id	sid	eid	entity	type
ejpam-1878	1	1	output.dvi european journal	ORG
ejpam-1878	1	2	8	CARDINAL
ejpam-1878	1	3	1	CARDINAL
ejpam-1878	1	4	2015	DATE
ejpam-1878	1	5	15	CARDINAL
ejpam-1878	1	6	sankar sagi college	PERSON
ejpam-1878	1	7	sohar, ministry of higher education	ORG
ejpam-1878	1	8	oman	GPE
ejpam-1878	2	1	z+	ORG
ejpam-1878	2	2	z+	ORG
ejpam-1878	2	3	z+	ORG
ejpam-1878	2	4	n ∈ z+	ORG
ejpam-1878	2	5	d(n	PERSON
ejpam-1878	3	1	z+	ORG
ejpam-1878	4	1	∈	ORG
ejpam-1878	5	1	z+	ORG
ejpam-1878	7	1	2010	DATE
ejpam-1878	7	2	06b10,11a99	CARDINAL
ejpam-1878	7	3	1	CARDINAL
ejpam-1878	8	1	z+	ORG
ejpam-1878	8	2	z+	ORG
ejpam-1878	9	1	⋃ m∈c	PERSON
ejpam-1878	9	2	n ∈ z+	ORG
ejpam-1878	10	1	d(n	PERSON
ejpam-1878	10	2	n ∈ z+	ORG
ejpam-1878	11	1	z+	ORG
ejpam-1878	11	2	m≤c	PERSON
ejpam-1878	12	1	∈	ORG
ejpam-1878	12	2	z+	ORG
ejpam-1878	13	1	2	CARDINAL
ejpam-1878	14	1	z+	ORG
ejpam-1878	14	2	sagi_sankar@yahoo.co.in	PERSON
ejpam-1878	14	3	15	CARDINAL
ejpam-1878	14	4	2015	CARDINAL
ejpam-1878	15	1	s. sagi	PERSON
ejpam-1878	16	1	j. pure	PERSON
ejpam-1878	16	2	8 (	PERCENT
ejpam-1878	16	3	15	CARDINAL
ejpam-1878	16	4	16	CARDINAL
ejpam-1878	17	1	z+	ORG
ejpam-1878	18	1	∈	PRODUCT
ejpam-1878	18	2	⊆	CARDINAL
ejpam-1878	19	1	z+,≤c	ORG
ejpam-1878	19	2	z+	ORG
ejpam-1878	20	1	z+	ORG
ejpam-1878	21	1	first	ORDINAL
ejpam-1878	22	1	2	CARDINAL
ejpam-1878	24	1	⊆	CARDINAL
ejpam-1878	25	1	a(lub of a	ORG
ejpam-1878	25	2	a1 ∧ a2 ∧ ·	PRODUCT
ejpam-1878	26	1	a1∨ a2∨	PERSON
ejpam-1878	27	1	∈	ORG
ejpam-1878	28	1	∈	ORG
ejpam-1878	30	1	commutative	ORG
ejpam-1878	33	1	z+	ORG
ejpam-1878	34	1	1	CARDINAL
ejpam-1878	35	1	z+	ORG
ejpam-1878	35	2	z+	ORG
ejpam-1878	35	3	n ∈ z+	ORG
ejpam-1878	36	1	1	CARDINAL
ejpam-1878	37	1	2	CARDINAL
ejpam-1878	39	1	j. pure	PERSON
ejpam-1878	39	2	8 (	PERCENT
ejpam-1878	39	3	15-25 17	DATE
ejpam-1878	39	4	3	CARDINAL
ejpam-1878	40	1	⋃ m∈c	PERSON
ejpam-1878	41	1	2	CARDINAL
ejpam-1878	42	1	n ∈ z+	ORG
ejpam-1878	43	1	∈	ORG
ejpam-1878	43	2	z+	ORG
ejpam-1878	43	3	z+	ORG
ejpam-1878	44	1	z+	ORG
ejpam-1878	44	2	z+	ORG
ejpam-1878	44	3	1	CARDINAL
ejpam-1878	44	4	4	CARDINAL
ejpam-1878	45	1	3	CARDINAL
ejpam-1878	50	1	1	CARDINAL
ejpam-1878	52	1	1	CARDINAL
ejpam-1878	53	1	z+,≤c	ORG
ejpam-1878	53	2	2	CARDINAL
ejpam-1878	54	1	z+,≤c	ORG
ejpam-1878	54	2	3	CARDINAL
ejpam-1878	54	3	dirichlet	PERSON
ejpam-1878	54	4	z+	ORG
ejpam-1878	54	5	3	CARDINAL
ejpam-1878	57	1	4	DATE
ejpam-1878	59	1	∈	ORG
ejpam-1878	61	1	5	CARDINAL
ejpam-1878	63	1	1	CARDINAL
ejpam-1878	64	1	∈	ORG
ejpam-1878	66	1	2	CARDINAL
ejpam-1878	68	1	j. pure	PERSON
ejpam-1878	68	2	8 (	PERCENT
ejpam-1878	68	3	15	CARDINAL
ejpam-1878	68	4	6	DATE
ejpam-1878	69	1	∈	ORG
ejpam-1878	70	1	s containing a. now	ORG
ejpam-1878	70	2	2	CARDINAL
ejpam-1878	70	3	s,∧	ORG
ejpam-1878	72	1	1	CARDINAL
ejpam-1878	73	1	2	CARDINAL
ejpam-1878	74	1	s.	ORG
ejpam-1878	74	2	3	CARDINAL
ejpam-1878	75	1	s. proof	PERSON
ejpam-1878	76	1	1)⇐⇒	DATE
ejpam-1878	76	2	2	CARDINAL
ejpam-1878	77	1	1	CARDINAL
ejpam-1878	77	2	3	CARDINAL
ejpam-1878	77	3	⊆	CARDINAL
ejpam-1878	80	1	3	CARDINAL
ejpam-1878	80	2	1	CARDINAL
ejpam-1878	83	1	⊆	CARDINAL
ejpam-1878	85	1	3	CARDINAL
ejpam-1878	87	1	7→	CARDINAL
ejpam-1878	87	2	s,∧	ORG
ejpam-1878	89	1	⊆	CARDINAL
ejpam-1878	89	2	∈	ORG
ejpam-1878	89	3	7→	CARDINAL
ejpam-1878	90	1	4	CARDINAL
ejpam-1878	91	1	s,∧	ORG
ejpam-1878	92	1	7→	CARDINAL
ejpam-1878	94	1	s. sagi	PERSON
ejpam-1878	95	1	j. pure	PERSON
ejpam-1878	95	2	8 (	PERCENT
ejpam-1878	95	3	15	CARDINAL
ejpam-1878	100	1	7→	CARDINAL
ejpam-1878	104	1	2	CARDINAL
ejpam-1878	104	2	s.	PERSON
ejpam-1878	108	1	∈	ORG
ejpam-1878	108	2	∈	ORG
ejpam-1878	108	3	5	CARDINAL
ejpam-1878	109	1	s.	ORG
ejpam-1878	109	2	1	CARDINAL
ejpam-1878	110	1	∈	ORG
ejpam-1878	110	2	∈	ORG
ejpam-1878	110	3	2	CARDINAL
ejpam-1878	111	1	⊆	CARDINAL
ejpam-1878	111	2	⊆	CARDINAL
ejpam-1878	111	3	j ⊆ p	ORG
ejpam-1878	111	4	3	CARDINAL
ejpam-1878	113	1	s. proof	PERSON
ejpam-1878	114	1	1	CARDINAL
ejpam-1878	114	2	2	CARDINAL
ejpam-1878	114	3	s.	PERSON
ejpam-1878	114	4	6⊆	DATE
ejpam-1878	114	5	∈	ORG
ejpam-1878	114	6	∈	ORG
ejpam-1878	115	1	1	CARDINAL
ejpam-1878	119	1	2	CARDINAL
ejpam-1878	120	1	3	CARDINAL
ejpam-1878	120	2	∈	ORG
ejpam-1878	122	1	6⊆	DATE
ejpam-1878	122	2	6⊆	CARDINAL
ejpam-1878	122	3	⇒(a	CARDINAL
ejpam-1878	122	4	6⊆	DATE
ejpam-1878	123	1	s.	PERSON
ejpam-1878	123	2	3	CARDINAL
ejpam-1878	123	3	1	CARDINAL
ejpam-1878	123	4	∈	PRODUCT
ejpam-1878	123	5	s. sagi	PERSON
ejpam-1878	124	1	j. pure	PERSON
ejpam-1878	124	2	8 (	PERCENT
ejpam-1878	124	3	15-25 20	QUANTITY
ejpam-1878	127	1	8	CARDINAL
ejpam-1878	128	1	s,∧	ORG
ejpam-1878	128	2	one	CARDINAL
ejpam-1878	128	3	5	CARDINAL
ejpam-1878	129	1	4	CARDINAL
ejpam-1878	129	2	z+	ORG
ejpam-1878	131	1	first	ORDINAL
ejpam-1878	131	2	n ∈ n	PRODUCT
ejpam-1878	135	1	9	CARDINAL
ejpam-1878	135	2	∈	ORG
ejpam-1878	137	1	6	CARDINAL
ejpam-1878	142	1	1	CARDINAL
ejpam-1878	142	2	1)(p	DATE
ejpam-1878	142	3	0 ≤ α(p	QUANTITY
ejpam-1878	142	4	z+	ORG
ejpam-1878	143	1	max{θ	PERSON
ejpam-1878	143	2	∈	ORG
ejpam-1878	143	3	s. sagi	PERSON
ejpam-1878	144	1	j. pure	PERSON
ejpam-1878	144	2	8 (	PERCENT
ejpam-1878	144	3	15-25 21	DATE
ejpam-1878	144	4	n)(p)≤ α(p	PERSON
ejpam-1878	146	1	∈	ORG
ejpam-1878	146	2	α(p	PERSON
ejpam-1878	147	1	n ∞. n ∈	ORG
ejpam-1878	148	1	⊆	CARDINAL
ejpam-1878	150	1	≤ α(p	PERSON
ejpam-1878	150	2	∈	ORG
ejpam-1878	151	1	θ (n	ORG
ejpam-1878	151	2	n)|	ORG
ejpam-1878	152	1	n)|= φ	ORG
ejpam-1878	152	2	n)|	ORG
ejpam-1878	154	1	6=	CARDINAL
ejpam-1878	154	2	1 ≤	QUANTITY
ejpam-1878	155	1	1 ≤	QUANTITY
ejpam-1878	155	2	m)(pi)|m	PERSON
ejpam-1878	157	1	∈	ORG
ejpam-1878	157	2	max{θ (m1)(pi	GPE
ejpam-1878	159	1	r.	NORP
ejpam-1878	159	2	6=	CARDINAL
ejpam-1878	159	3	m)(p	ORG
ejpam-1878	159	4	∈	ORG
ejpam-1878	162	1	⊆	CARDINAL
ejpam-1878	163	1	α(p	PERSON
ejpam-1878	165	1	1	CARDINAL
ejpam-1878	166	1	10	CARDINAL
ejpam-1878	168	1	β(p	PERSON
ejpam-1878	168	2	∈	ORG
ejpam-1878	174	1	⊆	CARDINAL
ejpam-1878	175	1	⊆	CARDINAL
ejpam-1878	176	1	≤ β(p	PERSON
ejpam-1878	178	1	β(p	ORG
ejpam-1878	180	1	≤ β(p	PERSON
ejpam-1878	181	1	0	CARDINAL
ejpam-1878	182	1	= β(p	PERSON
ejpam-1878	184	1	s. sagi	PERSON
ejpam-1878	185	1	j. pure	PERSON
ejpam-1878	185	2	8 (	PERCENT
ejpam-1878	185	3	15-25 22	TIME
ejpam-1878	187	1	⊆	CARDINAL
ejpam-1878	187	2	n /∈	NORP
ejpam-1878	187	3	∈	ORG
ejpam-1878	189	1	6=	CARDINAL
ejpam-1878	189	2	β(p	ORG
ejpam-1878	190	1	+ 1	DATE
ejpam-1878	190	2	n)(p	ORG
ejpam-1878	190	3	6≤	CARDINAL
ejpam-1878	191	1	+ 1	DATE
ejpam-1878	191	2	≤ β(p	PERSON
ejpam-1878	192	1	∈	ORG
ejpam-1878	195	1	7→	CARDINAL
ejpam-1878	196	1	1	CARDINAL
ejpam-1878	200	1	first	ORDINAL
ejpam-1878	200	2	two	CARDINAL
ejpam-1878	200	3	z+	ORG
ejpam-1878	201	1	3	CARDINAL
ejpam-1878	202	1	8	CARDINAL
ejpam-1878	203	1	z+	ORG
ejpam-1878	204	1	z+,≤c	ORG
ejpam-1878	206	1	9	CARDINAL
ejpam-1878	208	1	1	CARDINAL
ejpam-1878	209	1	z+,≤c	ORG
ejpam-1878	209	2	2	CARDINAL
ejpam-1878	210	1	z+,≤c	ORG
ejpam-1878	210	2	10	CARDINAL
ejpam-1878	215	1	1	CARDINAL
ejpam-1878	216	1	z+,≤c	ORG
ejpam-1878	217	1	2	CARDINAL
ejpam-1878	218	1	z+,≤c	ORG
ejpam-1878	218	2	3	CARDINAL
ejpam-1878	219	1	z+,≤c	ORG
ejpam-1878	221	1	2)⇔	CARDINAL
ejpam-1878	221	2	3	CARDINAL
ejpam-1878	221	3	8 (1)⇒	CARDINAL
ejpam-1878	221	4	2	CARDINAL
ejpam-1878	221	5	α(p	PERSON
ejpam-1878	225	1	1	CARDINAL
ejpam-1878	225	2	z+	ORG
ejpam-1878	225	3	z+,≤c	ORG
ejpam-1878	225	4	z+,≤c	ORG
ejpam-1878	226	1	1	CARDINAL
ejpam-1878	226	2	3	CARDINAL
ejpam-1878	226	3	8 and 9	DATE
ejpam-1878	226	4	∈	ORG
ejpam-1878	226	5	s. sagi	PERSON
ejpam-1878	227	1	j. pure	PERSON
ejpam-1878	227	2	8 (	PERCENT
ejpam-1878	227	3	15	CARDINAL
ejpam-1878	227	4	∨ n)(p	PERSON
ejpam-1878	227	5	m)(p	ORG
ejpam-1878	227	6	n)(p	ORG
ejpam-1878	227	7	n ∈ z+	ORG
ejpam-1878	229	1	n ∈ z+	ORG
ejpam-1878	229	2	∈	ORG
ejpam-1878	230	1	∈	ORG
ejpam-1878	231	1	c α(p	PERSON
ejpam-1878	231	2	∈	ORG
ejpam-1878	232	1	c α(p	PERSON
ejpam-1878	232	2	∈	ORG
ejpam-1878	233	1	z+,≤c	ORG
ejpam-1878	235	1	11	CARDINAL
ejpam-1878	238	1	1	CARDINAL
ejpam-1878	240	1	2	CARDINAL
ejpam-1878	241	1	α(p	PERSON
ejpam-1878	242	1	6=∞	CARDINAL
ejpam-1878	243	1	3	CARDINAL
ejpam-1878	244	1	α(p	PERSON
ejpam-1878	244	2	6=∞	CARDINAL
ejpam-1878	244	3	α(q	PERSON
ejpam-1878	245	1	6=	CARDINAL
ejpam-1878	247	1	1	CARDINAL
ejpam-1878	247	2	2	CARDINAL
ejpam-1878	247	3	7	CARDINAL
ejpam-1878	247	4	7→	CARDINAL
ejpam-1878	248	1	∩	NORP
ejpam-1878	248	2	α(p	PERSON
ejpam-1878	248	3	n)(p	ORG
ejpam-1878	248	4	z+	ORG
ejpam-1878	249	1	α(p	PERSON
ejpam-1878	250	1	6=∞	CARDINAL
ejpam-1878	251	1	2	CARDINAL
ejpam-1878	251	2	3	CARDINAL
ejpam-1878	251	3	2	CARDINAL
ejpam-1878	252	1	α(p	PERSON
ejpam-1878	253	1	6=∞.	DATE
ejpam-1878	254	1	β(q	ORG
ejpam-1878	257	1	6=	CARDINAL
ejpam-1878	258	1	j. pure	PERSON
ejpam-1878	258	2	8 (	PERCENT
ejpam-1878	258	3	15-25 24	TIME
ejpam-1878	258	4	γ(q	ORG
ejpam-1878	259	1	0	CARDINAL
ejpam-1878	259	2	6=	CARDINAL
ejpam-1878	259	3	∈	ORG
ejpam-1878	261	1	β(q)∧ γ(q	PERSON
ejpam-1878	261	2	α(q	PERSON
ejpam-1878	261	3	∈	ORG
ejpam-1878	262	1	α(p	PERSON
ejpam-1878	262	2	6=∞	CARDINAL
ejpam-1878	262	3	6≤	CARDINAL
ejpam-1878	262	4	6≤	CARDINAL
ejpam-1878	263	1	2	CARDINAL
ejpam-1878	263	2	α(q	PERSON
ejpam-1878	263	3	6=	CARDINAL
ejpam-1878	265	1	6=	CARDINAL
ejpam-1878	266	1	3	CARDINAL
ejpam-1878	267	1	1	CARDINAL
ejpam-1878	267	2	α(p	PERSON
ejpam-1878	267	3	6=∞	CARDINAL
ejpam-1878	267	4	α(q	PERSON
ejpam-1878	268	1	6=	CARDINAL
ejpam-1878	270	1	j ∩ k ⊆	PERSON
ejpam-1878	271	1	k = iγ	PERSON
ejpam-1878	272	1	∩	PERSON
ejpam-1878	272	2	j ∩ k ⊆	WORK_OF_ART
ejpam-1878	274	1	β(p)≤ α(p	PERSON
ejpam-1878	274	2	γ(p)≤ α(p	PERSON
ejpam-1878	275	1	α(q	PERSON
ejpam-1878	276	1	6=	CARDINAL
ejpam-1878	276	2	γ ≤ α	FAC
ejpam-1878	276	3	⊆	CARDINAL
ejpam-1878	277	1	j ⊆ iα	PERSON
ejpam-1878	277	2	k ⊆	ORG
ejpam-1878	278	1	11	DATE
ejpam-1878	282	1	α(q	PERSON
ejpam-1878	283	1	6=	CARDINAL
ejpam-1878	284	1	12	CARDINAL
ejpam-1878	291	1	11	CARDINAL
ejpam-1878	291	2	α(p	PERSON
ejpam-1878	291	3	6=∞	CARDINAL
ejpam-1878	291	4	α(q	PERSON
ejpam-1878	291	5	6=	CARDINAL
ejpam-1878	294	1	13	CARDINAL
ejpam-1878	295	1	∈	ORG
ejpam-1878	295	2	⊆	CARDINAL
ejpam-1878	295	3	25	CARDINAL
ejpam-1878	296	1	n ∈	ORG
ejpam-1878	296	2	⊆	CARDINAL
ejpam-1878	296	3	⊆	CARDINAL
ejpam-1878	296	4	6=	CARDINAL
ejpam-1878	296	5	0≤	CARDINAL
ejpam-1878	296	6	⊆	CARDINAL
ejpam-1878	296	7	qb+1)(b)≤	CARDINAL
ejpam-1878	298	1	⊆	CARDINAL
ejpam-1878	300	1	13	CARDINAL
ejpam-1878	300	2	2	CARDINAL
ejpam-1878	302	1	1	CARDINAL
ejpam-1878	303	1	∈	ORG
ejpam-1878	304	1	2	CARDINAL
ejpam-1878	306	1	6=	CARDINAL
ejpam-1878	306	2	∈	ORG
ejpam-1878	307	1	3	CARDINAL
ejpam-1878	308	1	⋃	PERSON
ejpam-1878	309	1	3	CARDINAL
ejpam-1878	311	1	n ∈ z	ORG
ejpam-1878	312	1	1	CARDINAL
ejpam-1878	312	2	s. sagi	PERSON
ejpam-1878	313	1	ph.d	ORG
ejpam-1878	314	1	andhra university	ORG
ejpam-1878	314	2	waltair	ORG
ejpam-1878	314	3	visakhapatnam	GPE
ejpam-1878	314	4	india	GPE
ejpam-1878	314	5	2010	DATE
ejpam-1878	315	1	2	CARDINAL
ejpam-1878	315	2	u.m. swamy	GPE
ejpam-1878	315	3	g.c. rao	PERSON
ejpam-1878	315	4	v. s. ramaiah	PERSON
ejpam-1878	317	1	indian	NORP
ejpam-1878	317	2	14(12	CARDINAL
ejpam-1878	317	3	1519-1530	CARDINAL
ejpam-1878	318	1	1983	DATE
ejpam-1878	319	1	3	CARDINAL
ejpam-1878	319	2	u.m. swamy	GPE
ejpam-1878	319	3	s. sagi	PERSON
ejpam-1878	320	1	european	NORP
ejpam-1878	320	2	424	CARDINAL
ejpam-1878	320	3	2011	DATE
ejpam-1878	321	1	4	CARDINAL
ejpam-1878	321	2	u.m. swamy	GPE
ejpam-1878	321	3	s. sagi	PERSON
ejpam-1878	323	1	2(1	CARDINAL
ejpam-1878	323	2	2011	DATE
ejpam-1878	323	3	25	CARDINAL