id	sid	eid	entity	type
ejpam-6106	1	1	european journal	ORG
ejpam-6106	1	2	2025	DATE
ejpam-6106	1	3	18	CARDINAL
ejpam-6106	1	4	4	CARDINAL
ejpam-6106	1	5	6106	DATE
ejpam-6106	1	6	new york	GPE
ejpam-6106	1	7	muhammad nazam1,∗	PERSON
ejpam-6106	1	8	manuel de la	PERSON
ejpam-6106	1	9	1	CARDINAL
ejpam-6106	1	10	allama iqbal	PERSON
ejpam-6106	1	11	islamabad	GPE
ejpam-6106	1	12	pakistan 2	ORG
ejpam-6106	1	13	48940	DATE
ejpam-6106	1	14	spain	GPE
ejpam-6106	4	1	petrov	PERSON
ejpam-6106	8	1	2020	DATE
ejpam-6106	8	2	47h09	CARDINAL
ejpam-6106	8	3	47h10	CARDINAL
ejpam-6106	8	4	30l15	CARDINAL
ejpam-6106	8	5	1	CARDINAL
ejpam-6106	9	1	polygon	ORG
ejpam-6106	14	1	m. nazam	PERSON
ejpam-6106	14	2	m. de la	PERSON
ejpam-6106	14	3	1	CARDINAL
ejpam-6106	15	1	2025	CARDINAL
ejpam-6106	16	1	m. nazam	PERSON
ejpam-6106	16	2	habiba	ORG
ejpam-6106	16	3	m. de la	PERSON
ejpam-6106	17	1	j. pure	PERSON
ejpam-6106	17	2	18	CARDINAL
ejpam-6106	17	3	4	CARDINAL
ejpam-6106	17	4	2025	CARDINAL
ejpam-6106	17	5	6106 2	DATE
ejpam-6106	17	6	10	CARDINAL
ejpam-6106	21	1	1	CARDINAL
ejpam-6106	23	1	1	CARDINAL
ejpam-6106	24	1	2023	CARDINAL
ejpam-6106	25	1	three	CARDINAL
ejpam-6106	25	2	two	CARDINAL
ejpam-6106	26	1	l(l(y	PERSON
ejpam-6106	27	1	one	CARDINAL
ejpam-6106	28	1	1922	DATE
ejpam-6106	28	2	2	CARDINAL
ejpam-6106	30	1	first	ORDINAL
ejpam-6106	32	1	three	CARDINAL
ejpam-6106	33	1	nadler	ORG
ejpam-6106	34	1	petrov	PERSON
ejpam-6106	36	1	polygon	ORG
ejpam-6106	36	2	n0	GPE
ejpam-6106	36	3	n0	GPE
ejpam-6106	37	1	7	CARDINAL
ejpam-6106	37	2	8	CARDINAL
ejpam-6106	37	3	9–13	CARDINAL
ejpam-6106	42	1	2	CARDINAL
ejpam-6106	43	1	shoaib	PERSON
ejpam-6106	44	1	7	CARDINAL
ejpam-6106	44	2	m. nazam	PERSON
ejpam-6106	44	3	habiba	ORG
ejpam-6106	44	4	m. de la	PERSON
ejpam-6106	45	1	j. pure	PERSON
ejpam-6106	45	2	18	CARDINAL
ejpam-6106	45	3	4	CARDINAL
ejpam-6106	45	4	2025	CARDINAL
ejpam-6106	45	5	6106 3	DATE
ejpam-6106	45	6	shoaib	PERSON
ejpam-6106	45	7	8	CARDINAL
ejpam-6106	47	1	two	CARDINAL
ejpam-6106	48	1	3	CARDINAL
ejpam-6106	52	1	3	CARDINAL
ejpam-6106	53	1	1	CARDINAL
ejpam-6106	56	1	0	CARDINAL
ejpam-6106	56	2	2) s(l1	DATE
ejpam-6106	57	1	∈	ORG
ejpam-6106	57	2	l ∈ z	PERSON
ejpam-6106	58	1	2	CARDINAL
ejpam-6106	62	1	0	CARDINAL
ejpam-6106	62	2	1	CARDINAL
ejpam-6106	63	1	+ s	PERSON
ejpam-6106	63	2	lln−1	ORG
ejpam-6106	64	1	+ s	PERSON
ejpam-6106	64	2	ln−1	NORP
ejpam-6106	64	3	1	CARDINAL
ejpam-6106	64	4	l3	ORG
ejpam-6106	64	5	∈	ORG
ejpam-6106	66	1	z.	GPE
ejpam-6106	66	2	m. nazam	PERSON
ejpam-6106	66	3	habiba	ORG
ejpam-6106	66	4	m. de la	PERSON
ejpam-6106	67	1	j. pure	PERSON
ejpam-6106	67	2	18	CARDINAL
ejpam-6106	67	3	4	CARDINAL
ejpam-6106	67	4	2025	CARDINAL
ejpam-6106	67	5	6106 4	DATE
ejpam-6106	67	6	10	CARDINAL
ejpam-6106	69	1	l0	NORP
ejpam-6106	70	1	∃ l ∈ z	ORG
ejpam-6106	75	1	+ s(ln−1	PERCENT
ejpam-6106	75	2	l0	ORG
ejpam-6106	76	1	β(s(l0	PRODUCT
ejpam-6106	76	2	+ s(ln−2	PERSON
ejpam-6106	78	1	4	CARDINAL
ejpam-6106	79	1	l(l(l	PERSON
ejpam-6106	81	1	1	CARDINAL
ejpam-6106	84	1	li ̸= l(li	PERSON
ejpam-6106	84	2	0	CARDINAL
ejpam-6106	84	3	1	DATE
ejpam-6106	84	4	2	CARDINAL
ejpam-6106	85	1	li ̸= li+1	PERSON
ejpam-6106	85	2	lli	ORG
ejpam-6106	86	1	̸= li	PERSON
ejpam-6106	87	1	li	PERSON
ejpam-6106	87	2	li+n	ORG
ejpam-6106	90	1	+ s(l2	GPE
ejpam-6106	91	1	+ s(ln−1	PERCENT
ejpam-6106	91	2	l0	ORG
ejpam-6106	91	3	p1 = s(l1	PERSON
ejpam-6106	92	1	+ s(l2	GPE
ejpam-6106	92	2	l4	ORG
ejpam-6106	92	3	+ s(ln	PERCENT
ejpam-6106	92	4	1	CARDINAL
ejpam-6106	94	1	2	CARDINAL
ejpam-6106	94	2	j ≥ n	PERSON
ejpam-6106	94	3	= li	PERSON
ejpam-6106	94	4	0 ≤	MONEY
ejpam-6106	97	1	2	CARDINAL
ejpam-6106	98	1	m. nazam	PERSON
ejpam-6106	98	2	habiba	ORG
ejpam-6106	98	3	m. de la	PERSON
ejpam-6106	99	1	j. pure	PERSON
ejpam-6106	99	2	18	CARDINAL
ejpam-6106	99	3	4	CARDINAL
ejpam-6106	99	4	2025	CARDINAL
ejpam-6106	99	5	6106 5	DATE
ejpam-6106	99	6	10	CARDINAL
ejpam-6106	99	7	l4	ORG
ejpam-6106	100	1	pk−1 ≤ βk−1p0	ORG
ejpam-6106	102	1	βp−1)p0	NORP
ejpam-6106	102	2	βk−1	ORG
ejpam-6106	102	3	1− βp 1−	TIME
ejpam-6106	103	1	0 ≤	MONEY
ejpam-6106	103	2	1	CARDINAL
ejpam-6106	104	1	βk−1	ORG
ejpam-6106	104	2	1 1−βp0	TIME
ejpam-6106	107	1	1	CARDINAL
ejpam-6106	107	2	+ s(llk−1	DATE
ejpam-6106	107	3	∗	CARDINAL
ejpam-6106	111	1	l ∗	ORG
ejpam-6106	113	1	0	CARDINAL
ejpam-6106	113	2	zero	CARDINAL
ejpam-6106	113	3	k → ∞.	ORG
ejpam-6106	113	4	1	CARDINAL
ejpam-6106	114	1	polygon	ORG
ejpam-6106	114	2	polygon	ORG
ejpam-6106	116	1	petrov	PERSON
ejpam-6106	117	1	5	CARDINAL
ejpam-6106	119	1	only one	CARDINAL
ejpam-6106	119	2	̸=	ORG
ejpam-6106	120	1	1	CARDINAL
ejpam-6106	122	1	̸=	ORG
ejpam-6106	122	2	1	CARDINAL
ejpam-6106	123	1	∀ n ≥ 1	ORG
ejpam-6106	123	2	l ∗	PERSON
ejpam-6106	125	1	ll2∗	PERSON
ejpam-6106	125	2	s(ln	GPE
ejpam-6106	125	3	l∗	ORG
ejpam-6106	126	1	+ s(l∗	GPE
ejpam-6106	126	2	l∗	ORG
ejpam-6106	126	3	+ s(l∗	GPE
ejpam-6106	127	1	1	CARDINAL
ejpam-6106	128	1	m. nazam	PERSON
ejpam-6106	128	2	habiba	ORG
ejpam-6106	128	3	m. de la	PERSON
ejpam-6106	129	1	j. pure	PERSON
ejpam-6106	129	2	18	CARDINAL
ejpam-6106	129	3	4	CARDINAL
ejpam-6106	129	4	2025	CARDINAL
ejpam-6106	129	5	6106 6	DATE
ejpam-6106	129	6	10	CARDINAL
ejpam-6106	130	1	1	CARDINAL
ejpam-6106	131	1	l3	ORG
ejpam-6106	132	1	1	CARDINAL
ejpam-6106	134	1	4	CARDINAL
ejpam-6106	135	1	7	CARDINAL
ejpam-6106	135	2	4	CARDINAL
ejpam-6106	136	1	l3	ORG
ejpam-6106	137	1	ll4 = l3	PERSON
ejpam-6106	138	1	4	CARDINAL
ejpam-6106	141	1	0	CARDINAL
ejpam-6106	141	2	1	CARDINAL
ejpam-6106	142	1	3	CARDINAL
ejpam-6106	145	1	∃ l ∈ z	ORG
ejpam-6106	145	2	l(l(l	PERSON
ejpam-6106	146	1	3	CARDINAL
ejpam-6106	148	1	l3	ORG
ejpam-6106	148	2	∈	ORG
ejpam-6106	153	1	y ∈ z	PERSON
ejpam-6106	154	1	3	CARDINAL
ejpam-6106	156	1	8	CARDINAL
ejpam-6106	158	1	l∗	GPE
ejpam-6106	160	1	li	PERSON
ejpam-6106	161	1	li	PERSON
ejpam-6106	162	1	2(n−	CARDINAL
ejpam-6106	162	2	li	PERSON
ejpam-6106	163	1	li	PERSON
ejpam-6106	164	1	⌊.⌋	ORG
ejpam-6106	165	1	lli	ORG
ejpam-6106	165	2	0	CARDINAL
ejpam-6106	165	3	1	DATE
ejpam-6106	165	4	0	CARDINAL
ejpam-6106	165	5	1	CARDINAL
ejpam-6106	166	1	1	CARDINAL
ejpam-6106	167	1	inequality(1	NORP
ejpam-6106	167	2	ln−1	GPE
ejpam-6106	167	3	l ∗ ∈ z.	ORG
ejpam-6106	169	1	+ s(l∗	GPE
ejpam-6106	169	2	li+(n−1	PERSON
ejpam-6106	170	1	li+n	ORG
ejpam-6106	170	2	m. nazam	PERSON
ejpam-6106	170	3	habiba	ORG
ejpam-6106	170	4	m. de la	PERSON
ejpam-6106	171	1	j. pure	PERSON
ejpam-6106	171	2	18	CARDINAL
ejpam-6106	171	3	4	CARDINAL
ejpam-6106	171	4	2025	CARDINAL
ejpam-6106	171	5	6106 7	DATE
ejpam-6106	171	6	10	CARDINAL
ejpam-6106	171	7	1)s(li	DATE
ejpam-6106	172	1	1)(2(n− 1)a−	DATE
ejpam-6106	172	2	lli+1)+s(lli+1	GPE
ejpam-6106	174	1	1)(2(n− 1)b−	DATE
ejpam-6106	175	1	li	PERSON
ejpam-6106	175	2	2(n− 1)b(1−	ORG
ejpam-6106	176	1	1	CARDINAL
ejpam-6106	176	2	2(n−	CARDINAL
ejpam-6106	176	3	1 2n	CARDINAL
ejpam-6106	177	1	2n−1	CARDINAL
ejpam-6106	177	2	1)− 1	DATE
ejpam-6106	177	3	s(t0	ORG
ejpam-6106	177	4	ti+1	GPE
ejpam-6106	177	5	2⌊i	CARDINAL
ejpam-6106	179	1	lli+n−1	NORP
ejpam-6106	179	2	+ s(lli+n−1	PERSON
ejpam-6106	180	1	+ s(l∗	GPE
ejpam-6106	180	2	li+n−1	GPE
ejpam-6106	181	1	li+n	ORG
ejpam-6106	181	2	1)(2(n− 1)b−	DATE
ejpam-6106	181	3	s(l0, li+1	DATE
ejpam-6106	182	1	1)(2(n− 1)b−	DATE
ejpam-6106	182	2	li	PERSON
ejpam-6106	184	1	2(n− 1)b− s(l0, li+1	DATE
ejpam-6106	184	2	2(n− 1)b−	DATE
ejpam-6106	184	3	li	PERSON
ejpam-6106	185	1	2(n−	CARDINAL
ejpam-6106	185	2	1)b−	CARDINAL
ejpam-6106	185	3	2(n− 1)b−	DATE
ejpam-6106	185	4	li	PERSON
ejpam-6106	185	5		ORG
ejpam-6106	185	6	2(n−1)b−2b(n−1)(1−1/2n	CARDINAL
ejpam-6106	186	1	1	CARDINAL
ejpam-6106	186	2	2(n−1)b−2(n−1)b(1−1/2n)+a/2n−1−b/2⌊i	CARDINAL
ejpam-6106	187	1	2(n−1)b−2(n−1)b(1−1/2n)−b/2n−1	CARDINAL
ejpam-6106	187	2	1)− 1	DATE
ejpam-6106	187	3	2n−3 2n−2	CARDINAL
ejpam-6106	187	4	1	CARDINAL
ejpam-6106	187	5	1)− 1	DATE
ejpam-6106	189	1	li+n ∈	ORG
ejpam-6106	189	2	z.	PERSON
ejpam-6106	189	3	li+n	ORG
ejpam-6106	191	1	+ s(lli+n−1	PERSON
ejpam-6106	192	1	1)(b/2⌊i/(n−1)⌋ −	DATE
ejpam-6106	194	1	ri	GPE
ejpam-6106	194	2	k = s(lli+1	PERSON
ejpam-6106	195	1	+ s(lli+n−1	PERSON
ejpam-6106	196	1	li+n	ORG
ejpam-6106	196	2	li+n)− (n−	GPE
ejpam-6106	196	3	1)(b/2⌊i/(n−1)⌋ −	DATE
ejpam-6106	199	1	li+n	ORG
ejpam-6106	199	2	m. nazam	PERSON
ejpam-6106	199	3	habiba	ORG
ejpam-6106	199	4	m. de la	PERSON
ejpam-6106	200	1	j. pure	PERSON
ejpam-6106	200	2	18	CARDINAL
ejpam-6106	200	3	4	CARDINAL
ejpam-6106	200	4	2025	CARDINAL
ejpam-6106	200	5	6106 8	DATE
ejpam-6106	200	6	10	CARDINAL
ejpam-6106	200	7	1−	CARDINAL
ejpam-6106	200	8	1)(b/2⌊i/(n−1)⌋	CARDINAL
ejpam-6106	201	1	li+n	ORG
ejpam-6106	202	1	2	CARDINAL
ejpam-6106	202	2	4	CARDINAL
ejpam-6106	202	3	s(li+k	PERSON
ejpam-6106	204	1	s(li+k	PERSON
ejpam-6106	207	1	li+n	ORG
ejpam-6106	208	1	1)s(li+m	DATE
ejpam-6106	209	1	2(n− 1)2b	ORG
ejpam-6106	210	1	4	CARDINAL
ejpam-6106	210	2	ri	GPE
ejpam-6106	210	3	k ≤ 1−	PERSON
ejpam-6106	211	1	1	CARDINAL
ejpam-6106	213	1	5	CARDINAL
ejpam-6106	214	1	1	CARDINAL
ejpam-6106	216	1	1	CARDINAL
ejpam-6106	217	1	2	CARDINAL
ejpam-6106	218	1	3	CARDINAL
ejpam-6106	219	1	polygon	ORG
ejpam-6106	219	2	polygon p1 fixed	ORG
ejpam-6106	219	3	m. nazam	PERSON
ejpam-6106	219	4	habiba	ORG
ejpam-6106	219	5	m. de la	PERSON
ejpam-6106	220	1	j. pure	PERSON
ejpam-6106	220	2	18	CARDINAL
ejpam-6106	220	3	4	CARDINAL
ejpam-6106	220	4	2025	CARDINAL
ejpam-6106	220	5	6106 9	DATE
ejpam-6106	220	6	10	CARDINAL
ejpam-6106	220	7	hexagon	ORG
ejpam-6106	220	8	heptagon g0 heptagon	PERSON
ejpam-6106	220	9	4	CARDINAL
ejpam-6106	221	1	petrov	PERSON
ejpam-6106	221	2	3	CARDINAL
ejpam-6106	222	1	petrov	PERSON
ejpam-6106	229	1	the european journal	ORG
ejpam-6106	230	1	m. nazam	PERSON
ejpam-6106	230	2	habiba	ORG
ejpam-6106	230	3	m. de la	PERSON
ejpam-6106	231	1	j. pure	PERSON
ejpam-6106	231	2	18	CARDINAL
ejpam-6106	231	3	4	CARDINAL
ejpam-6106	231	4	2025	CARDINAL
ejpam-6106	231	5	6106 10	DATE
ejpam-6106	232	1	m.n.	GPE
ejpam-6106	232	2	u.h.	GPE
ejpam-6106	232	3	first	ORDINAL
ejpam-6106	233	1	m.n.	GPE
ejpam-6106	233	2	m. d. s.	PERSON
ejpam-6106	233	3	second	ORDINAL
ejpam-6106	233	4	m. d. s.	PERSON
ejpam-6106	235	1	1	CARDINAL
ejpam-6106	235	2	evgeniy petrov	PERSON
ejpam-6106	237	1	2023	CARDINAL
ejpam-6106	238	1	2	CARDINAL
ejpam-6106	239	1	sur les options	ORG
ejpam-6106	239	2	dans les	ORG
ejpam-6106	239	3	aux ations intales	PERSON
ejpam-6106	240	1	fundamenta mathematicae	PERSON
ejpam-6106	240	2	3:133–181	CARDINAL
ejpam-6106	240	3	1922	DATE
ejpam-6106	241	1	3	CARDINAL
ejpam-6106	241	2	w. a. kirk	PERSON
ejpam-6106	241	3	n. shahzad	PERSON
ejpam-6106	243	1	2014	DATE
ejpam-6106	244	1	4	CARDINAL
ejpam-6106	244	2	w. a. kirk	PERSON
ejpam-6106	246	1	american	NORP
ejpam-6106	246	2	monthly	DATE
ejpam-6106	246	3	72:1004–1006	CARDINAL
ejpam-6106	246	4	1965	DATE
ejpam-6106	247	1	5	CARDINAL
ejpam-6106	247	2	james caristi	PERSON
ejpam-6106	249	1	american	NORP
ejpam-6106	249	2	215:241–251	CARDINAL
ejpam-6106	249	3	1976	DATE
ejpam-6106	250	1	6	CARDINAL
ejpam-6106	250	2	s. b. nadler jr.	PERSON
ejpam-6106	251	1	pacific journal of mathematics	ORG
ejpam-6106	251	2	30:475–488	CARDINAL
ejpam-6106	251	3	1969	DATE
ejpam-6106	252	1	7	CARDINAL
ejpam-6106	252	2	a. shoaib	PERSON
ejpam-6106	252	3	m. mehmood	PERSON
ejpam-6106	254	1	2024(157	CARDINAL
ejpam-6106	254	2	2024	DATE
ejpam-6106	255	1	8	CARDINAL
ejpam-6106	255	2	a. shoaib	PERSON
ejpam-6106	256	1	mathematical sciences	ORG
ejpam-6106	256	2	18(1):9–16	CARDINAL
ejpam-6106	256	3	2024	DATE
ejpam-6106	257	1	9	CARDINAL
ejpam-6106	257	2	c. tunç	PERSON
ejpam-6106	260	1	47:4014–4028	CARDINAL
ejpam-6106	260	2	2024	DATE
ejpam-6106	261	1	10	CARDINAL
ejpam-6106	261	2	hammerstein	PERSON
ejpam-6106	262	1	15(9):1736	CARDINAL
ejpam-6106	262	2	2023	CARDINAL
ejpam-6106	263	1	11	CARDINAL
ejpam-6106	264	1	revista de la	PERSON
ejpam-6106	264	2	academia de ciencias exactas	ORG
ejpam-6106	265	1	serie a. matemcas	PERSON
ejpam-6106	265	2	164	CARDINAL
ejpam-6106	265	3	22	CARDINAL
ejpam-6106	265	4	2021	CARDINAL
ejpam-6106	266	1	12	CARDINAL
ejpam-6106	266	2	c. tunç	PERSON
ejpam-6106	267	1	wang	PERSON
ejpam-6106	270	1	9(11):1355	ORG
ejpam-6106	270	2	2021	CARDINAL
ejpam-6106	271	1	13	CARDINAL
ejpam-6106	271	2	c. tunç	PERSON
ejpam-6106	272	1	23(3):435–448	ORG
ejpam-6106	272	2	2022	CARDINAL