id	sid	eid	entity	type
ejpam-2406	1	1	output.dvi european journal	ORG
ejpam-2406	1	2	8	CARDINAL
ejpam-2406	1	3	2	CARDINAL
ejpam-2406	1	4	2015	DATE
ejpam-2406	1	5	172	CARDINAL
ejpam-2406	1	6	1307-5543	CARDINAL
ejpam-2406	1	7	c. s. manjarekar 1	PERSON
ejpam-2406	1	8	2,∗	CARDINAL
ejpam-2406	1	9	1	CARDINAL
ejpam-2406	1	10	shivaji university	ORG
ejpam-2406	1	11	kolhapur	GPE
ejpam-2406	1	12	india	GPE
ejpam-2406	1	13	2	CARDINAL
ejpam-2406	1	14	sharad institute	ORG
ejpam-2406	1	15	shivaji university	ORG
ejpam-2406	1	16	kolhapur	GPE
ejpam-2406	1	17	india	GPE
ejpam-2406	4	1	2010	DATE
ejpam-2406	4	2	13a99	CARDINAL
ejpam-2406	5	1	1	CARDINAL
ejpam-2406	5	2	multiplicative lattice l	ORG
ejpam-2406	5	3	1	CARDINAL
ejpam-2406	5	4	multiplicative	NORP
ejpam-2406	6	1	ab ¶	ORG
ejpam-2406	7	1	ab ¶ p	ORG
ejpam-2406	10	1	multiplicative	NORP
ejpam-2406	11	1	∀aα ∈ l, a∈	ORG
ejpam-2406	13	1	∀a ∈ l	ORG
ejpam-2406	13	2	∈	ORG
ejpam-2406	15	1	csmanjrekar@yahoo.co.in	PERSON
ejpam-2406	15	2	c. manjarekar	PERSON
ejpam-2406	16	1	172	CARDINAL
ejpam-2406	16	2	2015	CARDINAL
ejpam-2406	17	1	c. manjarekar	PERSON
ejpam-2406	18	1	j. pure	PERSON
ejpam-2406	18	2	8 (	PERCENT
ejpam-2406	18	3	172	CARDINAL
ejpam-2406	18	4	184 173	CARDINAL
ejpam-2406	20	1	1	CARDINAL
ejpam-2406	24	1	multiplicative	NORP
ejpam-2406	25	1	∈	ORG
ejpam-2406	25	2	•	CARDINAL
ejpam-2406	25	3	cb ¶ a,	ORG
ejpam-2406	25	4	•	CARDINAL
ejpam-2406	25	5	bc	ORG
ejpam-2406	25	6	a and •	CARDINAL
ejpam-2406	25	7	ab ¶ a.	ORG
ejpam-2406	25	8	∈	ORG
ejpam-2406	26	1	∈	ORG
ejpam-2406	27	1	q1,q2	PERSON
ejpam-2406	29	1	qk	PERSON
ejpam-2406	30	1	∧ qk	PERSON
ejpam-2406	35	1	d. d. anderson	PERSON
ejpam-2406	36	1	1	CARDINAL
ejpam-2406	36	2	r. p. dilworth	PERSON
ejpam-2406	37	1	2	CARDINAL
ejpam-2406	38	1	2	CARDINAL
ejpam-2406	38	2	fuchs	ORG
ejpam-2406	38	3	4	CARDINAL
ejpam-2406	40	1	1	CARDINAL
ejpam-2406	42	1	1	CARDINAL
ejpam-2406	43	1	multiplicative	NORP
ejpam-2406	43	2	abr ¶ q	ORG
ejpam-2406	43	3	∈	ORG
ejpam-2406	43	4	2	CARDINAL
ejpam-2406	43	5	multiplicative	NORP
ejpam-2406	43	6	abr ¶ q	ORG
ejpam-2406	43	7	∈	ORG
ejpam-2406	43	8	3	CARDINAL
ejpam-2406	44	1	multiplicative	NORP
ejpam-2406	44	2	ab ¶ p	ORG
ejpam-2406	44	3	k. c. manjarekar	PERSON
ejpam-2406	45	1	j. pure	PERSON
ejpam-2406	45	2	8 (	PERCENT
ejpam-2406	45	3	172	CARDINAL
ejpam-2406	45	4	4	CARDINAL
ejpam-2406	46	1	multiplicative	NORP
ejpam-2406	46	2	¶q	NORP
ejpam-2406	47	1	∈	ORG
ejpam-2406	47	2	¶q	NORP
ejpam-2406	47	3	¶q	GPE
ejpam-2406	47	4	5	CARDINAL
ejpam-2406	48	1	¶q	NORP
ejpam-2406	49	1	∈	ORG
ejpam-2406	50	1	akn ¶q	PERSON
ejpam-2406	50	2	¶q	GPE
ejpam-2406	50	3	6	CARDINAL
ejpam-2406	51	1	l. example	ORG
ejpam-2406	52	1	1	CARDINAL
ejpam-2406	53	1	l(r	PERSON
ejpam-2406	53	2	r.	NORP
ejpam-2406	53	3	l(r	PERSON
ejpam-2406	53	4	multiplicative	NORP
ejpam-2406	55	1	l(f	PERSON
ejpam-2406	56	1	multiplicative	NORP
ejpam-2406	56	2	l(r	PERSON
ejpam-2406	57	1	r.	NORP
ejpam-2406	57	2	∈	ORG
ejpam-2406	57	3	0	CARDINAL
ejpam-2406	58	1	1	CARDINAL
ejpam-2406	59	1	2	CARDINAL
ejpam-2406	59	2	l(z	PERSON
ejpam-2406	60	1	z(p∞	ORG
ejpam-2406	61	1	= l(z(p∞	PERSON
ejpam-2406	62	1	z(p∞	PRODUCT
ejpam-2406	63	1	multiplicative	NORP
ejpam-2406	63	2	l(z	PERSON
ejpam-2406	64	1	z(p∞	PRODUCT
ejpam-2406	64	2	1	CARDINAL
ejpam-2406	65	1	3	CARDINAL
ejpam-2406	66	1	= z. let l(r	PERSON
ejpam-2406	67	1	l(r	PERSON
ejpam-2406	71	1	1	CARDINAL
ejpam-2406	71	2	1 5	CARDINAL
ejpam-2406	71	3	2.3	CARDINAL
ejpam-2406	71	4	1 2.3	CARDINAL
ejpam-2406	71	5	⊆	CARDINAL
ejpam-2406	71	6	2k	CARDINAL
ejpam-2406	71	7	1 2.3	CARDINAL
ejpam-2406	71	8	6⊆	DATE
ejpam-2406	71	9	3k	CARDINAL
ejpam-2406	71	10	1 2.3	CARDINAL
ejpam-2406	71	11	6⊆	DATE
ejpam-2406	72	1	1	CARDINAL
ejpam-2406	74	1	4	CARDINAL
ejpam-2406	75	1	l(r	PERSON
ejpam-2406	75	2	l(m	ORG
ejpam-2406	75	3	l(r	PERSON
ejpam-2406	76	1	⊕	PERSON
ejpam-2406	76	2	0	CARDINAL
ejpam-2406	77	1	l(m	ORG
ejpam-2406	77	2	l(m	ORG
ejpam-2406	78	1	1	CARDINAL
ejpam-2406	79	1	multiplicative	NORP
ejpam-2406	80	1	1	CARDINAL
ejpam-2406	81	1	c. manjarekar	PERSON
ejpam-2406	82	1	j. pure	PERSON
ejpam-2406	82	2	8 (	PERCENT
ejpam-2406	82	3	172	CARDINAL
ejpam-2406	82	4	1	CARDINAL
ejpam-2406	84	1	vii)⇒	PRODUCT
ejpam-2406	87	1	abr ¶ q	ORG
ejpam-2406	87	2	abr ¶ q	ORG
ejpam-2406	87	3	6¶	CARDINAL
ejpam-2406	87	4	integer k. hence	PERSON
ejpam-2406	87	5	akr ¶ q.	PERSON
ejpam-2406	87	6	ab ¶	ORG
ejpam-2406	87	7	ac ¶ q or bkc ¶ q	ORG
ejpam-2406	87	8	integer k.	PERSON
ejpam-2406	88	1	6¶	CARDINAL
ejpam-2406	88	2	6¶	CARDINAL
ejpam-2406	89	1	1	CARDINAL
ejpam-2406	90	1	1	CARDINAL
ejpam-2406	91	1	ab ¶ q.	ORG
ejpam-2406	92	1	1	CARDINAL
ejpam-2406	92	2	1	CARDINAL
ejpam-2406	92	3	1	CARDINAL
ejpam-2406	95	1	6¶	CARDINAL
ejpam-2406	96	1	ab ¶ p	ORG
ejpam-2406	96	2	6¶	CARDINAL
ejpam-2406	97	1	integer k.	PERSON
ejpam-2406	98	1	¶ q.	PERSON
ejpam-2406	98	2	kt ∈	PERSON
ejpam-2406	98	3	z+	ORG
ejpam-2406	101	1	6¶	CARDINAL
ejpam-2406	101	2	abr ¶	ORG
ejpam-2406	101	3	ab ¶	ORG
ejpam-2406	103	1	bnr ¶	PERSON
ejpam-2406	104	1	6¶	CARDINAL
ejpam-2406	104	2	ab ¶ p	ORG
ejpam-2406	105	1	integer k.	PERSON
ejpam-2406	105	2	1	CARDINAL
ejpam-2406	106	1	1	CARDINAL
ejpam-2406	106	2	1	CARDINAL
ejpam-2406	106	3	ab ¶ p	ORG
ejpam-2406	106	4	1	CARDINAL
ejpam-2406	107	1	1	CARDINAL
ejpam-2406	107	2	1	CARDINAL
ejpam-2406	110	1	vii)⇒	PRODUCT
ejpam-2406	112	1	ab ¶ p	ORG
ejpam-2406	113	1	ab)m	ORG
ejpam-2406	114	1	integer m.	PERSON
ejpam-2406	114	2	bm ¶	ORG
ejpam-2406	118	1	c. manjarekar	PERSON
ejpam-2406	119	1	j. pure	PERSON
ejpam-2406	119	2	8 (	PERCENT
ejpam-2406	119	3	172	CARDINAL
ejpam-2406	119	4	184 176	CARDINAL
ejpam-2406	119	5	multiplicative	NORP
ejpam-2406	119	6	multiplicative	NORP
ejpam-2406	120	1	2	CARDINAL
ejpam-2406	121	1	m.	PERSON
ejpam-2406	122	1	n 6¶q	ORG
ejpam-2406	122	2	l. (ii	ORG
ejpam-2406	122	3	n 6¶	ORG
ejpam-2406	123	1	ab ¶	ORG
ejpam-2406	124	1	integer k.	PERSON
ejpam-2406	126	1	¶ q.	PERSON
ejpam-2406	126	2	ab ¶	ORG
ejpam-2406	128	1	n ¶ q.	ORG
ejpam-2406	128	2	1	CARDINAL
ejpam-2406	128	3	ab ¶	ORG
ejpam-2406	129	1	1.	CARDINAL
ejpam-2406	130	1	¶q	GPE
ejpam-2406	131	1	m. (ii	ORG
ejpam-2406	131	2	ab ¶ p	ORG
ejpam-2406	131	3	integer k. since	PERSON
ejpam-2406	131	4	ann ¶ q	PERSON
ejpam-2406	131	5	bnn ¶	PERSON
ejpam-2406	134	1	¶q	NORP
ejpam-2406	134	2	ab ¶	ORG
ejpam-2406	137	1	akn ¶	PERSON
ejpam-2406	139	1	1	CARDINAL
ejpam-2406	140	1	ab ¶	ORG
ejpam-2406	141	1	1	CARDINAL
ejpam-2406	142	1	¶q	GPE
ejpam-2406	142	2	¶q	GPE
ejpam-2406	144	1	3	CARDINAL
ejpam-2406	145	1	m. (i) the following	ORG
ejpam-2406	146	1	k ∈	PERSON
ejpam-2406	146	2	n 6¶q	ORG
ejpam-2406	146	3	l. (ii	ORG
ejpam-2406	148	1	akn ¶	PERSON
ejpam-2406	148	2	k ∈	PERSON
ejpam-2406	148	3	c. manjarekar	PERSON
ejpam-2406	149	1	j. pure	PERSON
ejpam-2406	149	2	8 (	PERCENT
ejpam-2406	149	3	172	CARDINAL
ejpam-2406	149	4	184 177	CARDINAL
ejpam-2406	149	5	n 6¶q	ORG
ejpam-2406	149	6	l. theorem 4	ORG
ejpam-2406	150	1	m.	PERSON
ejpam-2406	152	1	m1, m2 6¶	PRODUCT
ejpam-2406	155	1	¶q	GPE
ejpam-2406	155	2	xn2 m2 ¶q	PERSON
ejpam-2406	158	1	æ	PERSON
ejpam-2406	159	1	æ	PERSON
ejpam-2406	160	1	m1 ∨ m2 6¶	ORG
ejpam-2406	160	2	1	CARDINAL
ejpam-2406	161	1	m1)¶	PERSON
ejpam-2406	162	1	∨{x ∈ l	ORG
ejpam-2406	165	1	xk2 m2 ¶q	PERSON
ejpam-2406	166	1	xk1 m1 ¶q	PERSON
ejpam-2406	166	2	xk2 m2 ¶q	PERSON
ejpam-2406	167	1	∨{x ∈ l	ORG
ejpam-2406	173	1	{p(q : n	PERSON
ejpam-2406	174	1	multiplicative	NORP
ejpam-2406	175	1	5	CARDINAL
ejpam-2406	177	1	m. (ii	ORG
ejpam-2406	177	2	l (iv	ORG
ejpam-2406	178	1	∈	ORG
ejpam-2406	179	1	¶q	GPE
ejpam-2406	180	1	ab ¶	ORG
ejpam-2406	180	2	6¶	CARDINAL
ejpam-2406	181	1	3	CARDINAL
ejpam-2406	181	2	l. hence, ak	ORG
ejpam-2406	182	1	¶q	GPE
ejpam-2406	182	2	k ∈ z+	PERSON
ejpam-2406	183	1	m. c. manjarekar	PERSON
ejpam-2406	184	1	j. pure	PERSON
ejpam-2406	184	2	8 (	PERCENT
ejpam-2406	184	3	172	CARDINAL
ejpam-2406	184	4	184 178	CARDINAL
ejpam-2406	184	5	m. let ab ¶	ORG
ejpam-2406	185	1	¶ q.	PERSON
ejpam-2406	188	1	¶ qim	ORG
ejpam-2406	190	1	q⇒	PERSON
ejpam-2406	193	1	abc ¶	ORG
ejpam-2406	194	1	¶ q.	PERSON
ejpam-2406	194	2	6¶	CARDINAL
ejpam-2406	194	3	bc 6¶	LAW
ejpam-2406	194	4	¶ q.	PERSON
ejpam-2406	194	5	abc ¶ q	ORG
ejpam-2406	194	6	6¶	CARDINAL
ejpam-2406	194	7	k ∈ z+	PERSON
ejpam-2406	195	1	akn ¶	PERSON
ejpam-2406	196	1	multiplicative	NORP
ejpam-2406	197	1	6	CARDINAL
ejpam-2406	204	1	m. let	PERSON
ejpam-2406	204	2	abr ¶ q	ORG
ejpam-2406	204	3	¶ q.	PERSON
ejpam-2406	204	4	k ∈ z+	PERSON
ejpam-2406	206	1	6¶	CARDINAL
ejpam-2406	206	2	l i.e.	CARDINAL
ejpam-2406	206	3	5	CARDINAL
ejpam-2406	206	4	ab ¶ p	ORG
ejpam-2406	209	1	bkr ¶	ORG
ejpam-2406	210	1	∈	ORG
ejpam-2406	211	1	q.	PERSON
ejpam-2406	217	1	∈	ORG
ejpam-2406	217	2	6¶	CARDINAL
ejpam-2406	218	1	j. pure	PERSON
ejpam-2406	218	2	8 (	PERCENT
ejpam-2406	218	3	172	CARDINAL
ejpam-2406	219	1	abc ¶	ORG
ejpam-2406	220	1	abc ¶ q	ORG
ejpam-2406	220	2	6¶	CARDINAL
ejpam-2406	223	1	akcim ¶ qim	PERSON
ejpam-2406	223	2	akn ¶ qim	PERSON
ejpam-2406	224	1	m. 3	ORG
ejpam-2406	224	2	3	CARDINAL
ejpam-2406	226	1	1	CARDINAL
ejpam-2406	229	1	7	CARDINAL
ejpam-2406	232	1	p1 ¶ p2 ¶	ORG
ejpam-2406	234	1	¶q	GPE
ejpam-2406	234	2	n 6¶q	ORG
ejpam-2406	237	1	t (1¶ t ¶ n	ORG
ejpam-2406	237	2	n 6¶q	ORG
ejpam-2406	238	1	∧q	CARDINAL
ejpam-2406	241	1	∈	PRODUCT
ejpam-2406	241	2	ab ¶ p	ORG
ejpam-2406	250	1	k ∈ z+	PERSON
ejpam-2406	250	2	n 6¶q	ORG
ejpam-2406	251	1	n 6¶q	ORG
ejpam-2406	253	1	n 6¶qn	DATE
ejpam-2406	254	1	¶q	GPE
ejpam-2406	255	1	¶q	GPE
ejpam-2406	257	1	¶q	GPE
ejpam-2406	257	2	∧q	ORG
ejpam-2406	257	3	¶q	PERSON
ejpam-2406	257	4	∧q	ORG
ejpam-2406	258	1	k ∈ z+	PERSON
ejpam-2406	259	1	∧q	CARDINAL
ejpam-2406	260	1	akn ¶	PERSON
ejpam-2406	262	1	¶q	GPE
ejpam-2406	262	2	¶q	GPE
ejpam-2406	262	3	¶q	GPE
ejpam-2406	262	4	¶q	GPE
ejpam-2406	267	1	1	CARDINAL
ejpam-2406	268	1	q1,q2	PERSON
ejpam-2406	271	1	5	CARDINAL
ejpam-2406	273	1	⊕	GPE
ejpam-2406	273	2	z3 ⊕	DATE
ejpam-2406	275	1	l(r	PERSON
ejpam-2406	275	2	l(m	ORG
ejpam-2406	275	3	l(r	PERSON
ejpam-2406	275	4	l(r	PERSON
ejpam-2406	275	5	multiplicative	NORP
ejpam-2406	276	1	0)⊕	CARDINAL
ejpam-2406	277	1	0)⊕	CARDINAL
ejpam-2406	277	2	z3 ⊕	GPE
ejpam-2406	277	3	0	CARDINAL
ejpam-2406	278	1	l(m	PRODUCT
ejpam-2406	279	1	l(m	PRODUCT
ejpam-2406	283	1	0	CARDINAL
ejpam-2406	284	1	6⊆	DATE
ejpam-2406	284	2	0	CARDINAL
ejpam-2406	284	3	3k(z2⊕z3⊕(0	CARDINAL
ejpam-2406	285	1	6⊆	DATE
ejpam-2406	286	1	⊂	GPE
ejpam-2406	287	1	2	CARDINAL
ejpam-2406	288	1	7	CARDINAL
ejpam-2406	290	1	8	CARDINAL
ejpam-2406	291	1	m. if n 6¶q	ORG
ejpam-2406	293	1	c. manjarekar	PERSON
ejpam-2406	294	1	j. pure	PERSON
ejpam-2406	294	2	8 (	PERCENT
ejpam-2406	294	3	172	CARDINAL
ejpam-2406	295	1	first	ORDINAL
ejpam-2406	296	1	ab ¶	ORG
ejpam-2406	296	2	6¶	CARDINAL
ejpam-2406	297	1	ab ¶	ORG
ejpam-2406	297	2	¶q	GPE
ejpam-2406	298	1	¶q	GPE
ejpam-2406	298	2	bnn ¶q	PERSON
ejpam-2406	301	1	ann ¶q	PERSON
ejpam-2406	308	1	ann ¶	PERSON
ejpam-2406	312	1	9	CARDINAL
ejpam-2406	319	1	6¶	CARDINAL
ejpam-2406	320	1	∧ q2 ∧	PRODUCT
ejpam-2406	321	1	∧ qk	PERSON
ejpam-2406	321	2	n.	ORG
ejpam-2406	321	3	first	ORDINAL
ejpam-2406	323	1	1,2	CARDINAL
ejpam-2406	325	1	k.	PERSON
ejpam-2406	328	1	∧ qk	PERSON
ejpam-2406	328	2	1,2	CARDINAL
ejpam-2406	329	1	k.	PERSON
ejpam-2406	333	1	6¶q1	CARDINAL
ejpam-2406	337	1	2,3	CARDINAL
ejpam-2406	339	1	1	CARDINAL
ejpam-2406	340	1	2	CARDINAL
ejpam-2406	342	1	k.	PERSON
ejpam-2406	342	2	2,3	CARDINAL
ejpam-2406	343	1	k.	PERSON
ejpam-2406	344	1	2,3	CARDINAL
ejpam-2406	346	1	k.	PERSON
ejpam-2406	347	1	1 ¶	CARDINAL
ejpam-2406	348	1	1	CARDINAL
ejpam-2406	348	2	1	CARDINAL
ejpam-2406	348	3	2,3	CARDINAL
ejpam-2406	349	1	k. hence	PERSON
ejpam-2406	351	1	∈	ORG
ejpam-2406	353	1	i.	PERSON
ejpam-2406	358	1	∧ æ	PERSON
ejpam-2406	359	1	1	CARDINAL
ejpam-2406	359	2	at least one	CARDINAL
ejpam-2406	359	3	i.	PERSON
ejpam-2406	360	1	6¶	CARDINAL
ejpam-2406	360	2	at least one	CARDINAL
ejpam-2406	360	3	1 ¶	CARDINAL
ejpam-2406	361	1	6¶	CARDINAL
ejpam-2406	361	2	1 ¶	CARDINAL
ejpam-2406	361	3	¶ k	PERSON
ejpam-2406	365	1	6=	CARDINAL
ejpam-2406	366	1	c. manjarekar	PERSON
ejpam-2406	367	1	j. pure	PERSON
ejpam-2406	367	2	8 (	PERCENT
ejpam-2406	367	3	172	CARDINAL
ejpam-2406	367	4	∈	ORG
ejpam-2406	369	1	6=	CARDINAL
ejpam-2406	369	2	∈	ORG
ejpam-2406	369	3	1	CARDINAL
ejpam-2406	369	4	6=	CARDINAL
ejpam-2406	369	5	r.	NORP
ejpam-2406	371	1	¶ 1	DATE
ejpam-2406	371	2	r.	NORP
ejpam-2406	371	3	1	CARDINAL
ejpam-2406	371	4	r.	NORP
ejpam-2406	371	5	6¶	CARDINAL
ejpam-2406	373	1	6¶qr	CARDINAL
ejpam-2406	381	1	6¶	CARDINAL
ejpam-2406	383	1	1	CARDINAL
ejpam-2406	383	2	at least one	CARDINAL
ejpam-2406	390	1	i.	PERSON
ejpam-2406	390	2	1,2	CARDINAL
ejpam-2406	392	1	l.	PERSON
ejpam-2406	392	2	6=	CARDINAL
ejpam-2406	392	3	6¶	CARDINAL
ejpam-2406	392	4	1,2	CARDINAL
ejpam-2406	396	1	6¶	CARDINAL
ejpam-2406	396	2	1,2	CARDINAL
ejpam-2406	397	1	l.	PERSON
ejpam-2406	401	1	at least one	CARDINAL
ejpam-2406	401	2	1 ¶	CARDINAL
ejpam-2406	402	1	at least one	CARDINAL
ejpam-2406	402	2	i.	PERSON
ejpam-2406	403	1	10	CARDINAL
ejpam-2406	406	1	q.	PERSON
ejpam-2406	412	1	7	CARDINAL
ejpam-2406	412	2	1 ¶	CARDINAL
ejpam-2406	417	1	6¶	CARDINAL
ejpam-2406	418	1	6=	CARDINAL
ejpam-2406	418	2	j. select	PERSON
ejpam-2406	418	3	6¶	CARDINAL
ejpam-2406	418	4	6¶	CARDINAL
ejpam-2406	419	1	6¶	CARDINAL
ejpam-2406	419	2	6¶p(q	CARDINAL
ejpam-2406	420	1	1,2	CARDINAL
ejpam-2406	424	1	6¶æ(q	CARDINAL
ejpam-2406	428	1	6¶	CARDINAL
ejpam-2406	429	1	j 6¶	LAW
ejpam-2406	429	2	bkai	PERSON
ejpam-2406	429	3	6¶	CARDINAL
ejpam-2406	429	4	j ∨ bkai	PERSON
ejpam-2406	429	5	6¶	CARDINAL
ejpam-2406	429	6	k j	PERSON
ejpam-2406	430	1	ak bkai	ORG
ejpam-2406	430	2	j = ak bk(a	ORG
ejpam-2406	430	3	j ∨	PERSON
ejpam-2406	430	4	bs(ai ∨	PERSON
ejpam-2406	430	5	integer s. therefore	PERSON
ejpam-2406	433	1	7	CARDINAL
ejpam-2406	433	2	3	CARDINAL
ejpam-2406	434	1	8	CARDINAL
ejpam-2406	437	1	6	CARDINAL
ejpam-2406	438	1	⊕ z. let l(r	PERSON
ejpam-2406	438	2	l(m	ORG
ejpam-2406	438	3	= z.	PERSON
ejpam-2406	438	4	l(m	PRODUCT
ejpam-2406	438	5	l(r	PERSON
ejpam-2406	439	1	c. manjarekar	PERSON
ejpam-2406	440	1	j. pure	PERSON
ejpam-2406	440	2	8 (	PERCENT
ejpam-2406	440	3	172	CARDINAL
ejpam-2406	440	4	q3 = z	PERSON
ejpam-2406	440	5	0	CARDINAL
ejpam-2406	440	6	q4 =	PERSON
ejpam-2406	440	7	0)⊕	CARDINAL
ejpam-2406	440	8	z.	PERSON
ejpam-2406	440	9	q3	ORG
ejpam-2406	440	10	q4	PERSON
ejpam-2406	441	1	2z	CARDINAL
ejpam-2406	441	2	3z	CARDINAL
ejpam-2406	442	1	0	CARDINAL
ejpam-2406	443	1	l(m	ORG
ejpam-2406	444	1	2z	CARDINAL
ejpam-2406	444	2	3z	CARDINAL
ejpam-2406	444	3	2z	CARDINAL
ejpam-2406	444	4	3z	CARDINAL
ejpam-2406	444	5	l(r	PERSON
ejpam-2406	450	1	two	CARDINAL
ejpam-2406	450	2	∧q	CARDINAL
ejpam-2406	451	1	∧q	CARDINAL
ejpam-2406	453	1	⊆	CARDINAL
ejpam-2406	453	2	1,2	CARDINAL
ejpam-2406	453	3	t ¾ 2	DATE
ejpam-2406	456	1	2	CARDINAL
ejpam-2406	461	1	11	CARDINAL
ejpam-2406	465	1	æ	PERSON
ejpam-2406	468	1	∧ æ	PERSON
ejpam-2406	469	1	∧ pk	PERSON
ejpam-2406	470	1	¶	DATE
ejpam-2406	472	1	pk	PERSON
ejpam-2406	472	2	1,2	CARDINAL
ejpam-2406	475	1	qk	ORG
ejpam-2406	478	1	pk ¶	PERSON
ejpam-2406	479	1	i.	PERSON
ejpam-2406	479	2	i.	PERSON
ejpam-2406	482	1	c. manjarekar	PERSON
ejpam-2406	483	1	j. pure	PERSON
ejpam-2406	483	2	8 (	PERCENT
ejpam-2406	483	3	172	CARDINAL
ejpam-2406	483	4	184 183	CARDINAL
ejpam-2406	483	5	12	CARDINAL
ejpam-2406	487	1	1,2	CARDINAL
ejpam-2406	490	1	1,2	CARDINAL
ejpam-2406	491	1	min(n	ORG
ejpam-2406	492	1	1,2	CARDINAL
ejpam-2406	496	1	first	ORDINAL
ejpam-2406	496	2	min(n	ORG
ejpam-2406	497	1	⊆	CARDINAL
ejpam-2406	498	1	1,2,3	DATE
ejpam-2406	505	1	6¶	CARDINAL
ejpam-2406	505	2	1 ¶	DATE
ejpam-2406	509	1	1 ¶	CARDINAL
ejpam-2406	519	1	1	CARDINAL
ejpam-2406	528	1	∃	PERSON
ejpam-2406	528	2	1,2	CARDINAL
ejpam-2406	528	3	min(n	ORG
ejpam-2406	529	1	⊆	CARDINAL
ejpam-2406	530	1	1,2,3	DATE
ejpam-2406	533	1	2	CARDINAL
ejpam-2406	535	1	5	CARDINAL
ejpam-2406	537	1	∧q1s	PERSON
ejpam-2406	537	2	æ	PERSON
ejpam-2406	538	1	1 ¶	CARDINAL
ejpam-2406	541	1	8	CARDINAL
ejpam-2406	542	1	1 ¶ j ¶	CARDINAL
ejpam-2406	542	2	{p2 j |	PERSON
ejpam-2406	543	1	1 ¶ j ¶	CARDINAL
ejpam-2406	544	1	⊆	CARDINAL
ejpam-2406	544	2	⊆	CARDINAL
ejpam-2406	545	1	⊆	CARDINAL
ejpam-2406	545	2	⊆	CARDINAL
ejpam-2406	545	3	⊆	CARDINAL
ejpam-2406	546	1	⊆	CARDINAL
ejpam-2406	549	1	∧q1s	PERSON
ejpam-2406	556	1	t∧	NORP
ejpam-2406	558	1	⊆	CARDINAL
ejpam-2406	558	2	⊆	CARDINAL
ejpam-2406	558	3	⊆	CARDINAL
ejpam-2406	559	1	⊆	CARDINAL
ejpam-2406	559	2	8	DATE
ejpam-2406	559	3	∧q1s	ORG
ejpam-2406	562	1	∧q1s)∧	DATE
ejpam-2406	562	2	∧q2t)∧q3	DATE
ejpam-2406	562	3	∧q11 ∧	ORG
ejpam-2406	562	4	∧q1s)∧	DATE
ejpam-2406	562	5	q3 ∧	ORG
ejpam-2406	563	1	′ 1	DATE
ejpam-2406	569	1	3	CARDINAL
ejpam-2406	570	1	∃	PERSON
ejpam-2406	571	1	3 ¶	CARDINAL
ejpam-2406	572	1	184	CARDINAL
ejpam-2406	577	1	′′ 1 ∧	ORG
ejpam-2406	577	2	′′	ORG
ejpam-2406	577	3	2	CARDINAL
ejpam-2406	578	1	′′	ORG
ejpam-2406	578	2	′′	ORG
ejpam-2406	580	1	1,2,3,4	DATE
ejpam-2406	581	1	⊆	CARDINAL
ejpam-2406	582	1	2	CARDINAL
ejpam-2406	589	1	1,2,3	DATE
ejpam-2406	591	1	1,2	CARDINAL
ejpam-2406	593	1	1,2	CARDINAL
ejpam-2406	594	1	min(n	ORG
ejpam-2406	595	1	european journal	ORG
ejpam-2406	596	1	dr n k	PERSON
ejpam-2406	596	2	76	CARDINAL
ejpam-2406	597	1	1	CARDINAL
ejpam-2406	597	2	m. behboodi	PERSON
ejpam-2406	597	3	r. jahani-nezhad	PERSON
ejpam-2406	597	4	m. h. naderi	PERSON
ejpam-2406	598	1	iranian	NORP
ejpam-2406	598	2	51	CARDINAL
ejpam-2406	598	3	2011	DATE
ejpam-2406	599	1	2	CARDINAL
ejpam-2406	599	2	m. baziar	PERSON
ejpam-2406	600	1	8(3	DATE
ejpam-2406	600	2	351-362	CARDINAL
ejpam-2406	600	3	2009	DATE
ejpam-2406	601	1	3	CARDINAL
ejpam-2406	602	1	pacific j.	LOC
ejpam-2406	602	2	12	CARDINAL
ejpam-2406	602	3	481	CARDINAL
ejpam-2406	603	1	1962	DATE
ejpam-2406	604	1	4	CARDINAL
ejpam-2406	605	1	mathematicarum	DATE
ejpam-2406	605	2	11	DATE
ejpam-2406	605	3	174	CARDINAL
ejpam-2406	605	4	1947	DATE
ejpam-2406	606	1	5	CARDINAL
ejpam-2406	606	2	r. y.	PERSON
ejpam-2406	607	1	london	GPE
ejpam-2406	607	2	cambridge university press	ORG
ejpam-2406	607	3	cambridge	GPE
ejpam-2406	607	4	1990	DATE