id	sid	eid	entity	type
ma-208	1	1	2024	CARDINAL
ma-208	2	1	j. math	PERSON
ma-208	4	1	4 (2024	CARDINAL
ma-208	5	1	10.28924	CARDINAL
ma-208	5	2	muhammad naeem abbas1,∗	PERSON
ma-208	5	3	mukhtar ahmad1,∗	PERSON
ma-208	5	4	abdul rauf khan2	PERSON
ma-208	6	1	khawaja fareed university	PERSON
ma-208	6	2	yar khan	PERSON
ma-208	6	3	pakistan	GPE
ma-208	7	1	2department	TIME
ma-208	7	2	ghazi university	ORG
ma-208	7	3	d.g.khan	GPE
ma-208	7	4	pakistan	GPE
ma-208	7	5	3institute	CARDINAL
ma-208	7	6	universiti malaya	GPE
ma-208	7	7	malaysia	GPE
ma-208	13	1	1	CARDINAL
ma-208	13	2	bell	ORG
ma-208	13	3	martindale	ORG
ma-208	14	1	3	CARDINAL
ma-208	15	1	belland martindale	PERSON
ma-208	16	1	3	CARDINAL
ma-208	16	2	∈	ORG
ma-208	17	1	r. bell	PERSON
ma-208	17	2	2	CARDINAL
ma-208	18	1	ali	PERSON
ma-208	18	2	1	CARDINAL
ma-208	18	3	bell	ORG
ma-208	18	4	martindale	ORG
ma-208	19	1	3	CARDINAL
ma-208	20	1	6=	CARDINAL
ma-208	20	2	0is	ORDINAL
ma-208	20	3	two	CARDINAL
ma-208	20	4	∈	ORG
ma-208	20	5	5	CARDINAL
ma-208	21	1	12	CARDINAL
ma-208	21	2	4	CARDINAL
ma-208	22	1	m. samman	PERSON
ma-208	22	2	n. al yamani	PERSON
ma-208	23	1	8	CARDINAL
ma-208	25	1	mukhtar ahmad et.al[9	PERSON
ma-208	26	1	19 nov 2023	CARDINAL
ma-208	28	1	derivation;r	ORG
ma-208	29	1	1	CARDINAL
ma-208	30	1	j. math	PERSON
ma-208	32	1	10.28924	CARDINAL
ma-208	32	2	2of	CARDINAL
ma-208	33	1	4	CARDINAL
ma-208	36	1	kashif	PERSON
ma-208	37	1	2	CARDINAL
ma-208	37	2	2.1	CARDINAL
ma-208	38	1	6=	CARDINAL
ma-208	38	2	0	CARDINAL
ma-208	38	3	0	CARDINAL
ma-208	39	1	2.2	CARDINAL
ma-208	42	1	2.3	CARDINAL
ma-208	45	1	2.4	CARDINAL
ma-208	47	1	2.5	CARDINAL
ma-208	54	1	2.6	CARDINAL
ma-208	56	1	r.	NORP
ma-208	56	2	2.7	CARDINAL
ma-208	59	1	r. lemma 2.8	PERSON
ma-208	60	1	6=	CARDINAL
ma-208	60	2	z(center	GPE
ma-208	61	1	2.9	CARDINAL
ma-208	62	1	∈	ORG
ma-208	62	2	∈	ORG
ma-208	62	3	z. lemma	PERSON
ma-208	62	4	2.10	CARDINAL
ma-208	64	1	r.	NORP
ma-208	64	2	z. 2.1	PERSON
ma-208	66	1	2.11	CARDINAL
ma-208	68	1	r.	NORP
ma-208	68	2	6=	CARDINAL
ma-208	68	3	r.	NORP
ma-208	68	4	g(w1	NORP
ma-208	71	1	j. math	PERSON
ma-208	73	1	10.28924	CARDINAL
ma-208	73	2	3this	CARDINAL
ma-208	74	1	al l	PERSON
ma-208	74	2	1	CARDINAL
ma-208	74	3	1	CARDINAL
ma-208	76	1	al l	PERSON
ma-208	76	2	2	CARDINAL
ma-208	77	1	g(u1v1)g(w1	ORG
ma-208	78	1	g(u1v1)g(w1	ORG
ma-208	78	2	2	CARDINAL
ma-208	79	1	al l	PERSON
ma-208	79	2	3	CARDINAL
ma-208	79	3	2	CARDINAL
ma-208	79	4	3	CARDINAL
ma-208	81	1	al l	PERSON
ma-208	81	2	4	CARDINAL
ma-208	82	1	4	CARDINAL
ma-208	84	1	0.by	CARDINAL
ma-208	84	2	β(v1	PRODUCT
ma-208	85	1	d(u1)(g([w1	PERSON
ma-208	91	1	j. math	PERSON
ma-208	93	1	10.28924	CARDINAL
ma-208	93	2	4as g	GPE
ma-208	93	3	g(w1	NORP
ma-208	94	1	2.12	CARDINAL
ma-208	95	1	6=	CARDINAL
ma-208	96	1	gis	PERSON
ma-208	98	1	2.11	CARDINAL
ma-208	99	1	5	CARDINAL
ma-208	99	2	5	CARDINAL
ma-208	103	1	5	CARDINAL
ma-208	105	1	0	CARDINAL
ma-208	106	1	6	CARDINAL
ma-208	107	1	5	CARDINAL
ma-208	108	1	g(v1)]by	GPE
ma-208	108	2	5	CARDINAL
ma-208	108	3	g(u1)− β(u1))β([u1	ORG
ma-208	109	1	0	CARDINAL
ma-208	110	1	7	CARDINAL
ma-208	110	2	6	CARDINAL
ma-208	114	1	r1])rb(g(u1)−	PERSON
ma-208	116	1	0,by	CARDINAL
ma-208	116	2	w	PERSON
ma-208	116	3	∈	ORG
ma-208	117	1	⊆	CARDINAL
ma-208	118	1	∃ v1 ∈	ORG
ma-208	119	1	b(g(v1	PERSON
ma-208	120	1	⊆	CARDINAL
ma-208	122	1	⊆	CARDINAL
ma-208	124	1	⊆	CARDINAL
ma-208	125	1	β(v1 +w1	PRODUCT
ma-208	126	1	⊆	CARDINAL
ma-208	126	2	b(g(v1	GPE
ma-208	126	3	β(v1 +w1	PRODUCT
ma-208	127	1	⊆	CARDINAL
ma-208	129	1	j. math	PERSON
ma-208	131	1	10.28924	CARDINAL
ma-208	131	2	5it	TIME
ma-208	132	1	⊆	CARDINAL
ma-208	133	1	⊆	CARDINAL
ma-208	134	1	⊆	CARDINAL
ma-208	134	2	∈	ORG
ma-208	136	1	2.10	CARDINAL
ma-208	136	2	6	CARDINAL
ma-208	139	1	∈	ORG
ma-208	140	1	∈	ORG
ma-208	140	2	2.13	CARDINAL
ma-208	142	1	0	CARDINAL
ma-208	143	1	r. proof	PERSON
ma-208	144	1	0	CARDINAL
ma-208	144	2	al l	PERSON
ma-208	148	1	0.by	CARDINAL
ma-208	148	2	0	CARDINAL
ma-208	148	3	al l	PERSON
ma-208	148	4	9	CARDINAL
ma-208	149	1	9	CARDINAL
ma-208	149	2	0,we	CARDINAL
ma-208	151	1	2.1	CARDINAL
ma-208	153	1	α(u1	CARDINAL
ma-208	155	1	0	CARDINAL
ma-208	155	2	al l	PERSON
ma-208	156	1	10	CARDINAL
ma-208	156	2	10	CARDINAL
ma-208	156	3	0	CARDINAL
ma-208	157	1	j. math	PERSON
ma-208	159	1	10.28924	CARDINAL
ma-208	159	2	6we	ORDINAL
ma-208	159	3	β(r1)[β(v1)d(u1	GPE
ma-208	160	1	0.by	CARDINAL
ma-208	160	2	10	CARDINAL
ma-208	162	1	0	CARDINAL
ma-208	162	2	∈	ORG
ma-208	162	3	r1 ∈	ORG
ma-208	162	4	∃	ORG
ma-208	162	5	ω	CARDINAL
ma-208	162	6	∈ ω	ORG
ma-208	162	7	∈	ORG
ma-208	162	8	10	CARDINAL
ma-208	164	1	⊆	CARDINAL
ma-208	165	1	0 6=	CARDINAL
ma-208	165	2	7	CARDINAL
ma-208	165	3	∈	ORG
ma-208	166	1	⊆	CARDINAL
ma-208	166	2	z.	PERSON
ma-208	166	3	⊆	CARDINAL
ma-208	166	4	⊆	CARDINAL
ma-208	166	5	d(u1)p	ORG
ma-208	167	1	∈	ORG
ma-208	167	2	r.	NORP
ma-208	167	3	2.14	CARDINAL
ma-208	168	1	6=	DATE
ma-208	168	2	r.	NORP
ma-208	168	3	r.	NORP
ma-208	169	1	6=	DATE
ma-208	169	2	2.12	CARDINAL
ma-208	170	1	∈	ORG
ma-208	170	2	11	CARDINAL
ma-208	170	3	11	CARDINAL
ma-208	171	1	∈	ORG
ma-208	172	1	∈	ORG
ma-208	174	1	∈	ORG
ma-208	174	2	11	CARDINAL
ma-208	175	1	al l	PERSON
ma-208	175	2	12	CARDINAL
ma-208	175	3	12	CARDINAL
ma-208	179	1	∈	ORG
ma-208	180	1	j. math	PERSON
ma-208	182	1	10.28924	CARDINAL
ma-208	182	2	7	CARDINAL
ma-208	183	1	12	CARDINAL
ma-208	184	1	2.8	CARDINAL
ma-208	184	2	[d(v1	PERSON
ma-208	185	1	3	CARDINAL
ma-208	187	1	1	CARDINAL
ma-208	187	2	a. ali	PERSON
ma-208	187	3	t. shah	PERSON
ma-208	187	4	60	CARDINAL
ma-208	187	5	1-2.[2	TIME
ma-208	187	6	m.n.	GPE
ma-208	189	1	bull	PERSON
ma-208	190	1	37	CARDINAL
ma-208	190	2	1994),443-447.[3	CARDINAL
ma-208	190	3	w.s. martindale	PERSON
ma-208	193	1	30	CARDINAL
ma-208	193	2	1987	DATE
ma-208	193	3	92-101.[4	CARDINAL
ma-208	193	4	m. bresar	PERSON
ma-208	193	5	j. vukman	PERSON
ma-208	195	1	38	CARDINAL
ma-208	195	2	1989	DATE
ma-208	195	3	178-185.[5	CARDINAL
ma-208	195	4	m. bresar	PERSON
ma-208	195	5	j. algebra	PERSON
ma-208	195	6	156	CARDINAL
ma-208	195	7	1993	DATE
ma-208	195	8	385	CARDINAL
ma-208	195	9	m.n. daig	GPE
ma-208	196	1	j. math	PERSON
ma-208	198	1	sci	ORG
ma-208	198	2	15 (1992	DATE
ma-208	198	3	205-206.[7	QUANTITY
ma-208	200	1	bull	PERSON
ma-208	201	1	27	CARDINAL
ma-208	201	2	1984	DATE
ma-208	201	3	122	CARDINAL
ma-208	201	4	niazi	GPE
ma-208	201	5	bhatti	PERSON
ma-208	201	6	m. aslam	PERSON
ma-208	201	7	y. qayyum	PERSON
ma-208	201	8	m. ibrahim	PERSON
ma-208	201	9	a. qayyum	PERSON
ma-208	201	10	amer	PERSON
ma-208	202	1	j. math	PERSON
ma-208	204	1	10	CARDINAL
ma-208	204	2	2022	CARDINAL
ma-208	204	3	3-11.[9	CARDINAL
ma-208	204	4	m. ahmad	PERSON
ma-208	204	5	s. hussain	PERSON
ma-208	204	6	i. zahid	PERSON
ma-208	204	7	m. sultan	PERSON
ma-208	204	8	a. qayyum	PERSON
ma-208	204	9	topological	ORG
ma-208	205	1	j. math	PERSON
ma-208	207	1	3 (	CARDINAL
ma-208	207	2	2023	CARDINAL
ma-208	207	3	20[10	CARDINAL
ma-208	207	4	m. ahmad	PERSON
ma-208	207	5	m.j.	PERSON
ma-208	207	6	hussain	PERSON
ma-208	207	7	g. atta	PERSON
ma-208	207	8	s. raza	PERSON
ma-208	207	9	i. waheed	PERSON
ma-208	207	10	a. qayyum	PERSON
ma-208	207	11	four	CARDINAL
ma-208	208	1	j. anal	PERSON
ma-208	210	1	21	CARDINAL
ma-208	210	2	2023	CARDINAL
ma-208	210	3	66.[11	CARDINAL
ma-208	211	1	iqbal	PERSON
ma-208	211	2	m. ahmad	PERSON
ma-208	211	3	a. qayyum	PERSON
ma-208	211	4	s.s. supadi	PERSON
ma-208	211	5	hussain	GPE
ma-208	211	6	s. raza	PERSON
ma-208	211	7	topological	ORG
ma-208	212	1	j. anal	PERSON
ma-208	214	1	21	CARDINAL
ma-208	214	2	2023	CARDINAL
ma-208	214	3	111.[12	CARDINAL
ma-208	214	4	a. asghar	PERSON
ma-208	214	5	a. qayyum	PERSON
ma-208	214	6	n. muhammad	PERSON
ma-208	215	1	j. math	PERSON
ma-208	217	1	3(2022	CARDINAL
ma-208	218	1	3	CARDINAL
ma-208	218	2	1	CARDINAL
ma-208	219	1	2	CARDINAL
ma-208	219	2	2.1	CARDINAL