id	sid	eid	entity	type
ejpam-6429	1	1	european journal	ORG
ejpam-6429	1	2	2025	DATE
ejpam-6429	1	3	18	CARDINAL
ejpam-6429	1	4	4	CARDINAL
ejpam-6429	1	5	6429	CARDINAL
ejpam-6429	1	6	1307-5543	DATE
ejpam-6429	1	7	new york	GPE
ejpam-6429	1	8	jamil j. hamja1,5	PERSON
ejpam-6429	1	9	seyed mahmoud sheikholeslami2,∗	PERSON
ejpam-6429	1	10	lutz volkmann3	PERSON
ejpam-6429	1	11	imelda s. aniversario4,5	PERSON
ejpam-6429	1	12	lucille m.	PERSON
ejpam-6429	2	1	msu	ORG
ejpam-6429	2	2	7500	CARDINAL
ejpam-6429	2	3	2	CARDINAL
ejpam-6429	2	4	shahid madani university	PERSON
ejpam-6429	2	5	tabriz	GPE
ejpam-6429	2	6	i.r.	GPE
ejpam-6429	2	7	iran	GPE
ejpam-6429	2	8	3 lehrstuhl ii für mathematik	QUANTITY
ejpam-6429	2	9	52056	CARDINAL
ejpam-6429	2	10	germany	GPE
ejpam-6429	2	11	4	CARDINAL
ejpam-6429	2	12	msu-iligan institute of technology	ORG
ejpam-6429	2	13	9200	CARDINAL
ejpam-6429	2	14	iligan city	GPE
ejpam-6429	2	15	5	CARDINAL
ejpam-6429	2	16	institute of science	ORG
ejpam-6429	2	17	msu-iligan institute of technology	ORG
ejpam-6429	2	18	9200	CARDINAL
ejpam-6429	2	19	iligan city	GPE
ejpam-6429	2	20	philippines	GPE
ejpam-6429	3	1	0	CARDINAL
ejpam-6429	3	2	1	DATE
ejpam-6429	3	3	2	DATE
ejpam-6429	3	4	3	CARDINAL
ejpam-6429	6	1	2	CARDINAL
ejpam-6429	7	1	0	CARDINAL
ejpam-6429	7	2	at least one	CARDINAL
ejpam-6429	7	3	2	CARDINAL
ejpam-6429	7	4	0	CARDINAL
ejpam-6429	7	5	1	DATE
ejpam-6429	7	6	2	DATE
ejpam-6429	7	7	3	CARDINAL
ejpam-6429	9	1	1	CARDINAL
ejpam-6429	9	2	2	CARDINAL
ejpam-6429	12	1	γgr(g	ORG
ejpam-6429	13	1	γgr(g	ORG
ejpam-6429	16	1	2020	DATE
ejpam-6429	16	2	05c69	CARDINAL
ejpam-6429	17	1	j. j. hamja	PERSON
ejpam-6429	17	2	s. m. sheikholeslami	PERSON
ejpam-6429	17	3	m. esmaeili	PERSON
ejpam-6429	17	4	l. volkmann	PERSON
ejpam-6429	17	5	imelda.aniversario@g.msuiit.edu.ph	GPE
ejpam-6429	17	6	i. s. aniversario	PERSON
ejpam-6429	17	7	lucille.bugo@g.msuiit.edu.ph	GPE
ejpam-6429	17	8	l. m. bugo	PERSON
ejpam-6429	17	9	1	CARDINAL
ejpam-6429	17	10	2025	CARDINAL
ejpam-6429	18	1	j. j. hamja	PERSON
ejpam-6429	20	1	j. pure	PERSON
ejpam-6429	20	2	18	CARDINAL
ejpam-6429	20	3	4	CARDINAL
ejpam-6429	20	4	2025	CARDINAL
ejpam-6429	20	5	6429 2	DATE
ejpam-6429	20	6	16 1	CARDINAL
ejpam-6429	21	1	revelle	PERSON
ejpam-6429	21	2	1	CARDINAL
ejpam-6429	22	1	2	CARDINAL
ejpam-6429	22	2	2004	DATE
ejpam-6429	22	3	3	CARDINAL
ejpam-6429	23	1	2}-domination	CARDINAL
ejpam-6429	23	2	two hundred	CARDINAL
ejpam-6429	24	1	jafari rad	GPE
ejpam-6429	25	1	4	CARDINAL
ejpam-6429	25	2	5	CARDINAL
ejpam-6429	27	1	6–8	CARDINAL
ejpam-6429	27	2	9	CARDINAL
ejpam-6429	27	3	10	CARDINAL
ejpam-6429	28	1	1	CARDINAL
ejpam-6429	28	2	2	CARDINAL
ejpam-6429	28	3	4–6	CARDINAL
ejpam-6429	28	4	9	DATE
ejpam-6429	28	5	10	CARDINAL
ejpam-6429	29	1	2024	CARDINAL
ejpam-6429	29	2	11	CARDINAL
ejpam-6429	30	1	more than one	CARDINAL
ejpam-6429	33	1	kor	ORG
ejpam-6429	34	1	12	CARDINAL
ejpam-6429	34	2	2025	CARDINAL
ejpam-6429	37	1	at least three	CARDINAL
ejpam-6429	41	1	11	CARDINAL
ejpam-6429	42	1	12	CARDINAL
ejpam-6429	42	2	13	CARDINAL
ejpam-6429	43	1	j. j. hamja et al	PERSON
ejpam-6429	44	1	j. pure	PERSON
ejpam-6429	44	2	18	CARDINAL
ejpam-6429	44	3	4	CARDINAL
ejpam-6429	44	4	2025	CARDINAL
ejpam-6429	44	5	6429 3	DATE
ejpam-6429	44	6	16	CARDINAL
ejpam-6429	44	7	extremal	GPE
ejpam-6429	45	1	the years	DATE
ejpam-6429	47	1	14	CARDINAL
ejpam-6429	48	1	15–22	CARDINAL
ejpam-6429	52	1	2	CARDINAL
ejpam-6429	53	1	n(v	ORG
ejpam-6429	53	2	∈	ORG
ejpam-6429	53	3	n(v	ORG
ejpam-6429	55	1	cn, k1,n−1	PERSON
ejpam-6429	55	2	kn	PERSON
ejpam-6429	56	1	kn	PERSON
ejpam-6429	56	2	bipartite	NORP
ejpam-6429	56	3	dsp	ORG
ejpam-6429	58	1	at least two	CARDINAL
ejpam-6429	59	1	cartesian	NORP
ejpam-6429	59	2	g□h	ORG
ejpam-6429	59	3	two	CARDINAL
ejpam-6429	59	4	p)(u	ORG
ejpam-6429	60	1	⊆	CARDINAL
ejpam-6429	61	1	x∈a f(x	PERSON
ejpam-6429	62	1	f(v	PRODUCT
ejpam-6429	63	1	0	CARDINAL
ejpam-6429	63	2	1	DATE
ejpam-6429	63	3	2	DATE
ejpam-6429	63	4	3	CARDINAL
ejpam-6429	66	1	2	CARDINAL
ejpam-6429	67	1	j. j. hamja et al	PERSON
ejpam-6429	68	1	j. pure	PERSON
ejpam-6429	68	2	18	CARDINAL
ejpam-6429	68	3	4	CARDINAL
ejpam-6429	68	4	2025	CARDINAL
ejpam-6429	68	5	6429 4	DATE
ejpam-6429	68	6	16	CARDINAL
ejpam-6429	69	1	0	CARDINAL
ejpam-6429	69	2	at least one	CARDINAL
ejpam-6429	69	3	f(v	PERSON
ejpam-6429	69	4	2	CARDINAL
ejpam-6429	69	5	0	CARDINAL
ejpam-6429	69	6	1	DATE
ejpam-6429	69	7	2	DATE
ejpam-6429	69	8	3	CARDINAL
ejpam-6429	69	9	g(u	PRODUCT
ejpam-6429	69	10	g(v	PERSON
ejpam-6429	69	11	= f(v	PERSON
ejpam-6429	70	1	1	CARDINAL
ejpam-6429	70	2	2	CARDINAL
ejpam-6429	70	3	g(w	ORG
ejpam-6429	73	1	f(v	PRODUCT
ejpam-6429	73	2	ωg r(f	PERSON
ejpam-6429	73	3	γgr(g	ORG
ejpam-6429	74	1	11	CARDINAL
ejpam-6429	76	1	0	CARDINAL
ejpam-6429	76	2	1	DATE
ejpam-6429	76	3	2	DATE
ejpam-6429	76	4	3	CARDINAL
ejpam-6429	77	1	four	CARDINAL
ejpam-6429	80	1	g1	ORG
ejpam-6429	82	1	gs	ORG
ejpam-6429	84	1	g1	ORG
ejpam-6429	86	1	gs	PERSON
ejpam-6429	86	2	at least 2	CARDINAL
ejpam-6429	87	1	1 ≤	QUANTITY
ejpam-6429	88	1	at least two	CARDINAL
ejpam-6429	89	1	3	CARDINAL
ejpam-6429	91	1	n ≥ 2	ORG
ejpam-6429	91	2	g′	PERSON
ejpam-6429	91	3	γgr(g ′	ORG
ejpam-6429	94	1	first	ORDINAL
ejpam-6429	95	1	1	CARDINAL
ejpam-6429	96	1	g′	PERSON
ejpam-6429	98	1	1	CARDINAL
ejpam-6429	99	1	0	CARDINAL
ejpam-6429	99	2	1	DATE
ejpam-6429	99	3	2	DATE
ejpam-6429	99	4	3	CARDINAL
ejpam-6429	99	5	g(u	PRODUCT
ejpam-6429	99	6	f(u)+f(x	ORG
ejpam-6429	101	1	γgr(g ′	ORG
ejpam-6429	102	1	1 ≤	QUANTITY
ejpam-6429	105	1	k ≥ 2	ORG
ejpam-6429	105	2	g′	PERSON
ejpam-6429	106	1	g′′	PERSON
ejpam-6429	106	2	γgr(g ′′	ORG
ejpam-6429	107	1	2	CARDINAL
ejpam-6429	108	1	n ≥ 2	ORG
ejpam-6429	109	1	1 or 3	CARDINAL
ejpam-6429	109	2	γgr(g ′	ORG
ejpam-6429	111	1	∈	ORG
ejpam-6429	111	2	x.	ORG
ejpam-6429	111	3	f(x	ORG
ejpam-6429	111	4	1	CARDINAL
ejpam-6429	111	5	3	CARDINAL
ejpam-6429	112	1	g′′	PERSON
ejpam-6429	112	2	f(x	ORG
ejpam-6429	113	1	1	CARDINAL
ejpam-6429	113	2	g′′	PERSON
ejpam-6429	113	3	j. j. hamja et al	PERSON
ejpam-6429	114	1	j. pure	PERSON
ejpam-6429	114	2	18	CARDINAL
ejpam-6429	114	3	4	CARDINAL
ejpam-6429	114	4	2025	CARDINAL
ejpam-6429	114	5	6429 5	DATE
ejpam-6429	114	6	γgr(g ′	PRODUCT
ejpam-6429	114	7	γgr(g ′′	ORG
ejpam-6429	115	1	f(x	ORG
ejpam-6429	116	1	3	CARDINAL
ejpam-6429	116	2	g′′	PERSON
ejpam-6429	116	3	f(u	GPE
ejpam-6429	116	4	f(v	PRODUCT
ejpam-6429	116	5	g(z	PERSON
ejpam-6429	117	1	γgr(g ′	ORG
ejpam-6429	117	2	γgr(g ′′	ORG
ejpam-6429	119	1	4	CARDINAL
ejpam-6429	119	2	11	CARDINAL
ejpam-6429	120	1	3	CARDINAL
ejpam-6429	121	1	11	CARDINAL
ejpam-6429	121	2	n ≥ 1	DATE
ejpam-6429	122	1	6n 7	DATE
ejpam-6429	123	1	4	CARDINAL
ejpam-6429	124	1	11	CARDINAL
ejpam-6429	124	2	n ≥ 4	DATE
ejpam-6429	125	1	6n 7	DATE
ejpam-6429	126	1	3	CARDINAL
ejpam-6429	126	2	1	CARDINAL
ejpam-6429	126	3	n ≥ 2	ORG
ejpam-6429	126	4	2	CARDINAL
ejpam-6429	126	5	n ≡ 6 (mod 7	ORG
ejpam-6429	126	6	1	CARDINAL
ejpam-6429	127	1	2	CARDINAL
ejpam-6429	127	2	n ≥ 4	DATE
ejpam-6429	127	3	2	CARDINAL
ejpam-6429	127	4	n ≡ 6 (mod 7	ORG
ejpam-6429	127	5	1	CARDINAL
ejpam-6429	128	1	5	CARDINAL
ejpam-6429	129	1	11	CARDINAL
ejpam-6429	129	2	2	CARDINAL
ejpam-6429	129	3	g = kn	PERSON
ejpam-6429	130	1	6	CARDINAL
ejpam-6429	131	1	13	CARDINAL
ejpam-6429	131	2	3	CARDINAL
ejpam-6429	132	1	3	CARDINAL
ejpam-6429	132	2	1	CARDINAL
ejpam-6429	133	1	5	CARDINAL
ejpam-6429	133	2	6	CARDINAL
ejpam-6429	133	3	3	CARDINAL
ejpam-6429	134	1	n ≥ 2 with	ORG
ejpam-6429	134	2	γgr(g	ORG
ejpam-6429	134	3	2	CARDINAL
ejpam-6429	134	4	3	CARDINAL
ejpam-6429	134	5	1	CARDINAL
ejpam-6429	135	1	2	CARDINAL
ejpam-6429	135	2	5	CARDINAL
ejpam-6429	135	3	g = kn	PERSON
ejpam-6429	136	1	5	CARDINAL
ejpam-6429	137	1	1	CARDINAL
ejpam-6429	137	2	γgr(g	ORG
ejpam-6429	137	3	3	CARDINAL
ejpam-6429	137	4	n + 1	PRODUCT
ejpam-6429	137	5	1	CARDINAL
ejpam-6429	137	6	γgr(g	ORG
ejpam-6429	137	7	3	CARDINAL
ejpam-6429	138	1	1	CARDINAL
ejpam-6429	138	2	3	CARDINAL
ejpam-6429	139	1	4	CARDINAL
ejpam-6429	140	1	2	CARDINAL
ejpam-6429	140	2	γgr(g	ORG
ejpam-6429	140	3	4	CARDINAL
ejpam-6429	141	1	1	CARDINAL
ejpam-6429	141	2	4	CARDINAL
ejpam-6429	142	1	ui	PERSON
ejpam-6429	142	2	vi	PERSON
ejpam-6429	142	3	1	CARDINAL
ejpam-6429	142	4	2	DATE
ejpam-6429	145	1	12	CARDINAL
ejpam-6429	146	1	1	CARDINAL
ejpam-6429	146	2	n ≥ 1	DATE
ejpam-6429	147	1	2 ⌉. j. j. hamja et al	QUANTITY
ejpam-6429	148	1	j. pure	PERSON
ejpam-6429	148	2	18	CARDINAL
ejpam-6429	148	3	4	CARDINAL
ejpam-6429	148	4	2025	CARDINAL
ejpam-6429	148	5	6429 6	DATE
ejpam-6429	148	6	16	CARDINAL
ejpam-6429	149	1	1	CARDINAL
ejpam-6429	150	1	g′	PERSON
ejpam-6429	153	1	f(x	ORG
ejpam-6429	153	2	1	CARDINAL
ejpam-6429	153	3	3	CARDINAL
ejpam-6429	153	4	2	CARDINAL
ejpam-6429	153	5	γgr(g ′	PRODUCT
ejpam-6429	154	1	two	CARDINAL
ejpam-6429	155	1	1	CARDINAL
ejpam-6429	158	1	2	CARDINAL
ejpam-6429	158	2	f(u2	GPE
ejpam-6429	158	3	1	CARDINAL
ejpam-6429	158	4	1	CARDINAL
ejpam-6429	160	1	0	CARDINAL
ejpam-6429	161	1	2	CARDINAL
ejpam-6429	162	1	4	CARDINAL
ejpam-6429	162	2	8	CARDINAL
ejpam-6429	162	3	7	CARDINAL
ejpam-6429	162	4	1	CARDINAL
ejpam-6429	163	1	2	CARDINAL
ejpam-6429	165	1	0	CARDINAL
ejpam-6429	167	1	2	CARDINAL
ejpam-6429	169	1	3	CARDINAL
ejpam-6429	169	2	5	CARDINAL
ejpam-6429	169	3	8	CARDINAL
ejpam-6429	171	1	2	CARDINAL
ejpam-6429	171	2	f(u2)+	PERSON
ejpam-6429	172	1	1	CARDINAL
ejpam-6429	172	2	2	CARDINAL
ejpam-6429	173	1	first	ORDINAL
ejpam-6429	174	1	2	CARDINAL
ejpam-6429	174	2	3	CARDINAL
ejpam-6429	175	1	2	CARDINAL
ejpam-6429	175	2	t ≥ 5	DATE
ejpam-6429	176	1	t ≥ 6	DATE
ejpam-6429	178	1	2	CARDINAL
ejpam-6429	178	2	8	CARDINAL
ejpam-6429	179	1	5	CARDINAL
ejpam-6429	180	1	1	CARDINAL
ejpam-6429	180	2	0	CARDINAL
ejpam-6429	183	1	3	CARDINAL
ejpam-6429	183	2	8	CARDINAL
ejpam-6429	185	1	x.	GPE
ejpam-6429	185	2	1	CARDINAL
ejpam-6429	186	1	2	CARDINAL
ejpam-6429	186	2	0	CARDINAL
ejpam-6429	186	3	2	CARDINAL
ejpam-6429	188	1	f(v1	DATE
ejpam-6429	189	1	2	CARDINAL
ejpam-6429	190	1	f(v1	DATE
ejpam-6429	190	2	3	CARDINAL
ejpam-6429	190	3	8	CARDINAL
ejpam-6429	192	1	2	CARDINAL
ejpam-6429	192	2	2	CARDINAL
ejpam-6429	193	1	0	CARDINAL
ejpam-6429	195	1	2	CARDINAL
ejpam-6429	197	1	3	CARDINAL
ejpam-6429	199	1	2	CARDINAL
ejpam-6429	199	2	2	CARDINAL
ejpam-6429	199	3	8	CARDINAL
ejpam-6429	201	1	2	CARDINAL
ejpam-6429	202	1	n ≥ 1	DATE
ejpam-6429	202	2	1	CARDINAL
ejpam-6429	205	1	1	CARDINAL
ejpam-6429	205	2	n ≥ 3	DATE
ejpam-6429	206	1	f(x	ORG
ejpam-6429	206	2	1	CARDINAL
ejpam-6429	206	3	3	CARDINAL
ejpam-6429	206	4	2	CARDINAL
ejpam-6429	206	5	γgr(g ′	ORG
ejpam-6429	207	1	1	CARDINAL
ejpam-6429	208	1	two	CARDINAL
ejpam-6429	209	1	j. j. hamja et al	PERSON
ejpam-6429	210	1	j. pure	PERSON
ejpam-6429	210	2	18	CARDINAL
ejpam-6429	210	3	4	CARDINAL
ejpam-6429	210	4	2025	CARDINAL
ejpam-6429	210	5	6429 7	DATE
ejpam-6429	210	6	16	CARDINAL
ejpam-6429	210	7	1	CARDINAL
ejpam-6429	213	1	2	CARDINAL
ejpam-6429	213	2	1	CARDINAL
ejpam-6429	213	3	f(v1	DATE
ejpam-6429	213	4	1	CARDINAL
ejpam-6429	213	5	1	CARDINAL
ejpam-6429	214	1	1	CARDINAL
ejpam-6429	215	1	0	CARDINAL
ejpam-6429	216	1	min{f(u2	GPE
ejpam-6429	216	2	2	CARDINAL
ejpam-6429	216	3	1	CARDINAL
ejpam-6429	216	4	2	CARDINAL
ejpam-6429	216	5	0	CARDINAL
ejpam-6429	217	1	1	CARDINAL
ejpam-6429	220	1	2	CARDINAL
ejpam-6429	221	1	ωg r(f)− 2	DATE
ejpam-6429	221	2	1	CARDINAL
ejpam-6429	222	1	3n+1 2	DATE
ejpam-6429	222	2	1	CARDINAL
ejpam-6429	222	3	2	CARDINAL
ejpam-6429	224	1	2	CARDINAL
ejpam-6429	226	1	3	CARDINAL
ejpam-6429	226	2	2	CARDINAL
ejpam-6429	227	1	1	CARDINAL
ejpam-6429	227	2	1	CARDINAL
ejpam-6429	228	1	2	CARDINAL
ejpam-6429	228	2	f(v1	DATE
ejpam-6429	228	3	2	CARDINAL
ejpam-6429	228	4	g(z	PERSON
ejpam-6429	229	1	1	CARDINAL
ejpam-6429	229	2	3(n−2)+1 2	DATE
ejpam-6429	229	3	3n+1 2	DATE
ejpam-6429	230	1	1	CARDINAL
ejpam-6429	230	2	0	CARDINAL
ejpam-6429	231	1	1	CARDINAL
ejpam-6429	232	1	1	CARDINAL
ejpam-6429	234	1	0	CARDINAL
ejpam-6429	236	1	2	CARDINAL
ejpam-6429	236	2	3	CARDINAL
ejpam-6429	236	3	2	CARDINAL
ejpam-6429	236	4	1	CARDINAL
ejpam-6429	236	5	1	CARDINAL
ejpam-6429	236	6	1	CARDINAL
ejpam-6429	236	7	2	CARDINAL
ejpam-6429	238	1	0	CARDINAL
ejpam-6429	238	2	f(x	ORG
ejpam-6429	240	1	2	CARDINAL
ejpam-6429	241	1	3	CARDINAL
ejpam-6429	241	2	6	CARDINAL
ejpam-6429	241	3	3n+1 2	DATE
ejpam-6429	242	1	n ≥ 5	DATE
ejpam-6429	243	1	3 or f(v3	CARDINAL
ejpam-6429	243	2	1	CARDINAL
ejpam-6429	244	1	3n+1 2	DATE
ejpam-6429	245	1	1	CARDINAL
ejpam-6429	245	2	2	CARDINAL
ejpam-6429	246	1	0	CARDINAL
ejpam-6429	247	1	f(u4	PRODUCT
ejpam-6429	247	2	1	CARDINAL
ejpam-6429	247	3	2	CARDINAL
ejpam-6429	248	1	4	CARDINAL
ejpam-6429	249	1	3n+1 2	DATE
ejpam-6429	249	2	1	CARDINAL
ejpam-6429	250	1	f(u4	ORG
ejpam-6429	252	1	1	CARDINAL
ejpam-6429	252	2	1 ≤	QUANTITY
ejpam-6429	252	3	7	CARDINAL
ejpam-6429	252	4	1	CARDINAL
ejpam-6429	252	5	7 + ⌈ 3(n−4)+1 2	DATE
ejpam-6429	252	6	3n+1 2	DATE
ejpam-6429	253	1	1	CARDINAL
ejpam-6429	255	1	2	CARDINAL
ejpam-6429	255	2	f(u5	PERSON
ejpam-6429	256	1	2	CARDINAL
ejpam-6429	257	1	5	CARDINAL
ejpam-6429	257	2	10	CARDINAL
ejpam-6429	257	3	3n+1 2	DATE
ejpam-6429	260	1	1 ≤	QUANTITY
ejpam-6429	260	2	ωg r(f)− 10	DATE
ejpam-6429	261	1	1	CARDINAL
ejpam-6429	262	1	+ 10	DATE
ejpam-6429	262	2	3(n−6	CARDINAL
ejpam-6429	262	3	2	CARDINAL
ejpam-6429	262	4	3n+1 2	DATE
ejpam-6429	264	1	1	CARDINAL
ejpam-6429	264	2	j. j. hamja et al	PERSON
ejpam-6429	265	1	j. pure	PERSON
ejpam-6429	265	2	18	CARDINAL
ejpam-6429	265	3	4	CARDINAL
ejpam-6429	265	4	2025	CARDINAL
ejpam-6429	265	5	6429 8	DATE
ejpam-6429	266	1	8	CARDINAL
ejpam-6429	267	1	at least three	CARDINAL
ejpam-6429	268	1	1	CARDINAL
ejpam-6429	270	1	3	CARDINAL
ejpam-6429	270	2	3	CARDINAL
ejpam-6429	271	1	1	CARDINAL
ejpam-6429	272	1	three	CARDINAL
ejpam-6429	272	2	w. let g′	ORG
ejpam-6429	273	1	+ f(z	DATE
ejpam-6429	274	1	3	CARDINAL
ejpam-6429	274	2	0	CARDINAL
ejpam-6429	275	1	1	CARDINAL
ejpam-6429	275	2	0	CARDINAL
ejpam-6429	276	1	1	CARDINAL
ejpam-6429	278	1	2	CARDINAL
ejpam-6429	278	2	f(v	PERSON
ejpam-6429	278	3	1 or f(y	DATE
ejpam-6429	278	4	1	CARDINAL
ejpam-6429	278	5	3	CARDINAL
ejpam-6429	278	6	0	CARDINAL
ejpam-6429	278	7	g(w	ORG
ejpam-6429	281	1	+ f(z	DATE
ejpam-6429	283	1	0	CARDINAL
ejpam-6429	285	1	1	CARDINAL
ejpam-6429	285	2	1	CARDINAL
ejpam-6429	285	3	2	CARDINAL
ejpam-6429	285	4	0	CARDINAL
ejpam-6429	285	5	g(w	ORG
ejpam-6429	288	1	+ f(z	DATE
ejpam-6429	290	1	0	CARDINAL
ejpam-6429	291	1	1	CARDINAL
ejpam-6429	292	1	2	CARDINAL
ejpam-6429	292	2	w	GPE
ejpam-6429	292	3	3	CARDINAL
ejpam-6429	292	4	1	DATE
ejpam-6429	292	5	0	DATE
ejpam-6429	292	6	0	CARDINAL
ejpam-6429	296	1	1	CARDINAL
ejpam-6429	297	1	at least two	CARDINAL
ejpam-6429	299	1	3	CARDINAL
ejpam-6429	299	2	w	ORG
ejpam-6429	299	3	at least three	CARDINAL
ejpam-6429	300	1	w	ORG
ejpam-6429	300	2	two	CARDINAL
ejpam-6429	300	3	w	GPE
ejpam-6429	300	4	vw	GPE
ejpam-6429	304	1	3	CARDINAL
ejpam-6429	304	2	1	CARDINAL
ejpam-6429	304	3	0	CARDINAL
ejpam-6429	304	4	2	CARDINAL
ejpam-6429	304	5	+ f(v	PERSON
ejpam-6429	306	1	3	CARDINAL
ejpam-6429	307	1	3	CARDINAL
ejpam-6429	307	2	0	CARDINAL
ejpam-6429	307	3	0	CARDINAL
ejpam-6429	308	1	4	CARDINAL
ejpam-6429	308	2	10	CARDINAL
ejpam-6429	310	1	j. j. hamja et al	PERSON
ejpam-6429	311	1	j. pure	PERSON
ejpam-6429	311	2	18	CARDINAL
ejpam-6429	311	3	4	CARDINAL
ejpam-6429	311	4	2025	CARDINAL
ejpam-6429	311	5	6429 9	DATE
ejpam-6429	311	6	16	CARDINAL
ejpam-6429	312	1	3	CARDINAL
ejpam-6429	315	1	vertex xk	ORG
ejpam-6429	317	1	2	CARDINAL
ejpam-6429	319	1	f(x3	DATE
ejpam-6429	321	1	4	CARDINAL
ejpam-6429	322	1	0	CARDINAL
ejpam-6429	322	2	2	CARDINAL
ejpam-6429	322	3	less than ωg	MONEY
ejpam-6429	323	1	f(x3	DATE
ejpam-6429	323	2	2	CARDINAL
ejpam-6429	323	3	3	CARDINAL
ejpam-6429	323	4	0	CARDINAL
ejpam-6429	323	5	2	CARDINAL
ejpam-6429	323	6	less than ωg	MONEY
ejpam-6429	324	1	11	CARDINAL
ejpam-6429	329	1	vw	GPE
ejpam-6429	329	2	x3	PERSON
ejpam-6429	331	1	g1	ORG
ejpam-6429	332	1	2	CARDINAL
ejpam-6429	332	2	1	CARDINAL
ejpam-6429	332	3	2	DATE
ejpam-6429	332	4	3	CARDINAL
ejpam-6429	333	1	1	CARDINAL
ejpam-6429	333	2	3	CARDINAL
ejpam-6429	334	1	two	CARDINAL
ejpam-6429	334	2	+ g(x2	GPE
ejpam-6429	334	3	4	CARDINAL
ejpam-6429	334	4	3	CARDINAL
ejpam-6429	334	5	less than ωg	QUANTITY
ejpam-6429	335	1	g(x2	GPE
ejpam-6429	336	1	+ g(w	PERSON
ejpam-6429	336	2	2	CARDINAL
ejpam-6429	336	3	3	CARDINAL
ejpam-6429	336	4	less than ωg	QUANTITY
ejpam-6429	337	1	0	CARDINAL
ejpam-6429	339	1	4	CARDINAL
ejpam-6429	340	1	less than ωg	QUANTITY
ejpam-6429	342	1	6	CARDINAL
ejpam-6429	343	1	3	CARDINAL
ejpam-6429	345	1	∈	ORG
ejpam-6429	345	2	at least two	CARDINAL
ejpam-6429	347	1	n(x	GPE
ejpam-6429	349	1	xx1	ORG
ejpam-6429	356	1	2	CARDINAL
ejpam-6429	357	1	1	CARDINAL
ejpam-6429	357	2	3	CARDINAL
ejpam-6429	358	1	i=1 f(yi	PERSON
ejpam-6429	359	1	4	CARDINAL
ejpam-6429	359	2	3	CARDINAL
ejpam-6429	360	1	i=1 f(yi	PERSON
ejpam-6429	362	1	f(x	ORG
ejpam-6429	362	2	2	CARDINAL
ejpam-6429	362	3	3	CARDINAL
ejpam-6429	362	4	i=1 f(yi	PERSON
ejpam-6429	364	1	j. j. hamja et al	PERSON
ejpam-6429	365	1	j. pure	PERSON
ejpam-6429	365	2	18	CARDINAL
ejpam-6429	365	3	4	CARDINAL
ejpam-6429	365	4	2025	CARDINAL
ejpam-6429	365	5	6429 10	DATE
ejpam-6429	365	6	16	CARDINAL
ejpam-6429	365	7	i.	PERSON
ejpam-6429	365	8	1	CARDINAL
ejpam-6429	366	1	f(x	ORG
ejpam-6429	367	1	1	CARDINAL
ejpam-6429	367	2	2	CARDINAL
ejpam-6429	369	1	2	CARDINAL
ejpam-6429	370	1	f(x	ORG
ejpam-6429	371	1	0	CARDINAL
ejpam-6429	372	1	one	CARDINAL
ejpam-6429	372	2	2	CARDINAL
ejpam-6429	372	3	i=1 f(yi	PERSON
ejpam-6429	373	1	0	CARDINAL
ejpam-6429	373	2	2	CARDINAL
ejpam-6429	375	1	2	CARDINAL
ejpam-6429	375	2	2	CARDINAL
ejpam-6429	379	1	1	CARDINAL
ejpam-6429	379	2	3	CARDINAL
ejpam-6429	379	3	n ≥ 2	ORG
ejpam-6429	381	1	5	CARDINAL
ejpam-6429	382	1	2	CARDINAL
ejpam-6429	383	1	6	CARDINAL
ejpam-6429	384	1	1	CARDINAL
ejpam-6429	386	1	3	CARDINAL
ejpam-6429	387	1	∈	ORG
ejpam-6429	387	2	2	CARDINAL
ejpam-6429	387	3	10	CARDINAL
ejpam-6429	388	1	3	CARDINAL
ejpam-6429	388	2	two	CARDINAL
ejpam-6429	389	1	g1	ORG
ejpam-6429	389	2	x3	GPE
ejpam-6429	390	1	2	CARDINAL
ejpam-6429	391	1	1	CARDINAL
ejpam-6429	391	2	3	CARDINAL
ejpam-6429	391	3	1	CARDINAL
ejpam-6429	391	4	2	DATE
ejpam-6429	391	5	3	CARDINAL
ejpam-6429	392	1	f(v	PERSON
ejpam-6429	392	2	i=1 f(xi	GPE
ejpam-6429	392	3	4	CARDINAL
ejpam-6429	392	4	3	CARDINAL
ejpam-6429	393	1	f(v	PERSON
ejpam-6429	395	1	f(v	PERSON
ejpam-6429	395	2	0	CARDINAL
ejpam-6429	395	3	1	DATE
ejpam-6429	395	4	2	CARDINAL
ejpam-6429	396	1	f(v	PERSON
ejpam-6429	396	2	2	CARDINAL
ejpam-6429	398	1	0	CARDINAL
ejpam-6429	399	1	1	CARDINAL
ejpam-6429	399	2	2	CARDINAL
ejpam-6429	399	3	3	DATE
ejpam-6429	400	1	2	CARDINAL
ejpam-6429	400	2	1 and f(xi	PERCENT
ejpam-6429	401	1	1	CARDINAL
ejpam-6429	401	2	2	DATE
ejpam-6429	401	3	3	CARDINAL
ejpam-6429	402	1	0	CARDINAL
ejpam-6429	404	1	at least one	CARDINAL
ejpam-6429	404	2	five	CARDINAL
ejpam-6429	404	3	5	CARDINAL
ejpam-6429	404	4	6	CARDINAL
ejpam-6429	406	1	2	CARDINAL
ejpam-6429	407	1	∈	ORG
ejpam-6429	407	2	two	CARDINAL
ejpam-6429	410	1	2	CARDINAL
ejpam-6429	411	1	j. j. hamja et al	PERSON
ejpam-6429	412	1	j. pure	PERSON
ejpam-6429	412	2	18	CARDINAL
ejpam-6429	412	3	4	CARDINAL
ejpam-6429	412	4	2025	CARDINAL
ejpam-6429	412	5	6429 11	DATE
ejpam-6429	412	6	16	CARDINAL
ejpam-6429	413	1	17	CARDINAL
ejpam-6429	414	1	1	CARDINAL
ejpam-6429	416	1	n(v3)−n	ORG
ejpam-6429	417	1	v1]|	PRODUCT
ejpam-6429	423	1	2	CARDINAL
ejpam-6429	423	2	1	CARDINAL
ejpam-6429	423	3	3	CARDINAL
ejpam-6429	426	1	11	CARDINAL
ejpam-6429	428	1	+ f(z	DATE
ejpam-6429	429	1	4	CARDINAL
ejpam-6429	429	2	0	CARDINAL
ejpam-6429	429	3	1	DATE
ejpam-6429	429	4	2	DATE
ejpam-6429	429	5	3	CARDINAL
ejpam-6429	429	6	3	CARDINAL
ejpam-6429	429	7	0	CARDINAL
ejpam-6429	429	8	1 ≤	QUANTITY
ejpam-6429	430	1	g(t	NORP
ejpam-6429	430	2	∈	ORG
ejpam-6429	430	3	wi	GPE
ejpam-6429	430	4	1 ≤	QUANTITY
ejpam-6429	433	1	2	CARDINAL
ejpam-6429	434	1	at least 2	CARDINAL
ejpam-6429	434	2	\n	ORG
ejpam-6429	435	1	\n	ORG
ejpam-6429	438	1	n(x	GPE
ejpam-6429	442	1	first	ORDINAL
ejpam-6429	442	2	n(x	GPE
ejpam-6429	446	1	n(x	GPE
ejpam-6429	447	1	1	CARDINAL
ejpam-6429	447	2	2	DATE
ejpam-6429	448	1	xi1	ORG
ejpam-6429	448	2	xi2	GPE
ejpam-6429	450	1	g1	ORG
ejpam-6429	450	2	xx1	ORG
ejpam-6429	451	1	1	CARDINAL
ejpam-6429	451	2	2	DATE
ejpam-6429	452	1	1 ≤ j ≤ li	QUANTITY
ejpam-6429	453	1	wi	ORG
ejpam-6429	453	2	1 ≤ j ≤ li	QUANTITY
ejpam-6429	453	3	⋃ 1≤i≤swi	DATE
ejpam-6429	456	1	2	CARDINAL
ejpam-6429	456	2	1 or	CARDINAL
ejpam-6429	457	1	first	ORDINAL
ejpam-6429	458	1	11	CARDINAL
ejpam-6429	458	2	4	CARDINAL
ejpam-6429	459	1	3	CARDINAL
ejpam-6429	459	2	0	CARDINAL
ejpam-6429	459	3	f(xij	CARDINAL
ejpam-6429	464	1	j. j. hamja et al	PERSON
ejpam-6429	465	1	j. pure	PERSON
ejpam-6429	465	2	18	CARDINAL
ejpam-6429	465	3	4	CARDINAL
ejpam-6429	465	4	2025	CARDINAL
ejpam-6429	465	5	6429 12	DATE
ejpam-6429	465	6	16 3	CARDINAL
ejpam-6429	469	1	i=1 f(xi	GPE
ejpam-6429	469	2	4	CARDINAL
ejpam-6429	469	3	3	CARDINAL
ejpam-6429	469	4	0	CARDINAL
ejpam-6429	469	5	1	CARDINAL
ejpam-6429	469	6	2	DATE
ejpam-6429	470	1	f(xij	CARDINAL
ejpam-6429	477	1	f(x	ORG
ejpam-6429	477	2	0	CARDINAL
ejpam-6429	477	3	1	DATE
ejpam-6429	477	4	2	CARDINAL
ejpam-6429	477	5	f(x1)+f(x2)+f(u1)+f(u2	ORG
ejpam-6429	477	6	4	CARDINAL
ejpam-6429	478	1	f(x	ORG
ejpam-6429	479	1	3	CARDINAL
ejpam-6429	483	1	4	CARDINAL
ejpam-6429	483	2	1	CARDINAL
ejpam-6429	483	3	3	CARDINAL
ejpam-6429	483	4	f(xij	CARDINAL
ejpam-6429	484	1	2	CARDINAL
ejpam-6429	486	1	1	CARDINAL
ejpam-6429	486	2	2	DATE
ejpam-6429	487	1	li	PERSON
ejpam-6429	489	1	1	CARDINAL
ejpam-6429	489	2	2	DATE
ejpam-6429	491	1	first	ORDINAL
ejpam-6429	491	2	1	CARDINAL
ejpam-6429	491	3	2	DATE
ejpam-6429	493	1	1	CARDINAL
ejpam-6429	493	2	2	DATE
ejpam-6429	494	1	li	PERSON
ejpam-6429	495	1	2	CARDINAL
ejpam-6429	496	1	1	CARDINAL
ejpam-6429	499	1	2	CARDINAL
ejpam-6429	499	2	j. clearly	PERSON
ejpam-6429	499	3	2	CARDINAL
ejpam-6429	501	1	g1	ORG
ejpam-6429	501	2	3 +	QUANTITY
ejpam-6429	503	1	3	CARDINAL
ejpam-6429	504	1	at least 2	CARDINAL
ejpam-6429	504	2	\n	CARDINAL
ejpam-6429	505	1	y ∈ n(v	ORG
ejpam-6429	505	2	n(v	ORG
ejpam-6429	505	3	\n	CARDINAL
ejpam-6429	506	1	3 + |n2(v)|	DATE
ejpam-6429	507	1	3+ |n2(v)|	DATE
ejpam-6429	507	2	3	CARDINAL
ejpam-6429	508	1	4 + |n2(v)|	DATE
ejpam-6429	509	1	n(v	ORG
ejpam-6429	515	1	y ∈ n(v	ORG
ejpam-6429	515	2	n(v	ORG
ejpam-6429	515	3	⊆	CARDINAL
ejpam-6429	518	1	at least one	CARDINAL
ejpam-6429	518	2	⊆ k∪n(s	QUANTITY
ejpam-6429	519	1	n(v	ORG
ejpam-6429	520	1	4+|k|+|s|	CARDINAL
ejpam-6429	524	1	g1	ORG
ejpam-6429	524	2	new vertices yj	ORG
ejpam-6429	524	3	1	CARDINAL
ejpam-6429	526	1	1 ≤	QUANTITY
ejpam-6429	526	2	1 ≤ i ≤ 3	QUANTITY
ejpam-6429	526	3	+ 3	DATE
ejpam-6429	529	1	3	CARDINAL
ejpam-6429	530	1	1	CARDINAL
ejpam-6429	530	2	3	CARDINAL
ejpam-6429	531	1	z. j. j. hamja et al	PERSON
ejpam-6429	532	1	j. pure	PERSON
ejpam-6429	532	2	18	CARDINAL
ejpam-6429	532	3	4	CARDINAL
ejpam-6429	532	4	2025	CARDINAL
ejpam-6429	532	5	6429 13	DATE
ejpam-6429	532	6	16	CARDINAL
ejpam-6429	532	7	4	CARDINAL
ejpam-6429	532	8	3	CARDINAL
ejpam-6429	532	9	0	CARDINAL
ejpam-6429	532	10	f(wj	ORG
ejpam-6429	532	11	1	CARDINAL
ejpam-6429	535	1	f(v	PERSON
ejpam-6429	536	1	1	CARDINAL
ejpam-6429	536	2	four	CARDINAL
ejpam-6429	537	1	1	CARDINAL
ejpam-6429	538	1	3	CARDINAL
ejpam-6429	538	2	1	CARDINAL
ejpam-6429	540	1	0	CARDINAL
ejpam-6429	541	1	4	CARDINAL
ejpam-6429	541	2	3	CARDINAL
ejpam-6429	542	1	i=1 f(yi	PERSON
ejpam-6429	543	1	j ∈	PERSON
ejpam-6429	543	2	1	CARDINAL
ejpam-6429	543	3	2	DATE
ejpam-6429	545	1	j = 1	PERSON
ejpam-6429	545	2	2	CARDINAL
ejpam-6429	545	3	2	CARDINAL
ejpam-6429	550	1	2	CARDINAL
ejpam-6429	550	2	1	CARDINAL
ejpam-6429	550	3	2	DATE
ejpam-6429	553	1	2	CARDINAL
ejpam-6429	554	1	2	CARDINAL
ejpam-6429	555	1	2	CARDINAL
ejpam-6429	555	2	1	CARDINAL
ejpam-6429	557	1	0	CARDINAL
ejpam-6429	558	1	1	CARDINAL
ejpam-6429	558	2	0	CARDINAL
ejpam-6429	559	1	wi	ORG
ejpam-6429	559	2	1	CARDINAL
ejpam-6429	559	3	2	DATE
ejpam-6429	563	1	0	CARDINAL
ejpam-6429	564	1	vi	PERSON
ejpam-6429	565	1	2	CARDINAL
ejpam-6429	565	2	2	CARDINAL
ejpam-6429	565	3	3	DATE
ejpam-6429	566	1	s + 2	PRODUCT
ejpam-6429	567	1	4	CARDINAL
ejpam-6429	567	2	3	CARDINAL
ejpam-6429	568	1	1	CARDINAL
ejpam-6429	568	2	2	DATE
ejpam-6429	569	1	2	CARDINAL
ejpam-6429	569	2	one	CARDINAL
ejpam-6429	569	3	first	ORDINAL
ejpam-6429	569	4	f(wj	ORG
ejpam-6429	569	5	2	CARDINAL
ejpam-6429	569	6	wj	PERSON
ejpam-6429	569	7	2	CARDINAL
ejpam-6429	569	8	1	CARDINAL
ejpam-6429	570	1	second	ORDINAL
ejpam-6429	570	2	1	CARDINAL
ejpam-6429	570	3	wj	PERSON
ejpam-6429	570	4	wi	ORG
ejpam-6429	571	1	3	CARDINAL
ejpam-6429	572	1	1	CARDINAL
ejpam-6429	572	2	2	CARDINAL
ejpam-6429	572	3	1	CARDINAL
ejpam-6429	573	1	0	CARDINAL
ejpam-6429	574	1	2	CARDINAL
ejpam-6429	575	1	0	CARDINAL
ejpam-6429	576	1	wi	ORG
ejpam-6429	576	2	1	CARDINAL
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