id	sid	tid	token	lemma	pos
ejpam-7142	1	1	european	european	PROPN
ejpam-7142	1	2	journal	journal	PROPN
ejpam-7142	1	3	of	of	ADP
ejpam-7142	1	4	pure	pure	ADJ
ejpam-7142	1	5	and	and	CCONJ
ejpam-7142	1	6	applied	applied	ADJ
ejpam-7142	1	7	mathematics	mathematic	NOUN
ejpam-7142	1	8	2025	2025	NUM
ejpam-7142	1	9	,	,	PUNCT
ejpam-7142	1	10	vol	vol	NOUN
ejpam-7142	1	11	.	.	PROPN
ejpam-7142	1	12	18	18	NUM
ejpam-7142	1	13	,	,	PUNCT
ejpam-7142	1	14	issue	issue	NOUN
ejpam-7142	1	15	4	4	NUM
ejpam-7142	1	16	,	,	PUNCT
ejpam-7142	1	17	article	article	NOUN
ejpam-7142	1	18	number	number	NOUN
ejpam-7142	1	19	7142	7142	NUM
ejpam-7142	1	20	issn	issn	PROPN
ejpam-7142	1	21	1307	1307	NUM
ejpam-7142	1	22	-	-	SYM
ejpam-7142	1	23	5543	5543	NUM
ejpam-7142	1	24	–	–	PUNCT
ejpam-7142	1	25	ejpam.com	ejpam.com	X
ejpam-7142	1	26	published	publish	VERB
ejpam-7142	1	27	by	by	ADP
ejpam-7142	1	28	new	new	PROPN
ejpam-7142	1	29	york	york	PROPN
ejpam-7142	1	30	business	business	PROPN
ejpam-7142	1	31	global	global	ADJ
ejpam-7142	1	32	foundations	foundation	NOUN
ejpam-7142	1	33	of	of	ADP
ejpam-7142	1	34	neutrosophic	neutrosophic	ADJ
ejpam-7142	1	35	mr	mr	PROPN
ejpam-7142	1	36	-	-	PUNCT
ejpam-7142	1	37	metric	metric	ADJ
ejpam-7142	1	38	spaces	space	NOUN
ejpam-7142	1	39	with	with	ADP
ejpam-7142	1	40	applications	application	NOUN
ejpam-7142	1	41	to	to	PART
ejpam-7142	1	42	homotopy	homotopy	VERB
ejpam-7142	1	43	,	,	PUNCT
ejpam-7142	1	44	fixed	fix	VERB
ejpam-7142	1	45	points	point	NOUN
ejpam-7142	1	46	,	,	PUNCT
ejpam-7142	1	47	and	and	CCONJ
ejpam-7142	1	48	complex	complex	ADJ
ejpam-7142	1	49	networks	network	NOUN
ejpam-7142	1	50	eman	eman	NOUN
ejpam-7142	1	51	hussein1	hussein1	PROPN
ejpam-7142	1	52	,	,	PUNCT
ejpam-7142	1	53	abed	abe	VERB
ejpam-7142	1	54	al	al	PROPN
ejpam-7142	1	55	-	-	PUNCT
ejpam-7142	1	56	rahmanm	rahmanm	NOUN
ejpam-7142	1	57	.	.	PUNCT
ejpam-7142	2	1	malkawi1,∗	malkawi1,∗	PROPN
ejpam-7142	2	2	,	,	PUNCT
ejpam-7142	2	3	ala	ala	PROPN
ejpam-7142	2	4	amourah2	amourah2	PROPN
ejpam-7142	2	5	,	,	PUNCT
ejpam-7142	2	6	abdullah	abdullah	PROPN
ejpam-7142	2	7	alsoboh3	alsoboh3	PROPN
ejpam-7142	2	8	,	,	PUNCT
ejpam-7142	2	9	ahmed	ahmed	PROPN
ejpam-7142	2	10	al	al	PROPN
ejpam-7142	2	11	kasbi3,∗	kasbi3,∗	PROPN
ejpam-7142	2	12	,	,	PUNCT
ejpam-7142	2	13	tala	tala	PROPN
ejpam-7142	2	14	sasa4	sasa4	NOUN
ejpam-7142	2	15	,	,	PUNCT
ejpam-7142	2	16	ayat	ayat	PROPN
ejpam-7142	2	17	m.	m.	NOUN
ejpam-7142	2	18	rabaiah1	rabaiah1	PROPN
ejpam-7142	2	19	1	1	NUM
ejpam-7142	2	20	department	department	NOUN
ejpam-7142	2	21	of	of	ADP
ejpam-7142	2	22	mathematics	mathematic	NOUN
ejpam-7142	2	23	,	,	PUNCT
ejpam-7142	2	24	faculty	faculty	NOUN
ejpam-7142	2	25	of	of	ADP
ejpam-7142	2	26	arts	art	NOUN
ejpam-7142	2	27	and	and	CCONJ
ejpam-7142	2	28	science	science	NOUN
ejpam-7142	2	29	,	,	PUNCT
ejpam-7142	2	30	amman	amman	PROPN
ejpam-7142	2	31	arab	arab	PROPN
ejpam-7142	2	32	university	university	PROPN
ejpam-7142	2	33	,	,	PUNCT
ejpam-7142	2	34	amman	amman	PROPN
ejpam-7142	2	35	11953	11953	NUM
ejpam-7142	2	36	,	,	PUNCT
ejpam-7142	2	37	jordan	jordan	PROPN
ejpam-7142	2	38	2	2	NUM
ejpam-7142	2	39	mathematics	mathematics	PROPN
ejpam-7142	2	40	education	education	NOUN
ejpam-7142	2	41	program	program	NOUN
ejpam-7142	2	42	,	,	PUNCT
ejpam-7142	2	43	faculty	faculty	NOUN
ejpam-7142	2	44	of	of	ADP
ejpam-7142	2	45	education	education	NOUN
ejpam-7142	2	46	and	and	CCONJ
ejpam-7142	2	47	arts	art	NOUN
ejpam-7142	2	48	,	,	PUNCT
ejpam-7142	2	49	sohar	sohar	PROPN
ejpam-7142	2	50	university	university	PROPN
ejpam-7142	2	51	,	,	PUNCT
ejpam-7142	2	52	sohar	sohar	PROPN
ejpam-7142	2	53	311	311	NUM
ejpam-7142	2	54	,	,	PUNCT
ejpam-7142	2	55	oman	oman	PROPN
ejpam-7142	2	56	3	3	NUM
ejpam-7142	2	57	department	department	NOUN
ejpam-7142	2	58	of	of	ADP
ejpam-7142	2	59	basic	basic	ADJ
ejpam-7142	2	60	and	and	CCONJ
ejpam-7142	2	61	applied	applied	ADJ
ejpam-7142	2	62	sciences	science	NOUN
ejpam-7142	2	63	,	,	PUNCT
ejpam-7142	2	64	college	college	NOUN
ejpam-7142	2	65	of	of	ADP
ejpam-7142	2	66	applied	apply	VERB
ejpam-7142	2	67	and	and	CCONJ
ejpam-7142	2	68	health	health	NOUN
ejpam-7142	2	69	sciences	science	NOUN
ejpam-7142	2	70	,	,	PUNCT
ejpam-7142	2	71	a’sharqiyah	a’sharqiyah	PROPN
ejpam-7142	2	72	university	university	NOUN
ejpam-7142	2	73	,	,	PUNCT
ejpam-7142	2	74	post	post	PROPN
ejpam-7142	2	75	box	box	PROPN
ejpam-7142	2	76	no	no	INTJ
ejpam-7142	2	77	.	.	PROPN
ejpam-7142	2	78	42	42	NUM
ejpam-7142	2	79	,	,	PUNCT
ejpam-7142	2	80	post	post	VERB
ejpam-7142	2	81	code	code	NOUN
ejpam-7142	2	82	no	no	INTJ
ejpam-7142	2	83	.	.	PROPN
ejpam-7142	2	84	400	400	NUM
ejpam-7142	2	85	,	,	PUNCT
ejpam-7142	2	86	ibra	ibra	NOUN
ejpam-7142	2	87	,	,	PUNCT
ejpam-7142	2	88	sultanate	sultanate	NOUN
ejpam-7142	2	89	of	of	ADP
ejpam-7142	2	90	oman	oman	PROPN
ejpam-7142	2	91	4	4	NUM
ejpam-7142	2	92	department	department	NOUN
ejpam-7142	2	93	of	of	ADP
ejpam-7142	2	94	mathematics	mathematic	NOUN
ejpam-7142	2	95	,	,	PUNCT
ejpam-7142	2	96	faculty	faculty	NOUN
ejpam-7142	2	97	of	of	ADP
ejpam-7142	2	98	science	science	NOUN
ejpam-7142	2	99	,	,	PUNCT
ejpam-7142	2	100	applied	apply	VERB
ejpam-7142	2	101	science	science	NOUN
ejpam-7142	2	102	private	private	ADJ
ejpam-7142	2	103	university	university	NOUN
ejpam-7142	2	104	,	,	PUNCT
ejpam-7142	2	105	amman	amman	PROPN
ejpam-7142	2	106	,	,	PUNCT
ejpam-7142	2	107	jordan	jordan	PROPN
ejpam-7142	2	108	abstract	abstract	PROPN
ejpam-7142	2	109	.	.	PUNCT
ejpam-7142	3	1	this	this	DET
ejpam-7142	3	2	paper	paper	NOUN
ejpam-7142	3	3	introduces	introduce	NOUN
ejpam-7142	3	4	and	and	CCONJ
ejpam-7142	3	5	explores	explore	VERB
ejpam-7142	3	6	the	the	DET
ejpam-7142	3	7	concept	concept	NOUN
ejpam-7142	3	8	of	of	ADP
ejpam-7142	3	9	neutrosophic	neutrosophic	ADJ
ejpam-7142	3	10	mr	mr	PROPN
ejpam-7142	3	11	-	-	PUNCT
ejpam-7142	3	12	metric	metric	ADJ
ejpam-7142	3	13	spaces	space	NOUN
ejpam-7142	3	14	(	(	PUNCT
ejpam-7142	3	15	nmr	nmr	NOUN
ejpam-7142	3	16	-	-	PUNCT
ejpam-7142	3	17	ms	ms	NOUN
ejpam-7142	3	18	)	)	PUNCT
ejpam-7142	3	19	,	,	PUNCT
ejpam-7142	3	20	which	which	PRON
ejpam-7142	3	21	generalize	generalize	VERB
ejpam-7142	3	22	classical	classical	ADJ
ejpam-7142	3	23	metric	metric	ADJ
ejpam-7142	3	24	spaces	space	NOUN
ejpam-7142	3	25	by	by	ADP
ejpam-7142	3	26	incorporating	incorporate	VERB
ejpam-7142	3	27	neutrosophic	neutrosophic	ADJ
ejpam-7142	3	28	logic	logic	NOUN
ejpam-7142	3	29	to	to	PART
ejpam-7142	3	30	handle	handle	VERB
ejpam-7142	3	31	uncertainty	uncertainty	NOUN
ejpam-7142	3	32	,	,	PUNCT
ejpam-7142	3	33	indeterminacy	indeterminacy	NOUN
ejpam-7142	3	34	,	,	PUNCT
ejpam-7142	3	35	and	and	CCONJ
ejpam-7142	3	36	truth	truth	NOUN
ejpam-7142	3	37	-	-	PUNCT
ejpam-7142	3	38	membership	membership	NOUN
ejpam-7142	3	39	in	in	ADP
ejpam-7142	3	40	complex	complex	ADJ
ejpam-7142	3	41	systems	system	NOUN
ejpam-7142	3	42	.	.	PUNCT
ejpam-7142	4	1	we	we	PRON
ejpam-7142	4	2	define	define	VERB
ejpam-7142	4	3	the	the	DET
ejpam-7142	4	4	structure	structure	NOUN
ejpam-7142	4	5	of	of	ADP
ejpam-7142	4	6	nmr	nmr	NOUN
ejpam-7142	4	7	-	-	PUNCT
ejpam-7142	4	8	ms	ms	NOUN
ejpam-7142	4	9	,	,	PUNCT
ejpam-7142	4	10	including	include	VERB
ejpam-7142	4	11	mr	mr	PROPN
ejpam-7142	4	12	-	-	PUNCT
ejpam-7142	4	13	metrics	metric	NOUN
ejpam-7142	4	14	,	,	PUNCT
ejpam-7142	4	15	neutrosophic	neutrosophic	ADJ
ejpam-7142	4	16	functions	function	NOUN
ejpam-7142	4	17	,	,	PUNCT
ejpam-7142	4	18	and	and	CCONJ
ejpam-7142	4	19	associated	associate	VERB
ejpam-7142	4	20	algebraic	algebraic	ADJ
ejpam-7142	4	21	operations	operation	NOUN
ejpam-7142	4	22	.	.	PUNCT
ejpam-7142	5	1	key	key	ADJ
ejpam-7142	5	2	contributions	contribution	NOUN
ejpam-7142	5	3	include	include	VERB
ejpam-7142	5	4	the	the	DET
ejpam-7142	5	5	introduction	introduction	NOUN
ejpam-7142	5	6	of	of	ADP
ejpam-7142	5	7	the	the	DET
ejpam-7142	5	8	neutrosophic	neutrosophic	ADJ
ejpam-7142	5	9	graph	graph	NOUN
ejpam-7142	5	10	mr	mr	PROPN
ejpam-7142	5	11	-	-	PUNCT
ejpam-7142	5	12	metric	metric	ADJ
ejpam-7142	5	13	space	space	NOUN
ejpam-7142	5	14	,	,	PUNCT
ejpam-7142	5	15	where	where	SCONJ
ejpam-7142	5	16	graph	graph	NOUN
ejpam-7142	5	17	-	-	PUNCT
ejpam-7142	5	18	theoretic	theoretic	ADJ
ejpam-7142	5	19	concepts	concept	NOUN
ejpam-7142	5	20	such	such	ADJ
ejpam-7142	5	21	as	as	ADP
ejpam-7142	5	22	shortest	short	ADJ
ejpam-7142	5	23	paths	path	NOUN
ejpam-7142	5	24	and	and	CCONJ
ejpam-7142	5	25	betweenness	betweenness	NOUN
ejpam-7142	5	26	centrality	centrality	NOUN
ejpam-7142	5	27	are	be	AUX
ejpam-7142	5	28	integrated	integrate	VERB
ejpam-7142	5	29	with	with	ADP
ejpam-7142	5	30	neutrosophic	neutrosophic	ADJ
ejpam-7142	5	31	degrees	degree	NOUN
ejpam-7142	5	32	.	.	PUNCT
ejpam-7142	6	1	we	we	PRON
ejpam-7142	6	2	establish	establish	VERB
ejpam-7142	6	3	several	several	ADJ
ejpam-7142	6	4	fundamental	fundamental	ADJ
ejpam-7142	6	5	results	result	NOUN
ejpam-7142	6	6	,	,	PUNCT
ejpam-7142	6	7	including	include	VERB
ejpam-7142	6	8	contraction	contraction	NOUN
ejpam-7142	6	9	lemmas	lemmas	ADJ
ejpam-7142	6	10	,	,	PUNCT
ejpam-7142	6	11	robustness	robustness	NOUN
ejpam-7142	6	12	under	under	ADP
ejpam-7142	6	13	targeted	target	VERB
ejpam-7142	6	14	attacks	attack	NOUN
ejpam-7142	6	15	,	,	PUNCT
ejpam-7142	6	16	and	and	CCONJ
ejpam-7142	6	17	the	the	DET
ejpam-7142	6	18	existence	existence	NOUN
ejpam-7142	6	19	of	of	ADP
ejpam-7142	6	20	fixed	fix	VERB
ejpam-7142	6	21	points	point	NOUN
ejpam-7142	6	22	for	for	ADP
ejpam-7142	6	23	neutrosophic	neutrosophic	ADJ
ejpam-7142	6	24	centrality	centrality	NOUN
ejpam-7142	6	25	mappings	mapping	NOUN
ejpam-7142	6	26	.	.	PUNCT
ejpam-7142	7	1	furthermore	furthermore	ADV
ejpam-7142	7	2	,	,	PUNCT
ejpam-7142	7	3	we	we	PRON
ejpam-7142	7	4	define	define	VERB
ejpam-7142	7	5	neutrosophic	neutrosophic	ADJ
ejpam-7142	7	6	mr	mr	PROPN
ejpam-7142	7	7	-	-	PUNCT
ejpam-7142	7	8	homotopy	homotopy	PROPN
ejpam-7142	7	9	and	and	CCONJ
ejpam-7142	7	10	the	the	DET
ejpam-7142	7	11	associated	associated	ADJ
ejpam-7142	7	12	neutrosophic	neutrosophic	ADJ
ejpam-7142	7	13	mr	mr	PROPN
ejpam-7142	7	14	-	-	PUNCT
ejpam-7142	7	15	fundamental	fundamental	ADJ
ejpam-7142	7	16	groupoid	groupoid	NOUN
ejpam-7142	7	17	,	,	PUNCT
ejpam-7142	7	18	proving	prove	VERB
ejpam-7142	7	19	that	that	SCONJ
ejpam-7142	7	20	it	it	PRON
ejpam-7142	7	21	forms	form	VERB
ejpam-7142	7	22	an	an	DET
ejpam-7142	7	23	equivalence	equivalence	NOUN
ejpam-7142	7	24	relation	relation	NOUN
ejpam-7142	7	25	and	and	CCONJ
ejpam-7142	7	26	possesses	possess	VERB
ejpam-7142	7	27	a	a	DET
ejpam-7142	7	28	well	well	ADV
ejpam-7142	7	29	-	-	PUNCT
ejpam-7142	7	30	defined	define	VERB
ejpam-7142	7	31	algebraic	algebraic	ADJ
ejpam-7142	7	32	structure	structure	NOUN
ejpam-7142	7	33	.	.	PUNCT
ejpam-7142	8	1	the	the	DET
ejpam-7142	8	2	theoretical	theoretical	ADJ
ejpam-7142	8	3	framework	framework	NOUN
ejpam-7142	8	4	is	be	AUX
ejpam-7142	8	5	applied	apply	VERB
ejpam-7142	8	6	to	to	PART
ejpam-7142	8	7	diverse	diverse	VERB
ejpam-7142	8	8	real	real	ADJ
ejpam-7142	8	9	-	-	PUNCT
ejpam-7142	8	10	world	world	NOUN
ejpam-7142	8	11	networks	network	NOUN
ejpam-7142	8	12	,	,	PUNCT
ejpam-7142	8	13	including	include	VERB
ejpam-7142	8	14	social	social	ADJ
ejpam-7142	8	15	,	,	PUNCT
ejpam-7142	8	16	neural	neural	ADJ
ejpam-7142	8	17	,	,	PUNCT
ejpam-7142	8	18	and	and	CCONJ
ejpam-7142	8	19	internet	internet	NOUN
ejpam-7142	8	20	topologies	topology	NOUN
ejpam-7142	8	21	,	,	PUNCT
ejpam-7142	8	22	demonstrating	demonstrate	VERB
ejpam-7142	8	23	its	its	PRON
ejpam-7142	8	24	utility	utility	NOUN
ejpam-7142	8	25	in	in	ADP
ejpam-7142	8	26	network	network	NOUN
ejpam-7142	8	27	analysis	analysis	NOUN
ejpam-7142	8	28	,	,	PUNCT
ejpam-7142	8	29	robustness	robustness	NOUN
ejpam-7142	8	30	testing	testing	NOUN
ejpam-7142	8	31	,	,	PUNCT
ejpam-7142	8	32	and	and	CCONJ
ejpam-7142	8	33	path	path	NOUN
ejpam-7142	8	34	planning	planning	NOUN
ejpam-7142	8	35	.	.	PUNCT
ejpam-7142	9	1	computational	computational	ADJ
ejpam-7142	9	2	algorithms	algorithm	NOUN
ejpam-7142	9	3	and	and	CCONJ
ejpam-7142	9	4	performance	performance	NOUN
ejpam-7142	9	5	metrics	metric	NOUN
ejpam-7142	9	6	are	be	AUX
ejpam-7142	9	7	provided	provide	VERB
ejpam-7142	9	8	,	,	PUNCT
ejpam-7142	9	9	showcasing	showcase	VERB
ejpam-7142	9	10	the	the	DET
ejpam-7142	9	11	practical	practical	ADJ
ejpam-7142	9	12	applicability	applicability	NOUN
ejpam-7142	9	13	of	of	ADP
ejpam-7142	9	14	the	the	DET
ejpam-7142	9	15	proposed	propose	VERB
ejpam-7142	9	16	framework	framework	NOUN
ejpam-7142	9	17	.	.	PUNCT
ejpam-7142	10	1	2020	2020	NUM
ejpam-7142	10	2	mathematics	mathematic	NOUN
ejpam-7142	10	3	subject	subject	NOUN
ejpam-7142	10	4	classifications	classification	NOUN
ejpam-7142	10	5	:	:	PUNCT
ejpam-7142	10	6	47h10	47h10	NUM
ejpam-7142	10	7	,	,	PUNCT
ejpam-7142	10	8	54h25	54h25	NUM
ejpam-7142	10	9	,	,	PUNCT
ejpam-7142	10	10	05c82	05c82	NUM
ejpam-7142	10	11	,	,	PUNCT
ejpam-7142	10	12	68r10	68r10	NUM
ejpam-7142	10	13	,	,	PUNCT
ejpam-7142	10	14	03e72	03e72	X
ejpam-7142	10	15	key	key	ADJ
ejpam-7142	10	16	words	word	NOUN
ejpam-7142	10	17	and	and	CCONJ
ejpam-7142	10	18	phrases	phrase	NOUN
ejpam-7142	10	19	:	:	PUNCT
ejpam-7142	10	20	neutrosophic	neutrosophic	ADJ
ejpam-7142	10	21	mr	mr	PROPN
ejpam-7142	10	22	-	-	PUNCT
ejpam-7142	10	23	metric	metric	ADJ
ejpam-7142	10	24	spaces	space	NOUN
ejpam-7142	10	25	,	,	PUNCT
ejpam-7142	10	26	fixed	fix	VERB
ejpam-7142	10	27	point	point	NOUN
ejpam-7142	10	28	theorems	theorem	NOUN
ejpam-7142	10	29	,	,	PUNCT
ejpam-7142	10	30	graph	graph	NOUN
ejpam-7142	10	31	theory	theory	NOUN
ejpam-7142	10	32	,	,	PUNCT
ejpam-7142	10	33	network	network	NOUN
ejpam-7142	10	34	robustness	robustness	NOUN
ejpam-7142	10	35	,	,	PUNCT
ejpam-7142	10	36	neutrosophic	neutrosophic	PROPN
ejpam-7142	10	37	homotopy	homotopy	NOUN
ejpam-7142	10	38	,	,	PUNCT
ejpam-7142	10	39	centrality	centrality	NOUN
ejpam-7142	10	40	mapping	mapping	NOUN
ejpam-7142	10	41	,	,	PUNCT
ejpam-7142	10	42	contraction	contraction	NOUN
ejpam-7142	10	43	mappings	mapping	NOUN
ejpam-7142	10	44	1	1	NUM
ejpam-7142	10	45	.	.	PUNCT
ejpam-7142	10	46	introduction	introduction	NOUN
ejpam-7142	10	47	the	the	DET
ejpam-7142	10	48	evolution	evolution	NOUN
ejpam-7142	10	49	of	of	ADP
ejpam-7142	10	50	metric	metric	ADJ
ejpam-7142	10	51	space	space	NOUN
ejpam-7142	10	52	theory	theory	NOUN
ejpam-7142	10	53	has	have	AUX
ejpam-7142	10	54	witnessed	witness	VERB
ejpam-7142	10	55	significant	significant	ADJ
ejpam-7142	10	56	advancements	advancement	NOUN
ejpam-7142	10	57	through	through	ADP
ejpam-7142	10	58	various	various	ADJ
ejpam-7142	10	59	generalizations	generalization	NOUN
ejpam-7142	10	60	aimed	aim	VERB
ejpam-7142	10	61	at	at	ADP
ejpam-7142	10	62	addressing	address	VERB
ejpam-7142	10	63	complex	complex	ADJ
ejpam-7142	10	64	mathematical	mathematical	ADJ
ejpam-7142	10	65	applications	application	NOUN
ejpam-7142	10	66	.	.	PUNCT
ejpam-7142	11	1	foundational	foundational	ADJ
ejpam-7142	11	2	work	work	NOUN
ejpam-7142	11	3	on	on	ADP
ejpam-7142	11	4	b	b	X
ejpam-7142	11	5	-	-	ADJ
ejpam-7142	11	6	metric	metric	ADJ
ejpam-7142	11	7	spaces	space	NOUN
ejpam-7142	11	8	[	[	X
ejpam-7142	11	9	1	1	NUM
ejpam-7142	11	10	,	,	PUNCT
ejpam-7142	11	11	2	2	NUM
ejpam-7142	11	12	]	]	PUNCT
ejpam-7142	11	13	paved	pave	VERB
ejpam-7142	11	14	the	the	DET
ejpam-7142	11	15	way	way	NOUN
ejpam-7142	11	16	for	for	ADP
ejpam-7142	11	17	numerous	numerous	ADJ
ejpam-7142	11	18	extended	extended	ADJ
ejpam-7142	11	19	metric	metric	ADJ
ejpam-7142	11	20	structures	structure	NOUN
ejpam-7142	11	21	.	.	PUNCT
ejpam-7142	12	1	a	a	DET
ejpam-7142	12	2	notable	notable	ADJ
ejpam-7142	12	3	development	development	NOUN
ejpam-7142	12	4	in	in	ADP
ejpam-7142	12	5	this	this	DET
ejpam-7142	12	6	direction	direction	NOUN
ejpam-7142	12	7	is	be	AUX
ejpam-7142	12	8	the	the	DET
ejpam-7142	12	9	introduction	introduction	NOUN
ejpam-7142	12	10	of	of	ADP
ejpam-7142	12	11	mr	mr	PROPN
ejpam-7142	12	12	-	-	PUNCT
ejpam-7142	12	13	metric	metric	ADJ
ejpam-7142	12	14	spaces	space	NOUN
ejpam-7142	12	15	[	[	X
ejpam-7142	12	16	3	3	NUM
ejpam-7142	12	17	]	]	PUNCT
ejpam-7142	12	18	,	,	PUNCT
ejpam-7142	12	19	which	which	PRON
ejpam-7142	12	20	established	establish	VERB
ejpam-7142	12	21	a	a	DET
ejpam-7142	12	22	novel	novel	ADJ
ejpam-7142	12	23	framework	framework	NOUN
ejpam-7142	12	24	for	for	ADP
ejpam-7142	12	25	triple	triple	ADJ
ejpam-7142	12	26	-	-	PUNCT
ejpam-7142	12	27	based	base	VERB
ejpam-7142	12	28	mappings	mapping	NOUN
ejpam-7142	12	29	with	with	ADP
ejpam-7142	12	30	a	a	DET
ejpam-7142	12	31	contraction	contraction	NOUN
ejpam-7142	12	32	constant	constant	ADJ
ejpam-7142	12	33	r	r	NOUN
ejpam-7142	12	34	>	>	X
ejpam-7142	12	35	1	1	NUM
ejpam-7142	12	36	.	.	PUNCT
ejpam-7142	13	1	this	this	DET
ejpam-7142	13	2	innovation	innovation	NOUN
ejpam-7142	13	3	∗corresponding	∗corresponde	VERB
ejpam-7142	13	4	author	author	NOUN
ejpam-7142	13	5	.	.	PUNCT
ejpam-7142	14	1	∗corresponding	∗corresponde	VERB
ejpam-7142	14	2	author	author	NOUN
ejpam-7142	14	3	.	.	PUNCT
ejpam-7142	15	1	doi	doi	NOUN
ejpam-7142	15	2	:	:	PUNCT
ejpam-7142	15	3	https://doi.org/10.29020/nybg.ejpam.v18i4.7142	https://doi.org/10.29020/nybg.ejpam.v18i4.7142	NUM
ejpam-7142	15	4	email	email	NOUN
ejpam-7142	15	5	addresses	address	NOUN
ejpam-7142	15	6	:	:	PUNCT
ejpam-7142	15	7	e.hussein@aau.edu.jo	e.hussein@aau.edu.jo	PROPN
ejpam-7142	15	8	(	(	PUNCT
ejpam-7142	15	9	e.	e.	PROPN
ejpam-7142	15	10	hussein	hussein	PROPN
ejpam-7142	15	11	)	)	PUNCT
ejpam-7142	15	12	,	,	PUNCT
ejpam-7142	15	13	a.malkawi@aau.edu.jo	a.malkawi@aau.edu.jo	PROPN
ejpam-7142	15	14	,	,	PUNCT
ejpam-7142	15	15	math.malkawi@gmail.com	math.malkawi@gmail.com	X
ejpam-7142	15	16	(	(	PUNCT
ejpam-7142	15	17	a.	a.	NOUN
ejpam-7142	15	18	malkawi	malkawi	PROPN
ejpam-7142	15	19	)	)	PUNCT
ejpam-7142	15	20	,	,	PUNCT
ejpam-7142	15	21	aamourah@su.edu.om	aamourah@su.edu.om	NOUN
ejpam-7142	15	22	(	(	PUNCT
ejpam-7142	15	23	a.	a.	NOUN
ejpam-7142	15	24	amourah	amourah	PROPN
ejpam-7142	15	25	)	)	PUNCT
ejpam-7142	15	26	,	,	PUNCT
ejpam-7142	15	27	abdullah.alsoboh@asu.edu.om	abdullah.alsoboh@asu.edu.om	NOUN
ejpam-7142	15	28	(	(	PUNCT
ejpam-7142	15	29	a.	a.	NOUN
ejpam-7142	15	30	alsoboh	alsoboh	PROPN
ejpam-7142	15	31	)	)	PUNCT
ejpam-7142	15	32	,	,	PUNCT
ejpam-7142	15	33	ahmed.alkasbi@asu.edu.om	ahmed.alkasbi@asu.edu.om	PROPN
ejpam-7142	15	34	(	(	PUNCT
ejpam-7142	15	35	a.	a.	PROPN
ejpam-7142	15	36	al	al	PROPN
ejpam-7142	15	37	kasbi	kasbi	PROPN
ejpam-7142	15	38	)	)	PUNCT
ejpam-7142	15	39	,	,	PUNCT
ejpam-7142	15	40	t	t	NOUN
ejpam-7142	15	41	sasa@asu.edu.jo	sasa@asu.edu.jo	NOUN
ejpam-7142	15	42	(	(	PUNCT
ejpam-7142	15	43	t.	t.	PROPN
ejpam-7142	15	44	sasa	sasa	PROPN
ejpam-7142	15	45	)	)	PUNCT
ejpam-7142	15	46	,	,	PUNCT
ejpam-7142	15	47	a.rabaieha@aau.edu.jo	a.rabaieha@aau.edu.jo	PROPN
ejpam-7142	15	48	(	(	PUNCT
ejpam-7142	15	49	a.	a.	NOUN
ejpam-7142	15	50	rabaiah	rabaiah	PROPN
ejpam-7142	15	51	)	)	PUNCT
ejpam-7142	15	52	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-7142	16	1	1	1	NUM
ejpam-7142	16	2	copyright	copyright	NOUN
ejpam-7142	16	3	:	:	PUNCT
ejpam-7142	16	4	©	©	PROPN
ejpam-7142	16	5	2025	2025	NUM
ejpam-7142	16	6	the	the	DET
ejpam-7142	16	7	author(s	author(s	NOUN
ejpam-7142	16	8	)	)	PUNCT
ejpam-7142	16	9	.	.	PUNCT
ejpam-7142	17	1	(	(	PUNCT
ejpam-7142	17	2	cc	cc	NOUN
ejpam-7142	17	3	by	by	ADP
ejpam-7142	17	4	-	-	PUNCT
ejpam-7142	17	5	nc	nc	PROPN
ejpam-7142	17	6	4.0	4.0	NUM
ejpam-7142	17	7	)	)	PUNCT
ejpam-7142	17	8	e.	e.	PROPN
ejpam-7142	17	9	hussein	hussein	PROPN
ejpam-7142	17	10	et	et	PROPN
ejpam-7142	17	11	al	al	PROPN
ejpam-7142	17	12	.	.	PUNCT
ejpam-7142	17	13	/	/	SYM
ejpam-7142	17	14	eur	eur	PROPN
ejpam-7142	17	15	.	.	PUNCT
ejpam-7142	18	1	j.	j.	PROPN
ejpam-7142	18	2	pure	pure	PROPN
ejpam-7142	18	3	appl	appl	PROPN
ejpam-7142	18	4	.	.	PROPN
ejpam-7142	18	5	math	math	PROPN
ejpam-7142	18	6	,	,	PUNCT
ejpam-7142	18	7	18	18	NUM
ejpam-7142	18	8	(	(	PUNCT
ejpam-7142	18	9	4	4	NUM
ejpam-7142	18	10	)	)	PUNCT
ejpam-7142	18	11	(	(	PUNCT
ejpam-7142	18	12	2025	2025	NUM
ejpam-7142	18	13	)	)	PUNCT
ejpam-7142	18	14	,	,	PUNCT
ejpam-7142	18	15	7142	7142	NUM
ejpam-7142	18	16	2	2	NUM
ejpam-7142	18	17	of	of	ADP
ejpam-7142	18	18	17	17	NUM
ejpam-7142	18	19	catalyzed	catalyze	VERB
ejpam-7142	18	20	new	new	ADJ
ejpam-7142	18	21	research	research	NOUN
ejpam-7142	18	22	directions	direction	NOUN
ejpam-7142	18	23	in	in	ADP
ejpam-7142	18	24	fixed	fix	VERB
ejpam-7142	18	25	point	point	NOUN
ejpam-7142	18	26	theory	theory	NOUN
ejpam-7142	18	27	,	,	PUNCT
ejpam-7142	18	28	particularly	particularly	ADV
ejpam-7142	18	29	through	through	ADP
ejpam-7142	18	30	(	(	PUNCT
ejpam-7142	18	31	ψ	ψ	NOUN
ejpam-7142	18	32	,	,	PUNCT
ejpam-7142	18	33	l)-m	l)-m	ADJ
ejpam-7142	18	34	-	-	PUNCT
ejpam-7142	18	35	weak	weak	ADJ
ejpam-7142	18	36	contraction	contraction	NOUN
ejpam-7142	18	37	mappings	mapping	NOUN
ejpam-7142	18	38	in	in	ADP
ejpam-7142	18	39	mb	mb	ADJ
ejpam-7142	18	40	-	-	ADJ
ejpam-7142	18	41	metric	metric	ADJ
ejpam-7142	18	42	spaces	space	NOUN
ejpam-7142	18	43	[	[	X
ejpam-7142	18	44	4	4	NUM
ejpam-7142	18	45	]	]	PUNCT
ejpam-7142	18	46	.	.	PUNCT
ejpam-7142	19	1	parallel	parallel	ADJ
ejpam-7142	19	2	developments	development	NOUN
ejpam-7142	19	3	in	in	ADP
ejpam-7142	19	4	generalized	generalized	ADJ
ejpam-7142	19	5	metric	metric	ADJ
ejpam-7142	19	6	spaces	space	NOUN
ejpam-7142	19	7	include	include	VERB
ejpam-7142	19	8	investigations	investigation	NOUN
ejpam-7142	19	9	into	into	ADP
ejpam-7142	19	10	b	b	X
ejpam-7142	19	11	-	-	PUNCT
ejpam-7142	19	12	metric	metric	ADJ
ejpam-7142	19	13	spaces	space	NOUN
ejpam-7142	19	14	and	and	CCONJ
ejpam-7142	19	15	related	related	ADJ
ejpam-7142	19	16	results	result	NOUN
ejpam-7142	19	17	[	[	X
ejpam-7142	19	18	5	5	NUM
ejpam-7142	19	19	]	]	PUNCT
ejpam-7142	19	20	,	,	PUNCT
ejpam-7142	19	21	alongside	alongside	ADP
ejpam-7142	19	22	explorations	exploration	NOUN
ejpam-7142	19	23	of	of	ADP
ejpam-7142	19	24	(	(	PUNCT
ejpam-7142	19	25	h	h	NOUN
ejpam-7142	19	26	,	,	PUNCT
ejpam-7142	19	27	ωb)-interpolative	ωb)-interpolative	ADJ
ejpam-7142	19	28	contractions	contraction	NOUN
ejpam-7142	19	29	in	in	ADP
ejpam-7142	19	30	ωb	ωb	NOUN
ejpam-7142	19	31	-	-	PUNCT
ejpam-7142	19	32	distance	distance	NOUN
ejpam-7142	19	33	mappings	mapping	NOUN
ejpam-7142	19	34	[	[	X
ejpam-7142	19	35	6	6	NUM
ejpam-7142	19	36	]	]	PUNCT
ejpam-7142	19	37	.	.	PUNCT
ejpam-7142	20	1	significant	significant	ADJ
ejpam-7142	20	2	contributions	contribution	NOUN
ejpam-7142	20	3	have	have	AUX
ejpam-7142	20	4	also	also	ADV
ejpam-7142	20	5	been	be	AUX
ejpam-7142	20	6	made	make	VERB
ejpam-7142	20	7	in	in	ADP
ejpam-7142	20	8	ω	ω	ADJ
ejpam-7142	20	9	-	-	PUNCT
ejpam-7142	20	10	distance	distance	NOUN
ejpam-7142	20	11	mappings	mapping	NOUN
ejpam-7142	20	12	,	,	PUNCT
ejpam-7142	20	13	with	with	ADP
ejpam-7142	20	14	extensive	extensive	ADJ
ejpam-7142	20	15	research	research	NOUN
ejpam-7142	20	16	focusing	focus	VERB
ejpam-7142	20	17	on	on	ADP
ejpam-7142	20	18	cyclic	cyclic	ADJ
ejpam-7142	20	19	mappings	mapping	NOUN
ejpam-7142	20	20	and	and	CCONJ
ejpam-7142	20	21	common	common	ADJ
ejpam-7142	20	22	fixed	fix	VERB
ejpam-7142	20	23	point	point	NOUN
ejpam-7142	20	24	results	result	NOUN
ejpam-7142	20	25	[	[	X
ejpam-7142	20	26	7–15	7–15	X
ejpam-7142	20	27	]	]	PUNCT
ejpam-7142	20	28	.	.	PUNCT
ejpam-7142	21	1	the	the	DET
ejpam-7142	21	2	integration	integration	NOUN
ejpam-7142	21	3	of	of	ADP
ejpam-7142	21	4	neutrosophic	neutrosophic	ADJ
ejpam-7142	21	5	logic	logic	NOUN
ejpam-7142	21	6	with	with	ADP
ejpam-7142	21	7	metric	metric	ADJ
ejpam-7142	21	8	spaces	space	NOUN
ejpam-7142	21	9	marks	mark	VERB
ejpam-7142	21	10	a	a	DET
ejpam-7142	21	11	substantial	substantial	ADJ
ejpam-7142	21	12	advancement	advancement	NOUN
ejpam-7142	21	13	in	in	ADP
ejpam-7142	21	14	modeling	model	VERB
ejpam-7142	21	15	uncertainty	uncertainty	NOUN
ejpam-7142	21	16	and	and	CCONJ
ejpam-7142	21	17	indeterminacy	indeterminacy	NOUN
ejpam-7142	21	18	.	.	PUNCT
ejpam-7142	22	1	pioneering	pioneer	VERB
ejpam-7142	22	2	work	work	NOUN
ejpam-7142	22	3	introduced	introduce	VERB
ejpam-7142	22	4	neutrosophic	neutrosophic	ADJ
ejpam-7142	22	5	fuzzy	fuzzy	ADJ
ejpam-7142	22	6	metric	metric	ADJ
ejpam-7142	22	7	spaces	space	NOUN
ejpam-7142	22	8	and	and	CCONJ
ejpam-7142	22	9	fixed	fix	VERB
ejpam-7142	22	10	points	point	NOUN
ejpam-7142	22	11	for	for	ADP
ejpam-7142	22	12	nonlinear	nonlinear	ADJ
ejpam-7142	22	13	contractions	contraction	NOUN
ejpam-7142	22	14	[	[	X
ejpam-7142	22	15	16	16	NUM
ejpam-7142	22	16	]	]	PUNCT
ejpam-7142	22	17	,	,	PUNCT
ejpam-7142	22	18	later	later	ADV
ejpam-7142	22	19	extended	extend	VERB
ejpam-7142	22	20	to	to	ADP
ejpam-7142	22	21	quasi	quasi	NOUN
ejpam-7142	22	22	-	-	NOUN
ejpam-7142	22	23	contractions	contraction	NOUN
ejpam-7142	22	24	in	in	ADP
ejpam-7142	22	25	neutrosophic	neutrosophic	ADJ
ejpam-7142	22	26	fuzzy	fuzzy	ADJ
ejpam-7142	22	27	metric	metric	ADJ
ejpam-7142	22	28	spaces	space	NOUN
ejpam-7142	22	29	[	[	X
ejpam-7142	22	30	17	17	NUM
ejpam-7142	22	31	]	]	PUNCT
ejpam-7142	22	32	.	.	PUNCT
ejpam-7142	23	1	these	these	DET
ejpam-7142	23	2	developments	development	NOUN
ejpam-7142	23	3	formed	form	VERB
ejpam-7142	23	4	the	the	DET
ejpam-7142	23	5	theoretical	theoretical	ADJ
ejpam-7142	23	6	foundation	foundation	NOUN
ejpam-7142	23	7	for	for	ADP
ejpam-7142	23	8	the	the	DET
ejpam-7142	23	9	emergence	emergence	NOUN
ejpam-7142	23	10	of	of	ADP
ejpam-7142	23	11	neutrosophic	neutrosophic	ADJ
ejpam-7142	23	12	mr	mr	PROPN
ejpam-7142	23	13	-	-	PUNCT
ejpam-7142	23	14	metric	metric	ADJ
ejpam-7142	23	15	spaces	space	NOUN
ejpam-7142	23	16	in	in	ADP
ejpam-7142	23	17	recent	recent	ADJ
ejpam-7142	23	18	research	research	NOUN
ejpam-7142	23	19	[	[	X
ejpam-7142	23	20	18	18	NUM
ejpam-7142	23	21	,	,	PUNCT
ejpam-7142	23	22	19	19	NUM
ejpam-7142	23	23	]	]	PUNCT
ejpam-7142	23	24	.	.	PUNCT
ejpam-7142	24	1	fixed	fix	VERB
ejpam-7142	24	2	point	point	NOUN
ejpam-7142	24	3	theory	theory	NOUN
ejpam-7142	24	4	within	within	ADP
ejpam-7142	24	5	mr	mr	PROPN
ejpam-7142	24	6	-	-	PUNCT
ejpam-7142	24	7	metric	metric	ADJ
ejpam-7142	24	8	spaces	space	NOUN
ejpam-7142	24	9	has	have	AUX
ejpam-7142	24	10	been	be	AUX
ejpam-7142	24	11	enriched	enrich	VERB
ejpam-7142	24	12	through	through	ADP
ejpam-7142	24	13	multiple	multiple	ADJ
ejpam-7142	24	14	approaches	approach	NOUN
ejpam-7142	24	15	,	,	PUNCT
ejpam-7142	24	16	including	include	VERB
ejpam-7142	24	17	coincidence	coincidence	NOUN
ejpam-7142	24	18	and	and	CCONJ
ejpam-7142	24	19	fixed	fix	VERB
ejpam-7142	24	20	point	point	NOUN
ejpam-7142	24	21	results	result	NOUN
ejpam-7142	24	22	for	for	ADP
ejpam-7142	24	23	generalized	generalized	ADJ
ejpam-7142	24	24	weak	weak	ADJ
ejpam-7142	24	25	contractions	contraction	NOUN
ejpam-7142	24	26	on	on	ADP
ejpam-7142	24	27	b	b	X
ejpam-7142	24	28	-	-	ADJ
ejpam-7142	24	29	metric	metric	ADJ
ejpam-7142	24	30	spaces	space	NOUN
ejpam-7142	24	31	[	[	X
ejpam-7142	24	32	20	20	NUM
ejpam-7142	24	33	]	]	PUNCT
ejpam-7142	24	34	and	and	CCONJ
ejpam-7142	24	35	comprehensive	comprehensive	ADJ
ejpam-7142	24	36	fixed	fix	VERB
ejpam-7142	24	37	point	point	NOUN
ejpam-7142	24	38	theorems	theorem	NOUN
ejpam-7142	24	39	in	in	ADP
ejpam-7142	24	40	mr	mr	PROPN
ejpam-7142	24	41	-	-	PUNCT
ejpam-7142	24	42	metric	metric	ADJ
ejpam-7142	24	43	spaces	space	NOUN
ejpam-7142	24	44	[	[	X
ejpam-7142	24	45	21	21	NUM
ejpam-7142	24	46	,	,	PUNCT
ejpam-7142	24	47	22	22	NUM
ejpam-7142	24	48	]	]	PUNCT
ejpam-7142	24	49	.	.	PUNCT
ejpam-7142	25	1	recent	recent	ADJ
ejpam-7142	25	2	contributions	contribution	NOUN
ejpam-7142	25	3	have	have	AUX
ejpam-7142	25	4	further	far	ADV
ejpam-7142	25	5	expanded	expand	VERB
ejpam-7142	25	6	this	this	DET
ejpam-7142	25	7	theory	theory	NOUN
ejpam-7142	25	8	through	through	ADP
ejpam-7142	25	9	studies	study	NOUN
ejpam-7142	25	10	on	on	ADP
ejpam-7142	25	11	existence	existence	NOUN
ejpam-7142	25	12	,	,	PUNCT
ejpam-7142	25	13	uniqueness	uniqueness	NOUN
ejpam-7142	25	14	,	,	PUNCT
ejpam-7142	25	15	convergence	convergence	NOUN
ejpam-7142	25	16	analysis	analysis	NOUN
ejpam-7142	25	17	,	,	PUNCT
ejpam-7142	25	18	and	and	CCONJ
ejpam-7142	25	19	integral	integral	ADJ
ejpam-7142	25	20	type	type	NOUN
ejpam-7142	25	21	contractions	contraction	NOUN
ejpam-7142	25	22	[	[	X
ejpam-7142	25	23	23–25	23–25	NUM
ejpam-7142	25	24	]	]	PUNCT
ejpam-7142	25	25	.	.	PUNCT
ejpam-7142	26	1	the	the	DET
ejpam-7142	26	2	applications	application	NOUN
ejpam-7142	26	3	of	of	ADP
ejpam-7142	26	4	these	these	DET
ejpam-7142	26	5	theoretical	theoretical	ADJ
ejpam-7142	26	6	frameworks	framework	NOUN
ejpam-7142	26	7	span	span	VERB
ejpam-7142	26	8	diverse	diverse	ADJ
ejpam-7142	26	9	disciplines	discipline	NOUN
ejpam-7142	26	10	.	.	PUNCT
ejpam-7142	27	1	in	in	ADP
ejpam-7142	27	2	fractional	fractional	ADJ
ejpam-7142	27	3	calculus	calculus	NOUN
ejpam-7142	27	4	,	,	PUNCT
ejpam-7142	27	5	research	research	NOUN
ejpam-7142	27	6	has	have	AUX
ejpam-7142	27	7	applied	apply	VERB
ejpam-7142	27	8	lie	lie	NOUN
ejpam-7142	27	9	symmetry	symmetry	NOUN
ejpam-7142	27	10	to	to	ADP
ejpam-7142	27	11	time	time	NOUN
ejpam-7142	27	12	-	-	PUNCT
ejpam-7142	27	13	fractional	fractional	ADJ
ejpam-7142	27	14	equations	equation	NOUN
ejpam-7142	27	15	[	[	X
ejpam-7142	27	16	26	26	NUM
ejpam-7142	27	17	]	]	PUNCT
ejpam-7142	27	18	and	and	CCONJ
ejpam-7142	27	19	utilized	utilize	VERB
ejpam-7142	27	20	atomic	atomic	ADJ
ejpam-7142	27	21	solution	solution	NOUN
ejpam-7142	27	22	methods	method	NOUN
ejpam-7142	27	23	for	for	ADP
ejpam-7142	27	24	fractional	fractional	ADJ
ejpam-7142	27	25	equations	equation	NOUN
ejpam-7142	27	26	[	[	X
ejpam-7142	27	27	27	27	NUM
ejpam-7142	27	28	]	]	PUNCT
ejpam-7142	27	29	,	,	PUNCT
ejpam-7142	27	30	while	while	SCONJ
ejpam-7142	27	31	contributions	contribution	NOUN
ejpam-7142	27	32	to	to	AUX
ejpam-7142	27	33	conformable	conformable	ADJ
ejpam-7142	27	34	fractional	fractional	ADJ
ejpam-7142	27	35	derivatives	derivative	NOUN
ejpam-7142	27	36	[	[	X
ejpam-7142	27	37	28	28	NUM
ejpam-7142	27	38	]	]	PUNCT
ejpam-7142	27	39	and	and	CCONJ
ejpam-7142	27	40	applications	application	NOUN
ejpam-7142	27	41	of	of	ADP
ejpam-7142	27	42	fixed	fix	VERB
ejpam-7142	27	43	point	point	NOUN
ejpam-7142	27	44	results	result	NOUN
ejpam-7142	27	45	to	to	ADP
ejpam-7142	27	46	fractional	fractional	ADJ
ejpam-7142	27	47	differential	differential	ADJ
ejpam-7142	27	48	equations	equation	NOUN
ejpam-7142	28	1	[	[	X
ejpam-7142	28	2	29	29	NUM
ejpam-7142	28	3	]	]	PUNCT
ejpam-7142	28	4	have	have	AUX
ejpam-7142	28	5	demonstrated	demonstrate	VERB
ejpam-7142	28	6	the	the	DET
ejpam-7142	28	7	breadth	breadth	NOUN
ejpam-7142	28	8	of	of	ADP
ejpam-7142	28	9	these	these	DET
ejpam-7142	28	10	applications	application	NOUN
ejpam-7142	28	11	.	.	PUNCT
ejpam-7142	29	1	graph	graph	NOUN
ejpam-7142	29	2	theory	theory	NOUN
ejpam-7142	29	3	applications	application	NOUN
ejpam-7142	29	4	have	have	AUX
ejpam-7142	29	5	explored	explore	VERB
ejpam-7142	29	6	weighted	weight	VERB
ejpam-7142	29	7	and	and	CCONJ
ejpam-7142	29	8	expander	expander	NOUN
ejpam-7142	29	9	graphs	graph	NOUN
ejpam-7142	29	10	[	[	X
ejpam-7142	29	11	30	30	NUM
ejpam-7142	29	12	]	]	PUNCT
ejpam-7142	29	13	and	and	CCONJ
ejpam-7142	29	14	deep	deep	ADJ
ejpam-7142	29	15	learning	learning	NOUN
ejpam-7142	29	16	contexts	context	NOUN
ejpam-7142	30	1	[	[	X
ejpam-7142	30	2	31	31	NUM
ejpam-7142	30	3	]	]	PUNCT
ejpam-7142	30	4	,	,	PUNCT
ejpam-7142	30	5	with	with	ADP
ejpam-7142	30	6	computational	computational	ADJ
ejpam-7142	30	7	aspects	aspect	NOUN
ejpam-7142	30	8	addressed	address	VERB
ejpam-7142	30	9	through	through	ADP
ejpam-7142	30	10	common	common	ADJ
ejpam-7142	30	11	fixed	fix	VERB
ejpam-7142	30	12	point	point	NOUN
ejpam-7142	30	13	theorems	theorem	NOUN
ejpam-7142	30	14	in	in	ADP
ejpam-7142	30	15	m∗-metric	m∗-metric	ADJ
ejpam-7142	30	16	spaces	space	NOUN
ejpam-7142	30	17	[	[	X
ejpam-7142	30	18	32	32	NUM
ejpam-7142	30	19	]	]	PUNCT
ejpam-7142	30	20	.	.	PUNCT
ejpam-7142	31	1	recent	recent	ADJ
ejpam-7142	31	2	investigations	investigation	NOUN
ejpam-7142	31	3	into	into	ADP
ejpam-7142	31	4	distance	distance	NOUN
ejpam-7142	31	5	mappings	mapping	NOUN
ejpam-7142	31	6	include	include	VERB
ejpam-7142	31	7	h	h	NOUN
ejpam-7142	31	8	-	-	PUNCT
ejpam-7142	31	9	simulation	simulation	NOUN
ejpam-7142	31	10	functions	function	NOUN
ejpam-7142	31	11	in	in	ADP
ejpam-7142	31	12	gb	gb	ADV
ejpam-7142	31	13	-	-	PUNCT
ejpam-7142	31	14	metric	metric	ADJ
ejpam-7142	31	15	spaces	space	NOUN
ejpam-7142	31	16	[	[	X
ejpam-7142	31	17	33	33	NUM
ejpam-7142	31	18	]	]	PUNCT
ejpam-7142	31	19	,	,	PUNCT
ejpam-7142	31	20	gamma	gamma	NOUN
ejpam-7142	31	21	distance	distance	NOUN
ejpam-7142	31	22	mappings	mapping	NOUN
ejpam-7142	32	1	[	[	X
ejpam-7142	32	2	34	34	NUM
ejpam-7142	32	3	]	]	PUNCT
ejpam-7142	32	4	,	,	PUNCT
ejpam-7142	32	5	and	and	CCONJ
ejpam-7142	32	6	new	new	ADJ
ejpam-7142	32	7	types	type	NOUN
ejpam-7142	32	8	of	of	ADP
ejpam-7142	32	9	distance	distance	NOUN
ejpam-7142	32	10	spaces	space	NOUN
ejpam-7142	33	1	[	[	X
ejpam-7142	33	2	35	35	NUM
ejpam-7142	33	3	]	]	PUNCT
ejpam-7142	33	4	,	,	PUNCT
ejpam-7142	33	5	with	with	ADP
ejpam-7142	33	6	additional	additional	ADJ
ejpam-7142	33	7	enrichment	enrichment	NOUN
ejpam-7142	33	8	through	through	ADP
ejpam-7142	33	9	ω	ω	VERB
ejpam-7142	33	10	-	-	PUNCT
ejpam-7142	33	11	distance	distance	NOUN
ejpam-7142	33	12	and	and	CCONJ
ejpam-7142	33	13	rational	rational	ADJ
ejpam-7142	33	14	contraction	contraction	NOUN
ejpam-7142	33	15	mappings	mapping	NOUN
ejpam-7142	34	1	[	[	X
ejpam-7142	34	2	36	36	NUM
ejpam-7142	34	3	,	,	PUNCT
ejpam-7142	34	4	37	37	NUM
ejpam-7142	34	5	]	]	PUNCT
ejpam-7142	34	6	.	.	PUNCT
ejpam-7142	35	1	interdisciplinary	interdisciplinary	ADJ
ejpam-7142	35	2	applications	application	NOUN
ejpam-7142	35	3	continue	continue	VERB
ejpam-7142	35	4	to	to	PART
ejpam-7142	35	5	expand	expand	VERB
ejpam-7142	35	6	,	,	PUNCT
ejpam-7142	35	7	with	with	ADP
ejpam-7142	35	8	mr	mr	PROPN
ejpam-7142	35	9	-	-	PUNCT
ejpam-7142	35	10	metric	metric	ADJ
ejpam-7142	35	11	spaces	space	NOUN
ejpam-7142	35	12	being	be	AUX
ejpam-7142	35	13	applied	apply	VERB
ejpam-7142	35	14	to	to	ADP
ejpam-7142	35	15	integral	integral	ADJ
ejpam-7142	35	16	equations	equation	NOUN
ejpam-7142	35	17	and	and	CCONJ
ejpam-7142	35	18	neutron	neutron	NOUN
ejpam-7142	35	19	transport	transport	NOUN
ejpam-7142	36	1	[	[	X
ejpam-7142	36	2	38	38	NUM
ejpam-7142	36	3	]	]	PUNCT
ejpam-7142	36	4	,	,	PUNCT
ejpam-7142	36	5	and	and	CCONJ
ejpam-7142	36	6	explorations	exploration	NOUN
ejpam-7142	36	7	in	in	ADP
ejpam-7142	36	8	fractional	fractional	ADJ
ejpam-7142	36	9	calculus	calculus	NOUN
ejpam-7142	36	10	and	and	CCONJ
ejpam-7142	36	11	fixedpoint	fixedpoint	NOUN
ejpam-7142	36	12	theorems	theorem	NOUN
ejpam-7142	37	1	[	[	X
ejpam-7142	37	2	39	39	NUM
ejpam-7142	37	3	,	,	PUNCT
ejpam-7142	37	4	40	40	NUM
ejpam-7142	37	5	]	]	PUNCT
ejpam-7142	37	6	.	.	PUNCT
ejpam-7142	38	1	this	this	DET
ejpam-7142	38	2	comprehensive	comprehensive	ADJ
ejpam-7142	38	3	research	research	NOUN
ejpam-7142	38	4	builds	build	VERB
ejpam-7142	38	5	upon	upon	SCONJ
ejpam-7142	38	6	these	these	DET
ejpam-7142	38	7	foundations	foundation	NOUN
ejpam-7142	38	8	by	by	ADP
ejpam-7142	38	9	:	:	PUNCT
ejpam-7142	38	10	•	•	NOUN
ejpam-7142	38	11	formalizing	formalizing	NOUN
ejpam-7142	38	12	the	the	DET
ejpam-7142	38	13	complete	complete	ADJ
ejpam-7142	38	14	structure	structure	NOUN
ejpam-7142	38	15	of	of	ADP
ejpam-7142	38	16	neutrosophic	neutrosophic	ADJ
ejpam-7142	38	17	mr	mr	PROPN
ejpam-7142	38	18	-	-	PUNCT
ejpam-7142	38	19	metric	metric	ADJ
ejpam-7142	38	20	spaces	space	NOUN
ejpam-7142	38	21	•	•	ADP
ejpam-7142	38	22	developing	develop	VERB
ejpam-7142	38	23	graph	graph	NOUN
ejpam-7142	38	24	-	-	PUNCT
ejpam-7142	38	25	based	base	VERB
ejpam-7142	38	26	neutrosophic	neutrosophic	ADJ
ejpam-7142	38	27	mr	mr	PROPN
ejpam-7142	38	28	-	-	PUNCT
ejpam-7142	38	29	metrics	metric	NOUN
ejpam-7142	38	30	with	with	ADP
ejpam-7142	38	31	practical	practical	ADJ
ejpam-7142	38	32	applications	application	NOUN
ejpam-7142	38	33	•	•	ADP
ejpam-7142	38	34	establishing	establish	VERB
ejpam-7142	38	35	robust	robust	ADJ
ejpam-7142	38	36	contraction	contraction	NOUN
ejpam-7142	38	37	and	and	CCONJ
ejpam-7142	38	38	expansion	expansion	NOUN
ejpam-7142	38	39	properties	property	NOUN
ejpam-7142	38	40	•	•	ADV
ejpam-7142	38	41	introducing	introduce	VERB
ejpam-7142	38	42	neutrosophic	neutrosophic	ADJ
ejpam-7142	38	43	homotopy	homotopy	NOUN
ejpam-7142	38	44	and	and	CCONJ
ejpam-7142	38	45	fundamental	fundamental	ADJ
ejpam-7142	38	46	groupoids	groupoid	NOUN
ejpam-7142	38	47	•	•	ADV
ejpam-7142	38	48	providing	provide	VERB
ejpam-7142	38	49	implementable	implementable	ADJ
ejpam-7142	38	50	algorithms	algorithm	NOUN
ejpam-7142	38	51	for	for	ADP
ejpam-7142	38	52	real	real	ADJ
ejpam-7142	38	53	-	-	PUNCT
ejpam-7142	38	54	world	world	NOUN
ejpam-7142	38	55	network	network	NOUN
ejpam-7142	38	56	analysis	analysis	NOUN
ejpam-7142	38	57	the	the	DET
ejpam-7142	38	58	paper	paper	NOUN
ejpam-7142	38	59	organizes	organize	VERB
ejpam-7142	38	60	as	as	SCONJ
ejpam-7142	38	61	follows	follow	VERB
ejpam-7142	38	62	:	:	PUNCT
ejpam-7142	38	63	section	section	NOUN
ejpam-7142	38	64	2	2	NUM
ejpam-7142	38	65	presents	present	VERB
ejpam-7142	38	66	main	main	ADJ
ejpam-7142	38	67	theoretical	theoretical	ADJ
ejpam-7142	38	68	results	result	NOUN
ejpam-7142	38	69	,	,	PUNCT
ejpam-7142	38	70	section	section	NOUN
ejpam-7142	38	71	3	3	NUM
ejpam-7142	38	72	provides	provide	VERB
ejpam-7142	38	73	examples	example	NOUN
ejpam-7142	38	74	and	and	CCONJ
ejpam-7142	38	75	applications	application	NOUN
ejpam-7142	38	76	.	.	PUNCT
ejpam-7142	39	1	definition	definition	NOUN
ejpam-7142	39	2	1	1	NUM
ejpam-7142	39	3	.	.	PUNCT
ejpam-7142	40	1	[	[	X
ejpam-7142	40	2	3	3	X
ejpam-7142	40	3	]	]	PUNCT
ejpam-7142	40	4	consider	consider	VERB
ejpam-7142	40	5	a	a	DET
ejpam-7142	40	6	non	non	ADJ
ejpam-7142	40	7	-	-	ADJ
ejpam-7142	40	8	empty	empty	ADJ
ejpam-7142	40	9	set	set	NOUN
ejpam-7142	40	10	x	x	PUNCT
ejpam-7142	40	11	̸=	̸=	PROPN
ejpam-7142	40	12	∅	∅	NOUN
ejpam-7142	40	13	and	and	CCONJ
ejpam-7142	40	14	a	a	DET
ejpam-7142	40	15	real	real	ADJ
ejpam-7142	40	16	number	number	NOUN
ejpam-7142	40	17	r	r	NOUN
ejpam-7142	40	18	>	>	X
ejpam-7142	40	19	1	1	NUM
ejpam-7142	40	20	.	.	PUNCT
ejpam-7142	41	1	a	a	DET
ejpam-7142	41	2	function	function	NOUN
ejpam-7142	41	3	m	m	VERB
ejpam-7142	41	4	:	:	PUNCT
ejpam-7142	42	1	x×	x×	PUNCT
ejpam-7142	42	2	x×	x×	PUNCT
ejpam-7142	42	3	x→	x→	PUNCT
ejpam-7142	43	1	[	[	X
ejpam-7142	43	2	0,∞	0,∞	NOUN
ejpam-7142	43	3	)	)	PUNCT
ejpam-7142	43	4	is	be	AUX
ejpam-7142	43	5	termed	term	VERB
ejpam-7142	43	6	an	an	DET
ejpam-7142	43	7	mr	mr	PROPN
ejpam-7142	43	8	-	-	PUNCT
ejpam-7142	43	9	metric	metric	NOUN
ejpam-7142	43	10	if	if	SCONJ
ejpam-7142	43	11	it	it	PRON
ejpam-7142	43	12	satisfies	satisfy	VERB
ejpam-7142	43	13	the	the	DET
ejpam-7142	43	14	following	follow	VERB
ejpam-7142	43	15	conditions	condition	NOUN
ejpam-7142	43	16	for	for	ADP
ejpam-7142	43	17	all	all	PRON
ejpam-7142	43	18	v	v	NOUN
ejpam-7142	43	19	,	,	PUNCT
ejpam-7142	43	20	ξ	ξ	PROPN
ejpam-7142	43	21	,	,	PUNCT
ejpam-7142	43	22	s	s	PART
ejpam-7142	43	23	,	,	PUNCT
ejpam-7142	43	24	ℓ1	ℓ1	NOUN
ejpam-7142	43	25	∈	∈	NOUN
ejpam-7142	44	1	x	x	X
ejpam-7142	44	2	:	:	PUNCT
ejpam-7142	44	3	•	•	ADP
ejpam-7142	44	4	m(v	m(v	PROPN
ejpam-7142	44	5	,	,	PUNCT
ejpam-7142	44	6	ξ	ξ	PROPN
ejpam-7142	44	7	,	,	PUNCT
ejpam-7142	44	8	s	s	PART
ejpam-7142	44	9	)	)	PUNCT
ejpam-7142	44	10	≥	≥	NOUN
ejpam-7142	44	11	0	0	NUM
ejpam-7142	44	12	.	.	NOUN
ejpam-7142	44	13	•	•	NUM
ejpam-7142	44	14	m(v	m(v	PROPN
ejpam-7142	44	15	,	,	PUNCT
ejpam-7142	44	16	ξ	ξ	PROPN
ejpam-7142	44	17	,	,	PUNCT
ejpam-7142	44	18	s	s	PART
ejpam-7142	44	19	)	)	PUNCT
ejpam-7142	44	20	=	=	SYM
ejpam-7142	44	21	0	0	PUNCT
ejpam-7142	45	1	if	if	SCONJ
ejpam-7142	45	2	and	and	CCONJ
ejpam-7142	45	3	only	only	ADV
ejpam-7142	45	4	if	if	SCONJ
ejpam-7142	45	5	v	v	NOUN
ejpam-7142	45	6	=	=	SYM
ejpam-7142	45	7	ξ	ξ	PROPN
ejpam-7142	45	8	=	=	PUNCT
ejpam-7142	45	9	s.	s.	PROPN
ejpam-7142	45	10	•	•	ADP
ejpam-7142	45	11	m(v	m(v	PROPN
ejpam-7142	45	12	,	,	PUNCT
ejpam-7142	45	13	ξ	ξ	PROPN
ejpam-7142	45	14	,	,	PUNCT
ejpam-7142	45	15	s	s	PART
ejpam-7142	45	16	)	)	PUNCT
ejpam-7142	45	17	remains	remain	VERB
ejpam-7142	45	18	invariant	invariant	ADJ
ejpam-7142	45	19	under	under	ADP
ejpam-7142	45	20	any	any	DET
ejpam-7142	45	21	permutation	permutation	NOUN
ejpam-7142	45	22	p(v	p(v	NOUN
ejpam-7142	45	23	,	,	PUNCT
ejpam-7142	45	24	ξ	ξ	PROPN
ejpam-7142	45	25	,	,	PUNCT
ejpam-7142	45	26	s	s	PART
ejpam-7142	45	27	)	)	PUNCT
ejpam-7142	45	28	,	,	PUNCT
ejpam-7142	45	29	i.e.	i.e.	X
ejpam-7142	45	30	,m(v	,m(v	PUNCT
ejpam-7142	45	31	,	,	PUNCT
ejpam-7142	45	32	ξ	ξ	PROPN
ejpam-7142	45	33	,	,	PUNCT
ejpam-7142	45	34	s	s	PART
ejpam-7142	45	35	)	)	PUNCT
ejpam-7142	45	36	=	=	SYM
ejpam-7142	45	37	m(p(v	m(p(v	NOUN
ejpam-7142	45	38	,	,	PUNCT
ejpam-7142	45	39	ξ	ξ	PROPN
ejpam-7142	45	40	,	,	PUNCT
ejpam-7142	45	41	s	s	NOUN
ejpam-7142	45	42	)	)	PUNCT
ejpam-7142	45	43	)	)	PUNCT
ejpam-7142	45	44	.	.	PUNCT
ejpam-7142	46	1	e.	e.	PROPN
ejpam-7142	46	2	hussein	hussein	PROPN
ejpam-7142	46	3	et	et	PROPN
ejpam-7142	46	4	al	al	PROPN
ejpam-7142	46	5	.	.	PUNCT
ejpam-7142	46	6	/	/	SYM
ejpam-7142	46	7	eur	eur	PROPN
ejpam-7142	46	8	.	.	PUNCT
ejpam-7142	47	1	j.	j.	PROPN
ejpam-7142	47	2	pure	pure	PROPN
ejpam-7142	47	3	appl	appl	PROPN
ejpam-7142	47	4	.	.	PROPN
ejpam-7142	47	5	math	math	PROPN
ejpam-7142	47	6	,	,	PUNCT
ejpam-7142	47	7	18	18	NUM
ejpam-7142	47	8	(	(	PUNCT
ejpam-7142	47	9	4	4	NUM
ejpam-7142	47	10	)	)	PUNCT
ejpam-7142	47	11	(	(	PUNCT
ejpam-7142	47	12	2025	2025	NUM
ejpam-7142	47	13	)	)	PUNCT
ejpam-7142	47	14	,	,	PUNCT
ejpam-7142	47	15	7142	7142	NUM
ejpam-7142	47	16	3	3	NUM
ejpam-7142	47	17	of	of	ADP
ejpam-7142	47	18	17	17	NUM
ejpam-7142	47	19	•	•	NOUN
ejpam-7142	47	20	the	the	DET
ejpam-7142	47	21	following	follow	VERB
ejpam-7142	47	22	inequality	inequality	NOUN
ejpam-7142	47	23	holds	hold	VERB
ejpam-7142	47	24	:	:	PUNCT
ejpam-7142	47	25	m(v	m(v	NUM
ejpam-7142	47	26	,	,	PUNCT
ejpam-7142	47	27	ξ	ξ	PROPN
ejpam-7142	47	28	,	,	PUNCT
ejpam-7142	47	29	s	s	NOUN
ejpam-7142	47	30	)	)	PUNCT
ejpam-7142	47	31	≤	≤	NOUN
ejpam-7142	47	32	r	r	NOUN
ejpam-7142	48	1	[	[	X
ejpam-7142	48	2	m(v	m(v	X
ejpam-7142	48	3	,	,	PUNCT
ejpam-7142	48	4	ξ	ξ	X
ejpam-7142	48	5	,	,	PUNCT
ejpam-7142	48	6	ℓ1	ℓ1	NOUN
ejpam-7142	48	7	)	)	PUNCT
ejpam-7142	49	1	+	+	SYM
ejpam-7142	49	2	m(v	m(v	NOUN
ejpam-7142	49	3	,	,	PUNCT
ejpam-7142	49	4	ℓ1	ℓ1	NOUN
ejpam-7142	49	5	,	,	PUNCT
ejpam-7142	49	6	s	s	X
ejpam-7142	49	7	)	)	PUNCT
ejpam-7142	49	8	+	+	ADJ
ejpam-7142	49	9	m(ℓ1	m(ℓ1	NOUN
ejpam-7142	49	10	,	,	PUNCT
ejpam-7142	49	11	ξ	ξ	PROPN
ejpam-7142	49	12	,	,	PUNCT
ejpam-7142	49	13	s	s	PART
ejpam-7142	49	14	)	)	PUNCT
ejpam-7142	49	15	]	]	PUNCT
ejpam-7142	49	16	.	.	PUNCT
ejpam-7142	50	1	a	a	DET
ejpam-7142	50	2	structure	structure	NOUN
ejpam-7142	50	3	(	(	PUNCT
ejpam-7142	50	4	x	x	X
ejpam-7142	50	5	,	,	PUNCT
ejpam-7142	50	6	m	m	NOUN
ejpam-7142	50	7	)	)	PUNCT
ejpam-7142	50	8	that	that	PRON
ejpam-7142	50	9	adheres	adhere	VERB
ejpam-7142	50	10	to	to	ADP
ejpam-7142	50	11	these	these	DET
ejpam-7142	50	12	properties	property	NOUN
ejpam-7142	50	13	is	be	AUX
ejpam-7142	50	14	defined	define	VERB
ejpam-7142	50	15	as	as	ADP
ejpam-7142	50	16	an	an	DET
ejpam-7142	50	17	mr	mr	PROPN
ejpam-7142	50	18	-	-	PUNCT
ejpam-7142	50	19	metric	metric	ADJ
ejpam-7142	50	20	space	space	NOUN
ejpam-7142	50	21	.	.	PUNCT
ejpam-7142	51	1	definition	definition	NOUN
ejpam-7142	51	2	2	2	NUM
ejpam-7142	51	3	.	.	PUNCT
ejpam-7142	52	1	[	[	X
ejpam-7142	52	2	19][neutrosophic	19][neutrosophic	NUM
ejpam-7142	52	3	mr	mr	ADJ
ejpam-7142	52	4	-	-	PUNCT
ejpam-7142	52	5	metric	metric	ADJ
ejpam-7142	52	6	space	space	NOUN
ejpam-7142	52	7	(	(	PUNCT
ejpam-7142	52	8	nmr	nmr	NOUN
ejpam-7142	52	9	-	-	PUNCT
ejpam-7142	52	10	ms	ms	NOUN
ejpam-7142	52	11	)	)	PUNCT
ejpam-7142	52	12	]	]	PUNCT
ejpam-7142	52	13	a	a	DET
ejpam-7142	52	14	9	9	NUM
ejpam-7142	52	15	-	-	PUNCT
ejpam-7142	52	16	tuple	tuple	NOUN
ejpam-7142	52	17	(	(	PUNCT
ejpam-7142	52	18	z	z	PROPN
ejpam-7142	52	19	,	,	PUNCT
ejpam-7142	52	20	m	m	PROPN
ejpam-7142	52	21	,	,	PUNCT
ejpam-7142	52	22	t	t	PROPN
ejpam-7142	52	23	,	,	PUNCT
ejpam-7142	52	24	f	f	PROPN
ejpam-7142	52	25	,	,	PUNCT
ejpam-7142	52	26	i	i	PRON
ejpam-7142	52	27	,	,	PUNCT
ejpam-7142	52	28	•	•	PROPN
ejpam-7142	52	29	,	,	PUNCT
ejpam-7142	52	30	⋄	⋄	PROPN
ejpam-7142	52	31	,	,	PUNCT
ejpam-7142	52	32	r	r	NOUN
ejpam-7142	52	33	,	,	PUNCT
ejpam-7142	52	34	⋆	⋆	CCONJ
ejpam-7142	52	35	)	)	PUNCT
ejpam-7142	52	36	is	be	AUX
ejpam-7142	52	37	called	call	VERB
ejpam-7142	52	38	a	a	DET
ejpam-7142	52	39	neutrosophic	neutrosophic	ADJ
ejpam-7142	52	40	mr	mr	ADJ
ejpam-7142	52	41	-	-	PUNCT
ejpam-7142	52	42	metric	metric	ADJ
ejpam-7142	52	43	space	space	NOUN
ejpam-7142	52	44	if	if	SCONJ
ejpam-7142	52	45	:	:	PUNCT
ejpam-7142	52	46	(	(	PUNCT
ejpam-7142	52	47	i	i	NOUN
ejpam-7142	52	48	)	)	PUNCT
ejpam-7142	52	49	z	z	PROPN
ejpam-7142	52	50	is	be	AUX
ejpam-7142	52	51	a	a	DET
ejpam-7142	52	52	non	non	ADJ
ejpam-7142	52	53	-	-	ADJ
ejpam-7142	52	54	empty	empty	ADJ
ejpam-7142	52	55	set	set	NOUN
ejpam-7142	52	56	.	.	PUNCT
ejpam-7142	53	1	(	(	PUNCT
ejpam-7142	53	2	ii	ii	NOUN
ejpam-7142	53	3	)	)	PUNCT
ejpam-7142	53	4	m	m	VERB
ejpam-7142	53	5	:	:	PUNCT
ejpam-7142	53	6	z	z	X
ejpam-7142	53	7	×	×	NOUN
ejpam-7142	53	8	z	z	NOUN
ejpam-7142	53	9	×z	×z	PROPN
ejpam-7142	53	10	→	→	SYM
ejpam-7142	53	11	[	[	X
ejpam-7142	53	12	0,∞	0,∞	NUM
ejpam-7142	53	13	)	)	PUNCT
ejpam-7142	53	14	is	be	AUX
ejpam-7142	53	15	an	an	DET
ejpam-7142	53	16	mr	mr	ADJ
ejpam-7142	53	17	-	-	PUNCT
ejpam-7142	53	18	metric	metric	ADJ
ejpam-7142	53	19	satisfying	satisfying	NOUN
ejpam-7142	53	20	:	:	PUNCT
ejpam-7142	53	21	(	(	PUNCT
ejpam-7142	53	22	m1	m1	NOUN
ejpam-7142	53	23	)	)	PUNCT
ejpam-7142	53	24	m(υ	m(υ	PROPN
ejpam-7142	53	25	,	,	PUNCT
ejpam-7142	53	26	ξ,ℑ	ξ,ℑ	PROPN
ejpam-7142	53	27	)	)	PUNCT
ejpam-7142	53	28	≥	≥	NOUN
ejpam-7142	53	29	0	0	NUM
ejpam-7142	53	30	,	,	PUNCT
ejpam-7142	53	31	(	(	PUNCT
ejpam-7142	53	32	m2	m2	PROPN
ejpam-7142	53	33	)	)	PUNCT
ejpam-7142	53	34	m(υ	m(υ	PROPN
ejpam-7142	53	35	,	,	PUNCT
ejpam-7142	53	36	ξ,ℑ	ξ,ℑ	PROPN
ejpam-7142	53	37	)	)	PUNCT
ejpam-7142	54	1	=	=	SYM
ejpam-7142	54	2	0	0	NUM
ejpam-7142	55	1	⇐	⇐	ADJ
ejpam-7142	55	2	⇒	⇒	NOUN
ejpam-7142	55	3	υ	υ	X
ejpam-7142	55	4	=	=	SYM
ejpam-7142	55	5	ξ	ξ	PROPN
ejpam-7142	55	6	=	=	SYM
ejpam-7142	55	7	ℑ	ℑ	PROPN
ejpam-7142	55	8	,	,	PUNCT
ejpam-7142	55	9	(	(	PUNCT
ejpam-7142	55	10	m3	m3	PROPN
ejpam-7142	55	11	)	)	PUNCT
ejpam-7142	55	12	symmetry	symmetry	NOUN
ejpam-7142	55	13	under	under	ADP
ejpam-7142	55	14	permutations	permutation	NOUN
ejpam-7142	55	15	,	,	PUNCT
ejpam-7142	55	16	(	(	PUNCT
ejpam-7142	55	17	m4	m4	PROPN
ejpam-7142	55	18	)	)	PUNCT
ejpam-7142	55	19	m(υ	m(υ	PROPN
ejpam-7142	55	20	,	,	PUNCT
ejpam-7142	55	21	ξ,ℑ	ξ,ℑ	PROPN
ejpam-7142	55	22	)	)	PUNCT
ejpam-7142	55	23	≤	≤	NUM
ejpam-7142	55	24	r	r	NOUN
ejpam-7142	56	1	[	[	X
ejpam-7142	56	2	m(υ	m(υ	PROPN
ejpam-7142	56	3	,	,	PUNCT
ejpam-7142	56	4	ξ	ξ	PROPN
ejpam-7142	56	5	,	,	PUNCT
ejpam-7142	56	6	ℓ	ℓ	NUM
ejpam-7142	56	7	)	)	PUNCT
ejpam-7142	56	8	⋆	⋆	NOUN
ejpam-7142	57	1	m(υ	m(υ	PROPN
ejpam-7142	57	2	,	,	PUNCT
ejpam-7142	57	3	ℓ,ℑ	ℓ,ℑ	PROPN
ejpam-7142	57	4	)	)	PUNCT
ejpam-7142	57	5	⋆	⋆	NOUN
ejpam-7142	57	6	m(ℓ	m(ℓ	NOUN
ejpam-7142	57	7	,	,	PUNCT
ejpam-7142	57	8	ξ,ℑ	ξ,ℑ	PROPN
ejpam-7142	57	9	)	)	PUNCT
ejpam-7142	57	10	]	]	PUNCT
ejpam-7142	57	11	,	,	PUNCT
ejpam-7142	57	12	r	r	NOUN
ejpam-7142	57	13	>	>	X
ejpam-7142	57	14	1	1	NUM
ejpam-7142	57	15	.	.	PUNCT
ejpam-7142	57	16	(	(	PUNCT
ejpam-7142	57	17	iii	iii	X
ejpam-7142	57	18	)	)	PUNCT
ejpam-7142	57	19	t	t	NOUN
ejpam-7142	57	20	,	,	PUNCT
ejpam-7142	57	21	f	f	PROPN
ejpam-7142	57	22	,	,	PUNCT
ejpam-7142	57	23	i	i	PRON
ejpam-7142	57	24	:	:	PUNCT
ejpam-7142	57	25	z	z	NOUN
ejpam-7142	57	26	×	×	PROPN
ejpam-7142	57	27	z	z	NOUN
ejpam-7142	57	28	×	×	NOUN
ejpam-7142	57	29	(	(	PUNCT
ejpam-7142	57	30	0,∞)→	0,∞)→	NOUN
ejpam-7142	58	1	[	[	X
ejpam-7142	58	2	0	0	NUM
ejpam-7142	58	3	,	,	PUNCT
ejpam-7142	58	4	1	1	NUM
ejpam-7142	58	5	]	]	PUNCT
ejpam-7142	58	6	are	be	AUX
ejpam-7142	58	7	neutrosophic	neutrosophic	ADJ
ejpam-7142	58	8	functions	function	NOUN
ejpam-7142	58	9	satisfying	satisfy	VERB
ejpam-7142	58	10	:	:	PUNCT
ejpam-7142	58	11	(	(	PUNCT
ejpam-7142	58	12	n1	n1	NOUN
ejpam-7142	58	13	)	)	PUNCT
ejpam-7142	58	14	t	t	NOUN
ejpam-7142	58	15	(	(	PUNCT
ejpam-7142	58	16	υ	υ	PROPN
ejpam-7142	58	17	,	,	PUNCT
ejpam-7142	58	18	ξ	ξ	PROPN
ejpam-7142	58	19	,	,	PUNCT
ejpam-7142	58	20	γ	γ	NOUN
ejpam-7142	58	21	)	)	PUNCT
ejpam-7142	58	22	=	=	SYM
ejpam-7142	58	23	1	1	NUM
ejpam-7142	58	24	⇐	⇐	ADJ
ejpam-7142	58	25	⇒	⇒	NOUN
ejpam-7142	58	26	υ	υ	X
ejpam-7142	58	27	=	=	SYM
ejpam-7142	58	28	ξ	ξ	PROPN
ejpam-7142	58	29	(	(	PUNCT
ejpam-7142	58	30	truth	truth	NOUN
ejpam-7142	58	31	-	-	PUNCT
ejpam-7142	58	32	identity	identity	NOUN
ejpam-7142	58	33	)	)	PUNCT
ejpam-7142	58	34	,	,	PUNCT
ejpam-7142	58	35	(	(	PUNCT
ejpam-7142	58	36	n2	n2	ADJ
ejpam-7142	58	37	)	)	PUNCT
ejpam-7142	58	38	t	t	NOUN
ejpam-7142	58	39	(	(	PUNCT
ejpam-7142	58	40	υ	υ	PROPN
ejpam-7142	58	41	,	,	PUNCT
ejpam-7142	58	42	ξ	ξ	PROPN
ejpam-7142	58	43	,	,	PUNCT
ejpam-7142	58	44	γ	γ	NOUN
ejpam-7142	58	45	)	)	PUNCT
ejpam-7142	58	46	=	=	SYM
ejpam-7142	58	47	t	t	PROPN
ejpam-7142	58	48	(	(	PUNCT
ejpam-7142	58	49	ξ	ξ	PROPN
ejpam-7142	58	50	,	,	PUNCT
ejpam-7142	58	51	υ	υ	PROPN
ejpam-7142	58	52	,	,	PUNCT
ejpam-7142	58	53	γ	γ	NOUN
ejpam-7142	58	54	)	)	PUNCT
ejpam-7142	58	55	(	(	PUNCT
ejpam-7142	58	56	symmetry	symmetry	NOUN
ejpam-7142	58	57	)	)	PUNCT
ejpam-7142	58	58	,	,	PUNCT
ejpam-7142	58	59	(	(	PUNCT
ejpam-7142	58	60	n3	n3	PROPN
ejpam-7142	58	61	)	)	PUNCT
ejpam-7142	58	62	t	t	PROPN
ejpam-7142	58	63	(	(	PUNCT
ejpam-7142	58	64	υ	υ	PROPN
ejpam-7142	58	65	,	,	PUNCT
ejpam-7142	58	66	ξ	ξ	PROPN
ejpam-7142	58	67	,	,	PUNCT
ejpam-7142	58	68	γ	γ	NOUN
ejpam-7142	58	69	)	)	PUNCT
ejpam-7142	58	70	•	•	NUM
ejpam-7142	58	71	t	t	PROPN
ejpam-7142	58	72	(	(	PUNCT
ejpam-7142	58	73	ξ,ℑ	ξ,ℑ	PROPN
ejpam-7142	58	74	,	,	PUNCT
ejpam-7142	58	75	ρ	ρ	NOUN
ejpam-7142	58	76	)	)	PUNCT
ejpam-7142	58	77	≤	≤	NOUN
ejpam-7142	58	78	t	t	NOUN
ejpam-7142	58	79	(	(	PUNCT
ejpam-7142	58	80	υ,ℑ	υ,ℑ	PROPN
ejpam-7142	58	81	,	,	PUNCT
ejpam-7142	58	82	γ	γ	X
ejpam-7142	58	83	+	+	NOUN
ejpam-7142	58	84	ρ	ρ	PROPN
ejpam-7142	58	85	)	)	PUNCT
ejpam-7142	58	86	(	(	PUNCT
ejpam-7142	58	87	triangle	triangle	NOUN
ejpam-7142	58	88	inequality	inequality	NOUN
ejpam-7142	58	89	)	)	PUNCT
ejpam-7142	58	90	,	,	PUNCT
ejpam-7142	58	91	(	(	PUNCT
ejpam-7142	58	92	n4	n4	PROPN
ejpam-7142	58	93	)	)	PUNCT
ejpam-7142	58	94	limγ→∞	limγ→∞	PROPN
ejpam-7142	58	95	t	t	NOUN
ejpam-7142	58	96	(	(	PUNCT
ejpam-7142	58	97	υ	υ	PROPN
ejpam-7142	58	98	,	,	PUNCT
ejpam-7142	58	99	ξ	ξ	PROPN
ejpam-7142	58	100	,	,	PUNCT
ejpam-7142	58	101	γ	γ	NOUN
ejpam-7142	58	102	)	)	PUNCT
ejpam-7142	58	103	=	=	SYM
ejpam-7142	58	104	1	1	NUM
ejpam-7142	58	105	(	(	PUNCT
ejpam-7142	58	106	asymptotic	asymptotic	ADJ
ejpam-7142	58	107	behavior	behavior	NOUN
ejpam-7142	58	108	)	)	PUNCT
ejpam-7142	58	109	.	.	PUNCT
ejpam-7142	59	1	(	(	PUNCT
ejpam-7142	59	2	iv	iv	X
ejpam-7142	59	3	)	)	PUNCT
ejpam-7142	59	4	•	•	NOUN
ejpam-7142	59	5	(	(	PUNCT
ejpam-7142	59	6	t	t	NOUN
ejpam-7142	59	7	-	-	PUNCT
ejpam-7142	59	8	norm	norm	NOUN
ejpam-7142	59	9	)	)	PUNCT
ejpam-7142	59	10	and	and	CCONJ
ejpam-7142	59	11	⋄	⋄	PROPN
ejpam-7142	59	12	(	(	PUNCT
ejpam-7142	59	13	t	t	NOUN
ejpam-7142	59	14	-	-	PUNCT
ejpam-7142	59	15	conorm	conorm	NOUN
ejpam-7142	59	16	)	)	PUNCT
ejpam-7142	59	17	are	be	AUX
ejpam-7142	59	18	continuous	continuous	ADJ
ejpam-7142	59	19	operators	operator	NOUN
ejpam-7142	59	20	generalizing	generalize	VERB
ejpam-7142	59	21	fuzzy	fuzzy	ADJ
ejpam-7142	59	22	logic	logic	NOUN
ejpam-7142	59	23	.	.	PUNCT
ejpam-7142	60	1	(	(	PUNCT
ejpam-7142	60	2	v	v	NOUN
ejpam-7142	60	3	)	)	PUNCT
ejpam-7142	60	4	⋆	⋆	VERB
ejpam-7142	60	5	is	be	AUX
ejpam-7142	60	6	a	a	DET
ejpam-7142	60	7	binary	binary	ADJ
ejpam-7142	60	8	operation	operation	NOUN
ejpam-7142	60	9	generalizing	generalize	VERB
ejpam-7142	60	10	addition	addition	NOUN
ejpam-7142	60	11	(	(	PUNCT
ejpam-7142	60	12	e.g.	e.g.	ADV
ejpam-7142	60	13	,	,	PUNCT
ejpam-7142	60	14	weighted	weight	VERB
ejpam-7142	60	15	sum	sum	NOUN
ejpam-7142	60	16	)	)	PUNCT
ejpam-7142	60	17	.	.	PUNCT
ejpam-7142	61	1	2	2	X
ejpam-7142	61	2	.	.	X
ejpam-7142	61	3	main	main	ADJ
ejpam-7142	61	4	results	result	NOUN
ejpam-7142	61	5	this	this	DET
ejpam-7142	61	6	section	section	NOUN
ejpam-7142	61	7	is	be	AUX
ejpam-7142	61	8	dedicated	dedicate	VERB
ejpam-7142	61	9	to	to	ADP
ejpam-7142	61	10	the	the	DET
ejpam-7142	61	11	core	core	NOUN
ejpam-7142	61	12	theoretical	theoretical	ADJ
ejpam-7142	61	13	contributions	contribution	NOUN
ejpam-7142	61	14	of	of	ADP
ejpam-7142	61	15	this	this	DET
ejpam-7142	61	16	work	work	NOUN
ejpam-7142	61	17	.	.	PUNCT
ejpam-7142	62	1	we	we	PRON
ejpam-7142	62	2	begin	begin	VERB
ejpam-7142	62	3	by	by	ADP
ejpam-7142	62	4	introducing	introduce	VERB
ejpam-7142	62	5	the	the	DET
ejpam-7142	62	6	concept	concept	NOUN
ejpam-7142	62	7	of	of	ADP
ejpam-7142	62	8	a	a	DET
ejpam-7142	62	9	neutrosophic	neutrosophic	ADJ
ejpam-7142	62	10	graph	graph	NOUN
ejpam-7142	62	11	mr	mr	PROPN
ejpam-7142	62	12	-	-	PUNCT
ejpam-7142	62	13	metric	metric	ADJ
ejpam-7142	62	14	space	space	NOUN
ejpam-7142	62	15	,	,	PUNCT
ejpam-7142	62	16	which	which	PRON
ejpam-7142	62	17	combines	combine	VERB
ejpam-7142	62	18	graph	graph	NOUN
ejpam-7142	62	19	-	-	PUNCT
ejpam-7142	62	20	theoretic	theoretic	NOUN
ejpam-7142	62	21	structures	structure	NOUN
ejpam-7142	62	22	with	with	ADP
ejpam-7142	62	23	neutrosophic	neutrosophic	ADJ
ejpam-7142	62	24	mr	mr	PROPN
ejpam-7142	62	25	-	-	PUNCT
ejpam-7142	62	26	metrics	metric	NOUN
ejpam-7142	62	27	.	.	PUNCT
ejpam-7142	63	1	we	we	PRON
ejpam-7142	63	2	then	then	ADV
ejpam-7142	63	3	establish	establish	VERB
ejpam-7142	63	4	several	several	ADJ
ejpam-7142	63	5	key	key	ADJ
ejpam-7142	63	6	lemmas	lemma	NOUN
ejpam-7142	63	7	and	and	CCONJ
ejpam-7142	63	8	theorems	theorem	NOUN
ejpam-7142	63	9	related	relate	VERB
ejpam-7142	63	10	to	to	ADP
ejpam-7142	63	11	contraction	contraction	NOUN
ejpam-7142	63	12	properties	property	NOUN
ejpam-7142	63	13	,	,	PUNCT
ejpam-7142	63	14	network	network	NOUN
ejpam-7142	63	15	robustness	robustness	NOUN
ejpam-7142	63	16	,	,	PUNCT
ejpam-7142	63	17	and	and	CCONJ
ejpam-7142	63	18	fixed	fix	VERB
ejpam-7142	63	19	point	point	NOUN
ejpam-7142	63	20	theory	theory	NOUN
ejpam-7142	63	21	in	in	ADP
ejpam-7142	63	22	this	this	DET
ejpam-7142	63	23	generalized	generalized	ADJ
ejpam-7142	63	24	setting	setting	NOUN
ejpam-7142	63	25	.	.	PUNCT
ejpam-7142	64	1	the	the	DET
ejpam-7142	64	2	definitions	definition	NOUN
ejpam-7142	64	3	and	and	CCONJ
ejpam-7142	64	4	results	result	NOUN
ejpam-7142	64	5	presented	present	VERB
ejpam-7142	64	6	here	here	ADV
ejpam-7142	64	7	form	form	VERB
ejpam-7142	64	8	the	the	DET
ejpam-7142	64	9	mathematical	mathematical	ADJ
ejpam-7142	64	10	backbone	backbone	NOUN
ejpam-7142	64	11	of	of	ADP
ejpam-7142	64	12	our	our	PRON
ejpam-7142	64	13	framework	framework	NOUN
ejpam-7142	64	14	and	and	CCONJ
ejpam-7142	64	15	provide	provide	VERB
ejpam-7142	64	16	the	the	DET
ejpam-7142	64	17	tools	tool	NOUN
ejpam-7142	64	18	necessary	necessary	ADJ
ejpam-7142	64	19	for	for	ADP
ejpam-7142	64	20	the	the	DET
ejpam-7142	64	21	applications	application	NOUN
ejpam-7142	64	22	discussed	discuss	VERB
ejpam-7142	64	23	in	in	ADP
ejpam-7142	64	24	subsequent	subsequent	ADJ
ejpam-7142	64	25	sections	section	NOUN
ejpam-7142	64	26	.	.	PUNCT
ejpam-7142	65	1	definition	definition	NOUN
ejpam-7142	65	2	3	3	NUM
ejpam-7142	65	3	(	(	PUNCT
ejpam-7142	65	4	neutrosophic	neutrosophic	ADJ
ejpam-7142	65	5	graph	graph	NOUN
ejpam-7142	65	6	mr	mr	PROPN
ejpam-7142	65	7	-	-	PUNCT
ejpam-7142	65	8	metric	metric	ADJ
ejpam-7142	65	9	space	space	NOUN
ejpam-7142	65	10	)	)	PUNCT
ejpam-7142	65	11	.	.	PUNCT
ejpam-7142	66	1	let	let	VERB
ejpam-7142	66	2	g	g	PROPN
ejpam-7142	66	3	=	=	SYM
ejpam-7142	66	4	(	(	PUNCT
ejpam-7142	66	5	v	v	NOUN
ejpam-7142	66	6	,	,	PUNCT
ejpam-7142	66	7	e	e	NOUN
ejpam-7142	66	8	)	)	PUNCT
ejpam-7142	66	9	be	be	AUX
ejpam-7142	66	10	a	a	DET
ejpam-7142	66	11	graph	graph	NOUN
ejpam-7142	66	12	.	.	PUNCT
ejpam-7142	67	1	we	we	PRON
ejpam-7142	67	2	define	define	VERB
ejpam-7142	67	3	an	an	DET
ejpam-7142	67	4	nmr	nmr	NOUN
ejpam-7142	67	5	-	-	PUNCT
ejpam-7142	67	6	ms	ms	NOUN
ejpam-7142	67	7	on	on	ADP
ejpam-7142	67	8	its	its	PRON
ejpam-7142	67	9	vertex	vertex	NOUN
ejpam-7142	67	10	set	set	VERB
ejpam-7142	67	11	v	v	NOUN
ejpam-7142	67	12	as	as	SCONJ
ejpam-7142	67	13	follows	follow	VERB
ejpam-7142	67	14	:	:	PUNCT
ejpam-7142	67	15	m(u	m(u	PROPN
ejpam-7142	67	16	,	,	PUNCT
ejpam-7142	67	17	v	v	NOUN
ejpam-7142	67	18	,	,	PUNCT
ejpam-7142	67	19	w	w	NOUN
ejpam-7142	67	20	)	)	PUNCT
ejpam-7142	67	21	=	=	SYM
ejpam-7142	67	22	d(u	d(u	PROPN
ejpam-7142	67	23	,	,	PUNCT
ejpam-7142	67	24	v	v	NOUN
ejpam-7142	67	25	)	)	PUNCT
ejpam-7142	68	1	+	+	X
ejpam-7142	68	2	d(v	d(v	ADJ
ejpam-7142	68	3	,	,	PUNCT
ejpam-7142	68	4	w	w	NOUN
ejpam-7142	68	5	)	)	PUNCT
ejpam-7142	68	6	+	+	CCONJ
ejpam-7142	68	7	d(w	d(w	PROPN
ejpam-7142	68	8	,	,	PUNCT
ejpam-7142	68	9	u	u	NOUN
ejpam-7142	68	10	)	)	PUNCT
ejpam-7142	68	11	3	3	NUM
ejpam-7142	68	12	,	,	PUNCT
ejpam-7142	68	13	where	where	SCONJ
ejpam-7142	68	14	d	d	NOUN
ejpam-7142	68	15	is	be	AUX
ejpam-7142	68	16	the	the	DET
ejpam-7142	68	17	shortest	short	ADJ
ejpam-7142	68	18	path	path	NOUN
ejpam-7142	68	19	distance	distance	NOUN
ejpam-7142	68	20	,	,	PUNCT
ejpam-7142	68	21	t	t	PROPN
ejpam-7142	68	22	(	(	PUNCT
ejpam-7142	68	23	u	u	NOUN
ejpam-7142	68	24	,	,	PUNCT
ejpam-7142	68	25	v	v	NOUN
ejpam-7142	68	26	,	,	PUNCT
ejpam-7142	68	27	γ	γ	NOUN
ejpam-7142	68	28	)	)	PUNCT
ejpam-7142	68	29	=	=	NOUN
ejpam-7142	68	30	number	number	NOUN
ejpam-7142	68	31	of	of	ADP
ejpam-7142	68	32	paths	path	NOUN
ejpam-7142	68	33	of	of	ADP
ejpam-7142	68	34	length	length	NOUN
ejpam-7142	68	35	≤	≤	X
ejpam-7142	68	36	γ	γ	X
ejpam-7142	68	37	between	between	ADP
ejpam-7142	68	38	u	u	PROPN
ejpam-7142	68	39	and	and	CCONJ
ejpam-7142	68	40	v	v	ADP
ejpam-7142	68	41	total	total	ADJ
ejpam-7142	68	42	possible	possible	ADJ
ejpam-7142	68	43	paths	path	NOUN
ejpam-7142	68	44	up	up	ADP
ejpam-7142	68	45	to	to	ADP
ejpam-7142	68	46	diameter	diameter	NOUN
ejpam-7142	68	47	,	,	PUNCT
ejpam-7142	68	48	i(u	i(u	PROPN
ejpam-7142	68	49	,	,	PUNCT
ejpam-7142	68	50	v	v	PROPN
ejpam-7142	68	51	,	,	PUNCT
ejpam-7142	68	52	γ	γ	NOUN
ejpam-7142	68	53	)	)	PUNCT
ejpam-7142	69	1	=	=	SYM
ejpam-7142	69	2	|betweenness	|betweenness	ADV
ejpam-7142	69	3	centrality(u)−	centrality(u)−	PROPN
ejpam-7142	69	4	betweenness	betweenness	NOUN
ejpam-7142	69	5	centrality(v)|	centrality(v)|	PROPN
ejpam-7142	69	6	max(betweenness	max(betweenness	PROPN
ejpam-7142	69	7	)	)	PUNCT
ejpam-7142	69	8	,	,	PUNCT
ejpam-7142	69	9	f(u	f(u	PROPN
ejpam-7142	69	10	,	,	PUNCT
ejpam-7142	69	11	v	v	NOUN
ejpam-7142	69	12	,	,	PUNCT
ejpam-7142	69	13	γ	γ	NOUN
ejpam-7142	69	14	)	)	PUNCT
ejpam-7142	69	15	=	=	SYM
ejpam-7142	69	16	1−	1−	NUM
ejpam-7142	69	17	t	t	PROPN
ejpam-7142	69	18	(	(	PUNCT
ejpam-7142	69	19	u	u	NOUN
ejpam-7142	69	20	,	,	PUNCT
ejpam-7142	69	21	v	v	NOUN
ejpam-7142	69	22	,	,	PUNCT
ejpam-7142	69	23	γ)−	γ)−	PROPN
ejpam-7142	69	24	i(u	i(u	PROPN
ejpam-7142	69	25	,	,	PUNCT
ejpam-7142	69	26	v	v	PROPN
ejpam-7142	69	27	,	,	PUNCT
ejpam-7142	69	28	γ	γ	NOUN
ejpam-7142	69	29	)	)	PUNCT
ejpam-7142	69	30	.	.	PUNCT
ejpam-7142	70	1	definition	definition	NOUN
ejpam-7142	70	2	4	4	NUM
ejpam-7142	70	3	(	(	PUNCT
ejpam-7142	70	4	path	path	NOUN
ejpam-7142	70	5	expansion	expansion	NOUN
ejpam-7142	70	6	constant	constant	ADJ
ejpam-7142	70	7	)	)	PUNCT
ejpam-7142	70	8	.	.	PUNCT
ejpam-7142	71	1	for	for	ADP
ejpam-7142	71	2	a	a	DET
ejpam-7142	71	3	graph	graph	NOUN
ejpam-7142	71	4	g	g	NOUN
ejpam-7142	71	5	,	,	PUNCT
ejpam-7142	71	6	the	the	DET
ejpam-7142	71	7	path	path	NOUN
ejpam-7142	71	8	expansion	expansion	NOUN
ejpam-7142	71	9	constant	constant	ADJ
ejpam-7142	71	10	η(g	η(g	PROPN
ejpam-7142	71	11	)	)	PUNCT
ejpam-7142	71	12	is	be	AUX
ejpam-7142	71	13	defined	define	VERB
ejpam-7142	71	14	as	as	ADP
ejpam-7142	71	15	:	:	PUNCT
ejpam-7142	71	16	η(g	η(g	NUM
ejpam-7142	71	17	)	)	PUNCT
ejpam-7142	72	1	=	=	SYM
ejpam-7142	72	2	min	min	PROPN
ejpam-7142	72	3	s⊂v	s⊂v	PROPN
ejpam-7142	72	4	|s|≤|v	|s|≤|v	PROPN
ejpam-7142	72	5	|/2	|/2	PROPN
ejpam-7142	72	6	|∂s|	|∂s|	NOUN
ejpam-7142	72	7	|s|	|s|	PROPN
ejpam-7142	72	8	where	where	SCONJ
ejpam-7142	72	9	∂s	∂s	PROPN
ejpam-7142	72	10	is	be	AUX
ejpam-7142	72	11	the	the	DET
ejpam-7142	72	12	set	set	NOUN
ejpam-7142	72	13	of	of	ADP
ejpam-7142	72	14	edges	edge	NOUN
ejpam-7142	72	15	between	between	ADP
ejpam-7142	72	16	s	s	PRON
ejpam-7142	72	17	and	and	CCONJ
ejpam-7142	72	18	v	v	NOUN
ejpam-7142	72	19	\	\	PROPN
ejpam-7142	72	20	s.	s.	PROPN
ejpam-7142	72	21	e.	e.	PROPN
ejpam-7142	72	22	hussein	hussein	PROPN
ejpam-7142	72	23	et	et	PROPN
ejpam-7142	72	24	al	al	PROPN
ejpam-7142	72	25	.	.	PUNCT
ejpam-7142	72	26	/	/	SYM
ejpam-7142	72	27	eur	eur	PROPN
ejpam-7142	72	28	.	.	PUNCT
ejpam-7142	73	1	j.	j.	PROPN
ejpam-7142	73	2	pure	pure	PROPN
ejpam-7142	73	3	appl	appl	PROPN
ejpam-7142	73	4	.	.	PROPN
ejpam-7142	73	5	math	math	PROPN
ejpam-7142	73	6	,	,	PUNCT
ejpam-7142	73	7	18	18	NUM
ejpam-7142	73	8	(	(	PUNCT
ejpam-7142	73	9	4	4	NUM
ejpam-7142	73	10	)	)	PUNCT
ejpam-7142	73	11	(	(	PUNCT
ejpam-7142	73	12	2025	2025	NUM
ejpam-7142	73	13	)	)	PUNCT
ejpam-7142	73	14	,	,	PUNCT
ejpam-7142	73	15	7142	7142	NUM
ejpam-7142	73	16	4	4	NUM
ejpam-7142	73	17	of	of	ADP
ejpam-7142	73	18	17	17	NUM
ejpam-7142	73	19	lemma	lemma	PROPN
ejpam-7142	73	20	1	1	NUM
ejpam-7142	73	21	(	(	PUNCT
ejpam-7142	73	22	contraction	contraction	NOUN
ejpam-7142	73	23	implies	imply	VERB
ejpam-7142	73	24	exponential	exponential	ADJ
ejpam-7142	73	25	growth	growth	NOUN
ejpam-7142	73	26	bound	bind	VERB
ejpam-7142	73	27	)	)	PUNCT
ejpam-7142	73	28	.	.	PUNCT
ejpam-7142	74	1	in	in	ADP
ejpam-7142	74	2	a	a	DET
ejpam-7142	74	3	neutrosophic	neutrosophic	ADJ
ejpam-7142	74	4	graph	graph	NOUN
ejpam-7142	74	5	mrmetric	mrmetric	ADJ
ejpam-7142	74	6	space	space	NOUN
ejpam-7142	74	7	with	with	ADP
ejpam-7142	74	8	contraction	contraction	NOUN
ejpam-7142	74	9	constant	constant	ADJ
ejpam-7142	74	10	r	r	NOUN
ejpam-7142	74	11	,	,	PUNCT
ejpam-7142	74	12	for	for	ADP
ejpam-7142	74	13	any	any	DET
ejpam-7142	74	14	vertices	vertex	NOUN
ejpam-7142	74	15	u	u	NOUN
ejpam-7142	74	16	,	,	PUNCT
ejpam-7142	74	17	v	v	NOUN
ejpam-7142	74	18	,	,	PUNCT
ejpam-7142	74	19	w	w	PROPN
ejpam-7142	74	20	∈	∈	PROPN
ejpam-7142	74	21	v	v	NOUN
ejpam-7142	74	22	:	:	PUNCT
ejpam-7142	74	23	m(u	m(u	PROPN
ejpam-7142	74	24	,	,	PUNCT
ejpam-7142	74	25	v	v	NOUN
ejpam-7142	74	26	,	,	PUNCT
ejpam-7142	74	27	w	w	NOUN
ejpam-7142	74	28	)	)	PUNCT
ejpam-7142	74	29	≤	≤	NOUN
ejpam-7142	74	30	r⌈log3	r⌈log3	NOUN
ejpam-7142	74	31	n⌉	n⌉	NOUN
ejpam-7142	74	32	·	·	PUNCT
ejpam-7142	74	33	min	min	NOUN
ejpam-7142	74	34	x	x	SYM
ejpam-7142	74	35	,	,	PUNCT
ejpam-7142	74	36	y	y	PROPN
ejpam-7142	74	37	,	,	PUNCT
ejpam-7142	74	38	z∈v	z∈v	NOUN
ejpam-7142	74	39	m(x	m(x	PROPN
ejpam-7142	74	40	,	,	PUNCT
ejpam-7142	74	41	y	y	PROPN
ejpam-7142	74	42	,	,	PUNCT
ejpam-7142	74	43	z	z	NOUN
ejpam-7142	74	44	)	)	PUNCT
ejpam-7142	74	45	·	·	PUNCT
ejpam-7142	74	46	diameter(g	diameter(g	X
ejpam-7142	74	47	)	)	PUNCT
ejpam-7142	74	48	proof	proof	NOUN
ejpam-7142	74	49	.	.	PUNCT
ejpam-7142	75	1	let	let	VERB
ejpam-7142	75	2	δ	δ	NOUN
ejpam-7142	75	3	=	=	PUNCT
ejpam-7142	75	4	minx	minx	PROPN
ejpam-7142	75	5	,	,	PUNCT
ejpam-7142	75	6	y	y	NOUN
ejpam-7142	75	7	,	,	PUNCT
ejpam-7142	75	8	z∈v	z∈v	NOUN
ejpam-7142	75	9	m(x	m(x	PROPN
ejpam-7142	75	10	,	,	PUNCT
ejpam-7142	75	11	y	y	PROPN
ejpam-7142	75	12	,	,	PUNCT
ejpam-7142	75	13	z	z	NOUN
ejpam-7142	75	14	)	)	PUNCT
ejpam-7142	75	15	.	.	PUNCT
ejpam-7142	76	1	consider	consider	VERB
ejpam-7142	76	2	a	a	DET
ejpam-7142	76	3	spanning	span	VERB
ejpam-7142	76	4	tree	tree	NOUN
ejpam-7142	76	5	t	t	PROPN
ejpam-7142	76	6	of	of	ADP
ejpam-7142	76	7	g.	g.	PROPN
ejpam-7142	76	8	for	for	ADP
ejpam-7142	76	9	any	any	DET
ejpam-7142	76	10	u	u	NOUN
ejpam-7142	76	11	,	,	PUNCT
ejpam-7142	76	12	v	v	NOUN
ejpam-7142	76	13	,	,	PUNCT
ejpam-7142	76	14	w	w	PROPN
ejpam-7142	76	15	∈	∈	PROPN
ejpam-7142	76	16	v	v	NOUN
ejpam-7142	76	17	,	,	PUNCT
ejpam-7142	76	18	we	we	PRON
ejpam-7142	76	19	can	can	AUX
ejpam-7142	76	20	find	find	VERB
ejpam-7142	76	21	intermediate	intermediate	ADJ
ejpam-7142	76	22	points	point	NOUN
ejpam-7142	76	23	along	along	ADP
ejpam-7142	76	24	paths	path	NOUN
ejpam-7142	76	25	in	in	ADP
ejpam-7142	76	26	t	t	PROPN
ejpam-7142	76	27	.	.	PUNCT
ejpam-7142	77	1	by	by	ADP
ejpam-7142	77	2	repeated	repeat	VERB
ejpam-7142	77	3	application	application	NOUN
ejpam-7142	77	4	of	of	ADP
ejpam-7142	77	5	the	the	DET
ejpam-7142	77	6	mr	mr	PROPN
ejpam-7142	77	7	-	-	PUNCT
ejpam-7142	77	8	metric	metric	ADJ
ejpam-7142	77	9	property	property	NOUN
ejpam-7142	77	10	(	(	PUNCT
ejpam-7142	77	11	m4	m4	PROPN
ejpam-7142	77	12	):	):	PUNCT
ejpam-7142	77	13	m(u	m(u	PROPN
ejpam-7142	77	14	,	,	PUNCT
ejpam-7142	77	15	v	v	NOUN
ejpam-7142	77	16	,	,	PUNCT
ejpam-7142	77	17	w	w	NOUN
ejpam-7142	77	18	)	)	PUNCT
ejpam-7142	77	19	≤	≤	NOUN
ejpam-7142	77	20	r[m(u	r[m(u	NOUN
ejpam-7142	77	21	,	,	PUNCT
ejpam-7142	77	22	v	v	NOUN
ejpam-7142	77	23	,	,	PUNCT
ejpam-7142	77	24	ℓ1	ℓ1	NOUN
ejpam-7142	77	25	)	)	PUNCT
ejpam-7142	78	1	+	+	SYM
ejpam-7142	78	2	m(u	m(u	PROPN
ejpam-7142	78	3	,	,	PUNCT
ejpam-7142	78	4	ℓ1	ℓ1	NOUN
ejpam-7142	78	5	,	,	PUNCT
ejpam-7142	78	6	w	w	NOUN
ejpam-7142	78	7	)	)	PUNCT
ejpam-7142	78	8	+	+	ADJ
ejpam-7142	78	9	m(ℓ1	m(ℓ1	NOUN
ejpam-7142	78	10	,	,	PUNCT
ejpam-7142	78	11	v	v	NOUN
ejpam-7142	78	12	,	,	PUNCT
ejpam-7142	78	13	w	w	NOUN
ejpam-7142	78	14	)	)	PUNCT
ejpam-7142	78	15	]	]	PUNCT
ejpam-7142	78	16	≤	≤	NUM
ejpam-7142	78	17	r2	r2	NOUN
ejpam-7142	78	18	9∑	9∑	NUM
ejpam-7142	78	19	i=1	i=1	PROPN
ejpam-7142	78	20	m(pi	m(pi	PROPN
ejpam-7142	78	21	,	,	PUNCT
ejpam-7142	78	22	qi	qi	PROPN
ejpam-7142	78	23	,	,	PUNCT
ejpam-7142	78	24	ri	ri	PROPN
ejpam-7142	78	25	)	)	PUNCT
ejpam-7142	78	26	...	...	PUNCT
ejpam-7142	79	1	≤	≤	NUM
ejpam-7142	79	2	r⌈log3	r⌈log3	NOUN
ejpam-7142	79	3	n⌉	n⌉	NOUN
ejpam-7142	79	4	·	·	PUNCT
ejpam-7142	80	1	3⌈log3	3⌈log3	NUM
ejpam-7142	80	2	n⌉	n⌉	NOUN
ejpam-7142	80	3	·	·	PUNCT
ejpam-7142	80	4	δ	δ	X
ejpam-7142	80	5	·	·	PUNCT
ejpam-7142	80	6	diameter(g	diameter(g	PROPN
ejpam-7142	80	7	)	)	PUNCT
ejpam-7142	80	8	since	since	SCONJ
ejpam-7142	80	9	3⌈log3	3⌈log3	NUM
ejpam-7142	80	10	n⌉	n⌉	PUNCT
ejpam-7142	80	11	≤	≤	NOUN
ejpam-7142	80	12	3n	3n	NUM
ejpam-7142	80	13	,	,	PUNCT
ejpam-7142	80	14	we	we	PRON
ejpam-7142	80	15	obtain	obtain	VERB
ejpam-7142	80	16	the	the	DET
ejpam-7142	80	17	stated	state	VERB
ejpam-7142	80	18	bound	bind	VERB
ejpam-7142	80	19	.	.	PUNCT
ejpam-7142	81	1	lemma	lemma	PROPN
ejpam-7142	81	2	2	2	NUM
ejpam-7142	81	3	(	(	PUNCT
ejpam-7142	81	4	small	small	ADJ
ejpam-7142	81	5	contraction	contraction	NOUN
ejpam-7142	81	6	implies	imply	VERB
ejpam-7142	81	7	good	good	ADJ
ejpam-7142	81	8	expansion	expansion	NOUN
ejpam-7142	81	9	)	)	PUNCT
ejpam-7142	81	10	.	.	PUNCT
ejpam-7142	82	1	if	if	SCONJ
ejpam-7142	82	2	r	r	NOUN
ejpam-7142	82	3	<	<	X
ejpam-7142	82	4	1	1	NUM
ejpam-7142	82	5	+	+	CCONJ
ejpam-7142	82	6	c	c	AUX
ejpam-7142	82	7	logn	logn	NOUN
ejpam-7142	82	8	for	for	ADP
ejpam-7142	82	9	some	some	DET
ejpam-7142	82	10	constant	constant	ADJ
ejpam-7142	82	11	c	c	NOUN
ejpam-7142	82	12	>	>	X
ejpam-7142	82	13	0	0	NUM
ejpam-7142	82	14	,	,	PUNCT
ejpam-7142	82	15	then	then	ADV
ejpam-7142	82	16	:	:	PUNCT
ejpam-7142	82	17	η(g	η(g	NUM
ejpam-7142	82	18	)	)	PUNCT
ejpam-7142	82	19	≥	≥	NOUN
ejpam-7142	82	20	1	1	NUM
ejpam-7142	82	21	2r2	2r2	NUM
ejpam-7142	82	22	proof	proof	NOUN
ejpam-7142	82	23	.	.	PUNCT
ejpam-7142	83	1	suppose	suppose	VERB
ejpam-7142	83	2	for	for	ADP
ejpam-7142	83	3	contradiction	contradiction	NOUN
ejpam-7142	83	4	that	that	PRON
ejpam-7142	83	5	η(g	η(g	PROPN
ejpam-7142	83	6	)	)	PUNCT
ejpam-7142	83	7	<	<	X
ejpam-7142	83	8	1	1	NUM
ejpam-7142	83	9	2r2	2r2	NUM
ejpam-7142	83	10	.	.	PUNCT
ejpam-7142	84	1	then	then	ADV
ejpam-7142	84	2	there	there	PRON
ejpam-7142	84	3	exists	exist	VERB
ejpam-7142	84	4	s	s	PROPN
ejpam-7142	84	5	⊂	⊂	PROPN
ejpam-7142	84	6	v	v	NOUN
ejpam-7142	84	7	with	with	ADP
ejpam-7142	84	8	|s|	|s|	NOUN
ejpam-7142	84	9	≤	≤	NOUN
ejpam-7142	84	10	n/2	n/2	NOUN
ejpam-7142	84	11	and	and	CCONJ
ejpam-7142	84	12	|∂s|	|∂s|	NOUN
ejpam-7142	84	13	<	<	X
ejpam-7142	84	14	|s|	|s|	NOUN
ejpam-7142	84	15	2r2	2r2	NUM
ejpam-7142	84	16	.	.	PUNCT
ejpam-7142	85	1	consider	consider	VERB
ejpam-7142	85	2	vertices	vertice	VERB
ejpam-7142	85	3	u	u	PROPN
ejpam-7142	85	4	∈	∈	PROPN
ejpam-7142	85	5	s	s	NOUN
ejpam-7142	85	6	,	,	PUNCT
ejpam-7142	85	7	v	v	PROPN
ejpam-7142	85	8	∈	∈	PROPN
ejpam-7142	85	9	v	v	ADP
ejpam-7142	85	10	\	\	NOUN
ejpam-7142	85	11	s.	s.	PROPN
ejpam-7142	86	1	the	the	DET
ejpam-7142	86	2	contraction	contraction	NOUN
ejpam-7142	86	3	property	property	NOUN
ejpam-7142	86	4	gives	give	VERB
ejpam-7142	86	5	:	:	PUNCT
ejpam-7142	86	6	m(u	m(u	PROPN
ejpam-7142	86	7	,	,	PUNCT
ejpam-7142	86	8	v	v	NOUN
ejpam-7142	86	9	,	,	PUNCT
ejpam-7142	86	10	w	w	NOUN
ejpam-7142	86	11	)	)	PUNCT
ejpam-7142	86	12	≤	≤	NOUN
ejpam-7142	86	13	r[m(u	r[m(u	NOUN
ejpam-7142	86	14	,	,	PUNCT
ejpam-7142	86	15	v	v	NOUN
ejpam-7142	86	16	,	,	PUNCT
ejpam-7142	86	17	ℓ	ℓ	NOUN
ejpam-7142	86	18	)	)	PUNCT
ejpam-7142	87	1	+	+	NOUN
ejpam-7142	87	2	m(u	m(u	PROPN
ejpam-7142	87	3	,	,	PUNCT
ejpam-7142	87	4	ℓ	ℓ	NOUN
ejpam-7142	87	5	,	,	PUNCT
ejpam-7142	87	6	w	w	NOUN
ejpam-7142	87	7	)	)	PUNCT
ejpam-7142	87	8	+	+	NOUN
ejpam-7142	87	9	m(ℓ	m(ℓ	NOUN
ejpam-7142	87	10	,	,	PUNCT
ejpam-7142	87	11	v	v	NOUN
ejpam-7142	87	12	,	,	PUNCT
ejpam-7142	87	13	w	w	NOUN
ejpam-7142	87	14	)	)	PUNCT
ejpam-7142	87	15	]	]	PUNCT
ejpam-7142	87	16	for	for	ADP
ejpam-7142	87	17	the	the	DET
ejpam-7142	87	18	cut	cut	NOUN
ejpam-7142	87	19	(	(	PUNCT
ejpam-7142	87	20	s	s	PROPN
ejpam-7142	87	21	,	,	PUNCT
ejpam-7142	87	22	v	v	ADJ
ejpam-7142	87	23	\	\	PROPN
ejpam-7142	87	24	s	s	NOUN
ejpam-7142	87	25	)	)	PUNCT
ejpam-7142	87	26	,	,	PUNCT
ejpam-7142	87	27	the	the	DET
ejpam-7142	87	28	limited	limited	ADJ
ejpam-7142	87	29	boundary	boundary	ADJ
ejpam-7142	87	30	forces	force	NOUN
ejpam-7142	87	31	some	some	DET
ejpam-7142	87	32	terms	term	NOUN
ejpam-7142	87	33	to	to	PART
ejpam-7142	87	34	be	be	AUX
ejpam-7142	87	35	large	large	ADJ
ejpam-7142	87	36	,	,	PUNCT
ejpam-7142	87	37	contradicting	contradict	VERB
ejpam-7142	87	38	small	small	ADJ
ejpam-7142	87	39	r.	r.	PROPN
ejpam-7142	87	40	specifically	specifically	ADV
ejpam-7142	87	41	,	,	PUNCT
ejpam-7142	87	42	the	the	DET
ejpam-7142	87	43	average	average	ADJ
ejpam-7142	87	44	path	path	NOUN
ejpam-7142	87	45	length	length	NOUN
ejpam-7142	87	46	across	across	ADP
ejpam-7142	87	47	the	the	DET
ejpam-7142	87	48	cut	cut	NOUN
ejpam-7142	87	49	must	must	AUX
ejpam-7142	87	50	satisfy	satisfy	VERB
ejpam-7142	87	51	:	:	PUNCT
ejpam-7142	88	1	e[d(u	e[d(u	NUM
ejpam-7142	88	2	,	,	PUNCT
ejpam-7142	88	3	v	v	NOUN
ejpam-7142	88	4	)	)	PUNCT
ejpam-7142	88	5	]	]	PUNCT
ejpam-7142	88	6	≥	≥	X
ejpam-7142	88	7	|s|	|s|	PROPN
ejpam-7142	88	8	·	·	PUNCT
ejpam-7142	88	9	|v	|v	PROPN
ejpam-7142	88	10	\	\	PROPN
ejpam-7142	88	11	s|	s|	PROPN
ejpam-7142	88	12	|∂s|	|∂s|	NOUN
ejpam-7142	88	13	≥	≥	NOUN
ejpam-7142	88	14	2r2	2r2	NUM
ejpam-7142	88	15	but	but	CCONJ
ejpam-7142	88	16	from	from	ADP
ejpam-7142	88	17	lemma	lemma	PROPN
ejpam-7142	88	18	1	1	NUM
ejpam-7142	88	19	,	,	PUNCT
ejpam-7142	88	20	small	small	ADJ
ejpam-7142	88	21	r	r	NOUN
ejpam-7142	88	22	implies	imply	VERB
ejpam-7142	88	23	small	small	ADJ
ejpam-7142	88	24	average	average	ADJ
ejpam-7142	88	25	path	path	NOUN
ejpam-7142	88	26	length	length	NOUN
ejpam-7142	88	27	.	.	PUNCT
ejpam-7142	89	1	lemma	lemma	PROPN
ejpam-7142	89	2	3	3	NUM
ejpam-7142	89	3	(	(	PUNCT
ejpam-7142	89	4	robust	robust	ADJ
ejpam-7142	89	5	connectivity	connectivity	NOUN
ejpam-7142	89	6	under	under	ADP
ejpam-7142	89	7	attacks	attack	NOUN
ejpam-7142	89	8	)	)	PUNCT
ejpam-7142	89	9	.	.	PUNCT
ejpam-7142	90	1	let	let	VERB
ejpam-7142	90	2	a	a	DET
ejpam-7142	90	3	⊂	⊂	PROPN
ejpam-7142	90	4	v	v	NOUN
ejpam-7142	90	5	with	with	ADP
ejpam-7142	90	6	|a|	|a|	PROPN
ejpam-7142	90	7	=	=	PROPN
ejpam-7142	90	8	k.	k.	NOUN
ejpam-7142	90	9	if	if	SCONJ
ejpam-7142	90	10	r	r	NOUN
ejpam-7142	90	11	<	<	X
ejpam-7142	90	12	1	1	NUM
ejpam-7142	90	13	+	+	SYM
ejpam-7142	90	14	1	1	NUM
ejpam-7142	90	15	logn	logn	NOUN
ejpam-7142	90	16	and	and	CCONJ
ejpam-7142	90	17	k	k	X
ejpam-7142	90	18	<	<	X
ejpam-7142	90	19	n	n	PROPN
ejpam-7142	90	20	4r4	4r4	NUM
ejpam-7142	90	21	,	,	PUNCT
ejpam-7142	91	1	then	then	ADV
ejpam-7142	91	2	the	the	DET
ejpam-7142	91	3	graph	graph	NOUN
ejpam-7142	91	4	g′	g′	NOUN
ejpam-7142	91	5	=	=	SYM
ejpam-7142	91	6	g	g	PROPN
ejpam-7142	91	7	\a	\a	ADJ
ejpam-7142	91	8	remains	remain	VERB
ejpam-7142	91	9	connected	connected	ADJ
ejpam-7142	91	10	and	and	CCONJ
ejpam-7142	91	11	:	:	PUNCT
ejpam-7142	91	12	diameter(g′	diameter(g′	X
ejpam-7142	91	13	)	)	PUNCT
ejpam-7142	91	14	≤	≤	NOUN
ejpam-7142	91	15	2r4	2r4	NUM
ejpam-7142	91	16	·	·	PUNCT
ejpam-7142	91	17	diameter(g	diameter(g	X
ejpam-7142	91	18	)	)	PUNCT
ejpam-7142	91	19	proof	proof	NOUN
ejpam-7142	91	20	.	.	PUNCT
ejpam-7142	92	1	from	from	ADP
ejpam-7142	92	2	lemma	lemma	PROPN
ejpam-7142	92	3	2	2	NUM
ejpam-7142	92	4	,	,	PUNCT
ejpam-7142	92	5	the	the	DET
ejpam-7142	92	6	original	original	ADJ
ejpam-7142	92	7	graph	graph	NOUN
ejpam-7142	92	8	has	have	VERB
ejpam-7142	92	9	expansion	expansion	NOUN
ejpam-7142	92	10	η(g	η(g	PROPN
ejpam-7142	92	11	)	)	PUNCT
ejpam-7142	92	12	≥	≥	NOUN
ejpam-7142	92	13	1	1	NUM
ejpam-7142	92	14	2r2	2r2	NUM
ejpam-7142	92	15	.	.	PUNCT
ejpam-7142	93	1	after	after	ADP
ejpam-7142	93	2	removing	remove	VERB
ejpam-7142	93	3	k	k	PROPN
ejpam-7142	93	4	vertices	vertex	NOUN
ejpam-7142	93	5	,	,	PUNCT
ejpam-7142	93	6	the	the	DET
ejpam-7142	93	7	minimum	minimum	NOUN
ejpam-7142	93	8	degree	degree	NOUN
ejpam-7142	93	9	in	in	ADP
ejpam-7142	93	10	g′	g′	NOUN
ejpam-7142	93	11	satisfies	satisfie	NOUN
ejpam-7142	93	12	:	:	PUNCT
ejpam-7142	93	13	δ(g′	δ(g′	NUM
ejpam-7142	93	14	)	)	PUNCT
ejpam-7142	93	15	≥	≥	NOUN
ejpam-7142	93	16	η(g	η(g	PROPN
ejpam-7142	93	17	)	)	PUNCT
ejpam-7142	93	18	·	·	PUNCT
ejpam-7142	94	1	(	(	PUNCT
ejpam-7142	94	2	n−	n−	NOUN
ejpam-7142	94	3	k)−	k)−	PROPN
ejpam-7142	94	4	k	k	PROPN
ejpam-7142	94	5	≥	≥	NUM
ejpam-7142	94	6	n−	n−	NOUN
ejpam-7142	94	7	k	k	NOUN
ejpam-7142	94	8	2r2	2r2	NUM
ejpam-7142	94	9	−	−	PROPN
ejpam-7142	95	1	k	k	NOUN
ejpam-7142	95	2	with	with	ADP
ejpam-7142	95	3	k	k	PROPN
ejpam-7142	95	4	<	<	X
ejpam-7142	95	5	n	n	PROPN
ejpam-7142	95	6	4r4	4r4	NUM
ejpam-7142	95	7	,	,	PUNCT
ejpam-7142	95	8	we	we	PRON
ejpam-7142	95	9	have	have	VERB
ejpam-7142	95	10	δ(g′	δ(g′	NOUN
ejpam-7142	95	11	)	)	PUNCT
ejpam-7142	95	12	≥	≥	PROPN
ejpam-7142	96	1	n	n	PROPN
ejpam-7142	96	2	4r4	4r4	NUM
ejpam-7142	96	3	>	>	X
ejpam-7142	96	4	0	0	NUM
ejpam-7142	96	5	,	,	PUNCT
ejpam-7142	96	6	so	so	SCONJ
ejpam-7142	96	7	g′	g′	NOUN
ejpam-7142	96	8	remains	remain	VERB
ejpam-7142	96	9	connected	connect	VERB
ejpam-7142	96	10	.	.	PUNCT
ejpam-7142	97	1	for	for	SCONJ
ejpam-7142	97	2	the	the	DET
ejpam-7142	97	3	diameter	diameter	NOUN
ejpam-7142	97	4	bound	bind	VERB
ejpam-7142	97	5	,	,	PUNCT
ejpam-7142	97	6	consider	consider	VERB
ejpam-7142	97	7	any	any	DET
ejpam-7142	97	8	u	u	NOUN
ejpam-7142	97	9	,	,	PUNCT
ejpam-7142	97	10	v	v	NOUN
ejpam-7142	97	11	∈	∈	NOUN
ejpam-7142	97	12	g′.	g′.	NOUN
ejpam-7142	97	13	in	in	ADP
ejpam-7142	97	14	g	g	NOUN
ejpam-7142	97	15	,	,	PUNCT
ejpam-7142	97	16	there	there	PRON
ejpam-7142	97	17	was	be	VERB
ejpam-7142	97	18	a	a	DET
ejpam-7142	97	19	path	path	NOUN
ejpam-7142	97	20	of	of	ADP
ejpam-7142	97	21	length	length	NOUN
ejpam-7142	97	22	≤	≤	NUM
ejpam-7142	97	23	diameter(g	diameter(g	PROPN
ejpam-7142	97	24	)	)	PUNCT
ejpam-7142	97	25	.	.	PUNCT
ejpam-7142	98	1	in	in	ADP
ejpam-7142	98	2	g′	g′	PROPN
ejpam-7142	98	3	,	,	PUNCT
ejpam-7142	98	4	we	we	PRON
ejpam-7142	98	5	may	may	AUX
ejpam-7142	98	6	need	need	VERB
ejpam-7142	98	7	to	to	PART
ejpam-7142	98	8	detour	detour	VERB
ejpam-7142	98	9	around	around	ADP
ejpam-7142	98	10	removed	removed	ADJ
ejpam-7142	98	11	vertices	vertex	NOUN
ejpam-7142	98	12	,	,	PUNCT
ejpam-7142	98	13	but	but	CCONJ
ejpam-7142	98	14	the	the	DET
ejpam-7142	98	15	expansion	expansion	NOUN
ejpam-7142	98	16	property	property	NOUN
ejpam-7142	98	17	ensures	ensure	VERB
ejpam-7142	98	18	detours	detour	NOUN
ejpam-7142	98	19	increase	increase	VERB
ejpam-7142	98	20	length	length	NOUN
ejpam-7142	98	21	by	by	ADP
ejpam-7142	98	22	at	at	ADP
ejpam-7142	98	23	most	most	ADJ
ejpam-7142	98	24	factor	factor	NOUN
ejpam-7142	98	25	2r4	2r4	NUM
ejpam-7142	98	26	.	.	PUNCT
ejpam-7142	99	1	e.	e.	PROPN
ejpam-7142	99	2	hussein	hussein	PROPN
ejpam-7142	99	3	et	et	PROPN
ejpam-7142	99	4	al	al	PROPN
ejpam-7142	99	5	.	.	PUNCT
ejpam-7142	99	6	/	/	SYM
ejpam-7142	99	7	eur	eur	PROPN
ejpam-7142	99	8	.	.	PUNCT
ejpam-7142	100	1	j.	j.	PROPN
ejpam-7142	100	2	pure	pure	PROPN
ejpam-7142	100	3	appl	appl	PROPN
ejpam-7142	100	4	.	.	PROPN
ejpam-7142	100	5	math	math	PROPN
ejpam-7142	100	6	,	,	PUNCT
ejpam-7142	100	7	18	18	NUM
ejpam-7142	100	8	(	(	PUNCT
ejpam-7142	100	9	4	4	NUM
ejpam-7142	100	10	)	)	PUNCT
ejpam-7142	100	11	(	(	PUNCT
ejpam-7142	100	12	2025	2025	NUM
ejpam-7142	100	13	)	)	PUNCT
ejpam-7142	100	14	,	,	PUNCT
ejpam-7142	100	15	7142	7142	NUM
ejpam-7142	100	16	5	5	NUM
ejpam-7142	100	17	of	of	ADP
ejpam-7142	100	18	17	17	NUM
ejpam-7142	100	19	definition	definition	NOUN
ejpam-7142	100	20	5	5	NUM
ejpam-7142	100	21	(	(	PUNCT
ejpam-7142	100	22	neutrosophic	neutrosophic	ADJ
ejpam-7142	100	23	centrality	centrality	NOUN
ejpam-7142	100	24	mapping	mapping	NOUN
ejpam-7142	100	25	)	)	PUNCT
ejpam-7142	100	26	.	.	PUNCT
ejpam-7142	101	1	the	the	DET
ejpam-7142	101	2	neutrosophic	neutrosophic	ADJ
ejpam-7142	101	3	centrality	centrality	NOUN
ejpam-7142	101	4	mapping	mapping	NOUN
ejpam-7142	101	5	f	f	NOUN
ejpam-7142	101	6	:	:	PUNCT
ejpam-7142	101	7	v	v	X
ejpam-7142	101	8	→	→	SYM
ejpam-7142	101	9	v	v	NOUN
ejpam-7142	101	10	is	be	AUX
ejpam-7142	101	11	defined	define	VERB
ejpam-7142	101	12	by	by	ADP
ejpam-7142	101	13	:	:	PUNCT
ejpam-7142	101	14	f(v	f(v	NOUN
ejpam-7142	101	15	)	)	PUNCT
ejpam-7142	102	1	=	=	SYM
ejpam-7142	102	2	argmin	argmin	NOUN
ejpam-7142	102	3	u∈v	u∈v	NOUN
ejpam-7142	102	4	max	max	PROPN
ejpam-7142	102	5	w∈v	w∈v	PROPN
ejpam-7142	103	1	[	[	X
ejpam-7142	103	2	m(u	m(u	PROPN
ejpam-7142	103	3	,	,	PUNCT
ejpam-7142	103	4	v	v	NOUN
ejpam-7142	103	5	,	,	PUNCT
ejpam-7142	103	6	w	w	NOUN
ejpam-7142	103	7	)	)	PUNCT
ejpam-7142	103	8	⋆	⋆	VERB
ejpam-7142	103	9	i(u	i(u	PROPN
ejpam-7142	103	10	,	,	PUNCT
ejpam-7142	103	11	v	v	PROPN
ejpam-7142	103	12	,	,	PUNCT
ejpam-7142	103	13	γ	γ	NOUN
ejpam-7142	103	14	)	)	PUNCT
ejpam-7142	103	15	]	]	PUNCT
ejpam-7142	103	16	where	where	SCONJ
ejpam-7142	103	17	⋆	⋆	NOUN
ejpam-7142	103	18	is	be	AUX
ejpam-7142	103	19	the	the	DET
ejpam-7142	103	20	generalized	generalized	ADJ
ejpam-7142	103	21	addition	addition	NOUN
ejpam-7142	103	22	operation	operation	NOUN
ejpam-7142	103	23	.	.	PUNCT
ejpam-7142	104	1	lemma	lemma	PROPN
ejpam-7142	104	2	4	4	NUM
ejpam-7142	104	3	(	(	PUNCT
ejpam-7142	104	4	contraction	contraction	NOUN
ejpam-7142	104	5	property	property	NOUN
ejpam-7142	104	6	of	of	ADP
ejpam-7142	104	7	centrality	centrality	NOUN
ejpam-7142	104	8	mapping	mapping	NOUN
ejpam-7142	104	9	)	)	PUNCT
ejpam-7142	104	10	.	.	PUNCT
ejpam-7142	105	1	the	the	DET
ejpam-7142	105	2	mapping	mapping	NOUN
ejpam-7142	105	3	f	f	X
ejpam-7142	105	4	is	be	AUX
ejpam-7142	105	5	a	a	DET
ejpam-7142	105	6	contraction	contraction	NOUN
ejpam-7142	105	7	on	on	ADP
ejpam-7142	105	8	the	the	DET
ejpam-7142	105	9	mr	mr	PROPN
ejpam-7142	105	10	-	-	PUNCT
ejpam-7142	105	11	metric	metric	ADJ
ejpam-7142	105	12	space	space	NOUN
ejpam-7142	105	13	:	:	PUNCT
ejpam-7142	105	14	m(f(v1	m(f(v1	PROPN
ejpam-7142	105	15	)	)	PUNCT
ejpam-7142	105	16	,	,	PUNCT
ejpam-7142	105	17	f(v2	f(v2	NOUN
ejpam-7142	105	18	)	)	PUNCT
ejpam-7142	105	19	,	,	PUNCT
ejpam-7142	105	20	w	w	X
ejpam-7142	105	21	)	)	PUNCT
ejpam-7142	105	22	≤	≤	NUM
ejpam-7142	105	23	λm(v1	λm(v1	NOUN
ejpam-7142	105	24	,	,	PUNCT
ejpam-7142	105	25	v2	v2	PROPN
ejpam-7142	105	26	,	,	PUNCT
ejpam-7142	105	27	w	w	NOUN
ejpam-7142	105	28	)	)	PUNCT
ejpam-7142	105	29	for	for	ADP
ejpam-7142	105	30	some	some	DET
ejpam-7142	105	31	λ	λ	NOUN
ejpam-7142	105	32	<	<	X
ejpam-7142	105	33	1	1	NUM
ejpam-7142	105	34	depending	depend	VERB
ejpam-7142	105	35	on	on	ADP
ejpam-7142	105	36	r	r	NOUN
ejpam-7142	105	37	and	and	CCONJ
ejpam-7142	105	38	the	the	DET
ejpam-7142	105	39	graph	graph	NOUN
ejpam-7142	105	40	structure	structure	NOUN
ejpam-7142	105	41	.	.	PUNCT
ejpam-7142	106	1	proof	proof	NOUN
ejpam-7142	106	2	.	.	PUNCT
ejpam-7142	107	1	let	let	VERB
ejpam-7142	107	2	u1	u1	NOUN
ejpam-7142	107	3	=	=	SYM
ejpam-7142	107	4	f(v1	f(v1	NOUN
ejpam-7142	107	5	)	)	PUNCT
ejpam-7142	107	6	,	,	PUNCT
ejpam-7142	107	7	u2	u2	NOUN
ejpam-7142	107	8	=	=	PUNCT
ejpam-7142	107	9	f(v2	f(v2	NOUN
ejpam-7142	107	10	)	)	PUNCT
ejpam-7142	107	11	.	.	PUNCT
ejpam-7142	108	1	by	by	ADP
ejpam-7142	108	2	definition	definition	NOUN
ejpam-7142	108	3	:	:	PUNCT
ejpam-7142	108	4	max	max	PROPN
ejpam-7142	108	5	w	w	PROPN
ejpam-7142	108	6	m(u1	m(u1	NOUN
ejpam-7142	108	7	,	,	PUNCT
ejpam-7142	108	8	v1	v1	NOUN
ejpam-7142	108	9	,	,	PUNCT
ejpam-7142	108	10	w	w	NOUN
ejpam-7142	108	11	)	)	PUNCT
ejpam-7142	108	12	⋆	⋆	NOUN
ejpam-7142	108	13	i(u1	i(u1	NOUN
ejpam-7142	108	14	,	,	PUNCT
ejpam-7142	108	15	v1	v1	NOUN
ejpam-7142	108	16	,	,	PUNCT
ejpam-7142	108	17	γ	γ	NOUN
ejpam-7142	108	18	)	)	PUNCT
ejpam-7142	108	19	≤	≤	NOUN
ejpam-7142	108	20	max	max	PROPN
ejpam-7142	108	21	w	w	PROPN
ejpam-7142	108	22	m(u2	m(u2	PROPN
ejpam-7142	108	23	,	,	PUNCT
ejpam-7142	108	24	v1	v1	PROPN
ejpam-7142	108	25	,	,	PUNCT
ejpam-7142	108	26	w	w	NOUN
ejpam-7142	108	27	)	)	PUNCT
ejpam-7142	108	28	⋆	⋆	NOUN
ejpam-7142	108	29	i(u2	i(u2	PROPN
ejpam-7142	108	30	,	,	PUNCT
ejpam-7142	108	31	v1	v1	PROPN
ejpam-7142	108	32	,	,	PUNCT
ejpam-7142	108	33	γ	γ	NOUN
ejpam-7142	108	34	)	)	PUNCT
ejpam-7142	108	35	max	max	PROPN
ejpam-7142	108	36	w	w	PROPN
ejpam-7142	108	37	m(u2	m(u2	PROPN
ejpam-7142	108	38	,	,	PUNCT
ejpam-7142	108	39	v2	v2	PROPN
ejpam-7142	108	40	,	,	PUNCT
ejpam-7142	108	41	w	w	NOUN
ejpam-7142	108	42	)	)	PUNCT
ejpam-7142	108	43	⋆	⋆	NOUN
ejpam-7142	108	44	i(u2	i(u2	NOUN
ejpam-7142	108	45	,	,	PUNCT
ejpam-7142	108	46	v2	v2	PROPN
ejpam-7142	108	47	,	,	PUNCT
ejpam-7142	108	48	γ	γ	NOUN
ejpam-7142	108	49	)	)	PUNCT
ejpam-7142	108	50	≤	≤	NOUN
ejpam-7142	108	51	max	max	PROPN
ejpam-7142	108	52	w	w	PROPN
ejpam-7142	108	53	m(u1	m(u1	NOUN
ejpam-7142	108	54	,	,	PUNCT
ejpam-7142	108	55	v2	v2	PROPN
ejpam-7142	108	56	,	,	PUNCT
ejpam-7142	108	57	w	w	NOUN
ejpam-7142	108	58	)	)	PUNCT
ejpam-7142	108	59	⋆	⋆	NOUN
ejpam-7142	108	60	i(u1	i(u1	NOUN
ejpam-7142	108	61	,	,	PUNCT
ejpam-7142	108	62	v2	v2	PROPN
ejpam-7142	108	63	,	,	PUNCT
ejpam-7142	108	64	γ	γ	NOUN
ejpam-7142	108	65	)	)	PUNCT
ejpam-7142	108	66	using	use	VERB
ejpam-7142	108	67	the	the	DET
ejpam-7142	108	68	mr	mr	PROPN
ejpam-7142	108	69	-	-	PUNCT
ejpam-7142	108	70	metric	metric	ADJ
ejpam-7142	108	71	property	property	NOUN
ejpam-7142	108	72	and	and	CCONJ
ejpam-7142	108	73	the	the	DET
ejpam-7142	108	74	fact	fact	NOUN
ejpam-7142	108	75	that	that	SCONJ
ejpam-7142	108	76	i	i	PRON
ejpam-7142	108	77	captures	capture	VERB
ejpam-7142	108	78	betweenness	betweenness	ADJ
ejpam-7142	108	79	differences	difference	NOUN
ejpam-7142	108	80	,	,	PUNCT
ejpam-7142	108	81	we	we	PRON
ejpam-7142	108	82	can	can	AUX
ejpam-7142	108	83	derive	derive	VERB
ejpam-7142	108	84	:	:	PUNCT
ejpam-7142	108	85	m(u1	m(u1	NOUN
ejpam-7142	108	86	,	,	PUNCT
ejpam-7142	108	87	u2	u2	PROPN
ejpam-7142	108	88	,	,	PUNCT
ejpam-7142	108	89	w	w	NOUN
ejpam-7142	108	90	)	)	PUNCT
ejpam-7142	108	91	≤	≤	NUM
ejpam-7142	108	92	r2	r2	NOUN
ejpam-7142	108	93	·	·	PUNCT
ejpam-7142	108	94	maxbetweenness−minbetweenness	maxbetweenness−minbetweenness	ADP
ejpam-7142	108	95	maxbetweenness	maxbetweenness	NOUN
ejpam-7142	108	96	·	·	SYM
ejpam-7142	108	97	m(v1	m(v1	NOUN
ejpam-7142	108	98	,	,	PUNCT
ejpam-7142	108	99	v2	v2	PROPN
ejpam-7142	108	100	,	,	PUNCT
ejpam-7142	108	101	w	w	NOUN
ejpam-7142	108	102	)	)	PUNCT
ejpam-7142	108	103	the	the	DET
ejpam-7142	108	104	coefficient	coefficient	NOUN
ejpam-7142	108	105	λ	λ	NOUN
ejpam-7142	108	106	=	=	VERB
ejpam-7142	108	107	r2	r2	PROPN
ejpam-7142	108	108	·	·	PUNCT
ejpam-7142	108	109	(	(	PUNCT
ejpam-7142	108	110	1−	1−	NUM
ejpam-7142	108	111	minbetweenness	minbetweenness	PROPN
ejpam-7142	108	112	maxbetweenness	maxbetweenness	NOUN
ejpam-7142	108	113	)	)	PUNCT
ejpam-7142	108	114	<	<	X
ejpam-7142	108	115	1	1	NUM
ejpam-7142	108	116	for	for	ADP
ejpam-7142	108	117	connected	connected	ADJ
ejpam-7142	108	118	non	non	ADJ
ejpam-7142	108	119	-	-	ADJ
ejpam-7142	108	120	complete	complete	ADJ
ejpam-7142	108	121	graphs	graph	NOUN
ejpam-7142	108	122	.	.	PUNCT
ejpam-7142	109	1	theorem	theorem	ADJ
ejpam-7142	109	2	1	1	NUM
ejpam-7142	109	3	(	(	PUNCT
ejpam-7142	109	4	robustness	robustness	NOUN
ejpam-7142	109	5	of	of	ADP
ejpam-7142	109	6	complex	complex	ADJ
ejpam-7142	109	7	networks	network	NOUN
ejpam-7142	109	8	in	in	ADP
ejpam-7142	109	9	neutrosophic	neutrosophic	ADJ
ejpam-7142	109	10	mr	mr	PROPN
ejpam-7142	109	11	-	-	PUNCT
ejpam-7142	109	12	metric	metric	ADJ
ejpam-7142	109	13	spaces	space	NOUN
ejpam-7142	109	14	)	)	PUNCT
ejpam-7142	109	15	.	.	PUNCT
ejpam-7142	110	1	in	in	ADP
ejpam-7142	110	2	a	a	DET
ejpam-7142	110	3	neutrosophic	neutrosophic	ADJ
ejpam-7142	110	4	graph	graph	NOUN
ejpam-7142	110	5	mr	mr	PROPN
ejpam-7142	110	6	-	-	ADJ
ejpam-7142	110	7	metric	metric	ADJ
ejpam-7142	110	8	space	space	NOUN
ejpam-7142	110	9	with	with	ADP
ejpam-7142	110	10	contraction	contraction	NOUN
ejpam-7142	110	11	constant	constant	ADJ
ejpam-7142	110	12	r	r	NOUN
ejpam-7142	110	13	<	<	X
ejpam-7142	110	14	1	1	NUM
ejpam-7142	110	15	+	+	SYM
ejpam-7142	110	16	1	1	NUM
ejpam-7142	110	17	logn	logn	NOUN
ejpam-7142	110	18	:	:	PUNCT
ejpam-7142	110	19	(	(	PUNCT
ejpam-7142	110	20	i	i	NOUN
ejpam-7142	110	21	)	)	PUNCT
ejpam-7142	110	22	small	small	ADJ
ejpam-7142	110	23	-	-	PUNCT
ejpam-7142	110	24	world	world	NOUN
ejpam-7142	110	25	property	property	NOUN
ejpam-7142	110	26	:	:	PUNCT
ejpam-7142	110	27	the	the	DET
ejpam-7142	110	28	average	average	ADJ
ejpam-7142	110	29	shortest	short	ADJ
ejpam-7142	110	30	path	path	NOUN
ejpam-7142	110	31	length	length	NOUN
ejpam-7142	110	32	satisfies	satisfy	VERB
ejpam-7142	110	33	l(g	l(g	NOUN
ejpam-7142	110	34	)	)	PUNCT
ejpam-7142	111	1	=	=	SYM
ejpam-7142	111	2	o(logn	o(logn	PROPN
ejpam-7142	111	3	)	)	PUNCT
ejpam-7142	111	4	(	(	PUNCT
ejpam-7142	111	5	ii	ii	NOUN
ejpam-7142	111	6	)	)	PUNCT
ejpam-7142	111	7	robustness	robustness	NOUN
ejpam-7142	111	8	to	to	ADP
ejpam-7142	111	9	targeted	target	VERB
ejpam-7142	111	10	attacks	attack	NOUN
ejpam-7142	111	11	:	:	PUNCT
ejpam-7142	111	12	after	after	ADP
ejpam-7142	111	13	removal	removal	NOUN
ejpam-7142	111	14	of	of	ADP
ejpam-7142	111	15	any	any	DET
ejpam-7142	111	16	k	k	NOUN
ejpam-7142	111	17	<	<	X
ejpam-7142	111	18	n	n	PRON
ejpam-7142	111	19	4r4	4r4	NUM
ejpam-7142	111	20	high	high	ADJ
ejpam-7142	111	21	-	-	PUNCT
ejpam-7142	111	22	centrality	centrality	NOUN
ejpam-7142	111	23	nodes	node	NOUN
ejpam-7142	111	24	,	,	PUNCT
ejpam-7142	111	25	the	the	DET
ejpam-7142	111	26	network	network	NOUN
ejpam-7142	111	27	remains	remain	VERB
ejpam-7142	111	28	connected	connect	VERB
ejpam-7142	111	29	with	with	ADP
ejpam-7142	111	30	diameter	diameter	NOUN
ejpam-7142	111	31	o(logn	o(logn	PROPN
ejpam-7142	111	32	)	)	PUNCT
ejpam-7142	111	33	(	(	PUNCT
ejpam-7142	111	34	iii	iii	X
ejpam-7142	111	35	)	)	PUNCT
ejpam-7142	111	36	central	central	ADJ
ejpam-7142	111	37	node	node	ADJ
ejpam-7142	111	38	identification	identification	NOUN
ejpam-7142	111	39	:	:	PUNCT
ejpam-7142	111	40	the	the	DET
ejpam-7142	111	41	fixed	fix	VERB
ejpam-7142	111	42	point	point	NOUN
ejpam-7142	111	43	v∗	v∗	PROPN
ejpam-7142	111	44	of	of	ADP
ejpam-7142	111	45	the	the	DET
ejpam-7142	111	46	neutrosophic	neutrosophic	ADJ
ejpam-7142	111	47	centrality	centrality	NOUN
ejpam-7142	111	48	mapping	mapping	NOUN
ejpam-7142	111	49	corresponds	correspond	VERB
ejpam-7142	111	50	to	to	ADP
ejpam-7142	111	51	the	the	DET
ejpam-7142	111	52	most	most	ADV
ejpam-7142	111	53	influential	influential	ADJ
ejpam-7142	111	54	node	node	NOUN
ejpam-7142	111	55	,	,	PUNCT
ejpam-7142	111	56	maximizing	maximize	VERB
ejpam-7142	111	57	:	:	PUNCT
ejpam-7142	111	58	cn	cn	PROPN
ejpam-7142	111	59	(	(	PUNCT
ejpam-7142	111	60	v	v	NOUN
ejpam-7142	111	61	)	)	PUNCT
ejpam-7142	111	62	=	=	VERB
ejpam-7142	112	1	lim	lim	PROPN
ejpam-7142	112	2	γ→∞	γ→∞	NUM
ejpam-7142	113	1	[	[	X
ejpam-7142	113	2	t	t	X
ejpam-7142	113	3	(	(	PUNCT
ejpam-7142	113	4	v∗	v∗	PROPN
ejpam-7142	113	5	,	,	PUNCT
ejpam-7142	113	6	v	v	NOUN
ejpam-7142	113	7	,	,	PUNCT
ejpam-7142	113	8	γ)−	γ)−	PROPN
ejpam-7142	113	9	i(v∗	i(v∗	PROPN
ejpam-7142	113	10	,	,	PUNCT
ejpam-7142	113	11	v	v	PROPN
ejpam-7142	113	12	,	,	PUNCT
ejpam-7142	113	13	γ	γ	NOUN
ejpam-7142	113	14	)	)	PUNCT
ejpam-7142	113	15	]	]	PUNCT
ejpam-7142	113	16	proof	proof	NOUN
ejpam-7142	113	17	.	.	PUNCT
ejpam-7142	114	1	part	part	NOUN
ejpam-7142	114	2	1	1	NUM
ejpam-7142	114	3	:	:	PUNCT
ejpam-7142	114	4	small	small	ADJ
ejpam-7142	114	5	-	-	PUNCT
ejpam-7142	114	6	world	world	NOUN
ejpam-7142	114	7	property	property	NOUN
ejpam-7142	114	8	from	from	ADP
ejpam-7142	114	9	lemma	lemma	PROPN
ejpam-7142	114	10	1	1	NUM
ejpam-7142	114	11	:	:	PUNCT
ejpam-7142	114	12	m(u	m(u	PROPN
ejpam-7142	114	13	,	,	PUNCT
ejpam-7142	114	14	v	v	NOUN
ejpam-7142	114	15	,	,	PUNCT
ejpam-7142	114	16	w	w	NOUN
ejpam-7142	114	17	)	)	PUNCT
ejpam-7142	114	18	≤	≤	NOUN
ejpam-7142	114	19	r⌈log3	r⌈log3	NOUN
ejpam-7142	114	20	n⌉	n⌉	NOUN
ejpam-7142	114	21	·	·	PUNCT
ejpam-7142	115	1	δ	δ	X
ejpam-7142	115	2	·	·	PUNCT
ejpam-7142	115	3	diameter(g	diameter(g	PROPN
ejpam-7142	115	4	)	)	PUNCT
ejpam-7142	115	5	since	since	SCONJ
ejpam-7142	115	6	r	r	NOUN
ejpam-7142	115	7	<	<	X
ejpam-7142	115	8	1	1	NUM
ejpam-7142	115	9	+	+	SYM
ejpam-7142	115	10	1	1	NUM
ejpam-7142	115	11	logn	logn	NOUN
ejpam-7142	115	12	,	,	PUNCT
ejpam-7142	115	13	we	we	PRON
ejpam-7142	115	14	have	have	VERB
ejpam-7142	115	15	:	:	PUNCT
ejpam-7142	115	16	r⌈log3	r⌈log3	VERB
ejpam-7142	115	17	n⌉	n⌉	NOUN
ejpam-7142	115	18	≤	≤	PROPN
ejpam-7142	115	19	e⌈log3	e⌈log3	VERB
ejpam-7142	115	20	n⌉	n⌉	X
ejpam-7142	115	21	·	·	PUNCT
ejpam-7142	115	22	1	1	NUM
ejpam-7142	115	23	logn	logn	NOUN
ejpam-7142	115	24	=	=	SYM
ejpam-7142	115	25	o(1	o(1	PROPN
ejpam-7142	115	26	)	)	PUNCT
ejpam-7142	115	27	also	also	ADV
ejpam-7142	115	28	,	,	PUNCT
ejpam-7142	115	29	from	from	ADP
ejpam-7142	115	30	lemma	lemma	PROPN
ejpam-7142	115	31	2	2	NUM
ejpam-7142	115	32	,	,	PUNCT
ejpam-7142	115	33	good	good	ADJ
ejpam-7142	115	34	expansion	expansion	NOUN
ejpam-7142	115	35	implies	imply	VERB
ejpam-7142	115	36	:	:	PUNCT
ejpam-7142	115	37	diameter(g	diameter(g	NUM
ejpam-7142	115	38	)	)	PUNCT
ejpam-7142	115	39	=	=	SYM
ejpam-7142	115	40	o(log	o(log	PROPN
ejpam-7142	115	41	n	n	CCONJ
ejpam-7142	115	42	)	)	PUNCT
ejpam-7142	115	43	therefore	therefore	ADV
ejpam-7142	115	44	:	:	PUNCT
ejpam-7142	115	45	e[m(u	e[m(u	NOUN
ejpam-7142	115	46	,	,	PUNCT
ejpam-7142	115	47	v	v	NOUN
ejpam-7142	115	48	,	,	PUNCT
ejpam-7142	115	49	w	w	NOUN
ejpam-7142	115	50	)	)	PUNCT
ejpam-7142	115	51	]	]	PUNCT
ejpam-7142	116	1	=	=	PUNCT
ejpam-7142	116	2	o(log	o(log	PROPN
ejpam-7142	116	3	n)⇒	n)⇒	PROPN
ejpam-7142	116	4	e[d(u	e[d(u	PROPN
ejpam-7142	116	5	,	,	PUNCT
ejpam-7142	116	6	v	v	NOUN
ejpam-7142	116	7	)	)	PUNCT
ejpam-7142	116	8	]	]	PUNCT
ejpam-7142	117	1	=	=	PUNCT
ejpam-7142	117	2	o(log	o(log	PROPN
ejpam-7142	117	3	n	n	CCONJ
ejpam-7142	117	4	)	)	PUNCT
ejpam-7142	117	5	part	part	NOUN
ejpam-7142	117	6	2	2	NUM
ejpam-7142	117	7	:	:	PUNCT
ejpam-7142	117	8	robustness	robustness	NOUN
ejpam-7142	117	9	to	to	ADP
ejpam-7142	117	10	targeted	target	VERB
ejpam-7142	117	11	attacks	attack	NOUN
ejpam-7142	117	12	e.	e.	PROPN
ejpam-7142	117	13	hussein	hussein	PROPN
ejpam-7142	117	14	et	et	PROPN
ejpam-7142	117	15	al	al	PROPN
ejpam-7142	117	16	.	.	PUNCT
ejpam-7142	117	17	/	/	SYM
ejpam-7142	117	18	eur	eur	PROPN
ejpam-7142	117	19	.	.	PUNCT
ejpam-7142	118	1	j.	j.	PROPN
ejpam-7142	118	2	pure	pure	PROPN
ejpam-7142	118	3	appl	appl	PROPN
ejpam-7142	118	4	.	.	PROPN
ejpam-7142	118	5	math	math	PROPN
ejpam-7142	118	6	,	,	PUNCT
ejpam-7142	118	7	18	18	NUM
ejpam-7142	118	8	(	(	PUNCT
ejpam-7142	118	9	4	4	NUM
ejpam-7142	118	10	)	)	PUNCT
ejpam-7142	118	11	(	(	PUNCT
ejpam-7142	118	12	2025	2025	NUM
ejpam-7142	118	13	)	)	PUNCT
ejpam-7142	118	14	,	,	PUNCT
ejpam-7142	118	15	7142	7142	NUM
ejpam-7142	118	16	6	6	NUM
ejpam-7142	118	17	of	of	ADP
ejpam-7142	118	18	17	17	NUM
ejpam-7142	118	19	direct	direct	ADJ
ejpam-7142	118	20	from	from	ADP
ejpam-7142	118	21	lemma	lemma	PROPN
ejpam-7142	118	22	3	3	NUM
ejpam-7142	118	23	.	.	PUNCT
ejpam-7142	119	1	the	the	DET
ejpam-7142	119	2	bound	bind	VERB
ejpam-7142	119	3	k	k	PROPN
ejpam-7142	119	4	<	<	X
ejpam-7142	119	5	n	n	X
ejpam-7142	119	6	4r4	4r4	NUM
ejpam-7142	119	7	allows	allow	VERB
ejpam-7142	119	8	removal	removal	NOUN
ejpam-7142	119	9	of	of	ADP
ejpam-7142	119	10	a	a	DET
ejpam-7142	119	11	constant	constant	ADJ
ejpam-7142	119	12	fraction	fraction	NOUN
ejpam-7142	119	13	of	of	ADP
ejpam-7142	119	14	nodes	node	NOUN
ejpam-7142	119	15	while	while	SCONJ
ejpam-7142	119	16	maintaining	maintain	VERB
ejpam-7142	119	17	connectivity	connectivity	NOUN
ejpam-7142	119	18	and	and	CCONJ
ejpam-7142	119	19	logarithmic	logarithmic	ADJ
ejpam-7142	119	20	diameter	diameter	NOUN
ejpam-7142	119	21	.	.	PUNCT
ejpam-7142	120	1	part	part	NOUN
ejpam-7142	120	2	3	3	NUM
ejpam-7142	120	3	:	:	PUNCT
ejpam-7142	120	4	central	central	ADJ
ejpam-7142	120	5	node	node	ADJ
ejpam-7142	120	6	identification	identification	NOUN
ejpam-7142	120	7	from	from	ADP
ejpam-7142	120	8	lemma	lemma	PROPN
ejpam-7142	120	9	4	4	NUM
ejpam-7142	120	10	,	,	PUNCT
ejpam-7142	120	11	f	f	PROPN
ejpam-7142	120	12	is	be	AUX
ejpam-7142	120	13	a	a	DET
ejpam-7142	120	14	contraction	contraction	NOUN
ejpam-7142	120	15	mapping	mapping	NOUN
ejpam-7142	120	16	.	.	PUNCT
ejpam-7142	121	1	by	by	ADP
ejpam-7142	121	2	the	the	DET
ejpam-7142	121	3	banach	banach	ADV
ejpam-7142	121	4	fixed	fix	VERB
ejpam-7142	121	5	-	-	PUNCT
ejpam-7142	121	6	point	point	NOUN
ejpam-7142	121	7	theorem	theorem	NOUN
ejpam-7142	121	8	in	in	ADP
ejpam-7142	121	9	complete	complete	ADJ
ejpam-7142	121	10	mr	mr	PROPN
ejpam-7142	121	11	-	-	PUNCT
ejpam-7142	121	12	metric	metric	ADJ
ejpam-7142	121	13	spaces	space	NOUN
ejpam-7142	121	14	,	,	PUNCT
ejpam-7142	121	15	f	f	PROPN
ejpam-7142	121	16	has	have	VERB
ejpam-7142	121	17	a	a	DET
ejpam-7142	121	18	unique	unique	ADJ
ejpam-7142	121	19	fixed	fix	VERB
ejpam-7142	121	20	point	point	NOUN
ejpam-7142	121	21	v∗.	v∗.	PROPN
ejpam-7142	121	22	at	at	ADP
ejpam-7142	121	23	the	the	DET
ejpam-7142	121	24	fixed	fixed	ADJ
ejpam-7142	121	25	point	point	NOUN
ejpam-7142	121	26	:	:	PUNCT
ejpam-7142	121	27	v∗	v∗	PROPN
ejpam-7142	121	28	=	=	SYM
ejpam-7142	121	29	f(v∗	f(v∗	NOUN
ejpam-7142	121	30	)	)	PUNCT
ejpam-7142	122	1	=	=	NOUN
ejpam-7142	122	2	argmin	argmin	NOUN
ejpam-7142	122	3	u∈v	u∈v	NOUN
ejpam-7142	122	4	max	max	PROPN
ejpam-7142	122	5	w∈v	w∈v	PROPN
ejpam-7142	123	1	[	[	X
ejpam-7142	123	2	m(u	m(u	PROPN
ejpam-7142	123	3	,	,	PUNCT
ejpam-7142	123	4	v∗	v∗	NOUN
ejpam-7142	123	5	,	,	PUNCT
ejpam-7142	123	6	w	w	NOUN
ejpam-7142	123	7	)	)	PUNCT
ejpam-7142	123	8	⋆	⋆	VERB
ejpam-7142	123	9	i(u	i(u	PROPN
ejpam-7142	123	10	,	,	PUNCT
ejpam-7142	123	11	v∗	v∗	PROPN
ejpam-7142	123	12	,	,	PUNCT
ejpam-7142	123	13	γ	γ	NOUN
ejpam-7142	123	14	)	)	PUNCT
ejpam-7142	123	15	]	]	PUNCT
ejpam-7142	124	1	this	this	PRON
ejpam-7142	124	2	minimizes	minimize	VERB
ejpam-7142	124	3	the	the	DET
ejpam-7142	124	4	maximum	maximum	ADJ
ejpam-7142	124	5	combined	combine	VERB
ejpam-7142	124	6	distance	distance	NOUN
ejpam-7142	124	7	and	and	CCONJ
ejpam-7142	124	8	indeterminacy	indeterminacy	NOUN
ejpam-7142	124	9	,	,	PUNCT
ejpam-7142	124	10	which	which	PRON
ejpam-7142	124	11	corresponds	correspond	VERB
ejpam-7142	124	12	to	to	ADP
ejpam-7142	124	13	maximizing	maximize	VERB
ejpam-7142	124	14	:	:	PUNCT
ejpam-7142	124	15	cn	cn	PROPN
ejpam-7142	124	16	(	(	PUNCT
ejpam-7142	124	17	v	v	NOUN
ejpam-7142	124	18	)	)	PUNCT
ejpam-7142	124	19	=	=	VERB
ejpam-7142	124	20	lim	lim	PROPN
ejpam-7142	124	21	γ→∞	γ→∞	NUM
ejpam-7142	125	1	[	[	X
ejpam-7142	125	2	t	t	X
ejpam-7142	125	3	(	(	PUNCT
ejpam-7142	125	4	v∗	v∗	PROPN
ejpam-7142	125	5	,	,	PUNCT
ejpam-7142	125	6	v	v	NOUN
ejpam-7142	125	7	,	,	PUNCT
ejpam-7142	125	8	γ)−	γ)−	PROPN
ejpam-7142	125	9	i(v∗	i(v∗	PROPN
ejpam-7142	125	10	,	,	PUNCT
ejpam-7142	125	11	v	v	PROPN
ejpam-7142	125	12	,	,	PUNCT
ejpam-7142	125	13	γ	γ	NOUN
ejpam-7142	125	14	)	)	PUNCT
ejpam-7142	125	15	]	]	PUNCT
ejpam-7142	125	16	the	the	DET
ejpam-7142	125	17	node	node	PROPN
ejpam-7142	125	18	v∗	v∗	PROPN
ejpam-7142	125	19	achieves	achieve	VERB
ejpam-7142	125	20	the	the	DET
ejpam-7142	125	21	optimal	optimal	ADJ
ejpam-7142	125	22	balance	balance	NOUN
ejpam-7142	125	23	of	of	ADP
ejpam-7142	125	24	high	high	ADJ
ejpam-7142	125	25	truth	truth	NOUN
ejpam-7142	125	26	-	-	PUNCT
ejpam-7142	125	27	membership	membership	NOUN
ejpam-7142	125	28	(	(	PUNCT
ejpam-7142	125	29	connectivity	connectivity	NOUN
ejpam-7142	125	30	)	)	PUNCT
ejpam-7142	125	31	and	and	CCONJ
ejpam-7142	125	32	low	low	ADJ
ejpam-7142	125	33	indeterminacy	indeterminacy	NOUN
ejpam-7142	125	34	(	(	PUNCT
ejpam-7142	125	35	consistent	consistent	ADJ
ejpam-7142	125	36	betweenness	betweenness	NOUN
ejpam-7142	125	37	)	)	PUNCT
ejpam-7142	125	38	with	with	ADP
ejpam-7142	125	39	all	all	DET
ejpam-7142	125	40	other	other	ADJ
ejpam-7142	125	41	nodes	node	NOUN
ejpam-7142	125	42	.	.	PUNCT
ejpam-7142	126	1	corollary	corollary	ADJ
ejpam-7142	126	2	1	1	NUM
ejpam-7142	126	3	(	(	PUNCT
ejpam-7142	126	4	network	network	NOUN
ejpam-7142	126	5	design	design	NOUN
ejpam-7142	126	6	implications	implication	NOUN
ejpam-7142	126	7	)	)	PUNCT
ejpam-7142	126	8	.	.	PUNCT
ejpam-7142	127	1	for	for	ADP
ejpam-7142	127	2	network	network	NOUN
ejpam-7142	127	3	design	design	NOUN
ejpam-7142	127	4	,	,	PUNCT
ejpam-7142	127	5	choosing	choose	VERB
ejpam-7142	127	6	topologies	topology	NOUN
ejpam-7142	127	7	with	with	ADP
ejpam-7142	127	8	small	small	ADJ
ejpam-7142	127	9	mr	mr	PROPN
ejpam-7142	127	10	-	-	PUNCT
ejpam-7142	127	11	contraction	contraction	NOUN
ejpam-7142	127	12	constant	constant	ADJ
ejpam-7142	127	13	r	r	NOUN
ejpam-7142	127	14	ensures	ensure	VERB
ejpam-7142	127	15	both	both	CCONJ
ejpam-7142	127	16	small	small	ADJ
ejpam-7142	127	17	-	-	PUNCT
ejpam-7142	127	18	world	world	NOUN
ejpam-7142	127	19	properties	property	NOUN
ejpam-7142	127	20	and	and	CCONJ
ejpam-7142	127	21	robustness	robustness	NOUN
ejpam-7142	127	22	to	to	ADP
ejpam-7142	127	23	targeted	target	VERB
ejpam-7142	127	24	attacks	attack	NOUN
ejpam-7142	127	25	.	.	PUNCT
ejpam-7142	128	1	definition	definition	NOUN
ejpam-7142	128	2	6	6	NUM
ejpam-7142	128	3	(	(	PUNCT
ejpam-7142	128	4	path	path	NOUN
ejpam-7142	128	5	triple	triple	ADJ
ejpam-7142	128	6	in	in	ADP
ejpam-7142	128	7	nmr	nmr	NOUN
ejpam-7142	128	8	-	-	PUNCT
ejpam-7142	128	9	ms	ms	NOUN
ejpam-7142	128	10	)	)	PUNCT
ejpam-7142	128	11	.	.	PUNCT
ejpam-7142	129	1	a	a	DET
ejpam-7142	129	2	path	path	NOUN
ejpam-7142	129	3	triple	triple	ADV
ejpam-7142	129	4	in	in	ADP
ejpam-7142	129	5	an	an	DET
ejpam-7142	129	6	nmr	nmr	NOUN
ejpam-7142	129	7	-	-	PUNCT
ejpam-7142	129	8	ms	ms	NOUN
ejpam-7142	129	9	is	be	AUX
ejpam-7142	129	10	a	a	DET
ejpam-7142	129	11	triple	triple	NOUN
ejpam-7142	129	12	of	of	ADP
ejpam-7142	129	13	continuous	continuous	ADJ
ejpam-7142	129	14	functions	function	NOUN
ejpam-7142	129	15	(	(	PUNCT
ejpam-7142	129	16	α	α	NOUN
ejpam-7142	129	17	,	,	PUNCT
ejpam-7142	129	18	β	β	X
ejpam-7142	129	19	,	,	PUNCT
ejpam-7142	129	20	γ	γ	NOUN
ejpam-7142	129	21	)	)	PUNCT
ejpam-7142	129	22	:	:	PUNCT
ejpam-7142	129	23	i3	i3	NOUN
ejpam-7142	129	24	→	→	SYM
ejpam-7142	129	25	z	z	X
ejpam-7142	129	26	,	,	PUNCT
ejpam-7142	129	27	where	where	SCONJ
ejpam-7142	129	28	i	i	PRON
ejpam-7142	129	29	=	=	PUNCT
ejpam-7142	130	1	[	[	X
ejpam-7142	130	2	0	0	NUM
ejpam-7142	130	3	,	,	PUNCT
ejpam-7142	130	4	1	1	NUM
ejpam-7142	130	5	]	]	PUNCT
ejpam-7142	130	6	.	.	PUNCT
ejpam-7142	131	1	we	we	PRON
ejpam-7142	131	2	interpret	interpret	VERB
ejpam-7142	131	3	these	these	PRON
ejpam-7142	131	4	as	as	ADP
ejpam-7142	131	5	three	three	NUM
ejpam-7142	131	6	paths	path	NOUN
ejpam-7142	131	7	parameterized	parameterize	VERB
ejpam-7142	131	8	by	by	ADP
ejpam-7142	131	9	the	the	DET
ejpam-7142	131	10	unit	unit	NOUN
ejpam-7142	131	11	cube	cube	NOUN
ejpam-7142	131	12	.	.	PUNCT
ejpam-7142	132	1	definition	definition	NOUN
ejpam-7142	132	2	7	7	NUM
ejpam-7142	132	3	(	(	PUNCT
ejpam-7142	132	4	neutrosophic	neutrosophic	ADJ
ejpam-7142	132	5	mr	mr	PROPN
ejpam-7142	132	6	-	-	PUNCT
ejpam-7142	132	7	homotopy	homotopy	NOUN
ejpam-7142	132	8	)	)	PUNCT
ejpam-7142	132	9	.	.	PUNCT
ejpam-7142	133	1	let	let	AUX
ejpam-7142	133	2	(	(	PUNCT
ejpam-7142	133	3	z	z	NOUN
ejpam-7142	133	4	,	,	PUNCT
ejpam-7142	133	5	m	m	PROPN
ejpam-7142	133	6	,	,	PUNCT
ejpam-7142	133	7	t	t	PROPN
ejpam-7142	133	8	,	,	PUNCT
ejpam-7142	133	9	f	f	PROPN
ejpam-7142	133	10	,	,	PUNCT
ejpam-7142	133	11	i	i	PRON
ejpam-7142	133	12	,	,	PUNCT
ejpam-7142	133	13	•	•	PROPN
ejpam-7142	133	14	,	,	PUNCT
ejpam-7142	133	15	⋄	⋄	PROPN
ejpam-7142	133	16	,	,	PUNCT
ejpam-7142	133	17	r	r	NOUN
ejpam-7142	133	18	,	,	PUNCT
ejpam-7142	133	19	⋆	⋆	ADJ
ejpam-7142	133	20	)	)	PUNCT
ejpam-7142	133	21	be	be	AUX
ejpam-7142	133	22	an	an	DET
ejpam-7142	133	23	nmr	nmr	NOUN
ejpam-7142	133	24	-	-	PUNCT
ejpam-7142	133	25	ms	ms	NOUN
ejpam-7142	133	26	.	.	PROPN
ejpam-7142	133	27	two	two	NUM
ejpam-7142	133	28	path	path	NOUN
ejpam-7142	133	29	triples	triple	NOUN
ejpam-7142	133	30	(	(	PUNCT
ejpam-7142	133	31	α	α	X
ejpam-7142	133	32	,	,	PUNCT
ejpam-7142	133	33	β	β	X
ejpam-7142	133	34	,	,	PUNCT
ejpam-7142	133	35	γ	γ	NOUN
ejpam-7142	133	36	)	)	PUNCT
ejpam-7142	133	37	,	,	PUNCT
ejpam-7142	133	38	(	(	PUNCT
ejpam-7142	133	39	α′	α′	NUM
ejpam-7142	133	40	,	,	PUNCT
ejpam-7142	133	41	β′	β′	NUM
ejpam-7142	133	42	,	,	PUNCT
ejpam-7142	133	43	γ′	γ′	PROPN
ejpam-7142	133	44	)	)	PUNCT
ejpam-7142	133	45	:	:	PUNCT
ejpam-7142	133	46	i3	i3	NOUN
ejpam-7142	133	47	→	→	SYM
ejpam-7142	133	48	z	z	X
ejpam-7142	133	49	are	be	AUX
ejpam-7142	133	50	said	say	VERB
ejpam-7142	133	51	to	to	PART
ejpam-7142	133	52	be	be	AUX
ejpam-7142	133	53	neutrosophic	neutrosophic	ADJ
ejpam-7142	133	54	mr	mr	PROPN
ejpam-7142	133	55	-	-	PUNCT
ejpam-7142	133	56	homotopic	homotopic	PROPN
ejpam-7142	133	57	if	if	SCONJ
ejpam-7142	133	58	there	there	PRON
ejpam-7142	133	59	exists	exist	VERB
ejpam-7142	133	60	a	a	DET
ejpam-7142	133	61	continuous	continuous	ADJ
ejpam-7142	133	62	map	map	NOUN
ejpam-7142	133	63	h	h	NOUN
ejpam-7142	133	64	:	:	PUNCT
ejpam-7142	133	65	i3	i3	NOUN
ejpam-7142	133	66	×	×	NOUN
ejpam-7142	133	67	i	i	INTJ
ejpam-7142	133	68	→	→	PUNCT
ejpam-7142	133	69	z	z	NOUN
ejpam-7142	133	70	such	such	ADJ
ejpam-7142	133	71	that	that	PRON
ejpam-7142	133	72	:	:	PUNCT
ejpam-7142	133	73	(	(	PUNCT
ejpam-7142	133	74	i	i	NOUN
ejpam-7142	133	75	)	)	PUNCT
ejpam-7142	133	76	boundary	boundary	ADJ
ejpam-7142	133	77	conditions	condition	NOUN
ejpam-7142	133	78	:	:	PUNCT
ejpam-7142	134	1	h(x	h(x	PROPN
ejpam-7142	134	2	,	,	PUNCT
ejpam-7142	134	3	y	y	PROPN
ejpam-7142	134	4	,	,	PUNCT
ejpam-7142	134	5	z	z	PROPN
ejpam-7142	134	6	,	,	PUNCT
ejpam-7142	134	7	0	0	NUM
ejpam-7142	134	8	)	)	PUNCT
ejpam-7142	134	9	=	=	SYM
ejpam-7142	134	10	(	(	PUNCT
ejpam-7142	134	11	α(x	α(x	PROPN
ejpam-7142	134	12	,	,	PUNCT
ejpam-7142	134	13	y	y	PROPN
ejpam-7142	134	14	,	,	PUNCT
ejpam-7142	134	15	z	z	NOUN
ejpam-7142	134	16	)	)	PUNCT
ejpam-7142	134	17	,	,	PUNCT
ejpam-7142	134	18	β(x	β(x	PROPN
ejpam-7142	134	19	,	,	PUNCT
ejpam-7142	134	20	y	y	PROPN
ejpam-7142	134	21	,	,	PUNCT
ejpam-7142	134	22	z	z	NOUN
ejpam-7142	134	23	)	)	PUNCT
ejpam-7142	134	24	,	,	PUNCT
ejpam-7142	134	25	γ(x	γ(x	PROPN
ejpam-7142	134	26	,	,	PUNCT
ejpam-7142	134	27	y	y	PROPN
ejpam-7142	134	28	,	,	PUNCT
ejpam-7142	134	29	z	z	NOUN
ejpam-7142	134	30	)	)	PUNCT
ejpam-7142	134	31	)	)	PUNCT
ejpam-7142	135	1	h(x	h(x	PROPN
ejpam-7142	135	2	,	,	PUNCT
ejpam-7142	135	3	y	y	PROPN
ejpam-7142	135	4	,	,	PUNCT
ejpam-7142	135	5	z	z	PROPN
ejpam-7142	135	6	,	,	PUNCT
ejpam-7142	135	7	1	1	NUM
ejpam-7142	135	8	)	)	PUNCT
ejpam-7142	135	9	=	=	SYM
ejpam-7142	135	10	(	(	PUNCT
ejpam-7142	135	11	α′(x	α′(x	PROPN
ejpam-7142	135	12	,	,	PUNCT
ejpam-7142	135	13	y	y	PROPN
ejpam-7142	135	14	,	,	PUNCT
ejpam-7142	135	15	z	z	NOUN
ejpam-7142	135	16	)	)	PUNCT
ejpam-7142	135	17	,	,	PUNCT
ejpam-7142	135	18	β′(x	β′(x	PROPN
ejpam-7142	135	19	,	,	PUNCT
ejpam-7142	135	20	y	y	PROPN
ejpam-7142	135	21	,	,	PUNCT
ejpam-7142	135	22	z	z	NOUN
ejpam-7142	135	23	)	)	PUNCT
ejpam-7142	135	24	,	,	PUNCT
ejpam-7142	135	25	γ′(x	γ′(x	PROPN
ejpam-7142	135	26	,	,	PUNCT
ejpam-7142	135	27	y	y	PROPN
ejpam-7142	135	28	,	,	PUNCT
ejpam-7142	135	29	z	z	NOUN
ejpam-7142	135	30	)	)	PUNCT
ejpam-7142	135	31	)	)	PUNCT
ejpam-7142	135	32	for	for	ADP
ejpam-7142	135	33	all	all	PRON
ejpam-7142	135	34	(	(	PUNCT
ejpam-7142	135	35	x	x	NOUN
ejpam-7142	135	36	,	,	PUNCT
ejpam-7142	135	37	y	y	PROPN
ejpam-7142	135	38	,	,	PUNCT
ejpam-7142	135	39	z	z	NOUN
ejpam-7142	135	40	)	)	PUNCT
ejpam-7142	135	41	∈	∈	PROPN
ejpam-7142	135	42	i3	i3	NOUN
ejpam-7142	135	43	.	.	PUNCT
ejpam-7142	136	1	(	(	PUNCT
ejpam-7142	136	2	ii	ii	X
ejpam-7142	136	3	)	)	PUNCT
ejpam-7142	136	4	monotonicity	monotonicity	NOUN
ejpam-7142	136	5	condition	condition	NOUN
ejpam-7142	136	6	:	:	PUNCT
ejpam-7142	136	7	for	for	ADP
ejpam-7142	136	8	the	the	DET
ejpam-7142	136	9	family	family	NOUN
ejpam-7142	136	10	ht	ht	PROPN
ejpam-7142	136	11	(	(	PUNCT
ejpam-7142	136	12	·	·	PUNCT
ejpam-7142	136	13	)	)	PUNCT
ejpam-7142	137	1	=	=	SYM
ejpam-7142	137	2	h	h	NOUN
ejpam-7142	137	3	(	(	PUNCT
ejpam-7142	137	4	·	·	PROPN
ejpam-7142	137	5	,	,	PUNCT
ejpam-7142	137	6	t	t	PROPN
ejpam-7142	137	7	)	)	PUNCT
ejpam-7142	137	8	,	,	PUNCT
ejpam-7142	137	9	the	the	DET
ejpam-7142	137	10	function	function	NOUN
ejpam-7142	137	11	:	:	PUNCT
ejpam-7142	137	12	φ(t	φ(t	NOUN
ejpam-7142	137	13	)	)	PUNCT
ejpam-7142	137	14	=	=	NOUN
ejpam-7142	137	15	m(ht(α),ht(β),ht(γ	m(ht(α),ht(β),ht(γ	NOUN
ejpam-7142	137	16	)	)	PUNCT
ejpam-7142	137	17	)	)	PUNCT
ejpam-7142	138	1	⋆	⋆	CCONJ
ejpam-7142	138	2	i(ht(α),ht(β	i(ht(α),ht(β	NOUN
ejpam-7142	138	3	)	)	PUNCT
ejpam-7142	138	4	,	,	PUNCT
ejpam-7142	138	5	γ	γ	X
ejpam-7142	138	6	)	)	PUNCT
ejpam-7142	138	7	is	be	AUX
ejpam-7142	138	8	monotonically	monotonically	ADV
ejpam-7142	138	9	decreasing	decrease	VERB
ejpam-7142	138	10	in	in	ADP
ejpam-7142	138	11	t.	t.	PROPN
ejpam-7142	138	12	(	(	PUNCT
ejpam-7142	138	13	iii	iii	NOUN
ejpam-7142	138	14	)	)	PUNCT
ejpam-7142	138	15	truth	truth	NOUN
ejpam-7142	138	16	convergence	convergence	NOUN
ejpam-7142	138	17	condition	condition	NOUN
ejpam-7142	138	18	:	:	PUNCT
ejpam-7142	139	1	lim	lim	PROPN
ejpam-7142	139	2	t→1	t→1	PROPN
ejpam-7142	139	3	t	t	PROPN
ejpam-7142	139	4	(	(	PUNCT
ejpam-7142	139	5	“	"	PUNCT
ejpam-7142	139	6	(	(	PUNCT
ejpam-7142	139	7	α	α	NOUN
ejpam-7142	139	8	,	,	PUNCT
ejpam-7142	139	9	β	β	X
ejpam-7142	139	10	,	,	PUNCT
ejpam-7142	139	11	γ	γ	NOUN
ejpam-7142	139	12	)	)	PUNCT
ejpam-7142	139	13	∼	∼	NOUN
ejpam-7142	139	14	(	(	PUNCT
ejpam-7142	139	15	α′	α′	NUM
ejpam-7142	139	16	,	,	PUNCT
ejpam-7142	139	17	β′	β′	NUM
ejpam-7142	139	18	,	,	PUNCT
ejpam-7142	139	19	γ′	γ′	NOUN
ejpam-7142	139	20	)	)	PUNCT
ejpam-7142	139	21	”	"	PUNCT
ejpam-7142	139	22	,	,	PUNCT
ejpam-7142	139	23	t	t	NOUN
ejpam-7142	139	24	)	)	PUNCT
ejpam-7142	139	25	=	=	SYM
ejpam-7142	140	1	1	1	NUM
ejpam-7142	140	2	we	we	PRON
ejpam-7142	140	3	denote	denote	VERB
ejpam-7142	140	4	this	this	DET
ejpam-7142	140	5	relation	relation	NOUN
ejpam-7142	140	6	by	by	ADP
ejpam-7142	140	7	(	(	PUNCT
ejpam-7142	140	8	α	α	X
ejpam-7142	140	9	,	,	PUNCT
ejpam-7142	140	10	β	β	X
ejpam-7142	140	11	,	,	PUNCT
ejpam-7142	140	12	γ	γ	NOUN
ejpam-7142	140	13	)	)	PUNCT
ejpam-7142	140	14	∼n	∼n	PROPN
ejpam-7142	140	15	(	(	PUNCT
ejpam-7142	140	16	α′	α′	NUM
ejpam-7142	140	17	,	,	PUNCT
ejpam-7142	140	18	β′	β′	NUM
ejpam-7142	140	19	,	,	PUNCT
ejpam-7142	140	20	γ′	γ′	NOUN
ejpam-7142	140	21	)	)	PUNCT
ejpam-7142	140	22	.	.	PUNCT
ejpam-7142	141	1	lemma	lemma	PROPN
ejpam-7142	141	2	5	5	NUM
ejpam-7142	141	3	(	(	PUNCT
ejpam-7142	141	4	reflexivity	reflexivity	NOUN
ejpam-7142	141	5	of	of	ADP
ejpam-7142	141	6	neutrosophic	neutrosophic	ADJ
ejpam-7142	141	7	mr	mr	PROPN
ejpam-7142	141	8	-	-	PUNCT
ejpam-7142	141	9	homotopy	homotopy	NOUN
ejpam-7142	141	10	)	)	PUNCT
ejpam-7142	141	11	.	.	PUNCT
ejpam-7142	142	1	for	for	ADP
ejpam-7142	142	2	any	any	DET
ejpam-7142	142	3	path	path	NOUN
ejpam-7142	142	4	triple	triple	ADJ
ejpam-7142	142	5	(	(	PUNCT
ejpam-7142	142	6	α	α	NOUN
ejpam-7142	142	7	,	,	PUNCT
ejpam-7142	142	8	β	β	X
ejpam-7142	142	9	,	,	PUNCT
ejpam-7142	142	10	γ	γ	NOUN
ejpam-7142	142	11	)	)	PUNCT
ejpam-7142	142	12	:	:	PUNCT
ejpam-7142	142	13	i3	i3	NOUN
ejpam-7142	142	14	→	→	SYM
ejpam-7142	142	15	z	z	X
ejpam-7142	142	16	,	,	PUNCT
ejpam-7142	142	17	we	we	PRON
ejpam-7142	142	18	have	have	AUX
ejpam-7142	142	19	(	(	PUNCT
ejpam-7142	142	20	α	α	X
ejpam-7142	142	21	,	,	PUNCT
ejpam-7142	142	22	β	β	X
ejpam-7142	142	23	,	,	PUNCT
ejpam-7142	142	24	γ	γ	NOUN
ejpam-7142	142	25	)	)	PUNCT
ejpam-7142	142	26	∼n	∼n	PROPN
ejpam-7142	142	27	(	(	PUNCT
ejpam-7142	142	28	α	α	PROPN
ejpam-7142	142	29	,	,	PUNCT
ejpam-7142	142	30	β	β	X
ejpam-7142	142	31	,	,	PUNCT
ejpam-7142	142	32	γ	γ	NOUN
ejpam-7142	142	33	)	)	PUNCT
ejpam-7142	142	34	.	.	PUNCT
ejpam-7142	143	1	proof	proof	NOUN
ejpam-7142	143	2	.	.	PUNCT
ejpam-7142	144	1	define	define	VERB
ejpam-7142	144	2	the	the	DET
ejpam-7142	144	3	constant	constant	ADJ
ejpam-7142	144	4	homotopy	homotopy	NOUN
ejpam-7142	144	5	h	h	NOUN
ejpam-7142	144	6	:	:	PUNCT
ejpam-7142	144	7	i3	i3	NOUN
ejpam-7142	144	8	×	×	NOUN
ejpam-7142	144	9	i	i	INTJ
ejpam-7142	144	10	→	→	SYM
ejpam-7142	144	11	z	z	NOUN
ejpam-7142	144	12	by	by	ADP
ejpam-7142	144	13	:	:	PUNCT
ejpam-7142	144	14	h(x	h(x	PROPN
ejpam-7142	144	15	,	,	PUNCT
ejpam-7142	144	16	y	y	PROPN
ejpam-7142	144	17	,	,	PUNCT
ejpam-7142	144	18	z	z	PROPN
ejpam-7142	144	19	,	,	PUNCT
ejpam-7142	144	20	t	t	PROPN
ejpam-7142	144	21	)	)	PUNCT
ejpam-7142	144	22	=	=	PUNCT
ejpam-7142	144	23	(	(	PUNCT
ejpam-7142	144	24	α(x	α(x	PROPN
ejpam-7142	144	25	,	,	PUNCT
ejpam-7142	144	26	y	y	PROPN
ejpam-7142	144	27	,	,	PUNCT
ejpam-7142	144	28	z	z	NOUN
ejpam-7142	144	29	)	)	PUNCT
ejpam-7142	144	30	,	,	PUNCT
ejpam-7142	144	31	β(x	β(x	PROPN
ejpam-7142	144	32	,	,	PUNCT
ejpam-7142	144	33	y	y	PROPN
ejpam-7142	144	34	,	,	PUNCT
ejpam-7142	144	35	z	z	NOUN
ejpam-7142	144	36	)	)	PUNCT
ejpam-7142	144	37	,	,	PUNCT
ejpam-7142	144	38	γ(x	γ(x	PROPN
ejpam-7142	144	39	,	,	PUNCT
ejpam-7142	144	40	y	y	PROPN
ejpam-7142	144	41	,	,	PUNCT
ejpam-7142	144	42	z	z	NOUN
ejpam-7142	144	43	)	)	PUNCT
ejpam-7142	144	44	)	)	PUNCT
ejpam-7142	144	45	for	for	ADP
ejpam-7142	144	46	all	all	DET
ejpam-7142	144	47	t	t	NOUN
ejpam-7142	144	48	∈	∈	PROPN
ejpam-7142	145	1	i	i	PRON
ejpam-7142	145	2	•	•	VERB
ejpam-7142	145	3	boundary	boundary	ADJ
ejpam-7142	145	4	conditions	condition	NOUN
ejpam-7142	145	5	:	:	PUNCT
ejpam-7142	145	6	clearly	clearly	ADV
ejpam-7142	145	7	satisfied	satisfied	ADJ
ejpam-7142	145	8	since	since	SCONJ
ejpam-7142	145	9	h0	h0	NOUN
ejpam-7142	145	10	=	=	PROPN
ejpam-7142	145	11	h1	h1	PROPN
ejpam-7142	145	12	=	=	SYM
ejpam-7142	145	13	(	(	PUNCT
ejpam-7142	145	14	α	α	X
ejpam-7142	145	15	,	,	PUNCT
ejpam-7142	145	16	β	β	X
ejpam-7142	145	17	,	,	PUNCT
ejpam-7142	145	18	γ	γ	NOUN
ejpam-7142	145	19	)	)	PUNCT
ejpam-7142	145	20	.	.	PUNCT
ejpam-7142	146	1	e.	e.	PROPN
ejpam-7142	146	2	hussein	hussein	PROPN
ejpam-7142	146	3	et	et	PROPN
ejpam-7142	146	4	al	al	PROPN
ejpam-7142	146	5	.	.	PUNCT
ejpam-7142	146	6	/	/	SYM
ejpam-7142	146	7	eur	eur	PROPN
ejpam-7142	146	8	.	.	PUNCT
ejpam-7142	147	1	j.	j.	PROPN
ejpam-7142	147	2	pure	pure	PROPN
ejpam-7142	147	3	appl	appl	PROPN
ejpam-7142	147	4	.	.	PROPN
ejpam-7142	147	5	math	math	PROPN
ejpam-7142	147	6	,	,	PUNCT
ejpam-7142	147	7	18	18	NUM
ejpam-7142	147	8	(	(	PUNCT
ejpam-7142	147	9	4	4	NUM
ejpam-7142	147	10	)	)	PUNCT
ejpam-7142	147	11	(	(	PUNCT
ejpam-7142	147	12	2025	2025	NUM
ejpam-7142	147	13	)	)	PUNCT
ejpam-7142	147	14	,	,	PUNCT
ejpam-7142	147	15	7142	7142	NUM
ejpam-7142	147	16	7	7	NUM
ejpam-7142	147	17	of	of	ADP
ejpam-7142	147	18	17	17	NUM
ejpam-7142	147	19	•	•	NOUN
ejpam-7142	147	20	monotonicity	monotonicity	NOUN
ejpam-7142	147	21	:	:	PUNCT
ejpam-7142	147	22	for	for	ADP
ejpam-7142	147	23	all	all	DET
ejpam-7142	147	24	t	t	NOUN
ejpam-7142	147	25	∈	∈	PROPN
ejpam-7142	148	1	i	i	PRON
ejpam-7142	148	2	:	:	PUNCT
ejpam-7142	148	3	φ(t	φ(t	PROPN
ejpam-7142	148	4	)	)	PUNCT
ejpam-7142	149	1	=	=	SYM
ejpam-7142	149	2	m(α	m(α	PROPN
ejpam-7142	149	3	,	,	PUNCT
ejpam-7142	149	4	β	β	X
ejpam-7142	149	5	,	,	PUNCT
ejpam-7142	149	6	γ	γ	NOUN
ejpam-7142	149	7	)	)	PUNCT
ejpam-7142	149	8	⋆	⋆	PROPN
ejpam-7142	149	9	i(α	i(α	PROPN
ejpam-7142	149	10	,	,	PUNCT
ejpam-7142	149	11	β	β	X
ejpam-7142	149	12	,	,	PUNCT
ejpam-7142	149	13	γ	γ	PROPN
ejpam-7142	149	14	)	)	PUNCT
ejpam-7142	149	15	which	which	PRON
ejpam-7142	149	16	is	be	AUX
ejpam-7142	149	17	constant	constant	ADJ
ejpam-7142	149	18	,	,	PUNCT
ejpam-7142	149	19	hence	hence	ADV
ejpam-7142	149	20	monotonically	monotonically	ADV
ejpam-7142	149	21	decreasing	decrease	VERB
ejpam-7142	149	22	.	.	PUNCT
ejpam-7142	150	1	•	•	NOUN
ejpam-7142	150	2	truth	truth	NOUN
ejpam-7142	150	3	convergence	convergence	NOUN
ejpam-7142	150	4	:	:	PUNCT
ejpam-7142	151	1	lim	lim	PROPN
ejpam-7142	151	2	t→1	t→1	PROPN
ejpam-7142	151	3	t	t	PROPN
ejpam-7142	151	4	(	(	PUNCT
ejpam-7142	151	5	“	"	PUNCT
ejpam-7142	151	6	equivalence	equivalence	NOUN
ejpam-7142	151	7	”	"	PUNCT
ejpam-7142	151	8	,	,	PUNCT
ejpam-7142	151	9	t	t	PROPN
ejpam-7142	151	10	)	)	PUNCT
ejpam-7142	151	11	=	=	SYM
ejpam-7142	151	12	t	t	PROPN
ejpam-7142	151	13	(	(	PUNCT
ejpam-7142	151	14	“	"	PUNCT
ejpam-7142	151	15	equivalence	equivalence	NOUN
ejpam-7142	151	16	”	"	PUNCT
ejpam-7142	151	17	,	,	PUNCT
ejpam-7142	151	18	1	1	X
ejpam-7142	151	19	)	)	PUNCT
ejpam-7142	151	20	=	=	SYM
ejpam-7142	151	21	1	1	NUM
ejpam-7142	151	22	by	by	ADP
ejpam-7142	151	23	the	the	DET
ejpam-7142	151	24	identity	identity	NOUN
ejpam-7142	151	25	property	property	NOUN
ejpam-7142	151	26	(	(	PUNCT
ejpam-7142	151	27	n1	n1	NOUN
ejpam-7142	151	28	)	)	PUNCT
ejpam-7142	151	29	of	of	ADP
ejpam-7142	151	30	the	the	DET
ejpam-7142	151	31	neutrosophic	neutrosophic	ADJ
ejpam-7142	151	32	truth	truth	NOUN
ejpam-7142	151	33	function	function	NOUN
ejpam-7142	151	34	.	.	PUNCT
ejpam-7142	152	1	therefore	therefore	ADV
ejpam-7142	152	2	,	,	PUNCT
ejpam-7142	152	3	the	the	DET
ejpam-7142	152	4	relation	relation	NOUN
ejpam-7142	152	5	is	be	AUX
ejpam-7142	152	6	reflexive	reflexive	ADJ
ejpam-7142	152	7	.	.	PUNCT
ejpam-7142	153	1	lemma	lemma	PROPN
ejpam-7142	153	2	6	6	NUM
ejpam-7142	153	3	(	(	PUNCT
ejpam-7142	153	4	symmetry	symmetry	NOUN
ejpam-7142	153	5	of	of	ADP
ejpam-7142	153	6	neutrosophic	neutrosophic	ADJ
ejpam-7142	153	7	mr	mr	PROPN
ejpam-7142	153	8	-	-	PUNCT
ejpam-7142	153	9	homotopy	homotopy	NOUN
ejpam-7142	153	10	)	)	PUNCT
ejpam-7142	153	11	.	.	PUNCT
ejpam-7142	154	1	if	if	SCONJ
ejpam-7142	154	2	(	(	PUNCT
ejpam-7142	154	3	α	α	X
ejpam-7142	154	4	,	,	PUNCT
ejpam-7142	154	5	β	β	X
ejpam-7142	154	6	,	,	PUNCT
ejpam-7142	154	7	γ	γ	NOUN
ejpam-7142	154	8	)	)	PUNCT
ejpam-7142	154	9	∼n	∼n	PROPN
ejpam-7142	154	10	(	(	PUNCT
ejpam-7142	154	11	α′	α′	NUM
ejpam-7142	154	12	,	,	PUNCT
ejpam-7142	154	13	β′	β′	NUM
ejpam-7142	154	14	,	,	PUNCT
ejpam-7142	154	15	γ′	γ′	PROPN
ejpam-7142	154	16	)	)	PUNCT
ejpam-7142	154	17	,	,	PUNCT
ejpam-7142	154	18	then	then	ADV
ejpam-7142	154	19	(	(	PUNCT
ejpam-7142	154	20	α′	α′	NUM
ejpam-7142	154	21	,	,	PUNCT
ejpam-7142	154	22	β′	β′	NUM
ejpam-7142	154	23	,	,	PUNCT
ejpam-7142	154	24	γ′	γ′	NOUN
ejpam-7142	154	25	)	)	PUNCT
ejpam-7142	154	26	∼n	∼n	NOUN
ejpam-7142	154	27	(	(	PUNCT
ejpam-7142	154	28	α	α	PROPN
ejpam-7142	154	29	,	,	PUNCT
ejpam-7142	154	30	β	β	X
ejpam-7142	154	31	,	,	PUNCT
ejpam-7142	154	32	γ	γ	NOUN
ejpam-7142	154	33	)	)	PUNCT
ejpam-7142	154	34	.	.	PUNCT
ejpam-7142	155	1	proof	proof	NOUN
ejpam-7142	155	2	.	.	PUNCT
ejpam-7142	156	1	let	let	VERB
ejpam-7142	156	2	h	h	NOUN
ejpam-7142	156	3	:	:	PUNCT
ejpam-7142	156	4	i3	i3	VERB
ejpam-7142	156	5	×	×	NOUN
ejpam-7142	157	1	i	i	INTJ
ejpam-7142	157	2	→	→	SYM
ejpam-7142	157	3	z	z	AUX
ejpam-7142	157	4	be	be	AUX
ejpam-7142	157	5	a	a	DET
ejpam-7142	157	6	neutrosophic	neutrosophic	ADJ
ejpam-7142	157	7	mr	mr	PROPN
ejpam-7142	157	8	-	-	PUNCT
ejpam-7142	157	9	homotopy	homotopy	PROPN
ejpam-7142	157	10	from	from	ADP
ejpam-7142	157	11	(	(	PUNCT
ejpam-7142	157	12	α	α	NOUN
ejpam-7142	157	13	,	,	PUNCT
ejpam-7142	157	14	β	β	X
ejpam-7142	157	15	,	,	PUNCT
ejpam-7142	157	16	γ	γ	NOUN
ejpam-7142	157	17	)	)	PUNCT
ejpam-7142	157	18	to	to	ADP
ejpam-7142	157	19	(	(	PUNCT
ejpam-7142	157	20	α′	α′	NUM
ejpam-7142	157	21	,	,	PUNCT
ejpam-7142	157	22	β′	β′	NUM
ejpam-7142	157	23	,	,	PUNCT
ejpam-7142	157	24	γ′	γ′	NOUN
ejpam-7142	157	25	)	)	PUNCT
ejpam-7142	157	26	.	.	PUNCT
ejpam-7142	158	1	define	define	VERB
ejpam-7142	158	2	the	the	DET
ejpam-7142	158	3	reverse	reverse	NOUN
ejpam-7142	158	4	homotopy	homotopy	VERB
ejpam-7142	158	5	h̃	h̃	PROPN
ejpam-7142	158	6	:	:	PUNCT
ejpam-7142	158	7	i3	i3	NOUN
ejpam-7142	158	8	×	×	NOUN
ejpam-7142	158	9	i	i	INTJ
ejpam-7142	158	10	→	→	SYM
ejpam-7142	158	11	z	z	NOUN
ejpam-7142	158	12	by	by	ADP
ejpam-7142	158	13	:	:	PUNCT
ejpam-7142	158	14	h̃(x	h̃(x	PROPN
ejpam-7142	158	15	,	,	PUNCT
ejpam-7142	158	16	y	y	PROPN
ejpam-7142	158	17	,	,	PUNCT
ejpam-7142	158	18	z	z	PROPN
ejpam-7142	158	19	,	,	PUNCT
ejpam-7142	158	20	t	t	PROPN
ejpam-7142	158	21	)	)	PUNCT
ejpam-7142	158	22	=	=	SYM
ejpam-7142	158	23	h(x	h(x	PROPN
ejpam-7142	158	24	,	,	PUNCT
ejpam-7142	158	25	y	y	PROPN
ejpam-7142	158	26	,	,	PUNCT
ejpam-7142	158	27	z	z	PROPN
ejpam-7142	158	28	,	,	PUNCT
ejpam-7142	158	29	1−	1−	NUM
ejpam-7142	158	30	t	t	PROPN
ejpam-7142	158	31	)	)	PUNCT
ejpam-7142	158	32	•	•	NUM
ejpam-7142	158	33	boundary	boundary	ADJ
ejpam-7142	158	34	conditions	condition	NOUN
ejpam-7142	158	35	:	:	PUNCT
ejpam-7142	158	36	h̃(x	h̃(x	PROPN
ejpam-7142	158	37	,	,	PUNCT
ejpam-7142	158	38	y	y	PROPN
ejpam-7142	158	39	,	,	PUNCT
ejpam-7142	158	40	z	z	PROPN
ejpam-7142	158	41	,	,	PUNCT
ejpam-7142	158	42	0	0	NUM
ejpam-7142	158	43	)	)	PUNCT
ejpam-7142	159	1	=	=	SYM
ejpam-7142	159	2	h(x	h(x	PROPN
ejpam-7142	159	3	,	,	PUNCT
ejpam-7142	159	4	y	y	PROPN
ejpam-7142	159	5	,	,	PUNCT
ejpam-7142	159	6	z	z	PROPN
ejpam-7142	159	7	,	,	PUNCT
ejpam-7142	159	8	1	1	NUM
ejpam-7142	159	9	)	)	PUNCT
ejpam-7142	159	10	=	=	SYM
ejpam-7142	159	11	(	(	PUNCT
ejpam-7142	159	12	α′(x	α′(x	PROPN
ejpam-7142	159	13	,	,	PUNCT
ejpam-7142	159	14	y	y	PROPN
ejpam-7142	159	15	,	,	PUNCT
ejpam-7142	159	16	z	z	NOUN
ejpam-7142	159	17	)	)	PUNCT
ejpam-7142	159	18	,	,	PUNCT
ejpam-7142	159	19	β′(x	β′(x	PROPN
ejpam-7142	159	20	,	,	PUNCT
ejpam-7142	159	21	y	y	PROPN
ejpam-7142	159	22	,	,	PUNCT
ejpam-7142	159	23	z	z	NOUN
ejpam-7142	159	24	)	)	PUNCT
ejpam-7142	159	25	,	,	PUNCT
ejpam-7142	159	26	γ′(x	γ′(x	PROPN
ejpam-7142	159	27	,	,	PUNCT
ejpam-7142	159	28	y	y	PROPN
ejpam-7142	159	29	,	,	PUNCT
ejpam-7142	159	30	z	z	NOUN
ejpam-7142	159	31	)	)	PUNCT
ejpam-7142	159	32	)	)	PUNCT
ejpam-7142	160	1	h̃(x	h̃(x	PROPN
ejpam-7142	160	2	,	,	PUNCT
ejpam-7142	160	3	y	y	PROPN
ejpam-7142	160	4	,	,	PUNCT
ejpam-7142	160	5	z	z	PROPN
ejpam-7142	160	6	,	,	PUNCT
ejpam-7142	160	7	1	1	NUM
ejpam-7142	160	8	)	)	PUNCT
ejpam-7142	160	9	=	=	SYM
ejpam-7142	160	10	h(x	h(x	PROPN
ejpam-7142	160	11	,	,	PUNCT
ejpam-7142	160	12	y	y	PROPN
ejpam-7142	160	13	,	,	PUNCT
ejpam-7142	160	14	z	z	PROPN
ejpam-7142	160	15	,	,	PUNCT
ejpam-7142	160	16	0	0	NUM
ejpam-7142	160	17	)	)	PUNCT
ejpam-7142	160	18	=	=	SYM
ejpam-7142	160	19	(	(	PUNCT
ejpam-7142	160	20	α(x	α(x	PROPN
ejpam-7142	160	21	,	,	PUNCT
ejpam-7142	160	22	y	y	PROPN
ejpam-7142	160	23	,	,	PUNCT
ejpam-7142	160	24	z	z	NOUN
ejpam-7142	160	25	)	)	PUNCT
ejpam-7142	160	26	,	,	PUNCT
ejpam-7142	160	27	β(x	β(x	PROPN
ejpam-7142	160	28	,	,	PUNCT
ejpam-7142	160	29	y	y	PROPN
ejpam-7142	160	30	,	,	PUNCT
ejpam-7142	160	31	z	z	NOUN
ejpam-7142	160	32	)	)	PUNCT
ejpam-7142	160	33	,	,	PUNCT
ejpam-7142	160	34	γ(x	γ(x	PROPN
ejpam-7142	160	35	,	,	PUNCT
ejpam-7142	160	36	y	y	PROPN
ejpam-7142	160	37	,	,	PUNCT
ejpam-7142	160	38	z	z	NOUN
ejpam-7142	160	39	)	)	PUNCT
ejpam-7142	160	40	)	)	PUNCT
ejpam-7142	160	41	•	•	ADP
ejpam-7142	160	42	monotonicity	monotonicity	NOUN
ejpam-7142	160	43	:	:	PUNCT
ejpam-7142	160	44	for	for	ADP
ejpam-7142	160	45	φ̃(t	φ̃(t	NOUN
ejpam-7142	160	46	)	)	PUNCT
ejpam-7142	161	1	=	=	SYM
ejpam-7142	161	2	m(h̃t(α	m(h̃t(α	NOUN
ejpam-7142	161	3	′	′	NOUN
ejpam-7142	161	4	)	)	PUNCT
ejpam-7142	161	5	,	,	PUNCT
ejpam-7142	161	6	h̃t(β	h̃t(β	PROPN
ejpam-7142	161	7	′	′	NUM
ejpam-7142	161	8	)	)	PUNCT
ejpam-7142	161	9	,	,	PUNCT
ejpam-7142	161	10	h̃t(γ	h̃t(γ	NOUN
ejpam-7142	161	11	′	′	NUM
ejpam-7142	161	12	)	)	PUNCT
ejpam-7142	161	13	)	)	PUNCT
ejpam-7142	162	1	⋆	⋆	X
ejpam-7142	162	2	i(h̃t(α	i(h̃t(α	NOUN
ejpam-7142	162	3	′	′	NUM
ejpam-7142	162	4	)	)	PUNCT
ejpam-7142	162	5	,	,	PUNCT
ejpam-7142	162	6	h̃t(β	h̃t(β	PROPN
ejpam-7142	162	7	′	′	NUM
ejpam-7142	162	8	)	)	PUNCT
ejpam-7142	162	9	,	,	PUNCT
ejpam-7142	162	10	γ′	γ′	PROPN
ejpam-7142	162	11	)	)	PUNCT
ejpam-7142	162	12	,	,	PUNCT
ejpam-7142	162	13	we	we	PRON
ejpam-7142	162	14	have	have	VERB
ejpam-7142	162	15	:	:	PUNCT
ejpam-7142	162	16	φ̃(t	φ̃(t	NOUN
ejpam-7142	162	17	)	)	PUNCT
ejpam-7142	162	18	=	=	SYM
ejpam-7142	163	1	φ(1−	φ(1−	PROPN
ejpam-7142	163	2	t	t	PROPN
ejpam-7142	163	3	)	)	PUNCT
ejpam-7142	163	4	since	since	SCONJ
ejpam-7142	163	5	φ	φ	PROPN
ejpam-7142	163	6	is	be	AUX
ejpam-7142	163	7	monotonically	monotonically	ADV
ejpam-7142	163	8	decreasing	decrease	VERB
ejpam-7142	163	9	,	,	PUNCT
ejpam-7142	163	10	φ̃	φ̃	PROPN
ejpam-7142	163	11	is	be	AUX
ejpam-7142	163	12	monotonically	monotonically	ADV
ejpam-7142	163	13	increasing	increase	VERB
ejpam-7142	163	14	.	.	PUNCT
ejpam-7142	164	1	however	however	ADV
ejpam-7142	164	2	,	,	PUNCT
ejpam-7142	164	3	we	we	PRON
ejpam-7142	164	4	can	can	AUX
ejpam-7142	164	5	redefine	redefine	VERB
ejpam-7142	164	6	the	the	DET
ejpam-7142	164	7	homotopy	homotopy	NOUN
ejpam-7142	164	8	parameter	parameter	NOUN
ejpam-7142	164	9	to	to	PART
ejpam-7142	164	10	maintain	maintain	VERB
ejpam-7142	164	11	monotonic	monotonic	ADJ
ejpam-7142	164	12	decrease	decrease	NOUN
ejpam-7142	164	13	.	.	PUNCT
ejpam-7142	165	1	•	•	NOUN
ejpam-7142	165	2	truth	truth	NOUN
ejpam-7142	165	3	convergence	convergence	NOUN
ejpam-7142	165	4	:	:	PUNCT
ejpam-7142	165	5	by	by	ADP
ejpam-7142	165	6	the	the	DET
ejpam-7142	165	7	symmetry	symmetry	NOUN
ejpam-7142	165	8	property	property	NOUN
ejpam-7142	165	9	(	(	PUNCT
ejpam-7142	165	10	n2	n2	NOUN
ejpam-7142	165	11	)	)	PUNCT
ejpam-7142	165	12	of	of	ADP
ejpam-7142	165	13	t	t	PROPN
ejpam-7142	165	14	:	:	PUNCT
ejpam-7142	165	15	t	t	PROPN
ejpam-7142	165	16	(	(	PUNCT
ejpam-7142	165	17	“	"	PUNCT
ejpam-7142	165	18	(	(	PUNCT
ejpam-7142	165	19	α′	α′	NUM
ejpam-7142	165	20	,	,	PUNCT
ejpam-7142	165	21	β′	β′	NUM
ejpam-7142	165	22	,	,	PUNCT
ejpam-7142	165	23	γ′	γ′	NOUN
ejpam-7142	165	24	)	)	PUNCT
ejpam-7142	165	25	∼	∼	NOUN
ejpam-7142	165	26	(	(	PUNCT
ejpam-7142	165	27	α	α	NOUN
ejpam-7142	165	28	,	,	PUNCT
ejpam-7142	165	29	β	β	X
ejpam-7142	165	30	,	,	PUNCT
ejpam-7142	165	31	γ	γ	NOUN
ejpam-7142	165	32	)	)	PUNCT
ejpam-7142	165	33	”	"	PUNCT
ejpam-7142	165	34	,	,	PUNCT
ejpam-7142	165	35	t	t	PROPN
ejpam-7142	165	36	)	)	PUNCT
ejpam-7142	165	37	=	=	SYM
ejpam-7142	165	38	t	t	PROPN
ejpam-7142	165	39	(	(	PUNCT
ejpam-7142	165	40	“	"	PUNCT
ejpam-7142	165	41	(	(	PUNCT
ejpam-7142	165	42	α	α	NOUN
ejpam-7142	165	43	,	,	PUNCT
ejpam-7142	165	44	β	β	X
ejpam-7142	165	45	,	,	PUNCT
ejpam-7142	165	46	γ	γ	NOUN
ejpam-7142	165	47	)	)	PUNCT
ejpam-7142	165	48	∼	∼	NOUN
ejpam-7142	165	49	(	(	PUNCT
ejpam-7142	165	50	α′	α′	NUM
ejpam-7142	165	51	,	,	PUNCT
ejpam-7142	165	52	β′	β′	NUM
ejpam-7142	165	53	,	,	PUNCT
ejpam-7142	165	54	γ′	γ′	NOUN
ejpam-7142	165	55	)	)	PUNCT
ejpam-7142	165	56	”	"	PUNCT
ejpam-7142	165	57	,	,	PUNCT
ejpam-7142	165	58	1−	1−	NUM
ejpam-7142	165	59	t	t	NOUN
ejpam-7142	165	60	)	)	PUNCT
ejpam-7142	165	61	thus	thus	ADV
ejpam-7142	165	62	:	:	PUNCT
ejpam-7142	166	1	lim	lim	PROPN
ejpam-7142	166	2	t→1	t→1	PROPN
ejpam-7142	166	3	t	t	PROPN
ejpam-7142	166	4	(	(	PUNCT
ejpam-7142	166	5	“	"	PUNCT
ejpam-7142	166	6	reverse	reverse	ADJ
ejpam-7142	166	7	equivalence	equivalence	NOUN
ejpam-7142	166	8	”	"	PUNCT
ejpam-7142	166	9	,	,	PUNCT
ejpam-7142	166	10	t	t	PROPN
ejpam-7142	166	11	)	)	PUNCT
ejpam-7142	166	12	=	=	PROPN
ejpam-7142	167	1	lim	lim	PROPN
ejpam-7142	167	2	t→1	t→1	PROPN
ejpam-7142	167	3	t	t	PROPN
ejpam-7142	167	4	(	(	PUNCT
ejpam-7142	167	5	“	"	PUNCT
ejpam-7142	167	6	original	original	ADJ
ejpam-7142	167	7	equivalence	equivalence	NOUN
ejpam-7142	167	8	”	"	PUNCT
ejpam-7142	167	9	,	,	PUNCT
ejpam-7142	167	10	1−	1−	NUM
ejpam-7142	167	11	t	t	NOUN
ejpam-7142	167	12	)	)	PUNCT
ejpam-7142	167	13	=	=	SYM
ejpam-7142	167	14	1	1	NUM
ejpam-7142	167	15	therefore	therefore	ADV
ejpam-7142	167	16	,	,	PUNCT
ejpam-7142	167	17	the	the	DET
ejpam-7142	167	18	relation	relation	NOUN
ejpam-7142	167	19	is	be	AUX
ejpam-7142	167	20	symmetric	symmetric	ADJ
ejpam-7142	167	21	.	.	PUNCT
ejpam-7142	168	1	lemma	lemma	PROPN
ejpam-7142	168	2	7	7	NUM
ejpam-7142	168	3	(	(	PUNCT
ejpam-7142	168	4	transitivity	transitivity	NOUN
ejpam-7142	168	5	of	of	ADP
ejpam-7142	168	6	neutrosophic	neutrosophic	ADJ
ejpam-7142	168	7	mr	mr	PROPN
ejpam-7142	168	8	-	-	PUNCT
ejpam-7142	168	9	homotopy	homotopy	NOUN
ejpam-7142	168	10	)	)	PUNCT
ejpam-7142	168	11	.	.	PUNCT
ejpam-7142	169	1	if	if	SCONJ
ejpam-7142	169	2	(	(	PUNCT
ejpam-7142	169	3	α	α	X
ejpam-7142	169	4	,	,	PUNCT
ejpam-7142	169	5	β	β	X
ejpam-7142	169	6	,	,	PUNCT
ejpam-7142	169	7	γ	γ	NOUN
ejpam-7142	169	8	)	)	PUNCT
ejpam-7142	169	9	∼n	∼n	PROPN
ejpam-7142	169	10	(	(	PUNCT
ejpam-7142	169	11	α′	α′	NUM
ejpam-7142	169	12	,	,	PUNCT
ejpam-7142	169	13	β′	β′	NUM
ejpam-7142	169	14	,	,	PUNCT
ejpam-7142	169	15	γ′	γ′	PROPN
ejpam-7142	169	16	)	)	PUNCT
ejpam-7142	169	17	and	and	CCONJ
ejpam-7142	169	18	(	(	PUNCT
ejpam-7142	169	19	α′	α′	NUM
ejpam-7142	169	20	,	,	PUNCT
ejpam-7142	169	21	β′	β′	NUM
ejpam-7142	169	22	,	,	PUNCT
ejpam-7142	169	23	γ′	γ′	NOUN
ejpam-7142	169	24	)	)	PUNCT
ejpam-7142	169	25	∼n	∼n	NOUN
ejpam-7142	169	26	(	(	PUNCT
ejpam-7142	169	27	α′′	α′′	NOUN
ejpam-7142	169	28	,	,	PUNCT
ejpam-7142	169	29	β′′	β′′	NOUN
ejpam-7142	169	30	,	,	PUNCT
ejpam-7142	169	31	γ′′	γ′′	PROPN
ejpam-7142	169	32	)	)	PUNCT
ejpam-7142	169	33	,	,	PUNCT
ejpam-7142	169	34	then	then	ADV
ejpam-7142	169	35	(	(	PUNCT
ejpam-7142	169	36	α	α	NOUN
ejpam-7142	169	37	,	,	PUNCT
ejpam-7142	169	38	β	β	X
ejpam-7142	169	39	,	,	PUNCT
ejpam-7142	169	40	γ	γ	NOUN
ejpam-7142	169	41	)	)	PUNCT
ejpam-7142	169	42	∼n	∼n	PROPN
ejpam-7142	169	43	(	(	PUNCT
ejpam-7142	169	44	α′′	α′′	NOUN
ejpam-7142	169	45	,	,	PUNCT
ejpam-7142	169	46	β′′	β′′	NOUN
ejpam-7142	169	47	,	,	PUNCT
ejpam-7142	169	48	γ′′	γ′′	PROPN
ejpam-7142	169	49	)	)	PUNCT
ejpam-7142	169	50	.	.	PUNCT
ejpam-7142	170	1	proof	proof	NOUN
ejpam-7142	170	2	.	.	PUNCT
ejpam-7142	171	1	let	let	VERB
ejpam-7142	171	2	h1	h1	PROPN
ejpam-7142	171	3	be	be	AUX
ejpam-7142	171	4	a	a	DET
ejpam-7142	171	5	homotopy	homotopy	NOUN
ejpam-7142	171	6	from	from	ADP
ejpam-7142	171	7	(	(	PUNCT
ejpam-7142	171	8	α	α	NOUN
ejpam-7142	171	9	,	,	PUNCT
ejpam-7142	171	10	β	β	X
ejpam-7142	171	11	,	,	PUNCT
ejpam-7142	171	12	γ	γ	NOUN
ejpam-7142	171	13	)	)	PUNCT
ejpam-7142	171	14	to	to	ADP
ejpam-7142	171	15	(	(	PUNCT
ejpam-7142	171	16	α′	α′	NUM
ejpam-7142	171	17	,	,	PUNCT
ejpam-7142	171	18	β′	β′	NUM
ejpam-7142	171	19	,	,	PUNCT
ejpam-7142	171	20	γ′	γ′	NOUN
ejpam-7142	171	21	)	)	PUNCT
ejpam-7142	171	22	and	and	CCONJ
ejpam-7142	171	23	h2	h2	NOUN
ejpam-7142	171	24	be	be	AUX
ejpam-7142	171	25	a	a	DET
ejpam-7142	171	26	homotopy	homotopy	NOUN
ejpam-7142	171	27	from	from	ADP
ejpam-7142	171	28	(	(	PUNCT
ejpam-7142	171	29	α′	α′	NUM
ejpam-7142	171	30	,	,	PUNCT
ejpam-7142	171	31	β′	β′	NUM
ejpam-7142	171	32	,	,	PUNCT
ejpam-7142	171	33	γ′	γ′	NOUN
ejpam-7142	171	34	)	)	PUNCT
ejpam-7142	171	35	to	to	ADP
ejpam-7142	171	36	(	(	PUNCT
ejpam-7142	171	37	α′′	α′′	NOUN
ejpam-7142	171	38	,	,	PUNCT
ejpam-7142	171	39	β′′	β′′	NOUN
ejpam-7142	171	40	,	,	PUNCT
ejpam-7142	171	41	γ′′	γ′′	PROPN
ejpam-7142	171	42	)	)	PUNCT
ejpam-7142	171	43	.	.	PUNCT
ejpam-7142	172	1	define	define	VERB
ejpam-7142	172	2	the	the	DET
ejpam-7142	172	3	concatenated	concatenate	VERB
ejpam-7142	172	4	homotopy	homotopy	NOUN
ejpam-7142	172	5	h	h	NOUN
ejpam-7142	172	6	:	:	PUNCT
ejpam-7142	172	7	i3	i3	NOUN
ejpam-7142	172	8	×	×	NOUN
ejpam-7142	172	9	i	i	INTJ
ejpam-7142	172	10	→	→	SYM
ejpam-7142	172	11	z	z	NOUN
ejpam-7142	172	12	by	by	ADP
ejpam-7142	172	13	:	:	PUNCT
ejpam-7142	172	14	h(x	h(x	PROPN
ejpam-7142	172	15	,	,	PUNCT
ejpam-7142	172	16	y	y	PROPN
ejpam-7142	172	17	,	,	PUNCT
ejpam-7142	172	18	z	z	PROPN
ejpam-7142	172	19	,	,	PUNCT
ejpam-7142	172	20	t	t	PROPN
ejpam-7142	172	21	)	)	PUNCT
ejpam-7142	172	22	=	=	PRON
ejpam-7142	172	23	{	{	PUNCT
ejpam-7142	172	24	h1(x	h1(x	NOUN
ejpam-7142	172	25	,	,	PUNCT
ejpam-7142	172	26	y	y	PROPN
ejpam-7142	172	27	,	,	PUNCT
ejpam-7142	172	28	z	z	PROPN
ejpam-7142	172	29	,	,	PUNCT
ejpam-7142	172	30	2	2	NUM
ejpam-7142	172	31	t	t	NOUN
ejpam-7142	172	32	)	)	PUNCT
ejpam-7142	172	33	if	if	SCONJ
ejpam-7142	172	34	0	0	NUM
ejpam-7142	172	35	≤	≤	NUM
ejpam-7142	172	36	t	t	NOUN
ejpam-7142	172	37	≤	≤	NUM
ejpam-7142	172	38	1	1	NUM
ejpam-7142	172	39	2	2	NUM
ejpam-7142	172	40	h2(x	h2(x	PROPN
ejpam-7142	172	41	,	,	PUNCT
ejpam-7142	172	42	y	y	PROPN
ejpam-7142	172	43	,	,	PUNCT
ejpam-7142	172	44	z	z	PROPN
ejpam-7142	172	45	,	,	PUNCT
ejpam-7142	172	46	2t−	2t−	NOUN
ejpam-7142	172	47	1	1	NUM
ejpam-7142	172	48	)	)	PUNCT
ejpam-7142	172	49	if	if	SCONJ
ejpam-7142	172	50	1	1	NUM
ejpam-7142	172	51	2	2	NUM
ejpam-7142	172	52	≤	≤	NOUN
ejpam-7142	172	53	t	t	NOUN
ejpam-7142	172	54	≤	≤	NUM
ejpam-7142	172	55	1	1	NUM
ejpam-7142	172	56	•	•	NOUN
ejpam-7142	172	57	boundary	boundary	ADJ
ejpam-7142	172	58	conditions	condition	NOUN
ejpam-7142	172	59	:	:	PUNCT
ejpam-7142	172	60	h(x	h(x	PROPN
ejpam-7142	172	61	,	,	PUNCT
ejpam-7142	172	62	y	y	PROPN
ejpam-7142	172	63	,	,	PUNCT
ejpam-7142	172	64	z	z	PROPN
ejpam-7142	172	65	,	,	PUNCT
ejpam-7142	172	66	0	0	NUM
ejpam-7142	172	67	)	)	PUNCT
ejpam-7142	173	1	=	=	SYM
ejpam-7142	173	2	h1(x	h1(x	PROPN
ejpam-7142	173	3	,	,	PUNCT
ejpam-7142	173	4	y	y	PROPN
ejpam-7142	173	5	,	,	PUNCT
ejpam-7142	173	6	z	z	PROPN
ejpam-7142	173	7	,	,	PUNCT
ejpam-7142	173	8	0	0	NUM
ejpam-7142	173	9	)	)	PUNCT
ejpam-7142	173	10	=	=	SYM
ejpam-7142	173	11	(	(	PUNCT
ejpam-7142	173	12	α	α	X
ejpam-7142	173	13	,	,	PUNCT
ejpam-7142	173	14	β	β	X
ejpam-7142	173	15	,	,	PUNCT
ejpam-7142	173	16	γ	γ	PROPN
ejpam-7142	173	17	)	)	PUNCT
ejpam-7142	173	18	h(x	h(x	PROPN
ejpam-7142	173	19	,	,	PUNCT
ejpam-7142	173	20	y	y	PROPN
ejpam-7142	173	21	,	,	PUNCT
ejpam-7142	173	22	z	z	PROPN
ejpam-7142	173	23	,	,	PUNCT
ejpam-7142	173	24	1	1	NUM
ejpam-7142	173	25	)	)	PUNCT
ejpam-7142	173	26	=	=	SYM
ejpam-7142	173	27	h2(x	h2(x	PROPN
ejpam-7142	173	28	,	,	PUNCT
ejpam-7142	173	29	y	y	PROPN
ejpam-7142	173	30	,	,	PUNCT
ejpam-7142	173	31	z	z	PROPN
ejpam-7142	173	32	,	,	PUNCT
ejpam-7142	173	33	1	1	NUM
ejpam-7142	173	34	)	)	PUNCT
ejpam-7142	173	35	=	=	SYM
ejpam-7142	173	36	(	(	PUNCT
ejpam-7142	173	37	α′′	α′′	NOUN
ejpam-7142	173	38	,	,	PUNCT
ejpam-7142	173	39	β′′	β′′	NOUN
ejpam-7142	173	40	,	,	PUNCT
ejpam-7142	173	41	γ′′	γ′′	PROPN
ejpam-7142	173	42	)	)	PUNCT
ejpam-7142	173	43	e.	e.	PROPN
ejpam-7142	173	44	hussein	hussein	PROPN
ejpam-7142	173	45	et	et	PROPN
ejpam-7142	173	46	al	al	PROPN
ejpam-7142	173	47	.	.	PUNCT
ejpam-7142	173	48	/	/	SYM
ejpam-7142	173	49	eur	eur	PROPN
ejpam-7142	173	50	.	.	PUNCT
ejpam-7142	174	1	j.	j.	PROPN
ejpam-7142	174	2	pure	pure	PROPN
ejpam-7142	174	3	appl	appl	PROPN
ejpam-7142	174	4	.	.	PROPN
ejpam-7142	174	5	math	math	PROPN
ejpam-7142	174	6	,	,	PUNCT
ejpam-7142	174	7	18	18	NUM
ejpam-7142	174	8	(	(	PUNCT
ejpam-7142	174	9	4	4	NUM
ejpam-7142	174	10	)	)	PUNCT
ejpam-7142	174	11	(	(	PUNCT
ejpam-7142	174	12	2025	2025	NUM
ejpam-7142	174	13	)	)	PUNCT
ejpam-7142	174	14	,	,	PUNCT
ejpam-7142	174	15	7142	7142	NUM
ejpam-7142	174	16	8	8	NUM
ejpam-7142	174	17	of	of	ADP
ejpam-7142	174	18	17	17	NUM
ejpam-7142	174	19	•	•	NOUN
ejpam-7142	174	20	monotonicity	monotonicity	NOUN
ejpam-7142	174	21	:	:	PUNCT
ejpam-7142	174	22	define	define	VERB
ejpam-7142	174	23	φ(t	φ(t	PROPN
ejpam-7142	174	24	)	)	PUNCT
ejpam-7142	174	25	as	as	ADP
ejpam-7142	174	26	in	in	ADP
ejpam-7142	174	27	definition	definition	NOUN
ejpam-7142	174	28	7	7	NUM
ejpam-7142	174	29	.	.	PUNCT
ejpam-7142	175	1	for	for	ADP
ejpam-7142	175	2	t	t	PROPN
ejpam-7142	175	3	∈	∈	PROPN
ejpam-7142	176	1	[	[	X
ejpam-7142	176	2	0	0	NUM
ejpam-7142	176	3	,	,	PUNCT
ejpam-7142	176	4	12	12	NUM
ejpam-7142	176	5	]	]	X
ejpam-7142	176	6	:	:	PUNCT
ejpam-7142	176	7	φ(t	φ(t	NUM
ejpam-7142	176	8	)	)	PUNCT
ejpam-7142	176	9	=	=	PUNCT
ejpam-7142	176	10	φ1(2	φ1(2	PROPN
ejpam-7142	176	11	t	t	PROPN
ejpam-7142	176	12	)	)	PUNCT
ejpam-7142	176	13	which	which	PRON
ejpam-7142	176	14	is	be	AUX
ejpam-7142	176	15	decreasing	decrease	VERB
ejpam-7142	176	16	since	since	SCONJ
ejpam-7142	176	17	φ1	φ1	PROPN
ejpam-7142	176	18	is	be	AUX
ejpam-7142	176	19	decreasing	decrease	VERB
ejpam-7142	176	20	.	.	PUNCT
ejpam-7142	177	1	for	for	ADP
ejpam-7142	177	2	t	t	PROPN
ejpam-7142	177	3	∈	∈	PROPN
ejpam-7142	178	1	[	[	X
ejpam-7142	178	2	12	12	NUM
ejpam-7142	178	3	,	,	PUNCT
ejpam-7142	178	4	1	1	NUM
ejpam-7142	178	5	]	]	NOUN
ejpam-7142	178	6	:	:	PUNCT
ejpam-7142	178	7	φ(t	φ(t	NUM
ejpam-7142	178	8	)	)	PUNCT
ejpam-7142	178	9	=	=	PRON
ejpam-7142	178	10	φ2(2t−	φ2(2t−	NOUN
ejpam-7142	178	11	1	1	NUM
ejpam-7142	178	12	)	)	PUNCT
ejpam-7142	178	13	which	which	PRON
ejpam-7142	178	14	is	be	AUX
ejpam-7142	178	15	also	also	ADV
ejpam-7142	178	16	decreasing	decrease	VERB
ejpam-7142	178	17	.	.	PUNCT
ejpam-7142	179	1	at	at	ADP
ejpam-7142	179	2	t	t	NOUN
ejpam-7142	179	3	=	=	SYM
ejpam-7142	179	4	1	1	NUM
ejpam-7142	179	5	2	2	NUM
ejpam-7142	179	6	,	,	PUNCT
ejpam-7142	179	7	we	we	PRON
ejpam-7142	179	8	have	have	VERB
ejpam-7142	179	9	continuity	continuity	NOUN
ejpam-7142	179	10	by	by	ADP
ejpam-7142	179	11	construction	construction	NOUN
ejpam-7142	179	12	.	.	PUNCT
ejpam-7142	180	1	•	•	NOUN
ejpam-7142	180	2	truth	truth	NOUN
ejpam-7142	180	3	convergence	convergence	NOUN
ejpam-7142	180	4	:	:	PUNCT
ejpam-7142	180	5	using	use	VERB
ejpam-7142	180	6	the	the	DET
ejpam-7142	180	7	triangle	triangle	NOUN
ejpam-7142	180	8	inequality	inequality	NOUN
ejpam-7142	180	9	(	(	PUNCT
ejpam-7142	180	10	n3	n3	NOUN
ejpam-7142	180	11	)	)	PUNCT
ejpam-7142	180	12	for	for	ADP
ejpam-7142	180	13	t	t	PROPN
ejpam-7142	180	14	:	:	PUNCT
ejpam-7142	180	15	t	t	PROPN
ejpam-7142	180	16	(	(	PUNCT
ejpam-7142	180	17	“	"	PUNCT
ejpam-7142	180	18	(	(	PUNCT
ejpam-7142	180	19	α	α	NOUN
ejpam-7142	180	20	,	,	PUNCT
ejpam-7142	180	21	β	β	X
ejpam-7142	180	22	,	,	PUNCT
ejpam-7142	180	23	γ	γ	NOUN
ejpam-7142	180	24	)	)	PUNCT
ejpam-7142	180	25	∼	∼	NOUN
ejpam-7142	180	26	(	(	PUNCT
ejpam-7142	180	27	α′′	α′′	NOUN
ejpam-7142	180	28	,	,	PUNCT
ejpam-7142	180	29	β′′	β′′	NOUN
ejpam-7142	180	30	,	,	PUNCT
ejpam-7142	180	31	γ′′	γ′′	PROPN
ejpam-7142	180	32	)	)	PUNCT
ejpam-7142	180	33	”	"	PUNCT
ejpam-7142	180	34	,	,	PUNCT
ejpam-7142	180	35	t	t	PROPN
ejpam-7142	180	36	)	)	PUNCT
ejpam-7142	180	37	≥	≥	PROPN
ejpam-7142	180	38	t	t	PROPN
ejpam-7142	180	39	(	(	PUNCT
ejpam-7142	180	40	“	"	PUNCT
ejpam-7142	180	41	(	(	PUNCT
ejpam-7142	180	42	α	α	NOUN
ejpam-7142	180	43	,	,	PUNCT
ejpam-7142	180	44	β	β	X
ejpam-7142	180	45	,	,	PUNCT
ejpam-7142	180	46	γ	γ	NOUN
ejpam-7142	180	47	)	)	PUNCT
ejpam-7142	180	48	∼	∼	NOUN
ejpam-7142	180	49	(	(	PUNCT
ejpam-7142	180	50	α′	α′	NUM
ejpam-7142	180	51	,	,	PUNCT
ejpam-7142	180	52	β′	β′	NUM
ejpam-7142	180	53	,	,	PUNCT
ejpam-7142	180	54	γ′	γ′	NOUN
ejpam-7142	180	55	)	)	PUNCT
ejpam-7142	180	56	”	"	PUNCT
ejpam-7142	180	57	,	,	PUNCT
ejpam-7142	180	58	2	2	NUM
ejpam-7142	180	59	t	t	NOUN
ejpam-7142	180	60	)	)	PUNCT
ejpam-7142	180	61	•	•	NUM
ejpam-7142	180	62	t	t	PROPN
ejpam-7142	180	63	(	(	PUNCT
ejpam-7142	180	64	“	"	PUNCT
ejpam-7142	180	65	(	(	PUNCT
ejpam-7142	180	66	α′	α′	NUM
ejpam-7142	180	67	,	,	PUNCT
ejpam-7142	180	68	β′	β′	NUM
ejpam-7142	180	69	,	,	PUNCT
ejpam-7142	180	70	γ′	γ′	NOUN
ejpam-7142	180	71	)	)	PUNCT
ejpam-7142	180	72	∼	∼	NOUN
ejpam-7142	180	73	(	(	PUNCT
ejpam-7142	180	74	α′′	α′′	NOUN
ejpam-7142	180	75	,	,	PUNCT
ejpam-7142	180	76	β′′	β′′	NOUN
ejpam-7142	180	77	,	,	PUNCT
ejpam-7142	180	78	γ′′	γ′′	PROPN
ejpam-7142	180	79	)	)	PUNCT
ejpam-7142	180	80	”	"	PUNCT
ejpam-7142	180	81	,	,	PUNCT
ejpam-7142	180	82	2t−	2t−	NOUN
ejpam-7142	180	83	1	1	NUM
ejpam-7142	180	84	)	)	PUNCT
ejpam-7142	180	85	taking	take	VERB
ejpam-7142	180	86	limit	limit	NOUN
ejpam-7142	180	87	as	as	ADP
ejpam-7142	180	88	t→	t→	X
ejpam-7142	180	89	1	1	NUM
ejpam-7142	180	90	:	:	PUNCT
ejpam-7142	180	91	lim	lim	PROPN
ejpam-7142	180	92	t→1	t→1	PROPN
ejpam-7142	180	93	t	t	PROPN
ejpam-7142	180	94	(	(	PUNCT
ejpam-7142	180	95	“	"	PUNCT
ejpam-7142	180	96	transitive	transitive	ADJ
ejpam-7142	180	97	equivalence	equivalence	NOUN
ejpam-7142	180	98	”	"	PUNCT
ejpam-7142	180	99	,	,	PUNCT
ejpam-7142	180	100	t	t	PROPN
ejpam-7142	180	101	)	)	PUNCT
ejpam-7142	180	102	≥	≥	NOUN
ejpam-7142	180	103	1	1	NUM
ejpam-7142	180	104	•	•	NUM
ejpam-7142	180	105	1	1	NUM
ejpam-7142	180	106	=	=	SYM
ejpam-7142	180	107	1	1	NUM
ejpam-7142	180	108	therefore	therefore	ADV
ejpam-7142	180	109	,	,	PUNCT
ejpam-7142	180	110	the	the	DET
ejpam-7142	180	111	relation	relation	NOUN
ejpam-7142	180	112	is	be	AUX
ejpam-7142	180	113	transitive	transitive	ADJ
ejpam-7142	180	114	.	.	PUNCT
ejpam-7142	181	1	theorem	theorem	ADJ
ejpam-7142	181	2	2	2	NUM
ejpam-7142	181	3	(	(	PUNCT
ejpam-7142	181	4	neutrosophic	neutrosophic	ADJ
ejpam-7142	181	5	mr	mr	PROPN
ejpam-7142	181	6	-	-	PUNCT
ejpam-7142	181	7	homotopy	homotopy	NOUN
ejpam-7142	181	8	is	be	AUX
ejpam-7142	181	9	an	an	DET
ejpam-7142	181	10	equivalence	equivalence	NOUN
ejpam-7142	181	11	relation	relation	NOUN
ejpam-7142	181	12	)	)	PUNCT
ejpam-7142	181	13	.	.	PUNCT
ejpam-7142	182	1	the	the	DET
ejpam-7142	182	2	relation	relation	NOUN
ejpam-7142	182	3	∼n	∼n	PROPN
ejpam-7142	182	4	of	of	ADP
ejpam-7142	182	5	neutrosophic	neutrosophic	ADJ
ejpam-7142	182	6	mr	mr	PROPN
ejpam-7142	182	7	-	-	PUNCT
ejpam-7142	182	8	homotopy	homotopy	NOUN
ejpam-7142	182	9	is	be	AUX
ejpam-7142	182	10	an	an	DET
ejpam-7142	182	11	equivalence	equivalence	NOUN
ejpam-7142	182	12	relation	relation	NOUN
ejpam-7142	182	13	on	on	ADP
ejpam-7142	182	14	the	the	DET
ejpam-7142	182	15	set	set	NOUN
ejpam-7142	182	16	of	of	ADP
ejpam-7142	182	17	path	path	NOUN
ejpam-7142	182	18	triples	triple	NOUN
ejpam-7142	182	19	in	in	ADP
ejpam-7142	182	20	an	an	DET
ejpam-7142	182	21	nmrms	nmrm	NOUN
ejpam-7142	182	22	.	.	PUNCT
ejpam-7142	183	1	proof	proof	NOUN
ejpam-7142	183	2	.	.	PUNCT
ejpam-7142	184	1	immediate	immediate	ADJ
ejpam-7142	184	2	from	from	ADP
ejpam-7142	184	3	lemmas	lemmas	PROPN
ejpam-7142	184	4	5	5	NUM
ejpam-7142	184	5	,	,	PUNCT
ejpam-7142	184	6	6	6	NUM
ejpam-7142	184	7	,	,	PUNCT
ejpam-7142	184	8	and	and	CCONJ
ejpam-7142	184	9	7	7	NUM
ejpam-7142	184	10	.	.	X
ejpam-7142	184	11	definition	definition	NOUN
ejpam-7142	184	12	8	8	NUM
ejpam-7142	184	13	(	(	PUNCT
ejpam-7142	184	14	neutrosophic	neutrosophic	ADJ
ejpam-7142	184	15	mr	mr	PROPN
ejpam-7142	184	16	-	-	PUNCT
ejpam-7142	184	17	fundamental	fundamental	ADJ
ejpam-7142	184	18	groupoid	groupoid	NOUN
ejpam-7142	184	19	)	)	PUNCT
ejpam-7142	184	20	.	.	PUNCT
ejpam-7142	185	1	let	let	AUX
ejpam-7142	185	2	(	(	PUNCT
ejpam-7142	185	3	z	z	NOUN
ejpam-7142	185	4	,	,	PUNCT
ejpam-7142	185	5	m	m	PROPN
ejpam-7142	185	6	,	,	PUNCT
ejpam-7142	185	7	t	t	PROPN
ejpam-7142	185	8	,	,	PUNCT
ejpam-7142	185	9	f	f	PROPN
ejpam-7142	185	10	,	,	PUNCT
ejpam-7142	185	11	i	i	PRON
ejpam-7142	185	12	,	,	PUNCT
ejpam-7142	185	13	•	•	PROPN
ejpam-7142	185	14	,	,	PUNCT
ejpam-7142	185	15	⋄	⋄	PROPN
ejpam-7142	185	16	,	,	PUNCT
ejpam-7142	185	17	r	r	NOUN
ejpam-7142	185	18	,	,	PUNCT
ejpam-7142	185	19	⋆	⋆	ADJ
ejpam-7142	185	20	)	)	PUNCT
ejpam-7142	185	21	be	be	AUX
ejpam-7142	185	22	an	an	DET
ejpam-7142	185	23	nmr	nmr	NOUN
ejpam-7142	185	24	-	-	PUNCT
ejpam-7142	185	25	ms	ms	NOUN
ejpam-7142	185	26	and	and	CCONJ
ejpam-7142	185	27	let	let	VERB
ejpam-7142	185	28	(	(	PUNCT
ejpam-7142	185	29	v	v	NOUN
ejpam-7142	185	30	,	,	PUNCT
ejpam-7142	185	31	ξ,ℑ	ξ,ℑ	PROPN
ejpam-7142	185	32	)	)	PUNCT
ejpam-7142	185	33	be	be	AUX
ejpam-7142	185	34	a	a	DET
ejpam-7142	185	35	triple	triple	NOUN
ejpam-7142	185	36	of	of	ADP
ejpam-7142	185	37	base	base	ADJ
ejpam-7142	185	38	points	point	NOUN
ejpam-7142	185	39	in	in	ADP
ejpam-7142	185	40	z.	z.	PROPN
ejpam-7142	185	41	the	the	DET
ejpam-7142	185	42	neutrosophic	neutrosophic	ADJ
ejpam-7142	185	43	mr	mr	PROPN
ejpam-7142	185	44	-	-	PUNCT
ejpam-7142	185	45	fundamental	fundamental	ADJ
ejpam-7142	185	46	groupoid	groupoid	NOUN
ejpam-7142	185	47	πn1	πn1	NOUN
ejpam-7142	185	48	(	(	PUNCT
ejpam-7142	185	49	z	z	NOUN
ejpam-7142	185	50	,	,	PUNCT
ejpam-7142	185	51	v	v	NOUN
ejpam-7142	185	52	,	,	PUNCT
ejpam-7142	185	53	ξ,ℑ	ξ,ℑ	PROPN
ejpam-7142	185	54	)	)	PUNCT
ejpam-7142	185	55	is	be	AUX
ejpam-7142	185	56	defined	define	VERB
ejpam-7142	185	57	as	as	ADP
ejpam-7142	185	58	:	:	PUNCT
ejpam-7142	185	59	•	•	NUM
ejpam-7142	185	60	objects	object	NOUN
ejpam-7142	185	61	:	:	PUNCT
ejpam-7142	185	62	the	the	DET
ejpam-7142	185	63	set	set	NOUN
ejpam-7142	185	64	of	of	ADP
ejpam-7142	185	65	path	path	NOUN
ejpam-7142	185	66	triples	triple	NOUN
ejpam-7142	185	67	(	(	PUNCT
ejpam-7142	185	68	α	α	X
ejpam-7142	185	69	,	,	PUNCT
ejpam-7142	185	70	β	β	X
ejpam-7142	185	71	,	,	PUNCT
ejpam-7142	185	72	γ	γ	NOUN
ejpam-7142	185	73	)	)	PUNCT
ejpam-7142	185	74	:	:	PUNCT
ejpam-7142	185	75	i3	i3	NOUN
ejpam-7142	185	76	→	→	SYM
ejpam-7142	185	77	z	z	NOUN
ejpam-7142	185	78	such	such	ADJ
ejpam-7142	185	79	that	that	SCONJ
ejpam-7142	185	80	:	:	PUNCT
ejpam-7142	185	81	α(0	α(0	NOUN
ejpam-7142	185	82	,	,	PUNCT
ejpam-7142	185	83	0	0	NUM
ejpam-7142	185	84	,	,	PUNCT
ejpam-7142	185	85	0	0	NUM
ejpam-7142	185	86	)	)	PUNCT
ejpam-7142	185	87	=	=	SYM
ejpam-7142	185	88	v	v	NOUN
ejpam-7142	185	89	,	,	PUNCT
ejpam-7142	185	90	α(1	α(1	PROPN
ejpam-7142	185	91	,	,	PUNCT
ejpam-7142	185	92	1	1	NUM
ejpam-7142	185	93	,	,	PUNCT
ejpam-7142	185	94	1	1	NUM
ejpam-7142	185	95	)	)	PUNCT
ejpam-7142	185	96	=	=	NOUN
ejpam-7142	185	97	v	v	ADP
ejpam-7142	185	98	β(0	β(0	PROPN
ejpam-7142	185	99	,	,	PUNCT
ejpam-7142	185	100	0	0	NUM
ejpam-7142	185	101	,	,	PUNCT
ejpam-7142	185	102	0	0	NUM
ejpam-7142	185	103	)	)	PUNCT
ejpam-7142	185	104	=	=	SYM
ejpam-7142	185	105	ξ	ξ	PROPN
ejpam-7142	185	106	,	,	PUNCT
ejpam-7142	185	107	β(1	β(1	PROPN
ejpam-7142	185	108	,	,	PUNCT
ejpam-7142	185	109	1	1	NUM
ejpam-7142	185	110	,	,	PUNCT
ejpam-7142	185	111	1	1	NUM
ejpam-7142	185	112	)	)	PUNCT
ejpam-7142	185	113	=	=	SYM
ejpam-7142	186	1	ξ	ξ	DET
ejpam-7142	186	2	γ(0	γ(0	PROPN
ejpam-7142	186	3	,	,	PUNCT
ejpam-7142	186	4	0	0	NUM
ejpam-7142	186	5	,	,	PUNCT
ejpam-7142	186	6	0	0	NUM
ejpam-7142	186	7	)	)	PUNCT
ejpam-7142	186	8	=	=	SYM
ejpam-7142	186	9	ℑ	ℑ	PROPN
ejpam-7142	186	10	,	,	PUNCT
ejpam-7142	186	11	γ(1	γ(1	PROPN
ejpam-7142	186	12	,	,	PUNCT
ejpam-7142	186	13	1	1	NUM
ejpam-7142	186	14	,	,	PUNCT
ejpam-7142	186	15	1	1	NUM
ejpam-7142	186	16	)	)	PUNCT
ejpam-7142	186	17	=	=	SYM
ejpam-7142	186	18	ℑ	ℑ	NOUN
ejpam-7142	186	19	•	•	ADV
ejpam-7142	186	20	morphisms	morphisms	ADV
ejpam-7142	186	21	:	:	PUNCT
ejpam-7142	186	22	equivalence	equivalence	NOUN
ejpam-7142	186	23	classes	class	NOUN
ejpam-7142	187	1	[	[	X
ejpam-7142	187	2	(	(	PUNCT
ejpam-7142	187	3	α	α	X
ejpam-7142	187	4	,	,	PUNCT
ejpam-7142	187	5	β	β	X
ejpam-7142	187	6	,	,	PUNCT
ejpam-7142	187	7	γ	γ	NOUN
ejpam-7142	187	8	)	)	PUNCT
ejpam-7142	187	9	]	]	PUNCT
ejpam-7142	187	10	under	under	ADP
ejpam-7142	187	11	the	the	DET
ejpam-7142	187	12	neutrosophic	neutrosophic	ADJ
ejpam-7142	187	13	mr	mr	PROPN
ejpam-7142	187	14	-	-	PUNCT
ejpam-7142	187	15	homotopy	homotopy	PROPN
ejpam-7142	187	16	relation	relation	NOUN
ejpam-7142	187	17	∼n	∼n	PROPN
ejpam-7142	187	18	.	.	PUNCT
ejpam-7142	188	1	•	•	NUM
ejpam-7142	188	2	composition	composition	NOUN
ejpam-7142	188	3	:	:	PUNCT
ejpam-7142	188	4	defined	define	VERB
ejpam-7142	188	5	by	by	ADP
ejpam-7142	188	6	concatenation	concatenation	NOUN
ejpam-7142	188	7	of	of	ADP
ejpam-7142	188	8	path	path	NOUN
ejpam-7142	188	9	triples	triple	NOUN
ejpam-7142	188	10	with	with	ADP
ejpam-7142	188	11	neutrosophic	neutrosophic	ADJ
ejpam-7142	188	12	degree	degree	NOUN
ejpam-7142	188	13	:	:	PUNCT
ejpam-7142	188	14	t	t	X
ejpam-7142	188	15	(	(	PUNCT
ejpam-7142	188	16	[	[	X
ejpam-7142	188	17	(	(	PUNCT
ejpam-7142	188	18	α	α	X
ejpam-7142	188	19	,	,	PUNCT
ejpam-7142	188	20	β	β	X
ejpam-7142	188	21	,	,	PUNCT
ejpam-7142	188	22	γ	γ	NOUN
ejpam-7142	188	23	)	)	PUNCT
ejpam-7142	188	24	]	]	PUNCT
ejpam-7142	189	1	◦	◦	NOUN
ejpam-7142	190	1	[	[	X
ejpam-7142	190	2	(	(	PUNCT
ejpam-7142	190	3	α′	α′	NUM
ejpam-7142	190	4	,	,	PUNCT
ejpam-7142	190	5	β′	β′	NUM
ejpam-7142	190	6	,	,	PUNCT
ejpam-7142	190	7	γ′	γ′	NOUN
ejpam-7142	190	8	)	)	PUNCT
ejpam-7142	190	9	]	]	PUNCT
ejpam-7142	190	10	)	)	PUNCT
ejpam-7142	191	1	=	=	SYM
ejpam-7142	191	2	t	t	PROPN
ejpam-7142	191	3	(	(	PUNCT
ejpam-7142	191	4	[	[	X
ejpam-7142	191	5	(	(	PUNCT
ejpam-7142	191	6	α	α	X
ejpam-7142	191	7	,	,	PUNCT
ejpam-7142	191	8	β	β	X
ejpam-7142	191	9	,	,	PUNCT
ejpam-7142	191	10	γ	γ	NOUN
ejpam-7142	191	11	)	)	PUNCT
ejpam-7142	191	12	]	]	PUNCT
ejpam-7142	191	13	)	)	PUNCT
ejpam-7142	191	14	•	•	NUM
ejpam-7142	191	15	t	t	NOUN
ejpam-7142	191	16	(	(	PUNCT
ejpam-7142	191	17	[	[	X
ejpam-7142	191	18	(	(	PUNCT
ejpam-7142	191	19	α′	α′	NUM
ejpam-7142	191	20	,	,	PUNCT
ejpam-7142	191	21	β′	β′	NUM
ejpam-7142	191	22	,	,	PUNCT
ejpam-7142	191	23	γ′	γ′	NOUN
ejpam-7142	191	24	)	)	PUNCT
ejpam-7142	191	25	]	]	PUNCT
ejpam-7142	191	26	)	)	PUNCT
ejpam-7142	191	27	•	•	NUM
ejpam-7142	191	28	neutrosophic	neutrosophic	ADJ
ejpam-7142	191	29	structure	structure	NOUN
ejpam-7142	191	30	:	:	PUNCT
ejpam-7142	191	31	each	each	DET
ejpam-7142	191	32	equivalence	equivalence	NOUN
ejpam-7142	191	33	class	class	NOUN
ejpam-7142	191	34	carries	carry	VERB
ejpam-7142	191	35	neutrosophic	neutrosophic	ADJ
ejpam-7142	191	36	degrees	degree	NOUN
ejpam-7142	191	37	:	:	PUNCT
ejpam-7142	191	38	(	(	PUNCT
ejpam-7142	191	39	[	[	X
ejpam-7142	191	40	(	(	PUNCT
ejpam-7142	191	41	α	α	X
ejpam-7142	191	42	,	,	PUNCT
ejpam-7142	191	43	β	β	X
ejpam-7142	191	44	,	,	PUNCT
ejpam-7142	191	45	γ	γ	NOUN
ejpam-7142	191	46	)	)	PUNCT
ejpam-7142	191	47	]	]	PUNCT
ejpam-7142	191	48	;	;	PUNCT
ejpam-7142	191	49	t	t	X
ejpam-7142	191	50	,	,	PUNCT
ejpam-7142	191	51	i	i	PRON
ejpam-7142	191	52	,	,	PUNCT
ejpam-7142	191	53	f	f	PROPN
ejpam-7142	191	54	)	)	PUNCT
ejpam-7142	191	55	where	where	SCONJ
ejpam-7142	191	56	the	the	DET
ejpam-7142	191	57	degrees	degree	NOUN
ejpam-7142	191	58	are	be	AUX
ejpam-7142	191	59	computed	compute	VERB
ejpam-7142	191	60	from	from	ADP
ejpam-7142	191	61	the	the	DET
ejpam-7142	191	62	homotopy	homotopy	NOUN
ejpam-7142	191	63	invariants	invariant	NOUN
ejpam-7142	191	64	.	.	PUNCT
ejpam-7142	192	1	theorem	theorem	NOUN
ejpam-7142	192	2	3	3	NUM
ejpam-7142	192	3	(	(	PUNCT
ejpam-7142	192	4	algebraic	algebraic	ADJ
ejpam-7142	192	5	structure	structure	NOUN
ejpam-7142	192	6	of	of	ADP
ejpam-7142	192	7	neutrosophic	neutrosophic	ADJ
ejpam-7142	192	8	mr	mr	PROPN
ejpam-7142	192	9	-	-	PUNCT
ejpam-7142	192	10	fundamental	fundamental	ADJ
ejpam-7142	192	11	groupoid	groupoid	NOUN
ejpam-7142	192	12	)	)	PUNCT
ejpam-7142	192	13	.	.	PUNCT
ejpam-7142	193	1	the	the	DET
ejpam-7142	193	2	neutrosophic	neutrosophic	ADJ
ejpam-7142	193	3	mr	mr	PROPN
ejpam-7142	193	4	-	-	PUNCT
ejpam-7142	193	5	fundamental	fundamental	ADJ
ejpam-7142	193	6	groupoid	groupoid	NOUN
ejpam-7142	193	7	πn1	πn1	NOUN
ejpam-7142	193	8	(	(	PUNCT
ejpam-7142	193	9	z	z	NOUN
ejpam-7142	193	10	,	,	PUNCT
ejpam-7142	193	11	v	v	NOUN
ejpam-7142	193	12	,	,	PUNCT
ejpam-7142	193	13	ξ,ℑ	ξ,ℑ	PROPN
ejpam-7142	193	14	)	)	PUNCT
ejpam-7142	193	15	has	have	VERB
ejpam-7142	193	16	the	the	DET
ejpam-7142	193	17	following	follow	VERB
ejpam-7142	193	18	properties	property	NOUN
ejpam-7142	193	19	:	:	PUNCT
ejpam-7142	193	20	(	(	PUNCT
ejpam-7142	193	21	i	i	NOUN
ejpam-7142	193	22	)	)	PUNCT
ejpam-7142	193	23	it	it	PRON
ejpam-7142	193	24	is	be	AUX
ejpam-7142	193	25	a	a	DET
ejpam-7142	193	26	groupoid	groupoid	NOUN
ejpam-7142	193	27	with	with	ADP
ejpam-7142	193	28	objects	object	NOUN
ejpam-7142	193	29	as	as	ADP
ejpam-7142	193	30	base	base	NOUN
ejpam-7142	193	31	-	-	PUNCT
ejpam-7142	193	32	pointed	point	VERB
ejpam-7142	193	33	path	path	NOUN
ejpam-7142	193	34	triples	triple	NOUN
ejpam-7142	193	35	and	and	CCONJ
ejpam-7142	193	36	morphisms	morphism	NOUN
ejpam-7142	193	37	as	as	ADP
ejpam-7142	193	38	neutrosophic	neutrosophic	ADJ
ejpam-7142	193	39	homotopy	homotopy	NOUN
ejpam-7142	193	40	classes	class	NOUN
ejpam-7142	193	41	.	.	PUNCT
ejpam-7142	194	1	e.	e.	PROPN
ejpam-7142	194	2	hussein	hussein	PROPN
ejpam-7142	194	3	et	et	PROPN
ejpam-7142	194	4	al	al	PROPN
ejpam-7142	194	5	.	.	PUNCT
ejpam-7142	194	6	/	/	SYM
ejpam-7142	194	7	eur	eur	PROPN
ejpam-7142	194	8	.	.	PUNCT
ejpam-7142	195	1	j.	j.	PROPN
ejpam-7142	195	2	pure	pure	PROPN
ejpam-7142	195	3	appl	appl	PROPN
ejpam-7142	195	4	.	.	PROPN
ejpam-7142	195	5	math	math	PROPN
ejpam-7142	195	6	,	,	PUNCT
ejpam-7142	195	7	18	18	NUM
ejpam-7142	195	8	(	(	PUNCT
ejpam-7142	195	9	4	4	NUM
ejpam-7142	195	10	)	)	PUNCT
ejpam-7142	195	11	(	(	PUNCT
ejpam-7142	195	12	2025	2025	NUM
ejpam-7142	195	13	)	)	PUNCT
ejpam-7142	195	14	,	,	PUNCT
ejpam-7142	195	15	7142	7142	NUM
ejpam-7142	195	16	9	9	NUM
ejpam-7142	195	17	of	of	ADP
ejpam-7142	195	18	17	17	NUM
ejpam-7142	195	19	(	(	PUNCT
ejpam-7142	195	20	ii	ii	NOUN
ejpam-7142	195	21	)	)	PUNCT
ejpam-7142	195	22	the	the	DET
ejpam-7142	195	23	composition	composition	NOUN
ejpam-7142	195	24	operation	operation	NOUN
ejpam-7142	195	25	is	be	AUX
ejpam-7142	195	26	associative	associative	ADJ
ejpam-7142	195	27	up	up	ADP
ejpam-7142	195	28	to	to	ADP
ejpam-7142	195	29	neutrosophic	neutrosophic	ADJ
ejpam-7142	195	30	homotopy	homotopy	NOUN
ejpam-7142	195	31	:	:	PUNCT
ejpam-7142	195	32	(	(	PUNCT
ejpam-7142	195	33	[	[	X
ejpam-7142	195	34	(	(	PUNCT
ejpam-7142	195	35	α	α	X
ejpam-7142	195	36	,	,	PUNCT
ejpam-7142	195	37	β	β	X
ejpam-7142	195	38	,	,	PUNCT
ejpam-7142	195	39	γ	γ	NOUN
ejpam-7142	195	40	)	)	PUNCT
ejpam-7142	195	41	]	]	PUNCT
ejpam-7142	196	1	◦	◦	NOUN
ejpam-7142	197	1	[	[	X
ejpam-7142	197	2	(	(	PUNCT
ejpam-7142	197	3	α′	α′	NUM
ejpam-7142	197	4	,	,	PUNCT
ejpam-7142	197	5	β′	β′	NUM
ejpam-7142	197	6	,	,	PUNCT
ejpam-7142	197	7	γ′	γ′	NOUN
ejpam-7142	197	8	)	)	PUNCT
ejpam-7142	197	9	]	]	PUNCT
ejpam-7142	197	10	)	)	PUNCT
ejpam-7142	198	1	◦	◦	NOUN
ejpam-7142	199	1	[	[	X
ejpam-7142	199	2	(	(	PUNCT
ejpam-7142	199	3	α′′	α′′	NOUN
ejpam-7142	199	4	,	,	PUNCT
ejpam-7142	199	5	β′′	β′′	NOUN
ejpam-7142	199	6	,	,	PUNCT
ejpam-7142	199	7	γ′′	γ′′	PROPN
ejpam-7142	199	8	)	)	PUNCT
ejpam-7142	199	9	]	]	PUNCT
ejpam-7142	200	1	∼n	∼n	PROPN
ejpam-7142	200	2	[	[	X
ejpam-7142	200	3	(	(	PUNCT
ejpam-7142	200	4	α	α	X
ejpam-7142	200	5	,	,	PUNCT
ejpam-7142	200	6	β	β	X
ejpam-7142	200	7	,	,	PUNCT
ejpam-7142	200	8	γ	γ	NOUN
ejpam-7142	200	9	)	)	PUNCT
ejpam-7142	200	10	]	]	PUNCT
ejpam-7142	200	11	◦	◦	NOUN
ejpam-7142	200	12	(	(	PUNCT
ejpam-7142	200	13	[	[	X
ejpam-7142	200	14	(	(	PUNCT
ejpam-7142	200	15	α′	α′	NUM
ejpam-7142	200	16	,	,	PUNCT
ejpam-7142	200	17	β′	β′	NUM
ejpam-7142	200	18	,	,	PUNCT
ejpam-7142	200	19	γ′	γ′	NOUN
ejpam-7142	200	20	)	)	PUNCT
ejpam-7142	200	21	]	]	PUNCT
ejpam-7142	201	1	◦	◦	NOUN
ejpam-7142	202	1	[	[	X
ejpam-7142	202	2	(	(	PUNCT
ejpam-7142	202	3	α′′	α′′	NOUN
ejpam-7142	202	4	,	,	PUNCT
ejpam-7142	202	5	β′′	β′′	NOUN
ejpam-7142	202	6	,	,	PUNCT
ejpam-7142	202	7	γ′′	γ′′	PROPN
ejpam-7142	202	8	)	)	PUNCT
ejpam-7142	202	9	]	]	PUNCT
ejpam-7142	202	10	)	)	PUNCT
ejpam-7142	202	11	(	(	PUNCT
ejpam-7142	202	12	iii	iii	X
ejpam-7142	202	13	)	)	PUNCT
ejpam-7142	202	14	identity	identity	NOUN
ejpam-7142	202	15	morphisms	morphism	NOUN
ejpam-7142	202	16	exist	exist	VERB
ejpam-7142	202	17	and	and	CCONJ
ejpam-7142	202	18	are	be	AUX
ejpam-7142	202	19	given	give	VERB
ejpam-7142	202	20	by	by	ADP
ejpam-7142	202	21	constant	constant	ADJ
ejpam-7142	202	22	path	path	NOUN
ejpam-7142	202	23	triples	triple	NOUN
ejpam-7142	202	24	.	.	PUNCT
ejpam-7142	203	1	(	(	PUNCT
ejpam-7142	203	2	iv	iv	X
ejpam-7142	203	3	)	)	PUNCT
ejpam-7142	203	4	every	every	DET
ejpam-7142	203	5	morphism	morphism	NOUN
ejpam-7142	203	6	has	have	VERB
ejpam-7142	203	7	an	an	DET
ejpam-7142	203	8	inverse	inverse	NOUN
ejpam-7142	203	9	up	up	ADP
ejpam-7142	203	10	to	to	ADP
ejpam-7142	203	11	neutrosophic	neutrosophic	ADJ
ejpam-7142	203	12	homotopy	homotopy	NOUN
ejpam-7142	203	13	.	.	PUNCT
ejpam-7142	204	1	(	(	PUNCT
ejpam-7142	204	2	v	v	X
ejpam-7142	204	3	)	)	PUNCT
ejpam-7142	204	4	the	the	DET
ejpam-7142	204	5	neutrosophic	neutrosophic	ADJ
ejpam-7142	204	6	degrees	degree	NOUN
ejpam-7142	204	7	satisfy	satisfy	VERB
ejpam-7142	204	8	the	the	DET
ejpam-7142	204	9	groupoid	groupoid	PROPN
ejpam-7142	204	10	axioms	axiom	VERB
ejpam-7142	204	11	with	with	ADP
ejpam-7142	204	12	t	t	NOUN
ejpam-7142	204	13	-	-	PUNCT
ejpam-7142	204	14	norm	norm	NOUN
ejpam-7142	204	15	and	and	CCONJ
ejpam-7142	204	16	t	t	NOUN
ejpam-7142	204	17	-	-	PUNCT
ejpam-7142	204	18	conorm	conorm	NOUN
ejpam-7142	204	19	operations	operation	NOUN
ejpam-7142	204	20	.	.	PUNCT
ejpam-7142	205	1	proof	proof	NOUN
ejpam-7142	205	2	.	.	PUNCT
ejpam-7142	206	1	we	we	PRON
ejpam-7142	206	2	prove	prove	VERB
ejpam-7142	206	3	each	each	DET
ejpam-7142	206	4	property	property	NOUN
ejpam-7142	206	5	:	:	PUNCT
ejpam-7142	206	6	(	(	PUNCT
ejpam-7142	206	7	i	i	NOUN
ejpam-7142	206	8	)	)	PUNCT
ejpam-7142	206	9	groupoid	groupoid	PROPN
ejpam-7142	206	10	structure	structure	NOUN
ejpam-7142	206	11	:	:	PUNCT
ejpam-7142	206	12	follows	follow	VERB
ejpam-7142	206	13	from	from	ADP
ejpam-7142	206	14	the	the	DET
ejpam-7142	206	15	equivalence	equivalence	NOUN
ejpam-7142	206	16	relation	relation	NOUN
ejpam-7142	206	17	established	establish	VERB
ejpam-7142	206	18	in	in	ADP
ejpam-7142	206	19	theorem	theorem	NOUN
ejpam-7142	206	20	2	2	NUM
ejpam-7142	206	21	and	and	CCONJ
ejpam-7142	206	22	the	the	DET
ejpam-7142	206	23	well	well	NOUN
ejpam-7142	206	24	-	-	PUNCT
ejpam-7142	206	25	definedness	definedness	NOUN
ejpam-7142	206	26	of	of	ADP
ejpam-7142	206	27	composition	composition	NOUN
ejpam-7142	206	28	.	.	PUNCT
ejpam-7142	207	1	(	(	PUNCT
ejpam-7142	207	2	ii	ii	NOUN
ejpam-7142	207	3	)	)	PUNCT
ejpam-7142	207	4	associativity	associativity	NOUN
ejpam-7142	207	5	:	:	PUNCT
ejpam-7142	207	6	given	give	VERB
ejpam-7142	207	7	three	three	NUM
ejpam-7142	207	8	composable	composable	ADJ
ejpam-7142	207	9	path	path	NOUN
ejpam-7142	207	10	triples	triple	NOUN
ejpam-7142	207	11	,	,	PUNCT
ejpam-7142	207	12	the	the	DET
ejpam-7142	207	13	associativity	associativity	NOUN
ejpam-7142	207	14	homotopy	homotopy	NOUN
ejpam-7142	207	15	can	can	AUX
ejpam-7142	207	16	be	be	AUX
ejpam-7142	207	17	constructed	construct	VERB
ejpam-7142	207	18	by	by	ADP
ejpam-7142	207	19	reparameterization	reparameterization	NOUN
ejpam-7142	207	20	.	.	PUNCT
ejpam-7142	208	1	the	the	DET
ejpam-7142	208	2	neutrosophic	neutrosophic	ADJ
ejpam-7142	208	3	conditions	condition	NOUN
ejpam-7142	208	4	are	be	AUX
ejpam-7142	208	5	satisfied	satisfied	ADJ
ejpam-7142	208	6	by	by	ADP
ejpam-7142	208	7	the	the	DET
ejpam-7142	208	8	properties	property	NOUN
ejpam-7142	208	9	of	of	ADP
ejpam-7142	208	10	•	•	NOUN
ejpam-7142	208	11	and	and	CCONJ
ejpam-7142	208	12	⋄.	⋄.	ADJ
ejpam-7142	208	13	(	(	PUNCT
ejpam-7142	208	14	iii	iii	NOUN
ejpam-7142	208	15	)	)	PUNCT
ejpam-7142	208	16	identities	identity	NOUN
ejpam-7142	208	17	:	:	PUNCT
ejpam-7142	208	18	for	for	ADP
ejpam-7142	208	19	any	any	DET
ejpam-7142	208	20	object	object	NOUN
ejpam-7142	208	21	[	[	X
ejpam-7142	208	22	(	(	PUNCT
ejpam-7142	208	23	α	α	X
ejpam-7142	208	24	,	,	PUNCT
ejpam-7142	208	25	β	β	X
ejpam-7142	208	26	,	,	PUNCT
ejpam-7142	208	27	γ	γ	NOUN
ejpam-7142	208	28	)	)	PUNCT
ejpam-7142	208	29	]	]	PUNCT
ejpam-7142	208	30	,	,	PUNCT
ejpam-7142	208	31	the	the	DET
ejpam-7142	208	32	identity	identity	NOUN
ejpam-7142	208	33	is	be	AUX
ejpam-7142	208	34	[	[	X
ejpam-7142	208	35	(	(	PUNCT
ejpam-7142	208	36	constv	constv	NOUN
ejpam-7142	208	37	,	,	PUNCT
ejpam-7142	208	38	constξ	constξ	NOUN
ejpam-7142	208	39	,	,	PUNCT
ejpam-7142	208	40	constℑ	constℑ	PROPN
ejpam-7142	208	41	)	)	PUNCT
ejpam-7142	208	42	]	]	PUNCT
ejpam-7142	208	43	.	.	PUNCT
ejpam-7142	209	1	the	the	DET
ejpam-7142	209	2	homotopy	homotopy	NOUN
ejpam-7142	209	3	to	to	ADP
ejpam-7142	209	4	the	the	DET
ejpam-7142	209	5	constant	constant	ADJ
ejpam-7142	209	6	path	path	NOUN
ejpam-7142	209	7	triple	triple	ADJ
ejpam-7142	209	8	satisfies	satisfie	NOUN
ejpam-7142	209	9	all	all	DET
ejpam-7142	209	10	neutrosophic	neutrosophic	ADJ
ejpam-7142	209	11	conditions	condition	NOUN
ejpam-7142	209	12	.	.	PUNCT
ejpam-7142	210	1	(	(	PUNCT
ejpam-7142	210	2	iv	iv	X
ejpam-7142	210	3	)	)	PUNCT
ejpam-7142	210	4	inverses	inverse	NOUN
ejpam-7142	210	5	:	:	PUNCT
ejpam-7142	210	6	the	the	DET
ejpam-7142	210	7	inverse	inverse	NOUN
ejpam-7142	210	8	of	of	ADP
ejpam-7142	210	9	[	[	X
ejpam-7142	210	10	(	(	PUNCT
ejpam-7142	210	11	α	α	X
ejpam-7142	210	12	,	,	PUNCT
ejpam-7142	210	13	β	β	X
ejpam-7142	210	14	,	,	PUNCT
ejpam-7142	210	15	γ	γ	NOUN
ejpam-7142	210	16	)	)	PUNCT
ejpam-7142	210	17	]	]	PUNCT
ejpam-7142	210	18	is	be	AUX
ejpam-7142	210	19	[	[	X
ejpam-7142	210	20	(	(	PUNCT
ejpam-7142	210	21	α−1	α−1	PROPN
ejpam-7142	210	22	,	,	PUNCT
ejpam-7142	210	23	β−1	β−1	NUM
ejpam-7142	210	24	,	,	PUNCT
ejpam-7142	210	25	γ−1	γ−1	PROPN
ejpam-7142	210	26	)	)	PUNCT
ejpam-7142	210	27	]	]	PUNCT
ejpam-7142	210	28	where	where	SCONJ
ejpam-7142	210	29	paths	path	NOUN
ejpam-7142	210	30	are	be	AUX
ejpam-7142	210	31	reversed	reverse	VERB
ejpam-7142	210	32	.	.	PUNCT
ejpam-7142	211	1	the	the	DET
ejpam-7142	211	2	homotopy	homotopy	NOUN
ejpam-7142	211	3	to	to	ADP
ejpam-7142	211	4	the	the	DET
ejpam-7142	211	5	constant	constant	ADJ
ejpam-7142	211	6	triple	triple	ADJ
ejpam-7142	211	7	satisfies	satisfie	NOUN
ejpam-7142	211	8	the	the	DET
ejpam-7142	211	9	neutrosophic	neutrosophic	ADJ
ejpam-7142	211	10	conditions	condition	NOUN
ejpam-7142	211	11	by	by	ADP
ejpam-7142	211	12	symmetry	symmetry	NOUN
ejpam-7142	211	13	.	.	PUNCT
ejpam-7142	212	1	(	(	PUNCT
ejpam-7142	212	2	v	v	NOUN
ejpam-7142	212	3	)	)	PUNCT
ejpam-7142	212	4	neutrosophic	neutrosophic	ADJ
ejpam-7142	212	5	axioms	axiom	NOUN
ejpam-7142	212	6	:	:	PUNCT
ejpam-7142	212	7	the	the	DET
ejpam-7142	212	8	t	t	NOUN
ejpam-7142	212	9	-	-	PUNCT
ejpam-7142	212	10	norm	norm	NOUN
ejpam-7142	212	11	•	•	NOUN
ejpam-7142	212	12	and	and	CCONJ
ejpam-7142	212	13	t	t	NOUN
ejpam-7142	212	14	-	-	PUNCT
ejpam-7142	212	15	conorm	conorm	NOUN
ejpam-7142	212	16	⋄	⋄	PROPN
ejpam-7142	212	17	operations	operation	NOUN
ejpam-7142	212	18	ensure	ensure	VERB
ejpam-7142	212	19	that	that	SCONJ
ejpam-7142	212	20	the	the	DET
ejpam-7142	212	21	neutrosophic	neutrosophic	ADJ
ejpam-7142	212	22	degrees	degree	NOUN
ejpam-7142	212	23	behave	behave	VERB
ejpam-7142	212	24	consistently	consistently	ADV
ejpam-7142	212	25	under	under	ADP
ejpam-7142	212	26	composition	composition	NOUN
ejpam-7142	212	27	and	and	CCONJ
ejpam-7142	212	28	inversion	inversion	NOUN
ejpam-7142	212	29	.	.	PUNCT
ejpam-7142	213	1	this	this	PRON
ejpam-7142	213	2	completes	complete	VERB
ejpam-7142	213	3	the	the	DET
ejpam-7142	213	4	proof	proof	NOUN
ejpam-7142	213	5	that	that	SCONJ
ejpam-7142	213	6	πn1	πn1	ADV
ejpam-7142	213	7	(	(	PUNCT
ejpam-7142	213	8	z	z	NOUN
ejpam-7142	213	9	,	,	PUNCT
ejpam-7142	213	10	v	v	NOUN
ejpam-7142	213	11	,	,	PUNCT
ejpam-7142	213	12	ξ,ℑ	ξ,ℑ	PROPN
ejpam-7142	213	13	)	)	PUNCT
ejpam-7142	213	14	is	be	AUX
ejpam-7142	213	15	indeed	indeed	ADV
ejpam-7142	213	16	a	a	DET
ejpam-7142	213	17	well	well	ADV
ejpam-7142	213	18	-	-	PUNCT
ejpam-7142	213	19	defined	define	VERB
ejpam-7142	213	20	neutrosophic	neutrosophic	ADJ
ejpam-7142	213	21	groupoid	groupoid	PROPN
ejpam-7142	213	22	.	.	PUNCT
ejpam-7142	214	1	corollary	corollary	ADJ
ejpam-7142	214	2	2	2	NUM
ejpam-7142	214	3	(	(	PUNCT
ejpam-7142	214	4	classical	classical	ADJ
ejpam-7142	214	5	fundamental	fundamental	ADJ
ejpam-7142	214	6	groupoid	groupoid	NOUN
ejpam-7142	214	7	as	as	ADP
ejpam-7142	214	8	special	special	ADJ
ejpam-7142	214	9	case	case	NOUN
ejpam-7142	214	10	)	)	PUNCT
ejpam-7142	214	11	.	.	PUNCT
ejpam-7142	215	1	when	when	SCONJ
ejpam-7142	215	2	t	t	PROPN
ejpam-7142	215	3	≡	≡	PROPN
ejpam-7142	215	4	1	1	NUM
ejpam-7142	215	5	,	,	PUNCT
ejpam-7142	215	6	i	i	PRON
ejpam-7142	215	7	≡	≡	PROPN
ejpam-7142	215	8	0	0	NUM
ejpam-7142	215	9	,	,	PUNCT
ejpam-7142	215	10	f	f	PROPN
ejpam-7142	215	11	≡	≡	PROPN
ejpam-7142	215	12	0	0	NUM
ejpam-7142	215	13	,	,	PUNCT
ejpam-7142	215	14	and	and	CCONJ
ejpam-7142	215	15	r	r	NOUN
ejpam-7142	215	16	=	=	SYM
ejpam-7142	215	17	1	1	NUM
ejpam-7142	215	18	,	,	PUNCT
ejpam-7142	215	19	the	the	DET
ejpam-7142	215	20	neutrosophic	neutrosophic	ADJ
ejpam-7142	215	21	mr	mr	PROPN
ejpam-7142	215	22	-	-	PUNCT
ejpam-7142	215	23	fundamental	fundamental	ADJ
ejpam-7142	215	24	groupoid	groupoid	NOUN
ejpam-7142	215	25	reduces	reduce	VERB
ejpam-7142	215	26	to	to	ADP
ejpam-7142	215	27	the	the	DET
ejpam-7142	215	28	classical	classical	ADJ
ejpam-7142	215	29	fundamental	fundamental	ADJ
ejpam-7142	215	30	groupoid	groupoid	NOUN
ejpam-7142	215	31	of	of	ADP
ejpam-7142	215	32	the	the	DET
ejpam-7142	215	33	space	space	NOUN
ejpam-7142	215	34	z.	z.	PROPN
ejpam-7142	215	35	proof	proof	NOUN
ejpam-7142	215	36	.	.	PUNCT
ejpam-7142	216	1	in	in	ADP
ejpam-7142	216	2	this	this	DET
ejpam-7142	216	3	limiting	limit	VERB
ejpam-7142	216	4	case	case	NOUN
ejpam-7142	216	5	,	,	PUNCT
ejpam-7142	216	6	all	all	DET
ejpam-7142	216	7	neutrosophic	neutrosophic	ADJ
ejpam-7142	216	8	conditions	condition	NOUN
ejpam-7142	216	9	become	become	VERB
ejpam-7142	216	10	trivial	trivial	ADJ
ejpam-7142	216	11	,	,	PUNCT
ejpam-7142	216	12	and	and	CCONJ
ejpam-7142	216	13	the	the	DET
ejpam-7142	216	14	homotopy	homotopy	NOUN
ejpam-7142	216	15	relation	relation	NOUN
ejpam-7142	216	16	reduces	reduce	VERB
ejpam-7142	216	17	to	to	ADP
ejpam-7142	216	18	the	the	DET
ejpam-7142	216	19	standard	standard	PROPN
ejpam-7142	216	20	homotopy	homotopy	NOUN
ejpam-7142	216	21	of	of	ADP
ejpam-7142	216	22	path	path	NOUN
ejpam-7142	216	23	triples	triple	NOUN
ejpam-7142	216	24	.	.	PUNCT
ejpam-7142	217	1	the	the	DET
ejpam-7142	217	2	groupoid	groupoid	PROPN
ejpam-7142	217	3	structure	structure	NOUN
ejpam-7142	217	4	coincides	coincide	VERB
ejpam-7142	217	5	with	with	ADP
ejpam-7142	217	6	the	the	DET
ejpam-7142	217	7	classical	classical	ADJ
ejpam-7142	217	8	fundamental	fundamental	ADJ
ejpam-7142	217	9	groupoid	groupoid	NOUN
ejpam-7142	217	10	.	.	PUNCT
ejpam-7142	218	1	3	3	X
ejpam-7142	218	2	.	.	X
ejpam-7142	218	3	examples	example	NOUN
ejpam-7142	218	4	and	and	CCONJ
ejpam-7142	218	5	applications	application	NOUN
ejpam-7142	218	6	in	in	ADP
ejpam-7142	218	7	this	this	DET
ejpam-7142	218	8	section	section	NOUN
ejpam-7142	218	9	,	,	PUNCT
ejpam-7142	218	10	we	we	PRON
ejpam-7142	218	11	illustrate	illustrate	VERB
ejpam-7142	218	12	the	the	DET
ejpam-7142	218	13	practical	practical	ADJ
ejpam-7142	218	14	relevance	relevance	NOUN
ejpam-7142	218	15	and	and	CCONJ
ejpam-7142	218	16	versatility	versatility	NOUN
ejpam-7142	218	17	of	of	ADP
ejpam-7142	218	18	neutrosophic	neutrosophic	ADJ
ejpam-7142	218	19	mrmetric	mrmetric	ADJ
ejpam-7142	218	20	spaces	space	NOUN
ejpam-7142	218	21	through	through	ADP
ejpam-7142	218	22	a	a	DET
ejpam-7142	218	23	series	series	NOUN
ejpam-7142	218	24	of	of	ADP
ejpam-7142	218	25	examples	example	NOUN
ejpam-7142	218	26	and	and	CCONJ
ejpam-7142	218	27	real	real	ADJ
ejpam-7142	218	28	-	-	PUNCT
ejpam-7142	218	29	world	world	NOUN
ejpam-7142	218	30	applications	application	NOUN
ejpam-7142	218	31	.	.	PUNCT
ejpam-7142	219	1	we	we	PRON
ejpam-7142	219	2	begin	begin	VERB
ejpam-7142	219	3	with	with	ADP
ejpam-7142	219	4	theoretical	theoretical	ADJ
ejpam-7142	219	5	examples	example	NOUN
ejpam-7142	219	6	on	on	ADP
ejpam-7142	219	7	common	common	ADJ
ejpam-7142	219	8	graph	graph	NOUN
ejpam-7142	219	9	structures	structure	NOUN
ejpam-7142	219	10	such	such	ADJ
ejpam-7142	219	11	as	as	ADP
ejpam-7142	219	12	complete	complete	ADJ
ejpam-7142	219	13	graphs	graph	NOUN
ejpam-7142	219	14	,	,	PUNCT
ejpam-7142	219	15	cycle	cycle	NOUN
ejpam-7142	219	16	graphs	graph	NOUN
ejpam-7142	219	17	,	,	PUNCT
ejpam-7142	219	18	and	and	CCONJ
ejpam-7142	219	19	scale	scale	NOUN
ejpam-7142	219	20	-	-	PUNCT
ejpam-7142	219	21	free	free	ADJ
ejpam-7142	219	22	networks	network	NOUN
ejpam-7142	219	23	,	,	PUNCT
ejpam-7142	219	24	demonstrating	demonstrate	VERB
ejpam-7142	219	25	how	how	SCONJ
ejpam-7142	219	26	neutrosophic	neutrosophic	ADJ
ejpam-7142	219	27	components	component	NOUN
ejpam-7142	219	28	and	and	CCONJ
ejpam-7142	219	29	contraction	contraction	NOUN
ejpam-7142	219	30	constants	constant	NOUN
ejpam-7142	219	31	behave	behave	VERB
ejpam-7142	219	32	in	in	ADP
ejpam-7142	219	33	each	each	DET
ejpam-7142	219	34	case	case	NOUN
ejpam-7142	219	35	.	.	PUNCT
ejpam-7142	220	1	we	we	PRON
ejpam-7142	220	2	then	then	ADV
ejpam-7142	220	3	transition	transition	VERB
ejpam-7142	220	4	to	to	ADP
ejpam-7142	220	5	applied	apply	VERB
ejpam-7142	220	6	scenarios	scenario	NOUN
ejpam-7142	220	7	,	,	PUNCT
ejpam-7142	220	8	including	include	VERB
ejpam-7142	220	9	social	social	ADJ
ejpam-7142	220	10	network	network	NOUN
ejpam-7142	220	11	analysis	analysis	NOUN
ejpam-7142	220	12	,	,	PUNCT
ejpam-7142	220	13	biological	biological	ADJ
ejpam-7142	220	14	neural	neural	ADJ
ejpam-7142	220	15	networks	network	NOUN
ejpam-7142	220	16	,	,	PUNCT
ejpam-7142	220	17	internet	internet	NOUN
ejpam-7142	220	18	topology	topology	NOUN
ejpam-7142	220	19	,	,	PUNCT
ejpam-7142	220	20	and	and	CCONJ
ejpam-7142	220	21	robotics	robotic	NOUN
ejpam-7142	220	22	path	path	NOUN
ejpam-7142	220	23	planning	planning	NOUN
ejpam-7142	220	24	.	.	PUNCT
ejpam-7142	221	1	each	each	DET
ejpam-7142	221	2	application	application	NOUN
ejpam-7142	221	3	is	be	AUX
ejpam-7142	221	4	accompanied	accompany	VERB
ejpam-7142	221	5	by	by	ADP
ejpam-7142	221	6	quantitative	quantitative	ADJ
ejpam-7142	221	7	results	result	NOUN
ejpam-7142	221	8	,	,	PUNCT
ejpam-7142	221	9	performance	performance	NOUN
ejpam-7142	221	10	metrics	metric	NOUN
ejpam-7142	221	11	,	,	PUNCT
ejpam-7142	221	12	and	and	CCONJ
ejpam-7142	221	13	computational	computational	ADJ
ejpam-7142	221	14	algorithms	algorithm	NOUN
ejpam-7142	221	15	,	,	PUNCT
ejpam-7142	221	16	highlighting	highlight	VERB
ejpam-7142	221	17	the	the	DET
ejpam-7142	221	18	framework	framework	NOUN
ejpam-7142	221	19	’s	’s	PART
ejpam-7142	221	20	ability	ability	NOUN
ejpam-7142	221	21	to	to	PART
ejpam-7142	221	22	model	model	VERB
ejpam-7142	221	23	uncertainty	uncertainty	NOUN
ejpam-7142	221	24	,	,	PUNCT
ejpam-7142	221	25	identify	identify	VERB
ejpam-7142	221	26	critical	critical	ADJ
ejpam-7142	221	27	nodes	node	NOUN
ejpam-7142	221	28	,	,	PUNCT
ejpam-7142	221	29	and	and	CCONJ
ejpam-7142	221	30	assess	assess	VERB
ejpam-7142	221	31	network	network	NOUN
ejpam-7142	221	32	robustness	robustness	NOUN
ejpam-7142	221	33	in	in	ADP
ejpam-7142	221	34	diverse	diverse	ADJ
ejpam-7142	221	35	contexts	contexts	NOUN
ejpam-7142	221	36	.	.	PUNCT
ejpam-7142	222	1	e.	e.	PROPN
ejpam-7142	222	2	hussein	hussein	PROPN
ejpam-7142	222	3	et	et	PROPN
ejpam-7142	222	4	al	al	PROPN
ejpam-7142	222	5	.	.	PUNCT
ejpam-7142	222	6	/	/	SYM
ejpam-7142	222	7	eur	eur	PROPN
ejpam-7142	222	8	.	.	PUNCT
ejpam-7142	223	1	j.	j.	PROPN
ejpam-7142	223	2	pure	pure	PROPN
ejpam-7142	223	3	appl	appl	PROPN
ejpam-7142	223	4	.	.	PROPN
ejpam-7142	223	5	math	math	PROPN
ejpam-7142	223	6	,	,	PUNCT
ejpam-7142	223	7	18	18	NUM
ejpam-7142	223	8	(	(	PUNCT
ejpam-7142	223	9	4	4	NUM
ejpam-7142	223	10	)	)	PUNCT
ejpam-7142	223	11	(	(	PUNCT
ejpam-7142	223	12	2025	2025	NUM
ejpam-7142	223	13	)	)	PUNCT
ejpam-7142	223	14	,	,	PUNCT
ejpam-7142	223	15	7142	7142	NUM
ejpam-7142	223	16	10	10	NUM
ejpam-7142	223	17	of	of	ADP
ejpam-7142	223	18	17	17	NUM
ejpam-7142	223	19	3.1	3.1	NUM
ejpam-7142	223	20	.	.	PUNCT
ejpam-7142	224	1	examples	example	NOUN
ejpam-7142	224	2	of	of	ADP
ejpam-7142	224	3	neutrosophic	neutrosophic	ADJ
ejpam-7142	224	4	graph	graph	NOUN
ejpam-7142	224	5	mr	mr	PROPN
ejpam-7142	224	6	-	-	ADJ
ejpam-7142	224	7	metric	metric	ADJ
ejpam-7142	224	8	spaces	space	NOUN
ejpam-7142	224	9	example	example	NOUN
ejpam-7142	224	10	1	1	NUM
ejpam-7142	224	11	(	(	PUNCT
ejpam-7142	224	12	complete	complete	ADJ
ejpam-7142	224	13	graph	graph	NOUN
ejpam-7142	224	14	kn	kn	PROPN
ejpam-7142	224	15	)	)	PUNCT
ejpam-7142	224	16	.	.	PUNCT
ejpam-7142	225	1	consider	consider	VERB
ejpam-7142	225	2	the	the	DET
ejpam-7142	225	3	complete	complete	ADJ
ejpam-7142	225	4	graph	graph	NOUN
ejpam-7142	225	5	kn	kn	PROPN
ejpam-7142	225	6	with	with	ADP
ejpam-7142	225	7	n	n	SYM
ejpam-7142	225	8	vertices	vertex	NOUN
ejpam-7142	225	9	.	.	PUNCT
ejpam-7142	226	1	the	the	DET
ejpam-7142	226	2	neutrosophic	neutrosophic	ADJ
ejpam-7142	226	3	graph	graph	NOUN
ejpam-7142	226	4	mr	mr	PROPN
ejpam-7142	226	5	-	-	ADJ
ejpam-7142	226	6	metric	metric	ADJ
ejpam-7142	226	7	space	space	NOUN
ejpam-7142	226	8	structure	structure	NOUN
ejpam-7142	226	9	is	be	AUX
ejpam-7142	226	10	given	give	VERB
ejpam-7142	226	11	by	by	ADP
ejpam-7142	226	12	:	:	PUNCT
ejpam-7142	226	13	•	•	NUM
ejpam-7142	226	14	mr	mr	PROPN
ejpam-7142	226	15	-	-	PUNCT
ejpam-7142	226	16	metric	metric	NOUN
ejpam-7142	226	17	:	:	PUNCT
ejpam-7142	226	18	for	for	ADP
ejpam-7142	226	19	any	any	DET
ejpam-7142	226	20	vertices	vertex	NOUN
ejpam-7142	226	21	u	u	NOUN
ejpam-7142	226	22	,	,	PUNCT
ejpam-7142	226	23	v	v	NOUN
ejpam-7142	226	24	,	,	PUNCT
ejpam-7142	226	25	w	w	PROPN
ejpam-7142	226	26	∈	∈	PROPN
ejpam-7142	226	27	v	v	X
ejpam-7142	226	28	(	(	PUNCT
ejpam-7142	226	29	kn	kn	PROPN
ejpam-7142	226	30	):	):	PUNCT
ejpam-7142	226	31	m(u	m(u	PROPN
ejpam-7142	226	32	,	,	PUNCT
ejpam-7142	226	33	v	v	NOUN
ejpam-7142	226	34	,	,	PUNCT
ejpam-7142	226	35	w	w	NOUN
ejpam-7142	226	36	)	)	PUNCT
ejpam-7142	226	37	=	=	SYM
ejpam-7142	226	38	d(u	d(u	PROPN
ejpam-7142	226	39	,	,	PUNCT
ejpam-7142	226	40	v	v	NOUN
ejpam-7142	226	41	)	)	PUNCT
ejpam-7142	226	42	+	+	X
ejpam-7142	226	43	d(v	d(v	ADJ
ejpam-7142	226	44	,	,	PUNCT
ejpam-7142	226	45	w	w	NOUN
ejpam-7142	226	46	)	)	PUNCT
ejpam-7142	226	47	+	+	CCONJ
ejpam-7142	226	48	d(w	d(w	PROPN
ejpam-7142	226	49	,	,	PUNCT
ejpam-7142	226	50	u	u	NOUN
ejpam-7142	226	51	)	)	PUNCT
ejpam-7142	226	52	3	3	NUM
ejpam-7142	226	53	=	=	SYM
ejpam-7142	226	54	1	1	NUM
ejpam-7142	226	55	+	+	NUM
ejpam-7142	226	56	1	1	NUM
ejpam-7142	226	57	+	+	SYM
ejpam-7142	226	58	1	1	NUM
ejpam-7142	226	59	3	3	NUM
ejpam-7142	226	60	=	=	SYM
ejpam-7142	226	61	1	1	NUM
ejpam-7142	226	62	since	since	SCONJ
ejpam-7142	226	63	all	all	DET
ejpam-7142	226	64	pairwise	pairwise	NOUN
ejpam-7142	226	65	distances	distance	NOUN
ejpam-7142	226	66	are	be	AUX
ejpam-7142	226	67	1	1	NUM
ejpam-7142	226	68	.	.	NOUN
ejpam-7142	226	69	•	•	NUM
ejpam-7142	226	70	truth	truth	NOUN
ejpam-7142	226	71	-	-	PUNCT
ejpam-7142	226	72	membership	membership	NOUN
ejpam-7142	226	73	:	:	PUNCT
ejpam-7142	226	74	for	for	ADP
ejpam-7142	226	75	any	any	DET
ejpam-7142	226	76	u	u	NOUN
ejpam-7142	226	77	,	,	PUNCT
ejpam-7142	226	78	v	v	NOUN
ejpam-7142	226	79	∈	∈	PROPN
ejpam-7142	226	80	v	v	NOUN
ejpam-7142	226	81	(	(	PUNCT
ejpam-7142	226	82	kn	kn	PROPN
ejpam-7142	226	83	)	)	PUNCT
ejpam-7142	226	84	and	and	CCONJ
ejpam-7142	226	85	γ	γ	X
ejpam-7142	226	86	≥	≥	NUM
ejpam-7142	226	87	1	1	NUM
ejpam-7142	226	88	:	:	PUNCT
ejpam-7142	226	89	t	t	PROPN
ejpam-7142	226	90	(	(	PUNCT
ejpam-7142	226	91	u	u	NOUN
ejpam-7142	226	92	,	,	PUNCT
ejpam-7142	226	93	v	v	NOUN
ejpam-7142	226	94	,	,	PUNCT
ejpam-7142	226	95	γ	γ	NOUN
ejpam-7142	226	96	)	)	PUNCT
ejpam-7142	226	97	=	=	NOUN
ejpam-7142	226	98	number	number	NOUN
ejpam-7142	226	99	of	of	ADP
ejpam-7142	226	100	paths	path	NOUN
ejpam-7142	226	101	of	of	ADP
ejpam-7142	226	102	length	length	NOUN
ejpam-7142	226	103	≤	≤	X
ejpam-7142	226	104	γ	γ	PROPN
ejpam-7142	226	105	total	total	ADJ
ejpam-7142	226	106	possible	possible	ADJ
ejpam-7142	226	107	paths	path	NOUN
ejpam-7142	226	108	=	=	SYM
ejpam-7142	226	109	1	1	NUM
ejpam-7142	226	110	because	because	SCONJ
ejpam-7142	226	111	in	in	ADP
ejpam-7142	226	112	a	a	DET
ejpam-7142	226	113	complete	complete	ADJ
ejpam-7142	226	114	graph	graph	NOUN
ejpam-7142	226	115	,	,	PUNCT
ejpam-7142	226	116	there	there	PRON
ejpam-7142	226	117	exists	exist	VERB
ejpam-7142	226	118	at	at	ADP
ejpam-7142	226	119	least	least	ADV
ejpam-7142	226	120	one	one	NUM
ejpam-7142	226	121	direct	direct	ADJ
ejpam-7142	226	122	path	path	NOUN
ejpam-7142	226	123	of	of	ADP
ejpam-7142	226	124	length	length	NOUN
ejpam-7142	226	125	1	1	NUM
ejpam-7142	226	126	between	between	ADP
ejpam-7142	226	127	any	any	DET
ejpam-7142	226	128	two	two	NUM
ejpam-7142	226	129	vertices	vertex	NOUN
ejpam-7142	226	130	.	.	PUNCT
ejpam-7142	227	1	•	•	ADP
ejpam-7142	227	2	indeterminacy	indeterminacy	NOUN
ejpam-7142	227	3	-	-	PUNCT
ejpam-7142	227	4	membership	membership	NOUN
ejpam-7142	227	5	:	:	PUNCT
ejpam-7142	227	6	the	the	DET
ejpam-7142	227	7	betweenness	betweenness	NOUN
ejpam-7142	227	8	centrality	centrality	NOUN
ejpam-7142	227	9	for	for	ADP
ejpam-7142	227	10	any	any	DET
ejpam-7142	227	11	vertex	vertex	NOUN
ejpam-7142	227	12	in	in	ADP
ejpam-7142	227	13	kn	kn	PROPN
ejpam-7142	227	14	is	be	AUX
ejpam-7142	227	15	:	:	PUNCT
ejpam-7142	227	16	betweenness(u	betweenness(u	NOUN
ejpam-7142	227	17	)	)	PUNCT
ejpam-7142	227	18	=	=	PUNCT
ejpam-7142	227	19	∑	∑	PUNCT
ejpam-7142	227	20	s̸=u̸=t	s̸=u̸=t	NOUN
ejpam-7142	227	21	σst(u	σst(u	PROPN
ejpam-7142	227	22	)	)	PUNCT
ejpam-7142	227	23	σst	σst	NOUN
ejpam-7142	228	1	=	=	SYM
ejpam-7142	228	2	0	0	PUNCT
ejpam-7142	228	3	since	since	SCONJ
ejpam-7142	228	4	all	all	DET
ejpam-7142	228	5	shortest	short	ADJ
ejpam-7142	228	6	paths	path	NOUN
ejpam-7142	228	7	are	be	AUX
ejpam-7142	228	8	direct	direct	ADJ
ejpam-7142	228	9	edges	edge	NOUN
ejpam-7142	228	10	.	.	PUNCT
ejpam-7142	229	1	therefore	therefore	ADV
ejpam-7142	229	2	:	:	PUNCT
ejpam-7142	229	3	i(u	i(u	PROPN
ejpam-7142	229	4	,	,	PUNCT
ejpam-7142	229	5	v	v	PROPN
ejpam-7142	229	6	,	,	PUNCT
ejpam-7142	229	7	γ	γ	NOUN
ejpam-7142	229	8	)	)	PUNCT
ejpam-7142	229	9	=	=	SYM
ejpam-7142	229	10	|0−	|0−	NOUN
ejpam-7142	229	11	0|	0|	VERB
ejpam-7142	229	12	max(betweenness	max(betweenness	NOUN
ejpam-7142	229	13	)	)	PUNCT
ejpam-7142	229	14	=	=	SYM
ejpam-7142	229	15	0	0	NUM
ejpam-7142	229	16	•	•	NUM
ejpam-7142	229	17	falsity	falsity	NOUN
ejpam-7142	229	18	-	-	PUNCT
ejpam-7142	229	19	membership	membership	NOUN
ejpam-7142	229	20	:	:	PUNCT
ejpam-7142	229	21	f(u	f(u	PROPN
ejpam-7142	229	22	,	,	PUNCT
ejpam-7142	229	23	v	v	NOUN
ejpam-7142	229	24	,	,	PUNCT
ejpam-7142	229	25	γ	γ	NOUN
ejpam-7142	229	26	)	)	PUNCT
ejpam-7142	229	27	=	=	SYM
ejpam-7142	229	28	1−	1−	NUM
ejpam-7142	229	29	t	t	PROPN
ejpam-7142	229	30	(	(	PUNCT
ejpam-7142	229	31	u	u	NOUN
ejpam-7142	229	32	,	,	PUNCT
ejpam-7142	229	33	v	v	NOUN
ejpam-7142	229	34	,	,	PUNCT
ejpam-7142	229	35	γ)−	γ)−	PROPN
ejpam-7142	229	36	i(u	i(u	PROPN
ejpam-7142	229	37	,	,	PUNCT
ejpam-7142	229	38	v	v	PROPN
ejpam-7142	229	39	,	,	PUNCT
ejpam-7142	229	40	γ	γ	NOUN
ejpam-7142	229	41	)	)	PUNCT
ejpam-7142	229	42	=	=	SYM
ejpam-7142	229	43	0	0	NOUN
ejpam-7142	230	1	the	the	DET
ejpam-7142	230	2	contraction	contraction	NOUN
ejpam-7142	230	3	constant	constant	ADJ
ejpam-7142	230	4	r	r	NOUN
ejpam-7142	230	5	can	can	AUX
ejpam-7142	230	6	be	be	AUX
ejpam-7142	230	7	chosen	choose	VERB
ejpam-7142	230	8	as	as	ADP
ejpam-7142	230	9	r	r	NOUN
ejpam-7142	230	10	=	=	SYM
ejpam-7142	230	11	1	1	NUM
ejpam-7142	230	12	+	+	CCONJ
ejpam-7142	230	13	ϵ	ϵ	X
ejpam-7142	230	14	for	for	ADP
ejpam-7142	230	15	small	small	ADJ
ejpam-7142	230	16	ϵ	ϵ	X
ejpam-7142	230	17	>	>	X
ejpam-7142	230	18	0	0	NUM
ejpam-7142	230	19	,	,	PUNCT
ejpam-7142	230	20	satisfying	satisfy	VERB
ejpam-7142	230	21	the	the	DET
ejpam-7142	230	22	small	small	ADJ
ejpam-7142	230	23	-	-	PUNCT
ejpam-7142	230	24	world	world	NOUN
ejpam-7142	230	25	property	property	NOUN
ejpam-7142	230	26	trivially	trivially	ADV
ejpam-7142	230	27	.	.	PUNCT
ejpam-7142	231	1	example	example	NOUN
ejpam-7142	231	2	2	2	NUM
ejpam-7142	231	3	(	(	PUNCT
ejpam-7142	231	4	cycle	cycle	NOUN
ejpam-7142	231	5	graph	graph	NOUN
ejpam-7142	231	6	cn	cn	PROPN
ejpam-7142	231	7	)	)	PUNCT
ejpam-7142	231	8	.	.	PUNCT
ejpam-7142	232	1	consider	consider	VERB
ejpam-7142	232	2	the	the	DET
ejpam-7142	232	3	cycle	cycle	NOUN
ejpam-7142	232	4	graph	graph	NOUN
ejpam-7142	232	5	cn	cn	VERB
ejpam-7142	232	6	with	with	ADP
ejpam-7142	232	7	n	n	NOUN
ejpam-7142	232	8	vertices	vertex	NOUN
ejpam-7142	232	9	arranged	arrange	VERB
ejpam-7142	232	10	in	in	ADP
ejpam-7142	232	11	a	a	DET
ejpam-7142	232	12	circle	circle	NOUN
ejpam-7142	232	13	.	.	PUNCT
ejpam-7142	233	1	•	•	NUM
ejpam-7142	233	2	mr	mr	PROPN
ejpam-7142	233	3	-	-	PUNCT
ejpam-7142	233	4	metric	metric	NOUN
ejpam-7142	233	5	:	:	PUNCT
ejpam-7142	233	6	for	for	ADP
ejpam-7142	233	7	vertices	vertex	NOUN
ejpam-7142	233	8	u	u	NOUN
ejpam-7142	233	9	,	,	PUNCT
ejpam-7142	233	10	v	v	NOUN
ejpam-7142	233	11	,	,	PUNCT
ejpam-7142	233	12	w	w	NOUN
ejpam-7142	233	13	:	:	PUNCT
ejpam-7142	233	14	m(u	m(u	PROPN
ejpam-7142	233	15	,	,	PUNCT
ejpam-7142	233	16	v	v	NOUN
ejpam-7142	233	17	,	,	PUNCT
ejpam-7142	233	18	w	w	NOUN
ejpam-7142	233	19	)	)	PUNCT
ejpam-7142	234	1	=	=	SYM
ejpam-7142	234	2	d(u	d(u	PROPN
ejpam-7142	234	3	,	,	PUNCT
ejpam-7142	234	4	v	v	NOUN
ejpam-7142	234	5	)	)	PUNCT
ejpam-7142	234	6	+	+	X
ejpam-7142	235	1	d(v	d(v	ADJ
ejpam-7142	235	2	,	,	PUNCT
ejpam-7142	235	3	w	w	NOUN
ejpam-7142	235	4	)	)	PUNCT
ejpam-7142	235	5	+	+	CCONJ
ejpam-7142	235	6	d(w	d(w	PROPN
ejpam-7142	235	7	,	,	PUNCT
ejpam-7142	235	8	u	u	NOUN
ejpam-7142	235	9	)	)	PUNCT
ejpam-7142	235	10	3	3	NUM
ejpam-7142	235	11	where	where	SCONJ
ejpam-7142	235	12	d(u	d(u	PROPN
ejpam-7142	235	13	,	,	PUNCT
ejpam-7142	235	14	v	v	NOUN
ejpam-7142	235	15	)	)	PUNCT
ejpam-7142	235	16	is	be	AUX
ejpam-7142	235	17	the	the	DET
ejpam-7142	235	18	shorter	short	ADJ
ejpam-7142	235	19	arc	arc	NOUN
ejpam-7142	235	20	distance	distance	NOUN
ejpam-7142	235	21	between	between	ADP
ejpam-7142	235	22	u	u	NOUN
ejpam-7142	235	23	and	and	CCONJ
ejpam-7142	235	24	v.	v.	ADP
ejpam-7142	235	25	•	•	NOUN
ejpam-7142	235	26	truth	truth	NOUN
ejpam-7142	235	27	-	-	PUNCT
ejpam-7142	235	28	membership	membership	NOUN
ejpam-7142	235	29	:	:	PUNCT
ejpam-7142	235	30	for	for	ADP
ejpam-7142	235	31	γ	γ	X
ejpam-7142	235	32	<	<	X
ejpam-7142	235	33	⌊n/2⌋	⌊n/2⌋	PROPN
ejpam-7142	235	34	:	:	PUNCT
ejpam-7142	235	35	t	t	PROPN
ejpam-7142	235	36	(	(	PUNCT
ejpam-7142	235	37	u	u	NOUN
ejpam-7142	235	38	,	,	PUNCT
ejpam-7142	235	39	v	v	NOUN
ejpam-7142	235	40	,	,	PUNCT
ejpam-7142	235	41	γ	γ	NOUN
ejpam-7142	235	42	)	)	PUNCT
ejpam-7142	235	43	=	=	NOUN
ejpam-7142	235	44	2γ	2γ	NUM
ejpam-7142	235	45	n−	n−	NOUN
ejpam-7142	235	46	1	1	NUM
ejpam-7142	235	47	since	since	SCONJ
ejpam-7142	235	48	there	there	PRON
ejpam-7142	235	49	are	be	VERB
ejpam-7142	235	50	exactly	exactly	ADV
ejpam-7142	235	51	2	2	NUM
ejpam-7142	235	52	paths	path	NOUN
ejpam-7142	235	53	of	of	ADP
ejpam-7142	235	54	length	length	NOUN
ejpam-7142	235	55	≤	≤	X
ejpam-7142	235	56	γ	γ	X
ejpam-7142	235	57	(	(	PUNCT
ejpam-7142	235	58	clockwise	clockwise	NOUN
ejpam-7142	235	59	and	and	CCONJ
ejpam-7142	235	60	counterclockwise	counterclockwise	NOUN
ejpam-7142	235	61	)	)	PUNCT
ejpam-7142	235	62	.	.	PUNCT
ejpam-7142	236	1	•	•	ADP
ejpam-7142	236	2	indeterminacy	indeterminacy	NOUN
ejpam-7142	236	3	-	-	PUNCT
ejpam-7142	236	4	membership	membership	NOUN
ejpam-7142	236	5	:	:	PUNCT
ejpam-7142	236	6	the	the	DET
ejpam-7142	236	7	betweenness	betweenness	ADJ
ejpam-7142	236	8	centrality	centrality	NOUN
ejpam-7142	236	9	in	in	ADP
ejpam-7142	236	10	cn	cn	PROPN
ejpam-7142	236	11	is	be	AUX
ejpam-7142	236	12	uniform	uniform	ADJ
ejpam-7142	236	13	:	:	PUNCT
ejpam-7142	236	14	betweenness(u	betweenness(u	NOUN
ejpam-7142	236	15	)	)	PUNCT
ejpam-7142	236	16	=	=	PUNCT
ejpam-7142	237	1	(	(	PUNCT
ejpam-7142	237	2	n−	n−	NOUN
ejpam-7142	237	3	1)(n−	1)(n−	NOUN
ejpam-7142	237	4	2	2	NUM
ejpam-7142	237	5	)	)	PUNCT
ejpam-7142	237	6	2	2	NUM
ejpam-7142	237	7	therefore	therefore	ADV
ejpam-7142	237	8	i(u	i(u	PROPN
ejpam-7142	237	9	,	,	PUNCT
ejpam-7142	237	10	v	v	PROPN
ejpam-7142	237	11	,	,	PUNCT
ejpam-7142	237	12	γ	γ	NOUN
ejpam-7142	237	13	)	)	PUNCT
ejpam-7142	237	14	=	=	SYM
ejpam-7142	237	15	0	0	NUM
ejpam-7142	237	16	for	for	ADP
ejpam-7142	237	17	all	all	DET
ejpam-7142	237	18	u	u	NOUN
ejpam-7142	237	19	,	,	PUNCT
ejpam-7142	237	20	v.	v.	PROPN
ejpam-7142	237	21	e.	e.	PROPN
ejpam-7142	237	22	hussein	hussein	PROPN
ejpam-7142	237	23	et	et	PROPN
ejpam-7142	237	24	al	al	PROPN
ejpam-7142	237	25	.	.	PUNCT
ejpam-7142	237	26	/	/	SYM
ejpam-7142	237	27	eur	eur	PROPN
ejpam-7142	237	28	.	.	PUNCT
ejpam-7142	238	1	j.	j.	PROPN
ejpam-7142	238	2	pure	pure	PROPN
ejpam-7142	238	3	appl	appl	PROPN
ejpam-7142	238	4	.	.	PROPN
ejpam-7142	238	5	math	math	PROPN
ejpam-7142	238	6	,	,	PUNCT
ejpam-7142	238	7	18	18	NUM
ejpam-7142	238	8	(	(	PUNCT
ejpam-7142	238	9	4	4	NUM
ejpam-7142	238	10	)	)	PUNCT
ejpam-7142	238	11	(	(	PUNCT
ejpam-7142	238	12	2025	2025	NUM
ejpam-7142	238	13	)	)	PUNCT
ejpam-7142	238	14	,	,	PUNCT
ejpam-7142	238	15	7142	7142	NUM
ejpam-7142	238	16	11	11	NUM
ejpam-7142	238	17	of	of	ADP
ejpam-7142	238	18	17	17	NUM
ejpam-7142	238	19	•	•	NOUN
ejpam-7142	238	20	contraction	contraction	NOUN
ejpam-7142	238	21	analysis	analysis	NOUN
ejpam-7142	238	22	:	:	PUNCT
ejpam-7142	238	23	the	the	DET
ejpam-7142	238	24	diameter	diameter	NOUN
ejpam-7142	238	25	is	be	AUX
ejpam-7142	238	26	⌊n/2⌋	⌊n/2⌋	NOUN
ejpam-7142	238	27	,	,	PUNCT
ejpam-7142	238	28	and	and	CCONJ
ejpam-7142	238	29	the	the	DET
ejpam-7142	238	30	contraction	contraction	NOUN
ejpam-7142	238	31	constant	constant	ADJ
ejpam-7142	238	32	r	r	NOUN
ejpam-7142	238	33	satisfies	satisfie	NOUN
ejpam-7142	238	34	:	:	PUNCT
ejpam-7142	238	35	r	r	NOUN
ejpam-7142	238	36	≥	≥	NOUN
ejpam-7142	238	37	1	1	NUM
ejpam-7142	238	38	+	+	CCONJ
ejpam-7142	238	39	c	c	NOUN
ejpam-7142	238	40	log	log	NOUN
ejpam-7142	238	41	n	n	NOUN
ejpam-7142	238	42	for	for	ADP
ejpam-7142	238	43	some	some	DET
ejpam-7142	238	44	constant	constant	ADJ
ejpam-7142	238	45	c	c	NOUN
ejpam-7142	238	46	>	>	X
ejpam-7142	238	47	0	0	PROPN
ejpam-7142	238	48	,	,	PUNCT
ejpam-7142	238	49	indicating	indicate	VERB
ejpam-7142	238	50	weak	weak	ADJ
ejpam-7142	238	51	small	small	ADJ
ejpam-7142	238	52	-	-	PUNCT
ejpam-7142	238	53	world	world	NOUN
ejpam-7142	238	54	properties	property	NOUN
ejpam-7142	238	55	.	.	PUNCT
ejpam-7142	239	1	example	example	NOUN
ejpam-7142	239	2	3	3	NUM
ejpam-7142	239	3	(	(	PUNCT
ejpam-7142	239	4	scale	scale	NOUN
ejpam-7142	239	5	-	-	PUNCT
ejpam-7142	239	6	free	free	ADJ
ejpam-7142	239	7	network	network	NOUN
ejpam-7142	239	8	model	model	NOUN
ejpam-7142	239	9	)	)	PUNCT
ejpam-7142	239	10	.	.	PUNCT
ejpam-7142	240	1	consider	consider	VERB
ejpam-7142	240	2	a	a	DET
ejpam-7142	240	3	scale	scale	NOUN
ejpam-7142	240	4	-	-	PUNCT
ejpam-7142	240	5	free	free	ADJ
ejpam-7142	240	6	network	network	NOUN
ejpam-7142	240	7	generated	generate	VERB
ejpam-7142	240	8	by	by	ADP
ejpam-7142	240	9	the	the	DET
ejpam-7142	240	10	barabásialbert	barabásialbert	NOUN
ejpam-7142	240	11	model	model	NOUN
ejpam-7142	240	12	with	with	ADP
ejpam-7142	240	13	n	n	ADP
ejpam-7142	240	14	vertices	vertex	NOUN
ejpam-7142	240	15	and	and	CCONJ
ejpam-7142	240	16	preferential	preferential	ADJ
ejpam-7142	240	17	attachment	attachment	NOUN
ejpam-7142	240	18	.	.	PUNCT
ejpam-7142	241	1	•	•	NUM
ejpam-7142	241	2	distance	distance	NOUN
ejpam-7142	241	3	distribution	distribution	NOUN
ejpam-7142	241	4	:	:	PUNCT
ejpam-7142	241	5	the	the	DET
ejpam-7142	241	6	average	average	ADJ
ejpam-7142	241	7	distance	distance	NOUN
ejpam-7142	241	8	scales	scale	VERB
ejpam-7142	241	9	as	as	ADP
ejpam-7142	241	10	:	:	PUNCT
ejpam-7142	241	11	l(g	l(g	NOUN
ejpam-7142	241	12	)	)	PUNCT
ejpam-7142	241	13	∼	∼	NOUN
ejpam-7142	241	14	logn	logn	NOUN
ejpam-7142	241	15	log	log	NOUN
ejpam-7142	241	16	logn	logn	VERB
ejpam-7142	241	17	•	•	NOUN
ejpam-7142	241	18	betweenness	betweenness	NOUN
ejpam-7142	241	19	centrality	centrality	NOUN
ejpam-7142	241	20	:	:	PUNCT
ejpam-7142	241	21	follows	follow	VERB
ejpam-7142	241	22	a	a	DET
ejpam-7142	241	23	power	power	NOUN
ejpam-7142	241	24	-	-	PUNCT
ejpam-7142	241	25	law	law	NOUN
ejpam-7142	241	26	distribution	distribution	NOUN
ejpam-7142	241	27	:	:	PUNCT
ejpam-7142	241	28	p	p	X
ejpam-7142	241	29	(	(	PUNCT
ejpam-7142	241	30	betweenness	betweenness	NOUN
ejpam-7142	241	31	=	=	SYM
ejpam-7142	241	32	b	b	X
ejpam-7142	241	33	)	)	PUNCT
ejpam-7142	241	34	∼	∼	NOUN
ejpam-7142	241	35	b−γ	b−γ	NOUN
ejpam-7142	241	36	with	with	ADP
ejpam-7142	241	37	γ	γ	PROPN
ejpam-7142	241	38	≈	≈	PROPN
ejpam-7142	241	39	2.2	2.2	NUM
ejpam-7142	241	40	.	.	PUNCT
ejpam-7142	241	41	•	•	NUM
ejpam-7142	241	42	neutrosophic	neutrosophic	ADJ
ejpam-7142	241	43	components	component	NOUN
ejpam-7142	241	44	:	:	PUNCT
ejpam-7142	241	45	t	t	PROPN
ejpam-7142	241	46	(	(	PUNCT
ejpam-7142	241	47	u	u	NOUN
ejpam-7142	241	48	,	,	PUNCT
ejpam-7142	241	49	v	v	NOUN
ejpam-7142	241	50	,	,	PUNCT
ejpam-7142	241	51	γ	γ	NOUN
ejpam-7142	241	52	)	)	PUNCT
ejpam-7142	241	53	=	=	PROPN
ejpam-7142	241	54	∑γ	∑γ	PROPN
ejpam-7142	241	55	k=1nk(u	k=1nk(u	NOUN
ejpam-7142	241	56	,	,	PUNCT
ejpam-7142	241	57	v)∑diameter	v)∑diameter	PUNCT
ejpam-7142	241	58	k=1	k=1	PROPN
ejpam-7142	241	59	nk(u	nk(u	NUM
ejpam-7142	241	60	,	,	PUNCT
ejpam-7142	241	61	v	v	NOUN
ejpam-7142	241	62	)	)	PUNCT
ejpam-7142	241	63	i(u	i(u	PROPN
ejpam-7142	241	64	,	,	PUNCT
ejpam-7142	241	65	v	v	PROPN
ejpam-7142	241	66	,	,	PUNCT
ejpam-7142	241	67	γ	γ	NOUN
ejpam-7142	241	68	)	)	PUNCT
ejpam-7142	241	69	=	=	PUNCT
ejpam-7142	241	70	|b(u)−b(v)|	|b(u)−b(v)|	PROPN
ejpam-7142	241	71	maxb	maxb	PROPN
ejpam-7142	241	72	f(u	f(u	PROPN
ejpam-7142	241	73	,	,	PUNCT
ejpam-7142	241	74	v	v	NOUN
ejpam-7142	241	75	,	,	PUNCT
ejpam-7142	241	76	γ	γ	NOUN
ejpam-7142	241	77	)	)	PUNCT
ejpam-7142	241	78	=	=	SYM
ejpam-7142	241	79	1−	1−	NUM
ejpam-7142	241	80	t	t	PROPN
ejpam-7142	241	81	(	(	PUNCT
ejpam-7142	241	82	u	u	NOUN
ejpam-7142	241	83	,	,	PUNCT
ejpam-7142	241	84	v	v	NOUN
ejpam-7142	241	85	,	,	PUNCT
ejpam-7142	241	86	γ)−	γ)−	PROPN
ejpam-7142	241	87	i(u	i(u	PROPN
ejpam-7142	241	88	,	,	PUNCT
ejpam-7142	241	89	v	v	PROPN
ejpam-7142	241	90	,	,	PUNCT
ejpam-7142	241	91	γ	γ	NOUN
ejpam-7142	241	92	)	)	PUNCT
ejpam-7142	241	93	where	where	SCONJ
ejpam-7142	241	94	nk(u	nk(u	NUM
ejpam-7142	241	95	,	,	PUNCT
ejpam-7142	241	96	v	v	NOUN
ejpam-7142	241	97	)	)	PUNCT
ejpam-7142	241	98	is	be	AUX
ejpam-7142	241	99	the	the	DET
ejpam-7142	241	100	number	number	NOUN
ejpam-7142	241	101	of	of	ADP
ejpam-7142	241	102	paths	path	NOUN
ejpam-7142	241	103	of	of	ADP
ejpam-7142	241	104	length	length	NOUN
ejpam-7142	241	105	exactly	exactly	ADV
ejpam-7142	241	106	k	k	X
ejpam-7142	241	107	between	between	ADP
ejpam-7142	241	108	u	u	PROPN
ejpam-7142	241	109	and	and	CCONJ
ejpam-7142	241	110	v.	v.	CCONJ
ejpam-7142	241	111	•	•	NOUN
ejpam-7142	241	112	contraction	contraction	NOUN
ejpam-7142	241	113	constant	constant	ADJ
ejpam-7142	241	114	:	:	PUNCT
ejpam-7142	241	115	empirical	empirical	ADJ
ejpam-7142	241	116	studies	study	NOUN
ejpam-7142	241	117	show	show	VERB
ejpam-7142	241	118	:	:	PUNCT
ejpam-7142	241	119	r	r	NOUN
ejpam-7142	241	120	≈	≈	PROPN
ejpam-7142	241	121	1	1	NUM
ejpam-7142	241	122	+	+	NUM
ejpam-7142	241	123	1.2	1.2	NUM
ejpam-7142	241	124	log	log	NOUN
ejpam-7142	241	125	n	n	CCONJ
ejpam-7142	241	126	satisfying	satisfy	VERB
ejpam-7142	241	127	the	the	DET
ejpam-7142	241	128	small	small	ADJ
ejpam-7142	241	129	-	-	PUNCT
ejpam-7142	241	130	world	world	NOUN
ejpam-7142	241	131	condition	condition	NOUN
ejpam-7142	241	132	.	.	PUNCT
ejpam-7142	242	1	3.2	3.2	NUM
ejpam-7142	242	2	.	.	PUNCT
ejpam-7142	242	3	applications	application	NOUN
ejpam-7142	242	4	to	to	ADP
ejpam-7142	242	5	real	real	ADJ
ejpam-7142	242	6	-	-	PUNCT
ejpam-7142	242	7	world	world	NOUN
ejpam-7142	242	8	networks	network	NOUN
ejpam-7142	242	9	application	application	NOUN
ejpam-7142	242	10	social	social	ADJ
ejpam-7142	242	11	network	network	NOUN
ejpam-7142	242	12	analysis	analysis	NOUN
ejpam-7142	242	13	.	.	PUNCT
ejpam-7142	243	1	consider	consider	VERB
ejpam-7142	243	2	a	a	DET
ejpam-7142	243	3	social	social	ADJ
ejpam-7142	243	4	network	network	NOUN
ejpam-7142	243	5	(	(	PUNCT
ejpam-7142	243	6	e.g.	e.g.	ADV
ejpam-7142	243	7	,	,	PUNCT
ejpam-7142	243	8	facebook	facebook	NOUN
ejpam-7142	243	9	friendships	friendship	NOUN
ejpam-7142	243	10	)	)	PUNCT
ejpam-7142	243	11	as	as	ADP
ejpam-7142	243	12	a	a	DET
ejpam-7142	243	13	neutrosophic	neutrosophic	ADJ
ejpam-7142	243	14	graph	graph	NOUN
ejpam-7142	243	15	mr	mr	PROPN
ejpam-7142	243	16	-	-	PUNCT
ejpam-7142	243	17	metric	metric	ADJ
ejpam-7142	243	18	space	space	NOUN
ejpam-7142	243	19	:	:	PUNCT
ejpam-7142	243	20	•	•	NOUN
ejpam-7142	243	21	vertices	vertex	NOUN
ejpam-7142	243	22	:	:	PUNCT
ejpam-7142	243	23	individuals	individual	NOUN
ejpam-7142	243	24	in	in	ADP
ejpam-7142	243	25	the	the	DET
ejpam-7142	243	26	social	social	ADJ
ejpam-7142	243	27	network	network	NOUN
ejpam-7142	243	28	•	•	NOUN
ejpam-7142	243	29	edges	edge	NOUN
ejpam-7142	243	30	:	:	PUNCT
ejpam-7142	243	31	friendship	friendship	NOUN
ejpam-7142	243	32	relationships	relationship	NOUN
ejpam-7142	243	33	•	•	ADP
ejpam-7142	243	34	mr	mr	PROPN
ejpam-7142	243	35	-	-	PUNCT
ejpam-7142	243	36	metric	metric	NOUN
ejpam-7142	243	37	:	:	PUNCT
ejpam-7142	243	38	measures	measure	VERB
ejpam-7142	243	39	the	the	DET
ejpam-7142	243	40	average	average	ADJ
ejpam-7142	243	41	social	social	ADJ
ejpam-7142	243	42	distance	distance	NOUN
ejpam-7142	243	43	between	between	ADP
ejpam-7142	243	44	triples	triple	NOUN
ejpam-7142	243	45	of	of	ADP
ejpam-7142	243	46	individuals	individual	NOUN
ejpam-7142	243	47	•	•	ADP
ejpam-7142	243	48	truth	truth	NOUN
ejpam-7142	243	49	-	-	PUNCT
ejpam-7142	243	50	membership	membership	NOUN
ejpam-7142	243	51	:	:	PUNCT
ejpam-7142	243	52	probability	probability	NOUN
ejpam-7142	243	53	that	that	SCONJ
ejpam-7142	243	54	two	two	NUM
ejpam-7142	243	55	individuals	individual	NOUN
ejpam-7142	243	56	can	can	AUX
ejpam-7142	243	57	communicate	communicate	VERB
ejpam-7142	243	58	through	through	ADP
ejpam-7142	243	59	short	short	ADJ
ejpam-7142	243	60	chains	chain	NOUN
ejpam-7142	243	61	•	•	ADP
ejpam-7142	243	62	indeterminacy	indeterminacy	NOUN
ejpam-7142	243	63	-	-	PUNCT
ejpam-7142	243	64	membership	membership	NOUN
ejpam-7142	243	65	:	:	PUNCT
ejpam-7142	243	66	difference	difference	NOUN
ejpam-7142	243	67	in	in	ADP
ejpam-7142	243	68	social	social	ADJ
ejpam-7142	243	69	influence	influence	NOUN
ejpam-7142	243	70	(	(	PUNCT
ejpam-7142	243	71	betweenness	betweenness	NOUN
ejpam-7142	243	72	centrality	centrality	NOUN
ejpam-7142	243	73	)	)	PUNCT
ejpam-7142	243	74	implementation	implementation	NOUN
ejpam-7142	243	75	results	result	NOUN
ejpam-7142	243	76	:	:	PUNCT
ejpam-7142	243	77	e.	e.	PROPN
ejpam-7142	243	78	hussein	hussein	PROPN
ejpam-7142	243	79	et	et	PROPN
ejpam-7142	243	80	al	al	PROPN
ejpam-7142	243	81	.	.	PUNCT
ejpam-7142	243	82	/	/	SYM
ejpam-7142	243	83	eur	eur	PROPN
ejpam-7142	243	84	.	.	PUNCT
ejpam-7142	244	1	j.	j.	PROPN
ejpam-7142	244	2	pure	pure	PROPN
ejpam-7142	244	3	appl	appl	PROPN
ejpam-7142	244	4	.	.	PROPN
ejpam-7142	244	5	math	math	PROPN
ejpam-7142	244	6	,	,	PUNCT
ejpam-7142	244	7	18	18	NUM
ejpam-7142	244	8	(	(	PUNCT
ejpam-7142	244	9	4	4	NUM
ejpam-7142	244	10	)	)	PUNCT
ejpam-7142	244	11	(	(	PUNCT
ejpam-7142	244	12	2025	2025	NUM
ejpam-7142	244	13	)	)	PUNCT
ejpam-7142	244	14	,	,	PUNCT
ejpam-7142	244	15	7142	7142	NUM
ejpam-7142	244	16	12	12	NUM
ejpam-7142	244	17	of	of	ADP
ejpam-7142	244	18	17	17	NUM
ejpam-7142	244	19	(	(	PUNCT
ejpam-7142	244	20	i	i	NOUN
ejpam-7142	244	21	)	)	PUNCT
ejpam-7142	244	22	for	for	ADP
ejpam-7142	244	23	the	the	DET
ejpam-7142	244	24	facebook	facebook	NOUN
ejpam-7142	244	25	social	social	ADJ
ejpam-7142	244	26	graph	graph	NOUN
ejpam-7142	244	27	with	with	ADP
ejpam-7142	244	28	n	n	PROPN
ejpam-7142	244	29	≈	≈	PROPN
ejpam-7142	244	30	2.8	2.8	NUM
ejpam-7142	244	31	billion	billion	NUM
ejpam-7142	244	32	vertices	vertex	NOUN
ejpam-7142	244	33	:	:	PUNCT
ejpam-7142	244	34	l(g	l(g	X
ejpam-7142	244	35	)	)	PUNCT
ejpam-7142	245	1	≈	≈	PROPN
ejpam-7142	245	2	4.7	4.7	NUM
ejpam-7142	245	3	,	,	PUNCT
ejpam-7142	245	4	r	r	NOUN
ejpam-7142	245	5	≈	≈	PROPN
ejpam-7142	245	6	1.08	1.08	NUM
ejpam-7142	245	7	(	(	PUNCT
ejpam-7142	245	8	ii	ii	NOUN
ejpam-7142	245	9	)	)	PUNCT
ejpam-7142	245	10	the	the	DET
ejpam-7142	245	11	fixed	fixed	ADJ
ejpam-7142	245	12	point	point	NOUN
ejpam-7142	245	13	v∗	v∗	PROPN
ejpam-7142	245	14	of	of	ADP
ejpam-7142	245	15	the	the	DET
ejpam-7142	245	16	neutrosophic	neutrosophic	ADJ
ejpam-7142	245	17	centrality	centrality	NOUN
ejpam-7142	245	18	mapping	mapping	NOUN
ejpam-7142	245	19	identifies	identify	VERB
ejpam-7142	245	20	the	the	DET
ejpam-7142	245	21	most	most	ADV
ejpam-7142	245	22	influential	influential	ADJ
ejpam-7142	245	23	user	user	NOUN
ejpam-7142	245	24	(	(	PUNCT
ejpam-7142	245	25	iii	iii	NOUN
ejpam-7142	245	26	)	)	PUNCT
ejpam-7142	245	27	network	network	NOUN
ejpam-7142	245	28	remains	remain	VERB
ejpam-7142	245	29	connected	connected	ADJ
ejpam-7142	245	30	(	(	PUNCT
ejpam-7142	245	31	η(g	η(g	PROPN
ejpam-7142	245	32	)	)	PUNCT
ejpam-7142	245	33	>	>	X
ejpam-7142	245	34	0.1	0.1	NUM
ejpam-7142	245	35	)	)	PUNCT
ejpam-7142	245	36	even	even	ADV
ejpam-7142	245	37	after	after	ADP
ejpam-7142	245	38	removing	remove	VERB
ejpam-7142	245	39	top	top	ADJ
ejpam-7142	245	40	5	5	NUM
ejpam-7142	245	41	%	%	NOUN
ejpam-7142	245	42	of	of	ADP
ejpam-7142	245	43	high	high	ADJ
ejpam-7142	245	44	-	-	PUNCT
ejpam-7142	245	45	centrality	centrality	NOUN
ejpam-7142	245	46	nodes	node	NOUN
ejpam-7142	245	47	application	application	NOUN
ejpam-7142	245	48	biological	biological	ADJ
ejpam-7142	245	49	neural	neural	ADJ
ejpam-7142	245	50	networks	network	NOUN
ejpam-7142	245	51	.	.	PUNCT
ejpam-7142	246	1	model	model	VERB
ejpam-7142	246	2	the	the	DET
ejpam-7142	246	3	c.	c.	PROPN
ejpam-7142	246	4	elegans	elegan	VERB
ejpam-7142	246	5	neural	neural	ADJ
ejpam-7142	246	6	network	network	NOUN
ejpam-7142	246	7	as	as	ADP
ejpam-7142	246	8	a	a	DET
ejpam-7142	246	9	neutrosophic	neutrosophic	ADJ
ejpam-7142	246	10	graph	graph	NOUN
ejpam-7142	246	11	mr	mr	PROPN
ejpam-7142	246	12	-	-	PUNCT
ejpam-7142	246	13	metric	metric	ADJ
ejpam-7142	246	14	space	space	NOUN
ejpam-7142	246	15	:	:	PUNCT
ejpam-7142	246	16	•	•	NOUN
ejpam-7142	246	17	vertices	vertex	NOUN
ejpam-7142	246	18	:	:	PUNCT
ejpam-7142	246	19	302	302	NUM
ejpam-7142	246	20	neurons	neuron	NOUN
ejpam-7142	246	21	•	•	NOUN
ejpam-7142	246	22	edges	edge	NOUN
ejpam-7142	246	23	:	:	PUNCT
ejpam-7142	246	24	synaptic	synaptic	ADJ
ejpam-7142	246	25	connections	connection	NOUN
ejpam-7142	246	26	•	•	ADP
ejpam-7142	246	27	mr	mr	PROPN
ejpam-7142	246	28	-	-	PUNCT
ejpam-7142	246	29	metric	metric	ADJ
ejpam-7142	246	30	:	:	PUNCT
ejpam-7142	246	31	information	information	NOUN
ejpam-7142	246	32	processing	processing	NOUN
ejpam-7142	246	33	efficiency	efficiency	NOUN
ejpam-7142	246	34	between	between	ADP
ejpam-7142	246	35	neuron	neuron	NOUN
ejpam-7142	246	36	triples	triple	NOUN
ejpam-7142	246	37	•	•	NUM
ejpam-7142	246	38	truth	truth	NOUN
ejpam-7142	246	39	-	-	PUNCT
ejpam-7142	246	40	membership	membership	NOUN
ejpam-7142	246	41	:	:	PUNCT
ejpam-7142	246	42	signal	signal	VERB
ejpam-7142	246	43	transmission	transmission	NOUN
ejpam-7142	246	44	reliability	reliability	NOUN
ejpam-7142	246	45	•	•	NOUN
ejpam-7142	246	46	indeterminacy	indeterminacy	NOUN
ejpam-7142	246	47	-	-	PUNCT
ejpam-7142	246	48	membership	membership	NOUN
ejpam-7142	246	49	:	:	PUNCT
ejpam-7142	246	50	functional	functional	ADJ
ejpam-7142	246	51	redundancy	redundancy	NOUN
ejpam-7142	246	52	differences	difference	NOUN
ejpam-7142	246	53	experimental	experimental	ADJ
ejpam-7142	246	54	findings	finding	NOUN
ejpam-7142	246	55	:	:	PUNCT
ejpam-7142	246	56	mavg	mavg	NOUN
ejpam-7142	246	57	=	=	PUNCT
ejpam-7142	246	58	2.34±	2.34±	PROPN
ejpam-7142	246	59	0.67	0.67	NUM
ejpam-7142	246	60	e[t	e[t	X
ejpam-7142	246	61	]	]	PUNCT
ejpam-7142	247	1	=	=	PUNCT
ejpam-7142	247	2	0.89±	0.89±	NOUN
ejpam-7142	247	3	0.08	0.08	NUM
ejpam-7142	247	4	e[i	e[i	NOUN
ejpam-7142	247	5	]	]	PUNCT
ejpam-7142	247	6	=	=	SYM
ejpam-7142	247	7	0.12±	0.12±	NOUN
ejpam-7142	247	8	0.05	0.05	NUM
ejpam-7142	247	9	r	r	NOUN
ejpam-7142	247	10	=	=	NOUN
ejpam-7142	247	11	1.23	1.23	NUM
ejpam-7142	247	12	the	the	DET
ejpam-7142	247	13	small	small	ADJ
ejpam-7142	247	14	contraction	contraction	NOUN
ejpam-7142	247	15	constant	constant	ADJ
ejpam-7142	247	16	r	r	NOUN
ejpam-7142	247	17	indicates	indicate	VERB
ejpam-7142	247	18	robust	robust	ADJ
ejpam-7142	247	19	information	information	NOUN
ejpam-7142	247	20	flow	flow	NOUN
ejpam-7142	247	21	despite	despite	SCONJ
ejpam-7142	247	22	neuronal	neuronal	ADJ
ejpam-7142	247	23	damage	damage	NOUN
ejpam-7142	247	24	.	.	PUNCT
ejpam-7142	248	1	application	application	NOUN
ejpam-7142	248	2	internet	internet	NOUN
ejpam-7142	248	3	topology	topology	NOUN
ejpam-7142	248	4	analysis	analysis	NOUN
ejpam-7142	248	5	.	.	PUNCT
ejpam-7142	249	1	apply	apply	VERB
ejpam-7142	249	2	neutrosophic	neutrosophic	ADJ
ejpam-7142	249	3	mr	mr	PROPN
ejpam-7142	249	4	-	-	PUNCT
ejpam-7142	249	5	metric	metric	ADJ
ejpam-7142	249	6	spaces	space	NOUN
ejpam-7142	249	7	to	to	ADP
ejpam-7142	249	8	the	the	DET
ejpam-7142	249	9	internet	internet	NOUN
ejpam-7142	249	10	as	as	ADP
ejpam-7142	249	11	-	-	PUNCT
ejpam-7142	249	12	level	level	NOUN
ejpam-7142	249	13	topology	topology	NOUN
ejpam-7142	249	14	:	:	PUNCT
ejpam-7142	249	15	•	•	NOUN
ejpam-7142	249	16	vertices	vertex	NOUN
ejpam-7142	249	17	:	:	PUNCT
ejpam-7142	249	18	autonomous	autonomous	ADJ
ejpam-7142	249	19	systems	system	NOUN
ejpam-7142	249	20	(	(	PUNCT
ejpam-7142	249	21	as	as	ADP
ejpam-7142	249	22	)	)	PUNCT
ejpam-7142	249	23	•	•	NOUN
ejpam-7142	249	24	edges	edge	NOUN
ejpam-7142	249	25	:	:	PUNCT
ejpam-7142	249	26	bgp	bgp	PROPN
ejpam-7142	249	27	peerings	peering	NOUN
ejpam-7142	249	28	•	•	ADP
ejpam-7142	249	29	mr	mr	PROPN
ejpam-7142	249	30	-	-	PUNCT
ejpam-7142	249	31	metric	metric	ADJ
ejpam-7142	249	32	:	:	PUNCT
ejpam-7142	249	33	routing	route	VERB
ejpam-7142	249	34	efficiency	efficiency	NOUN
ejpam-7142	249	35	between	between	ADP
ejpam-7142	249	36	as	as	ADP
ejpam-7142	249	37	triples	triple	NOUN
ejpam-7142	249	38	•	•	NUM
ejpam-7142	249	39	truth	truth	NOUN
ejpam-7142	249	40	-	-	PUNCT
ejpam-7142	249	41	membership	membership	NOUN
ejpam-7142	249	42	:	:	PUNCT
ejpam-7142	249	43	path	path	NOUN
ejpam-7142	249	44	availability	availability	NOUN
ejpam-7142	249	45	probability	probability	NOUN
ejpam-7142	249	46	•	•	NOUN
ejpam-7142	249	47	indeterminacy	indeterminacy	NOUN
ejpam-7142	249	48	-	-	PUNCT
ejpam-7142	249	49	membership	membership	NOUN
ejpam-7142	249	50	:	:	PUNCT
ejpam-7142	249	51	traffic	traffic	NOUN
ejpam-7142	249	52	handling	handling	NOUN
ejpam-7142	249	53	capacity	capacity	NOUN
ejpam-7142	249	54	differences	difference	NOUN
ejpam-7142	249	55	performance	performance	NOUN
ejpam-7142	249	56	metrics	metric	NOUN
ejpam-7142	249	57	:	:	PUNCT
ejpam-7142	249	58	(	(	PUNCT
ejpam-7142	249	59	i	i	NOUN
ejpam-7142	249	60	)	)	PUNCT
ejpam-7142	249	61	average	average	ADJ
ejpam-7142	249	62	path	path	NOUN
ejpam-7142	249	63	length	length	NOUN
ejpam-7142	249	64	:	:	PUNCT
ejpam-7142	250	1	l(g	l(g	X
ejpam-7142	250	2	)	)	PUNCT
ejpam-7142	251	1	≈	≈	PROPN
ejpam-7142	251	2	3.2	3.2	NUM
ejpam-7142	251	3	(	(	PUNCT
ejpam-7142	251	4	ii	ii	NOUN
ejpam-7142	251	5	)	)	PUNCT
ejpam-7142	251	6	contraction	contraction	NOUN
ejpam-7142	251	7	constant	constant	ADJ
ejpam-7142	251	8	:	:	PUNCT
ejpam-7142	251	9	r	r	NOUN
ejpam-7142	251	10	≈	≈	PROPN
ejpam-7142	251	11	1.15	1.15	NUM
ejpam-7142	251	12	(	(	PUNCT
ejpam-7142	251	13	iii	iii	NOUN
ejpam-7142	251	14	)	)	PUNCT
ejpam-7142	251	15	network	network	NOUN
ejpam-7142	251	16	remains	remain	VERB
ejpam-7142	251	17	connected	connect	VERB
ejpam-7142	251	18	after	after	ADP
ejpam-7142	251	19	removing	remove	VERB
ejpam-7142	251	20	15	15	NUM
ejpam-7142	251	21	%	%	NOUN
ejpam-7142	251	22	of	of	ADP
ejpam-7142	251	23	core	core	NOUN
ejpam-7142	251	24	ases	as	NOUN
ejpam-7142	251	25	(	(	PUNCT
ejpam-7142	251	26	iv	iv	NOUN
ejpam-7142	251	27	)	)	PUNCT
ejpam-7142	251	28	fixed	fix	VERB
ejpam-7142	251	29	point	point	NOUN
ejpam-7142	251	30	identification	identification	NOUN
ejpam-7142	251	31	matches	match	NOUN
ejpam-7142	251	32	known	know	VERB
ejpam-7142	251	33	tier-1	tier-1	NUM
ejpam-7142	251	34	isps	isps	PROPN
ejpam-7142	251	35	e.	e.	PROPN
ejpam-7142	251	36	hussein	hussein	PROPN
ejpam-7142	251	37	et	et	PROPN
ejpam-7142	251	38	al	al	PROPN
ejpam-7142	251	39	.	.	PUNCT
ejpam-7142	251	40	/	/	SYM
ejpam-7142	251	41	eur	eur	PROPN
ejpam-7142	251	42	.	.	PUNCT
ejpam-7142	252	1	j.	j.	PROPN
ejpam-7142	252	2	pure	pure	PROPN
ejpam-7142	252	3	appl	appl	PROPN
ejpam-7142	252	4	.	.	PROPN
ejpam-7142	252	5	math	math	PROPN
ejpam-7142	252	6	,	,	PUNCT
ejpam-7142	252	7	18	18	NUM
ejpam-7142	252	8	(	(	PUNCT
ejpam-7142	252	9	4	4	NUM
ejpam-7142	252	10	)	)	PUNCT
ejpam-7142	252	11	(	(	PUNCT
ejpam-7142	252	12	2025	2025	NUM
ejpam-7142	252	13	)	)	PUNCT
ejpam-7142	252	14	,	,	PUNCT
ejpam-7142	252	15	7142	7142	NUM
ejpam-7142	252	16	13	13	NUM
ejpam-7142	252	17	of	of	ADP
ejpam-7142	252	18	17	17	NUM
ejpam-7142	252	19	3.3	3.3	NUM
ejpam-7142	252	20	.	.	PUNCT
ejpam-7142	253	1	computational	computational	ADJ
ejpam-7142	253	2	implementation	implementation	NOUN
ejpam-7142	253	3	and	and	CCONJ
ejpam-7142	253	4	algorithms	algorithms	NOUN
ejpam-7142	253	5	application	application	NOUN
ejpam-7142	253	6	neutrosophic	neutrosophic	ADJ
ejpam-7142	253	7	centrality	centrality	NOUN
ejpam-7142	253	8	computation	computation	NOUN
ejpam-7142	253	9	.	.	PUNCT
ejpam-7142	254	1	algorithm	algorithm	NOUN
ejpam-7142	254	2	for	for	ADP
ejpam-7142	254	3	computing	compute	VERB
ejpam-7142	254	4	the	the	DET
ejpam-7142	254	5	neutrosophic	neutrosophic	ADJ
ejpam-7142	254	6	centrality	centrality	NOUN
ejpam-7142	254	7	fixed	fix	VERB
ejpam-7142	254	8	point	point	NOUN
ejpam-7142	254	9	:	:	PUNCT
ejpam-7142	254	10	(	(	PUNCT
ejpam-7142	254	11	i	i	NOUN
ejpam-7142	254	12	)	)	PUNCT
ejpam-7142	254	13	input	input	NOUN
ejpam-7142	254	14	:	:	PUNCT
ejpam-7142	254	15	graph	graph	NOUN
ejpam-7142	254	16	g	g	PROPN
ejpam-7142	254	17	=	=	SYM
ejpam-7142	254	18	(	(	PUNCT
ejpam-7142	254	19	v	v	NOUN
ejpam-7142	254	20	,	,	PUNCT
ejpam-7142	254	21	e	e	NOUN
ejpam-7142	254	22	)	)	PUNCT
ejpam-7142	254	23	,	,	PUNCT
ejpam-7142	254	24	tolerance	tolerance	NOUN
ejpam-7142	254	25	ϵ	ϵ	X
ejpam-7142	254	26	>	>	X
ejpam-7142	254	27	0	0	PUNCT
ejpam-7142	254	28	(	(	PUNCT
ejpam-7142	254	29	ii	ii	NOUN
ejpam-7142	254	30	)	)	PUNCT
ejpam-7142	254	31	initialize	initialize	NOUN
ejpam-7142	254	32	:	:	PUNCT
ejpam-7142	254	33	v0	v0	NOUN
ejpam-7142	254	34	←	←	PROPN
ejpam-7142	254	35	random	random	ADJ
ejpam-7142	254	36	vertex	vertex	NOUN
ejpam-7142	254	37	,	,	PUNCT
ejpam-7142	254	38	t←	t←	X
ejpam-7142	254	39	0	0	NUM
ejpam-7142	254	40	(	(	PUNCT
ejpam-7142	254	41	iii	iii	NOUN
ejpam-7142	254	42	)	)	PUNCT
ejpam-7142	254	43	repeat	repeat	NOUN
ejpam-7142	254	44	:	:	PUNCT
ejpam-7142	254	45	vt+1	vt+1	NUM
ejpam-7142	254	46	←	←	PROPN
ejpam-7142	254	47	argmin	argmin	PROPN
ejpam-7142	254	48	u∈v	u∈v	PROPN
ejpam-7142	254	49	max	max	PROPN
ejpam-7142	254	50	w∈v	w∈v	PROPN
ejpam-7142	255	1	[	[	X
ejpam-7142	255	2	m(u	m(u	PROPN
ejpam-7142	255	3	,	,	PUNCT
ejpam-7142	255	4	vt	vt	NOUN
ejpam-7142	255	5	,	,	PUNCT
ejpam-7142	255	6	w	w	PROPN
ejpam-7142	255	7	)	)	PUNCT
ejpam-7142	255	8	⋆	⋆	VERB
ejpam-7142	255	9	i(u	i(u	PROPN
ejpam-7142	255	10	,	,	PUNCT
ejpam-7142	255	11	vt	vt	PROPN
ejpam-7142	255	12	,	,	PUNCT
ejpam-7142	255	13	γ	γ	PROPN
ejpam-7142	255	14	)	)	PUNCT
ejpam-7142	255	15	]	]	PUNCT
ejpam-7142	256	1	δ	δ	PROPN
ejpam-7142	256	2	←m(vt+1	←m(vt+1	PROPN
ejpam-7142	256	3	,	,	PUNCT
ejpam-7142	256	4	vt	vt	PROPN
ejpam-7142	256	5	,	,	PUNCT
ejpam-7142	256	6	w	w	PROPN
ejpam-7142	256	7	∗	∗	NOUN
ejpam-7142	256	8	)	)	PUNCT
ejpam-7142	256	9	for	for	ADP
ejpam-7142	256	10	some	some	DET
ejpam-7142	256	11	w∗	w∗	NOUN
ejpam-7142	256	12	(	(	PUNCT
ejpam-7142	256	13	iv	iv	NUM
ejpam-7142	256	14	)	)	PUNCT
ejpam-7142	256	15	until	until	ADP
ejpam-7142	256	16	δ	δ	PROPN
ejpam-7142	256	17	<	<	X
ejpam-7142	256	18	ϵ	ϵ	X
ejpam-7142	256	19	(	(	PUNCT
ejpam-7142	256	20	v	v	NOUN
ejpam-7142	256	21	)	)	PUNCT
ejpam-7142	256	22	output	output	NOUN
ejpam-7142	256	23	:	:	PUNCT
ejpam-7142	256	24	v∗	v∗	PROPN
ejpam-7142	256	25	←	←	PROPN
ejpam-7142	256	26	vt+1	vt+1	PROPN
ejpam-7142	257	1	(	(	PUNCT
ejpam-7142	257	2	most	most	ADV
ejpam-7142	257	3	influential	influential	ADJ
ejpam-7142	257	4	node	node	NOUN
ejpam-7142	257	5	)	)	PUNCT
ejpam-7142	257	6	complexity	complexity	NOUN
ejpam-7142	257	7	analysis	analysis	NOUN
ejpam-7142	257	8	:	:	PUNCT
ejpam-7142	257	9	•	•	ADP
ejpam-7142	257	10	mr	mr	ADJ
ejpam-7142	257	11	-	-	PUNCT
ejpam-7142	257	12	metric	metric	ADJ
ejpam-7142	257	13	computation	computation	NOUN
ejpam-7142	257	14	:	:	PUNCT
ejpam-7142	257	15	o(n3	o(n3	NOUN
ejpam-7142	257	16	)	)	PUNCT
ejpam-7142	257	17	using	use	VERB
ejpam-7142	257	18	floyd	floyd	PROPN
ejpam-7142	257	19	-	-	PUNCT
ejpam-7142	257	20	warshall	warshall	PROPN
ejpam-7142	257	21	•	•	ADV
ejpam-7142	257	22	betweenness	betweenness	NOUN
ejpam-7142	257	23	centrality	centrality	NOUN
ejpam-7142	257	24	:	:	PUNCT
ejpam-7142	257	25	o(nm	o(nm	NOUN
ejpam-7142	257	26	)	)	PUNCT
ejpam-7142	257	27	using	use	VERB
ejpam-7142	257	28	brandes	brande	NOUN
ejpam-7142	257	29	’	'	PUNCT
ejpam-7142	257	30	algorithm	algorithm	NOUN
ejpam-7142	257	31	•	•	ADP
ejpam-7142	257	32	fixed	fix	VERB
ejpam-7142	257	33	point	point	NOUN
ejpam-7142	257	34	iteration	iteration	NOUN
ejpam-7142	257	35	:	:	PUNCT
ejpam-7142	257	36	o(k	o(k	PROPN
ejpam-7142	257	37	·	·	PUNCT
ejpam-7142	257	38	n2	n2	NOUN
ejpam-7142	257	39	)	)	PUNCT
ejpam-7142	257	40	where	where	SCONJ
ejpam-7142	257	41	k	k	PROPN
ejpam-7142	257	42	is	be	AUX
ejpam-7142	257	43	iterations	iteration	NOUN
ejpam-7142	257	44	•	•	DET
ejpam-7142	257	45	total	total	NOUN
ejpam-7142	257	46	:	:	PUNCT
ejpam-7142	257	47	o(n3	o(n3	NOUN
ejpam-7142	257	48	)	)	PUNCT
ejpam-7142	257	49	for	for	ADP
ejpam-7142	257	50	dense	dense	ADJ
ejpam-7142	257	51	graphs	graph	NOUN
ejpam-7142	257	52	,	,	PUNCT
ejpam-7142	257	53	o(nm	o(nm	NOUN
ejpam-7142	257	54	)	)	PUNCT
ejpam-7142	257	55	for	for	ADP
ejpam-7142	257	56	sparse	sparse	ADJ
ejpam-7142	257	57	graphs	graph	NOUN
ejpam-7142	257	58	application	application	NOUN
ejpam-7142	257	59	network	network	NOUN
ejpam-7142	257	60	robustness	robustness	NOUN
ejpam-7142	257	61	testing	testing	NOUN
ejpam-7142	257	62	.	.	PUNCT
ejpam-7142	258	1	procedure	procedure	NOUN
ejpam-7142	258	2	for	for	ADP
ejpam-7142	258	3	testing	testing	NOUN
ejpam-7142	258	4	network	network	NOUN
ejpam-7142	258	5	robustness	robustness	NOUN
ejpam-7142	258	6	using	use	VERB
ejpam-7142	258	7	neutrosophic	neutrosophic	ADJ
ejpam-7142	258	8	framework	framework	NOUN
ejpam-7142	258	9	:	:	PUNCT
ejpam-7142	258	10	(	(	PUNCT
ejpam-7142	258	11	i	i	NOUN
ejpam-7142	258	12	)	)	PUNCT
ejpam-7142	258	13	compute	compute	PROPN
ejpam-7142	258	14	contraction	contraction	NOUN
ejpam-7142	258	15	constant	constant	ADJ
ejpam-7142	258	16	r	r	NOUN
ejpam-7142	258	17	from	from	ADP
ejpam-7142	258	18	mr	mr	PROPN
ejpam-7142	258	19	-	-	PUNCT
ejpam-7142	258	20	metric	metric	ADJ
ejpam-7142	258	21	properties	property	NOUN
ejpam-7142	258	22	(	(	PUNCT
ejpam-7142	258	23	ii	ii	NOUN
ejpam-7142	258	24	)	)	PUNCT
ejpam-7142	258	25	verify	verify	VERB
ejpam-7142	258	26	small	small	ADJ
ejpam-7142	258	27	-	-	PUNCT
ejpam-7142	258	28	world	world	NOUN
ejpam-7142	258	29	condition	condition	NOUN
ejpam-7142	258	30	:	:	PUNCT
ejpam-7142	258	31	r	r	NOUN
ejpam-7142	258	32	<	<	X
ejpam-7142	258	33	1	1	NUM
ejpam-7142	258	34	+	+	SYM
ejpam-7142	258	35	1	1	NUM
ejpam-7142	258	36	logn	logn	NOUN
ejpam-7142	258	37	(	(	PUNCT
ejpam-7142	258	38	iii	iii	NOUN
ejpam-7142	258	39	)	)	PUNCT
ejpam-7142	258	40	calculate	calculate	NOUN
ejpam-7142	258	41	expansion	expansion	NOUN
ejpam-7142	258	42	constant	constant	ADJ
ejpam-7142	258	43	η(g	η(g	PROPN
ejpam-7142	258	44	)	)	PUNCT
ejpam-7142	258	45	(	(	PUNCT
ejpam-7142	258	46	iv	iv	X
ejpam-7142	258	47	)	)	PUNCT
ejpam-7142	258	48	determine	determine	VERB
ejpam-7142	258	49	critical	critical	ADJ
ejpam-7142	258	50	attack	attack	NOUN
ejpam-7142	258	51	size	size	NOUN
ejpam-7142	258	52	:	:	PUNCT
ejpam-7142	258	53	kmax	kmax	PROPN
ejpam-7142	258	54	=	=	SYM
ejpam-7142	259	1	n	n	PROPN
ejpam-7142	259	2	4r4	4r4	NUM
ejpam-7142	259	3	(	(	PUNCT
ejpam-7142	259	4	v	v	NOUN
ejpam-7142	259	5	)	)	PUNCT
ejpam-7142	259	6	test	test	NOUN
ejpam-7142	259	7	connectivity	connectivity	NOUN
ejpam-7142	259	8	after	after	ADP
ejpam-7142	259	9	removing	remove	VERB
ejpam-7142	259	10	top	top	ADJ
ejpam-7142	259	11	k	k	ADJ
ejpam-7142	259	12	central	central	ADJ
ejpam-7142	259	13	nodes	node	NOUN
ejpam-7142	259	14	(	(	PUNCT
ejpam-7142	259	15	vi	vi	NOUN
ejpam-7142	259	16	)	)	PUNCT
ejpam-7142	259	17	measure	measure	NOUN
ejpam-7142	259	18	diameter	diameter	NOUN
ejpam-7142	259	19	increase	increase	NOUN
ejpam-7142	259	20	factor	factor	NOUN
ejpam-7142	259	21	:	:	PUNCT
ejpam-7142	259	22	diameter(g′	diameter(g′	NUM
ejpam-7142	259	23	)	)	PUNCT
ejpam-7142	259	24	diameter(g	diameter(g	PROPN
ejpam-7142	259	25	)	)	PUNCT
ejpam-7142	259	26	≤	≤	NOUN
ejpam-7142	259	27	2r4	2r4	NUM
ejpam-7142	259	28	case	case	NOUN
ejpam-7142	259	29	study	study	NOUN
ejpam-7142	259	30	power	power	NOUN
ejpam-7142	259	31	grid	grid	NOUN
ejpam-7142	259	32	network	network	NOUN
ejpam-7142	259	33	:	:	PUNCT
ejpam-7142	259	34	n	n	PROPN
ejpam-7142	259	35	=	=	SYM
ejpam-7142	259	36	4941	4941	NUM
ejpam-7142	259	37	,	,	PUNCT
ejpam-7142	259	38	m	m	VERB
ejpam-7142	259	39	=	=	SYM
ejpam-7142	259	40	6594	6594	NUM
ejpam-7142	259	41	r	r	NOUN
ejpam-7142	259	42	=	=	SYM
ejpam-7142	259	43	1.32	1.32	NUM
ejpam-7142	259	44	,	,	PUNCT
ejpam-7142	259	45	η(g	η(g	NUM
ejpam-7142	259	46	)	)	PUNCT
ejpam-7142	259	47	=	=	PUNCT
ejpam-7142	259	48	0.08	0.08	NUM
ejpam-7142	259	49	kmax	kmax	NOUN
ejpam-7142	259	50	=	=	SYM
ejpam-7142	259	51	164	164	NUM
ejpam-7142	259	52	,	,	PUNCT
ejpam-7142	259	53	diameter	diameter	NOUN
ejpam-7142	259	54	increase	increase	NOUN
ejpam-7142	259	55	:	:	PUNCT
ejpam-7142	259	56	1.47×	1.47×	NUM
ejpam-7142	259	57	e.	e.	PROPN
ejpam-7142	259	58	hussein	hussein	PROPN
ejpam-7142	259	59	et	et	PROPN
ejpam-7142	259	60	al	al	PROPN
ejpam-7142	259	61	.	.	PUNCT
ejpam-7142	259	62	/	/	SYM
ejpam-7142	259	63	eur	eur	PROPN
ejpam-7142	259	64	.	.	PUNCT
ejpam-7142	260	1	j.	j.	PROPN
ejpam-7142	260	2	pure	pure	PROPN
ejpam-7142	260	3	appl	appl	PROPN
ejpam-7142	260	4	.	.	PROPN
ejpam-7142	260	5	math	math	PROPN
ejpam-7142	260	6	,	,	PUNCT
ejpam-7142	260	7	18	18	NUM
ejpam-7142	260	8	(	(	PUNCT
ejpam-7142	260	9	4	4	NUM
ejpam-7142	260	10	)	)	PUNCT
ejpam-7142	260	11	(	(	PUNCT
ejpam-7142	260	12	2025	2025	NUM
ejpam-7142	260	13	)	)	PUNCT
ejpam-7142	260	14	,	,	PUNCT
ejpam-7142	260	15	7142	7142	NUM
ejpam-7142	260	16	14	14	NUM
ejpam-7142	260	17	of	of	ADP
ejpam-7142	260	18	17	17	NUM
ejpam-7142	260	19	3.4	3.4	NUM
ejpam-7142	260	20	.	.	PUNCT
ejpam-7142	261	1	neutrosophic	neutrosophic	PROPN
ejpam-7142	261	2	mr	mr	PROPN
ejpam-7142	261	3	-	-	PUNCT
ejpam-7142	261	4	homotopy	homotopy	NOUN
ejpam-7142	261	5	in	in	ADP
ejpam-7142	261	6	practical	practical	ADJ
ejpam-7142	261	7	scenarios	scenario	NOUN
ejpam-7142	261	8	application	application	NOUN
ejpam-7142	261	9	path	path	NOUN
ejpam-7142	261	10	planning	planning	NOUN
ejpam-7142	261	11	in	in	ADP
ejpam-7142	261	12	robotics	robotic	NOUN
ejpam-7142	261	13	.	.	PUNCT
ejpam-7142	262	1	use	use	VERB
ejpam-7142	262	2	neutrosophic	neutrosophic	ADJ
ejpam-7142	262	3	mr	mr	PROPN
ejpam-7142	262	4	-	-	PUNCT
ejpam-7142	262	5	homotopy	homotopy	NOUN
ejpam-7142	262	6	for	for	ADP
ejpam-7142	262	7	multi	multi	ADJ
ejpam-7142	262	8	-	-	ADJ
ejpam-7142	262	9	robot	robot	ADJ
ejpam-7142	262	10	path	path	NOUN
ejpam-7142	262	11	planning	planning	NOUN
ejpam-7142	262	12	:	:	PUNCT
ejpam-7142	262	13	•	•	NUM
ejpam-7142	262	14	configuration	configuration	NOUN
ejpam-7142	262	15	space	space	NOUN
ejpam-7142	262	16	:	:	PUNCT
ejpam-7142	262	17	z	z	NOUN
ejpam-7142	262	18	=	=	SYM
ejpam-7142	262	19	r3	r3	PROPN
ejpam-7142	262	20	m	m	PROPN
ejpam-7142	262	21	for	for	ADP
ejpam-7142	262	22	m	m	PROPN
ejpam-7142	262	23	robots	robot	NOUN
ejpam-7142	262	24	•	•	ADP
ejpam-7142	262	25	mr	mr	PROPN
ejpam-7142	262	26	-	-	PUNCT
ejpam-7142	262	27	metric	metric	NOUN
ejpam-7142	262	28	:	:	PUNCT
ejpam-7142	262	29	measures	measure	NOUN
ejpam-7142	262	30	collective	collective	ADJ
ejpam-7142	262	31	path	path	NOUN
ejpam-7142	262	32	efficiency	efficiency	NOUN
ejpam-7142	262	33	•	•	NUM
ejpam-7142	262	34	homotopy	homotopy	NOUN
ejpam-7142	262	35	classes	class	NOUN
ejpam-7142	262	36	:	:	PUNCT
ejpam-7142	262	37	different	different	ADJ
ejpam-7142	262	38	collision	collision	NOUN
ejpam-7142	262	39	-	-	PUNCT
ejpam-7142	262	40	free	free	ADJ
ejpam-7142	262	41	path	path	NOUN
ejpam-7142	262	42	strategies	strategy	NOUN
ejpam-7142	262	43	•	•	ADP
ejpam-7142	262	44	truth	truth	NOUN
ejpam-7142	262	45	-	-	PUNCT
ejpam-7142	262	46	membership	membership	NOUN
ejpam-7142	262	47	:	:	PUNCT
ejpam-7142	262	48	path	path	VERB
ejpam-7142	262	49	feasibility	feasibility	NOUN
ejpam-7142	262	50	confidence	confidence	NOUN
ejpam-7142	262	51	•	•	NOUN
ejpam-7142	262	52	indeterminacy	indeterminacy	NOUN
ejpam-7142	262	53	-	-	PUNCT
ejpam-7142	262	54	membership	membership	NOUN
ejpam-7142	262	55	:	:	PUNCT
ejpam-7142	263	1	uncertainty	uncertainty	NOUN
ejpam-7142	263	2	in	in	ADP
ejpam-7142	263	3	obstacle	obstacle	NOUN
ejpam-7142	263	4	positions	position	NOUN
ejpam-7142	263	5	implementation	implementation	NOUN
ejpam-7142	263	6	:	:	PUNCT
ejpam-7142	263	7	ht(α	ht(α	NUM
ejpam-7142	263	8	,	,	PUNCT
ejpam-7142	263	9	β	β	X
ejpam-7142	263	10	,	,	PUNCT
ejpam-7142	263	11	γ	γ	NOUN
ejpam-7142	263	12	)	)	PUNCT
ejpam-7142	263	13	=	=	PUNCT
ejpam-7142	263	14	(	(	PUNCT
ejpam-7142	263	15	1−	1−	NUM
ejpam-7142	263	16	t	t	PROPN
ejpam-7142	263	17	)	)	PUNCT
ejpam-7142	263	18	·	·	PUNCT
ejpam-7142	263	19	initial	initial	ADJ
ejpam-7142	263	20	paths	path	NOUN
ejpam-7142	263	21	+	+	CCONJ
ejpam-7142	263	22	t	t	NOUN
ejpam-7142	263	23	·	·	PUNCT
ejpam-7142	263	24	final	final	ADJ
ejpam-7142	263	25	paths	path	NOUN
ejpam-7142	263	26	+	+	CCONJ
ejpam-7142	263	27	obstacle	obstacle	NOUN
ejpam-7142	263	28	avoidance	avoidance	NOUN
ejpam-7142	263	29	the	the	DET
ejpam-7142	263	30	monotonic	monotonic	ADJ
ejpam-7142	263	31	decrease	decrease	NOUN
ejpam-7142	263	32	of	of	ADP
ejpam-7142	263	33	φ(t	φ(t	PROPN
ejpam-7142	263	34	)	)	PUNCT
ejpam-7142	263	35	ensures	ensure	VERB
ejpam-7142	263	36	continuous	continuous	ADJ
ejpam-7142	263	37	improvement	improvement	NOUN
ejpam-7142	263	38	in	in	ADP
ejpam-7142	263	39	path	path	NOUN
ejpam-7142	263	40	quality	quality	NOUN
ejpam-7142	263	41	.	.	PUNCT
ejpam-7142	264	1	application	application	NOUN
ejpam-7142	264	2	protein	protein	NOUN
ejpam-7142	264	3	folding	fold	VERB
ejpam-7142	264	4	pathways	pathway	NOUN
ejpam-7142	264	5	.	.	PUNCT
ejpam-7142	265	1	model	model	NOUN
ejpam-7142	265	2	protein	protein	NOUN
ejpam-7142	265	3	folding	fold	VERB
ejpam-7142	265	4	as	as	ADP
ejpam-7142	265	5	neutrosophic	neutrosophic	ADJ
ejpam-7142	265	6	mr	mr	PROPN
ejpam-7142	265	7	-	-	PUNCT
ejpam-7142	265	8	homotopy	homotopy	PROPN
ejpam-7142	265	9	:	:	PUNCT
ejpam-7142	265	10	•	•	NUM
ejpam-7142	265	11	space	space	NOUN
ejpam-7142	265	12	:	:	PUNCT
ejpam-7142	265	13	z	z	NOUN
ejpam-7142	265	14	=	=	SYM
ejpam-7142	265	15	conformation	conformation	NOUN
ejpam-7142	265	16	space	space	NOUN
ejpam-7142	265	17	of	of	ADP
ejpam-7142	265	18	amino	amino	ADJ
ejpam-7142	265	19	acids	acid	NOUN
ejpam-7142	265	20	•	•	NUM
ejpam-7142	265	21	path	path	NOUN
ejpam-7142	265	22	triples	triple	NOUN
ejpam-7142	265	23	:	:	PUNCT
ejpam-7142	265	24	(	(	PUNCT
ejpam-7142	265	25	α	α	X
ejpam-7142	265	26	,	,	PUNCT
ejpam-7142	265	27	β	β	X
ejpam-7142	265	28	,	,	PUNCT
ejpam-7142	265	29	γ	γ	NOUN
ejpam-7142	265	30	)	)	PUNCT
ejpam-7142	265	31	represent	represent	VERB
ejpam-7142	265	32	different	different	ADJ
ejpam-7142	265	33	folding	folding	NOUN
ejpam-7142	265	34	trajectories	trajectory	NOUN
ejpam-7142	265	35	•	•	NUM
ejpam-7142	265	36	homotopy	homotopy	VERB
ejpam-7142	265	37	:	:	PUNCT
ejpam-7142	265	38	continuous	continuous	ADJ
ejpam-7142	265	39	deformation	deformation	NOUN
ejpam-7142	265	40	between	between	ADP
ejpam-7142	265	41	folding	fold	VERB
ejpam-7142	265	42	pathways	pathway	NOUN
ejpam-7142	265	43	•	•	ADP
ejpam-7142	265	44	truth	truth	NOUN
ejpam-7142	265	45	-	-	PUNCT
ejpam-7142	265	46	membership	membership	NOUN
ejpam-7142	265	47	:	:	PUNCT
ejpam-7142	265	48	native	native	ADJ
ejpam-7142	265	49	state	state	NOUN
ejpam-7142	265	50	reachability	reachability	NOUN
ejpam-7142	265	51	probability	probability	NOUN
ejpam-7142	265	52	•	•	NOUN
ejpam-7142	265	53	indeterminacy	indeterminacy	NOUN
ejpam-7142	265	54	-	-	PUNCT
ejpam-7142	265	55	membership	membership	NOUN
ejpam-7142	265	56	:	:	PUNCT
ejpam-7142	265	57	uncertainty	uncertainty	NOUN
ejpam-7142	265	58	in	in	ADP
ejpam-7142	265	59	intermediate	intermediate	ADJ
ejpam-7142	265	60	states	state	NOUN
ejpam-7142	265	61	biological	biological	ADJ
ejpam-7142	265	62	insight	insight	NOUN
ejpam-7142	265	63	:	:	PUNCT
ejpam-7142	265	64	the	the	DET
ejpam-7142	265	65	neutrosophic	neutrosophic	ADJ
ejpam-7142	265	66	fundamental	fundamental	ADJ
ejpam-7142	265	67	groupoid	groupoid	NOUN
ejpam-7142	265	68	reveals	reveal	VERB
ejpam-7142	265	69	equivalent	equivalent	ADJ
ejpam-7142	265	70	folding	fold	VERB
ejpam-7142	265	71	mechanisms	mechanism	NOUN
ejpam-7142	265	72	with	with	ADP
ejpam-7142	265	73	different	different	ADJ
ejpam-7142	265	74	energy	energy	NOUN
ejpam-7142	265	75	landscapes	landscape	NOUN
ejpam-7142	265	76	.	.	PUNCT
ejpam-7142	266	1	3.5	3.5	NUM
ejpam-7142	266	2	.	.	PUNCT
ejpam-7142	267	1	quantitative	quantitative	ADJ
ejpam-7142	267	2	results	result	NOUN
ejpam-7142	267	3	and	and	CCONJ
ejpam-7142	267	4	performance	performance	NOUN
ejpam-7142	267	5	analysis	analysis	NOUN
ejpam-7142	267	6	network	network	NOUN
ejpam-7142	267	7	type	type	NOUN
ejpam-7142	267	8	n	n	CCONJ
ejpam-7142	267	9	r	r	NOUN
ejpam-7142	267	10	l(g	l(g	PROPN
ejpam-7142	267	11	)	)	PUNCT
ejpam-7142	267	12	η(g	η(g	PROPN
ejpam-7142	267	13	)	)	PUNCT
ejpam-7142	267	14	social	social	ADJ
ejpam-7142	267	15	(	(	PUNCT
ejpam-7142	267	16	facebook	facebook	PROPN
ejpam-7142	267	17	)	)	PUNCT
ejpam-7142	267	18	2.8b	2.8b	NOUN
ejpam-7142	267	19	1.08	1.08	NUM
ejpam-7142	267	20	4.7	4.7	NUM
ejpam-7142	267	21	0.15	0.15	NUM
ejpam-7142	267	22	neural	neural	ADJ
ejpam-7142	267	23	(	(	PUNCT
ejpam-7142	267	24	c.	c.	PROPN
ejpam-7142	267	25	elegans	elegans	PROPN
ejpam-7142	267	26	)	)	PUNCT
ejpam-7142	267	27	302	302	NUM
ejpam-7142	267	28	1.23	1.23	NUM
ejpam-7142	267	29	2.3	2.3	NUM
ejpam-7142	267	30	0.22	0.22	NUM
ejpam-7142	267	31	internet	internet	NOUN
ejpam-7142	267	32	as	as	ADP
ejpam-7142	267	33	74k	74k	PROPN
ejpam-7142	267	34	1.15	1.15	NUM
ejpam-7142	267	35	3.2	3.2	NUM
ejpam-7142	267	36	0.08	0.08	NUM
ejpam-7142	267	37	power	power	NOUN
ejpam-7142	267	38	grid	grid	NOUN
ejpam-7142	267	39	4.9k	4.9k	NOUN
ejpam-7142	267	40	1.32	1.32	NUM
ejpam-7142	267	41	18.7	18.7	NUM
ejpam-7142	267	42	0.08	0.08	NUM
ejpam-7142	267	43	protein	protein	NOUN
ejpam-7142	267	44	interaction	interaction	NOUN
ejpam-7142	267	45	6.5k	6.5k	NUM
ejpam-7142	267	46	1.19	1.19	NUM
ejpam-7142	267	47	4.1	4.1	NUM
ejpam-7142	267	48	0.12	0.12	NUM
ejpam-7142	267	49	table	table	NOUN
ejpam-7142	267	50	1	1	NUM
ejpam-7142	267	51	:	:	PUNCT
ejpam-7142	267	52	neutrosophic	neutrosophic	ADJ
ejpam-7142	267	53	mr	mr	PROPN
ejpam-7142	267	54	-	-	PUNCT
ejpam-7142	267	55	metric	metric	ADJ
ejpam-7142	267	56	parameters	parameter	NOUN
ejpam-7142	267	57	for	for	ADP
ejpam-7142	267	58	real	real	ADJ
ejpam-7142	267	59	networks	network	NOUN
ejpam-7142	267	60	application	application	NOUN
ejpam-7142	267	61	success	success	NOUN
ejpam-7142	267	62	rate	rate	NOUN
ejpam-7142	267	63	computation	computation	NOUN
ejpam-7142	267	64	time	time	NOUN
ejpam-7142	267	65	robustness	robustness	NOUN
ejpam-7142	267	66	gain	gain	NOUN
ejpam-7142	267	67	influencer	influencer	NOUN
ejpam-7142	267	68	identification	identification	NOUN
ejpam-7142	267	69	92	92	NUM
ejpam-7142	267	70	%	%	NOUN
ejpam-7142	267	71	45min	45min	NOUN
ejpam-7142	267	72	1.8×	1.8×	NUM
ejpam-7142	267	73	network	network	NOUN
ejpam-7142	267	74	hardening	harden	VERB
ejpam-7142	267	75	88	88	NUM
ejpam-7142	267	76	%	%	NOUN
ejpam-7142	267	77	2.3hr	2.3hr	NUM
ejpam-7142	267	78	2.1×	2.1×	NUM
ejpam-7142	267	79	path	path	NOUN
ejpam-7142	267	80	planning	plan	VERB
ejpam-7142	267	81	95	95	NUM
ejpam-7142	267	82	%	%	NOUN
ejpam-7142	267	83	8.7s	8.7s	NUM
ejpam-7142	267	84	1.5×	1.5×	NUM
ejpam-7142	267	85	folding	fold	VERB
ejpam-7142	267	86	analysis	analysis	NOUN
ejpam-7142	267	87	83	83	NUM
ejpam-7142	267	88	%	%	NOUN
ejpam-7142	267	89	34min	34min	NOUN
ejpam-7142	267	90	1.9×	1.9×	NUM
ejpam-7142	267	91	table	table	NOUN
ejpam-7142	267	92	2	2	NUM
ejpam-7142	267	93	:	:	PUNCT
ejpam-7142	267	94	performance	performance	NOUN
ejpam-7142	267	95	metrics	metric	NOUN
ejpam-7142	267	96	for	for	ADP
ejpam-7142	267	97	neutrosophic	neutrosophic	ADJ
ejpam-7142	267	98	mr	mr	PROPN
ejpam-7142	267	99	-	-	PUNCT
ejpam-7142	267	100	metric	metric	ADJ
ejpam-7142	267	101	applications	application	NOUN
ejpam-7142	267	102	remark	remark	VERB
ejpam-7142	267	103	1	1	NUM
ejpam-7142	267	104	(	(	PUNCT
ejpam-7142	267	105	practical	practical	ADJ
ejpam-7142	267	106	implementation	implementation	NOUN
ejpam-7142	267	107	considerations	consideration	NOUN
ejpam-7142	267	108	)	)	PUNCT
ejpam-7142	267	109	.	.	PUNCT
ejpam-7142	268	1	(	(	PUNCT
ejpam-7142	268	2	i	i	NOUN
ejpam-7142	268	3	)	)	PUNCT
ejpam-7142	268	4	computational	computational	ADJ
ejpam-7142	268	5	efficiency	efficiency	NOUN
ejpam-7142	268	6	:	:	PUNCT
ejpam-7142	268	7	use	use	VERB
ejpam-7142	268	8	approximate	approximate	ADJ
ejpam-7142	268	9	algorithms	algorithm	NOUN
ejpam-7142	268	10	for	for	ADP
ejpam-7142	268	11	large	large	ADJ
ejpam-7142	268	12	-	-	PUNCT
ejpam-7142	268	13	scale	scale	NOUN
ejpam-7142	268	14	networks	network	NOUN
ejpam-7142	268	15	e.	e.	PROPN
ejpam-7142	268	16	hussein	hussein	PROPN
ejpam-7142	268	17	et	et	PROPN
ejpam-7142	268	18	al	al	PROPN
ejpam-7142	268	19	.	.	PUNCT
ejpam-7142	268	20	/	/	SYM
ejpam-7142	268	21	eur	eur	PROPN
ejpam-7142	268	22	.	.	PUNCT
ejpam-7142	269	1	j.	j.	PROPN
ejpam-7142	269	2	pure	pure	PROPN
ejpam-7142	269	3	appl	appl	PROPN
ejpam-7142	269	4	.	.	PROPN
ejpam-7142	269	5	math	math	PROPN
ejpam-7142	269	6	,	,	PUNCT
ejpam-7142	269	7	18	18	NUM
ejpam-7142	269	8	(	(	PUNCT
ejpam-7142	269	9	4	4	NUM
ejpam-7142	269	10	)	)	PUNCT
ejpam-7142	269	11	(	(	PUNCT
ejpam-7142	269	12	2025	2025	NUM
ejpam-7142	269	13	)	)	PUNCT
ejpam-7142	269	14	,	,	PUNCT
ejpam-7142	269	15	7142	7142	NUM
ejpam-7142	269	16	15	15	NUM
ejpam-7142	269	17	of	of	ADP
ejpam-7142	269	18	17	17	NUM
ejpam-7142	269	19	(	(	PUNCT
ejpam-7142	269	20	ii	ii	NOUN
ejpam-7142	269	21	)	)	PUNCT
ejpam-7142	269	22	parameter	parameter	NOUN
ejpam-7142	269	23	tuning	tuning	NOUN
ejpam-7142	269	24	:	:	PUNCT
ejpam-7142	269	25	optimize	optimize	VERB
ejpam-7142	269	26	t	t	PROPN
ejpam-7142	269	27	-	-	PUNCT
ejpam-7142	269	28	norm	norm	NOUN
ejpam-7142	269	29	operations	operation	NOUN
ejpam-7142	269	30	for	for	ADP
ejpam-7142	269	31	specific	specific	ADJ
ejpam-7142	269	32	applications	application	NOUN
ejpam-7142	269	33	(	(	PUNCT
ejpam-7142	269	34	iii	iii	NOUN
ejpam-7142	269	35	)	)	PUNCT
ejpam-7142	269	36	uncertainty	uncertainty	NOUN
ejpam-7142	269	37	quantification	quantification	NOUN
ejpam-7142	269	38	:	:	PUNCT
ejpam-7142	269	39	employ	employ	NOUN
ejpam-7142	269	40	monte	monte	PROPN
ejpam-7142	269	41	carlo	carlo	PROPN
ejpam-7142	269	42	methods	method	NOUN
ejpam-7142	269	43	for	for	ADP
ejpam-7142	269	44	neutrosophic	neutrosophic	ADJ
ejpam-7142	269	45	degrees	degree	NOUN
ejpam-7142	269	46	(	(	PUNCT
ejpam-7142	269	47	iv	iv	NOUN
ejpam-7142	269	48	)	)	PUNCT
ejpam-7142	269	49	scalability	scalability	NOUN
ejpam-7142	269	50	:	:	PUNCT
ejpam-7142	269	51	distributed	distribute	VERB
ejpam-7142	269	52	computation	computation	NOUN
ejpam-7142	269	53	for	for	ADP
ejpam-7142	269	54	billion	billion	NUM
ejpam-7142	269	55	-	-	PUNCT
ejpam-7142	269	56	scale	scale	NOUN
ejpam-7142	269	57	networks	network	NOUN
ejpam-7142	269	58	3.6	3.6	NUM
ejpam-7142	269	59	.	.	PUNCT
ejpam-7142	270	1	conclusion	conclusion	NOUN
ejpam-7142	270	2	of	of	ADP
ejpam-7142	270	3	applications	application	NOUN
ejpam-7142	270	4	the	the	DET
ejpam-7142	270	5	examples	example	NOUN
ejpam-7142	270	6	and	and	CCONJ
ejpam-7142	270	7	applications	application	NOUN
ejpam-7142	270	8	demonstrate	demonstrate	VERB
ejpam-7142	270	9	the	the	DET
ejpam-7142	270	10	versatility	versatility	NOUN
ejpam-7142	270	11	of	of	ADP
ejpam-7142	270	12	neutrosophic	neutrosophic	ADJ
ejpam-7142	270	13	mr	mr	PROPN
ejpam-7142	270	14	-	-	PUNCT
ejpam-7142	270	15	metric	metric	ADJ
ejpam-7142	270	16	spaces	space	NOUN
ejpam-7142	270	17	in	in	ADP
ejpam-7142	270	18	:	:	PUNCT
ejpam-7142	270	19	•	•	NUM
ejpam-7142	270	20	modeling	model	VERB
ejpam-7142	270	21	complex	complex	ADJ
ejpam-7142	270	22	real	real	ADJ
ejpam-7142	270	23	-	-	PUNCT
ejpam-7142	270	24	world	world	NOUN
ejpam-7142	270	25	networks	network	NOUN
ejpam-7142	270	26	with	with	ADP
ejpam-7142	270	27	uncertainty	uncertainty	NOUN
ejpam-7142	270	28	•	•	ADP
ejpam-7142	270	29	identifying	identify	VERB
ejpam-7142	270	30	critical	critical	ADJ
ejpam-7142	270	31	components	component	NOUN
ejpam-7142	270	32	and	and	CCONJ
ejpam-7142	270	33	influencers	influencer	NOUN
ejpam-7142	270	34	•	•	NOUN
ejpam-7142	270	35	analyzing	analyze	VERB
ejpam-7142	270	36	network	network	NOUN
ejpam-7142	270	37	robustness	robustness	NOUN
ejpam-7142	270	38	and	and	CCONJ
ejpam-7142	270	39	vulnerability	vulnerability	NOUN
ejpam-7142	270	40	•	•	NOUN
ejpam-7142	270	41	providing	provide	VERB
ejpam-7142	270	42	computational	computational	ADJ
ejpam-7142	270	43	frameworks	framework	NOUN
ejpam-7142	270	44	for	for	ADP
ejpam-7142	270	45	path	path	NOUN
ejpam-7142	270	46	planning	planning	NOUN
ejpam-7142	270	47	and	and	CCONJ
ejpam-7142	270	48	structural	structural	ADJ
ejpam-7142	270	49	analysis	analysis	NOUN
ejpam-7142	270	50	•	•	NOUN
ejpam-7142	270	51	offering	offer	VERB
ejpam-7142	270	52	quantitative	quantitative	ADJ
ejpam-7142	270	53	metrics	metric	NOUN
ejpam-7142	270	54	for	for	ADP
ejpam-7142	270	55	network	network	NOUN
ejpam-7142	270	56	design	design	NOUN
ejpam-7142	270	57	and	and	CCONJ
ejpam-7142	270	58	optimization	optimization	NOUN
ejpam-7142	270	59	the	the	DET
ejpam-7142	270	60	integration	integration	NOUN
ejpam-7142	270	61	of	of	ADP
ejpam-7142	270	62	neutrosophic	neutrosophic	ADJ
ejpam-7142	270	63	logic	logic	NOUN
ejpam-7142	270	64	with	with	ADP
ejpam-7142	270	65	mr	mr	PROPN
ejpam-7142	270	66	-	-	PUNCT
ejpam-7142	270	67	metric	metric	ADJ
ejpam-7142	270	68	spaces	space	NOUN
ejpam-7142	270	69	provides	provide	VERB
ejpam-7142	270	70	a	a	DET
ejpam-7142	270	71	powerful	powerful	ADJ
ejpam-7142	270	72	mathematical	mathematical	ADJ
ejpam-7142	270	73	foundation	foundation	NOUN
ejpam-7142	270	74	for	for	ADP
ejpam-7142	270	75	handling	handle	VERB
ejpam-7142	270	76	uncertainty	uncertainty	NOUN
ejpam-7142	270	77	,	,	PUNCT
ejpam-7142	270	78	indeterminacy	indeterminacy	NOUN
ejpam-7142	270	79	,	,	PUNCT
ejpam-7142	270	80	and	and	CCONJ
ejpam-7142	270	81	complexity	complexity	NOUN
ejpam-7142	270	82	in	in	ADP
ejpam-7142	270	83	modern	modern	ADJ
ejpam-7142	270	84	network	network	NOUN
ejpam-7142	270	85	science	science	NOUN
ejpam-7142	270	86	applications	application	NOUN
ejpam-7142	270	87	.	.	PUNCT
ejpam-7142	271	1	references	reference	NOUN
ejpam-7142	271	2	[	[	X
ejpam-7142	271	3	1	1	NUM
ejpam-7142	271	4	]	]	PUNCT
ejpam-7142	271	5	i.	i.	PROPN
ejpam-7142	271	6	a.	a.	PROPN
ejpam-7142	271	7	bakhtin	bakhtin	PROPN
ejpam-7142	271	8	.	.	PUNCT
ejpam-7142	272	1	the	the	DET
ejpam-7142	272	2	contraction	contraction	NOUN
ejpam-7142	272	3	mapping	map	VERB
ejpam-7142	272	4	principle	principle	NOUN
ejpam-7142	272	5	in	in	ADP
ejpam-7142	272	6	almost	almost	ADV
ejpam-7142	272	7	metric	metric	ADJ
ejpam-7142	272	8	spaces	space	NOUN
ejpam-7142	272	9	.	.	PUNCT
ejpam-7142	273	1	functional	functional	ADJ
ejpam-7142	273	2	analysis	analysis	NOUN
ejpam-7142	273	3	,	,	PUNCT
ejpam-7142	273	4	30:26–37	30:26–37	PROPN
ejpam-7142	273	5	,	,	PUNCT
ejpam-7142	273	6	1989	1989	NUM
ejpam-7142	273	7	.	.	PUNCT
ejpam-7142	274	1	[	[	X
ejpam-7142	274	2	2	2	X
ejpam-7142	274	3	]	]	PUNCT
ejpam-7142	274	4	s.	s.	PROPN
ejpam-7142	274	5	czerwik	czerwik	PROPN
ejpam-7142	274	6	.	.	PUNCT
ejpam-7142	275	1	contraction	contraction	NOUN
ejpam-7142	275	2	mappings	mapping	NOUN
ejpam-7142	275	3	in	in	ADP
ejpam-7142	275	4	b	b	NOUN
ejpam-7142	275	5	-	-	ADJ
ejpam-7142	275	6	metric	metric	ADJ
ejpam-7142	275	7	spaces	space	NOUN
ejpam-7142	275	8	.	.	PUNCT
ejpam-7142	276	1	acta	acta	PROPN
ejpam-7142	276	2	mathematica	mathematica	PROPN
ejpam-7142	276	3	et	et	PROPN
ejpam-7142	276	4	informatica	informatica	PROPN
ejpam-7142	276	5	universitatis	universitatis	PROPN
ejpam-7142	276	6	ostraviensis	ostraviensis	PROPN
ejpam-7142	276	7	,	,	PUNCT
ejpam-7142	276	8	1:5–11	1:5–11	NUM
ejpam-7142	276	9	,	,	PUNCT
ejpam-7142	276	10	1993	1993	NUM
ejpam-7142	276	11	.	.	PUNCT
ejpam-7142	277	1	[	[	X
ejpam-7142	277	2	3	3	NUM
ejpam-7142	277	3	]	]	X
ejpam-7142	277	4	a.	a.	NOUN
ejpam-7142	277	5	malkawi	malkawi	PROPN
ejpam-7142	277	6	,	,	PUNCT
ejpam-7142	277	7	a.	a.	PROPN
ejpam-7142	277	8	rabaiah	rabaiah	PROPN
ejpam-7142	277	9	,	,	PUNCT
ejpam-7142	277	10	w.	w.	PROPN
ejpam-7142	277	11	shatanawi	shatanawi	PROPN
ejpam-7142	277	12	,	,	PUNCT
ejpam-7142	277	13	and	and	CCONJ
ejpam-7142	277	14	a.	a.	NOUN
ejpam-7142	277	15	talafhah	talafhah	PROPN
ejpam-7142	277	16	.	.	PUNCT
ejpam-7142	278	1	mr	mr	PROPN
ejpam-7142	278	2	-	-	PUNCT
ejpam-7142	278	3	metric	metric	ADJ
ejpam-7142	278	4	spaces	space	NOUN
ejpam-7142	278	5	and	and	CCONJ
ejpam-7142	278	6	an	an	DET
ejpam-7142	278	7	application	application	NOUN
ejpam-7142	278	8	,	,	PUNCT
ejpam-7142	278	9	2021	2021	NUM
ejpam-7142	278	10	.	.	PUNCT
ejpam-7142	279	1	preprint	preprint	NOUN
ejpam-7142	279	2	.	.	PUNCT
ejpam-7142	280	1	[	[	X
ejpam-7142	280	2	4	4	X
ejpam-7142	280	3	]	]	X
ejpam-7142	280	4	a.	a.	NOUN
ejpam-7142	280	5	malkawi	malkawi	PROPN
ejpam-7142	280	6	,	,	PUNCT
ejpam-7142	280	7	a.	a.	NOUN
ejpam-7142	280	8	talafhah	talafhah	PROPN
ejpam-7142	280	9	,	,	PUNCT
ejpam-7142	280	10	and	and	CCONJ
ejpam-7142	280	11	w.	w.	PROPN
ejpam-7142	280	12	shatanawi	shatanawi	PROPN
ejpam-7142	280	13	.	.	PUNCT
ejpam-7142	281	1	coincidence	coincidence	NOUN
ejpam-7142	281	2	and	and	CCONJ
ejpam-7142	281	3	fixed	fix	VERB
ejpam-7142	281	4	point	point	NOUN
ejpam-7142	281	5	results	result	NOUN
ejpam-7142	281	6	for	for	ADP
ejpam-7142	281	7	(	(	PUNCT
ejpam-7142	281	8	ψ	ψ	X
ejpam-7142	281	9	,	,	PUNCT
ejpam-7142	281	10	l)-mweak	l)-mweak	NOUN
ejpam-7142	281	11	contraction	contraction	NOUN
ejpam-7142	281	12	mapping	mapping	NOUN
ejpam-7142	281	13	on	on	ADP
ejpam-7142	281	14	mb	mb	ADJ
ejpam-7142	281	15	-	-	ADJ
ejpam-7142	281	16	metric	metric	ADJ
ejpam-7142	281	17	spaces	space	NOUN
ejpam-7142	281	18	.	.	PUNCT
ejpam-7142	282	1	italian	italian	ADJ
ejpam-7142	282	2	journal	journal	NOUN
ejpam-7142	282	3	of	of	ADP
ejpam-7142	282	4	pure	pure	ADJ
ejpam-7142	282	5	and	and	CCONJ
ejpam-7142	282	6	applied	applied	ADJ
ejpam-7142	282	7	mathematics	mathematic	NOUN
ejpam-7142	282	8	,	,	PUNCT
ejpam-7142	282	9	(	(	PUNCT
ejpam-7142	282	10	47):751–768	47):751–768	NOUN
ejpam-7142	282	11	,	,	PUNCT
ejpam-7142	282	12	2022	2022	NUM
ejpam-7142	282	13	.	.	PUNCT
ejpam-7142	283	1	[	[	X
ejpam-7142	283	2	5	5	X
ejpam-7142	283	3	]	]	PUNCT
ejpam-7142	283	4	anwar	anwar	PROPN
ejpam-7142	283	5	bataihah	bataihah	PROPN
ejpam-7142	283	6	,	,	PUNCT
ejpam-7142	283	7	tariq	tariq	NOUN
ejpam-7142	283	8	qawasmeh	qawasmeh	NOUN
ejpam-7142	283	9	,	,	PUNCT
ejpam-7142	283	10	and	and	CCONJ
ejpam-7142	283	11	mutaz	mutaz	NOUN
ejpam-7142	283	12	shatnawi	shatnawi	ADJ
ejpam-7142	283	13	.	.	PUNCT
ejpam-7142	284	1	discussion	discussion	NOUN
ejpam-7142	284	2	on	on	ADP
ejpam-7142	284	3	b	b	X
ejpam-7142	284	4	-	-	ADJ
ejpam-7142	284	5	metric	metric	ADJ
ejpam-7142	284	6	spaces	space	NOUN
ejpam-7142	284	7	and	and	CCONJ
ejpam-7142	284	8	related	relate	VERB
ejpam-7142	284	9	results	result	NOUN
ejpam-7142	284	10	in	in	ADP
ejpam-7142	284	11	metric	metric	ADJ
ejpam-7142	284	12	and	and	CCONJ
ejpam-7142	284	13	g	g	NOUN
ejpam-7142	284	14	-	-	PUNCT
ejpam-7142	284	15	metric	metric	ADJ
ejpam-7142	284	16	spaces	space	NOUN
ejpam-7142	284	17	.	.	PUNCT
ejpam-7142	285	1	nonlinear	nonlinear	ADJ
ejpam-7142	285	2	functional	functional	ADJ
ejpam-7142	285	3	analysis	analysis	NOUN
ejpam-7142	285	4	and	and	CCONJ
ejpam-7142	285	5	applications	application	NOUN
ejpam-7142	285	6	,	,	PUNCT
ejpam-7142	285	7	27:233–247	27:233–247	NUM
ejpam-7142	285	8	,	,	PUNCT
ejpam-7142	285	9	2022	2022	NUM
ejpam-7142	285	10	.	.	PUNCT
ejpam-7142	286	1	[	[	X
ejpam-7142	286	2	6	6	NUM
ejpam-7142	286	3	]	]	PUNCT
ejpam-7142	286	4	t.	t.	NOUN
ejpam-7142	286	5	qawasmeh	qawasmeh	NOUN
ejpam-7142	286	6	.	.	PUNCT
ejpam-7142	287	1	(	(	PUNCT
ejpam-7142	287	2	h	h	NOUN
ejpam-7142	287	3	,	,	PUNCT
ejpam-7142	287	4	ωb)-interpolative	ωb)-interpolative	ADJ
ejpam-7142	287	5	contractions	contraction	NOUN
ejpam-7142	287	6	in	in	ADP
ejpam-7142	287	7	ωb	ωb	NOUN
ejpam-7142	287	8	-	-	PUNCT
ejpam-7142	287	9	distance	distance	NOUN
ejpam-7142	287	10	mappings	mapping	NOUN
ejpam-7142	287	11	with	with	ADP
ejpam-7142	287	12	applications	application	NOUN
ejpam-7142	287	13	.	.	PUNCT
ejpam-7142	288	1	european	european	ADJ
ejpam-7142	288	2	journal	journal	PROPN
ejpam-7142	288	3	of	of	ADP
ejpam-7142	288	4	pure	pure	ADJ
ejpam-7142	288	5	and	and	CCONJ
ejpam-7142	288	6	applied	applied	ADJ
ejpam-7142	288	7	mathematics	mathematic	NOUN
ejpam-7142	288	8	,	,	PUNCT
ejpam-7142	288	9	16(3):1717–1730	16(3):1717–1730	NUM
ejpam-7142	288	10	,	,	PUNCT
ejpam-7142	288	11	2023	2023	NUM
ejpam-7142	288	12	.	.	PUNCT
ejpam-7142	289	1	[	[	X
ejpam-7142	289	2	7	7	X
ejpam-7142	289	3	]	]	PUNCT
ejpam-7142	289	4	wasfi	wasfi	NOUN
ejpam-7142	289	5	shatanawi	shatanawi	PROPN
ejpam-7142	289	6	,	,	PUNCT
ejpam-7142	289	7	georgeta	georgeta	PROPN
ejpam-7142	289	8	maniu	maniu	PROPN
ejpam-7142	289	9	,	,	PUNCT
ejpam-7142	289	10	anwar	anwar	PROPN
ejpam-7142	289	11	bataihah	bataihah	PROPN
ejpam-7142	289	12	,	,	PUNCT
ejpam-7142	289	13	and	and	CCONJ
ejpam-7142	289	14	f.	f.	PROPN
ejpam-7142	289	15	b.	b.	PROPN
ejpam-7142	289	16	ahmad	ahmad	PROPN
ejpam-7142	289	17	.	.	PUNCT
ejpam-7142	290	1	common	common	ADJ
ejpam-7142	290	2	fixed	fix	VERB
ejpam-7142	290	3	points	point	NOUN
ejpam-7142	290	4	for	for	ADP
ejpam-7142	290	5	mappings	mapping	NOUN
ejpam-7142	290	6	of	of	ADP
ejpam-7142	290	7	cyclic	cyclic	ADJ
ejpam-7142	290	8	form	form	NOUN
ejpam-7142	290	9	satisfying	satisfy	VERB
ejpam-7142	290	10	linear	linear	PROPN
ejpam-7142	290	11	contractive	contractive	ADJ
ejpam-7142	290	12	conditions	condition	NOUN
ejpam-7142	290	13	with	with	ADP
ejpam-7142	290	14	omegadistance	omegadistance	NOUN
ejpam-7142	290	15	.	.	PUNCT
ejpam-7142	291	1	upb	upb	ADJ
ejpam-7142	291	2	scientific	scientific	ADJ
ejpam-7142	291	3	bulletin	bulletin	NOUN
ejpam-7142	291	4	,	,	PUNCT
ejpam-7142	291	5	series	series	PROPN
ejpam-7142	291	6	a	a	PRON
ejpam-7142	291	7	:	:	PUNCT
ejpam-7142	291	8	applied	apply	VERB
ejpam-7142	291	9	mathematics	mathematic	NOUN
ejpam-7142	291	10	and	and	CCONJ
ejpam-7142	291	11	physics	physics	NOUN
ejpam-7142	291	12	,	,	PUNCT
ejpam-7142	291	13	79:11–20	79:11–20	NUM
ejpam-7142	291	14	,	,	PUNCT
ejpam-7142	291	15	2017	2017	NUM
ejpam-7142	291	16	.	.	PUNCT
ejpam-7142	292	1	[	[	X
ejpam-7142	292	2	8	8	NUM
ejpam-7142	292	3	]	]	X
ejpam-7142	292	4	i.	i.	PROPN
ejpam-7142	292	5	abu	abu	PROPN
ejpam-7142	292	6	-	-	PUNCT
ejpam-7142	292	7	irwaq	irwaq	PROPN
ejpam-7142	292	8	,	,	PUNCT
ejpam-7142	292	9	w.	w.	PROPN
ejpam-7142	292	10	shatanawi	shatanawi	PROPN
ejpam-7142	292	11	,	,	PUNCT
ejpam-7142	292	12	a.	a.	NOUN
ejpam-7142	292	13	bataihah	bataihah	PROPN
ejpam-7142	292	14	,	,	PUNCT
ejpam-7142	292	15	and	and	CCONJ
ejpam-7142	292	16	i.	i.	PROPN
ejpam-7142	292	17	nuseir	nuseir	PROPN
ejpam-7142	292	18	.	.	PUNCT
ejpam-7142	293	1	fixed	fix	VERB
ejpam-7142	293	2	point	point	NOUN
ejpam-7142	293	3	results	result	NOUN
ejpam-7142	293	4	for	for	ADP
ejpam-7142	293	5	nonlinear	nonlinear	ADJ
ejpam-7142	293	6	contractions	contraction	NOUN
ejpam-7142	293	7	with	with	ADP
ejpam-7142	293	8	generalized	generalized	ADJ
ejpam-7142	293	9	ω	ω	NUM
ejpam-7142	293	10	-	-	PUNCT
ejpam-7142	293	11	distance	distance	NOUN
ejpam-7142	293	12	mappings	mapping	NOUN
ejpam-7142	293	13	.	.	PUNCT
ejpam-7142	294	1	upb	upb	ADJ
ejpam-7142	294	2	scientific	scientific	ADJ
ejpam-7142	294	3	bulletin	bulletin	NOUN
ejpam-7142	294	4	,	,	PUNCT
ejpam-7142	294	5	series	series	NOUN
ejpam-7142	294	6	a	a	NOUN
ejpam-7142	294	7	,	,	PUNCT
ejpam-7142	294	8	81(1):57–64	81(1):57–64	NUM
ejpam-7142	294	9	,	,	PUNCT
ejpam-7142	294	10	2019	2019	NUM
ejpam-7142	294	11	.	.	PUNCT
ejpam-7142	295	1	[	[	X
ejpam-7142	295	2	9	9	NUM
ejpam-7142	295	3	]	]	PUNCT
ejpam-7142	295	4	wasfi	wasfi	NOUN
ejpam-7142	295	5	shatanawi	shatanawi	PROPN
ejpam-7142	295	6	,	,	PUNCT
ejpam-7142	295	7	anwar	anwar	PROPN
ejpam-7142	295	8	bataihah	bataihah	PROPN
ejpam-7142	295	9	,	,	PUNCT
ejpam-7142	295	10	and	and	CCONJ
ejpam-7142	295	11	ariana	ariana	PROPN
ejpam-7142	295	12	pitea	pitea	NOUN
ejpam-7142	295	13	.	.	PUNCT
ejpam-7142	296	1	fixed	fix	VERB
ejpam-7142	296	2	and	and	CCONJ
ejpam-7142	296	3	common	common	ADJ
ejpam-7142	296	4	fixed	fix	VERB
ejpam-7142	296	5	point	point	NOUN
ejpam-7142	296	6	results	result	NOUN
ejpam-7142	296	7	for	for	ADP
ejpam-7142	296	8	cyclic	cyclic	ADJ
ejpam-7142	296	9	mappings	mapping	NOUN
ejpam-7142	296	10	of	of	ADP
ejpam-7142	296	11	ω	ω	NOUN
ejpam-7142	296	12	-	-	PUNCT
ejpam-7142	296	13	distance	distance	NOUN
ejpam-7142	296	14	.	.	PUNCT
ejpam-7142	297	1	journal	journal	PROPN
ejpam-7142	297	2	of	of	ADP
ejpam-7142	297	3	nonlinear	nonlinear	ADJ
ejpam-7142	297	4	science	science	NOUN
ejpam-7142	297	5	and	and	CCONJ
ejpam-7142	297	6	applications	application	NOUN
ejpam-7142	297	7	,	,	PUNCT
ejpam-7142	297	8	9:727–735	9:727–735	NUM
ejpam-7142	297	9	,	,	PUNCT
ejpam-7142	297	10	2016	2016	NUM
ejpam-7142	297	11	.	.	PUNCT
ejpam-7142	298	1	[	[	X
ejpam-7142	298	2	10	10	NUM
ejpam-7142	298	3	]	]	PUNCT
ejpam-7142	298	4	a.	a.	NOUN
ejpam-7142	298	5	rabaiah	rabaiah	PROPN
ejpam-7142	298	6	,	,	PUNCT
ejpam-7142	298	7	a.	a.	NOUN
ejpam-7142	298	8	tallafha	tallafha	NOUN
ejpam-7142	298	9	,	,	PUNCT
ejpam-7142	298	10	and	and	CCONJ
ejpam-7142	298	11	w.	w.	PROPN
ejpam-7142	298	12	shatanawi	shatanawi	PROPN
ejpam-7142	298	13	.	.	PUNCT
ejpam-7142	299	1	common	common	ADJ
ejpam-7142	299	2	fixed	fix	VERB
ejpam-7142	299	3	point	point	NOUN
ejpam-7142	299	4	results	result	NOUN
ejpam-7142	299	5	for	for	ADP
ejpam-7142	299	6	mappings	mapping	NOUN
ejpam-7142	299	7	under	under	ADP
ejpam-7142	299	8	nonlinear	nonlinear	ADJ
ejpam-7142	299	9	contraction	contraction	NOUN
ejpam-7142	299	10	of	of	ADP
ejpam-7142	299	11	cyclic	cyclic	ADJ
ejpam-7142	299	12	form	form	NOUN
ejpam-7142	299	13	in	in	ADP
ejpam-7142	299	14	b	b	NOUN
ejpam-7142	299	15	-	-	ADJ
ejpam-7142	299	16	metric	metric	ADJ
ejpam-7142	299	17	spaces	space	NOUN
ejpam-7142	299	18	.	.	PUNCT
ejpam-7142	300	1	advances	advance	NOUN
ejpam-7142	300	2	in	in	ADP
ejpam-7142	300	3	mathematics	mathematics	NOUN
ejpam-7142	300	4	scientific	scientific	ADJ
ejpam-7142	300	5	journal	journal	NOUN
ejpam-7142	300	6	,	,	PUNCT
ejpam-7142	300	7	26(2):289–301	26(2):289–301	PROPN
ejpam-7142	300	8	,	,	PUNCT
ejpam-7142	300	9	2021	2021	NUM
ejpam-7142	300	10	.	.	PUNCT
ejpam-7142	301	1	e.	e.	PROPN
ejpam-7142	301	2	hussein	hussein	PROPN
ejpam-7142	301	3	et	et	PROPN
ejpam-7142	301	4	al	al	PROPN
ejpam-7142	301	5	.	.	PUNCT
ejpam-7142	301	6	/	/	SYM
ejpam-7142	301	7	eur	eur	PROPN
ejpam-7142	301	8	.	.	PUNCT
ejpam-7142	302	1	j.	j.	PROPN
ejpam-7142	302	2	pure	pure	PROPN
ejpam-7142	302	3	appl	appl	PROPN
ejpam-7142	302	4	.	.	PROPN
ejpam-7142	302	5	math	math	PROPN
ejpam-7142	302	6	,	,	PUNCT
ejpam-7142	302	7	18	18	NUM
ejpam-7142	302	8	(	(	PUNCT
ejpam-7142	302	9	4	4	NUM
ejpam-7142	302	10	)	)	PUNCT
ejpam-7142	302	11	(	(	PUNCT
ejpam-7142	302	12	2025	2025	NUM
ejpam-7142	302	13	)	)	PUNCT
ejpam-7142	302	14	,	,	PUNCT
ejpam-7142	302	15	7142	7142	NUM
ejpam-7142	302	16	16	16	NUM
ejpam-7142	302	17	of	of	ADP
ejpam-7142	302	18	17	17	NUM
ejpam-7142	303	1	[	[	X
ejpam-7142	303	2	11	11	NUM
ejpam-7142	303	3	]	]	PUNCT
ejpam-7142	303	4	bataihah	bataihah	PROPN
ejpam-7142	303	5	,	,	PUNCT
ejpam-7142	303	6	t.	t.	NOUN
ejpam-7142	303	7	qawasmeh	qawasmeh	NOUN
ejpam-7142	303	8	,	,	PUNCT
ejpam-7142	303	9	i.	i.	PROPN
ejpam-7142	303	10	batiha	batiha	PROPN
ejpam-7142	303	11	,	,	PUNCT
ejpam-7142	303	12	i.	i.	PROPN
ejpam-7142	303	13	m.	m.	PROPN
ejpam-7142	303	14	batiha	batiha	PROPN
ejpam-7142	303	15	,	,	PUNCT
ejpam-7142	303	16	and	and	CCONJ
ejpam-7142	303	17	t.	t.	PROPN
ejpam-7142	303	18	abdeljawad	abdeljawad	NOUN
ejpam-7142	303	19	.	.	PUNCT
ejpam-7142	304	1	gamma	gamma	NOUN
ejpam-7142	304	2	distance	distance	NOUN
ejpam-7142	304	3	mappings	mapping	NOUN
ejpam-7142	304	4	with	with	ADP
ejpam-7142	304	5	application	application	NOUN
ejpam-7142	304	6	to	to	ADP
ejpam-7142	304	7	fractional	fractional	ADJ
ejpam-7142	304	8	boundary	boundary	ADJ
ejpam-7142	304	9	differential	differential	NOUN
ejpam-7142	304	10	equation	equation	NOUN
ejpam-7142	304	11	.	.	PUNCT
ejpam-7142	305	1	journal	journal	PROPN
ejpam-7142	305	2	of	of	ADP
ejpam-7142	305	3	mathematical	mathematical	ADJ
ejpam-7142	305	4	analysis	analysis	NOUN
ejpam-7142	305	5	,	,	PUNCT
ejpam-7142	305	6	15(5):99–106	15(5):99–106	NUM
ejpam-7142	305	7	,	,	PUNCT
ejpam-7142	305	8	2024	2024	NUM
ejpam-7142	305	9	.	.	PUNCT
ejpam-7142	306	1	[	[	X
ejpam-7142	306	2	12	12	NUM
ejpam-7142	306	3	]	]	PUNCT
ejpam-7142	306	4	a.	a.	PROPN
ejpam-7142	306	5	al	al	PROPN
ejpam-7142	306	6	-	-	PUNCT
ejpam-7142	306	7	zghoul	zghoul	PROPN
ejpam-7142	306	8	,	,	PUNCT
ejpam-7142	306	9	t.	t.	NOUN
ejpam-7142	306	10	qawasmeh	qawasmeh	NOUN
ejpam-7142	306	11	,	,	PUNCT
ejpam-7142	306	12	r.	r.	PROPN
ejpam-7142	306	13	hatamleh	hatamleh	PROPN
ejpam-7142	306	14	,	,	PUNCT
ejpam-7142	306	15	and	and	CCONJ
ejpam-7142	306	16	a.	a.	NOUN
ejpam-7142	306	17	alhazimeh	alhazimeh	NOUN
ejpam-7142	306	18	.	.	PUNCT
ejpam-7142	307	1	a	a	DET
ejpam-7142	307	2	new	new	ADJ
ejpam-7142	307	3	contraction	contraction	NOUN
ejpam-7142	307	4	by	by	ADP
ejpam-7142	307	5	utilizing	utilize	VERB
ejpam-7142	307	6	h	h	NOUN
ejpam-7142	307	7	-	-	PUNCT
ejpam-7142	307	8	simulition	simulition	NOUN
ejpam-7142	307	9	functions	function	NOUN
ejpam-7142	307	10	and	and	CCONJ
ejpam-7142	307	11	ω	ω	NUM
ejpam-7142	307	12	-	-	PUNCT
ejpam-7142	307	13	distance	distance	NOUN
ejpam-7142	307	14	mappings	mapping	NOUN
ejpam-7142	307	15	in	in	ADP
ejpam-7142	307	16	the	the	DET
ejpam-7142	307	17	frame	frame	NOUN
ejpam-7142	307	18	of	of	ADP
ejpam-7142	307	19	complete	complete	ADJ
ejpam-7142	307	20	g	g	NOUN
ejpam-7142	307	21	-	-	PUNCT
ejpam-7142	307	22	metric	metric	ADJ
ejpam-7142	307	23	spaces	space	NOUN
ejpam-7142	307	24	.	.	PUNCT
ejpam-7142	308	1	journal	journal	NOUN
ejpam-7142	308	2	of	of	ADP
ejpam-7142	308	3	applied	apply	VERB
ejpam-7142	308	4	mathematics	mathematics	PROPN
ejpam-7142	308	5	&	&	CCONJ
ejpam-7142	308	6	informatics	informatic	NOUN
ejpam-7142	308	7	,	,	PUNCT
ejpam-7142	308	8	42(4):749–759	42(4):749–759	PROPN
ejpam-7142	308	9	,	,	PUNCT
ejpam-7142	308	10	2024	2024	NUM
ejpam-7142	308	11	.	.	PUNCT
ejpam-7142	309	1	[	[	X
ejpam-7142	309	2	13	13	NUM
ejpam-7142	309	3	]	]	PUNCT
ejpam-7142	309	4	t.	t.	NOUN
ejpam-7142	309	5	qawasmeh	qawasmeh	NOUN
ejpam-7142	309	6	,	,	PUNCT
ejpam-7142	309	7	a.	a.	NOUN
ejpam-7142	309	8	tallafha	tallafha	NOUN
ejpam-7142	309	9	,	,	PUNCT
ejpam-7142	309	10	and	and	CCONJ
ejpam-7142	309	11	w.	w.	PROPN
ejpam-7142	309	12	shatanawi	shatanawi	PROPN
ejpam-7142	309	13	.	.	PUNCT
ejpam-7142	310	1	fixed	fix	VERB
ejpam-7142	310	2	and	and	CCONJ
ejpam-7142	310	3	common	common	ADJ
ejpam-7142	310	4	fixed	fix	VERB
ejpam-7142	310	5	point	point	NOUN
ejpam-7142	310	6	theorems	theorem	NOUN
ejpam-7142	310	7	through	through	ADP
ejpam-7142	310	8	modified	modify	VERB
ejpam-7142	310	9	ω	ω	NUM
ejpam-7142	310	10	-	-	PUNCT
ejpam-7142	310	11	distance	distance	NOUN
ejpam-7142	310	12	mappings	mapping	NOUN
ejpam-7142	310	13	.	.	PUNCT
ejpam-7142	311	1	nonlinear	nonlinear	ADJ
ejpam-7142	311	2	functional	functional	ADJ
ejpam-7142	311	3	analysis	analysis	NOUN
ejpam-7142	311	4	and	and	CCONJ
ejpam-7142	311	5	applications	application	NOUN
ejpam-7142	311	6	,	,	PUNCT
ejpam-7142	311	7	24(2):221–239	24(2):221–239	NUM
ejpam-7142	311	8	,	,	PUNCT
ejpam-7142	311	9	2021	2021	NUM
ejpam-7142	311	10	.	.	PUNCT
ejpam-7142	312	1	[	[	X
ejpam-7142	312	2	14	14	NUM
ejpam-7142	312	3	]	]	PUNCT
ejpam-7142	312	4	k.	k.	PROPN
ejpam-7142	312	5	abodayeh	abodayeh	PROPN
ejpam-7142	312	6	,	,	PUNCT
ejpam-7142	312	7	t.	t.	NOUN
ejpam-7142	312	8	qawasmeh	qawasmeh	NOUN
ejpam-7142	312	9	,	,	PUNCT
ejpam-7142	312	10	w.	w.	PROPN
ejpam-7142	312	11	shatanawi	shatanawi	PROPN
ejpam-7142	312	12	,	,	PUNCT
ejpam-7142	312	13	and	and	CCONJ
ejpam-7142	312	14	k.	k.	PROPN
ejpam-7142	312	15	tallafha	tallafha	PROPN
ejpam-7142	312	16	.	.	PUNCT
ejpam-7142	313	1	ϵφ	ϵφ	NOUN
ejpam-7142	313	2	-	-	NOUN
ejpam-7142	313	3	contraction	contraction	NOUN
ejpam-7142	313	4	and	and	CCONJ
ejpam-7142	313	5	some	some	DET
ejpam-7142	313	6	fixed	fix	VERB
ejpam-7142	313	7	point	point	NOUN
ejpam-7142	313	8	results	result	NOUN
ejpam-7142	313	9	via	via	ADP
ejpam-7142	313	10	modified	modify	VERB
ejpam-7142	313	11	ω	ω	VERB
ejpam-7142	313	12	-	-	PUNCT
ejpam-7142	313	13	distance	distance	NOUN
ejpam-7142	313	14	mappings	mapping	NOUN
ejpam-7142	313	15	in	in	ADP
ejpam-7142	313	16	the	the	DET
ejpam-7142	313	17	frame	frame	NOUN
ejpam-7142	313	18	of	of	ADP
ejpam-7142	313	19	complete	complete	ADJ
ejpam-7142	313	20	quasi	quasi	ADJ
ejpam-7142	313	21	metric	metric	ADJ
ejpam-7142	313	22	spaces	space	NOUN
ejpam-7142	313	23	and	and	CCONJ
ejpam-7142	313	24	applications	application	NOUN
ejpam-7142	313	25	.	.	PUNCT
ejpam-7142	314	1	international	international	ADJ
ejpam-7142	314	2	journal	journal	NOUN
ejpam-7142	314	3	of	of	ADP
ejpam-7142	314	4	electrical	electrical	ADJ
ejpam-7142	314	5	and	and	CCONJ
ejpam-7142	314	6	computer	computer	NOUN
ejpam-7142	314	7	engineering	engineering	NOUN
ejpam-7142	314	8	,	,	PUNCT
ejpam-7142	314	9	10(4):3839–3853	10(4):3839–3853	NUM
ejpam-7142	314	10	,	,	PUNCT
ejpam-7142	314	11	2020	2020	NUM
ejpam-7142	314	12	.	.	PUNCT
ejpam-7142	315	1	[	[	X
ejpam-7142	315	2	15	15	NUM
ejpam-7142	315	3	]	]	PUNCT
ejpam-7142	315	4	t.	t.	NOUN
ejpam-7142	315	5	qawasmeh	qawasmeh	NOUN
ejpam-7142	315	6	,	,	PUNCT
ejpam-7142	315	7	a.	a.	NOUN
ejpam-7142	315	8	bataihah	bataihah	PROPN
ejpam-7142	315	9	,	,	PUNCT
ejpam-7142	315	10	a.	a.	NOUN
ejpam-7142	315	11	a.	a.	NOUN
ejpam-7142	315	12	hazaymeh	hazaymeh	PROPN
ejpam-7142	315	13	,	,	PUNCT
ejpam-7142	315	14	r.	r.	PROPN
ejpam-7142	315	15	hatamleh	hatamleh	PROPN
ejpam-7142	315	16	,	,	PUNCT
ejpam-7142	315	17	r.	r.	PROPN
ejpam-7142	315	18	abdelrahim	abdelrahim	PROPN
ejpam-7142	315	19	,	,	PUNCT
ejpam-7142	315	20	and	and	CCONJ
ejpam-7142	315	21	a.	a.	NOUN
ejpam-7142	315	22	a.	a.	PROPN
ejpam-7142	315	23	hassan	hassan	PROPN
ejpam-7142	315	24	.	.	PUNCT
ejpam-7142	316	1	new	new	ADJ
ejpam-7142	316	2	fixed	fix	VERB
ejpam-7142	316	3	point	point	NOUN
ejpam-7142	316	4	results	result	NOUN
ejpam-7142	316	5	for	for	ADP
ejpam-7142	316	6	gamma	gamma	NOUN
ejpam-7142	316	7	interpolative	interpolative	ADJ
ejpam-7142	316	8	contractions	contraction	NOUN
ejpam-7142	316	9	through	through	ADP
ejpam-7142	316	10	gamma	gamma	NOUN
ejpam-7142	316	11	distance	distance	NOUN
ejpam-7142	316	12	mappings	mapping	NOUN
ejpam-7142	316	13	.	.	PUNCT
ejpam-7142	317	1	wseas	wseas	NOUN
ejpam-7142	317	2	transactions	transaction	NOUN
ejpam-7142	317	3	on	on	ADP
ejpam-7142	317	4	mathematics	mathematic	NOUN
ejpam-7142	317	5	,	,	PUNCT
ejpam-7142	317	6	24:424–430	24:424–430	PROPN
ejpam-7142	317	7	,	,	PUNCT
ejpam-7142	317	8	2025	2025	NUM
ejpam-7142	317	9	.	.	PUNCT
ejpam-7142	318	1	[	[	X
ejpam-7142	318	2	16	16	NUM
ejpam-7142	318	3	]	]	X
ejpam-7142	318	4	ayman	ayman	PROPN
ejpam-7142	318	5	a.	a.	PROPN
ejpam-7142	318	6	hazaymeh	hazaymeh	NOUN
ejpam-7142	318	7	and	and	CCONJ
ejpam-7142	318	8	anwar	anwar	PROPN
ejpam-7142	318	9	bataihah	bataihah	PROPN
ejpam-7142	318	10	.	.	PUNCT
ejpam-7142	319	1	neutrosophic	neutrosophic	ADJ
ejpam-7142	319	2	fuzzy	fuzzy	ADJ
ejpam-7142	319	3	metric	metric	ADJ
ejpam-7142	319	4	spaces	space	NOUN
ejpam-7142	319	5	and	and	CCONJ
ejpam-7142	319	6	fixed	fix	VERB
ejpam-7142	319	7	points	point	NOUN
ejpam-7142	319	8	for	for	ADP
ejpam-7142	319	9	contractions	contraction	NOUN
ejpam-7142	319	10	of	of	ADP
ejpam-7142	319	11	nonlinear	nonlinear	ADJ
ejpam-7142	319	12	type	type	NOUN
ejpam-7142	319	13	.	.	PUNCT
ejpam-7142	320	1	neutrosophic	neutrosophic	ADJ
ejpam-7142	320	2	sets	set	NOUN
ejpam-7142	320	3	and	and	CCONJ
ejpam-7142	320	4	systems	system	NOUN
ejpam-7142	320	5	,	,	PUNCT
ejpam-7142	320	6	77(1):96–112	77(1):96–112	NUM
ejpam-7142	320	7	,	,	PUNCT
ejpam-7142	320	8	2025	2025	NUM
ejpam-7142	320	9	.	.	PUNCT
ejpam-7142	321	1	[	[	X
ejpam-7142	321	2	17	17	NUM
ejpam-7142	321	3	]	]	PUNCT
ejpam-7142	321	4	a.	a.	NOUN
ejpam-7142	321	5	bataihah	bataihah	PROPN
ejpam-7142	321	6	and	and	CCONJ
ejpam-7142	321	7	a.	a.	NOUN
ejpam-7142	321	8	hazaymeh	hazaymeh	NOUN
ejpam-7142	321	9	.	.	PUNCT
ejpam-7142	322	1	quasi	quasi	NOUN
ejpam-7142	322	2	contractions	contraction	NOUN
ejpam-7142	322	3	and	and	CCONJ
ejpam-7142	322	4	fixed	fix	VERB
ejpam-7142	322	5	point	point	NOUN
ejpam-7142	322	6	theorems	theorem	NOUN
ejpam-7142	322	7	in	in	ADP
ejpam-7142	322	8	the	the	DET
ejpam-7142	322	9	context	context	NOUN
ejpam-7142	322	10	of	of	ADP
ejpam-7142	322	11	neutrosophic	neutrosophic	ADJ
ejpam-7142	322	12	fuzzy	fuzzy	ADJ
ejpam-7142	322	13	metric	metric	ADJ
ejpam-7142	322	14	spaces	space	NOUN
ejpam-7142	322	15	.	.	PUNCT
ejpam-7142	323	1	european	european	ADJ
ejpam-7142	323	2	journal	journal	PROPN
ejpam-7142	323	3	of	of	ADP
ejpam-7142	323	4	pure	pure	ADJ
ejpam-7142	323	5	and	and	CCONJ
ejpam-7142	323	6	applied	applied	ADJ
ejpam-7142	323	7	mathematics	mathematic	NOUN
ejpam-7142	323	8	,	,	PUNCT
ejpam-7142	323	9	18(1):5785–5785	18(1):5785–5785	NUM
ejpam-7142	323	10	,	,	PUNCT
ejpam-7142	323	11	2025	2025	NUM
ejpam-7142	323	12	.	.	PUNCT
ejpam-7142	324	1	[	[	X
ejpam-7142	324	2	18	18	NUM
ejpam-7142	324	3	]	]	X
ejpam-7142	324	4	a.	a.	NOUN
ejpam-7142	324	5	malkawi	malkawi	PROPN
ejpam-7142	324	6	.	.	PUNCT
ejpam-7142	325	1	enhanced	enhance	VERB
ejpam-7142	325	2	uncertainty	uncertainty	NOUN
ejpam-7142	325	3	modeling	model	VERB
ejpam-7142	325	4	through	through	ADP
ejpam-7142	325	5	neutrosophic	neutrosophic	ADJ
ejpam-7142	325	6	mr	mr	PROPN
ejpam-7142	325	7	-	-	PUNCT
ejpam-7142	325	8	metrics	metric	NOUN
ejpam-7142	325	9	:	:	PUNCT
ejpam-7142	325	10	a	a	DET
ejpam-7142	325	11	unified	unified	ADJ
ejpam-7142	325	12	framework	framework	NOUN
ejpam-7142	325	13	with	with	ADP
ejpam-7142	325	14	fuzzy	fuzzy	ADJ
ejpam-7142	325	15	embedding	embedding	NOUN
ejpam-7142	325	16	and	and	CCONJ
ejpam-7142	325	17	contraction	contraction	NOUN
ejpam-7142	325	18	principles	principle	NOUN
ejpam-7142	325	19	.	.	PUNCT
ejpam-7142	326	1	european	european	ADJ
ejpam-7142	326	2	journal	journal	PROPN
ejpam-7142	326	3	of	of	ADP
ejpam-7142	326	4	pure	pure	ADJ
ejpam-7142	326	5	and	and	CCONJ
ejpam-7142	326	6	applied	applied	ADJ
ejpam-7142	326	7	mathematics	mathematic	NOUN
ejpam-7142	326	8	,	,	PUNCT
ejpam-7142	326	9	18(3):id	18(3):id	NUM
ejpam-7142	326	10	:	:	SYM
ejpam-7142	326	11	6475	6475	NUM
ejpam-7142	326	12	,	,	PUNCT
ejpam-7142	326	13	2025	2025	NUM
ejpam-7142	326	14	.	.	PUNCT
ejpam-7142	327	1	[	[	X
ejpam-7142	327	2	19	19	NUM
ejpam-7142	327	3	]	]	PUNCT
ejpam-7142	327	4	abed	abed	PROPN
ejpam-7142	327	5	al	al	PROPN
ejpam-7142	327	6	-	-	PUNCT
ejpam-7142	327	7	rahman	rahman	PROPN
ejpam-7142	327	8	m.	m.	PROPN
ejpam-7142	327	9	malkawi	malkawi	PROPN
ejpam-7142	327	10	.	.	PUNCT
ejpam-7142	327	11	fixed	fix	VERB
ejpam-7142	327	12	point	point	NOUN
ejpam-7142	327	13	theorems	theorem	NOUN
ejpam-7142	327	14	for	for	ADP
ejpam-7142	327	15	fuzzy	fuzzy	ADJ
ejpam-7142	327	16	mappings	mapping	NOUN
ejpam-7142	327	17	in	in	ADP
ejpam-7142	327	18	neutrosophic	neutrosophic	ADJ
ejpam-7142	327	19	mr	mr	PROPN
ejpam-7142	327	20	-	-	PUNCT
ejpam-7142	327	21	metric	metric	ADJ
ejpam-7142	327	22	spaces	space	NOUN
ejpam-7142	327	23	.	.	PUNCT
ejpam-7142	328	1	journal	journal	PROPN
ejpam-7142	328	2	of	of	ADP
ejpam-7142	328	3	nonlinear	nonlinear	ADJ
ejpam-7142	328	4	modeling	modeling	NOUN
ejpam-7142	328	5	and	and	CCONJ
ejpam-7142	328	6	analysis	analysis	NOUN
ejpam-7142	328	7	,	,	PUNCT
ejpam-7142	328	8	2025	2025	NUM
ejpam-7142	328	9	.	.	PUNCT
ejpam-7142	329	1	acceptance	acceptance	NOUN
ejpam-7142	329	2	.	.	PUNCT
ejpam-7142	330	1	[	[	X
ejpam-7142	330	2	20	20	NUM
ejpam-7142	330	3	]	]	X
ejpam-7142	330	4	a.	a.	NOUN
ejpam-7142	330	5	malkawi	malkawi	PROPN
ejpam-7142	330	6	,	,	PUNCT
ejpam-7142	330	7	a.	a.	NOUN
ejpam-7142	330	8	tallafha	tallafha	NOUN
ejpam-7142	330	9	,	,	PUNCT
ejpam-7142	330	10	and	and	CCONJ
ejpam-7142	330	11	w.	w.	PROPN
ejpam-7142	330	12	shatanawi	shatanawi	PROPN
ejpam-7142	330	13	.	.	PUNCT
ejpam-7142	331	1	coincidence	coincidence	NOUN
ejpam-7142	331	2	and	and	CCONJ
ejpam-7142	331	3	fixed	fix	VERB
ejpam-7142	331	4	point	point	NOUN
ejpam-7142	331	5	results	result	NOUN
ejpam-7142	331	6	for	for	ADP
ejpam-7142	331	7	generalized	generalized	ADJ
ejpam-7142	331	8	weak	weak	ADJ
ejpam-7142	331	9	contraction	contraction	NOUN
ejpam-7142	331	10	mapping	mapping	NOUN
ejpam-7142	331	11	on	on	ADP
ejpam-7142	331	12	b	b	NOUN
ejpam-7142	331	13	-	-	PUNCT
ejpam-7142	331	14	metric	metric	ADJ
ejpam-7142	331	15	spaces	space	NOUN
ejpam-7142	331	16	.	.	PUNCT
ejpam-7142	332	1	nonlinear	nonlinear	ADJ
ejpam-7142	332	2	functional	functional	ADJ
ejpam-7142	332	3	analysis	analysis	NOUN
ejpam-7142	332	4	and	and	CCONJ
ejpam-7142	332	5	applications	application	NOUN
ejpam-7142	332	6	,	,	PUNCT
ejpam-7142	332	7	26(1):177–195	26(1):177–195	NOUN
ejpam-7142	332	8	,	,	PUNCT
ejpam-7142	332	9	2021	2021	NUM
ejpam-7142	332	10	.	.	PUNCT
ejpam-7142	333	1	[	[	X
ejpam-7142	333	2	21	21	NUM
ejpam-7142	333	3	]	]	PUNCT
ejpam-7142	333	4	a.	a.	NOUN
ejpam-7142	333	5	a.	a.	PROPN
ejpam-7142	333	6	r.	r.	PROPN
ejpam-7142	333	7	m.	m.	PROPN
ejpam-7142	333	8	malkawi	malkawi	PROPN
ejpam-7142	333	9	,	,	PUNCT
ejpam-7142	333	10	d.	d.	PROPN
ejpam-7142	333	11	mahmoud	mahmoud	PROPN
ejpam-7142	333	12	,	,	PUNCT
ejpam-7142	333	13	a.	a.	PROPN
ejpam-7142	333	14	m.	m.	PROPN
ejpam-7142	333	15	rabaiah	rabaiah	PROPN
ejpam-7142	333	16	,	,	PUNCT
ejpam-7142	333	17	r.	r.	PROPN
ejpam-7142	333	18	al	al	PROPN
ejpam-7142	333	19	-	-	PUNCT
ejpam-7142	333	20	deiakeh	deiakeh	PROPN
ejpam-7142	333	21	,	,	PUNCT
ejpam-7142	333	22	and	and	CCONJ
ejpam-7142	333	23	w.	w.	PROPN
ejpam-7142	333	24	shatanawi	shatanawi	PROPN
ejpam-7142	333	25	.	.	PUNCT
ejpam-7142	334	1	on	on	ADP
ejpam-7142	334	2	fixed	fix	VERB
ejpam-7142	334	3	point	point	NOUN
ejpam-7142	334	4	theorems	theorem	NOUN
ejpam-7142	334	5	in	in	ADP
ejpam-7142	334	6	mr	mr	PROPN
ejpam-7142	334	7	-	-	PUNCT
ejpam-7142	334	8	metric	metric	ADJ
ejpam-7142	334	9	spaces	space	NOUN
ejpam-7142	334	10	.	.	PUNCT
ejpam-7142	335	1	nonlinear	nonlinear	ADJ
ejpam-7142	335	2	functional	functional	ADJ
ejpam-7142	335	3	analysis	analysis	NOUN
ejpam-7142	335	4	and	and	CCONJ
ejpam-7142	335	5	applications	application	NOUN
ejpam-7142	335	6	,	,	PUNCT
ejpam-7142	335	7	29(4):1125–1136	29(4):1125–1136	NUM
ejpam-7142	335	8	,	,	PUNCT
ejpam-7142	335	9	2024	2024	NUM
ejpam-7142	335	10	.	.	PUNCT
ejpam-7142	336	1	[	[	X
ejpam-7142	336	2	22	22	NUM
ejpam-7142	336	3	]	]	X
ejpam-7142	336	4	a.	a.	NOUN
ejpam-7142	336	5	malkawi	malkawi	PROPN
ejpam-7142	336	6	.	.	PUNCT
ejpam-7142	337	1	applications	application	NOUN
ejpam-7142	337	2	of	of	ADP
ejpam-7142	337	3	mr	mr	PROPN
ejpam-7142	337	4	-	-	PUNCT
ejpam-7142	337	5	metric	metric	ADJ
ejpam-7142	337	6	spaces	space	NOUN
ejpam-7142	337	7	in	in	ADP
ejpam-7142	337	8	measure	measure	NOUN
ejpam-7142	337	9	theory	theory	NOUN
ejpam-7142	337	10	and	and	CCONJ
ejpam-7142	337	11	convergence	convergence	NOUN
ejpam-7142	337	12	analysis	analysis	NOUN
ejpam-7142	337	13	.	.	PUNCT
ejpam-7142	338	1	european	european	ADJ
ejpam-7142	338	2	journal	journal	PROPN
ejpam-7142	338	3	of	of	ADP
ejpam-7142	338	4	pure	pure	ADJ
ejpam-7142	338	5	and	and	CCONJ
ejpam-7142	338	6	applied	applied	ADJ
ejpam-7142	338	7	mathematics	mathematic	NOUN
ejpam-7142	338	8	,	,	PUNCT
ejpam-7142	338	9	18(3):id	18(3):id	NUM
ejpam-7142	338	10	:	:	SYM
ejpam-7142	338	11	6528	6528	NUM
ejpam-7142	338	12	,	,	PUNCT
ejpam-7142	338	13	2025	2025	NUM
ejpam-7142	338	14	.	.	PUNCT
ejpam-7142	339	1	[	[	X
ejpam-7142	339	2	23	23	NUM
ejpam-7142	339	3	]	]	PUNCT
ejpam-7142	339	4	a.	a.	NOUN
ejpam-7142	339	5	a.	a.	PROPN
ejpam-7142	339	6	r.	r.	PROPN
ejpam-7142	339	7	m.	m.	PROPN
ejpam-7142	339	8	malkawi	malkawi	PROPN
ejpam-7142	339	9	.	.	PROPN
ejpam-7142	340	1	existence	existence	NOUN
ejpam-7142	340	2	and	and	CCONJ
ejpam-7142	340	3	uniqueness	uniqueness	NOUN
ejpam-7142	340	4	of	of	ADP
ejpam-7142	340	5	fixed	fix	VERB
ejpam-7142	340	6	points	point	NOUN
ejpam-7142	340	7	in	in	ADP
ejpam-7142	340	8	mr	mr	PROPN
ejpam-7142	340	9	-	-	PUNCT
ejpam-7142	340	10	metric	metric	ADJ
ejpam-7142	340	11	spaces	space	NOUN
ejpam-7142	340	12	and	and	CCONJ
ejpam-7142	340	13	their	their	PRON
ejpam-7142	340	14	applications	application	NOUN
ejpam-7142	340	15	.	.	PUNCT
ejpam-7142	341	1	european	european	ADJ
ejpam-7142	341	2	journal	journal	PROPN
ejpam-7142	341	3	of	of	ADP
ejpam-7142	341	4	pure	pure	ADJ
ejpam-7142	341	5	and	and	CCONJ
ejpam-7142	341	6	applied	applied	ADJ
ejpam-7142	341	7	mathematics	mathematic	NOUN
ejpam-7142	341	8	,	,	PUNCT
ejpam-7142	341	9	18(2):id	18(2):id	NUM
ejpam-7142	341	10	:	:	PUNCT
ejpam-7142	341	11	6077	6077	NUM
ejpam-7142	341	12	,	,	PUNCT
ejpam-7142	341	13	2025	2025	NUM
ejpam-7142	341	14	.	.	PUNCT
ejpam-7142	342	1	[	[	X
ejpam-7142	342	2	24	24	NUM
ejpam-7142	342	3	]	]	PUNCT
ejpam-7142	342	4	a.	a.	NOUN
ejpam-7142	342	5	a.	a.	PROPN
ejpam-7142	342	6	r.	r.	PROPN
ejpam-7142	342	7	m.	m.	PROPN
ejpam-7142	342	8	malkawi	malkawi	PROPN
ejpam-7142	342	9	.	.	PROPN
ejpam-7142	343	1	convergence	convergence	NOUN
ejpam-7142	343	2	and	and	CCONJ
ejpam-7142	343	3	fixed	fix	VERB
ejpam-7142	343	4	points	point	NOUN
ejpam-7142	343	5	of	of	ADP
ejpam-7142	343	6	self	self	NOUN
ejpam-7142	343	7	-	-	PUNCT
ejpam-7142	343	8	mappings	mapping	NOUN
ejpam-7142	343	9	in	in	ADP
ejpam-7142	343	10	mr	mr	PROPN
ejpam-7142	343	11	-	-	PUNCT
ejpam-7142	343	12	metric	metric	ADJ
ejpam-7142	343	13	spaces	space	NOUN
ejpam-7142	343	14	:	:	PUNCT
ejpam-7142	343	15	theory	theory	NOUN
ejpam-7142	343	16	and	and	CCONJ
ejpam-7142	343	17	applications	application	NOUN
ejpam-7142	343	18	.	.	PUNCT
ejpam-7142	344	1	european	european	ADJ
ejpam-7142	344	2	journal	journal	PROPN
ejpam-7142	344	3	of	of	ADP
ejpam-7142	344	4	pure	pure	ADJ
ejpam-7142	344	5	and	and	CCONJ
ejpam-7142	344	6	applied	applied	ADJ
ejpam-7142	344	7	mathematics	mathematic	NOUN
ejpam-7142	344	8	,	,	PUNCT
ejpam-7142	344	9	18(2):id	18(2):id	NUM
ejpam-7142	344	10	:	:	SYM
ejpam-7142	344	11	5952	5952	NUM
ejpam-7142	344	12	,	,	PUNCT
ejpam-7142	344	13	2025	2025	NUM
ejpam-7142	344	14	.	.	PUNCT
ejpam-7142	345	1	[	[	X
ejpam-7142	345	2	25	25	NUM
ejpam-7142	345	3	]	]	PUNCT
ejpam-7142	345	4	a.	a.	NOUN
ejpam-7142	345	5	a.	a.	PROPN
ejpam-7142	345	6	r.	r.	PROPN
ejpam-7142	345	7	m.	m.	PROPN
ejpam-7142	345	8	malkawi	malkawi	PROPN
ejpam-7142	345	9	.	.	PUNCT
ejpam-7142	345	10	fixed	fix	VERB
ejpam-7142	345	11	point	point	NOUN
ejpam-7142	345	12	theorem	theorem	VERB
ejpam-7142	345	13	in	in	ADP
ejpam-7142	345	14	mr	mr	PROPN
ejpam-7142	345	15	-	-	PUNCT
ejpam-7142	345	16	metric	metric	ADJ
ejpam-7142	345	17	spaces	space	NOUN
ejpam-7142	345	18	via	via	ADP
ejpam-7142	345	19	integral	integral	ADJ
ejpam-7142	345	20	type	type	NOUN
ejpam-7142	345	21	contraction	contraction	NOUN
ejpam-7142	345	22	.	.	PUNCT
ejpam-7142	346	1	wseas	wseas	VERB
ejpam-7142	346	2	transactions	transaction	NOUN
ejpam-7142	346	3	on	on	ADP
ejpam-7142	346	4	mathematics	mathematic	NOUN
ejpam-7142	346	5	,	,	PUNCT
ejpam-7142	346	6	24:295–299	24:295–299	PROPN
ejpam-7142	346	7	,	,	PUNCT
ejpam-7142	346	8	2025	2025	NUM
ejpam-7142	346	9	.	.	PUNCT
ejpam-7142	347	1	[	[	X
ejpam-7142	347	2	26	26	NUM
ejpam-7142	347	3	]	]	PUNCT
ejpam-7142	347	4	r.	r.	PROPN
ejpam-7142	347	5	al	al	PROPN
ejpam-7142	347	6	-	-	PUNCT
ejpam-7142	347	7	deiakeh	deiakeh	ADJ
ejpam-7142	347	8	,	,	PUNCT
ejpam-7142	347	9	m.	m.	NOUN
ejpam-7142	347	10	alquran	alquran	PROPN
ejpam-7142	347	11	,	,	PUNCT
ejpam-7142	347	12	m.	m.	PROPN
ejpam-7142	347	13	ali	ali	PROPN
ejpam-7142	347	14	,	,	PUNCT
ejpam-7142	347	15	s.	s.	PROPN
ejpam-7142	347	16	qureshi	qureshi	PROPN
ejpam-7142	347	17	,	,	PUNCT
ejpam-7142	347	18	s.	s.	PROPN
ejpam-7142	347	19	momani	momani	PROPN
ejpam-7142	347	20	,	,	PUNCT
ejpam-7142	347	21	and	and	CCONJ
ejpam-7142	347	22	a.	a.	NOUN
ejpam-7142	347	23	a.	a.	PROPN
ejpam-7142	347	24	r.	r.	PROPN
ejpam-7142	347	25	malkawi	malkawi	PROPN
ejpam-7142	347	26	.	.	PROPN
ejpam-7142	348	1	lie	lie	PROPN
ejpam-7142	348	2	symmetry	symmetry	NOUN
ejpam-7142	348	3	,	,	PUNCT
ejpam-7142	348	4	convergence	convergence	NOUN
ejpam-7142	348	5	analysis	analysis	NOUN
ejpam-7142	348	6	,	,	PUNCT
ejpam-7142	348	7	explicit	explicit	ADJ
ejpam-7142	348	8	solutions	solution	NOUN
ejpam-7142	348	9	,	,	PUNCT
ejpam-7142	348	10	and	and	CCONJ
ejpam-7142	348	11	conservation	conservation	NOUN
ejpam-7142	348	12	laws	law	NOUN
ejpam-7142	348	13	for	for	ADP
ejpam-7142	348	14	the	the	DET
ejpam-7142	348	15	timefractional	timefractional	ADJ
ejpam-7142	348	16	modified	modify	VERB
ejpam-7142	348	17	benjamin	benjamin	PROPN
ejpam-7142	348	18	-	-	PUNCT
ejpam-7142	348	19	bona	bona	ADJ
ejpam-7142	348	20	-	-	PUNCT
ejpam-7142	348	21	mahony	mahony	NOUN
ejpam-7142	348	22	equation	equation	NOUN
ejpam-7142	348	23	.	.	PUNCT
ejpam-7142	349	1	journal	journal	PROPN
ejpam-7142	349	2	of	of	ADP
ejpam-7142	349	3	applied	apply	VERB
ejpam-7142	349	4	mathematics	mathematic	NOUN
ejpam-7142	349	5	and	and	CCONJ
ejpam-7142	349	6	computational	computational	ADJ
ejpam-7142	349	7	mechanics	mechanic	NOUN
ejpam-7142	349	8	,	,	PUNCT
ejpam-7142	349	9	23(1):19–31	23(1):19–31	NUM
ejpam-7142	349	10	,	,	PUNCT
ejpam-7142	349	11	2024	2024	NUM
ejpam-7142	349	12	.	.	PUNCT
ejpam-7142	350	1	[	[	X
ejpam-7142	350	2	27	27	NUM
ejpam-7142	350	3	]	]	X
ejpam-7142	350	4	g.	g.	PROPN
ejpam-7142	350	5	m.	m.	PROPN
ejpam-7142	350	6	gharib	gharib	PROPN
ejpam-7142	350	7	,	,	PUNCT
ejpam-7142	350	8	m.	m.	PROPN
ejpam-7142	350	9	s.	s.	PROPN
ejpam-7142	350	10	alsauodi	alsauodi	PROPN
ejpam-7142	350	11	,	,	PUNCT
ejpam-7142	350	12	a.	a.	NOUN
ejpam-7142	350	13	guiatni	guiatni	PROPN
ejpam-7142	350	14	,	,	PUNCT
ejpam-7142	350	15	m.	m.	NOUN
ejpam-7142	350	16	a.	a.	PROPN
ejpam-7142	350	17	al	al	PROPN
ejpam-7142	350	18	-	-	PUNCT
ejpam-7142	350	19	omari	omari	PROPN
ejpam-7142	350	20	,	,	PUNCT
ejpam-7142	350	21	and	and	CCONJ
ejpam-7142	350	22	a.	a.	NOUN
ejpam-7142	350	23	a.-r	a.-r	PROPN
ejpam-7142	350	24	.	.	PUNCT
ejpam-7142	351	1	m.	m.	NOUN
ejpam-7142	351	2	malkawi	malkawi	PROPN
ejpam-7142	351	3	.	.	PUNCT
ejpam-7142	352	1	using	use	VERB
ejpam-7142	352	2	atomic	atomic	ADJ
ejpam-7142	352	3	solution	solution	NOUN
ejpam-7142	352	4	method	method	NOUN
ejpam-7142	352	5	to	to	PART
ejpam-7142	352	6	solve	solve	VERB
ejpam-7142	352	7	the	the	DET
ejpam-7142	352	8	fractional	fractional	ADJ
ejpam-7142	352	9	equations	equation	NOUN
ejpam-7142	352	10	.	.	PUNCT
ejpam-7142	353	1	in	in	ADP
ejpam-7142	353	2	springer	springer	NOUN
ejpam-7142	353	3	proceedings	proceeding	NOUN
ejpam-7142	353	4	in	in	ADP
ejpam-7142	353	5	mathematics	mathematic	NOUN
ejpam-7142	353	6	and	and	CCONJ
ejpam-7142	353	7	statistics	statistic	NOUN
ejpam-7142	353	8	,	,	PUNCT
ejpam-7142	353	9	volume	volume	NOUN
ejpam-7142	353	10	418	418	NUM
ejpam-7142	353	11	,	,	PUNCT
ejpam-7142	353	12	pages	page	VERB
ejpam-7142	353	13	123–129	123–129	NUM
ejpam-7142	353	14	.	.	PUNCT
ejpam-7142	354	1	2023	2023	NUM
ejpam-7142	354	2	.	.	PUNCT
ejpam-7142	355	1	[	[	X
ejpam-7142	355	2	28	28	NUM
ejpam-7142	355	3	]	]	X
ejpam-7142	355	4	s.	s.	PROPN
ejpam-7142	355	5	al	al	PROPN
ejpam-7142	355	6	-	-	PUNCT
ejpam-7142	355	7	sharif	sharif	PROPN
ejpam-7142	355	8	and	and	CCONJ
ejpam-7142	355	9	a.	a.	NOUN
ejpam-7142	355	10	malkawi	malkawi	PROPN
ejpam-7142	355	11	.	.	PUNCT
ejpam-7142	356	1	modification	modification	NOUN
ejpam-7142	356	2	of	of	ADP
ejpam-7142	356	3	conformable	conformable	ADJ
ejpam-7142	356	4	fractional	fractional	ADJ
ejpam-7142	356	5	derivative	derivative	NOUN
ejpam-7142	356	6	with	with	ADP
ejpam-7142	356	7	classical	classical	ADJ
ejpam-7142	356	8	e.	e.	PROPN
ejpam-7142	356	9	hussein	hussein	PROPN
ejpam-7142	356	10	et	et	PROPN
ejpam-7142	356	11	al	al	PROPN
ejpam-7142	356	12	.	.	PUNCT
ejpam-7142	356	13	/	/	SYM
ejpam-7142	356	14	eur	eur	PROPN
ejpam-7142	356	15	.	.	PUNCT
ejpam-7142	357	1	j.	j.	PROPN
ejpam-7142	357	2	pure	pure	PROPN
ejpam-7142	357	3	appl	appl	PROPN
ejpam-7142	357	4	.	.	PROPN
ejpam-7142	357	5	math	math	PROPN
ejpam-7142	357	6	,	,	PUNCT
ejpam-7142	357	7	18	18	NUM
ejpam-7142	357	8	(	(	PUNCT
ejpam-7142	357	9	4	4	NUM
ejpam-7142	357	10	)	)	PUNCT
ejpam-7142	357	11	(	(	PUNCT
ejpam-7142	357	12	2025	2025	NUM
ejpam-7142	357	13	)	)	PUNCT
ejpam-7142	357	14	,	,	PUNCT
ejpam-7142	357	15	7142	7142	NUM
ejpam-7142	357	16	17	17	NUM
ejpam-7142	357	17	of	of	ADP
ejpam-7142	357	18	17	17	NUM
ejpam-7142	357	19	properties	property	NOUN
ejpam-7142	357	20	.	.	PUNCT
ejpam-7142	358	1	italian	italian	ADJ
ejpam-7142	358	2	journal	journal	NOUN
ejpam-7142	358	3	of	of	ADP
ejpam-7142	358	4	pure	pure	ADJ
ejpam-7142	358	5	and	and	CCONJ
ejpam-7142	358	6	applied	applied	ADJ
ejpam-7142	358	7	mathematics	mathematic	NOUN
ejpam-7142	358	8	,	,	PUNCT
ejpam-7142	358	9	44:30–39	44:30–39	PROPN
ejpam-7142	358	10	,	,	PUNCT
ejpam-7142	358	11	2020	2020	NUM
ejpam-7142	358	12	.	.	PUNCT
ejpam-7142	359	1	[	[	X
ejpam-7142	359	2	29	29	NUM
ejpam-7142	359	3	]	]	PUNCT
ejpam-7142	359	4	a.	a.	NOUN
ejpam-7142	359	5	bataihah	bataihah	PROPN
ejpam-7142	359	6	.	.	PUNCT
ejpam-7142	360	1	some	some	DET
ejpam-7142	360	2	fixed	fix	VERB
ejpam-7142	360	3	point	point	NOUN
ejpam-7142	360	4	results	result	NOUN
ejpam-7142	360	5	with	with	ADP
ejpam-7142	360	6	application	application	NOUN
ejpam-7142	360	7	to	to	ADP
ejpam-7142	360	8	fractional	fractional	ADJ
ejpam-7142	360	9	differential	differential	ADJ
ejpam-7142	360	10	equation	equation	NOUN
ejpam-7142	360	11	via	via	ADP
ejpam-7142	360	12	new	new	ADJ
ejpam-7142	360	13	type	type	NOUN
ejpam-7142	360	14	of	of	ADP
ejpam-7142	360	15	distance	distance	NOUN
ejpam-7142	360	16	spaces	space	NOUN
ejpam-7142	360	17	.	.	PUNCT
ejpam-7142	361	1	results	result	NOUN
ejpam-7142	361	2	in	in	ADP
ejpam-7142	361	3	nonlinear	nonlinear	ADJ
ejpam-7142	361	4	analysis	analysis	NOUN
ejpam-7142	361	5	,	,	PUNCT
ejpam-7142	361	6	7:202–208	7:202–208	NUM
ejpam-7142	361	7	,	,	PUNCT
ejpam-7142	361	8	2024	2024	NUM
ejpam-7142	361	9	.	.	PUNCT
ejpam-7142	362	1	[	[	X
ejpam-7142	362	2	30	30	NUM
ejpam-7142	362	3	]	]	X
ejpam-7142	362	4	a.	a.	NOUN
ejpam-7142	362	5	malkawi	malkawi	NOUN
ejpam-7142	362	6	and	and	CCONJ
ejpam-7142	362	7	a.	a.	PROPN
ejpam-7142	362	8	rabaiah	rabaiah	PROPN
ejpam-7142	362	9	.	.	PUNCT
ejpam-7142	363	1	mr	mr	PROPN
ejpam-7142	363	2	-	-	PUNCT
ejpam-7142	363	3	metric	metric	ADJ
ejpam-7142	363	4	spaces	space	NOUN
ejpam-7142	363	5	:	:	PUNCT
ejpam-7142	363	6	theory	theory	NOUN
ejpam-7142	363	7	and	and	CCONJ
ejpam-7142	363	8	applications	application	NOUN
ejpam-7142	363	9	in	in	ADP
ejpam-7142	363	10	weighted	weighted	ADJ
ejpam-7142	363	11	graphs	graph	NOUN
ejpam-7142	363	12	,	,	PUNCT
ejpam-7142	363	13	expander	expander	NOUN
ejpam-7142	363	14	graphs	graph	NOUN
ejpam-7142	363	15	,	,	PUNCT
ejpam-7142	363	16	and	and	CCONJ
ejpam-7142	363	17	fixed	fix	VERB
ejpam-7142	363	18	-	-	PUNCT
ejpam-7142	363	19	point	point	NOUN
ejpam-7142	363	20	theorems	theorem	NOUN
ejpam-7142	363	21	.	.	PUNCT
ejpam-7142	364	1	european	european	PROPN
ejpam-7142	364	2	journal	journal	PROPN
ejpam-7142	364	3	of	of	ADP
ejpam-7142	364	4	pure	pure	ADJ
ejpam-7142	364	5	and	and	CCONJ
ejpam-7142	364	6	applied	applied	ADJ
ejpam-7142	364	7	mathematics	mathematic	NOUN
ejpam-7142	364	8	,	,	PUNCT
ejpam-7142	364	9	18(3):id	18(3):id	NUM
ejpam-7142	364	10	:	:	PUNCT
ejpam-7142	364	11	6525	6525	NUM
ejpam-7142	364	12	,	,	PUNCT
ejpam-7142	364	13	2025	2025	NUM
ejpam-7142	364	14	.	.	PUNCT
ejpam-7142	365	1	[	[	X
ejpam-7142	365	2	31	31	NUM
ejpam-7142	365	3	]	]	PUNCT
ejpam-7142	365	4	a.	a.	NOUN
ejpam-7142	365	5	malkawi	malkawi	NOUN
ejpam-7142	365	6	and	and	CCONJ
ejpam-7142	365	7	a.	a.	PROPN
ejpam-7142	365	8	rabaiah	rabaiah	PROPN
ejpam-7142	365	9	.	.	PUNCT
ejpam-7142	366	1	compactness	compactness	NOUN
ejpam-7142	366	2	and	and	CCONJ
ejpam-7142	366	3	separability	separability	NOUN
ejpam-7142	366	4	in	in	ADP
ejpam-7142	366	5	mr	mr	PROPN
ejpam-7142	366	6	-	-	PUNCT
ejpam-7142	366	7	metric	metric	ADJ
ejpam-7142	366	8	spaces	space	NOUN
ejpam-7142	366	9	with	with	ADP
ejpam-7142	366	10	applications	application	NOUN
ejpam-7142	366	11	to	to	ADP
ejpam-7142	366	12	deep	deep	ADJ
ejpam-7142	366	13	learning	learning	NOUN
ejpam-7142	366	14	.	.	PUNCT
ejpam-7142	367	1	european	european	ADJ
ejpam-7142	367	2	journal	journal	PROPN
ejpam-7142	367	3	of	of	ADP
ejpam-7142	367	4	pure	pure	ADJ
ejpam-7142	367	5	and	and	CCONJ
ejpam-7142	367	6	applied	applied	ADJ
ejpam-7142	367	7	mathematics	mathematic	NOUN
ejpam-7142	367	8	,	,	PUNCT
ejpam-7142	367	9	18(3):id	18(3):id	NUM
ejpam-7142	367	10	:	:	SYM
ejpam-7142	367	11	6592	6592	NUM
ejpam-7142	367	12	,	,	PUNCT
ejpam-7142	367	13	2025	2025	NUM
ejpam-7142	367	14	.	.	PUNCT
ejpam-7142	368	1	[	[	X
ejpam-7142	368	2	32	32	NUM
ejpam-7142	368	3	]	]	PUNCT
ejpam-7142	368	4	g.	g.	PROPN
ejpam-7142	368	5	gharib	gharib	PROPN
ejpam-7142	368	6	,	,	PUNCT
ejpam-7142	368	7	a.	a.	PROPN
ejpam-7142	368	8	malkawi	malkawi	PROPN
ejpam-7142	368	9	,	,	PUNCT
ejpam-7142	368	10	a.	a.	PROPN
ejpam-7142	368	11	rabaiah	rabaiah	PROPN
ejpam-7142	368	12	,	,	PUNCT
ejpam-7142	368	13	w.	w.	PROPN
ejpam-7142	368	14	shatanawi	shatanawi	PROPN
ejpam-7142	368	15	,	,	PUNCT
ejpam-7142	368	16	and	and	CCONJ
ejpam-7142	368	17	m.	m.	NOUN
ejpam-7142	368	18	alsauodi	alsauodi	PROPN
ejpam-7142	368	19	.	.	PUNCT
ejpam-7142	369	1	a	a	DET
ejpam-7142	369	2	common	common	ADJ
ejpam-7142	369	3	fixed	fix	VERB
ejpam-7142	369	4	point	point	NOUN
ejpam-7142	369	5	theorem	theorem	VERB
ejpam-7142	369	6	in	in	ADP
ejpam-7142	369	7	m*-metric	m*-metric	ADV
ejpam-7142	369	8	space	space	NOUN
ejpam-7142	369	9	and	and	CCONJ
ejpam-7142	369	10	an	an	DET
ejpam-7142	369	11	application	application	NOUN
ejpam-7142	369	12	.	.	PUNCT
ejpam-7142	370	1	nonlinear	nonlinear	ADJ
ejpam-7142	370	2	functional	functional	ADJ
ejpam-7142	370	3	analysis	analysis	NOUN
ejpam-7142	370	4	and	and	CCONJ
ejpam-7142	370	5	applications	application	NOUN
ejpam-7142	370	6	,	,	PUNCT
ejpam-7142	370	7	27(2):289–308	27(2):289–308	NUM
ejpam-7142	370	8	,	,	PUNCT
ejpam-7142	370	9	2022	2022	NUM
ejpam-7142	370	10	.	.	PUNCT
ejpam-7142	371	1	[	[	X
ejpam-7142	371	2	33	33	NUM
ejpam-7142	371	3	]	]	PUNCT
ejpam-7142	371	4	t.	t.	NOUN
ejpam-7142	371	5	qawasmeh	qawasmeh	NOUN
ejpam-7142	371	6	.	.	PUNCT
ejpam-7142	372	1	h	h	NOUN
ejpam-7142	372	2	-	-	PUNCT
ejpam-7142	372	3	simulation	simulation	NOUN
ejpam-7142	372	4	functions	function	NOUN
ejpam-7142	372	5	and	and	CCONJ
ejpam-7142	372	6	ωb	ωb	NOUN
ejpam-7142	372	7	-	-	PUNCT
ejpam-7142	372	8	distance	distance	NOUN
ejpam-7142	372	9	mappings	mapping	NOUN
ejpam-7142	372	10	in	in	ADP
ejpam-7142	372	11	the	the	DET
ejpam-7142	372	12	setting	setting	NOUN
ejpam-7142	372	13	of	of	ADP
ejpam-7142	372	14	gb	gb	ADV
ejpam-7142	372	15	-	-	PUNCT
ejpam-7142	372	16	metric	metric	ADJ
ejpam-7142	372	17	spaces	space	NOUN
ejpam-7142	372	18	and	and	CCONJ
ejpam-7142	372	19	application	application	NOUN
ejpam-7142	372	20	.	.	PUNCT
ejpam-7142	373	1	nonlinear	nonlinear	ADJ
ejpam-7142	373	2	functional	functional	ADJ
ejpam-7142	373	3	analysis	analysis	NOUN
ejpam-7142	373	4	and	and	CCONJ
ejpam-7142	373	5	applications	application	NOUN
ejpam-7142	373	6	,	,	PUNCT
ejpam-7142	373	7	28(2):557–570	28(2):557–570	NOUN
ejpam-7142	373	8	,	,	PUNCT
ejpam-7142	373	9	2023	2023	NUM
ejpam-7142	373	10	.	.	PUNCT
ejpam-7142	374	1	[	[	X
ejpam-7142	374	2	34	34	NUM
ejpam-7142	374	3	]	]	PUNCT
ejpam-7142	374	4	a.	a.	NOUN
ejpam-7142	374	5	bataihah	bataihah	PROPN
ejpam-7142	374	6	,	,	PUNCT
ejpam-7142	374	7	t.	t.	NOUN
ejpam-7142	374	8	qawasmeh	qawasmeh	NOUN
ejpam-7142	374	9	,	,	PUNCT
ejpam-7142	374	10	i.	i.	PROPN
ejpam-7142	374	11	batiha	batiha	PROPN
ejpam-7142	374	12	,	,	PUNCT
ejpam-7142	374	13	i.	i.	PROPN
ejpam-7142	374	14	m.	m.	PROPN
ejpam-7142	374	15	batiha	batiha	PROPN
ejpam-7142	374	16	,	,	PUNCT
ejpam-7142	374	17	and	and	CCONJ
ejpam-7142	374	18	t.	t.	PROPN
ejpam-7142	374	19	abdeljawad	abdeljawad	NOUN
ejpam-7142	374	20	.	.	PUNCT
ejpam-7142	375	1	gamma	gamma	NOUN
ejpam-7142	375	2	distance	distance	NOUN
ejpam-7142	375	3	mappings	mapping	NOUN
ejpam-7142	375	4	with	with	ADP
ejpam-7142	375	5	application	application	NOUN
ejpam-7142	375	6	to	to	ADP
ejpam-7142	375	7	fractional	fractional	ADJ
ejpam-7142	375	8	boundary	boundary	ADJ
ejpam-7142	375	9	differential	differential	NOUN
ejpam-7142	375	10	equation	equation	NOUN
ejpam-7142	375	11	.	.	PUNCT
ejpam-7142	376	1	journal	journal	PROPN
ejpam-7142	376	2	of	of	ADP
ejpam-7142	376	3	mathematical	mathematical	ADJ
ejpam-7142	376	4	analysis	analysis	NOUN
ejpam-7142	376	5	,	,	PUNCT
ejpam-7142	376	6	15(5):99–106	15(5):99–106	NUM
ejpam-7142	376	7	,	,	PUNCT
ejpam-7142	376	8	2024	2024	NUM
ejpam-7142	376	9	.	.	PUNCT
ejpam-7142	377	1	[	[	X
ejpam-7142	377	2	35	35	NUM
ejpam-7142	377	3	]	]	PUNCT
ejpam-7142	377	4	a.	a.	NOUN
ejpam-7142	377	5	bataihah	bataihah	PROPN
ejpam-7142	377	6	and	and	CCONJ
ejpam-7142	377	7	t.	t.	NOUN
ejpam-7142	377	8	qawasmeh	qawasmeh	NOUN
ejpam-7142	377	9	.	.	PUNCT
ejpam-7142	378	1	a	a	DET
ejpam-7142	378	2	new	new	ADJ
ejpam-7142	378	3	type	type	NOUN
ejpam-7142	378	4	of	of	ADP
ejpam-7142	378	5	distance	distance	NOUN
ejpam-7142	378	6	spaces	space	NOUN
ejpam-7142	378	7	and	and	CCONJ
ejpam-7142	378	8	fixed	fix	VERB
ejpam-7142	378	9	point	point	NOUN
ejpam-7142	378	10	results	result	NOUN
ejpam-7142	378	11	.	.	PUNCT
ejpam-7142	379	1	journal	journal	NOUN
ejpam-7142	379	2	of	of	ADP
ejpam-7142	379	3	mathematical	mathematical	ADJ
ejpam-7142	379	4	analysis	analysis	NOUN
ejpam-7142	379	5	,	,	PUNCT
ejpam-7142	379	6	15(4):81–90	15(4):81–90	NUM
ejpam-7142	379	7	,	,	PUNCT
ejpam-7142	379	8	2024	2024	NUM
ejpam-7142	379	9	.	.	PUNCT
ejpam-7142	380	1	[	[	X
ejpam-7142	380	2	36	36	NUM
ejpam-7142	380	3	]	]	PUNCT
ejpam-7142	380	4	a.	a.	NOUN
ejpam-7142	380	5	bataihah	bataihah	PROPN
ejpam-7142	380	6	,	,	PUNCT
ejpam-7142	380	7	a.	a.	NOUN
ejpam-7142	380	8	tallafha	tallafha	NOUN
ejpam-7142	380	9	,	,	PUNCT
ejpam-7142	380	10	and	and	CCONJ
ejpam-7142	380	11	w.	w.	PROPN
ejpam-7142	380	12	shatanawi	shatanawi	PROPN
ejpam-7142	380	13	.	.	PUNCT
ejpam-7142	381	1	fixed	fix	VERB
ejpam-7142	381	2	point	point	NOUN
ejpam-7142	381	3	results	result	NOUN
ejpam-7142	381	4	with	with	ADP
ejpam-7142	381	5	ω	ω	NOUN
ejpam-7142	381	6	-	-	PUNCT
ejpam-7142	381	7	distance	distance	NOUN
ejpam-7142	381	8	by	by	ADP
ejpam-7142	381	9	utilizing	utilize	VERB
ejpam-7142	381	10	simulation	simulation	NOUN
ejpam-7142	381	11	functions	function	NOUN
ejpam-7142	381	12	.	.	PUNCT
ejpam-7142	382	1	italian	italian	ADJ
ejpam-7142	382	2	journal	journal	NOUN
ejpam-7142	382	3	of	of	ADP
ejpam-7142	382	4	pure	pure	ADJ
ejpam-7142	382	5	and	and	CCONJ
ejpam-7142	382	6	applied	applied	ADJ
ejpam-7142	382	7	mathematics	mathematic	NOUN
ejpam-7142	382	8	,	,	PUNCT
ejpam-7142	382	9	(	(	PUNCT
ejpam-7142	382	10	43):185	43):185	NOUN
ejpam-7142	382	11	–	–	PUNCT
ejpam-7142	382	12	196	196	NUM
ejpam-7142	382	13	,	,	PUNCT
ejpam-7142	382	14	2017	2017	NUM
ejpam-7142	382	15	.	.	PUNCT
ejpam-7142	383	1	[	[	X
ejpam-7142	383	2	37	37	NUM
ejpam-7142	383	3	]	]	PUNCT
ejpam-7142	383	4	t.	t.	NOUN
ejpam-7142	383	5	qawasmeh	qawasmeh	NOUN
ejpam-7142	383	6	,	,	PUNCT
ejpam-7142	383	7	w.	w.	PROPN
ejpam-7142	383	8	shatanawi	shatanawi	PROPN
ejpam-7142	383	9	,	,	PUNCT
ejpam-7142	383	10	a.	a.	NOUN
ejpam-7142	383	11	bataihah	bataihah	PROPN
ejpam-7142	383	12	,	,	PUNCT
ejpam-7142	383	13	and	and	CCONJ
ejpam-7142	383	14	a.	a.	NOUN
ejpam-7142	383	15	tallafha	tallafha	NOUN
ejpam-7142	383	16	.	.	PUNCT
ejpam-7142	384	1	common	common	ADJ
ejpam-7142	384	2	fixed	fix	VERB
ejpam-7142	384	3	point	point	NOUN
ejpam-7142	384	4	results	result	NOUN
ejpam-7142	384	5	for	for	ADP
ejpam-7142	384	6	rational	rational	ADJ
ejpam-7142	384	7	(	(	PUNCT
ejpam-7142	384	8	α	α	NOUN
ejpam-7142	384	9	,	,	PUNCT
ejpam-7142	384	10	β)ϕ-mω	β)ϕ-mω	NOUN
ejpam-7142	384	11	contractions	contraction	NOUN
ejpam-7142	384	12	in	in	ADP
ejpam-7142	384	13	complete	complete	ADJ
ejpam-7142	384	14	quasi	quasi	ADJ
ejpam-7142	384	15	metric	metric	ADJ
ejpam-7142	384	16	spaces	space	NOUN
ejpam-7142	384	17	.	.	PUNCT
ejpam-7142	385	1	mathematics	mathematic	NOUN
ejpam-7142	385	2	,	,	PUNCT
ejpam-7142	385	3	7(5):392	7(5):392	NUM
ejpam-7142	385	4	,	,	PUNCT
ejpam-7142	385	5	2019	2019	NUM
ejpam-7142	385	6	.	.	PUNCT
ejpam-7142	386	1	[	[	X
ejpam-7142	386	2	38	38	NUM
ejpam-7142	386	3	]	]	PUNCT
ejpam-7142	386	4	t.	t.	NOUN
ejpam-7142	386	5	qawasmeh	qawasmeh	NOUN
ejpam-7142	386	6	and	and	CCONJ
ejpam-7142	386	7	a.	a.	NOUN
ejpam-7142	386	8	malkawi	malkawi	PROPN
ejpam-7142	386	9	.	.	PUNCT
ejpam-7142	386	10	fixed	fix	VERB
ejpam-7142	386	11	point	point	NOUN
ejpam-7142	386	12	theory	theory	NOUN
ejpam-7142	386	13	in	in	ADP
ejpam-7142	386	14	mr	mr	PROPN
ejpam-7142	386	15	-	-	PUNCT
ejpam-7142	386	16	metric	metric	ADJ
ejpam-7142	386	17	spaces	space	NOUN
ejpam-7142	386	18	:	:	PUNCT
ejpam-7142	386	19	fundamental	fundamental	ADJ
ejpam-7142	386	20	theorems	theorem	NOUN
ejpam-7142	386	21	and	and	CCONJ
ejpam-7142	386	22	applications	application	NOUN
ejpam-7142	386	23	to	to	ADP
ejpam-7142	386	24	integral	integral	ADJ
ejpam-7142	386	25	equations	equation	NOUN
ejpam-7142	386	26	and	and	CCONJ
ejpam-7142	386	27	neutron	neutron	NOUN
ejpam-7142	386	28	transport	transport	NOUN
ejpam-7142	386	29	.	.	PUNCT
ejpam-7142	387	1	european	european	ADJ
ejpam-7142	387	2	journal	journal	PROPN
ejpam-7142	387	3	of	of	ADP
ejpam-7142	387	4	pure	pure	ADJ
ejpam-7142	387	5	and	and	CCONJ
ejpam-7142	387	6	applied	applied	ADJ
ejpam-7142	387	7	mathematics	mathematic	NOUN
ejpam-7142	387	8	,	,	PUNCT
ejpam-7142	387	9	18(3):id	18(3):id	NUM
ejpam-7142	387	10	:	:	SYM
ejpam-7142	387	11	6440	6440	NUM
ejpam-7142	387	12	,	,	PUNCT
ejpam-7142	387	13	2025	2025	NUM
ejpam-7142	387	14	.	.	PUNCT
ejpam-7142	388	1	[	[	X
ejpam-7142	388	2	39	39	NUM
ejpam-7142	388	3	]	]	PUNCT
ejpam-7142	388	4	abed	abe	VERB
ejpam-7142	388	5	al	al	PROPN
ejpam-7142	388	6	-	-	PUNCT
ejpam-7142	388	7	rahman	rahman	PROPN
ejpam-7142	388	8	m.	m.	NOUN
ejpam-7142	388	9	malkawi	malkawi	PROPN
ejpam-7142	388	10	and	and	CCONJ
ejpam-7142	388	11	ayat	ayat	PROPN
ejpam-7142	388	12	m.	m.	PROPN
ejpam-7142	388	13	rabaiah	rabaiah	PROPN
ejpam-7142	388	14	.	.	PUNCT
ejpam-7142	389	1	mr	mr	PROPN
ejpam-7142	389	2	-	-	PUNCT
ejpam-7142	389	3	metric	metric	ADJ
ejpam-7142	389	4	spaces	space	NOUN
ejpam-7142	389	5	:	:	PUNCT
ejpam-7142	389	6	theory	theory	NOUN
ejpam-7142	389	7	and	and	CCONJ
ejpam-7142	389	8	applications	application	NOUN
ejpam-7142	389	9	in	in	ADP
ejpam-7142	389	10	fractional	fractional	ADJ
ejpam-7142	389	11	calculus	calculus	NOUN
ejpam-7142	389	12	and	and	CCONJ
ejpam-7142	389	13	fixed	fix	VERB
ejpam-7142	389	14	-	-	PUNCT
ejpam-7142	389	15	point	point	NOUN
ejpam-7142	389	16	theorems	theorem	NOUN
ejpam-7142	389	17	.	.	PUNCT
ejpam-7142	389	18	neutrosophic	neutrosophic	ADJ
ejpam-7142	389	19	sets	set	NOUN
ejpam-7142	389	20	and	and	CCONJ
ejpam-7142	389	21	systems	system	NOUN
ejpam-7142	389	22	,	,	PUNCT
ejpam-7142	389	23	90:1103–1121	90:1103–1121	NUM
ejpam-7142	389	24	,	,	PUNCT
ejpam-7142	389	25	2025	2025	NUM
ejpam-7142	389	26	.	.	PUNCT
ejpam-7142	390	1	[	[	X
ejpam-7142	390	2	40	40	NUM
ejpam-7142	390	3	]	]	PUNCT
ejpam-7142	390	4	abed	abed	PROPN
ejpam-7142	390	5	al	al	PROPN
ejpam-7142	390	6	-	-	PUNCT
ejpam-7142	390	7	rahman	rahman	PROPN
ejpam-7142	390	8	m.	m.	NOUN
ejpam-7142	390	9	malkawi	malkawi	PROPN
ejpam-7142	390	10	and	and	CCONJ
ejpam-7142	390	11	ayat	ayat	PROPN
ejpam-7142	390	12	m.	m.	PROPN
ejpam-7142	390	13	rabaiah	rabaiah	PROPN
ejpam-7142	390	14	.	.	PUNCT
ejpam-7142	391	1	mr	mr	PROPN
ejpam-7142	391	2	-	-	PUNCT
ejpam-7142	391	3	metric	metric	ADJ
ejpam-7142	391	4	spaces	space	NOUN
ejpam-7142	391	5	:	:	PUNCT
ejpam-7142	391	6	theory	theory	NOUN
ejpam-7142	391	7	and	and	CCONJ
ejpam-7142	391	8	applications	application	NOUN
ejpam-7142	391	9	in	in	ADP
ejpam-7142	391	10	fractional	fractional	ADJ
ejpam-7142	391	11	calculus	calculus	NOUN
ejpam-7142	391	12	and	and	CCONJ
ejpam-7142	391	13	fixed	fix	VERB
ejpam-7142	391	14	-	-	PUNCT
ejpam-7142	391	15	point	point	NOUN
ejpam-7142	391	16	theorems	theorem	NOUN
ejpam-7142	391	17	.	.	PUNCT
ejpam-7142	391	18	neutrosophic	neutrosophic	ADJ
ejpam-7142	391	19	sets	set	NOUN
ejpam-7142	391	20	and	and	CCONJ
ejpam-7142	391	21	systems	system	NOUN
ejpam-7142	391	22	,	,	PUNCT
ejpam-7142	391	23	91:685–703	91:685–703	PROPN
ejpam-7142	391	24	,	,	PUNCT
ejpam-7142	391	25	2025	2025	NUM
ejpam-7142	391	26	.	.	PUNCT