id	sid	tid	token	lemma	pos
mdp.39015104955862	1	1	41	41	NUM
mdp.39015104955862	1	2	ad	ad	NOUN
mdp.39015104955862	1	3	-	-	PUNCT
mdp.39015104955862	1	4	a271	a271	PROPN
mdp.39015104955862	1	5	435	435	NUM
mdp.39015104955862	1	6	pl	pl	PROPN
mdp.39015104955862	1	7	-	-	PUNCT
mdp.39015104955862	1	8	tr-92	tr-92	NOUN
mdp.39015104955862	1	9	-	-	PUNCT
mdp.39015104955862	1	10	2325	2325	NUM
mdp.39015104955862	1	11	convergence	convergence	NOUN
mdp.39015104955862	1	12	of	of	ADP
mdp.39015104955862	1	13	the	the	DET
mdp.39015104955862	1	14	hermite	hermite	PROPN
mdp.39015104955862	1	15	wavelet	wavelet	PROPN
mdp.39015104955862	1	16	expansion	expansion	PROPN
mdp.39015104955862	1	17	g.	g.	PROPN
mdp.39015104955862	1	18	v.	v.	PROPN
mdp.39015104955862	1	19	h.	h.	PROPN
mdp.39015104955862	1	20	sandri	sandri	PROPN
mdp.39015104955862	1	21	boston	boston	PROPN
mdp.39015104955862	1	22	university	university	PROPN
mdp.39015104955862	1	23	college	college	PROPN
mdp.39015104955862	1	24	of	of	ADP
mdp.39015104955862	1	25	engineering	engineering	NOUN
mdp.39015104955862	1	26	and	and	CCONJ
mdp.39015104955862	1	27	center	center	NOUN
mdp.39015104955862	1	28	for	for	ADP
mdp.39015104955862	1	29	space	space	NOUN
mdp.39015104955862	1	30	physics	physics	PROPN
mdp.39015104955862	1	31	boston	boston	PROPN
mdp.39015104955862	1	32	,	,	PUNCT
mdp.39015104955862	1	33	ma	ma	PROPN
mdp.39015104955862	1	34	02215	02215	NUM
mdp.39015104955862	1	35	november	november	PROPN
mdp.39015104955862	1	36	1992	1992	NUM
mdp.39015104955862	1	37	final	final	ADJ
mdp.39015104955862	1	38	report	report	NOUN
mdp.39015104955862	1	39	1	1	NUM
mdp.39015104955862	1	40	november	november	PROPN
mdp.39015104955862	1	41	1988	1988	NUM
mdp.39015104955862	1	42	31	31	NUM
mdp.39015104955862	1	43	october	october	PROPN
mdp.39015104955862	1	44	1992	1992	NUM
mdp.39015104955862	1	45	phillips	phillip	NOUN
mdp.39015104955862	1	46	$	$	SYM
mdp.39015104955862	1	47	boratory	boratory	NOUN
mdp.39015104955862	1	48	approved	approve	VERB
mdp.39015104955862	1	49	for	for	ADP
mdp.39015104955862	1	50	public	public	ADJ
mdp.39015104955862	1	51	release	release	NOUN
mdp.39015104955862	1	52	;	;	PUNCT
mdp.39015104955862	1	53	distribution	distribution	NOUN
mdp.39015104955862	1	54	unlimited	unlimited	ADJ
mdp.39015104955862	1	55	dtic	dtic	ADJ
mdp.39015104955862	1	56	electe	electe	NOUN
mdp.39015104955862	1	57	oct	oct	PROPN
mdp.39015104955862	1	58	2	2	NUM
mdp.39015104955862	1	59	2	2	NUM
mdp.39015104955862	1	60	1993	1993	NUM
mdp.39015104955862	1	61	phillips	phillip	NOUN
mdp.39015104955862	1	62	laboratory	laboratory	PROPN
mdp.39015104955862	1	63	directorate	directorate	NOUN
mdp.39015104955862	1	64	of	of	ADP
mdp.39015104955862	1	65	geophysics	geophysic	NOUN
mdp.39015104955862	1	66	93	93	NUM
mdp.39015104955862	1	67	10	10	NUM
mdp.39015104955862	1	68	21	21	NUM
mdp.39015104955862	1	69	air	air	NOUN
mdp.39015104955862	1	70	force	force	NOUN
mdp.39015104955862	1	71	systems	systems	PROPN
mdp.39015104955862	1	72	command	command	PROPN
mdp.39015104955862	1	73	hanscom	hanscom	PROPN
mdp.39015104955862	1	74	air	air	PROPN
mdp.39015104955862	1	75	force	force	PROPN
mdp.39015104955862	1	76	base	base	PROPN
mdp.39015104955862	1	77	,	,	PUNCT
mdp.39015104955862	1	78	ma	ma	PROPN
mdp.39015104955862	1	79	01731	01731	NUM
mdp.39015104955862	1	80	-	-	SYM
mdp.39015104955862	1	81	5000	5000	NUM
mdp.39015104955862	1	82	93	93	NUM
mdp.39015104955862	1	83	-	-	SYM
mdp.39015104955862	1	84	25482	25482	NUM
mdp.39015104955862	1	85	d	d	NOUN
mdp.39015104955862	1	86	university	university	PROPN
mdp.39015104955862	1	87	of	of	ADP
mdp.39015104955862	1	88	michigan	michigan	PROPN
mdp.39015104955862	1	89	3	3	NUM
mdp.39015104955862	1	90	9015	9015	NUM
mdp.39015104955862	1	91	10495	10495	NUM
mdp.39015104955862	1	92	5862	5862	NUM
mdp.39015104955862	2	1	38115	38115	NUM
mdp.39015104955862	3	1	"	"	PUNCT
mdp.39015104955862	3	2	this	this	DET
mdp.39015104955862	3	3	technical	technical	ADJ
mdp.39015104955862	3	4	report	report	NOUN
mdp.39015104955862	3	5	has	have	AUX
mdp.39015104955862	3	6	been	be	AUX
mdp.39015104955862	3	7	reviewed	review	VERB
mdp.39015104955862	3	8	and	and	CCONJ
mdp.39015104955862	3	9	is	be	AUX
mdp.39015104955862	3	10	approved	approve	VERB
mdp.39015104955862	3	11	for	for	ADP
mdp.39015104955862	3	12	publication	publication	NOUN
mdp.39015104955862	3	13	"	"	PUNCT
mdp.39015104955862	3	14	arad	arad	PROPN
mdp.39015104955862	3	15	robert	robert	PROPN
mdp.39015104955862	3	16	r.	r.	PROPN
mdp.39015104955862	3	17	beland	beland	PROPN
mdp.39015104955862	3	18	contract	contract	PROPN
mdp.39015104955862	3	19	manager	manager	PROPN
mdp.39015104955862	3	20	beland	beland	PROPN
mdp.39015104955862	3	21	donald	donald	PROPN
mdp.39015104955862	3	22	&	&	CCONJ
mdp.39015104955862	3	23	bedo	bedo	PROPN
mdp.39015104955862	3	24	donald	donald	PROPN
mdp.39015104955862	3	25	e.	e.	PROPN
mdp.39015104955862	3	26	bedo	bedo	PROPN
mdp.39015104955862	3	27	branch	branch	PROPN
mdp.39015104955862	3	28	chief	chief	PROPN
mdp.39015104955862	3	29	roger	roger	PROPN
mdp.39015104955862	3	30	aiken	aiken	PROPN
mdp.39015104955862	3	31	sacul	sacul	PROPN
mdp.39015104955862	3	32	roger	roger	PROPN
mdp.39015104955862	3	33	van	van	PROPN
mdp.39015104955862	3	34	tassel	tassel	PROPN
mdp.39015104955862	3	35	division	division	NOUN
mdp.39015104955862	3	36	director	director	NOUN
mdp.39015104955862	3	37	ناست	ناست	PROPN
mdp.39015104955862	4	1	this	this	DET
mdp.39015104955862	4	2	report	report	NOUN
mdp.39015104955862	4	3	has	have	AUX
mdp.39015104955862	4	4	been	be	AUX
mdp.39015104955862	4	5	reviewed	review	VERB
mdp.39015104955862	4	6	by	by	ADP
mdp.39015104955862	4	7	the	the	DET
mdp.39015104955862	4	8	esd	esd	PROPN
mdp.39015104955862	4	9	public	public	PROPN
mdp.39015104955862	4	10	affairs	affair	NOUN
mdp.39015104955862	4	11	office	office	PROPN
mdp.39015104955862	4	12	(	(	PUNCT
mdp.39015104955862	4	13	pa	pa	PROPN
mdp.39015104955862	4	14	)	)	PUNCT
mdp.39015104955862	4	15	and	and	CCONJ
mdp.39015104955862	4	16	is	be	AUX
mdp.39015104955862	4	17	releasable	releasable	ADJ
mdp.39015104955862	4	18	to	to	ADP
mdp.39015104955862	4	19	the	the	DET
mdp.39015104955862	4	20	national	national	ADJ
mdp.39015104955862	4	21	technical	technical	ADJ
mdp.39015104955862	4	22	information	information	NOUN
mdp.39015104955862	4	23	service	service	NOUN
mdp.39015104955862	4	24	(	(	PUNCT
mdp.39015104955862	4	25	ntis	ntis	PROPN
mdp.39015104955862	4	26	)	)	PUNCT
mdp.39015104955862	4	27	.	.	PUNCT
mdp.39015104955862	5	1	qualified	qualified	ADJ
mdp.39015104955862	5	2	requestors	requestor	NOUN
mdp.39015104955862	5	3	may	may	AUX
mdp.39015104955862	5	4	obtain	obtain	VERB
mdp.39015104955862	5	5	additional	additional	ADJ
mdp.39015104955862	5	6	copies	copy	NOUN
mdp.39015104955862	5	7	from	from	ADP
mdp.39015104955862	5	8	the	the	DET
mdp.39015104955862	5	9	defense	defense	NOUN
mdp.39015104955862	5	10	technical	technical	ADJ
mdp.39015104955862	5	11	information	information	NOUN
mdp.39015104955862	5	12	center	center	NOUN
mdp.39015104955862	5	13	.	.	PUNCT
mdp.39015104955862	6	1	all	all	DET
mdp.39015104955862	6	2	others	other	NOUN
mdp.39015104955862	6	3	should	should	AUX
mdp.39015104955862	6	4	apply	apply	VERB
mdp.39015104955862	6	5	to	to	ADP
mdp.39015104955862	6	6	the	the	DET
mdp.39015104955862	6	7	national	national	ADJ
mdp.39015104955862	6	8	technical	technical	ADJ
mdp.39015104955862	6	9	information	information	NOUN
mdp.39015104955862	6	10	service	service	NOUN
mdp.39015104955862	6	11	.	.	PUNCT
mdp.39015104955862	7	1	if	if	SCONJ
mdp.39015104955862	7	2	your	your	PRON
mdp.39015104955862	7	3	address	address	NOUN
mdp.39015104955862	7	4	has	have	AUX
mdp.39015104955862	7	5	changed	change	VERB
mdp.39015104955862	7	6	,	,	PUNCT
mdp.39015104955862	7	7	or	or	CCONJ
mdp.39015104955862	7	8	if	if	SCONJ
mdp.39015104955862	7	9	you	you	PRON
mdp.39015104955862	7	10	wish	wish	VERB
mdp.39015104955862	7	11	to	to	PART
mdp.39015104955862	7	12	be	be	AUX
mdp.39015104955862	7	13	removed	remove	VERB
mdp.39015104955862	7	14	from	from	ADP
mdp.39015104955862	7	15	the	the	DET
mdp.39015104955862	7	16	mailing	mailing	NOUN
mdp.39015104955862	7	17	list	list	NOUN
mdp.39015104955862	7	18	,	,	PUNCT
mdp.39015104955862	7	19	or	or	CCONJ
mdp.39015104955862	7	20	if	if	SCONJ
mdp.39015104955862	7	21	the	the	DET
mdp.39015104955862	7	22	addressee	addressee	NOUN
mdp.39015104955862	7	23	is	be	AUX
mdp.39015104955862	7	24	no	no	ADV
mdp.39015104955862	7	25	longer	long	ADV
mdp.39015104955862	7	26	employed	employ	VERB
mdp.39015104955862	7	27	by	by	ADP
mdp.39015104955862	7	28	your	your	PRON
mdp.39015104955862	7	29	organization	organization	NOUN
mdp.39015104955862	7	30	,	,	PUNCT
mdp.39015104955862	7	31	please	please	INTJ
mdp.39015104955862	7	32	notify	notify	VERB
mdp.39015104955862	7	33	pl	pl	PROPN
mdp.39015104955862	7	34	/	/	SYM
mdp.39015104955862	7	35	tsi	tsi	PROPN
mdp.39015104955862	7	36	,	,	PUNCT
mdp.39015104955862	7	37	hanscom	hanscom	PROPN
mdp.39015104955862	7	38	afb	afb	PROPN
mdp.39015104955862	7	39	,	,	PUNCT
mdp.39015104955862	7	40	ma	ma	PROPN
mdp.39015104955862	7	41	01731	01731	NUM
mdp.39015104955862	7	42	-	-	SYM
mdp.39015104955862	7	43	5000	5000	NUM
mdp.39015104955862	7	44	.	.	PUNCT
mdp.39015104955862	8	1	this	this	PRON
mdp.39015104955862	8	2	will	will	AUX
mdp.39015104955862	8	3	assist	assist	VERB
mdp.39015104955862	8	4	us	we	PRON
mdp.39015104955862	8	5	in	in	ADP
mdp.39015104955862	8	6	maintaining	maintain	VERB
mdp.39015104955862	8	7	a	a	DET
mdp.39015104955862	8	8	current	current	ADJ
mdp.39015104955862	8	9	mailing	mailing	NOUN
mdp.39015104955862	8	10	list	list	NOUN
mdp.39015104955862	8	11	.	.	PUNCT
mdp.39015104955862	9	1	do	do	AUX
mdp.39015104955862	9	2	not	not	PART
mdp.39015104955862	9	3	return	return	VERB
mdp.39015104955862	9	4	copies	copy	NOUN
mdp.39015104955862	9	5	of	of	ADP
mdp.39015104955862	9	6	this	this	DET
mdp.39015104955862	9	7	report	report	NOUN
mdp.39015104955862	9	8	unless	unless	SCONJ
mdp.39015104955862	9	9	contractual	contractual	ADJ
mdp.39015104955862	9	10	obligations	obligation	NOUN
mdp.39015104955862	9	11	or	or	CCONJ
mdp.39015104955862	9	12	notices	notice	NOUN
mdp.39015104955862	9	13	on	on	ADP
mdp.39015104955862	9	14	a	a	DET
mdp.39015104955862	9	15	specific	specific	ADJ
mdp.39015104955862	9	16	document	document	NOUN
mdp.39015104955862	9	17	requires	require	VERB
mdp.39015104955862	9	18	that	that	SCONJ
mdp.39015104955862	9	19	it	it	PRON
mdp.39015104955862	9	20	be	be	AUX
mdp.39015104955862	9	21	returned	return	VERB
mdp.39015104955862	9	22	.	.	PUNCT
mdp.39015104955862	10	1	report	report	VERB
mdp.39015104955862	10	2	documentation	documentation	NOUN
mdp.39015104955862	10	3	page	page	NOUN
mdp.39015104955862	10	4	public	public	ADJ
mdp.39015104955862	10	5	reporting	reporting	NOUN
mdp.39015104955862	10	6	burden	burden	NOUN
mdp.39015104955862	10	7	for	for	ADP
mdp.39015104955862	10	8	this	this	DET
mdp.39015104955862	10	9	collection	collection	NOUN
mdp.39015104955862	10	10	of	of	ADP
mdp.39015104955862	10	11	information	information	NOUN
mdp.39015104955862	10	12	is	be	AUX
mdp.39015104955862	10	13	estimated	estimate	VERB
mdp.39015104955862	10	14	to	to	PART
mdp.39015104955862	10	15	average	average	VERB
mdp.39015104955862	10	16	1	1	NUM
mdp.39015104955862	10	17	hour	hour	NOUN
mdp.39015104955862	10	18	per	per	ADP
mdp.39015104955862	10	19	response	response	NOUN
mdp.39015104955862	10	20	,	,	PUNCT
mdp.39015104955862	10	21	including	include	VERB
mdp.39015104955862	10	22	the	the	DET
mdp.39015104955862	10	23	time	time	NOUN
mdp.39015104955862	10	24	for	for	ADP
mdp.39015104955862	10	25	reviewing	review	VERB
mdp.39015104955862	10	26	instructions	instruction	NOUN
mdp.39015104955862	10	27	,	,	PUNCT
mdp.39015104955862	10	28	searching	search	VERB
mdp.39015104955862	10	29	existing	exist	VERB
mdp.39015104955862	10	30	data	datum	NOUN
mdp.39015104955862	10	31	sources	source	NOUN
mdp.39015104955862	10	32	.	.	PUNCT
mdp.39015104955862	11	1	gathering	gather	VERB
mdp.39015104955862	11	2	and	and	CCONJ
mdp.39015104955862	11	3	maintaining	maintain	VERB
mdp.39015104955862	11	4	the	the	DET
mdp.39015104955862	11	5	data	datum	NOUN
mdp.39015104955862	11	6	needed	need	VERB
mdp.39015104955862	11	7	and	and	CCONJ
mdp.39015104955862	11	8	completing	complete	VERB
mdp.39015104955862	11	9	and	and	CCONJ
mdp.39015104955862	11	10	reviewing	review	VERB
mdp.39015104955862	11	11	the	the	DET
mdp.39015104955862	11	12	collection	collection	NOUN
mdp.39015104955862	11	13	of	of	ADP
mdp.39015104955862	11	14	information	information	NOUN
mdp.39015104955862	11	15	send	send	VERB
mdp.39015104955862	11	16	comments	comment	NOUN
mdp.39015104955862	11	17	regarding	regard	VERB
mdp.39015104955862	11	18	this	this	DET
mdp.39015104955862	11	19	burden	burden	NOUN
mdp.39015104955862	11	20	estimate	estimate	NOUN
mdp.39015104955862	11	21	or	or	CCONJ
mdp.39015104955862	11	22	any	any	DET
mdp.39015104955862	11	23	other	other	ADJ
mdp.39015104955862	11	24	aspect	aspect	NOUN
mdp.39015104955862	11	25	of	of	ADP
mdp.39015104955862	11	26	this	this	DET
mdp.39015104955862	11	27	collection	collection	NOUN
mdp.39015104955862	11	28	of	of	ADP
mdp.39015104955862	11	29	information	information	NOUN
mdp.39015104955862	11	30	,	,	PUNCT
mdp.39015104955862	11	31	including	include	VERB
mdp.39015104955862	11	32	suggestions	suggestion	NOUN
mdp.39015104955862	11	33	for	for	ADP
mdp.39015104955862	11	34	reducing	reduce	VERB
mdp.39015104955862	11	35	this	this	DET
mdp.39015104955862	11	36	burden	burden	NOUN
mdp.39015104955862	11	37	to	to	ADP
mdp.39015104955862	11	38	washington	washington	PROPN
mdp.39015104955862	11	39	headquarters	headquarters	PROPN
mdp.39015104955862	11	40	services	service	NOUN
mdp.39015104955862	11	41	.	.	PUNCT
mdp.39015104955862	12	1	directorate	directorate	VERB
mdp.39015104955862	12	2	for	for	ADP
mdp.39015104955862	12	3	information	information	NOUN
mdp.39015104955862	12	4	operations	operation	NOUN
mdp.39015104955862	12	5	and	and	CCONJ
mdp.39015104955862	12	6	reports	report	NOUN
mdp.39015104955862	12	7	,	,	PUNCT
mdp.39015104955862	12	8	1415	1415	NUM
mdp.39015104955862	12	9	jetterson	jetterson	PROPN
mdp.39015104955862	12	10	davis	davis	PROPN
mdp.39015104955862	12	11	highway	highway	PROPN
mdp.39015104955862	12	12	,	,	PUNCT
mdp.39015104955862	12	13	suite	suite	NOUN
mdp.39015104955862	12	14	1204	1204	NUM
mdp.39015104955862	12	15	,	,	PUNCT
mdp.39015104955862	12	16	arlington	arlington	PROPN
mdp.39015104955862	12	17	,	,	PUNCT
mdp.39015104955862	12	18	va	va	PROPN
mdp.39015104955862	12	19	22202	22202	NUM
mdp.39015104955862	12	20	-	-	SYM
mdp.39015104955862	12	21	4302	4302	NUM
mdp.39015104955862	12	22	,	,	PUNCT
mdp.39015104955862	12	23	and	and	CCONJ
mdp.39015104955862	12	24	to	to	ADP
mdp.39015104955862	12	25	the	the	DET
mdp.39015104955862	12	26	office	office	NOUN
mdp.39015104955862	12	27	of	of	ADP
mdp.39015104955862	12	28	management	management	NOUN
mdp.39015104955862	12	29	and	and	CCONJ
mdp.39015104955862	12	30	budget	budget	NOUN
mdp.39015104955862	12	31	.	.	PUNCT
mdp.39015104955862	12	32	paperwork	paperwork	NOUN
mdp.39015104955862	12	33	reduction	reduction	NOUN
mdp.39015104955862	12	34	project	project	NOUN
mdp.39015104955862	12	35	(	(	PUNCT
mdp.39015104955862	12	36	0704	0704	NUM
mdp.39015104955862	12	37	-	-	SYM
mdp.39015104955862	12	38	0188	0188	NUM
mdp.39015104955862	12	39	)	)	PUNCT
mdp.39015104955862	12	40	,	,	PUNCT
mdp.39015104955862	12	41	washington	washington	PROPN
mdp.39015104955862	12	42	,	,	PUNCT
mdp.39015104955862	12	43	dc	dc	PROPN
mdp.39015104955862	12	44	20503	20503	NUM
mdp.39015104955862	12	45	1	1	NUM
mdp.39015104955862	12	46	.	.	PUNCT
mdp.39015104955862	13	1	agency	agency	NOUN
mdp.39015104955862	13	2	use	use	NOUN
mdp.39015104955862	13	3	only	only	ADV
mdp.39015104955862	13	4	(	(	PUNCT
mdp.39015104955862	13	5	leave	leave	VERB
mdp.39015104955862	13	6	blank	blank	ADJ
mdp.39015104955862	13	7	)	)	PUNCT
mdp.39015104955862	13	8	2	2	NUM
mdp.39015104955862	13	9	.	.	PUNCT
mdp.39015104955862	14	1	report	report	VERB
mdp.39015104955862	14	2	date	date	NOUN
mdp.39015104955862	14	3	3	3	NUM
mdp.39015104955862	14	4	.	.	PUNCT
mdp.39015104955862	15	1	report	report	NOUN
mdp.39015104955862	15	2	type	type	NOUN
mdp.39015104955862	15	3	and	and	CCONJ
mdp.39015104955862	15	4	dates	date	NOUN
mdp.39015104955862	15	5	covered	cover	VERB
mdp.39015104955862	15	6	final	final	ADJ
mdp.39015104955862	15	7	.	.	PUNCT
mdp.39015104955862	16	1	nov	nov	PROPN
mdp.39015104955862	16	2	.	.	PROPN
mdp.39015104955862	16	3	november	november	PROPN
mdp.39015104955862	16	4	1992	1992	NUM
mdp.39015104955862	16	5	4	4	NUM
mdp.39015104955862	16	6	.	.	PUNCT
mdp.39015104955862	17	1	title	title	NOUN
mdp.39015104955862	17	2	and	and	CCONJ
mdp.39015104955862	17	3	subtitle	subtitle	NOUN
mdp.39015104955862	17	4	convergence	convergence	NOUN
mdp.39015104955862	17	5	of	of	ADP
mdp.39015104955862	17	6	the	the	DET
mdp.39015104955862	17	7	hermite	hermite	PROPN
mdp.39015104955862	17	8	wavelet	wavelet	PROPN
mdp.39015104955862	17	9	expansion	expansion	NOUN
mdp.39015104955862	17	10	6	6	NUM
mdp.39015104955862	17	11	.	.	X
mdp.39015104955862	18	1	author(s	author(s	NOUN
mdp.39015104955862	18	2	)	)	PUNCT
mdp.39015104955862	18	3	g.	g.	PROPN
mdp.39015104955862	18	4	v.	v.	PROPN
mdp.39015104955862	18	5	h.	h.	PROPN
mdp.39015104955862	18	6	sandri	sandri	PROPN
mdp.39015104955862	18	7	7	7	NUM
mdp.39015104955862	18	8	.	.	PUNCT
mdp.39015104955862	19	1	performing	perform	VERB
mdp.39015104955862	19	2	organization	organization	NOUN
mdp.39015104955862	19	3	name(s	name(s	NOUN
mdp.39015104955862	19	4	)	)	PUNCT
mdp.39015104955862	19	5	and	and	CCONJ
mdp.39015104955862	19	6	address(es	address(es	PROPN
mdp.39015104955862	19	7	)	)	PUNCT
mdp.39015104955862	19	8	boston	boston	PROPN
mdp.39015104955862	19	9	university	university	PROPN
mdp.39015104955862	19	10	college	college	PROPN
mdp.39015104955862	19	11	of	of	ADP
mdp.39015104955862	19	12	engineering	engineering	NOUN
mdp.39015104955862	19	13	and	and	CCONJ
mdp.39015104955862	19	14	center	center	NOUN
mdp.39015104955862	19	15	for	for	ADP
mdp.39015104955862	19	16	space	space	NOUN
mdp.39015104955862	19	17	physics	physics	PROPN
mdp.39015104955862	19	18	boston	boston	PROPN
mdp.39015104955862	19	19	,	,	PUNCT
mdp.39015104955862	19	20	ma	ma	PROPN
mdp.39015104955862	19	21	02215	02215	NUM
mdp.39015104955862	19	22	9	9	NUM
mdp.39015104955862	19	23	.	.	PUNCT
mdp.39015104955862	20	1	sponsoring	sponsor	VERB
mdp.39015104955862	20	2	/	/	SYM
mdp.39015104955862	20	3	monitoring	monitoring	NOUN
mdp.39015104955862	20	4	agency	agency	NOUN
mdp.39015104955862	20	5	name(s	name(s	NOUN
mdp.39015104955862	20	6	)	)	PUNCT
mdp.39015104955862	20	7	and	and	CCONJ
mdp.39015104955862	20	8	address(es	address(es	PROPN
mdp.39015104955862	20	9	)	)	PUNCT
mdp.39015104955862	20	10	phillips	phillips	PROPN
mdp.39015104955862	20	11	laboratory	laboratory	PROPN
mdp.39015104955862	20	12	hanscom	hanscom	PROPN
mdp.39015104955862	20	13	afb	afb	PROPN
mdp.39015104955862	20	14	,	,	PUNCT
mdp.39015104955862	20	15	ma	ma	PROPN
mdp.39015104955862	20	16	01731	01731	NUM
mdp.39015104955862	20	17	-	-	SYM
mdp.39015104955862	20	18	5000	5000	NUM
mdp.39015104955862	20	19	contract	contract	NOUN
mdp.39015104955862	20	20	manager	manager	NOUN
mdp.39015104955862	20	21	:	:	PUNCT
mdp.39015104955862	20	22	robert	robert	PROPN
mdp.39015104955862	20	23	beland	beland	PROPN
mdp.39015104955862	20	24	/	/	SYM
mdp.39015104955862	20	25	gpoa	gpoa	PROPN
mdp.39015104955862	20	26	11	11	NUM
mdp.39015104955862	20	27	.	.	PUNCT
mdp.39015104955862	21	1	supplementary	supplementary	PROPN
mdp.39015104955862	21	2	notes	note	NOUN
mdp.39015104955862	21	3	12a	12a	PROPN
mdp.39015104955862	21	4	.	.	PUNCT
mdp.39015104955862	22	1	distribution	distribution	NOUN
mdp.39015104955862	22	2	/	/	SYM
mdp.39015104955862	22	3	availability	availability	NOUN
mdp.39015104955862	22	4	statement	statement	NOUN
mdp.39015104955862	22	5	approved	approve	VERB
mdp.39015104955862	22	6	for	for	ADP
mdp.39015104955862	22	7	public	public	ADJ
mdp.39015104955862	22	8	release	release	NOUN
mdp.39015104955862	22	9	;	;	PUNCT
mdp.39015104955862	22	10	distribution	distribution	NOUN
mdp.39015104955862	22	11	unlimited	unlimited	ADJ
mdp.39015104955862	22	12	.	.	PUNCT
mdp.39015104955862	23	1	13	13	X
mdp.39015104955862	23	2	.	.	X
mdp.39015104955862	24	1	abstract	abstract	ADJ
mdp.39015104955862	24	2	(	(	PUNCT
mdp.39015104955862	24	3	maximum	maximum	ADJ
mdp.39015104955862	24	4	200	200	NUM
mdp.39015104955862	24	5	words	word	NOUN
mdp.39015104955862	24	6	)	)	PUNCT
mdp.39015104955862	24	7	14	14	NUM
mdp.39015104955862	24	8	.	.	PUNCT
mdp.39015104955862	25	1	subject	subject	ADJ
mdp.39015104955862	25	2	terms	term	NOUN
mdp.39015104955862	25	3	unclassified	unclassifie	VERB
mdp.39015104955862	25	4	nsn	nsn	PROPN
mdp.39015104955862	25	5	7540	7540	NUM
mdp.39015104955862	25	6	-	-	SYM
mdp.39015104955862	25	7	01	01	NUM
mdp.39015104955862	25	8	-	-	PUNCT
mdp.39015104955862	25	9	280	280	NUM
mdp.39015104955862	25	10	-	-	SYM
mdp.39015104955862	25	11	5500	5500	NUM
mdp.39015104955862	25	12	form	form	NOUN
mdp.39015104955862	25	13	approved	approve	VERB
mdp.39015104955862	25	14	omb	omb	NOUN
mdp.39015104955862	25	15	no	no	NOUN
mdp.39015104955862	25	16	.	.	PROPN
mdp.39015104955862	25	17	0704	0704	NUM
mdp.39015104955862	25	18	-	-	SYM
mdp.39015104955862	25	19	0188	0188	NUM
mdp.39015104955862	25	20	of	of	ADP
mdp.39015104955862	25	21	abstract	abstract	ADJ
mdp.39015104955862	25	22	unclassified	unclassified	ADJ
mdp.39015104955862	25	23	1	1	NUM
mdp.39015104955862	25	24	,	,	PUNCT
mdp.39015104955862	25	25	1988	1988	NUM
mdp.39015104955862	25	26	to	to	ADP
mdp.39015104955862	25	27	oct	oct	PROPN
mdp.39015104955862	25	28	.	.	PROPN
mdp.39015104955862	25	29	31	31	NUM
mdp.39015104955862	25	30	,	,	PUNCT
mdp.39015104955862	25	31	1992	1992	NUM
mdp.39015104955862	25	32	5	5	NUM
mdp.39015104955862	25	33	.	.	PUNCT
mdp.39015104955862	26	1	funding	funding	NOUN
mdp.39015104955862	26	2	numbers	number	NOUN
mdp.39015104955862	26	3	trail	trail	VERB
mdp.39015104955862	26	4	pe	pe	PRON
mdp.39015104955862	26	5	61101f	61101f	NUM
mdp.39015104955862	26	6	pr	pr	NOUN
mdp.39015104955862	26	7	7670	7670	NUM
mdp.39015104955862	26	8	ta	ta	ADP
mdp.39015104955862	26	9	15	15	NUM
mdp.39015104955862	26	10	wu	wu	PROPN
mdp.39015104955862	26	11	ar	ar	PROPN
mdp.39015104955862	26	12	contract	contract	PROPN
mdp.39015104955862	26	13	f19628	f19628	PROPN
mdp.39015104955862	26	14	-	-	PUNCT
mdp.39015104955862	26	15	88	88	NUM
mdp.39015104955862	26	16	-	-	PUNCT
mdp.39015104955862	26	17	kin	kin	NOUN
mdp.39015104955862	26	18	this	this	DET
mdp.39015104955862	26	19	report	report	NOUN
mdp.39015104955862	26	20	we	we	PRON
mdp.39015104955862	26	21	summarize	summarize	VERB
mdp.39015104955862	26	22	the	the	DET
mdp.39015104955862	26	23	research	research	NOUN
mdp.39015104955862	26	24	carried	carry	VERB
mdp.39015104955862	26	25	out	out	ADP
mdp.39015104955862	26	26	under	under	ADP
mdp.39015104955862	26	27	this	this	DET
mdp.39015104955862	26	28	contract	contract	NOUN
mdp.39015104955862	26	29	on	on	ADP
mdp.39015104955862	26	30	the	the	DET
mdp.39015104955862	26	31	chaos	chaos	NOUN
mdp.39015104955862	26	32	dynamics	dynamic	NOUN
mdp.39015104955862	26	33	anlysis	anlysis	ADV
mdp.39015104955862	26	34	of	of	ADP
mdp.39015104955862	26	35	the	the	DET
mdp.39015104955862	26	36	free	free	ADJ
mdp.39015104955862	26	37	sheared	sheared	ADJ
mdp.39015104955862	26	38	atmosphere	atmosphere	NOUN
mdp.39015104955862	26	39	.	.	PUNCT
mdp.39015104955862	27	1	our	our	PRON
mdp.39015104955862	27	2	approach	approach	NOUN
mdp.39015104955862	27	3	is	be	AUX
mdp.39015104955862	27	4	to	to	PART
mdp.39015104955862	27	5	expand	expand	VERB
mdp.39015104955862	27	6	the	the	DET
mdp.39015104955862	27	7	fluid	fluid	ADJ
mdp.39015104955862	27	8	equations	equation	NOUN
mdp.39015104955862	27	9	into	into	ADP
mdp.39015104955862	27	10	finite	finite	ADJ
mdp.39015104955862	27	11	energy	energy	NOUN
mdp.39015104955862	27	12	modes	mode	NOUN
mdp.39015104955862	27	13	rather	rather	ADV
mdp.39015104955862	27	14	then	then	ADV
mdp.39015104955862	27	15	in	in	ADP
mdp.39015104955862	27	16	the	the	DET
mdp.39015104955862	27	17	conventional	conventional	ADJ
mdp.39015104955862	27	18	fourier	fourier	NOUN
mdp.39015104955862	27	19	analysis	analysis	NOUN
mdp.39015104955862	27	20	.	.	PUNCT
mdp.39015104955862	28	1	we	we	PRON
mdp.39015104955862	28	2	prove	prove	VERB
mdp.39015104955862	28	3	rigorously	rigorously	ADV
mdp.39015104955862	28	4	that	that	SCONJ
mdp.39015104955862	28	5	our	our	PRON
mdp.39015104955862	28	6	expansion	expansion	NOUN
mdp.39015104955862	28	7	method	method	NOUN
mdp.39015104955862	28	8	has	have	VERB
mdp.39015104955862	28	9	the	the	DET
mdp.39015104955862	28	10	required	require	VERB
mdp.39015104955862	28	11	convergence	convergence	NOUN
mdp.39015104955862	28	12	properties	property	NOUN
mdp.39015104955862	28	13	to	to	PART
mdp.39015104955862	28	14	ensure	ensure	VERB
mdp.39015104955862	28	15	a	a	DET
mdp.39015104955862	28	16	satisfactory	satisfactory	ADJ
mdp.39015104955862	28	17	physical	physical	ADJ
mdp.39015104955862	28	18	interpretation	interpretation	NOUN
mdp.39015104955862	28	19	of	of	ADP
mdp.39015104955862	28	20	the	the	DET
mdp.39015104955862	28	21	results	result	NOUN
mdp.39015104955862	28	22	.	.	PUNCT
mdp.39015104955862	29	1	for	for	ADP
mdp.39015104955862	29	2	the	the	DET
mdp.39015104955862	29	3	taylor	taylor	PROPN
mdp.39015104955862	29	4	-	-	PUNCT
mdp.39015104955862	29	5	dyson	dyson	NOUN
mdp.39015104955862	29	6	atmosphere	atmosphere	NOUN
mdp.39015104955862	29	7	,	,	PUNCT
mdp.39015104955862	29	8	our	our	PRON
mdp.39015104955862	29	9	analysis	analysis	NOUN
mdp.39015104955862	29	10	,	,	PUNCT
mdp.39015104955862	29	11	like	like	ADP
mdp.39015104955862	29	12	the	the	DET
mdp.39015104955862	29	13	fourier	fourier	NOUN
mdp.39015104955862	29	14	analysis	analysis	NOUN
mdp.39015104955862	29	15	yields	yield	VERB
mdp.39015104955862	29	16	no	no	DET
mdp.39015104955862	29	17	unstable	unstable	ADJ
mdp.39015104955862	29	18	modes	mode	NOUN
mdp.39015104955862	29	19	.	.	PUNCT
mdp.39015104955862	30	1	8	8	X
mdp.39015104955862	30	2	.	.	X
mdp.39015104955862	30	3	performing	perform	VERB
mdp.39015104955862	30	4	organization	organization	NOUN
mdp.39015104955862	30	5	report	report	NOUN
mdp.39015104955862	30	6	number	number	NOUN
mdp.39015104955862	30	7	taylor	taylor	PROPN
mdp.39015104955862	30	8	-	-	PUNCT
mdp.39015104955862	30	9	dyson	dyson	NOUN
mdp.39015104955862	30	10	atmosphere	atmosphere	NOUN
mdp.39015104955862	30	11	,	,	PUNCT
mdp.39015104955862	30	12	hermite	hermite	PROPN
mdp.39015104955862	30	13	wavelet	wavelet	PROPN
mdp.39015104955862	30	14	expansion	expansion	NOUN
mdp.39015104955862	30	15	.	.	PUNCT
mdp.39015104955862	31	1	17	17	NUM
mdp.39015104955862	31	2	.	.	PUNCT
mdp.39015104955862	31	3	security	security	NOUN
mdp.39015104955862	31	4	classification	classification	NOUN
mdp.39015104955862	31	5	18	18	NUM
mdp.39015104955862	31	6	.	.	PUNCT
mdp.39015104955862	32	1	security	security	NOUN
mdp.39015104955862	32	2	classification	classification	NOUN
mdp.39015104955862	32	3	19	19	NUM
mdp.39015104955862	32	4	.	.	PUNCT
mdp.39015104955862	33	1	security	security	NOUN
mdp.39015104955862	33	2	classification	classification	NOUN
mdp.39015104955862	33	3	of	of	ADP
mdp.39015104955862	33	4	report	report	NOUN
mdp.39015104955862	33	5	of	of	ADP
mdp.39015104955862	33	6	this	this	DET
mdp.39015104955862	33	7	page	page	NOUN
mdp.39015104955862	33	8	unclassified	unclassifie	VERB
mdp.39015104955862	33	9	10	10	NUM
mdp.39015104955862	33	10	.	.	PUNCT
mdp.39015104955862	34	1	sponsoring	sponsor	VERB
mdp.39015104955862	34	2	/	/	SYM
mdp.39015104955862	34	3	monitoring	monitor	VERB
mdp.39015104955862	34	4	agency	agency	NOUN
mdp.39015104955862	34	5	report	report	NOUN
mdp.39015104955862	34	6	number	number	NOUN
mdp.39015104955862	34	7	pl	pl	NOUN
mdp.39015104955862	34	8	-	-	PUNCT
mdp.39015104955862	34	9	tr-92	tr-92	NOUN
mdp.39015104955862	34	10	-	-	PUNCT
mdp.39015104955862	34	11	2325	2325	NUM
mdp.39015104955862	34	12	12b	12b	NOUN
mdp.39015104955862	34	13	.	.	PUNCT
mdp.39015104955862	35	1	distribution	distribution	NOUN
mdp.39015104955862	35	2	code	code	NOUN
mdp.39015104955862	35	3	0017	0017	NUM
mdp.39015104955862	35	4	15	15	NUM
mdp.39015104955862	35	5	.	.	PUNCT
mdp.39015104955862	36	1	number	number	NOUN
mdp.39015104955862	36	2	of	of	ADP
mdp.39015104955862	36	3	pages	page	NOUN
mdp.39015104955862	36	4	38	38	NUM
mdp.39015104955862	36	5	16	16	NUM
mdp.39015104955862	36	6	.	.	PUNCT
mdp.39015104955862	37	1	frice	frice	NOUN
mdp.39015104955862	37	2	code	code	PROPN
mdp.39015104955862	37	3	20	20	NUM
mdp.39015104955862	37	4	.	.	PUNCT
mdp.39015104955862	38	1	limitation	limitation	NOUN
mdp.39015104955862	38	2	of	of	ADP
mdp.39015104955862	38	3	abstract	abstract	ADJ
mdp.39015104955862	38	4	sar	sar	PROPN
mdp.39015104955862	38	5	standard	standard	ADJ
mdp.39015104955862	38	6	form	form	NOUN
mdp.39015104955862	38	7	298	298	NUM
mdp.39015104955862	38	8	(	(	PUNCT
mdp.39015104955862	38	9	rev	rev	VERB
mdp.39015104955862	38	10	2	2	NUM
mdp.39015104955862	38	11	-	-	SYM
mdp.39015104955862	38	12	89	89	NUM
mdp.39015104955862	38	13	)	)	PUNCT
mdp.39015104955862	38	14	prescribed	prescribe	VERB
mdp.39015104955862	38	15	by	by	ADP
mdp.39015104955862	38	16	ali	ali	PROPN
mdp.39015104955862	38	17	std	std	PROPN
mdp.39015104955862	38	18	259	259	NUM
mdp.39015104955862	38	19	-	-	SYM
mdp.39015104955862	38	20	18	18	NUM
mdp.39015104955862	38	21	240	240	NUM
mdp.39015104955862	38	22	2	2	NUM
mdp.39015104955862	38	23	introduction	introduction	NOUN
mdp.39015104955862	38	24	2	2	NUM
mdp.39015104955862	38	25	.	.	PUNCT
mdp.39015104955862	38	26	mathematical	mathematical	ADJ
mdp.39015104955862	38	27	framework	framework	NOUN
mdp.39015104955862	38	28	1	1	NUM
mdp.39015104955862	38	29	.	.	PUNCT
mdp.39015104955862	39	1	ત	ત	PROPN
mdp.39015104955862	39	2	3	3	NUM
mdp.39015104955862	39	3	.	.	PROPN
mdp.39015104955862	39	4	4	4	NUM
mdp.39015104955862	39	5	.	.	NUM
mdp.39015104955862	39	6	5	5	NUM
mdp.39015104955862	39	7	.	.	PUNCT
mdp.39015104955862	39	8	definitions	definition	NOUN
mdp.39015104955862	39	9	and	and	CCONJ
mdp.39015104955862	39	10	notation	notation	NOUN
mdp.39015104955862	39	11	characterization	characterization	NOUN
mdp.39015104955862	39	12	of	of	ADP
mdp.39015104955862	39	13	hyperdistributions	hyperdistribution	NOUN
mdp.39015104955862	39	14	classes	class	NOUN
mdp.39015104955862	39	15	d({m	d({m	PROPN
mdp.39015104955862	39	16	}	}	PUNCT
mdp.39015104955862	39	17	)	)	PUNCT
mdp.39015104955862	39	18	and	and	CCONJ
mdp.39015104955862	39	19	the	the	DET
mdp.39015104955862	39	20	diffusion	diffusion	NOUN
mdp.39015104955862	39	21	group	group	NOUN
mdp.39015104955862	39	22	6	6	NUM
mdp.39015104955862	39	23	.	.	PUNCT
mdp.39015104955862	40	1	summary	summary	NOUN
mdp.39015104955862	40	2	and	and	CCONJ
mdp.39015104955862	40	3	conclusions	conclusion	NOUN
mdp.39015104955862	40	4	references	reference	VERB
mdp.39015104955862	40	5	iii	iii	X
mdp.39015104955862	40	6	accesion	accesion	NOUN
mdp.39015104955862	40	7	for	for	ADP
mdp.39015104955862	40	8	ntis	ntis	PROPN
mdp.39015104955862	40	9	crasi	crasi	PROPN
mdp.39015104955862	40	10	dtic	dtic	PROPN
mdp.39015104955862	40	11	tas	tas	PROPN
mdp.39015104955862	40	12	chama	chama	PROPN
mdp.39015104955862	40	13	ced	ced	PROPN
mdp.39015104955862	40	14	j	j	PROPN
mdp.39015104955862	40	15	by	by	ADP
mdp.39015104955862	40	16	caton	caton	PROPN
mdp.39015104955862	40	17	distributor	distributor	PROPN
mdp.39015104955862	40	18	!	!	PUNCT
mdp.39015104955862	41	1	cist	cist	PROPN
mdp.39015104955862	41	2	avarieti	avarieti	X
mdp.39015104955862	41	3	|a-11	|a-11	X
mdp.39015104955862	41	4	contents	content	NOUN
mdp.39015104955862	41	5	500	500	NUM
mdp.39015104955862	41	6	dedes	dede	NOUN
mdp.39015104955862	41	7	avid	avid	ADJ
mdp.39015104955862	41	8	and	and	CCONJ
mdp.39015104955862	41	9	or	or	CCONJ
mdp.39015104955862	41	10	special	special	ADJ
mdp.39015104955862	41	11	1	1	NUM
mdp.39015104955862	41	12	2	2	NUM
mdp.39015104955862	41	13	~	~	PUNCT
mdp.39015104955862	41	14	~	~	PUNCT
mdp.39015104955862	41	15	7	7	NUM
mdp.39015104955862	41	16	11	11	NUM
mdp.39015104955862	41	17	21	21	NUM
mdp.39015104955862	41	18	22	22	NUM
mdp.39015104955862	41	19	332323	332323	NUM
mdp.39015104955862	41	20	31	31	NUM
mdp.39015104955862	41	21	3	3	NUM
mdp.39015104955862	41	22	כי	כי	ADP
mdp.39015104955862	41	23	1	1	NUM
mdp.39015104955862	41	24	introduction	introduction	NOUN
mdp.39015104955862	41	25	in	in	ADP
mdp.39015104955862	41	26	this	this	DET
mdp.39015104955862	41	27	contract	contract	NOUN
mdp.39015104955862	41	28	we	we	PRON
mdp.39015104955862	41	29	have	have	AUX
mdp.39015104955862	41	30	first	first	ADV
mdp.39015104955862	41	31	investigated	investigate	VERB
mdp.39015104955862	41	32	a	a	DET
mdp.39015104955862	41	33	phenomenological	phenomenological	ADJ
mdp.39015104955862	41	34	approach	approach	NOUN
mdp.39015104955862	41	35	to	to	ADP
mdp.39015104955862	41	36	a	a	DET
mdp.39015104955862	41	37	chaos	chaos	NOUN
mdp.39015104955862	41	38	dynamical	dynamical	ADJ
mdp.39015104955862	41	39	analysis	analysis	NOUN
mdp.39015104955862	41	40	at	at	ADP
mdp.39015104955862	41	41	the	the	DET
mdp.39015104955862	41	42	free	free	ADJ
mdp.39015104955862	41	43	sheered	sheered	ADJ
mdp.39015104955862	41	44	atmosphere	atmosphere	NOUN
mdp.39015104955862	41	45	.	.	PUNCT
mdp.39015104955862	42	1	we	we	PRON
mdp.39015104955862	42	2	have	have	AUX
mdp.39015104955862	42	3	then	then	ADV
mdp.39015104955862	42	4	turned	turn	VERB
mdp.39015104955862	42	5	to	to	ADP
mdp.39015104955862	42	6	a	a	DET
mdp.39015104955862	42	7	theoretical	theoretical	ADJ
mdp.39015104955862	42	8	phase	phase	NOUN
mdp.39015104955862	42	9	in	in	ADP
mdp.39015104955862	42	10	which	which	PRON
mdp.39015104955862	42	11	we	we	PRON
mdp.39015104955862	42	12	have	have	AUX
mdp.39015104955862	42	13	developed	develop	VERB
mdp.39015104955862	42	14	a	a	DET
mdp.39015104955862	42	15	novel	novel	ADJ
mdp.39015104955862	42	16	expansion	expansion	NOUN
mdp.39015104955862	42	17	of	of	ADP
mdp.39015104955862	42	18	the	the	DET
mdp.39015104955862	42	19	equations	equation	NOUN
mdp.39015104955862	42	20	for	for	ADP
mdp.39015104955862	42	21	the	the	DET
mdp.39015104955862	42	22	free	free	ADJ
mdp.39015104955862	42	23	sheared	shear	VERB
mdp.39015104955862	42	24	atmosphere	atmosphere	NOUN
mdp.39015104955862	42	25	which	which	PRON
mdp.39015104955862	42	26	hinge	hinge	VERB
mdp.39015104955862	42	27	on	on	ADP
mdp.39015104955862	42	28	properties	property	NOUN
mdp.39015104955862	42	29	of	of	ADP
mdp.39015104955862	42	30	hermite	hermite	ADJ
mdp.39015104955862	42	31	polynomials	polynomial	NOUN
mdp.39015104955862	42	32	and	and	CCONJ
mdp.39015104955862	42	33	the	the	DET
mdp.39015104955862	42	34	gaussian	gaussian	ADJ
mdp.39015104955862	42	35	function	function	NOUN
mdp.39015104955862	42	36	.	.	PUNCT
mdp.39015104955862	43	1	in	in	ADP
mdp.39015104955862	43	2	this	this	DET
mdp.39015104955862	43	3	final	final	ADJ
mdp.39015104955862	43	4	scientific	scientific	ADJ
mdp.39015104955862	43	5	report	report	NOUN
mdp.39015104955862	43	6	we	we	PRON
mdp.39015104955862	43	7	give	give	VERB
mdp.39015104955862	43	8	the	the	DET
mdp.39015104955862	43	9	conditions	condition	NOUN
mdp.39015104955862	43	10	for	for	ADP
mdp.39015104955862	43	11	the	the	DET
mdp.39015104955862	43	12	basic	basic	ADJ
mdp.39015104955862	43	13	expansions	expansion	NOUN
mdp.39015104955862	43	14	used	use	VERB
mdp.39015104955862	43	15	during	during	ADP
mdp.39015104955862	43	16	our	our	PRON
mdp.39015104955862	43	17	analysis	analysis	NOUN
mdp.39015104955862	43	18	to	to	PART
mdp.39015104955862	43	19	converge	converge	VERB
mdp.39015104955862	43	20	.	.	PUNCT
mdp.39015104955862	44	1	more	more	ADV
mdp.39015104955862	44	2	specifically	specifically	ADV
mdp.39015104955862	44	3	,	,	PUNCT
mdp.39015104955862	44	4	the	the	DET
mdp.39015104955862	44	5	necessary	necessary	ADJ
mdp.39015104955862	44	6	and	and	CCONJ
mdp.39015104955862	44	7	sufficient	sufficient	ADJ
mdp.39015104955862	44	8	conditions	condition	NOUN
mdp.39015104955862	44	9	are	be	AUX
mdp.39015104955862	44	10	given	give	VERB
mdp.39015104955862	44	11	for	for	ADP
mdp.39015104955862	44	12	the	the	DET
mdp.39015104955862	44	13	quasianalytic	quasianalytic	ADJ
mdp.39015104955862	44	14	function	function	NOUN
mdp.39015104955862	44	15	classes	class	NOUN
mdp.39015104955862	44	16	d({m	d({m	PROPN
mdp.39015104955862	44	17	}	}	PUNCT
mdp.39015104955862	44	18	)	)	PUNCT
mdp.39015104955862	44	19	and	and	CCONJ
mdp.39015104955862	44	20	the	the	DET
mdp.39015104955862	44	21	corresponding	correspond	VERB
mdp.39015104955862	44	22	classes	class	NOUN
mdp.39015104955862	44	23	of	of	ADP
mdp.39015104955862	44	24	distributions	distribution	NOUN
mdp.39015104955862	44	25	d'({m	d'({m	ADV
mdp.39015104955862	44	26	}	}	PUNCT
mdp.39015104955862	44	27	)	)	PUNCT
mdp.39015104955862	44	28	to	to	PART
mdp.39015104955862	44	29	be	be	AUX
mdp.39015104955862	44	30	invariant	invariant	ADJ
mdp.39015104955862	44	31	with	with	ADP
mdp.39015104955862	44	32	respect	respect	NOUN
mdp.39015104955862	44	33	to	to	ADP
mdp.39015104955862	44	34	the	the	DET
mdp.39015104955862	44	35	complex	complex	ADJ
mdp.39015104955862	44	36	-	-	PUNCT
mdp.39015104955862	44	37	time	time	NOUN
mdp.39015104955862	44	38	diffusion	diffusion	NOUN
mdp.39015104955862	44	39	group	group	NOUN
mdp.39015104955862	44	40	∞	∞	X
mdp.39015104955862	44	41	zk	zk	PROPN
mdp.39015104955862	44	42	82k	82k	NOUN
mdp.39015104955862	44	43	u₁	u₁	PROPN
mdp.39015104955862	44	44	=	=	SYM
mdp.39015104955862	44	45	σ	σ	PROPN
mdp.39015104955862	44	46	uz	uz	PROPN
mdp.39015104955862	44	47	k=0	k=0	PROPN
mdp.39015104955862	44	48	x	x	PUNCT
mdp.39015104955862	44	49	k	k	X
mdp.39015104955862	44	50	!	!	PUNCT
mdp.39015104955862	44	51	əx²k	əx²k	SPACE
mdp.39015104955862	44	52	'	'	PUNCT
mdp.39015104955862	44	53	≈	≈	PROPN
mdp.39015104955862	44	54	є	є	PROPN
mdp.39015104955862	44	55	r¹	r¹	PROPN
mdp.39015104955862	44	56	,	,	PUNCT
mdp.39015104955862	44	57	z	z	PROPN
mdp.39015104955862	44	58	є	є	PROPN
mdp.39015104955862	44	59	c.	c.	PROPN
mdp.39015104955862	44	60	in	in	ADP
mdp.39015104955862	44	61	addition	addition	NOUN
mdp.39015104955862	44	62	,	,	PUNCT
mdp.39015104955862	44	63	the	the	DET
mdp.39015104955862	44	64	properties	property	NOUN
mdp.39015104955862	44	65	of	of	ADP
mdp.39015104955862	44	66	hyperdistributions	hyperdistribution	NOUN
mdp.39015104955862	44	67	moments	moment	NOUN
mdp.39015104955862	44	68	r	r	X
mdp.39015104955862	44	69	=	=	SYM
mdp.39015104955862	44	70	σ	σ	PROPN
mdp.39015104955862	44	71	ακδία	ακδία	NUM
mdp.39015104955862	44	72	)	)	PUNCT
mdp.39015104955862	44	73	(	(	PUNCT
mdp.39015104955862	44	74	4	4	X
mdp.39015104955862	44	75	)	)	PUNCT
mdp.39015104955862	44	76	k=0	k=0	NOUN
mdp.39015104955862	44	77	are	be	AUX
mdp.39015104955862	44	78	studied	study	VERB
mdp.39015104955862	44	79	.	.	PUNCT
mdp.39015104955862	45	1	it	it	PRON
mdp.39015104955862	45	2	is	be	AUX
mdp.39015104955862	45	3	shown	show	VERB
mdp.39015104955862	45	4	that	that	SCONJ
mdp.39015104955862	45	5	hyperdistributions	hyperdistribution	NOUN
mdp.39015104955862	45	6	are	be	AUX
mdp.39015104955862	45	7	characterized	characterize	VERB
mdp.39015104955862	45	8	by	by	ADP
mdp.39015104955862	45	9	the	the	DET
mdp.39015104955862	45	10	behavior	behavior	NOUN
mdp.39015104955862	45	11	of	of	ADP
mdp.39015104955862	45	12	their	their	PRON
mdp.39015104955862	45	13	µk(t	µk(t	SPACE
mdp.39015104955862	45	14	)	)	PUNCT
mdp.39015104955862	45	15	=	=	X
mdp.39015104955862	45	16	г(x	г(x	X
mdp.39015104955862	45	17	*	*	PUNCT
mdp.39015104955862	45	18	)	)	PUNCT
mdp.39015104955862	45	19	.	.	PUNCT
mdp.39015104955862	46	1	we	we	PRON
mdp.39015104955862	46	2	conclude	conclude	VERB
mdp.39015104955862	46	3	that	that	SCONJ
mdp.39015104955862	46	4	expansions	expansion	NOUN
mdp.39015104955862	46	5	based	base	VERB
mdp.39015104955862	46	6	on	on	ADP
mdp.39015104955862	46	7	hermite	hermite	ADJ
mdp.39015104955862	46	8	polynomials	polynomial	NOUN
mdp.39015104955862	46	9	multipied	multipie	VERB
mdp.39015104955862	46	10	by	by	ADP
mdp.39015104955862	46	11	a	a	DET
mdp.39015104955862	46	12	gaussian	gaussian	NOUN
mdp.39015104955862	46	13	have	have	VERB
mdp.39015104955862	46	14	a	a	DET
mdp.39015104955862	46	15	proper	proper	ADJ
mdp.39015104955862	46	16	limiting	limit	VERB
mdp.39015104955862	46	17	behaviour	behaviour	NOUN
mdp.39015104955862	46	18	.	.	PUNCT
mdp.39015104955862	47	1	the	the	DET
mdp.39015104955862	47	2	objective	objective	NOUN
mdp.39015104955862	47	3	to	to	PART
mdp.39015104955862	47	4	give	give	VERB
mdp.39015104955862	47	5	complete	complete	ADJ
mdp.39015104955862	47	6	mathematical	mathematical	ADJ
mdp.39015104955862	47	7	foundations	foundation	NOUN
mdp.39015104955862	47	8	for	for	ADP
mdp.39015104955862	47	9	our	our	PRON
mdp.39015104955862	47	10	analysis	analysis	NOUN
mdp.39015104955862	47	11	has	have	AUX
mdp.39015104955862	47	12	been	be	AUX
mdp.39015104955862	47	13	accomplished	accomplish	VERB
mdp.39015104955862	47	14	.	.	PUNCT
mdp.39015104955862	48	1	1	1	NUM
mdp.39015104955862	48	2	1	1	NUM
mdp.39015104955862	48	3	2	2	NUM
mdp.39015104955862	48	4	mathematical	mathematical	ADJ
mdp.39015104955862	48	5	framework	framework	NOUN
mdp.39015104955862	48	6	many	many	ADJ
mdp.39015104955862	48	7	physical	physical	ADJ
mdp.39015104955862	48	8	processes	process	NOUN
mdp.39015104955862	48	9	have	have	VERB
mdp.39015104955862	48	10	diffusive	diffusive	ADJ
mdp.39015104955862	48	11	character	character	NOUN
mdp.39015104955862	48	12	:	:	PUNCT
mdp.39015104955862	48	13	the	the	DET
mdp.39015104955862	48	14	spreading	spreading	NOUN
mdp.39015104955862	48	15	of	of	ADP
mdp.39015104955862	48	16	smoke	smoke	NOUN
mdp.39015104955862	48	17	in	in	ADP
mdp.39015104955862	48	18	air	air	NOUN
mdp.39015104955862	48	19	,	,	PUNCT
mdp.39015104955862	48	20	the	the	DET
mdp.39015104955862	48	21	behavior	behavior	NOUN
mdp.39015104955862	48	22	of	of	ADP
mdp.39015104955862	48	23	the	the	DET
mdp.39015104955862	48	24	temperature	temperature	NOUN
mdp.39015104955862	48	25	in	in	ADP
mdp.39015104955862	48	26	a	a	DET
mdp.39015104955862	48	27	material	material	ADJ
mdp.39015104955862	48	28	body	body	NOUN
mdp.39015104955862	48	29	,	,	PUNCT
mdp.39015104955862	48	30	and	and	CCONJ
mdp.39015104955862	48	31	the	the	DET
mdp.39015104955862	48	32	vorticity	vorticity	NOUN
mdp.39015104955862	48	33	in	in	ADP
mdp.39015104955862	48	34	a	a	DET
mdp.39015104955862	48	35	fluid	fluid	ADJ
mdp.39015104955862	48	36	flow	flow	NOUN
mdp.39015104955862	48	37	are	be	AUX
mdp.39015104955862	48	38	examples	example	NOUN
mdp.39015104955862	48	39	illustrating	illustrate	VERB
mdp.39015104955862	48	40	this	this	DET
mdp.39015104955862	48	41	feature	feature	NOUN
mdp.39015104955862	48	42	.	.	PUNCT
mdp.39015104955862	49	1	the	the	DET
mdp.39015104955862	49	2	engineer	engineer	NOUN
mdp.39015104955862	49	3	's	's	PART
mdp.39015104955862	49	4	notion	notion	NOUN
mdp.39015104955862	49	5	of	of	ADP
mdp.39015104955862	49	6	blurring	blur	VERB
mdp.39015104955862	49	7	and	and	CCONJ
mdp.39015104955862	49	8	filtering	filtering	NOUN
mdp.39015104955862	49	9	have	have	VERB
mdp.39015104955862	49	10	similar	similar	ADJ
mdp.39015104955862	49	11	nature	nature	NOUN
mdp.39015104955862	49	12	.	.	PUNCT
mdp.39015104955862	50	1	the	the	DET
mdp.39015104955862	50	2	one	one	NUM
mdp.39015104955862	50	3	-	-	PUNCT
mdp.39015104955862	50	4	dimensional	dimensional	ADJ
mdp.39015104955862	50	5	diffusion	diffusion	NOUN
mdp.39015104955862	50	6	processes	process	NOUN
mdp.39015104955862	50	7	are	be	AUX
mdp.39015104955862	50	8	governed	govern	VERB
mdp.39015104955862	50	9	by	by	ADP
mdp.39015104955862	50	10	the	the	DET
mdp.39015104955862	50	11	heat	heat	NOUN
mdp.39015104955862	50	12	equation	equation	NOUN
mdp.39015104955862	50	13	jv(x	jv(x	PROPN
mdp.39015104955862	50	14	,	,	PUNCT
mdp.39015104955862	50	15	t	t	PROPN
mdp.39015104955862	50	16	)	)	PUNCT
mdp.39015104955862	50	17	_	_	NUM
mdp.39015104955862	51	1	0²¥(x	0²¥(x	NOUN
mdp.39015104955862	51	2	,	,	PUNCT
mdp.39015104955862	51	3	t	t	PROPN
mdp.39015104955862	51	4	)	)	PUNCT
mdp.39015104955862	51	5	at	at	ADP
mdp.39015104955862	51	6	8x2	8x2	NUM
mdp.39015104955862	51	7	in	in	ADP
mdp.39015104955862	51	8	order	order	NOUN
mdp.39015104955862	51	9	to	to	PART
mdp.39015104955862	51	10	determine	determine	VERB
mdp.39015104955862	51	11	the	the	DET
mdp.39015104955862	51	12	behavior	behavior	NOUN
mdp.39015104955862	51	13	of	of	ADP
mdp.39015104955862	51	14	the	the	DET
mdp.39015104955862	51	15	physical	physical	ADJ
mdp.39015104955862	51	16	quantity	quantity	NOUN
mdp.39015104955862	51	17	v	v	NOUN
mdp.39015104955862	51	18	under	under	ADP
mdp.39015104955862	51	19	consideration	consideration	NOUN
mdp.39015104955862	51	20	,	,	PUNCT
mdp.39015104955862	51	21	provided	provide	VERB
mdp.39015104955862	51	22	its	its	PRON
mdp.39015104955862	51	23	initial	initial	ADJ
mdp.39015104955862	51	24	value	value	NOUN
mdp.39015104955862	51	25	y(x	y(x	PROPN
mdp.39015104955862	51	26	,	,	PUNCT
mdp.39015104955862	51	27	0	0	NUM
mdp.39015104955862	51	28	)	)	PUNCT
mdp.39015104955862	51	29	=	=	PROPN
mdp.39015104955862	51	30	x(x	x(x	PROPN
mdp.39015104955862	51	31	)	)	PUNCT
mdp.39015104955862	51	32	,	,	PUNCT
mdp.39015104955862	51	33	x	x	PUNCT
mdp.39015104955862	51	34	є	є	CCONJ
mdp.39015104955862	51	35	r¹	r¹	PROPN
mdp.39015104955862	51	36	,	,	PUNCT
mdp.39015104955862	51	37	is	be	AUX
mdp.39015104955862	51	38	given	give	VERB
mdp.39015104955862	51	39	,	,	PUNCT
mdp.39015104955862	51	40	we	we	PRON
mdp.39015104955862	51	41	have	have	VERB
mdp.39015104955862	51	42	to	to	PART
mdp.39015104955862	51	43	solve	solve	VERB
mdp.39015104955862	51	44	the	the	DET
mdp.39015104955862	51	45	cauchy	cauchy	ADJ
mdp.39015104955862	51	46	problem	problem	NOUN
mdp.39015104955862	51	47	(	(	PUNCT
mdp.39015104955862	51	48	1	1	X
mdp.39015104955862	51	49	)	)	PUNCT
mdp.39015104955862	51	50	(	(	PUNCT
mdp.39015104955862	51	51	2	2	NUM
mdp.39015104955862	51	52	)	)	PUNCT
mdp.39015104955862	51	53	for	for	ADP
mdp.39015104955862	51	54	the	the	DET
mdp.39015104955862	51	55	heat	heat	NOUN
mdp.39015104955862	51	56	equation	equation	NOUN
mdp.39015104955862	51	57	.	.	PUNCT
mdp.39015104955862	52	1	it	it	PRON
mdp.39015104955862	52	2	is	be	AUX
mdp.39015104955862	52	3	well	well	ADV
mdp.39015104955862	52	4	-	-	PUNCT
mdp.39015104955862	52	5	known	know	VERB
mdp.39015104955862	52	6	that	that	SCONJ
mdp.39015104955862	52	7	the	the	DET
mdp.39015104955862	52	8	solution	solution	NOUN
mdp.39015104955862	52	9	of	of	ADP
mdp.39015104955862	52	10	the	the	DET
mdp.39015104955862	52	11	cauchy	cauchy	ADJ
mdp.39015104955862	52	12	problem	problem	NOUN
mdp.39015104955862	52	13	(	(	PUNCT
mdp.39015104955862	52	14	1	1	X
mdp.39015104955862	52	15	)	)	PUNCT
mdp.39015104955862	52	16	(	(	PUNCT
mdp.39015104955862	52	17	2	2	NUM
mdp.39015104955862	52	18	)	)	PUNCT
mdp.39015104955862	52	19	with	with	ADP
mdp.39015104955862	52	20	appropriately	appropriately	ADV
mdp.39015104955862	52	21	chosen	choose	VERB
mdp.39015104955862	52	22	initial	initial	ADJ
mdp.39015104955862	52	23	condition	condition	NOUN
mdp.39015104955862	52	24	is	be	AUX
mdp.39015104955862	52	25	given	give	VERB
mdp.39015104955862	52	26	by	by	ADP
mdp.39015104955862	52	27	poisson	poisson	PROPN
mdp.39015104955862	52	28	's	's	PART
mdp.39015104955862	52	29	formula	formula	NOUN
mdp.39015104955862	52	30	4(x	4(x	NUM
mdp.39015104955862	52	31	,	,	PUNCT
mdp.39015104955862	52	32	t	t	PROPN
mdp.39015104955862	52	33	)	)	PUNCT
mdp.39015104955862	52	34	=	=	VERB
mdp.39015104955862	52	35	√√a=	√√a=	PROPN
mdp.39015104955862	52	36	√1	√1	PROPN
mdp.39015104955862	52	37	.	.	PUNCT
mdp.39015104955862	53	1	p(3	p(3	PROPN
mdp.39015104955862	53	2	)	)	PUNCT
mdp.39015104955862	54	1	e(=x	e(=x	NOUN
mdp.39015104955862	54	2	)	)	PUNCT
mdp.39015104955862	54	3	"	"	PUNCT
mdp.39015104955862	54	4	dy	dy	PROPN
mdp.39015104955862	54	5	,	,	PUNCT
mdp.39015104955862	54	6	1	1	NUM
mdp.39015104955862	54	7	4πt	4πt	NOUN
mdp.39015104955862	54	8	jv(x	jv(x	NOUN
mdp.39015104955862	54	9	,	,	PUNCT
mdp.39015104955862	54	10	t	t	PROPN
mdp.39015104955862	54	11	)	)	PUNCT
mdp.39015104955862	54	12	at	at	ADP
mdp.39015104955862	54	13	≈	≈	PROPN
mdp.39015104955862	54	14	є	є	PROPN
mdp.39015104955862	54	15	r',t	r',t	PROPN
mdp.39015104955862	54	16	>	>	PUNCT
mdp.39015104955862	54	17	0	0	NUM
mdp.39015104955862	54	18	.	.	PUNCT
mdp.39015104955862	55	1	g²y(x	g²y(x	PROPN
mdp.39015104955862	55	2	,	,	PUNCT
mdp.39015104955862	55	3	t	t	PROPN
mdp.39015104955862	55	4	)	)	PUNCT
mdp.39015104955862	55	5	,	,	PUNCT
mdp.39015104955862	55	6	მუ2	მუ2	NOUN
mdp.39015104955862	55	7	(	(	PUNCT
mdp.39015104955862	55	8	3	3	X
mdp.39015104955862	55	9	)	)	PUNCT
mdp.39015104955862	55	10	the	the	DET
mdp.39015104955862	55	11	following	follow	VERB
mdp.39015104955862	55	12	interpretation	interpretation	NOUN
mdp.39015104955862	55	13	of	of	ADP
mdp.39015104955862	55	14	formula	formula	NOUN
mdp.39015104955862	55	15	(	(	PUNCT
mdp.39015104955862	55	16	3	3	X
mdp.39015104955862	55	17	)	)	PUNCT
mdp.39015104955862	55	18	is	be	AUX
mdp.39015104955862	55	19	possible	possible	ADJ
mdp.39015104955862	55	20	.	.	PUNCT
mdp.39015104955862	56	1	we	we	PRON
mdp.39015104955862	56	2	get	get	VERB
mdp.39015104955862	56	3	the	the	DET
mdp.39015104955862	56	4	solution	solution	NOUN
mdp.39015104955862	56	5	(	(	PUNCT
mdp.39015104955862	56	6	x	x	PROPN
mdp.39015104955862	56	7	,	,	PUNCT
mdp.39015104955862	56	8	t	t	PROPN
mdp.39015104955862	56	9	)	)	PUNCT
mdp.39015104955862	56	10	as	as	ADP
mdp.39015104955862	56	11	a	a	DET
mdp.39015104955862	56	12	result	result	NOUN
mdp.39015104955862	56	13	of	of	ADP
mdp.39015104955862	56	14	filtering	filter	VERB
mdp.39015104955862	56	15	the	the	DET
mdp.39015104955862	56	16	given	give	VERB
mdp.39015104955862	56	17	data	datum	NOUN
mdp.39015104955862	56	18	y	y	PROPN
mdp.39015104955862	56	19	through	through	ADP
mdp.39015104955862	56	20	a	a	DET
mdp.39015104955862	56	21	gassian	gassian	ADJ
mdp.39015104955862	56	22	filter	filter	NOUN
mdp.39015104955862	56	23	of	of	ADP
mdp.39015104955862	56	24	width	width	NOUN
mdp.39015104955862	56	25	√t	√t	SPACE
mdp.39015104955862	56	26	.	.	PUNCT
mdp.39015104955862	57	1	suppose	suppose	VERB
mdp.39015104955862	57	2	we	we	PRON
mdp.39015104955862	57	3	would	would	AUX
mdp.39015104955862	57	4	like	like	VERB
mdp.39015104955862	57	5	to	to	PART
mdp.39015104955862	57	6	reverse	reverse	VERB
mdp.39015104955862	57	7	the	the	DET
mdp.39015104955862	57	8	process	process	NOUN
mdp.39015104955862	57	9	of	of	ADP
mdp.39015104955862	57	10	filtering	filtering	PROPN
mdp.39015104955862	57	11	.	.	PUNCT
mdp.39015104955862	58	1	this	this	PRON
mdp.39015104955862	58	2	is	be	AUX
mdp.39015104955862	58	3	important	important	ADJ
mdp.39015104955862	58	4	,	,	PUNCT
mdp.39015104955862	58	5	for	for	ADP
mdp.39015104955862	58	6	example	example	NOUN
mdp.39015104955862	58	7	,	,	PUNCT
mdp.39015104955862	58	8	when	when	SCONJ
mdp.39015104955862	58	9	we	we	PRON
mdp.39015104955862	58	10	are	be	AUX
mdp.39015104955862	58	11	concerned	concerned	ADJ
mdp.39015104955862	58	12	with	with	ADP
mdp.39015104955862	58	13	the	the	DET
mdp.39015104955862	58	14	problem	problem	NOUN
mdp.39015104955862	58	15	of	of	ADP
mdp.39015104955862	58	16	reconstructing	reconstruct	VERB
mdp.39015104955862	58	17	sharp	sharp	ADJ
mdp.39015104955862	58	18	images	image	NOUN
mdp.39015104955862	58	19	from	from	ADP
mdp.39015104955862	58	20	degraded	degraded	ADJ
mdp.39015104955862	58	21	pictures	picture	NOUN
mdp.39015104955862	58	22	.	.	PUNCT
mdp.39015104955862	59	1	it	it	PRON
mdp.39015104955862	59	2	is	be	AUX
mdp.39015104955862	59	3	clear	clear	ADJ
mdp.39015104955862	59	4	that	that	SCONJ
mdp.39015104955862	59	5	the	the	DET
mdp.39015104955862	59	6	inverse	inverse	ADJ
mdp.39015104955862	59	7	filtering	filtering	NOUN
mdp.39015104955862	59	8	is	be	AUX
mdp.39015104955862	59	9	described	describe	VERB
mdp.39015104955862	59	10	by	by	ADP
mdp.39015104955862	59	11	the	the	DET
mdp.39015104955862	59	12	inverse	inverse	ADJ
mdp.39015104955862	59	13	heat	heat	NOUN
mdp.39015104955862	59	14	equation	equation	NOUN
mdp.39015104955862	59	15	(	(	PUNCT
mdp.39015104955862	59	16	1	1	X
mdp.39015104955862	59	17	)	)	PUNCT
mdp.39015104955862	59	18	≈	≈	PROPN
mdp.39015104955862	60	1	€	€	SYM
mdp.39015104955862	60	2	r¹,t	r¹,t	PROPN
mdp.39015104955862	60	3	>	>	X
mdp.39015104955862	60	4	0	0	NUM
mdp.39015104955862	60	5	.	.	PUNCT
mdp.39015104955862	61	1	≈	≈	PROPN
mdp.39015104955862	61	2	€	€	PROPN
mdp.39015104955862	61	3	r¹	r¹	PROPN
mdp.39015104955862	61	4	,	,	PUNCT
mdp.39015104955862	61	5	t	t	PROPN
mdp.39015104955862	61	6	>	>	SYM
mdp.39015104955862	61	7	0	0	NUM
mdp.39015104955862	61	8	.	.	PUNCT
mdp.39015104955862	62	1	(	(	PUNCT
mdp.39015104955862	62	2	2	2	X
mdp.39015104955862	62	3	)	)	PUNCT
mdp.39015104955862	62	4	(	(	PUNCT
mdp.39015104955862	62	5	4	4	NUM
mdp.39015104955862	62	6	)	)	PUNCT
mdp.39015104955862	62	7	2	2	NUM
mdp.39015104955862	63	1	it	it	PRON
mdp.39015104955862	63	2	is	be	AUX
mdp.39015104955862	63	3	possible	possible	ADJ
mdp.39015104955862	63	4	to	to	PART
mdp.39015104955862	63	5	incorporate	incorporate	VERB
mdp.39015104955862	63	6	the	the	DET
mdp.39015104955862	63	7	heat	heat	NOUN
mdp.39015104955862	63	8	equation	equation	NOUN
mdp.39015104955862	63	9	(	(	PUNCT
mdp.39015104955862	63	10	1	1	NUM
mdp.39015104955862	63	11	)	)	PUNCT
mdp.39015104955862	63	12	,	,	PUNCT
mdp.39015104955862	63	13	the	the	DET
mdp.39015104955862	63	14	inverse	inverse	ADJ
mdp.39015104955862	63	15	heat	heat	NOUN
mdp.39015104955862	63	16	equation	equation	NOUN
mdp.39015104955862	63	17	(	(	PUNCT
mdp.39015104955862	63	18	4	4	NUM
mdp.39015104955862	63	19	)	)	PUNCT
mdp.39015104955862	63	20	,	,	PUNCT
mdp.39015104955862	63	21	and	and	CCONJ
mdp.39015104955862	63	22	the	the	DET
mdp.39015104955862	63	23	schrödinger	schrödinger	ADJ
mdp.39015104955862	63	24	equation	equation	NOUN
mdp.39015104955862	63	25	ov	ov	INTJ
mdp.39015104955862	63	26	(	(	PUNCT
mdp.39015104955862	63	27	z	z	PROPN
mdp.39015104955862	63	28	,	,	PUNCT
mdp.39015104955862	63	29	t	t	PROPN
mdp.39015104955862	63	30	)	)	PUNCT
mdp.39015104955862	63	31	,	,	PUNCT
mdp.39015104955862	63	32	0²	0²	NUM
mdp.39015104955862	63	33	v	v	NOUN
mdp.39015104955862	63	34	(	(	PUNCT
mdp.39015104955862	63	35	z	z	PROPN
mdp.39015104955862	63	36	,	,	PUNCT
mdp.39015104955862	63	37	t	t	PROPN
mdp.39015104955862	63	38	)	)	PUNCT
mdp.39015104955862	63	39	,	,	PUNCT
mdp.39015104955862	63	40	=	=	VERB
mdp.39015104955862	63	41	at	at	ADP
mdp.39015104955862	63	42	მე2	მე2	PUNCT
mdp.39015104955862	63	43	which	which	PRON
mdp.39015104955862	63	44	describes	describe	VERB
mdp.39015104955862	63	45	the	the	DET
mdp.39015104955862	63	46	one	one	NUM
mdp.39015104955862	63	47	-	-	PUNCT
mdp.39015104955862	63	48	dimensional	dimensional	ADJ
mdp.39015104955862	63	49	motion	motion	NOUN
mdp.39015104955862	63	50	of	of	ADP
mdp.39015104955862	63	51	a	a	DET
mdp.39015104955862	63	52	free	free	ADJ
mdp.39015104955862	63	53	particle	particle	NOUN
mdp.39015104955862	63	54	in	in	ADP
mdp.39015104955862	63	55	quantum	quantum	NOUN
mdp.39015104955862	63	56	mechanics	mechanic	NOUN
mdp.39015104955862	63	57	,	,	PUNCT
mdp.39015104955862	63	58	into	into	ADP
mdp.39015104955862	63	59	the	the	DET
mdp.39015104955862	63	60	so	so	ADV
mdp.39015104955862	63	61	-	-	PUNCT
mdp.39015104955862	63	62	called	call	VERB
mdp.39015104955862	63	63	complex	complex	ADJ
mdp.39015104955862	63	64	-	-	PUNCT
mdp.39015104955862	63	65	time	time	NOUN
mdp.39015104955862	63	66	diffusion	diffusion	NOUN
mdp.39015104955862	63	67	equation	equation	NOUN
mdp.39015104955862	63	68	jy(x	jy(x	SPACE
mdp.39015104955862	63	69	,	,	PUNCT
mdp.39015104955862	63	70	z	z	PROPN
mdp.39015104955862	63	71	)	)	PUNCT
mdp.39015104955862	63	72	_	_	PUNCT
mdp.39015104955862	63	73	_	_	PUNCT
mdp.39015104955862	64	1	ə²y(x	ə²y(x	PROPN
mdp.39015104955862	64	2	,	,	PUNCT
mdp.39015104955862	64	3	z	z	PROPN
mdp.39015104955862	64	4	)	)	PUNCT
mdp.39015104955862	64	5	əz	əz	NOUN
mdp.39015104955862	64	6	მუ2	მუ2	NOUN
mdp.39015104955862	64	7	consider	consider	VERB
mdp.39015104955862	64	8	now	now	ADV
mdp.39015104955862	64	9	the	the	DET
mdp.39015104955862	64	10	following	follow	VERB
mdp.39015104955862	64	11	formal	formal	ADJ
mdp.39015104955862	64	12	semi	semi	NOUN
mdp.39015104955862	64	13	-	-	NOUN
mdp.39015104955862	64	14	group	group	NOUN
mdp.39015104955862	64	15	of	of	ADP
mdp.39015104955862	64	16	operators	operator	NOUN
mdp.39015104955862	64	17	u₁	u₁	PROPN
mdp.39015104955862	64	18	=	=	VERB
mdp.39015104955862	64	19	∞	∞	X
mdp.39015104955862	64	20	tk	tk	PROPN
mdp.39015104955862	64	21	82k	82k	VERB
mdp.39015104955862	64	22	σ	σ	NOUN
mdp.39015104955862	64	23	k=0	k=0	PROPN
mdp.39015104955862	64	24	u₁	u₁	PROPN
mdp.39015104955862	64	25	=	=	PROPN
mdp.39015104955862	64	26	e	e	X
mdp.39015104955862	64	27	'	'	PROPN
mdp.39015104955862	64	28	,	,	PUNCT
mdp.39015104955862	64	29	(	(	PUNCT
mdp.39015104955862	64	30	the	the	DET
mdp.39015104955862	64	31	diffusion	diffusion	NOUN
mdp.39015104955862	64	32	semi	semi	NOUN
mdp.39015104955862	64	33	-	-	NOUN
mdp.39015104955862	64	34	group	group	NOUN
mdp.39015104955862	64	35	)	)	PUNCT
mdp.39015104955862	64	36	.	.	PUNCT
mdp.39015104955862	65	1	it	it	PRON
mdp.39015104955862	65	2	can	can	AUX
mdp.39015104955862	65	3	be	be	AUX
mdp.39015104955862	65	4	easily	easily	ADV
mdp.39015104955862	65	5	seen	see	VERB
mdp.39015104955862	65	6	[	[	X
mdp.39015104955862	65	7	6	6	X
mdp.39015104955862	65	8	]	]	PUNCT
mdp.39015104955862	65	9	that	that	SCONJ
mdp.39015104955862	65	10	the	the	DET
mdp.39015104955862	65	11	formula	formula	NOUN
mdp.39015104955862	65	12	¥	¥	SYM
mdp.39015104955862	65	13	(	(	PUNCT
mdp.39015104955862	65	14	x	x	PROPN
mdp.39015104955862	65	15	,	,	PUNCT
mdp.39015104955862	65	16	t	t	PROPN
mdp.39015104955862	65	17	)	)	PUNCT
mdp.39015104955862	65	18	=	=	X
mdp.39015104955862	65	19	u₁y(x	u₁y(x	PROPN
mdp.39015104955862	65	20	)	)	PUNCT
mdp.39015104955862	65	21	,	,	PUNCT
mdp.39015104955862	65	22	≈	≈	PROPN
mdp.39015104955862	65	23	є	є	ADP
mdp.39015104955862	65	24	r¹‚t	r¹‚t	NOUN
mdp.39015104955862	65	25	>	>	SYM
mdp.39015104955862	65	26	0	0	NUM
mdp.39015104955862	65	27	defines	define	VERB
mdp.39015104955862	65	28	the	the	DET
mdp.39015104955862	65	29	formal	formal	ADJ
mdp.39015104955862	65	30	solution	solution	NOUN
mdp.39015104955862	65	31	of	of	ADP
mdp.39015104955862	65	32	the	the	DET
mdp.39015104955862	65	33	cauchy	cauchy	ADJ
mdp.39015104955862	65	34	problem	problem	NOUN
mdp.39015104955862	65	35	(	(	PUNCT
mdp.39015104955862	65	36	1	1	X
mdp.39015104955862	65	37	)	)	PUNCT
mdp.39015104955862	65	38	–	–	PUNCT
mdp.39015104955862	65	39	(	(	PUNCT
mdp.39015104955862	65	40	2	2	NUM
mdp.39015104955862	65	41	)	)	PUNCT
mdp.39015104955862	65	42	.	.	PUNCT
mdp.39015104955862	66	1	using	use	VERB
mdp.39015104955862	66	2	the	the	DET
mdp.39015104955862	66	3	taylor	taylor	PROPN
mdp.39015104955862	66	4	expansion	expansion	NOUN
mdp.39015104955862	66	5	of	of	ADP
mdp.39015104955862	66	6	the	the	DET
mdp.39015104955862	66	7	function	function	NOUN
mdp.39015104955862	66	8	etu	etu	PROPN
mdp.39015104955862	66	9	,	,	PUNCT
mdp.39015104955862	66	10	u	u	PROPN
mdp.39015104955862	66	11	€	€	SYM
mdp.39015104955862	66	12	r¹	r¹	ADV
mdp.39015104955862	66	13	in	in	ADP
mdp.39015104955862	66	14	(	(	PUNCT
mdp.39015104955862	66	15	6	6	NUM
mdp.39015104955862	66	16	)	)	PUNCT
mdp.39015104955862	66	17	,	,	PUNCT
mdp.39015104955862	66	18	we	we	PRON
mdp.39015104955862	66	19	can	can	AUX
mdp.39015104955862	66	20	represent	represent	VERB
mdp.39015104955862	66	21	{	{	PUNCT
mdp.39015104955862	66	22	u₁	u₁	NOUN
mdp.39015104955862	66	23	}	}	PUNCT
mdp.39015104955862	66	24	as	as	ADP
mdp.39015104955862	66	25	a	a	DET
mdp.39015104955862	66	26	semi	semi	NOUN
mdp.39015104955862	66	27	-	-	NOUN
mdp.39015104955862	66	28	group	group	NOUN
mdp.39015104955862	66	29	of	of	ADP
mdp.39015104955862	66	30	differential	differential	ADJ
mdp.39015104955862	66	31	operators	operator	NOUN
mdp.39015104955862	66	32	of	of	ADP
mdp.39015104955862	66	33	infinite	infinite	ADJ
mdp.39015104955862	66	34	order	order	PROPN
mdp.39015104955862	66	35	k	k	PROPN
mdp.39015104955862	66	36	!	!	PUNCT
mdp.39015104955862	66	37	ox²k	ox²k	X
mdp.39015104955862	66	38	'	'	PUNCT
mdp.39015104955862	66	39	,	,	PUNCT
mdp.39015104955862	66	40	=	=	PROPN
mdp.39015104955862	66	41	σ	σ	PROPN
mdp.39015104955862	66	42	k=0	k=0	PROPN
mdp.39015104955862	66	43	x	x	PUNCT
mdp.39015104955862	66	44	є	є	ADP
mdp.39015104955862	66	45	r¹‚t	r¹‚t	CCONJ
mdp.39015104955862	66	46	є	є	ADJ
mdp.39015104955862	66	47	r¹.	r¹.	NOUN
mdp.39015104955862	66	48	მ2k	მ2k	PROPN
mdp.39015104955862	67	1	k	k	X
mdp.39015104955862	67	2	!	!	PUNCT
mdp.39015104955862	67	3	jx²k	jx²k	SPACE
mdp.39015104955862	67	4	'	'	PUNCT
mdp.39015104955862	67	5	≈	≈	PROPN
mdp.39015104955862	67	6	є	є	PROPN
mdp.39015104955862	67	7	r¹	r¹	PROPN
mdp.39015104955862	67	8	,	,	PUNCT
mdp.39015104955862	67	9	z	z	PROPN
mdp.39015104955862	67	10	є	є	PROPN
mdp.39015104955862	67	11	c.	c.	PROPN
mdp.39015104955862	67	12	t>0	t>0	PROPN
mdp.39015104955862	67	13	t	t	PROPN
mdp.39015104955862	67	14	>	>	X
mdp.39015104955862	67	15	0	0	NUM
mdp.39015104955862	67	16	.	.	PUNCT
mdp.39015104955862	68	1	(	(	PUNCT
mdp.39015104955862	68	2	5	5	X
mdp.39015104955862	68	3	)	)	PUNCT
mdp.39015104955862	68	4	if	if	SCONJ
mdp.39015104955862	68	5	we	we	PRON
mdp.39015104955862	68	6	put	put	VERB
mdp.39015104955862	68	7	a	a	DET
mdp.39015104955862	68	8	complex	complex	ADJ
mdp.39015104955862	68	9	number	number	NOUN
mdp.39015104955862	68	10	z	z	PROPN
mdp.39015104955862	68	11	ec	ec	PROPN
mdp.39015104955862	68	12	instead	instead	ADV
mdp.39015104955862	68	13	of	of	ADP
mdp.39015104955862	68	14	t	t	PROPN
mdp.39015104955862	68	15	in	in	ADP
mdp.39015104955862	68	16	(	(	PUNCT
mdp.39015104955862	68	17	7	7	NUM
mdp.39015104955862	68	18	)	)	PUNCT
mdp.39015104955862	68	19	,	,	PUNCT
mdp.39015104955862	68	20	we	we	PRON
mdp.39015104955862	68	21	obtain	obtain	VERB
mdp.39015104955862	68	22	the	the	DET
mdp.39015104955862	68	23	complex	complex	ADJ
mdp.39015104955862	68	24	-	-	PUNCT
mdp.39015104955862	68	25	time	time	NOUN
mdp.39015104955862	68	26	diffusion	diffusion	NOUN
mdp.39015104955862	68	27	group	group	NOUN
mdp.39015104955862	68	28	of	of	ADP
mdp.39015104955862	68	29	operators	operator	NOUN
mdp.39015104955862	68	30	(	(	PUNCT
mdp.39015104955862	68	31	6	6	X
mdp.39015104955862	68	32	)	)	PUNCT
mdp.39015104955862	68	33	zє	zє	NOUN
mdp.39015104955862	68	34	c.	c.	PROPN
mdp.39015104955862	68	35	(	(	PUNCT
mdp.39015104955862	68	36	7	7	X
mdp.39015104955862	68	37	)	)	PUNCT
mdp.39015104955862	68	38	(	(	PUNCT
mdp.39015104955862	68	39	8)	8)	NUM
mdp.39015104955862	68	40	the	the	DET
mdp.39015104955862	68	41	group	group	NOUN
mdp.39015104955862	68	42	{	{	PUNCT
mdp.39015104955862	68	43	u₂	u₂	PROPN
mdp.39015104955862	68	44	}	}	PUNCT
mdp.39015104955862	68	45	provides	provide	VERB
mdp.39015104955862	68	46	a	a	DET
mdp.39015104955862	68	47	formal	formal	ADJ
mdp.39015104955862	68	48	solution	solution	NOUN
mdp.39015104955862	68	49	of	of	ADP
mdp.39015104955862	68	50	the	the	DET
mdp.39015104955862	68	51	complex	complex	ADJ
mdp.39015104955862	68	52	-	-	PUNCT
mdp.39015104955862	68	53	time	time	NOUN
mdp.39015104955862	68	54	diffusion	diffusion	NOUN
mdp.39015104955862	68	55	equation	equation	NOUN
mdp.39015104955862	68	56	(	(	PUNCT
mdp.39015104955862	68	57	5	5	NUM
mdp.39015104955862	68	58	)	)	PUNCT
mdp.39015104955862	68	59	.	.	PUNCT
mdp.39015104955862	69	1	moreover	moreover	ADV
mdp.39015104955862	69	2	,	,	PUNCT
mdp.39015104955862	69	3	it	it	PRON
mdp.39015104955862	69	4	is	be	AUX
mdp.39015104955862	69	5	a	a	DET
mdp.39015104955862	69	6	formal	formal	ADJ
mdp.39015104955862	69	7	analytic	analytic	ADJ
mdp.39015104955862	69	8	continuation	continuation	NOUN
mdp.39015104955862	69	9	of	of	ADP
mdp.39015104955862	69	10	the	the	DET
mdp.39015104955862	69	11	semi	semi	ADJ
mdp.39015104955862	69	12	-	-	NOUN
mdp.39015104955862	69	13	group	group	NOUN
mdp.39015104955862	69	14	(	(	PUNCT
mdp.39015104955862	69	15	7	7	NUM
mdp.39015104955862	69	16	)	)	PUNCT
mdp.39015104955862	69	17	.	.	PUNCT
mdp.39015104955862	70	1	we	we	PRON
mdp.39015104955862	70	2	use	use	VERB
mdp.39015104955862	70	3	the	the	DET
mdp.39015104955862	70	4	word	word	NOUN
mdp.39015104955862	70	5	"	"	PUNCT
mdp.39015104955862	70	6	formal	formal	ADJ
mdp.39015104955862	70	7	”	"	PUNCT
mdp.39015104955862	70	8	in	in	ADP
mdp.39015104955862	70	9	3	3	NUM
mdp.39015104955862	70	10	considerations	consideration	NOUN
mdp.39015104955862	70	11	above	above	ADV
mdp.39015104955862	70	12	,	,	PUNCT
mdp.39015104955862	70	13	because	because	SCONJ
mdp.39015104955862	70	14	we	we	PRON
mdp.39015104955862	70	15	have	have	AUX
mdp.39015104955862	70	16	not	not	PART
mdp.39015104955862	70	17	yet	yet	ADV
mdp.39015104955862	70	18	defined	define	VERB
mdp.39015104955862	70	19	the	the	DET
mdp.39015104955862	70	20	domain	domain	NOUN
mdp.39015104955862	70	21	of	of	ADP
mdp.39015104955862	70	22	the	the	DET
mdp.39015104955862	70	23	operators	operator	NOUN
mdp.39015104955862	70	24	u	u	PROPN
mdp.39015104955862	70	25	,	,	PUNCT
mdp.39015104955862	70	26	given	give	VERB
mdp.39015104955862	70	27	by	by	ADP
mdp.39015104955862	70	28	(	(	PUNCT
mdp.39015104955862	70	29	8)	8)	NUM
mdp.39015104955862	70	30	.	.	PUNCT
mdp.39015104955862	70	31	suppose	suppose	VERB
mdp.39015104955862	70	32	{	{	PUNCT
mdp.39015104955862	70	33	m	m	VERB
mdp.39015104955862	70	34	}	}	PUNCT
mdp.39015104955862	70	35	is	be	AUX
mdp.39015104955862	70	36	a	a	DET
mdp.39015104955862	70	37	sequence	sequence	NOUN
mdp.39015104955862	70	38	of	of	ADP
mdp.39015104955862	70	39	positive	positive	ADJ
mdp.39015104955862	70	40	numbers	number	NOUN
mdp.39015104955862	70	41	.	.	PUNCT
mdp.39015104955862	71	1	define	define	VERB
mdp.39015104955862	71	2	a	a	DET
mdp.39015104955862	71	3	function	function	NOUN
mdp.39015104955862	71	4	class	class	NOUN
mdp.39015104955862	71	5	d({m	d({m	NOUN
mdp.39015104955862	71	6	}	}	PUNCT
mdp.39015104955862	71	7	)	)	PUNCT
mdp.39015104955862	71	8	on	on	ADP
mdp.39015104955862	71	9	r¹	r¹	PROPN
mdp.39015104955862	71	10	by	by	ADP
mdp.39015104955862	71	11	the	the	DET
mdp.39015104955862	71	12	following	following	ADJ
mdp.39015104955862	71	13	formula	formula	NOUN
mdp.39015104955862	71	14	d({m₁	d({m₁	ADJ
mdp.39015104955862	71	15	}	}	PUNCT
mdp.39015104955862	71	16	)	)	PUNCT
mdp.39015104955862	71	17	=	=	PUNCT
mdp.39015104955862	71	18	{	{	PUNCT
mdp.39015104955862	71	19	y	y	X
mdp.39015104955862	71	20	€	€	PROPN
mdp.39015104955862	71	21	c∞(r¹	c∞(r¹	PROPN
mdp.39015104955862	71	22	)	)	PUNCT
mdp.39015104955862	71	23	:	:	PUNCT
mdp.39015104955862	71	24	|p	|p	SPACE
mdp.39015104955862	71	25	(	(	PUNCT
mdp.39015104955862	71	26	*	*	NOUN
mdp.39015104955862	71	27	)	)	PUNCT
mdp.39015104955862	71	28	(	(	PUNCT
mdp.39015104955862	71	29	x)|	x)|	PROPN
mdp.39015104955862	71	30	≤	≤	PROPN
mdp.39015104955862	71	31	ah*mk	ah*mk	X
mdp.39015104955862	71	32	,	,	PUNCT
mdp.39015104955862	71	33	k	k	PROPN
mdp.39015104955862	71	34	≥	≥	X
mdp.39015104955862	71	35	0	0	NUM
mdp.39015104955862	71	36	,	,	PUNCT
mdp.39015104955862	71	37	≈	≈	PROPN
mdp.39015104955862	71	38	€	€	PROPN
mdp.39015104955862	71	39	r¹	r¹	PROPN
mdp.39015104955862	71	40	}	}	PUNCT
mdp.39015104955862	71	41	,	,	PUNCT
mdp.39015104955862	71	42	where	where	SCONJ
mdp.39015104955862	71	43	positive	positive	ADJ
mdp.39015104955862	71	44	constants	constant	NOUN
mdp.39015104955862	71	45	a	a	PRON
mdp.39015104955862	71	46	and	and	CCONJ
mdp.39015104955862	71	47	h	h	NOUN
mdp.39015104955862	71	48	depend	depend	VERB
mdp.39015104955862	71	49	on	on	ADP
mdp.39015104955862	71	50	y.	y.	PROPN
mdp.39015104955862	71	51	these	these	DET
mdp.39015104955862	71	52	classes	class	NOUN
mdp.39015104955862	71	53	are	be	AUX
mdp.39015104955862	71	54	important	important	ADJ
mdp.39015104955862	71	55	in	in	ADP
mdp.39015104955862	71	56	making	make	VERB
mdp.39015104955862	71	57	the	the	DET
mdp.39015104955862	71	58	formal	formal	ADJ
mdp.39015104955862	71	59	considerations	consideration	NOUN
mdp.39015104955862	71	60	above	above	ADP
mdp.39015104955862	71	61	precise	precise	ADJ
mdp.39015104955862	71	62	.	.	PUNCT
mdp.39015104955862	72	1	perhaps	perhaps	ADV
mdp.39015104955862	72	2	,	,	PUNCT
mdp.39015104955862	72	3	hadamard	hadamard	NOUN
mdp.39015104955862	72	4	[	[	X
mdp.39015104955862	72	5	4	4	NUM
mdp.39015104955862	72	6	]	]	PUNCT
mdp.39015104955862	72	7	,	,	PUNCT
mdp.39015104955862	72	8	[	[	X
mdp.39015104955862	72	9	5	5	X
mdp.39015104955862	72	10	]	]	PUNCT
mdp.39015104955862	72	11	was	be	AUX
mdp.39015104955862	72	12	one	one	NUM
mdp.39015104955862	72	13	of	of	ADP
mdp.39015104955862	72	14	the	the	DET
mdp.39015104955862	72	15	first	first	ADJ
mdp.39015104955862	72	16	who	who	PRON
mdp.39015104955862	72	17	understood	understand	VERB
mdp.39015104955862	72	18	the	the	DET
mdp.39015104955862	72	19	importance	importance	NOUN
mdp.39015104955862	72	20	of	of	ADP
mdp.39015104955862	72	21	classes	class	NOUN
mdp.39015104955862	72	22	,	,	PUNCT
mdp.39015104955862	72	23	defined	define	VERB
mdp.39015104955862	72	24	by	by	ADP
mdp.39015104955862	72	25	given	give	VERB
mdp.39015104955862	72	26	upper	upper	ADJ
mdp.39015104955862	72	27	bounds	bound	NOUN
mdp.39015104955862	72	28	for	for	ADP
mdp.39015104955862	72	29	the	the	DET
mdp.39015104955862	72	30	successive	successive	ADJ
mdp.39015104955862	72	31	derivatives	derivative	NOUN
mdp.39015104955862	72	32	of	of	ADP
mdp.39015104955862	72	33	functions	function	NOUN
mdp.39015104955862	72	34	,	,	PUNCT
mdp.39015104955862	72	35	in	in	ADP
mdp.39015104955862	72	36	dealing	deal	VERB
mdp.39015104955862	72	37	with	with	ADP
mdp.39015104955862	72	38	the	the	DET
mdp.39015104955862	72	39	cauchy	cauchy	ADJ
mdp.39015104955862	72	40	problem	problem	NOUN
mdp.39015104955862	72	41	for	for	ADP
mdp.39015104955862	72	42	the	the	DET
mdp.39015104955862	72	43	heat	heat	NOUN
mdp.39015104955862	72	44	equation	equation	NOUN
mdp.39015104955862	72	45	.	.	PUNCT
mdp.39015104955862	73	1	hadamard	hadamard	PROPN
mdp.39015104955862	73	2	posed	pose	VERB
mdp.39015104955862	73	3	in	in	ADP
mdp.39015104955862	73	4	[	[	X
mdp.39015104955862	73	5	4	4	NUM
mdp.39015104955862	73	6	]	]	PUNCT
mdp.39015104955862	73	7	the	the	DET
mdp.39015104955862	73	8	problem	problem	NOUN
mdp.39015104955862	73	9	of	of	ADP
mdp.39015104955862	73	10	characterizing	characterize	VERB
mdp.39015104955862	73	11	those	those	DET
mdp.39015104955862	73	12	classes	class	NOUN
mdp.39015104955862	73	13	d({m	d({m	PROPN
mdp.39015104955862	73	14	}	}	PUNCT
mdp.39015104955862	73	15	)	)	PUNCT
mdp.39015104955862	73	16	,	,	PUNCT
mdp.39015104955862	73	17	for	for	ADP
mdp.39015104955862	73	18	which	which	PRON
mdp.39015104955862	73	19	every	every	DET
mdp.39015104955862	73	20	function	function	NOUN
mdp.39015104955862	73	21	↳	↳	X
mdp.39015104955862	73	22	€	€	SYM
mdp.39015104955862	73	23	d({m	d({m	NOUN
mdp.39015104955862	73	24	}	}	PUNCT
mdp.39015104955862	73	25	)	)	PUNCT
mdp.39015104955862	73	26	can	can	AUX
mdp.39015104955862	73	27	be	be	AUX
mdp.39015104955862	73	28	uniquely	uniquely	ADV
mdp.39015104955862	73	29	determined	determine	VERB
mdp.39015104955862	73	30	by	by	ADP
mdp.39015104955862	73	31	the	the	DET
mdp.39015104955862	73	32	sequence	sequence	NOUN
mdp.39015104955862	73	33	(	(	PUNCT
mdp.39015104955862	73	34	*	*	PUNCT
mdp.39015104955862	73	35	)	)	PUNCT
mdp.39015104955862	73	36	(	(	PUNCT
mdp.39015104955862	73	37	xo	xo	PROPN
mdp.39015104955862	73	38	)	)	PUNCT
mdp.39015104955862	73	39	,	,	PUNCT
mdp.39015104955862	73	40	k	k	PROPN
mdp.39015104955862	73	41	≥	≥	X
mdp.39015104955862	73	42	0	0	NUM
mdp.39015104955862	73	43	for	for	ADP
mdp.39015104955862	73	44	any	any	DET
mdp.39015104955862	73	45	given	give	VERB
mdp.39015104955862	73	46	a	a	DET
mdp.39015104955862	73	47	€	€	PROPN
mdp.39015104955862	73	48	r¹.	r¹.	NOUN
mdp.39015104955862	73	49	such	such	ADJ
mdp.39015104955862	73	50	classes	class	NOUN
mdp.39015104955862	73	51	d({m	d({m	PROPN
mdp.39015104955862	73	52	}	}	PUNCT
mdp.39015104955862	73	53	)	)	PUNCT
mdp.39015104955862	73	54	are	be	AUX
mdp.39015104955862	73	55	called	call	VERB
mdp.39015104955862	73	56	the	the	DET
mdp.39015104955862	73	57	quasianalytic	quasianalytic	ADJ
mdp.39015104955862	73	58	classes	class	NOUN
mdp.39015104955862	73	59	.	.	PUNCT
mdp.39015104955862	74	1	hadamard	hadamard	PROPN
mdp.39015104955862	74	2	's	's	PART
mdp.39015104955862	74	3	problem	problem	NOUN
mdp.39015104955862	74	4	has	have	AUX
mdp.39015104955862	74	5	been	be	AUX
mdp.39015104955862	74	6	solved	solve	VERB
mdp.39015104955862	74	7	by	by	ADP
mdp.39015104955862	74	8	denjoy	denjoy	PROPN
mdp.39015104955862	74	9	and	and	CCONJ
mdp.39015104955862	74	10	carleman	carleman	PROPN
mdp.39015104955862	74	11	(	(	PUNCT
mdp.39015104955862	74	12	see	see	VERB
mdp.39015104955862	74	13	section	section	NOUN
mdp.39015104955862	74	14	2	2	NUM
mdp.39015104955862	74	15	below	below	ADV
mdp.39015104955862	74	16	,	,	PUNCT
mdp.39015104955862	74	17	where	where	SCONJ
mdp.39015104955862	74	18	we	we	PRON
mdp.39015104955862	74	19	formulate	formulate	VERB
mdp.39015104955862	74	20	the	the	DET
mdp.39015104955862	74	21	denjoy	denjoy	NOUN
mdp.39015104955862	74	22	-	-	PUNCT
mdp.39015104955862	74	23	carleman	carleman	PROPN
mdp.39015104955862	74	24	theorem	theorem	PROPN
mdp.39015104955862	74	25	)	)	PUNCT
mdp.39015104955862	74	26	.	.	PUNCT
mdp.39015104955862	75	1	the	the	DET
mdp.39015104955862	75	2	classes	class	NOUN
mdp.39015104955862	75	3	d({m	d({m	PROPN
mdp.39015104955862	75	4	}	}	PUNCT
mdp.39015104955862	75	5	)	)	PUNCT
mdp.39015104955862	75	6	have	have	AUX
mdp.39015104955862	75	7	become	become	VERB
mdp.39015104955862	75	8	useful	useful	ADJ
mdp.39015104955862	75	9	tools	tool	NOUN
mdp.39015104955862	75	10	in	in	ADP
mdp.39015104955862	75	11	complex	complex	ADJ
mdp.39015104955862	75	12	analysis	analysis	NOUN
mdp.39015104955862	75	13	[	[	X
mdp.39015104955862	75	14	8	8	NUM
mdp.39015104955862	75	15	]	]	PUNCT
mdp.39015104955862	75	16	,	,	PUNCT
mdp.39015104955862	75	17	[	[	X
mdp.39015104955862	75	18	10	10	X
mdp.39015104955862	75	19	]	]	PUNCT
mdp.39015104955862	75	20	–	–	PUNCT
mdp.39015104955862	75	21	[	[	X
mdp.39015104955862	75	22	11	11	NUM
mdp.39015104955862	75	23	]	]	PUNCT
mdp.39015104955862	75	24	,	,	PUNCT
mdp.39015104955862	75	25	in	in	ADP
mdp.39015104955862	75	26	the	the	DET
mdp.39015104955862	75	27	theory	theory	NOUN
mdp.39015104955862	75	28	of	of	ADP
mdp.39015104955862	75	29	distributions	distribution	NOUN
mdp.39015104955862	75	30	[	[	X
mdp.39015104955862	75	31	2	2	NUM
mdp.39015104955862	75	32	]	]	PUNCT
mdp.39015104955862	75	33	,	,	PUNCT
mdp.39015104955862	75	34	[	[	X
mdp.39015104955862	75	35	13	13	NUM
mdp.39015104955862	75	36	]	]	PUNCT
mdp.39015104955862	75	37	,	,	PUNCT
mdp.39015104955862	75	38	and	and	CCONJ
mdp.39015104955862	75	39	in	in	ADP
mdp.39015104955862	75	40	the	the	DET
mdp.39015104955862	75	41	theory	theory	NOUN
mdp.39015104955862	75	42	of	of	ADP
mdp.39015104955862	75	43	differential	differential	ADJ
mdp.39015104955862	75	44	operators	operator	NOUN
mdp.39015104955862	75	45	of	of	ADP
mdp.39015104955862	75	46	infinite	infinite	ADJ
mdp.39015104955862	75	47	order	order	NOUN
mdp.39015104955862	75	48	[	[	X
mdp.39015104955862	75	49	1	1	NUM
mdp.39015104955862	75	50	]	]	PUNCT
mdp.39015104955862	75	51	.	.	PUNCT
mdp.39015104955862	76	1	the	the	DET
mdp.39015104955862	76	2	simple	simple	ADJ
mdp.39015104955862	76	3	example	example	NOUN
mdp.39015104955862	76	4	of	of	ADP
mdp.39015104955862	76	5	their	their	PRON
mdp.39015104955862	76	6	usefulness	usefulness	NOUN
mdp.39015104955862	76	7	in	in	ADP
mdp.39015104955862	76	8	the	the	DET
mdp.39015104955862	76	9	cauchy	cauchy	ADJ
mdp.39015104955862	76	10	problem	problem	NOUN
mdp.39015104955862	76	11	for	for	SCONJ
mdp.39015104955862	76	12	the	the	DET
mdp.39015104955862	76	13	heat	heat	NOUN
mdp.39015104955862	76	14	equation	equation	NOUN
mdp.39015104955862	76	15	is	be	AUX
mdp.39015104955862	76	16	given	give	VERB
mdp.39015104955862	76	17	by	by	ADP
mdp.39015104955862	76	18	the	the	DET
mdp.39015104955862	76	19	following	following	NOUN
mdp.39015104955862	76	20	.	.	PUNCT
mdp.39015104955862	77	1	for	for	ADP
mdp.39015104955862	77	2	an	an	DET
mdp.39015104955862	77	3	appropriately	appropriately	ADV
mdp.39015104955862	77	4	chosen	choose	VERB
mdp.39015104955862	77	5	class	class	NOUN
mdp.39015104955862	77	6	d({m	d({m	PROPN
mdp.39015104955862	77	7	}	}	PUNCT
mdp.39015104955862	77	8	)	)	PUNCT
mdp.39015104955862	77	9	,	,	PUNCT
mdp.39015104955862	77	10	the	the	DET
mdp.39015104955862	77	11	functions	function	NOUN
mdp.39015104955862	77	12	∞0	∞0	VERB
mdp.39015104955862	77	13	tk	tk	PRON
mdp.39015104955862	77	14	82k	82k	VERB
mdp.39015104955862	77	15	p(x	p(x	X
mdp.39015104955862	77	16	)	)	PUNCT
mdp.39015104955862	77	17	u₁y(x	u₁y(x	PROPN
mdp.39015104955862	77	18	)	)	PUNCT
mdp.39015104955862	77	19	=	=	PROPN
mdp.39015104955862	77	20	σ	σ	PROPN
mdp.39015104955862	77	21	k	k	PROPN
mdp.39015104955862	77	22	!	!	PROPN
mdp.39015104955862	77	23	8x2k	8x2k	PROPN
mdp.39015104955862	77	24	k=0	k=0	PROPN
mdp.39015104955862	77	25	are	be	AUX
mdp.39015104955862	77	26	defined	define	VERB
mdp.39015104955862	77	27	for	for	ADP
mdp.39015104955862	77	28	every	every	DET
mdp.39015104955862	77	29	function	function	NOUN
mdp.39015104955862	77	30	y	y	PROPN
mdp.39015104955862	77	31	є	є	PROPN
mdp.39015104955862	77	32	d({m₁	d({m₁	ADJ
mdp.39015104955862	77	33	}	}	PUNCT
mdp.39015104955862	77	34	)	)	PUNCT
mdp.39015104955862	77	35	and	and	CCONJ
mdp.39015104955862	77	36	u₁y(x	u₁y(x	PROPN
mdp.39015104955862	77	37	)	)	PUNCT
mdp.39015104955862	77	38	=	=	VERB
mdp.39015104955862	78	1	v(x	v(x	PROPN
mdp.39015104955862	78	2	,	,	PUNCT
mdp.39015104955862	78	3	t	t	PROPN
mdp.39015104955862	78	4	)	)	PUNCT
mdp.39015104955862	78	5	,	,	PUNCT
mdp.39015104955862	78	6	t	t	PROPN
mdp.39015104955862	78	7	>	>	X
mdp.39015104955862	78	8	0	0	NUM
mdp.39015104955862	78	9	x	x	SYM
mdp.39015104955862	78	10	є	є	PROPN
mdp.39015104955862	78	11	r¹	r¹	PROPN
mdp.39015104955862	78	12	,	,	PUNCT
mdp.39015104955862	78	13	t	t	PROPN
mdp.39015104955862	78	14	>	>	SYM
mdp.39015104955862	78	15	0	0	NUM
mdp.39015104955862	78	16	,	,	PUNCT
mdp.39015104955862	78	17	4	4	NUM
mdp.39015104955862	78	18	where	where	SCONJ
mdp.39015104955862	78	19	is	be	AUX
mdp.39015104955862	78	20	given	give	VERB
mdp.39015104955862	78	21	by	by	ADP
mdp.39015104955862	78	22	(	(	PUNCT
mdp.39015104955862	78	23	3	3	NUM
mdp.39015104955862	78	24	)	)	PUNCT
mdp.39015104955862	78	25	.	.	PUNCT
mdp.39015104955862	79	1	an	an	DET
mdp.39015104955862	79	2	important	important	ADJ
mdp.39015104955862	79	3	contribution	contribution	NOUN
mdp.39015104955862	79	4	to	to	ADP
mdp.39015104955862	79	5	the	the	DET
mdp.39015104955862	79	6	application	application	NOUN
mdp.39015104955862	79	7	of	of	ADP
mdp.39015104955862	79	8	the	the	DET
mdp.39015104955862	79	9	quasianalytic	quasianalytic	ADJ
mdp.39015104955862	79	10	classes	class	NOUN
mdp.39015104955862	79	11	in	in	ADP
mdp.39015104955862	79	12	the	the	DET
mdp.39015104955862	79	13	theory	theory	NOUN
mdp.39015104955862	79	14	of	of	ADP
mdp.39015104955862	79	15	partial	partial	ADJ
mdp.39015104955862	79	16	differential	differential	ADJ
mdp.39015104955862	79	17	equations	equation	NOUN
mdp.39015104955862	79	18	is	be	AUX
mdp.39015104955862	79	19	due	due	ADJ
mdp.39015104955862	79	20	to	to	ADP
mdp.39015104955862	79	21	gelfand	gelfand	PROPN
mdp.39015104955862	79	22	and	and	CCONJ
mdp.39015104955862	79	23	shilov	shilov	PROPN
mdp.39015104955862	80	1	[	[	X
mdp.39015104955862	80	2	2	2	NUM
mdp.39015104955862	80	3	]	]	PUNCT
mdp.39015104955862	80	4	,	,	PUNCT
mdp.39015104955862	80	5	[	[	X
mdp.39015104955862	80	6	3	3	X
mdp.39015104955862	80	7	]	]	PUNCT
mdp.39015104955862	80	8	.	.	PUNCT
mdp.39015104955862	81	1	they	they	PRON
mdp.39015104955862	81	2	contributed	contribute	VERB
mdp.39015104955862	81	3	substantially	substantially	ADV
mdp.39015104955862	81	4	to	to	ADP
mdp.39015104955862	81	5	the	the	DET
mdp.39015104955862	81	6	theory	theory	NOUN
mdp.39015104955862	81	7	of	of	ADP
mdp.39015104955862	81	8	distributions	distribution	NOUN
mdp.39015104955862	81	9	over	over	ADP
mdp.39015104955862	81	10	quasianalytic	quasianalytic	ADJ
mdp.39015104955862	81	11	classes	class	NOUN
mdp.39015104955862	81	12	and	and	CCONJ
mdp.39015104955862	81	13	to	to	ADP
mdp.39015104955862	81	14	the	the	DET
mdp.39015104955862	81	15	uniqueness	uniqueness	NOUN
mdp.39015104955862	81	16	and	and	CCONJ
mdp.39015104955862	81	17	well	well	ADJ
mdp.39015104955862	81	18	-	-	PUNCT
mdp.39015104955862	81	19	posedness	posedness	NOUN
mdp.39015104955862	81	20	problems	problem	NOUN
mdp.39015104955862	81	21	for	for	ADP
mdp.39015104955862	81	22	the	the	DET
mdp.39015104955862	81	23	heat	heat	NOUN
mdp.39015104955862	81	24	equation	equation	NOUN
mdp.39015104955862	81	25	with	with	ADP
mdp.39015104955862	81	26	complex	complex	ADJ
mdp.39015104955862	81	27	diffusion	diffusion	NOUN
mdp.39015104955862	81	28	coefficient	coefficient	NOUN
mdp.39015104955862	81	29	a	a	DET
mdp.39015104955862	81	30	,	,	PUNCT
mdp.39015104955862	81	31	namely	namely	ADV
mdp.39015104955862	81	32	jy(x	jy(x	X
mdp.39015104955862	81	33	,	,	PUNCT
mdp.39015104955862	81	34	t	t	PROPN
mdp.39015104955862	81	35	)	)	PUNCT
mdp.39015104955862	81	36	ə²y(x	ə²y(x	PROPN
mdp.39015104955862	81	37	,	,	PUNCT
mdp.39015104955862	81	38	t	t	PROPN
mdp.39015104955862	81	39	)	)	PUNCT
mdp.39015104955862	81	40	at	at	ADP
mdp.39015104955862	81	41	მუ2	მუ2	NUM
mdp.39015104955862	81	42	=	=	NUM
mdp.39015104955862	81	43	a	a	DET
mdp.39015104955862	81	44	≈	≈	PROPN
mdp.39015104955862	81	45	€	€	PROPN
mdp.39015104955862	81	46	r¹	r¹	PROPN
mdp.39015104955862	81	47	,	,	PUNCT
mdp.39015104955862	81	48	a	a	DET
mdp.39015104955862	81	49	є	є	PROPN
mdp.39015104955862	81	50	c.	c.	PROPN
mdp.39015104955862	81	51	gelfland	gelfland	PROPN
mdp.39015104955862	81	52	and	and	CCONJ
mdp.39015104955862	81	53	shilov	shilov	PROPN
mdp.39015104955862	81	54	found	find	VERB
mdp.39015104955862	81	55	in	in	ADP
mdp.39015104955862	81	56	[	[	X
mdp.39015104955862	81	57	2	2	NUM
mdp.39015104955862	81	58	]	]	PUNCT
mdp.39015104955862	81	59	the	the	DET
mdp.39015104955862	81	60	classes	class	NOUN
mdp.39015104955862	81	61	of	of	ADP
mdp.39015104955862	81	62	generalized	generalized	ADJ
mdp.39015104955862	81	63	distributions	distribution	NOUN
mdp.39015104955862	81	64	which	which	PRON
mdp.39015104955862	81	65	provide	provide	VERB
mdp.39015104955862	81	66	solutions	solution	NOUN
mdp.39015104955862	81	67	to	to	ADP
mdp.39015104955862	81	68	these	these	DET
mdp.39015104955862	81	69	problems	problem	NOUN
mdp.39015104955862	81	70	.	.	PUNCT
mdp.39015104955862	82	1	they	they	PRON
mdp.39015104955862	82	2	wrote	write	VERB
mdp.39015104955862	82	3	in	in	ADP
mdp.39015104955862	82	4	[	[	X
mdp.39015104955862	82	5	2	2	NUM
mdp.39015104955862	82	6	]	]	X
mdp.39015104955862	82	7	:	:	PUNCT
mdp.39015104955862	82	8	"	"	PUNCT
mdp.39015104955862	82	9	applications	application	NOUN
mdp.39015104955862	82	10	of	of	ADP
mdp.39015104955862	82	11	these	these	DET
mdp.39015104955862	82	12	spaces	space	NOUN
mdp.39015104955862	82	13	to	to	ADP
mdp.39015104955862	82	14	the	the	DET
mdp.39015104955862	82	15	cauchy	cauchy	ADJ
mdp.39015104955862	82	16	problem	problem	NOUN
mdp.39015104955862	82	17	in	in	ADP
mdp.39015104955862	82	18	vol	vol	NOUN
mdp.39015104955862	82	19	.	.	PUNCT
mdp.39015104955862	83	1	3	3	NUM
mdp.39015104955862	83	2	will	will	AUX
mdp.39015104955862	83	3	illustrate	illustrate	VERB
mdp.39015104955862	83	4	the	the	DET
mdp.39015104955862	83	5	well	well	ADV
mdp.39015104955862	83	6	-	-	PUNCT
mdp.39015104955862	83	7	known	know	VERB
mdp.39015104955862	83	8	statement	statement	NOUN
mdp.39015104955862	83	9	of	of	ADP
mdp.39015104955862	83	10	hadamard	hadamard	NOUN
mdp.39015104955862	83	11	's	's	PART
mdp.39015104955862	83	12	on	on	ADP
mdp.39015104955862	83	13	the	the	DET
mdp.39015104955862	83	14	relation	relation	NOUN
mdp.39015104955862	83	15	between	between	ADP
mdp.39015104955862	83	16	uniqueness	uniqueness	ADJ
mdp.39015104955862	83	17	theorems	theorem	NOUN
mdp.39015104955862	83	18	in	in	ADP
mdp.39015104955862	83	19	the	the	DET
mdp.39015104955862	83	20	cauchy	cauchy	ADJ
mdp.39015104955862	83	21	problem	problem	NOUN
mdp.39015104955862	83	22	on	on	ADP
mdp.39015104955862	83	23	the	the	DET
mdp.39015104955862	83	24	one	one	NUM
mdp.39015104955862	83	25	hand	hand	NOUN
mdp.39015104955862	83	26	,	,	PUNCT
mdp.39015104955862	83	27	and	and	CCONJ
mdp.39015104955862	83	28	the	the	DET
mdp.39015104955862	83	29	theory	theory	NOUN
mdp.39015104955862	83	30	of	of	ADP
mdp.39015104955862	83	31	quasianalytic	quasianalytic	ADJ
mdp.39015104955862	83	32	functions	function	NOUN
mdp.39015104955862	83	33	and	and	CCONJ
mdp.39015104955862	83	34	the	the	DET
mdp.39015104955862	83	35	general	general	ADJ
mdp.39015104955862	83	36	theory	theory	NOUN
mdp.39015104955862	83	37	of	of	ADP
mdp.39015104955862	83	38	functions	function	NOUN
mdp.39015104955862	83	39	of	of	ADP
mdp.39015104955862	83	40	a	a	DET
mdp.39015104955862	83	41	complex	complex	ADJ
mdp.39015104955862	83	42	variable	variable	NOUN
mdp.39015104955862	83	43	,	,	PUNCT
mdp.39015104955862	83	44	on	on	ADP
mdp.39015104955862	83	45	the	the	DET
mdp.39015104955862	83	46	other	other	ADJ
mdp.39015104955862	83	47	.	.	PUNCT
mdp.39015104955862	83	48	"	"	PUNCT
mdp.39015104955862	84	1	one	one	NUM
mdp.39015104955862	84	2	of	of	ADP
mdp.39015104955862	84	3	the	the	DET
mdp.39015104955862	84	4	problems	problem	NOUN
mdp.39015104955862	84	5	we	we	PRON
mdp.39015104955862	84	6	consider	consider	VERB
mdp.39015104955862	84	7	in	in	ADP
mdp.39015104955862	84	8	this	this	DET
mdp.39015104955862	84	9	work	work	NOUN
mdp.39015104955862	84	10	is	be	AUX
mdp.39015104955862	84	11	to	to	PART
mdp.39015104955862	84	12	characterize	characterize	VERB
mdp.39015104955862	84	13	those	those	DET
mdp.39015104955862	84	14	classes	class	NOUN
mdp.39015104955862	84	15	d({mk	d({mk	SPACE
mdp.39015104955862	84	16	}	}	PUNCT
mdp.39015104955862	84	17	)	)	PUNCT
mdp.39015104955862	84	18	,	,	PUNCT
mdp.39015104955862	84	19	which	which	PRON
mdp.39015104955862	84	20	are	be	AUX
mdp.39015104955862	84	21	invariant	invariant	ADJ
mdp.39015104955862	84	22	with	with	ADP
mdp.39015104955862	84	23	respect	respect	NOUN
mdp.39015104955862	84	24	to	to	ADP
mdp.39015104955862	84	25	the	the	DET
mdp.39015104955862	84	26	complex	complex	ADJ
mdp.39015104955862	84	27	-	-	PUNCT
mdp.39015104955862	84	28	time	time	NOUN
mdp.39015104955862	84	29	diffusion	diffusion	NOUN
mdp.39015104955862	84	30	group	group	NOUN
mdp.39015104955862	84	31	(	(	PUNCT
mdp.39015104955862	84	32	8)	8)	NUM
mdp.39015104955862	84	33	,	,	PUNCT
mdp.39015104955862	84	34	which	which	PRON
mdp.39015104955862	84	35	means	mean	VERB
mdp.39015104955862	84	36	that	that	SCONJ
mdp.39015104955862	84	37	u₂(d({m₁	u₂(d({m₁	NOUN
mdp.39015104955862	84	38	}	}	PUNCT
mdp.39015104955862	84	39	)	)	PUNCT
mdp.39015104955862	84	40	)	)	PUNCT
mdp.39015104955862	85	1	c	c	PROPN
mdp.39015104955862	85	2	d({mk	d({mk	PROPN
mdp.39015104955862	85	3	}	}	PUNCT
mdp.39015104955862	85	4	)	)	PUNCT
mdp.39015104955862	85	5	,	,	PUNCT
mdp.39015104955862	85	6	we	we	PRON
mdp.39015104955862	85	7	answer	answer	VERB
mdp.39015104955862	85	8	this	this	DET
mdp.39015104955862	85	9	question	question	NOUN
mdp.39015104955862	85	10	in	in	ADP
mdp.39015104955862	85	11	section	section	NOUN
mdp.39015104955862	85	12	5	5	NUM
mdp.39015104955862	85	13	.	.	PUNCT
mdp.39015104955862	86	1	the	the	DET
mdp.39015104955862	86	2	u	u	NOUN
mdp.39015104955862	86	3	-	-	NOUN
mdp.39015104955862	86	4	invariance	invariance	NOUN
mdp.39015104955862	86	5	of	of	ADP
mdp.39015104955862	86	6	d({m	d({m	PROPN
mdp.39015104955862	86	7	}	}	PUNCT
mdp.39015104955862	86	8	)	)	PUNCT
mdp.39015104955862	86	9	implies	imply	VERB
mdp.39015104955862	86	10	that	that	SCONJ
mdp.39015104955862	86	11	we	we	PRON
mdp.39015104955862	86	12	can	can	AUX
mdp.39015104955862	86	13	diffuse	diffuse	VERB
mdp.39015104955862	86	14	,	,	PUNCT
mdp.39015104955862	86	15	anti	anti	ADJ
mdp.39015104955862	86	16	-	-	NOUN
mdp.39015104955862	86	17	diffuse	diffuse	NOUN
mdp.39015104955862	86	18	,	,	PUNCT
mdp.39015104955862	86	19	disperse	disperse	VERB
mdp.39015104955862	86	20	,	,	PUNCT
mdp.39015104955862	86	21	and	and	CCONJ
mdp.39015104955862	86	22	anti	anti	ADJ
mdp.39015104955862	86	23	-	-	ADJ
mdp.39015104955862	86	24	disperse¹	disperse¹	ADJ
mdp.39015104955862	86	25	,	,	PUNCT
mdp.39015104955862	86	26	staying	stay	VERB
mdp.39015104955862	86	27	in	in	ADP
mdp.39015104955862	86	28	the	the	DET
mdp.39015104955862	86	29	same	same	ADJ
mdp.39015104955862	86	30	class	class	NOUN
mdp.39015104955862	86	31	.	.	PUNCT
mdp.39015104955862	87	1	it	it	PRON
mdp.39015104955862	87	2	is	be	AUX
mdp.39015104955862	87	3	easy	easy	ADJ
mdp.39015104955862	87	4	to	to	PART
mdp.39015104955862	87	5	see	see	VERB
mdp.39015104955862	87	6	that	that	SCONJ
mdp.39015104955862	87	7	the	the	DET
mdp.39015104955862	87	8	operator	operator	NOUN
mdp.39015104955862	87	9	u	u	PROPN
mdp.39015104955862	87	10	,	,	PUNCT
mdp.39015104955862	87	11	in	in	ADP
mdp.39015104955862	87	12	(	(	PUNCT
mdp.39015104955862	87	13	8)	8)	NUM
mdp.39015104955862	87	14	is	be	AUX
mdp.39015104955862	87	15	a	a	DET
mdp.39015104955862	87	16	convolution	convolution	NOUN
mdp.39015104955862	87	17	operator	operator	NOUN
mdp.39015104955862	87	18	,	,	PUNCT
mdp.39015104955862	87	19	defined	define	VERB
mdp.39015104955862	87	20	by	by	ADP
mdp.39015104955862	87	21	the	the	DET
mdp.39015104955862	87	22	formula	formula	NOUN
mdp.39015104955862	87	23	zє	zє	PROPN
mdp.39015104955862	87	24	c.	c.	PROPN
mdp.39015104955862	87	25	u₂y	u₂y	PROPN
mdp.39015104955862	87	26	=	=	PROPN
mdp.39015104955862	87	27	y	y	PROPN
mdp.39015104955862	87	28	*	*	PUNCT
mdp.39015104955862	87	29	г₂	г₂	PROPN
mdp.39015104955862	87	30	,	,	PUNCT
mdp.39015104955862	87	31	¹dispersion	¹dispersion	PROPN
mdp.39015104955862	87	32	and	and	CCONJ
mdp.39015104955862	87	33	anti	anti	ADJ
mdp.39015104955862	87	34	-	-	NOUN
mdp.39015104955862	87	35	dispersion	dispersion	NOUN
mdp.39015104955862	87	36	correspond	correspond	NOUN
mdp.39015104955862	87	37	to	to	ADP
mdp.39015104955862	87	38	the	the	DET
mdp.39015104955862	87	39	schrödinger	schrödinger	ADJ
mdp.39015104955862	87	40	equation	equation	NOUN
mdp.39015104955862	87	41	for	for	ADP
mdp.39015104955862	87	42	the	the	DET
mdp.39015104955862	87	43	free	free	ADJ
mdp.39015104955862	87	44	particle	particle	NOUN
mdp.39015104955862	87	45	.	.	PUNCT
mdp.39015104955862	88	1	5	5	NUM
mdp.39015104955862	88	2	where	where	SCONJ
mdp.39015104955862	88	3	t	t	PROPN
mdp.39015104955862	88	4	,	,	PUNCT
mdp.39015104955862	88	5	is	be	AUX
mdp.39015104955862	88	6	the	the	DET
mdp.39015104955862	88	7	green	green	NOUN
mdp.39015104955862	88	8	's	's	PART
mdp.39015104955862	88	9	function	function	NOUN
mdp.39015104955862	88	10	for	for	ADP
mdp.39015104955862	88	11	equation	equation	NOUN
mdp.39015104955862	88	12	(	(	PUNCT
mdp.39015104955862	88	13	5	5	NUM
mdp.39015104955862	88	14	)	)	PUNCT
mdp.39015104955862	88	15	,	,	PUNCT
mdp.39015104955862	88	16	namely	namely	ADV
mdp.39015104955862	88	17	σ	σ	NOUN
mdp.39015104955862	88	18	=	=	SYM
mdp.39015104955862	88	19	8	8	NUM
mdp.39015104955862	88	20	(	(	PUNCT
mdp.39015104955862	88	21	2k	2k	NUM
mdp.39015104955862	88	22	)	)	PUNCT
mdp.39015104955862	88	23	k=0	k=0	NOUN
mdp.39015104955862	88	24	r₁	r₁	VERB
mdp.39015104955862	88	25	=	=	PUNCT
mdp.39015104955862	88	26	the	the	DET
mdp.39015104955862	88	27	symbol	symbol	NOUN
mdp.39015104955862	88	28	do	do	AUX
mdp.39015104955862	88	29	in	in	ADP
mdp.39015104955862	88	30	(	(	PUNCT
mdp.39015104955862	88	31	9	9	NUM
mdp.39015104955862	88	32	)	)	PUNCT
mdp.39015104955862	88	33	denotes	denote	VERB
mdp.39015104955862	88	34	the	the	DET
mdp.39015104955862	88	35	dirac	dirac	NOUN
mdp.39015104955862	88	36	's	's	PART
mdp.39015104955862	88	37	delta	delta	NOUN
mdp.39015104955862	88	38	function	function	NOUN
mdp.39015104955862	88	39	at	at	ADP
mdp.39015104955862	88	40	0	0	NUM
mdp.39015104955862	88	41	.	.	PUNCT
mdp.39015104955862	89	1	the	the	DET
mdp.39015104955862	89	2	formal	formal	ADJ
mdp.39015104955862	89	3	series	series	NOUN
mdp.39015104955862	89	4	,	,	PUNCT
mdp.39015104955862	89	5	invloving	invlove	VERB
mdp.39015104955862	89	6	all	all	DET
mdp.39015104955862	89	7	the	the	DET
mdp.39015104955862	89	8	derivatives	derivative	NOUN
mdp.39015104955862	89	9	of	of	ADP
mdp.39015104955862	89	10	the	the	DET
mdp.39015104955862	89	11	delta	delta	NOUN
mdp.39015104955862	89	12	-	-	PUNCT
mdp.39015104955862	89	13	function	function	NOUN
mdp.39015104955862	89	14	,	,	PUNCT
mdp.39015104955862	89	15	namely	namely	ADV
mdp.39015104955862	89	16	r	r	NOUN
mdp.39015104955862	89	17	=	=	PUNCT
mdp.39015104955862	89	18	σax	σax	PROPN
mdp.39015104955862	89	19	(	(	PUNCT
mdp.39015104955862	89	20	*	*	PROPN
mdp.39015104955862	89	21	)	)	PUNCT
mdp.39015104955862	89	22	,	,	PUNCT
mdp.39015104955862	89	23	k=0	k=0	PROPN
mdp.39015104955862	89	24	r₁	r₁	VERB
mdp.39015104955862	89	25	=	=	NOUN
mdp.39015104955862	89	26	i	i	PRON
mdp.39015104955862	89	27	'	'	VERB
mdp.39015104955862	89	28	are	be	AUX
mdp.39015104955862	89	29	called	call	VERB
mdp.39015104955862	89	30	hyperdistributions	hyperdistribution	NOUN
mdp.39015104955862	89	31	.	.	PUNCT
mdp.39015104955862	90	1	they	they	PRON
mdp.39015104955862	90	2	are	be	AUX
mdp.39015104955862	90	3	highly	highly	ADV
mdp.39015104955862	90	4	singular	singular	ADJ
mdp.39015104955862	90	5	objects	object	NOUN
mdp.39015104955862	90	6	and	and	CCONJ
mdp.39015104955862	90	7	schwartz	schwartz	NOUN
mdp.39015104955862	90	8	's	's	PART
mdp.39015104955862	90	9	theory	theory	NOUN
mdp.39015104955862	90	10	of	of	ADP
mdp.39015104955862	90	11	distributions	distribution	NOUN
mdp.39015104955862	90	12	(	(	PUNCT
mdp.39015104955862	90	13	see	see	VERB
mdp.39015104955862	90	14	[	[	X
mdp.39015104955862	90	15	9	9	NUM
mdp.39015104955862	90	16	]	]	PUNCT
mdp.39015104955862	90	17	,	,	PUNCT
mdp.39015104955862	90	18	[	[	X
mdp.39015104955862	90	19	14	14	NUM
mdp.39015104955862	90	20	]	]	PUNCT
mdp.39015104955862	90	21	,	,	PUNCT
mdp.39015104955862	90	22	[	[	X
mdp.39015104955862	90	23	2	2	X
mdp.39015104955862	90	24	]	]	PUNCT
mdp.39015104955862	90	25	)	)	PUNCT
mdp.39015104955862	90	26	does	do	AUX
mdp.39015104955862	90	27	not	not	PART
mdp.39015104955862	90	28	include	include	VERB
mdp.39015104955862	90	29	them	they	PRON
mdp.39015104955862	90	30	.	.	PUNCT
mdp.39015104955862	91	1	the	the	DET
mdp.39015104955862	91	2	most	most	ADV
mdp.39015104955862	91	3	appropriate	appropriate	ADJ
mdp.39015104955862	91	4	theory	theory	NOUN
mdp.39015104955862	91	5	,	,	PUNCT
mdp.39015104955862	91	6	which	which	PRON
mdp.39015104955862	91	7	involves	involve	VERB
mdp.39015104955862	91	8	hyperdistributions	hyperdistribution	NOUN
mdp.39015104955862	91	9	,	,	PUNCT
mdp.39015104955862	91	10	is	be	AUX
mdp.39015104955862	91	11	that	that	PRON
mdp.39015104955862	91	12	of	of	ADP
mdp.39015104955862	91	13	the	the	DET
mdp.39015104955862	91	14	distributions	distribution	NOUN
mdp.39015104955862	91	15	over	over	ADP
mdp.39015104955862	91	16	the	the	DET
mdp.39015104955862	91	17	classes	class	NOUN
mdp.39015104955862	91	18	d({m	d({m	PROPN
mdp.39015104955862	91	19	}	}	PUNCT
mdp.39015104955862	91	20	)	)	PUNCT
mdp.39015104955862	91	21	(	(	PUNCT
mdp.39015104955862	91	22	see	see	VERB
mdp.39015104955862	91	23	[	[	X
mdp.39015104955862	91	24	2	2	NUM
mdp.39015104955862	91	25	]	]	PUNCT
mdp.39015104955862	91	26	,	,	PUNCT
mdp.39015104955862	91	27	[	[	X
mdp.39015104955862	91	28	3	3	X
mdp.39015104955862	91	29	]	]	PUNCT
mdp.39015104955862	91	30	,	,	PUNCT
mdp.39015104955862	91	31	[	[	X
mdp.39015104955862	91	32	13	13	NUM
mdp.39015104955862	91	33	]	]	PUNCT
mdp.39015104955862	91	34	)	)	PUNCT
mdp.39015104955862	91	35	.	.	PUNCT
mdp.39015104955862	92	1	in	in	ADP
mdp.39015104955862	92	2	this	this	DET
mdp.39015104955862	92	3	theory	theory	NOUN
mdp.39015104955862	92	4	the	the	DET
mdp.39015104955862	92	5	functions	function	NOUN
mdp.39015104955862	92	6	y	y	X
mdp.39015104955862	92	7	€	€	SYM
mdp.39015104955862	92	8	d({m	d({m	NOUN
mdp.39015104955862	92	9	}	}	PUNCT
mdp.39015104955862	92	10	)	)	PUNCT
mdp.39015104955862	92	11	are	be	AUX
mdp.39015104955862	92	12	considered	consider	VERB
mdp.39015104955862	92	13	as	as	ADP
mdp.39015104955862	92	14	test	test	NOUN
mdp.39015104955862	92	15	functions	function	NOUN
mdp.39015104955862	92	16	and	and	CCONJ
mdp.39015104955862	92	17	the	the	DET
mdp.39015104955862	92	18	distributions	distribution	NOUN
mdp.39015104955862	92	19	are	be	AUX
mdp.39015104955862	92	20	defined	define	VERB
mdp.39015104955862	92	21	as	as	ADP
mdp.39015104955862	92	22	bounded	bound	VERB
mdp.39015104955862	92	23	linear	linear	ADJ
mdp.39015104955862	92	24	functionals	functional	NOUN
mdp.39015104955862	92	25	on	on	ADP
mdp.39015104955862	92	26	the	the	DET
mdp.39015104955862	92	27	class	class	NOUN
mdp.39015104955862	92	28	d({m₁	d({m₁	ADJ
mdp.39015104955862	92	29	}	}	PUNCT
mdp.39015104955862	92	30	)	)	PUNCT
mdp.39015104955862	92	31	,	,	PUNCT
mdp.39015104955862	92	32	equipped	equip	VERB
mdp.39015104955862	92	33	with	with	ADP
mdp.39015104955862	92	34	appropriate	appropriate	ADJ
mdp.39015104955862	92	35	topology	topology	NOUN
mdp.39015104955862	92	36	.	.	PUNCT
mdp.39015104955862	93	1	in	in	ADP
mdp.39015104955862	93	2	[	[	PUNCT
mdp.39015104955862	93	3	13	13	NUM
mdp.39015104955862	93	4	]	]	PUNCT
mdp.39015104955862	93	5	the	the	DET
mdp.39015104955862	93	6	formal	formal	ADJ
mdp.39015104955862	93	7	series	series	NOUN
mdp.39015104955862	93	8	(	(	PUNCT
mdp.39015104955862	93	9	10	10	NUM
mdp.39015104955862	93	10	)	)	PUNCT
mdp.39015104955862	93	11	were	be	AUX
mdp.39015104955862	93	12	considered	consider	VERB
mdp.39015104955862	93	13	as	as	ADP
mdp.39015104955862	93	14	distributions	distribution	NOUN
mdp.39015104955862	93	15	over	over	ADP
mdp.39015104955862	93	16	non	non	ADJ
mdp.39015104955862	93	17	-	-	ADJ
mdp.39015104955862	93	18	quasianalysitc	quasianalysitc	ADJ
mdp.39015104955862	93	19	classes	class	NOUN
mdp.39015104955862	93	20	d({mk	d({mk	SPACE
mdp.39015104955862	93	21	}	}	PUNCT
mdp.39015104955862	93	22	)	)	PUNCT
mdp.39015104955862	93	23	(	(	PUNCT
mdp.39015104955862	93	24	see	see	VERB
mdp.39015104955862	93	25	[	[	X
mdp.39015104955862	93	26	13	13	NUM
mdp.39015104955862	93	27	]	]	PUNCT
mdp.39015104955862	93	28	,	,	PUNCT
mdp.39015104955862	93	29	p.	p.	NOUN
mdp.39015104955862	93	30	51	51	NUM
mdp.39015104955862	93	31	)	)	PUNCT
mdp.39015104955862	93	32	.	.	PUNCT
mdp.39015104955862	94	1	hyperdistributions	hyperdistribution	NOUN
mdp.39015104955862	94	2	are	be	AUX
mdp.39015104955862	94	3	of	of	ADP
mdp.39015104955862	94	4	much	much	ADJ
mdp.39015104955862	94	5	use	use	NOUN
mdp.39015104955862	94	6	in	in	ADP
mdp.39015104955862	94	7	image	image	NOUN
mdp.39015104955862	94	8	processing	processing	NOUN
mdp.39015104955862	94	9	(	(	PUNCT
mdp.39015104955862	94	10	see	see	VERB
mdp.39015104955862	94	11	[	[	X
mdp.39015104955862	94	12	6	6	NUM
mdp.39015104955862	94	13	]	]	PUNCT
mdp.39015104955862	94	14	,	,	PUNCT
mdp.39015104955862	94	15	[	[	X
mdp.39015104955862	94	16	7	7	X
mdp.39015104955862	94	17	]	]	PUNCT
mdp.39015104955862	94	18	)	)	PUNCT
mdp.39015104955862	94	19	.	.	PUNCT
mdp.39015104955862	95	1	they	they	PRON
mdp.39015104955862	95	2	have	have	AUX
mdp.39015104955862	95	3	been	be	AUX
mdp.39015104955862	95	4	used	use	VERB
mdp.39015104955862	95	5	for	for	ADP
mdp.39015104955862	95	6	deblurring	deblurre	VERB
mdp.39015104955862	95	7	and	and	CCONJ
mdp.39015104955862	95	8	compressing	compressing	NOUN
mdp.39015104955862	95	9	of	of	ADP
mdp.39015104955862	95	10	images	image	NOUN
mdp.39015104955862	95	11	.	.	PUNCT
mdp.39015104955862	96	1	this	this	PRON
mdp.39015104955862	96	2	is	be	AUX
mdp.39015104955862	96	3	easy	easy	ADJ
mdp.39015104955862	96	4	to	to	PART
mdp.39015104955862	96	5	understand	understand	VERB
mdp.39015104955862	96	6	if	if	SCONJ
mdp.39015104955862	96	7	we	we	PRON
mdp.39015104955862	96	8	recall	recall	VERB
mdp.39015104955862	96	9	that	that	SCONJ
mdp.39015104955862	96	10	a	a	DET
mdp.39015104955862	96	11	hyperdistribution	hyperdistribution	NOUN
mdp.39015104955862	96	12	(	(	PUNCT
mdp.39015104955862	96	13	9	9	NUM
mdp.39015104955862	96	14	)	)	PUNCT
mdp.39015104955862	96	15	=(	=(	NOUN
mdp.39015104955862	96	16	-1	-1	X
mdp.39015104955862	96	17	)	)	PUNCT
mdp.39015104955862	96	18	*	*	PUNCT
mdp.39015104955862	96	19	(	(	PUNCT
mdp.39015104955862	96	20	24	24	NUM
mdp.39015104955862	96	21	)	)	PUNCT
mdp.39015104955862	96	22	,	,	PUNCT
mdp.39015104955862	96	23	(	(	PUNCT
mdp.39015104955862	96	24	−t)k	−t)k	VERB
mdp.39015104955862	96	25	(	(	PUNCT
mdp.39015104955862	96	26	11	11	NUM
mdp.39015104955862	96	27	)	)	PUNCT
mdp.39015104955862	96	28	k	k	PROPN
mdp.39015104955862	96	29	!	!	PUNCT
mdp.39015104955862	96	30	k=0	k=0	PROPN
mdp.39015104955862	96	31	is	be	AUX
mdp.39015104955862	96	32	the	the	DET
mdp.39015104955862	96	33	green	green	NOUN
mdp.39015104955862	96	34	's	's	PART
mdp.39015104955862	96	35	function	function	NOUN
mdp.39015104955862	96	36	for	for	ADP
mdp.39015104955862	96	37	the	the	DET
mdp.39015104955862	96	38	inverse	inverse	ADJ
mdp.39015104955862	96	39	heat	heat	NOUN
mdp.39015104955862	96	40	equation	equation	NOUN
mdp.39015104955862	96	41	and	and	CCONJ
mdp.39015104955862	96	42	thus	thus	ADV
mdp.39015104955862	96	43	we	we	PRON
mdp.39015104955862	96	44	may	may	AUX
mdp.39015104955862	96	45	reconstruct	reconstruct	VERB
mdp.39015104955862	96	46	sharp	sharp	ADJ
mdp.39015104955862	96	47	images	image	NOUN
mdp.39015104955862	96	48	from	from	ADP
mdp.39015104955862	96	49	damaged	damage	VERB
mdp.39015104955862	96	50	ones	one	NOUN
mdp.39015104955862	96	51	by	by	ADP
mdp.39015104955862	96	52	convolving	convolve	VERB
mdp.39015104955862	96	53	them	they	PRON
mdp.39015104955862	96	54	with	with	ADP
mdp.39015104955862	96	55	hyperdistributions	hyperdistribution	NOUN
mdp.39015104955862	96	56	(	(	PUNCT
mdp.39015104955862	96	57	11	11	NUM
mdp.39015104955862	96	58	)	)	PUNCT
mdp.39015104955862	96	59	.	.	PUNCT
mdp.39015104955862	97	1	this	this	DET
mdp.39015104955862	97	2	paper	paper	NOUN
mdp.39015104955862	97	3	is	be	AUX
mdp.39015104955862	97	4	organized	organize	VERB
mdp.39015104955862	97	5	as	as	SCONJ
mdp.39015104955862	97	6	follows	follow	VERB
mdp.39015104955862	97	7	:	:	PUNCT
mdp.39015104955862	97	8	in	in	ADP
mdp.39015104955862	97	9	section	section	NOUN
mdp.39015104955862	97	10	3	3	NUM
mdp.39015104955862	97	11	the	the	DET
mdp.39015104955862	97	12	necessary	necessary	ADJ
mdp.39015104955862	97	13	definitions	definition	NOUN
mdp.39015104955862	97	14	and	and	CCONJ
mdp.39015104955862	97	15	known	known	ADJ
mdp.39015104955862	97	16	results	result	NOUN
mdp.39015104955862	97	17	are	be	AUX
mdp.39015104955862	97	18	gathered	gather	VERB
mdp.39015104955862	97	19	.	.	PUNCT
mdp.39015104955862	98	1	section	section	NOUN
mdp.39015104955862	98	2	4	4	NUM
mdp.39015104955862	98	3	is	be	AUX
mdp.39015104955862	98	4	concerned	concern	VERB
mdp.39015104955862	98	5	with	with	ADP
mdp.39015104955862	98	6	the	the	DET
mdp.39015104955862	98	7	structure	structure	NOUN
mdp.39015104955862	98	8	of	of	ADP
mdp.39015104955862	98	9	hyperdistributions	hyperdistribution	NOUN
mdp.39015104955862	98	10	.	.	PUNCT
mdp.39015104955862	99	1	we	we	PRON
mdp.39015104955862	99	2	prove	prove	VERB
mdp.39015104955862	99	3	(	(	PUNCT
mdp.39015104955862	99	4	see	see	VERB
mdp.39015104955862	99	5	theorems	theorem	NOUN
mdp.39015104955862	99	6	3	3	NUM
mdp.39015104955862	99	7	and	and	CCONJ
mdp.39015104955862	99	8	4	4	NUM
mdp.39015104955862	99	9	)	)	PUNCT
mdp.39015104955862	99	10	that	that	SCONJ
mdp.39015104955862	99	11	,	,	PUNCT
mdp.39015104955862	99	12	roughly	roughly	ADV
mdp.39015104955862	99	13	speaking	speak	VERB
mdp.39015104955862	99	14	,	,	PUNCT
mdp.39015104955862	99	15	the	the	DET
mdp.39015104955862	99	16	hyperdistributions	hyperdistribution	NOUN
mdp.39015104955862	99	17	are	be	AUX
mdp.39015104955862	99	18	distributions	distribution	NOUN
mdp.39015104955862	99	19	over	over	ADP
mdp.39015104955862	99	20	classes	class	NOUN
mdp.39015104955862	99	21	d({m	d({m	PROPN
mdp.39015104955862	99	22	}	}	PUNCT
mdp.39015104955862	99	23	)	)	PUNCT
mdp.39015104955862	99	24	,	,	PUNCT
mdp.39015104955862	99	25	which	which	PRON
mdp.39015104955862	99	26	have	have	VERB
mdp.39015104955862	99	27	moments	moment	NOUN
mdp.39015104955862	99	28	of	of	ADP
mdp.39015104955862	99	29	all	all	DET
mdp.39015104955862	99	30	orders	order	NOUN
mdp.39015104955862	99	31	,	,	PUNCT
mdp.39015104955862	99	32	and	and	CCONJ
mdp.39015104955862	99	33	their	their	PRON
mdp.39015104955862	99	34	moments	moment	NOUN
mdp.39015104955862	99	35	should	should	AUX
mdp.39015104955862	99	36	satisfy	satisfy	VERB
mdp.39015104955862	99	37	special	special	ADJ
mdp.39015104955862	99	38	(	(	PUNCT
mdp.39015104955862	99	39	10	10	NUM
mdp.39015104955862	99	40	)	)	PUNCT
mdp.39015104955862	99	41	t	t	PROPN
mdp.39015104955862	99	42	>	>	X
mdp.39015104955862	99	43	0	0	NUM
mdp.39015104955862	99	44	6	6	NUM
mdp.39015104955862	99	45	conditions	condition	NOUN
mdp.39015104955862	99	46	.	.	PUNCT
mdp.39015104955862	100	1	in	in	ADP
mdp.39015104955862	100	2	section	section	NOUN
mdp.39015104955862	100	3	5	5	NUM
mdp.39015104955862	100	4	we	we	PRON
mdp.39015104955862	100	5	give	give	VERB
mdp.39015104955862	100	6	a	a	DET
mdp.39015104955862	100	7	characterization	characterization	NOUN
mdp.39015104955862	100	8	of	of	ADP
mdp.39015104955862	100	9	the	the	DET
mdp.39015104955862	100	10	u₂-invariant	u₂-invariant	PROPN
mdp.39015104955862	100	11	classes	class	NOUN
mdp.39015104955862	100	12	d({m	d({m	PROPN
mdp.39015104955862	100	13	}	}	PUNCT
mdp.39015104955862	100	14	)	)	PUNCT
mdp.39015104955862	100	15	and	and	CCONJ
mdp.39015104955862	100	16	the	the	DET
mdp.39015104955862	100	17	u	u	PROPN
mdp.39015104955862	100	18	,	,	PUNCT
mdp.39015104955862	100	19	invariant	invariant	ADJ
mdp.39015104955862	100	20	classes	class	NOUN
mdp.39015104955862	100	21	of	of	ADP
mdp.39015104955862	100	22	distributions	distribution	NOUN
mdp.39015104955862	100	23	d'({m	d'({m	ADV
mdp.39015104955862	100	24	}	}	PUNCT
mdp.39015104955862	100	25	)	)	PUNCT
mdp.39015104955862	100	26	(	(	PUNCT
mdp.39015104955862	100	27	see	see	VERB
mdp.39015104955862	100	28	theorems	theorem	NOUN
mdp.39015104955862	100	29	5	5	NUM
mdp.39015104955862	100	30	and	and	CCONJ
mdp.39015104955862	100	31	6	6	NUM
mdp.39015104955862	100	32	)	)	PUNCT
mdp.39015104955862	100	33	.	.	PUNCT
mdp.39015104955862	101	1	as	as	SCONJ
mdp.39015104955862	101	2	the	the	DET
mdp.39015104955862	101	3	corollary	corollary	NOUN
mdp.39015104955862	101	4	of	of	ADP
mdp.39015104955862	101	5	theorem	theorem	NOUN
mdp.39015104955862	101	6	5	5	NUM
mdp.39015104955862	101	7	we	we	PRON
mdp.39015104955862	101	8	get	get	VERB
mdp.39015104955862	101	9	the	the	DET
mdp.39015104955862	101	10	following	following	ADJ
mdp.39015104955862	101	11	result	result	NOUN
mdp.39015104955862	101	12	.	.	PUNCT
mdp.39015104955862	102	1	the	the	DET
mdp.39015104955862	102	2	quasianalytic	quasianalytic	ADJ
mdp.39015104955862	102	3	classes	class	NOUN
mdp.39015104955862	102	4	d({k	d({k	NOUN
mdp.39015104955862	102	5	}	}	PUNCT
mdp.39015104955862	102	6	)	)	PUNCT
mdp.39015104955862	102	7	,	,	PUNCT
mdp.39015104955862	102	8	0	0	NUM
mdp.39015104955862	102	9	≤	≤	X
mdp.39015104955862	103	1	y	y	X
mdp.39015104955862	103	2	<	<	X
mdp.39015104955862	103	3	1	1	NUM
mdp.39015104955862	103	4	,	,	PUNCT
mdp.39015104955862	103	5	are	be	AUX
mdp.39015104955862	103	6	u	u	ADJ
mdp.39015104955862	103	7	-	-	ADJ
mdp.39015104955862	103	8	invariant	invariant	ADJ
mdp.39015104955862	103	9	,	,	PUNCT
mdp.39015104955862	103	10	while	while	SCONJ
mdp.39015104955862	103	11	the	the	DET
mdp.39015104955862	103	12	class	class	NOUN
mdp.39015104955862	103	13	d({**/2	d({**/2	SPACE
mdp.39015104955862	103	14	}	}	PUNCT
mdp.39015104955862	103	15	)	)	PUNCT
mdp.39015104955862	103	16	is	be	AUX
mdp.39015104955862	103	17	not	not	PART
mdp.39015104955862	103	18	(	(	PUNCT
mdp.39015104955862	103	19	see	see	VERB
mdp.39015104955862	103	20	corollaries	corollary	NOUN
mdp.39015104955862	103	21	2	2	NUM
mdp.39015104955862	103	22	and	and	CCONJ
mdp.39015104955862	103	23	3	3	NUM
mdp.39015104955862	103	24	)	)	PUNCT
mdp.39015104955862	103	25	.	.	PUNCT
mdp.39015104955862	104	1	3	3	NUM
mdp.39015104955862	104	2	definitions	definition	NOUN
mdp.39015104955862	104	3	and	and	CCONJ
mdp.39015104955862	104	4	notation	notation	NOUN
mdp.39015104955862	104	5	definition	definition	NOUN
mdp.39015104955862	104	6	1	1	NUM
mdp.39015104955862	104	7	(	(	PUNCT
mdp.39015104955862	104	8	see	see	VERB
mdp.39015104955862	104	9	[	[	X
mdp.39015104955862	104	10	8],[11],[12	8],[11],[12	NUM
mdp.39015104955862	104	11	]	]	PUNCT
mdp.39015104955862	104	12	)	)	PUNCT
mdp.39015104955862	104	13	.	.	PUNCT
mdp.39015104955862	105	1	suppose	suppose	VERB
mdp.39015104955862	105	2	{	{	PUNCT
mdp.39015104955862	105	3	m	m	VERB
mdp.39015104955862	105	4	}	}	PUNCT
mdp.39015104955862	105	5	is	be	AUX
mdp.39015104955862	105	6	a	a	DET
mdp.39015104955862	105	7	sequence	sequence	NOUN
mdp.39015104955862	105	8	of	of	ADP
mdp.39015104955862	105	9	positive	positive	ADJ
mdp.39015104955862	105	10	numbers	number	NOUN
mdp.39015104955862	105	11	.	.	PUNCT
mdp.39015104955862	106	1	we	we	PRON
mdp.39015104955862	106	2	say	say	VERB
mdp.39015104955862	106	3	that	that	SCONJ
mdp.39015104955862	106	4	an	an	DET
mdp.39015104955862	106	5	infinitely	infinitely	ADV
mdp.39015104955862	106	6	differentiable	differentiable	ADJ
mdp.39015104955862	106	7	function	function	NOUN
mdp.39015104955862	106	8	&	&	CCONJ
mdp.39015104955862	106	9	on	on	ADP
mdp.39015104955862	106	10	the	the	DET
mdp.39015104955862	106	11	real	real	ADJ
mdp.39015104955862	106	12	line	line	NOUN
mdp.39015104955862	106	13	belongs	belong	VERB
mdp.39015104955862	106	14	to	to	ADP
mdp.39015104955862	106	15	the	the	DET
mdp.39015104955862	106	16	class	class	NOUN
mdp.39015104955862	106	17	d({mx	d({mx	SPACE
mdp.39015104955862	106	18	}	}	PUNCT
mdp.39015104955862	106	19	)	)	PUNCT
mdp.39015104955862	106	20	if	if	SCONJ
mdp.39015104955862	106	21	there	there	PRON
mdp.39015104955862	106	22	exist	exist	VERB
mdp.39015104955862	106	23	positive	positive	ADJ
mdp.39015104955862	106	24	constants	constant	NOUN
mdp.39015104955862	106	25	a	a	PRON
mdp.39015104955862	106	26	,	,	PUNCT
mdp.39015104955862	106	27	and	and	CCONJ
mdp.39015104955862	106	28	ho	ho	ADJ
mdp.39015104955862	106	29	,	,	PUNCT
mdp.39015104955862	106	30	depending	depend	VERB
mdp.39015104955862	106	31	on	on	ADP
mdp.39015104955862	106	32	4	4	NUM
mdp.39015104955862	106	33	,	,	PUNCT
mdp.39015104955862	106	34	such	such	ADJ
mdp.39015104955862	106	35	that	that	SCONJ
mdp.39015104955862	106	36	the	the	DET
mdp.39015104955862	106	37	following	following	ADJ
mdp.39015104955862	106	38	estimates	estimate	NOUN
mdp.39015104955862	106	39	hold	hold	VERB
mdp.39015104955862	106	40	for	for	ADP
mdp.39015104955862	106	41	the	the	DET
mdp.39015104955862	106	42	successive	successive	ADJ
mdp.39015104955862	106	43	derivatives	derivative	NOUN
mdp.39015104955862	106	44	(	(	PUNCT
mdp.39015104955862	106	45	*	*	PUNCT
mdp.39015104955862	106	46	)	)	PUNCT
mdp.39015104955862	106	47	of	of	ADP
mdp.39015104955862	106	48	the	the	DET
mdp.39015104955862	106	49	function	function	NOUN
mdp.39015104955862	106	50	4	4	NUM
mdp.39015104955862	106	51	,	,	PUNCT
mdp.39015104955862	106	52	|ø(k	|ø(k	SPACE
mdp.39015104955862	106	53	)	)	PUNCT
mdp.39015104955862	106	54	(	(	PUNCT
mdp.39015104955862	106	55	x)|	x)|	PROPN
mdp.39015104955862	106	56	≤	≤	PROPN
mdp.39015104955862	106	57	a¢h*mk	a¢h*mk	PROPN
mdp.39015104955862	106	58	,	,	PUNCT
mdp.39015104955862	106	59	x	x	PUNCT
mdp.39015104955862	106	60	є	є	PRON
mdp.39015104955862	106	61	r¹.	r¹.	PROPN
mdp.39015104955862	106	62	definition	definition	NOUN
mdp.39015104955862	106	63	2	2	NUM
mdp.39015104955862	106	64	(	(	PUNCT
mdp.39015104955862	106	65	see	see	VERB
mdp.39015104955862	106	66	[	[	X
mdp.39015104955862	106	67	8],[11],[12	8],[11],[12	NUM
mdp.39015104955862	106	68	]	]	PUNCT
mdp.39015104955862	106	69	)	)	PUNCT
mdp.39015104955862	106	70	.	.	PUNCT
mdp.39015104955862	107	1	the	the	DET
mdp.39015104955862	107	2	class	class	NOUN
mdp.39015104955862	107	3	d({m	d({m	PROPN
mdp.39015104955862	107	4	}	}	PUNCT
mdp.39015104955862	107	5	)	)	PUNCT
mdp.39015104955862	107	6	is	be	AUX
mdp.39015104955862	107	7	called	call	VERB
mdp.39015104955862	107	8	quasianalytic	quasianalytic	ADJ
mdp.39015104955862	107	9	if	if	SCONJ
mdp.39015104955862	107	10	$	$	SYM
mdp.39015104955862	107	11	€	€	SYM
mdp.39015104955862	107	12	d({mx	d({mx	ADV
mdp.39015104955862	107	13	}	}	PUNCT
mdp.39015104955862	107	14	)	)	PUNCT
mdp.39015104955862	107	15	,	,	PUNCT
mdp.39015104955862	107	16	$	$	SYM
mdp.39015104955862	107	17	(	(	PUNCT
mdp.39015104955862	107	18	k	k	PROPN
mdp.39015104955862	107	19	)	)	PUNCT
mdp.39015104955862	107	20	(	(	PUNCT
mdp.39015104955862	107	21	x0	x0	PROPN
mdp.39015104955862	107	22	)	)	PUNCT
mdp.39015104955862	107	23	=	=	PROPN
mdp.39015104955862	107	24	0	0	NUM
mdp.39015104955862	107	25	for	for	ADP
mdp.39015104955862	107	26	some	some	DET
mdp.39015104955862	107	27	xo	xo	X
mdp.39015104955862	107	28	€	€	PROPN
mdp.39015104955862	107	29	r¹	r¹	PROPN
mdp.39015104955862	107	30	and	and	CCONJ
mdp.39015104955862	107	31	all	all	DET
mdp.39015104955862	107	32	k	k	X
mdp.39015104955862	107	33	≥	≥	X
mdp.39015104955862	107	34	0	0	NUM
mdp.39015104955862	107	35	⇒	⇒	NOUN
mdp.39015104955862	107	36	☀	☀	PUNCT
mdp.39015104955862	107	37	=	=	SYM
mdp.39015104955862	107	38	0	0	NUM
mdp.39015104955862	107	39	,	,	PUNCT
mdp.39015104955862	107	40	while	while	SCONJ
mdp.39015104955862	107	41	all	all	DET
mdp.39015104955862	107	42	the	the	DET
mdp.39015104955862	107	43	classes	class	NOUN
mdp.39015104955862	107	44	d({m	d({m	PROPN
mdp.39015104955862	107	45	}	}	PUNCT
mdp.39015104955862	107	46	)	)	PUNCT
mdp.39015104955862	107	47	,	,	PUNCT
mdp.39015104955862	107	48	which	which	PRON
mdp.39015104955862	107	49	does	do	AUX
mdp.39015104955862	107	50	not	not	PART
mdp.39015104955862	107	51	satisfy	satisfy	VERB
mdp.39015104955862	107	52	the	the	DET
mdp.39015104955862	107	53	quasianalyticity	quasianalyticity	NOUN
mdp.39015104955862	107	54	condition	condition	NOUN
mdp.39015104955862	107	55	(	(	PUNCT
mdp.39015104955862	107	56	12	12	NUM
mdp.39015104955862	107	57	)	)	PUNCT
mdp.39015104955862	107	58	are	be	AUX
mdp.39015104955862	107	59	called	call	VERB
mdp.39015104955862	107	60	non	non	ADJ
mdp.39015104955862	107	61	-	-	ADJ
mdp.39015104955862	107	62	quasianalytic	quasianalytic	ADJ
mdp.39015104955862	107	63	.	.	PUNCT
mdp.39015104955862	108	1	(	(	PUNCT
mdp.39015104955862	108	2	12	12	NUM
mdp.39015104955862	108	3	)	)	PUNCT
mdp.39015104955862	108	4	it	it	PRON
mdp.39015104955862	108	5	is	be	AUX
mdp.39015104955862	108	6	easy	easy	ADJ
mdp.39015104955862	108	7	to	to	PART
mdp.39015104955862	108	8	see	see	VERB
mdp.39015104955862	108	9	that	that	SCONJ
mdp.39015104955862	108	10	classes	class	NOUN
mdp.39015104955862	108	11	d({m	d({m	PROPN
mdp.39015104955862	108	12	}	}	PUNCT
mdp.39015104955862	108	13	)	)	PUNCT
mdp.39015104955862	108	14	are	be	AUX
mdp.39015104955862	108	15	linear	linear	ADJ
mdp.39015104955862	108	16	and	and	CCONJ
mdp.39015104955862	108	17	dilation	dilation	NOUN
mdp.39015104955862	108	18	-	-	PUNCT
mdp.39015104955862	108	19	invariant	invariant	ADJ
mdp.39015104955862	108	20	.	.	PUNCT
mdp.39015104955862	109	1	the	the	DET
mdp.39015104955862	109	2	quasianalytic	quasianalytic	ADJ
mdp.39015104955862	109	3	classes	class	NOUN
mdp.39015104955862	109	4	d({m	d({m	PROPN
mdp.39015104955862	109	5	}	}	PUNCT
mdp.39015104955862	109	6	)	)	PUNCT
mdp.39015104955862	109	7	can	can	AUX
mdp.39015104955862	109	8	not	not	PART
mdp.39015104955862	109	9	contain	contain	VERB
mdp.39015104955862	109	10	functions	function	NOUN
mdp.39015104955862	109	11	with	with	ADP
mdp.39015104955862	109	12	compact	compact	ADJ
mdp.39015104955862	109	13	support	support	NOUN
mdp.39015104955862	109	14	.	.	PUNCT
mdp.39015104955862	110	1	definition	definition	NOUN
mdp.39015104955862	110	2	3	3	NUM
mdp.39015104955862	110	3	(	(	PUNCT
mdp.39015104955862	110	4	see	see	VERB
mdp.39015104955862	110	5	[	[	X
mdp.39015104955862	110	6	13	13	NUM
mdp.39015104955862	110	7	]	]	PUNCT
mdp.39015104955862	110	8	)	)	PUNCT
mdp.39015104955862	110	9	.	.	PUNCT
mdp.39015104955862	111	1	in	in	ADP
mdp.39015104955862	111	2	this	this	DET
mdp.39015104955862	111	3	definition	definition	NOUN
mdp.39015104955862	111	4	we	we	PRON
mdp.39015104955862	111	5	equip	equip	VERB
mdp.39015104955862	111	6	the	the	DET
mdp.39015104955862	111	7	class	class	NOUN
mdp.39015104955862	111	8	d({m	d({m	NOUN
mdp.39015104955862	111	9	}	}	PUNCT
mdp.39015104955862	111	10	)	)	PUNCT
mdp.39015104955862	111	11	with	with	ADP
mdp.39015104955862	111	12	the	the	DET
mdp.39015104955862	111	13	locally	locally	ADV
mdp.39015104955862	111	14	conver	conver	ADJ
mdp.39015104955862	111	15	topology	topology	NOUN
mdp.39015104955862	111	16	.	.	PUNCT
mdp.39015104955862	112	1	first	first	ADV
mdp.39015104955862	112	2	we	we	PRON
mdp.39015104955862	112	3	consider	consider	VERB
mdp.39015104955862	112	4	linear	linear	ADJ
mdp.39015104955862	112	5	subclasses	subclass	NOUN
mdp.39015104955862	112	6	,	,	PUNCT
mdp.39015104955862	112	7	dm({mx	dm({mx	PROPN
mdp.39015104955862	112	8	}	}	PUNCT
mdp.39015104955862	112	9	)	)	PUNCT
mdp.39015104955862	112	10	=	=	X
mdp.39015104955862	112	11	{	{	PUNCT
mdp.39015104955862	112	12	$	$	SYM
mdp.39015104955862	112	13	€	€	SYM
mdp.39015104955862	112	14	d({mx	d({mx	NOUN
mdp.39015104955862	112	15	}	}	PUNCT
mdp.39015104955862	112	16	)	)	PUNCT
mdp.39015104955862	112	17	:	:	PUNCT
mdp.39015104955862	112	18	|ø(*)(x)|	|ø(*)(x)|	NOUN
mdp.39015104955862	112	19	≤	≤	NOUN
mdp.39015104955862	112	20	аøm*μk	аøm*μk	PUNCT
mdp.39015104955862	112	21	,	,	PUNCT
mdp.39015104955862	112	22	k≥	k≥	PROPN
mdp.39015104955862	112	23	0	0	NUM
mdp.39015104955862	112	24	}	}	PUNCT
mdp.39015104955862	112	25	,	,	PUNCT
mdp.39015104955862	112	26	m	m	PROPN
mdp.39015104955862	112	27	≥	≥	X
mdp.39015104955862	112	28	1	1	NUM
mdp.39015104955862	112	29	7	7	NUM
mdp.39015104955862	112	30	of	of	ADP
mdp.39015104955862	112	31	d({mk	d({mk	PROPN
mdp.39015104955862	112	32	}	}	PUNCT
mdp.39015104955862	112	33	)	)	PUNCT
mdp.39015104955862	112	34	.	.	PUNCT
mdp.39015104955862	113	1	each	each	PRON
mdp.39015104955862	113	2	of	of	ADP
mdp.39015104955862	113	3	the	the	DET
mdp.39015104955862	113	4	classes	class	NOUN
mdp.39015104955862	113	5	d({m₁	d({m₁	ADJ
mdp.39015104955862	113	6	}	}	PUNCT
mdp.39015104955862	113	7	)	)	PUNCT
mdp.39015104955862	114	1	is	be	AUX
mdp.39015104955862	114	2	a	a	DET
mdp.39015104955862	114	3	banach	banach	NOUN
mdp.39015104955862	114	4	space	space	NOUN
mdp.39015104955862	114	5	with	with	ADP
mdp.39015104955862	114	6	the	the	DET
mdp.39015104955862	114	7	norm	norm	NOUN
mdp.39015104955862	114	8	defined	define	VERB
mdp.39015104955862	114	9	by	by	ADP
mdp.39015104955862	114	10	10(*)(x)|	10(*)(x)|	NUM
mdp.39015104955862	114	11	pm	pm	NOUN
mdp.39015104955862	114	12	(	(	PUNCT
mdp.39015104955862	114	13	4	4	X
mdp.39015104955862	114	14	)	)	PUNCT
mdp.39015104955862	114	15	=	=	PUNCT
mdp.39015104955862	115	1	sup	sup	X
mdp.39015104955862	115	2	sup	sup	PROPN
mdp.39015104955862	115	3	зer¹	зer¹	PROPN
mdp.39015104955862	115	4	k≥⁰	k≥⁰	PROPN
mdp.39015104955862	115	5	m	m	PROPN
mdp.39015104955862	115	6	⭑	⭑	NOUN
mdp.39015104955862	115	7	m	m	NOUN
mdp.39015104955862	115	8	*	*	NOUN
mdp.39015104955862	116	1	it	it	PRON
mdp.39015104955862	116	2	is	be	AUX
mdp.39015104955862	116	3	clear	clear	ADJ
mdp.39015104955862	116	4	that	that	SCONJ
mdp.39015104955862	116	5	d({i	d({i	PROPN
mdp.39015104955862	116	6	}	}	PUNCT
mdp.39015104955862	116	7	=	=	PROPN
mdp.39015104955862	116	8	udm({mx	udm({mx	PROPN
mdp.39015104955862	116	9	}	}	PUNCT
mdp.39015104955862	116	10	)	)	PUNCT
mdp.39015104955862	116	11	.	.	PUNCT
mdp.39015104955862	117	1	we	we	PRON
mdp.39015104955862	117	2	equip	equip	VERB
mdp.39015104955862	117	3	d({m	d({m	PROPN
mdp.39015104955862	117	4	}	}	PUNCT
mdp.39015104955862	117	5	)	)	PUNCT
mdp.39015104955862	117	6	with	with	ADP
mdp.39015104955862	117	7	the	the	DET
mdp.39015104955862	117	8	inductivet	inductivet	ADJ
mdp.39015104955862	117	9	topology	topology	NOUN
mdp.39015104955862	117	10	with	with	ADP
mdp.39015104955862	117	11	respect	respect	NOUN
mdp.39015104955862	117	12	to	to	ADP
mdp.39015104955862	117	13	the	the	DET
mdp.39015104955862	117	14	family	family	NOUN
mdp.39015104955862	117	15	of	of	ADP
mdp.39015104955862	117	16	its	its	PRON
mdp.39015104955862	117	17	subspaces	subspace	NOUN
mdp.39015104955862	117	18	dm({mx	dm({mx	ADP
mdp.39015104955862	117	19	}	}	PUNCT
mdp.39015104955862	117	20	)	)	PUNCT
mdp.39015104955862	117	21	,	,	PUNCT
mdp.39015104955862	117	22	m	m	PROPN
mdp.39015104955862	117	23	≥	≥	X
mdp.39015104955862	117	24	1	1	NUM
mdp.39015104955862	117	25	(	(	PUNCT
mdp.39015104955862	117	26	see	see	VERB
mdp.39015104955862	117	27	[	[	X
mdp.39015104955862	117	28	12	12	NUM
mdp.39015104955862	117	29	]	]	PUNCT
mdp.39015104955862	117	30	for	for	ADP
mdp.39015104955862	117	31	the	the	DET
mdp.39015104955862	117	32	definition	definition	NOUN
mdp.39015104955862	117	33	of	of	ADP
mdp.39015104955862	117	34	the	the	DET
mdp.39015104955862	117	35	inductive	inductive	ADJ
mdp.39015104955862	117	36	limit	limit	NOUN
mdp.39015104955862	117	37	)	)	PUNCT
mdp.39015104955862	117	38	.	.	PUNCT
mdp.39015104955862	118	1	definition	definition	NOUN
mdp.39015104955862	118	2	4	4	NUM
mdp.39015104955862	118	3	(	(	PUNCT
mdp.39015104955862	118	4	see	see	VERB
mdp.39015104955862	118	5	[	[	X
mdp.39015104955862	118	6	13	13	NUM
mdp.39015104955862	118	7	]	]	PUNCT
mdp.39015104955862	118	8	)	)	PUNCT
mdp.39015104955862	118	9	.	.	PUNCT
mdp.39015104955862	119	1	the	the	DET
mdp.39015104955862	119	2	space	space	NOUN
mdp.39015104955862	119	3	d'({m	d'({m	NOUN
mdp.39015104955862	119	4	}	}	PUNCT
mdp.39015104955862	119	5	)	)	PUNCT
mdp.39015104955862	119	6	of	of	ADP
mdp.39015104955862	119	7	all	all	DET
mdp.39015104955862	119	8	bounded	bound	VERB
mdp.39015104955862	119	9	linear	linear	ADJ
mdp.39015104955862	119	10	functionals	functional	NOUN
mdp.39015104955862	119	11	on	on	ADP
mdp.39015104955862	119	12	the	the	DET
mdp.39015104955862	119	13	locally	locally	ADV
mdp.39015104955862	119	14	compact	compact	ADJ
mdp.39015104955862	119	15	space	space	NOUN
mdp.39015104955862	119	16	d({m	d({m	PROPN
mdp.39015104955862	119	17	}	}	PUNCT
mdp.39015104955862	119	18	)	)	PUNCT
mdp.39015104955862	119	19	,	,	PUNCT
mdp.39015104955862	119	20	equipped	equip	VERB
mdp.39015104955862	119	21	with	with	ADP
mdp.39015104955862	119	22	the	the	DET
mdp.39015104955862	119	23	strong	strong	ADJ
mdp.39015104955862	119	24	topology	topology	NOUN
mdp.39015104955862	119	25	(	(	PUNCT
mdp.39015104955862	119	26	see	see	VERB
mdp.39015104955862	119	27	[	[	X
mdp.39015104955862	119	28	12	12	NUM
mdp.39015104955862	119	29	]	]	PUNCT
mdp.39015104955862	119	30	)	)	PUNCT
mdp.39015104955862	119	31	,	,	PUNCT
mdp.39015104955862	119	32	will	will	AUX
mdp.39015104955862	119	33	be	be	AUX
mdp.39015104955862	119	34	called	call	VERB
mdp.39015104955862	119	35	the	the	DET
mdp.39015104955862	119	36	space	space	NOUN
mdp.39015104955862	119	37	of	of	ADP
mdp.39015104955862	119	38	distributions	distribution	NOUN
mdp.39015104955862	119	39	over	over	ADP
mdp.39015104955862	119	40	the	the	DET
mdp.39015104955862	119	41	class	class	NOUN
mdp.39015104955862	119	42	d({m₁	d({m₁	ADJ
mdp.39015104955862	119	43	}	}	PUNCT
mdp.39015104955862	119	44	)	)	PUNCT
mdp.39015104955862	119	45	.	.	PUNCT
mdp.39015104955862	120	1	it	it	PRON
mdp.39015104955862	120	2	is	be	AUX
mdp.39015104955862	120	3	not	not	PART
mdp.39015104955862	120	4	difficult	difficult	ADJ
mdp.39015104955862	120	5	to	to	PART
mdp.39015104955862	120	6	prove	prove	VERB
mdp.39015104955862	120	7	that	that	SCONJ
mdp.39015104955862	120	8	every	every	DET
mdp.39015104955862	120	9	band	band	NOUN
mdp.39015104955862	120	10	-	-	PUNCT
mdp.39015104955862	120	11	limited	limit	VERB
mdp.39015104955862	120	12	function	function	NOUN
mdp.39015104955862	120	13	&	&	CCONJ
mdp.39015104955862	120	14	є	є	PRON
mdp.39015104955862	120	15	l²(r¹	l²(r¹	PROPN
mdp.39015104955862	120	16	)	)	PUNCT
mdp.39015104955862	120	17	belongs	belong	VERB
mdp.39015104955862	120	18	to	to	ADP
mdp.39015104955862	120	19	the	the	DET
mdp.39015104955862	120	20	class	class	NOUN
mdp.39015104955862	120	21	d({m	d({m	NOUN
mdp.39015104955862	120	22	}	}	PUNCT
mdp.39015104955862	120	23	)	)	PUNCT
mdp.39015104955862	120	24	with	with	ADP
mdp.39015104955862	120	25	m	m	NOUN
mdp.39015104955862	120	26	=	=	SYM
mdp.39015104955862	120	27	1	1	NUM
mdp.39015104955862	120	28	,	,	PUNCT
mdp.39015104955862	120	29	k	k	X
mdp.39015104955862	120	30	≥	≥	X
mdp.39015104955862	120	31	0	0	NUM
mdp.39015104955862	120	32	.	.	PUNCT
mdp.39015104955862	121	1	the	the	DET
mdp.39015104955862	121	2	tand	tand	NOUN
mdp.39015104955862	121	3	-	-	PUNCT
mdp.39015104955862	121	4	limitedness	limitedness	PROPN
mdp.39015104955862	121	5	means	mean	VERB
mdp.39015104955862	121	6	that	that	SCONJ
mdp.39015104955862	121	7	the	the	DET
mdp.39015104955862	121	8	support	support	NOUN
mdp.39015104955862	121	9	of	of	ADP
mdp.39015104955862	121	10	the	the	DET
mdp.39015104955862	121	11	fourier	fourier	NOUN
mdp.39015104955862	121	12	transform	transform	NOUN
mdp.39015104955862	121	13	of	of	ADP
mdp.39015104955862	121	14	4	4	NUM
mdp.39015104955862	121	15	is	be	AUX
mdp.39015104955862	121	16	bounded	bound	VERB
mdp.39015104955862	121	17	.	.	PUNCT
mdp.39015104955862	122	1	one	one	NUM
mdp.39015104955862	122	2	more	more	ADJ
mdp.39015104955862	122	3	example	example	NOUN
mdp.39015104955862	122	4	is	be	AUX
mdp.39015104955862	122	5	given	give	VERB
mdp.39015104955862	122	6	by	by	ADP
mdp.39015104955862	122	7	the	the	DET
mdp.39015104955862	122	8	gaussian	gaussian	PROPN
mdp.39015104955862	122	9	☀	☀	PROPN
mdp.39015104955862	122	10	(	(	PUNCT
mdp.39015104955862	122	11	x	x	SYM
mdp.39015104955862	122	12	)	)	PUNCT
mdp.39015104955862	122	13	=	=	X
mdp.39015104955862	122	14	e−r²	e−r²	X
mdp.39015104955862	122	15	which	which	PRON
mdp.39015104955862	122	16	belongs	belong	VERB
mdp.39015104955862	122	17	to	to	ADP
mdp.39015104955862	122	18	the	the	DET
mdp.39015104955862	122	19	class	class	NOUN
mdp.39015104955862	122	20	d({k*/2	d({k*/2	SPACE
mdp.39015104955862	122	21	}	}	PUNCT
mdp.39015104955862	122	22	)	)	PUNCT
mdp.39015104955862	122	23	.	.	PUNCT
mdp.39015104955862	123	1	in	in	ADP
mdp.39015104955862	123	2	the	the	DET
mdp.39015104955862	123	3	book	book	NOUN
mdp.39015104955862	123	4	by	by	ADP
mdp.39015104955862	123	5	mandelbrojt	mandelbrojt	PROPN
mdp.39015104955862	123	6	[	[	X
mdp.39015104955862	123	7	11	11	NUM
mdp.39015104955862	123	8	]	]	PUNCT
mdp.39015104955862	123	9	(	(	PUNCT
mdp.39015104955862	123	10	see	see	VERB
mdp.39015104955862	123	11	p.	p.	NOUN
mdp.39015104955862	123	12	89	89	NUM
mdp.39015104955862	123	13	)	)	PUNCT
mdp.39015104955862	124	1	there	there	PRON
mdp.39015104955862	124	2	are	be	VERB
mdp.39015104955862	124	3	examples	example	NOUN
mdp.39015104955862	124	4	of	of	ADP
mdp.39015104955862	124	5	functions	function	NOUN
mdp.39015104955862	124	6	&	&	CCONJ
mdp.39015104955862	124	7	€	€	SYM
mdp.39015104955862	124	8	d({m	d({m	NOUN
mdp.39015104955862	124	9	}	}	PUNCT
mdp.39015104955862	124	10	)	)	PUNCT
mdp.39015104955862	124	11	,	,	PUNCT
mdp.39015104955862	124	12	which	which	PRON
mdp.39015104955862	124	13	do	do	AUX
mdp.39015104955862	124	14	not	not	PART
mdp.39015104955862	124	15	belong	belong	VERB
mdp.39015104955862	124	16	to	to	ADP
mdp.39015104955862	124	17	any	any	DET
mdp.39015104955862	124	18	proper	proper	ADJ
mdp.39015104955862	124	19	subclass	subclass	NOUN
mdp.39015104955862	124	20	d({m	d({m	NOUN
mdp.39015104955862	124	21	}	}	PUNCT
mdp.39015104955862	124	22	)	)	PUNCT
mdp.39015104955862	124	23	of	of	ADP
mdp.39015104955862	124	24	d({m	d({m	PROPN
mdp.39015104955862	124	25	}	}	PUNCT
mdp.39015104955862	124	26	)	)	PUNCT
mdp.39015104955862	124	27	.	.	PUNCT
mdp.39015104955862	125	1	our	our	PRON
mdp.39015104955862	125	2	next	next	ADJ
mdp.39015104955862	125	3	goal	goal	NOUN
mdp.39015104955862	125	4	is	be	AUX
mdp.39015104955862	125	5	to	to	PART
mdp.39015104955862	125	6	introduce	introduce	VERB
mdp.39015104955862	125	7	new	new	ADJ
mdp.39015104955862	125	8	classes	class	NOUN
mdp.39015104955862	125	9	ď({m	ď({m	ADV
mdp.39015104955862	125	10	}	}	PUNCT
mdp.39015104955862	125	11	)	)	PUNCT
mdp.39015104955862	125	12	,	,	PUNCT
mdp.39015104955862	125	13	which	which	PRON
mdp.39015104955862	125	14	contain	contain	VERB
mdp.39015104955862	125	15	d({m	d({m	PROPN
mdp.39015104955862	125	16	}	}	PUNCT
mdp.39015104955862	125	17	)	)	PUNCT
mdp.39015104955862	125	18	and	and	CCONJ
mdp.39015104955862	125	19	all	all	DET
mdp.39015104955862	125	20	the	the	DET
mdp.39015104955862	125	21	polynomials	polynomial	NOUN
mdp.39015104955862	125	22	.	.	PUNCT
mdp.39015104955862	126	1	definition	definition	NOUN
mdp.39015104955862	126	2	5	5	NUM
mdp.39015104955862	126	3	for	for	ADP
mdp.39015104955862	126	4	given	give	VERB
mdp.39015104955862	126	5	sequence	sequence	NOUN
mdp.39015104955862	126	6	{	{	PUNCT
mdp.39015104955862	126	7	m	m	VERB
mdp.39015104955862	126	8	}	}	PUNCT
mdp.39015104955862	126	9	consider	consider	VERB
mdp.39015104955862	126	10	a	a	DET
mdp.39015104955862	126	11	class	class	NOUN
mdp.39015104955862	126	12	ď{{x	ď{{x	NUM
mdp.39015104955862	126	13	}	}	PUNCT
mdp.39015104955862	126	14	}	}	PUNCT
mdp.39015104955862	126	15	of	of	ADP
mdp.39015104955862	126	16	infinitely	infinitely	ADV
mdp.39015104955862	126	17	differentiable	differentiable	ADJ
mdp.39015104955862	126	18	functions	function	NOUN
mdp.39015104955862	126	19	on	on	ADP
mdp.39015104955862	126	20	the	the	DET
mdp.39015104955862	126	21	real	real	ADJ
mdp.39015104955862	126	22	line	line	NOUN
mdp.39015104955862	126	23	such	such	ADJ
mdp.39015104955862	126	24	that	that	SCONJ
mdp.39015104955862	126	25	there	there	PRON
mdp.39015104955862	126	26	exists	exist	VERB
mdp.39015104955862	126	27	a	a	DET
mdp.39015104955862	126	28	constant	constant	ADJ
mdp.39015104955862	126	29	ho	ho	NOUN
mdp.39015104955862	126	30	,	,	PUNCT
mdp.39015104955862	126	31	depending	depend	VERB
mdp.39015104955862	126	32	only	only	ADV
mdp.39015104955862	126	33	on	on	ADP
mdp.39015104955862	126	34	4	4	NUM
mdp.39015104955862	126	35	,	,	PUNCT
mdp.39015104955862	126	36	and	and	CCONJ
mdp.39015104955862	126	37	for	for	ADP
mdp.39015104955862	126	38	every	every	DET
mdp.39015104955862	126	39	finite	finite	NOUN
mdp.39015104955862	126	40	interval	interval	NOUN
mdp.39015104955862	127	1	ic	ic	INTJ
mdp.39015104955862	127	2	r¹	r¹	NOUN
mdp.39015104955862	127	3	there	there	PRON
mdp.39015104955862	127	4	exists	exist	VERB
mdp.39015104955862	127	5	a	a	DET
mdp.39015104955862	127	6	constant	constant	ADJ
mdp.39015104955862	127	7	a1	a1	NOUN
mdp.39015104955862	127	8	,	,	PUNCT
mdp.39015104955862	127	9	,	,	PUNCT
mdp.39015104955862	127	10	depending	depend	VERB
mdp.39015104955862	127	11	on	on	ADP
mdp.39015104955862	127	12	!	!	PUNCT
mdp.39015104955862	128	1	and	and	CCONJ
mdp.39015104955862	128	2	4	4	NUM
mdp.39015104955862	128	3	,	,	PUNCT
mdp.39015104955862	128	4	for	for	ADP
mdp.39015104955862	128	5	which	which	PRON
mdp.39015104955862	128	6	|ø(k	|ø(k	NOUN
mdp.39015104955862	128	7	)	)	PUNCT
mdp.39015104955862	128	8	(	(	PUNCT
mdp.39015104955862	128	9	x)|	x)|	PROPN
mdp.39015104955862	128	10	≤	≤	X
mdp.39015104955862	128	11	a1,øht	a1,øht	SPACE
mdp.39015104955862	128	12	,	,	PUNCT
mdp.39015104955862	128	13	m½	m½	PROPN
mdp.39015104955862	128	14	,	,	PUNCT
mdp.39015104955862	128	15	≈	≈	PROPN
mdp.39015104955862	128	16	€	€	PROPN
mdp.39015104955862	128	17	i	i	PROPN
mdp.39015104955862	128	18	,	,	PUNCT
mdp.39015104955862	128	19	k	k	PROPN
mdp.39015104955862	128	20	≥	≥	X
mdp.39015104955862	128	21	0	0	NUM
mdp.39015104955862	128	22	.	.	NOUN
mdp.39015104955862	128	23	8	8	NUM
mdp.39015104955862	128	24	definition	definition	NOUN
mdp.39015104955862	128	25	6	6	NUM
mdp.39015104955862	128	26	we	we	PRON
mdp.39015104955862	128	27	introduce	introduce	VERB
mdp.39015104955862	128	28	the	the	DET
mdp.39015104955862	128	29	locally	locally	ADV
mdp.39015104955862	128	30	convex	convex	ADJ
mdp.39015104955862	128	31	topology	topology	NOUN
mdp.39015104955862	128	32	of	of	ADP
mdp.39015104955862	128	33	the	the	DET
mdp.39015104955862	128	34	class	class	NOUN
mdp.39015104955862	128	35	ď({m	ď({m	NOUN
mdp.39015104955862	128	36	}	}	PUNCT
mdp.39015104955862	128	37	)	)	PUNCT
mdp.39015104955862	128	38	in	in	ADP
mdp.39015104955862	128	39	the	the	DET
mdp.39015104955862	128	40	following	following	ADJ
mdp.39015104955862	128	41	way	way	NOUN
mdp.39015104955862	128	42	.	.	PUNCT
mdp.39015104955862	129	1	consider	consider	VERB
mdp.39015104955862	129	2	linear	linear	ADJ
mdp.39015104955862	129	3	subspaces	subspace	NOUN
mdp.39015104955862	129	4	ďm({mx	ďm({mx	VERB
mdp.39015104955862	129	5	}	}	PUNCT
mdp.39015104955862	129	6	)	)	PUNCT
mdp.39015104955862	130	1	=	=	PUNCT
mdp.39015104955862	130	2	{	{	PUNCT
mdp.39015104955862	130	3	þ	þ	X
mdp.39015104955862	130	4	€	€	X
mdp.39015104955862	130	5	ď({mk	ď({mk	PROPN
mdp.39015104955862	130	6	}	}	PUNCT
mdp.39015104955862	130	7	)	)	PUNCT
mdp.39015104955862	130	8	:	:	PUNCT
mdp.39015104955862	130	9	p1,m(4	p1,m(4	X
mdp.39015104955862	130	10	)	)	PUNCT
mdp.39015104955862	130	11	=	=	VERB
mdp.39015104955862	130	12	sup	sup	X
mdp.39015104955862	130	13	sup	sup	X
mdp.39015104955862	130	14	<	<	X
mdp.39015104955862	130	15	∞	∞	PROPN
mdp.39015104955862	130	16	,	,	PUNCT
mdp.39015104955862	130	17	icr¹	icr¹	PROPN
mdp.39015104955862	130	18	}	}	PUNCT
mdp.39015104955862	130	19	.	.	PUNCT
mdp.39015104955862	131	1	(	(	PUNCT
mdp.39015104955862	131	2	13	13	X
mdp.39015104955862	131	3	)	)	PUNCT
mdp.39015104955862	131	4	the	the	DET
mdp.39015104955862	131	5	family	family	NOUN
mdp.39015104955862	131	6	of	of	ADP
mdp.39015104955862	131	7	semi	semi	ADJ
mdp.39015104955862	131	8	-	-	ADJ
mdp.39015104955862	131	9	norms	norms	ADJ
mdp.39015104955862	131	10	p1,m	p1,m	PROPN
mdp.39015104955862	131	11	generates	generate	VERB
mdp.39015104955862	131	12	the	the	DET
mdp.39015104955862	131	13	frechet	frechet	PROPN
mdp.39015104955862	131	14	space	space	PROPN
mdp.39015104955862	131	15	topology	topology	PROPN
mdp.39015104955862	131	16	on	on	ADP
mdp.39015104955862	131	17	d({m	d({m	PROPN
mdp.39015104955862	131	18	}	}	PUNCT
mdp.39015104955862	131	19	)	)	PUNCT
mdp.39015104955862	131	20	.	.	PUNCT
mdp.39015104955862	132	1	it	it	PRON
mdp.39015104955862	132	2	is	be	AUX
mdp.39015104955862	132	3	clear	clear	ADJ
mdp.39015104955862	132	4	that	that	SCONJ
mdp.39015104955862	132	5	10(*)(x)|	10(*)(x)|	NUM
mdp.39015104955862	132	6	el	el	PROPN
mdp.39015104955862	132	7	k>0	k>0	PROPN
mdp.39015104955862	132	8	mk	mk	PROPN
mdp.39015104955862	132	9	mk	mk	PROPN
mdp.39015104955862	132	10	ď({mk	ď({mk	PROPN
mdp.39015104955862	132	11	}	}	PUNCT
mdp.39015104955862	132	12	)	)	PUNCT
mdp.39015104955862	132	13	=	=	X
mdp.39015104955862	132	14	||ďm({mk	||ďm({mk	SPACE
mdp.39015104955862	132	15	}	}	PUNCT
mdp.39015104955862	132	16	)	)	PUNCT
mdp.39015104955862	132	17	.	.	PUNCT
mdp.39015104955862	133	1	m	m	VERB
mdp.39015104955862	133	2	we	we	PRON
mdp.39015104955862	133	3	equip	equip	VERB
mdp.39015104955862	133	4	d({mk	d({mk	PROPN
mdp.39015104955862	133	5	}	}	PUNCT
mdp.39015104955862	133	6	)	)	PUNCT
mdp.39015104955862	133	7	with	with	ADP
mdp.39015104955862	133	8	the	the	DET
mdp.39015104955862	133	9	inductive	inductive	ADJ
mdp.39015104955862	133	10	limit	limit	NOUN
mdp.39015104955862	133	11	topology	topology	NOUN
mdp.39015104955862	133	12	with	with	ADP
mdp.39015104955862	133	13	respect	respect	NOUN
mdp.39015104955862	133	14	to	to	ADP
mdp.39015104955862	133	15	the	the	DET
mdp.39015104955862	133	16	family	family	NOUN
mdp.39015104955862	133	17	of	of	ADP
mdp.39015104955862	133	18	its	its	PRON
mdp.39015104955862	133	19	linear	linear	ADJ
mdp.39015104955862	133	20	subspaces	subspace	NOUN
mdp.39015104955862	133	21	{	{	PUNCT
mdp.39015104955862	133	22	ďm({m	ďm({m	PROPN
mdp.39015104955862	133	23	}	}	PUNCT
mdp.39015104955862	133	24	)	)	PUNCT
mdp.39015104955862	133	25	}	}	PUNCT
mdp.39015104955862	133	26	,	,	PUNCT
mdp.39015104955862	133	27	m	m	PROPN
mdp.39015104955862	133	28	≥	≥	X
mdp.39015104955862	133	29	1	1	NUM
mdp.39015104955862	133	30	(	(	PUNCT
mdp.39015104955862	133	31	see	see	VERB
mdp.39015104955862	133	32	[	[	X
mdp.39015104955862	133	33	12	12	NUM
mdp.39015104955862	133	34	]	]	PUNCT
mdp.39015104955862	133	35	for	for	ADP
mdp.39015104955862	133	36	the	the	DET
mdp.39015104955862	133	37	definition	definition	NOUN
mdp.39015104955862	133	38	of	of	ADP
mdp.39015104955862	133	39	the	the	DET
mdp.39015104955862	133	40	inductive	inductive	ADJ
mdp.39015104955862	133	41	limit	limit	NOUN
mdp.39015104955862	133	42	)	)	PUNCT
mdp.39015104955862	133	43	.	.	PUNCT
mdp.39015104955862	134	1	are	be	AUX
mdp.39015104955862	134	2	called	call	VERB
mdp.39015104955862	134	3	the	the	DET
mdp.39015104955862	134	4	moments	moment	NOUN
mdp.39015104955862	134	5	of	of	ADP
mdp.39015104955862	134	6	г	г	PROPN
mdp.39015104955862	134	7	.	.	PUNCT
mdp.39015104955862	135	1	suppose	suppose	VERB
mdp.39015104955862	135	2	i	i	PRON
mdp.39015104955862	135	3	is	be	AUX
mdp.39015104955862	135	4	a	a	DET
mdp.39015104955862	135	5	bounded	bounded	ADJ
mdp.39015104955862	135	6	linear	linear	NOUN
mdp.39015104955862	135	7	functional	functional	NOUN
mdp.39015104955862	135	8	on	on	ADP
mdp.39015104955862	135	9	the	the	DET
mdp.39015104955862	135	10	space	space	NOUN
mdp.39015104955862	135	11	ď({m	ď({m	NOUN
mdp.39015104955862	135	12	}	}	PUNCT
mdp.39015104955862	135	13	)	)	PUNCT
mdp.39015104955862	135	14	.	.	PUNCT
mdp.39015104955862	136	1	the	the	DET
mdp.39015104955862	136	2	next	next	ADJ
mdp.39015104955862	136	3	definition	definition	NOUN
mdp.39015104955862	136	4	introduces	introduce	VERB
mdp.39015104955862	136	5	the	the	DET
mdp.39015104955862	136	6	moments	moment	NOUN
mdp.39015104955862	136	7	of	of	ADP
mdp.39015104955862	136	8	such	such	ADJ
mdp.39015104955862	136	9	functionals	functional	NOUN
mdp.39015104955862	136	10	.	.	PUNCT
mdp.39015104955862	137	1	definition	definition	NOUN
mdp.39015104955862	137	2	7	7	NUM
mdp.39015104955862	137	3	for	for	ADP
mdp.39015104955862	137	4	the	the	DET
mdp.39015104955862	137	5	functional	functional	ADJ
mdp.39015104955862	137	6	г	г	PROPN
mdp.39015104955862	137	7	as	as	ADP
mdp.39015104955862	137	8	above	above	ADV
mdp.39015104955862	137	9	,	,	PUNCT
mdp.39015104955862	137	10	the	the	DET
mdp.39015104955862	137	11	numbers	number	NOUN
mdp.39015104955862	137	12	µk(t	µk(t	SPACE
mdp.39015104955862	137	13	)	)	PUNCT
mdp.39015104955862	137	14	=	=	X
mdp.39015104955862	137	15	t(x^	t(x^	PROPN
mdp.39015104955862	137	16	)	)	PUNCT
mdp.39015104955862	137	17	,	,	PUNCT
mdp.39015104955862	137	18	k≥0	k≥0	PROPN
mdp.39015104955862	137	19	(	(	PUNCT
mdp.39015104955862	137	20	14	14	NUM
mdp.39015104955862	137	21	)	)	PUNCT
mdp.39015104955862	138	1	it	it	PRON
mdp.39015104955862	138	2	is	be	AUX
mdp.39015104955862	138	3	clear	clear	ADJ
mdp.39015104955862	138	4	that	that	SCONJ
mdp.39015104955862	138	5	d({mx	d({mx	SPACE
mdp.39015104955862	138	6	}	}	PUNCT
mdp.39015104955862	138	7	)	)	PUNCT
mdp.39015104955862	138	8	℃	℃	PROPN
mdp.39015104955862	138	9	ď({mx	ď({mx	NUM
mdp.39015104955862	138	10	}	}	PUNCT
mdp.39015104955862	138	11	)	)	PUNCT
mdp.39015104955862	138	12	.	.	PUNCT
mdp.39015104955862	139	1	thus	thus	ADV
mdp.39015104955862	139	2	,	,	PUNCT
mdp.39015104955862	139	3	every	every	DET
mdp.39015104955862	139	4	bounded	bound	VERB
mdp.39015104955862	139	5	linear	linear	PROPN
mdp.39015104955862	139	6	functional	functional	PROPN
mdp.39015104955862	139	7	г	г	X
mdp.39015104955862	139	8	on	on	ADP
mdp.39015104955862	139	9	ď({m	ď({m	NOUN
mdp.39015104955862	139	10	}	}	PUNCT
mdp.39015104955862	139	11	)	)	PUNCT
mdp.39015104955862	139	12	belongs	belong	VERB
mdp.39015104955862	139	13	to	to	ADP
mdp.39015104955862	139	14	the	the	DET
mdp.39015104955862	139	15	space	space	NOUN
mdp.39015104955862	139	16	d'({mk	d'({mk	NOUN
mdp.39015104955862	139	17	}	}	PUNCT
mdp.39015104955862	139	18	)	)	PUNCT
mdp.39015104955862	139	19	.	.	PUNCT
mdp.39015104955862	140	1	definition	definition	NOUN
mdp.39015104955862	140	2	8	8	NUM
mdp.39015104955862	140	3	the	the	DET
mdp.39015104955862	140	4	space	space	NOUN
mdp.39015104955862	140	5	ď'({m	ď'({m	SPACE
mdp.39015104955862	140	6	}	}	PUNCT
mdp.39015104955862	140	7	)	)	PUNCT
mdp.39015104955862	140	8	of	of	ADP
mdp.39015104955862	140	9	all	all	DET
mdp.39015104955862	140	10	bounded	bound	VERB
mdp.39015104955862	140	11	linear	linear	ADJ
mdp.39015104955862	140	12	functionals	functional	NOUN
mdp.39015104955862	140	13	on	on	ADP
mdp.39015104955862	140	14	the	the	DET
mdp.39015104955862	140	15	locally	locally	ADV
mdp.39015104955862	140	16	conver	conver	ADJ
mdp.39015104955862	140	17	space	space	NOUN
mdp.39015104955862	140	18	d({m	d({m	PROPN
mdp.39015104955862	140	19	}	}	PUNCT
mdp.39015104955862	140	20	)	)	PUNCT
mdp.39015104955862	140	21	,	,	PUNCT
mdp.39015104955862	140	22	equipped	equip	VERB
mdp.39015104955862	140	23	with	with	ADP
mdp.39015104955862	140	24	the	the	DET
mdp.39015104955862	140	25	strong	strong	ADJ
mdp.39015104955862	140	26	topology	topology	NOUN
mdp.39015104955862	140	27	(	(	PUNCT
mdp.39015104955862	140	28	see	see	VERB
mdp.39015104955862	140	29	[	[	X
mdp.39015104955862	140	30	12	12	NUM
mdp.39015104955862	140	31	]	]	PUNCT
mdp.39015104955862	140	32	)	)	PUNCT
mdp.39015104955862	140	33	,	,	PUNCT
mdp.39015104955862	140	34	will	will	AUX
mdp.39015104955862	140	35	be	be	AUX
mdp.39015104955862	140	36	called	call	VERB
mdp.39015104955862	140	37	the	the	DET
mdp.39015104955862	140	38	space	space	NOUN
mdp.39015104955862	140	39	of	of	ADP
mdp.39015104955862	140	40	distributions	distribution	NOUN
mdp.39015104955862	140	41	over	over	ADP
mdp.39015104955862	140	42	the	the	DET
mdp.39015104955862	140	43	class	class	NOUN
mdp.39015104955862	140	44	d{{m	d{{m	NUM
mdp.39015104955862	140	45	}	}	PUNCT
mdp.39015104955862	140	46	)	)	PUNCT
mdp.39015104955862	140	47	,	,	PUNCT
mdp.39015104955862	140	48	which	which	PRON
mdp.39015104955862	140	49	have	have	VERB
mdp.39015104955862	140	50	moments	moment	NOUN
mdp.39015104955862	140	51	.	.	PUNCT
mdp.39015104955862	141	1	9	9	NUM
mdp.39015104955862	141	2	the	the	DET
mdp.39015104955862	141	3	quasianalyticity	quasianalyticity	NOUN
mdp.39015104955862	141	4	property	property	NOUN
mdp.39015104955862	141	5	of	of	ADP
mdp.39015104955862	141	6	the	the	DET
mdp.39015104955862	141	7	class	class	NOUN
mdp.39015104955862	141	8	d({m	d({m	NOUN
mdp.39015104955862	141	9	}	}	PUNCT
mdp.39015104955862	141	10	)	)	PUNCT
mdp.39015104955862	141	11	depends	depend	VERB
mdp.39015104955862	141	12	on	on	ADP
mdp.39015104955862	141	13	the	the	DET
mdp.39015104955862	141	14	behavior	behavior	NOUN
mdp.39015104955862	141	15	of	of	ADP
mdp.39015104955862	141	16	the	the	DET
mdp.39015104955862	141	17	ostrovski	ostrovski	NOUN
mdp.39015104955862	141	18	function	function	NOUN
mdp.39015104955862	141	19	k≥0	k≥0	PROPN
mdp.39015104955862	141	20	mk	mk	PROPN
mdp.39015104955862	141	21	(	(	PUNCT
mdp.39015104955862	141	22	see	see	VERB
mdp.39015104955862	141	23	[	[	X
mdp.39015104955862	141	24	8	8	NUM
mdp.39015104955862	141	25	]	]	PUNCT
mdp.39015104955862	141	26	)	)	PUNCT
mdp.39015104955862	141	27	.	.	PUNCT
mdp.39015104955862	142	1	for	for	ADP
mdp.39015104955862	142	2	every	every	DET
mdp.39015104955862	142	3	sequence	sequence	NOUN
mdp.39015104955862	142	4	{	{	PUNCT
mdp.39015104955862	142	5	m	m	NOUN
mdp.39015104955862	142	6	}	}	PUNCT
mdp.39015104955862	142	7	,	,	PUNCT
mdp.39015104955862	142	8	the	the	DET
mdp.39015104955862	142	9	new	new	ADJ
mdp.39015104955862	142	10	sequence	sequence	NOUN
mdp.39015104955862	142	11	{	{	PUNCT
mdp.39015104955862	142	12	m	m	NOUN
mdp.39015104955862	142	13	}	}	PUNCT
mdp.39015104955862	142	14	,	,	PUNCT
mdp.39015104955862	142	15	defined	define	VERB
mdp.39015104955862	142	16	by	by	ADP
mdp.39015104955862	142	17	t(r	t(r	NOUN
mdp.39015104955862	142	18	)	)	PUNCT
mdp.39015104955862	142	19	=	=	PROPN
mdp.39015104955862	142	20	sup	sup	PROPN
mdp.39015104955862	142	21	(	(	PUNCT
mdp.39015104955862	142	22	15	15	NUM
mdp.39015104955862	142	23	)	)	PUNCT
mdp.39015104955862	142	24	is	be	AUX
mdp.39015104955862	142	25	called	call	VERB
mdp.39015104955862	142	26	the	the	DET
mdp.39015104955862	142	27	convex	convex	ADJ
mdp.39015104955862	142	28	logarithmic	logarithmic	ADJ
mdp.39015104955862	142	29	regularization	regularization	NOUN
mdp.39015104955862	142	30	of	of	ADP
mdp.39015104955862	142	31	the	the	DET
mdp.39015104955862	142	32	sequence	sequence	NOUN
mdp.39015104955862	142	33	{	{	PUNCT
mdp.39015104955862	142	34	m	m	NOUN
mdp.39015104955862	142	35	}	}	PUNCT
mdp.39015104955862	142	36	.	.	PUNCT
mdp.39015104955862	143	1	the	the	DET
mdp.39015104955862	143	2	sequence	sequence	NOUN
mdp.39015104955862	143	3	{	{	PUNCT
mdp.39015104955862	143	4	ln	ln	PROPN
mdp.39015104955862	143	5	mx	mx	PROPN
mdp.39015104955862	143	6	}	}	PUNCT
mdp.39015104955862	143	7	is	be	AUX
mdp.39015104955862	143	8	the	the	DET
mdp.39015104955862	143	9	largest	large	ADJ
mdp.39015104955862	143	10	convex	convex	ADJ
mdp.39015104955862	143	11	sequence	sequence	NOUN
mdp.39015104955862	143	12	,	,	PUNCT
mdp.39015104955862	143	13	minorizing	minorize	VERB
mdp.39015104955862	143	14	the	the	DET
mdp.39015104955862	143	15	sequence	sequence	NOUN
mdp.39015104955862	143	16	{	{	PUNCT
mdp.39015104955862	143	17	ln	ln	ADV
mdp.39015104955862	143	18	m	m	PROPN
mdp.39015104955862	143	19	}	}	PUNCT
mdp.39015104955862	143	20	.	.	PUNCT
mdp.39015104955862	144	1	if	if	SCONJ
mdp.39015104955862	144	2	the	the	DET
mdp.39015104955862	144	3	initial	initial	ADJ
mdp.39015104955862	144	4	sequence	sequence	NOUN
mdp.39015104955862	144	5	{	{	PUNCT
mdp.39015104955862	144	6	mk	mk	PROPN
mdp.39015104955862	144	7	}	}	PUNCT
mdp.39015104955862	144	8	is	be	AUX
mdp.39015104955862	144	9	logarithmically	logarithmically	ADV
mdp.39015104955862	144	10	convex	convex	ADJ
mdp.39015104955862	144	11	,	,	PUNCT
mdp.39015104955862	144	12	namely	namely	ADV
mdp.39015104955862	144	13	if	if	SCONJ
mdp.39015104955862	144	14	m²	m²	PROPN
mdp.39015104955862	144	15	≤	≤	X
mdp.39015104955862	144	16	mk−1	mk−1	NOUN
mdp.39015104955862	144	17	mk+1	mk+1	PROPN
mdp.39015104955862	144	18	,	,	PUNCT
mdp.39015104955862	144	19	k	k	PROPN
mdp.39015104955862	144	20	≥	≥	PROPN
mdp.39015104955862	144	21	1	1	NUM
mdp.39015104955862	144	22	,	,	PUNCT
mdp.39015104955862	144	23	2	2	NUM
mdp.39015104955862	144	24	.	.	PUNCT
mdp.39015104955862	144	25	then	then	ADV
mdp.39015104955862	144	26	m	m	VERB
mdp.39015104955862	144	27	=	=	PROPN
mdp.39015104955862	144	28	mk	mk	PROPN
mdp.39015104955862	144	29	,	,	PUNCT
mdp.39015104955862	144	30	k≥	k≥	PROPN
mdp.39015104955862	144	31	0	0	NUM
mdp.39015104955862	144	32	.	.	PUNCT
mdp.39015104955862	145	1	the	the	DET
mdp.39015104955862	145	2	main	main	ADJ
mdp.39015104955862	145	3	result	result	NOUN
mdp.39015104955862	145	4	in	in	ADP
mdp.39015104955862	145	5	the	the	DET
mdp.39015104955862	145	6	theory	theory	NOUN
mdp.39015104955862	145	7	of	of	ADP
mdp.39015104955862	145	8	quasianalytic	quasianalytic	ADJ
mdp.39015104955862	145	9	classes	class	NOUN
mdp.39015104955862	145	10	is	be	AUX
mdp.39015104955862	145	11	called	call	VERB
mdp.39015104955862	145	12	the	the	DET
mdp.39015104955862	145	13	denjoy	denjoy	NOUN
mdp.39015104955862	145	14	-	-	PUNCT
mdp.39015104955862	145	15	carleman	carleman	PROPN
mdp.39015104955862	145	16	theorem	theorem	NOUN
mdp.39015104955862	145	17	(	(	PUNCT
mdp.39015104955862	145	18	see	see	VERB
mdp.39015104955862	145	19	[	[	X
mdp.39015104955862	145	20	8	8	NUM
mdp.39015104955862	145	21	]	]	PUNCT
mdp.39015104955862	145	22	)	)	PUNCT
mdp.39015104955862	145	23	.	.	PUNCT
mdp.39015104955862	146	1	3	3	X
mdp.39015104955862	146	2	.	.	X
mdp.39015104955862	146	3	theorem	theorem	PROPN
mdp.39015104955862	146	4	1	1	NUM
mdp.39015104955862	146	5	(	(	PUNCT
mdp.39015104955862	146	6	denjoy	denjoy	NOUN
mdp.39015104955862	146	7	-	-	PUNCT
mdp.39015104955862	146	8	carleman	carleman	PROPN
mdp.39015104955862	146	9	)	)	PUNCT
mdp.39015104955862	146	10	the	the	DET
mdp.39015104955862	146	11	following	follow	VERB
mdp.39015104955862	146	12	conditions	condition	NOUN
mdp.39015104955862	146	13	are	be	AUX
mdp.39015104955862	146	14	equivalent	equivalent	ADJ
mdp.39015104955862	146	15	:	:	PUNCT
mdp.39015104955862	146	16	1	1	X
mdp.39015104955862	146	17	.	.	X
mdp.39015104955862	146	18	the	the	DET
mdp.39015104955862	146	19	class	class	NOUN
mdp.39015104955862	146	20	d({m	d({m	PROPN
mdp.39015104955862	146	21	}	}	PUNCT
mdp.39015104955862	146	22	)	)	PUNCT
mdp.39015104955862	146	23	is	be	AUX
mdp.39015104955862	146	24	quasianalytic	quasianalytic	ADJ
mdp.39015104955862	146	25	.	.	PUNCT
mdp.39015104955862	147	1	4	4	X
mdp.39015104955862	147	2	.	.	PUNCT
mdp.39015104955862	148	1	in	in	ADP
mdp.39015104955862	148	2	m	m	NOUN
mdp.39015104955862	148	3	=	=	NOUN
mdp.39015104955862	148	4	sup(k	sup(k	PROPN
mdp.39015104955862	148	5	ln	ln	ADJ
mdp.39015104955862	148	6	r	r	NOUN
mdp.39015104955862	148	7	—	—	PUNCT
mdp.39015104955862	148	8	ln	ln	ADV
mdp.39015104955862	148	9	t(r	t(r	PROPN
mdp.39015104955862	148	10	)	)	PUNCT
mdp.39015104955862	148	11	)	)	PUNCT
mdp.39015104955862	148	12	,	,	PUNCT
mdp.39015104955862	148	13	r>0	r>0	PROPN
mdp.39015104955862	148	14	∞	∞	NUM
mdp.39015104955862	148	15	ln	ln	ADV
mdp.39015104955862	148	16	t(r	t(r	NOUN
mdp.39015104955862	148	17	)	)	PUNCT
mdp.39015104955862	148	18	1	1	NUM
mdp.39015104955862	148	19	+	+	NUM
mdp.39015104955862	148	20	2	2	NUM
mdp.39015104955862	148	21	%	%	NOUN
mdp.39015104955862	148	22	°	°	PROPN
mdp.39015104955862	148	23	°	°	X
mdp.39015104955862	148	24	!	!	PUNCT
mdp.39015104955862	149	1	m8	m8	PROPN
mdp.39015104955862	149	2	r>0	r>0	PROPN
mdp.39015104955862	149	3	k=0	k=0	PROPN
mdp.39015104955862	149	4	k=0	k=0	PROPN
mdp.39015104955862	149	5	m	m	VERB
mdp.39015104955862	149	6	mkti	mkti	PROPN
mdp.39015104955862	149	7	σ(mk)−¹/	σ(mk)−¹/	PROPN
mdp.39015104955862	150	1	*	*	PROPN
mdp.39015104955862	150	2	dr	dr	PROPN
mdp.39015104955862	150	3	=	=	PRON
mdp.39015104955862	150	4	∞.	∞.	PROPN
mdp.39015104955862	150	5	∞.	∞.	PROPN
mdp.39015104955862	150	6	=	=	PUNCT
mdp.39015104955862	150	7	∞.	∞.	PROPN
mdp.39015104955862	150	8	10	10	NUM
mdp.39015104955862	150	9	the	the	DET
mdp.39015104955862	150	10	following	follow	VERB
mdp.39015104955862	150	11	theorem	theorem	NOUN
mdp.39015104955862	150	12	reduces	reduce	VERB
mdp.39015104955862	150	13	the	the	DET
mdp.39015104955862	150	14	case	case	NOUN
mdp.39015104955862	150	15	of	of	ADP
mdp.39015104955862	150	16	the	the	DET
mdp.39015104955862	150	17	general	general	ADJ
mdp.39015104955862	150	18	classes	class	NOUN
mdp.39015104955862	150	19	d({m	d({m	PROPN
mdp.39015104955862	150	20	}	}	PUNCT
mdp.39015104955862	150	21	)	)	PUNCT
mdp.39015104955862	150	22	to	to	ADP
mdp.39015104955862	150	23	the	the	DET
mdp.39015104955862	150	24	case	case	NOUN
mdp.39015104955862	150	25	of	of	ADP
mdp.39015104955862	150	26	classes	class	NOUN
mdp.39015104955862	150	27	with	with	ADP
mdp.39015104955862	150	28	logarithmically	logarithmically	ADV
mdp.39015104955862	150	29	convex	convex	ADJ
mdp.39015104955862	150	30	defining	define	VERB
mdp.39015104955862	150	31	sequences	sequence	NOUN
mdp.39015104955862	150	32	.	.	PUNCT
mdp.39015104955862	151	1	theorem	theorem	PROPN
mdp.39015104955862	151	2	2	2	NUM
mdp.39015104955862	151	3	(	(	PUNCT
mdp.39015104955862	151	4	cartan	cartan	ADV
mdp.39015104955862	151	5	-	-	PUNCT
mdp.39015104955862	151	6	gorny	gorny	PROPN
mdp.39015104955862	151	7	)	)	PUNCT
mdp.39015104955862	151	8	(	(	PUNCT
mdp.39015104955862	151	9	see	see	VERB
mdp.39015104955862	151	10	[	[	X
mdp.39015104955862	151	11	8	8	NUM
mdp.39015104955862	151	12	]	]	PUNCT
mdp.39015104955862	151	13	)	)	PUNCT
mdp.39015104955862	151	14	for	for	ADP
mdp.39015104955862	151	15	every	every	DET
mdp.39015104955862	151	16	positive	positive	ADJ
mdp.39015104955862	151	17	sequence	sequence	NOUN
mdp.39015104955862	151	18	{	{	PUNCT
mdp.39015104955862	151	19	m	m	NOUN
mdp.39015104955862	151	20	}	}	PUNCT
mdp.39015104955862	151	21	we	we	PRON
mdp.39015104955862	151	22	have	have	VERB
mdp.39015104955862	151	23	d({m	d({m	PROPN
mdp.39015104955862	151	24	}	}	PUNCT
mdp.39015104955862	151	25	)	)	PUNCT
mdp.39015104955862	151	26	=	=	VERB
mdp.39015104955862	151	27	d({m	d({m	PROPN
mdp.39015104955862	151	28	}	}	PUNCT
mdp.39015104955862	151	29	)	)	PUNCT
mdp.39015104955862	151	30	.	.	PUNCT
mdp.39015104955862	152	1	as	as	SCONJ
mdp.39015104955862	152	2	we	we	PRON
mdp.39015104955862	152	3	have	have	AUX
mdp.39015104955862	152	4	already	already	ADV
mdp.39015104955862	152	5	mentioned	mention	VERB
mdp.39015104955862	152	6	in	in	ADP
mdp.39015104955862	152	7	the	the	DET
mdp.39015104955862	152	8	introduction	introduction	NOUN
mdp.39015104955862	152	9	,	,	PUNCT
mdp.39015104955862	152	10	the	the	DET
mdp.39015104955862	152	11	formal	formal	ADJ
mdp.39015104955862	152	12	infinite	infinite	ADJ
mdp.39015104955862	152	13	series	series	PROPN
mdp.39015104955862	152	14	,	,	PUNCT
mdp.39015104955862	152	15	f	f	PROPN
mdp.39015104955862	152	16	=	=	SYM
mdp.39015104955862	152	17	σ	σ	PROPN
mdp.39015104955862	152	18	αιδία	αιδία	NOUN
mdp.39015104955862	152	19	)	)	PUNCT
mdp.39015104955862	152	20	ž	ž	X
mdp.39015104955862	152	21	k=0	k=0	PROPN
mdp.39015104955862	152	22	will	will	AUX
mdp.39015104955862	152	23	be	be	AUX
mdp.39015104955862	152	24	called	call	VERB
mdp.39015104955862	152	25	hyperdistributions	hyperdistribution	NOUN
mdp.39015104955862	152	26	.	.	PUNCT
mdp.39015104955862	153	1	we	we	PRON
mdp.39015104955862	153	2	have	have	VERB
mdp.39015104955862	153	3	(	(	PUNCT
mdp.39015104955862	153	4	formally	formally	ADV
mdp.39015104955862	153	5	)	)	PUNCT
mdp.39015104955862	153	6	the	the	DET
mdp.39015104955862	153	7	following	follow	VERB
mdp.39015104955862	153	8	formula	formula	NOUN
mdp.39015104955862	153	9	for	for	ADP
mdp.39015104955862	153	10	the	the	DET
mdp.39015104955862	153	11	moments	moment	NOUN
mdp.39015104955862	153	12	(	(	PUNCT
mdp.39015104955862	153	13	14	14	NUM
mdp.39015104955862	153	14	)	)	PUNCT
mdp.39015104955862	153	15	of	of	ADP
mdp.39015104955862	153	16	г	г	PROPN
mdp.39015104955862	153	17	:	:	PUNCT
mdp.39015104955862	153	18	µk(t	µk(t	SPACE
mdp.39015104955862	153	19	)	)	PUNCT
mdp.39015104955862	153	20	=	=	X
mdp.39015104955862	153	21	(	(	PUNCT
mdp.39015104955862	153	22	−1)^k!ak	−1)^k!ak	SPACE
mdp.39015104955862	153	23	,	,	PUNCT
mdp.39015104955862	153	24	k≥0	k≥0	PROPN
mdp.39015104955862	153	25	and	and	CCONJ
mdp.39015104955862	153	26	the	the	DET
mdp.39015104955862	153	27	following	following	ADJ
mdp.39015104955862	153	28	moment	moment	NOUN
mdp.39015104955862	153	29	representation	representation	NOUN
mdp.39015104955862	153	30	for	for	ADP
mdp.39015104955862	153	31	r	r	NOUN
mdp.39015104955862	153	32	:	:	PUNCT
mdp.39015104955862	153	33	r	r	NOUN
mdp.39015104955862	153	34	=	=	PUNCT
mdp.39015104955862	153	35	√	√	PROPN
mdp.39015104955862	153	36	(	(	PUNCT
mdp.39015104955862	153	37	−	−	PROPN
mdp.39015104955862	153	38	1)^	1)^	NUM
mdp.39015104955862	153	39	k	k	X
mdp.39015104955862	153	40	!	!	PUNCT
mdp.39015104955862	153	41	k=0	k=0	NOUN
mdp.39015104955862	153	42	4	4	NUM
mdp.39015104955862	153	43	in	in	ADP
mdp.39015104955862	153	44	section	section	NOUN
mdp.39015104955862	153	45	4	4	NUM
mdp.39015104955862	153	46	formulas	formula	NOUN
mdp.39015104955862	153	47	(	(	PUNCT
mdp.39015104955862	153	48	16	16	NUM
mdp.39015104955862	153	49	)	)	PUNCT
mdp.39015104955862	153	50	and	and	CCONJ
mdp.39015104955862	153	51	(	(	PUNCT
mdp.39015104955862	153	52	17	17	NUM
mdp.39015104955862	153	53	)	)	PUNCT
mdp.39015104955862	153	54	will	will	AUX
mdp.39015104955862	153	55	be	be	AUX
mdp.39015104955862	153	56	given	give	VERB
mdp.39015104955862	153	57	exact	exact	ADJ
mdp.39015104955862	153	58	meaning	meaning	NOUN
mdp.39015104955862	153	59	.	.	PUNCT
mdp.39015104955862	154	1	-ha(t)s(a	-ha(t)s(a	X
mdp.39015104955862	154	2	)	)	PUNCT
mdp.39015104955862	154	3	characterization	characterization	NOUN
mdp.39015104955862	154	4	of	of	ADP
mdp.39015104955862	154	5	hyperdistributions	hyperdistribution	NOUN
mdp.39015104955862	154	6	the	the	DET
mdp.39015104955862	154	7	first	first	ADJ
mdp.39015104955862	154	8	result	result	NOUN
mdp.39015104955862	154	9	in	in	ADP
mdp.39015104955862	154	10	this	this	DET
mdp.39015104955862	154	11	section	section	NOUN
mdp.39015104955862	154	12	provides	provide	VERB
mdp.39015104955862	154	13	conditions	condition	NOUN
mdp.39015104955862	154	14	for	for	ADP
mdp.39015104955862	154	15	a	a	DET
mdp.39015104955862	154	16	hyperdistribution	hyperdistribution	NOUN
mdp.39015104955862	154	17	r	r	NOUN
mdp.39015104955862	154	18	=	=	SYM
mdp.39015104955862	154	19	σ	σ	PROPN
mdp.39015104955862	154	20	a₁d	a₁d	NOUN
mdp.39015104955862	154	21	(	(	PUNCT
mdp.39015104955862	154	22	*	*	PUNCT
mdp.39015104955862	154	23	)	)	PUNCT
mdp.39015104955862	154	24	k=0	k=0	NOUN
mdp.39015104955862	154	25	to	to	PART
mdp.39015104955862	154	26	be	be	AUX
mdp.39015104955862	154	27	a	a	DET
mdp.39015104955862	154	28	distribution	distribution	NOUN
mdp.39015104955862	154	29	,	,	PUNCT
mdp.39015104955862	154	30	belonging	belong	VERB
mdp.39015104955862	154	31	to	to	ADP
mdp.39015104955862	154	32	the	the	DET
mdp.39015104955862	154	33	class	class	NOUN
mdp.39015104955862	154	34	ď'({mâ	ď'({mâ	PROPN
mdp.39015104955862	154	35	}	}	PUNCT
mdp.39015104955862	154	36	)	)	PUNCT
mdp.39015104955862	154	37	.	.	PUNCT
mdp.39015104955862	155	1	(	(	PUNCT
mdp.39015104955862	155	2	16	16	NUM
mdp.39015104955862	155	3	)	)	PUNCT
mdp.39015104955862	155	4	(	(	PUNCT
mdp.39015104955862	155	5	17	17	NUM
mdp.39015104955862	155	6	)	)	PUNCT
mdp.39015104955862	155	7	(	(	PUNCT
mdp.39015104955862	155	8	18	18	NUM
mdp.39015104955862	155	9	)	)	PUNCT
mdp.39015104955862	155	10	11	11	NUM
mdp.39015104955862	155	11	theorem	theorem	NOUN
mdp.39015104955862	155	12	3	3	NUM
mdp.39015104955862	155	13	suppose	suppose	VERB
mdp.39015104955862	155	14	a	a	DET
mdp.39015104955862	155	15	hyperdistribution	hyperdistribution	NOUN
mdp.39015104955862	155	16	(	(	PUNCT
mdp.39015104955862	155	17	18	18	NUM
mdp.39015104955862	155	18	)	)	PUNCT
mdp.39015104955862	155	19	and	and	CCONJ
mdp.39015104955862	155	20	a	a	DET
mdp.39015104955862	155	21	sequence	sequence	NOUN
mdp.39015104955862	155	22	{	{	PUNCT
mdp.39015104955862	155	23	m	m	AUX
mdp.39015104955862	155	24	}	}	PUNCT
mdp.39015104955862	155	25	are	be	AUX
mdp.39015104955862	155	26	given	give	VERB
mdp.39015104955862	155	27	.	.	PUNCT
mdp.39015104955862	156	1	if	if	SCONJ
mdp.39015104955862	156	2	σ|ax|mxh	σ|ax|mxh	NOUN
mdp.39015104955862	156	3	*	*	PUNCT
mdp.39015104955862	156	4	<	<	X
mdp.39015104955862	156	5	∞	∞	NUM
mdp.39015104955862	156	6	for	for	ADP
mdp.39015104955862	156	7	every	every	DET
mdp.39015104955862	156	8	h	h	NOUN
mdp.39015104955862	156	9	>	>	SYM
mdp.39015104955862	156	10	0	0	NUM
mdp.39015104955862	156	11	,	,	PUNCT
mdp.39015104955862	156	12	then	then	ADV
mdp.39015104955862	156	13	г	г	PROPN
mdp.39015104955862	156	14	€	€	PROPN
mdp.39015104955862	156	15	ď'({mx	ď'({mx	PROPN
mdp.39015104955862	156	16	}	}	PUNCT
mdp.39015104955862	156	17	)	)	PUNCT
mdp.39015104955862	156	18	and	and	CCONJ
mdp.39015104955862	156	19	is	be	AUX
mdp.39015104955862	156	20	true	true	ADJ
mdp.39015104955862	156	21	for	for	ADP
mdp.39015104955862	156	22	г	г	PROPN
mdp.39015104955862	156	23	.	.	PUNCT
mdp.39015104955862	156	24	k=0	k=0	PROPN
mdp.39015104955862	156	25	(	(	PUNCT
mdp.39015104955862	156	26	20	20	NUM
mdp.39015104955862	156	27	)	)	PUNCT
mdp.39015104955862	156	28	remark	remark	NOUN
mdp.39015104955862	156	29	1	1	NUM
mdp.39015104955862	156	30	theorem	theorem	NOUN
mdp.39015104955862	156	31	1	1	NUM
mdp.39015104955862	156	32	shows	show	VERB
mdp.39015104955862	156	33	that	that	SCONJ
mdp.39015104955862	156	34	for	for	ADP
mdp.39015104955862	156	35	a	a	DET
mdp.39015104955862	156	36	given	give	VERB
mdp.39015104955862	156	37	sequence	sequence	NOUN
mdp.39015104955862	156	38	{	{	PUNCT
mdp.39015104955862	156	39	m	m	NOUN
mdp.39015104955862	156	40	}	}	PUNCT
mdp.39015104955862	156	41	all	all	DET
mdp.39015104955862	156	42	hyperdistributions	hyperdistribution	NOUN
mdp.39015104955862	156	43	(	(	PUNCT
mdp.39015104955862	156	44	18	18	NUM
mdp.39015104955862	156	45	)	)	PUNCT
mdp.39015104955862	156	46	,	,	PUNCT
mdp.39015104955862	156	47	satisfying	satisfy	VERB
mdp.39015104955862	156	48	condition	condition	NOUN
mdp.39015104955862	156	49	(	(	PUNCT
mdp.39015104955862	156	50	19	19	NUM
mdp.39015104955862	156	51	)	)	PUNCT
mdp.39015104955862	156	52	,	,	PUNCT
mdp.39015104955862	156	53	have	have	VERB
mdp.39015104955862	156	54	moments	moment	NOUN
mdp.39015104955862	156	55	µ(г	µ(г	SPACE
mdp.39015104955862	156	56	)	)	PUNCT
mdp.39015104955862	156	57	of	of	ADP
mdp.39015104955862	156	58	all	all	DET
mdp.39015104955862	156	59	orders	order	NOUN
mdp.39015104955862	156	60	.	.	PUNCT
mdp.39015104955862	157	1	moreover	moreover	ADV
mdp.39015104955862	157	2	,	,	PUNCT
mdp.39015104955862	157	3	ak	ak	PROPN
mdp.39015104955862	157	4	=	=	PROPN
mdp.39015104955862	157	5	(	(	PUNCT
mdp.39015104955862	157	6	−1)*µk(t)(k!)−¹	−1)*µk(t)(k!)−¹	SPACE
mdp.39015104955862	157	7	,	,	PUNCT
mdp.39015104955862	157	8	k≥0	k≥0	PROPN
mdp.39015104955862	157	9	.	.	PUNCT
mdp.39015104955862	158	1	1	1	X
mdp.39015104955862	158	2	.	.	PUNCT
mdp.39015104955862	159	1	for	for	ADP
mdp.39015104955862	159	2	every	every	DET
mdp.39015104955862	159	3	h	h	NOUN
mdp.39015104955862	159	4	>	>	X
mdp.39015104955862	159	5	0	0	NUM
mdp.39015104955862	159	6	and	and	CCONJ
mdp.39015104955862	159	7	the	the	DET
mdp.39015104955862	159	8	moment	moment	NOUN
mdp.39015104955862	159	9	representation	representation	NOUN
mdp.39015104955862	159	10	formula	formula	NOUN
mdp.39015104955862	159	11	r	r	NOUN
mdp.39015104955862	159	12	=	=	X
mdp.39015104955862	159	13	√	√	PROPN
mdp.39015104955862	159	14	(	(	PUNCT
mdp.39015104955862	159	15	−1	−1	NUM
mdp.39015104955862	159	16	)	)	PUNCT
mdp.39015104955862	159	17	^	^	NOUN
mdp.39015104955862	159	18	k=0	k=0	NOUN
mdp.39015104955862	159	19	2	2	NUM
mdp.39015104955862	159	20	.	.	PUNCT
mdp.39015104955862	159	21	k=0	k=0	PROPN
mdp.39015104955862	159	22	lux(i	lux(i	PROPN
mdp.39015104955862	159	23	)	)	PUNCT
mdp.39015104955862	159	24	minh	minh	PROPN
mdp.39015104955862	159	25	cao	cao	PROPN
mdp.39015104955862	159	26	k	k	PROPN
mdp.39015104955862	159	27	!	!	PUNCT
mdp.39015104955862	160	1	then	then	ADV
mdp.39015104955862	160	2	the	the	DET
mdp.39015104955862	160	3	following	following	ADJ
mdp.39015104955862	160	4	result	result	NOUN
mdp.39015104955862	160	5	holds	hold	VERB
mdp.39015104955862	160	6	.	.	PUNCT
mdp.39015104955862	161	1	k	k	PROPN
mdp.39015104955862	161	2	!	!	PROPN
mdp.39015104955862	161	3	hk	hk	PROPN
mdp.39015104955862	161	4	(	(	PUNCT
mdp.39015104955862	161	5	i)ε	i)ε	NOUN
mdp.39015104955862	161	6	(	(	PUNCT
mdp.39015104955862	161	7	*	*	NOUN
mdp.39015104955862	161	8	)	)	PUNCT
mdp.39015104955862	161	9	we	we	PRON
mdp.39015104955862	161	10	now	now	ADV
mdp.39015104955862	161	11	formulate	formulate	VERB
mdp.39015104955862	161	12	the	the	DET
mdp.39015104955862	161	13	main	main	ADJ
mdp.39015104955862	161	14	result	result	NOUN
mdp.39015104955862	161	15	of	of	ADP
mdp.39015104955862	161	16	this	this	DET
mdp.39015104955862	161	17	section	section	NOUN
mdp.39015104955862	161	18	.	.	PUNCT
mdp.39015104955862	162	1	it	it	PRON
mdp.39015104955862	162	2	will	will	AUX
mdp.39015104955862	162	3	be	be	AUX
mdp.39015104955862	162	4	shown	show	VERB
mdp.39015104955862	162	5	that	that	SCONJ
mdp.39015104955862	162	6	for	for	ADP
mdp.39015104955862	162	7	some	some	DET
mdp.39015104955862	162	8	sequences	sequence	NOUN
mdp.39015104955862	162	9	{	{	PUNCT
mdp.39015104955862	162	10	m	m	VERB
mdp.39015104955862	162	11	}	}	PUNCT
mdp.39015104955862	162	12	the	the	DET
mdp.39015104955862	162	13	inverse	inverse	NOUN
mdp.39015104955862	162	14	to	to	ADP
mdp.39015104955862	162	15	theorem	theorem	NOUN
mdp.39015104955862	162	16	3	3	NUM
mdp.39015104955862	162	17	holds	hold	VERB
mdp.39015104955862	162	18	.	.	PUNCT
mdp.39015104955862	163	1	the	the	DET
mdp.39015104955862	163	2	restriction	restriction	NOUN
mdp.39015104955862	163	3	for	for	ADP
mdp.39015104955862	163	4	sequences	sequence	NOUN
mdp.39015104955862	163	5	{	{	PUNCT
mdp.39015104955862	163	6	m	m	VERB
mdp.39015104955862	163	7	}	}	PUNCT
mdp.39015104955862	163	8	will	will	AUX
mdp.39015104955862	163	9	be	be	AUX
mdp.39015104955862	163	10	as	as	SCONJ
mdp.39015104955862	163	11	follows	follow	VERB
mdp.39015104955862	163	12	:	:	PUNCT
mdp.39015104955862	163	13	there	there	PRON
mdp.39015104955862	163	14	exists	exist	VERB
mdp.39015104955862	163	15	a	a	DET
mdp.39015104955862	163	16	positive	positive	ADJ
mdp.39015104955862	163	17	function	function	NOUN
mdp.39015104955862	163	18	p(h	p(h	PROPN
mdp.39015104955862	163	19	)	)	PUNCT
mdp.39015104955862	163	20	,	,	PUNCT
mdp.39015104955862	163	21	h≥	h≥	X
mdp.39015104955862	163	22	0	0	NUM
mdp.39015104955862	163	23	and	and	CCONJ
mdp.39015104955862	163	24	a	a	DET
mdp.39015104955862	163	25	positive	positive	ADJ
mdp.39015104955862	163	26	sequence	sequence	NOUN
mdp.39015104955862	163	27	{	{	PUNCT
mdp.39015104955862	163	28	}	}	PUNCT
mdp.39015104955862	163	29	such	such	ADJ
mdp.39015104955862	163	30	that	that	PRON
mdp.39015104955862	163	31	σμπτη	σμπτη	VERB
mdp.39015104955862	163	32	200	200	NUM
mdp.39015104955862	163	33	n=0	n=0	PUNCT
mdp.39015104955862	163	34	mn+mh	mn+mh	SPACE
mdp.39015104955862	163	35	"	"	PUNCT
mdp.39015104955862	163	36	<	<	X
mdp.39015104955862	163	37	p(h)m+(n!)tnmm,,m>0	p(h)m+(n!)tnmm,,m>0	PROPN
mdp.39015104955862	163	38	,	,	PUNCT
mdp.39015104955862	163	39	n	n	CCONJ
mdp.39015104955862	163	40	>	>	X
mdp.39015104955862	163	41	0	0	NUM
mdp.39015104955862	163	42	,	,	PUNCT
mdp.39015104955862	163	43	h	h	PROPN
mdp.39015104955862	163	44	>	>	X
mdp.39015104955862	163	45	họ	họ	PROPN
mdp.39015104955862	163	46	.	.	PUNCT
mdp.39015104955862	164	1	(	(	PUNCT
mdp.39015104955862	164	2	19	19	NUM
mdp.39015104955862	164	3	)	)	PUNCT
mdp.39015104955862	164	4	(	(	PUNCT
mdp.39015104955862	164	5	21	21	NUM
mdp.39015104955862	164	6	)	)	PUNCT
mdp.39015104955862	164	7	(	(	PUNCT
mdp.39015104955862	164	8	22	22	NUM
mdp.39015104955862	164	9	)	)	PUNCT
mdp.39015104955862	164	10	12	12	NUM
mdp.39015104955862	164	11	theorem	theorem	NOUN
mdp.39015104955862	164	12	4	4	NUM
mdp.39015104955862	164	13	suppose	suppose	VERB
mdp.39015104955862	164	14	a	a	DET
mdp.39015104955862	164	15	sequence	sequence	NOUN
mdp.39015104955862	164	16	{	{	PUNCT
mdp.39015104955862	164	17	m	m	NOUN
mdp.39015104955862	164	18	}	}	PUNCT
mdp.39015104955862	164	19	satisfies	satisfie	NOUN
mdp.39015104955862	164	20	the	the	DET
mdp.39015104955862	164	21	conditions	condition	NOUN
mdp.39015104955862	164	22	above	above	ADV
mdp.39015104955862	164	23	.	.	PUNCT
mdp.39015104955862	165	1	then	then	ADV
mdp.39015104955862	165	2	every	every	DET
mdp.39015104955862	165	3	distribution	distribution	NOUN
mdp.39015104955862	165	4	г	г	X
mdp.39015104955862	165	5	€	€	SYM
mdp.39015104955862	165	6	ď¹({mx	ď¹({mx	SPACE
mdp.39015104955862	165	7	}	}	PUNCT
mdp.39015104955862	165	8	)	)	PUNCT
mdp.39015104955862	165	9	is	be	AUX
mdp.39015104955862	165	10	a	a	DET
mdp.39015104955862	165	11	hyperdistribution	hyperdistribution	NOUN
mdp.39015104955862	165	12	(	(	PUNCT
mdp.39015104955862	165	13	18	18	NUM
mdp.39015104955862	165	14	)	)	PUNCT
mdp.39015104955862	165	15	,	,	PUNCT
mdp.39015104955862	165	16	for	for	ADP
mdp.39015104955862	165	17	which	which	PRON
mdp.39015104955862	165	18	(	(	PUNCT
mdp.39015104955862	165	19	20	20	NUM
mdp.39015104955862	165	20	)	)	PUNCT
mdp.39015104955862	165	21	,	,	PUNCT
mdp.39015104955862	165	22	(	(	PUNCT
mdp.39015104955862	165	23	21	21	NUM
mdp.39015104955862	165	24	)	)	PUNCT
mdp.39015104955862	165	25	,	,	PUNCT
mdp.39015104955862	165	26	and	and	CCONJ
mdp.39015104955862	165	27	(	(	PUNCT
mdp.39015104955862	165	28	22	22	X
mdp.39015104955862	165	29	)	)	PUNCT
mdp.39015104955862	165	30	hold	hold	NOUN
mdp.39015104955862	165	31	.	.	PUNCT
mdp.39015104955862	166	1	remark	remark	NOUN
mdp.39015104955862	166	2	2	2	NUM
mdp.39015104955862	166	3	the	the	DET
mdp.39015104955862	166	4	conditions	condition	NOUN
mdp.39015104955862	166	5	1)-2	1)-2	NUM
mdp.39015104955862	166	6	)	)	PUNCT
mdp.39015104955862	166	7	above	above	ADP
mdp.39015104955862	166	8	and	and	CCONJ
mdp.39015104955862	166	9	the	the	DET
mdp.39015104955862	166	10	similar	similar	ADJ
mdp.39015104955862	166	11	conditions	condition	NOUN
mdp.39015104955862	166	12	in	in	ADP
mdp.39015104955862	166	13	section	section	NOUN
mdp.39015104955862	166	14	4	4	NUM
mdp.39015104955862	166	15	are	be	AUX
mdp.39015104955862	166	16	useful	useful	ADJ
mdp.39015104955862	166	17	in	in	ADP
mdp.39015104955862	166	18	problems	problem	NOUN
mdp.39015104955862	166	19	,	,	PUNCT
mdp.39015104955862	166	20	which	which	PRON
mdp.39015104955862	166	21	we	we	PRON
mdp.39015104955862	166	22	consider	consider	VERB
mdp.39015104955862	166	23	in	in	ADP
mdp.39015104955862	166	24	this	this	DET
mdp.39015104955862	166	25	paper	paper	NOUN
mdp.39015104955862	166	26	.	.	PUNCT
mdp.39015104955862	167	1	the	the	DET
mdp.39015104955862	167	2	conditions	condition	NOUN
mdp.39015104955862	167	3	1)-2	1)-2	NUM
mdp.39015104955862	167	4	)	)	PUNCT
mdp.39015104955862	167	5	imply	imply	VERB
mdp.39015104955862	167	6	,	,	PUNCT
mdp.39015104955862	167	7	on	on	ADP
mdp.39015104955862	167	8	the	the	DET
mdp.39015104955862	167	9	one	one	NUM
mdp.39015104955862	167	10	hand	hand	NOUN
mdp.39015104955862	167	11	,	,	PUNCT
mdp.39015104955862	167	12	the	the	DET
mdp.39015104955862	167	13	differentiability	differentiability	NOUN
mdp.39015104955862	167	14	condition	condition	NOUN
mdp.39015104955862	167	15	for	for	ADP
mdp.39015104955862	167	16	the	the	DET
mdp.39015104955862	167	17	classes	class	NOUN
mdp.39015104955862	167	18	d({mk	d({mk	SPACE
mdp.39015104955862	167	19	}	}	PUNCT
mdp.39015104955862	167	20	)	)	PUNCT
mdp.39015104955862	167	21	,	,	PUNCT
mdp.39015104955862	167	22	namely	namely	ADV
mdp.39015104955862	167	23	mk+1	mk+1	NOUN
mdp.39015104955862	167	24	≤	≤	X
mdp.39015104955862	167	25	c	c	X
mdp.39015104955862	167	26	*	*	PUNCT
mdp.39015104955862	167	27	mk	mk	PROPN
mdp.39015104955862	167	28	with	with	ADP
mdp.39015104955862	167	29	some	some	PRON
mdp.39015104955862	167	30	c	c	X
mdp.39015104955862	167	31	>	>	SYM
mdp.39015104955862	167	32	0	0	NUM
mdp.39015104955862	167	33	.	.	PUNCT
mdp.39015104955862	168	1	this	this	DET
mdp.39015104955862	168	2	condition	condition	NOUN
mdp.39015104955862	168	3	is	be	AUX
mdp.39015104955862	168	4	necessary	necessary	ADJ
mdp.39015104955862	168	5	and	and	CCONJ
mdp.39015104955862	168	6	sufficient	sufficient	ADJ
mdp.39015104955862	168	7	for	for	ADP
mdp.39015104955862	168	8	the	the	DET
mdp.39015104955862	168	9	differentiation	differentiation	NOUN
mdp.39015104955862	168	10	invariance	invariance	NOUN
mdp.39015104955862	168	11	of	of	ADP
mdp.39015104955862	168	12	the	the	DET
mdp.39015104955862	168	13	class	class	NOUN
mdp.39015104955862	168	14	d({m	d({m	NOUN
mdp.39015104955862	168	15	}	}	PUNCT
mdp.39015104955862	168	16	)	)	PUNCT
mdp.39015104955862	168	17	(	(	PUNCT
mdp.39015104955862	168	18	see	see	VERB
mdp.39015104955862	168	19	[	[	X
mdp.39015104955862	168	20	13	13	NUM
mdp.39015104955862	168	21	]	]	PUNCT
mdp.39015104955862	168	22	,	,	PUNCT
mdp.39015104955862	168	23	p.	p.	NOUN
mdp.39015104955862	168	24	57	57	NUM
mdp.39015104955862	168	25	)	)	PUNCT
mdp.39015104955862	168	26	.	.	PUNCT
mdp.39015104955862	169	1	on	on	ADP
mdp.39015104955862	169	2	the	the	DET
mdp.39015104955862	169	3	other	other	ADJ
mdp.39015104955862	169	4	hand	hand	NOUN
mdp.39015104955862	169	5	,	,	PUNCT
mdp.39015104955862	169	6	conditions	condition	NOUN
mdp.39015104955862	169	7	1)-2	1)-2	NUM
mdp.39015104955862	169	8	)	)	PUNCT
mdp.39015104955862	169	9	above	above	ADP
mdp.39015104955862	169	10	imply	imply	NOUN
mdp.39015104955862	169	11	h	h	PROPN
mdp.39015104955862	169	12	*	*	SYM
mdp.39015104955862	169	13	mk(k!)−¹	mk(k!)−¹	PROPN
mdp.39015104955862	169	14	→	→	SYM
mdp.39015104955862	169	15	0	0	NUM
mdp.39015104955862	169	16	as	as	ADP
mdp.39015104955862	169	17	k	k	PROPN
mdp.39015104955862	169	18	→	→	SYM
mdp.39015104955862	169	19	∞	∞	NUM
mdp.39015104955862	169	20	for	for	ADP
mdp.39015104955862	169	21	each	each	DET
mdp.39015104955862	169	22	h>0	h>0	PROPN
mdp.39015104955862	169	23	.	.	PUNCT
mdp.39015104955862	169	24	condition	condition	NOUN
mdp.39015104955862	169	25	(	(	PUNCT
mdp.39015104955862	169	26	23	23	NUM
mdp.39015104955862	169	27	)	)	PUNCT
mdp.39015104955862	169	28	guarantees	guarantee	VERB
mdp.39015104955862	169	29	the	the	DET
mdp.39015104955862	169	30	convergence	convergence	NOUN
mdp.39015104955862	169	31	of	of	ADP
mdp.39015104955862	169	32	taylor	taylor	PROPN
mdp.39015104955862	169	33	series	series	PROPN
mdp.39015104955862	169	34	=	=	PUNCT
mdp.39015104955862	169	35	=	=	PROPN
mdp.39015104955862	169	36	6)(0	6)(0	NUM
mdp.39015104955862	169	37	)	)	PUNCT
mdp.39015104955862	169	38	=	=	PROPN
mdp.39015104955862	169	39	,	,	PUNCT
mdp.39015104955862	169	40	φ(2	φ(2	PROPN
mdp.39015104955862	169	41	)	)	PUNCT
mdp.39015104955862	170	1	=	=	PROPN
mdp.39015104955862	170	2	σ	σ	PROPN
mdp.39015104955862	170	3	¿	¿	PROPN
mdp.39015104955862	170	4	(	(	PUNCT
mdp.39015104955862	170	5	³	³	PROPN
mdp.39015104955862	170	6	)	)	PUNCT
mdp.39015104955862	170	7	(	(	PUNCT
mdp.39015104955862	170	8	0)µ³¸	0)µ³¸	NUM
mdp.39015104955862	170	9	þ€	þ€	CCONJ
mdp.39015104955862	170	10	ď{{mk	ď{{mk	SPACE
mdp.39015104955862	170	11	}	}	PUNCT
mdp.39015104955862	170	12	)	)	PUNCT
mdp.39015104955862	170	13	j	j	PROPN
mdp.39015104955862	170	14	!	!	PROPN
mdp.39015104955862	170	15	j=0	j=0	VERB
mdp.39015104955862	170	16	everywhere	everywhere	ADV
mdp.39015104955862	170	17	on	on	ADP
mdp.39015104955862	170	18	the	the	DET
mdp.39015104955862	170	19	real	real	ADJ
mdp.39015104955862	170	20	line	line	NOUN
mdp.39015104955862	170	21	.	.	PUNCT
mdp.39015104955862	171	1	remainder	remainder	NOUN
mdp.39015104955862	171	2	of	of	ADP
mdp.39015104955862	171	3	the	the	DET
mdp.39015104955862	171	4	series	series	NOUN
mdp.39015104955862	171	5	in	in	ADP
mdp.39015104955862	171	6	(	(	PUNCT
mdp.39015104955862	171	7	24	24	NUM
mdp.39015104955862	171	8	)	)	PUNCT
mdp.39015104955862	171	9	.	.	PUNCT
mdp.39015104955862	172	1	similarly	similarly	ADV
mdp.39015104955862	172	2	,	,	PUNCT
mdp.39015104955862	172	3	all	all	DET
mdp.39015104955862	172	4	the	the	DET
mdp.39015104955862	172	5	taylor	taylor	PROPN
mdp.39015104955862	172	6	series	series	NOUN
mdp.39015104955862	172	7	this	this	PRON
mdp.39015104955862	172	8	can	can	AUX
mdp.39015104955862	172	9	be	be	AUX
mdp.39015104955862	172	10	shown	show	VERB
mdp.39015104955862	172	11	by	by	ADP
mdp.39015104955862	172	12	estimating	estimate	VERB
mdp.39015104955862	172	13	the	the	DET
mdp.39015104955862	172	14	lagrange	lagrange	NOUN
mdp.39015104955862	172	15	form	form	NOUN
mdp.39015104955862	172	16	of	of	ADP
mdp.39015104955862	172	17	the	the	DET
mdp.39015104955862	172	18	85	85	NUM
mdp.39015104955862	172	19	(	(	PUNCT
mdp.39015104955862	172	20	k	k	PROPN
mdp.39015104955862	172	21	)	)	PUNCT
mdp.39015104955862	172	22	(	(	PUNCT
mdp.39015104955862	172	23	x	x	NOUN
mdp.39015104955862	172	24	)	)	PUNCT
mdp.39015104955862	172	25	=	=	X
mdp.39015104955862	172	26	£	£	SYM
mdp.39015104955862	172	27	¤(³+k	¤(³+k	PROPN
mdp.39015104955862	172	28	)	)	PUNCT
mdp.39015104955862	172	29	(	(	PUNCT
mdp.39015104955862	172	30	0	0	X
mdp.39015104955862	172	31	)	)	PUNCT
mdp.39015104955862	172	32	µ³	µ³	PROPN
mdp.39015104955862	172	33	,	,	PUNCT
mdp.39015104955862	172	34	k	k	PROPN
mdp.39015104955862	172	35	≥0	≥0	PROPN
mdp.39015104955862	172	36	,	,	PUNCT
mdp.39015104955862	172	37	¢	¢	NOUN
mdp.39015104955862	172	38	€	€	X
mdp.39015104955862	172	39	ď({mk	ď({mk	PROPN
mdp.39015104955862	172	40	}	}	PUNCT
mdp.39015104955862	172	41	)	)	PUNCT
mdp.39015104955862	172	42	j	j	PROPN
mdp.39015104955862	172	43	!	!	PROPN
mdp.39015104955862	172	44	j=0	j=0	NUM
mdp.39015104955862	172	45	converge	converge	VERB
mdp.39015104955862	172	46	uniformly	uniformly	ADV
mdp.39015104955862	172	47	on	on	ADP
mdp.39015104955862	172	48	all	all	DET
mdp.39015104955862	172	49	subintervals	subinterval	NOUN
mdp.39015104955862	172	50	of	of	ADP
mdp.39015104955862	172	51	r¹.	r¹.	NOUN
mdp.39015104955862	172	52	(	(	PUNCT
mdp.39015104955862	172	53	23	23	NUM
mdp.39015104955862	172	54	)	)	PUNCT
mdp.39015104955862	172	55	г(ø	г(ø	SPACE
mdp.39015104955862	172	56	)	)	PUNCT
mdp.39015104955862	173	1	=	=	PROPN
mdp.39015104955862	174	1	(	(	PUNCT
mdp.39015104955862	174	2	-1)*a*(*)(0	-1)*a*(*)(0	NOUN
mdp.39015104955862	174	3	)	)	PUNCT
mdp.39015104955862	174	4	.	.	PUNCT
mdp.39015104955862	175	1	k=0	k=0	NOUN
mdp.39015104955862	175	2	(	(	PUNCT
mdp.39015104955862	175	3	24	24	NUM
mdp.39015104955862	175	4	)	)	PUNCT
mdp.39015104955862	175	5	proof	proof	NOUN
mdp.39015104955862	175	6	of	of	ADP
mdp.39015104955862	175	7	theorem	theorem	NOUN
mdp.39015104955862	175	8	3	3	NUM
mdp.39015104955862	175	9	.	.	PUNCT
mdp.39015104955862	176	1	if	if	SCONJ
mdp.39015104955862	176	2	a	a	DET
mdp.39015104955862	176	3	hyperdistribution	hyperdistribution	NOUN
mdp.39015104955862	176	4	(	(	PUNCT
mdp.39015104955862	176	5	18	18	NUM
mdp.39015104955862	176	6	)	)	PUNCT
mdp.39015104955862	176	7	is	be	AUX
mdp.39015104955862	176	8	given	give	VERB
mdp.39015104955862	176	9	and	and	CCONJ
mdp.39015104955862	176	10	if	if	SCONJ
mdp.39015104955862	176	11	a	a	DET
mdp.39015104955862	176	12	function	function	NOUN
mdp.39015104955862	176	13	belongs	belong	VERB
mdp.39015104955862	176	14	to	to	ADP
mdp.39015104955862	176	15	the	the	DET
mdp.39015104955862	176	16	class	class	NOUN
mdp.39015104955862	176	17	ď({m	ď({m	NOUN
mdp.39015104955862	176	18	}	}	PUNCT
mdp.39015104955862	176	19	)	)	PUNCT
mdp.39015104955862	176	20	,	,	PUNCT
mdp.39015104955862	176	21	then	then	ADV
mdp.39015104955862	176	22	(	(	PUNCT
mdp.39015104955862	176	23	19	19	NUM
mdp.39015104955862	176	24	)	)	PUNCT
mdp.39015104955862	176	25	implies	imply	VERB
mdp.39015104955862	176	26	the	the	DET
mdp.39015104955862	176	27	absolute	absolute	ADJ
mdp.39015104955862	176	28	convergence	convergence	NOUN
mdp.39015104955862	176	29	of	of	ADP
mdp.39015104955862	176	30	the	the	DET
mdp.39015104955862	176	31	series	series	NOUN
mdp.39015104955862	176	32	(	(	PUNCT
mdp.39015104955862	176	33	25	25	NUM
mdp.39015104955862	176	34	)	)	PUNCT
mdp.39015104955862	176	35	13	13	NUM
mdp.39015104955862	176	36	moreover	moreover	ADV
mdp.39015104955862	176	37	,	,	PUNCT
mdp.39015104955862	176	38	if	if	SCONJ
mdp.39015104955862	176	39	i	i	PRON
mdp.39015104955862	176	40	is	be	AUX
mdp.39015104955862	176	41	any	any	DET
mdp.39015104955862	176	42	interval	interval	NOUN
mdp.39015104955862	176	43	,	,	PUNCT
mdp.39015104955862	177	1	for	for	ADP
mdp.39015104955862	177	2	which	which	PRON
mdp.39015104955862	177	3	0	0	NUM
mdp.39015104955862	177	4	€	€	PROPN
mdp.39015104955862	177	5	i	i	PRON
mdp.39015104955862	177	6	,	,	PUNCT
mdp.39015104955862	177	7	we	we	PRON
mdp.39015104955862	177	8	have	have	AUX
mdp.39015104955862	177	9	|t(0)|	|t(0)|	NOUN
mdp.39015104955862	177	10	≤	≤	PUNCT
mdp.39015104955862	177	11	p1,m(4	p1,m(4	X
mdp.39015104955862	177	12	)	)	PUNCT
mdp.39015104955862	177	13	σ|ax|m	σ|ax|m	NOUN
mdp.39015104955862	177	14	*	*	PUNCT
mdp.39015104955862	177	15	mk	mk	PROPN
mdp.39015104955862	177	16	,	,	PUNCT
mdp.39015104955862	177	17	m≥1	m≥1	PROPN
mdp.39015104955862	177	18	,	,	PUNCT
mdp.39015104955862	177	19	k=0	k=0	PROPN
mdp.39015104955862	177	20	where	where	SCONJ
mdp.39015104955862	177	21	the	the	DET
mdp.39015104955862	177	22	semi	semi	ADJ
mdp.39015104955862	177	23	-	-	ADJ
mdp.39015104955862	177	24	norms	norms	ADJ
mdp.39015104955862	177	25	pi	pi	NOUN
mdp.39015104955862	177	26	,	,	PUNCT
mdp.39015104955862	177	27	m	m	AUX
mdp.39015104955862	177	28	are	be	AUX
mdp.39015104955862	177	29	defined	define	VERB
mdp.39015104955862	177	30	in	in	ADP
mdp.39015104955862	177	31	(	(	PUNCT
mdp.39015104955862	177	32	13	13	NUM
mdp.39015104955862	177	33	)	)	PUNCT
mdp.39015104955862	177	34	.	.	PUNCT
mdp.39015104955862	178	1	it	it	PRON
mdp.39015104955862	178	2	follows	follow	VERB
mdp.39015104955862	178	3	from	from	ADP
mdp.39015104955862	178	4	(	(	PUNCT
mdp.39015104955862	178	5	26	26	NUM
mdp.39015104955862	178	6	)	)	PUNCT
mdp.39015104955862	178	7	that	that	SCONJ
mdp.39015104955862	178	8	the	the	DET
mdp.39015104955862	178	9	functional	functional	ADJ
mdp.39015104955862	178	10	i	i	PRON
mdp.39015104955862	178	11	is	be	AUX
mdp.39015104955862	178	12	bounded	bound	VERB
mdp.39015104955862	178	13	on	on	ADP
mdp.39015104955862	178	14	the	the	DET
mdp.39015104955862	178	15	space	space	NOUN
mdp.39015104955862	178	16	ďm({m	ďm({m	X
mdp.39015104955862	178	17	}	}	PUNCT
mdp.39015104955862	178	18	)	)	PUNCT
mdp.39015104955862	178	19	,	,	PUNCT
mdp.39015104955862	178	20	m	m	PROPN
mdp.39015104955862	178	21	≥	≥	PROPN
mdp.39015104955862	178	22	1	1	NUM
mdp.39015104955862	178	23	.	.	PUNCT
mdp.39015104955862	179	1	hence	hence	ADV
mdp.39015104955862	179	2	,	,	PUNCT
mdp.39015104955862	179	3	it	it	PRON
mdp.39015104955862	179	4	is	be	AUX
mdp.39015104955862	179	5	bounded	bound	VERB
mdp.39015104955862	179	6	on	on	ADP
mdp.39015104955862	179	7	the	the	DET
mdp.39015104955862	179	8	inductive	inductive	ADJ
mdp.39015104955862	179	9	limit	limit	NOUN
mdp.39015104955862	179	10	ď({m	ď({m	PROPN
mdp.39015104955862	179	11	}	}	PUNCT
mdp.39015104955862	179	12	)	)	PUNCT
mdp.39015104955862	179	13	of	of	ADP
mdp.39015104955862	179	14	the	the	DET
mdp.39015104955862	179	15	spaces	space	NOUN
mdp.39015104955862	179	16	ďm({mk}),m	ďm({mk}),m	ADJ
mdp.39015104955862	179	17	≥	≥	X
mdp.39015104955862	179	18	1	1	NUM
mdp.39015104955862	179	19	(	(	PUNCT
mdp.39015104955862	179	20	see	see	VERB
mdp.39015104955862	179	21	[	[	X
mdp.39015104955862	179	22	12	12	NUM
mdp.39015104955862	179	23	]	]	PUNCT
mdp.39015104955862	179	24	for	for	ADP
mdp.39015104955862	179	25	the	the	DET
mdp.39015104955862	179	26	properties	property	NOUN
mdp.39015104955862	179	27	of	of	ADP
mdp.39015104955862	179	28	the	the	DET
mdp.39015104955862	179	29	inductive	inductive	ADJ
mdp.39015104955862	179	30	limits	limit	NOUN
mdp.39015104955862	179	31	)	)	PUNCT
mdp.39015104955862	179	32	.	.	PUNCT
mdp.39015104955862	180	1	formula	formula	NOUN
mdp.39015104955862	180	2	(	(	PUNCT
mdp.39015104955862	180	3	20	20	NUM
mdp.39015104955862	180	4	)	)	PUNCT
mdp.39015104955862	180	5	follows	follow	VERB
mdp.39015104955862	180	6	easily	easily	ADV
mdp.39015104955862	180	7	from	from	ADP
mdp.39015104955862	180	8	the	the	DET
mdp.39015104955862	180	9	definition	definition	NOUN
mdp.39015104955862	180	10	of	of	ADP
mdp.39015104955862	180	11	the	the	DET
mdp.39015104955862	180	12	moments	moment	NOUN
mdp.39015104955862	180	13	.	.	PUNCT
mdp.39015104955862	181	1	theorem	theorem	NOUN
mdp.39015104955862	181	2	3	3	NUM
mdp.39015104955862	181	3	is	be	AUX
mdp.39015104955862	181	4	proved	prove	VERB
mdp.39015104955862	181	5	.	.	PUNCT
mdp.39015104955862	182	1	proof	proof	NOUN
mdp.39015104955862	182	2	of	of	ADP
mdp.39015104955862	182	3	theorem	theorem	NOUN
mdp.39015104955862	182	4	4	4	NUM
mdp.39015104955862	182	5	.	.	PUNCT
mdp.39015104955862	183	1	we	we	PRON
mdp.39015104955862	183	2	will	will	AUX
mdp.39015104955862	183	3	need	need	VERB
mdp.39015104955862	183	4	the	the	DET
mdp.39015104955862	183	5	following	follow	VERB
mdp.39015104955862	183	6	lemma	lemma	NOUN
mdp.39015104955862	183	7	.	.	PUNCT
mdp.39015104955862	184	1	lemma	lemma	NOUN
mdp.39015104955862	184	2	1	1	NUM
mdp.39015104955862	184	3	suppose	suppose	VERB
mdp.39015104955862	184	4	conditions	condition	NOUN
mdp.39015104955862	184	5	1)-2	1)-2	NUM
mdp.39015104955862	184	6	)	)	PUNCT
mdp.39015104955862	184	7	hold	hold	VERB
mdp.39015104955862	184	8	for	for	ADP
mdp.39015104955862	184	9	a	a	DET
mdp.39015104955862	184	10	sequence	sequence	NOUN
mdp.39015104955862	184	11	{	{	PUNCT
mdp.39015104955862	184	12	m	m	NOUN
mdp.39015104955862	184	13	}	}	PUNCT
mdp.39015104955862	184	14	.	.	PUNCT
mdp.39015104955862	185	1	then	then	ADV
mdp.39015104955862	185	2	the	the	DET
mdp.39015104955862	185	3	taylor	taylor	PROPN
mdp.39015104955862	185	4	series	series	PROPN
mdp.39015104955862	185	5	(	(	PUNCT
mdp.39015104955862	185	6	24	24	NUM
mdp.39015104955862	185	7	)	)	PUNCT
mdp.39015104955862	185	8	of	of	ADP
mdp.39015104955862	185	9	a	a	DET
mdp.39015104955862	185	10	function	function	NOUN
mdp.39015104955862	185	11	&	&	CCONJ
mdp.39015104955862	185	12	€	€	SYM
mdp.39015104955862	185	13	ď({m	ď({m	NOUN
mdp.39015104955862	185	14	}	}	PUNCT
mdp.39015104955862	185	15	)	)	PUNCT
mdp.39015104955862	185	16	converges	converge	VERB
mdp.39015104955862	185	17	to	to	ADP
mdp.39015104955862	185	18	&	&	CCONJ
mdp.39015104955862	185	19	in	in	ADP
mdp.39015104955862	185	20	the	the	DET
mdp.39015104955862	185	21	topology	topology	NOUN
mdp.39015104955862	185	22	of	of	ADP
mdp.39015104955862	185	23	the	the	DET
mdp.39015104955862	185	24	space	space	NOUN
mdp.39015104955862	185	25	ď({mx	ď({mx	SPACE
mdp.39015104955862	185	26	}	}	PUNCT
mdp.39015104955862	185	27	)	)	PUNCT
mdp.39015104955862	185	28	.	.	PUNCT
mdp.39015104955862	186	1	proof	proof	PROPN
mdp.39015104955862	186	2	.	.	PUNCT
mdp.39015104955862	187	1	consider	consider	VERB
mdp.39015104955862	187	2	a	a	DET
mdp.39015104955862	187	3	sequence	sequence	NOUN
mdp.39015104955862	187	4	of	of	ADP
mdp.39015104955862	187	5	remainders	remainder	NOUN
mdp.39015104955862	187	6	of	of	ADP
mdp.39015104955862	187	7	the	the	DET
mdp.39015104955862	187	8	taylor	taylor	PROPN
mdp.39015104955862	187	9	series	series	PROPN
mdp.39015104955862	187	10	of	of	ADP
mdp.39015104955862	187	11	p	p	PROPN
mdp.39015104955862	187	12	,	,	PUNCT
mdp.39015104955862	187	13	namely	namely	ADV
mdp.39015104955862	187	14	$	$	SYM
mdp.39015104955862	187	15	(	(	PUNCT
mdp.39015104955862	187	16	m)(0	m)(0	NUM
mdp.39015104955862	187	17	)	)	PUNCT
mdp.39015104955862	187	18	m	m	PROPN
mdp.39015104955862	187	19	!	!	PUNCT
mdp.39015104955862	187	20	φ;(x	φ;(x	SPACE
mdp.39015104955862	187	21	)	)	PUNCT
mdp.39015104955862	188	1	=	=	PROPN
mdp.39015104955862	188	2	σ	σ	X
mdp.39015104955862	189	1	m	m	VERB
mdp.39015104955862	189	2	=	=	NOUN
mdp.39015104955862	189	3	j	j	X
mdp.39015104955862	189	4	x	x	SYM
mdp.39015104955862	189	5	"	"	PUNCT
mdp.39015104955862	189	6	,	,	PUNCT
mdp.39015104955862	189	7	j≥0	j≥0	PROPN
mdp.39015104955862	189	8	.	.	PUNCT
mdp.39015104955862	190	1	by	by	ADP
mdp.39015104955862	190	2	remark	remark	NOUN
mdp.39015104955862	190	3	2	2	NUM
mdp.39015104955862	190	4	,	,	PUNCT
mdp.39015104955862	190	5	the	the	DET
mdp.39015104955862	190	6	sequence	sequence	NOUN
mdp.39015104955862	190	7	;	;	PUNCT
mdp.39015104955862	190	8	tends	tend	VERB
mdp.39015104955862	190	9	to	to	PART
mdp.39015104955862	190	10	0	0	NUM
mdp.39015104955862	190	11	as	as	ADP
mdp.39015104955862	190	12	j→	j→	PROPN
mdp.39015104955862	190	13	∞	∞	X
mdp.39015104955862	190	14	uniformly	uniformly	ADV
mdp.39015104955862	190	15	on	on	ADP
mdp.39015104955862	190	16	every	every	DET
mdp.39015104955862	190	17	interval	interval	NOUN
mdp.39015104955862	190	18	.	.	PUNCT
mdp.39015104955862	191	1	moreover	moreover	ADV
mdp.39015104955862	191	2	,	,	PUNCT
mdp.39015104955862	191	3	we	we	PRON
mdp.39015104955862	191	4	may	may	AUX
mdp.39015104955862	191	5	differentiate	differentiate	VERB
mdp.39015104955862	191	6	k	k	NOUN
mdp.39015104955862	191	7	-	-	PUNCT
mdp.39015104955862	191	8	times	time	NOUN
mdp.39015104955862	191	9	under	under	ADP
mdp.39015104955862	191	10	the	the	DET
mdp.39015104955862	191	11	summation	summation	NOUN
mdp.39015104955862	191	12	sign	sign	NOUN
mdp.39015104955862	191	13	(	(	PUNCT
mdp.39015104955862	191	14	see	see	VERB
mdp.39015104955862	191	15	(	(	PUNCT
mdp.39015104955862	191	16	25	25	NUM
mdp.39015104955862	191	17	)	)	PUNCT
mdp.39015104955862	191	18	in	in	ADP
mdp.39015104955862	191	19	remark	remark	NOUN
mdp.39015104955862	191	20	2	2	NUM
mdp.39015104955862	191	21	)	)	PUNCT
mdp.39015104955862	191	22	.	.	PUNCT
mdp.39015104955862	192	1	differentiating	differentiate	VERB
mdp.39015104955862	192	2	k	k	PROPN
mdp.39015104955862	192	3	times	time	NOUN
mdp.39015104955862	192	4	,	,	PUNCT
mdp.39015104955862	192	5	we	we	PRON
mdp.39015104955862	192	6	get	get	VERB
mdp.39015104955862	192	7	(	(	PUNCT
mdp.39015104955862	192	8	514	514	NUM
mdp.39015104955862	192	9	)	)	PUNCT
mdp.39015104955862	192	10	(	(	PUNCT
mdp.39015104955862	192	11	2	2	X
mdp.39015104955862	192	12	)	)	PUNCT
mdp.39015104955862	192	13	=	=	PUNCT
mdp.39015104955862	192	14	{	{	PUNCT
mdp.39015104955862	192	15	m	m	PROPN
mdp.39015104955862	192	16	¿	¿	NUM
mdp.39015104955862	192	17	(	(	PUNCT
mdp.39015104955862	192	18	m+k	m+k	SPACE
mdp.39015104955862	192	19	)	)	PUNCT
mdp.39015104955862	192	20	(	(	PUNCT
mdp.39015104955862	192	21	0	0	X
mdp.39015104955862	192	22	)	)	PUNCT
mdp.39015104955862	192	23	x²	x²	PROPN
mdp.39015104955862	192	24	σm=0+)(0	σm=0+)(0	SPACE
mdp.39015104955862	192	25	)	)	PUNCT
mdp.39015104955862	192	26	σm	σm	PROPN
mdp.39015104955862	192	27	-	-	PUNCT
mdp.39015104955862	192	28	j	j	PROPN
mdp.39015104955862	192	29	-	-	PUNCT
mdp.39015104955862	192	30	k	k	PROPN
mdp.39015104955862	192	31	(	(	PUNCT
mdp.39015104955862	192	32	26	26	NUM
mdp.39015104955862	192	33	)	)	PUNCT
mdp.39015104955862	192	34	m	m	NOUN
mdp.39015104955862	192	35	!	!	PUNCT
mdp.39015104955862	193	1	otherwise	otherwise	ADV
mdp.39015104955862	193	2	if	if	SCONJ
mdp.39015104955862	193	3	kj	kj	PROPN
mdp.39015104955862	193	4	(	(	PUNCT
mdp.39015104955862	193	5	27	27	NUM
mdp.39015104955862	193	6	)	)	PUNCT
mdp.39015104955862	193	7	it	it	PRON
mdp.39015104955862	193	8	follows	follow	VERB
mdp.39015104955862	193	9	from	from	ADP
mdp.39015104955862	193	10	the	the	DET
mdp.39015104955862	193	11	properties	property	NOUN
mdp.39015104955862	193	12	of	of	ADP
mdp.39015104955862	193	13	inductive	inductive	ADJ
mdp.39015104955862	193	14	limits	limit	NOUN
mdp.39015104955862	193	15	(	(	PUNCT
mdp.39015104955862	193	16	see	see	VERB
mdp.39015104955862	193	17	[	[	X
mdp.39015104955862	193	18	12	12	NUM
mdp.39015104955862	193	19	]	]	PUNCT
mdp.39015104955862	193	20	)	)	PUNCT
mdp.39015104955862	193	21	that	that	SCONJ
mdp.39015104955862	193	22	lemma	lemma	NOUN
mdp.39015104955862	193	23	1	1	NUM
mdp.39015104955862	193	24	will	will	AUX
mdp.39015104955862	193	25	be	be	AUX
mdp.39015104955862	193	26	proved	prove	VERB
mdp.39015104955862	193	27	if	if	SCONJ
mdp.39015104955862	193	28	we	we	PRON
mdp.39015104955862	193	29	show	show	VERB
mdp.39015104955862	193	30	that	that	SCONJ
mdp.39015104955862	193	31	there	there	PRON
mdp.39015104955862	193	32	exists	exist	VERB
mdp.39015104955862	193	33	p	p	PROPN
mdp.39015104955862	193	34	>	>	X
mdp.39015104955862	193	35	1	1	NUM
mdp.39015104955862	193	36	such	such	ADJ
mdp.39015104955862	193	37	that	that	DET
mdp.39015104955862	193	38	þ	þ	PROPN
mdp.39015104955862	193	39	;	;	PUNCT
mdp.39015104955862	193	40	€	€	X
mdp.39015104955862	193	41	ďp({mx	ďp({mx	NOUN
mdp.39015104955862	193	42	}	}	PUNCT
mdp.39015104955862	193	43	)	)	PUNCT
mdp.39015104955862	193	44	for	for	ADP
mdp.39015104955862	193	45	j	j	PROPN
mdp.39015104955862	193	46	≥	≥	PROPN
mdp.39015104955862	193	47	jo	jo	PROPN
mdp.39015104955862	193	48	and	and	CCONJ
mdp.39015104955862	193	49	pl	pl	PROPN
mdp.39015104955862	193	50	,	,	PUNCT
mdp.39015104955862	193	51	p(øj	p(øj	PROPN
mdp.39015104955862	193	52	)	)	PUNCT
mdp.39015104955862	193	53	→	→	SYM
mdp.39015104955862	193	54	0	0	NUM
mdp.39015104955862	193	55	(	(	PUNCT
mdp.39015104955862	193	56	28	28	NUM
mdp.39015104955862	193	57	)	)	PUNCT
mdp.39015104955862	193	58	14	14	NUM
mdp.39015104955862	193	59	as	as	SCONJ
mdp.39015104955862	193	60	j→	j→	PROPN
mdp.39015104955862	193	61	∞o	∞o	VERB
mdp.39015104955862	193	62	for	for	ADP
mdp.39015104955862	193	63	every	every	DET
mdp.39015104955862	193	64	interval	interval	NOUN
mdp.39015104955862	193	65	i.	i.	NOUN
mdp.39015104955862	193	66	from	from	ADP
mdp.39015104955862	193	67	(	(	PUNCT
mdp.39015104955862	193	68	13	13	NUM
mdp.39015104955862	193	69	)	)	PUNCT
mdp.39015104955862	193	70	and	and	CCONJ
mdp.39015104955862	193	71	(	(	PUNCT
mdp.39015104955862	193	72	27	27	X
mdp.39015104955862	193	73	)	)	PUNCT
mdp.39015104955862	193	74	we	we	PRON
mdp.39015104955862	193	75	get	get	VERB
mdp.39015104955862	193	76	for	for	ADP
mdp.39015104955862	193	77	≈	≈	PROPN
mdp.39015104955862	193	78	€	€	PROPN
mdp.39015104955862	193	79	i	i	PROPN
mdp.39015104955862	193	80	,	,	PUNCT
mdp.39015104955862	193	81	k	k	PROPN
mdp.39015104955862	193	82	≥	≥	PROPN
mdp.39015104955862	193	83	j/2	j/2	X
mdp.39015104955862	193	84	bm	bm	PROPN
mdp.39015104955862	193	85	|ø	|ø	PROPN
mdp.39015104955862	193	86	(	(	PUNCT
mdp.39015104955862	193	87	*	*	PUNCT
mdp.39015104955862	193	88	)	)	PUNCT
mdp.39015104955862	193	89	(	(	PUNCT
mdp.39015104955862	193	90	z)|	z)|	VERB
mdp.39015104955862	193	91	≤	≤	X
mdp.39015104955862	193	92	σ	σ	X
mdp.39015104955862	194	1	[	[	X
mdp.39015104955862	194	2	ø(m+k)(0)|	ø(m+k)(0)|	X
mdp.39015104955862	194	3	|x|″	|x|″	NUM
mdp.39015104955862	194	4	<	<	X
mdp.39015104955862	194	5	alights	alight	NOUN
mdp.39015104955862	194	6	||=|	||=|	NOUN
mdp.39015104955862	194	7	≤	≤	PROPN
mdp.39015104955862	194	8	aight	aight	PROPN
mdp.39015104955862	194	9	mm+kh	mm+kh	SPACE
mdp.39015104955862	194	10	™	™	PROPN
mdp.39015104955862	194	11	b	b	PROPN
mdp.39015104955862	194	12	™	™	PROPN
mdp.39015104955862	194	13	m	m	NOUN
mdp.39015104955862	194	14	!	!	PUNCT
mdp.39015104955862	194	15	m=0	m=0	PROPN
mdp.39015104955862	194	16	using	use	VERB
mdp.39015104955862	194	17	1	1	NUM
mdp.39015104955862	194	18	)	)	PUNCT
mdp.39015104955862	194	19	and	and	CCONJ
mdp.39015104955862	194	20	2	2	X
mdp.39015104955862	194	21	)	)	PUNCT
mdp.39015104955862	194	22	,	,	PUNCT
mdp.39015104955862	194	23	we	we	PRON
mdp.39015104955862	194	24	obtain	obtain	VERB
mdp.39015104955862	194	25	|ø(*)(x)|	|ø(*)(x)|	PROPN
mdp.39015104955862	194	26	≤	≤	NOUN
mdp.39015104955862	194	27	a1‚¢h*p(ho)*+¹	a1‚¢h*p(ho)*+¹	X
mdp.39015104955862	194	28	mk	mk	PROPN
mdp.39015104955862	194	29	σ	σ	PROPN
mdp.39015104955862	194	30	tmbm	tmbm	VERB
mdp.39015104955862	194	31	≤	≤	PROPN
mdp.39015104955862	194	32	ã1,h	ã1,h	PROPN
mdp.39015104955862	194	33	™	™	PROPN
mdp.39015104955862	194	34	mx	mx	PROPN
mdp.39015104955862	194	35	,	,	PUNCT
mdp.39015104955862	194	36	,	,	PUNCT
mdp.39015104955862	194	37	k≥	k≥	PROPN
mdp.39015104955862	194	38	j/2	j/2	PROPN
mdp.39015104955862	194	39	,	,	PUNCT
mdp.39015104955862	194	40	≈	≈	PROPN
mdp.39015104955862	194	41	€	€	PROPN
mdp.39015104955862	194	42	i.	i.	PROPN
mdp.39015104955862	194	43	(	(	PUNCT
mdp.39015104955862	194	44	29	29	NUM
mdp.39015104955862	194	45	)	)	PUNCT
mdp.39015104955862	194	46	m=0	m=0	PROPN
mdp.39015104955862	194	47	in	in	ADP
mdp.39015104955862	194	48	the	the	DET
mdp.39015104955862	194	49	case	case	NOUN
mdp.39015104955862	194	50	k	k	PROPN
mdp.39015104955862	194	51	<	<	X
mdp.39015104955862	194	52	j/2	j/2	PROPN
mdp.39015104955862	194	53	,	,	PUNCT
mdp.39015104955862	194	54	x	x	PUNCT
mdp.39015104955862	194	55	€	€	X
mdp.39015104955862	194	56	i	i	PRON
mdp.39015104955862	194	57	we	we	PRON
mdp.39015104955862	194	58	get	get	VERB
mdp.39015104955862	194	59	|0(*)(z)|	|0(*)(z)|	X
mdp.39015104955862	194	60	≤	≤	PROPN
mdp.39015104955862	194	61	a1,øh*p(ho)*+¹	a1,øh*p(ho)*+¹	PROPN
mdp.39015104955862	194	62	mk	mk	PROPN
mdp.39015104955862	194	63	σ	σ	PROPN
mdp.39015104955862	194	64	tm	tm	PROPN
mdp.39015104955862	194	65	bt	bt	PROPN
mdp.39015104955862	194	66	≤	≤	PROPN
mdp.39015104955862	194	67	alo(h	alo(h	PROPN
mdp.39015104955862	194	68	)	)	PUNCT
mdp.39015104955862	194	69	*	*	PUNCT
mdp.39015104955862	195	1	mk	mk	PROPN
mdp.39015104955862	195	2	σ	σ	PROPN
mdp.39015104955862	195	3	tmbt	tmbt	PROPN
mdp.39015104955862	195	4	.	.	PUNCT
mdp.39015104955862	196	1	m	m	NOUN
mdp.39015104955862	196	2	:	:	PUNCT
mdp.39015104955862	196	3	m	m	PUNCT
mdp.39015104955862	196	4	>	>	X
mdp.39015104955862	196	5	j/2	j/2	X
mdp.39015104955862	196	6	m	m	PROPN
mdp.39015104955862	196	7	:	:	PUNCT
mdp.39015104955862	196	8	m	m	NOUN
mdp.39015104955862	196	9	>	>	X
mdp.39015104955862	196	10	j/2	j/2	X
mdp.39015104955862	196	11	it	it	PRON
mdp.39015104955862	196	12	follows	follow	VERB
mdp.39015104955862	196	13	from	from	ADP
mdp.39015104955862	196	14	the	the	DET
mdp.39015104955862	196	15	previous	previous	ADJ
mdp.39015104955862	196	16	inequality	inequality	NOUN
mdp.39015104955862	196	17	and	and	CCONJ
mdp.39015104955862	196	18	from	from	ADP
mdp.39015104955862	196	19	(	(	PUNCT
mdp.39015104955862	196	20	29	29	NUM
mdp.39015104955862	196	21	)	)	PUNCT
mdp.39015104955862	196	22	that	that	SCONJ
mdp.39015104955862	196	23	there	there	PRON
mdp.39015104955862	196	24	exists	exist	VERB
mdp.39015104955862	196	25	a	a	DET
mdp.39015104955862	196	26	constant	constant	ADJ
mdp.39015104955862	196	27	h	h	NOUN
mdp.39015104955862	196	28	¿	¿	NUM
mdp.39015104955862	196	29	,	,	PUNCT
mdp.39015104955862	196	30	depending	depend	VERB
mdp.39015104955862	196	31	only	only	ADV
mdp.39015104955862	196	32	on	on	ADP
mdp.39015104955862	196	33	ø	ø	PROPN
mdp.39015104955862	196	34	,	,	PUNCT
mdp.39015104955862	196	35	and	and	CCONJ
mdp.39015104955862	196	36	for	for	ADP
mdp.39015104955862	196	37	every	every	DET
mdp.39015104955862	196	38	interval	interval	NOUN
mdp.39015104955862	197	1	ic	ic	INTJ
mdp.39015104955862	197	2	r¹	r¹	NOUN
mdp.39015104955862	197	3	there	there	PRON
mdp.39015104955862	197	4	exists	exist	VERB
mdp.39015104955862	197	5	a	a	DET
mdp.39015104955862	197	6	constant	constant	ADJ
mdp.39015104955862	197	7	a	a	PRON
mdp.39015104955862	197	8	,	,	PUNCT
mdp.39015104955862	197	9	,	,	PUNCT
mdp.39015104955862	197	10	depending	depend	VERB
mdp.39015104955862	197	11	on	on	ADP
mdp.39015104955862	197	12	i	i	PRON
mdp.39015104955862	197	13	and	and	CCONJ
mdp.39015104955862	197	14	o	o	NOUN
mdp.39015104955862	197	15	,	,	PUNCT
mdp.39015104955862	197	16	for	for	ADP
mdp.39015104955862	197	17	which	which	PRON
mdp.39015104955862	197	18	3=0	3=0	NUM
mdp.39015104955862	197	19	p1,p($	p1,p($	NOUN
mdp.39015104955862	197	20	;)	;)	PUNCT
mdp.39015104955862	197	21	=	=	PROPN
mdp.39015104955862	197	22	supmax	supmax	PROPN
mdp.39015104955862	197	23	{	{	PUNCT
mdp.39015104955862	197	24	sup_[\¿(*)(x)|(p*mx)¯¹	sup_[\¿(*)(x)|(p*mx)¯¹	NOUN
mdp.39015104955862	197	25	]	]	PUNCT
mdp.39015104955862	197	26	,	,	PUNCT
mdp.39015104955862	197	27	sup_[|ø(*)(x)|(p*mk)¯¹	sup_[|ø(*)(x)|(p*mk)¯¹	NOUN
mdp.39015104955862	197	28	]	]	PUNCT
mdp.39015104955862	197	29	≤	≤	X
mdp.39015104955862	197	30	τε	τε	X
mdp.39015104955862	197	31	!	!	PUNCT
mdp.39015104955862	198	1	hence	hence	ADV
mdp.39015104955862	198	2	,	,	PUNCT
mdp.39015104955862	198	3	k	k	X
mdp.39015104955862	198	4	:	:	PUNCT
mdp.39015104955862	198	5	k	k	PROPN
mdp.39015104955862	198	6	>	>	X
mdp.39015104955862	198	7	j/2	j/2	X
mdp.39015104955862	198	8	k	k	PROPN
mdp.39015104955862	198	9	:	:	PUNCT
mdp.39015104955862	198	10	k≤j/2	k≤j/2	PROPN
mdp.39015104955862	198	11	-k	-k	SYM
mdp.39015104955862	198	12	a1	a1	PROPN
mdp.39015104955862	198	13	,	,	PUNCT
mdp.39015104955862	198	14	max	max	PROPN
mdp.39015104955862	198	15	sup	sup	NOUN
mdp.39015104955862	198	16	[	[	X
mdp.39015104955862	198	17	hp-	hp-	X
mdp.39015104955862	198	18	*	*	PUNCT
mdp.39015104955862	198	19	]	]	X
mdp.39015104955862	198	20	,	,	PUNCT
mdp.39015104955862	198	21	sup	sup	NOUN
mdp.39015104955862	198	22	[	[	X
mdp.39015104955862	198	23	hp	hp	X
mdp.39015104955862	198	24	σ	σ	PROPN
mdp.39015104955862	198	25	tmbm	tmbm	NOUN
mdp.39015104955862	198	26	]	]	PUNCT
mdp.39015104955862	198	27	}	}	PUNCT
mdp.39015104955862	198	28	.	.	PUNCT
mdp.39015104955862	199	1	k	k	X
mdp.39015104955862	199	2	:	:	PUNCT
mdp.39015104955862	200	1	k	k	PROPN
mdp.39015104955862	200	2	>	>	X
mdp.39015104955862	200	3	j/2	j/2	X
mdp.39015104955862	200	4	k	k	PROPN
mdp.39015104955862	200	5	<	<	X
mdp.39015104955862	200	6	j/2	j/2	X
mdp.39015104955862	200	7	m	m	PROPN
mdp.39015104955862	200	8	:	:	PUNCT
mdp.39015104955862	200	9	m	m	X
mdp.39015104955862	200	10	>	>	X
mdp.39015104955862	200	11	j/2	j/2	NUM
mdp.39015104955862	200	12	using	use	VERB
mdp.39015104955862	200	13	(	(	PUNCT
mdp.39015104955862	200	14	30	30	NUM
mdp.39015104955862	200	15	)	)	PUNCT
mdp.39015104955862	200	16	,	,	PUNCT
mdp.39015104955862	200	17	we	we	PRON
mdp.39015104955862	200	18	show	show	VERB
mdp.39015104955862	200	19	that	that	SCONJ
mdp.39015104955862	200	20	for	for	ADP
mdp.39015104955862	200	21	p	p	PROPN
mdp.39015104955862	200	22	>	>	X
mdp.39015104955862	200	23	he	he	PRON
mdp.39015104955862	200	24	condition	condition	NOUN
mdp.39015104955862	200	25	(	(	PUNCT
mdp.39015104955862	200	26	28	28	NUM
mdp.39015104955862	200	27	)	)	PUNCT
mdp.39015104955862	200	28	is	be	AUX
mdp.39015104955862	200	29	satisfied	satisfied	ADJ
mdp.39015104955862	200	30	.	.	PUNCT
mdp.39015104955862	201	1	this	this	PRON
mdp.39015104955862	201	2	proves	prove	VERB
mdp.39015104955862	201	3	lemma	lemma	NOUN
mdp.39015104955862	201	4	1	1	X
mdp.39015104955862	201	5	.	.	X
mdp.39015104955862	202	1	let	let	VERB
mdp.39015104955862	202	2	us	we	PRON
mdp.39015104955862	202	3	proceed	proceed	VERB
mdp.39015104955862	202	4	with	with	ADP
mdp.39015104955862	202	5	the	the	DET
mdp.39015104955862	202	6	proof	proof	NOUN
mdp.39015104955862	202	7	of	of	ADP
mdp.39015104955862	202	8	theorem	theorem	NOUN
mdp.39015104955862	202	9	4	4	NUM
mdp.39015104955862	202	10	.	.	PUNCT
mdp.39015104955862	203	1	suppose	suppose	VERB
mdp.39015104955862	203	2	г	г	PRON
mdp.39015104955862	203	3	€	€	SYM
mdp.39015104955862	203	4	ď'({m	ď'({m	NUM
mdp.39015104955862	203	5	}	}	PUNCT
mdp.39015104955862	203	6	)	)	PUNCT
mdp.39015104955862	203	7	.	.	PUNCT
mdp.39015104955862	204	1	by	by	ADP
mdp.39015104955862	204	2	lemma	lemma	NOUN
mdp.39015104955862	204	3	1	1	NUM
mdp.39015104955862	204	4	,	,	PUNCT
mdp.39015104955862	204	5	we	we	PRON
mdp.39015104955862	204	6	get	get	VERB
mdp.39015104955862	204	7	for	for	ADP
mdp.39015104955862	204	8	every	every	DET
mdp.39015104955862	204	9	$	$	SYM
mdp.39015104955862	204	10	€	€	SYM
mdp.39015104955862	204	11	ď({mk	ď({mk	PROPN
mdp.39015104955862	204	12	}	}	PUNCT
mdp.39015104955862	204	13	)	)	PUNCT
mdp.39015104955862	204	14	i(ø	i(ø	PROPN
mdp.39015104955862	204	15	)	)	PUNCT
mdp.39015104955862	204	16	=	=	PUNCT
mdp.39015104955862	205	1	_	_	PUNCT
mdp.39015104955862	205	2	*	*	PUNCT
mdp.39015104955862	206	1	*	*	PUNCT
mdp.39015104955862	206	2	)	)	PUNCT
mdp.39015104955862	206	3	(	(	PUNCT
mdp.39015104955862	206	4	0	0	X
mdp.39015104955862	206	5	)	)	PUNCT
mdp.39015104955862	206	6	r(2	r(2	SPACE
mdp.39015104955862	206	7	*	*	PUNCT
mdp.39015104955862	206	8	)	)	PUNCT
mdp.39015104955862	206	9	=	=	PUNCT
mdp.39015104955862	206	10	_	_	PUNCT
mdp.39015104955862	206	11	ø(^)(0	ø(^)(0	SPACE
mdp.39015104955862	206	12	)	)	PUNCT
mdp.39015104955862	206	13	k	k	PROPN
mdp.39015104955862	206	14	!	!	PUNCT
mdp.39015104955862	206	15	k=0	k=0	PROPN
mdp.39015104955862	207	1	k=0	k=0	PROPN
mdp.39015104955862	207	2	r	r	X
mdp.39015104955862	207	3	=	=	PUNCT
mdp.39015104955862	207	4	σ(−1	σ(−1	PROPN
mdp.39015104955862	207	5	)	)	PUNCT
mdp.39015104955862	207	6	*	*	PUNCT
mdp.39015104955862	207	7	h*(t	h*(t	NOUN
mdp.39015104955862	207	8	)	)	PUNCT
mdp.39015104955862	207	9	¿	¿	PROPN
mdp.39015104955862	207	10	(	(	PUNCT
mdp.39015104955862	207	11	k	k	PROPN
mdp.39015104955862	207	12	)	)	PUNCT
mdp.39015104955862	207	13	με	με	PROPN
mdp.39015104955862	207	14	k	k	PROPN
mdp.39015104955862	207	15	!	!	PUNCT
mdp.39015104955862	207	16	k=0	k=0	PROPN
mdp.39015104955862	207	17	∞	∞	X
mdp.39015104955862	207	18	lk	lk	PROPN
mdp.39015104955862	207	19	(	(	PUNCT
mdp.39015104955862	207	20	i	i	NOUN
mdp.39015104955862	207	21	)	)	PUNCT
mdp.39015104955862	207	22	g(k	g(k	PROPN
mdp.39015104955862	207	23	)	)	PUNCT
mdp.39015104955862	207	24	(	(	PUNCT
mdp.39015104955862	207	25	$	$	SYM
mdp.39015104955862	207	26	)	)	PUNCT
mdp.39015104955862	207	27	.	.	PUNCT
mdp.39015104955862	208	1	·	·	PUNCT
mdp.39015104955862	208	2	µk(t	µk(t	SPACE
mdp.39015104955862	208	3	)	)	PUNCT
mdp.39015104955862	208	4	=	=	PUNCT
mdp.39015104955862	208	5	σ(−1	σ(−1	PROPN
mdp.39015104955862	208	6	)	)	PUNCT
mdp.39015104955862	208	7	*	*	PUNCT
mdp.39015104955862	208	8	!	!	PUNCT
mdp.39015104955862	208	9	*	*	PUNCT
mdp.39015104955862	209	1	(	(	PUNCT
mdp.39015104955862	209	2	k	k	PROPN
mdp.39015104955862	209	3	!	!	PUNCT
mdp.39015104955862	209	4	k=0	k=0	PROPN
mdp.39015104955862	209	5	(	(	PUNCT
mdp.39015104955862	209	6	30	30	NUM
mdp.39015104955862	209	7	)	)	PUNCT
mdp.39015104955862	209	8	(	(	PUNCT
mdp.39015104955862	209	9	31	31	NUM
mdp.39015104955862	209	10	)	)	PUNCT
mdp.39015104955862	209	11	15	15	NUM
mdp.39015104955862	210	1	and	and	CCONJ
mdp.39015104955862	210	2	i	i	PRON
mdp.39015104955862	210	3	is	be	AUX
mdp.39015104955862	210	4	a	a	DET
mdp.39015104955862	210	5	hyperdistribution	hyperdistribution	NOUN
mdp.39015104955862	210	6	.	.	PUNCT
mdp.39015104955862	211	1	to	to	PART
mdp.39015104955862	211	2	complete	complete	VERB
mdp.39015104955862	211	3	the	the	DET
mdp.39015104955862	211	4	proof	proof	NOUN
mdp.39015104955862	211	5	of	of	ADP
mdp.39015104955862	211	6	theorem	theorem	NOUN
mdp.39015104955862	211	7	4	4	NUM
mdp.39015104955862	211	8	we	we	PRON
mdp.39015104955862	211	9	need	need	VERB
mdp.39015104955862	211	10	only	only	ADV
mdp.39015104955862	211	11	to	to	PART
mdp.39015104955862	211	12	show	show	VERB
mdp.39015104955862	211	13	that	that	SCONJ
mdp.39015104955862	211	14	our	our	PRON
mdp.39015104955862	211	15	goal	goal	NOUN
mdp.39015104955862	211	16	is	be	AUX
mdp.39015104955862	211	17	to	to	PART
mdp.39015104955862	211	18	prove	prove	VERB
mdp.39015104955862	211	19	that	that	SCONJ
mdp.39015104955862	211	20	fix	fix	NOUN
mdp.39015104955862	211	21	h	h	NOUN
mdp.39015104955862	211	22	>	>	X
mdp.39015104955862	211	23	0	0	NUM
mdp.39015104955862	211	24	and	and	CCONJ
mdp.39015104955862	211	25	consider	consider	VERB
mdp.39015104955862	211	26	a	a	DET
mdp.39015104955862	211	27	function	function	NOUN
mdp.39015104955862	212	1	oh	oh	INTJ
mdp.39015104955862	212	2	,	,	PUNCT
mdp.39015104955862	212	3	given	give	VERB
mdp.39015104955862	212	4	by	by	ADP
mdp.39015104955862	212	5	the	the	DET
mdp.39015104955862	212	6	following	following	ADJ
mdp.39015104955862	212	7	infinite	infinite	ADJ
mdp.39015104955862	212	8	series	series	PROPN
mdp.39015104955862	212	9	:	:	PUNCT
mdp.39015104955862	212	10	‡n(≈	‡n(≈	PROPN
mdp.39015104955862	212	11	)	)	PUNCT
mdp.39015104955862	212	12	=	=	PROPN
mdp.39015104955862	212	13	†	†	X
mdp.39015104955862	212	14	sign(µ;(t	sign(µ;(t	PROPN
mdp.39015104955862	212	15	)	)	PUNCT
mdp.39015104955862	212	16	)	)	PUNCT
mdp.39015104955862	213	1	m;h³z³	m;h³z³	PROPN
mdp.39015104955862	213	2	,	,	PUNCT
mdp.39015104955862	213	3	≈	≈	PROPN
mdp.39015104955862	213	4	€	€	PROPN
mdp.39015104955862	213	5	r¹.	r¹.	PROPN
mdp.39015104955862	213	6	j	j	NOUN
mdp.39015104955862	213	7	!	!	PUNCT
mdp.39015104955862	213	8	j=0	j=0	VERB
mdp.39015104955862	213	9	if	if	SCONJ
mdp.39015104955862	213	10	(	(	PUNCT
mdp.39015104955862	213	11	32	32	NUM
mdp.39015104955862	213	12	)	)	PUNCT
mdp.39015104955862	213	13	is	be	AUX
mdp.39015104955862	213	14	proved	prove	VERB
mdp.39015104955862	213	15	,	,	PUNCT
mdp.39015104955862	213	16	then	then	ADV
mdp.39015104955862	213	17	σ	σ	PROPN
mdp.39015104955862	213	18	k=0	k=0	PROPN
mdp.39015104955862	213	19	\µk(i)\	\µk(i)\	CCONJ
mdp.39015104955862	213	20	mμxh	mμxh	NOUN
mdp.39015104955862	213	21	*	*	PUNCT
mdp.39015104955862	213	22	<	<	X
mdp.39015104955862	213	23	∞	∞	X
mdp.39015104955862	213	24	,	,	PUNCT
mdp.39015104955862	213	25	h>0	h>0	PROPN
mdp.39015104955862	213	26	.	.	PUNCT
mdp.39015104955862	214	1	k	k	PROPN
mdp.39015104955862	214	2	!	!	PROPN
mdp.39015104955862	214	3	and	and	CCONJ
mdp.39015104955862	214	4	(	(	PUNCT
mdp.39015104955862	214	5	34	34	NUM
mdp.39015104955862	214	6	)	)	PUNCT
mdp.39015104955862	214	7	gives	give	VERB
mdp.39015104955862	214	8	t(n	t(n	SPACE
mdp.39015104955862	214	9	):	):	PUNCT
mdp.39015104955862	214	10	=	=	SYM
mdp.39015104955862	214	11	j=0	j=0	VERB
mdp.39015104955862	214	12	and	and	CCONJ
mdp.39015104955862	214	13	theorem	theorem	NOUN
mdp.39015104955862	214	14	4	4	NUM
mdp.39015104955862	214	15	will	will	AUX
mdp.39015104955862	214	16	follow	follow	VERB
mdp.39015104955862	214	17	from	from	ADP
mdp.39015104955862	214	18	(	(	PUNCT
mdp.39015104955862	214	19	31	31	NUM
mdp.39015104955862	214	20	)	)	PUNCT
mdp.39015104955862	214	21	and	and	CCONJ
mdp.39015104955862	214	22	(	(	PUNCT
mdp.39015104955862	214	23	33	33	NUM
mdp.39015104955862	214	24	)	)	PUNCT
mdp.39015104955862	214	25	.	.	PUNCT
mdp.39015104955862	215	1	we	we	PRON
mdp.39015104955862	215	2	have	have	VERB
mdp.39015104955862	215	3	oh	oh	INTJ
mdp.39015104955862	215	4	€	€	SYM
mdp.39015104955862	215	5	ď({mk	ď({mk	PROPN
mdp.39015104955862	215	6	}	}	PUNCT
mdp.39015104955862	215	7	)	)	PUNCT
mdp.39015104955862	215	8	.	.	PUNCT
mdp.39015104955862	216	1	from	from	ADP
mdp.39015104955862	216	2	conditions	condition	NOUN
mdp.39015104955862	216	3	1)-2	1)-2	NUM
mdp.39015104955862	216	4	)	)	PUNCT
mdp.39015104955862	216	5	we	we	PRON
mdp.39015104955862	216	6	obtain	obtain	VERB
mdp.39015104955862	216	7	|µ,(t)|m;h³	|µ,(t)|m;h³	SPACE
mdp.39015104955862	216	8	j	j	X
mdp.39015104955862	216	9	!	!	PUNCT
mdp.39015104955862	216	10	|øn(x)|	|øn(x)|	X
mdp.39015104955862	217	1	≤	≤	X
mdp.39015104955862	217	2	ĉ	ĉ	ADP
mdp.39015104955862	217	3	h³	h³	PROPN
mdp.39015104955862	217	4	\x\¿m	\x\¿m	PROPN
mdp.39015104955862	217	5	;	;	PUNCT
mdp.39015104955862	217	6	j=0	j=0	NUM
mdp.39015104955862	217	7	j	j	NOUN
mdp.39015104955862	217	8	!	!	PUNCT
mdp.39015104955862	217	9	∞	∞	X
mdp.39015104955862	217	10	>	>	X
mdp.39015104955862	217	11	m	m	X
mdp.39015104955862	217	12	;	;	PUNCT
mdp.39015104955862	217	13	≤	≤	PROPN
mdp.39015104955862	217	14	c(j!)t;mo	c(j!)t;mo	PROPN
mdp.39015104955862	217	15	,	,	PUNCT
mdp.39015104955862	217	16	j≥0	j≥0	PROPN
mdp.39015104955862	217	17	|4n(z)|	|4n(z)|	VERB
mdp.39015104955862	217	18	≤	≤	X
mdp.39015104955862	217	19	cmoσh³|z|³t	cmoσh³|z|³t	SPACE
mdp.39015104955862	217	20	;	;	PUNCT
mdp.39015104955862	217	21	.	.	PUNCT
mdp.39015104955862	217	22	j=0	j=0	VERB
mdp.39015104955862	217	23	therefore	therefore	ADV
mdp.39015104955862	217	24	,	,	PUNCT
mdp.39015104955862	217	25	the	the	DET
mdp.39015104955862	217	26	series	series	NOUN
mdp.39015104955862	217	27	,	,	PUNCT
mdp.39015104955862	217	28	defining	define	VERB
mdp.39015104955862	217	29	oh	oh	INTJ
mdp.39015104955862	217	30	,	,	PUNCT
mdp.39015104955862	217	31	is	be	AUX
mdp.39015104955862	217	32	uniformly	uniformly	ADV
mdp.39015104955862	217	33	convergent	convergent	ADJ
mdp.39015104955862	217	34	on	on	ADP
mdp.39015104955862	217	35	intervals	interval	NOUN
mdp.39015104955862	217	36	.	.	PUNCT
mdp.39015104955862	218	1	similarly	similarly	ADV
mdp.39015104955862	218	2	,	,	PUNCT
mdp.39015104955862	218	3	the	the	DET
mdp.39015104955862	218	4	k	k	PROPN
mdp.39015104955862	218	5	-	-	PUNCT
mdp.39015104955862	218	6	times	times	NOUN
mdp.39015104955862	218	7	differentiated	differentiate	VERB
mdp.39015104955862	218	8	series	series	NOUN
mdp.39015104955862	218	9	,	,	PUNCT
mdp.39015104955862	218	10	namely	namely	ADV
mdp.39015104955862	218	11	zi	zi	PROPN
mdp.39015104955862	218	12	ik(2	ik(2	PROPN
mdp.39015104955862	218	13	)	)	PUNCT
mdp.39015104955862	218	14	=	=	PROPN
mdp.39015104955862	218	15	σ	σ	PROPN
mdp.39015104955862	218	16	=	=	SYM
mdp.39015104955862	218	17	sign(µ;+k(t))mj+khi+k	sign(µ;+k(t))mj+khi+k	PROPN
mdp.39015104955862	218	18	j=0	j=0	NUM
mdp.39015104955862	218	19	is	be	AUX
mdp.39015104955862	218	20	uniformly	uniformly	ADV
mdp.39015104955862	218	21	convergent	convergent	ADJ
mdp.39015104955862	218	22	on	on	ADP
mdp.39015104955862	218	23	intervals	interval	NOUN
mdp.39015104955862	218	24	.	.	PUNCT
mdp.39015104955862	219	1	this	this	PRON
mdp.39015104955862	219	2	can	can	AUX
mdp.39015104955862	219	3	be	be	AUX
mdp.39015104955862	219	4	shown	show	VERB
mdp.39015104955862	219	5	as	as	SCONJ
mdp.39015104955862	219	6	follows	follow	NOUN
mdp.39015104955862	219	7	.	.	PUNCT
mdp.39015104955862	220	1	(	(	PUNCT
mdp.39015104955862	220	2	32	32	NUM
mdp.39015104955862	220	3	)	)	PUNCT
mdp.39015104955862	220	4	(	(	PUNCT
mdp.39015104955862	220	5	33	33	NUM
mdp.39015104955862	220	6	)	)	PUNCT
mdp.39015104955862	220	7	(	(	PUNCT
mdp.39015104955862	220	8	34	34	NUM
mdp.39015104955862	220	9	)	)	PUNCT
mdp.39015104955862	220	10	(	(	PUNCT
mdp.39015104955862	220	11	35	35	NUM
mdp.39015104955862	220	12	)	)	PUNCT
mdp.39015104955862	220	13	(	(	PUNCT
mdp.39015104955862	220	14	36	36	NUM
mdp.39015104955862	220	15	)	)	PUNCT
mdp.39015104955862	220	16	i	i	PRON
mdp.39015104955862	220	17	16	16	NUM
mdp.39015104955862	220	18	by	by	ADP
mdp.39015104955862	220	19	conditions	condition	NOUN
mdp.39015104955862	220	20	1)-2	1)-2	NUM
mdp.39015104955862	220	21	)	)	PUNCT
mdp.39015104955862	220	22	and	and	CCONJ
mdp.39015104955862	220	23	by	by	ADP
mdp.39015104955862	220	24	(	(	PUNCT
mdp.39015104955862	220	25	36	36	NUM
mdp.39015104955862	220	26	)	)	PUNCT
mdp.39015104955862	220	27	,	,	PUNCT
mdp.39015104955862	220	28	we	we	PRON
mdp.39015104955862	220	29	get	get	VERB
mdp.39015104955862	220	30	\ik(2)|	\ik(2)|	X
mdp.39015104955862	220	31	≤	≤	X
mdp.39015104955862	220	32	h*c*mk	h*c*mk	NOUN
mdp.39015104955862	220	33	σ	σ	NOUN
mdp.39015104955862	220	34	h³z³tj	h³z³tj	NOUN
mdp.39015104955862	220	35	,	,	PUNCT
mdp.39015104955862	220	36	j=0	j=0	VERB
mdp.39015104955862	220	37	which	which	PRON
mdp.39015104955862	220	38	shows	show	VERB
mdp.39015104955862	220	39	that	that	SCONJ
mdp.39015104955862	220	40	the	the	DET
mdp.39015104955862	220	41	series	series	NOUN
mdp.39015104955862	220	42	in	in	ADP
mdp.39015104955862	220	43	(	(	PUNCT
mdp.39015104955862	220	44	36	36	NUM
mdp.39015104955862	220	45	)	)	PUNCT
mdp.39015104955862	220	46	converges	converge	VERB
mdp.39015104955862	220	47	uniformly	uniformly	ADV
mdp.39015104955862	220	48	.	.	PUNCT
mdp.39015104955862	221	1	hence	hence	ADV
mdp.39015104955862	221	2	,	,	PUNCT
mdp.39015104955862	221	3	4(*)(x	4(*)(x	NUM
mdp.39015104955862	221	4	)	)	PUNCT
mdp.39015104955862	221	5	=	=	X
mdp.39015104955862	221	6	ik(x	ik(x	PROPN
mdp.39015104955862	221	7	)	)	PUNCT
mdp.39015104955862	221	8	,	,	PUNCT
mdp.39015104955862	221	9	xɛ	xɛ	X
mdp.39015104955862	221	10	r¹.	r¹.	PROPN
mdp.39015104955862	221	11	moreover	moreover	ADV
mdp.39015104955862	221	12	,	,	PUNCT
mdp.39015104955862	221	13	from	from	ADP
mdp.39015104955862	221	14	(	(	PUNCT
mdp.39015104955862	221	15	36	36	NUM
mdp.39015104955862	221	16	)	)	PUNCT
mdp.39015104955862	221	17	,	,	PUNCT
mdp.39015104955862	221	18	(	(	PUNCT
mdp.39015104955862	221	19	37	37	NUM
mdp.39015104955862	221	20	)	)	PUNCT
mdp.39015104955862	221	21	,	,	PUNCT
mdp.39015104955862	221	22	and	and	CCONJ
mdp.39015104955862	221	23	(	(	PUNCT
mdp.39015104955862	221	24	38	38	X
mdp.39015104955862	221	25	)	)	PUNCT
mdp.39015104955862	221	26	we	we	PRON
mdp.39015104955862	221	27	get	get	VERB
mdp.39015104955862	221	28	-k	-k	PUNCT
mdp.39015104955862	221	29	|0	|0	PUNCT
mdp.39015104955862	221	30	(	(	PUNCT
mdp.39015104955862	221	31	*	*	PUNCT
mdp.39015104955862	221	32	)	)	PUNCT
mdp.39015104955862	221	33	(	(	PUNCT
mdp.39015104955862	221	34	x)|	x)|	PROPN
mdp.39015104955862	221	35	≤	≤	X
mdp.39015104955862	221	36	ahh	ahh	PROPN
mdp.39015104955862	221	37	*	*	NOUN
mdp.39015104955862	221	38	mx	mx	PROPN
mdp.39015104955862	221	39	,	,	PUNCT
mdp.39015104955862	221	40	k	k	PROPN
mdp.39015104955862	221	41	≥	≥	X
mdp.39015104955862	221	42	0	0	NUM
mdp.39015104955862	221	43	,	,	PUNCT
mdp.39015104955862	221	44	x	x	PUNCT
mdp.39015104955862	221	45	є	є	INTJ
mdp.39015104955862	222	1	i	i	PRON
mdp.39015104955862	222	2	denote	denote	VERB
mdp.39015104955862	222	3	mk	mk	PROPN
mdp.39015104955862	222	4	=	=	PROPN
mdp.39015104955862	222	5	k*(k	k*(k	PROPN
mdp.39015104955862	222	6	)	)	PUNCT
mdp.39015104955862	222	7	,	,	PUNCT
mdp.39015104955862	222	8	k	k	PROPN
mdp.39015104955862	222	9	≥	≥	X
mdp.39015104955862	222	10	0	0	NUM
mdp.39015104955862	222	11	,	,	PUNCT
mdp.39015104955862	222	12	where	where	SCONJ
mdp.39015104955862	222	13	κ(u	κ(u	PROPN
mdp.39015104955862	222	14	)	)	PUNCT
mdp.39015104955862	222	15	,	,	PUNCT
mdp.39015104955862	222	16	u	u	PROPN
mdp.39015104955862	222	17	≥	≥	X
mdp.39015104955862	222	18	0	0	NUM
mdp.39015104955862	222	19	is	be	AUX
mdp.39015104955862	222	20	a	a	DET
mdp.39015104955862	222	21	smooth	smooth	ADJ
mdp.39015104955862	222	22	increasing	increase	VERB
mdp.39015104955862	222	23	function	function	NOUN
mdp.39015104955862	222	24	on	on	ADP
mdp.39015104955862	222	25	[	[	X
mdp.39015104955862	222	26	0,∞	0,∞	NUM
mdp.39015104955862	222	27	)	)	PUNCT
mdp.39015104955862	222	28	,	,	PUNCT
mdp.39015104955862	222	29	for	for	ADP
mdp.39015104955862	222	30	which	which	PRON
mdp.39015104955862	222	31	k'(u	k'(u	PROPN
mdp.39015104955862	222	32	)	)	PUNCT
mdp.39015104955862	222	33	≤	≤	PROPN
mdp.39015104955862	222	34	1−ɛ	1−ɛ	NUM
mdp.39015104955862	222	35	,	,	PUNCT
mdp.39015104955862	222	36	,	,	PUNCT
mdp.39015104955862	222	37	u	u	PROPN
mdp.39015104955862	222	38	>	>	X
mdp.39015104955862	222	39	0	0	NUM
mdp.39015104955862	222	40	for	for	ADP
mdp.39015104955862	222	41	some	some	DET
mdp.39015104955862	222	42	ε	ε	PROPN
mdp.39015104955862	222	43	,	,	PUNCT
mdp.39015104955862	222	44	0	0	NUM
mdp.39015104955862	222	45	<	<	X
mdp.39015104955862	222	46	ε	ε	X
mdp.39015104955862	222	47	<	<	X
mdp.39015104955862	222	48	1	1	NUM
mdp.39015104955862	222	49	.	.	PUNCT
mdp.39015104955862	223	1	then	then	ADV
mdp.39015104955862	223	2	conditions	condition	NOUN
mdp.39015104955862	223	3	1)-2	1)-2	NUM
mdp.39015104955862	223	4	)	)	PUNCT
mdp.39015104955862	223	5	hold	hold	VERB
mdp.39015104955862	223	6	for	for	ADP
mdp.39015104955862	223	7	{	{	PUNCT
mdp.39015104955862	223	8	mk	mk	PROPN
mdp.39015104955862	223	9	}	}	PUNCT
mdp.39015104955862	223	10	·	·	PUNCT
mdp.39015104955862	223	11	proof	proof	NOUN
mdp.39015104955862	223	12	.	.	PUNCT
mdp.39015104955862	224	1	it	it	PRON
mdp.39015104955862	224	2	is	be	AUX
mdp.39015104955862	224	3	clear	clear	ADJ
mdp.39015104955862	224	4	that	that	SCONJ
mdp.39015104955862	224	5	(	(	PUNCT
mdp.39015104955862	224	6	40	40	NUM
mdp.39015104955862	224	7	)	)	PUNCT
mdp.39015104955862	224	8	implies	imply	VERB
mdp.39015104955862	224	9	for	for	ADP
mdp.39015104955862	224	10	every	every	DET
mdp.39015104955862	224	11	interval	interval	NOUN
mdp.39015104955862	224	12	i.	i.	NOUN
mdp.39015104955862	224	13	this	this	PRON
mdp.39015104955862	224	14	shows	show	VERB
mdp.39015104955862	224	15	that	that	SCONJ
mdp.39015104955862	224	16	on	on	ADP
mdp.39015104955862	224	17	€	€	SYM
mdp.39015104955862	224	18	ɖ({mx	ɖ({mx	PROPN
mdp.39015104955862	224	19	}	}	PUNCT
mdp.39015104955862	224	20	)	)	PUNCT
mdp.39015104955862	224	21	,	,	PUNCT
mdp.39015104955862	224	22	and	and	CCONJ
mdp.39015104955862	224	23	hence	hence	ADV
mdp.39015104955862	224	24	the	the	DET
mdp.39015104955862	224	25	proof	proof	NOUN
mdp.39015104955862	224	26	of	of	ADP
mdp.39015104955862	224	27	theorem	theorem	NOUN
mdp.39015104955862	224	28	4	4	NUM
mdp.39015104955862	224	29	is	be	AUX
mdp.39015104955862	224	30	completed	complete	VERB
mdp.39015104955862	224	31	.	.	PUNCT
mdp.39015104955862	225	1	the	the	DET
mdp.39015104955862	225	2	next	next	ADJ
mdp.39015104955862	225	3	lemma	lemma	NOUN
mdp.39015104955862	225	4	allows	allow	VERB
mdp.39015104955862	225	5	us	we	PRON
mdp.39015104955862	225	6	to	to	PART
mdp.39015104955862	225	7	construct	construct	VERB
mdp.39015104955862	225	8	examples	example	NOUN
mdp.39015104955862	225	9	of	of	ADP
mdp.39015104955862	225	10	sequences	sequence	NOUN
mdp.39015104955862	225	11	{	{	PUNCT
mdp.39015104955862	225	12	m	m	NOUN
mdp.39015104955862	225	13	}	}	PUNCT
mdp.39015104955862	225	14	,	,	PUNCT
mdp.39015104955862	225	15	satisfying	satisfy	VERB
mdp.39015104955862	225	16	conditions	condition	NOUN
mdp.39015104955862	225	17	1)-2	1)-2	NUM
mdp.39015104955862	225	18	)	)	PUNCT
mdp.39015104955862	225	19	.	.	PUNCT
mdp.39015104955862	226	1	lemma	lemma	NOUN
mdp.39015104955862	226	2	2	2	NUM
mdp.39015104955862	226	3	suppose	suppose	VERB
mdp.39015104955862	226	4	lim	lim	PROPN
mdp.39015104955862	226	5	sup	sup	NOUN
mdp.39015104955862	226	6	811	811	NUM
mdp.39015104955862	226	7	k(u	k(u	PROPN
mdp.39015104955862	226	8	)	)	PUNCT
mdp.39015104955862	226	9	น	น	PROPN
mdp.39015104955862	226	10	≤	≤	NOUN
mdp.39015104955862	226	11	1	1	NUM
mdp.39015104955862	226	12	−	−	PROPN
mdp.39015104955862	226	13	ɛ	ɛ	X
mdp.39015104955862	226	14	.	.	PUNCT
mdp.39015104955862	226	15	m(u	m(u	PROPN
mdp.39015104955862	226	16	)	)	PUNCT
mdp.39015104955862	226	17	=	=	PROPN
mdp.39015104955862	226	18	u*(u	u*(u	PROPN
mdp.39015104955862	226	19	)	)	PUNCT
mdp.39015104955862	226	20	,	,	PUNCT
mdp.39015104955862	226	21	u	u	PROPN
mdp.39015104955862	226	22	≥	≥	PROPN
mdp.39015104955862	226	23	0	0	NUM
mdp.39015104955862	226	24	.	.	PUNCT
mdp.39015104955862	227	1	(	(	PUNCT
mdp.39015104955862	227	2	37	37	NUM
mdp.39015104955862	227	3	)	)	PUNCT
mdp.39015104955862	227	4	(	(	PUNCT
mdp.39015104955862	227	5	38	38	NUM
mdp.39015104955862	227	6	)	)	PUNCT
mdp.39015104955862	227	7	(	(	PUNCT
mdp.39015104955862	227	8	39	39	NUM
mdp.39015104955862	227	9	)	)	PUNCT
mdp.39015104955862	227	10	(	(	PUNCT
mdp.39015104955862	227	11	40	40	NUM
mdp.39015104955862	227	12	)	)	PUNCT
mdp.39015104955862	227	13	(	(	PUNCT
mdp.39015104955862	227	14	41	41	NUM
mdp.39015104955862	227	15	)	)	PUNCT
mdp.39015104955862	227	16	(	(	PUNCT
mdp.39015104955862	227	17	42	42	NUM
mdp.39015104955862	227	18	)	)	PUNCT
mdp.39015104955862	227	19	17	17	NUM
mdp.39015104955862	227	20	then	then	ADV
mdp.39015104955862	227	21	,	,	PUNCT
mdp.39015104955862	227	22	by	by	ADP
mdp.39015104955862	227	23	(	(	PUNCT
mdp.39015104955862	227	24	39	39	NUM
mdp.39015104955862	227	25	)	)	PUNCT
mdp.39015104955862	227	26	and	and	CCONJ
mdp.39015104955862	227	27	(	(	PUNCT
mdp.39015104955862	227	28	42	42	NUM
mdp.39015104955862	227	29	)	)	PUNCT
mdp.39015104955862	227	30	,	,	PUNCT
mdp.39015104955862	227	31	we	we	PRON
mdp.39015104955862	227	32	have	have	VERB
mdp.39015104955862	227	33	m₂	m₂	PROPN
mdp.39015104955862	227	34	=	=	PUNCT
mdp.39015104955862	227	35	m(n	m(n	SPACE
mdp.39015104955862	227	36	)	)	PUNCT
mdp.39015104955862	227	37	,	,	PUNCT
mdp.39015104955862	227	38	n	n	CCONJ
mdp.39015104955862	227	39	≥	≥	X
mdp.39015104955862	227	40	0	0	NUM
mdp.39015104955862	227	41	.	.	PUNCT
mdp.39015104955862	227	42	now	now	ADV
mdp.39015104955862	227	43	suppose	suppose	VERB
mdp.39015104955862	227	44	where	where	SCONJ
mdp.39015104955862	227	45	8	8	NUM
mdp.39015104955862	227	46	<	<	X
mdp.39015104955862	227	47	ε/2	ε/2	NUM
mdp.39015104955862	227	48	(	(	PUNCT
mdp.39015104955862	227	49	43	43	NUM
mdp.39015104955862	227	50	)	)	PUNCT
mdp.39015104955862	227	51	is	be	AUX
mdp.39015104955862	227	52	fixed	fix	VERB
mdp.39015104955862	227	53	.	.	PUNCT
mdp.39015104955862	228	1	then	then	ADV
mdp.39015104955862	228	2	condition	condition	NOUN
mdp.39015104955862	228	3	1	1	NUM
mdp.39015104955862	228	4	)	)	PUNCT
mdp.39015104955862	228	5	with	with	ADP
mdp.39015104955862	228	6	t₂	t₂	NOUN
mdp.39015104955862	228	7	=	=	SYM
mdp.39015104955862	228	8	t(n	t(n	SPACE
mdp.39015104955862	228	9	)	)	PUNCT
mdp.39015104955862	228	10	,	,	PUNCT
mdp.39015104955862	228	11	n	n	CCONJ
mdp.39015104955862	228	12	≥	≥	X
mdp.39015104955862	228	13	0	0	NUM
mdp.39015104955862	228	14	is	be	AUX
mdp.39015104955862	228	15	satisfied	satisfied	ADJ
mdp.39015104955862	228	16	.	.	PUNCT
mdp.39015104955862	229	1	as	as	ADP
mdp.39015104955862	229	2	for	for	ADP
mdp.39015104955862	229	3	condition	condition	NOUN
mdp.39015104955862	229	4	2	2	NUM
mdp.39015104955862	229	5	)	)	PUNCT
mdp.39015104955862	229	6	,	,	PUNCT
mdp.39015104955862	229	7	it	it	PRON
mdp.39015104955862	229	8	is	be	AUX
mdp.39015104955862	229	9	easy	easy	ADJ
mdp.39015104955862	229	10	to	to	PART
mdp.39015104955862	229	11	see	see	VERB
mdp.39015104955862	229	12	that	that	SCONJ
mdp.39015104955862	229	13	it	it	PRON
mdp.39015104955862	229	14	follows	follow	VERB
mdp.39015104955862	229	15	from	from	ADP
mdp.39015104955862	229	16	the	the	DET
mdp.39015104955862	229	17	inequality	inequality	NOUN
mdp.39015104955862	229	18	where	where	SCONJ
mdp.39015104955862	229	19	≥	≥	PROPN
mdp.39015104955862	229	20	1	1	NUM
mdp.39015104955862	229	21	,	,	PUNCT
mdp.39015104955862	229	22	μ≥	μ≥	PROPN
mdp.39015104955862	229	23	1	1	NUM
mdp.39015104955862	229	24	,	,	PUNCT
mdp.39015104955862	229	25	h	h	NOUN
mdp.39015104955862	229	26	>	>	X
mdp.39015104955862	229	27	ho	ho	PROPN
mdp.39015104955862	229	28	,	,	PUNCT
mdp.39015104955862	229	29	and	and	CCONJ
mdp.39015104955862	229	30	m	m	VERB
mdp.39015104955862	229	31	is	be	AUX
mdp.39015104955862	229	32	defined	define	VERB
mdp.39015104955862	229	33	in	in	ADP
mdp.39015104955862	229	34	(	(	PUNCT
mdp.39015104955862	229	35	42	42	NUM
mdp.39015104955862	229	36	)	)	PUNCT
mdp.39015104955862	229	37	.	.	PUNCT
mdp.39015104955862	230	1	our	our	PRON
mdp.39015104955862	230	2	goal	goal	NOUN
mdp.39015104955862	230	3	will	will	AUX
mdp.39015104955862	230	4	be	be	AUX
mdp.39015104955862	230	5	to	to	PART
mdp.39015104955862	230	6	prove	prove	VERB
mdp.39015104955862	230	7	(	(	PUNCT
mdp.39015104955862	230	8	44	44	NUM
mdp.39015104955862	230	9	)	)	PUNCT
mdp.39015104955862	230	10	.	.	PUNCT
mdp.39015104955862	231	1	by	by	ADP
mdp.39015104955862	231	2	(	(	PUNCT
mdp.39015104955862	231	3	40	40	NUM
mdp.39015104955862	231	4	)	)	PUNCT
mdp.39015104955862	231	5	,	,	PUNCT
mdp.39015104955862	231	6	we	we	PRON
mdp.39015104955862	231	7	get	get	VERB
mdp.39015104955862	231	8	т(u	т(u	SPACE
mdp.39015104955862	231	9	)	)	PUNCT
mdp.39015104955862	231	10	=	=	VERB
mdp.39015104955862	231	11	u	u	PROPN
mdp.39015104955862	231	12	-	-	ADJ
mdp.39015104955862	231	13	bu	bu	PROPN
mdp.39015104955862	231	14	,	,	PUNCT
mdp.39015104955862	231	15	u≥	u≥	ADJ
mdp.39015104955862	231	16	0	0	NUM
mdp.39015104955862	231	17	,	,	PUNCT
mdp.39015104955862	231	18	น	น	PROPN
mdp.39015104955862	231	19	m(µλ)¹/¹h	m(µλ)¹/¹h	PROPN
mdp.39015104955862	231	20	"	"	PUNCT
mdp.39015104955862	231	21	≤	≤	NOUN
mdp.39015104955862	231	22	p(h)\(µ−1)(1−6	p(h)\(µ−1)(1−6	SPACE
mdp.39015104955862	231	23	)	)	PUNCT
mdp.39015104955862	231	24	(	(	PUNCT
mdp.39015104955862	231	25	µ	µ	PROPN
mdp.39015104955862	231	26	−	−	PROPN
mdp.39015104955862	231	27	1)(µ−1)(1−5	1)(µ−1)(1−5	NUM
mdp.39015104955862	231	28	)	)	PUNCT
mdp.39015104955862	231	29	m	m	NOUN
mdp.39015104955862	231	30	(	(	PUNCT
mdp.39015104955862	231	31	a)¹/^	a)¹/^	PROPN
mdp.39015104955862	231	32	,	,	PUNCT
mdp.39015104955862	231	33	it	it	PRON
mdp.39015104955862	231	34	follows	follow	VERB
mdp.39015104955862	231	35	from	from	ADP
mdp.39015104955862	231	36	(	(	PUNCT
mdp.39015104955862	231	37	41	41	NUM
mdp.39015104955862	231	38	)	)	PUNCT
mdp.39015104955862	231	39	that	that	SCONJ
mdp.39015104955862	231	40	since	since	SCONJ
mdp.39015104955862	231	41	(	(	PUNCT
mdp.39015104955862	231	42	45	45	NUM
mdp.39015104955862	231	43	)	)	PUNCT
mdp.39015104955862	231	44	and	and	CCONJ
mdp.39015104955862	231	45	denoting	denote	VERB
mdp.39015104955862	231	46	the	the	DET
mdp.39015104955862	231	47	left	left	ADJ
mdp.39015104955862	231	48	-	-	PUNCT
mdp.39015104955862	231	49	hand	hand	NOUN
mdp.39015104955862	231	50	side	side	NOUN
mdp.39015104955862	231	51	of	of	ADP
mdp.39015104955862	231	52	(	(	PUNCT
mdp.39015104955862	231	53	45	45	NUM
mdp.39015104955862	231	54	)	)	PUNCT
mdp.39015104955862	231	55	by	by	ADP
mdp.39015104955862	231	56	§	§	PROPN
mdp.39015104955862	231	57	¡	¡	PROPN
mdp.39015104955862	231	58	(	(	PUNCT
mdp.39015104955862	231	59	λ,µ	λ,µ	NOUN
mdp.39015104955862	231	60	)	)	PUNCT
mdp.39015104955862	231	61	and	and	CCONJ
mdp.39015104955862	231	62	the	the	DET
mdp.39015104955862	231	63	right	right	ADJ
mdp.39015104955862	231	64	-	-	PUNCT
mdp.39015104955862	231	65	hand	hand	NOUN
mdp.39015104955862	231	66	side	side	NOUN
mdp.39015104955862	231	67	by	by	ADP
mdp.39015104955862	231	68	§	§	PROPN
mdp.39015104955862	231	69	2(λ,µ	2(λ,µ	NUM
mdp.39015104955862	231	70	)	)	PUNCT
mdp.39015104955862	231	71	,	,	PUNCT
mdp.39015104955862	231	72	we	we	PRON
mdp.39015104955862	231	73	obtain	obtain	VERB
mdp.39015104955862	231	74	there	there	PRON
mdp.39015104955862	231	75	exists	exist	VERB
mdp.39015104955862	231	76	μo	μo	NOUN
mdp.39015104955862	231	77	,	,	PUNCT
mdp.39015104955862	231	78	satisfying	satisfy	VERB
mdp.39015104955862	231	79	for	for	ADP
mdp.39015104955862	231	80	which	which	PRON
mdp.39015104955862	231	81	*	*	PUNCT
mdp.39015104955862	231	82	(	(	PUNCT
mdp.39015104955862	231	83	aµ	aµ	NOUN
mdp.39015104955862	231	84	)	)	PUNCT
mdp.39015104955862	231	85	≤	≤	PROPN
mdp.39015104955862	231	86	(	(	PUNCT
mdp.39015104955862	231	87	1	1	NUM
mdp.39015104955862	231	88	−	−	NOUN
mdp.39015104955862	231	89	e)(µ	e)(µ	X
mdp.39015104955862	231	90	−	−	PROPN
mdp.39015104955862	231	91	1	1	X
mdp.39015104955862	231	92	)	)	PUNCT
mdp.39015104955862	231	93	—	—	PUNCT
mdp.39015104955862	231	94	*	*	PROPN
mdp.39015104955862	231	95	(	(	PUNCT
mdp.39015104955862	231	96	1	1	NUM
mdp.39015104955862	231	97	)	)	PUNCT
mdp.39015104955862	231	98	,	,	PUNCT
mdp.39015104955862	231	99	:	:	PUNCT
mdp.39015104955862	231	100	d	d	X
mdp.39015104955862	231	101	®	®	NOUN
mdp.39015104955862	231	102	1	1	NUM
mdp.39015104955862	231	103	(	(	PUNCT
mdp.39015104955862	231	104	1,µ	1,µ	PROPN
mdp.39015104955862	231	105	)	)	PUNCT
mdp.39015104955862	231	106	≤	≤	PROPN
mdp.39015104955862	232	1	d	d	X
mdp.39015104955862	232	2	$	$	SYM
mdp.39015104955862	232	3	2	2	NUM
mdp.39015104955862	232	4	(	(	PUNCT
mdp.39015104955862	232	5	^‚µ	^‚µ	X
mdp.39015104955862	232	6	)	)	PUNCT
mdp.39015104955862	232	7	.	.	PUNCT
mdp.39015104955862	233	1	k(u	k(u	X
mdp.39015104955862	233	2	)	)	PUNCT
mdp.39015104955862	234	1	น	น	PROPN
mdp.39015104955862	234	2	lim	lim	PROPN
mdp.39015104955862	234	3	848	848	NUM
mdp.39015104955862	234	4	<	<	SYM
mdp.39015104955862	234	5	1	1	NUM
mdp.39015104955862	234	6	-	-	PUNCT
mdp.39015104955862	234	7	ε	ε	NOUN
mdp.39015104955862	234	8	,	,	PUNCT
mdp.39015104955862	234	9	u≥	u≥	ADJ
mdp.39015104955862	234	10	uo	uo	NOUN
mdp.39015104955862	234	11	.	.	PUNCT
mdp.39015104955862	235	1	(	(	PUNCT
mdp.39015104955862	235	2	µ	µ	PROPN
mdp.39015104955862	235	3	−	−	PROPN
mdp.39015104955862	235	4	1	1	NUM
mdp.39015104955862	235	5	)	)	PUNCT
mdp.39015104955862	235	6	ln(µ	ln(µ	ADJ
mdp.39015104955862	235	7	−	−	PROPN
mdp.39015104955862	235	8	1	1	X
mdp.39015104955862	235	9	)	)	PUNCT
mdp.39015104955862	235	10	uln	uln	PROPN
mdp.39015104955862	235	11	houo	houo	PROPN
mdp.39015104955862	235	12	,	,	PUNCT
mdp.39015104955862	235	13	(	(	PUNCT
mdp.39015104955862	235	14	µ	µ	X
mdp.39015104955862	235	15	−	−	PROPN
mdp.39015104955862	235	16	1	1	NUM
mdp.39015104955862	235	17	)	)	PUNCT
mdp.39015104955862	235	18	ln(µ	ln(µ	ADJ
mdp.39015104955862	235	19	−	−	PROPN
mdp.39015104955862	235	20	1	1	X
mdp.39015104955862	235	21	)	)	PUNCT
mdp.39015104955862	235	22	>	>	X
mdp.39015104955862	236	1	ln	ln	ADV
mdp.39015104955862	236	2	=	=	PROPN
mdp.39015104955862	236	3	1	1	NUM
mdp.39015104955862	236	4	,	,	PUNCT
mdp.39015104955862	236	5	>	>	X
mdp.39015104955862	236	6	1	1	NUM
mdp.39015104955862	236	7	-	-	PUNCT
mdp.39015104955862	236	8	v	v	NOUN
mdp.39015104955862	236	9	,	,	PUNCT
mdp.39015104955862	236	10	µ	µ	PROPN
mdp.39015104955862	236	11	>	>	X
mdp.39015104955862	236	12	ho(44	ho(44	PROPN
mdp.39015104955862	236	13	)	)	PUNCT
mdp.39015104955862	236	14	(	(	PUNCT
mdp.39015104955862	236	15	46	46	NUM
mdp.39015104955862	236	16	)	)	PUNCT
mdp.39015104955862	236	17	(	(	PUNCT
mdp.39015104955862	236	18	47	47	NUM
mdp.39015104955862	236	19	)	)	PUNCT
mdp.39015104955862	236	20	(	(	PUNCT
mdp.39015104955862	236	21	48	48	NUM
mdp.39015104955862	236	22	)	)	PUNCT
mdp.39015104955862	236	23	(	(	PUNCT
mdp.39015104955862	236	24	49	49	NUM
mdp.39015104955862	236	25	)	)	PUNCT
mdp.39015104955862	236	26	18	18	NUM
mdp.39015104955862	236	27	here	here	ADV
mdp.39015104955862	236	28	v	v	ADV
mdp.39015104955862	236	29	is	be	AUX
mdp.39015104955862	236	30	a	a	DET
mdp.39015104955862	236	31	positive	positive	ADJ
mdp.39015104955862	236	32	number	number	NOUN
mdp.39015104955862	236	33	such	such	ADJ
mdp.39015104955862	236	34	that	that	PRON
mdp.39015104955862	236	35	suppose	suppose	VERB
mdp.39015104955862	236	36	the	the	DET
mdp.39015104955862	236	37	number	number	NOUN
mdp.39015104955862	236	38	v	v	NOUN
mdp.39015104955862	236	39	,	,	PUNCT
mdp.39015104955862	236	40	satisfying	satisfy	VERB
mdp.39015104955862	236	41	(	(	PUNCT
mdp.39015104955862	236	42	50	50	NUM
mdp.39015104955862	236	43	)	)	PUNCT
mdp.39015104955862	236	44	,	,	PUNCT
mdp.39015104955862	236	45	always	always	ADV
mdp.39015104955862	236	46	exists	exist	VERB
mdp.39015104955862	236	47	,	,	PUNCT
mdp.39015104955862	236	48	because	because	SCONJ
mdp.39015104955862	236	49	,	,	PUNCT
mdp.39015104955862	236	50	by	by	ADP
mdp.39015104955862	236	51	(	(	PUNCT
mdp.39015104955862	236	52	43	43	NUM
mdp.39015104955862	236	53	)	)	PUNCT
mdp.39015104955862	236	54	,	,	PUNCT
mdp.39015104955862	236	55	we	we	PRON
mdp.39015104955862	236	56	have	have	VERB
mdp.39015104955862	236	57	then	then	ADV
mdp.39015104955862	236	58	where	where	SCONJ
mdp.39015104955862	236	59	for	for	ADP
mdp.39015104955862	236	60	h	h	PROPN
mdp.39015104955862	236	61	>	>	X
mdp.39015104955862	236	62	hi	hi	PROPN
mdp.39015104955862	236	63	,	,	PUNCT
mdp.39015104955862	236	64	≥	≥	PRON
mdp.39015104955862	236	65	1	1	NUM
mdp.39015104955862	237	1	we	we	PRON
mdp.39015104955862	237	2	have	have	VERB
mdp.39015104955862	237	3	thus	thus	ADV
mdp.39015104955862	237	4	,	,	PUNCT
mdp.39015104955862	237	5	by	by	ADP
mdp.39015104955862	237	6	(	(	PUNCT
mdp.39015104955862	237	7	47	47	NUM
mdp.39015104955862	237	8	)	)	PUNCT
mdp.39015104955862	237	9	,	,	PUNCT
mdp.39015104955862	237	10	(	(	PUNCT
mdp.39015104955862	237	11	52	52	NUM
mdp.39015104955862	237	12	)	)	PUNCT
mdp.39015104955862	237	13	,	,	PUNCT
mdp.39015104955862	237	14	and	and	CCONJ
mdp.39015104955862	237	15	(	(	PUNCT
mdp.39015104955862	237	16	53	53	NUM
mdp.39015104955862	237	17	)	)	PUNCT
mdp.39015104955862	237	18	,	,	PUNCT
mdp.39015104955862	237	19	it	it	PRON
mdp.39015104955862	237	20	follows	follow	VERB
mdp.39015104955862	237	21	from	from	ADP
mdp.39015104955862	237	22	(	(	PUNCT
mdp.39015104955862	237	23	51	51	NUM
mdp.39015104955862	237	24	)	)	PUNCT
mdp.39015104955862	237	25	that	that	SCONJ
mdp.39015104955862	237	26	!	!	PUNCT
mdp.39015104955862	238	1	1	1	NUM
mdp.39015104955862	238	2	-	-	PUNCT
mdp.39015104955862	238	3	ε+8	ε+8	NUM
mdp.39015104955862	238	4	(	(	PUNCT
mdp.39015104955862	238	5	1	1	NUM
mdp.39015104955862	238	6	-	-	NUM
mdp.39015104955862	238	7	6)(1v	6)(1v	NUM
mdp.39015104955862	238	8	)	)	PUNCT
mdp.39015104955862	238	9	.	.	PUNCT
mdp.39015104955862	239	1	1	1	NUM
mdp.39015104955862	239	2	-	-	PUNCT
mdp.39015104955862	239	3	ε+8<1	ε+8<1	NOUN
mdp.39015104955862	239	4	–	–	PUNCT
mdp.39015104955862	239	5	8	8	NUM
mdp.39015104955862	239	6	.	.	X
mdp.39015104955862	239	7	μ	μ	NUM
mdp.39015104955862	239	8	<	<	SYM
mdp.39015104955862	239	9	h.	h.	NOUN
mdp.39015104955862	239	10	where	where	SCONJ
mdp.39015104955862	239	11	p	p	PROPN
mdp.39015104955862	239	12	is	be	AUX
mdp.39015104955862	239	13	some	some	DET
mdp.39015104955862	239	14	positive	positive	ADJ
mdp.39015104955862	239	15	function	function	NOUN
mdp.39015104955862	239	16	.	.	PUNCT
mdp.39015104955862	240	1	now	now	ADV
mdp.39015104955862	240	2	suppose	suppose	VERB
mdp.39015104955862	240	3	h	h	PROPN
mdp.39015104955862	240	4	“	"	PUNCT
mdp.39015104955862	240	5	µ	µ	X
mdp.39015104955862	240	6	®	®	PROPN
mdp.39015104955862	240	7	1	1	NUM
mdp.39015104955862	240	8	(	(	PUNCT
mdp.39015104955862	240	9	µ,x	µ,x	NOUN
mdp.39015104955862	240	10	)	)	PUNCT
mdp.39015104955862	240	11	<	<	X
mdp.39015104955862	240	12	h	h	PROPN
mdp.39015104955862	240	13	®	®	PROPN
mdp.39015104955862	240	14	(	(	PUNCT
mdp.39015104955862	240	15	h	h	PROPN
mdp.39015104955862	240	16	,	,	PUNCT
mdp.39015104955862	240	17	x	x	PROPN
mdp.39015104955862	240	18	)	)	PUNCT
mdp.39015104955862	240	19	,	,	PUNCT
mdp.39015104955862	240	20	$	$	SYM
mdp.39015104955862	240	21	(	(	PUNCT
mdp.39015104955862	240	22	h	h	PROPN
mdp.39015104955862	240	23	,	,	PUNCT
mdp.39015104955862	240	24	λ	λ	NOUN
mdp.39015104955862	240	25	)	)	PUNCT
mdp.39015104955862	240	26	=	=	X
mdp.39015104955862	241	1	h¹³	h¹³	INTJ
mdp.39015104955862	241	2	+	+	ADV
mdp.39015104955862	241	3	{	{	PUNCT
mdp.39015104955862	241	4	}	}	PUNCT
mdp.39015104955862	241	5	{	{	PUNCT
mdp.39015104955862	241	6	×	×	PROPN
mdp.39015104955862	241	7	(	(	PUNCT
mdp.39015104955862	241	8	¿	¿	PROPN
mdp.39015104955862	241	9	¹º	¹º	PROPN
mdp.39015104955862	241	10	λ	λ	NOUN
mdp.39015104955862	241	11	)	)	PUNCT
mdp.39015104955862	241	12	.	.	PUNCT
mdp.39015104955862	242	1	ah	ah	INTJ
mdp.39015104955862	242	2	!	!	PUNCT
mdp.39015104955862	242	3	>	>	X
mdp.39015104955862	243	1	uo	uo	PROPN
mdp.39015104955862	243	2	§	§	PROPN
mdp.39015104955862	243	3	(	(	PUNCT
mdp.39015104955862	243	4	h	h	PROPN
mdp.39015104955862	243	5	,	,	PUNCT
mdp.39015104955862	243	6	λ	λ	NOUN
mdp.39015104955862	243	7	)	)	PUNCT
mdp.39015104955862	243	8	≤	≤	NOUN
mdp.39015104955862	243	9	h¹/5	h¹/5	VERB
mdp.39015104955862	243	10	+	+	NUM
mdp.39015104955862	243	11	1/8h¹.	1/8h¹.	NUM
mdp.39015104955862	243	12	h"µ1	h"µ1	X
mdp.39015104955862	243	13	(	(	PUNCT
mdp.39015104955862	243	14	h,\	h,\	PROPN
mdp.39015104955862	243	15	)	)	PUNCT
mdp.39015104955862	243	16	≤p(h	≤p(h	PROPN
mdp.39015104955862	243	17	)	)	PUNCT
mdp.39015104955862	243	18	,	,	PUNCT
mdp.39015104955862	243	19	h	h	PROPN
mdp.39015104955862	243	20	>	>	X
mdp.39015104955862	243	21	h₁	h₁	PROPN
mdp.39015104955862	243	22	,	,	PUNCT
mdp.39015104955862	243	23	h≤μs	h≤μs	PROPN
mdp.39015104955862	243	24	.	.	PUNCT
mdp.39015104955862	244	1	(	(	PUNCT
mdp.39015104955862	244	2	50	50	NUM
mdp.39015104955862	244	3	)	)	PUNCT
mdp.39015104955862	244	4	(	(	PUNCT
mdp.39015104955862	244	5	51	51	NUM
mdp.39015104955862	244	6	)	)	PUNCT
mdp.39015104955862	244	7	(	(	PUNCT
mdp.39015104955862	244	8	52	52	NUM
mdp.39015104955862	244	9	)	)	PUNCT
mdp.39015104955862	244	10	(	(	PUNCT
mdp.39015104955862	244	11	53	53	NUM
mdp.39015104955862	244	12	)	)	PUNCT
mdp.39015104955862	244	13	(	(	PUNCT
mdp.39015104955862	244	14	54	54	NUM
mdp.39015104955862	244	15	)	)	PUNCT
mdp.39015104955862	244	16	(	(	PUNCT
mdp.39015104955862	244	17	55	55	NUM
mdp.39015104955862	244	18	)	)	PUNCT
mdp.39015104955862	244	19	19	19	NUM
mdp.39015104955862	244	20	then	then	ADV
mdp.39015104955862	244	21	oh	oh	INTJ
mdp.39015104955862	244	22	implies	imply	VERB
mdp.39015104955862	244	23	μo	μo	ADP
mdp.39015104955862	244	24	<	<	X
mdp.39015104955862	244	25	μ	μ	PROPN
mdp.39015104955862	244	26	and	and	CCONJ
mdp.39015104955862	244	27	since	since	SCONJ
mdp.39015104955862	244	28	we	we	PRON
mdp.39015104955862	244	29	have	have	AUX
mdp.39015104955862	244	30	by	by	ADP
mdp.39015104955862	244	31	(	(	PUNCT
mdp.39015104955862	244	32	49	49	NUM
mdp.39015104955862	244	33	)	)	PUNCT
mdp.39015104955862	244	34	,	,	PUNCT
mdp.39015104955862	244	35	moreover	moreover	ADV
mdp.39015104955862	244	36	,	,	PUNCT
mdp.39015104955862	244	37	(	(	PUNCT
mdp.39015104955862	244	38	50	50	NUM
mdp.39015104955862	244	39	)	)	PUNCT
mdp.39015104955862	244	40	and	and	CCONJ
mdp.39015104955862	244	41	(	(	PUNCT
mdp.39015104955862	244	42	57	57	NUM
mdp.39015104955862	244	43	)	)	PUNCT
mdp.39015104955862	244	44	give	give	VERB
mdp.39015104955862	244	45	from	from	ADP
mdp.39015104955862	244	46	(	(	PUNCT
mdp.39015104955862	244	47	54	54	NUM
mdp.39015104955862	244	48	)	)	PUNCT
mdp.39015104955862	244	49	and	and	CCONJ
mdp.39015104955862	244	50	(	(	PUNCT
mdp.39015104955862	244	51	58	58	NUM
mdp.39015104955862	244	52	)	)	PUNCT
mdp.39015104955862	244	53	we	we	PRON
mdp.39015104955862	244	54	get	get	VERB
mdp.39015104955862	244	55	μο	μο	INTJ
mdp.39015104955862	245	1	<	<	X
mdp.39015104955862	245	2	λμ	λμ	INTJ
mdp.39015104955862	245	3	.	.	PUNCT
mdp.39015104955862	246	1	(	(	PUNCT
mdp.39015104955862	246	2	µ	µ	X
mdp.39015104955862	246	3	−	−	PROPN
mdp.39015104955862	246	4	1)μ−1	1)μ−1	NUM
mdp.39015104955862	246	5	=	=	SYM
mdp.39015104955862	246	6	µ	µ	PROPN
mdp.39015104955862	246	7	µ(1−6	µ(1−6	NOUN
mdp.39015104955862	246	8	)	)	PUNCT
mdp.39015104955862	246	9	(	(	PUNCT
mdp.39015104955862	246	10	1−v)µ	1−v)µ	NUM
mdp.39015104955862	246	11	≤	≤	NOUN
mdp.39015104955862	246	12	(	(	PUNCT
mdp.39015104955862	246	13	µ	µ	X
mdp.39015104955862	246	14	−	−	PROPN
mdp.39015104955862	246	15	1)(1−6)(µ−1	1)(1−6)(µ−1	NUM
mdp.39015104955862	246	16	)	)	PUNCT
mdp.39015104955862	246	17	,	,	PUNCT
mdp.39015104955862	246	18	now	now	ADV
mdp.39015104955862	246	19	it	it	PRON
mdp.39015104955862	246	20	follows	follow	VERB
mdp.39015104955862	246	21	from	from	ADP
mdp.39015104955862	246	22	(	(	PUNCT
mdp.39015104955862	246	23	55	55	NUM
mdp.39015104955862	246	24	)	)	PUNCT
mdp.39015104955862	246	25	,	,	PUNCT
mdp.39015104955862	246	26	(	(	PUNCT
mdp.39015104955862	246	27	48	48	NUM
mdp.39015104955862	246	28	)	)	PUNCT
mdp.39015104955862	246	29	,	,	PUNCT
mdp.39015104955862	246	30	(	(	PUNCT
mdp.39015104955862	246	31	56	56	NUM
mdp.39015104955862	246	32	)	)	PUNCT
mdp.39015104955862	246	33	,	,	PUNCT
mdp.39015104955862	246	34	and	and	CCONJ
mdp.39015104955862	246	35	(	(	PUNCT
mdp.39015104955862	246	36	47	47	NUM
mdp.39015104955862	246	37	)	)	PUNCT
mdp.39015104955862	246	38	that	that	SCONJ
mdp.39015104955862	246	39	h"µ	h"µ	PROPN
mdp.39015104955862	246	40	®	®	PROPN
mdp.39015104955862	246	41	1	1	NUM
mdp.39015104955862	246	42	(	(	PUNCT
mdp.39015104955862	246	43	μ	μ	PROPN
mdp.39015104955862	246	44	,	,	PUNCT
mdp.39015104955862	246	45	x	x	NOUN
mdp.39015104955862	246	46	)	)	PUNCT
mdp.39015104955862	247	1	<	<	X
mdp.39015104955862	247	2	µ(6	µ(6	SPACE
mdp.39015104955862	247	3	+	+	NUM
mdp.39015104955862	247	4	1−c)µ¸	1−c)µ¸	NUM
mdp.39015104955862	247	5	corollary	corollary	NOUN
mdp.39015104955862	247	6	1	1	NUM
mdp.39015104955862	247	7	suppose	suppose	VERB
mdp.39015104955862	247	8	(	(	PUNCT
mdp.39015104955862	247	9	4	4	NUM
mdp.39015104955862	247	10	-	-	SYM
mdp.39015104955862	247	11	1)in(μ-1	1)in(μ-1	NUM
mdp.39015104955862	247	12	)	)	PUNCT
mdp.39015104955862	247	13	ا	ا	VERB
mdp.39015104955862	248	1	ما	ما	PROPN
mdp.39015104955862	248	2	then	then	ADV
mdp.39015104955862	248	3	theorem	theorem	PROPN
mdp.39015104955862	248	4	4	4	NUM
mdp.39015104955862	248	5	is	be	AUX
mdp.39015104955862	248	6	true	true	ADJ
mdp.39015104955862	248	7	for	for	ADP
mdp.39015104955862	248	8	{	{	PUNCT
mdp.39015104955862	248	9	mx	mx	PROPN
mdp.39015104955862	248	10	}	}	PUNCT
mdp.39015104955862	248	11	.	.	PUNCT
mdp.39015104955862	248	12	"	"	PUNCT
mdp.39015104955862	249	1	h"µ	h"µ	PROPN
mdp.39015104955862	249	2	*	*	PROPN
mdp.39015104955862	249	3	(	(	PUNCT
mdp.39015104955862	249	4	μ₁λ	μ₁λ	PROPN
mdp.39015104955862	249	5	)	)	PUNCT
mdp.39015104955862	249	6	≤	≤	PROPN
mdp.39015104955862	249	7	(	(	PUNCT
mdp.39015104955862	249	8	μ1)(1−6)(µ−1)¸	μ1)(1−6)(µ−1)¸	PROPN
mdp.39015104955862	249	9	(	(	PUNCT
mdp.39015104955862	249	10	4,x	4,x	PROPN
mdp.39015104955862	249	11	)	)	PUNCT
mdp.39015104955862	249	12	(	(	PUNCT
mdp.39015104955862	249	13	µ	µ	PROPN
mdp.39015104955862	249	14	−	−	PROPN
mdp.39015104955862	249	15	h"µ	h"µ	PROPN
mdp.39015104955862	249	16	®	®	PROPN
mdp.39015104955862	249	17	(	(	PUNCT
mdp.39015104955862	249	18	1,λ	1,λ	NUM
mdp.39015104955862	249	19	)	)	PUNCT
mdp.39015104955862	249	20	≤	≤	X
mdp.39015104955862	249	21	p(h)(µ	p(h)(µ	X
mdp.39015104955862	249	22	−	−	NOUN
mdp.39015104955862	249	23	1)(1	1)(1	NUM
mdp.39015104955862	249	24	-	-	SYM
mdp.39015104955862	249	25	6	6	NUM
mdp.39015104955862	249	26	)	)	PUNCT
mdp.39015104955862	249	27	(	(	PUNCT
mdp.39015104955862	249	28	μ-1	μ-1	PROPN
mdp.39015104955862	249	29	)	)	PUNCT
mdp.39015104955862	249	30	,	,	PUNCT
mdp.39015104955862	249	31	h	h	PROPN
mdp.39015104955862	249	32	>	>	X
mdp.39015104955862	249	33	max(h₁,h	max(h₁,h	PROPN
mdp.39015104955862	249	34	)	)	PUNCT
mdp.39015104955862	249	35	.	.	PUNCT
mdp.39015104955862	250	1	µ	µ	PROPN
mdp.39015104955862	250	2	>	>	X
mdp.39015104955862	250	3	ho	ho	PROPN
mdp.39015104955862	250	4	.	.	PUNCT
mdp.39015104955862	251	1	mk	mk	PROPN
mdp.39015104955862	251	2	=	=	PROPN
mdp.39015104955862	251	3	k	k	PROPN
mdp.39015104955862	251	4	™	™	PROPN
mdp.39015104955862	251	5	k	k	PROPN
mdp.39015104955862	251	6	,	,	PUNCT
mdp.39015104955862	251	7	k≥	k≥	PROPN
mdp.39015104955862	251	8	0	0	NUM
mdp.39015104955862	251	9	,	,	PUNCT
mdp.39015104955862	251	10	0	0	PUNCT
mdp.39015104955862	251	11	<	<	X
mdp.39015104955862	252	1	y	y	X
mdp.39015104955862	252	2	<	<	X
mdp.39015104955862	252	3	1	1	X
mdp.39015104955862	252	4	.	.	PUNCT
mdp.39015104955862	253	1	now	now	ADV
mdp.39015104955862	253	2	it	it	PRON
mdp.39015104955862	253	3	is	be	AUX
mdp.39015104955862	253	4	sufficient	sufficient	ADJ
mdp.39015104955862	253	5	to	to	PART
mdp.39015104955862	253	6	multiply	multiply	VERB
mdp.39015104955862	253	7	the	the	DET
mdp.39015104955862	253	8	inequalities	inequality	NOUN
mdp.39015104955862	253	9	(	(	PUNCT
mdp.39015104955862	253	10	46	46	NUM
mdp.39015104955862	253	11	)	)	PUNCT
mdp.39015104955862	253	12	and	and	CCONJ
mdp.39015104955862	253	13	(	(	PUNCT
mdp.39015104955862	253	14	59	59	NUM
mdp.39015104955862	253	15	)	)	PUNCT
mdp.39015104955862	253	16	and	and	CCONJ
mdp.39015104955862	253	17	remember	remember	VERB
mdp.39015104955862	253	18	the	the	DET
mdp.39015104955862	253	19	definition	definition	NOUN
mdp.39015104955862	253	20	of	of	ADP
mdp.39015104955862	253	21	§	§	PROPN
mdp.39015104955862	253	22	1	1	NUM
mdp.39015104955862	253	23	,	,	PUNCT
mdp.39015104955862	253	24	§	§	NUM
mdp.39015104955862	253	25	2	2	NUM
mdp.39015104955862	253	26	,	,	PUNCT
mdp.39015104955862	253	27	and	and	CCONJ
mdp.39015104955862	253	28	m.	m.	VERB
mdp.39015104955862	253	29	it	it	PRON
mdp.39015104955862	253	30	is	be	AUX
mdp.39015104955862	253	31	easy	easy	ADJ
mdp.39015104955862	253	32	to	to	PART
mdp.39015104955862	253	33	see	see	VERB
mdp.39015104955862	253	34	that	that	SCONJ
mdp.39015104955862	253	35	we	we	PRON
mdp.39015104955862	253	36	get	get	VERB
mdp.39015104955862	253	37	(	(	PUNCT
mdp.39015104955862	253	38	44	44	NUM
mdp.39015104955862	253	39	)	)	PUNCT
mdp.39015104955862	253	40	as	as	ADP
mdp.39015104955862	253	41	the	the	DET
mdp.39015104955862	253	42	result	result	NOUN
mdp.39015104955862	253	43	.	.	PUNCT
mdp.39015104955862	254	1	hence	hence	ADV
mdp.39015104955862	254	2	,	,	PUNCT
mdp.39015104955862	254	3	inequality	inequality	NOUN
mdp.39015104955862	254	4	(	(	PUNCT
mdp.39015104955862	254	5	44	44	NUM
mdp.39015104955862	254	6	)	)	PUNCT
mdp.39015104955862	254	7	holds	hold	VERB
mdp.39015104955862	254	8	and	and	CCONJ
mdp.39015104955862	254	9	lemma	lemma	NOUN
mdp.39015104955862	254	10	2	2	NUM
mdp.39015104955862	254	11	is	be	AUX
mdp.39015104955862	254	12	proved	prove	VERB
mdp.39015104955862	254	13	.	.	PUNCT
mdp.39015104955862	255	1	corollary	corollary	ADJ
mdp.39015104955862	255	2	1	1	NUM
mdp.39015104955862	255	3	follows	follow	VERB
mdp.39015104955862	255	4	easily	easily	ADV
mdp.39015104955862	255	5	from	from	ADP
mdp.39015104955862	255	6	lemma	lemma	NOUN
mdp.39015104955862	255	7	2	2	NUM
mdp.39015104955862	255	8	and	and	CCONJ
mdp.39015104955862	255	9	theorem	theorem	NOUN
mdp.39015104955862	255	10	4	4	NUM
mdp.39015104955862	255	11	.	.	PUNCT
mdp.39015104955862	256	1	(	(	PUNCT
mdp.39015104955862	256	2	56	56	NUM
mdp.39015104955862	256	3	)	)	PUNCT
mdp.39015104955862	256	4	(	(	PUNCT
mdp.39015104955862	256	5	57	57	NUM
mdp.39015104955862	256	6	)	)	PUNCT
mdp.39015104955862	256	7	(	(	PUNCT
mdp.39015104955862	256	8	58	58	NUM
mdp.39015104955862	256	9	)	)	PUNCT
mdp.39015104955862	256	10	(	(	PUNCT
mdp.39015104955862	256	11	59	59	NUM
mdp.39015104955862	256	12	)	)	PUNCT
mdp.39015104955862	256	13	20	20	NUM
mdp.39015104955862	256	14	classes	class	NOUN
mdp.39015104955862	256	15	d({m	d({m	PROPN
mdp.39015104955862	256	16	}	}	PUNCT
mdp.39015104955862	256	17	)	)	PUNCT
mdp.39015104955862	256	18	and	and	CCONJ
mdp.39015104955862	256	19	the	the	DET
mdp.39015104955862	256	20	diffusion	diffusion	NOUN
mdp.39015104955862	256	21	group	group	NOUN
mdp.39015104955862	256	22	in	in	ADP
mdp.39015104955862	256	23	this	this	DET
mdp.39015104955862	256	24	section	section	NOUN
mdp.39015104955862	256	25	we	we	PRON
mdp.39015104955862	256	26	consider	consider	VERB
mdp.39015104955862	256	27	classes	class	NOUN
mdp.39015104955862	256	28	d({m	d({m	PROPN
mdp.39015104955862	256	29	}	}	PUNCT
mdp.39015104955862	256	30	)	)	PUNCT
mdp.39015104955862	256	31	,	,	PUNCT
mdp.39015104955862	256	32	satisfying	satisfy	VERB
mdp.39015104955862	256	33	the	the	DET
mdp.39015104955862	256	34	following	following	ADJ
mdp.39015104955862	256	35	condition	condition	NOUN
mdp.39015104955862	256	36	:	:	PUNCT
mdp.39015104955862	256	37	ln	ln	PROPN
mdp.39015104955862	256	38	mk	mk	PROPN
mdp.39015104955862	256	39	lim	lim	PROPN
mdp.39015104955862	256	40	k	k	PROPN
mdp.39015104955862	256	41	5	5	NUM
mdp.39015104955862	256	42	818	818	NUM
mdp.39015104955862	257	1	it	it	PRON
mdp.39015104955862	257	2	is	be	AUX
mdp.39015104955862	257	3	easy	easy	ADJ
mdp.39015104955862	257	4	to	to	PART
mdp.39015104955862	257	5	see	see	VERB
mdp.39015104955862	257	6	that	that	SCONJ
mdp.39015104955862	257	7	if	if	SCONJ
mdp.39015104955862	257	8	condition	condition	NOUN
mdp.39015104955862	257	9	(	(	PUNCT
mdp.39015104955862	257	10	60	60	NUM
mdp.39015104955862	257	11	)	)	PUNCT
mdp.39015104955862	257	12	holds	hold	VERB
mdp.39015104955862	257	13	then	then	ADV
mdp.39015104955862	257	14	lim	lim	PROPN
mdp.39015104955862	257	15	814	814	NUM
mdp.39015104955862	257	16	and	and	CCONJ
mdp.39015104955862	257	17	the	the	DET
mdp.39015104955862	257	18	inequality	inequality	NOUN
mdp.39015104955862	257	19	in	in	ADP
mdp.39015104955862	257	20	mx	mx	PROPN
mdp.39015104955862	257	21	k	k	PROPN
mdp.39015104955862	257	22	where	where	SCONJ
mdp.39015104955862	257	23	{	{	PUNCT
mdp.39015104955862	257	24	m	m	VERB
mdp.39015104955862	257	25	}	}	PUNCT
mdp.39015104955862	257	26	is	be	AUX
mdp.39015104955862	257	27	the	the	DET
mdp.39015104955862	257	28	logarithmic	logarithmic	ADJ
mdp.39015104955862	257	29	regularization	regularization	NOUN
mdp.39015104955862	257	30	of	of	ADP
mdp.39015104955862	257	31	{	{	PUNCT
mdp.39015104955862	257	32	m	m	NOUN
mdp.39015104955862	257	33	}	}	PUNCT
mdp.39015104955862	257	34	,	,	PUNCT
mdp.39015104955862	257	35	defined	define	VERB
mdp.39015104955862	257	36	in	in	ADP
mdp.39015104955862	257	37	(	(	PUNCT
mdp.39015104955862	257	38	15	15	NUM
mdp.39015104955862	257	39	)	)	PUNCT
mdp.39015104955862	257	40	.	.	PUNCT
mdp.39015104955862	258	1	the	the	DET
mdp.39015104955862	258	2	following	following	ADJ
mdp.39015104955862	258	3	theorem	theorem	NOUN
mdp.39015104955862	258	4	characterizes	characterize	VERB
mdp.39015104955862	258	5	classes	class	NOUN
mdp.39015104955862	258	6	d({m	d({m	PROPN
mdp.39015104955862	258	7	}	}	PUNCT
mdp.39015104955862	258	8	)	)	PUNCT
mdp.39015104955862	258	9	,	,	PUNCT
mdp.39015104955862	258	10	which	which	PRON
mdp.39015104955862	258	11	are	be	AUX
mdp.39015104955862	258	12	invariant	invariant	ADJ
mdp.39015104955862	258	13	with	with	ADP
mdp.39015104955862	258	14	respect	respect	NOUN
mdp.39015104955862	258	15	to	to	ADP
mdp.39015104955862	258	16	the	the	DET
mdp.39015104955862	258	17	complex	complex	ADJ
mdp.39015104955862	258	18	-	-	PUNCT
mdp.39015104955862	258	19	time	time	NOUN
mdp.39015104955862	258	20	diffusion	diffusion	NOUN
mdp.39015104955862	258	21	group	group	NOUN
mdp.39015104955862	258	22	∞.	∞.	PROPN
mdp.39015104955862	258	23	∞	∞	NUM
mdp.39015104955862	258	24	zk	zk	X
mdp.39015104955862	258	25	u₂¢(x	u₂¢(x	NOUN
mdp.39015104955862	258	26	)	)	PUNCT
mdp.39015104955862	258	27	x	x	PUNCT
mdp.39015104955862	258	28	€	€	PROPN
mdp.39015104955862	258	29	r¹	r¹	NOUN
mdp.39015104955862	258	30	,	,	PUNCT
mdp.39015104955862	258	31	z	z	PROPN
mdp.39015104955862	258	32	ɛ	ɛ	X
mdp.39015104955862	258	33	c.	c.	PROPN
mdp.39015104955862	258	34	=	=	NOUN
mdp.39015104955862	258	35	σ	σ	NOUN
mdp.39015104955862	258	36	=	=	PUNCT
mdp.39015104955862	258	37	=	=	PUNCT
mdp.39015104955862	258	38	=	=	PROPN
mdp.39015104955862	258	39	10	10	NUM
mdp.39015104955862	258	40	(	(	PUNCT
mdp.39015104955862	258	41	24	24	NUM
mdp.39015104955862	258	42	)	)	PUNCT
mdp.39015104955862	258	43	(	(	PUNCT
mdp.39015104955862	258	44	2	2	NUM
mdp.39015104955862	258	45	k=0	k=0	PROPN
mdp.39015104955862	258	46	theorem	theorem	VERB
mdp.39015104955862	258	47	5	5	NUM
mdp.39015104955862	258	48	let	let	VERB
mdp.39015104955862	258	49	{	{	PUNCT
mdp.39015104955862	258	50	m	m	VERB
mdp.39015104955862	258	51	}	}	PUNCT
mdp.39015104955862	258	52	be	be	AUX
mdp.39015104955862	258	53	a	a	DET
mdp.39015104955862	258	54	sequence	sequence	NOUN
mdp.39015104955862	258	55	,	,	PUNCT
mdp.39015104955862	258	56	satisfying	satisfy	VERB
mdp.39015104955862	258	57	(	(	PUNCT
mdp.39015104955862	258	58	60	60	NUM
mdp.39015104955862	258	59	)	)	PUNCT
mdp.39015104955862	258	60	.	.	PUNCT
mdp.39015104955862	259	1	then	then	ADV
mdp.39015104955862	259	2	the	the	DET
mdp.39015104955862	259	3	following	following	ADJ
mdp.39015104955862	259	4	assertions	assertion	NOUN
mdp.39015104955862	259	5	are	be	AUX
mdp.39015104955862	259	6	equivalent	equivalent	ADJ
mdp.39015104955862	259	7	.	.	PUNCT
mdp.39015104955862	260	1	a	a	DET
mdp.39015104955862	260	2	)	)	PUNCT
mdp.39015104955862	260	3	u₂(d({mx	u₂(d({mx	NOUN
mdp.39015104955862	260	4	}	}	PUNCT
mdp.39015104955862	260	5	)	)	PUNCT
mdp.39015104955862	260	6	)	)	PUNCT
mdp.39015104955862	260	7	cd({m	cd({m	PROPN
mdp.39015104955862	260	8	}	}	PUNCT
mdp.39015104955862	260	9	)	)	PUNCT
mdp.39015104955862	260	10	,	,	PUNCT
mdp.39015104955862	260	11	z	z	PROPN
mdp.39015104955862	260	12	e	e	X
mdp.39015104955862	260	13	c.	c.	PROPN
mdp.39015104955862	260	14	b	b	PROPN
mdp.39015104955862	260	15	)	)	PUNCT
mdp.39015104955862	260	16	there	there	PRON
mdp.39015104955862	260	17	exists	exist	VERB
mdp.39015104955862	260	18	a	a	DET
mdp.39015104955862	260	19	positive	positive	ADJ
mdp.39015104955862	260	20	function	function	NOUN
mdp.39015104955862	260	21	p(h	p(h	PROPN
mdp.39015104955862	260	22	)	)	PUNCT
mdp.39015104955862	260	23	,	,	PUNCT
mdp.39015104955862	260	24	h	h	PROPN
mdp.39015104955862	260	25	≥	≥	X
mdp.39015104955862	260	26	0	0	NUM
mdp.39015104955862	260	27	such	such	ADJ
mdp.39015104955862	260	28	that	that	SCONJ
mdp.39015104955862	260	29	m2n+mh	m2n+mh	PROPN
mdp.39015104955862	260	30	"	"	PUNCT
mdp.39015104955862	260	31	<	<	X
mdp.39015104955862	260	32	p(h)m+1	p(h)m+1	PROPN
mdp.39015104955862	260	33	"	"	PUNCT
mdp.39015104955862	260	34	mm	mm	PROPN
mdp.39015104955862	260	35	,	,	PUNCT
mdp.39015104955862	260	36	m>0	m>0	PROPN
mdp.39015104955862	260	37	,	,	PUNCT
mdp.39015104955862	260	38	n	n	CCONJ
mdp.39015104955862	260	39	≥	≥	X
mdp.39015104955862	260	40	0	0	NUM
mdp.39015104955862	260	41	,	,	PUNCT
mdp.39015104955862	260	42	h	h	PROPN
mdp.39015104955862	260	43	>	>	X
mdp.39015104955862	260	44	họ	họ	PROPN
mdp.39015104955862	260	45	.	.	PUNCT
mdp.39015104955862	261	1	η	η	PROPN
mdp.39015104955862	261	2	c	c	PROPN
mdp.39015104955862	261	3	)	)	PUNCT
mdp.39015104955862	261	4	there	there	PRON
mdp.39015104955862	261	5	exist	exist	VERB
mdp.39015104955862	261	6	two	two	NUM
mdp.39015104955862	261	7	positive	positive	ADJ
mdp.39015104955862	261	8	functions	function	NOUN
mdp.39015104955862	261	9	m	m	NOUN
mdp.39015104955862	261	10	and	and	CCONJ
mdp.39015104955862	261	11	p	p	NOUN
mdp.39015104955862	261	12	on	on	ADP
mdp.39015104955862	261	13	[	[	X
mdp.39015104955862	261	14	0,∞	0,∞	SPACE
mdp.39015104955862	261	15	)	)	PUNCT
mdp.39015104955862	261	16	such	such	ADJ
mdp.39015104955862	261	17	that	that	DET
mdp.39015104955862	261	18	m(k	m(k	PROPN
mdp.39015104955862	261	19	)	)	PUNCT
mdp.39015104955862	261	20	=	=	PROPN
mdp.39015104955862	261	21	mk	mk	PROPN
mdp.39015104955862	261	22	,	,	PUNCT
mdp.39015104955862	261	23	k≥0	k≥0	PROPN
mdp.39015104955862	261	24	holds	hold	VERB
mdp.39015104955862	261	25	for	for	ADP
mdp.39015104955862	261	26	all	all	PRON
mdp.39015104955862	261	27	>	>	SYM
mdp.39015104955862	261	28	1	1	NUM
mdp.39015104955862	261	29	,	,	PUNCT
mdp.39015104955862	261	30	μ	μ	PROPN
mdp.39015104955862	261	31	≥	≥	X
mdp.39015104955862	261	32	1	1	NUM
mdp.39015104955862	261	33	,	,	PUNCT
mdp.39015104955862	261	34	and	and	CCONJ
mdp.39015104955862	261	35	h	h	PROPN
mdp.39015104955862	261	36	>	>	X
mdp.39015104955862	261	37	ho	ho	PROPN
mdp.39015104955862	261	38	.	.	PUNCT
mdp.39015104955862	262	1	h“m(µλ)¹¹	h“m(µλ)¹¹	PROPN
mdp.39015104955862	262	2	≤	≤	X
mdp.39015104955862	262	3	p(h)(µ	p(h)(µ	X
mdp.39015104955862	262	4	−	−	PROPN
mdp.39015104955862	262	5	1)am(a)¹	1)am(a)¹	ADV
mdp.39015104955862	262	6	(	(	PUNCT
mdp.39015104955862	262	7	60	60	NUM
mdp.39015104955862	262	8	)	)	PUNCT
mdp.39015104955862	262	9	(	(	PUNCT
mdp.39015104955862	262	10	61	61	NUM
mdp.39015104955862	262	11	)	)	PUNCT
mdp.39015104955862	262	12	(	(	PUNCT
mdp.39015104955862	262	13	62	62	NUM
mdp.39015104955862	262	14	)	)	PUNCT
mdp.39015104955862	262	15	21	21	NUM
mdp.39015104955862	262	16	proof	proof	NOUN
mdp.39015104955862	262	17	.	.	PUNCT
mdp.39015104955862	263	1	we	we	PRON
mdp.39015104955862	263	2	begin	begin	VERB
mdp.39015104955862	263	3	by	by	ADP
mdp.39015104955862	263	4	showing	show	VERB
mdp.39015104955862	263	5	that	that	SCONJ
mdp.39015104955862	263	6	if	if	SCONJ
mdp.39015104955862	263	7	there	there	PRON
mdp.39015104955862	263	8	exists	exist	VERB
mdp.39015104955862	263	9	a	a	DET
mdp.39015104955862	263	10	positive	positive	ADJ
mdp.39015104955862	263	11	function	function	NOUN
mdp.39015104955862	263	12	p	p	PROPN
mdp.39015104955862	263	13	such	such	ADJ
mdp.39015104955862	263	14	that	that	SCONJ
mdp.39015104955862	263	15	man+mh	man+mh	PROPN
mdp.39015104955862	263	16	"	"	PUNCT
mdp.39015104955862	263	17	<	<	X
mdp.39015104955862	263	18	p(h)m+¹n"mm	p(h)m+¹n"mm	PROPN
mdp.39015104955862	263	19	,	,	PUNCT
mdp.39015104955862	263	20	m≥0	m≥0	PROPN
mdp.39015104955862	263	21	,	,	PUNCT
mdp.39015104955862	263	22	n	n	CCONJ
mdp.39015104955862	263	23	≥	≥	X
mdp.39015104955862	263	24	0	0	NUM
mdp.39015104955862	263	25	,	,	PUNCT
mdp.39015104955862	263	26	h	h	PROPN
mdp.39015104955862	263	27	>	>	X
mdp.39015104955862	263	28	ho	ho	PROPN
mdp.39015104955862	263	29	,	,	PUNCT
mdp.39015104955862	263	30	then	then	ADV
mdp.39015104955862	263	31	assertion	assertion	VERB
mdp.39015104955862	263	32	a	a	DET
mdp.39015104955862	263	33	)	)	PUNCT
mdp.39015104955862	263	34	holds	hold	VERB
mdp.39015104955862	263	35	.	.	PUNCT
mdp.39015104955862	264	1	suppose	suppose	VERB
mdp.39015104955862	264	2	(	(	PUNCT
mdp.39015104955862	264	3	63	63	NUM
mdp.39015104955862	264	4	)	)	PUNCT
mdp.39015104955862	264	5	is	be	AUX
mdp.39015104955862	264	6	true	true	ADJ
mdp.39015104955862	264	7	and	and	CCONJ
mdp.39015104955862	264	8	let	let	VERB
mdp.39015104955862	264	9	€	€	SYM
mdp.39015104955862	264	10	d({m	d({m	NOUN
mdp.39015104955862	264	11	}	}	PUNCT
mdp.39015104955862	264	12	)	)	PUNCT
mdp.39015104955862	264	13	.	.	PUNCT
mdp.39015104955862	265	1	then	then	ADV
mdp.39015104955862	265	2	121k	121k	NOUN
mdp.39015104955862	265	3	2	2	NUM
mdp.39015104955862	265	4	+	+	NUM
mdp.39015104955862	265	5	|ø	|ø	NOUN
mdp.39015104955862	265	6	(	(	PUNCT
mdp.39015104955862	265	7	2k+j	2k+j	NUM
mdp.39015104955862	265	8	)	)	PUNCT
mdp.39015104955862	265	9	(	(	PUNCT
mdp.39015104955862	265	10	x	x	SYM
mdp.39015104955862	265	11	)	)	PUNCT
mdp.39015104955862	265	12	|	|	ADP
mdp.39015104955862	265	13	≤	≤	PUNCT
mdp.39015104955862	266	1	ash³	ash³	VERB
mdp.39015104955862	266	2	k=0	k=0	NOUN
mdp.39015104955862	266	3	applying	apply	VERB
mdp.39015104955862	266	4	(	(	PUNCT
mdp.39015104955862	266	5	63	63	NUM
mdp.39015104955862	266	6	)	)	PUNCT
mdp.39015104955862	266	7	with	with	ADP
mdp.39015104955862	266	8	h	h	NOUN
mdp.39015104955862	266	9	=	=	SYM
mdp.39015104955862	266	10	2h2|z|	2h2|z|	NOUN
mdp.39015104955862	266	11	,	,	PUNCT
mdp.39015104955862	266	12	we	we	PRON
mdp.39015104955862	266	13	get	get	VERB
mdp.39015104955862	266	14	and	and	CCONJ
mdp.39015104955862	266	15	it	it	PRON
mdp.39015104955862	266	16	follows	follow	VERB
mdp.39015104955862	266	17	from	from	ADP
mdp.39015104955862	266	18	(	(	PUNCT
mdp.39015104955862	266	19	64	64	NUM
mdp.39015104955862	266	20	)	)	PUNCT
mdp.39015104955862	266	21	and	and	CCONJ
mdp.39015104955862	266	22	(	(	PUNCT
mdp.39015104955862	266	23	65	65	NUM
mdp.39015104955862	266	24	)	)	PUNCT
mdp.39015104955862	266	25	that	that	PRON
mdp.39015104955862	266	26	[	[	X
mdp.39015104955862	266	27	u₁6(x	u₁6(x	X
mdp.39015104955862	266	28	)	)	PUNCT
mdp.39015104955862	266	29	]	]	PUNCT
mdp.39015104955862	266	30	(	(	PUNCT
mdp.39015104955862	266	31	)	)	PUNCT
mdp.39015104955862	266	32	=	=	VERB
mdp.39015104955862	266	33	m2k+i	m2k+i	ADJ
mdp.39015104955862	266	34	h2	h2	NOUN
mdp.39015104955862	266	35	*	*	PUNCT
mdp.39015104955862	266	36	|z|	|z|	X
mdp.39015104955862	266	37	*	*	PUNCT
mdp.39015104955862	266	38	<	<	X
mdp.39015104955862	266	39	2−*p(2h3|z|)i+¹mj	2−*p(2h3|z|)i+¹mj	NUM
mdp.39015104955862	266	40	.	.	PUNCT
mdp.39015104955862	267	1	2k	2k	NUM
mdp.39015104955862	267	2	k	k	X
mdp.39015104955862	267	3	!	!	PROPN
mdp.39015104955862	267	4	σ	σ	PROPN
mdp.39015104955862	267	5	—	—	PUNCT
mdp.39015104955862	267	6	+	+	CCONJ
mdp.39015104955862	267	7	k=0	k=0	NOUN
mdp.39015104955862	267	8	k=0	k=0	NOUN
mdp.39015104955862	267	9	121	121	NUM
mdp.39015104955862	267	10	*	*	SYM
mdp.39015104955862	267	11	2k	2k	NUM
mdp.39015104955862	267	12	k	k	X
mdp.39015104955862	267	13	!	!	PUNCT
mdp.39015104955862	268	1	-h2	-h2	NOUN
mdp.39015104955862	268	2	m2k+j⋅	m2k+j⋅	NOUN
mdp.39015104955862	268	3	$	$	SYM
mdp.39015104955862	268	4	(	(	PUNCT
mdp.39015104955862	268	5	2k+j	2k+j	NUM
mdp.39015104955862	268	6	)	)	PUNCT
mdp.39015104955862	268	7	(	(	PUNCT
mdp.39015104955862	268	8	x	x	PROPN
mdp.39015104955862	268	9	)	)	PUNCT
mdp.39015104955862	268	10	,	,	PUNCT
mdp.39015104955862	268	11	(	(	PUNCT
mdp.39015104955862	268	12	63	63	NUM
mdp.39015104955862	268	13	)	)	PUNCT
mdp.39015104955862	268	14	(	(	PUNCT
mdp.39015104955862	268	15	64	64	NUM
mdp.39015104955862	268	16	)	)	PUNCT
mdp.39015104955862	268	17	(	(	PUNCT
mdp.39015104955862	268	18	65	65	NUM
mdp.39015104955862	268	19	)	)	PUNCT
mdp.39015104955862	269	1	[	[	X
mdp.39015104955862	269	2	[	[	X
mdp.39015104955862	269	3	u₂6(x)](i)|	u₂6(x)](i)|	X
mdp.39015104955862	269	4	≤	≤	NOUN
mdp.39015104955862	269	5	c₂‚øh²¿mj	c₂‚øh²¿mj	PROPN
mdp.39015104955862	269	6	,	,	PUNCT
mdp.39015104955862	269	7	z€	z€	PROPN
mdp.39015104955862	269	8	c	c	NOUN
mdp.39015104955862	269	9	,	,	PUNCT
mdp.39015104955862	269	10	j≥	j≥	PROPN
mdp.39015104955862	269	11	0	0	NUM
mdp.39015104955862	269	12	,	,	PUNCT
mdp.39015104955862	269	13	which	which	PRON
mdp.39015104955862	269	14	proves	prove	VERB
mdp.39015104955862	269	15	that	that	SCONJ
mdp.39015104955862	269	16	(	(	PUNCT
mdp.39015104955862	269	17	63	63	NUM
mdp.39015104955862	269	18	)	)	PUNCT
mdp.39015104955862	269	19	implies	imply	VERB
mdp.39015104955862	269	20	a	a	PRON
mdp.39015104955862	269	21	)	)	PUNCT
mdp.39015104955862	269	22	.	.	PUNCT
mdp.39015104955862	270	1	using	use	VERB
mdp.39015104955862	270	2	cartan	cartan	ADJ
mdp.39015104955862	270	3	-	-	PUNCT
mdp.39015104955862	270	4	gorny	gorny	ADJ
mdp.39015104955862	270	5	theorem	theorem	NOUN
mdp.39015104955862	270	6	(	(	PUNCT
mdp.39015104955862	270	7	see	see	VERB
mdp.39015104955862	270	8	theorem	theorem	NOUN
mdp.39015104955862	270	9	2	2	NUM
mdp.39015104955862	270	10	in	in	ADP
mdp.39015104955862	270	11	section	section	NOUN
mdp.39015104955862	270	12	3	3	NUM
mdp.39015104955862	270	13	,	,	PUNCT
mdp.39015104955862	270	14	we	we	PRON
mdp.39015104955862	270	15	conclude	conclude	VERB
mdp.39015104955862	270	16	that	that	SCONJ
mdp.39015104955862	270	17	a	a	PRON
mdp.39015104955862	270	18	)	)	PUNCT
mdp.39015104955862	270	19	follows	follow	VERB
mdp.39015104955862	270	20	from	from	ADP
mdp.39015104955862	270	21	b	b	PROPN
mdp.39015104955862	270	22	)	)	PUNCT
mdp.39015104955862	270	23	.	.	PUNCT
mdp.39015104955862	271	1	remark	remark	NOUN
mdp.39015104955862	271	2	3	3	NUM
mdp.39015104955862	271	3	analyzing	analyze	VERB
mdp.39015104955862	271	4	the	the	DET
mdp.39015104955862	271	5	previous	previous	ADJ
mdp.39015104955862	271	6	part	part	NOUN
mdp.39015104955862	271	7	ot	ot	INTJ
mdp.39015104955862	271	8	the	the	DET
mdp.39015104955862	271	9	proof	proof	NOUN
mdp.39015104955862	271	10	of	of	ADP
mdp.39015104955862	271	11	theorem	theorem	NOUN
mdp.39015104955862	271	12	3	3	NUM
mdp.39015104955862	271	13	,	,	PUNCT
mdp.39015104955862	271	14	we	we	PRON
mdp.39015104955862	271	15	see	see	VERB
mdp.39015104955862	271	16	that	that	DET
mdp.39015104955862	271	17	condition	condition	NOUN
mdp.39015104955862	271	18	(	(	PUNCT
mdp.39015104955862	271	19	63	63	NUM
mdp.39015104955862	271	20	)	)	PUNCT
mdp.39015104955862	271	21	implies	imply	VERB
mdp.39015104955862	271	22	not	not	PART
mdp.39015104955862	271	23	only	only	ADV
mdp.39015104955862	271	24	the	the	DET
mdp.39015104955862	271	25	validity	validity	NOUN
mdp.39015104955862	271	26	of	of	ADP
mdp.39015104955862	271	27	inclusion	inclusion	NOUN
mdp.39015104955862	271	28	a	a	PRON
mdp.39015104955862	271	29	)	)	PUNCT
mdp.39015104955862	271	30	,	,	PUNCT
mdp.39015104955862	271	31	but	but	CCONJ
mdp.39015104955862	271	32	also	also	ADV
mdp.39015104955862	271	33	the	the	DET
mdp.39015104955862	271	34	continuity	continuity	NOUN
mdp.39015104955862	271	35	of	of	ADP
mdp.39015104955862	271	36	the	the	DET
mdp.39015104955862	271	37	operators	operator	NOUN
mdp.39015104955862	271	38	u	u	PROPN
mdp.39015104955862	271	39	,	,	PUNCT
mdp.39015104955862	271	40	,	,	PUNCT
mdp.39015104955862	271	41	z	z	PROPN
mdp.39015104955862	271	42	>	>	X
mdp.39015104955862	271	43	0	0	NUM
mdp.39015104955862	271	44	on	on	ADP
mdp.39015104955862	271	45	d({m	d({m	PROPN
mdp.39015104955862	271	46	}	}	PUNCT
mdp.39015104955862	271	47	)	)	PUNCT
mdp.39015104955862	271	48	.	.	PUNCT
mdp.39015104955862	272	1	since	since	SCONJ
mdp.39015104955862	272	2	the	the	DET
mdp.39015104955862	272	3	topologies	topology	NOUN
mdp.39015104955862	272	4	of	of	ADP
mdp.39015104955862	272	5	the	the	DET
mdp.39015104955862	272	6	classes	class	NOUN
mdp.39015104955862	272	7	d({m	d({m	PROPN
mdp.39015104955862	272	8	}	}	PUNCT
mdp.39015104955862	272	9	)	)	PUNCT
mdp.39015104955862	272	10	and	and	CCONJ
mdp.39015104955862	272	11	d({m	d({m	PROPN
mdp.39015104955862	272	12	}	}	PUNCT
mdp.39015104955862	272	13	)	)	PUNCT
mdp.39015104955862	272	14	coincide	coincide	NOUN
mdp.39015104955862	272	15	(	(	PUNCT
mdp.39015104955862	272	16	see	see	VERB
mdp.39015104955862	272	17	the	the	DET
mdp.39015104955862	272	18	proof	proof	NOUN
mdp.39015104955862	272	19	of	of	ADP
mdp.39015104955862	272	20	cartan	cartan	PROPN
mdp.39015104955862	272	21	-	-	PUNCT
mdp.39015104955862	272	22	gorny	gorny	ADJ
mdp.39015104955862	272	23	theorem	theorem	NOUN
mdp.39015104955862	272	24	in	in	ADP
mdp.39015104955862	272	25	[	[	X
mdp.39015104955862	272	26	8	8	NUM
mdp.39015104955862	272	27	]	]	PUNCT
mdp.39015104955862	272	28	)	)	PUNCT
mdp.39015104955862	273	1	,	,	PUNCT
mdp.39015104955862	273	2	the	the	DET
mdp.39015104955862	273	3	validity	validity	NOUN
mdp.39015104955862	273	4	of	of	ADP
mdp.39015104955862	273	5	condition	condition	NOUN
mdp.39015104955862	273	6	b	b	PROPN
mdp.39015104955862	273	7	)	)	PUNCT
mdp.39015104955862	273	8	in	in	ADP
mdp.39015104955862	273	9	theorem	theorem	NOUN
mdp.39015104955862	273	10	3	3	NUM
mdp.39015104955862	273	11	implies	imply	VERB
mdp.39015104955862	273	12	the	the	DET
mdp.39015104955862	273	13	continuity	continuity	NOUN
mdp.39015104955862	273	14	of	of	ADP
mdp.39015104955862	273	15	u	u	PROPN
mdp.39015104955862	273	16	,	,	PUNCT
mdp.39015104955862	273	17	on	on	ADP
mdp.39015104955862	273	18	the	the	DET
mdp.39015104955862	273	19	class	class	NOUN
mdp.39015104955862	273	20	d({mx	d({mx	SPACE
mdp.39015104955862	273	21	}	}	PUNCT
mdp.39015104955862	273	22	)	)	PUNCT
mdp.39015104955862	273	23	.	.	PUNCT
mdp.39015104955862	274	1	22	22	NUM
mdp.39015104955862	275	1	the	the	DET
mdp.39015104955862	275	2	next	next	ADJ
mdp.39015104955862	275	3	step	step	NOUN
mdp.39015104955862	275	4	consists	consist	VERB
mdp.39015104955862	275	5	in	in	ADP
mdp.39015104955862	275	6	proving	prove	VERB
mdp.39015104955862	275	7	that	that	PRON
mdp.39015104955862	275	8	a	a	PRON
mdp.39015104955862	275	9	)	)	PUNCT
mdp.39015104955862	275	10	implies	imply	VERB
mdp.39015104955862	275	11	b	b	NOUN
mdp.39015104955862	275	12	)	)	PUNCT
mdp.39015104955862	275	13	.	.	PUNCT
mdp.39015104955862	276	1	appealing	appeal	VERB
mdp.39015104955862	276	2	again	again	ADV
mdp.39015104955862	276	3	to	to	ADP
mdp.39015104955862	276	4	cartan	cartan	ADV
mdp.39015104955862	276	5	-	-	PUNCT
mdp.39015104955862	276	6	gorny	gorny	ADJ
mdp.39015104955862	276	7	theorem	theorem	NOUN
mdp.39015104955862	276	8	,	,	PUNCT
mdp.39015104955862	276	9	we	we	PRON
mdp.39015104955862	276	10	see	see	VERB
mdp.39015104955862	276	11	that	that	DET
mdp.39015104955862	276	12	condition	condition	NOUN
mdp.39015104955862	276	13	a	a	X
mdp.39015104955862	276	14	)	)	PUNCT
mdp.39015104955862	276	15	is	be	AUX
mdp.39015104955862	276	16	equivalent	equivalent	ADJ
mdp.39015104955862	276	17	to	to	ADP
mdp.39015104955862	276	18	the	the	DET
mdp.39015104955862	276	19	condition	condition	NOUN
mdp.39015104955862	276	20	u₂(d({m	u₂(d({m	PROPN
mdp.39015104955862	276	21	}	}	PUNCT
mdp.39015104955862	276	22	)	)	PUNCT
mdp.39015104955862	276	23	)	)	PUNCT
mdp.39015104955862	276	24	cd({m	cd({m	PROPN
mdp.39015104955862	276	25	}	}	PUNCT
mdp.39015104955862	276	26	)	)	PUNCT
mdp.39015104955862	276	27	,	,	PUNCT
mdp.39015104955862	276	28	z	z	PROPN
mdp.39015104955862	276	29	e	e	X
mdp.39015104955862	276	30	c.	c.	PROPN
mdp.39015104955862	276	31	therefore	therefore	ADV
mdp.39015104955862	276	32	,	,	PUNCT
mdp.39015104955862	276	33	we	we	PRON
mdp.39015104955862	276	34	should	should	AUX
mdp.39015104955862	276	35	prove	prove	VERB
mdp.39015104955862	276	36	that	that	SCONJ
mdp.39015104955862	276	37	b	b	NOUN
mdp.39015104955862	276	38	)	)	PUNCT
mdp.39015104955862	276	39	follows	follow	VERB
mdp.39015104955862	276	40	from	from	ADP
mdp.39015104955862	276	41	(	(	PUNCT
mdp.39015104955862	276	42	66	66	NUM
mdp.39015104955862	276	43	)	)	PUNCT
mdp.39015104955862	276	44	.	.	PUNCT
mdp.39015104955862	277	1	the	the	DET
mdp.39015104955862	277	2	sequence	sequence	NOUN
mdp.39015104955862	277	3	{	{	PUNCT
mdp.39015104955862	277	4	m	m	VERB
mdp.39015104955862	277	5	}	}	PUNCT
mdp.39015104955862	277	6	is	be	AUX
mdp.39015104955862	277	7	logarithmically	logarithmically	ADV
mdp.39015104955862	277	8	convex	convex	ADJ
mdp.39015104955862	277	9	and	and	CCONJ
mdp.39015104955862	277	10	hence	hence	ADV
mdp.39015104955862	277	11	convex	convex	ADJ
mdp.39015104955862	277	12	.	.	PUNCT
mdp.39015104955862	278	1	without	without	ADP
mdp.39015104955862	278	2	loss	loss	NOUN
mdp.39015104955862	278	3	of	of	ADP
mdp.39015104955862	278	4	generality	generality	NOUN
mdp.39015104955862	278	5	we	we	PRON
mdp.39015104955862	278	6	may	may	AUX
mdp.39015104955862	278	7	suppose	suppose	VERB
mdp.39015104955862	278	8	that	that	SCONJ
mdp.39015104955862	278	9	m	m	VERB
mdp.39015104955862	278	10	increases	increase	NOUN
mdp.39015104955862	278	11	and	and	CCONJ
mdp.39015104955862	278	12	that	that	SCONJ
mdp.39015104955862	278	13	m₁	m₁	NOUN
mdp.39015104955862	278	14	=	=	PROPN
mdp.39015104955862	278	15	1	1	NUM
mdp.39015104955862	278	16	.	.	PUNCT
mdp.39015104955862	279	1	it	it	PRON
mdp.39015104955862	279	2	is	be	AUX
mdp.39015104955862	279	3	easy	easy	ADJ
mdp.39015104955862	279	4	to	to	PART
mdp.39015104955862	279	5	see	see	VERB
mdp.39015104955862	279	6	that	that	SCONJ
mdp.39015104955862	279	7	for	for	ADP
mdp.39015104955862	279	8	such	such	ADJ
mdp.39015104955862	279	9	{	{	PUNCT
mdp.39015104955862	279	10	m	m	NOUN
mdp.39015104955862	279	11	}	}	PUNCT
mdp.39015104955862	279	12	there	there	PRON
mdp.39015104955862	279	13	always	always	ADV
mdp.39015104955862	279	14	exists	exist	VERB
mdp.39015104955862	279	15	a	a	DET
mdp.39015104955862	279	16	smooth	smooth	ADJ
mdp.39015104955862	279	17	logarithmically	logarithmically	ADV
mdp.39015104955862	279	18	convex	convex	ADJ
mdp.39015104955862	279	19	increasing	increase	VERB
mdp.39015104955862	279	20	function	function	NOUN
mdp.39015104955862	279	21	m	m	VERB
mdp.39015104955862	279	22	on	on	ADP
mdp.39015104955862	279	23	[	[	X
mdp.39015104955862	279	24	0,∞	0,∞	NUM
mdp.39015104955862	279	25	)	)	PUNCT
mdp.39015104955862	279	26	,	,	PUNCT
mdp.39015104955862	279	27	for	for	ADP
mdp.39015104955862	279	28	which	which	PRON
mdp.39015104955862	279	29	and	and	CCONJ
mdp.39015104955862	279	30	m(k	m(k	PROPN
mdp.39015104955862	279	31	)	)	PUNCT
mdp.39015104955862	279	32	=	=	PROPN
mdp.39015104955862	279	33	mk	mk	PROPN
mdp.39015104955862	279	34	,	,	PUNCT
mdp.39015104955862	279	35	k≥0	k≥0	PROPN
mdp.39015104955862	279	36	denote	denote	PROPN
mdp.39015104955862	279	37	lim	lim	PROPN
mdp.39015104955862	279	38	818	818	NUM
mdp.39015104955862	279	39	(	(	PUNCT
mdp.39015104955862	279	40	68	68	NUM
mdp.39015104955862	279	41	)	)	PUNCT
mdp.39015104955862	279	42	now	now	ADV
mdp.39015104955862	279	43	consider	consider	VERB
mdp.39015104955862	279	44	the	the	DET
mdp.39015104955862	279	45	following	follow	VERB
mdp.39015104955862	279	46	continuous	continuous	ADJ
mdp.39015104955862	279	47	version	version	NOUN
mdp.39015104955862	279	48	of	of	ADP
mdp.39015104955862	279	49	the	the	DET
mdp.39015104955862	279	50	ostrovski	ostrovski	NOUN
mdp.39015104955862	279	51	function	function	NOUN
mdp.39015104955862	279	52	(	(	PUNCT
mdp.39015104955862	279	53	see	see	VERB
mdp.39015104955862	279	54	section	section	NOUN
mdp.39015104955862	279	55	3	3	NUM
mdp.39015104955862	279	56	)	)	PUNCT
mdp.39015104955862	279	57	(	(	PUNCT
mdp.39015104955862	279	58	69	69	NUM
mdp.39015104955862	279	59	)	)	PUNCT
mdp.39015104955862	279	60	in	in	ADP
mdp.39015104955862	279	61	m(u	m(u	PROPN
mdp.39015104955862	279	62	)	)	PUNCT
mdp.39015104955862	280	1	น	น	PROPN
mdp.39015104955862	280	2	t₁(r	t₁(r	SPACE
mdp.39015104955862	280	3	)	)	PUNCT
mdp.39015104955862	280	4	=	=	PROPN
mdp.39015104955862	280	5	sup	sup	PROPN
mdp.39015104955862	280	6	w,(u	w,(u	VERB
mdp.39015104955862	280	7	)	)	PUNCT
mdp.39015104955862	280	8	=	=	VERB
mdp.39015104955862	280	9	ru	ru	PROPN
mdp.39015104955862	280	10	m(u	m(u	PROPN
mdp.39015104955862	280	11	)	)	PUNCT
mdp.39015104955862	280	12	'	'	PUNCT
mdp.39015104955862	280	13	you	you	PRON
mdp.39015104955862	280	14	m(u	m(u	SPACE
mdp.39015104955862	280	15	)	)	PUNCT
mdp.39015104955862	280	16	'	'	PUNCT
mdp.39015104955862	280	17	since	since	SCONJ
mdp.39015104955862	280	18	v(0	v(0	X
mdp.39015104955862	280	19	)	)	PUNCT
mdp.39015104955862	280	20	=	=	PROPN
mdp.39015104955862	280	21	1	1	NUM
mdp.39015104955862	280	22	and	and	CCONJ
mdp.39015104955862	280	23	equality	equality	NOUN
mdp.39015104955862	280	24	(	(	PUNCT
mdp.39015104955862	280	25	68	68	NUM
mdp.39015104955862	280	26	)	)	PUNCT
mdp.39015104955862	280	27	is	be	AUX
mdp.39015104955862	280	28	true	true	ADJ
mdp.39015104955862	280	29	,	,	PUNCT
mdp.39015104955862	280	30	we	we	PRON
mdp.39015104955862	280	31	have	have	VERB
mdp.39015104955862	280	32	∞.	∞.	NUM
mdp.39015104955862	280	33	t	t	NOUN
mdp.39015104955862	280	34	>	>	SYM
mdp.39015104955862	280	35	0	0	NUM
mdp.39015104955862	280	36	.	.	PUNCT
mdp.39015104955862	281	1	u	u	PROPN
mdp.39015104955862	281	2	>	>	X
mdp.39015104955862	281	3	0	0	NUM
mdp.39015104955862	281	4	,	,	PUNCT
mdp.39015104955862	281	5	r	r	X
mdp.39015104955862	281	6	>	>	X
mdp.39015104955862	281	7	1	1	NUM
mdp.39015104955862	281	8	.	.	X
mdp.39015104955862	281	9	w,(0	w,(0	PROPN
mdp.39015104955862	281	10	)	)	PUNCT
mdp.39015104955862	281	11	=	=	PROPN
mdp.39015104955862	281	12	1	1	NUM
mdp.39015104955862	281	13	,	,	PUNCT
mdp.39015104955862	281	14	lim.—∞	lim.—∞	PROPN
mdp.39015104955862	281	15	w‚(u	w‚(u	SPACE
mdp.39015104955862	281	16	)	)	PUNCT
mdp.39015104955862	281	17	=	=	PROPN
mdp.39015104955862	281	18	0	0	NUM
mdp.39015104955862	281	19	.	.	PUNCT
mdp.39015104955862	282	1	therefore	therefore	ADV
mdp.39015104955862	282	2	,	,	PUNCT
mdp.39015104955862	282	3	the	the	DET
mdp.39015104955862	282	4	continuous	continuous	ADJ
mdp.39015104955862	282	5	function	function	NOUN
mdp.39015104955862	282	6	w	w	PROPN
mdp.39015104955862	282	7	,	,	PUNCT
mdp.39015104955862	282	8	attains	attain	VERB
mdp.39015104955862	282	9	its	its	PRON
mdp.39015104955862	282	10	maximum	maximum	NOUN
mdp.39015104955862	282	11	on	on	ADP
mdp.39015104955862	282	12	[	[	X
mdp.39015104955862	282	13	0,∞	0,∞	NUM
mdp.39015104955862	282	14	)	)	PUNCT
mdp.39015104955862	282	15	.	.	PUNCT
mdp.39015104955862	283	1	denote	denote	ADJ
mdp.39015104955862	283	2	(	(	PUNCT
mdp.39015104955862	283	3	66	66	NUM
mdp.39015104955862	283	4	)	)	PUNCT
mdp.39015104955862	283	5	p(u	p(u	PROPN
mdp.39015104955862	283	6	)	)	PUNCT
mdp.39015104955862	283	7	=	=	PROPN
mdp.39015104955862	283	8	ln	ln	PROPN
mdp.39015104955862	283	9	m(u	m(u	PROPN
mdp.39015104955862	283	10	)	)	PUNCT
mdp.39015104955862	283	11	น	น	PROPN
mdp.39015104955862	283	12	since	since	SCONJ
mdp.39015104955862	283	13	m	m	NOUN
mdp.39015104955862	283	14	is	be	AUX
mdp.39015104955862	283	15	logarithmically	logarithmically	ADV
mdp.39015104955862	283	16	convex	convex	ADJ
mdp.39015104955862	283	17	,	,	PUNCT
mdp.39015104955862	283	18	the	the	DET
mdp.39015104955862	283	19	function	function	NOUN
mdp.39015104955862	283	20	p	p	NOUN
mdp.39015104955862	283	21	increases	increase	NOUN
mdp.39015104955862	283	22	.	.	PUNCT
mdp.39015104955862	284	1	(	(	PUNCT
mdp.39015104955862	284	2	67	67	NUM
mdp.39015104955862	284	3	)	)	PUNCT
mdp.39015104955862	284	4	23	23	NUM
mdp.39015104955862	284	5	it	it	PRON
mdp.39015104955862	284	6	is	be	AUX
mdp.39015104955862	284	7	easy	easy	ADJ
mdp.39015104955862	284	8	to	to	PART
mdp.39015104955862	284	9	see	see	VERB
mdp.39015104955862	284	10	that	that	SCONJ
mdp.39015104955862	284	11	the	the	DET
mdp.39015104955862	284	12	point	point	NOUN
mdp.39015104955862	284	13	u	u	NOUN
mdp.39015104955862	284	14	。	。	PROPN
mdp.39015104955862	284	15	=	=	VERB
mdp.39015104955862	284	16	u。(r	u。(r	ADP
mdp.39015104955862	284	17	)	)	PUNCT
mdp.39015104955862	284	18	,	,	PUNCT
mdp.39015104955862	284	19	at	at	ADP
mdp.39015104955862	284	20	which	which	PRON
mdp.39015104955862	284	21	the	the	DET
mdp.39015104955862	284	22	maximal	maximal	ADJ
mdp.39015104955862	284	23	value	value	NOUN
mdp.39015104955862	284	24	of	of	ADP
mdp.39015104955862	284	25	w	w	PROPN
mdp.39015104955862	284	26	,	,	PUNCT
mdp.39015104955862	284	27	is	be	AUX
mdp.39015104955862	284	28	attained	attain	VERB
mdp.39015104955862	284	29	,	,	PUNCT
mdp.39015104955862	284	30	satisfies	satisfy	VERB
mdp.39015104955862	284	31	thus	thus	ADV
mdp.39015104955862	284	32	it	it	PRON
mdp.39015104955862	284	33	is	be	AUX
mdp.39015104955862	284	34	clear	clear	ADJ
mdp.39015104955862	284	35	that	that	SCONJ
mdp.39015104955862	284	36	where	where	SCONJ
mdp.39015104955862	284	37	u。(r	u。(r	ADP
mdp.39015104955862	284	38	)	)	PUNCT
mdp.39015104955862	284	39	=	=	X
mdp.39015104955862	284	40	p−¹(lnr	p−¹(lnr	PROPN
mdp.39015104955862	284	41	)	)	PUNCT
mdp.39015104955862	284	42	.	.	PUNCT
mdp.39015104955862	285	1	p(u。(t	p(u。(t	NOUN
mdp.39015104955862	285	2	)	)	PUNCT
mdp.39015104955862	285	3	)	)	PUNCT
mdp.39015104955862	286	1	=	=	PROPN
mdp.39015104955862	287	1	ln	ln	PROPN
mdp.39015104955862	287	2	r.	r.	PROPN
mdp.39015104955862	287	3	t₁(r	t₁(r	SPACE
mdp.39015104955862	287	4	)	)	PUNCT
mdp.39015104955862	287	5	=	=	NOUN
mdp.39015104955862	288	1	go40	go40	NOUN
mdp.39015104955862	288	2	(	(	PUNCT
mdp.39015104955862	288	3	r	r	NOUN
mdp.39015104955862	288	4	)	)	PUNCT
mdp.39015104955862	288	5	m(uo(t	m(uo(t	NUM
mdp.39015104955862	288	6	)	)	PUNCT
mdp.39015104955862	288	7	)	)	PUNCT
mdp.39015104955862	288	8	'	'	PUNCT
mdp.39015104955862	288	9	(	(	PUNCT
mdp.39015104955862	288	10	71	71	NUM
mdp.39015104955862	288	11	)	)	PUNCT
mdp.39015104955862	288	12	after	after	ADP
mdp.39015104955862	288	13	these	these	DET
mdp.39015104955862	288	14	prelimimary	prelimimary	ADJ
mdp.39015104955862	288	15	considerations	consideration	NOUN
mdp.39015104955862	288	16	we	we	PRON
mdp.39015104955862	288	17	proceed	proceed	VERB
mdp.39015104955862	288	18	with	with	ADP
mdp.39015104955862	288	19	the	the	DET
mdp.39015104955862	288	20	proof	proof	NOUN
mdp.39015104955862	288	21	of	of	ADP
mdp.39015104955862	288	22	the	the	DET
mdp.39015104955862	288	23	implication	implication	NOUN
mdp.39015104955862	288	24	a	a	DET
mdp.39015104955862	288	25	)	)	PUNCT
mdp.39015104955862	288	26	⇒	⇒	PROPN
mdp.39015104955862	288	27	b	b	NOUN
mdp.39015104955862	288	28	)	)	PUNCT
mdp.39015104955862	288	29	.	.	PUNCT
mdp.39015104955862	289	1	suppose	suppose	VERB
mdp.39015104955862	289	2	(	(	PUNCT
mdp.39015104955862	289	3	66	66	NUM
mdp.39015104955862	289	4	)	)	PUNCT
mdp.39015104955862	289	5	holds	hold	VERB
mdp.39015104955862	289	6	.	.	PUNCT
mdp.39015104955862	290	1	define	define	VERB
mdp.39015104955862	290	2	a	a	DET
mdp.39015104955862	290	3	function	function	NOUN
mdp.39015104955862	290	4	by	by	ADP
mdp.39015104955862	290	5	φ(z	φ(z	SPACE
mdp.39015104955862	290	6	)	)	PUNCT
mdp.39015104955862	291	1	=	=	PROPN
mdp.39015104955862	291	2	σ	σ	PROPN
mdp.39015104955862	291	3	σ	σ	X
mdp.39015104955862	291	4	k=1	k=1	PROPN
mdp.39015104955862	291	5	differentiating	differentiate	VERB
mdp.39015104955862	291	6	formally	formally	ADV
mdp.39015104955862	291	7	,	,	PUNCT
mdp.39015104955862	291	8	we	we	PRON
mdp.39015104955862	291	9	obtain	obtain	VERB
mdp.39015104955862	291	10	cos(t(k)x	cos(t(k)x	ADJ
mdp.39015104955862	291	11	)	)	PUNCT
mdp.39015104955862	291	12	k²	k²	PROPN
mdp.39015104955862	291	13	t₁(t(k	t₁(t(k	PROPN
mdp.39015104955862	291	14	)	)	PUNCT
mdp.39015104955862	291	15	)	)	PUNCT
mdp.39015104955862	291	16	'	'	PUNCT
mdp.39015104955862	291	17	from	from	ADP
mdp.39015104955862	291	18	(	(	PUNCT
mdp.39015104955862	291	19	67	67	NUM
mdp.39015104955862	291	20	)	)	PUNCT
mdp.39015104955862	291	21	and	and	CCONJ
mdp.39015104955862	291	22	(	(	PUNCT
mdp.39015104955862	291	23	69	69	NUM
mdp.39015104955862	291	24	)	)	PUNCT
mdp.39015104955862	291	25	it	it	PRON
mdp.39015104955862	291	26	is	be	AUX
mdp.39015104955862	291	27	clear	clear	ADJ
mdp.39015104955862	291	28	that	that	SCONJ
mdp.39015104955862	291	29	r	r	X
mdp.39015104955862	291	30	>	>	X
mdp.39015104955862	291	31	1	1	NUM
mdp.39015104955862	291	32	.	.	PUNCT
mdp.39015104955862	291	33	t(k	t(k	NOUN
mdp.39015104955862	291	34	)	)	PUNCT
mdp.39015104955862	292	1	=	=	NOUN
mdp.39015104955862	292	2	ep(k	ep(k	SPACE
mdp.39015104955862	292	3	)	)	PUNCT
mdp.39015104955862	292	4	,	,	PUNCT
mdp.39015104955862	293	1	k	k	PROPN
mdp.39015104955862	293	2	≥	≥	PROPN
mdp.39015104955862	293	3	1	1	NUM
mdp.39015104955862	293	4	.	.	PUNCT
mdp.39015104955862	293	5	(	(	PUNCT
mdp.39015104955862	293	6	73	73	NUM
mdp.39015104955862	293	7	)	)	PUNCT
mdp.39015104955862	293	8	let	let	VERB
mdp.39015104955862	293	9	us	we	PRON
mdp.39015104955862	293	10	show	show	VERB
mdp.39015104955862	293	11	that	that	SCONJ
mdp.39015104955862	293	12	the	the	DET
mdp.39015104955862	293	13	series	series	NOUN
mdp.39015104955862	293	14	in	in	ADP
mdp.39015104955862	293	15	(	(	PUNCT
mdp.39015104955862	293	16	72	72	NUM
mdp.39015104955862	293	17	)	)	PUNCT
mdp.39015104955862	293	18	and	and	CCONJ
mdp.39015104955862	293	19	all	all	DET
mdp.39015104955862	293	20	the	the	DET
mdp.39015104955862	293	21	m	m	NOUN
mdp.39015104955862	293	22	-	-	NOUN
mdp.39015104955862	293	23	times	time	NOUN
mdp.39015104955862	293	24	termwise	termwise	NOUN
mdp.39015104955862	293	25	differentiated	differentiate	VERB
mdp.39015104955862	293	26	series	series	NOUN
mdp.39015104955862	293	27	converge	converge	VERB
mdp.39015104955862	293	28	absolutely	absolutely	ADV
mdp.39015104955862	293	29	.	.	PUNCT
mdp.39015104955862	294	1	|ø(m	|ø(m	NOUN
mdp.39015104955862	294	2	)	)	PUNCT
mdp.39015104955862	294	3	(	(	PUNCT
mdp.39015104955862	294	4	x)|	x)|	PROPN
mdp.39015104955862	294	5	≤	≤	PROPN
mdp.39015104955862	294	6	σ	σ	PROPN
mdp.39015104955862	294	7	k²t₁(7(k	k²t₁(7(k	PROPN
mdp.39015104955862	294	8	)	)	PUNCT
mdp.39015104955862	294	9	)	)	PUNCT
mdp.39015104955862	294	10	*	*	PUNCT
mdp.39015104955862	295	1	t(k)m	t(k)m	X
mdp.39015104955862	295	2	x	x	SYM
mdp.39015104955862	295	3	є	є	PROPN
mdp.39015104955862	295	4	r¹	r¹	PROPN
mdp.39015104955862	295	5	,	,	PUNCT
mdp.39015104955862	295	6	t₁(t(k	t₁(t(k	SPACE
mdp.39015104955862	295	7	)	)	PUNCT
mdp.39015104955862	295	8	)	)	PUNCT
mdp.39015104955862	295	9	>	>	X
mdp.39015104955862	295	10	t(k)n	t(k)n	X
mdp.39015104955862	295	11	m	m	NOUN
mdp.39015104955862	295	12	for	for	ADP
mdp.39015104955862	295	13	every	every	DET
mdp.39015104955862	295	14	k	k	PROPN
mdp.39015104955862	295	15	and	and	CCONJ
mdp.39015104955862	295	16	n.	n.	PROPN
mdp.39015104955862	295	17	applying	applying	NOUN
mdp.39015104955862	295	18	(	(	PUNCT
mdp.39015104955862	295	19	75	75	NUM
mdp.39015104955862	295	20	)	)	PUNCT
mdp.39015104955862	295	21	with	with	ADP
mdp.39015104955862	295	22	n	n	NOUN
mdp.39015104955862	295	23	=	=	ADP
mdp.39015104955862	295	24	m	m	VERB
mdp.39015104955862	295	25	to	to	ADP
mdp.39015104955862	295	26	(	(	PUNCT
mdp.39015104955862	295	27	74	74	NUM
mdp.39015104955862	295	28	)	)	PUNCT
mdp.39015104955862	295	29	,	,	PUNCT
mdp.39015104955862	295	30	we	we	PRON
mdp.39015104955862	295	31	get	get	VERB
mdp.39015104955862	295	32	(	(	PUNCT
mdp.39015104955862	295	33	70	70	NUM
mdp.39015104955862	295	34	)	)	PUNCT
mdp.39015104955862	295	35	|ø(m	|ø(m	NOUN
mdp.39015104955862	295	36	)	)	PUNCT
mdp.39015104955862	295	37	(	(	PUNCT
mdp.39015104955862	295	38	x)|	x)|	PROPN
mdp.39015104955862	295	39	≤	≤	X
mdp.39015104955862	295	40	mmσk-²	mmσk-²	PROPN
mdp.39015104955862	295	41	,	,	PUNCT
mdp.39015104955862	295	42	m≥0	m≥0	PROPN
mdp.39015104955862	295	43	,	,	PUNCT
mdp.39015104955862	295	44	k=1	k=1	PROPN
mdp.39015104955862	295	45	(	(	PUNCT
mdp.39015104955862	295	46	72	72	NUM
mdp.39015104955862	295	47	)	)	PUNCT
mdp.39015104955862	295	48	(	(	PUNCT
mdp.39015104955862	295	49	74	74	NUM
mdp.39015104955862	295	50	)	)	PUNCT
mdp.39015104955862	295	51	(	(	PUNCT
mdp.39015104955862	295	52	75	75	NUM
mdp.39015104955862	295	53	)	)	PUNCT
mdp.39015104955862	295	54	24	24	NUM
mdp.39015104955862	295	55	which	which	PRON
mdp.39015104955862	295	56	means	mean	VERB
mdp.39015104955862	295	57	that	that	SCONJ
mdp.39015104955862	295	58	$	$	SYM
mdp.39015104955862	295	59	€	€	SYM
mdp.39015104955862	295	60	d({m₁	d({m₁	ADJ
mdp.39015104955862	295	61	}	}	PUNCT
mdp.39015104955862	295	62	)	)	PUNCT
mdp.39015104955862	295	63	.	.	PUNCT
mdp.39015104955862	296	1	using	use	VERB
mdp.39015104955862	296	2	(	(	PUNCT
mdp.39015104955862	296	3	66	66	NUM
mdp.39015104955862	296	4	)	)	PUNCT
mdp.39015104955862	296	5	,	,	PUNCT
mdp.39015104955862	296	6	we	we	PRON
mdp.39015104955862	296	7	obtain	obtain	VERB
mdp.39015104955862	296	8	u_h(4	u_h(4	SPACE
mdp.39015104955862	296	9	)	)	PUNCT
mdp.39015104955862	296	10	€	€	SYM
mdp.39015104955862	296	11	d({m	d({m	PROPN
mdp.39015104955862	296	12	}	}	PUNCT
mdp.39015104955862	296	13	)	)	PUNCT
mdp.39015104955862	296	14	,	,	PUNCT
mdp.39015104955862	296	15	and	and	CCONJ
mdp.39015104955862	296	16	recalling	recall	VERB
mdp.39015104955862	296	17	the	the	DET
mdp.39015104955862	296	18	definition	definition	NOUN
mdp.39015104955862	296	19	of	of	ADP
mdp.39015104955862	296	20	the	the	DET
mdp.39015104955862	296	21	class	class	NOUN
mdp.39015104955862	296	22	d({m	d({m	PROPN
mdp.39015104955862	296	23	}	}	PUNCT
mdp.39015104955862	296	24	)	)	PUNCT
mdp.39015104955862	296	25	,	,	PUNCT
mdp.39015104955862	296	26	we	we	PRON
mdp.39015104955862	296	27	get	get	VERB
mdp.39015104955862	296	28	k=0	k=0	NOUN
mdp.39015104955862	296	29	with	with	ADP
mdp.39015104955862	296	30	some	some	DET
mdp.39015104955862	296	31	positive	positive	ADJ
mdp.39015104955862	296	32	function	function	NOUN
mdp.39015104955862	296	33	p.	p.	NOUN
mdp.39015104955862	297	1	it	it	PRON
mdp.39015104955862	297	2	is	be	AUX
mdp.39015104955862	297	3	clear	clear	ADJ
mdp.39015104955862	297	4	that	that	SCONJ
mdp.39015104955862	297	5	(	(	PUNCT
mdp.39015104955862	297	6	−h	−h	PROPN
mdp.39015104955862	297	7	)	)	PUNCT
mdp.39015104955862	297	8	*	*	PUNCT
mdp.39015104955862	297	9	$	$	SYM
mdp.39015104955862	297	10	(	(	PUNCT
mdp.39015104955862	297	11	2k+j	2k+j	NUM
mdp.39015104955862	297	12	)	)	PUNCT
mdp.39015104955862	297	13	(	(	PUNCT
mdp.39015104955862	297	14	0)|	0)|	NUM
mdp.39015104955862	297	15	≤	≤	X
mdp.39015104955862	297	16	chp(h)³m	chp(h)³m	NOUN
mdp.39015104955862	297	17	,	,	PUNCT
mdp.39015104955862	297	18	,	,	PUNCT
mdp.39015104955862	297	19	j≥0	j≥0	PROPN
mdp.39015104955862	297	20	k	k	PROPN
mdp.39015104955862	297	21	!	!	PUNCT
mdp.39015104955862	297	22	$	$	SYM
mdp.39015104955862	297	23	(	(	PUNCT
mdp.39015104955862	297	24	2k+m	2k+m	NUM
mdp.39015104955862	297	25	)	)	PUNCT
mdp.39015104955862	297	26	(	(	PUNCT
mdp.39015104955862	297	27	0	0	X
mdp.39015104955862	297	28	)	)	PUNCT
mdp.39015104955862	297	29	=	=	VERB
mdp.39015104955862	297	30	0	0	NUM
mdp.39015104955862	298	1	for	for	ADP
mdp.39015104955862	298	2	every	every	DET
mdp.39015104955862	298	3	odd	odd	ADJ
mdp.39015104955862	298	4	integer	integer	ADJ
mdp.39015104955862	298	5	m.	m.	NOUN
mdp.39015104955862	298	6	in	in	ADP
mdp.39015104955862	298	7	the	the	DET
mdp.39015104955862	298	8	case	case	NOUN
mdp.39015104955862	298	9	of	of	ADP
mdp.39015104955862	298	10	the	the	DET
mdp.39015104955862	298	11	even	even	ADV
mdp.39015104955862	298	12	integer	integer	ADJ
mdp.39015104955862	298	13	m	m	PROPN
mdp.39015104955862	298	14	=	=	PROPN
mdp.39015104955862	298	15	2j	2j	NUM
mdp.39015104955862	298	16	we	we	PRON
mdp.39015104955862	298	17	get	get	VERB
mdp.39015104955862	298	18	from	from	ADP
mdp.39015104955862	298	19	(	(	PUNCT
mdp.39015104955862	298	20	70	70	NUM
mdp.39015104955862	298	21	)	)	PUNCT
mdp.39015104955862	298	22	,	,	PUNCT
mdp.39015104955862	298	23	(	(	PUNCT
mdp.39015104955862	298	24	71	71	NUM
mdp.39015104955862	298	25	)	)	PUNCT
mdp.39015104955862	298	26	,	,	PUNCT
mdp.39015104955862	298	27	and	and	CCONJ
mdp.39015104955862	298	28	(	(	PUNCT
mdp.39015104955862	298	29	73	73	NUM
mdp.39015104955862	298	30	)	)	PUNCT
mdp.39015104955862	298	31	that	that	SCONJ
mdp.39015104955862	298	32	t(m)2k+2j	t(m)2k+2j	X
mdp.39015104955862	298	33	ø	ø	X
mdp.39015104955862	298	34	(	(	PUNCT
mdp.39015104955862	298	35	2k+2	2k+2	NUM
mdp.39015104955862	298	36	;)	;)	PUNCT
mdp.39015104955862	298	37	(	(	PUNCT
mdp.39015104955862	298	38	0	0	NUM
mdp.39015104955862	298	39	)	)	PUNCT
mdp.39015104955862	298	40	=	=	PUNCT
mdp.39015104955862	298	41	(	(	PUNCT
mdp.39015104955862	298	42	−	−	PROPN
mdp.39015104955862	298	43	1)k+	1)k+	NUM
mdp.39015104955862	298	44	;	;	PUNCT
mdp.39015104955862	298	45	†	†	PROPN
mdp.39015104955862	298	46	t(m	t(m	PROPN
mdp.39015104955862	298	47	)	)	PUNCT
mdp.39015104955862	298	48	2k+2	2k+2	NUM
mdp.39015104955862	298	49	;	;	PUNCT
mdp.39015104955862	298	50	m²t₁(t(m	m²t₁(t(m	PROPN
mdp.39015104955862	298	51	)	)	PUNCT
mdp.39015104955862	298	52	)	)	PUNCT
mdp.39015104955862	299	1	σ	σ	NOUN
mdp.39015104955862	299	2	m=1	m=1	PROPN
mdp.39015104955862	300	1	it	it	PRON
mdp.39015104955862	300	2	follows	follow	VERB
mdp.39015104955862	300	3	from	from	ADP
mdp.39015104955862	300	4	(	(	PUNCT
mdp.39015104955862	300	5	76	76	NUM
mdp.39015104955862	300	6	)	)	PUNCT
mdp.39015104955862	300	7	that	that	SCONJ
mdp.39015104955862	300	8	242	242	NUM
mdp.39015104955862	300	9	k=	k=	INTJ
mdp.39015104955862	300	10	mmt(m	mmt(m	PROPN
mdp.39015104955862	300	11	)	)	PUNCT
mdp.39015104955862	300	12	2k+2j	2k+2j	NUM
mdp.39015104955862	300	13	m²τ(m)m	m²τ(m)m	PROPN
mdp.39015104955862	300	14	=	=	VERB
mdp.39015104955862	300	15	1	1	NUM
mdp.39015104955862	300	16	=(	=(	NUM
mdp.39015104955862	300	17	−1)k+immt	−1)k+immt	PROPN
mdp.39015104955862	300	18	(	(	PUNCT
mdp.39015104955862	300	19	m)²k+2j	m)²k+2j	PROPN
mdp.39015104955862	300	20	m²r(m)m	m²r(m)m	PROPN
mdp.39015104955862	300	21	m=1	m=1	PROPN
mdp.39015104955862	300	22	<	<	X
mdp.39015104955862	300	23	chp(h)¹³	chp(h)¹³	PROPN
mdp.39015104955862	300	24	m₂j	m₂j	NOUN
mdp.39015104955862	300	25	.	.	PUNCT
mdp.39015104955862	301	1	taking	take	VERB
mdp.39015104955862	301	2	into	into	ADP
mdp.39015104955862	301	3	account	account	NOUN
mdp.39015104955862	301	4	only	only	ADV
mdp.39015104955862	301	5	the	the	DET
mdp.39015104955862	301	6	term	term	NOUN
mdp.39015104955862	301	7	with	with	ADP
mdp.39015104955862	301	8	m	m	NOUN
mdp.39015104955862	301	9	=	=	SYM
mdp.39015104955862	301	10	2k	2k	NUM
mdp.39015104955862	301	11	+	+	CCONJ
mdp.39015104955862	301	12	2j	2j	NUM
mdp.39015104955862	301	13	in	in	ADP
mdp.39015104955862	301	14	the	the	DET
mdp.39015104955862	301	15	infinite	infinite	ADJ
mdp.39015104955862	301	16	sum	sum	NOUN
mdp.39015104955862	301	17	on	on	ADP
mdp.39015104955862	301	18	the	the	DET
mdp.39015104955862	301	19	left	left	ADJ
mdp.39015104955862	301	20	-	-	PUNCT
mdp.39015104955862	301	21	hand	hand	NOUN
mdp.39015104955862	301	22	side	side	NOUN
mdp.39015104955862	301	23	of	of	ADP
mdp.39015104955862	301	24	(	(	PUNCT
mdp.39015104955862	301	25	78	78	NUM
mdp.39015104955862	301	26	)	)	PUNCT
mdp.39015104955862	301	27	,	,	PUNCT
mdp.39015104955862	301	28	we	we	PRON
mdp.39015104955862	301	29	get	get	VERB
mdp.39015104955862	301	30	(	(	PUNCT
mdp.39015104955862	301	31	76	76	NUM
mdp.39015104955862	301	32	)	)	PUNCT
mdp.39015104955862	301	33	k=0	k=0	NOUN
mdp.39015104955862	301	34	(	(	PUNCT
mdp.39015104955862	301	35	77	77	NUM
mdp.39015104955862	301	36	)	)	PUNCT
mdp.39015104955862	301	37	h	h	NOUN
mdp.39015104955862	301	38	*	*	NOUN
mdp.39015104955862	302	1	m2k+2j	m2k+2j	INTJ
mdp.39015104955862	302	2	k	k	PROPN
mdp.39015104955862	302	3	!	!	PROPN
mdp.39015104955862	302	4	e4k+4j	e4k+4j	PROPN
mdp.39015104955862	302	5	hk	hk	PROPN
mdp.39015104955862	302	6	m2k+2j	m2k+2j	INTJ
mdp.39015104955862	302	7	chp(h)²	chp(h)²	NOUN
mdp.39015104955862	302	8	;	;	PUNCT
mdp.39015104955862	302	9	m2	m2	PROPN
mdp.39015104955862	302	10	;	;	PUNCT
mdp.39015104955862	302	11	≥	≥	PROPN
mdp.39015104955862	302	12	σk	σk	PROPN
mdp.39015104955862	302	13	!	!	PUNCT
mdp.39015104955862	302	14	(	(	PUNCT
mdp.39015104955862	303	1	2k	2k	NUM
mdp.39015104955862	303	2	+	+	NUM
mdp.39015104955862	303	3	2j)²	2j)²	NUM
mdp.39015104955862	303	4	>	>	PUNCT
mdp.39015104955862	303	5	(	(	PUNCT
mdp.39015104955862	303	6	79	79	NUM
mdp.39015104955862	303	7	)	)	PUNCT
mdp.39015104955862	303	8	k=0	k=0	NOUN
mdp.39015104955862	303	9	it	it	PRON
mdp.39015104955862	303	10	is	be	AUX
mdp.39015104955862	303	11	seen	see	VERB
mdp.39015104955862	303	12	from	from	ADP
mdp.39015104955862	303	13	(	(	PUNCT
mdp.39015104955862	303	14	79	79	NUM
mdp.39015104955862	303	15	)	)	PUNCT
mdp.39015104955862	303	16	that	that	DET
mdp.39015104955862	303	17	assertion	assertion	PROPN
mdp.39015104955862	303	18	b	b	X
mdp.39015104955862	303	19	)	)	PUNCT
mdp.39015104955862	303	20	follows	follow	VERB
mdp.39015104955862	303	21	from	from	ADP
mdp.39015104955862	303	22	(	(	PUNCT
mdp.39015104955862	303	23	66	66	NUM
mdp.39015104955862	303	24	)	)	PUNCT
mdp.39015104955862	303	25	in	in	ADP
mdp.39015104955862	303	26	the	the	DET
mdp.39015104955862	303	27	case	case	NOUN
mdp.39015104955862	303	28	of	of	ADP
mdp.39015104955862	303	29	an	an	DET
mdp.39015104955862	303	30	even	even	ADV
mdp.39015104955862	303	31	integer	integer	ADJ
mdp.39015104955862	303	32	m.	m.	NOUN
mdp.39015104955862	303	33	the	the	DET
mdp.39015104955862	303	34	case	case	NOUN
mdp.39015104955862	303	35	of	of	ADP
mdp.39015104955862	303	36	odd	odd	ADJ
mdp.39015104955862	303	37	m	m	PROPN
mdp.39015104955862	303	38	's	's	PART
mdp.39015104955862	303	39	can	can	AUX
mdp.39015104955862	303	40	be	be	AUX
mdp.39015104955862	303	41	treated	treat	VERB
mdp.39015104955862	303	42	similarly	similarly	ADV
mdp.39015104955862	303	43	with	with	ADP
mdp.39015104955862	303	44	only	only	ADV
mdp.39015104955862	303	45	one	one	NUM
mdp.39015104955862	303	46	difference	difference	NOUN
mdp.39015104955862	303	47	that	that	PRON
mdp.39015104955862	303	48	we	we	PRON
mdp.39015104955862	303	49	take	take	VERB
mdp.39015104955862	303	50	sines	sine	NOUN
mdp.39015104955862	303	51	instead	instead	ADV
mdp.39015104955862	303	52	of	of	ADP
mdp.39015104955862	303	53	cosines	cosine	NOUN
mdp.39015104955862	303	54	in	in	ADP
mdp.39015104955862	303	55	the	the	DET
mdp.39015104955862	303	56	definition	definition	NOUN
mdp.39015104955862	303	57	(	(	PUNCT
mdp.39015104955862	303	58	72	72	NUM
mdp.39015104955862	303	59	)	)	PUNCT
mdp.39015104955862	303	60	of	of	ADP
mdp.39015104955862	303	61	the	the	DET
mdp.39015104955862	303	62	function	function	NOUN
mdp.39015104955862	303	63	.	.	PUNCT
mdp.39015104955862	304	1	we	we	PRON
mdp.39015104955862	304	2	complete	complete	VERB
mdp.39015104955862	304	3	the	the	DET
mdp.39015104955862	304	4	proof	proof	NOUN
mdp.39015104955862	304	5	of	of	ADP
mdp.39015104955862	304	6	theorem	theorem	NOUN
mdp.39015104955862	304	7	3	3	NUM
mdp.39015104955862	304	8	by	by	ADP
mdp.39015104955862	304	9	showing	show	VERB
mdp.39015104955862	304	10	that	that	DET
mdp.39015104955862	304	11	b	b	NOUN
mdp.39015104955862	304	12	)	)	PUNCT
mdp.39015104955862	304	13	is	be	AUX
mdp.39015104955862	304	14	equivalent	equivalent	ADJ
mdp.39015104955862	304	15	to	to	ADP
mdp.39015104955862	304	16	c	c	PROPN
mdp.39015104955862	304	17	)	)	PUNCT
mdp.39015104955862	304	18	.	.	PUNCT
mdp.39015104955862	305	1	(	(	PUNCT
mdp.39015104955862	305	2	78	78	NUM
mdp.39015104955862	305	3	)	)	PUNCT
mdp.39015104955862	305	4	the	the	DET
mdp.39015104955862	305	5	kap	kap	PROPN
mdp.39015104955862	305	6	25	25	NUM
mdp.39015104955862	305	7	let	let	VERB
mdp.39015104955862	305	8	us	we	PRON
mdp.39015104955862	305	9	first	first	ADV
mdp.39015104955862	305	10	prove	prove	VERB
mdp.39015104955862	305	11	that	that	SCONJ
mdp.39015104955862	305	12	b	b	NOUN
mdp.39015104955862	305	13	)	)	PUNCT
mdp.39015104955862	305	14	is	be	AUX
mdp.39015104955862	305	15	equivalent	equivalent	ADJ
mdp.39015104955862	305	16	to	to	ADP
mdp.39015104955862	305	17	the	the	DET
mdp.39015104955862	305	18	existence	existence	NOUN
mdp.39015104955862	305	19	of	of	ADP
mdp.39015104955862	305	20	positive	positive	ADJ
mdp.39015104955862	305	21	functions	function	NOUN
mdp.39015104955862	305	22	m	m	PROPN
mdp.39015104955862	305	23	and	and	CCONJ
mdp.39015104955862	305	24	p	p	PROPN
mdp.39015104955862	305	25	such	such	ADJ
mdp.39015104955862	305	26	that	that	SCONJ
mdp.39015104955862	305	27	and	and	CCONJ
mdp.39015104955862	305	28	the	the	DET
mdp.39015104955862	305	29	inequality	inequality	NOUN
mdp.39015104955862	305	30	m(k	m(k	PROPN
mdp.39015104955862	305	31	)	)	PUNCT
mdp.39015104955862	305	32	=	=	PROPN
mdp.39015104955862	305	33	mk	mk	PROPN
mdp.39015104955862	305	34	,	,	PUNCT
mdp.39015104955862	305	35	k≥0	k≥0	PROPN
mdp.39015104955862	305	36	m(2	m(2	PROPN
mdp.39015104955862	305	37	€	€	PROPN
mdp.39015104955862	305	38	+	+	NUM
mdp.39015104955862	305	39	v)he	v)he	NOUN
mdp.39015104955862	305	40	≤	≤	NOUN
mdp.39015104955862	305	41	p(h)+¹¤	p(h)+¹¤	X
mdp.39015104955862	305	42	m(v	m(v	PROPN
mdp.39015104955862	305	43	)	)	PUNCT
mdp.39015104955862	305	44	where	where	SCONJ
mdp.39015104955862	305	45	[	[	X
mdp.39015104955862	305	46	a	a	PRON
mdp.39015104955862	305	47	]	]	PUNCT
mdp.39015104955862	305	48	denotes	denote	VERB
mdp.39015104955862	305	49	the	the	DET
mdp.39015104955862	305	50	integer	integer	ADJ
mdp.39015104955862	305	51	part	part	NOUN
mdp.39015104955862	305	52	of	of	ADP
mdp.39015104955862	305	53	a.	a.	NOUN
mdp.39015104955862	305	54	it	it	PRON
mdp.39015104955862	305	55	follows	follow	VERB
mdp.39015104955862	305	56	from	from	ADP
mdp.39015104955862	305	57	(	(	PUNCT
mdp.39015104955862	305	58	82	82	NUM
mdp.39015104955862	305	59	)	)	PUNCT
mdp.39015104955862	305	60	that	that	PRON
mdp.39015104955862	305	61	m(2§	m(2§	VERB
mdp.39015104955862	305	62	+	+	SYM
mdp.39015104955862	305	63	v)h€	v)h€	NUM
mdp.39015104955862	305	64	≤	≤	NOUN
mdp.39015104955862	305	65	p(h)~+¹§¤	p(h)~+¹§¤	NOUN
mdp.39015104955862	305	66	m[v]+1•	m[v]+1•	PROPN
mdp.39015104955862	305	67	is	be	AUX
mdp.39015104955862	305	68	true	true	ADJ
mdp.39015104955862	305	69	for	for	ADP
mdp.39015104955862	305	70	all	all	DET
mdp.39015104955862	305	71	≥	≥	SYM
mdp.39015104955862	305	72	0	0	NUM
mdp.39015104955862	305	73	,	,	PUNCT
mdp.39015104955862	305	74	v	v	NOUN
mdp.39015104955862	305	75	≥	≥	X
mdp.39015104955862	305	76	0	0	NUM
mdp.39015104955862	305	77	,	,	PUNCT
mdp.39015104955862	305	78	and	and	CCONJ
mdp.39015104955862	305	79	h	h	X
mdp.39015104955862	305	80	>	>	X
mdp.39015104955862	305	81	họ	họ	PROPN
mdp.39015104955862	305	82	.	.	PUNCT
mdp.39015104955862	306	1	it	it	PRON
mdp.39015104955862	306	2	is	be	AUX
mdp.39015104955862	306	3	clear	clear	ADJ
mdp.39015104955862	306	4	that	that	SCONJ
mdp.39015104955862	306	5	this	this	DET
mdp.39015104955862	306	6	assertion	assertion	NOUN
mdp.39015104955862	306	7	implies	imply	VERB
mdp.39015104955862	306	8	b	b	NOUN
mdp.39015104955862	306	9	)	)	PUNCT
mdp.39015104955862	306	10	.	.	PUNCT
mdp.39015104955862	307	1	now	now	ADV
mdp.39015104955862	307	2	suppose	suppose	VERB
mdp.39015104955862	307	3	b	b	X
mdp.39015104955862	307	4	)	)	PUNCT
mdp.39015104955862	307	5	holds	hold	VERB
mdp.39015104955862	307	6	.	.	PUNCT
mdp.39015104955862	308	1	consider	consider	VERB
mdp.39015104955862	308	2	the	the	DET
mdp.39015104955862	308	3	function	function	NOUN
mdp.39015104955862	308	4	m	m	INTJ
mdp.39015104955862	308	5	,	,	PUNCT
mdp.39015104955862	308	6	defined	define	VERB
mdp.39015104955862	308	7	above	above	ADV
mdp.39015104955862	308	8	in	in	ADP
mdp.39015104955862	308	9	the	the	DET
mdp.39015104955862	308	10	previous	previous	ADJ
mdp.39015104955862	308	11	part	part	NOUN
mdp.39015104955862	308	12	of	of	ADP
mdp.39015104955862	308	13	the	the	DET
mdp.39015104955862	308	14	proof	proof	NOUN
mdp.39015104955862	308	15	.	.	PUNCT
mdp.39015104955862	309	1	then	then	ADV
mdp.39015104955862	309	2	inequality	inequality	NOUN
mdp.39015104955862	309	3	(	(	PUNCT
mdp.39015104955862	309	4	80	80	NUM
mdp.39015104955862	309	5	)	)	PUNCT
mdp.39015104955862	309	6	holds	hold	VERB
mdp.39015104955862	309	7	and	and	CCONJ
mdp.39015104955862	309	8	,	,	PUNCT
mdp.39015104955862	309	9	using	use	VERB
mdp.39015104955862	309	10	(	(	PUNCT
mdp.39015104955862	309	11	80	80	NUM
mdp.39015104955862	309	12	)	)	PUNCT
mdp.39015104955862	309	13	and	and	CCONJ
mdp.39015104955862	309	14	(	(	PUNCT
mdp.39015104955862	309	15	81	81	NUM
mdp.39015104955862	309	16	)	)	PUNCT
mdp.39015104955862	309	17	,	,	PUNCT
mdp.39015104955862	309	18	we	we	PRON
mdp.39015104955862	309	19	get	get	VERB
mdp.39015104955862	309	20	for	for	ADP
mdp.39015104955862	309	21	h	h	X
mdp.39015104955862	309	22	>	>	X
mdp.39015104955862	309	23	ho	ho	PROPN
mdp.39015104955862	310	1	m(2	m(2	PROPN
mdp.39015104955862	310	2	€	€	SYM
mdp.39015104955862	310	3	+	+	NUM
mdp.39015104955862	310	4	v)h€	v)h€	NUM
mdp.39015104955862	310	5	≤	≤	X
mdp.39015104955862	310	6	m(2([e	m(2([e	PROPN
mdp.39015104955862	310	7	]	]	PUNCT
mdp.39015104955862	311	1	+	+	NUM
mdp.39015104955862	311	2	1	1	X
mdp.39015104955862	311	3	)	)	PUNCT
mdp.39015104955862	311	4	+	+	PUNCT
mdp.39015104955862	312	1	[	[	X
mdp.39015104955862	312	2	v	v	X
mdp.39015104955862	312	3	]	]	X
mdp.39015104955862	312	4	+	+	NUM
mdp.39015104955862	312	5	1)hl€)+¹	1)hl€)+¹	NUM
mdp.39015104955862	312	6	≤	≤	X
mdp.39015104955862	312	7	p(h)[~]+²([e	p(h)[~]+²([e	X
mdp.39015104955862	312	8	]	]	PUNCT
mdp.39015104955862	313	1	+	+	CCONJ
mdp.39015104955862	313	2	1)[€]+¹	1)[€]+¹	NUM
mdp.39015104955862	313	3	m{v}+1	m{v}+1	NOUN
mdp.39015104955862	313	4	taking	take	VERB
mdp.39015104955862	313	5	n	n	NOUN
mdp.39015104955862	313	6	=	=	SYM
mdp.39015104955862	313	7	1	1	NUM
mdp.39015104955862	313	8	,	,	PUNCT
mdp.39015104955862	313	9	h	h	NOUN
mdp.39015104955862	313	10	=	=	SYM
mdp.39015104955862	313	11	1	1	NUM
mdp.39015104955862	313	12	in	in	ADP
mdp.39015104955862	313	13	(	(	PUNCT
mdp.39015104955862	313	14	61	61	NUM
mdp.39015104955862	313	15	)	)	PUNCT
mdp.39015104955862	313	16	,	,	PUNCT
mdp.39015104955862	313	17	we	we	PRON
mdp.39015104955862	313	18	obtain	obtain	VERB
mdp.39015104955862	313	19	(	(	PUNCT
mdp.39015104955862	313	20	80	80	NUM
mdp.39015104955862	313	21	)	)	PUNCT
mdp.39015104955862	313	22	show	show	VERB
mdp.39015104955862	313	23	that	that	SCONJ
mdp.39015104955862	313	24	(	(	PUNCT
mdp.39015104955862	313	25	81	81	NUM
mdp.39015104955862	313	26	)	)	PUNCT
mdp.39015104955862	313	27	is	be	AUX
mdp.39015104955862	313	28	equivalent	equivalent	ADJ
mdp.39015104955862	313	29	to	to	ADP
mdp.39015104955862	313	30	assertion	assertion	NOUN
mdp.39015104955862	313	31	c	c	PROPN
mdp.39015104955862	313	32	)	)	PUNCT
mdp.39015104955862	313	33	.	.	PUNCT
mdp.39015104955862	314	1	theorem	theorem	NOUN
mdp.39015104955862	314	2	5	5	NUM
mdp.39015104955862	314	3	is	be	AUX
mdp.39015104955862	314	4	proved	prove	VERB
mdp.39015104955862	314	5	.	.	PUNCT
mdp.39015104955862	315	1	f	f	PROPN
mdp.39015104955862	315	2	(	(	PUNCT
mdp.39015104955862	315	3	81	81	NUM
mdp.39015104955862	315	4	)	)	PUNCT
mdp.39015104955862	315	5	(	(	PUNCT
mdp.39015104955862	315	6	82	82	NUM
mdp.39015104955862	315	7	)	)	PUNCT
mdp.39015104955862	315	8	mm+2	mm+2	PROPN
mdp.39015104955862	315	9	≤	≤	X
mdp.39015104955862	316	1	cm+¹	cm+¹	INTJ
mdp.39015104955862	316	2	mm	mm	INTJ
mdp.39015104955862	316	3	,	,	PUNCT
mdp.39015104955862	316	4	m≥0	m≥0	PROPN
mdp.39015104955862	316	5	.	.	PUNCT
mdp.39015104955862	317	1	now	now	ADV
mdp.39015104955862	317	2	it	it	PRON
mdp.39015104955862	317	3	is	be	AUX
mdp.39015104955862	317	4	clear	clear	ADJ
mdp.39015104955862	317	5	that	that	SCONJ
mdp.39015104955862	317	6	(	(	PUNCT
mdp.39015104955862	317	7	81	81	NUM
mdp.39015104955862	317	8	)	)	PUNCT
mdp.39015104955862	317	9	follows	follow	VERB
mdp.39015104955862	317	10	from	from	ADP
mdp.39015104955862	317	11	(	(	PUNCT
mdp.39015104955862	317	12	83	83	NUM
mdp.39015104955862	317	13	)	)	PUNCT
mdp.39015104955862	317	14	and	and	CCONJ
mdp.39015104955862	317	15	(	(	PUNCT
mdp.39015104955862	317	16	84	84	NUM
mdp.39015104955862	317	17	)	)	PUNCT
mdp.39015104955862	317	18	.	.	PUNCT
mdp.39015104955862	318	1	therefore	therefore	ADV
mdp.39015104955862	318	2	,	,	PUNCT
mdp.39015104955862	318	3	(	(	PUNCT
mdp.39015104955862	318	4	81	81	NUM
mdp.39015104955862	318	5	)	)	PUNCT
mdp.39015104955862	318	6	is	be	AUX
mdp.39015104955862	318	7	equivalent	equivalent	ADJ
mdp.39015104955862	318	8	to	to	ADP
mdp.39015104955862	318	9	b	b	NOUN
mdp.39015104955862	318	10	)	)	PUNCT
mdp.39015104955862	318	11	.	.	PUNCT
mdp.39015104955862	319	1	taking	take	VERB
mdp.39015104955862	319	2	=	=	X
mdp.39015104955862	319	3	kv	kv	PROPN
mdp.39015104955862	319	4	,	,	PUNCT
mdp.39015104955862	319	5	2k	2k	NUM
mdp.39015104955862	319	6	+	+	NUM
mdp.39015104955862	319	7	1	1	NUM
mdp.39015104955862	319	8	=	=	SYM
mdp.39015104955862	319	9	µ	µ	PROPN
mdp.39015104955862	319	10	,	,	PUNCT
mdp.39015104955862	319	11	and	and	CCONJ
mdp.39015104955862	319	12	v	v	ADP
mdp.39015104955862	319	13	=	=	PROPN
mdp.39015104955862	319	14	&	&	CCONJ
mdp.39015104955862	319	15	µ	µ	PROPN
mdp.39015104955862	319	16	,	,	PUNCT
mdp.39015104955862	319	17	and	and	CCONJ
mdp.39015104955862	319	18	v	v	ADP
mdp.39015104955862	319	19	=	=	NOUN
mdp.39015104955862	319	20	λ	λ	X
mdp.39015104955862	319	21	in	in	ADP
mdp.39015104955862	319	22	(	(	PUNCT
mdp.39015104955862	319	23	81	81	NUM
mdp.39015104955862	319	24	)	)	PUNCT
mdp.39015104955862	319	25	and	and	CCONJ
mdp.39015104955862	319	26	making	make	VERB
mdp.39015104955862	319	27	simple	simple	ADJ
mdp.39015104955862	319	28	transformations	transformation	NOUN
mdp.39015104955862	319	29	,	,	PUNCT
mdp.39015104955862	319	30	we	we	PRON
mdp.39015104955862	319	31	(	(	PUNCT
mdp.39015104955862	319	32	83	83	NUM
mdp.39015104955862	319	33	)	)	PUNCT
mdp.39015104955862	319	34	(	(	PUNCT
mdp.39015104955862	319	35	84	84	NUM
mdp.39015104955862	319	36	)	)	PUNCT
mdp.39015104955862	319	37	26	26	NUM
mdp.39015104955862	319	38	remark	remark	NOUN
mdp.39015104955862	319	39	4	4	NUM
mdp.39015104955862	319	40	in	in	ADP
mdp.39015104955862	319	41	the	the	DET
mdp.39015104955862	319	42	first	first	ADJ
mdp.39015104955862	319	43	part	part	NOUN
mdp.39015104955862	319	44	of	of	ADP
mdp.39015104955862	319	45	the	the	DET
mdp.39015104955862	319	46	proof	proof	NOUN
mdp.39015104955862	319	47	of	of	ADP
mdp.39015104955862	319	48	theorem	theorem	NOUN
mdp.39015104955862	319	49	5	5	NUM
mdp.39015104955862	319	50	we	we	PRON
mdp.39015104955862	319	51	showed	show	VERB
mdp.39015104955862	319	52	that	that	DET
mdp.39015104955862	319	53	condition	condition	NOUN
mdp.39015104955862	319	54	(	(	PUNCT
mdp.39015104955862	319	55	63	63	NUM
mdp.39015104955862	319	56	)	)	PUNCT
mdp.39015104955862	319	57	implies	imply	VERB
mdp.39015104955862	319	58	the	the	DET
mdp.39015104955862	319	59	u	u	PROPN
mdp.39015104955862	319	60	,	,	PUNCT
mdp.39015104955862	319	61	invariance	invariance	NOUN
mdp.39015104955862	319	62	of	of	ADP
mdp.39015104955862	319	63	the	the	DET
mdp.39015104955862	319	64	class	class	NOUN
mdp.39015104955862	319	65	d({m	d({m	PROPN
mdp.39015104955862	319	66	}	}	PUNCT
mdp.39015104955862	319	67	)	)	PUNCT
mdp.39015104955862	319	68	.	.	PUNCT
mdp.39015104955862	320	1	moreover	moreover	ADV
mdp.39015104955862	320	2	,	,	PUNCT
mdp.39015104955862	320	3	we	we	PRON
mdp.39015104955862	320	4	did	do	AUX
mdp.39015104955862	320	5	not	not	PART
mdp.39015104955862	320	6	use	use	VERB
mdp.39015104955862	320	7	condition	condition	NOUN
mdp.39015104955862	320	8	(	(	PUNCT
mdp.39015104955862	320	9	60	60	NUM
mdp.39015104955862	320	10	)	)	PUNCT
mdp.39015104955862	320	11	in	in	ADP
mdp.39015104955862	320	12	this	this	DET
mdp.39015104955862	320	13	part	part	NOUN
mdp.39015104955862	320	14	of	of	ADP
mdp.39015104955862	320	15	the	the	DET
mdp.39015104955862	320	16	proof	proof	NOUN
mdp.39015104955862	320	17	.	.	PUNCT
mdp.39015104955862	321	1	if	if	SCONJ
mdp.39015104955862	321	2	we	we	PRON
mdp.39015104955862	321	3	apply	apply	VERB
mdp.39015104955862	321	4	theorem	theorem	NOUN
mdp.39015104955862	321	5	3	3	NUM
mdp.39015104955862	321	6	,	,	PUNCT
mdp.39015104955862	321	7	we	we	PRON
mdp.39015104955862	321	8	see	see	VERB
mdp.39015104955862	321	9	that	that	DET
mdp.39015104955862	321	10	condition	condition	NOUN
mdp.39015104955862	321	11	(	(	PUNCT
mdp.39015104955862	321	12	63	63	NUM
mdp.39015104955862	321	13	)	)	PUNCT
mdp.39015104955862	321	14	for	for	ADP
mdp.39015104955862	321	15	the	the	DET
mdp.39015104955862	321	16	sequence	sequence	NOUN
mdp.39015104955862	321	17	{	{	PUNCT
mdp.39015104955862	321	18	m	m	NOUN
mdp.39015104955862	321	19	}	}	PUNCT
mdp.39015104955862	321	20	,	,	PUNCT
mdp.39015104955862	321	21	satisfying	satisfy	VERB
mdp.39015104955862	321	22	(	(	PUNCT
mdp.39015104955862	321	23	60	60	NUM
mdp.39015104955862	321	24	)	)	PUNCT
mdp.39015104955862	321	25	,	,	PUNCT
mdp.39015104955862	321	26	implies	imply	VERB
mdp.39015104955862	321	27	the	the	DET
mdp.39015104955862	321	28	similar	similar	ADJ
mdp.39015104955862	321	29	condition	condition	NOUN
mdp.39015104955862	321	30	(	(	PUNCT
mdp.39015104955862	321	31	61	61	NUM
mdp.39015104955862	321	32	)	)	PUNCT
mdp.39015104955862	321	33	for	for	ADP
mdp.39015104955862	321	34	the	the	DET
mdp.39015104955862	321	35	sequence	sequence	NOUN
mdp.39015104955862	321	36	{	{	PUNCT
mdp.39015104955862	321	37	m	m	NOUN
mdp.39015104955862	321	38	}	}	PUNCT
mdp.39015104955862	321	39	.	.	PUNCT
mdp.39015104955862	322	1	the	the	DET
mdp.39015104955862	322	2	inverse	inverse	ADJ
mdp.39015104955862	322	3	assertion	assertion	NOUN
mdp.39015104955862	322	4	does	do	AUX
mdp.39015104955862	322	5	not	not	PART
mdp.39015104955862	322	6	hold	hold	VERB
mdp.39015104955862	322	7	,	,	PUNCT
mdp.39015104955862	322	8	as	as	SCONJ
mdp.39015104955862	322	9	it	it	PRON
mdp.39015104955862	322	10	can	can	AUX
mdp.39015104955862	322	11	be	be	AUX
mdp.39015104955862	322	12	easily	easily	ADV
mdp.39015104955862	322	13	shown	show	VERB
mdp.39015104955862	322	14	by	by	ADP
mdp.39015104955862	322	15	simple	simple	ADJ
mdp.39015104955862	322	16	examples	example	NOUN
mdp.39015104955862	322	17	.	.	PUNCT
mdp.39015104955862	323	1	hence	hence	ADV
mdp.39015104955862	323	2	,	,	PUNCT
mdp.39015104955862	323	3	condition	condition	NOUN
mdp.39015104955862	323	4	(	(	PUNCT
mdp.39015104955862	323	5	61	61	NUM
mdp.39015104955862	323	6	)	)	PUNCT
mdp.39015104955862	323	7	is	be	AUX
mdp.39015104955862	323	8	only	only	ADV
mdp.39015104955862	323	9	suffisient	suffisient	ADJ
mdp.39015104955862	323	10	but	but	CCONJ
mdp.39015104955862	323	11	not	not	PART
mdp.39015104955862	323	12	necessary	necessary	ADJ
mdp.39015104955862	323	13	for	for	ADP
mdp.39015104955862	323	14	the	the	DET
mdp.39015104955862	323	15	u,-invariance	u,-invariance	NOUN
mdp.39015104955862	323	16	of	of	ADP
mdp.39015104955862	323	17	the	the	DET
mdp.39015104955862	323	18	class	class	NOUN
mdp.39015104955862	323	19	d({m	d({m	PROPN
mdp.39015104955862	323	20	}	}	PUNCT
mdp.39015104955862	323	21	)	)	PUNCT
mdp.39015104955862	323	22	.	.	PUNCT
mdp.39015104955862	324	1	corollary	corollary	ADJ
mdp.39015104955862	324	2	2	2	NUM
mdp.39015104955862	324	3	suppose	suppose	VERB
mdp.39015104955862	324	4	mk	mk	PROPN
mdp.39015104955862	324	5	=	=	PROPN
mdp.39015104955862	324	6	k*(k	k*(k	PROPN
mdp.39015104955862	324	7	)	)	PUNCT
mdp.39015104955862	324	8	,	,	PUNCT
mdp.39015104955862	324	9	k	k	PROPN
mdp.39015104955862	324	10	≥	≥	X
mdp.39015104955862	324	11	0	0	NUM
mdp.39015104955862	324	12	,	,	PUNCT
mdp.39015104955862	324	13	where	where	SCONJ
mdp.39015104955862	324	14	κ	κ	PROPN
mdp.39015104955862	324	15	is	be	AUX
mdp.39015104955862	324	16	a	a	DET
mdp.39015104955862	324	17	smooth	smooth	ADJ
mdp.39015104955862	324	18	increasing	increase	VERB
mdp.39015104955862	324	19	function	function	NOUN
mdp.39015104955862	324	20	on	on	ADP
mdp.39015104955862	324	21	(	(	PUNCT
mdp.39015104955862	324	22	0,∞	0,∞	NUM
mdp.39015104955862	324	23	)	)	PUNCT
mdp.39015104955862	324	24	such	such	ADJ
mdp.39015104955862	324	25	that	that	DET
mdp.39015104955862	324	26	1	1	NUM
mdp.39015104955862	324	27	.	.	SYM
mdp.39015104955862	324	28	2	2	NUM
mdp.39015104955862	324	29	.	.	PUNCT
mdp.39015104955862	324	30	lim	lim	PROPN
mdp.39015104955862	324	31	sup	sup	PROPN
mdp.39015104955862	324	32	818	818	NUM
mdp.39015104955862	324	33	it	it	PRON
mdp.39015104955862	324	34	follows	follow	VERB
mdp.39015104955862	324	35	that	that	SCONJ
mdp.39015104955862	324	36	k(u	k(u	SPACE
mdp.39015104955862	324	37	)	)	PUNCT
mdp.39015104955862	325	1	น	น	PROPN
mdp.39015104955862	325	2	<	<	X
mdp.39015104955862	325	3	1/2	1/2	NUM
mdp.39015104955862	325	4	.	.	PUNCT
mdp.39015104955862	325	5	κ'(u	κ'(u	PROPN
mdp.39015104955862	325	6	)	)	PUNCT
mdp.39015104955862	325	7	≤	≤	PROPN
mdp.39015104955862	325	8	1/2	1/2	NUM
mdp.39015104955862	325	9	,	,	PUNCT
mdp.39015104955862	325	10	u	u	PROPN
mdp.39015104955862	325	11	¿	¿	ADJ
mdp.39015104955862	325	12	0	0	NUM
mdp.39015104955862	325	13	.	.	PUNCT
mdp.39015104955862	326	1	then	then	ADV
mdp.39015104955862	326	2	the	the	DET
mdp.39015104955862	326	3	class	class	NOUN
mdp.39015104955862	326	4	d({m	d({m	NOUN
mdp.39015104955862	326	5	}	}	PUNCT
mdp.39015104955862	326	6	)	)	PUNCT
mdp.39015104955862	326	7	is	be	AUX
mdp.39015104955862	326	8	u₂-invariant	u₂-invariant	PROPN
mdp.39015104955862	326	9	.	.	PUNCT
mdp.39015104955862	327	1	proof	proof	PROPN
mdp.39015104955862	327	2	.	.	PUNCT
mdp.39015104955862	328	1	it	it	PRON
mdp.39015104955862	328	2	is	be	AUX
mdp.39015104955862	328	3	sufficient	sufficient	ADJ
mdp.39015104955862	328	4	to	to	PART
mdp.39015104955862	328	5	check	check	VERB
mdp.39015104955862	328	6	that	that	DET
mdp.39015104955862	328	7	inequality	inequality	NOUN
mdp.39015104955862	328	8	(	(	PUNCT
mdp.39015104955862	328	9	62	62	NUM
mdp.39015104955862	328	10	)	)	PUNCT
mdp.39015104955862	328	11	with	with	ADP
mdp.39015104955862	328	12	m(u	m(u	PROPN
mdp.39015104955862	328	13	)	)	PUNCT
mdp.39015104955862	328	14	=	=	PROPN
mdp.39015104955862	328	15	u(u	u(u	PROPN
mdp.39015104955862	328	16	)	)	PUNCT
mdp.39015104955862	328	17	instead	instead	ADV
mdp.39015104955862	328	18	of	of	ADP
mdp.39015104955862	328	19	m(u	m(u	PROPN
mdp.39015104955862	328	20	)	)	PUNCT
mdp.39015104955862	328	21	holds	hold	VERB
mdp.39015104955862	328	22	.	.	PUNCT
mdp.39015104955862	329	1	then	then	ADV
mdp.39015104955862	329	2	(	(	PUNCT
mdp.39015104955862	329	3	63	63	NUM
mdp.39015104955862	329	4	)	)	PUNCT
mdp.39015104955862	329	5	will	will	AUX
mdp.39015104955862	329	6	hold	hold	VERB
mdp.39015104955862	329	7	and	and	CCONJ
mdp.39015104955862	329	8	the	the	DET
mdp.39015104955862	329	9	class	class	NOUN
mdp.39015104955862	329	10	d({m	d({m	NOUN
mdp.39015104955862	329	11	}	}	PUNCT
mdp.39015104955862	329	12	)	)	PUNCT
mdp.39015104955862	329	13	will	will	AUX
mdp.39015104955862	329	14	be	be	AUX
mdp.39015104955862	329	15	u₂-invariant	u₂-invariant	ADJ
mdp.39015104955862	329	16	by	by	ADP
mdp.39015104955862	329	17	remark	remark	NOUN
mdp.39015104955862	329	18	4	4	NUM
mdp.39015104955862	329	19	.	.	PUNCT
mdp.39015104955862	329	20	condition	condition	NOUN
mdp.39015104955862	329	21	2	2	NUM
mdp.39015104955862	329	22	)	)	PUNCT
mdp.39015104955862	329	23	of	of	ADP
mdp.39015104955862	329	24	corollary	corollary	ADJ
mdp.39015104955862	329	25	2	2	NUM
mdp.39015104955862	329	26	gives	give	VERB
mdp.39015104955862	329	27	k(hλ	k(hλ	PROPN
mdp.39015104955862	329	28	)	)	PUNCT
mdp.39015104955862	329	29	≤	≤	PROPN
mdp.39015104955862	329	30	p	p	PROPN
mdp.39015104955862	329	31	−	−	PROPN
mdp.39015104955862	329	32	1	1	NUM
mdp.39015104955862	329	33	+	+	NUM
mdp.39015104955862	329	34	k(a	k(a	PROPN
mdp.39015104955862	329	35	)	)	PUNCT
mdp.39015104955862	329	36	32	32	NUM
mdp.39015104955862	329	37	.	.	PUNCT
mdp.39015104955862	330	1	d^(μλ)2	d^(μλ)2	SPACE
mdp.39015104955862	330	2	/	/	SYM
mdp.39015104955862	330	3	x	x	PUNCT
mdp.39015104955862	330	4	<	<	X
mdp.39015104955862	330	5	14	14	NUM
mdp.39015104955862	330	6	-	-	SYM
mdp.39015104955862	330	7	1+x(a)2	1+x(a)2	NUM
mdp.39015104955862	330	8	/	/	SYM
mdp.39015104955862	330	9	λ¸	λ¸	PROPN
mdp.39015104955862	330	10	(	(	PUNCT
mdp.39015104955862	330	11	85	85	NUM
mdp.39015104955862	330	12	)	)	PUNCT
mdp.39015104955862	330	13	27	27	NUM
mdp.39015104955862	330	14	from	from	ADP
mdp.39015104955862	330	15	condition	condition	NOUN
mdp.39015104955862	330	16	1	1	NUM
mdp.39015104955862	330	17	)	)	PUNCT
mdp.39015104955862	330	18	we	we	PRON
mdp.39015104955862	330	19	get	get	VERB
mdp.39015104955862	330	20	thus	thus	ADV
mdp.39015104955862	330	21	,	,	PUNCT
mdp.39015104955862	330	22	there	there	PRON
mdp.39015104955862	330	23	exists	exist	VERB
mdp.39015104955862	330	24	t	t	NOUN
mdp.39015104955862	330	25	>	>	X
mdp.39015104955862	330	26	0	0	NUM
mdp.39015104955862	330	27	such	such	ADJ
mdp.39015104955862	330	28	that	that	SCONJ
mdp.39015104955862	330	29	there	there	PRON
mdp.39015104955862	330	30	exists	exist	VERB
mdp.39015104955862	330	31	fix	fix	VERB
mdp.39015104955862	330	32	any	any	DET
mdp.39015104955862	330	33	such	such	ADJ
mdp.39015104955862	330	34	that	that	SCONJ
mdp.39015104955862	330	35	2	2	NUM
mdp.39015104955862	330	36	≤7	≤7	PROPN
mdp.39015104955862	330	37	.	.	PUNCT
mdp.39015104955862	331	1	since	since	SCONJ
mdp.39015104955862	331	2	for	for	ADP
mdp.39015104955862	331	3	which	which	PRON
mdp.39015104955862	331	4	suppose	suppose	VERB
mdp.39015104955862	331	5	then	then	ADV
mdp.39015104955862	331	6	where	where	SCONJ
mdp.39015104955862	331	7	k(u)<u/2	k(u)<u/2	PROPN
mdp.39015104955862	331	8	,	,	PUNCT
mdp.39015104955862	331	9	u≥	u≥	ADJ
mdp.39015104955862	331	10	uo	uo	NOUN
mdp.39015104955862	331	11	.	.	PUNCT
mdp.39015104955862	332	1	for	for	ADP
mdp.39015104955862	332	2	h	h	PROPN
mdp.39015104955862	332	3	>	>	X
mdp.39015104955862	332	4	ho	ho	PROPN
mdp.39015104955862	332	5	,	,	PUNCT
mdp.39015104955862	332	6	≥	≥	PRON
mdp.39015104955862	332	7	1	1	NUM
mdp.39015104955862	332	8	we	we	PRON
mdp.39015104955862	332	9	have	have	VERB
mdp.39015104955862	332	10	thus	thus	ADV
mdp.39015104955862	332	11	,	,	PUNCT
mdp.39015104955862	332	12	by	by	ADP
mdp.39015104955862	332	13	(	(	PUNCT
mdp.39015104955862	332	14	86	86	NUM
mdp.39015104955862	332	15	)	)	PUNCT
mdp.39015104955862	332	16	and	and	CCONJ
mdp.39015104955862	332	17	(	(	PUNCT
mdp.39015104955862	332	18	90	90	NUM
mdp.39015104955862	332	19	)	)	PUNCT
mdp.39015104955862	332	20	,	,	PUNCT
mdp.39015104955862	332	21	2k(u	2k(u	PROPN
mdp.39015104955862	332	22	)	)	PUNCT
mdp.39015104955862	333	1	น	น	PROPN
mdp.39015104955862	333	2	lim	lim	PROPN
mdp.39015104955862	333	3	818	818	NUM
mdp.39015104955862	334	1	+	+	PROPN
mdp.39015104955862	334	2	t	t	X
mdp.39015104955862	334	3	<	<	X
mdp.39015104955862	334	4	1	1	NUM
mdp.39015104955862	334	5	,	,	PUNCT
mdp.39015104955862	334	6	u≥	u≥	ADJ
mdp.39015104955862	334	7	u	u	PROPN
mdp.39015104955862	334	8	。	。	PROPN
mdp.39015104955862	334	9	.	.	PUNCT
mdp.39015104955862	335	1	(	(	PUNCT
mdp.39015104955862	335	2	µ	µ	PROPN
mdp.39015104955862	335	3	−	−	PROPN
mdp.39015104955862	335	4	1	1	NUM
mdp.39015104955862	335	5	)	)	PUNCT
mdp.39015104955862	335	6	ln(µ	ln(µ	ADJ
mdp.39015104955862	335	7	−	−	PROPN
mdp.39015104955862	335	8	1	1	X
mdp.39015104955862	335	9	)	)	PUNCT
mdp.39015104955862	335	10	uln	uln	ADV
mdp.39015104955862	335	11	ho	ho	PROPN
mdp.39015104955862	335	12	uo	uo	PROPN
mdp.39015104955862	335	13	,	,	PUNCT
mdp.39015104955862	335	14	(	(	PUNCT
mdp.39015104955862	335	15	µ	µ	X
mdp.39015104955862	335	16	−	−	PROPN
mdp.39015104955862	335	17	1	1	NUM
mdp.39015104955862	335	18	)	)	PUNCT
mdp.39015104955862	335	19	ln(µ	ln(µ	ADJ
mdp.39015104955862	335	20	−	−	PROPN
mdp.39015104955862	335	21	1	1	X
mdp.39015104955862	335	22	)	)	PUNCT
mdp.39015104955862	335	23	>	>	X
mdp.39015104955862	335	24	1	1	NUM
mdp.39015104955862	335	25	−	−	PROPN
mdp.39015104955862	335	26	§	§	SPACE
mdp.39015104955862	335	27	,	,	PUNCT
mdp.39015104955862	335	28	µ	µ	PROPN
mdp.39015104955862	335	29	>	>	X
mdp.39015104955862	335	30	ho	ho	PROPN
mdp.39015104955862	335	31	.	.	PUNCT
mdp.39015104955862	336	1	μη	μη	INTJ
mdp.39015104955862	336	2	μ	μ	NOUN
mdp.39015104955862	336	3	µ¤	µ¤	NOUN
mdp.39015104955862	336	4	<	<	X
mdp.39015104955862	336	5	h.	h.	NOUN
mdp.39015104955862	336	6	þ(h	þ(h	PROPN
mdp.39015104955862	336	7	,	,	PUNCT
mdp.39015104955862	336	8	d	d	PROPN
mdp.39015104955862	336	9	)	)	PUNCT
mdp.39015104955862	336	10	=	=	X
mdp.39015104955862	336	11	h¹/e	h¹/e	VERB
mdp.39015104955862	336	12	h	h	PROPN
mdp.39015104955862	336	13	"	"	PUNCT
mdp.39015104955862	336	14	µ*(hd)2/^	µ*(hd)2/^	X
mdp.39015104955862	336	15	<	<	PROPN
mdp.39015104955862	336	16	h	h	PROPN
mdp.39015104955862	336	17	®	®	PROPN
mdp.39015104955862	336	18	(	(	PUNCT
mdp.39015104955862	336	19	h	h	PROPN
mdp.39015104955862	336	20	,	,	PUNCT
mdp.39015104955862	336	21	a	a	NOUN
mdp.39015104955862	336	22	)	)	PUNCT
mdp.39015104955862	336	23	,	,	PUNCT
mdp.39015104955862	336	24	+	+	CCONJ
mdp.39015104955862	336	25	=	=	SYM
mdp.39015104955862	336	26	1	1	NUM
mdp.39015104955862	336	27	,	,	PUNCT
mdp.39015104955862	336	28	dh¹le	dh¹le	NOUN
mdp.39015104955862	336	29	>	>	X
mdp.39015104955862	336	30	40	40	NUM
mdp.39015104955862	336	31	.	.	PUNCT
mdp.39015104955862	337	1	=	=	NOUN
mdp.39015104955862	337	2	1	1	NUM
mdp.39015104955862	337	3	2	2	NUM
mdp.39015104955862	337	4	supx(h),v	supx(h),v	NOUN
mdp.39015104955862	337	5	/	/	SYM
mdp.39015104955862	337	6	x	x	SYM
mdp.39015104955862	337	7	{	{	PUNCT
mdp.39015104955862	337	8	{	{	PUNCT
mdp.39015104955862	337	9	^(21/6x	^(21/6x	SPACE
mdp.39015104955862	337	10	)	)	PUNCT
mdp.39015104955862	337	11	.	.	PUNCT
mdp.39015104955862	338	1	≤1	≤1	X
mdp.39015104955862	338	2	.	.	PUNCT
mdp.39015104955862	338	3	(	(	PUNCT
mdp.39015104955862	338	4	86	86	NUM
mdp.39015104955862	338	5	)	)	PUNCT
mdp.39015104955862	338	6	(	(	PUNCT
mdp.39015104955862	338	7	87	87	NUM
mdp.39015104955862	338	8	)	)	PUNCT
mdp.39015104955862	338	9	(	(	PUNCT
mdp.39015104955862	338	10	88	88	NUM
mdp.39015104955862	338	11	)	)	PUNCT
mdp.39015104955862	338	12	(	(	PUNCT
mdp.39015104955862	338	13	89	89	NUM
mdp.39015104955862	338	14	)	)	PUNCT
mdp.39015104955862	338	15	(	(	PUNCT
mdp.39015104955862	338	16	90	90	NUM
mdp.39015104955862	338	17	)	)	PUNCT
mdp.39015104955862	338	18	(	(	PUNCT
mdp.39015104955862	338	19	91	91	NUM
mdp.39015104955862	338	20	)	)	PUNCT
mdp.39015104955862	338	21	28	28	NUM
mdp.39015104955862	338	22	it	it	PRON
mdp.39015104955862	338	23	follows	follow	VERB
mdp.39015104955862	338	24	from	from	ADP
mdp.39015104955862	338	25	(	(	PUNCT
mdp.39015104955862	338	26	89	89	NUM
mdp.39015104955862	338	27	)	)	PUNCT
mdp.39015104955862	338	28	and	and	CCONJ
mdp.39015104955862	338	29	(	(	PUNCT
mdp.39015104955862	338	30	91	91	NUM
mdp.39015104955862	338	31	)	)	PUNCT
mdp.39015104955862	338	32	that	that	PRON
mdp.39015104955862	338	33	and	and	CCONJ
mdp.39015104955862	338	34	where	where	SCONJ
mdp.39015104955862	338	35	p	p	PROPN
mdp.39015104955862	338	36	is	be	AUX
mdp.39015104955862	338	37	some	some	DET
mdp.39015104955862	338	38	positive	positive	ADJ
mdp.39015104955862	338	39	function	function	NOUN
mdp.39015104955862	338	40	.	.	PUNCT
mdp.39015104955862	339	1	now	now	ADV
mdp.39015104955862	339	2	suppose	suppose	VERB
mdp.39015104955862	339	3	then	then	ADV
mdp.39015104955862	339	4	h	h	PROPN
mdp.39015104955862	339	5	>	>	X
mdp.39015104955862	339	6	implies	imply	VERB
mdp.39015104955862	339	7	μ	μ	PROPN
mdp.39015104955862	339	8	>	>	X
mdp.39015104955862	339	9	μo	μo	NOUN
mdp.39015104955862	339	10	and	and	CCONJ
mdp.39015104955862	339	11	since	since	SCONJ
mdp.39015104955862	339	12	§	§	PROPN
mdp.39015104955862	339	13	(	(	PUNCT
mdp.39015104955862	339	14	h	h	PROPN
mdp.39015104955862	339	15	,	,	PUNCT
mdp.39015104955862	339	16	λ	λ	NOUN
mdp.39015104955862	339	17	)	)	PUNCT
mdp.39015104955862	339	18	≤	≤	X
mdp.39015104955862	339	19	h¹/	h¹/	X
mdp.39015104955862	340	1	+	+	NUM
mdp.39015104955862	340	2	1/§h¹/	1/§h¹/	NUM
mdp.39015104955862	340	3	h"µ^(μx)2/1	h"µ^(μx)2/1	ADV
mdp.39015104955862	340	4	≤p(h	≤p(h	PROPN
mdp.39015104955862	340	5	)	)	PUNCT
mdp.39015104955862	340	6	,	,	PUNCT
mdp.39015104955862	340	7	h	h	PROPN
mdp.39015104955862	340	8	>	>	X
mdp.39015104955862	340	9	ho	ho	PROPN
mdp.39015104955862	340	10	,	,	PUNCT
mdp.39015104955862	340	11	we	we	PRON
mdp.39015104955862	340	12	have	have	VERB
mdp.39015104955862	340	13	h	h	PROPN
mdp.39015104955862	340	14	σμ	σμ	PROPN
mdp.39015104955862	340	15	.	.	PUNCT
mdp.39015104955862	341	1	λμ	λμ	X
mdp.39015104955862	341	2	>	>	X
mdp.39015104955862	341	3	μο	μο	PROPN
mdp.39015104955862	341	4	·	·	PUNCT
mdp.39015104955862	341	5	(	(	PUNCT
mdp.39015104955862	341	6	µ	µ	X
mdp.39015104955862	341	7	−	−	PROPN
mdp.39015104955862	341	8	1)μ−¹	1)μ−¹	NUM
mdp.39015104955862	341	9	(	(	PUNCT
mdp.39015104955862	341	10	4	4	NUM
mdp.39015104955862	341	11	-	-	SYM
mdp.39015104955862	341	12	1	1	NUM
mdp.39015104955862	341	13	)	)	PUNCT
mdp.39015104955862	341	14	in(μ-1	in(μ-1	PROPN
mdp.39015104955862	341	15	)	)	PUNCT
mdp.39015104955862	341	16	in	in	ADP
mdp.39015104955862	341	17	μ	μ	PROPN
mdp.39015104955862	341	18	=	=	SYM
mdp.39015104955862	341	19	μ	μ	PROPN
mdp.39015104955862	341	20	(	(	PUNCT
mdp.39015104955862	341	21	µ	µ	X
mdp.39015104955862	341	22	−	−	PROPN
mdp.39015104955862	341	23	1)μ-¹	1)μ-¹	NUM
mdp.39015104955862	341	24	≥	≥	NOUN
mdp.39015104955862	341	25	µ(¹−ε)µ	µ(¹−ε)µ	SPACE
mdp.39015104955862	341	26	,	,	PUNCT
mdp.39015104955862	341	27	µ	µ	PROPN
mdp.39015104955862	341	28	>	>	X
mdp.39015104955862	341	29	μo	μo	PROPN
mdp.39015104955862	341	30	.	.	PUNCT
mdp.39015104955862	342	1	it	it	PRON
mdp.39015104955862	342	2	follows	follow	VERB
mdp.39015104955862	342	3	from	from	ADP
mdp.39015104955862	342	4	(	(	PUNCT
mdp.39015104955862	342	5	93	93	NUM
mdp.39015104955862	342	6	)	)	PUNCT
mdp.39015104955862	342	7	,	,	PUNCT
mdp.39015104955862	342	8	(	(	PUNCT
mdp.39015104955862	342	9	94	94	NUM
mdp.39015104955862	342	10	)	)	PUNCT
mdp.39015104955862	342	11	,	,	PUNCT
mdp.39015104955862	342	12	(	(	PUNCT
mdp.39015104955862	342	13	88	88	NUM
mdp.39015104955862	342	14	)	)	PUNCT
mdp.39015104955862	342	15	,	,	PUNCT
mdp.39015104955862	342	16	and	and	CCONJ
mdp.39015104955862	342	17	(	(	PUNCT
mdp.39015104955862	342	18	95	95	NUM
mdp.39015104955862	342	19	)	)	PUNCT
mdp.39015104955862	342	20	that	that	SCONJ
mdp.39015104955862	342	21	h^h^(hx)2/^	h^h^(hx)2/^	PROPN
mdp.39015104955862	342	22	huμ^(μλ)2/1	huμ^(μλ)2/1	PROPN
mdp.39015104955862	342	23	<	<	PROPN
mdp.39015104955862	342	24	heμta	heμta	NOUN
mdp.39015104955862	342	25	(	(	PUNCT
mdp.39015104955862	342	26	w+)?/	w+)?/	VERB
mdp.39015104955862	342	27	>	>	X
mdp.39015104955862	342	28	<	<	X
mdp.39015104955862	342	29	µh({+1	µh({+1	PROPN
mdp.39015104955862	342	30	-	-	SYM
mdp.39015104955862	342	31	7	7	NUM
mdp.39015104955862	342	32	)	)	PUNCT
mdp.39015104955862	342	33	≤	≤	X
mdp.39015104955862	342	34	μ(1	μ(1	NOUN
mdp.39015104955862	342	35	-	-	PUNCT
mdp.39015104955862	342	36	e)μ	e)μ	X
mdp.39015104955862	342	37	<	<	X
mdp.39015104955862	342	38	(	(	PUNCT
mdp.39015104955862	342	39	μ	μ	PROPN
mdp.39015104955862	342	40	1)“–¹.	1)“–¹.	NUM
mdp.39015104955862	342	41	<	<	X
mdp.39015104955862	342	42	≤	≤	PROPN
mdp.39015104955862	342	43	(	(	PUNCT
mdp.39015104955862	342	44	µ	µ	X
mdp.39015104955862	342	45	−	−	NOUN
mdp.39015104955862	342	46	from	from	ADP
mdp.39015104955862	342	47	(	(	PUNCT
mdp.39015104955862	342	48	92	92	NUM
mdp.39015104955862	342	49	)	)	PUNCT
mdp.39015104955862	342	50	and	and	CCONJ
mdp.39015104955862	342	51	(	(	PUNCT
mdp.39015104955862	342	52	96	96	NUM
mdp.39015104955862	342	53	)	)	PUNCT
mdp.39015104955862	342	54	we	we	PRON
mdp.39015104955862	342	55	get	get	VERB
mdp.39015104955862	342	56	h"µ^(μλ)2/1	h"µ^(μλ)2/1	PROPN
mdp.39015104955862	342	57	≤	≤	PROPN
mdp.39015104955862	342	58	p(h	p(h	PROPN
mdp.39015104955862	342	59	)	)	PUNCT
mdp.39015104955862	342	60	(	(	PUNCT
mdp.39015104955862	342	61	µ	µ	X
mdp.39015104955862	342	62	−	−	PROPN
mdp.39015104955862	342	63	1)μ−¹	1)μ−¹	NUM
mdp.39015104955862	342	64	(	(	PUNCT
mdp.39015104955862	342	65	92	92	NUM
mdp.39015104955862	342	66	)	)	PUNCT
mdp.39015104955862	342	67	(	(	PUNCT
mdp.39015104955862	342	68	93	93	NUM
mdp.39015104955862	342	69	)	)	PUNCT
mdp.39015104955862	342	70	(	(	PUNCT
mdp.39015104955862	342	71	94	94	NUM
mdp.39015104955862	342	72	)	)	PUNCT
mdp.39015104955862	342	73	(	(	PUNCT
mdp.39015104955862	342	74	95	95	NUM
mdp.39015104955862	342	75	)	)	PUNCT
mdp.39015104955862	342	76	(	(	PUNCT
mdp.39015104955862	342	77	96	96	NUM
mdp.39015104955862	342	78	)	)	PUNCT
mdp.39015104955862	342	79	(	(	PUNCT
mdp.39015104955862	342	80	97	97	NUM
mdp.39015104955862	342	81	)	)	PUNCT
mdp.39015104955862	342	82	for	for	ADP
mdp.39015104955862	342	83	h	h	NOUN
mdp.39015104955862	342	84	>	>	PUNCT
mdp.39015104955862	342	85	max(ho	max(ho	NUM
mdp.39015104955862	342	86	,	,	PUNCT
mdp.39015104955862	342	87	he	he	PRON
mdp.39015104955862	342	88	)	)	PUNCT
mdp.39015104955862	342	89	.	.	PUNCT
mdp.39015104955862	343	1	multiplying	multiply	VERB
mdp.39015104955862	343	2	inequalities	inequality	NOUN
mdp.39015104955862	343	3	(	(	PUNCT
mdp.39015104955862	343	4	85	85	NUM
mdp.39015104955862	343	5	)	)	PUNCT
mdp.39015104955862	343	6	and	and	CCONJ
mdp.39015104955862	343	7	(	(	PUNCT
mdp.39015104955862	343	8	97	97	NUM
mdp.39015104955862	343	9	)	)	PUNCT
mdp.39015104955862	343	10	,	,	PUNCT
mdp.39015104955862	343	11	taking	take	VERB
mdp.39015104955862	343	12	the	the	DET
mdp.39015104955862	343	13	square	square	ADJ
mdp.39015104955862	343	14	roots	root	NOUN
mdp.39015104955862	343	15	of	of	ADP
mdp.39015104955862	343	16	the	the	DET
mdp.39015104955862	343	17	products	product	NOUN
mdp.39015104955862	343	18	and	and	CCONJ
mdp.39015104955862	343	19	recalling	recall	VERB
mdp.39015104955862	343	20	the	the	DET
mdp.39015104955862	343	21	definition	definition	NOUN
mdp.39015104955862	343	22	of	of	ADP
mdp.39015104955862	343	23	the	the	DET
mdp.39015104955862	343	24	function	function	NOUN
mdp.39015104955862	343	25	m	m	VERB
mdp.39015104955862	343	26	in	in	ADP
mdp.39015104955862	343	27	corollary	corollary	ADJ
mdp.39015104955862	343	28	2	2	NUM
mdp.39015104955862	343	29	,	,	PUNCT
mdp.39015104955862	343	30	we	we	PRON
mdp.39015104955862	343	31	see	see	VERB
mdp.39015104955862	343	32	that	that	DET
mdp.39015104955862	343	33	inequality	inequality	NOUN
mdp.39015104955862	343	34	(	(	PUNCT
mdp.39015104955862	343	35	62	62	NUM
mdp.39015104955862	343	36	)	)	PUNCT
mdp.39015104955862	343	37	with	with	ADP
mdp.39015104955862	343	38	m	m	PROPN
mdp.39015104955862	343	39	29	29	NUM
mdp.39015104955862	343	40	instead	instead	ADV
mdp.39015104955862	343	41	of	of	ADP
mdp.39015104955862	343	42	m	m	ADV
mdp.39015104955862	343	43	holds	hold	VERB
mdp.39015104955862	343	44	for	for	ADP
mdp.39015104955862	343	45	all	all	DET
mdp.39015104955862	343	46	h	h	NOUN
mdp.39015104955862	343	47	>	>	X
mdp.39015104955862	343	48	max(ho	max(ho	NUM
mdp.39015104955862	343	49	,	,	PUNCT
mdp.39015104955862	343	50	µ¶	µ¶	SPACE
mdp.39015104955862	343	51	)	)	PUNCT
mdp.39015104955862	343	52	.	.	PUNCT
mdp.39015104955862	344	1	as	as	SCONJ
mdp.39015104955862	344	2	we	we	PRON
mdp.39015104955862	344	3	have	have	AUX
mdp.39015104955862	344	4	already	already	ADV
mdp.39015104955862	344	5	mentioned	mention	VERB
mdp.39015104955862	344	6	above	above	ADV
mdp.39015104955862	344	7	,	,	PUNCT
mdp.39015104955862	344	8	this	this	PRON
mdp.39015104955862	344	9	implies	imply	VERB
mdp.39015104955862	344	10	the	the	DET
mdp.39015104955862	344	11	u₂-invariance	u₂-invariance	NOUN
mdp.39015104955862	344	12	of	of	ADP
mdp.39015104955862	344	13	the	the	DET
mdp.39015104955862	344	14	class	class	NOUN
mdp.39015104955862	344	15	d({mk	d({mk	PROPN
mdp.39015104955862	344	16	}	}	PUNCT
mdp.39015104955862	344	17	)	)	PUNCT
mdp.39015104955862	344	18	.	.	PUNCT
mdp.39015104955862	345	1	corollary	corollary	ADJ
mdp.39015104955862	345	2	2	2	NUM
mdp.39015104955862	345	3	is	be	AUX
mdp.39015104955862	345	4	established	establish	VERB
mdp.39015104955862	345	5	.	.	PUNCT
mdp.39015104955862	346	1	the	the	DET
mdp.39015104955862	346	2	next	next	ADJ
mdp.39015104955862	346	3	assertion	assertion	NOUN
mdp.39015104955862	346	4	follows	follow	VERB
mdp.39015104955862	346	5	from	from	ADP
mdp.39015104955862	346	6	corollary	corollary	ADJ
mdp.39015104955862	346	7	2	2	NUM
mdp.39015104955862	346	8	.	.	PUNCT
mdp.39015104955862	347	1	corollary	corollary	ADJ
mdp.39015104955862	347	2	3	3	NUM
mdp.39015104955862	347	3	suppose	suppose	VERB
mdp.39015104955862	347	4	mk	mk	PROPN
mdp.39015104955862	347	5	=	=	PROPN
mdp.39015104955862	347	6	k	k	PROPN
mdp.39015104955862	347	7	*	*	PROPN
mdp.39015104955862	347	8	,	,	PUNCT
mdp.39015104955862	347	9	k	k	PROPN
mdp.39015104955862	347	10	≥	≥	X
mdp.39015104955862	347	11	0	0	NUM
mdp.39015104955862	347	12	,	,	PUNCT
mdp.39015104955862	347	13	where	where	SCONJ
mdp.39015104955862	347	14	0	0	PUNCT
mdp.39015104955862	347	15	<	<	X
mdp.39015104955862	347	16	1	1	NUM
mdp.39015104955862	347	17	.	.	PUNCT
mdp.39015104955862	348	1	then	then	ADV
mdp.39015104955862	348	2	the	the	DET
mdp.39015104955862	348	3	class	class	NOUN
mdp.39015104955862	348	4	d({m	d({m	NOUN
mdp.39015104955862	348	5	}	}	PUNCT
mdp.39015104955862	348	6	)	)	PUNCT
mdp.39015104955862	348	7	is	be	AUX
mdp.39015104955862	348	8	u₂-invariant	u₂-invariant	PROPN
mdp.39015104955862	348	9	.	.	PUNCT
mdp.39015104955862	349	1	corollary	corollary	ADJ
mdp.39015104955862	349	2	4	4	NUM
mdp.39015104955862	349	3	if	if	SCONJ
mdp.39015104955862	349	4	mk	mk	PROPN
mdp.39015104955862	349	5	mx	mx	PROPN
mdp.39015104955862	349	6	=	=	PROPN
mdp.39015104955862	349	7	kk/²	kk/²	PROPN
mdp.39015104955862	349	8	,	,	PUNCT
mdp.39015104955862	349	9	k	k	PROPN
mdp.39015104955862	349	10	≥	≥	X
mdp.39015104955862	349	11	0	0	NUM
mdp.39015104955862	349	12	,	,	PUNCT
mdp.39015104955862	349	13	then	then	ADV
mdp.39015104955862	349	14	the	the	DET
mdp.39015104955862	349	15	class	class	NOUN
mdp.39015104955862	349	16	d({m	d({m	NOUN
mdp.39015104955862	349	17	}	}	PUNCT
mdp.39015104955862	349	18	)	)	PUNCT
mdp.39015104955862	349	19	is	be	AUX
mdp.39015104955862	349	20	not	not	PART
mdp.39015104955862	349	21	u₂-invariant	u₂-invariant	ADJ
mdp.39015104955862	349	22	.	.	PUNCT
mdp.39015104955862	350	1	proof	proof	PROPN
mdp.39015104955862	350	2	.	.	PUNCT
mdp.39015104955862	351	1	assume	assume	VERB
mdp.39015104955862	351	2	d({m₁	d({m₁	ADJ
mdp.39015104955862	351	3	}	}	PUNCT
mdp.39015104955862	351	4	)	)	PUNCT
mdp.39015104955862	351	5	is	be	AUX
mdp.39015104955862	351	6	u₂-invariant	u₂-invariant	PROPN
mdp.39015104955862	351	7	.	.	PUNCT
mdp.39015104955862	352	1	then	then	ADV
mdp.39015104955862	352	2	,	,	PUNCT
mdp.39015104955862	352	3	by	by	ADP
mdp.39015104955862	352	4	theorem	theorem	NOUN
mdp.39015104955862	352	5	5	5	NUM
mdp.39015104955862	352	6	,	,	PUNCT
mdp.39015104955862	352	7	the	the	DET
mdp.39015104955862	352	8	inequality	inequality	NOUN
mdp.39015104955862	352	9	(	(	PUNCT
mdp.39015104955862	352	10	80	80	NUM
mdp.39015104955862	352	11	)	)	PUNCT
mdp.39015104955862	352	12	should	should	AUX
mdp.39015104955862	352	13	be	be	AUX
mdp.39015104955862	352	14	true	true	ADJ
mdp.39015104955862	352	15	.	.	PUNCT
mdp.39015104955862	353	1	we	we	PRON
mdp.39015104955862	353	2	get	get	VERB
mdp.39015104955862	353	3	in	in	ADP
mdp.39015104955862	353	4	this	this	DET
mdp.39015104955862	353	5	case	case	NOUN
mdp.39015104955862	353	6	(	(	PUNCT
mdp.39015104955862	353	7	2n	2n	X
mdp.39015104955862	353	8	+	+	PUNCT
mdp.39015104955862	353	9	m)n+m/2	m)n+m/2	PROPN
mdp.39015104955862	353	10	n	n	CCONJ
mdp.39015104955862	353	11	!	!	PUNCT
mdp.39015104955862	354	1	for	for	ADP
mdp.39015104955862	354	2	all	all	DET
mdp.39015104955862	354	3	h	h	NOUN
mdp.39015104955862	354	4	>	>	X
mdp.39015104955862	354	5	ho	ho	PROPN
mdp.39015104955862	354	6	,	,	PUNCT
mdp.39015104955862	354	7	n	n	CCONJ
mdp.39015104955862	354	8	≥	≥	X
mdp.39015104955862	354	9	0	0	NUM
mdp.39015104955862	354	10	,	,	PUNCT
mdp.39015104955862	354	11	and	and	CCONJ
mdp.39015104955862	354	12	m	m	X
mdp.39015104955862	354	13	≥	≥	X
mdp.39015104955862	354	14	0	0	NUM
mdp.39015104955862	354	15	.	.	PUNCT
mdp.39015104955862	355	1	since	since	SCONJ
mdp.39015104955862	355	2	n">n	n">n	PROPN
mdp.39015104955862	355	3	!	!	PUNCT
mdp.39015104955862	356	1	and	and	CCONJ
mdp.39015104955862	356	2	n	n	X
mdp.39015104955862	356	3	<	<	X
mdp.39015104955862	356	4	2n	2n	NUM
mdp.39015104955862	356	5	+	+	ADV
mdp.39015104955862	356	6	m	m	NOUN
mdp.39015104955862	356	7	,	,	PUNCT
mdp.39015104955862	356	8	we	we	PRON
mdp.39015104955862	356	9	get	get	VERB
mdp.39015104955862	356	10	from	from	ADP
mdp.39015104955862	356	11	(	(	PUNCT
mdp.39015104955862	356	12	98	98	NUM
mdp.39015104955862	356	13	)	)	PUNCT
mdp.39015104955862	356	14	(	(	PUNCT
mdp.39015104955862	356	15	2n	2n	NUM
mdp.39015104955862	356	16	+	+	CCONJ
mdp.39015104955862	356	17	m)m/2h	m)m/2h	PROPN
mdp.39015104955862	356	18	"	"	PUNCT
mdp.39015104955862	356	19	≤	≤	PROPN
mdp.39015104955862	356	20	p(h)m+1	p(h)m+1	PROPN
mdp.39015104955862	356	21	mm/2	mm/2	NOUN
mdp.39015104955862	356	22	.	.	PUNCT
mdp.39015104955862	357	1	·	·	PUNCT
mdp.39015104955862	357	2	h	h	PROPN
mdp.39015104955862	357	3	"	"	PUNCT
mdp.39015104955862	357	4	≤	≤	PROPN
mdp.39015104955862	357	5	p(h)m+¹mm/2	p(h)m+¹mm/2	PROPN
mdp.39015104955862	357	6	(	(	PUNCT
mdp.39015104955862	357	7	98	98	NUM
mdp.39015104955862	357	8	)	)	PUNCT
mdp.39015104955862	357	9	fixing	fix	VERB
mdp.39015104955862	357	10	m	m	NOUN
mdp.39015104955862	357	11	and	and	CCONJ
mdp.39015104955862	357	12	allowing	allow	VERB
mdp.39015104955862	357	13	n	n	CCONJ
mdp.39015104955862	357	14	to	to	PART
mdp.39015104955862	357	15	tend	tend	VERB
mdp.39015104955862	357	16	to	to	PART
mdp.39015104955862	357	17	infinity	infinity	VERB
mdp.39015104955862	357	18	,	,	PUNCT
mdp.39015104955862	357	19	we	we	PRON
mdp.39015104955862	357	20	get	get	VERB
mdp.39015104955862	357	21	a	a	DET
mdp.39015104955862	357	22	contradiction	contradiction	NOUN
mdp.39015104955862	357	23	.	.	PUNCT
mdp.39015104955862	358	1	hence	hence	ADV
mdp.39015104955862	358	2	,	,	PUNCT
mdp.39015104955862	358	3	the	the	DET
mdp.39015104955862	358	4	class	class	NOUN
mdp.39015104955862	358	5	d({m	d({m	NOUN
mdp.39015104955862	358	6	}	}	PUNCT
mdp.39015104955862	358	7	)	)	PUNCT
mdp.39015104955862	358	8	is	be	AUX
mdp.39015104955862	358	9	not	not	PART
mdp.39015104955862	358	10	u	u	ADJ
mdp.39015104955862	358	11	-	-	ADJ
mdp.39015104955862	358	12	invariant	invariant	ADJ
mdp.39015104955862	358	13	.	.	PUNCT
mdp.39015104955862	359	1	corollary	corollary	ADJ
mdp.39015104955862	359	2	4	4	NUM
mdp.39015104955862	359	3	is	be	AUX
mdp.39015104955862	359	4	proved	prove	VERB
mdp.39015104955862	359	5	.	.	PUNCT
mdp.39015104955862	360	1	the	the	DET
mdp.39015104955862	360	2	next	next	ADJ
mdp.39015104955862	360	3	theorem	theorem	NOUN
mdp.39015104955862	360	4	is	be	AUX
mdp.39015104955862	360	5	analogous	analogous	ADJ
mdp.39015104955862	360	6	to	to	ADP
mdp.39015104955862	360	7	theorem	theorem	NOUN
mdp.39015104955862	360	8	5	5	NUM
mdp.39015104955862	360	9	.	.	PUNCT
mdp.39015104955862	361	1	it	it	PRON
mdp.39015104955862	361	2	concerns	concern	VERB
mdp.39015104955862	361	3	the	the	DET
mdp.39015104955862	361	4	u₂-invariance	u₂-invariance	NOUN
mdp.39015104955862	361	5	of	of	ADP
mdp.39015104955862	361	6	classes	class	NOUN
mdp.39015104955862	361	7	d'({m	d'({m	PROPN
mdp.39015104955862	361	8	}	}	PUNCT
mdp.39015104955862	361	9	)	)	PUNCT
mdp.39015104955862	361	10	.	.	PUNCT
mdp.39015104955862	362	1	the	the	DET
mdp.39015104955862	362	2	action	action	NOUN
mdp.39015104955862	362	3	of	of	ADP
mdp.39015104955862	362	4	{	{	PUNCT
mdp.39015104955862	362	5	u₂	u₂	ADJ
mdp.39015104955862	362	6	}	}	PUNCT
mdp.39015104955862	362	7	on	on	ADP
mdp.39015104955862	362	8	d'({m	d'({m	PROPN
mdp.39015104955862	362	9	}	}	PUNCT
mdp.39015104955862	362	10	)	)	PUNCT
mdp.39015104955862	362	11	is	be	AUX
mdp.39015104955862	362	12	defined	define	VERB
mdp.39015104955862	362	13	by	by	ADP
mdp.39015104955862	362	14	u.(t)($	u.(t)($	ADJ
mdp.39015104955862	362	15	)	)	PUNCT
mdp.39015104955862	362	16	=	=	NOUN
mdp.39015104955862	362	17	г(u₂	г(u₂	PROPN
mdp.39015104955862	362	18	(	(	PUNCT
mdp.39015104955862	362	19	)	)	PUNCT
mdp.39015104955862	362	20	)	)	PUNCT
mdp.39015104955862	362	21	,	,	PUNCT
mdp.39015104955862	362	22	t€	t€	NUM
mdp.39015104955862	362	23	d'({mk	d'({mk	NOUN
mdp.39015104955862	362	24	}	}	PUNCT
mdp.39015104955862	362	25	)	)	PUNCT
mdp.39015104955862	362	26	,	,	PUNCT
mdp.39015104955862	362	27	¢	¢	PROPN
mdp.39015104955862	362	28	€	€	PUNCT
mdp.39015104955862	362	29	d({m	d({m	PROPN
mdp.39015104955862	362	30	⭑	⭑	NOUN
mdp.39015104955862	362	31	}	}	PUNCT
mdp.39015104955862	362	32	)	)	PUNCT
mdp.39015104955862	362	33	.	.	PUNCT
mdp.39015104955862	363	1	30	30	NUM
mdp.39015104955862	363	2	theorem	theorem	NOUN
mdp.39015104955862	363	3	6	6	NUM
mdp.39015104955862	363	4	let	let	VERB
mdp.39015104955862	363	5	{	{	PUNCT
mdp.39015104955862	363	6	m	m	VERB
mdp.39015104955862	363	7	}	}	PUNCT
mdp.39015104955862	363	8	be	be	AUX
mdp.39015104955862	363	9	a	a	DET
mdp.39015104955862	363	10	sequence	sequence	NOUN
mdp.39015104955862	363	11	,	,	PUNCT
mdp.39015104955862	363	12	satisfying	satisfy	VERB
mdp.39015104955862	363	13	(	(	PUNCT
mdp.39015104955862	363	14	60	60	NUM
mdp.39015104955862	363	15	)	)	PUNCT
mdp.39015104955862	363	16	.	.	PUNCT
mdp.39015104955862	364	1	then	then	ADV
mdp.39015104955862	364	2	the	the	DET
mdp.39015104955862	364	3	validity	validity	NOUN
mdp.39015104955862	364	4	of	of	ADP
mdp.39015104955862	364	5	inclusion	inclusion	NOUN
mdp.39015104955862	364	6	u₂(d'({m	u₂(d'({m	PROPN
mdp.39015104955862	364	7	}	}	PUNCT
mdp.39015104955862	364	8	)	)	PUNCT
mdp.39015104955862	364	9	)	)	PUNCT
mdp.39015104955862	365	1	c	c	NOUN
mdp.39015104955862	365	2	d'({mk	d'({mk	NOUN
mdp.39015104955862	365	3	}	}	PUNCT
mdp.39015104955862	365	4	)	)	PUNCT
mdp.39015104955862	365	5	is	be	AUX
mdp.39015104955862	365	6	equivalent	equivalent	ADJ
mdp.39015104955862	365	7	to	to	ADP
mdp.39015104955862	365	8	condition	condition	NOUN
mdp.39015104955862	365	9	b	b	PROPN
mdp.39015104955862	365	10	)	)	PUNCT
mdp.39015104955862	365	11	or	or	CCONJ
mdp.39015104955862	365	12	condition	condition	NOUN
mdp.39015104955862	365	13	c	c	PROPN
mdp.39015104955862	365	14	)	)	PUNCT
mdp.39015104955862	365	15	in	in	ADP
mdp.39015104955862	365	16	theorem	theorem	PROPN
mdp.39015104955862	365	17	5	5	NUM
mdp.39015104955862	365	18	.	.	PUNCT
mdp.39015104955862	366	1	theorem	theorem	PROPN
mdp.39015104955862	366	2	6	6	NUM
mdp.39015104955862	366	3	follows	follow	VERB
mdp.39015104955862	366	4	easily	easily	ADV
mdp.39015104955862	366	5	from	from	ADP
mdp.39015104955862	366	6	theorem	theorem	NOUN
mdp.39015104955862	366	7	5	5	NUM
mdp.39015104955862	366	8	and	and	CCONJ
mdp.39015104955862	366	9	remark	remark	VERB
mdp.39015104955862	366	10	3	3	NUM
mdp.39015104955862	366	11	.	.	SYM
mdp.39015104955862	366	12	6	6	NUM
mdp.39015104955862	366	13	summary	summary	NOUN
mdp.39015104955862	366	14	and	and	CCONJ
mdp.39015104955862	366	15	conclusions	conclusion	VERB
mdp.39015104955862	366	16	the	the	DET
mdp.39015104955862	366	17	purpose	purpose	NOUN
mdp.39015104955862	366	18	of	of	ADP
mdp.39015104955862	366	19	the	the	DET
mdp.39015104955862	366	20	research	research	NOUN
mdp.39015104955862	366	21	carried	carry	VERB
mdp.39015104955862	366	22	out	out	ADP
mdp.39015104955862	366	23	under	under	ADP
mdp.39015104955862	366	24	this	this	DET
mdp.39015104955862	366	25	contract	contract	NOUN
mdp.39015104955862	366	26	is	be	AUX
mdp.39015104955862	366	27	that	that	PRON
mdp.39015104955862	366	28	of	of	ADP
mdp.39015104955862	366	29	develop	develop	VERB
mdp.39015104955862	366	30	、	、	X
mdp.39015104955862	367	1	g	g	ADP
mdp.39015104955862	367	2	the	the	DET
mdp.39015104955862	367	3	"	"	PUNCT
mdp.39015104955862	367	4	chaos	chaos	NOUN
mdp.39015104955862	367	5	dynamics	dynamic	NOUN
mdp.39015104955862	367	6	"	"	PUNCT
mdp.39015104955862	367	7	approach	approach	NOUN
mdp.39015104955862	367	8	to	to	ADP
mdp.39015104955862	367	9	the	the	DET
mdp.39015104955862	367	10	free	free	ADJ
mdp.39015104955862	367	11	sheared	shear	VERB
mdp.39015104955862	367	12	atmosphere	atmosphere	NOUN
mdp.39015104955862	367	13	which	which	PRON
mdp.39015104955862	367	14	parallels	parallel	VERB
mdp.39015104955862	367	15	the	the	DET
mdp.39015104955862	367	16	successful	successful	ADJ
mdp.39015104955862	367	17	analysis	analysis	NOUN
mdp.39015104955862	367	18	carried	carry	VERB
mdp.39015104955862	367	19	out	out	ADP
mdp.39015104955862	367	20	by	by	ADP
mdp.39015104955862	367	21	ed	ed	PROPN
mdp.39015104955862	367	22	lorenz	lorenz	PROPN
mdp.39015104955862	367	23	on	on	ADP
mdp.39015104955862	367	24	the	the	DET
mdp.39015104955862	367	25	benard	benard	NOUN
mdp.39015104955862	367	26	flow	flow	NOUN
mdp.39015104955862	367	27	(	(	PUNCT
mdp.39015104955862	367	28	which	which	PRON
mdp.39015104955862	367	29	is	be	AUX
mdp.39015104955862	367	30	a	a	DET
mdp.39015104955862	367	31	physical	physical	ADJ
mdp.39015104955862	367	32	model	model	NOUN
mdp.39015104955862	367	33	of	of	ADP
mdp.39015104955862	367	34	the	the	DET
mdp.39015104955862	367	35	troposphere	troposphere	NOUN
mdp.39015104955862	367	36	)	)	PUNCT
mdp.39015104955862	367	37	.	.	PUNCT
mdp.39015104955862	368	1	the	the	DET
mdp.39015104955862	368	2	basic	basic	ADJ
mdp.39015104955862	368	3	idea	idea	NOUN
mdp.39015104955862	368	4	of	of	ADP
mdp.39015104955862	368	5	the	the	DET
mdp.39015104955862	368	6	chaos	chaos	NOUN
mdp.39015104955862	368	7	dynamical	dynamical	ADJ
mdp.39015104955862	368	8	analysis	analysis	NOUN
mdp.39015104955862	368	9	is	be	AUX
mdp.39015104955862	368	10	that	that	PRON
mdp.39015104955862	368	11	of	of	ADP
mdp.39015104955862	368	12	(	(	PUNCT
mdp.39015104955862	368	13	1	1	X
mdp.39015104955862	368	14	)	)	PUNCT
mdp.39015104955862	368	15	expanding	expand	VERB
mdp.39015104955862	368	16	the	the	DET
mdp.39015104955862	368	17	fluid	fluid	ADJ
mdp.39015104955862	368	18	equations	equation	NOUN
mdp.39015104955862	368	19	in	in	ADP
mdp.39015104955862	368	20	terms	term	NOUN
mdp.39015104955862	368	21	of	of	ADP
mdp.39015104955862	368	22	basis	basis	NOUN
mdp.39015104955862	368	23	functions	function	NOUN
mdp.39015104955862	368	24	suited	suit	VERB
mdp.39015104955862	368	25	to	to	ADP
mdp.39015104955862	368	26	the	the	DET
mdp.39015104955862	368	27	geometry	geometry	NOUN
mdp.39015104955862	368	28	and	and	CCONJ
mdp.39015104955862	368	29	physics	physics	NOUN
mdp.39015104955862	368	30	of	of	ADP
mdp.39015104955862	368	31	the	the	DET
mdp.39015104955862	368	32	problem	problem	NOUN
mdp.39015104955862	368	33	,	,	PUNCT
mdp.39015104955862	368	34	(	(	PUNCT
mdp.39015104955862	368	35	2	2	X
mdp.39015104955862	368	36	)	)	PUNCT
mdp.39015104955862	368	37	truncate	truncate	ADJ
mdp.39015104955862	368	38	the	the	DET
mdp.39015104955862	368	39	expansion	expansion	NOUN
mdp.39015104955862	368	40	to	to	ADP
mdp.39015104955862	368	41	the	the	DET
mdp.39015104955862	368	42	"	"	PUNCT
mdp.39015104955862	368	43	lowest	low	ADJ
mdp.39015104955862	368	44	"	"	PUNCT
mdp.39015104955862	368	45	post	post	ADJ
mdp.39015104955862	368	46	-	-	ADJ
mdp.39015104955862	368	47	linear	linear	ADJ
mdp.39015104955862	368	48	terms	term	NOUN
mdp.39015104955862	368	49	(	(	PUNCT
mdp.39015104955862	368	50	quadratic	quadratic	ADJ
mdp.39015104955862	368	51	in	in	ADP
mdp.39015104955862	368	52	lorenz	lorenz	PROPN
mdp.39015104955862	368	53	'	'	PART
mdp.39015104955862	368	54	work	work	NOUN
mdp.39015104955862	368	55	)	)	PUNCT
mdp.39015104955862	368	56	,	,	PUNCT
mdp.39015104955862	368	57	(	(	PUNCT
mdp.39015104955862	368	58	3	3	X
mdp.39015104955862	368	59	)	)	PUNCT
mdp.39015104955862	368	60	deduce	deduce	VERB
mdp.39015104955862	368	61	an	an	DET
mdp.39015104955862	368	62	iterative	iterative	ADJ
mdp.39015104955862	368	63	map	map	NOUN
mdp.39015104955862	368	64	appropriate	appropriate	ADJ
mdp.39015104955862	368	65	to	to	ADP
mdp.39015104955862	368	66	the	the	DET
mdp.39015104955862	368	67	(	(	PUNCT
mdp.39015104955862	368	68	strange	strange	ADJ
mdp.39015104955862	368	69	)	)	PUNCT
mdp.39015104955862	368	70	attractor	attractor	NOUN
mdp.39015104955862	368	71	given	give	VERB
mdp.39015104955862	368	72	by	by	ADP
mdp.39015104955862	368	73	the	the	DET
mdp.39015104955862	368	74	truncated	truncated	ADJ
mdp.39015104955862	368	75	postlinear	postlinear	ADJ
mdp.39015104955862	368	76	dynamics	dynamic	NOUN
mdp.39015104955862	368	77	(	(	PUNCT
mdp.39015104955862	368	78	the	the	DET
mdp.39015104955862	368	79	lorenz	lorenz	NOUN
mdp.39015104955862	368	80	"	"	PUNCT
mdp.39015104955862	368	81	mask	mask	NOUN
mdp.39015104955862	368	82	"	"	PUNCT
mdp.39015104955862	368	83	in	in	ADP
mdp.39015104955862	368	84	the	the	DET
mdp.39015104955862	368	85	case	case	NOUN
mdp.39015104955862	368	86	of	of	ADP
mdp.39015104955862	368	87	the	the	DET
mdp.39015104955862	368	88	benard	benard	ADJ
mdp.39015104955862	368	89	problem	problem	NOUN
mdp.39015104955862	368	90	)	)	PUNCT
mdp.39015104955862	368	91	,	,	PUNCT
mdp.39015104955862	368	92	and	and	CCONJ
mdp.39015104955862	368	93	(	(	PUNCT
mdp.39015104955862	368	94	4	4	X
mdp.39015104955862	368	95	)	)	PUNCT
mdp.39015104955862	368	96	calculate	calculate	VERB
mdp.39015104955862	368	97	the	the	DET
mdp.39015104955862	368	98	critical	critical	ADJ
mdp.39015104955862	368	99	value	value	NOUN
mdp.39015104955862	368	100	of	of	ADP
mdp.39015104955862	368	101	the	the	DET
mdp.39015104955862	368	102	parameter(s	parameter(s	NOUN
mdp.39015104955862	368	103	)	)	PUNCT
mdp.39015104955862	368	104	that	that	PRON
mdp.39015104955862	368	105	correspond	correspond	VERB
mdp.39015104955862	368	106	to	to	ADP
mdp.39015104955862	368	107	both	both	DET
mdp.39015104955862	368	108	the	the	DET
mdp.39015104955862	368	109	onset	onset	NOUN
mdp.39015104955862	368	110	of	of	ADP
mdp.39015104955862	368	111	instability	instability	NOUN
mdp.39015104955862	368	112	(	(	PUNCT
mdp.39015104955862	368	113	this	this	DET
mdp.39015104955862	368	114	critical	critical	ADJ
mdp.39015104955862	368	115	value	value	NOUN
mdp.39015104955862	368	116	can	can	AUX
mdp.39015104955862	368	117	usually	usually	ADV
mdp.39015104955862	368	118	be	be	AUX
mdp.39015104955862	368	119	reached	reach	VERB
mdp.39015104955862	368	120	by	by	ADP
mdp.39015104955862	368	121	the	the	DET
mdp.39015104955862	368	122	linear	linear	PROPN
mdp.39015104955862	368	123	theory	theory	NOUN
mdp.39015104955862	368	124	)	)	PUNCT
mdp.39015104955862	368	125	and	and	CCONJ
mdp.39015104955862	368	126	,	,	PUNCT
mdp.39015104955862	368	127	most	most	ADV
mdp.39015104955862	368	128	important	important	ADJ
mdp.39015104955862	368	129	,	,	PUNCT
mdp.39015104955862	368	130	to	to	ADP
mdp.39015104955862	368	131	the	the	DET
mdp.39015104955862	368	132	onset	onset	NOUN
mdp.39015104955862	368	133	of	of	ADP
mdp.39015104955862	368	134	chaos	chaos	NOUN
mdp.39015104955862	368	135	,	,	PUNCT
mdp.39015104955862	368	136	which	which	PRON
mdp.39015104955862	368	137	is	be	AUX
mdp.39015104955862	368	138	interpreted	interpret	VERB
mdp.39015104955862	368	139	as	as	ADP
mdp.39015104955862	368	140	the	the	DET
mdp.39015104955862	368	141	onset	onset	NOUN
mdp.39015104955862	368	142	of	of	ADP
mdp.39015104955862	368	143	turbulence	turbulence	NOUN
mdp.39015104955862	368	144	.	.	PUNCT
mdp.39015104955862	369	1	in	in	ADP
mdp.39015104955862	369	2	the	the	DET
mdp.39015104955862	369	3	case	case	NOUN
mdp.39015104955862	369	4	of	of	ADP
mdp.39015104955862	369	5	the	the	DET
mdp.39015104955862	369	6	free	free	ADJ
mdp.39015104955862	369	7	sheared	shear	VERB
mdp.39015104955862	369	8	atmosphere	atmosphere	NOUN
mdp.39015104955862	369	9	the	the	DET
mdp.39015104955862	369	10	relevant	relevant	ADJ
mdp.39015104955862	369	11	parameter	parameter	NOUN
mdp.39015104955862	369	12	is	be	AUX
mdp.39015104955862	369	13	the	the	DET
mdp.39015104955862	369	14	richardson	richardson	PROPN
mdp.39015104955862	369	15	number	number	NOUN
mdp.39015104955862	369	16	.	.	PUNCT
mdp.39015104955862	370	1	its	its	PRON
mdp.39015104955862	370	2	critical	critical	ADJ
mdp.39015104955862	370	3	values	value	NOUN
mdp.39015104955862	370	4	are	be	AUX
mdp.39015104955862	370	5	at	at	ADP
mdp.39015104955862	370	6	the	the	DET
mdp.39015104955862	370	7	present	present	ADJ
mdp.39015104955862	370	8	not	not	PART
mdp.39015104955862	370	9	understood	understand	VERB
mdp.39015104955862	370	10	.	.	PUNCT
mdp.39015104955862	371	1	the	the	DET
mdp.39015104955862	371	2	major	major	ADJ
mdp.39015104955862	371	3	portion	portion	NOUN
mdp.39015104955862	371	4	of	of	ADP
mdp.39015104955862	371	5	our	our	PRON
mdp.39015104955862	371	6	calculations	calculation	NOUN
mdp.39015104955862	371	7	have	have	AUX
mdp.39015104955862	371	8	been	be	AUX
mdp.39015104955862	371	9	carried	carry	VERB
mdp.39015104955862	371	10	out	out	ADP
mdp.39015104955862	371	11	for	for	ADP
mdp.39015104955862	371	12	the	the	DET
mdp.39015104955862	371	13	taylordyson	taylordyson	NOUN
mdp.39015104955862	371	14	atmosphere	atmosphere	NOUN
mdp.39015104955862	371	15	in	in	ADP
mdp.39015104955862	371	16	which	which	PRON
mdp.39015104955862	371	17	both	both	CCONJ
mdp.39015104955862	371	18	the	the	DET
mdp.39015104955862	371	19	pressure	pressure	NOUN
mdp.39015104955862	371	20	and	and	CCONJ
mdp.39015104955862	371	21	the	the	DET
mdp.39015104955862	371	22	density	density	NOUN
mdp.39015104955862	371	23	decrease	decrease	NOUN
mdp.39015104955862	371	24	exponentially	exponentially	ADV
mdp.39015104955862	371	25	with	with	ADP
mdp.39015104955862	371	26	height	height	NOUN
mdp.39015104955862	371	27	above	above	ADP
mdp.39015104955862	371	28	the	the	DET
mdp.39015104955862	371	29	ground	ground	NOUN
mdp.39015104955862	371	30	and	and	CCONJ
mdp.39015104955862	371	31	the	the	DET
mdp.39015104955862	371	32	horizontal	horizontal	ADJ
mdp.39015104955862	371	33	shear	shear	NOUN
mdp.39015104955862	371	34	is	be	AUX
mdp.39015104955862	371	35	given	give	VERB
mdp.39015104955862	371	36	by	by	ADP
mdp.39015104955862	371	37	a	a	DET
mdp.39015104955862	371	38	couette	couette	NOUN
mdp.39015104955862	371	39	flow	flow	NOUN
mdp.39015104955862	371	40	.	.	PUNCT
mdp.39015104955862	372	1	this	this	DET
mdp.39015104955862	372	2	model	model	NOUN
mdp.39015104955862	372	3	has	have	AUX
mdp.39015104955862	372	4	been	be	AUX
mdp.39015104955862	372	5	analyzed	analyze	VERB
mdp.39015104955862	372	6	with	with	ADP
mdp.39015104955862	372	7	fourier	fourier	NOUN
mdp.39015104955862	372	8	analasis	analasis	NOUN
mdp.39015104955862	372	9	which	which	PRON
mdp.39015104955862	372	10	fails	fail	VERB
mdp.39015104955862	372	11	to	to	PART
mdp.39015104955862	372	12	yield	yield	VERB
mdp.39015104955862	372	13	unstable	unstable	ADJ
mdp.39015104955862	372	14	!	!	PUNCT
mdp.39015104955862	373	1	31	31	NUM
mdp.39015104955862	373	2	modes	mode	NOUN
mdp.39015104955862	373	3	even	even	ADV
mdp.39015104955862	373	4	in	in	ADP
mdp.39015104955862	373	5	the	the	DET
mdp.39015104955862	373	6	most	most	ADV
mdp.39015104955862	373	7	refined	refined	ADJ
mdp.39015104955862	373	8	forms.since	forms.since	NOUN
mdp.39015104955862	373	9	the	the	DET
mdp.39015104955862	373	10	standard	standard	ADJ
mdp.39015104955862	373	11	method	method	NOUN
mdp.39015104955862	373	12	fails	fail	VERB
mdp.39015104955862	373	13	to	to	PART
mdp.39015104955862	373	14	give	give	VERB
mdp.39015104955862	373	15	insight	insight	NOUN
mdp.39015104955862	373	16	into	into	ADP
mdp.39015104955862	373	17	the	the	DET
mdp.39015104955862	373	18	critical	critical	ADJ
mdp.39015104955862	373	19	richardson	richardson	PROPN
mdp.39015104955862	373	20	number	number	NOUN
mdp.39015104955862	373	21	,	,	PUNCT
mdp.39015104955862	373	22	we	we	PRON
mdp.39015104955862	373	23	study	study	VERB
mdp.39015104955862	373	24	an	an	DET
mdp.39015104955862	373	25	alternative	alternative	NOUN
mdp.39015104955862	373	26	that	that	PRON
mdp.39015104955862	373	27	utilizes	utilize	VERB
mdp.39015104955862	373	28	modes	mode	NOUN
mdp.39015104955862	373	29	with	with	ADP
mdp.39015104955862	373	30	finite	finite	ADJ
mdp.39015104955862	373	31	energy	energy	NOUN
mdp.39015104955862	373	32	from	from	ADP
mdp.39015104955862	373	33	the	the	DET
mdp.39015104955862	373	34	start	start	NOUN
mdp.39015104955862	373	35	.	.	PUNCT
mdp.39015104955862	374	1	our	our	PRON
mdp.39015104955862	374	2	methodology	methodology	NOUN
mdp.39015104955862	374	3	uses	use	VERB
mdp.39015104955862	374	4	hermite	hermite	NOUN
mdp.39015104955862	374	5	polynomials	polynomial	NOUN
mdp.39015104955862	374	6	for	for	ADP
mdp.39015104955862	374	7	the	the	DET
mdp.39015104955862	374	8	infinite	infinite	ADJ
mdp.39015104955862	374	9	interval	interval	NOUN
mdp.39015104955862	374	10	(	(	PUNCT
mdp.39015104955862	374	11	tapered	taper	VERB
mdp.39015104955862	374	12	by	by	ADP
mdp.39015104955862	374	13	a	a	DET
mdp.39015104955862	374	14	gaussian	gaussian	NOUN
mdp.39015104955862	374	15	)	)	PUNCT
mdp.39015104955862	374	16	and	and	CCONJ
mdp.39015104955862	374	17	laguerre	laguerre	PROPN
mdp.39015104955862	374	18	polynomials	polynomial	NOUN
mdp.39015104955862	374	19	for	for	ADP
mdp.39015104955862	374	20	the	the	DET
mdp.39015104955862	374	21	semiinfinite	semiinfinite	PROPN
mdp.39015104955862	374	22	interval	interval	NOUN
mdp.39015104955862	374	23	(	(	PUNCT
mdp.39015104955862	374	24	tapered	taper	VERB
mdp.39015104955862	374	25	by	by	ADP
mdp.39015104955862	374	26	an	an	DET
mdp.39015104955862	374	27	exponential	exponential	NOUN
mdp.39015104955862	374	28	)	)	PUNCT
mdp.39015104955862	374	29	.	.	PUNCT
mdp.39015104955862	375	1	our	our	PRON
mdp.39015104955862	375	2	expansion	expansion	NOUN
mdp.39015104955862	375	3	method	method	NOUN
mdp.39015104955862	375	4	also	also	ADV
mdp.39015104955862	375	5	fails	fail	VERB
mdp.39015104955862	375	6	to	to	PART
mdp.39015104955862	375	7	reveal	reveal	VERB
mdp.39015104955862	375	8	unstable	unstable	ADJ
mdp.39015104955862	375	9	modes	mode	NOUN
mdp.39015104955862	375	10	,	,	PUNCT
mdp.39015104955862	375	11	just	just	ADV
mdp.39015104955862	375	12	like	like	ADP
mdp.39015104955862	375	13	the	the	DET
mdp.39015104955862	375	14	conventional	conventional	ADJ
mdp.39015104955862	375	15	method	method	NOUN
mdp.39015104955862	375	16	.	.	PUNCT
mdp.39015104955862	376	1	a	a	DET
mdp.39015104955862	376	2	question	question	NOUN
mdp.39015104955862	376	3	of	of	ADP
mdp.39015104955862	376	4	fundamental	fundamental	ADJ
mdp.39015104955862	376	5	significance	significance	NOUN
mdp.39015104955862	376	6	that	that	PRON
mdp.39015104955862	376	7	arises	arise	VERB
mdp.39015104955862	376	8	is	be	AUX
mdp.39015104955862	376	9	wether	wether	ADV
mdp.39015104955862	376	10	the	the	DET
mdp.39015104955862	376	11	parameter	parameter	NOUN
mdp.39015104955862	376	12	(	(	PUNCT
mdp.39015104955862	376	13	scale	scale	NOUN
mdp.39015104955862	376	14	height	height	NOUN
mdp.39015104955862	376	15	)	)	PUNCT
mdp.39015104955862	376	16	that	that	PRON
mdp.39015104955862	376	17	tapers	taper	VERB
mdp.39015104955862	376	18	the	the	DET
mdp.39015104955862	376	19	polynomials	polynomial	NOUN
mdp.39015104955862	376	20	requires	require	VERB
mdp.39015104955862	376	21	such	such	ADJ
mdp.39015104955862	376	22	fine	fine	ADJ
mdp.39015104955862	376	23	adjustment	adjustment	NOUN
mdp.39015104955862	376	24	that	that	SCONJ
mdp.39015104955862	376	25	only	only	ADV
mdp.39015104955862	376	26	a	a	DET
mdp.39015104955862	376	27	very	very	ADV
mdp.39015104955862	376	28	special	special	ADJ
mdp.39015104955862	376	29	choice	choice	NOUN
mdp.39015104955862	376	30	would	would	AUX
mdp.39015104955862	376	31	correspond	correspond	VERB
mdp.39015104955862	376	32	to	to	ADP
mdp.39015104955862	376	33	the	the	DET
mdp.39015104955862	376	34	physical	physical	ADJ
mdp.39015104955862	376	35	conditions	condition	NOUN
mdp.39015104955862	376	36	envisioned	envision	VERB
mdp.39015104955862	376	37	.	.	PUNCT
mdp.39015104955862	377	1	we	we	PRON
mdp.39015104955862	377	2	have	have	AUX
mdp.39015104955862	377	3	established	establish	VERB
mdp.39015104955862	377	4	that	that	SCONJ
mdp.39015104955862	377	5	this	this	PRON
mdp.39015104955862	377	6	is	be	AUX
mdp.39015104955862	377	7	not	not	PART
mdp.39015104955862	377	8	the	the	DET
mdp.39015104955862	377	9	case	case	NOUN
mdp.39015104955862	377	10	and	and	CCONJ
mdp.39015104955862	377	11	we	we	PRON
mdp.39015104955862	377	12	prove	prove	VERB
mdp.39015104955862	377	13	this	this	DET
mdp.39015104955862	377	14	fact	fact	NOUN
mdp.39015104955862	377	15	below	below	ADV
mdp.39015104955862	377	16	by	by	ADP
mdp.39015104955862	377	17	showing	show	VERB
mdp.39015104955862	377	18	that	that	SCONJ
mdp.39015104955862	377	19	taking	take	VERB
mdp.39015104955862	377	20	the	the	DET
mdp.39015104955862	377	21	scale	scale	NOUN
mdp.39015104955862	377	22	height	height	NOUN
mdp.39015104955862	377	23	to	to	ADP
mdp.39015104955862	377	24	arbitrarily	arbitrarily	ADV
mdp.39015104955862	377	25	small	small	ADJ
mdp.39015104955862	377	26	values	value	NOUN
mdp.39015104955862	377	27	does	do	AUX
mdp.39015104955862	377	28	not	not	PART
mdp.39015104955862	377	29	destroy	destroy	VERB
mdp.39015104955862	377	30	the	the	DET
mdp.39015104955862	377	31	convergence	convergence	NOUN
mdp.39015104955862	377	32	of	of	ADP
mdp.39015104955862	377	33	the	the	DET
mdp.39015104955862	377	34	expansion	expansion	NOUN
mdp.39015104955862	377	35	.	.	PUNCT
mdp.39015104955862	378	1	in	in	ADP
mdp.39015104955862	378	2	fact	fact	NOUN
mdp.39015104955862	378	3	the	the	DET
mdp.39015104955862	378	4	analysis	analysis	NOUN
mdp.39015104955862	378	5	given	give	VERB
mdp.39015104955862	378	6	below	below	ADP
mdp.39015104955862	378	7	establishes	establishe	NOUN
mdp.39015104955862	378	8	with	with	ADP
mdp.39015104955862	378	9	mathematical	mathematical	ADJ
mdp.39015104955862	378	10	rigor	rigor	NOUN
mdp.39015104955862	378	11	the	the	DET
mdp.39015104955862	378	12	validity	validity	NOUN
mdp.39015104955862	378	13	of	of	ADP
mdp.39015104955862	378	14	our	our	PRON
mdp.39015104955862	378	15	expansion	expansion	NOUN
mdp.39015104955862	378	16	method	method	NOUN
mdp.39015104955862	378	17	.	.	PUNCT
mdp.39015104955862	379	1	7	7	NUM
mdp.39015104955862	379	2	aknowledgements	aknowledgement	NOUN
mdp.39015104955862	379	3	it	it	PRON
mdp.39015104955862	379	4	is	be	AUX
mdp.39015104955862	379	5	a	a	DET
mdp.39015104955862	379	6	pleasure	pleasure	NOUN
mdp.39015104955862	379	7	to	to	PART
mdp.39015104955862	379	8	acknowledge	acknowledge	VERB
mdp.39015104955862	379	9	deep	deep	ADJ
mdp.39015104955862	379	10	and	and	CCONJ
mdp.39015104955862	379	11	fruitful	fruitful	ADJ
mdp.39015104955862	379	12	discussions	discussion	NOUN
mdp.39015104955862	379	13	with	with	ADP
mdp.39015104955862	379	14	prof	prof	PROPN
mdp.39015104955862	379	15	.	.	PUNCT
mdp.39015104955862	380	1	robert	robert	PROPN
mdp.39015104955862	380	2	hohlfeld	hohlfeld	PROPN
mdp.39015104955862	380	3	,	,	PUNCT
mdp.39015104955862	380	4	the	the	DET
mdp.39015104955862	380	5	great	great	ADJ
mdp.39015104955862	380	6	help	help	NOUN
mdp.39015104955862	380	7	given	give	VERB
mdp.39015104955862	380	8	in	in	ADP
mdp.39015104955862	380	9	many	many	ADJ
mdp.39015104955862	380	10	of	of	ADP
mdp.39015104955862	380	11	the	the	DET
mdp.39015104955862	380	12	calculations	calculation	NOUN
mdp.39015104955862	380	13	by	by	ADP
mdp.39015104955862	380	14	a.	a.	PROPN
mdp.39015104955862	380	15	gulisashvili	gulisashvili	PROPN
mdp.39015104955862	380	16	.	.	PUNCT
mdp.39015104955862	381	1	special	special	ADJ
mdp.39015104955862	381	2	thanks	thank	NOUN
mdp.39015104955862	381	3	are	be	AUX
mdp.39015104955862	381	4	due	due	ADJ
mdp.39015104955862	381	5	to	to	ADP
mdp.39015104955862	381	6	dr	dr	PROPN
mdp.39015104955862	381	7	.	.	PROPN
mdp.39015104955862	381	8	robert	robert	PROPN
mdp.39015104955862	381	9	beland	beland	PROPN
mdp.39015104955862	381	10	and	and	CCONJ
mdp.39015104955862	381	11	to	to	ADP
mdp.39015104955862	381	12	peter	peter	PROPN
mdp.39015104955862	381	13	thomas	thomas	PROPN
mdp.39015104955862	381	14	for	for	ADP
mdp.39015104955862	381	15	introducing	introduce	VERB
mdp.39015104955862	381	16	us	we	PRON
mdp.39015104955862	381	17	to	to	ADP
mdp.39015104955862	381	18	the	the	DET
mdp.39015104955862	381	19	problems	problem	NOUN
mdp.39015104955862	381	20	and	and	CCONJ
mdp.39015104955862	381	21	for	for	ADP
mdp.39015104955862	381	22	much	much	ADJ
mdp.39015104955862	381	23	support	support	NOUN
mdp.39015104955862	381	24	.	.	PUNCT
mdp.39015104955862	382	1	32	32	NUM
mdp.39015104955862	382	2	1	1	NUM
mdp.39015104955862	382	3	8	8	NUM
mdp.39015104955862	382	4	references	reference	NOUN
mdp.39015104955862	382	5	1	1	NUM
mdp.39015104955862	382	6	.	.	PUNCT
mdp.39015104955862	382	7	j.	j.	PROPN
mdp.39015104955862	382	8	a.	a.	PROPN
mdp.39015104955862	382	9	dubinskij	dubinskij	PROPN
mdp.39015104955862	382	10	,	,	PUNCT
mdp.39015104955862	382	11	"	"	PUNCT
mdp.39015104955862	382	12	sobolev	sobolev	NOUN
mdp.39015104955862	382	13	spaces	space	NOUN
mdp.39015104955862	382	14	of	of	ADP
mdp.39015104955862	382	15	infinte	infinte	PROPN
mdp.39015104955862	382	16	order	order	NOUN
mdp.39015104955862	382	17	and	and	CCONJ
mdp.39015104955862	382	18	differential	differential	ADJ
mdp.39015104955862	382	19	equations	equation	NOUN
mdp.39015104955862	382	20	,	,	PUNCT
mdp.39015104955862	382	21	"	"	PUNCT
mdp.39015104955862	382	22	reidel	reidel	PROPN
mdp.39015104955862	382	23	,	,	PUNCT
mdp.39015104955862	382	24	dordrecht	dordrecht	NOUN
mdp.39015104955862	382	25	et	et	PROPN
mdp.39015104955862	382	26	al	al	PROPN
mdp.39015104955862	382	27	,	,	PUNCT
mdp.39015104955862	382	28	1986	1986	NUM
mdp.39015104955862	382	29	.	.	PUNCT
mdp.39015104955862	383	1	2	2	NUM
mdp.39015104955862	383	2	.	.	X
mdp.39015104955862	383	3	i.	i.	PROPN
mdp.39015104955862	383	4	m.	m.	PROPN
mdp.39015104955862	383	5	gelfand	gelfand	PROPN
mdp.39015104955862	383	6	and	and	CCONJ
mdp.39015104955862	383	7	g.	g.	PROPN
mdp.39015104955862	383	8	e.	e.	PROPN
mdp.39015104955862	383	9	shilov	shilov	PROPN
mdp.39015104955862	383	10	,	,	PUNCT
mdp.39015104955862	383	11	"	"	PUNCT
mdp.39015104955862	383	12	generalized	generalized	ADJ
mdp.39015104955862	383	13	functions	function	NOUN
mdp.39015104955862	383	14	,	,	PUNCT
mdp.39015104955862	383	15	"	"	PUNCT
mdp.39015104955862	383	16	academic	academic	ADJ
mdp.39015104955862	383	17	press	press	NOUN
mdp.39015104955862	383	18	,	,	PUNCT
mdp.39015104955862	383	19	new	new	PROPN
mdp.39015104955862	383	20	york	york	PROPN
mdp.39015104955862	383	21	,	,	PUNCT
mdp.39015104955862	383	22	1964	1964	NUM
mdp.39015104955862	383	23	.	.	PUNCT
mdp.39015104955862	384	1	3	3	X
mdp.39015104955862	384	2	.	.	X
mdp.39015104955862	384	3	i.	i.	PROPN
mdp.39015104955862	384	4	m.	m.	PROPN
mdp.39015104955862	384	5	gelfand	gelfand	PROPN
mdp.39015104955862	384	6	and	and	CCONJ
mdp.39015104955862	384	7	g.	g.	PROPN
mdp.39015104955862	384	8	e.	e.	PROPN
mdp.39015104955862	384	9	shilov	shilov	PROPN
mdp.39015104955862	384	10	,	,	PUNCT
mdp.39015104955862	384	11	quelques	quelques	X
mdp.39015104955862	384	12	applications	application	NOUN
mdp.39015104955862	384	13	de	de	X
mdp.39015104955862	384	14	la	la	X
mdp.39015104955862	384	15	théorie	théorie	X
mdp.39015104955862	384	16	des	des	X
mdp.39015104955862	384	17	fonctions	fonctions	PROPN
mdp.39015104955862	384	18	généralisées	généralisées	PROPN
mdp.39015104955862	384	19	,	,	PUNCT
mdp.39015104955862	384	20	j.	j.	PROPN
mdp.39015104955862	384	21	math	math	PROPN
mdp.39015104955862	384	22	.	.	PUNCT
mdp.39015104955862	385	1	pures	pure	NOUN
mdp.39015104955862	385	2	et	et	PROPN
mdp.39015104955862	385	3	appl	appl	VERB
mdp.39015104955862	385	4	.	.	PUNCT
mdp.39015104955862	386	1	35	35	NUM
mdp.39015104955862	386	2	(	(	PUNCT
mdp.39015104955862	386	3	1956	1956	NUM
mdp.39015104955862	386	4	)	)	PUNCT
mdp.39015104955862	386	5	,	,	PUNCT
mdp.39015104955862	386	6	383	383	NUM
mdp.39015104955862	386	7	-	-	SYM
mdp.39015104955862	386	8	413	413	NUM
mdp.39015104955862	386	9	.	.	PUNCT
mdp.39015104955862	387	1	4	4	NUM
mdp.39015104955862	387	2	.	.	X
mdp.39015104955862	387	3	j.	j.	PROPN
mdp.39015104955862	387	4	hadamard	hadamard	PROPN
mdp.39015104955862	387	5	,	,	PUNCT
mdp.39015104955862	387	6	sur	sur	PROPN
mdp.39015104955862	387	7	la	la	PROPN
mdp.39015104955862	387	8	généralisation	généralisation	PROPN
mdp.39015104955862	387	9	de	de	ADP
mdp.39015104955862	387	10	la	la	PROPN
mdp.39015104955862	387	11	notion	notion	NOUN
mdp.39015104955862	387	12	de	de	ADP
mdp.39015104955862	387	13	fonction	fonction	NOUN
mdp.39015104955862	387	14	analytique	analytique	NOUN
mdp.39015104955862	387	15	,	,	PUNCT
mdp.39015104955862	387	16	bull	bull	NOUN
mdp.39015104955862	387	17	.	.	PUNCT
mdp.39015104955862	388	1	de	de	X
mdp.39015104955862	388	2	la	la	X
mdp.39015104955862	388	3	societe	societe	ADJ
mdp.39015104955862	388	4	math	math	NOUN
mdp.39015104955862	388	5	.	.	PUNCT
mdp.39015104955862	389	1	fr	fr	PROPN
mdp.39015104955862	389	2	.	.	PROPN
mdp.39015104955862	390	1	40	40	NUM
mdp.39015104955862	390	2	(	(	PUNCT
mdp.39015104955862	390	3	1912	1912	NUM
mdp.39015104955862	390	4	)	)	PUNCT
mdp.39015104955862	390	5	,	,	PUNCT
mdp.39015104955862	390	6	28	28	NUM
mdp.39015104955862	390	7	.	.	SYM
mdp.39015104955862	390	8	5	5	NUM
mdp.39015104955862	390	9	.	.	PROPN
mdp.39015104955862	391	1	j.	j.	PROPN
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mdp.39015104955862	391	3	,	,	PUNCT
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mdp.39015104955862	391	21	,	,	PUNCT
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mdp.39015104955862	391	23	.	.	PUNCT
mdp.39015104955862	392	1	6	6	NUM
mdp.39015104955862	392	2	.	.	X
mdp.39015104955862	392	3	c.	c.	PROPN
mdp.39015104955862	392	4	konstantopoulos	konstantopoulos	PROPN
mdp.39015104955862	392	5	,	,	PUNCT
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mdp.39015104955862	392	7	problems	problem	NOUN
mdp.39015104955862	392	8	and	and	CCONJ
mdp.39015104955862	392	9	anti	anti	ADJ
mdp.39015104955862	392	10	-	-	ADJ
mdp.39015104955862	392	11	diffision	diffision	NOUN
mdp.39015104955862	392	12	,	,	PUNCT
mdp.39015104955862	392	13	ph.d	ph.d	PROPN
mdp.39015104955862	392	14	.	.	PUNCT
mdp.39015104955862	393	1	thesis	thesis	PROPN
mdp.39015104955862	393	2	,	,	PUNCT
mdp.39015104955862	393	3	boston	boston	PROPN
mdp.39015104955862	393	4	university	university	PROPN
mdp.39015104955862	393	5	,	,	PUNCT
mdp.39015104955862	393	6	1992	1992	NUM
mdp.39015104955862	393	7	.	.	PUNCT
mdp.39015104955862	394	1	7	7	X
mdp.39015104955862	394	2	.	.	X
mdp.39015104955862	394	3	c.	c.	PROPN
mdp.39015104955862	394	4	konstantopoulos	konstantopoulos	PROPN
mdp.39015104955862	394	5	,	,	PUNCT
mdp.39015104955862	394	6	l.	l.	PROPN
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mdp.39015104955862	394	8	and	and	CCONJ
mdp.39015104955862	394	9	g.	g.	PROPN
mdp.39015104955862	394	10	sandri	sandri	PROPN
mdp.39015104955862	394	11	,	,	PUNCT
mdp.39015104955862	394	12	deconvolution	deconvolution	NOUN
mdp.39015104955862	394	13	of	of	ADP
mdp.39015104955862	394	14	gaussian	gaussian	ADJ
mdp.39015104955862	394	15	filters	filter	NOUN
mdp.39015104955862	394	16	and	and	CCONJ
mdp.39015104955862	394	17	antidiffusion	antidiffusion	NOUN
mdp.39015104955862	394	18	,	,	PUNCT
mdp.39015104955862	394	19	j.	j.	PROPN
mdp.39015104955862	394	20	appl	appl	PROPN
mdp.39015104955862	394	21	.	.	PUNCT
mdp.39015104955862	395	1	phys	phy	NOUN
mdp.39015104955862	395	2	.	.	PROPN
mdp.39015104955862	395	3	,	,	PUNCT
mdp.39015104955862	395	4	68	68	NUM
mdp.39015104955862	395	5	(	(	PUNCT
mdp.39015104955862	395	6	1990	1990	NUM
mdp.39015104955862	395	7	)	)	PUNCT
mdp.39015104955862	395	8	,	,	PUNCT
mdp.39015104955862	395	9	1415	1415	NUM
mdp.39015104955862	395	10	-	-	SYM
mdp.39015104955862	395	11	1420	1420	NUM
mdp.39015104955862	395	12	.	.	PUNCT
mdp.39015104955862	396	1	8	8	NUM
mdp.39015104955862	396	2	.	.	PUNCT
mdp.39015104955862	397	1	p.	p.	NOUN
mdp.39015104955862	397	2	koosis	koosis	NOUN
mdp.39015104955862	397	3	,	,	PUNCT
mdp.39015104955862	397	4	"	"	PUNCT
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mdp.39015104955862	397	7	integral	integral	NOUN
mdp.39015104955862	397	8	,	,	PUNCT
mdp.39015104955862	397	9	"	"	PUNCT
mdp.39015104955862	397	10	cambridge	cambridge	PROPN
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mdp.39015104955862	397	13	,	,	PUNCT
mdp.39015104955862	397	14	cambridge	cambridge	PROPN
mdp.39015104955862	397	15	,	,	PUNCT
mdp.39015104955862	397	16	1988	1988	NUM
mdp.39015104955862	397	17	.	.	PUNCT
mdp.39015104955862	398	1	9	9	NUM
mdp.39015104955862	398	2	.	.	NUM
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mdp.39015104955862	398	4	lighthill	lighthill	PROPN
mdp.39015104955862	398	5	,	,	PUNCT
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mdp.39015104955862	398	8	to	to	ADP
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mdp.39015104955862	398	10	analysis	analysis	NOUN
mdp.39015104955862	398	11	and	and	CCONJ
mdp.39015104955862	398	12	generalized	generalized	ADJ
mdp.39015104955862	398	13	functions	function	NOUN
mdp.39015104955862	398	14	,	,	PUNCT
mdp.39015104955862	398	15	"	"	PUNCT
mdp.39015104955862	398	16	cambridge	cambridge	PROPN
mdp.39015104955862	398	17	university	university	PROPN
mdp.39015104955862	398	18	press	press	PROPN
mdp.39015104955862	398	19	,	,	PUNCT
mdp.39015104955862	398	20	cambridge	cambridge	PROPN
mdp.39015104955862	398	21	,	,	PUNCT
mdp.39015104955862	398	22	1970	1970	NUM
mdp.39015104955862	398	23	.	.	PUNCT
mdp.39015104955862	399	1	10	10	NUM
mdp.39015104955862	399	2	.	.	PUNCT
mdp.39015104955862	399	3	s.	s.	PROPN
mdp.39015104955862	399	4	mandelbrojt	mandelbrojt	PROPN
mdp.39015104955862	399	5	,	,	PUNCT
mdp.39015104955862	399	6	"	"	PUNCT
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mdp.39015104955862	399	9	,	,	PUNCT
mdp.39015104955862	399	10	régularization	régularization	NOUN
mdp.39015104955862	399	11	des	des	X
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mdp.39015104955862	399	13	,	,	PUNCT
mdp.39015104955862	399	14	"	"	PUNCT
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mdp.39015104955862	399	16	,	,	PUNCT
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mdp.39015104955862	399	18	,	,	PUNCT
mdp.39015104955862	399	19	paris	paris	PROPN
mdp.39015104955862	399	20	,	,	PUNCT
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mdp.39015104955862	399	22	.	.	PUNCT
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mdp.39015104955862	400	3	.	.	PUNCT
mdp.39015104955862	401	1	s.	s.	PROPN
mdp.39015104955862	401	2	mandelbrojt	mandelbrojt	PROPN
mdp.39015104955862	401	3	,	,	PUNCT
mdp.39015104955862	401	4	"	"	PUNCT
mdp.39015104955862	401	5	s'eries	s'erie	NOUN
mdp.39015104955862	401	6	de	de	X
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mdp.39015104955862	401	8	et	et	NOUN
mdp.39015104955862	401	9	classes	class	NOUN
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mdp.39015104955862	401	11	de	de	PROPN
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mdp.39015104955862	401	13	,	,	PUNCT
mdp.39015104955862	401	14	"	"	PUNCT
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mdp.39015104955862	401	16	,	,	PUNCT
mdp.39015104955862	401	17	paris	paris	PROPN
mdp.39015104955862	401	18	,	,	PUNCT
mdp.39015104955862	401	19	1935	1935	NUM
mdp.39015104955862	401	20	.	.	PUNCT
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mdp.39015104955862	402	2	.	.	PUNCT
mdp.39015104955862	403	1	a.	a.	NOUN
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mdp.39015104955862	403	4	and	and	CCONJ
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mdp.39015104955862	403	7	,	,	PUNCT
mdp.39015104955862	403	8	"	"	PUNCT
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mdp.39015104955862	403	10	vector	vector	NOUN
mdp.39015104955862	403	11	spaces	space	NOUN
mdp.39015104955862	403	12	,	,	PUNCT
mdp.39015104955862	403	13	"	"	PUNCT
mdp.39015104955862	403	14	cambridge	cambridge	PROPN
mdp.39015104955862	403	15	university	university	PROPN
mdp.39015104955862	403	16	press	press	PROPN
mdp.39015104955862	403	17	,	,	PUNCT
mdp.39015104955862	403	18	cambridge	cambridge	PROPN
mdp.39015104955862	403	19	,	,	PUNCT
mdp.39015104955862	403	20	1964	1964	NUM
mdp.39015104955862	403	21	.	.	PUNCT
mdp.39015104955862	404	1	13	13	NUM
mdp.39015104955862	404	2	.	.	PUNCT
mdp.39015104955862	405	1	c.	c.	PROPN
mdp.39015104955862	405	2	roumieu	roumieu	PROPN
mdp.39015104955862	405	3	,	,	PUNCT
mdp.39015104955862	405	4	sur	sur	X
mdp.39015104955862	405	5	quelques	quelques	X
mdp.39015104955862	405	6	extensions	extension	NOUN
mdp.39015104955862	405	7	de	de	X
mdp.39015104955862	405	8	la	la	X
mdp.39015104955862	405	9	rotion	rotion	PROPN
mdp.39015104955862	405	10	de	de	ADP
mdp.39015104955862	405	11	distribution	distribution	NOUN
mdp.39015104955862	405	12	,	,	PUNCT
mdp.39015104955862	405	13	ann	ann	PROPN
mdp.39015104955862	405	14	.	.	PROPN
mdp.39015104955862	405	15	sci	sci	PROPN
mdp.39015104955862	405	16	.	.	PROPN
mdp.39015104955862	405	17	ec	ec	PROPN
mdp.39015104955862	405	18	.	.	PROPN
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mdp.39015104955862	405	20	.	.	PUNCT
mdp.39015104955862	406	1	sup	sup	PROPN
mdp.39015104955862	406	2	.	.	PROPN
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mdp.39015104955862	406	4	(	(	PUNCT
mdp.39015104955862	406	5	1960	1960	NUM
mdp.39015104955862	406	6	)	)	PUNCT
mdp.39015104955862	406	7	,	,	PUNCT
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mdp.39015104955862	406	9	-	-	SYM
mdp.39015104955862	406	10	121	121	NUM
mdp.39015104955862	406	11	.	.	PUNCT
mdp.39015104955862	407	1	14	14	NUM
mdp.39015104955862	407	2	.	.	PUNCT
mdp.39015104955862	408	1	l.	l.	PROPN
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mdp.39015104955862	408	3	,	,	PUNCT
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mdp.39015104955862	408	8	,	,	PUNCT
mdp.39015104955862	408	9	"	"	PUNCT
mdp.39015104955862	408	10	hermann	hermann	PROPN
mdp.39015104955862	408	11	et	et	PROPN
mdp.39015104955862	408	12	cie	cie	PROPN
mdp.39015104955862	408	13	.	.	PROPN
mdp.39015104955862	408	14	,	,	PUNCT
mdp.39015104955862	408	15	paris	paris	PROPN
mdp.39015104955862	408	16	,	,	PUNCT
mdp.39015104955862	408	17	1951	1951	NUM
mdp.39015104955862	408	18	.	.	PUNCT
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mdp.39015104955862	409	5	-	-	SYM
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