id	sid	tid	token	lemma	pos
ejpam-2498	1	1	compile	compile	NOUN
ejpam-2498	1	2	/	/	SYM
ejpam-2498	1	3	output.dvi	output.dvi	NOUN
ejpam-2498	1	4	european	european	ADJ
ejpam-2498	1	5	journal	journal	NOUN
ejpam-2498	1	6	of	of	ADP
ejpam-2498	1	7	pure	pure	ADJ
ejpam-2498	1	8	and	and	CCONJ
ejpam-2498	1	9	applied	apply	VERB
ejpam-2498	1	10	mathematics	mathematic	NOUN
ejpam-2498	1	11	vol	vol	NOUN
ejpam-2498	1	12	.	.	PROPN
ejpam-2498	2	1	9	9	NUM
ejpam-2498	2	2	,	,	PUNCT
ejpam-2498	2	3	no	no	INTJ
ejpam-2498	2	4	.	.	NOUN
ejpam-2498	2	5	3	3	NUM
ejpam-2498	2	6	,	,	PUNCT
ejpam-2498	2	7	2016	2016	NUM
ejpam-2498	2	8	,	,	PUNCT
ejpam-2498	2	9	314	314	NUM
ejpam-2498	2	10	-	-	SYM
ejpam-2498	2	11	321	321	NUM
ejpam-2498	2	12	issn	issn	PROPN
ejpam-2498	2	13	1307	1307	NUM
ejpam-2498	2	14	-	-	SYM
ejpam-2498	2	15	5543	5543	NUM
ejpam-2498	2	16	–	–	PUNCT
ejpam-2498	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-2498	2	18	perfect	perfect	ADJ
ejpam-2498	2	19	morse	morse	ADJ
ejpam-2498	2	20	function	function	NOUN
ejpam-2498	2	21	on	on	ADP
ejpam-2498	2	22	so(n	so(n	PROPN
ejpam-2498	2	23	)	)	PUNCT
ejpam-2498	2	24	mehmet	mehmet	PROPN
ejpam-2498	2	25	solgun	solgun	PROPN
ejpam-2498	2	26	bilecik	bilecik	PROPN
ejpam-2498	2	27	seyh	seyh	PROPN
ejpam-2498	2	28	edebali	edebali	VERB
ejpam-2498	2	29	university	university	NOUN
ejpam-2498	2	30	,	,	PUNCT
ejpam-2498	2	31	faculty	faculty	NOUN
ejpam-2498	2	32	of	of	ADP
ejpam-2498	2	33	sciences	science	NOUN
ejpam-2498	2	34	and	and	CCONJ
ejpam-2498	2	35	arts	art	NOUN
ejpam-2498	2	36	,	,	PUNCT
ejpam-2498	2	37	department	department	NOUN
ejpam-2498	2	38	of	of	ADP
ejpam-2498	2	39	mathematics	mathematics	PROPN
ejpam-2498	2	40	,	,	PUNCT
ejpam-2498	2	41	bilecik	bilecik	PROPN
ejpam-2498	2	42	,	,	PUNCT
ejpam-2498	2	43	turkey	turkey	PROPN
ejpam-2498	2	44	abstract	abstract	NOUN
ejpam-2498	2	45	.	.	PUNCT
ejpam-2498	3	1	in	in	ADP
ejpam-2498	3	2	this	this	DET
ejpam-2498	3	3	work	work	NOUN
ejpam-2498	3	4	,	,	PUNCT
ejpam-2498	3	5	we	we	PRON
ejpam-2498	3	6	define	define	VERB
ejpam-2498	3	7	a	a	DET
ejpam-2498	3	8	morse	morse	ADJ
ejpam-2498	3	9	function	function	NOUN
ejpam-2498	3	10	on	on	ADP
ejpam-2498	3	11	so(n	so(n	PROPN
ejpam-2498	3	12	)	)	PUNCT
ejpam-2498	3	13	and	and	CCONJ
ejpam-2498	3	14	show	show	VERB
ejpam-2498	3	15	that	that	SCONJ
ejpam-2498	3	16	this	this	DET
ejpam-2498	3	17	function	function	NOUN
ejpam-2498	3	18	is	be	AUX
ejpam-2498	3	19	indeed	indeed	ADV
ejpam-2498	3	20	a	a	DET
ejpam-2498	3	21	perfect	perfect	ADJ
ejpam-2498	3	22	morse	morse	NOUN
ejpam-2498	3	23	function	function	NOUN
ejpam-2498	3	24	.	.	PUNCT
ejpam-2498	4	1	2010	2010	NUM
ejpam-2498	4	2	mathematics	mathematic	NOUN
ejpam-2498	4	3	subject	subject	NOUN
ejpam-2498	4	4	classifications	classification	NOUN
ejpam-2498	4	5	:	:	PUNCT
ejpam-2498	4	6	57r70	57r70	NUM
ejpam-2498	4	7	,	,	PUNCT
ejpam-2498	4	8	58e05	58e05	NUM
ejpam-2498	4	9	key	key	ADJ
ejpam-2498	4	10	words	word	NOUN
ejpam-2498	4	11	and	and	CCONJ
ejpam-2498	4	12	phrases	phrase	NOUN
ejpam-2498	4	13	:	:	PUNCT
ejpam-2498	4	14	so(n	so(n	NUM
ejpam-2498	4	15	)	)	PUNCT
ejpam-2498	4	16	,	,	PUNCT
ejpam-2498	4	17	morse	morse	NOUN
ejpam-2498	4	18	functions	function	NOUN
ejpam-2498	4	19	,	,	PUNCT
ejpam-2498	4	20	perfect	perfect	ADJ
ejpam-2498	4	21	morse	morse	NOUN
ejpam-2498	4	22	functions	function	NOUN
ejpam-2498	4	23	.	.	PUNCT
ejpam-2498	5	1	1	1	X
ejpam-2498	5	2	.	.	X
ejpam-2498	5	3	introduction	introduction	NOUN
ejpam-2498	5	4	the	the	DET
ejpam-2498	5	5	main	main	ADJ
ejpam-2498	5	6	point	point	NOUN
ejpam-2498	5	7	of	of	ADP
ejpam-2498	5	8	morse	morse	PROPN
ejpam-2498	5	9	theory	theory	NOUN
ejpam-2498	5	10	,	,	PUNCT
ejpam-2498	5	11	which	which	PRON
ejpam-2498	5	12	was	be	AUX
ejpam-2498	5	13	introduced	introduce	VERB
ejpam-2498	5	14	in	in	ADP
ejpam-2498	5	15	[	[	X
ejpam-2498	5	16	6	6	NUM
ejpam-2498	5	17	]	]	PUNCT
ejpam-2498	5	18	,	,	PUNCT
ejpam-2498	5	19	is	be	AUX
ejpam-2498	5	20	investigating	investigate	VERB
ejpam-2498	5	21	the	the	DET
ejpam-2498	5	22	relation	relation	NOUN
ejpam-2498	5	23	between	between	ADP
ejpam-2498	5	24	shape	shape	NOUN
ejpam-2498	5	25	of	of	ADP
ejpam-2498	5	26	a	a	DET
ejpam-2498	5	27	smooth	smooth	ADJ
ejpam-2498	5	28	manifold	manifold	ADJ
ejpam-2498	5	29	m	m	NOUN
ejpam-2498	5	30	and	and	CCONJ
ejpam-2498	5	31	critical	critical	ADJ
ejpam-2498	5	32	points	point	NOUN
ejpam-2498	5	33	of	of	ADP
ejpam-2498	5	34	a	a	DET
ejpam-2498	5	35	specific	specific	ADJ
ejpam-2498	5	36	real	real	ADV
ejpam-2498	5	37	-	-	PUNCT
ejpam-2498	5	38	valued	value	VERB
ejpam-2498	5	39	function	function	NOUN
ejpam-2498	5	40	f	f	NOUN
ejpam-2498	5	41	:	:	PUNCT
ejpam-2498	5	42	m	m	VERB
ejpam-2498	5	43	→	→	SYM
ejpam-2498	5	44	r	r	NOUN
ejpam-2498	5	45	,	,	PUNCT
ejpam-2498	5	46	that	that	PRON
ejpam-2498	5	47	is	be	AUX
ejpam-2498	5	48	called	call	VERB
ejpam-2498	5	49	morse	morse	ADJ
ejpam-2498	5	50	function	function	NOUN
ejpam-2498	5	51	.	.	PUNCT
ejpam-2498	6	1	[	[	X
ejpam-2498	6	2	5	5	NUM
ejpam-2498	6	3	]	]	PUNCT
ejpam-2498	6	4	and	and	CCONJ
ejpam-2498	6	5	[	[	X
ejpam-2498	6	6	4	4	NUM
ejpam-2498	6	7	]	]	PUNCT
ejpam-2498	6	8	are	be	AUX
ejpam-2498	6	9	two	two	NUM
ejpam-2498	6	10	of	of	ADP
ejpam-2498	6	11	main	main	ADJ
ejpam-2498	6	12	sources	source	NOUN
ejpam-2498	6	13	about	about	ADP
ejpam-2498	6	14	this	this	DET
ejpam-2498	6	15	subject	subject	NOUN
ejpam-2498	6	16	,	,	PUNCT
ejpam-2498	6	17	so	so	SCONJ
ejpam-2498	6	18	mostly	mostly	ADV
ejpam-2498	6	19	we	we	PRON
ejpam-2498	6	20	will	will	AUX
ejpam-2498	6	21	use	use	VERB
ejpam-2498	6	22	their	their	PRON
ejpam-2498	6	23	beautiful	beautiful	ADJ
ejpam-2498	6	24	tools	tool	NOUN
ejpam-2498	6	25	for	for	ADP
ejpam-2498	6	26	defining	define	VERB
ejpam-2498	6	27	a	a	DET
ejpam-2498	6	28	morse	morse	ADJ
ejpam-2498	6	29	function	function	NOUN
ejpam-2498	6	30	on	on	ADP
ejpam-2498	6	31	so(n	so(n	PROPN
ejpam-2498	6	32	)	)	PUNCT
ejpam-2498	6	33	.	.	PUNCT
ejpam-2498	7	1	also	also	ADV
ejpam-2498	7	2	,	,	PUNCT
ejpam-2498	7	3	we	we	PRON
ejpam-2498	7	4	will	will	AUX
ejpam-2498	7	5	refer	refer	VERB
ejpam-2498	7	6	[	[	X
ejpam-2498	7	7	2	2	NUM
ejpam-2498	7	8	]	]	PUNCT
ejpam-2498	7	9	to	to	PART
ejpam-2498	7	10	use	use	VERB
ejpam-2498	7	11	homological	homological	ADJ
ejpam-2498	7	12	properties	property	NOUN
ejpam-2498	7	13	and	and	CCONJ
ejpam-2498	7	14	to	to	PART
ejpam-2498	7	15	determine	determine	VERB
ejpam-2498	7	16	the	the	DET
ejpam-2498	7	17	poincaré	poincaré	PROPN
ejpam-2498	7	18	polynomial	polynomial	PROPN
ejpam-2498	7	19	of	of	ADP
ejpam-2498	7	20	so(n	so(n	PROPN
ejpam-2498	7	21	)	)	PUNCT
ejpam-2498	7	22	.	.	PUNCT
ejpam-2498	8	1	perfect	perfect	ADJ
ejpam-2498	8	2	morse	morse	NOUN
ejpam-2498	8	3	functions	function	NOUN
ejpam-2498	8	4	are	be	AUX
ejpam-2498	8	5	widely	widely	ADV
ejpam-2498	8	6	studied	study	VERB
ejpam-2498	8	7	in	in	ADP
ejpam-2498	8	8	[	[	X
ejpam-2498	8	9	7	7	NUM
ejpam-2498	8	10	]	]	PUNCT
ejpam-2498	8	11	,	,	PUNCT
ejpam-2498	8	12	that	that	PRON
ejpam-2498	8	13	is	be	AUX
ejpam-2498	8	14	one	one	NUM
ejpam-2498	8	15	of	of	ADP
ejpam-2498	8	16	our	our	PRON
ejpam-2498	8	17	inspiration	inspiration	NOUN
ejpam-2498	8	18	to	to	PART
ejpam-2498	8	19	show	show	VERB
ejpam-2498	8	20	that	that	SCONJ
ejpam-2498	8	21	the	the	DET
ejpam-2498	8	22	function	function	NOUN
ejpam-2498	8	23	,	,	PUNCT
ejpam-2498	8	24	we	we	PRON
ejpam-2498	8	25	defined	define	VERB
ejpam-2498	8	26	,	,	PUNCT
ejpam-2498	8	27	is	be	AUX
ejpam-2498	8	28	also	also	ADV
ejpam-2498	8	29	perfect	perfect	ADJ
ejpam-2498	8	30	.	.	PUNCT
ejpam-2498	9	1	2	2	X
ejpam-2498	9	2	.	.	X
ejpam-2498	9	3	preliminaries	preliminary	NOUN
ejpam-2498	9	4	in	in	ADP
ejpam-2498	9	5	this	this	DET
ejpam-2498	9	6	section	section	NOUN
ejpam-2498	9	7	,	,	PUNCT
ejpam-2498	9	8	we	we	PRON
ejpam-2498	9	9	give	give	VERB
ejpam-2498	9	10	some	some	DET
ejpam-2498	9	11	definitions	definition	NOUN
ejpam-2498	9	12	and	and	CCONJ
ejpam-2498	9	13	theorems	theorem	NOUN
ejpam-2498	9	14	which	which	PRON
ejpam-2498	9	15	will	will	AUX
ejpam-2498	9	16	be	be	AUX
ejpam-2498	9	17	used	use	VERB
ejpam-2498	9	18	in	in	ADP
ejpam-2498	9	19	this	this	DET
ejpam-2498	9	20	paper	paper	NOUN
ejpam-2498	9	21	.	.	PUNCT
ejpam-2498	10	1	definition	definition	NOUN
ejpam-2498	10	2	1	1	NUM
ejpam-2498	10	3	.	.	PUNCT
ejpam-2498	11	1	let	let	VERB
ejpam-2498	11	2	m	m	PRON
ejpam-2498	11	3	be	be	AUX
ejpam-2498	11	4	an	an	DET
ejpam-2498	11	5	n	n	ADV
ejpam-2498	11	6	-	-	PUNCT
ejpam-2498	11	7	dimensional	dimensional	ADJ
ejpam-2498	11	8	smooth	smooth	ADJ
ejpam-2498	11	9	manifold	manifold	NOUN
ejpam-2498	11	10	and	and	CCONJ
ejpam-2498	11	11	f	f	NOUN
ejpam-2498	11	12	:	:	PUNCT
ejpam-2498	11	13	m	m	VERB
ejpam-2498	11	14	→	→	SYM
ejpam-2498	11	15	r	r	NOUN
ejpam-2498	11	16	be	be	AUX
ejpam-2498	11	17	a	a	DET
ejpam-2498	11	18	smooth	smooth	ADJ
ejpam-2498	11	19	function	function	NOUN
ejpam-2498	11	20	.	.	PUNCT
ejpam-2498	12	1	a	a	DET
ejpam-2498	12	2	point	point	NOUN
ejpam-2498	12	3	p0	p0	NOUN
ejpam-2498	12	4	∈	∈	PROPN
ejpam-2498	12	5	m	m	VERB
ejpam-2498	12	6	is	be	AUX
ejpam-2498	12	7	said	say	VERB
ejpam-2498	12	8	to	to	PART
ejpam-2498	12	9	be	be	AUX
ejpam-2498	12	10	a	a	DET
ejpam-2498	12	11	critical	critical	ADJ
ejpam-2498	12	12	point	point	NOUN
ejpam-2498	12	13	of	of	ADP
ejpam-2498	12	14	m	m	PRON
ejpam-2498	12	15	if	if	SCONJ
ejpam-2498	12	16	we	we	PRON
ejpam-2498	12	17	have	have	VERB
ejpam-2498	12	18	∂	∂	NUM
ejpam-2498	12	19	f	f	NOUN
ejpam-2498	12	20	∂	∂	NOUN
ejpam-2498	12	21	x1	x1	NOUN
ejpam-2498	13	1	=	=	SYM
ejpam-2498	13	2	0	0	NUM
ejpam-2498	13	3	,	,	PUNCT
ejpam-2498	13	4	∂	∂	NUM
ejpam-2498	13	5	f	f	NOUN
ejpam-2498	13	6	∂	∂	NOUN
ejpam-2498	13	7	x2	x2	NOUN
ejpam-2498	13	8	=	=	SYM
ejpam-2498	13	9	0	0	PROPN
ejpam-2498	13	10	,	,	PUNCT
ejpam-2498	13	11	.	.	PUNCT
ejpam-2498	13	12	.	.	PUNCT
ejpam-2498	14	1	.	.	PUNCT
ejpam-2498	15	1	,	,	PUNCT
ejpam-2498	15	2	∂	∂	NUM
ejpam-2498	15	3	f	f	NOUN
ejpam-2498	15	4	∂	∂	NOUN
ejpam-2498	15	5	xn	xn	PROPN
ejpam-2498	15	6	=	=	SYM
ejpam-2498	15	7	0	0	NUM
ejpam-2498	15	8	(	(	PUNCT
ejpam-2498	15	9	1	1	NUM
ejpam-2498	15	10	)	)	PUNCT
ejpam-2498	15	11	with	with	ADP
ejpam-2498	15	12	respect	respect	NOUN
ejpam-2498	15	13	to	to	ADP
ejpam-2498	15	14	a	a	DET
ejpam-2498	15	15	coordinate	coordinate	NOUN
ejpam-2498	15	16	system	system	NOUN
ejpam-2498	15	17	{	{	PUNCT
ejpam-2498	15	18	x1	x1	PROPN
ejpam-2498	15	19	,	,	PUNCT
ejpam-2498	15	20	x2	x2	PROPN
ejpam-2498	15	21	,	,	PUNCT
ejpam-2498	15	22	.	.	PUNCT
ejpam-2498	15	23	.	.	PUNCT
ejpam-2498	16	1	.	.	PUNCT
ejpam-2498	17	1	,	,	PUNCT
ejpam-2498	17	2	xn	xn	X
ejpam-2498	17	3	}	}	PUNCT
ejpam-2498	17	4	around	around	ADP
ejpam-2498	17	5	p0	p0	NOUN
ejpam-2498	17	6	.	.	PUNCT
ejpam-2498	18	1	email	email	NOUN
ejpam-2498	18	2	address	address	NOUN
ejpam-2498	18	3	:	:	PUNCT
ejpam-2498	18	4	mehmet.solgun@bilecik.edu.tr	mehmet.solgun@bilecik.edu.tr	ADV
ejpam-2498	18	5	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2498	18	6	314	314	NUM
ejpam-2498	18	7	c	c	NOUN
ejpam-2498	18	8	©	©	PROPN
ejpam-2498	18	9	2016	2016	NUM
ejpam-2498	18	10	ejpam	ejpam	VERB
ejpam-2498	18	11	all	all	DET
ejpam-2498	18	12	rights	right	NOUN
ejpam-2498	18	13	reserved	reserve	VERB
ejpam-2498	18	14	.	.	PUNCT
ejpam-2498	19	1	m.	m.	NOUN
ejpam-2498	19	2	solgun	solgun	PROPN
ejpam-2498	19	3	/	/	SYM
ejpam-2498	19	4	eur	eur	PROPN
ejpam-2498	19	5	.	.	PUNCT
ejpam-2498	20	1	j.	j.	PROPN
ejpam-2498	20	2	pure	pure	PROPN
ejpam-2498	20	3	appl	appl	PROPN
ejpam-2498	20	4	.	.	PROPN
ejpam-2498	20	5	math	math	PROPN
ejpam-2498	20	6	,	,	PUNCT
ejpam-2498	20	7	9	9	NUM
ejpam-2498	20	8	(	(	PUNCT
ejpam-2498	20	9	2016	2016	NUM
ejpam-2498	20	10	)	)	PUNCT
ejpam-2498	20	11	,	,	PUNCT
ejpam-2498	20	12	314	314	NUM
ejpam-2498	20	13	-	-	SYM
ejpam-2498	20	14	321	321	NUM
ejpam-2498	20	15	315	315	NUM
ejpam-2498	20	16	a	a	DET
ejpam-2498	20	17	point	point	NOUN
ejpam-2498	20	18	c	c	X
ejpam-2498	20	19	∈	∈	NOUN
ejpam-2498	20	20	r	r	NOUN
ejpam-2498	20	21	is	be	AUX
ejpam-2498	20	22	said	say	VERB
ejpam-2498	20	23	to	to	PART
ejpam-2498	20	24	be	be	AUX
ejpam-2498	20	25	a	a	DET
ejpam-2498	20	26	critical	critical	ADJ
ejpam-2498	20	27	value	value	NOUN
ejpam-2498	20	28	of	of	ADP
ejpam-2498	20	29	f	f	PROPN
ejpam-2498	20	30	:	:	PUNCT
ejpam-2498	20	31	m	m	VERB
ejpam-2498	20	32	→	→	SYM
ejpam-2498	20	33	r	r	NOUN
ejpam-2498	20	34	,	,	PUNCT
ejpam-2498	20	35	if	if	SCONJ
ejpam-2498	20	36	f	f	PROPN
ejpam-2498	20	37	(	(	PUNCT
ejpam-2498	20	38	p0	p0	PROPN
ejpam-2498	20	39	)	)	PUNCT
ejpam-2498	20	40	=	=	SYM
ejpam-2498	21	1	c	c	NOUN
ejpam-2498	21	2	for	for	ADP
ejpam-2498	21	3	a	a	DET
ejpam-2498	21	4	critical	critical	ADJ
ejpam-2498	21	5	point	point	NOUN
ejpam-2498	21	6	p0	p0	NOUN
ejpam-2498	21	7	of	of	ADP
ejpam-2498	21	8	f	f	PROPN
ejpam-2498	21	9	.	.	PUNCT
ejpam-2498	22	1	definition	definition	NOUN
ejpam-2498	22	2	2	2	NUM
ejpam-2498	22	3	.	.	PUNCT
ejpam-2498	23	1	let	let	VERB
ejpam-2498	23	2	p0	p0	NOUN
ejpam-2498	23	3	be	be	AUX
ejpam-2498	23	4	a	a	DET
ejpam-2498	23	5	critical	critical	ADJ
ejpam-2498	23	6	point	point	NOUN
ejpam-2498	23	7	of	of	ADP
ejpam-2498	23	8	the	the	DET
ejpam-2498	23	9	function	function	NOUN
ejpam-2498	23	10	f	f	NOUN
ejpam-2498	23	11	:	:	PUNCT
ejpam-2498	23	12	m	m	VERB
ejpam-2498	23	13	→	→	SYM
ejpam-2498	23	14	r.	r.	X
ejpam-2498	23	15	the	the	DET
ejpam-2498	23	16	hessian	hessian	NOUN
ejpam-2498	23	17	of	of	ADP
ejpam-2498	23	18	f	f	PROPN
ejpam-2498	23	19	at	at	ADP
ejpam-2498	23	20	he	he	PRON
ejpam-2498	23	21	point	point	VERB
ejpam-2498	23	22	p0	p0	NOUN
ejpam-2498	23	23	is	be	AUX
ejpam-2498	24	1	the	the	DET
ejpam-2498	24	2	n×	n×	PROPN
ejpam-2498	24	3	n	n	NOUN
ejpam-2498	24	4	matrix	matrix	NOUN
ejpam-2498	24	5	h	h	NOUN
ejpam-2498	25	1	f	f	PROPN
ejpam-2498	26	1	(	(	PUNCT
ejpam-2498	26	2	p0	p0	PROPN
ejpam-2498	26	3	)	)	PUNCT
ejpam-2498	27	1	=	=	NOUN
ejpam-2498	27	2			NOUN
ejpam-2498	27	3			ADJ
ejpam-2498	27	4			ADJ
ejpam-2498	27	5			NOUN
ejpam-2498	27	6	∂	∂	NUM
ejpam-2498	27	7	2	2	NUM
ejpam-2498	27	8	f	f	SYM
ejpam-2498	27	9	∂	∂	NOUN
ejpam-2498	27	10	x1	x1	NOUN
ejpam-2498	27	11	2	2	NUM
ejpam-2498	27	12	(	(	PUNCT
ejpam-2498	27	13	p0	p0	NOUN
ejpam-2498	27	14	)	)	PUNCT
ejpam-2498	27	15	·	·	PUNCT
ejpam-2498	27	16	·	·	PUNCT
ejpam-2498	27	17	·	·	PUNCT
ejpam-2498	27	18	∂	∂	NUM
ejpam-2498	27	19	2	2	NUM
ejpam-2498	27	20	f	f	PROPN
ejpam-2498	27	21	∂	∂	NOUN
ejpam-2498	27	22	x1∂	x1∂	PROPN
ejpam-2498	27	23	xn	xn	PROPN
ejpam-2498	27	24	(	(	PUNCT
ejpam-2498	27	25	p0	p0	PROPN
ejpam-2498	27	26	)	)	PUNCT
ejpam-2498	27	27	...	...	PUNCT
ejpam-2498	27	28	.	.	PUNCT
ejpam-2498	27	29	.	.	PUNCT
ejpam-2498	27	30	.	.	PUNCT
ejpam-2498	28	1	...	...	PUNCT
ejpam-2498	29	1	∂	∂	NUM
ejpam-2498	29	2	2	2	NUM
ejpam-2498	29	3	f	f	SYM
ejpam-2498	29	4	∂	∂	NOUN
ejpam-2498	30	1	xn∂	xn∂	NUM
ejpam-2498	31	1	x1	x1	PROPN
ejpam-2498	31	2	(	(	PUNCT
ejpam-2498	31	3	p0	p0	PROPN
ejpam-2498	31	4	)	)	PUNCT
ejpam-2498	31	5	·	·	PUNCT
ejpam-2498	31	6	·	·	PUNCT
ejpam-2498	31	7	·	·	PUNCT
ejpam-2498	31	8	∂	∂	NUM
ejpam-2498	31	9	2	2	NUM
ejpam-2498	31	10	f	f	PROPN
ejpam-2498	31	11	∂	∂	NOUN
ejpam-2498	31	12	xn	xn	PROPN
ejpam-2498	31	13	2	2	NUM
ejpam-2498	31	14	(	(	PUNCT
ejpam-2498	31	15	p0	p0	NOUN
ejpam-2498	31	16	)	)	PUNCT
ejpam-2498	31	17			PROPN
ejpam-2498	31	18			PROPN
ejpam-2498	31	19			PROPN
ejpam-2498	31	20			PROPN
ejpam-2498	31	21	(	(	PUNCT
ejpam-2498	31	22	2	2	NUM
ejpam-2498	31	23	)	)	PUNCT
ejpam-2498	31	24	since	since	SCONJ
ejpam-2498	31	25	∂	∂	NUM
ejpam-2498	31	26	2	2	NUM
ejpam-2498	31	27	f	f	NOUN
ejpam-2498	31	28	∂	∂	NOUN
ejpam-2498	31	29	x	x	VERB
ejpam-2498	31	30	i∂	i∂	VERB
ejpam-2498	31	31	x	x	PUNCT
ejpam-2498	31	32	j	j	PROPN
ejpam-2498	31	33	(	(	PUNCT
ejpam-2498	31	34	p0	p0	PROPN
ejpam-2498	31	35	)	)	PUNCT
ejpam-2498	31	36	=	=	SYM
ejpam-2498	31	37	∂	∂	NUM
ejpam-2498	31	38	2	2	NUM
ejpam-2498	31	39	f	f	NOUN
ejpam-2498	31	40	∂	∂	NUM
ejpam-2498	31	41	x	x	NOUN
ejpam-2498	31	42	j∂	j∂	PROPN
ejpam-2498	31	43	x	x	X
ejpam-2498	31	44	i	i	PRON
ejpam-2498	31	45	(	(	PUNCT
ejpam-2498	31	46	p0	p0	NOUN
ejpam-2498	31	47	)	)	PUNCT
ejpam-2498	31	48	,	,	PUNCT
ejpam-2498	31	49	the	the	DET
ejpam-2498	31	50	hessian	hessian	NOUN
ejpam-2498	31	51	of	of	ADP
ejpam-2498	31	52	f	f	PROPN
ejpam-2498	31	53	is	be	AUX
ejpam-2498	31	54	a	a	DET
ejpam-2498	31	55	symmetric	symmetric	ADJ
ejpam-2498	31	56	matrix	matrix	NOUN
ejpam-2498	31	57	.	.	PUNCT
ejpam-2498	32	1	let	let	VERB
ejpam-2498	32	2	p0	p0	NOUN
ejpam-2498	32	3	be	be	AUX
ejpam-2498	32	4	a	a	DET
ejpam-2498	32	5	critical	critical	ADJ
ejpam-2498	32	6	point	point	NOUN
ejpam-2498	32	7	of	of	ADP
ejpam-2498	32	8	f	f	PROPN
ejpam-2498	32	9	and	and	CCONJ
ejpam-2498	32	10	c0	c0	PROPN
ejpam-2498	32	11	∈	∈	PROPN
ejpam-2498	32	12	r	r	NOUN
ejpam-2498	33	1	such	such	ADJ
ejpam-2498	33	2	that	that	SCONJ
ejpam-2498	33	3	f	f	PROPN
ejpam-2498	33	4	(	(	PUNCT
ejpam-2498	33	5	p0	p0	PROPN
ejpam-2498	33	6	)	)	PUNCT
ejpam-2498	33	7	=	=	SYM
ejpam-2498	33	8	c0	c0	PROPN
ejpam-2498	33	9	.	.	PUNCT
ejpam-2498	34	1	then	then	ADV
ejpam-2498	34	2	,	,	PUNCT
ejpam-2498	34	3	c0	c0	PROPN
ejpam-2498	34	4	is	be	AUX
ejpam-2498	34	5	said	say	VERB
ejpam-2498	34	6	to	to	PART
ejpam-2498	34	7	be	be	AUX
ejpam-2498	34	8	a	a	DET
ejpam-2498	34	9	critical	critical	ADJ
ejpam-2498	34	10	value	value	NOUN
ejpam-2498	34	11	of	of	ADP
ejpam-2498	34	12	f	f	PROPN
ejpam-2498	34	13	.	.	PUNCT
ejpam-2498	35	1	if	if	SCONJ
ejpam-2498	35	2	p0	p0	NOUN
ejpam-2498	35	3	is	be	AUX
ejpam-2498	35	4	a	a	DET
ejpam-2498	35	5	regular	regular	ADJ
ejpam-2498	35	6	point	point	NOUN
ejpam-2498	35	7	of	of	ADP
ejpam-2498	35	8	f	f	PROPN
ejpam-2498	35	9	,	,	PUNCT
ejpam-2498	35	10	then	then	ADV
ejpam-2498	35	11	c0	c0	PROPN
ejpam-2498	35	12	is	be	AUX
ejpam-2498	35	13	said	say	VERB
ejpam-2498	35	14	to	to	PART
ejpam-2498	35	15	be	be	AUX
ejpam-2498	35	16	a	a	DET
ejpam-2498	35	17	regular	regular	ADJ
ejpam-2498	35	18	value	value	NOUN
ejpam-2498	35	19	of	of	ADP
ejpam-2498	35	20	f	f	PROPN
ejpam-2498	35	21	.	.	PUNCT
ejpam-2498	36	1	if	if	SCONJ
ejpam-2498	36	2	a	a	PRON
ejpam-2498	36	3	is	be	AUX
ejpam-2498	36	4	a	a	DET
ejpam-2498	36	5	regular	regular	ADJ
ejpam-2498	36	6	value	value	NOUN
ejpam-2498	36	7	of	of	ADP
ejpam-2498	36	8	f	f	PROPN
ejpam-2498	36	9	,	,	PUNCT
ejpam-2498	36	10	it	it	PRON
ejpam-2498	36	11	can	can	AUX
ejpam-2498	36	12	be	be	AUX
ejpam-2498	36	13	shown	show	VERB
ejpam-2498	36	14	that	that	SCONJ
ejpam-2498	36	15	the	the	DET
ejpam-2498	36	16	set	set	NOUN
ejpam-2498	36	17	f	f	PROPN
ejpam-2498	36	18	−1(a	−1(a	PROPN
ejpam-2498	36	19	)	)	PUNCT
ejpam-2498	36	20	=	=	PRON
ejpam-2498	36	21	{	{	PUNCT
ejpam-2498	36	22	p	p	X
ejpam-2498	36	23	∈	∈	PROPN
ejpam-2498	36	24	m	m	VERB
ejpam-2498	36	25	|	|	ADV
ejpam-2498	36	26	f	f	X
ejpam-2498	36	27	(	(	PUNCT
ejpam-2498	36	28	p	p	NOUN
ejpam-2498	36	29	)	)	PUNCT
ejpam-2498	36	30	=	=	SYM
ejpam-2498	36	31	a	a	PRON
ejpam-2498	36	32	}	}	PUNCT
ejpam-2498	36	33	is	be	AUX
ejpam-2498	36	34	an	an	DET
ejpam-2498	36	35	n−	n−	NOUN
ejpam-2498	36	36	1	1	NUM
ejpam-2498	36	37	dimensional	dimensional	ADJ
ejpam-2498	36	38	manifold	manifold	ADJ
ejpam-2498	37	1	[	[	X
ejpam-2498	37	2	1	1	NUM
ejpam-2498	37	3	]	]	PUNCT
ejpam-2498	37	4	.	.	PUNCT
ejpam-2498	38	1	definition	definition	NOUN
ejpam-2498	38	2	3	3	NUM
ejpam-2498	38	3	.	.	PUNCT
ejpam-2498	39	1	a	a	DET
ejpam-2498	39	2	critical	critical	ADJ
ejpam-2498	39	3	point	point	NOUN
ejpam-2498	39	4	of	of	ADP
ejpam-2498	39	5	a	a	DET
ejpam-2498	39	6	function	function	NOUN
ejpam-2498	39	7	f	f	NOUN
ejpam-2498	39	8	:	:	PUNCT
ejpam-2498	39	9	m	m	AUX
ejpam-2498	39	10	→	→	SYM
ejpam-2498	39	11	r	r	NOUN
ejpam-2498	39	12	is	be	AUX
ejpam-2498	39	13	called	call	VERB
ejpam-2498	39	14	"	"	PUNCT
ejpam-2498	39	15	non	non	ADJ
ejpam-2498	39	16	-	-	ADJ
ejpam-2498	39	17	degenerate	degenerate	ADJ
ejpam-2498	39	18	point	point	NOUN
ejpam-2498	39	19	of	of	ADP
ejpam-2498	39	20	f	f	PROPN
ejpam-2498	39	21	"	"	PUNCT
ejpam-2498	39	22	if	if	SCONJ
ejpam-2498	39	23	deth	deth	PROPN
ejpam-2498	39	24	f	f	X
ejpam-2498	39	25	(	(	PUNCT
ejpam-2498	39	26	p0	p0	PROPN
ejpam-2498	39	27	)	)	PUNCT
ejpam-2498	39	28	6=	6=	ADP
ejpam-2498	39	29	0	0	X
ejpam-2498	39	30	.	.	PUNCT
ejpam-2498	40	1	otherwise	otherwise	ADV
ejpam-2498	40	2	,	,	PUNCT
ejpam-2498	40	3	it	it	PRON
ejpam-2498	40	4	is	be	AUX
ejpam-2498	40	5	called	call	VERB
ejpam-2498	40	6	"	"	PUNCT
ejpam-2498	40	7	degenerate	degenerate	ADJ
ejpam-2498	40	8	critical	critical	ADJ
ejpam-2498	40	9	point	point	NOUN
ejpam-2498	40	10	"	"	PUNCT
ejpam-2498	40	11	.	.	PUNCT
ejpam-2498	41	1	lemma	lemma	PROPN
ejpam-2498	41	2	1	1	X
ejpam-2498	41	3	.	.	PUNCT
ejpam-2498	42	1	let	let	VERB
ejpam-2498	42	2	p0	p0	NOUN
ejpam-2498	42	3	be	be	AUX
ejpam-2498	42	4	a	a	DET
ejpam-2498	42	5	critical	critical	ADJ
ejpam-2498	42	6	point	point	NOUN
ejpam-2498	42	7	of	of	ADP
ejpam-2498	42	8	a	a	DET
ejpam-2498	42	9	smooth	smooth	ADJ
ejpam-2498	42	10	function	function	NOUN
ejpam-2498	42	11	f	f	NOUN
ejpam-2498	42	12	:	:	PUNCT
ejpam-2498	42	13	m	m	VERB
ejpam-2498	42	14	→	→	SYM
ejpam-2498	42	15	r	r	NOUN
ejpam-2498	42	16	,	,	PUNCT
ejpam-2498	42	17	(	(	PUNCT
ejpam-2498	42	18	u	u	NOUN
ejpam-2498	42	19	,	,	PUNCT
ejpam-2498	42	20	ϕ	ϕ	NOUN
ejpam-2498	42	21	=	=	PUNCT
ejpam-2498	42	22	(	(	PUNCT
ejpam-2498	42	23	x1	x1	PROPN
ejpam-2498	42	24	,	,	PUNCT
ejpam-2498	42	25	.	.	PUNCT
ejpam-2498	42	26	.	.	PUNCT
ejpam-2498	43	1	.	.	PUNCT
ejpam-2498	44	1	,	,	PUNCT
ejpam-2498	44	2	xn	xn	PROPN
ejpam-2498	44	3	)	)	PUNCT
ejpam-2498	44	4	)	)	PUNCT
ejpam-2498	44	5	,	,	PUNCT
ejpam-2498	44	6	(	(	PUNCT
ejpam-2498	44	7	v	v	NOUN
ejpam-2498	44	8	,	,	PUNCT
ejpam-2498	44	9	ψ=	ψ=	PUNCT
ejpam-2498	44	10	(	(	PUNCT
ejpam-2498	44	11	x1	x1	PROPN
ejpam-2498	44	12	,	,	PUNCT
ejpam-2498	44	13	.	.	PUNCT
ejpam-2498	44	14	.	.	PUNCT
ejpam-2498	44	15	.	.	PUNCT
ejpam-2498	45	1	,	,	PUNCT
ejpam-2498	45	2	xn	xn	PROPN
ejpam-2498	45	3	)	)	PUNCT
ejpam-2498	45	4	)	)	PUNCT
ejpam-2498	45	5	be	be	AUX
ejpam-2498	45	6	two	two	NUM
ejpam-2498	45	7	charts	chart	NOUN
ejpam-2498	45	8	of	of	ADP
ejpam-2498	45	9	p0	p0	NOUN
ejpam-2498	45	10	,	,	PUNCT
ejpam-2498	45	11	and	and	CCONJ
ejpam-2498	45	12	h	h	NOUN
ejpam-2498	45	13	f	f	PROPN
ejpam-2498	45	14	(	(	PUNCT
ejpam-2498	45	15	p0),h	p0),h	PROPN
ejpam-2498	45	16	f	f	PROPN
ejpam-2498	45	17	(	(	PUNCT
ejpam-2498	45	18	p0	p0	PROPN
ejpam-2498	45	19	)	)	PUNCT
ejpam-2498	45	20	be	be	VERB
ejpam-2498	45	21	the	the	DET
ejpam-2498	45	22	hessians	hessian	NOUN
ejpam-2498	45	23	of	of	ADP
ejpam-2498	45	24	f	f	PROPN
ejpam-2498	45	25	at	at	ADP
ejpam-2498	45	26	p0	p0	NOUN
ejpam-2498	45	27	,	,	PUNCT
ejpam-2498	45	28	using	use	VERB
ejpam-2498	45	29	the	the	DET
ejpam-2498	45	30	charts	chart	NOUN
ejpam-2498	45	31	(	(	PUNCT
ejpam-2498	45	32	u	u	NOUN
ejpam-2498	45	33	,	,	PUNCT
ejpam-2498	45	34	ϕ	ϕ	PROPN
ejpam-2498	45	35	)	)	PUNCT
ejpam-2498	45	36	,	,	PUNCT
ejpam-2498	45	37	(	(	PUNCT
ejpam-2498	45	38	v	v	NOUN
ejpam-2498	45	39	,	,	PUNCT
ejpam-2498	45	40	ψ	ψ	NOUN
ejpam-2498	45	41	)	)	PUNCT
ejpam-2498	45	42	respectively	respectively	ADV
ejpam-2498	45	43	.	.	PUNCT
ejpam-2498	46	1	then	then	ADV
ejpam-2498	46	2	the	the	DET
ejpam-2498	46	3	following	follow	VERB
ejpam-2498	46	4	holds	hold	VERB
ejpam-2498	46	5	:	:	PUNCT
ejpam-2498	46	6	h	h	PROPN
ejpam-2498	46	7	f	f	X
ejpam-2498	46	8	(	(	PUNCT
ejpam-2498	46	9	p0	p0	PROPN
ejpam-2498	46	10	)	)	PUNCT
ejpam-2498	46	11	=	=	SYM
ejpam-2498	46	12	j(p0	j(p0	NOUN
ejpam-2498	46	13	)	)	PUNCT
ejpam-2498	46	14	t	t	PROPN
ejpam-2498	46	15	h	h	NOUN
ejpam-2498	46	16	f	f	PROPN
ejpam-2498	46	17	(	(	PUNCT
ejpam-2498	46	18	p0)j(p0	p0)j(p0	NOUN
ejpam-2498	46	19	)	)	PUNCT
ejpam-2498	46	20	(	(	PUNCT
ejpam-2498	46	21	3	3	X
ejpam-2498	46	22	)	)	PUNCT
ejpam-2498	46	23	where	where	SCONJ
ejpam-2498	46	24	j(p0	j(p0	NOUN
ejpam-2498	46	25	)	)	PUNCT
ejpam-2498	46	26	is	be	AUX
ejpam-2498	46	27	the	the	DET
ejpam-2498	46	28	jacobian	jacobian	ADJ
ejpam-2498	46	29	matrix	matrix	NOUN
ejpam-2498	46	30	for	for	ADP
ejpam-2498	46	31	the	the	DET
ejpam-2498	46	32	given	give	VERB
ejpam-2498	46	33	coordinate	coordinate	NOUN
ejpam-2498	46	34	transformation	transformation	NOUN
ejpam-2498	46	35	,	,	PUNCT
ejpam-2498	46	36	defined	define	VERB
ejpam-2498	46	37	by	by	ADP
ejpam-2498	46	38	j(p0	j(p0	NOUN
ejpam-2498	46	39	)	)	PUNCT
ejpam-2498	47	1	=	=	NOUN
ejpam-2498	47	2			NOUN
ejpam-2498	47	3			ADJ
ejpam-2498	47	4			ADJ
ejpam-2498	47	5			NOUN
ejpam-2498	47	6	∂	∂	NOUN
ejpam-2498	48	1	x1	x1	PRON
ejpam-2498	48	2	∂	∂	NOUN
ejpam-2498	49	1	x1	x1	PROPN
ejpam-2498	49	2	(	(	PUNCT
ejpam-2498	49	3	p0	p0	PROPN
ejpam-2498	49	4	)	)	PUNCT
ejpam-2498	49	5	·	·	PUNCT
ejpam-2498	49	6	·	·	PUNCT
ejpam-2498	49	7	·	·	PUNCT
ejpam-2498	49	8	∂	∂	NUM
ejpam-2498	50	1	x1	x1	PRON
ejpam-2498	50	2	∂	∂	NOUN
ejpam-2498	50	3	xn	xn	PROPN
ejpam-2498	50	4	(	(	PUNCT
ejpam-2498	50	5	p0	p0	PROPN
ejpam-2498	50	6	)	)	PUNCT
ejpam-2498	50	7	...	...	PUNCT
ejpam-2498	50	8	.	.	PUNCT
ejpam-2498	50	9	.	.	PUNCT
ejpam-2498	50	10	.	.	PUNCT
ejpam-2498	51	1	...	...	PUNCT
ejpam-2498	52	1	∂	∂	NUM
ejpam-2498	52	2	xn	xn	SYM
ejpam-2498	52	3	∂	∂	NUM
ejpam-2498	53	1	x1	x1	PROPN
ejpam-2498	53	2	(	(	PUNCT
ejpam-2498	53	3	p0	p0	PROPN
ejpam-2498	53	4	)	)	PUNCT
ejpam-2498	53	5	·	·	PUNCT
ejpam-2498	53	6	·	·	PUNCT
ejpam-2498	53	7	·	·	PUNCT
ejpam-2498	53	8	∂	∂	NUM
ejpam-2498	53	9	xn	xn	PROPN
ejpam-2498	53	10	∂	∂	NUM
ejpam-2498	53	11	xn	xn	PROPN
ejpam-2498	53	12	(	(	PUNCT
ejpam-2498	53	13	p0	p0	NOUN
ejpam-2498	53	14	)	)	PUNCT
ejpam-2498	53	15			PROPN
ejpam-2498	53	16			PROPN
ejpam-2498	53	17			PROPN
ejpam-2498	53	18			PROPN
ejpam-2498	53	19	(	(	PUNCT
ejpam-2498	53	20	4	4	NUM
ejpam-2498	53	21	)	)	PUNCT
ejpam-2498	53	22	and	and	CCONJ
ejpam-2498	53	23	the	the	DET
ejpam-2498	53	24	matrix	matrix	NOUN
ejpam-2498	53	25	j(p0	j(p0	NOUN
ejpam-2498	53	26	)	)	PUNCT
ejpam-2498	53	27	t	t	PROPN
ejpam-2498	53	28	is	be	AUX
ejpam-2498	53	29	the	the	DET
ejpam-2498	53	30	transpose	transpose	NOUN
ejpam-2498	53	31	of	of	ADP
ejpam-2498	53	32	j(p0	j(p0	NOUN
ejpam-2498	53	33	)	)	PUNCT
ejpam-2498	53	34	.	.	PUNCT
ejpam-2498	54	1	for	for	ADP
ejpam-2498	54	2	a	a	DET
ejpam-2498	54	3	critical	critical	ADJ
ejpam-2498	54	4	point	point	NOUN
ejpam-2498	54	5	p0	p0	NOUN
ejpam-2498	54	6	,	,	PUNCT
ejpam-2498	54	7	non	non	ADJ
ejpam-2498	54	8	-	-	NOUN
ejpam-2498	54	9	degeneracy	degeneracy	NOUN
ejpam-2498	54	10	does	do	AUX
ejpam-2498	54	11	not	not	PART
ejpam-2498	54	12	depend	depend	VERB
ejpam-2498	54	13	on	on	ADP
ejpam-2498	54	14	the	the	DET
ejpam-2498	54	15	choice	choice	NOUN
ejpam-2498	54	16	of	of	ADP
ejpam-2498	54	17	charts	chart	NOUN
ejpam-2498	54	18	around	around	ADP
ejpam-2498	54	19	p0	p0	NOUN
ejpam-2498	54	20	.	.	PUNCT
ejpam-2498	55	1	the	the	DET
ejpam-2498	55	2	same	same	ADJ
ejpam-2498	55	3	argument	argument	NOUN
ejpam-2498	55	4	is	be	AUX
ejpam-2498	55	5	also	also	ADV
ejpam-2498	55	6	true	true	ADJ
ejpam-2498	55	7	for	for	ADP
ejpam-2498	55	8	degenerate	degenerate	ADJ
ejpam-2498	55	9	critical	critical	ADJ
ejpam-2498	55	10	points	point	NOUN
ejpam-2498	55	11	.	.	PUNCT
ejpam-2498	56	1	in	in	ADP
ejpam-2498	56	2	fact	fact	NOUN
ejpam-2498	56	3	we	we	PRON
ejpam-2498	56	4	have	have	VERB
ejpam-2498	56	5	h	h	PROPN
ejpam-2498	56	6	f	f	PROPN
ejpam-2498	56	7	(	(	PUNCT
ejpam-2498	56	8	p0	p0	PROPN
ejpam-2498	56	9	)	)	PUNCT
ejpam-2498	56	10	=	=	SYM
ejpam-2498	56	11	j(p0	j(p0	NOUN
ejpam-2498	56	12	)	)	PUNCT
ejpam-2498	56	13	t	t	PROPN
ejpam-2498	56	14	h	h	NOUN
ejpam-2498	56	15	f	f	PROPN
ejpam-2498	56	16	(	(	PUNCT
ejpam-2498	56	17	p0)j(p0	p0)j(p0	NOUN
ejpam-2498	56	18	)	)	PUNCT
ejpam-2498	56	19	by	by	ADP
ejpam-2498	56	20	the	the	DET
ejpam-2498	56	21	previous	previous	ADJ
ejpam-2498	56	22	lemma	lemma	PROPN
ejpam-2498	56	23	,	,	PUNCT
ejpam-2498	56	24	and	and	CCONJ
ejpam-2498	56	25	hence	hence	ADV
ejpam-2498	56	26	deth	deth	PROPN
ejpam-2498	56	27	f	f	PROPN
ejpam-2498	56	28	(	(	PUNCT
ejpam-2498	56	29	p0	p0	PROPN
ejpam-2498	56	30	)	)	PUNCT
ejpam-2498	56	31	=	=	SYM
ejpam-2498	56	32	detj(p0	detj(p0	NOUN
ejpam-2498	56	33	)	)	PUNCT
ejpam-2498	56	34	t	t	PROPN
ejpam-2498	56	35	deth	deth	PROPN
ejpam-2498	56	36	f	f	PROPN
ejpam-2498	56	37	(	(	PUNCT
ejpam-2498	56	38	p0)detj(p0	p0)detj(p0	NOUN
ejpam-2498	56	39	)	)	PUNCT
ejpam-2498	56	40	(	(	PUNCT
ejpam-2498	56	41	5	5	X
ejpam-2498	56	42	)	)	PUNCT
ejpam-2498	56	43	m.	m.	NOUN
ejpam-2498	56	44	solgun	solgun	PROPN
ejpam-2498	56	45	/	/	SYM
ejpam-2498	56	46	eur	eur	PROPN
ejpam-2498	56	47	.	.	PUNCT
ejpam-2498	57	1	j.	j.	PROPN
ejpam-2498	57	2	pure	pure	PROPN
ejpam-2498	57	3	appl	appl	PROPN
ejpam-2498	57	4	.	.	PROPN
ejpam-2498	57	5	math	math	PROPN
ejpam-2498	57	6	,	,	PUNCT
ejpam-2498	57	7	9	9	NUM
ejpam-2498	57	8	(	(	PUNCT
ejpam-2498	57	9	2016	2016	NUM
ejpam-2498	57	10	)	)	PUNCT
ejpam-2498	57	11	,	,	PUNCT
ejpam-2498	57	12	314	314	NUM
ejpam-2498	57	13	-	-	SYM
ejpam-2498	57	14	321	321	NUM
ejpam-2498	57	15	316	316	NUM
ejpam-2498	57	16	by	by	ADP
ejpam-2498	57	17	using	use	VERB
ejpam-2498	57	18	determinant	determinant	ADJ
ejpam-2498	57	19	function	function	NOUN
ejpam-2498	57	20	on	on	ADP
ejpam-2498	57	21	both	both	DET
ejpam-2498	57	22	sides	side	NOUN
ejpam-2498	57	23	.	.	PUNCT
ejpam-2498	58	1	on	on	ADP
ejpam-2498	58	2	the	the	DET
ejpam-2498	58	3	other	other	ADJ
ejpam-2498	58	4	hand	hand	NOUN
ejpam-2498	58	5	,	,	PUNCT
ejpam-2498	58	6	the	the	DET
ejpam-2498	58	7	determinant	determinant	NOUN
ejpam-2498	58	8	of	of	ADP
ejpam-2498	58	9	the	the	DET
ejpam-2498	58	10	jacobian	jacobian	ADJ
ejpam-2498	58	11	matrix	matrix	NOUN
ejpam-2498	58	12	is	be	AUX
ejpam-2498	58	13	non	non	ADJ
ejpam-2498	58	14	-	-	ADJ
ejpam-2498	58	15	zero	zero	NUM
ejpam-2498	58	16	.	.	PUNCT
ejpam-2498	59	1	so	so	ADV
ejpam-2498	59	2	the	the	DET
ejpam-2498	59	3	statement	statement	NOUN
ejpam-2498	59	4	"	"	PUNCT
ejpam-2498	59	5	deth	deth	PROPN
ejpam-2498	59	6	f	f	X
ejpam-2498	59	7	(	(	PUNCT
ejpam-2498	59	8	p0	p0	PROPN
ejpam-2498	59	9	)	)	PUNCT
ejpam-2498	59	10	6=	6=	ADP
ejpam-2498	59	11	0	0	NUM
ejpam-2498	59	12	"	"	PUNCT
ejpam-2498	59	13	and	and	CCONJ
ejpam-2498	59	14	"	"	PUNCT
ejpam-2498	59	15	deth	deth	PROPN
ejpam-2498	59	16	f	f	X
ejpam-2498	59	17	(	(	PUNCT
ejpam-2498	59	18	p0	p0	PROPN
ejpam-2498	59	19	)	)	PUNCT
ejpam-2498	59	20	6=	6=	ADP
ejpam-2498	59	21	0	0	NUM
ejpam-2498	59	22	"	"	PUNCT
ejpam-2498	59	23	are	be	AUX
ejpam-2498	59	24	equivalent	equivalent	ADJ
ejpam-2498	59	25	.	.	PUNCT
ejpam-2498	60	1	in	in	ADP
ejpam-2498	60	2	other	other	ADJ
ejpam-2498	60	3	words	word	NOUN
ejpam-2498	60	4	,	,	PUNCT
ejpam-2498	60	5	deth	deth	PROPN
ejpam-2498	60	6	f	f	X
ejpam-2498	60	7	(	(	PUNCT
ejpam-2498	60	8	p0	p0	PROPN
ejpam-2498	60	9	)	)	PUNCT
ejpam-2498	60	10	6=	6=	NUM
ejpam-2498	60	11	0⇔	0⇔	PROPN
ejpam-2498	60	12	deth	deth	PROPN
ejpam-2498	60	13	f	f	PROPN
ejpam-2498	60	14	(	(	PUNCT
ejpam-2498	60	15	p0	p0	PROPN
ejpam-2498	60	16	)	)	PUNCT
ejpam-2498	60	17	6=	6=	ADP
ejpam-2498	60	18	0	0	X
ejpam-2498	60	19	.	.	PUNCT
ejpam-2498	61	1	now	now	ADV
ejpam-2498	61	2	a	a	DET
ejpam-2498	61	3	function	function	NOUN
ejpam-2498	61	4	f	f	NOUN
ejpam-2498	62	1	:	:	PUNCT
ejpam-2498	62	2	m	m	AUX
ejpam-2498	62	3	→	→	SYM
ejpam-2498	62	4	r	r	NOUN
ejpam-2498	62	5	is	be	AUX
ejpam-2498	62	6	called	call	VERB
ejpam-2498	62	7	a	a	DET
ejpam-2498	62	8	morse	morse	ADJ
ejpam-2498	62	9	function	function	NOUN
ejpam-2498	62	10	if	if	SCONJ
ejpam-2498	62	11	any	any	DET
ejpam-2498	62	12	critical	critical	ADJ
ejpam-2498	62	13	point	point	NOUN
ejpam-2498	62	14	of	of	ADP
ejpam-2498	62	15	f	f	PROPN
ejpam-2498	62	16	is	be	AUX
ejpam-2498	62	17	non	non	ADJ
ejpam-2498	62	18	-	-	ADJ
ejpam-2498	62	19	degenerate	degenerate	ADJ
ejpam-2498	62	20	.	.	PUNCT
ejpam-2498	63	1	from	from	ADP
ejpam-2498	63	2	now	now	ADV
ejpam-2498	63	3	on	on	ADV
ejpam-2498	63	4	,	,	PUNCT
ejpam-2498	63	5	we	we	PRON
ejpam-2498	63	6	only	only	ADV
ejpam-2498	63	7	consider	consider	VERB
ejpam-2498	63	8	a	a	DET
ejpam-2498	63	9	morse	morse	ADJ
ejpam-2498	63	10	function	function	NOUN
ejpam-2498	63	11	f	f	PROPN
ejpam-2498	63	12	.	.	PUNCT
ejpam-2498	64	1	now	now	ADV
ejpam-2498	64	2	,	,	PUNCT
ejpam-2498	64	3	we	we	PRON
ejpam-2498	64	4	introduce	introduce	VERB
ejpam-2498	64	5	morse	morse	PROPN
ejpam-2498	64	6	lemma	lemma	PROPN
ejpam-2498	64	7	on	on	ADP
ejpam-2498	64	8	manifolds	manifold	NOUN
ejpam-2498	64	9	.	.	PUNCT
ejpam-2498	65	1	theorem	theorem	NOUN
ejpam-2498	65	2	1	1	NUM
ejpam-2498	65	3	(	(	PUNCT
ejpam-2498	65	4	the	the	DET
ejpam-2498	65	5	morse	morse	NOUN
ejpam-2498	65	6	lemma	lemma	PROPN
ejpam-2498	65	7	)	)	PUNCT
ejpam-2498	65	8	.	.	PUNCT
ejpam-2498	66	1	let	let	VERB
ejpam-2498	66	2	m	m	PRON
ejpam-2498	66	3	be	be	AUX
ejpam-2498	66	4	an	an	DET
ejpam-2498	66	5	n	n	ADV
ejpam-2498	66	6	-	-	PUNCT
ejpam-2498	66	7	dimensional	dimensional	ADJ
ejpam-2498	66	8	smooth	smooth	ADJ
ejpam-2498	66	9	manifold	manifold	NOUN
ejpam-2498	66	10	and	and	CCONJ
ejpam-2498	66	11	p0	p0	NOUN
ejpam-2498	66	12	be	be	AUX
ejpam-2498	66	13	a	a	DET
ejpam-2498	66	14	nondegenerate	nondegenerate	ADJ
ejpam-2498	66	15	critical	critical	ADJ
ejpam-2498	66	16	point	point	NOUN
ejpam-2498	66	17	of	of	ADP
ejpam-2498	66	18	a	a	DET
ejpam-2498	66	19	morse	morse	ADJ
ejpam-2498	66	20	function	function	NOUN
ejpam-2498	66	21	f	f	NOUN
ejpam-2498	66	22	:	:	PUNCT
ejpam-2498	66	23	m	m	PROPN
ejpam-2498	66	24	→	→	SYM
ejpam-2498	66	25	r.	r.	PROPN
ejpam-2498	66	26	then	then	ADV
ejpam-2498	66	27	,	,	PUNCT
ejpam-2498	66	28	there	there	PRON
ejpam-2498	66	29	exists	exist	VERB
ejpam-2498	66	30	a	a	DET
ejpam-2498	66	31	local	local	ADJ
ejpam-2498	66	32	coordinate	coordinate	NOUN
ejpam-2498	66	33	system	system	NOUN
ejpam-2498	66	34	(	(	PUNCT
ejpam-2498	66	35	x1	x1	PROPN
ejpam-2498	66	36	,	,	PUNCT
ejpam-2498	66	37	x2	x2	PROPN
ejpam-2498	66	38	,	,	PUNCT
ejpam-2498	66	39	.	.	PUNCT
ejpam-2498	66	40	.	.	PUNCT
ejpam-2498	67	1	.	.	PUNCT
ejpam-2498	68	1	,	,	PUNCT
ejpam-2498	68	2	xn	xn	X
ejpam-2498	68	3	)	)	PUNCT
ejpam-2498	68	4	around	around	ADP
ejpam-2498	68	5	p0	p0	NOUN
ejpam-2498	68	6	such	such	ADJ
ejpam-2498	68	7	that	that	SCONJ
ejpam-2498	68	8	the	the	DET
ejpam-2498	68	9	coordinate	coordinate	NOUN
ejpam-2498	68	10	representation	representation	NOUN
ejpam-2498	68	11	of	of	ADP
ejpam-2498	68	12	f	f	PROPN
ejpam-2498	68	13	has	have	VERB
ejpam-2498	68	14	the	the	DET
ejpam-2498	68	15	following	follow	VERB
ejpam-2498	68	16	form	form	NOUN
ejpam-2498	68	17	:	:	PUNCT
ejpam-2498	68	18	f	f	X
ejpam-2498	68	19	=	=	PUNCT
ejpam-2498	68	20	−x	−x	NOUN
ejpam-2498	68	21	2	2	NUM
ejpam-2498	68	22	1	1	NUM
ejpam-2498	68	23	−	−	NOUN
ejpam-2498	68	24	x	x	SYM
ejpam-2498	68	25	2	2	NUM
ejpam-2498	68	26	2	2	NUM
ejpam-2498	68	27	.	.	PUNCT
ejpam-2498	68	28	.	.	PUNCT
ejpam-2498	69	1	.−	.−	PUNCT
ejpam-2498	70	1	x	x	SYM
ejpam-2498	70	2	2	2	NUM
ejpam-2498	70	3	λ	λ	NOUN
ejpam-2498	70	4	+	+	NOUN
ejpam-2498	70	5	x	x	SYM
ejpam-2498	70	6	2	2	NUM
ejpam-2498	70	7	λ+1	λ+1	X
ejpam-2498	70	8	+	+	CCONJ
ejpam-2498	70	9	.	.	PUNCT
ejpam-2498	70	10	.	.	PUNCT
ejpam-2498	71	1	.+	.+	NOUN
ejpam-2498	71	2	x	x	PUNCT
ejpam-2498	71	3	2	2	NUM
ejpam-2498	71	4	n	n	NOUN
ejpam-2498	71	5	+	+	X
ejpam-2498	71	6	c	c	X
ejpam-2498	71	7	(	(	PUNCT
ejpam-2498	71	8	6	6	NUM
ejpam-2498	71	9	)	)	PUNCT
ejpam-2498	71	10	where	where	SCONJ
ejpam-2498	71	11	c	c	NOUN
ejpam-2498	71	12	=	=	SYM
ejpam-2498	71	13	f	f	PROPN
ejpam-2498	71	14	(	(	PUNCT
ejpam-2498	71	15	p0	p0	PROPN
ejpam-2498	71	16	)	)	PUNCT
ejpam-2498	71	17	and	and	CCONJ
ejpam-2498	71	18	p0	p0	NOUN
ejpam-2498	71	19	corresponds	correspond	VERB
ejpam-2498	71	20	to	to	ADP
ejpam-2498	71	21	the	the	DET
ejpam-2498	71	22	origin	origin	NOUN
ejpam-2498	71	23	(	(	PUNCT
ejpam-2498	71	24	0,0	0,0	NOUN
ejpam-2498	71	25	,	,	PUNCT
ejpam-2498	71	26	.	.	PUNCT
ejpam-2498	71	27	.	.	PUNCT
ejpam-2498	72	1	.	.	PUNCT
ejpam-2498	73	1	,	,	PUNCT
ejpam-2498	73	2	0	0	NUM
ejpam-2498	73	3	)	)	PUNCT
ejpam-2498	73	4	.	.	PUNCT
ejpam-2498	74	1	one	one	PRON
ejpam-2498	74	2	may	may	AUX
ejpam-2498	74	3	refer	refer	VERB
ejpam-2498	74	4	to	to	ADP
ejpam-2498	74	5	[	[	X
ejpam-2498	74	6	5	5	NUM
ejpam-2498	74	7	]	]	PUNCT
ejpam-2498	74	8	for	for	ADP
ejpam-2498	74	9	the	the	DET
ejpam-2498	74	10	proof	proof	NOUN
ejpam-2498	74	11	.	.	PUNCT
ejpam-2498	75	1	the	the	DET
ejpam-2498	75	2	number	number	NOUN
ejpam-2498	75	3	λ	λ	PROPN
ejpam-2498	75	4	of	of	ADP
ejpam-2498	75	5	minus	minus	NOUN
ejpam-2498	75	6	signs	sign	NOUN
ejpam-2498	75	7	in	in	ADP
ejpam-2498	75	8	the	the	DET
ejpam-2498	75	9	equation	equation	NOUN
ejpam-2498	75	10	(	(	PUNCT
ejpam-2498	75	11	6	6	NUM
ejpam-2498	75	12	)	)	PUNCT
ejpam-2498	75	13	is	be	AUX
ejpam-2498	75	14	the	the	DET
ejpam-2498	75	15	number	number	NOUN
ejpam-2498	75	16	of	of	ADP
ejpam-2498	75	17	negative	negative	ADJ
ejpam-2498	75	18	diagonal	diagonal	ADJ
ejpam-2498	75	19	entries	entry	NOUN
ejpam-2498	75	20	of	of	ADP
ejpam-2498	75	21	the	the	DET
ejpam-2498	75	22	matrix	matrix	NOUN
ejpam-2498	75	23	h	h	NOUN
ejpam-2498	76	1	f	f	PROPN
ejpam-2498	76	2	(	(	PUNCT
ejpam-2498	76	3	p0	p0	NOUN
ejpam-2498	76	4	)	)	PUNCT
ejpam-2498	76	5	after	after	ADP
ejpam-2498	76	6	diagonalization	diagonalization	NOUN
ejpam-2498	76	7	.	.	PUNCT
ejpam-2498	77	1	by	by	ADP
ejpam-2498	77	2	sylvester	sylvester	PROPN
ejpam-2498	77	3	’s	’s	PART
ejpam-2498	77	4	law	law	NOUN
ejpam-2498	77	5	,	,	PUNCT
ejpam-2498	77	6	λ	λ	PROPN
ejpam-2498	77	7	does	do	AUX
ejpam-2498	77	8	not	not	PART
ejpam-2498	77	9	depend	depend	VERB
ejpam-2498	77	10	on	on	ADP
ejpam-2498	77	11	how	how	SCONJ
ejpam-2498	77	12	h	h	NOUN
ejpam-2498	77	13	f	f	X
ejpam-2498	77	14	(	(	PUNCT
ejpam-2498	77	15	p0	p0	NOUN
ejpam-2498	77	16	)	)	PUNCT
ejpam-2498	77	17	is	be	AUX
ejpam-2498	77	18	diagonalized	diagonalize	VERB
ejpam-2498	77	19	.	.	PUNCT
ejpam-2498	78	1	so	so	ADV
ejpam-2498	78	2	,	,	PUNCT
ejpam-2498	78	3	λ	λ	PROPN
ejpam-2498	78	4	is	be	AUX
ejpam-2498	78	5	determined	determine	VERB
ejpam-2498	78	6	by	by	ADP
ejpam-2498	78	7	f	f	PROPN
ejpam-2498	78	8	and	and	CCONJ
ejpam-2498	78	9	p0	p0	NOUN
ejpam-2498	78	10	.	.	PUNCT
ejpam-2498	79	1	the	the	DET
ejpam-2498	79	2	number	number	NOUN
ejpam-2498	79	3	λ	λ	PROPN
ejpam-2498	79	4	is	be	AUX
ejpam-2498	79	5	called	call	VERB
ejpam-2498	79	6	"	"	PUNCT
ejpam-2498	79	7	the	the	DET
ejpam-2498	79	8	index	index	NOUN
ejpam-2498	79	9	of	of	ADP
ejpam-2498	79	10	the	the	DET
ejpam-2498	79	11	non	non	ADJ
ejpam-2498	79	12	-	-	ADJ
ejpam-2498	79	13	degenerate	degenerate	ADJ
ejpam-2498	79	14	critical	critical	ADJ
ejpam-2498	79	15	point	point	NOUN
ejpam-2498	79	16	p0	p0	NOUN
ejpam-2498	79	17	"	"	PUNCT
ejpam-2498	79	18	.	.	PUNCT
ejpam-2498	80	1	obviously	obviously	ADV
ejpam-2498	80	2	,	,	PUNCT
ejpam-2498	80	3	λ	λ	PROPN
ejpam-2498	80	4	is	be	AUX
ejpam-2498	80	5	an	an	DET
ejpam-2498	80	6	integer	integer	NOUN
ejpam-2498	80	7	between	between	ADP
ejpam-2498	80	8	0	0	NUM
ejpam-2498	80	9	and	and	CCONJ
ejpam-2498	80	10	n.	n.	NOUN
ejpam-2498	80	11	note	note	VERB
ejpam-2498	80	12	that	that	SCONJ
ejpam-2498	80	13	,	,	PUNCT
ejpam-2498	80	14	(	(	PUNCT
ejpam-2498	80	15	i	i	NOUN
ejpam-2498	80	16	)	)	PUNCT
ejpam-2498	80	17	a	a	DET
ejpam-2498	80	18	non	non	ADJ
ejpam-2498	80	19	-	-	ADJ
ejpam-2498	80	20	degenerate	degenerate	ADJ
ejpam-2498	80	21	critical	critical	ADJ
ejpam-2498	80	22	point	point	NOUN
ejpam-2498	80	23	is	be	AUX
ejpam-2498	80	24	isolated	isolate	VERB
ejpam-2498	80	25	.	.	PUNCT
ejpam-2498	81	1	(	(	PUNCT
ejpam-2498	81	2	ii	ii	X
ejpam-2498	81	3	)	)	PUNCT
ejpam-2498	81	4	a	a	DET
ejpam-2498	81	5	morse	morse	ADJ
ejpam-2498	81	6	function	function	NOUN
ejpam-2498	81	7	on	on	ADP
ejpam-2498	81	8	a	a	DET
ejpam-2498	81	9	compact	compact	ADJ
ejpam-2498	81	10	manifold	manifold	NOUN
ejpam-2498	81	11	has	have	VERB
ejpam-2498	81	12	only	only	ADV
ejpam-2498	81	13	finitely	finitely	ADV
ejpam-2498	81	14	many	many	ADJ
ejpam-2498	81	15	critical	critical	ADJ
ejpam-2498	81	16	points	point	NOUN
ejpam-2498	82	1	[	[	X
ejpam-2498	82	2	5	5	NUM
ejpam-2498	82	3	]	]	PUNCT
ejpam-2498	82	4	.	.	PUNCT
ejpam-2498	83	1	3	3	X
ejpam-2498	83	2	.	.	X
ejpam-2498	83	3	a	a	DET
ejpam-2498	83	4	morse	morse	ADJ
ejpam-2498	83	5	function	function	NOUN
ejpam-2498	83	6	on	on	ADP
ejpam-2498	83	7	so(n	so(n	NOUN
ejpam-2498	83	8	)	)	PUNCT
ejpam-2498	83	9	in	in	ADP
ejpam-2498	83	10	this	this	DET
ejpam-2498	83	11	section	section	NOUN
ejpam-2498	83	12	,	,	PUNCT
ejpam-2498	83	13	we	we	PRON
ejpam-2498	83	14	will	will	AUX
ejpam-2498	83	15	define	define	VERB
ejpam-2498	83	16	a	a	DET
ejpam-2498	83	17	morse	morse	ADJ
ejpam-2498	83	18	function	function	NOUN
ejpam-2498	83	19	on	on	ADP
ejpam-2498	83	20	so(n	so(n	PROPN
ejpam-2498	83	21	)	)	PUNCT
ejpam-2498	83	22	.	.	PUNCT
ejpam-2498	84	1	the	the	DET
ejpam-2498	84	2	set	set	NOUN
ejpam-2498	84	3	of	of	ADP
ejpam-2498	84	4	all	all	DET
ejpam-2498	84	5	n×	n×	PRON
ejpam-2498	84	6	n	n	PRON
ejpam-2498	84	7	orthogonal	orthogonal	ADJ
ejpam-2498	84	8	matrices	matrix	NOUN
ejpam-2498	84	9	,	,	PUNCT
ejpam-2498	84	10	o(n	o(n	NOUN
ejpam-2498	84	11	)	)	PUNCT
ejpam-2498	84	12	=	=	PRON
ejpam-2498	84	13	{	{	PUNCT
ejpam-2498	84	14	a=	a=	VERB
ejpam-2498	84	15	(	(	PUNCT
ejpam-2498	84	16	ai	ai	VERB
ejpam-2498	84	17	j	j	PROPN
ejpam-2498	84	18	)	)	PUNCT
ejpam-2498	84	19	∈	∈	PROPN
ejpam-2498	84	20	mn(r	mn(r	NOUN
ejpam-2498	84	21	)	)	PUNCT
ejpam-2498	84	22	:	:	PUNCT
ejpam-2498	84	23	aat	aat	X
ejpam-2498	84	24	=	=	PUNCT
ejpam-2498	84	25	in	in	SCONJ
ejpam-2498	84	26	}	}	PUNCT
ejpam-2498	84	27	is	be	AUX
ejpam-2498	84	28	a	a	DET
ejpam-2498	84	29	group	group	NOUN
ejpam-2498	84	30	with	with	ADP
ejpam-2498	84	31	matrix	matrix	NOUN
ejpam-2498	84	32	multiplication	multiplication	NOUN
ejpam-2498	84	33	.	.	PUNCT
ejpam-2498	85	1	from	from	ADP
ejpam-2498	85	2	the	the	DET
ejpam-2498	85	3	definition	definition	NOUN
ejpam-2498	85	4	of	of	ADP
ejpam-2498	85	5	o(n	o(n	PROPN
ejpam-2498	85	6	)	)	PUNCT
ejpam-2498	85	7	,	,	PUNCT
ejpam-2498	85	8	deta=	deta=	NUM
ejpam-2498	85	9	±1	±1	VERB
ejpam-2498	85	10	,	,	PUNCT
ejpam-2498	85	11	for	for	ADP
ejpam-2498	85	12	any	any	DET
ejpam-2498	85	13	a∈	a∈	PROPN
ejpam-2498	85	14	o(n	o(n	PROPN
ejpam-2498	85	15	)	)	PUNCT
ejpam-2498	85	16	.	.	PUNCT
ejpam-2498	86	1	an	an	DET
ejpam-2498	86	2	orthogonal	orthogonal	ADJ
ejpam-2498	86	3	matrix	matrix	NOUN
ejpam-2498	86	4	with	with	ADP
ejpam-2498	86	5	determinant	determinant	ADJ
ejpam-2498	86	6	1	1	NUM
ejpam-2498	86	7	is	be	AUX
ejpam-2498	86	8	called	call	VERB
ejpam-2498	86	9	rotation	rotation	NOUN
ejpam-2498	86	10	matrix	matrix	NOUN
ejpam-2498	86	11	and	and	CCONJ
ejpam-2498	86	12	the	the	DET
ejpam-2498	86	13	set	set	NOUN
ejpam-2498	86	14	of	of	ADP
ejpam-2498	86	15	this	this	DET
ejpam-2498	86	16	kind	kind	NOUN
ejpam-2498	86	17	of	of	ADP
ejpam-2498	86	18	matrices	matrix	NOUN
ejpam-2498	86	19	is	be	AUX
ejpam-2498	86	20	also	also	ADV
ejpam-2498	86	21	a	a	DET
ejpam-2498	86	22	group	group	NOUN
ejpam-2498	86	23	,	,	PUNCT
ejpam-2498	86	24	called	call	VERB
ejpam-2498	86	25	special	special	ADJ
ejpam-2498	86	26	orthogonal	orthogonal	ADJ
ejpam-2498	86	27	group	group	NOUN
ejpam-2498	86	28	and	and	CCONJ
ejpam-2498	86	29	denoted	denote	VERB
ejpam-2498	86	30	by	by	ADP
ejpam-2498	86	31	so(n	so(n	PROPN
ejpam-2498	86	32	)	)	PUNCT
ejpam-2498	86	33	.	.	PUNCT
ejpam-2498	87	1	on	on	ADP
ejpam-2498	87	2	the	the	DET
ejpam-2498	87	3	other	other	ADJ
ejpam-2498	87	4	hand	hand	NOUN
ejpam-2498	87	5	,	,	PUNCT
ejpam-2498	87	6	let	let	VERB
ejpam-2498	87	7	sn(r	sn(r	PRON
ejpam-2498	87	8	)	)	PUNCT
ejpam-2498	87	9	denote	denote	VERB
ejpam-2498	87	10	the	the	DET
ejpam-2498	87	11	set	set	NOUN
ejpam-2498	87	12	of	of	ADP
ejpam-2498	87	13	symmetric	symmetric	ADJ
ejpam-2498	87	14	n	n	NUM
ejpam-2498	87	15	×	×	NOUN
ejpam-2498	87	16	n	n	PRON
ejpam-2498	87	17	matrices	matrix	NOUN
ejpam-2498	87	18	.	.	PUNCT
ejpam-2498	88	1	since	since	SCONJ
ejpam-2498	88	2	each	each	DET
ejpam-2498	88	3	symmetric	symmetric	ADJ
ejpam-2498	88	4	matrix	matrix	NOUN
ejpam-2498	88	5	is	be	AUX
ejpam-2498	88	6	uniquely	uniquely	ADV
ejpam-2498	88	7	determined	determine	VERB
ejpam-2498	88	8	by	by	ADP
ejpam-2498	88	9	its	its	PRON
ejpam-2498	88	10	entries	entry	NOUN
ejpam-2498	88	11	on	on	ADP
ejpam-2498	88	12	and	and	CCONJ
ejpam-2498	88	13	above	above	ADP
ejpam-2498	88	14	the	the	DET
ejpam-2498	88	15	main	main	ADJ
ejpam-2498	88	16	diagonal	diagonal	NOUN
ejpam-2498	88	17	,	,	PUNCT
ejpam-2498	88	18	that	that	PRON
ejpam-2498	88	19	is	be	AUX
ejpam-2498	88	20	a	a	DET
ejpam-2498	88	21	linear	linear	ADJ
ejpam-2498	88	22	subspace	subspace	NOUN
ejpam-2498	88	23	of	of	ADP
ejpam-2498	88	24	mn(r	mn(r	NOUN
ejpam-2498	88	25	)	)	PUNCT
ejpam-2498	88	26	of	of	ADP
ejpam-2498	88	27	dimension	dimension	NOUN
ejpam-2498	88	28	n(n+	n(n+	PROPN
ejpam-2498	89	1	1)/2	1)/2	NUM
ejpam-2498	89	2	.	.	PUNCT
ejpam-2498	90	1	now	now	ADV
ejpam-2498	90	2	we	we	PRON
ejpam-2498	90	3	define	define	VERB
ejpam-2498	90	4	a	a	DET
ejpam-2498	90	5	function	function	NOUN
ejpam-2498	90	6	ϕ	ϕ	NOUN
ejpam-2498	90	7	:	:	PUNCT
ejpam-2498	90	8	gln(r	gln(r	NOUN
ejpam-2498	90	9	)	)	PUNCT
ejpam-2498	90	10	−→	−→	NOUN
ejpam-2498	90	11	sn(r	sn(r	NUM
ejpam-2498	90	12	)	)	PUNCT
ejpam-2498	90	13	by	by	ADP
ejpam-2498	90	14	ϕ(a	ϕ(a	NOUN
ejpam-2498	90	15	)	)	PUNCT
ejpam-2498	90	16	:	:	PUNCT
ejpam-2498	91	1	=	=	PUNCT
ejpam-2498	91	2	ata	ata	PROPN
ejpam-2498	91	3	.	.	PUNCT
ejpam-2498	92	1	then	then	ADV
ejpam-2498	92	2	,	,	PUNCT
ejpam-2498	92	3	the	the	DET
ejpam-2498	92	4	identity	identity	NOUN
ejpam-2498	92	5	matrix	matrix	NOUN
ejpam-2498	92	6	in	in	ADP
ejpam-2498	92	7	is	be	AUX
ejpam-2498	92	8	a	a	DET
ejpam-2498	92	9	regular	regular	ADJ
ejpam-2498	92	10	value	value	NOUN
ejpam-2498	92	11	of	of	ADP
ejpam-2498	92	12	ϕ	ϕ	NOUN
ejpam-2498	93	1	[	[	X
ejpam-2498	93	2	3	3	NUM
ejpam-2498	93	3	]	]	PUNCT
ejpam-2498	93	4	.	.	PUNCT
ejpam-2498	94	1	m.	m.	NOUN
ejpam-2498	94	2	solgun	solgun	PROPN
ejpam-2498	94	3	/	/	SYM
ejpam-2498	94	4	eur	eur	PROPN
ejpam-2498	94	5	.	.	PUNCT
ejpam-2498	95	1	j.	j.	PROPN
ejpam-2498	95	2	pure	pure	PROPN
ejpam-2498	95	3	appl	appl	PROPN
ejpam-2498	95	4	.	.	PROPN
ejpam-2498	95	5	math	math	PROPN
ejpam-2498	95	6	,	,	PUNCT
ejpam-2498	95	7	9	9	NUM
ejpam-2498	95	8	(	(	PUNCT
ejpam-2498	95	9	2016	2016	NUM
ejpam-2498	95	10	)	)	PUNCT
ejpam-2498	95	11	,	,	PUNCT
ejpam-2498	95	12	314	314	NUM
ejpam-2498	95	13	-	-	SYM
ejpam-2498	95	14	321	321	NUM
ejpam-2498	95	15	317	317	NUM
ejpam-2498	95	16	let	let	VERB
ejpam-2498	95	17	c	c	PROPN
ejpam-2498	95	18	∈	∈	PROPN
ejpam-2498	95	19	sn(r	sn(r	PRON
ejpam-2498	95	20	)	)	PUNCT
ejpam-2498	95	21	with	with	ADP
ejpam-2498	95	22	entries	entry	NOUN
ejpam-2498	95	23	ci	ci	PROPN
ejpam-2498	95	24	,	,	PUNCT
ejpam-2498	95	25	with	with	ADP
ejpam-2498	95	26	0≤	0≤	ADJ
ejpam-2498	95	27	c1	c1	NOUN
ejpam-2498	95	28	<	<	X
ejpam-2498	95	29	c2	c2	PROPN
ejpam-2498	95	30	<	<	X
ejpam-2498	95	31	.	.	PUNCT
ejpam-2498	95	32	.	.	PUNCT
ejpam-2498	95	33	.	.	PUNCT
ejpam-2498	96	1	<	<	X
ejpam-2498	96	2	cn	cn	PROPN
ejpam-2498	96	3	fixed	fix	VERB
ejpam-2498	96	4	real	real	ADJ
ejpam-2498	96	5	numbers	number	NOUN
ejpam-2498	96	6	and	and	CCONJ
ejpam-2498	96	7	fc	fc	INTJ
ejpam-2498	96	8	:	:	PUNCT
ejpam-2498	96	9	so(n)→	so(n)→	VERB
ejpam-2498	96	10	r	r	NOUN
ejpam-2498	96	11	be	be	AUX
ejpam-2498	96	12	given	give	VERB
ejpam-2498	96	13	by	by	ADP
ejpam-2498	96	14	,	,	PUNCT
ejpam-2498	96	15	fc(a	fc(a	X
ejpam-2498	96	16	)	)	PUNCT
ejpam-2498	96	17	:	:	PUNCT
ejpam-2498	97	1	=	=	X
ejpam-2498	97	2	<	<	X
ejpam-2498	97	3	c	c	X
ejpam-2498	97	4	,	,	PUNCT
ejpam-2498	97	5	a>=	a>=	X
ejpam-2498	97	6	c1	c1	PROPN
ejpam-2498	97	7	x11	x11	PROPN
ejpam-2498	98	1	+	+	CCONJ
ejpam-2498	98	2	c2	c2	PROPN
ejpam-2498	98	3	x22	x22	PROPN
ejpam-2498	99	1	+	+	CCONJ
ejpam-2498	99	2	.	.	PUNCT
ejpam-2498	99	3	.	.	PUNCT
ejpam-2498	100	1	.+	.+	NOUN
ejpam-2498	100	2	cn	cn	PROPN
ejpam-2498	100	3	xnn	xnn	PROPN
ejpam-2498	100	4	,	,	PUNCT
ejpam-2498	100	5	(	(	PUNCT
ejpam-2498	100	6	7	7	X
ejpam-2498	100	7	)	)	PUNCT
ejpam-2498	100	8	where	where	SCONJ
ejpam-2498	100	9	a=	a=	PROPN
ejpam-2498	100	10	(	(	PUNCT
ejpam-2498	100	11	x	x	SYM
ejpam-2498	100	12	i	i	PROPN
ejpam-2498	100	13	j	j	PROPN
ejpam-2498	100	14	)	)	PUNCT
ejpam-2498	100	15	∈	∈	PROPN
ejpam-2498	100	16	so(n	so(n	NOUN
ejpam-2498	100	17	)	)	PUNCT
ejpam-2498	100	18	.	.	PUNCT
ejpam-2498	101	1	obviously	obviously	ADV
ejpam-2498	101	2	,	,	PUNCT
ejpam-2498	101	3	fc	fc	PROPN
ejpam-2498	101	4	is	be	AUX
ejpam-2498	101	5	a	a	DET
ejpam-2498	101	6	smooth	smooth	ADJ
ejpam-2498	101	7	function	function	NOUN
ejpam-2498	101	8	.	.	PUNCT
ejpam-2498	102	1	now	now	ADV
ejpam-2498	102	2	,	,	PUNCT
ejpam-2498	102	3	we	we	PRON
ejpam-2498	102	4	will	will	AUX
ejpam-2498	102	5	determine	determine	VERB
ejpam-2498	102	6	its	its	PRON
ejpam-2498	102	7	critical	critical	ADJ
ejpam-2498	102	8	points	point	NOUN
ejpam-2498	102	9	.	.	PUNCT
ejpam-2498	103	1	lemma	lemma	PROPN
ejpam-2498	103	2	2	2	NUM
ejpam-2498	103	3	.	.	PUNCT
ejpam-2498	104	1	the	the	DET
ejpam-2498	104	2	critical	critical	ADJ
ejpam-2498	104	3	points	point	NOUN
ejpam-2498	104	4	of	of	ADP
ejpam-2498	104	5	the	the	DET
ejpam-2498	104	6	function	function	NOUN
ejpam-2498	104	7	fc	fc	PROPN
ejpam-2498	104	8	defined	define	VERB
ejpam-2498	104	9	above	above	ADP
ejpam-2498	104	10	are	be	AUX
ejpam-2498	104	11	:	:	PUNCT
ejpam-2498	104	12			NOUN
ejpam-2498	104	13			ADJ
ejpam-2498	104	14			ADJ
ejpam-2498	104	15			ADJ
ejpam-2498	104	16			NUM
ejpam-2498	104	17	±1	±1	VERB
ejpam-2498	104	18	0	0	NUM
ejpam-2498	104	19	·	·	PUNCT
ejpam-2498	104	20	·	·	PUNCT
ejpam-2498	104	21	·	·	PUNCT
ejpam-2498	104	22	0	0	SYM
ejpam-2498	104	23	0	0	NUM
ejpam-2498	104	24	±1	±1	VERB
ejpam-2498	104	25	.	.	PUNCT
ejpam-2498	104	26	.	.	PUNCT
ejpam-2498	104	27	.	.	PUNCT
ejpam-2498	105	1	...	...	PUNCT
ejpam-2498	105	2	...	...	PUNCT
ejpam-2498	105	3	.	.	PUNCT
ejpam-2498	105	4	.	.	PUNCT
ejpam-2498	105	5	.	.	PUNCT
ejpam-2498	106	1	.	.	PUNCT
ejpam-2498	106	2	.	.	PUNCT
ejpam-2498	107	1	.	.	PUNCT
ejpam-2498	108	1	0	0	NUM
ejpam-2498	108	2	0	0	NUM
ejpam-2498	108	3	·	·	PUNCT
ejpam-2498	108	4	·	·	PUNCT
ejpam-2498	108	5	·	·	PUNCT
ejpam-2498	108	6	0	0	NUM
ejpam-2498	108	7	±1	±1	VERB
ejpam-2498	108	8			PROPN
ejpam-2498	108	9			PROPN
ejpam-2498	108	10			PROPN
ejpam-2498	108	11			PROPN
ejpam-2498	108	12			PROPN
ejpam-2498	108	13	(	(	PUNCT
ejpam-2498	108	14	8)	8)	NUM
ejpam-2498	108	15	proof	proof	NOUN
ejpam-2498	108	16	.	.	PUNCT
ejpam-2498	109	1	let	let	VERB
ejpam-2498	109	2	a	a	DET
ejpam-2498	109	3	be	be	AUX
ejpam-2498	109	4	a	a	DET
ejpam-2498	109	5	critical	critical	ADJ
ejpam-2498	109	6	point	point	NOUN
ejpam-2498	109	7	of	of	ADP
ejpam-2498	109	8	fc	fc	PROPN
ejpam-2498	109	9	.	.	PUNCT
ejpam-2498	110	1	then	then	ADV
ejpam-2498	110	2	the	the	DET
ejpam-2498	110	3	derivative	derivative	NOUN
ejpam-2498	110	4	of	of	ADP
ejpam-2498	110	5	fc	fc	PROPN
ejpam-2498	110	6	at	at	ADP
ejpam-2498	110	7	a	a	PRON
ejpam-2498	110	8	must	must	AUX
ejpam-2498	110	9	be	be	AUX
ejpam-2498	110	10	zero	zero	NUM
ejpam-2498	110	11	.	.	PUNCT
ejpam-2498	111	1	consider	consider	VERB
ejpam-2498	111	2	the	the	DET
ejpam-2498	111	3	matrix	matrix	NOUN
ejpam-2498	111	4	given	give	VERB
ejpam-2498	111	5	by	by	ADP
ejpam-2498	111	6	a	a	DET
ejpam-2498	111	7	rotation	rotation	NOUN
ejpam-2498	111	8	of	of	ADP
ejpam-2498	111	9	first	first	ADJ
ejpam-2498	111	10	and	and	CCONJ
ejpam-2498	111	11	second	second	ADJ
ejpam-2498	111	12	coordinate	coordinate	NOUN
ejpam-2498	111	13	b12(θ	b12(θ	NOUN
ejpam-2498	111	14	)	)	PUNCT
ejpam-2498	111	15	defined	define	VERB
ejpam-2498	111	16	by	by	ADP
ejpam-2498	111	17	b12(θ	b12(θ	NOUN
ejpam-2498	111	18	)	)	PUNCT
ejpam-2498	112	1	=	=	VERB
ejpam-2498	112	2			NOUN
ejpam-2498	112	3			ADJ
ejpam-2498	112	4			ADJ
ejpam-2498	112	5			ADJ
ejpam-2498	112	6			ADJ
ejpam-2498	112	7			ADJ
ejpam-2498	112	8			NUM
ejpam-2498	112	9	cosθ	cosθ	X
ejpam-2498	112	10	−sinθ	−sinθ	NOUN
ejpam-2498	112	11	0	0	NUM
ejpam-2498	112	12	·	·	PUNCT
ejpam-2498	112	13	·	·	PUNCT
ejpam-2498	112	14	·	·	PUNCT
ejpam-2498	112	15	0	0	NUM
ejpam-2498	113	1	sinθ	sinθ	PROPN
ejpam-2498	113	2	cosθ	cosθ	X
ejpam-2498	113	3	0	0	PUNCT
ejpam-2498	113	4	·	·	PUNCT
ejpam-2498	113	5	·	·	PUNCT
ejpam-2498	113	6	·	·	PUNCT
ejpam-2498	113	7	0	0	NUM
ejpam-2498	113	8	0	0	NUM
ejpam-2498	113	9	0	0	NUM
ejpam-2498	113	10	1	1	NUM
ejpam-2498	113	11	...	...	PUNCT
ejpam-2498	113	12	...	...	PUNCT
ejpam-2498	113	13	...	...	PUNCT
ejpam-2498	113	14	.	.	PUNCT
ejpam-2498	113	15	.	.	PUNCT
ejpam-2498	113	16	.	.	PUNCT
ejpam-2498	114	1	...	...	PUNCT
ejpam-2498	115	1	0	0	NUM
ejpam-2498	115	2	0	0	NUM
ejpam-2498	115	3	·	·	PUNCT
ejpam-2498	115	4	·	·	PUNCT
ejpam-2498	115	5	·	·	PUNCT
ejpam-2498	115	6	0	0	NUM
ejpam-2498	115	7	1	1	NUM
ejpam-2498	115	8			PROPN
ejpam-2498	115	9			PROPN
ejpam-2498	115	10			PROPN
ejpam-2498	115	11			PROPN
ejpam-2498	115	12			PROPN
ejpam-2498	115	13			PROPN
ejpam-2498	115	14			PROPN
ejpam-2498	115	15	.	.	PUNCT
ejpam-2498	116	1	then	then	ADV
ejpam-2498	116	2	,	,	PUNCT
ejpam-2498	116	3	ab12(θ	ab12(θ	ADJ
ejpam-2498	116	4	)	)	PUNCT
ejpam-2498	116	5	∈	∈	PROPN
ejpam-2498	116	6	so(n	so(n	NOUN
ejpam-2498	116	7	)	)	PUNCT
ejpam-2498	116	8	and	and	CCONJ
ejpam-2498	116	9	the	the	DET
ejpam-2498	116	10	matrix	matrix	NOUN
ejpam-2498	116	11	b12(θ	b12(θ	NOUN
ejpam-2498	116	12	)	)	PUNCT
ejpam-2498	116	13	forms	form	VERB
ejpam-2498	116	14	a	a	DET
ejpam-2498	116	15	curve	curve	NOUN
ejpam-2498	116	16	on	on	ADP
ejpam-2498	116	17	so(n	so(n	PROPN
ejpam-2498	116	18	)	)	PUNCT
ejpam-2498	116	19	.	.	PUNCT
ejpam-2498	117	1	moreover	moreover	ADV
ejpam-2498	117	2	,	,	PUNCT
ejpam-2498	117	3	b12(θ	b12(θ	NOUN
ejpam-2498	117	4	)	)	PUNCT
ejpam-2498	117	5	=	=	PUNCT
ejpam-2498	118	1	a	a	PRON
ejpam-2498	118	2	for	for	ADP
ejpam-2498	118	3	θ	θ	PROPN
ejpam-2498	118	4	=	=	SYM
ejpam-2498	118	5	0	0	NUM
ejpam-2498	118	6	.	.	PUNCT
ejpam-2498	119	1	by	by	ADP
ejpam-2498	119	2	the	the	DET
ejpam-2498	119	3	definition	definition	NOUN
ejpam-2498	119	4	of	of	ADP
ejpam-2498	119	5	fc	fc	PROPN
ejpam-2498	119	6	,	,	PUNCT
ejpam-2498	119	7	and	and	CCONJ
ejpam-2498	119	8	after	after	ADP
ejpam-2498	119	9	computing	compute	VERB
ejpam-2498	119	10	the	the	DET
ejpam-2498	119	11	matrix	matrix	NOUN
ejpam-2498	119	12	product	product	NOUN
ejpam-2498	119	13	,	,	PUNCT
ejpam-2498	119	14	we	we	PRON
ejpam-2498	119	15	have	have	VERB
ejpam-2498	119	16	fc(ab12(θ	fc(ab12(θ	NOUN
ejpam-2498	119	17	)	)	PUNCT
ejpam-2498	119	18	)	)	PUNCT
ejpam-2498	120	1	=	=	SYM
ejpam-2498	120	2	c1(x11cosθ	c1(x11cosθ	NOUN
ejpam-2498	120	3	+	+	CCONJ
ejpam-2498	120	4	x12sinθ	x12sinθ	NOUN
ejpam-2498	120	5	)	)	PUNCT
ejpam-2498	121	1	+	+	CCONJ
ejpam-2498	121	2	c2(−x21sinθ	c2(−x21sinθ	NOUN
ejpam-2498	121	3	+	+	CCONJ
ejpam-2498	121	4	x22cosθ	x22cosθ	PROPN
ejpam-2498	121	5	)	)	PUNCT
ejpam-2498	121	6	+	+	CCONJ
ejpam-2498	121	7	c3	c3	X
ejpam-2498	121	8	x33	x33	PROPN
ejpam-2498	122	1	+	+	X
ejpam-2498	122	2	.	.	PUNCT
ejpam-2498	122	3	.	.	PUNCT
ejpam-2498	123	1	.+	.+	NOUN
ejpam-2498	123	2	cn	cn	PROPN
ejpam-2498	123	3	xnn	xnn	PROPN
ejpam-2498	123	4	.	.	PUNCT
ejpam-2498	124	1	(	(	PUNCT
ejpam-2498	124	2	9	9	NUM
ejpam-2498	124	3	)	)	PUNCT
ejpam-2498	124	4	by	by	ADP
ejpam-2498	124	5	differentiating	differentiate	VERB
ejpam-2498	124	6	f	f	PROPN
ejpam-2498	124	7	in	in	ADP
ejpam-2498	124	8	the	the	DET
ejpam-2498	124	9	direction	direction	NOUN
ejpam-2498	124	10	of	of	ADP
ejpam-2498	124	11	the	the	DET
ejpam-2498	124	12	velocity	velocity	NOUN
ejpam-2498	124	13	vector	vector	NOUN
ejpam-2498	124	14	d	d	PROPN
ejpam-2498	124	15	dθ	dθ	PROPN
ejpam-2498	124	16	ab12(θ	ab12(θ	PROPN
ejpam-2498	124	17	)	)	PUNCT
ejpam-2498	124	18	|θ=0	|θ=0	NOUN
ejpam-2498	124	19	of	of	ADP
ejpam-2498	124	20	the	the	DET
ejpam-2498	124	21	curve	curve	NOUN
ejpam-2498	124	22	ab12(θ	ab12(θ	PROPN
ejpam-2498	124	23	)	)	PUNCT
ejpam-2498	124	24	at	at	ADP
ejpam-2498	124	25	a	a	PRON
ejpam-2498	124	26	,	,	PUNCT
ejpam-2498	124	27	we	we	PRON
ejpam-2498	124	28	have	have	VERB
ejpam-2498	124	29	d	d	PROPN
ejpam-2498	124	30	dθ	dθ	PROPN
ejpam-2498	124	31	fc(ab12(θ	fc(ab12(θ	PROPN
ejpam-2498	124	32	)	)	PUNCT
ejpam-2498	124	33	)	)	PUNCT
ejpam-2498	125	1	|θ=0	|θ=0	PROPN
ejpam-2498	125	2	=	=	PROPN
ejpam-2498	125	3	c1	c1	PROPN
ejpam-2498	125	4	x12	x12	NUM
ejpam-2498	126	1	−	−	PROPN
ejpam-2498	126	2	c2	c2	PROPN
ejpam-2498	126	3	x21	x21	PROPN
ejpam-2498	126	4	(	(	PUNCT
ejpam-2498	126	5	10	10	NUM
ejpam-2498	126	6	)	)	PUNCT
ejpam-2498	126	7	and	and	CCONJ
ejpam-2498	126	8	d	d	PROPN
ejpam-2498	126	9	dθ	dθ	PROPN
ejpam-2498	126	10	fc(b12(θ	fc(b12(θ	NOUN
ejpam-2498	126	11	)	)	PUNCT
ejpam-2498	127	1	a)|θ=0	a)|θ=0	PROPN
ejpam-2498	127	2	=	=	PROPN
ejpam-2498	128	1	−c1	−c1	PROPN
ejpam-2498	128	2	x21	x21	PROPN
ejpam-2498	129	1	+	+	CCONJ
ejpam-2498	129	2	c2	c2	PROPN
ejpam-2498	129	3	x12	x12	NUM
ejpam-2498	129	4	.	.	PUNCT
ejpam-2498	130	1	(	(	PUNCT
ejpam-2498	130	2	11	11	NUM
ejpam-2498	130	3	)	)	PUNCT
ejpam-2498	130	4	however	however	ADV
ejpam-2498	130	5	,	,	PUNCT
ejpam-2498	130	6	by	by	ADP
ejpam-2498	130	7	the	the	DET
ejpam-2498	130	8	assumption	assumption	NOUN
ejpam-2498	130	9	that	that	SCONJ
ejpam-2498	130	10	a	a	PRON
ejpam-2498	130	11	is	be	AUX
ejpam-2498	130	12	a	a	DET
ejpam-2498	130	13	critical	critical	ADJ
ejpam-2498	130	14	point	point	NOUN
ejpam-2498	130	15	of	of	ADP
ejpam-2498	130	16	fc	fc	PROPN
ejpam-2498	130	17	,	,	PUNCT
ejpam-2498	130	18	we	we	PRON
ejpam-2498	130	19	require	require	VERB
ejpam-2498	130	20	these	these	DET
ejpam-2498	130	21	derivatives	derivative	NOUN
ejpam-2498	130	22	to	to	PART
ejpam-2498	130	23	be	be	AUX
ejpam-2498	130	24	zero	zero	NUM
ejpam-2498	130	25	.	.	PUNCT
ejpam-2498	131	1	i.e.	i.e.	X
ejpam-2498	131	2	c1	c1	PROPN
ejpam-2498	131	3	x12	x12	NUM
ejpam-2498	131	4	−	−	PROPN
ejpam-2498	131	5	c2	c2	PROPN
ejpam-2498	131	6	x12	x12	NUM
ejpam-2498	131	7	=	=	SYM
ejpam-2498	131	8	0	0	PROPN
ejpam-2498	132	1	−c1	−c1	PROPN
ejpam-2498	132	2	x21	x21	PROPN
ejpam-2498	133	1	+	+	CCONJ
ejpam-2498	133	2	c2	c2	PROPN
ejpam-2498	133	3	x12	x12	NUM
ejpam-2498	133	4	=	=	SYM
ejpam-2498	133	5	0	0	NUM
ejpam-2498	133	6	solving	solve	VERB
ejpam-2498	133	7	this	this	DET
ejpam-2498	133	8	system	system	NOUN
ejpam-2498	133	9	for	for	ADP
ejpam-2498	133	10	x12	x12	NUM
ejpam-2498	133	11	,	,	PUNCT
ejpam-2498	133	12	x21	x21	PROPN
ejpam-2498	133	13	gives	give	VERB
ejpam-2498	133	14	x12	x12	NUM
ejpam-2498	133	15	=	=	SYM
ejpam-2498	133	16	x21	x21	PROPN
ejpam-2498	134	1	=	=	SYM
ejpam-2498	134	2	0	0	X
ejpam-2498	134	3	.	.	PUNCT
ejpam-2498	135	1	we	we	PRON
ejpam-2498	135	2	can	can	AUX
ejpam-2498	135	3	carry	carry	VERB
ejpam-2498	135	4	out	out	ADP
ejpam-2498	135	5	the	the	DET
ejpam-2498	135	6	similar	similar	ADJ
ejpam-2498	135	7	calculation	calculation	NOUN
ejpam-2498	135	8	for	for	ADP
ejpam-2498	135	9	bi	bi	NOUN
ejpam-2498	135	10	j(θ	j(θ	PROPN
ejpam-2498	135	11	)	)	PUNCT
ejpam-2498	135	12	with	with	ADP
ejpam-2498	135	13	i	i	PRON
ejpam-2498	135	14	<	<	X
ejpam-2498	135	15	j	j	PROPN
ejpam-2498	135	16	,	,	PUNCT
ejpam-2498	135	17	where	where	SCONJ
ejpam-2498	135	18	bi	bi	PROPN
ejpam-2498	135	19	j(θ	j(θ	PROPN
ejpam-2498	135	20	)	)	PUNCT
ejpam-2498	135	21	is	be	AUX
ejpam-2498	135	22	with	with	ADP
ejpam-2498	135	23	the	the	DET
ejpam-2498	135	24	entries	entry	NOUN
ejpam-2498	135	25	:	:	PUNCT
ejpam-2498	135	26	(	(	PUNCT
ejpam-2498	135	27	i	i	PRON
ejpam-2498	135	28	,	,	PUNCT
ejpam-2498	135	29	i	i	NOUN
ejpam-2498	135	30	)	)	PUNCT
ejpam-2498	136	1	=	=	SYM
ejpam-2498	136	2	cosθ	cosθ	NOUN
ejpam-2498	136	3	,	,	PUNCT
ejpam-2498	136	4	(	(	PUNCT
ejpam-2498	136	5	i	i	PROPN
ejpam-2498	136	6	,	,	PUNCT
ejpam-2498	136	7	j	j	PROPN
ejpam-2498	136	8	)	)	PUNCT
ejpam-2498	136	9	=	=	PUNCT
ejpam-2498	136	10	−sinθ	−sinθ	NOUN
ejpam-2498	136	11	,	,	PUNCT
ejpam-2498	136	12	(	(	PUNCT
ejpam-2498	136	13	j	j	PROPN
ejpam-2498	136	14	,	,	PUNCT
ejpam-2498	136	15	i	i	NOUN
ejpam-2498	136	16	)	)	PUNCT
ejpam-2498	136	17	=	=	SYM
ejpam-2498	136	18	sinθ	sinθ	PROPN
ejpam-2498	136	19	m.	m.	NOUN
ejpam-2498	136	20	solgun	solgun	PROPN
ejpam-2498	136	21	/	/	SYM
ejpam-2498	136	22	eur	eur	PROPN
ejpam-2498	136	23	.	.	PUNCT
ejpam-2498	137	1	j.	j.	PROPN
ejpam-2498	137	2	pure	pure	PROPN
ejpam-2498	137	3	appl	appl	PROPN
ejpam-2498	137	4	.	.	PROPN
ejpam-2498	137	5	math	math	PROPN
ejpam-2498	137	6	,	,	PUNCT
ejpam-2498	137	7	9	9	NUM
ejpam-2498	137	8	(	(	PUNCT
ejpam-2498	137	9	2016	2016	NUM
ejpam-2498	137	10	)	)	PUNCT
ejpam-2498	137	11	,	,	PUNCT
ejpam-2498	137	12	314	314	NUM
ejpam-2498	137	13	-	-	SYM
ejpam-2498	137	14	321	321	NUM
ejpam-2498	137	15	318	318	NUM
ejpam-2498	137	16	and	and	CCONJ
ejpam-2498	137	17	(	(	PUNCT
ejpam-2498	137	18	j	j	PROPN
ejpam-2498	137	19	,	,	PUNCT
ejpam-2498	137	20	j	j	PROPN
ejpam-2498	137	21	)	)	PUNCT
ejpam-2498	137	22	=	=	PUNCT
ejpam-2498	138	1	cosθ	cosθ	PROPN
ejpam-2498	138	2	.	.	PUNCT
ejpam-2498	139	1	thus	thus	ADV
ejpam-2498	139	2	,	,	PUNCT
ejpam-2498	139	3	for	for	ADP
ejpam-2498	139	4	the	the	DET
ejpam-2498	139	5	matrix	matrix	NOUN
ejpam-2498	139	6	a	a	PRON
ejpam-2498	139	7	,	,	PUNCT
ejpam-2498	139	8	x	x	PROPN
ejpam-2498	139	9	i	i	PRON
ejpam-2498	139	10	j	j	NOUN
ejpam-2498	140	1	=	=	PUNCT
ejpam-2498	140	2	0	0	PUNCT
ejpam-2498	141	1	whenever	whenever	SCONJ
ejpam-2498	141	2	i	i	PRON
ejpam-2498	141	3	6=	6=	VERB
ejpam-2498	141	4	j.	j.	PROPN
ejpam-2498	142	1	so	so	ADV
ejpam-2498	142	2	,	,	PUNCT
ejpam-2498	142	3	that	that	ADV
ejpam-2498	142	4	is	is	ADV
ejpam-2498	142	5	,	,	PUNCT
ejpam-2498	142	6	a	a	DET
ejpam-2498	142	7	critical	critical	ADJ
ejpam-2498	142	8	point	point	NOUN
ejpam-2498	142	9	of	of	ADP
ejpam-2498	142	10	fc	fc	PROPN
ejpam-2498	142	11	is	be	AUX
ejpam-2498	142	12	a	a	DET
ejpam-2498	142	13	diagonal	diagonal	ADJ
ejpam-2498	142	14	matrix	matrix	NOUN
ejpam-2498	142	15	.	.	PUNCT
ejpam-2498	143	1	on	on	ADP
ejpam-2498	143	2	the	the	DET
ejpam-2498	143	3	other	other	ADJ
ejpam-2498	143	4	hand	hand	NOUN
ejpam-2498	143	5	a∈	a∈	PROPN
ejpam-2498	143	6	so(n	so(n	PROPN
ejpam-2498	143	7	)	)	PUNCT
ejpam-2498	143	8	,	,	PUNCT
ejpam-2498	143	9	so	so	ADV
ejpam-2498	143	10	we	we	PRON
ejpam-2498	143	11	have	have	AUX
ejpam-2498	143	12	aat	aat	VERB
ejpam-2498	143	13	=	=	PUNCT
ejpam-2498	143	14	in	in	ADP
ejpam-2498	143	15	.	.	PUNCT
ejpam-2498	144	1	so	so	ADV
ejpam-2498	144	2	each	each	DET
ejpam-2498	144	3	entry	entry	NOUN
ejpam-2498	144	4	on	on	ADP
ejpam-2498	144	5	the	the	DET
ejpam-2498	144	6	main	main	ADJ
ejpam-2498	144	7	diagonal	diagonal	NOUN
ejpam-2498	144	8	of	of	ADP
ejpam-2498	144	9	a	a	PRON
ejpam-2498	144	10	must	must	AUX
ejpam-2498	144	11	be	be	AUX
ejpam-2498	144	12	±1	±1	VERB
ejpam-2498	144	13	.	.	PUNCT
ejpam-2498	145	1	conversely	conversely	ADV
ejpam-2498	145	2	,	,	PUNCT
ejpam-2498	145	3	let	let	VERB
ejpam-2498	145	4	a	a	PRON
ejpam-2498	145	5	be	be	AUX
ejpam-2498	145	6	a	a	DET
ejpam-2498	145	7	matrix	matrix	NOUN
ejpam-2498	145	8	in	in	ADP
ejpam-2498	145	9	the	the	DET
ejpam-2498	145	10	form	form	NOUN
ejpam-2498	145	11	(	(	PUNCT
ejpam-2498	145	12	8)	8)	NUM
ejpam-2498	145	13	.	.	PUNCT
ejpam-2498	146	1	in	in	ADP
ejpam-2498	146	2	order	order	NOUN
ejpam-2498	146	3	to	to	PART
ejpam-2498	146	4	check	check	VERB
ejpam-2498	146	5	that	that	SCONJ
ejpam-2498	146	6	a	a	PRON
ejpam-2498	146	7	is	be	AUX
ejpam-2498	146	8	a	a	DET
ejpam-2498	146	9	critical	critical	ADJ
ejpam-2498	146	10	point	point	NOUN
ejpam-2498	146	11	,	,	PUNCT
ejpam-2498	146	12	we	we	PRON
ejpam-2498	146	13	need	need	VERB
ejpam-2498	146	14	to	to	PART
ejpam-2498	146	15	compute	compute	VERB
ejpam-2498	146	16	the	the	DET
ejpam-2498	146	17	derivative	derivative	NOUN
ejpam-2498	146	18	of	of	ADP
ejpam-2498	146	19	fc	fc	PROPN
ejpam-2498	146	20	.	.	PUNCT
ejpam-2498	147	1	if	if	SCONJ
ejpam-2498	147	2	we	we	PRON
ejpam-2498	147	3	could	could	AUX
ejpam-2498	147	4	find	find	VERB
ejpam-2498	147	5	n(n−	n(n−	PROPN
ejpam-2498	147	6	1)/2	1)/2	NUM
ejpam-2498	147	7	curves	curve	NOUN
ejpam-2498	147	8	ci	ci	NOUN
ejpam-2498	147	9	going	go	VERB
ejpam-2498	147	10	through	through	ADP
ejpam-2498	147	11	a	a	PRON
ejpam-2498	147	12	with	with	ADP
ejpam-2498	147	13	velocity	velocity	NOUN
ejpam-2498	147	14	vector	vector	NOUN
ejpam-2498	147	15	at	at	ADP
ejpam-2498	147	16	a	a	PRON
ejpam-2498	147	17	and	and	CCONJ
ejpam-2498	147	18	linearly	linearly	ADV
ejpam-2498	147	19	independent	independent	ADJ
ejpam-2498	147	20	from	from	ADP
ejpam-2498	147	21	each	each	DET
ejpam-2498	147	22	other	other	ADJ
ejpam-2498	147	23	.	.	PUNCT
ejpam-2498	148	1	since	since	SCONJ
ejpam-2498	148	2	the	the	DET
ejpam-2498	148	3	velocity	velocity	NOUN
ejpam-2498	148	4	vector	vector	NOUN
ejpam-2498	148	5	of	of	ADP
ejpam-2498	148	6	ci	ci	NOUN
ejpam-2498	148	7	at	at	ADP
ejpam-2498	148	8	a	a	DET
ejpam-2498	148	9	plays	play	NOUN
ejpam-2498	148	10	a	a	DET
ejpam-2498	148	11	role	role	NOUN
ejpam-2498	148	12	of	of	ADP
ejpam-2498	148	13	a	a	DET
ejpam-2498	148	14	local	local	ADJ
ejpam-2498	148	15	coordinate	coordinate	NOUN
ejpam-2498	148	16	of	of	ADP
ejpam-2498	148	17	a	a	PRON
ejpam-2498	148	18	,	,	PUNCT
ejpam-2498	148	19	we	we	PRON
ejpam-2498	148	20	only	only	ADV
ejpam-2498	148	21	need	need	VERB
ejpam-2498	148	22	to	to	PART
ejpam-2498	148	23	check	check	VERB
ejpam-2498	148	24	that	that	SCONJ
ejpam-2498	148	25	the	the	DET
ejpam-2498	148	26	derivative	derivative	NOUN
ejpam-2498	148	27	of	of	ADP
ejpam-2498	148	28	fc(ci	fc(ci	PROPN
ejpam-2498	148	29	)	)	PUNCT
ejpam-2498	148	30	vanishes	vanish	VERB
ejpam-2498	148	31	to	to	PART
ejpam-2498	148	32	see	see	VERB
ejpam-2498	148	33	that	that	PRON
ejpam-2498	148	34	d	d	PROPN
ejpam-2498	148	35	f	f	X
ejpam-2498	148	36	(	(	PUNCT
ejpam-2498	148	37	a	a	NOUN
ejpam-2498	148	38	)	)	PUNCT
ejpam-2498	148	39	=	=	SYM
ejpam-2498	148	40	0	0	X
ejpam-2498	148	41	.	.	PUNCT
ejpam-2498	149	1	now	now	ADV
ejpam-2498	149	2	,	,	PUNCT
ejpam-2498	149	3	the	the	DET
ejpam-2498	149	4	claim	claim	NOUN
ejpam-2498	149	5	is	be	AUX
ejpam-2498	149	6	the	the	DET
ejpam-2498	149	7	curves	curve	NOUN
ejpam-2498	149	8	ci	ci	NOUN
ejpam-2498	149	9	’s	’	VERB
ejpam-2498	149	10	are	be	AUX
ejpam-2498	149	11	in	in	ADP
ejpam-2498	149	12	fact	fact	NOUN
ejpam-2498	149	13	abi	abi	PROPN
ejpam-2498	149	14	jθ	jθ	PROPN
ejpam-2498	150	1	’s	’s	AUX
ejpam-2498	150	2	defined	define	VERB
ejpam-2498	150	3	above	above	ADV
ejpam-2498	150	4	.	.	PUNCT
ejpam-2498	151	1	let	let	VERB
ejpam-2498	151	2	εi	εi	NOUN
ejpam-2498	151	3	=	=	VERB
ejpam-2498	151	4	aii	aii	NOUN
ejpam-2498	151	5	where	where	SCONJ
ejpam-2498	151	6	aii	aii	PROPN
ejpam-2498	151	7	is	be	AUX
ejpam-2498	151	8	the	the	DET
ejpam-2498	151	9	i	i	PROPN
ejpam-2498	151	10	-	-	PUNCT
ejpam-2498	151	11	th	th	X
ejpam-2498	151	12	diagonal	diagonal	ADJ
ejpam-2498	151	13	entry	entry	NOUN
ejpam-2498	151	14	of	of	ADP
ejpam-2498	151	15	a(εi	a(εi	NOUN
ejpam-2498	151	16	=	=	SYM
ejpam-2498	151	17	±1	±1	VERB
ejpam-2498	151	18	)	)	PUNCT
ejpam-2498	151	19	.	.	PUNCT
ejpam-2498	152	1	then	then	ADV
ejpam-2498	152	2	,	,	PUNCT
ejpam-2498	152	3	the	the	DET
ejpam-2498	152	4	derivative	derivative	NOUN
ejpam-2498	152	5	of	of	ADP
ejpam-2498	152	6	the	the	DET
ejpam-2498	152	7	matrix	matrix	NOUN
ejpam-2498	152	8	abi	abi	PROPN
ejpam-2498	152	9	j(θ	j(θ	PROPN
ejpam-2498	152	10	)	)	PUNCT
ejpam-2498	152	11	at	at	ADP
ejpam-2498	152	12	a	a	PRON
ejpam-2498	152	13	is	be	AUX
ejpam-2498	152	14	(	(	PUNCT
ejpam-2498	152	15	we	we	PRON
ejpam-2498	152	16	did	do	VERB
ejpam-2498	152	17	for	for	ADP
ejpam-2498	152	18	the	the	DET
ejpam-2498	152	19	case	case	NOUN
ejpam-2498	152	20	b12	b12	NOUN
ejpam-2498	152	21	,	,	PUNCT
ejpam-2498	152	22	but	but	CCONJ
ejpam-2498	152	23	it	it	PRON
ejpam-2498	152	24	is	be	AUX
ejpam-2498	152	25	same	same	ADJ
ejpam-2498	152	26	for	for	ADP
ejpam-2498	152	27	other	other	ADJ
ejpam-2498	152	28	indices	index	NOUN
ejpam-2498	152	29	with	with	ADP
ejpam-2498	152	30	i	i	PRON
ejpam-2498	152	31	<	<	X
ejpam-2498	152	32	j	j	PROPN
ejpam-2498	152	33	)	)	PUNCT
ejpam-2498	152	34	,	,	PUNCT
ejpam-2498	153	1	d	d	PROPN
ejpam-2498	153	2	dθ	dθ	PROPN
ejpam-2498	153	3	ab12(θ	ab12(θ	PROPN
ejpam-2498	153	4	)	)	PUNCT
ejpam-2498	153	5	|θ=0	|θ=0	PROPN
ejpam-2498	153	6	=	=	NOUN
ejpam-2498	153	7			NOUN
ejpam-2498	153	8			ADJ
ejpam-2498	153	9			ADJ
ejpam-2498	153	10			ADJ
ejpam-2498	153	11			ADJ
ejpam-2498	153	12			ADJ
ejpam-2498	153	13			NOUN
ejpam-2498	153	14	0	0	PUNCT
ejpam-2498	154	1	−ε1	−ε1	PROPN
ejpam-2498	154	2	0	0	NUM
ejpam-2498	154	3	·	·	PUNCT
ejpam-2498	154	4	·	·	PUNCT
ejpam-2498	154	5	·	·	PUNCT
ejpam-2498	154	6	0	0	PUNCT
ejpam-2498	155	1	ε2	ε2	ADJ
ejpam-2498	155	2	0	0	NUM
ejpam-2498	155	3	0	0	NUM
ejpam-2498	155	4	·	·	PUNCT
ejpam-2498	155	5	·	·	PUNCT
ejpam-2498	155	6	·	·	PUNCT
ejpam-2498	155	7	0	0	NUM
ejpam-2498	156	1	0	0	NUM
ejpam-2498	156	2	0	0	NUM
ejpam-2498	156	3	...	...	PUNCT
ejpam-2498	156	4	0	0	NUM
ejpam-2498	156	5	...	...	PUNCT
ejpam-2498	156	6	...	...	PUNCT
ejpam-2498	156	7	...	...	PUNCT
ejpam-2498	157	1	0	0	NUM
ejpam-2498	157	2	0	0	NUM
ejpam-2498	157	3	·	·	PUNCT
ejpam-2498	157	4	·	·	PUNCT
ejpam-2498	157	5	·	·	PUNCT
ejpam-2498	157	6	0	0	NUM
ejpam-2498	158	1			PROPN
ejpam-2498	158	2			PROPN
ejpam-2498	158	3			PROPN
ejpam-2498	158	4			PROPN
ejpam-2498	158	5			PROPN
ejpam-2498	158	6			PROPN
ejpam-2498	158	7			PROPN
ejpam-2498	158	8	this	this	DET
ejpam-2498	158	9	matrix	matrix	NOUN
ejpam-2498	158	10	is	be	AUX
ejpam-2498	158	11	regarded	regard	VERB
ejpam-2498	158	12	as	as	ADP
ejpam-2498	158	13	a	a	DET
ejpam-2498	158	14	vector	vector	NOUN
ejpam-2498	158	15	in	in	ADP
ejpam-2498	158	16	rn2	rn2	PROPN
ejpam-2498	158	17	.	.	PUNCT
ejpam-2498	159	1	by	by	ADP
ejpam-2498	159	2	considering	consider	VERB
ejpam-2498	159	3	all	all	DET
ejpam-2498	159	4	1	1	NUM
ejpam-2498	159	5	≤	≤	NUM
ejpam-2498	159	6	i	i	PRON
ejpam-2498	159	7	≤	≤	NUM
ejpam-2498	159	8	j	j	PROPN
ejpam-2498	159	9	≤	≤	NUM
ejpam-2498	159	10	n	n	CCONJ
ejpam-2498	159	11	,	,	PUNCT
ejpam-2498	159	12	these	these	DET
ejpam-2498	159	13	matrices	matrix	NOUN
ejpam-2498	159	14	(	(	PUNCT
ejpam-2498	159	15	vectors	vector	NOUN
ejpam-2498	159	16	)	)	PUNCT
ejpam-2498	159	17	form	form	VERB
ejpam-2498	159	18	a	a	DET
ejpam-2498	159	19	basis	basis	NOUN
ejpam-2498	159	20	for	for	ADP
ejpam-2498	159	21	the	the	DET
ejpam-2498	159	22	tangent	tangent	ADJ
ejpam-2498	159	23	space	space	NOUN
ejpam-2498	159	24	taso(n	taso(n	PROPN
ejpam-2498	159	25	)	)	PUNCT
ejpam-2498	159	26	.	.	PUNCT
ejpam-2498	160	1	so	so	ADV
ejpam-2498	160	2	,	,	PUNCT
ejpam-2498	160	3	for	for	ADP
ejpam-2498	160	4	a	a	DET
ejpam-2498	160	5	given	give	VERB
ejpam-2498	160	6	matrix	matrix	NOUN
ejpam-2498	160	7	a	a	PRON
ejpam-2498	160	8	in	in	ADP
ejpam-2498	160	9	the	the	DET
ejpam-2498	160	10	form	form	NOUN
ejpam-2498	160	11	(	(	PUNCT
ejpam-2498	160	12	8)	8)	NUM
ejpam-2498	160	13	,	,	PUNCT
ejpam-2498	160	14	it	it	PRON
ejpam-2498	160	15	is	be	AUX
ejpam-2498	160	16	easy	easy	ADJ
ejpam-2498	160	17	to	to	PART
ejpam-2498	160	18	compute	compute	VERB
ejpam-2498	160	19	that	that	SCONJ
ejpam-2498	160	20	,	,	PUNCT
ejpam-2498	160	21	the	the	DET
ejpam-2498	160	22	derivative	derivative	NOUN
ejpam-2498	160	23	of	of	ADP
ejpam-2498	160	24	fc	fc	PROPN
ejpam-2498	160	25	at	at	ADP
ejpam-2498	160	26	a	a	PRON
ejpam-2498	160	27	is	be	AUX
ejpam-2498	160	28	zero	zero	NUM
ejpam-2498	160	29	.	.	PUNCT
ejpam-2498	161	1	this	this	PRON
ejpam-2498	161	2	means	mean	VERB
ejpam-2498	161	3	nothing	nothing	PRON
ejpam-2498	161	4	but	but	SCONJ
ejpam-2498	161	5	a	a	PRON
ejpam-2498	161	6	is	be	AUX
ejpam-2498	161	7	a	a	DET
ejpam-2498	161	8	critical	critical	ADJ
ejpam-2498	161	9	point	point	NOUN
ejpam-2498	161	10	of	of	ADP
ejpam-2498	161	11	fc	fc	PROPN
ejpam-2498	161	12	.	.	PUNCT
ejpam-2498	162	1	after	after	ADP
ejpam-2498	162	2	now	now	ADV
ejpam-2498	162	3	,	,	PUNCT
ejpam-2498	162	4	we	we	PRON
ejpam-2498	162	5	know	know	VERB
ejpam-2498	162	6	the	the	DET
ejpam-2498	162	7	coordinate	coordinate	NOUN
ejpam-2498	162	8	system	system	NOUN
ejpam-2498	162	9	of	of	ADP
ejpam-2498	162	10	so(n	so(n	NOUN
ejpam-2498	162	11	)	)	PUNCT
ejpam-2498	162	12	and	and	CCONJ
ejpam-2498	162	13	the	the	DET
ejpam-2498	162	14	critical	critical	ADJ
ejpam-2498	162	15	points	point	NOUN
ejpam-2498	162	16	of	of	ADP
ejpam-2498	162	17	the	the	DET
ejpam-2498	162	18	the	the	DET
ejpam-2498	162	19	given	give	VERB
ejpam-2498	162	20	function	function	NOUN
ejpam-2498	162	21	fc	fc	PROPN
ejpam-2498	162	22	.	.	PUNCT
ejpam-2498	163	1	it	it	PRON
ejpam-2498	163	2	is	be	AUX
ejpam-2498	163	3	straightforward	straightforward	ADJ
ejpam-2498	163	4	to	to	PART
ejpam-2498	163	5	compute	compute	VERB
ejpam-2498	163	6	the	the	DET
ejpam-2498	163	7	hessian	hessian	NOUN
ejpam-2498	163	8	of	of	ADP
ejpam-2498	163	9	fc	fc	PROPN
ejpam-2498	163	10	at	at	ADP
ejpam-2498	163	11	a.	a.	NOUN
ejpam-2498	163	12	suppose	suppose	VERB
ejpam-2498	163	13	that	that	SCONJ
ejpam-2498	163	14	a	a	PRON
ejpam-2498	163	15	is	be	AUX
ejpam-2498	163	16	a	a	DET
ejpam-2498	163	17	critical	critical	ADJ
ejpam-2498	163	18	matrix	matrix	NOUN
ejpam-2498	163	19	with	with	ADP
ejpam-2498	163	20	diagonal	diagonal	ADJ
ejpam-2498	163	21	entries	entry	NOUN
ejpam-2498	163	22	aii	aii	NOUN
ejpam-2498	163	23	=	=	SYM
ejpam-2498	163	24	εi	εi	PROPN
ejpam-2498	163	25	=	=	SYM
ejpam-2498	163	26	±1	±1	ADJ
ejpam-2498	163	27	.	.	PUNCT
ejpam-2498	164	1	then	then	ADV
ejpam-2498	164	2	,	,	PUNCT
ejpam-2498	164	3	we	we	PRON
ejpam-2498	164	4	want	want	VERB
ejpam-2498	164	5	to	to	PART
ejpam-2498	164	6	compute	compute	VERB
ejpam-2498	164	7	∂	∂	NUM
ejpam-2498	164	8	2	2	NUM
ejpam-2498	164	9	∂	∂	NUM
ejpam-2498	164	10	θ∂	θ∂	NOUN
ejpam-2498	164	11	ϕ	ϕ	PROPN
ejpam-2498	164	12	fc(abαβ	fc(abαβ	PROPN
ejpam-2498	164	13	(	(	PUNCT
ejpam-2498	164	14	θ	θ	NOUN
ejpam-2498	164	15	)	)	PUNCT
ejpam-2498	164	16	bγδ(ϕ))|θ=0,ϕ=0	bγδ(ϕ))|θ=0,ϕ=0	PROPN
ejpam-2498	164	17	.	.	PUNCT
ejpam-2498	165	1	notice	notice	NOUN
ejpam-2498	165	2	that	that	PRON
ejpam-2498	165	3	is	be	AUX
ejpam-2498	165	4	linear	linear	PROPN
ejpam-2498	165	5	abαβ	abαβ	PROPN
ejpam-2498	165	6	(	(	PUNCT
ejpam-2498	165	7	θ	θ	NOUN
ejpam-2498	165	8	)	)	PUNCT
ejpam-2498	165	9	bγδ(ϕ	bγδ(ϕ	PROPN
ejpam-2498	165	10	)	)	PUNCT
ejpam-2498	165	11	is	be	AUX
ejpam-2498	165	12	linear	linear	ADJ
ejpam-2498	165	13	in	in	ADP
ejpam-2498	165	14	θ	θ	PROPN
ejpam-2498	165	15	and	and	CCONJ
ejpam-2498	165	16	in	in	ADP
ejpam-2498	165	17	ϕ	ϕ	NOUN
ejpam-2498	165	18	,	,	PUNCT
ejpam-2498	165	19	and	and	CCONJ
ejpam-2498	165	20	fc	fc	PROPN
ejpam-2498	165	21	is	be	AUX
ejpam-2498	165	22	a	a	DET
ejpam-2498	165	23	linear	linear	ADJ
ejpam-2498	165	24	function	function	NOUN
ejpam-2498	165	25	.	.	PUNCT
ejpam-2498	166	1	thus	thus	ADV
ejpam-2498	166	2	,	,	PUNCT
ejpam-2498	166	3	we	we	PRON
ejpam-2498	166	4	can	can	AUX
ejpam-2498	166	5	bring	bring	VERB
ejpam-2498	166	6	the	the	DET
ejpam-2498	166	7	derivative	derivative	NOUN
ejpam-2498	166	8	inside	inside	ADP
ejpam-2498	166	9	fc	fc	PROPN
ejpam-2498	166	10	.	.	PUNCT
ejpam-2498	167	1	so	so	ADV
ejpam-2498	167	2	,	,	PUNCT
ejpam-2498	167	3	∂	∂	NUM
ejpam-2498	167	4	2	2	NUM
ejpam-2498	167	5	∂	∂	NUM
ejpam-2498	167	6	θ∂	θ∂	PROPN
ejpam-2498	167	7	ϕ	ϕ	PROPN
ejpam-2498	167	8	fc(abαβ(θ	fc(abαβ(θ	PROPN
ejpam-2498	167	9	)	)	PUNCT
ejpam-2498	167	10	bγδ(ϕ))|θ=0,ϕ=0	bγδ(ϕ))|θ=0,ϕ=0	VERB
ejpam-2498	168	1	=	=	SYM
ejpam-2498	168	2	fc(a	fc(a	PROPN
ejpam-2498	168	3	d	d	PROPN
ejpam-2498	168	4	dθ	dθ	PROPN
ejpam-2498	168	5	bαβ	bαβ	PROPN
ejpam-2498	168	6	(	(	PUNCT
ejpam-2498	168	7	θ	θ	NOUN
ejpam-2498	168	8	)	)	PUNCT
ejpam-2498	168	9	|θ=0	|θ=0	PROPN
ejpam-2498	168	10	d	d	NOUN
ejpam-2498	168	11	dϕ	dϕ	NOUN
ejpam-2498	168	12	bγδ(ϕ)|ϕ=0	bγδ(ϕ)|ϕ=0	ADV
ejpam-2498	168	13	=	=	PUNCT
ejpam-2498	169	1	¨	¨	NOUN
ejpam-2498	169	2	−cαεα	−cαεα	NOUN
ejpam-2498	169	3	−	−	PROPN
ejpam-2498	169	4	cβεβ	cβεβ	NOUN
ejpam-2498	170	1	if	if	SCONJ
ejpam-2498	170	2	α=	α=	PROPN
ejpam-2498	170	3	γ	γ	X
ejpam-2498	170	4	,	,	PUNCT
ejpam-2498	170	5	β	β	X
ejpam-2498	170	6	=	=	SYM
ejpam-2498	170	7	δ	δ	PROPN
ejpam-2498	170	8	0	0	PUNCT
ejpam-2498	171	1	otherwise	otherwise	ADV
ejpam-2498	171	2	this	this	DET
ejpam-2498	171	3	calculation	calculation	NOUN
ejpam-2498	171	4	becomes	become	VERB
ejpam-2498	171	5	easier	easy	ADJ
ejpam-2498	171	6	if	if	SCONJ
ejpam-2498	171	7	we	we	PRON
ejpam-2498	171	8	consider	consider	VERB
ejpam-2498	171	9	the	the	DET
ejpam-2498	171	10	matrix	matrix	NOUN
ejpam-2498	171	11	multiplication	multiplication	NOUN
ejpam-2498	171	12	ci	ci	PROPN
ejpam-2498	171	13	j	j	PROPN
ejpam-2498	171	14	=	=	PUNCT
ejpam-2498	171	15	∑	∑	PUNCT
ejpam-2498	171	16	k	k	PROPN
ejpam-2498	171	17	aik	aik	PROPN
ejpam-2498	171	18	bk	bk	PROPN
ejpam-2498	171	19	j	j	PROPN
ejpam-2498	171	20	.	.	PUNCT
ejpam-2498	172	1	the	the	DET
ejpam-2498	172	2	calculation	calculation	NOUN
ejpam-2498	172	3	above	above	ADV
ejpam-2498	172	4	shows	show	VERB
ejpam-2498	172	5	that	that	SCONJ
ejpam-2498	172	6	the	the	DET
ejpam-2498	172	7	hessian	hessian	ADJ
ejpam-2498	172	8	matrix	matrix	NOUN
ejpam-2498	172	9	is	be	AUX
ejpam-2498	172	10	diagonal	diagonal	ADJ
ejpam-2498	172	11	.	.	PUNCT
ejpam-2498	173	1	since	since	SCONJ
ejpam-2498	173	2	cα	cα	PROPN
ejpam-2498	173	3	6=	6=	PROPN
ejpam-2498	173	4	cβ	cβ	NOUN
ejpam-2498	173	5	for	for	ADP
ejpam-2498	173	6	α	α	PROPN
ejpam-2498	173	7	6=	6=	ADP
ejpam-2498	173	8	β	β	NOUN
ejpam-2498	173	9	,	,	PUNCT
ejpam-2498	173	10	the	the	DET
ejpam-2498	173	11	entries	entry	NOUN
ejpam-2498	173	12	on	on	ADP
ejpam-2498	173	13	the	the	DET
ejpam-2498	173	14	diagonal	diagonal	NOUN
ejpam-2498	173	15	are	be	AUX
ejpam-2498	173	16	non	non	ADJ
ejpam-2498	173	17	-	-	ADJ
ejpam-2498	173	18	zero	zero	NUM
ejpam-2498	173	19	.	.	PUNCT
ejpam-2498	174	1	therefore	therefore	ADV
ejpam-2498	174	2	,	,	PUNCT
ejpam-2498	174	3	a	a	PRON
ejpam-2498	174	4	is	be	AUX
ejpam-2498	174	5	a	a	DET
ejpam-2498	174	6	non	non	ADJ
ejpam-2498	174	7	-	-	ADJ
ejpam-2498	174	8	degenerate	degenerate	ADJ
ejpam-2498	174	9	critical	critical	ADJ
ejpam-2498	174	10	point	point	NOUN
ejpam-2498	174	11	of	of	ADP
ejpam-2498	174	12	fc	fc	PROPN
ejpam-2498	174	13	,	,	PUNCT
ejpam-2498	174	14	meaning	mean	VERB
ejpam-2498	174	15	that	that	SCONJ
ejpam-2498	174	16	fc	fc	PROPN
ejpam-2498	174	17	is	be	AUX
ejpam-2498	174	18	a	a	DET
ejpam-2498	174	19	morse	morse	ADJ
ejpam-2498	174	20	function	function	NOUN
ejpam-2498	174	21	on	on	ADP
ejpam-2498	174	22	so(n	so(n	PROPN
ejpam-2498	174	23	)	)	PUNCT
ejpam-2498	174	24	.	.	PUNCT
ejpam-2498	175	1	assume	assume	VERB
ejpam-2498	175	2	that	that	SCONJ
ejpam-2498	175	3	the	the	DET
ejpam-2498	175	4	subscripts	subscript	NOUN
ejpam-2498	175	5	i	i	PRON
ejpam-2498	175	6	of	of	ADP
ejpam-2498	175	7	the	the	DET
ejpam-2498	175	8	diagonal	diagonal	ADJ
ejpam-2498	175	9	entries	entry	NOUN
ejpam-2498	175	10	εi	εi	VERB
ejpam-2498	175	11	of	of	ADP
ejpam-2498	175	12	a	a	PRON
ejpam-2498	175	13	,	,	PUNCT
ejpam-2498	175	14	1≤	1≤	NUM
ejpam-2498	175	15	i	i	PROPN
ejpam-2498	175	16	≤	≤	PROPN
ejpam-2498	175	17	n	n	CCONJ
ejpam-2498	175	18	,	,	PUNCT
ejpam-2498	175	19	with	with	ADP
ejpam-2498	175	20	εi	εi	NOUN
ejpam-2498	175	21	=	=	SYM
ejpam-2498	175	22	1	1	NUM
ejpam-2498	175	23	are	be	AUX
ejpam-2498	175	24	i1	i1	PROPN
ejpam-2498	175	25	,	,	PUNCT
ejpam-2498	175	26	i2	i2	PROPN
ejpam-2498	175	27	,	,	PUNCT
ejpam-2498	175	28	.	.	PUNCT
ejpam-2498	175	29	.	.	PUNCT
ejpam-2498	176	1	.	.	PUNCT
ejpam-2498	177	1	,	,	PUNCT
ejpam-2498	178	1	i	i	PRON
ejpam-2498	178	2	m	m	VERB
ejpam-2498	178	3	m.	m.	NOUN
ejpam-2498	178	4	solgun	solgun	PROPN
ejpam-2498	178	5	/	/	SYM
ejpam-2498	178	6	eur	eur	PROPN
ejpam-2498	178	7	.	.	PUNCT
ejpam-2498	179	1	j.	j.	PROPN
ejpam-2498	179	2	pure	pure	PROPN
ejpam-2498	179	3	appl	appl	PROPN
ejpam-2498	179	4	.	.	PROPN
ejpam-2498	179	5	math	math	PROPN
ejpam-2498	179	6	,	,	PUNCT
ejpam-2498	179	7	9	9	NUM
ejpam-2498	179	8	(	(	PUNCT
ejpam-2498	179	9	2016	2016	NUM
ejpam-2498	179	10	)	)	PUNCT
ejpam-2498	179	11	,	,	PUNCT
ejpam-2498	179	12	314	314	NUM
ejpam-2498	179	13	-	-	SYM
ejpam-2498	179	14	321	321	NUM
ejpam-2498	179	15	319	319	NUM
ejpam-2498	179	16	in	in	ADP
ejpam-2498	179	17	ascending	ascend	VERB
ejpam-2498	179	18	order	order	NOUN
ejpam-2498	179	19	.	.	PUNCT
ejpam-2498	180	1	then	then	ADV
ejpam-2498	180	2	the	the	DET
ejpam-2498	180	3	index	index	NOUN
ejpam-2498	180	4	of	of	ADP
ejpam-2498	180	5	the	the	DET
ejpam-2498	180	6	critical	critical	ADJ
ejpam-2498	180	7	point	point	NOUN
ejpam-2498	180	8	a	a	PRON
ejpam-2498	180	9	(	(	PUNCT
ejpam-2498	180	10	the	the	DET
ejpam-2498	180	11	number	number	NOUN
ejpam-2498	180	12	of	of	ADP
ejpam-2498	180	13	minus	minus	ADJ
ejpam-2498	180	14	signs	sign	NOUN
ejpam-2498	180	15	on	on	ADP
ejpam-2498	180	16	the	the	DET
ejpam-2498	180	17	diagonal	diagonal	NOUN
ejpam-2498	180	18	of	of	ADP
ejpam-2498	180	19	hessian	hessian	NOUN
ejpam-2498	180	20	)	)	PUNCT
ejpam-2498	180	21	is	be	AUX
ejpam-2498	180	22	(	(	PUNCT
ejpam-2498	180	23	i1	i1	PROPN
ejpam-2498	180	24	−	−	PROPN
ejpam-2498	180	25	1	1	NUM
ejpam-2498	180	26	)	)	PUNCT
ejpam-2498	181	1	+	+	CCONJ
ejpam-2498	181	2	(	(	PUNCT
ejpam-2498	181	3	i2	i2	PROPN
ejpam-2498	181	4	−	−	PROPN
ejpam-2498	181	5	1	1	NUM
ejpam-2498	181	6	)	)	PUNCT
ejpam-2498	181	7	+	+	CCONJ
ejpam-2498	181	8	.	.	PUNCT
ejpam-2498	181	9	.	.	PUNCT
ejpam-2498	182	1	.+	.+	NOUN
ejpam-2498	182	2	(	(	PUNCT
ejpam-2498	182	3	i	i	NOUN
ejpam-2498	182	4	m	m	VERB
ejpam-2498	182	5	−	−	NOUN
ejpam-2498	182	6	1	1	NUM
ejpam-2498	182	7	)	)	PUNCT
ejpam-2498	182	8	.	.	PUNCT
ejpam-2498	183	1	and	and	CCONJ
ejpam-2498	183	2	the	the	DET
ejpam-2498	183	3	index	index	NOUN
ejpam-2498	183	4	is	be	AUX
ejpam-2498	183	5	0	0	NUM
ejpam-2498	183	6	if	if	SCONJ
ejpam-2498	183	7	all	all	PRON
ejpam-2498	183	8	εi	εi	PRON
ejpam-2498	183	9	’s	’	NOUN
ejpam-2498	183	10	are	be	AUX
ejpam-2498	183	11	-1	-1	PUNCT
ejpam-2498	183	12	.	.	PUNCT
ejpam-2498	184	1	also	also	ADV
ejpam-2498	184	2	,	,	PUNCT
ejpam-2498	184	3	the	the	DET
ejpam-2498	184	4	critical	critical	ADJ
ejpam-2498	184	5	value	value	NOUN
ejpam-2498	184	6	at	at	ADP
ejpam-2498	184	7	the	the	DET
ejpam-2498	184	8	critical	critical	ADJ
ejpam-2498	184	9	point	point	NOUN
ejpam-2498	184	10	is	be	AUX
ejpam-2498	184	11	2(ci1	2(ci1	NUM
ejpam-2498	184	12	+	+	CCONJ
ejpam-2498	184	13	ci2	ci2	NOUN
ejpam-2498	184	14	+	+	CCONJ
ejpam-2498	184	15	·	·	PUNCT
ejpam-2498	184	16	·	·	PUNCT
ejpam-2498	184	17	·	·	PUNCT
ejpam-2498	184	18	+	+	CCONJ
ejpam-2498	184	19	cim)−	cim)−	PROPN
ejpam-2498	184	20	n	n	CCONJ
ejpam-2498	184	21	∑	∑	ADP
ejpam-2498	184	22	i=0	i=0	PROPN
ejpam-2498	184	23	ci	ci	PROPN
ejpam-2498	184	24	.	.	PUNCT
ejpam-2498	185	1	considering	consider	VERB
ejpam-2498	185	2	that	that	SCONJ
ejpam-2498	185	3	deta=	deta=	NUM
ejpam-2498	185	4	1	1	NUM
ejpam-2498	185	5	,	,	PUNCT
ejpam-2498	185	6	there	there	PRON
ejpam-2498	185	7	are	be	VERB
ejpam-2498	185	8	2n−1	2n−1	NUM
ejpam-2498	185	9	critical	critical	ADJ
ejpam-2498	185	10	points	point	NOUN
ejpam-2498	186	1	[	[	X
ejpam-2498	186	2	4	4	NUM
ejpam-2498	186	3	]	]	PUNCT
ejpam-2498	186	4	.	.	PUNCT
ejpam-2498	187	1	4	4	X
ejpam-2498	187	2	.	.	X
ejpam-2498	187	3	perfect	perfect	ADJ
ejpam-2498	187	4	morse	morse	NOUN
ejpam-2498	187	5	functions	function	NOUN
ejpam-2498	187	6	first	first	ADV
ejpam-2498	187	7	,	,	PUNCT
ejpam-2498	187	8	we	we	PRON
ejpam-2498	187	9	will	will	AUX
ejpam-2498	187	10	give	give	VERB
ejpam-2498	187	11	the	the	DET
ejpam-2498	187	12	basic	basic	ADJ
ejpam-2498	187	13	notions	notion	NOUN
ejpam-2498	187	14	.	.	PUNCT
ejpam-2498	188	1	definition	definition	NOUN
ejpam-2498	188	2	4	4	NUM
ejpam-2498	188	3	.	.	PUNCT
ejpam-2498	189	1	the	the	DET
ejpam-2498	189	2	poincaré	poincaré	PROPN
ejpam-2498	189	3	polynomial	polynomial	NOUN
ejpam-2498	189	4	of	of	ADP
ejpam-2498	189	5	the	the	DET
ejpam-2498	189	6	n	n	ADV
ejpam-2498	189	7	-	-	PUNCT
ejpam-2498	189	8	dimensional	dimensional	ADJ
ejpam-2498	189	9	manifold	manifold	ADJ
ejpam-2498	189	10	m	m	VERB
ejpam-2498	189	11	is	be	AUX
ejpam-2498	189	12	defined	define	VERB
ejpam-2498	189	13	to	to	PART
ejpam-2498	189	14	be	be	AUX
ejpam-2498	189	15	pm	pm	NOUN
ejpam-2498	189	16	(	(	PUNCT
ejpam-2498	189	17	t	t	NOUN
ejpam-2498	189	18	)	)	PUNCT
ejpam-2498	189	19	=	=	SYM
ejpam-2498	190	1	n	n	PROPN
ejpam-2498	190	2	∑	∑	PUNCT
ejpam-2498	190	3	k=0	k=0	PROPN
ejpam-2498	190	4	bk(m)t	bk(m)t	PROPN
ejpam-2498	191	1	k	k	X
ejpam-2498	191	2	(	(	PUNCT
ejpam-2498	191	3	12	12	NUM
ejpam-2498	191	4	)	)	PUNCT
ejpam-2498	191	5	where	where	SCONJ
ejpam-2498	191	6	bk(m	bk(m	PUNCT
ejpam-2498	191	7	)	)	PUNCT
ejpam-2498	191	8	is	be	AUX
ejpam-2498	191	9	the	the	DET
ejpam-2498	191	10	k	k	PROPN
ejpam-2498	191	11	-	-	PUNCT
ejpam-2498	191	12	th	th	VERB
ejpam-2498	191	13	betti	betti	ADJ
ejpam-2498	191	14	number	number	NOUN
ejpam-2498	191	15	of	of	ADP
ejpam-2498	191	16	m.	m.	NOUN
ejpam-2498	191	17	definition	definition	NOUN
ejpam-2498	191	18	5	5	NUM
ejpam-2498	191	19	.	.	PUNCT
ejpam-2498	192	1	let	let	VERB
ejpam-2498	192	2	f	f	NOUN
ejpam-2498	192	3	:	:	PUNCT
ejpam-2498	192	4	m	m	VERB
ejpam-2498	192	5	→	→	SYM
ejpam-2498	192	6	r	r	NOUN
ejpam-2498	192	7	be	be	AUX
ejpam-2498	192	8	a	a	DET
ejpam-2498	192	9	morse	morse	ADJ
ejpam-2498	192	10	function	function	NOUN
ejpam-2498	192	11	.	.	PUNCT
ejpam-2498	193	1	then	then	ADV
ejpam-2498	193	2	,	,	PUNCT
ejpam-2498	193	3	the	the	DET
ejpam-2498	193	4	morse	morse	ADJ
ejpam-2498	193	5	polynomial	polynomial	NOUN
ejpam-2498	193	6	of	of	ADP
ejpam-2498	193	7	f	f	PROPN
ejpam-2498	193	8	is	be	AUX
ejpam-2498	193	9	defined	define	VERB
ejpam-2498	193	10	to	to	PART
ejpam-2498	193	11	be	be	AUX
ejpam-2498	193	12	pf	pf	PROPN
ejpam-2498	193	13	(	(	PUNCT
ejpam-2498	193	14	t	t	NOUN
ejpam-2498	193	15	)	)	PUNCT
ejpam-2498	193	16	=	=	SYM
ejpam-2498	194	1	n	n	PROPN
ejpam-2498	194	2	∑	∑	ADP
ejpam-2498	194	3	k=0	k=0	PROPN
ejpam-2498	194	4	µk	µk	PRON
ejpam-2498	194	5	tk	tk	PROPN
ejpam-2498	194	6	(	(	PUNCT
ejpam-2498	194	7	13	13	NUM
ejpam-2498	194	8	)	)	PUNCT
ejpam-2498	194	9	where	where	SCONJ
ejpam-2498	194	10	µk	µk	NOUN
ejpam-2498	194	11	is	be	AUX
ejpam-2498	194	12	the	the	DET
ejpam-2498	194	13	number	number	NOUN
ejpam-2498	194	14	of	of	ADP
ejpam-2498	194	15	critical	critical	ADJ
ejpam-2498	194	16	points	point	NOUN
ejpam-2498	194	17	of	of	ADP
ejpam-2498	194	18	f	f	PROPN
ejpam-2498	194	19	of	of	ADP
ejpam-2498	194	20	index	index	PROPN
ejpam-2498	194	21	k.	k.	PROPN
ejpam-2498	194	22	theorem	theorem	VERB
ejpam-2498	194	23	2	2	NUM
ejpam-2498	194	24	(	(	PUNCT
ejpam-2498	194	25	the	the	DET
ejpam-2498	194	26	morse	morse	PROPN
ejpam-2498	194	27	inequality	inequality	NOUN
ejpam-2498	194	28	)	)	PUNCT
ejpam-2498	194	29	.	.	PUNCT
ejpam-2498	195	1	let	let	VERB
ejpam-2498	195	2	f	f	NOUN
ejpam-2498	195	3	:	:	PUNCT
ejpam-2498	195	4	m	m	VERB
ejpam-2498	195	5	→	→	SYM
ejpam-2498	195	6	r	r	NOUN
ejpam-2498	195	7	be	be	AUX
ejpam-2498	195	8	a	a	DET
ejpam-2498	195	9	morse	morse	ADJ
ejpam-2498	195	10	function	function	NOUN
ejpam-2498	195	11	on	on	ADP
ejpam-2498	195	12	a	a	DET
ejpam-2498	195	13	smooth	smooth	ADJ
ejpam-2498	195	14	manifold	manifold	ADJ
ejpam-2498	195	15	m.	m.	NOUN
ejpam-2498	195	16	then	then	ADV
ejpam-2498	195	17	,	,	PUNCT
ejpam-2498	195	18	there	there	PRON
ejpam-2498	195	19	exists	exist	VERB
ejpam-2498	195	20	a	a	DET
ejpam-2498	195	21	polynomial	polynomial	ADJ
ejpam-2498	195	22	r(t	r(t	NOUN
ejpam-2498	195	23	)	)	PUNCT
ejpam-2498	195	24	with	with	ADP
ejpam-2498	195	25	non	non	ADJ
ejpam-2498	195	26	-	-	ADJ
ejpam-2498	195	27	negative	negative	ADJ
ejpam-2498	195	28	integer	integer	NOUN
ejpam-2498	195	29	coefficients	coefficient	NOUN
ejpam-2498	195	30	such	such	ADJ
ejpam-2498	195	31	that	that	SCONJ
ejpam-2498	195	32	pf	pf	PROPN
ejpam-2498	195	33	(	(	PUNCT
ejpam-2498	195	34	t	t	PROPN
ejpam-2498	195	35	)	)	PUNCT
ejpam-2498	195	36	=	=	SYM
ejpam-2498	196	1	pm	pm	NOUN
ejpam-2498	196	2	(	(	PUNCT
ejpam-2498	196	3	t	t	NOUN
ejpam-2498	196	4	)	)	PUNCT
ejpam-2498	196	5	+	+	CCONJ
ejpam-2498	196	6	(	(	PUNCT
ejpam-2498	196	7	1	1	NUM
ejpam-2498	196	8	+	+	NUM
ejpam-2498	196	9	t)r(t	t)r(t	NOUN
ejpam-2498	196	10	)	)	PUNCT
ejpam-2498	196	11	.	.	PUNCT
ejpam-2498	197	1	one	one	PRON
ejpam-2498	197	2	may	may	AUX
ejpam-2498	197	3	refer	refer	VERB
ejpam-2498	197	4	to	to	ADP
ejpam-2498	197	5	[	[	X
ejpam-2498	197	6	7	7	X
ejpam-2498	197	7	]	]	PUNCT
ejpam-2498	197	8	for	for	ADP
ejpam-2498	197	9	proof	proof	NOUN
ejpam-2498	197	10	.	.	PUNCT
ejpam-2498	198	1	a	a	DET
ejpam-2498	198	2	morse	morse	ADJ
ejpam-2498	198	3	function	function	NOUN
ejpam-2498	198	4	f	f	NOUN
ejpam-2498	198	5	:	:	PUNCT
ejpam-2498	198	6	m	m	AUX
ejpam-2498	198	7	→	→	SYM
ejpam-2498	198	8	r	r	NOUN
ejpam-2498	198	9	is	be	AUX
ejpam-2498	198	10	called	call	VERB
ejpam-2498	198	11	a	a	DET
ejpam-2498	198	12	perfect	perfect	ADJ
ejpam-2498	198	13	morse	morse	NOUN
ejpam-2498	198	14	function	function	NOUN
ejpam-2498	198	15	if	if	SCONJ
ejpam-2498	198	16	pf	pf	PROPN
ejpam-2498	198	17	(	(	PUNCT
ejpam-2498	198	18	t	t	PROPN
ejpam-2498	198	19	)	)	PUNCT
ejpam-2498	198	20	=	=	SYM
ejpam-2498	199	1	pm	pm	NOUN
ejpam-2498	199	2	(	(	PUNCT
ejpam-2498	199	3	t	t	NOUN
ejpam-2498	199	4	)	)	PUNCT
ejpam-2498	200	1	[	[	X
ejpam-2498	200	2	7	7	NUM
ejpam-2498	200	3	]	]	PUNCT
ejpam-2498	200	4	.	.	PUNCT
ejpam-2498	201	1	now	now	ADV
ejpam-2498	201	2	,	,	PUNCT
ejpam-2498	201	3	we	we	PRON
ejpam-2498	201	4	show	show	VERB
ejpam-2498	201	5	that	that	SCONJ
ejpam-2498	201	6	the	the	DET
ejpam-2498	201	7	function	function	NOUN
ejpam-2498	201	8	fc	fc	PROPN
ejpam-2498	201	9	on	on	ADP
ejpam-2498	201	10	so(n	so(n	NOUN
ejpam-2498	201	11	)	)	PUNCT
ejpam-2498	201	12	defined	define	VERB
ejpam-2498	201	13	in	in	ADP
ejpam-2498	201	14	the	the	DET
ejpam-2498	201	15	previous	previous	ADJ
ejpam-2498	201	16	section	section	NOUN
ejpam-2498	201	17	is	be	AUX
ejpam-2498	201	18	also	also	ADV
ejpam-2498	201	19	a	a	DET
ejpam-2498	201	20	perfect	perfect	ADJ
ejpam-2498	201	21	morse	morse	NOUN
ejpam-2498	201	22	function	function	NOUN
ejpam-2498	201	23	.	.	PUNCT
ejpam-2498	202	1	theorem	theorem	NOUN
ejpam-2498	202	2	3	3	NUM
ejpam-2498	202	3	.	.	PUNCT
ejpam-2498	203	1	the	the	DET
ejpam-2498	203	2	function	function	NOUN
ejpam-2498	203	3	fc	fc	PROPN
ejpam-2498	203	4	:	:	PUNCT
ejpam-2498	203	5	so(n)→	so(n)→	VERB
ejpam-2498	203	6	r	r	NOUN
ejpam-2498	203	7	,	,	PUNCT
ejpam-2498	203	8	fc(a	fc(a	X
ejpam-2498	203	9	)	)	PUNCT
ejpam-2498	203	10	:	:	PUNCT
ejpam-2498	204	1	=	=	PUNCT
ejpam-2498	204	2	〈	〈	PROPN
ejpam-2498	204	3	c	c	PROPN
ejpam-2498	204	4	,	,	PUNCT
ejpam-2498	204	5	a	a	DET
ejpam-2498	204	6	〉	〉	NOUN
ejpam-2498	204	7	is	be	AUX
ejpam-2498	204	8	a	a	DET
ejpam-2498	204	9	perfect	perfect	ADJ
ejpam-2498	204	10	morse	morse	NOUN
ejpam-2498	204	11	function	function	NOUN
ejpam-2498	204	12	where	where	SCONJ
ejpam-2498	204	13	c	c	PROPN
ejpam-2498	204	14	∈	∈	PROPN
ejpam-2498	204	15	sn(r	sn(r	PRON
ejpam-2498	204	16	)	)	PUNCT
ejpam-2498	204	17	.	.	PUNCT
ejpam-2498	205	1	m.	m.	NOUN
ejpam-2498	205	2	solgun	solgun	PROPN
ejpam-2498	205	3	/	/	SYM
ejpam-2498	205	4	eur	eur	PROPN
ejpam-2498	205	5	.	.	PUNCT
ejpam-2498	206	1	j.	j.	PROPN
ejpam-2498	206	2	pure	pure	PROPN
ejpam-2498	206	3	appl	appl	PROPN
ejpam-2498	206	4	.	.	PROPN
ejpam-2498	206	5	math	math	PROPN
ejpam-2498	206	6	,	,	PUNCT
ejpam-2498	206	7	9	9	NUM
ejpam-2498	206	8	(	(	PUNCT
ejpam-2498	206	9	2016	2016	NUM
ejpam-2498	206	10	)	)	PUNCT
ejpam-2498	206	11	,	,	PUNCT
ejpam-2498	206	12	314	314	NUM
ejpam-2498	206	13	-	-	SYM
ejpam-2498	206	14	321	321	NUM
ejpam-2498	206	15	320	320	NUM
ejpam-2498	206	16	proof	proof	NOUN
ejpam-2498	206	17	.	.	PUNCT
ejpam-2498	207	1	first	first	ADV
ejpam-2498	207	2	we	we	PRON
ejpam-2498	207	3	show	show	VERB
ejpam-2498	207	4	that	that	SCONJ
ejpam-2498	207	5	the	the	DET
ejpam-2498	207	6	morse	morse	ADJ
ejpam-2498	207	7	polynomial	polynomial	NOUN
ejpam-2498	207	8	is	be	AUX
ejpam-2498	207	9	,	,	PUNCT
ejpam-2498	207	10	pfc	pfc	PROPN
ejpam-2498	207	11	(	(	PUNCT
ejpam-2498	207	12	t	t	PROPN
ejpam-2498	207	13	)	)	PUNCT
ejpam-2498	207	14	=	=	PUNCT
ejpam-2498	207	15	(	(	PUNCT
ejpam-2498	207	16	1	1	NUM
ejpam-2498	207	17	+	+	NUM
ejpam-2498	207	18	t)(1	t)(1	NOUN
ejpam-2498	207	19	+	+	ADJ
ejpam-2498	208	1	t2	t2	NOUN
ejpam-2498	209	1	)	)	PUNCT
ejpam-2498	210	1	·	·	PUNCT
ejpam-2498	210	2	·	·	PUNCT
ejpam-2498	210	3	·	·	PUNCT
ejpam-2498	210	4	(	(	PUNCT
ejpam-2498	210	5	1	1	NUM
ejpam-2498	210	6	+	+	CCONJ
ejpam-2498	210	7	tn−1	tn−1	ADJ
ejpam-2498	210	8	)	)	PUNCT
ejpam-2498	210	9	.	.	PUNCT
ejpam-2498	211	1	(	(	PUNCT
ejpam-2498	211	2	14	14	NUM
ejpam-2498	211	3	)	)	PUNCT
ejpam-2498	211	4	we	we	PRON
ejpam-2498	211	5	use	use	VERB
ejpam-2498	211	6	induction	induction	NOUN
ejpam-2498	211	7	method	method	NOUN
ejpam-2498	211	8	.	.	PUNCT
ejpam-2498	212	1	for	for	ADP
ejpam-2498	212	2	making	make	VERB
ejpam-2498	212	3	it	it	PRON
ejpam-2498	212	4	easier	easy	ADJ
ejpam-2498	212	5	,	,	PUNCT
ejpam-2498	212	6	we	we	PRON
ejpam-2498	212	7	label	label	VERB
ejpam-2498	212	8	the	the	DET
ejpam-2498	212	9	function	function	NOUN
ejpam-2498	212	10	fc	fc	PROPN
ejpam-2498	212	11	with	with	ADP
ejpam-2498	212	12	n	n	PROPN
ejpam-2498	212	13	as	as	ADP
ejpam-2498	212	14	fc	fc	PROPN
ejpam-2498	212	15	n	n	PROPN
ejpam-2498	212	16	:	:	PUNCT
ejpam-2498	212	17	so(n)→	so(n)→	PROPN
ejpam-2498	212	18	r.	r.	PROPN
ejpam-2498	212	19	trivially	trivially	ADV
ejpam-2498	212	20	,	,	PUNCT
ejpam-2498	212	21	for	for	ADP
ejpam-2498	212	22	n=	n=	ADJ
ejpam-2498	212	23	1	1	NUM
ejpam-2498	212	24	,	,	PUNCT
ejpam-2498	212	25	pfc	pfc	NOUN
ejpam-2498	212	26	1	1	NUM
ejpam-2498	212	27	(	(	PUNCT
ejpam-2498	212	28	t	t	NOUN
ejpam-2498	212	29	)	)	PUNCT
ejpam-2498	212	30	=	=	SYM
ejpam-2498	212	31	1	1	NUM
ejpam-2498	212	32	and	and	CCONJ
ejpam-2498	212	33	for	for	ADP
ejpam-2498	212	34	n=	n=	ADJ
ejpam-2498	212	35	2	2	NUM
ejpam-2498	212	36	,	,	PUNCT
ejpam-2498	212	37	pfc	pfc	NOUN
ejpam-2498	212	38	2	2	NUM
ejpam-2498	212	39	(	(	PUNCT
ejpam-2498	212	40	t	t	NOUN
ejpam-2498	212	41	)	)	PUNCT
ejpam-2498	212	42	=	=	SYM
ejpam-2498	213	1	1	1	NUM
ejpam-2498	213	2	+	+	NUM
ejpam-2498	213	3	t.	t.	NOUN
ejpam-2498	213	4	assume	assume	VERB
ejpam-2498	213	5	that	that	SCONJ
ejpam-2498	213	6	pfc	pfc	NOUN
ejpam-2498	213	7	n	n	PROPN
ejpam-2498	213	8	(	(	PUNCT
ejpam-2498	213	9	t	t	PROPN
ejpam-2498	213	10	)	)	PUNCT
ejpam-2498	213	11	=	=	PUNCT
ejpam-2498	214	1	(	(	PUNCT
ejpam-2498	214	2	1	1	NUM
ejpam-2498	214	3	+	+	NUM
ejpam-2498	214	4	t)(1	t)(1	NOUN
ejpam-2498	214	5	+	+	ADJ
ejpam-2498	214	6	t2	t2	NOUN
ejpam-2498	214	7	)	)	PUNCT
ejpam-2498	215	1	+	+	CCONJ
ejpam-2498	215	2	.	.	PUNCT
ejpam-2498	215	3	.	.	PUNCT
ejpam-2498	216	1	.+	.+	NOUN
ejpam-2498	216	2	(	(	PUNCT
ejpam-2498	216	3	1	1	NUM
ejpam-2498	216	4	+	+	CCONJ
ejpam-2498	216	5	tn−1	tn−1	ADJ
ejpam-2498	216	6	)	)	PUNCT
ejpam-2498	216	7	.	.	PUNCT
ejpam-2498	217	1	then	then	ADV
ejpam-2498	217	2	,	,	PUNCT
ejpam-2498	217	3	we	we	PRON
ejpam-2498	217	4	need	need	VERB
ejpam-2498	217	5	to	to	PART
ejpam-2498	217	6	show	show	VERB
ejpam-2498	217	7	that	that	DET
ejpam-2498	217	8	pfc	pfc	NOUN
ejpam-2498	217	9	n+1	n+1	PROPN
ejpam-2498	217	10	(	(	PUNCT
ejpam-2498	217	11	t	t	NOUN
ejpam-2498	217	12	)	)	PUNCT
ejpam-2498	217	13	satisfies	satisfy	VERB
ejpam-2498	217	14	the	the	DET
ejpam-2498	217	15	form	form	NOUN
ejpam-2498	217	16	(	(	PUNCT
ejpam-2498	217	17	14	14	NUM
ejpam-2498	217	18	)	)	PUNCT
ejpam-2498	217	19	.	.	PUNCT
ejpam-2498	218	1	we	we	PRON
ejpam-2498	218	2	may	may	AUX
ejpam-2498	218	3	consider	consider	VERB
ejpam-2498	218	4	that	that	SCONJ
ejpam-2498	218	5	so(n+	so(n+	PROPN
ejpam-2498	218	6	1	1	NUM
ejpam-2498	218	7	)	)	PUNCT
ejpam-2498	218	8	gets	get	VERB
ejpam-2498	218	9	all	all	DET
ejpam-2498	218	10	the	the	DET
ejpam-2498	218	11	critical	critical	ADJ
ejpam-2498	218	12	points	point	NOUN
ejpam-2498	218	13	from	from	ADP
ejpam-2498	218	14	so(n	so(n	PROPN
ejpam-2498	218	15	)	)	PUNCT
ejpam-2498	218	16	with	with	ADP
ejpam-2498	218	17	extra	extra	ADJ
ejpam-2498	218	18	bottom	bottom	ADJ
ejpam-2498	218	19	entry	entry	NOUN
ejpam-2498	218	20	(	(	PUNCT
ejpam-2498	218	21	(	(	PUNCT
ejpam-2498	218	22	n+	n+	NUM
ejpam-2498	218	23	1)-th	1)-th	NUM
ejpam-2498	218	24	diagonal	diagonal	ADJ
ejpam-2498	218	25	entry	entry	NOUN
ejpam-2498	218	26	)	)	PUNCT
ejpam-2498	218	27	,	,	PUNCT
ejpam-2498	218	28	which	which	PRON
ejpam-2498	218	29	is	be	AUX
ejpam-2498	218	30	either	either	CCONJ
ejpam-2498	218	31	+1	+1	PROPN
ejpam-2498	218	32	or	or	CCONJ
ejpam-2498	218	33	-1	-1	PUNCT
ejpam-2498	218	34	.	.	PUNCT
ejpam-2498	219	1	say	say	VERB
ejpam-2498	219	2	the	the	DET
ejpam-2498	219	3	set	set	NOUN
ejpam-2498	219	4	of	of	ADP
ejpam-2498	219	5	all	all	DET
ejpam-2498	219	6	these	these	DET
ejpam-2498	219	7	points	point	NOUN
ejpam-2498	219	8	are	be	AUX
ejpam-2498	219	9	c+	c+	ADV
ejpam-2498	219	10	n+1	n+1	ADV
ejpam-2498	219	11	and	and	CCONJ
ejpam-2498	219	12	c−	c−	NOUN
ejpam-2498	219	13	n+1	n+1	NUM
ejpam-2498	219	14	respectively	respectively	ADV
ejpam-2498	219	15	.	.	PUNCT
ejpam-2498	220	1	let	let	VERB
ejpam-2498	220	2	a∈	a∈	PROPN
ejpam-2498	220	3	c−	c−	NOUN
ejpam-2498	220	4	n+1	n+1	PROPN
ejpam-2498	220	5	.	.	PUNCT
ejpam-2498	221	1	then	then	ADV
ejpam-2498	221	2	we	we	PRON
ejpam-2498	221	3	have	have	VERB
ejpam-2498	221	4	ã∈	ã∈	PROPN
ejpam-2498	221	5	o(n	o(n	NOUN
ejpam-2498	221	6	)	)	PUNCT
ejpam-2498	221	7	such	such	ADJ
ejpam-2498	221	8	that	that	SCONJ
ejpam-2498	221	9	,	,	PUNCT
ejpam-2498	221	10	a	a	PRON
ejpam-2498	221	11	is	be	AUX
ejpam-2498	221	12	the	the	DET
ejpam-2498	221	13	matrix	matrix	NOUN
ejpam-2498	221	14	ã	ã	PROPN
ejpam-2498	221	15	with	with	ADP
ejpam-2498	221	16	extra	extra	ADJ
ejpam-2498	221	17	bottom	bottom	ADJ
ejpam-2498	221	18	entry	entry	NOUN
ejpam-2498	221	19	-1	-1	NOUN
ejpam-2498	221	20	.	.	PUNCT
ejpam-2498	222	1	then	then	ADV
ejpam-2498	222	2	,	,	PUNCT
ejpam-2498	222	3	by	by	ADP
ejpam-2498	222	4	the	the	DET
ejpam-2498	222	5	definition	definition	NOUN
ejpam-2498	222	6	of	of	ADP
ejpam-2498	222	7	index	index	NOUN
ejpam-2498	222	8	,	,	PUNCT
ejpam-2498	222	9	we	we	PRON
ejpam-2498	222	10	obtain	obtain	VERB
ejpam-2498	222	11	ind(a	ind(a	PROPN
ejpam-2498	222	12	)	)	PUNCT
ejpam-2498	222	13	=	=	SYM
ejpam-2498	222	14	ind(ã	ind(ã	NOUN
ejpam-2498	222	15	)	)	PUNCT
ejpam-2498	222	16	.	.	PUNCT
ejpam-2498	223	1	thus	thus	ADV
ejpam-2498	223	2	,	,	PUNCT
ejpam-2498	223	3	for	for	ADP
ejpam-2498	223	4	the	the	DET
ejpam-2498	223	5	elements	element	NOUN
ejpam-2498	223	6	of	of	ADP
ejpam-2498	223	7	c−	c−	NOUN
ejpam-2498	223	8	n+1	n+1	PROPN
ejpam-2498	223	9	the	the	DET
ejpam-2498	223	10	equation	equation	NOUN
ejpam-2498	223	11	(	(	PUNCT
ejpam-2498	223	12	14	14	NUM
ejpam-2498	223	13	)	)	PUNCT
ejpam-2498	223	14	holds	hold	VERB
ejpam-2498	223	15	.	.	PUNCT
ejpam-2498	224	1	let	let	VERB
ejpam-2498	224	2	a∈	a∈	PROPN
ejpam-2498	224	3	c+	c+	VERB
ejpam-2498	224	4	n+1	n+1	PROPN
ejpam-2498	224	5	.	.	PUNCT
ejpam-2498	225	1	then	then	ADV
ejpam-2498	225	2	we	we	PRON
ejpam-2498	225	3	have	have	VERB
ejpam-2498	225	4	ã∈	ã∈	ADJ
ejpam-2498	225	5	so(n	so(n	NOUN
ejpam-2498	225	6	)	)	PUNCT
ejpam-2498	225	7	such	such	ADJ
ejpam-2498	225	8	that	that	SCONJ
ejpam-2498	225	9	,	,	PUNCT
ejpam-2498	225	10	a	a	PRON
ejpam-2498	225	11	is	be	AUX
ejpam-2498	225	12	the	the	DET
ejpam-2498	225	13	matrix	matrix	NOUN
ejpam-2498	225	14	with	with	ADP
ejpam-2498	225	15	ã	ã	PROPN
ejpam-2498	225	16	with	with	ADP
ejpam-2498	225	17	the	the	DET
ejpam-2498	225	18	bottom	bottom	ADJ
ejpam-2498	225	19	entry	entry	NOUN
ejpam-2498	225	20	+1	+1	PROPN
ejpam-2498	225	21	.	.	PUNCT
ejpam-2498	226	1	thus	thus	ADV
ejpam-2498	226	2	,	,	PUNCT
ejpam-2498	226	3	by	by	ADP
ejpam-2498	226	4	the	the	DET
ejpam-2498	226	5	definition	definition	NOUN
ejpam-2498	226	6	of	of	ADP
ejpam-2498	226	7	index	index	NOUN
ejpam-2498	226	8	,	,	PUNCT
ejpam-2498	226	9	we	we	PRON
ejpam-2498	226	10	obtain	obtain	VERB
ejpam-2498	226	11	ind(a	ind(a	PROPN
ejpam-2498	226	12	)	)	PUNCT
ejpam-2498	226	13	=	=	SYM
ejpam-2498	226	14	ind(ã	ind(ã	NOUN
ejpam-2498	226	15	)	)	PUNCT
ejpam-2498	227	1	+	+	CCONJ
ejpam-2498	227	2	n.	n.	NOUN
ejpam-2498	227	3	so	so	ADV
ejpam-2498	227	4	,	,	PUNCT
ejpam-2498	227	5	by	by	ADP
ejpam-2498	227	6	the	the	DET
ejpam-2498	227	7	definition	definition	NOUN
ejpam-2498	227	8	of	of	ADP
ejpam-2498	227	9	morse	morse	ADJ
ejpam-2498	227	10	polynomial	polynomial	ADJ
ejpam-2498	227	11	,	,	PUNCT
ejpam-2498	227	12	we	we	PRON
ejpam-2498	227	13	gain	gain	VERB
ejpam-2498	227	14	pfc	pfc	NOUN
ejpam-2498	227	15	n+1	n+1	PROPN
ejpam-2498	227	16	(	(	PUNCT
ejpam-2498	227	17	t	t	NOUN
ejpam-2498	227	18	)	)	PUNCT
ejpam-2498	228	1	=	=	SYM
ejpam-2498	228	2	pfc	pfc	NOUN
ejpam-2498	228	3	n	n	CCONJ
ejpam-2498	228	4	(	(	PUNCT
ejpam-2498	228	5	t)(1	t)(1	PROPN
ejpam-2498	228	6	+	+	X
ejpam-2498	228	7	tn	tn	NOUN
ejpam-2498	228	8	)	)	PUNCT
ejpam-2498	228	9	=	=	PUNCT
ejpam-2498	228	10	(	(	PUNCT
ejpam-2498	228	11	1	1	NUM
ejpam-2498	228	12	+	+	NUM
ejpam-2498	228	13	t)(1	t)(1	NOUN
ejpam-2498	228	14	+	+	ADJ
ejpam-2498	228	15	t2	t2	NOUN
ejpam-2498	228	16	)	)	PUNCT
ejpam-2498	228	17	.	.	PUNCT
ejpam-2498	228	18	.	.	PUNCT
ejpam-2498	228	19	.	.	PUNCT
ejpam-2498	229	1	(	(	PUNCT
ejpam-2498	229	2	1	1	NUM
ejpam-2498	229	3	+	+	NUM
ejpam-2498	229	4	tn−1)(1	tn−1)(1	NOUN
ejpam-2498	229	5	+	+	X
ejpam-2498	229	6	tn	tn	NOUN
ejpam-2498	229	7	)	)	PUNCT
ejpam-2498	229	8	.	.	PUNCT
ejpam-2498	230	1	(	(	PUNCT
ejpam-2498	230	2	15	15	NUM
ejpam-2498	230	3	)	)	PUNCT
ejpam-2498	230	4	now	now	ADV
ejpam-2498	230	5	,	,	PUNCT
ejpam-2498	230	6	we	we	PRON
ejpam-2498	230	7	find	find	VERB
ejpam-2498	230	8	out	out	ADP
ejpam-2498	230	9	the	the	DET
ejpam-2498	230	10	poincaré	poincaré	PROPN
ejpam-2498	230	11	polynomial	polynomial	PROPN
ejpam-2498	230	12	of	of	ADP
ejpam-2498	230	13	so(n	so(n	PROPN
ejpam-2498	230	14	)	)	PUNCT
ejpam-2498	230	15	.	.	PUNCT
ejpam-2498	231	1	the	the	DET
ejpam-2498	231	2	graded	grade	VERB
ejpam-2498	231	3	abelian	abelian	PROPN
ejpam-2498	231	4	group	group	NOUN
ejpam-2498	231	5	h∗(so(n),z2	h∗(so(n),z2	PROPN
ejpam-2498	231	6	)	)	PUNCT
ejpam-2498	231	7	is	be	AUX
ejpam-2498	231	8	isomorphic	isomorphic	ADJ
ejpam-2498	231	9	to	to	ADP
ejpam-2498	231	10	the	the	DET
ejpam-2498	231	11	graded	grade	VERB
ejpam-2498	231	12	group	group	NOUN
ejpam-2498	231	13	coming	come	VERB
ejpam-2498	231	14	from	from	ADP
ejpam-2498	231	15	the	the	DET
ejpam-2498	231	16	exterior	exterior	ADJ
ejpam-2498	231	17	algebra	algebra	NOUN
ejpam-2498	231	18	[	[	X
ejpam-2498	231	19	2	2	NUM
ejpam-2498	231	20	]	]	PUNCT
ejpam-2498	231	21	∧z2	∧z2	PROPN
ejpam-2498	231	22	[	[	X
ejpam-2498	231	23	e1	e1	PROPN
ejpam-2498	231	24	,	,	PUNCT
ejpam-2498	231	25	e2	e2	PROPN
ejpam-2498	231	26	,	,	PUNCT
ejpam-2498	231	27	.	.	PUNCT
ejpam-2498	231	28	.	.	PUNCT
ejpam-2498	232	1	.	.	PUNCT
ejpam-2498	233	1	,	,	PUNCT
ejpam-2498	233	2	en−1	en−1	PROPN
ejpam-2498	233	3	]	]	PUNCT
ejpam-2498	233	4	.	.	PUNCT
ejpam-2498	234	1	let	let	AUX
ejpam-2498	234	2	say	say	VERB
ejpam-2498	234	3	a(n	a(n	NOUN
ejpam-2498	234	4	)	)	PUNCT
ejpam-2498	235	1	=	=	PUNCT
ejpam-2498	236	1	∧z2	∧z2	PROPN
ejpam-2498	237	1	[	[	X
ejpam-2498	237	2	e1	e1	PROPN
ejpam-2498	237	3	,	,	PUNCT
ejpam-2498	237	4	e2	e2	PROPN
ejpam-2498	237	5	,	,	PUNCT
ejpam-2498	237	6	.	.	PUNCT
ejpam-2498	237	7	.	.	PUNCT
ejpam-2498	237	8	.	.	PUNCT
ejpam-2498	238	1	,	,	PUNCT
ejpam-2498	238	2	en−1	en−1	PROPN
ejpam-2498	238	3	]	]	PUNCT
ejpam-2498	238	4	where	where	SCONJ
ejpam-2498	238	5	the	the	DET
ejpam-2498	238	6	degree	degree	NOUN
ejpam-2498	238	7	of	of	ADP
ejpam-2498	238	8	ei	ei	NOUN
ejpam-2498	238	9	,	,	PUNCT
ejpam-2498	238	10	|ei	|ei	X
ejpam-2498	238	11	|=	|=	NOUN
ejpam-2498	238	12	i.	i.	NOUN
ejpam-2498	238	13	then	then	ADV
ejpam-2498	238	14	,	,	PUNCT
ejpam-2498	238	15	we	we	PRON
ejpam-2498	238	16	obtain	obtain	VERB
ejpam-2498	238	17	|ei1	|ei1	PROPN
ejpam-2498	238	18	∧	∧	NOUN
ejpam-2498	238	19	ei2	ei2	NOUN
ejpam-2498	238	20	∧	∧	PROPN
ejpam-2498	238	21	.	.	PUNCT
ejpam-2498	238	22	.	.	PUNCT
ejpam-2498	238	23	.∧	.∧	PUNCT
ejpam-2498	239	1	eik	eik	PROPN
ejpam-2498	239	2	|=	|=	VERB
ejpam-2498	240	1	k	k	NOUN
ejpam-2498	240	2	∑	∑	PUNCT
ejpam-2498	240	3	j=1	j=1	X
ejpam-2498	240	4	|ei	|ei	PUNCT
ejpam-2498	240	5	j	j	NOUN
ejpam-2498	240	6	|=	|=	PUNCT
ejpam-2498	240	7	k	k	NOUN
ejpam-2498	240	8	∑	∑	PUNCT
ejpam-2498	240	9	j=1	j=1	PROPN
ejpam-2498	241	1	i	i	PRON
ejpam-2498	241	2	j	j	PROPN
ejpam-2498	241	3	.	.	PUNCT
ejpam-2498	242	1	if	if	SCONJ
ejpam-2498	242	2	we	we	PRON
ejpam-2498	242	3	define	define	VERB
ejpam-2498	242	4	a(n)k	a(n)k	PROPN
ejpam-2498	242	5	=	=	PUNCT
ejpam-2498	242	6	dimz2(a(n)k	dimz2(a(n)k	PROPN
ejpam-2498	242	7	)	)	PUNCT
ejpam-2498	242	8	,	,	PUNCT
ejpam-2498	242	9	then	then	ADV
ejpam-2498	242	10	by	by	ADP
ejpam-2498	242	11	the	the	DET
ejpam-2498	242	12	result	result	NOUN
ejpam-2498	242	13	in	in	ADP
ejpam-2498	242	14	[	[	X
ejpam-2498	242	15	2	2	NUM
ejpam-2498	242	16	]	]	PUNCT
ejpam-2498	242	17	,	,	PUNCT
ejpam-2498	242	18	a(n)k	a(n)k	PROPN
ejpam-2498	242	19	is	be	AUX
ejpam-2498	242	20	nothing	nothing	PRON
ejpam-2498	242	21	but	but	SCONJ
ejpam-2498	242	22	the	the	DET
ejpam-2498	242	23	k	k	PROPN
ejpam-2498	242	24	-	-	PUNCT
ejpam-2498	242	25	th	th	VERB
ejpam-2498	242	26	betti	betti	ADJ
ejpam-2498	242	27	number	number	NOUN
ejpam-2498	242	28	of	of	ADP
ejpam-2498	242	29	so(n	so(n	PROPN
ejpam-2498	242	30	)	)	PUNCT
ejpam-2498	242	31	.	.	PUNCT
ejpam-2498	243	1	hence	hence	ADV
ejpam-2498	243	2	,	,	PUNCT
ejpam-2498	243	3	the	the	DET
ejpam-2498	243	4	polynomial	polynomial	ADJ
ejpam-2498	243	5	p(a(n	p(a(n	NOUN
ejpam-2498	243	6	)	)	PUNCT
ejpam-2498	243	7	)	)	PUNCT
ejpam-2498	244	1	=	=	SYM
ejpam-2498	244	2	∞	∞	NUM
ejpam-2498	244	3	∑	∑	PUNCT
ejpam-2498	244	4	i=0	i=0	PROPN
ejpam-2498	244	5	a(n)i	a(n)i	PROPN
ejpam-2498	245	1	t	t	X
ejpam-2498	245	2	i	i	PRON
ejpam-2498	245	3	is	be	AUX
ejpam-2498	245	4	the	the	DET
ejpam-2498	245	5	poincaré	poincaré	PROPN
ejpam-2498	245	6	polynomial	polynomial	PROPN
ejpam-2498	245	7	of	of	ADP
ejpam-2498	245	8	so(n	so(n	PROPN
ejpam-2498	245	9	)	)	PUNCT
ejpam-2498	245	10	.	.	PUNCT
ejpam-2498	246	1	now	now	ADV
ejpam-2498	246	2	,	,	PUNCT
ejpam-2498	246	3	our	our	PRON
ejpam-2498	246	4	claim	claim	NOUN
ejpam-2498	246	5	is	be	AUX
ejpam-2498	246	6	that	that	SCONJ
ejpam-2498	246	7	the	the	DET
ejpam-2498	246	8	poincaré	poincaré	PROPN
ejpam-2498	246	9	polynomial	polynomial	PROPN
ejpam-2498	246	10	of	of	ADP
ejpam-2498	246	11	so(n	so(n	PROPN
ejpam-2498	246	12	)	)	PUNCT
ejpam-2498	246	13	is	be	AUX
ejpam-2498	246	14	p(a(n	p(a(n	NOUN
ejpam-2498	246	15	)	)	PUNCT
ejpam-2498	246	16	)	)	PUNCT
ejpam-2498	247	1	=	=	PUNCT
ejpam-2498	247	2	(	(	PUNCT
ejpam-2498	247	3	1	1	NUM
ejpam-2498	247	4	+	+	NUM
ejpam-2498	247	5	t)(1	t)(1	NOUN
ejpam-2498	247	6	+	+	ADJ
ejpam-2498	247	7	t2	t2	NOUN
ejpam-2498	247	8	)	)	PUNCT
ejpam-2498	247	9	.	.	PUNCT
ejpam-2498	247	10	.	.	PUNCT
ejpam-2498	247	11	.	.	PUNCT
ejpam-2498	248	1	(	(	PUNCT
ejpam-2498	248	2	1	1	NUM
ejpam-2498	248	3	+	+	CCONJ
ejpam-2498	248	4	tn−1	tn−1	ADJ
ejpam-2498	248	5	)	)	PUNCT
ejpam-2498	248	6	.	.	PUNCT
ejpam-2498	249	1	references	reference	NOUN
ejpam-2498	249	2	321	321	NUM
ejpam-2498	249	3	let	let	VERB
ejpam-2498	249	4	b(a(n	b(a(n	PROPN
ejpam-2498	249	5	)	)	PUNCT
ejpam-2498	249	6	)	)	PUNCT
ejpam-2498	250	1	be	be	AUX
ejpam-2498	250	2	the	the	DET
ejpam-2498	250	3	basis	basis	NOUN
ejpam-2498	250	4	of	of	ADP
ejpam-2498	250	5	a(n	a(n	NOUN
ejpam-2498	250	6	)	)	PUNCT
ejpam-2498	250	7	.	.	PUNCT
ejpam-2498	251	1	for	for	ADP
ejpam-2498	251	2	instance	instance	NOUN
ejpam-2498	251	3	,	,	PUNCT
ejpam-2498	251	4	b(a(1	b(a(1	NOUN
ejpam-2498	251	5	)	)	PUNCT
ejpam-2498	251	6	)	)	PUNCT
ejpam-2498	252	1	=	=	PUNCT
ejpam-2498	252	2	trivial	trivial	ADJ
ejpam-2498	252	3	,	,	PUNCT
ejpam-2498	252	4	b(a(2	b(a(2	NOUN
ejpam-2498	252	5	)	)	PUNCT
ejpam-2498	252	6	)	)	PUNCT
ejpam-2498	253	1	=	=	PRON
ejpam-2498	253	2	{	{	PUNCT
ejpam-2498	253	3	1	1	NUM
ejpam-2498	253	4	,	,	PUNCT
ejpam-2498	253	5	e1	e1	PROPN
ejpam-2498	253	6	}	}	PUNCT
ejpam-2498	253	7	,	,	PUNCT
ejpam-2498	253	8	b(a(3	b(a(3	NOUN
ejpam-2498	253	9	)	)	PUNCT
ejpam-2498	253	10	)	)	PUNCT
ejpam-2498	254	1	=	=	PRON
ejpam-2498	254	2	{	{	PUNCT
ejpam-2498	254	3	1	1	NUM
ejpam-2498	254	4	,	,	PUNCT
ejpam-2498	254	5	e1	e1	PROPN
ejpam-2498	254	6	,	,	PUNCT
ejpam-2498	254	7	e2	e2	NOUN
ejpam-2498	254	8	,	,	PUNCT
ejpam-2498	254	9	e1	e1	PROPN
ejpam-2498	254	10	∧	∧	PROPN
ejpam-2498	254	11	e2	e2	PROPN
ejpam-2498	254	12	}	}	PUNCT
ejpam-2498	254	13	etc	etc	X
ejpam-2498	254	14	.	.	X
ejpam-2498	254	15	in	in	ADP
ejpam-2498	254	16	this	this	DET
ejpam-2498	254	17	sense	sense	NOUN
ejpam-2498	254	18	,	,	PUNCT
ejpam-2498	254	19	we	we	PRON
ejpam-2498	254	20	obtain	obtain	VERB
ejpam-2498	254	21	b(a(n+	b(a(n+	NOUN
ejpam-2498	254	22	1	1	NUM
ejpam-2498	254	23	)	)	PUNCT
ejpam-2498	254	24	)	)	PUNCT
ejpam-2498	255	1	=	=	PRON
ejpam-2498	255	2	(	(	PUNCT
ejpam-2498	255	3	b(a(n))∧	b(a(n))∧	VERB
ejpam-2498	255	4	en)⊔	en)⊔	PROPN
ejpam-2498	255	5	b(a(n	b(a(n	PROPN
ejpam-2498	255	6	)	)	PUNCT
ejpam-2498	255	7	)	)	PUNCT
ejpam-2498	255	8	.	.	PUNCT
ejpam-2498	256	1	we	we	PRON
ejpam-2498	256	2	use	use	VERB
ejpam-2498	256	3	induction	induction	NOUN
ejpam-2498	256	4	method	method	NOUN
ejpam-2498	256	5	.	.	PUNCT
ejpam-2498	257	1	indeed	indeed	ADV
ejpam-2498	257	2	,	,	PUNCT
ejpam-2498	257	3	here	here	ADV
ejpam-2498	257	4	we	we	PRON
ejpam-2498	257	5	have	have	VERB
ejpam-2498	257	6	very	very	ADV
ejpam-2498	257	7	similar	similar	ADJ
ejpam-2498	257	8	arguments	argument	NOUN
ejpam-2498	257	9	with	with	ADP
ejpam-2498	257	10	the	the	DET
ejpam-2498	257	11	previous	previous	ADJ
ejpam-2498	257	12	claim	claim	NOUN
ejpam-2498	257	13	.	.	PUNCT
ejpam-2498	258	1	the	the	DET
ejpam-2498	258	2	variable	variable	NOUN
ejpam-2498	258	3	en	en	ADV
ejpam-2498	258	4	has	have	VERB
ejpam-2498	258	5	the	the	DET
ejpam-2498	258	6	same	same	ADJ
ejpam-2498	258	7	role	role	NOUN
ejpam-2498	258	8	with	with	ADP
ejpam-2498	258	9	"	"	PUNCT
ejpam-2498	258	10	the	the	DET
ejpam-2498	258	11	extra	extra	ADJ
ejpam-2498	258	12	bottom	bottom	ADJ
ejpam-2498	258	13	entry	entry	NOUN
ejpam-2498	258	14	±1	±1	NOUN
ejpam-2498	258	15	"	"	PUNCT
ejpam-2498	258	16	.	.	PUNCT
ejpam-2498	259	1	then	then	ADV
ejpam-2498	259	2	,	,	PUNCT
ejpam-2498	259	3	we	we	PRON
ejpam-2498	259	4	have	have	VERB
ejpam-2498	259	5	the	the	DET
ejpam-2498	259	6	polynomial	polynomial	ADJ
ejpam-2498	259	7	p(a(n	p(a(n	NOUN
ejpam-2498	259	8	)	)	PUNCT
ejpam-2498	259	9	)	)	PUNCT
ejpam-2498	260	1	=	=	PUNCT
ejpam-2498	260	2	∑	∑	PUNCT
ejpam-2498	260	3	b∈b(a(n	b∈b(a(n	NOUN
ejpam-2498	260	4	)	)	PUNCT
ejpam-2498	260	5	)	)	PUNCT
ejpam-2498	261	1	a(n)b	a(n)b	PROPN
ejpam-2498	261	2	t	t	PROPN
ejpam-2498	261	3	|b|	|b|	PROPN
ejpam-2498	261	4	.	.	PROPN
ejpam-2498	261	5	trivially	trivially	ADV
ejpam-2498	261	6	,	,	PUNCT
ejpam-2498	261	7	p(a(1	p(a(1	ADP
ejpam-2498	261	8	)	)	PUNCT
ejpam-2498	261	9	)	)	PUNCT
ejpam-2498	262	1	=	=	SYM
ejpam-2498	262	2	1	1	NUM
ejpam-2498	262	3	and	and	CCONJ
ejpam-2498	262	4	p(a(2	p(a(2	NOUN
ejpam-2498	262	5	)	)	PUNCT
ejpam-2498	262	6	)	)	PUNCT
ejpam-2498	263	1	=	=	PUNCT
ejpam-2498	264	1	1	1	NUM
ejpam-2498	264	2	+	+	NUM
ejpam-2498	264	3	t.	t.	NOUN
ejpam-2498	264	4	by	by	ADP
ejpam-2498	264	5	the	the	DET
ejpam-2498	264	6	induction	induction	NOUN
ejpam-2498	264	7	hypothesis	hypothesis	NOUN
ejpam-2498	264	8	,	,	PUNCT
ejpam-2498	264	9	assume	assume	VERB
ejpam-2498	264	10	that	that	SCONJ
ejpam-2498	264	11	p(a(n	p(a(n	NOUN
ejpam-2498	264	12	)	)	PUNCT
ejpam-2498	264	13	)	)	PUNCT
ejpam-2498	265	1	=	=	PUNCT
ejpam-2498	265	2	∑	∑	PUNCT
ejpam-2498	265	3	b∈b(a(n	b∈b(a(n	NOUN
ejpam-2498	265	4	)	)	PUNCT
ejpam-2498	265	5	)	)	PUNCT
ejpam-2498	266	1	a(n)b	a(n)b	PROPN
ejpam-2498	266	2	t	t	NOUN
ejpam-2498	266	3	|b|	|b|	PROPN
ejpam-2498	266	4	=	=	PUNCT
ejpam-2498	266	5	(	(	PUNCT
ejpam-2498	266	6	1	1	NUM
ejpam-2498	266	7	+	+	NUM
ejpam-2498	266	8	t)(1	t)(1	NOUN
ejpam-2498	266	9	+	+	ADJ
ejpam-2498	266	10	t2	t2	NOUN
ejpam-2498	266	11	)	)	PUNCT
ejpam-2498	266	12	·	·	PUNCT
ejpam-2498	266	13	·	·	PUNCT
ejpam-2498	266	14	·	·	PUNCT
ejpam-2498	266	15	(	(	PUNCT
ejpam-2498	266	16	1	1	NUM
ejpam-2498	266	17	+	+	CCONJ
ejpam-2498	266	18	tn−1	tn−1	ADJ
ejpam-2498	266	19	)	)	PUNCT
ejpam-2498	266	20	.	.	PUNCT
ejpam-2498	267	1	for	for	ADP
ejpam-2498	267	2	the	the	DET
ejpam-2498	267	3	polynomial	polynomial	ADJ
ejpam-2498	267	4	p(a(n+1	p(a(n+1	NOUN
ejpam-2498	267	5	)	)	PUNCT
ejpam-2498	267	6	)	)	PUNCT
ejpam-2498	267	7	,	,	PUNCT
ejpam-2498	267	8	pick	pick	VERB
ejpam-2498	267	9	an	an	DET
ejpam-2498	267	10	element	element	NOUN
ejpam-2498	267	11	b	b	PROPN
ejpam-2498	267	12	∈	∈	PROPN
ejpam-2498	267	13	b(a(n+1	b(a(n+1	NOUN
ejpam-2498	267	14	)	)	PUNCT
ejpam-2498	267	15	)	)	PUNCT
ejpam-2498	267	16	.	.	PUNCT
ejpam-2498	268	1	then	then	ADV
ejpam-2498	268	2	,	,	PUNCT
ejpam-2498	268	3	b	b	PROPN
ejpam-2498	268	4	is	be	AUX
ejpam-2498	268	5	in	in	ADP
ejpam-2498	268	6	either	either	CCONJ
ejpam-2498	268	7	b(a(n	b(a(n	PROPN
ejpam-2498	268	8	)	)	PUNCT
ejpam-2498	268	9	)	)	PUNCT
ejpam-2498	268	10	or	or	CCONJ
ejpam-2498	268	11	b(a(n))∧en	b(a(n))∧en	PROPN
ejpam-2498	268	12	.	.	PROPN
ejpam-2498	269	1	for	for	ADP
ejpam-2498	269	2	b	b	PROPN
ejpam-2498	269	3	∈	∈	PROPN
ejpam-2498	269	4	b(a(n+1	b(a(n+1	NOUN
ejpam-2498	269	5	)	)	PUNCT
ejpam-2498	269	6	)	)	PUNCT
ejpam-2498	269	7	,	,	PUNCT
ejpam-2498	269	8	trivially	trivially	ADV
ejpam-2498	269	9	,	,	PUNCT
ejpam-2498	269	10	p(a(n+1	p(a(n+1	NUM
ejpam-2498	269	11	)	)	PUNCT
ejpam-2498	269	12	)	)	PUNCT
ejpam-2498	269	13	has	have	VERB
ejpam-2498	269	14	the	the	DET
ejpam-2498	269	15	desired	desire	VERB
ejpam-2498	269	16	form	form	NOUN
ejpam-2498	269	17	.	.	PUNCT
ejpam-2498	270	1	if	if	SCONJ
ejpam-2498	270	2	b	b	PROPN
ejpam-2498	270	3	∈	∈	PROPN
ejpam-2498	270	4	b(a(n))∧en	b(a(n))∧en	PROPN
ejpam-2498	270	5	,	,	PUNCT
ejpam-2498	270	6	then	then	ADV
ejpam-2498	270	7	by	by	ADP
ejpam-2498	270	8	the	the	DET
ejpam-2498	270	9	definition	definition	NOUN
ejpam-2498	270	10	of	of	ADP
ejpam-2498	270	11	degree	degree	NOUN
ejpam-2498	270	12	,	,	PUNCT
ejpam-2498	270	13	there	there	PRON
ejpam-2498	270	14	is	be	VERB
ejpam-2498	270	15	b̃	b̃	PROPN
ejpam-2498	270	16	∈	∈	PROPN
ejpam-2498	270	17	b(a(n	b(a(n	PROPN
ejpam-2498	270	18	)	)	PUNCT
ejpam-2498	270	19	)	)	PUNCT
ejpam-2498	271	1	such	such	ADJ
ejpam-2498	271	2	that	that	SCONJ
ejpam-2498	271	3	|b|	|b|	PROPN
ejpam-2498	271	4	=	=	PUNCT
ejpam-2498	271	5	|b̃|	|b̃|	PROPN
ejpam-2498	271	6	+	+	NUM
ejpam-2498	271	7	n.	n.	PROPN
ejpam-2498	271	8	thus	thus	ADV
ejpam-2498	271	9	,	,	PUNCT
ejpam-2498	271	10	by	by	ADP
ejpam-2498	271	11	the	the	DET
ejpam-2498	271	12	definition	definition	NOUN
ejpam-2498	271	13	of	of	ADP
ejpam-2498	271	14	p(a(n	p(a(n	NOUN
ejpam-2498	271	15	)	)	PUNCT
ejpam-2498	271	16	)	)	PUNCT
ejpam-2498	271	17	,	,	PUNCT
ejpam-2498	271	18	we	we	PRON
ejpam-2498	271	19	obtain	obtain	VERB
ejpam-2498	271	20	p(a(n+	p(a(n+	NOUN
ejpam-2498	271	21	1	1	NUM
ejpam-2498	271	22	)	)	PUNCT
ejpam-2498	271	23	)	)	PUNCT
ejpam-2498	272	1	=	=	PUNCT
ejpam-2498	272	2	(	(	PUNCT
ejpam-2498	272	3	1	1	NUM
ejpam-2498	272	4	+	+	NUM
ejpam-2498	272	5	t)(1	t)(1	NOUN
ejpam-2498	272	6	+	+	ADJ
ejpam-2498	272	7	t2	t2	NOUN
ejpam-2498	272	8	)	)	PUNCT
ejpam-2498	272	9	·	·	PUNCT
ejpam-2498	272	10	·	·	PUNCT
ejpam-2498	272	11	·	·	PUNCT
ejpam-2498	272	12	(	(	PUNCT
ejpam-2498	272	13	1	1	NUM
ejpam-2498	272	14	+	+	NUM
ejpam-2498	272	15	tn	tn	NOUN
ejpam-2498	272	16	)	)	PUNCT
ejpam-2498	272	17	(	(	PUNCT
ejpam-2498	272	18	16	16	NUM
ejpam-2498	272	19	)	)	PUNCT
ejpam-2498	272	20	which	which	PRON
ejpam-2498	272	21	completes	complete	VERB
ejpam-2498	272	22	the	the	DET
ejpam-2498	272	23	proof	proof	NOUN
ejpam-2498	272	24	.	.	PUNCT
ejpam-2498	273	1	thereby	thereby	ADV
ejpam-2498	273	2	,	,	PUNCT
ejpam-2498	273	3	we	we	PRON
ejpam-2498	273	4	have	have	AUX
ejpam-2498	273	5	shown	show	VERB
ejpam-2498	273	6	that	that	SCONJ
ejpam-2498	273	7	,	,	PUNCT
ejpam-2498	273	8	for	for	ADP
ejpam-2498	273	9	the	the	DET
ejpam-2498	273	10	given	give	VERB
ejpam-2498	273	11	morse	morse	NOUN
ejpam-2498	273	12	function	function	NOUN
ejpam-2498	273	13	fc	fc	PROPN
ejpam-2498	273	14	:	:	PUNCT
ejpam-2498	273	15	so(n)→	so(n)→	VERB
ejpam-2498	273	16	r	r	NOUN
ejpam-2498	273	17	,	,	PUNCT
ejpam-2498	273	18	pm	pm	NOUN
ejpam-2498	273	19	(	(	PUNCT
ejpam-2498	273	20	t	t	NOUN
ejpam-2498	273	21	)	)	PUNCT
ejpam-2498	273	22	=	=	NOUN
ejpam-2498	273	23	pfc	pfc	NOUN
ejpam-2498	273	24	(	(	PUNCT
ejpam-2498	273	25	t	t	PROPN
ejpam-2498	273	26	)	)	PUNCT
ejpam-2498	273	27	,	,	PUNCT
ejpam-2498	273	28	meaning	mean	VERB
ejpam-2498	273	29	that	that	SCONJ
ejpam-2498	273	30	fc	fc	PROPN
ejpam-2498	273	31	is	be	AUX
ejpam-2498	273	32	a	a	DET
ejpam-2498	273	33	perfect	perfect	ADJ
ejpam-2498	273	34	morse	morse	NOUN
ejpam-2498	273	35	function	function	NOUN
ejpam-2498	273	36	.	.	PUNCT
ejpam-2498	274	1	references	reference	NOUN
ejpam-2498	274	2	[	[	X
ejpam-2498	274	3	1	1	NUM
ejpam-2498	274	4	]	]	X
ejpam-2498	274	5	d.b	d.b	PROPN
ejpam-2498	274	6	.	.	PROPN
ejpam-2498	274	7	gauld	gauld	PROPN
ejpam-2498	274	8	.	.	PUNCT
ejpam-2498	275	1	differential	differential	PROPN
ejpam-2498	275	2	topology	topology	NOUN
ejpam-2498	275	3	:	:	PUNCT
ejpam-2498	275	4	an	an	DET
ejpam-2498	275	5	introduction	introduction	NOUN
ejpam-2498	275	6	.	.	PUNCT
ejpam-2498	276	1	marcel	marcel	PROPN
ejpam-2498	276	2	dekker	dekker	PROPN
ejpam-2498	276	3	,	,	PUNCT
ejpam-2498	276	4	new	new	PROPN
ejpam-2498	276	5	york	york	PROPN
ejpam-2498	276	6	,	,	PUNCT
ejpam-2498	276	7	1982	1982	NUM
ejpam-2498	276	8	.	.	PUNCT
ejpam-2498	277	1	[	[	X
ejpam-2498	277	2	2	2	NUM
ejpam-2498	277	3	]	]	PUNCT
ejpam-2498	277	4	a.	a.	NOUN
ejpam-2498	277	5	hatcher	hatcher	PROPN
ejpam-2498	277	6	.	.	PUNCT
ejpam-2498	278	1	algebraic	algebraic	ADJ
ejpam-2498	278	2	topology	topology	PROPN
ejpam-2498	278	3	.	.	PUNCT
ejpam-2498	279	1	cambridge	cambridge	PROPN
ejpam-2498	279	2	university	university	PROPN
ejpam-2498	279	3	press	press	PROPN
ejpam-2498	279	4	,	,	PUNCT
ejpam-2498	279	5	new	new	PROPN
ejpam-2498	279	6	york	york	PROPN
ejpam-2498	279	7	,	,	PUNCT
ejpam-2498	279	8	3rd	3rd	ADJ
ejpam-2498	279	9	edition	edition	NOUN
ejpam-2498	279	10	,	,	PUNCT
ejpam-2498	279	11	2002	2002	NUM
ejpam-2498	279	12	.	.	PUNCT
ejpam-2498	280	1	[	[	X
ejpam-2498	280	2	3	3	X
ejpam-2498	280	3	]	]	X
ejpam-2498	280	4	j.m	j.m	PROPN
ejpam-2498	280	5	.	.	PROPN
ejpam-2498	280	6	lee	lee	PROPN
ejpam-2498	280	7	.	.	PROPN
ejpam-2498	280	8	introduction	introduction	NOUN
ejpam-2498	280	9	to	to	ADP
ejpam-2498	280	10	smooth	smooth	ADJ
ejpam-2498	280	11	manifolds	manifold	NOUN
ejpam-2498	280	12	.	.	PUNCT
ejpam-2498	281	1	springer	springer	NOUN
ejpam-2498	281	2	,	,	PUNCT
ejpam-2498	281	3	new	new	PROPN
ejpam-2498	281	4	york	york	PROPN
ejpam-2498	281	5	,	,	PUNCT
ejpam-2498	281	6	2nd	2nd	PROPN
ejpam-2498	281	7	edition	edition	NOUN
ejpam-2498	281	8	,	,	PUNCT
ejpam-2498	281	9	2012	2012	NUM
ejpam-2498	281	10	.	.	PUNCT
ejpam-2498	282	1	[	[	X
ejpam-2498	282	2	4	4	NUM
ejpam-2498	282	3	]	]	X
ejpam-2498	282	4	y.	y.	PROPN
ejpam-2498	282	5	matsumoto	matsumoto	PROPN
ejpam-2498	282	6	.	.	PUNCT
ejpam-2498	283	1	an	an	DET
ejpam-2498	283	2	introduction	introduction	NOUN
ejpam-2498	283	3	to	to	ADP
ejpam-2498	283	4	morse	morse	PROPN
ejpam-2498	283	5	theory	theory	NOUN
ejpam-2498	283	6	.	.	PUNCT
ejpam-2498	284	1	american	american	PROPN
ejpam-2498	284	2	mathematical	mathematical	PROPN
ejpam-2498	284	3	society	society	NOUN
ejpam-2498	284	4	,	,	PUNCT
ejpam-2498	284	5	translations	translation	NOUN
ejpam-2498	284	6	of	of	ADP
ejpam-2498	284	7	mathematical	mathematical	ADJ
ejpam-2498	284	8	monographs	monograph	NOUN
ejpam-2498	284	9	,	,	PUNCT
ejpam-2498	284	10	208	208	NUM
ejpam-2498	284	11	,	,	PUNCT
ejpam-2498	284	12	providence	providence	NOUN
ejpam-2498	284	13	,	,	PUNCT
ejpam-2498	284	14	ri	ri	NOUN
ejpam-2498	284	15	,	,	PUNCT
ejpam-2498	284	16	2002	2002	NUM
ejpam-2498	284	17	.	.	PUNCT
ejpam-2498	285	1	[	[	X
ejpam-2498	285	2	5	5	X
ejpam-2498	285	3	]	]	X
ejpam-2498	285	4	j.w	j.w	PROPN
ejpam-2498	285	5	.	.	PROPN
ejpam-2498	285	6	milnor	milnor	PROPN
ejpam-2498	285	7	.	.	PUNCT
ejpam-2498	286	1	morse	morse	PROPN
ejpam-2498	286	2	theory	theory	PROPN
ejpam-2498	286	3	.	.	PUNCT
ejpam-2498	287	1	princeton	princeton	PROPN
ejpam-2498	287	2	university	university	PROPN
ejpam-2498	287	3	press	press	NOUN
ejpam-2498	287	4	,	,	PUNCT
ejpam-2498	287	5	new	new	PROPN
ejpam-2498	287	6	jersey	jersey	PROPN
ejpam-2498	287	7	,	,	PUNCT
ejpam-2498	287	8	usa	usa	PROPN
ejpam-2498	287	9	,	,	PUNCT
ejpam-2498	287	10	1963	1963	NUM
ejpam-2498	287	11	.	.	PUNCT
ejpam-2498	288	1	[	[	X
ejpam-2498	288	2	6	6	NUM
ejpam-2498	288	3	]	]	PUNCT
ejpam-2498	288	4	j.	j.	PROPN
ejpam-2498	288	5	morse	morse	PROPN
ejpam-2498	288	6	.	.	PUNCT
ejpam-2498	289	1	the	the	DET
ejpam-2498	289	2	foundations	foundation	NOUN
ejpam-2498	289	3	of	of	ADP
ejpam-2498	289	4	a	a	DET
ejpam-2498	289	5	theory	theory	NOUN
ejpam-2498	289	6	of	of	ADP
ejpam-2498	289	7	the	the	DET
ejpam-2498	289	8	calculus	calculus	NOUN
ejpam-2498	289	9	of	of	ADP
ejpam-2498	289	10	variations	variation	NOUN
ejpam-2498	289	11	in	in	ADP
ejpam-2498	289	12	the	the	DET
ejpam-2498	289	13	large	large	ADJ
ejpam-2498	289	14	in	in	ADP
ejpam-2498	289	15	m	m	NOUN
ejpam-2498	289	16	-	-	NOUN
ejpam-2498	289	17	space	space	NOUN
ejpam-2498	289	18	.	.	PUNCT
ejpam-2498	290	1	transactions	transaction	NOUN
ejpam-2498	290	2	of	of	ADP
ejpam-2498	290	3	the	the	DET
ejpam-2498	290	4	american	american	PROPN
ejpam-2498	290	5	mathematical	mathematical	PROPN
ejpam-2498	290	6	society	society	NOUN
ejpam-2498	290	7	,	,	PUNCT
ejpam-2498	290	8	30:213–274	30:213–274	NUM
ejpam-2498	290	9	,	,	PUNCT
ejpam-2498	290	10	1928	1928	NUM
ejpam-2498	290	11	.	.	PUNCT
ejpam-2498	291	1	[	[	X
ejpam-2498	291	2	7	7	X
ejpam-2498	291	3	]	]	X
ejpam-2498	291	4	l.i	l.i	PROPN
ejpam-2498	291	5	.	.	PROPN
ejpam-2498	291	6	nicolaescu	nicolaescu	PROPN
ejpam-2498	291	7	.	.	PUNCT
ejpam-2498	292	1	an	an	DET
ejpam-2498	292	2	invitation	invitation	NOUN
ejpam-2498	292	3	to	to	PART
ejpam-2498	292	4	morse	morse	VERB
ejpam-2498	292	5	theory	theory	NOUN
ejpam-2498	292	6	.	.	PUNCT
ejpam-2498	293	1	springer	springer	NOUN
ejpam-2498	293	2	,	,	PUNCT
ejpam-2498	293	3	new	new	PROPN
ejpam-2498	293	4	york	york	PROPN
ejpam-2498	293	5	,	,	PUNCT
ejpam-2498	293	6	2nd	2nd	PROPN
ejpam-2498	293	7	edition	edition	NOUN
ejpam-2498	293	8	,	,	PUNCT
ejpam-2498	293	9	2011	2011	NUM
ejpam-2498	293	10	.	.	PUNCT