id	sid	eid	entity	type
ejpam-5135	1	1	european journal	ORG
ejpam-5135	2	1	17	CARDINAL
ejpam-5135	2	2	2	CARDINAL
ejpam-5135	2	3	2024	DATE
ejpam-5135	2	4	663	CARDINAL
ejpam-5135	2	5	1307-5543	DATE
ejpam-5135	2	6	new york	GPE
ejpam-5135	2	7	justine bryle c. macaso1,∗	PERSON
ejpam-5135	2	8	cherry mae r. balingit1 1	ORG
ejpam-5135	2	9	central mindanao university	ORG
ejpam-5135	2	10	8710	CARDINAL
ejpam-5135	2	11	bukidnon	GPE
ejpam-5135	2	12	philippines	GPE
ejpam-5135	5	1	11	CARDINAL
ejpam-5135	10	1	2020	DATE
ejpam-5135	10	2	37f20	CARDINAL
ejpam-5135	10	3	54c35	CARDINAL
ejpam-5135	10	4	1	CARDINAL
ejpam-5135	11	1	1	CARDINAL
ejpam-5135	11	2	3	CARDINAL
ejpam-5135	11	3	5	CARDINAL
ejpam-5135	11	4	6	CARDINAL
ejpam-5135	11	5	8	CARDINAL
ejpam-5135	12	1	hassan	PERSON
ejpam-5135	14	1	1	CARDINAL
ejpam-5135	14	2	two	CARDINAL
ejpam-5135	16	1	alsanaia et.al	DATE
ejpam-5135	17	1	2	CARDINAL
ejpam-5135	18	1	macaso	PERSON
ejpam-5135	18	2	f.cherrymae.balingit@cmu.edu.ph	CARDINAL
ejpam-5135	18	3	balingit	PERSON
ejpam-5135	18	4	663	CARDINAL
ejpam-5135	18	5	2024	CARDINAL
ejpam-5135	19	1	justine bryle c. macaso	PERSON
ejpam-5135	19	2	cherry mae	PERSON
ejpam-5135	19	3	r. balingit	PERSON
ejpam-5135	20	1	j. pure	PERSON
ejpam-5135	20	2	17	CARDINAL
ejpam-5135	20	3	2	CARDINAL
ejpam-5135	20	4	2024	CARDINAL
ejpam-5135	20	5	663	CARDINAL
ejpam-5135	21	1	g[s	ORG
ejpam-5135	21	2	two	CARDINAL
ejpam-5135	21	3	g[s	GPE
ejpam-5135	22	1	two	CARDINAL
ejpam-5135	23	1	two	CARDINAL
ejpam-5135	24	1	κ(g	PERSON
ejpam-5135	25	1	κ(g −	PERSON
ejpam-5135	25	2	κ(g	PERSON
ejpam-5135	26	1	gm	ORG
ejpam-5135	26	2	2	CARDINAL
ejpam-5135	26	3	4	CARDINAL
ejpam-5135	27	1	11	CARDINAL
ejpam-5135	28	1	zero	CARDINAL
ejpam-5135	29	1	two	CARDINAL
ejpam-5135	29	2	one	CARDINAL
ejpam-5135	29	3	4	CARDINAL
ejpam-5135	30	1	⋃k	CARDINAL
ejpam-5135	33	1	x.	GPE
ejpam-5135	33	2	γ	GPE
ejpam-5135	34	1	k ∈ z+,wi ∈	ORG
ejpam-5135	34	2	x[10	GPE
ejpam-5135	35	1	x.	GPE
ejpam-5135	36	1	9	CARDINAL
ejpam-5135	37	1	two	CARDINAL
ejpam-5135	37	2	x[10	GPE
ejpam-5135	43	1	2	CARDINAL
ejpam-5135	45	1	justine bryle c. macaso	PERSON
ejpam-5135	45	2	cherry mae	PERSON
ejpam-5135	45	3	r. balingit	PERSON
ejpam-5135	46	1	j. pure	PERSON
ejpam-5135	46	2	17	CARDINAL
ejpam-5135	46	3	2	CARDINAL
ejpam-5135	46	4	2024	CARDINAL
ejpam-5135	46	5	663-675	CARDINAL
ejpam-5135	46	6	665	CARDINAL
ejpam-5135	46	7	1	CARDINAL
ejpam-5135	46	8	1 ≤	QUANTITY
ejpam-5135	47	1	ci	PERSON
ejpam-5135	47	2	ci	PERSON
ejpam-5135	47	3	2	CARDINAL
ejpam-5135	47	4	ci	PERSON
ejpam-5135	47	5	vi1	PERSON
ejpam-5135	48	1	3	CARDINAL
ejpam-5135	48	2	vi1	PERSON
ejpam-5135	49	1	4	CARDINAL
ejpam-5135	49	2	one	CARDINAL
ejpam-5135	50	1	5	CARDINAL
ejpam-5135	51	1	6	CARDINAL
ejpam-5135	52	1	7	CARDINAL
ejpam-5135	53	1	1	CARDINAL
ejpam-5135	54	1	1	CARDINAL
ejpam-5135	54	2	2	CARDINAL
ejpam-5135	54	3	justine bryle c. macaso	PERSON
ejpam-5135	54	4	cherry mae	PERSON
ejpam-5135	54	5	r. balingit	PERSON
ejpam-5135	55	1	j. pure	PERSON
ejpam-5135	55	2	17	CARDINAL
ejpam-5135	55	3	2	CARDINAL
ejpam-5135	55	4	2024	CARDINAL
ejpam-5135	55	5	663-675	CARDINAL
ejpam-5135	55	6	c3	PERSON
ejpam-5135	55	7	2	CARDINAL
ejpam-5135	55	8	3	CARDINAL
ejpam-5135	55	9	3	CARDINAL
ejpam-5135	55	10	one	CARDINAL
ejpam-5135	57	1	4	CARDINAL
ejpam-5135	57	2	4	CARDINAL
ejpam-5135	57	3	justine bryle c. macaso	PERSON
ejpam-5135	57	4	cherry mae	PERSON
ejpam-5135	57	5	r. balingit	PERSON
ejpam-5135	58	1	j. pure	PERSON
ejpam-5135	58	2	17	CARDINAL
ejpam-5135	58	3	2	CARDINAL
ejpam-5135	58	4	2024	CARDINAL
ejpam-5135	58	5	663	CARDINAL
ejpam-5135	58	6	667	CARDINAL
ejpam-5135	59	1	5	CARDINAL
ejpam-5135	60	1	5	CARDINAL
ejpam-5135	60	2	5	CARDINAL
ejpam-5135	60	3	6	CARDINAL
ejpam-5135	60	4	6	CARDINAL
ejpam-5135	60	5	3	CARDINAL
ejpam-5135	61	1	1	CARDINAL
ejpam-5135	62	1	k ∈ z+	PERSON
ejpam-5135	65	1	ac	ORG
ejpam-5135	66	1	1	CARDINAL
ejpam-5135	66	2	7	CARDINAL
ejpam-5135	67	1	1	CARDINAL
ejpam-5135	67	2	justine bryle c. macaso	PERSON
ejpam-5135	67	3	cherry mae	PERSON
ejpam-5135	67	4	r. balingit	PERSON
ejpam-5135	68	1	j. pure	PERSON
ejpam-5135	68	2	17	CARDINAL
ejpam-5135	68	3	2	CARDINAL
ejpam-5135	68	4	2024	CARDINAL
ejpam-5135	68	5	663	CARDINAL
ejpam-5135	71	1	v1 v2 v3 v4 v1 v2 v3 v4 v5 v6 v5 v6	PERSON
ejpam-5135	71	2	7	CARDINAL
ejpam-5135	71	3	two	CARDINAL
ejpam-5135	71	4	one	CARDINAL
ejpam-5135	74	1	1	CARDINAL
ejpam-5135	79	1	⊆	CARDINAL
ejpam-5135	79	2	1	CARDINAL
ejpam-5135	79	3	2	DATE
ejpam-5135	79	4	k}	PERSON
ejpam-5135	80	1	1	CARDINAL
ejpam-5135	80	2	g[{v	ORG
ejpam-5135	81	1	1	CARDINAL
ejpam-5135	81	2	two	CARDINAL
ejpam-5135	83	1	1	CARDINAL
ejpam-5135	83	2	2	DATE
ejpam-5135	83	3	1	CARDINAL
ejpam-5135	83	4	2	DATE
ejpam-5135	83	5	bri	PERSON
ejpam-5135	83	6	τb(g)-open	DATE
ejpam-5135	84	1	i=1bri	ORG
ejpam-5135	84	2	τb(g)-open	DATE
ejpam-5135	85	1	2	CARDINAL
ejpam-5135	89	1	1	CARDINAL
ejpam-5135	92	1	∈	ORG
ejpam-5135	92	2	τb(g)-open	DATE
ejpam-5135	94	1	1	CARDINAL
ejpam-5135	94	2	2	CARDINAL
ejpam-5135	95	1	at least two	CARDINAL
ejpam-5135	95	2	w.	PERSON
ejpam-5135	95	3	theorem justine bryle c. macaso	PERSON
ejpam-5135	95	4	cherry mae	PERSON
ejpam-5135	95	5	r. balingit	PERSON
ejpam-5135	96	1	j. pure	PERSON
ejpam-5135	96	2	17	CARDINAL
ejpam-5135	96	3	2	CARDINAL
ejpam-5135	96	4	2024	CARDINAL
ejpam-5135	96	5	663-675	CARDINAL
ejpam-5135	99	1	1	CARDINAL
ejpam-5135	102	1	3	CARDINAL
ejpam-5135	110	1	two	CARDINAL
ejpam-5135	115	1	1	CARDINAL
ejpam-5135	117	1	two	CARDINAL
ejpam-5135	117	2	one	CARDINAL
ejpam-5135	117	3	4	CARDINAL
ejpam-5135	118	1	1	CARDINAL
ejpam-5135	119	1	4	CARDINAL
ejpam-5135	120	1	⊆	CARDINAL
ejpam-5135	120	2	t ⊆	CARDINAL
ejpam-5135	124	1	two	CARDINAL
ejpam-5135	124	2	one	CARDINAL
ejpam-5135	126	1	∈	ORG
ejpam-5135	126	2	t ⊆	CARDINAL
ejpam-5135	127	1	1	CARDINAL
ejpam-5135	127	2	1	CARDINAL
ejpam-5135	128	1	1	CARDINAL
ejpam-5135	129	1	more than one	CARDINAL
ejpam-5135	131	1	2	CARDINAL
ejpam-5135	134	1	4	CARDINAL
ejpam-5135	134	2	2	CARDINAL
ejpam-5135	134	3	8	CARDINAL
ejpam-5135	137	1	justine bryle c. macaso	PERSON
ejpam-5135	137	2	cherry mae	PERSON
ejpam-5135	137	3	r. balingit	PERSON
ejpam-5135	138	1	j. pure	PERSON
ejpam-5135	138	2	17	CARDINAL
ejpam-5135	138	3	2	CARDINAL
ejpam-5135	138	4	2024	CARDINAL
ejpam-5135	138	5	663-675	CARDINAL
ejpam-5135	138	6	8	CARDINAL
ejpam-5135	138	7	5	CARDINAL
ejpam-5135	139	1	1	CARDINAL
ejpam-5135	140	1	w	GPE
ejpam-5135	140	2	w. proof	PERSON
ejpam-5135	141	1	1	CARDINAL
ejpam-5135	141	2	w. let o	PERSON
ejpam-5135	141	3	w /∈	NORP
ejpam-5135	144	1	w ∈	PERSON
ejpam-5135	145	1	∈	ORG
ejpam-5135	145	2	⊆	CARDINAL
ejpam-5135	146	1	two	CARDINAL
ejpam-5135	146	2	one	CARDINAL
ejpam-5135	147	1	w ∈	PERSON
ejpam-5135	147	2	two	CARDINAL
ejpam-5135	147	3	two	CARDINAL
ejpam-5135	147	4	9	CARDINAL
ejpam-5135	149	1	6	CARDINAL
ejpam-5135	153	1	two	CARDINAL
ejpam-5135	153	2	two	CARDINAL
ejpam-5135	154	1	1	CARDINAL
ejpam-5135	155	1	more than one	CARDINAL
ejpam-5135	156	1	w.	PERSON
ejpam-5135	156	2	5	CARDINAL
ejpam-5135	156	3	w.	PERSON
ejpam-5135	159	1	2	CARDINAL
ejpam-5135	161	1	3	CARDINAL
ejpam-5135	161	2	9	CARDINAL
ejpam-5135	161	3	w.	PERSON
ejpam-5135	161	4	5	CARDINAL
ejpam-5135	161	5	w. hence	PERSON
ejpam-5135	162	1	2	CARDINAL
ejpam-5135	164	1	justine bryle c. macaso	PERSON
ejpam-5135	164	2	cherry mae	PERSON
ejpam-5135	164	3	r. balingit	PERSON
ejpam-5135	165	1	j. pure	PERSON
ejpam-5135	165	2	17	CARDINAL
ejpam-5135	165	3	2	CARDINAL
ejpam-5135	165	4	2024	CARDINAL
ejpam-5135	165	5	663	CARDINAL
ejpam-5135	165	6	9	CARDINAL
ejpam-5135	165	7	7	CARDINAL
ejpam-5135	167	1	one	CARDINAL
ejpam-5135	167	2	one	CARDINAL
ejpam-5135	171	1	one	CARDINAL
ejpam-5135	171	2	one	CARDINAL
ejpam-5135	174	1	one	CARDINAL
ejpam-5135	176	1	1	CARDINAL
ejpam-5135	176	2	2	CARDINAL
ejpam-5135	178	1	3	CARDINAL
ejpam-5135	182	1	2	CARDINAL
ejpam-5135	182	2	∈	ORG
ejpam-5135	182	3	∖	PERSON
ejpam-5135	182	4	w}	GPE
ejpam-5135	182	5	wv	GPE
ejpam-5135	183	1	f−1(w	ORG
ejpam-5135	184	1	1	CARDINAL
ejpam-5135	190	1	g[{v	ORG
ejpam-5135	190	2	τb(g)-open	DATE
ejpam-5135	192	1	f−1(w	ORG
ejpam-5135	193	1	1	CARDINAL
ejpam-5135	194	1	3	CARDINAL
ejpam-5135	195	1	g = p1	PERSON
ejpam-5135	196	1	justine bryle c. macaso	PERSON
ejpam-5135	196	2	cherry mae	PERSON
ejpam-5135	196	3	r. balingit	PERSON
ejpam-5135	197	1	j. pure	PERSON
ejpam-5135	197	2	17	CARDINAL
ejpam-5135	197	3	2	CARDINAL
ejpam-5135	197	4	2024	CARDINAL
ejpam-5135	197	5	663	CARDINAL
ejpam-5135	197	6	672	CARDINAL
ejpam-5135	198	1	n ≥ 4	ORG
ejpam-5135	199	1	at least two	CARDINAL
ejpam-5135	199	2	one	CARDINAL
ejpam-5135	199	3	one	CARDINAL
ejpam-5135	201	1	at least two	CARDINAL
ejpam-5135	202	1	at least 1	CARDINAL
ejpam-5135	202	2	at least two	CARDINAL
ejpam-5135	205	1	1	CARDINAL
ejpam-5135	205	2	2	DATE
ejpam-5135	205	3	1	CARDINAL
ejpam-5135	207	1	= vi.	PERSON
ejpam-5135	207	2	one	CARDINAL
ejpam-5135	207	3	one	CARDINAL
ejpam-5135	211	1	∈	ORG
ejpam-5135	213	1	1	CARDINAL
ejpam-5135	214	1	5	CARDINAL
ejpam-5135	214	2	v2 ∈ a.	ORG
ejpam-5135	215	1	∈	ORG
ejpam-5135	216	1	∈	ORG
ejpam-5135	216	2	f−1(vj	ORG
ejpam-5135	218	1	∈	ORG
ejpam-5135	218	2	2	CARDINAL
ejpam-5135	218	3	∈	ORG
ejpam-5135	221	1	⊆	CARDINAL
ejpam-5135	222	1	τb(g)-open	DATE
ejpam-5135	223	1	3	CARDINAL
ejpam-5135	225	1	⊆	CARDINAL
ejpam-5135	225	2	τb(g)-open	DATE
ejpam-5135	227	1	one	CARDINAL
ejpam-5135	227	2	one	CARDINAL
ejpam-5135	228	1	1	CARDINAL
ejpam-5135	228	2	2	CARDINAL
ejpam-5135	228	3	1	CARDINAL
ejpam-5135	228	4	3	CARDINAL
ejpam-5135	229	1	1	CARDINAL
ejpam-5135	229	2	g = kn	PERSON
ejpam-5135	233	1	2	CARDINAL
ejpam-5135	233	2	1	CARDINAL
ejpam-5135	234	1	vw	GPE
ejpam-5135	236	1	f−1(w	ORG
ejpam-5135	238	1	τb(g)-open	DATE
ejpam-5135	240	1	1	CARDINAL
ejpam-5135	240	2	3	CARDINAL
ejpam-5135	241	1	justine bryle c. macaso	PERSON
ejpam-5135	241	2	cherry mae	PERSON
ejpam-5135	241	3	r. balingit	PERSON
ejpam-5135	242	1	j. pure	PERSON
ejpam-5135	242	2	17	CARDINAL
ejpam-5135	242	3	2	CARDINAL
ejpam-5135	242	4	2024	CARDINAL
ejpam-5135	242	5	663	CARDINAL
ejpam-5135	243	1	1	CARDINAL
ejpam-5135	243	2	xy ∈	PERSON
ejpam-5135	245	1	τb(g)-open	DATE
ejpam-5135	249	1	4	CARDINAL
ejpam-5135	251	1	2	CARDINAL
ejpam-5135	251	2	xy /∈ e(g	PERSON
ejpam-5135	252	1	g[{v	ORG
ejpam-5135	252	2	τb(g)-open	DATE
ejpam-5135	256	1	4.	CARDINAL
ejpam-5135	256	2	2	CARDINAL
ejpam-5135	261	1	⊆	CARDINAL
ejpam-5135	261	2	∈	ORG
ejpam-5135	263	1	4	CARDINAL
ejpam-5135	264	1	7	CARDINAL
ejpam-5135	264	2	10	CARDINAL
ejpam-5135	265	1	v2, v3	GPE
ejpam-5135	265	2	10	CARDINAL
ejpam-5135	265	3	674	CARDINAL
ejpam-5135	265	4	4	CARDINAL
ejpam-5135	267	1	2	CARDINAL
ejpam-5135	270	1	5	CARDINAL
ejpam-5135	272	1	one	CARDINAL
ejpam-5135	273	1	13	CARDINAL
ejpam-5135	273	2	12	CARDINAL
ejpam-5135	273	3	14	CARDINAL
ejpam-5135	273	4	15	CARDINAL
ejpam-5135	273	5	9	CARDINAL
ejpam-5135	273	6	hassan	PERSON
ejpam-5135	273	7	7	CARDINAL
ejpam-5135	276	1	rolito g. eballe	PERSON
ejpam-5135	276	2	two	CARDINAL
ejpam-5135	277	1	central mindanao university	ORG
ejpam-5135	278	1	1	CARDINAL
ejpam-5135	278	2	abdu	PERSON
ejpam-5135	278	3	a. kilicman	PERSON
ejpam-5135	280	1	2018	DATE
ejpam-5135	281	1	2	CARDINAL
ejpam-5135	284	1	3	CARDINAL
ejpam-5135	286	1	2(2):45–50	CARDINAL
ejpam-5135	286	2	1999	DATE
ejpam-5135	287	1	675	CARDINAL
ejpam-5135	287	2	4	CARDINAL
ejpam-5135	287	3	l lesniak	PERSON
ejpam-5135	287	4	p zhang	PERSON
ejpam-5135	288	1	crc press	ORG
ejpam-5135	288	2	western michigan university	ORG
ejpam-5135	288	3	2010	DATE
ejpam-5135	289	1	5	CARDINAL
ejpam-5135	291	1	journal of research and development	ORG
ejpam-5135	291	2	1(1):76–81, 1983	DATE
ejpam-5135	292	1	6	CARDINAL
ejpam-5135	292	2	a. e. gamorez	PERSON
ejpam-5135	292	3	c. g. nianga	PERSON
ejpam-5135	294	1	european journal	ORG
ejpam-5135	294	2	12(3):749–755	CARDINAL
ejpam-5135	294	3	2019	DATE
ejpam-5135	295	1	7	CARDINAL
ejpam-5135	295	2	hassan	PERSON
ejpam-5135	295	3	z.i.	GPE
ejpam-5135	296	1	biomathematices	GPE
ejpam-5135	297	1	journal of physics	ORG
ejpam-5135	297	2	1591(1	CARDINAL
ejpam-5135	297	3	2020	DATE
ejpam-5135	298	1	8	CARDINAL
ejpam-5135	298	2	laping	PERSON
ejpam-5135	298	3	balingit	GPE
ejpam-5135	300	1	asian research journal	ORG
ejpam-5135	300	2	2022	CARDINAL
ejpam-5135	301	1	9	CARDINAL
ejpam-5135	302	1	schaum	ORG
ejpam-5135	303	1	mcgraw hill	ORG
ejpam-5135	303	2	temple university	ORG
ejpam-5135	303	3	1965	DATE
ejpam-5135	304	1	10	CARDINAL
ejpam-5135	305	1	viro	GPE
ejpam-5135	305	2	o.a. ivanov	PERSON
ejpam-5135	305	3	n.y.	GPE
ejpam-5135	305	4	netsvetaev	DATE
ejpam-5135	305	5	v.m. kharlamov	PERSON
ejpam-5135	307	1	11	CARDINAL
ejpam-5135	309	1	mathworld	PERSON
ejpam-5135	310	1	12	CARDINAL
ejpam-5135	310	2	g şenel	PERSON
ejpam-5135	312	1	2016	DATE
ejpam-5135	313	1	13	CARDINAL
ejpam-5135	313	2	g şenel	PERSON
ejpam-5135	315	1	3(5):57–66, 2014	DATE
ejpam-5135	316	1	14	CARDINAL
ejpam-5135	316	2	g şenel	PERSON
ejpam-5135	318	1	10(4):525–535	DATE
ejpam-5135	318	2	2015	DATE
ejpam-5135	319	1	15	CARDINAL
ejpam-5135	319	2	a.p.	GPE
ejpam-5135	321	1	13th	ORDINAL
ejpam-5135	321	2	89–103, 1985	DATE