id	sid	tid	token	lemma	pos
ejpam-6741	1	1	european	european	PROPN
ejpam-6741	1	2	journal	journal	PROPN
ejpam-6741	1	3	of	of	ADP
ejpam-6741	1	4	pure	pure	ADJ
ejpam-6741	1	5	and	and	CCONJ
ejpam-6741	1	6	applied	applied	ADJ
ejpam-6741	1	7	mathematics	mathematic	NOUN
ejpam-6741	1	8	2025	2025	NUM
ejpam-6741	1	9	,	,	PUNCT
ejpam-6741	1	10	vol	vol	NOUN
ejpam-6741	1	11	.	.	PROPN
ejpam-6741	1	12	18	18	NUM
ejpam-6741	1	13	,	,	PUNCT
ejpam-6741	1	14	issue	issue	NOUN
ejpam-6741	1	15	4	4	NUM
ejpam-6741	1	16	,	,	PUNCT
ejpam-6741	1	17	article	article	NOUN
ejpam-6741	1	18	number	number	NOUN
ejpam-6741	1	19	6741	6741	NUM
ejpam-6741	1	20	issn	issn	PROPN
ejpam-6741	1	21	1307	1307	NUM
ejpam-6741	1	22	-	-	SYM
ejpam-6741	1	23	5543	5543	NUM
ejpam-6741	1	24	–	–	PUNCT
ejpam-6741	1	25	ejpam.com	ejpam.com	X
ejpam-6741	1	26	published	publish	VERB
ejpam-6741	1	27	by	by	ADP
ejpam-6741	1	28	new	new	PROPN
ejpam-6741	1	29	york	york	PROPN
ejpam-6741	1	30	business	business	PROPN
ejpam-6741	1	31	global	global	PROPN
ejpam-6741	1	32	ricci	ricci	PROPN
ejpam-6741	1	33	solitons	soliton	NOUN
ejpam-6741	1	34	and	and	CCONJ
ejpam-6741	1	35	their	their	PRON
ejpam-6741	1	36	associated	associated	ADJ
ejpam-6741	1	37	vector	vector	NOUN
ejpam-6741	1	38	fields	field	NOUN
ejpam-6741	1	39	in	in	ADP
ejpam-6741	1	40	lrs	lrs	PROPN
ejpam-6741	1	41	bianchi	bianchi	NOUN
ejpam-6741	1	42	type	type	NOUN
ejpam-6741	1	43	i	i	PRON
ejpam-6741	1	44	spacetime	spacetime	PROPN
ejpam-6741	1	45	uzma	uzma	PROPN
ejpam-6741	1	46	nasib1	nasib1	PROPN
ejpam-6741	1	47	,	,	PUNCT
ejpam-6741	1	48	jamshed	jamshe	VERB
ejpam-6741	1	49	khan2	khan2	PROPN
ejpam-6741	1	50	,	,	PUNCT
ejpam-6741	1	51	sumaira	sumaira	PROPN
ejpam-6741	1	52	saleem	saleem	PROPN
ejpam-6741	1	53	akhtar3	akhtar3	PROPN
ejpam-6741	1	54	,	,	PUNCT
ejpam-6741	1	55	salma	salma	PROPN
ejpam-6741	1	56	haque4	haque4	PROPN
ejpam-6741	1	57	,	,	PUNCT
ejpam-6741	1	58	nabil	nabil	PROPN
ejpam-6741	1	59	mlaiki4,∗	mlaiki4,∗	NOUN
ejpam-6741	1	60	1	1	NUM
ejpam-6741	1	61	government	government	NOUN
ejpam-6741	1	62	girls	girl	NOUN
ejpam-6741	1	63	degree	degree	NOUN
ejpam-6741	1	64	college	college	NOUN
ejpam-6741	1	65	landi	landi	PROPN
ejpam-6741	1	66	kotal	kotal	PROPN
ejpam-6741	1	67	,	,	PUNCT
ejpam-6741	1	68	khyber	khyber	PROPN
ejpam-6741	1	69	,	,	PUNCT
ejpam-6741	1	70	khyber	khyber	PROPN
ejpam-6741	1	71	pakhtunkhwa	pakhtunkhwa	PROPN
ejpam-6741	1	72	,	,	PUNCT
ejpam-6741	1	73	pakistan	pakistan	PROPN
ejpam-6741	1	74	2	2	NUM
ejpam-6741	1	75	government	government	NOUN
ejpam-6741	1	76	post	post	NOUN
ejpam-6741	1	77	graduate	graduate	PROPN
ejpam-6741	1	78	college	college	NOUN
ejpam-6741	1	79	lakki	lakki	PROPN
ejpam-6741	1	80	marwat	marwat	NOUN
ejpam-6741	1	81	,	,	PUNCT
ejpam-6741	1	82	khyber	khyber	PROPN
ejpam-6741	1	83	pakhtunkhwa	pakhtunkhwa	PROPN
ejpam-6741	1	84	,	,	PUNCT
ejpam-6741	1	85	pakistan	pakistan	PROPN
ejpam-6741	1	86	3	3	NUM
ejpam-6741	1	87	department	department	NOUN
ejpam-6741	1	88	of	of	ADP
ejpam-6741	1	89	mathematics	mathematic	NOUN
ejpam-6741	1	90	,	,	PUNCT
ejpam-6741	1	91	women	woman	NOUN
ejpam-6741	1	92	university	university	PROPN
ejpam-6741	1	93	mardan	mardan	PROPN
ejpam-6741	1	94	,	,	PUNCT
ejpam-6741	1	95	khyber	khyber	PROPN
ejpam-6741	1	96	pakhtunkhwa	pakhtunkhwa	PROPN
ejpam-6741	1	97	,	,	PUNCT
ejpam-6741	1	98	pakistan	pakistan	PROPN
ejpam-6741	1	99	4	4	NUM
ejpam-6741	1	100	department	department	NOUN
ejpam-6741	1	101	of	of	ADP
ejpam-6741	1	102	mathematics	mathematic	NOUN
ejpam-6741	1	103	and	and	CCONJ
ejpam-6741	1	104	sciences	science	NOUN
ejpam-6741	1	105	,	,	PUNCT
ejpam-6741	1	106	prince	prince	PROPN
ejpam-6741	1	107	sultan	sultan	PROPN
ejpam-6741	1	108	university	university	PROPN
ejpam-6741	1	109	,	,	PUNCT
ejpam-6741	1	110	riyadh	riyadh	PROPN
ejpam-6741	1	111	11586	11586	NUM
ejpam-6741	1	112	,	,	PUNCT
ejpam-6741	1	113	saudi	saudi	PROPN
ejpam-6741	1	114	arabia	arabia	PROPN
ejpam-6741	1	115	abstract	abstract	NOUN
ejpam-6741	1	116	.	.	PUNCT
ejpam-6741	2	1	this	this	DET
ejpam-6741	2	2	article	article	NOUN
ejpam-6741	2	3	presents	present	VERB
ejpam-6741	2	4	a	a	DET
ejpam-6741	2	5	complete	complete	ADJ
ejpam-6741	2	6	classification	classification	NOUN
ejpam-6741	2	7	of	of	ADP
ejpam-6741	2	8	ricci	ricci	PROPN
ejpam-6741	2	9	solitons	soliton	NOUN
ejpam-6741	2	10	and	and	CCONJ
ejpam-6741	2	11	their	their	PRON
ejpam-6741	2	12	associated	associated	ADJ
ejpam-6741	2	13	vector	vector	NOUN
ejpam-6741	2	14	fields	field	NOUN
ejpam-6741	2	15	in	in	ADP
ejpam-6741	2	16	the	the	DET
ejpam-6741	2	17	context	context	NOUN
ejpam-6741	2	18	of	of	ADP
ejpam-6741	2	19	locally	locally	ADV
ejpam-6741	2	20	rotationally	rotationally	ADV
ejpam-6741	2	21	symmetric	symmetric	ADJ
ejpam-6741	2	22	(	(	PUNCT
ejpam-6741	2	23	lrs	lrs	PROPN
ejpam-6741	2	24	)	)	PUNCT
ejpam-6741	2	25	bianchi	bianchi	NOUN
ejpam-6741	2	26	type	type	NOUN
ejpam-6741	2	27	i	i	PRON
ejpam-6741	2	28	spacetime	spacetime	NOUN
ejpam-6741	2	29	,	,	PUNCT
ejpam-6741	2	30	a	a	DET
ejpam-6741	2	31	crucial	crucial	ADJ
ejpam-6741	2	32	model	model	NOUN
ejpam-6741	2	33	in	in	ADP
ejpam-6741	2	34	cosmological	cosmological	ADJ
ejpam-6741	2	35	studies	study	NOUN
ejpam-6741	2	36	.	.	PUNCT
ejpam-6741	3	1	to	to	PART
ejpam-6741	3	2	systematically	systematically	ADV
ejpam-6741	3	3	address	address	VERB
ejpam-6741	3	4	the	the	DET
ejpam-6741	3	5	complexities	complexity	NOUN
ejpam-6741	3	6	inherent	inherent	ADJ
ejpam-6741	3	7	in	in	ADP
ejpam-6741	3	8	the	the	DET
ejpam-6741	3	9	ricci	ricci	PROPN
ejpam-6741	3	10	soliton	soliton	PROPN
ejpam-6741	3	11	equations	equation	NOUN
ejpam-6741	3	12	,	,	PUNCT
ejpam-6741	3	13	we	we	PRON
ejpam-6741	3	14	adopt	adopt	VERB
ejpam-6741	3	15	the	the	DET
ejpam-6741	3	16	rif	rif	PROPN
ejpam-6741	3	17	tree	tree	NOUN
ejpam-6741	3	18	technique	technique	NOUN
ejpam-6741	3	19	.	.	PUNCT
ejpam-6741	4	1	the	the	DET
ejpam-6741	4	2	equations	equation	NOUN
ejpam-6741	4	3	defining	define	VERB
ejpam-6741	4	4	the	the	DET
ejpam-6741	4	5	ricci	ricci	PROPN
ejpam-6741	4	6	soliton	soliton	NOUN
ejpam-6741	4	7	and	and	CCONJ
ejpam-6741	4	8	its	its	PRON
ejpam-6741	4	9	vector	vector	NOUN
ejpam-6741	4	10	field	field	NOUN
ejpam-6741	4	11	are	be	AUX
ejpam-6741	4	12	transformed	transform	VERB
ejpam-6741	4	13	into	into	ADP
ejpam-6741	4	14	a	a	DET
ejpam-6741	4	15	reduced	reduce	VERB
ejpam-6741	4	16	involutive	involutive	ADJ
ejpam-6741	4	17	form	form	NOUN
ejpam-6741	4	18	using	use	VERB
ejpam-6741	4	19	a	a	DET
ejpam-6741	4	20	computational	computational	ADJ
ejpam-6741	4	21	algorithm	algorithm	NOUN
ejpam-6741	4	22	,	,	PUNCT
ejpam-6741	4	23	which	which	PRON
ejpam-6741	4	24	assists	assist	VERB
ejpam-6741	4	25	in	in	ADP
ejpam-6741	4	26	dividing	divide	VERB
ejpam-6741	4	27	the	the	DET
ejpam-6741	4	28	integration	integration	NOUN
ejpam-6741	4	29	process	process	NOUN
ejpam-6741	4	30	into	into	ADP
ejpam-6741	4	31	a	a	DET
ejpam-6741	4	32	collection	collection	NOUN
ejpam-6741	4	33	of	of	ADP
ejpam-6741	4	34	cases	case	NOUN
ejpam-6741	4	35	organized	organize	VERB
ejpam-6741	4	36	in	in	ADP
ejpam-6741	4	37	a	a	DET
ejpam-6741	4	38	tree	tree	NOUN
ejpam-6741	4	39	-	-	PUNCT
ejpam-6741	4	40	like	like	ADJ
ejpam-6741	4	41	structure	structure	NOUN
ejpam-6741	4	42	.	.	PUNCT
ejpam-6741	5	1	each	each	PRON
ejpam-6741	5	2	of	of	ADP
ejpam-6741	5	3	these	these	DET
ejpam-6741	5	4	cases	case	NOUN
ejpam-6741	5	5	is	be	AUX
ejpam-6741	5	6	governed	govern	VERB
ejpam-6741	5	7	by	by	ADP
ejpam-6741	5	8	specific	specific	ADJ
ejpam-6741	5	9	constraints	constraint	NOUN
ejpam-6741	5	10	on	on	ADP
ejpam-6741	5	11	the	the	DET
ejpam-6741	5	12	metric	metric	ADJ
ejpam-6741	5	13	functions	function	NOUN
ejpam-6741	5	14	,	,	PUNCT
ejpam-6741	5	15	which	which	PRON
ejpam-6741	5	16	facilitates	facilitate	VERB
ejpam-6741	5	17	the	the	DET
ejpam-6741	5	18	solution	solution	NOUN
ejpam-6741	5	19	process	process	NOUN
ejpam-6741	5	20	.	.	PUNCT
ejpam-6741	6	1	definite	definite	ADJ
ejpam-6741	6	2	expressions	expression	NOUN
ejpam-6741	6	3	for	for	ADP
ejpam-6741	6	4	the	the	DET
ejpam-6741	6	5	metric	metric	ADJ
ejpam-6741	6	6	functions	function	NOUN
ejpam-6741	6	7	and	and	CCONJ
ejpam-6741	6	8	the	the	DET
ejpam-6741	6	9	corresponding	correspond	VERB
ejpam-6741	6	10	vector	vector	NOUN
ejpam-6741	6	11	field	field	NOUN
ejpam-6741	6	12	of	of	ADP
ejpam-6741	6	13	the	the	DET
ejpam-6741	6	14	ricci	ricci	PROPN
ejpam-6741	6	15	soliton	soliton	NOUN
ejpam-6741	6	16	are	be	AUX
ejpam-6741	6	17	obtained	obtain	VERB
ejpam-6741	6	18	by	by	ADP
ejpam-6741	6	19	efficiently	efficiently	ADV
ejpam-6741	6	20	solving	solve	VERB
ejpam-6741	6	21	the	the	DET
ejpam-6741	6	22	system	system	NOUN
ejpam-6741	6	23	of	of	ADP
ejpam-6741	6	24	equations	equation	NOUN
ejpam-6741	6	25	characterizing	characterize	VERB
ejpam-6741	6	26	the	the	DET
ejpam-6741	6	27	soliton	soliton	NOUN
ejpam-6741	6	28	vector	vector	NOUN
ejpam-6741	6	29	field	field	NOUN
ejpam-6741	6	30	through	through	ADP
ejpam-6741	6	31	the	the	DET
ejpam-6741	6	32	application	application	NOUN
ejpam-6741	6	33	of	of	ADP
ejpam-6741	6	34	these	these	DET
ejpam-6741	6	35	constraints	constraint	NOUN
ejpam-6741	6	36	.	.	PUNCT
ejpam-6741	7	1	this	this	DET
ejpam-6741	7	2	powerful	powerful	ADJ
ejpam-6741	7	3	approach	approach	NOUN
ejpam-6741	7	4	enables	enable	VERB
ejpam-6741	7	5	us	we	PRON
ejpam-6741	7	6	to	to	PART
ejpam-6741	7	7	derive	derive	VERB
ejpam-6741	7	8	novel	novel	NOUN
ejpam-6741	7	9	and	and	CCONJ
ejpam-6741	7	10	exact	exact	ADJ
ejpam-6741	7	11	solutions	solution	NOUN
ejpam-6741	7	12	that	that	SCONJ
ejpam-6741	7	13	previous	previous	ADJ
ejpam-6741	7	14	methods	method	NOUN
ejpam-6741	7	15	have	have	AUX
ejpam-6741	7	16	overlooked	overlook	VERB
ejpam-6741	7	17	.	.	PUNCT
ejpam-6741	8	1	our	our	PRON
ejpam-6741	8	2	results	result	NOUN
ejpam-6741	8	3	demonstrate	demonstrate	VERB
ejpam-6741	8	4	that	that	SCONJ
ejpam-6741	8	5	this	this	DET
ejpam-6741	8	6	spacetime	spacetime	NOUN
ejpam-6741	8	7	admits	admit	VERB
ejpam-6741	8	8	ricci	ricci	PROPN
ejpam-6741	8	9	solitons	soliton	NOUN
ejpam-6741	8	10	of	of	ADP
ejpam-6741	8	11	shrinking	shrinking	NOUN
ejpam-6741	8	12	,	,	PUNCT
ejpam-6741	8	13	steady	steady	ADJ
ejpam-6741	8	14	,	,	PUNCT
ejpam-6741	8	15	and	and	CCONJ
ejpam-6741	8	16	expanding	expand	VERB
ejpam-6741	8	17	natures	nature	NOUN
ejpam-6741	8	18	,	,	PUNCT
ejpam-6741	8	19	characterized	characterize	VERB
ejpam-6741	8	20	by	by	ADP
ejpam-6741	8	21	vector	vector	NOUN
ejpam-6741	8	22	fields	field	NOUN
ejpam-6741	8	23	with	with	ADP
ejpam-6741	8	24	up	up	ADP
ejpam-6741	8	25	to	to	PART
ejpam-6741	8	26	11	11	NUM
ejpam-6741	8	27	free	free	ADJ
ejpam-6741	8	28	parameters	parameter	NOUN
ejpam-6741	8	29	.	.	PUNCT
ejpam-6741	9	1	crucially	crucially	ADV
ejpam-6741	9	2	,	,	PUNCT
ejpam-6741	9	3	we	we	PRON
ejpam-6741	9	4	conduct	conduct	VERB
ejpam-6741	9	5	a	a	DET
ejpam-6741	9	6	thorough	thorough	ADJ
ejpam-6741	9	7	physical	physical	ADJ
ejpam-6741	9	8	analysis	analysis	NOUN
ejpam-6741	9	9	of	of	ADP
ejpam-6741	9	10	the	the	DET
ejpam-6741	9	11	resulting	result	VERB
ejpam-6741	9	12	models	model	NOUN
ejpam-6741	9	13	,	,	PUNCT
ejpam-6741	9	14	determining	determine	VERB
ejpam-6741	9	15	their	their	PRON
ejpam-6741	9	16	matter	matter	NOUN
ejpam-6741	9	17	content	content	NOUN
ejpam-6741	9	18	through	through	ADP
ejpam-6741	9	19	the	the	DET
ejpam-6741	9	20	equation	equation	NOUN
ejpam-6741	9	21	of	of	ADP
ejpam-6741	9	22	state	state	NOUN
ejpam-6741	9	23	and	and	CCONJ
ejpam-6741	9	24	testing	test	VERB
ejpam-6741	9	25	their	their	PRON
ejpam-6741	9	26	physical	physical	ADJ
ejpam-6741	9	27	viability	viability	NOUN
ejpam-6741	9	28	via	via	ADP
ejpam-6741	9	29	the	the	DET
ejpam-6741	9	30	standard	standard	ADJ
ejpam-6741	9	31	energy	energy	NOUN
ejpam-6741	9	32	conditions	condition	NOUN
ejpam-6741	9	33	.	.	PUNCT
ejpam-6741	10	1	we	we	PRON
ejpam-6741	10	2	find	find	VERB
ejpam-6741	10	3	specific	specific	ADJ
ejpam-6741	10	4	families	family	NOUN
ejpam-6741	10	5	of	of	ADP
ejpam-6741	10	6	solutions	solution	NOUN
ejpam-6741	10	7	that	that	PRON
ejpam-6741	10	8	correspond	correspond	VERB
ejpam-6741	10	9	to	to	ADP
ejpam-6741	10	10	physically	physically	ADV
ejpam-6741	10	11	significant	significant	ADJ
ejpam-6741	10	12	scenarios	scenario	NOUN
ejpam-6741	10	13	,	,	PUNCT
ejpam-6741	10	14	such	such	ADJ
ejpam-6741	10	15	as	as	ADP
ejpam-6741	10	16	a	a	DET
ejpam-6741	10	17	spacetime	spacetime	NOUN
ejpam-6741	10	18	filled	fill	VERB
ejpam-6741	10	19	with	with	ADP
ejpam-6741	10	20	vacuum	vacuum	NOUN
ejpam-6741	10	21	energy	energy	NOUN
ejpam-6741	10	22	(	(	PUNCT
ejpam-6741	10	23	a	a	DET
ejpam-6741	10	24	cosmological	cosmological	ADJ
ejpam-6741	10	25	constant	constant	ADJ
ejpam-6741	10	26	)	)	PUNCT
ejpam-6741	10	27	.	.	PUNCT
ejpam-6741	11	1	this	this	DET
ejpam-6741	11	2	work	work	NOUN
ejpam-6741	11	3	not	not	PART
ejpam-6741	11	4	only	only	ADV
ejpam-6741	11	5	provides	provide	VERB
ejpam-6741	11	6	a	a	DET
ejpam-6741	11	7	comprehensive	comprehensive	ADJ
ejpam-6741	11	8	mathematical	mathematical	ADJ
ejpam-6741	11	9	classification	classification	NOUN
ejpam-6741	11	10	but	but	CCONJ
ejpam-6741	11	11	also	also	ADV
ejpam-6741	11	12	establishes	establish	VERB
ejpam-6741	11	13	a	a	DET
ejpam-6741	11	14	direct	direct	ADJ
ejpam-6741	11	15	link	link	NOUN
ejpam-6741	11	16	between	between	ADP
ejpam-6741	11	17	these	these	DET
ejpam-6741	11	18	geometric	geometric	ADJ
ejpam-6741	11	19	structures	structure	NOUN
ejpam-6741	11	20	and	and	CCONJ
ejpam-6741	11	21	potentially	potentially	ADV
ejpam-6741	11	22	realistic	realistic	ADJ
ejpam-6741	11	23	cosmological	cosmological	ADJ
ejpam-6741	11	24	models	model	NOUN
ejpam-6741	11	25	.	.	PUNCT
ejpam-6741	12	1	2020	2020	NUM
ejpam-6741	12	2	mathematics	mathematic	NOUN
ejpam-6741	12	3	subject	subject	NOUN
ejpam-6741	12	4	classifications	classification	NOUN
ejpam-6741	12	5	:	:	PUNCT
ejpam-6741	12	6	83c15	83c15	NUM
ejpam-6741	12	7	,	,	PUNCT
ejpam-6741	12	8	83f05	83f05	NUM
ejpam-6741	12	9	,	,	PUNCT
ejpam-6741	12	10	53c50	53c50	NUM
ejpam-6741	12	11	key	key	ADJ
ejpam-6741	12	12	words	word	NOUN
ejpam-6741	12	13	and	and	CCONJ
ejpam-6741	12	14	phrases	phrase	NOUN
ejpam-6741	12	15	:	:	PUNCT
ejpam-6741	12	16	soliton	soliton	NOUN
ejpam-6741	12	17	vector	vector	NOUN
ejpam-6741	12	18	fields	field	NOUN
ejpam-6741	12	19	,	,	PUNCT
ejpam-6741	12	20	locally	locally	ADV
ejpam-6741	12	21	rotationally	rotationally	ADV
ejpam-6741	12	22	symmetric	symmetric	ADJ
ejpam-6741	12	23	bianchi	bianchi	NOUN
ejpam-6741	12	24	type	type	NOUN
ejpam-6741	12	25	i	i	PRON
ejpam-6741	12	26	spacetime	spacetime	NOUN
ejpam-6741	12	27	,	,	PUNCT
ejpam-6741	12	28	rif	rif	PROPN
ejpam-6741	12	29	tree	tree	NOUN
ejpam-6741	12	30	,	,	PUNCT
ejpam-6741	12	31	energy	energy	NOUN
ejpam-6741	12	32	conditions	condition	NOUN
ejpam-6741	12	33	∗corresponding	∗corresponde	VERB
ejpam-6741	12	34	author	author	NOUN
ejpam-6741	12	35	.	.	PUNCT
ejpam-6741	13	1	doi	doi	NOUN
ejpam-6741	13	2	:	:	PUNCT
ejpam-6741	13	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6741	https://doi.org/10.29020/nybg.ejpam.v18i4.6741	ADJ
ejpam-6741	13	4	email	email	NOUN
ejpam-6741	13	5	addresses	address	NOUN
ejpam-6741	13	6	:	:	PUNCT
ejpam-6741	13	7	nmlaiki@psu.edu.sa	nmlaiki@psu.edu.sa	PROPN
ejpam-6741	13	8	,	,	PUNCT
ejpam-6741	13	9	nmlaiki2012@gmail.com	nmlaiki2012@gmail.com	PUNCT
ejpam-6741	14	1	(	(	PUNCT
ejpam-6741	14	2	n.	n.	PROPN
ejpam-6741	14	3	mlaiki	mlaiki	PROPN
ejpam-6741	14	4	)	)	PUNCT
ejpam-6741	14	5	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6741	15	1	1	1	NUM
ejpam-6741	15	2	copyright	copyright	NOUN
ejpam-6741	15	3	:	:	PUNCT
ejpam-6741	15	4	©	©	PROPN
ejpam-6741	15	5	2025	2025	NUM
ejpam-6741	15	6	the	the	DET
ejpam-6741	15	7	author(s	author(s	NOUN
ejpam-6741	15	8	)	)	PUNCT
ejpam-6741	15	9	.	.	PUNCT
ejpam-6741	16	1	(	(	PUNCT
ejpam-6741	16	2	cc	cc	NOUN
ejpam-6741	16	3	by	by	ADP
ejpam-6741	16	4	-	-	PUNCT
ejpam-6741	16	5	nc	nc	PROPN
ejpam-6741	16	6	4.0	4.0	NUM
ejpam-6741	16	7	)	)	PUNCT
ejpam-6741	16	8	u.	u.	PROPN
ejpam-6741	16	9	nasib	nasib	PROPN
ejpam-6741	16	10	et	et	PROPN
ejpam-6741	16	11	al	al	PROPN
ejpam-6741	16	12	.	.	PUNCT
ejpam-6741	16	13	/	/	SYM
ejpam-6741	16	14	eur	eur	PROPN
ejpam-6741	16	15	.	.	PUNCT
ejpam-6741	17	1	j.	j.	PROPN
ejpam-6741	17	2	pure	pure	PROPN
ejpam-6741	17	3	appl	appl	PROPN
ejpam-6741	17	4	.	.	PROPN
ejpam-6741	17	5	math	math	PROPN
ejpam-6741	17	6	,	,	PUNCT
ejpam-6741	17	7	18	18	NUM
ejpam-6741	17	8	(	(	PUNCT
ejpam-6741	17	9	4	4	NUM
ejpam-6741	17	10	)	)	PUNCT
ejpam-6741	17	11	(	(	PUNCT
ejpam-6741	17	12	2025	2025	NUM
ejpam-6741	17	13	)	)	PUNCT
ejpam-6741	17	14	,	,	PUNCT
ejpam-6741	17	15	6741	6741	NUM
ejpam-6741	17	16	2	2	NUM
ejpam-6741	17	17	of	of	ADP
ejpam-6741	17	18	14	14	NUM
ejpam-6741	17	19	1	1	NUM
ejpam-6741	17	20	.	.	PUNCT
ejpam-6741	18	1	introduction	introduction	NOUN
ejpam-6741	18	2	in	in	ADP
ejpam-6741	18	3	the	the	DET
ejpam-6741	18	4	theory	theory	NOUN
ejpam-6741	18	5	of	of	ADP
ejpam-6741	18	6	general	general	ADJ
ejpam-6741	18	7	relativity	relativity	NOUN
ejpam-6741	18	8	(	(	PUNCT
ejpam-6741	18	9	gr	gr	NOUN
ejpam-6741	18	10	)	)	PUNCT
ejpam-6741	18	11	,	,	PUNCT
ejpam-6741	18	12	a	a	DET
ejpam-6741	18	13	primary	primary	ADJ
ejpam-6741	18	14	aim	aim	NOUN
ejpam-6741	18	15	of	of	ADP
ejpam-6741	18	16	researchers	researcher	NOUN
ejpam-6741	18	17	is	be	AUX
ejpam-6741	18	18	to	to	PART
ejpam-6741	18	19	construct	construct	VERB
ejpam-6741	18	20	gravitational	gravitational	ADJ
ejpam-6741	18	21	potentials	potential	NOUN
ejpam-6741	18	22	that	that	PRON
ejpam-6741	18	23	satisfy	satisfy	VERB
ejpam-6741	18	24	the	the	DET
ejpam-6741	18	25	einstein	einstein	ADJ
ejpam-6741	18	26	field	field	NOUN
ejpam-6741	18	27	equations	equation	NOUN
ejpam-6741	18	28	(	(	PUNCT
ejpam-6741	18	29	efes	efe	NOUN
ejpam-6741	18	30	)	)	PUNCT
ejpam-6741	18	31	.	.	PUNCT
ejpam-6741	19	1	for	for	ADP
ejpam-6741	19	2	this	this	DET
ejpam-6741	19	3	purpose	purpose	NOUN
ejpam-6741	19	4	,	,	PUNCT
ejpam-6741	19	5	various	various	ADJ
ejpam-6741	19	6	symmetry	symmetry	NOUN
ejpam-6741	19	7	assumptions	assumption	NOUN
ejpam-6741	19	8	are	be	AUX
ejpam-6741	19	9	frequently	frequently	ADV
ejpam-6741	19	10	imposed	impose	VERB
ejpam-6741	19	11	on	on	ADP
ejpam-6741	19	12	the	the	DET
ejpam-6741	19	13	geometry	geometry	NOUN
ejpam-6741	19	14	of	of	ADP
ejpam-6741	19	15	the	the	DET
ejpam-6741	19	16	spacetime	spacetime	NOUN
ejpam-6741	19	17	,	,	PUNCT
ejpam-6741	19	18	along	along	ADP
ejpam-6741	19	19	with	with	ADP
ejpam-6741	19	20	a	a	DET
ejpam-6741	19	21	choice	choice	NOUN
ejpam-6741	19	22	of	of	ADP
ejpam-6741	19	23	the	the	DET
ejpam-6741	19	24	particular	particular	ADJ
ejpam-6741	19	25	matter	matter	NOUN
ejpam-6741	19	26	distribution	distribution	NOUN
ejpam-6741	19	27	under	under	ADP
ejpam-6741	19	28	consideration	consideration	NOUN
ejpam-6741	19	29	.	.	PUNCT
ejpam-6741	20	1	these	these	DET
ejpam-6741	20	2	symmetries	symmetry	NOUN
ejpam-6741	20	3	are	be	AUX
ejpam-6741	20	4	expressed	express	VERB
ejpam-6741	20	5	through	through	ADP
ejpam-6741	20	6	vector	vector	NOUN
ejpam-6741	20	7	fields	field	NOUN
ejpam-6741	20	8	that	that	PRON
ejpam-6741	20	9	preserve	preserve	VERB
ejpam-6741	20	10	different	different	ADJ
ejpam-6741	20	11	kinds	kind	NOUN
ejpam-6741	20	12	of	of	ADP
ejpam-6741	20	13	tensors	tensor	NOUN
ejpam-6741	20	14	.	.	PUNCT
ejpam-6741	21	1	among	among	ADP
ejpam-6741	21	2	the	the	DET
ejpam-6741	21	3	various	various	ADJ
ejpam-6741	21	4	symmetries	symmetry	NOUN
ejpam-6741	21	5	in	in	ADP
ejpam-6741	21	6	the	the	DET
ejpam-6741	21	7	literature	literature	NOUN
ejpam-6741	21	8	[	[	X
ejpam-6741	21	9	1]-[2	1]-[2	NUM
ejpam-6741	21	10	]	]	PUNCT
ejpam-6741	21	11	,	,	PUNCT
ejpam-6741	21	12	some	some	PRON
ejpam-6741	21	13	of	of	ADP
ejpam-6741	21	14	the	the	DET
ejpam-6741	21	15	more	more	ADV
ejpam-6741	21	16	significant	significant	ADJ
ejpam-6741	21	17	ones	one	NOUN
ejpam-6741	21	18	are	be	AUX
ejpam-6741	21	19	killing	kill	VERB
ejpam-6741	21	20	,	,	PUNCT
ejpam-6741	21	21	homothetic	homothetic	ADJ
ejpam-6741	21	22	,	,	PUNCT
ejpam-6741	21	23	and	and	CCONJ
ejpam-6741	21	24	conformal	conformal	ADJ
ejpam-6741	21	25	vector	vector	NOUN
ejpam-6741	21	26	fields	field	NOUN
ejpam-6741	21	27	,	,	PUNCT
ejpam-6741	21	28	as	as	ADV
ejpam-6741	21	29	well	well	ADV
ejpam-6741	21	30	as	as	ADP
ejpam-6741	21	31	noether	noether	ADJ
ejpam-6741	21	32	symmetries	symmetry	NOUN
ejpam-6741	21	33	.	.	PUNCT
ejpam-6741	22	1	in	in	ADP
ejpam-6741	22	2	terms	term	NOUN
ejpam-6741	22	3	of	of	ADP
ejpam-6741	22	4	physical	physical	ADJ
ejpam-6741	22	5	importance	importance	NOUN
ejpam-6741	22	6	,	,	PUNCT
ejpam-6741	22	7	these	these	DET
ejpam-6741	22	8	symmetries	symmetry	NOUN
ejpam-6741	22	9	are	be	AUX
ejpam-6741	22	10	connected	connect	VERB
ejpam-6741	22	11	to	to	ADP
ejpam-6741	22	12	conservation	conservation	NOUN
ejpam-6741	22	13	laws	law	NOUN
ejpam-6741	22	14	of	of	ADP
ejpam-6741	22	15	energy	energy	NOUN
ejpam-6741	22	16	and	and	CCONJ
ejpam-6741	22	17	momentum	momentum	NOUN
ejpam-6741	22	18	,	,	PUNCT
ejpam-6741	22	19	among	among	ADP
ejpam-6741	22	20	others	other	NOUN
ejpam-6741	22	21	.	.	PUNCT
ejpam-6741	23	1	their	their	PRON
ejpam-6741	23	2	role	role	NOUN
ejpam-6741	23	3	also	also	ADV
ejpam-6741	23	4	extends	extend	VERB
ejpam-6741	23	5	to	to	ADP
ejpam-6741	23	6	the	the	DET
ejpam-6741	23	7	study	study	NOUN
ejpam-6741	23	8	of	of	ADP
ejpam-6741	23	9	singularities	singularity	NOUN
ejpam-6741	23	10	in	in	ADP
ejpam-6741	23	11	gr	gr	ADP
ejpam-6741	23	12	,	,	PUNCT
ejpam-6741	23	13	cosmological	cosmological	ADJ
ejpam-6741	23	14	problems	problem	NOUN
ejpam-6741	23	15	,	,	PUNCT
ejpam-6741	23	16	and	and	CCONJ
ejpam-6741	23	17	astrophysics	astrophysic	NOUN
ejpam-6741	23	18	.	.	PUNCT
ejpam-6741	24	1	apart	apart	ADV
ejpam-6741	24	2	from	from	ADP
ejpam-6741	24	3	these	these	PRON
ejpam-6741	24	4	,	,	PUNCT
ejpam-6741	24	5	noether	noether	ADJ
ejpam-6741	24	6	symmetries	symmetry	NOUN
ejpam-6741	24	7	are	be	AUX
ejpam-6741	24	8	considered	consider	VERB
ejpam-6741	24	9	a	a	DET
ejpam-6741	24	10	crucial	crucial	ADJ
ejpam-6741	24	11	tool	tool	NOUN
ejpam-6741	24	12	for	for	ADP
ejpam-6741	24	13	classifying	classify	VERB
ejpam-6741	24	14	spacetime	spacetime	NOUN
ejpam-6741	24	15	lagrangians	lagrangian	NOUN
ejpam-6741	24	16	to	to	PART
ejpam-6741	24	17	obtain	obtain	VERB
ejpam-6741	24	18	exact	exact	ADJ
ejpam-6741	24	19	solutions	solution	NOUN
ejpam-6741	24	20	of	of	ADP
ejpam-6741	24	21	efes	efes	PROPN
ejpam-6741	24	22	and	and	CCONJ
ejpam-6741	24	23	to	to	PART
ejpam-6741	24	24	reduce	reduce	VERB
ejpam-6741	24	25	the	the	DET
ejpam-6741	24	26	number	number	NOUN
ejpam-6741	24	27	of	of	ADP
ejpam-6741	24	28	variables	variable	NOUN
ejpam-6741	24	29	and	and	CCONJ
ejpam-6741	24	30	the	the	DET
ejpam-6741	24	31	order	order	NOUN
ejpam-6741	24	32	of	of	ADP
ejpam-6741	24	33	partial	partial	ADJ
ejpam-6741	24	34	differential	differential	ADJ
ejpam-6741	24	35	equations	equation	NOUN
ejpam-6741	24	36	[	[	X
ejpam-6741	24	37	3	3	NUM
ejpam-6741	24	38	]	]	PUNCT
ejpam-6741	24	39	.	.	PUNCT
ejpam-6741	25	1	it	it	PRON
ejpam-6741	25	2	is	be	AUX
ejpam-6741	25	3	crucial	crucial	ADJ
ejpam-6741	25	4	to	to	PART
ejpam-6741	25	5	distinguish	distinguish	VERB
ejpam-6741	25	6	the	the	DET
ejpam-6741	25	7	aforementioned	aforementioned	ADJ
ejpam-6741	25	8	symmetries	symmetry	NOUN
ejpam-6741	25	9	from	from	ADP
ejpam-6741	25	10	the	the	DET
ejpam-6741	25	11	structure	structure	NOUN
ejpam-6741	25	12	of	of	ADP
ejpam-6741	25	13	a	a	DET
ejpam-6741	25	14	ricci	ricci	PROPN
ejpam-6741	25	15	soliton	soliton	NOUN
ejpam-6741	25	16	.	.	PUNCT
ejpam-6741	26	1	a	a	DET
ejpam-6741	26	2	ricci	ricci	PROPN
ejpam-6741	26	3	soliton	soliton	NOUN
ejpam-6741	26	4	is	be	AUX
ejpam-6741	26	5	defined	define	VERB
ejpam-6741	26	6	as	as	ADP
ejpam-6741	26	7	a	a	DET
ejpam-6741	26	8	pseudo	pseudo	NOUN
ejpam-6741	26	9	-	-	ADJ
ejpam-6741	26	10	riemannian	riemannian	ADJ
ejpam-6741	26	11	manifold	manifold	NOUN
ejpam-6741	26	12	(	(	PUNCT
ejpam-6741	26	13	m	m	PROPN
ejpam-6741	26	14	,	,	PUNCT
ejpam-6741	26	15	g	g	NOUN
ejpam-6741	26	16	)	)	PUNCT
ejpam-6741	26	17	that	that	PRON
ejpam-6741	26	18	admits	admit	VERB
ejpam-6741	26	19	a	a	DET
ejpam-6741	26	20	smooth	smooth	ADJ
ejpam-6741	26	21	vector	vector	NOUN
ejpam-6741	26	22	field	field	NOUN
ejpam-6741	26	23	v	v	ADP
ejpam-6741	26	24	satisfying	satisfy	VERB
ejpam-6741	26	25	equation	equation	NOUN
ejpam-6741	26	26	(	(	PUNCT
ejpam-6741	26	27	1	1	NUM
ejpam-6741	26	28	)	)	PUNCT
ejpam-6741	26	29	.	.	PUNCT
ejpam-6741	27	1	in	in	ADP
ejpam-6741	27	2	contrast	contrast	NOUN
ejpam-6741	27	3	to	to	ADP
ejpam-6741	27	4	a	a	DET
ejpam-6741	27	5	symmetry	symmetry	NOUN
ejpam-6741	27	6	vector	vector	NOUN
ejpam-6741	27	7	field	field	NOUN
ejpam-6741	27	8	,	,	PUNCT
ejpam-6741	27	9	which	which	PRON
ejpam-6741	27	10	generates	generate	VERB
ejpam-6741	27	11	a	a	DET
ejpam-6741	27	12	transformation	transformation	NOUN
ejpam-6741	27	13	preserving	preserve	VERB
ejpam-6741	27	14	certain	certain	ADJ
ejpam-6741	27	15	properties	property	NOUN
ejpam-6741	27	16	of	of	ADP
ejpam-6741	27	17	a	a	DET
ejpam-6741	27	18	given	give	VERB
ejpam-6741	27	19	metric	metric	NOUN
ejpam-6741	27	20	,	,	PUNCT
ejpam-6741	27	21	the	the	DET
ejpam-6741	27	22	vector	vector	NOUN
ejpam-6741	27	23	field	field	NOUN
ejpam-6741	27	24	v	v	NOUN
ejpam-6741	27	25	is	be	AUX
ejpam-6741	27	26	an	an	DET
ejpam-6741	27	27	intrinsic	intrinsic	ADJ
ejpam-6741	27	28	part	part	NOUN
ejpam-6741	27	29	of	of	ADP
ejpam-6741	27	30	the	the	DET
ejpam-6741	27	31	soliton	soliton	NOUN
ejpam-6741	27	32	structure	structure	NOUN
ejpam-6741	27	33	itself	itself	PRON
ejpam-6741	27	34	.	.	PUNCT
ejpam-6741	28	1	the	the	DET
ejpam-6741	28	2	metric	metric	ADJ
ejpam-6741	28	3	g	g	NOUN
ejpam-6741	28	4	and	and	CCONJ
ejpam-6741	28	5	the	the	DET
ejpam-6741	28	6	vector	vector	NOUN
ejpam-6741	28	7	field	field	NOUN
ejpam-6741	28	8	v	v	AUX
ejpam-6741	28	9	together	together	ADV
ejpam-6741	28	10	satisfy	satisfy	VERB
ejpam-6741	28	11	the	the	DET
ejpam-6741	28	12	soliton	soliton	NOUN
ejpam-6741	28	13	equation	equation	NOUN
ejpam-6741	28	14	.	.	PUNCT
ejpam-6741	29	1	in	in	ADP
ejpam-6741	29	2	this	this	DET
ejpam-6741	29	3	paper	paper	NOUN
ejpam-6741	29	4	,	,	PUNCT
ejpam-6741	29	5	we	we	PRON
ejpam-6741	29	6	study	study	VERB
ejpam-6741	29	7	the	the	DET
ejpam-6741	29	8	lrs	lrs	PROPN
ejpam-6741	29	9	bianchi	bianchi	PROPN
ejpam-6741	29	10	-	-	PUNCT
ejpam-6741	29	11	i	i	PRON
ejpam-6741	29	12	spacetime	spacetime	VERB
ejpam-6741	29	13	as	as	ADP
ejpam-6741	29	14	a	a	DET
ejpam-6741	29	15	ricci	ricci	PROPN
ejpam-6741	29	16	soliton	soliton	NOUN
ejpam-6741	29	17	,	,	PUNCT
ejpam-6741	29	18	and	and	CCONJ
ejpam-6741	29	19	our	our	PRON
ejpam-6741	29	20	objective	objective	NOUN
ejpam-6741	29	21	is	be	AUX
ejpam-6741	29	22	to	to	PART
ejpam-6741	29	23	solve	solve	VERB
ejpam-6741	29	24	equation	equation	NOUN
ejpam-6741	29	25	(	(	PUNCT
ejpam-6741	29	26	1	1	NUM
ejpam-6741	29	27	)	)	PUNCT
ejpam-6741	29	28	to	to	PART
ejpam-6741	29	29	find	find	VERB
ejpam-6741	29	30	the	the	DET
ejpam-6741	29	31	metric	metric	ADJ
ejpam-6741	29	32	functions	function	NOUN
ejpam-6741	29	33	p(t	p(t	NOUN
ejpam-6741	29	34	)	)	PUNCT
ejpam-6741	29	35	,	,	PUNCT
ejpam-6741	29	36	q(t	q(t	PROPN
ejpam-6741	29	37	)	)	PUNCT
ejpam-6741	29	38	and	and	CCONJ
ejpam-6741	29	39	the	the	DET
ejpam-6741	29	40	components	component	NOUN
ejpam-6741	29	41	of	of	ADP
ejpam-6741	29	42	the	the	DET
ejpam-6741	29	43	associated	associated	ADJ
ejpam-6741	29	44	vector	vector	NOUN
ejpam-6741	29	45	field	field	NOUN
ejpam-6741	29	46	v	v	NOUN
ejpam-6741	29	47	.	.	PUNCT
ejpam-6741	30	1	the	the	DET
ejpam-6741	30	2	study	study	NOUN
ejpam-6741	30	3	of	of	ADP
ejpam-6741	30	4	ricci	ricci	PROPN
ejpam-6741	30	5	solitons	soliton	NOUN
ejpam-6741	30	6	on	on	ADP
ejpam-6741	30	7	spacetimes	spacetime	NOUN
ejpam-6741	30	8	has	have	AUX
ejpam-6741	30	9	gained	gain	VERB
ejpam-6741	30	10	considerable	considerable	ADJ
ejpam-6741	30	11	momentum	momentum	NOUN
ejpam-6741	30	12	,	,	PUNCT
ejpam-6741	30	13	with	with	ADP
ejpam-6741	30	14	recent	recent	ADJ
ejpam-6741	30	15	works	work	NOUN
ejpam-6741	30	16	providing	provide	VERB
ejpam-6741	30	17	important	important	ADJ
ejpam-6741	30	18	classifications	classification	NOUN
ejpam-6741	30	19	regarding	regard	VERB
ejpam-6741	30	20	rsvfs	rsvfs	NOUN
ejpam-6741	30	21	.	.	PUNCT
ejpam-6741	31	1	for	for	ADP
ejpam-6741	31	2	instance	instance	NOUN
ejpam-6741	31	3	,	,	PUNCT
ejpam-6741	31	4	ibrar	ibrar	NOUN
ejpam-6741	31	5	et	et	PROPN
ejpam-6741	31	6	al	al	PROPN
ejpam-6741	31	7	.	.	PUNCT
ejpam-6741	32	1	[	[	X
ejpam-6741	32	2	4	4	NUM
ejpam-6741	32	3	]	]	X
ejpam-6741	32	4	classified	classified	ADJ
ejpam-6741	32	5	ricci	ricci	PROPN
ejpam-6741	32	6	solitons	soliton	NOUN
ejpam-6741	32	7	in	in	ADP
ejpam-6741	32	8	plane	plane	NOUN
ejpam-6741	32	9	symmetric	symmetric	ADJ
ejpam-6741	32	10	static	static	ADJ
ejpam-6741	32	11	spacetimes	spacetime	NOUN
ejpam-6741	32	12	,	,	PUNCT
ejpam-6741	32	13	finding	find	VERB
ejpam-6741	32	14	a	a	DET
ejpam-6741	32	15	sixor	sixor	ADJ
ejpam-6741	32	16	ten	ten	ADJ
ejpam-6741	32	17	-	-	PUNCT
ejpam-6741	32	18	dimensional	dimensional	ADJ
ejpam-6741	32	19	lie	lie	NOUN
ejpam-6741	32	20	algebra	algebra	NOUN
ejpam-6741	32	21	for	for	ADP
ejpam-6741	32	22	the	the	DET
ejpam-6741	32	23	soliton	soliton	NOUN
ejpam-6741	32	24	vectors	vector	NOUN
ejpam-6741	32	25	.	.	PUNCT
ejpam-6741	33	1	similarly	similarly	ADV
ejpam-6741	33	2	,	,	PUNCT
ejpam-6741	33	3	mahmood	mahmood	PROPN
ejpam-6741	33	4	et	et	PROPN
ejpam-6741	33	5	al	al	PROPN
ejpam-6741	33	6	.	.	PUNCT
ejpam-6741	34	1	[	[	X
ejpam-6741	34	2	5	5	NUM
ejpam-6741	34	3	]	]	PUNCT
ejpam-6741	34	4	and	and	CCONJ
ejpam-6741	34	5	tahirullah	tahirullah	INTJ
ejpam-6741	34	6	et	et	PROPN
ejpam-6741	34	7	al	al	PROPN
ejpam-6741	34	8	.	.	PUNCT
ejpam-6741	35	1	[	[	X
ejpam-6741	35	2	6	6	NUM
ejpam-6741	35	3	]	]	PUNCT
ejpam-6741	35	4	examined	examine	VERB
ejpam-6741	35	5	lrs	lrs	PROPN
ejpam-6741	35	6	bianchi	bianchi	PROPN
ejpam-6741	35	7	type	type	NOUN
ejpam-6741	35	8	v	v	NOUN
ejpam-6741	35	9	and	and	CCONJ
ejpam-6741	35	10	static	static	ADJ
ejpam-6741	35	11	spherically	spherically	PROPN
ejpam-6741	35	12	symmetric	symmetric	PROPN
ejpam-6741	35	13	spacetimes	spacetime	NOUN
ejpam-6741	35	14	,	,	PUNCT
ejpam-6741	35	15	respectively	respectively	ADV
ejpam-6741	35	16	,	,	PUNCT
ejpam-6741	35	17	identifying	identify	VERB
ejpam-6741	35	18	solutions	solution	NOUN
ejpam-6741	35	19	with	with	ADP
ejpam-6741	35	20	expanding	expand	VERB
ejpam-6741	35	21	,	,	PUNCT
ejpam-6741	35	22	steady	steady	ADJ
ejpam-6741	35	23	,	,	PUNCT
ejpam-6741	35	24	and	and	CCONJ
ejpam-6741	35	25	shrinking	shrink	VERB
ejpam-6741	35	26	natures	nature	NOUN
ejpam-6741	35	27	.	.	PUNCT
ejpam-6741	36	1	ali	ali	PROPN
ejpam-6741	36	2	and	and	CCONJ
ejpam-6741	36	3	khan	khan	PROPN
ejpam-6741	37	1	[	[	X
ejpam-6741	37	2	7	7	NUM
ejpam-6741	37	3	]	]	PUNCT
ejpam-6741	37	4	investigated	investigate	VERB
ejpam-6741	37	5	kantowski	kantowski	ADJ
ejpam-6741	37	6	-	-	PUNCT
ejpam-6741	37	7	sachs	sachs	NOUN
ejpam-6741	37	8	spacetimes	spacetime	NOUN
ejpam-6741	37	9	,	,	PUNCT
ejpam-6741	37	10	concluding	conclude	VERB
ejpam-6741	37	11	they	they	PRON
ejpam-6741	37	12	only	only	ADV
ejpam-6741	37	13	admit	admit	VERB
ejpam-6741	37	14	expanding	expand	VERB
ejpam-6741	37	15	solitons	soliton	NOUN
ejpam-6741	37	16	.	.	PUNCT
ejpam-6741	38	1	furthermore	furthermore	ADV
ejpam-6741	38	2	,	,	PUNCT
ejpam-6741	38	3	the	the	DET
ejpam-6741	38	4	exploration	exploration	NOUN
ejpam-6741	38	5	has	have	AUX
ejpam-6741	38	6	extended	extend	VERB
ejpam-6741	38	7	to	to	ADP
ejpam-6741	38	8	modified	modify	VERB
ejpam-6741	38	9	theories	theory	NOUN
ejpam-6741	38	10	of	of	ADP
ejpam-6741	38	11	gravity	gravity	NOUN
ejpam-6741	38	12	;	;	PUNCT
ejpam-6741	38	13	uzma	uzma	PROPN
ejpam-6741	38	14	et	et	PROPN
ejpam-6741	38	15	al	al	PROPN
ejpam-6741	38	16	.	.	PUNCT
ejpam-6741	39	1	[	[	X
ejpam-6741	39	2	8	8	NUM
ejpam-6741	39	3	]	]	PUNCT
ejpam-6741	39	4	found	find	VERB
ejpam-6741	39	5	all	all	DET
ejpam-6741	39	6	three	three	NUM
ejpam-6741	39	7	types	type	NOUN
ejpam-6741	39	8	of	of	ADP
ejpam-6741	39	9	solitons	soliton	NOUN
ejpam-6741	39	10	for	for	ADP
ejpam-6741	39	11	bianchi	bianchi	NOUN
ejpam-6741	39	12	type	type	NOUN
ejpam-6741	39	13	i	i	PRON
ejpam-6741	39	14	spacetimes	spacetime	VERB
ejpam-6741	39	15	in	in	ADP
ejpam-6741	39	16	f(t	f(t	PROPN
ejpam-6741	39	17	)	)	PUNCT
ejpam-6741	39	18	gravity	gravity	NOUN
ejpam-6741	39	19	,	,	PUNCT
ejpam-6741	39	20	while	while	SCONJ
ejpam-6741	39	21	siddiqi	siddiqi	NOUN
ejpam-6741	39	22	et	et	NOUN
ejpam-6741	39	23	al	al	PROPN
ejpam-6741	39	24	.	.	PUNCT
ejpam-6741	40	1	[	[	X
ejpam-6741	40	2	9	9	NUM
ejpam-6741	40	3	,	,	PUNCT
ejpam-6741	40	4	10	10	NUM
ejpam-6741	40	5	]	]	PUNCT
ejpam-6741	40	6	have	have	AUX
ejpam-6741	40	7	classified	classify	VERB
ejpam-6741	40	8	them	they	PRON
ejpam-6741	40	9	in	in	ADP
ejpam-6741	40	10	f(r	f(r	NOUN
ejpam-6741	40	11	)	)	PUNCT
ejpam-6741	40	12	and	and	CCONJ
ejpam-6741	40	13	f(r	f(r	PROPN
ejpam-6741	40	14	,	,	PUNCT
ejpam-6741	40	15	t	t	NOUN
ejpam-6741	40	16	)	)	PUNCT
ejpam-6741	40	17	theories	theory	NOUN
ejpam-6741	40	18	.	.	PUNCT
ejpam-6741	41	1	the	the	DET
ejpam-6741	41	2	exploration	exploration	NOUN
ejpam-6741	41	3	of	of	ADP
ejpam-6741	41	4	solitons	soliton	NOUN
ejpam-6741	41	5	extends	extend	VERB
ejpam-6741	41	6	beyond	beyond	ADP
ejpam-6741	41	7	ricci	ricci	PROPN
ejpam-6741	41	8	solitons	soliton	NOUN
ejpam-6741	41	9	to	to	ADP
ejpam-6741	41	10	other	other	ADJ
ejpam-6741	41	11	geometrically	geometrically	ADV
ejpam-6741	41	12	significant	significant	ADJ
ejpam-6741	41	13	types	type	NOUN
ejpam-6741	41	14	.	.	PUNCT
ejpam-6741	42	1	recently	recently	ADV
ejpam-6741	42	2	,	,	PUNCT
ejpam-6741	42	3	ali	ali	PROPN
ejpam-6741	42	4	et	et	PROPN
ejpam-6741	42	5	al	al	PROPN
ejpam-6741	42	6	.	.	PUNCT
ejpam-6741	43	1	[	[	X
ejpam-6741	43	2	11	11	NUM
ejpam-6741	43	3	]	]	PUNCT
ejpam-6741	43	4	conducted	conduct	VERB
ejpam-6741	43	5	a	a	DET
ejpam-6741	43	6	comprehensive	comprehensive	ADJ
ejpam-6741	43	7	analysis	analysis	NOUN
ejpam-6741	43	8	of	of	ADP
ejpam-6741	43	9	conformal	conformal	ADJ
ejpam-6741	43	10	ricci	ricci	NOUN
ejpam-6741	43	11	solitons	soliton	NOUN
ejpam-6741	43	12	within	within	ADP
ejpam-6741	43	13	the	the	DET
ejpam-6741	43	14	framework	framework	NOUN
ejpam-6741	43	15	of	of	ADP
ejpam-6741	43	16	kenmotsu	kenmotsu	PROPN
ejpam-6741	43	17	manifolds	manifold	NOUN
ejpam-6741	43	18	,	,	PUNCT
ejpam-6741	43	19	uncovering	uncover	VERB
ejpam-6741	43	20	conditions	condition	NOUN
ejpam-6741	43	21	under	under	ADP
ejpam-6741	43	22	which	which	PRON
ejpam-6741	43	23	such	such	ADJ
ejpam-6741	43	24	solitons	soliton	NOUN
ejpam-6741	43	25	become	become	VERB
ejpam-6741	43	26	einstein	einstein	ADV
ejpam-6741	43	27	and	and	CCONJ
ejpam-6741	43	28	providing	provide	VERB
ejpam-6741	43	29	valuable	valuable	ADJ
ejpam-6741	43	30	insights	insight	NOUN
ejpam-6741	43	31	into	into	ADP
ejpam-6741	43	32	the	the	DET
ejpam-6741	43	33	interplay	interplay	NOUN
ejpam-6741	43	34	between	between	ADP
ejpam-6741	43	35	curvature	curvature	NOUN
ejpam-6741	43	36	and	and	CCONJ
ejpam-6741	43	37	soliton	soliton	NOUN
ejpam-6741	43	38	structures	structure	NOUN
ejpam-6741	43	39	.	.	PUNCT
ejpam-6741	44	1	in	in	ADP
ejpam-6741	44	2	the	the	DET
ejpam-6741	44	3	realm	realm	NOUN
ejpam-6741	44	4	of	of	ADP
ejpam-6741	44	5	almost	almost	ADV
ejpam-6741	44	6	paracontact	paracontact	NOUN
ejpam-6741	44	7	geometry	geometry	NOUN
ejpam-6741	44	8	,	,	PUNCT
ejpam-6741	44	9	naik	naik	PROPN
ejpam-6741	44	10	et	et	PROPN
ejpam-6741	44	11	al	al	PROPN
ejpam-6741	44	12	.	.	PUNCT
ejpam-6741	45	1	[	[	X
ejpam-6741	45	2	12	12	NUM
ejpam-6741	45	3	]	]	PUNCT
ejpam-6741	45	4	investigated	investigate	VERB
ejpam-6741	45	5	generalized	generalized	ADJ
ejpam-6741	45	6	ricci	ricci	NOUN
ejpam-6741	45	7	solitons	soliton	NOUN
ejpam-6741	45	8	,	,	PUNCT
ejpam-6741	45	9	establishing	establish	VERB
ejpam-6741	45	10	key	key	ADJ
ejpam-6741	45	11	theorems	theorem	NOUN
ejpam-6741	45	12	that	that	PRON
ejpam-6741	45	13	determine	determine	VERB
ejpam-6741	45	14	when	when	SCONJ
ejpam-6741	45	15	these	these	DET
ejpam-6741	45	16	solitons	soliton	NOUN
ejpam-6741	45	17	transition	transition	NOUN
ejpam-6741	45	18	to	to	ADP
ejpam-6741	45	19	a	a	DET
ejpam-6741	45	20	nearly	nearly	ADV
ejpam-6741	45	21	para	para	NOUN
ejpam-6741	45	22	-	-	PUNCT
ejpam-6741	45	23	einstein	einstein	NOUN
ejpam-6741	45	24	form	form	NOUN
ejpam-6741	45	25	,	,	PUNCT
ejpam-6741	45	26	thereby	thereby	ADV
ejpam-6741	45	27	enriching	enrich	VERB
ejpam-6741	45	28	the	the	DET
ejpam-6741	45	29	classification	classification	NOUN
ejpam-6741	45	30	of	of	ADP
ejpam-6741	45	31	solitons	soliton	NOUN
ejpam-6741	45	32	in	in	ADP
ejpam-6741	45	33	this	this	DET
ejpam-6741	45	34	specific	specific	ADJ
ejpam-6741	45	35	geometric	geometric	ADJ
ejpam-6741	45	36	setting	setting	NOUN
ejpam-6741	45	37	.	.	PUNCT
ejpam-6741	46	1	furthermore	furthermore	ADV
ejpam-6741	46	2	,	,	PUNCT
ejpam-6741	46	3	the	the	DET
ejpam-6741	46	4	study	study	NOUN
ejpam-6741	46	5	of	of	ADP
ejpam-6741	46	6	solitons	soliton	NOUN
ejpam-6741	46	7	has	have	AUX
ejpam-6741	46	8	been	be	AUX
ejpam-6741	46	9	advanced	advance	VERB
ejpam-6741	46	10	through	through	ADP
ejpam-6741	46	11	the	the	DET
ejpam-6741	46	12	lens	lens	NOUN
ejpam-6741	46	13	of	of	ADP
ejpam-6741	46	14	symmetry	symmetry	NOUN
ejpam-6741	46	15	,	,	PUNCT
ejpam-6741	46	16	as	as	SCONJ
ejpam-6741	46	17	demonstrated	demonstrate	VERB
ejpam-6741	46	18	by	by	ADP
ejpam-6741	46	19	raza	raza	PROPN
ejpam-6741	46	20	et	et	PROPN
ejpam-6741	46	21	al	al	PROPN
ejpam-6741	46	22	.	.	PUNCT
ejpam-6741	47	1	[	[	X
ejpam-6741	47	2	13	13	NUM
ejpam-6741	47	3	]	]	PUNCT
ejpam-6741	47	4	,	,	PUNCT
ejpam-6741	47	5	who	who	PRON
ejpam-6741	47	6	explored	explore	VERB
ejpam-6741	47	7	the	the	DET
ejpam-6741	47	8	relationship	relationship	NOUN
ejpam-6741	47	9	between	between	ADP
ejpam-6741	47	10	ricci	ricci	PROPN
ejpam-6741	47	11	solitons	soliton	NOUN
ejpam-6741	47	12	and	and	CCONJ
ejpam-6741	47	13	curvature	curvature	NOUN
ejpam-6741	47	14	inheritance	inheritance	NOUN
ejpam-6741	47	15	u.	u.	PROPN
ejpam-6741	47	16	nasib	nasib	PROPN
ejpam-6741	47	17	et	et	PROPN
ejpam-6741	47	18	al	al	PROPN
ejpam-6741	47	19	.	.	PUNCT
ejpam-6741	47	20	/	/	SYM
ejpam-6741	47	21	eur	eur	PROPN
ejpam-6741	47	22	.	.	PUNCT
ejpam-6741	48	1	j.	j.	PROPN
ejpam-6741	48	2	pure	pure	PROPN
ejpam-6741	48	3	appl	appl	PROPN
ejpam-6741	48	4	.	.	PROPN
ejpam-6741	48	5	math	math	PROPN
ejpam-6741	48	6	,	,	PUNCT
ejpam-6741	48	7	18	18	NUM
ejpam-6741	48	8	(	(	PUNCT
ejpam-6741	48	9	4	4	NUM
ejpam-6741	48	10	)	)	PUNCT
ejpam-6741	48	11	(	(	PUNCT
ejpam-6741	48	12	2025	2025	NUM
ejpam-6741	48	13	)	)	PUNCT
ejpam-6741	48	14	,	,	PUNCT
ejpam-6741	48	15	6741	6741	NUM
ejpam-6741	48	16	3	3	NUM
ejpam-6741	48	17	of	of	ADP
ejpam-6741	48	18	14	14	NUM
ejpam-6741	48	19	symmetry	symmetry	NOUN
ejpam-6741	48	20	in	in	ADP
ejpam-6741	48	21	riemannian	riemannian	ADJ
ejpam-6741	48	22	manifolds	manifold	NOUN
ejpam-6741	48	23	.	.	PUNCT
ejpam-6741	49	1	their	their	PRON
ejpam-6741	49	2	work	work	NOUN
ejpam-6741	49	3	is	be	AUX
ejpam-6741	49	4	particularly	particularly	ADV
ejpam-6741	49	5	relevant	relevant	ADJ
ejpam-6741	49	6	as	as	SCONJ
ejpam-6741	49	7	it	it	PRON
ejpam-6741	49	8	bridges	bridge	VERB
ejpam-6741	49	9	the	the	DET
ejpam-6741	49	10	study	study	NOUN
ejpam-6741	49	11	of	of	ADP
ejpam-6741	49	12	solitons	soliton	NOUN
ejpam-6741	49	13	with	with	ADP
ejpam-6741	49	14	other	other	ADJ
ejpam-6741	49	15	fundamental	fundamental	ADJ
ejpam-6741	49	16	symmetry	symmetry	NOUN
ejpam-6741	49	17	principles	principle	NOUN
ejpam-6741	49	18	in	in	ADP
ejpam-6741	49	19	geometry	geometry	NOUN
ejpam-6741	49	20	,	,	PUNCT
ejpam-6741	49	21	suggesting	suggest	VERB
ejpam-6741	49	22	a	a	DET
ejpam-6741	49	23	deeper	deep	ADJ
ejpam-6741	49	24	underlying	underlying	ADJ
ejpam-6741	49	25	structure	structure	NOUN
ejpam-6741	49	26	.	.	PUNCT
ejpam-6741	50	1	a	a	DET
ejpam-6741	50	2	common	common	ADJ
ejpam-6741	50	3	thread	thread	NOUN
ejpam-6741	50	4	in	in	ADP
ejpam-6741	50	5	these	these	DET
ejpam-6741	50	6	studies	study	NOUN
ejpam-6741	50	7	is	be	AUX
ejpam-6741	50	8	the	the	DET
ejpam-6741	50	9	reliance	reliance	NOUN
ejpam-6741	50	10	on	on	ADP
ejpam-6741	50	11	the	the	DET
ejpam-6741	50	12	direct	direct	ADJ
ejpam-6741	50	13	integration	integration	NOUN
ejpam-6741	50	14	approach	approach	NOUN
ejpam-6741	50	15	to	to	PART
ejpam-6741	50	16	solve	solve	VERB
ejpam-6741	50	17	the	the	DET
ejpam-6741	50	18	highly	highly	ADV
ejpam-6741	50	19	complex	complex	ADJ
ejpam-6741	50	20	,	,	PUNCT
ejpam-6741	50	21	coupled	couple	VERB
ejpam-6741	50	22	non	non	ADJ
ejpam-6741	50	23	-	-	ADJ
ejpam-6741	50	24	linear	linear	ADJ
ejpam-6741	50	25	system	system	NOUN
ejpam-6741	50	26	of	of	ADP
ejpam-6741	50	27	ricci	ricci	PROPN
ejpam-6741	50	28	soliton	soliton	PROPN
ejpam-6741	50	29	equations	equation	NOUN
ejpam-6741	50	30	.	.	PUNCT
ejpam-6741	51	1	while	while	SCONJ
ejpam-6741	51	2	this	this	DET
ejpam-6741	51	3	method	method	NOUN
ejpam-6741	51	4	has	have	AUX
ejpam-6741	51	5	yielded	yield	VERB
ejpam-6741	51	6	valuable	valuable	ADJ
ejpam-6741	51	7	results	result	NOUN
ejpam-6741	51	8	,	,	PUNCT
ejpam-6741	51	9	it	it	PRON
ejpam-6741	51	10	is	be	AUX
ejpam-6741	51	11	inherently	inherently	ADV
ejpam-6741	51	12	burdensome	burdensome	ADJ
ejpam-6741	51	13	,	,	PUNCT
ejpam-6741	51	14	time	time	NOUN
ejpam-6741	51	15	-	-	PUNCT
ejpam-6741	51	16	consuming	consume	VERB
ejpam-6741	51	17	,	,	PUNCT
ejpam-6741	51	18	and	and	CCONJ
ejpam-6741	51	19	prone	prone	ADJ
ejpam-6741	51	20	to	to	ADP
ejpam-6741	51	21	human	human	ADJ
ejpam-6741	51	22	error	error	NOUN
ejpam-6741	51	23	.	.	PUNCT
ejpam-6741	52	1	most	most	ADV
ejpam-6741	52	2	critically	critically	ADV
ejpam-6741	52	3	,	,	PUNCT
ejpam-6741	52	4	this	this	DET
ejpam-6741	52	5	methodological	methodological	ADJ
ejpam-6741	52	6	limitation	limitation	NOUN
ejpam-6741	52	7	carries	carry	VERB
ejpam-6741	52	8	a	a	DET
ejpam-6741	52	9	significant	significant	ADJ
ejpam-6741	52	10	risk	risk	NOUN
ejpam-6741	52	11	of	of	ADP
ejpam-6741	52	12	overlooking	overlook	VERB
ejpam-6741	52	13	particular	particular	ADJ
ejpam-6741	52	14	classes	class	NOUN
ejpam-6741	52	15	of	of	ADP
ejpam-6741	52	16	metrics	metric	NOUN
ejpam-6741	52	17	or	or	CCONJ
ejpam-6741	52	18	special	special	ADJ
ejpam-6741	52	19	solutions	solution	NOUN
ejpam-6741	52	20	that	that	PRON
ejpam-6741	52	21	satisfy	satisfy	VERB
ejpam-6741	52	22	the	the	DET
ejpam-6741	52	23	governing	govern	VERB
ejpam-6741	52	24	equations	equation	NOUN
ejpam-6741	52	25	only	only	ADV
ejpam-6741	52	26	under	under	ADP
ejpam-6741	52	27	specific	specific	ADJ
ejpam-6741	52	28	,	,	PUNCT
ejpam-6741	52	29	non	non	ADJ
ejpam-6741	52	30	-	-	ADJ
ejpam-6741	52	31	generic	generic	ADJ
ejpam-6741	52	32	conditions	condition	NOUN
ejpam-6741	52	33	.	.	PUNCT
ejpam-6741	53	1	this	this	PRON
ejpam-6741	53	2	means	mean	VERB
ejpam-6741	53	3	that	that	SCONJ
ejpam-6741	53	4	prior	prior	ADJ
ejpam-6741	53	5	classifications	classification	NOUN
ejpam-6741	53	6	,	,	PUNCT
ejpam-6741	53	7	while	while	SCONJ
ejpam-6741	53	8	insightful	insightful	ADJ
ejpam-6741	53	9	,	,	PUNCT
ejpam-6741	53	10	are	be	AUX
ejpam-6741	53	11	likely	likely	ADJ
ejpam-6741	53	12	not	not	PART
ejpam-6741	53	13	exhaustive	exhaustive	ADJ
ejpam-6741	53	14	and	and	CCONJ
ejpam-6741	53	15	may	may	AUX
ejpam-6741	53	16	have	have	AUX
ejpam-6741	53	17	missed	miss	VERB
ejpam-6741	53	18	entire	entire	ADJ
ejpam-6741	53	19	branches	branch	NOUN
ejpam-6741	53	20	of	of	ADP
ejpam-6741	53	21	solutions	solution	NOUN
ejpam-6741	53	22	.	.	PUNCT
ejpam-6741	54	1	this	this	PRON
ejpam-6741	54	2	constitutes	constitute	VERB
ejpam-6741	54	3	a	a	DET
ejpam-6741	54	4	fundamental	fundamental	ADJ
ejpam-6741	54	5	gap	gap	NOUN
ejpam-6741	54	6	in	in	ADP
ejpam-6741	54	7	the	the	DET
ejpam-6741	54	8	literature	literature	NOUN
ejpam-6741	54	9	,	,	PUNCT
ejpam-6741	54	10	as	as	SCONJ
ejpam-6741	54	11	an	an	DET
ejpam-6741	54	12	incomplete	incomplete	ADJ
ejpam-6741	54	13	classification	classification	NOUN
ejpam-6741	54	14	hinders	hinder	VERB
ejpam-6741	54	15	a	a	DET
ejpam-6741	54	16	full	full	ADJ
ejpam-6741	54	17	understanding	understanding	NOUN
ejpam-6741	54	18	of	of	ADP
ejpam-6741	54	19	the	the	DET
ejpam-6741	54	20	spacetime	spacetime	NOUN
ejpam-6741	54	21	’s	’s	PART
ejpam-6741	54	22	geometric	geometric	ADJ
ejpam-6741	54	23	and	and	CCONJ
ejpam-6741	54	24	physical	physical	ADJ
ejpam-6741	54	25	properties	property	NOUN
ejpam-6741	54	26	.	.	PUNCT
ejpam-6741	55	1	furthermore	furthermore	ADV
ejpam-6741	55	2	,	,	PUNCT
ejpam-6741	55	3	the	the	DET
ejpam-6741	55	4	absence	absence	NOUN
ejpam-6741	55	5	of	of	ADP
ejpam-6741	55	6	a	a	DET
ejpam-6741	55	7	systematic	systematic	ADJ
ejpam-6741	55	8	method	method	NOUN
ejpam-6741	55	9	makes	make	VERB
ejpam-6741	55	10	it	it	PRON
ejpam-6741	55	11	difficult	difficult	ADJ
ejpam-6741	55	12	to	to	PART
ejpam-6741	55	13	compare	compare	VERB
ejpam-6741	55	14	results	result	NOUN
ejpam-6741	55	15	across	across	ADP
ejpam-6741	55	16	different	different	ADJ
ejpam-6741	55	17	studies	study	NOUN
ejpam-6741	55	18	or	or	CCONJ
ejpam-6741	55	19	to	to	PART
ejpam-6741	55	20	ensure	ensure	VERB
ejpam-6741	55	21	reproducibility	reproducibility	NOUN
ejpam-6741	55	22	.	.	PUNCT
ejpam-6741	56	1	our	our	PRON
ejpam-6741	56	2	work	work	NOUN
ejpam-6741	56	3	advances	advance	VERB
ejpam-6741	56	4	beyond	beyond	ADP
ejpam-6741	56	5	these	these	DET
ejpam-6741	56	6	prior	prior	ADJ
ejpam-6741	56	7	studies	study	NOUN
ejpam-6741	56	8	by	by	ADP
ejpam-6741	56	9	implementing	implement	VERB
ejpam-6741	56	10	a	a	DET
ejpam-6741	56	11	systematic	systematic	ADJ
ejpam-6741	56	12	and	and	CCONJ
ejpam-6741	56	13	exhaustive	exhaustive	ADJ
ejpam-6741	56	14	classification	classification	NOUN
ejpam-6741	56	15	methodology	methodology	NOUN
ejpam-6741	56	16	.	.	PUNCT
ejpam-6741	57	1	we	we	PRON
ejpam-6741	57	2	employ	employ	VERB
ejpam-6741	57	3	the	the	DET
ejpam-6741	57	4	rif	rif	PROPN
ejpam-6741	57	5	tree	tree	NOUN
ejpam-6741	57	6	algorithm	algorithm	NOUN
ejpam-6741	58	1	[	[	X
ejpam-6741	58	2	14	14	NUM
ejpam-6741	58	3	,	,	PUNCT
ejpam-6741	58	4	15	15	NUM
ejpam-6741	58	5	]	]	X
ejpam-6741	58	6	,	,	PUNCT
ejpam-6741	58	7	a	a	DET
ejpam-6741	58	8	powerful	powerful	ADJ
ejpam-6741	58	9	computational	computational	ADJ
ejpam-6741	58	10	differential	differential	NOUN
ejpam-6741	58	11	elimination	elimination	NOUN
ejpam-6741	58	12	tool	tool	NOUN
ejpam-6741	58	13	,	,	PUNCT
ejpam-6741	58	14	to	to	PART
ejpam-6741	58	15	address	address	VERB
ejpam-6741	58	16	the	the	DET
ejpam-6741	58	17	aforementioned	aforementioned	ADJ
ejpam-6741	58	18	limitations	limitation	NOUN
ejpam-6741	58	19	.	.	PUNCT
ejpam-6741	59	1	this	this	DET
ejpam-6741	59	2	approach	approach	NOUN
ejpam-6741	59	3	algorithmically	algorithmically	ADV
ejpam-6741	59	4	simplifies	simplify	VERB
ejpam-6741	59	5	the	the	DET
ejpam-6741	59	6	ricci	ricci	PROPN
ejpam-6741	59	7	soliton	soliton	PROPN
ejpam-6741	59	8	equations	equation	NOUN
ejpam-6741	59	9	into	into	ADP
ejpam-6741	59	10	a	a	DET
ejpam-6741	59	11	reduced	reduce	VERB
ejpam-6741	59	12	involutive	involutive	ADJ
ejpam-6741	59	13	form	form	NOUN
ejpam-6741	59	14	and	and	CCONJ
ejpam-6741	59	15	partitions	partition	VERB
ejpam-6741	59	16	the	the	DET
ejpam-6741	59	17	entire	entire	ADJ
ejpam-6741	59	18	solution	solution	NOUN
ejpam-6741	59	19	space	space	NOUN
ejpam-6741	59	20	into	into	ADP
ejpam-6741	59	21	a	a	DET
ejpam-6741	59	22	tree	tree	NOUN
ejpam-6741	59	23	-	-	PUNCT
ejpam-6741	59	24	like	like	ADJ
ejpam-6741	59	25	structure	structure	NOUN
ejpam-6741	59	26	of	of	ADP
ejpam-6741	59	27	mutually	mutually	ADV
ejpam-6741	59	28	exclusive	exclusive	ADJ
ejpam-6741	59	29	cases	case	NOUN
ejpam-6741	59	30	.	.	PUNCT
ejpam-6741	60	1	each	each	DET
ejpam-6741	60	2	branch	branch	NOUN
ejpam-6741	60	3	of	of	ADP
ejpam-6741	60	4	this	this	DET
ejpam-6741	60	5	rif	rif	PROPN
ejpam-6741	60	6	tree	tree	NOUN
ejpam-6741	60	7	represents	represent	VERB
ejpam-6741	60	8	a	a	DET
ejpam-6741	60	9	distinct	distinct	ADJ
ejpam-6741	60	10	set	set	NOUN
ejpam-6741	60	11	of	of	ADP
ejpam-6741	60	12	constraints	constraint	NOUN
ejpam-6741	60	13	on	on	ADP
ejpam-6741	60	14	the	the	DET
ejpam-6741	60	15	metric	metric	ADJ
ejpam-6741	60	16	functions	function	NOUN
ejpam-6741	60	17	p(t	p(t	NOUN
ejpam-6741	60	18	)	)	PUNCT
ejpam-6741	60	19	and	and	CCONJ
ejpam-6741	60	20	q(t	q(t	NOUN
ejpam-6741	60	21	)	)	PUNCT
ejpam-6741	60	22	.	.	PUNCT
ejpam-6741	61	1	this	this	PRON
ejpam-6741	61	2	ensures	ensure	VERB
ejpam-6741	61	3	that	that	SCONJ
ejpam-6741	61	4	no	no	DET
ejpam-6741	61	5	possible	possible	ADJ
ejpam-6741	61	6	case	case	NOUN
ejpam-6741	61	7	is	be	AUX
ejpam-6741	61	8	overlooked	overlook	VERB
ejpam-6741	61	9	,	,	PUNCT
ejpam-6741	61	10	thereby	thereby	ADV
ejpam-6741	61	11	guaranteeing	guarantee	VERB
ejpam-6741	61	12	a	a	DET
ejpam-6741	61	13	complete	complete	ADJ
ejpam-6741	61	14	classification	classification	NOUN
ejpam-6741	61	15	-	-	PUNCT
ejpam-6741	61	16	a	a	DET
ejpam-6741	61	17	feat	feat	NOUN
ejpam-6741	61	18	difficult	difficult	ADJ
ejpam-6741	61	19	to	to	PART
ejpam-6741	61	20	achieve	achieve	VERB
ejpam-6741	61	21	through	through	ADP
ejpam-6741	61	22	manual	manual	ADJ
ejpam-6741	61	23	computation	computation	NOUN
ejpam-6741	61	24	alone	alone	ADV
ejpam-6741	61	25	.	.	PUNCT
ejpam-6741	62	1	the	the	DET
ejpam-6741	62	2	application	application	NOUN
ejpam-6741	62	3	of	of	ADP
ejpam-6741	62	4	the	the	DET
ejpam-6741	62	5	rif	rif	PROPN
ejpam-6741	62	6	tree	tree	NOUN
ejpam-6741	62	7	approach	approach	NOUN
ejpam-6741	62	8	in	in	ADP
ejpam-6741	62	9	gr	gr	PROPN
ejpam-6741	62	10	has	have	AUX
ejpam-6741	62	11	recently	recently	ADV
ejpam-6741	62	12	proven	prove	VERB
ejpam-6741	62	13	its	its	PRON
ejpam-6741	62	14	value	value	NOUN
ejpam-6741	62	15	in	in	ADP
ejpam-6741	62	16	classifying	classify	VERB
ejpam-6741	62	17	spacetimes	spacetime	NOUN
ejpam-6741	62	18	by	by	ADP
ejpam-6741	62	19	other	other	ADJ
ejpam-6741	62	20	symmetries	symmetry	NOUN
ejpam-6741	62	21	[	[	X
ejpam-6741	62	22	16–19	16–19	NUM
ejpam-6741	62	23	]	]	PUNCT
ejpam-6741	62	24	,	,	PUNCT
ejpam-6741	62	25	often	often	ADV
ejpam-6741	62	26	uncovering	uncover	VERB
ejpam-6741	62	27	new	new	ADJ
ejpam-6741	62	28	metrics	metric	NOUN
ejpam-6741	62	29	missed	miss	VERB
ejpam-6741	62	30	by	by	ADP
ejpam-6741	62	31	direct	direct	ADJ
ejpam-6741	62	32	integration	integration	NOUN
ejpam-6741	62	33	.	.	PUNCT
ejpam-6741	63	1	we	we	PRON
ejpam-6741	63	2	apply	apply	VERB
ejpam-6741	63	3	this	this	DET
ejpam-6741	63	4	innovative	innovative	ADJ
ejpam-6741	63	5	technique	technique	NOUN
ejpam-6741	63	6	for	for	ADP
ejpam-6741	63	7	the	the	DET
ejpam-6741	63	8	first	first	ADJ
ejpam-6741	63	9	time	time	NOUN
ejpam-6741	63	10	to	to	ADP
ejpam-6741	63	11	the	the	DET
ejpam-6741	63	12	problem	problem	NOUN
ejpam-6741	63	13	of	of	ADP
ejpam-6741	63	14	classifying	classify	VERB
ejpam-6741	63	15	ricci	ricci	PROPN
ejpam-6741	63	16	solitons	soliton	NOUN
ejpam-6741	63	17	in	in	ADP
ejpam-6741	63	18	lrs	lrs	PROPN
ejpam-6741	63	19	bianchi	bianchi	NOUN
ejpam-6741	63	20	type	type	NOUN
ejpam-6741	63	21	i	i	PRON
ejpam-6741	63	22	spacetime	spacetime	NOUN
ejpam-6741	63	23	.	.	PUNCT
ejpam-6741	64	1	this	this	PRON
ejpam-6741	64	2	allows	allow	VERB
ejpam-6741	64	3	us	we	PRON
ejpam-6741	64	4	to	to	PART
ejpam-6741	64	5	not	not	PART
ejpam-6741	64	6	only	only	ADV
ejpam-6741	64	7	recover	recover	VERB
ejpam-6741	64	8	all	all	DET
ejpam-6741	64	9	solutions	solution	NOUN
ejpam-6741	64	10	that	that	PRON
ejpam-6741	64	11	might	might	AUX
ejpam-6741	64	12	be	be	AUX
ejpam-6741	64	13	found	find	VERB
ejpam-6741	64	14	by	by	ADP
ejpam-6741	64	15	direct	direct	ADJ
ejpam-6741	64	16	methods	method	NOUN
ejpam-6741	64	17	but	but	CCONJ
ejpam-6741	64	18	,	,	PUNCT
ejpam-6741	64	19	more	more	ADV
ejpam-6741	64	20	importantly	importantly	ADV
ejpam-6741	64	21	,	,	PUNCT
ejpam-6741	64	22	to	to	PART
ejpam-6741	64	23	discover	discover	VERB
ejpam-6741	64	24	novel	novel	NOUN
ejpam-6741	64	25	and	and	CCONJ
ejpam-6741	64	26	previously	previously	ADV
ejpam-6741	64	27	unreported	unreported	ADJ
ejpam-6741	64	28	solutions	solution	NOUN
ejpam-6741	64	29	that	that	PRON
ejpam-6741	64	30	exist	exist	VERB
ejpam-6741	64	31	under	under	ADP
ejpam-6741	64	32	specific	specific	ADJ
ejpam-6741	64	33	differential	differential	ADJ
ejpam-6741	64	34	constraints	constraint	NOUN
ejpam-6741	64	35	.	.	PUNCT
ejpam-6741	65	1	our	our	PRON
ejpam-6741	65	2	study	study	NOUN
ejpam-6741	65	3	therefore	therefore	ADV
ejpam-6741	65	4	provides	provide	VERB
ejpam-6741	65	5	the	the	DET
ejpam-6741	65	6	first	first	ADJ
ejpam-6741	65	7	complete	complete	ADJ
ejpam-6741	65	8	picture	picture	NOUN
ejpam-6741	65	9	of	of	ADP
ejpam-6741	65	10	ricci	ricci	PROPN
ejpam-6741	65	11	solitons	soliton	NOUN
ejpam-6741	65	12	in	in	ADP
ejpam-6741	65	13	this	this	DET
ejpam-6741	65	14	important	important	ADJ
ejpam-6741	65	15	cosmological	cosmological	ADJ
ejpam-6741	65	16	spacetime	spacetime	NOUN
ejpam-6741	65	17	.	.	PUNCT
ejpam-6741	66	1	in	in	ADP
ejpam-6741	66	2	the	the	DET
ejpam-6741	66	3	theories	theory	NOUN
ejpam-6741	66	4	of	of	ADP
ejpam-6741	66	5	gr	gr	PRON
ejpam-6741	66	6	and	and	CCONJ
ejpam-6741	66	7	riemannian	riemannian	ADJ
ejpam-6741	66	8	geometry	geometry	NOUN
ejpam-6741	66	9	,	,	PUNCT
ejpam-6741	66	10	geometric	geometric	ADJ
ejpam-6741	66	11	flows	flow	NOUN
ejpam-6741	66	12	are	be	AUX
ejpam-6741	66	13	essential	essential	ADJ
ejpam-6741	66	14	tools	tool	NOUN
ejpam-6741	66	15	.	.	PUNCT
ejpam-6741	67	1	among	among	ADP
ejpam-6741	67	2	these	these	PRON
ejpam-6741	67	3	,	,	PUNCT
ejpam-6741	67	4	the	the	DET
ejpam-6741	67	5	ricci	ricci	PROPN
ejpam-6741	67	6	flow	flow	NOUN
ejpam-6741	67	7	,	,	PUNCT
ejpam-6741	67	8	initially	initially	ADV
ejpam-6741	67	9	proposed	propose	VERB
ejpam-6741	67	10	by	by	ADP
ejpam-6741	67	11	hamilton	hamilton	PROPN
ejpam-6741	68	1	[	[	X
ejpam-6741	68	2	20	20	NUM
ejpam-6741	68	3	]	]	PUNCT
ejpam-6741	68	4	,	,	PUNCT
ejpam-6741	68	5	is	be	AUX
ejpam-6741	68	6	of	of	ADP
ejpam-6741	68	7	fundamental	fundamental	ADJ
ejpam-6741	68	8	importance	importance	NOUN
ejpam-6741	68	9	.	.	PUNCT
ejpam-6741	69	1	hamilton	hamilton	PROPN
ejpam-6741	69	2	also	also	ADV
ejpam-6741	69	3	introduced	introduce	VERB
ejpam-6741	69	4	self	self	NOUN
ejpam-6741	69	5	-	-	PUNCT
ejpam-6741	69	6	similar	similar	ADJ
ejpam-6741	69	7	solutions	solution	NOUN
ejpam-6741	69	8	for	for	ADP
ejpam-6741	69	9	the	the	DET
ejpam-6741	69	10	ricci	ricci	PROPN
ejpam-6741	69	11	flow	flow	NOUN
ejpam-6741	69	12	,	,	PUNCT
ejpam-6741	69	13	defined	define	VERB
ejpam-6741	69	14	as	as	ADP
ejpam-6741	69	15	ricci	ricci	PROPN
ejpam-6741	69	16	soliton	soliton	PROPN
ejpam-6741	69	17	vector	vector	NOUN
ejpam-6741	69	18	fields	field	NOUN
ejpam-6741	69	19	(	(	PUNCT
ejpam-6741	69	20	rsvfs	rsvfs	NOUN
ejpam-6741	69	21	)	)	PUNCT
ejpam-6741	70	1	[	[	X
ejpam-6741	70	2	21	21	NUM
ejpam-6741	70	3	]	]	PUNCT
ejpam-6741	70	4	,	,	PUNCT
ejpam-6741	70	5	given	give	VERB
ejpam-6741	70	6	by	by	ADP
ejpam-6741	70	7	:	:	PUNCT
ejpam-6741	70	8	lv	lv	PROPN
ejpam-6741	70	9	gmn	gmn	NOUN
ejpam-6741	70	10	+	+	CCONJ
ejpam-6741	70	11	2rmn	2rmn	NUM
ejpam-6741	70	12	=	=	SYM
ejpam-6741	70	13	2δgmn	2δgmn	NUM
ejpam-6741	70	14	.	.	PUNCT
ejpam-6741	70	15	(	(	PUNCT
ejpam-6741	70	16	1	1	X
ejpam-6741	70	17	)	)	PUNCT
ejpam-6741	70	18	here	here	ADV
ejpam-6741	70	19	,	,	PUNCT
ejpam-6741	70	20	lv	lv	PROPN
ejpam-6741	70	21	gmn	gmn	PROPN
ejpam-6741	70	22	represents	represent	VERB
ejpam-6741	70	23	the	the	DET
ejpam-6741	70	24	lie	lie	NOUN
ejpam-6741	70	25	derivative	derivative	NOUN
ejpam-6741	70	26	of	of	ADP
ejpam-6741	70	27	the	the	DET
ejpam-6741	70	28	metric	metric	ADJ
ejpam-6741	70	29	tensor	tensor	NOUN
ejpam-6741	70	30	gmn	gmn	NOUN
ejpam-6741	70	31	along	along	ADP
ejpam-6741	70	32	the	the	DET
ejpam-6741	70	33	vector	vector	NOUN
ejpam-6741	70	34	field	field	NOUN
ejpam-6741	70	35	v	v	NOUN
ejpam-6741	70	36	,	,	PUNCT
ejpam-6741	70	37	rmn	rmn	PROPN
ejpam-6741	70	38	denotes	denote	VERB
ejpam-6741	70	39	the	the	DET
ejpam-6741	70	40	ricci	ricci	PROPN
ejpam-6741	70	41	tensor	tensor	NOUN
ejpam-6741	70	42	,	,	PUNCT
ejpam-6741	70	43	and	and	CCONJ
ejpam-6741	70	44	δ	δ	PROPN
ejpam-6741	70	45	is	be	AUX
ejpam-6741	70	46	a	a	DET
ejpam-6741	70	47	constant	constant	ADJ
ejpam-6741	70	48	.	.	PUNCT
ejpam-6741	71	1	depending	depend	VERB
ejpam-6741	71	2	on	on	ADP
ejpam-6741	71	3	the	the	DET
ejpam-6741	71	4	value	value	NOUN
ejpam-6741	71	5	of	of	ADP
ejpam-6741	71	6	δ	δ	PROPN
ejpam-6741	71	7	,	,	PUNCT
ejpam-6741	71	8	an	an	DET
ejpam-6741	71	9	rsvf	rsvf	NOUN
ejpam-6741	71	10	may	may	AUX
ejpam-6741	71	11	be	be	AUX
ejpam-6741	71	12	shrinking	shrink	VERB
ejpam-6741	71	13	,	,	PUNCT
ejpam-6741	71	14	expanding	expand	VERB
ejpam-6741	71	15	,	,	PUNCT
ejpam-6741	71	16	or	or	CCONJ
ejpam-6741	71	17	steady	steady	ADJ
ejpam-6741	71	18	when	when	SCONJ
ejpam-6741	71	19	δ	δ	PROPN
ejpam-6741	71	20	>	>	X
ejpam-6741	71	21	0	0	PROPN
ejpam-6741	71	22	,	,	PUNCT
ejpam-6741	71	23	δ	δ	PROPN
ejpam-6741	71	24	<	<	X
ejpam-6741	71	25	0	0	NUM
ejpam-6741	71	26	or	or	CCONJ
ejpam-6741	71	27	δ	δ	PROPN
ejpam-6741	71	28	=	=	SYM
ejpam-6741	71	29	0	0	NUM
ejpam-6741	71	30	,	,	PUNCT
ejpam-6741	71	31	respectively	respectively	ADV
ejpam-6741	71	32	.	.	PUNCT
ejpam-6741	72	1	rsvfs	rsvfs	NOUN
ejpam-6741	72	2	are	be	AUX
ejpam-6741	72	3	not	not	PART
ejpam-6741	72	4	only	only	ADV
ejpam-6741	72	5	considered	consider	VERB
ejpam-6741	72	6	a	a	DET
ejpam-6741	72	7	fruitful	fruitful	ADJ
ejpam-6741	72	8	tool	tool	NOUN
ejpam-6741	72	9	for	for	ADP
ejpam-6741	72	10	the	the	DET
ejpam-6741	72	11	simplification	simplification	NOUN
ejpam-6741	72	12	of	of	ADP
ejpam-6741	72	13	efes	efes	PROPN
ejpam-6741	72	14	but	but	CCONJ
ejpam-6741	72	15	are	be	AUX
ejpam-6741	72	16	also	also	ADV
ejpam-6741	72	17	helpful	helpful	ADJ
ejpam-6741	72	18	in	in	ADP
ejpam-6741	72	19	understanding	understand	VERB
ejpam-6741	72	20	singularity	singularity	NOUN
ejpam-6741	72	21	formation	formation	NOUN
ejpam-6741	72	22	.	.	PUNCT
ejpam-6741	73	1	they	they	PRON
ejpam-6741	73	2	establish	establish	VERB
ejpam-6741	73	3	a	a	DET
ejpam-6741	73	4	relationship	relationship	NOUN
ejpam-6741	73	5	between	between	ADP
ejpam-6741	73	6	physical	physical	ADJ
ejpam-6741	73	7	spacetime	spacetime	NOUN
ejpam-6741	73	8	models	model	NOUN
ejpam-6741	73	9	and	and	CCONJ
ejpam-6741	73	10	theoretical	theoretical	ADJ
ejpam-6741	73	11	geometric	geometric	ADJ
ejpam-6741	73	12	flows	flow	NOUN
ejpam-6741	73	13	,	,	PUNCT
ejpam-6741	73	14	providing	provide	VERB
ejpam-6741	73	15	a	a	DET
ejpam-6741	73	16	framework	framework	NOUN
ejpam-6741	73	17	for	for	ADP
ejpam-6741	73	18	exploring	explore	VERB
ejpam-6741	73	19	u.	u.	PROPN
ejpam-6741	73	20	nasib	nasib	PROPN
ejpam-6741	73	21	et	et	PROPN
ejpam-6741	73	22	al	al	PROPN
ejpam-6741	73	23	.	.	PUNCT
ejpam-6741	73	24	/	/	SYM
ejpam-6741	73	25	eur	eur	PROPN
ejpam-6741	73	26	.	.	PUNCT
ejpam-6741	74	1	j.	j.	PROPN
ejpam-6741	74	2	pure	pure	PROPN
ejpam-6741	74	3	appl	appl	PROPN
ejpam-6741	74	4	.	.	PROPN
ejpam-6741	74	5	math	math	PROPN
ejpam-6741	74	6	,	,	PUNCT
ejpam-6741	74	7	18	18	NUM
ejpam-6741	74	8	(	(	PUNCT
ejpam-6741	74	9	4	4	NUM
ejpam-6741	74	10	)	)	PUNCT
ejpam-6741	74	11	(	(	PUNCT
ejpam-6741	74	12	2025	2025	NUM
ejpam-6741	74	13	)	)	PUNCT
ejpam-6741	74	14	,	,	PUNCT
ejpam-6741	74	15	6741	6741	NUM
ejpam-6741	74	16	4	4	NUM
ejpam-6741	74	17	of	of	ADP
ejpam-6741	74	18	14	14	NUM
ejpam-6741	74	19	fundamental	fundamental	ADJ
ejpam-6741	74	20	questions	question	NOUN
ejpam-6741	74	21	in	in	ADP
ejpam-6741	74	22	both	both	DET
ejpam-6741	74	23	mathematics	mathematic	NOUN
ejpam-6741	74	24	and	and	CCONJ
ejpam-6741	74	25	theoretical	theoretical	ADJ
ejpam-6741	74	26	physics	physics	NOUN
ejpam-6741	74	27	.	.	PUNCT
ejpam-6741	75	1	another	another	DET
ejpam-6741	75	2	important	important	ADJ
ejpam-6741	75	3	feature	feature	NOUN
ejpam-6741	75	4	of	of	ADP
ejpam-6741	75	5	rsvfs	rsvfs	NOUN
ejpam-6741	75	6	is	be	AUX
ejpam-6741	75	7	that	that	SCONJ
ejpam-6741	75	8	when	when	SCONJ
ejpam-6741	75	9	they	they	PRON
ejpam-6741	75	10	reduce	reduce	VERB
ejpam-6741	75	11	to	to	ADP
ejpam-6741	75	12	an	an	DET
ejpam-6741	75	13	einstein	einstein	PROPN
ejpam-6741	75	14	tensor	tensor	NOUN
ejpam-6741	75	15	,	,	PUNCT
ejpam-6741	75	16	they	they	PRON
ejpam-6741	75	17	provide	provide	VERB
ejpam-6741	75	18	a	a	DET
ejpam-6741	75	19	solution	solution	NOUN
ejpam-6741	75	20	to	to	ADP
ejpam-6741	75	21	the	the	DET
ejpam-6741	75	22	efes	efe	NOUN
ejpam-6741	75	23	with	with	ADP
ejpam-6741	75	24	a	a	DET
ejpam-6741	75	25	cosmological	cosmological	ADJ
ejpam-6741	75	26	constant	constant	NOUN
ejpam-6741	75	27	,	,	PUNCT
ejpam-6741	75	28	which	which	PRON
ejpam-6741	75	29	makes	make	VERB
ejpam-6741	75	30	them	they	PRON
ejpam-6741	75	31	beneficial	beneficial	ADJ
ejpam-6741	75	32	for	for	ADP
ejpam-6741	75	33	investigating	investigate	VERB
ejpam-6741	75	34	various	various	ADJ
ejpam-6741	75	35	cosmological	cosmological	ADJ
ejpam-6741	75	36	models	model	NOUN
ejpam-6741	75	37	.	.	PUNCT
ejpam-6741	76	1	furthermore	furthermore	ADV
ejpam-6741	76	2	,	,	PUNCT
ejpam-6741	76	3	ricci	ricci	PROPN
ejpam-6741	76	4	solitons	soliton	NOUN
ejpam-6741	76	5	are	be	AUX
ejpam-6741	76	6	important	important	ADJ
ejpam-6741	76	7	for	for	ADP
ejpam-6741	76	8	examining	examine	VERB
ejpam-6741	76	9	how	how	SCONJ
ejpam-6741	76	10	spacetime	spacetime	NOUN
ejpam-6741	76	11	evolves	evolve	VERB
ejpam-6741	76	12	.	.	PUNCT
ejpam-6741	77	1	for	for	ADP
ejpam-6741	77	2	example	example	NOUN
ejpam-6741	77	3	,	,	PUNCT
ejpam-6741	77	4	they	they	PRON
ejpam-6741	77	5	can	can	AUX
ejpam-6741	77	6	help	help	VERB
ejpam-6741	77	7	analyze	analyze	VERB
ejpam-6741	77	8	how	how	SCONJ
ejpam-6741	77	9	the	the	DET
ejpam-6741	77	10	ricci	ricci	PROPN
ejpam-6741	77	11	flow	flow	NOUN
ejpam-6741	77	12	affects	affect	VERB
ejpam-6741	77	13	the	the	DET
ejpam-6741	77	14	spacetime	spacetime	ADJ
ejpam-6741	77	15	structure	structure	NOUN
ejpam-6741	77	16	over	over	ADP
ejpam-6741	77	17	time	time	NOUN
ejpam-6741	77	18	.	.	PUNCT
ejpam-6741	78	1	they	they	PRON
ejpam-6741	78	2	are	be	AUX
ejpam-6741	78	3	also	also	ADV
ejpam-6741	78	4	significant	significant	ADJ
ejpam-6741	78	5	for	for	ADP
ejpam-6741	78	6	observing	observe	VERB
ejpam-6741	78	7	how	how	SCONJ
ejpam-6741	78	8	a	a	DET
ejpam-6741	78	9	manifold	manifold	ADJ
ejpam-6741	78	10	behaves	behave	NOUN
ejpam-6741	78	11	under	under	ADP
ejpam-6741	78	12	the	the	DET
ejpam-6741	78	13	flow	flow	NOUN
ejpam-6741	78	14	and	and	CCONJ
ejpam-6741	78	15	can	can	AUX
ejpam-6741	78	16	offer	offer	VERB
ejpam-6741	78	17	insights	insight	NOUN
ejpam-6741	78	18	into	into	ADP
ejpam-6741	78	19	the	the	DET
ejpam-6741	78	20	flow	flow	NOUN
ejpam-6741	78	21	’s	’s	PART
ejpam-6741	78	22	behavior	behavior	NOUN
ejpam-6741	78	23	near	near	ADP
ejpam-6741	78	24	singularities	singularity	NOUN
ejpam-6741	78	25	.	.	PUNCT
ejpam-6741	79	1	drawing	draw	VERB
ejpam-6741	79	2	inspiration	inspiration	NOUN
ejpam-6741	79	3	from	from	ADP
ejpam-6741	79	4	the	the	DET
ejpam-6741	79	5	existing	exist	VERB
ejpam-6741	79	6	literature	literature	NOUN
ejpam-6741	79	7	and	and	CCONJ
ejpam-6741	79	8	the	the	DET
ejpam-6741	79	9	identified	identify	VERB
ejpam-6741	79	10	gap	gap	NOUN
ejpam-6741	79	11	in	in	ADP
ejpam-6741	79	12	methodology	methodology	NOUN
ejpam-6741	79	13	,	,	PUNCT
ejpam-6741	79	14	the	the	DET
ejpam-6741	79	15	objective	objective	NOUN
ejpam-6741	79	16	of	of	ADP
ejpam-6741	79	17	this	this	DET
ejpam-6741	79	18	paper	paper	NOUN
ejpam-6741	79	19	is	be	AUX
ejpam-6741	79	20	to	to	PART
ejpam-6741	79	21	present	present	VERB
ejpam-6741	79	22	a	a	DET
ejpam-6741	79	23	complete	complete	ADJ
ejpam-6741	79	24	and	and	CCONJ
ejpam-6741	79	25	exhaustive	exhaustive	ADJ
ejpam-6741	79	26	classification	classification	NOUN
ejpam-6741	79	27	of	of	ADP
ejpam-6741	79	28	ricci	ricci	PROPN
ejpam-6741	79	29	solitons	soliton	NOUN
ejpam-6741	79	30	in	in	ADP
ejpam-6741	79	31	the	the	DET
ejpam-6741	79	32	context	context	NOUN
ejpam-6741	79	33	of	of	ADP
ejpam-6741	79	34	lrs	lrs	PROPN
ejpam-6741	79	35	bianchi	bianchi	PROPN
ejpam-6741	79	36	type	type	NOUN
ejpam-6741	79	37	i	i	PRON
ejpam-6741	79	38	spacetime	spacetime	VERB
ejpam-6741	79	39	within	within	ADP
ejpam-6741	79	40	the	the	DET
ejpam-6741	79	41	framework	framework	NOUN
ejpam-6741	79	42	of	of	ADP
ejpam-6741	79	43	gr	gr	PROPN
ejpam-6741	79	44	,	,	PUNCT
ejpam-6741	79	45	by	by	ADP
ejpam-6741	79	46	adopting	adopt	VERB
ejpam-6741	79	47	the	the	DET
ejpam-6741	79	48	innovative	innovative	ADJ
ejpam-6741	79	49	rif	rif	PROPN
ejpam-6741	79	50	tree	tree	NOUN
ejpam-6741	79	51	approach	approach	NOUN
ejpam-6741	79	52	.	.	PUNCT
ejpam-6741	80	1	2	2	X
ejpam-6741	80	2	.	.	X
ejpam-6741	80	3	ricci	ricci	PROPN
ejpam-6741	80	4	soliton	soliton	PROPN
ejpam-6741	80	5	equations	equation	NOUN
ejpam-6741	80	6	the	the	DET
ejpam-6741	80	7	line	line	NOUN
ejpam-6741	80	8	element	element	NOUN
ejpam-6741	80	9	for	for	ADP
ejpam-6741	80	10	lrs	lrs	PROPN
ejpam-6741	80	11	bianchi	bianchi	PROPN
ejpam-6741	80	12	type	type	NOUN
ejpam-6741	80	13	i	i	PRON
ejpam-6741	80	14	spacetime	spacetime	NOUN
ejpam-6741	80	15	is	be	AUX
ejpam-6741	80	16	given	give	VERB
ejpam-6741	80	17	as	as	ADP
ejpam-6741	80	18	:	:	PUNCT
ejpam-6741	80	19	ds2	ds2	PROPN
ejpam-6741	80	20	=	=	SYM
ejpam-6741	80	21	−dt2	−dt2	SYM
ejpam-6741	80	22	+	+	CCONJ
ejpam-6741	80	23	p2(t	p2(t	PROPN
ejpam-6741	80	24	)	)	PUNCT
ejpam-6741	80	25	dx2	dx2	NOUN
ejpam-6741	80	26	+	+	CCONJ
ejpam-6741	80	27	q2(t	q2(t	PROPN
ejpam-6741	80	28	)	)	PUNCT
ejpam-6741	80	29	(	(	PUNCT
ejpam-6741	80	30	dy2	dy2	PROPN
ejpam-6741	80	31	+	+	CCONJ
ejpam-6741	80	32	dz2	dz2	NOUN
ejpam-6741	80	33	)	)	PUNCT
ejpam-6741	80	34	,	,	PUNCT
ejpam-6741	80	35	(	(	PUNCT
ejpam-6741	80	36	2	2	X
ejpam-6741	80	37	)	)	PUNCT
ejpam-6741	80	38	where	where	SCONJ
ejpam-6741	80	39	p	p	PRON
ejpam-6741	80	40	̸=	̸=	PROPN
ejpam-6741	80	41	0	0	NUM
ejpam-6741	80	42	and	and	CCONJ
ejpam-6741	80	43	q	q	ADJ
ejpam-6741	80	44	̸=	̸=	PROPN
ejpam-6741	80	45	0	0	NUM
ejpam-6741	80	46	.	.	PUNCT
ejpam-6741	81	1	the	the	DET
ejpam-6741	81	2	set	set	NOUN
ejpam-6741	81	3	{	{	PUNCT
ejpam-6741	81	4	∂x	∂x	PROPN
ejpam-6741	81	5	,	,	PUNCT
ejpam-6741	81	6	∂y	∂y	PROPN
ejpam-6741	81	7	,	,	PUNCT
ejpam-6741	81	8	∂z	∂z	PROPN
ejpam-6741	81	9	,	,	PUNCT
ejpam-6741	81	10	y∂z	y∂z	X
ejpam-6741	81	11	−	−	PROPN
ejpam-6741	81	12	z∂y	z∂y	NOUN
ejpam-6741	81	13	}	}	PUNCT
ejpam-6741	81	14	represents	represent	VERB
ejpam-6741	81	15	the	the	DET
ejpam-6741	81	16	minimal	minimal	ADJ
ejpam-6741	81	17	set	set	NOUN
ejpam-6741	81	18	of	of	ADP
ejpam-6741	81	19	killing	kill	VERB
ejpam-6741	81	20	vector	vector	NOUN
ejpam-6741	81	21	fields	field	NOUN
ejpam-6741	81	22	(	(	PUNCT
ejpam-6741	81	23	kvfs	kvfs	NOUN
ejpam-6741	81	24	)	)	PUNCT
ejpam-6741	81	25	possessed	possess	VERB
ejpam-6741	81	26	by	by	ADP
ejpam-6741	81	27	the	the	DET
ejpam-6741	81	28	above	above	ADJ
ejpam-6741	81	29	spacetime	spacetime	NOUN
ejpam-6741	81	30	.	.	PUNCT
ejpam-6741	82	1	the	the	DET
ejpam-6741	82	2	following	follow	VERB
ejpam-6741	82	3	expressions	expression	NOUN
ejpam-6741	82	4	demonstrate	demonstrate	VERB
ejpam-6741	82	5	the	the	DET
ejpam-6741	82	6	non	non	ADJ
ejpam-6741	82	7	-	-	ADJ
ejpam-6741	82	8	vanishing	vanishing	ADJ
ejpam-6741	82	9	components	component	NOUN
ejpam-6741	82	10	of	of	ADP
ejpam-6741	82	11	rmn	rmn	PROPN
ejpam-6741	82	12	:	:	PUNCT
ejpam-6741	82	13	r00	r00	NOUN
ejpam-6741	82	14	=	=	SYM
ejpam-6741	82	15	−	−	PROPN
ejpam-6741	82	16	1	1	NUM
ejpam-6741	82	17	pq	pq	NOUN
ejpam-6741	82	18	{	{	PUNCT
ejpam-6741	82	19	p′′q	p′′q	PROPN
ejpam-6741	82	20	+	+	CCONJ
ejpam-6741	82	21	2q′′p	2q′′p	NUM
ejpam-6741	82	22	}	}	PUNCT
ejpam-6741	82	23	,	,	PUNCT
ejpam-6741	82	24	r11	r11	NOUN
ejpam-6741	82	25	=	=	SYM
ejpam-6741	82	26	p	p	NOUN
ejpam-6741	82	27	q	q	X
ejpam-6741	82	28	{	{	PUNCT
ejpam-6741	82	29	p′′q	p′′q	NOUN
ejpam-6741	82	30	+	+	CCONJ
ejpam-6741	83	1	2p′q′	2p′q′	NUM
ejpam-6741	83	2	}	}	PUNCT
ejpam-6741	83	3	,	,	PUNCT
ejpam-6741	83	4	r22	r22	NOUN
ejpam-6741	83	5	=	=	SYM
ejpam-6741	83	6	1	1	NUM
ejpam-6741	83	7	p	p	NOUN
ejpam-6741	83	8	{	{	PUNCT
ejpam-6741	83	9	pqq′′	pqq′′	PROPN
ejpam-6741	83	10	+	+	CCONJ
ejpam-6741	83	11	pq′2	pq′2	NOUN
ejpam-6741	83	12	+	+	CCONJ
ejpam-6741	83	13	qp′q′	qp′q′	ADJ
ejpam-6741	83	14	}	}	PUNCT
ejpam-6741	83	15	,	,	PUNCT
ejpam-6741	83	16	r33	r33	NUM
ejpam-6741	83	17	=	=	SYM
ejpam-6741	83	18	r22	r22	NOUN
ejpam-6741	83	19	.	.	PUNCT
ejpam-6741	84	1	(	(	PUNCT
ejpam-6741	84	2	3	3	X
ejpam-6741	84	3	)	)	PUNCT
ejpam-6741	84	4	substituting	substitute	VERB
ejpam-6741	84	5	the	the	DET
ejpam-6741	84	6	metric	metric	ADJ
ejpam-6741	84	7	tensor	tensor	NOUN
ejpam-6741	84	8	from	from	ADP
ejpam-6741	84	9	eq	eq	PROPN
ejpam-6741	84	10	.	.	PUNCT
ejpam-6741	85	1	(	(	PUNCT
ejpam-6741	85	2	2	2	NUM
ejpam-6741	85	3	)	)	PUNCT
ejpam-6741	85	4	along	along	ADP
ejpam-6741	85	5	with	with	ADP
ejpam-6741	85	6	the	the	DET
ejpam-6741	85	7	components	component	NOUN
ejpam-6741	85	8	of	of	ADP
ejpam-6741	85	9	rmn	rmn	PROPN
ejpam-6741	85	10	from	from	ADP
ejpam-6741	85	11	eq	eq	PROPN
ejpam-6741	85	12	.	.	PUNCT
ejpam-6741	86	1	(	(	PUNCT
ejpam-6741	86	2	3	3	X
ejpam-6741	86	3	)	)	PUNCT
ejpam-6741	86	4	into	into	ADP
ejpam-6741	86	5	eq	eq	NOUN
ejpam-6741	86	6	.	.	PUNCT
ejpam-6741	87	1	(	(	PUNCT
ejpam-6741	87	2	1	1	X
ejpam-6741	87	3	)	)	PUNCT
ejpam-6741	87	4	results	result	NOUN
ejpam-6741	87	5	in	in	ADP
ejpam-6741	87	6	the	the	DET
ejpam-6741	87	7	following	follow	VERB
ejpam-6741	87	8	system	system	NOUN
ejpam-6741	87	9	of	of	ADP
ejpam-6741	87	10	differential	differential	ADJ
ejpam-6741	87	11	equations	equation	NOUN
ejpam-6741	87	12	:	:	PUNCT
ejpam-6741	87	13	v	v	NOUN
ejpam-6741	87	14	0	0	NUM
ejpam-6741	87	15	,	,	PUNCT
ejpam-6741	87	16	0	0	NUM
ejpam-6741	87	17	=	=	SYM
ejpam-6741	87	18	δ	δ	PROPN
ejpam-6741	87	19	+	+	NOUN
ejpam-6741	87	20	r00	r00	ADJ
ejpam-6741	87	21	,	,	PUNCT
ejpam-6741	87	22	(	(	PUNCT
ejpam-6741	87	23	4	4	X
ejpam-6741	87	24	)	)	PUNCT
ejpam-6741	87	25	p2v	p2v	PROPN
ejpam-6741	87	26	1	1	NUM
ejpam-6741	87	27	,	,	PUNCT
ejpam-6741	87	28	0	0	NUM
ejpam-6741	87	29	−	−	NOUN
ejpam-6741	87	30	v	v	NOUN
ejpam-6741	87	31	0	0	NUM
ejpam-6741	87	32	,	,	PUNCT
ejpam-6741	87	33	1	1	NUM
ejpam-6741	87	34	=	=	SYM
ejpam-6741	87	35	0	0	NUM
ejpam-6741	87	36	,	,	PUNCT
ejpam-6741	87	37	(	(	PUNCT
ejpam-6741	87	38	5	5	NUM
ejpam-6741	87	39	)	)	PUNCT
ejpam-6741	87	40	q2v	q2v	CCONJ
ejpam-6741	87	41	2	2	NUM
ejpam-6741	87	42	,	,	PUNCT
ejpam-6741	87	43	0	0	NUM
ejpam-6741	87	44	−	−	NOUN
ejpam-6741	87	45	v	v	NOUN
ejpam-6741	87	46	0	0	NUM
ejpam-6741	87	47	,	,	PUNCT
ejpam-6741	87	48	2	2	NUM
ejpam-6741	87	49	=	=	SYM
ejpam-6741	87	50	0	0	NUM
ejpam-6741	87	51	,	,	PUNCT
ejpam-6741	87	52	(	(	PUNCT
ejpam-6741	87	53	6	6	NUM
ejpam-6741	87	54	)	)	PUNCT
ejpam-6741	87	55	q2v	q2v	CCONJ
ejpam-6741	87	56	3	3	NUM
ejpam-6741	87	57	,	,	PUNCT
ejpam-6741	87	58	0	0	NUM
ejpam-6741	87	59	−	−	NOUN
ejpam-6741	87	60	v	v	NOUN
ejpam-6741	87	61	0	0	NUM
ejpam-6741	87	62	,	,	PUNCT
ejpam-6741	87	63	3	3	NUM
ejpam-6741	87	64	=	=	SYM
ejpam-6741	87	65	0	0	NUM
ejpam-6741	87	66	,	,	PUNCT
ejpam-6741	87	67	(	(	PUNCT
ejpam-6741	87	68	7	7	X
ejpam-6741	87	69	)	)	PUNCT
ejpam-6741	87	70	v	v	NOUN
ejpam-6741	87	71	1	1	NUM
ejpam-6741	87	72	,	,	PUNCT
ejpam-6741	87	73	1	1	NUM
ejpam-6741	87	74	+	+	NUM
ejpam-6741	87	75	p′	p′	NOUN
ejpam-6741	87	76	p	p	X
ejpam-6741	87	77	v	v	ADP
ejpam-6741	87	78	0	0	NUM
ejpam-6741	88	1	=	=	SYM
ejpam-6741	88	2	δ	δ	NOUN
ejpam-6741	88	3	−	−	NOUN
ejpam-6741	88	4	1	1	NUM
ejpam-6741	88	5	p2	p2	PROPN
ejpam-6741	88	6	r11	r11	NOUN
ejpam-6741	88	7	,	,	PUNCT
ejpam-6741	88	8	(	(	PUNCT
ejpam-6741	88	9	8)	8)	NUM
ejpam-6741	88	10	p2	p2	NOUN
ejpam-6741	88	11	v	v	ADP
ejpam-6741	88	12	1	1	NUM
ejpam-6741	88	13	,	,	PUNCT
ejpam-6741	88	14	2	2	NUM
ejpam-6741	88	15	+	+	NUM
ejpam-6741	88	16	q2	q2	NOUN
ejpam-6741	88	17	v	v	ADP
ejpam-6741	88	18	2	2	NUM
ejpam-6741	88	19	,	,	PUNCT
ejpam-6741	88	20	1	1	NUM
ejpam-6741	88	21	=	=	SYM
ejpam-6741	88	22	0	0	NUM
ejpam-6741	88	23	,	,	PUNCT
ejpam-6741	88	24	(	(	PUNCT
ejpam-6741	88	25	9	9	X
ejpam-6741	88	26	)	)	PUNCT
ejpam-6741	88	27	p2	p2	NOUN
ejpam-6741	88	28	v	v	ADP
ejpam-6741	88	29	1	1	NUM
ejpam-6741	88	30	,	,	PUNCT
ejpam-6741	88	31	3	3	NUM
ejpam-6741	88	32	+	+	CCONJ
ejpam-6741	88	33	q2v	q2v	CCONJ
ejpam-6741	88	34	3	3	NUM
ejpam-6741	88	35	,	,	PUNCT
ejpam-6741	88	36	1	1	NUM
ejpam-6741	88	37	=	=	SYM
ejpam-6741	88	38	0	0	NUM
ejpam-6741	88	39	,	,	PUNCT
ejpam-6741	88	40	(	(	PUNCT
ejpam-6741	88	41	10	10	NUM
ejpam-6741	88	42	)	)	PUNCT
ejpam-6741	88	43	v	v	ADP
ejpam-6741	88	44	2	2	NUM
ejpam-6741	88	45	,	,	PUNCT
ejpam-6741	88	46	2	2	NUM
ejpam-6741	88	47	+	+	NUM
ejpam-6741	88	48	q′	q′	NOUN
ejpam-6741	88	49	q	q	NOUN
ejpam-6741	88	50	v	v	NOUN
ejpam-6741	88	51	0	0	NUM
ejpam-6741	88	52	=	=	SYM
ejpam-6741	88	53	δ	δ	NOUN
ejpam-6741	88	54	−	−	NUM
ejpam-6741	88	55	1	1	NUM
ejpam-6741	88	56	q2	q2	NOUN
ejpam-6741	88	57	r22	r22	NOUN
ejpam-6741	88	58	,	,	PUNCT
ejpam-6741	88	59	(	(	PUNCT
ejpam-6741	88	60	11	11	NUM
ejpam-6741	88	61	)	)	PUNCT
ejpam-6741	88	62	u.	u.	NOUN
ejpam-6741	88	63	nasib	nasib	PROPN
ejpam-6741	88	64	et	et	PROPN
ejpam-6741	88	65	al	al	PROPN
ejpam-6741	88	66	.	.	PUNCT
ejpam-6741	88	67	/	/	SYM
ejpam-6741	88	68	eur	eur	PROPN
ejpam-6741	88	69	.	.	PUNCT
ejpam-6741	89	1	j.	j.	PROPN
ejpam-6741	89	2	pure	pure	PROPN
ejpam-6741	89	3	appl	appl	PROPN
ejpam-6741	89	4	.	.	PROPN
ejpam-6741	89	5	math	math	PROPN
ejpam-6741	89	6	,	,	PUNCT
ejpam-6741	89	7	18	18	NUM
ejpam-6741	89	8	(	(	PUNCT
ejpam-6741	89	9	4	4	NUM
ejpam-6741	89	10	)	)	PUNCT
ejpam-6741	89	11	(	(	PUNCT
ejpam-6741	89	12	2025	2025	NUM
ejpam-6741	89	13	)	)	PUNCT
ejpam-6741	89	14	,	,	PUNCT
ejpam-6741	89	15	6741	6741	NUM
ejpam-6741	89	16	5	5	NUM
ejpam-6741	89	17	of	of	ADP
ejpam-6741	89	18	14	14	NUM
ejpam-6741	89	19	v	v	NUM
ejpam-6741	89	20	2	2	NUM
ejpam-6741	89	21	,	,	PUNCT
ejpam-6741	89	22	3	3	NUM
ejpam-6741	89	23	+	+	SYM
ejpam-6741	89	24	v	v	NUM
ejpam-6741	89	25	3	3	NUM
ejpam-6741	89	26	,	,	PUNCT
ejpam-6741	89	27	2	2	NUM
ejpam-6741	89	28	=	=	SYM
ejpam-6741	89	29	0	0	NUM
ejpam-6741	89	30	,	,	PUNCT
ejpam-6741	89	31	(	(	PUNCT
ejpam-6741	89	32	12	12	NUM
ejpam-6741	89	33	)	)	PUNCT
ejpam-6741	89	34	v	v	ADP
ejpam-6741	89	35	3	3	NUM
ejpam-6741	89	36	,	,	PUNCT
ejpam-6741	89	37	3	3	NUM
ejpam-6741	89	38	+	+	NUM
ejpam-6741	89	39	q′	q′	NOUN
ejpam-6741	89	40	q	q	NOUN
ejpam-6741	89	41	v	v	NOUN
ejpam-6741	89	42	0	0	NUM
ejpam-6741	89	43	=	=	SYM
ejpam-6741	89	44	δ	δ	NOUN
ejpam-6741	89	45	−	−	NUM
ejpam-6741	89	46	1	1	NUM
ejpam-6741	89	47	q2	q2	NOUN
ejpam-6741	89	48	r22	r22	NOUN
ejpam-6741	89	49	.	.	PUNCT
ejpam-6741	90	1	(	(	PUNCT
ejpam-6741	90	2	13	13	NUM
ejpam-6741	90	3	)	)	PUNCT
ejpam-6741	90	4	we	we	PRON
ejpam-6741	90	5	begin	begin	VERB
ejpam-6741	90	6	by	by	ADP
ejpam-6741	90	7	analyzing	analyze	VERB
ejpam-6741	90	8	the	the	DET
ejpam-6741	90	9	system	system	NOUN
ejpam-6741	90	10	of	of	ADP
ejpam-6741	90	11	rsvf	rsvf	ADJ
ejpam-6741	90	12	equations	equation	NOUN
ejpam-6741	90	13	(	(	PUNCT
ejpam-6741	90	14	eqs	eqs	X
ejpam-6741	90	15	.	.	PROPN
ejpam-6741	90	16	4	4	NUM
ejpam-6741	90	17	-	-	SYM
ejpam-6741	90	18	13	13	NUM
ejpam-6741	90	19	)	)	PUNCT
ejpam-6741	90	20	using	use	VERB
ejpam-6741	90	21	the	the	DET
ejpam-6741	90	22	rif	rif	PROPN
ejpam-6741	90	23	algorithm	algorithm	NOUN
ejpam-6741	90	24	through	through	ADP
ejpam-6741	90	25	maple	maple	NOUN
ejpam-6741	90	26	software	software	NOUN
ejpam-6741	90	27	,	,	PUNCT
ejpam-6741	90	28	which	which	PRON
ejpam-6741	90	29	produces	produce	VERB
ejpam-6741	90	30	the	the	DET
ejpam-6741	90	31	rif	rif	PROPN
ejpam-6741	90	32	tree	tree	NOUN
ejpam-6741	90	33	shown	show	VERB
ejpam-6741	90	34	in	in	ADP
ejpam-6741	90	35	fig	fig	NOUN
ejpam-6741	90	36	.	.	PUNCT
ejpam-6741	91	1	(	(	PUNCT
ejpam-6741	91	2	1	1	NUM
ejpam-6741	91	3	)	)	PUNCT
ejpam-6741	91	4	.	.	PUNCT
ejpam-6741	92	1	the	the	DET
ejpam-6741	92	2	rif	rif	PROPN
ejpam-6741	92	3	algorithm	algorithm	PROPN
ejpam-6741	92	4	not	not	PART
ejpam-6741	92	5	only	only	ADV
ejpam-6741	92	6	simplifies	simplify	VERB
ejpam-6741	92	7	the	the	DET
ejpam-6741	92	8	system	system	NOUN
ejpam-6741	92	9	but	but	CCONJ
ejpam-6741	92	10	also	also	ADV
ejpam-6741	92	11	identifies	identify	VERB
ejpam-6741	92	12	and	and	CCONJ
ejpam-6741	92	13	prunes	prune	NOUN
ejpam-6741	92	14	branches	branch	NOUN
ejpam-6741	92	15	that	that	PRON
ejpam-6741	92	16	lead	lead	VERB
ejpam-6741	92	17	to	to	ADP
ejpam-6741	92	18	mathematical	mathematical	ADJ
ejpam-6741	92	19	inconsistencies	inconsistency	NOUN
ejpam-6741	92	20	(	(	PUNCT
ejpam-6741	92	21	e.g.	e.g.	ADV
ejpam-6741	92	22	,	,	PUNCT
ejpam-6741	92	23	a	a	DET
ejpam-6741	92	24	condition	condition	NOUN
ejpam-6741	92	25	that	that	PRON
ejpam-6741	92	26	implies	imply	VERB
ejpam-6741	92	27	p′	p′	NOUN
ejpam-6741	92	28	=	=	SYM
ejpam-6741	92	29	0	0	PUNCT
ejpam-6741	92	30	while	while	SCONJ
ejpam-6741	92	31	another	another	DET
ejpam-6741	92	32	condition	condition	NOUN
ejpam-6741	92	33	in	in	ADP
ejpam-6741	92	34	the	the	DET
ejpam-6741	92	35	same	same	ADJ
ejpam-6741	92	36	branch	branch	NOUN
ejpam-6741	92	37	implies	imply	VERB
ejpam-6741	92	38	p′	p′	NOUN
ejpam-6741	92	39	̸=	̸=	PROPN
ejpam-6741	92	40	0	0	NUM
ejpam-6741	92	41	)	)	PUNCT
ejpam-6741	92	42	.	.	PUNCT
ejpam-6741	93	1	these	these	DET
ejpam-6741	93	2	inconsistent	inconsistent	ADJ
ejpam-6741	93	3	branches	branch	NOUN
ejpam-6741	93	4	are	be	AUX
ejpam-6741	93	5	shown	show	VERB
ejpam-6741	93	6	in	in	ADP
ejpam-6741	93	7	the	the	DET
ejpam-6741	93	8	tree	tree	NOUN
ejpam-6741	93	9	(	(	PUNCT
ejpam-6741	93	10	fig	fig	NOUN
ejpam-6741	93	11	.	.	NOUN
ejpam-6741	94	1	1	1	NUM
ejpam-6741	94	2	)	)	PUNCT
ejpam-6741	94	3	as	as	ADP
ejpam-6741	94	4	terminating	terminate	VERB
ejpam-6741	94	5	without	without	ADP
ejpam-6741	94	6	further	further	ADJ
ejpam-6741	94	7	subdivision	subdivision	NOUN
ejpam-6741	94	8	(	(	PUNCT
ejpam-6741	94	9	often	often	ADV
ejpam-6741	94	10	marked	mark	VERB
ejpam-6741	94	11	as	as	ADP
ejpam-6741	94	12	”	"	PUNCT
ejpam-6741	94	13	0	0	NUM
ejpam-6741	94	14	=	=	SYM
ejpam-6741	94	15	1	1	NUM
ejpam-6741	94	16	”	"	PUNCT
ejpam-6741	94	17	or	or	CCONJ
ejpam-6741	94	18	similar	similar	ADJ
ejpam-6741	94	19	in	in	ADP
ejpam-6741	94	20	maple	maple	NOUN
ejpam-6741	94	21	’s	’s	PART
ejpam-6741	94	22	output	output	NOUN
ejpam-6741	94	23	)	)	PUNCT
ejpam-6741	94	24	.	.	PUNCT
ejpam-6741	95	1	the	the	DET
ejpam-6741	95	2	branches	branch	NOUN
ejpam-6741	95	3	presented	present	VERB
ejpam-6741	95	4	in	in	ADP
ejpam-6741	95	5	the	the	DET
ejpam-6741	95	6	figure	figure	NOUN
ejpam-6741	95	7	are	be	AUX
ejpam-6741	95	8	the	the	DET
ejpam-6741	95	9	consistent	consistent	ADJ
ejpam-6741	95	10	,	,	PUNCT
ejpam-6741	95	11	non	non	ADJ
ejpam-6741	95	12	-	-	ADJ
ejpam-6741	95	13	singular	singular	ADJ
ejpam-6741	95	14	cases	case	NOUN
ejpam-6741	95	15	that	that	PRON
ejpam-6741	95	16	require	require	VERB
ejpam-6741	95	17	further	further	ADJ
ejpam-6741	95	18	analysis	analysis	NOUN
ejpam-6741	95	19	.	.	PUNCT
ejpam-6741	96	1	the	the	DET
ejpam-6741	96	2	pivots	pivot	NOUN
ejpam-6741	96	3	leading	lead	VERB
ejpam-6741	96	4	to	to	ADP
ejpam-6741	96	5	these	these	DET
ejpam-6741	96	6	dead	dead	ADJ
ejpam-6741	96	7	ends	end	NOUN
ejpam-6741	96	8	are	be	AUX
ejpam-6741	96	9	not	not	PART
ejpam-6741	96	10	listed	list	VERB
ejpam-6741	96	11	in	in	ADP
ejpam-6741	96	12	equation	equation	NOUN
ejpam-6741	96	13	(	(	PUNCT
ejpam-6741	96	14	14	14	NUM
ejpam-6741	96	15	)	)	PUNCT
ejpam-6741	96	16	as	as	SCONJ
ejpam-6741	96	17	they	they	PRON
ejpam-6741	96	18	are	be	AUX
ejpam-6741	96	19	automatically	automatically	ADV
ejpam-6741	96	20	discarded	discard	VERB
ejpam-6741	96	21	by	by	ADP
ejpam-6741	96	22	the	the	DET
ejpam-6741	96	23	algorithm	algorithm	NOUN
ejpam-6741	96	24	.	.	PUNCT
ejpam-6741	97	1	each	each	DET
ejpam-6741	97	2	branch	branch	NOUN
ejpam-6741	97	3	of	of	ADP
ejpam-6741	97	4	the	the	DET
ejpam-6741	97	5	rif	rif	PROPN
ejpam-6741	97	6	tree	tree	NOUN
ejpam-6741	97	7	includes	include	VERB
ejpam-6741	97	8	nodes	node	NOUN
ejpam-6741	97	9	labeled	label	VERB
ejpam-6741	97	10	p1	p1	NOUN
ejpam-6741	97	11	,	,	PUNCT
ejpam-6741	97	12	p2	p2	NOUN
ejpam-6741	97	13	,	,	PUNCT
ejpam-6741	97	14	p3	p3	PROPN
ejpam-6741	97	15	,	,	PUNCT
ejpam-6741	97	16	...	...	PUNCT
ejpam-6741	97	17	,	,	PUNCT
ejpam-6741	97	18	p10	p10	PROPN
ejpam-6741	97	19	,	,	PUNCT
ejpam-6741	97	20	known	know	VERB
ejpam-6741	97	21	as	as	ADP
ejpam-6741	97	22	pivots	pivot	NOUN
ejpam-6741	97	23	,	,	PUNCT
ejpam-6741	97	24	with	with	ADP
ejpam-6741	97	25	their	their	PRON
ejpam-6741	97	26	expressions	expression	NOUN
ejpam-6741	97	27	listed	list	VERB
ejpam-6741	97	28	in	in	ADP
ejpam-6741	97	29	eq	eq	PROPN
ejpam-6741	97	30	.	.	PUNCT
ejpam-6741	98	1	(	(	PUNCT
ejpam-6741	98	2	14	14	NUM
ejpam-6741	98	3	)	)	PUNCT
ejpam-6741	98	4	.	.	PUNCT
ejpam-6741	99	1	these	these	DET
ejpam-6741	99	2	pivot	pivot	NOUN
ejpam-6741	99	3	expressions	expression	NOUN
ejpam-6741	99	4	demonstrate	demonstrate	VERB
ejpam-6741	99	5	the	the	DET
ejpam-6741	99	6	conditions	condition	NOUN
ejpam-6741	99	7	on	on	ADP
ejpam-6741	99	8	p	p	NOUN
ejpam-6741	99	9	and	and	CCONJ
ejpam-6741	99	10	q	q	PROPN
ejpam-6741	99	11	under	under	ADP
ejpam-6741	99	12	which	which	PRON
ejpam-6741	99	13	the	the	DET
ejpam-6741	99	14	rsvf	rsvf	PROPN
ejpam-6741	99	15	eqs	eqs	PROPN
ejpam-6741	99	16	.	.	PUNCT
ejpam-6741	100	1	(	(	PUNCT
ejpam-6741	100	2	4)-(13	4)-(13	X
ejpam-6741	100	3	)	)	PUNCT
ejpam-6741	100	4	are	be	AUX
ejpam-6741	100	5	required	require	VERB
ejpam-6741	100	6	to	to	PART
ejpam-6741	100	7	be	be	AUX
ejpam-6741	100	8	solved	solve	VERB
ejpam-6741	100	9	.	.	PUNCT
ejpam-6741	101	1	the	the	DET
ejpam-6741	101	2	solution	solution	NOUN
ejpam-6741	101	3	of	of	ADP
ejpam-6741	101	4	eqs	eqs	PROPN
ejpam-6741	101	5	.	.	PUNCT
ejpam-6741	101	6	(	(	PUNCT
ejpam-6741	101	7	4)-(13	4)-(13	NUM
ejpam-6741	101	8	)	)	PUNCT
ejpam-6741	101	9	,	,	PUNCT
ejpam-6741	101	10	based	base	VERB
ejpam-6741	101	11	on	on	ADP
ejpam-6741	101	12	the	the	DET
ejpam-6741	101	13	conditions	condition	NOUN
ejpam-6741	101	14	from	from	ADP
ejpam-6741	101	15	every	every	DET
ejpam-6741	101	16	branch	branch	NOUN
ejpam-6741	101	17	,	,	PUNCT
ejpam-6741	101	18	provides	provide	VERB
ejpam-6741	101	19	the	the	DET
ejpam-6741	101	20	precise	precise	ADJ
ejpam-6741	101	21	form	form	NOUN
ejpam-6741	101	22	of	of	ADP
ejpam-6741	101	23	the	the	DET
ejpam-6741	101	24	rsvfs	rsvfs	NOUN
ejpam-6741	101	25	.	.	PUNCT
ejpam-6741	102	1	moreover	moreover	ADV
ejpam-6741	102	2	,	,	PUNCT
ejpam-6741	102	3	in	in	ADP
ejpam-6741	102	4	the	the	DET
ejpam-6741	102	5	figure	figure	NOUN
ejpam-6741	102	6	,	,	PUNCT
ejpam-6741	102	7	the	the	DET
ejpam-6741	102	8	indications	indication	NOUN
ejpam-6741	102	9	”	"	PUNCT
ejpam-6741	102	10	=	=	SYM
ejpam-6741	102	11	”	"	PUNCT
ejpam-6741	102	12	and	and	CCONJ
ejpam-6741	102	13	”	"	PUNCT
ejpam-6741	102	14	<	<	X
ejpam-6741	102	15	>	>	X
ejpam-6741	102	16	”	"	PUNCT
ejpam-6741	102	17	denote	denote	VERB
ejpam-6741	102	18	the	the	DET
ejpam-6741	102	19	vanishing	vanishing	NOUN
ejpam-6741	102	20	and	and	CCONJ
ejpam-6741	102	21	non	non	ADJ
ejpam-6741	102	22	-	-	ADJ
ejpam-6741	102	23	vanishing	vanishing	ADJ
ejpam-6741	102	24	nature	nature	NOUN
ejpam-6741	102	25	of	of	ADP
ejpam-6741	102	26	the	the	DET
ejpam-6741	102	27	pivot	pivot	NOUN
ejpam-6741	102	28	,	,	PUNCT
ejpam-6741	102	29	respectively	respectively	ADV
ejpam-6741	102	30	.	.	PUNCT
ejpam-6741	103	1	p1	p1	PROPN
ejpam-6741	103	2	=	=	SYM
ejpam-6741	103	3	p′	p′	PROPN
ejpam-6741	103	4	,	,	PUNCT
ejpam-6741	103	5	p2	p2	X
ejpam-6741	103	6	=	=	SYM
ejpam-6741	104	1	qq′′	qq′′	NOUN
ejpam-6741	104	2	−	−	PROPN
ejpam-6741	104	3	q′2	q′2	PROPN
ejpam-6741	104	4	,	,	PUNCT
ejpam-6741	104	5	p3	p3	PROPN
ejpam-6741	104	6	=	=	SYM
ejpam-6741	104	7	q′′p−	q′′p−	PROPN
ejpam-6741	104	8	p′′q	p′′q	PROPN
ejpam-6741	104	9	,	,	PUNCT
ejpam-6741	104	10	p4	p4	ADJ
ejpam-6741	104	11	=	=	ADJ
ejpam-6741	104	12	pq′	pq′	NOUN
ejpam-6741	104	13	−	−	NOUN
ejpam-6741	104	14	p′q	p′q	NOUN
ejpam-6741	104	15	,	,	PUNCT
ejpam-6741	105	1	p5	p5	PROPN
ejpam-6741	105	2	=	=	SYM
ejpam-6741	105	3	p′′q	p′′q	NOUN
ejpam-6741	105	4	−	−	PROPN
ejpam-6741	105	5	p′q′	p′q′	PROPN
ejpam-6741	105	6	,	,	PUNCT
ejpam-6741	105	7	p6	p6	ADJ
ejpam-6741	105	8	=	=	PUNCT
ejpam-6741	105	9	p′′p′	p′′p′	NOUN
ejpam-6741	106	1	−	−	PROPN
ejpam-6741	107	1	pp′′′	pp′′′	PROPN
ejpam-6741	107	2	,	,	PUNCT
ejpam-6741	107	3	p7	p7	ADJ
ejpam-6741	107	4	=	=	SYM
ejpam-6741	107	5	p′′q2	p′′q2	NOUN
ejpam-6741	107	6	−	−	PROPN
ejpam-6741	107	7	pq′2	pq′2	PROPN
ejpam-6741	107	8	,	,	PUNCT
ejpam-6741	107	9	p8	p8	PROPN
ejpam-6741	107	10	=	=	SYM
ejpam-6741	107	11	q′	q′	NOUN
ejpam-6741	107	12	,	,	PUNCT
ejpam-6741	107	13	p9	p9	PROPN
ejpam-6741	107	14	=	=	PUNCT
ejpam-6741	107	15	p′′p−	p′′p−	PROPN
ejpam-6741	107	16	p′2	p′2	NOUN
ejpam-6741	107	17	,	,	PUNCT
ejpam-6741	107	18	p10	p10	NOUN
ejpam-6741	107	19	=	=	SYM
ejpam-6741	107	20	pq′	pq′	NOUN
ejpam-6741	107	21	+	+	CCONJ
ejpam-6741	107	22	p′q	p′q	NOUN
ejpam-6741	107	23	,	,	PUNCT
ejpam-6741	107	24	p11	p11	ADJ
ejpam-6741	107	25	=	=	SYM
ejpam-6741	107	26	q′(pq′	q′(pq′	NOUN
ejpam-6741	107	27	−	−	NOUN
ejpam-6741	107	28	p′q	p′q	NOUN
ejpam-6741	107	29	)	)	PUNCT
ejpam-6741	107	30	.	.	PUNCT
ejpam-6741	108	1	(	(	PUNCT
ejpam-6741	108	2	14	14	X
ejpam-6741	108	3	)	)	PUNCT
ejpam-6741	108	4	u.	u.	PROPN
ejpam-6741	108	5	nasib	nasib	PROPN
ejpam-6741	108	6	et	et	PROPN
ejpam-6741	108	7	al	al	PROPN
ejpam-6741	108	8	.	.	PUNCT
ejpam-6741	108	9	/	/	SYM
ejpam-6741	108	10	eur	eur	PROPN
ejpam-6741	108	11	.	.	PUNCT
ejpam-6741	109	1	j.	j.	PROPN
ejpam-6741	109	2	pure	pure	PROPN
ejpam-6741	109	3	appl	appl	PROPN
ejpam-6741	109	4	.	.	PROPN
ejpam-6741	109	5	math	math	PROPN
ejpam-6741	109	6	,	,	PUNCT
ejpam-6741	109	7	18	18	NUM
ejpam-6741	109	8	(	(	PUNCT
ejpam-6741	109	9	4	4	NUM
ejpam-6741	109	10	)	)	PUNCT
ejpam-6741	109	11	(	(	PUNCT
ejpam-6741	109	12	2025	2025	NUM
ejpam-6741	109	13	)	)	PUNCT
ejpam-6741	109	14	,	,	PUNCT
ejpam-6741	109	15	6741	6741	NUM
ejpam-6741	109	16	6	6	NUM
ejpam-6741	109	17	of	of	ADP
ejpam-6741	109	18	14	14	NUM
ejpam-6741	109	19	figure	figure	NOUN
ejpam-6741	109	20	1	1	NUM
ejpam-6741	109	21	:	:	PUNCT
ejpam-6741	109	22	rif	rif	PROPN
ejpam-6741	109	23	tree	tree	NOUN
ejpam-6741	109	24	structure	structure	NOUN
ejpam-6741	109	25	for	for	ADP
ejpam-6741	109	26	the	the	DET
ejpam-6741	109	27	system	system	NOUN
ejpam-6741	109	28	of	of	ADP
ejpam-6741	109	29	rsvf	rsvf	ADJ
ejpam-6741	109	30	equations	equation	NOUN
ejpam-6741	109	31	.	.	PUNCT
ejpam-6741	110	1	branches	branch	NOUN
ejpam-6741	110	2	that	that	PRON
ejpam-6741	110	3	terminate	terminate	VERB
ejpam-6741	110	4	prematurely	prematurely	ADV
ejpam-6741	110	5	were	be	AUX
ejpam-6741	110	6	pruned	prune	VERB
ejpam-6741	110	7	by	by	ADP
ejpam-6741	110	8	the	the	DET
ejpam-6741	110	9	algorithm	algorithm	NOUN
ejpam-6741	110	10	as	as	SCONJ
ejpam-6741	110	11	they	they	PRON
ejpam-6741	110	12	led	lead	VERB
ejpam-6741	110	13	to	to	ADP
ejpam-6741	110	14	mathematical	mathematical	ADJ
ejpam-6741	110	15	inconsistencies	inconsistency	NOUN
ejpam-6741	110	16	(	(	PUNCT
ejpam-6741	110	17	e.g.	e.g.	ADV
ejpam-6741	110	18	,	,	PUNCT
ejpam-6741	110	19	p1	p1	PROPN
ejpam-6741	110	20	=	=	SYM
ejpam-6741	110	21	p′	p′	PROPN
ejpam-6741	110	22	=	=	SYM
ejpam-6741	110	23	0	0	PUNCT
ejpam-6741	110	24	and	and	CCONJ
ejpam-6741	110	25	p1	p1	PROPN
ejpam-6741	110	26	̸=	̸=	PROPN
ejpam-6741	110	27	0	0	NUM
ejpam-6741	111	1	arising	arise	VERB
ejpam-6741	111	2	in	in	ADP
ejpam-6741	111	3	the	the	DET
ejpam-6741	111	4	same	same	ADJ
ejpam-6741	111	5	branch	branch	NOUN
ejpam-6741	111	6	)	)	PUNCT
ejpam-6741	111	7	.	.	PUNCT
ejpam-6741	112	1	the	the	DET
ejpam-6741	112	2	displayed	display	VERB
ejpam-6741	112	3	branches	branch	NOUN
ejpam-6741	112	4	represent	represent	VERB
ejpam-6741	112	5	all	all	ADV
ejpam-6741	112	6	consistent	consistent	ADJ
ejpam-6741	112	7	,	,	PUNCT
ejpam-6741	112	8	solvable	solvable	ADJ
ejpam-6741	112	9	cases	case	NOUN
ejpam-6741	112	10	..	..	PUNCT
ejpam-6741	112	11	the	the	DET
ejpam-6741	112	12	general	general	ADJ
ejpam-6741	112	13	solution	solution	NOUN
ejpam-6741	112	14	for	for	ADP
ejpam-6741	112	15	the	the	DET
ejpam-6741	112	16	vector	vector	NOUN
ejpam-6741	112	17	field	field	NOUN
ejpam-6741	112	18	v	v	NOUN
ejpam-6741	112	19	in	in	ADP
ejpam-6741	112	20	branches	branch	NOUN
ejpam-6741	112	21	1	1	NUM
ejpam-6741	112	22	and	and	CCONJ
ejpam-6741	112	23	2	2	NUM
ejpam-6741	112	24	contains	contain	VERB
ejpam-6741	112	25	8	8	NUM
ejpam-6741	112	26	and	and	CCONJ
ejpam-6741	112	27	9	9	NUM
ejpam-6741	112	28	independent	independent	ADJ
ejpam-6741	112	29	arbitrary	arbitrary	ADJ
ejpam-6741	112	30	constants	constant	NOUN
ejpam-6741	112	31	(	(	PUNCT
ejpam-6741	112	32	e1	e1	NOUN
ejpam-6741	112	33	,	,	PUNCT
ejpam-6741	112	34	e2	e2	PROPN
ejpam-6741	112	35	,	,	PUNCT
ejpam-6741	112	36	...	...	PUNCT
ejpam-6741	112	37	)	)	PUNCT
ejpam-6741	112	38	respectively	respectively	ADV
ejpam-6741	112	39	,	,	PUNCT
ejpam-6741	112	40	while	while	SCONJ
ejpam-6741	112	41	δ	δ	PROPN
ejpam-6741	112	42	is	be	AUX
ejpam-6741	112	43	arbitrary	arbitrary	ADJ
ejpam-6741	112	44	.	.	PUNCT
ejpam-6741	113	1	in	in	ADP
ejpam-6741	113	2	both	both	DET
ejpam-6741	113	3	branches	branch	NOUN
ejpam-6741	113	4	,	,	PUNCT
ejpam-6741	113	5	u.	u.	PROPN
ejpam-6741	113	6	nasib	nasib	PROPN
ejpam-6741	113	7	et	et	PROPN
ejpam-6741	113	8	al	al	PROPN
ejpam-6741	113	9	.	.	PUNCT
ejpam-6741	113	10	/	/	SYM
ejpam-6741	113	11	eur	eur	PROPN
ejpam-6741	113	12	.	.	PUNCT
ejpam-6741	114	1	j.	j.	PROPN
ejpam-6741	114	2	pure	pure	PROPN
ejpam-6741	114	3	appl	appl	PROPN
ejpam-6741	114	4	.	.	PROPN
ejpam-6741	114	5	math	math	PROPN
ejpam-6741	114	6	,	,	PUNCT
ejpam-6741	114	7	18	18	NUM
ejpam-6741	114	8	(	(	PUNCT
ejpam-6741	114	9	4	4	NUM
ejpam-6741	114	10	)	)	PUNCT
ejpam-6741	114	11	(	(	PUNCT
ejpam-6741	114	12	2025	2025	NUM
ejpam-6741	114	13	)	)	PUNCT
ejpam-6741	114	14	,	,	PUNCT
ejpam-6741	114	15	6741	6741	NUM
ejpam-6741	114	16	7	7	NUM
ejpam-6741	114	17	of	of	ADP
ejpam-6741	114	18	14	14	NUM
ejpam-6741	114	19	branch	branch	NOUN
ejpam-6741	114	20	no	no	INTJ
ejpam-6741	114	21	.	.	PUNCT
ejpam-6741	115	1	metric	metric	ADJ
ejpam-6741	115	2	functions	function	NOUN
ejpam-6741	115	3	components	component	NOUN
ejpam-6741	115	4	of	of	ADP
ejpam-6741	115	5	v	v	NOUN
ejpam-6741	115	6	p	p	X
ejpam-6741	115	7	̸=	̸=	PROPN
ejpam-6741	115	8	q	q	NOUN
ejpam-6741	115	9	,	,	PUNCT
ejpam-6741	115	10	p′	p′	NOUN
ejpam-6741	115	11	̸=	̸=	PROPN
ejpam-6741	115	12	0	0	NUM
ejpam-6741	115	13	,	,	PUNCT
ejpam-6741	115	14	v	v	NOUN
ejpam-6741	115	15	0	0	NUM
ejpam-6741	115	16	=	=	SYM
ejpam-6741	115	17	δt−	δt−	NUM
ejpam-6741	115	18	∫	∫	PROPN
ejpam-6741	116	1	p′′	p′′	PROPN
ejpam-6741	116	2	p	p	PROPN
ejpam-6741	116	3	dt−	dt−	PROPN
ejpam-6741	116	4	2	2	NUM
ejpam-6741	116	5	∫	∫	NOUN
ejpam-6741	116	6	q′′	q′′	ADP
ejpam-6741	116	7	q	q	NOUN
ejpam-6741	116	8	dt+	dt+	NOUN
ejpam-6741	116	9	e1	e1	NOUN
ejpam-6741	116	10	,	,	PUNCT
ejpam-6741	116	11	1	1	NUM
ejpam-6741	116	12	qq′′	qq′′	NOUN
ejpam-6741	116	13	−	−	PROPN
ejpam-6741	116	14	q′2	q′2	NOUN
ejpam-6741	116	15	̸=	̸=	PROPN
ejpam-6741	116	16	0	0	NUM
ejpam-6741	116	17	,	,	PUNCT
ejpam-6741	116	18	v	v	NOUN
ejpam-6741	116	19	1	1	NUM
ejpam-6741	116	20	=	=	NOUN
ejpam-6741	116	21	e2x+	e2x+	PRON
ejpam-6741	116	22	e3	e3	PROPN
ejpam-6741	116	23	,	,	PUNCT
ejpam-6741	116	24	p′′q	p′′q	NOUN
ejpam-6741	116	25	−	−	NOUN
ejpam-6741	117	1	q′′p	q′′p	PROPN
ejpam-6741	117	2	=	=	SYM
ejpam-6741	117	3	0	0	NUM
ejpam-6741	117	4	.	.	NOUN
ejpam-6741	117	5	v	v	ADP
ejpam-6741	117	6	2	2	NUM
ejpam-6741	117	7	=	=	SYM
ejpam-6741	117	8	e4z	e4z	NOUN
ejpam-6741	117	9	+	+	CCONJ
ejpam-6741	117	10	e5y	e5y	PROPN
ejpam-6741	118	1	+	+	NUM
ejpam-6741	118	2	e6	e6	NOUN
ejpam-6741	118	3	,	,	PUNCT
ejpam-6741	118	4	v	v	NOUN
ejpam-6741	118	5	3	3	NUM
ejpam-6741	118	6	=	=	SYM
ejpam-6741	118	7	−e4y	−e4y	PROPN
ejpam-6741	119	1	+	+	CCONJ
ejpam-6741	119	2	e5z	e5z	PROPN
ejpam-6741	119	3	+	+	CCONJ
ejpam-6741	119	4	e7	e7	PROPN
ejpam-6741	119	5	.	.	PUNCT
ejpam-6741	120	1	where	where	SCONJ
ejpam-6741	120	2	p	p	NOUN
ejpam-6741	120	3	and	and	CCONJ
ejpam-6741	120	4	q	q	NOUN
ejpam-6741	120	5	must	must	AUX
ejpam-6741	120	6	satisfy	satisfy	VERB
ejpam-6741	120	7	the	the	DET
ejpam-6741	120	8	following	follow	VERB
ejpam-6741	120	9	expressions	expression	NOUN
ejpam-6741	120	10	:	:	PUNCT
ejpam-6741	120	11	e2	e2	NOUN
ejpam-6741	120	12	+	+	CCONJ
ejpam-6741	120	13	p′	p′	NOUN
ejpam-6741	120	14	p	p	X
ejpam-6741	120	15	{	{	PUNCT
ejpam-6741	120	16	δt−	δt−	NUM
ejpam-6741	120	17	∫	∫	PROPN
ejpam-6741	121	1	p′′	p′′	PROPN
ejpam-6741	121	2	p	p	PROPN
ejpam-6741	121	3	dt−	dt−	PROPN
ejpam-6741	121	4	2	2	NUM
ejpam-6741	121	5	∫	∫	NOUN
ejpam-6741	121	6	q′′	q′′	ADP
ejpam-6741	121	7	q	q	ADJ
ejpam-6741	121	8	dt+	dt+	NOUN
ejpam-6741	121	9	e1}+	e1}+	NOUN
ejpam-6741	121	10	qp′′+2p′q′	qp′′+2p′q′	PROPN
ejpam-6741	121	11	pq	pq	PROPN
ejpam-6741	121	12	=	=	SYM
ejpam-6741	121	13	δ	δ	PROPN
ejpam-6741	121	14	.	.	PUNCT
ejpam-6741	122	1	e5	e5	PROPN
ejpam-6741	123	1	+	+	CCONJ
ejpam-6741	123	2	q′	q′	NOUN
ejpam-6741	123	3	q	q	X
ejpam-6741	123	4	{	{	PUNCT
ejpam-6741	123	5	δt−	δt−	NUM
ejpam-6741	123	6	∫	∫	PROPN
ejpam-6741	124	1	p′′	p′′	PROPN
ejpam-6741	124	2	p	p	PROPN
ejpam-6741	124	3	dt−	dt−	PROPN
ejpam-6741	124	4	2	2	NUM
ejpam-6741	124	5	∫	∫	NOUN
ejpam-6741	124	6	q′′	q′′	ADP
ejpam-6741	124	7	q	q	ADJ
ejpam-6741	124	8	dt+	dt+	NOUN
ejpam-6741	124	9	e1}+	e1}+	VERB
ejpam-6741	124	10	q′′	q′′	ADP
ejpam-6741	124	11	q	q	PROPN
ejpam-6741	124	12	+	+	PUNCT
ejpam-6741	124	13	q′2	q′2	ADJ
ejpam-6741	124	14	q2	q2	NOUN
ejpam-6741	124	15	+	+	CCONJ
ejpam-6741	125	1	p′q′	p′q′	PROPN
ejpam-6741	125	2	pq	pq	NOUN
ejpam-6741	125	3	=	=	SYM
ejpam-6741	125	4	δ	δ	PROPN
ejpam-6741	125	5	.	.	PUNCT
ejpam-6741	126	1	p	p	X
ejpam-6741	126	2	=	=	PUNCT
ejpam-6741	126	3	q	q	NOUN
ejpam-6741	126	4	,	,	PUNCT
ejpam-6741	126	5	p′	p′	NOUN
ejpam-6741	126	6	̸=	̸=	PROPN
ejpam-6741	126	7	0	0	NUM
ejpam-6741	126	8	,	,	PUNCT
ejpam-6741	126	9	v	v	NOUN
ejpam-6741	126	10	0	0	NUM
ejpam-6741	126	11	=	=	SYM
ejpam-6741	126	12	δt−	δt−	NUM
ejpam-6741	126	13	3	3	NUM
ejpam-6741	126	14	∫	∫	NOUN
ejpam-6741	126	15	p′′	p′′	PROPN
ejpam-6741	126	16	p	p	PROPN
ejpam-6741	126	17	dt+	dt+	NOUN
ejpam-6741	126	18	e1	e1	NOUN
ejpam-6741	126	19	,	,	PUNCT
ejpam-6741	126	20	2	2	NUM
ejpam-6741	126	21	pp′′	pp′′	NOUN
ejpam-6741	126	22	−	−	PROPN
ejpam-6741	126	23	p′2	p′2	NOUN
ejpam-6741	127	1	̸=	̸=	PROPN
ejpam-6741	127	2	0	0	NUM
ejpam-6741	127	3	.	.	PUNCT
ejpam-6741	128	1	v	v	ADP
ejpam-6741	128	2	1	1	NUM
ejpam-6741	128	3	=	=	SYM
ejpam-6741	128	4	e2x−	e2x−	NOUN
ejpam-6741	128	5	e3y	e3y	PROPN
ejpam-6741	128	6	−	−	PROPN
ejpam-6741	128	7	e4z	e4z	PROPN
ejpam-6741	128	8	+	+	CCONJ
ejpam-6741	128	9	e5	e5	PROPN
ejpam-6741	128	10	,	,	PUNCT
ejpam-6741	128	11	v	v	NOUN
ejpam-6741	128	12	2	2	NUM
ejpam-6741	128	13	=	=	SYM
ejpam-6741	128	14	e6z	e6z	VERB
ejpam-6741	129	1	+	+	CCONJ
ejpam-6741	129	2	e2y	e2y	PROPN
ejpam-6741	129	3	+	+	CCONJ
ejpam-6741	129	4	e3x+	e3x+	PROPN
ejpam-6741	129	5	e7	e7	PROPN
ejpam-6741	129	6	,	,	PUNCT
ejpam-6741	129	7	v	v	NOUN
ejpam-6741	129	8	3	3	NUM
ejpam-6741	129	9	=	=	SYM
ejpam-6741	129	10	e2z	e2z	NOUN
ejpam-6741	129	11	−	−	PROPN
ejpam-6741	129	12	e6y	e6y	ADV
ejpam-6741	129	13	+	+	CCONJ
ejpam-6741	129	14	e4x+	e4x+	PROPN
ejpam-6741	129	15	e8	e8	PROPN
ejpam-6741	129	16	.	.	PUNCT
ejpam-6741	129	17	where	where	SCONJ
ejpam-6741	129	18	p	p	PROPN
ejpam-6741	129	19	satisfies	satisfy	VERB
ejpam-6741	129	20	the	the	DET
ejpam-6741	129	21	non	non	ADJ
ejpam-6741	129	22	-	-	ADJ
ejpam-6741	129	23	linear	linear	ADJ
ejpam-6741	129	24	equation	equation	NOUN
ejpam-6741	129	25	given	give	VERB
ejpam-6741	129	26	by	by	ADP
ejpam-6741	129	27	:	:	PUNCT
ejpam-6741	129	28	e2	e2	PROPN
ejpam-6741	129	29	+	+	CCONJ
ejpam-6741	129	30	p′	p′	NOUN
ejpam-6741	129	31	p	p	X
ejpam-6741	129	32	{	{	PUNCT
ejpam-6741	129	33	δt−	δt−	NUM
ejpam-6741	129	34	3	3	NUM
ejpam-6741	129	35	∫	∫	NOUN
ejpam-6741	129	36	p′′	p′′	PROPN
ejpam-6741	129	37	p	p	PROPN
ejpam-6741	129	38	dt+	dt+	NOUN
ejpam-6741	129	39	e1}+	e1}+	NOUN
ejpam-6741	129	40	pp′′+2p′2	pp′′+2p′2	NOUN
ejpam-6741	129	41	p2	p2	PROPN
ejpam-6741	129	42	=	=	SYM
ejpam-6741	129	43	δ	δ	PROPN
ejpam-6741	129	44	.	.	PUNCT
ejpam-6741	130	1	p	p	X
ejpam-6741	131	1	=	=	PROPN
ejpam-6741	131	2	tan	tan	PROPN
ejpam-6741	131	3	t	t	PROPN
ejpam-6741	131	4	,	,	PUNCT
ejpam-6741	131	5	v	v	NOUN
ejpam-6741	131	6	0	0	NUM
ejpam-6741	131	7	=	=	SYM
ejpam-6741	132	1	−2	−2	PROPN
ejpam-6741	132	2	tan	tan	PROPN
ejpam-6741	132	3	t	t	PROPN
ejpam-6741	132	4	,	,	PUNCT
ejpam-6741	132	5	3	3	NUM
ejpam-6741	132	6	q	q	NOUN
ejpam-6741	132	7	=	=	SYM
ejpam-6741	132	8	ekt	ekt	PROPN
ejpam-6741	132	9	,	,	PUNCT
ejpam-6741	132	10	v	v	NOUN
ejpam-6741	132	11	1	1	NUM
ejpam-6741	132	12	=	=	SYM
ejpam-6741	132	13	e1	e1	NOUN
ejpam-6741	132	14	,	,	PUNCT
ejpam-6741	132	15	k	k	PROPN
ejpam-6741	132	16	̸=	̸=	PROPN
ejpam-6741	132	17	0	0	NUM
ejpam-6741	132	18	.	.	PUNCT
ejpam-6741	133	1	v	v	ADP
ejpam-6741	133	2	2	2	NUM
ejpam-6741	133	3	=	=	SYM
ejpam-6741	133	4	e2z	e2z	NOUN
ejpam-6741	133	5	+	+	NUM
ejpam-6741	133	6	e3	e3	NOUN
ejpam-6741	133	7	,	,	PUNCT
ejpam-6741	133	8	v	v	NOUN
ejpam-6741	133	9	3	3	NUM
ejpam-6741	133	10	=	=	SYM
ejpam-6741	133	11	−e2y	−e2y	PUNCT
ejpam-6741	133	12	+	+	X
ejpam-6741	133	13	e4	e4	PROPN
ejpam-6741	133	14	.	.	PUNCT
ejpam-6741	134	1	p	p	X
ejpam-6741	134	2	=	=	PUNCT
ejpam-6741	134	3	ek1	ek1	PROPN
ejpam-6741	134	4	t	t	PROPN
ejpam-6741	134	5	,	,	PUNCT
ejpam-6741	134	6	v	v	NOUN
ejpam-6741	134	7	0	0	NUM
ejpam-6741	134	8	=	=	SYM
ejpam-6741	134	9	e1	e1	NOUN
ejpam-6741	134	10	,	,	PUNCT
ejpam-6741	134	11	4	4	NUM
ejpam-6741	134	12	q	q	NOUN
ejpam-6741	134	13	=	=	PUNCT
ejpam-6741	134	14	ek2	ek2	NOUN
ejpam-6741	134	15	t	t	PROPN
ejpam-6741	134	16	,	,	PUNCT
ejpam-6741	134	17	v	v	NOUN
ejpam-6741	134	18	1	1	NUM
ejpam-6741	134	19	=	=	SYM
ejpam-6741	134	20	2k2(k2	2k2(k2	NUM
ejpam-6741	134	21	−	−	NOUN
ejpam-6741	134	22	k1)x−	k1)x−	NOUN
ejpam-6741	134	23	e1k1x+	e1k1x+	PROPN
ejpam-6741	134	24	e2	e2	PROPN
ejpam-6741	134	25	,	,	PUNCT
ejpam-6741	134	26	k1	k1	PROPN
ejpam-6741	134	27	̸=	̸=	PROPN
ejpam-6741	134	28	k2	k2	NOUN
ejpam-6741	134	29	,	,	PUNCT
ejpam-6741	134	30	v	v	NOUN
ejpam-6741	134	31	2	2	NUM
ejpam-6741	134	32	=	=	NOUN
ejpam-6741	134	33	e3z	e3z	VERB
ejpam-6741	134	34	+	+	CCONJ
ejpam-6741	134	35	k1(k1	k1(k1	PROPN
ejpam-6741	134	36	−	−	PROPN
ejpam-6741	134	37	k2)y	k2)y	NOUN
ejpam-6741	134	38	−	−	PROPN
ejpam-6741	134	39	e1k2y	e1k2y	SYM
ejpam-6741	135	1	+	+	CCONJ
ejpam-6741	135	2	e4	e4	PROPN
ejpam-6741	135	3	,	,	PUNCT
ejpam-6741	135	4	and	and	CCONJ
ejpam-6741	135	5	δ	δ	PROPN
ejpam-6741	135	6	=	=	PROPN
ejpam-6741	135	7	k2	k2	PROPN
ejpam-6741	135	8	1	1	NUM
ejpam-6741	135	9	+	+	NUM
ejpam-6741	135	10	2k2	2k2	NUM
ejpam-6741	135	11	2	2	NUM
ejpam-6741	135	12	.	.	PUNCT
ejpam-6741	135	13	v	v	NUM
ejpam-6741	135	14	3	3	NUM
ejpam-6741	135	15	=	=	SYM
ejpam-6741	135	16	k1(k1	k1(k1	NOUN
ejpam-6741	135	17	−	−	PROPN
ejpam-6741	135	18	k2)z	k2)z	NOUN
ejpam-6741	135	19	−	−	PROPN
ejpam-6741	135	20	e3y	e3y	PUNCT
ejpam-6741	135	21	−	−	PROPN
ejpam-6741	135	22	e1k2z	e1k2z	X
ejpam-6741	135	23	+	+	CCONJ
ejpam-6741	135	24	e5	e5	INTJ
ejpam-6741	135	25	.	.	PUNCT
ejpam-6741	136	1	p	p	X
ejpam-6741	137	1	=	=	PUNCT
ejpam-6741	137	2	k2e	k2e	PROPN
ejpam-6741	137	3	kt	kt	PROPN
ejpam-6741	137	4	+	+	CCONJ
ejpam-6741	137	5	k3e	k3e	PROPN
ejpam-6741	137	6	−kt	−kt	PROPN
ejpam-6741	137	7	,	,	PUNCT
ejpam-6741	137	8	v	v	NOUN
ejpam-6741	137	9	0	0	NUM
ejpam-6741	137	10	=	=	SYM
ejpam-6741	137	11	1	1	NUM
ejpam-6741	137	12	α	α	NOUN
ejpam-6741	137	13	{	{	PUNCT
ejpam-6741	137	14	e1	e1	NOUN
ejpam-6741	137	15	sinαx−	sinαx−	NOUN
ejpam-6741	137	16	e2	e2	PROPN
ejpam-6741	137	17	cosαx	cosαx	PROPN
ejpam-6741	137	18	}	}	PUNCT
ejpam-6741	137	19	,	,	PUNCT
ejpam-6741	137	20	5	5	NUM
ejpam-6741	137	21	q	q	NOUN
ejpam-6741	137	22	=	=	NOUN
ejpam-6741	137	23	k1	k1	NOUN
ejpam-6741	137	24	̸=	̸=	PROPN
ejpam-6741	137	25	0	0	NUM
ejpam-6741	137	26	,	,	PUNCT
ejpam-6741	137	27	v	v	NOUN
ejpam-6741	137	28	1	1	NUM
ejpam-6741	137	29	=	=	SYM
ejpam-6741	137	30	k(k2e	k(k2e	ADP
ejpam-6741	137	31	kt−k3e	kt−k3e	NOUN
ejpam-6741	137	32	−kt	−kt	NOUN
ejpam-6741	137	33	)	)	PUNCT
ejpam-6741	137	34	α2(k2ekt+k3e−kt	α2(k2ekt+k3e−kt	NOUN
ejpam-6741	137	35	)	)	PUNCT
ejpam-6741	137	36	{	{	PUNCT
ejpam-6741	137	37	e1	e1	PROPN
ejpam-6741	137	38	cosαx+	cosαx+	CCONJ
ejpam-6741	137	39	e2	e2	PROPN
ejpam-6741	137	40	sinαx}+	sinαx}+	PROPN
ejpam-6741	137	41	e3	e3	PROPN
ejpam-6741	137	42	,	,	PUNCT
ejpam-6741	137	43	k	k	PROPN
ejpam-6741	137	44	̸=	̸=	PROPN
ejpam-6741	137	45	0	0	NUM
ejpam-6741	137	46	,	,	PUNCT
ejpam-6741	137	47	δ	δ	PROPN
ejpam-6741	137	48	=	=	SYM
ejpam-6741	137	49	k2	k2	PROPN
ejpam-6741	137	50	,	,	PUNCT
ejpam-6741	137	51	v	v	NOUN
ejpam-6741	137	52	2	2	NUM
ejpam-6741	137	53	=	=	SYM
ejpam-6741	137	54	e4z	e4z	NOUN
ejpam-6741	138	1	+	+	CCONJ
ejpam-6741	138	2	k2y	k2y	PROPN
ejpam-6741	138	3	+	+	CCONJ
ejpam-6741	138	4	e5	e5	PROPN
ejpam-6741	138	5	,	,	PUNCT
ejpam-6741	138	6	α	α	NOUN
ejpam-6741	138	7	=	=	SYM
ejpam-6741	138	8	2k	2k	NUM
ejpam-6741	138	9	√	√	NUM
ejpam-6741	139	1	k2k3	k2k3	NOUN
ejpam-6741	139	2	.	.	PUNCT
ejpam-6741	140	1	v	v	ADP
ejpam-6741	140	2	3	3	NUM
ejpam-6741	140	3	=	=	SYM
ejpam-6741	140	4	−e4y	−e4y	PROPN
ejpam-6741	141	1	+	+	NUM
ejpam-6741	141	2	k2z	k2z	NOUN
ejpam-6741	141	3	+	+	CCONJ
ejpam-6741	141	4	e6	e6	NOUN
ejpam-6741	141	5	.	.	PUNCT
ejpam-6741	142	1	p	p	X
ejpam-6741	142	2	=	=	PROPN
ejpam-6741	142	3	e−k1	e−k1	PROPN
ejpam-6741	142	4	t	t	PROPN
ejpam-6741	142	5	,	,	PUNCT
ejpam-6741	142	6	v	v	NOUN
ejpam-6741	142	7	0	0	NUM
ejpam-6741	143	1	=	=	SYM
ejpam-6741	143	2	4k2	4k2	NUM
ejpam-6741	143	3	1	1	NUM
ejpam-6741	143	4	−	−	NOUN
ejpam-6741	143	5	e1	e1	NOUN
ejpam-6741	143	6	,	,	PUNCT
ejpam-6741	143	7	6	6	NUM
ejpam-6741	143	8	q	q	NOUN
ejpam-6741	143	9	=	=	PUNCT
ejpam-6741	143	10	ek1	ek1	NOUN
ejpam-6741	143	11	t	t	PROPN
ejpam-6741	143	12	v	v	NOUN
ejpam-6741	143	13	1	1	NUM
ejpam-6741	143	14	=	=	SYM
ejpam-6741	143	15	{	{	PUNCT
ejpam-6741	143	16	4k2	4k2	NUM
ejpam-6741	143	17	1	1	NUM
ejpam-6741	143	18	−	−	NOUN
ejpam-6741	143	19	k1(4k	k1(4k	NOUN
ejpam-6741	143	20	2	2	NUM
ejpam-6741	143	21	1	1	NUM
ejpam-6741	143	22	−	−	PROPN
ejpam-6741	143	23	e1)}x+	e1)}x+	PROPN
ejpam-6741	143	24	e2	e2	NOUN
ejpam-6741	143	25	,	,	PUNCT
ejpam-6741	143	26	where	where	SCONJ
ejpam-6741	143	27	k1	k1	NOUN
ejpam-6741	143	28	̸=	̸=	PROPN
ejpam-6741	143	29	0	0	NUM
ejpam-6741	143	30	and	and	CCONJ
ejpam-6741	143	31	δ	δ	PROPN
ejpam-6741	143	32	=	=	PUNCT
ejpam-6741	144	1	3k2	3k2	NUM
ejpam-6741	145	1	1	1	NUM
ejpam-6741	145	2	.	.	PUNCT
ejpam-6741	145	3	v	v	SYM
ejpam-6741	145	4	2	2	NUM
ejpam-6741	145	5	=	=	SYM
ejpam-6741	145	6	e3z	e3z	NOUN
ejpam-6741	145	7	+	+	CCONJ
ejpam-6741	145	8	e1y	e1y	X
ejpam-6741	145	9	+	+	X
ejpam-6741	145	10	e4	e4	PROPN
ejpam-6741	145	11	,	,	PUNCT
ejpam-6741	145	12	v	v	NOUN
ejpam-6741	145	13	3	3	NUM
ejpam-6741	145	14	=	=	SYM
ejpam-6741	145	15	−e3y	−e3y	PROPN
ejpam-6741	146	1	+	+	CCONJ
ejpam-6741	146	2	e1z	e1z	PROPN
ejpam-6741	146	3	+	+	NUM
ejpam-6741	146	4	e5	e5	PROPN
ejpam-6741	146	5	.	.	PUNCT
ejpam-6741	147	1	p	p	X
ejpam-6741	147	2	=	=	SYM
ejpam-6741	147	3	1	1	NUM
ejpam-6741	147	4	k1	k1	PROPN
ejpam-6741	147	5	ek1	ek1	PROPN
ejpam-6741	147	6	t	t	PROPN
ejpam-6741	147	7	,	,	PUNCT
ejpam-6741	147	8	v	v	NOUN
ejpam-6741	147	9	0	0	NUM
ejpam-6741	147	10	=	=	SYM
ejpam-6741	147	11	1	1	NUM
ejpam-6741	147	12	k1	k1	NOUN
ejpam-6741	147	13	{	{	PUNCT
ejpam-6741	147	14	e1z	e1z	PROPN
ejpam-6741	147	15	−	−	PROPN
ejpam-6741	147	16	e2y	e2y	PROPN
ejpam-6741	147	17	−	−	PROPN
ejpam-6741	147	18	e3x−	e3x−	PROPN
ejpam-6741	147	19	e4	e4	PROPN
ejpam-6741	147	20	}	}	PUNCT
ejpam-6741	147	21	,	,	PUNCT
ejpam-6741	147	22	7	7	NUM
ejpam-6741	147	23	q	q	NOUN
ejpam-6741	147	24	=	=	SYM
ejpam-6741	147	25	ek1	ek1	NOUN
ejpam-6741	147	26	t	t	PROPN
ejpam-6741	147	27	v	v	NOUN
ejpam-6741	147	28	1	1	NUM
ejpam-6741	147	29	=	=	PUNCT
ejpam-6741	147	30	e3	e3	NOUN
ejpam-6741	147	31	2	2	NUM
ejpam-6741	147	32	(	(	PUNCT
ejpam-6741	147	33	x2	x2	NOUN
ejpam-6741	148	1	+	+	CCONJ
ejpam-6741	148	2	y2	y2	PROPN
ejpam-6741	149	1	+	+	CCONJ
ejpam-6741	149	2	z2	z2	PROPN
ejpam-6741	149	3	+	+	CCONJ
ejpam-6741	149	4	e−2k1	e−2k1	PROPN
ejpam-6741	149	5	t	t	NOUN
ejpam-6741	149	6	k2	k2	NOUN
ejpam-6741	149	7	1	1	NUM
ejpam-6741	149	8	)	)	PUNCT
ejpam-6741	149	9	+	+	CCONJ
ejpam-6741	149	10	(	(	PUNCT
ejpam-6741	149	11	e2x−	e2x−	NOUN
ejpam-6741	149	12	e5)y	e5)y	NOUN
ejpam-6741	149	13	+	+	PROPN
ejpam-6741	149	14	(	(	PUNCT
ejpam-6741	149	15	e6	e6	NOUN
ejpam-6741	149	16	−	−	PROPN
ejpam-6741	149	17	e1x)z	e1x)z	PUNCT
ejpam-6741	150	1	+	+	CCONJ
ejpam-6741	150	2	e4x+	e4x+	PROPN
ejpam-6741	150	3	e7	e7	PROPN
ejpam-6741	150	4	,	,	PUNCT
ejpam-6741	150	5	where	where	SCONJ
ejpam-6741	150	6	k1	k1	NOUN
ejpam-6741	150	7	̸=	̸=	PROPN
ejpam-6741	150	8	0	0	NUM
ejpam-6741	150	9	,	,	PUNCT
ejpam-6741	150	10	1	1	NUM
ejpam-6741	150	11	and	and	CCONJ
ejpam-6741	150	12	δ	δ	PROPN
ejpam-6741	150	13	=	=	PUNCT
ejpam-6741	150	14	3k2	3k2	NUM
ejpam-6741	150	15	1	1	NUM
ejpam-6741	150	16	.	.	PUNCT
ejpam-6741	150	17	v	v	SYM
ejpam-6741	150	18	2	2	NUM
ejpam-6741	150	19	=	=	SYM
ejpam-6741	150	20	e2	e2	NOUN
ejpam-6741	150	21	2	2	NUM
ejpam-6741	150	22	(	(	PUNCT
ejpam-6741	150	23	2yz	2yz	NOUN
ejpam-6741	150	24	+	+	ADP
ejpam-6741	150	25	e−2k1	e−2k1	NOUN
ejpam-6741	150	26	t	t	NOUN
ejpam-6741	150	27	k2	k2	NOUN
ejpam-6741	150	28	1	1	NUM
ejpam-6741	150	29	+	+	CCONJ
ejpam-6741	150	30	x2	x2	ADJ
ejpam-6741	150	31	)	)	PUNCT
ejpam-6741	150	32	+	+	CCONJ
ejpam-6741	150	33	e1	e1	NOUN
ejpam-6741	150	34	2	2	NUM
ejpam-6741	150	35	(	(	PUNCT
ejpam-6741	150	36	z2	z2	NOUN
ejpam-6741	150	37	−	−	PROPN
ejpam-6741	150	38	y2	y2	PROPN
ejpam-6741	150	39	)	)	PUNCT
ejpam-6741	151	1	+	+	ADJ
ejpam-6741	151	2	e8z	e8z	PROPN
ejpam-6741	151	3	+	+	CCONJ
ejpam-6741	151	4	(	(	PUNCT
ejpam-6741	151	5	e3x+	e3x+	INTJ
ejpam-6741	151	6	e4)y	e4)y	PROPN
ejpam-6741	151	7	+	+	CCONJ
ejpam-6741	151	8	e5x+	e5x+	PROPN
ejpam-6741	151	9	e9	e9	PROPN
ejpam-6741	151	10	,	,	PUNCT
ejpam-6741	151	11	v	v	NOUN
ejpam-6741	151	12	3	3	NUM
ejpam-6741	151	13	=	=	SYM
ejpam-6741	151	14	−	−	PROPN
ejpam-6741	151	15	e1	e1	NOUN
ejpam-6741	151	16	2	2	NUM
ejpam-6741	151	17	(	(	PUNCT
ejpam-6741	151	18	2yz	2yz	NOUN
ejpam-6741	151	19	+	+	ADP
ejpam-6741	151	20	e−2k1	e−2k1	NOUN
ejpam-6741	151	21	t	t	NOUN
ejpam-6741	151	22	k2	k2	NOUN
ejpam-6741	151	23	1	1	NUM
ejpam-6741	151	24	−	−	PROPN
ejpam-6741	151	25	x2	x2	PROPN
ejpam-6741	151	26	)	)	PUNCT
ejpam-6741	152	1	+	+	CCONJ
ejpam-6741	152	2	e2	e2	PROPN
ejpam-6741	152	3	2	2	NUM
ejpam-6741	152	4	(	(	PUNCT
ejpam-6741	152	5	z2	z2	NOUN
ejpam-6741	152	6	−	−	PROPN
ejpam-6741	152	7	y2	y2	PROPN
ejpam-6741	152	8	)	)	PUNCT
ejpam-6741	152	9	−e8y	−e8y	PUNCT
ejpam-6741	153	1	+	+	CCONJ
ejpam-6741	153	2	(	(	PUNCT
ejpam-6741	153	3	e3x+	e3x+	INTJ
ejpam-6741	153	4	e4)z	e4)z	NOUN
ejpam-6741	153	5	+	+	CCONJ
ejpam-6741	153	6	e6x+	e6x+	ADJ
ejpam-6741	153	7	e10	e10	NOUN
ejpam-6741	153	8	.	.	PUNCT
ejpam-6741	153	9	table	table	NOUN
ejpam-6741	153	10	1	1	NUM
ejpam-6741	153	11	:	:	PUNCT
ejpam-6741	153	12	metrics	metric	NOUN
ejpam-6741	153	13	admitting	admit	VERB
ejpam-6741	153	14	rsvfs	rsvfs	NOUN
ejpam-6741	153	15	the	the	DET
ejpam-6741	153	16	nature	nature	NOUN
ejpam-6741	153	17	of	of	ADP
ejpam-6741	153	18	the	the	DET
ejpam-6741	153	19	rsvfs	rsvfs	NOUN
ejpam-6741	153	20	can	can	AUX
ejpam-6741	153	21	be	be	AUX
ejpam-6741	153	22	shrinking	shrink	VERB
ejpam-6741	153	23	,	,	PUNCT
ejpam-6741	153	24	expanding	expand	VERB
ejpam-6741	153	25	,	,	PUNCT
ejpam-6741	153	26	or	or	CCONJ
ejpam-6741	153	27	steady	steady	ADJ
ejpam-6741	153	28	.	.	PUNCT
ejpam-6741	154	1	in	in	ADP
ejpam-6741	154	2	the	the	DET
ejpam-6741	154	3	case	case	NOUN
ejpam-6741	154	4	of	of	ADP
ejpam-6741	154	5	a	a	DET
ejpam-6741	154	6	steady	steady	ADJ
ejpam-6741	154	7	u.	u.	PROPN
ejpam-6741	154	8	nasib	nasib	PROPN
ejpam-6741	154	9	et	et	PROPN
ejpam-6741	154	10	al	al	PROPN
ejpam-6741	154	11	.	.	PUNCT
ejpam-6741	154	12	/	/	SYM
ejpam-6741	154	13	eur	eur	PROPN
ejpam-6741	154	14	.	.	PUNCT
ejpam-6741	155	1	j.	j.	PROPN
ejpam-6741	155	2	pure	pure	PROPN
ejpam-6741	155	3	appl	appl	PROPN
ejpam-6741	155	4	.	.	PROPN
ejpam-6741	155	5	math	math	PROPN
ejpam-6741	155	6	,	,	PUNCT
ejpam-6741	155	7	18	18	NUM
ejpam-6741	155	8	(	(	PUNCT
ejpam-6741	155	9	4	4	NUM
ejpam-6741	155	10	)	)	PUNCT
ejpam-6741	155	11	(	(	PUNCT
ejpam-6741	155	12	2025	2025	NUM
ejpam-6741	155	13	)	)	PUNCT
ejpam-6741	155	14	,	,	PUNCT
ejpam-6741	155	15	6741	6741	NUM
ejpam-6741	155	16	8	8	NUM
ejpam-6741	155	17	of	of	ADP
ejpam-6741	155	18	14	14	NUM
ejpam-6741	155	19	branch	branch	NOUN
ejpam-6741	155	20	no	no	INTJ
ejpam-6741	155	21	.	.	PUNCT
ejpam-6741	156	1	metric	metric	ADJ
ejpam-6741	156	2	functions	function	NOUN
ejpam-6741	156	3	components	component	NOUN
ejpam-6741	156	4	of	of	ADP
ejpam-6741	156	5	v	v	NOUN
ejpam-6741	156	6	p	p	NOUN
ejpam-6741	156	7	=	=	PUNCT
ejpam-6741	156	8	ek1	ek1	PROPN
ejpam-6741	156	9	t	t	PROPN
ejpam-6741	156	10	,	,	PUNCT
ejpam-6741	156	11	v	v	NOUN
ejpam-6741	156	12	0	0	NUM
ejpam-6741	156	13	=	=	SYM
ejpam-6741	156	14	1	1	NUM
ejpam-6741	156	15	k1	k1	NOUN
ejpam-6741	156	16	{	{	PUNCT
ejpam-6741	156	17	e1z	e1z	PROPN
ejpam-6741	156	18	−	−	PROPN
ejpam-6741	156	19	e2y	e2y	PROPN
ejpam-6741	156	20	−	−	PROPN
ejpam-6741	156	21	e3x−	e3x−	PROPN
ejpam-6741	156	22	e4	e4	PROPN
ejpam-6741	156	23	}	}	PUNCT
ejpam-6741	156	24	,	,	PUNCT
ejpam-6741	156	25	8	8	NUM
ejpam-6741	156	26	q	q	NOUN
ejpam-6741	156	27	=	=	PUNCT
ejpam-6741	156	28	ek1	ek1	NOUN
ejpam-6741	156	29	t	t	PROPN
ejpam-6741	156	30	v	v	NOUN
ejpam-6741	156	31	1	1	NUM
ejpam-6741	156	32	=	=	PUNCT
ejpam-6741	156	33	e3	e3	NOUN
ejpam-6741	156	34	2	2	NUM
ejpam-6741	156	35	(	(	PUNCT
ejpam-6741	156	36	x2	x2	NOUN
ejpam-6741	157	1	+	+	CCONJ
ejpam-6741	157	2	y2	y2	PROPN
ejpam-6741	158	1	+	+	CCONJ
ejpam-6741	158	2	z2	z2	PROPN
ejpam-6741	158	3	+	+	CCONJ
ejpam-6741	158	4	e−2k1	e−2k1	PROPN
ejpam-6741	158	5	t	t	NOUN
ejpam-6741	158	6	k2	k2	NOUN
ejpam-6741	158	7	1	1	NUM
ejpam-6741	158	8	)	)	PUNCT
ejpam-6741	158	9	+	+	CCONJ
ejpam-6741	158	10	(	(	PUNCT
ejpam-6741	158	11	e2x−	e2x−	NOUN
ejpam-6741	158	12	e5)y	e5)y	NOUN
ejpam-6741	158	13	+	+	PROPN
ejpam-6741	158	14	(	(	PUNCT
ejpam-6741	158	15	e6	e6	NOUN
ejpam-6741	158	16	−	−	PROPN
ejpam-6741	158	17	e1x)z	e1x)z	PUNCT
ejpam-6741	159	1	+	+	CCONJ
ejpam-6741	159	2	e4x+	e4x+	PROPN
ejpam-6741	159	3	e7	e7	PROPN
ejpam-6741	159	4	,	,	PUNCT
ejpam-6741	159	5	where	where	SCONJ
ejpam-6741	159	6	k1	k1	NOUN
ejpam-6741	159	7	̸=	̸=	PROPN
ejpam-6741	159	8	0	0	NUM
ejpam-6741	159	9	and	and	CCONJ
ejpam-6741	159	10	δ	δ	PROPN
ejpam-6741	159	11	=	=	PUNCT
ejpam-6741	159	12	3k2	3k2	NUM
ejpam-6741	159	13	1	1	NUM
ejpam-6741	159	14	.	.	PUNCT
ejpam-6741	159	15	v	v	SYM
ejpam-6741	159	16	2	2	NUM
ejpam-6741	159	17	=	=	SYM
ejpam-6741	159	18	e2	e2	NOUN
ejpam-6741	159	19	2	2	NUM
ejpam-6741	159	20	(	(	PUNCT
ejpam-6741	159	21	2yz	2yz	NOUN
ejpam-6741	159	22	+	+	ADP
ejpam-6741	159	23	e−2k1	e−2k1	NOUN
ejpam-6741	159	24	t	t	NOUN
ejpam-6741	159	25	k2	k2	NOUN
ejpam-6741	159	26	1	1	NUM
ejpam-6741	159	27	+	+	CCONJ
ejpam-6741	159	28	x2	x2	ADJ
ejpam-6741	159	29	)	)	PUNCT
ejpam-6741	159	30	+	+	CCONJ
ejpam-6741	159	31	e1	e1	NOUN
ejpam-6741	159	32	2	2	NUM
ejpam-6741	159	33	(	(	PUNCT
ejpam-6741	159	34	z2	z2	NOUN
ejpam-6741	159	35	−	−	PROPN
ejpam-6741	159	36	y2	y2	PROPN
ejpam-6741	159	37	)	)	PUNCT
ejpam-6741	160	1	+	+	ADJ
ejpam-6741	160	2	e8z	e8z	PROPN
ejpam-6741	160	3	+	+	CCONJ
ejpam-6741	160	4	(	(	PUNCT
ejpam-6741	160	5	e3x+	e3x+	INTJ
ejpam-6741	160	6	e4)y	e4)y	PROPN
ejpam-6741	160	7	+	+	CCONJ
ejpam-6741	160	8	e5x+	e5x+	PROPN
ejpam-6741	160	9	e9	e9	PROPN
ejpam-6741	160	10	,	,	PUNCT
ejpam-6741	160	11	v	v	NOUN
ejpam-6741	160	12	3	3	NUM
ejpam-6741	160	13	=	=	SYM
ejpam-6741	160	14	−	−	PROPN
ejpam-6741	160	15	e1	e1	NOUN
ejpam-6741	160	16	2	2	NUM
ejpam-6741	160	17	(	(	PUNCT
ejpam-6741	160	18	2yz	2yz	NOUN
ejpam-6741	160	19	+	+	ADP
ejpam-6741	160	20	e−2k1	e−2k1	NOUN
ejpam-6741	160	21	t	t	NOUN
ejpam-6741	160	22	k2	k2	NOUN
ejpam-6741	160	23	1	1	NUM
ejpam-6741	160	24	−	−	PROPN
ejpam-6741	160	25	x2	x2	PROPN
ejpam-6741	160	26	)	)	PUNCT
ejpam-6741	161	1	+	+	CCONJ
ejpam-6741	161	2	e2	e2	PROPN
ejpam-6741	161	3	2	2	NUM
ejpam-6741	161	4	(	(	PUNCT
ejpam-6741	161	5	z2	z2	NOUN
ejpam-6741	161	6	−	−	PROPN
ejpam-6741	161	7	y2	y2	PROPN
ejpam-6741	161	8	)	)	PUNCT
ejpam-6741	161	9	−e8y	−e8y	PUNCT
ejpam-6741	162	1	+	+	CCONJ
ejpam-6741	162	2	(	(	PUNCT
ejpam-6741	162	3	e3x+	e3x+	INTJ
ejpam-6741	162	4	e4)z	e4)z	NOUN
ejpam-6741	162	5	+	+	CCONJ
ejpam-6741	162	6	e6x+	e6x+	X
ejpam-6741	162	7	e10	e10	NOUN
ejpam-6741	162	8	.	.	PUNCT
ejpam-6741	163	1	p	p	X
ejpam-6741	163	2	=	=	PROPN
ejpam-6741	163	3	k1t+	k1t+	PROPN
ejpam-6741	163	4	k2	k2	PROPN
ejpam-6741	163	5	,	,	PUNCT
ejpam-6741	163	6	v	v	NOUN
ejpam-6741	163	7	0	0	NUM
ejpam-6741	163	8	=	=	SYM
ejpam-6741	163	9	δt+	δt+	ADJ
ejpam-6741	163	10	e1	e1	PROPN
ejpam-6741	163	11	,	,	PUNCT
ejpam-6741	163	12	9	9	NUM
ejpam-6741	163	13	q	q	NOUN
ejpam-6741	163	14	=	=	PRON
ejpam-6741	163	15	k3	k3	VERB
ejpam-6741	163	16	̸=	̸=	PROPN
ejpam-6741	163	17	0	0	NUM
ejpam-6741	163	18	,	,	PUNCT
ejpam-6741	163	19	v	v	NOUN
ejpam-6741	163	20	1	1	NUM
ejpam-6741	163	21	=	=	NOUN
ejpam-6741	163	22	e2x+	e2x+	X
ejpam-6741	163	23	e3	e3	NOUN
ejpam-6741	163	24	,	,	PUNCT
ejpam-6741	163	25	where	where	SCONJ
ejpam-6741	163	26	k1	k1	NOUN
ejpam-6741	163	27	̸=	̸=	PROPN
ejpam-6741	163	28	0	0	NUM
ejpam-6741	163	29	,	,	PUNCT
ejpam-6741	163	30	k2	k2	ADJ
ejpam-6741	163	31	̸=	̸=	PROPN
ejpam-6741	163	32	0	0	NUM
ejpam-6741	163	33	v	v	ADP
ejpam-6741	163	34	2	2	NUM
ejpam-6741	163	35	=	=	SYM
ejpam-6741	163	36	δy	δy	NOUN
ejpam-6741	163	37	+	+	CCONJ
ejpam-6741	163	38	e4z	e4z	PROPN
ejpam-6741	163	39	+	+	CCONJ
ejpam-6741	163	40	e5	e5	PROPN
ejpam-6741	163	41	,	,	PUNCT
ejpam-6741	163	42	δ	δ	PROPN
ejpam-6741	163	43	=	=	PROPN
ejpam-6741	163	44	k1	k1	PROPN
ejpam-6741	163	45	k2	k2	PROPN
ejpam-6741	163	46	e1	e1	PROPN
ejpam-6741	163	47	.	.	PUNCT
ejpam-6741	164	1	v	v	X
ejpam-6741	164	2	3	3	NUM
ejpam-6741	164	3	=	=	SYM
ejpam-6741	164	4	δz	δz	PROPN
ejpam-6741	164	5	−	−	PROPN
ejpam-6741	164	6	e4y	e4y	PROPN
ejpam-6741	164	7	+	+	NUM
ejpam-6741	164	8	e6	e6	NOUN
ejpam-6741	164	9	.	.	PUNCT
ejpam-6741	165	1	p	p	X
ejpam-6741	165	2	=	=	PROPN
ejpam-6741	165	3	k1	k1	PROPN
ejpam-6741	165	4	,	,	PUNCT
ejpam-6741	165	5	v	v	NOUN
ejpam-6741	165	6	0	0	NUM
ejpam-6741	165	7	=	=	NOUN
ejpam-6741	165	8	δt+	δt+	NOUN
ejpam-6741	165	9	e1	e1	NOUN
ejpam-6741	165	10	−	−	PROPN
ejpam-6741	165	11	2	2	NUM
ejpam-6741	165	12	∫	∫	NOUN
ejpam-6741	165	13	q′′	q′′	ADP
ejpam-6741	165	14	q	q	PROPN
ejpam-6741	165	15	dt	dt	X
ejpam-6741	165	16	,	,	PUNCT
ejpam-6741	165	17	10	10	NUM
ejpam-6741	165	18	q′	q′	NOUN
ejpam-6741	165	19	̸=	̸=	PROPN
ejpam-6741	165	20	0	0	NUM
ejpam-6741	165	21	,	,	PUNCT
ejpam-6741	165	22	v	v	NOUN
ejpam-6741	165	23	1	1	NUM
ejpam-6741	165	24	=	=	SYM
ejpam-6741	165	25	δx+	δx+	PROPN
ejpam-6741	165	26	e2	e2	PROPN
ejpam-6741	165	27	,	,	PUNCT
ejpam-6741	165	28	where	where	SCONJ
ejpam-6741	165	29	qq′′	qq′′	NOUN
ejpam-6741	165	30	−	−	PROPN
ejpam-6741	165	31	q′2	q′2	NOUN
ejpam-6741	165	32	̸=	̸=	PROPN
ejpam-6741	165	33	0	0	NUM
ejpam-6741	165	34	.	.	PUNCT
ejpam-6741	166	1	v	v	ADP
ejpam-6741	166	2	2	2	NUM
ejpam-6741	166	3	=	=	SYM
ejpam-6741	166	4	e3z	e3z	VERB
ejpam-6741	166	5	+	+	CCONJ
ejpam-6741	166	6	e4y	e4y	PROPN
ejpam-6741	166	7	+	+	NUM
ejpam-6741	166	8	e5	e5	PROPN
ejpam-6741	166	9	,	,	PUNCT
ejpam-6741	166	10	v	v	NOUN
ejpam-6741	166	11	3	3	NUM
ejpam-6741	166	12	=	=	SYM
ejpam-6741	166	13	−e3y	−e3y	PROPN
ejpam-6741	166	14	+	+	NUM
ejpam-6741	166	15	e4z	e4z	PROPN
ejpam-6741	167	1	+	+	CCONJ
ejpam-6741	167	2	e6	e6	PROPN
ejpam-6741	167	3	.	.	PUNCT
ejpam-6741	168	1	where	where	SCONJ
ejpam-6741	168	2	q	q	PROPN
ejpam-6741	168	3	satisfies	satisfy	VERB
ejpam-6741	168	4	the	the	DET
ejpam-6741	168	5	non	non	ADJ
ejpam-6741	168	6	-	-	ADJ
ejpam-6741	168	7	linear	linear	ADJ
ejpam-6741	168	8	expression	expression	NOUN
ejpam-6741	168	9	given	give	VERB
ejpam-6741	168	10	by	by	ADP
ejpam-6741	168	11	e4	e4	PROPN
ejpam-6741	168	12	+	+	CCONJ
ejpam-6741	168	13	q′	q′	NOUN
ejpam-6741	168	14	q	q	X
ejpam-6741	168	15	{	{	PUNCT
ejpam-6741	168	16	δt−	δt−	NUM
ejpam-6741	168	17	3	3	NUM
ejpam-6741	168	18	∫	∫	NOUN
ejpam-6741	168	19	q′′	q′′	ADP
ejpam-6741	168	20	q	q	ADJ
ejpam-6741	168	21	dt+	dt+	NOUN
ejpam-6741	168	22	e1}+	e1}+	NOUN
ejpam-6741	168	23	qq′′+2q′2	qq′′+2q′2	PUNCT
ejpam-6741	168	24	q2	q2	NOUN
ejpam-6741	168	25	=	=	SYM
ejpam-6741	168	26	δ	δ	PROPN
ejpam-6741	168	27	.	.	PUNCT
ejpam-6741	169	1	p	p	X
ejpam-6741	169	2	=	=	PROPN
ejpam-6741	169	3	k1	k1	PROPN
ejpam-6741	169	4	̸=	̸=	PROPN
ejpam-6741	169	5	0	0	NUM
ejpam-6741	169	6	,	,	PUNCT
ejpam-6741	169	7	v	v	NOUN
ejpam-6741	169	8	0	0	NUM
ejpam-6741	169	9	=	=	SYM
ejpam-6741	169	10	e1	e1	NOUN
ejpam-6741	169	11	,	,	PUNCT
ejpam-6741	169	12	11	11	NUM
ejpam-6741	169	13	q	q	NOUN
ejpam-6741	169	14	=	=	PUNCT
ejpam-6741	169	15	ek2	ek2	NOUN
ejpam-6741	169	16	t	t	PROPN
ejpam-6741	169	17	,	,	PUNCT
ejpam-6741	169	18	v	v	NOUN
ejpam-6741	169	19	1	1	NUM
ejpam-6741	169	20	=	=	SYM
ejpam-6741	169	21	δx+	δx+	PROPN
ejpam-6741	169	22	e2	e2	PROPN
ejpam-6741	169	23	,	,	PUNCT
ejpam-6741	169	24	where	where	SCONJ
ejpam-6741	169	25	k2	k2	PROPN
ejpam-6741	169	26	̸=	̸=	PROPN
ejpam-6741	169	27	0	0	NUM
ejpam-6741	169	28	,	,	PUNCT
ejpam-6741	169	29	δ	δ	PROPN
ejpam-6741	169	30	=	=	SYM
ejpam-6741	169	31	2k2	2k2	NUM
ejpam-6741	170	1	2	2	NUM
ejpam-6741	170	2	.	.	X
ejpam-6741	170	3	v	v	SYM
ejpam-6741	170	4	2	2	NUM
ejpam-6741	170	5	=	=	SYM
ejpam-6741	170	6	e3z	e3z	VERB
ejpam-6741	170	7	−	−	PROPN
ejpam-6741	170	8	e1k2y	e1k2y	SYM
ejpam-6741	171	1	+	+	CCONJ
ejpam-6741	171	2	e4	e4	PROPN
ejpam-6741	171	3	,	,	PUNCT
ejpam-6741	171	4	v	v	NOUN
ejpam-6741	171	5	3	3	NUM
ejpam-6741	171	6	=	=	SYM
ejpam-6741	171	7	−e3y	−e3y	NOUN
ejpam-6741	171	8	−	−	NOUN
ejpam-6741	171	9	e1k2z	e1k2z	X
ejpam-6741	171	10	+	+	CCONJ
ejpam-6741	171	11	e5	e5	INTJ
ejpam-6741	171	12	.	.	PUNCT
ejpam-6741	172	1	p	p	X
ejpam-6741	172	2	=	=	PROPN
ejpam-6741	172	3	k1	k1	PROPN
ejpam-6741	172	4	̸=	̸=	PROPN
ejpam-6741	172	5	0	0	NUM
ejpam-6741	172	6	,	,	PUNCT
ejpam-6741	172	7	v	v	NOUN
ejpam-6741	172	8	0	0	NUM
ejpam-6741	172	9	=	=	SYM
ejpam-6741	172	10	δt+	δt+	PROPN
ejpam-6741	172	11	k2	k2	PROPN
ejpam-6741	172	12	2(e1y	2(e1y	PROPN
ejpam-6741	172	13	+	+	CCONJ
ejpam-6741	172	14	e2z	e2z	PROPN
ejpam-6741	172	15	)	)	PUNCT
ejpam-6741	173	1	+	+	CCONJ
ejpam-6741	173	2	k2	k2	PROPN
ejpam-6741	173	3	1e3t+	1e3t+	NUM
ejpam-6741	173	4	e4	e4	PROPN
ejpam-6741	173	5	,	,	PUNCT
ejpam-6741	173	6	12	12	NUM
ejpam-6741	173	7	q	q	NOUN
ejpam-6741	173	8	=	=	SYM
ejpam-6741	173	9	k2	k2	NOUN
ejpam-6741	173	10	̸=	̸=	PROPN
ejpam-6741	173	11	0	0	NUM
ejpam-6741	173	12	.	.	PUNCT
ejpam-6741	174	1	v	v	ADP
ejpam-6741	174	2	1	1	NUM
ejpam-6741	174	3	=	=	SYM
ejpam-6741	174	4	δx−	δx−	NUM
ejpam-6741	174	5	k2	k2	ADJ
ejpam-6741	174	6	2	2	NUM
ejpam-6741	174	7	k2	k2	NOUN
ejpam-6741	174	8	1	1	NUM
ejpam-6741	174	9	(	(	PUNCT
ejpam-6741	174	10	e5y	e5y	X
ejpam-6741	174	11	+	+	PUNCT
ejpam-6741	174	12	e6z	e6z	NUM
ejpam-6741	174	13	)	)	PUNCT
ejpam-6741	175	1	+	+	CCONJ
ejpam-6741	175	2	e3x+	e3x+	PROPN
ejpam-6741	175	3	e7	e7	PROPN
ejpam-6741	175	4	,	,	PUNCT
ejpam-6741	175	5	v	v	NOUN
ejpam-6741	175	6	2	2	NUM
ejpam-6741	175	7	=	=	SYM
ejpam-6741	175	8	δy	δy	NOUN
ejpam-6741	175	9	+	+	CCONJ
ejpam-6741	175	10	e8z	e8z	PROPN
ejpam-6741	175	11	+	+	CCONJ
ejpam-6741	175	12	e5x+	e5x+	ADJ
ejpam-6741	175	13	e1t+	e1t+	NOUN
ejpam-6741	175	14	a9	a9	PROPN
ejpam-6741	175	15	,	,	PUNCT
ejpam-6741	175	16	v	v	NOUN
ejpam-6741	175	17	3	3	NUM
ejpam-6741	175	18	=	=	SYM
ejpam-6741	175	19	δz	δz	PROPN
ejpam-6741	175	20	−	−	NUM
ejpam-6741	175	21	e8y	e8y	NOUN
ejpam-6741	175	22	+	+	CCONJ
ejpam-6741	175	23	e6x+	e6x+	ADJ
ejpam-6741	175	24	e2t+	e2t+	PROPN
ejpam-6741	175	25	a10	a10	PROPN
ejpam-6741	175	26	.	.	PUNCT
ejpam-6741	176	1	table	table	NOUN
ejpam-6741	176	2	2	2	NUM
ejpam-6741	176	3	:	:	PUNCT
ejpam-6741	176	4	metrics	metric	NOUN
ejpam-6741	176	5	admitting	admit	VERB
ejpam-6741	176	6	rsvfs	rsvfs	NOUN
ejpam-6741	176	7	nature	nature	NOUN
ejpam-6741	176	8	(	(	PUNCT
ejpam-6741	176	9	δ	δ	NOUN
ejpam-6741	176	10	=	=	SYM
ejpam-6741	176	11	0	0	NUM
ejpam-6741	176	12	)	)	PUNCT
ejpam-6741	176	13	,	,	PUNCT
ejpam-6741	176	14	the	the	DET
ejpam-6741	176	15	number	number	NOUN
ejpam-6741	176	16	of	of	ADP
ejpam-6741	176	17	independent	independent	ADJ
ejpam-6741	176	18	arbitrary	arbitrary	ADJ
ejpam-6741	176	19	constants	constant	NOUN
ejpam-6741	176	20	in	in	ADP
ejpam-6741	176	21	the	the	DET
ejpam-6741	176	22	solution	solution	NOUN
ejpam-6741	176	23	for	for	ADP
ejpam-6741	176	24	v	v	NOUN
ejpam-6741	176	25	is	be	AUX
ejpam-6741	176	26	reduced	reduce	VERB
ejpam-6741	176	27	by	by	ADP
ejpam-6741	176	28	one	one	NUM
ejpam-6741	176	29	for	for	ADP
ejpam-6741	176	30	both	both	DET
ejpam-6741	176	31	branches	branch	NOUN
ejpam-6741	176	32	.	.	PUNCT
ejpam-6741	177	1	branch	branch	NOUN
ejpam-6741	177	2	3	3	NUM
ejpam-6741	177	3	shows	show	VERB
ejpam-6741	177	4	that	that	SCONJ
ejpam-6741	177	5	the	the	DET
ejpam-6741	177	6	spacetime	spacetime	NOUN
ejpam-6741	177	7	under	under	ADP
ejpam-6741	177	8	study	study	NOUN
ejpam-6741	177	9	possesses	possesse	NOUN
ejpam-6741	177	10	rsvfs	rsvfs	NOUN
ejpam-6741	177	11	of	of	ADP
ejpam-6741	177	12	a	a	DET
ejpam-6741	177	13	steady	steady	ADJ
ejpam-6741	177	14	nature	nature	NOUN
ejpam-6741	177	15	(	(	PUNCT
ejpam-6741	177	16	δ	δ	NOUN
ejpam-6741	177	17	=	=	SYM
ejpam-6741	177	18	0	0	NUM
ejpam-6741	177	19	implied	imply	VERB
ejpam-6741	177	20	by	by	ADP
ejpam-6741	177	21	the	the	DET
ejpam-6741	177	22	solution	solution	NOUN
ejpam-6741	177	23	)	)	PUNCT
ejpam-6741	177	24	with	with	ADP
ejpam-6741	177	25	a	a	DET
ejpam-6741	177	26	expanding	expanding	NOUN
ejpam-6741	177	27	,	,	PUNCT
ejpam-6741	177	28	and	and	CCONJ
ejpam-6741	177	29	the	the	DET
ejpam-6741	177	30	solution	solution	NOUN
ejpam-6741	177	31	for	for	ADP
ejpam-6741	177	32	v	v	NOUN
ejpam-6741	177	33	is	be	AUX
ejpam-6741	177	34	characterized	characterize	VERB
ejpam-6741	177	35	by	by	ADP
ejpam-6741	177	36	3	3	NUM
ejpam-6741	177	37	independent	independent	ADJ
ejpam-6741	177	38	parameters	parameter	NOUN
ejpam-6741	177	39	.	.	PUNCT
ejpam-6741	178	1	our	our	PRON
ejpam-6741	178	2	analysis	analysis	NOUN
ejpam-6741	178	3	shows	show	VERB
ejpam-6741	178	4	that	that	SCONJ
ejpam-6741	178	5	the	the	DET
ejpam-6741	178	6	constant	constant	ADJ
ejpam-6741	178	7	δ	δ	PROPN
ejpam-6741	178	8	is	be	AUX
ejpam-6741	178	9	positive	positive	ADJ
ejpam-6741	178	10	for	for	ADP
ejpam-6741	178	11	both	both	DET
ejpam-6741	178	12	branches	branch	NOUN
ejpam-6741	178	13	4	4	NUM
ejpam-6741	178	14	and	and	CCONJ
ejpam-6741	178	15	6	6	NUM
ejpam-6741	178	16	,	,	PUNCT
ejpam-6741	178	17	indicating	indicate	VERB
ejpam-6741	178	18	that	that	SCONJ
ejpam-6741	178	19	the	the	DET
ejpam-6741	178	20	rsvfs	rsvfs	NOUN
ejpam-6741	178	21	found	find	VERB
ejpam-6741	178	22	are	be	AUX
ejpam-6741	178	23	naturally	naturally	ADV
ejpam-6741	178	24	expanding	expand	VERB
ejpam-6741	178	25	with	with	ADP
ejpam-6741	178	26	a	a	DET
ejpam-6741	178	27	expanding	expanding	NOUN
ejpam-6741	178	28	,	,	PUNCT
ejpam-6741	178	29	and	and	CCONJ
ejpam-6741	178	30	the	the	DET
ejpam-6741	178	31	solution	solution	NOUN
ejpam-6741	178	32	for	for	ADP
ejpam-6741	178	33	v	v	NOUN
ejpam-6741	178	34	is	be	AUX
ejpam-6741	178	35	characterized	characterize	VERB
ejpam-6741	178	36	by	by	ADP
ejpam-6741	178	37	5	5	NUM
ejpam-6741	178	38	independent	independent	ADJ
ejpam-6741	178	39	parameters	parameter	NOUN
ejpam-6741	178	40	.	.	PUNCT
ejpam-6741	179	1	the	the	DET
ejpam-6741	179	2	dimension	dimension	NOUN
ejpam-6741	179	3	of	of	ADP
ejpam-6741	179	4	the	the	DET
ejpam-6741	179	5	rsvfs	rsvfs	NOUN
ejpam-6741	179	6	is	be	AUX
ejpam-6741	179	7	7	7	NUM
ejpam-6741	179	8	under	under	ADP
ejpam-6741	179	9	the	the	DET
ejpam-6741	179	10	conditions	condition	NOUN
ejpam-6741	179	11	of	of	ADP
ejpam-6741	179	12	branches	branch	NOUN
ejpam-6741	179	13	5	5	NUM
ejpam-6741	179	14	and	and	CCONJ
ejpam-6741	179	15	10	10	NUM
ejpam-6741	179	16	.	.	PUNCT
ejpam-6741	180	1	for	for	ADP
ejpam-6741	180	2	branch	branch	NOUN
ejpam-6741	180	3	5	5	NUM
ejpam-6741	180	4	,	,	PUNCT
ejpam-6741	180	5	δ	δ	PROPN
ejpam-6741	180	6	=	=	SYM
ejpam-6741	180	7	k2	k2	PROPN
ejpam-6741	180	8	,	,	PUNCT
ejpam-6741	180	9	which	which	PRON
ejpam-6741	180	10	reveals	reveal	VERB
ejpam-6741	180	11	that	that	SCONJ
ejpam-6741	180	12	the	the	DET
ejpam-6741	180	13	nature	nature	NOUN
ejpam-6741	180	14	of	of	ADP
ejpam-6741	180	15	the	the	DET
ejpam-6741	180	16	rsvfs	rsvfs	NOUN
ejpam-6741	180	17	is	be	AUX
ejpam-6741	180	18	only	only	ADV
ejpam-6741	180	19	expanding	expand	VERB
ejpam-6741	180	20	.	.	PUNCT
ejpam-6741	181	1	in	in	ADP
ejpam-6741	181	2	branch	branch	NOUN
ejpam-6741	181	3	10	10	NUM
ejpam-6741	181	4	,	,	PUNCT
ejpam-6741	181	5	the	the	DET
ejpam-6741	181	6	nature	nature	NOUN
ejpam-6741	181	7	of	of	ADP
ejpam-6741	181	8	the	the	DET
ejpam-6741	181	9	rsvfs	rsvfs	NOUN
ejpam-6741	181	10	may	may	AUX
ejpam-6741	181	11	be	be	AUX
ejpam-6741	181	12	expanding	expand	VERB
ejpam-6741	181	13	,	,	PUNCT
ejpam-6741	181	14	shrinking	shrinking	NOUN
ejpam-6741	181	15	,	,	PUNCT
ejpam-6741	181	16	or	or	CCONJ
ejpam-6741	181	17	steady	steady	ADJ
ejpam-6741	181	18	,	,	PUNCT
ejpam-6741	181	19	corresponding	correspond	VERB
ejpam-6741	181	20	to	to	ADP
ejpam-6741	181	21	δ	δ	PROPN
ejpam-6741	181	22	being	be	AUX
ejpam-6741	181	23	positive	positive	ADJ
ejpam-6741	181	24	,	,	PUNCT
ejpam-6741	181	25	negative	negative	ADJ
ejpam-6741	181	26	,	,	PUNCT
ejpam-6741	181	27	or	or	CCONJ
ejpam-6741	181	28	zero	zero	NUM
ejpam-6741	181	29	,	,	PUNCT
ejpam-6741	181	30	respectively	respectively	ADV
ejpam-6741	181	31	.	.	PUNCT
ejpam-6741	182	1	u.	u.	PROPN
ejpam-6741	182	2	nasib	nasib	PROPN
ejpam-6741	182	3	et	et	PROPN
ejpam-6741	182	4	al	al	PROPN
ejpam-6741	182	5	.	.	PUNCT
ejpam-6741	182	6	/	/	SYM
ejpam-6741	182	7	eur	eur	PROPN
ejpam-6741	182	8	.	.	PUNCT
ejpam-6741	183	1	j.	j.	PROPN
ejpam-6741	183	2	pure	pure	PROPN
ejpam-6741	183	3	appl	appl	PROPN
ejpam-6741	183	4	.	.	PROPN
ejpam-6741	183	5	math	math	PROPN
ejpam-6741	183	6	,	,	PUNCT
ejpam-6741	183	7	18	18	NUM
ejpam-6741	183	8	(	(	PUNCT
ejpam-6741	183	9	4	4	NUM
ejpam-6741	183	10	)	)	PUNCT
ejpam-6741	183	11	(	(	PUNCT
ejpam-6741	183	12	2025	2025	NUM
ejpam-6741	183	13	)	)	PUNCT
ejpam-6741	183	14	,	,	PUNCT
ejpam-6741	183	15	6741	6741	NUM
ejpam-6741	183	16	9	9	NUM
ejpam-6741	183	17	of	of	ADP
ejpam-6741	183	18	14	14	NUM
ejpam-6741	183	19	the	the	DET
ejpam-6741	183	20	solution	solution	NOUN
ejpam-6741	183	21	of	of	ADP
ejpam-6741	183	22	eqs.(4)-(13	eqs.(4)-(13	NOUN
ejpam-6741	183	23	)	)	PUNCT
ejpam-6741	183	24	,	,	PUNCT
ejpam-6741	183	25	under	under	ADP
ejpam-6741	183	26	the	the	DET
ejpam-6741	183	27	limitations	limitation	NOUN
ejpam-6741	183	28	of	of	ADP
ejpam-6741	183	29	branching	branch	VERB
ejpam-6741	183	30	scenarios	scenario	NOUN
ejpam-6741	183	31	7	7	NUM
ejpam-6741	183	32	and	and	CCONJ
ejpam-6741	183	33	8	8	NUM
ejpam-6741	183	34	,	,	PUNCT
ejpam-6741	183	35	provides	provide	VERB
ejpam-6741	183	36	a	a	DET
ejpam-6741	183	37	solution	solution	NOUN
ejpam-6741	183	38	for	for	ADP
ejpam-6741	183	39	v	v	NOUN
ejpam-6741	183	40	containing	contain	VERB
ejpam-6741	183	41	10	10	NUM
ejpam-6741	183	42	independent	independent	ADJ
ejpam-6741	183	43	parameters	parameter	NOUN
ejpam-6741	183	44	,	,	PUNCT
ejpam-6741	183	45	which	which	PRON
ejpam-6741	183	46	are	be	AUX
ejpam-6741	183	47	only	only	ADV
ejpam-6741	183	48	expanding	expand	VERB
ejpam-6741	183	49	by	by	ADP
ejpam-6741	183	50	nature	nature	NOUN
ejpam-6741	183	51	(	(	PUNCT
ejpam-6741	183	52	δ	δ	NOUN
ejpam-6741	183	53	=	=	SYM
ejpam-6741	183	54	3k21	3k21	PROPN
ejpam-6741	183	55	>	>	X
ejpam-6741	183	56	0	0	NUM
ejpam-6741	183	57	)	)	PUNCT
ejpam-6741	183	58	.	.	PUNCT
ejpam-6741	184	1	investigation	investigation	NOUN
ejpam-6741	184	2	of	of	ADP
ejpam-6741	184	3	rsvfs	rsvfs	NOUN
ejpam-6741	184	4	for	for	ADP
ejpam-6741	184	5	lrs	lrs	PROPN
ejpam-6741	184	6	bianchi	bianchi	PROPN
ejpam-6741	184	7	type	type	NOUN
ejpam-6741	184	8	i	i	PRON
ejpam-6741	184	9	spacetime	spacetime	VERB
ejpam-6741	184	10	,	,	PUNCT
ejpam-6741	184	11	within	within	ADP
ejpam-6741	184	12	the	the	DET
ejpam-6741	184	13	limits	limit	NOUN
ejpam-6741	184	14	of	of	ADP
ejpam-6741	184	15	the	the	DET
ejpam-6741	184	16	branching	branch	VERB
ejpam-6741	184	17	constraints	constraint	NOUN
ejpam-6741	184	18	of	of	ADP
ejpam-6741	184	19	9	9	NUM
ejpam-6741	184	20	and	and	CCONJ
ejpam-6741	184	21	11	11	NUM
ejpam-6741	184	22	,	,	PUNCT
ejpam-6741	184	23	gives	give	VERB
ejpam-6741	184	24	a	a	DET
ejpam-6741	184	25	solution	solution	NOUN
ejpam-6741	184	26	for	for	ADP
ejpam-6741	184	27	v	v	NOUN
ejpam-6741	184	28	characterized	characterize	VERB
ejpam-6741	184	29	by	by	ADP
ejpam-6741	184	30	6	6	NUM
ejpam-6741	184	31	independent	independent	ADJ
ejpam-6741	184	32	parameters	parameter	NOUN
ejpam-6741	184	33	..	..	PUNCT
ejpam-6741	184	34	in	in	ADP
ejpam-6741	184	35	branch	branch	NOUN
ejpam-6741	184	36	9	9	NUM
ejpam-6741	184	37	,	,	PUNCT
ejpam-6741	184	38	δ	δ	PROPN
ejpam-6741	184	39	may	may	AUX
ejpam-6741	184	40	take	take	VERB
ejpam-6741	184	41	any	any	DET
ejpam-6741	184	42	value	value	NOUN
ejpam-6741	184	43	(	(	PUNCT
ejpam-6741	184	44	as	as	SCONJ
ejpam-6741	184	45	it	it	PRON
ejpam-6741	184	46	is	be	AUX
ejpam-6741	184	47	proportional	proportional	ADJ
ejpam-6741	184	48	to	to	ADP
ejpam-6741	184	49	e1	e1	PROPN
ejpam-6741	184	50	)	)	PUNCT
ejpam-6741	184	51	,	,	PUNCT
ejpam-6741	184	52	which	which	PRON
ejpam-6741	184	53	indicates	indicate	VERB
ejpam-6741	184	54	that	that	SCONJ
ejpam-6741	184	55	the	the	DET
ejpam-6741	184	56	nature	nature	NOUN
ejpam-6741	184	57	of	of	ADP
ejpam-6741	184	58	the	the	DET
ejpam-6741	184	59	found	find	VERB
ejpam-6741	184	60	rsvfs	rsvfs	NOUN
ejpam-6741	184	61	may	may	AUX
ejpam-6741	184	62	be	be	AUX
ejpam-6741	184	63	steady	steady	ADJ
ejpam-6741	184	64	,	,	PUNCT
ejpam-6741	184	65	shrinking	shrinking	NOUN
ejpam-6741	184	66	,	,	PUNCT
ejpam-6741	184	67	or	or	CCONJ
ejpam-6741	184	68	expanding	expand	VERB
ejpam-6741	184	69	.	.	PUNCT
ejpam-6741	185	1	in	in	ADP
ejpam-6741	185	2	contrast	contrast	NOUN
ejpam-6741	185	3	,	,	PUNCT
ejpam-6741	185	4	δ	δ	PROPN
ejpam-6741	185	5	turns	turn	VERB
ejpam-6741	185	6	out	out	ADP
ejpam-6741	185	7	to	to	PART
ejpam-6741	185	8	be	be	AUX
ejpam-6741	185	9	positive	positive	ADJ
ejpam-6741	185	10	in	in	ADP
ejpam-6741	185	11	branch	branch	NOUN
ejpam-6741	185	12	11	11	NUM
ejpam-6741	185	13	(	(	PUNCT
ejpam-6741	185	14	δ	δ	NOUN
ejpam-6741	185	15	=	=	SYM
ejpam-6741	185	16	2k22	2k22	NUM
ejpam-6741	185	17	)	)	PUNCT
ejpam-6741	185	18	,	,	PUNCT
ejpam-6741	185	19	showing	show	VERB
ejpam-6741	185	20	that	that	SCONJ
ejpam-6741	185	21	the	the	DET
ejpam-6741	185	22	rsvfs	rsvfs	NOUN
ejpam-6741	185	23	are	be	AUX
ejpam-6741	185	24	expanding	expand	VERB
ejpam-6741	185	25	.	.	PUNCT
ejpam-6741	186	1	the	the	DET
ejpam-6741	186	2	solution	solution	NOUN
ejpam-6741	186	3	of	of	ADP
ejpam-6741	186	4	eqs.(4)-(13	eqs.(4)-(13	NOUN
ejpam-6741	186	5	)	)	PUNCT
ejpam-6741	186	6	leads	lead	VERB
ejpam-6741	186	7	to	to	ADP
ejpam-6741	186	8	the	the	DET
ejpam-6741	186	9	precise	precise	ADJ
ejpam-6741	186	10	form	form	NOUN
ejpam-6741	186	11	of	of	ADP
ejpam-6741	186	12	a	a	DET
ejpam-6741	186	13	solution	solution	NOUN
ejpam-6741	186	14	for	for	ADP
ejpam-6741	186	15	v	v	NOUN
ejpam-6741	186	16	characterized	characterize	VERB
ejpam-6741	186	17	by	by	ADP
ejpam-6741	186	18	11	11	NUM
ejpam-6741	186	19	independent	independent	ADJ
ejpam-6741	186	20	parameters	parameter	NOUN
ejpam-6741	186	21	.	.	PUNCT
ejpam-6741	187	1	under	under	ADP
ejpam-6741	187	2	the	the	DET
ejpam-6741	187	3	conditions	condition	NOUN
ejpam-6741	187	4	imposed	impose	VERB
ejpam-6741	187	5	by	by	ADP
ejpam-6741	187	6	branch	branch	NOUN
ejpam-6741	187	7	12	12	NUM
ejpam-6741	187	8	.	.	PUNCT
ejpam-6741	188	1	here	here	ADV
ejpam-6741	188	2	the	the	DET
ejpam-6741	188	3	constant	constant	ADJ
ejpam-6741	188	4	δ	δ	PROPN
ejpam-6741	188	5	is	be	AUX
ejpam-6741	188	6	arbitrary	arbitrary	ADJ
ejpam-6741	188	7	,	,	PUNCT
ejpam-6741	188	8	and	and	CCONJ
ejpam-6741	188	9	the	the	DET
ejpam-6741	188	10	rsvfs	rsvfs	NOUN
ejpam-6741	188	11	can	can	AUX
ejpam-6741	188	12	be	be	AUX
ejpam-6741	188	13	of	of	ADP
ejpam-6741	188	14	any	any	DET
ejpam-6741	188	15	nature	nature	NOUN
ejpam-6741	188	16	among	among	ADP
ejpam-6741	188	17	the	the	DET
ejpam-6741	188	18	three	three	NUM
ejpam-6741	188	19	mentioned	mention	VERB
ejpam-6741	188	20	.	.	PUNCT
ejpam-6741	189	1	3	3	X
ejpam-6741	189	2	.	.	X
ejpam-6741	189	3	physical	physical	ADJ
ejpam-6741	189	4	implications	implication	NOUN
ejpam-6741	189	5	to	to	PART
ejpam-6741	189	6	ensure	ensure	VERB
ejpam-6741	189	7	the	the	DET
ejpam-6741	189	8	physical	physical	ADJ
ejpam-6741	189	9	validity	validity	NOUN
ejpam-6741	189	10	of	of	ADP
ejpam-6741	189	11	the	the	DET
ejpam-6741	189	12	obtained	obtain	VERB
ejpam-6741	189	13	metrics	metric	NOUN
ejpam-6741	189	14	,	,	PUNCT
ejpam-6741	189	15	it	it	PRON
ejpam-6741	189	16	is	be	AUX
ejpam-6741	189	17	necessary	necessary	ADJ
ejpam-6741	189	18	to	to	PART
ejpam-6741	189	19	find	find	VERB
ejpam-6741	189	20	the	the	DET
ejpam-6741	189	21	nonvanishing	nonvanishe	VERB
ejpam-6741	189	22	components	component	NOUN
ejpam-6741	189	23	of	of	ADP
ejpam-6741	189	24	the	the	DET
ejpam-6741	189	25	energy	energy	NOUN
ejpam-6741	189	26	-	-	PUNCT
ejpam-6741	189	27	momentum	momentum	NOUN
ejpam-6741	189	28	tensor	tensor	NOUN
ejpam-6741	189	29	(	(	PUNCT
ejpam-6741	189	30	emt	emt	PROPN
ejpam-6741	189	31	)	)	PUNCT
ejpam-6741	189	32	,	,	PUNCT
ejpam-6741	189	33	denoted	denote	VERB
ejpam-6741	189	34	by	by	ADP
ejpam-6741	189	35	tmn	tmn	NOUN
ejpam-6741	189	36	,	,	PUNCT
ejpam-6741	189	37	for	for	ADP
ejpam-6741	189	38	the	the	DET
ejpam-6741	189	39	specified	specified	ADJ
ejpam-6741	189	40	spacetime	spacetime	NOUN
ejpam-6741	189	41	.	.	PUNCT
ejpam-6741	190	1	equation	equation	NOUN
ejpam-6741	190	2	(	(	PUNCT
ejpam-6741	190	3	15	15	NUM
ejpam-6741	190	4	)	)	PUNCT
ejpam-6741	190	5	gives	give	VERB
ejpam-6741	190	6	these	these	DET
ejpam-6741	190	7	terms	term	NOUN
ejpam-6741	190	8	for	for	ADP
ejpam-6741	190	9	the	the	DET
ejpam-6741	190	10	spacetime	spacetime	NOUN
ejpam-6741	190	11	(	(	PUNCT
ejpam-6741	190	12	2	2	NUM
ejpam-6741	190	13	)	)	PUNCT
ejpam-6741	190	14	.	.	PUNCT
ejpam-6741	191	1	t00	t00	NOUN
ejpam-6741	191	2	=	=	PUNCT
ejpam-6741	192	1	2p′q′	2p′q′	NUM
ejpam-6741	192	2	pq	pq	NOUN
ejpam-6741	192	3	+	+	CCONJ
ejpam-6741	192	4	q′2	q′2	PROPN
ejpam-6741	192	5	q2	q2	PROPN
ejpam-6741	192	6	,	,	PUNCT
ejpam-6741	192	7	t11	t11	NOUN
ejpam-6741	192	8	=	=	SYM
ejpam-6741	192	9	−p2	−p2	PROPN
ejpam-6741	192	10	q2	q2	NOUN
ejpam-6741	192	11	(	(	PUNCT
ejpam-6741	192	12	2qq′′	2qq′′	PROPN
ejpam-6741	192	13	+	+	CCONJ
ejpam-6741	192	14	q′2	q′2	CCONJ
ejpam-6741	192	15	)	)	PUNCT
ejpam-6741	192	16	,	,	PUNCT
ejpam-6741	192	17	t22	t22	PROPN
ejpam-6741	192	18	=	=	SYM
ejpam-6741	192	19	−p	−p	ADJ
ejpam-6741	192	20	q	q	NOUN
ejpam-6741	192	21	(	(	PUNCT
ejpam-6741	192	22	pq′′	pq′′	X
ejpam-6741	192	23	+	+	NOUN
ejpam-6741	192	24	qp′′	qp′′	PROPN
ejpam-6741	192	25	+	+	CCONJ
ejpam-6741	192	26	p′q′	p′q′	PROPN
ejpam-6741	192	27	)	)	PUNCT
ejpam-6741	192	28	,	,	PUNCT
ejpam-6741	192	29	t33	t33	PROPN
ejpam-6741	192	30	=	=	SYM
ejpam-6741	192	31	t22	t22	PROPN
ejpam-6741	192	32	.	.	PUNCT
ejpam-6741	193	1	(	(	PUNCT
ejpam-6741	193	2	15	15	NUM
ejpam-6741	193	3	)	)	PUNCT
ejpam-6741	193	4	based	base	VERB
ejpam-6741	193	5	on	on	ADP
ejpam-6741	193	6	the	the	DET
ejpam-6741	193	7	type	type	NOUN
ejpam-6741	193	8	of	of	ADP
ejpam-6741	193	9	matter	matter	NOUN
ejpam-6741	193	10	it	it	PRON
ejpam-6741	193	11	describes	describe	VERB
ejpam-6741	193	12	,	,	PUNCT
ejpam-6741	193	13	the	the	DET
ejpam-6741	193	14	emt	emt	NOUN
ejpam-6741	193	15	takes	take	VERB
ejpam-6741	193	16	distinct	distinct	ADJ
ejpam-6741	193	17	forms	form	NOUN
ejpam-6741	193	18	.	.	PUNCT
ejpam-6741	194	1	the	the	DET
ejpam-6741	194	2	form	form	NOUN
ejpam-6741	194	3	tmn	tmn	NOUN
ejpam-6741	194	4	=	=	PUNCT
ejpam-6741	194	5	(	(	PUNCT
ejpam-6741	194	6	ρ+p	ρ+p	NUM
ejpam-6741	194	7	)	)	PUNCT
ejpam-6741	194	8	umun+pgmn	umun+pgmn	PROPN
ejpam-6741	194	9	indicates	indicate	VERB
ejpam-6741	194	10	a	a	DET
ejpam-6741	194	11	perfect	perfect	ADJ
ejpam-6741	194	12	fluid	fluid	NOUN
ejpam-6741	194	13	,	,	PUNCT
ejpam-6741	194	14	while	while	SCONJ
ejpam-6741	194	15	the	the	DET
ejpam-6741	194	16	form	form	NOUN
ejpam-6741	194	17	tmn	tmn	NOUN
ejpam-6741	194	18	=	=	SYM
ejpam-6741	194	19	(	(	PUNCT
ejpam-6741	194	20	ρ+p∥)umun+(p∥−	ρ+p∥)umun+(p∥−	PROPN
ejpam-6741	194	21	p⊥)vmvn+p⊥gmn	p⊥)vmvn+p⊥gmn	PROPN
ejpam-6741	194	22	illustrates	illustrate	VERB
ejpam-6741	194	23	an	an	DET
ejpam-6741	194	24	anisotropic	anisotropic	NOUN
ejpam-6741	194	25	fluid	fluid	NOUN
ejpam-6741	194	26	.	.	PUNCT
ejpam-6741	195	1	here	here	ADV
ejpam-6741	195	2	the	the	DET
ejpam-6741	195	3	symbols	symbol	NOUN
ejpam-6741	195	4	ρ	ρ	PROPN
ejpam-6741	195	5	,	,	PUNCT
ejpam-6741	195	6	p	p	NOUN
ejpam-6741	195	7	,	,	PUNCT
ejpam-6741	195	8	p∥	p∥	NOUN
ejpam-6741	195	9	,	,	PUNCT
ejpam-6741	195	10	p⊥	p⊥	NOUN
ejpam-6741	195	11	stand	stand	VERB
ejpam-6741	195	12	for	for	ADP
ejpam-6741	195	13	energy	energy	NOUN
ejpam-6741	195	14	density	density	NOUN
ejpam-6741	195	15	,	,	PUNCT
ejpam-6741	195	16	isotropic	isotropic	ADJ
ejpam-6741	195	17	pressure	pressure	NOUN
ejpam-6741	195	18	,	,	PUNCT
ejpam-6741	195	19	pressure	pressure	NOUN
ejpam-6741	195	20	parallel	parallel	NOUN
ejpam-6741	195	21	to	to	ADP
ejpam-6741	195	22	the	the	DET
ejpam-6741	195	23	preferred	preferred	ADJ
ejpam-6741	195	24	spatial	spatial	ADJ
ejpam-6741	195	25	direction	direction	NOUN
ejpam-6741	195	26	,	,	PUNCT
ejpam-6741	195	27	and	and	CCONJ
ejpam-6741	195	28	pressure	pressure	NOUN
ejpam-6741	195	29	perpendicular	perpendicular	NOUN
ejpam-6741	195	30	to	to	ADP
ejpam-6741	195	31	it	it	PRON
ejpam-6741	195	32	,	,	PUNCT
ejpam-6741	195	33	respectively	respectively	ADV
ejpam-6741	195	34	.	.	PUNCT
ejpam-6741	196	1	moreover	moreover	ADV
ejpam-6741	196	2	,	,	PUNCT
ejpam-6741	196	3	um	um	INTJ
ejpam-6741	196	4	and	and	CCONJ
ejpam-6741	196	5	vm	vm	PROPN
ejpam-6741	196	6	indicate	indicate	VERB
ejpam-6741	196	7	the	the	DET
ejpam-6741	196	8	four	four	NUM
ejpam-6741	196	9	-	-	PUNCT
ejpam-6741	196	10	velocity	velocity	NOUN
ejpam-6741	196	11	vector	vector	NOUN
ejpam-6741	196	12	and	and	CCONJ
ejpam-6741	196	13	a	a	DET
ejpam-6741	196	14	space	space	NOUN
ejpam-6741	196	15	-	-	PUNCT
ejpam-6741	196	16	like	like	ADJ
ejpam-6741	196	17	unit	unit	NOUN
ejpam-6741	196	18	vector	vector	NOUN
ejpam-6741	196	19	,	,	PUNCT
ejpam-6741	196	20	respectively	respectively	ADV
ejpam-6741	196	21	,	,	PUNCT
ejpam-6741	196	22	such	such	ADJ
ejpam-6741	196	23	that	that	DET
ejpam-6741	196	24	umum	umum	NOUN
ejpam-6741	196	25	=	=	SYM
ejpam-6741	196	26	−1	−1	NOUN
ejpam-6741	196	27	,	,	PUNCT
ejpam-6741	196	28	vmvm	vmvm	NOUN
ejpam-6741	196	29	=	=	SYM
ejpam-6741	196	30	1	1	NUM
ejpam-6741	196	31	and	and	CCONJ
ejpam-6741	196	32	umvm	umvm	ADJ
ejpam-6741	196	33	=	=	SYM
ejpam-6741	196	34	0	0	PUNCT
ejpam-6741	197	1	[	[	X
ejpam-6741	197	2	22	22	NUM
ejpam-6741	197	3	]	]	PUNCT
ejpam-6741	197	4	.	.	PUNCT
ejpam-6741	198	1	the	the	DET
ejpam-6741	198	2	terms	term	NOUN
ejpam-6741	198	3	p∥	p∥	NOUN
ejpam-6741	198	4	and	and	CCONJ
ejpam-6741	198	5	p⊥	p⊥	NOUN
ejpam-6741	198	6	become	become	VERB
ejpam-6741	198	7	equal	equal	ADJ
ejpam-6741	198	8	when	when	SCONJ
ejpam-6741	198	9	the	the	DET
ejpam-6741	198	10	matter	matter	NOUN
ejpam-6741	198	11	is	be	AUX
ejpam-6741	198	12	a	a	DET
ejpam-6741	198	13	perfect	perfect	ADJ
ejpam-6741	198	14	fluid	fluid	NOUN
ejpam-6741	198	15	.	.	PUNCT
ejpam-6741	199	1	the	the	DET
ejpam-6741	199	2	equation	equation	NOUN
ejpam-6741	199	3	of	of	ADP
ejpam-6741	199	4	state	state	NOUN
ejpam-6741	199	5	(	(	PUNCT
ejpam-6741	199	6	eos	eos	PROPN
ejpam-6741	199	7	)	)	PUNCT
ejpam-6741	199	8	for	for	ADP
ejpam-6741	199	9	a	a	DET
ejpam-6741	199	10	perfect	perfect	ADJ
ejpam-6741	199	11	fluid	fluid	NOUN
ejpam-6741	199	12	has	have	VERB
ejpam-6741	199	13	the	the	DET
ejpam-6741	199	14	form	form	NOUN
ejpam-6741	199	15	p	p	NOUN
ejpam-6741	199	16	=	=	NOUN
ejpam-6741	199	17	wρ	wρ	NOUN
ejpam-6741	199	18	,	,	PUNCT
ejpam-6741	199	19	where	where	SCONJ
ejpam-6741	199	20	w	w	NOUN
ejpam-6741	199	21	is	be	AUX
ejpam-6741	199	22	the	the	DET
ejpam-6741	199	23	eos	eos	PROPN
ejpam-6741	199	24	parameter	parameter	NOUN
ejpam-6741	199	25	.	.	PUNCT
ejpam-6741	200	1	to	to	PART
ejpam-6741	200	2	ensure	ensure	VERB
ejpam-6741	200	3	that	that	SCONJ
ejpam-6741	200	4	the	the	DET
ejpam-6741	200	5	system	system	NOUN
ejpam-6741	200	6	preserves	preserve	VERB
ejpam-6741	200	7	mechanical	mechanical	ADJ
ejpam-6741	200	8	stability	stability	NOUN
ejpam-6741	200	9	and	and	CCONJ
ejpam-6741	200	10	adheres	adhere	VERB
ejpam-6741	200	11	to	to	ADP
ejpam-6741	200	12	causality	causality	NOUN
ejpam-6741	200	13	,	,	PUNCT
ejpam-6741	200	14	the	the	DET
ejpam-6741	200	15	condition	condition	NOUN
ejpam-6741	200	16	−1	−1	NOUN
ejpam-6741	200	17	≤	≤	NUM
ejpam-6741	200	18	w	w	NOUN
ejpam-6741	200	19	≤	≤	NUM
ejpam-6741	200	20	1	1	NUM
ejpam-6741	200	21	should	should	AUX
ejpam-6741	200	22	hold	hold	VERB
ejpam-6741	200	23	.	.	PUNCT
ejpam-6741	201	1	different	different	ADJ
ejpam-6741	201	2	values	value	NOUN
ejpam-6741	201	3	of	of	ADP
ejpam-6741	201	4	w	w	PROPN
ejpam-6741	201	5	indicate	indicate	VERB
ejpam-6741	201	6	various	various	ADJ
ejpam-6741	201	7	matter	matter	NOUN
ejpam-6741	201	8	sources	source	NOUN
ejpam-6741	201	9	.	.	PUNCT
ejpam-6741	202	1	for	for	ADP
ejpam-6741	202	2	w	w	PROPN
ejpam-6741	202	3	=	=	SYM
ejpam-6741	202	4	−1	−1	NOUN
ejpam-6741	202	5	,	,	PUNCT
ejpam-6741	202	6	the	the	DET
ejpam-6741	202	7	matter	matter	NOUN
ejpam-6741	202	8	source	source	NOUN
ejpam-6741	202	9	is	be	AUX
ejpam-6741	202	10	a	a	DET
ejpam-6741	202	11	cosmological	cosmological	ADJ
ejpam-6741	202	12	constant	constant	ADJ
ejpam-6741	202	13	,	,	PUNCT
ejpam-6741	202	14	also	also	ADV
ejpam-6741	202	15	called	call	VERB
ejpam-6741	202	16	vacuum	vacuum	NOUN
ejpam-6741	202	17	energy	energy	NOUN
ejpam-6741	202	18	.	.	PUNCT
ejpam-6741	203	1	taking	take	VERB
ejpam-6741	203	2	w	w	NOUN
ejpam-6741	203	3	=	=	NOUN
ejpam-6741	203	4	0	0	NUM
ejpam-6741	203	5	,	,	PUNCT
ejpam-6741	203	6	the	the	DET
ejpam-6741	203	7	matter	matter	NOUN
ejpam-6741	203	8	source	source	NOUN
ejpam-6741	203	9	is	be	AUX
ejpam-6741	203	10	dust	dust	NOUN
ejpam-6741	203	11	,	,	PUNCT
ejpam-6741	203	12	also	also	ADV
ejpam-6741	203	13	referred	refer	VERB
ejpam-6741	203	14	to	to	ADP
ejpam-6741	203	15	as	as	ADP
ejpam-6741	203	16	nonrelativistic	nonrelativistic	ADJ
ejpam-6741	203	17	matter	matter	NOUN
ejpam-6741	203	18	.	.	PUNCT
ejpam-6741	204	1	the	the	DET
ejpam-6741	204	2	matter	matter	NOUN
ejpam-6741	204	3	source	source	NOUN
ejpam-6741	204	4	will	will	AUX
ejpam-6741	204	5	be	be	AUX
ejpam-6741	204	6	stiff	stiff	ADJ
ejpam-6741	204	7	matter	matter	NOUN
ejpam-6741	204	8	(	(	PUNCT
ejpam-6741	204	9	zel’dovich	zel’dovich	NOUN
ejpam-6741	204	10	matter	matter	NOUN
ejpam-6741	204	11	)	)	PUNCT
ejpam-6741	204	12	when	when	SCONJ
ejpam-6741	204	13	w	w	PROPN
ejpam-6741	204	14	=	=	SYM
ejpam-6741	204	15	1	1	NUM
ejpam-6741	204	16	[	[	X
ejpam-6741	204	17	23	23	NUM
ejpam-6741	204	18	]	]	PUNCT
ejpam-6741	204	19	.	.	PUNCT
ejpam-6741	205	1	for	for	ADP
ejpam-6741	205	2	branches	branch	NOUN
ejpam-6741	205	3	7	7	NUM
ejpam-6741	205	4	and	and	CCONJ
ejpam-6741	205	5	8	8	NUM
ejpam-6741	205	6	,	,	PUNCT
ejpam-6741	205	7	we	we	PRON
ejpam-6741	205	8	obtained	obtain	VERB
ejpam-6741	205	9	the	the	DET
ejpam-6741	205	10	physical	physical	ADJ
ejpam-6741	205	11	terms	term	NOUN
ejpam-6741	205	12	as	as	ADP
ejpam-6741	205	13	ρ	ρ	PROPN
ejpam-6741	205	14	=	=	SYM
ejpam-6741	205	15	3k21	3k21	NOUN
ejpam-6741	205	16	and	and	CCONJ
ejpam-6741	205	17	p	p	NOUN
ejpam-6741	205	18	=	=	SYM
ejpam-6741	205	19	−3k21	−3k21	PROPN
ejpam-6741	205	20	,	,	PUNCT
ejpam-6741	205	21	for	for	ADP
ejpam-6741	205	22	which	which	PRON
ejpam-6741	205	23	the	the	DET
ejpam-6741	205	24	eos	eos	PROPN
ejpam-6741	205	25	parameter	parameter	NOUN
ejpam-6741	205	26	turns	turn	VERB
ejpam-6741	205	27	out	out	ADP
ejpam-6741	205	28	to	to	PART
ejpam-6741	205	29	be	be	AUX
ejpam-6741	205	30	w	w	NOUN
ejpam-6741	205	31	=	=	SYM
ejpam-6741	205	32	−1	−1	NOUN
ejpam-6741	205	33	,	,	PUNCT
ejpam-6741	205	34	identifying	identify	VERB
ejpam-6741	205	35	that	that	SCONJ
ejpam-6741	205	36	the	the	DET
ejpam-6741	205	37	source	source	NOUN
ejpam-6741	205	38	of	of	ADP
ejpam-6741	205	39	matter	matter	NOUN
ejpam-6741	205	40	in	in	ADP
ejpam-6741	205	41	the	the	DET
ejpam-6741	205	42	branches	branch	NOUN
ejpam-6741	205	43	under	under	ADP
ejpam-6741	205	44	study	study	NOUN
ejpam-6741	205	45	corresponds	correspond	NOUN
ejpam-6741	205	46	to	to	ADP
ejpam-6741	205	47	the	the	DET
ejpam-6741	205	48	cosmological	cosmological	ADJ
ejpam-6741	205	49	constant	constant	ADJ
ejpam-6741	205	50	,	,	PUNCT
ejpam-6741	205	51	or	or	CCONJ
ejpam-6741	205	52	vacuum	vacuum	NOUN
ejpam-6741	205	53	energy	energy	NOUN
ejpam-6741	205	54	.	.	PUNCT
ejpam-6741	206	1	u.	u.	PROPN
ejpam-6741	206	2	nasib	nasib	PROPN
ejpam-6741	206	3	et	et	PROPN
ejpam-6741	206	4	al	al	PROPN
ejpam-6741	206	5	.	.	PUNCT
ejpam-6741	206	6	/	/	SYM
ejpam-6741	206	7	eur	eur	PROPN
ejpam-6741	206	8	.	.	PUNCT
ejpam-6741	207	1	j.	j.	PROPN
ejpam-6741	207	2	pure	pure	PROPN
ejpam-6741	207	3	appl	appl	PROPN
ejpam-6741	207	4	.	.	PROPN
ejpam-6741	207	5	math	math	PROPN
ejpam-6741	207	6	,	,	PUNCT
ejpam-6741	207	7	18	18	NUM
ejpam-6741	207	8	(	(	PUNCT
ejpam-6741	207	9	4	4	NUM
ejpam-6741	207	10	)	)	PUNCT
ejpam-6741	207	11	(	(	PUNCT
ejpam-6741	207	12	2025	2025	NUM
ejpam-6741	207	13	)	)	PUNCT
ejpam-6741	207	14	,	,	PUNCT
ejpam-6741	207	15	6741	6741	NUM
ejpam-6741	207	16	10	10	NUM
ejpam-6741	207	17	of	of	ADP
ejpam-6741	207	18	14	14	NUM
ejpam-6741	207	19	this	this	DET
ejpam-6741	207	20	result	result	NOUN
ejpam-6741	207	21	reveals	reveal	VERB
ejpam-6741	207	22	that	that	SCONJ
ejpam-6741	207	23	these	these	DET
ejpam-6741	207	24	branches	branch	NOUN
ejpam-6741	207	25	represent	represent	VERB
ejpam-6741	207	26	a	a	DET
ejpam-6741	207	27	constant	constant	ADJ
ejpam-6741	207	28	energy	energy	NOUN
ejpam-6741	207	29	density	density	NOUN
ejpam-6741	207	30	that	that	PRON
ejpam-6741	207	31	drives	drive	VERB
ejpam-6741	207	32	cosmic	cosmic	ADJ
ejpam-6741	207	33	acceleration	acceleration	NOUN
ejpam-6741	207	34	.	.	PUNCT
ejpam-6741	208	1	in	in	ADP
ejpam-6741	208	2	a	a	DET
ejpam-6741	208	3	similar	similar	ADJ
ejpam-6741	208	4	way	way	NOUN
ejpam-6741	208	5	,	,	PUNCT
ejpam-6741	208	6	one	one	PRON
ejpam-6741	208	7	can	can	AUX
ejpam-6741	208	8	study	study	VERB
ejpam-6741	208	9	all	all	DET
ejpam-6741	208	10	metrics	metric	NOUN
ejpam-6741	208	11	obtained	obtain	VERB
ejpam-6741	208	12	in	in	ADP
ejpam-6741	208	13	all	all	DET
ejpam-6741	208	14	branches	branch	NOUN
ejpam-6741	208	15	with	with	ADP
ejpam-6741	208	16	respect	respect	NOUN
ejpam-6741	208	17	to	to	ADP
ejpam-6741	208	18	the	the	DET
ejpam-6741	208	19	eos	eos	PROPN
ejpam-6741	208	20	.	.	PUNCT
ejpam-6741	209	1	for	for	ADP
ejpam-6741	209	2	an	an	DET
ejpam-6741	209	3	anisotropic	anisotropic	NOUN
ejpam-6741	209	4	fluid	fluid	NOUN
ejpam-6741	209	5	,	,	PUNCT
ejpam-6741	209	6	once	once	SCONJ
ejpam-6741	209	7	the	the	DET
ejpam-6741	209	8	values	value	NOUN
ejpam-6741	209	9	of	of	ADP
ejpam-6741	209	10	density	density	NOUN
ejpam-6741	209	11	and	and	CCONJ
ejpam-6741	209	12	pressure	pressure	NOUN
ejpam-6741	209	13	are	be	AUX
ejpam-6741	209	14	determined	determine	VERB
ejpam-6741	209	15	,	,	PUNCT
ejpam-6741	209	16	the	the	DET
ejpam-6741	209	17	following	follow	VERB
ejpam-6741	209	18	energy	energy	NOUN
ejpam-6741	209	19	conditions	condition	NOUN
ejpam-6741	209	20	are	be	AUX
ejpam-6741	209	21	evaluated	evaluate	VERB
ejpam-6741	209	22	in	in	ADP
ejpam-6741	209	23	detail	detail	NOUN
ejpam-6741	209	24	to	to	PART
ejpam-6741	209	25	analyze	analyze	VERB
ejpam-6741	209	26	the	the	DET
ejpam-6741	209	27	physical	physical	ADJ
ejpam-6741	209	28	viability	viability	NOUN
ejpam-6741	209	29	of	of	ADP
ejpam-6741	209	30	the	the	DET
ejpam-6741	209	31	obtained	obtain	VERB
ejpam-6741	209	32	models	model	NOUN
ejpam-6741	209	33	[	[	X
ejpam-6741	209	34	22	22	NUM
ejpam-6741	209	35	]	]	SYM
ejpam-6741	209	36	:	:	PUNCT
ejpam-6741	209	37	1	1	X
ejpam-6741	209	38	.	.	PUNCT
ejpam-6741	209	39	null	null	ADJ
ejpam-6741	209	40	energy	energy	NOUN
ejpam-6741	209	41	condition	condition	NOUN
ejpam-6741	209	42	(	(	PUNCT
ejpam-6741	209	43	nec	nec	PROPN
ejpam-6741	209	44	)	)	PUNCT
ejpam-6741	209	45	requires	require	VERB
ejpam-6741	209	46	that	that	SCONJ
ejpam-6741	209	47	(	(	PUNCT
ejpam-6741	209	48	ρ+	ρ+	NUM
ejpam-6741	209	49	p∥	p∥	X
ejpam-6741	209	50	≥	≥	NOUN
ejpam-6741	209	51	0	0	NUM
ejpam-6741	209	52	,	,	PUNCT
ejpam-6741	209	53	ρ+	ρ+	NUM
ejpam-6741	209	54	p⊥	p⊥	NOUN
ejpam-6741	209	55	≥	≥	NOUN
ejpam-6741	209	56	0	0	NUM
ejpam-6741	209	57	)	)	PUNCT
ejpam-6741	209	58	.	.	PUNCT
ejpam-6741	210	1	2	2	X
ejpam-6741	210	2	.	.	X
ejpam-6741	210	3	weak	weak	ADJ
ejpam-6741	210	4	energy	energy	NOUN
ejpam-6741	210	5	condition	condition	NOUN
ejpam-6741	210	6	(	(	PUNCT
ejpam-6741	210	7	wec	wec	NOUN
ejpam-6741	210	8	)	)	PUNCT
ejpam-6741	210	9	requires	require	VERB
ejpam-6741	210	10	(	(	PUNCT
ejpam-6741	210	11	ρ	ρ	X
ejpam-6741	210	12	≥	≥	NOUN
ejpam-6741	210	13	0	0	NUM
ejpam-6741	210	14	)	)	PUNCT
ejpam-6741	210	15	in	in	ADP
ejpam-6741	210	16	addition	addition	NOUN
ejpam-6741	210	17	to	to	ADP
ejpam-6741	210	18	the	the	DET
ejpam-6741	210	19	nec	nec	PROPN
ejpam-6741	210	20	.	.	PROPN
ejpam-6741	211	1	3	3	X
ejpam-6741	211	2	.	.	X
ejpam-6741	211	3	strong	strong	ADJ
ejpam-6741	211	4	energy	energy	NOUN
ejpam-6741	211	5	condition	condition	NOUN
ejpam-6741	211	6	(	(	PUNCT
ejpam-6741	211	7	sec	sec	PROPN
ejpam-6741	211	8	)	)	PUNCT
ejpam-6741	211	9	,	,	PUNCT
ejpam-6741	211	10	in	in	ADP
ejpam-6741	211	11	addition	addition	NOUN
ejpam-6741	211	12	to	to	ADP
ejpam-6741	211	13	the	the	DET
ejpam-6741	211	14	nec	nec	PROPN
ejpam-6741	211	15	,	,	PUNCT
ejpam-6741	211	16	requires	require	VERB
ejpam-6741	211	17	(	(	PUNCT
ejpam-6741	211	18	ρ+	ρ+	NUM
ejpam-6741	211	19	p∥	p∥	NOUN
ejpam-6741	211	20	+	+	CCONJ
ejpam-6741	211	21	2p⊥	2p⊥	NUM
ejpam-6741	211	22	≥	≥	NOUN
ejpam-6741	211	23	0	0	NUM
ejpam-6741	211	24	)	)	PUNCT
ejpam-6741	211	25	.	.	PUNCT
ejpam-6741	212	1	4	4	X
ejpam-6741	212	2	.	.	X
ejpam-6741	212	3	dominant	dominant	ADJ
ejpam-6741	212	4	energy	energy	NOUN
ejpam-6741	212	5	condition	condition	NOUN
ejpam-6741	212	6	(	(	PUNCT
ejpam-6741	212	7	dec	dec	PROPN
ejpam-6741	212	8	)	)	PUNCT
ejpam-6741	212	9	demands	demand	NOUN
ejpam-6741	212	10	(	(	PUNCT
ejpam-6741	212	11	ρ	ρ	NOUN
ejpam-6741	212	12	≥	≥	NOUN
ejpam-6741	212	13	0	0	NUM
ejpam-6741	212	14	,	,	PUNCT
ejpam-6741	212	15	ρ	ρ	PROPN
ejpam-6741	212	16	≥	≥	NOUN
ejpam-6741	212	17	∣∣p∥	∣∣p∥	ADJ
ejpam-6741	212	18	∣∣	∣∣	NUM
ejpam-6741	212	19	,	,	PUNCT
ejpam-6741	212	20	ρ	ρ	PROPN
ejpam-6741	212	21	≥	≥	NOUN
ejpam-6741	212	22	|p⊥|	|p⊥|	NUM
ejpam-6741	212	23	)	)	PUNCT
ejpam-6741	212	24	.	.	PUNCT
ejpam-6741	213	1	in	in	ADP
ejpam-6741	213	2	branch	branch	NOUN
ejpam-6741	213	3	4	4	NUM
ejpam-6741	213	4	,	,	PUNCT
ejpam-6741	213	5	we	we	PRON
ejpam-6741	213	6	get	get	VERB
ejpam-6741	213	7	ρ	ρ	NOUN
ejpam-6741	213	8	=	=	SYM
ejpam-6741	213	9	2k1k2	2k1k2	NUM
ejpam-6741	213	10	+	+	CCONJ
ejpam-6741	213	11	k22	k22	NOUN
ejpam-6741	213	12	,	,	PUNCT
ejpam-6741	213	13	p∥	p∥	NOUN
ejpam-6741	213	14	=	=	SYM
ejpam-6741	213	15	−3k22	−3k22	PROPN
ejpam-6741	213	16	and	and	CCONJ
ejpam-6741	213	17	p⊥	p⊥	NOUN
ejpam-6741	213	18	=	=	NOUN
ejpam-6741	213	19	−e2(k1−k2)t(k21	−e2(k1−k2)t(k21	NOUN
ejpam-6741	213	20	+	+	CCONJ
ejpam-6741	213	21	k22	k22	NOUN
ejpam-6741	213	22	+	+	CCONJ
ejpam-6741	213	23	k1k2	k1k2	NOUN
ejpam-6741	213	24	)	)	PUNCT
ejpam-6741	213	25	.	.	PUNCT
ejpam-6741	214	1	the	the	DET
ejpam-6741	214	2	nec	nec	PROPN
ejpam-6741	214	3	holds	hold	VERB
ejpam-6741	214	4	true	true	ADJ
ejpam-6741	214	5	when	when	SCONJ
ejpam-6741	214	6	k1	k1	PROPN
ejpam-6741	214	7	>	>	X
ejpam-6741	214	8	k2	k2	PROPN
ejpam-6741	214	9	and	and	CCONJ
ejpam-6741	214	10	2k1k2	2k1k2	NUM
ejpam-6741	214	11	+	+	CCONJ
ejpam-6741	214	12	k22	k22	NOUN
ejpam-6741	214	13	−	−	PROPN
ejpam-6741	214	14	e2(k1−k2)t(k21	e2(k1−k2)t(k21	PROPN
ejpam-6741	215	1	+	+	CCONJ
ejpam-6741	215	2	k22	k22	NOUN
ejpam-6741	215	3	+	+	CCONJ
ejpam-6741	215	4	k1k2	k1k2	NOUN
ejpam-6741	215	5	)	)	PUNCT
ejpam-6741	215	6	≥	≥	NOUN
ejpam-6741	215	7	0	0	NUM
ejpam-6741	215	8	.	.	PUNCT
ejpam-6741	216	1	additionally	additionally	ADV
ejpam-6741	216	2	,	,	PUNCT
ejpam-6741	216	3	if	if	SCONJ
ejpam-6741	216	4	2k1k2	2k1k2	NUM
ejpam-6741	216	5	+	+	CCONJ
ejpam-6741	216	6	k22	k22	NOUN
ejpam-6741	216	7	≥	≥	NOUN
ejpam-6741	216	8	0	0	NUM
ejpam-6741	216	9	,	,	PUNCT
ejpam-6741	216	10	then	then	ADV
ejpam-6741	216	11	the	the	DET
ejpam-6741	216	12	wec	wec	PROPN
ejpam-6741	216	13	is	be	AUX
ejpam-6741	216	14	also	also	ADV
ejpam-6741	216	15	satisfied	satisfied	ADJ
ejpam-6741	216	16	.	.	PUNCT
ejpam-6741	217	1	furthermore	furthermore	ADV
ejpam-6741	217	2	,	,	PUNCT
ejpam-6741	217	3	2k1k2	2k1k2	NUM
ejpam-6741	217	4	−	−	NOUN
ejpam-6741	218	1	2k22	2k22	NOUN
ejpam-6741	218	2	−	−	NOUN
ejpam-6741	218	3	e2(k1−k2)t(k21	e2(k1−k2)t(k21	PROPN
ejpam-6741	219	1	+	+	PUNCT
ejpam-6741	219	2	k22	k22	NOUN
ejpam-6741	219	3	+	+	CCONJ
ejpam-6741	219	4	k1k2	k1k2	NOUN
ejpam-6741	219	5	)	)	PUNCT
ejpam-6741	219	6	≥	≥	X
ejpam-6741	219	7	0	0	NUM
ejpam-6741	219	8	reveals	reveal	VERB
ejpam-6741	219	9	that	that	SCONJ
ejpam-6741	219	10	the	the	DET
ejpam-6741	219	11	sec	sec	PROPN
ejpam-6741	219	12	is	be	AUX
ejpam-6741	219	13	fulfilled	fulfil	VERB
ejpam-6741	219	14	.	.	PUNCT
ejpam-6741	220	1	the	the	DET
ejpam-6741	220	2	restrictions	restriction	NOUN
ejpam-6741	220	3	k1	k1	PROPN
ejpam-6741	220	4	>	>	X
ejpam-6741	220	5	k2	k2	PROPN
ejpam-6741	220	6	and	and	CCONJ
ejpam-6741	220	7	2k1k2	2k1k2	NUM
ejpam-6741	220	8	+	+	CCONJ
ejpam-6741	220	9	k22	k22	NOUN
ejpam-6741	220	10	≥	≥	NOUN
ejpam-6741	220	11	e2(k1−k2)t(k21	e2(k1−k2)t(k21	PROPN
ejpam-6741	221	1	+	+	PUNCT
ejpam-6741	221	2	k22	k22	NOUN
ejpam-6741	221	3	+	+	CCONJ
ejpam-6741	221	4	k1k2	k1k2	NOUN
ejpam-6741	221	5	)	)	PUNCT
ejpam-6741	221	6	confirm	confirm	VERB
ejpam-6741	221	7	the	the	DET
ejpam-6741	221	8	satisfaction	satisfaction	NOUN
ejpam-6741	221	9	of	of	ADP
ejpam-6741	221	10	the	the	DET
ejpam-6741	221	11	dec	dec	PROPN
ejpam-6741	221	12	.	.	PROPN
ejpam-6741	222	1	for	for	ADP
ejpam-6741	222	2	branch	branch	NOUN
ejpam-6741	222	3	5	5	NUM
ejpam-6741	222	4	,	,	PUNCT
ejpam-6741	222	5	the	the	DET
ejpam-6741	222	6	physical	physical	ADJ
ejpam-6741	222	7	terms	term	NOUN
ejpam-6741	222	8	are	be	AUX
ejpam-6741	222	9	obtained	obtain	VERB
ejpam-6741	222	10	as	as	ADP
ejpam-6741	222	11	ρ	ρ	NOUN
ejpam-6741	222	12	=	=	SYM
ejpam-6741	222	13	p∥	p∥	NOUN
ejpam-6741	222	14	=	=	SYM
ejpam-6741	222	15	0	0	NUM
ejpam-6741	222	16	and	and	CCONJ
ejpam-6741	222	17	p⊥	p⊥	NOUN
ejpam-6741	222	18	=	=	SYM
ejpam-6741	222	19	−k2	−k2	PROPN
ejpam-6741	222	20	k21	k21	NOUN
ejpam-6741	222	21	(	(	PUNCT
ejpam-6741	222	22	k2e	k2e	PROPN
ejpam-6741	222	23	kt	kt	PROPN
ejpam-6741	222	24	+	+	CCONJ
ejpam-6741	222	25	k3e	k3e	PROPN
ejpam-6741	222	26	−kt	−kt	PROPN
ejpam-6741	222	27	)	)	PUNCT
ejpam-6741	222	28	.	.	PUNCT
ejpam-6741	223	1	under	under	ADP
ejpam-6741	223	2	the	the	DET
ejpam-6741	223	3	condition	condition	NOUN
ejpam-6741	223	4	k2	k2	PROPN
ejpam-6741	223	5	k21	k21	PROPN
ejpam-6741	223	6	(	(	PUNCT
ejpam-6741	223	7	k2e	k2e	PROPN
ejpam-6741	223	8	kt	kt	PROPN
ejpam-6741	223	9	+	+	CCONJ
ejpam-6741	223	10	k3e	k3e	PROPN
ejpam-6741	223	11	−kt	−kt	PROPN
ejpam-6741	223	12	)	)	PUNCT
ejpam-6741	223	13	<	<	X
ejpam-6741	223	14	0	0	PUNCT
ejpam-6741	223	15	(	(	PUNCT
ejpam-6741	223	16	i.e.	i.e.	X
ejpam-6741	223	17	,	,	PUNCT
ejpam-6741	223	18	p⊥	p⊥	NOUN
ejpam-6741	223	19	>	>	X
ejpam-6741	223	20	0	0	NUM
ejpam-6741	223	21	)	)	PUNCT
ejpam-6741	223	22	,	,	PUNCT
ejpam-6741	223	23	the	the	DET
ejpam-6741	223	24	nec	nec	PROPN
ejpam-6741	223	25	,	,	PUNCT
ejpam-6741	223	26	wec	wec	PROPN
ejpam-6741	223	27	,	,	PUNCT
ejpam-6741	223	28	and	and	CCONJ
ejpam-6741	223	29	sec	sec	PROPN
ejpam-6741	223	30	hold	hold	VERB
ejpam-6741	223	31	true	true	ADJ
ejpam-6741	223	32	,	,	PUNCT
ejpam-6741	223	33	while	while	SCONJ
ejpam-6741	223	34	the	the	DET
ejpam-6741	223	35	dec	dec	PROPN
ejpam-6741	223	36	does	do	AUX
ejpam-6741	223	37	not	not	PART
ejpam-6741	223	38	hold	hold	VERB
ejpam-6741	223	39	(	(	PUNCT
ejpam-6741	223	40	as	as	ADP
ejpam-6741	223	41	ρ	ρ	PROPN
ejpam-6741	223	42	=	=	SYM
ejpam-6741	223	43	0	0	NUM
ejpam-6741	223	44	is	be	AUX
ejpam-6741	223	45	not	not	PART
ejpam-6741	223	46	greater	great	ADJ
ejpam-6741	223	47	than	than	ADP
ejpam-6741	223	48	|p⊥|	|p⊥|	PROPN
ejpam-6741	223	49	>	>	X
ejpam-6741	223	50	0	0	NUM
ejpam-6741	223	51	)	)	PUNCT
ejpam-6741	223	52	.	.	PUNCT
ejpam-6741	224	1	for	for	ADP
ejpam-6741	224	2	the	the	DET
ejpam-6741	224	3	metric	metric	NOUN
ejpam-6741	224	4	of	of	ADP
ejpam-6741	224	5	branch	branch	NOUN
ejpam-6741	224	6	9	9	NUM
ejpam-6741	224	7	,	,	PUNCT
ejpam-6741	224	8	the	the	DET
ejpam-6741	224	9	values	value	NOUN
ejpam-6741	224	10	of	of	ADP
ejpam-6741	224	11	ρ	ρ	PROPN
ejpam-6741	224	12	,	,	PUNCT
ejpam-6741	224	13	p∥	p∥	NOUN
ejpam-6741	224	14	,	,	PUNCT
ejpam-6741	224	15	and	and	CCONJ
ejpam-6741	224	16	p⊥	p⊥	NOUN
ejpam-6741	224	17	turn	turn	VERB
ejpam-6741	224	18	out	out	ADP
ejpam-6741	224	19	to	to	PART
ejpam-6741	224	20	be	be	AUX
ejpam-6741	224	21	zero	zero	NUM
ejpam-6741	224	22	,	,	PUNCT
ejpam-6741	224	23	which	which	PRON
ejpam-6741	224	24	demonstrates	demonstrate	VERB
ejpam-6741	224	25	the	the	DET
ejpam-6741	224	26	presence	presence	NOUN
ejpam-6741	224	27	of	of	ADP
ejpam-6741	224	28	a	a	DET
ejpam-6741	224	29	vacuum	vacuum	NOUN
ejpam-6741	224	30	space	space	NOUN
ejpam-6741	224	31	,	,	PUNCT
ejpam-6741	224	32	and	and	CCONJ
ejpam-6741	224	33	all	all	DET
ejpam-6741	224	34	the	the	DET
ejpam-6741	224	35	energy	energy	NOUN
ejpam-6741	224	36	conditions	condition	NOUN
ejpam-6741	224	37	are	be	AUX
ejpam-6741	224	38	satisfied	satisfied	ADJ
ejpam-6741	224	39	trivially	trivially	ADV
ejpam-6741	224	40	.	.	PUNCT
ejpam-6741	225	1	in	in	ADP
ejpam-6741	225	2	the	the	DET
ejpam-6741	225	3	case	case	NOUN
ejpam-6741	225	4	of	of	ADP
ejpam-6741	225	5	branch	branch	NOUN
ejpam-6741	225	6	10	10	NUM
ejpam-6741	225	7	,	,	PUNCT
ejpam-6741	225	8	ρ	ρ	PROPN
ejpam-6741	225	9	=	=	PROPN
ejpam-6741	225	10	q′2	q′2	PROPN
ejpam-6741	225	11	q2	q2	PROPN
ejpam-6741	225	12	,	,	PUNCT
ejpam-6741	225	13	p∥	p∥	X
ejpam-6741	225	14	=	=	SYM
ejpam-6741	225	15	−	−	PROPN
ejpam-6741	225	16	1	1	NUM
ejpam-6741	225	17	q2	q2	NOUN
ejpam-6741	225	18	(	(	PUNCT
ejpam-6741	225	19	2qq′′	2qq′′	PROPN
ejpam-6741	225	20	+	+	X
ejpam-6741	225	21	q′2	q′2	NOUN
ejpam-6741	225	22	)	)	PUNCT
ejpam-6741	225	23	,	,	PUNCT
ejpam-6741	225	24	and	and	CCONJ
ejpam-6741	225	25	p⊥	p⊥	NOUN
ejpam-6741	225	26	=	=	PUNCT
ejpam-6741	225	27	−k21	−k21	ADP
ejpam-6741	225	28	q′′	q′′	ADP
ejpam-6741	225	29	q3	q3	NOUN
ejpam-6741	225	30	.	.	PUNCT
ejpam-6741	226	1	if	if	SCONJ
ejpam-6741	226	2	q′′	q′′	ADP
ejpam-6741	226	3	<	<	X
ejpam-6741	226	4	0	0	X
ejpam-6741	226	5	(	(	PUNCT
ejpam-6741	226	6	making	make	VERB
ejpam-6741	226	7	p⊥	p⊥	PRON
ejpam-6741	226	8	>	>	X
ejpam-6741	226	9	0	0	NUM
ejpam-6741	226	10	)	)	PUNCT
ejpam-6741	226	11	and	and	CCONJ
ejpam-6741	226	12	qq′2	qq′2	VERB
ejpam-6741	226	13	−	−	PROPN
ejpam-6741	226	14	k1q	k1q	PROPN
ejpam-6741	226	15	′′	′′	PROPN
ejpam-6741	226	16	≥	≥	PRON
ejpam-6741	226	17	0	0	NUM
ejpam-6741	226	18	(	(	PUNCT
ejpam-6741	226	19	ensuring	ensure	VERB
ejpam-6741	226	20	ρ	ρ	NOUN
ejpam-6741	226	21	+	+	NOUN
ejpam-6741	226	22	p⊥	p⊥	NOUN
ejpam-6741	226	23	≥	≥	NOUN
ejpam-6741	226	24	0	0	NUM
ejpam-6741	226	25	)	)	PUNCT
ejpam-6741	226	26	,	,	PUNCT
ejpam-6741	226	27	then	then	ADV
ejpam-6741	226	28	the	the	DET
ejpam-6741	226	29	nec	nec	PROPN
ejpam-6741	226	30	,	,	PUNCT
ejpam-6741	226	31	wec	wec	PROPN
ejpam-6741	226	32	,	,	PUNCT
ejpam-6741	226	33	and	and	CCONJ
ejpam-6741	226	34	sec	sec	PROPN
ejpam-6741	226	35	hold	hold	VERB
ejpam-6741	226	36	true	true	ADJ
ejpam-6741	226	37	.	.	PUNCT
ejpam-6741	227	1	additionally	additionally	ADV
ejpam-6741	227	2	,	,	PUNCT
ejpam-6741	227	3	the	the	DET
ejpam-6741	227	4	dec	dec	PROPN
ejpam-6741	227	5	requires	require	VERB
ejpam-6741	227	6	q′2	q′2	PROPN
ejpam-6741	227	7	≥	≥	PROPN
ejpam-6741	227	8	k21	k21	PROPN
ejpam-6741	227	9	∣∣∣	∣∣∣	PROPN
ejpam-6741	227	10	q′′q	q′′q	PROPN
ejpam-6741	227	11	∣∣∣	∣∣∣	NOUN
ejpam-6741	227	12	(	(	PUNCT
ejpam-6741	227	13	since	since	SCONJ
ejpam-6741	227	14	p⊥	p⊥	NOUN
ejpam-6741	227	15	is	be	AUX
ejpam-6741	227	16	positive	positive	ADJ
ejpam-6741	227	17	under	under	ADP
ejpam-6741	227	18	q′′	q′′	ADP
ejpam-6741	227	19	<	<	X
ejpam-6741	227	20	0	0	NUM
ejpam-6741	227	21	,	,	PUNCT
ejpam-6741	227	22	this	this	PRON
ejpam-6741	227	23	becomes	become	VERB
ejpam-6741	227	24	q′2	q′2	ADP
ejpam-6741	227	25	≥	≥	NOUN
ejpam-6741	227	26	−k21	−k21	ADP
ejpam-6741	227	27	q′′	q′′	ADP
ejpam-6741	227	28	q	q	PROPN
ejpam-6741	227	29	)	)	PUNCT
ejpam-6741	227	30	.	.	PUNCT
ejpam-6741	228	1	by	by	ADP
ejpam-6741	228	2	adopting	adopt	VERB
ejpam-6741	228	3	the	the	DET
ejpam-6741	228	4	same	same	ADJ
ejpam-6741	228	5	procedure	procedure	NOUN
ejpam-6741	228	6	,	,	PUNCT
ejpam-6741	228	7	one	one	PRON
ejpam-6741	228	8	can	can	AUX
ejpam-6741	228	9	easily	easily	ADV
ejpam-6741	228	10	examine	examine	VERB
ejpam-6741	228	11	the	the	DET
ejpam-6741	228	12	above	above	ADV
ejpam-6741	228	13	-	-	PUNCT
ejpam-6741	228	14	mentioned	mention	VERB
ejpam-6741	228	15	energy	energy	NOUN
ejpam-6741	228	16	conditions	condition	NOUN
ejpam-6741	228	17	for	for	ADP
ejpam-6741	228	18	the	the	DET
ejpam-6741	228	19	remaining	remain	VERB
ejpam-6741	228	20	metrics	metric	NOUN
ejpam-6741	228	21	.	.	PUNCT
ejpam-6741	229	1	3.1	3.1	NUM
ejpam-6741	229	2	.	.	PUNCT
ejpam-6741	229	3	implications	implication	NOUN
ejpam-6741	229	4	for	for	ADP
ejpam-6741	229	5	spacetime	spacetime	NOUN
ejpam-6741	229	6	evolution	evolution	NOUN
ejpam-6741	229	7	and	and	CCONJ
ejpam-6741	229	8	stability	stability	NOUN
ejpam-6741	229	9	the	the	DET
ejpam-6741	229	10	discovery	discovery	NOUN
ejpam-6741	229	11	of	of	ADP
ejpam-6741	229	12	ricci	ricci	PROPN
ejpam-6741	229	13	soliton	soliton	NOUN
ejpam-6741	229	14	solutions	solution	NOUN
ejpam-6741	229	15	within	within	ADP
ejpam-6741	229	16	the	the	DET
ejpam-6741	229	17	lrs	lrs	PROPN
ejpam-6741	229	18	bianchi	bianchi	PROPN
ejpam-6741	229	19	-	-	PUNCT
ejpam-6741	229	20	i	i	PRON
ejpam-6741	229	21	framework	framework	NOUN
ejpam-6741	229	22	has	have	VERB
ejpam-6741	229	23	profound	profound	ADJ
ejpam-6741	229	24	implications	implication	NOUN
ejpam-6741	229	25	for	for	ADP
ejpam-6741	229	26	understanding	understand	VERB
ejpam-6741	229	27	the	the	DET
ejpam-6741	229	28	possible	possible	ADJ
ejpam-6741	229	29	evolution	evolution	NOUN
ejpam-6741	229	30	and	and	CCONJ
ejpam-6741	229	31	stability	stability	NOUN
ejpam-6741	229	32	of	of	ADP
ejpam-6741	229	33	such	such	ADJ
ejpam-6741	229	34	spacetimes	spacetime	NOUN
ejpam-6741	229	35	.	.	PUNCT
ejpam-6741	230	1	a	a	DET
ejpam-6741	230	2	ricci	ricci	PROPN
ejpam-6741	230	3	soliton	soliton	NOUN
ejpam-6741	230	4	metric	metric	NOUN
ejpam-6741	230	5	is	be	AUX
ejpam-6741	230	6	,	,	PUNCT
ejpam-6741	230	7	by	by	ADP
ejpam-6741	230	8	definition	definition	NOUN
ejpam-6741	230	9	,	,	PUNCT
ejpam-6741	230	10	a	a	DET
ejpam-6741	230	11	fixed	fix	VERB
ejpam-6741	230	12	point	point	NOUN
ejpam-6741	230	13	(	(	PUNCT
ejpam-6741	230	14	or	or	CCONJ
ejpam-6741	230	15	equilibrium	equilibrium	NOUN
ejpam-6741	230	16	solution	solution	NOUN
ejpam-6741	230	17	)	)	PUNCT
ejpam-6741	230	18	of	of	ADP
ejpam-6741	230	19	the	the	DET
ejpam-6741	230	20	ricci	ricci	PROPN
ejpam-6741	230	21	flow	flow	NOUN
ejpam-6741	230	22	∂gmn	∂gmn	X
ejpam-6741	230	23	∂λ	∂λ	PROPN
ejpam-6741	230	24	=	=	PUNCT
ejpam-6741	230	25	−2rmn	−2rmn	NOUN
ejpam-6741	230	26	under	under	ADP
ejpam-6741	230	27	a	a	DET
ejpam-6741	230	28	combination	combination	NOUN
ejpam-6741	230	29	of	of	ADP
ejpam-6741	230	30	the	the	DET
ejpam-6741	230	31	flow	flow	NOUN
ejpam-6741	230	32	and	and	CCONJ
ejpam-6741	230	33	diffeomorphisms	diffeomorphism	NOUN
ejpam-6741	230	34	generated	generate	VERB
ejpam-6741	230	35	by	by	ADP
ejpam-6741	230	36	the	the	DET
ejpam-6741	230	37	vector	vector	NOUN
ejpam-6741	230	38	field	field	NOUN
ejpam-6741	230	39	v	v	ADP
ejpam-6741	230	40	[	[	X
ejpam-6741	230	41	20	20	NUM
ejpam-6741	230	42	]	]	PUNCT
ejpam-6741	230	43	.	.	PUNCT
ejpam-6741	231	1	this	this	DET
ejpam-6741	231	2	connection	connection	NOUN
ejpam-6741	231	3	allows	allow	VERB
ejpam-6741	231	4	us	we	PRON
ejpam-6741	231	5	to	to	PART
ejpam-6741	231	6	interpret	interpret	VERB
ejpam-6741	231	7	our	our	PRON
ejpam-6741	231	8	results	result	NOUN
ejpam-6741	231	9	in	in	ADP
ejpam-6741	231	10	a	a	DET
ejpam-6741	231	11	dynamical	dynamical	ADJ
ejpam-6741	231	12	context	context	NOUN
ejpam-6741	231	13	.	.	PUNCT
ejpam-6741	232	1	the	the	DET
ejpam-6741	232	2	nature	nature	NOUN
ejpam-6741	232	3	of	of	ADP
ejpam-6741	232	4	the	the	DET
ejpam-6741	232	5	soliton	soliton	NOUN
ejpam-6741	232	6	-	-	PUNCT
ejpam-6741	232	7	shrinking	shrink	VERB
ejpam-6741	232	8	(	(	PUNCT
ejpam-6741	232	9	δ	δ	X
ejpam-6741	232	10	>	>	X
ejpam-6741	232	11	0	0	NUM
ejpam-6741	232	12	)	)	PUNCT
ejpam-6741	232	13	,	,	PUNCT
ejpam-6741	232	14	steady	steady	ADJ
ejpam-6741	232	15	(	(	PUNCT
ejpam-6741	232	16	δ	δ	NOUN
ejpam-6741	232	17	=	=	PROPN
ejpam-6741	232	18	0	0	NUM
ejpam-6741	232	19	)	)	PUNCT
ejpam-6741	232	20	,	,	PUNCT
ejpam-6741	232	21	or	or	CCONJ
ejpam-6741	232	22	expanding	expand	VERB
ejpam-6741	232	23	(	(	PUNCT
ejpam-6741	232	24	δ	δ	X
ejpam-6741	232	25	<	<	X
ejpam-6741	232	26	0)provides	0)provides	NUM
ejpam-6741	232	27	a	a	DET
ejpam-6741	232	28	direct	direct	ADJ
ejpam-6741	232	29	classification	classification	NOUN
ejpam-6741	232	30	of	of	ADP
ejpam-6741	232	31	the	the	DET
ejpam-6741	232	32	spacetime	spacetime	NOUN
ejpam-6741	232	33	’s	’s	PART
ejpam-6741	232	34	behavior	behavior	NOUN
ejpam-6741	232	35	under	under	ADP
ejpam-6741	232	36	the	the	DET
ejpam-6741	232	37	ricci	ricci	PROPN
ejpam-6741	232	38	flow	flow	NOUN
ejpam-6741	232	39	.	.	PUNCT
ejpam-6741	233	1	for	for	ADP
ejpam-6741	233	2	instance	instance	NOUN
ejpam-6741	233	3	,	,	PUNCT
ejpam-6741	233	4	the	the	DET
ejpam-6741	233	5	expanding	expand	VERB
ejpam-6741	233	6	solitons	soliton	NOUN
ejpam-6741	233	7	found	find	VERB
ejpam-6741	233	8	in	in	ADP
ejpam-6741	233	9	branches	branch	NOUN
ejpam-6741	233	10	4	4	NUM
ejpam-6741	233	11	,	,	PUNCT
ejpam-6741	233	12	5	5	NUM
ejpam-6741	233	13	,	,	PUNCT
ejpam-6741	233	14	7	7	NUM
ejpam-6741	233	15	,	,	PUNCT
ejpam-6741	233	16	8	8	NUM
ejpam-6741	233	17	,	,	PUNCT
ejpam-6741	233	18	and	and	CCONJ
ejpam-6741	233	19	11	11	NUM
ejpam-6741	233	20	suggest	suggest	VERB
ejpam-6741	233	21	a	a	DET
ejpam-6741	233	22	spacetime	spacetime	NOUN
ejpam-6741	233	23	that	that	SCONJ
ejpam-6741	233	24	,	,	PUNCT
ejpam-6741	233	25	under	under	ADP
ejpam-6741	233	26	the	the	DET
ejpam-6741	233	27	flow	flow	NOUN
ejpam-6741	233	28	,	,	PUNCT
ejpam-6741	233	29	exhibits	exhibit	VERB
ejpam-6741	233	30	inflationary	inflationary	ADJ
ejpam-6741	233	31	-	-	PUNCT
ejpam-6741	233	32	like	like	ADJ
ejpam-6741	233	33	expansion	expansion	NOUN
ejpam-6741	233	34	.	.	PUNCT
ejpam-6741	234	1	this	this	PRON
ejpam-6741	234	2	is	be	AUX
ejpam-6741	234	3	not	not	PART
ejpam-6741	234	4	a	a	DET
ejpam-6741	234	5	physical	physical	ADJ
ejpam-6741	234	6	expansion	expansion	NOUN
ejpam-6741	234	7	in	in	ADP
ejpam-6741	234	8	time	time	NOUN
ejpam-6741	234	9	t	t	PROPN
ejpam-6741	234	10	,	,	PUNCT
ejpam-6741	234	11	but	but	CCONJ
ejpam-6741	234	12	an	an	DET
ejpam-6741	234	13	expansion	expansion	NOUN
ejpam-6741	234	14	in	in	ADP
ejpam-6741	234	15	the	the	DET
ejpam-6741	234	16	flow	flow	NOUN
ejpam-6741	234	17	parameter	parameter	NOUN
ejpam-6741	234	18	λ	λ	PROPN
ejpam-6741	234	19	,	,	PUNCT
ejpam-6741	234	20	which	which	PRON
ejpam-6741	234	21	can	can	AUX
ejpam-6741	234	22	be	be	AUX
ejpam-6741	234	23	interpreted	interpret	VERB
ejpam-6741	234	24	as	as	ADP
ejpam-6741	234	25	a	a	DET
ejpam-6741	234	26	coarseu	coarseu	NOUN
ejpam-6741	234	27	.	.	PUNCT
ejpam-6741	235	1	nasib	nasib	INTJ
ejpam-6741	235	2	et	et	PROPN
ejpam-6741	235	3	al	al	PROPN
ejpam-6741	235	4	.	.	PUNCT
ejpam-6741	235	5	/	/	SYM
ejpam-6741	235	6	eur	eur	PROPN
ejpam-6741	235	7	.	.	PUNCT
ejpam-6741	236	1	j.	j.	PROPN
ejpam-6741	236	2	pure	pure	PROPN
ejpam-6741	236	3	appl	appl	PROPN
ejpam-6741	236	4	.	.	PROPN
ejpam-6741	236	5	math	math	PROPN
ejpam-6741	236	6	,	,	PUNCT
ejpam-6741	236	7	18	18	NUM
ejpam-6741	236	8	(	(	PUNCT
ejpam-6741	236	9	4	4	NUM
ejpam-6741	236	10	)	)	PUNCT
ejpam-6741	236	11	(	(	PUNCT
ejpam-6741	236	12	2025	2025	NUM
ejpam-6741	236	13	)	)	PUNCT
ejpam-6741	236	14	,	,	PUNCT
ejpam-6741	236	15	6741	6741	NUM
ejpam-6741	236	16	11	11	NUM
ejpam-6741	236	17	of	of	ADP
ejpam-6741	236	18	14	14	NUM
ejpam-6741	236	19	grained	grain	VERB
ejpam-6741	236	20	or	or	CCONJ
ejpam-6741	236	21	averaged	average	VERB
ejpam-6741	236	22	evolution	evolution	NOUN
ejpam-6741	236	23	of	of	ADP
ejpam-6741	236	24	the	the	DET
ejpam-6741	236	25	geometry	geometry	NOUN
ejpam-6741	236	26	.	.	PUNCT
ejpam-6741	237	1	the	the	DET
ejpam-6741	237	2	prevalence	prevalence	NOUN
ejpam-6741	237	3	of	of	ADP
ejpam-6741	237	4	expanding	expand	VERB
ejpam-6741	237	5	solutions	solution	NOUN
ejpam-6741	237	6	in	in	ADP
ejpam-6741	237	7	our	our	PRON
ejpam-6741	237	8	classification	classification	NOUN
ejpam-6741	237	9	indicates	indicate	VERB
ejpam-6741	237	10	that	that	SCONJ
ejpam-6741	237	11	the	the	DET
ejpam-6741	237	12	lrs	lrs	PROPN
ejpam-6741	237	13	bianchi	bianchi	PROPN
ejpam-6741	237	14	-	-	PUNCT
ejpam-6741	237	15	i	i	PROPN
ejpam-6741	237	16	geometry	geometry	NOUN
ejpam-6741	237	17	naturally	naturally	ADV
ejpam-6741	237	18	tends	tend	VERB
ejpam-6741	237	19	towards	towards	ADP
ejpam-6741	237	20	less	less	ADV
ejpam-6741	237	21	curved	curved	ADJ
ejpam-6741	237	22	,	,	PUNCT
ejpam-6741	237	23	more	more	ADV
ejpam-6741	237	24	voluminous	voluminous	ADJ
ejpam-6741	237	25	states	state	NOUN
ejpam-6741	237	26	under	under	ADP
ejpam-6741	237	27	this	this	DET
ejpam-6741	237	28	geometric	geometric	ADJ
ejpam-6741	237	29	flow	flow	NOUN
ejpam-6741	237	30	.	.	PUNCT
ejpam-6741	238	1	conversely	conversely	ADV
ejpam-6741	238	2	,	,	PUNCT
ejpam-6741	238	3	the	the	DET
ejpam-6741	238	4	existence	existence	NOUN
ejpam-6741	238	5	of	of	ADP
ejpam-6741	238	6	steady	steady	ADJ
ejpam-6741	238	7	solitons	soliton	NOUN
ejpam-6741	238	8	(	(	PUNCT
ejpam-6741	238	9	e.g.	e.g.	ADV
ejpam-6741	238	10	,	,	PUNCT
ejpam-6741	238	11	when	when	SCONJ
ejpam-6741	238	12	δ	δ	PROPN
ejpam-6741	238	13	=	=	NOUN
ejpam-6741	238	14	0	0	NUM
ejpam-6741	238	15	in	in	ADP
ejpam-6741	238	16	branches	branch	NOUN
ejpam-6741	238	17	1	1	NUM
ejpam-6741	238	18	,	,	PUNCT
ejpam-6741	238	19	2	2	NUM
ejpam-6741	238	20	,	,	PUNCT
ejpam-6741	238	21	9	9	NUM
ejpam-6741	238	22	,	,	PUNCT
ejpam-6741	238	23	10	10	NUM
ejpam-6741	238	24	,	,	PUNCT
ejpam-6741	238	25	and	and	CCONJ
ejpam-6741	238	26	12	12	NUM
ejpam-6741	238	27	)	)	PUNCT
ejpam-6741	238	28	represents	represent	VERB
ejpam-6741	238	29	equilibrium	equilibrium	NOUN
ejpam-6741	238	30	configurations	configuration	NOUN
ejpam-6741	238	31	.	.	PUNCT
ejpam-6741	239	1	these	these	DET
ejpam-6741	239	2	spacetimes	spacetime	NOUN
ejpam-6741	239	3	are	be	AUX
ejpam-6741	239	4	stable	stable	ADJ
ejpam-6741	239	5	under	under	ADP
ejpam-6741	239	6	the	the	DET
ejpam-6741	239	7	combined	combine	VERB
ejpam-6741	239	8	action	action	NOUN
ejpam-6741	239	9	of	of	ADP
ejpam-6741	239	10	the	the	DET
ejpam-6741	239	11	ricci	ricci	PROPN
ejpam-6741	239	12	flow	flow	NOUN
ejpam-6741	239	13	and	and	CCONJ
ejpam-6741	239	14	the	the	DET
ejpam-6741	239	15	diffeomorphism	diffeomorphism	NOUN
ejpam-6741	239	16	generated	generate	VERB
ejpam-6741	239	17	by	by	ADP
ejpam-6741	239	18	their	their	PRON
ejpam-6741	239	19	associated	associated	ADJ
ejpam-6741	239	20	vector	vector	NOUN
ejpam-6741	239	21	field	field	NOUN
ejpam-6741	239	22	v	v	NOUN
ejpam-6741	239	23	.	.	PUNCT
ejpam-6741	240	1	a	a	DET
ejpam-6741	240	2	prime	prime	ADJ
ejpam-6741	240	3	example	example	NOUN
ejpam-6741	240	4	is	be	AUX
ejpam-6741	240	5	branch	branch	NOUN
ejpam-6741	240	6	9	9	NUM
ejpam-6741	240	7	,	,	PUNCT
ejpam-6741	240	8	where	where	SCONJ
ejpam-6741	240	9	we	we	PRON
ejpam-6741	240	10	found	find	VERB
ejpam-6741	240	11	a	a	DET
ejpam-6741	240	12	vacuum	vacuum	NOUN
ejpam-6741	240	13	solution	solution	NOUN
ejpam-6741	240	14	(	(	PUNCT
ejpam-6741	240	15	ρ	ρ	NOUN
ejpam-6741	240	16	=	=	SYM
ejpam-6741	240	17	p∥	p∥	NOUN
ejpam-6741	240	18	=	=	PUNCT
ejpam-6741	240	19	p⊥	p⊥	NOUN
ejpam-6741	240	20	=	=	NOUN
ejpam-6741	240	21	0	0	X
ejpam-6741	240	22	)	)	PUNCT
ejpam-6741	240	23	satisfying	satisfy	VERB
ejpam-6741	240	24	all	all	DET
ejpam-6741	240	25	energy	energy	NOUN
ejpam-6741	240	26	conditions	condition	NOUN
ejpam-6741	240	27	.	.	PUNCT
ejpam-6741	241	1	this	this	DET
ejpam-6741	241	2	steady	steady	ADJ
ejpam-6741	241	3	soliton	soliton	NOUN
ejpam-6741	241	4	can	can	AUX
ejpam-6741	241	5	be	be	AUX
ejpam-6741	241	6	viewed	view	VERB
ejpam-6741	241	7	as	as	ADP
ejpam-6741	241	8	a	a	DET
ejpam-6741	241	9	stable	stable	ADJ
ejpam-6741	241	10	,	,	PUNCT
ejpam-6741	241	11	fixed	fix	VERB
ejpam-6741	241	12	-	-	PUNCT
ejpam-6741	241	13	point	point	NOUN
ejpam-6741	241	14	geometry	geometry	NOUN
ejpam-6741	241	15	within	within	ADP
ejpam-6741	241	16	this	this	DET
ejpam-6741	241	17	class	class	NOUN
ejpam-6741	241	18	of	of	ADP
ejpam-6741	241	19	models	model	NOUN
ejpam-6741	241	20	.	.	PUNCT
ejpam-6741	242	1	the	the	DET
ejpam-6741	242	2	shrinking	shrink	VERB
ejpam-6741	242	3	solitons	soliton	NOUN
ejpam-6741	242	4	(	(	PUNCT
ejpam-6741	242	5	possible	possible	ADJ
ejpam-6741	242	6	in	in	ADP
ejpam-6741	242	7	branches	branch	NOUN
ejpam-6741	242	8	1	1	NUM
ejpam-6741	242	9	,	,	PUNCT
ejpam-6741	242	10	2	2	NUM
ejpam-6741	242	11	,	,	PUNCT
ejpam-6741	242	12	9	9	NUM
ejpam-6741	242	13	,	,	PUNCT
ejpam-6741	242	14	10	10	NUM
ejpam-6741	242	15	,	,	PUNCT
ejpam-6741	242	16	and	and	CCONJ
ejpam-6741	242	17	12	12	NUM
ejpam-6741	242	18	for	for	ADP
ejpam-6741	242	19	δ	δ	PROPN
ejpam-6741	242	20	>	>	X
ejpam-6741	242	21	0	0	NUM
ejpam-6741	242	22	)	)	PUNCT
ejpam-6741	242	23	are	be	AUX
ejpam-6741	242	24	perhaps	perhaps	ADV
ejpam-6741	242	25	the	the	DET
ejpam-6741	242	26	most	most	ADV
ejpam-6741	242	27	significant	significant	ADJ
ejpam-6741	242	28	from	from	ADP
ejpam-6741	242	29	a	a	DET
ejpam-6741	242	30	gravitational	gravitational	ADJ
ejpam-6741	242	31	perspective	perspective	NOUN
ejpam-6741	242	32	.	.	PUNCT
ejpam-6741	243	1	in	in	ADP
ejpam-6741	243	2	the	the	DET
ejpam-6741	243	3	ricci	ricci	PROPN
ejpam-6741	243	4	flow	flow	NOUN
ejpam-6741	243	5	,	,	PUNCT
ejpam-6741	243	6	shrinking	shrink	VERB
ejpam-6741	243	7	solitons	soliton	NOUN
ejpam-6741	243	8	evolve	evolve	VERB
ejpam-6741	243	9	towards	towards	ADP
ejpam-6741	243	10	a	a	DET
ejpam-6741	243	11	singularity	singularity	NOUN
ejpam-6741	243	12	(	(	PUNCT
ejpam-6741	243	13	a	a	DET
ejpam-6741	243	14	curvature	curvature	NOUN
ejpam-6741	243	15	blow	blow	NOUN
ejpam-6741	243	16	-	-	PUNCT
ejpam-6741	243	17	up	up	NOUN
ejpam-6741	243	18	)	)	PUNCT
ejpam-6741	243	19	in	in	ADP
ejpam-6741	243	20	finite	finite	ADJ
ejpam-6741	243	21	flow	flow	NOUN
ejpam-6741	243	22	time	time	NOUN
ejpam-6741	243	23	.	.	PUNCT
ejpam-6741	244	1	this	this	DET
ejpam-6741	244	2	mathematical	mathematical	ADJ
ejpam-6741	244	3	behavior	behavior	NOUN
ejpam-6741	244	4	is	be	AUX
ejpam-6741	244	5	analogous	analogous	ADJ
ejpam-6741	244	6	to	to	ADP
ejpam-6741	244	7	the	the	DET
ejpam-6741	244	8	formation	formation	NOUN
ejpam-6741	244	9	of	of	ADP
ejpam-6741	244	10	a	a	DET
ejpam-6741	244	11	spacetime	spacetime	NOUN
ejpam-6741	244	12	singularity	singularity	NOUN
ejpam-6741	244	13	in	in	ADP
ejpam-6741	244	14	gr	gr	PROPN
ejpam-6741	244	15	,	,	PUNCT
ejpam-6741	244	16	such	such	ADJ
ejpam-6741	244	17	as	as	ADP
ejpam-6741	244	18	those	those	PRON
ejpam-6741	244	19	inside	inside	ADP
ejpam-6741	244	20	black	black	ADJ
ejpam-6741	244	21	holes	hole	NOUN
ejpam-6741	244	22	or	or	CCONJ
ejpam-6741	244	23	in	in	ADP
ejpam-6741	244	24	cosmological	cosmological	ADJ
ejpam-6741	244	25	scenarios	scenario	NOUN
ejpam-6741	244	26	like	like	ADP
ejpam-6741	244	27	the	the	DET
ejpam-6741	244	28	big	big	PROPN
ejpam-6741	244	29	bang	bang	PROPN
ejpam-6741	244	30	.	.	PUNCT
ejpam-6741	245	1	therefore	therefore	ADV
ejpam-6741	245	2	,	,	PUNCT
ejpam-6741	245	3	our	our	PRON
ejpam-6741	245	4	identification	identification	NOUN
ejpam-6741	245	5	of	of	ADP
ejpam-6741	245	6	these	these	DET
ejpam-6741	245	7	shrinking	shrink	VERB
ejpam-6741	245	8	soliton	soliton	NOUN
ejpam-6741	245	9	solutions	solution	NOUN
ejpam-6741	245	10	provides	provide	VERB
ejpam-6741	245	11	concrete	concrete	ADJ
ejpam-6741	245	12	examples	example	NOUN
ejpam-6741	245	13	of	of	ADP
ejpam-6741	245	14	lrs	lrs	PROPN
ejpam-6741	245	15	bianchi	bianchi	PROPN
ejpam-6741	245	16	-	-	PUNCT
ejpam-6741	245	17	i	i	PRON
ejpam-6741	245	18	spacetimes	spacetime	VERB
ejpam-6741	245	19	whose	whose	DET
ejpam-6741	245	20	intrinsic	intrinsic	ADJ
ejpam-6741	245	21	geometry	geometry	NOUN
ejpam-6741	245	22	is	be	AUX
ejpam-6741	245	23	predisposed	predispose	VERB
ejpam-6741	245	24	to	to	PART
ejpam-6741	245	25	evolve	evolve	VERB
ejpam-6741	245	26	into	into	ADP
ejpam-6741	245	27	a	a	DET
ejpam-6741	245	28	singular	singular	ADJ
ejpam-6741	245	29	state	state	NOUN
ejpam-6741	245	30	,	,	PUNCT
ejpam-6741	245	31	offering	offer	VERB
ejpam-6741	245	32	a	a	DET
ejpam-6741	245	33	geometric	geometric	ADJ
ejpam-6741	245	34	flow	flow	NOUN
ejpam-6741	245	35	perspective	perspective	NOUN
ejpam-6741	245	36	on	on	ADP
ejpam-6741	245	37	singularity	singularity	NOUN
ejpam-6741	245	38	formation	formation	NOUN
ejpam-6741	245	39	.	.	PUNCT
ejpam-6741	246	1	finally	finally	ADV
ejpam-6741	246	2	,	,	PUNCT
ejpam-6741	246	3	the	the	DET
ejpam-6741	246	4	high	high	ADJ
ejpam-6741	246	5	dimensionality	dimensionality	NOUN
ejpam-6741	246	6	of	of	ADP
ejpam-6741	246	7	the	the	DET
ejpam-6741	246	8	soliton	soliton	NOUN
ejpam-6741	246	9	vector	vector	NOUN
ejpam-6741	246	10	fields	field	NOUN
ejpam-6741	246	11	(	(	PUNCT
ejpam-6741	246	12	e.g.	e.g.	ADV
ejpam-6741	246	13	,	,	PUNCT
ejpam-6741	246	14	up	up	ADP
ejpam-6741	246	15	to	to	PART
ejpam-6741	246	16	11	11	NUM
ejpam-6741	246	17	parameters	parameter	NOUN
ejpam-6741	246	18	in	in	ADP
ejpam-6741	246	19	branch	branch	NOUN
ejpam-6741	246	20	12	12	NUM
ejpam-6741	246	21	)	)	PUNCT
ejpam-6741	246	22	indicates	indicate	VERB
ejpam-6741	246	23	a	a	DET
ejpam-6741	246	24	significant	significant	ADJ
ejpam-6741	246	25	degree	degree	NOUN
ejpam-6741	246	26	of	of	ADP
ejpam-6741	246	27	geometric	geometric	ADJ
ejpam-6741	246	28	rigidity	rigidity	NOUN
ejpam-6741	246	29	.	.	PUNCT
ejpam-6741	247	1	the	the	DET
ejpam-6741	247	2	spacetime	spacetime	NOUN
ejpam-6741	247	3	admits	admit	VERB
ejpam-6741	247	4	a	a	DET
ejpam-6741	247	5	large	large	ADJ
ejpam-6741	247	6	family	family	NOUN
ejpam-6741	247	7	of	of	ADP
ejpam-6741	247	8	deformations	deformation	NOUN
ejpam-6741	247	9	(	(	PUNCT
ejpam-6741	247	10	generated	generate	VERB
ejpam-6741	247	11	by	by	ADP
ejpam-6741	247	12	v	v	NOUN
ejpam-6741	247	13	)	)	PUNCT
ejpam-6741	247	14	that	that	PRON
ejpam-6741	247	15	preserve	preserve	VERB
ejpam-6741	247	16	the	the	DET
ejpam-6741	247	17	soliton	soliton	NOUN
ejpam-6741	247	18	structure	structure	NOUN
ejpam-6741	247	19	.	.	PUNCT
ejpam-6741	248	1	this	this	PRON
ejpam-6741	248	2	suggests	suggest	VERB
ejpam-6741	248	3	a	a	DET
ejpam-6741	248	4	form	form	NOUN
ejpam-6741	248	5	of	of	ADP
ejpam-6741	248	6	stability	stability	NOUN
ejpam-6741	248	7	:	:	PUNCT
ejpam-6741	248	8	the	the	DET
ejpam-6741	248	9	spacetime	spacetime	NOUN
ejpam-6741	248	10	is	be	AUX
ejpam-6741	248	11	not	not	PART
ejpam-6741	248	12	a	a	DET
ejpam-6741	248	13	isolated	isolated	ADJ
ejpam-6741	248	14	solution	solution	NOUN
ejpam-6741	248	15	but	but	CCONJ
ejpam-6741	248	16	part	part	NOUN
ejpam-6741	248	17	of	of	ADP
ejpam-6741	248	18	a	a	DET
ejpam-6741	248	19	larger	large	ADJ
ejpam-6741	248	20	family	family	NOUN
ejpam-6741	248	21	of	of	ADP
ejpam-6741	248	22	solutions	solution	NOUN
ejpam-6741	248	23	with	with	ADP
ejpam-6741	248	24	similar	similar	ADJ
ejpam-6741	248	25	geometric	geometric	ADJ
ejpam-6741	248	26	properties	property	NOUN
ejpam-6741	248	27	,	,	PUNCT
ejpam-6741	248	28	making	make	VERB
ejpam-6741	248	29	it	it	PRON
ejpam-6741	248	30	a	a	DET
ejpam-6741	248	31	more	more	ADV
ejpam-6741	248	32	robust	robust	ADJ
ejpam-6741	248	33	and	and	CCONJ
ejpam-6741	248	34	physically	physically	ADV
ejpam-6741	248	35	plausible	plausible	ADJ
ejpam-6741	248	36	model	model	NOUN
ejpam-6741	248	37	.	.	PUNCT
ejpam-6741	249	1	in	in	ADP
ejpam-6741	249	2	conclusion	conclusion	NOUN
ejpam-6741	249	3	,	,	PUNCT
ejpam-6741	249	4	our	our	PRON
ejpam-6741	249	5	classification	classification	NOUN
ejpam-6741	249	6	does	do	VERB
ejpam-6741	249	7	more	more	ADJ
ejpam-6741	249	8	than	than	ADP
ejpam-6741	249	9	list	list	NOUN
ejpam-6741	249	10	solutions	solution	NOUN
ejpam-6741	249	11	;	;	PUNCT
ejpam-6741	249	12	it	it	PRON
ejpam-6741	249	13	reveals	reveal	VERB
ejpam-6741	249	14	the	the	DET
ejpam-6741	249	15	dynamical	dynamical	ADJ
ejpam-6741	249	16	tendencies	tendency	NOUN
ejpam-6741	249	17	of	of	ADP
ejpam-6741	249	18	lrs	lrs	PROPN
ejpam-6741	249	19	bianchi	bianchi	PROPN
ejpam-6741	249	20	-	-	PUNCT
ejpam-6741	249	21	i	i	PRON
ejpam-6741	249	22	spacetimes	spacetime	VERB
ejpam-6741	249	23	.	.	PUNCT
ejpam-6741	250	1	the	the	DET
ejpam-6741	250	2	expanding	expand	VERB
ejpam-6741	250	3	,	,	PUNCT
ejpam-6741	250	4	steady	steady	ADJ
ejpam-6741	250	5	,	,	PUNCT
ejpam-6741	250	6	and	and	CCONJ
ejpam-6741	250	7	shrinking	shrink	VERB
ejpam-6741	250	8	solitons	soliton	NOUN
ejpam-6741	250	9	map	map	NOUN
ejpam-6741	250	10	onto	onto	ADP
ejpam-6741	250	11	possible	possible	ADJ
ejpam-6741	250	12	evolutionary	evolutionary	ADJ
ejpam-6741	250	13	pathways	pathway	NOUN
ejpam-6741	250	14	-	-	PUNCT
ejpam-6741	250	15	inflationary	inflationary	ADJ
ejpam-6741	250	16	expansion	expansion	NOUN
ejpam-6741	250	17	,	,	PUNCT
ejpam-6741	250	18	stable	stable	ADJ
ejpam-6741	250	19	equilibrium	equilibrium	NOUN
ejpam-6741	250	20	,	,	PUNCT
ejpam-6741	250	21	or	or	CCONJ
ejpam-6741	250	22	gravitational	gravitational	ADJ
ejpam-6741	250	23	collapse	collapse	NOUN
ejpam-6741	250	24	-	-	PUNCT
ejpam-6741	250	25	linking	link	VERB
ejpam-6741	250	26	the	the	DET
ejpam-6741	250	27	algebraic	algebraic	ADJ
ejpam-6741	250	28	structure	structure	NOUN
ejpam-6741	250	29	of	of	ADP
ejpam-6741	250	30	the	the	DET
ejpam-6741	250	31	ricci	ricci	PROPN
ejpam-6741	250	32	soliton	soliton	NOUN
ejpam-6741	250	33	equation	equation	NOUN
ejpam-6741	250	34	to	to	PART
ejpam-6741	250	35	profound	profound	VERB
ejpam-6741	250	36	physical	physical	ADJ
ejpam-6741	250	37	phenomena	phenomenon	NOUN
ejpam-6741	250	38	in	in	ADP
ejpam-6741	250	39	cosmology	cosmology	NOUN
ejpam-6741	250	40	and	and	CCONJ
ejpam-6741	250	41	gravitation	gravitation	NOUN
ejpam-6741	250	42	.	.	PUNCT
ejpam-6741	251	1	4	4	X
ejpam-6741	251	2	.	.	X
ejpam-6741	251	3	conclusion	conclusion	NOUN
ejpam-6741	251	4	this	this	DET
ejpam-6741	251	5	work	work	NOUN
ejpam-6741	251	6	presents	present	VERB
ejpam-6741	251	7	a	a	DET
ejpam-6741	251	8	detailed	detailed	ADJ
ejpam-6741	251	9	theoretical	theoretical	ADJ
ejpam-6741	251	10	study	study	NOUN
ejpam-6741	251	11	of	of	ADP
ejpam-6741	251	12	ricci	ricci	PROPN
ejpam-6741	251	13	solitons	soliton	NOUN
ejpam-6741	251	14	in	in	ADP
ejpam-6741	251	15	lrs	lrs	PROPN
ejpam-6741	251	16	bianchi	bianchi	PROPN
ejpam-6741	251	17	-	-	PUNCT
ejpam-6741	251	18	i	i	PROPN
ejpam-6741	251	19	spacetime	spacetime	NOUN
ejpam-6741	251	20	,	,	PUNCT
ejpam-6741	251	21	culminating	culminate	VERB
ejpam-6741	251	22	in	in	ADP
ejpam-6741	251	23	a	a	DET
ejpam-6741	251	24	complete	complete	ADJ
ejpam-6741	251	25	classification	classification	NOUN
ejpam-6741	251	26	.	.	PUNCT
ejpam-6741	252	1	the	the	DET
ejpam-6741	252	2	investigation	investigation	NOUN
ejpam-6741	252	3	was	be	AUX
ejpam-6741	252	4	carried	carry	VERB
ejpam-6741	252	5	out	out	ADP
ejpam-6741	252	6	in	in	ADP
ejpam-6741	252	7	multiple	multiple	ADJ
ejpam-6741	252	8	,	,	PUNCT
ejpam-6741	252	9	comprehensive	comprehensive	ADJ
ejpam-6741	252	10	stages	stage	NOUN
ejpam-6741	252	11	:	:	PUNCT
ejpam-6741	252	12	first	first	ADV
ejpam-6741	252	13	,	,	PUNCT
ejpam-6741	252	14	the	the	DET
ejpam-6741	252	15	highly	highly	ADV
ejpam-6741	252	16	complex	complex	ADJ
ejpam-6741	252	17	,	,	PUNCT
ejpam-6741	252	18	coupled	couple	VERB
ejpam-6741	252	19	system	system	NOUN
ejpam-6741	252	20	of	of	ADP
ejpam-6741	252	21	partial	partial	ADJ
ejpam-6741	252	22	differential	differential	ADJ
ejpam-6741	252	23	equations	equation	NOUN
ejpam-6741	252	24	defining	define	VERB
ejpam-6741	252	25	the	the	DET
ejpam-6741	252	26	ricci	ricci	PROPN
ejpam-6741	252	27	soliton	soliton	NOUN
ejpam-6741	252	28	and	and	CCONJ
ejpam-6741	252	29	its	its	PRON
ejpam-6741	252	30	vector	vector	NOUN
ejpam-6741	252	31	field	field	NOUN
ejpam-6741	252	32	was	be	AUX
ejpam-6741	252	33	derived	derive	VERB
ejpam-6741	252	34	.	.	PUNCT
ejpam-6741	253	1	second	second	ADJ
ejpam-6741	253	2	,	,	PUNCT
ejpam-6741	253	3	the	the	DET
ejpam-6741	253	4	rif	rif	PROPN
ejpam-6741	253	5	tree	tree	NOUN
ejpam-6741	253	6	algorithm	algorithm	NOUN
ejpam-6741	253	7	was	be	AUX
ejpam-6741	253	8	employed	employ	VERB
ejpam-6741	253	9	to	to	PART
ejpam-6741	253	10	perform	perform	VERB
ejpam-6741	253	11	a	a	DET
ejpam-6741	253	12	systematic	systematic	ADJ
ejpam-6741	253	13	and	and	CCONJ
ejpam-6741	253	14	exhaustive	exhaustive	ADJ
ejpam-6741	253	15	analysis	analysis	NOUN
ejpam-6741	253	16	of	of	ADP
ejpam-6741	253	17	this	this	DET
ejpam-6741	253	18	system	system	NOUN
ejpam-6741	253	19	,	,	PUNCT
ejpam-6741	253	20	leading	lead	VERB
ejpam-6741	253	21	to	to	ADP
ejpam-6741	253	22	the	the	DET
ejpam-6741	253	23	identification	identification	NOUN
ejpam-6741	253	24	of	of	ADP
ejpam-6741	253	25	twelve	twelve	NUM
ejpam-6741	253	26	distinct	distinct	ADJ
ejpam-6741	253	27	branches	branch	NOUN
ejpam-6741	253	28	of	of	ADP
ejpam-6741	253	29	solutions	solution	NOUN
ejpam-6741	253	30	,	,	PUNCT
ejpam-6741	253	31	each	each	PRON
ejpam-6741	253	32	governed	govern	VERB
ejpam-6741	253	33	by	by	ADP
ejpam-6741	253	34	specific	specific	ADJ
ejpam-6741	253	35	geometric	geometric	ADJ
ejpam-6741	253	36	constraints	constraint	NOUN
ejpam-6741	253	37	on	on	ADP
ejpam-6741	253	38	the	the	DET
ejpam-6741	253	39	metric	metric	ADJ
ejpam-6741	253	40	functions	function	NOUN
ejpam-6741	253	41	p(t	p(t	NOUN
ejpam-6741	253	42	)	)	PUNCT
ejpam-6741	253	43	and	and	CCONJ
ejpam-6741	253	44	q(t	q(t	NOUN
ejpam-6741	253	45	)	)	PUNCT
ejpam-6741	253	46	.	.	PUNCT
ejpam-6741	254	1	third	third	ADJ
ejpam-6741	254	2	,	,	PUNCT
ejpam-6741	254	3	the	the	DET
ejpam-6741	254	4	resulting	result	VERB
ejpam-6741	254	5	equations	equation	NOUN
ejpam-6741	254	6	were	be	AUX
ejpam-6741	254	7	solved	solve	VERB
ejpam-6741	254	8	to	to	PART
ejpam-6741	254	9	determine	determine	VERB
ejpam-6741	254	10	the	the	DET
ejpam-6741	254	11	exact	exact	ADJ
ejpam-6741	254	12	form	form	NOUN
ejpam-6741	254	13	of	of	ADP
ejpam-6741	254	14	the	the	DET
ejpam-6741	254	15	soliton	soliton	NOUN
ejpam-6741	254	16	vector	vector	NOUN
ejpam-6741	254	17	field	field	NOUN
ejpam-6741	254	18	v	v	NOUN
ejpam-6741	254	19	for	for	ADP
ejpam-6741	254	20	each	each	DET
ejpam-6741	254	21	case	case	NOUN
ejpam-6741	254	22	,	,	PUNCT
ejpam-6741	254	23	revealing	reveal	VERB
ejpam-6741	254	24	solutions	solution	NOUN
ejpam-6741	254	25	characterized	characterize	VERB
ejpam-6741	254	26	by	by	ADP
ejpam-6741	254	27	a	a	DET
ejpam-6741	254	28	number	number	NOUN
ejpam-6741	254	29	of	of	ADP
ejpam-6741	254	30	free	free	ADJ
ejpam-6741	254	31	parameters	parameter	NOUN
ejpam-6741	254	32	ranging	range	VERB
ejpam-6741	254	33	from	from	ADP
ejpam-6741	254	34	3	3	NUM
ejpam-6741	254	35	to	to	ADP
ejpam-6741	254	36	11	11	NUM
ejpam-6741	254	37	.	.	PUNCT
ejpam-6741	255	1	finally	finally	ADV
ejpam-6741	255	2	,	,	PUNCT
ejpam-6741	255	3	a	a	DET
ejpam-6741	255	4	thorough	thorough	ADJ
ejpam-6741	255	5	physical	physical	ADJ
ejpam-6741	255	6	analysis	analysis	NOUN
ejpam-6741	255	7	was	be	AUX
ejpam-6741	255	8	conducted	conduct	VERB
ejpam-6741	255	9	,	,	PUNCT
ejpam-6741	255	10	determining	determine	VERB
ejpam-6741	255	11	the	the	DET
ejpam-6741	255	12	matter	matter	NOUN
ejpam-6741	255	13	content	content	NOUN
ejpam-6741	255	14	via	via	ADP
ejpam-6741	255	15	the	the	DET
ejpam-6741	255	16	equation	equation	NOUN
ejpam-6741	255	17	of	of	ADP
ejpam-6741	255	18	state	state	NOUN
ejpam-6741	255	19	and	and	CCONJ
ejpam-6741	255	20	testing	test	VERB
ejpam-6741	255	21	the	the	DET
ejpam-6741	255	22	physical	physical	ADJ
ejpam-6741	255	23	viability	viability	NOUN
ejpam-6741	255	24	of	of	ADP
ejpam-6741	255	25	the	the	DET
ejpam-6741	255	26	resulting	result	VERB
ejpam-6741	255	27	models	model	NOUN
ejpam-6741	255	28	through	through	ADP
ejpam-6741	255	29	the	the	DET
ejpam-6741	255	30	standard	standard	ADJ
ejpam-6741	255	31	energy	energy	NOUN
ejpam-6741	255	32	conditions	condition	NOUN
ejpam-6741	255	33	.	.	PUNCT
ejpam-6741	256	1	u.	u.	PROPN
ejpam-6741	256	2	nasib	nasib	PROPN
ejpam-6741	256	3	et	et	PROPN
ejpam-6741	256	4	al	al	PROPN
ejpam-6741	256	5	.	.	PUNCT
ejpam-6741	256	6	/	/	SYM
ejpam-6741	256	7	eur	eur	PROPN
ejpam-6741	256	8	.	.	PUNCT
ejpam-6741	257	1	j.	j.	PROPN
ejpam-6741	257	2	pure	pure	PROPN
ejpam-6741	257	3	appl	appl	PROPN
ejpam-6741	257	4	.	.	PROPN
ejpam-6741	257	5	math	math	PROPN
ejpam-6741	257	6	,	,	PUNCT
ejpam-6741	257	7	18	18	NUM
ejpam-6741	257	8	(	(	PUNCT
ejpam-6741	257	9	4	4	NUM
ejpam-6741	257	10	)	)	PUNCT
ejpam-6741	257	11	(	(	PUNCT
ejpam-6741	257	12	2025	2025	NUM
ejpam-6741	257	13	)	)	PUNCT
ejpam-6741	257	14	,	,	PUNCT
ejpam-6741	257	15	6741	6741	NUM
ejpam-6741	257	16	12	12	NUM
ejpam-6741	257	17	of	of	ADP
ejpam-6741	257	18	14	14	NUM
ejpam-6741	257	19	the	the	DET
ejpam-6741	257	20	main	main	ADJ
ejpam-6741	257	21	results	result	NOUN
ejpam-6741	257	22	and	and	CCONJ
ejpam-6741	257	23	findings	finding	NOUN
ejpam-6741	257	24	reported	report	VERB
ejpam-6741	257	25	in	in	ADP
ejpam-6741	257	26	this	this	DET
ejpam-6741	257	27	manuscript	manuscript	NOUN
ejpam-6741	257	28	are	be	AUX
ejpam-6741	257	29	summarized	summarize	VERB
ejpam-6741	257	30	as	as	SCONJ
ejpam-6741	257	31	follows	follow	VERB
ejpam-6741	257	32	:	:	PUNCT
ejpam-6741	257	33	(	(	PUNCT
ejpam-6741	257	34	i	i	NOUN
ejpam-6741	257	35	)	)	PUNCT
ejpam-6741	257	36	the	the	DET
ejpam-6741	257	37	rif	rif	PROPN
ejpam-6741	257	38	tree	tree	NOUN
ejpam-6741	257	39	algorithm	algorithm	NOUN
ejpam-6741	257	40	proved	prove	VERB
ejpam-6741	257	41	to	to	PART
ejpam-6741	257	42	be	be	AUX
ejpam-6741	257	43	a	a	DET
ejpam-6741	257	44	powerful	powerful	ADJ
ejpam-6741	257	45	and	and	CCONJ
ejpam-6741	257	46	essential	essential	ADJ
ejpam-6741	257	47	tool	tool	NOUN
ejpam-6741	257	48	for	for	ADP
ejpam-6741	257	49	this	this	DET
ejpam-6741	257	50	classification	classification	NOUN
ejpam-6741	257	51	,	,	PUNCT
ejpam-6741	257	52	successfully	successfully	ADV
ejpam-6741	257	53	managing	manage	VERB
ejpam-6741	257	54	the	the	DET
ejpam-6741	257	55	high	high	ADJ
ejpam-6741	257	56	complexity	complexity	NOUN
ejpam-6741	257	57	of	of	ADP
ejpam-6741	257	58	the	the	DET
ejpam-6741	257	59	pde	pde	NOUN
ejpam-6741	257	60	system	system	NOUN
ejpam-6741	257	61	and	and	CCONJ
ejpam-6741	257	62	guaranteeing	guarantee	VERB
ejpam-6741	257	63	that	that	SCONJ
ejpam-6741	257	64	no	no	DET
ejpam-6741	257	65	possible	possible	ADJ
ejpam-6741	257	66	solution	solution	NOUN
ejpam-6741	257	67	branch	branch	NOUN
ejpam-6741	257	68	was	be	AUX
ejpam-6741	257	69	overlooked	overlook	VERB
ejpam-6741	257	70	.	.	PUNCT
ejpam-6741	258	1	this	this	PRON
ejpam-6741	258	2	represents	represent	VERB
ejpam-6741	258	3	a	a	DET
ejpam-6741	258	4	significant	significant	ADJ
ejpam-6741	258	5	methodological	methodological	ADJ
ejpam-6741	258	6	advancement	advancement	NOUN
ejpam-6741	258	7	over	over	ADP
ejpam-6741	258	8	the	the	DET
ejpam-6741	258	9	direct	direct	ADJ
ejpam-6741	258	10	integration	integration	NOUN
ejpam-6741	258	11	approach	approach	NOUN
ejpam-6741	258	12	used	use	VERB
ejpam-6741	258	13	in	in	ADP
ejpam-6741	258	14	prior	prior	ADJ
ejpam-6741	258	15	studies	study	NOUN
ejpam-6741	258	16	.	.	PUNCT
ejpam-6741	259	1	(	(	PUNCT
ejpam-6741	259	2	ii	ii	NOUN
ejpam-6741	259	3	)	)	PUNCT
ejpam-6741	259	4	the	the	DET
ejpam-6741	259	5	lrs	lrs	PROPN
ejpam-6741	259	6	bianchi	bianchi	PROPN
ejpam-6741	259	7	-	-	PUNCT
ejpam-6741	259	8	i	i	PROPN
ejpam-6741	259	9	spacetime	spacetime	PROPN
ejpam-6741	259	10	admits	admit	VERB
ejpam-6741	259	11	a	a	DET
ejpam-6741	259	12	rich	rich	ADJ
ejpam-6741	259	13	variety	variety	NOUN
ejpam-6741	259	14	of	of	ADP
ejpam-6741	259	15	ricci	ricci	PROPN
ejpam-6741	259	16	soliton	soliton	PROPN
ejpam-6741	259	17	solutions	solution	NOUN
ejpam-6741	259	18	,	,	PUNCT
ejpam-6741	259	19	including	include	VERB
ejpam-6741	259	20	shrinking	shrink	VERB
ejpam-6741	259	21	(	(	PUNCT
ejpam-6741	259	22	δ	δ	X
ejpam-6741	259	23	>	>	X
ejpam-6741	259	24	0	0	NUM
ejpam-6741	259	25	)	)	PUNCT
ejpam-6741	259	26	,	,	PUNCT
ejpam-6741	259	27	steady	steady	ADJ
ejpam-6741	259	28	(	(	PUNCT
ejpam-6741	259	29	δ	δ	NOUN
ejpam-6741	259	30	=	=	PROPN
ejpam-6741	259	31	0	0	NUM
ejpam-6741	259	32	)	)	PUNCT
ejpam-6741	259	33	,	,	PUNCT
ejpam-6741	259	34	and	and	CCONJ
ejpam-6741	259	35	expanding	expand	VERB
ejpam-6741	259	36	(	(	PUNCT
ejpam-6741	259	37	δ	δ	X
ejpam-6741	259	38	<	<	X
ejpam-6741	259	39	0	0	NUM
ejpam-6741	259	40	)	)	PUNCT
ejpam-6741	259	41	types	type	NOUN
ejpam-6741	259	42	.	.	PUNCT
ejpam-6741	260	1	their	their	PRON
ejpam-6741	260	2	existence	existence	NOUN
ejpam-6741	260	3	depends	depend	VERB
ejpam-6741	260	4	critically	critically	ADV
ejpam-6741	260	5	on	on	ADP
ejpam-6741	260	6	the	the	DET
ejpam-6741	260	7	specific	specific	ADJ
ejpam-6741	260	8	differential	differential	NOUN
ejpam-6741	260	9	constraints	constraint	NOUN
ejpam-6741	260	10	satisfied	satisfy	VERB
ejpam-6741	260	11	by	by	ADP
ejpam-6741	260	12	the	the	DET
ejpam-6741	260	13	metric	metric	ADJ
ejpam-6741	260	14	functions	function	NOUN
ejpam-6741	260	15	p(t	p(t	NOUN
ejpam-6741	260	16	)	)	PUNCT
ejpam-6741	260	17	and	and	CCONJ
ejpam-6741	260	18	q(t	q(t	NOUN
ejpam-6741	260	19	)	)	PUNCT
ejpam-6741	260	20	.	.	PUNCT
ejpam-6741	261	1	(	(	PUNCT
ejpam-6741	261	2	iii	iii	X
ejpam-6741	261	3	)	)	PUNCT
ejpam-6741	261	4	the	the	DET
ejpam-6741	261	5	dimensionality	dimensionality	NOUN
ejpam-6741	261	6	of	of	ADP
ejpam-6741	261	7	the	the	DET
ejpam-6741	261	8	associated	associated	ADJ
ejpam-6741	261	9	soliton	soliton	NOUN
ejpam-6741	261	10	vector	vector	NOUN
ejpam-6741	261	11	fields	field	NOUN
ejpam-6741	261	12	v	v	NOUN
ejpam-6741	261	13	varies	vary	VERB
ejpam-6741	261	14	significantly	significantly	ADV
ejpam-6741	261	15	across	across	ADP
ejpam-6741	261	16	the	the	DET
ejpam-6741	261	17	different	different	ADJ
ejpam-6741	261	18	branches	branch	NOUN
ejpam-6741	261	19	,	,	PUNCT
ejpam-6741	261	20	ranging	range	VERB
ejpam-6741	261	21	from	from	ADP
ejpam-6741	261	22	3	3	NUM
ejpam-6741	261	23	to	to	ADP
ejpam-6741	261	24	11	11	NUM
ejpam-6741	261	25	independent	independent	ADJ
ejpam-6741	261	26	parameters	parameter	NOUN
ejpam-6741	261	27	.	.	PUNCT
ejpam-6741	262	1	this	this	DET
ejpam-6741	262	2	diversity	diversity	NOUN
ejpam-6741	262	3	indicates	indicate	VERB
ejpam-6741	262	4	varying	vary	VERB
ejpam-6741	262	5	degrees	degree	NOUN
ejpam-6741	262	6	of	of	ADP
ejpam-6741	262	7	geometric	geometric	ADJ
ejpam-6741	262	8	rigidity	rigidity	NOUN
ejpam-6741	262	9	within	within	ADP
ejpam-6741	262	10	the	the	DET
ejpam-6741	262	11	solution	solution	NOUN
ejpam-6741	262	12	space	space	NOUN
ejpam-6741	262	13	.	.	PUNCT
ejpam-6741	263	1	(	(	PUNCT
ejpam-6741	263	2	iv	iv	X
ejpam-6741	263	3	)	)	PUNCT
ejpam-6741	263	4	the	the	DET
ejpam-6741	263	5	physical	physical	ADJ
ejpam-6741	263	6	analysis	analysis	NOUN
ejpam-6741	263	7	,	,	PUNCT
ejpam-6741	263	8	based	base	VERB
ejpam-6741	263	9	on	on	ADP
ejpam-6741	263	10	the	the	DET
ejpam-6741	263	11	equation	equation	NOUN
ejpam-6741	263	12	of	of	ADP
ejpam-6741	263	13	state	state	NOUN
ejpam-6741	263	14	and	and	CCONJ
ejpam-6741	263	15	energy	energy	NOUN
ejpam-6741	263	16	conditions	condition	NOUN
ejpam-6741	263	17	,	,	PUNCT
ejpam-6741	263	18	confirmed	confirm	VERB
ejpam-6741	263	19	that	that	SCONJ
ejpam-6741	263	20	several	several	ADJ
ejpam-6741	263	21	of	of	ADP
ejpam-6741	263	22	the	the	DET
ejpam-6741	263	23	obtained	obtain	VERB
ejpam-6741	263	24	solutions	solution	NOUN
ejpam-6741	263	25	correspond	correspond	VERB
ejpam-6741	263	26	to	to	ADP
ejpam-6741	263	27	physically	physically	ADV
ejpam-6741	263	28	meaningful	meaningful	ADJ
ejpam-6741	263	29	scenarios	scenario	NOUN
ejpam-6741	263	30	.	.	PUNCT
ejpam-6741	264	1	notably	notably	ADV
ejpam-6741	264	2	,	,	PUNCT
ejpam-6741	264	3	the	the	DET
ejpam-6741	264	4	solutions	solution	NOUN
ejpam-6741	264	5	in	in	ADP
ejpam-6741	264	6	branches	branch	NOUN
ejpam-6741	264	7	7	7	NUM
ejpam-6741	264	8	and	and	CCONJ
ejpam-6741	264	9	8	8	NUM
ejpam-6741	264	10	were	be	AUX
ejpam-6741	264	11	found	find	VERB
ejpam-6741	264	12	to	to	PART
ejpam-6741	264	13	perfectly	perfectly	ADV
ejpam-6741	264	14	describe	describe	VERB
ejpam-6741	264	15	a	a	DET
ejpam-6741	264	16	spacetime	spacetime	NOUN
ejpam-6741	264	17	filled	fill	VERB
ejpam-6741	264	18	with	with	ADP
ejpam-6741	264	19	a	a	DET
ejpam-6741	264	20	cosmological	cosmological	ADJ
ejpam-6741	264	21	constant	constant	ADJ
ejpam-6741	264	22	(	(	PUNCT
ejpam-6741	264	23	w	w	NOUN
ejpam-6741	264	24	=	=	PUNCT
ejpam-6741	264	25	−1	−1	NOUN
ejpam-6741	264	26	)	)	PUNCT
ejpam-6741	264	27	,	,	PUNCT
ejpam-6741	264	28	while	while	SCONJ
ejpam-6741	264	29	the	the	DET
ejpam-6741	264	30	solution	solution	NOUN
ejpam-6741	264	31	in	in	ADP
ejpam-6741	264	32	branch	branch	NOUN
ejpam-6741	264	33	9	9	NUM
ejpam-6741	264	34	describes	describe	VERB
ejpam-6741	264	35	a	a	DET
ejpam-6741	264	36	vacuum	vacuum	NOUN
ejpam-6741	264	37	.	.	PUNCT
ejpam-6741	265	1	in	in	ADP
ejpam-6741	265	2	conclusion	conclusion	NOUN
ejpam-6741	265	3	,	,	PUNCT
ejpam-6741	265	4	our	our	PRON
ejpam-6741	265	5	classification	classification	NOUN
ejpam-6741	265	6	does	do	VERB
ejpam-6741	265	7	more	more	ADJ
ejpam-6741	265	8	than	than	ADP
ejpam-6741	265	9	list	list	NOUN
ejpam-6741	265	10	solutions	solution	NOUN
ejpam-6741	265	11	;	;	PUNCT
ejpam-6741	265	12	it	it	PRON
ejpam-6741	265	13	reveals	reveal	VERB
ejpam-6741	265	14	the	the	DET
ejpam-6741	265	15	dynamical	dynamical	ADJ
ejpam-6741	265	16	tendencies	tendency	NOUN
ejpam-6741	265	17	and	and	CCONJ
ejpam-6741	265	18	stability	stability	NOUN
ejpam-6741	265	19	properties	property	NOUN
ejpam-6741	265	20	of	of	ADP
ejpam-6741	265	21	lrs	lrs	PROPN
ejpam-6741	265	22	bianchi	bianchi	PROPN
ejpam-6741	265	23	-	-	PUNCT
ejpam-6741	265	24	i	i	PRON
ejpam-6741	265	25	spacetimes	spacetime	VERB
ejpam-6741	265	26	.	.	PUNCT
ejpam-6741	266	1	the	the	DET
ejpam-6741	266	2	expanding	expand	VERB
ejpam-6741	266	3	,	,	PUNCT
ejpam-6741	266	4	steady	steady	ADJ
ejpam-6741	266	5	,	,	PUNCT
ejpam-6741	266	6	and	and	CCONJ
ejpam-6741	266	7	shrinking	shrink	VERB
ejpam-6741	266	8	solitons	soliton	NOUN
ejpam-6741	266	9	map	map	NOUN
ejpam-6741	266	10	onto	onto	ADP
ejpam-6741	266	11	possible	possible	ADJ
ejpam-6741	266	12	evolutionary	evolutionary	ADJ
ejpam-6741	266	13	pathways	pathway	NOUN
ejpam-6741	266	14	-	-	PUNCT
ejpam-6741	266	15	inflationary	inflationary	ADJ
ejpam-6741	266	16	expansion	expansion	NOUN
ejpam-6741	266	17	,	,	PUNCT
ejpam-6741	266	18	stable	stable	ADJ
ejpam-6741	266	19	equilibrium	equilibrium	NOUN
ejpam-6741	266	20	,	,	PUNCT
ejpam-6741	266	21	or	or	CCONJ
ejpam-6741	266	22	gravitational	gravitational	ADJ
ejpam-6741	266	23	collapse	collapse	NOUN
ejpam-6741	266	24	-	-	PUNCT
ejpam-6741	266	25	linking	link	VERB
ejpam-6741	266	26	the	the	DET
ejpam-6741	266	27	algebraic	algebraic	ADJ
ejpam-6741	266	28	structure	structure	NOUN
ejpam-6741	266	29	of	of	ADP
ejpam-6741	266	30	the	the	DET
ejpam-6741	266	31	ricci	ricci	PROPN
ejpam-6741	266	32	soliton	soliton	NOUN
ejpam-6741	266	33	equation	equation	NOUN
ejpam-6741	266	34	to	to	PART
ejpam-6741	266	35	profound	profound	VERB
ejpam-6741	266	36	physical	physical	ADJ
ejpam-6741	266	37	phenomena	phenomenon	NOUN
ejpam-6741	266	38	in	in	ADP
ejpam-6741	266	39	cosmology	cosmology	NOUN
ejpam-6741	266	40	and	and	CCONJ
ejpam-6741	266	41	gravitation	gravitation	NOUN
ejpam-6741	266	42	.	.	PUNCT
ejpam-6741	267	1	the	the	DET
ejpam-6741	267	2	cases	case	NOUN
ejpam-6741	267	3	involving	involve	VERB
ejpam-6741	267	4	non	non	ADJ
ejpam-6741	267	5	-	-	ADJ
ejpam-6741	267	6	linear	linear	ADJ
ejpam-6741	267	7	constraints	constraint	NOUN
ejpam-6741	267	8	on	on	ADP
ejpam-6741	267	9	p(t	p(t	NOUN
ejpam-6741	267	10	)	)	PUNCT
ejpam-6741	267	11	and	and	CCONJ
ejpam-6741	267	12	q(t	q(t	X
ejpam-6741	267	13	)	)	PUNCT
ejpam-6741	267	14	present	present	ADJ
ejpam-6741	267	15	promising	promise	VERB
ejpam-6741	267	16	avenues	avenue	NOUN
ejpam-6741	267	17	for	for	ADP
ejpam-6741	267	18	future	future	ADJ
ejpam-6741	267	19	work	work	NOUN
ejpam-6741	267	20	,	,	PUNCT
ejpam-6741	267	21	potentially	potentially	ADV
ejpam-6741	267	22	requiring	require	VERB
ejpam-6741	267	23	numerical	numerical	ADJ
ejpam-6741	267	24	analysis	analysis	NOUN
ejpam-6741	267	25	to	to	PART
ejpam-6741	267	26	fully	fully	ADV
ejpam-6741	267	27	explore	explore	VERB
ejpam-6741	267	28	their	their	PRON
ejpam-6741	267	29	dynamics	dynamic	NOUN
ejpam-6741	267	30	and	and	CCONJ
ejpam-6741	267	31	stability	stability	NOUN
ejpam-6741	267	32	.	.	PUNCT
ejpam-6741	268	1	declarations	declaration	NOUN
ejpam-6741	268	2	acknowledgements	acknowledgement	VERB
ejpam-6741	268	3	the	the	DET
ejpam-6741	268	4	authors	author	NOUN
ejpam-6741	268	5	s.	s.	PROPN
ejpam-6741	268	6	haque	haque	PROPN
ejpam-6741	268	7	and	and	CCONJ
ejpam-6741	268	8	n.	n.	PROPN
ejpam-6741	268	9	mlaiki	mlaiki	PROPN
ejpam-6741	268	10	would	would	AUX
ejpam-6741	268	11	like	like	VERB
ejpam-6741	268	12	to	to	PART
ejpam-6741	268	13	thank	thank	VERB
ejpam-6741	268	14	the	the	DET
ejpam-6741	268	15	prince	prince	PROPN
ejpam-6741	268	16	sultan	sultan	PROPN
ejpam-6741	268	17	university	university	PROPN
ejpam-6741	268	18	for	for	ADP
ejpam-6741	268	19	paying	pay	VERB
ejpam-6741	268	20	the	the	DET
ejpam-6741	268	21	publication	publication	NOUN
ejpam-6741	268	22	fees	fee	NOUN
ejpam-6741	268	23	for	for	ADP
ejpam-6741	268	24	this	this	DET
ejpam-6741	268	25	work	work	NOUN
ejpam-6741	268	26	through	through	ADP
ejpam-6741	268	27	tas	ta	NOUN
ejpam-6741	268	28	lab	lab	NOUN
ejpam-6741	268	29	.	.	PUNCT
ejpam-6741	269	1	funding	fund	VERB
ejpam-6741	269	2	this	this	DET
ejpam-6741	269	3	research	research	NOUN
ejpam-6741	269	4	work	work	NOUN
ejpam-6741	269	5	did	do	AUX
ejpam-6741	269	6	not	not	PART
ejpam-6741	269	7	receive	receive	VERB
ejpam-6741	269	8	any	any	DET
ejpam-6741	269	9	external	external	ADJ
ejpam-6741	269	10	funding	funding	NOUN
ejpam-6741	269	11	.	.	PUNCT
ejpam-6741	270	1	references	reference	NOUN
ejpam-6741	270	2	[	[	X
ejpam-6741	270	3	1	1	NUM
ejpam-6741	270	4	]	]	PUNCT
ejpam-6741	270	5	a.	a.	PROPN
ejpam-6741	270	6	ali	ali	PROPN
ejpam-6741	270	7	and	and	CCONJ
ejpam-6741	270	8	z.	z.	PROPN
ejpam-6741	270	9	minullah	minullah	PROPN
ejpam-6741	270	10	.	.	PUNCT
ejpam-6741	271	1	classification	classification	NOUN
ejpam-6741	271	2	of	of	ADP
ejpam-6741	271	3	spherically	spherically	PROPN
ejpam-6741	271	4	symmetric	symmetric	PROPN
ejpam-6741	271	5	non	non	ADJ
ejpam-6741	271	6	static	static	ADJ
ejpam-6741	271	7	space	space	NOUN
ejpam-6741	271	8	-	-	PUNCT
ejpam-6741	271	9	times	time	NOUN
ejpam-6741	271	10	according	accord	VERB
ejpam-6741	271	11	to	to	ADP
ejpam-6741	271	12	their	their	PRON
ejpam-6741	271	13	killing	kill	VERB
ejpam-6741	271	14	vector	vector	NOUN
ejpam-6741	271	15	fields	field	NOUN
ejpam-6741	271	16	.	.	PUNCT
ejpam-6741	272	1	appl	appl	PROPN
ejpam-6741	272	2	.	.	PROPN
ejpam-6741	272	3	math	math	PROPN
ejpam-6741	272	4	.	.	PUNCT
ejpam-6741	273	1	sci	sci	PROPN
ejpam-6741	273	2	.	.	PROPN
ejpam-6741	273	3	,	,	PUNCT
ejpam-6741	273	4	6:2681–2686	6:2681–2686	NUM
ejpam-6741	273	5	,	,	PUNCT
ejpam-6741	273	6	2012	2012	NUM
ejpam-6741	273	7	.	.	PUNCT
ejpam-6741	274	1	u.	u.	PROPN
ejpam-6741	274	2	nasib	nasib	PROPN
ejpam-6741	274	3	et	et	PROPN
ejpam-6741	274	4	al	al	PROPN
ejpam-6741	274	5	.	.	PUNCT
ejpam-6741	274	6	/	/	SYM
ejpam-6741	274	7	eur	eur	PROPN
ejpam-6741	274	8	.	.	PUNCT
ejpam-6741	275	1	j.	j.	PROPN
ejpam-6741	275	2	pure	pure	PROPN
ejpam-6741	275	3	appl	appl	PROPN
ejpam-6741	275	4	.	.	PROPN
ejpam-6741	275	5	math	math	PROPN
ejpam-6741	275	6	,	,	PUNCT
ejpam-6741	275	7	18	18	NUM
ejpam-6741	275	8	(	(	PUNCT
ejpam-6741	275	9	4	4	NUM
ejpam-6741	275	10	)	)	PUNCT
ejpam-6741	275	11	(	(	PUNCT
ejpam-6741	275	12	2025	2025	NUM
ejpam-6741	275	13	)	)	PUNCT
ejpam-6741	275	14	,	,	PUNCT
ejpam-6741	275	15	6741	6741	NUM
ejpam-6741	275	16	13	13	NUM
ejpam-6741	275	17	of	of	ADP
ejpam-6741	275	18	14	14	NUM
ejpam-6741	275	19	[	[	X
ejpam-6741	275	20	2	2	X
ejpam-6741	275	21	]	]	PUNCT
ejpam-6741	275	22	t.	t.	PROPN
ejpam-6741	275	23	hussain	hussain	PROPN
ejpam-6741	275	24	,	,	PUNCT
ejpam-6741	275	25	s.	s.	PROPN
ejpam-6741	275	26	s.	s.	PROPN
ejpam-6741	275	27	akhtar	akhtar	PROPN
ejpam-6741	275	28	,	,	PUNCT
ejpam-6741	275	29	and	and	CCONJ
ejpam-6741	275	30	a.	a.	PROPN
ejpam-6741	275	31	h.	h.	PROPN
ejpam-6741	275	32	bokhari	bokhari	PROPN
ejpam-6741	275	33	.	.	PUNCT
ejpam-6741	276	1	a	a	DET
ejpam-6741	276	2	study	study	NOUN
ejpam-6741	276	3	of	of	ADP
ejpam-6741	276	4	energy	energy	NOUN
ejpam-6741	276	5	conditions	condition	NOUN
ejpam-6741	276	6	in	in	ADP
ejpam-6741	276	7	nonstatic	nonstatic	ADJ
ejpam-6741	276	8	spherically	spherically	NOUN
ejpam-6741	276	9	symmetric	symmetric	ADJ
ejpam-6741	276	10	spacetimes	spacetime	NOUN
ejpam-6741	276	11	via	via	ADP
ejpam-6741	276	12	noether	noether	ADJ
ejpam-6741	276	13	symmetries	symmetry	NOUN
ejpam-6741	276	14	.	.	PUNCT
ejpam-6741	277	1	j.	j.	PROPN
ejpam-6741	277	2	math	math	PROPN
ejpam-6741	277	3	.	.	PUNCT
ejpam-6741	278	1	anal	anal	PROPN
ejpam-6741	278	2	.	.	PUNCT
ejpam-6741	279	1	appl	appl	PROPN
ejpam-6741	279	2	.	.	PROPN
ejpam-6741	279	3	,	,	PUNCT
ejpam-6741	279	4	483:123574	483:123574	NUM
ejpam-6741	279	5	,	,	PUNCT
ejpam-6741	279	6	2020	2020	NUM
ejpam-6741	279	7	.	.	PUNCT
ejpam-6741	280	1	[	[	X
ejpam-6741	280	2	3	3	X
ejpam-6741	280	3	]	]	X
ejpam-6741	280	4	g.	g.	PROPN
ejpam-6741	280	5	w.	w.	PROPN
ejpam-6741	280	6	bluman	bluman	PROPN
ejpam-6741	280	7	and	and	CCONJ
ejpam-6741	280	8	s.	s.	PROPN
ejpam-6741	280	9	kumei	kumei	PROPN
ejpam-6741	280	10	.	.	PUNCT
ejpam-6741	281	1	symmetries	symmetry	NOUN
ejpam-6741	281	2	and	and	CCONJ
ejpam-6741	281	3	differential	differential	ADJ
ejpam-6741	281	4	equations	equation	NOUN
ejpam-6741	281	5	.	.	PUNCT
ejpam-6741	282	1	springer	springer	NOUN
ejpam-6741	282	2	,	,	PUNCT
ejpam-6741	282	3	new	new	PROPN
ejpam-6741	282	4	york	york	PROPN
ejpam-6741	282	5	,	,	PUNCT
ejpam-6741	282	6	1989	1989	NUM
ejpam-6741	282	7	.	.	PUNCT
ejpam-6741	283	1	[	[	X
ejpam-6741	283	2	4	4	NUM
ejpam-6741	283	3	]	]	PUNCT
ejpam-6741	283	4	i.	i.	PROPN
ejpam-6741	283	5	hussain	hussain	PROPN
ejpam-6741	283	6	,	,	PUNCT
ejpam-6741	283	7	tahirullah	tahirullah	ADJ
ejpam-6741	283	8	,	,	PUNCT
ejpam-6741	283	9	and	and	CCONJ
ejpam-6741	283	10	s.	s.	PROPN
ejpam-6741	283	11	khan	khan	PROPN
ejpam-6741	283	12	.	.	PUNCT
ejpam-6741	284	1	four	four	NUM
ejpam-6741	284	2	-	-	PUNCT
ejpam-6741	284	3	dimensional	dimensional	ADJ
ejpam-6741	284	4	lorentzian	lorentzian	ADJ
ejpam-6741	284	5	plane	plane	NOUN
ejpam-6741	284	6	symmetric	symmetric	ADJ
ejpam-6741	284	7	static	static	PROPN
ejpam-6741	284	8	ricci	ricci	PROPN
ejpam-6741	284	9	solitons	soliton	NOUN
ejpam-6741	284	10	.	.	PUNCT
ejpam-6741	285	1	int	int	NOUN
ejpam-6741	285	2	.	.	PUNCT
ejpam-6741	286	1	j.	j.	PROPN
ejpam-6741	286	2	mod	mod	PROPN
ejpam-6741	286	3	.	.	PUNCT
ejpam-6741	287	1	phys	phy	NOUN
ejpam-6741	287	2	.	.	PUNCT
ejpam-6741	288	1	d	d	X
ejpam-6741	288	2	,	,	PUNCT
ejpam-6741	288	3	28:2040010	28:2040010	NUM
ejpam-6741	288	4	,	,	PUNCT
ejpam-6741	288	5	2019	2019	NUM
ejpam-6741	288	6	.	.	PUNCT
ejpam-6741	289	1	[	[	X
ejpam-6741	289	2	5	5	NUM
ejpam-6741	289	3	]	]	PUNCT
ejpam-6741	289	4	a.	a.	NOUN
ejpam-6741	289	5	mahmood	mahmood	PROPN
ejpam-6741	289	6	,	,	PUNCT
ejpam-6741	289	7	a.	a.	PROPN
ejpam-6741	289	8	t.	t.	PROPN
ejpam-6741	289	9	ali	ali	PROPN
ejpam-6741	289	10	,	,	PUNCT
ejpam-6741	289	11	and	and	CCONJ
ejpam-6741	289	12	s.	s.	PROPN
ejpam-6741	289	13	khan	khan	PROPN
ejpam-6741	289	14	.	.	PUNCT
ejpam-6741	290	1	concircular	concircular	ADJ
ejpam-6741	290	2	vector	vector	NOUN
ejpam-6741	290	3	fields	field	NOUN
ejpam-6741	290	4	and	and	CCONJ
ejpam-6741	290	5	the	the	DET
ejpam-6741	290	6	ricci	ricci	PROPN
ejpam-6741	290	7	solitons	soliton	NOUN
ejpam-6741	290	8	for	for	ADP
ejpam-6741	290	9	the	the	DET
ejpam-6741	290	10	lrs	lrs	PROPN
ejpam-6741	290	11	bianchi	bianchi	PROPN
ejpam-6741	290	12	type	type	NOUN
ejpam-6741	290	13	-	-	PUNCT
ejpam-6741	290	14	v	v	NOUN
ejpam-6741	290	15	spacetimes	spacetime	NOUN
ejpam-6741	290	16	.	.	PUNCT
ejpam-6741	291	1	mod	mod	PROPN
ejpam-6741	291	2	.	.	PUNCT
ejpam-6741	292	1	phys	phys	PROPN
ejpam-6741	292	2	.	.	PUNCT
ejpam-6741	293	1	lett	lett	PROPN
ejpam-6741	293	2	.	.	PUNCT
ejpam-6741	294	1	a	a	DET
ejpam-6741	294	2	,	,	PUNCT
ejpam-6741	294	3	35:2050169	35:2050169	NUM
ejpam-6741	294	4	,	,	PUNCT
ejpam-6741	294	5	2020	2020	NUM
ejpam-6741	294	6	.	.	PUNCT
ejpam-6741	295	1	[	[	X
ejpam-6741	295	2	6	6	NUM
ejpam-6741	295	3	]	]	PUNCT
ejpam-6741	295	4	tahirullah	tahirullah	ADV
ejpam-6741	295	5	,	,	PUNCT
ejpam-6741	295	6	a.	a.	PROPN
ejpam-6741	295	7	t.	t.	PROPN
ejpam-6741	295	8	ali	ali	PROPN
ejpam-6741	295	9	,	,	PUNCT
ejpam-6741	295	10	and	and	CCONJ
ejpam-6741	295	11	s.	s.	PROPN
ejpam-6741	295	12	khan	khan	PROPN
ejpam-6741	295	13	.	.	PUNCT
ejpam-6741	296	1	ricci	ricci	PROPN
ejpam-6741	296	2	soliton	soliton	PROPN
ejpam-6741	296	3	vector	vector	NOUN
ejpam-6741	296	4	fields	field	NOUN
ejpam-6741	296	5	of	of	ADP
ejpam-6741	296	6	spherically	spherically	PROPN
ejpam-6741	296	7	symmetric	symmetric	ADJ
ejpam-6741	296	8	static	static	ADJ
ejpam-6741	296	9	spacetimes	spacetime	NOUN
ejpam-6741	296	10	.	.	PUNCT
ejpam-6741	297	1	mod	mod	PROPN
ejpam-6741	297	2	.	.	PUNCT
ejpam-6741	298	1	phys	phys	PROPN
ejpam-6741	298	2	.	.	PUNCT
ejpam-6741	299	1	lett	lett	PROPN
ejpam-6741	299	2	.	.	PUNCT
ejpam-6741	300	1	a	a	DET
ejpam-6741	300	2	,	,	PUNCT
ejpam-6741	300	3	36:2150014	36:2150014	NUM
ejpam-6741	300	4	,	,	PUNCT
ejpam-6741	300	5	2021	2021	NUM
ejpam-6741	300	6	.	.	PUNCT
ejpam-6741	301	1	[	[	X
ejpam-6741	301	2	7	7	NUM
ejpam-6741	301	3	]	]	PUNCT
ejpam-6741	301	4	a.	a.	NOUN
ejpam-6741	301	5	t.	t.	PROPN
ejpam-6741	301	6	ali	ali	PROPN
ejpam-6741	301	7	and	and	CCONJ
ejpam-6741	301	8	s.	s.	PROPN
ejpam-6741	301	9	khan	khan	PROPN
ejpam-6741	301	10	.	.	PUNCT
ejpam-6741	302	1	ricci	ricci	PROPN
ejpam-6741	302	2	soliton	soliton	PROPN
ejpam-6741	302	3	vector	vector	NOUN
ejpam-6741	302	4	fields	field	NOUN
ejpam-6741	302	5	of	of	ADP
ejpam-6741	302	6	kantowski	kantowski	ADJ
ejpam-6741	302	7	sachs	sachs	PROPN
ejpam-6741	302	8	spacetimes	spacetime	NOUN
ejpam-6741	302	9	.	.	PUNCT
ejpam-6741	303	1	mod	mod	PROPN
ejpam-6741	303	2	.	.	PUNCT
ejpam-6741	304	1	phys	phys	PROPN
ejpam-6741	304	2	.	.	PUNCT
ejpam-6741	305	1	lett	lett	PROPN
ejpam-6741	305	2	.	.	PUNCT
ejpam-6741	306	1	a	a	DET
ejpam-6741	306	2	,	,	PUNCT
ejpam-6741	306	3	37:2250146	37:2250146	NUM
ejpam-6741	306	4	,	,	PUNCT
ejpam-6741	306	5	2022	2022	NUM
ejpam-6741	306	6	.	.	PUNCT
ejpam-6741	307	1	[	[	X
ejpam-6741	307	2	8	8	NUM
ejpam-6741	307	3	]	]	X
ejpam-6741	307	4	u.	u.	NOUN
ejpam-6741	307	5	gull	gull	PROPN
ejpam-6741	307	6	,	,	PUNCT
ejpam-6741	307	7	a.	a.	PROPN
ejpam-6741	307	8	t.	t.	PROPN
ejpam-6741	307	9	ali	ali	PROPN
ejpam-6741	307	10	,	,	PUNCT
ejpam-6741	307	11	s.	s.	PROPN
ejpam-6741	307	12	khan	khan	PROPN
ejpam-6741	307	13	,	,	PUNCT
ejpam-6741	307	14	and	and	CCONJ
ejpam-6741	307	15	a.	a.	PROPN
ejpam-6741	307	16	h.	h.	PROPN
ejpam-6741	307	17	alkasasbeh	alkasasbeh	PROPN
ejpam-6741	307	18	.	.	PUNCT
ejpam-6741	308	1	ricci	ricci	PROPN
ejpam-6741	308	2	soliton	soliton	PROPN
ejpam-6741	308	3	vector	vector	NOUN
ejpam-6741	308	4	fields	field	NOUN
ejpam-6741	308	5	of	of	ADP
ejpam-6741	308	6	a	a	DET
ejpam-6741	308	7	sub	sub	NOUN
ejpam-6741	308	8	-	-	NOUN
ejpam-6741	308	9	class	class	NOUN
ejpam-6741	308	10	of	of	ADP
ejpam-6741	308	11	perfect	perfect	ADJ
ejpam-6741	308	12	fluid	fluid	ADJ
ejpam-6741	308	13	bianchi	bianchi	NOUN
ejpam-6741	308	14	type	type	NOUN
ejpam-6741	308	15	-	-	PUNCT
ejpam-6741	308	16	i	i	PRON
ejpam-6741	308	17	spacetimes	spacetime	VERB
ejpam-6741	308	18	in	in	ADP
ejpam-6741	308	19	f(t	f(t	PROPN
ejpam-6741	308	20	)	)	PUNCT
ejpam-6741	308	21	theory	theory	NOUN
ejpam-6741	308	22	of	of	ADP
ejpam-6741	308	23	gravity	gravity	NOUN
ejpam-6741	308	24	.	.	PUNCT
ejpam-6741	309	1	int	int	NOUN
ejpam-6741	309	2	.	.	PUNCT
ejpam-6741	310	1	j.	j.	PROPN
ejpam-6741	310	2	theor	theor	PROPN
ejpam-6741	310	3	.	.	PUNCT
ejpam-6741	311	1	phys	phy	NOUN
ejpam-6741	311	2	.	.	PUNCT
ejpam-6741	311	3	,	,	PUNCT
ejpam-6741	311	4	63:203	63:203	NUM
ejpam-6741	311	5	,	,	PUNCT
ejpam-6741	311	6	2024	2024	NUM
ejpam-6741	311	7	.	.	PUNCT
ejpam-6741	312	1	[	[	X
ejpam-6741	312	2	9	9	NUM
ejpam-6741	312	3	]	]	PUNCT
ejpam-6741	312	4	m.	m.	NOUN
ejpam-6741	312	5	d.	d.	PROPN
ejpam-6741	312	6	siddiqi	siddiqi	PROPN
ejpam-6741	312	7	.	.	PUNCT
ejpam-6741	313	1	ricci	ricci	PROPN
ejpam-6741	313	2	solitons	soliton	NOUN
ejpam-6741	313	3	in	in	ADP
ejpam-6741	313	4	f(r	f(r	NOUN
ejpam-6741	313	5	)	)	PUNCT
ejpam-6741	313	6	gravity	gravity	NOUN
ejpam-6741	313	7	.	.	PUNCT
ejpam-6741	314	1	balk	balk	VERB
ejpam-6741	314	2	.	.	PUNCT
ejpam-6741	315	1	j.	j.	PROPN
ejpam-6741	315	2	geom	geom	PROPN
ejpam-6741	315	3	.	.	PUNCT
ejpam-6741	316	1	appl	appl	PROPN
ejpam-6741	316	2	.	.	PROPN
ejpam-6741	316	3	,	,	PUNCT
ejpam-6741	316	4	27:162–17x	27:162–17x	NUM
ejpam-6741	316	5	,	,	PUNCT
ejpam-6741	316	6	2022	2022	NUM
ejpam-6741	316	7	.	.	PUNCT
ejpam-6741	317	1	[	[	X
ejpam-6741	317	2	10	10	NUM
ejpam-6741	317	3	]	]	PUNCT
ejpam-6741	317	4	m.	m.	NOUN
ejpam-6741	317	5	d.	d.	PROPN
ejpam-6741	317	6	siddiqi	siddiqi	PROPN
ejpam-6741	317	7	,	,	PUNCT
ejpam-6741	317	8	s.	s.	PROPN
ejpam-6741	317	9	k.	k.	PROPN
ejpam-6741	317	10	chaubey	chaubey	PROPN
ejpam-6741	317	11	,	,	PUNCT
ejpam-6741	317	12	and	and	CCONJ
ejpam-6741	317	13	m.	m.	PROPN
ejpam-6741	317	14	n.	n.	PROPN
ejpam-6741	317	15	i.	i.	PROPN
ejpam-6741	317	16	khan	khan	PROPN
ejpam-6741	317	17	.	.	PUNCT
ejpam-6741	318	1	f(r	f(r	PROPN
ejpam-6741	318	2	,	,	PUNCT
ejpam-6741	318	3	t	t	NOUN
ejpam-6741	318	4	)	)	PUNCT
ejpam-6741	318	5	gravity	gravity	NOUN
ejpam-6741	318	6	model	model	NOUN
ejpam-6741	318	7	with	with	ADP
ejpam-6741	318	8	perfect	perfect	ADJ
ejpam-6741	318	9	fluid	fluid	NOUN
ejpam-6741	318	10	admitting	admit	VERB
ejpam-6741	318	11	einstein	einstein	ADJ
ejpam-6741	318	12	solitons	soliton	NOUN
ejpam-6741	318	13	.	.	PUNCT
ejpam-6741	319	1	mathematics	mathematic	NOUN
ejpam-6741	319	2	,	,	PUNCT
ejpam-6741	319	3	10:82	10:82	NUM
ejpam-6741	319	4	,	,	PUNCT
ejpam-6741	319	5	2022	2022	NUM
ejpam-6741	319	6	.	.	PUNCT
ejpam-6741	320	1	[	[	X
ejpam-6741	320	2	11	11	NUM
ejpam-6741	320	3	]	]	PUNCT
ejpam-6741	320	4	a.	a.	PROPN
ejpam-6741	320	5	ali	ali	PROPN
ejpam-6741	320	6	,	,	PUNCT
ejpam-6741	320	7	m.	m.	PROPN
ejpam-6741	320	8	ali	ali	PROPN
ejpam-6741	320	9	,	,	PUNCT
ejpam-6741	320	10	and	and	CCONJ
ejpam-6741	320	11	v.	v.	ADP
ejpam-6741	320	12	a.	a.	PROPN
ejpam-6741	320	13	khan	khan	PROPN
ejpam-6741	320	14	.	.	PUNCT
ejpam-6741	321	1	conformal	conformal	ADJ
ejpam-6741	321	2	ricci	ricci	PROPN
ejpam-6741	321	3	solitons	soliton	NOUN
ejpam-6741	321	4	on	on	ADP
ejpam-6741	321	5	kenmotsu	kenmotsu	PROPN
ejpam-6741	321	6	manifolds	manifolds	PROPN
ejpam-6741	321	7	.	.	PUNCT
ejpam-6741	322	1	results	result	VERB
ejpam-6741	322	2	phys	phy	NOUN
ejpam-6741	322	3	.	.	PUNCT
ejpam-6741	322	4	,	,	PUNCT
ejpam-6741	322	5	46:106761	46:106761	NOUN
ejpam-6741	322	6	,	,	PUNCT
ejpam-6741	322	7	2023	2023	NUM
ejpam-6741	322	8	.	.	PUNCT
ejpam-6741	323	1	[	[	X
ejpam-6741	323	2	12	12	NUM
ejpam-6741	323	3	]	]	X
ejpam-6741	323	4	d.	d.	PROPN
ejpam-6741	323	5	m.	m.	PROPN
ejpam-6741	323	6	naik	naik	PROPN
ejpam-6741	323	7	,	,	PUNCT
ejpam-6741	323	8	venkatesha	venkatesha	PROPN
ejpam-6741	323	9	,	,	PUNCT
ejpam-6741	323	10	and	and	CCONJ
ejpam-6741	323	11	h.	h.	PROPN
ejpam-6741	323	12	a.	a.	PROPN
ejpam-6741	323	13	kumara	kumara	PROPN
ejpam-6741	323	14	.	.	PUNCT
ejpam-6741	324	1	generalized	generalize	VERB
ejpam-6741	324	2	ricci	ricci	PROPN
ejpam-6741	324	3	solitons	soliton	NOUN
ejpam-6741	324	4	on	on	ADP
ejpam-6741	324	5	almost	almost	ADV
ejpam-6741	324	6	paracontact	paracontact	VERB
ejpam-6741	324	7	metric	metric	ADJ
ejpam-6741	324	8	manifolds	manifold	NOUN
ejpam-6741	324	9	.	.	PUNCT
ejpam-6741	325	1	int	int	NOUN
ejpam-6741	325	2	.	.	PUNCT
ejpam-6741	326	1	j.	j.	PROPN
ejpam-6741	326	2	mod	mod	PROPN
ejpam-6741	326	3	.	.	PUNCT
ejpam-6741	327	1	phys	phys	PROPN
ejpam-6741	327	2	.	.	PUNCT
ejpam-6741	328	1	a	a	DET
ejpam-6741	328	2	,	,	PUNCT
ejpam-6741	328	3	37:2250193	37:2250193	NUM
ejpam-6741	328	4	,	,	PUNCT
ejpam-6741	328	5	2022	2022	NUM
ejpam-6741	328	6	.	.	PUNCT
ejpam-6741	329	1	[	[	X
ejpam-6741	329	2	13	13	NUM
ejpam-6741	329	3	]	]	X
ejpam-6741	329	4	n.	n.	PROPN
ejpam-6741	329	5	raza	raza	PROPN
ejpam-6741	329	6	,	,	PUNCT
ejpam-6741	329	7	m.	m.	NOUN
ejpam-6741	329	8	h.	h.	PROPN
ejpam-6741	329	9	shahid	shahid	PROPN
ejpam-6741	329	10	,	,	PUNCT
ejpam-6741	329	11	and	and	CCONJ
ejpam-6741	329	12	a.	a.	PROPN
ejpam-6741	329	13	ali	ali	PROPN
ejpam-6741	329	14	.	.	PROPN
ejpam-6741	330	1	curvature	curvature	PROPN
ejpam-6741	330	2	inheritance	inheritance	NOUN
ejpam-6741	330	3	symmetry	symmetry	NOUN
ejpam-6741	330	4	in	in	ADP
ejpam-6741	330	5	riemannian	riemannian	ADJ
ejpam-6741	330	6	manifolds	manifold	NOUN
ejpam-6741	330	7	with	with	ADP
ejpam-6741	330	8	applications	application	NOUN
ejpam-6741	330	9	.	.	PUNCT
ejpam-6741	331	1	results	result	VERB
ejpam-6741	331	2	phys	phy	NOUN
ejpam-6741	331	3	.	.	PUNCT
ejpam-6741	331	4	,	,	PUNCT
ejpam-6741	331	5	20:103825	20:103825	PROPN
ejpam-6741	331	6	,	,	PUNCT
ejpam-6741	331	7	2021	2021	NUM
ejpam-6741	331	8	.	.	PUNCT
ejpam-6741	332	1	[	[	X
ejpam-6741	332	2	14	14	NUM
ejpam-6741	332	3	]	]	X
ejpam-6741	332	4	g.	g.	PROPN
ejpam-6741	332	5	reid	reid	PROPN
ejpam-6741	332	6	,	,	PUNCT
ejpam-6741	332	7	a.	a.	NOUN
ejpam-6741	332	8	wittkopf	wittkopf	NOUN
ejpam-6741	332	9	,	,	PUNCT
ejpam-6741	332	10	and	and	CCONJ
ejpam-6741	332	11	a.	a.	PROPN
ejpam-6741	332	12	boulton	boulton	PROPN
ejpam-6741	332	13	.	.	PUNCT
ejpam-6741	333	1	reduction	reduction	NOUN
ejpam-6741	333	2	of	of	ADP
ejpam-6741	333	3	systems	system	NOUN
ejpam-6741	333	4	of	of	ADP
ejpam-6741	333	5	nonlinear	nonlinear	ADJ
ejpam-6741	333	6	partial	partial	ADJ
ejpam-6741	333	7	differential	differential	ADJ
ejpam-6741	333	8	equations	equation	NOUN
ejpam-6741	333	9	to	to	PART
ejpam-6741	333	10	simplified	simplify	VERB
ejpam-6741	333	11	involutive	involutive	ADJ
ejpam-6741	333	12	forms	form	NOUN
ejpam-6741	333	13	.	.	PUNCT
ejpam-6741	334	1	eur	eur	PROPN
ejpam-6741	334	2	.	.	PUNCT
ejpam-6741	335	1	j.	j.	PROPN
ejpam-6741	335	2	appl	appl	PROPN
ejpam-6741	335	3	.	.	PROPN
ejpam-6741	335	4	math	math	PROPN
ejpam-6741	335	5	.	.	PUNCT
ejpam-6741	335	6	,	,	PUNCT
ejpam-6741	335	7	7:604–635	7:604–635	NUM
ejpam-6741	335	8	,	,	PUNCT
ejpam-6741	335	9	1996	1996	NUM
ejpam-6741	335	10	.	.	PUNCT
ejpam-6741	336	1	[	[	X
ejpam-6741	336	2	15	15	NUM
ejpam-6741	336	3	]	]	X
ejpam-6741	336	4	a.	a.	NOUN
ejpam-6741	336	5	d.	d.	PROPN
ejpam-6741	336	6	wittkopf	wittkopf	PROPN
ejpam-6741	336	7	.	.	PUNCT
ejpam-6741	337	1	algorithms	algorithm	NOUN
ejpam-6741	337	2	and	and	CCONJ
ejpam-6741	337	3	implementations	implementation	NOUN
ejpam-6741	337	4	for	for	ADP
ejpam-6741	337	5	differential	differential	ADJ
ejpam-6741	337	6	elimination	elimination	NOUN
ejpam-6741	337	7	.	.	PUNCT
ejpam-6741	338	1	phd	phd	NOUN
ejpam-6741	338	2	thesis	thesis	PROPN
ejpam-6741	338	3	,	,	PUNCT
ejpam-6741	338	4	simon	simon	PROPN
ejpam-6741	338	5	fraser	fraser	PROPN
ejpam-6741	338	6	university	university	PROPN
ejpam-6741	338	7	,	,	PUNCT
ejpam-6741	338	8	canada	canada	PROPN
ejpam-6741	338	9	,	,	PUNCT
ejpam-6741	338	10	2004	2004	NUM
ejpam-6741	338	11	.	.	PUNCT
ejpam-6741	339	1	[	[	X
ejpam-6741	339	2	16	16	NUM
ejpam-6741	339	3	]	]	PUNCT
ejpam-6741	339	4	t.	t.	PROPN
ejpam-6741	339	5	hussain	hussain	PROPN
ejpam-6741	339	6	,	,	PUNCT
ejpam-6741	339	7	u.	u.	PROPN
ejpam-6741	339	8	nasib	nasib	PROPN
ejpam-6741	339	9	,	,	PUNCT
ejpam-6741	339	10	m.	m.	NOUN
ejpam-6741	339	11	farhan	farhan	PROPN
ejpam-6741	339	12	,	,	PUNCT
ejpam-6741	339	13	and	and	CCONJ
ejpam-6741	339	14	a.	a.	PROPN
ejpam-6741	339	15	h.	h.	PROPN
ejpam-6741	339	16	bokhari	bokhari	PROPN
ejpam-6741	339	17	.	.	PUNCT
ejpam-6741	340	1	a	a	DET
ejpam-6741	340	2	study	study	NOUN
ejpam-6741	340	3	of	of	ADP
ejpam-6741	340	4	energy	energy	NOUN
ejpam-6741	340	5	conditions	condition	NOUN
ejpam-6741	340	6	in	in	ADP
ejpam-6741	340	7	kantowski	kantowski	ADJ
ejpam-6741	340	8	-	-	PUNCT
ejpam-6741	340	9	sachs	sachs	NOUN
ejpam-6741	340	10	spacetimes	spacetime	NOUN
ejpam-6741	340	11	via	via	ADP
ejpam-6741	340	12	homothetic	homothetic	ADJ
ejpam-6741	340	13	vector	vector	NOUN
ejpam-6741	340	14	fields	field	NOUN
ejpam-6741	340	15	.	.	PUNCT
ejpam-6741	341	1	int	int	NOUN
ejpam-6741	341	2	.	.	PUNCT
ejpam-6741	342	1	j.	j.	PROPN
ejpam-6741	342	2	geom	geom	PROPN
ejpam-6741	342	3	.	.	PUNCT
ejpam-6741	343	1	methods	methods	PROPN
ejpam-6741	343	2	mod	mod	PROPN
ejpam-6741	343	3	.	.	PUNCT
ejpam-6741	344	1	phys	phy	NOUN
ejpam-6741	344	2	.	.	PUNCT
ejpam-6741	344	3	,	,	PUNCT
ejpam-6741	344	4	17:2050035	17:2050035	NUM
ejpam-6741	344	5	,	,	PUNCT
ejpam-6741	344	6	2020	2020	NUM
ejpam-6741	344	7	.	.	PUNCT
ejpam-6741	345	1	[	[	X
ejpam-6741	345	2	17	17	NUM
ejpam-6741	345	3	]	]	PUNCT
ejpam-6741	345	4	t.	t.	PROPN
ejpam-6741	345	5	hussain	hussain	PROPN
ejpam-6741	345	6	,	,	PUNCT
ejpam-6741	345	7	u.	u.	PROPN
ejpam-6741	345	8	nasib	nasib	PROPN
ejpam-6741	345	9	,	,	PUNCT
ejpam-6741	345	10	m.	m.	NOUN
ejpam-6741	345	11	farhan	farhan	PROPN
ejpam-6741	345	12	,	,	PUNCT
ejpam-6741	345	13	and	and	CCONJ
ejpam-6741	345	14	a.	a.	PROPN
ejpam-6741	345	15	h.	h.	PROPN
ejpam-6741	345	16	bokhari	bokhari	PROPN
ejpam-6741	345	17	.	.	PUNCT
ejpam-6741	346	1	a	a	DET
ejpam-6741	346	2	study	study	NOUN
ejpam-6741	346	3	of	of	ADP
ejpam-6741	346	4	energy	energy	NOUN
ejpam-6741	346	5	conditions	condition	NOUN
ejpam-6741	346	6	in	in	ADP
ejpam-6741	346	7	static	static	ADJ
ejpam-6741	346	8	plane	plane	NOUN
ejpam-6741	346	9	symmetric	symmetric	ADJ
ejpam-6741	346	10	spacetimes	spacetime	NOUN
ejpam-6741	346	11	via	via	ADP
ejpam-6741	346	12	homothetic	homothetic	ADJ
ejpam-6741	346	13	symmetries	symmetry	NOUN
ejpam-6741	346	14	.	.	PUNCT
ejpam-6741	347	1	int	int	NOUN
ejpam-6741	347	2	.	.	PUNCT
ejpam-6741	348	1	j.	j.	PROPN
ejpam-6741	348	2	mod	mod	PROPN
ejpam-6741	348	3	.	.	PUNCT
ejpam-6741	349	1	phys	phys	PROPN
ejpam-6741	349	2	.	.	PUNCT
ejpam-6741	350	1	a	a	DET
ejpam-6741	350	2	,	,	PUNCT
ejpam-6741	350	3	34:1950238	34:1950238	NUM
ejpam-6741	350	4	,	,	PUNCT
ejpam-6741	350	5	2019	2019	NUM
ejpam-6741	350	6	.	.	PUNCT
ejpam-6741	351	1	[	[	X
ejpam-6741	351	2	18	18	NUM
ejpam-6741	351	3	]	]	X
ejpam-6741	351	4	j.	j.	PROPN
ejpam-6741	351	5	khan	khan	PROPN
ejpam-6741	351	6	,	,	PUNCT
ejpam-6741	351	7	t.	t.	PROPN
ejpam-6741	351	8	hussain	hussain	PROPN
ejpam-6741	351	9	,	,	PUNCT
ejpam-6741	351	10	d.	d.	PROPN
ejpam-6741	351	11	santina	santina	PROPN
ejpam-6741	351	12	,	,	PUNCT
ejpam-6741	351	13	and	and	CCONJ
ejpam-6741	351	14	n.	n.	PROPN
ejpam-6741	351	15	mlaiki	mlaiki	PROPN
ejpam-6741	351	16	.	.	PUNCT
ejpam-6741	352	1	homothetic	homothetic	ADJ
ejpam-6741	352	2	symmetries	symmetry	NOUN
ejpam-6741	352	3	of	of	ADP
ejpam-6741	352	4	static	static	ADJ
ejpam-6741	352	5	cylindrically	cylindrically	ADV
ejpam-6741	352	6	symmetric	symmetric	ADJ
ejpam-6741	352	7	spacetimes	spacetime	NOUN
ejpam-6741	352	8	a	a	DET
ejpam-6741	352	9	rif	rif	PROPN
ejpam-6741	352	10	tree	tree	NOUN
ejpam-6741	352	11	approach	approach	NOUN
ejpam-6741	352	12	.	.	PUNCT
ejpam-6741	353	1	axioms	axiom	NOUN
ejpam-6741	353	2	,	,	PUNCT
ejpam-6741	353	3	11:506	11:506	NUM
ejpam-6741	353	4	,	,	PUNCT
ejpam-6741	353	5	2022	2022	NUM
ejpam-6741	353	6	.	.	PUNCT
ejpam-6741	354	1	[	[	X
ejpam-6741	354	2	19	19	NUM
ejpam-6741	354	3	]	]	PUNCT
ejpam-6741	354	4	a.	a.	NOUN
ejpam-6741	354	5	h.	h.	PROPN
ejpam-6741	354	6	bokhari	bokhari	PROPN
ejpam-6741	354	7	,	,	PUNCT
ejpam-6741	354	8	t.	t.	PROPN
ejpam-6741	354	9	hussain	hussain	PROPN
ejpam-6741	354	10	,	,	PUNCT
ejpam-6741	354	11	j.	j.	PROPN
ejpam-6741	354	12	khan	khan	PROPN
ejpam-6741	354	13	,	,	PUNCT
ejpam-6741	354	14	and	and	CCONJ
ejpam-6741	354	15	u.	u.	PROPN
ejpam-6741	354	16	nasib	nasib	PROPN
ejpam-6741	354	17	.	.	PUNCT
ejpam-6741	354	18	proper	proper	ADJ
ejpam-6741	354	19	hvfs	hvfs	NOUN
ejpam-6741	354	20	of	of	ADP
ejpam-6741	354	21	bianchi	bianchi	NOUN
ejpam-6741	354	22	type	type	NOUN
ejpam-6741	354	23	i	i	PRON
ejpam-6741	354	24	spacetimes	spacetime	VERB
ejpam-6741	354	25	via	via	ADP
ejpam-6741	354	26	rif	rif	PROPN
ejpam-6741	354	27	tree	tree	PROPN
ejpam-6741	354	28	approach	approach	NOUN
ejpam-6741	354	29	.	.	PUNCT
ejpam-6741	355	1	results	result	VERB
ejpam-6741	355	2	phys	phy	NOUN
ejpam-6741	355	3	.	.	PUNCT
ejpam-6741	355	4	,	,	PUNCT
ejpam-6741	355	5	25:104299	25:104299	NOUN
ejpam-6741	355	6	,	,	PUNCT
ejpam-6741	355	7	2021	2021	NUM
ejpam-6741	355	8	.	.	PUNCT
ejpam-6741	356	1	[	[	X
ejpam-6741	356	2	20	20	NUM
ejpam-6741	356	3	]	]	PUNCT
ejpam-6741	356	4	r.	r.	PROPN
ejpam-6741	356	5	s.	s.	PROPN
ejpam-6741	356	6	hamilton	hamilton	PROPN
ejpam-6741	356	7	.	.	PUNCT
ejpam-6741	357	1	three	three	NUM
ejpam-6741	357	2	-	-	PUNCT
ejpam-6741	357	3	manifolds	manifold	NOUN
ejpam-6741	357	4	with	with	ADP
ejpam-6741	357	5	positive	positive	ADJ
ejpam-6741	357	6	ricci	ricci	PROPN
ejpam-6741	357	7	curvature	curvature	NOUN
ejpam-6741	357	8	.	.	PUNCT
ejpam-6741	358	1	j.	j.	PROPN
ejpam-6741	358	2	differ	differ	VERB
ejpam-6741	358	3	.	.	PUNCT
ejpam-6741	359	1	geom	geom	PROPN
ejpam-6741	359	2	.	.	PROPN
ejpam-6741	359	3	,	,	PUNCT
ejpam-6741	360	1	17:255–306	17:255–306	NUM
ejpam-6741	360	2	,	,	PUNCT
ejpam-6741	360	3	1982	1982	NUM
ejpam-6741	360	4	.	.	PUNCT
ejpam-6741	361	1	[	[	X
ejpam-6741	361	2	21	21	NUM
ejpam-6741	361	3	]	]	X
ejpam-6741	361	4	r.	r.	PROPN
ejpam-6741	361	5	s.	s.	PROPN
ejpam-6741	361	6	hamilton	hamilton	PROPN
ejpam-6741	361	7	.	.	PUNCT
ejpam-6741	362	1	the	the	DET
ejpam-6741	362	2	ricci	ricci	PROPN
ejpam-6741	362	3	flow	flow	NOUN
ejpam-6741	362	4	on	on	ADP
ejpam-6741	362	5	surfaces	surface	NOUN
ejpam-6741	362	6	.	.	PUNCT
ejpam-6741	363	1	contemp	contemp	NOUN
ejpam-6741	363	2	.	.	PUNCT
ejpam-6741	364	1	math	math	NOUN
ejpam-6741	364	2	.	.	PUNCT
ejpam-6741	364	3	,	,	PUNCT
ejpam-6741	365	1	71:237–262	71:237–262	PROPN
ejpam-6741	365	2	,	,	PUNCT
ejpam-6741	365	3	1988	1988	NUM
ejpam-6741	365	4	.	.	PUNCT
ejpam-6741	366	1	u.	u.	PROPN
ejpam-6741	366	2	nasib	nasib	PROPN
ejpam-6741	366	3	et	et	PROPN
ejpam-6741	366	4	al	al	PROPN
ejpam-6741	366	5	.	.	PUNCT
ejpam-6741	366	6	/	/	SYM
ejpam-6741	366	7	eur	eur	PROPN
ejpam-6741	366	8	.	.	PUNCT
ejpam-6741	367	1	j.	j.	PROPN
ejpam-6741	367	2	pure	pure	PROPN
ejpam-6741	367	3	appl	appl	PROPN
ejpam-6741	367	4	.	.	PROPN
ejpam-6741	367	5	math	math	PROPN
ejpam-6741	367	6	,	,	PUNCT
ejpam-6741	367	7	18	18	NUM
ejpam-6741	367	8	(	(	PUNCT
ejpam-6741	367	9	4	4	NUM
ejpam-6741	367	10	)	)	PUNCT
ejpam-6741	367	11	(	(	PUNCT
ejpam-6741	367	12	2025	2025	NUM
ejpam-6741	367	13	)	)	PUNCT
ejpam-6741	367	14	,	,	PUNCT
ejpam-6741	367	15	6741	6741	NUM
ejpam-6741	367	16	14	14	NUM
ejpam-6741	367	17	of	of	ADP
ejpam-6741	367	18	14	14	NUM
ejpam-6741	367	19	[	[	SYM
ejpam-6741	367	20	22	22	NUM
ejpam-6741	367	21	]	]	PUNCT
ejpam-6741	367	22	a.	a.	NOUN
ejpam-6741	367	23	a.	a.	NOUN
ejpam-6741	367	24	coley	coley	PROPN
ejpam-6741	367	25	and	and	CCONJ
ejpam-6741	367	26	b.	b.	PROPN
ejpam-6741	367	27	o.	o.	PROPN
ejpam-6741	367	28	j.	j.	PROPN
ejpam-6741	367	29	tupper	tupper	PROPN
ejpam-6741	367	30	.	.	PUNCT
ejpam-6741	368	1	spherically	spherically	PROPN
ejpam-6741	368	2	symmetric	symmetric	ADJ
ejpam-6741	368	3	anisotropic	anisotropic	NOUN
ejpam-6741	368	4	fluid	fluid	NOUN
ejpam-6741	368	5	ickv	ickv	NOUN
ejpam-6741	368	6	spacetimes	spacetime	NOUN
ejpam-6741	368	7	.	.	PUNCT
ejpam-6741	369	1	class	class	NOUN
ejpam-6741	369	2	.	.	PUNCT
ejpam-6741	370	1	quantum	quantum	ADJ
ejpam-6741	370	2	gravity	gravity	NOUN
ejpam-6741	370	3	,	,	PUNCT
ejpam-6741	370	4	11:2553–2574	11:2553–2574	NUM
ejpam-6741	370	5	,	,	PUNCT
ejpam-6741	370	6	1994	1994	NUM
ejpam-6741	370	7	.	.	PUNCT
ejpam-6741	371	1	[	[	X
ejpam-6741	371	2	23	23	X
ejpam-6741	371	3	]	]	X
ejpam-6741	371	4	v.	v.	ADP
ejpam-6741	371	5	singh	singh	PROPN
ejpam-6741	371	6	and	and	CCONJ
ejpam-6741	371	7	a.	a.	NOUN
ejpam-6741	371	8	beesham	beesham	PROPN
ejpam-6741	371	9	.	.	PUNCT
ejpam-6741	372	1	lrs	lrs	PROPN
ejpam-6741	372	2	bianchi	bianchi	PROPN
ejpam-6741	372	3	-	-	PUNCT
ejpam-6741	372	4	i	i	PRON
ejpam-6741	372	5	model	model	VERB
ejpam-6741	372	6	with	with	ADP
ejpam-6741	372	7	perfect	perfect	ADJ
ejpam-6741	372	8	fluid	fluid	ADJ
ejpam-6741	372	9	equation	equation	NOUN
ejpam-6741	372	10	of	of	ADP
ejpam-6741	372	11	state	state	NOUN
ejpam-6741	372	12	.	.	PUNCT
ejpam-6741	373	1	int	int	NOUN
ejpam-6741	373	2	.	.	PUNCT
ejpam-6741	374	1	j.	j.	PROPN
ejpam-6741	374	2	mod	mod	PROPN
ejpam-6741	374	3	.	.	PUNCT
ejpam-6741	375	1	phys	phy	NOUN
ejpam-6741	375	2	.	.	PUNCT
ejpam-6741	376	1	d	d	X
ejpam-6741	376	2	,	,	PUNCT
ejpam-6741	376	3	12:1950xxx	12:1950xxx	NUM
ejpam-6741	376	4	,	,	PUNCT
ejpam-6741	376	5	2019	2019	NUM
ejpam-6741	376	6	.	.	PUNCT