id	sid	tid	token	lemma	pos
ap-1199	1	1	ap-3-10.dvi	ap-3-10.dvi	PROPN
ap-1199	1	2	acta	acta	PROPN
ap-1199	1	3	polytechnica	polytechnica	PROPN
ap-1199	1	4	vol	vol	NOUN
ap-1199	1	5	.	.	PROPN
ap-1199	2	1	50	50	NUM
ap-1199	2	2	no	no	NOUN
ap-1199	2	3	.	.	PUNCT
ap-1199	3	1	3/2010	3/2010	NUM
ap-1199	3	2	asymptotic	asymptotic	ADJ
ap-1199	3	3	power	power	NOUN
ap-1199	3	4	series	series	NOUN
ap-1199	3	5	of	of	ADP
ap-1199	3	6	field	field	NOUN
ap-1199	3	7	correlators	correlators	PROPN
ap-1199	3	8	i.	i.	PROPN
ap-1199	3	9	caprini	caprini	PROPN
ap-1199	3	10	,	,	PUNCT
ap-1199	3	11	j.	j.	PROPN
ap-1199	3	12	fischer	fischer	PROPN
ap-1199	3	13	,	,	PUNCT
ap-1199	3	14	i.	i.	PROPN
ap-1199	3	15	vrkoč	vrkoč	PROPN
ap-1199	3	16	abstract	abstract	PROPN
ap-1199	3	17	we	we	PRON
ap-1199	3	18	address	address	VERB
ap-1199	3	19	the	the	DET
ap-1199	3	20	problem	problem	NOUN
ap-1199	3	21	of	of	ADP
ap-1199	3	22	ambiguity	ambiguity	NOUN
ap-1199	3	23	of	of	ADP
ap-1199	3	24	a	a	DET
ap-1199	3	25	function	function	NOUN
ap-1199	3	26	determined	determine	VERB
ap-1199	3	27	by	by	ADP
ap-1199	3	28	an	an	DET
ap-1199	3	29	asymptotic	asymptotic	ADJ
ap-1199	3	30	perturbation	perturbation	NOUN
ap-1199	3	31	expansion	expansion	NOUN
ap-1199	3	32	.	.	PUNCT
ap-1199	4	1	using	use	VERB
ap-1199	4	2	a	a	DET
ap-1199	4	3	modified	modify	VERB
ap-1199	4	4	form	form	NOUN
ap-1199	4	5	of	of	ADP
ap-1199	4	6	the	the	DET
ap-1199	4	7	watson	watson	PROPN
ap-1199	4	8	lemma	lemma	PROPN
ap-1199	4	9	recently	recently	ADV
ap-1199	4	10	proved	prove	VERB
ap-1199	4	11	elsewhere	elsewhere	ADV
ap-1199	4	12	,	,	PUNCT
ap-1199	4	13	we	we	PRON
ap-1199	4	14	discuss	discuss	VERB
ap-1199	4	15	a	a	DET
ap-1199	4	16	large	large	ADJ
ap-1199	4	17	class	class	NOUN
ap-1199	4	18	of	of	ADP
ap-1199	4	19	functions	function	NOUN
ap-1199	4	20	determined	determine	VERB
ap-1199	4	21	by	by	ADP
ap-1199	4	22	the	the	DET
ap-1199	4	23	same	same	ADJ
ap-1199	4	24	asymptotic	asymptotic	ADJ
ap-1199	4	25	power	power	NOUN
ap-1199	4	26	expansion	expansion	NOUN
ap-1199	4	27	and	and	CCONJ
ap-1199	4	28	represented	represent	VERB
ap-1199	4	29	by	by	ADP
ap-1199	4	30	various	various	ADJ
ap-1199	4	31	forms	form	NOUN
ap-1199	4	32	of	of	ADP
ap-1199	4	33	integrals	integral	NOUN
ap-1199	4	34	of	of	ADP
ap-1199	4	35	the	the	DET
ap-1199	4	36	laplace	laplace	NOUN
ap-1199	4	37	-	-	PUNCT
ap-1199	4	38	borel	borel	NOUN
ap-1199	4	39	type	type	NOUN
ap-1199	4	40	along	along	ADP
ap-1199	4	41	a	a	DET
ap-1199	4	42	general	general	ADJ
ap-1199	4	43	contour	contour	NOUN
ap-1199	4	44	in	in	ADP
ap-1199	4	45	the	the	DET
ap-1199	4	46	borel	borel	NOUN
ap-1199	4	47	complex	complex	ADJ
ap-1199	4	48	plane	plane	NOUN
ap-1199	4	49	.	.	PUNCT
ap-1199	5	1	some	some	DET
ap-1199	5	2	remarks	remark	NOUN
ap-1199	5	3	on	on	ADP
ap-1199	5	4	possible	possible	ADJ
ap-1199	5	5	applications	application	NOUN
ap-1199	5	6	in	in	ADP
ap-1199	5	7	qcd	qcd	PROPN
ap-1199	5	8	are	be	AUX
ap-1199	5	9	made	make	VERB
ap-1199	5	10	.	.	PUNCT
ap-1199	6	1	1	1	NUM
ap-1199	6	2	asymptotic	asymptotic	ADJ
ap-1199	6	3	perturbation	perturbation	NOUN
ap-1199	6	4	expansions	expansion	VERB
ap-1199	6	5	perturbation	perturbation	NOUN
ap-1199	6	6	expansions	expansion	NOUN
ap-1199	6	7	are	be	AUX
ap-1199	6	8	known	know	VERB
ap-1199	6	9	to	to	PART
ap-1199	6	10	be	be	AUX
ap-1199	6	11	divergent	divergent	ADJ
ap-1199	6	12	both	both	CCONJ
ap-1199	6	13	in	in	ADP
ap-1199	6	14	quantum	quantum	ADJ
ap-1199	6	15	electrodynamics	electrodynamic	NOUN
ap-1199	6	16	and	and	CCONJ
ap-1199	6	17	in	in	ADP
ap-1199	6	18	quantum	quantum	ADJ
ap-1199	6	19	chromodynamics	chromodynamic	NOUN
ap-1199	6	20	,	,	PUNCT
ap-1199	6	21	as	as	ADV
ap-1199	6	22	well	well	ADV
ap-1199	6	23	as	as	ADP
ap-1199	6	24	in	in	ADP
ap-1199	6	25	many	many	ADJ
ap-1199	6	26	other	other	ADJ
ap-1199	6	27	physically	physically	ADV
ap-1199	6	28	interesting	interesting	ADJ
ap-1199	6	29	theories	theory	NOUN
ap-1199	6	30	and	and	CCONJ
ap-1199	6	31	models	model	NOUN
ap-1199	6	32	.	.	PUNCT
ap-1199	7	1	in	in	ADP
ap-1199	7	2	qed	qed	PROPN
ap-1199	7	3	,	,	PUNCT
ap-1199	7	4	divergence	divergence	NOUN
ap-1199	7	5	was	be	AUX
ap-1199	7	6	proved	prove	VERB
ap-1199	7	7	by	by	ADP
ap-1199	7	8	f.	f.	PROPN
ap-1199	7	9	j.	j.	PROPN
ap-1199	7	10	dyson	dyson	PROPN
ap-1199	7	11	in	in	ADP
ap-1199	7	12	1952	1952	NUM
ap-1199	7	13	(	(	PUNCT
ap-1199	7	14	see	see	VERB
ap-1199	7	15	[	[	X
ap-1199	7	16	1	1	NUM
ap-1199	7	17	]	]	NUM
ap-1199	7	18	)	)	PUNCT
ap-1199	7	19	.	.	PUNCT
ap-1199	8	1	his	his	PRON
ap-1199	8	2	result	result	NOUN
ap-1199	8	3	has	have	AUX
ap-1199	8	4	been	be	AUX
ap-1199	8	5	revisited	revisit	VERB
ap-1199	8	6	and	and	CCONJ
ap-1199	8	7	reformulated	reformulate	VERB
ap-1199	8	8	by	by	ADP
ap-1199	8	9	many	many	ADJ
ap-1199	8	10	authors	author	NOUN
ap-1199	8	11	(	(	PUNCT
ap-1199	8	12	[	[	X
ap-1199	8	13	2	2	NUM
ap-1199	8	14	,	,	PUNCT
ap-1199	8	15	3	3	NUM
ap-1199	8	16	]	]	PUNCT
ap-1199	8	17	,	,	PUNCT
ap-1199	8	18	see	see	VERB
ap-1199	8	19	also	also	ADV
ap-1199	8	20	a	a	DET
ap-1199	8	21	review	review	NOUN
ap-1199	8	22	in	in	ADP
ap-1199	8	23	[	[	X
ap-1199	8	24	4	4	NUM
ap-1199	8	25	]	]	NUM
ap-1199	8	26	)	)	PUNCT
ap-1199	8	27	.	.	PUNCT
ap-1199	9	1	dyson	dyson	PROPN
ap-1199	9	2	proposed	propose	VERB
ap-1199	9	3	to	to	PART
ap-1199	9	4	give	give	VERB
ap-1199	9	5	the	the	DET
ap-1199	9	6	divergent	divergent	ADJ
ap-1199	9	7	series	series	NOUN
ap-1199	9	8	mathematical	mathematical	ADJ
ap-1199	9	9	meaning	meaning	NOUN
ap-1199	9	10	by	by	ADP
ap-1199	9	11	interpreting	interpret	VERB
ap-1199	9	12	it	it	PRON
ap-1199	9	13	as	as	ADP
ap-1199	9	14	an	an	DET
ap-1199	9	15	asymptotic	asymptotic	ADJ
ap-1199	9	16	series	series	NOUN
ap-1199	9	17	to	to	ADP
ap-1199	9	18	f	f	PROPN
ap-1199	9	19	(	(	PUNCT
ap-1199	9	20	z	z	NOUN
ap-1199	9	21	)	)	PUNCT
ap-1199	9	22	,	,	PUNCT
ap-1199	9	23	the	the	DET
ap-1199	9	24	sought	seek	VERB
ap-1199	9	25	function	function	NOUN
ap-1199	9	26	:	:	PUNCT
ap-1199	9	27	f	f	PROPN
ap-1199	9	28	(	(	PUNCT
ap-1199	9	29	z	z	NOUN
ap-1199	9	30	)	)	PUNCT
ap-1199	9	31	∼	∼	VERB
ap-1199	9	32	∞∑	∞∑	PRON
ap-1199	9	33	n=0	n=0	NUM
ap-1199	9	34	fnzn	fnzn	NOUN
ap-1199	9	35	,	,	PUNCT
ap-1199	9	36	z	z	PROPN
ap-1199	9	37	∈	∈	PROPN
ap-1199	9	38	s	s	NOUN
ap-1199	9	39	,	,	PUNCT
ap-1199	9	40	z	z	PROPN
ap-1199	9	41	→	→	SYM
ap-1199	9	42	0	0	NUM
ap-1199	9	43	,	,	PUNCT
ap-1199	9	44	(	(	PUNCT
ap-1199	9	45	1	1	X
ap-1199	9	46	)	)	PUNCT
ap-1199	9	47	where	where	SCONJ
ap-1199	9	48	s	s	NOUN
ap-1199	9	49	is	be	AUX
ap-1199	9	50	a	a	DET
ap-1199	9	51	point	point	NOUN
ap-1199	9	52	set	set	VERB
ap-1199	9	53	having	have	VERB
ap-1199	9	54	the	the	DET
ap-1199	9	55	origin	origin	NOUN
ap-1199	9	56	as	as	ADP
ap-1199	9	57	an	an	DET
ap-1199	9	58	accumulation	accumulation	NOUN
ap-1199	9	59	point	point	NOUN
ap-1199	9	60	,	,	PUNCT
ap-1199	9	61	z	z	NOUN
ap-1199	9	62	being	be	AUX
ap-1199	9	63	the	the	DET
ap-1199	9	64	perturbation	perturbation	NOUN
ap-1199	9	65	parameter	parameter	NOUN
ap-1199	9	66	.	.	PUNCT
ap-1199	10	1	to	to	PART
ap-1199	10	2	see	see	VERB
ap-1199	10	3	how	how	SCONJ
ap-1199	10	4	dramatically	dramatically	ADV
ap-1199	10	5	the	the	DET
ap-1199	10	6	philosophy	philosophy	NOUN
ap-1199	10	7	of	of	ADP
ap-1199	10	8	perturbation	perturbation	NOUN
ap-1199	10	9	theory	theory	NOUN
ap-1199	10	10	was	be	AUX
ap-1199	10	11	changed	change	VERB
ap-1199	10	12	by	by	ADP
ap-1199	10	13	this	this	DET
ap-1199	10	14	step	step	NOUN
ap-1199	10	15	,	,	PUNCT
ap-1199	10	16	let	let	VERB
ap-1199	10	17	us	we	PRON
ap-1199	10	18	first	first	ADV
ap-1199	10	19	recall	recall	VERB
ap-1199	10	20	the	the	DET
ap-1199	10	21	definition	definition	NOUN
ap-1199	10	22	of	of	ADP
ap-1199	10	23	an	an	DET
ap-1199	10	24	asymptotic	asymptotic	ADJ
ap-1199	10	25	series	series	NOUN
ap-1199	10	26	:	:	PUNCT
ap-1199	10	27	definition	definition	NOUN
ap-1199	10	28	:	:	PUNCT
ap-1199	10	29	let	let	VERB
ap-1199	10	30	s	s	PRON
ap-1199	10	31	be	be	AUX
ap-1199	10	32	a	a	DET
ap-1199	10	33	region	region	NOUN
ap-1199	10	34	or	or	CCONJ
ap-1199	10	35	point	point	NOUN
ap-1199	10	36	set	set	VERB
ap-1199	10	37	having	have	VERB
ap-1199	10	38	the	the	DET
ap-1199	10	39	origin	origin	NOUN
ap-1199	10	40	as	as	ADP
ap-1199	10	41	an	an	DET
ap-1199	10	42	accumulation	accumulation	NOUN
ap-1199	10	43	point	point	NOUN
ap-1199	10	44	.	.	PUNCT
ap-1199	11	1	the	the	DET
ap-1199	11	2	power	power	NOUN
ap-1199	11	3	series	series	NOUN
ap-1199	11	4	∞∑	∞∑	PROPN
ap-1199	11	5	n=0	n=0	NUM
ap-1199	11	6	fnzn	fnzn	NOUN
ap-1199	11	7	is	be	AUX
ap-1199	11	8	said	say	VERB
ap-1199	11	9	to	to	PART
ap-1199	11	10	be	be	AUX
ap-1199	11	11	asymptotic	asymptotic	ADJ
ap-1199	11	12	to	to	ADP
ap-1199	11	13	the	the	DET
ap-1199	11	14	function	function	NOUN
ap-1199	11	15	f	f	PROPN
ap-1199	11	16	(	(	PUNCT
ap-1199	11	17	z	z	NOUN
ap-1199	11	18	)	)	PUNCT
ap-1199	11	19	as	as	ADP
ap-1199	11	20	z	z	PROPN
ap-1199	11	21	→	→	SYM
ap-1199	11	22	0	0	NUM
ap-1199	11	23	on	on	ADP
ap-1199	11	24	s	s	PROPN
ap-1199	11	25	,	,	PUNCT
ap-1199	11	26	and	and	CCONJ
ap-1199	11	27	we	we	PRON
ap-1199	11	28	write	write	VERB
ap-1199	11	29	eq	eq	X
ap-1199	11	30	.	.	PUNCT
ap-1199	12	1	(	(	PUNCT
ap-1199	12	2	1	1	NUM
ap-1199	12	3	)	)	PUNCT
ap-1199	12	4	,	,	PUNCT
ap-1199	12	5	if	if	SCONJ
ap-1199	12	6	the	the	DET
ap-1199	12	7	set	set	NOUN
ap-1199	12	8	of	of	ADP
ap-1199	12	9	functions	function	NOUN
ap-1199	12	10	rn	rn	PROPN
ap-1199	12	11	(	(	PUNCT
ap-1199	12	12	z	z	PROPN
ap-1199	12	13	)	)	PUNCT
ap-1199	12	14	,	,	PUNCT
ap-1199	12	15	rn	rn	PROPN
ap-1199	12	16	(	(	PUNCT
ap-1199	12	17	z	z	NOUN
ap-1199	12	18	)	)	PUNCT
ap-1199	12	19	=	=	SYM
ap-1199	12	20	f	f	X
ap-1199	12	21	(	(	PUNCT
ap-1199	12	22	z)−	z)−	PROPN
ap-1199	12	23	n∑	n∑	NOUN
ap-1199	12	24	n=0	n=0	NUM
ap-1199	12	25	fnzn	fnzn	NOUN
ap-1199	12	26	,	,	PUNCT
ap-1199	12	27	(	(	PUNCT
ap-1199	12	28	2	2	X
ap-1199	12	29	)	)	PUNCT
ap-1199	12	30	satisfies	satisfy	VERB
ap-1199	12	31	the	the	DET
ap-1199	12	32	condition	condition	NOUN
ap-1199	12	33	rn	rn	PROPN
ap-1199	12	34	(	(	PUNCT
ap-1199	12	35	z	z	NOUN
ap-1199	12	36	)	)	PUNCT
ap-1199	12	37	=	=	SYM
ap-1199	12	38	o(zn	o(zn	NOUN
ap-1199	12	39	)	)	PUNCT
ap-1199	12	40	(	(	PUNCT
ap-1199	12	41	3	3	X
ap-1199	12	42	)	)	PUNCT
ap-1199	12	43	for	for	ADP
ap-1199	12	44	all	all	DET
ap-1199	12	45	n	n	NOUN
ap-1199	12	46	=	=	SYM
ap-1199	12	47	0	0	NUM
ap-1199	12	48	,	,	PUNCT
ap-1199	12	49	1	1	NUM
ap-1199	12	50	,	,	PUNCT
ap-1199	12	51	2	2	NUM
ap-1199	12	52	,	,	PUNCT
ap-1199	12	53	.	.	PUNCT
ap-1199	12	54	.	.	PUNCT
ap-1199	13	1	.	.	PUNCT
ap-1199	14	1	,	,	PUNCT
ap-1199	14	2	z	z	PROPN
ap-1199	14	3	→	→	SYM
ap-1199	14	4	0	0	NUM
ap-1199	14	5	and	and	CCONJ
ap-1199	14	6	z	z	PROPN
ap-1199	14	7	∈	∈	PROPN
ap-1199	14	8	s.	s.	PROPN
ap-1199	14	9	note	note	VERB
ap-1199	14	10	that	that	SCONJ
ap-1199	14	11	the	the	DET
ap-1199	14	12	asymptotic	asymptotic	ADJ
ap-1199	14	13	series	series	NOUN
ap-1199	14	14	is	be	AUX
ap-1199	14	15	defined	define	VERB
ap-1199	14	16	by	by	ADP
ap-1199	14	17	a	a	DET
ap-1199	14	18	different	different	ADJ
ap-1199	14	19	limiting	limit	VERB
ap-1199	14	20	procedure	procedure	NOUN
ap-1199	14	21	than	than	ADP
ap-1199	14	22	the	the	DET
ap-1199	14	23	taylor	taylor	PROPN
ap-1199	14	24	one	one	NUM
ap-1199	14	25	:	:	PUNCT
ap-1199	14	26	taking	take	VERB
ap-1199	14	27	n	n	NOUN
ap-1199	14	28	fixed	fix	VERB
ap-1199	14	29	,	,	PUNCT
ap-1199	14	30	one	one	PRON
ap-1199	14	31	observes	observe	VERB
ap-1199	14	32	how	how	SCONJ
ap-1199	14	33	rn	rn	PROPN
ap-1199	14	34	(	(	PUNCT
ap-1199	14	35	z	z	NOUN
ap-1199	14	36	)	)	PUNCT
ap-1199	14	37	behaves	behave	NOUN
ap-1199	14	38	for	for	ADP
ap-1199	14	39	z	z	NOUN
ap-1199	14	40	→	→	SYM
ap-1199	14	41	0	0	NUM
ap-1199	14	42	,	,	PUNCT
ap-1199	14	43	z	z	PROPN
ap-1199	14	44	∈	∈	PROPN
ap-1199	14	45	s	s	PART
ap-1199	14	46	,	,	PUNCT
ap-1199	14	47	the	the	DET
ap-1199	14	48	procedure	procedure	NOUN
ap-1199	14	49	being	be	AUX
ap-1199	14	50	repeated	repeat	VERB
ap-1199	14	51	for	for	ADP
ap-1199	14	52	all	all	DET
ap-1199	14	53	n	n	DET
ap-1199	14	54	≥	≥	NOUN
ap-1199	14	55	0	0	NUM
ap-1199	14	56	integers	integer	NOUN
ap-1199	14	57	.	.	PUNCT
ap-1199	15	1	convergence	convergence	NOUN
ap-1199	15	2	may	may	AUX
ap-1199	15	3	be	be	AUX
ap-1199	15	4	provable	provable	ADJ
ap-1199	15	5	without	without	ADP
ap-1199	15	6	knowing	know	VERB
ap-1199	15	7	f	f	PROPN
ap-1199	15	8	(	(	PUNCT
ap-1199	15	9	z	z	NOUN
ap-1199	15	10	)	)	PUNCT
ap-1199	15	11	,	,	PUNCT
ap-1199	15	12	but	but	CCONJ
ap-1199	15	13	asymptoticity	asymptoticity	NOUN
ap-1199	15	14	can	can	AUX
ap-1199	15	15	be	be	AUX
ap-1199	15	16	tested	test	VERB
ap-1199	15	17	only	only	ADV
ap-1199	15	18	if	if	SCONJ
ap-1199	15	19	one	one	PRON
ap-1199	15	20	knows	know	VERB
ap-1199	15	21	both	both	CCONJ
ap-1199	15	22	the	the	DET
ap-1199	15	23	fn	fn	NOUN
ap-1199	15	24	and	and	CCONJ
ap-1199	15	25	f	f	PROPN
ap-1199	15	26	(	(	PUNCT
ap-1199	15	27	z	z	NOUN
ap-1199	15	28	)	)	PUNCT
ap-1199	15	29	.	.	PUNCT
ap-1199	16	1	by	by	ADP
ap-1199	16	2	(	(	PUNCT
ap-1199	16	3	1	1	NUM
ap-1199	16	4	)	)	PUNCT
ap-1199	16	5	,	,	PUNCT
ap-1199	16	6	f	f	PROPN
ap-1199	16	7	(	(	PUNCT
ap-1199	16	8	z	z	NOUN
ap-1199	16	9	)	)	PUNCT
ap-1199	16	10	is	be	AUX
ap-1199	16	11	not	not	PART
ap-1199	16	12	uniquely	uniquely	ADV
ap-1199	16	13	determined	determine	VERB
ap-1199	16	14	;	;	PUNCT
ap-1199	16	15	there	there	PRON
ap-1199	16	16	are	be	VERB
ap-1199	16	17	many	many	ADJ
ap-1199	16	18	different	different	ADJ
ap-1199	16	19	functions	function	NOUN
ap-1199	16	20	having	have	VERB
ap-1199	16	21	the	the	DET
ap-1199	16	22	same	same	ADJ
ap-1199	16	23	asymptotic	asymptotic	ADJ
ap-1199	16	24	series	series	NOUN
ap-1199	16	25	,	,	PUNCT
ap-1199	16	26	(	(	PUNCT
ap-1199	16	27	1	1	X
ap-1199	16	28	)	)	PUNCT
ap-1199	16	29	say	say	INTJ
ap-1199	16	30	.	.	PUNCT
ap-1199	17	1	the	the	DET
ap-1199	17	2	ambiguity	ambiguity	NOUN
ap-1199	17	3	of	of	ADP
ap-1199	17	4	a	a	DET
ap-1199	17	5	function	function	NOUN
ap-1199	17	6	given	give	VERB
ap-1199	17	7	by	by	ADP
ap-1199	17	8	an	an	DET
ap-1199	17	9	asymptotic	asymptotic	ADJ
ap-1199	17	10	series	series	NOUN
ap-1199	17	11	is	be	AUX
ap-1199	17	12	illustrated	illustrate	VERB
ap-1199	17	13	by	by	ADP
ap-1199	17	14	the	the	DET
ap-1199	17	15	lemma	lemma	PROPN
ap-1199	17	16	of	of	ADP
ap-1199	17	17	watson	watson	PROPN
ap-1199	17	18	.	.	PUNCT
ap-1199	18	1	2	2	NUM
ap-1199	18	2	watson	watson	PROPN
ap-1199	18	3	lemma	lemma	PROPN
ap-1199	18	4	consider	consider	VERB
ap-1199	18	5	the	the	DET
ap-1199	18	6	following	follow	VERB
ap-1199	18	7	integral	integral	ADJ
ap-1199	18	8	φ0,c(λ	φ0,c(λ	NOUN
ap-1199	18	9	)	)	PUNCT
ap-1199	18	10	=	=	SYM
ap-1199	18	11	∫	∫	PROPN
ap-1199	18	12	c	c	NOUN
ap-1199	18	13	0	0	NUM
ap-1199	18	14	e−λxα	e−λxα	PROPN
ap-1199	18	15	xβ−1f(x)dx	xβ−1f(x)dx	PROPN
ap-1199	18	16	,	,	PUNCT
ap-1199	18	17	(	(	PUNCT
ap-1199	18	18	4	4	X
ap-1199	18	19	)	)	PUNCT
ap-1199	18	20	where	where	SCONJ
ap-1199	18	21	0	0	NUM
ap-1199	18	22	<	<	X
ap-1199	18	23	c	c	X
ap-1199	18	24	<	<	X
ap-1199	18	25	∞	∞	PROPN
ap-1199	18	26	and	and	CCONJ
ap-1199	18	27	α	α	NOUN
ap-1199	18	28	>	>	X
ap-1199	18	29	0	0	PROPN
ap-1199	18	30	,	,	PUNCT
ap-1199	18	31	β	β	X
ap-1199	18	32	>	>	X
ap-1199	18	33	0	0	X
ap-1199	18	34	.	.	PUNCT
ap-1199	19	1	let	let	VERB
ap-1199	19	2	f(x	f(x	PROPN
ap-1199	19	3	)	)	PUNCT
ap-1199	19	4	∈	∈	PROPN
ap-1199	19	5	c∞[0	c∞[0	NOUN
ap-1199	19	6	,	,	PUNCT
ap-1199	19	7	c	c	NOUN
ap-1199	19	8	]	]	PUNCT
ap-1199	19	9	and	and	CCONJ
ap-1199	19	10	f	f	X
ap-1199	19	11	(	(	PUNCT
ap-1199	19	12	k)(0	k)(0	X
ap-1199	19	13	)	)	PUNCT
ap-1199	19	14	defined	define	VERB
ap-1199	19	15	as	as	ADP
ap-1199	19	16	lim	lim	PROPN
ap-1199	19	17	x→0	x→0	PROPN
ap-1199	20	1	+	+	PROPN
ap-1199	20	2	f	f	X
ap-1199	20	3	(	(	PUNCT
ap-1199	20	4	k)(x	k)(x	PROPN
ap-1199	20	5	)	)	PUNCT
ap-1199	20	6	.	.	PUNCT
ap-1199	21	1	let	let	VERB
ap-1199	21	2	ε	ε	PROPN
ap-1199	21	3	be	be	AUX
ap-1199	21	4	any	any	DET
ap-1199	21	5	number	number	NOUN
ap-1199	21	6	from	from	ADP
ap-1199	21	7	the	the	DET
ap-1199	21	8	interval	interval	NOUN
ap-1199	21	9	0	0	PUNCT
ap-1199	21	10	<	<	X
ap-1199	21	11	ε	ε	PROPN
ap-1199	21	12	<	<	X
ap-1199	21	13	π/2	π/2	NUM
ap-1199	21	14	.	.	PUNCT
ap-1199	22	1	lemma	lemma	PROPN
ap-1199	22	2	1	1	NUM
ap-1199	22	3	(	(	PUNCT
ap-1199	22	4	g.	g.	PROPN
ap-1199	22	5	n.	n.	PROPN
ap-1199	22	6	watson	watson	PROPN
ap-1199	22	7	):	):	PUNCT
ap-1199	22	8	if	if	SCONJ
ap-1199	22	9	the	the	DET
ap-1199	22	10	above	above	ADJ
ap-1199	22	11	conditions	condition	NOUN
ap-1199	22	12	are	be	AUX
ap-1199	22	13	fulfilled	fulfil	VERB
ap-1199	22	14	,	,	PUNCT
ap-1199	22	15	the	the	DET
ap-1199	22	16	asymptotic	asymptotic	ADJ
ap-1199	22	17	expansion	expansion	NOUN
ap-1199	22	18	φ0,c(λ	φ0,c(λ	NOUN
ap-1199	22	19	)	)	PUNCT
ap-1199	22	20	∼	∼	NOUN
ap-1199	22	21	1	1	NUM
ap-1199	22	22	α	α	NOUN
ap-1199	22	23	∞∑	∞∑	PROPN
ap-1199	22	24	k=0	k=0	PUNCT
ap-1199	22	25	λ−	λ−	PROPN
ap-1199	22	26	k+β	k+β	PROPN
ap-1199	22	27	α	α	NUM
ap-1199	22	28	γ	γ	X
ap-1199	22	29	(	(	PUNCT
ap-1199	22	30	k	k	PROPN
ap-1199	22	31	+	+	CCONJ
ap-1199	22	32	β	β	X
ap-1199	22	33	α	α	NOUN
ap-1199	22	34	)	)	PUNCT
ap-1199	22	35	f	f	PROPN
ap-1199	22	36	(	(	PUNCT
ap-1199	22	37	k)(0	k)(0	PROPN
ap-1199	22	38	)	)	PUNCT
ap-1199	22	39	k	k	X
ap-1199	22	40	!	!	PUNCT
ap-1199	23	1	(	(	PUNCT
ap-1199	23	2	5	5	X
ap-1199	23	3	)	)	PUNCT
ap-1199	23	4	holds	hold	VERB
ap-1199	23	5	for	for	ADP
ap-1199	23	6	λ	λ	PROPN
ap-1199	23	7	→∞	→∞	PROPN
ap-1199	23	8	,	,	PUNCT
ap-1199	23	9	λ	λ	PROPN
ap-1199	23	10	∈	∈	PROPN
ap-1199	23	11	sε	sε	NOUN
ap-1199	23	12	,	,	PUNCT
ap-1199	23	13	where	where	SCONJ
ap-1199	23	14	sε	sε	PRON
ap-1199	23	15	is	be	AUX
ap-1199	23	16	the	the	DET
ap-1199	23	17	angle	angle	NOUN
ap-1199	24	1	|	|	ADV
ap-1199	24	2	argλ|	argλ|	NOUN
ap-1199	24	3	≤	≤	NUM
ap-1199	24	4	π	π	NOUN
ap-1199	24	5	2	2	NUM
ap-1199	24	6	−	−	PROPN
ap-1199	24	7	ε	ε	PROPN
ap-1199	24	8	.	.	PUNCT
ap-1199	25	1	(	(	PUNCT
ap-1199	25	2	6	6	NUM
ap-1199	25	3	)	)	PUNCT
ap-1199	25	4	the	the	DET
ap-1199	25	5	expansion	expansion	NOUN
ap-1199	25	6	(	(	PUNCT
ap-1199	25	7	5	5	X
ap-1199	25	8	)	)	PUNCT
ap-1199	25	9	can	can	AUX
ap-1199	25	10	be	be	AUX
ap-1199	25	11	differentiated	differentiate	VERB
ap-1199	25	12	with	with	ADP
ap-1199	25	13	respect	respect	NOUN
ap-1199	25	14	to	to	ADP
ap-1199	25	15	λ	λ	PROPN
ap-1199	25	16	any	any	DET
ap-1199	25	17	number	number	NOUN
ap-1199	25	18	of	of	ADP
ap-1199	25	19	times	time	NOUN
ap-1199	25	20	.	.	PUNCT
ap-1199	26	1	for	for	ADP
ap-1199	26	2	the	the	DET
ap-1199	26	3	proof	proof	NOUN
ap-1199	26	4	,	,	PUNCT
ap-1199	26	5	see	see	VERB
ap-1199	26	6	for	for	ADP
ap-1199	26	7	instance	instance	NOUN
ap-1199	26	8	[	[	X
ap-1199	26	9	5	5	NUM
ap-1199	26	10	]	]	PUNCT
ap-1199	26	11	.	.	PUNCT
ap-1199	27	1	let	let	VERB
ap-1199	27	2	us	we	PRON
ap-1199	27	3	add	add	VERB
ap-1199	27	4	several	several	ADJ
ap-1199	27	5	remarks	remark	NOUN
ap-1199	27	6	:	:	PUNCT
ap-1199	27	7	1	1	X
ap-1199	27	8	)	)	PUNCT
ap-1199	27	9	the	the	DET
ap-1199	27	10	angle	angle	NOUN
ap-1199	27	11	sε	sε	NOUN
ap-1199	27	12	of	of	ADP
ap-1199	27	13	validity	validity	NOUN
ap-1199	27	14	of	of	ADP
ap-1199	27	15	(	(	PUNCT
ap-1199	27	16	5	5	NUM
ap-1199	27	17	)	)	PUNCT
ap-1199	27	18	,	,	PUNCT
ap-1199	27	19	(	(	PUNCT
ap-1199	27	20	6	6	NUM
ap-1199	27	21	)	)	PUNCT
ap-1199	27	22	,	,	PUNCT
ap-1199	27	23	is	be	AUX
ap-1199	27	24	independent	independent	ADJ
ap-1199	27	25	of	of	ADP
ap-1199	27	26	α	α	PROPN
ap-1199	27	27	,	,	PUNCT
ap-1199	27	28	β	β	X
ap-1199	27	29	and	and	CCONJ
ap-1199	27	30	c.	c.	PROPN
ap-1199	27	31	2	2	NUM
ap-1199	27	32	)	)	PUNCT
ap-1199	27	33	thanks	thank	NOUN
ap-1199	27	34	to	to	ADP
ap-1199	27	35	the	the	DET
ap-1199	27	36	factor	factor	NOUN
ap-1199	27	37	γ	γ	X
ap-1199	27	38	(	(	PUNCT
ap-1199	27	39	k	k	PROPN
ap-1199	28	1	+	+	CCONJ
ap-1199	28	2	β	β	X
ap-1199	28	3	α	α	NOUN
ap-1199	28	4	)	)	PUNCT
ap-1199	28	5	,	,	PUNCT
ap-1199	28	6	the	the	DET
ap-1199	28	7	expansion	expansion	NOUN
ap-1199	28	8	coefficients	coefficient	VERB
ap-1199	28	9	in	in	ADP
ap-1199	28	10	(	(	PUNCT
ap-1199	28	11	5	5	X
ap-1199	28	12	)	)	PUNCT
ap-1199	28	13	grow	grow	VERB
ap-1199	28	14	faster	fast	ADV
ap-1199	28	15	with	with	ADP
ap-1199	28	16	k	k	PROPN
ap-1199	28	17	than	than	ADP
ap-1199	28	18	those	those	PRON
ap-1199	28	19	of	of	ADP
ap-1199	28	20	the	the	DET
ap-1199	28	21	taylor	taylor	PROPN
ap-1199	28	22	series	series	NOUN
ap-1199	28	23	for	for	ADP
ap-1199	28	24	f(x	f(x	PROPN
ap-1199	28	25	)	)	PUNCT
ap-1199	28	26	.	.	PUNCT
ap-1199	29	1	3	3	X
ap-1199	29	2	)	)	PUNCT
ap-1199	29	3	the	the	DET
ap-1199	29	4	expansion	expansion	NOUN
ap-1199	29	5	coefficients	coefficient	VERB
ap-1199	29	6	in	in	ADP
ap-1199	29	7	(	(	PUNCT
ap-1199	29	8	5	5	NUM
ap-1199	29	9	)	)	PUNCT
ap-1199	29	10	are	be	AUX
ap-1199	29	11	independent	independent	ADJ
ap-1199	29	12	of	of	ADP
ap-1199	29	13	c.	c.	PROPN
ap-1199	29	14	this	this	PRON
ap-1199	29	15	illustrates	illustrate	VERB
ap-1199	29	16	the	the	DET
ap-1199	29	17	impossibility	impossibility	NOUN
ap-1199	29	18	of	of	ADP
ap-1199	29	19	a	a	DET
ap-1199	29	20	unique	unique	ADJ
ap-1199	29	21	determination	determination	NOUN
ap-1199	29	22	of	of	ADP
ap-1199	29	23	a	a	DET
ap-1199	29	24	function	function	NOUN
ap-1199	29	25	from	from	ADP
ap-1199	29	26	its	its	PRON
ap-1199	29	27	asymptotic	asymptotic	ADJ
ap-1199	29	28	expansion	expansion	NOUN
ap-1199	29	29	.	.	PUNCT
ap-1199	30	1	presented	present	VERB
ap-1199	30	2	at	at	ADP
ap-1199	30	3	the	the	DET
ap-1199	30	4	international	international	ADJ
ap-1199	30	5	conference	conference	NOUN
ap-1199	30	6	“	"	PUNCT
ap-1199	30	7	selected	select	VERB
ap-1199	30	8	topics	topic	NOUN
ap-1199	30	9	in	in	ADP
ap-1199	30	10	mathematical	mathematical	ADJ
ap-1199	30	11	and	and	CCONJ
ap-1199	30	12	particle	particle	NOUN
ap-1199	30	13	physics	physics	NOUN
ap-1199	30	14	”	"	PUNCT
ap-1199	30	15	organized	organize	VERB
ap-1199	30	16	in	in	ADP
ap-1199	30	17	honour	honour	NOUN
ap-1199	30	18	of	of	ADP
ap-1199	30	19	the	the	DET
ap-1199	30	20	70th	70th	ADJ
ap-1199	30	21	anniversary	anniversary	NOUN
ap-1199	30	22	of	of	ADP
ap-1199	30	23	professor	professor	NOUN
ap-1199	30	24	jiří	jiří	NOUN
ap-1199	30	25	niederle	niederle	NOUN
ap-1199	30	26	at	at	ADP
ap-1199	30	27	new	new	PROPN
ap-1199	30	28	york	york	PROPN
ap-1199	30	29	university	university	PROPN
ap-1199	30	30	,	,	PUNCT
ap-1199	30	31	prague	prague	PROPN
ap-1199	30	32	,	,	PUNCT
ap-1199	30	33	5–7	5–7	PROPN
ap-1199	30	34	may	may	PROPN
ap-1199	30	35	2009	2009	NUM
ap-1199	30	36	.	.	PUNCT
ap-1199	31	1	71	71	NUM
ap-1199	31	2	acta	acta	PROPN
ap-1199	31	3	polytechnica	polytechnica	PROPN
ap-1199	31	4	vol	vol	NOUN
ap-1199	31	5	.	.	PROPN
ap-1199	32	1	50	50	NUM
ap-1199	32	2	no	no	NOUN
ap-1199	32	3	.	.	PUNCT
ap-1199	33	1	3/2010	3/2010	NUM
ap-1199	33	2	in	in	ADP
ap-1199	33	3	the	the	DET
ap-1199	33	4	next	next	ADJ
ap-1199	33	5	section	section	NOUN
ap-1199	33	6	we	we	PRON
ap-1199	33	7	shall	shall	AUX
ap-1199	33	8	give	give	VERB
ap-1199	33	9	a	a	DET
ap-1199	33	10	modification	modification	NOUN
ap-1199	33	11	to	to	ADP
ap-1199	33	12	the	the	DET
ap-1199	33	13	watson	watson	PROPN
ap-1199	33	14	lemma	lemma	PROPN
ap-1199	33	15	,	,	PUNCT
ap-1199	33	16	which	which	PRON
ap-1199	33	17	shows	show	VERB
ap-1199	33	18	that	that	SCONJ
ap-1199	33	19	under	under	ADP
ap-1199	33	20	plausible	plausible	ADJ
ap-1199	33	21	assumptions	assumption	NOUN
ap-1199	33	22	the	the	DET
ap-1199	33	23	straight	straight	ADJ
ap-1199	33	24	integration	integration	NOUN
ap-1199	33	25	contour	contour	NOUN
ap-1199	33	26	can	can	AUX
ap-1199	33	27	be	be	AUX
ap-1199	33	28	bent	bent	ADJ
ap-1199	33	29	.	.	PUNCT
ap-1199	34	1	3	3	NUM
ap-1199	34	2	modified	modify	VERB
ap-1199	34	3	watson	watson	PROPN
ap-1199	34	4	lemma	lemma	PROPN
ap-1199	34	5	the	the	DET
ap-1199	34	6	modified	modified	PROPN
ap-1199	34	7	watson	watson	PROPN
ap-1199	34	8	lemma	lemma	PROPN
ap-1199	35	1	we	we	PRON
ap-1199	35	2	present	present	VERB
ap-1199	35	3	below	below	ADV
ap-1199	35	4	(	(	PUNCT
ap-1199	35	5	and	and	CCONJ
ap-1199	35	6	call	call	VERB
ap-1199	35	7	lemma	lemma	PROPN
ap-1199	35	8	2	2	NUM
ap-1199	35	9	’	'	PUNCT
ap-1199	35	10	)	)	PUNCT
ap-1199	35	11	is	be	AUX
ap-1199	35	12	a	a	DET
ap-1199	35	13	special	special	ADJ
ap-1199	35	14	case	case	NOUN
ap-1199	35	15	of	of	ADP
ap-1199	35	16	lemma	lemma	PROPN
ap-1199	35	17	2	2	NUM
ap-1199	35	18	,	,	PUNCT
ap-1199	35	19	which	which	PRON
ap-1199	35	20	we	we	PRON
ap-1199	35	21	publish	publish	VERB
ap-1199	35	22	and	and	CCONJ
ap-1199	35	23	prove	prove	VERB
ap-1199	35	24	in	in	ADP
ap-1199	35	25	ref	ref	NOUN
ap-1199	35	26	.	.	PUNCT
ap-1199	36	1	[	[	X
ap-1199	36	2	6	6	NUM
ap-1199	36	3	]	]	PUNCT
ap-1199	36	4	.	.	PUNCT
ap-1199	37	1	the	the	DET
ap-1199	37	2	special	special	ADJ
ap-1199	37	3	form	form	NOUN
ap-1199	37	4	given	give	VERB
ap-1199	37	5	here	here	ADV
ap-1199	37	6	is	be	AUX
ap-1199	37	7	obtained	obtain	VERB
ap-1199	37	8	from	from	ADP
ap-1199	37	9	that	that	PRON
ap-1199	37	10	given	give	VERB
ap-1199	37	11	in	in	ADP
ap-1199	37	12	[	[	X
ap-1199	37	13	6	6	NUM
ap-1199	37	14	]	]	PUNCT
ap-1199	37	15	by	by	ADP
ap-1199	37	16	setting	set	VERB
ap-1199	37	17	α	α	NOUN
ap-1199	37	18	=	=	PUNCT
ap-1199	37	19	β	β	X
ap-1199	37	20	=	=	SYM
ap-1199	37	21	1	1	X
ap-1199	37	22	.	.	PUNCT
ap-1199	38	1	let	let	AUX
ap-1199	38	2	g(r	g(r	PROPN
ap-1199	38	3	)	)	PUNCT
ap-1199	38	4	be	be	AUX
ap-1199	38	5	a	a	DET
ap-1199	38	6	continuous	continuous	ADJ
ap-1199	38	7	complex	complex	ADJ
ap-1199	38	8	function	function	NOUN
ap-1199	38	9	of	of	ADP
ap-1199	38	10	the	the	DET
ap-1199	38	11	form	form	NOUN
ap-1199	38	12	g(r	g(r	NOUN
ap-1199	38	13	)	)	PUNCT
ap-1199	39	1	=	=	PUNCT
ap-1199	39	2	r	r	NOUN
ap-1199	39	3	exp(ig(r	exp(ig(r	PROPN
ap-1199	39	4	)	)	PUNCT
ap-1199	39	5	)	)	PUNCT
ap-1199	39	6	,	,	PUNCT
ap-1199	39	7	where	where	SCONJ
ap-1199	39	8	g(r	g(r	NOUN
ap-1199	39	9	)	)	PUNCT
ap-1199	39	10	is	be	AUX
ap-1199	39	11	a	a	DET
ap-1199	39	12	real	real	ADV
ap-1199	39	13	-	-	PUNCT
ap-1199	39	14	valued	value	VERB
ap-1199	39	15	function	function	NOUN
ap-1199	39	16	given	give	VERB
ap-1199	39	17	on	on	ADP
ap-1199	39	18	0	0	NUM
ap-1199	39	19	≤	≤	NUM
ap-1199	39	20	r	r	NOUN
ap-1199	39	21	<	<	X
ap-1199	39	22	c	c	NOUN
ap-1199	39	23	,	,	PUNCT
ap-1199	39	24	with	with	ADP
ap-1199	39	25	0	0	NUM
ap-1199	39	26	<	<	X
ap-1199	39	27	c	c	NOUN
ap-1199	39	28	≤	≤	PUNCT
ap-1199	39	29	∞.	∞.	PROPN
ap-1199	39	30	assume	assume	VERB
ap-1199	39	31	that	that	SCONJ
ap-1199	39	32	the	the	DET
ap-1199	39	33	derivative	derivative	ADJ
ap-1199	39	34	g′(r	g′(r	NOUN
ap-1199	39	35	)	)	PUNCT
ap-1199	39	36	is	be	AUX
ap-1199	39	37	continuous	continuous	ADJ
ap-1199	39	38	on	on	ADP
ap-1199	39	39	the	the	DET
ap-1199	39	40	interval	interval	NOUN
ap-1199	39	41	0	0	NUM
ap-1199	40	1	≤	≤	NUM
ap-1199	40	2	r	r	NOUN
ap-1199	40	3	<	<	X
ap-1199	40	4	c	c	NOUN
ap-1199	40	5	and	and	CCONJ
ap-1199	40	6	a	a	DET
ap-1199	40	7	constant	constant	ADJ
ap-1199	40	8	r0	r0	NOUN
ap-1199	40	9	>	>	X
ap-1199	40	10	0	0	NUM
ap-1199	40	11	exists	exist	VERB
ap-1199	40	12	such	such	ADJ
ap-1199	40	13	that	that	SCONJ
ap-1199	40	14	|g′(r)|	|g′(r)|	PROPN
ap-1199	40	15	≤	≤	ADJ
ap-1199	40	16	k1r	k1r	NOUN
ap-1199	40	17	γ1	γ1	NOUN
ap-1199	40	18	,	,	PUNCT
ap-1199	40	19	r0	r0	NOUN
ap-1199	40	20	≤	≤	NOUN
ap-1199	40	21	r	r	NOUN
ap-1199	40	22	<	<	X
ap-1199	40	23	c	c	NOUN
ap-1199	40	24	,	,	PUNCT
ap-1199	40	25	(	(	PUNCT
ap-1199	40	26	7	7	X
ap-1199	40	27	)	)	PUNCT
ap-1199	40	28	for	for	ADP
ap-1199	40	29	a	a	DET
ap-1199	40	30	nonnegative	nonnegative	ADJ
ap-1199	40	31	k1	k1	NOUN
ap-1199	40	32	and	and	CCONJ
ap-1199	40	33	a	a	DET
ap-1199	40	34	real	real	ADJ
ap-1199	40	35	γ1	γ1	NOUN
ap-1199	40	36	.	.	PUNCT
ap-1199	41	1	assume	assume	VERB
ap-1199	41	2	that	that	SCONJ
ap-1199	41	3	the	the	DET
ap-1199	41	4	parameter	parameter	NOUN
ap-1199	41	5	ε	ε	PROPN
ap-1199	41	6	>	>	X
ap-1199	41	7	0	0	NUM
ap-1199	41	8	exists	exist	VERB
ap-1199	41	9	such	such	ADJ
ap-1199	41	10	that	that	SCONJ
ap-1199	41	11	the	the	DET
ap-1199	41	12	quantities	quantity	NOUN
ap-1199	41	13	a	a	DET
ap-1199	41	14	=	=	X
ap-1199	41	15	inf	inf	NOUN
ap-1199	41	16	r0≤r	r0≤r	PROPN
ap-1199	41	17	<	<	X
ap-1199	41	18	c	c	PROPN
ap-1199	41	19	g(r	g(r	PROPN
ap-1199	41	20	)	)	PUNCT
ap-1199	41	21	,	,	PUNCT
ap-1199	41	22	b	b	X
ap-1199	41	23	=	=	SYM
ap-1199	41	24	sup	sup	NUM
ap-1199	41	25	r0≤r	r0≤r	PROPN
ap-1199	41	26	<	<	X
ap-1199	41	27	c	c	PROPN
ap-1199	41	28	g(r	g(r	PROPN
ap-1199	41	29	)	)	PUNCT
ap-1199	41	30	(	(	PUNCT
ap-1199	41	31	8)	8)	NUM
ap-1199	41	32	satisfy	satisfy	VERB
ap-1199	41	33	the	the	DET
ap-1199	41	34	inequality	inequality	NOUN
ap-1199	42	1	b	b	PROPN
ap-1199	42	2	−a	−a	NOUN
ap-1199	42	3	<	<	X
ap-1199	42	4	π	π	X
ap-1199	42	5	−	−	PROPN
ap-1199	42	6	2ε	2ε	PROPN
ap-1199	42	7	.	.	PUNCT
ap-1199	43	1	(	(	PUNCT
ap-1199	43	2	9	9	X
ap-1199	43	3	)	)	PUNCT
ap-1199	43	4	let	let	VERB
ap-1199	43	5	the	the	DET
ap-1199	43	6	function	function	NOUN
ap-1199	43	7	f(u	f(u	PROPN
ap-1199	43	8	)	)	PUNCT
ap-1199	43	9	be	be	AUX
ap-1199	43	10	defined	define	VERB
ap-1199	43	11	along	along	ADP
ap-1199	43	12	the	the	DET
ap-1199	43	13	curve	curve	NOUN
ap-1199	43	14	u	u	NOUN
ap-1199	43	15	=	=	PROPN
ap-1199	43	16	g(r	g(r	PROPN
ap-1199	43	17	)	)	PUNCT
ap-1199	43	18	and	and	CCONJ
ap-1199	43	19	on	on	ADP
ap-1199	43	20	the	the	DET
ap-1199	43	21	disc	disc	NOUN
ap-1199	43	22	|u|	|u|	PROPN
ap-1199	43	23	<	<	X
ap-1199	43	24	ρ	ρ	PROPN
ap-1199	43	25	,	,	PUNCT
ap-1199	43	26	where	where	SCONJ
ap-1199	43	27	ρ	ρ	NOUN
ap-1199	43	28	>	>	X
ap-1199	43	29	r0	r0	NOUN
ap-1199	43	30	.	.	PUNCT
ap-1199	44	1	let	let	AUX
ap-1199	44	2	f(u	f(u	PROPN
ap-1199	44	3	)	)	PUNCT
ap-1199	44	4	be	be	AUX
ap-1199	44	5	holomorphic	holomorphic	ADJ
ap-1199	44	6	on	on	ADP
ap-1199	44	7	the	the	DET
ap-1199	44	8	disc	disc	NOUN
ap-1199	44	9	and	and	CCONJ
ap-1199	44	10	measurable	measurable	ADJ
ap-1199	44	11	on	on	ADP
ap-1199	44	12	the	the	DET
ap-1199	44	13	curve	curve	NOUN
ap-1199	44	14	.	.	PUNCT
ap-1199	45	1	assume	assume	VERB
ap-1199	45	2	that	that	SCONJ
ap-1199	45	3	|f(g(r))|	|f(g(r))|	ADJ
ap-1199	45	4	≤	≤	PROPN
ap-1199	45	5	k2r	k2r	VERB
ap-1199	45	6	γ2	γ2	PROPN
ap-1199	45	7	,	,	PUNCT
ap-1199	45	8	r0	r0	VERB
ap-1199	45	9	≤	≤	NOUN
ap-1199	45	10	r	r	NOUN
ap-1199	45	11	<	<	X
ap-1199	45	12	c	c	NOUN
ap-1199	45	13	,	,	PUNCT
ap-1199	45	14	(	(	PUNCT
ap-1199	45	15	10	10	X
ap-1199	45	16	)	)	PUNCT
ap-1199	45	17	hold	hold	VERB
ap-1199	45	18	for	for	ADP
ap-1199	45	19	a	a	DET
ap-1199	45	20	nonnegative	nonnegative	ADJ
ap-1199	45	21	k2	k2	NOUN
ap-1199	45	22	and	and	CCONJ
ap-1199	45	23	a	a	DET
ap-1199	45	24	real	real	ADJ
ap-1199	45	25	γ2	γ2	NOUN
ap-1199	45	26	.	.	PUNCT
ap-1199	46	1	define	define	VERB
ap-1199	46	2	the	the	DET
ap-1199	46	3	function	function	NOUN
ap-1199	46	4	φ(g)b	φ(g)b	PROPN
ap-1199	46	5	,	,	PUNCT
ap-1199	46	6	c	c	NOUN
ap-1199	46	7	(	(	PUNCT
ap-1199	46	8	λ	λ	NOUN
ap-1199	46	9	)	)	PUNCT
ap-1199	46	10	for	for	ADP
ap-1199	46	11	0	0	NUM
ap-1199	46	12	≤	≤	NUM
ap-1199	46	13	b	b	NOUN
ap-1199	46	14	<	<	X
ap-1199	46	15	c	c	X
ap-1199	46	16	by1	by1	PROPN
ap-1199	46	17	φ(g)b	φ(g)b	PROPN
ap-1199	46	18	,	,	PUNCT
ap-1199	46	19	c	c	PROPN
ap-1199	46	20	(	(	PUNCT
ap-1199	46	21	λ	λ	NOUN
ap-1199	46	22	)	)	PUNCT
ap-1199	46	23	=	=	SYM
ap-1199	47	1	∫	∫	PROPN
ap-1199	47	2	c	c	NOUN
ap-1199	47	3	r	r	NOUN
ap-1199	47	4	=	=	PROPN
ap-1199	47	5	b	b	NOUN
ap-1199	47	6	e−λg(r)g(r)f(g(r))dg(r	e−λg(r)g(r)f(g(r))dg(r	NUM
ap-1199	47	7	)	)	PUNCT
ap-1199	47	8	.	.	PUNCT
ap-1199	48	1	(	(	PUNCT
ap-1199	48	2	11	11	X
ap-1199	48	3	)	)	PUNCT
ap-1199	48	4	lemma	lemma	PROPN
ap-1199	48	5	2	2	NUM
ap-1199	48	6	’	'	PUNCT
ap-1199	48	7	:	:	PUNCT
ap-1199	48	8	if	if	SCONJ
ap-1199	48	9	the	the	DET
ap-1199	48	10	above	above	ADJ
ap-1199	48	11	assumptions	assumption	NOUN
ap-1199	48	12	are	be	AUX
ap-1199	48	13	fulfilled	fulfil	VERB
ap-1199	48	14	,	,	PUNCT
ap-1199	48	15	then	then	ADV
ap-1199	48	16	the	the	DET
ap-1199	48	17	asymptotic	asymptotic	ADJ
ap-1199	48	18	expansion	expansion	NOUN
ap-1199	48	19	φ(g)0,c	φ(g)0,c	NOUN
ap-1199	48	20	(	(	PUNCT
ap-1199	48	21	λ	λ	NOUN
ap-1199	48	22	)	)	PUNCT
ap-1199	48	23	∼	∼	VERB
ap-1199	48	24	∞∑	∞∑	PRON
ap-1199	48	25	k=0	k=0	PROPN
ap-1199	48	26	λ−(k+1	λ−(k+1	PROPN
ap-1199	48	27	)	)	PUNCT
ap-1199	48	28	γ(k	γ(k	NOUN
ap-1199	48	29	+	+	CCONJ
ap-1199	48	30	1	1	X
ap-1199	48	31	)	)	PUNCT
ap-1199	48	32	f	f	NOUN
ap-1199	48	33	(	(	PUNCT
ap-1199	48	34	k)(0	k)(0	X
ap-1199	48	35	)	)	PUNCT
ap-1199	49	1	k	k	X
ap-1199	49	2	!	!	PUNCT
ap-1199	50	1	(	(	PUNCT
ap-1199	50	2	12	12	NUM
ap-1199	50	3	)	)	PUNCT
ap-1199	50	4	holds	hold	VERB
ap-1199	50	5	for	for	ADP
ap-1199	50	6	λ	λ	PROPN
ap-1199	50	7	→∞	→∞	PROPN
ap-1199	50	8	,	,	PUNCT
ap-1199	50	9	λ	λ	PROPN
ap-1199	50	10	∈	∈	PROPN
ap-1199	50	11	tε	tε	NOUN
ap-1199	50	12	,	,	PUNCT
ap-1199	50	13	where	where	SCONJ
ap-1199	50	14	tε=	tε=	PROPN
ap-1199	50	15	{	{	PUNCT
ap-1199	50	16	λ	λ	X
ap-1199	50	17	:	:	PUNCT
ap-1199	51	1	λ	λ	X
ap-1199	51	2	=	=	SYM
ap-1199	51	3	|λ|	|λ|	PROPN
ap-1199	51	4	exp(iϕ	exp(iϕ	ADJ
ap-1199	51	5	)	)	PUNCT
ap-1199	51	6	,	,	PUNCT
ap-1199	51	7	−π	−π	ADV
ap-1199	51	8	2	2	X
ap-1199	51	9	−a+	−a+	X
ap-1199	51	10	ε	ε	X
ap-1199	51	11	<	<	X
ap-1199	51	12	ϕ	ϕ	X
ap-1199	51	13	<	<	X
ap-1199	51	14	π	π	PROPN
ap-1199	51	15	2	2	NUM
ap-1199	51	16	−b	−b	ADV
ap-1199	51	17	−	−	X
ap-1199	51	18	ε	ε	PROPN
ap-1199	51	19	}	}	PUNCT
ap-1199	51	20	.	.	PUNCT
ap-1199	52	1	(	(	PUNCT
ap-1199	52	2	13	13	NUM
ap-1199	52	3	)	)	PUNCT
ap-1199	52	4	we	we	PRON
ap-1199	52	5	refer	refer	VERB
ap-1199	52	6	the	the	DET
ap-1199	52	7	reader	reader	NOUN
ap-1199	52	8	to	to	PART
ap-1199	52	9	ref	ref	VERB
ap-1199	52	10	.	.	PUNCT
ap-1199	53	1	[	[	X
ap-1199	53	2	6	6	NUM
ap-1199	53	3	]	]	PUNCT
ap-1199	53	4	for	for	ADP
ap-1199	53	5	the	the	DET
ap-1199	53	6	proof	proof	NOUN
ap-1199	53	7	of	of	ADP
ap-1199	53	8	lemma	lemma	PROPN
ap-1199	53	9	2	2	NUM
ap-1199	53	10	and	and	CCONJ
ap-1199	53	11	its	its	PRON
ap-1199	53	12	discussion	discussion	NOUN
ap-1199	53	13	.	.	PUNCT
ap-1199	54	1	the	the	DET
ap-1199	54	2	above	above	ADJ
ap-1199	54	3	simplified	simplified	ADJ
ap-1199	54	4	version	version	NOUN
ap-1199	54	5	,	,	PUNCT
ap-1199	54	6	lemma	lemma	PROPN
ap-1199	54	7	2	2	NUM
ap-1199	54	8	’	'	PUNCT
ap-1199	54	9	,	,	PUNCT
ap-1199	54	10	is	be	AUX
ap-1199	54	11	given	give	VERB
ap-1199	54	12	here	here	ADV
ap-1199	54	13	to	to	PART
ap-1199	54	14	illustrate	illustrate	VERB
ap-1199	54	15	some	some	DET
ap-1199	54	16	special	special	ADJ
ap-1199	54	17	features	feature	NOUN
ap-1199	54	18	of	of	ADP
ap-1199	54	19	the	the	DET
ap-1199	54	20	general	general	ADJ
ap-1199	54	21	lemma	lemma	PROPN
ap-1199	54	22	2	2	NUM
ap-1199	54	23	and	and	CCONJ
ap-1199	54	24	its	its	PRON
ap-1199	54	25	possible	possible	ADJ
ap-1199	54	26	applications	application	NOUN
ap-1199	54	27	.	.	PUNCT
ap-1199	55	1	let	let	VERB
ap-1199	55	2	us	we	PRON
ap-1199	55	3	add	add	VERB
ap-1199	55	4	several	several	ADJ
ap-1199	55	5	remarks	remark	NOUN
ap-1199	55	6	to	to	ADP
ap-1199	55	7	lemma	lemma	PROPN
ap-1199	55	8	2	2	NUM
ap-1199	55	9	’	'	PUNCT
ap-1199	55	10	:	:	PUNCT
ap-1199	55	11	1/	1/	NUM
ap-1199	55	12	lemma	lemma	NOUN
ap-1199	55	13	2	2	NUM
ap-1199	55	14	’	'	PUNCT
ap-1199	55	15	implies	imply	VERB
ap-1199	55	16	watson	watson	PROPN
ap-1199	55	17	’s	’s	PART
ap-1199	55	18	lemma	lemma	PROPN
ap-1199	55	19	when	when	SCONJ
ap-1199	55	20	the	the	DET
ap-1199	55	21	integration	integration	NOUN
ap-1199	55	22	contour	contour	NOUN
ap-1199	55	23	is	be	AUX
ap-1199	55	24	chosen	choose	VERB
ap-1199	55	25	to	to	PART
ap-1199	55	26	have	have	VERB
ap-1199	55	27	the	the	DET
ap-1199	55	28	special	special	ADJ
ap-1199	55	29	form	form	NOUN
ap-1199	55	30	of	of	ADP
ap-1199	55	31	a	a	DET
ap-1199	55	32	segment	segment	NOUN
ap-1199	55	33	of	of	ADP
ap-1199	55	34	the	the	DET
ap-1199	55	35	real	real	ADJ
ap-1199	55	36	positive	positive	ADJ
ap-1199	55	37	semiaxis	semiaxis	NOUN
ap-1199	55	38	,	,	PUNCT
ap-1199	55	39	i.e.	i.e.	X
ap-1199	55	40	g(r	g(r	ADJ
ap-1199	55	41	)	)	PUNCT
ap-1199	55	42	≡	≡	PROPN
ap-1199	55	43	0	0	NUM
ap-1199	55	44	,	,	PUNCT
ap-1199	55	45	and	and	CCONJ
ap-1199	55	46	f(r	f(r	NOUN
ap-1199	55	47	)	)	PUNCT
ap-1199	55	48	∈	∈	PROPN
ap-1199	55	49	c∞[0	c∞[0	NOUN
ap-1199	55	50	,	,	PUNCT
ap-1199	55	51	c	c	NOUN
ap-1199	55	52	]	]	X
ap-1199	55	53	.	.	PUNCT
ap-1199	56	1	2/	2/	NUM
ap-1199	56	2	perturbation	perturbation	NOUN
ap-1199	56	3	theory	theory	NOUN
ap-1199	56	4	is	be	AUX
ap-1199	56	5	obtained	obtain	VERB
ap-1199	56	6	by	by	ADP
ap-1199	56	7	setting	set	VERB
ap-1199	56	8	λ	λ	PROPN
ap-1199	56	9	=	=	SYM
ap-1199	56	10	1	1	NUM
ap-1199	56	11	/	/	SYM
ap-1199	56	12	z	z	NOUN
ap-1199	56	13	in	in	ADP
ap-1199	56	14	(	(	PUNCT
ap-1199	56	15	10	10	NUM
ap-1199	56	16	)	)	PUNCT
ap-1199	56	17	,	,	PUNCT
ap-1199	56	18	(	(	PUNCT
ap-1199	56	19	11	11	NUM
ap-1199	56	20	)	)	PUNCT
ap-1199	56	21	.	.	PUNCT
ap-1199	57	1	then	then	ADV
ap-1199	57	2	,	,	PUNCT
ap-1199	57	3	the	the	DET
ap-1199	57	4	function	function	NOUN
ap-1199	57	5	f	f	X
ap-1199	57	6	(	(	PUNCT
ap-1199	57	7	g	g	NOUN
ap-1199	57	8	)	)	PUNCT
ap-1199	57	9	0,c	0,c	NOUN
ap-1199	57	10	(	(	PUNCT
ap-1199	57	11	z	z	X
ap-1199	57	12	)	)	PUNCT
ap-1199	57	13	=	=	SYM
ap-1199	58	1	∫	∫	PROPN
ap-1199	58	2	c	c	PROPN
ap-1199	58	3	r=0	r=0	PROPN
ap-1199	58	4	e−g(r)/z	e−g(r)/z	NOUN
ap-1199	58	5	f(g(r	f(g(r	PROPN
ap-1199	58	6	)	)	PUNCT
ap-1199	58	7	)	)	PUNCT
ap-1199	58	8	dg(r	dg(r	ADP
ap-1199	58	9	)	)	PUNCT
ap-1199	58	10	(	(	PUNCT
ap-1199	58	11	14	14	NUM
ap-1199	58	12	)	)	PUNCT
ap-1199	58	13	has	have	VERB
ap-1199	58	14	the	the	DET
ap-1199	58	15	asymptotic	asymptotic	ADJ
ap-1199	58	16	expansion	expansion	NOUN
ap-1199	58	17	f	f	X
ap-1199	58	18	(	(	PUNCT
ap-1199	58	19	g	g	NOUN
ap-1199	58	20	)	)	PUNCT
ap-1199	58	21	0,c	0,c	NOUN
ap-1199	59	1	(	(	PUNCT
ap-1199	59	2	z	z	NOUN
ap-1199	59	3	)	)	PUNCT
ap-1199	59	4	∼	∼	VERB
ap-1199	59	5	∞∑	∞∑	PRON
ap-1199	59	6	k=0	k=0	PROPN
ap-1199	59	7	zk+1f	zk+1f	NOUN
ap-1199	59	8	(	(	PUNCT
ap-1199	59	9	k)(0	k)(0	NUM
ap-1199	59	10	)	)	PUNCT
ap-1199	59	11	(	(	PUNCT
ap-1199	59	12	15	15	NUM
ap-1199	59	13	)	)	PUNCT
ap-1199	59	14	for	for	ADP
ap-1199	59	15	z	z	NOUN
ap-1199	59	16	→	→	SYM
ap-1199	59	17	0	0	NUM
ap-1199	59	18	and	and	CCONJ
ap-1199	59	19	z	z	PROPN
ap-1199	59	20	∈	∈	PROPN
ap-1199	59	21	zε	zε	NOUN
ap-1199	59	22	,	,	PUNCT
ap-1199	59	23	where	where	SCONJ
ap-1199	59	24	zε=	zε=	PROPN
ap-1199	59	25	{	{	PUNCT
ap-1199	59	26	z	z	NOUN
ap-1199	59	27	:	:	PUNCT
ap-1199	59	28	z	z	X
ap-1199	60	1	=	=	PUNCT
ap-1199	60	2	|z|	|z|	PROPN
ap-1199	60	3	exp	exp	NOUN
ap-1199	60	4	(	(	PUNCT
ap-1199	60	5	iχ	iχ	PROPN
ap-1199	60	6	)	)	PUNCT
ap-1199	60	7	,	,	PUNCT
ap-1199	60	8	−π	−π	ADV
ap-1199	60	9	2	2	NUM
ap-1199	61	1	+	+	SYM
ap-1199	61	2	b	b	NOUN
ap-1199	61	3	+	+	CCONJ
ap-1199	61	4	ε	ε	X
ap-1199	61	5	<	<	X
ap-1199	61	6	χ	χ	X
ap-1199	61	7	<	<	X
ap-1199	61	8	π	π	X
ap-1199	61	9	2	2	NUM
ap-1199	61	10	+	+	ADJ
ap-1199	61	11	a−	a−	PROPN
ap-1199	61	12	ε	ε	PROPN
ap-1199	61	13	}	}	PUNCT
ap-1199	61	14	.	.	PUNCT
ap-1199	62	1	(	(	PUNCT
ap-1199	62	2	16	16	NUM
ap-1199	62	3	)	)	PUNCT
ap-1199	62	4	3/	3/	NUM
ap-1199	62	5	the	the	DET
ap-1199	62	6	parameter	parameter	NOUN
ap-1199	62	7	ε	ε	PROPN
ap-1199	62	8	in	in	ADP
ap-1199	62	9	(	(	PUNCT
ap-1199	62	10	9	9	NUM
ap-1199	62	11	)	)	PUNCT
ap-1199	62	12	is	be	AUX
ap-1199	62	13	limited	limit	VERB
ap-1199	62	14	by	by	ADP
ap-1199	62	15	0	0	NUM
ap-1199	62	16	<	<	X
ap-1199	62	17	ε	ε	X
ap-1199	62	18	<	<	X
ap-1199	62	19	π/2−(b−a)/2	π/2−(b−a)/2	NOUN
ap-1199	62	20	,	,	PUNCT
ap-1199	62	21	but	but	CCONJ
ap-1199	62	22	is	be	AUX
ap-1199	62	23	otherwise	otherwise	ADV
ap-1199	62	24	arbitrary	arbitrary	ADJ
ap-1199	62	25	.	.	PUNCT
ap-1199	63	1	note	note	VERB
ap-1199	63	2	however	however	ADV
ap-1199	63	3	that	that	SCONJ
ap-1199	63	4	the	the	DET
ap-1199	63	5	upper	upper	ADJ
ap-1199	63	6	limit	limit	NOUN
ap-1199	63	7	of	of	ADP
ap-1199	63	8	ε	ε	PROPN
ap-1199	63	9	depends	depend	VERB
ap-1199	63	10	on	on	ADP
ap-1199	63	11	b	b	NOUN
ap-1199	63	12	−	−	NOUN
ap-1199	63	13	a	a	PROPN
ap-1199	63	14	and	and	CCONJ
ap-1199	63	15	may	may	AUX
ap-1199	63	16	be	be	AUX
ap-1199	63	17	considerably	considerably	ADV
ap-1199	63	18	less	less	ADJ
ap-1199	63	19	than	than	ADP
ap-1199	63	20	π/2	π/2	NUM
ap-1199	63	21	.	.	PUNCT
ap-1199	64	1	this	this	PRON
ap-1199	64	2	happens	happen	VERB
ap-1199	64	3	,	,	PUNCT
ap-1199	64	4	for	for	ADP
ap-1199	64	5	instance	instance	NOUN
ap-1199	64	6	,	,	PUNCT
ap-1199	64	7	if	if	SCONJ
ap-1199	64	8	the	the	DET
ap-1199	64	9	integration	integration	NOUN
ap-1199	64	10	contour	contour	NOUN
ap-1199	64	11	is	be	AUX
ap-1199	64	12	bent	bent	ADJ
ap-1199	64	13	or	or	CCONJ
ap-1199	64	14	meandering	meander	VERB
ap-1199	64	15	.	.	PUNCT
ap-1199	65	1	4/	4/	NUM
ap-1199	65	2	the	the	DET
ap-1199	65	3	parametrization	parametrization	NOUN
ap-1199	65	4	g(r	g(r	NOUN
ap-1199	65	5	)	)	PUNCT
ap-1199	65	6	=	=	SYM
ap-1199	66	1	r	r	NOUN
ap-1199	66	2	exp	exp	NOUN
ap-1199	66	3	(	(	PUNCT
ap-1199	66	4	ig(r	ig(r	NOUN
ap-1199	66	5	)	)	PUNCT
ap-1199	66	6	)	)	PUNCT
ap-1199	66	7	does	do	AUX
ap-1199	66	8	not	not	PART
ap-1199	66	9	include	include	VERB
ap-1199	66	10	contours	contour	NOUN
ap-1199	66	11	that	that	PRON
ap-1199	66	12	cross	cross	VERB
ap-1199	66	13	a	a	DET
ap-1199	66	14	circle	circle	NOUN
ap-1199	66	15	centred	centre	VERB
ap-1199	66	16	at	at	ADP
ap-1199	66	17	r	r	NOUN
ap-1199	66	18	=	=	SYM
ap-1199	66	19	0	0	NUM
ap-1199	66	20	,	,	PUNCT
ap-1199	66	21	either	either	CCONJ
ap-1199	66	22	touching	touching	ADJ
ap-1199	66	23	or	or	CCONJ
ap-1199	66	24	doubly	doubly	ADV
ap-1199	66	25	intersecting	intersect	VERB
ap-1199	66	26	it	it	PRON
ap-1199	66	27	,	,	PUNCT
ap-1199	66	28	so	so	SCONJ
ap-1199	66	29	that	that	SCONJ
ap-1199	66	30	the	the	DET
ap-1199	66	31	derivative	derivative	ADJ
ap-1199	66	32	g′(r	g′(r	NOUN
ap-1199	66	33	)	)	PUNCT
ap-1199	66	34	either	either	CCONJ
ap-1199	66	35	does	do	AUX
ap-1199	66	36	not	not	PART
ap-1199	66	37	exist	exist	VERB
ap-1199	66	38	or	or	CCONJ
ap-1199	66	39	is	be	AUX
ap-1199	66	40	not	not	PART
ap-1199	66	41	bounded	bound	VERB
ap-1199	66	42	.	.	PUNCT
ap-1199	67	1	in	in	ADP
ap-1199	67	2	such	such	ADJ
ap-1199	67	3	cases	case	NOUN
ap-1199	67	4	,	,	PUNCT
ap-1199	67	5	the	the	DET
ap-1199	67	6	parametrization	parametrization	NOUN
ap-1199	67	7	has	have	VERB
ap-1199	67	8	to	to	PART
ap-1199	67	9	be	be	AUX
ap-1199	67	10	modified	modify	VERB
ap-1199	67	11	.	.	PUNCT
ap-1199	68	1	5/	5/	NUM
ap-1199	68	2	let	let	VERB
ap-1199	68	3	us	we	PRON
ap-1199	68	4	remark	remark	VERB
ap-1199	68	5	that	that	SCONJ
ap-1199	68	6	the	the	DET
ap-1199	68	7	proof	proof	NOUN
ap-1199	68	8	of	of	ADP
ap-1199	68	9	lemma	lemma	PROPN
ap-1199	68	10	2	2	NUM
ap-1199	68	11	in	in	ADP
ap-1199	68	12	ref	ref	NOUN
ap-1199	68	13	.	.	PUNCT
ap-1199	69	1	[	[	X
ap-1199	69	2	6	6	NUM
ap-1199	69	3	]	]	PUNCT
ap-1199	69	4	allows	allow	VERB
ap-1199	69	5	us	we	PRON
ap-1199	69	6	to	to	PART
ap-1199	69	7	obtain	obtain	VERB
ap-1199	69	8	remarkable	remarkable	ADJ
ap-1199	69	9	correlations	correlation	NOUN
ap-1199	69	10	between	between	ADP
ap-1199	69	11	the	the	DET
ap-1199	69	12	strength	strength	NOUN
ap-1199	69	13	of	of	ADP
ap-1199	69	14	the	the	DET
ap-1199	69	15	bounds	bound	NOUN
ap-1199	69	16	on	on	ADP
ap-1199	69	17	the	the	DET
ap-1199	69	18	remainder	remainder	NOUN
ap-1199	69	19	and	and	CCONJ
ap-1199	69	20	the	the	DET
ap-1199	69	21	size	size	NOUN
ap-1199	69	22	of	of	ADP
ap-1199	69	23	the	the	DET
ap-1199	69	24	angles	angle	NOUN
ap-1199	69	25	within	within	ADP
ap-1199	69	26	which	which	PRON
ap-1199	69	27	the	the	DET
ap-1199	69	28	asymptotic	asymptotic	ADJ
ap-1199	69	29	expansion	expansion	NOUN
ap-1199	69	30	is	be	AUX
ap-1199	69	31	valid	valid	ADJ
ap-1199	69	32	.	.	PUNCT
ap-1199	70	1	it	it	PRON
ap-1199	70	2	follows	follow	VERB
ap-1199	70	3	from	from	ADP
ap-1199	70	4	[	[	X
ap-1199	70	5	6	6	NUM
ap-1199	70	6	]	]	PUNCT
ap-1199	70	7	that	that	SCONJ
ap-1199	70	8	the	the	DET
ap-1199	70	9	bounds	bound	NOUN
ap-1199	70	10	are	be	AUX
ap-1199	70	11	proportional	proportional	ADJ
ap-1199	70	12	to	to	ADP
ap-1199	70	13	1	1	NUM
ap-1199	70	14	(	(	PUNCT
ap-1199	70	15	|λ|	|λ|	NOUN
ap-1199	70	16	−	−	PROPN
ap-1199	70	17	1	1	X
ap-1199	70	18	)	)	PUNCT
ap-1199	70	19	sin	sin	NOUN
ap-1199	70	20	ε	ε	PROPN
ap-1199	70	21	e−(|λ|−1)r0	e−(|λ|−1)r0	PROPN
ap-1199	70	22	sin	sin	NOUN
ap-1199	70	23	ε	ε	PROPN
ap-1199	70	24	(	(	PUNCT
ap-1199	70	25	17	17	NUM
ap-1199	70	26	)	)	PUNCT
ap-1199	70	27	or	or	CCONJ
ap-1199	70	28	to	to	ADP
ap-1199	70	29	cn	cn	PROPN
ap-1199	70	30	(	(	PUNCT
ap-1199	70	31	|λ|	|λ|	PROPN
ap-1199	70	32	sin	sin	NOUN
ap-1199	70	33	ε)−(n+2	ε)−(n+2	NOUN
ap-1199	70	34	)	)	PUNCT
ap-1199	70	35	,	,	PUNCT
ap-1199	70	36	(	(	PUNCT
ap-1199	70	37	18	18	NUM
ap-1199	70	38	)	)	PUNCT
ap-1199	70	39	where	where	SCONJ
ap-1199	70	40	n	n	PRON
ap-1199	70	41	is	be	AUX
ap-1199	70	42	the	the	DET
ap-1199	70	43	truncation	truncation	NOUN
ap-1199	70	44	order	order	NOUN
ap-1199	70	45	and	and	CCONJ
ap-1199	70	46	the	the	DET
ap-1199	70	47	cn	cn	PROPN
ap-1199	70	48	,	,	PUNCT
ap-1199	70	49	n	n	PROPN
ap-1199	70	50	=	=	SYM
ap-1199	70	51	0	0	NUM
ap-1199	70	52	,	,	PUNCT
ap-1199	70	53	1	1	NUM
ap-1199	70	54	,	,	PUNCT
ap-1199	70	55	2	2	NUM
ap-1199	70	56	,	,	PUNCT
ap-1199	70	57	.	.	PUNCT
ap-1199	70	58	.	.	PUNCT
ap-1199	71	1	.	.	PUNCT
ap-1199	72	1	are	be	AUX
ap-1199	72	2	λ	λ	ADJ
ap-1199	72	3	-	-	ADJ
ap-1199	72	4	independent	independent	ADJ
ap-1199	72	5	positive	positive	ADJ
ap-1199	72	6	numbers	number	NOUN
ap-1199	72	7	.	.	PUNCT
ap-1199	73	1	the	the	DET
ap-1199	73	2	bounds	bound	NOUN
ap-1199	73	3	decrease	decrease	VERB
ap-1199	73	4	with	with	ADP
ap-1199	73	5	increasing	increase	VERB
ap-1199	73	6	ε	ε	PROPN
ap-1199	73	7	,	,	PUNCT
ap-1199	73	8	the	the	DET
ap-1199	73	9	parameter	parameter	NOUN
ap-1199	73	10	,	,	PUNCT
ap-1199	73	11	which	which	PRON
ap-1199	73	12	determines	determine	VERB
ap-1199	73	13	the	the	DET
ap-1199	73	14	angles	angle	NOUN
ap-1199	73	15	tε	tε	NOUN
ap-1199	73	16	and	and	CCONJ
ap-1199	73	17	zε	zε	VERB
ap-1199	73	18	,	,	PUNCT
ap-1199	73	19	see	see	VERB
ap-1199	73	20	(	(	PUNCT
ap-1199	73	21	13	13	NUM
ap-1199	73	22	)	)	PUNCT
ap-1199	73	23	and	and	CCONJ
ap-1199	73	24	(	(	PUNCT
ap-1199	73	25	16	16	NUM
ap-1199	73	26	)	)	PUNCT
ap-1199	73	27	respectively	respectively	ADV
ap-1199	73	28	.	.	PUNCT
ap-1199	74	1	as	as	ADP
ap-1199	74	2	a	a	DET
ap-1199	74	3	consequence	consequence	NOUN
ap-1199	74	4	,	,	PUNCT
ap-1199	74	5	the	the	PRON
ap-1199	74	6	larger	large	ADJ
ap-1199	74	7	the	the	DET
ap-1199	74	8	angle	angle	NOUN
ap-1199	74	9	of	of	ADP
ap-1199	74	10	validity	validity	NOUN
ap-1199	74	11	,	,	PUNCT
ap-1199	74	12	the	the	PRON
ap-1199	74	13	looser	loose	ADJ
ap-1199	74	14	the	the	DET
ap-1199	74	15	bound	bind	VERB
ap-1199	74	16	,	,	PUNCT
ap-1199	74	17	and	and	CCONJ
ap-1199	74	18	vice	vice	ADV
ap-1199	74	19	versa	versa	ADV
ap-1199	74	20	.	.	PUNCT
ap-1199	75	1	1this	1this	NUM
ap-1199	75	2	integral	integral	ADJ
ap-1199	75	3	exists	exist	NOUN
ap-1199	75	4	since	since	SCONJ
ap-1199	75	5	we	we	PRON
ap-1199	75	6	assume	assume	VERB
ap-1199	75	7	that	that	SCONJ
ap-1199	75	8	f(u	f(u	PROPN
ap-1199	75	9	)	)	PUNCT
ap-1199	75	10	is	be	AUX
ap-1199	75	11	measurable	measurable	ADJ
ap-1199	75	12	along	along	ADP
ap-1199	75	13	the	the	DET
ap-1199	75	14	curve	curve	NOUN
ap-1199	75	15	u	u	NOUN
ap-1199	75	16	=	=	PROPN
ap-1199	75	17	g(r	g(r	PROPN
ap-1199	75	18	)	)	PUNCT
ap-1199	75	19	and	and	CCONJ
ap-1199	75	20	bounded	bound	VERB
ap-1199	75	21	by	by	ADP
ap-1199	75	22	(	(	PUNCT
ap-1199	75	23	10	10	NUM
ap-1199	75	24	)	)	PUNCT
ap-1199	75	25	.	.	PUNCT
ap-1199	76	1	72	72	NUM
ap-1199	76	2	acta	acta	PROPN
ap-1199	76	3	polytechnica	polytechnica	PROPN
ap-1199	76	4	vol	vol	NOUN
ap-1199	76	5	.	.	PROPN
ap-1199	77	1	50	50	NUM
ap-1199	77	2	no	no	NOUN
ap-1199	77	3	.	.	PUNCT
ap-1199	78	1	3/2010	3/2010	NUM
ap-1199	78	2	4	4	NUM
ap-1199	78	3	some	some	DET
ap-1199	78	4	applications	application	NOUN
ap-1199	78	5	to	to	PART
ap-1199	78	6	perturbative	perturbative	VERB
ap-1199	78	7	qcd	qcd	PROPN
ap-1199	78	8	to	to	PART
ap-1199	78	9	discuss	discuss	VERB
ap-1199	78	10	some	some	DET
ap-1199	78	11	applications	application	NOUN
ap-1199	78	12	of	of	ADP
ap-1199	78	13	lemma	lemma	PROPN
ap-1199	78	14	2	2	NUM
ap-1199	78	15	’	'	PUNCT
ap-1199	78	16	,	,	PUNCT
ap-1199	78	17	we	we	PRON
ap-1199	78	18	take	take	VERB
ap-1199	78	19	the	the	DET
ap-1199	78	20	adler	adler	NOUN
ap-1199	78	21	function	function	NOUN
ap-1199	79	1	[	[	X
ap-1199	79	2	7	7	NUM
ap-1199	79	3	]	]	PUNCT
ap-1199	79	4	,	,	PUNCT
ap-1199	79	5	d(s	d(s	PROPN
ap-1199	79	6	)	)	PUNCT
ap-1199	79	7	=	=	SYM
ap-1199	79	8	−s	−s	NOUN
ap-1199	79	9	dπ(s	dπ(s	PRON
ap-1199	79	10	)	)	PUNCT
ap-1199	80	1	ds	ds	ADP
ap-1199	80	2	−	−	NOUN
ap-1199	80	3	1	1	NUM
ap-1199	80	4	.	.	PUNCT
ap-1199	81	1	(	(	PUNCT
ap-1199	81	2	19	19	NUM
ap-1199	81	3	)	)	PUNCT
ap-1199	81	4	where	where	SCONJ
ap-1199	81	5	π(s	π(s	PROPN
ap-1199	81	6	)	)	PUNCT
ap-1199	81	7	is	be	AUX
ap-1199	81	8	the	the	DET
ap-1199	81	9	polarization	polarization	NOUN
ap-1199	81	10	amplitude	amplitude	NOUN
ap-1199	81	11	defined	define	VERB
ap-1199	81	12	in	in	ADP
ap-1199	81	13	terms	term	NOUN
ap-1199	81	14	of	of	ADP
ap-1199	81	15	the	the	DET
ap-1199	81	16	vector	vector	NOUN
ap-1199	81	17	current	current	ADJ
ap-1199	81	18	products	product	NOUN
ap-1199	81	19	for	for	ADP
ap-1199	81	20	light	light	ADJ
ap-1199	81	21	quarks	quark	NOUN
ap-1199	81	22	.	.	PUNCT
ap-1199	82	1	the	the	DET
ap-1199	82	2	adler	adler	PROPN
ap-1199	82	3	function	function	PROPN
ap-1199	82	4	d(s	d(s	PROPN
ap-1199	82	5	)	)	PUNCT
ap-1199	82	6	is	be	AUX
ap-1199	82	7	real	real	ADV
ap-1199	82	8	analytic	analytic	ADJ
ap-1199	82	9	in	in	ADP
ap-1199	82	10	the	the	DET
ap-1199	82	11	s	s	NOUN
ap-1199	82	12	-	-	NOUN
ap-1199	82	13	plane	plane	NOUN
ap-1199	82	14	,	,	PUNCT
ap-1199	82	15	except	except	SCONJ
ap-1199	82	16	for	for	ADP
ap-1199	82	17	a	a	DET
ap-1199	82	18	cut	cut	NOUN
ap-1199	82	19	along	along	ADP
ap-1199	82	20	the	the	DET
ap-1199	82	21	timelike	timelike	NOUN
ap-1199	82	22	axis	axis	NOUN
ap-1199	82	23	produced	produce	VERB
ap-1199	82	24	by	by	ADP
ap-1199	82	25	unitarity	unitarity	NOUN
ap-1199	82	26	[	[	X
ap-1199	82	27	7	7	NUM
ap-1199	82	28	,	,	PUNCT
ap-1199	82	29	8	8	NUM
ap-1199	82	30	]	]	PUNCT
ap-1199	82	31	.	.	PUNCT
ap-1199	83	1	in	in	ADP
ap-1199	83	2	perturbative	perturbative	ADJ
ap-1199	83	3	qcd	qcd	PROPN
ap-1199	83	4	,	,	PUNCT
ap-1199	83	5	any	any	DET
ap-1199	83	6	finite	finite	ADJ
ap-1199	83	7	-	-	PUNCT
ap-1199	83	8	order	order	NOUN
ap-1199	83	9	approximant	approximant	NOUN
ap-1199	83	10	has	have	AUX
ap-1199	83	11	cuts	cut	NOUN
ap-1199	83	12	along	along	ADP
ap-1199	83	13	the	the	DET
ap-1199	83	14	timelike	timelike	NOUN
ap-1199	83	15	axis	axis	NOUN
ap-1199	83	16	,	,	PUNCT
ap-1199	83	17	while	while	SCONJ
ap-1199	83	18	the	the	DET
ap-1199	83	19	renormalization	renormalization	NOUN
ap-1199	83	20	-	-	PUNCT
ap-1199	83	21	group	group	NOUN
ap-1199	83	22	improved	improve	VERB
ap-1199	83	23	expansion	expansion	NOUN
ap-1199	83	24	,	,	PUNCT
ap-1199	83	25	d(s	d(s	PROPN
ap-1199	83	26	)	)	PUNCT
ap-1199	84	1	=	=	X
ap-1199	84	2	d1	d1	NOUN
ap-1199	84	3	αs(s)/π	αs(s)/π	PUNCT
ap-1199	84	4	+	+	NUM
ap-1199	84	5	d2	d2	PROPN
ap-1199	84	6	(	(	PUNCT
ap-1199	84	7	αs(s)/π)2	αs(s)/π)2	PROPN
ap-1199	84	8	+	+	CCONJ
ap-1199	84	9	d3	d3	PROPN
ap-1199	84	10	(	(	PUNCT
ap-1199	84	11	αs(s)/π)3	αs(s)/π)3	PROPN
ap-1199	84	12	+	+	PUNCT
ap-1199	84	13	.	.	PUNCT
ap-1199	84	14	.	.	PUNCT
ap-1199	84	15	.	.	PUNCT
ap-1199	85	1	,	,	PUNCT
ap-1199	85	2	(	(	PUNCT
ap-1199	85	3	20	20	NUM
ap-1199	85	4	)	)	PUNCT
ap-1199	85	5	has	have	AUX
ap-1199	85	6	,	,	PUNCT
ap-1199	85	7	in	in	ADP
ap-1199	85	8	addition	addition	NOUN
ap-1199	85	9	,	,	PUNCT
ap-1199	85	10	an	an	DET
ap-1199	85	11	unphysical	unphysical	ADJ
ap-1199	85	12	singularity	singularity	NOUN
ap-1199	85	13	due	due	ADP
ap-1199	85	14	to	to	ADP
ap-1199	85	15	the	the	DET
ap-1199	85	16	landau	landau	NOUN
ap-1199	85	17	pole	pole	VERB
ap-1199	85	18	in	in	ADP
ap-1199	85	19	the	the	DET
ap-1199	85	20	running	running	NOUN
ap-1199	85	21	coupling	coupling	NOUN
ap-1199	85	22	αs(s	αs(s	NUM
ap-1199	85	23	)	)	PUNCT
ap-1199	85	24	.	.	PUNCT
ap-1199	86	1	(	(	PUNCT
ap-1199	86	2	20	20	NUM
ap-1199	86	3	)	)	PUNCT
ap-1199	86	4	is	be	AUX
ap-1199	86	5	known	know	VERB
ap-1199	86	6	to	to	PART
ap-1199	86	7	be	be	AUX
ap-1199	86	8	divergent	divergent	ADJ
ap-1199	86	9	,	,	PUNCT
ap-1199	86	10	the	the	DET
ap-1199	86	11	dn	dn	NOUN
ap-1199	86	12	growing	grow	VERB
ap-1199	86	13	as	as	ADP
ap-1199	86	14	n	n	X
ap-1199	86	15	!	!	PUNCT
ap-1199	87	1	at	at	ADP
ap-1199	87	2	large	large	ADJ
ap-1199	87	3	orders	order	NOUN
ap-1199	87	4	[	[	X
ap-1199	87	5	9]–[12	9]–[12	NUM
ap-1199	87	6	]	]	X
ap-1199	87	7	.	.	PUNCT
ap-1199	87	8	4.1	4.1	NUM
ap-1199	87	9	on	on	ADP
ap-1199	87	10	the	the	DET
ap-1199	87	11	high	high	ADJ
ap-1199	87	12	ambiguity	ambiguity	NOUN
ap-1199	87	13	of	of	ADP
ap-1199	87	14	perturbative	perturbative	ADJ
ap-1199	87	15	qcd	qcd	PROPN
ap-1199	87	16	to	to	PART
ap-1199	87	17	discuss	discuss	VERB
ap-1199	87	18	the	the	DET
ap-1199	87	19	implications	implication	NOUN
ap-1199	87	20	of	of	ADP
ap-1199	87	21	lemma	lemma	PROPN
ap-1199	87	22	2	2	NUM
ap-1199	87	23	’	'	PUNCT
ap-1199	87	24	,	,	PUNCT
ap-1199	87	25	we	we	PRON
ap-1199	87	26	first	first	ADV
ap-1199	87	27	define	define	VERB
ap-1199	87	28	the	the	DET
ap-1199	87	29	borel	borel	PROPN
ap-1199	87	30	transform	transform	VERB
ap-1199	87	31	b(u	b(u	PROPN
ap-1199	87	32	)	)	PUNCT
ap-1199	87	33	by	by	ADP
ap-1199	87	34	[	[	X
ap-1199	87	35	11	11	NUM
ap-1199	87	36	]	]	PUNCT
ap-1199	87	37	,	,	PUNCT
ap-1199	87	38	b(u	b(u	PROPN
ap-1199	87	39	)	)	PUNCT
ap-1199	87	40	=	=	PUNCT
ap-1199	88	1	∑	∑	PUNCT
ap-1199	88	2	n≥0	n≥0	PROPN
ap-1199	88	3	bn	bn	PROPN
ap-1199	88	4	un	un	NOUN
ap-1199	88	5	,	,	PUNCT
ap-1199	88	6	bn	bn	NOUN
ap-1199	88	7	=	=	SYM
ap-1199	88	8	dn+1	dn+1	X
ap-1199	88	9	βn	βn	X
ap-1199	88	10	0	0	NUM
ap-1199	88	11	n	n	CCONJ
ap-1199	88	12	!	!	PUNCT
ap-1199	88	13	.	.	PUNCT
ap-1199	89	1	(	(	PUNCT
ap-1199	89	2	21	21	NUM
ap-1199	89	3	)	)	PUNCT
ap-1199	89	4	it	it	PRON
ap-1199	89	5	is	be	AUX
ap-1199	89	6	usually	usually	ADV
ap-1199	89	7	assumed	assume	VERB
ap-1199	89	8	that	that	SCONJ
ap-1199	89	9	the	the	DET
ap-1199	89	10	series	series	NOUN
ap-1199	89	11	(	(	PUNCT
ap-1199	89	12	21	21	NUM
ap-1199	89	13	)	)	PUNCT
ap-1199	89	14	is	be	AUX
ap-1199	89	15	convergent	convergent	ADJ
ap-1199	89	16	on	on	ADP
ap-1199	89	17	a	a	DET
ap-1199	89	18	disc	disc	NOUN
ap-1199	89	19	of	of	ADP
ap-1199	89	20	nonvanishing	nonvanishe	VERB
ap-1199	89	21	radius	radius	NOUN
ap-1199	89	22	(	(	PUNCT
ap-1199	89	23	this	this	DET
ap-1199	89	24	result	result	NOUN
ap-1199	89	25	was	be	AUX
ap-1199	89	26	rigorously	rigorously	ADV
ap-1199	89	27	proved	prove	VERB
ap-1199	89	28	by	by	ADP
ap-1199	89	29	david	david	PROPN
ap-1199	89	30	et	et	PROPN
ap-1199	89	31	al	al	PROPN
ap-1199	89	32	.	.	PUNCT
ap-1199	90	1	[	[	X
ap-1199	90	2	13	13	NUM
ap-1199	90	3	]	]	PUNCT
ap-1199	90	4	for	for	ADP
ap-1199	90	5	the	the	DET
ap-1199	90	6	scalar	scalar	ADJ
ap-1199	90	7	ϕ4	ϕ4	PROPN
ap-1199	90	8	theory	theory	NOUN
ap-1199	90	9	in	in	ADP
ap-1199	90	10	four	four	NUM
ap-1199	90	11	dimensions	dimension	NOUN
ap-1199	90	12	)	)	PUNCT
ap-1199	90	13	.	.	PUNCT
ap-1199	91	1	this	this	PRON
ap-1199	91	2	is	be	AUX
ap-1199	91	3	what	what	PRON
ap-1199	91	4	is	be	AUX
ap-1199	91	5	required	require	VERB
ap-1199	91	6	in	in	ADP
ap-1199	91	7	lemma	lemma	PROPN
ap-1199	91	8	2	2	NUM
ap-1199	91	9	’	'	PUNCT
ap-1199	91	10	for	for	ADP
ap-1199	91	11	the	the	DET
ap-1199	91	12	generalized	generalized	ADJ
ap-1199	91	13	borel	borel	NOUN
ap-1199	91	14	transform	transform	VERB
ap-1199	91	15	f(g(r	f(g(r	PROPN
ap-1199	91	16	)	)	PUNCT
ap-1199	91	17	)	)	PUNCT
ap-1199	91	18	.	.	PUNCT
ap-1199	92	1	if	if	SCONJ
ap-1199	92	2	we	we	PRON
ap-1199	92	3	assume	assume	VERB
ap-1199	92	4	that	that	SCONJ
ap-1199	92	5	the	the	DET
ap-1199	92	6	series	series	NOUN
ap-1199	92	7	(	(	PUNCT
ap-1199	92	8	20	20	NUM
ap-1199	92	9	)	)	PUNCT
ap-1199	92	10	is	be	AUX
ap-1199	92	11	asymptotic	asymptotic	ADJ
ap-1199	92	12	,	,	PUNCT
ap-1199	92	13	lemma	lemma	PROPN
ap-1199	92	14	2	2	NUM
ap-1199	92	15	’	'	PUNCT
ap-1199	92	16	implies	imply	VERB
ap-1199	92	17	a	a	DET
ap-1199	92	18	large	large	ADJ
ap-1199	92	19	freedom	freedom	NOUN
ap-1199	92	20	in	in	ADP
ap-1199	92	21	recovering	recover	VERB
ap-1199	92	22	the	the	DET
ap-1199	92	23	true	true	ADJ
ap-1199	92	24	function	function	NOUN
ap-1199	92	25	from	from	ADP
ap-1199	92	26	its	its	PRON
ap-1199	92	27	coefficients	coefficient	NOUN
ap-1199	92	28	.	.	PUNCT
ap-1199	93	1	all	all	DET
ap-1199	93	2	the	the	DET
ap-1199	93	3	functions	function	NOUN
ap-1199	93	4	dg	dg	VERB
ap-1199	93	5	0,c(s	0,c(	NOUN
ap-1199	93	6	)	)	PUNCT
ap-1199	93	7	of	of	ADP
ap-1199	93	8	the	the	DET
ap-1199	93	9	form	form	NOUN
ap-1199	93	10	dg	dg	VERB
ap-1199	93	11	0,c(s	0,c(s	NUM
ap-1199	93	12	)	)	PUNCT
ap-1199	93	13	=	=	SYM
ap-1199	93	14	1	1	NUM
ap-1199	93	15	β0	β0	NUM
ap-1199	93	16	∫	∫	PROPN
ap-1199	93	17	c	c	PROPN
ap-1199	94	1	r=0	r=0	PROPN
ap-1199	94	2	e	e	PROPN
ap-1199	94	3	−	−	PROPN
ap-1199	94	4	g(r	g(r	PROPN
ap-1199	94	5	)	)	PUNCT
ap-1199	94	6	β0	β0	PROPN
ap-1199	94	7	a(s	a(s	PROPN
ap-1199	94	8	)	)	PUNCT
ap-1199	94	9	b(g(r	b(g(r	PROPN
ap-1199	94	10	)	)	PUNCT
ap-1199	94	11	)	)	PUNCT
ap-1199	95	1	dg(r	dg(r	ADP
ap-1199	95	2	)	)	PUNCT
ap-1199	95	3	,	,	PUNCT
ap-1199	95	4	(	(	PUNCT
ap-1199	95	5	22	22	NUM
ap-1199	95	6	)	)	PUNCT
ap-1199	95	7	where	where	SCONJ
ap-1199	95	8	a(s	a(	NOUN
ap-1199	95	9	)	)	PUNCT
ap-1199	95	10	=	=	SYM
ap-1199	95	11	αs(s)/π	αs(s)/π	NOUN
ap-1199	95	12	,	,	PUNCT
ap-1199	95	13	admit	admit	VERB
ap-1199	95	14	the	the	DET
ap-1199	95	15	asymptotic	asymptotic	ADJ
ap-1199	95	16	expansion	expansion	NOUN
ap-1199	95	17	dg	dg	VERB
ap-1199	95	18	0,c(s	0,c(	NOUN
ap-1199	95	19	)	)	PUNCT
ap-1199	95	20	∼	∼	NOUN
ap-1199	95	21	∞∑	∞∑	NUM
ap-1199	95	22	n=1	n=1	PART
ap-1199	95	23	dn	dn	PROPN
ap-1199	95	24	(	(	PUNCT
ap-1199	95	25	a(s))n	a(s))n	PROPN
ap-1199	95	26	,	,	PUNCT
ap-1199	95	27	as(s)→	as(s)→	NOUN
ap-1199	95	28	0	0	NUM
ap-1199	95	29	,	,	PUNCT
ap-1199	95	30	(	(	PUNCT
ap-1199	95	31	23	23	NUM
ap-1199	95	32	)	)	PUNCT
ap-1199	95	33	in	in	ADP
ap-1199	95	34	a	a	DET
ap-1199	95	35	certain	certain	ADJ
ap-1199	95	36	domain	domain	NOUN
ap-1199	95	37	of	of	ADP
ap-1199	95	38	the	the	DET
ap-1199	95	39	s	s	NOUN
ap-1199	95	40	-	-	NOUN
ap-1199	95	41	plane	plane	NOUN
ap-1199	95	42	,	,	PUNCT
ap-1199	95	43	which	which	PRON
ap-1199	95	44	follows	follow	VERB
ap-1199	95	45	from	from	ADP
ap-1199	95	46	(	(	PUNCT
ap-1199	95	47	13	13	NUM
ap-1199	95	48	)	)	PUNCT
ap-1199	95	49	and	and	CCONJ
ap-1199	95	50	the	the	DET
ap-1199	95	51	expression	expression	NOUN
ap-1199	95	52	of	of	ADP
ap-1199	95	53	the	the	DET
ap-1199	95	54	running	running	NOUN
ap-1199	95	55	coupling	couple	VERB
ap-1199	95	56	a(s	a(	NOUN
ap-1199	95	57	)	)	PUNCT
ap-1199	95	58	given	give	VERB
ap-1199	95	59	by	by	ADP
ap-1199	95	60	the	the	DET
ap-1199	95	61	renormalization	renormalization	NOUN
ap-1199	95	62	group	group	NOUN
ap-1199	95	63	.	.	PUNCT
ap-1199	96	1	no	no	DET
ap-1199	96	2	function	function	NOUN
ap-1199	96	3	of	of	ADP
ap-1199	96	4	the	the	DET
ap-1199	96	5	form	form	NOUN
ap-1199	96	6	dg	dg	VERB
ap-1199	96	7	0,c(s	0,c(	NOUN
ap-1199	96	8	)	)	PUNCT
ap-1199	96	9	,	,	PUNCT
ap-1199	96	10	(	(	PUNCT
ap-1199	96	11	22	22	NUM
ap-1199	96	12	)	)	PUNCT
ap-1199	96	13	,	,	PUNCT
ap-1199	96	14	can	can	AUX
ap-1199	96	15	be	be	AUX
ap-1199	96	16	a	a	DET
ap-1199	96	17	priori	priori	ADV
ap-1199	96	18	preferred	prefer	VERB
ap-1199	96	19	when	when	SCONJ
ap-1199	96	20	looking	look	VERB
ap-1199	96	21	for	for	ADP
ap-1199	96	22	the	the	DET
ap-1199	96	23	true	true	ADJ
ap-1199	96	24	adler	adler	NOUN
ap-1199	96	25	function	function	NOUN
ap-1199	96	26	.	.	PUNCT
ap-1199	97	1	contributing	contribute	VERB
ap-1199	97	2	only	only	ADV
ap-1199	97	3	to	to	ADP
ap-1199	97	4	the	the	DET
ap-1199	97	5	exponentially	exponentially	ADV
ap-1199	97	6	suppressed	suppress	VERB
ap-1199	97	7	remainder	remainder	NOUN
ap-1199	97	8	,	,	PUNCT
ap-1199	97	9	neither	neither	CCONJ
ap-1199	97	10	the	the	DET
ap-1199	97	11	form	form	NOUN
ap-1199	97	12	or	or	CCONJ
ap-1199	97	13	length	length	NOUN
ap-1199	97	14	of	of	ADP
ap-1199	97	15	the	the	DET
ap-1199	97	16	contour	contour	NOUN
ap-1199	97	17	,	,	PUNCT
ap-1199	97	18	nor	nor	CCONJ
ap-1199	97	19	the	the	DET
ap-1199	97	20	values	value	NOUN
ap-1199	97	21	of	of	ADP
ap-1199	97	22	b(u	b(u	PROPN
ap-1199	97	23	)	)	PUNCT
ap-1199	97	24	outside	outside	ADP
ap-1199	97	25	the	the	DET
ap-1199	97	26	convergence	convergence	NOUN
ap-1199	97	27	disc	disc	NOUN
ap-1199	97	28	can	can	AUX
ap-1199	97	29	affect	affect	VERB
ap-1199	97	30	(	(	PUNCT
ap-1199	97	31	23	23	NUM
ap-1199	97	32	)	)	PUNCT
ap-1199	97	33	.	.	PUNCT
ap-1199	98	1	the	the	DET
ap-1199	98	2	remainder	remainder	NOUN
ap-1199	98	3	to	to	ADP
ap-1199	98	4	(	(	PUNCT
ap-1199	98	5	23	23	NUM
ap-1199	98	6	)	)	PUNCT
ap-1199	98	7	is	be	AUX
ap-1199	98	8	of	of	ADP
ap-1199	98	9	the	the	DET
ap-1199	98	10	form	form	NOUN
ap-1199	98	11	h	h	NOUN
ap-1199	98	12	exp(−d	exp(−d	PROPN
ap-1199	98	13	/	/	SYM
ap-1199	98	14	β0a(s	β0a(s	PROPN
ap-1199	98	15	)	)	PUNCT
ap-1199	98	16	)	)	PUNCT
ap-1199	98	17	∼	∼	NOUN
ap-1199	98	18	h	h	NOUN
ap-1199	98	19	(	(	PUNCT
ap-1199	98	20	−λ2	−λ2	PROPN
ap-1199	98	21	/	/	SYM
ap-1199	98	22	s	s	PART
ap-1199	98	23	)	)	PUNCT
ap-1199	98	24	d	d	NOUN
ap-1199	98	25	.	.	PUNCT
ap-1199	99	1	the	the	DET
ap-1199	99	2	quantities	quantity	NOUN
ap-1199	99	3	h	h	NOUN
ap-1199	99	4	and	and	CCONJ
ap-1199	99	5	d	d	X
ap-1199	99	6	>	>	X
ap-1199	99	7	0	0	PUNCT
ap-1199	99	8	depend	depend	VERB
ap-1199	99	9	on	on	ADP
ap-1199	99	10	the	the	DET
ap-1199	99	11	contour	contour	NOUN
ap-1199	99	12	and	and	CCONJ
ap-1199	99	13	on	on	ADP
ap-1199	99	14	b(u	b(u	PROPN
ap-1199	99	15	)	)	PUNCT
ap-1199	99	16	outside	outside	ADP
ap-1199	99	17	the	the	DET
ap-1199	99	18	disc	disc	NOUN
ap-1199	99	19	,	,	PUNCT
ap-1199	99	20	which	which	PRON
ap-1199	99	21	can	can	AUX
ap-1199	99	22	be	be	AUX
ap-1199	99	23	chosen	choose	VERB
ap-1199	99	24	rather	rather	ADV
ap-1199	99	25	freely	freely	ADV
ap-1199	99	26	.	.	PUNCT
ap-1199	100	1	as	as	ADP
ap-1199	100	2	a	a	DET
ap-1199	100	3	consequence	consequence	NOUN
ap-1199	100	4	,	,	PUNCT
ap-1199	100	5	(	(	PUNCT
ap-1199	100	6	22	22	NUM
ap-1199	100	7	)	)	PUNCT
ap-1199	100	8	contains	contain	VERB
ap-1199	100	9	arbitrary	arbitrary	ADJ
ap-1199	100	10	power	power	NOUN
ap-1199	100	11	terms	term	NOUN
ap-1199	100	12	,	,	PUNCT
ap-1199	100	13	to	to	PART
ap-1199	100	14	be	be	AUX
ap-1199	100	15	added	add	VERB
ap-1199	100	16	to	to	ADP
ap-1199	100	17	(	(	PUNCT
ap-1199	100	18	23	23	NUM
ap-1199	100	19	)	)	PUNCT
ap-1199	100	20	.	.	PUNCT
ap-1199	101	1	4.2	4.2	NUM
ap-1199	101	2	analyticity	analyticity	NOUN
ap-1199	101	3	and	and	CCONJ
ap-1199	101	4	optimal	optimal	ADJ
ap-1199	101	5	conformal	conformal	ADJ
ap-1199	101	6	mapping	mapping	NOUN
ap-1199	101	7	in	in	ADP
ap-1199	101	8	discussing	discuss	VERB
ap-1199	101	9	the	the	DET
ap-1199	101	10	divergence	divergence	NOUN
ap-1199	101	11	of	of	ADP
ap-1199	101	12	(	(	PUNCT
ap-1199	101	13	20	20	NUM
ap-1199	101	14	)	)	PUNCT
ap-1199	101	15	and	and	CCONJ
ap-1199	101	16	(	(	PUNCT
ap-1199	101	17	21	21	NUM
ap-1199	101	18	)	)	PUNCT
ap-1199	101	19	,	,	PUNCT
ap-1199	101	20	the	the	DET
ap-1199	101	21	singularities	singularity	NOUN
ap-1199	101	22	of	of	ADP
ap-1199	101	23	d(s	d(s	PROPN
ap-1199	101	24	)	)	PUNCT
ap-1199	101	25	in	in	ADP
ap-1199	101	26	the	the	DET
ap-1199	101	27	αs(s	αs(	NOUN
ap-1199	101	28	)	)	PUNCT
ap-1199	101	29	plane	plane	NOUN
ap-1199	101	30	and	and	CCONJ
ap-1199	101	31	,	,	PUNCT
ap-1199	101	32	respectively	respectively	ADV
ap-1199	101	33	,	,	PUNCT
ap-1199	101	34	those	those	PRON
ap-1199	101	35	of	of	ADP
ap-1199	101	36	b(u	b(u	PROPN
ap-1199	101	37	)	)	PUNCT
ap-1199	101	38	in	in	ADP
ap-1199	101	39	the	the	DET
ap-1199	101	40	borel	borel	NOUN
ap-1199	101	41	plane	plane	NOUN
ap-1199	101	42	are	be	AUX
ap-1199	101	43	of	of	ADP
ap-1199	101	44	importance	importance	NOUN
ap-1199	101	45	.	.	PUNCT
ap-1199	102	1	as	as	ADP
ap-1199	102	2	for	for	ADP
ap-1199	102	3	b(u	b(u	PROPN
ap-1199	102	4	)	)	PUNCT
ap-1199	102	5	,	,	PUNCT
ap-1199	102	6	some	some	DET
ap-1199	102	7	information	information	NOUN
ap-1199	102	8	about	about	ADP
ap-1199	102	9	the	the	DET
ap-1199	102	10	location	location	NOUN
ap-1199	102	11	and	and	CCONJ
ap-1199	102	12	nature	nature	NOUN
ap-1199	102	13	of	of	ADP
ap-1199	102	14	the	the	DET
ap-1199	102	15	singularities	singularity	NOUN
ap-1199	102	16	can	can	AUX
ap-1199	102	17	be	be	AUX
ap-1199	102	18	obtained	obtain	VERB
ap-1199	102	19	from	from	ADP
ap-1199	102	20	certain	certain	ADJ
ap-1199	102	21	classes	class	NOUN
ap-1199	102	22	of	of	ADP
ap-1199	102	23	feynman	feynman	PROPN
ap-1199	102	24	diagrams	diagram	NOUN
ap-1199	102	25	(	(	PUNCT
ap-1199	102	26	which	which	PRON
ap-1199	102	27	can	can	AUX
ap-1199	102	28	be	be	AUX
ap-1199	102	29	summed	sum	VERB
ap-1199	102	30	,	,	PUNCT
ap-1199	102	31	see	see	VERB
ap-1199	102	32	[	[	X
ap-1199	102	33	10]–[12	10]–[12	NOUN
ap-1199	102	34	]	]	NOUN
ap-1199	102	35	)	)	PUNCT
ap-1199	102	36	,	,	PUNCT
ap-1199	102	37	and	and	CCONJ
ap-1199	102	38	from	from	ADP
ap-1199	102	39	general	general	ADJ
ap-1199	102	40	arguments	argument	NOUN
ap-1199	102	41	based	base	VERB
ap-1199	102	42	on	on	ADP
ap-1199	102	43	renormalization	renormalization	NOUN
ap-1199	102	44	theory	theory	NOUN
ap-1199	102	45	,	,	PUNCT
ap-1199	102	46	[	[	X
ap-1199	102	47	9	9	NUM
ap-1199	102	48	,	,	PUNCT
ap-1199	102	49	14	14	NUM
ap-1199	102	50	]	]	PUNCT
ap-1199	102	51	.	.	PUNCT
ap-1199	103	1	it	it	PRON
ap-1199	103	2	follows	follow	VERB
ap-1199	103	3	that	that	SCONJ
ap-1199	103	4	b(u	b(u	PROPN
ap-1199	103	5	)	)	PUNCT
ap-1199	103	6	has	have	VERB
ap-1199	103	7	branch	branch	NOUN
ap-1199	103	8	points	point	NOUN
ap-1199	103	9	along	along	ADP
ap-1199	103	10	the	the	DET
ap-1199	103	11	rays	ray	NOUN
ap-1199	103	12	u	u	PROPN
ap-1199	103	13	≥	≥	NUM
ap-1199	103	14	2	2	NUM
ap-1199	103	15	and	and	CCONJ
ap-1199	103	16	u	u	NOUN
ap-1199	103	17	≤	≤	X
ap-1199	103	18	−1	−1	NOUN
ap-1199	103	19	(	(	PUNCT
ap-1199	103	20	ir	ir	NOUN
ap-1199	103	21	and	and	CCONJ
ap-1199	103	22	uv	uv	NOUN
ap-1199	103	23	renormalons	renormalon	NOUN
ap-1199	103	24	respectively	respectively	ADV
ap-1199	103	25	)	)	PUNCT
ap-1199	103	26	.	.	PUNCT
ap-1199	104	1	other	other	ADJ
ap-1199	104	2	(	(	PUNCT
ap-1199	104	3	though	though	SCONJ
ap-1199	104	4	nonperturbative	nonperturbative	ADJ
ap-1199	104	5	)	)	PUNCT
ap-1199	104	6	singularities	singularity	NOUN
ap-1199	104	7	,	,	PUNCT
ap-1199	104	8	for	for	ADP
ap-1199	104	9	u	u	PRON
ap-1199	104	10	≥	≥	NOUN
ap-1199	104	11	4	4	NUM
ap-1199	104	12	,	,	PUNCT
ap-1199	104	13	are	be	AUX
ap-1199	104	14	produced	produce	VERB
ap-1199	104	15	by	by	ADP
ap-1199	104	16	instanton	instanton	NOUN
ap-1199	104	17	-	-	PUNCT
ap-1199	104	18	antiinstanton	antiinstanton	NOUN
ap-1199	104	19	pairs	pair	NOUN
ap-1199	104	20	.	.	PUNCT
ap-1199	105	1	(	(	PUNCT
ap-1199	105	2	due	due	ADP
ap-1199	105	3	to	to	ADP
ap-1199	105	4	the	the	DET
ap-1199	105	5	singularities	singularity	NOUN
ap-1199	105	6	at	at	ADP
ap-1199	105	7	u	u	PROPN
ap-1199	105	8	>	>	X
ap-1199	105	9	0	0	PROPN
ap-1199	105	10	,	,	PUNCT
ap-1199	105	11	the	the	DET
ap-1199	105	12	series	series	NOUN
ap-1199	105	13	(	(	PUNCT
ap-1199	105	14	20	20	NUM
ap-1199	105	15	)	)	PUNCT
ap-1199	105	16	is	be	AUX
ap-1199	105	17	not	not	PART
ap-1199	105	18	borel	borel	NOUN
ap-1199	105	19	summable	summable	ADJ
ap-1199	105	20	.	.	PUNCT
ap-1199	105	21	)	)	PUNCT
ap-1199	106	1	no	no	DET
ap-1199	106	2	other	other	ADJ
ap-1199	106	3	singularities	singularity	NOUN
ap-1199	106	4	of	of	ADP
ap-1199	106	5	b(u	b(u	PROPN
ap-1199	106	6	)	)	PUNCT
ap-1199	106	7	in	in	ADP
ap-1199	106	8	the	the	DET
ap-1199	106	9	borel	borel	NOUN
ap-1199	106	10	plane	plane	NOUN
ap-1199	106	11	are	be	AUX
ap-1199	106	12	known	know	VERB
ap-1199	106	13	,	,	PUNCT
ap-1199	106	14	however	however	ADV
ap-1199	106	15	.	.	PUNCT
ap-1199	107	1	it	it	PRON
ap-1199	107	2	is	be	AUX
ap-1199	107	3	usually	usually	ADV
ap-1199	107	4	assumed	assume	VERB
ap-1199	107	5	that	that	SCONJ
ap-1199	107	6	b(u	b(u	PROPN
ap-1199	107	7	)	)	PUNCT
ap-1199	107	8	is	be	AUX
ap-1199	107	9	holomorphic	holomorphic	ADJ
ap-1199	107	10	elsewhere	elsewhere	ADV
ap-1199	107	11	.	.	PUNCT
ap-1199	108	1	to	to	PART
ap-1199	108	2	make	make	VERB
ap-1199	108	3	full	full	ADJ
ap-1199	108	4	use	use	NOUN
ap-1199	108	5	of	of	ADP
ap-1199	108	6	the	the	DET
ap-1199	108	7	analyticity	analyticity	NOUN
ap-1199	108	8	of	of	ADP
ap-1199	108	9	b(u	b(u	PROPN
ap-1199	108	10	)	)	PUNCT
ap-1199	108	11	in	in	ADP
ap-1199	108	12	the	the	DET
ap-1199	108	13	whole	whole	ADJ
ap-1199	108	14	b	b	NOUN
ap-1199	108	15	,	,	PUNCT
ap-1199	108	16	we	we	PRON
ap-1199	108	17	shall	shall	AUX
ap-1199	108	18	use	use	VERB
ap-1199	108	19	the	the	DET
ap-1199	108	20	method	method	NOUN
ap-1199	108	21	of	of	ADP
ap-1199	108	22	optimal	optimal	ADJ
ap-1199	108	23	conformal	conformal	ADJ
ap-1199	108	24	mapping	mapping	NOUN
ap-1199	108	25	[	[	X
ap-1199	108	26	15	15	NUM
ap-1199	108	27	]	]	PUNCT
ap-1199	108	28	.	.	PUNCT
ap-1199	109	1	let	let	VERB
ap-1199	109	2	k	k	X
ap-1199	109	3	be	be	AUX
ap-1199	109	4	the	the	DET
ap-1199	109	5	disc	disc	NOUN
ap-1199	109	6	of	of	ADP
ap-1199	109	7	convergence	convergence	NOUN
ap-1199	109	8	of	of	ADP
ap-1199	109	9	the	the	DET
ap-1199	109	10	series	series	NOUN
ap-1199	109	11	(	(	PUNCT
ap-1199	109	12	21	21	NUM
ap-1199	109	13	)	)	PUNCT
ap-1199	109	14	;	;	PUNCT
ap-1199	109	15	clearly	clearly	ADV
ap-1199	109	16	,	,	PUNCT
ap-1199	109	17	k	k	PROPN
ap-1199	109	18	⊂	⊂	PROPN
ap-1199	109	19	b.	b.	PROPN
ap-1199	109	20	then	then	ADV
ap-1199	109	21	,	,	PUNCT
ap-1199	109	22	evidently	evidently	ADV
ap-1199	109	23	,	,	PUNCT
ap-1199	109	24	the	the	DET
ap-1199	109	25	expansion	expansion	NOUN
ap-1199	109	26	(	(	PUNCT
ap-1199	109	27	21	21	NUM
ap-1199	109	28	)	)	PUNCT
ap-1199	109	29	in	in	ADP
ap-1199	109	30	powers	power	NOUN
ap-1199	109	31	of	of	ADP
ap-1199	109	32	u	u	NOUN
ap-1199	109	33	can	can	AUX
ap-1199	109	34	be	be	AUX
ap-1199	109	35	replaced	replace	VERB
ap-1199	109	36	by	by	ADP
ap-1199	109	37	that	that	PRON
ap-1199	109	38	in	in	ADP
ap-1199	109	39	powers	power	NOUN
ap-1199	109	40	of	of	ADP
ap-1199	109	41	w(u	w(u	PROPN
ap-1199	109	42	)	)	PUNCT
ap-1199	109	43	,	,	PUNCT
ap-1199	109	44	b(u	b(u	PROPN
ap-1199	109	45	)	)	PUNCT
ap-1199	109	46	=	=	PUNCT
ap-1199	110	1	∑	∑	PUNCT
ap-1199	110	2	n≥0	n≥0	PROPN
ap-1199	110	3	cn	cn	PROPN
ap-1199	110	4	wn	wn	PROPN
ap-1199	110	5	,	,	PUNCT
ap-1199	110	6	(	(	PUNCT
ap-1199	110	7	24	24	NUM
ap-1199	110	8	)	)	PUNCT
ap-1199	110	9	where	where	SCONJ
ap-1199	110	10	the	the	DET
ap-1199	110	11	function	function	NOUN
ap-1199	110	12	w	w	PROPN
ap-1199	110	13	=	=	SYM
ap-1199	110	14	w(u	w(u	PROPN
ap-1199	110	15	)	)	PUNCT
ap-1199	110	16	with	with	ADP
ap-1199	110	17	the	the	DET
ap-1199	110	18	property	property	NOUN
ap-1199	110	19	w(0	w(0	PROPN
ap-1199	110	20	)	)	PUNCT
ap-1199	110	21	=	=	SYM
ap-1199	110	22	0	0	PUNCT
ap-1199	110	23	represents	represent	VERB
ap-1199	110	24	the	the	DET
ap-1199	110	25	conformal	conformal	ADJ
ap-1199	110	26	mapping	mapping	NOUN
ap-1199	110	27	of	of	ADP
ap-1199	110	28	the	the	DET
ap-1199	110	29	region	region	NOUN
ap-1199	110	30	of	of	ADP
ap-1199	110	31	b	b	NOUN
ap-1199	110	32	onto	onto	ADP
ap-1199	110	33	the	the	DET
ap-1199	110	34	disc	disc	NOUN
ap-1199	110	35	|w|	|w|	PROPN
ap-1199	110	36	<	<	X
ap-1199	110	37	1	1	NUM
ap-1199	110	38	,	,	PUNCT
ap-1199	110	39	on	on	ADP
ap-1199	110	40	which	which	PRON
ap-1199	110	41	(	(	PUNCT
ap-1199	110	42	24	24	NUM
ap-1199	110	43	)	)	PUNCT
ap-1199	110	44	converges	converge	VERB
ap-1199	110	45	.	.	PUNCT
ap-1199	111	1	it	it	PRON
ap-1199	111	2	can	can	AUX
ap-1199	111	3	easily	easily	ADV
ap-1199	111	4	be	be	AUX
ap-1199	111	5	seen	see	VERB
ap-1199	111	6	that	that	SCONJ
ap-1199	111	7	(	(	PUNCT
ap-1199	111	8	24	24	NUM
ap-1199	111	9	)	)	PUNCT
ap-1199	111	10	has	have	VERB
ap-1199	111	11	better	well	ADJ
ap-1199	111	12	convergence	convergence	NOUN
ap-1199	111	13	properties	property	NOUN
ap-1199	111	14	than	than	ADP
ap-1199	111	15	(	(	PUNCT
ap-1199	111	16	21	21	NUM
ap-1199	111	17	)	)	PUNCT
ap-1199	111	18	in	in	ADP
ap-1199	111	19	this	this	DET
ap-1199	111	20	case	case	NOUN
ap-1199	111	21	:	:	PUNCT
ap-1199	111	22	indeed	indeed	ADV
ap-1199	111	23	,	,	PUNCT
ap-1199	111	24	as	as	SCONJ
ap-1199	111	25	was	be	AUX
ap-1199	111	26	proved	prove	VERB
ap-1199	111	27	in	in	ADP
ap-1199	111	28	[	[	X
ap-1199	111	29	15	15	NUM
ap-1199	111	30	]	]	PUNCT
ap-1199	111	31	by	by	ADP
ap-1199	111	32	using	use	VERB
ap-1199	111	33	the	the	DET
ap-1199	111	34	schwarz	schwarz	PROPN
ap-1199	111	35	lemma	lemma	PROPN
ap-1199	111	36	,	,	PUNCT
ap-1199	111	37	the	the	PRON
ap-1199	111	38	larger	large	ADJ
ap-1199	111	39	the	the	DET
ap-1199	111	40	region	region	NOUN
ap-1199	111	41	mapped	map	VERB
ap-1199	111	42	by	by	ADP
ap-1199	111	43	w(u	w(u	NOUN
ap-1199	111	44	)	)	PUNCT
ap-1199	111	45	onto	onto	ADP
ap-1199	111	46	|w|	|w|	ADJ
ap-1199	111	47	<	<	X
ap-1199	111	48	1	1	NUM
ap-1199	111	49	,	,	PUNCT
ap-1199	111	50	the	the	PRON
ap-1199	111	51	faster	fast	ADJ
ap-1199	111	52	the	the	DET
ap-1199	111	53	large	large	ADJ
ap-1199	111	54	-	-	PUNCT
ap-1199	111	55	order	order	NOUN
ap-1199	111	56	convergence	convergence	NOUN
ap-1199	111	57	rate	rate	NOUN
ap-1199	111	58	of	of	ADP
ap-1199	111	59	(	(	PUNCT
ap-1199	111	60	24	24	NUM
ap-1199	111	61	)	)	PUNCT
ap-1199	111	62	.	.	PUNCT
ap-1199	112	1	if	if	SCONJ
ap-1199	112	2	w(u	w(u	NOUN
ap-1199	112	3	)	)	PUNCT
ap-1199	112	4	maps	map	VERB
ap-1199	112	5	the	the	DET
ap-1199	112	6	whole	whole	ADJ
ap-1199	112	7	b	b	NOUN
ap-1199	112	8	onto	onto	ADP
ap-1199	112	9	the	the	DET
ap-1199	112	10	unit	unit	NOUN
ap-1199	112	11	disc	disc	VERB
ap-1199	112	12	|w|	|w|	PROPN
ap-1199	112	13	<	<	X
ap-1199	112	14	1	1	NUM
ap-1199	112	15	in	in	ADP
ap-1199	112	16	the	the	DET
ap-1199	112	17	w	w	PROPN
ap-1199	112	18	plane	plane	NOUN
ap-1199	112	19	,	,	PUNCT
ap-1199	112	20	the	the	DET
ap-1199	112	21	mapping	mapping	NOUN
ap-1199	112	22	is	be	AUX
ap-1199	112	23	called	call	VERB
ap-1199	112	24	optimal	optimal	ADJ
ap-1199	112	25	.	.	PUNCT
ap-1199	113	1	in	in	ADP
ap-1199	113	2	this	this	DET
ap-1199	113	3	case	case	NOUN
ap-1199	113	4	,	,	PUNCT
ap-1199	113	5	(	(	PUNCT
ap-1199	113	6	24	24	NUM
ap-1199	113	7	)	)	PUNCT
ap-1199	113	8	converges	converge	VERB
ap-1199	113	9	everywhere	everywhere	ADV
ap-1199	113	10	on	on	ADP
ap-1199	113	11	b	b	NOUN
ap-1199	113	12	and	and	CCONJ
ap-1199	113	13	the	the	DET
ap-1199	113	14	convergence	convergence	NOUN
ap-1199	113	15	rate	rate	NOUN
ap-1199	113	16	is	be	AUX
ap-1199	113	17	the	the	DET
ap-1199	113	18	fastest	fast	ADJ
ap-1199	113	19	[	[	X
ap-1199	113	20	15	15	NUM
ap-1199	113	21	]	]	PUNCT
ap-1199	113	22	.	.	PUNCT
ap-1199	114	1	the	the	DET
ap-1199	114	2	region	region	NOUN
ap-1199	114	3	of	of	ADP
ap-1199	114	4	convergence	convergence	NOUN
ap-1199	114	5	of	of	ADP
ap-1199	114	6	(	(	PUNCT
ap-1199	114	7	24	24	NUM
ap-1199	114	8	)	)	PUNCT
ap-1199	114	9	coincides	coincide	VERB
ap-1199	114	10	with	with	ADP
ap-1199	114	11	b	b	PROPN
ap-1199	114	12	,	,	PUNCT
ap-1199	114	13	the	the	DET
ap-1199	114	14	region	region	NOUN
ap-1199	114	15	of	of	ADP
ap-1199	114	16	analyticity	analyticity	NOUN
ap-1199	114	17	.	.	PUNCT
ap-1199	115	1	in	in	ADP
ap-1199	115	2	this	this	DET
ap-1199	115	3	way	way	NOUN
ap-1199	115	4	,	,	PUNCT
ap-1199	115	5	the	the	DET
ap-1199	115	6	optimal	optimal	ADJ
ap-1199	115	7	conformal	conformal	ADJ
ap-1199	115	8	mapping	mapping	NOUN
ap-1199	115	9	can	can	AUX
ap-1199	115	10	express	express	VERB
ap-1199	115	11	analyticity	analyticity	NOUN
ap-1199	115	12	in	in	ADP
ap-1199	115	13	terms	term	NOUN
ap-1199	115	14	of	of	ADP
ap-1199	115	15	convergence	convergence	NOUN
ap-1199	115	16	.	.	PUNCT
ap-1199	116	1	inserting	insert	VERB
ap-1199	116	2	(	(	PUNCT
ap-1199	116	3	24	24	NUM
ap-1199	116	4	)	)	PUNCT
ap-1199	116	5	into	into	ADP
ap-1199	116	6	(	(	PUNCT
ap-1199	116	7	22	22	NUM
ap-1199	116	8	)	)	PUNCT
ap-1199	116	9	we	we	PRON
ap-1199	116	10	obtain	obtain	VERB
ap-1199	116	11	an	an	DET
ap-1199	116	12	alternative	alternative	ADJ
ap-1199	116	13	asymptotic	asymptotic	ADJ
ap-1199	116	14	expansion	expansion	NOUN
ap-1199	116	15	:	:	PUNCT
ap-1199	116	16	dg	dg	PROPN
ap-1199	116	17	0,c(s)=	0,c(s)=	NOUN
ap-1199	116	18	1	1	NUM
ap-1199	116	19	β0	β0	NOUN
ap-1199	116	20	∫	∫	PROPN
ap-1199	117	1	c	c	PROPN
ap-1199	117	2	r=0	r=0	PROPN
ap-1199	117	3	e	e	PROPN
ap-1199	117	4	−	−	PROPN
ap-1199	117	5	g(r	g(r	PROPN
ap-1199	117	6	)	)	PUNCT
ap-1199	117	7	β0	β0	PROPN
ap-1199	117	8	a(s	a(s	PROPN
ap-1199	117	9	)	)	PUNCT
ap-1199	117	10	·	·	PUNCT
ap-1199	117	11	∑	∑	PUNCT
ap-1199	117	12	n≥0	n≥0	PROPN
ap-1199	117	13	cn	cn	PROPN
ap-1199	118	1	[	[	X
ap-1199	118	2	w(g(r))]n	w(g(r))]n	ADJ
ap-1199	118	3	dg(r	dg(r	NUM
ap-1199	118	4	)	)	PUNCT
ap-1199	118	5	.	.	PUNCT
ap-1199	119	1	(	(	PUNCT
ap-1199	119	2	25	25	NUM
ap-1199	119	3	)	)	PUNCT
ap-1199	119	4	73	73	NUM
ap-1199	119	5	acta	acta	PROPN
ap-1199	119	6	polytechnica	polytechnica	PROPN
ap-1199	119	7	vol	vol	NOUN
ap-1199	119	8	.	.	PROPN
ap-1199	120	1	50	50	NUM
ap-1199	120	2	no	no	NOUN
ap-1199	120	3	.	.	PUNCT
ap-1199	121	1	3/2010	3/2010	NUM
ap-1199	121	2	containing	contain	VERB
ap-1199	121	3	powers	power	NOUN
ap-1199	121	4	of	of	ADP
ap-1199	121	5	the	the	DET
ap-1199	121	6	optimal	optimal	ADJ
ap-1199	121	7	conformal	conformal	ADJ
ap-1199	121	8	mapping	mapping	NOUN
ap-1199	121	9	w(u	w(u	PROPN
ap-1199	121	10	)	)	PUNCT
ap-1199	121	11	(	(	PUNCT
ap-1199	121	12	which	which	PRON
ap-1199	121	13	has	have	AUX
ap-1199	121	14	the	the	DET
ap-1199	121	15	same	same	ADJ
ap-1199	121	16	location	location	NOUN
ap-1199	121	17	of	of	ADP
ap-1199	121	18	singularities	singularity	NOUN
ap-1199	121	19	as	as	ADP
ap-1199	121	20	the	the	DET
ap-1199	121	21	expanded	expand	VERB
ap-1199	121	22	function	function	NOUN
ap-1199	121	23	b(u	b(u	PROPN
ap-1199	121	24	)	)	PUNCT
ap-1199	121	25	)	)	PUNCT
ap-1199	122	1	,	,	PUNCT
ap-1199	122	2	this	this	DET
ap-1199	122	3	representation	representation	NOUN
ap-1199	122	4	implements	implement	VERB
ap-1199	122	5	more	more	ADJ
ap-1199	122	6	information	information	NOUN
ap-1199	122	7	about	about	ADP
ap-1199	122	8	the	the	DET
ap-1199	122	9	singularities	singularity	NOUN
ap-1199	122	10	of	of	ADP
ap-1199	122	11	b(u	b(u	PROPN
ap-1199	122	12	)	)	PUNCT
ap-1199	122	13	than	than	ADP
ap-1199	122	14	the	the	DET
ap-1199	122	15	series	series	NOUN
ap-1199	122	16	(	(	PUNCT
ap-1199	122	17	21	21	NUM
ap-1199	122	18	)	)	PUNCT
ap-1199	122	19	in	in	ADP
ap-1199	122	20	powers	power	NOUN
ap-1199	122	21	of	of	ADP
ap-1199	122	22	u	u	NOUN
ap-1199	122	23	,	,	PUNCT
ap-1199	122	24	even	even	ADV
ap-1199	122	25	at	at	ADP
ap-1199	122	26	finite	finite	ADJ
ap-1199	122	27	orders	order	NOUN
ap-1199	122	28	.	.	PUNCT
ap-1199	123	1	thus	thus	ADV
ap-1199	123	2	,	,	PUNCT
ap-1199	123	3	it	it	PRON
ap-1199	123	4	is	be	AUX
ap-1199	123	5	to	to	PART
ap-1199	123	6	be	be	AUX
ap-1199	123	7	expected	expect	VERB
ap-1199	123	8	that	that	SCONJ
ap-1199	123	9	even	even	ADV
ap-1199	123	10	the	the	DET
ap-1199	123	11	finiteorder	finiteorder	NOUN
ap-1199	123	12	approximants	approximant	NOUN
ap-1199	123	13	of	of	ADP
ap-1199	123	14	(	(	PUNCT
ap-1199	123	15	25	25	NUM
ap-1199	123	16	)	)	PUNCT
ap-1199	123	17	will	will	AUX
ap-1199	123	18	provide	provide	VERB
ap-1199	123	19	a	a	DET
ap-1199	123	20	more	more	ADV
ap-1199	123	21	precise	precise	ADJ
ap-1199	123	22	description	description	NOUN
ap-1199	123	23	of	of	ADP
ap-1199	123	24	the	the	DET
ap-1199	123	25	function	function	NOUN
ap-1199	123	26	searched	search	VERB
ap-1199	123	27	for	for	ADP
ap-1199	123	28	[	[	NOUN
ap-1199	123	29	16	16	NUM
ap-1199	123	30	,	,	PUNCT
ap-1199	123	31	17	17	NUM
ap-1199	123	32	]	]	PUNCT
ap-1199	123	33	.	.	PUNCT
ap-1199	124	1	4.3	4.3	NUM
ap-1199	124	2	analyticity	analyticity	NOUN
ap-1199	124	3	may	may	AUX
ap-1199	124	4	easily	easily	ADV
ap-1199	124	5	get	get	AUX
ap-1199	124	6	lost	lose	VERB
ap-1199	124	7	we	we	PRON
ap-1199	124	8	shall	shall	AUX
ap-1199	124	9	briefly	briefly	ADV
ap-1199	124	10	mention	mention	VERB
ap-1199	124	11	an	an	DET
ap-1199	124	12	intriguing	intriguing	ADJ
ap-1199	124	13	situation	situation	NOUN
ap-1199	124	14	showing	show	VERB
ap-1199	124	15	that	that	DET
ap-1199	124	16	careless	careless	ADJ
ap-1199	124	17	manipulation	manipulation	NOUN
ap-1199	124	18	with	with	ADP
ap-1199	124	19	the	the	DET
ap-1199	124	20	integration	integration	NOUN
ap-1199	124	21	contour	contour	NOUN
ap-1199	124	22	may	may	AUX
ap-1199	124	23	have	have	VERB
ap-1199	124	24	a	a	DET
ap-1199	124	25	fateful	fateful	ADJ
ap-1199	124	26	impact	impact	NOUN
ap-1199	124	27	on	on	ADP
ap-1199	124	28	analyticity	analyticity	NOUN
ap-1199	124	29	.	.	PUNCT
ap-1199	125	1	in	in	ADP
ap-1199	125	2	[	[	X
ap-1199	125	3	18	18	NUM
ap-1199	125	4	]	]	PUNCT
ap-1199	125	5	,	,	PUNCT
ap-1199	125	6	two	two	NUM
ap-1199	125	7	different	different	ADJ
ap-1199	125	8	integration	integration	NOUN
ap-1199	125	9	contours	contours	NOUN
ap-1199	125	10	in	in	ADP
ap-1199	125	11	the	the	DET
ap-1199	125	12	u	u	NOUN
ap-1199	125	13	-	-	NOUN
ap-1199	125	14	plane	plane	NOUN
ap-1199	125	15	were	be	AUX
ap-1199	125	16	chosen	choose	VERB
ap-1199	125	17	for	for	ADP
ap-1199	125	18	the	the	DET
ap-1199	125	19	summation	summation	NOUN
ap-1199	125	20	of	of	ADP
ap-1199	125	21	the	the	DET
ap-1199	125	22	so	so	ADV
ap-1199	125	23	-	-	PUNCT
ap-1199	125	24	called	call	VERB
ap-1199	125	25	renormalon	renormalon	NOUN
ap-1199	125	26	chains	chain	NOUN
ap-1199	125	27	[	[	X
ap-1199	125	28	10	10	NUM
ap-1199	125	29	]	]	X
ap-1199	125	30	:	:	PUNCT
ap-1199	125	31	for	for	ADP
ap-1199	125	32	a(s	a(	NOUN
ap-1199	125	33	)	)	PUNCT
ap-1199	125	34	>	>	SYM
ap-1199	125	35	0	0	NUM
ap-1199	125	36	and	and	CCONJ
ap-1199	125	37	a(s	a(	NOUN
ap-1199	125	38	)	)	PUNCT
ap-1199	125	39	<	<	X
ap-1199	125	40	0	0	NUM
ap-1199	125	41	,	,	PUNCT
ap-1199	125	42	a	a	DET
ap-1199	125	43	ray	ray	NOUN
ap-1199	125	44	parallel	parallel	NOUN
ap-1199	125	45	and	and	CCONJ
ap-1199	125	46	close	close	ADJ
ap-1199	125	47	to	to	ADP
ap-1199	125	48	the	the	DET
ap-1199	125	49	positive	positive	ADJ
ap-1199	125	50	and	and	CCONJ
ap-1199	125	51	,	,	PUNCT
ap-1199	125	52	respectively	respectively	ADV
ap-1199	125	53	,	,	PUNCT
ap-1199	125	54	negative	negative	ADJ
ap-1199	125	55	semiaxis	semiaxis	NOUN
ap-1199	125	56	is	be	AUX
ap-1199	125	57	chosen	choose	VERB
ap-1199	125	58	.	.	PUNCT
ap-1199	126	1	as	as	SCONJ
ap-1199	126	2	was	be	AUX
ap-1199	126	3	expected	expect	VERB
ap-1199	126	4	and	and	CCONJ
ap-1199	126	5	later	later	ADV
ap-1199	126	6	proved	prove	VERB
ap-1199	126	7	[	[	X
ap-1199	126	8	19	19	NUM
ap-1199	126	9	]	]	PUNCT
ap-1199	126	10	,	,	PUNCT
ap-1199	126	11	analyticity	analyticity	NOUN
ap-1199	126	12	is	be	AUX
ap-1199	126	13	lost	lose	VERB
ap-1199	126	14	with	with	ADP
ap-1199	126	15	this	this	DET
ap-1199	126	16	choice	choice	NOUN
ap-1199	126	17	,	,	PUNCT
ap-1199	126	18	the	the	DET
ap-1199	126	19	summation	summation	NOUN
ap-1199	126	20	being	be	AUX
ap-1199	126	21	only	only	ADV
ap-1199	126	22	piecewise	piecewise	NOUN
ap-1199	126	23	analytic	analytic	ADJ
ap-1199	126	24	in	in	ADP
ap-1199	126	25	s.	s.	PROPN
ap-1199	126	26	on	on	ADP
ap-1199	126	27	the	the	DET
ap-1199	126	28	other	other	ADJ
ap-1199	126	29	hand	hand	NOUN
ap-1199	126	30	,	,	PUNCT
ap-1199	126	31	as	as	SCONJ
ap-1199	126	32	shown	show	VERB
ap-1199	126	33	in	in	ADP
ap-1199	126	34	[	[	X
ap-1199	126	35	20	20	NUM
ap-1199	126	36	,	,	PUNCT
ap-1199	126	37	21	21	NUM
ap-1199	126	38	]	]	PUNCT
ap-1199	126	39	,	,	PUNCT
ap-1199	126	40	the	the	DET
ap-1199	126	41	borel	borel	NOUN
ap-1199	126	42	summation	summation	NOUN
ap-1199	126	43	with	with	ADP
ap-1199	126	44	the	the	DET
ap-1199	126	45	principal	principal	ADJ
ap-1199	126	46	value	value	NOUN
ap-1199	126	47	(	(	PUNCT
ap-1199	126	48	pv	pv	NOUN
ap-1199	126	49	)	)	PUNCT
ap-1199	126	50	prescription	prescription	NOUN
ap-1199	126	51	of	of	ADP
ap-1199	126	52	the	the	DET
ap-1199	126	53	same	same	ADJ
ap-1199	126	54	class	class	NOUN
ap-1199	126	55	of	of	ADP
ap-1199	126	56	diagrams	diagram	NOUN
ap-1199	126	57	admits	admit	VERB
ap-1199	126	58	an	an	DET
ap-1199	126	59	analytic	analytic	ADJ
ap-1199	126	60	continuation	continuation	NOUN
ap-1199	126	61	in	in	ADP
ap-1199	126	62	the	the	DET
ap-1199	126	63	s	s	NOUN
ap-1199	126	64	-	-	NOUN
ap-1199	126	65	plane	plane	NOUN
ap-1199	126	66	,	,	PUNCT
ap-1199	126	67	in	in	ADP
ap-1199	126	68	agreement	agreement	NOUN
ap-1199	126	69	with	with	ADP
ap-1199	126	70	analyticity	analyticity	NOUN
ap-1199	126	71	except	except	SCONJ
ap-1199	126	72	for	for	ADP
ap-1199	126	73	a	a	DET
ap-1199	126	74	cut	cut	NOUN
ap-1199	126	75	along	along	ADP
ap-1199	126	76	a	a	DET
ap-1199	126	77	segment	segment	NOUN
ap-1199	126	78	of	of	ADP
ap-1199	126	79	the	the	DET
ap-1199	126	80	spacelike	spacelike	ADJ
ap-1199	126	81	axis	axis	NOUN
ap-1199	126	82	,	,	PUNCT
ap-1199	126	83	related	relate	VERB
ap-1199	126	84	to	to	ADP
ap-1199	126	85	the	the	DET
ap-1199	126	86	landau	landau	NOUN
ap-1199	126	87	pole	pole	VERB
ap-1199	126	88	.	.	PUNCT
ap-1199	127	1	5	5	NUM
ap-1199	127	2	conclusion	conclusion	NOUN
ap-1199	127	3	in	in	ADP
ap-1199	127	4	this	this	DET
ap-1199	127	5	paper	paper	NOUN
ap-1199	127	6	we	we	PRON
ap-1199	127	7	have	have	AUX
ap-1199	127	8	discussed	discuss	VERB
ap-1199	127	9	some	some	DET
ap-1199	127	10	special	special	ADJ
ap-1199	127	11	consequences	consequence	NOUN
ap-1199	127	12	of	of	ADP
ap-1199	127	13	our	our	PRON
ap-1199	127	14	general	general	ADJ
ap-1199	127	15	result	result	NOUN
ap-1199	127	16	published	publish	VERB
ap-1199	127	17	in	in	ADP
ap-1199	127	18	[	[	X
ap-1199	127	19	6	6	NUM
ap-1199	127	20	]	]	PUNCT
ap-1199	127	21	,	,	PUNCT
ap-1199	127	22	which	which	PRON
ap-1199	127	23	is	be	AUX
ap-1199	127	24	based	base	VERB
ap-1199	127	25	on	on	ADP
ap-1199	127	26	a	a	DET
ap-1199	127	27	modification	modification	NOUN
ap-1199	127	28	of	of	ADP
ap-1199	127	29	the	the	DET
ap-1199	127	30	watson	watson	PROPN
ap-1199	127	31	lemma	lemma	PROPN
ap-1199	127	32	.	.	PUNCT
ap-1199	128	1	it	it	PRON
ap-1199	128	2	follows	follow	VERB
ap-1199	128	3	that	that	SCONJ
ap-1199	128	4	a	a	DET
ap-1199	128	5	perturbation	perturbation	NOUN
ap-1199	128	6	series	series	NOUN
ap-1199	128	7	,	,	PUNCT
ap-1199	128	8	if	if	SCONJ
ap-1199	128	9	regarded	regard	VERB
ap-1199	128	10	as	as	ADP
ap-1199	128	11	asymptotic	asymptotic	ADJ
ap-1199	128	12	,	,	PUNCT
ap-1199	128	13	implies	imply	VERB
ap-1199	128	14	a	a	DET
ap-1199	128	15	huge	huge	ADJ
ap-1199	128	16	ambiguity	ambiguity	NOUN
ap-1199	128	17	of	of	ADP
ap-1199	128	18	possible	possible	ADJ
ap-1199	128	19	expanded	expand	VERB
ap-1199	128	20	functions	function	NOUN
ap-1199	128	21	having	have	VERB
ap-1199	128	22	the	the	DET
ap-1199	128	23	same	same	ADJ
ap-1199	128	24	asymptotic	asymptotic	ADJ
ap-1199	128	25	expansion	expansion	NOUN
ap-1199	128	26	of	of	ADP
ap-1199	128	27	the	the	DET
ap-1199	128	28	type	type	NOUN
ap-1199	128	29	(	(	PUNCT
ap-1199	128	30	1	1	NUM
ap-1199	128	31	)	)	PUNCT
ap-1199	128	32	.	.	PUNCT
ap-1199	129	1	this	this	DET
ap-1199	129	2	mathematical	mathematical	ADJ
ap-1199	129	3	fact	fact	NOUN
ap-1199	129	4	is	be	AUX
ap-1199	129	5	often	often	ADV
ap-1199	129	6	ignored	ignore	VERB
ap-1199	129	7	or	or	CCONJ
ap-1199	129	8	overlooked	overlook	VERB
ap-1199	129	9	in	in	ADP
ap-1199	129	10	physical	physical	ADJ
ap-1199	129	11	applications	application	NOUN
ap-1199	129	12	.	.	PUNCT
ap-1199	130	1	our	our	PRON
ap-1199	130	2	contribution	contribution	NOUN
ap-1199	130	3	consists	consist	VERB
ap-1199	130	4	in	in	ADP
ap-1199	130	5	the	the	DET
ap-1199	130	6	fact	fact	NOUN
ap-1199	130	7	that	that	SCONJ
ap-1199	130	8	we	we	PRON
ap-1199	130	9	have	have	AUX
ap-1199	130	10	specified	specify	VERB
ap-1199	130	11	its	its	PRON
ap-1199	130	12	special	special	ADJ
ap-1199	130	13	subclass	subclass	NOUN
ap-1199	130	14	by	by	ADP
ap-1199	130	15	lemma	lemma	PROPN
ap-1199	130	16	2	2	NUM
ap-1199	130	17	of	of	ADP
ap-1199	130	18	ref	ref	NOUN
ap-1199	130	19	.	.	PUNCT
ap-1199	131	1	[	[	X
ap-1199	131	2	6	6	NUM
ap-1199	131	3	]	]	PUNCT
ap-1199	131	4	.	.	PUNCT
ap-1199	132	1	moreover	moreover	ADV
ap-1199	132	2	,	,	PUNCT
ap-1199	132	3	in	in	ADP
ap-1199	132	4	the	the	DET
ap-1199	132	5	present	present	ADJ
ap-1199	132	6	paper	paper	NOUN
ap-1199	132	7	,	,	PUNCT
ap-1199	132	8	we	we	PRON
ap-1199	132	9	have	have	AUX
ap-1199	132	10	considered	consider	VERB
ap-1199	132	11	a	a	DET
ap-1199	132	12	special	special	ADJ
ap-1199	132	13	subclass	subclass	NOUN
ap-1199	132	14	of	of	ADP
ap-1199	132	15	lemma	lemma	PROPN
ap-1199	132	16	2	2	NUM
ap-1199	132	17	(	(	PUNCT
ap-1199	132	18	as	as	SCONJ
ap-1199	132	19	defined	define	VERB
ap-1199	132	20	by	by	ADP
ap-1199	132	21	lemma	lemma	PROPN
ap-1199	132	22	2	2	NUM
ap-1199	132	23	’	'	PUNCT
ap-1199	132	24	in	in	ADP
ap-1199	132	25	section	section	NOUN
ap-1199	132	26	3	3	NUM
ap-1199	132	27	of	of	ADP
ap-1199	132	28	this	this	DET
ap-1199	132	29	paper	paper	NOUN
ap-1199	132	30	)	)	PUNCT
ap-1199	132	31	,	,	PUNCT
ap-1199	132	32	which	which	PRON
ap-1199	132	33	we	we	PRON
ap-1199	132	34	discuss	discuss	VERB
ap-1199	132	35	here	here	ADV
ap-1199	132	36	in	in	ADP
ap-1199	132	37	more	more	ADJ
ap-1199	132	38	detail	detail	NOUN
ap-1199	132	39	due	due	ADP
ap-1199	132	40	to	to	ADP
ap-1199	132	41	its	its	PRON
ap-1199	132	42	direct	direct	ADJ
ap-1199	132	43	applicability	applicability	NOUN
ap-1199	132	44	to	to	ADP
ap-1199	132	45	perturbative	perturbative	ADJ
ap-1199	132	46	qcd	qcd	PROPN
ap-1199	132	47	.	.	PUNCT
ap-1199	132	48	to	to	PART
ap-1199	132	49	find	find	VERB
ap-1199	132	50	the	the	DET
ap-1199	132	51	true	true	ADJ
ap-1199	132	52	solution	solution	NOUN
ap-1199	132	53	,	,	PUNCT
ap-1199	132	54	additional	additional	ADJ
ap-1199	132	55	information	information	NOUN
ap-1199	132	56	inputs	input	NOUN
ap-1199	132	57	are	be	AUX
ap-1199	132	58	unavoidable	unavoidable	ADJ
ap-1199	132	59	.	.	PUNCT
ap-1199	133	1	applying	apply	VERB
ap-1199	133	2	the	the	DET
ap-1199	133	3	result	result	NOUN
ap-1199	133	4	to	to	PART
ap-1199	133	5	qcd	qcd	VERB
ap-1199	133	6	,	,	PUNCT
ap-1199	133	7	we	we	PRON
ap-1199	133	8	conclude	conclude	VERB
ap-1199	133	9	that	that	SCONJ
ap-1199	133	10	the	the	DET
ap-1199	133	11	contour	contour	NOUN
ap-1199	133	12	of	of	ADP
ap-1199	133	13	the	the	DET
ap-1199	133	14	integral	integral	ADJ
ap-1199	133	15	representing	represent	VERB
ap-1199	133	16	the	the	DET
ap-1199	133	17	qcd	qcd	PROPN
ap-1199	133	18	correlator	correlator	NOUN
ap-1199	133	19	can	can	AUX
ap-1199	133	20	be	be	AUX
ap-1199	133	21	chosen	choose	VERB
ap-1199	133	22	very	very	ADV
ap-1199	133	23	freely	freely	ADV
ap-1199	133	24	.	.	PUNCT
ap-1199	134	1	the	the	DET
ap-1199	134	2	same	same	ADJ
ap-1199	134	3	holds	hold	VERB
ap-1199	134	4	for	for	ADP
ap-1199	134	5	the	the	DET
ap-1199	134	6	borel	borel	PROPN
ap-1199	134	7	transform	transform	VERB
ap-1199	134	8	b(u	b(u	PROPN
ap-1199	134	9	)	)	PUNCT
ap-1199	134	10	outside	outside	ADP
ap-1199	134	11	the	the	DET
ap-1199	134	12	convergence	convergence	NOUN
ap-1199	134	13	circle	circle	NOUN
ap-1199	134	14	.	.	PUNCT
ap-1199	135	1	we	we	PRON
ap-1199	135	2	have	have	AUX
ap-1199	135	3	kept	keep	VERB
ap-1199	135	4	our	our	PRON
ap-1199	135	5	discussion	discussion	NOUN
ap-1199	135	6	on	on	ADP
ap-1199	135	7	a	a	DET
ap-1199	135	8	general	general	ADJ
ap-1199	135	9	level	level	NOUN
ap-1199	135	10	,	,	PUNCT
ap-1199	135	11	bearing	bear	VERB
ap-1199	135	12	in	in	ADP
ap-1199	135	13	mind	mind	NOUN
ap-1199	135	14	that	that	SCONJ
ap-1199	135	15	little	little	ADJ
ap-1199	135	16	is	be	AUX
ap-1199	135	17	known	know	VERB
ap-1199	135	18	,	,	PUNCT
ap-1199	135	19	in	in	ADP
ap-1199	135	20	a	a	DET
ap-1199	135	21	rigorous	rigorous	ADJ
ap-1199	135	22	framework	framework	NOUN
ap-1199	135	23	,	,	PUNCT
ap-1199	135	24	about	about	ADP
ap-1199	135	25	the	the	DET
ap-1199	135	26	analytic	analytic	ADJ
ap-1199	135	27	properties	property	NOUN
ap-1199	135	28	of	of	ADP
ap-1199	135	29	the	the	DET
ap-1199	135	30	qcd	qcd	PROPN
ap-1199	135	31	correlators	correlator	NOUN
ap-1199	135	32	in	in	ADP
ap-1199	135	33	the	the	DET
ap-1199	135	34	borel	borel	NOUN
ap-1199	135	35	plane	plane	NOUN
ap-1199	135	36	.	.	PUNCT
ap-1199	136	1	if	if	SCONJ
ap-1199	136	2	some	some	DET
ap-1199	136	3	specific	specific	ADJ
ap-1199	136	4	properties	property	NOUN
ap-1199	136	5	are	be	AUX
ap-1199	136	6	known	know	VERB
ap-1199	136	7	or	or	CCONJ
ap-1199	136	8	assumed	assume	VERB
ap-1199	136	9	,	,	PUNCT
ap-1199	136	10	the	the	DET
ap-1199	136	11	integral	integral	ADJ
ap-1199	136	12	representations	representation	NOUN
ap-1199	136	13	will	will	AUX
ap-1199	136	14	have	have	VERB
ap-1199	136	15	additional	additional	ADJ
ap-1199	136	16	analytic	analytic	ADJ
ap-1199	136	17	properties	property	NOUN
ap-1199	136	18	.	.	PUNCT
ap-1199	137	1	naturally	naturally	ADV
ap-1199	137	2	,	,	PUNCT
ap-1199	137	3	the	the	DET
ap-1199	137	4	results	result	NOUN
ap-1199	137	5	obtained	obtain	VERB
ap-1199	137	6	in	in	ADP
ap-1199	137	7	[	[	X
ap-1199	137	8	6	6	NUM
ap-1199	137	9	]	]	PUNCT
ap-1199	137	10	may	may	AUX
ap-1199	137	11	also	also	ADV
ap-1199	137	12	be	be	AUX
ap-1199	137	13	useful	useful	ADJ
ap-1199	137	14	in	in	ADP
ap-1199	137	15	other	other	ADJ
ap-1199	137	16	branches	branch	NOUN
ap-1199	137	17	of	of	ADP
ap-1199	137	18	physics	physics	NOUN
ap-1199	137	19	where	where	SCONJ
ap-1199	137	20	perturbation	perturbation	NOUN
ap-1199	137	21	series	series	NOUN
ap-1199	137	22	are	be	AUX
ap-1199	137	23	divergent	divergent	ADJ
ap-1199	137	24	.	.	PUNCT
ap-1199	138	1	acknowledgement	acknowledgement	NOUN
ap-1199	138	2	one	one	NUM
ap-1199	138	3	of	of	ADP
ap-1199	138	4	us	we	PRON
ap-1199	138	5	(	(	PUNCT
ap-1199	138	6	i.c	i.c	PROPN
ap-1199	138	7	.	.	PROPN
ap-1199	138	8	)	)	PUNCT
ap-1199	139	1	thanks	thank	NOUN
ap-1199	139	2	prof	prof	PROPN
ap-1199	139	3	.	.	PUNCT
ap-1199	140	1	j.	j.	PROPN
ap-1199	140	2	chýla	chýla	PROPN
ap-1199	140	3	and	and	CCONJ
ap-1199	140	4	the	the	DET
ap-1199	140	5	institute	institute	PROPN
ap-1199	140	6	of	of	ADP
ap-1199	140	7	physics	physics	PROPN
ap-1199	140	8	of	of	ADP
ap-1199	140	9	the	the	DET
ap-1199	140	10	czech	czech	PROPN
ap-1199	140	11	academy	academy	PROPN
ap-1199	140	12	in	in	ADP
ap-1199	140	13	prague	prague	PROPN
ap-1199	140	14	for	for	ADP
ap-1199	140	15	hospitality	hospitality	NOUN
ap-1199	140	16	.	.	PUNCT
ap-1199	141	1	j.	j.	PROPN
ap-1199	141	2	f.	f.	PROPN
ap-1199	141	3	thanks	thanks	PROPN
ap-1199	141	4	prof	prof	PROPN
ap-1199	141	5	.	.	PUNCT
ap-1199	142	1	p.	p.	NOUN
ap-1199	142	2	ra̧czka	ra̧czka	PROPN
ap-1199	142	3	and	and	CCONJ
ap-1199	142	4	the	the	DET
ap-1199	142	5	institute	institute	NOUN
ap-1199	142	6	of	of	ADP
ap-1199	142	7	theoretical	theoretical	ADJ
ap-1199	142	8	physics	physics	PROPN
ap-1199	142	9	of	of	ADP
ap-1199	142	10	warsaw	warsaw	PROPN
ap-1199	142	11	university	university	PROPN
ap-1199	142	12	for	for	ADP
ap-1199	142	13	hospitality	hospitality	NOUN
ap-1199	142	14	.	.	PUNCT
ap-1199	143	1	supported	support	VERB
ap-1199	143	2	by	by	ADP
ap-1199	143	3	cncsis	cncsis	NOUN
ap-1199	143	4	in	in	ADP
ap-1199	143	5	the	the	DET
ap-1199	143	6	framework	framework	NOUN
ap-1199	143	7	of	of	ADP
ap-1199	143	8	program	program	NOUN
ap-1199	143	9	idei	idei	VERB
ap-1199	143	10	,	,	PUNCT
ap-1199	143	11	contract	contract	NOUN
ap-1199	143	12	no	no	NOUN
ap-1199	143	13	.	.	PUNCT
ap-1199	144	1	464/2009	464/2009	NUM
ap-1199	144	2	,	,	PUNCT
ap-1199	144	3	and	and	CCONJ
ap-1199	144	4	by	by	ADP
ap-1199	144	5	projects	project	NOUN
ap-1199	144	6	no	no	NOUN
ap-1199	144	7	.	.	PUNCT
ap-1199	145	1	la08015	la08015	NOUN
ap-1199	145	2	of	of	ADP
ap-1199	145	3	the	the	DET
ap-1199	145	4	ministry	ministry	PROPN
ap-1199	145	5	of	of	ADP
ap-1199	145	6	education	education	PROPN
ap-1199	145	7	and	and	CCONJ
ap-1199	145	8	av0z10100502	av0z10100502	NOUN
ap-1199	145	9	of	of	ADP
ap-1199	145	10	the	the	DET
ap-1199	145	11	academy	academy	PROPN
ap-1199	145	12	of	of	ADP
ap-1199	145	13	sciences	sciences	PROPN
ap-1199	145	14	of	of	ADP
ap-1199	145	15	the	the	DET
ap-1199	145	16	czech	czech	PROPN
ap-1199	145	17	republic	republic	NOUN
ap-1199	145	18	.	.	PUNCT
ap-1199	146	1	references	reference	NOUN
ap-1199	146	2	[	[	X
ap-1199	146	3	1	1	NUM
ap-1199	146	4	]	]	PUNCT
ap-1199	146	5	dyson	dyson	PROPN
ap-1199	146	6	,	,	PUNCT
ap-1199	146	7	f.	f.	PROPN
ap-1199	146	8	j.	j.	PROPN
ap-1199	146	9	:	:	PUNCT
ap-1199	146	10	phys	phy	NOUN
ap-1199	146	11	.	.	PUNCT
ap-1199	147	1	rev	rev	PROPN
ap-1199	147	2	.	.	PROPN
ap-1199	147	3	85	85	NUM
ap-1199	147	4	,	,	PUNCT
ap-1199	147	5	631	631	NUM
ap-1199	147	6	(	(	PUNCT
ap-1199	147	7	1952	1952	NUM
ap-1199	147	8	)	)	PUNCT
ap-1199	147	9	.	.	PUNCT
ap-1199	148	1	[	[	X
ap-1199	148	2	2	2	NUM
ap-1199	148	3	]	]	X
ap-1199	148	4	lautrup	lautrup	NOUN
ap-1199	148	5	,	,	PUNCT
ap-1199	148	6	b.	b.	NOUN
ap-1199	148	7	:	:	PUNCT
ap-1199	149	1	phys	phy	NOUN
ap-1199	149	2	.	.	PUNCT
ap-1199	150	1	lett	lett	PROPN
ap-1199	150	2	.	.	PUNCT
ap-1199	150	3	b69	b69	PROPN
ap-1199	150	4	,	,	PUNCT
ap-1199	150	5	109	109	NUM
ap-1199	150	6	(	(	PUNCT
ap-1199	150	7	1977	1977	NUM
ap-1199	150	8	)	)	PUNCT
ap-1199	150	9	;	;	PUNCT
ap-1199	150	10	lipatov	lipatov	PROPN
ap-1199	150	11	,	,	PUNCT
ap-1199	150	12	l.	l.	PROPN
ap-1199	150	13	n.	n.	PROPN
ap-1199	150	14	:	:	PUNCT
ap-1199	150	15	sov	sov	NOUN
ap-1199	150	16	.	.	PUNCT
ap-1199	151	1	phys	phy	NOUN
ap-1199	151	2	.	.	PUNCT
ap-1199	152	1	jetp	jetp	PROPN
ap-1199	152	2	45	45	NUM
ap-1199	152	3	,	,	PUNCT
ap-1199	152	4	216	216	NUM
ap-1199	152	5	(	(	PUNCT
ap-1199	152	6	1977	1977	NUM
ap-1199	152	7	)	)	PUNCT
ap-1199	152	8	;	;	PUNCT
ap-1199	152	9	parisi	parisi	PROPN
ap-1199	152	10	,	,	PUNCT
ap-1199	152	11	g.	g.	NOUN
ap-1199	152	12	:	:	PUNCT
ap-1199	152	13	phys	phy	NOUN
ap-1199	152	14	.	.	PUNCT
ap-1199	153	1	lett	lett	PROPN
ap-1199	153	2	.	.	PUNCT
ap-1199	153	3	b76	b76	PROPN
ap-1199	153	4	,	,	PUNCT
ap-1199	153	5	65	65	NUM
ap-1199	153	6	(	(	PUNCT
ap-1199	153	7	1978	1978	NUM
ap-1199	153	8	)	)	PUNCT
ap-1199	153	9	;	;	PUNCT
ap-1199	153	10	mueller	mueller	PROPN
ap-1199	153	11	,	,	PUNCT
ap-1199	153	12	a.	a.	PROPN
ap-1199	153	13	h.	h.	PROPN
ap-1199	153	14	:	:	PUNCT
ap-1199	153	15	nucl	nucl	PROPN
ap-1199	153	16	.	.	PUNCT
ap-1199	154	1	phys	phy	NOUN
ap-1199	154	2	.	.	PUNCT
ap-1199	155	1	b250	b250	PROPN
ap-1199	155	2	,	,	PUNCT
ap-1199	155	3	327	327	NUM
ap-1199	155	4	(	(	PUNCT
ap-1199	155	5	1985	1985	NUM
ap-1199	155	6	)	)	PUNCT
ap-1199	155	7	.	.	PUNCT
ap-1199	156	1	[	[	X
ap-1199	156	2	3	3	NUM
ap-1199	156	3	]	]	X
ap-1199	156	4	hooft	hooft	NOUN
ap-1199	156	5	,	,	PUNCT
ap-1199	156	6	g.	g.	NOUN
ap-1199	156	7	’t	’t	NOUN
ap-1199	156	8	:	:	PUNCT
ap-1199	156	9	in	in	ADP
ap-1199	156	10	:	:	PUNCT
ap-1199	156	11	the	the	DET
ap-1199	156	12	why	why	SCONJ
ap-1199	156	13	s	s	X
ap-1199	156	14	of	of	ADP
ap-1199	156	15	subnuclear	subnuclear	NOUN
ap-1199	156	16	physics	physics	PROPN
ap-1199	156	17	,	,	PUNCT
ap-1199	156	18	proc	proc	NOUN
ap-1199	156	19	.	.	PROPN
ap-1199	157	1	of	of	ADP
ap-1199	157	2	the	the	DET
ap-1199	157	3	15th	15th	ADJ
ap-1199	157	4	intern	intern	NOUN
ap-1199	157	5	.	.	PUNCT
ap-1199	158	1	school	school	NOUN
ap-1199	158	2	on	on	ADP
ap-1199	158	3	subnucl	subnucl	PROPN
ap-1199	158	4	.	.	PUNCT
ap-1199	159	1	physics	physics	PROPN
ap-1199	159	2	,	,	PUNCT
ap-1199	159	3	erice	erice	NOUN
ap-1199	159	4	,	,	PUNCT
ap-1199	159	5	1977	1977	NUM
ap-1199	159	6	,	,	PUNCT
ap-1199	159	7	ed	ed	NOUN
ap-1199	159	8	.	.	PUNCT
ap-1199	159	9	by	by	ADP
ap-1199	159	10	a.	a.	PROPN
ap-1199	159	11	zichichi	zichichi	PROPN
ap-1199	159	12	(	(	PUNCT
ap-1199	159	13	plenum	plenum	PROPN
ap-1199	159	14	press	press	PROPN
ap-1199	159	15	,	,	PUNCT
ap-1199	159	16	new	new	PROPN
ap-1199	159	17	york	york	PROPN
ap-1199	159	18	,	,	PUNCT
ap-1199	159	19	1979	1979	NUM
ap-1199	159	20	)	)	PUNCT
ap-1199	159	21	,	,	PUNCT
ap-1199	159	22	943	943	NUM
ap-1199	159	23	.	.	PUNCT
ap-1199	160	1	[	[	X
ap-1199	160	2	4	4	NUM
ap-1199	160	3	]	]	X
ap-1199	160	4	fischer	fischer	PROPN
ap-1199	160	5	,	,	PUNCT
ap-1199	160	6	j	j	NOUN
ap-1199	160	7	:	:	PUNCT
ap-1199	160	8	int	int	NOUN
ap-1199	160	9	.	.	PUNCT
ap-1199	161	1	j.	j.	PROPN
ap-1199	161	2	mod	mod	PROPN
ap-1199	161	3	.	.	PUNCT
ap-1199	162	1	phys	phys	PROPN
ap-1199	162	2	.	.	PUNCT
ap-1199	163	1	a12	a12	PROPN
ap-1199	163	2	,	,	PUNCT
ap-1199	163	3	3625	3625	NUM
ap-1199	163	4	(	(	PUNCT
ap-1199	163	5	1997	1997	NUM
ap-1199	163	6	)	)	PUNCT
ap-1199	163	7	.	.	PUNCT
ap-1199	164	1	[	[	X
ap-1199	164	2	5	5	NUM
ap-1199	164	3	]	]	X
ap-1199	164	4	jeffreys	jeffrey	NOUN
ap-1199	164	5	,	,	PUNCT
ap-1199	164	6	h.	h.	NOUN
ap-1199	164	7	:	:	PUNCT
ap-1199	164	8	asymptotic	asymptotic	ADJ
ap-1199	164	9	approximations	approximation	NOUN
ap-1199	164	10	,	,	PUNCT
ap-1199	164	11	clarendon	clarendon	PROPN
ap-1199	164	12	press	press	NOUN
ap-1199	164	13	,	,	PUNCT
ap-1199	164	14	oxford	oxford	PROPN
ap-1199	164	15	,	,	PUNCT
ap-1199	164	16	1962	1962	NUM
ap-1199	164	17	;	;	PUNCT
ap-1199	164	18	dingle	dingle	PROPN
ap-1199	164	19	,	,	PUNCT
ap-1199	164	20	r.	r.	PROPN
ap-1199	164	21	b.	b.	PROPN
ap-1199	164	22	:	:	PUNCT
ap-1199	164	23	asymptotic	asymptotic	ADJ
ap-1199	164	24	expansions	expansion	NOUN
ap-1199	164	25	:	:	PUNCT
ap-1199	164	26	their	their	PRON
ap-1199	164	27	derivation	derivation	NOUN
ap-1199	164	28	and	and	CCONJ
ap-1199	164	29	interpretation	interpretation	NOUN
ap-1199	164	30	,	,	PUNCT
ap-1199	164	31	academic	academic	ADJ
ap-1199	164	32	press	press	NOUN
ap-1199	164	33	,	,	PUNCT
ap-1199	164	34	1972	1972	NUM
ap-1199	164	35	;	;	PUNCT
ap-1199	164	36	fedoryuk	fedoryuk	NOUN
ap-1199	164	37	,	,	PUNCT
ap-1199	164	38	m.	m.	NOUN
ap-1199	165	1	v.	v.	NOUN
ap-1199	165	2	:	:	PUNCT
ap-1199	165	3	asymptotics	asymptotic	NOUN
ap-1199	165	4	,	,	PUNCT
ap-1199	165	5	integrals	integral	NOUN
ap-1199	165	6	and	and	CCONJ
ap-1199	165	7	series	series	NOUN
ap-1199	165	8	(	(	PUNCT
ap-1199	165	9	in	in	ADP
ap-1199	165	10	russian	russian	PROPN
ap-1199	165	11	)	)	PUNCT
ap-1199	165	12	,	,	PUNCT
ap-1199	165	13	moscow	moscow	PROPN
ap-1199	165	14	,	,	PUNCT
ap-1199	165	15	nauka	nauka	PROPN
ap-1199	165	16	,	,	PUNCT
ap-1199	165	17	1987	1987	NUM
ap-1199	165	18	,	,	PUNCT
ap-1199	165	19	58	58	NUM
ap-1199	165	20	.	.	PUNCT
ap-1199	166	1	[	[	X
ap-1199	166	2	6	6	NUM
ap-1199	166	3	]	]	SYM
ap-1199	166	4	caprini	caprini	PROPN
ap-1199	166	5	,	,	PUNCT
ap-1199	166	6	i.	i.	PROPN
ap-1199	166	7	,	,	PUNCT
ap-1199	166	8	fischer	fischer	PROPN
ap-1199	166	9	,	,	PUNCT
ap-1199	166	10	j.	j.	PROPN
ap-1199	166	11	,	,	PUNCT
ap-1199	166	12	vrkoč	vrkoč	NOUN
ap-1199	166	13	,	,	PUNCT
ap-1199	166	14	i.	i.	PROPN
ap-1199	166	15	:	:	PUNCT
ap-1199	166	16	j.	j.	PROPN
ap-1199	166	17	phys	phys	PROPN
ap-1199	166	18	.	.	PUNCT
ap-1199	167	1	a42	a42	PROPN
ap-1199	167	2	395403	395403	NUM
ap-1199	167	3	,	,	PUNCT
ap-1199	167	4	2009	2009	NUM
ap-1199	167	5	.	.	PUNCT
ap-1199	168	1	[	[	X
ap-1199	168	2	7	7	NUM
ap-1199	168	3	]	]	X
ap-1199	168	4	adler	adler	NOUN
ap-1199	168	5	,	,	PUNCT
ap-1199	168	6	s.	s.	PROPN
ap-1199	168	7	l.	l.	PROPN
ap-1199	168	8	:	:	PUNCT
ap-1199	168	9	phys	phy	NOUN
ap-1199	168	10	.	.	PUNCT
ap-1199	168	11	rev	rev	PROPN
ap-1199	168	12	.	.	PROPN
ap-1199	168	13	d10	d10	PROPN
ap-1199	168	14	,	,	PUNCT
ap-1199	168	15	3714	3714	NUM
ap-1199	168	16	(	(	PUNCT
ap-1199	168	17	1974	1974	NUM
ap-1199	168	18	)	)	PUNCT
ap-1199	168	19	.	.	PUNCT
ap-1199	169	1	[	[	X
ap-1199	169	2	8	8	NUM
ap-1199	169	3	]	]	SYM
ap-1199	169	4	bogoliubov	bogoliubov	NOUN
ap-1199	169	5	,	,	PUNCT
ap-1199	169	6	n.	n.	PROPN
ap-1199	169	7	n.	n.	PROPN
ap-1199	169	8	,	,	PUNCT
ap-1199	169	9	shirkov	shirkov	PROPN
ap-1199	169	10	,	,	PUNCT
ap-1199	169	11	d.	d.	PROPN
ap-1199	169	12	v.	v.	PROPN
ap-1199	169	13	:	:	PUNCT
ap-1199	169	14	introduction	introduction	NOUN
ap-1199	169	15	to	to	ADP
ap-1199	169	16	the	the	DET
ap-1199	169	17	theory	theory	NOUN
ap-1199	169	18	of	of	ADP
ap-1199	169	19	quantized	quantize	VERB
ap-1199	169	20	fields	field	NOUN
ap-1199	169	21	,	,	PUNCT
ap-1199	169	22	interscience	interscience	NOUN
ap-1199	169	23	,	,	PUNCT
ap-1199	169	24	1959	1959	NUM
ap-1199	169	25	.	.	PUNCT
ap-1199	170	1	[	[	X
ap-1199	170	2	9	9	NUM
ap-1199	170	3	]	]	SYM
ap-1199	170	4	mueller	mueller	PROPN
ap-1199	170	5	,	,	PUNCT
ap-1199	170	6	a.	a.	PROPN
ap-1199	170	7	h.	h.	PROPN
ap-1199	170	8	:	:	PUNCT
ap-1199	170	9	in	in	ADP
ap-1199	170	10	:	:	PUNCT
ap-1199	170	11	qcd	qcd	PROPN
ap-1199	170	12	–	–	PUNCT
ap-1199	170	13	twenty	twenty	NUM
ap-1199	170	14	years	year	NOUN
ap-1199	170	15	later	later	ADV
ap-1199	170	16	,	,	PUNCT
ap-1199	170	17	aachen	aachen	PROPN
ap-1199	170	18	1992	1992	NUM
ap-1199	170	19	,	,	PUNCT
ap-1199	170	20	edited	edit	VERB
ap-1199	170	21	by	by	ADP
ap-1199	170	22	p.	p.	PROPN
ap-1199	170	23	zerwas	zerwas	PROPN
ap-1199	170	24	and	and	CCONJ
ap-1199	170	25	h.	h.	PROPN
ap-1199	170	26	a.	a.	PROPN
ap-1199	170	27	kastrup	kastrup	PROPN
ap-1199	170	28	(	(	PUNCT
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ap-1199	170	33	,	,	PUNCT
ap-1199	170	34	1992	1992	NUM
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ap-1199	171	3	]	]	X
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ap-1199	171	5	,	,	PUNCT
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ap-1199	171	7	:	:	PUNCT
ap-1199	171	8	nucl	nucl	PROPN
ap-1199	171	9	.	.	PUNCT
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ap-1199	172	2	.	.	PUNCT
ap-1199	173	1	b405	b405	PROPN
ap-1199	173	2	,	,	PUNCT
ap-1199	173	3	424	424	NUM
ap-1199	173	4	(	(	PUNCT
ap-1199	173	5	1993	1993	NUM
ap-1199	173	6	)	)	PUNCT
ap-1199	173	7	;	;	PUNCT
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ap-1199	173	9	,	,	PUNCT
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ap-1199	173	12	:	:	PUNCT
ap-1199	173	13	z.	z.	PROPN
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ap-1199	173	15	.	.	PUNCT
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ap-1199	174	2	,	,	PUNCT
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ap-1199	174	4	(	(	PUNCT
ap-1199	174	5	1993	1993	NUM
ap-1199	174	6	)	)	PUNCT
ap-1199	174	7	.	.	PUNCT
ap-1199	175	1	[	[	X
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ap-1199	175	3	]	]	X
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ap-1199	175	5	,	,	PUNCT
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ap-1199	175	7	:	:	PUNCT
ap-1199	175	8	nucl	nucl	PROPN
ap-1199	175	9	.	.	PUNCT
ap-1199	176	1	phys	phy	NOUN
ap-1199	176	2	.	.	PUNCT
ap-1199	177	1	b463	b463	NUM
ap-1199	177	2	,	,	PUNCT
ap-1199	177	3	511	511	NUM
ap-1199	177	4	(	(	PUNCT
ap-1199	177	5	1996	1996	NUM
ap-1199	177	6	)	)	PUNCT
ap-1199	177	7	.	.	PUNCT
ap-1199	178	1	[	[	X
ap-1199	178	2	12	12	NUM
ap-1199	178	3	]	]	X
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ap-1199	178	5	,	,	PUNCT
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ap-1199	178	7	:	:	PUNCT
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ap-1199	178	9	.	.	PUNCT
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ap-1199	179	2	.	.	PUNCT
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ap-1199	180	2	,	,	PUNCT
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ap-1199	180	4	(	(	PUNCT
ap-1199	180	5	1999	1999	NUM
ap-1199	180	6	)	)	PUNCT
ap-1199	180	7	.	.	PUNCT
ap-1199	181	1	[	[	X
ap-1199	181	2	13	13	NUM
ap-1199	181	3	]	]	X
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ap-1199	181	5	,	,	PUNCT
ap-1199	181	6	f.	f.	PROPN
ap-1199	181	7	,	,	PUNCT
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ap-1199	181	9	,	,	PUNCT
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ap-1199	181	11	,	,	PUNCT
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ap-1199	181	13	,	,	PUNCT
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ap-1199	181	15	:	:	PUNCT
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ap-1199	181	17	.	.	PUNCT
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ap-1199	182	2	.	.	PUNCT
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ap-1199	183	2	,	,	PUNCT
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ap-1199	183	4	(	(	PUNCT
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ap-1199	183	6	)	)	PUNCT
ap-1199	183	7	.	.	PUNCT
ap-1199	184	1	[	[	X
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ap-1199	184	5	,	,	PUNCT
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ap-1199	184	7	,	,	PUNCT
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ap-1199	184	9	,	,	PUNCT
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ap-1199	184	14	,	,	PUNCT
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ap-1199	184	16	:	:	PUNCT
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ap-1199	184	18	.	.	PUNCT
ap-1199	185	1	lett	lett	PROPN
ap-1199	185	2	.	.	PUNCT
ap-1199	186	1	b404	b404	PROPN
ap-1199	186	2	,	,	PUNCT
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ap-1199	186	4	(	(	PUNCT
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ap-1199	186	6	)	)	PUNCT
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ap-1199	187	1	[	[	X
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ap-1199	187	5	,	,	PUNCT
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ap-1199	187	7	,	,	PUNCT
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ap-1199	187	11	:	:	PUNCT
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ap-1199	187	13	.	.	PUNCT
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ap-1199	188	2	.	.	PUNCT
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ap-1199	189	2	,	,	PUNCT
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ap-1199	189	4	(	(	PUNCT
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ap-1199	189	6	)	)	PUNCT
ap-1199	189	7	.	.	PUNCT
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ap-1199	192	6	,	,	PUNCT
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ap-1199	194	2	,	,	PUNCT
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ap-1199	194	4	(	(	PUNCT
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ap-1199	194	6	)	)	PUNCT
ap-1199	194	7	;	;	PUNCT
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ap-1199	194	9	,	,	PUNCT
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ap-1199	194	15	:	:	PUNCT
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ap-1199	194	17	.	.	PUNCT
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ap-1199	195	4	,	,	PUNCT
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ap-1199	195	6	(	(	PUNCT
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ap-1199	195	8	)	)	PUNCT
ap-1199	195	9	.	.	PUNCT
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ap-1199	196	5	,	,	PUNCT
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ap-1199	196	9	,	,	PUNCT
ap-1199	196	10	t.	t.	PROPN
ap-1199	196	11	:	:	PUNCT
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ap-1199	196	13	.	.	PUNCT
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ap-1199	197	2	.	.	PROPN
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ap-1199	197	4	,	,	PUNCT
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ap-1199	197	6	(	(	PUNCT
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ap-1199	197	8	)	)	PUNCT
ap-1199	197	9	.	.	PUNCT
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ap-1199	198	3	]	]	PUNCT
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ap-1199	198	5	,	,	PUNCT
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ap-1199	198	13	:	:	PUNCT
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ap-1199	198	17	.	.	PUNCT
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ap-1199	199	3	,	,	PUNCT
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ap-1199	199	5	(	(	PUNCT
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ap-1199	199	7	)	)	PUNCT
ap-1199	199	8	;	;	PUNCT
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ap-1199	200	10	:	:	PUNCT
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ap-1199	201	2	.	.	PROPN
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ap-1199	201	4	,	,	PUNCT
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ap-1199	201	6	(	(	PUNCT
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ap-1199	201	8	)	)	PUNCT
ap-1199	201	9	.	.	PUNCT
ap-1199	202	1	[	[	X
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ap-1199	202	11	:	:	PUNCT
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ap-1199	202	13	.	.	PUNCT
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ap-1199	202	17	,	,	PUNCT
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ap-1199	202	19	(	(	PUNCT
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ap-1199	203	7	,	,	PUNCT
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ap-1199	203	9	,	,	PUNCT
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ap-1199	203	11	:	:	PUNCT
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ap-1199	203	14	,	,	PUNCT
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ap-1199	203	16	(	(	PUNCT
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ap-1199	203	18	)	)	PUNCT
ap-1199	203	19	.	.	PUNCT
ap-1199	204	1	[	[	X
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ap-1199	204	11	:	:	PUNCT
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ap-1199	204	13	.	.	PUNCT
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ap-1199	204	17	,	,	PUNCT
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ap-1199	204	19	(	(	PUNCT
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ap-1199	204	22	.	.	PUNCT
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