id	sid	tid	token	lemma	pos
ijassa-111	1	1	advances	advance	NOUN
ijassa-111	1	2	in	in	ADP
ijassa-111	1	3	systems	system	NOUN
ijassa-111	1	4	science	science	NOUN
ijassa-111	1	5	and	and	CCONJ
ijassa-111	1	6	applications	application	NOUN
ijassa-111	1	7	(	(	PUNCT
ijassa-111	1	8	2012	2012	NUM
ijassa-111	1	9	)	)	PUNCT
ijassa-111	1	10	vol.12	vol.12	NOUN
ijassa-111	1	11	no.3	no.3	VERB
ijassa-111	1	12	258	258	NUM
ijassa-111	1	13	-	-	SYM
ijassa-111	1	14	271	271	NUM
ijassa-111	1	15	a	a	DET
ijassa-111	1	16	geometric	geometric	ADJ
ijassa-111	1	17	interpretation	interpretation	NOUN
ijassa-111	1	18	of	of	ADP
ijassa-111	1	19	gravity	gravity	NOUN
ijassa-111	1	20	theory	theory	NOUN
ijassa-111	1	21	n.n	n.n	PROPN
ijassa-111	1	22	.	.	PROPN
ijassa-111	1	23	popov	popov	PROPN
ijassa-111	1	24	dorodnitsyn	dorodnitsyn	PROPN
ijassa-111	1	25	computer	computer	NOUN
ijassa-111	1	26	centre	centre	NOUN
ijassa-111	1	27	of	of	ADP
ijassa-111	1	28	russian	russian	PROPN
ijassa-111	1	29	academy	academy	PROPN
ijassa-111	1	30	of	of	ADP
ijassa-111	1	31	science	science	PROPN
ijassa-111	1	32	abstract	abstract	VERB
ijassa-111	1	33	a	a	DET
ijassa-111	1	34	system	system	NOUN
ijassa-111	1	35	of	of	ADP
ijassa-111	1	36	postulates	postulate	NOUN
ijassa-111	1	37	which	which	PRON
ijassa-111	1	38	give	give	VERB
ijassa-111	1	39	a	a	DET
ijassa-111	1	40	geometric	geometric	ADJ
ijassa-111	1	41	meaning	meaning	NOUN
ijassa-111	1	42	to	to	ADP
ijassa-111	1	43	the	the	DET
ijassa-111	1	44	fundamental	fundamental	ADJ
ijassa-111	1	45	notions	notion	NOUN
ijassa-111	1	46	of	of	ADP
ijassa-111	1	47	gravity	gravity	NOUN
ijassa-111	1	48	theory	theory	NOUN
ijassa-111	1	49	is	be	AUX
ijassa-111	1	50	introduced	introduce	VERB
ijassa-111	1	51	.	.	PUNCT
ijassa-111	2	1	the	the	DET
ijassa-111	2	2	fundamental	fundamental	ADJ
ijassa-111	2	3	equation	equation	NOUN
ijassa-111	2	4	of	of	ADP
ijassa-111	2	5	geometric	geometric	ADJ
ijassa-111	2	6	gravity	gravity	NOUN
ijassa-111	2	7	theory	theory	NOUN
ijassa-111	2	8	is	be	AUX
ijassa-111	2	9	derived	derive	VERB
ijassa-111	2	10	.	.	PUNCT
ijassa-111	3	1	the	the	DET
ijassa-111	3	2	consistency	consistency	NOUN
ijassa-111	3	3	of	of	ADP
ijassa-111	3	4	the	the	DET
ijassa-111	3	5	system	system	NOUN
ijassa-111	3	6	of	of	ADP
ijassa-111	3	7	postulates	postulate	NOUN
ijassa-111	3	8	is	be	AUX
ijassa-111	3	9	shown	show	VERB
ijassa-111	3	10	.	.	PUNCT
ijassa-111	4	1	a	a	DET
ijassa-111	4	2	series	series	NOUN
ijassa-111	4	3	of	of	ADP
ijassa-111	4	4	examples	example	NOUN
ijassa-111	4	5	adequately	adequately	ADV
ijassa-111	4	6	describing	describe	VERB
ijassa-111	4	7	the	the	DET
ijassa-111	4	8	gravitational	gravitational	ADJ
ijassa-111	4	9	field	field	NOUN
ijassa-111	4	10	are	be	AUX
ijassa-111	4	11	considered	consider	VERB
ijassa-111	4	12	.	.	PUNCT
ijassa-111	5	1	mathematically	mathematically	ADV
ijassa-111	5	2	rigorous	rigorous	ADJ
ijassa-111	5	3	definitions	definition	NOUN
ijassa-111	5	4	of	of	ADP
ijassa-111	5	5	a	a	DET
ijassa-111	5	6	black	black	ADJ
ijassa-111	5	7	hole	hole	NOUN
ijassa-111	5	8	and	and	CCONJ
ijassa-111	5	9	dark	dark	ADJ
ijassa-111	5	10	energy	energy	NOUN
ijassa-111	5	11	are	be	AUX
ijassa-111	5	12	given	give	VERB
ijassa-111	5	13	.	.	PUNCT
ijassa-111	6	1	keywords	keyword	VERB
ijassa-111	6	2	pseudo	pseudo	NOUN
ijassa-111	6	3	-	-	ADJ
ijassa-111	6	4	riemannian	riemannian	ADJ
ijassa-111	6	5	space	space	NOUN
ijassa-111	6	6	,	,	PUNCT
ijassa-111	6	7	scalar	scalar	ADJ
ijassa-111	6	8	curvature	curvature	NOUN
ijassa-111	6	9	,	,	PUNCT
ijassa-111	6	10	metric	metric	ADJ
ijassa-111	6	11	gravity	gravity	NOUN
ijassa-111	6	12	equation	equation	NOUN
ijassa-111	6	13	,	,	PUNCT
ijassa-111	6	14	spherically	spherically	NOUN
ijassa-111	6	15	symmetric	symmetric	PROPN
ijassa-111	6	16	spatial	spatial	ADJ
ijassa-111	6	17	black	black	ADJ
ijassa-111	6	18	hole	hole	NOUN
ijassa-111	6	19	,	,	PUNCT
ijassa-111	6	20	dark	dark	ADJ
ijassa-111	6	21	energy	energy	NOUN
ijassa-111	6	22	1	1	NUM
ijassa-111	6	23	introduction	introduction	NOUN
ijassa-111	6	24	hilbert	hilbert	NOUN
ijassa-111	6	25	’s	’s	PART
ijassa-111	6	26	sixth	sixth	ADJ
ijassa-111	6	27	problem	problem	NOUN
ijassa-111	6	28	of	of	ADP
ijassa-111	6	29	axiomatizing	axiomatize	VERB
ijassa-111	6	30	those	those	DET
ijassa-111	6	31	branches	branch	NOUN
ijassa-111	6	32	of	of	ADP
ijassa-111	6	33	physics	physics	NOUN
ijassa-111	6	34	in	in	ADP
ijassa-111	6	35	which	which	PRON
ijassa-111	6	36	mathematics	mathematic	NOUN
ijassa-111	6	37	is	be	AUX
ijassa-111	6	38	prevalent	prevalent	ADJ
ijassa-111	6	39	,	,	PUNCT
ijassa-111	6	40	posed	pose	VERB
ijassa-111	6	41	by	by	ADP
ijassa-111	6	42	hilbert	hilbert	PROPN
ijassa-111	6	43	in	in	ADP
ijassa-111	6	44	1900	1900	NUM
ijassa-111	6	45	among	among	ADP
ijassa-111	6	46	other	other	ADJ
ijassa-111	6	47	problems	problem	NOUN
ijassa-111	6	48	,	,	PUNCT
ijassa-111	6	49	has	have	VERB
ijassa-111	6	50	the	the	DET
ijassa-111	6	51	status	status	NOUN
ijassa-111	6	52	of	of	ADP
ijassa-111	6	53	being	be	AUX
ijassa-111	6	54	too	too	ADV
ijassa-111	6	55	vague	vague	ADJ
ijassa-111	6	56	.	.	PUNCT
ijassa-111	7	1	however	however	ADV
ijassa-111	7	2	,	,	PUNCT
ijassa-111	7	3	in	in	ADP
ijassa-111	7	4	the	the	DET
ijassa-111	7	5	context	context	NOUN
ijassa-111	7	6	of	of	ADP
ijassa-111	7	7	some	some	DET
ijassa-111	7	8	particular	particular	ADJ
ijassa-111	7	9	area	area	NOUN
ijassa-111	7	10	of	of	ADP
ijassa-111	7	11	physics	physics	NOUN
ijassa-111	7	12	,	,	PUNCT
ijassa-111	7	13	such	such	ADJ
ijassa-111	7	14	as	as	ADP
ijassa-111	7	15	gravity	gravity	NOUN
ijassa-111	7	16	theory	theory	NOUN
ijassa-111	7	17	,	,	PUNCT
ijassa-111	7	18	this	this	DET
ijassa-111	7	19	problem	problem	NOUN
ijassa-111	7	20	can	can	AUX
ijassa-111	7	21	be	be	AUX
ijassa-111	7	22	stated	state	VERB
ijassa-111	7	23	rigorously	rigorously	ADV
ijassa-111	7	24	.	.	PUNCT
ijassa-111	8	1	the	the	DET
ijassa-111	8	2	foundation	foundation	NOUN
ijassa-111	8	3	of	of	ADP
ijassa-111	8	4	physical	physical	ADJ
ijassa-111	8	5	gravity	gravity	NOUN
ijassa-111	8	6	theory	theory	NOUN
ijassa-111	8	7	is	be	AUX
ijassa-111	8	8	two	two	NUM
ijassa-111	8	9	fundamental	fundamental	ADJ
ijassa-111	8	10	physical	physical	ADJ
ijassa-111	8	11	concepts	concept	NOUN
ijassa-111	8	12	,	,	PUNCT
ijassa-111	8	13	of	of	ADP
ijassa-111	8	14	the	the	DET
ijassa-111	8	15	gravitational	gravitational	ADJ
ijassa-111	8	16	field	field	NOUN
ijassa-111	8	17	and	and	CCONJ
ijassa-111	8	18	of	of	ADP
ijassa-111	8	19	the	the	DET
ijassa-111	8	20	mass	mass	NOUN
ijassa-111	8	21	of	of	ADP
ijassa-111	8	22	a	a	DET
ijassa-111	8	23	body	body	NOUN
ijassa-111	8	24	.	.	PUNCT
ijassa-111	9	1	in	in	ADP
ijassa-111	9	2	general	general	ADJ
ijassa-111	9	3	relativity	relativity	NOUN
ijassa-111	9	4	theory	theory	NOUN
ijassa-111	9	5	(	(	PUNCT
ijassa-111	9	6	grt	grt	PROPN
ijassa-111	9	7	)	)	PUNCT
ijassa-111	9	8	,	,	PUNCT
ijassa-111	9	9	which	which	PRON
ijassa-111	9	10	is	be	AUX
ijassa-111	9	11	essentially	essentially	ADV
ijassa-111	9	12	relativistic	relativistic	ADJ
ijassa-111	9	13	gravity	gravity	NOUN
ijassa-111	9	14	theory	theory	NOUN
ijassa-111	9	15	,	,	PUNCT
ijassa-111	9	16	a	a	DET
ijassa-111	9	17	substantial	substantial	ADJ
ijassa-111	9	18	progress	progress	NOUN
ijassa-111	9	19	in	in	ADP
ijassa-111	9	20	the	the	DET
ijassa-111	9	21	mathematical	mathematical	ADJ
ijassa-111	9	22	interpretation	interpretation	NOUN
ijassa-111	9	23	of	of	ADP
ijassa-111	9	24	one	one	NUM
ijassa-111	9	25	of	of	ADP
ijassa-111	9	26	the	the	DET
ijassa-111	9	27	basic	basic	ADJ
ijassa-111	9	28	concepts	concept	NOUN
ijassa-111	9	29	of	of	ADP
ijassa-111	9	30	the	the	DET
ijassa-111	9	31	theory	theory	NOUN
ijassa-111	9	32	,	,	PUNCT
ijassa-111	9	33	namely	namely	ADV
ijassa-111	9	34	,	,	PUNCT
ijassa-111	9	35	that	that	PRON
ijassa-111	9	36	of	of	ADP
ijassa-111	9	37	the	the	DET
ijassa-111	9	38	gravitational	gravitational	ADJ
ijassa-111	9	39	field	field	NOUN
ijassa-111	9	40	,	,	PUNCT
ijassa-111	9	41	has	have	AUX
ijassa-111	9	42	been	be	AUX
ijassa-111	9	43	made	make	VERB
ijassa-111	9	44	.	.	PUNCT
ijassa-111	10	1	from	from	ADP
ijassa-111	10	2	the	the	DET
ijassa-111	10	3	geometrical	geometrical	ADJ
ijassa-111	10	4	point	point	NOUN
ijassa-111	10	5	of	of	ADP
ijassa-111	10	6	view	view	NOUN
ijassa-111	10	7	,	,	PUNCT
ijassa-111	10	8	the	the	DET
ijassa-111	10	9	gravitational	gravitational	ADJ
ijassa-111	10	10	field	field	NOUN
ijassa-111	10	11	is	be	AUX
ijassa-111	10	12	interpreted	interpret	VERB
ijassa-111	10	13	as	as	ADP
ijassa-111	10	14	a	a	DET
ijassa-111	10	15	metric	metric	ADJ
ijassa-111	10	16	pseudo	pseudo	NOUN
ijassa-111	10	17	-	-	NOUN
ijassa-111	10	18	riemannian	riemannian	ADJ
ijassa-111	10	19	4space	4space	NUM
ijassa-111	10	20	.	.	PUNCT
ijassa-111	11	1	however	however	ADV
ijassa-111	11	2	,	,	PUNCT
ijassa-111	11	3	grt	grt	PROPN
ijassa-111	11	4	does	do	AUX
ijassa-111	11	5	not	not	PART
ijassa-111	11	6	provide	provide	VERB
ijassa-111	11	7	such	such	DET
ijassa-111	11	8	a	a	DET
ijassa-111	11	9	precise	precise	ADJ
ijassa-111	11	10	mathematical	mathematical	ADJ
ijassa-111	11	11	definition	definition	NOUN
ijassa-111	11	12	of	of	ADP
ijassa-111	11	13	mass	mass	PROPN
ijassa-111	11	14	,	,	PUNCT
ijassa-111	11	15	or	or	CCONJ
ijassa-111	11	16	,	,	PUNCT
ijassa-111	11	17	to	to	PART
ijassa-111	11	18	be	be	AUX
ijassa-111	11	19	more	more	ADV
ijassa-111	11	20	precise	precise	ADJ
ijassa-111	11	21	,	,	PUNCT
ijassa-111	11	22	the	the	DET
ijassa-111	11	23	distribution	distribution	NOUN
ijassa-111	11	24	density	density	NOUN
ijassa-111	11	25	of	of	ADP
ijassa-111	11	26	mass	mass	PROPN
ijassa-111	11	27	.	.	PUNCT
ijassa-111	12	1	thus	thus	ADV
ijassa-111	12	2	,	,	PUNCT
ijassa-111	12	3	the	the	DET
ijassa-111	12	4	grt	grt	PROPN
ijassa-111	12	5	fundamental	fundamental	ADJ
ijassa-111	12	6	equation	equation	NOUN
ijassa-111	12	7	contains	contain	VERB
ijassa-111	12	8	both	both	PRON
ijassa-111	12	9	a	a	DET
ijassa-111	12	10	purely	purely	ADV
ijassa-111	12	11	mathematical	mathematical	ADJ
ijassa-111	12	12	left	left	ADJ
ijassa-111	12	13	-	-	PUNCT
ijassa-111	12	14	hand	hand	NOUN
ijassa-111	12	15	side	side	NOUN
ijassa-111	12	16	,	,	PUNCT
ijassa-111	12	17	which	which	PRON
ijassa-111	12	18	is	be	AUX
ijassa-111	12	19	generated	generate	VERB
ijassa-111	12	20	by	by	ADP
ijassa-111	12	21	a	a	DET
ijassa-111	12	22	metric	metric	ADJ
ijassa-111	12	23	space	space	NOUN
ijassa-111	12	24	,	,	PUNCT
ijassa-111	12	25	and	and	CCONJ
ijassa-111	12	26	a	a	DET
ijassa-111	12	27	purely	purely	ADV
ijassa-111	12	28	physical	physical	ADJ
ijassa-111	12	29	right	right	ADJ
ijassa-111	12	30	-	-	PUNCT
ijassa-111	12	31	hand	hand	NOUN
ijassa-111	12	32	side	side	NOUN
ijassa-111	12	33	,	,	PUNCT
ijassa-111	12	34	which	which	PRON
ijassa-111	12	35	is	be	AUX
ijassa-111	12	36	the	the	DET
ijassa-111	12	37	energy	energy	NOUN
ijassa-111	12	38	-	-	PUNCT
ijassa-111	12	39	momentum	momentum	NOUN
ijassa-111	12	40	tensor	tensor	NOUN
ijassa-111	12	41	of	of	ADP
ijassa-111	12	42	the	the	DET
ijassa-111	12	43	physical	physical	ADJ
ijassa-111	12	44	system	system	NOUN
ijassa-111	12	45	under	under	ADP
ijassa-111	12	46	consideration	consideration	NOUN
ijassa-111	12	47	.	.	PUNCT
ijassa-111	13	1	note	note	VERB
ijassa-111	13	2	that	that	SCONJ
ijassa-111	13	3	grt	grt	PROPN
ijassa-111	13	4	imposes	impose	VERB
ijassa-111	13	5	no	no	DET
ijassa-111	13	6	constraints	constraint	NOUN
ijassa-111	13	7	on	on	ADP
ijassa-111	13	8	the	the	DET
ijassa-111	13	9	choice	choice	NOUN
ijassa-111	13	10	of	of	ADP
ijassa-111	13	11	the	the	DET
ijassa-111	13	12	energy	energy	NOUN
ijassa-111	13	13	-	-	PUNCT
ijassa-111	13	14	momentum	momentum	NOUN
ijassa-111	13	15	tensor	tensor	NOUN
ijassa-111	13	16	;	;	PUNCT
ijassa-111	13	17	this	this	PRON
ijassa-111	13	18	leads	lead	VERB
ijassa-111	13	19	to	to	ADP
ijassa-111	13	20	the	the	DET
ijassa-111	13	21	possibility	possibility	NOUN
ijassa-111	13	22	of	of	ADP
ijassa-111	13	23	constructing	construct	VERB
ijassa-111	13	24	unrealistic	unrealistic	ADJ
ijassa-111	13	25	models	model	NOUN
ijassa-111	13	26	and	and	CCONJ
ijassa-111	13	27	,	,	PUNCT
ijassa-111	13	28	thereby	thereby	ADV
ijassa-111	13	29	,	,	PUNCT
ijassa-111	13	30	provides	provide	VERB
ijassa-111	13	31	evidence	evidence	NOUN
ijassa-111	13	32	for	for	ADP
ijassa-111	13	33	the	the	DET
ijassa-111	13	34	insufficiency	insufficiency	NOUN
ijassa-111	13	35	of	of	ADP
ijassa-111	13	36	the	the	DET
ijassa-111	13	37	principles	principle	NOUN
ijassa-111	13	38	on	on	ADP
ijassa-111	13	39	which	which	PRON
ijassa-111	13	40	grt	grt	PROPN
ijassa-111	13	41	is	be	AUX
ijassa-111	13	42	founded	found	VERB
ijassa-111	13	43	.	.	PUNCT
ijassa-111	14	1	our	our	PRON
ijassa-111	14	2	purpose	purpose	NOUN
ijassa-111	14	3	in	in	ADP
ijassa-111	14	4	this	this	DET
ijassa-111	14	5	paper	paper	NOUN
ijassa-111	14	6	is	be	AUX
ijassa-111	14	7	to	to	PART
ijassa-111	14	8	present	present	VERB
ijassa-111	14	9	a	a	DET
ijassa-111	14	10	complete	complete	ADJ
ijassa-111	14	11	translation	translation	NOUN
ijassa-111	14	12	of	of	ADP
ijassa-111	14	13	gravity	gravity	NOUN
ijassa-111	14	14	theory	theory	NOUN
ijassa-111	14	15	into	into	ADP
ijassa-111	14	16	the	the	DET
ijassa-111	14	17	language	language	NOUN
ijassa-111	14	18	of	of	ADP
ijassa-111	14	19	differential	differential	ADJ
ijassa-111	14	20	geometry	geometry	NOUN
ijassa-111	14	21	,	,	PUNCT
ijassa-111	14	22	in	in	ADP
ijassa-111	14	23	which	which	PRON
ijassa-111	14	24	the	the	DET
ijassa-111	14	25	physical	physical	ADJ
ijassa-111	14	26	notion	notion	NOUN
ijassa-111	14	27	of	of	ADP
ijassa-111	14	28	the	the	DET
ijassa-111	14	29	mass	mass	ADJ
ijassa-111	14	30	distribution	distribution	NOUN
ijassa-111	14	31	density	density	NOUN
ijassa-111	14	32	has	have	VERB
ijassa-111	14	33	a	a	DET
ijassa-111	14	34	purely	purely	ADV
ijassa-111	14	35	geometric	geometric	ADJ
ijassa-111	14	36	interpretation	interpretation	NOUN
ijassa-111	14	37	.	.	PUNCT
ijassa-111	15	1	2	2	NUM
ijassa-111	15	2	the	the	DET
ijassa-111	15	3	first	first	ADJ
ijassa-111	15	4	postulates	postulate	NOUN
ijassa-111	15	5	of	of	ADP
ijassa-111	15	6	mathematical	mathematical	ADJ
ijassa-111	15	7	gravity	gravity	NOUN
ijassa-111	15	8	theory	theory	NOUN
ijassa-111	15	9	the	the	DET
ijassa-111	15	10	notion	notion	NOUN
ijassa-111	15	11	of	of	ADP
ijassa-111	15	12	a	a	DET
ijassa-111	15	13	metric	metric	ADJ
ijassa-111	15	14	space	space	NOUN
ijassa-111	15	15	is	be	AUX
ijassa-111	15	16	the	the	DET
ijassa-111	15	17	basis	basis	NOUN
ijassa-111	15	18	on	on	ADP
ijassa-111	15	19	which	which	PRON
ijassa-111	15	20	mathematical	mathematical	ADJ
ijassa-111	15	21	gravity	gravity	NOUN
ijassa-111	15	22	theory	theory	NOUN
ijassa-111	15	23	is	be	AUX
ijassa-111	15	24	constructed	construct	VERB
ijassa-111	15	25	.	.	PUNCT
ijassa-111	16	1	to	to	PART
ijassa-111	16	2	construct	construct	VERB
ijassa-111	16	3	the	the	DET
ijassa-111	16	4	theory	theory	NOUN
ijassa-111	16	5	,	,	PUNCT
ijassa-111	16	6	it	it	PRON
ijassa-111	16	7	suffices	suffice	VERB
ijassa-111	16	8	to	to	PART
ijassa-111	16	9	choose	choose	VERB
ijassa-111	16	10	a	a	DET
ijassa-111	16	11	pseudo	pseudo	NOUN
ijassa-111	16	12	-	-	ADJ
ijassa-111	16	13	riemannian	riemannian	ADJ
ijassa-111	16	14	4	4	NUM
ijassa-111	16	15	-	-	PUNCT
ijassa-111	16	16	space	space	NOUN
ijassa-111	16	17	of	of	ADP
ijassa-111	16	18	signature	signature	NOUN
ijassa-111	16	19	(	(	PUNCT
ijassa-111	16	20	−−−+	−−−+	NOUN
ijassa-111	16	21	)	)	PUNCT
ijassa-111	16	22	,	,	PUNCT
ijassa-111	16	23	on	on	ADP
ijassa-111	16	24	which	which	PRON
ijassa-111	16	25	a	a	DET
ijassa-111	16	26	twice	twice	ADV
ijassa-111	16	27	covariant	covariant	ADJ
ijassa-111	16	28	symmetric	symmetric	ADJ
ijassa-111	16	29	nondegenerate	nondegenerate	PROPN
ijassa-111	16	30	tensor	tensor	NOUN
ijassa-111	16	31	field	field	NOUN
ijassa-111	16	32	gij(x1,k	gij(x1,k	PROPN
ijassa-111	16	33	,	,	PUNCT
ijassa-111	16	34	x4	x4	PROPN
ijassa-111	16	35	)	)	PUNCT
ijassa-111	16	36	is	be	AUX
ijassa-111	16	37	defined	define	VERB
ijassa-111	16	38	;	;	PUNCT
ijassa-111	16	39	we	we	PRON
ijassa-111	16	40	have	have	VERB
ijassa-111	16	41	advances	advance	NOUN
ijassa-111	16	42	in	in	ADP
ijassa-111	16	43	systems	system	NOUN
ijassa-111	16	44	science	science	NOUN
ijassa-111	16	45	and	and	CCONJ
ijassa-111	16	46	applications	application	NOUN
ijassa-111	16	47	(	(	PUNCT
ijassa-111	16	48	2012	2012	NUM
ijassa-111	16	49	)	)	PUNCT
ijassa-111	16	50	vol.12	vol.12	NOUN
ijassa-111	16	51	no.3	no.3	VERB
ijassa-111	16	52	259	259	NUM
ijassa-111	16	53	det	det	PROPN
ijassa-111	16	54	|gij	|gij	PROPN
ijassa-111	16	55	|	|	ADV
ijassa-111	16	56	̸=	̸=	PROPN
ijassa-111	16	57	0	0	NUM
ijassa-111	16	58	,	,	PUNCT
ijassa-111	16	59	gij	gij	NOUN
ijassa-111	16	60	=	=	SYM
ijassa-111	16	61	gji	gji	PROPN
ijassa-111	16	62	,	,	PUNCT
ijassa-111	16	63	i	i	PRON
ijassa-111	16	64	,	,	PUNCT
ijassa-111	16	65	j	j	PROPN
ijassa-111	16	66	=	=	SYM
ijassa-111	16	67	1	1	NUM
ijassa-111	16	68	,	,	PUNCT
ijassa-111	16	69	.	.	PUNCT
ijassa-111	16	70	.	.	PUNCT
ijassa-111	17	1	.	.	PUNCT
ijassa-111	18	1	,	,	PUNCT
ijassa-111	18	2	4	4	NUM
ijassa-111	18	3	we	we	PRON
ijassa-111	18	4	refer	refer	VERB
ijassa-111	18	5	to	to	ADP
ijassa-111	18	6	the	the	DET
ijassa-111	18	7	tensor	tensor	NOUN
ijassa-111	18	8	as	as	ADP
ijassa-111	18	9	the	the	DET
ijassa-111	18	10	metric	metric	NOUN
ijassa-111	18	11	of	of	ADP
ijassa-111	18	12	the	the	DET
ijassa-111	18	13	pseudo	pseudo	NOUN
ijassa-111	18	14	-	-	ADJ
ijassa-111	18	15	riemannian	riemannian	ADJ
ijassa-111	18	16	space	space	NOUN
ijassa-111	18	17	.	.	PUNCT
ijassa-111	19	1	general	general	ADJ
ijassa-111	19	2	requirements	requirement	NOUN
ijassa-111	19	3	to	to	ADP
ijassa-111	19	4	a	a	DET
ijassa-111	19	5	metric	metric	ADJ
ijassa-111	19	6	space	space	NOUN
ijassa-111	19	7	are	be	AUX
ijassa-111	19	8	as	as	SCONJ
ijassa-111	19	9	follows	follow	VERB
ijassa-111	19	10	:	:	PUNCT
ijassa-111	19	11	(	(	PUNCT
ijassa-111	19	12	1	1	X
ijassa-111	19	13	)	)	PUNCT
ijassa-111	19	14	smoothness	smoothness	NOUN
ijassa-111	19	15	,	,	PUNCT
ijassa-111	19	16	i.e.	i.e.	X
ijassa-111	19	17	,	,	PUNCT
ijassa-111	19	18	the	the	DET
ijassa-111	19	19	continuity	continuity	NOUN
ijassa-111	19	20	of	of	ADP
ijassa-111	19	21	all	all	DET
ijassa-111	19	22	components	component	NOUN
ijassa-111	19	23	of	of	ADP
ijassa-111	19	24	the	the	DET
ijassa-111	19	25	metric	metric	NOUN
ijassa-111	19	26	on	on	ADP
ijassa-111	19	27	the	the	DET
ijassa-111	19	28	entire	entire	ADJ
ijassa-111	19	29	space	space	NOUN
ijassa-111	19	30	and	and	CCONJ
ijassa-111	19	31	the	the	DET
ijassa-111	19	32	continuous	continuous	ADJ
ijassa-111	19	33	differentiability	differentiability	NOUN
ijassa-111	19	34	of	of	ADP
ijassa-111	19	35	the	the	DET
ijassa-111	19	36	components	component	NOUN
ijassa-111	19	37	up	up	ADP
ijassa-111	19	38	to	to	ADP
ijassa-111	19	39	the	the	DET
ijassa-111	19	40	second	second	ADJ
ijassa-111	19	41	order	order	NOUN
ijassa-111	19	42	with	with	ADP
ijassa-111	19	43	respect	respect	NOUN
ijassa-111	19	44	to	to	ADP
ijassa-111	19	45	all	all	DET
ijassa-111	19	46	variables	variable	NOUN
ijassa-111	19	47	almost	almost	ADV
ijassa-111	19	48	everywhere	everywhere	ADV
ijassa-111	19	49	except	except	SCONJ
ijassa-111	19	50	,	,	PUNCT
ijassa-111	19	51	possibly	possibly	ADV
ijassa-111	19	52	,	,	PUNCT
ijassa-111	19	53	on	on	ADP
ijassa-111	19	54	singular	singular	ADJ
ijassa-111	19	55	sets	set	NOUN
ijassa-111	19	56	;	;	PUNCT
ijassa-111	19	57	(	(	PUNCT
ijassa-111	19	58	2	2	X
ijassa-111	19	59	)	)	PUNCT
ijassa-111	19	60	the	the	DET
ijassa-111	19	61	preservation	preservation	NOUN
ijassa-111	19	62	of	of	ADP
ijassa-111	19	63	the	the	DET
ijassa-111	19	64	metric	metric	ADJ
ijassa-111	19	65	signature	signature	NOUN
ijassa-111	19	66	at	at	ADP
ijassa-111	19	67	each	each	DET
ijassa-111	19	68	point	point	NOUN
ijassa-111	19	69	of	of	ADP
ijassa-111	19	70	the	the	DET
ijassa-111	19	71	space	space	NOUN
ijassa-111	19	72	.	.	PUNCT
ijassa-111	20	1	note	note	VERB
ijassa-111	20	2	that	that	SCONJ
ijassa-111	20	3	the	the	DET
ijassa-111	20	4	metric	metric	ADJ
ijassa-111	20	5	smoothness	smoothness	ADJ
ijassa-111	20	6	condition	condition	NOUN
ijassa-111	20	7	is	be	AUX
ijassa-111	20	8	stated	state	VERB
ijassa-111	20	9	in	in	ADP
ijassa-111	20	10	a	a	DET
ijassa-111	20	11	somewhat	somewhat	ADV
ijassa-111	20	12	relaxed	relaxed	ADJ
ijassa-111	20	13	form	form	NOUN
ijassa-111	20	14	in	in	ADP
ijassa-111	20	15	order	order	NOUN
ijassa-111	20	16	to	to	PART
ijassa-111	20	17	make	make	VERB
ijassa-111	20	18	it	it	PRON
ijassa-111	20	19	possible	possible	ADJ
ijassa-111	20	20	to	to	PART
ijassa-111	20	21	consider	consider	VERB
ijassa-111	20	22	pseudo	pseudo	NOUN
ijassa-111	20	23	-	-	ADJ
ijassa-111	20	24	riemannian	riemannian	ADJ
ijassa-111	20	25	spaces	space	NOUN
ijassa-111	20	26	with	with	ADP
ijassa-111	20	27	discontinuous	discontinuous	ADJ
ijassa-111	20	28	scalar	scalar	ADJ
ijassa-111	20	29	curvature	curvature	NOUN
ijassa-111	20	30	.	.	PUNCT
ijassa-111	21	1	note	note	VERB
ijassa-111	21	2	that	that	SCONJ
ijassa-111	21	3	the	the	DET
ijassa-111	21	4	space	space	NOUN
ijassa-111	21	5	structure	structure	NOUN
ijassa-111	21	6	and	and	CCONJ
ijassa-111	21	7	dimension	dimension	NOUN
ijassa-111	21	8	chosen	choose	VERB
ijassa-111	21	9	above	above	ADV
ijassa-111	21	10	are	be	AUX
ijassa-111	21	11	not	not	PART
ijassa-111	21	12	regarded	regard	VERB
ijassa-111	21	13	to	to	PART
ijassa-111	21	14	be	be	AUX
ijassa-111	21	15	final	final	ADJ
ijassa-111	21	16	.	.	PUNCT
ijassa-111	22	1	they	they	PRON
ijassa-111	22	2	are	be	AUX
ijassa-111	22	3	only	only	ADV
ijassa-111	22	4	sufficient	sufficient	ADJ
ijassa-111	22	5	for	for	ADP
ijassa-111	22	6	constructing	construct	VERB
ijassa-111	22	7	geometric	geometric	ADJ
ijassa-111	22	8	gravity	gravity	NOUN
ijassa-111	22	9	theory	theory	NOUN
ijassa-111	22	10	;	;	PUNCT
ijassa-111	22	11	thus	thus	ADV
ijassa-111	22	12	,	,	PUNCT
ijassa-111	22	13	we	we	PRON
ijassa-111	22	14	introduce	introduce	VERB
ijassa-111	22	15	them	they	PRON
ijassa-111	22	16	as	as	ADP
ijassa-111	22	17	sufficient	sufficient	ADJ
ijassa-111	22	18	conditions	condition	NOUN
ijassa-111	22	19	for	for	ADP
ijassa-111	22	20	constructing	construct	VERB
ijassa-111	22	21	an	an	DET
ijassa-111	22	22	adequate	adequate	ADJ
ijassa-111	22	23	theory	theory	NOUN
ijassa-111	22	24	rather	rather	ADV
ijassa-111	22	25	than	than	ADP
ijassa-111	22	26	as	as	ADP
ijassa-111	22	27	fundamental	fundamental	ADJ
ijassa-111	22	28	postulates	postulate	NOUN
ijassa-111	22	29	.	.	PUNCT
ijassa-111	23	1	we	we	PRON
ijassa-111	23	2	proceed	proceed	VERB
ijassa-111	23	3	to	to	PART
ijassa-111	23	4	state	state	VERB
ijassa-111	23	5	two	two	NUM
ijassa-111	23	6	postulates	postulate	NOUN
ijassa-111	23	7	of	of	ADP
ijassa-111	23	8	geometric	geometric	ADJ
ijassa-111	23	9	gravity	gravity	NOUN
ijassa-111	23	10	theory	theory	NOUN
ijassa-111	23	11	.	.	PUNCT
ijassa-111	24	1	as	as	SCONJ
ijassa-111	24	2	mentioned	mention	VERB
ijassa-111	24	3	above	above	ADV
ijassa-111	24	4	,	,	PUNCT
ijassa-111	24	5	the	the	DET
ijassa-111	24	6	main	main	ADJ
ijassa-111	24	7	physical	physical	ADJ
ijassa-111	24	8	objects	object	NOUN
ijassa-111	24	9	of	of	ADP
ijassa-111	24	10	gravity	gravity	NOUN
ijassa-111	24	11	theory	theory	NOUN
ijassa-111	24	12	are	be	AUX
ijassa-111	24	13	the	the	DET
ijassa-111	24	14	gravitational	gravitational	ADJ
ijassa-111	24	15	field	field	NOUN
ijassa-111	24	16	and	and	CCONJ
ijassa-111	24	17	the	the	DET
ijassa-111	24	18	distribution	distribution	NOUN
ijassa-111	24	19	density	density	NOUN
ijassa-111	24	20	of	of	ADP
ijassa-111	24	21	the	the	DET
ijassa-111	24	22	matter	matter	NOUN
ijassa-111	24	23	mass	mass	PROPN
ijassa-111	24	24	.	.	PUNCT
ijassa-111	25	1	the	the	DET
ijassa-111	25	2	objective	objective	NOUN
ijassa-111	25	3	of	of	ADP
ijassa-111	25	4	gravity	gravity	NOUN
ijassa-111	25	5	theory	theory	NOUN
ijassa-111	25	6	is	be	AUX
ijassa-111	25	7	determining	determine	VERB
ijassa-111	25	8	laws	law	NOUN
ijassa-111	25	9	governing	govern	VERB
ijassa-111	25	10	the	the	DET
ijassa-111	25	11	interaction	interaction	NOUN
ijassa-111	25	12	of	of	ADP
ijassa-111	25	13	the	the	DET
ijassa-111	25	14	gravitational	gravitational	ADJ
ijassa-111	25	15	field	field	NOUN
ijassa-111	25	16	with	with	ADP
ijassa-111	25	17	the	the	DET
ijassa-111	25	18	distribution	distribution	NOUN
ijassa-111	25	19	density	density	NOUN
ijassa-111	25	20	of	of	ADP
ijassa-111	25	21	gravitational	gravitational	ADJ
ijassa-111	25	22	mass	mass	PROPN
ijassa-111	25	23	.	.	PUNCT
ijassa-111	26	1	the	the	DET
ijassa-111	26	2	first	first	ADJ
ijassa-111	26	3	postulate	postulate	NOUN
ijassa-111	26	4	of	of	ADP
ijassa-111	26	5	geometric	geometric	ADJ
ijassa-111	26	6	gravity	gravity	NOUN
ijassa-111	26	7	theory	theory	NOUN
ijassa-111	26	8	can	can	AUX
ijassa-111	26	9	be	be	AUX
ijassa-111	26	10	stated	state	VERB
ijassa-111	26	11	as	as	SCONJ
ijassa-111	26	12	follows	follow	VERB
ijassa-111	26	13	.	.	PUNCT
ijassa-111	27	1	postulate	postulate	VERB
ijassa-111	27	2	1	1	NUM
ijassa-111	27	3	.	.	PUNCT
ijassa-111	28	1	the	the	DET
ijassa-111	28	2	gravitational	gravitational	ADJ
ijassa-111	28	3	field	field	NOUN
ijassa-111	28	4	is	be	AUX
ijassa-111	28	5	a	a	DET
ijassa-111	28	6	metric	metric	NOUN
ijassa-111	28	7	of	of	ADP
ijassa-111	28	8	a	a	DET
ijassa-111	28	9	pseudo	pseudo	NOUN
ijassa-111	28	10	-	-	ADJ
ijassa-111	28	11	riemannian	riemannian	ADJ
ijassa-111	28	12	space	space	NOUN
ijassa-111	28	13	.	.	PUNCT
ijassa-111	29	1	this	this	DET
ijassa-111	29	2	assertion	assertion	NOUN
ijassa-111	29	3	is	be	AUX
ijassa-111	29	4	the	the	DET
ijassa-111	29	5	basis	basis	NOUN
ijassa-111	29	6	of	of	ADP
ijassa-111	29	7	grt	grt	PROPN
ijassa-111	29	8	and	and	CCONJ
ijassa-111	29	9	does	do	AUX
ijassa-111	29	10	not	not	PART
ijassa-111	29	11	need	need	VERB
ijassa-111	29	12	any	any	DET
ijassa-111	29	13	comments	comment	NOUN
ijassa-111	29	14	.	.	PUNCT
ijassa-111	30	1	before	before	ADP
ijassa-111	30	2	stating	state	VERB
ijassa-111	30	3	the	the	DET
ijassa-111	30	4	second	second	ADJ
ijassa-111	30	5	postulate	postulate	NOUN
ijassa-111	30	6	,	,	PUNCT
ijassa-111	30	7	we	we	PRON
ijassa-111	30	8	introduce	introduce	VERB
ijassa-111	30	9	the	the	DET
ijassa-111	30	10	following	following	ADJ
ijassa-111	30	11	notation[1	notation[1	PROPN
ijassa-111	30	12	-	-	SYM
ijassa-111	30	13	2	2	NUM
ijassa-111	30	14	]	]	PUNCT
ijassa-111	30	15	:	:	PUNCT
ijassa-111	30	16	γk	γk	X
ijassa-111	30	17	ij	ij	NOUN
ijassa-111	30	18	is	be	AUX
ijassa-111	30	19	the	the	DET
ijassa-111	30	20	pseudo	pseudo	NOUN
ijassa-111	30	21	-	-	ADJ
ijassa-111	30	22	riemannian	riemannian	ADJ
ijassa-111	30	23	connection	connection	NOUN
ijassa-111	30	24	,	,	PUNCT
ijassa-111	30	25	which	which	PRON
ijassa-111	30	26	is	be	AUX
ijassa-111	30	27	defined	define	VERB
ijassa-111	30	28	by	by	ADP
ijassa-111	30	29	γk	γk	PROPN
ijassa-111	30	30	ij	ij	INTJ
ijassa-111	30	31	=	=	SYM
ijassa-111	30	32	−1	−1	NOUN
ijassa-111	30	33	2	2	NUM
ijassa-111	30	34	gkl	gkl	NOUN
ijassa-111	30	35	(	(	PUNCT
ijassa-111	30	36	∂glj	∂glj	PUNCT
ijassa-111	30	37	∂xi	∂xi	NOUN
ijassa-111	30	38	+	+	CCONJ
ijassa-111	30	39	∂gli	∂gli	ADJ
ijassa-111	30	40	∂xj	∂xj	NOUN
ijassa-111	30	41	+	+	CCONJ
ijassa-111	30	42	∂gij	∂gij	PUNCT
ijassa-111	30	43	∂xl	∂xl	PROPN
ijassa-111	30	44	)	)	PUNCT
ijassa-111	30	45	;	;	PUNCT
ijassa-111	30	46	(	(	PUNCT
ijassa-111	30	47	1	1	X
ijassa-111	30	48	)	)	PUNCT
ijassa-111	30	49	rij	rij	X
ijassa-111	30	50	is	be	AUX
ijassa-111	30	51	the	the	DET
ijassa-111	30	52	ricci	ricci	PROPN
ijassa-111	30	53	tensor	tensor	NOUN
ijassa-111	30	54	,	,	PUNCT
ijassa-111	30	55	that	that	ADV
ijassa-111	30	56	is	is	ADV
ijassa-111	30	57	,	,	PUNCT
ijassa-111	30	58	rij	rij	ADJ
ijassa-111	30	59	=	=	SYM
ijassa-111	30	60	γk	γk	PROPN
ijassa-111	30	61	ij	ij	PROPN
ijassa-111	30	62	∂xk	∂xk	PROPN
ijassa-111	30	63	−	−	PROPN
ijassa-111	30	64	γk	γk	PROPN
ijassa-111	30	65	ik	ik	PROPN
ijassa-111	30	66	∂xj	∂xj	PROPN
ijassa-111	30	67	+	+	CCONJ
ijassa-111	31	1	γk	γk	PROPN
ijassa-111	31	2	pkγ	pkγ	NOUN
ijassa-111	31	3	p	p	X
ijassa-111	31	4	ij	ij	INTJ
ijassa-111	31	5	−	−	PROPN
ijassa-111	31	6	γk	γk	PROPN
ijassa-111	31	7	pjγ	pjγ	PROPN
ijassa-111	31	8	p	p	PROPN
ijassa-111	31	9	ik	ik	PROPN
ijassa-111	31	10	;	;	PUNCT
ijassa-111	31	11	(	(	PUNCT
ijassa-111	31	12	2	2	X
ijassa-111	31	13	)	)	PUNCT
ijassa-111	31	14	r	r	NOUN
ijassa-111	31	15	is	be	AUX
ijassa-111	31	16	the	the	DET
ijassa-111	31	17	scalar	scalar	ADJ
ijassa-111	31	18	curvature	curvature	NOUN
ijassa-111	31	19	,	,	PUNCT
ijassa-111	31	20	that	that	ADV
ijassa-111	31	21	is	is	ADV
ijassa-111	31	22	,	,	PUNCT
ijassa-111	31	23	r	r	NOUN
ijassa-111	31	24	=	=	SYM
ijassa-111	31	25	gijrij	gijrij	NOUN
ijassa-111	31	26	;	;	PUNCT
ijassa-111	31	27	(	(	PUNCT
ijassa-111	31	28	3	3	X
ijassa-111	31	29	)	)	PUNCT
ijassa-111	31	30	where	where	SCONJ
ijassa-111	31	31	the	the	DET
ijassa-111	31	32	summation	summation	NOUN
ijassa-111	31	33	over	over	ADP
ijassa-111	31	34	repeated	repeat	VERB
ijassa-111	31	35	indices	index	NOUN
ijassa-111	31	36	is	be	AUX
ijassa-111	31	37	implied	imply	VERB
ijassa-111	31	38	;	;	PUNCT
ijassa-111	31	39	and	and	CCONJ
ijassa-111	31	40	is	be	AUX
ijassa-111	31	41	the	the	DET
ijassa-111	31	42	contravariant	contravariant	PROPN
ijassa-111	31	43	metric	metric	ADJ
ijassa-111	31	44	tensor	tensor	NOUN
ijassa-111	31	45	.	.	PUNCT
ijassa-111	32	1	postulate	postulate	VERB
ijassa-111	32	2	2′	2′	NUM
ijassa-111	32	3	(	(	PUNCT
ijassa-111	32	4	weak	weak	ADJ
ijassa-111	32	5	statement	statement	NOUN
ijassa-111	32	6	)	)	PUNCT
ijassa-111	32	7	.	.	PUNCT
ijassa-111	33	1	if	if	SCONJ
ijassa-111	33	2	the	the	DET
ijassa-111	33	3	mass	mass	ADJ
ijassa-111	33	4	density	density	NOUN
ijassa-111	33	5	of	of	ADP
ijassa-111	33	6	the	the	DET
ijassa-111	33	7	matter	matter	NOUN
ijassa-111	33	8	is	be	AUX
ijassa-111	33	9	nonzero	nonzero	NOUN
ijassa-111	33	10	at	at	ADP
ijassa-111	33	11	some	some	DET
ijassa-111	33	12	point	point	NOUN
ijassa-111	33	13	of	of	ADP
ijassa-111	33	14	the	the	DET
ijassa-111	33	15	space	space	NOUN
ijassa-111	33	16	,	,	PUNCT
ijassa-111	33	17	then	then	ADV
ijassa-111	33	18	so	so	ADV
ijassa-111	33	19	is	be	AUX
ijassa-111	33	20	the	the	DET
ijassa-111	33	21	scalar	scalar	ADJ
ijassa-111	33	22	curvature	curvature	NOUN
ijassa-111	33	23	of	of	ADP
ijassa-111	33	24	the	the	DET
ijassa-111	33	25	space	space	NOUN
ijassa-111	33	26	at	at	ADP
ijassa-111	33	27	this	this	DET
ijassa-111	33	28	point	point	NOUN
ijassa-111	33	29	,	,	PUNCT
ijassa-111	33	30	260	260	NUM
ijassa-111	33	31	n.n	n.n	PROPN
ijassa-111	33	32	.	.	PROPN
ijassa-111	33	33	popov	popov	PROPN
ijassa-111	33	34	:	:	PUNCT
ijassa-111	33	35	a	a	DET
ijassa-111	33	36	geometric	geometric	ADJ
ijassa-111	33	37	interpretation	interpretation	NOUN
ijassa-111	33	38	of	of	ADP
ijassa-111	33	39	gravity	gravity	NOUN
ijassa-111	33	40	theory	theory	NOUN
ijassa-111	33	41	and	and	CCONJ
ijassa-111	33	42	vice	vice	NOUN
ijassa-111	33	43	versa	versa	ADV
ijassa-111	33	44	.	.	PUNCT
ijassa-111	34	1	this	this	DET
ijassa-111	34	2	postulate	postulate	NOUN
ijassa-111	34	3	says	say	VERB
ijassa-111	34	4	nothing	nothing	PRON
ijassa-111	34	5	about	about	ADP
ijassa-111	34	6	the	the	DET
ijassa-111	34	7	form	form	NOUN
ijassa-111	34	8	of	of	ADP
ijassa-111	34	9	the	the	DET
ijassa-111	34	10	dependence	dependence	NOUN
ijassa-111	34	11	between	between	ADP
ijassa-111	34	12	these	these	DET
ijassa-111	34	13	scalar	scalar	ADJ
ijassa-111	34	14	functions	function	NOUN
ijassa-111	34	15	.	.	PUNCT
ijassa-111	35	1	it	it	PRON
ijassa-111	35	2	only	only	ADV
ijassa-111	35	3	indicates	indicate	VERB
ijassa-111	35	4	the	the	DET
ijassa-111	35	5	existence	existence	NOUN
ijassa-111	35	6	of	of	ADP
ijassa-111	35	7	a	a	DET
ijassa-111	35	8	relation	relation	NOUN
ijassa-111	35	9	between	between	ADP
ijassa-111	35	10	them	they	PRON
ijassa-111	35	11	.	.	PUNCT
ijassa-111	36	1	to	to	PART
ijassa-111	36	2	determine	determine	VERB
ijassa-111	36	3	this	this	DET
ijassa-111	36	4	relation	relation	NOUN
ijassa-111	36	5	,	,	PUNCT
ijassa-111	36	6	we	we	PRON
ijassa-111	36	7	use	use	VERB
ijassa-111	36	8	two	two	NUM
ijassa-111	36	9	principles	principle	NOUN
ijassa-111	36	10	;	;	PUNCT
ijassa-111	36	11	namely	namely	ADV
ijassa-111	36	12	,	,	PUNCT
ijassa-111	36	13	the	the	DET
ijassa-111	36	14	principle	principle	NOUN
ijassa-111	36	15	of	of	ADP
ijassa-111	36	16	minimal	minimal	ADJ
ijassa-111	36	17	action	action	NOUN
ijassa-111	36	18	and	and	CCONJ
ijassa-111	36	19	the	the	DET
ijassa-111	36	20	correspondence	correspondence	NOUN
ijassa-111	36	21	principle	principle	NOUN
ijassa-111	36	22	.	.	PUNCT
ijassa-111	37	1	these	these	DET
ijassa-111	37	2	principles	principle	NOUN
ijassa-111	37	3	make	make	VERB
ijassa-111	37	4	it	it	PRON
ijassa-111	37	5	possible	possible	ADJ
ijassa-111	37	6	to	to	PART
ijassa-111	37	7	derive	derive	VERB
ijassa-111	37	8	the	the	DET
ijassa-111	37	9	fundamental	fundamental	ADJ
ijassa-111	37	10	equation	equation	NOUN
ijassa-111	37	11	of	of	ADP
ijassa-111	37	12	geometric	geometric	ADJ
ijassa-111	37	13	gravity	gravity	NOUN
ijassa-111	37	14	theory	theory	NOUN
ijassa-111	37	15	and	and	CCONJ
ijassa-111	37	16	refine	refine	VERB
ijassa-111	37	17	the	the	DET
ijassa-111	37	18	statement	statement	NOUN
ijassa-111	37	19	of	of	ADP
ijassa-111	37	20	postulate	postulate	NOUN
ijassa-111	37	21	2	2	NUM
ijassa-111	37	22	.	.	NOUN
ijassa-111	37	23	3	3	NUM
ijassa-111	37	24	the	the	DET
ijassa-111	37	25	third	third	ADJ
ijassa-111	37	26	postulate	postulate	NOUN
ijassa-111	37	27	,	,	PUNCT
ijassa-111	37	28	the	the	DET
ijassa-111	37	29	fundamental	fundamental	ADJ
ijassa-111	37	30	equation	equation	NOUN
ijassa-111	37	31	of	of	ADP
ijassa-111	37	32	gravity	gravity	NOUN
ijassa-111	37	33	theory	theory	NOUN
ijassa-111	37	34	,	,	PUNCT
ijassa-111	37	35	and	and	CCONJ
ijassa-111	37	36	the	the	DET
ijassa-111	37	37	strengthened	strengthen	VERB
ijassa-111	37	38	statement	statement	NOUN
ijassa-111	37	39	of	of	ADP
ijassa-111	37	40	postulate	postulate	NOUN
ijassa-111	37	41	2′	2′	NUM
ijassa-111	37	42	according	accord	VERB
ijassa-111	37	43	to	to	PART
ijassa-111	37	44	postulate	postulate	VERB
ijassa-111	37	45	2′	2′	NUM
ijassa-111	37	46	,	,	PUNCT
ijassa-111	37	47	there	there	PRON
ijassa-111	37	48	is	be	VERB
ijassa-111	37	49	a	a	DET
ijassa-111	37	50	dependence	dependence	NOUN
ijassa-111	37	51	between	between	ADP
ijassa-111	37	52	the	the	DET
ijassa-111	37	53	scalar	scalar	ADJ
ijassa-111	37	54	function	function	NOUN
ijassa-111	37	55	of	of	ADP
ijassa-111	37	56	the	the	DET
ijassa-111	37	57	matter	matter	NOUN
ijassa-111	37	58	mass	mass	NOUN
ijassa-111	37	59	density	density	NOUN
ijassa-111	37	60	and	and	CCONJ
ijassa-111	37	61	the	the	DET
ijassa-111	37	62	function	function	NOUN
ijassa-111	37	63	of	of	ADP
ijassa-111	37	64	the	the	DET
ijassa-111	37	65	space	space	NOUN
ijassa-111	37	66	scalar	scalar	NOUN
ijassa-111	37	67	curvature	curvature	NOUN
ijassa-111	37	68	.	.	PUNCT
ijassa-111	38	1	to	to	PART
ijassa-111	38	2	find	find	VERB
ijassa-111	38	3	this	this	DET
ijassa-111	38	4	dependence	dependence	NOUN
ijassa-111	38	5	,	,	PUNCT
ijassa-111	38	6	we	we	PRON
ijassa-111	38	7	introduce	introduce	VERB
ijassa-111	38	8	a	a	DET
ijassa-111	38	9	composite	composite	ADJ
ijassa-111	38	10	scalar	scalar	ADJ
ijassa-111	38	11	function	function	NOUN
ijassa-111	38	12	χ	χ	X
ijassa-111	38	13	(	(	PUNCT
ijassa-111	38	14	ρ	ρ	PROPN
ijassa-111	38	15	)	)	PUNCT
ijassa-111	38	16	,	,	PUNCT
ijassa-111	38	17	which	which	PRON
ijassa-111	38	18	depends	depend	VERB
ijassa-111	38	19	on	on	ADP
ijassa-111	38	20	the	the	DET
ijassa-111	38	21	matter	matter	NOUN
ijassa-111	38	22	mass	mass	NOUN
ijassa-111	38	23	density	density	NOUN
ijassa-111	38	24	ρ	ρ	PROPN
ijassa-111	38	25	in	in	ADP
ijassa-111	38	26	an	an	DET
ijassa-111	38	27	unknown	unknown	ADJ
ijassa-111	38	28	way	way	NOUN
ijassa-111	38	29	,	,	PUNCT
ijassa-111	38	30	and	and	CCONJ
ijassa-111	38	31	a	a	DET
ijassa-111	38	32	scalar	scalar	ADJ
ijassa-111	38	33	curvature	curvature	NOUN
ijassa-111	38	34	function	function	NOUN
ijassa-111	38	35	r(gij	r(gij	PROPN
ijassa-111	38	36	)	)	PUNCT
ijassa-111	38	37	,	,	PUNCT
ijassa-111	38	38	which	which	PRON
ijassa-111	38	39	is	be	AUX
ijassa-111	38	40	a	a	DET
ijassa-111	38	41	composite	composite	ADJ
ijassa-111	38	42	function	function	NOUN
ijassa-111	38	43	depending	depend	VERB
ijassa-111	38	44	on	on	ADP
ijassa-111	38	45	the	the	DET
ijassa-111	38	46	metric	metric	ADJ
ijassa-111	38	47	gij	gij	NOUN
ijassa-111	38	48	.	.	PUNCT
ijassa-111	39	1	the	the	DET
ijassa-111	39	2	general	general	ADJ
ijassa-111	39	3	form	form	NOUN
ijassa-111	39	4	of	of	ADP
ijassa-111	39	5	the	the	DET
ijassa-111	39	6	gravitational	gravitational	ADJ
ijassa-111	39	7	field	field	NOUN
ijassa-111	39	8	equations	equation	NOUN
ijassa-111	39	9	can	can	AUX
ijassa-111	39	10	be	be	AUX
ijassa-111	39	11	obtained	obtain	VERB
ijassa-111	39	12	by	by	ADP
ijassa-111	39	13	applying	apply	VERB
ijassa-111	39	14	the	the	DET
ijassa-111	39	15	principle	principle	NOUN
ijassa-111	39	16	of	of	ADP
ijassa-111	39	17	minimal	minimal	ADJ
ijassa-111	39	18	action	action	NOUN
ijassa-111	39	19	.	.	PUNCT
ijassa-111	40	1	the	the	DET
ijassa-111	40	2	field	field	NOUN
ijassa-111	40	3	equations	equation	NOUN
ijassa-111	40	4	are	be	AUX
ijassa-111	40	5	obtained	obtain	VERB
ijassa-111	40	6	as	as	ADP
ijassa-111	40	7	the	the	DET
ijassa-111	40	8	eulerclagrange	eulerclagrange	NOUN
ijassa-111	40	9	equations	equation	NOUN
ijassa-111	40	10	under	under	ADP
ijassa-111	40	11	the	the	DET
ijassa-111	40	12	variation	variation	NOUN
ijassa-111	40	13	of	of	ADP
ijassa-111	40	14	the	the	DET
ijassa-111	40	15	field	field	NOUN
ijassa-111	40	16	action	action	NOUN
ijassa-111	40	17	.	.	PUNCT
ijassa-111	41	1	for	for	ADP
ijassa-111	41	2	the	the	DET
ijassa-111	41	3	field	field	NOUN
ijassa-111	41	4	action	action	NOUN
ijassa-111	41	5	functional	functional	ADJ
ijassa-111	41	6	we	we	PRON
ijassa-111	41	7	take	take	VERB
ijassa-111	41	8	the	the	DET
ijassa-111	41	9	quantity	quantity	NOUN
ijassa-111	41	10	sg	sg	ADP
ijassa-111	41	11	=	=	SYM
ijassa-111	41	12	∫	∫	PROPN
ijassa-111	41	13	ω	ω	PROPN
ijassa-111	41	14	(	(	PUNCT
ijassa-111	41	15	r	r	NOUN
ijassa-111	41	16	+	+	NUM
ijassa-111	41	17	χ	χ	NOUN
ijassa-111	41	18	)	)	PUNCT
ijassa-111	42	1	√	√	NUM
ijassa-111	42	2	|g|d4x	|g|d4x	NOUN
ijassa-111	42	3	,	,	PUNCT
ijassa-111	42	4	(	(	PUNCT
ijassa-111	42	5	4	4	X
ijassa-111	42	6	)	)	PUNCT
ijassa-111	42	7	where	where	SCONJ
ijassa-111	42	8	dω	dω	NOUN
ijassa-111	42	9	=	=	SYM
ijassa-111	42	10	√	√	NUM
ijassa-111	42	11	|g|d4x	|g|d4x	NOUN
ijassa-111	42	12	is	be	AUX
ijassa-111	42	13	the	the	DET
ijassa-111	42	14	standard	standard	ADJ
ijassa-111	42	15	volume	volume	NOUN
ijassa-111	42	16	4	4	NUM
ijassa-111	42	17	-	-	PUNCT
ijassa-111	42	18	form	form	NOUN
ijassa-111	42	19	on	on	ADP
ijassa-111	42	20	the	the	DET
ijassa-111	42	21	pseudo	pseudo	NOUN
ijassa-111	42	22	-	-	ADJ
ijassa-111	42	23	riemannian	riemannian	ADJ
ijassa-111	42	24	space	space	NOUN
ijassa-111	42	25	,	,	PUNCT
ijassa-111	42	26	g	g	PROPN
ijassa-111	42	27	=	=	SYM
ijassa-111	42	28	det(gij	det(gij	PROPN
ijassa-111	42	29	)	)	PUNCT
ijassa-111	42	30	,	,	PUNCT
ijassa-111	42	31	and	and	CCONJ
ijassa-111	42	32	the	the	DET
ijassa-111	42	33	integral	integral	ADJ
ijassa-111	42	34	is	be	AUX
ijassa-111	42	35	the	the	DET
ijassa-111	42	36	whole	whole	ADJ
ijassa-111	42	37	3	3	NUM
ijassa-111	42	38	-	-	PUNCT
ijassa-111	42	39	space	space	NOUN
ijassa-111	42	40	(	(	PUNCT
ijassa-111	42	41	x1	x1	PROPN
ijassa-111	42	42	,	,	PUNCT
ijassa-111	42	43	x2	x2	PROPN
ijassa-111	42	44	,	,	PUNCT
ijassa-111	42	45	x3	x3	ADJ
ijassa-111	42	46	)	)	PUNCT
ijassa-111	42	47	and	and	CCONJ
ijassa-111	42	48	over	over	ADP
ijassa-111	42	49	the	the	DET
ijassa-111	42	50	interval	interval	NOUN
ijassa-111	42	51	x41	x41	NOUN
ijassa-111	42	52	≤	≤	PROPN
ijassa-111	42	53	x4	x4	PROPN
ijassa-111	42	54	≤	≤	ADJ
ijassa-111	42	55	x42	x42	NOUN
ijassa-111	42	56	of	of	ADP
ijassa-111	42	57	the	the	DET
ijassa-111	42	58	time	time	NOUN
ijassa-111	42	59	coordinate	coordinate	NOUN
ijassa-111	42	60	x4	x4	PROPN
ijassa-111	42	61	.	.	PUNCT
ijassa-111	43	1	postulate	postulate	VERB
ijassa-111	43	2	3	3	NUM
ijassa-111	43	3	.	.	PUNCT
ijassa-111	44	1	in	in	ADP
ijassa-111	44	2	geometric	geometric	ADJ
ijassa-111	44	3	gravity	gravity	NOUN
ijassa-111	44	4	theory	theory	NOUN
ijassa-111	44	5	,	,	PUNCT
ijassa-111	44	6	the	the	DET
ijassa-111	44	7	following	follow	VERB
ijassa-111	44	8	relation	relation	NOUN
ijassa-111	44	9	holds	hold	VERB
ijassa-111	44	10	:	:	PUNCT
ijassa-111	44	11	δsg	δsg	NOUN
ijassa-111	44	12	δgij	δgij	NOUN
ijassa-111	44	13	=	=	SYM
ijassa-111	44	14	0	0	X
ijassa-111	44	15	.	.	PUNCT
ijassa-111	45	1	postulate	postulate	VERB
ijassa-111	45	2	3	3	NUM
ijassa-111	45	3	means	mean	VERB
ijassa-111	45	4	that	that	SCONJ
ijassa-111	45	5	the	the	DET
ijassa-111	45	6	sought	seek	VERB
ijassa-111	45	7	dependence	dependence	NOUN
ijassa-111	45	8	between	between	ADP
ijassa-111	45	9	the	the	DET
ijassa-111	45	10	composite	composite	ADJ
ijassa-111	45	11	functions	function	NOUN
ijassa-111	45	12	r(g	r(g	NUM
ijassa-111	45	13	)	)	PUNCT
ijassa-111	45	14	and	and	CCONJ
ijassa-111	45	15	χ(ρ	χ(ρ	NOUN
ijassa-111	45	16	)	)	PUNCT
ijassa-111	45	17	minimizes	minimize	VERB
ijassa-111	45	18	the	the	DET
ijassa-111	45	19	action	action	NOUN
ijassa-111	45	20	functional	functional	ADJ
ijassa-111	45	21	(	(	PUNCT
ijassa-111	45	22	4	4	NUM
ijassa-111	45	23	)	)	PUNCT
ijassa-111	45	24	with	with	ADP
ijassa-111	45	25	respect	respect	NOUN
ijassa-111	45	26	to	to	ADP
ijassa-111	45	27	the	the	DET
ijassa-111	45	28	contravariance	contravariance	NOUN
ijassa-111	45	29	metric	metric	NOUN
ijassa-111	45	30	of	of	ADP
ijassa-111	45	31	the	the	DET
ijassa-111	45	32	pseudo	pseudo	NOUN
ijassa-111	45	33	-	-	ADJ
ijassa-111	45	34	riemannian	riemannian	ADJ
ijassa-111	45	35	space	space	NOUN
ijassa-111	45	36	gij	gij	NOUN
ijassa-111	45	37	.	.	PUNCT
ijassa-111	46	1	theorem	theorem	VERB
ijassa-111	46	2	1	1	NUM
ijassa-111	46	3	.	.	PUNCT
ijassa-111	47	1	if	if	SCONJ
ijassa-111	47	2	postulate	postulate	VERB
ijassa-111	47	3	3	3	NUM
ijassa-111	47	4	holds	hold	VERB
ijassa-111	47	5	for	for	ADP
ijassa-111	47	6	functional	functional	ADJ
ijassa-111	47	7	(	(	PUNCT
ijassa-111	47	8	4	4	NUM
ijassa-111	47	9	)	)	PUNCT
ijassa-111	47	10	,	,	PUNCT
ijassa-111	47	11	then	then	ADV
ijassa-111	47	12	rij	rij	VERB
ijassa-111	47	13	−	−	NUM
ijassa-111	47	14	1	1	NUM
ijassa-111	47	15	2	2	NUM
ijassa-111	47	16	rgij	rgij	NOUN
ijassa-111	47	17	=	=	NOUN
ijassa-111	47	18	1	1	NUM
ijassa-111	47	19	2	2	NUM
ijassa-111	47	20	χgij	χgij	NOUN
ijassa-111	47	21	.	.	PUNCT
ijassa-111	48	1	(	(	PUNCT
ijassa-111	48	2	5	5	X
ijassa-111	48	3	)	)	PUNCT
ijassa-111	48	4	proof	proof	NOUN
ijassa-111	48	5	.	.	PUNCT
ijassa-111	49	1	relation	relation	NOUN
ijassa-111	49	2	(	(	PUNCT
ijassa-111	49	3	4	4	NUM
ijassa-111	49	4	)	)	PUNCT
ijassa-111	49	5	implies	imply	VERB
ijassa-111	49	6	δsg	δsg	PROPN
ijassa-111	49	7	δgij	δgij	NOUN
ijassa-111	49	8	=	=	SYM
ijassa-111	49	9	δ	δ	PROPN
ijassa-111	49	10	∫	∫	PROPN
ijassa-111	49	11	ωr(g	ωr(g	PROPN
ijassa-111	49	12	)	)	PUNCT
ijassa-111	49	13	√	√	NUM
ijassa-111	49	14	|g|d4x	|g|d4x	NOUN
ijassa-111	49	15	δgij	δgij	NOUN
ijassa-111	49	16	+	+	CCONJ
ijassa-111	49	17	δ	δ	PROPN
ijassa-111	49	18	∫	∫	PROPN
ijassa-111	49	19	ω	ω	NUM
ijassa-111	49	20	χ(ρ	χ(ρ	NOUN
ijassa-111	49	21	)	)	PUNCT
ijassa-111	49	22	√	√	NUM
ijassa-111	49	23	|g|d4x	|g|d4x	NOUN
ijassa-111	49	24	δgij	δgij	NOUN
ijassa-111	49	25	.	.	PUNCT
ijassa-111	50	1	advances	advance	NOUN
ijassa-111	50	2	in	in	ADP
ijassa-111	50	3	systems	system	NOUN
ijassa-111	50	4	science	science	NOUN
ijassa-111	50	5	and	and	CCONJ
ijassa-111	50	6	applications	application	NOUN
ijassa-111	50	7	(	(	PUNCT
ijassa-111	50	8	2012	2012	NUM
ijassa-111	50	9	)	)	PUNCT
ijassa-111	50	10	vol.12	vol.12	NOUN
ijassa-111	50	11	no.3	no.3	VERB
ijassa-111	50	12	261	261	NUM
ijassa-111	50	13	the	the	DET
ijassa-111	50	14	first	first	ADJ
ijassa-111	50	15	term	term	NOUN
ijassa-111	50	16	is	be	AUX
ijassa-111	50	17	the	the	DET
ijassa-111	50	18	hilbert	hilbert	NOUN
ijassa-111	50	19	variational	variational	ADJ
ijassa-111	50	20	derivative[3	derivative[3	PROPN
ijassa-111	50	21	]	]	X
ijassa-111	50	22	δ	δ	PROPN
ijassa-111	50	23	∫	∫	PROPN
ijassa-111	50	24	ωr(g	ωr(g	PROPN
ijassa-111	50	25	)	)	PUNCT
ijassa-111	50	26	√	√	NUM
ijassa-111	50	27	|g|d4x	|g|d4x	NOUN
ijassa-111	50	28	δgij	δgij	NOUN
ijassa-111	50	29	=	=	SYM
ijassa-111	50	30	rij	rij	ADJ
ijassa-111	50	31	−	−	NOUN
ijassa-111	50	32	r	r	NOUN
ijassa-111	50	33	2	2	NUM
ijassa-111	50	34	gij	gij	NOUN
ijassa-111	50	35	.	.	PUNCT
ijassa-111	51	1	the	the	DET
ijassa-111	51	2	second	second	ADJ
ijassa-111	51	3	term	term	NOUN
ijassa-111	51	4	can	can	AUX
ijassa-111	51	5	be	be	AUX
ijassa-111	51	6	represented	represent	VERB
ijassa-111	51	7	in	in	ADP
ijassa-111	51	8	the	the	DET
ijassa-111	51	9	form	form	NOUN
ijassa-111	51	10	δ	δ	PROPN
ijassa-111	51	11	∫	∫	PROPN
ijassa-111	51	12	ω	ω	NUM
ijassa-111	51	13	χ(ρ	χ(ρ	NOUN
ijassa-111	51	14	)	)	PUNCT
ijassa-111	51	15	√	√	NUM
ijassa-111	51	16	|g|d4x	|g|d4x	NOUN
ijassa-111	51	17	δgij	δgij	NOUN
ijassa-111	51	18	=	=	SYM
ijassa-111	51	19	∫	∫	PROPN
ijassa-111	51	20	ω(δχ(ρ	ω(δχ(ρ	PROPN
ijassa-111	51	21	)	)	PUNCT
ijassa-111	51	22	√	√	VERB
ijassa-111	52	1	|g|+	|g|+	DET
ijassa-111	52	2	χ(ρ)δ	χ(ρ)δ	NOUN
ijassa-111	52	3	√	√	ADP
ijassa-111	52	4	|g|)d4x	|g|)d4x	NUM
ijassa-111	52	5	δgij	δgij	NOUN
ijassa-111	52	6	.	.	PUNCT
ijassa-111	53	1	taking	take	VERB
ijassa-111	53	2	into	into	ADP
ijassa-111	53	3	account	account	NOUN
ijassa-111	53	4	the	the	DET
ijassa-111	53	5	relation	relation	NOUN
ijassa-111	53	6	δ	δ	PROPN
ijassa-111	53	7	√	√	VERB
ijassa-111	53	8	|g|	|g|	PROPN
ijassa-111	53	9	=	=	SYM
ijassa-111	53	10	−1	−1	NOUN
ijassa-111	53	11	2	2	NUM
ijassa-111	53	12	√	√	NUM
ijassa-111	53	13	|g|gijδgij	|g|gijδgij	NOUN
ijassa-111	54	1	and	and	CCONJ
ijassa-111	54	2	the	the	DET
ijassa-111	54	3	fact	fact	NOUN
ijassa-111	54	4	that	that	SCONJ
ijassa-111	54	5	the	the	DET
ijassa-111	54	6	variation	variation	NOUN
ijassa-111	54	7	of	of	ADP
ijassa-111	54	8	the	the	DET
ijassa-111	54	9	scalar	scalar	NOUN
ijassa-111	54	10	.	.	PUNCT
ijassa-111	55	1	function	function	NOUN
ijassa-111	55	2	χ(ρ	χ(ρ	PROPN
ijassa-111	55	3	)	)	PUNCT
ijassa-111	55	4	,	,	PUNCT
ijassa-111	55	5	which	which	PRON
ijassa-111	55	6	does	do	AUX
ijassa-111	55	7	not	not	PART
ijassa-111	55	8	depend	depend	VERB
ijassa-111	55	9	on	on	ADP
ijassa-111	55	10	the	the	DET
ijassa-111	55	11	metric	metric	ADJ
ijassa-111	55	12	gij	gij	NOUN
ijassa-111	55	13	,	,	PUNCT
ijassa-111	55	14	vanishes	vanish	VERB
ijassa-111	55	15	,	,	PUNCT
ijassa-111	55	16	we	we	PRON
ijassa-111	55	17	obtain	obtain	VERB
ijassa-111	55	18	δ	δ	PROPN
ijassa-111	55	19	∫	∫	PROPN
ijassa-111	55	20	ω	ω	NUM
ijassa-111	55	21	χ(ρ	χ(ρ	NOUN
ijassa-111	55	22	)	)	PUNCT
ijassa-111	55	23	√	√	NUM
ijassa-111	55	24	|g|d4x	|g|d4x	NOUN
ijassa-111	55	25	δgij	δgij	NOUN
ijassa-111	55	26	=	=	PUNCT
ijassa-111	55	27	−χ(ρ	−χ(ρ	NOUN
ijassa-111	55	28	)	)	PUNCT
ijassa-111	55	29	2	2	NUM
ijassa-111	55	30	gij	gij	NOUN
ijassa-111	55	31	.	.	PUNCT
ijassa-111	56	1	it	it	PRON
ijassa-111	56	2	follows	follow	VERB
ijassa-111	56	3	that	that	SCONJ
ijassa-111	56	4	δsg	δsg	NOUN
ijassa-111	56	5	δgij	δgij	NOUN
ijassa-111	56	6	=	=	SYM
ijassa-111	56	7	rij	rij	ADJ
ijassa-111	56	8	−	−	NOUN
ijassa-111	56	9	r	r	NOUN
ijassa-111	56	10	2	2	NUM
ijassa-111	56	11	gij	gij	NOUN
ijassa-111	56	12	−	−	NOUN
ijassa-111	56	13	χ(ρ	χ(ρ	NOUN
ijassa-111	56	14	)	)	PUNCT
ijassa-111	56	15	2	2	NUM
ijassa-111	56	16	gij	gij	NOUN
ijassa-111	56	17	=	=	SYM
ijassa-111	56	18	0	0	PROPN
ijassa-111	56	19	,	,	PUNCT
ijassa-111	56	20	which	which	PRON
ijassa-111	56	21	completes	complete	VERB
ijassa-111	56	22	the	the	DET
ijassa-111	56	23	proof	proof	NOUN
ijassa-111	56	24	of	of	ADP
ijassa-111	56	25	the	the	DET
ijassa-111	56	26	theorem	theorem	NOUN
ijassa-111	56	27	.	.	PUNCT
ijassa-111	57	1	equation	equation	NOUN
ijassa-111	57	2	(	(	PUNCT
ijassa-111	57	3	5	5	NUM
ijassa-111	57	4	)	)	PUNCT
ijassa-111	57	5	implies	imply	VERB
ijassa-111	57	6	the	the	DET
ijassa-111	57	7	presence	presence	NOUN
ijassa-111	57	8	of	of	ADP
ijassa-111	57	9	a	a	DET
ijassa-111	57	10	linear	linear	ADJ
ijassa-111	57	11	dependence	dependence	NOUN
ijassa-111	57	12	between	between	ADP
ijassa-111	57	13	the	the	DET
ijassa-111	57	14	functions	function	NOUN
ijassa-111	57	15	r	r	NOUN
ijassa-111	57	16	and	and	CCONJ
ijassa-111	57	17	χ	χ	NOUN
ijassa-111	57	18	.	.	PUNCT
ijassa-111	58	1	indeed	indeed	ADV
ijassa-111	58	2	,	,	PUNCT
ijassa-111	58	3	multiplying	multiply	VERB
ijassa-111	58	4	the	the	DET
ijassa-111	58	5	rightand	rightand	NOUN
ijassa-111	58	6	left	left	ADJ
ijassa-111	58	7	-	-	PUNCT
ijassa-111	58	8	hand	hand	NOUN
ijassa-111	58	9	sides	side	NOUN
ijassa-111	58	10	of	of	ADP
ijassa-111	58	11	equation	equation	NOUN
ijassa-111	58	12	(	(	PUNCT
ijassa-111	58	13	5	5	NUM
ijassa-111	58	14	)	)	PUNCT
ijassa-111	58	15	by	by	ADP
ijassa-111	58	16	the	the	DET
ijassa-111	58	17	contravariant	contravariant	PROPN
ijassa-111	58	18	metric	metric	ADJ
ijassa-111	58	19	tensor	tensor	NOUN
ijassa-111	58	20	gij	gij	NOUN
ijassa-111	58	21	and	and	CCONJ
ijassa-111	58	22	convolving	convolve	VERB
ijassa-111	58	23	both	both	DET
ijassa-111	58	24	sides	side	NOUN
ijassa-111	58	25	over	over	ADP
ijassa-111	58	26	the	the	DET
ijassa-111	58	27	indices	index	NOUN
ijassa-111	58	28	i	i	PRON
ijassa-111	58	29	and	and	CCONJ
ijassa-111	58	30	j	j	PROPN
ijassa-111	58	31	,	,	PUNCT
ijassa-111	58	32	we	we	PRON
ijassa-111	58	33	obtain	obtain	VERB
ijassa-111	58	34	the	the	DET
ijassa-111	58	35	relation	relation	NOUN
ijassa-111	58	36	χ	χ	NOUN
ijassa-111	58	37	=	=	PUNCT
ijassa-111	58	38	−r	−r	ADJ
ijassa-111	58	39	2	2	NUM
ijassa-111	58	40	.	.	PUNCT
ijassa-111	59	1	(	(	PUNCT
ijassa-111	59	2	6	6	NUM
ijassa-111	59	3	)	)	PUNCT
ijassa-111	59	4	according	accord	VERB
ijassa-111	59	5	to	to	ADP
ijassa-111	59	6	(	(	PUNCT
ijassa-111	59	7	6	6	NUM
ijassa-111	59	8	)	)	PUNCT
ijassa-111	59	9	,	,	PUNCT
ijassa-111	59	10	the	the	DET
ijassa-111	59	11	scalar	scalar	ADJ
ijassa-111	59	12	curvature	curvature	NOUN
ijassa-111	59	13	r	r	NOUN
ijassa-111	59	14	turns	turn	VERB
ijassa-111	59	15	out	out	ADP
ijassa-111	59	16	to	to	PART
ijassa-111	59	17	depend	depend	VERB
ijassa-111	59	18	on	on	ADP
ijassa-111	59	19	the	the	DET
ijassa-111	59	20	matter	matter	NOUN
ijassa-111	59	21	mass	mass	PROPN
ijassa-111	59	22	density	density	PROPN
ijassa-111	59	23	ρ	ρ	PROPN
ijassa-111	59	24	.	.	PUNCT
ijassa-111	60	1	however	however	ADV
ijassa-111	60	2	,	,	PUNCT
ijassa-111	60	3	we	we	PRON
ijassa-111	60	4	do	do	AUX
ijassa-111	60	5	not	not	PART
ijassa-111	60	6	know	know	VERB
ijassa-111	60	7	the	the	DET
ijassa-111	60	8	particular	particular	ADJ
ijassa-111	60	9	form	form	NOUN
ijassa-111	60	10	of	of	ADP
ijassa-111	60	11	this	this	DET
ijassa-111	60	12	dependence	dependence	NOUN
ijassa-111	60	13	so	so	ADV
ijassa-111	60	14	far	far	ADV
ijassa-111	60	15	.	.	PUNCT
ijassa-111	61	1	to	to	PART
ijassa-111	61	2	determine	determine	VERB
ijassa-111	61	3	it	it	PRON
ijassa-111	61	4	,	,	PUNCT
ijassa-111	61	5	we	we	PRON
ijassa-111	61	6	apply	apply	VERB
ijassa-111	61	7	the	the	DET
ijassa-111	61	8	correspondence	correspondence	NOUN
ijassa-111	61	9	principle	principle	NOUN
ijassa-111	61	10	,	,	PUNCT
ijassa-111	61	11	which	which	PRON
ijassa-111	61	12	can	can	AUX
ijassa-111	61	13	be	be	AUX
ijassa-111	61	14	stated	state	VERB
ijassa-111	61	15	as	as	SCONJ
ijassa-111	61	16	follows	follow	VERB
ijassa-111	61	17	:	:	PUNCT
ijassa-111	61	18	if	if	SCONJ
ijassa-111	61	19	the	the	DET
ijassa-111	61	20	metric	metric	ADJ
ijassa-111	61	21	gij	gij	NOUN
ijassa-111	61	22	weakly	weakly	ADJ
ijassa-111	61	23	converges	converge	NOUN
ijassa-111	61	24	to	to	ADP
ijassa-111	61	25	the	the	DET
ijassa-111	61	26	minkowski	minkowski	ADJ
ijassa-111	61	27	metric	metric	ADJ
ijassa-111	61	28	ηij	ηij	NOUN
ijassa-111	61	29	and	and	CCONJ
ijassa-111	61	30	,	,	PUNCT
ijassa-111	61	31	moreover	moreover	ADV
ijassa-111	61	32	,	,	PUNCT
ijassa-111	61	33	g44	g44	NOUN
ijassa-111	61	34	=	=	SYM
ijassa-111	61	35	1	1	NUM
ijassa-111	61	36	+	+	CCONJ
ijassa-111	61	37	aφ	aφ	ADP
ijassa-111	61	38	c2	c2	PROPN
ijassa-111	61	39	+	+	CCONJ
ijassa-111	61	40	o	o	PROPN
ijassa-111	61	41	(	(	PUNCT
ijassa-111	61	42	1	1	NUM
ijassa-111	61	43	c3	c3	NOUN
ijassa-111	61	44	)	)	PUNCT
ijassa-111	61	45	and	and	CCONJ
ijassa-111	61	46	gij	gij	ADJ
ijassa-111	61	47	=	=	SYM
ijassa-111	61	48	−δij	−δij	NOUN
ijassa-111	62	1	+	+	CCONJ
ijassa-111	62	2	o	o	NOUN
ijassa-111	62	3	(	(	PUNCT
ijassa-111	62	4	1	1	NUM
ijassa-111	62	5	c3	c3	NOUN
ijassa-111	62	6	)	)	PUNCT
ijassa-111	62	7	for	for	ADP
ijassa-111	62	8	i	i	PRON
ijassa-111	62	9	,	,	PUNCT
ijassa-111	62	10	j	j	PROPN
ijassa-111	62	11	=	=	SYM
ijassa-111	62	12	1	1	NUM
ijassa-111	62	13	,	,	PUNCT
ijassa-111	62	14	.	.	PUNCT
ijassa-111	62	15	.	.	PUNCT
ijassa-111	62	16	.	.	PUNCT
ijassa-111	63	1	,	,	PUNCT
ijassa-111	63	2	4	4	NUM
ijassa-111	63	3	,	,	PUNCT
ijassa-111	63	4	i	i	PRON
ijassa-111	63	5	̸=	̸=	PROPN
ijassa-111	63	6	j	j	PROPN
ijassa-111	63	7	,	,	PUNCT
ijassa-111	63	8	where	where	SCONJ
ijassa-111	63	9	c−1	c−1	PROPN
ijassa-111	63	10	is	be	AUX
ijassa-111	63	11	a	a	DET
ijassa-111	63	12	small	small	ADJ
ijassa-111	63	13	parameter	parameter	NOUN
ijassa-111	63	14	and	and	CCONJ
ijassa-111	63	15	φ	φ	PROPN
ijassa-111	63	16	is	be	AUX
ijassa-111	63	17	a	a	DET
ijassa-111	63	18	twice	twice	ADV
ijassa-111	63	19	differentiable	differentiable	ADJ
ijassa-111	63	20	function	function	NOUN
ijassa-111	63	21	,	,	PUNCT
ijassa-111	63	22	then	then	ADV
ijassa-111	63	23	equation	equation	NOUN
ijassa-111	63	24	(	(	PUNCT
ijassa-111	63	25	5	5	NUM
ijassa-111	63	26	)	)	PUNCT
ijassa-111	63	27	must	must	AUX
ijassa-111	63	28	degenerate	degenerate	VERB
ijassa-111	63	29	into	into	ADP
ijassa-111	63	30	the	the	DET
ijassa-111	63	31	poisson	poisson	NOUN
ijassa-111	63	32	equation	equation	NOUN
ijassa-111	63	33	for	for	ADP
ijassa-111	63	34	newtonian	newtonian	ADJ
ijassa-111	63	35	gravity	gravity	NOUN
ijassa-111	63	36	theory	theory	NOUN
ijassa-111	63	37	,	,	PUNCT
ijassa-111	63	38	which	which	PRON
ijassa-111	63	39	is	be	AUX
ijassa-111	63	40	∆φ	∆φ	PROPN
ijassa-111	63	41	=	=	SYM
ijassa-111	63	42	4πgρ	4πgρ	PROPN
ijassa-111	63	43	,	,	PUNCT
ijassa-111	63	44	(	(	PUNCT
ijassa-111	63	45	7	7	NUM
ijassa-111	63	46	)	)	PUNCT
ijassa-111	63	47	where	where	SCONJ
ijassa-111	63	48	∆	∆	PROPN
ijassa-111	63	49	is	be	AUX
ijassa-111	63	50	the	the	DET
ijassa-111	63	51	laplace	laplace	NOUN
ijassa-111	63	52	operator	operator	NOUN
ijassa-111	63	53	,	,	PUNCT
ijassa-111	63	54	φ	φ	PROPN
ijassa-111	63	55	is	be	AUX
ijassa-111	63	56	the	the	DET
ijassa-111	63	57	newtonian	newtonian	ADJ
ijassa-111	63	58	gravitational	gravitational	ADJ
ijassa-111	63	59	potential	potential	NOUN
ijassa-111	63	60	,	,	PUNCT
ijassa-111	63	61	g	g	PROPN
ijassa-111	63	62	is	be	AUX
ijassa-111	63	63	the	the	DET
ijassa-111	63	64	gravitational	gravitational	ADJ
ijassa-111	63	65	constant	constant	ADJ
ijassa-111	63	66	,	,	PUNCT
ijassa-111	63	67	and	and	CCONJ
ijassa-111	63	68	c	c	NOUN
ijassa-111	63	69	is	be	AUX
ijassa-111	63	70	the	the	DET
ijassa-111	63	71	speed	speed	NOUN
ijassa-111	63	72	of	of	ADP
ijassa-111	63	73	light	light	NOUN
ijassa-111	63	74	.	.	PUNCT
ijassa-111	64	1	simple	simple	ADJ
ijassa-111	64	2	calculations	calculation	NOUN
ijassa-111	64	3	show	show	VERB
ijassa-111	64	4	that	that	SCONJ
ijassa-111	64	5	equation	equation	NOUN
ijassa-111	64	6	(	(	PUNCT
ijassa-111	64	7	5	5	X
ijassa-111	64	8	)	)	PUNCT
ijassa-111	64	9	does	do	AUX
ijassa-111	64	10	degenerate	degenerate	VERB
ijassa-111	64	11	into	into	ADP
ijassa-111	64	12	the	the	DET
ijassa-111	64	13	poisson	poisson	NOUN
ijassa-111	64	14	equation	equation	NOUN
ijassa-111	64	15	(	(	PUNCT
ijassa-111	64	16	7	7	NUM
ijassa-111	64	17	)	)	PUNCT
ijassa-111	64	18	under	under	ADP
ijassa-111	64	19	the	the	DET
ijassa-111	64	20	condition	condition	NOUN
ijassa-111	64	21	ρ	ρ	NOUN
ijassa-111	64	22	=	=	PROPN
ijassa-111	64	23	c2	c2	PROPN
ijassa-111	64	24	32πg	32πg	PROPN
ijassa-111	64	25	r.	r.	PROPN
ijassa-111	64	26	(	(	PUNCT
ijassa-111	64	27	8)	8)	NUM
ijassa-111	64	28	relation	relation	NOUN
ijassa-111	64	29	(	(	PUNCT
ijassa-111	64	30	8)	8)	NUM
ijassa-111	64	31	can	can	AUX
ijassa-111	64	32	be	be	AUX
ijassa-111	64	33	regarded	regard	VERB
ijassa-111	64	34	as	as	ADP
ijassa-111	64	35	a	a	DET
ijassa-111	64	36	stronger	strong	ADJ
ijassa-111	64	37	statement	statement	NOUN
ijassa-111	64	38	of	of	ADP
ijassa-111	64	39	postulate	postulate	NOUN
ijassa-111	64	40	2	2	NUM
ijassa-111	64	41	’	'	PUNCT
ijassa-111	64	42	.	.	PUNCT
ijassa-111	65	1	postulate	postulate	VERB
ijassa-111	65	2	2	2	NUM
ijassa-111	65	3	(	(	PUNCT
ijassa-111	65	4	strong	strong	ADJ
ijassa-111	65	5	statement	statement	NOUN
ijassa-111	65	6	)	)	PUNCT
ijassa-111	65	7	.	.	PUNCT
ijassa-111	66	1	the	the	DET
ijassa-111	66	2	matter	matter	NOUN
ijassa-111	66	3	mass	mass	ADJ
ijassa-111	66	4	distribution	distribution	NOUN
ijassa-111	66	5	density	density	NOUN
ijassa-111	66	6	in	in	ADP
ijassa-111	66	7	space	space	NOUN
ijassa-111	66	8	262	262	NUM
ijassa-111	66	9	n.n	n.n	PROPN
ijassa-111	66	10	.	.	PROPN
ijassa-111	66	11	popov	popov	PROPN
ijassa-111	66	12	:	:	PUNCT
ijassa-111	66	13	a	a	DET
ijassa-111	66	14	geometric	geometric	ADJ
ijassa-111	66	15	interpretation	interpretation	NOUN
ijassa-111	66	16	of	of	ADP
ijassa-111	66	17	gravity	gravity	NOUN
ijassa-111	66	18	theory	theory	NOUN
ijassa-111	66	19	is	be	AUX
ijassa-111	66	20	directly	directly	ADV
ijassa-111	66	21	proportional	proportional	ADJ
ijassa-111	66	22	to	to	ADP
ijassa-111	66	23	the	the	DET
ijassa-111	66	24	scalar	scalar	ADJ
ijassa-111	66	25	curvature	curvature	NOUN
ijassa-111	66	26	of	of	ADP
ijassa-111	66	27	the	the	DET
ijassa-111	66	28	pseudo	pseudo	NOUN
ijassa-111	66	29	-	-	ADJ
ijassa-111	66	30	riemannian	riemannian	ADJ
ijassa-111	66	31	space	space	NOUN
ijassa-111	66	32	:	:	PUNCT
ijassa-111	66	33	ρ	ρ	PROPN
ijassa-111	66	34	=	=	SYM
ijassa-111	66	35	ær	ær	INTJ
ijassa-111	66	36	,	,	PUNCT
ijassa-111	66	37	where	where	SCONJ
ijassa-111	66	38	æ	æ	PROPN
ijassa-111	66	39	=	=	SYM
ijassa-111	66	40	c2	c2	PROPN
ijassa-111	66	41	32πg	32πg	PROPN
ijassa-111	66	42	.it	.it	PUNCT
ijassa-111	66	43	follows	follow	VERB
ijassa-111	66	44	from	from	ADP
ijassa-111	66	45	postulate	postulate	NOUN
ijassa-111	66	46	2	2	NUM
ijassa-111	66	47	and	and	CCONJ
ijassa-111	66	48	equation	equation	NOUN
ijassa-111	66	49	(	(	PUNCT
ijassa-111	66	50	5	5	NUM
ijassa-111	66	51	)	)	PUNCT
ijassa-111	66	52	,	,	PUNCT
ijassa-111	66	53	based	base	VERB
ijassa-111	66	54	on	on	ADP
ijassa-111	66	55	postulate	postulate	NOUN
ijassa-111	66	56	3	3	NUM
ijassa-111	66	57	,	,	PUNCT
ijassa-111	66	58	that	that	SCONJ
ijassa-111	66	59	the	the	DET
ijassa-111	66	60	fundamental	fundamental	ADJ
ijassa-111	66	61	equation	equation	NOUN
ijassa-111	66	62	of	of	ADP
ijassa-111	66	63	gravity	gravity	NOUN
ijassa-111	66	64	theory	theory	NOUN
ijassa-111	66	65	can	can	AUX
ijassa-111	66	66	be	be	AUX
ijassa-111	66	67	represented	represent	VERB
ijassa-111	66	68	in	in	ADP
ijassa-111	66	69	the	the	DET
ijassa-111	66	70	form	form	NOUN
ijassa-111	66	71	rij	rij	ADJ
ijassa-111	66	72	−	−	NUM
ijassa-111	66	73	1	1	NUM
ijassa-111	66	74	2	2	NUM
ijassa-111	66	75	rgij	rgij	NOUN
ijassa-111	66	76	=	=	SYM
ijassa-111	66	77	−8πg	−8πg	PROPN
ijassa-111	66	78	c2	c2	PROPN
ijassa-111	66	79	ρgij	ρgij	NOUN
ijassa-111	66	80	,	,	PUNCT
ijassa-111	66	81	i	i	PRON
ijassa-111	66	82	,	,	PUNCT
ijassa-111	66	83	j	j	PROPN
ijassa-111	66	84	=	=	SYM
ijassa-111	66	85	1	1	NUM
ijassa-111	66	86	,	,	PUNCT
ijassa-111	66	87	.	.	PUNCT
ijassa-111	66	88	.	.	PUNCT
ijassa-111	67	1	.	.	PUNCT
ijassa-111	68	1	,	,	PUNCT
ijassa-111	69	1	4	4	NUM
ijassa-111	69	2	,	,	PUNCT
ijassa-111	69	3	(	(	PUNCT
ijassa-111	69	4	9	9	NUM
ijassa-111	69	5	)	)	PUNCT
ijassa-111	69	6	or	or	CCONJ
ijassa-111	69	7	in	in	ADP
ijassa-111	69	8	the	the	DET
ijassa-111	69	9	form	form	NOUN
ijassa-111	69	10	of	of	ADP
ijassa-111	69	11	the	the	DET
ijassa-111	69	12	system	system	NOUN
ijassa-111	69	13	of	of	ADP
ijassa-111	69	14	two	two	NUM
ijassa-111	69	15	relations	relation	NOUN
ijassa-111	69	16	rij	rij	ADJ
ijassa-111	69	17	=	=	SYM
ijassa-111	69	18	r	r	NOUN
ijassa-111	69	19	4	4	NUM
ijassa-111	69	20	gij	gij	NOUN
ijassa-111	69	21	,	,	PUNCT
ijassa-111	69	22	i	i	PRON
ijassa-111	69	23	,	,	PUNCT
ijassa-111	69	24	j	j	PROPN
ijassa-111	69	25	=	=	SYM
ijassa-111	69	26	1	1	NUM
ijassa-111	69	27	,	,	PUNCT
ijassa-111	69	28	.	.	PUNCT
ijassa-111	69	29	.	.	PUNCT
ijassa-111	70	1	.	.	PUNCT
ijassa-111	71	1	,	,	PUNCT
ijassa-111	71	2	4	4	NUM
ijassa-111	71	3	,	,	PUNCT
ijassa-111	71	4	(	(	PUNCT
ijassa-111	71	5	10	10	NUM
ijassa-111	71	6	)	)	PUNCT
ijassa-111	71	7	r	r	NOUN
ijassa-111	71	8	=	=	SYM
ijassa-111	71	9	32πg	32πg	ADJ
ijassa-111	71	10	c2	c2	PROPN
ijassa-111	71	11	ρ	ρ	NUM
ijassa-111	71	12	the	the	DET
ijassa-111	71	13	first	first	ADJ
ijassa-111	71	14	of	of	ADP
ijassa-111	71	15	which	which	PRON
ijassa-111	71	16	is	be	AUX
ijassa-111	71	17	a	a	DET
ijassa-111	71	18	direct	direct	ADJ
ijassa-111	71	19	consequence	consequence	NOUN
ijassa-111	71	20	of	of	ADP
ijassa-111	71	21	postulate	postulate	NOUN
ijassa-111	71	22	3	3	NUM
ijassa-111	71	23	and	and	CCONJ
ijassa-111	71	24	the	the	DET
ijassa-111	71	25	second	second	ADJ
ijassa-111	71	26	,	,	PUNCT
ijassa-111	71	27	of	of	ADP
ijassa-111	71	28	postulate	postulate	NOUN
ijassa-111	71	29	2	2	NUM
ijassa-111	71	30	.	.	PUNCT
ijassa-111	72	1	thus	thus	ADV
ijassa-111	72	2	,	,	PUNCT
ijassa-111	72	3	physical	physical	ADJ
ijassa-111	72	4	theory	theory	NOUN
ijassa-111	72	5	of	of	ADP
ijassa-111	72	6	gravitational	gravitational	ADJ
ijassa-111	72	7	fields	field	NOUN
ijassa-111	72	8	can	can	AUX
ijassa-111	72	9	be	be	AUX
ijassa-111	72	10	translated	translate	VERB
ijassa-111	72	11	into	into	ADP
ijassa-111	72	12	the	the	DET
ijassa-111	72	13	language	language	NOUN
ijassa-111	72	14	of	of	ADP
ijassa-111	72	15	differential	differential	ADJ
ijassa-111	72	16	geometry	geometry	NOUN
ijassa-111	72	17	.	.	PUNCT
ijassa-111	73	1	according	accord	VERB
ijassa-111	73	2	to	to	ADP
ijassa-111	73	3	postulates	postulate	NOUN
ijassa-111	73	4	1	1	NUM
ijassa-111	73	5	and	and	CCONJ
ijassa-111	73	6	2	2	NUM
ijassa-111	73	7	,	,	PUNCT
ijassa-111	73	8	the	the	DET
ijassa-111	73	9	fundamental	fundamental	ADJ
ijassa-111	73	10	physical	physical	ADJ
ijassa-111	73	11	concepts	concept	NOUN
ijassa-111	73	12	of	of	ADP
ijassa-111	73	13	gravitational	gravitational	ADJ
ijassa-111	73	14	theory	theory	NOUN
ijassa-111	73	15	,	,	PUNCT
ijassa-111	73	16	such	such	ADJ
ijassa-111	73	17	as	as	ADP
ijassa-111	73	18	gravitational	gravitational	ADJ
ijassa-111	73	19	field	field	NOUN
ijassa-111	73	20	and	and	CCONJ
ijassa-111	73	21	matter	matter	VERB
ijassa-111	73	22	mass	mass	ADJ
ijassa-111	73	23	density	density	NOUN
ijassa-111	73	24	,	,	PUNCT
ijassa-111	73	25	are	be	AUX
ijassa-111	73	26	interpreted	interpret	VERB
ijassa-111	73	27	in	in	ADP
ijassa-111	73	28	the	the	DET
ijassa-111	73	29	geometric	geometric	NOUN
ijassa-111	73	30	as	as	ADP
ijassa-111	73	31	the	the	DET
ijassa-111	73	32	metric	metric	NOUN
ijassa-111	73	33	and	and	CCONJ
ijassa-111	73	34	the	the	DET
ijassa-111	73	35	scalar	scalar	ADJ
ijassa-111	73	36	curvature	curvature	NOUN
ijassa-111	73	37	(	(	PUNCT
ijassa-111	73	38	up	up	ADP
ijassa-111	73	39	to	to	ADP
ijassa-111	73	40	proportionality	proportionality	NOUN
ijassa-111	73	41	)	)	PUNCT
ijassa-111	73	42	,	,	PUNCT
ijassa-111	73	43	respectively	respectively	ADV
ijassa-111	73	44	,	,	PUNCT
ijassa-111	73	45	of	of	ADP
ijassa-111	73	46	a	a	DET
ijassa-111	73	47	pseudo	pseudo	NOUN
ijassa-111	73	48	-	-	ADJ
ijassa-111	73	49	riemannian	riemannian	ADJ
ijassa-111	73	50	space	space	NOUN
ijassa-111	73	51	.	.	PUNCT
ijassa-111	74	1	4	4	NUM
ijassa-111	74	2	consistency	consistency	NOUN
ijassa-111	74	3	and	and	CCONJ
ijassa-111	74	4	physical	physical	ADJ
ijassa-111	74	5	adequacy	adequacy	NOUN
ijassa-111	74	6	of	of	ADP
ijassa-111	74	7	postulates	postulate	NOUN
ijassa-111	74	8	1	1	NUM
ijassa-111	74	9	-	-	SYM
ijassa-111	74	10	3	3	NUM
ijassa-111	74	11	to	to	PART
ijassa-111	74	12	verify	verify	VERB
ijassa-111	74	13	the	the	DET
ijassa-111	74	14	consistency	consistency	NOUN
ijassa-111	74	15	of	of	ADP
ijassa-111	74	16	the	the	DET
ijassa-111	74	17	system	system	NOUN
ijassa-111	74	18	of	of	ADP
ijassa-111	74	19	postulates	postulate	NOUN
ijassa-111	74	20	stated	state	VERB
ijassa-111	74	21	above	above	ADP
ijassa-111	74	22	and	and	CCONJ
ijassa-111	74	23	the	the	DET
ijassa-111	74	24	physical	physical	ADJ
ijassa-111	74	25	adequacy	adequacy	NOUN
ijassa-111	74	26	of	of	ADP
ijassa-111	74	27	these	these	DET
ijassa-111	74	28	postulates	postulate	NOUN
ijassa-111	74	29	,	,	PUNCT
ijassa-111	74	30	consider	consider	VERB
ijassa-111	74	31	a	a	DET
ijassa-111	74	32	model	model	NOUN
ijassa-111	74	33	of	of	ADP
ijassa-111	74	34	a	a	DET
ijassa-111	74	35	spherically	spherically	NOUN
ijassa-111	74	36	symmetric	symmetric	ADJ
ijassa-111	74	37	space	space	NOUN
ijassa-111	74	38	with	with	ADP
ijassa-111	74	39	a	a	DET
ijassa-111	74	40	ball	ball	NOUN
ijassa-111	74	41	of	of	ADP
ijassa-111	74	42	radius	radius	NOUN
ijassa-111	74	43	r1	r1	PROPN
ijassa-111	74	44	at	at	ADP
ijassa-111	74	45	the	the	DET
ijassa-111	74	46	center	center	NOUN
ijassa-111	74	47	of	of	ADP
ijassa-111	74	48	symmetry	symmetry	NOUN
ijassa-111	74	49	.	.	PUNCT
ijassa-111	75	1	the	the	DET
ijassa-111	75	2	ball	ball	NOUN
ijassa-111	75	3	is	be	AUX
ijassa-111	75	4	uniformly	uniformly	ADV
ijassa-111	75	5	filled	fill	VERB
ijassa-111	75	6	with	with	ADP
ijassa-111	75	7	a	a	DET
ijassa-111	75	8	matter	matter	NOUN
ijassa-111	75	9	of	of	ADP
ijassa-111	75	10	mass	mass	NOUN
ijassa-111	75	11	ρ	ρ	NOUN
ijassa-111	75	12	and	and	CCONJ
ijassa-111	75	13	constant	constant	ADJ
ijassa-111	75	14	density	density	NOUN
ijassa-111	75	15	;	;	PUNCT
ijassa-111	75	16	outside	outside	ADP
ijassa-111	75	17	the	the	DET
ijassa-111	75	18	ball	ball	NOUN
ijassa-111	75	19	,	,	PUNCT
ijassa-111	75	20	there	there	PRON
ijassa-111	75	21	is	be	VERB
ijassa-111	75	22	no	no	DET
ijassa-111	75	23	matter	matter	NOUN
ijassa-111	75	24	.	.	PUNCT
ijassa-111	76	1	from	from	ADP
ijassa-111	76	2	the	the	DET
ijassa-111	76	3	geometric	geometric	ADJ
ijassa-111	76	4	point	point	NOUN
ijassa-111	76	5	of	of	ADP
ijassa-111	76	6	view	view	NOUN
ijassa-111	76	7	,	,	PUNCT
ijassa-111	76	8	we	we	PRON
ijassa-111	76	9	have	have	VERB
ijassa-111	76	10	a	a	DET
ijassa-111	76	11	spherically	spherically	NOUN
ijassa-111	76	12	symmetric	symmetric	ADJ
ijassa-111	76	13	pseudo	pseudo	NOUN
ijassa-111	76	14	-	-	ADJ
ijassa-111	76	15	riemannian	riemannian	ADJ
ijassa-111	76	16	space	space	NOUN
ijassa-111	76	17	with	with	ADP
ijassa-111	76	18	constant	constant	ADJ
ijassa-111	76	19	scalar	scalar	ADJ
ijassa-111	76	20	curvature	curvature	NOUN
ijassa-111	76	21	r	r	NOUN
ijassa-111	76	22	=	=	SYM
ijassa-111	76	23	32πg	32πg	ADJ
ijassa-111	76	24	c2	c2	PROPN
ijassa-111	76	25	ρ	ρ	PROPN
ijassa-111	76	26	inside	inside	ADP
ijassa-111	76	27	a	a	DET
ijassa-111	76	28	ball	ball	NOUN
ijassa-111	76	29	of	of	ADP
ijassa-111	76	30	radius	radius	NOUN
ijassa-111	76	31	r1	r1	PROPN
ijassa-111	76	32	and	and	CCONJ
ijassa-111	76	33	vanishing	vanish	VERB
ijassa-111	76	34	scalar	scalar	ADJ
ijassa-111	76	35	curvature	curvature	NOUN
ijassa-111	76	36	outside	outside	ADP
ijassa-111	76	37	the	the	DET
ijassa-111	76	38	ball	ball	NOUN
ijassa-111	76	39	.	.	PUNCT
ijassa-111	77	1	the	the	DET
ijassa-111	77	2	problem	problem	NOUN
ijassa-111	77	3	is	be	AUX
ijassa-111	77	4	to	to	PART
ijassa-111	77	5	determine	determine	VERB
ijassa-111	77	6	the	the	DET
ijassa-111	77	7	metric	metric	NOUN
ijassa-111	77	8	of	of	ADP
ijassa-111	77	9	such	such	DET
ijassa-111	77	10	a	a	DET
ijassa-111	77	11	space	space	NOUN
ijassa-111	77	12	.	.	PUNCT
ijassa-111	78	1	hereafter	hereafter	ADV
ijassa-111	78	2	,	,	PUNCT
ijassa-111	78	3	we	we	PRON
ijassa-111	78	4	always	always	ADV
ijassa-111	78	5	assume	assume	VERB
ijassa-111	78	6	that	that	SCONJ
ijassa-111	78	7	the	the	DET
ijassa-111	78	8	system	system	NOUN
ijassa-111	78	9	units	unit	NOUN
ijassa-111	78	10	used	use	VERB
ijassa-111	78	11	for	for	ADP
ijassa-111	78	12	measuring	measure	VERB
ijassa-111	78	13	physical	physical	ADJ
ijassa-111	78	14	quantities	quantity	NOUN
ijassa-111	78	15	is	be	AUX
ijassa-111	78	16	chosen	choose	VERB
ijassa-111	78	17	so	so	SCONJ
ijassa-111	78	18	that	that	SCONJ
ijassa-111	78	19	g	g	NOUN
ijassa-111	78	20	,	,	PUNCT
ijassa-111	78	21	c	c	NOUN
ijassa-111	78	22	=	=	SYM
ijassa-111	78	23	1	1	NUM
ijassa-111	78	24	.	.	PUNCT
ijassa-111	79	1	the	the	DET
ijassa-111	79	2	general	general	ADJ
ijassa-111	79	3	form	form	NOUN
ijassa-111	79	4	of	of	ADP
ijassa-111	79	5	a	a	DET
ijassa-111	79	6	stationary	stationary	ADJ
ijassa-111	79	7	spherically	spherically	NOUN
ijassa-111	79	8	symmetric	symmetric	ADJ
ijassa-111	79	9	metric	metric	NOUN
ijassa-111	79	10	of	of	ADP
ijassa-111	79	11	a	a	DET
ijassa-111	79	12	pseudoriemannian	pseudoriemannian	ADJ
ijassa-111	79	13	4	4	NUM
ijassa-111	79	14	-	-	PUNCT
ijassa-111	79	15	space	space	NOUN
ijassa-111	79	16	in	in	ADP
ijassa-111	79	17	spherical	spherical	ADJ
ijassa-111	79	18	coordinates	coordinate	NOUN
ijassa-111	79	19	t	t	PROPN
ijassa-111	79	20	,	,	PUNCT
ijassa-111	79	21	r	r	NOUN
ijassa-111	79	22	,	,	PUNCT
ijassa-111	79	23	θ	θ	PROPN
ijassa-111	79	24	,	,	PUNCT
ijassa-111	79	25	φ	φ	PROPN
ijassa-111	79	26	is[4	is[4	X
ijassa-111	79	27	]	]	X
ijassa-111	79	28	ds2	ds2	PROPN
ijassa-111	79	29	=	=	SYM
ijassa-111	79	30	g44(r)dt	g44(r)dt	NOUN
ijassa-111	79	31	2	2	NUM
ijassa-111	79	32	+	+	SYM
ijassa-111	79	33	g11(r)dr	g11(r)dr	NUM
ijassa-111	79	34	2	2	NUM
ijassa-111	79	35	+	+	CCONJ
ijassa-111	79	36	g22(r)(dθ	g22(r)(dθ	NOUN
ijassa-111	79	37	2	2	NUM
ijassa-111	79	38	+	+	NUM
ijassa-111	79	39	sin2θdφ2	sin2θdφ2	PROPN
ijassa-111	79	40	)	)	PUNCT
ijassa-111	79	41	,	,	PUNCT
ijassa-111	79	42	(	(	PUNCT
ijassa-111	79	43	11	11	NUM
ijassa-111	79	44	)	)	PUNCT
ijassa-111	79	45	where	where	SCONJ
ijassa-111	79	46	g11	g11	NOUN
ijassa-111	79	47	and	and	CCONJ
ijassa-111	79	48	g22	g22	NOUN
ijassa-111	79	49	are	be	AUX
ijassa-111	79	50	negative	negative	ADJ
ijassa-111	79	51	unknown	unknown	ADJ
ijassa-111	79	52	functions	function	NOUN
ijassa-111	79	53	and	and	CCONJ
ijassa-111	79	54	g44	g44	NOUN
ijassa-111	79	55	is	be	AUX
ijassa-111	79	56	a	a	DET
ijassa-111	79	57	positive	positive	ADJ
ijassa-111	79	58	function	function	NOUN
ijassa-111	79	59	,	,	PUNCT
ijassa-111	79	60	which	which	PRON
ijassa-111	79	61	depend	depend	VERB
ijassa-111	79	62	on	on	ADP
ijassa-111	79	63	the	the	DET
ijassa-111	79	64	variable	variable	ADJ
ijassa-111	79	65	r	r	NOUN
ijassa-111	79	66	,	,	PUNCT
ijassa-111	79	67	and	and	CCONJ
ijassa-111	79	68	r	r	NOUN
ijassa-111	79	69	,	,	PUNCT
ijassa-111	79	70	t	t	PROPN
ijassa-111	79	71	∈	∈	PROPN
ijassa-111	79	72	(	(	PUNCT
ijassa-111	79	73	0,∞	0,∞	NOUN
ijassa-111	79	74	)	)	PUNCT
ijassa-111	79	75	,	,	PUNCT
ijassa-111	79	76	r	r	NOUN
ijassa-111	79	77	∈	∈	PROPN
ijassa-111	79	78	(	(	PUNCT
ijassa-111	79	79	0,∞	0,∞	NOUN
ijassa-111	79	80	)	)	PUNCT
ijassa-111	79	81	,	,	PUNCT
ijassa-111	79	82	θ	θ	PROPN
ijassa-111	79	83	∈	∈	PROPN
ijassa-111	80	1	[	[	X
ijassa-111	80	2	0	0	NUM
ijassa-111	80	3	,	,	PUNCT
ijassa-111	80	4	π	π	PROPN
ijassa-111	80	5	]	]	X
ijassa-111	80	6	,	,	PUNCT
ijassa-111	80	7	φ	φ	PROPN
ijassa-111	80	8	∈	∈	PROPN
ijassa-111	81	1	[	[	X
ijassa-111	81	2	0	0	NUM
ijassa-111	81	3	,	,	PUNCT
ijassa-111	81	4	2π	2π	NOUN
ijassa-111	81	5	)	)	PUNCT
ijassa-111	81	6	.	.	PUNCT
ijassa-111	82	1	the	the	DET
ijassa-111	82	2	components	component	NOUN
ijassa-111	82	3	of	of	ADP
ijassa-111	82	4	metric	metric	ADJ
ijassa-111	82	5	(	(	PUNCT
ijassa-111	82	6	11	11	NUM
ijassa-111	82	7	)	)	PUNCT
ijassa-111	82	8	must	must	AUX
ijassa-111	82	9	satisfy	satisfy	VERB
ijassa-111	82	10	system	system	NOUN
ijassa-111	82	11	(	(	PUNCT
ijassa-111	82	12	10	10	NUM
ijassa-111	82	13	)	)	PUNCT
ijassa-111	82	14	.	.	PUNCT
ijassa-111	83	1	using	use	VERB
ijassa-111	83	2	relations	relation	NOUN
ijassa-111	83	3	(	(	PUNCT
ijassa-111	83	4	1	1	X
ijassa-111	83	5	)	)	PUNCT
ijassa-111	83	6	advances	advance	NOUN
ijassa-111	83	7	in	in	ADP
ijassa-111	83	8	systems	system	NOUN
ijassa-111	83	9	science	science	NOUN
ijassa-111	83	10	and	and	CCONJ
ijassa-111	83	11	applications	application	NOUN
ijassa-111	83	12	(	(	PUNCT
ijassa-111	83	13	2012	2012	NUM
ijassa-111	83	14	)	)	PUNCT
ijassa-111	83	15	vol.12	vol.12	NOUN
ijassa-111	83	16	no.3	no.3	VERB
ijassa-111	83	17	263	263	NUM
ijassa-111	83	18	and	and	CCONJ
ijassa-111	83	19	(	(	PUNCT
ijassa-111	83	20	2	2	NUM
ijassa-111	83	21	)	)	PUNCT
ijassa-111	83	22	,	,	PUNCT
ijassa-111	83	23	we	we	PRON
ijassa-111	83	24	can	can	AUX
ijassa-111	83	25	reduce	reduce	VERB
ijassa-111	83	26	system	system	NOUN
ijassa-111	83	27	(	(	PUNCT
ijassa-111	83	28	10	10	NUM
ijassa-111	83	29	)	)	PUNCT
ijassa-111	83	30	for	for	ADP
ijassa-111	83	31	metric	metric	ADJ
ijassa-111	83	32	(	(	PUNCT
ijassa-111	83	33	11	11	NUM
ijassa-111	83	34	)	)	PUNCT
ijassa-111	83	35	to	to	ADP
ijassa-111	83	36	the	the	DET
ijassa-111	83	37	form	form	NOUN
ijassa-111	83	38	(	(	PUNCT
ijassa-111	83	39	g′22	g′22	ADJ
ijassa-111	83	40	g22	g22	NOUN
ijassa-111	83	41	)	)	PUNCT
ijassa-111	83	42	′	′	PUNCT
ijassa-111	84	1	+	+	CCONJ
ijassa-111	84	2	1	1	NUM
ijassa-111	84	3	2	2	NUM
ijassa-111	84	4	(	(	PUNCT
ijassa-111	84	5	g′44	g′44	NOUN
ijassa-111	84	6	g44	g44	NOUN
ijassa-111	84	7	)	)	PUNCT
ijassa-111	84	8	′	′	NUM
ijassa-111	85	1	−	−	NOUN
ijassa-111	85	2	1	1	NUM
ijassa-111	85	3	2	2	NUM
ijassa-111	85	4	(	(	PUNCT
ijassa-111	85	5	g′11	g′11	VERB
ijassa-111	85	6	g11	g11	PROPN
ijassa-111	85	7	)	)	PUNCT
ijassa-111	85	8	(	(	PUNCT
ijassa-111	85	9	g′22	g′22	ADJ
ijassa-111	85	10	g22	g22	NOUN
ijassa-111	85	11	+	+	CCONJ
ijassa-111	85	12	g′44	g′44	NOUN
ijassa-111	85	13	2g44	2g44	NOUN
ijassa-111	85	14	)	)	PUNCT
ijassa-111	86	1	+	+	CCONJ
ijassa-111	86	2	1	1	NUM
ijassa-111	86	3	2	2	NUM
ijassa-111	86	4	(	(	PUNCT
ijassa-111	86	5	g′22	g′22	ADJ
ijassa-111	86	6	g22	g22	NOUN
ijassa-111	86	7	)	)	PUNCT
ijassa-111	86	8	2	2	NUM
ijassa-111	87	1	+	+	CCONJ
ijassa-111	87	2	1	1	NUM
ijassa-111	87	3	4	4	NUM
ijassa-111	87	4	(	(	PUNCT
ijassa-111	87	5	g′44	g′44	NOUN
ijassa-111	87	6	g44	g44	NOUN
ijassa-111	87	7	)	)	PUNCT
ijassa-111	87	8	2	2	NUM
ijassa-111	88	1	=	=	SYM
ijassa-111	88	2	r	r	NOUN
ijassa-111	88	3	4	4	NUM
ijassa-111	88	4	g11	g11	NOUN
ijassa-111	88	5	,	,	PUNCT
ijassa-111	88	6	1	1	NUM
ijassa-111	88	7	2	2	NUM
ijassa-111	88	8	(	(	PUNCT
ijassa-111	88	9	g′22	g′22	PROPN
ijassa-111	88	10	g11	g11	NOUN
ijassa-111	88	11	)	)	PUNCT
ijassa-111	88	12	′	′	NUM
ijassa-111	89	1	+	+	CCONJ
ijassa-111	90	1	g′22	g′22	ADJ
ijassa-111	90	2	2g11	2g11	NOUN
ijassa-111	90	3	(	(	PUNCT
ijassa-111	90	4	g′11	g′11	VERB
ijassa-111	90	5	2g11	2g11	NUM
ijassa-111	90	6	+	+	CCONJ
ijassa-111	90	7	g′22	g′22	ADJ
ijassa-111	90	8	g22	g22	NOUN
ijassa-111	90	9	+	+	CCONJ
ijassa-111	90	10	g′44	g′44	NOUN
ijassa-111	90	11	2g44	2g44	NOUN
ijassa-111	90	12	)	)	PUNCT
ijassa-111	90	13	−	−	PROPN
ijassa-111	91	1	1	1	NUM
ijassa-111	91	2	2g11g22	2g11g22	NOUN
ijassa-111	91	3	(	(	PUNCT
ijassa-111	91	4	g′22	g′22	PROPN
ijassa-111	91	5	)	)	PUNCT
ijassa-111	91	6	2	2	NUM
ijassa-111	91	7	−	−	NOUN
ijassa-111	91	8	1	1	NUM
ijassa-111	91	9	=	=	SYM
ijassa-111	91	10	r	r	NOUN
ijassa-111	91	11	4	4	NUM
ijassa-111	91	12	g22	g22	NOUN
ijassa-111	91	13	,	,	PUNCT
ijassa-111	91	14	(	(	PUNCT
ijassa-111	91	15	12	12	NUM
ijassa-111	91	16	)	)	PUNCT
ijassa-111	91	17	−1	−1	NOUN
ijassa-111	91	18	2	2	NUM
ijassa-111	91	19	(	(	PUNCT
ijassa-111	91	20	g′44	g′44	NOUN
ijassa-111	91	21	g11	g11	NOUN
ijassa-111	91	22	)	)	PUNCT
ijassa-111	91	23	′	′	NUM
ijassa-111	92	1	−	−	NOUN
ijassa-111	92	2	g′44	g′44	VERB
ijassa-111	92	3	2g11	2g11	NOUN
ijassa-111	92	4	(	(	PUNCT
ijassa-111	92	5	g′11	g′11	VERB
ijassa-111	92	6	2g11	2g11	NUM
ijassa-111	92	7	+	+	CCONJ
ijassa-111	92	8	g′22	g′22	ADJ
ijassa-111	92	9	g22	g22	NOUN
ijassa-111	92	10	+	+	CCONJ
ijassa-111	92	11	g′44	g′44	NOUN
ijassa-111	92	12	2g44	2g44	NOUN
ijassa-111	92	13	)	)	PUNCT
ijassa-111	93	1	+	+	CCONJ
ijassa-111	93	2	1	1	NUM
ijassa-111	93	3	2g11g44	2g11g44	NUM
ijassa-111	93	4	(	(	PUNCT
ijassa-111	93	5	g′44	g′44	NOUN
ijassa-111	93	6	)	)	PUNCT
ijassa-111	93	7	2	2	NUM
ijassa-111	93	8	=	=	SYM
ijassa-111	93	9	r	r	NOUN
ijassa-111	93	10	4	4	NUM
ijassa-111	93	11	g44	g44	NOUN
ijassa-111	93	12	,	,	PUNCT
ijassa-111	93	13	where	where	SCONJ
ijassa-111	93	14	g′ij	g′ij	NOUN
ijassa-111	93	15	=	=	PUNCT
ijassa-111	93	16	dgij	dgij	PROPN
ijassa-111	93	17	dr	dr	PROPN
ijassa-111	93	18	,	,	PUNCT
ijassa-111	93	19	r	r	NOUN
ijassa-111	93	20	>	>	X
ijassa-111	93	21	0	0	NUM
ijassa-111	93	22	,	,	PUNCT
ijassa-111	93	23	at	at	ADP
ijassa-111	93	24	r	r	NOUN
ijassa-111	93	25	≤	≤	NUM
ijassa-111	93	26	r1	r1	NOUN
ijassa-111	93	27	,	,	PUNCT
ijassa-111	93	28	and	and	CCONJ
ijassa-111	93	29	r	r	NOUN
ijassa-111	93	30	=	=	SYM
ijassa-111	93	31	0	0	NUM
ijassa-111	93	32	at	at	ADP
ijassa-111	93	33	r	r	X
ijassa-111	93	34	>	>	X
ijassa-111	93	35	r1	r1	PROPN
ijassa-111	93	36	.	.	PUNCT
ijassa-111	94	1	for	for	ADP
ijassa-111	94	2	the	the	DET
ijassa-111	94	3	sake	sake	NOUN
ijassa-111	94	4	of	of	ADP
ijassa-111	94	5	generality	generality	NOUN
ijassa-111	94	6	,	,	PUNCT
ijassa-111	94	7	we	we	PRON
ijassa-111	94	8	assume	assume	VERB
ijassa-111	94	9	that	that	SCONJ
ijassa-111	94	10	the	the	DET
ijassa-111	94	11	unknown	unknown	ADJ
ijassa-111	94	12	scalar	scalar	ADJ
ijassa-111	94	13	function	function	NOUN
ijassa-111	94	14	r	r	NOUN
ijassa-111	94	15	in	in	ADP
ijassa-111	94	16	system	system	NOUN
ijassa-111	94	17	(	(	PUNCT
ijassa-111	94	18	12	12	NUM
ijassa-111	94	19	)	)	PUNCT
ijassa-111	94	20	depends	depend	VERB
ijassa-111	94	21	on	on	ADP
ijassa-111	94	22	the	the	DET
ijassa-111	94	23	r	r	NOUN
ijassa-111	94	24	coordinate	coordinate	NOUN
ijassa-111	94	25	.	.	PUNCT
ijassa-111	95	1	the	the	DET
ijassa-111	95	2	following	follow	VERB
ijassa-111	95	3	theorem	theorem	NOUN
ijassa-111	95	4	is	be	AUX
ijassa-111	95	5	valid	valid	ADJ
ijassa-111	95	6	.	.	PUNCT
ijassa-111	96	1	theorem	theorem	NOUN
ijassa-111	96	2	2	2	NUM
ijassa-111	96	3	.	.	PUNCT
ijassa-111	97	1	if	if	SCONJ
ijassa-111	97	2	g22(0	g22(0	NOUN
ijassa-111	97	3	)	)	PUNCT
ijassa-111	98	1	=	=	SYM
ijassa-111	98	2	0	0	NUM
ijassa-111	98	3	and	and	CCONJ
ijassa-111	98	4	g44(0	g44(0	NOUN
ijassa-111	98	5	)	)	PUNCT
ijassa-111	98	6	<	<	X
ijassa-111	98	7	∞	∞	PROPN
ijassa-111	98	8	,	,	PUNCT
ijassa-111	98	9	then	then	ADV
ijassa-111	98	10	the	the	DET
ijassa-111	98	11	scalar	scalar	ADJ
ijassa-111	98	12	curvature	curvature	NOUN
ijassa-111	98	13	r(r	r(r	PROPN
ijassa-111	98	14	)	)	PUNCT
ijassa-111	98	15	does	do	AUX
ijassa-111	98	16	not	not	PART
ijassa-111	98	17	depend	depend	VERB
ijassa-111	98	18	on	on	ADP
ijassa-111	98	19	r	r	NOUN
ijassa-111	98	20	in	in	ADP
ijassa-111	98	21	the	the	DET
ijassa-111	98	22	domain	domain	NOUN
ijassa-111	98	23	where	where	SCONJ
ijassa-111	98	24	it	it	PRON
ijassa-111	98	25	is	be	AUX
ijassa-111	98	26	nonzero	nonzero	ADJ
ijassa-111	98	27	,	,	PUNCT
ijassa-111	98	28	and	and	CCONJ
ijassa-111	98	29	system	system	NOUN
ijassa-111	98	30	(	(	PUNCT
ijassa-111	98	31	12	12	NUM
ijassa-111	98	32	)	)	PUNCT
ijassa-111	98	33	has	have	VERB
ijassa-111	98	34	a	a	DET
ijassa-111	98	35	unique	unique	ADJ
ijassa-111	98	36	solution	solution	NOUN
ijassa-111	98	37	depending	depend	VERB
ijassa-111	98	38	on	on	ADP
ijassa-111	98	39	one	one	NUM
ijassa-111	98	40	free	free	ADJ
ijassa-111	98	41	parameter	parameter	NOUN
ijassa-111	98	42	.	.	PUNCT
ijassa-111	99	1	if	if	SCONJ
ijassa-111	99	2	,	,	PUNCT
ijassa-111	99	3	in	in	ADP
ijassa-111	99	4	addition	addition	NOUN
ijassa-111	99	5	,	,	PUNCT
ijassa-111	99	6	g44(0	g44(0	NOUN
ijassa-111	99	7	)	)	PUNCT
ijassa-111	99	8	=	=	SYM
ijassa-111	100	1	1	1	NUM
ijassa-111	100	2	,	,	PUNCT
ijassa-111	100	3	then	then	ADV
ijassa-111	100	4	the	the	DET
ijassa-111	100	5	solution	solution	NOUN
ijassa-111	100	6	of	of	ADP
ijassa-111	100	7	system	system	NOUN
ijassa-111	100	8	(	(	PUNCT
ijassa-111	100	9	12	12	NUM
ijassa-111	100	10	)	)	PUNCT
ijassa-111	100	11	is	be	AUX
ijassa-111	100	12	unique	unique	ADJ
ijassa-111	100	13	;	;	PUNCT
ijassa-111	100	14	moreover	moreover	ADV
ijassa-111	100	15	,	,	PUNCT
ijassa-111	100	16	at	at	ADP
ijassa-111	100	17	r	r	NOUN
ijassa-111	100	18	≤	≤	NUM
ijassa-111	100	19	r1	r1	NOUN
ijassa-111	100	20	,	,	PUNCT
ijassa-111	100	21	where	where	SCONJ
ijassa-111	100	22	r1	r1	PROPN
ijassa-111	100	23	<	<	X
ijassa-111	100	24	√	√	PROPN
ijassa-111	100	25	12	12	NUM
ijassa-111	100	26	r	r	NOUN
ijassa-111	100	27	,	,	PUNCT
ijassa-111	100	28	it	it	PRON
ijassa-111	100	29	coincides	coincide	VERB
ijassa-111	100	30	with	with	ADP
ijassa-111	100	31	the	the	DET
ijassa-111	100	32	de	de	X
ijassa-111	100	33	sitter	sitter	NOUN
ijassa-111	100	34	metric[5	metric[5	PROPN
ijassa-111	100	35	]	]	X
ijassa-111	100	36	ds2	ds2	PROPN
ijassa-111	100	37	=	=	SYM
ijassa-111	100	38	(	(	PUNCT
ijassa-111	100	39	1−	1−	NUM
ijassa-111	100	40	r	r	NOUN
ijassa-111	100	41	12	12	NUM
ijassa-111	100	42	r2)dt2	r2)dt2	NOUN
ijassa-111	100	43	−	−	NOUN
ijassa-111	101	1	dr2	dr2	NOUN
ijassa-111	101	2	1−	1−	NUM
ijassa-111	101	3	r	r	NOUN
ijassa-111	101	4	12r	12r	NUM
ijassa-111	101	5	2	2	NUM
ijassa-111	101	6	−	−	NOUN
ijassa-111	101	7	r2(dθ2	r2(dθ2	NOUN
ijassa-111	101	8	+	+	CCONJ
ijassa-111	101	9	sin2θdφ2	sin2θdφ2	NOUN
ijassa-111	101	10	)	)	PUNCT
ijassa-111	101	11	,	,	PUNCT
ijassa-111	101	12	(	(	PUNCT
ijassa-111	101	13	13	13	NUM
ijassa-111	101	14	)	)	PUNCT
ijassa-111	101	15	and	and	CCONJ
ijassa-111	101	16	at	at	ADP
ijassa-111	101	17	r	r	NOUN
ijassa-111	101	18	>	>	X
ijassa-111	101	19	r1	r1	PROPN
ijassa-111	101	20	,	,	PUNCT
ijassa-111	101	21	it	it	PRON
ijassa-111	101	22	coincides	coincide	VERB
ijassa-111	101	23	with	with	ADP
ijassa-111	101	24	the	the	DET
ijassa-111	101	25	schwarzschild	schwarzschild	NOUN
ijassa-111	101	26	metric[6	metric[6	NOUN
ijassa-111	101	27	]	]	X
ijassa-111	101	28	ds2	ds2	PROPN
ijassa-111	101	29	=	=	SYM
ijassa-111	101	30	(	(	PUNCT
ijassa-111	101	31	1−	1−	NUM
ijassa-111	101	32	r	r	NOUN
ijassa-111	101	33	12	12	NUM
ijassa-111	101	34	r31	r31	NOUN
ijassa-111	101	35	r	r	NOUN
ijassa-111	101	36	)	)	PUNCT
ijassa-111	101	37	dt2	dt2	PROPN
ijassa-111	101	38	−	−	PROPN
ijassa-111	101	39	dr2	dr2	PROPN
ijassa-111	101	40	1−	1−	NUM
ijassa-111	101	41	r	r	NOUN
ijassa-111	101	42	12	12	NUM
ijassa-111	101	43	r31	r31	NOUN
ijassa-111	101	44	r	r	NOUN
ijassa-111	101	45	−	−	NOUN
ijassa-111	101	46	r2(dθ2	r2(dθ2	NOUN
ijassa-111	101	47	+	+	CCONJ
ijassa-111	101	48	sin	sin	NOUN
ijassa-111	101	49	θ2dφ2	θ2dφ2	NOUN
ijassa-111	101	50	)	)	PUNCT
ijassa-111	101	51	.	.	PUNCT
ijassa-111	102	1	(	(	PUNCT
ijassa-111	102	2	14	14	NUM
ijassa-111	102	3	)	)	PUNCT
ijassa-111	102	4	proof	proof	NOUN
ijassa-111	102	5	.	.	PUNCT
ijassa-111	103	1	system	system	NOUN
ijassa-111	103	2	of	of	ADP
ijassa-111	103	3	equations	equation	NOUN
ijassa-111	103	4	(	(	PUNCT
ijassa-111	103	5	12	12	NUM
ijassa-111	103	6	)	)	PUNCT
ijassa-111	103	7	can	can	AUX
ijassa-111	103	8	be	be	AUX
ijassa-111	103	9	simplified	simplify	VERB
ijassa-111	103	10	by	by	ADP
ijassa-111	103	11	passing	pass	VERB
ijassa-111	103	12	to	to	ADP
ijassa-111	103	13	the	the	DET
ijassa-111	103	14	generalized	generalized	ADJ
ijassa-111	103	15	spherical	spherical	ADJ
ijassa-111	103	16	coordinates	coordinate	NOUN
ijassa-111	103	17	x1	x1	PROPN
ijassa-111	103	18	,	,	PUNCT
ijassa-111	103	19	.	.	PUNCT
ijassa-111	103	20	.	.	PUNCT
ijassa-111	104	1	.	.	PUNCT
ijassa-111	105	1	,	,	PUNCT
ijassa-111	106	1	x4,where	x4,where	X
ijassa-111	106	2	x1	x1	PROPN
ijassa-111	106	3	=	=	SYM
ijassa-111	106	4	r3	r3	PROPN
ijassa-111	106	5	3	3	NUM
ijassa-111	106	6	,	,	PUNCT
ijassa-111	107	1	x2	x2	PROPN
ijassa-111	107	2	=	=	PUNCT
ijassa-111	107	3	−	−	PROPN
ijassa-111	107	4	cos	cos	PROPN
ijassa-111	107	5	θ	θ	PROPN
ijassa-111	107	6	,	,	PUNCT
ijassa-111	107	7	x3	x3	NOUN
ijassa-111	107	8	=	=	SYM
ijassa-111	107	9	φ	φ	NUM
ijassa-111	107	10	,	,	PUNCT
ijassa-111	107	11	and	and	CCONJ
ijassa-111	107	12	x4	x4	PROPN
ijassa-111	107	13	=	=	PROPN
ijassa-111	108	1	t.	t.	NOUN
ijassa-111	108	2	let	let	VERB
ijassa-111	108	3	us	we	PRON
ijassa-111	108	4	introduce	introduce	VERB
ijassa-111	108	5	the	the	DET
ijassa-111	108	6	following	follow	VERB
ijassa-111	108	7	new	new	ADJ
ijassa-111	108	8	notation	notation	NOUN
ijassa-111	108	9	for	for	ADP
ijassa-111	108	10	the	the	DET
ijassa-111	108	11	components	component	NOUN
ijassa-111	108	12	of	of	ADP
ijassa-111	108	13	the	the	DET
ijassa-111	108	14	metric	metric	ADJ
ijassa-111	108	15	tensor	tensor	NOUN
ijassa-111	108	16	:	:	PUNCT
ijassa-111	108	17	g11	g11	PROPN
ijassa-111	108	18	=	=	SYM
ijassa-111	108	19	−(3x1	−(3x1	NOUN
ijassa-111	108	20	)	)	PUNCT
ijassa-111	108	21	4	4	NUM
ijassa-111	108	22	3	3	NUM
ijassa-111	108	23	f1(x1	f1(x1	NOUN
ijassa-111	108	24	)	)	PUNCT
ijassa-111	108	25	,	,	PUNCT
ijassa-111	108	26	g22	g22	NOUN
ijassa-111	108	27	=	=	SYM
ijassa-111	108	28	−f2(x1	−f2(x1	PROPN
ijassa-111	108	29	)	)	PUNCT
ijassa-111	108	30	,	,	PUNCT
ijassa-111	108	31	g44	g44	NOUN
ijassa-111	108	32	=	=	SYM
ijassa-111	108	33	f4(x1	f4(x1	PROPN
ijassa-111	108	34	)	)	PUNCT
ijassa-111	108	35	.	.	PUNCT
ijassa-111	109	1	in	in	ADP
ijassa-111	109	2	this	this	DET
ijassa-111	109	3	notation	notation	NOUN
ijassa-111	109	4	,	,	PUNCT
ijassa-111	109	5	metric	metric	ADJ
ijassa-111	109	6	(	(	PUNCT
ijassa-111	109	7	11	11	NUM
ijassa-111	109	8	)	)	PUNCT
ijassa-111	109	9	takes	take	VERB
ijassa-111	109	10	the	the	DET
ijassa-111	109	11	following	follow	VERB
ijassa-111	109	12	form	form	NOUN
ijassa-111	109	13	in	in	ADP
ijassa-111	109	14	the	the	DET
ijassa-111	109	15	generalized	generalized	ADJ
ijassa-111	109	16	spherical	spherical	ADJ
ijassa-111	109	17	coordinates	coordinate	NOUN
ijassa-111	109	18	:	:	PUNCT
ijassa-111	109	19	ds2	ds2	PROPN
ijassa-111	109	20	=	=	PUNCT
ijassa-111	109	21	f4dx4	f4dx4	VERB
ijassa-111	109	22	2	2	NUM
ijassa-111	109	23	−	−	NOUN
ijassa-111	109	24	f1dx1	f1dx1	NOUN
ijassa-111	109	25	2	2	NUM
ijassa-111	109	26	−	−	NOUN
ijassa-111	110	1	f2	f2	PROPN
ijassa-111	111	1	(	(	PUNCT
ijassa-111	111	2	dx2	dx2	PROPN
ijassa-111	111	3	2	2	NUM
ijassa-111	111	4	1−	1−	NUM
ijassa-111	111	5	x22	x22	NOUN
ijassa-111	111	6	+	+	CCONJ
ijassa-111	111	7	(	(	PUNCT
ijassa-111	111	8	1−	1−	NUM
ijassa-111	111	9	x2)dx3	x2)dx3	PROPN
ijassa-111	111	10	2	2	NUM
ijassa-111	111	11	)	)	PUNCT
ijassa-111	111	12	.	.	PUNCT
ijassa-111	112	1	(	(	PUNCT
ijassa-111	112	2	15	15	X
ijassa-111	112	3	)	)	PUNCT
ijassa-111	112	4	using	use	VERB
ijassa-111	112	5	the	the	DET
ijassa-111	112	6	arbitrariness	arbitrariness	NOUN
ijassa-111	112	7	of	of	ADP
ijassa-111	112	8	the	the	DET
ijassa-111	112	9	scaling	scale	VERB
ijassa-111	112	10	multiplier	multiplier	ADV
ijassa-111	112	11	of	of	ADP
ijassa-111	112	12	the	the	DET
ijassa-111	112	13	coordinate	coordinate	NOUN
ijassa-111	112	14	x1	x1	INTJ
ijassa-111	112	15	,	,	PUNCT
ijassa-111	112	16	we	we	PRON
ijassa-111	112	17	can	can	AUX
ijassa-111	112	18	achieve	achieve	VERB
ijassa-111	112	19	f1f2	f1f2	PROPN
ijassa-111	112	20	2f4	2f4	NUM
ijassa-111	112	21	=	=	SYM
ijassa-111	112	22	1	1	NUM
ijassa-111	112	23	.	.	PUNCT
ijassa-111	113	1	(	(	PUNCT
ijassa-111	113	2	16	16	NUM
ijassa-111	113	3	)	)	PUNCT
ijassa-111	113	4	264	264	NUM
ijassa-111	113	5	n.n	n.n	PROPN
ijassa-111	113	6	.	.	PROPN
ijassa-111	113	7	popov	popov	PROPN
ijassa-111	113	8	:	:	PUNCT
ijassa-111	113	9	a	a	DET
ijassa-111	113	10	geometric	geometric	ADJ
ijassa-111	113	11	interpretation	interpretation	NOUN
ijassa-111	113	12	of	of	ADP
ijassa-111	113	13	gravity	gravity	NOUN
ijassa-111	113	14	theory	theory	NOUN
ijassa-111	113	15	system	system	NOUN
ijassa-111	113	16	(	(	PUNCT
ijassa-111	113	17	10	10	NUM
ijassa-111	113	18	)	)	PUNCT
ijassa-111	113	19	for	for	ADP
ijassa-111	113	20	metric	metric	ADJ
ijassa-111	113	21	(	(	PUNCT
ijassa-111	113	22	15	15	NUM
ijassa-111	113	23	)	)	PUNCT
ijassa-111	113	24	can	can	AUX
ijassa-111	113	25	be	be	AUX
ijassa-111	113	26	represented	represent	VERB
ijassa-111	113	27	as	as	ADP
ijassa-111	113	28	−1	−1	NOUN
ijassa-111	113	29	2	2	NUM
ijassa-111	113	30	(	(	PUNCT
ijassa-111	113	31	f	f	NOUN
ijassa-111	113	32	′	′	NOUN
ijassa-111	113	33	1	1	NUM
ijassa-111	113	34	f1	f1	NOUN
ijassa-111	113	35	)	)	PUNCT
ijassa-111	113	36	′	′	NUM
ijassa-111	114	1	+	+	CCONJ
ijassa-111	114	2	1	1	NUM
ijassa-111	114	3	2	2	NUM
ijassa-111	114	4	(	(	PUNCT
ijassa-111	114	5	f	f	NOUN
ijassa-111	114	6	′	′	NUM
ijassa-111	114	7	2	2	NUM
ijassa-111	114	8	f2	f2	ADJ
ijassa-111	114	9	)	)	PUNCT
ijassa-111	114	10	2	2	NUM
ijassa-111	114	11	+	+	CCONJ
ijassa-111	114	12	1	1	NUM
ijassa-111	114	13	4	4	NUM
ijassa-111	114	14	(	(	PUNCT
ijassa-111	114	15	f	f	NOUN
ijassa-111	114	16	′	′	NOUN
ijassa-111	114	17	1	1	NUM
ijassa-111	114	18	f1	f1	NOUN
ijassa-111	114	19	)	)	PUNCT
ijassa-111	114	20	2	2	NUM
ijassa-111	114	21	+	+	CCONJ
ijassa-111	114	22	1	1	NUM
ijassa-111	114	23	4	4	NUM
ijassa-111	114	24	(	(	PUNCT
ijassa-111	114	25	f	f	NOUN
ijassa-111	115	1	′	′	NOUN
ijassa-111	115	2	4	4	NUM
ijassa-111	115	3	f4	f4	NUM
ijassa-111	115	4	)	)	PUNCT
ijassa-111	115	5	2	2	NUM
ijassa-111	115	6	=	=	NUM
ijassa-111	115	7	−r	−r	ADJ
ijassa-111	115	8	4	4	NUM
ijassa-111	115	9	f1	f1	NOUN
ijassa-111	115	10	,	,	PUNCT
ijassa-111	115	11	1	1	NUM
ijassa-111	115	12	2	2	NUM
ijassa-111	115	13	(	(	PUNCT
ijassa-111	115	14	f	f	NOUN
ijassa-111	115	15	′	′	NOUN
ijassa-111	115	16	2	2	NUM
ijassa-111	115	17	f1	f1	NOUN
ijassa-111	115	18	)	)	PUNCT
ijassa-111	115	19	′	′	NUM
ijassa-111	116	1	−	−	NUM
ijassa-111	116	2	1	1	NUM
ijassa-111	116	3	2f1f2	2f1f2	NUM
ijassa-111	116	4	(	(	PUNCT
ijassa-111	116	5	f	f	NOUN
ijassa-111	116	6	′	′	NUM
ijassa-111	116	7	2	2	NUM
ijassa-111	116	8	)	)	PUNCT
ijassa-111	116	9	2	2	NUM
ijassa-111	116	10	−	−	NOUN
ijassa-111	116	11	1	1	NUM
ijassa-111	116	12	=	=	NUM
ijassa-111	116	13	−r	−r	ADJ
ijassa-111	116	14	4	4	NUM
ijassa-111	116	15	f2	f2	ADJ
ijassa-111	116	16	,	,	PUNCT
ijassa-111	116	17	(	(	PUNCT
ijassa-111	116	18	17	17	NUM
ijassa-111	116	19	)	)	PUNCT
ijassa-111	116	20	−1	−1	NOUN
ijassa-111	116	21	2	2	NUM
ijassa-111	116	22	(	(	PUNCT
ijassa-111	116	23	f	f	NOUN
ijassa-111	116	24	′	′	NOUN
ijassa-111	116	25	4	4	NUM
ijassa-111	116	26	f1	f1	NOUN
ijassa-111	116	27	)	)	PUNCT
ijassa-111	116	28	′	′	NUM
ijassa-111	117	1	+	+	CCONJ
ijassa-111	117	2	1	1	NUM
ijassa-111	117	3	2f1f4	2f1f4	NUM
ijassa-111	117	4	(	(	PUNCT
ijassa-111	117	5	f	f	NOUN
ijassa-111	117	6	′	′	NUM
ijassa-111	117	7	4	4	NUM
ijassa-111	117	8	)	)	PUNCT
ijassa-111	117	9	2	2	NUM
ijassa-111	117	10	=	=	SYM
ijassa-111	117	11	r	r	NOUN
ijassa-111	117	12	4	4	NUM
ijassa-111	117	13	f4	f4	NOUN
ijassa-111	117	14	.	.	PUNCT
ijassa-111	118	1	condition	condition	NOUN
ijassa-111	118	2	(	(	PUNCT
ijassa-111	118	3	16	16	NUM
ijassa-111	118	4	)	)	PUNCT
ijassa-111	118	5	gives	give	VERB
ijassa-111	118	6	the	the	DET
ijassa-111	118	7	additional	additional	ADJ
ijassa-111	118	8	equation	equation	NOUN
ijassa-111	118	9	f	f	NOUN
ijassa-111	118	10	′	′	NOUN
ijassa-111	118	11	1	1	NUM
ijassa-111	118	12	f1	f1	NOUN
ijassa-111	118	13	+	+	CCONJ
ijassa-111	118	14	2f	2f	NUM
ijassa-111	118	15	′	′	NUM
ijassa-111	118	16	2	2	NUM
ijassa-111	118	17	f2	f2	PROPN
ijassa-111	119	1	+	+	NOUN
ijassa-111	119	2	f	f	NOUN
ijassa-111	119	3	′	′	NOUN
ijassa-111	119	4	4	4	NUM
ijassa-111	119	5	f4	f4	NOUN
ijassa-111	119	6	=	=	SYM
ijassa-111	119	7	0	0	NUM
ijassa-111	119	8	,	,	PUNCT
ijassa-111	119	9	(	(	PUNCT
ijassa-111	119	10	18	18	NUM
ijassa-111	119	11	)	)	PUNCT
ijassa-111	119	12	where	where	SCONJ
ijassa-111	119	13	f	f	NOUN
ijassa-111	120	1	′	′	VERB
ijassa-111	121	1	i	i	PRON
ijassa-111	122	1	=	=	SYM
ijassa-111	122	2	dfi	dfi	PROPN
ijassa-111	122	3	dxi	dxi	NOUN
ijassa-111	122	4	.	.	PUNCT
ijassa-111	123	1	system	system	NOUN
ijassa-111	123	2	(	(	PUNCT
ijassa-111	123	3	17	17	NUM
ijassa-111	123	4	)	)	PUNCT
ijassa-111	123	5	,	,	PUNCT
ijassa-111	123	6	(	(	PUNCT
ijassa-111	123	7	18	18	NUM
ijassa-111	123	8	)	)	PUNCT
ijassa-111	123	9	contains	contain	VERB
ijassa-111	123	10	four	four	NUM
ijassa-111	123	11	unknown	unknown	ADJ
ijassa-111	123	12	functions	function	NOUN
ijassa-111	123	13	f1	f1	NOUN
ijassa-111	123	14	,	,	PUNCT
ijassa-111	123	15	f2	f2	PROPN
ijassa-111	123	16	,	,	PUNCT
ijassa-111	123	17	f4	f4	PROPN
ijassa-111	123	18	,	,	PUNCT
ijassa-111	123	19	and	and	CCONJ
ijassa-111	123	20	r	r	NOUN
ijassa-111	123	21	;	;	PUNCT
ijassa-111	123	22	only	only	ADV
ijassa-111	123	23	two	two	NUM
ijassa-111	123	24	of	of	ADP
ijassa-111	123	25	these	these	DET
ijassa-111	123	26	functions	function	NOUN
ijassa-111	123	27	,	,	PUNCT
ijassa-111	123	28	say	say	VERB
ijassa-111	123	29	f2	f2	PROPN
ijassa-111	123	30	and	and	CCONJ
ijassa-111	123	31	r	r	NOUN
ijassa-111	123	32	,	,	PUNCT
ijassa-111	123	33	can	can	AUX
ijassa-111	123	34	be	be	AUX
ijassa-111	123	35	regarded	regard	VERB
ijassa-111	123	36	to	to	PART
ijassa-111	123	37	be	be	AUX
ijassa-111	123	38	independent	independent	ADJ
ijassa-111	123	39	.	.	PUNCT
ijassa-111	124	1	this	this	PRON
ijassa-111	124	2	follows	follow	VERB
ijassa-111	124	3	from	from	ADP
ijassa-111	124	4	relations	relation	NOUN
ijassa-111	124	5	(	(	PUNCT
ijassa-111	124	6	3	3	NUM
ijassa-111	124	7	)	)	PUNCT
ijassa-111	124	8	and	and	CCONJ
ijassa-111	124	9	(	(	PUNCT
ijassa-111	124	10	16	16	NUM
ijassa-111	124	11	)	)	PUNCT
ijassa-111	124	12	.	.	PUNCT
ijassa-111	125	1	let	let	VERB
ijassa-111	125	2	us	we	PRON
ijassa-111	125	3	express	express	VERB
ijassa-111	125	4	the	the	DET
ijassa-111	125	5	unknown	unknown	ADJ
ijassa-111	125	6	functions	function	NOUN
ijassa-111	125	7	f1	f1	NOUN
ijassa-111	125	8	and	and	CCONJ
ijassa-111	125	9	f4	f4	NOUN
ijassa-111	125	10	in	in	ADP
ijassa-111	125	11	terms	term	NOUN
ijassa-111	125	12	of	of	ADP
ijassa-111	125	13	f2	f2	PROPN
ijassa-111	125	14	and	and	CCONJ
ijassa-111	125	15	r	r	NOUN
ijassa-111	125	16	.	.	PUNCT
ijassa-111	126	1	for	for	ADP
ijassa-111	126	2	this	this	DET
ijassa-111	126	3	purpose	purpose	NOUN
ijassa-111	126	4	,	,	PUNCT
ijassa-111	126	5	note	note	VERB
ijassa-111	126	6	that	that	SCONJ
ijassa-111	126	7	the	the	DET
ijassa-111	126	8	third	third	ADJ
ijassa-111	126	9	equation	equation	NOUN
ijassa-111	126	10	in	in	ADP
ijassa-111	126	11	system	system	NOUN
ijassa-111	126	12	(	(	PUNCT
ijassa-111	126	13	17	17	NUM
ijassa-111	126	14	)	)	PUNCT
ijassa-111	126	15	can	can	AUX
ijassa-111	126	16	be	be	AUX
ijassa-111	126	17	represented	represent	VERB
ijassa-111	126	18	as	as	ADP
ijassa-111	126	19	1	1	NUM
ijassa-111	126	20	2f1f4	2f1f4	NUM
ijassa-111	126	21	f	f	NOUN
ijassa-111	126	22	′	′	NUM
ijassa-111	126	23	1f	1f	NUM
ijassa-111	127	1	′	′	NUM
ijassa-111	127	2	4	4	NUM
ijassa-111	127	3	−	−	NUM
ijassa-111	127	4	1	1	NUM
ijassa-111	127	5	2	2	NUM
ijassa-111	127	6	(	(	PUNCT
ijassa-111	127	7	f	f	NOUN
ijassa-111	127	8	′	′	NOUN
ijassa-111	127	9	4	4	NUM
ijassa-111	127	10	f4	f4	NUM
ijassa-111	127	11	)	)	PUNCT
ijassa-111	127	12	′	′	NUM
ijassa-111	128	1	=	=	PUNCT
ijassa-111	128	2	r	r	NOUN
ijassa-111	128	3	4	4	NUM
ijassa-111	128	4	f1	f1	NOUN
ijassa-111	128	5	.	.	PUNCT
ijassa-111	129	1	(	(	PUNCT
ijassa-111	129	2	19	19	NUM
ijassa-111	129	3	)	)	PUNCT
ijassa-111	129	4	adding	add	VERB
ijassa-111	129	5	the	the	DET
ijassa-111	129	6	first	first	ADJ
ijassa-111	129	7	equation	equation	NOUN
ijassa-111	129	8	in	in	ADP
ijassa-111	129	9	system	system	NOUN
ijassa-111	129	10	(	(	PUNCT
ijassa-111	129	11	17	17	NUM
ijassa-111	129	12	)	)	PUNCT
ijassa-111	129	13	to	to	ADP
ijassa-111	129	14	equation	equation	NOUN
ijassa-111	129	15	(	(	PUNCT
ijassa-111	129	16	19	19	NUM
ijassa-111	129	17	)	)	PUNCT
ijassa-111	129	18	and	and	CCONJ
ijassa-111	129	19	using	use	VERB
ijassa-111	129	20	(	(	PUNCT
ijassa-111	129	21	18	18	NUM
ijassa-111	129	22	)	)	PUNCT
ijassa-111	129	23	,	,	PUNCT
ijassa-111	129	24	we	we	PRON
ijassa-111	129	25	obtain	obtain	VERB
ijassa-111	129	26	the	the	DET
ijassa-111	129	27	relation	relation	NOUN
ijassa-111	129	28	(	(	PUNCT
ijassa-111	129	29	f	f	NOUN
ijassa-111	129	30	′	′	NOUN
ijassa-111	129	31	2	2	NUM
ijassa-111	129	32	f2	f2	ADV
ijassa-111	129	33	)	)	PUNCT
ijassa-111	129	34	′	′	PUNCT
ijassa-111	130	1	+	+	CCONJ
ijassa-111	130	2	3	3	NUM
ijassa-111	130	3	2	2	NUM
ijassa-111	130	4	(	(	PUNCT
ijassa-111	130	5	f	f	NOUN
ijassa-111	130	6	′	′	NUM
ijassa-111	130	7	2	2	NUM
ijassa-111	130	8	f2	f2	ADJ
ijassa-111	130	9	)	)	PUNCT
ijassa-111	130	10	2	2	NUM
ijassa-111	130	11	=	=	SYM
ijassa-111	130	12	0	0	NUM
ijassa-111	130	13	.	.	PUNCT
ijassa-111	131	1	twice	twice	ADV
ijassa-111	131	2	integrating	integrate	VERB
ijassa-111	131	3	it	it	PRON
ijassa-111	131	4	,	,	PUNCT
ijassa-111	131	5	we	we	PRON
ijassa-111	131	6	obtain	obtain	VERB
ijassa-111	131	7	f2	f2	ADV
ijassa-111	131	8	=	=	PUNCT
ijassa-111	131	9	λ(3x1	λ(3x1	X
ijassa-111	131	10	+	+	NUM
ijassa-111	131	11	α	α	X
ijassa-111	131	12	)	)	PUNCT
ijassa-111	131	13	2	2	NUM
ijassa-111	131	14	3	3	NUM
ijassa-111	131	15	,	,	PUNCT
ijassa-111	131	16	where	where	SCONJ
ijassa-111	131	17	λ	λ	PROPN
ijassa-111	131	18	and	and	CCONJ
ijassa-111	131	19	α	α	NOUN
ijassa-111	131	20	are	be	AUX
ijassa-111	131	21	arbitrary	arbitrary	ADJ
ijassa-111	131	22	constants	constant	NOUN
ijassa-111	131	23	of	of	ADP
ijassa-111	131	24	integration	integration	NOUN
ijassa-111	131	25	.	.	PUNCT
ijassa-111	132	1	by	by	ADP
ijassa-111	132	2	the	the	DET
ijassa-111	132	3	assumption	assumption	NOUN
ijassa-111	132	4	of	of	ADP
ijassa-111	132	5	the	the	DET
ijassa-111	132	6	theorem	theorem	NOUN
ijassa-111	132	7	,	,	PUNCT
ijassa-111	132	8	we	we	PRON
ijassa-111	132	9	have	have	AUX
ijassa-111	132	10	f2(0	f2(0	VERB
ijassa-111	132	11	)	)	PUNCT
ijassa-111	133	1	=	=	SYM
ijassa-111	133	2	0	0	NUM
ijassa-111	133	3	,	,	PUNCT
ijassa-111	133	4	which	which	PRON
ijassa-111	133	5	implies	imply	VERB
ijassa-111	133	6	α	α	X
ijassa-111	133	7	=	=	SYM
ijassa-111	133	8	0	0	NUM
ijassa-111	133	9	and	and	CCONJ
ijassa-111	133	10	f2	f2	X
ijassa-111	133	11	=	=	SYM
ijassa-111	133	12	λ(3x1	λ(3x1	ADJ
ijassa-111	133	13	)	)	PUNCT
ijassa-111	133	14	2	2	NUM
ijassa-111	133	15	3	3	NUM
ijassa-111	133	16	.	.	PUNCT
ijassa-111	134	1	(	(	PUNCT
ijassa-111	134	2	20	20	NUM
ijassa-111	134	3	)	)	PUNCT
ijassa-111	134	4	we	we	PRON
ijassa-111	134	5	seek	seek	VERB
ijassa-111	134	6	f	f	NOUN
ijassa-111	135	1	′	′	NOUN
ijassa-111	135	2	4	4	NUM
ijassa-111	135	3	f4	f4	NOUN
ijassa-111	135	4	in	in	ADP
ijassa-111	135	5	(	(	PUNCT
ijassa-111	135	6	19	19	NUM
ijassa-111	135	7	)	)	PUNCT
ijassa-111	135	8	in	in	ADP
ijassa-111	135	9	the	the	DET
ijassa-111	135	10	form	form	NOUN
ijassa-111	135	11	f	f	PROPN
ijassa-111	136	1	′	′	NOUN
ijassa-111	136	2	4	4	NUM
ijassa-111	136	3	f4	f4	NOUN
ijassa-111	136	4	=	=	NOUN
ijassa-111	136	5	c(x1)f1	c(x1)f1	NOUN
ijassa-111	136	6	.	.	PUNCT
ijassa-111	137	1	substituting	substitute	VERB
ijassa-111	137	2	the	the	DET
ijassa-111	137	3	last	last	ADJ
ijassa-111	137	4	relation	relation	NOUN
ijassa-111	137	5	into	into	ADP
ijassa-111	137	6	equation	equation	NOUN
ijassa-111	137	7	(	(	PUNCT
ijassa-111	137	8	19	19	NUM
ijassa-111	137	9	)	)	PUNCT
ijassa-111	137	10	,	,	PUNCT
ijassa-111	137	11	we	we	PRON
ijassa-111	137	12	obtain	obtain	VERB
ijassa-111	137	13	f	f	PROPN
ijassa-111	138	1	′	′	NUM
ijassa-111	138	2	4	4	NUM
ijassa-111	138	3	=	=	SYM
ijassa-111	138	4	c	c	NOUN
ijassa-111	138	5	−	−	NOUN
ijassa-111	138	6	1	1	NUM
ijassa-111	138	7	2	2	NUM
ijassa-111	138	8	∫	∫	NOUN
ijassa-111	138	9	rdx1	rdx1	PROPN
ijassa-111	138	10	λ2(3x1	λ2(3x1	ADV
ijassa-111	138	11	)	)	PUNCT
ijassa-111	138	12	4	4	NUM
ijassa-111	138	13	3	3	NUM
ijassa-111	138	14	,	,	PUNCT
ijassa-111	138	15	where	where	SCONJ
ijassa-111	138	16	c	c	NOUN
ijassa-111	138	17	is	be	AUX
ijassa-111	138	18	a	a	DET
ijassa-111	138	19	constant	constant	ADJ
ijassa-111	138	20	.	.	PUNCT
ijassa-111	139	1	integrating	integrate	VERB
ijassa-111	139	2	both	both	DET
ijassa-111	139	3	sides	side	NOUN
ijassa-111	139	4	of	of	ADP
ijassa-111	139	5	this	this	DET
ijassa-111	139	6	relation	relation	NOUN
ijassa-111	139	7	,	,	PUNCT
ijassa-111	139	8	we	we	PRON
ijassa-111	139	9	arrive	arrive	VERB
ijassa-111	139	10	at	at	ADP
ijassa-111	139	11	the	the	DET
ijassa-111	139	12	formula	formula	NOUN
ijassa-111	139	13	f4	f4	NOUN
ijassa-111	139	14	=	=	SYM
ijassa-111	139	15	β	β	X
ijassa-111	139	16	−	−	NOUN
ijassa-111	139	17	c	c	NOUN
ijassa-111	139	18	λ2(3x1	λ2(3x1	NOUN
ijassa-111	139	19	)	)	PUNCT
ijassa-111	139	20	1	1	NUM
ijassa-111	139	21	3	3	NUM
ijassa-111	139	22	+	+	SYM
ijassa-111	139	23	1	1	NUM
ijassa-111	139	24	2λ2	2λ2	NUM
ijassa-111	139	25	∫	∫	NOUN
ijassa-111	139	26	rdx1	rdx1	PROPN
ijassa-111	139	27	(	(	PUNCT
ijassa-111	139	28	3x1	3x1	NUM
ijassa-111	139	29	)	)	PUNCT
ijassa-111	139	30	1	1	NUM
ijassa-111	139	31	3	3	NUM
ijassa-111	139	32	−	−	NUM
ijassa-111	139	33	1	1	NUM
ijassa-111	139	34	2λ2	2λ2	NUM
ijassa-111	139	35	∫	∫	NOUN
ijassa-111	139	36	r	r	NOUN
ijassa-111	139	37	(	(	PUNCT
ijassa-111	139	38	3x1	3x1	NUM
ijassa-111	139	39	)	)	PUNCT
ijassa-111	139	40	1	1	NUM
ijassa-111	139	41	3	3	NUM
ijassa-111	139	42	dx1	dx1	PROPN
ijassa-111	139	43	,	,	PUNCT
ijassa-111	139	44	(	(	PUNCT
ijassa-111	139	45	21	21	NUM
ijassa-111	139	46	)	)	PUNCT
ijassa-111	139	47	advances	advance	NOUN
ijassa-111	139	48	in	in	ADP
ijassa-111	139	49	systems	system	NOUN
ijassa-111	139	50	science	science	NOUN
ijassa-111	139	51	and	and	CCONJ
ijassa-111	139	52	applications	application	NOUN
ijassa-111	139	53	(	(	PUNCT
ijassa-111	139	54	2012	2012	NUM
ijassa-111	139	55	)	)	PUNCT
ijassa-111	139	56	vol.12	vol.12	NOUN
ijassa-111	139	57	no.3	no.3	VERB
ijassa-111	139	58	265	265	NUM
ijassa-111	139	59	where	where	SCONJ
ijassa-111	139	60	β	β	NOUN
ijassa-111	139	61	is	be	AUX
ijassa-111	139	62	constant	constant	ADJ
ijassa-111	139	63	of	of	ADP
ijassa-111	139	64	integration	integration	NOUN
ijassa-111	139	65	.	.	PUNCT
ijassa-111	140	1	by	by	ADP
ijassa-111	140	2	the	the	DET
ijassa-111	140	3	assumption	assumption	NOUN
ijassa-111	140	4	of	of	ADP
ijassa-111	140	5	the	the	DET
ijassa-111	140	6	theorem	theorem	NOUN
ijassa-111	140	7	,	,	PUNCT
ijassa-111	140	8	the	the	DET
ijassa-111	140	9	function	function	NOUN
ijassa-111	140	10	f4(0	f4(0	NOUN
ijassa-111	140	11	)	)	PUNCT
ijassa-111	140	12	is	be	AUX
ijassa-111	140	13	bounded	bound	VERB
ijassa-111	140	14	;	;	PUNCT
ijassa-111	140	15	therefore	therefore	ADV
ijassa-111	140	16	,	,	PUNCT
ijassa-111	140	17	considering	consider	VERB
ijassa-111	140	18	a	a	DET
ijassa-111	140	19	solution	solution	NOUN
ijassa-111	140	20	in	in	ADP
ijassa-111	140	21	some	some	DET
ijassa-111	140	22	neighborhood	neighborhood	NOUN
ijassa-111	140	23	of	of	ADP
ijassa-111	140	24	zero	zero	NUM
ijassa-111	140	25	,	,	PUNCT
ijassa-111	140	26	we	we	PRON
ijassa-111	140	27	must	must	AUX
ijassa-111	140	28	set	set	VERB
ijassa-111	140	29	c	c	NOUN
ijassa-111	140	30	=	=	SYM
ijassa-111	140	31	0	0	NUM
ijassa-111	140	32	,	,	PUNCT
ijassa-111	140	33	and	and	CCONJ
ijassa-111	140	34	the	the	DET
ijassa-111	140	35	formula	formula	NOUN
ijassa-111	140	36	for	for	ADP
ijassa-111	140	37	f4	f4	PROPN
ijassa-111	140	38	takes	take	VERB
ijassa-111	140	39	the	the	DET
ijassa-111	140	40	form	form	NOUN
ijassa-111	140	41	f4	f4	NOUN
ijassa-111	140	42	=	=	SYM
ijassa-111	140	43	β	β	NOUN
ijassa-111	140	44	+	+	CCONJ
ijassa-111	140	45	∫	∫	PROPN
ijassa-111	140	46	r(x1)dx1	r(x1)dx1	PROPN
ijassa-111	140	47	2λ2(3x1	2λ2(3x1	NUM
ijassa-111	140	48	)	)	PUNCT
ijassa-111	140	49	1	1	NUM
ijassa-111	140	50	3	3	NUM
ijassa-111	140	51	−	−	PROPN
ijassa-111	140	52	1	1	NUM
ijassa-111	140	53	2λ2	2λ2	NUM
ijassa-111	140	54	∫	∫	NOUN
ijassa-111	140	55	r(x1	r(x1	PROPN
ijassa-111	140	56	)	)	PUNCT
ijassa-111	140	57	(	(	PUNCT
ijassa-111	140	58	3x1	3x1	NUM
ijassa-111	140	59	)	)	PUNCT
ijassa-111	140	60	1	1	NUM
ijassa-111	140	61	3	3	NUM
ijassa-111	140	62	dx1	dx1	X
ijassa-111	140	63	.	.	PUNCT
ijassa-111	141	1	(	(	PUNCT
ijassa-111	141	2	22	22	NUM
ijassa-111	141	3	)	)	PUNCT
ijassa-111	141	4	condition	condition	NOUN
ijassa-111	141	5	(	(	PUNCT
ijassa-111	141	6	16	16	NUM
ijassa-111	141	7	)	)	PUNCT
ijassa-111	141	8	implies	imply	VERB
ijassa-111	141	9	f1	f1	NOUN
ijassa-111	141	10	=	=	NOUN
ijassa-111	141	11	1	1	NUM
ijassa-111	141	12	λ2(3x1	λ2(3x1	NUM
ijassa-111	141	13	)	)	PUNCT
ijassa-111	141	14	4	4	NUM
ijassa-111	141	15	3	3	NUM
ijassa-111	141	16	1	1	NUM
ijassa-111	141	17	f4	f4	NOUN
ijassa-111	141	18	.	.	PUNCT
ijassa-111	142	1	(	(	PUNCT
ijassa-111	142	2	23	23	NUM
ijassa-111	142	3	)	)	PUNCT
ijassa-111	142	4	the	the	DET
ijassa-111	142	5	functions	function	NOUN
ijassa-111	142	6	f1	f1	NOUN
ijassa-111	142	7	,	,	PUNCT
ijassa-111	142	8	f2	f2	PROPN
ijassa-111	142	9	,	,	PUNCT
ijassa-111	142	10	and	and	CCONJ
ijassa-111	142	11	f4	f4	PRON
ijassa-111	142	12	specified	specify	VERB
ijassa-111	142	13	by	by	ADP
ijassa-111	142	14	(	(	PUNCT
ijassa-111	142	15	20	20	NUM
ijassa-111	142	16	)	)	PUNCT
ijassa-111	142	17	,	,	PUNCT
ijassa-111	142	18	(	(	PUNCT
ijassa-111	142	19	22	22	NUM
ijassa-111	142	20	)	)	PUNCT
ijassa-111	142	21	,	,	PUNCT
ijassa-111	142	22	and	and	CCONJ
ijassa-111	142	23	(	(	PUNCT
ijassa-111	142	24	23	23	NUM
ijassa-111	142	25	)	)	PUNCT
ijassa-111	142	26	satisfy	satisfy	NOUN
ijassa-111	142	27	system	system	NOUN
ijassa-111	142	28	(	(	PUNCT
ijassa-111	142	29	17	17	NUM
ijassa-111	142	30	)	)	PUNCT
ijassa-111	142	31	of	of	ADP
ijassa-111	142	32	differential	differential	ADJ
ijassa-111	142	33	equations	equation	NOUN
ijassa-111	142	34	only	only	ADV
ijassa-111	142	35	if	if	SCONJ
ijassa-111	142	36	βλ3	βλ3	NOUN
ijassa-111	142	37	=	=	SYM
ijassa-111	142	38	1,∫	1,∫	NUM
ijassa-111	142	39	r(x1	r(x1	NOUN
ijassa-111	142	40	)	)	PUNCT
ijassa-111	142	41	(	(	PUNCT
ijassa-111	142	42	3x1	3x1	NUM
ijassa-111	142	43	)	)	PUNCT
ijassa-111	142	44	1	1	NUM
ijassa-111	142	45	3	3	NUM
ijassa-111	142	46	dx1	dx1	X
ijassa-111	142	47	=	=	SYM
ijassa-111	142	48	r(x1	r(x1	PROPN
ijassa-111	142	49	)	)	PUNCT
ijassa-111	142	50	2	2	NUM
ijassa-111	142	51	(	(	PUNCT
ijassa-111	142	52	3x1	3x1	NUM
ijassa-111	142	53	)	)	PUNCT
ijassa-111	142	54	2	2	NUM
ijassa-111	142	55	3	3	NUM
ijassa-111	142	56	.	.	PUNCT
ijassa-111	143	1	(	(	PUNCT
ijassa-111	143	2	24	24	NUM
ijassa-111	143	3	)	)	PUNCT
ijassa-111	143	4	it	it	PRON
ijassa-111	143	5	follows	follow	VERB
ijassa-111	143	6	from	from	ADP
ijassa-111	143	7	relation	relation	NOUN
ijassa-111	143	8	(	(	PUNCT
ijassa-111	143	9	24	24	NUM
ijassa-111	143	10	)	)	PUNCT
ijassa-111	143	11	that	that	SCONJ
ijassa-111	143	12	the	the	DET
ijassa-111	143	13	function	function	NOUN
ijassa-111	143	14	r(x1	r(x1	NOUN
ijassa-111	143	15	)	)	PUNCT
ijassa-111	143	16	must	must	AUX
ijassa-111	143	17	be	be	AUX
ijassa-111	143	18	constant	constant	ADJ
ijassa-111	143	19	in	in	ADP
ijassa-111	143	20	the	the	DET
ijassa-111	143	21	domain	domain	NOUN
ijassa-111	143	22	where	where	SCONJ
ijassa-111	143	23	it	it	PRON
ijassa-111	143	24	is	be	AUX
ijassa-111	143	25	nonzero	nonzero	NOUN
ijassa-111	143	26	.	.	PUNCT
ijassa-111	144	1	thus	thus	ADV
ijassa-111	144	2	,	,	PUNCT
ijassa-111	144	3	inside	inside	ADP
ijassa-111	144	4	the	the	DET
ijassa-111	144	5	ball	ball	NOUN
ijassa-111	144	6	of	of	ADP
ijassa-111	144	7	radius	radius	NOUN
ijassa-111	144	8	r1	r1	PROPN
ijassa-111	144	9	,	,	PUNCT
ijassa-111	144	10	the	the	DET
ijassa-111	144	11	components	component	NOUN
ijassa-111	144	12	of	of	ADP
ijassa-111	144	13	metric	metric	ADJ
ijassa-111	144	14	(	(	PUNCT
ijassa-111	144	15	25	25	NUM
ijassa-111	144	16	)	)	PUNCT
ijassa-111	144	17	have	have	VERB
ijassa-111	144	18	the	the	DET
ijassa-111	144	19	form	form	NOUN
ijassa-111	144	20	f2	f2	ADV
ijassa-111	144	21	=	=	SYM
ijassa-111	144	22	λ(3x1	λ(3x1	NUM
ijassa-111	144	23	)	)	PUNCT
ijassa-111	144	24	2	2	NUM
ijassa-111	144	25	3	3	NUM
ijassa-111	144	26	,	,	PUNCT
ijassa-111	144	27	f4	f4	NOUN
ijassa-111	144	28	=	=	SYM
ijassa-111	144	29	1	1	NUM
ijassa-111	144	30	λ3	λ3	PROPN
ijassa-111	144	31	−	−	NOUN
ijassa-111	144	32	r	r	NOUN
ijassa-111	144	33	12	12	NUM
ijassa-111	144	34	(	(	PUNCT
ijassa-111	144	35	3x1	3x1	NUM
ijassa-111	144	36	)	)	PUNCT
ijassa-111	144	37	2	2	NUM
ijassa-111	144	38	3	3	NUM
ijassa-111	144	39	λ2	λ2	NOUN
ijassa-111	144	40	,	,	PUNCT
ijassa-111	144	41	f1	f1	NOUN
ijassa-111	144	42	=	=	NOUN
ijassa-111	144	43	1	1	NUM
ijassa-111	144	44	λ2(3x1	λ2(3x1	NUM
ijassa-111	144	45	)	)	PUNCT
ijassa-111	144	46	4	4	NUM
ijassa-111	144	47	3	3	NUM
ijassa-111	144	48	1	1	NUM
ijassa-111	144	49	f4	f4	NOUN
ijassa-111	144	50	.	.	PUNCT
ijassa-111	145	1	(	(	PUNCT
ijassa-111	145	2	25	25	NUM
ijassa-111	145	3	)	)	PUNCT
ijassa-111	145	4	outside	outside	ADP
ijassa-111	145	5	the	the	DET
ijassa-111	145	6	ball	ball	NOUN
ijassa-111	145	7	,	,	PUNCT
ijassa-111	145	8	the	the	DET
ijassa-111	145	9	scalar	scalar	ADJ
ijassa-111	145	10	curvature	curvature	NOUN
ijassa-111	145	11	vanishes	vanish	VERB
ijassa-111	145	12	,	,	PUNCT
ijassa-111	145	13	and	and	CCONJ
ijassa-111	145	14	relation	relation	NOUN
ijassa-111	145	15	(	(	PUNCT
ijassa-111	145	16	21	21	NUM
ijassa-111	145	17	)	)	PUNCT
ijassa-111	145	18	implies	imply	VERB
ijassa-111	145	19	that	that	SCONJ
ijassa-111	145	20	the	the	DET
ijassa-111	145	21	components	component	NOUN
ijassa-111	145	22	of	of	ADP
ijassa-111	145	23	metric	metric	ADJ
ijassa-111	145	24	(	(	PUNCT
ijassa-111	145	25	15	15	NUM
ijassa-111	145	26	)	)	PUNCT
ijassa-111	145	27	have	have	VERB
ijassa-111	145	28	the	the	DET
ijassa-111	145	29	form	form	NOUN
ijassa-111	145	30	f2	f2	ADV
ijassa-111	145	31	=	=	SYM
ijassa-111	145	32	λ(3x1	λ(3x1	NUM
ijassa-111	145	33	)	)	PUNCT
ijassa-111	145	34	2	2	NUM
ijassa-111	145	35	3	3	NUM
ijassa-111	145	36	,	,	PUNCT
ijassa-111	145	37	f4	f4	NOUN
ijassa-111	145	38	=	=	SYM
ijassa-111	145	39	1	1	NUM
ijassa-111	145	40	λ3	λ3	PROPN
ijassa-111	146	1	−	−	PROPN
ijassa-111	146	2	c	c	NOUN
ijassa-111	146	3	λ2(3x1	λ2(3x1	NOUN
ijassa-111	146	4	)	)	PUNCT
ijassa-111	146	5	1	1	NUM
ijassa-111	146	6	3	3	NUM
ijassa-111	146	7	.	.	PUNCT
ijassa-111	147	1	(	(	PUNCT
ijassa-111	147	2	26	26	NUM
ijassa-111	147	3	)	)	PUNCT
ijassa-111	147	4	these	these	DET
ijassa-111	147	5	components	component	NOUN
ijassa-111	147	6	satisfy	satisfy	VERB
ijassa-111	147	7	also	also	ADV
ijassa-111	147	8	system	system	NOUN
ijassa-111	147	9	(	(	PUNCT
ijassa-111	147	10	17),(18	17),(18	NUM
ijassa-111	147	11	)	)	PUNCT
ijassa-111	147	12	.	.	PUNCT
ijassa-111	148	1	the	the	DET
ijassa-111	148	2	constant	constant	ADJ
ijassa-111	148	3	c	c	NOUN
ijassa-111	148	4	in	in	ADP
ijassa-111	148	5	(	(	PUNCT
ijassa-111	148	6	26	26	NUM
ijassa-111	148	7	)	)	PUNCT
ijassa-111	148	8	is	be	AUX
ijassa-111	148	9	found	find	VERB
ijassa-111	148	10	from	from	ADP
ijassa-111	148	11	the	the	DET
ijassa-111	148	12	condition	condition	NOUN
ijassa-111	148	13	that	that	SCONJ
ijassa-111	148	14	the	the	DET
ijassa-111	148	15	metric	metric	ADJ
ijassa-111	148	16	components	component	NOUN
ijassa-111	148	17	must	must	AUX
ijassa-111	148	18	be	be	AUX
ijassa-111	148	19	continuous	continuous	ADJ
ijassa-111	148	20	on	on	ADP
ijassa-111	148	21	the	the	DET
ijassa-111	148	22	entire	entire	ADJ
ijassa-111	148	23	space	space	NOUN
ijassa-111	148	24	,	,	PUNCT
ijassa-111	148	25	which	which	PRON
ijassa-111	148	26	implies	imply	VERB
ijassa-111	148	27	c	c	NOUN
ijassa-111	148	28	=	=	SYM
ijassa-111	148	29	r	r	NOUN
ijassa-111	148	30	12r1	12r1	NUM
ijassa-111	148	31	3	3	NUM
ijassa-111	148	32	.	.	PUNCT
ijassa-111	148	33	system	system	NOUN
ijassa-111	148	34	(	(	PUNCT
ijassa-111	148	35	17	17	NUM
ijassa-111	148	36	)	)	PUNCT
ijassa-111	148	37	,	,	PUNCT
ijassa-111	148	38	(	(	PUNCT
ijassa-111	148	39	18	18	NUM
ijassa-111	148	40	)	)	PUNCT
ijassa-111	148	41	has	have	VERB
ijassa-111	148	42	the	the	DET
ijassa-111	148	43	unique	unique	ADJ
ijassa-111	148	44	solution	solution	NOUN
ijassa-111	148	45	(	(	PUNCT
ijassa-111	148	46	25	25	NUM
ijassa-111	148	47	)	)	PUNCT
ijassa-111	148	48	,	,	PUNCT
ijassa-111	148	49	(	(	PUNCT
ijassa-111	148	50	26	26	NUM
ijassa-111	148	51	)	)	PUNCT
ijassa-111	148	52	,	,	PUNCT
ijassa-111	148	53	which	which	PRON
ijassa-111	148	54	contains	contain	VERB
ijassa-111	148	55	one	one	NUM
ijassa-111	148	56	free	free	ADJ
ijassa-111	148	57	parameter	parameter	NOUN
ijassa-111	148	58	λ	λ	PROPN
ijassa-111	148	59	.	.	PUNCT
ijassa-111	149	1	taking	take	VERB
ijassa-111	149	2	into	into	ADP
ijassa-111	149	3	account	account	NOUN
ijassa-111	149	4	the	the	DET
ijassa-111	149	5	additional	additional	ADJ
ijassa-111	149	6	condition	condition	NOUN
ijassa-111	149	7	g44(0	g44(0	NOUN
ijassa-111	149	8	)	)	PUNCT
ijassa-111	149	9	=	=	SYM
ijassa-111	149	10	1	1	NUM
ijassa-111	149	11	in	in	ADP
ijassa-111	149	12	the	the	DET
ijassa-111	149	13	theorem	theorem	NOUN
ijassa-111	149	14	,	,	PUNCT
ijassa-111	149	15	which	which	PRON
ijassa-111	149	16	implies	imply	VERB
ijassa-111	149	17	λ	λ	PROPN
ijassa-111	149	18	=	=	SYM
ijassa-111	149	19	1	1	NUM
ijassa-111	149	20	,	,	PUNCT
ijassa-111	149	21	and	and	CCONJ
ijassa-111	149	22	passing	pass	VERB
ijassa-111	149	23	to	to	ADP
ijassa-111	149	24	the	the	DET
ijassa-111	149	25	usual	usual	ADJ
ijassa-111	149	26	spherical	spherical	ADJ
ijassa-111	149	27	coordinates	coordinate	NOUN
ijassa-111	149	28	,	,	PUNCT
ijassa-111	149	29	we	we	PRON
ijassa-111	149	30	see	see	VERB
ijassa-111	149	31	that	that	SCONJ
ijassa-111	149	32	relations	relation	NOUN
ijassa-111	149	33	(	(	PUNCT
ijassa-111	149	34	13	13	NUM
ijassa-111	149	35	)	)	PUNCT
ijassa-111	149	36	and	and	CCONJ
ijassa-111	149	37	(	(	PUNCT
ijassa-111	149	38	14	14	NUM
ijassa-111	149	39	)	)	PUNCT
ijassa-111	149	40	hold	hold	NOUN
ijassa-111	149	41	.	.	PUNCT
ijassa-111	150	1	this	this	PRON
ijassa-111	150	2	completes	complete	VERB
ijassa-111	150	3	the	the	DET
ijassa-111	150	4	proof	proof	NOUN
ijassa-111	150	5	of	of	ADP
ijassa-111	150	6	the	the	DET
ijassa-111	150	7	theorem	theorem	NOUN
ijassa-111	150	8	.	.	PUNCT
ijassa-111	151	1	thus	thus	ADV
ijassa-111	151	2	,	,	PUNCT
ijassa-111	151	3	in	in	ADP
ijassa-111	151	4	the	the	DET
ijassa-111	151	5	framework	framework	NOUN
ijassa-111	151	6	of	of	ADP
ijassa-111	151	7	the	the	DET
ijassa-111	151	8	proposed	propose	VERB
ijassa-111	151	9	axiomatics	axiomatic	NOUN
ijassa-111	151	10	,	,	PUNCT
ijassa-111	151	11	we	we	PRON
ijassa-111	151	12	have	have	AUX
ijassa-111	151	13	constructed	construct	VERB
ijassa-111	151	14	a	a	DET
ijassa-111	151	15	mathematically	mathematically	ADV
ijassa-111	151	16	rigorous	rigorous	ADJ
ijassa-111	151	17	model	model	NOUN
ijassa-111	151	18	of	of	ADP
ijassa-111	151	19	a	a	DET
ijassa-111	151	20	spherically	spherically	NOUN
ijassa-111	151	21	symmetric	symmetric	ADJ
ijassa-111	151	22	space	space	NOUN
ijassa-111	151	23	adequately	adequately	ADV
ijassa-111	151	24	describing	describe	VERB
ijassa-111	151	25	the	the	DET
ijassa-111	151	26	spherically	spherically	NOUN
ijassa-111	151	27	symmetric	symmetric	PROPN
ijassa-111	151	28	gravitational	gravitational	ADJ
ijassa-111	151	29	field	field	NOUN
ijassa-111	151	30	generated	generate	VERB
ijassa-111	151	31	by	by	ADP
ijassa-111	151	32	a	a	DET
ijassa-111	151	33	spherical	spherical	ADJ
ijassa-111	151	34	gravitational	gravitational	ADJ
ijassa-111	151	35	source	source	NOUN
ijassa-111	151	36	with	with	ADP
ijassa-111	151	37	constant	constant	ADJ
ijassa-111	151	38	mass	mass	NOUN
ijassa-111	151	39	density	density	NOUN
ijassa-111	151	40	.	.	PUNCT
ijassa-111	152	1	theorem	theorem	NOUN
ijassa-111	152	2	2	2	NUM
ijassa-111	152	3	are	be	AUX
ijassa-111	152	4	easy	easy	ADJ
ijassa-111	152	5	to	to	PART
ijassa-111	152	6	extend	extend	VERB
ijassa-111	152	7	to	to	ADP
ijassa-111	152	8	a	a	DET
ijassa-111	152	9	more	more	ADV
ijassa-111	152	10	general	general	ADJ
ijassa-111	152	11	case	case	NOUN
ijassa-111	152	12	.	.	PUNCT
ijassa-111	153	1	266	266	NUM
ijassa-111	153	2	n.n	n.n	PROPN
ijassa-111	153	3	.	.	PROPN
ijassa-111	153	4	popov	popov	PROPN
ijassa-111	153	5	:	:	PUNCT
ijassa-111	153	6	a	a	DET
ijassa-111	153	7	geometric	geometric	ADJ
ijassa-111	153	8	interpretation	interpretation	NOUN
ijassa-111	153	9	of	of	ADP
ijassa-111	153	10	gravity	gravity	NOUN
ijassa-111	153	11	theory	theory	NOUN
ijassa-111	153	12	5	5	NUM
ijassa-111	153	13	stationary	stationary	ADJ
ijassa-111	153	14	spherically	spherically	NOUN
ijassa-111	153	15	symmetric	symmetric	ADJ
ijassa-111	153	16	spaces	space	NOUN
ijassa-111	153	17	with	with	ADP
ijassa-111	153	18	scalar	scalar	ADJ
ijassa-111	153	19	curvature	curvature	NOUN
ijassa-111	153	20	having	have	VERB
ijassa-111	153	21	finitely	finitely	ADV
ijassa-111	153	22	or	or	CCONJ
ijassa-111	153	23	countably	countably	ADV
ijassa-111	153	24	many	many	ADJ
ijassa-111	153	25	discontinuities	discontinuity	NOUN
ijassa-111	153	26	of	of	ADP
ijassa-111	153	27	the	the	DET
ijassa-111	153	28	first	first	ADJ
ijassa-111	153	29	kind	kind	NOUN
ijassa-111	153	30	and	and	CCONJ
ijassa-111	153	31	a	a	DET
ijassa-111	153	32	mathematically	mathematically	ADV
ijassa-111	153	33	rigorous	rigorous	ADJ
ijassa-111	153	34	definition	definition	NOUN
ijassa-111	153	35	of	of	ADP
ijassa-111	153	36	spherically	spherically	PROPN
ijassa-111	153	37	symmetric	symmetric	ADJ
ijassa-111	153	38	black	black	ADJ
ijassa-111	153	39	holes	hole	NOUN
ijassa-111	153	40	consider	consider	VERB
ijassa-111	153	41	a	a	DET
ijassa-111	153	42	stationary	stationary	ADJ
ijassa-111	153	43	spherically	spherically	NOUN
ijassa-111	153	44	symmetric	symmetric	ADJ
ijassa-111	153	45	space	space	NOUN
ijassa-111	153	46	endowed	endow	VERB
ijassa-111	153	47	with	with	ADP
ijassa-111	153	48	a	a	DET
ijassa-111	153	49	metric	metric	NOUN
ijassa-111	153	50	of	of	ADP
ijassa-111	153	51	the	the	DET
ijassa-111	153	52	general	general	ADJ
ijassa-111	153	53	form	form	NOUN
ijassa-111	153	54	(	(	PUNCT
ijassa-111	153	55	11	11	NUM
ijassa-111	153	56	)	)	PUNCT
ijassa-111	153	57	.	.	PUNCT
ijassa-111	154	1	suppose	suppose	VERB
ijassa-111	154	2	that	that	SCONJ
ijassa-111	154	3	the	the	DET
ijassa-111	154	4	scalar	scalar	ADJ
ijassa-111	154	5	curvature	curvature	NOUN
ijassa-111	154	6	of	of	ADP
ijassa-111	154	7	this	this	DET
ijassa-111	154	8	space	space	NOUN
ijassa-111	154	9	is	be	AUX
ijassa-111	154	10	a	a	DET
ijassa-111	154	11	piecewise	piecewise	NOUN
ijassa-111	154	12	smooth	smooth	ADJ
ijassa-111	154	13	function	function	NOUN
ijassa-111	154	14	r(r	r(r	PROPN
ijassa-111	154	15	)	)	PUNCT
ijassa-111	154	16	with	with	ADP
ijassa-111	154	17	at	at	ADV
ijassa-111	154	18	most	most	ADV
ijassa-111	154	19	countably	countably	ADV
ijassa-111	154	20	many	many	ADJ
ijassa-111	154	21	discontinuities	discontinuity	NOUN
ijassa-111	154	22	of	of	ADP
ijassa-111	154	23	the	the	DET
ijassa-111	154	24	first	first	ADJ
ijassa-111	154	25	kind	kind	NOUN
ijassa-111	154	26	at	at	ADP
ijassa-111	154	27	points	point	NOUN
ijassa-111	154	28	r1	r1	PROPN
ijassa-111	154	29	,	,	PUNCT
ijassa-111	154	30	r2	r2	PROPN
ijassa-111	154	31	,	,	PUNCT
ijassa-111	154	32	.	.	PUNCT
ijassa-111	154	33	.	.	PUNCT
ijassa-111	155	1	.	.	PUNCT
ijassa-111	156	1	,	,	PUNCT
ijassa-111	156	2	rn	rn	PROPN
ijassa-111	156	3	,	,	PUNCT
ijassa-111	156	4	.	.	PUNCT
ijassa-111	156	5	.	.	PUNCT
ijassa-111	157	1	.	.	PUNCT
ijassa-111	158	1	numbered	number	VERB
ijassa-111	158	2	in	in	ADP
ijassa-111	158	3	increasing	increase	VERB
ijassa-111	158	4	order	order	NOUN
ijassa-111	158	5	.	.	PUNCT
ijassa-111	159	1	for	for	ADP
ijassa-111	159	2	such	such	DET
ijassa-111	159	3	a	a	DET
ijassa-111	159	4	space	space	NOUN
ijassa-111	159	5	,	,	PUNCT
ijassa-111	159	6	the	the	DET
ijassa-111	159	7	following	follow	VERB
ijassa-111	159	8	theorem	theorem	NOUN
ijassa-111	159	9	is	be	AUX
ijassa-111	159	10	valid	valid	ADJ
ijassa-111	159	11	.	.	PUNCT
ijassa-111	160	1	theorem	theorem	NOUN
ijassa-111	160	2	3	3	NUM
ijassa-111	160	3	.	.	PUNCT
ijassa-111	161	1	if	if	SCONJ
ijassa-111	161	2	the	the	DET
ijassa-111	161	3	components	component	NOUN
ijassa-111	161	4	of	of	ADP
ijassa-111	161	5	metric	metric	ADJ
ijassa-111	161	6	(	(	PUNCT
ijassa-111	161	7	11	11	NUM
ijassa-111	161	8	)	)	PUNCT
ijassa-111	161	9	satisfy	satisfy	VERB
ijassa-111	161	10	the	the	DET
ijassa-111	161	11	conditions	condition	NOUN
ijassa-111	161	12	g22(0	g22(0	NOUN
ijassa-111	161	13	)	)	PUNCT
ijassa-111	162	1	=	=	SYM
ijassa-111	162	2	0	0	NUM
ijassa-111	162	3	and	and	CCONJ
ijassa-111	162	4	g44(0	g44(0	NOUN
ijassa-111	162	5	)	)	PUNCT
ijassa-111	163	1	=	=	SYM
ijassa-111	163	2	1	1	NUM
ijassa-111	163	3	,	,	PUNCT
ijassa-111	163	4	then	then	ADV
ijassa-111	163	5	the	the	DET
ijassa-111	163	6	scalar	scalar	ADJ
ijassa-111	163	7	curvature	curvature	NOUN
ijassa-111	163	8	of	of	ADP
ijassa-111	163	9	the	the	DET
ijassa-111	163	10	spherically	spherically	NOUN
ijassa-111	163	11	symmetric	symmetric	ADJ
ijassa-111	163	12	space	space	NOUN
ijassa-111	163	13	under	under	ADP
ijassa-111	163	14	consideration	consideration	NOUN
ijassa-111	163	15	is	be	AUX
ijassa-111	163	16	a	a	DET
ijassa-111	163	17	piecewise	piecewise	NOUN
ijassa-111	163	18	constant	constant	ADJ
ijassa-111	163	19	function	function	NOUN
ijassa-111	163	20	taking	take	VERB
ijassa-111	163	21	the	the	DET
ijassa-111	163	22	constant	constant	ADJ
ijassa-111	163	23	values	value	NOUN
ijassa-111	163	24	r(r	r(r	NOUN
ijassa-111	163	25	)	)	PUNCT
ijassa-111	164	1	=	=	PRON
ijassa-111	164	2	rk	rk	NOUN
ijassa-111	164	3	at	at	ADP
ijassa-111	164	4	rk−1	rk−1	NOUN
ijassa-111	164	5	<	<	X
ijassa-111	164	6	r	r	NOUN
ijassa-111	164	7	≤	≤	NUM
ijassa-111	164	8	rk	rk	NOUN
ijassa-111	164	9	for	for	ADP
ijassa-111	164	10	k	k	PROPN
ijassa-111	164	11	=	=	SYM
ijassa-111	164	12	1	1	NUM
ijassa-111	164	13	,	,	PUNCT
ijassa-111	164	14	.	.	PUNCT
ijassa-111	164	15	.	.	PUNCT
ijassa-111	165	1	.	.	PUNCT
ijassa-111	166	1	,	,	PUNCT
ijassa-111	167	1	n	n	CCONJ
ijassa-111	167	2	,	,	PUNCT
ijassa-111	167	3	.	.	PUNCT
ijassa-111	167	4	.	.	PUNCT
ijassa-111	168	1	.	.	PUNCT
ijassa-111	169	1	,	,	PUNCT
ijassa-111	169	2	where	where	SCONJ
ijassa-111	169	3	r0	r0	NOUN
ijassa-111	169	4	=	=	NOUN
ijassa-111	169	5	0	0	PROPN
ijassa-111	169	6	.	.	PUNCT
ijassa-111	170	1	the	the	DET
ijassa-111	170	2	metric	metric	NOUN
ijassa-111	170	3	of	of	ADP
ijassa-111	170	4	such	such	DET
ijassa-111	170	5	a	a	DET
ijassa-111	170	6	space	space	NOUN
ijassa-111	170	7	is	be	AUX
ijassa-111	170	8	everywhere	everywhere	ADV
ijassa-111	170	9	continuous	continuous	ADJ
ijassa-111	170	10	,	,	PUNCT
ijassa-111	170	11	provided	provide	VERB
ijassa-111	170	12	that	that	PRON
ijassa-111	170	13	2m(r	2m(r	NOUN
ijassa-111	170	14	)	)	PUNCT
ijassa-111	171	1	r	r	NOUN
ijassa-111	171	2	<	<	X
ijassa-111	171	3	1	1	NUM
ijassa-111	171	4	for	for	ADP
ijassa-111	171	5	r	r	NOUN
ijassa-111	171	6	∈	∈	PROPN
ijassa-111	171	7	(	(	PUNCT
ijassa-111	171	8	0,∞	0,∞	NOUN
ijassa-111	171	9	)	)	PUNCT
ijassa-111	171	10	,	,	PUNCT
ijassa-111	171	11	and	and	CCONJ
ijassa-111	171	12	has	have	VERB
ijassa-111	171	13	the	the	DET
ijassa-111	171	14	form	form	NOUN
ijassa-111	171	15	ds2	ds2	PROPN
ijassa-111	171	16	=	=	PUNCT
ijassa-111	171	17	(	(	PUNCT
ijassa-111	171	18	1−	1−	NUM
ijassa-111	171	19	2m(r	2m(r	NUM
ijassa-111	171	20	)	)	PUNCT
ijassa-111	172	1	r	r	NOUN
ijassa-111	172	2	)	)	PUNCT
ijassa-111	172	3	dt2	dt2	PROPN
ijassa-111	173	1	−	−	PROPN
ijassa-111	173	2	dr2	dr2	PROPN
ijassa-111	173	3	1−	1−	NUM
ijassa-111	173	4	2m(r	2m(r	NUM
ijassa-111	173	5	)	)	PUNCT
ijassa-111	174	1	r	r	NOUN
ijassa-111	174	2	−	−	NOUN
ijassa-111	174	3	r2(dθ2	r2(dθ2	NOUN
ijassa-111	174	4	+	+	X
ijassa-111	174	5	sin2θdφ	sin2θdφ	NOUN
ijassa-111	174	6	)	)	PUNCT
ijassa-111	174	7	,	,	PUNCT
ijassa-111	174	8	(	(	PUNCT
ijassa-111	174	9	27	27	NUM
ijassa-111	174	10	)	)	PUNCT
ijassa-111	174	11	where	where	SCONJ
ijassa-111	174	12	m(r	m(r	NOUN
ijassa-111	174	13	)	)	PUNCT
ijassa-111	175	1	=	=	PUNCT
ijassa-111	175	2	r∫	r∫	PROPN
ijassa-111	175	3	0	0	PUNCT
ijassa-111	175	4	∑	∑	PUNCT
ijassa-111	175	5	k>0	k>0	ADP
ijassa-111	175	6	rk	rk	PROPN
ijassa-111	175	7	4	4	NUM
ijassa-111	175	8	[	[	X
ijassa-111	175	9	θ(x−	θ(x−	ADP
ijassa-111	175	10	rk−1)−	rk−1)−	NUM
ijassa-111	175	11	θ(x−	θ(x−	PROPN
ijassa-111	175	12	rk)]x	rk)]x	PROPN
ijassa-111	175	13	2dx	2dx	NOUN
ijassa-111	175	14	.	.	PUNCT
ijassa-111	176	1	the	the	DET
ijassa-111	176	2	components	component	NOUN
ijassa-111	176	3	of	of	ADP
ijassa-111	176	4	metric	metric	ADJ
ijassa-111	176	5	(	(	PUNCT
ijassa-111	176	6	27	27	NUM
ijassa-111	176	7	)	)	PUNCT
ijassa-111	176	8	satisfy	satisfy	NOUN
ijassa-111	176	9	system	system	NOUN
ijassa-111	176	10	(	(	PUNCT
ijassa-111	176	11	12	12	NUM
ijassa-111	176	12	)	)	PUNCT
ijassa-111	176	13	of	of	ADP
ijassa-111	176	14	differential	differential	ADJ
ijassa-111	176	15	equations	equation	NOUN
ijassa-111	176	16	everywhere	everywhere	ADV
ijassa-111	176	17	except	except	SCONJ
ijassa-111	176	18	at	at	ADP
ijassa-111	176	19	a	a	DET
ijassa-111	176	20	finite	finite	NOUN
ijassa-111	176	21	or	or	CCONJ
ijassa-111	176	22	countable	countable	ADJ
ijassa-111	176	23	set	set	NOUN
ijassa-111	176	24	of	of	ADP
ijassa-111	176	25	points	point	NOUN
ijassa-111	176	26	r1	r1	PROPN
ijassa-111	176	27	,	,	PUNCT
ijassa-111	176	28	.	.	PUNCT
ijassa-111	176	29	.	.	PUNCT
ijassa-111	177	1	.	.	PUNCT
ijassa-111	178	1	,	,	PUNCT
ijassa-111	178	2	rn	rn	PROPN
ijassa-111	178	3	,	,	PUNCT
ijassa-111	178	4	.	.	PUNCT
ijassa-111	178	5	.	.	PUNCT
ijassa-111	178	6	.	.	PUNCT
ijassa-111	178	7	.	.	PUNCT
ijassa-111	179	1	proof	proof	NOUN
ijassa-111	179	2	.	.	PUNCT
ijassa-111	180	1	this	this	DET
ijassa-111	180	2	theorem	theorem	NOUN
ijassa-111	180	3	is	be	AUX
ijassa-111	180	4	proved	prove	VERB
ijassa-111	180	5	by	by	ADP
ijassa-111	180	6	the	the	DET
ijassa-111	180	7	same	same	ADJ
ijassa-111	180	8	method	method	NOUN
ijassa-111	180	9	as	as	ADP
ijassa-111	180	10	theorem	theorem	ADJ
ijassa-111	180	11	2	2	NUM
ijassa-111	180	12	.	.	PUNCT
ijassa-111	181	1	as	as	ADP
ijassa-111	181	2	in	in	ADP
ijassa-111	181	3	theorem	theorem	NOUN
ijassa-111	181	4	2	2	NUM
ijassa-111	181	5	,	,	PUNCT
ijassa-111	181	6	we	we	PRON
ijassa-111	181	7	show	show	VERB
ijassa-111	181	8	that	that	SCONJ
ijassa-111	181	9	,	,	PUNCT
ijassa-111	181	10	under	under	ADP
ijassa-111	181	11	the	the	DET
ijassa-111	181	12	assumptions	assumption	NOUN
ijassa-111	181	13	of	of	ADP
ijassa-111	181	14	theorem	theorem	NOUN
ijassa-111	181	15	3	3	NUM
ijassa-111	181	16	,	,	PUNCT
ijassa-111	181	17	the	the	DET
ijassa-111	181	18	components	component	NOUN
ijassa-111	181	19	of	of	ADP
ijassa-111	181	20	metric	metric	ADJ
ijassa-111	181	21	(	(	PUNCT
ijassa-111	181	22	11	11	NUM
ijassa-111	181	23	)	)	PUNCT
ijassa-111	181	24	in	in	ADP
ijassa-111	181	25	the	the	DET
ijassa-111	181	26	spherical	spherical	ADJ
ijassa-111	181	27	coordinate	coordinate	NOUN
ijassa-111	181	28	system	system	NOUN
ijassa-111	181	29	have	have	VERB
ijassa-111	181	30	the	the	DET
ijassa-111	181	31	form	form	NOUN
ijassa-111	181	32	g44	g44	NOUN
ijassa-111	181	33	=	=	SYM
ijassa-111	181	34	1−	1−	NUM
ijassa-111	181	35	1	1	NUM
ijassa-111	181	36	4r	4r	NUM
ijassa-111	181	37	r∫	r∫	PROPN
ijassa-111	181	38	0	0	PUNCT
ijassa-111	182	1	r(x)x2dx	r(x)x2dx	ADJ
ijassa-111	182	2	,	,	PUNCT
ijassa-111	182	3	g22	g22	NOUN
ijassa-111	182	4	=	=	SYM
ijassa-111	182	5	−r2	−r2	PROPN
ijassa-111	182	6	,	,	PUNCT
ijassa-111	182	7	g11	g11	NOUN
ijassa-111	182	8	=	=	SYM
ijassa-111	182	9	−g44	−g44	X
ijassa-111	182	10	−1	−1	NOUN
ijassa-111	182	11	,	,	PUNCT
ijassa-111	182	12	(	(	PUNCT
ijassa-111	182	13	28	28	NUM
ijassa-111	182	14	)	)	PUNCT
ijassa-111	182	15	where	where	SCONJ
ijassa-111	182	16	r	r	NOUN
ijassa-111	182	17	is	be	AUX
ijassa-111	182	18	a	a	DET
ijassa-111	182	19	piecewise	piecewise	NOUN
ijassa-111	182	20	smooth	smooth	ADJ
ijassa-111	182	21	function	function	NOUN
ijassa-111	182	22	with	with	ADP
ijassa-111	182	23	at	at	ADP
ijassa-111	182	24	most	most	ADV
ijassa-111	182	25	countably	countably	ADV
ijassa-111	182	26	many	many	ADJ
ijassa-111	182	27	discontinuities	discontinuity	NOUN
ijassa-111	182	28	of	of	ADP
ijassa-111	182	29	the	the	DET
ijassa-111	182	30	first	first	ADJ
ijassa-111	182	31	kind	kind	NOUN
ijassa-111	182	32	at	at	ADP
ijassa-111	182	33	points	point	NOUN
ijassa-111	182	34	r1	r1	PROPN
ijassa-111	182	35	,	,	PUNCT
ijassa-111	182	36	r2	r2	PROPN
ijassa-111	182	37	,	,	PUNCT
ijassa-111	182	38	.	.	PUNCT
ijassa-111	182	39	.	.	PUNCT
ijassa-111	182	40	.	.	PUNCT
ijassa-111	182	41	.	.	PUNCT
ijassa-111	183	1	the	the	DET
ijassa-111	183	2	functions	function	NOUN
ijassa-111	183	3	in	in	ADP
ijassa-111	183	4	(	(	PUNCT
ijassa-111	183	5	28	28	NUM
ijassa-111	183	6	)	)	PUNCT
ijassa-111	183	7	satisfy	satisfy	NOUN
ijassa-111	183	8	system	system	NOUN
ijassa-111	183	9	(	(	PUNCT
ijassa-111	183	10	12	12	NUM
ijassa-111	183	11	)	)	PUNCT
ijassa-111	183	12	only	only	ADV
ijassa-111	183	13	under	under	ADP
ijassa-111	183	14	the	the	DET
ijassa-111	183	15	condition	condition	NOUN
ijassa-111	183	16	dr	dr	PROPN
ijassa-111	183	17	dr	dr	PROPN
ijassa-111	183	18	=	=	PROPN
ijassa-111	183	19	0	0	PROPN
ijassa-111	183	20	,	,	PUNCT
ijassa-111	183	21	(	(	PUNCT
ijassa-111	183	22	29	29	NUM
ijassa-111	183	23	)	)	PUNCT
ijassa-111	183	24	which	which	PRON
ijassa-111	183	25	is	be	AUX
ijassa-111	183	26	an	an	DET
ijassa-111	183	27	analogue	analogue	NOUN
ijassa-111	183	28	of	of	ADP
ijassa-111	183	29	condition	condition	NOUN
ijassa-111	183	30	(	(	PUNCT
ijassa-111	183	31	24	24	NUM
ijassa-111	183	32	)	)	PUNCT
ijassa-111	183	33	in	in	ADP
ijassa-111	183	34	the	the	DET
ijassa-111	183	35	proof	proof	NOUN
ijassa-111	183	36	of	of	ADP
ijassa-111	183	37	theorem	theorem	ADJ
ijassa-111	183	38	2	2	NUM
ijassa-111	183	39	.	.	PUNCT
ijassa-111	183	40	relation	relation	NOUN
ijassa-111	183	41	(	(	PUNCT
ijassa-111	183	42	29	29	NUM
ijassa-111	183	43	)	)	PUNCT
ijassa-111	183	44	implies	imply	VERB
ijassa-111	183	45	that	that	SCONJ
ijassa-111	183	46	r(r	r(r	PROPN
ijassa-111	183	47	)	)	PUNCT
ijassa-111	183	48	must	must	AUX
ijassa-111	183	49	take	take	VERB
ijassa-111	183	50	constant	constant	ADJ
ijassa-111	183	51	values	value	NOUN
ijassa-111	183	52	in	in	ADP
ijassa-111	183	53	its	its	PRON
ijassa-111	183	54	domains	domain	NOUN
ijassa-111	183	55	of	of	ADP
ijassa-111	183	56	continuity	continuity	NOUN
ijassa-111	183	57	.	.	PUNCT
ijassa-111	184	1	suppose	suppose	VERB
ijassa-111	184	2	that	that	SCONJ
ijassa-111	184	3	r(r	r(r	PROPN
ijassa-111	184	4	)	)	PUNCT
ijassa-111	184	5	takes	take	VERB
ijassa-111	184	6	a	a	DET
ijassa-111	184	7	value	value	NOUN
ijassa-111	184	8	rk	rk	NOUN
ijassa-111	184	9	at	at	ADP
ijassa-111	184	10	rk−1	rk−1	NOUN
ijassa-111	184	11	<	<	X
ijassa-111	184	12	r	r	NOUN
ijassa-111	184	13	≤	≤	NUM
ijassa-111	184	14	rk	rk	NOUN
ijassa-111	184	15	;	;	PUNCT
ijassa-111	184	16	then	then	ADV
ijassa-111	184	17	r(r	r(r	PROPN
ijassa-111	184	18	)	)	PUNCT
ijassa-111	184	19	=	=	PUNCT
ijassa-111	185	1	∑	∑	PUNCT
ijassa-111	185	2	k=1	k=1	PROPN
ijassa-111	185	3	rk(θ(r	rk(θ(r	X
ijassa-111	185	4	−	−	PROPN
ijassa-111	185	5	rk−1)−	rk−1)−	NUM
ijassa-111	185	6	θ(r	θ(r	X
ijassa-111	185	7	−	−	VERB
ijassa-111	185	8	rk	rk	NOUN
ijassa-111	185	9	)	)	PUNCT
ijassa-111	185	10	)	)	PUNCT
ijassa-111	186	1	,	,	PUNCT
ijassa-111	186	2	advances	advance	NOUN
ijassa-111	186	3	in	in	ADP
ijassa-111	186	4	systems	system	NOUN
ijassa-111	186	5	science	science	NOUN
ijassa-111	186	6	and	and	CCONJ
ijassa-111	186	7	applications	application	NOUN
ijassa-111	186	8	(	(	PUNCT
ijassa-111	186	9	2012	2012	NUM
ijassa-111	186	10	)	)	PUNCT
ijassa-111	186	11	vol.12	vol.12	NOUN
ijassa-111	186	12	no.3	no.3	VERB
ijassa-111	186	13	267	267	NUM
ijassa-111	186	14	which	which	PRON
ijassa-111	186	15	implies	imply	VERB
ijassa-111	186	16	the	the	DET
ijassa-111	186	17	assertion	assertion	NOUN
ijassa-111	186	18	theorem	theorem	VERB
ijassa-111	186	19	3	3	NUM
ijassa-111	186	20	.	.	PUNCT
ijassa-111	187	1	the	the	DET
ijassa-111	187	2	components	component	NOUN
ijassa-111	187	3	of	of	ADP
ijassa-111	187	4	metric	metric	ADJ
ijassa-111	187	5	(	(	PUNCT
ijassa-111	187	6	27	27	NUM
ijassa-111	187	7	)	)	PUNCT
ijassa-111	187	8	are	be	AUX
ijassa-111	187	9	everywhere	everywhere	ADV
ijassa-111	187	10	continuous	continuous	ADJ
ijassa-111	187	11	if	if	SCONJ
ijassa-111	187	12	2m(r	2m(r	NUM
ijassa-111	187	13	)	)	PUNCT
ijassa-111	188	1	r	r	NOUN
ijassa-111	188	2	<	<	X
ijassa-111	188	3	1	1	NUM
ijassa-111	188	4	for	for	ADP
ijassa-111	188	5	r	r	NOUN
ijassa-111	188	6	∈	∈	PROPN
ijassa-111	188	7	(	(	PUNCT
ijassa-111	188	8	0,∞	0,∞	NOUN
ijassa-111	188	9	)	)	PUNCT
ijassa-111	188	10	.	.	PUNCT
ijassa-111	189	1	if	if	SCONJ
ijassa-111	189	2	2m(r	2m(r	NUM
ijassa-111	189	3	)	)	PUNCT
ijassa-111	190	1	r	r	NOUN
ijassa-111	190	2	=	=	NOUN
ijassa-111	190	3	1	1	NUM
ijassa-111	190	4	at	at	ADP
ijassa-111	190	5	some	some	DET
ijassa-111	190	6	r	r	NOUN
ijassa-111	190	7	=	=	SYM
ijassa-111	190	8	rg	rg	PROPN
ijassa-111	190	9	.	.	PUNCT
ijassa-111	191	1	in	in	ADP
ijassa-111	191	2	this	this	DET
ijassa-111	191	3	case	case	NOUN
ijassa-111	191	4	,	,	PUNCT
ijassa-111	191	5	there	there	PRON
ijassa-111	191	6	are	be	VERB
ijassa-111	191	7	two	two	NUM
ijassa-111	191	8	possibilities	possibility	NOUN
ijassa-111	191	9	:	:	PUNCT
ijassa-111	191	10	either	either	CCONJ
ijassa-111	191	11	the	the	DET
ijassa-111	191	12	spherically	spherically	PROPN
ijassa-111	191	13	symmetric	symmetric	ADJ
ijassa-111	191	14	space	space	NOUN
ijassa-111	191	15	is	be	AUX
ijassa-111	191	16	bounded	bound	VERB
ijassa-111	191	17	by	by	ADP
ijassa-111	191	18	a	a	DET
ijassa-111	191	19	hypersphere	hypersphere	NOUN
ijassa-111	191	20	with	with	ADP
ijassa-111	191	21	radial	radial	ADJ
ijassa-111	191	22	parameter	parameter	NOUN
ijassa-111	191	23	rg	rg	PROPN
ijassa-111	191	24	(	(	PUNCT
ijassa-111	191	25	if	if	SCONJ
ijassa-111	191	26	2m(r	2m(r	NUM
ijassa-111	191	27	)	)	PUNCT
ijassa-111	192	1	r	r	NOUN
ijassa-111	192	2	>	>	X
ijassa-111	192	3	1	1	NUM
ijassa-111	192	4	at	at	ADP
ijassa-111	192	5	r	r	NOUN
ijassa-111	192	6	>	>	X
ijassa-111	192	7	rg	rg	PROPN
ijassa-111	192	8	)	)	PUNCT
ijassa-111	192	9	,	,	PUNCT
ijassa-111	192	10	or	or	CCONJ
ijassa-111	192	11	this	this	DET
ijassa-111	192	12	space	space	NOUN
ijassa-111	192	13	can	can	AUX
ijassa-111	192	14	be	be	AUX
ijassa-111	192	15	extended	extend	VERB
ijassa-111	192	16	(	(	PUNCT
ijassa-111	192	17	if	if	SCONJ
ijassa-111	192	18	2m(r	2m(r	NUM
ijassa-111	192	19	)	)	PUNCT
ijassa-111	193	1	r	r	NOUN
ijassa-111	193	2	<	<	X
ijassa-111	193	3	1	1	NUM
ijassa-111	193	4	at	at	ADP
ijassa-111	193	5	r	r	NOUN
ijassa-111	193	6	>	>	X
ijassa-111	193	7	rg	rg	PROPN
ijassa-111	193	8	)	)	PUNCT
ijassa-111	193	9	.	.	PUNCT
ijassa-111	194	1	in	in	ADP
ijassa-111	194	2	the	the	DET
ijassa-111	194	3	latter	latter	ADJ
ijassa-111	194	4	case	case	NOUN
ijassa-111	194	5	,	,	PUNCT
ijassa-111	194	6	the	the	DET
ijassa-111	194	7	space	space	NOUN
ijassa-111	194	8	contains	contain	VERB
ijassa-111	194	9	a	a	DET
ijassa-111	194	10	spherically	spherically	NOUN
ijassa-111	194	11	symmetric	symmetric	ADJ
ijassa-111	194	12	body	body	NOUN
ijassa-111	194	13	of	of	ADP
ijassa-111	194	14	radius	radius	NOUN
ijassa-111	194	15	rg	rg	PROPN
ijassa-111	194	16	with	with	ADP
ijassa-111	194	17	generally	generally	ADV
ijassa-111	194	18	nonuniform	nonuniform	ADJ
ijassa-111	194	19	mass	mass	ADJ
ijassa-111	194	20	distribution	distribution	NOUN
ijassa-111	194	21	density	density	NOUN
ijassa-111	194	22	,	,	PUNCT
ijassa-111	194	23	and	and	CCONJ
ijassa-111	194	24	on	on	ADP
ijassa-111	194	25	the	the	DET
ijassa-111	194	26	boundary	boundary	NOUN
ijassa-111	194	27	of	of	ADP
ijassa-111	194	28	this	this	DET
ijassa-111	194	29	body	body	NOUN
ijassa-111	194	30	,	,	PUNCT
ijassa-111	194	31	the	the	DET
ijassa-111	194	32	metric	metric	NOUN
ijassa-111	194	33	exhibits	exhibit	VERB
ijassa-111	194	34	an	an	DET
ijassa-111	194	35	irregular	irregular	ADJ
ijassa-111	194	36	behavior	behavior	NOUN
ijassa-111	194	37	.	.	PUNCT
ijassa-111	195	1	we	we	PRON
ijassa-111	195	2	refer	refer	VERB
ijassa-111	195	3	to	to	ADP
ijassa-111	195	4	such	such	ADJ
ijassa-111	195	5	bodies	body	NOUN
ijassa-111	195	6	as	as	ADP
ijassa-111	195	7	spherically	spherically	NOUN
ijassa-111	195	8	symmetric	symmetric	ADJ
ijassa-111	195	9	stationary	stationary	ADJ
ijassa-111	195	10	black	black	ADJ
ijassa-111	195	11	holes	hole	NOUN
ijassa-111	195	12	.	.	PUNCT
ijassa-111	196	1	below	below	ADV
ijassa-111	196	2	we	we	PRON
ijassa-111	196	3	give	give	VERB
ijassa-111	196	4	the	the	DET
ijassa-111	196	5	definition	definition	NOUN
ijassa-111	196	6	of	of	ADP
ijassa-111	196	7	the	the	DET
ijassa-111	196	8	simplest	simple	ADJ
ijassa-111	196	9	stationary	stationary	ADJ
ijassa-111	196	10	black	black	ADJ
ijassa-111	196	11	hole	hole	NOUN
ijassa-111	196	12	.	.	PUNCT
ijassa-111	197	1	definition	definition	NOUN
ijassa-111	197	2	1	1	NUM
ijassa-111	197	3	.	.	PUNCT
ijassa-111	198	1	a	a	DET
ijassa-111	198	2	globular	globular	ADJ
ijassa-111	198	3	body	body	NOUN
ijassa-111	198	4	of	of	ADP
ijassa-111	198	5	radius	radius	NOUN
ijassa-111	198	6	rg	rg	PROPN
ijassa-111	198	7	with	with	ADP
ijassa-111	198	8	constant	constant	ADJ
ijassa-111	198	9	mass	mass	NOUN
ijassa-111	198	10	density	density	NOUN
ijassa-111	198	11	satisfying	satisfy	VERB
ijassa-111	198	12	the	the	DET
ijassa-111	198	13	condition	condition	NOUN
ijassa-111	198	14	r	r	NOUN
ijassa-111	198	15	=	=	SYM
ijassa-111	198	16	12	12	NUM
ijassa-111	198	17	rg2	rg2	NOUN
ijassa-111	198	18	is	be	AUX
ijassa-111	198	19	called	call	VERB
ijassa-111	198	20	a	a	DET
ijassa-111	198	21	stationary	stationary	ADJ
ijassa-111	198	22	spherical	spherical	ADJ
ijassa-111	198	23	black	black	ADJ
ijassa-111	198	24	hole	hole	NOUN
ijassa-111	198	25	.	.	PUNCT
ijassa-111	199	1	the	the	DET
ijassa-111	199	2	sphere	sphere	NOUN
ijassa-111	199	3	of	of	ADP
ijassa-111	199	4	radius	radius	NOUN
ijassa-111	199	5	rg	rg	PROPN
ijassa-111	199	6	being	be	AUX
ijassa-111	199	7	the	the	DET
ijassa-111	199	8	surface	surface	NOUN
ijassa-111	199	9	of	of	ADP
ijassa-111	199	10	a	a	DET
ijassa-111	199	11	black	black	ADJ
ijassa-111	199	12	hole	hole	NOUN
ijassa-111	199	13	is	be	AUX
ijassa-111	199	14	called	call	VERB
ijassa-111	199	15	its	its	PRON
ijassa-111	199	16	horizon	horizon	NOUN
ijassa-111	199	17	level	level	NOUN
ijassa-111	199	18	,	,	PUNCT
ijassa-111	199	19	or	or	CCONJ
ijassa-111	199	20	the	the	DET
ijassa-111	199	21	schwarzschild	schwarzschild	NOUN
ijassa-111	199	22	sphere	sphere	NOUN
ijassa-111	199	23	.	.	PUNCT
ijassa-111	200	1	it	it	PRON
ijassa-111	200	2	follows	follow	VERB
ijassa-111	200	3	from	from	ADP
ijassa-111	200	4	the	the	DET
ijassa-111	200	5	definition	definition	NOUN
ijassa-111	200	6	that	that	PRON
ijassa-111	200	7	rg	rg	PROPN
ijassa-111	200	8	=	=	NOUN
ijassa-111	200	9	√	√	PROPN
ijassa-111	200	10	12	12	NUM
ijassa-111	200	11	r	r	NOUN
ijassa-111	200	12	.	.	PUNCT
ijassa-111	201	1	note	note	VERB
ijassa-111	201	2	that	that	SCONJ
ijassa-111	201	3	the	the	DET
ijassa-111	201	4	signature	signature	NOUN
ijassa-111	201	5	of	of	ADP
ijassa-111	201	6	the	the	DET
ijassa-111	201	7	space	space	NOUN
ijassa-111	201	8	inside	inside	ADP
ijassa-111	201	9	a	a	DET
ijassa-111	201	10	black	black	ADJ
ijassa-111	201	11	hole	hole	NOUN
ijassa-111	201	12	and	and	CCONJ
ijassa-111	201	13	outside	outside	ADP
ijassa-111	201	14	it	it	PRON
ijassa-111	201	15	remains	remain	VERB
ijassa-111	201	16	invariable	invariable	ADJ
ijassa-111	201	17	,	,	PUNCT
ijassa-111	201	18	which	which	PRON
ijassa-111	201	19	agrees	agree	VERB
ijassa-111	201	20	with	with	ADP
ijassa-111	201	21	condition	condition	NOUN
ijassa-111	201	22	(	(	PUNCT
ijassa-111	201	23	2	2	NUM
ijassa-111	201	24	)	)	PUNCT
ijassa-111	201	25	on	on	ADP
ijassa-111	201	26	the	the	DET
ijassa-111	201	27	metric	metric	NOUN
ijassa-111	201	28	of	of	ADP
ijassa-111	201	29	a	a	DET
ijassa-111	201	30	pseudo	pseudo	NOUN
ijassa-111	201	31	-	-	ADJ
ijassa-111	201	32	riemannian	riemannian	ADJ
ijassa-111	201	33	space	space	NOUN
ijassa-111	201	34	.	.	PUNCT
ijassa-111	202	1	all	all	DET
ijassa-111	202	2	components	component	NOUN
ijassa-111	202	3	of	of	ADP
ijassa-111	202	4	metric	metric	ADJ
ijassa-111	202	5	(	(	PUNCT
ijassa-111	202	6	27	27	NUM
ijassa-111	202	7	)	)	PUNCT
ijassa-111	202	8	are	be	AUX
ijassa-111	202	9	continuously	continuously	ADV
ijassa-111	202	10	differentiable	differentiable	ADJ
ijassa-111	202	11	on	on	ADP
ijassa-111	202	12	the	the	DET
ijassa-111	202	13	entire	entire	ADJ
ijassa-111	202	14	space	space	NOUN
ijassa-111	202	15	except	except	SCONJ
ijassa-111	202	16	on	on	ADP
ijassa-111	202	17	the	the	DET
ijassa-111	202	18	surface	surface	NOUN
ijassa-111	202	19	of	of	ADP
ijassa-111	202	20	the	the	DET
ijassa-111	202	21	black	black	ADJ
ijassa-111	202	22	hole	hole	NOUN
ijassa-111	202	23	,	,	PUNCT
ijassa-111	202	24	on	on	ADP
ijassa-111	202	25	which	which	PRON
ijassa-111	202	26	the	the	DET
ijassa-111	202	27	behavior	behavior	NOUN
ijassa-111	202	28	of	of	ADP
ijassa-111	202	29	metric	metric	ADJ
ijassa-111	202	30	(	(	PUNCT
ijassa-111	202	31	27	27	NUM
ijassa-111	202	32	)	)	PUNCT
ijassa-111	202	33	is	be	AUX
ijassa-111	202	34	irregular	irregular	ADJ
ijassa-111	202	35	,	,	PUNCT
ijassa-111	202	36	namely	namely	ADV
ijassa-111	202	37	,	,	PUNCT
ijassa-111	202	38	g11(rg	g11(rg	NOUN
ijassa-111	202	39	)	)	PUNCT
ijassa-111	202	40	=	=	VERB
ijassa-111	202	41	−∞.	−∞.	PROPN
ijassa-111	202	42	the	the	DET
ijassa-111	202	43	mathematical	mathematical	ADJ
ijassa-111	202	44	properties	property	NOUN
ijassa-111	202	45	of	of	ADP
ijassa-111	202	46	a	a	DET
ijassa-111	202	47	stationary	stationary	ADJ
ijassa-111	202	48	spherically	spherically	NOUN
ijassa-111	202	49	symmetric	symmetric	ADJ
ijassa-111	202	50	black	black	ADJ
ijassa-111	202	51	hole	hole	NOUN
ijassa-111	202	52	in	in	ADP
ijassa-111	202	53	the	the	DET
ijassa-111	202	54	formalism	formalism	NOUN
ijassa-111	202	55	suggested	suggest	VERB
ijassa-111	202	56	here	here	ADV
ijassa-111	202	57	substantially	substantially	ADV
ijassa-111	202	58	differ	differ	VERB
ijassa-111	202	59	from	from	ADP
ijassa-111	202	60	the	the	DET
ijassa-111	202	61	properties	property	NOUN
ijassa-111	202	62	of	of	ADP
ijassa-111	202	63	black	black	ADJ
ijassa-111	202	64	holes	hole	NOUN
ijassa-111	202	65	investigated	investigate	VERB
ijassa-111	202	66	in	in	ADP
ijassa-111	202	67	the	the	DET
ijassa-111	202	68	framework	framework	NOUN
ijassa-111	202	69	of	of	ADP
ijassa-111	202	70	grt[7	grt[7	PROPN
ijassa-111	202	71	]	]	PUNCT
ijassa-111	202	72	.	.	PUNCT
ijassa-111	203	1	if	if	SCONJ
ijassa-111	203	2	the	the	DET
ijassa-111	203	3	spherically	spherically	NOUN
ijassa-111	203	4	symmetric	symmetric	ADJ
ijassa-111	203	5	space	space	NOUN
ijassa-111	203	6	has	have	VERB
ijassa-111	203	7	the	the	DET
ijassa-111	203	8	same	same	ADJ
ijassa-111	203	9	scalar	scalar	ADJ
ijassa-111	203	10	curvature	curvature	NOUN
ijassa-111	203	11	r	r	NOUN
ijassa-111	203	12	at	at	ADV
ijassa-111	203	13	all	all	DET
ijassa-111	203	14	points	point	NOUN
ijassa-111	203	15	,	,	PUNCT
ijassa-111	203	16	then	then	ADV
ijassa-111	203	17	the	the	DET
ijassa-111	203	18	space	space	NOUN
ijassa-111	203	19	is	be	AUX
ijassa-111	203	20	the	the	DET
ijassa-111	203	21	de	de	PROPN
ijassa-111	203	22	sitter	sitter	NOUN
ijassa-111	203	23	closed	close	VERB
ijassa-111	203	24	elliptic	elliptic	ADJ
ijassa-111	203	25	space[5	space[5	PROPN
ijassa-111	203	26	]	]	PUNCT
ijassa-111	203	27	determined	determine	VERB
ijassa-111	203	28	by	by	ADP
ijassa-111	203	29	metric	metric	ADJ
ijassa-111	203	30	(	(	PUNCT
ijassa-111	203	31	27	27	NUM
ijassa-111	203	32	)	)	PUNCT
ijassa-111	203	33	of	of	ADP
ijassa-111	203	34	the	the	DET
ijassa-111	203	35	form	form	NOUN
ijassa-111	203	36	ds2	ds2	PROPN
ijassa-111	203	37	=	=	PUNCT
ijassa-111	203	38	(	(	PUNCT
ijassa-111	203	39	1−	1−	NUM
ijassa-111	203	40	r	r	NOUN
ijassa-111	203	41	12	12	NUM
ijassa-111	203	42	r2)dt2	r2)dt2	NOUN
ijassa-111	203	43	−	−	NOUN
ijassa-111	204	1	dr2	dr2	NOUN
ijassa-111	204	2	1−	1−	NUM
ijassa-111	204	3	r	r	NOUN
ijassa-111	204	4	12r	12r	NUM
ijassa-111	204	5	2	2	NUM
ijassa-111	204	6	−	−	NOUN
ijassa-111	204	7	r2(dθ2	r2(dθ2	NOUN
ijassa-111	204	8	+	+	X
ijassa-111	204	9	sin2θdφ	sin2θdφ	NOUN
ijassa-111	204	10	)	)	PUNCT
ijassa-111	204	11	with	with	ADP
ijassa-111	204	12	r	r	NOUN
ijassa-111	204	13	<	<	X
ijassa-111	204	14	√	√	PROPN
ijassa-111	204	15	12	12	NUM
ijassa-111	204	16	r	r	NOUN
ijassa-111	204	17	.	.	PUNCT
ijassa-111	205	1	this	this	DET
ijassa-111	205	2	space	space	NOUN
ijassa-111	205	3	is	be	AUX
ijassa-111	205	4	bounded	bound	VERB
ijassa-111	205	5	by	by	ADP
ijassa-111	205	6	a	a	DET
ijassa-111	205	7	sphere	sphere	NOUN
ijassa-111	205	8	with	with	ADP
ijassa-111	205	9	radial	radial	ADJ
ijassa-111	205	10	parameter	parameter	NOUN
ijassa-111	205	11	r	r	NOUN
ijassa-111	205	12	<	<	X
ijassa-111	205	13	√	√	PROPN
ijassa-111	205	14	12	12	NUM
ijassa-111	205	15	r	r	NOUN
ijassa-111	205	16	.	.	PUNCT
ijassa-111	206	1	such	such	DET
ijassa-111	206	2	a	a	DET
ijassa-111	206	3	model	model	NOUN
ijassa-111	206	4	corresponds	correspond	VERB
ijassa-111	206	5	to	to	ADP
ijassa-111	206	6	a	a	DET
ijassa-111	206	7	homogeneous	homogeneous	ADJ
ijassa-111	206	8	closed	closed	ADJ
ijassa-111	206	9	space	space	NOUN
ijassa-111	206	10	filled	fill	VERB
ijassa-111	206	11	with	with	ADP
ijassa-111	206	12	a	a	DET
ijassa-111	206	13	matter	matter	NOUN
ijassa-111	206	14	with	with	ADP
ijassa-111	206	15	constant	constant	ADJ
ijassa-111	206	16	mass	mass	NOUN
ijassa-111	206	17	density	density	NOUN
ijassa-111	206	18	.	.	PUNCT
ijassa-111	207	1	consider	consider	VERB
ijassa-111	207	2	yet	yet	ADV
ijassa-111	207	3	another	another	DET
ijassa-111	207	4	parameter	parameter	NOUN
ijassa-111	207	5	of	of	ADP
ijassa-111	207	6	the	the	DET
ijassa-111	207	7	spherically	spherically	PROPN
ijassa-111	207	8	symmetric	symmetric	ADJ
ijassa-111	207	9	space	space	NOUN
ijassa-111	207	10	generated	generate	VERB
ijassa-111	207	11	by	by	ADP
ijassa-111	207	12	a	a	DET
ijassa-111	207	13	ball	ball	NOUN
ijassa-111	207	14	of	of	ADP
ijassa-111	207	15	radius	radius	NOUN
ijassa-111	207	16	r1	r1	PROPN
ijassa-111	207	17	with	with	ADP
ijassa-111	207	18	constant	constant	ADJ
ijassa-111	207	19	mass	mass	NOUN
ijassa-111	207	20	density	density	NOUN
ijassa-111	207	21	ρ1	ρ1	NOUN
ijassa-111	207	22	and	and	CCONJ
ijassa-111	207	23	a	a	DET
ijassa-111	207	24	matter	matter	NOUN
ijassa-111	207	25	with	with	ADP
ijassa-111	207	26	constant	constant	ADJ
ijassa-111	207	27	mass	mass	NOUN
ijassa-111	207	28	density	density	NOUN
ijassa-111	207	29	ρ2	ρ2	NOUN
ijassa-111	207	30	filling	fill	VERB
ijassa-111	207	31	the	the	DET
ijassa-111	207	32	whole	whole	ADJ
ijassa-111	207	33	space	space	NOUN
ijassa-111	207	34	outside	outside	ADP
ijassa-111	207	35	the	the	DET
ijassa-111	207	36	ball	ball	NOUN
ijassa-111	207	37	.	.	PUNCT
ijassa-111	208	1	the	the	DET
ijassa-111	208	2	scalar	scalar	ADJ
ijassa-111	208	3	curvature	curvature	NOUN
ijassa-111	208	4	of	of	ADP
ijassa-111	208	5	the	the	DET
ijassa-111	208	6	space	space	NOUN
ijassa-111	208	7	inside	inside	ADP
ijassa-111	208	8	the	the	DET
ijassa-111	208	9	ball	ball	NOUN
ijassa-111	208	10	is	be	AUX
ijassa-111	208	11	calculated	calculate	VERB
ijassa-111	208	12	by	by	ADP
ijassa-111	208	13	r1	r1	PROPN
ijassa-111	208	14	=	=	PUNCT
ijassa-111	208	15	32πρ1	32πρ1	NUM
ijassa-111	208	16	and	and	CCONJ
ijassa-111	208	17	outside	outside	ADP
ijassa-111	208	18	the	the	DET
ijassa-111	208	19	ball	ball	NOUN
ijassa-111	208	20	,	,	PUNCT
ijassa-111	208	21	by	by	ADP
ijassa-111	208	22	268	268	NUM
ijassa-111	208	23	n.n	n.n	PROPN
ijassa-111	208	24	.	.	PROPN
ijassa-111	208	25	popov	popov	PROPN
ijassa-111	208	26	:	:	PUNCT
ijassa-111	208	27	a	a	DET
ijassa-111	208	28	geometric	geometric	ADJ
ijassa-111	208	29	interpretation	interpretation	NOUN
ijassa-111	208	30	of	of	ADP
ijassa-111	208	31	gravity	gravity	NOUN
ijassa-111	208	32	theory	theory	NOUN
ijassa-111	208	33	r2	r2	NOUN
ijassa-111	208	34	=	=	SYM
ijassa-111	208	35	32πρ2	32πρ2	PROPN
ijassa-111	208	36	.	.	PUNCT
ijassa-111	209	1	the	the	DET
ijassa-111	209	2	components	component	NOUN
ijassa-111	209	3	of	of	ADP
ijassa-111	209	4	metric	metric	ADJ
ijassa-111	209	5	(	(	PUNCT
ijassa-111	209	6	27	27	NUM
ijassa-111	209	7	)	)	PUNCT
ijassa-111	209	8	for	for	ADP
ijassa-111	209	9	each	each	DET
ijassa-111	209	10	space	space	NOUN
ijassa-111	209	11	have	have	VERB
ijassa-111	209	12	the	the	DET
ijassa-111	209	13	form	form	NOUN
ijassa-111	209	14	g44	g44	NOUN
ijassa-111	209	15	=	=	SYM
ijassa-111	209	16	1−	1−	NUM
ijassa-111	209	17	r1	r1	NOUN
ijassa-111	209	18	12	12	NUM
ijassa-111	209	19	r2	r2	NOUN
ijassa-111	209	20	at	at	ADP
ijassa-111	209	21	r	r	NOUN
ijassa-111	209	22	<	<	X
ijassa-111	209	23	r1	r1	NOUN
ijassa-111	209	24	,	,	PUNCT
ijassa-111	209	25	g44	g44	NOUN
ijassa-111	209	26	=	=	SYM
ijassa-111	209	27	1−	1−	NUM
ijassa-111	209	28	r1	r1	NOUN
ijassa-111	209	29	−r2	−r2	PROPN
ijassa-111	209	30	12	12	NUM
ijassa-111	209	31	r1	r1	NOUN
ijassa-111	209	32	3	3	NUM
ijassa-111	209	33	r	r	NOUN
ijassa-111	209	34	−	−	PROPN
ijassa-111	209	35	r2	r2	NOUN
ijassa-111	209	36	12	12	NUM
ijassa-111	209	37	r2	r2	NOUN
ijassa-111	209	38	at	at	ADP
ijassa-111	209	39	r	r	PROPN
ijassa-111	209	40	≥	≥	NUM
ijassa-111	209	41	r1	r1	NOUN
ijassa-111	209	42	,	,	PUNCT
ijassa-111	209	43	and	and	CCONJ
ijassa-111	209	44	g22	g22	NOUN
ijassa-111	209	45	=	=	SYM
ijassa-111	209	46	−r2	−r2	PROPN
ijassa-111	209	47	,	,	PUNCT
ijassa-111	209	48	g11	g11	NOUN
ijassa-111	209	49	=	=	SYM
ijassa-111	209	50	−g44	−g44	PROPN
ijassa-111	209	51	−1(r	−1(r	NOUN
ijassa-111	209	52	)	)	PUNCT
ijassa-111	209	53	if	if	SCONJ
ijassa-111	209	54	r1	r1	PROPN
ijassa-111	209	55	12	12	NUM
ijassa-111	209	56	r1	r1	NOUN
ijassa-111	209	57	2	2	NUM
ijassa-111	209	58	<	<	X
ijassa-111	209	59	1	1	NUM
ijassa-111	209	60	.	.	PUNCT
ijassa-111	210	1	the	the	DET
ijassa-111	210	2	spherically	spherically	PROPN
ijassa-111	210	3	symmetric	symmetric	ADJ
ijassa-111	210	4	space	space	NOUN
ijassa-111	210	5	is	be	AUX
ijassa-111	210	6	bounded	bound	VERB
ijassa-111	210	7	by	by	ADP
ijassa-111	210	8	a	a	DET
ijassa-111	210	9	sphere	sphere	NOUN
ijassa-111	210	10	of	of	ADP
ijassa-111	210	11	radius	radius	NOUN
ijassa-111	210	12	r2	r2	NOUN
ijassa-111	210	13	,	,	PUNCT
ijassa-111	210	14	which	which	PRON
ijassa-111	210	15	is	be	AUX
ijassa-111	210	16	the	the	DET
ijassa-111	210	17	least	least	ADV
ijassa-111	210	18	positive	positive	ADJ
ijassa-111	210	19	root	root	NOUN
ijassa-111	210	20	of	of	ADP
ijassa-111	210	21	the	the	DET
ijassa-111	210	22	cubic	cubic	ADJ
ijassa-111	210	23	equation	equation	NOUN
ijassa-111	210	24	r3	r3	PROPN
ijassa-111	210	25	−	−	NUM
ijassa-111	210	26	12	12	NUM
ijassa-111	210	27	r2	r2	NOUN
ijassa-111	210	28	r	r	NOUN
ijassa-111	210	29	+	+	CCONJ
ijassa-111	210	30	r1	r1	NOUN
ijassa-111	210	31	−r2	−r2	PROPN
ijassa-111	210	32	r2	r2	PROPN
ijassa-111	210	33	r1	r1	NOUN
ijassa-111	210	34	3	3	NUM
ijassa-111	210	35	=	=	SYM
ijassa-111	210	36	0	0	NUM
ijassa-111	210	37	.	.	PUNCT
ijassa-111	211	1	a	a	DET
ijassa-111	211	2	criterion	criterion	NOUN
ijassa-111	211	3	for	for	ADP
ijassa-111	211	4	the	the	DET
ijassa-111	211	5	transformation	transformation	NOUN
ijassa-111	211	6	of	of	ADP
ijassa-111	211	7	the	the	DET
ijassa-111	211	8	ball	ball	NOUN
ijassa-111	211	9	into	into	ADP
ijassa-111	211	10	a	a	DET
ijassa-111	211	11	black	black	ADJ
ijassa-111	211	12	hole	hole	NOUN
ijassa-111	211	13	is	be	AUX
ijassa-111	211	14	r1	r1	PROPN
ijassa-111	211	15	12	12	NUM
ijassa-111	211	16	r1	r1	NOUN
ijassa-111	211	17	2	2	NUM
ijassa-111	211	18	=	=	SYM
ijassa-111	211	19	1	1	NUM
ijassa-111	211	20	.	.	NOUN
ijassa-111	211	21	6	6	NUM
ijassa-111	211	22	a	a	DET
ijassa-111	211	23	model	model	NOUN
ijassa-111	211	24	of	of	ADP
ijassa-111	211	25	a	a	DET
ijassa-111	211	26	nonstationary	nonstationary	ADJ
ijassa-111	211	27	spherically	spherically	NOUN
ijassa-111	211	28	symmetric	symmetric	ADJ
ijassa-111	211	29	pseudo	pseudo	NOUN
ijassa-111	211	30	-	-	ADJ
ijassa-111	211	31	riemannian	riemannian	ADJ
ijassa-111	211	32	space	space	NOUN
ijassa-111	211	33	with	with	ADP
ijassa-111	211	34	constant	constant	ADJ
ijassa-111	211	35	scalar	scalar	ADJ
ijassa-111	211	36	curvature	curvature	NOUN
ijassa-111	211	37	and	and	CCONJ
ijassa-111	211	38	the	the	DET
ijassa-111	211	39	definition	definition	NOUN
ijassa-111	211	40	of	of	ADP
ijassa-111	211	41	dark	dark	ADJ
ijassa-111	211	42	energy	energy	NOUN
ijassa-111	211	43	in	in	ADP
ijassa-111	211	44	the	the	DET
ijassa-111	211	45	preceding	precede	VERB
ijassa-111	211	46	section	section	NOUN
ijassa-111	211	47	,	,	PUNCT
ijassa-111	211	48	we	we	PRON
ijassa-111	211	49	described	describe	VERB
ijassa-111	211	50	a	a	DET
ijassa-111	211	51	stationary	stationary	ADJ
ijassa-111	211	52	spherically	spherically	NOUN
ijassa-111	211	53	symmetric	symmetric	ADJ
ijassa-111	211	54	space	space	NOUN
ijassa-111	211	55	with	with	ADP
ijassa-111	211	56	discontinuous	discontinuous	ADJ
ijassa-111	211	57	scalar	scalar	ADJ
ijassa-111	211	58	curvature	curvature	NOUN
ijassa-111	211	59	.	.	PUNCT
ijassa-111	212	1	here	here	ADV
ijassa-111	212	2	,	,	PUNCT
ijassa-111	212	3	we	we	PRON
ijassa-111	212	4	consider	consider	VERB
ijassa-111	212	5	a	a	DET
ijassa-111	212	6	mathematical	mathematical	ADJ
ijassa-111	212	7	model	model	NOUN
ijassa-111	212	8	of	of	ADP
ijassa-111	212	9	a	a	DET
ijassa-111	212	10	spherically	spherically	NOUN
ijassa-111	212	11	symmetric	symmetric	ADJ
ijassa-111	212	12	pseudo	pseudo	NOUN
ijassa-111	212	13	-	-	ADJ
ijassa-111	212	14	riemannian	riemannian	ADJ
ijassa-111	212	15	space	space	NOUN
ijassa-111	212	16	with	with	ADP
ijassa-111	212	17	nonstationary	nonstationary	ADJ
ijassa-111	212	18	fridmantype	fridmantype	NOUN
ijassa-111	212	19	metric[8	metric[8	NOUN
ijassa-111	212	20	]	]	X
ijassa-111	212	21	ds2	ds2	PROPN
ijassa-111	212	22	=	=	SYM
ijassa-111	212	23	dx4	dx4	VERB
ijassa-111	212	24	2	2	NUM
ijassa-111	212	25	−	−	NOUN
ijassa-111	212	26	r2(x4)(dx1	r2(x4)(dx1	PROPN
ijassa-111	212	27	2	2	NUM
ijassa-111	212	28	+	+	CCONJ
ijassa-111	212	29	sin2x1(x2	sin2x1(x2	PROPN
ijassa-111	212	30	2	2	NUM
ijassa-111	212	31	+	+	CCONJ
ijassa-111	212	32	sin2x2dx3	sin2x2dx3	NUM
ijassa-111	212	33	2	2	NUM
ijassa-111	212	34	)	)	PUNCT
ijassa-111	212	35	)	)	PUNCT
ijassa-111	212	36	,	,	PUNCT
ijassa-111	212	37	(	(	PUNCT
ijassa-111	212	38	30	30	NUM
ijassa-111	212	39	)	)	PUNCT
ijassa-111	212	40	where	where	SCONJ
ijassa-111	212	41	r	r	NOUN
ijassa-111	212	42	is	be	AUX
ijassa-111	212	43	the	the	DET
ijassa-111	212	44	curvature	curvature	NOUN
ijassa-111	212	45	radius	radius	NOUN
ijassa-111	212	46	of	of	ADP
ijassa-111	212	47	the	the	DET
ijassa-111	212	48	three	three	NUM
ijassa-111	212	49	-	-	PUNCT
ijassa-111	212	50	dimensional	dimensional	ADJ
ijassa-111	212	51	hypersphere	hypersphere	NOUN
ijassa-111	212	52	,	,	PUNCT
ijassa-111	212	53	which	which	PRON
ijassa-111	212	54	depends	depend	VERB
ijassa-111	212	55	on	on	ADP
ijassa-111	212	56	the	the	DET
ijassa-111	212	57	parameter	parameter	NOUN
ijassa-111	212	58	x4	x4	PROPN
ijassa-111	212	59	;	;	PUNCT
ijassa-111	212	60	x1	x1	PROPN
ijassa-111	212	61	∈	∈	PROPN
ijassa-111	212	62	(	(	PUNCT
ijassa-111	212	63	0	0	NUM
ijassa-111	212	64	,	,	PUNCT
ijassa-111	212	65	2π	2π	NOUN
ijassa-111	212	66	)	)	PUNCT
ijassa-111	212	67	;	;	PUNCT
ijassa-111	212	68	x2	x2	PROPN
ijassa-111	212	69	∈	∈	PROPN
ijassa-111	212	70	(	(	PUNCT
ijassa-111	212	71	0	0	NUM
ijassa-111	212	72	,	,	PUNCT
ijassa-111	212	73	π	π	NOUN
ijassa-111	212	74	)	)	PUNCT
ijassa-111	212	75	;	;	PUNCT
ijassa-111	212	76	x3	x3	PROPN
ijassa-111	212	77	∈	∈	PROPN
ijassa-111	212	78	(	(	PUNCT
ijassa-111	212	79	0	0	NUM
ijassa-111	212	80	,	,	PUNCT
ijassa-111	212	81	2π	2π	NOUN
ijassa-111	212	82	)	)	PUNCT
ijassa-111	212	83	;	;	PUNCT
ijassa-111	212	84	and	and	CCONJ
ijassa-111	212	85	x4	x4	PROPN
ijassa-111	212	86	∈	∈	PROPN
ijassa-111	212	87	(	(	PUNCT
ijassa-111	212	88	0,∞	0,∞	NOUN
ijassa-111	212	89	)	)	PUNCT
ijassa-111	212	90	.	.	PUNCT
ijassa-111	213	1	the	the	DET
ijassa-111	213	2	following	follow	VERB
ijassa-111	213	3	theorem	theorem	NOUN
ijassa-111	213	4	is	be	AUX
ijassa-111	213	5	valid	valid	ADJ
ijassa-111	213	6	.	.	PUNCT
ijassa-111	214	1	theorem	theorem	ADJ
ijassa-111	214	2	4	4	NUM
ijassa-111	214	3	.	.	PUNCT
ijassa-111	214	4	system	system	NOUN
ijassa-111	214	5	(	(	PUNCT
ijassa-111	214	6	10	10	NUM
ijassa-111	214	7	)	)	PUNCT
ijassa-111	214	8	for	for	ADP
ijassa-111	214	9	metric	metric	ADJ
ijassa-111	214	10	(	(	PUNCT
ijassa-111	214	11	30	30	NUM
ijassa-111	214	12	)	)	PUNCT
ijassa-111	214	13	reduces	reduce	VERB
ijassa-111	214	14	to	to	ADP
ijassa-111	214	15	the	the	DET
ijassa-111	214	16	single	single	ADJ
ijassa-111	214	17	second	second	ADJ
ijassa-111	214	18	-	-	PUNCT
ijassa-111	214	19	order	order	NOUN
ijassa-111	214	20	nonlinear	nonlinear	ADJ
ijassa-111	214	21	differential	differential	ADJ
ijassa-111	214	22	equation	equation	NOUN
ijassa-111	214	23	r	r	NOUN
ijassa-111	214	24	d2r	d2r	ADJ
ijassa-111	214	25	dx42	dx42	PROPN
ijassa-111	214	26	−	−	PROPN
ijassa-111	214	27	(	(	PUNCT
ijassa-111	214	28	dr	dr	PROPN
ijassa-111	214	29	dx4	dx4	PROPN
ijassa-111	214	30	)	)	PUNCT
ijassa-111	214	31	2	2	NUM
ijassa-111	214	32	−	−	NOUN
ijassa-111	214	33	1	1	NUM
ijassa-111	214	34	=	=	SYM
ijassa-111	214	35	0	0	NUM
ijassa-111	214	36	for	for	ADP
ijassa-111	214	37	the	the	DET
ijassa-111	214	38	unknown	unknown	ADJ
ijassa-111	214	39	function	function	NOUN
ijassa-111	214	40	r(x4	r(x4	NOUN
ijassa-111	214	41	)	)	PUNCT
ijassa-111	214	42	.	.	PUNCT
ijassa-111	215	1	this	this	DET
ijassa-111	215	2	equation	equation	NOUN
ijassa-111	215	3	has	have	VERB
ijassa-111	215	4	a	a	DET
ijassa-111	215	5	real	real	ADJ
ijassa-111	215	6	solution	solution	NOUN
ijassa-111	215	7	r	r	NOUN
ijassa-111	215	8	=	=	SYM
ijassa-111	215	9	r0	r0	NOUN
ijassa-111	215	10	cosh	cosh	NOUN
ijassa-111	215	11	x4	x4	PROPN
ijassa-111	215	12	r0	r0	PROPN
ijassa-111	215	13	,	,	PUNCT
ijassa-111	215	14	where	where	SCONJ
ijassa-111	215	15	r0	r0	NOUN
ijassa-111	215	16	is	be	AUX
ijassa-111	215	17	a	a	DET
ijassa-111	215	18	some	some	ADV
ijassa-111	215	19	constant	constant	ADJ
ijassa-111	215	20	.	.	PUNCT
ijassa-111	216	1	the	the	DET
ijassa-111	216	2	scalar	scalar	ADJ
ijassa-111	216	3	curvature	curvature	NOUN
ijassa-111	216	4	of	of	ADP
ijassa-111	216	5	the	the	DET
ijassa-111	216	6	space	space	NOUN
ijassa-111	216	7	is	be	AUX
ijassa-111	216	8	everywhere	everywhere	ADV
ijassa-111	216	9	constant	constant	ADJ
ijassa-111	216	10	and	and	CCONJ
ijassa-111	216	11	has	have	VERB
ijassa-111	216	12	the	the	DET
ijassa-111	216	13	form	form	NOUN
ijassa-111	216	14	r	r	NOUN
ijassa-111	216	15	=	=	SYM
ijassa-111	216	16	12	12	NUM
ijassa-111	216	17	r02	r02	NOUN
ijassa-111	216	18	.	.	PUNCT
ijassa-111	217	1	proof	proof	NOUN
ijassa-111	217	2	.	.	PUNCT
ijassa-111	218	1	according	accord	VERB
ijassa-111	218	2	to	to	ADP
ijassa-111	218	3	(	(	PUNCT
ijassa-111	218	4	30	30	NUM
ijassa-111	218	5	)	)	PUNCT
ijassa-111	218	6	,	,	PUNCT
ijassa-111	218	7	the	the	DET
ijassa-111	218	8	nonzero	nonzero	PROPN
ijassa-111	218	9	components	component	NOUN
ijassa-111	218	10	of	of	ADP
ijassa-111	218	11	the	the	DET
ijassa-111	218	12	covariant	covariant	ADJ
ijassa-111	218	13	metric	metric	ADJ
ijassa-111	218	14	tensor	tensor	NOUN
ijassa-111	218	15	gij	gij	NOUN
ijassa-111	218	16	have	have	VERB
ijassa-111	218	17	the	the	DET
ijassa-111	218	18	form	form	NOUN
ijassa-111	218	19	g11	g11	X
ijassa-111	218	20	=	=	SYM
ijassa-111	218	21	−r2	−r2	PROPN
ijassa-111	218	22	,	,	PUNCT
ijassa-111	218	23	g22	g22	NOUN
ijassa-111	218	24	=	=	SYM
ijassa-111	218	25	−r2sin2x1	−r2sin2x1	PROPN
ijassa-111	218	26	,	,	PUNCT
ijassa-111	218	27	g33	g33	PROPN
ijassa-111	218	28	=	=	SYM
ijassa-111	218	29	−r2sin2x1sin	−r2sin2x1sin	PROPN
ijassa-111	218	30	2x2	2x2	NUM
ijassa-111	218	31	,	,	PUNCT
ijassa-111	218	32	g44	g44	NOUN
ijassa-111	218	33	=	=	SYM
ijassa-111	218	34	1	1	X
ijassa-111	218	35	.	.	PUNCT
ijassa-111	219	1	(	(	PUNCT
ijassa-111	219	2	31	31	NUM
ijassa-111	219	3	)	)	PUNCT
ijassa-111	219	4	advances	advance	NOUN
ijassa-111	219	5	in	in	ADP
ijassa-111	219	6	systems	system	NOUN
ijassa-111	219	7	science	science	NOUN
ijassa-111	219	8	and	and	CCONJ
ijassa-111	219	9	applications	application	NOUN
ijassa-111	219	10	(	(	PUNCT
ijassa-111	219	11	2012	2012	NUM
ijassa-111	219	12	)	)	PUNCT
ijassa-111	219	13	vol.12	vol.12	NOUN
ijassa-111	219	14	no.3	no.3	VERB
ijassa-111	219	15	269	269	NUM
ijassa-111	219	16	the	the	DET
ijassa-111	219	17	components	component	NOUN
ijassa-111	219	18	of	of	ADP
ijassa-111	219	19	the	the	DET
ijassa-111	219	20	contravariant	contravariant	PROPN
ijassa-111	219	21	metric	metric	PROPN
ijassa-111	219	22	tensor	tensor	NOUN
ijassa-111	219	23	gij	gij	NOUN
ijassa-111	219	24	have	have	VERB
ijassa-111	219	25	the	the	DET
ijassa-111	219	26	form	form	NOUN
ijassa-111	219	27	g11	g11	NOUN
ijassa-111	219	28	=	=	SYM
ijassa-111	219	29	−r−2	−r−2	NUM
ijassa-111	219	30	,	,	PUNCT
ijassa-111	219	31	g22	g22	NOUN
ijassa-111	219	32	=	=	SYM
ijassa-111	219	33	−	−	PROPN
ijassa-111	219	34	1	1	NUM
ijassa-111	219	35	r2sin2x1	r2sin2x1	NOUN
ijassa-111	219	36	,	,	PUNCT
ijassa-111	219	37	g33	g33	PROPN
ijassa-111	219	38	=	=	SYM
ijassa-111	219	39	−	−	PROPN
ijassa-111	219	40	1	1	NUM
ijassa-111	219	41	r2sin2x1sin	r2sin2x1sin	NOUN
ijassa-111	219	42	2x2	2x2	NUM
ijassa-111	219	43	,	,	PUNCT
ijassa-111	219	44	g44	g44	NOUN
ijassa-111	219	45	=	=	SYM
ijassa-111	219	46	1	1	X
ijassa-111	219	47	.	.	PUNCT
ijassa-111	220	1	(	(	PUNCT
ijassa-111	220	2	32	32	NUM
ijassa-111	220	3	)	)	PUNCT
ijassa-111	220	4	substituting	substitute	VERB
ijassa-111	220	5	the	the	DET
ijassa-111	220	6	metric	metric	ADJ
ijassa-111	220	7	components	component	NOUN
ijassa-111	220	8	(	(	PUNCT
ijassa-111	220	9	31	31	NUM
ijassa-111	220	10	)	)	PUNCT
ijassa-111	220	11	and	and	CCONJ
ijassa-111	220	12	(	(	PUNCT
ijassa-111	220	13	32	32	NUM
ijassa-111	220	14	)	)	PUNCT
ijassa-111	220	15	into	into	ADP
ijassa-111	220	16	relation	relation	NOUN
ijassa-111	220	17	(	(	PUNCT
ijassa-111	220	18	1	1	NUM
ijassa-111	220	19	)	)	PUNCT
ijassa-111	220	20	,	,	PUNCT
ijassa-111	220	21	we	we	PRON
ijassa-111	220	22	find	find	VERB
ijassa-111	220	23	all	all	DET
ijassa-111	220	24	nonzero	nonzero	ADJ
ijassa-111	220	25	elements	element	NOUN
ijassa-111	220	26	of	of	ADP
ijassa-111	220	27	the	the	DET
ijassa-111	220	28	pseudo	pseudo	NOUN
ijassa-111	220	29	-	-	ADJ
ijassa-111	220	30	riemannian	riemannian	ADJ
ijassa-111	220	31	connection	connection	NOUN
ijassa-111	220	32	;	;	PUNCT
ijassa-111	220	33	these	these	PRON
ijassa-111	220	34	are	be	AUX
ijassa-111	220	35	γ22	γ22	NOUN
ijassa-111	220	36	1	1	NUM
ijassa-111	220	37	=	=	SYM
ijassa-111	220	38	−	−	NOUN
ijassa-111	221	1	sinx1	sinx1	NOUN
ijassa-111	221	2	cosx1,γ33	cosx1,γ33	VERB
ijassa-111	221	3	1	1	NUM
ijassa-111	221	4	=	=	SYM
ijassa-111	221	5	−	−	NOUN
ijassa-111	221	6	sinx1	sinx1	NOUN
ijassa-111	221	7	cosx1sin	cosx1sin	VERB
ijassa-111	222	1	2x2,γ14	2x2,γ14	NUM
ijassa-111	222	2	1	1	NUM
ijassa-111	222	3	=	=	SYM
ijassa-111	222	4	1	1	NUM
ijassa-111	222	5	r	r	NOUN
ijassa-111	222	6	dr	dr	PROPN
ijassa-111	222	7	dx4	dx4	PROPN
ijassa-111	222	8	,	,	PUNCT
ijassa-111	222	9	γ12	γ12	NOUN
ijassa-111	222	10	2	2	NUM
ijassa-111	222	11	=	=	NOUN
ijassa-111	222	12	cotx1,γ33	cotx1,γ33	NOUN
ijassa-111	222	13	2	2	NUM
ijassa-111	222	14	=	=	SYM
ijassa-111	222	15	−	−	NOUN
ijassa-111	222	16	sinx2	sinx2	NOUN
ijassa-111	222	17	cosx2,γ24	cosx2,γ24	NOUN
ijassa-111	222	18	2	2	NUM
ijassa-111	222	19	=	=	SYM
ijassa-111	222	20	1	1	NUM
ijassa-111	222	21	r	r	NOUN
ijassa-111	222	22	dr	dr	PROPN
ijassa-111	222	23	dx4	dx4	PROPN
ijassa-111	222	24	,	,	PUNCT
ijassa-111	222	25	(	(	PUNCT
ijassa-111	222	26	33	33	NUM
ijassa-111	222	27	)	)	PUNCT
ijassa-111	222	28	γ13	γ13	NOUN
ijassa-111	222	29	3	3	NUM
ijassa-111	222	30	=	=	SYM
ijassa-111	222	31	cotx1,γ23	cotx1,γ23	PROPN
ijassa-111	222	32	3	3	NUM
ijassa-111	222	33	=	=	SYM
ijassa-111	222	34	cotx2,γ34	cotx2,γ34	NOUN
ijassa-111	222	35	3	3	NUM
ijassa-111	222	36	=	=	SYM
ijassa-111	222	37	1	1	NUM
ijassa-111	222	38	r	r	NOUN
ijassa-111	222	39	dr	dr	PROPN
ijassa-111	222	40	dx4	dx4	PROPN
ijassa-111	222	41	,	,	PUNCT
ijassa-111	222	42	γ11	γ11	PROPN
ijassa-111	222	43	4	4	NUM
ijassa-111	222	44	=	=	SYM
ijassa-111	222	45	r	r	NOUN
ijassa-111	222	46	dr	dr	PROPN
ijassa-111	222	47	dx4	dx4	PROPN
ijassa-111	222	48	,	,	PUNCT
ijassa-111	222	49	γ22	γ22	NOUN
ijassa-111	222	50	4	4	NUM
ijassa-111	222	51	=	=	SYM
ijassa-111	222	52	r	r	NOUN
ijassa-111	222	53	dr	dr	NOUN
ijassa-111	222	54	dx4	dx4	INTJ
ijassa-111	222	55	sin2x1,γ33	sin2x1,γ33	PROPN
ijassa-111	222	56	4	4	NUM
ijassa-111	222	57	=	=	SYM
ijassa-111	222	58	r	r	NOUN
ijassa-111	222	59	dr	dr	PROPN
ijassa-111	222	60	dx4	dx4	PROPN
ijassa-111	222	61	sin2x1sin	sin2x1sin	PROPN
ijassa-111	222	62	2x2	2x2	NUM
ijassa-111	222	63	.	.	PUNCT
ijassa-111	223	1	using	use	VERB
ijassa-111	223	2	the	the	DET
ijassa-111	223	3	components	component	NOUN
ijassa-111	223	4	(	(	PUNCT
ijassa-111	223	5	33	33	NUM
ijassa-111	223	6	)	)	PUNCT
ijassa-111	223	7	of	of	ADP
ijassa-111	223	8	the	the	DET
ijassa-111	223	9	connection	connection	NOUN
ijassa-111	223	10	and	and	CCONJ
ijassa-111	223	11	applying	apply	VERB
ijassa-111	223	12	formula	formula	NOUN
ijassa-111	223	13	(	(	PUNCT
ijassa-111	223	14	2	2	NUM
ijassa-111	223	15	)	)	PUNCT
ijassa-111	223	16	,	,	PUNCT
ijassa-111	223	17	we	we	PRON
ijassa-111	223	18	obtain	obtain	VERB
ijassa-111	223	19	all	all	DET
ijassa-111	223	20	nonzero	nonzero	ADJ
ijassa-111	223	21	components	component	NOUN
ijassa-111	223	22	of	of	ADP
ijassa-111	223	23	the	the	DET
ijassa-111	223	24	ricci	ricci	PROPN
ijassa-111	223	25	tensor	tensor	NOUN
ijassa-111	223	26	rij	rij	PROPN
ijassa-111	223	27	:	:	PUNCT
ijassa-111	223	28	r11	r11	NOUN
ijassa-111	223	29	=	=	SYM
ijassa-111	223	30	−2	−2	NOUN
ijassa-111	223	31	(	(	PUNCT
ijassa-111	223	32	dr	dr	PROPN
ijassa-111	223	33	dx4	dx4	PROPN
ijassa-111	223	34	)	)	PUNCT
ijassa-111	223	35	2	2	NUM
ijassa-111	223	36	−	−	NOUN
ijassa-111	223	37	r	r	NOUN
ijassa-111	223	38	d2r	d2r	ADJ
ijassa-111	223	39	dx42	dx42	PROPN
ijassa-111	223	40	−	−	NUM
ijassa-111	223	41	2	2	NUM
ijassa-111	223	42	,	,	PUNCT
ijassa-111	223	43	r22	r22	NOUN
ijassa-111	223	44	=	=	SYM
ijassa-111	223	45	sin2x1r11	sin2x1r11	PROPN
ijassa-111	223	46	,	,	PUNCT
ijassa-111	223	47	(	(	PUNCT
ijassa-111	223	48	34	34	NUM
ijassa-111	223	49	)	)	PUNCT
ijassa-111	223	50	r33	r33	NOUN
ijassa-111	223	51	=	=	SYM
ijassa-111	223	52	sin2x1sin	sin2x1sin	NOUN
ijassa-111	223	53	2x2r11	2x2r11	NUM
ijassa-111	223	54	,	,	PUNCT
ijassa-111	223	55	r44	r44	NOUN
ijassa-111	223	56	=	=	SYM
ijassa-111	223	57	3	3	NUM
ijassa-111	223	58	r	r	NOUN
ijassa-111	223	59	d2r	d2r	ADJ
ijassa-111	223	60	dx42	dx42	PROPN
ijassa-111	223	61	.	.	PUNCT
ijassa-111	224	1	it	it	PRON
ijassa-111	224	2	follows	follow	VERB
ijassa-111	224	3	from	from	ADP
ijassa-111	224	4	(	(	PUNCT
ijassa-111	224	5	10	10	NUM
ijassa-111	224	6	)	)	PUNCT
ijassa-111	224	7	,	,	PUNCT
ijassa-111	224	8	(	(	PUNCT
ijassa-111	224	9	32	32	NUM
ijassa-111	224	10	)	)	PUNCT
ijassa-111	224	11	,	,	PUNCT
ijassa-111	224	12	and	and	CCONJ
ijassa-111	224	13	(	(	PUNCT
ijassa-111	224	14	34	34	NUM
ijassa-111	224	15	)	)	PUNCT
ijassa-111	224	16	that	that	SCONJ
ijassa-111	224	17	the	the	DET
ijassa-111	224	18	scalar	scalar	ADJ
ijassa-111	224	19	curvature	curvature	NOUN
ijassa-111	224	20	is	be	AUX
ijassa-111	225	1	r	r	NOUN
ijassa-111	225	2	=	=	SYM
ijassa-111	225	3	6	6	NUM
ijassa-111	225	4	r	r	NOUN
ijassa-111	225	5	d2r	d2r	ADJ
ijassa-111	225	6	dx42	dx42	PROPN
ijassa-111	225	7	+	+	CCONJ
ijassa-111	225	8	6	6	NUM
ijassa-111	225	9	r2	r2	NOUN
ijassa-111	225	10	(	(	PUNCT
ijassa-111	225	11	dr	dr	PROPN
ijassa-111	225	12	dx4	dx4	PROPN
ijassa-111	225	13	)	)	PUNCT
ijassa-111	225	14	2	2	NUM
ijassa-111	225	15	+	+	SYM
ijassa-111	225	16	6	6	NUM
ijassa-111	225	17	r2	r2	NOUN
ijassa-111	225	18	.	.	PUNCT
ijassa-111	226	1	(	(	PUNCT
ijassa-111	226	2	35	35	NUM
ijassa-111	226	3	)	)	PUNCT
ijassa-111	226	4	by	by	ADP
ijassa-111	226	5	virtue	virtue	NOUN
ijassa-111	226	6	of	of	ADP
ijassa-111	226	7	(	(	PUNCT
ijassa-111	226	8	31	31	NUM
ijassa-111	226	9	)	)	PUNCT
ijassa-111	226	10	,	,	PUNCT
ijassa-111	226	11	(	(	PUNCT
ijassa-111	226	12	34	34	NUM
ijassa-111	226	13	)	)	PUNCT
ijassa-111	226	14	,	,	PUNCT
ijassa-111	226	15	and	and	CCONJ
ijassa-111	226	16	(	(	PUNCT
ijassa-111	226	17	35	35	NUM
ijassa-111	226	18	)	)	PUNCT
ijassa-111	226	19	,	,	PUNCT
ijassa-111	226	20	system	system	NOUN
ijassa-111	226	21	(	(	PUNCT
ijassa-111	226	22	10	10	NUM
ijassa-111	226	23	)	)	PUNCT
ijassa-111	226	24	degenerates	degenerate	NOUN
ijassa-111	226	25	into	into	ADP
ijassa-111	226	26	a	a	DET
ijassa-111	226	27	single	single	ADJ
ijassa-111	226	28	equation	equation	NOUN
ijassa-111	226	29	of	of	ADP
ijassa-111	226	30	the	the	DET
ijassa-111	226	31	form	form	NOUN
ijassa-111	226	32	r	r	NOUN
ijassa-111	226	33	d2r	d2r	ADJ
ijassa-111	226	34	dx42	dx42	PROPN
ijassa-111	226	35	−	−	PROPN
ijassa-111	226	36	(	(	PUNCT
ijassa-111	226	37	dr	dr	PROPN
ijassa-111	226	38	dx4	dx4	PROPN
ijassa-111	226	39	)	)	PUNCT
ijassa-111	226	40	2	2	NUM
ijassa-111	226	41	−	−	NOUN
ijassa-111	226	42	1	1	NUM
ijassa-111	226	43	=	=	SYM
ijassa-111	226	44	0	0	NUM
ijassa-111	226	45	.	.	PUNCT
ijassa-111	227	1	(	(	PUNCT
ijassa-111	227	2	36	36	NUM
ijassa-111	227	3	)	)	PUNCT
ijassa-111	227	4	we	we	PRON
ijassa-111	227	5	seek	seek	VERB
ijassa-111	227	6	a	a	DET
ijassa-111	227	7	solution	solution	NOUN
ijassa-111	227	8	of	of	ADP
ijassa-111	227	9	equation	equation	NOUN
ijassa-111	227	10	(	(	PUNCT
ijassa-111	227	11	36	36	NUM
ijassa-111	227	12	)	)	PUNCT
ijassa-111	227	13	in	in	ADP
ijassa-111	227	14	the	the	DET
ijassa-111	227	15	form	form	NOUN
ijassa-111	227	16	r	r	NOUN
ijassa-111	227	17	=	=	PUNCT
ijassa-111	227	18	a1e	a1e	PART
ijassa-111	227	19	β1x4	β1x4	PUNCT
ijassa-111	227	20	+	+	CCONJ
ijassa-111	227	21	a2e	a2e	ADJ
ijassa-111	227	22	−β2x4	−β2x4	NOUN
ijassa-111	227	23	,	,	PUNCT
ijassa-111	227	24	where	where	SCONJ
ijassa-111	227	25	a1	a1	NOUN
ijassa-111	227	26	,	,	PUNCT
ijassa-111	227	27	a2	a2	PROPN
ijassa-111	227	28	,	,	PUNCT
ijassa-111	227	29	β1	β1	PROPN
ijassa-111	227	30	,	,	PUNCT
ijassa-111	227	31	and	and	CCONJ
ijassa-111	227	32	are	be	AUX
ijassa-111	227	33	some	some	DET
ijassa-111	227	34	constants	constant	NOUN
ijassa-111	227	35	.	.	PUNCT
ijassa-111	228	1	then	then	ADV
ijassa-111	228	2	equation	equation	NOUN
ijassa-111	228	3	(	(	PUNCT
ijassa-111	228	4	36	36	NUM
ijassa-111	228	5	)	)	PUNCT
ijassa-111	228	6	transforms	transform	VERB
ijassa-111	228	7	into	into	ADP
ijassa-111	228	8	the	the	DET
ijassa-111	228	9	relation	relation	NOUN
ijassa-111	228	10	a1a2(β1	a1a2(β1	NOUN
ijassa-111	228	11	+	+	CCONJ
ijassa-111	228	12	β2	β2	ADJ
ijassa-111	228	13	)	)	PUNCT
ijassa-111	228	14	2	2	NUM
ijassa-111	229	1	=	=	SYM
ijassa-111	229	2	e(β2−β1)x4	e(β2−β1)x4	PROPN
ijassa-111	229	3	,	,	PUNCT
ijassa-111	229	4	which	which	PRON
ijassa-111	229	5	implies	imply	VERB
ijassa-111	229	6	β1	β1	PROPN
ijassa-111	229	7	=	=	SYM
ijassa-111	229	8	β2	β2	PROPN
ijassa-111	229	9	and	and	CCONJ
ijassa-111	229	10	a1a2	a1a2	X
ijassa-111	229	11	=	=	NOUN
ijassa-111	229	12	1	1	NUM
ijassa-111	229	13	4β1	4β1	NUM
ijassa-111	229	14	2	2	NUM
ijassa-111	229	15	.	.	PUNCT
ijassa-111	230	1	since	since	SCONJ
ijassa-111	230	2	r	r	NOUN
ijassa-111	230	3	>	>	X
ijassa-111	230	4	0	0	NUM
ijassa-111	230	5	,	,	PUNCT
ijassa-111	230	6	it	it	PRON
ijassa-111	230	7	follows	follow	VERB
ijassa-111	230	8	that	that	DET
ijassa-111	230	9	a1	a1	NOUN
ijassa-111	230	10	>	>	X
ijassa-111	230	11	0	0	PUNCT
ijassa-111	231	1	if	if	SCONJ
ijassa-111	231	2	β1	β1	PROPN
ijassa-111	231	3	>	>	X
ijassa-111	231	4	0	0	NUM
ijassa-111	231	5	,	,	PUNCT
ijassa-111	231	6	and	and	CCONJ
ijassa-111	231	7	we	we	PRON
ijassa-111	231	8	can	can	AUX
ijassa-111	231	9	set	set	VERB
ijassa-111	231	10	a1	a1	NOUN
ijassa-111	231	11	=	=	SYM
ijassa-111	231	12	ea	ea	PROPN
ijassa-111	231	13	2β1	2β1	NUM
ijassa-111	231	14	and	and	CCONJ
ijassa-111	231	15	a2	a2	PROPN
ijassa-111	231	16	=	=	SYM
ijassa-111	231	17	e−a	e−a	PROPN
ijassa-111	231	18	2β1	2β1	NUM
ijassa-111	231	19	.	.	PUNCT
ijassa-111	232	1	if	if	SCONJ
ijassa-111	232	2	dr	dr	PROPN
ijassa-111	232	3	dx4	dx4	VERB
ijassa-111	232	4	|	|	ADV
ijassa-111	232	5	x4=0	x4=0	PUNCT
ijassa-111	232	6	=	=	SYM
ijassa-111	232	7	0	0	NUM
ijassa-111	232	8	,	,	PUNCT
ijassa-111	232	9	then	then	ADV
ijassa-111	232	10	a	a	DET
ijassa-111	232	11	=	=	NOUN
ijassa-111	232	12	0	0	X
ijassa-111	232	13	.	.	PUNCT
ijassa-111	233	1	setting	set	VERB
ijassa-111	233	2	a1	a1	NOUN
ijassa-111	233	3	=	=	SYM
ijassa-111	233	4	r0	r0	NOUN
ijassa-111	233	5	,	,	PUNCT
ijassa-111	233	6	we	we	PRON
ijassa-111	233	7	finally	finally	ADV
ijassa-111	233	8	obtain	obtain	VERB
ijassa-111	233	9	r(x4	r(x4	NOUN
ijassa-111	233	10	)	)	PUNCT
ijassa-111	233	11	=	=	SYM
ijassa-111	233	12	r0	r0	NOUN
ijassa-111	233	13	cosh	cosh	NOUN
ijassa-111	233	14	x4	x4	PROPN
ijassa-111	233	15	r0	r0	PROPN
ijassa-111	233	16	.	.	PUNCT
ijassa-111	234	1	270	270	NUM
ijassa-111	234	2	n.n	n.n	PROPN
ijassa-111	234	3	.	.	PROPN
ijassa-111	234	4	popov	popov	PROPN
ijassa-111	234	5	:	:	PUNCT
ijassa-111	234	6	a	a	DET
ijassa-111	234	7	geometric	geometric	ADJ
ijassa-111	234	8	interpretation	interpretation	NOUN
ijassa-111	234	9	of	of	ADP
ijassa-111	234	10	gravity	gravity	NOUN
ijassa-111	234	11	theory	theory	NOUN
ijassa-111	234	12	there	there	PRON
ijassa-111	234	13	exists	exist	VERB
ijassa-111	234	14	yet	yet	ADV
ijassa-111	234	15	another	another	PRON
ijassa-111	234	16	,	,	PUNCT
ijassa-111	234	17	complex	complex	ADJ
ijassa-111	234	18	,	,	PUNCT
ijassa-111	234	19	solution	solution	NOUN
ijassa-111	234	20	of	of	ADP
ijassa-111	234	21	equation	equation	NOUN
ijassa-111	234	22	(	(	PUNCT
ijassa-111	234	23	36	36	NUM
ijassa-111	234	24	)	)	PUNCT
ijassa-111	234	25	,	,	PUNCT
ijassa-111	234	26	namely	namely	ADV
ijassa-111	234	27	,	,	PUNCT
ijassa-111	234	28	r	r	NOUN
ijassa-111	234	29	=	=	NOUN
ijassa-111	234	30	ix4	ix4	VERB
ijassa-111	234	31	,	,	PUNCT
ijassa-111	234	32	but	but	CCONJ
ijassa-111	234	33	we	we	PRON
ijassa-111	234	34	are	be	AUX
ijassa-111	234	35	interested	interested	ADJ
ijassa-111	234	36	only	only	ADV
ijassa-111	234	37	in	in	ADP
ijassa-111	234	38	real	real	ADJ
ijassa-111	234	39	positive	positive	ADJ
ijassa-111	234	40	solutions	solution	NOUN
ijassa-111	234	41	.	.	PUNCT
ijassa-111	235	1	substituting	substitute	VERB
ijassa-111	235	2	the	the	DET
ijassa-111	235	3	solution	solution	NOUN
ijassa-111	235	4	r(x4	r(x4	NOUN
ijassa-111	235	5	)	)	PUNCT
ijassa-111	235	6	=	=	SYM
ijassa-111	235	7	r0	r0	NOUN
ijassa-111	235	8	cosh	cosh	NOUN
ijassa-111	235	9	x4	x4	PROPN
ijassa-111	235	10	r0	r0	PROPN
ijassa-111	235	11	into	into	ADP
ijassa-111	235	12	(	(	PUNCT
ijassa-111	235	13	35	35	NUM
ijassa-111	235	14	)	)	PUNCT
ijassa-111	235	15	,	,	PUNCT
ijassa-111	235	16	we	we	PRON
ijassa-111	235	17	obtain	obtain	VERB
ijassa-111	235	18	the	the	DET
ijassa-111	235	19	following	follow	VERB
ijassa-111	235	20	expression	expression	NOUN
ijassa-111	235	21	r	r	NOUN
ijassa-111	235	22	=	=	SYM
ijassa-111	235	23	12	12	NUM
ijassa-111	235	24	r02	r02	NOUN
ijassa-111	235	25	for	for	ADP
ijassa-111	235	26	the	the	DET
ijassa-111	235	27	scalar	scalar	ADJ
ijassa-111	235	28	curvature	curvature	NOUN
ijassa-111	235	29	,	,	PUNCT
ijassa-111	235	30	which	which	PRON
ijassa-111	235	31	proves	prove	VERB
ijassa-111	235	32	the	the	DET
ijassa-111	235	33	theorem	theorem	NOUN
ijassa-111	235	34	.	.	PUNCT
ijassa-111	236	1	at	at	ADP
ijassa-111	236	2	first	first	ADJ
ijassa-111	236	3	glance	glance	NOUN
ijassa-111	236	4	,	,	PUNCT
ijassa-111	236	5	the	the	DET
ijassa-111	236	6	physical	physical	ADJ
ijassa-111	236	7	interpretation	interpretation	NOUN
ijassa-111	236	8	of	of	ADP
ijassa-111	236	9	the	the	DET
ijassa-111	236	10	assertion	assertion	NOUN
ijassa-111	236	11	of	of	ADP
ijassa-111	236	12	theorem	theorem	NOUN
ijassa-111	236	13	4	4	NUM
ijassa-111	236	14	may	may	AUX
ijassa-111	236	15	seem	seem	VERB
ijassa-111	236	16	rather	rather	ADV
ijassa-111	236	17	contradictory	contradictory	ADJ
ijassa-111	236	18	.	.	PUNCT
ijassa-111	237	1	on	on	ADP
ijassa-111	237	2	the	the	DET
ijassa-111	237	3	one	one	NUM
ijassa-111	237	4	hand	hand	NOUN
ijassa-111	237	5	,	,	PUNCT
ijassa-111	237	6	the	the	DET
ijassa-111	237	7	hyperspherical	hyperspherical	ADJ
ijassa-111	237	8	space	space	NOUN
ijassa-111	237	9	expands	expand	VERB
ijassa-111	237	10	by	by	ADP
ijassa-111	237	11	an	an	DET
ijassa-111	237	12	almost	almost	ADV
ijassa-111	237	13	exponential	exponential	ADJ
ijassa-111	237	14	law	law	NOUN
ijassa-111	237	15	,	,	PUNCT
ijassa-111	237	16	i.e.	i.e.	X
ijassa-111	237	17	,	,	PUNCT
ijassa-111	237	18	the	the	DET
ijassa-111	237	19	curvature	curvature	NOUN
ijassa-111	237	20	radius	radius	NOUN
ijassa-111	237	21	increases	increase	NOUN
ijassa-111	237	22	as	as	ADP
ijassa-111	237	23	r	r	NOUN
ijassa-111	237	24	=	=	SYM
ijassa-111	237	25	r0	r0	NOUN
ijassa-111	237	26	cosh	cosh	NOUN
ijassa-111	237	27	x4	x4	PROPN
ijassa-111	237	28	r0	r0	NOUN
ijassa-111	237	29	,	,	PUNCT
ijassa-111	237	30	while	while	SCONJ
ijassa-111	237	31	the	the	DET
ijassa-111	237	32	scalar	scalar	ADJ
ijassa-111	237	33	curvature	curvature	NOUN
ijassa-111	237	34	r	r	NOUN
ijassa-111	237	35	itself	itself	PRON
ijassa-111	237	36	does	do	AUX
ijassa-111	237	37	not	not	PART
ijassa-111	237	38	depend	depend	VERB
ijassa-111	237	39	on	on	ADP
ijassa-111	237	40	the	the	DET
ijassa-111	237	41	parameter	parameter	NOUN
ijassa-111	237	42	x4	x4	PROPN
ijassa-111	237	43	and	and	CCONJ
ijassa-111	237	44	remains	remain	VERB
ijassa-111	237	45	everywhere	everywhere	ADV
ijassa-111	237	46	constant	constant	ADJ
ijassa-111	237	47	.	.	PUNCT
ijassa-111	238	1	according	accord	VERB
ijassa-111	238	2	to	to	PART
ijassa-111	238	3	postulate	postulate	VERB
ijassa-111	238	4	2	2	NUM
ijassa-111	238	5	,	,	PUNCT
ijassa-111	238	6	this	this	PRON
ijassa-111	238	7	means	mean	VERB
ijassa-111	238	8	that	that	SCONJ
ijassa-111	238	9	the	the	DET
ijassa-111	238	10	mass	mass	ADJ
ijassa-111	238	11	density	density	NOUN
ijassa-111	238	12	of	of	ADP
ijassa-111	238	13	the	the	DET
ijassa-111	238	14	matter	matter	NOUN
ijassa-111	238	15	uniformly	uniformly	ADV
ijassa-111	238	16	filling	fill	VERB
ijassa-111	238	17	the	the	DET
ijassa-111	238	18	expanding	expand	VERB
ijassa-111	238	19	space	space	NOUN
ijassa-111	238	20	remains	remain	VERB
ijassa-111	238	21	constant	constant	ADJ
ijassa-111	238	22	as	as	ADV
ijassa-111	238	23	well	well	ADV
ijassa-111	238	24	.	.	PUNCT
ijassa-111	239	1	in	in	ADP
ijassa-111	239	2	reality	reality	NOUN
ijassa-111	239	3	,	,	PUNCT
ijassa-111	239	4	these	these	DET
ijassa-111	239	5	results	result	NOUN
ijassa-111	239	6	involve	involve	VERB
ijassa-111	239	7	no	no	DET
ijassa-111	239	8	contradiction	contradiction	NOUN
ijassa-111	239	9	.	.	PUNCT
ijassa-111	240	1	at	at	ADP
ijassa-111	240	2	present	present	ADJ
ijassa-111	240	3	,	,	PUNCT
ijassa-111	240	4	the	the	DET
ijassa-111	240	5	existence	existence	NOUN
ijassa-111	240	6	of	of	ADP
ijassa-111	240	7	a	a	DET
ijassa-111	240	8	new	new	ADJ
ijassa-111	240	9	type	type	NOUN
ijassa-111	240	10	of	of	ADP
ijassa-111	240	11	matter	matter	NOUN
ijassa-111	240	12	in	in	ADP
ijassa-111	240	13	our	our	PRON
ijassa-111	240	14	universe	universe	NOUN
ijassa-111	240	15	,	,	PUNCT
ijassa-111	240	16	which	which	PRON
ijassa-111	240	17	is	be	AUX
ijassa-111	240	18	known	know	VERB
ijassa-111	240	19	as	as	ADP
ijassa-111	240	20	dark	dark	ADJ
ijassa-111	240	21	energy	energy	NOUN
ijassa-111	240	22	,	,	PUNCT
ijassa-111	240	23	has	have	AUX
ijassa-111	240	24	been	be	AUX
ijassa-111	240	25	reliably	reliably	ADV
ijassa-111	240	26	established	establish	VERB
ijassa-111	240	27	in	in	ADP
ijassa-111	240	28	cosmology	cosmology	NOUN
ijassa-111	240	29	;	;	PUNCT
ijassa-111	240	30	this	this	DET
ijassa-111	240	31	matter	matter	NOUN
ijassa-111	240	32	fills	fill	VERB
ijassa-111	240	33	uniformly	uniformly	ADV
ijassa-111	240	34	whole	whole	ADJ
ijassa-111	240	35	space	space	NOUN
ijassa-111	240	36	and	and	CCONJ
ijassa-111	240	37	is	be	AUX
ijassa-111	240	38	characterized	characterize	VERB
ijassa-111	240	39	by	by	ADP
ijassa-111	240	40	constant	constant	ADJ
ijassa-111	240	41	mass	mass	NOUN
ijassa-111	240	42	density	density	NOUN
ijassa-111	240	43	not	not	PART
ijassa-111	240	44	depending	depend	VERB
ijassa-111	240	45	on	on	ADP
ijassa-111	240	46	the	the	DET
ijassa-111	240	47	time	time	NOUN
ijassa-111	240	48	parameter	parameter	PROPN
ijassa-111	240	49	x4	x4	PROPN
ijassa-111	240	50	.	.	PUNCT
ijassa-111	241	1	the	the	DET
ijassa-111	241	2	model	model	NOUN
ijassa-111	241	3	suggested	suggest	VERB
ijassa-111	241	4	above	above	ADV
ijassa-111	241	5	can	can	AUX
ijassa-111	241	6	be	be	AUX
ijassa-111	241	7	regarded	regard	VERB
ijassa-111	241	8	as	as	ADP
ijassa-111	241	9	an	an	DET
ijassa-111	241	10	example	example	NOUN
ijassa-111	241	11	confirming	confirm	VERB
ijassa-111	241	12	the	the	DET
ijassa-111	241	13	existence	existence	NOUN
ijassa-111	241	14	of	of	ADP
ijassa-111	241	15	this	this	DET
ijassa-111	241	16	type	type	NOUN
ijassa-111	241	17	matter	matter	NOUN
ijassa-111	241	18	with	with	ADP
ijassa-111	241	19	such	such	ADJ
ijassa-111	241	20	unusual	unusual	ADJ
ijassa-111	241	21	physical	physical	ADJ
ijassa-111	241	22	properties	property	NOUN
ijassa-111	241	23	.	.	PUNCT
ijassa-111	242	1	7	7	NUM
ijassa-111	242	2	conclusion	conclusion	NOUN
ijassa-111	242	3	the	the	DET
ijassa-111	242	4	axiomatization	axiomatization	NOUN
ijassa-111	242	5	of	of	ADP
ijassa-111	242	6	gravity	gravity	NOUN
ijassa-111	242	7	theory	theory	NOUN
ijassa-111	242	8	proposed	propose	VERB
ijassa-111	242	9	in	in	ADP
ijassa-111	242	10	this	this	DET
ijassa-111	242	11	paper	paper	NOUN
ijassa-111	242	12	and	and	CCONJ
ijassa-111	242	13	the	the	DET
ijassa-111	242	14	fundamental	fundamental	ADJ
ijassa-111	242	15	gravity	gravity	NOUN
ijassa-111	242	16	equation	equation	NOUN
ijassa-111	242	17	obtained	obtain	VERB
ijassa-111	242	18	on	on	ADP
ijassa-111	242	19	the	the	DET
ijassa-111	242	20	basis	basis	NOUN
ijassa-111	242	21	of	of	ADP
ijassa-111	242	22	these	these	DET
ijassa-111	242	23	axioms	axiom	NOUN
ijassa-111	242	24	make	make	VERB
ijassa-111	242	25	it	it	PRON
ijassa-111	242	26	possible	possible	ADJ
ijassa-111	242	27	to	to	PART
ijassa-111	242	28	demonstrate	demonstrate	VERB
ijassa-111	242	29	the	the	DET
ijassa-111	242	30	effectiveness	effectiveness	NOUN
ijassa-111	242	31	of	of	ADP
ijassa-111	242	32	the	the	DET
ijassa-111	242	33	suggested	suggest	VERB
ijassa-111	242	34	approach	approach	NOUN
ijassa-111	242	35	for	for	ADP
ijassa-111	242	36	a	a	DET
ijassa-111	242	37	number	number	NOUN
ijassa-111	242	38	of	of	ADP
ijassa-111	242	39	physical	physical	ADJ
ijassa-111	242	40	examples	example	NOUN
ijassa-111	242	41	considered	consider	VERB
ijassa-111	242	42	in	in	ADP
ijassa-111	242	43	the	the	DET
ijassa-111	242	44	paper	paper	NOUN
ijassa-111	242	45	.	.	PUNCT
ijassa-111	243	1	it	it	PRON
ijassa-111	243	2	suffices	suffice	VERB
ijassa-111	243	3	to	to	PART
ijassa-111	243	4	mention	mention	VERB
ijassa-111	243	5	that	that	SCONJ
ijassa-111	243	6	the	the	DET
ijassa-111	243	7	problem	problem	NOUN
ijassa-111	243	8	of	of	ADP
ijassa-111	243	9	constructing	construct	VERB
ijassa-111	243	10	an	an	DET
ijassa-111	243	11	everywhere	everywhere	ADV
ijassa-111	243	12	continuous	continuous	ADJ
ijassa-111	243	13	spherically	spherically	NOUN
ijassa-111	243	14	symmetric	symmetric	ADJ
ijassa-111	243	15	stationary	stationary	ADJ
ijassa-111	243	16	metric	metric	NOUN
ijassa-111	243	17	of	of	ADP
ijassa-111	243	18	a	a	DET
ijassa-111	243	19	pseudo	pseudo	NOUN
ijassa-111	243	20	-	-	ADJ
ijassa-111	243	21	riemannian	riemannian	ADJ
ijassa-111	243	22	space	space	NOUN
ijassa-111	243	23	with	with	ADP
ijassa-111	243	24	discontinuous	discontinuous	ADJ
ijassa-111	243	25	scalar	scalar	ADJ
ijassa-111	243	26	curvature	curvature	NOUN
ijassa-111	243	27	,	,	PUNCT
ijassa-111	243	28	which	which	PRON
ijassa-111	243	29	is	be	AUX
ijassa-111	243	30	solved	solve	VERB
ijassa-111	243	31	in	in	ADP
ijassa-111	243	32	general	general	ADJ
ijassa-111	243	33	form	form	NOUN
ijassa-111	243	34	in	in	ADP
ijassa-111	243	35	section	section	NOUN
ijassa-111	243	36	4	4	NUM
ijassa-111	243	37	,	,	PUNCT
ijassa-111	243	38	still	still	ADV
ijassa-111	243	39	remains	remain	VERB
ijassa-111	243	40	unsolved	unsolved	ADJ
ijassa-111	243	41	in	in	ADP
ijassa-111	243	42	the	the	DET
ijassa-111	243	43	framework	framework	NOUN
ijassa-111	243	44	of	of	ADP
ijassa-111	243	45	grt	grt	PROPN
ijassa-111	243	46	,	,	PUNCT
ijassa-111	243	47	in	in	ADP
ijassa-111	243	48	which	which	PRON
ijassa-111	243	49	solving	solve	VERB
ijassa-111	243	50	this	this	DET
ijassa-111	243	51	problem	problem	NOUN
ijassa-111	243	52	involves	involve	VERB
ijassa-111	243	53	fundamental	fundamental	ADJ
ijassa-111	243	54	difficulties	difficulty	NOUN
ijassa-111	243	55	.	.	PUNCT
ijassa-111	244	1	in	in	ADP
ijassa-111	244	2	the	the	DET
ijassa-111	244	3	framework	framework	NOUN
ijassa-111	244	4	of	of	ADP
ijassa-111	244	5	the	the	DET
ijassa-111	244	6	formalism	formalism	NOUN
ijassa-111	244	7	suggested	suggest	VERB
ijassa-111	244	8	here	here	ADV
ijassa-111	244	9	,	,	PUNCT
ijassa-111	244	10	the	the	DET
ijassa-111	244	11	concepts	concept	NOUN
ijassa-111	244	12	of	of	ADP
ijassa-111	244	13	a	a	DET
ijassa-111	244	14	stationary	stationary	ADJ
ijassa-111	244	15	black	black	ADJ
ijassa-111	244	16	hole	hole	NOUN
ijassa-111	244	17	and	and	CCONJ
ijassa-111	244	18	dark	dark	ADJ
ijassa-111	244	19	energy	energy	NOUN
ijassa-111	244	20	are	be	AUX
ijassa-111	244	21	defined	define	VERB
ijassa-111	244	22	more	more	ADV
ijassa-111	244	23	rigorously	rigorously	ADV
ijassa-111	244	24	from	from	ADP
ijassa-111	244	25	the	the	DET
ijassa-111	244	26	mathematical	mathematical	ADJ
ijassa-111	244	27	point	point	NOUN
ijassa-111	244	28	of	of	ADP
ijassa-111	244	29	view	view	NOUN
ijassa-111	244	30	.	.	PUNCT
ijassa-111	245	1	importantly	importantly	ADV
ijassa-111	245	2	,	,	PUNCT
ijassa-111	245	3	dark	dark	ADJ
ijassa-111	245	4	energy	energy	NOUN
ijassa-111	245	5	arises	arise	VERB
ijassa-111	245	6	in	in	ADP
ijassa-111	245	7	a	a	DET
ijassa-111	245	8	natural	natural	ADJ
ijassa-111	245	9	way	way	NOUN
ijassa-111	245	10	as	as	ADP
ijassa-111	245	11	one	one	NUM
ijassa-111	245	12	of	of	ADP
ijassa-111	245	13	the	the	DET
ijassa-111	245	14	solutions	solution	NOUN
ijassa-111	245	15	of	of	ADP
ijassa-111	245	16	the	the	DET
ijassa-111	245	17	system	system	NOUN
ijassa-111	245	18	(	(	PUNCT
ijassa-111	245	19	10	10	NUM
ijassa-111	245	20	)	)	PUNCT
ijassa-111	245	21	of	of	ADP
ijassa-111	245	22	gravity	gravity	NOUN
ijassa-111	245	23	equations	equation	NOUN
ijassa-111	245	24	,	,	PUNCT
ijassa-111	245	25	which	which	PRON
ijassa-111	245	26	,	,	PUNCT
ijassa-111	245	27	unlike	unlike	ADP
ijassa-111	245	28	in	in	ADP
ijassa-111	245	29	grt[9	grt[9	PROPN
ijassa-111	245	30	]	]	PUNCT
ijassa-111	245	31	,	,	PUNCT
ijassa-111	245	32	does	do	AUX
ijassa-111	245	33	not	not	PART
ijassa-111	245	34	require	require	VERB
ijassa-111	245	35	introduce	introduce	VERB
ijassa-111	245	36	any	any	DET
ijassa-111	245	37	additional	additional	ADJ
ijassa-111	245	38	empirical	empirical	ADJ
ijassa-111	245	39	constants	constant	NOUN
ijassa-111	245	40	into	into	ADP
ijassa-111	245	41	the	the	DET
ijassa-111	245	42	main	main	ADJ
ijassa-111	245	43	equation	equation	NOUN
ijassa-111	245	44	,	,	PUNCT
ijassa-111	245	45	such	such	ADJ
ijassa-111	245	46	as	as	ADP
ijassa-111	245	47	the	the	DET
ijassa-111	245	48	cosmological	cosmological	ADJ
ijassa-111	245	49	constant	constant	ADJ
ijassa-111	245	50	and	and	CCONJ
ijassa-111	245	51	its	its	PRON
ijassa-111	245	52	comparatively	comparatively	ADV
ijassa-111	245	53	recent	recent	ADJ
ijassa-111	245	54	interpretation	interpretation	NOUN
ijassa-111	245	55	as	as	ADP
ijassa-111	245	56	the	the	DET
ijassa-111	245	57	mass	mass	ADJ
ijassa-111	245	58	density	density	NOUN
ijassa-111	245	59	of	of	ADP
ijassa-111	245	60	dark	dark	ADJ
ijassa-111	245	61	energy[10	energy[10	PROPN
ijassa-111	245	62	]	]	PUNCT
ijassa-111	245	63	.	.	PUNCT
ijassa-111	246	1	references	reference	NOUN
ijassa-111	246	2	[	[	X
ijassa-111	246	3	1	1	NUM
ijassa-111	246	4	]	]	PUNCT
ijassa-111	246	5	p.	p.	NOUN
ijassa-111	246	6	k.	k.	PROPN
ijassa-111	247	1	rashevskii	rashevskii	PROPN
ijassa-111	247	2	.	.	PUNCT
ijassa-111	248	1	(	(	PUNCT
ijassa-111	248	2	1967	1967	NUM
ijassa-111	248	3	)	)	PUNCT
ijassa-111	248	4	,	,	PUNCT
ijassa-111	248	5	riemannian	riemannian	ADJ
ijassa-111	248	6	geometry	geometry	NOUN
ijassa-111	248	7	and	and	CCONJ
ijassa-111	248	8	tensor	tensor	NOUN
ijassa-111	248	9	analysis	analysis	NOUN
ijassa-111	248	10	,	,	PUNCT
ijassa-111	248	11	(	(	PUNCT
ijassa-111	248	12	nauka	nauka	PROPN
ijassa-111	248	13	,	,	PUNCT
ijassa-111	248	14	moscow	moscow	PROPN
ijassa-111	248	15	)	)	PUNCT
ijassa-111	249	1	[	[	X
ijassa-111	249	2	in	in	ADP
ijassa-111	249	3	russian	russian	PROPN
ijassa-111	249	4	]	]	PUNCT
ijassa-111	249	5	.	.	PUNCT
ijassa-111	250	1	[	[	X
ijassa-111	250	2	2	2	NUM
ijassa-111	250	3	]	]	PUNCT
ijassa-111	250	4	b.	b.	PROPN
ijassa-111	250	5	a.	a.	PROPN
ijassa-111	250	6	dubrovin	dubrovin	PROPN
ijassa-111	250	7	,	,	PUNCT
ijassa-111	250	8	s.	s.	PROPN
ijassa-111	250	9	p.	p.	PROPN
ijassa-111	250	10	novikov	novikov	PROPN
ijassa-111	250	11	and	and	CCONJ
ijassa-111	250	12	a.	a.	NOUN
ijassa-111	250	13	t.	t.	PROPN
ijassa-111	250	14	fomenko	fomenko	PROPN
ijassa-111	250	15	.	.	PUNCT
ijassa-111	251	1	(	(	PUNCT
ijassa-111	251	2	1979	1979	NUM
ijassa-111	251	3	)	)	PUNCT
ijassa-111	251	4	,	,	PUNCT
ijassa-111	251	5	modern	modern	ADJ
ijassa-111	251	6	geometry	geometry	NOUN
ijassa-111	251	7	,	,	PUNCT
ijassa-111	251	8	(	(	PUNCT
ijassa-111	251	9	nauka	nauka	PROPN
ijassa-111	251	10	,	,	PUNCT
ijassa-111	251	11	moscow	moscow	PROPN
ijassa-111	251	12	)	)	PUNCT
ijassa-111	252	1	[	[	X
ijassa-111	252	2	in	in	ADP
ijassa-111	252	3	russian	russian	PROPN
ijassa-111	252	4	]	]	PUNCT
ijassa-111	252	5	.	.	PUNCT
ijassa-111	253	1	advances	advance	NOUN
ijassa-111	253	2	in	in	ADP
ijassa-111	253	3	systems	system	NOUN
ijassa-111	253	4	science	science	NOUN
ijassa-111	253	5	and	and	CCONJ
ijassa-111	253	6	applications	application	NOUN
ijassa-111	253	7	(	(	PUNCT
ijassa-111	253	8	2012	2012	NUM
ijassa-111	253	9	)	)	PUNCT
ijassa-111	253	10	vol.12	vol.12	NOUN
ijassa-111	253	11	no.3	no.3	VERB
ijassa-111	253	12	271	271	NUM
ijassa-111	253	13	[	[	X
ijassa-111	253	14	3	3	NUM
ijassa-111	253	15	]	]	X
ijassa-111	253	16	d.	d.	PROPN
ijassa-111	253	17	hilbert	hilbert	PROPN
ijassa-111	253	18	.	.	PUNCT
ijassa-111	254	1	(	(	PUNCT
ijassa-111	254	2	1915	1915	NUM
ijassa-111	254	3	)	)	PUNCT
ijassa-111	254	4	,	,	PUNCT
ijassa-111	254	5	“	"	PUNCT
ijassa-111	254	6	die	die	VERB
ijassa-111	254	7	grundlagen	grundlagen	PROPN
ijassa-111	254	8	der	der	PROPN
ijassa-111	254	9	physik	physik	PROPN
ijassa-111	254	10	(	(	PUNCT
ijassa-111	254	11	erste	erste	PROPN
ijassa-111	254	12	mitteilung	mitteilung	PROPN
ijassa-111	254	13	)	)	PUNCT
ijassa-111	254	14	,	,	PUNCT
ijassa-111	254	15	nachr	nachr	PROPN
ijassa-111	254	16	.	.	PUNCT
ijassa-111	255	1	königl	königl	NOUN
ijassa-111	255	2	.	.	PUNCT
ijassa-111	256	1	gesellschaft	gesellschaft	PROPN
ijassa-111	256	2	d.	d.	PROPN
ijassa-111	256	3	wiss	wiss	PROPN
ijassa-111	256	4	.	.	PUNCT
ijassa-111	257	1	göttingen”,math	göttingen”,math	NOUN
ijassa-111	257	2	.	.	PUNCT
ijassa-111	258	1	phys	phy	NOUN
ijassa-111	258	2	.	.	PUNCT
ijassa-111	259	1	klasse	klasse	PROPN
ijassa-111	259	2	,	,	PUNCT
ijassa-111	259	3	heft	heft	ADJ
ijassa-111	259	4	3	3	NUM
ijassa-111	259	5	,	,	PUNCT
ijassa-111	259	6	pp.395407	pp.395407	PROPN
ijassa-111	259	7	.	.	PUNCT
ijassa-111	260	1	[	[	X
ijassa-111	260	2	4	4	NUM
ijassa-111	260	3	]	]	PUNCT
ijassa-111	260	4	a.	a.	NOUN
ijassa-111	260	5	z.	z.	PROPN
ijassa-111	260	6	petrov	petrov	PROPN
ijassa-111	260	7	.	.	PUNCT
ijassa-111	261	1	(	(	PUNCT
ijassa-111	261	2	1967	1967	NUM
ijassa-111	261	3	)	)	PUNCT
ijassa-111	261	4	,	,	PUNCT
ijassa-111	261	5	newest	new	ADJ
ijassa-111	261	6	methods	method	NOUN
ijassa-111	261	7	in	in	ADP
ijassa-111	261	8	general	general	ADJ
ijassa-111	261	9	relativity	relativity	NOUN
ijassa-111	261	10	theory	theory	NOUN
ijassa-111	261	11	,	,	PUNCT
ijassa-111	261	12	(	(	PUNCT
ijassa-111	261	13	nauka	nauka	PROPN
ijassa-111	261	14	,	,	PUNCT
ijassa-111	261	15	moscow	moscow	PROPN
ijassa-111	261	16	)	)	PUNCT
ijassa-111	262	1	[	[	X
ijassa-111	262	2	in	in	ADP
ijassa-111	262	3	russian	russian	PROPN
ijassa-111	262	4	]	]	PUNCT
ijassa-111	262	5	.	.	PUNCT
ijassa-111	263	1	[	[	X
ijassa-111	263	2	5	5	X
ijassa-111	263	3	]	]	PUNCT
ijassa-111	263	4	w.	w.	PROPN
ijassa-111	263	5	de	de	PROPN
ijassa-111	263	6	sitter	sitter	PROPN
ijassa-111	263	7	.	.	PUNCT
ijassa-111	264	1	(	(	PUNCT
ijassa-111	264	2	1917	1917	NUM
ijassa-111	264	3	)	)	PUNCT
ijassa-111	264	4	,	,	PUNCT
ijassa-111	264	5	“	"	PUNCT
ijassa-111	264	6	on	on	ADP
ijassa-111	264	7	einstein	einstein	PROPN
ijassa-111	264	8	’s	’s	PART
ijassa-111	264	9	theory	theory	NOUN
ijassa-111	264	10	of	of	ADP
ijassa-111	264	11	gravitation	gravitation	NOUN
ijassa-111	264	12	and	and	CCONJ
ijassa-111	264	13	its	its	PRON
ijassa-111	264	14	astronomical	astronomical	ADJ
ijassa-111	264	15	consequences	consequence	NOUN
ijassa-111	264	16	”	"	PUNCT
ijassa-111	264	17	,	,	PUNCT
ijassa-111	264	18	third	third	ADJ
ijassa-111	264	19	paper	paper	NOUN
ijassa-111	264	20	,	,	PUNCT
ijassa-111	264	21	monthly	monthly	ADJ
ijassa-111	264	22	notices	notice	NOUN
ijassa-111	264	23	roy	roy	PROPN
ijassa-111	264	24	.	.	PROPN
ijassa-111	265	1	astron	astron	PROPN
ijassa-111	265	2	,	,	PUNCT
ijassa-111	265	3	soc	soc	NOUN
ijassa-111	265	4	.	.	PUNCT
ijassa-111	266	1	vol.78	vol.78	ADJ
ijassa-111	266	2	,	,	PUNCT
ijassa-111	266	3	no.3	no.3	PROPN
ijassa-111	266	4	.	.	PUNCT
ijassa-111	267	1	[	[	X
ijassa-111	267	2	6	6	NUM
ijassa-111	267	3	]	]	PUNCT
ijassa-111	267	4	schwarzschild	schwarzschild	NOUN
ijassa-111	267	5	,	,	PUNCT
ijassa-111	267	6	k.	k.	PROPN
ijassa-111	267	7	(	(	PUNCT
ijassa-111	267	8	1916	1916	NUM
ijassa-111	267	9	)	)	PUNCT
ijassa-111	267	10	,	,	PUNCT
ijassa-111	267	11	“	"	PUNCT
ijassa-111	267	12	on	on	ADP
ijassa-111	267	13	the	the	DET
ijassa-111	267	14	gravitational	gravitational	ADJ
ijassa-111	267	15	field	field	NOUN
ijassa-111	267	16	of	of	ADP
ijassa-111	267	17	a	a	DET
ijassa-111	267	18	point	point	NOUN
ijassa-111	267	19	-	-	PUNCT
ijassa-111	267	20	mass	mass	NOUN
ijassa-111	267	21	,	,	PUNCT
ijassa-111	267	22	according	accord	VERB
ijassa-111	267	23	to	to	ADP
ijassa-111	267	24	einstein	einstein	PROPN
ijassa-111	267	25	’s	’s	PART
ijassa-111	267	26	theory	theory	NOUN
ijassa-111	267	27	sitzungsber	sitzungsber	NOUN
ijassa-111	267	28	”	"	PUNCT
ijassa-111	267	29	,	,	PUNCT
ijassa-111	267	30	preuss	preuss	ADJ
ijassa-111	267	31	.	.	PUNCT
ijassa-111	268	1	akad	akad	PROPN
ijassa-111	268	2	.	.	PUNCT
ijassa-111	269	1	wiss	wiss	PROPN
ijassa-111	269	2	.	.	PROPN
ijassa-111	269	3	,	,	PUNCT
ijassa-111	269	4	phys	phy	NOUN
ijassa-111	269	5	.	.	PUNCT
ijassa-111	269	6	math	math	NOUN
ijassa-111	269	7	.	.	PUNCT
ijassa-111	270	1	kl	kl	PROPN
ijassa-111	270	2	.	.	PUNCT
ijassa-111	270	3	vol.189	vol.189	PROPN
ijassa-111	270	4	.	.	PUNCT
ijassa-111	271	1	[	[	X
ijassa-111	271	2	7	7	X
ijassa-111	271	3	]	]	PUNCT
ijassa-111	271	4	s.	s.	PROPN
ijassa-111	271	5	chandrasekhar	chandrasekhar	PROPN
ijassa-111	271	6	.	.	PUNCT
ijassa-111	272	1	(	(	PUNCT
ijassa-111	272	2	1983	1983	NUM
ijassa-111	272	3	)	)	PUNCT
ijassa-111	272	4	,	,	PUNCT
ijassa-111	272	5	“	"	PUNCT
ijassa-111	272	6	the	the	DET
ijassa-111	272	7	mathematical	mathematical	ADJ
ijassa-111	272	8	theory	theory	NOUN
ijassa-111	272	9	of	of	ADP
ijassa-111	272	10	black	black	ADJ
ijassa-111	272	11	holes	hole	NOUN
ijassa-111	272	12	,	,	PUNCT
ijassa-111	272	13	research	research	NOUN
ijassa-111	272	14	supported	support	VERB
ijassa-111	272	15	by	by	ADP
ijassa-111	272	16	nsf	nsf	PROPN
ijassa-111	272	17	”	"	PUNCT
ijassa-111	272	18	,	,	PUNCT
ijassa-111	272	19	international	international	ADJ
ijassa-111	272	20	series	series	NOUN
ijassa-111	272	21	of	of	ADP
ijassa-111	272	22	monographs	monograph	NOUN
ijassa-111	272	23	on	on	ADP
ijassa-111	272	24	physics	physics	NOUN
ijassa-111	272	25	,	,	PUNCT
ijassa-111	272	26	vol.69	vol.69	ADP
ijassa-111	272	27	(	(	PUNCT
ijassa-111	272	28	clarendon	clarendon	PROPN
ijassa-111	272	29	press	press	NOUN
ijassa-111	272	30	-	-	PUNCT
ijassa-111	272	31	oxford	oxford	PROPN
ijassa-111	272	32	university	university	NOUN
ijassa-111	272	33	press	press	NOUN
ijassa-111	272	34	,	,	PUNCT
ijassa-111	272	35	oxford	oxford	PROPN
ijassa-111	272	36	-	-	PUNCT
ijassa-111	272	37	new	new	PROPN
ijassa-111	272	38	york	york	PROPN
ijassa-111	272	39	)	)	PUNCT
ijassa-111	272	40	.	.	PUNCT
ijassa-111	273	1	[	[	X
ijassa-111	273	2	8	8	NUM
ijassa-111	273	3	]	]	PUNCT
ijassa-111	273	4	a.	a.	NOUN
ijassa-111	273	5	a.	a.	NOUN
ijassa-111	273	6	fridman	fridman	NOUN
ijassa-111	273	7	.	.	PUNCT
ijassa-111	274	1	(	(	PUNCT
ijassa-111	274	2	1966	1966	NUM
ijassa-111	274	3	)	)	PUNCT
ijassa-111	275	1	,	,	PUNCT
ijassa-111	275	2	on	on	ADP
ijassa-111	275	3	space	space	NOUN
ijassa-111	275	4	curvature	curvature	NOUN
ijassa-111	275	5	,	,	PUNCT
ijassa-111	275	6	sselected	sselecte	VERB
ijassa-111	275	7	works	work	NOUN
ijassa-111	275	8	,	,	PUNCT
ijassa-111	275	9	(	(	PUNCT
ijassa-111	275	10	nauka	nauka	PROPN
ijassa-111	275	11	,	,	PUNCT
ijassa-111	275	12	moscow	moscow	PROPN
ijassa-111	275	13	)	)	PUNCT
ijassa-111	276	1	[	[	X
ijassa-111	276	2	in	in	ADP
ijassa-111	276	3	russian	russian	PROPN
ijassa-111	276	4	]	]	PUNCT
ijassa-111	276	5	.	.	PUNCT
ijassa-111	277	1	[	[	X
ijassa-111	277	2	9	9	NUM
ijassa-111	277	3	]	]	PUNCT
ijassa-111	277	4	a.	a.	NOUN
ijassa-111	277	5	einstein	einstein	NOUN
ijassa-111	277	6	.	.	PUNCT
ijassa-111	278	1	(	(	PUNCT
ijassa-111	278	2	1917	1917	NUM
ijassa-111	278	3	)	)	PUNCT
ijassa-111	278	4	,	,	PUNCT
ijassa-111	278	5	kosmologische	kosmologische	NOUN
ijassa-111	278	6	betrachtungen	betrachtungen	PROPN
ijassa-111	278	7	zur	zur	NUM
ijassa-111	278	8	allgemeinen	allgemeinen	NOUN
ijassa-111	278	9	relativitätstheorie	relativitätstheorie	NOUN
ijassa-111	278	10	,	,	PUNCT
ijassa-111	278	11	ber	ber	PROPN
ijassa-111	278	12	.	.	PUNCT
ijassa-111	279	1	preuß	preuß	NOUN
ijassa-111	279	2	.	.	PUNCT
ijassa-111	280	1	akad	akad	PROPN
ijassa-111	280	2	.	.	PUNCT
ijassa-111	281	1	wiss	wiss	PROPN
ijassa-111	281	2	.	.	PROPN
ijassa-111	281	3	,	,	PUNCT
ijassa-111	281	4	berlin	berlin	PROPN
ijassa-111	281	5	.	.	PUNCT
ijassa-111	282	1	[	[	X
ijassa-111	282	2	10	10	NUM
ijassa-111	282	3	]	]	X
ijassa-111	282	4	a.d	a.d	PROPN
ijassa-111	282	5	.	.	PROPN
ijassa-111	282	6	chernin	chernin	PROPN
ijassa-111	282	7	.	.	PUNCT
ijassa-111	283	1	(	(	PUNCT
ijassa-111	283	2	2008	2008	NUM
ijassa-111	283	3	)	)	PUNCT
ijassa-111	283	4	,	,	PUNCT
ijassa-111	283	5	“	"	PUNCT
ijassa-111	283	6	dark	dark	ADJ
ijassa-111	283	7	energy	energy	NOUN
ijassa-111	283	8	and	and	CCONJ
ijassa-111	283	9	universal	universal	ADJ
ijassa-111	283	10	antigravitation	antigravitation	NOUN
ijassa-111	283	11	”	"	PUNCT
ijassa-111	283	12	,	,	PUNCT
ijassa-111	283	13	uspekhi	uspekhi	PROPN
ijassa-111	283	14	fiz	fiz	PROPN
ijassa-111	283	15	.	.	PUNCT
ijassa-111	284	1	nauk	nauk	PROPN
ijassa-111	284	2	,	,	PUNCT
ijassa-111	284	3	vol.178	vol.178	PROPN
ijassa-111	284	4	no.3	no.3	PROPN
ijassa-111	284	5	,	,	PUNCT
ijassa-111	284	6	pp.267	pp.267	PROPN
ijassa-111	284	7	-	-	PUNCT
ijassa-111	284	8	298	298	NUM
ijassa-111	285	1	[	[	X
ijassa-111	285	2	physics	physics	NOUN
ijassa-111	285	3	-	-	PUNCT
ijassa-111	285	4	uspekhi	uspekhi	PROPN
ijassa-111	285	5	,	,	PUNCT
ijassa-111	285	6	vol.51	vol.51	PROPN
ijassa-111	285	7	,	,	PUNCT
ijassa-111	285	8	no	no	INTJ
ijassa-111	285	9	.	.	NOUN
ijassa-111	285	10	3	3	NUM
ijassa-111	285	11	,	,	PUNCT
ijassa-111	285	12	pp.253282	pp.253282	PROPN
ijassa-111	285	13	]	]	PUNCT
ijassa-111	285	14	.	.	PUNCT
ijassa-111	286	1	corresponding	correspond	VERB
ijassa-111	286	2	author	author	NOUN
ijassa-111	286	3	n.n	n.n	PROPN
ijassa-111	286	4	.	.	PROPN
ijassa-111	286	5	popov	popov	PROPN
ijassa-111	286	6	can	can	AUX
ijassa-111	286	7	be	be	AUX
ijassa-111	286	8	contacted	contact	VERB
ijassa-111	286	9	at	at	ADP
ijassa-111	286	10	:	:	PUNCT
ijassa-111	286	11	nnpopov@mail.ru	nnpopov@mail.ru	ADV