id	sid	tid	token	lemma	pos
ejpam-5290	1	1	european	european	PROPN
ejpam-5290	1	2	journal	journal	PROPN
ejpam-5290	1	3	of	of	ADP
ejpam-5290	1	4	pure	pure	ADJ
ejpam-5290	1	5	and	and	CCONJ
ejpam-5290	1	6	applied	apply	VERB
ejpam-5290	1	7	mathematics	mathematic	NOUN
ejpam-5290	1	8	vol	vol	NOUN
ejpam-5290	1	9	.	.	PROPN
ejpam-5290	2	1	17	17	NUM
ejpam-5290	2	2	,	,	PUNCT
ejpam-5290	2	3	no	no	INTJ
ejpam-5290	2	4	.	.	NOUN
ejpam-5290	2	5	4	4	NUM
ejpam-5290	2	6	,	,	PUNCT
ejpam-5290	2	7	2024	2024	NUM
ejpam-5290	2	8	,	,	PUNCT
ejpam-5290	2	9	3079	3079	NUM
ejpam-5290	2	10	-	-	SYM
ejpam-5290	2	11	3092	3092	NUM
ejpam-5290	2	12	issn	issn	PROPN
ejpam-5290	2	13	1307	1307	NUM
ejpam-5290	2	14	-	-	SYM
ejpam-5290	2	15	5543	5543	NUM
ejpam-5290	2	16	–	–	PUNCT
ejpam-5290	2	17	ejpam.com	ejpam.com	X
ejpam-5290	2	18	published	publish	VERB
ejpam-5290	2	19	by	by	ADP
ejpam-5290	2	20	new	new	PROPN
ejpam-5290	2	21	york	york	PROPN
ejpam-5290	2	22	business	business	PROPN
ejpam-5290	2	23	global	global	ADJ
ejpam-5290	2	24	infinitesimal	infinitesimal	ADJ
ejpam-5290	2	25	rigidity	rigidity	NOUN
ejpam-5290	2	26	analysis	analysis	NOUN
ejpam-5290	2	27	of	of	ADP
ejpam-5290	2	28	a	a	DET
ejpam-5290	2	29	bar	bar	NOUN
ejpam-5290	2	30	-	-	PUNCT
ejpam-5290	2	31	joint	joint	NOUN
ejpam-5290	2	32	framework	framework	NOUN
ejpam-5290	2	33	with	with	ADP
ejpam-5290	2	34	connected	connected	ADJ
ejpam-5290	2	35	braced	braced	ADJ
ejpam-5290	2	36	triangles	triangle	NOUN
ejpam-5290	2	37	ghada	ghada	NOUN
ejpam-5290	2	38	matooq	matooq	PROPN
ejpam-5290	2	39	badri	badri	PROPN
ejpam-5290	2	40	mathematics	mathematics	PROPN
ejpam-5290	2	41	department	department	PROPN
ejpam-5290	2	42	,	,	PUNCT
ejpam-5290	2	43	faculty	faculty	NOUN
ejpam-5290	2	44	of	of	ADP
ejpam-5290	2	45	sciences	science	NOUN
ejpam-5290	2	46	,	,	PUNCT
ejpam-5290	2	47	umm	umm	INTJ
ejpam-5290	2	48	al	al	PROPN
ejpam-5290	2	49	-	-	PUNCT
ejpam-5290	2	50	qura	qura	PROPN
ejpam-5290	2	51	university	university	PROPN
ejpam-5290	2	52	,	,	PUNCT
ejpam-5290	2	53	makkah	makkah	PROPN
ejpam-5290	2	54	,	,	PUNCT
ejpam-5290	2	55	saudi	saudi	PROPN
ejpam-5290	2	56	arabia	arabia	PROPN
ejpam-5290	2	57	abstract	abstract	NOUN
ejpam-5290	2	58	.	.	PUNCT
ejpam-5290	3	1	the	the	DET
ejpam-5290	3	2	aim	aim	NOUN
ejpam-5290	3	3	of	of	ADP
ejpam-5290	3	4	this	this	DET
ejpam-5290	3	5	paper	paper	NOUN
ejpam-5290	3	6	is	be	AUX
ejpam-5290	3	7	to	to	PART
ejpam-5290	3	8	provide	provide	VERB
ejpam-5290	3	9	detailed	detailed	ADJ
ejpam-5290	3	10	infinitesimal	infinitesimal	ADJ
ejpam-5290	3	11	rigidity	rigidity	NOUN
ejpam-5290	3	12	analysis	analysis	NOUN
ejpam-5290	3	13	of	of	ADP
ejpam-5290	3	14	a	a	DET
ejpam-5290	3	15	planar	planar	ADJ
ejpam-5290	3	16	infinite	infinite	ADJ
ejpam-5290	3	17	bar	bar	NOUN
ejpam-5290	3	18	-	-	PUNCT
ejpam-5290	3	19	joint	joint	NOUN
ejpam-5290	3	20	framework	framework	NOUN
ejpam-5290	3	21	consisting	consist	VERB
ejpam-5290	3	22	of	of	ADP
ejpam-5290	3	23	connected	connected	ADJ
ejpam-5290	3	24	braced	braced	ADJ
ejpam-5290	3	25	triangles	triangle	NOUN
ejpam-5290	3	26	.	.	PUNCT
ejpam-5290	4	1	this	this	PRON
ejpam-5290	4	2	is	be	AUX
ejpam-5290	4	3	achieved	achieve	VERB
ejpam-5290	4	4	in	in	ADP
ejpam-5290	4	5	a	a	DET
ejpam-5290	4	6	purely	purely	ADV
ejpam-5290	4	7	mathematical	mathematical	ADJ
ejpam-5290	4	8	manner	manner	NOUN
ejpam-5290	4	9	,	,	PUNCT
ejpam-5290	4	10	using	use	VERB
ejpam-5290	4	11	the	the	DET
ejpam-5290	4	12	infinitesimal	infinitesimal	ADJ
ejpam-5290	4	13	flex	flex	ADJ
ejpam-5290	4	14	condition	condition	NOUN
ejpam-5290	4	15	,	,	PUNCT
ejpam-5290	4	16	as	as	SCONJ
ejpam-5290	4	17	we	we	PRON
ejpam-5290	4	18	identify	identify	VERB
ejpam-5290	4	19	the	the	DET
ejpam-5290	4	20	non	non	ADJ
ejpam-5290	4	21	trivial	trivial	ADJ
ejpam-5290	4	22	infinitesimal	infinitesimal	ADJ
ejpam-5290	4	23	flexes	flex	NOUN
ejpam-5290	4	24	of	of	ADP
ejpam-5290	4	25	the	the	DET
ejpam-5290	4	26	finite	finite	ADJ
ejpam-5290	4	27	framework	framework	NOUN
ejpam-5290	4	28	consisting	consist	VERB
ejpam-5290	4	29	of	of	ADP
ejpam-5290	4	30	n	n	DET
ejpam-5290	4	31	connected	connected	ADJ
ejpam-5290	4	32	triangles	triangle	NOUN
ejpam-5290	4	33	.	.	PUNCT
ejpam-5290	5	1	the	the	DET
ejpam-5290	5	2	result	result	NOUN
ejpam-5290	5	3	is	be	AUX
ejpam-5290	5	4	then	then	ADV
ejpam-5290	5	5	generalized	generalize	VERB
ejpam-5290	5	6	to	to	ADP
ejpam-5290	5	7	the	the	DET
ejpam-5290	5	8	infinite	infinite	ADJ
ejpam-5290	5	9	case	case	NOUN
ejpam-5290	5	10	leading	lead	VERB
ejpam-5290	5	11	to	to	ADP
ejpam-5290	5	12	the	the	DET
ejpam-5290	5	13	identification	identification	NOUN
ejpam-5290	5	14	of	of	ADP
ejpam-5290	5	15	a	a	DET
ejpam-5290	5	16	base	base	NOUN
ejpam-5290	5	17	for	for	ADP
ejpam-5290	5	18	the	the	DET
ejpam-5290	5	19	space	space	NOUN
ejpam-5290	5	20	of	of	ADP
ejpam-5290	5	21	all	all	DET
ejpam-5290	5	22	infinitesimal	infinitesimal	ADJ
ejpam-5290	5	23	flexes	flex	NOUN
ejpam-5290	5	24	.	.	PUNCT
ejpam-5290	6	1	2020	2020	NUM
ejpam-5290	6	2	mathematics	mathematic	NOUN
ejpam-5290	6	3	subject	subject	NOUN
ejpam-5290	6	4	classifications	classification	NOUN
ejpam-5290	6	5	:	:	PUNCT
ejpam-5290	6	6	52c25	52c25	NUM
ejpam-5290	6	7	,	,	PUNCT
ejpam-5290	6	8	51m05	51m05	NUM
ejpam-5290	6	9	,	,	PUNCT
ejpam-5290	6	10	47n50	47n50	NUM
ejpam-5290	6	11	key	key	ADJ
ejpam-5290	6	12	words	word	NOUN
ejpam-5290	6	13	and	and	CCONJ
ejpam-5290	6	14	phrases	phrase	NOUN
ejpam-5290	6	15	:	:	PUNCT
ejpam-5290	6	16	bar	bar	NOUN
ejpam-5290	6	17	-	-	PUNCT
ejpam-5290	6	18	joint	joint	NOUN
ejpam-5290	6	19	framework	framework	NOUN
ejpam-5290	6	20	,	,	PUNCT
ejpam-5290	6	21	infinitesimal	infinitesimal	ADJ
ejpam-5290	6	22	rigidity	rigidity	NOUN
ejpam-5290	6	23	,	,	PUNCT
ejpam-5290	6	24	non	non	ADJ
ejpam-5290	6	25	trivial	trivial	ADJ
ejpam-5290	6	26	flex	flex	ADJ
ejpam-5290	6	27	1	1	NUM
ejpam-5290	6	28	.	.	PUNCT
ejpam-5290	7	1	introduction	introduction	NOUN
ejpam-5290	7	2	there	there	PRON
ejpam-5290	7	3	has	have	AUX
ejpam-5290	7	4	been	be	AUX
ejpam-5290	7	5	increasing	increase	VERB
ejpam-5290	7	6	interest	interest	NOUN
ejpam-5290	7	7	in	in	ADP
ejpam-5290	7	8	the	the	DET
ejpam-5290	7	9	analysis	analysis	NOUN
ejpam-5290	7	10	of	of	ADP
ejpam-5290	7	11	mathematical	mathematical	ADJ
ejpam-5290	7	12	bar	bar	NOUN
ejpam-5290	7	13	-	-	PUNCT
ejpam-5290	7	14	joint	joint	NOUN
ejpam-5290	7	15	frameworks	framework	NOUN
ejpam-5290	7	16	,	,	PUNCT
ejpam-5290	7	17	both	both	CCONJ
ejpam-5290	7	18	in	in	ADP
ejpam-5290	7	19	the	the	DET
ejpam-5290	7	20	finite	finite	NOUN
ejpam-5290	7	21	and	and	CCONJ
ejpam-5290	7	22	infinite	infinite	ADJ
ejpam-5290	7	23	sense	sense	NOUN
ejpam-5290	7	24	.	.	PUNCT
ejpam-5290	8	1	the	the	DET
ejpam-5290	8	2	realization	realization	NOUN
ejpam-5290	8	3	of	of	ADP
ejpam-5290	8	4	a	a	DET
ejpam-5290	8	5	framework	framework	NOUN
ejpam-5290	8	6	in	in	ADP
ejpam-5290	8	7	the	the	DET
ejpam-5290	8	8	euclidean	euclidean	ADJ
ejpam-5290	8	9	space	space	NOUN
ejpam-5290	8	10	enables	enable	VERB
ejpam-5290	8	11	us	we	PRON
ejpam-5290	8	12	to	to	PART
ejpam-5290	8	13	mathematically	mathematically	ADV
ejpam-5290	8	14	investigate	investigate	VERB
ejpam-5290	8	15	properties	property	NOUN
ejpam-5290	8	16	of	of	ADP
ejpam-5290	8	17	physical	physical	ADJ
ejpam-5290	8	18	structures	structure	NOUN
ejpam-5290	8	19	and	and	CCONJ
ejpam-5290	8	20	crystalline	crystalline	NOUN
ejpam-5290	8	21	materials	material	NOUN
ejpam-5290	8	22	.	.	PUNCT
ejpam-5290	9	1	applications	application	NOUN
ejpam-5290	9	2	of	of	ADP
ejpam-5290	9	3	rigidity	rigidity	NOUN
ejpam-5290	9	4	now	now	ADV
ejpam-5290	9	5	extend	extend	VERB
ejpam-5290	9	6	beyond	beyond	ADP
ejpam-5290	9	7	physics	physics	NOUN
ejpam-5290	9	8	and	and	CCONJ
ejpam-5290	9	9	structure	structure	NOUN
ejpam-5290	9	10	engineering	engineering	NOUN
ejpam-5290	9	11	finding	find	VERB
ejpam-5290	9	12	their	their	PRON
ejpam-5290	9	13	way	way	NOUN
ejpam-5290	9	14	to	to	PART
ejpam-5290	9	15	molecule	molecule	VERB
ejpam-5290	9	16	analysis	analysis	NOUN
ejpam-5290	9	17	[	[	X
ejpam-5290	9	18	8	8	NUM
ejpam-5290	9	19	]	]	PUNCT
ejpam-5290	9	20	,	,	PUNCT
ejpam-5290	9	21	[	[	X
ejpam-5290	9	22	13	13	NUM
ejpam-5290	9	23	]	]	PUNCT
ejpam-5290	9	24	,	,	PUNCT
ejpam-5290	9	25	robotics	robotic	NOUN
ejpam-5290	9	26	[	[	X
ejpam-5290	9	27	26	26	NUM
ejpam-5290	9	28	]	]	PUNCT
ejpam-5290	9	29	and	and	CCONJ
ejpam-5290	9	30	much	much	ADV
ejpam-5290	9	31	more	more	ADJ
ejpam-5290	9	32	.	.	PUNCT
ejpam-5290	10	1	formally	formally	ADV
ejpam-5290	10	2	,	,	PUNCT
ejpam-5290	10	3	a	a	DET
ejpam-5290	10	4	pair	pair	NOUN
ejpam-5290	10	5	(	(	PUNCT
ejpam-5290	10	6	g	g	NOUN
ejpam-5290	10	7	,	,	PUNCT
ejpam-5290	10	8	p	p	NOUN
ejpam-5290	10	9	)	)	PUNCT
ejpam-5290	10	10	in	in	ADP
ejpam-5290	10	11	the	the	DET
ejpam-5290	10	12	euclidean	euclidean	ADJ
ejpam-5290	10	13	plane	plane	NOUN
ejpam-5290	10	14	r2	r2	NOUN
ejpam-5290	10	15	is	be	AUX
ejpam-5290	10	16	a	a	DET
ejpam-5290	10	17	mathematical	mathematical	ADJ
ejpam-5290	10	18	bar	bar	NOUN
ejpam-5290	10	19	-	-	PUNCT
ejpam-5290	10	20	joint	joint	NOUN
ejpam-5290	10	21	framework	framework	NOUN
ejpam-5290	10	22	g	g	NOUN
ejpam-5290	10	23	where	where	SCONJ
ejpam-5290	10	24	g	g	NOUN
ejpam-5290	10	25	=	=	SYM
ejpam-5290	10	26	(	(	PUNCT
ejpam-5290	10	27	v	v	NOUN
ejpam-5290	10	28	,	,	PUNCT
ejpam-5290	10	29	e	e	NOUN
ejpam-5290	10	30	)	)	PUNCT
ejpam-5290	10	31	represents	represent	VERB
ejpam-5290	10	32	a	a	DET
ejpam-5290	10	33	simple	simple	ADJ
ejpam-5290	10	34	graph	graph	NOUN
ejpam-5290	10	35	,	,	PUNCT
ejpam-5290	10	36	and	and	CCONJ
ejpam-5290	10	37	p	p	NOUN
ejpam-5290	10	38	=	=	SYM
ejpam-5290	10	39	(	(	PUNCT
ejpam-5290	10	40	p1	p1	PROPN
ejpam-5290	10	41	,	,	PUNCT
ejpam-5290	10	42	p2	p2	NOUN
ejpam-5290	10	43	,	,	PUNCT
ejpam-5290	10	44	p3	p3	NOUN
ejpam-5290	10	45	,	,	PUNCT
ejpam-5290	10	46	.	.	PUNCT
ejpam-5290	10	47	.	.	PUNCT
ejpam-5290	10	48	.	.	PUNCT
ejpam-5290	10	49	)	)	PUNCT
ejpam-5290	11	1	represents	represent	VERB
ejpam-5290	11	2	a	a	DET
ejpam-5290	11	3	placement	placement	NOUN
ejpam-5290	11	4	of	of	ADP
ejpam-5290	11	5	the	the	DET
ejpam-5290	11	6	graph	graph	NOUN
ejpam-5290	11	7	’s	’s	PART
ejpam-5290	11	8	vertices	vertex	NOUN
ejpam-5290	11	9	in	in	ADP
ejpam-5290	11	10	r2	r2	PROPN
ejpam-5290	11	11	,	,	PUNCT
ejpam-5290	11	12	with	with	ADP
ejpam-5290	11	13	pi	pi	NOUN
ejpam-5290	11	14	̸=	̸=	PROPN
ejpam-5290	11	15	pj	pj	PROPN
ejpam-5290	11	16	if	if	SCONJ
ejpam-5290	11	17	(	(	PUNCT
ejpam-5290	11	18	vi	vi	NOUN
ejpam-5290	11	19	,	,	PUNCT
ejpam-5290	11	20	vj	vj	NOUN
ejpam-5290	11	21	)	)	PUNCT
ejpam-5290	11	22	is	be	AUX
ejpam-5290	11	23	an	an	DET
ejpam-5290	11	24	edge	edge	NOUN
ejpam-5290	11	25	.	.	PUNCT
ejpam-5290	12	1	the	the	DET
ejpam-5290	12	2	line	line	NOUN
ejpam-5290	12	3	segments	segment	NOUN
ejpam-5290	13	1	[	[	X
ejpam-5290	13	2	pi	pi	NOUN
ejpam-5290	13	3	,	,	PUNCT
ejpam-5290	13	4	pj	pj	PROPN
ejpam-5290	13	5	]	]	PUNCT
ejpam-5290	13	6	connected	connect	VERB
ejpam-5290	13	7	to	to	ADP
ejpam-5290	13	8	the	the	DET
ejpam-5290	13	9	edges	edge	NOUN
ejpam-5290	13	10	of	of	ADP
ejpam-5290	13	11	g	g	NOUN
ejpam-5290	13	12	are	be	AUX
ejpam-5290	13	13	the	the	DET
ejpam-5290	13	14	framework	framework	NOUN
ejpam-5290	13	15	edges	edge	NOUN
ejpam-5290	13	16	.	.	PUNCT
ejpam-5290	14	1	definition	definition	NOUN
ejpam-5290	14	2	1	1	NUM
ejpam-5290	14	3	.	.	PUNCT
ejpam-5290	15	1	let	let	VERB
ejpam-5290	15	2	g	g	PROPN
ejpam-5290	15	3	=	=	SYM
ejpam-5290	15	4	(	(	PUNCT
ejpam-5290	15	5	v	v	NOUN
ejpam-5290	15	6	,	,	PUNCT
ejpam-5290	15	7	e	e	NOUN
ejpam-5290	15	8	)	)	PUNCT
ejpam-5290	15	9	be	be	AUX
ejpam-5290	15	10	a	a	DET
ejpam-5290	15	11	graph	graph	NOUN
ejpam-5290	15	12	with	with	ADP
ejpam-5290	15	13	p	p	PROPN
ejpam-5290	15	14	∈	∈	PROPN
ejpam-5290	15	15	v	v	NOUN
ejpam-5290	15	16	.	.	PUNCT
ejpam-5290	16	1	the	the	DET
ejpam-5290	16	2	number	number	NOUN
ejpam-5290	16	3	|e(p)|	|e(p)|	PROPN
ejpam-5290	16	4	of	of	ADP
ejpam-5290	16	5	edges	edge	NOUN
ejpam-5290	16	6	in	in	ADP
ejpam-5290	16	7	the	the	DET
ejpam-5290	16	8	graph	graph	NOUN
ejpam-5290	16	9	with	with	ADP
ejpam-5290	16	10	the	the	DET
ejpam-5290	16	11	vertex	vertex	NOUN
ejpam-5290	16	12	p	p	NOUN
ejpam-5290	16	13	as	as	ADP
ejpam-5290	16	14	an	an	DET
ejpam-5290	16	15	endpoint	endpoint	NOUN
ejpam-5290	16	16	is	be	AUX
ejpam-5290	16	17	the	the	DET
ejpam-5290	16	18	degree	degree	NOUN
ejpam-5290	16	19	of	of	ADP
ejpam-5290	16	20	p	p	NOUN
ejpam-5290	16	21	,	,	PUNCT
ejpam-5290	16	22	or	or	CCONJ
ejpam-5290	16	23	d(p	d(p	PROPN
ejpam-5290	16	24	)	)	PUNCT
ejpam-5290	16	25	.	.	PUNCT
ejpam-5290	17	1	the	the	DET
ejpam-5290	17	2	minimum	minimum	NOUN
ejpam-5290	17	3	degree	degree	NOUN
ejpam-5290	17	4	of	of	ADP
ejpam-5290	17	5	g	g	PROPN
ejpam-5290	17	6	is	be	AUX
ejpam-5290	17	7	δ(g	δ(g	ADV
ejpam-5290	17	8	)	)	PUNCT
ejpam-5290	17	9	:	:	PUNCT
ejpam-5290	18	1	=	=	SYM
ejpam-5290	18	2	min{d(p	min{d(p	PROPN
ejpam-5290	18	3	)	)	PUNCT
ejpam-5290	18	4	,	,	PUNCT
ejpam-5290	18	5	p	p	PROPN
ejpam-5290	18	6	∈	∈	PROPN
ejpam-5290	18	7	v	v	ADP
ejpam-5290	18	8	}	}	PUNCT
ejpam-5290	18	9	,	,	PUNCT
ejpam-5290	18	10	and	and	CCONJ
ejpam-5290	18	11	the	the	DET
ejpam-5290	18	12	maximum	maximum	ADJ
ejpam-5290	18	13	degree	degree	NOUN
ejpam-5290	18	14	is	be	AUX
ejpam-5290	18	15	∆(g	∆(g	NOUN
ejpam-5290	18	16	)	)	PUNCT
ejpam-5290	18	17	:	:	PUNCT
ejpam-5290	19	1	=	=	SYM
ejpam-5290	19	2	max{d(p	max{d(p	PROPN
ejpam-5290	19	3	)	)	PUNCT
ejpam-5290	19	4	,	,	PUNCT
ejpam-5290	19	5	p	p	PROPN
ejpam-5290	19	6	∈	∈	PROPN
ejpam-5290	19	7	v	v	ADP
ejpam-5290	19	8	}	}	PUNCT
ejpam-5290	19	9	.	.	PUNCT
ejpam-5290	20	1	g	g	NOUN
ejpam-5290	20	2	=	=	SYM
ejpam-5290	20	3	(	(	PUNCT
ejpam-5290	20	4	v	v	NOUN
ejpam-5290	20	5	,	,	PUNCT
ejpam-5290	20	6	e	e	NOUN
ejpam-5290	20	7	)	)	PUNCT
ejpam-5290	20	8	is	be	AUX
ejpam-5290	20	9	said	say	VERB
ejpam-5290	20	10	to	to	PART
ejpam-5290	20	11	be	be	AUX
ejpam-5290	20	12	n	n	ADV
ejpam-5290	20	13	-	-	PUNCT
ejpam-5290	20	14	regular	regular	ADJ
ejpam-5290	20	15	if	if	SCONJ
ejpam-5290	20	16	all	all	PRON
ejpam-5290	20	17	of	of	ADP
ejpam-5290	20	18	the	the	DET
ejpam-5290	20	19	vertices	vertex	NOUN
ejpam-5290	20	20	have	have	VERB
ejpam-5290	20	21	the	the	DET
ejpam-5290	20	22	same	same	ADJ
ejpam-5290	20	23	degree	degree	NOUN
ejpam-5290	20	24	n.	n.	NOUN
ejpam-5290	20	25	doi	doi	PROPN
ejpam-5290	20	26	:	:	PUNCT
ejpam-5290	20	27	https://doi.org/10.29020/nybg.ejpam.v17i4.5290	https://doi.org/10.29020/nybg.ejpam.v17i4.5290	DET
ejpam-5290	20	28	email	email	NOUN
ejpam-5290	20	29	address	address	NOUN
ejpam-5290	20	30	:	:	PUNCT
ejpam-5290	20	31	gmbadri@uqu.edu.sa	gmbadri@uqu.edu.sa	NOUN
ejpam-5290	20	32	(	(	PUNCT
ejpam-5290	20	33	g.	g.	PROPN
ejpam-5290	20	34	m.	m.	PROPN
ejpam-5290	20	35	badri	badri	PROPN
ejpam-5290	20	36	)	)	PUNCT
ejpam-5290	20	37	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5290	20	38	3079	3079	NUM
ejpam-5290	20	39	copyright	copyright	NOUN
ejpam-5290	20	40	:	:	PUNCT
ejpam-5290	20	41	©	©	PROPN
ejpam-5290	20	42	2024	2024	NUM
ejpam-5290	20	43	the	the	DET
ejpam-5290	20	44	author(s	author(s	NOUN
ejpam-5290	20	45	)	)	PUNCT
ejpam-5290	20	46	.	.	PUNCT
ejpam-5290	21	1	(	(	PUNCT
ejpam-5290	21	2	cc	cc	NOUN
ejpam-5290	21	3	by	by	ADP
ejpam-5290	21	4	-	-	PUNCT
ejpam-5290	21	5	nc	nc	PROPN
ejpam-5290	21	6	4.0	4.0	NUM
ejpam-5290	21	7	)	)	PUNCT
ejpam-5290	21	8	g.	g.	PROPN
ejpam-5290	21	9	m.	m.	PROPN
ejpam-5290	21	10	badri	badri	PROPN
ejpam-5290	21	11	/	/	SYM
ejpam-5290	21	12	eur	eur	PROPN
ejpam-5290	21	13	.	.	PUNCT
ejpam-5290	22	1	j.	j.	PROPN
ejpam-5290	22	2	pure	pure	PROPN
ejpam-5290	22	3	appl	appl	PROPN
ejpam-5290	22	4	.	.	PROPN
ejpam-5290	22	5	math	math	PROPN
ejpam-5290	22	6	,	,	PUNCT
ejpam-5290	22	7	17	17	NUM
ejpam-5290	22	8	(	(	PUNCT
ejpam-5290	22	9	4	4	NUM
ejpam-5290	22	10	)	)	PUNCT
ejpam-5290	22	11	(	(	PUNCT
ejpam-5290	22	12	2024	2024	NUM
ejpam-5290	22	13	)	)	PUNCT
ejpam-5290	22	14	,	,	PUNCT
ejpam-5290	22	15	3079	3079	NUM
ejpam-5290	22	16	-	-	SYM
ejpam-5290	22	17	3092	3092	NUM
ejpam-5290	22	18	3080	3080	NUM
ejpam-5290	22	19	any	any	DET
ejpam-5290	22	20	displacement	displacement	NOUN
ejpam-5290	22	21	of	of	ADP
ejpam-5290	22	22	the	the	DET
ejpam-5290	22	23	framework	framework	NOUN
ejpam-5290	22	24	that	that	PRON
ejpam-5290	22	25	preserves	preserve	VERB
ejpam-5290	22	26	the	the	DET
ejpam-5290	22	27	distances	distance	NOUN
ejpam-5290	22	28	between	between	ADP
ejpam-5290	22	29	each	each	DET
ejpam-5290	22	30	pair	pair	NOUN
ejpam-5290	22	31	of	of	ADP
ejpam-5290	22	32	framework	framework	NOUN
ejpam-5290	22	33	vertices	vertex	NOUN
ejpam-5290	22	34	is	be	AUX
ejpam-5290	22	35	called	call	VERB
ejpam-5290	22	36	a	a	DET
ejpam-5290	22	37	rigid	rigid	ADJ
ejpam-5290	22	38	body	body	NOUN
ejpam-5290	22	39	motion	motion	NOUN
ejpam-5290	22	40	.	.	PUNCT
ejpam-5290	23	1	this	this	DET
ejpam-5290	23	2	transition	transition	NOUN
ejpam-5290	23	3	,	,	PUNCT
ejpam-5290	23	4	known	know	VERB
ejpam-5290	23	5	as	as	ADP
ejpam-5290	23	6	a	a	DET
ejpam-5290	23	7	flexing	flexing	NOUN
ejpam-5290	23	8	of	of	ADP
ejpam-5290	23	9	the	the	DET
ejpam-5290	23	10	structure	structure	NOUN
ejpam-5290	23	11	,	,	PUNCT
ejpam-5290	23	12	occurs	occur	VERB
ejpam-5290	23	13	when	when	SCONJ
ejpam-5290	23	14	the	the	DET
ejpam-5290	23	15	lengths	length	NOUN
ejpam-5290	23	16	between	between	ADP
ejpam-5290	23	17	vertices	vertex	NOUN
ejpam-5290	23	18	that	that	PRON
ejpam-5290	23	19	are	be	AUX
ejpam-5290	23	20	not	not	PART
ejpam-5290	23	21	connected	connect	VERB
ejpam-5290	23	22	by	by	ADP
ejpam-5290	23	23	an	an	DET
ejpam-5290	23	24	edge	edge	NOUN
ejpam-5290	23	25	change	change	NOUN
ejpam-5290	23	26	.	.	PUNCT
ejpam-5290	24	1	the	the	DET
ejpam-5290	24	2	outcome	outcome	NOUN
ejpam-5290	24	3	is	be	AUX
ejpam-5290	24	4	a	a	DET
ejpam-5290	24	5	new	new	ADJ
ejpam-5290	24	6	configuration	configuration	NOUN
ejpam-5290	24	7	that	that	PRON
ejpam-5290	24	8	differs	differ	VERB
ejpam-5290	24	9	from	from	ADP
ejpam-5290	24	10	the	the	DET
ejpam-5290	24	11	previous	previous	ADJ
ejpam-5290	24	12	one	one	NUM
ejpam-5290	24	13	.	.	PUNCT
ejpam-5290	25	1	in	in	ADP
ejpam-5290	25	2	the	the	DET
ejpam-5290	25	3	euclidean	euclidean	ADJ
ejpam-5290	25	4	plane	plane	NOUN
ejpam-5290	25	5	r2	r2	NOUN
ejpam-5290	25	6	,	,	PUNCT
ejpam-5290	25	7	it	it	PRON
ejpam-5290	25	8	is	be	AUX
ejpam-5290	25	9	evident	evident	ADJ
ejpam-5290	25	10	that	that	SCONJ
ejpam-5290	25	11	rigid	rigid	ADJ
ejpam-5290	25	12	body	body	NOUN
ejpam-5290	25	13	motions	motion	NOUN
ejpam-5290	25	14	result	result	VERB
ejpam-5290	25	15	form	form	NOUN
ejpam-5290	25	16	linear	linear	ADJ
ejpam-5290	25	17	combinations	combination	NOUN
ejpam-5290	25	18	of	of	ADP
ejpam-5290	25	19	rotations	rotation	NOUN
ejpam-5290	25	20	and	and	CCONJ
ejpam-5290	25	21	translations	translation	NOUN
ejpam-5290	25	22	in	in	ADP
ejpam-5290	25	23	either	either	CCONJ
ejpam-5290	25	24	coordinate	coordinate	ADJ
ejpam-5290	25	25	direction	direction	NOUN
ejpam-5290	25	26	.	.	PUNCT
ejpam-5290	26	1	definition	definition	NOUN
ejpam-5290	26	2	2	2	NUM
ejpam-5290	26	3	.	.	PUNCT
ejpam-5290	27	1	let	let	VERB
ejpam-5290	27	2	g	g	NOUN
ejpam-5290	27	3	=	=	PUNCT
ejpam-5290	27	4	(	(	PUNCT
ejpam-5290	27	5	g	g	PROPN
ejpam-5290	27	6	,	,	PUNCT
ejpam-5290	27	7	p	p	X
ejpam-5290	27	8	)	)	PUNCT
ejpam-5290	27	9	be	be	AUX
ejpam-5290	27	10	a	a	DET
ejpam-5290	27	11	finite	finite	ADJ
ejpam-5290	27	12	framework	framework	NOUN
ejpam-5290	27	13	with	with	ADP
ejpam-5290	27	14	|v	|v	PROPN
ejpam-5290	28	1	|	|	NOUN
ejpam-5290	28	2	=	=	SYM
ejpam-5290	28	3	n	n	X
ejpam-5290	28	4	in	in	ADP
ejpam-5290	28	5	r2	r2	PROPN
ejpam-5290	28	6	.	.	PUNCT
ejpam-5290	29	1	a	a	DET
ejpam-5290	29	2	vector	vector	NOUN
ejpam-5290	29	3	u	u	NOUN
ejpam-5290	29	4	=	=	PUNCT
ejpam-5290	29	5	(	(	PUNCT
ejpam-5290	29	6	u1	u1	PROPN
ejpam-5290	29	7	,	,	PUNCT
ejpam-5290	29	8	.	.	PUNCT
ejpam-5290	29	9	.	.	PUNCT
ejpam-5290	29	10	.	.	PUNCT
ejpam-5290	29	11	,	,	PUNCT
ejpam-5290	29	12	un	un	PROPN
ejpam-5290	29	13	)	)	PUNCT
ejpam-5290	29	14	in	in	ADP
ejpam-5290	29	15	the	the	DET
ejpam-5290	29	16	vector	vector	NOUN
ejpam-5290	29	17	space	space	NOUN
ejpam-5290	29	18	hv(g	hv(g	NOUN
ejpam-5290	29	19	)	)	PUNCT
ejpam-5290	29	20	=	=	SYM
ejpam-5290	30	1	n⊕	n⊕	PROPN
ejpam-5290	30	2	i=1	i=1	PROPN
ejpam-5290	30	3	r2	r2	PROPN
ejpam-5290	30	4	is	be	AUX
ejpam-5290	30	5	called	call	VERB
ejpam-5290	30	6	an	an	DET
ejpam-5290	30	7	infinitesimal	infinitesimal	ADJ
ejpam-5290	30	8	flex	flex	NOUN
ejpam-5290	30	9	if	if	SCONJ
ejpam-5290	30	10	and	and	CCONJ
ejpam-5290	30	11	only	only	ADV
ejpam-5290	30	12	if	if	SCONJ
ejpam-5290	30	13	the	the	DET
ejpam-5290	30	14	orthogonality	orthogonality	NOUN
ejpam-5290	30	15	relation	relation	NOUN
ejpam-5290	30	16	⟨pi	⟨pi	PROPN
ejpam-5290	30	17	−	−	PROPN
ejpam-5290	30	18	pj	pj	PROPN
ejpam-5290	30	19	,	,	PUNCT
ejpam-5290	30	20	ui	ui	PROPN
ejpam-5290	30	21	−	−	PROPN
ejpam-5290	30	22	uj⟩	uj⟩	PROPN
ejpam-5290	30	23	=	=	NOUN
ejpam-5290	30	24	0	0	NUM
ejpam-5290	30	25	is	be	AUX
ejpam-5290	30	26	held	hold	VERB
ejpam-5290	30	27	for	for	ADP
ejpam-5290	30	28	any	any	DET
ejpam-5290	30	29	edge	edge	NOUN
ejpam-5290	30	30	e	e	NOUN
ejpam-5290	31	1	=	=	PUNCT
ejpam-5290	32	1	[	[	X
ejpam-5290	32	2	pi	pi	NOUN
ejpam-5290	32	3	,	,	PUNCT
ejpam-5290	32	4	pj	pj	PROPN
ejpam-5290	32	5	]	]	PUNCT
ejpam-5290	32	6	.	.	PUNCT
ejpam-5290	33	1	a	a	DET
ejpam-5290	33	2	framework	framework	NOUN
ejpam-5290	33	3	g	g	NOUN
ejpam-5290	33	4	is	be	AUX
ejpam-5290	33	5	infinitesimally	infinitesimally	ADV
ejpam-5290	33	6	rigid	rigid	ADJ
ejpam-5290	33	7	if	if	SCONJ
ejpam-5290	33	8	every	every	DET
ejpam-5290	33	9	infinitesimal	infinitesimal	ADJ
ejpam-5290	33	10	flex	flex	NOUN
ejpam-5290	33	11	of	of	ADP
ejpam-5290	33	12	g	g	PROPN
ejpam-5290	33	13	is	be	AUX
ejpam-5290	33	14	trivial	trivial	ADJ
ejpam-5290	33	15	,	,	PUNCT
ejpam-5290	33	16	and	and	CCONJ
ejpam-5290	33	17	infinitesimally	infinitesimally	ADV
ejpam-5290	33	18	flexible	flexible	ADJ
ejpam-5290	33	19	otherwise	otherwise	ADV
ejpam-5290	33	20	.	.	PUNCT
ejpam-5290	34	1	if	if	SCONJ
ejpam-5290	34	2	,	,	PUNCT
ejpam-5290	34	3	however	however	ADV
ejpam-5290	34	4	,	,	PUNCT
ejpam-5290	34	5	all	all	DET
ejpam-5290	34	6	pairs	pair	NOUN
ejpam-5290	34	7	of	of	ADP
ejpam-5290	34	8	framework	framework	NOUN
ejpam-5290	34	9	vertices	vertex	NOUN
ejpam-5290	34	10	,	,	PUNCT
ejpam-5290	34	11	not	not	PART
ejpam-5290	34	12	just	just	ADV
ejpam-5290	34	13	those	those	PRON
ejpam-5290	34	14	that	that	PRON
ejpam-5290	34	15	form	form	NOUN
ejpam-5290	34	16	edges	edge	VERB
ejpam-5290	34	17	,	,	PUNCT
ejpam-5290	34	18	satisfy	satisfy	VERB
ejpam-5290	34	19	the	the	DET
ejpam-5290	34	20	above	above	ADJ
ejpam-5290	34	21	condition	condition	NOUN
ejpam-5290	34	22	,	,	PUNCT
ejpam-5290	34	23	then	then	ADV
ejpam-5290	34	24	u	u	NOUN
ejpam-5290	34	25	is	be	AUX
ejpam-5290	34	26	considered	consider	VERB
ejpam-5290	34	27	a	a	DET
ejpam-5290	34	28	trivial	trivial	ADJ
ejpam-5290	34	29	infinitesimal	infinitesimal	ADJ
ejpam-5290	34	30	flex	flex	ADJ
ejpam-5290	34	31	,	,	PUNCT
ejpam-5290	34	32	or	or	CCONJ
ejpam-5290	34	33	an	an	DET
ejpam-5290	34	34	infinitesimal	infinitesimal	ADJ
ejpam-5290	34	35	rigid	rigid	ADJ
ejpam-5290	34	36	body	body	NOUN
ejpam-5290	34	37	motion	motion	NOUN
ejpam-5290	34	38	.	.	PUNCT
ejpam-5290	35	1	hv(g	hv(g	PROPN
ejpam-5290	35	2	)	)	PUNCT
ejpam-5290	35	3	will	will	AUX
ejpam-5290	35	4	be	be	AUX
ejpam-5290	35	5	used	use	VERB
ejpam-5290	35	6	to	to	PART
ejpam-5290	35	7	represent	represent	VERB
ejpam-5290	35	8	the	the	DET
ejpam-5290	35	9	vector	vector	NOUN
ejpam-5290	35	10	space	space	NOUN
ejpam-5290	35	11	containing	contain	VERB
ejpam-5290	35	12	all	all	DET
ejpam-5290	35	13	velocity	velocity	NOUN
ejpam-5290	35	14	vectors	vector	NOUN
ejpam-5290	35	15	allocated	allocate	VERB
ejpam-5290	35	16	to	to	ADP
ejpam-5290	35	17	the	the	DET
ejpam-5290	35	18	vertices	vertex	NOUN
ejpam-5290	35	19	of	of	ADP
ejpam-5290	35	20	the	the	DET
ejpam-5290	35	21	framework	framework	NOUN
ejpam-5290	35	22	.	.	PUNCT
ejpam-5290	36	1	a	a	DET
ejpam-5290	36	2	vector	vector	NOUN
ejpam-5290	36	3	subspace	subspace	NOUN
ejpam-5290	36	4	of	of	ADP
ejpam-5290	36	5	hv(g	hv(g	PROPN
ejpam-5290	36	6	)	)	PUNCT
ejpam-5290	36	7	,	,	PUNCT
ejpam-5290	36	8	which	which	PRON
ejpam-5290	36	9	includes	include	VERB
ejpam-5290	36	10	the	the	DET
ejpam-5290	36	11	subspace	subspace	NOUN
ejpam-5290	36	12	of	of	ADP
ejpam-5290	36	13	all	all	DET
ejpam-5290	36	14	infinitesimal	infinitesimal	ADJ
ejpam-5290	36	15	rigid	rigid	ADJ
ejpam-5290	36	16	motions	motion	NOUN
ejpam-5290	36	17	hrig(g	hrig(g	NOUN
ejpam-5290	36	18	)	)	PUNCT
ejpam-5290	36	19	,	,	PUNCT
ejpam-5290	36	20	is	be	AUX
ejpam-5290	36	21	the	the	DET
ejpam-5290	36	22	space	space	NOUN
ejpam-5290	36	23	hfl(g	hfl(g	PROPN
ejpam-5290	36	24	)	)	PUNCT
ejpam-5290	36	25	of	of	ADP
ejpam-5290	36	26	all	all	DET
ejpam-5290	36	27	infinitesimal	infinitesimal	ADJ
ejpam-5290	36	28	flexes	flex	NOUN
ejpam-5290	36	29	of	of	ADP
ejpam-5290	36	30	g.	g.	PROPN
ejpam-5290	36	31	definition	definition	NOUN
ejpam-5290	36	32	3	3	NUM
ejpam-5290	36	33	.	.	PUNCT
ejpam-5290	37	1	in	in	ADP
ejpam-5290	37	2	r2	r2	PROPN
ejpam-5290	37	3	,	,	PUNCT
ejpam-5290	37	4	let	let	VERB
ejpam-5290	37	5	g	g	NOUN
ejpam-5290	37	6	=	=	PUNCT
ejpam-5290	37	7	(	(	PUNCT
ejpam-5290	37	8	g	g	PROPN
ejpam-5290	37	9	,	,	PUNCT
ejpam-5290	37	10	p	p	X
ejpam-5290	37	11	)	)	PUNCT
ejpam-5290	37	12	be	be	AUX
ejpam-5290	37	13	an	an	DET
ejpam-5290	37	14	infinite	infinite	ADJ
ejpam-5290	37	15	framework	framework	NOUN
ejpam-5290	37	16	.	.	PUNCT
ejpam-5290	38	1	a	a	DET
ejpam-5290	38	2	vector	vector	NOUN
ejpam-5290	38	3	in	in	ADP
ejpam-5290	38	4	hv(g	hv(g	PROPN
ejpam-5290	38	5	)	)	PUNCT
ejpam-5290	39	1	=	=	SYM
ejpam-5290	39	2	∏	∏	PROPN
ejpam-5290	39	3	v	v	NOUN
ejpam-5290	39	4	r2	r2	NOUN
ejpam-5290	39	5	=	=	SYM
ejpam-5290	39	6	r2	r2	PROPN
ejpam-5290	39	7	⊕	⊕	PROPN
ejpam-5290	39	8	r2	r2	PROPN
ejpam-5290	39	9	⊕	⊕	PROPN
ejpam-5290	39	10	+	+	PUNCT
ejpam-5290	39	11	.	.	PUNCT
ejpam-5290	39	12	.	.	PUNCT
ejpam-5290	39	13	.	.	PUNCT
ejpam-5290	40	1	is	be	AUX
ejpam-5290	40	2	an	an	DET
ejpam-5290	40	3	infinitesimal	infinitesimal	ADJ
ejpam-5290	40	4	flex	flex	NOUN
ejpam-5290	40	5	of	of	ADP
ejpam-5290	40	6	g	g	NOUN
ejpam-5290	40	7	for	for	ADP
ejpam-5290	40	8	which	which	PRON
ejpam-5290	40	9	,	,	PUNCT
ejpam-5290	40	10	just	just	ADV
ejpam-5290	40	11	like	like	INTJ
ejpam-5290	40	12	in	in	ADP
ejpam-5290	40	13	the	the	DET
ejpam-5290	40	14	finite	finite	ADJ
ejpam-5290	40	15	case	case	NOUN
ejpam-5290	40	16	,	,	PUNCT
ejpam-5290	40	17	⟨ui	⟨ui	PROPN
ejpam-5290	40	18	−	−	PROPN
ejpam-5290	40	19	uj	uj	PROPN
ejpam-5290	40	20	,	,	PUNCT
ejpam-5290	40	21	pi	pi	NOUN
ejpam-5290	40	22	−	−	PROPN
ejpam-5290	40	23	pj⟩	pj⟩	PROPN
ejpam-5290	40	24	=	=	SYM
ejpam-5290	40	25	0	0	NUM
ejpam-5290	40	26	is	be	AUX
ejpam-5290	40	27	held	hold	VERB
ejpam-5290	40	28	for	for	ADP
ejpam-5290	40	29	every	every	DET
ejpam-5290	40	30	edge	edge	NOUN
ejpam-5290	40	31	e	e	NOUN
ejpam-5290	40	32	=	=	PUNCT
ejpam-5290	41	1	[	[	X
ejpam-5290	41	2	pi	pi	NOUN
ejpam-5290	41	3	,	,	PUNCT
ejpam-5290	41	4	pj	pj	PROPN
ejpam-5290	41	5	]	]	PUNCT
ejpam-5290	41	6	.	.	PUNCT
ejpam-5290	42	1	let	let	VERB
ejpam-5290	42	2	hfl(g	hfl(g	PROPN
ejpam-5290	42	3	)	)	PUNCT
ejpam-5290	42	4	be	be	AUX
ejpam-5290	42	5	the	the	DET
ejpam-5290	42	6	linear	linear	ADJ
ejpam-5290	42	7	space	space	NOUN
ejpam-5290	42	8	of	of	ADP
ejpam-5290	42	9	all	all	DET
ejpam-5290	42	10	infinitesimal	infinitesimal	ADJ
ejpam-5290	42	11	flexes	flex	NOUN
ejpam-5290	42	12	,	,	PUNCT
ejpam-5290	42	13	adapting	adapt	VERB
ejpam-5290	42	14	the	the	DET
ejpam-5290	42	15	same	same	ADJ
ejpam-5290	42	16	notation	notation	NOUN
ejpam-5290	42	17	as	as	ADP
ejpam-5290	42	18	in	in	ADP
ejpam-5290	42	19	the	the	DET
ejpam-5290	42	20	finite	finite	ADJ
ejpam-5290	42	21	case	case	NOUN
ejpam-5290	42	22	.	.	PUNCT
ejpam-5290	43	1	this	this	PRON
ejpam-5290	43	2	includes	include	VERB
ejpam-5290	43	3	the	the	DET
ejpam-5290	43	4	three	three	NUM
ejpam-5290	43	5	dimensional	dimensional	ADJ
ejpam-5290	43	6	space	space	NOUN
ejpam-5290	43	7	of	of	ADP
ejpam-5290	43	8	rigid	rigid	ADJ
ejpam-5290	43	9	body	body	NOUN
ejpam-5290	43	10	motions	motion	NOUN
ejpam-5290	43	11	hrig(g	hrig(g	NOUN
ejpam-5290	43	12	)	)	PUNCT
ejpam-5290	43	13	which	which	PRON
ejpam-5290	43	14	is	be	AUX
ejpam-5290	43	15	spanned	span	VERB
ejpam-5290	43	16	by	by	ADP
ejpam-5290	43	17	two	two	NUM
ejpam-5290	43	18	translations	translation	NOUN
ejpam-5290	43	19	and	and	CCONJ
ejpam-5290	43	20	one	one	NUM
ejpam-5290	43	21	rotation	rotation	NOUN
ejpam-5290	43	22	.	.	PUNCT
ejpam-5290	44	1	see	see	VERB
ejpam-5290	44	2	[	[	X
ejpam-5290	44	3	5	5	NUM
ejpam-5290	44	4	]	]	PUNCT
ejpam-5290	44	5	,	,	PUNCT
ejpam-5290	44	6	[	[	X
ejpam-5290	44	7	11	11	NUM
ejpam-5290	44	8	]	]	PUNCT
ejpam-5290	44	9	,	,	PUNCT
ejpam-5290	44	10	[	[	X
ejpam-5290	44	11	14	14	NUM
ejpam-5290	44	12	]	]	PUNCT
ejpam-5290	44	13	and	and	CCONJ
ejpam-5290	44	14	[	[	X
ejpam-5290	44	15	24	24	NUM
ejpam-5290	44	16	]	]	PUNCT
ejpam-5290	44	17	for	for	ADP
ejpam-5290	44	18	a	a	DET
ejpam-5290	44	19	thorough	thorough	ADJ
ejpam-5290	44	20	introduction	introduction	NOUN
ejpam-5290	44	21	to	to	ADP
ejpam-5290	44	22	bar	bar	NOUN
ejpam-5290	44	23	-	-	PUNCT
ejpam-5290	44	24	joint	joint	ADJ
ejpam-5290	44	25	frameworks	framework	NOUN
ejpam-5290	44	26	.	.	PUNCT
ejpam-5290	45	1	definition	definition	NOUN
ejpam-5290	45	2	4	4	NUM
ejpam-5290	45	3	.	.	PUNCT
ejpam-5290	46	1	r(g	r(g	ADJ
ejpam-5290	46	2	,	,	PUNCT
ejpam-5290	46	3	p	p	NOUN
ejpam-5290	46	4	)	)	PUNCT
ejpam-5290	46	5	is	be	AUX
ejpam-5290	46	6	the	the	DET
ejpam-5290	46	7	rigidity	rigidity	NOUN
ejpam-5290	46	8	matrix	matrix	NOUN
ejpam-5290	46	9	of	of	ADP
ejpam-5290	46	10	the	the	DET
ejpam-5290	46	11	infinite	infinite	ADJ
ejpam-5290	46	12	framework	framework	NOUN
ejpam-5290	46	13	g	g	NOUN
ejpam-5290	46	14	=	=	PUNCT
ejpam-5290	46	15	(	(	PUNCT
ejpam-5290	46	16	g	g	NOUN
ejpam-5290	46	17	,	,	PUNCT
ejpam-5290	46	18	p	p	NOUN
ejpam-5290	46	19	)	)	PUNCT
ejpam-5290	46	20	.	.	PUNCT
ejpam-5290	47	1	in	in	ADP
ejpam-5290	47	2	r2	r2	PROPN
ejpam-5290	47	3	,	,	PUNCT
ejpam-5290	47	4	it	it	PRON
ejpam-5290	47	5	consists	consist	VERB
ejpam-5290	47	6	of	of	ADP
ejpam-5290	47	7	rows	row	NOUN
ejpam-5290	47	8	indexed	index	VERB
ejpam-5290	47	9	by	by	ADP
ejpam-5290	47	10	the	the	DET
ejpam-5290	47	11	framework	framework	NOUN
ejpam-5290	47	12	edges	edge	NOUN
ejpam-5290	47	13	and	and	CCONJ
ejpam-5290	47	14	columns	column	NOUN
ejpam-5290	47	15	labelled	label	VERB
ejpam-5290	47	16	by	by	ADP
ejpam-5290	47	17	the	the	DET
ejpam-5290	47	18	vertices	vertex	NOUN
ejpam-5290	47	19	but	but	CCONJ
ejpam-5290	47	20	with	with	ADP
ejpam-5290	47	21	multiplicity	multiplicity	NOUN
ejpam-5290	47	22	two	two	NUM
ejpam-5290	47	23	,	,	PUNCT
ejpam-5290	47	24	i.e.	i.e.	X
ejpam-5290	47	25	,	,	PUNCT
ejpam-5290	47	26	vx1	vx1	NOUN
ejpam-5290	47	27	,	,	PUNCT
ejpam-5290	47	28	v	v	NOUN
ejpam-5290	47	29	y	y	PROPN
ejpam-5290	47	30	1	1	NUM
ejpam-5290	47	31	,	,	PUNCT
ejpam-5290	47	32	v	v	NOUN
ejpam-5290	47	33	x	x	SYM
ejpam-5290	47	34	2	2	NUM
ejpam-5290	47	35	,	,	PUNCT
ejpam-5290	47	36	v	v	NOUN
ejpam-5290	47	37	y	y	PROPN
ejpam-5290	47	38	2	2	NUM
ejpam-5290	47	39	,	,	PUNCT
ejpam-5290	47	40	.	.	PUNCT
ejpam-5290	47	41	.	.	PUNCT
ejpam-5290	47	42	.	.	PUNCT
ejpam-5290	47	43	.	.	PUNCT
ejpam-5290	48	1	the	the	DET
ejpam-5290	48	2	entries	entry	NOUN
ejpam-5290	48	3	xi	xi	ADP
ejpam-5290	48	4	−	−	PROPN
ejpam-5290	48	5	xj	xj	PROPN
ejpam-5290	48	6	,	,	PUNCT
ejpam-5290	48	7	xj	xj	PROPN
ejpam-5290	48	8	−	−	PROPN
ejpam-5290	48	9	xi	xi	PROPN
ejpam-5290	48	10	,	,	PUNCT
ejpam-5290	48	11	yi	yi	PROPN
ejpam-5290	48	12	−	−	PROPN
ejpam-5290	48	13	yj	yj	PROPN
ejpam-5290	48	14	,	,	PUNCT
ejpam-5290	48	15	yj	yj	PROPN
ejpam-5290	48	16	−	−	PROPN
ejpam-5290	48	17	yi	yi	PROPN
ejpam-5290	48	18	occur	occur	VERB
ejpam-5290	48	19	in	in	ADP
ejpam-5290	48	20	the	the	DET
ejpam-5290	48	21	row	row	NOUN
ejpam-5290	48	22	labelled	label	VERB
ejpam-5290	48	23	e	e	NOUN
ejpam-5290	48	24	=	=	SYM
ejpam-5290	48	25	(	(	PUNCT
ejpam-5290	48	26	vi	vi	PROPN
ejpam-5290	48	27	,	,	PUNCT
ejpam-5290	48	28	vj	vj	NOUN
ejpam-5290	48	29	)	)	PUNCT
ejpam-5290	48	30	with	with	ADP
ejpam-5290	48	31	respective	respective	ADJ
ejpam-5290	48	32	column	column	NOUN
ejpam-5290	48	33	labels	label	VERB
ejpam-5290	48	34	vxi	vxi	ADV
ejpam-5290	48	35	,	,	PUNCT
ejpam-5290	48	36	v	v	NOUN
ejpam-5290	48	37	y	y	NOUN
ejpam-5290	49	1	i	i	PRON
ejpam-5290	49	2	,	,	PUNCT
ejpam-5290	49	3	v	v	X
ejpam-5290	49	4	x	x	SYM
ejpam-5290	49	5	j	j	PROPN
ejpam-5290	49	6	,	,	PUNCT
ejpam-5290	49	7	v	v	PROPN
ejpam-5290	49	8	y	y	PROPN
ejpam-5290	49	9	j	j	PROPN
ejpam-5290	49	10	and	and	CCONJ
ejpam-5290	49	11	equal	equal	ADJ
ejpam-5290	49	12	zero	zero	NUM
ejpam-5290	49	13	elsewhere	elsewhere	ADV
ejpam-5290	49	14	.	.	PUNCT
ejpam-5290	50	1	r(g	r(g	ADJ
ejpam-5290	50	2	,	,	PUNCT
ejpam-5290	50	3	p	p	NOUN
ejpam-5290	50	4	)	)	PUNCT
ejpam-5290	50	5	defines	define	VERB
ejpam-5290	50	6	a	a	DET
ejpam-5290	50	7	linear	linear	ADJ
ejpam-5290	50	8	transformation	transformation	NOUN
ejpam-5290	50	9	from	from	ADP
ejpam-5290	50	10	the	the	DET
ejpam-5290	50	11	space	space	NOUN
ejpam-5290	50	12	hv(g	hv(g	NOUN
ejpam-5290	50	13	)	)	PUNCT
ejpam-5290	51	1	=	=	SYM
ejpam-5290	51	2	∏	∏	PROPN
ejpam-5290	51	3	v	v	NUM
ejpam-5290	51	4	r2	r2	PROPN
ejpam-5290	51	5	to	to	ADP
ejpam-5290	51	6	he(g	he(g	PUNCT
ejpam-5290	51	7	)	)	PUNCT
ejpam-5290	52	1	=	=	SYM
ejpam-5290	52	2	∏	∏	NUM
ejpam-5290	52	3	e	e	NOUN
ejpam-5290	52	4	r	r	NOUN
ejpam-5290	52	5	and	and	CCONJ
ejpam-5290	52	6	it	it	PRON
ejpam-5290	52	7	can	can	AUX
ejpam-5290	52	8	be	be	AUX
ejpam-5290	52	9	seen	see	VERB
ejpam-5290	52	10	that	that	SCONJ
ejpam-5290	52	11	a	a	DET
ejpam-5290	52	12	vector	vector	NOUN
ejpam-5290	52	13	u	u	NOUN
ejpam-5290	52	14	in	in	ADP
ejpam-5290	52	15	hv(g	hv(g	PROPN
ejpam-5290	52	16	)	)	PUNCT
ejpam-5290	52	17	is	be	AUX
ejpam-5290	52	18	an	an	DET
ejpam-5290	52	19	infinitesimal	infinitesimal	ADJ
ejpam-5290	52	20	flex	flex	NOUN
ejpam-5290	52	21	if	if	SCONJ
ejpam-5290	53	1	and	and	CCONJ
ejpam-5290	53	2	only	only	ADV
ejpam-5290	53	3	if	if	SCONJ
ejpam-5290	53	4	r(g	r(g	NUM
ejpam-5290	53	5	,	,	PUNCT
ejpam-5290	53	6	p)u	p)u	PUNCT
ejpam-5290	53	7	=	=	PUNCT
ejpam-5290	54	1	0	0	X
ejpam-5290	54	2	.	.	PUNCT
ejpam-5290	54	3	g.	g.	PROPN
ejpam-5290	54	4	m.	m.	PROPN
ejpam-5290	54	5	badri	badri	PROPN
ejpam-5290	54	6	/	/	SYM
ejpam-5290	54	7	eur	eur	PROPN
ejpam-5290	54	8	.	.	PUNCT
ejpam-5290	55	1	j.	j.	PROPN
ejpam-5290	55	2	pure	pure	PROPN
ejpam-5290	55	3	appl	appl	PROPN
ejpam-5290	55	4	.	.	PROPN
ejpam-5290	55	5	math	math	PROPN
ejpam-5290	55	6	,	,	PUNCT
ejpam-5290	55	7	17	17	NUM
ejpam-5290	55	8	(	(	PUNCT
ejpam-5290	55	9	4	4	NUM
ejpam-5290	55	10	)	)	PUNCT
ejpam-5290	55	11	(	(	PUNCT
ejpam-5290	55	12	2024	2024	NUM
ejpam-5290	55	13	)	)	PUNCT
ejpam-5290	55	14	,	,	PUNCT
ejpam-5290	55	15	3079	3079	NUM
ejpam-5290	55	16	-	-	SYM
ejpam-5290	55	17	3092	3092	NUM
ejpam-5290	55	18	3081	3081	NUM
ejpam-5290	55	19	definition	definition	NOUN
ejpam-5290	55	20	5	5	NUM
ejpam-5290	55	21	.	.	PUNCT
ejpam-5290	56	1	a	a	DET
ejpam-5290	56	2	countably	countably	ADV
ejpam-5290	56	3	infinite	infinite	ADJ
ejpam-5290	56	4	framework	framework	NOUN
ejpam-5290	56	5	g	g	NOUN
ejpam-5290	56	6	=	=	PUNCT
ejpam-5290	56	7	(	(	PUNCT
ejpam-5290	56	8	g	g	PROPN
ejpam-5290	56	9	,	,	PUNCT
ejpam-5290	56	10	p	p	NOUN
ejpam-5290	56	11	)	)	PUNCT
ejpam-5290	56	12	is	be	AUX
ejpam-5290	56	13	edge	edge	NOUN
ejpam-5290	56	14	vanishing	vanish	VERB
ejpam-5290	56	15	if	if	SCONJ
ejpam-5290	56	16	the	the	DET
ejpam-5290	56	17	sequence	sequence	NOUN
ejpam-5290	56	18	(	(	PUNCT
ejpam-5290	56	19	dei	dei	NOUN
ejpam-5290	56	20	)	)	PUNCT
ejpam-5290	56	21	∞	∞	NUM
ejpam-5290	56	22	i=1	i=1	PROPN
ejpam-5290	56	23	formed	form	VERB
ejpam-5290	56	24	by	by	ADP
ejpam-5290	56	25	all	all	DET
ejpam-5290	56	26	bar	bar	NOUN
ejpam-5290	56	27	lengths	length	NOUN
ejpam-5290	56	28	has	have	VERB
ejpam-5290	56	29	no	no	PRON
ejpam-5290	56	30	lower	lower	ADV
ejpam-5290	56	31	bound	bind	VERB
ejpam-5290	56	32	.	.	PUNCT
ejpam-5290	57	1	g	g	PROPN
ejpam-5290	57	2	is	be	AUX
ejpam-5290	57	3	edge	edge	NOUN
ejpam-5290	57	4	unbounded	unbounded	ADJ
ejpam-5290	57	5	if	if	SCONJ
ejpam-5290	57	6	(	(	PUNCT
ejpam-5290	57	7	dei	dei	NOUN
ejpam-5290	57	8	)	)	PUNCT
ejpam-5290	57	9	∞	∞	NUM
ejpam-5290	57	10	i=1	i=1	PROPN
ejpam-5290	57	11	has	have	VERB
ejpam-5290	57	12	no	no	DET
ejpam-5290	57	13	upper	upper	ADJ
ejpam-5290	57	14	bound	bind	VERB
ejpam-5290	57	15	.	.	PUNCT
ejpam-5290	58	1	g	g	PROPN
ejpam-5290	58	2	is	be	AUX
ejpam-5290	58	3	distance	distance	NOUN
ejpam-5290	58	4	-	-	PUNCT
ejpam-5290	58	5	regular	regular	ADJ
ejpam-5290	58	6	if	if	SCONJ
ejpam-5290	58	7	(	(	PUNCT
ejpam-5290	58	8	dei	dei	NOUN
ejpam-5290	58	9	)	)	PUNCT
ejpam-5290	58	10	∞	∞	NUM
ejpam-5290	58	11	i=1	i=1	PROPN
ejpam-5290	58	12	is	be	AUX
ejpam-5290	58	13	bounded	bound	VERB
ejpam-5290	58	14	.	.	PUNCT
ejpam-5290	59	1	theorem	theorem	NOUN
ejpam-5290	59	2	1	1	NUM
ejpam-5290	59	3	.	.	PUNCT
ejpam-5290	60	1	[	[	X
ejpam-5290	60	2	20	20	NUM
ejpam-5290	60	3	]	]	PUNCT
ejpam-5290	60	4	for	for	ADP
ejpam-5290	60	5	a	a	DET
ejpam-5290	60	6	distance	distance	NOUN
ejpam-5290	60	7	regular	regular	ADJ
ejpam-5290	60	8	framework	framework	NOUN
ejpam-5290	60	9	in	in	ADP
ejpam-5290	60	10	r2	r2	PROPN
ejpam-5290	60	11	where	where	SCONJ
ejpam-5290	60	12	the	the	DET
ejpam-5290	60	13	degrees	degree	NOUN
ejpam-5290	60	14	of	of	ADP
ejpam-5290	60	15	the	the	DET
ejpam-5290	60	16	vertices	vertex	NOUN
ejpam-5290	60	17	are	be	AUX
ejpam-5290	60	18	uniformly	uniformly	ADV
ejpam-5290	60	19	bounded	bound	VERB
ejpam-5290	60	20	,	,	PUNCT
ejpam-5290	60	21	the	the	DET
ejpam-5290	60	22	rigidity	rigidity	NOUN
ejpam-5290	60	23	matrix	matrix	NOUN
ejpam-5290	60	24	determines	determine	VERB
ejpam-5290	60	25	a	a	DET
ejpam-5290	60	26	bounded	bounded	ADJ
ejpam-5290	60	27	hilbert	hilbert	PROPN
ejpam-5290	60	28	space	space	NOUN
ejpam-5290	60	29	transformation	transformation	NOUN
ejpam-5290	60	30	.	.	PUNCT
ejpam-5290	61	1	one	one	NUM
ejpam-5290	61	2	of	of	ADP
ejpam-5290	61	3	the	the	DET
ejpam-5290	61	4	earliest	early	ADJ
ejpam-5290	61	5	contributions	contribution	NOUN
ejpam-5290	61	6	towards	towards	ADP
ejpam-5290	61	7	rigidity	rigidity	NOUN
ejpam-5290	61	8	theory	theory	NOUN
ejpam-5290	61	9	is	be	AUX
ejpam-5290	61	10	due	due	ADJ
ejpam-5290	61	11	to	to	ADP
ejpam-5290	61	12	laman	laman	PROPN
ejpam-5290	61	13	,	,	PUNCT
ejpam-5290	61	14	[	[	X
ejpam-5290	61	15	16	16	NUM
ejpam-5290	61	16	]	]	PUNCT
ejpam-5290	61	17	.	.	PUNCT
ejpam-5290	62	1	laman	laman	PROPN
ejpam-5290	62	2	’s	’s	PART
ejpam-5290	62	3	theorem	theorem	NOUN
ejpam-5290	62	4	characterizes	characterize	VERB
ejpam-5290	62	5	the	the	DET
ejpam-5290	62	6	rigidity	rigidity	NOUN
ejpam-5290	62	7	of	of	ADP
ejpam-5290	62	8	a	a	DET
ejpam-5290	62	9	generic	generic	ADJ
ejpam-5290	62	10	framework	framework	NOUN
ejpam-5290	62	11	as	as	ADP
ejpam-5290	62	12	purely	purely	ADV
ejpam-5290	62	13	combinatorial	combinatorial	ADJ
ejpam-5290	62	14	,	,	PUNCT
ejpam-5290	62	15	regardless	regardless	ADV
ejpam-5290	62	16	of	of	ADP
ejpam-5290	62	17	its	its	PRON
ejpam-5290	62	18	geometry	geometry	NOUN
ejpam-5290	62	19	.	.	PUNCT
ejpam-5290	63	1	for	for	ADP
ejpam-5290	63	2	three	three	NUM
ejpam-5290	63	3	dimensional	dimensional	ADJ
ejpam-5290	63	4	frameworks	framework	NOUN
ejpam-5290	63	5	,	,	PUNCT
ejpam-5290	63	6	euler	euler	NOUN
ejpam-5290	63	7	conjectured	conjecture	VERB
ejpam-5290	63	8	that	that	SCONJ
ejpam-5290	63	9	“	"	PUNCT
ejpam-5290	63	10	a	a	DET
ejpam-5290	63	11	closed	closed	ADJ
ejpam-5290	63	12	spatial	spatial	ADJ
ejpam-5290	63	13	figure	figure	NOUN
ejpam-5290	63	14	allows	allow	VERB
ejpam-5290	63	15	no	no	DET
ejpam-5290	63	16	changes	change	NOUN
ejpam-5290	63	17	,	,	PUNCT
ejpam-5290	63	18	as	as	ADV
ejpam-5290	63	19	long	long	ADV
ejpam-5290	63	20	as	as	SCONJ
ejpam-5290	63	21	it	it	PRON
ejpam-5290	63	22	is	be	AUX
ejpam-5290	63	23	not	not	PART
ejpam-5290	63	24	ripped	rip	VERB
ejpam-5290	63	25	apart	apart	ADV
ejpam-5290	63	26	”	"	PUNCT
ejpam-5290	63	27	,	,	PUNCT
ejpam-5290	63	28	see	see	VERB
ejpam-5290	63	29	[	[	X
ejpam-5290	63	30	14	14	NUM
ejpam-5290	63	31	]	]	PUNCT
ejpam-5290	63	32	.	.	PUNCT
ejpam-5290	64	1	for	for	ADP
ejpam-5290	64	2	convex	convex	PROPN
ejpam-5290	64	3	polyhedra	polyhedra	NOUN
ejpam-5290	64	4	,	,	PUNCT
ejpam-5290	64	5	this	this	DET
ejpam-5290	64	6	conjecture	conjecture	NOUN
ejpam-5290	64	7	was	be	AUX
ejpam-5290	64	8	later	later	ADV
ejpam-5290	64	9	answered	answer	VERB
ejpam-5290	64	10	by	by	ADP
ejpam-5290	64	11	cauchy	cauchy	PROPN
ejpam-5290	64	12	[	[	X
ejpam-5290	64	13	9	9	NUM
ejpam-5290	64	14	]	]	PUNCT
ejpam-5290	64	15	,	,	PUNCT
ejpam-5290	64	16	who	who	PRON
ejpam-5290	64	17	proved	prove	VERB
ejpam-5290	64	18	that	that	SCONJ
ejpam-5290	64	19	“	"	PUNCT
ejpam-5290	64	20	if	if	SCONJ
ejpam-5290	64	21	there	there	PRON
ejpam-5290	64	22	is	be	VERB
ejpam-5290	64	23	an	an	DET
ejpam-5290	64	24	isometry	isometry	NOUN
ejpam-5290	64	25	between	between	ADP
ejpam-5290	64	26	the	the	DET
ejpam-5290	64	27	faces	face	NOUN
ejpam-5290	64	28	of	of	ADP
ejpam-5290	64	29	two	two	NUM
ejpam-5290	64	30	strictly	strictly	ADV
ejpam-5290	64	31	convex	convex	ADJ
ejpam-5290	64	32	polyhedra	polyhedra	NOUN
ejpam-5290	64	33	which	which	PRON
ejpam-5290	64	34	is	be	AUX
ejpam-5290	64	35	an	an	DET
ejpam-5290	64	36	isometry	isometry	NOUN
ejpam-5290	64	37	on	on	ADP
ejpam-5290	64	38	each	each	PRON
ejpam-5290	64	39	of	of	ADP
ejpam-5290	64	40	the	the	DET
ejpam-5290	64	41	faces	face	NOUN
ejpam-5290	64	42	,	,	PUNCT
ejpam-5290	64	43	then	then	ADV
ejpam-5290	64	44	the	the	DET
ejpam-5290	64	45	two	two	NUM
ejpam-5290	64	46	polyhedra	polyhedra	NOUN
ejpam-5290	64	47	are	be	AUX
ejpam-5290	64	48	congruent	congruent	ADJ
ejpam-5290	64	49	”	"	PUNCT
ejpam-5290	64	50	.	.	PUNCT
ejpam-5290	65	1	a	a	DET
ejpam-5290	65	2	corollary	corollary	NOUN
ejpam-5290	65	3	of	of	ADP
ejpam-5290	65	4	cauchy	cauchy	PROPN
ejpam-5290	65	5	’s	’s	PART
ejpam-5290	65	6	theorem	theorem	NOUN
ejpam-5290	65	7	is	be	AUX
ejpam-5290	65	8	that	that	SCONJ
ejpam-5290	65	9	all	all	DET
ejpam-5290	65	10	convex	convex	ADJ
ejpam-5290	65	11	polyhedrons	polyhedron	NOUN
ejpam-5290	65	12	are	be	AUX
ejpam-5290	65	13	in	in	ADP
ejpam-5290	65	14	fact	fact	NOUN
ejpam-5290	65	15	rigid	rigid	ADJ
ejpam-5290	65	16	.	.	PUNCT
ejpam-5290	66	1	the	the	DET
ejpam-5290	66	2	formal	formal	ADJ
ejpam-5290	66	3	identification	identification	NOUN
ejpam-5290	66	4	of	of	ADP
ejpam-5290	66	5	a	a	DET
ejpam-5290	66	6	mathematical	mathematical	ADJ
ejpam-5290	66	7	framework	framework	NOUN
ejpam-5290	66	8	as	as	ADP
ejpam-5290	66	9	a	a	DET
ejpam-5290	66	10	set	set	NOUN
ejpam-5290	66	11	of	of	ADP
ejpam-5290	66	12	bars	bar	NOUN
ejpam-5290	66	13	and	and	CCONJ
ejpam-5290	66	14	joints	joint	NOUN
ejpam-5290	66	15	was	be	AUX
ejpam-5290	66	16	first	first	ADV
ejpam-5290	66	17	introduced	introduce	VERB
ejpam-5290	66	18	by	by	ADP
ejpam-5290	66	19	asimov	asimov	PROPN
ejpam-5290	66	20	and	and	CCONJ
ejpam-5290	66	21	roth	roth	PROPN
ejpam-5290	66	22	[	[	X
ejpam-5290	66	23	3	3	NUM
ejpam-5290	66	24	]	]	PUNCT
ejpam-5290	66	25	,	,	PUNCT
ejpam-5290	66	26	[	[	X
ejpam-5290	66	27	4	4	NUM
ejpam-5290	66	28	]	]	PUNCT
ejpam-5290	66	29	,	,	PUNCT
ejpam-5290	66	30	[	[	X
ejpam-5290	66	31	22	22	NUM
ejpam-5290	66	32	]	]	PUNCT
ejpam-5290	66	33	where	where	SCONJ
ejpam-5290	66	34	each	each	DET
ejpam-5290	66	35	vertex	vertex	NOUN
ejpam-5290	66	36	corresponds	correspond	VERB
ejpam-5290	66	37	to	to	ADP
ejpam-5290	66	38	a	a	DET
ejpam-5290	66	39	joint	joint	NOUN
ejpam-5290	66	40	and	and	CCONJ
ejpam-5290	66	41	each	each	DET
ejpam-5290	66	42	bar	bar	NOUN
ejpam-5290	66	43	represents	represent	VERB
ejpam-5290	66	44	an	an	DET
ejpam-5290	66	45	edge	edge	NOUN
ejpam-5290	66	46	.	.	PUNCT
ejpam-5290	67	1	finally	finally	ADV
ejpam-5290	67	2	,	,	PUNCT
ejpam-5290	67	3	euler	euler	VERB
ejpam-5290	67	4	’s	’s	PART
ejpam-5290	67	5	conjecture	conjecture	NOUN
ejpam-5290	67	6	was	be	AUX
ejpam-5290	67	7	proven	prove	VERB
ejpam-5290	67	8	wrong	wrong	ADJ
ejpam-5290	67	9	by	by	ADP
ejpam-5290	67	10	connelly	connelly	PROPN
ejpam-5290	67	11	[	[	X
ejpam-5290	67	12	10	10	NUM
ejpam-5290	67	13	]	]	PUNCT
ejpam-5290	67	14	,	,	PUNCT
ejpam-5290	67	15	who	who	PRON
ejpam-5290	67	16	showed	show	VERB
ejpam-5290	67	17	that	that	SCONJ
ejpam-5290	67	18	there	there	PRON
ejpam-5290	67	19	exists	exist	VERB
ejpam-5290	67	20	a	a	DET
ejpam-5290	67	21	polyhedron	polyhedron	NOUN
ejpam-5290	67	22	that	that	PRON
ejpam-5290	67	23	is	be	AUX
ejpam-5290	67	24	not	not	PART
ejpam-5290	67	25	rigid	rigid	ADJ
ejpam-5290	67	26	.	.	PUNCT
ejpam-5290	68	1	recent	recent	ADJ
ejpam-5290	68	2	developments	development	NOUN
ejpam-5290	68	3	in	in	ADP
ejpam-5290	68	4	rigidity	rigidity	NOUN
ejpam-5290	68	5	theory	theory	NOUN
ejpam-5290	68	6	include	include	VERB
ejpam-5290	68	7	the	the	DET
ejpam-5290	68	8	formal	formal	ADJ
ejpam-5290	68	9	identification	identification	NOUN
ejpam-5290	68	10	of	of	ADP
ejpam-5290	68	11	an	an	DET
ejpam-5290	68	12	infinite	infinite	ADJ
ejpam-5290	68	13	bar	bar	NOUN
ejpam-5290	68	14	-	-	PUNCT
ejpam-5290	68	15	joint	joint	NOUN
ejpam-5290	68	16	framework	framework	NOUN
ejpam-5290	68	17	,	,	PUNCT
ejpam-5290	68	18	crystallographic	crystallographic	ADJ
ejpam-5290	68	19	bar	bar	NOUN
ejpam-5290	68	20	-	-	PUNCT
ejpam-5290	68	21	joint	joint	NOUN
ejpam-5290	68	22	frameworks	framework	NOUN
ejpam-5290	68	23	and	and	CCONJ
ejpam-5290	68	24	the	the	DET
ejpam-5290	68	25	rigidity	rigidity	NOUN
ejpam-5290	68	26	matrix	matrix	NOUN
ejpam-5290	68	27	by	by	ADP
ejpam-5290	68	28	owen	owen	NOUN
ejpam-5290	68	29	and	and	CCONJ
ejpam-5290	68	30	power	power	NOUN
ejpam-5290	68	31	,	,	PUNCT
ejpam-5290	68	32	[	[	X
ejpam-5290	68	33	20	20	NUM
ejpam-5290	68	34	]	]	PUNCT
ejpam-5290	68	35	.	.	PUNCT
ejpam-5290	69	1	the	the	DET
ejpam-5290	69	2	investigation	investigation	NOUN
ejpam-5290	69	3	of	of	ADP
ejpam-5290	69	4	various	various	ADJ
ejpam-5290	69	5	types	type	NOUN
ejpam-5290	69	6	of	of	ADP
ejpam-5290	69	7	flexes	flex	NOUN
ejpam-5290	69	8	admitted	admit	VERB
ejpam-5290	69	9	by	by	ADP
ejpam-5290	69	10	such	such	ADJ
ejpam-5290	69	11	frameworks	framework	NOUN
ejpam-5290	69	12	was	be	AUX
ejpam-5290	69	13	carried	carry	VERB
ejpam-5290	69	14	out	out	ADP
ejpam-5290	69	15	in	in	ADP
ejpam-5290	69	16	[	[	X
ejpam-5290	69	17	18	18	NUM
ejpam-5290	69	18	]	]	PUNCT
ejpam-5290	69	19	and	and	CCONJ
ejpam-5290	69	20	[	[	X
ejpam-5290	69	21	19	19	NUM
ejpam-5290	69	22	]	]	PUNCT
ejpam-5290	69	23	.	.	PUNCT
ejpam-5290	70	1	different	different	ADJ
ejpam-5290	70	2	forms	form	NOUN
ejpam-5290	70	3	of	of	ADP
ejpam-5290	70	4	rigidity	rigidity	NOUN
ejpam-5290	70	5	were	be	AUX
ejpam-5290	70	6	also	also	ADV
ejpam-5290	70	7	introduced	introduce	VERB
ejpam-5290	70	8	,	,	PUNCT
ejpam-5290	70	9	for	for	ADP
ejpam-5290	70	10	example	example	NOUN
ejpam-5290	70	11	,	,	PUNCT
ejpam-5290	70	12	dimensional	dimensional	ADJ
ejpam-5290	70	13	rigidity	rigidity	NOUN
ejpam-5290	70	14	[	[	X
ejpam-5290	70	15	1	1	NUM
ejpam-5290	70	16	]	]	PUNCT
ejpam-5290	70	17	,	,	PUNCT
ejpam-5290	70	18	global	global	ADJ
ejpam-5290	70	19	rigidity	rigidity	NOUN
ejpam-5290	71	1	[	[	X
ejpam-5290	71	2	12	12	NUM
ejpam-5290	71	3	]	]	PUNCT
ejpam-5290	71	4	,	,	PUNCT
ejpam-5290	71	5	almost	almost	ADV
ejpam-5290	71	6	periodic	periodic	ADJ
ejpam-5290	71	7	rigidity	rigidity	NOUN
ejpam-5290	71	8	[	[	X
ejpam-5290	71	9	6	6	NUM
ejpam-5290	71	10	]	]	PUNCT
ejpam-5290	71	11	and	and	CCONJ
ejpam-5290	71	12	bearing	bear	VERB
ejpam-5290	71	13	rigidity	rigidity	NOUN
ejpam-5290	71	14	[	[	X
ejpam-5290	71	15	17	17	NUM
ejpam-5290	71	16	]	]	PUNCT
ejpam-5290	71	17	.	.	PUNCT
ejpam-5290	72	1	for	for	ADP
ejpam-5290	72	2	more	more	ADJ
ejpam-5290	72	3	rigidity	rigidity	NOUN
ejpam-5290	72	4	considerations	consideration	NOUN
ejpam-5290	72	5	,	,	PUNCT
ejpam-5290	72	6	one	one	PRON
ejpam-5290	72	7	can	can	AUX
ejpam-5290	72	8	refer	refer	VERB
ejpam-5290	72	9	to	to	ADP
ejpam-5290	72	10	[	[	X
ejpam-5290	72	11	2	2	NUM
ejpam-5290	72	12	]	]	PUNCT
ejpam-5290	72	13	,	,	PUNCT
ejpam-5290	72	14	[	[	X
ejpam-5290	72	15	15	15	NUM
ejpam-5290	72	16	]	]	PUNCT
ejpam-5290	72	17	and	and	CCONJ
ejpam-5290	72	18	[	[	X
ejpam-5290	72	19	25	25	NUM
ejpam-5290	72	20	]	]	PUNCT
ejpam-5290	72	21	.	.	PUNCT
ejpam-5290	73	1	2	2	X
ejpam-5290	73	2	.	.	X
ejpam-5290	73	3	the	the	DET
ejpam-5290	73	4	connected	connect	VERB
ejpam-5290	73	5	braced	braced	ADJ
ejpam-5290	73	6	triangles	triangle	NOUN
ejpam-5290	73	7	finite	finite	NOUN
ejpam-5290	73	8	bar	bar	NOUN
ejpam-5290	73	9	-	-	PUNCT
ejpam-5290	73	10	joint	joint	NOUN
ejpam-5290	73	11	framework	framework	NOUN
ejpam-5290	73	12	let	let	VERB
ejpam-5290	73	13	f2tri	f2tri	PROPN
ejpam-5290	73	14	be	be	AUX
ejpam-5290	73	15	the	the	DET
ejpam-5290	73	16	finite	finite	ADJ
ejpam-5290	73	17	bar	bar	NOUN
ejpam-5290	73	18	-	-	PUNCT
ejpam-5290	73	19	joint	joint	NOUN
ejpam-5290	73	20	framework	framework	NOUN
ejpam-5290	73	21	constructed	construct	VERB
ejpam-5290	73	22	by	by	ADP
ejpam-5290	73	23	connecting	connect	VERB
ejpam-5290	73	24	two	two	NUM
ejpam-5290	73	25	braced	braced	ADJ
ejpam-5290	73	26	triangles	triangle	NOUN
ejpam-5290	73	27	,	,	PUNCT
ejpam-5290	73	28	with	with	ADP
ejpam-5290	73	29	the	the	DET
ejpam-5290	73	30	planar	planar	ADJ
ejpam-5290	73	31	placement	placement	NOUN
ejpam-5290	73	32	suggested	suggest	VERB
ejpam-5290	73	33	by	by	ADP
ejpam-5290	73	34	figure	figure	NOUN
ejpam-5290	73	35	1	1	NUM
ejpam-5290	73	36	.	.	PUNCT
ejpam-5290	74	1	although	although	SCONJ
ejpam-5290	74	2	any	any	DET
ejpam-5290	74	3	triangle	triangle	NOUN
ejpam-5290	74	4	in	in	ADP
ejpam-5290	74	5	the	the	DET
ejpam-5290	74	6	euclidean	euclidean	ADJ
ejpam-5290	74	7	plane	plane	NOUN
ejpam-5290	74	8	r2	r2	PROPN
ejpam-5290	74	9	is	be	AUX
ejpam-5290	74	10	rigid	rigid	ADJ
ejpam-5290	74	11	,	,	PUNCT
ejpam-5290	74	12	the	the	DET
ejpam-5290	74	13	presence	presence	NOUN
ejpam-5290	74	14	of	of	ADP
ejpam-5290	74	15	a	a	DET
ejpam-5290	74	16	vertex	vertex	NOUN
ejpam-5290	74	17	on	on	ADP
ejpam-5290	74	18	one	one	NUM
ejpam-5290	74	19	edge	edge	NOUN
ejpam-5290	74	20	implies	imply	VERB
ejpam-5290	74	21	the	the	DET
ejpam-5290	74	22	existence	existence	NOUN
ejpam-5290	74	23	of	of	ADP
ejpam-5290	74	24	a	a	DET
ejpam-5290	74	25	non	non	ADJ
ejpam-5290	74	26	trivial	trivial	ADJ
ejpam-5290	74	27	infinitesimal	infinitesimal	ADJ
ejpam-5290	74	28	flex	flex	NOUN
ejpam-5290	74	29	of	of	ADP
ejpam-5290	74	30	the	the	DET
ejpam-5290	74	31	triangle	triangle	NOUN
ejpam-5290	74	32	.	.	PUNCT
ejpam-5290	75	1	in	in	ADP
ejpam-5290	75	2	this	this	DET
ejpam-5290	75	3	case	case	NOUN
ejpam-5290	75	4	,	,	PUNCT
ejpam-5290	75	5	the	the	DET
ejpam-5290	75	6	addition	addition	NOUN
ejpam-5290	75	7	of	of	ADP
ejpam-5290	75	8	the	the	DET
ejpam-5290	75	9	internal	internal	ADJ
ejpam-5290	75	10	horizontal	horizontal	ADJ
ejpam-5290	75	11	edge	edge	NOUN
ejpam-5290	75	12	would	would	AUX
ejpam-5290	75	13	prevent	prevent	VERB
ejpam-5290	75	14	any	any	DET
ejpam-5290	75	15	flexing	flexing	NOUN
ejpam-5290	75	16	of	of	ADP
ejpam-5290	75	17	that	that	DET
ejpam-5290	75	18	edge	edge	NOUN
ejpam-5290	75	19	.	.	PUNCT
ejpam-5290	76	1	now	now	ADV
ejpam-5290	76	2	,	,	PUNCT
ejpam-5290	76	3	let	let	VERB
ejpam-5290	76	4	ui	ui	NOUN
ejpam-5290	76	5	=	=	PUNCT
ejpam-5290	76	6	(	(	PUNCT
ejpam-5290	76	7	uxi	uxi	NOUN
ejpam-5290	76	8	,	,	PUNCT
ejpam-5290	76	9	u	u	PRON
ejpam-5290	76	10	y	y	PROPN
ejpam-5290	76	11	i	i	PROPN
ejpam-5290	76	12	)	)	PUNCT
ejpam-5290	76	13	be	be	VERB
ejpam-5290	76	14	the	the	DET
ejpam-5290	76	15	infinitesimal	infinitesimal	ADJ
ejpam-5290	76	16	flex	flex	NOUN
ejpam-5290	76	17	applied	apply	VERB
ejpam-5290	76	18	to	to	ADP
ejpam-5290	76	19	the	the	DET
ejpam-5290	76	20	vertex	vertex	NOUN
ejpam-5290	76	21	pi	pi	NOUN
ejpam-5290	76	22	=	=	SYM
ejpam-5290	76	23	(	(	PUNCT
ejpam-5290	76	24	pxi	pxi	NOUN
ejpam-5290	76	25	,	,	PUNCT
ejpam-5290	76	26	p	p	NOUN
ejpam-5290	76	27	y	y	PROPN
ejpam-5290	76	28	i	i	PROPN
ejpam-5290	76	29	)	)	PUNCT
ejpam-5290	76	30	.	.	PUNCT
ejpam-5290	77	1	assuming	assume	VERB
ejpam-5290	77	2	that	that	SCONJ
ejpam-5290	77	3	all	all	DET
ejpam-5290	77	4	the	the	DET
ejpam-5290	77	5	flexes	flex	NOUN
ejpam-5290	77	6	at	at	ADP
ejpam-5290	77	7	the	the	DET
ejpam-5290	77	8	base	base	NOUN
ejpam-5290	77	9	vertices	vertex	NOUN
ejpam-5290	77	10	equal	equal	ADJ
ejpam-5290	77	11	zero	zero	NUM
ejpam-5290	77	12	,	,	PUNCT
ejpam-5290	77	13	this	this	PRON
ejpam-5290	77	14	would	would	AUX
ejpam-5290	77	15	prevent	prevent	VERB
ejpam-5290	77	16	any	any	DET
ejpam-5290	77	17	rigid	rigid	ADJ
ejpam-5290	77	18	body	body	NOUN
ejpam-5290	77	19	motion	motion	NOUN
ejpam-5290	77	20	and	and	CCONJ
ejpam-5290	77	21	any	any	DET
ejpam-5290	77	22	flexing	flexing	NOUN
ejpam-5290	77	23	of	of	ADP
ejpam-5290	77	24	the	the	DET
ejpam-5290	77	25	structure	structure	NOUN
ejpam-5290	77	26	would	would	AUX
ejpam-5290	77	27	be	be	AUX
ejpam-5290	77	28	non	non	X
ejpam-5290	77	29	trivial	trivial	ADJ
ejpam-5290	77	30	.	.	PUNCT
ejpam-5290	78	1	the	the	DET
ejpam-5290	78	2	following	follow	VERB
ejpam-5290	78	3	theorem	theorem	NOUN
ejpam-5290	78	4	proves	prove	VERB
ejpam-5290	78	5	that	that	SCONJ
ejpam-5290	78	6	this	this	DET
ejpam-5290	78	7	framework	framework	NOUN
ejpam-5290	78	8	admits	admit	VERB
ejpam-5290	78	9	a	a	DET
ejpam-5290	78	10	non	non	ADJ
ejpam-5290	78	11	trivial	trivial	ADJ
ejpam-5290	78	12	infinitesimal	infinitesimal	ADJ
ejpam-5290	78	13	flex	flex	NOUN
ejpam-5290	78	14	uniquely	uniquely	ADV
ejpam-5290	78	15	determined	determine	VERB
ejpam-5290	78	16	by	by	ADP
ejpam-5290	78	17	the	the	DET
ejpam-5290	78	18	velocity	velocity	NOUN
ejpam-5290	78	19	applied	apply	VERB
ejpam-5290	78	20	at	at	ADP
ejpam-5290	78	21	vertex	vertex	NOUN
ejpam-5290	78	22	p1	p1	PROPN
ejpam-5290	78	23	.	.	PUNCT
ejpam-5290	79	1	theorem	theorem	NOUN
ejpam-5290	79	2	2	2	NUM
ejpam-5290	79	3	.	.	PUNCT
ejpam-5290	80	1	let	let	VERB
ejpam-5290	80	2	f2tri	f2tri	PROPN
ejpam-5290	80	3	be	be	AUX
ejpam-5290	80	4	the	the	DET
ejpam-5290	80	5	finite	finite	ADJ
ejpam-5290	80	6	framework	framework	NOUN
ejpam-5290	80	7	with	with	ADP
ejpam-5290	80	8	two	two	NUM
ejpam-5290	80	9	braced	braced	ADJ
ejpam-5290	80	10	triangles	triangle	NOUN
ejpam-5290	80	11	,	,	PUNCT
ejpam-5290	80	12	then	then	ADV
ejpam-5290	80	13	f2tri	f2tri	PROPN
ejpam-5290	80	14	admits	admit	VERB
ejpam-5290	80	15	a	a	DET
ejpam-5290	80	16	one	one	NUM
ejpam-5290	80	17	dimensional	dimensional	ADJ
ejpam-5290	80	18	space	space	NOUN
ejpam-5290	80	19	of	of	ADP
ejpam-5290	80	20	non	non	ADJ
ejpam-5290	80	21	trivial	trivial	ADJ
ejpam-5290	80	22	infinitesimal	infinitesimal	ADJ
ejpam-5290	80	23	flexes	flex	NOUN
ejpam-5290	80	24	.	.	PUNCT
ejpam-5290	81	1	g.	g.	PROPN
ejpam-5290	81	2	m.	m.	PROPN
ejpam-5290	81	3	badri	badri	PROPN
ejpam-5290	81	4	/	/	SYM
ejpam-5290	81	5	eur	eur	PROPN
ejpam-5290	81	6	.	.	PUNCT
ejpam-5290	82	1	j.	j.	PROPN
ejpam-5290	82	2	pure	pure	PROPN
ejpam-5290	82	3	appl	appl	PROPN
ejpam-5290	82	4	.	.	PROPN
ejpam-5290	82	5	math	math	PROPN
ejpam-5290	82	6	,	,	PUNCT
ejpam-5290	82	7	17	17	NUM
ejpam-5290	82	8	(	(	PUNCT
ejpam-5290	82	9	4	4	NUM
ejpam-5290	82	10	)	)	PUNCT
ejpam-5290	82	11	(	(	PUNCT
ejpam-5290	82	12	2024	2024	NUM
ejpam-5290	82	13	)	)	PUNCT
ejpam-5290	82	14	,	,	PUNCT
ejpam-5290	82	15	3079	3079	NUM
ejpam-5290	82	16	-	-	SYM
ejpam-5290	82	17	3092	3092	NUM
ejpam-5290	82	18	3082	3082	NUM
ejpam-5290	82	19	p3	p3	PROPN
ejpam-5290	82	20	p2	p2	PROPN
ejpam-5290	82	21	p1	p1	PROPN
ejpam-5290	82	22	p4	p4	ADJ
ejpam-5290	82	23	p7	p7	ADJ
ejpam-5290	82	24	p6	p6	NOUN
ejpam-5290	82	25	p8	p8	ADJ
ejpam-5290	82	26	p5	p5	PROPN
ejpam-5290	82	27	x	x	PUNCT
ejpam-5290	82	28	y	y	PROPN
ejpam-5290	82	29	α1	α1	PROPN
ejpam-5290	82	30	β1	β1	PROPN
ejpam-5290	82	31	α2	α2	PROPN
ejpam-5290	82	32	β2	β2	PROPN
ejpam-5290	82	33	figure	figure	VERB
ejpam-5290	82	34	1	1	NUM
ejpam-5290	82	35	:	:	PUNCT
ejpam-5290	82	36	the	the	DET
ejpam-5290	82	37	finite	finite	NOUN
ejpam-5290	82	38	connected	connect	VERB
ejpam-5290	82	39	braced	braced	ADJ
ejpam-5290	82	40	triangles	triangle	NOUN
ejpam-5290	82	41	framework	framework	NOUN
ejpam-5290	82	42	f2tri	f2tri	ADJ
ejpam-5290	82	43	proof	proof	NOUN
ejpam-5290	82	44	.	.	PUNCT
ejpam-5290	83	1	the	the	DET
ejpam-5290	83	2	proof	proof	NOUN
ejpam-5290	83	3	makes	make	VERB
ejpam-5290	83	4	direct	direct	ADJ
ejpam-5290	83	5	use	use	NOUN
ejpam-5290	83	6	of	of	ADP
ejpam-5290	83	7	the	the	DET
ejpam-5290	83	8	infinitesimal	infinitesimal	ADJ
ejpam-5290	83	9	flex	flex	ADJ
ejpam-5290	83	10	condition	condition	NOUN
ejpam-5290	83	11	.	.	PUNCT
ejpam-5290	84	1	let	let	VERB
ejpam-5290	84	2	u	u	PRON
ejpam-5290	84	3	=	=	PUNCT
ejpam-5290	84	4	(	(	PUNCT
ejpam-5290	84	5	u1	u1	PROPN
ejpam-5290	84	6	,	,	PUNCT
ejpam-5290	84	7	.	.	PUNCT
ejpam-5290	84	8	.	.	PUNCT
ejpam-5290	85	1	.	.	PUNCT
ejpam-5290	86	1	,	,	PUNCT
ejpam-5290	86	2	u8	u8	PROPN
ejpam-5290	86	3	)	)	PUNCT
ejpam-5290	86	4	denote	denote	VERB
ejpam-5290	86	5	a	a	DET
ejpam-5290	86	6	flex	flex	NOUN
ejpam-5290	86	7	of	of	ADP
ejpam-5290	86	8	f2tri	f2tri	NOUN
ejpam-5290	86	9	with	with	ADP
ejpam-5290	86	10	the	the	DET
ejpam-5290	86	11	component	component	NOUN
ejpam-5290	86	12	ui	ui	NOUN
ejpam-5290	87	1	=	=	PUNCT
ejpam-5290	87	2	(	(	PUNCT
ejpam-5290	87	3	uxi	uxi	NOUN
ejpam-5290	87	4	,	,	PUNCT
ejpam-5290	87	5	u	u	NOUN
ejpam-5290	87	6	y	y	PROPN
ejpam-5290	87	7	i	i	PROPN
ejpam-5290	87	8	)	)	PUNCT
ejpam-5290	88	1	being	be	AUX
ejpam-5290	88	2	the	the	DET
ejpam-5290	88	3	velocity	velocity	NOUN
ejpam-5290	88	4	applied	apply	VERB
ejpam-5290	88	5	at	at	ADP
ejpam-5290	88	6	vertex	vertex	NOUN
ejpam-5290	88	7	pi	pi	NOUN
ejpam-5290	88	8	.	.	PUNCT
ejpam-5290	89	1	subtracting	subtract	VERB
ejpam-5290	89	2	appropriate	appropriate	ADJ
ejpam-5290	89	3	multiples	multiple	NOUN
ejpam-5290	89	4	of	of	ADP
ejpam-5290	89	5	rigid	rigid	ADJ
ejpam-5290	89	6	body	body	NOUN
ejpam-5290	89	7	motions	motion	NOUN
ejpam-5290	89	8	we	we	PRON
ejpam-5290	89	9	can	can	AUX
ejpam-5290	89	10	arrange	arrange	VERB
ejpam-5290	89	11	for	for	ADP
ejpam-5290	89	12	the	the	DET
ejpam-5290	89	13	vertices	vertex	NOUN
ejpam-5290	89	14	p3	p3	NOUN
ejpam-5290	89	15	and	and	CCONJ
ejpam-5290	89	16	p7	p7	ADJ
ejpam-5290	89	17	to	to	PART
ejpam-5290	89	18	have	have	VERB
ejpam-5290	89	19	zero	zero	NUM
ejpam-5290	89	20	velocity	velocity	NOUN
ejpam-5290	89	21	vectors	vector	NOUN
ejpam-5290	89	22	.	.	PUNCT
ejpam-5290	90	1	it	it	PRON
ejpam-5290	90	2	follows	follow	VERB
ejpam-5290	90	3	immediately	immediately	ADV
ejpam-5290	90	4	that	that	SCONJ
ejpam-5290	90	5	vertices	vertice	VERB
ejpam-5290	90	6	p1	p1	NOUN
ejpam-5290	90	7	,	,	PUNCT
ejpam-5290	90	8	p4	p4	ADJ
ejpam-5290	90	9	,	,	PUNCT
ejpam-5290	90	10	p5	p5	ADJ
ejpam-5290	90	11	and	and	CCONJ
ejpam-5290	90	12	p8	p8	NOUN
ejpam-5290	90	13	all	all	PRON
ejpam-5290	90	14	have	have	AUX
ejpam-5290	90	15	have	have	VERB
ejpam-5290	90	16	zero	zero	NUM
ejpam-5290	90	17	velocity	velocity	NOUN
ejpam-5290	90	18	components	component	NOUN
ejpam-5290	90	19	in	in	ADP
ejpam-5290	90	20	the	the	DET
ejpam-5290	90	21	y	y	PROPN
ejpam-5290	90	22	direction	direction	NOUN
ejpam-5290	90	23	.	.	PUNCT
ejpam-5290	91	1	applying	apply	VERB
ejpam-5290	91	2	the	the	DET
ejpam-5290	91	3	flex	flex	ADJ
ejpam-5290	91	4	condition	condition	NOUN
ejpam-5290	91	5	to	to	ADP
ejpam-5290	91	6	the	the	DET
ejpam-5290	91	7	edge	edge	NOUN
ejpam-5290	91	8	[	[	X
ejpam-5290	91	9	p2	p2	NOUN
ejpam-5290	91	10	,	,	PUNCT
ejpam-5290	91	11	p3	p3	PROPN
ejpam-5290	91	12	]	]	PUNCT
ejpam-5290	91	13	we	we	PRON
ejpam-5290	91	14	have	have	AUX
ejpam-5290	91	15	:	:	PUNCT
ejpam-5290	91	16	⟨p2	⟨p2	PROPN
ejpam-5290	91	17	−	−	PROPN
ejpam-5290	91	18	p3	p3	PROPN
ejpam-5290	91	19	,	,	PUNCT
ejpam-5290	91	20	u2⟩+	u2⟩+	VERB
ejpam-5290	91	21	⟨p3	⟨p3	PROPN
ejpam-5290	91	22	−	−	PROPN
ejpam-5290	91	23	p2	p2	NOUN
ejpam-5290	91	24	,	,	PUNCT
ejpam-5290	91	25	u3⟩	u3⟩	NOUN
ejpam-5290	91	26	=	=	SYM
ejpam-5290	91	27	0	0	NUM
ejpam-5290	92	1	(	(	PUNCT
ejpam-5290	92	2	px2	px2	NOUN
ejpam-5290	92	3	−	−	PROPN
ejpam-5290	92	4	px3)u	px3)u	NOUN
ejpam-5290	92	5	x	x	SYM
ejpam-5290	92	6	2	2	NUM
ejpam-5290	92	7	+	+	CCONJ
ejpam-5290	92	8	(	(	PUNCT
ejpam-5290	92	9	py2	py2	VERB
ejpam-5290	92	10	−	−	PROPN
ejpam-5290	92	11	py3)u	py3)u	NOUN
ejpam-5290	92	12	y	y	NOUN
ejpam-5290	92	13	2	2	NUM
ejpam-5290	92	14	+	+	CCONJ
ejpam-5290	92	15	(	(	PUNCT
ejpam-5290	92	16	px3	px3	NOUN
ejpam-5290	92	17	−	−	PROPN
ejpam-5290	92	18	px2)u	px2)u	PROPN
ejpam-5290	92	19	x	x	X
ejpam-5290	92	20	3	3	NUM
ejpam-5290	92	21	+	+	CCONJ
ejpam-5290	92	22	(	(	PUNCT
ejpam-5290	92	23	py3	py3	X
ejpam-5290	92	24	−	−	PROPN
ejpam-5290	92	25	py2)u	py2)u	PROPN
ejpam-5290	92	26	y	y	PROPN
ejpam-5290	92	27	3	3	NUM
ejpam-5290	92	28	=	=	SYM
ejpam-5290	92	29	0	0	PUNCT
ejpam-5290	92	30	ux2	ux2	PROPN
ejpam-5290	92	31	=	=	SYM
ejpam-5290	92	32	(	(	PUNCT
ejpam-5290	92	33	α1	α1	PROPN
ejpam-5290	92	34	γ1	γ1	PROPN
ejpam-5290	92	35	)	)	PUNCT
ejpam-5290	93	1	uy2	uy2	PROPN
ejpam-5290	93	2	applying	apply	VERB
ejpam-5290	93	3	the	the	DET
ejpam-5290	93	4	flex	flex	ADJ
ejpam-5290	93	5	condition	condition	NOUN
ejpam-5290	93	6	to	to	ADP
ejpam-5290	93	7	the	the	DET
ejpam-5290	93	8	edge	edge	NOUN
ejpam-5290	93	9	[	[	X
ejpam-5290	93	10	p1	p1	NOUN
ejpam-5290	93	11	,	,	PUNCT
ejpam-5290	93	12	p2	p2	X
ejpam-5290	93	13	]	]	PUNCT
ejpam-5290	93	14	:	:	PUNCT
ejpam-5290	94	1	⟨p1	⟨p1	ADP
ejpam-5290	94	2	−	−	NOUN
ejpam-5290	94	3	p2	p2	NOUN
ejpam-5290	94	4	,	,	PUNCT
ejpam-5290	94	5	u1⟩+	u1⟩+	VERB
ejpam-5290	94	6	⟨p2	⟨p2	NOUN
ejpam-5290	94	7	−	−	NOUN
ejpam-5290	94	8	p1	p1	NOUN
ejpam-5290	94	9	,	,	PUNCT
ejpam-5290	94	10	u2⟩	u2⟩	NOUN
ejpam-5290	94	11	=	=	ADJ
ejpam-5290	94	12	0	0	NUM
ejpam-5290	94	13	(	(	PUNCT
ejpam-5290	94	14	px1	px1	VERB
ejpam-5290	94	15	−	−	PROPN
ejpam-5290	94	16	px2)u	px2)u	NOUN
ejpam-5290	94	17	x	x	NOUN
ejpam-5290	94	18	1	1	NUM
ejpam-5290	94	19	+	+	CCONJ
ejpam-5290	94	20	(	(	PUNCT
ejpam-5290	94	21	py1	py1	NOUN
ejpam-5290	94	22	−	−	PROPN
ejpam-5290	94	23	py2)u	py2)u	NOUN
ejpam-5290	94	24	y	y	PROPN
ejpam-5290	94	25	1	1	NUM
ejpam-5290	94	26	+	+	CCONJ
ejpam-5290	94	27	(	(	PUNCT
ejpam-5290	94	28	px2	px2	NOUN
ejpam-5290	94	29	−	−	PROPN
ejpam-5290	94	30	px1)u	px1)u	NOUN
ejpam-5290	94	31	x	x	SYM
ejpam-5290	94	32	2	2	NUM
ejpam-5290	94	33	+	+	CCONJ
ejpam-5290	94	34	(	(	PUNCT
ejpam-5290	94	35	py2	py2	VERB
ejpam-5290	94	36	−	−	PROPN
ejpam-5290	95	1	py1)u	py1)u	PROPN
ejpam-5290	95	2	y	y	PROPN
ejpam-5290	95	3	2	2	NUM
ejpam-5290	95	4	=	=	SYM
ejpam-5290	95	5	0	0	NUM
ejpam-5290	95	6	γ1u	γ1u	NOUN
ejpam-5290	95	7	x	x	SYM
ejpam-5290	95	8	1	1	X
ejpam-5290	95	9	−	−	PROPN
ejpam-5290	95	10	γ1u	γ1u	NOUN
ejpam-5290	95	11	x	x	SYM
ejpam-5290	95	12	2	2	NUM
ejpam-5290	95	13	−	−	NOUN
ejpam-5290	95	14	β1u	β1u	NOUN
ejpam-5290	95	15	y	y	PROPN
ejpam-5290	95	16	2	2	NUM
ejpam-5290	95	17	=	=	SYM
ejpam-5290	95	18	0	0	NUM
ejpam-5290	95	19	substituting	substitute	VERB
ejpam-5290	95	20	ux2	ux2	NOUN
ejpam-5290	95	21	:	:	PUNCT
ejpam-5290	95	22	ux1	ux1	PROPN
ejpam-5290	95	23	=	=	PRON
ejpam-5290	95	24	(	(	PUNCT
ejpam-5290	95	25	α1	α1	PROPN
ejpam-5290	95	26	+	+	CCONJ
ejpam-5290	95	27	β1	β1	PROPN
ejpam-5290	95	28	γ1	γ1	PROPN
ejpam-5290	95	29	)	)	PUNCT
ejpam-5290	95	30	uy2	uy2	PROPN
ejpam-5290	95	31	the	the	DET
ejpam-5290	95	32	latter	latter	ADJ
ejpam-5290	95	33	expression	expression	NOUN
ejpam-5290	95	34	being	be	AUX
ejpam-5290	95	35	equivalent	equivalent	ADJ
ejpam-5290	95	36	to	to	ADP
ejpam-5290	95	37	:	:	PUNCT
ejpam-5290	95	38	g.	g.	PROPN
ejpam-5290	95	39	m.	m.	PROPN
ejpam-5290	95	40	badri	badri	PROPN
ejpam-5290	95	41	/	/	SYM
ejpam-5290	95	42	eur	eur	PROPN
ejpam-5290	95	43	.	.	PUNCT
ejpam-5290	96	1	j.	j.	PROPN
ejpam-5290	96	2	pure	pure	PROPN
ejpam-5290	96	3	appl	appl	PROPN
ejpam-5290	96	4	.	.	PROPN
ejpam-5290	96	5	math	math	PROPN
ejpam-5290	96	6	,	,	PUNCT
ejpam-5290	96	7	17	17	NUM
ejpam-5290	96	8	(	(	PUNCT
ejpam-5290	96	9	4	4	NUM
ejpam-5290	96	10	)	)	PUNCT
ejpam-5290	96	11	(	(	PUNCT
ejpam-5290	96	12	2024	2024	NUM
ejpam-5290	96	13	)	)	PUNCT
ejpam-5290	96	14	,	,	PUNCT
ejpam-5290	96	15	3079	3079	NUM
ejpam-5290	96	16	-	-	SYM
ejpam-5290	96	17	3092	3092	NUM
ejpam-5290	96	18	3083	3083	NUM
ejpam-5290	96	19	ux2	ux2	PROPN
ejpam-5290	96	20	=	=	SYM
ejpam-5290	96	21	(	(	PUNCT
ejpam-5290	96	22	1	1	NUM
ejpam-5290	96	23	1	1	NUM
ejpam-5290	96	24	+	+	CCONJ
ejpam-5290	96	25	β1	β1	PROPN
ejpam-5290	96	26	α1	α1	PROPN
ejpam-5290	96	27	)	)	PUNCT
ejpam-5290	96	28	ux1	ux1	NOUN
ejpam-5290	96	29	the	the	DET
ejpam-5290	96	30	application	application	NOUN
ejpam-5290	96	31	of	of	ADP
ejpam-5290	96	32	the	the	DET
ejpam-5290	96	33	flex	flex	ADJ
ejpam-5290	96	34	condition	condition	NOUN
ejpam-5290	96	35	to	to	ADP
ejpam-5290	96	36	both	both	DET
ejpam-5290	96	37	edges	edge	NOUN
ejpam-5290	96	38	[	[	X
ejpam-5290	96	39	p2	p2	NOUN
ejpam-5290	96	40	,	,	PUNCT
ejpam-5290	96	41	p4	p4	ADJ
ejpam-5290	96	42	]	]	PUNCT
ejpam-5290	96	43	and	and	CCONJ
ejpam-5290	96	44	[	[	X
ejpam-5290	96	45	p4	p4	ADJ
ejpam-5290	96	46	,	,	PUNCT
ejpam-5290	96	47	p5	p5	PROPN
ejpam-5290	96	48	]	]	PUNCT
ejpam-5290	96	49	implies	imply	VERB
ejpam-5290	96	50	that	that	SCONJ
ejpam-5290	97	1	:	:	PUNCT
ejpam-5290	97	2	ux2	ux2	PROPN
ejpam-5290	97	3	=	=	PUNCT
ejpam-5290	97	4	ux4	ux4	ADJ
ejpam-5290	97	5	=	=	PUNCT
ejpam-5290	97	6	ux5	ux5	NOUN
ejpam-5290	97	7	=	=	SYM
ejpam-5290	97	8	(	(	PUNCT
ejpam-5290	97	9	1	1	NUM
ejpam-5290	97	10	1	1	NUM
ejpam-5290	97	11	+	+	CCONJ
ejpam-5290	97	12	β1	β1	PROPN
ejpam-5290	97	13	α1	α1	PROPN
ejpam-5290	97	14	)	)	PUNCT
ejpam-5290	97	15	ux1	ux1	NOUN
ejpam-5290	97	16	applying	apply	VERB
ejpam-5290	97	17	the	the	DET
ejpam-5290	97	18	flex	flex	ADJ
ejpam-5290	97	19	condition	condition	NOUN
ejpam-5290	97	20	to	to	ADP
ejpam-5290	97	21	the	the	DET
ejpam-5290	97	22	edge	edge	NOUN
ejpam-5290	97	23	[	[	X
ejpam-5290	97	24	p5	p5	ADJ
ejpam-5290	97	25	,	,	PUNCT
ejpam-5290	97	26	p6	p6	PROPN
ejpam-5290	97	27	]	]	PUNCT
ejpam-5290	97	28	:	:	PUNCT
ejpam-5290	97	29	⟨p5	⟨p5	PROPN
ejpam-5290	97	30	−	−	PROPN
ejpam-5290	97	31	p6	p6	PROPN
ejpam-5290	97	32	,	,	PUNCT
ejpam-5290	97	33	u5⟩+	u5⟩+	PROPN
ejpam-5290	97	34	⟨p6	⟨p6	PROPN
ejpam-5290	97	35	−	−	PROPN
ejpam-5290	97	36	p5	p5	PROPN
ejpam-5290	97	37	,	,	PUNCT
ejpam-5290	97	38	u6⟩	u6⟩	ADV
ejpam-5290	97	39	=	=	SYM
ejpam-5290	97	40	0	0	NUM
ejpam-5290	98	1	(	(	PUNCT
ejpam-5290	98	2	px5	px5	ADJ
ejpam-5290	98	3	−	−	PROPN
ejpam-5290	98	4	px6)u	px6)u	NOUN
ejpam-5290	98	5	x	x	SYM
ejpam-5290	98	6	5	5	NUM
ejpam-5290	98	7	+	+	CCONJ
ejpam-5290	98	8	(	(	PUNCT
ejpam-5290	98	9	py5	py5	NOUN
ejpam-5290	98	10	−	−	PROPN
ejpam-5290	99	1	py6)u	py6)u	NOUN
ejpam-5290	100	1	y	y	PROPN
ejpam-5290	100	2	5	5	NUM
ejpam-5290	100	3	+	+	CCONJ
ejpam-5290	100	4	(	(	PUNCT
ejpam-5290	100	5	px6	px6	NOUN
ejpam-5290	100	6	−	−	PROPN
ejpam-5290	100	7	px5)u	px5)u	NOUN
ejpam-5290	100	8	x	x	PUNCT
ejpam-5290	100	9	6	6	NUM
ejpam-5290	100	10	+	+	CCONJ
ejpam-5290	100	11	(	(	PUNCT
ejpam-5290	100	12	py6	py6	NOUN
ejpam-5290	100	13	−	−	PROPN
ejpam-5290	100	14	py5)u	py5)u	NOUN
ejpam-5290	100	15	y	y	PROPN
ejpam-5290	100	16	6	6	NUM
ejpam-5290	100	17	=	=	SYM
ejpam-5290	100	18	0	0	NUM
ejpam-5290	100	19	substituting	substitute	VERB
ejpam-5290	100	20	ux6	ux6	NOUN
ejpam-5290	100	21	it	it	PRON
ejpam-5290	100	22	follows	follow	VERB
ejpam-5290	100	23	that	that	SCONJ
ejpam-5290	100	24	:	:	PUNCT
ejpam-5290	100	25	γ2u	γ2u	X
ejpam-5290	100	26	x	x	SYM
ejpam-5290	100	27	5	5	NUM
ejpam-5290	100	28	−	−	NUM
ejpam-5290	100	29	α2u	α2u	NOUN
ejpam-5290	100	30	y	y	PROPN
ejpam-5290	100	31	6	6	NUM
ejpam-5290	100	32	−	−	NOUN
ejpam-5290	100	33	β2u	β2u	SYM
ejpam-5290	100	34	y	y	PROPN
ejpam-5290	100	35	6	6	NUM
ejpam-5290	100	36	=	=	SYM
ejpam-5290	100	37	0	0	NUM
ejpam-5290	100	38	γ2u	γ2u	X
ejpam-5290	100	39	x	x	SYM
ejpam-5290	100	40	5	5	NUM
ejpam-5290	100	41	=	=	SYM
ejpam-5290	100	42	(	(	PUNCT
ejpam-5290	100	43	α2	α2	ADJ
ejpam-5290	100	44	+	+	CCONJ
ejpam-5290	100	45	β2)u	β2)u	ADJ
ejpam-5290	100	46	y	y	PROPN
ejpam-5290	100	47	6	6	NUM
ejpam-5290	100	48	ux5	ux5	NOUN
ejpam-5290	101	1	=	=	NOUN
ejpam-5290	102	1	(	(	PUNCT
ejpam-5290	102	2	α2	α2	ADJ
ejpam-5290	102	3	+	+	CCONJ
ejpam-5290	102	4	β2	β2	VERB
ejpam-5290	102	5	γ2	γ2	PROPN
ejpam-5290	102	6	)	)	PUNCT
ejpam-5290	103	1	uy6	uy6	INTJ
ejpam-5290	103	2	ux5	ux5	NOUN
ejpam-5290	103	3	=	=	PUNCT
ejpam-5290	103	4	(	(	PUNCT
ejpam-5290	103	5	1	1	NUM
ejpam-5290	103	6	+	+	CCONJ
ejpam-5290	103	7	β2	β2	VERB
ejpam-5290	103	8	α2	α2	ADJ
ejpam-5290	103	9	)	)	PUNCT
ejpam-5290	103	10	ux6	ux6	NOUN
ejpam-5290	103	11	equivalently	equivalently	ADV
ejpam-5290	103	12	,	,	PUNCT
ejpam-5290	103	13	ux6	ux6	NOUN
ejpam-5290	103	14	=	=	SYM
ejpam-5290	103	15	(	(	PUNCT
ejpam-5290	103	16	1	1	NUM
ejpam-5290	103	17	1	1	NUM
ejpam-5290	103	18	+	+	CCONJ
ejpam-5290	103	19	β2	β2	VERB
ejpam-5290	103	20	α2	α2	ADJ
ejpam-5290	103	21	)	)	PUNCT
ejpam-5290	103	22	ux5	ux5	NOUN
ejpam-5290	104	1	=	=	PUNCT
ejpam-5290	104	2	(	(	PUNCT
ejpam-5290	104	3	1	1	NUM
ejpam-5290	104	4	1	1	NUM
ejpam-5290	104	5	+	+	CCONJ
ejpam-5290	104	6	β1	β1	PROPN
ejpam-5290	104	7	α1	α1	PROPN
ejpam-5290	104	8	)	)	PUNCT
ejpam-5290	104	9	(	(	PUNCT
ejpam-5290	104	10	1	1	NUM
ejpam-5290	104	11	1	1	NUM
ejpam-5290	104	12	+	+	CCONJ
ejpam-5290	104	13	β2	β2	VERB
ejpam-5290	104	14	α2	α2	PROPN
ejpam-5290	104	15	)	)	PUNCT
ejpam-5290	104	16	ux1	ux1	PROPN
ejpam-5290	104	17	applying	apply	VERB
ejpam-5290	104	18	the	the	DET
ejpam-5290	104	19	flex	flex	ADJ
ejpam-5290	104	20	condition	condition	NOUN
ejpam-5290	104	21	to	to	ADP
ejpam-5290	104	22	the	the	DET
ejpam-5290	104	23	edge	edge	NOUN
ejpam-5290	104	24	[	[	X
ejpam-5290	104	25	p6	p6	X
ejpam-5290	104	26	,	,	PUNCT
ejpam-5290	104	27	p7	p7	PROPN
ejpam-5290	104	28	]	]	PUNCT
ejpam-5290	104	29	:	:	PUNCT
ejpam-5290	104	30	⟨p6	⟨p6	PROPN
ejpam-5290	104	31	−	−	PROPN
ejpam-5290	104	32	p7	p7	PROPN
ejpam-5290	104	33	,	,	PUNCT
ejpam-5290	104	34	u6⟩+	u6⟩+	VERB
ejpam-5290	104	35	⟨p7	⟨p7	ADJ
ejpam-5290	104	36	−	−	PROPN
ejpam-5290	104	37	p6	p6	PROPN
ejpam-5290	104	38	,	,	PUNCT
ejpam-5290	104	39	u7⟩	u7⟩	PUNCT
ejpam-5290	105	1	=	=	SYM
ejpam-5290	105	2	0	0	PUNCT
ejpam-5290	105	3	(	(	PUNCT
ejpam-5290	105	4	px6	px6	NOUN
ejpam-5290	105	5	−	−	PROPN
ejpam-5290	105	6	px7)u	px7)u	PROPN
ejpam-5290	105	7	x	x	SYM
ejpam-5290	105	8	6	6	NUM
ejpam-5290	105	9	+	+	CCONJ
ejpam-5290	105	10	(	(	PUNCT
ejpam-5290	105	11	py6	py6	NOUN
ejpam-5290	105	12	−	−	NOUN
ejpam-5290	105	13	py7)u	py7)u	NOUN
ejpam-5290	105	14	y	y	NOUN
ejpam-5290	105	15	6	6	NUM
ejpam-5290	105	16	+	+	CCONJ
ejpam-5290	105	17	(	(	PUNCT
ejpam-5290	105	18	px7	px7	NOUN
ejpam-5290	105	19	−	−	PROPN
ejpam-5290	105	20	px6)u	px6)u	NOUN
ejpam-5290	105	21	x	x	SYM
ejpam-5290	105	22	7	7	NUM
ejpam-5290	105	23	+	+	CCONJ
ejpam-5290	105	24	(	(	PUNCT
ejpam-5290	105	25	py7	py7	NOUN
ejpam-5290	105	26	−	−	PROPN
ejpam-5290	105	27	py6)u	py6)u	NOUN
ejpam-5290	106	1	y	y	NOUN
ejpam-5290	106	2	7	7	NUM
ejpam-5290	106	3	=	=	SYM
ejpam-5290	106	4	0	0	PUNCT
ejpam-5290	107	1	therefore	therefore	ADV
ejpam-5290	107	2	:	:	PUNCT
ejpam-5290	107	3	uy6	uy6	PROPN
ejpam-5290	107	4	=	=	PUNCT
ejpam-5290	107	5	(	(	PUNCT
ejpam-5290	107	6	γ2	γ2	ADJ
ejpam-5290	107	7	α2	α2	PROPN
ejpam-5290	107	8	)	)	PUNCT
ejpam-5290	108	1	ux6	ux6	NOUN
ejpam-5290	108	2	uy6	uy6	NOUN
ejpam-5290	108	3	=	=	SYM
ejpam-5290	108	4	(	(	PUNCT
ejpam-5290	108	5	γ2	γ2	ADJ
ejpam-5290	108	6	α2	α2	PROPN
ejpam-5290	108	7	)	)	PUNCT
ejpam-5290	108	8	(	(	PUNCT
ejpam-5290	108	9	1	1	NUM
ejpam-5290	108	10	1	1	NUM
ejpam-5290	108	11	+	+	CCONJ
ejpam-5290	108	12	β1	β1	PROPN
ejpam-5290	108	13	α1	α1	PROPN
ejpam-5290	108	14	)	)	PUNCT
ejpam-5290	108	15	(	(	PUNCT
ejpam-5290	108	16	1	1	NUM
ejpam-5290	108	17	1	1	NUM
ejpam-5290	108	18	+	+	CCONJ
ejpam-5290	108	19	β2	β2	VERB
ejpam-5290	108	20	α2	α2	PROPN
ejpam-5290	108	21	)	)	PUNCT
ejpam-5290	108	22	ux1	ux1	PROPN
ejpam-5290	109	1	uy6	uy6	INTJ
ejpam-5290	109	2	=	=	SYM
ejpam-5290	109	3	(	(	PUNCT
ejpam-5290	109	4	1	1	NUM
ejpam-5290	109	5	1	1	NUM
ejpam-5290	109	6	+	+	CCONJ
ejpam-5290	109	7	β1	β1	PROPN
ejpam-5290	109	8	α1	α1	PROPN
ejpam-5290	109	9	)	)	PUNCT
ejpam-5290	109	10	(	(	PUNCT
ejpam-5290	109	11	γ2	γ2	PROPN
ejpam-5290	109	12	α2	α2	PROPN
ejpam-5290	109	13	+	+	CCONJ
ejpam-5290	109	14	β2	β2	PROPN
ejpam-5290	109	15	)	)	PUNCT
ejpam-5290	109	16	ux1	ux1	PROPN
ejpam-5290	109	17	g.	g.	PROPN
ejpam-5290	109	18	m.	m.	PROPN
ejpam-5290	109	19	badri	badri	PROPN
ejpam-5290	109	20	/	/	SYM
ejpam-5290	109	21	eur	eur	PROPN
ejpam-5290	109	22	.	.	PUNCT
ejpam-5290	110	1	j.	j.	PROPN
ejpam-5290	110	2	pure	pure	PROPN
ejpam-5290	110	3	appl	appl	PROPN
ejpam-5290	110	4	.	.	PROPN
ejpam-5290	110	5	math	math	PROPN
ejpam-5290	110	6	,	,	PUNCT
ejpam-5290	110	7	17	17	NUM
ejpam-5290	110	8	(	(	PUNCT
ejpam-5290	110	9	4	4	NUM
ejpam-5290	110	10	)	)	PUNCT
ejpam-5290	110	11	(	(	PUNCT
ejpam-5290	110	12	2024	2024	NUM
ejpam-5290	110	13	)	)	PUNCT
ejpam-5290	110	14	,	,	PUNCT
ejpam-5290	110	15	3079	3079	NUM
ejpam-5290	110	16	-	-	SYM
ejpam-5290	110	17	3092	3092	NUM
ejpam-5290	110	18	3084	3084	NUM
ejpam-5290	110	19	finally	finally	ADV
ejpam-5290	110	20	,	,	PUNCT
ejpam-5290	110	21	applying	apply	VERB
ejpam-5290	110	22	the	the	DET
ejpam-5290	110	23	flex	flex	ADJ
ejpam-5290	110	24	condition	condition	NOUN
ejpam-5290	110	25	to	to	ADP
ejpam-5290	110	26	the	the	DET
ejpam-5290	110	27	edge	edge	NOUN
ejpam-5290	110	28	[	[	X
ejpam-5290	110	29	p6	p6	X
ejpam-5290	110	30	,	,	PUNCT
ejpam-5290	110	31	p8	p8	PROPN
ejpam-5290	110	32	]	]	PUNCT
ejpam-5290	110	33	:	:	PUNCT
ejpam-5290	110	34	⟨p6	⟨p6	PROPN
ejpam-5290	110	35	−	−	PROPN
ejpam-5290	110	36	p8	p8	PROPN
ejpam-5290	110	37	,	,	PUNCT
ejpam-5290	110	38	u6⟩+	u6⟩+	PROPN
ejpam-5290	110	39	⟨p8	⟨p8	PROPN
ejpam-5290	110	40	−	−	PROPN
ejpam-5290	110	41	p6	p6	PROPN
ejpam-5290	110	42	,	,	PUNCT
ejpam-5290	110	43	u7⟩	u7⟩	PUNCT
ejpam-5290	111	1	=	=	SYM
ejpam-5290	111	2	0	0	PUNCT
ejpam-5290	111	3	(	(	PUNCT
ejpam-5290	111	4	px6	px6	NOUN
ejpam-5290	111	5	−	−	PROPN
ejpam-5290	111	6	px8)u	px8)u	PROPN
ejpam-5290	111	7	x	x	PUNCT
ejpam-5290	111	8	6	6	NUM
ejpam-5290	111	9	+	+	CCONJ
ejpam-5290	111	10	(	(	PUNCT
ejpam-5290	111	11	py6	py6	NOUN
ejpam-5290	111	12	−	−	PROPN
ejpam-5290	111	13	py8)u	py8)u	PROPN
ejpam-5290	111	14	y	y	PROPN
ejpam-5290	111	15	6	6	NUM
ejpam-5290	111	16	+	+	CCONJ
ejpam-5290	111	17	(	(	PUNCT
ejpam-5290	111	18	px8	px8	NOUN
ejpam-5290	111	19	−	−	PROPN
ejpam-5290	111	20	px6)u	px6)u	NOUN
ejpam-5290	111	21	x	x	SYM
ejpam-5290	111	22	8	8	NUM
ejpam-5290	111	23	+	+	CCONJ
ejpam-5290	111	24	(	(	PUNCT
ejpam-5290	111	25	py8	py8	NOUN
ejpam-5290	111	26	−	−	PROPN
ejpam-5290	111	27	py6)u	py6)u	NOUN
ejpam-5290	111	28	y	y	PROPN
ejpam-5290	111	29	8	8	NUM
ejpam-5290	111	30	=	=	SYM
ejpam-5290	111	31	0	0	NUM
ejpam-5290	112	1	ux8	ux8	NOUN
ejpam-5290	113	1	=	=	NOUN
ejpam-5290	114	1	ux6	ux6	NOUN
ejpam-5290	114	2	the	the	DET
ejpam-5290	114	3	argument	argument	NOUN
ejpam-5290	114	4	above	above	ADV
ejpam-5290	114	5	,	,	PUNCT
ejpam-5290	114	6	together	together	ADV
ejpam-5290	114	7	with	with	ADP
ejpam-5290	114	8	the	the	DET
ejpam-5290	114	9	appropriate	appropriate	ADJ
ejpam-5290	114	10	substitutions	substitution	NOUN
ejpam-5290	114	11	we	we	PRON
ejpam-5290	114	12	can	can	AUX
ejpam-5290	114	13	identify	identify	VERB
ejpam-5290	114	14	the	the	DET
ejpam-5290	114	15	non	non	ADJ
ejpam-5290	114	16	trivial	trivial	ADJ
ejpam-5290	114	17	infinitesimal	infinitesimal	ADJ
ejpam-5290	114	18	flex	flex	ADJ
ejpam-5290	114	19	u	u	NOUN
ejpam-5290	114	20	=	=	PUNCT
ejpam-5290	114	21	(	(	PUNCT
ejpam-5290	114	22	u1	u1	PROPN
ejpam-5290	114	23	,	,	PUNCT
ejpam-5290	114	24	u2	u2	NOUN
ejpam-5290	114	25	,	,	PUNCT
ejpam-5290	114	26	.	.	PUNCT
ejpam-5290	114	27	.	.	PUNCT
ejpam-5290	115	1	.	.	PUNCT
ejpam-5290	116	1	,	,	PUNCT
ejpam-5290	116	2	u8	u8	PROPN
ejpam-5290	116	3	)	)	PUNCT
ejpam-5290	116	4	of	of	ADP
ejpam-5290	116	5	f2tri	f2tri	ADJ
ejpam-5290	116	6	with	with	ADP
ejpam-5290	116	7	the	the	DET
ejpam-5290	116	8	velocity	velocity	NOUN
ejpam-5290	116	9	components	component	NOUN
ejpam-5290	116	10	:	:	PUNCT
ejpam-5290	116	11	u1	u1	NOUN
ejpam-5290	116	12	=	=	SYM
ejpam-5290	116	13	(	(	PUNCT
ejpam-5290	116	14	ux1	ux1	PROPN
ejpam-5290	116	15	,	,	PUNCT
ejpam-5290	116	16	0	0	NUM
ejpam-5290	116	17	)	)	PUNCT
ejpam-5290	116	18	u2	u2	NOUN
ejpam-5290	116	19	=	=	PUNCT
ejpam-5290	116	20	(	(	PUNCT
ejpam-5290	116	21	(	(	PUNCT
ejpam-5290	116	22	1	1	NUM
ejpam-5290	116	23	1	1	NUM
ejpam-5290	116	24	+	+	CCONJ
ejpam-5290	116	25	β1	β1	PROPN
ejpam-5290	116	26	α1	α1	PROPN
ejpam-5290	116	27	)	)	PUNCT
ejpam-5290	116	28	ux1	ux1	NOUN
ejpam-5290	116	29	,	,	PUNCT
ejpam-5290	116	30	(	(	PUNCT
ejpam-5290	116	31	γ1	γ1	PROPN
ejpam-5290	116	32	α1	α1	PROPN
ejpam-5290	116	33	+	+	CCONJ
ejpam-5290	116	34	β1	β1	PROPN
ejpam-5290	116	35	)	)	PUNCT
ejpam-5290	116	36	ux1	ux1	NOUN
ejpam-5290	116	37	)	)	PUNCT
ejpam-5290	116	38	u3	u3	NOUN
ejpam-5290	116	39	=	=	SYM
ejpam-5290	116	40	(	(	PUNCT
ejpam-5290	116	41	0	0	NUM
ejpam-5290	116	42	,	,	PUNCT
ejpam-5290	116	43	0	0	NUM
ejpam-5290	116	44	)	)	PUNCT
ejpam-5290	117	1	u4	u4	NOUN
ejpam-5290	117	2	=	=	SYM
ejpam-5290	117	3	(	(	PUNCT
ejpam-5290	117	4	(	(	PUNCT
ejpam-5290	117	5	1	1	NUM
ejpam-5290	117	6	1	1	NUM
ejpam-5290	117	7	+	+	CCONJ
ejpam-5290	117	8	β1	β1	PROPN
ejpam-5290	117	9	α1	α1	PROPN
ejpam-5290	117	10	)	)	PUNCT
ejpam-5290	117	11	ux1	ux1	NOUN
ejpam-5290	117	12	,	,	PUNCT
ejpam-5290	117	13	0	0	NUM
ejpam-5290	117	14	)	)	PUNCT
ejpam-5290	117	15	u5	u5	PROPN
ejpam-5290	117	16	=	=	SYM
ejpam-5290	117	17	(	(	PUNCT
ejpam-5290	117	18	0	0	NUM
ejpam-5290	117	19	,	,	PUNCT
ejpam-5290	117	20	0	0	NUM
ejpam-5290	117	21	)	)	PUNCT
ejpam-5290	117	22	u6	u6	NOUN
ejpam-5290	117	23	=	=	SYM
ejpam-5290	117	24	(	(	PUNCT
ejpam-5290	117	25	(	(	PUNCT
ejpam-5290	117	26	1	1	NUM
ejpam-5290	117	27	1	1	NUM
ejpam-5290	117	28	+	+	CCONJ
ejpam-5290	117	29	β1	β1	PROPN
ejpam-5290	117	30	α1	α1	PROPN
ejpam-5290	117	31	)	)	PUNCT
ejpam-5290	117	32	(	(	PUNCT
ejpam-5290	117	33	1	1	NUM
ejpam-5290	117	34	1	1	NUM
ejpam-5290	117	35	+	+	CCONJ
ejpam-5290	117	36	β2	β2	VERB
ejpam-5290	117	37	α2	α2	PROPN
ejpam-5290	117	38	)	)	PUNCT
ejpam-5290	117	39	ux1	ux1	NOUN
ejpam-5290	117	40	,	,	PUNCT
ejpam-5290	117	41	(	(	PUNCT
ejpam-5290	117	42	1	1	NUM
ejpam-5290	117	43	1	1	NUM
ejpam-5290	117	44	+	+	CCONJ
ejpam-5290	117	45	β1	β1	PROPN
ejpam-5290	117	46	α1	α1	PROPN
ejpam-5290	117	47	)	)	PUNCT
ejpam-5290	117	48	(	(	PUNCT
ejpam-5290	117	49	γ2	γ2	PROPN
ejpam-5290	117	50	α2	α2	PROPN
ejpam-5290	117	51	+	+	CCONJ
ejpam-5290	117	52	β2	β2	PROPN
ejpam-5290	117	53	)	)	PUNCT
ejpam-5290	117	54	ux1	ux1	PROPN
ejpam-5290	117	55	)	)	PUNCT
ejpam-5290	117	56	u7	u7	PROPN
ejpam-5290	117	57	=	=	PUNCT
ejpam-5290	117	58	(	(	PUNCT
ejpam-5290	117	59	0	0	NUM
ejpam-5290	117	60	,	,	PUNCT
ejpam-5290	117	61	0	0	NUM
ejpam-5290	117	62	)	)	PUNCT
ejpam-5290	117	63	u8	u8	NOUN
ejpam-5290	117	64	=	=	PUNCT
ejpam-5290	117	65	(	(	PUNCT
ejpam-5290	117	66	(	(	PUNCT
ejpam-5290	117	67	1	1	NUM
ejpam-5290	117	68	1	1	NUM
ejpam-5290	117	69	+	+	CCONJ
ejpam-5290	117	70	β1	β1	PROPN
ejpam-5290	117	71	α1	α1	PROPN
ejpam-5290	117	72	)	)	PUNCT
ejpam-5290	117	73	(	(	PUNCT
ejpam-5290	117	74	1	1	NUM
ejpam-5290	117	75	1	1	NUM
ejpam-5290	117	76	+	+	CCONJ
ejpam-5290	117	77	β2	β2	VERB
ejpam-5290	117	78	α2	α2	PROPN
ejpam-5290	117	79	)	)	PUNCT
ejpam-5290	117	80	ux1	ux1	PROPN
ejpam-5290	117	81	,	,	PUNCT
ejpam-5290	117	82	0	0	NUM
ejpam-5290	117	83	)	)	PUNCT
ejpam-5290	117	84	clearly	clearly	ADV
ejpam-5290	117	85	,	,	PUNCT
ejpam-5290	117	86	u	u	NOUN
ejpam-5290	117	87	is	be	AUX
ejpam-5290	117	88	uniquely	uniquely	ADV
ejpam-5290	117	89	determined	determine	VERB
ejpam-5290	117	90	by	by	ADP
ejpam-5290	117	91	the	the	DET
ejpam-5290	117	92	initial	initial	ADJ
ejpam-5290	117	93	velocity	velocity	NOUN
ejpam-5290	117	94	applied	apply	VERB
ejpam-5290	117	95	at	at	ADP
ejpam-5290	117	96	u1	u1	NOUN
ejpam-5290	117	97	and	and	CCONJ
ejpam-5290	117	98	the	the	DET
ejpam-5290	117	99	conclusion	conclusion	NOUN
ejpam-5290	117	100	follows	follow	VERB
ejpam-5290	117	101	.	.	PUNCT
ejpam-5290	118	1	corollary	corollary	ADJ
ejpam-5290	118	2	1	1	NUM
ejpam-5290	118	3	.	.	PUNCT
ejpam-5290	119	1	let	let	AUX
ejpam-5290	119	2	hfl(f2tri	hfl(f2tri	VERB
ejpam-5290	119	3	)	)	PUNCT
ejpam-5290	119	4	denote	denote	VERB
ejpam-5290	119	5	the	the	DET
ejpam-5290	119	6	linear	linear	ADJ
ejpam-5290	119	7	space	space	NOUN
ejpam-5290	119	8	of	of	ADP
ejpam-5290	119	9	all	all	DET
ejpam-5290	119	10	infinitesimal	infinitesimal	ADJ
ejpam-5290	119	11	flexes	flex	NOUN
ejpam-5290	119	12	of	of	ADP
ejpam-5290	119	13	f2tri	f2tri	NOUN
ejpam-5290	119	14	.	.	PUNCT
ejpam-5290	120	1	then	then	ADV
ejpam-5290	120	2	dim(hfl(f2tri	dim(hfl(f2tri	ADJ
ejpam-5290	120	3	)	)	PUNCT
ejpam-5290	120	4	)	)	PUNCT
ejpam-5290	121	1	=	=	PUNCT
ejpam-5290	121	2	4	4	X
ejpam-5290	121	3	.	.	X
ejpam-5290	121	4	we	we	PRON
ejpam-5290	121	5	now	now	ADV
ejpam-5290	121	6	consider	consider	VERB
ejpam-5290	121	7	the	the	DET
ejpam-5290	121	8	finite	finite	ADJ
ejpam-5290	121	9	framework	framework	NOUN
ejpam-5290	121	10	constructed	construct	VERB
ejpam-5290	121	11	by	by	ADP
ejpam-5290	121	12	connecting	connect	VERB
ejpam-5290	121	13	three	three	NUM
ejpam-5290	121	14	braced	braced	ADJ
ejpam-5290	121	15	triangles	triangle	NOUN
ejpam-5290	121	16	,	,	PUNCT
ejpam-5290	121	17	f3tri	f3tri	PROPN
ejpam-5290	121	18	,	,	PUNCT
ejpam-5290	121	19	suggested	suggest	VERB
ejpam-5290	121	20	by	by	ADP
ejpam-5290	121	21	figure	figure	NOUN
ejpam-5290	121	22	2	2	NUM
ejpam-5290	121	23	.	.	PUNCT
ejpam-5290	122	1	in	in	ADP
ejpam-5290	122	2	addition	addition	NOUN
ejpam-5290	122	3	to	to	ADP
ejpam-5290	122	4	the	the	DET
ejpam-5290	122	5	flex	flex	ADJ
ejpam-5290	122	6	determined	determine	VERB
ejpam-5290	122	7	by	by	ADP
ejpam-5290	122	8	the	the	DET
ejpam-5290	122	9	velocity	velocity	NOUN
ejpam-5290	122	10	applied	apply	VERB
ejpam-5290	122	11	at	at	ADP
ejpam-5290	122	12	p1	p1	PROPN
ejpam-5290	122	13	,	,	PUNCT
ejpam-5290	122	14	the	the	DET
ejpam-5290	122	15	following	follow	VERB
ejpam-5290	122	16	theorem	theorem	NOUN
ejpam-5290	122	17	identifies	identify	VERB
ejpam-5290	122	18	a	a	DET
ejpam-5290	122	19	new	new	ADJ
ejpam-5290	122	20	infinitesimal	infinitesimal	ADJ
ejpam-5290	122	21	flex	flex	NOUN
ejpam-5290	122	22	of	of	ADP
ejpam-5290	122	23	this	this	DET
ejpam-5290	122	24	framework	framework	NOUN
ejpam-5290	122	25	.	.	PUNCT
ejpam-5290	123	1	theorem	theorem	NOUN
ejpam-5290	123	2	3	3	X
ejpam-5290	123	3	.	.	PUNCT
ejpam-5290	124	1	let	let	VERB
ejpam-5290	124	2	f3tri	f3tri	PROPN
ejpam-5290	124	3	be	be	AUX
ejpam-5290	124	4	the	the	DET
ejpam-5290	124	5	finite	finite	ADJ
ejpam-5290	124	6	framework	framework	NOUN
ejpam-5290	124	7	with	with	ADP
ejpam-5290	124	8	three	three	NUM
ejpam-5290	124	9	braced	braced	ADJ
ejpam-5290	124	10	triangles	triangle	NOUN
ejpam-5290	124	11	.	.	PUNCT
ejpam-5290	125	1	let	let	VERB
ejpam-5290	125	2	u	u	PRON
ejpam-5290	125	3	=	=	PUNCT
ejpam-5290	125	4	(	(	PUNCT
ejpam-5290	125	5	u1	u1	PROPN
ejpam-5290	125	6	,	,	PUNCT
ejpam-5290	125	7	u2	u2	NOUN
ejpam-5290	125	8	,	,	PUNCT
ejpam-5290	125	9	.	.	PUNCT
ejpam-5290	125	10	.	.	PUNCT
ejpam-5290	126	1	.	.	PUNCT
ejpam-5290	127	1	,	,	PUNCT
ejpam-5290	127	2	u12	u12	PROPN
ejpam-5290	127	3	)	)	PUNCT
ejpam-5290	127	4	be	be	VERB
ejpam-5290	127	5	the	the	DET
ejpam-5290	127	6	flex	flex	ADJ
ejpam-5290	127	7	of	of	ADP
ejpam-5290	127	8	f3tri	f3tri	PROPN
ejpam-5290	127	9	with	with	ADP
ejpam-5290	127	10	zero	zero	NUM
ejpam-5290	127	11	velocity	velocity	NOUN
ejpam-5290	127	12	components	component	NOUN
ejpam-5290	127	13	at	at	ADP
ejpam-5290	127	14	all	all	DET
ejpam-5290	127	15	the	the	DET
ejpam-5290	127	16	vertices	vertex	NOUN
ejpam-5290	127	17	of	of	ADP
ejpam-5290	127	18	the	the	DET
ejpam-5290	127	19	first	first	ADJ
ejpam-5290	127	20	and	and	CCONJ
ejpam-5290	127	21	third	third	ADJ
ejpam-5290	127	22	triangle	triangle	NOUN
ejpam-5290	127	23	.	.	PUNCT
ejpam-5290	128	1	then	then	ADV
ejpam-5290	128	2	f3tri	f3tri	PROPN
ejpam-5290	128	3	admits	admit	VERB
ejpam-5290	128	4	a	a	DET
ejpam-5290	128	5	non	non	ADJ
ejpam-5290	128	6	trivial	trivial	ADJ
ejpam-5290	128	7	infinitesimal	infinitesimal	ADJ
ejpam-5290	128	8	flex	flex	NOUN
ejpam-5290	128	9	uniquely	uniquely	ADV
ejpam-5290	128	10	determined	determine	VERB
ejpam-5290	128	11	by	by	ADP
ejpam-5290	128	12	uy7	uy7	PROPN
ejpam-5290	128	13	.	.	PUNCT
ejpam-5290	129	1	g.	g.	PROPN
ejpam-5290	129	2	m.	m.	PROPN
ejpam-5290	129	3	badri	badri	PROPN
ejpam-5290	129	4	/	/	SYM
ejpam-5290	129	5	eur	eur	PROPN
ejpam-5290	129	6	.	.	PUNCT
ejpam-5290	130	1	j.	j.	PROPN
ejpam-5290	130	2	pure	pure	PROPN
ejpam-5290	130	3	appl	appl	PROPN
ejpam-5290	130	4	.	.	PROPN
ejpam-5290	130	5	math	math	PROPN
ejpam-5290	130	6	,	,	PUNCT
ejpam-5290	130	7	17	17	NUM
ejpam-5290	130	8	(	(	PUNCT
ejpam-5290	130	9	4	4	NUM
ejpam-5290	130	10	)	)	PUNCT
ejpam-5290	130	11	(	(	PUNCT
ejpam-5290	130	12	2024	2024	NUM
ejpam-5290	130	13	)	)	PUNCT
ejpam-5290	130	14	,	,	PUNCT
ejpam-5290	130	15	3079	3079	NUM
ejpam-5290	130	16	-	-	SYM
ejpam-5290	130	17	3092	3092	NUM
ejpam-5290	130	18	3085	3085	NUM
ejpam-5290	130	19	p1	p1	NOUN
ejpam-5290	130	20	p2	p2	PROPN
ejpam-5290	130	21	p3	p3	PROPN
ejpam-5290	130	22	p4	p4	ADJ
ejpam-5290	130	23	p5	p5	ADJ
ejpam-5290	130	24	p6	p6	ADJ
ejpam-5290	130	25	p7	p7	VERB
ejpam-5290	130	26	p8	p8	ADJ
ejpam-5290	130	27	p9	p9	PROPN
ejpam-5290	130	28	p10	p10	NOUN
ejpam-5290	130	29	p11	p11	NOUN
ejpam-5290	130	30	p12	p12	ADJ
ejpam-5290	130	31	α1	α1	PROPN
ejpam-5290	130	32	β1	β1	PROPN
ejpam-5290	130	33	γ1	γ1	PROPN
ejpam-5290	130	34	α2	α2	PROPN
ejpam-5290	130	35	β2	β2	PROPN
ejpam-5290	130	36	γ2	γ2	PROPN
ejpam-5290	130	37	α3	α3	PROPN
ejpam-5290	130	38	β3	β3	VERB
ejpam-5290	130	39	γ3	γ3	PROPN
ejpam-5290	130	40	σ1	σ1	PROPN
ejpam-5290	130	41	σ2	σ2	PROPN
ejpam-5290	130	42	figure	figure	NOUN
ejpam-5290	130	43	2	2	NUM
ejpam-5290	130	44	:	:	PUNCT
ejpam-5290	130	45	the	the	DET
ejpam-5290	130	46	finite	finite	NOUN
ejpam-5290	130	47	connected	connect	VERB
ejpam-5290	130	48	braced	braced	ADJ
ejpam-5290	130	49	triangles	triangle	NOUN
ejpam-5290	130	50	framework	framework	NOUN
ejpam-5290	130	51	f3tri	f3tri	PROPN
ejpam-5290	130	52	proof	proof	NOUN
ejpam-5290	130	53	.	.	PUNCT
ejpam-5290	131	1	with	with	ADP
ejpam-5290	131	2	the	the	DET
ejpam-5290	131	3	first	first	ADJ
ejpam-5290	131	4	and	and	CCONJ
ejpam-5290	131	5	third	third	ADJ
ejpam-5290	131	6	framework	framework	NOUN
ejpam-5290	131	7	vertices	vertex	NOUN
ejpam-5290	131	8	all	all	PRON
ejpam-5290	131	9	having	have	VERB
ejpam-5290	131	10	zero	zero	NUM
ejpam-5290	131	11	velocity	velocity	NOUN
ejpam-5290	131	12	components	component	NOUN
ejpam-5290	131	13	,	,	PUNCT
ejpam-5290	131	14	u1	u1	NOUN
ejpam-5290	131	15	=	=	SYM
ejpam-5290	131	16	u2	u2	PROPN
ejpam-5290	131	17	=	=	PUNCT
ejpam-5290	131	18	u3	u3	PROPN
ejpam-5290	131	19	=	=	SYM
ejpam-5290	131	20	u4	u4	PROPN
ejpam-5290	131	21	=	=	PROPN
ejpam-5290	131	22	u9	u9	PROPN
ejpam-5290	131	23	=	=	SYM
ejpam-5290	131	24	u10	u10	PROPN
ejpam-5290	131	25	=	=	SYM
ejpam-5290	131	26	u11	u11	PROPN
ejpam-5290	131	27	=	=	PUNCT
ejpam-5290	131	28	u12	u12	NOUN
ejpam-5290	131	29	=	=	SYM
ejpam-5290	131	30	(	(	PUNCT
ejpam-5290	131	31	0	0	NUM
ejpam-5290	131	32	,	,	PUNCT
ejpam-5290	131	33	0	0	NUM
ejpam-5290	131	34	)	)	PUNCT
ejpam-5290	131	35	.	.	PUNCT
ejpam-5290	132	1	from	from	ADP
ejpam-5290	132	2	which	which	PRON
ejpam-5290	132	3	it	it	PRON
ejpam-5290	132	4	immediately	immediately	ADV
ejpam-5290	132	5	follows	follow	VERB
ejpam-5290	132	6	that	that	SCONJ
ejpam-5290	132	7	u7	u7	PROPN
ejpam-5290	132	8	only	only	ADV
ejpam-5290	132	9	admits	admit	VERB
ejpam-5290	132	10	a	a	DET
ejpam-5290	132	11	velocity	velocity	NOUN
ejpam-5290	132	12	component	component	NOUN
ejpam-5290	132	13	in	in	ADP
ejpam-5290	132	14	the	the	DET
ejpam-5290	132	15	y	y	PROPN
ejpam-5290	132	16	direction	direction	NOUN
ejpam-5290	132	17	,	,	PUNCT
ejpam-5290	132	18	the	the	DET
ejpam-5290	132	19	velocity	velocity	NOUN
ejpam-5290	132	20	in	in	ADP
ejpam-5290	132	21	the	the	DET
ejpam-5290	132	22	x	x	NOUN
ejpam-5290	132	23	direction	direction	NOUN
ejpam-5290	132	24	,	,	PUNCT
ejpam-5290	132	25	ux7	ux7	NOUN
ejpam-5290	132	26	,	,	PUNCT
ejpam-5290	132	27	being	be	AUX
ejpam-5290	132	28	zero	zero	NUM
ejpam-5290	132	29	.	.	PUNCT
ejpam-5290	133	1	applying	apply	VERB
ejpam-5290	133	2	the	the	DET
ejpam-5290	133	3	flex	flex	ADJ
ejpam-5290	133	4	condition	condition	NOUN
ejpam-5290	133	5	to	to	ADP
ejpam-5290	133	6	the	the	DET
ejpam-5290	133	7	edge	edge	NOUN
ejpam-5290	133	8	[	[	X
ejpam-5290	133	9	p4	p4	ADJ
ejpam-5290	133	10	,	,	PUNCT
ejpam-5290	133	11	p5	p5	PROPN
ejpam-5290	133	12	]	]	PUNCT
ejpam-5290	134	1	we	we	PRON
ejpam-5290	134	2	have	have	VERB
ejpam-5290	134	3	:	:	PUNCT
ejpam-5290	134	4	⟨p4	⟨p4	NOUN
ejpam-5290	134	5	−	−	PROPN
ejpam-5290	134	6	p5	p5	PROPN
ejpam-5290	134	7	,	,	PUNCT
ejpam-5290	134	8	u4⟩+	u4⟩+	PROPN
ejpam-5290	134	9	⟨p5	⟨p5	NOUN
ejpam-5290	134	10	−	−	NOUN
ejpam-5290	134	11	p4	p4	ADJ
ejpam-5290	134	12	,	,	PUNCT
ejpam-5290	134	13	u5⟩	u5⟩	ADP
ejpam-5290	134	14	=	=	SYM
ejpam-5290	134	15	0	0	PUNCT
ejpam-5290	134	16	(	(	PUNCT
ejpam-5290	134	17	px4	px4	X
ejpam-5290	134	18	−	−	NOUN
ejpam-5290	134	19	px5)u	px5)u	NOUN
ejpam-5290	134	20	x	x	SYM
ejpam-5290	134	21	4	4	NUM
ejpam-5290	134	22	+	+	CCONJ
ejpam-5290	134	23	(	(	PUNCT
ejpam-5290	134	24	py4	py4	NOUN
ejpam-5290	134	25	−	−	PROPN
ejpam-5290	134	26	py5)u	py5)u	PROPN
ejpam-5290	134	27	y	y	PROPN
ejpam-5290	134	28	4	4	NUM
ejpam-5290	134	29	+	+	CCONJ
ejpam-5290	134	30	(	(	PUNCT
ejpam-5290	134	31	px5	px5	ADJ
ejpam-5290	134	32	−	−	PROPN
ejpam-5290	134	33	px4)u	px4)u	NOUN
ejpam-5290	134	34	x	x	SYM
ejpam-5290	134	35	5	5	NUM
ejpam-5290	134	36	+	+	CCONJ
ejpam-5290	134	37	(	(	PUNCT
ejpam-5290	134	38	py5	py5	NOUN
ejpam-5290	134	39	−	−	PROPN
ejpam-5290	135	1	py4)u	py4)u	NOUN
ejpam-5290	135	2	y	y	PROPN
ejpam-5290	135	3	5	5	NUM
ejpam-5290	135	4	=	=	SYM
ejpam-5290	135	5	0	0	NUM
ejpam-5290	136	1	σ1u	σ1u	NOUN
ejpam-5290	136	2	x	x	SYM
ejpam-5290	136	3	5	5	NUM
ejpam-5290	136	4	+	+	CCONJ
ejpam-5290	136	5	(	(	PUNCT
ejpam-5290	136	6	α2	α2	ADJ
ejpam-5290	136	7	+	+	CCONJ
ejpam-5290	136	8	β2	β2	PROPN
ejpam-5290	136	9	−	−	PROPN
ejpam-5290	136	10	α1)u	α1)u	NOUN
ejpam-5290	136	11	y	y	PROPN
ejpam-5290	136	12	5	5	NUM
ejpam-5290	136	13	=	=	SYM
ejpam-5290	136	14	0	0	NUM
ejpam-5290	136	15	which	which	PRON
ejpam-5290	136	16	implies	imply	VERB
ejpam-5290	136	17	:	:	PUNCT
ejpam-5290	136	18	ux5	ux5	PROPN
ejpam-5290	136	19	=	=	SYM
ejpam-5290	136	20	(	(	PUNCT
ejpam-5290	136	21	α1	α1	PROPN
ejpam-5290	136	22	−	−	PROPN
ejpam-5290	136	23	(	(	PUNCT
ejpam-5290	136	24	α2	α2	PROPN
ejpam-5290	136	25	+	+	CCONJ
ejpam-5290	136	26	β2	β2	ADJ
ejpam-5290	136	27	)	)	PUNCT
ejpam-5290	136	28	σ1	σ1	PROPN
ejpam-5290	136	29	)	)	PUNCT
ejpam-5290	136	30	uy5	uy5	PROPN
ejpam-5290	137	1	applying	apply	VERB
ejpam-5290	137	2	the	the	DET
ejpam-5290	137	3	flex	flex	ADJ
ejpam-5290	137	4	condition	condition	NOUN
ejpam-5290	137	5	to	to	ADP
ejpam-5290	137	6	the	the	DET
ejpam-5290	137	7	edge	edge	NOUN
ejpam-5290	137	8	[	[	X
ejpam-5290	137	9	p7	p7	ADJ
ejpam-5290	137	10	,	,	PUNCT
ejpam-5290	137	11	p8	p8	PROPN
ejpam-5290	137	12	]	]	PUNCT
ejpam-5290	137	13	:	:	PUNCT
ejpam-5290	137	14	⟨p7	⟨p7	PROPN
ejpam-5290	137	15	−	−	PROPN
ejpam-5290	137	16	p8	p8	PROPN
ejpam-5290	137	17	,	,	PUNCT
ejpam-5290	137	18	u8⟩+	u8⟩+	PROPN
ejpam-5290	137	19	⟨p8	⟨p8	PROPN
ejpam-5290	137	20	−	−	PROPN
ejpam-5290	137	21	p7	p7	NOUN
ejpam-5290	137	22	,	,	PUNCT
ejpam-5290	137	23	u8⟩	u8⟩	NOUN
ejpam-5290	137	24	=	=	SYM
ejpam-5290	137	25	0	0	NUM
ejpam-5290	138	1	(	(	PUNCT
ejpam-5290	138	2	px7	px7	NOUN
ejpam-5290	138	3	−	−	PROPN
ejpam-5290	138	4	px8)u	px8)u	PROPN
ejpam-5290	138	5	x	x	SYM
ejpam-5290	138	6	7	7	NUM
ejpam-5290	138	7	+	+	CCONJ
ejpam-5290	138	8	(	(	PUNCT
ejpam-5290	138	9	py7	py7	NOUN
ejpam-5290	138	10	−	−	PROPN
ejpam-5290	138	11	py8)u	py8)u	PROPN
ejpam-5290	138	12	y	y	PROPN
ejpam-5290	138	13	7	7	NUM
ejpam-5290	139	1	+	+	CCONJ
ejpam-5290	139	2	(	(	PUNCT
ejpam-5290	139	3	px8	px8	NOUN
ejpam-5290	139	4	−	−	PROPN
ejpam-5290	139	5	px7)u	px7)u	PROPN
ejpam-5290	139	6	x	x	SYM
ejpam-5290	139	7	8	8	NUM
ejpam-5290	139	8	+	+	CCONJ
ejpam-5290	139	9	(	(	PUNCT
ejpam-5290	139	10	py8	py8	NOUN
ejpam-5290	139	11	−	−	NOUN
ejpam-5290	139	12	py7)u	py7)u	NOUN
ejpam-5290	139	13	y	y	NOUN
ejpam-5290	139	14	8	8	NUM
ejpam-5290	139	15	=	=	SYM
ejpam-5290	139	16	0	0	NUM
ejpam-5290	139	17	uy7	uy7	NOUN
ejpam-5290	139	18	=	=	X
ejpam-5290	140	1	uy8	uy8	ADV
ejpam-5290	140	2	applying	apply	VERB
ejpam-5290	140	3	the	the	DET
ejpam-5290	140	4	flex	flex	ADJ
ejpam-5290	140	5	condition	condition	NOUN
ejpam-5290	140	6	to	to	ADP
ejpam-5290	140	7	the	the	DET
ejpam-5290	140	8	edge	edge	NOUN
ejpam-5290	140	9	[	[	X
ejpam-5290	140	10	p5	p5	ADJ
ejpam-5290	140	11	,	,	PUNCT
ejpam-5290	140	12	p8	p8	PROPN
ejpam-5290	140	13	]	]	PUNCT
ejpam-5290	140	14	:	:	PUNCT
ejpam-5290	140	15	⟨p5	⟨p5	PROPN
ejpam-5290	140	16	−	−	PROPN
ejpam-5290	140	17	p8	p8	PROPN
ejpam-5290	140	18	,	,	PUNCT
ejpam-5290	140	19	u5⟩+	u5⟩+	PROPN
ejpam-5290	140	20	⟨p8	⟨p8	PROPN
ejpam-5290	140	21	−	−	PROPN
ejpam-5290	140	22	p5	p5	PROPN
ejpam-5290	140	23	,	,	PUNCT
ejpam-5290	140	24	u8⟩	u8⟩	NOUN
ejpam-5290	140	25	=	=	SYM
ejpam-5290	140	26	0	0	NUM
ejpam-5290	141	1	(	(	PUNCT
ejpam-5290	141	2	px5	px5	ADJ
ejpam-5290	141	3	−	−	PROPN
ejpam-5290	141	4	px8)u	px8)u	PROPN
ejpam-5290	141	5	x	x	SYM
ejpam-5290	141	6	5	5	NUM
ejpam-5290	141	7	+	+	CCONJ
ejpam-5290	141	8	(	(	PUNCT
ejpam-5290	141	9	py5	py5	NOUN
ejpam-5290	141	10	−	−	PROPN
ejpam-5290	141	11	py8)u	py8)u	PROPN
ejpam-5290	141	12	y	y	PROPN
ejpam-5290	141	13	5	5	NUM
ejpam-5290	141	14	+	+	CCONJ
ejpam-5290	141	15	(	(	PUNCT
ejpam-5290	141	16	px8	px8	VERB
ejpam-5290	141	17	−	−	PROPN
ejpam-5290	141	18	px5)u	px5)u	NOUN
ejpam-5290	141	19	x	x	SYM
ejpam-5290	141	20	8	8	NUM
ejpam-5290	141	21	+	+	CCONJ
ejpam-5290	141	22	(	(	PUNCT
ejpam-5290	141	23	py8	py8	NOUN
ejpam-5290	141	24	−	−	PROPN
ejpam-5290	141	25	py5)u	py5)u	NOUN
ejpam-5290	141	26	y	y	PROPN
ejpam-5290	141	27	8	8	NUM
ejpam-5290	141	28	=	=	SYM
ejpam-5290	141	29	0	0	NUM
ejpam-5290	141	30	uy5	uy5	PROPN
ejpam-5290	142	1	=	=	SYM
ejpam-5290	143	1	uy8	uy8	PROPN
ejpam-5290	143	2	g.	g.	PROPN
ejpam-5290	143	3	m.	m.	PROPN
ejpam-5290	143	4	badri	badri	PROPN
ejpam-5290	143	5	/	/	SYM
ejpam-5290	143	6	eur	eur	PROPN
ejpam-5290	143	7	.	.	PUNCT
ejpam-5290	144	1	j.	j.	PROPN
ejpam-5290	144	2	pure	pure	PROPN
ejpam-5290	144	3	appl	appl	PROPN
ejpam-5290	144	4	.	.	PROPN
ejpam-5290	144	5	math	math	PROPN
ejpam-5290	144	6	,	,	PUNCT
ejpam-5290	144	7	17	17	NUM
ejpam-5290	144	8	(	(	PUNCT
ejpam-5290	144	9	4	4	NUM
ejpam-5290	144	10	)	)	PUNCT
ejpam-5290	144	11	(	(	PUNCT
ejpam-5290	144	12	2024	2024	NUM
ejpam-5290	144	13	)	)	PUNCT
ejpam-5290	144	14	,	,	PUNCT
ejpam-5290	144	15	3079	3079	NUM
ejpam-5290	144	16	-	-	SYM
ejpam-5290	144	17	3092	3092	NUM
ejpam-5290	144	18	3086	3086	NUM
ejpam-5290	144	19	applying	apply	VERB
ejpam-5290	144	20	the	the	DET
ejpam-5290	144	21	flex	flex	ADJ
ejpam-5290	144	22	condition	condition	NOUN
ejpam-5290	144	23	to	to	ADP
ejpam-5290	144	24	the	the	DET
ejpam-5290	144	25	edge	edge	NOUN
ejpam-5290	144	26	[	[	X
ejpam-5290	144	27	p8	p8	X
ejpam-5290	144	28	,	,	PUNCT
ejpam-5290	144	29	p9	p9	PROPN
ejpam-5290	144	30	]	]	PUNCT
ejpam-5290	144	31	:	:	PUNCT
ejpam-5290	144	32	⟨p8	⟨p8	PROPN
ejpam-5290	144	33	−	−	PROPN
ejpam-5290	144	34	p9	p9	PROPN
ejpam-5290	144	35	,	,	PUNCT
ejpam-5290	144	36	u8⟩+	u8⟩+	PROPN
ejpam-5290	144	37	⟨p9	⟨p9	PROPN
ejpam-5290	144	38	−	−	PROPN
ejpam-5290	144	39	p8	p8	PROPN
ejpam-5290	144	40	,	,	PUNCT
ejpam-5290	144	41	u9⟩	u9⟩	NOUN
ejpam-5290	144	42	=	=	SYM
ejpam-5290	144	43	0	0	NUM
ejpam-5290	144	44	(	(	PUNCT
ejpam-5290	144	45	px8	px8	NOUN
ejpam-5290	144	46	−	−	NOUN
ejpam-5290	144	47	px9)u	px9)u	PROPN
ejpam-5290	144	48	x	x	SYM
ejpam-5290	144	49	8	8	NUM
ejpam-5290	144	50	+	+	CCONJ
ejpam-5290	144	51	(	(	PUNCT
ejpam-5290	144	52	py8	py8	NOUN
ejpam-5290	144	53	−	−	NOUN
ejpam-5290	145	1	py9)u	py9)u	ADJ
ejpam-5290	145	2	y	y	PROPN
ejpam-5290	145	3	8	8	NUM
ejpam-5290	145	4	+	+	CCONJ
ejpam-5290	145	5	(	(	PUNCT
ejpam-5290	145	6	px9	px9	NOUN
ejpam-5290	145	7	−	−	PROPN
ejpam-5290	145	8	px8)u	px8)u	PROPN
ejpam-5290	145	9	x	x	SYM
ejpam-5290	145	10	9	9	NUM
ejpam-5290	145	11	+	+	CCONJ
ejpam-5290	145	12	(	(	PUNCT
ejpam-5290	145	13	py9	py9	PROPN
ejpam-5290	145	14	−	−	PROPN
ejpam-5290	145	15	py8)u	py8)u	PROPN
ejpam-5290	145	16	y	y	PROPN
ejpam-5290	145	17	9	9	NUM
ejpam-5290	145	18	=	=	SYM
ejpam-5290	145	19	0	0	PUNCT
ejpam-5290	145	20	(	(	PUNCT
ejpam-5290	145	21	−σ1)u	−σ1)u	NOUN
ejpam-5290	145	22	x	x	SYM
ejpam-5290	145	23	8	8	NUM
ejpam-5290	145	24	+	+	CCONJ
ejpam-5290	145	25	(	(	PUNCT
ejpam-5290	145	26	α2	α2	ADJ
ejpam-5290	145	27	−	−	PROPN
ejpam-5290	145	28	(	(	PUNCT
ejpam-5290	145	29	α3	α3	PROPN
ejpam-5290	145	30	+	+	CCONJ
ejpam-5290	145	31	β3))u	β3))u	X
ejpam-5290	145	32	y	y	PROPN
ejpam-5290	145	33	8	8	NUM
ejpam-5290	145	34	=	=	SYM
ejpam-5290	145	35	0	0	PUNCT
ejpam-5290	146	1	and	and	CCONJ
ejpam-5290	146	2	it	it	PRON
ejpam-5290	146	3	follows	follow	VERB
ejpam-5290	146	4	that	that	SCONJ
ejpam-5290	146	5	ux8	ux8	NOUN
ejpam-5290	147	1	=	=	INTJ
ejpam-5290	147	2	(	(	PUNCT
ejpam-5290	147	3	α2	α2	ADV
ejpam-5290	147	4	−	−	PROPN
ejpam-5290	147	5	(	(	PUNCT
ejpam-5290	147	6	α3	α3	PROPN
ejpam-5290	147	7	+	+	CCONJ
ejpam-5290	147	8	β3	β3	ADJ
ejpam-5290	147	9	)	)	PUNCT
ejpam-5290	147	10	σ2	σ2	PROPN
ejpam-5290	147	11	)	)	PUNCT
ejpam-5290	148	1	uy8	uy8	INTJ
ejpam-5290	148	2	applying	apply	VERB
ejpam-5290	148	3	the	the	DET
ejpam-5290	148	4	flex	flex	ADJ
ejpam-5290	148	5	condition	condition	NOUN
ejpam-5290	148	6	to	to	ADP
ejpam-5290	148	7	the	the	DET
ejpam-5290	148	8	edge	edge	NOUN
ejpam-5290	148	9	[	[	X
ejpam-5290	148	10	p6	p6	X
ejpam-5290	148	11	,	,	PUNCT
ejpam-5290	148	12	p7	p7	PROPN
ejpam-5290	148	13	]	]	PUNCT
ejpam-5290	148	14	:	:	PUNCT
ejpam-5290	148	15	⟨p6	⟨p6	PROPN
ejpam-5290	148	16	−	−	PROPN
ejpam-5290	148	17	p7	p7	PROPN
ejpam-5290	148	18	,	,	PUNCT
ejpam-5290	148	19	u6⟩+	u6⟩+	VERB
ejpam-5290	148	20	⟨p7	⟨p7	ADJ
ejpam-5290	148	21	−	−	PROPN
ejpam-5290	148	22	p6	p6	PROPN
ejpam-5290	148	23	,	,	PUNCT
ejpam-5290	148	24	u7⟩	u7⟩	PUNCT
ejpam-5290	149	1	=	=	SYM
ejpam-5290	149	2	0	0	PUNCT
ejpam-5290	149	3	(	(	PUNCT
ejpam-5290	149	4	px6	px6	NOUN
ejpam-5290	149	5	−	−	PROPN
ejpam-5290	149	6	px7)u	px7)u	PROPN
ejpam-5290	149	7	x	x	SYM
ejpam-5290	149	8	6	6	NUM
ejpam-5290	149	9	+	+	CCONJ
ejpam-5290	149	10	(	(	PUNCT
ejpam-5290	149	11	py6	py6	NOUN
ejpam-5290	149	12	−	−	NOUN
ejpam-5290	149	13	py7)u	py7)u	NOUN
ejpam-5290	149	14	y	y	NOUN
ejpam-5290	149	15	6	6	NUM
ejpam-5290	149	16	+	+	CCONJ
ejpam-5290	149	17	(	(	PUNCT
ejpam-5290	149	18	px7	px7	NOUN
ejpam-5290	149	19	−	−	PROPN
ejpam-5290	149	20	px6)u	px6)u	NOUN
ejpam-5290	149	21	x	x	SYM
ejpam-5290	149	22	7	7	NUM
ejpam-5290	149	23	+	+	CCONJ
ejpam-5290	149	24	(	(	PUNCT
ejpam-5290	149	25	py7	py7	NOUN
ejpam-5290	149	26	−	−	PROPN
ejpam-5290	149	27	py6)u	py6)u	NOUN
ejpam-5290	150	1	y	y	NOUN
ejpam-5290	150	2	7	7	NUM
ejpam-5290	150	3	=	=	SYM
ejpam-5290	150	4	0	0	PUNCT
ejpam-5290	151	1	(	(	PUNCT
ejpam-5290	151	2	−γ2)u	−γ2)u	NOUN
ejpam-5290	151	3	x	x	SYM
ejpam-5290	151	4	6	6	NUM
ejpam-5290	151	5	=	=	SYM
ejpam-5290	151	6	α2u	α2u	PROPN
ejpam-5290	151	7	y	y	PROPN
ejpam-5290	151	8	6	6	NUM
ejpam-5290	151	9	uy6	uy6	NOUN
ejpam-5290	151	10	=	=	PUNCT
ejpam-5290	151	11	(	(	PUNCT
ejpam-5290	151	12	γ2	γ2	ADJ
ejpam-5290	151	13	α2	α2	PROPN
ejpam-5290	151	14	)	)	PUNCT
ejpam-5290	152	1	ux6	ux6	NOUN
ejpam-5290	152	2	applying	apply	VERB
ejpam-5290	152	3	the	the	DET
ejpam-5290	152	4	flex	flex	ADJ
ejpam-5290	152	5	condition	condition	NOUN
ejpam-5290	152	6	to	to	ADP
ejpam-5290	152	7	the	the	DET
ejpam-5290	152	8	edge	edge	NOUN
ejpam-5290	152	9	[	[	X
ejpam-5290	152	10	p6	p6	X
ejpam-5290	152	11	,	,	PUNCT
ejpam-5290	152	12	p8	p8	PROPN
ejpam-5290	152	13	]	]	PUNCT
ejpam-5290	152	14	:	:	PUNCT
ejpam-5290	152	15	⟨p6	⟨p6	PROPN
ejpam-5290	152	16	−	−	PROPN
ejpam-5290	152	17	p8	p8	PROPN
ejpam-5290	152	18	,	,	PUNCT
ejpam-5290	152	19	u6⟩+	u6⟩+	PROPN
ejpam-5290	152	20	⟨p8	⟨p8	PROPN
ejpam-5290	152	21	−	−	NOUN
ejpam-5290	152	22	p6	p6	PROPN
ejpam-5290	152	23	,	,	PUNCT
ejpam-5290	152	24	u8⟩	u8⟩	NOUN
ejpam-5290	152	25	=	=	SYM
ejpam-5290	152	26	0	0	PUNCT
ejpam-5290	152	27	(	(	PUNCT
ejpam-5290	152	28	px6	px6	NOUN
ejpam-5290	152	29	−	−	PROPN
ejpam-5290	152	30	px8)u	px8)u	PROPN
ejpam-5290	152	31	x	x	PUNCT
ejpam-5290	152	32	6	6	NUM
ejpam-5290	152	33	+	+	CCONJ
ejpam-5290	152	34	(	(	PUNCT
ejpam-5290	152	35	py6	py6	NOUN
ejpam-5290	152	36	−	−	PROPN
ejpam-5290	152	37	py8)u	py8)u	PROPN
ejpam-5290	152	38	y	y	PROPN
ejpam-5290	152	39	6	6	NUM
ejpam-5290	152	40	+	+	CCONJ
ejpam-5290	152	41	(	(	PUNCT
ejpam-5290	152	42	px8	px8	NOUN
ejpam-5290	152	43	−	−	PROPN
ejpam-5290	152	44	px6)u	px6)u	NOUN
ejpam-5290	152	45	x	x	SYM
ejpam-5290	152	46	8	8	NUM
ejpam-5290	152	47	+	+	CCONJ
ejpam-5290	152	48	(	(	PUNCT
ejpam-5290	152	49	py8	py8	NOUN
ejpam-5290	152	50	−	−	PROPN
ejpam-5290	152	51	py6)u	py6)u	NOUN
ejpam-5290	153	1	y	y	PROPN
ejpam-5290	153	2	8	8	NUM
ejpam-5290	153	3	=	=	SYM
ejpam-5290	153	4	0	0	NUM
ejpam-5290	154	1	ux6	ux6	NOUN
ejpam-5290	154	2	=	=	PUNCT
ejpam-5290	154	3	ux8	ux8	PROPN
ejpam-5290	154	4	finally	finally	ADV
ejpam-5290	154	5	,	,	PUNCT
ejpam-5290	154	6	applying	apply	VERB
ejpam-5290	154	7	the	the	DET
ejpam-5290	154	8	flex	flex	ADJ
ejpam-5290	154	9	condition	condition	NOUN
ejpam-5290	154	10	to	to	ADP
ejpam-5290	154	11	the	the	DET
ejpam-5290	154	12	edge	edge	NOUN
ejpam-5290	154	13	[	[	X
ejpam-5290	154	14	p5	p5	ADJ
ejpam-5290	154	15	,	,	PUNCT
ejpam-5290	154	16	p6	p6	PROPN
ejpam-5290	154	17	]	]	PUNCT
ejpam-5290	154	18	:	:	PUNCT
ejpam-5290	154	19	⟨p5	⟨p5	PROPN
ejpam-5290	154	20	−	−	PROPN
ejpam-5290	154	21	p6	p6	PROPN
ejpam-5290	154	22	,	,	PUNCT
ejpam-5290	154	23	u5⟩+	u5⟩+	PROPN
ejpam-5290	154	24	⟨p6	⟨p6	PROPN
ejpam-5290	154	25	−	−	PROPN
ejpam-5290	154	26	p5	p5	PROPN
ejpam-5290	154	27	,	,	PUNCT
ejpam-5290	154	28	u6⟩	u6⟩	ADV
ejpam-5290	155	1	=	=	SYM
ejpam-5290	155	2	0	0	NUM
ejpam-5290	155	3	(	(	PUNCT
ejpam-5290	155	4	px5	px5	ADJ
ejpam-5290	155	5	−	−	PROPN
ejpam-5290	155	6	px6)u	px6)u	NOUN
ejpam-5290	155	7	x	x	SYM
ejpam-5290	155	8	5	5	NUM
ejpam-5290	155	9	+	+	CCONJ
ejpam-5290	155	10	(	(	PUNCT
ejpam-5290	155	11	py5	py5	NOUN
ejpam-5290	155	12	−	−	PROPN
ejpam-5290	155	13	py6)u	py6)u	NOUN
ejpam-5290	156	1	y	y	PROPN
ejpam-5290	156	2	5	5	NUM
ejpam-5290	156	3	+	+	CCONJ
ejpam-5290	156	4	(	(	PUNCT
ejpam-5290	156	5	px6	px6	NOUN
ejpam-5290	156	6	−	−	PROPN
ejpam-5290	156	7	px5)u	px5)u	NOUN
ejpam-5290	156	8	x	x	PUNCT
ejpam-5290	156	9	6	6	NUM
ejpam-5290	156	10	+	+	CCONJ
ejpam-5290	156	11	(	(	PUNCT
ejpam-5290	156	12	py6	py6	NOUN
ejpam-5290	156	13	−	−	PROPN
ejpam-5290	156	14	py5)u	py5)u	NOUN
ejpam-5290	156	15	y	y	PROPN
ejpam-5290	156	16	6	6	NUM
ejpam-5290	156	17	=	=	SYM
ejpam-5290	156	18	0	0	NUM
ejpam-5290	156	19	from	from	ADP
ejpam-5290	156	20	which	which	PRON
ejpam-5290	156	21	it	it	PRON
ejpam-5290	156	22	follows	follow	VERB
ejpam-5290	156	23	that	that	SCONJ
ejpam-5290	156	24	:	:	PUNCT
ejpam-5290	156	25	γ2u	γ2u	X
ejpam-5290	156	26	x	x	SYM
ejpam-5290	156	27	5	5	NUM
ejpam-5290	156	28	+	+	CCONJ
ejpam-5290	156	29	β2u	β2u	PUNCT
ejpam-5290	156	30	y	y	PROPN
ejpam-5290	156	31	5	5	NUM
ejpam-5290	156	32	=	=	SYM
ejpam-5290	156	33	γ2u	γ2u	X
ejpam-5290	156	34	x	x	SYM
ejpam-5290	156	35	6	6	NUM
ejpam-5290	156	36	+	+	CCONJ
ejpam-5290	156	37	β2u	β2u	PUNCT
ejpam-5290	156	38	y	y	PROPN
ejpam-5290	156	39	6	6	NUM
ejpam-5290	156	40	substituting	substitute	VERB
ejpam-5290	156	41	uy6	uy6	PROPN
ejpam-5290	156	42	:	:	PUNCT
ejpam-5290	156	43	γ2u	γ2u	NOUN
ejpam-5290	156	44	x	x	SYM
ejpam-5290	156	45	5	5	NUM
ejpam-5290	156	46	+	+	CCONJ
ejpam-5290	156	47	β2u	β2u	PUNCT
ejpam-5290	156	48	y	y	PROPN
ejpam-5290	156	49	5	5	NUM
ejpam-5290	156	50	=	=	SYM
ejpam-5290	156	51	γ2u	γ2u	X
ejpam-5290	156	52	x	x	SYM
ejpam-5290	156	53	6	6	NUM
ejpam-5290	156	54	+	+	CCONJ
ejpam-5290	156	55	β2	β2	NOUN
ejpam-5290	156	56	(	(	PUNCT
ejpam-5290	156	57	γ2	γ2	ADJ
ejpam-5290	156	58	α2	α2	PROPN
ejpam-5290	156	59	)	)	PUNCT
ejpam-5290	157	1	ux6	ux6	NOUN
ejpam-5290	157	2	ux5	ux5	NOUN
ejpam-5290	157	3	=	=	SYM
ejpam-5290	157	4	(	(	PUNCT
ejpam-5290	157	5	1	1	NUM
ejpam-5290	157	6	+	+	CCONJ
ejpam-5290	157	7	β2	β2	VERB
ejpam-5290	157	8	α2	α2	ADJ
ejpam-5290	157	9	)	)	PUNCT
ejpam-5290	157	10	ux6	ux6	NOUN
ejpam-5290	157	11	−	−	PROPN
ejpam-5290	158	1	(	(	PUNCT
ejpam-5290	158	2	β2	β2	NOUN
ejpam-5290	158	3	γ2	γ2	PROPN
ejpam-5290	158	4	)	)	PUNCT
ejpam-5290	158	5	uy5	uy5	PROPN
ejpam-5290	158	6	g.	g.	PROPN
ejpam-5290	158	7	m.	m.	PROPN
ejpam-5290	158	8	badri	badri	PROPN
ejpam-5290	158	9	/	/	SYM
ejpam-5290	158	10	eur	eur	PROPN
ejpam-5290	158	11	.	.	PUNCT
ejpam-5290	159	1	j.	j.	PROPN
ejpam-5290	159	2	pure	pure	PROPN
ejpam-5290	159	3	appl	appl	PROPN
ejpam-5290	159	4	.	.	PROPN
ejpam-5290	159	5	math	math	PROPN
ejpam-5290	159	6	,	,	PUNCT
ejpam-5290	159	7	17	17	NUM
ejpam-5290	159	8	(	(	PUNCT
ejpam-5290	159	9	4	4	NUM
ejpam-5290	159	10	)	)	PUNCT
ejpam-5290	159	11	(	(	PUNCT
ejpam-5290	159	12	2024	2024	NUM
ejpam-5290	159	13	)	)	PUNCT
ejpam-5290	159	14	,	,	PUNCT
ejpam-5290	159	15	3079	3079	NUM
ejpam-5290	159	16	-	-	SYM
ejpam-5290	159	17	3092	3092	NUM
ejpam-5290	159	18	3087	3087	NUM
ejpam-5290	159	19	substituting	substitute	VERB
ejpam-5290	159	20	ux6	ux6	NOUN
ejpam-5290	159	21	=	=	PUNCT
ejpam-5290	159	22	ux8	ux8	NOUN
ejpam-5290	159	23	and	and	CCONJ
ejpam-5290	159	24	uy8	uy8	ADJ
ejpam-5290	159	25	=	=	SYM
ejpam-5290	159	26	uy5	uy5	NOUN
ejpam-5290	159	27	:	:	PUNCT
ejpam-5290	159	28	ux5	ux5	PROPN
ejpam-5290	160	1	=	=	PUNCT
ejpam-5290	160	2	(	(	PUNCT
ejpam-5290	160	3	1	1	NUM
ejpam-5290	160	4	+	+	CCONJ
ejpam-5290	160	5	β2	β2	VERB
ejpam-5290	160	6	α2	α2	PROPN
ejpam-5290	160	7	)	)	PUNCT
ejpam-5290	160	8	(	(	PUNCT
ejpam-5290	160	9	α2	α2	ADJ
ejpam-5290	160	10	+	+	CCONJ
ejpam-5290	160	11	(	(	PUNCT
ejpam-5290	160	12	α3	α3	ADJ
ejpam-5290	160	13	+	+	CCONJ
ejpam-5290	160	14	β3	β3	ADJ
ejpam-5290	160	15	)	)	PUNCT
ejpam-5290	160	16	σ2	σ2	PROPN
ejpam-5290	160	17	)	)	PUNCT
ejpam-5290	160	18	uy8	uy8	ADP
ejpam-5290	160	19	−	−	PROPN
ejpam-5290	160	20	(	(	PUNCT
ejpam-5290	160	21	β2	β2	NOUN
ejpam-5290	160	22	γ2	γ2	PROPN
ejpam-5290	160	23	)	)	PUNCT
ejpam-5290	160	24	uy5	uy5	PROPN
ejpam-5290	161	1	=	=	PUNCT
ejpam-5290	161	2	[	[	X
ejpam-5290	161	3	(	(	PUNCT
ejpam-5290	161	4	1	1	NUM
ejpam-5290	161	5	+	+	NUM
ejpam-5290	161	6	β2	β2	VERB
ejpam-5290	161	7	α2	α2	PROPN
ejpam-5290	161	8	)	)	PUNCT
ejpam-5290	161	9	(	(	PUNCT
ejpam-5290	161	10	α2	α2	ADJ
ejpam-5290	161	11	+	+	CCONJ
ejpam-5290	161	12	(	(	PUNCT
ejpam-5290	161	13	α3	α3	ADJ
ejpam-5290	161	14	+	+	CCONJ
ejpam-5290	161	15	β3	β3	ADJ
ejpam-5290	161	16	)	)	PUNCT
ejpam-5290	161	17	σ2	σ2	NOUN
ejpam-5290	161	18	)	)	PUNCT
ejpam-5290	161	19	−	−	PROPN
ejpam-5290	162	1	β2	β2	ADJ
ejpam-5290	162	2	γ2	γ2	NOUN
ejpam-5290	162	3	]	]	PUNCT
ejpam-5290	162	4	uy5	uy5	PROPN
ejpam-5290	162	5	with	with	ADP
ejpam-5290	162	6	the	the	DET
ejpam-5290	162	7	appropriate	appropriate	ADJ
ejpam-5290	162	8	substitutions	substitution	NOUN
ejpam-5290	162	9	we	we	PRON
ejpam-5290	162	10	arrive	arrive	VERB
ejpam-5290	162	11	at	at	ADP
ejpam-5290	162	12	an	an	DET
ejpam-5290	162	13	infinitesimal	infinitesimal	ADJ
ejpam-5290	162	14	flex	flex	NOUN
ejpam-5290	162	15	of	of	ADP
ejpam-5290	162	16	f3tri	f3tri	PROPN
ejpam-5290	162	17	with	with	ADP
ejpam-5290	162	18	the	the	DET
ejpam-5290	162	19	velocity	velocity	NOUN
ejpam-5290	162	20	components	component	NOUN
ejpam-5290	162	21	:	:	PUNCT
ejpam-5290	162	22	u5	u5	PROPN
ejpam-5290	162	23	=	=	SYM
ejpam-5290	162	24	(	(	PUNCT
ejpam-5290	162	25	[	[	X
ejpam-5290	162	26	(	(	PUNCT
ejpam-5290	162	27	1	1	NUM
ejpam-5290	162	28	+	+	NUM
ejpam-5290	162	29	β2	β2	VERB
ejpam-5290	162	30	α2	α2	PROPN
ejpam-5290	162	31	)	)	PUNCT
ejpam-5290	162	32	(	(	PUNCT
ejpam-5290	162	33	α2	α2	ADJ
ejpam-5290	162	34	+	+	CCONJ
ejpam-5290	162	35	(	(	PUNCT
ejpam-5290	162	36	α3	α3	ADJ
ejpam-5290	162	37	+	+	CCONJ
ejpam-5290	162	38	β3	β3	ADJ
ejpam-5290	162	39	)	)	PUNCT
ejpam-5290	162	40	σ2	σ2	NOUN
ejpam-5290	162	41	)	)	PUNCT
ejpam-5290	162	42	−	−	PROPN
ejpam-5290	163	1	β2	β2	ADJ
ejpam-5290	163	2	γ2	γ2	PROPN
ejpam-5290	163	3	]	]	PUNCT
ejpam-5290	164	1	uy7	uy7	PROPN
ejpam-5290	164	2	,	,	PUNCT
ejpam-5290	164	3	u	u	NOUN
ejpam-5290	164	4	y	y	PROPN
ejpam-5290	164	5	7	7	NUM
ejpam-5290	164	6	)	)	PUNCT
ejpam-5290	164	7	u6	u6	NOUN
ejpam-5290	164	8	=	=	SYM
ejpam-5290	164	9	(	(	PUNCT
ejpam-5290	164	10	(	(	PUNCT
ejpam-5290	164	11	α2	α2	ADJ
ejpam-5290	164	12	−	−	PROPN
ejpam-5290	165	1	(	(	PUNCT
ejpam-5290	165	2	α3	α3	PROPN
ejpam-5290	165	3	+	+	CCONJ
ejpam-5290	165	4	β3	β3	ADJ
ejpam-5290	165	5	)	)	PUNCT
ejpam-5290	165	6	σ2	σ2	PROPN
ejpam-5290	165	7	)	)	PUNCT
ejpam-5290	165	8	uy7	uy7	PROPN
ejpam-5290	165	9	,	,	PUNCT
ejpam-5290	165	10	(	(	PUNCT
ejpam-5290	165	11	γ2	γ2	ADJ
ejpam-5290	165	12	α2	α2	PROPN
ejpam-5290	165	13	)	)	PUNCT
ejpam-5290	165	14	(	(	PUNCT
ejpam-5290	165	15	α2	α2	ADV
ejpam-5290	165	16	−	−	PROPN
ejpam-5290	165	17	(	(	PUNCT
ejpam-5290	165	18	α3	α3	PROPN
ejpam-5290	165	19	+	+	CCONJ
ejpam-5290	165	20	β3	β3	ADJ
ejpam-5290	165	21	)	)	PUNCT
ejpam-5290	165	22	σ2	σ2	PROPN
ejpam-5290	165	23	)	)	PUNCT
ejpam-5290	165	24	uy7	uy7	PROPN
ejpam-5290	165	25	)	)	PUNCT
ejpam-5290	166	1	u7	u7	PROPN
ejpam-5290	166	2	=	=	SYM
ejpam-5290	166	3	(	(	PUNCT
ejpam-5290	166	4	0	0	NUM
ejpam-5290	166	5	,	,	PUNCT
ejpam-5290	166	6	uy7	uy7	X
ejpam-5290	166	7	)	)	PUNCT
ejpam-5290	166	8	u8	u8	PROPN
ejpam-5290	166	9	=	=	SYM
ejpam-5290	166	10	(	(	PUNCT
ejpam-5290	166	11	(	(	PUNCT
ejpam-5290	166	12	α2	α2	ADJ
ejpam-5290	166	13	−	−	PROPN
ejpam-5290	166	14	(	(	PUNCT
ejpam-5290	166	15	α3	α3	PROPN
ejpam-5290	166	16	+	+	CCONJ
ejpam-5290	166	17	β3	β3	ADJ
ejpam-5290	166	18	)	)	PUNCT
ejpam-5290	166	19	σ2	σ2	PROPN
ejpam-5290	166	20	)	)	PUNCT
ejpam-5290	166	21	uy7	uy7	PROPN
ejpam-5290	166	22	,	,	PUNCT
ejpam-5290	166	23	u	u	NOUN
ejpam-5290	166	24	y	y	PROPN
ejpam-5290	166	25	7	7	NUM
ejpam-5290	166	26	)	)	PUNCT
ejpam-5290	166	27	uniquely	uniquely	ADV
ejpam-5290	166	28	determined	determine	VERB
ejpam-5290	166	29	by	by	ADP
ejpam-5290	166	30	uy7	uy7	NOUN
ejpam-5290	166	31	and	and	CCONJ
ejpam-5290	166	32	with	with	ADP
ejpam-5290	166	33	zero	zero	NUM
ejpam-5290	166	34	velocities	velocity	NOUN
ejpam-5290	166	35	elsewhere	elsewhere	ADV
ejpam-5290	166	36	.	.	PUNCT
ejpam-5290	167	1	corollary	corollary	ADJ
ejpam-5290	167	2	2	2	NUM
ejpam-5290	167	3	.	.	PUNCT
ejpam-5290	168	1	let	let	AUX
ejpam-5290	168	2	hfl(f3tri	hfl(f3tri	ADJ
ejpam-5290	168	3	)	)	PUNCT
ejpam-5290	168	4	denote	denote	VERB
ejpam-5290	168	5	the	the	DET
ejpam-5290	168	6	linear	linear	ADJ
ejpam-5290	168	7	space	space	NOUN
ejpam-5290	168	8	of	of	ADP
ejpam-5290	168	9	all	all	DET
ejpam-5290	168	10	infinitesimal	infinitesimal	ADJ
ejpam-5290	168	11	flexes	flex	NOUN
ejpam-5290	168	12	of	of	ADP
ejpam-5290	168	13	f3tri	f3tri	PROPN
ejpam-5290	168	14	.	.	PROPN
ejpam-5290	168	15	then	then	ADV
ejpam-5290	168	16	dim(hfl(f3tri	dim(hfl(f3tri	ADJ
ejpam-5290	168	17	)	)	PUNCT
ejpam-5290	168	18	)	)	PUNCT
ejpam-5290	169	1	=	=	SYM
ejpam-5290	169	2	5	5	X
ejpam-5290	169	3	.	.	PUNCT
ejpam-5290	169	4	corollary	corollary	ADJ
ejpam-5290	169	5	3	3	NUM
ejpam-5290	169	6	.	.	PUNCT
ejpam-5290	170	1	let	let	AUX
ejpam-5290	170	2	hfl(fntri	hfl(fntri	NOUN
ejpam-5290	170	3	)	)	PUNCT
ejpam-5290	170	4	denote	denote	VERB
ejpam-5290	170	5	the	the	DET
ejpam-5290	170	6	linear	linear	ADJ
ejpam-5290	170	7	space	space	NOUN
ejpam-5290	170	8	of	of	ADP
ejpam-5290	170	9	all	all	DET
ejpam-5290	170	10	infinitesimal	infinitesimal	ADJ
ejpam-5290	170	11	flexes	flex	NOUN
ejpam-5290	170	12	of	of	ADP
ejpam-5290	170	13	the	the	DET
ejpam-5290	170	14	finite	finite	ADJ
ejpam-5290	170	15	framework	framework	NOUN
ejpam-5290	170	16	with	with	ADP
ejpam-5290	170	17	n	n	CCONJ
ejpam-5290	170	18	connected	connect	VERB
ejpam-5290	170	19	braced	braced	ADJ
ejpam-5290	170	20	triangles	triangle	NOUN
ejpam-5290	170	21	.	.	PUNCT
ejpam-5290	171	1	then	then	ADV
ejpam-5290	171	2	dim(hfl(fntri	dim(hfl(fntri	NOUN
ejpam-5290	171	3	)	)	PUNCT
ejpam-5290	171	4	)	)	PUNCT
ejpam-5290	172	1	=	=	SYM
ejpam-5290	172	2	n+	n+	PUNCT
ejpam-5290	173	1	2	2	NUM
ejpam-5290	173	2	.	.	SYM
ejpam-5290	173	3	3	3	NUM
ejpam-5290	173	4	.	.	PUNCT
ejpam-5290	174	1	the	the	DET
ejpam-5290	174	2	connected	connect	VERB
ejpam-5290	174	3	braced	braced	ADJ
ejpam-5290	174	4	triangles	triangle	NOUN
ejpam-5290	174	5	infinite	infinite	ADJ
ejpam-5290	174	6	bar	bar	NOUN
ejpam-5290	174	7	-	-	PUNCT
ejpam-5290	174	8	joint	joint	NOUN
ejpam-5290	174	9	framework	framework	NOUN
ejpam-5290	174	10	let	let	AUX
ejpam-5290	174	11	gtri	gtri	AUX
ejpam-5290	174	12	be	be	AUX
ejpam-5290	174	13	the	the	DET
ejpam-5290	174	14	infinite	infinite	ADJ
ejpam-5290	174	15	strip	strip	NOUN
ejpam-5290	174	16	bar	bar	NOUN
ejpam-5290	174	17	-	-	PUNCT
ejpam-5290	174	18	joint	joint	NOUN
ejpam-5290	174	19	framework	framework	NOUN
ejpam-5290	174	20	in	in	ADP
ejpam-5290	174	21	r2	r2	PROPN
ejpam-5290	174	22	constructed	construct	VERB
ejpam-5290	174	23	by	by	ADP
ejpam-5290	174	24	joining	join	VERB
ejpam-5290	174	25	copies	copy	NOUN
ejpam-5290	174	26	of	of	ADP
ejpam-5290	174	27	the	the	DET
ejpam-5290	174	28	connecting	connect	VERB
ejpam-5290	174	29	braced	braced	ADJ
ejpam-5290	174	30	triangles	triangle	NOUN
ejpam-5290	174	31	finite	finite	NOUN
ejpam-5290	174	32	framework	framework	NOUN
ejpam-5290	174	33	along	along	ADP
ejpam-5290	174	34	in	in	ADP
ejpam-5290	174	35	the	the	DET
ejpam-5290	174	36	positive	positive	ADJ
ejpam-5290	174	37	x	x	SYM
ejpam-5290	174	38	coordinate	coordinate	NOUN
ejpam-5290	174	39	direction	direction	NOUN
ejpam-5290	174	40	,	,	PUNCT
ejpam-5290	174	41	as	as	SCONJ
ejpam-5290	174	42	suggested	suggest	VERB
ejpam-5290	174	43	by	by	ADP
ejpam-5290	174	44	figure	figure	NOUN
ejpam-5290	174	45	3	3	NUM
ejpam-5290	174	46	.	.	PUNCT
ejpam-5290	174	47	.	.	PUNCT
ejpam-5290	174	48	.	.	PUNCT
ejpam-5290	175	1	.	.	PUNCT
ejpam-5290	176	1	figure	figure	VERB
ejpam-5290	176	2	3	3	NUM
ejpam-5290	176	3	:	:	PUNCT
ejpam-5290	176	4	the	the	DET
ejpam-5290	176	5	infinite	infinite	ADJ
ejpam-5290	176	6	connected	connect	VERB
ejpam-5290	176	7	braced	braced	ADJ
ejpam-5290	176	8	triangles	triangle	NOUN
ejpam-5290	176	9	framework	framework	NOUN
ejpam-5290	176	10	gtri	gtri	PROPN
ejpam-5290	176	11	g.	g.	PROPN
ejpam-5290	176	12	m.	m.	PROPN
ejpam-5290	176	13	badri	badri	PROPN
ejpam-5290	176	14	/	/	SYM
ejpam-5290	176	15	eur	eur	PROPN
ejpam-5290	176	16	.	.	PUNCT
ejpam-5290	177	1	j.	j.	PROPN
ejpam-5290	177	2	pure	pure	PROPN
ejpam-5290	177	3	appl	appl	PROPN
ejpam-5290	177	4	.	.	PROPN
ejpam-5290	177	5	math	math	PROPN
ejpam-5290	177	6	,	,	PUNCT
ejpam-5290	177	7	17	17	NUM
ejpam-5290	177	8	(	(	PUNCT
ejpam-5290	177	9	4	4	NUM
ejpam-5290	177	10	)	)	PUNCT
ejpam-5290	177	11	(	(	PUNCT
ejpam-5290	177	12	2024	2024	NUM
ejpam-5290	177	13	)	)	PUNCT
ejpam-5290	177	14	,	,	PUNCT
ejpam-5290	177	15	3079	3079	NUM
ejpam-5290	177	16	-	-	SYM
ejpam-5290	177	17	3092	3092	NUM
ejpam-5290	177	18	3088	3088	NUM
ejpam-5290	177	19	this	this	DET
ejpam-5290	177	20	section	section	NOUN
ejpam-5290	177	21	is	be	AUX
ejpam-5290	177	22	dedicated	dedicate	VERB
ejpam-5290	177	23	to	to	ADP
ejpam-5290	177	24	the	the	DET
ejpam-5290	177	25	identification	identification	NOUN
ejpam-5290	177	26	of	of	ADP
ejpam-5290	177	27	a	a	DET
ejpam-5290	177	28	base	base	NOUN
ejpam-5290	177	29	for	for	ADP
ejpam-5290	177	30	the	the	DET
ejpam-5290	177	31	space	space	NOUN
ejpam-5290	177	32	of	of	ADP
ejpam-5290	177	33	all	all	DET
ejpam-5290	177	34	infinitesimal	infinitesimal	ADJ
ejpam-5290	177	35	flexes	flex	NOUN
ejpam-5290	177	36	of	of	ADP
ejpam-5290	177	37	the	the	DET
ejpam-5290	177	38	infinite	infinite	ADJ
ejpam-5290	177	39	connected	connect	VERB
ejpam-5290	177	40	braced	braced	ADJ
ejpam-5290	177	41	triangles	triangle	NOUN
ejpam-5290	177	42	framework	framework	NOUN
ejpam-5290	177	43	.	.	PUNCT
ejpam-5290	178	1	in	in	ADP
ejpam-5290	178	2	fact	fact	NOUN
ejpam-5290	178	3	,	,	PUNCT
ejpam-5290	178	4	such	such	ADJ
ejpam-5290	178	5	bases	basis	NOUN
ejpam-5290	178	6	do	do	AUX
ejpam-5290	178	7	exist	exist	VERB
ejpam-5290	178	8	for	for	ADP
ejpam-5290	178	9	infinite	infinite	ADJ
ejpam-5290	178	10	frameworks	framework	NOUN
ejpam-5290	178	11	and	and	CCONJ
ejpam-5290	178	12	this	this	PRON
ejpam-5290	178	13	was	be	AUX
ejpam-5290	178	14	thoroughly	thoroughly	ADV
ejpam-5290	178	15	investigated	investigate	VERB
ejpam-5290	178	16	in	in	ADP
ejpam-5290	178	17	[	[	X
ejpam-5290	178	18	7	7	NUM
ejpam-5290	178	19	]	]	PUNCT
ejpam-5290	178	20	.	.	PUNCT
ejpam-5290	179	1	for	for	ADP
ejpam-5290	179	2	more	more	ADJ
ejpam-5290	179	3	considerations	consideration	NOUN
ejpam-5290	179	4	of	of	ADP
ejpam-5290	179	5	infinite	infinite	ADJ
ejpam-5290	179	6	strip	strip	NOUN
ejpam-5290	179	7	frameworks	framework	NOUN
ejpam-5290	179	8	see	see	VERB
ejpam-5290	179	9	[	[	X
ejpam-5290	179	10	20	20	NUM
ejpam-5290	179	11	]	]	PUNCT
ejpam-5290	179	12	,	,	PUNCT
ejpam-5290	179	13	[	[	X
ejpam-5290	179	14	21	21	NUM
ejpam-5290	179	15	]	]	PUNCT
ejpam-5290	179	16	and	and	CCONJ
ejpam-5290	179	17	[	[	X
ejpam-5290	179	18	23	23	NUM
ejpam-5290	179	19	]	]	PUNCT
ejpam-5290	179	20	.	.	PUNCT
ejpam-5290	180	1	similar	similar	ADJ
ejpam-5290	180	2	to	to	ADP
ejpam-5290	180	3	the	the	DET
ejpam-5290	180	4	finite	finite	ADJ
ejpam-5290	180	5	case	case	NOUN
ejpam-5290	180	6	,	,	PUNCT
ejpam-5290	180	7	with	with	SCONJ
ejpam-5290	180	8	the	the	DET
ejpam-5290	180	9	base	base	NOUN
ejpam-5290	180	10	vertices	vertice	VERB
ejpam-5290	180	11	having	have	VERB
ejpam-5290	180	12	zero	zero	NUM
ejpam-5290	180	13	velocity	velocity	NOUN
ejpam-5290	180	14	components	component	NOUN
ejpam-5290	180	15	,	,	PUNCT
ejpam-5290	180	16	the	the	DET
ejpam-5290	180	17	action	action	NOUN
ejpam-5290	180	18	implied	imply	VERB
ejpam-5290	180	19	by	by	ADP
ejpam-5290	180	20	the	the	DET
ejpam-5290	180	21	velocity	velocity	NOUN
ejpam-5290	180	22	at	at	ADP
ejpam-5290	180	23	vertex	vertex	NOUN
ejpam-5290	180	24	p1	p1	NOUN
ejpam-5290	180	25	does	do	AUX
ejpam-5290	180	26	in	in	ADP
ejpam-5290	180	27	fact	fact	NOUN
ejpam-5290	180	28	extend	extend	VERB
ejpam-5290	180	29	to	to	ADP
ejpam-5290	180	30	the	the	DET
ejpam-5290	180	31	rest	rest	NOUN
ejpam-5290	180	32	of	of	ADP
ejpam-5290	180	33	the	the	DET
ejpam-5290	180	34	framework	framework	NOUN
ejpam-5290	180	35	in	in	ADP
ejpam-5290	180	36	the	the	DET
ejpam-5290	180	37	infinite	infinite	ADJ
ejpam-5290	180	38	case	case	NOUN
ejpam-5290	180	39	.	.	PUNCT
ejpam-5290	181	1	theorem	theorem	NOUN
ejpam-5290	181	2	4	4	NUM
ejpam-5290	181	3	.	.	PUNCT
ejpam-5290	182	1	let	let	AUX
ejpam-5290	182	2	gtri	gtri	AUX
ejpam-5290	182	3	be	be	AUX
ejpam-5290	182	4	the	the	DET
ejpam-5290	182	5	connected	connect	VERB
ejpam-5290	182	6	braced	braced	ADJ
ejpam-5290	182	7	triangles	triangle	NOUN
ejpam-5290	182	8	infinite	infinite	ADJ
ejpam-5290	182	9	bar	bar	NOUN
ejpam-5290	182	10	-	-	PUNCT
ejpam-5290	182	11	joint	joint	NOUN
ejpam-5290	182	12	framework	framework	NOUN
ejpam-5290	182	13	in	in	ADP
ejpam-5290	182	14	r2	r2	PROPN
ejpam-5290	182	15	.	.	PUNCT
ejpam-5290	183	1	let	let	VERB
ejpam-5290	183	2	u	u	PRON
ejpam-5290	183	3	be	be	AUX
ejpam-5290	183	4	the	the	DET
ejpam-5290	183	5	non	non	ADJ
ejpam-5290	183	6	trivial	trivial	ADJ
ejpam-5290	183	7	infinitesimal	infinitesimal	ADJ
ejpam-5290	183	8	flex	flex	NOUN
ejpam-5290	183	9	of	of	ADP
ejpam-5290	183	10	gtri	gtri	NOUN
ejpam-5290	183	11	,	,	PUNCT
ejpam-5290	183	12	with	with	ADP
ejpam-5290	183	13	the	the	DET
ejpam-5290	183	14	velocity	velocity	NOUN
ejpam-5290	183	15	component	component	NOUN
ejpam-5290	183	16	un	un	PROPN
ejpam-5290	183	17	,	,	PUNCT
ejpam-5290	183	18	i	i	PRON
ejpam-5290	183	19	applied	apply	VERB
ejpam-5290	183	20	at	at	ADP
ejpam-5290	183	21	vertex	vertex	NOUN
ejpam-5290	183	22	pn	pn	PROPN
ejpam-5290	183	23	,	,	PUNCT
ejpam-5290	183	24	i	i	PRON
ejpam-5290	183	25	,	,	PUNCT
ejpam-5290	183	26	and	and	CCONJ
ejpam-5290	183	27	with	with	ADP
ejpam-5290	183	28	un,3	un,3	PROPN
ejpam-5290	183	29	=	=	SYM
ejpam-5290	183	30	(	(	PUNCT
ejpam-5290	183	31	0	0	NUM
ejpam-5290	183	32	,	,	PUNCT
ejpam-5290	183	33	0	0	NUM
ejpam-5290	183	34	)	)	PUNCT
ejpam-5290	183	35	for	for	ADP
ejpam-5290	183	36	all	all	PRON
ejpam-5290	183	37	n	n	DET
ejpam-5290	183	38	∈	∈	PROPN
ejpam-5290	183	39	n.	n.	NOUN
ejpam-5290	183	40	then	then	ADV
ejpam-5290	183	41	:	:	PUNCT
ejpam-5290	183	42	un,1	un,1	PROPN
ejpam-5290	183	43	=	=	PRON
ejpam-5290	183	44	(	(	PUNCT
ejpam-5290	183	45	n−1∏	n−1∏	PROPN
ejpam-5290	183	46	i=1	i=1	PROPN
ejpam-5290	183	47	(	(	PUNCT
ejpam-5290	183	48	1	1	NUM
ejpam-5290	183	49	1	1	NUM
ejpam-5290	183	50	+	+	CCONJ
ejpam-5290	183	51	βi	βi	PROPN
ejpam-5290	183	52	αi	αi	ADV
ejpam-5290	183	53	)	)	PUNCT
ejpam-5290	184	1	ux1,1	ux1,1	PROPN
ejpam-5290	184	2	,	,	PUNCT
ejpam-5290	184	3	0	0	NUM
ejpam-5290	184	4	)	)	PUNCT
ejpam-5290	184	5	.	.	PUNCT
ejpam-5290	184	6	.	.	PUNCT
ejpam-5290	184	7	.	.	PUNCT
ejpam-5290	184	8	.	.	PUNCT
ejpam-5290	184	9	.	.	PUNCT
ejpam-5290	184	10	.	.	PUNCT
ejpam-5290	185	1	pn,1	pn,1	PROPN
ejpam-5290	185	2	pn+1,1	pn+1,1	PROPN
ejpam-5290	185	3	pn,2	pn,2	VERB
ejpam-5290	185	4	pn,4	pn,4	PROPN
ejpam-5290	185	5	pn,3	pn,3	PROPN
ejpam-5290	185	6	αn	αn	NOUN
ejpam-5290	185	7	βn	βn	NOUN
ejpam-5290	185	8	γn	γn	ADP
ejpam-5290	185	9	pn+1,2	pn+1,2	PROPN
ejpam-5290	185	10	pn+1,3	pn+1,3	PROPN
ejpam-5290	185	11	pn+1,4	pn+1,4	PROPN
ejpam-5290	185	12	βn+1	βn+1	NUM
ejpam-5290	185	13	αn+1	αn+1	NUM
ejpam-5290	185	14	γn+1	γn+1	NUM
ejpam-5290	185	15	σn	σn	NOUN
ejpam-5290	185	16	figure	figure	NOUN
ejpam-5290	185	17	4	4	NUM
ejpam-5290	185	18	:	:	PUNCT
ejpam-5290	185	19	labelling	labelling	NOUN
ejpam-5290	185	20	of	of	ADP
ejpam-5290	185	21	the	the	DET
ejpam-5290	185	22	infinite	infinite	ADJ
ejpam-5290	185	23	connected	connect	VERB
ejpam-5290	185	24	braced	braced	ADJ
ejpam-5290	185	25	triangles	triangle	NOUN
ejpam-5290	185	26	framework	framework	NOUN
ejpam-5290	185	27	gtri	gtri	NOUN
ejpam-5290	185	28	proof	proof	NOUN
ejpam-5290	185	29	.	.	PUNCT
ejpam-5290	186	1	the	the	DET
ejpam-5290	186	2	proof	proof	NOUN
ejpam-5290	186	3	proceeds	proceed	VERB
ejpam-5290	186	4	by	by	ADP
ejpam-5290	186	5	mathematical	mathematical	ADJ
ejpam-5290	186	6	induction	induction	NOUN
ejpam-5290	186	7	.	.	PUNCT
ejpam-5290	187	1	the	the	DET
ejpam-5290	187	2	case	case	NOUN
ejpam-5290	187	3	n	n	NOUN
ejpam-5290	187	4	=	=	SYM
ejpam-5290	187	5	2	2	NUM
ejpam-5290	187	6	follows	follow	VERB
ejpam-5290	187	7	immediately	immediately	ADV
ejpam-5290	187	8	from	from	ADP
ejpam-5290	187	9	the	the	DET
ejpam-5290	187	10	proof	proof	NOUN
ejpam-5290	187	11	of	of	ADP
ejpam-5290	187	12	theorem	theorem	NOUN
ejpam-5290	187	13	2	2	X
ejpam-5290	187	14	.	.	PUNCT
ejpam-5290	187	15	we	we	PRON
ejpam-5290	187	16	now	now	ADV
ejpam-5290	187	17	assume	assume	VERB
ejpam-5290	187	18	that	that	SCONJ
ejpam-5290	187	19	this	this	PRON
ejpam-5290	187	20	is	be	AUX
ejpam-5290	187	21	true	true	ADJ
ejpam-5290	187	22	for	for	ADP
ejpam-5290	187	23	n	n	CCONJ
ejpam-5290	187	24	,	,	PUNCT
ejpam-5290	187	25	that	that	PRON
ejpam-5290	187	26	is	be	AUX
ejpam-5290	187	27	un,1	un,1	PROPN
ejpam-5290	187	28	=	=	SYM
ejpam-5290	187	29	(	(	PUNCT
ejpam-5290	187	30	n−1∏	n−1∏	PROPN
ejpam-5290	187	31	i=1	i=1	PROPN
ejpam-5290	187	32	(	(	PUNCT
ejpam-5290	187	33	1	1	NUM
ejpam-5290	187	34	1	1	NUM
ejpam-5290	187	35	+	+	CCONJ
ejpam-5290	187	36	βi	βi	PROPN
ejpam-5290	187	37	αi	αi	ADV
ejpam-5290	187	38	)	)	PUNCT
ejpam-5290	188	1	ux1,1	ux1,1	PROPN
ejpam-5290	188	2	,	,	PUNCT
ejpam-5290	188	3	0	0	NUM
ejpam-5290	188	4	)	)	PUNCT
ejpam-5290	188	5	.	.	PUNCT
ejpam-5290	189	1	the	the	DET
ejpam-5290	189	2	proof	proof	NOUN
ejpam-5290	189	3	for	for	ADP
ejpam-5290	189	4	n+1	n+1	PROPN
ejpam-5290	189	5	makes	make	VERB
ejpam-5290	189	6	direct	direct	ADJ
ejpam-5290	189	7	use	use	NOUN
ejpam-5290	189	8	of	of	ADP
ejpam-5290	189	9	the	the	DET
ejpam-5290	189	10	flex	flex	ADJ
ejpam-5290	189	11	condition	condition	NOUN
ejpam-5290	189	12	.	.	PUNCT
ejpam-5290	190	1	it	it	PRON
ejpam-5290	190	2	is	be	AUX
ejpam-5290	190	3	obvious	obvious	ADJ
ejpam-5290	190	4	that	that	SCONJ
ejpam-5290	190	5	each	each	DET
ejpam-5290	190	6	flex	flex	ADJ
ejpam-5290	190	7	un,1	un,1	PROPN
ejpam-5290	190	8	has	have	VERB
ejpam-5290	190	9	a	a	DET
ejpam-5290	190	10	zero	zero	NUM
ejpam-5290	190	11	velocity	velocity	NOUN
ejpam-5290	190	12	component	component	NOUN
ejpam-5290	190	13	in	in	ADP
ejpam-5290	190	14	the	the	DET
ejpam-5290	190	15	y	y	PROPN
ejpam-5290	190	16	direction	direction	NOUN
ejpam-5290	190	17	since	since	SCONJ
ejpam-5290	190	18	un,3	un,3	PROPN
ejpam-5290	190	19	=	=	X
ejpam-5290	190	20	(	(	PUNCT
ejpam-5290	190	21	0	0	NUM
ejpam-5290	190	22	,	,	PUNCT
ejpam-5290	190	23	0	0	NUM
ejpam-5290	190	24	)	)	PUNCT
ejpam-5290	190	25	for	for	ADP
ejpam-5290	190	26	all	all	DET
ejpam-5290	190	27	n.	n.	NOUN
ejpam-5290	190	28	to	to	PART
ejpam-5290	190	29	find	find	VERB
ejpam-5290	190	30	the	the	DET
ejpam-5290	190	31	g.	g.	PROPN
ejpam-5290	190	32	m.	m.	PROPN
ejpam-5290	190	33	badri	badri	PROPN
ejpam-5290	190	34	/	/	SYM
ejpam-5290	190	35	eur	eur	PROPN
ejpam-5290	190	36	.	.	PUNCT
ejpam-5290	191	1	j.	j.	PROPN
ejpam-5290	191	2	pure	pure	PROPN
ejpam-5290	191	3	appl	appl	PROPN
ejpam-5290	191	4	.	.	PROPN
ejpam-5290	191	5	math	math	PROPN
ejpam-5290	191	6	,	,	PUNCT
ejpam-5290	191	7	17	17	NUM
ejpam-5290	191	8	(	(	PUNCT
ejpam-5290	191	9	4	4	NUM
ejpam-5290	191	10	)	)	PUNCT
ejpam-5290	191	11	(	(	PUNCT
ejpam-5290	191	12	2024	2024	NUM
ejpam-5290	191	13	)	)	PUNCT
ejpam-5290	191	14	,	,	PUNCT
ejpam-5290	191	15	3079	3079	NUM
ejpam-5290	191	16	-	-	SYM
ejpam-5290	191	17	3092	3092	NUM
ejpam-5290	191	18	3089	3089	NUM
ejpam-5290	191	19	velocity	velocity	NOUN
ejpam-5290	191	20	component	component	NOUN
ejpam-5290	191	21	in	in	ADP
ejpam-5290	191	22	the	the	DET
ejpam-5290	191	23	x	x	NOUN
ejpam-5290	191	24	direction	direction	NOUN
ejpam-5290	191	25	we	we	PRON
ejpam-5290	191	26	first	first	ADV
ejpam-5290	191	27	start	start	VERB
ejpam-5290	191	28	by	by	ADP
ejpam-5290	191	29	applying	apply	VERB
ejpam-5290	191	30	the	the	DET
ejpam-5290	191	31	flex	flex	ADJ
ejpam-5290	191	32	condition	condition	NOUN
ejpam-5290	191	33	to	to	ADP
ejpam-5290	191	34	the	the	DET
ejpam-5290	191	35	edge	edge	NOUN
ejpam-5290	191	36	[	[	X
ejpam-5290	191	37	pn,2	pn,2	PROPN
ejpam-5290	191	38	,	,	PUNCT
ejpam-5290	191	39	pn,3	pn,3	PROPN
ejpam-5290	191	40	]	]	X
ejpam-5290	191	41	:	:	PUNCT
ejpam-5290	191	42	⟨pn,2	⟨pn,2	NUM
ejpam-5290	191	43	−	−	PROPN
ejpam-5290	191	44	pn,3	pn,3	PROPN
ejpam-5290	191	45	,	,	PUNCT
ejpam-5290	191	46	un,2⟩+	un,2⟩+	PRON
ejpam-5290	191	47	⟨pn,3	⟨pn,3	NUM
ejpam-5290	192	1	−	−	PROPN
ejpam-5290	192	2	pn,2	pn,2	PROPN
ejpam-5290	192	3	,	,	PUNCT
ejpam-5290	192	4	un,3⟩	un,3⟩	ADJ
ejpam-5290	192	5	=	=	SYM
ejpam-5290	192	6	0	0	PUNCT
ejpam-5290	193	1	(	(	PUNCT
ejpam-5290	193	2	pxn,2	pxn,2	VERB
ejpam-5290	193	3	−	−	PROPN
ejpam-5290	193	4	pxn,3)u	pxn,3)u	NOUN
ejpam-5290	193	5	x	x	NOUN
ejpam-5290	193	6	n,2	n,2	VERB
ejpam-5290	193	7	+	+	CCONJ
ejpam-5290	193	8	(	(	PUNCT
ejpam-5290	193	9	pyn,2	pyn,2	VERB
ejpam-5290	193	10	−	−	PROPN
ejpam-5290	193	11	pyn,3)u	pyn,3)u	NOUN
ejpam-5290	193	12	y	y	PROPN
ejpam-5290	193	13	n,2	n,2	VERB
ejpam-5290	193	14	+	+	CCONJ
ejpam-5290	194	1	(	(	PUNCT
ejpam-5290	194	2	pxn,3	pxn,3	ADV
ejpam-5290	194	3	−	−	PUNCT
ejpam-5290	194	4	pxn,2)u	pxn,2)u	NOUN
ejpam-5290	194	5	x	x	NOUN
ejpam-5290	194	6	n,3	n,3	NOUN
ejpam-5290	194	7	+	+	CCONJ
ejpam-5290	194	8	(	(	PUNCT
ejpam-5290	194	9	pyn,3	pyn,3	NOUN
ejpam-5290	194	10	−	−	PROPN
ejpam-5290	194	11	pyn,2)u	pyn,2)u	NOUN
ejpam-5290	194	12	y	y	NOUN
ejpam-5290	194	13	n,3	n,3	ADV
ejpam-5290	194	14	=	=	SYM
ejpam-5290	194	15	0	0	NUM
ejpam-5290	194	16	−γnu	−γnu	PROPN
ejpam-5290	194	17	x	x	PUNCT
ejpam-5290	194	18	n,2	n,2	ADJ
ejpam-5290	194	19	+	+	CCONJ
ejpam-5290	194	20	αnu	αnu	ADJ
ejpam-5290	194	21	y	y	NOUN
ejpam-5290	194	22	n,2	n,2	VERB
ejpam-5290	194	23	=	=	NOUN
ejpam-5290	194	24	0	0	NUM
ejpam-5290	194	25	from	from	ADP
ejpam-5290	194	26	which	which	PRON
ejpam-5290	194	27	it	it	PRON
ejpam-5290	194	28	follows	follow	VERB
ejpam-5290	194	29	that	that	SCONJ
ejpam-5290	194	30	:	:	PUNCT
ejpam-5290	194	31	uyn,2	uyn,2	ADJ
ejpam-5290	194	32	=	=	SYM
ejpam-5290	194	33	(	(	PUNCT
ejpam-5290	194	34	γn	γn	NOUN
ejpam-5290	194	35	αn	αn	NOUN
ejpam-5290	194	36	)	)	PUNCT
ejpam-5290	194	37	uxn,2	uxn,2	ADJ
ejpam-5290	194	38	applying	apply	VERB
ejpam-5290	194	39	the	the	DET
ejpam-5290	194	40	flex	flex	ADJ
ejpam-5290	194	41	condition	condition	NOUN
ejpam-5290	194	42	to	to	ADP
ejpam-5290	194	43	the	the	DET
ejpam-5290	194	44	edge	edge	NOUN
ejpam-5290	195	1	[	[	X
ejpam-5290	195	2	pn,1	pn,1	PROPN
ejpam-5290	195	3	,	,	PUNCT
ejpam-5290	195	4	pn,2	pn,2	VERB
ejpam-5290	195	5	]	]	PUNCT
ejpam-5290	195	6	:	:	PUNCT
ejpam-5290	195	7	⟨pn,1	⟨pn,1	X
ejpam-5290	195	8	−	−	PROPN
ejpam-5290	195	9	pn,2	pn,2	VERB
ejpam-5290	195	10	,	,	PUNCT
ejpam-5290	195	11	un,1⟩+	un,1⟩+	ADP
ejpam-5290	195	12	⟨pn,2	⟨pn,2	VERB
ejpam-5290	195	13	−	−	PROPN
ejpam-5290	195	14	pn,1	pn,1	PROPN
ejpam-5290	195	15	,	,	PUNCT
ejpam-5290	195	16	un,2⟩	un,2⟩	PROPN
ejpam-5290	195	17	=	=	SYM
ejpam-5290	195	18	0	0	PUNCT
ejpam-5290	195	19	(	(	PUNCT
ejpam-5290	196	1	pxn,1	pxn,1	NOUN
ejpam-5290	196	2	−	−	PROPN
ejpam-5290	196	3	pxn,2)u	pxn,2)u	NOUN
ejpam-5290	196	4	x	x	PUNCT
ejpam-5290	196	5	n,1	n,1	PROPN
ejpam-5290	196	6	+	+	CCONJ
ejpam-5290	196	7	(	(	PUNCT
ejpam-5290	196	8	pyn,1	pyn,1	INTJ
ejpam-5290	196	9	−	−	PROPN
ejpam-5290	196	10	pyn,2)u	pyn,2)u	NOUN
ejpam-5290	196	11	y	y	PROPN
ejpam-5290	196	12	n,1	n,1	PROPN
ejpam-5290	197	1	+	+	CCONJ
ejpam-5290	197	2	(	(	PUNCT
ejpam-5290	197	3	pxn,2	pxn,2	VERB
ejpam-5290	197	4	−	−	PROPN
ejpam-5290	197	5	pxn,1)u	pxn,1)u	NOUN
ejpam-5290	197	6	x	x	NOUN
ejpam-5290	197	7	n,2	n,2	VERB
ejpam-5290	197	8	+	+	CCONJ
ejpam-5290	197	9	(	(	PUNCT
ejpam-5290	197	10	pyn,2	pyn,2	VERB
ejpam-5290	197	11	−	−	PROPN
ejpam-5290	197	12	pyn,1)u	pyn,1)u	NOUN
ejpam-5290	197	13	y	y	PROPN
ejpam-5290	197	14	n,2	n,2	VERB
ejpam-5290	197	15	=	=	SYM
ejpam-5290	197	16	0	0	NUM
ejpam-5290	197	17	γnu	γnu	PROPN
ejpam-5290	197	18	x	x	SYM
ejpam-5290	197	19	n,1	n,1	NOUN
ejpam-5290	197	20	−	−	PROPN
ejpam-5290	197	21	γnu	γnu	PROPN
ejpam-5290	197	22	x	x	PUNCT
ejpam-5290	197	23	n,2	n,2	VERB
ejpam-5290	197	24	−	−	PROPN
ejpam-5290	197	25	βnu	βnu	ADV
ejpam-5290	197	26	y	y	PROPN
ejpam-5290	197	27	n,2	n,2	VERB
ejpam-5290	197	28	=	=	SYM
ejpam-5290	197	29	0	0	NUM
ejpam-5290	197	30	substituting	substitute	VERB
ejpam-5290	197	31	uyn,2	uyn,2	ADJ
ejpam-5290	197	32	:	:	PUNCT
ejpam-5290	197	33	γnu	γnu	PROPN
ejpam-5290	197	34	x	x	SYM
ejpam-5290	197	35	n,1	n,1	PROPN
ejpam-5290	197	36	−	−	PROPN
ejpam-5290	197	37	γnu	γnu	PROPN
ejpam-5290	197	38	x	x	PUNCT
ejpam-5290	197	39	n,2	n,2	VERB
ejpam-5290	197	40	−	−	X
ejpam-5290	197	41	βn	βn	VERB
ejpam-5290	197	42	(	(	PUNCT
ejpam-5290	197	43	γn	γn	NOUN
ejpam-5290	197	44	αn	αn	NOUN
ejpam-5290	197	45	)	)	PUNCT
ejpam-5290	197	46	uxn,2	uxn,2	ADJ
ejpam-5290	197	47	=	=	SYM
ejpam-5290	197	48	0	0	NUM
ejpam-5290	197	49	uxn,2	uxn,2	ADJ
ejpam-5290	197	50	=	=	SYM
ejpam-5290	197	51	(	(	PUNCT
ejpam-5290	197	52	1	1	NUM
ejpam-5290	197	53	1	1	NUM
ejpam-5290	197	54	+	+	CCONJ
ejpam-5290	197	55	βn	βn	ADJ
ejpam-5290	197	56	αn	αn	NOUN
ejpam-5290	197	57	)	)	PUNCT
ejpam-5290	197	58	uxn,1	uxn,1	NOUN
ejpam-5290	197	59	applying	apply	VERB
ejpam-5290	197	60	the	the	DET
ejpam-5290	197	61	flex	flex	ADJ
ejpam-5290	197	62	condition	condition	NOUN
ejpam-5290	197	63	to	to	ADP
ejpam-5290	197	64	the	the	DET
ejpam-5290	197	65	edge	edge	NOUN
ejpam-5290	197	66	[	[	X
ejpam-5290	197	67	pn,2	pn,2	PROPN
ejpam-5290	197	68	,	,	PUNCT
ejpam-5290	197	69	pn,4	pn,4	PROPN
ejpam-5290	197	70	]	]	PUNCT
ejpam-5290	197	71	:	:	PUNCT
ejpam-5290	197	72	⟨pn,2	⟨pn,2	NUM
ejpam-5290	197	73	−	−	PROPN
ejpam-5290	197	74	pn,4	pn,4	PROPN
ejpam-5290	197	75	,	,	PUNCT
ejpam-5290	197	76	un,2⟩+	un,2⟩+	X
ejpam-5290	197	77	⟨pn,4	⟨pn,4	PUNCT
ejpam-5290	197	78	−	−	PROPN
ejpam-5290	198	1	pn,2	pn,2	PROPN
ejpam-5290	198	2	,	,	PUNCT
ejpam-5290	198	3	un,4⟩	un,4⟩	NOUN
ejpam-5290	198	4	=	=	SYM
ejpam-5290	198	5	0	0	NUM
ejpam-5290	198	6	(	(	PUNCT
ejpam-5290	198	7	pxn,2	pxn,2	VERB
ejpam-5290	198	8	−	−	PROPN
ejpam-5290	198	9	pxn,4)u	pxn,4)u	NOUN
ejpam-5290	198	10	x	x	PUNCT
ejpam-5290	198	11	n,2	n,2	VERB
ejpam-5290	198	12	+	+	CCONJ
ejpam-5290	198	13	(	(	PUNCT
ejpam-5290	198	14	pyn,2	pyn,2	VERB
ejpam-5290	198	15	−	−	PROPN
ejpam-5290	198	16	pyn,4)u	pyn,4)u	VERB
ejpam-5290	198	17	y	y	PROPN
ejpam-5290	198	18	n,2	n,2	VERB
ejpam-5290	198	19	+	+	CCONJ
ejpam-5290	198	20	(	(	PUNCT
ejpam-5290	198	21	pxn,4	pxn,4	NOUN
ejpam-5290	198	22	−	−	PROPN
ejpam-5290	198	23	pxn,2)u	pxn,2)u	NOUN
ejpam-5290	198	24	x	x	NOUN
ejpam-5290	198	25	n,4	n,4	PROPN
ejpam-5290	198	26	+	+	CCONJ
ejpam-5290	198	27	(	(	PUNCT
ejpam-5290	198	28	pyn,4	pyn,4	NOUN
ejpam-5290	198	29	−	−	PROPN
ejpam-5290	198	30	pyn,2)u	pyn,2)u	NOUN
ejpam-5290	198	31	y	y	NOUN
ejpam-5290	198	32	n,4	n,4	PROPN
ejpam-5290	199	1	=	=	SYM
ejpam-5290	199	2	0	0	NUM
ejpam-5290	199	3	−γnu	−γnu	NOUN
ejpam-5290	199	4	x	x	PUNCT
ejpam-5290	199	5	n,2	n,2	PROPN
ejpam-5290	199	6	+	+	CCONJ
ejpam-5290	199	7	γnu	γnu	X
ejpam-5290	199	8	x	x	X
ejpam-5290	199	9	n,4	n,4	PROPN
ejpam-5290	200	1	=	=	SYM
ejpam-5290	200	2	0	0	PUNCT
ejpam-5290	200	3	hence	hence	ADV
ejpam-5290	200	4	,	,	PUNCT
ejpam-5290	200	5	uxn,4	uxn,4	ADJ
ejpam-5290	200	6	=	=	SYM
ejpam-5290	200	7	uxn,2	uxn,2	ADJ
ejpam-5290	200	8	=	=	SYM
ejpam-5290	200	9	(	(	PUNCT
ejpam-5290	200	10	1	1	NUM
ejpam-5290	200	11	1	1	NUM
ejpam-5290	200	12	+	+	CCONJ
ejpam-5290	200	13	βn	βn	ADJ
ejpam-5290	200	14	αn	αn	NOUN
ejpam-5290	200	15	)	)	PUNCT
ejpam-5290	200	16	uxn,1	uxn,1	NOUN
ejpam-5290	200	17	applying	apply	VERB
ejpam-5290	200	18	the	the	DET
ejpam-5290	200	19	flex	flex	ADJ
ejpam-5290	200	20	condition	condition	NOUN
ejpam-5290	200	21	to	to	ADP
ejpam-5290	200	22	the	the	DET
ejpam-5290	200	23	edge	edge	NOUN
ejpam-5290	200	24	[	[	X
ejpam-5290	200	25	pn,4	pn,4	PROPN
ejpam-5290	200	26	,	,	PUNCT
ejpam-5290	200	27	pn+1,1	pn+1,1	PROPN
ejpam-5290	200	28	]	]	PUNCT
ejpam-5290	200	29	:	:	PUNCT
ejpam-5290	200	30	⟨pn,4	⟨pn,4	PUNCT
ejpam-5290	201	1	−	−	PROPN
ejpam-5290	201	2	pn+1,1	pn+1,1	PROPN
ejpam-5290	201	3	,	,	PUNCT
ejpam-5290	201	4	un,4⟩+	un,4⟩+	PROPN
ejpam-5290	201	5	⟨pn+1,1	⟨pn+1,1	NOUN
ejpam-5290	201	6	−	−	PROPN
ejpam-5290	201	7	pn,4	pn,4	PROPN
ejpam-5290	201	8	,	,	PUNCT
ejpam-5290	201	9	un+1,1⟩	un+1,1⟩	X
ejpam-5290	201	10	=	=	SYM
ejpam-5290	201	11	0	0	NUM
ejpam-5290	201	12	(	(	PUNCT
ejpam-5290	201	13	pxn,4	pxn,4	NOUN
ejpam-5290	201	14	−	−	PROPN
ejpam-5290	201	15	pxn+1,1)u	pxn+1,1)u	NUM
ejpam-5290	201	16	x	x	SYM
ejpam-5290	201	17	n,4	n,4	PROPN
ejpam-5290	201	18	+	+	CCONJ
ejpam-5290	201	19	(	(	PUNCT
ejpam-5290	201	20	pyn,4	pyn,4	NOUN
ejpam-5290	201	21	−	−	PROPN
ejpam-5290	201	22	pyn+1,1)u	pyn+1,1)u	NOUN
ejpam-5290	201	23	y	y	PROPN
ejpam-5290	201	24	n,4	n,4	PROPN
ejpam-5290	201	25	+	+	CCONJ
ejpam-5290	201	26	(	(	PUNCT
ejpam-5290	201	27	pxn+1,1	pxn+1,1	NOUN
ejpam-5290	201	28	−	−	PROPN
ejpam-5290	201	29	pxn,4)u	pxn,4)u	NOUN
ejpam-5290	201	30	x	x	PROPN
ejpam-5290	201	31	n+1,1	n+1,1	PROPN
ejpam-5290	201	32	+	+	CCONJ
ejpam-5290	201	33	(	(	PUNCT
ejpam-5290	201	34	pyn+1,1	pyn+1,1	NOUN
ejpam-5290	201	35	−	−	NOUN
ejpam-5290	201	36	pyn,4)u	pyn,4)u	PROPN
ejpam-5290	201	37	y	y	PROPN
ejpam-5290	201	38	n+1,1	n+1,1	PROPN
ejpam-5290	201	39	=	=	SYM
ejpam-5290	201	40	0	0	PUNCT
ejpam-5290	202	1	uxn+1,1	uxn+1,1	NOUN
ejpam-5290	202	2	=	=	PUNCT
ejpam-5290	202	3	uxn,4	uxn,4	PROPN
ejpam-5290	202	4	g.	g.	PROPN
ejpam-5290	202	5	m.	m.	PROPN
ejpam-5290	202	6	badri	badri	PROPN
ejpam-5290	202	7	/	/	SYM
ejpam-5290	202	8	eur	eur	PROPN
ejpam-5290	202	9	.	.	PUNCT
ejpam-5290	203	1	j.	j.	PROPN
ejpam-5290	203	2	pure	pure	PROPN
ejpam-5290	203	3	appl	appl	PROPN
ejpam-5290	203	4	.	.	PROPN
ejpam-5290	203	5	math	math	PROPN
ejpam-5290	203	6	,	,	PUNCT
ejpam-5290	203	7	17	17	NUM
ejpam-5290	203	8	(	(	PUNCT
ejpam-5290	203	9	4	4	NUM
ejpam-5290	203	10	)	)	PUNCT
ejpam-5290	203	11	(	(	PUNCT
ejpam-5290	203	12	2024	2024	NUM
ejpam-5290	203	13	)	)	PUNCT
ejpam-5290	203	14	,	,	PUNCT
ejpam-5290	203	15	3079	3079	NUM
ejpam-5290	203	16	-	-	SYM
ejpam-5290	203	17	3092	3092	NUM
ejpam-5290	203	18	3090	3090	NUM
ejpam-5290	203	19	finally	finally	ADV
ejpam-5290	203	20	,	,	PUNCT
ejpam-5290	203	21	using	use	VERB
ejpam-5290	203	22	the	the	DET
ejpam-5290	203	23	induction	induction	NOUN
ejpam-5290	203	24	hypothesis	hypothesis	NOUN
ejpam-5290	203	25	:	:	PUNCT
ejpam-5290	203	26	uxn+1,1	uxn+1,1	NOUN
ejpam-5290	203	27	=	=	SYM
ejpam-5290	203	28	uxn,4	uxn,4	NOUN
ejpam-5290	204	1	=	=	SYM
ejpam-5290	204	2	(	(	PUNCT
ejpam-5290	204	3	1	1	NUM
ejpam-5290	204	4	1	1	NUM
ejpam-5290	204	5	+	+	CCONJ
ejpam-5290	204	6	βn	βn	ADJ
ejpam-5290	204	7	αn	αn	NOUN
ejpam-5290	204	8	)	)	PUNCT
ejpam-5290	204	9	uxn,1	uxn,1	NOUN
ejpam-5290	204	10	=	=	PUNCT
ejpam-5290	204	11	(	(	PUNCT
ejpam-5290	204	12	1	1	NUM
ejpam-5290	204	13	1	1	NUM
ejpam-5290	204	14	+	+	CCONJ
ejpam-5290	204	15	βn	βn	ADJ
ejpam-5290	204	16	αn	αn	NOUN
ejpam-5290	204	17	)	)	PUNCT
ejpam-5290	204	18	(	(	PUNCT
ejpam-5290	204	19	n−1∏	n−1∏	PROPN
ejpam-5290	204	20	i=1	i=1	PROPN
ejpam-5290	204	21	(	(	PUNCT
ejpam-5290	204	22	1	1	NUM
ejpam-5290	204	23	1	1	NUM
ejpam-5290	204	24	+	+	CCONJ
ejpam-5290	204	25	βi	βi	PRON
ejpam-5290	204	26	αi	αi	ADV
ejpam-5290	204	27	)	)	PUNCT
ejpam-5290	204	28	)	)	PUNCT
ejpam-5290	204	29	ux1,1	ux1,1	PROPN
ejpam-5290	205	1	=	=	PUNCT
ejpam-5290	205	2	n∏	n∏	PROPN
ejpam-5290	205	3	i=1	i=1	PROPN
ejpam-5290	206	1	(	(	PUNCT
ejpam-5290	206	2	1	1	NUM
ejpam-5290	206	3	1	1	NUM
ejpam-5290	206	4	+	+	CCONJ
ejpam-5290	206	5	βi	βi	PROPN
ejpam-5290	206	6	αi	αi	ADV
ejpam-5290	206	7	)	)	PUNCT
ejpam-5290	206	8	ux1,1	ux1,1	VERB
ejpam-5290	207	1	and	and	CCONJ
ejpam-5290	207	2	the	the	DET
ejpam-5290	207	3	result	result	NOUN
ejpam-5290	207	4	follows	follow	VERB
ejpam-5290	207	5	.	.	PUNCT
ejpam-5290	208	1	definition	definition	NOUN
ejpam-5290	208	2	6	6	NUM
ejpam-5290	208	3	.	.	PUNCT
ejpam-5290	209	1	let	let	VERB
ejpam-5290	209	2	g	g	NOUN
ejpam-5290	209	3	=	=	PUNCT
ejpam-5290	209	4	(	(	PUNCT
ejpam-5290	209	5	g	g	PROPN
ejpam-5290	209	6	,	,	PUNCT
ejpam-5290	209	7	p	p	X
ejpam-5290	209	8	)	)	PUNCT
ejpam-5290	209	9	be	be	AUX
ejpam-5290	209	10	an	an	DET
ejpam-5290	209	11	infinite	infinite	ADJ
ejpam-5290	209	12	framework	framework	NOUN
ejpam-5290	209	13	in	in	ADP
ejpam-5290	209	14	r2	r2	PROPN
ejpam-5290	209	15	.	.	PUNCT
ejpam-5290	210	1	an	an	DET
ejpam-5290	210	2	infinitesimal	infinitesimal	ADJ
ejpam-5290	210	3	flex	flex	ADJ
ejpam-5290	210	4	u	u	NOUN
ejpam-5290	210	5	=	=	SYM
ejpam-5290	210	6	(	(	PUNCT
ejpam-5290	210	7	un	un	PROPN
ejpam-5290	210	8	)	)	PUNCT
ejpam-5290	210	9	of	of	ADP
ejpam-5290	210	10	g	g	PROPN
ejpam-5290	210	11	is	be	AUX
ejpam-5290	210	12	called	call	VERB
ejpam-5290	210	13	local	local	ADJ
ejpam-5290	210	14	if	if	SCONJ
ejpam-5290	210	15	un	un	PROPN
ejpam-5290	210	16	=	=	SYM
ejpam-5290	210	17	(	(	PUNCT
ejpam-5290	210	18	0	0	NUM
ejpam-5290	210	19	,	,	PUNCT
ejpam-5290	210	20	0	0	NUM
ejpam-5290	210	21	)	)	PUNCT
ejpam-5290	210	22	for	for	ADP
ejpam-5290	210	23	all	all	PRON
ejpam-5290	210	24	but	but	ADV
ejpam-5290	210	25	finitely	finitely	ADV
ejpam-5290	210	26	many	many	ADJ
ejpam-5290	210	27	values	value	NOUN
ejpam-5290	210	28	of	of	ADP
ejpam-5290	210	29	n.	n.	NOUN
ejpam-5290	210	30	corollary	corollary	ADJ
ejpam-5290	210	31	4	4	NUM
ejpam-5290	210	32	.	.	PUNCT
ejpam-5290	211	1	let	let	AUX
ejpam-5290	211	2	gtri	gtri	AUX
ejpam-5290	211	3	be	be	AUX
ejpam-5290	211	4	the	the	DET
ejpam-5290	211	5	connected	connect	VERB
ejpam-5290	211	6	braced	braced	ADJ
ejpam-5290	211	7	triangles	triangle	NOUN
ejpam-5290	211	8	infinite	infinite	ADJ
ejpam-5290	211	9	bar	bar	NOUN
ejpam-5290	211	10	-	-	PUNCT
ejpam-5290	211	11	joint	joint	NOUN
ejpam-5290	211	12	framework	framework	NOUN
ejpam-5290	211	13	in	in	ADP
ejpam-5290	211	14	r2	r2	PROPN
ejpam-5290	211	15	.	.	PUNCT
ejpam-5290	212	1	if	if	SCONJ
ejpam-5290	212	2	the	the	DET
ejpam-5290	212	3	vertices	vertex	NOUN
ejpam-5290	212	4	of	of	ADP
ejpam-5290	212	5	all	all	DET
ejpam-5290	212	6	but	but	SCONJ
ejpam-5290	212	7	one	one	NUM
ejpam-5290	212	8	triangle	triangle	NOUN
ejpam-5290	212	9	have	have	VERB
ejpam-5290	212	10	zero	zero	NUM
ejpam-5290	212	11	velocity	velocity	NOUN
ejpam-5290	212	12	components	component	NOUN
ejpam-5290	212	13	,	,	PUNCT
ejpam-5290	212	14	then	then	ADV
ejpam-5290	212	15	gtri	gtri	AUX
ejpam-5290	212	16	admits	admit	VERB
ejpam-5290	212	17	the	the	DET
ejpam-5290	212	18	local	local	ADJ
ejpam-5290	212	19	flex	flex	ADJ
ejpam-5290	212	20	identified	identify	VERB
ejpam-5290	212	21	in	in	ADP
ejpam-5290	212	22	theorem	theorem	ADJ
ejpam-5290	212	23	3	3	NUM
ejpam-5290	212	24	.	.	PUNCT
ejpam-5290	212	25	theorem	theorem	NOUN
ejpam-5290	212	26	5	5	NUM
ejpam-5290	212	27	.	.	PUNCT
ejpam-5290	213	1	let	let	AUX
ejpam-5290	213	2	gtri	gtri	AUX
ejpam-5290	213	3	be	be	AUX
ejpam-5290	213	4	the	the	DET
ejpam-5290	213	5	connected	connect	VERB
ejpam-5290	213	6	braced	braced	ADJ
ejpam-5290	213	7	triangles	triangle	NOUN
ejpam-5290	213	8	infinite	infinite	ADJ
ejpam-5290	213	9	bar	bar	NOUN
ejpam-5290	213	10	-	-	PUNCT
ejpam-5290	213	11	joint	joint	NOUN
ejpam-5290	213	12	framework	framework	NOUN
ejpam-5290	213	13	in	in	ADP
ejpam-5290	213	14	r2	r2	PROPN
ejpam-5290	213	15	.	.	PUNCT
ejpam-5290	214	1	then	then	ADV
ejpam-5290	214	2	b	b	X
ejpam-5290	214	3	=	=	SYM
ejpam-5290	214	4	{	{	PUNCT
ejpam-5290	214	5	wx	wx	PROPN
ejpam-5290	214	6	,	,	PUNCT
ejpam-5290	214	7	wy	wy	PROPN
ejpam-5290	214	8	,	,	PUNCT
ejpam-5290	214	9	r	r	NOUN
ejpam-5290	214	10	}	}	PUNCT
ejpam-5290	214	11	⋃	⋃	NOUN
ejpam-5290	214	12	{	{	PUNCT
ejpam-5290	214	13	v	v	NOUN
ejpam-5290	214	14	}	}	PUNCT
ejpam-5290	214	15	⋃	⋃	NOUN
ejpam-5290	214	16	{	{	PUNCT
ejpam-5290	214	17	un	un	PROPN
ejpam-5290	214	18	:	:	PUNCT
ejpam-5290	214	19	n	n	CCONJ
ejpam-5290	214	20	∈	∈	PROPN
ejpam-5290	214	21	n	n	CCONJ
ejpam-5290	214	22	}	}	PUNCT
ejpam-5290	214	23	is	be	AUX
ejpam-5290	214	24	a	a	DET
ejpam-5290	214	25	base	base	NOUN
ejpam-5290	214	26	for	for	ADP
ejpam-5290	214	27	hfl(gtri	hfl(gtri	NOUN
ejpam-5290	214	28	)	)	PUNCT
ejpam-5290	214	29	,	,	PUNCT
ejpam-5290	214	30	where	where	SCONJ
ejpam-5290	214	31	wx	wx	PROPN
ejpam-5290	214	32	,	,	PUNCT
ejpam-5290	214	33	wy	wy	PROPN
ejpam-5290	214	34	,	,	PUNCT
ejpam-5290	214	35	r	r	NOUN
ejpam-5290	214	36	are	be	AUX
ejpam-5290	214	37	the	the	DET
ejpam-5290	214	38	three	three	NUM
ejpam-5290	214	39	planar	planar	ADJ
ejpam-5290	214	40	rigid	rigid	ADJ
ejpam-5290	214	41	body	body	NOUN
ejpam-5290	214	42	motions	motion	NOUN
ejpam-5290	214	43	,	,	PUNCT
ejpam-5290	214	44	v	v	NOUN
ejpam-5290	214	45	is	be	AUX
ejpam-5290	214	46	the	the	DET
ejpam-5290	214	47	non	non	ADJ
ejpam-5290	214	48	trivial	trivial	ADJ
ejpam-5290	214	49	flex	flex	NOUN
ejpam-5290	214	50	in	in	ADP
ejpam-5290	214	51	theorem	theorem	NOUN
ejpam-5290	214	52	4	4	NUM
ejpam-5290	214	53	and	and	CCONJ
ejpam-5290	214	54	un	un	PROPN
ejpam-5290	214	55	is	be	AUX
ejpam-5290	214	56	the	the	DET
ejpam-5290	214	57	local	local	ADJ
ejpam-5290	214	58	flex	flex	NOUN
ejpam-5290	214	59	with	with	ADP
ejpam-5290	214	60	non	non	ADJ
ejpam-5290	214	61	zero	zero	NUM
ejpam-5290	214	62	velocity	velocity	NOUN
ejpam-5290	214	63	components	component	NOUN
ejpam-5290	214	64	at	at	ADP
ejpam-5290	214	65	one	one	NUM
ejpam-5290	214	66	triangle	triangle	NOUN
ejpam-5290	214	67	and	and	CCONJ
ejpam-5290	214	68	zero	zero	NUM
ejpam-5290	214	69	velocities	velocity	NOUN
ejpam-5290	214	70	elsewhere	elsewhere	ADV
ejpam-5290	214	71	.	.	PUNCT
ejpam-5290	215	1	proof	proof	NOUN
ejpam-5290	215	2	.	.	PUNCT
ejpam-5290	216	1	the	the	DET
ejpam-5290	216	2	proof	proof	NOUN
ejpam-5290	216	3	proceeds	proceed	VERB
ejpam-5290	216	4	with	with	ADP
ejpam-5290	216	5	an	an	DET
ejpam-5290	216	6	exhaustion	exhaustion	NOUN
ejpam-5290	216	7	argument	argument	NOUN
ejpam-5290	216	8	where	where	SCONJ
ejpam-5290	216	9	appropriate	appropriate	ADJ
ejpam-5290	216	10	multiples	multiple	NOUN
ejpam-5290	216	11	are	be	AUX
ejpam-5290	216	12	subtracted	subtract	VERB
ejpam-5290	216	13	from	from	ADP
ejpam-5290	216	14	an	an	DET
ejpam-5290	216	15	arbitrary	arbitrary	ADJ
ejpam-5290	216	16	flex	flex	NOUN
ejpam-5290	216	17	until	until	SCONJ
ejpam-5290	216	18	we	we	PRON
ejpam-5290	216	19	achieve	achieve	VERB
ejpam-5290	216	20	zero	zero	NUM
ejpam-5290	216	21	flexing	flexing	NOUN
ejpam-5290	216	22	of	of	ADP
ejpam-5290	216	23	the	the	DET
ejpam-5290	216	24	structure	structure	NOUN
ejpam-5290	216	25	.	.	PUNCT
ejpam-5290	217	1	let	let	VERB
ejpam-5290	217	2	s	s	PRON
ejpam-5290	217	3	=	=	PUNCT
ejpam-5290	217	4	(	(	PUNCT
ejpam-5290	217	5	sn	sn	PROPN
ejpam-5290	217	6	)	)	PUNCT
ejpam-5290	217	7	=	=	SYM
ejpam-5290	218	1	(	(	PUNCT
ejpam-5290	218	2	(	(	PUNCT
ejpam-5290	218	3	sn	sn	INTJ
ejpam-5290	218	4	,	,	PUNCT
ejpam-5290	218	5	i	i	NOUN
ejpam-5290	218	6	)	)	PUNCT
ejpam-5290	218	7	4	4	NUM
ejpam-5290	218	8	i=1	i=1	NOUN
ejpam-5290	218	9	)	)	PUNCT
ejpam-5290	218	10	∞	∞	PROPN
ejpam-5290	218	11	n=1	n=1	PROPN
ejpam-5290	218	12	be	be	VERB
ejpam-5290	218	13	an	an	DET
ejpam-5290	218	14	arbitrary	arbitrary	ADJ
ejpam-5290	218	15	flex	flex	NOUN
ejpam-5290	218	16	of	of	ADP
ejpam-5290	218	17	gtri	gtri	NOUN
ejpam-5290	218	18	.	.	PUNCT
ejpam-5290	219	1	subtracting	subtract	VERB
ejpam-5290	219	2	sx1,3w	sx1,3w	ADJ
ejpam-5290	219	3	x	x	NOUN
ejpam-5290	220	1	+	+	CCONJ
ejpam-5290	220	2	sy1,3w	sy1,3w	PROPN
ejpam-5290	220	3	y	y	PROPN
ejpam-5290	220	4	from	from	ADP
ejpam-5290	220	5	the	the	DET
ejpam-5290	220	6	flex	flex	NOUN
ejpam-5290	220	7	s	s	NOUN
ejpam-5290	220	8	one	one	PRON
ejpam-5290	220	9	can	can	AUX
ejpam-5290	220	10	arrange	arrange	VERB
ejpam-5290	220	11	for	for	ADP
ejpam-5290	220	12	vertex	vertex	NOUN
ejpam-5290	220	13	p1,3	p1,3	PROPN
ejpam-5290	220	14	to	to	PART
ejpam-5290	220	15	have	have	VERB
ejpam-5290	220	16	a	a	DET
ejpam-5290	220	17	zero	zero	NUM
ejpam-5290	220	18	velocity	velocity	NOUN
ejpam-5290	220	19	.	.	PUNCT
ejpam-5290	221	1	subtracting	subtract	VERB
ejpam-5290	221	2	sy2,3r	sy2,3r	NOUN
ejpam-5290	221	3	,	,	PUNCT
ejpam-5290	221	4	vertex	vertex	NOUN
ejpam-5290	221	5	p2,3	p2,3	PROPN
ejpam-5290	221	6	now	now	ADV
ejpam-5290	221	7	has	have	VERB
ejpam-5290	221	8	a	a	DET
ejpam-5290	221	9	zero	zero	NUM
ejpam-5290	221	10	velocity	velocity	NOUN
ejpam-5290	221	11	implying	imply	VERB
ejpam-5290	221	12	that	that	SCONJ
ejpam-5290	221	13	any	any	DET
ejpam-5290	221	14	further	further	ADJ
ejpam-5290	221	15	flexing	flexing	NOUN
ejpam-5290	221	16	of	of	ADP
ejpam-5290	221	17	gtri	gtri	NOUN
ejpam-5290	221	18	would	would	AUX
ejpam-5290	221	19	be	be	AUX
ejpam-5290	221	20	non	non	X
ejpam-5290	221	21	trivial	trivial	ADJ
ejpam-5290	221	22	.	.	PUNCT
ejpam-5290	222	1	proceeding	proceed	VERB
ejpam-5290	222	2	in	in	ADP
ejpam-5290	222	3	the	the	DET
ejpam-5290	222	4	same	same	ADJ
ejpam-5290	222	5	manner	manner	NOUN
ejpam-5290	222	6	,	,	PUNCT
ejpam-5290	222	7	subtracting	subtract	VERB
ejpam-5290	222	8	sx1,1v	sx1,1v	NOUN
ejpam-5290	222	9	results	result	NOUN
ejpam-5290	222	10	in	in	ADP
ejpam-5290	222	11	a	a	DET
ejpam-5290	222	12	zero	zero	NUM
ejpam-5290	222	13	velocity	velocity	NOUN
ejpam-5290	222	14	at	at	ADP
ejpam-5290	222	15	vertex	vertex	NOUN
ejpam-5290	222	16	p1,1	p1,1	NOUN
ejpam-5290	222	17	from	from	ADP
ejpam-5290	222	18	which	which	PRON
ejpam-5290	222	19	it	it	PRON
ejpam-5290	222	20	follows	follow	VERB
ejpam-5290	222	21	that	that	SCONJ
ejpam-5290	222	22	vertex	vertex	NOUN
ejpam-5290	222	23	p2,1	p2,1	PROPN
ejpam-5290	222	24	is	be	AUX
ejpam-5290	222	25	also	also	ADV
ejpam-5290	222	26	assigned	assign	VERB
ejpam-5290	222	27	a	a	DET
ejpam-5290	222	28	zero	zero	NUM
ejpam-5290	222	29	velocity	velocity	NOUN
ejpam-5290	222	30	.	.	PUNCT
ejpam-5290	223	1	to	to	ADP
ejpam-5290	223	2	this	this	DET
ejpam-5290	223	3	end	end	NOUN
ejpam-5290	223	4	,	,	PUNCT
ejpam-5290	223	5	vertices	vertice	VERB
ejpam-5290	223	6	p1,1	p1,1	PROPN
ejpam-5290	223	7	,	,	PUNCT
ejpam-5290	223	8	p1,2	p1,2	PROPN
ejpam-5290	223	9	,	,	PUNCT
ejpam-5290	223	10	.	.	PUNCT
ejpam-5290	223	11	.	.	PUNCT
ejpam-5290	224	1	.	.	PUNCT
ejpam-5290	225	1	,	,	PUNCT
ejpam-5290	225	2	p2,3	p2,3	NOUN
ejpam-5290	225	3	,	,	PUNCT
ejpam-5290	225	4	p2,4	p2,4	NOUN
ejpam-5290	225	5	of	of	ADP
ejpam-5290	225	6	the	the	DET
ejpam-5290	225	7	first	first	ADJ
ejpam-5290	225	8	two	two	NUM
ejpam-5290	225	9	triangles	triangle	NOUN
ejpam-5290	225	10	are	be	AUX
ejpam-5290	225	11	all	all	PRON
ejpam-5290	225	12	fixed	fix	VERB
ejpam-5290	225	13	.	.	PUNCT
ejpam-5290	226	1	finally	finally	ADV
ejpam-5290	226	2	,	,	PUNCT
ejpam-5290	226	3	successive	successive	ADJ
ejpam-5290	226	4	subtraction	subtraction	NOUN
ejpam-5290	226	5	of	of	ADP
ejpam-5290	226	6	syn,3un	syn,3un	NOUN
ejpam-5290	226	7	,	,	PUNCT
ejpam-5290	226	8	assigns	assign	VERB
ejpam-5290	226	9	zero	zero	NUM
ejpam-5290	226	10	velocities	velocity	NOUN
ejpam-5290	226	11	to	to	ADP
ejpam-5290	226	12	the	the	DET
ejpam-5290	226	13	points	point	NOUN
ejpam-5290	226	14	pn,3	pn,3	PROPN
ejpam-5290	226	15	.	.	PUNCT
ejpam-5290	227	1	this	this	PRON
ejpam-5290	227	2	results	result	VERB
ejpam-5290	227	3	in	in	ADP
ejpam-5290	227	4	every	every	DET
ejpam-5290	227	5	vertex	vertex	NOUN
ejpam-5290	227	6	of	of	ADP
ejpam-5290	227	7	gtri	gtri	NOUN
ejpam-5290	227	8	admitting	admit	VERB
ejpam-5290	227	9	a	a	DET
ejpam-5290	227	10	zero	zero	NUM
ejpam-5290	227	11	velocity	velocity	NOUN
ejpam-5290	227	12	and	and	CCONJ
ejpam-5290	227	13	the	the	DET
ejpam-5290	227	14	conclusion	conclusion	NOUN
ejpam-5290	227	15	follows	follow	VERB
ejpam-5290	227	16	.	.	PUNCT
ejpam-5290	228	1	4	4	X
ejpam-5290	228	2	.	.	X
ejpam-5290	228	3	conclusion	conclusion	NOUN
ejpam-5290	228	4	in	in	ADP
ejpam-5290	228	5	this	this	DET
ejpam-5290	228	6	paper	paper	NOUN
ejpam-5290	228	7	we	we	PRON
ejpam-5290	228	8	determined	determine	VERB
ejpam-5290	228	9	the	the	DET
ejpam-5290	228	10	non	non	ADJ
ejpam-5290	228	11	trivial	trivial	ADJ
ejpam-5290	228	12	flexes	flex	NOUN
ejpam-5290	228	13	of	of	ADP
ejpam-5290	228	14	the	the	DET
ejpam-5290	228	15	planar	planar	ADJ
ejpam-5290	228	16	finite	finite	ADJ
ejpam-5290	228	17	frameworks	framework	NOUN
ejpam-5290	228	18	with	with	ADP
ejpam-5290	228	19	n	n	CCONJ
ejpam-5290	228	20	connected	connect	VERB
ejpam-5290	228	21	braced	braced	ADJ
ejpam-5290	228	22	triangles	triangle	NOUN
ejpam-5290	228	23	.	.	PUNCT
ejpam-5290	229	1	this	this	DET
ejpam-5290	229	2	lead	lead	NOUN
ejpam-5290	229	3	to	to	ADP
ejpam-5290	229	4	the	the	DET
ejpam-5290	229	5	identification	identification	NOUN
ejpam-5290	229	6	of	of	ADP
ejpam-5290	229	7	a	a	DET
ejpam-5290	229	8	bases	basis	NOUN
ejpam-5290	229	9	for	for	ADP
ejpam-5290	229	10	the	the	DET
ejpam-5290	229	11	spaces	space	NOUN
ejpam-5290	229	12	of	of	ADP
ejpam-5290	229	13	all	all	DET
ejpam-5290	229	14	infinitesimal	infinitesimal	ADJ
ejpam-5290	229	15	flexes	flex	NOUN
ejpam-5290	229	16	,	,	PUNCT
ejpam-5290	229	17	hfl(fntri	hfl(fntri	NOUN
ejpam-5290	229	18	)	)	PUNCT
ejpam-5290	229	19	.	.	PUNCT
ejpam-5290	230	1	the	the	DET
ejpam-5290	230	2	nature	nature	NOUN
ejpam-5290	230	3	of	of	ADP
ejpam-5290	230	4	the	the	DET
ejpam-5290	230	5	non	non	ADJ
ejpam-5290	230	6	trivial	trivial	ADJ
ejpam-5290	230	7	base	base	NOUN
ejpam-5290	230	8	elements	element	NOUN
ejpam-5290	230	9	emphasises	emphasise	VERB
ejpam-5290	230	10	how	how	SCONJ
ejpam-5290	230	11	the	the	DET
ejpam-5290	230	12	flexibility	flexibility	NOUN
ejpam-5290	230	13	of	of	ADP
ejpam-5290	230	14	a	a	DET
ejpam-5290	230	15	framework	framework	NOUN
ejpam-5290	230	16	is	be	AUX
ejpam-5290	230	17	impacted	impact	VERB
ejpam-5290	230	18	by	by	ADP
ejpam-5290	230	19	its	its	PRON
ejpam-5290	230	20	unique	unique	ADJ
ejpam-5290	230	21	geometry	geometry	NOUN
ejpam-5290	230	22	.	.	PUNCT
ejpam-5290	231	1	this	this	DET
ejpam-5290	231	2	knowledge	knowledge	NOUN
ejpam-5290	231	3	can	can	AUX
ejpam-5290	231	4	be	be	AUX
ejpam-5290	231	5	taken	take	VERB
ejpam-5290	231	6	forward	forward	ADV
ejpam-5290	231	7	to	to	PART
ejpam-5290	231	8	provide	provide	VERB
ejpam-5290	231	9	detailed	detailed	ADJ
ejpam-5290	231	10	rigidity	rigidity	NOUN
ejpam-5290	231	11	analysis	analysis	NOUN
ejpam-5290	231	12	of	of	ADP
ejpam-5290	231	13	infinite	infinite	ADJ
ejpam-5290	231	14	frameworks	framework	NOUN
ejpam-5290	231	15	references	reference	NOUN
ejpam-5290	231	16	3091	3091	NUM
ejpam-5290	231	17	by	by	ADP
ejpam-5290	231	18	understanding	understand	VERB
ejpam-5290	231	19	the	the	DET
ejpam-5290	231	20	rigidity	rigidity	NOUN
ejpam-5290	231	21	of	of	ADP
ejpam-5290	231	22	their	their	PRON
ejpam-5290	231	23	finite	finite	ADJ
ejpam-5290	231	24	subframeworks	subframework	NOUN
ejpam-5290	231	25	placed	place	VERB
ejpam-5290	231	26	in	in	ADP
ejpam-5290	231	27	euclidean	euclidean	ADJ
ejpam-5290	231	28	spaces	space	NOUN
ejpam-5290	231	29	.	.	PUNCT
ejpam-5290	232	1	in	in	ADP
ejpam-5290	232	2	this	this	DET
ejpam-5290	232	3	specific	specific	ADJ
ejpam-5290	232	4	case	case	NOUN
ejpam-5290	232	5	,	,	PUNCT
ejpam-5290	232	6	the	the	DET
ejpam-5290	232	7	infinite	infinite	ADJ
ejpam-5290	232	8	framework	framework	NOUN
ejpam-5290	232	9	admits	admit	VERB
ejpam-5290	232	10	similar	similar	ADJ
ejpam-5290	232	11	flexing	flex	VERB
ejpam-5290	232	12	properties	property	NOUN
ejpam-5290	232	13	to	to	ADP
ejpam-5290	232	14	those	those	PRON
ejpam-5290	232	15	of	of	ADP
ejpam-5290	232	16	the	the	DET
ejpam-5290	232	17	finite	finite	ADJ
ejpam-5290	232	18	frameworks	framework	NOUN
ejpam-5290	232	19	.	.	PUNCT
ejpam-5290	233	1	additionally	additionally	ADV
ejpam-5290	233	2	,	,	PUNCT
ejpam-5290	233	3	we	we	PRON
ejpam-5290	233	4	found	find	VERB
ejpam-5290	233	5	that	that	SCONJ
ejpam-5290	233	6	the	the	DET
ejpam-5290	233	7	action	action	NOUN
ejpam-5290	233	8	of	of	ADP
ejpam-5290	233	9	the	the	DET
ejpam-5290	233	10	non	non	ADJ
ejpam-5290	233	11	trivial	trivial	ADJ
ejpam-5290	233	12	infinitesimal	infinitesimal	ADJ
ejpam-5290	233	13	flex	flex	ADJ
ejpam-5290	233	14	with	with	ADP
ejpam-5290	233	15	zero	zero	NUM
ejpam-5290	233	16	velocities	velocity	NOUN
ejpam-5290	233	17	at	at	ADP
ejpam-5290	233	18	the	the	DET
ejpam-5290	233	19	points	point	NOUN
ejpam-5290	233	20	pn,3	pn,3	PROPN
ejpam-5290	233	21	extends	extend	VERB
ejpam-5290	233	22	to	to	ADP
ejpam-5290	233	23	the	the	DET
ejpam-5290	233	24	rest	rest	NOUN
ejpam-5290	233	25	of	of	ADP
ejpam-5290	233	26	the	the	DET
ejpam-5290	233	27	framework	framework	NOUN
ejpam-5290	233	28	and	and	CCONJ
ejpam-5290	233	29	is	be	AUX
ejpam-5290	233	30	uniquely	uniquely	ADV
ejpam-5290	233	31	determined	determine	VERB
ejpam-5290	233	32	by	by	ADP
ejpam-5290	233	33	the	the	DET
ejpam-5290	233	34	x	x	PROPN
ejpam-5290	233	35	component	component	NOUN
ejpam-5290	233	36	of	of	ADP
ejpam-5290	233	37	the	the	DET
ejpam-5290	233	38	velocity	velocity	NOUN
ejpam-5290	233	39	initially	initially	ADV
ejpam-5290	233	40	applied	apply	VERB
ejpam-5290	233	41	at	at	ADP
ejpam-5290	233	42	vertex	vertex	NOUN
ejpam-5290	233	43	p1,1	p1,1	NOUN
ejpam-5290	233	44	.	.	PUNCT
ejpam-5290	234	1	furthermore	furthermore	ADV
ejpam-5290	234	2	,	,	PUNCT
ejpam-5290	234	3	such	such	ADJ
ejpam-5290	234	4	analysis	analysis	NOUN
ejpam-5290	234	5	can	can	AUX
ejpam-5290	234	6	be	be	AUX
ejpam-5290	234	7	applied	apply	VERB
ejpam-5290	234	8	to	to	ADP
ejpam-5290	234	9	crystal	crystal	NOUN
ejpam-5290	234	10	frameworks	framework	NOUN
ejpam-5290	234	11	for	for	ADP
ejpam-5290	234	12	example	example	NOUN
ejpam-5290	234	13	,	,	PUNCT
ejpam-5290	234	14	a	a	DET
ejpam-5290	234	15	class	class	NOUN
ejpam-5290	234	16	of	of	ADP
ejpam-5290	234	17	bar	bar	NOUN
ejpam-5290	234	18	-	-	PUNCT
ejpam-5290	234	19	joint	joint	NOUN
ejpam-5290	234	20	frameworks	framework	NOUN
ejpam-5290	234	21	known	know	VERB
ejpam-5290	234	22	for	for	ADP
ejpam-5290	234	23	their	their	PRON
ejpam-5290	234	24	translational	translational	ADJ
ejpam-5290	234	25	symmetry	symmetry	NOUN
ejpam-5290	234	26	.	.	PUNCT
ejpam-5290	235	1	this	this	PRON
ejpam-5290	235	2	also	also	ADV
ejpam-5290	235	3	can	can	AUX
ejpam-5290	235	4	be	be	AUX
ejpam-5290	235	5	used	use	VERB
ejpam-5290	235	6	to	to	PART
ejpam-5290	235	7	identify	identify	VERB
ejpam-5290	235	8	special	special	ADJ
ejpam-5290	235	9	types	type	NOUN
ejpam-5290	235	10	of	of	ADP
ejpam-5290	235	11	flexes	flex	NOUN
ejpam-5290	235	12	such	such	ADJ
ejpam-5290	235	13	as	as	ADP
ejpam-5290	235	14	strictly	strictly	ADV
ejpam-5290	235	15	periodic	periodic	ADJ
ejpam-5290	235	16	,	,	PUNCT
ejpam-5290	235	17	phase	phase	NOUN
ejpam-5290	235	18	periodic	periodic	ADJ
ejpam-5290	235	19	and	and	CCONJ
ejpam-5290	235	20	supercell	supercell	VERB
ejpam-5290	235	21	periodic	periodic	ADJ
ejpam-5290	235	22	flexes	flex	NOUN
ejpam-5290	235	23	.	.	PUNCT
ejpam-5290	236	1	references	reference	NOUN
ejpam-5290	236	2	[	[	X
ejpam-5290	236	3	1	1	NUM
ejpam-5290	236	4	]	]	X
ejpam-5290	236	5	abdo	abdo	PROPN
ejpam-5290	236	6	y	y	PROPN
ejpam-5290	236	7	alfakih	alfakih	PROPN
ejpam-5290	236	8	.	.	PUNCT
ejpam-5290	237	1	on	on	ADP
ejpam-5290	237	2	dimensional	dimensional	ADJ
ejpam-5290	237	3	rigidity	rigidity	NOUN
ejpam-5290	237	4	of	of	ADP
ejpam-5290	237	5	bar	bar	NOUN
ejpam-5290	237	6	-	-	PUNCT
ejpam-5290	237	7	and	and	CCONJ
ejpam-5290	237	8	-	-	PUNCT
ejpam-5290	237	9	joint	joint	ADJ
ejpam-5290	237	10	frameworks	framework	NOUN
ejpam-5290	237	11	.	.	PUNCT
ejpam-5290	238	1	discrete	discrete	ADJ
ejpam-5290	238	2	applied	apply	VERB
ejpam-5290	238	3	mathematics	mathematic	NOUN
ejpam-5290	238	4	,	,	PUNCT
ejpam-5290	238	5	155(10):1244–1253	155(10):1244–1253	NUM
ejpam-5290	238	6	,	,	PUNCT
ejpam-5290	238	7	2007	2007	NUM
ejpam-5290	238	8	.	.	PUNCT
ejpam-5290	239	1	[	[	X
ejpam-5290	239	2	2	2	NUM
ejpam-5290	239	3	]	]	X
ejpam-5290	239	4	abdo	abdo	PROPN
ejpam-5290	239	5	y	y	PROPN
ejpam-5290	239	6	alfakih	alfakih	PROPN
ejpam-5290	239	7	.	.	PUNCT
ejpam-5290	240	1	euclidean	euclidean	ADJ
ejpam-5290	240	2	distance	distance	NOUN
ejpam-5290	240	3	matrices	matrix	NOUN
ejpam-5290	240	4	and	and	CCONJ
ejpam-5290	240	5	their	their	PRON
ejpam-5290	240	6	applications	application	NOUN
ejpam-5290	240	7	in	in	ADP
ejpam-5290	240	8	rigidity	rigidity	NOUN
ejpam-5290	240	9	theory	theory	NOUN
ejpam-5290	240	10	.	.	PUNCT
ejpam-5290	241	1	springer	springer	NOUN
ejpam-5290	241	2	,	,	PUNCT
ejpam-5290	241	3	2018	2018	NUM
ejpam-5290	241	4	.	.	PUNCT
ejpam-5290	242	1	[	[	X
ejpam-5290	242	2	3	3	X
ejpam-5290	242	3	]	]	X
ejpam-5290	242	4	leonard	leonard	PROPN
ejpam-5290	242	5	asimow	asimow	PROPN
ejpam-5290	242	6	and	and	CCONJ
ejpam-5290	242	7	ben	ben	PROPN
ejpam-5290	242	8	roth	roth	PROPN
ejpam-5290	242	9	.	.	PUNCT
ejpam-5290	243	1	the	the	DET
ejpam-5290	243	2	rigidity	rigidity	NOUN
ejpam-5290	243	3	of	of	ADP
ejpam-5290	243	4	graphs	graph	NOUN
ejpam-5290	243	5	.	.	PUNCT
ejpam-5290	244	1	transactions	transaction	NOUN
ejpam-5290	244	2	of	of	ADP
ejpam-5290	244	3	the	the	DET
ejpam-5290	244	4	american	american	PROPN
ejpam-5290	244	5	mathematical	mathematical	PROPN
ejpam-5290	244	6	society	society	NOUN
ejpam-5290	244	7	,	,	PUNCT
ejpam-5290	244	8	245:279–289	245:279–289	NUM
ejpam-5290	244	9	,	,	PUNCT
ejpam-5290	244	10	1978	1978	NUM
ejpam-5290	244	11	.	.	PUNCT
ejpam-5290	245	1	[	[	X
ejpam-5290	245	2	4	4	X
ejpam-5290	245	3	]	]	PUNCT
ejpam-5290	245	4	leonard	leonard	PROPN
ejpam-5290	245	5	asimow	asimow	PROPN
ejpam-5290	245	6	and	and	CCONJ
ejpam-5290	245	7	ben	ben	PROPN
ejpam-5290	245	8	roth	roth	PROPN
ejpam-5290	245	9	.	.	PUNCT
ejpam-5290	246	1	the	the	DET
ejpam-5290	246	2	rigidity	rigidity	NOUN
ejpam-5290	246	3	of	of	ADP
ejpam-5290	246	4	graphs	graph	NOUN
ejpam-5290	246	5	,	,	PUNCT
ejpam-5290	246	6	ii	ii	PROPN
ejpam-5290	246	7	.	.	PROPN
ejpam-5290	246	8	journal	journal	PROPN
ejpam-5290	246	9	of	of	ADP
ejpam-5290	246	10	mathematical	mathematical	ADJ
ejpam-5290	246	11	analysis	analysis	NOUN
ejpam-5290	246	12	and	and	CCONJ
ejpam-5290	246	13	applications	application	NOUN
ejpam-5290	246	14	,	,	PUNCT
ejpam-5290	246	15	68(1):171–190	68(1):171–190	NOUN
ejpam-5290	246	16	,	,	PUNCT
ejpam-5290	246	17	1979	1979	NUM
ejpam-5290	246	18	.	.	PUNCT
ejpam-5290	247	1	[	[	X
ejpam-5290	247	2	5	5	NUM
ejpam-5290	247	3	]	]	X
ejpam-5290	247	4	ghada	ghada	NOUN
ejpam-5290	247	5	badri	badri	PROPN
ejpam-5290	247	6	.	.	PUNCT
ejpam-5290	248	1	rigidity	rigidity	NOUN
ejpam-5290	248	2	operators	operator	NOUN
ejpam-5290	248	3	and	and	CCONJ
ejpam-5290	248	4	the	the	DET
ejpam-5290	248	5	flexibility	flexibility	NOUN
ejpam-5290	248	6	of	of	ADP
ejpam-5290	248	7	infinite	infinite	ADJ
ejpam-5290	248	8	bar	bar	NOUN
ejpam-5290	248	9	-	-	PUNCT
ejpam-5290	248	10	joint	joint	NOUN
ejpam-5290	248	11	frameworks	framework	NOUN
ejpam-5290	248	12	.	.	PUNCT
ejpam-5290	249	1	lancaster	lancaster	PROPN
ejpam-5290	249	2	university	university	PROPN
ejpam-5290	249	3	(	(	PUNCT
ejpam-5290	249	4	united	united	ADJ
ejpam-5290	249	5	kingdom	kingdom	PROPN
ejpam-5290	249	6	)	)	PUNCT
ejpam-5290	249	7	,	,	PUNCT
ejpam-5290	249	8	2015	2015	NUM
ejpam-5290	249	9	.	.	PUNCT
ejpam-5290	250	1	[	[	X
ejpam-5290	250	2	6	6	NUM
ejpam-5290	250	3	]	]	X
ejpam-5290	250	4	ghada	ghada	NOUN
ejpam-5290	250	5	badri	badri	PROPN
ejpam-5290	250	6	,	,	PUNCT
ejpam-5290	250	7	derek	derek	PROPN
ejpam-5290	250	8	kitson	kitson	PROPN
ejpam-5290	250	9	,	,	PUNCT
ejpam-5290	250	10	and	and	CCONJ
ejpam-5290	250	11	stephen	stephen	PROPN
ejpam-5290	250	12	c	c	PROPN
ejpam-5290	250	13	power	power	NOUN
ejpam-5290	250	14	.	.	PUNCT
ejpam-5290	251	1	the	the	DET
ejpam-5290	251	2	almost	almost	ADV
ejpam-5290	251	3	periodic	periodic	ADJ
ejpam-5290	251	4	rigidity	rigidity	NOUN
ejpam-5290	251	5	of	of	ADP
ejpam-5290	251	6	crystallographic	crystallographic	ADJ
ejpam-5290	251	7	bar	bar	NOUN
ejpam-5290	251	8	-	-	PUNCT
ejpam-5290	251	9	joint	joint	ADJ
ejpam-5290	251	10	frameworks	framework	NOUN
ejpam-5290	251	11	.	.	PUNCT
ejpam-5290	252	1	symmetry	symmetry	NOUN
ejpam-5290	252	2	,	,	PUNCT
ejpam-5290	252	3	6(2):308–328	6(2):308–328	NUM
ejpam-5290	252	4	,	,	PUNCT
ejpam-5290	252	5	2014	2014	NUM
ejpam-5290	252	6	.	.	PUNCT
ejpam-5290	253	1	[	[	X
ejpam-5290	253	2	7	7	X
ejpam-5290	253	3	]	]	X
ejpam-5290	253	4	ghada	ghada	NOUN
ejpam-5290	253	5	badri	badri	PROPN
ejpam-5290	253	6	,	,	PUNCT
ejpam-5290	253	7	derek	derek	PROPN
ejpam-5290	253	8	kitson	kitson	PROPN
ejpam-5290	253	9	,	,	PUNCT
ejpam-5290	253	10	and	and	CCONJ
ejpam-5290	253	11	stephen	stephen	PROPN
ejpam-5290	253	12	c	c	PROPN
ejpam-5290	253	13	power	power	PROPN
ejpam-5290	253	14	.	.	PUNCT
ejpam-5290	254	1	crystal	crystal	NOUN
ejpam-5290	254	2	flex	flex	ADJ
ejpam-5290	254	3	bases	basis	NOUN
ejpam-5290	254	4	and	and	CCONJ
ejpam-5290	254	5	the	the	DET
ejpam-5290	254	6	rum	rum	NOUN
ejpam-5290	254	7	spectrum	spectrum	NOUN
ejpam-5290	254	8	.	.	PUNCT
ejpam-5290	255	1	proceedings	proceeding	NOUN
ejpam-5290	255	2	of	of	ADP
ejpam-5290	255	3	the	the	DET
ejpam-5290	255	4	edinburgh	edinburgh	PROPN
ejpam-5290	255	5	mathematical	mathematical	PROPN
ejpam-5290	255	6	society	society	PROPN
ejpam-5290	255	7	,	,	PUNCT
ejpam-5290	255	8	64(4):735–761	64(4):735–761	NOUN
ejpam-5290	255	9	,	,	PUNCT
ejpam-5290	255	10	2021	2021	NUM
ejpam-5290	255	11	.	.	PUNCT
ejpam-5290	256	1	[	[	X
ejpam-5290	256	2	8	8	NUM
ejpam-5290	256	3	]	]	SYM
ejpam-5290	256	4	vladislav	vladislav	NOUN
ejpam-5290	256	5	a	a	DET
ejpam-5290	256	6	blatov	blatov	NOUN
ejpam-5290	256	7	,	,	PUNCT
ejpam-5290	256	8	olaf	olaf	PROPN
ejpam-5290	256	9	delgado	delgado	NOUN
ejpam-5290	256	10	-	-	PUNCT
ejpam-5290	256	11	friedrichs	friedrich	NOUN
ejpam-5290	256	12	,	,	PUNCT
ejpam-5290	256	13	michael	michael	PROPN
ejpam-5290	256	14	o’keeffe	o’keeffe	PROPN
ejpam-5290	256	15	,	,	PUNCT
ejpam-5290	256	16	and	and	CCONJ
ejpam-5290	256	17	davide	davide	PROPN
ejpam-5290	256	18	m	m	PROPN
ejpam-5290	256	19	proserpio	proserpio	NOUN
ejpam-5290	256	20	.	.	PUNCT
ejpam-5290	257	1	three	three	NUM
ejpam-5290	257	2	-	-	PUNCT
ejpam-5290	257	3	periodic	periodic	ADJ
ejpam-5290	257	4	nets	net	NOUN
ejpam-5290	257	5	and	and	CCONJ
ejpam-5290	257	6	tilings	tiling	NOUN
ejpam-5290	257	7	:	:	PUNCT
ejpam-5290	257	8	natural	natural	ADJ
ejpam-5290	257	9	tilings	tiling	NOUN
ejpam-5290	257	10	for	for	ADP
ejpam-5290	257	11	nets	net	NOUN
ejpam-5290	257	12	.	.	PUNCT
ejpam-5290	258	1	acta	acta	PROPN
ejpam-5290	258	2	crystallographica	crystallographica	PROPN
ejpam-5290	258	3	section	section	PROPN
ejpam-5290	258	4	a	a	DET
ejpam-5290	258	5	:	:	PUNCT
ejpam-5290	258	6	foundations	foundation	NOUN
ejpam-5290	258	7	of	of	ADP
ejpam-5290	258	8	crystallography	crystallography	NOUN
ejpam-5290	258	9	,	,	PUNCT
ejpam-5290	258	10	63(5):418–425	63(5):418–425	NOUN
ejpam-5290	258	11	,	,	PUNCT
ejpam-5290	258	12	2007	2007	NUM
ejpam-5290	258	13	.	.	PUNCT
ejpam-5290	259	1	[	[	X
ejpam-5290	259	2	9	9	NUM
ejpam-5290	259	3	]	]	SYM
ejpam-5290	259	4	augustin	augustin	PROPN
ejpam-5290	259	5	louis	louis	PROPN
ejpam-5290	259	6	cauchy	cauchy	PROPN
ejpam-5290	259	7	.	.	PUNCT
ejpam-5290	260	1	sur	sur	PROPN
ejpam-5290	260	2	les	les	PROPN
ejpam-5290	260	3	polygones	polygone	NOUN
ejpam-5290	260	4	et	et	PROPN
ejpam-5290	260	5	polyedres	polyedre	NOUN
ejpam-5290	260	6	.	.	PUNCT
ejpam-5290	261	1	j.	j.	PROPN
ejpam-5290	261	2	ec	ec	PROPN
ejpam-5290	261	3	.	.	PUNCT
ejpam-5290	262	1	polytechnique	polytechnique	PROPN
ejpam-5290	262	2	,	,	PUNCT
ejpam-5290	262	3	16:87	16:87	NUM
ejpam-5290	262	4	–	–	PUNCT
ejpam-5290	262	5	99	99	NUM
ejpam-5290	262	6	,	,	PUNCT
ejpam-5290	262	7	1813	1813	NUM
ejpam-5290	262	8	.	.	PUNCT
ejpam-5290	263	1	[	[	X
ejpam-5290	263	2	10	10	NUM
ejpam-5290	263	3	]	]	X
ejpam-5290	263	4	robert	robert	PROPN
ejpam-5290	263	5	connelly	connelly	PROPN
ejpam-5290	263	6	.	.	PUNCT
ejpam-5290	264	1	a	a	DET
ejpam-5290	264	2	flexible	flexible	ADJ
ejpam-5290	264	3	sphere	sphere	NOUN
ejpam-5290	264	4	.	.	PUNCT
ejpam-5290	265	1	the	the	DET
ejpam-5290	265	2	mathematical	mathematical	ADJ
ejpam-5290	265	3	intelligencer	intelligencer	NOUN
ejpam-5290	265	4	,	,	PUNCT
ejpam-5290	265	5	1:130–131	1:130–131	NUM
ejpam-5290	265	6	,	,	PUNCT
ejpam-5290	265	7	1978	1978	NUM
ejpam-5290	265	8	.	.	PUNCT
ejpam-5290	266	1	[	[	X
ejpam-5290	266	2	11	11	NUM
ejpam-5290	266	3	]	]	X
ejpam-5290	266	4	robert	robert	PROPN
ejpam-5290	266	5	connelly	connelly	PROPN
ejpam-5290	266	6	and	and	CCONJ
ejpam-5290	266	7	simon	simon	PROPN
ejpam-5290	266	8	d	d	PROPN
ejpam-5290	266	9	guest	guest	PROPN
ejpam-5290	266	10	.	.	PUNCT
ejpam-5290	267	1	frameworks	framework	NOUN
ejpam-5290	267	2	,	,	PUNCT
ejpam-5290	267	3	tensegrities	tensegritie	NOUN
ejpam-5290	267	4	,	,	PUNCT
ejpam-5290	267	5	and	and	CCONJ
ejpam-5290	267	6	symmetry	symmetry	PROPN
ejpam-5290	267	7	.	.	PUNCT
ejpam-5290	268	1	cambridge	cambridge	PROPN
ejpam-5290	268	2	university	university	PROPN
ejpam-5290	268	3	press	press	NOUN
ejpam-5290	268	4	,	,	PUNCT
ejpam-5290	268	5	2022	2022	NUM
ejpam-5290	268	6	.	.	PUNCT
ejpam-5290	269	1	[	[	X
ejpam-5290	269	2	12	12	NUM
ejpam-5290	269	3	]	]	X
ejpam-5290	269	4	robert	robert	PROPN
ejpam-5290	269	5	connelly	connelly	PROPN
ejpam-5290	269	6	,	,	PUNCT
ejpam-5290	269	7	tibor	tibor	PROPN
ejpam-5290	269	8	jordán	jordán	PROPN
ejpam-5290	269	9	,	,	PUNCT
ejpam-5290	269	10	and	and	CCONJ
ejpam-5290	269	11	walter	walter	PROPN
ejpam-5290	269	12	whiteley	whiteley	PROPN
ejpam-5290	269	13	.	.	PUNCT
ejpam-5290	270	1	generic	generic	ADJ
ejpam-5290	270	2	global	global	ADJ
ejpam-5290	270	3	rigidity	rigidity	NOUN
ejpam-5290	270	4	of	of	ADP
ejpam-5290	270	5	body	body	NOUN
ejpam-5290	270	6	–	–	PUNCT
ejpam-5290	270	7	bar	bar	NOUN
ejpam-5290	270	8	frameworks	framework	NOUN
ejpam-5290	270	9	.	.	PUNCT
ejpam-5290	271	1	journal	journal	NOUN
ejpam-5290	271	2	of	of	ADP
ejpam-5290	271	3	combinatorial	combinatorial	ADJ
ejpam-5290	271	4	theory	theory	NOUN
ejpam-5290	271	5	,	,	PUNCT
ejpam-5290	271	6	series	series	PROPN
ejpam-5290	271	7	b	b	PROPN
ejpam-5290	271	8	,	,	PUNCT
ejpam-5290	271	9	103(6):689–705	103(6):689–705	NUM
ejpam-5290	271	10	,	,	PUNCT
ejpam-5290	271	11	2013	2013	NUM
ejpam-5290	271	12	.	.	PUNCT
ejpam-5290	272	1	references	reference	NOUN
ejpam-5290	272	2	3092	3092	NUM
ejpam-5290	273	1	[	[	X
ejpam-5290	273	2	13	13	NUM
ejpam-5290	273	3	]	]	X
ejpam-5290	273	4	olaf	olaf	PROPN
ejpam-5290	273	5	delgado	delgado	NOUN
ejpam-5290	273	6	-	-	PUNCT
ejpam-5290	273	7	friedrichs	friedrich	NOUN
ejpam-5290	273	8	,	,	PUNCT
ejpam-5290	273	9	martin	martin	PROPN
ejpam-5290	273	10	d	d	PROPN
ejpam-5290	273	11	foster	foster	PROPN
ejpam-5290	273	12	,	,	PUNCT
ejpam-5290	273	13	michael	michael	PROPN
ejpam-5290	273	14	o’keeffe	o’keeffe	PROPN
ejpam-5290	273	15	,	,	PUNCT
ejpam-5290	273	16	davide	davide	PROPN
ejpam-5290	273	17	m	m	PROPN
ejpam-5290	273	18	proserpio	proserpio	NOUN
ejpam-5290	273	19	,	,	PUNCT
ejpam-5290	273	20	michael	michael	PROPN
ejpam-5290	273	21	mj	mj	PROPN
ejpam-5290	273	22	treacy	treacy	PROPN
ejpam-5290	273	23	,	,	PUNCT
ejpam-5290	273	24	and	and	CCONJ
ejpam-5290	273	25	omar	omar	PROPN
ejpam-5290	273	26	m	m	PROPN
ejpam-5290	273	27	yaghi	yaghi	PROPN
ejpam-5290	273	28	.	.	PUNCT
ejpam-5290	274	1	what	what	PRON
ejpam-5290	274	2	do	do	AUX
ejpam-5290	274	3	we	we	PRON
ejpam-5290	274	4	know	know	VERB
ejpam-5290	274	5	about	about	ADV
ejpam-5290	274	6	three	three	NUM
ejpam-5290	274	7	-	-	PUNCT
ejpam-5290	274	8	periodic	periodic	ADJ
ejpam-5290	274	9	nets	net	NOUN
ejpam-5290	274	10	?	?	PUNCT
ejpam-5290	275	1	journal	journal	NOUN
ejpam-5290	275	2	of	of	ADP
ejpam-5290	275	3	solid	solid	ADJ
ejpam-5290	275	4	state	state	NOUN
ejpam-5290	275	5	chemistry	chemistry	NOUN
ejpam-5290	275	6	,	,	PUNCT
ejpam-5290	275	7	178(8):2533–2554	178(8):2533–2554	NUM
ejpam-5290	275	8	,	,	PUNCT
ejpam-5290	275	9	2005	2005	NUM
ejpam-5290	275	10	.	.	PUNCT
ejpam-5290	276	1	[	[	X
ejpam-5290	276	2	14	14	NUM
ejpam-5290	276	3	]	]	X
ejpam-5290	276	4	jack	jack	NOUN
ejpam-5290	276	5	e	e	PROPN
ejpam-5290	276	6	graver	graver	X
ejpam-5290	276	7	.	.	PUNCT
ejpam-5290	277	1	counting	count	VERB
ejpam-5290	277	2	on	on	ADP
ejpam-5290	277	3	frameworks	framework	NOUN
ejpam-5290	277	4	:	:	PUNCT
ejpam-5290	277	5	mathematics	mathematic	NOUN
ejpam-5290	277	6	to	to	PART
ejpam-5290	277	7	aid	aid	VERB
ejpam-5290	277	8	the	the	DET
ejpam-5290	277	9	design	design	NOUN
ejpam-5290	277	10	of	of	ADP
ejpam-5290	277	11	rigid	rigid	ADJ
ejpam-5290	277	12	structures	structure	NOUN
ejpam-5290	277	13	.	.	PUNCT
ejpam-5290	278	1	number	number	NOUN
ejpam-5290	278	2	25	25	NUM
ejpam-5290	278	3	.	.	PUNCT
ejpam-5290	279	1	cambridge	cambridge	PROPN
ejpam-5290	279	2	university	university	PROPN
ejpam-5290	279	3	press	press	NOUN
ejpam-5290	279	4	,	,	PUNCT
ejpam-5290	279	5	2001	2001	NUM
ejpam-5290	279	6	.	.	PUNCT
ejpam-5290	280	1	[	[	X
ejpam-5290	280	2	15	15	NUM
ejpam-5290	280	3	]	]	X
ejpam-5290	280	4	derek	derek	PROPN
ejpam-5290	280	5	kitson	kitson	PROPN
ejpam-5290	280	6	and	and	CCONJ
ejpam-5290	280	7	stephen	stephen	PROPN
ejpam-5290	280	8	c	c	PROPN
ejpam-5290	280	9	power	power	NOUN
ejpam-5290	280	10	.	.	PUNCT
ejpam-5290	281	1	infinitesimal	infinitesimal	ADJ
ejpam-5290	281	2	rigidity	rigidity	NOUN
ejpam-5290	281	3	for	for	ADP
ejpam-5290	281	4	non	non	ADJ
ejpam-5290	281	5	-	-	ADJ
ejpam-5290	281	6	euclidean	euclidean	ADJ
ejpam-5290	281	7	bar	bar	NOUN
ejpam-5290	281	8	-	-	PUNCT
ejpam-5290	281	9	joint	joint	NOUN
ejpam-5290	281	10	frameworks	framework	NOUN
ejpam-5290	281	11	.	.	PUNCT
ejpam-5290	282	1	bulletin	bulletin	NOUN
ejpam-5290	282	2	of	of	ADP
ejpam-5290	282	3	the	the	DET
ejpam-5290	282	4	london	london	PROPN
ejpam-5290	282	5	mathematical	mathematical	ADJ
ejpam-5290	282	6	society	society	NOUN
ejpam-5290	282	7	,	,	PUNCT
ejpam-5290	282	8	page	page	NOUN
ejpam-5290	282	9	bdu017	bdu017	PROPN
ejpam-5290	282	10	,	,	PUNCT
ejpam-5290	282	11	2014	2014	NUM
ejpam-5290	282	12	.	.	PUNCT
ejpam-5290	283	1	[	[	X
ejpam-5290	283	2	16	16	NUM
ejpam-5290	283	3	]	]	X
ejpam-5290	283	4	gerard	gerard	PROPN
ejpam-5290	283	5	laman	laman	PROPN
ejpam-5290	283	6	.	.	PROPN
ejpam-5290	284	1	on	on	ADP
ejpam-5290	284	2	graphs	graph	NOUN
ejpam-5290	284	3	and	and	CCONJ
ejpam-5290	284	4	rigidity	rigidity	NOUN
ejpam-5290	284	5	of	of	ADP
ejpam-5290	284	6	plane	plane	NOUN
ejpam-5290	284	7	skeletal	skeletal	ADJ
ejpam-5290	284	8	structures	structure	NOUN
ejpam-5290	284	9	.	.	PUNCT
ejpam-5290	285	1	journal	journal	NOUN
ejpam-5290	285	2	of	of	ADP
ejpam-5290	285	3	engineering	engineering	NOUN
ejpam-5290	285	4	mathematics	mathematic	NOUN
ejpam-5290	285	5	,	,	PUNCT
ejpam-5290	285	6	4(4):331–340	4(4):331–340	NUM
ejpam-5290	285	7	,	,	PUNCT
ejpam-5290	285	8	1970	1970	NUM
ejpam-5290	285	9	.	.	PUNCT
ejpam-5290	286	1	[	[	X
ejpam-5290	286	2	17	17	NUM
ejpam-5290	286	3	]	]	X
ejpam-5290	286	4	giulia	giulia	PROPN
ejpam-5290	286	5	michieletto	michieletto	PROPN
ejpam-5290	286	6	,	,	PUNCT
ejpam-5290	286	7	angelo	angelo	PROPN
ejpam-5290	286	8	cenedese	cenedese	PROPN
ejpam-5290	286	9	,	,	PUNCT
ejpam-5290	286	10	and	and	CCONJ
ejpam-5290	286	11	daniel	daniel	PROPN
ejpam-5290	286	12	zelazo	zelazo	PROPN
ejpam-5290	286	13	.	.	PUNCT
ejpam-5290	287	1	a	a	DET
ejpam-5290	287	2	unified	unified	ADJ
ejpam-5290	287	3	dissertation	dissertation	NOUN
ejpam-5290	287	4	on	on	ADP
ejpam-5290	287	5	bearing	bear	VERB
ejpam-5290	287	6	rigidity	rigidity	NOUN
ejpam-5290	287	7	theory	theory	NOUN
ejpam-5290	287	8	.	.	PUNCT
ejpam-5290	288	1	ieee	ieee	NOUN
ejpam-5290	288	2	transactions	transaction	NOUN
ejpam-5290	288	3	on	on	ADP
ejpam-5290	288	4	control	control	NOUN
ejpam-5290	288	5	of	of	ADP
ejpam-5290	288	6	network	network	NOUN
ejpam-5290	288	7	systems	system	NOUN
ejpam-5290	288	8	,	,	PUNCT
ejpam-5290	288	9	8(4):1624–1636	8(4):1624–1636	NUM
ejpam-5290	288	10	,	,	PUNCT
ejpam-5290	288	11	2021	2021	NUM
ejpam-5290	288	12	.	.	PUNCT
ejpam-5290	289	1	[	[	X
ejpam-5290	289	2	18	18	NUM
ejpam-5290	289	3	]	]	X
ejpam-5290	289	4	john	john	PROPN
ejpam-5290	289	5	c	c	PROPN
ejpam-5290	289	6	owen	owen	PROPN
ejpam-5290	289	7	and	and	CCONJ
ejpam-5290	289	8	stephen	stephen	PROPN
ejpam-5290	289	9	c	c	PROPN
ejpam-5290	289	10	power	power	PROPN
ejpam-5290	289	11	.	.	PUNCT
ejpam-5290	290	1	infinite	infinite	ADJ
ejpam-5290	290	2	bar	bar	NOUN
ejpam-5290	290	3	-	-	PUNCT
ejpam-5290	290	4	joint	joint	NOUN
ejpam-5290	290	5	frameworks	framework	NOUN
ejpam-5290	290	6	.	.	PUNCT
ejpam-5290	291	1	in	in	ADP
ejpam-5290	291	2	proceedings	proceeding	NOUN
ejpam-5290	291	3	of	of	ADP
ejpam-5290	291	4	the	the	DET
ejpam-5290	291	5	2009	2009	NUM
ejpam-5290	291	6	acm	acm	NOUN
ejpam-5290	291	7	symposium	symposium	NOUN
ejpam-5290	291	8	on	on	ADP
ejpam-5290	291	9	applied	apply	VERB
ejpam-5290	291	10	computing	computing	NOUN
ejpam-5290	291	11	,	,	PUNCT
ejpam-5290	291	12	pages	page	NOUN
ejpam-5290	291	13	1116–1121	1116–1121	NUM
ejpam-5290	291	14	.	.	PUNCT
ejpam-5290	291	15	acm	acm	PROPN
ejpam-5290	291	16	,	,	PUNCT
ejpam-5290	291	17	2009	2009	NUM
ejpam-5290	291	18	.	.	PUNCT
ejpam-5290	292	1	[	[	X
ejpam-5290	292	2	19	19	NUM
ejpam-5290	292	3	]	]	X
ejpam-5290	292	4	john	john	PROPN
ejpam-5290	292	5	c	c	PROPN
ejpam-5290	292	6	owen	owen	PROPN
ejpam-5290	292	7	and	and	CCONJ
ejpam-5290	292	8	stephen	stephen	PROPN
ejpam-5290	292	9	c	c	PROPN
ejpam-5290	292	10	power	power	NOUN
ejpam-5290	292	11	.	.	PUNCT
ejpam-5290	293	1	frameworks	framework	NOUN
ejpam-5290	293	2	symmetry	symmetry	NOUN
ejpam-5290	293	3	and	and	CCONJ
ejpam-5290	293	4	rigidity	rigidity	NOUN
ejpam-5290	293	5	.	.	PUNCT
ejpam-5290	294	1	international	international	ADJ
ejpam-5290	294	2	journal	journal	NOUN
ejpam-5290	294	3	of	of	ADP
ejpam-5290	294	4	computational	computational	ADJ
ejpam-5290	294	5	geometry	geometry	NOUN
ejpam-5290	294	6	&	&	CCONJ
ejpam-5290	294	7	applications	application	NOUN
ejpam-5290	294	8	,	,	PUNCT
ejpam-5290	294	9	20(06):723–750	20(06):723–750	NUM
ejpam-5290	294	10	,	,	PUNCT
ejpam-5290	294	11	2010	2010	NUM
ejpam-5290	294	12	.	.	PUNCT
ejpam-5290	295	1	[	[	X
ejpam-5290	295	2	20	20	NUM
ejpam-5290	295	3	]	]	X
ejpam-5290	295	4	john	john	PROPN
ejpam-5290	295	5	c	c	PROPN
ejpam-5290	295	6	owen	owen	PROPN
ejpam-5290	295	7	and	and	CCONJ
ejpam-5290	295	8	stephen	stephen	PROPN
ejpam-5290	295	9	c	c	PROPN
ejpam-5290	295	10	power	power	PROPN
ejpam-5290	295	11	.	.	PUNCT
ejpam-5290	296	1	infinite	infinite	ADJ
ejpam-5290	296	2	bar	bar	NOUN
ejpam-5290	296	3	-	-	PUNCT
ejpam-5290	296	4	joint	joint	NOUN
ejpam-5290	296	5	frameworks	framework	NOUN
ejpam-5290	296	6	,	,	PUNCT
ejpam-5290	296	7	crystals	crystal	NOUN
ejpam-5290	296	8	and	and	CCONJ
ejpam-5290	296	9	operator	operator	NOUN
ejpam-5290	296	10	theory	theory	NOUN
ejpam-5290	296	11	.	.	PUNCT
ejpam-5290	297	1	new	new	PROPN
ejpam-5290	297	2	york	york	PROPN
ejpam-5290	297	3	journal	journal	PROPN
ejpam-5290	297	4	of	of	ADP
ejpam-5290	297	5	mathematics	mathematic	NOUN
ejpam-5290	297	6	,	,	PUNCT
ejpam-5290	297	7	17:445–490	17:445–490	NUM
ejpam-5290	297	8	,	,	PUNCT
ejpam-5290	297	9	2011	2011	NUM
ejpam-5290	297	10	.	.	PUNCT
ejpam-5290	298	1	[	[	X
ejpam-5290	298	2	21	21	NUM
ejpam-5290	298	3	]	]	X
ejpam-5290	298	4	stephen	stephen	PROPN
ejpam-5290	298	5	c	c	PROPN
ejpam-5290	298	6	power	power	NOUN
ejpam-5290	298	7	.	.	PUNCT
ejpam-5290	299	1	polynomials	polynomial	NOUN
ejpam-5290	299	2	for	for	ADP
ejpam-5290	299	3	crystal	crystal	NOUN
ejpam-5290	299	4	frameworks	framework	NOUN
ejpam-5290	299	5	and	and	CCONJ
ejpam-5290	299	6	the	the	DET
ejpam-5290	299	7	rigid	rigid	ADJ
ejpam-5290	299	8	unit	unit	NOUN
ejpam-5290	299	9	mode	mode	NOUN
ejpam-5290	299	10	spectrum	spectrum	NOUN
ejpam-5290	299	11	.	.	PUNCT
ejpam-5290	300	1	philosophical	philosophical	ADJ
ejpam-5290	300	2	transactions	transaction	NOUN
ejpam-5290	300	3	of	of	ADP
ejpam-5290	300	4	the	the	DET
ejpam-5290	300	5	royal	royal	ADJ
ejpam-5290	300	6	society	society	NOUN
ejpam-5290	300	7	a	a	DET
ejpam-5290	300	8	:	:	PUNCT
ejpam-5290	300	9	mathematical	mathematical	ADJ
ejpam-5290	300	10	,	,	PUNCT
ejpam-5290	300	11	physical	physical	ADJ
ejpam-5290	300	12	and	and	CCONJ
ejpam-5290	300	13	engineering	engineering	NOUN
ejpam-5290	300	14	sciences	science	NOUN
ejpam-5290	300	15	,	,	PUNCT
ejpam-5290	300	16	372(2008):20120030	372(2008):20120030	NUM
ejpam-5290	300	17	,	,	PUNCT
ejpam-5290	300	18	2014	2014	NUM
ejpam-5290	300	19	.	.	PUNCT
ejpam-5290	301	1	[	[	X
ejpam-5290	301	2	22	22	NUM
ejpam-5290	301	3	]	]	X
ejpam-5290	301	4	ben	ben	PROPN
ejpam-5290	301	5	roth	roth	PROPN
ejpam-5290	301	6	.	.	PUNCT
ejpam-5290	302	1	rigid	rigid	ADJ
ejpam-5290	302	2	and	and	CCONJ
ejpam-5290	302	3	flexible	flexible	ADJ
ejpam-5290	302	4	frameworks	framework	NOUN
ejpam-5290	302	5	.	.	PUNCT
ejpam-5290	303	1	american	american	PROPN
ejpam-5290	303	2	mathematical	mathematical	PROPN
ejpam-5290	303	3	monthly	monthly	ADV
ejpam-5290	303	4	,	,	PUNCT
ejpam-5290	303	5	pages	page	NOUN
ejpam-5290	303	6	6–21	6–21	PROPN
ejpam-5290	303	7	,	,	PUNCT
ejpam-5290	303	8	1981	1981	NUM
ejpam-5290	303	9	.	.	PUNCT
ejpam-5290	304	1	[	[	X
ejpam-5290	304	2	23	23	NUM
ejpam-5290	304	3	]	]	PUNCT
ejpam-5290	304	4	avais	avais	X
ejpam-5290	304	5	sait	sait	PROPN
ejpam-5290	304	6	.	.	PUNCT
ejpam-5290	305	1	rigidity	rigidity	NOUN
ejpam-5290	305	2	of	of	ADP
ejpam-5290	305	3	infinite	infinite	ADJ
ejpam-5290	305	4	frameworks	framework	NOUN
ejpam-5290	305	5	.	.	PUNCT
ejpam-5290	306	1	lancaster	lancaster	PROPN
ejpam-5290	306	2	university	university	PROPN
ejpam-5290	306	3	mphil	mphil	PROPN
ejpam-5290	306	4	thesis	thesis	NOUN
ejpam-5290	306	5	,	,	PUNCT
ejpam-5290	306	6	2011	2011	NUM
ejpam-5290	306	7	.	.	PUNCT
ejpam-5290	307	1	[	[	X
ejpam-5290	307	2	24	24	NUM
ejpam-5290	307	3	]	]	X
ejpam-5290	307	4	michael	michael	PROPN
ejpam-5290	307	5	f	f	PROPN
ejpam-5290	307	6	thorpe	thorpe	PROPN
ejpam-5290	307	7	and	and	CCONJ
ejpam-5290	307	8	phillip	phillip	PROPN
ejpam-5290	307	9	m	m	PROPN
ejpam-5290	307	10	duxbury	duxbury	PROPN
ejpam-5290	307	11	.	.	PUNCT
ejpam-5290	308	1	rigidity	rigidity	NOUN
ejpam-5290	308	2	theory	theory	NOUN
ejpam-5290	308	3	and	and	CCONJ
ejpam-5290	308	4	applications	application	NOUN
ejpam-5290	308	5	.	.	PUNCT
ejpam-5290	309	1	springer	springer	NOUN
ejpam-5290	309	2	science	science	PROPN
ejpam-5290	309	3	&	&	CCONJ
ejpam-5290	309	4	business	business	NOUN
ejpam-5290	309	5	media	medium	NOUN
ejpam-5290	309	6	,	,	PUNCT
ejpam-5290	309	7	2006	2006	NUM
ejpam-5290	309	8	.	.	PUNCT
ejpam-5290	310	1	[	[	X
ejpam-5290	310	2	25	25	NUM
ejpam-5290	310	3	]	]	X
ejpam-5290	310	4	walter	walter	PROPN
ejpam-5290	310	5	whiteley	whiteley	PROPN
ejpam-5290	310	6	.	.	PUNCT
ejpam-5290	311	1	some	some	DET
ejpam-5290	311	2	matroids	matroid	NOUN
ejpam-5290	311	3	from	from	ADP
ejpam-5290	311	4	discrete	discrete	ADJ
ejpam-5290	311	5	applied	apply	VERB
ejpam-5290	311	6	geometry	geometry	NOUN
ejpam-5290	311	7	.	.	PUNCT
ejpam-5290	312	1	contemporary	contemporary	ADJ
ejpam-5290	312	2	mathematics	mathematic	NOUN
ejpam-5290	312	3	,	,	PUNCT
ejpam-5290	312	4	197:171–312	197:171–312	NUM
ejpam-5290	312	5	,	,	PUNCT
ejpam-5290	312	6	1996	1996	NUM
ejpam-5290	312	7	.	.	PUNCT
ejpam-5290	313	1	[	[	X
ejpam-5290	313	2	26	26	NUM
ejpam-5290	313	3	]	]	X
ejpam-5290	313	4	daniel	daniel	PROPN
ejpam-5290	313	5	zelazo	zelazo	PROPN
ejpam-5290	313	6	,	,	PUNCT
ejpam-5290	313	7	antonio	antonio	PROPN
ejpam-5290	313	8	franchi	franchi	PROPN
ejpam-5290	313	9	,	,	PUNCT
ejpam-5290	313	10	frank	frank	PROPN
ejpam-5290	313	11	allgöwer	allgöwer	PROPN
ejpam-5290	313	12	,	,	PUNCT
ejpam-5290	313	13	heinrich	heinrich	PROPN
ejpam-5290	313	14	h	h	NOUN
ejpam-5290	313	15	bülthoff	bülthoff	NOUN
ejpam-5290	313	16	,	,	PUNCT
ejpam-5290	313	17	and	and	CCONJ
ejpam-5290	313	18	paolo	paolo	PROPN
ejpam-5290	313	19	robuffo	robuffo	PROPN
ejpam-5290	313	20	giordano	giordano	PROPN
ejpam-5290	313	21	.	.	PUNCT
ejpam-5290	314	1	rigidity	rigidity	NOUN
ejpam-5290	314	2	maintenance	maintenance	NOUN
ejpam-5290	314	3	control	control	NOUN
ejpam-5290	314	4	for	for	ADP
ejpam-5290	314	5	multi	multi	ADJ
ejpam-5290	314	6	-	-	ADJ
ejpam-5290	314	7	robot	robot	ADJ
ejpam-5290	314	8	systems	system	NOUN
ejpam-5290	314	9	.	.	PUNCT
ejpam-5290	315	1	in	in	ADP
ejpam-5290	315	2	robotics	robotic	NOUN
ejpam-5290	315	3	:	:	PUNCT
ejpam-5290	315	4	science	science	NOUN
ejpam-5290	315	5	and	and	CCONJ
ejpam-5290	315	6	systems	system	NOUN
ejpam-5290	315	7	,	,	PUNCT
ejpam-5290	315	8	volume	volume	NOUN
ejpam-5290	315	9	2012	2012	NUM
ejpam-5290	315	10	.	.	PUNCT
ejpam-5290	316	1	sydney	sydney	PROPN
ejpam-5290	316	2	,	,	PUNCT
ejpam-5290	316	3	australia	australia	PROPN
ejpam-5290	316	4	,	,	PUNCT
ejpam-5290	316	5	2012	2012	NUM
ejpam-5290	316	6	.	.	PUNCT