-3007	367	48	,	,	PUNCT
ejpam-3007	367	49	c2	c2	PROPN
ejpam-3007	367	50	=	=	PUNCT
ejpam-3007	368	1	t∫	t∫	ADJ
ejpam-3007	368	2	0	0	NUM
ejpam-3007	368	3	∣∣∣∇f̃1	∣∣∣∇f̃1	PROPN
ejpam-3007	368	4	∣∣∣2	∣∣∣2	PROPN
ejpam-3007	368	5	dτ	dτ	PROPN
ejpam-3007	368	6	,	,	PUNCT
ejpam-3007	368	7	c4	c4	NOUN
ejpam-3007	368	8	=	=	SYM
ejpam-3007	368	9	t∫	t∫	PROPN
ejpam-3007	368	10	0	0	NUM
ejpam-3007	368	11	∣∣∣∇2f̃1	∣∣∣∇2f̃1	PROPN
ejpam-3007	368	12	∣∣∣2	∣∣∣2	PROPN
ejpam-3007	368	13	dτ	dτ	PROPN
ejpam-3007	368	14	.	.	PROPN
ejpam-3007	368	15	(	(	PUNCT
ejpam-3007	368	16	72	72	NUM
ejpam-3007	368	17	)	)	PUNCT
ejpam-3007	368	18	proof	proof	NOUN
ejpam-3007	368	19	.	.	PUNCT
ejpam-3007	369	1	this	this	PRON
ejpam-3007	369	2	follows	follow	VERB
ejpam-3007	369	3	from	from	ADP
ejpam-3007	369	4	the	the	DET
ejpam-3007	369	5	a	a	DET
ejpam-3007	369	6	priori	priori	ADJ
ejpam-3007	369	7	estimation	estimation	NOUN
ejpam-3007	369	8	of	of	ADP
ejpam-3007	369	9	lemma	lemma	PROPN
ejpam-3007	369	10	21	21	NUM
ejpam-3007	369	11	,	,	PUNCT
ejpam-3007	369	12	the	the	DET
ejpam-3007	369	13	navier	navier	NOUN
ejpam-3007	369	14	–	–	PUNCT
ejpam-3007	369	15	stokes	stokes	PROPN
ejpam-3007	369	16	equations	equation	NOUN
ejpam-3007	369	17	.	.	PUNCT
ejpam-3007	370	1	lemma	lemma	PROPN
ejpam-3007	370	2	27	27	NUM
ejpam-3007	370	3	.	.	PUNCT
ejpam-3007	370	4	suppose	suppose	VERB
ejpam-3007	371	1	that	that	SCONJ
ejpam-3007	371	2	q	q	PROPN
ejpam-3007	371	3	∈	∈	PROPN
ejpam-3007	371	4	r	r	PROPN
ejpam-3007	371	5	,	,	PUNCT
ejpam-3007	371	6	max	max	PROPN
ejpam-3007	371	7	k	k	PROPN
ejpam-3007	371	8	|q̃|	|q̃|	PROPN
ejpam-3007	371	9	<	<	X
ejpam-3007	371	10	∞	∞	PROPN
ejpam-3007	371	11	,	,	PUNCT
ejpam-3007	371	12	then	then	ADV
ejpam-3007	371	13	∫	∫	PROPN
ejpam-3007	371	14	r3	r3	PROPN
ejpam-3007	371	15	∫	∫	PROPN
ejpam-3007	371	16	r3	r3	PROPN
ejpam-3007	371	17	q(x)q(y	q(x)q(y	PROPN
ejpam-3007	371	18	)	)	PUNCT
ejpam-3007	371	19	|x−	|x−	PROPN
ejpam-3007	371	20	y|2	y|2	PROPN
ejpam-3007	371	21	dxdy	dxdy	PROPN
ejpam-3007	371	22	≤	≤	PROPN
ejpam-3007	371	23	c(|q|l2	c(|q|l2	NOUN
ejpam-3007	372	1	+	+	NUM
ejpam-3007	372	2	max	max	PROPN
ejpam-3007	372	3	k	k	PROPN
ejpam-3007	372	4	|q̃|)2	|q̃|)2	PROPN
ejpam-3007	372	5	.	.	PUNCT
ejpam-3007	373	1	proof	proof	NOUN
ejpam-3007	373	2	.	.	PUNCT
ejpam-3007	374	1	using	use	VERB
ejpam-3007	374	2	plansherel	plansherel	NOUN
ejpam-3007	374	3	’s	’s	PART
ejpam-3007	374	4	theorem	theorem	NOUN
ejpam-3007	374	5	,	,	PUNCT
ejpam-3007	374	6	we	we	PRON
ejpam-3007	374	7	get	get	VERB
ejpam-3007	374	8	the	the	DET
ejpam-3007	374	9	statement	statement	NOUN
ejpam-3007	374	10	of	of	ADP
ejpam-3007	374	11	the	the	DET
ejpam-3007	374	12	lemma	lemma	PROPN
ejpam-3007	374	13	.	.	PUNCT
ejpam-3007	375	1	this	this	PRON
ejpam-3007	375	2	proves	prove	VERB
ejpam-3007	375	3	lemma	lemma	PROPN
ejpam-3007	375	4	27	27	NUM
ejpam-3007	375	5	.	.	PUNCT
ejpam-3007	376	1	let	let	VERB
ejpam-3007	376	2	’s	’s	NOUN
ejpam-3007	376	3	consider	consider	VERB
ejpam-3007	376	4	the	the	DET
ejpam-3007	376	5	influence	influence	NOUN
ejpam-3007	376	6	of	of	ADP
ejpam-3007	376	7	the	the	DET
ejpam-3007	376	8	following	follow	VERB
ejpam-3007	376	9	large	large	ADJ
ejpam-3007	376	10	scale	scale	NOUN
ejpam-3007	376	11	transformations	transformation	NOUN
ejpam-3007	376	12	in	in	ADP
ejpam-3007	376	13	navierstokes	navierstoke	NOUN
ejpam-3007	376	14	’	'	PUNCT
ejpam-3007	376	15	equation	equation	NOUN
ejpam-3007	376	16	on	on	ADP
ejpam-3007	376	17	k	k	PROPN
ejpam-3007	376	18	=	=	PUNCT
ejpam-3007	376	19	ν	ν	NOUN
ejpam-3007	376	20	1	1	NUM
ejpam-3007	376	21	2	2	NUM
ejpam-3007	376	22	ν	ν	NOUN
ejpam-3007	376	23	1	1	NUM
ejpam-3007	376	24	2	2	NUM
ejpam-3007	376	25	−	−	PROPN
ejpam-3007	376	26	4πcc	4πcc	PROPN
ejpam-3007	376	27	1	1	NUM
ejpam-3007	376	28	2	2	NUM
ejpam-3007	376	29	0	0	NUM
ejpam-3007	376	30	.	.	PUNCT
ejpam-3007	377	1	t′	t′	X
ejpam-3007	377	2	=	=	SYM
ejpam-3007	377	3	ta	ta	PROPN
ejpam-3007	377	4	,	,	PUNCT
ejpam-3007	377	5	ν	ν	X
ejpam-3007	377	6	′	′	NOUN
ejpam-3007	378	1	=	=	PUNCT
ejpam-3007	378	2	ν	ν	X
ejpam-3007	378	3	a	a	PRON
ejpam-3007	378	4	,	,	PUNCT
ejpam-3007	378	5	v′	v′	X
ejpam-3007	378	6	=	=	PUNCT
ejpam-3007	378	7	v	v	X
ejpam-3007	378	8	a	a	PRON
ejpam-3007	378	9	,	,	PUNCT
ejpam-3007	378	10	f	f	PROPN
ejpam-3007	378	11	′0	′0	PROPN
ejpam-3007	378	12	=	=	SYM
ejpam-3007	378	13	f0	f0	PROPN
ejpam-3007	378	14	a2	a2	PROPN
ejpam-3007	378	15	.	.	PUNCT
ejpam-3007	379	1	a.	a.	NOUN
ejpam-3007	379	2	durmagambetov	durmagambetov	PROPN
ejpam-3007	379	3	/	/	SYM
ejpam-3007	379	4	eur	eur	PROPN
ejpam-3007	379	5	.	.	PUNCT
ejpam-3007	380	1	j.	j.	PROPN
ejpam-3007	380	2	pure	pure	PROPN
ejpam-3007	380	3	appl	appl	PROPN
ejpam-3007	380	4	.	.	PROPN
ejpam-3007	380	5	math	math	PROPN
ejpam-3007	380	6	,	,	PUNCT
ejpam-3007	380	7	10	10	NUM
ejpam-3007	380	8	(	(	PUNCT
ejpam-3007	380	9	4	4	NUM
ejpam-3007	380	10	)	)	PUNCT
ejpam-3007	380	11	(	(	PUNCT
ejpam-3007	380	12	2017	2017	NUM
ejpam-3007	380	13	)	)	PUNCT
ejpam-3007	380	14	,	,	PUNCT
ejpam-3007	380	15	763	763	NUM
ejpam-3007	380	16	-	-	SYM
ejpam-3007	380	17	785	785	NUM
ejpam-3007	380	18	779	779	NUM
ejpam-3007	380	19	lemma	lemma	PROPN
ejpam-3007	380	20	28	28	NUM
ejpam-3007	380	21	.	.	PUNCT
ejpam-3007	381	1	let	let	VERB
ejpam-3007	381	2	a	a	DET
ejpam-3007	381	3	=	=	SYM
ejpam-3007	381	4	4	4	NUM
ejpam-3007	381	5	ν	ν	NOUN
ejpam-3007	381	6	1	1	NUM
ejpam-3007	381	7	3	3	NUM
ejpam-3007	381	8	(	(	PUNCT
ejpam-3007	381	9	cc0	cc0	NOUN
ejpam-3007	381	10	+	+	CCONJ
ejpam-3007	381	11	1	1	NUM
ejpam-3007	381	12	)	)	PUNCT
ejpam-3007	381	13	2	2	NUM
ejpam-3007	381	14	3	3	NUM
ejpam-3007	381	15	,	,	PUNCT
ejpam-3007	381	16	then	then	ADV
ejpam-3007	381	17	k	k	PROPN
ejpam-3007	381	18	≤	≤	PROPN
ejpam-3007	381	19	8	8	NUM
ejpam-3007	381	20	7	7	NUM
ejpam-3007	381	21	.	.	PUNCT
ejpam-3007	382	1	proof	proof	NOUN
ejpam-3007	382	2	.	.	PUNCT
ejpam-3007	383	1	by	by	ADP
ejpam-3007	383	2	the	the	DET
ejpam-3007	383	3	definitions	definition	NOUN
ejpam-3007	383	4	c	c	NOUN
ejpam-3007	383	5	and	and	CCONJ
ejpam-3007	383	6	c0	c0	PROPN
ejpam-3007	383	7	,	,	PUNCT
ejpam-3007	383	8	we	we	PRON
ejpam-3007	383	9	have	have	VERB
ejpam-3007	383	10	k	k	NOUN
ejpam-3007	383	11	=	=	PRON
ejpam-3007	383	12	(	(	PUNCT
ejpam-3007	383	13	ν	ν	NOUN
ejpam-3007	383	14	a	a	X
ejpam-3007	383	15	)	)	PUNCT
ejpam-3007	383	16	1	1	NUM
ejpam-3007	383	17	2	2	NUM
ejpam-3007	383	18	(	(	PUNCT
ejpam-3007	383	19	(	(	PUNCT
ejpam-3007	383	20	ν	ν	X
ejpam-3007	383	21	a	a	X
ejpam-3007	383	22	)	)	PUNCT
ejpam-3007	383	23	1	1	NUM
ejpam-3007	383	24	2	2	NUM
ejpam-3007	383	25	−4πcc0	−4πcc0	NOUN
ejpam-3007	383	26	a2	a2	PROPN
ejpam-3007	383	27	)	)	PUNCT
ejpam-3007	383	28	−1	−1	NOUN
ejpam-3007	383	29	=	=	PUNCT
ejpam-3007	384	1	ν	ν	NOUN
ejpam-3007	384	2	1	1	NUM
ejpam-3007	384	3	2	2	NUM
ejpam-3007	384	4	(	(	PUNCT
ejpam-3007	384	5	ν	ν	PROPN
ejpam-3007	384	6	1	1	NUM
ejpam-3007	384	7	2	2	NUM
ejpam-3007	384	8	−	−	NOUN
ejpam-3007	384	9	4πcc0	4πcc0	NOUN
ejpam-3007	384	10	a	a	DET
ejpam-3007	384	11	3	3	NUM
ejpam-3007	384	12	2	2	NUM
ejpam-3007	384	13	)	)	PUNCT
ejpam-3007	384	14	−1	−1	NOUN
ejpam-3007	384	15	<	<	X
ejpam-3007	384	16	8	8	NUM
ejpam-3007	384	17	7	7	NUM
ejpam-3007	384	18	.	.	PUNCT
ejpam-3007	385	1	this	this	PRON
ejpam-3007	385	2	proves	prove	VERB
ejpam-3007	385	3	lemma	lemma	PROPN
ejpam-3007	385	4	let	let	VERB
ejpam-3007	385	5	us	we	PRON
ejpam-3007	385	6	introduce	introduce	VERB
ejpam-3007	385	7	operator	operator	NOUN
ejpam-3007	385	8	fkk′	fkk′	VERB
ejpam-3007	385	9	,	,	PUNCT
ejpam-3007	385	10	as	as	ADP
ejpam-3007	385	11	fkk′f	fkk′f	ADV
ejpam-3007	385	12	=	=	SYM
ejpam-3007	385	13	∫	∫	PROPN
ejpam-3007	385	14	r3	r3	PROPN
ejpam-3007	385	15	e	e	PROPN
ejpam-3007	385	16	i(k	i(k	PROPN
ejpam-3007	385	17	,	,	PUNCT
ejpam-3007	385	18	x)−i(x	x)−i(x	PROPN
ejpam-3007	385	19	,	,	PUNCT
ejpam-3007	385	20	k′)f(x)dx	k′)f(x)dx	VERB
ejpam-3007	385	21	lemma	lemma	PROPN
ejpam-3007	385	22	29	29	NUM
ejpam-3007	385	23	.	.	PUNCT
ejpam-3007	386	1	let	let	VERB
ejpam-3007	386	2	q	q	PROPN
ejpam-3007	386	3	∈	∈	VERB
ejpam-3007	386	4	w	w	NOUN
ejpam-3007	386	5	1	1	NUM
ejpam-3007	386	6	2	2	NUM
ejpam-3007	386	7	(	(	PUNCT
ejpam-3007	386	8	r3	r3	PROPN
ejpam-3007	386	9	)	)	PUNCT
ejpam-3007	386	10	,	,	PUNCT
ejpam-3007	386	11	q	q	PROPN
ejpam-3007	386	12	∈	∈	PROPN
ejpam-3007	386	13	l2(qt	l2(qt	PROPN
ejpam-3007	386	14	)	)	PUNCT
ejpam-3007	386	15	,	,	PUNCT
ejpam-3007	386	16	νk(k	νk(k	X
ejpam-3007	386	17	,	,	PUNCT
ejpam-3007	386	18	k	k	PROPN
ejpam-3007	386	19	′	′	NOUN
ejpam-3007	386	20	)	)	PUNCT
ejpam-3007	386	21	=	=	PUNCT
ejpam-3007	386	22	ν|k	ν|k	PROPN
ejpam-3007	387	1	−	−	PROPN
ejpam-3007	387	2	k′|2.then	k′|2.then	ADV
ejpam-3007	387	3	,	,	PUNCT
ejpam-3007	387	4	the	the	DET
ejpam-3007	387	5	solution	solution	NOUN
ejpam-3007	387	6	of	of	ADP
ejpam-3007	387	7	(	(	PUNCT
ejpam-3007	387	8	57	57	NUM
ejpam-3007	387	9	)	)	PUNCT
ejpam-3007	387	10	,	,	PUNCT
ejpam-3007	387	11	(	(	PUNCT
ejpam-3007	387	12	58	58	NUM
ejpam-3007	387	13	)	)	PUNCT
ejpam-3007	387	14	,	,	PUNCT
ejpam-3007	387	15	(	(	PUNCT
ejpam-3007	387	16	59	59	NUM
ejpam-3007	387	17	)	)	PUNCT
ejpam-3007	387	18	in	in	ADP
ejpam-3007	387	19	theorem	theorem	ADJ
ejpam-3007	387	20	20	20	NUM
ejpam-3007	387	21	satisfies	satisfie	NOUN
ejpam-3007	387	22	the	the	DET
ejpam-3007	387	23	following	follow	VERB
ejpam-3007	387	24	inequalities	inequality	NOUN
ejpam-3007	387	25	:	:	PUNCT
ejpam-3007	387	26	sup	sup	NUM
ejpam-3007	387	27	(	(	PUNCT
ejpam-3007	387	28	ek	ek	NOUN
ejpam-3007	387	29	,	,	PUNCT
ejpam-3007	387	30	ek′	ek′	ADJ
ejpam-3007	387	31	)	)	PUNCT
ejpam-3007	387	32	∈s2	∈s2	PROPN
ejpam-3007	387	33	|q(k	|q(k	PROPN
ejpam-3007	387	34	,	,	PUNCT
ejpam-3007	387	35	k′)|	k′)|	X
ejpam-3007	387	36	<	<	X
ejpam-3007	387	37	c	c	X
ejpam-3007	387	38	,	,	PUNCT
ejpam-3007	387	39	sup	sup	NOUN
ejpam-3007	387	40	(	(	PUNCT
ejpam-3007	387	41	ek	ek	ADJ
ejpam-3007	387	42	,	,	PUNCT
ejpam-3007	387	43	ek′	ek′	ADJ
ejpam-3007	387	44	)	)	PUNCT
ejpam-3007	387	45	∈s2	∈s2	PROPN
ejpam-3007	387	46	k|q(k	k|q(k	PROPN
ejpam-3007	387	47	,	,	PUNCT
ejpam-3007	387	48	k′)|	k′)|	X
ejpam-3007	387	49	<	<	X
ejpam-3007	387	50	c√	c√	PROPN
ejpam-3007	387	51	(	(	PUNCT
ejpam-3007	387	52	1−	1−	NUM
ejpam-3007	387	53	cos(θ	cos(θ	NOUN
ejpam-3007	387	54	)	)	PUNCT
ejpam-3007	387	55	)	)	PUNCT
ejpam-3007	387	56	,	,	PUNCT
ejpam-3007	387	57	sup	sup	NOUN
ejpam-3007	387	58	(	(	PUNCT
ejpam-3007	387	59	ek	ek	ADJ
ejpam-3007	387	60	,	,	PUNCT
ejpam-3007	387	61	ek′	ek′	ADJ
ejpam-3007	387	62	)	)	PUNCT
ejpam-3007	387	63	∈s2	∈s2	PROPN
ejpam-3007	387	64	|a(k	|a(k	PROPN
ejpam-3007	387	65	,	,	PUNCT
ejpam-3007	387	66	k′)|	k′)|	X
ejpam-3007	387	67	<	<	X
ejpam-3007	387	68	c	c	X
ejpam-3007	387	69	,	,	PUNCT
ejpam-3007	387	70	sup	sup	NOUN
ejpam-3007	387	71	(	(	PUNCT
ejpam-3007	387	72	ek	ek	ADJ
ejpam-3007	387	73	,	,	PUNCT
ejpam-3007	387	74	ek′	ek′	ADJ
ejpam-3007	387	75	)	)	PUNCT
ejpam-3007	387	76	∈s2	∈s2	PROPN
ejpam-3007	387	77	k|a(k	k|a(k	PROPN
ejpam-3007	387	78	,	,	PUNCT
ejpam-3007	387	79	k′)|	k′)|	X
ejpam-3007	387	80	<	<	X
ejpam-3007	387	81	c√	c√	PROPN
ejpam-3007	387	82	(	(	PUNCT
ejpam-3007	387	83	1−	1−	NUM
ejpam-3007	387	84	cos(θ	cos(θ	NOUN
ejpam-3007	387	85	)	)	PUNCT
ejpam-3007	387	86	)	)	PUNCT
ejpam-3007	387	87	,	,	PUNCT
ejpam-3007	387	88	(	(	PUNCT
ejpam-3007	387	89	73	73	NUM
ejpam-3007	387	90	)	)	PUNCT
ejpam-3007	387	91	proof	proof	NOUN
ejpam-3007	387	92	.	.	PUNCT
ejpam-3007	388	1	this	this	PRON
ejpam-3007	388	2	follows	follow	VERB
ejpam-3007	388	3	from	from	ADP
ejpam-3007	388	4	q̇	q̇	NOUN
ejpam-3007	388	5	=	=	PUNCT
ejpam-3007	388	6	−fkk′[(q,∇)q	−fkk′[(q,∇)q	PROPN
ejpam-3007	388	7	]	]	X
ejpam-3007	388	8	+	+	NUM
ejpam-3007	388	9	fkk′(ν∆q	fkk′(ν∆q	PROPN
ejpam-3007	388	10	+	+	CCONJ
ejpam-3007	388	11	∇p	∇p	ADV
ejpam-3007	388	12	)	)	PUNCT
ejpam-3007	389	1	+	+	CCONJ
ejpam-3007	389	2	fkk′f	fkk′f	ADV
ejpam-3007	389	3	(	(	PUNCT
ejpam-3007	389	4	74	74	NUM
ejpam-3007	389	5	)	)	PUNCT
ejpam-3007	389	6	after	after	ADP
ejpam-3007	389	7	the	the	DET
ejpam-3007	389	8	transformations	transformation	NOUN
ejpam-3007	389	9	we	we	PRON
ejpam-3007	389	10	obtain	obtain	VERB
ejpam-3007	389	11	q̇	q̇	NOUN
ejpam-3007	389	12	=	=	SYM
ejpam-3007	389	13	−fkk′[(q,∇)q	−fkk′[(q,∇)q	PROPN
ejpam-3007	389	14	]	]	X
ejpam-3007	389	15	+	+	CCONJ
ejpam-3007	389	16	(	(	PUNCT
ejpam-3007	389	17	νkfkk′q	νkfkk′q	PROPN
ejpam-3007	389	18	+	+	X
ejpam-3007	389	19	fkk′∇p	fkk′∇p	PROPN
ejpam-3007	389	20	)	)	PUNCT
ejpam-3007	390	1	+	+	NUM
ejpam-3007	390	2	fkk′f	fkk′f	ADV
ejpam-3007	390	3	,	,	PUNCT
ejpam-3007	390	4	(	(	PUNCT
ejpam-3007	390	5	75	75	NUM
ejpam-3007	390	6	)	)	PUNCT
ejpam-3007	390	7	q	q	NOUN
ejpam-3007	391	1	=	=	PUNCT
ejpam-3007	391	2	q0	q0	PROPN
ejpam-3007	391	3	+	+	CCONJ
ejpam-3007	391	4	∫	∫	PROPN
ejpam-3007	391	5	t	t	PROPN
ejpam-3007	391	6	0	0	NUM
ejpam-3007	392	1	e−|k|	e−|k|	PROPN
ejpam-3007	392	2	2(1−cos(θ))(t−τ	2(1−cos(θ))(t−τ	NUM
ejpam-3007	392	3	)	)	PUNCT
ejpam-3007	392	4	(	(	PUNCT
ejpam-3007	392	5	−fkk′[(q,∇)q	−fkk′[(q,∇)q	PROPN
ejpam-3007	392	6	]	]	PUNCT
ejpam-3007	392	7	+	+	NUM
ejpam-3007	392	8	fkk′∇p+	fkk′∇p+	NOUN
ejpam-3007	392	9	fkk′f	fkk′f	ADV
ejpam-3007	392	10	)	)	PUNCT
ejpam-3007	392	11	.	.	PUNCT
ejpam-3007	393	1	from	from	ADP
ejpam-3007	393	2	last	last	ADJ
ejpam-3007	393	3	equation	equation	NOUN
ejpam-3007	393	4	we	we	PRON
ejpam-3007	393	5	have	have	AUX
ejpam-3007	393	6	|q|	|q|	VERB
ejpam-3007	393	7	≤	≤	NUM
ejpam-3007	393	8	|q0|+	|q0|+	NUM
ejpam-3007	393	9	ct	ct	NOUN
ejpam-3007	393	10	integrating	integrating	NOUN
ejpam-3007	393	11	by	by	ADP
ejpam-3007	393	12	θ	θ	PROPN
ejpam-3007	393	13	and	and	CCONJ
ejpam-3007	393	14	carrying	carry	VERB
ejpam-3007	393	15	out	out	ADP
ejpam-3007	393	16	the	the	DET
ejpam-3007	393	17	coordinate	coordinate	NOUN
ejpam-3007	393	18	transformations	transformation	NOUN
ejpam-3007	393	19	,	,	PUNCT
ejpam-3007	393	20	we	we	PRON
ejpam-3007	393	21	obtain	obtain	VERB
ejpam-3007	393	22	q	q	NOUN
ejpam-3007	393	23	=	=	PUNCT
ejpam-3007	393	24	q0	q0	PROPN
ejpam-3007	394	1	+	+	CCONJ
ejpam-3007	395	1	∫	∫	PROPN
ejpam-3007	395	2	t	t	PROPN
ejpam-3007	395	3	0	0	NUM
ejpam-3007	395	4	e−|k|	e−|k|	PROPN
ejpam-3007	395	5	2(1−cos(θ))(t−τ	2(1−cos(θ))(t−τ	NUM
ejpam-3007	395	6	)	)	PUNCT
ejpam-3007	395	7	(	(	PUNCT
ejpam-3007	395	8	−fkk′[(q,∇)q	−fkk′[(q,∇)q	PROPN
ejpam-3007	395	9	]	]	PUNCT
ejpam-3007	395	10	+	+	NUM
ejpam-3007	395	11	fkk′∇p+	fkk′∇p+	NOUN
ejpam-3007	395	12	fkk′f	fkk′f	ADV
ejpam-3007	395	13	)	)	PUNCT
ejpam-3007	395	14	.	.	PUNCT
ejpam-3007	396	1	|q|	|q|	VERB
ejpam-3007	396	2	≤	≤	NUM
ejpam-3007	396	3	|q0|+	|q0|+	PUNCT
ejpam-3007	396	4	c	c	NOUN
ejpam-3007	396	5	k	k	NOUN
ejpam-3007	396	6	√	√	PROPN
ejpam-3007	396	7	(	(	PUNCT
ejpam-3007	396	8	1−	1−	NUM
ejpam-3007	396	9	cos(θ	cos(θ	X
ejpam-3007	396	10	)	)	PUNCT
ejpam-3007	396	11	)	)	PUNCT
ejpam-3007	396	12	a.	a.	NOUN
ejpam-3007	396	13	durmagambetov	durmagambetov	PROPN
ejpam-3007	396	14	/	/	SYM
ejpam-3007	396	15	eur	eur	PROPN
ejpam-3007	396	16	.	.	PUNCT
ejpam-3007	397	1	j.	j.	PROPN
ejpam-3007	397	2	pure	pure	PROPN
ejpam-3007	397	3	appl	appl	PROPN
ejpam-3007	397	4	.	.	PROPN
ejpam-3007	397	5	math	math	PROPN
ejpam-3007	397	6	,	,	PUNCT
ejpam-3007	397	7	10	10	NUM
ejpam-3007	397	8	(	(	PUNCT
ejpam-3007	397	9	4	4	NUM
ejpam-3007	397	10	)	)	PUNCT
ejpam-3007	397	11	(	(	PUNCT
ejpam-3007	397	12	2017	2017	NUM
ejpam-3007	397	13	)	)	PUNCT
ejpam-3007	397	14	,	,	PUNCT
ejpam-3007	397	15	763	763	NUM
ejpam-3007	397	16	-	-	SYM
ejpam-3007	397	17	785	785	NUM
ejpam-3007	397	18	780	780	NUM
ejpam-3007	397	19	lemma	lemma	PROPN
ejpam-3007	397	20	30	30	NUM
ejpam-3007	397	21	.	.	PUNCT
ejpam-3007	398	1	let	let	VERB
ejpam-3007	398	2	q	q	PROPN
ejpam-3007	398	3	∈	∈	VERB
ejpam-3007	398	4	w	w	NOUN
ejpam-3007	398	5	1	1	NUM
ejpam-3007	398	6	2	2	NUM
ejpam-3007	398	7	(	(	PUNCT
ejpam-3007	398	8	r3	r3	PROPN
ejpam-3007	398	9	)	)	PUNCT
ejpam-3007	398	10	,	,	PUNCT
ejpam-3007	398	11	q	q	PROPN
ejpam-3007	398	12	∈	∈	PROPN
ejpam-3007	398	13	l2(qt	l2(qt	PROPN
ejpam-3007	398	14	)	)	PUNCT
ejpam-3007	398	15	,	,	PUNCT
ejpam-3007	398	16	νk(k	νk(k	X
ejpam-3007	398	17	,	,	PUNCT
ejpam-3007	398	18	k	k	PROPN
ejpam-3007	398	19	′	′	NOUN
ejpam-3007	398	20	)	)	PUNCT
ejpam-3007	398	21	=	=	PUNCT
ejpam-3007	398	22	ν|k	ν|k	PROPN
ejpam-3007	399	1	−	−	PROPN
ejpam-3007	399	2	k′|2.then	k′|2.then	ADV
ejpam-3007	399	3	,	,	PUNCT
ejpam-3007	399	4	the	the	DET
ejpam-3007	399	5	solution	solution	NOUN
ejpam-3007	399	6	of	of	ADP
ejpam-3007	399	7	(	(	PUNCT
ejpam-3007	399	8	57	57	NUM
ejpam-3007	399	9	)	)	PUNCT
ejpam-3007	399	10	,	,	PUNCT
ejpam-3007	399	11	(	(	PUNCT
ejpam-3007	399	12	58	58	NUM
ejpam-3007	399	13	)	)	PUNCT
ejpam-3007	399	14	,	,	PUNCT
ejpam-3007	399	15	(	(	PUNCT
ejpam-3007	399	16	59	59	NUM
ejpam-3007	399	17	)	)	PUNCT
ejpam-3007	399	18	in	in	ADP
ejpam-3007	399	19	theorem	theorem	ADJ
ejpam-3007	399	20	20	20	NUM
ejpam-3007	399	21	satisfies	satisfie	NOUN
ejpam-3007	399	22	the	the	DET
ejpam-3007	399	23	following	follow	VERB
ejpam-3007	399	24	inequalities	inequality	NOUN
ejpam-3007	399	25	:	:	PUNCT
ejpam-3007	399	26	sup	sup	NUM
ejpam-3007	399	27	(	(	PUNCT
ejpam-3007	399	28	ek	ek	NOUN
ejpam-3007	399	29	,	,	PUNCT
ejpam-3007	399	30	ek′	ek′	ADJ
ejpam-3007	399	31	)	)	PUNCT
ejpam-3007	399	32	∈s2	∈s2	PROPN
ejpam-3007	399	33	∣∣tq(k	∣∣tq(k	PROPN
ejpam-3007	399	34	,	,	PUNCT
ejpam-3007	399	35	k′	k′	NUM
ejpam-3007	399	36	)	)	PUNCT
ejpam-3007	399	37	∣∣	∣∣	X
ejpam-3007	399	38	<	<	X
ejpam-3007	399	39	c	c	X
ejpam-3007	399	40	,	,	PUNCT
ejpam-3007	399	41	sup	sup	NOUN
ejpam-3007	399	42	(	(	PUNCT
ejpam-3007	399	43	ek	ek	ADJ
ejpam-3007	399	44	,	,	PUNCT
ejpam-3007	399	45	ek′	ek′	ADJ
ejpam-3007	399	46	)	)	PUNCT
ejpam-3007	399	47	∈s2	∈s2	PROPN
ejpam-3007	399	48	∣∣λtq(k	∣∣λtq(k	PROPN
ejpam-3007	399	49	,	,	PUNCT
ejpam-3007	399	50	k′	k′	PROPN
ejpam-3007	399	51	)	)	PUNCT
ejpam-3007	399	52	∣∣	∣∣	X
ejpam-3007	400	1	<	<	X
ejpam-3007	400	2	c	c	X
ejpam-3007	400	3	,	,	PUNCT
ejpam-3007	400	4	sup	sup	NOUN
ejpam-3007	400	5	(	(	PUNCT
ejpam-3007	400	6	ek	ek	ADJ
ejpam-3007	400	7	,	,	PUNCT
ejpam-3007	400	8	ek′	ek′	ADJ
ejpam-3007	400	9	)	)	PUNCT
ejpam-3007	400	10	∈s2	∈s2	PROPN
ejpam-3007	400	11	|ta(k	|ta(k	PROPN
ejpam-3007	400	12	,	,	PUNCT
ejpam-3007	400	13	k′)|	k′)|	X
ejpam-3007	400	14	<	<	X
ejpam-3007	400	15	c	c	X
ejpam-3007	400	16	,	,	PUNCT
ejpam-3007	400	17	sup	sup	NOUN
ejpam-3007	400	18	(	(	PUNCT
ejpam-3007	400	19	ek	ek	ADJ
ejpam-3007	400	20	,	,	PUNCT
ejpam-3007	400	21	ek′	ek′	ADJ
ejpam-3007	400	22	)	)	PUNCT
ejpam-3007	400	23	∈s2	∈s2	PROPN
ejpam-3007	400	24	∣∣λta(k	∣∣λta(k	PROPN
ejpam-3007	400	25	,	,	PUNCT
ejpam-3007	400	26	k′	k′	NUM
ejpam-3007	400	27	)	)	PUNCT
ejpam-3007	400	28	∣∣	∣∣	X
ejpam-3007	400	29	<	<	X
ejpam-3007	400	30	c	c	X
ejpam-3007	400	31	,	,	PUNCT
ejpam-3007	400	32	(	(	PUNCT
ejpam-3007	400	33	76	76	NUM
ejpam-3007	400	34	)	)	PUNCT
ejpam-3007	400	35	proof	proof	NOUN
ejpam-3007	400	36	.	.	PUNCT
ejpam-3007	401	1	this	this	PRON
ejpam-3007	401	2	follows	follow	VERB
ejpam-3007	401	3	from	from	ADP
ejpam-3007	401	4	tq	tq	ADP
ejpam-3007	401	5	=	=	NOUN
ejpam-3007	401	6	tq0	tq0	NOUN
ejpam-3007	402	1	+	+	X
ejpam-3007	402	2	t	t	PROPN
ejpam-3007	402	3	∫	∫	PROPN
ejpam-3007	402	4	t	t	PROPN
ejpam-3007	402	5	0	0	NUM
ejpam-3007	402	6	e−|k|	e−|k|	PROPN
ejpam-3007	402	7	2(1−cos(θ))(t−τ	2(1−cos(θ))(t−τ	NUM
ejpam-3007	402	8	)	)	PUNCT
ejpam-3007	402	9	(	(	PUNCT
ejpam-3007	402	10	−fkk′[(q,∇)q	−fkk′[(q,∇)q	PROPN
ejpam-3007	402	11	]	]	PUNCT
ejpam-3007	402	12	+	+	NUM
ejpam-3007	402	13	fkk′∇p+	fkk′∇p+	NOUN
ejpam-3007	402	14	fkk′f	fkk′f	ADV
ejpam-3007	402	15	)	)	PUNCT
ejpam-3007	402	16	.	.	PUNCT
ejpam-3007	403	1	from	from	ADP
ejpam-3007	403	2	last	last	ADJ
ejpam-3007	403	3	equation	equation	NOUN
ejpam-3007	403	4	we	we	PRON
ejpam-3007	403	5	have	have	AUX
ejpam-3007	403	6	|tq|	|tq|	ADJ
ejpam-3007	403	7	≤	≤	NUM
ejpam-3007	403	8	|tq0|+	|tq0|+	NOUN
ejpam-3007	403	9	ct	ct	NOUN
ejpam-3007	403	10	using	use	VERB
ejpam-3007	403	11	operator	operator	NOUN
ejpam-3007	403	12	λ	λ	NOUN
ejpam-3007	403	13	=	=	NOUN
ejpam-3007	403	14	3∑	3∑	NUM
ejpam-3007	403	15	i=1	i=1	PRON
ejpam-3007	403	16	∂2	∂2	NOUN
ejpam-3007	403	17	∂k2i	∂k2i	NUM
ejpam-3007	403	18	λtq	λtq	PROPN
ejpam-3007	403	19	=	=	SYM
ejpam-3007	403	20	λtq0	λtq0	PROPN
ejpam-3007	403	21	+	+	CCONJ
ejpam-3007	403	22	λt	λt	ADP
ejpam-3007	403	23	∫	∫	PROPN
ejpam-3007	403	24	t	t	PROPN
ejpam-3007	403	25	0	0	PUNCT
ejpam-3007	404	1	e−|k|	e−|k|	PROPN
ejpam-3007	404	2	2(1−cos(θ))(t−τ	2(1−cos(θ))(t−τ	NUM
ejpam-3007	404	3	)	)	PUNCT
ejpam-3007	404	4	(	(	PUNCT
ejpam-3007	404	5	−fkk′[(q,∇)q	−fkk′[(q,∇)q	PROPN
ejpam-3007	404	6	]	]	PUNCT
ejpam-3007	404	7	+	+	NUM
ejpam-3007	404	8	fkk′∇p+	fkk′∇p+	NOUN
ejpam-3007	404	9	fkk′f	fkk′f	ADV
ejpam-3007	404	10	)	)	PUNCT
ejpam-3007	404	11	.	.	PUNCT
ejpam-3007	405	1	|λtq|	|λtq|	VERB
ejpam-3007	405	2	=	=	PUNCT
ejpam-3007	405	3	|λtq0|+	|λtq0|+	PROPN
ejpam-3007	405	4	ct	ct	NOUN
ejpam-3007	405	5	lemma	lemma	PROPN
ejpam-3007	405	6	31	31	NUM
ejpam-3007	405	7	.	.	PUNCT
ejpam-3007	406	1	let	let	VERB
ejpam-3007	406	2	q	q	PROPN
ejpam-3007	406	3	∈	∈	VERB
ejpam-3007	406	4	w	w	NOUN
ejpam-3007	406	5	1	1	NUM
ejpam-3007	406	6	2	2	NUM
ejpam-3007	406	7	(	(	PUNCT
ejpam-3007	406	8	r3	r3	PROPN
ejpam-3007	406	9	)	)	PUNCT
ejpam-3007	406	10	,	,	PUNCT
ejpam-3007	406	11	q	q	PROPN
ejpam-3007	406	12	∈	∈	PROPN
ejpam-3007	406	13	l2(qt	l2(qt	PROPN
ejpam-3007	406	14	)	)	PUNCT
ejpam-3007	406	15	,	,	PUNCT
ejpam-3007	406	16	νk(k	νk(k	X
ejpam-3007	406	17	,	,	PUNCT
ejpam-3007	406	18	k	k	PROPN
ejpam-3007	406	19	′	′	NOUN
ejpam-3007	406	20	)	)	PUNCT
ejpam-3007	406	21	=	=	PUNCT
ejpam-3007	406	22	ν|k	ν|k	PROPN
ejpam-3007	406	23	−	−	PROPN
ejpam-3007	406	24	k′|2	k′|2	PROPN
ejpam-3007	406	25	,	,	PUNCT
ejpam-3007	406	26	x(x	x(x	PROPN
ejpam-3007	406	27	)	)	PUNCT
ejpam-3007	407	1	=	=	SYM
ejpam-3007	407	2	x.then	x.then	PROPN
ejpam-3007	407	3	,	,	PUNCT
ejpam-3007	407	4	the	the	DET
ejpam-3007	407	5	solution	solution	NOUN
ejpam-3007	407	6	of	of	ADP
ejpam-3007	407	7	(	(	PUNCT
ejpam-3007	407	8	57	57	NUM
ejpam-3007	407	9	)	)	PUNCT
ejpam-3007	407	10	,	,	PUNCT
ejpam-3007	407	11	(	(	PUNCT
ejpam-3007	407	12	58	58	NUM
ejpam-3007	407	13	)	)	PUNCT
ejpam-3007	407	14	,	,	PUNCT
ejpam-3007	407	15	(	(	PUNCT
ejpam-3007	407	16	59	59	NUM
ejpam-3007	407	17	)	)	PUNCT
ejpam-3007	407	18	in	in	ADP
ejpam-3007	407	19	theorem	theorem	ADJ
ejpam-3007	407	20	20	20	NUM
ejpam-3007	407	21	satisfies	satisfie	NOUN
ejpam-3007	407	22	the	the	DET
ejpam-3007	407	23	following	follow	VERB
ejpam-3007	407	24	inequalities	inequality	NOUN
ejpam-3007	407	25	:	:	PUNCT
ejpam-3007	407	26	sup	sup	NUM
ejpam-3007	407	27	(	(	PUNCT
ejpam-3007	407	28	ek	ek	NOUN
ejpam-3007	407	29	,	,	PUNCT
ejpam-3007	407	30	ek′	ek′	ADJ
ejpam-3007	407	31	)	)	PUNCT
ejpam-3007	407	32	∈s2	∈s2	PROPN
ejpam-3007	407	33	∫	∫	PROPN
ejpam-3007	407	34	∞	∞	PROPN
ejpam-3007	407	35	0	0	NUM
ejpam-3007	407	36	|sφx0q(k	|sφx0q(k	ADV
ejpam-3007	407	37	,	,	PUNCT
ejpam-3007	407	38	k′)|dk	k′)|dk	VERB
ejpam-3007	407	39	<	<	X
ejpam-3007	407	40	c	c	X
ejpam-3007	407	41	∫	∫	PROPN
ejpam-3007	407	42	t	t	PROPN
ejpam-3007	407	43	0	0	NUM
ejpam-3007	407	44	sup	sup	NOUN
ejpam-3007	407	45	x∈r3	x∈r3	NOUN
ejpam-3007	407	46	|q(x)|	|q(x)|	NOUN
ejpam-3007	407	47	∥∥(1	∥∥(1	NUM
ejpam-3007	407	48	+	+	PROPN
ejpam-3007	407	49	x2)∇q	x2)∇q	PROPN
ejpam-3007	407	50	∥∥	∥∥	PRON
ejpam-3007	407	51	l2(r3	l2(r3	PROPN
ejpam-3007	407	52	)	)	PUNCT
ejpam-3007	407	53	dτ	dτ	NOUN
ejpam-3007	407	54	,	,	PUNCT
ejpam-3007	407	55	sup	sup	PROPN
ejpam-3007	407	56	(	(	PUNCT
ejpam-3007	407	57	ek	ek	NOUN
ejpam-3007	407	58	,	,	PUNCT
ejpam-3007	407	59	ek′	ek′	ADJ
ejpam-3007	407	60	)	)	PUNCT
ejpam-3007	408	1	∈s2	∈s2	PROPN
ejpam-3007	408	2	∫	∫	PROPN
ejpam-3007	409	1	∞	∞	PROPN
ejpam-3007	409	2	0	0	X
ejpam-3007	410	1	|λsφx0q(k	|λsφx0q(k	PROPN
ejpam-3007	410	2	,	,	PUNCT
ejpam-3007	410	3	k′)|dk	k′)|dk	VERB
ejpam-3007	410	4	<	<	X
ejpam-3007	410	5	c	c	X
ejpam-3007	410	6	∫	∫	PROPN
ejpam-3007	410	7	t	t	PROPN
ejpam-3007	410	8	0	0	NUM
ejpam-3007	410	9	supx∈r3	supx∈r3	PROPN
ejpam-3007	410	10	|q(x)|	|q(x)|	NOUN
ejpam-3007	410	11	∥∥(1	∥∥(1	NUM
ejpam-3007	410	12	+	+	PROPN
ejpam-3007	410	13	x2)∇q	x2)∇q	PROPN
ejpam-3007	410	14	∥∥	∥∥	PRON
ejpam-3007	410	15	l2(r3	l2(r3	ADJ
ejpam-3007	410	16	)	)	PUNCT
ejpam-3007	410	17	dτ	dτ	NOUN
ejpam-3007	410	18	(	(	PUNCT
ejpam-3007	410	19	77	77	NUM
ejpam-3007	410	20	)	)	PUNCT
ejpam-3007	410	21	proof	proof	NOUN
ejpam-3007	410	22	.	.	PUNCT
ejpam-3007	411	1	this	this	PRON
ejpam-3007	411	2	follows	follow	VERB
ejpam-3007	411	3	from	from	ADP
ejpam-3007	411	4	from	from	ADP
ejpam-3007	411	5	last	last	ADJ
ejpam-3007	411	6	equation	equation	NOUN
ejpam-3007	411	7	we	we	PRON
ejpam-3007	411	8	have	have	AUX
ejpam-3007	411	9	|sφx0q|	|sφx0q|	VERB
ejpam-3007	411	10	≤	≤	NUM
ejpam-3007	412	1	|sφx0q0|+	|sφx0q0|+	NUM
ejpam-3007	412	2	sup	sup	NOUN
ejpam-3007	412	3	(	(	PUNCT
ejpam-3007	412	4	ek	ek	NOUN
ejpam-3007	412	5	,	,	PUNCT
ejpam-3007	412	6	ek′	ek′	ADJ
ejpam-3007	412	7	)	)	PUNCT
ejpam-3007	412	8	∈s2	∈s2	PROPN
ejpam-3007	412	9	∫	∫	PROPN
ejpam-3007	412	10	∞	∞	PROPN
ejpam-3007	412	11	0	0	NUM
ejpam-3007	412	12	|sφx0q(k	|sφx0q(k	ADV
ejpam-3007	412	13	,	,	PUNCT
ejpam-3007	412	14	k′)|dk	k′)|dk	VERB
ejpam-3007	412	15	<	<	X
ejpam-3007	412	16	c	c	X
ejpam-3007	412	17	∫	∫	PROPN
ejpam-3007	412	18	t	t	PROPN
ejpam-3007	412	19	0	0	NUM
ejpam-3007	412	20	sup	sup	NOUN
ejpam-3007	412	21	x∈r3	x∈r3	NOUN
ejpam-3007	412	22	|q(x)|	|q(x)|	NOUN
ejpam-3007	412	23	∥∥(1	∥∥(1	NUM
ejpam-3007	412	24	+	+	PROPN
ejpam-3007	412	25	x2)∇q	x2)∇q	PROPN
ejpam-3007	412	26	∥∥	∥∥	PRON
ejpam-3007	412	27	l2(r3	l2(r3	ADJ
ejpam-3007	412	28	)	)	PUNCT
ejpam-3007	412	29	dτ	dτ	NOUN
ejpam-3007	412	30	using	use	VERB
ejpam-3007	412	31	operator	operator	NOUN
ejpam-3007	412	32	λ	λ	NOUN
ejpam-3007	412	33	=	=	NOUN
ejpam-3007	412	34	3∑	3∑	NUM
ejpam-3007	412	35	i=1	i=1	PRON
ejpam-3007	412	36	∂2	∂2	NOUN
ejpam-3007	412	37	∂k2i	∂k2i	NUM
ejpam-3007	412	38	a.	a.	NOUN
ejpam-3007	412	39	durmagambetov	durmagambetov	PROPN
ejpam-3007	412	40	/	/	SYM
ejpam-3007	412	41	eur	eur	PROPN
ejpam-3007	412	42	.	.	PUNCT
ejpam-3007	413	1	j.	j.	PROPN
ejpam-3007	413	2	pure	pure	PROPN
ejpam-3007	413	3	appl	appl	PROPN
ejpam-3007	413	4	.	.	PROPN
ejpam-3007	413	5	math	math	PROPN
ejpam-3007	413	6	,	,	PUNCT
ejpam-3007	413	7	10	10	NUM
ejpam-3007	413	8	(	(	PUNCT
ejpam-3007	413	9	4	4	NUM
ejpam-3007	413	10	)	)	PUNCT
ejpam-3007	413	11	(	(	PUNCT
ejpam-3007	413	12	2017	2017	NUM
ejpam-3007	413	13	)	)	PUNCT
ejpam-3007	413	14	,	,	PUNCT
ejpam-3007	413	15	763	763	NUM
ejpam-3007	413	16	-	-	SYM
ejpam-3007	413	17	785	785	NUM
ejpam-3007	413	18	781	781	NUM
ejpam-3007	413	19	|λsφx0q|	|λsφx0q|	PROPN
ejpam-3007	413	20	≤	≤	NUM
ejpam-3007	413	21	|sφx0q0|+	|sφx0q0|+	NUM
ejpam-3007	413	22	sup	sup	NOUN
ejpam-3007	413	23	(	(	PUNCT
ejpam-3007	413	24	ek	ek	NOUN
ejpam-3007	413	25	,	,	PUNCT
ejpam-3007	413	26	ek′	ek′	ADJ
ejpam-3007	413	27	)	)	PUNCT
ejpam-3007	414	1	∈s2	∈s2	PROPN
ejpam-3007	414	2	∣∣∣∣λsφx0	∣∣∣∣λsφx0	PROPN
ejpam-3007	414	3	∫	∫	PROPN
ejpam-3007	414	4	t	t	PROPN
ejpam-3007	414	5	0	0	PUNCT
ejpam-3007	414	6	e−|k|	e−|k|	PROPN
ejpam-3007	414	7	2(1−cos(θ))(t−τ	2(1−cos(θ))(t−τ	NUM
ejpam-3007	414	8	)	)	PUNCT
ejpam-3007	414	9	(	(	PUNCT
ejpam-3007	414	10	−fkk′[(q,∇)q	−fkk′[(q,∇)q	PROPN
ejpam-3007	414	11	]	]	PUNCT
ejpam-3007	414	12	+	+	NUM
ejpam-3007	414	13	fkk′∇p+	fkk′∇p+	NOUN
ejpam-3007	414	14	fkk′f	fkk′f	ADV
ejpam-3007	414	15	)	)	PUNCT
ejpam-3007	414	16	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3007	414	17	<	<	X
ejpam-3007	414	18	c	c	X
ejpam-3007	414	19	∫	∫	PROPN
ejpam-3007	414	20	t	t	NOUN
ejpam-3007	414	21	0	0	NUM
ejpam-3007	414	22	sup	sup	NOUN
ejpam-3007	414	23	x∈r3	x∈r3	NOUN
ejpam-3007	414	24	|q(x)|	|q(x)|	NOUN
ejpam-3007	414	25	∥∥(1	∥∥(1	NUM
ejpam-3007	414	26	+	+	PROPN
ejpam-3007	414	27	x2)∇q	x2)∇q	PROPN
ejpam-3007	414	28	∥∥	∥∥	PRON
ejpam-3007	414	29	l2(r3	l2(r3	ADJ
ejpam-3007	414	30	)	)	PUNCT
ejpam-3007	414	31	dτ	dτ	NOUN
ejpam-3007	414	32	lemma	lemma	PROPN
ejpam-3007	414	33	32	32	NUM
ejpam-3007	414	34	.	.	PUNCT
ejpam-3007	415	1	let	let	VERB
ejpam-3007	415	2	q	q	PROPN
ejpam-3007	415	3	∈	∈	PROPN
ejpam-3007	415	4	r	r	NOUN
ejpam-3007	415	5	∩	∩	NOUN
ejpam-3007	415	6	l2(r3	l2(r3	NOUN
ejpam-3007	415	7	)	)	PUNCT
ejpam-3007	415	8	,	,	PUNCT
ejpam-3007	415	9	and	and	CCONJ
ejpam-3007	415	10	csupek	csupek	PROPN
ejpam-3007	415	11	,	,	PUNCT
ejpam-3007	415	12	ek′	ek′	ADJ
ejpam-3007	415	13	,	,	PUNCT
ejpam-3007	415	14	k|tq(k	k|tq(k	ADJ
ejpam-3007	415	15	,	,	PUNCT
ejpam-3007	415	16	k′)|+	k′)|+	PROPN
ejpam-3007	415	17	csupek	csupek	PROPN
ejpam-3007	415	18	,	,	PUNCT
ejpam-3007	415	19	ek′	ek′	INTJ
ejpam-3007	415	20	,	,	PUNCT
ejpam-3007	415	21	k|q(k	k|q(k	PROPN
ejpam-3007	415	22	,	,	PUNCT
ejpam-3007	415	23	k′)|	k′)|	X
ejpam-3007	415	24	<	<	X
ejpam-3007	415	25	1	1	X
ejpam-3007	415	26	.	.	PUNCT
ejpam-3007	416	1	then	then	ADV
ejpam-3007	416	2	,	,	PUNCT
ejpam-3007	416	3	|λψ±q|	|λψ±q|	NUM
ejpam-3007	416	4	|x	|x	NOUN
ejpam-3007	416	5	=	=	SYM
ejpam-3007	416	6	x0	x0	PROPN
ejpam-3007	416	7	,	,	PUNCT
ejpam-3007	416	8	k=0	k=0	PROPN
ejpam-3007	416	9	≥	≥	NUM
ejpam-3007	416	10	x2	x2	NOUN
ejpam-3007	417	1	−	−	PROPN
ejpam-3007	417	2	c.	c.	NOUN
ejpam-3007	417	3	(	(	PUNCT
ejpam-3007	417	4	78	78	NUM
ejpam-3007	417	5	)	)	PUNCT
ejpam-3007	417	6	proof	proof	NOUN
ejpam-3007	417	7	.	.	PUNCT
ejpam-3007	417	8	|λψ−|k=0	|λψ−|k=0	X
ejpam-3007	418	1	=	=	PRON
ejpam-3007	418	2	|t−λg−	|t−λg−	NOUN
ejpam-3007	418	3	+	+	CCONJ
ejpam-3007	418	4	λφ0|k=0	λφ0|k=0	X
ejpam-3007	418	5	≥	≥	NOUN
ejpam-3007	418	6	x	x	SYM
ejpam-3007	418	7	2	2	NUM
ejpam-3007	418	8	−	−	NOUN
ejpam-3007	418	9	∣∣(i	∣∣(i	NOUN
ejpam-3007	418	10	−	−	PROPN
ejpam-3007	418	11	t−d)−1	t−d)−1	NOUN
ejpam-3007	418	12	(	(	PUNCT
ejpam-3007	418	13	t−(∇d,∇tg	t−(∇d,∇tg	NOUN
ejpam-3007	418	14	)	)	PUNCT
ejpam-3007	418	15	+	+	CCONJ
ejpam-3007	419	1	tλdφ0	tλdφ0	ADJ
ejpam-3007	419	2	)	)	PUNCT
ejpam-3007	419	3	∣∣	∣∣	PROPN
ejpam-3007	420	1	k=0	k=0	PROPN
ejpam-3007	420	2	≥	≥	NUM
ejpam-3007	421	1	x2	x2	NUM
ejpam-3007	421	2	−	−	PROPN
ejpam-3007	421	3	∣∣(i	∣∣(i	NOUN
ejpam-3007	421	4	−	−	PROPN
ejpam-3007	421	5	t−d)−1	t−d)−1	NOUN
ejpam-3007	421	6	(	(	PUNCT
ejpam-3007	421	7	t−(∇d,∇t	t−(∇d,∇t	PROPN
ejpam-3007	421	8	(	(	PUNCT
ejpam-3007	421	9	(	(	PUNCT
ejpam-3007	421	10	i	i	PRON
ejpam-3007	421	11	−	−	PROPN
ejpam-3007	421	12	t−d)−1t−dφ0))−	t−d)−1t−dφ0))−	ADJ
ejpam-3007	421	13	tλdφ0	tλdφ0	PROPN
ejpam-3007	421	14	)	)	PUNCT
ejpam-3007	422	1	∣∣	∣∣	X
ejpam-3007	422	2	k=0	k=0	PROPN
ejpam-3007	422	3	≥	≥	X
ejpam-3007	423	1	x2	x2	INTJ
ejpam-3007	423	2	−	−	PROPN
ejpam-3007	424	1	c	c	NOUN
ejpam-3007	424	2	(	(	PUNCT
ejpam-3007	424	3	79	79	NUM
ejpam-3007	424	4	)	)	PUNCT
ejpam-3007	424	5	lemma	lemma	PROPN
ejpam-3007	424	6	33	33	NUM
ejpam-3007	424	7	.	.	PUNCT
ejpam-3007	425	1	the	the	DET
ejpam-3007	425	2	following	follow	VERB
ejpam-3007	425	3	permutation	permutation	NOUN
ejpam-3007	425	4	formulas	formula	NOUN
ejpam-3007	425	5	hold	hold	VERB
ejpam-3007	425	6	true	true	ADJ
ejpam-3007	425	7	xn∏	xn∏	PROPN
ejpam-3007	425	8	0	0	PUNCT
ejpam-3007	425	9	<	<	X
ejpam-3007	425	10	i	i	X
ejpam-3007	425	11	<	<	X
ejpam-3007	425	12	n(xi+1	n(xi+1	PROPN
ejpam-3007	425	13	−	−	PROPN
ejpam-3007	425	14	xi)(xn	xi)(xn	PUNCT
ejpam-3007	426	1	−	−	PROPN
ejpam-3007	426	2	xn−1	xn−1	PROPN
ejpam-3007	426	3	)	)	PUNCT
ejpam-3007	426	4	=	=	PUNCT
ejpam-3007	427	1	1∏	1∏	NUM
ejpam-3007	427	2	0	0	PUNCT
ejpam-3007	427	3	<	<	X
ejpam-3007	427	4	i	i	X
ejpam-3007	427	5	<	<	X
ejpam-3007	427	6	n(xi+1	n(xi+1	NOUN
ejpam-3007	427	7	−	−	PROPN
ejpam-3007	427	8	xi	xi	PROPN
ejpam-3007	427	9	)	)	PUNCT
ejpam-3007	428	1	+	+	CCONJ
ejpam-3007	428	2	xn−1∏	xn−1∏	PROPN
ejpam-3007	428	3	0	0	PUNCT
ejpam-3007	428	4	<	<	X
ejpam-3007	428	5	i	i	X
ejpam-3007	428	6	<	<	X
ejpam-3007	428	7	n(xi+1	n(xi+1	PROPN
ejpam-3007	428	8	−	−	PROPN
ejpam-3007	428	9	xi)(xn	xi)(xn	PUNCT
ejpam-3007	428	10	−	−	PROPN
ejpam-3007	428	11	xn−1	xn−1	PROPN
ejpam-3007	428	12	)	)	PUNCT
ejpam-3007	428	13	xn−1∏	xn−1∏	NOUN
ejpam-3007	429	1	0	0	PUNCT
ejpam-3007	429	2	<	<	X
ejpam-3007	429	3	i	i	X
ejpam-3007	429	4	<	<	X
ejpam-3007	429	5	n(xi+1	n(xi+1	PROPN
ejpam-3007	429	6	−	−	PROPN
ejpam-3007	429	7	xi)(xn	xi)(xn	PUNCT
ejpam-3007	429	8	−	−	PROPN
ejpam-3007	429	9	xn−1	xn−1	PROPN
ejpam-3007	429	10	)	)	PUNCT
ejpam-3007	429	11	=	=	PUNCT
ejpam-3007	430	1	1∏	1∏	NUM
ejpam-3007	430	2	0	0	PUNCT
ejpam-3007	430	3	<	<	X
ejpam-3007	430	4	i	i	X
ejpam-3007	430	5	<	<	X
ejpam-3007	430	6	n	n	CCONJ
ejpam-3007	430	7	,	,	PUNCT
ejpam-3007	430	8	i	i	PROPN
ejpam-3007	430	9	6	6	NUM
ejpam-3007	430	10	=	=	NOUN
ejpam-3007	430	11	n−1(xi+1	n−1(xi+1	NOUN
ejpam-3007	430	12	−	−	PROPN
ejpam-3007	430	13	xi)(xn	xi)(xn	PUNCT
ejpam-3007	431	1	−	−	PROPN
ejpam-3007	431	2	xn−1	xn−1	PROPN
ejpam-3007	431	3	)	)	PUNCT
ejpam-3007	432	1	+	+	CCONJ
ejpam-3007	432	2	xn−2∏	xn−2∏	PROPN
ejpam-3007	432	3	0	0	PUNCT
ejpam-3007	432	4	<	<	X
ejpam-3007	432	5	i	i	PROPN
ejpam-3007	432	6	<	<	X
ejpam-3007	432	7	n(xi+1	n(xi+1	PROPN
ejpam-3007	432	8	−	−	PROPN
ejpam-3007	432	9	xi)(xn	xi)(xn	PUNCT
ejpam-3007	433	1	−	−	PROPN
ejpam-3007	433	2	xn−1	xn−1	PROPN
ejpam-3007	433	3	)	)	PUNCT
ejpam-3007	433	4	(	(	PUNCT
ejpam-3007	433	5	80	80	NUM
ejpam-3007	433	6	)	)	PUNCT
ejpam-3007	433	7	proof	proof	NOUN
ejpam-3007	433	8	.	.	PUNCT
ejpam-3007	434	1	simple	simple	ADJ
ejpam-3007	434	2	transformations	transformation	NOUN
ejpam-3007	434	3	,	,	PUNCT
ejpam-3007	434	4	but	but	CCONJ
ejpam-3007	434	5	in	in	ADP
ejpam-3007	434	6	the	the	DET
ejpam-3007	434	7	future	future	NOUN
ejpam-3007	434	8	plays	play	VERB
ejpam-3007	434	9	an	an	DET
ejpam-3007	434	10	important	important	ADJ
ejpam-3007	434	11	role	role	NOUN
ejpam-3007	434	12	.	.	PUNCT
ejpam-3007	435	1	with	with	ADP
ejpam-3007	435	2	the	the	DET
ejpam-3007	435	3	help	help	NOUN
ejpam-3007	435	4	of	of	ADP
ejpam-3007	435	5	this	this	DET
ejpam-3007	435	6	transformation	transformation	NOUN
ejpam-3007	435	7	we	we	PRON
ejpam-3007	435	8	will	will	AUX
ejpam-3007	435	9	be	be	AUX
ejpam-3007	435	10	able	able	ADJ
ejpam-3007	435	11	to	to	PART
ejpam-3007	435	12	prove	prove	VERB
ejpam-3007	435	13	a	a	DET
ejpam-3007	435	14	very	very	ADV
ejpam-3007	435	15	important	important	ADJ
ejpam-3007	435	16	estimate	estimate	NOUN
ejpam-3007	435	17	for	for	ADP
ejpam-3007	435	18	the	the	DET
ejpam-3007	435	19	derivatives	derivative	NOUN
ejpam-3007	435	20	of	of	ADP
ejpam-3007	435	21	wave	wave	NOUN
ejpam-3007	435	22	functions	function	NOUN
ejpam-3007	435	23	and	and	CCONJ
ejpam-3007	435	24	show	show	VERB
ejpam-3007	435	25	that	that	SCONJ
ejpam-3007	435	26	it	it	PRON
ejpam-3007	435	27	is	be	AUX
ejpam-3007	435	28	actually	actually	ADV
ejpam-3007	435	29	close	close	ADJ
ejpam-3007	435	30	to	to	ADP
ejpam-3007	435	31	an	an	DET
ejpam-3007	435	32	estimate	estimate	NOUN
ejpam-3007	435	33	without	without	ADP
ejpam-3007	435	34	derivatives	derivative	NOUN
ejpam-3007	435	35	lemma	lemma	PROPN
ejpam-3007	435	36	34	34	NUM
ejpam-3007	435	37	.	.	PUNCT
ejpam-3007	436	1	let	let	VERB
ejpam-3007	436	2	q	q	PROPN
ejpam-3007	436	3	∈	∈	VERB
ejpam-3007	436	4	w	w	NOUN
ejpam-3007	436	5	1	1	NUM
ejpam-3007	436	6	2	2	NUM
ejpam-3007	436	7	(	(	PUNCT
ejpam-3007	436	8	r3	r3	PROPN
ejpam-3007	436	9	)	)	PUNCT
ejpam-3007	436	10	,	,	PUNCT
ejpam-3007	436	11	q	q	PROPN
ejpam-3007	436	12	∈	∈	PROPN
ejpam-3007	436	13	l2(qt	l2(qt	PROPN
ejpam-3007	436	14	)	)	PUNCT
ejpam-3007	436	15	,	,	PUNCT
ejpam-3007	436	16	νk(k	νk(k	X
ejpam-3007	436	17	,	,	PUNCT
ejpam-3007	436	18	k	k	PROPN
ejpam-3007	436	19	′	′	NOUN
ejpam-3007	436	20	)	)	PUNCT
ejpam-3007	436	21	=	=	PUNCT
ejpam-3007	436	22	ν|k	ν|k	PROPN
ejpam-3007	437	1	−	−	PROPN
ejpam-3007	437	2	k′|2,k(k	k′|2,k(k	NOUN
ejpam-3007	437	3	)	)	PUNCT
ejpam-3007	437	4	=	=	SYM
ejpam-3007	437	5	k	k	PROPN
ejpam-3007	437	6	,	,	PUNCT
ejpam-3007	437	7	x(x	x(x	PROPN
ejpam-3007	437	8	)	)	PUNCT
ejpam-3007	437	9	=	=	SYM
ejpam-3007	438	1	x.then	x.then	PROPN
ejpam-3007	438	2	,	,	PUNCT
ejpam-3007	438	3	the	the	DET
ejpam-3007	438	4	solution	solution	NOUN
ejpam-3007	438	5	of	of	ADP
ejpam-3007	438	6	(	(	PUNCT
ejpam-3007	438	7	57	57	NUM
ejpam-3007	438	8	)	)	PUNCT
ejpam-3007	438	9	,	,	PUNCT
ejpam-3007	438	10	(	(	PUNCT
ejpam-3007	438	11	58	58	NUM
ejpam-3007	438	12	)	)	PUNCT
ejpam-3007	438	13	,	,	PUNCT
ejpam-3007	438	14	(	(	PUNCT
ejpam-3007	438	15	59	59	NUM
ejpam-3007	438	16	)	)	PUNCT
ejpam-3007	438	17	in	in	ADP
ejpam-3007	438	18	theorem	theorem	ADJ
ejpam-3007	438	19	20	20	NUM
ejpam-3007	438	20	satisfies	satisfie	NOUN
ejpam-3007	438	21	the	the	DET
ejpam-3007	438	22	following	follow	VERB
ejpam-3007	438	23	inequalities	inequality	NOUN
ejpam-3007	438	24	:	:	PUNCT
ejpam-3007	438	25	sup	sup	NOUN
ejpam-3007	438	26	x∈r3	x∈r3	PROPN
ejpam-3007	438	27	|q(x)|	|q(x)|	PROPN
ejpam-3007	438	28	<	<	X
ejpam-3007	438	29	∫	∫	PROPN
ejpam-3007	438	30	t	t	PROPN
ejpam-3007	438	31	0	0	NUM
ejpam-3007	438	32	sup	sup	NOUN
ejpam-3007	438	33	x∈r3	x∈r3	NOUN
ejpam-3007	438	34	|q(x)|	|q(x)|	NOUN
ejpam-3007	438	35	∥∥(1	∥∥(1	NUM
ejpam-3007	438	36	+	+	PROPN
ejpam-3007	438	37	x2)∇q	x2)∇q	PROPN
ejpam-3007	438	38	∥∥	∥∥	PRON
ejpam-3007	438	39	l2(r3	l2(r3	PROPN
ejpam-3007	438	40	)	)	PUNCT
ejpam-3007	438	41	dτ	dτ	NOUN
ejpam-3007	438	42	,	,	PUNCT
ejpam-3007	438	43	sup	sup	NOUN
ejpam-3007	438	44	x∈r3	x∈r3	PROPN
ejpam-3007	438	45	|q(x)|	|q(x)|	PROPN
ejpam-3007	438	46	<	<	X
ejpam-3007	438	47	c	c	X
ejpam-3007	438	48	(	(	PUNCT
ejpam-3007	438	49	81	81	NUM
ejpam-3007	438	50	)	)	PUNCT
ejpam-3007	438	51	a.	a.	NOUN
ejpam-3007	438	52	durmagambetov	durmagambetov	PROPN
ejpam-3007	438	53	/	/	SYM
ejpam-3007	438	54	eur	eur	PROPN
ejpam-3007	438	55	.	.	PUNCT
ejpam-3007	439	1	j.	j.	PROPN
ejpam-3007	439	2	pure	pure	PROPN
ejpam-3007	439	3	appl	appl	PROPN
ejpam-3007	439	4	.	.	PROPN
ejpam-3007	439	5	math	math	PROPN
ejpam-3007	439	6	,	,	PUNCT
ejpam-3007	439	7	10	10	NUM
ejpam-3007	439	8	(	(	PUNCT
ejpam-3007	439	9	4	4	NUM
ejpam-3007	439	10	)	)	PUNCT
ejpam-3007	439	11	(	(	PUNCT
ejpam-3007	439	12	2017	2017	NUM
ejpam-3007	439	13	)	)	PUNCT
ejpam-3007	439	14	,	,	PUNCT
ejpam-3007	439	15	763	763	NUM
ejpam-3007	439	16	-	-	SYM
ejpam-3007	439	17	785	785	NUM
ejpam-3007	439	18	782	782	NUM
ejpam-3007	439	19	proof	proof	NOUN
ejpam-3007	439	20	.	.	PUNCT
ejpam-3007	440	1	using	use	VERB
ejpam-3007	440	2	equation	equation	NOUN
ejpam-3007	440	3	q	q	NOUN
ejpam-3007	440	4	=	=	SYM
ejpam-3007	440	5	lim	lim	PROPN
ejpam-3007	440	6	z→0	z→0	X
ejpam-3007	440	7	λh0ψ−/λψ−	λh0ψ−/λψ−	PROPN
ejpam-3007	440	8	(	(	PUNCT
ejpam-3007	440	9	82	82	NUM
ejpam-3007	440	10	)	)	PUNCT
ejpam-3007	440	11	using	use	VERB
ejpam-3007	440	12	lemmas	lemmas	PROPN
ejpam-3007	440	13	(	(	PUNCT
ejpam-3007	440	14	11	11	NUM
ejpam-3007	440	15	-	-	SYM
ejpam-3007	440	16	21	21	NUM
ejpam-3007	440	17	)	)	PUNCT
ejpam-3007	440	18	we	we	PRON
ejpam-3007	440	19	have	have	VERB
ejpam-3007	440	20	|q(x)|	|q(x)|	NOUN
ejpam-3007	440	21	=	=	SYM
ejpam-3007	440	22	∣∣∣∣h0λψ−	∣∣∣∣h0λψ−	PROPN
ejpam-3007	440	23	λψ−	λψ−	PROPN
ejpam-3007	440	24	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3007	440	25	k=0	k=0	PROPN
ejpam-3007	440	26	,	,	PUNCT
ejpam-3007	440	27	|q(x0)|	|q(x0)|	NOUN
ejpam-3007	440	28	≤	≤	PROPN
ejpam-3007	440	29	∣∣∣∣h0λψ−	∣∣∣∣h0λψ−	PUNCT
ejpam-3007	440	30	x2	x2	PROPN
ejpam-3007	440	31	0	0	PUNCT
ejpam-3007	440	32	−	−	PROPN
ejpam-3007	440	33	α	α	PRON
ejpam-3007	440	34	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3007	440	35	k=0	k=0	PUNCT
ejpam-3007	440	36	≤	≤	NUM
ejpam-3007	440	37	c	c	NOUN
ejpam-3007	440	38	|h0λψ−|k=0	|h0λψ−|k=0	NOUN
ejpam-3007	441	1	=	=	PUNCT
ejpam-3007	441	2	c	c	X
ejpam-3007	441	3	|t−λg−|k=0	|t−λg−|k=0	PROPN
ejpam-3007	441	4	≤	≤	PROPN
ejpam-3007	441	5	c	c	PROPN
ejpam-3007	441	6	∣∣(i	∣∣(i	NOUN
ejpam-3007	441	7	−	−	PROPN
ejpam-3007	441	8	t−d)−1	t−d)−1	NOUN
ejpam-3007	441	9	(	(	PUNCT
ejpam-3007	441	10	t−(∇d,∇th0	t−(∇d,∇th0	NOUN
ejpam-3007	441	11	g	g	NOUN
ejpam-3007	441	12	)	)	PUNCT
ejpam-3007	442	1	+	+	NUM
ejpam-3007	442	2	tλdh0φ0	tλdh0φ0	NOUN
ejpam-3007	442	3	)	)	PUNCT
ejpam-3007	443	1	∣∣	∣∣	X
ejpam-3007	444	1	k=0	k=0	PROPN
ejpam-3007	444	2	c	c	PROPN
ejpam-3007	444	3	∣∣(i	∣∣(i	NOUN
ejpam-3007	444	4	−	−	PROPN
ejpam-3007	444	5	t−d)−1	t−d)−1	NOUN
ejpam-3007	444	6	(	(	PUNCT
ejpam-3007	444	7	t−(∇d,∇t	t−(∇d,∇t	PROPN
ejpam-3007	444	8	(	(	PUNCT
ejpam-3007	444	9	k2	k2	PROPN
ejpam-3007	444	10	g	g	PROPN
ejpam-3007	444	11	+	+	CCONJ
ejpam-3007	444	12	qg))−	qg))−	PROPN
ejpam-3007	444	13	tλdk2φ0	tλdk2φ0	NOUN
ejpam-3007	444	14	)	)	PUNCT
ejpam-3007	444	15	∣∣	∣∣	X
ejpam-3007	444	16	k=0	k=0	PROPN
ejpam-3007	444	17	≤	≤	PROPN
ejpam-3007	444	18	c	c	PROPN
ejpam-3007	444	19	∣∣(i	∣∣(i	NOUN
ejpam-3007	444	20	−	−	PROPN
ejpam-3007	444	21	t−d)−1	t−d)−1	NOUN
ejpam-3007	444	22	(	(	PUNCT
ejpam-3007	444	23	t−(∇d,∇tk2((i	t−(∇d,∇tk2((i	NOUN
ejpam-3007	444	24	−	−	PROPN
ejpam-3007	444	25	t−d)−1t−dφ0))−	t−d)−1t−dφ0))−	NOUN
ejpam-3007	444	26	tλdk2φ0	tλdk2φ0	NOUN
ejpam-3007	444	27	)	)	PUNCT
ejpam-3007	444	28	∣∣	∣∣	X
ejpam-3007	444	29	k=0	k=0	PROPN
ejpam-3007	444	30	≤	≤	X
ejpam-3007	444	31	c|sφx0q|+	c|sφx0q|+	NOUN
ejpam-3007	444	32	c|sλφx0	c|sλφx0	PART
ejpam-3007	444	33	q|	q|	NOUN
ejpam-3007	444	34	≤	≤	NUM
ejpam-3007	444	35	c	c	PROPN
ejpam-3007	444	36	∫	∫	PROPN
ejpam-3007	444	37	t	t	NOUN
ejpam-3007	444	38	0	0	NUM
ejpam-3007	444	39	sup	sup	NOUN
ejpam-3007	444	40	x∈r3	x∈r3	NOUN
ejpam-3007	444	41	|q(x)|	|q(x)|	NOUN
ejpam-3007	444	42	∥∥(1	∥∥(1	NUM
ejpam-3007	444	43	+	+	PROPN
ejpam-3007	444	44	x2)∇q	x2)∇q	PROPN
ejpam-3007	444	45	∥∥	∥∥	PRON
ejpam-3007	444	46	l2(r3	l2(r3	ADJ
ejpam-3007	444	47	)	)	PUNCT
ejpam-3007	444	48	dτ	dτ	NOUN
ejpam-3007	444	49	(	(	PUNCT
ejpam-3007	444	50	83	83	NUM
ejpam-3007	444	51	)	)	PUNCT
ejpam-3007	444	52	using	use	VERB
ejpam-3007	444	53	the	the	DET
ejpam-3007	444	54	grnwal	grnwal	NOUN
ejpam-3007	444	55	bellman	bellman	NOUN
ejpam-3007	444	56	inequality	inequality	NOUN
ejpam-3007	444	57	we	we	PRON
ejpam-3007	444	58	have	have	VERB
ejpam-3007	444	59	sup	sup	NOUN
ejpam-3007	444	60	x∈r3	x∈r3	PROPN
ejpam-3007	444	61	|q(x)|	|q(x)|	PROPN
ejpam-3007	444	62	<	<	X
ejpam-3007	444	63	c	c	PROPN
ejpam-3007	444	64	theorem	theorem	VERB
ejpam-3007	444	65	35	35	NUM
ejpam-3007	444	66	.	.	PUNCT
ejpam-3007	445	1	let	let	VERB
ejpam-3007	445	2	q0	q0	PROPN
ejpam-3007	445	3	∈w	∈w	PROPN
ejpam-3007	445	4	2	2	NUM
ejpam-3007	445	5	2	2	NUM
ejpam-3007	445	6	(	(	PUNCT
ejpam-3007	445	7	r3),∇2q̃0	r3),∇2q̃0	NOUN
ejpam-3007	445	8	∈	∈	NOUN
ejpam-3007	445	9	l2(r3	l2(r3	NOUN
ejpam-3007	445	10	)	)	PUNCT
ejpam-3007	445	11	,	,	PUNCT
ejpam-3007	445	12	f	f	PROPN
ejpam-3007	445	13	∈	∈	PROPN
ejpam-3007	445	14	l2(qt	l2(qt	PROPN
ejpam-3007	445	15	)	)	PUNCT
ejpam-3007	445	16	,	,	PUNCT
ejpam-3007	445	17	f̃	f̃	PROPN
ejpam-3007	445	18	∈	∈	PROPN
ejpam-3007	445	19	l1(qt	l1(qt	PROPN
ejpam-3007	445	20	)	)	PUNCT
ejpam-3007	445	21	∩l2(r3	∩l2(r3	NUM
ejpam-3007	445	22	)	)	PUNCT
ejpam-3007	445	23	,	,	PUNCT
ejpam-3007	445	24	∇2f̃	∇2f̃	NOUN
ejpam-3007	445	25	∈	∈	PROPN
ejpam-3007	445	26	l1(qt	l1(qt	PROPN
ejpam-3007	445	27	)	)	PUNCT
ejpam-3007	445	28	∩	∩	ADJ
ejpam-3007	445	29	l2(r3	l2(r3	ADJ
ejpam-3007	445	30	)	)	PUNCT
ejpam-3007	445	31	.	.	PUNCT
ejpam-3007	446	1	and	and	CCONJ
ejpam-3007	446	2	max	max	PROPN
ejpam-3007	446	3	k	k	PROPN
ejpam-3007	446	4	|t	|t	PROPN
ejpam-3007	446	5	q̃0|	q̃0|	INTJ
ejpam-3007	446	6	<	<	X
ejpam-3007	446	7	const	const	PROPN
ejpam-3007	446	8	,	,	PUNCT
ejpam-3007	446	9	max	max	PROPN
ejpam-3007	446	10	k	k	PROPN
ejpam-3007	447	1	|t∇2q̃0|	|t∇2q̃0|	PROPN
ejpam-3007	447	2	<	<	X
ejpam-3007	447	3	const	const	X
ejpam-3007	447	4	,	,	PUNCT
ejpam-3007	447	5	then	then	ADV
ejpam-3007	447	6	,	,	PUNCT
ejpam-3007	447	7	there	there	PRON
ejpam-3007	447	8	exists	exist	VERB
ejpam-3007	447	9	the	the	DET
ejpam-3007	447	10	following	follow	VERB
ejpam-3007	447	11	a	a	DET
ejpam-3007	447	12	unique	unique	ADJ
ejpam-3007	447	13	generalized	generalized	ADJ
ejpam-3007	447	14	solution	solution	NOUN
ejpam-3007	447	15	of	of	ADP
ejpam-3007	447	16	(	(	PUNCT
ejpam-3007	447	17	57	57	NUM
ejpam-3007	447	18	)	)	PUNCT
ejpam-3007	447	19	,	,	PUNCT
ejpam-3007	447	20	(	(	PUNCT
ejpam-3007	447	21	58	58	NUM
ejpam-3007	447	22	)	)	PUNCT
ejpam-3007	447	23	,	,	PUNCT
ejpam-3007	447	24	(	(	PUNCT
ejpam-3007	447	25	59)satisfying	59)satisfye	VERB
ejpam-3007	447	26	inequality	inequality	NOUN
ejpam-3007	447	27	:	:	PUNCT
ejpam-3007	447	28	sup	sup	NOUN
ejpam-3007	447	29	x	x	SYM
ejpam-3007	447	30	|qi|	|qi|	NOUN
ejpam-3007	447	31	≤	≤	NOUN
ejpam-3007	447	32	const	const	NOUN
ejpam-3007	447	33	,	,	PUNCT
ejpam-3007	447	34	where	where	SCONJ
ejpam-3007	447	35	the	the	DET
ejpam-3007	447	36	value	value	NOUN
ejpam-3007	447	37	of	of	ADP
ejpam-3007	447	38	const	const	NOUN
ejpam-3007	447	39	depends	depend	VERB
ejpam-3007	447	40	only	only	ADV
ejpam-3007	447	41	on	on	ADP
ejpam-3007	447	42	the	the	DET
ejpam-3007	447	43	conditions	condition	NOUN
ejpam-3007	447	44	of	of	ADP
ejpam-3007	447	45	the	the	DET
ejpam-3007	447	46	theorem	theorem	NOUN
ejpam-3007	447	47	.	.	PUNCT
ejpam-3007	448	1	proof	proof	NOUN
ejpam-3007	448	2	.	.	PUNCT
ejpam-3007	449	1	it	it	PRON
ejpam-3007	449	2	suffices	suffice	VERB
ejpam-3007	449	3	to	to	PART
ejpam-3007	449	4	obtain	obtain	VERB
ejpam-3007	449	5	uniform	uniform	ADJ
ejpam-3007	449	6	estimates	estimate	NOUN
ejpam-3007	449	7	of	of	ADP
ejpam-3007	449	8	the	the	DET
ejpam-3007	449	9	maximum	maximum	ADJ
ejpam-3007	449	10	velocity	velocity	NOUN
ejpam-3007	449	11	components	component	NOUN
ejpam-3007	449	12	qi	qi	PROPN
ejpam-3007	449	13	,	,	PUNCT
ejpam-3007	449	14	which	which	PRON
ejpam-3007	449	15	obviously	obviously	ADV
ejpam-3007	449	16	follow	follow	VERB
ejpam-3007	449	17	from	from	ADP
ejpam-3007	449	18	max	max	PROPN
ejpam-3007	449	19	x	x	SYM
ejpam-3007	449	20	|qi|	|qi|	PROPN
ejpam-3007	449	21	,	,	PUNCT
ejpam-3007	449	22	because	because	SCONJ
ejpam-3007	449	23	uniform	uniform	ADJ
ejpam-3007	449	24	estimates	estimate	NOUN
ejpam-3007	449	25	allow	allow	VERB
ejpam-3007	449	26	us	we	PRON
ejpam-3007	449	27	to	to	PART
ejpam-3007	449	28	extend	extend	VERB
ejpam-3007	449	29	the	the	DET
ejpam-3007	449	30	local	local	ADJ
ejpam-3007	449	31	existence	existence	NOUN
ejpam-3007	449	32	and	and	CCONJ
ejpam-3007	449	33	uniqueness	uniqueness	NOUN
ejpam-3007	449	34	theorem	theorem	VERB
ejpam-3007	449	35	over	over	ADP
ejpam-3007	449	36	the	the	DET
ejpam-3007	449	37	interval	interval	NOUN
ejpam-3007	449	38	in	in	ADP
ejpam-3007	449	39	which	which	PRON
ejpam-3007	449	40	they	they	PRON
ejpam-3007	449	41	are	be	AUX
ejpam-3007	449	42	valid	valid	ADJ
ejpam-3007	449	43	.	.	PUNCT
ejpam-3007	450	1	to	to	PART
ejpam-3007	450	2	estimate	estimate	VERB
ejpam-3007	450	3	the	the	DET
ejpam-3007	450	4	velocity	velocity	NOUN
ejpam-3007	450	5	components	component	NOUN
ejpam-3007	450	6	,	,	PUNCT
ejpam-3007	450	7	lemma	lemma	PROPN
ejpam-3007	450	8	(	(	PUNCT
ejpam-3007	450	9	15)can	15)can	NUM
ejpam-3007	450	10	be	be	AUX
ejpam-3007	450	11	used	use	VERB
ejpam-3007	450	12	:	:	PUNCT
ejpam-3007	450	13	vi	vi	ADJ
ejpam-3007	450	14	=	=	SYM
ejpam-3007	450	15	qi/	qi/	NOUN
ejpam-3007	450	16	(	(	PUNCT
ejpam-3007	450	17	∫	∫	PROPN
ejpam-3007	450	18	t	t	PROPN
ejpam-3007	450	19	0	0	PUNCT
ejpam-3007	451	1	||qx||2l2(r3)dt+a0	||qx||2l2(r3)dt+a0	PROPN
ejpam-3007	452	1	+	+	NUM
ejpam-3007	452	2	1	1	NUM
ejpam-3007	452	3	)	)	PUNCT
ejpam-3007	452	4	,	,	PUNCT
ejpam-3007	452	5	a0	a0	PROPN
ejpam-3007	452	6	=	=	SYM
ejpam-3007	452	7	4/(ν	4/(ν	PROPN
ejpam-3007	452	8	1	1	NUM
ejpam-3007	452	9	3	3	NUM
ejpam-3007	452	10	(	(	PUNCT
ejpam-3007	452	11	cc0	cc0	NOUN
ejpam-3007	452	12	+	+	CCONJ
ejpam-3007	452	13	1	1	NUM
ejpam-3007	452	14	)	)	PUNCT
ejpam-3007	452	15	2	2	NUM
ejpam-3007	452	16	3	3	NUM
ejpam-3007	452	17	)	)	PUNCT
ejpam-3007	452	18	.	.	PUNCT
ejpam-3007	453	1	using	use	VERB
ejpam-3007	453	2	lemmas	lemmas	PROPN
ejpam-3007	453	3	(	(	PUNCT
ejpam-3007	453	4	11)-(21	11)-(21	NOUN
ejpam-3007	453	5	)	)	PUNCT
ejpam-3007	453	6	for	for	ADP
ejpam-3007	453	7	vi	vi	NOUN
ejpam-3007	453	8	=	=	SYM
ejpam-3007	453	9	qi/	qi/	NOUN
ejpam-3007	453	10	(	(	PUNCT
ejpam-3007	453	11	∫	∫	PROPN
ejpam-3007	453	12	t	t	PROPN
ejpam-3007	453	13	0	0	PUNCT
ejpam-3007	454	1	||qx||2l2(r3)dt+a0	||qx||2l2(r3)dt+a0	PROPN
ejpam-3007	454	2	+	+	NUM
ejpam-3007	454	3	1	1	X
ejpam-3007	454	4	)	)	PUNCT
ejpam-3007	454	5	we	we	PRON
ejpam-3007	454	6	can	can	AUX
ejpam-3007	454	7	obtain	obtain	VERB
ejpam-3007	454	8	∫	∫	PROPN
ejpam-3007	454	9	s2	s2	VERB
ejpam-3007	454	10	||ai||tadθ′	||ai||tadθ′	NOUN
ejpam-3007	454	11	<	<	X
ejpam-3007	454	12	α	α	X
ejpam-3007	454	13	<	<	X
ejpam-3007	454	14	1	1	NUM
ejpam-3007	454	15	,	,	PUNCT
ejpam-3007	454	16	where	where	SCONJ
ejpam-3007	454	17	aiis	aiis	NOUN
ejpam-3007	454	18	the	the	DET
ejpam-3007	454	19	amplitude	amplitude	NOUN
ejpam-3007	454	20	of	of	ADP
ejpam-3007	454	21	potential	potential	ADJ
ejpam-3007	454	22	qi	qi	PROPN
ejpam-3007	454	23	and	and	CCONJ
ejpam-3007	454	24	n(qi	n(qi	NUM
ejpam-3007	454	25	)	)	PUNCT
ejpam-3007	454	26	<	<	X
ejpam-3007	455	1	1.that	1.that	NUM
ejpam-3007	455	2	is	be	AUX
ejpam-3007	455	3	,	,	PUNCT
ejpam-3007	455	4	discrete	discrete	ADJ
ejpam-3007	455	5	solutions	solution	NOUN
ejpam-3007	455	6	are	be	AUX
ejpam-3007	455	7	not	not	PART
ejpam-3007	455	8	significant	significant	ADJ
ejpam-3007	455	9	in	in	ADP
ejpam-3007	455	10	proving	prove	VERB
ejpam-3007	455	11	the	the	DET
ejpam-3007	455	12	theorem	theorem	NOUN
ejpam-3007	455	13	,	,	PUNCT
ejpam-3007	455	14	so	so	ADV
ejpam-3007	455	15	its	its	PRON
ejpam-3007	455	16	assertion	assertion	NOUN
ejpam-3007	455	17	follows	follow	VERB
ejpam-3007	455	18	the	the	DET
ejpam-3007	455	19	conditions	condition	NOUN
ejpam-3007	455	20	of	of	ADP
ejpam-3007	455	21	theorem	theorem	NOUN
ejpam-3007	455	22	35	35	NUM
ejpam-3007	455	23	,	,	PUNCT
ejpam-3007	455	24	which	which	PRON
ejpam-3007	455	25	defines	define	VERB
ejpam-3007	455	26	uniform	uniform	ADJ
ejpam-3007	455	27	time	time	NOUN
ejpam-3007	455	28	estimations	estimation	NOUN
ejpam-3007	455	29	for	for	ADP
ejpam-3007	455	30	the	the	DET
ejpam-3007	455	31	maximum	maximum	ADJ
ejpam-3007	455	32	values	value	NOUN
ejpam-3007	455	33	of	of	ADP
ejpam-3007	455	34	velocity	velocity	NOUN
ejpam-3007	455	35	components	component	NOUN
ejpam-3007	455	36	.	.	PUNCT
ejpam-3007	456	1	||∇q||l2(r3	||∇q||l2(r3	NUM
ejpam-3007	456	2	)	)	PUNCT
ejpam-3007	457	1	+	+	CCONJ
ejpam-3007	457	2	t∫	t∫	DET
ejpam-3007	457	3	0	0	NUM
ejpam-3007	457	4	∫	∫	PROPN
ejpam-3007	457	5	r3	r3	PROPN
ejpam-3007	457	6	|∇q|2dkdτ	|∇q|2dkdτ	PROPN
ejpam-3007	457	7	≤	≤	NOUN
ejpam-3007	457	8	const+	const+	NOUN
ejpam-3007	457	9	sup	sup	NOUN
ejpam-3007	457	10	x∈r3	x∈r3	NOUN
ejpam-3007	457	11	|q(x)|	|q(x)|	PROPN
ejpam-3007	457	12	t∫	t∫	DET
ejpam-3007	457	13	0	0	NUM
ejpam-3007	457	14	||∇q||l2(r3	||∇q||l2(r3	NUM
ejpam-3007	457	15	)	)	PUNCT
ejpam-3007	457	16	∣∣∣∣∇2q	∣∣∣∣∇2q	PROPN
ejpam-3007	457	17	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3007	457	18	l2(r3	l2(r3	ADJ
ejpam-3007	457	19	)	)	PUNCT
ejpam-3007	457	20	dτ	dτ	NOUN
ejpam-3007	457	21	,	,	PUNCT
ejpam-3007	457	22	(	(	PUNCT
ejpam-3007	457	23	84	84	NUM
ejpam-3007	457	24	)	)	PUNCT
ejpam-3007	457	25	references	reference	NOUN
ejpam-3007	457	26	783	783	NUM
ejpam-3007	457	27	theorem	theorem	VERB
ejpam-3007	457	28	35	35	NUM
ejpam-3007	457	29	asserts	assert	VERB
ejpam-3007	457	30	the	the	DET
ejpam-3007	457	31	global	global	ADJ
ejpam-3007	457	32	solvability	solvability	NOUN
ejpam-3007	457	33	and	and	CCONJ
ejpam-3007	457	34	uniqueness	uniqueness	NOUN
ejpam-3007	457	35	of	of	ADP
ejpam-3007	457	36	the	the	DET
ejpam-3007	457	37	cauchy	cauchy	ADJ
ejpam-3007	457	38	problem	problem	NOUN
ejpam-3007	457	39	for	for	ADP
ejpam-3007	457	40	the	the	DET
ejpam-3007	457	41	navier	navier	NOUN
ejpam-3007	457	42	-	-	PUNCT
ejpam-3007	457	43	stokes	stoke	NOUN
ejpam-3007	457	44	equations	equation	NOUN
ejpam-3007	457	45	.	.	PUNCT
ejpam-3007	458	1	theorem	theorem	VERB
ejpam-3007	458	2	36	36	NUM
ejpam-3007	458	3	.	.	PUNCT
ejpam-3007	459	1	let	let	VERB
ejpam-3007	459	2	q0	q0	PROPN
ejpam-3007	459	3	∈w	∈w	PROPN
ejpam-3007	459	4	2	2	NUM
ejpam-3007	459	5	2	2	NUM
ejpam-3007	459	6	(	(	PUNCT
ejpam-3007	459	7	r3),∇2q̃0	r3),∇2q̃0	NOUN
ejpam-3007	459	8	∈	∈	NOUN
ejpam-3007	459	9	l2(r3	l2(r3	NOUN
ejpam-3007	459	10	)	)	PUNCT
ejpam-3007	459	11	,	,	PUNCT
ejpam-3007	459	12	f	f	PROPN
ejpam-3007	459	13	∈	∈	PROPN
ejpam-3007	459	14	l2(qt	l2(qt	PROPN
ejpam-3007	459	15	)	)	PUNCT
ejpam-3007	459	16	,	,	PUNCT
ejpam-3007	459	17	f̃	f̃	PROPN
ejpam-3007	459	18	∈	∈	PROPN
ejpam-3007	459	19	l1(qt	l1(qt	PROPN
ejpam-3007	459	20	)	)	PUNCT
ejpam-3007	459	21	∩	∩	ADJ
ejpam-3007	459	22	l2(r3	l2(r3	PROPN
ejpam-3007	459	23	)	)	PUNCT
ejpam-3007	459	24	lim	lim	PROPN
ejpam-3007	459	25	t→t0	t→t0	VERB
ejpam-3007	459	26	||∇q||l2(r3	||∇q||l2(r3	PROPN
ejpam-3007	459	27	)	)	PUNCT
ejpam-3007	460	1	=	=	PRON
ejpam-3007	460	2	∞.	∞.	PROPN
ejpam-3007	460	3	(	(	PUNCT
ejpam-3007	460	4	85	85	NUM
ejpam-3007	460	5	)	)	PUNCT
ejpam-3007	460	6	then	then	ADV
ejpam-3007	460	7	,	,	PUNCT
ejpam-3007	460	8	there	there	PRON
ejpam-3007	460	9	exists	exist	VERB
ejpam-3007	460	10	i	i	PRON
ejpam-3007	460	11	,	,	PUNCT
ejpam-3007	460	12	j	j	PROPN
ejpam-3007	460	13	,	,	PUNCT
ejpam-3007	460	14	x0	x0	PROPN
ejpam-3007	460	15	lim	lim	PROPN
ejpam-3007	460	16	t→t0	t→t0	PROPN
ejpam-3007	460	17	ψj(x0	ψj(x0	PROPN
ejpam-3007	460	18	,	,	PUNCT
ejpam-3007	460	19	t	t	PROPN
ejpam-3007	460	20	)	)	PUNCT
ejpam-3007	460	21	=	=	NOUN
ejpam-3007	460	22	∞	∞	PROPN
ejpam-3007	460	23	or	or	CCONJ
ejpam-3007	460	24	lim	lim	PROPN
ejpam-3007	460	25	t→t0	t→t0	VERB
ejpam-3007	460	26	n(qi	n(qi	PROPN
ejpam-3007	460	27	)	)	PUNCT
ejpam-3007	460	28	=	=	NOUN
ejpam-3007	460	29	∞	∞	PROPN
ejpam-3007	460	30	(	(	PUNCT
ejpam-3007	460	31	86	86	NUM
ejpam-3007	460	32	)	)	PUNCT
ejpam-3007	460	33	proof	proof	NOUN
ejpam-3007	460	34	.	.	PUNCT
ejpam-3007	461	1	a	a	DET
ejpam-3007	461	2	proof	proof	NOUN
ejpam-3007	461	3	of	of	ADP
ejpam-3007	461	4	this	this	DET
ejpam-3007	461	5	lemma	lemma	PROPN
ejpam-3007	461	6	can	can	AUX
ejpam-3007	461	7	be	be	AUX
ejpam-3007	461	8	obtained	obtain	VERB
ejpam-3007	461	9	using	use	VERB
ejpam-3007	461	10	qi	qi	NOUN
ejpam-3007	461	11	=	=	SYM
ejpam-3007	461	12	pacqi	pacqi	NOUN
ejpam-3007	461	13	+	+	CCONJ
ejpam-3007	461	14	pdqi	pdqi	NOUN
ejpam-3007	461	15	and	and	CCONJ
ejpam-3007	461	16	uniform	uniform	ADJ
ejpam-3007	461	17	estimates	estimate	NOUN
ejpam-3007	461	18	pacqi	pacqi	VERB
ejpam-3007	461	19	.	.	PUNCT
ejpam-3007	462	1	theorem	theorem	VERB
ejpam-3007	462	2	36	36	NUM
ejpam-3007	462	3	describes	describe	VERB
ejpam-3007	462	4	the	the	DET
ejpam-3007	462	5	loss	loss	NOUN
ejpam-3007	462	6	of	of	ADP
ejpam-3007	462	7	smoothness	smoothness	NOUN
ejpam-3007	462	8	of	of	ADP
ejpam-3007	462	9	classical	classical	ADJ
ejpam-3007	462	10	solutions	solution	NOUN
ejpam-3007	462	11	for	for	ADP
ejpam-3007	462	12	the	the	DET
ejpam-3007	462	13	navier	navier	NOUN
ejpam-3007	462	14	–	–	PUNCT
ejpam-3007	462	15	stokes	stokes	PROPN
ejpam-3007	462	16	equations	equation	NOUN
ejpam-3007	462	17	.	.	PUNCT
ejpam-3007	463	1	theorem	theorem	VERB
ejpam-3007	463	2	36	36	NUM
ejpam-3007	463	3	describes	describe	VERB
ejpam-3007	463	4	the	the	DET
ejpam-3007	463	5	time	time	NOUN
ejpam-3007	463	6	blow	blow	VERB
ejpam-3007	463	7	up	up	ADP
ejpam-3007	463	8	of	of	ADP
ejpam-3007	463	9	the	the	DET
ejpam-3007	463	10	classical	classical	ADJ
ejpam-3007	463	11	solutions	solution	NOUN
ejpam-3007	463	12	for	for	ADP
ejpam-3007	463	13	the	the	DET
ejpam-3007	463	14	navier	navier	NOUN
ejpam-3007	463	15	-	-	PUNCT
ejpam-3007	463	16	stokes	stoke	NOUN
ejpam-3007	463	17	equations	equation	NOUN
ejpam-3007	463	18	arises	arise	VERB
ejpam-3007	463	19	,	,	PUNCT
ejpam-3007	463	20	and	and	CCONJ
ejpam-3007	463	21	complements	complement	VERB
ejpam-3007	463	22	the	the	DET
ejpam-3007	463	23	results	result	NOUN
ejpam-3007	463	24	of	of	ADP
ejpam-3007	463	25	terence	terence	NOUN
ejpam-3007	463	26	tao	tao	PROPN
ejpam-3007	464	1	[	[	X
ejpam-3007	464	2	1	1	NUM
ejpam-3007	464	3	]	]	PUNCT
ejpam-3007	464	4	.	.	PUNCT
ejpam-3007	465	1	7	7	X
ejpam-3007	465	2	.	.	X
ejpam-3007	465	3	conclusions	conclusion	NOUN
ejpam-3007	465	4	uniform	uniform	ADJ
ejpam-3007	465	5	global	global	ADJ
ejpam-3007	465	6	estimations	estimation	NOUN
ejpam-3007	465	7	of	of	ADP
ejpam-3007	465	8	the	the	DET
ejpam-3007	465	9	fourier	fourier	NOUN
ejpam-3007	465	10	transform	transform	NOUN
ejpam-3007	465	11	of	of	ADP
ejpam-3007	465	12	solutions	solution	NOUN
ejpam-3007	465	13	of	of	ADP
ejpam-3007	465	14	the	the	DET
ejpam-3007	465	15	navier	navier	NOUN
ejpam-3007	465	16	–	–	PUNCT
ejpam-3007	465	17	stokes	stokes	PROPN
ejpam-3007	465	18	equations	equation	NOUN
ejpam-3007	465	19	indicate	indicate	VERB
ejpam-3007	465	20	that	that	SCONJ
ejpam-3007	465	21	the	the	DET
ejpam-3007	465	22	principle	principle	NOUN
ejpam-3007	465	23	modeling	modeling	NOUN
ejpam-3007	465	24	of	of	ADP
ejpam-3007	465	25	complex	complex	ADJ
ejpam-3007	465	26	flows	flow	NOUN
ejpam-3007	465	27	and	and	CCONJ
ejpam-3007	465	28	related	related	ADJ
ejpam-3007	465	29	calculations	calculation	NOUN
ejpam-3007	465	30	can	can	AUX
ejpam-3007	465	31	be	be	AUX
ejpam-3007	465	32	based	base	VERB
ejpam-3007	465	33	on	on	ADP
ejpam-3007	465	34	the	the	DET
ejpam-3007	465	35	fourier	fourier	NOUN
ejpam-3007	465	36	transform	transform	NOUN
ejpam-3007	465	37	method	method	NOUN
ejpam-3007	465	38	.	.	PUNCT
ejpam-3007	466	1	in	in	ADP
ejpam-3007	466	2	terms	term	NOUN
ejpam-3007	466	3	of	of	ADP
ejpam-3007	466	4	the	the	DET
ejpam-3007	466	5	fourier	fourier	NOUN
ejpam-3007	466	6	transform	transform	NOUN
ejpam-3007	466	7	,	,	PUNCT
ejpam-3007	466	8	under	under	ADP
ejpam-3007	466	9	both	both	DET
ejpam-3007	466	10	smooth	smooth	ADJ
ejpam-3007	466	11	initial	initial	ADJ
ejpam-3007	466	12	conditions	condition	NOUN
ejpam-3007	466	13	and	and	CCONJ
ejpam-3007	466	14	right	right	ADJ
ejpam-3007	466	15	-	-	PUNCT
ejpam-3007	466	16	hand	hand	NOUN
ejpam-3007	466	17	sides	side	NOUN
ejpam-3007	466	18	,	,	PUNCT
ejpam-3007	466	19	no	no	PRON
ejpam-3007	466	20	appear	appear	NOUN
ejpam-3007	466	21	exacerbations	exacerbation	NOUN
ejpam-3007	466	22	appear	appear	VERB
ejpam-3007	466	23	in	in	ADP
ejpam-3007	466	24	the	the	DET
ejpam-3007	466	25	speed	speed	NOUN
ejpam-3007	466	26	and	and	CCONJ
ejpam-3007	466	27	pressure	pressure	NOUN
ejpam-3007	466	28	modes.a	modes.a	NOUN
ejpam-3007	466	29	loss	loss	NOUN
ejpam-3007	466	30	of	of	ADP
ejpam-3007	466	31	smoothness	smoothness	NOUN
ejpam-3007	466	32	in	in	ADP
ejpam-3007	466	33	terms	term	NOUN
ejpam-3007	466	34	of	of	ADP
ejpam-3007	466	35	the	the	DET
ejpam-3007	466	36	fourier	fourier	NOUN
ejpam-3007	466	37	transform	transform	NOUN
ejpam-3007	466	38	can	can	AUX
ejpam-3007	466	39	only	only	ADV
ejpam-3007	466	40	be	be	AUX
ejpam-3007	466	41	expected	expect	VERB
ejpam-3007	466	42	in	in	ADP
ejpam-3007	466	43	the	the	DET
ejpam-3007	466	44	case	case	NOUN
ejpam-3007	466	45	of	of	ADP
ejpam-3007	466	46	singular	singular	ADJ
ejpam-3007	466	47	initial	initial	ADJ
ejpam-3007	466	48	conditions	condition	NOUN
ejpam-3007	466	49	,	,	PUNCT
ejpam-3007	466	50	or	or	CCONJ
ejpam-3007	466	51	of	of	ADP
ejpam-3007	466	52	unlimited	unlimited	ADJ
ejpam-3007	466	53	forces	force	NOUN
ejpam-3007	466	54	in	in	ADP
ejpam-3007	466	55	l2(qt	l2(qt	PROPN
ejpam-3007	466	56	)	)	PUNCT
ejpam-3007	466	57	.	.	PUNCT
ejpam-3007	467	1	the	the	DET
ejpam-3007	467	2	theory	theory	NOUN
ejpam-3007	467	3	developed	develop	VERB
ejpam-3007	467	4	by	by	ADP
ejpam-3007	467	5	us	we	PRON
ejpam-3007	467	6	is	be	AUX
ejpam-3007	467	7	supported	support	VERB
ejpam-3007	467	8	by	by	ADP
ejpam-3007	467	9	numerical	numerical	ADJ
ejpam-3007	467	10	calculations	calculation	NOUN
ejpam-3007	467	11	carried	carry	VERB
ejpam-3007	467	12	out	out	ADP
ejpam-3007	467	13	in	in	ADP
ejpam-3007	467	14	the	the	DET
ejpam-3007	467	15	works	work	NOUN
ejpam-3007	467	16	[	[	X
ejpam-3007	467	17	21	21	NUM
ejpam-3007	467	18	-	-	SYM
ejpam-3007	467	19	23	23	NUM
ejpam-3007	467	20	]	]	PUNCT
ejpam-3007	467	21	where	where	SCONJ
ejpam-3007	467	22	the	the	DET
ejpam-3007	467	23	dependence	dependence	NOUN
ejpam-3007	467	24	of	of	ADP
ejpam-3007	467	25	the	the	DET
ejpam-3007	467	26	smoothness	smoothness	NOUN
ejpam-3007	467	27	of	of	ADP
ejpam-3007	467	28	the	the	DET
ejpam-3007	467	29	solution	solution	NOUN
ejpam-3007	467	30	on	on	ADP
ejpam-3007	467	31	the	the	DET
ejpam-3007	467	32	oscillations	oscillation	NOUN
ejpam-3007	467	33	of	of	ADP
ejpam-3007	467	34	the	the	DET
ejpam-3007	467	35	system	system	NOUN
ejpam-3007	467	36	is	be	AUX
ejpam-3007	467	37	clearly	clearly	ADV
ejpam-3007	467	38	deduced	deduce	VERB
ejpam-3007	467	39	.	.	PUNCT
ejpam-3007	468	1	acknowledgements	acknowledgement	NOUN
ejpam-3007	468	2	we	we	PRON
ejpam-3007	468	3	are	be	AUX
ejpam-3007	468	4	grateful	grateful	ADJ
ejpam-3007	468	5	to	to	ADP
ejpam-3007	468	6	the	the	DET
ejpam-3007	468	7	ministry	ministry	PROPN
ejpam-3007	468	8	of	of	ADP
ejpam-3007	468	9	education	education	PROPN
ejpam-3007	468	10	and	and	CCONJ
ejpam-3007	468	11	science	science	NOUN
ejpam-3007	468	12	of	of	ADP
ejpam-3007	468	13	the	the	DET
ejpam-3007	468	14	republic	republic	NOUN
ejpam-3007	468	15	of	of	ADP
ejpam-3007	468	16	kazakhstan	kazakhstan	PROPN
ejpam-3007	468	17	for	for	ADP
ejpam-3007	468	18	a	a	DET
ejpam-3007	468	19	grant	grant	NOUN
ejpam-3007	468	20	,	,	PUNCT
ejpam-3007	468	21	and	and	CCONJ
ejpam-3007	468	22	to	to	ADP
ejpam-3007	468	23	the	the	DET
ejpam-3007	468	24	system	system	NOUN
ejpam-3007	468	25	research	research	NOUN
ejpam-3007	468	26	”	"	PUNCT
ejpam-3007	468	27	factor	factor	NOUN
ejpam-3007	468	28	”	"	PUNCT
ejpam-3007	468	29	company	company	NOUN
ejpam-3007	468	30	for	for	ADP
ejpam-3007	468	31	combining	combine	VERB
ejpam-3007	468	32	our	our	PRON
ejpam-3007	468	33	efforts	effort	NOUN
ejpam-3007	468	34	in	in	ADP
ejpam-3007	468	35	this	this	DET
ejpam-3007	468	36	project	project	NOUN
ejpam-3007	468	37	.	.	PUNCT
ejpam-3007	469	1	the	the	DET
ejpam-3007	469	2	work	work	NOUN
ejpam-3007	469	3	was	be	AUX
ejpam-3007	469	4	performed	perform	VERB
ejpam-3007	469	5	as	as	ADP
ejpam-3007	469	6	part	part	NOUN
ejpam-3007	469	7	of	of	ADP
ejpam-3007	469	8	an	an	DET
ejpam-3007	469	9	international	international	ADJ
ejpam-3007	469	10	project	project	NOUN
ejpam-3007	469	11	,	,	PUNCT
ejpam-3007	469	12	”	"	PUNCT
ejpam-3007	469	13	joint	joint	ADJ
ejpam-3007	469	14	kazakhindian	kazakhindian	ADJ
ejpam-3007	469	15	studies	study	NOUN
ejpam-3007	469	16	of	of	ADP
ejpam-3007	469	17	the	the	DET
ejpam-3007	469	18	influence	influence	NOUN
ejpam-3007	469	19	of	of	ADP
ejpam-3007	469	20	anthropogenic	anthropogenic	ADJ
ejpam-3007	469	21	factors	factor	NOUN
ejpam-3007	469	22	on	on	ADP
ejpam-3007	469	23	atmospheric	atmospheric	ADJ
ejpam-3007	469	24	phenomena	phenomenon	NOUN
ejpam-3007	469	25	on	on	ADP
ejpam-3007	469	26	the	the	DET
ejpam-3007	469	27	basis	basis	NOUN
ejpam-3007	469	28	of	of	ADP
ejpam-3007	469	29	numerical	numerical	ADJ
ejpam-3007	469	30	weather	weather	PROPN
ejpam-3007	469	31	prediction	prediction	NOUN
ejpam-3007	469	32	models	model	NOUN
ejpam-3007	469	33	wrf	wrf	PROPN
ejpam-3007	469	34	(	(	PUNCT
ejpam-3007	469	35	weather	weather	NOUN
ejpam-3007	469	36	research	research	NOUN
ejpam-3007	469	37	and	and	CCONJ
ejpam-3007	469	38	forecasting	forecasting	NOUN
ejpam-3007	469	39	)	)	PUNCT
ejpam-3007	469	40	”	"	PUNCT
ejpam-3007	469	41	,	,	PUNCT
ejpam-3007	469	42	commissioned	commission	VERB
ejpam-3007	469	43	by	by	ADP
ejpam-3007	469	44	the	the	DET
ejpam-3007	469	45	ministry	ministry	PROPN
ejpam-3007	469	46	of	of	ADP
ejpam-3007	469	47	education	education	PROPN
ejpam-3007	469	48	and	and	CCONJ
ejpam-3007	469	49	science	science	NOUN
ejpam-3007	469	50	of	of	ADP
ejpam-3007	469	51	the	the	DET
ejpam-3007	469	52	republic	republic	NOUN
ejpam-3007	469	53	of	of	ADP
ejpam-3007	469	54	kazakhstan	kazakhstan	PROPN
ejpam-3007	469	55	.	.	PUNCT
ejpam-3007	470	1	references	reference	NOUN
ejpam-3007	470	2	[	[	X
ejpam-3007	470	3	1	1	NUM
ejpam-3007	470	4	]	]	X
ejpam-3007	470	5	terence	terence	NOUN
ejpam-3007	470	6	tao	tao	PROPN
ejpam-3007	470	7	,	,	PUNCT
ejpam-3007	470	8	finite	finite	ADJ
ejpam-3007	470	9	time	time	NOUN
ejpam-3007	470	10	blowup	blowup	ADJ
ejpam-3007	470	11	for	for	ADP
ejpam-3007	470	12	an	an	DET
ejpam-3007	470	13	averaged	average	VERB
ejpam-3007	470	14	three	three	NUM
ejpam-3007	470	15	-	-	PUNCT
ejpam-3007	470	16	dimensional	dimensional	ADJ
ejpam-3007	470	17	navier	navier	NOUN
ejpam-3007	470	18	-	-	PUNCT
ejpam-3007	470	19	stokes	stoke	NOUN
ejpam-3007	470	20	equation	equation	NOUN
ejpam-3007	470	21	,	,	PUNCT
ejpam-3007	470	22	-arxiv:1402.0290	-arxiv:1402.0290	PUNCT
ejpam-3007	470	23	[	[	X
ejpam-3007	470	24	math.ap	math.ap	X
ejpam-3007	470	25	]	]	X
ejpam-3007	470	26	references	reference	NOUN
ejpam-3007	470	27	784	784	NUM
ejpam-3007	470	28	[	[	X
ejpam-3007	470	29	2	2	NUM
ejpam-3007	470	30	]	]	PUNCT
ejpam-3007	470	31	l.	l.	PROPN
ejpam-3007	470	32	d.	d.	PROPN
ejpam-3007	470	33	faddeev	faddeev	PROPN
ejpam-3007	470	34	,	,	PUNCT
ejpam-3007	470	35	the	the	DET
ejpam-3007	470	36	inverse	inverse	NOUN
ejpam-3007	470	37	problem	problem	NOUN
ejpam-3007	470	38	in	in	ADP
ejpam-3007	470	39	the	the	DET
ejpam-3007	470	40	quantum	quantum	ADJ
ejpam-3007	470	41	theory	theory	NOUN
ejpam-3007	470	42	of	of	ADP
ejpam-3007	470	43	scattering	scattering	NOUN
ejpam-3007	470	44	.	.	PUNCT
ejpam-3007	471	1	ii	ii	PROPN
ejpam-3007	471	2	,	,	PUNCT
ejpam-3007	471	3	itogi	itogi	PROPN
ejpam-3007	471	4	nauki	nauki	PROPN
ejpam-3007	472	1	i	i	PRON
ejpam-3007	472	2	tekhniki	tekhniki	PROPN
ejpam-3007	472	3	.	.	PUNCT
ejpam-3007	473	1	ser	ser	PROPN
ejpam-3007	473	2	.	.	PUNCT
ejpam-3007	474	1	sovrem	sovrem	PROPN
ejpam-3007	474	2	.	.	PUNCT
ejpam-3007	475	1	probl	probl	PROPN
ejpam-3007	475	2	.	.	PUNCT
ejpam-3007	476	1	mat	mat	PROPN
ejpam-3007	476	2	.	.	PROPN
ejpam-3007	476	3	,	,	PUNCT
ejpam-3007	476	4	3	3	X
ejpam-3007	476	5	,	,	PUNCT
ejpam-3007	476	6	viniti	viniti	PROPN
ejpam-3007	476	7	,	,	PUNCT
ejpam-3007	476	8	moscow	moscow	PROPN
ejpam-3007	476	9	,	,	PUNCT
ejpam-3007	476	10	1974	1974	NUM
ejpam-3007	476	11	,	,	PUNCT
ejpam-3007	476	12	93180	93180	NUM
ejpam-3007	477	1	[	[	X
ejpam-3007	477	2	3	3	X
ejpam-3007	477	3	]	]	X
ejpam-3007	477	4	charles	charles	PROPN
ejpam-3007	477	5	l.	l.	PROPN
ejpam-3007	477	6	fefferman	fefferman	PROPN
ejpam-3007	477	7	existence	existence	NOUN
ejpam-3007	477	8	and	and	CCONJ
ejpam-3007	477	9	smoothness	smoothness	NOUN
ejpam-3007	477	10	of	of	ADP
ejpam-3007	477	11	the	the	DET
ejpam-3007	477	12	navier	navier	NOUN
ejpam-3007	477	13	-	-	PUNCT
ejpam-3007	477	14	stokes	stoke	NOUN
ejpam-3007	477	15	equation	equation	NOUN
ejpam-3007	477	16	.	.	PUNCT
ejpam-3007	478	1	the	the	DET
ejpam-3007	478	2	millennium	millennium	PROPN
ejpam-3007	478	3	prize	prize	PROPN
ejpam-3007	478	4	problems	problem	NOUN
ejpam-3007	478	5	,	,	PUNCT
ejpam-3007	478	6	5767	5767	NUM
ejpam-3007	478	7	,	,	PUNCT
ejpam-3007	478	8	clay	clay	NOUN
ejpam-3007	478	9	math	math	NOUN
ejpam-3007	478	10	.	.	PUNCT
ejpam-3007	479	1	inst	inst	PROPN
ejpam-3007	479	2	.	.	PROPN
ejpam-3007	479	3	,	,	PUNCT
ejpam-3007	479	4	cambridge	cambridge	PROPN
ejpam-3007	479	5	,	,	PUNCT
ejpam-3007	479	6	ma	ma	PROPN
ejpam-3007	479	7	,	,	PUNCT
ejpam-3007	479	8	2006	2006	NUM
ejpam-3007	479	9	.	.	PUNCT
ejpam-3007	480	1	[	[	X
ejpam-3007	480	2	4	4	NUM
ejpam-3007	480	3	]	]	PUNCT
ejpam-3007	480	4	asset	asset	NOUN
ejpam-3007	480	5	durmagambetov	durmagambetov	NOUN
ejpam-3007	480	6	,	,	PUNCT
ejpam-3007	480	7	leyla	leyla	PROPN
ejpam-3007	480	8	fazilova	fazilova	PROPN
ejpam-3007	480	9	.	.	PUNCT
ejpam-3007	481	1	global	global	ADJ
ejpam-3007	481	2	estimation	estimation	NOUN
ejpam-3007	481	3	of	of	ADP
ejpam-3007	481	4	the	the	DET
ejpam-3007	481	5	cauchy	cauchy	PROPN
ejpam-3007	481	6	problem	problem	NOUN
ejpam-3007	481	7	solutions	solution	NOUN
ejpam-3007	481	8	fourier	fourier	NOUN
ejpam-3007	481	9	transform	transform	VERB
ejpam-3007	481	10	derivatives	derivative	NOUN
ejpam-3007	481	11	for	for	ADP
ejpam-3007	481	12	the	the	DET
ejpam-3007	481	13	navier	navier	NOUN
ejpam-3007	481	14	-	-	PUNCT
ejpam-3007	481	15	stokes	stokes	PROPN
ejpam-3007	481	16	equation	equation	NOUN
ejpam-3007	481	17	international	international	PROPN
ejpam-3007	481	18	journal	journal	NOUN
ejpam-3007	481	19	of	of	ADP
ejpam-3007	481	20	modern	modern	ADJ
ejpam-3007	481	21	nonlinear	nonlinear	ADJ
ejpam-3007	481	22	theory	theory	NOUN
ejpam-3007	481	23	and	and	CCONJ
ejpam-3007	481	24	application	application	NOUN
ejpam-3007	481	25	vol.2	vol.2	PROPN
ejpam-3007	481	26	no.4	no.4	PROPN
ejpam-3007	481	27	,	,	PUNCT
ejpam-3007	481	28	december	december	PROPN
ejpam-3007	481	29	2	2	NUM
ejpam-3007	481	30	,	,	PUNCT
ejpam-3007	481	31	2013	2013	NUM
ejpam-3007	481	32	[	[	X
ejpam-3007	481	33	5	5	NUM
ejpam-3007	481	34	]	]	X
ejpam-3007	481	35	global	global	ADJ
ejpam-3007	481	36	estimation	estimation	NOUN
ejpam-3007	481	37	of	of	ADP
ejpam-3007	481	38	the	the	DET
ejpam-3007	481	39	cauchy	cauchy	PROPN
ejpam-3007	481	40	problem	problem	NOUN
ejpam-3007	481	41	solutions	solution	VERB
ejpam-3007	481	42	the	the	DET
ejpam-3007	481	43	navier	navier	NOUN
ejpam-3007	481	44	-	-	PUNCT
ejpam-3007	481	45	stokes	stokes	PROPN
ejpam-3007	481	46	equation	equation	NOUN
ejpam-3007	481	47	a.	a.	NOUN
ejpam-3007	481	48	a.	a.	NOUN
ejpam-3007	481	49	durmagambetov	durmagambetov	PROPN
ejpam-3007	481	50	,	,	PUNCT
ejpam-3007	481	51	l.	l.	PROPN
ejpam-3007	481	52	s.	s.	PROPN
ejpam-3007	481	53	fazilova	fazilova	PROPN
ejpam-3007	481	54	journal	journal	PROPN
ejpam-3007	481	55	of	of	ADP
ejpam-3007	481	56	applied	apply	VERB
ejpam-3007	481	57	mathematics	mathematics	PROPN
ejpam-3007	481	58	and	and	CCONJ
ejpam-3007	481	59	physics	physics	NOUN
ejpam-3007	481	60	volume	volume	NOUN
ejpam-3007	481	61	2	2	NUM
ejpam-3007	481	62	,	,	PUNCT
ejpam-3007	481	63	number	number	NOUN
ejpam-3007	481	64	4	4	NUM
ejpam-3007	481	65	,	,	PUNCT
ejpam-3007	481	66	march	march	PROPN
ejpam-3007	481	67	2014	2014	NUM
ejpam-3007	482	1	[	[	X
ejpam-3007	482	2	6	6	NUM
ejpam-3007	482	3	]	]	PUNCT
ejpam-3007	482	4	a.	a.	NOUN
ejpam-3007	482	5	durmagambetov	durmagambetov	NOUN
ejpam-3007	482	6	,	,	PUNCT
ejpam-3007	482	7	l.	l.	PROPN
ejpam-3007	482	8	s.	s.	PROPN
ejpam-3007	482	9	fazilova	fazilova	VERB
ejpam-3007	482	10	global	global	ADJ
ejpam-3007	482	11	estimation	estimation	NOUN
ejpam-3007	482	12	of	of	ADP
ejpam-3007	482	13	the	the	DET
ejpam-3007	482	14	cauchy	cauchy	PROPN
ejpam-3007	482	15	problem	problem	NOUN
ejpam-3007	482	16	solutions	solution	VERB
ejpam-3007	482	17	the	the	DET
ejpam-3007	482	18	navier	navier	NOUN
ejpam-3007	482	19	-	-	PUNCT
ejpam-3007	482	20	stokes	stokes	PROPN
ejpam-3007	482	21	equation	equation	NOUN
ejpam-3007	482	22	//	//	SYM
ejpam-3007	482	23	journal	journal	PROPN
ejpam-3007	482	24	of	of	ADP
ejpam-3007	482	25	applied	apply	VERB
ejpam-3007	482	26	mathematics	mathematic	NOUN
ejpam-3007	482	27	and	and	CCONJ
ejpam-3007	482	28	physics	physics	NOUN
ejpam-3007	482	29	.	.	PUNCT
ejpam-3007	483	1	2014	2014	NUM
ejpam-3007	483	2	.	.	PUNCT
ejpam-3007	484	1	vol	vol	NOUN
ejpam-3007	484	2	.	.	PROPN
ejpam-3007	485	1	2	2	NUM
ejpam-3007	485	2	.	.	X
ejpam-3007	485	3	.	.	PUNCT
ejpam-3007	486	1	4	4	X
ejpam-3007	486	2	.	.	PUNCT
ejpam-3007	487	1	p.	p.	NOUN
ejpam-3007	487	2	17	17	NUM
ejpam-3007	487	3	-	-	SYM
ejpam-3007	487	4	25	25	NUM
ejpam-3007	487	5	.	.	PUNCT
ejpam-3007	488	1	[	[	X
ejpam-3007	488	2	7	7	X
ejpam-3007	488	3	]	]	X
ejpam-3007	488	4	j.s.russell	j.s.russell	ADJ
ejpam-3007	488	5	report	report	NOUN
ejpam-3007	488	6	on	on	ADP
ejpam-3007	488	7	waves	wave	NOUN
ejpam-3007	488	8	:	:	PUNCT
ejpam-3007	488	9	(	(	PUNCT
ejpam-3007	488	10	report	report	NOUN
ejpam-3007	488	11	of	of	ADP
ejpam-3007	488	12	the	the	DET
ejpam-3007	488	13	fourteenth	fourteenth	ADJ
ejpam-3007	488	14	meeting	meeting	NOUN
ejpam-3007	488	15	of	of	ADP
ejpam-3007	488	16	the	the	DET
ejpam-3007	488	17	british	british	PROPN
ejpam-3007	488	18	association	association	PROPN
ejpam-3007	488	19	for	for	ADP
ejpam-3007	488	20	the	the	DET
ejpam-3007	488	21	advancement	advancement	NOUN
ejpam-3007	488	22	of	of	ADP
ejpam-3007	488	23	science	science	PROPN
ejpam-3007	488	24	,	,	PUNCT
ejpam-3007	488	25	york	york	PROPN
ejpam-3007	488	26	,	,	PUNCT
ejpam-3007	488	27	september	september	PROPN
ejpam-3007	488	28	1844	1844	NUM
ejpam-3007	488	29	(	(	PUNCT
ejpam-3007	488	30	london	london	PROPN
ejpam-3007	488	31	1845	1845	NUM
ejpam-3007	488	32	)	)	PUNCT
ejpam-3007	488	33	,	,	PUNCT
ejpam-3007	488	34	pp	pp	PROPN
ejpam-3007	488	35	311390	311390	NUM
ejpam-3007	488	36	,	,	PUNCT
ejpam-3007	488	37	plates	plate	NOUN
ejpam-3007	488	38	xlvii	xlvii	PROPN
ejpam-3007	488	39	-	-	PUNCT
ejpam-3007	488	40	lvii	lvii	ADJ
ejpam-3007	488	41	)	)	PUNCT
ejpam-3007	489	1	[	[	X
ejpam-3007	489	2	8	8	NUM
ejpam-3007	489	3	]	]	X
ejpam-3007	489	4	j.s.russell	j.s.russell	NOUN
ejpam-3007	489	5	(	(	PUNCT
ejpam-3007	489	6	1838	1838	NUM
ejpam-3007	489	7	)	)	PUNCT
ejpam-3007	489	8	,	,	PUNCT
ejpam-3007	489	9	report	report	NOUN
ejpam-3007	489	10	of	of	ADP
ejpam-3007	489	11	the	the	DET
ejpam-3007	489	12	committee	committee	NOUN
ejpam-3007	489	13	on	on	ADP
ejpam-3007	489	14	waves	wave	NOUN
ejpam-3007	489	15	,	,	PUNCT
ejpam-3007	489	16	report	report	NOUN
ejpam-3007	489	17	of	of	ADP
ejpam-3007	489	18	the	the	DET
ejpam-3007	489	19	7th	7th	ADJ
ejpam-3007	489	20	meeting	meeting	NOUN
ejpam-3007	489	21	of	of	ADP
ejpam-3007	489	22	british	british	PROPN
ejpam-3007	489	23	association	association	PROPN
ejpam-3007	489	24	for	for	ADP
ejpam-3007	489	25	the	the	DET
ejpam-3007	489	26	advancement	advancement	NOUN
ejpam-3007	489	27	of	of	ADP
ejpam-3007	489	28	science	science	NOUN
ejpam-3007	489	29	,	,	PUNCT
ejpam-3007	489	30	john	john	PROPN
ejpam-3007	489	31	murray	murray	PROPN
ejpam-3007	489	32	,	,	PUNCT
ejpam-3007	489	33	london	london	PROPN
ejpam-3007	489	34	,	,	PUNCT
ejpam-3007	489	35	pp.417	pp.417	PROPN
ejpam-3007	489	36	-	-	PUNCT
ejpam-3007	489	37	496	496	NUM
ejpam-3007	489	38	.	.	PUNCT
ejpam-3007	490	1	[	[	X
ejpam-3007	490	2	9	9	NUM
ejpam-3007	490	3	]	]	PUNCT
ejpam-3007	490	4	mark	mark	PROPN
ejpam-3007	490	5	j.	j.	PROPN
ejpam-3007	490	6	ablowitz	ablowitz	PROPN
ejpam-3007	490	7	,	,	PUNCT
ejpam-3007	490	8	harvey	harvey	PROPN
ejpam-3007	490	9	segur	segur	PROPN
ejpam-3007	490	10	solitons	solitons	PROPN
ejpam-3007	490	11	and	and	CCONJ
ejpam-3007	490	12	the	the	DET
ejpam-3007	490	13	inverse	inverse	NOUN
ejpam-3007	490	14	scattering	scattering	NOUN
ejpam-3007	490	15	transform	transform	NOUN
ejpam-3007	490	16	siam	siam	NOUN
ejpam-3007	490	17	,	,	PUNCT
ejpam-3007	490	18	1981p	1981p	NUM
ejpam-3007	490	19	.	.	PUNCT
ejpam-3007	491	1	435	435	NUM
ejpam-3007	491	2	.	.	PUNCT
ejpam-3007	492	1	[	[	X
ejpam-3007	492	2	10	10	NUM
ejpam-3007	492	3	]	]	SYM
ejpam-3007	492	4	n.j.zabusky	n.j.zabusky	NOUN
ejpam-3007	492	5	and	and	CCONJ
ejpam-3007	492	6	m.d.kruskal	m.d.kruskal	NOUN
ejpam-3007	492	7	(	(	PUNCT
ejpam-3007	492	8	1965	1965	NUM
ejpam-3007	492	9	)	)	PUNCT
ejpam-3007	492	10	,	,	PUNCT
ejpam-3007	492	11	interaction	interaction	NOUN
ejpam-3007	492	12	of	of	ADP
ejpam-3007	492	13	solitons	soliton	NOUN
ejpam-3007	492	14	in	in	ADP
ejpam-3007	492	15	a	a	DET
ejpam-3007	492	16	collisionless	collisionless	ADJ
ejpam-3007	492	17	plasma	plasma	NOUN
ejpam-3007	492	18	and	and	CCONJ
ejpam-3007	492	19	the	the	DET
ejpam-3007	492	20	recurrence	recurrence	NOUN
ejpam-3007	492	21	of	of	ADP
ejpam-3007	492	22	initial	initial	ADJ
ejpam-3007	492	23	states	state	NOUN
ejpam-3007	492	24	,	,	PUNCT
ejpam-3007	492	25	phys.rev.lett	phys.rev.lett	PROPN
ejpam-3007	492	26	.	.	PUNCT
ejpam-3007	492	27	,	,	PUNCT
ejpam-3007	492	28	15	15	NUM
ejpam-3007	492	29	pp	pp	NOUN
ejpam-3007	492	30	.	.	PUNCT
ejpam-3007	493	1	240243	240243	NUM
ejpam-3007	493	2	.	.	PUNCT
ejpam-3007	494	1	[	[	X
ejpam-3007	494	2	11	11	NUM
ejpam-3007	494	3	]	]	X
ejpam-3007	494	4	r.g	r.g	PROPN
ejpam-3007	494	5	newton	newton	PROPN
ejpam-3007	494	6	,	,	PUNCT
ejpam-3007	494	7	new	new	ADJ
ejpam-3007	494	8	result	result	NOUN
ejpam-3007	494	9	on	on	ADP
ejpam-3007	494	10	the	the	DET
ejpam-3007	494	11	inverse	inverse	NOUN
ejpam-3007	494	12	scattering	scattering	NOUN
ejpam-3007	494	13	problem	problem	NOUN
ejpam-3007	494	14	in	in	ADP
ejpam-3007	494	15	three	three	NUM
ejpam-3007	494	16	dimentions	dimention	NOUN
ejpam-3007	494	17	,	,	PUNCT
ejpam-3007	494	18	phys	phy	NOUN
ejpam-3007	494	19	.	.	PUNCT
ejpam-3007	495	1	rev	rev	PROPN
ejpam-3007	495	2	.	.	PROPN
ejpam-3007	495	3	lett	lett	PROPN
ejpam-3007	495	4	.	.	PUNCT
ejpam-3007	496	1	v43	v43	PROPN
ejpam-3007	496	2	,	,	PUNCT
ejpam-3007	496	3	8,pp.541	8,pp.541	NUM
ejpam-3007	496	4	-	-	SYM
ejpam-3007	496	5	542,1979	542,1979	NUM
ejpam-3007	496	6	[	[	X
ejpam-3007	496	7	12	12	NUM
ejpam-3007	496	8	]	]	X
ejpam-3007	496	9	r.g	r.g	PROPN
ejpam-3007	496	10	newton	newton	PROPN
ejpam-3007	496	11	,	,	PUNCT
ejpam-3007	496	12	inverse	inverse	NOUN
ejpam-3007	496	13	scattering	scatter	VERB
ejpam-3007	496	14	three	three	NUM
ejpam-3007	496	15	dimensions	dimension	NOUN
ejpam-3007	496	16	,	,	PUNCT
ejpam-3007	496	17	jour	jour	PROPN
ejpam-3007	496	18	.	.	PUNCT
ejpam-3007	496	19	math	math	NOUN
ejpam-3007	496	20	.	.	PUNCT
ejpam-3007	497	1	phys	phy	NOUN
ejpam-3007	497	2	.	.	PUNCT
ejpam-3007	498	1	21	21	NUM
ejpam-3007	498	2	,	,	PUNCT
ejpam-3007	498	3	pp.16981715,1980	pp.16981715,1980	NOUN
ejpam-3007	498	4	[	[	X
ejpam-3007	498	5	13	13	NUM
ejpam-3007	498	6	]	]	PUNCT
ejpam-3007	498	7	somersalo	somersalo	PROPN
ejpam-3007	498	8	e.	e.	PROPN
ejpam-3007	498	9	et	et	PROPN
ejpam-3007	498	10	al	al	PROPN
ejpam-3007	498	11	.	.	PROPN
ejpam-3007	498	12	inverse	inverse	ADJ
ejpam-3007	498	13	scattering	scattering	NOUN
ejpam-3007	498	14	problem	problem	NOUN
ejpam-3007	498	15	for	for	ADP
ejpam-3007	498	16	the	the	DET
ejpam-3007	498	17	schrodinger	schrodinger	NOUN
ejpam-3007	498	18	’s	’s	PART
ejpam-3007	498	19	equation	equation	NOUN
ejpam-3007	498	20	in	in	ADP
ejpam-3007	498	21	three	three	NUM
ejpam-3007	498	22	dimensions	dimension	NOUN
ejpam-3007	498	23	:	:	PUNCT
ejpam-3007	498	24	connections	connection	NOUN
ejpam-3007	498	25	between	between	ADP
ejpam-3007	498	26	exact	exact	ADJ
ejpam-3007	498	27	and	and	CCONJ
ejpam-3007	498	28	approximate	approximate	ADJ
ejpam-3007	498	29	methods	method	NOUN
ejpam-3007	498	30	.	.	PUNCT
ejpam-3007	499	1	1988	1988	NUM
ejpam-3007	499	2	.	.	PUNCT
ejpam-3007	500	1	[	[	X
ejpam-3007	500	2	14	14	NUM
ejpam-3007	500	3	]	]	PUNCT
ejpam-3007	500	4	a.	a.	NOUN
ejpam-3007	500	5	y.	y.	PROPN
ejpam-3007	500	6	povzner	povzner	PROPN
ejpam-3007	500	7	,	,	PUNCT
ejpam-3007	500	8	on	on	ADP
ejpam-3007	500	9	the	the	DET
ejpam-3007	500	10	expansion	expansion	NOUN
ejpam-3007	500	11	of	of	ADP
ejpam-3007	500	12	arbitrary	arbitrary	ADJ
ejpam-3007	500	13	functions	function	NOUN
ejpam-3007	500	14	in	in	ADP
ejpam-3007	500	15	characteristic	characteristic	ADJ
ejpam-3007	500	16	functions	function	NOUN
ejpam-3007	500	17	of	of	ADP
ejpam-3007	500	18	the	the	DET
ejpam-3007	500	19	operator	operator	NOUN
ejpam-3007	500	20	−∆u	−∆u	X
ejpam-3007	501	1	+	+	ADJ
ejpam-3007	501	2	cu	cu	PROPN
ejpam-3007	501	3	mat	mat	PROPN
ejpam-3007	501	4	.	.	PUNCT
ejpam-3007	501	5	sb	sb	PROPN
ejpam-3007	501	6	.	.	PROPN
ejpam-3007	502	1	(	(	PUNCT
ejpam-3007	502	2	n.s	n.s	PROPN
ejpam-3007	502	3	.	.	PROPN
ejpam-3007	502	4	)	)	PUNCT
ejpam-3007	502	5	,	,	PUNCT
ejpam-3007	502	6	32(74):1	32(74):1	NUM
ejpam-3007	502	7	(	(	PUNCT
ejpam-3007	502	8	1953	1953	NUM
ejpam-3007	502	9	)	)	PUNCT
ejpam-3007	502	10	,	,	PUNCT
ejpam-3007	502	11	109156	109156	NUM
ejpam-3007	502	12	.	.	PUNCT
ejpam-3007	503	1	[	[	X
ejpam-3007	503	2	15	15	NUM
ejpam-3007	503	3	]	]	X
ejpam-3007	503	4	birman	birman	NOUN
ejpam-3007	503	5	,	,	PUNCT
ejpam-3007	503	6	m.	m.	NOUN
ejpam-3007	503	7	.	.	PUNCT
ejpam-3007	504	1	on	on	ADP
ejpam-3007	504	2	the	the	DET
ejpam-3007	504	3	spectrum	spectrum	NOUN
ejpam-3007	504	4	of	of	ADP
ejpam-3007	504	5	singular	singular	ADJ
ejpam-3007	504	6	boundary	boundary	ADJ
ejpam-3007	504	7	-	-	PUNCT
ejpam-3007	504	8	value	value	NOUN
ejpam-3007	504	9	problems	problem	NOUN
ejpam-3007	504	10	.	.	PUNCT
ejpam-3007	505	1	(	(	PUNCT
ejpam-3007	505	2	russian	russian	ADJ
ejpam-3007	505	3	)	)	PUNCT
ejpam-3007	505	4	mat	mat	PROPN
ejpam-3007	505	5	.	.	PUNCT
ejpam-3007	505	6	sb	sb	PROPN
ejpam-3007	505	7	.	.	PROPN
ejpam-3007	506	1	(	(	PUNCT
ejpam-3007	506	2	n.s	n.s	PROPN
ejpam-3007	506	3	.	.	PROPN
ejpam-3007	506	4	)	)	PUNCT
ejpam-3007	507	1	55	55	NUM
ejpam-3007	507	2	(	(	PUNCT
ejpam-3007	507	3	97	97	NUM
ejpam-3007	507	4	)	)	PUNCT
ejpam-3007	507	5	1961	1961	NUM
ejpam-3007	507	6	125174	125174	NUM
ejpam-3007	507	7	.	.	PUNCT
ejpam-3007	508	1	[	[	X
ejpam-3007	508	2	16	16	NUM
ejpam-3007	508	3	]	]	X
ejpam-3007	508	4	poincare	poincare	PROPN
ejpam-3007	508	5	h.	h.	PROPN
ejpam-3007	508	6	,	,	PUNCT
ejpam-3007	508	7	lecons	lecon	NOUN
ejpam-3007	508	8	de	de	PROPN
ejpam-3007	508	9	mecanique	mecanique	PROPN
ejpam-3007	508	10	celeste	celeste	PROPN
ejpam-3007	508	11	,	,	PUNCT
ejpam-3007	508	12	t.	t.	NOUN
ejpam-3007	508	13	3	3	NUM
ejpam-3007	508	14	,	,	PUNCT
ejpam-3007	508	15	p.	p.	NOUN
ejpam-3007	508	16	,	,	PUNCT
ejpam-3007	508	17	1910	1910	NUM
ejpam-3007	508	18	.	.	PUNCT
ejpam-3007	509	1	references	reference	NOUN
ejpam-3007	509	2	785	785	NUM
ejpam-3007	510	1	[	[	X
ejpam-3007	510	2	17	17	NUM
ejpam-3007	510	3	]	]	X
ejpam-3007	510	4	leray	leray	PROPN
ejpam-3007	510	5	,	,	PUNCT
ejpam-3007	510	6	j.	j.	PROPN
ejpam-3007	510	7	(	(	PUNCT
ejpam-3007	510	8	1934	1934	NUM
ejpam-3007	510	9	)	)	PUNCT
ejpam-3007	510	10	.	.	PUNCT
ejpam-3007	511	1	”	"	PUNCT
ejpam-3007	511	2	sur	sur	PROPN
ejpam-3007	511	3	le	le	X
ejpam-3007	511	4	mouvement	mouvement	PROPN
ejpam-3007	511	5	d’un	d’un	PROPN
ejpam-3007	511	6	liquide	liquide	PROPN
ejpam-3007	511	7	visqueux	visqueux	PROPN
ejpam-3007	511	8	emplissant	emplissant	PROPN
ejpam-3007	511	9	l’espace	l’espace	PROPN
ejpam-3007	511	10	”	"	PUNCT
ejpam-3007	511	11	.	.	PUNCT
ejpam-3007	512	1	acta	acta	PROPN
ejpam-3007	512	2	mathematica	mathematica	PROPN
ejpam-3007	512	3	63	63	NUM
ejpam-3007	512	4	:	:	SYM
ejpam-3007	512	5	193248	193248	NUM
ejpam-3007	512	6	.	.	PUNCT
ejpam-3007	513	1	doi:10.1007	doi:10.1007	NOUN
ejpam-3007	513	2	/	/	SYM
ejpam-3007	513	3	bf02547354	bf02547354	PROPN
ejpam-3007	513	4	.	.	PUNCT
ejpam-3007	514	1	[	[	X
ejpam-3007	514	2	18	18	NUM
ejpam-3007	514	3	]	]	X
ejpam-3007	514	4	o.a	o.a	PROPN
ejpam-3007	514	5	.	.	PROPN
ejpam-3007	514	6	ladyzhenskaya	ladyzhenskaya	PROPN
ejpam-3007	514	7	,	,	PUNCT
ejpam-3007	514	8	mathematic	mathematic	ADJ
ejpam-3007	514	9	problems	problem	NOUN
ejpam-3007	514	10	of	of	ADP
ejpam-3007	514	11	viscous	viscous	ADJ
ejpam-3007	514	12	incondensable	incondensable	ADJ
ejpam-3007	514	13	liquid	liquid	ADJ
ejpam-3007	514	14	dynamics	dynamic	NOUN
ejpam-3007	514	15	.	.	PUNCT
ejpam-3007	515	1	m.	m.	NOUN
ejpam-3007	515	2	:	:	PUNCT
ejpam-3007	515	3	science	science	NOUN
ejpam-3007	515	4	,	,	PUNCT
ejpam-3007	515	5	1970	1970	NUM
ejpam-3007	515	6	.	.	PUNCT
ejpam-3007	516	1	p.	p.	NOUN
ejpam-3007	516	2	288	288	NUM
ejpam-3007	517	1	[	[	X
ejpam-3007	517	2	19	19	NUM
ejpam-3007	517	3	]	]	X
ejpam-3007	517	4	solonnikov	solonnikov	PROPN
ejpam-3007	517	5	v.a	v.a	PROPN
ejpam-3007	517	6	.	.	PROPN
ejpam-3007	517	7	estimates	estimate	NOUN
ejpam-3007	517	8	solving	solve	VERB
ejpam-3007	517	9	nonstationary	nonstationary	ADJ
ejpam-3007	517	10	linearized	linearize	VERB
ejpam-3007	517	11	systems	system	NOUN
ejpam-3007	517	12	of	of	ADP
ejpam-3007	517	13	navier	navier	NOUN
ejpam-3007	517	14	-	-	PUNCT
ejpam-3007	517	15	stokes	stoke	NOUN
ejpam-3007	517	16	’	'	PUNCT
ejpam-3007	517	17	equations	equation	NOUN
ejpam-3007	517	18	.	.	PUNCT
ejpam-3007	518	1	transactions	transaction	NOUN
ejpam-3007	518	2	academy	academy	PROPN
ejpam-3007	518	3	of	of	ADP
ejpam-3007	518	4	sciences	sciences	PROPN
ejpam-3007	518	5	ussr	ussr	ADJ
ejpam-3007	518	6	vol	vol	NOUN
ejpam-3007	518	7	.	.	PROPN
ejpam-3007	518	8	70	70	NUM
ejpam-3007	518	9	,	,	PUNCT
ejpam-3007	518	10	1964	1964	NUM
ejpam-3007	518	11	.	.	PUNCT
ejpam-3007	519	1	p.	p.	NOUN
ejpam-3007	519	2	213	213	NUM
ejpam-3007	519	3	–	–	PUNCT
ejpam-3007	519	4	317	317	NUM
ejpam-3007	519	5	.	.	PUNCT
ejpam-3007	520	1	[	[	X
ejpam-3007	520	2	20	20	NUM
ejpam-3007	520	3	]	]	X
ejpam-3007	520	4	huang	huang	PROPN
ejpam-3007	520	5	xiangdi	xiangdi	PROPN
ejpam-3007	520	6	,	,	PUNCT
ejpam-3007	520	7	li	li	PROPN
ejpam-3007	520	8	jing	jing	PROPN
ejpam-3007	520	9	,	,	PUNCT
ejpam-3007	520	10	wang	wang	PROPN
ejpam-3007	520	11	yong	yong	PROPN
ejpam-3007	520	12	.	.	PUNCT
ejpam-3007	521	1	serrin	serrin	ADJ
ejpam-3007	521	2	-	-	PUNCT
ejpam-3007	521	3	type	type	NOUN
ejpam-3007	521	4	blowup	blowup	ADJ
ejpam-3007	521	5	criterion	criterion	NOUN
ejpam-3007	521	6	for	for	ADP
ejpam-3007	521	7	full	full	ADJ
ejpam-3007	521	8	compressible	compressible	ADJ
ejpam-3007	521	9	navier	navier	NOUN
ejpam-3007	521	10	-	-	PUNCT
ejpam-3007	521	11	stokes	stoke	NOUN
ejpam-3007	521	12	system	system	NOUN
ejpam-3007	521	13	,	,	PUNCT
ejpam-3007	521	14	archive	archive	NOUN
ejpam-3007	521	15	for	for	ADP
ejpam-3007	521	16	rational	rational	ADJ
ejpam-3007	521	17	mechanics	mechanic	NOUN
ejpam-3007	521	18	and	and	CCONJ
ejpam-3007	521	19	analysis	analysis	NOUN
ejpam-3007	521	20	,	,	PUNCT
ejpam-3007	521	21	p.p	p.p	PROPN
ejpam-3007	521	22	.	.	NOUN
ejpam-3007	521	23	303	303	NUM
ejpam-3007	521	24	-	-	SYM
ejpam-3007	521	25	316	316	NUM
ejpam-3007	521	26	,	,	PUNCT
ejpam-3007	521	27	2013	2013	NUM
ejpam-3007	521	28	.	.	PUNCT
ejpam-3007	522	1	[	[	X
ejpam-3007	522	2	21	21	NUM
ejpam-3007	522	3	]	]	X
ejpam-3007	522	4	f.	f.	PROPN
ejpam-3007	522	5	mebarek	mebarek	PROPN
ejpam-3007	522	6	-	-	PUNCT
ejpam-3007	522	7	oudina	oudina	PROPN
ejpam-3007	522	8	r.	r.	PROPN
ejpam-3007	522	9	bessah	bessah	PROPN
ejpam-3007	522	10	,	,	PUNCT
ejpam-3007	522	11	magnetohydrodynamic	magnetohydrodynamic	ADJ
ejpam-3007	522	12	stability	stability	NOUN
ejpam-3007	522	13	of	of	ADP
ejpam-3007	522	14	natural	natural	ADJ
ejpam-3007	522	15	convection	convection	NOUN
ejpam-3007	522	16	flows	flow	NOUN
ejpam-3007	522	17	in	in	ADP
ejpam-3007	522	18	czochralski	czochralski	NOUN
ejpam-3007	522	19	crystal	crystal	NOUN
ejpam-3007	522	20	growth	growth	NOUN
ejpam-3007	522	21	.	.	PUNCT
ejpam-3007	523	1	world	world	PROPN
ejpam-3007	523	2	journal	journal	PROPN
ejpam-3007	523	3	of	of	ADP
ejpam-3007	523	4	engineering	engineering	NOUN
ejpam-3007	523	5	,	,	PUNCT
ejpam-3007	523	6	vol	vol	NOUN
ejpam-3007	523	7	.	.	PROPN
ejpam-3007	523	8	4	4	NUM
ejpam-3007	523	9	no.4	no.4	PROPN
ejpam-3007	523	10	,	,	PUNCT
ejpam-3007	523	11	pp	pp	X
ejpam-3007	523	12	.	.	PUNCT
ejpam-3007	523	13	1522	1522	NUM
ejpam-3007	523	14	,	,	PUNCT
ejpam-3007	523	15	2007	2007	NUM
ejpam-3007	523	16	.	.	PUNCT
ejpam-3007	524	1	[	[	X
ejpam-3007	524	2	22	22	NUM
ejpam-3007	524	3	]	]	X
ejpam-3007	524	4	f.	f.	PROPN
ejpam-3007	524	5	mebarek	mebarek	PROPN
ejpam-3007	524	6	-	-	PUNCT
ejpam-3007	524	7	oudina	oudina	PROPN
ejpam-3007	524	8	r.	r.	PROPN
ejpam-3007	524	9	bessah	bessah	PROPN
ejpam-3007	524	10	,	,	PUNCT
ejpam-3007	524	11	numerical	numerical	ADJ
ejpam-3007	524	12	modeling	modeling	NOUN
ejpam-3007	524	13	of	of	ADP
ejpam-3007	524	14	mhd	mhd	NOUN
ejpam-3007	524	15	stability	stability	NOUN
ejpam-3007	524	16	in	in	ADP
ejpam-3007	524	17	a	a	DET
ejpam-3007	524	18	cylindrical	cylindrical	ADJ
ejpam-3007	524	19	configuration	configuration	NOUN
ejpam-3007	524	20	.	.	PUNCT
ejpam-3007	525	1	journal	journal	NOUN
ejpam-3007	525	2	of	of	ADP
ejpam-3007	525	3	the	the	DET
ejpam-3007	525	4	franklin	franklin	PROPN
ejpam-3007	525	5	institute	institute	PROPN
ejpam-3007	525	6	,	,	PUNCT
ejpam-3007	525	7	vol	vol	NOUN
ejpam-3007	525	8	.	.	PROPN
ejpam-3007	525	9	351	351	NUM
ejpam-3007	525	10	,	,	PUNCT
ejpam-3007	525	11	issue	issue	NOUN
ejpam-3007	525	12	2	2	NUM
ejpam-3007	525	13	,	,	PUNCT
ejpam-3007	525	14	pp	pp	ADJ
ejpam-3007	525	15	.	.	PUNCT
ejpam-3007	525	16	667681	667681	NUM
ejpam-3007	525	17	,	,	PUNCT
ejpam-3007	525	18	2014	2014	NUM
ejpam-3007	525	19	.	.	PUNCT
ejpam-3007	526	1	[	[	X
ejpam-3007	526	2	23	23	NUM
ejpam-3007	526	3	]	]	X
ejpam-3007	526	4	f.	f.	PROPN
ejpam-3007	526	5	mebarek	mebarek	PROPN
ejpam-3007	526	6	-	-	PUNCT
ejpam-3007	526	7	oudina	oudina	PROPN
ejpam-3007	526	8	r.	r.	PROPN
ejpam-3007	526	9	bessah	bessah	PROPN
ejpam-3007	526	10	,	,	PUNCT
ejpam-3007	526	11	oscillatory	oscillatory	ADJ
ejpam-3007	526	12	magnetohydrodynamic	magnetohydrodynamic	ADJ
ejpam-3007	526	13	natural	natural	ADJ
ejpam-3007	526	14	convection	convection	NOUN
ejpam-3007	526	15	of	of	ADP
ejpam-3007	526	16	liquid	liquid	ADJ
ejpam-3007	526	17	metal	metal	NOUN
ejpam-3007	526	18	between	between	ADP
ejpam-3007	526	19	vertical	vertical	ADJ
ejpam-3007	526	20	coaxial	coaxial	ADJ
ejpam-3007	526	21	cylinders	cylinder	NOUN
ejpam-3007	526	22	,	,	PUNCT
ejpam-3007	526	23	j.	j.	PROPN
ejpam-3007	526	24	of	of	ADP
ejpam-3007	526	25	applied	apply	VERB
ejpam-3007	526	26	fluid	fluid	ADJ
ejpam-3007	526	27	mechanics	mechanic	NOUN
ejpam-3007	526	28	,	,	PUNCT
ejpam-3007	526	29	vol	vol	NOUN
ejpam-3007	526	30	.	.	NOUN
ejpam-3007	526	31	9	9	NUM
ejpam-3007	526	32	,	,	PUNCT
ejpam-3007	526	33	no	no	INTJ
ejpam-3007	526	34	.	.	NOUN
ejpam-3007	526	35	4	4	NUM
ejpam-3007	526	36	,	,	PUNCT
ejpam-3007	526	37	pp	pp	ADJ
ejpam-3007	526	38	.	.	PUNCT
ejpam-3007	527	1	1655	1655	NUM
ejpam-3007	527	2	-	-	SYM
ejpam-3007	527	3	1665	1665	NUM
ejpam-3007	527	4	,	,	PUNCT
ejpam-3007	527	5	2016	2016	NUM
ejpam-3007	527	6	.	.	PUNCT