id	sid	eid	entity	type
ejpam-3464	1	1	european journal	ORG
ejpam-3464	2	1	12	CARDINAL
ejpam-3464	2	2	3, 2019	DATE
ejpam-3464	2	3	749	CARDINAL
ejpam-3464	2	4	1307-5543	DATE
ejpam-3464	2	5	new york	GPE
ejpam-3464	2	6	anabel e. gamorez1,∗	PERSON
ejpam-3464	2	7	caen grace s. nianga2,3	PERSON
ejpam-3464	3	1	sergio r. canoy	PERSON
ejpam-3464	3	2	1	CARDINAL
ejpam-3464	3	3	7000	CARDINAL
ejpam-3464	3	4	zamboanga city	GPE
ejpam-3464	3	5	philippines 2 department	ORG
ejpam-3464	3	6	mindanao state university-iligan institute of technology	ORG
ejpam-3464	3	7	9200	CARDINAL
ejpam-3464	3	8	iligan city	GPE
ejpam-3464	3	9	3	CARDINAL
ejpam-3464	3	10	institute of science	ORG
ejpam-3464	3	11	mindanao state university-iligan institute of technology	ORG
ejpam-3464	3	12	9200	CARDINAL
ejpam-3464	3	13	iligan city	GPE
ejpam-3464	3	14	philippines	GPE
ejpam-3464	5	1	τg	ORG
ejpam-3464	5	2	xa ∈	PERSON
ejpam-3464	6	1	two	CARDINAL
ejpam-3464	7	1	2010	DATE
ejpam-3464	7	2	05c76	CARDINAL
ejpam-3464	7	3	1	CARDINAL
ejpam-3464	10	1	∈	ORG
ejpam-3464	12	1	⊆	CARDINAL
ejpam-3464	13	1	∪	ORG
ejpam-3464	19	1	1983	DATE
ejpam-3464	19	2	1	CARDINAL
ejpam-3464	19	3	∗corresponding	PERSON
ejpam-3464	20	1	a. gamorez	PERSON
ejpam-3464	21	1	sergio.canoy@g.msuiit.edu.ph	ORG
ejpam-3464	21	2	s. canoy jr.	PERSON
ejpam-3464	22	1	749	CARDINAL
ejpam-3464	22	2	2019	CARDINAL
ejpam-3464	23	1	a. gamorez	PERSON
ejpam-3464	23	2	c. nianga	GPE
ejpam-3464	23	3	s. canoy / eur	PERSON
ejpam-3464	24	1	j. pure	PERSON
ejpam-3464	24	2	12	CARDINAL
ejpam-3464	24	3	3	CARDINAL
ejpam-3464	24	4	2019	DATE
ejpam-3464	24	5	749-755 750	QUANTITY
ejpam-3464	26	1	guerrero	PERSON
ejpam-3464	26	2	2	CARDINAL
ejpam-3464	27	1	canoy	PERSON
ejpam-3464	27	2	4	CARDINAL
ejpam-3464	28	1	cartesian	NORP
ejpam-3464	28	2	two	CARDINAL
ejpam-3464	30	1	8	CARDINAL
ejpam-3464	31	1	1	CARDINAL
ejpam-3464	31	2	two	CARDINAL
ejpam-3464	33	1	3	CARDINAL
ejpam-3464	33	2	6	CARDINAL
ejpam-3464	34	1	2	CARDINAL
ejpam-3464	34	2	⊆	CARDINAL
ejpam-3464	40	1	first	ORDINAL
ejpam-3464	40	2	two	CARDINAL
ejpam-3464	40	3	1	CARDINAL
ejpam-3464	40	4	5	CARDINAL
ejpam-3464	41	1	1	CARDINAL
ejpam-3464	43	1	⊆	CARDINAL
ejpam-3464	44	1	τg	CARDINAL
ejpam-3464	44	2	1	CARDINAL
ejpam-3464	45	1	g. theorem 2	PERSON
ejpam-3464	47	1	∈	ORG
ejpam-3464	48	1	1	CARDINAL
ejpam-3464	49	1	3	CARDINAL
ejpam-3464	49	2	one	CARDINAL
ejpam-3464	49	3	∈	ORG
ejpam-3464	50	1	τg◦h	ORG
ejpam-3464	51	1	3	CARDINAL
ejpam-3464	52	1	∈	ORG
ejpam-3464	53	1	∈	ORG
ejpam-3464	54	1	⋃	DATE
ejpam-3464	54	2	hu	PERSON
ejpam-3464	55	1	a. gamorez	PERSON
ejpam-3464	55	2	c. nianga	GPE
ejpam-3464	55	3	s. canoy / eur	PERSON
ejpam-3464	56	1	j. pure	PERSON
ejpam-3464	56	2	12	CARDINAL
ejpam-3464	56	3	3	CARDINAL
ejpam-3464	56	4	2019	DATE
ejpam-3464	56	5	749-755 751	QUANTITY
ejpam-3464	56	6	∈	ORG
ejpam-3464	59	1	∈	ORG
ejpam-3464	60	1	nk	ORG
ejpam-3464	61	1	1	CARDINAL
ejpam-3464	64	1	⋃	DATE
ejpam-3464	64	2	hu	PERSON
ejpam-3464	65	1	∈	ORG
ejpam-3464	66	1	nk	ORG
ejpam-3464	67	1	1	CARDINAL
ejpam-3464	72	1	2	CARDINAL
ejpam-3464	73	1	3	CARDINAL
ejpam-3464	73	2	one	CARDINAL
ejpam-3464	75	1	4	CARDINAL
ejpam-3464	76	1	∈	ORG
ejpam-3464	77	1	∈	ORG
ejpam-3464	78	1	6	CARDINAL
ejpam-3464	79	1	∈	ORG
ejpam-3464	80	1	hpq	PERSON
ejpam-3464	80	2	a. gamorez	PERSON
ejpam-3464	80	3	c. nianga	GPE
ejpam-3464	80	4	s. canoy / eur	PERSON
ejpam-3464	81	1	j. pure	PERSON
ejpam-3464	81	2	12	CARDINAL
ejpam-3464	81	3	3	CARDINAL
ejpam-3464	81	4	2019	DATE
ejpam-3464	81	5	749-755 752 proof	QUANTITY
ejpam-3464	82	1	∈	ORG
ejpam-3464	83	1	2	CARDINAL
ejpam-3464	84	1	⋃ z∈ng(a	PERSON
ejpam-3464	86	1	6	CARDINAL
ejpam-3464	87	1	∈	ORG
ejpam-3464	88	1	2	CARDINAL
ejpam-3464	92	1	hpq	PERSON
ejpam-3464	93	1	3	CARDINAL
ejpam-3464	94	1	3	CARDINAL
ejpam-3464	95	1	′ ∈ e(h	ORG
ejpam-3464	96	1	5	CARDINAL
ejpam-3464	102	1	3	CARDINAL
ejpam-3464	102	2	∈	ORG
ejpam-3464	102	3	∈	ORG
ejpam-3464	103	1	∩	PERSON
ejpam-3464	114	1	a. gamorez	PERSON
ejpam-3464	114	2	c. nianga	GPE
ejpam-3464	114	3	s. canoy / eur	PERSON
ejpam-3464	115	1	j. pure	PERSON
ejpam-3464	115	2	12	CARDINAL
ejpam-3464	115	3	3	CARDINAL
ejpam-3464	115	4	2019	DATE
ejpam-3464	115	5	749-755 753	QUANTITY
ejpam-3464	116	1	∈	ORG
ejpam-3464	118	1	5	CARDINAL
ejpam-3464	118	2	fg	ORG
ejpam-3464	122	1	4	CARDINAL
ejpam-3464	123	1	3	CARDINAL
ejpam-3464	124	1	′ ∈ e(h	ORG
ejpam-3464	125	1	6	CARDINAL
ejpam-3464	132	1	∈	ORG
ejpam-3464	135	1	6= 1	DATE
ejpam-3464	135	2	1	CARDINAL
ejpam-3464	136	1	6=	CARDINAL
ejpam-3464	137	1	6= 1	DATE
ejpam-3464	141	1	2	CARDINAL
ejpam-3464	141	2	6=	CARDINAL
ejpam-3464	142	1	1	CARDINAL
ejpam-3464	144	1	6=	CARDINAL
ejpam-3464	149	1	⊆	CARDINAL
ejpam-3464	149	2	fh	PERSON
ejpam-3464	154	1	az 6= e(h	ORG
ejpam-3464	155	1	6=	DATE
ejpam-3464	155	2	4	DATE
ejpam-3464	155	3	z)(v	GPE
ejpam-3464	156	1	∈	ORG
ejpam-3464	158	1	6=	CARDINAL
ejpam-3464	158	2	az /∈	ORG
ejpam-3464	160	1	6=	DATE
ejpam-3464	160	2	4	DATE
ejpam-3464	160	3	z)(v	GPE
ejpam-3464	161	1	∈	ORG
ejpam-3464	163	1	⊆	CARDINAL
ejpam-3464	164	1	2	CARDINAL
ejpam-3464	169	1	∈	ORG
ejpam-3464	171	1	6	CARDINAL
ejpam-3464	174	1	5	CARDINAL
ejpam-3464	175	1	3	CARDINAL
ejpam-3464	183	1	a. gamorez	PERSON
ejpam-3464	183	2	c. nianga	GPE
ejpam-3464	183	3	s. canoy / eur	PERSON
ejpam-3464	184	1	j. pure	PERSON
ejpam-3464	184	2	12	CARDINAL
ejpam-3464	184	3	3	CARDINAL
ejpam-3464	184	4	2019	DATE
ejpam-3464	184	5	749-755 754	QUANTITY
ejpam-3464	188	1	g⊕h	GPE
ejpam-3464	188	2	∈	ORG
ejpam-3464	191	1	6= 1	DATE
ejpam-3464	191	2	1	CARDINAL
ejpam-3464	193	1	6=	CARDINAL
ejpam-3464	194	1	6= 1	DATE
ejpam-3464	198	1	2	CARDINAL
ejpam-3464	198	2	6=	CARDINAL
ejpam-3464	199	1	1	CARDINAL
ejpam-3464	202	1	6=	CARDINAL
ejpam-3464	202	2	∈	ORG
ejpam-3464	202	3	∈	ORG
ejpam-3464	206	1	⊆	CARDINAL
ejpam-3464	207	1	fh	PERSON
ejpam-3464	209	1	w.	PERSON
ejpam-3464	211	1	6=	CARDINAL
ejpam-3464	211	2	ac /∈	ORG
ejpam-3464	213	1	5	CARDINAL
ejpam-3464	213	2	c)(v	ORG
ejpam-3464	216	1	∈	ORG
ejpam-3464	216	2	5	CARDINAL
ejpam-3464	216	3	c)(v	ORG
ejpam-3464	219	1	6=	CARDINAL
ejpam-3464	219	2	ac /∈	ORG
ejpam-3464	221	1	5	CARDINAL
ejpam-3464	221	2	c)(v	ORG
ejpam-3464	224	1	w ⊆	ORG
ejpam-3464	225	1	w.	PERSON
ejpam-3464	225	2	3	CARDINAL
ejpam-3464	233	1	7	CARDINAL
ejpam-3464	236	1	6	CARDINAL
ejpam-3464	237	1	3	CARDINAL
ejpam-3464	238	1	′ ∈ e(h	ORG
ejpam-3464	239	1	8	CARDINAL
ejpam-3464	245	1	fg[v]×	NORP
ejpam-3464	252	1	∈	ORG
ejpam-3464	254	1	6= 1	DATE
ejpam-3464	254	2	1	CARDINAL
ejpam-3464	255	1	6=	CARDINAL
ejpam-3464	256	1	6= 1	DATE
ejpam-3464	259	1	2	CARDINAL
ejpam-3464	259	2	6=	CARDINAL
ejpam-3464	260	1	1	CARDINAL
ejpam-3464	263	1	6=	CARDINAL
ejpam-3464	263	2	∈	ORG
ejpam-3464	264	1	∈	ORG
ejpam-3464	265	1	∈	ORG
ejpam-3464	267	1	⊆	CARDINAL
ejpam-3464	268	1	755	CARDINAL
ejpam-3464	270	1	= z. next	PERSON
ejpam-3464	272	1	6=	DATE
ejpam-3464	272	2	6	DATE
ejpam-3464	274	1	∈	ORG
ejpam-3464	276	1	az /∈	ORG
ejpam-3464	278	1	6=	DATE
ejpam-3464	278	2	6	DATE
ejpam-3464	279	1	∈	ORG
ejpam-3464	285	1	⊗ kn	PERSON
ejpam-3464	290	1	8	CARDINAL
ejpam-3464	291	1	mindanao state university-iligan institute of technology	ORG
ejpam-3464	292	1	1	CARDINAL
ejpam-3464	292	2	s. diesto and	PERSON
ejpam-3464	292	3	s. gervacio	PERSON
ejpam-3464	294	1	journal of research and development	ORG
ejpam-3464	294	2	1(1):76–81, 1983	DATE
ejpam-3464	295	1	2	CARDINAL
ejpam-3464	295	2	r. guerrero	PERSON
ejpam-3464	295	3	s. gervacio.	PERSON
ejpam-3464	297	1	matimyas matematika	PERSON
ejpam-3464	297	2	1986	DATE
ejpam-3464	298	1	3	CARDINAL
ejpam-3464	298	2	f. harary	PERSON
ejpam-3464	300	1	addison-wesley publishing company, usa, 1969	ORG
ejpam-3464	301	1	4	CARDINAL
ejpam-3464	301	2	r. lemence	PERSON
ejpam-3464	301	3	s. canoy	PERSON
ejpam-3464	303	1	matimyas matematika	PERSON
ejpam-3464	303	2	21(2):1–7	CARDINAL
ejpam-3464	303	3	1998	DATE
ejpam-3464	304	1	5	CARDINAL
ejpam-3464	304	2	r. lemence	PERSON
ejpam-3464	304	3	s. canoy.	PERSON
ejpam-3464	306	1	2(2):45–50	CARDINAL
ejpam-3464	306	2	1999	DATE
ejpam-3464	307	1	6	CARDINAL
ejpam-3464	307	2	s. lipschutz	PERSON
ejpam-3464	308	1	schaum	ORG
ejpam-3464	309	1	mcgraw hill international publishing co.	ORG
ejpam-3464	309	2	1987	DATE
ejpam-3464	310	1	7	CARDINAL
ejpam-3464	310	2	s. canoy.	PERSON
ejpam-3464	312	1	21(1):79–89	CARDINAL
ejpam-3464	312	2	2019	DATE
ejpam-3464	313	1	8	CARDINAL
ejpam-3464	313	2	s. canoy	PERSON
ejpam-3464	315	1	european journal	ORG
ejpam-3464	315	2	12(2):499	CARDINAL
ejpam-3464	315	3	505	CARDINAL
ejpam-3464	315	4	2019	DATE