id	sid	eid	entity	type
ejpam-6576	1	1	european journal	ORG
ejpam-6576	1	2	2025	DATE
ejpam-6576	1	3	18	CARDINAL
ejpam-6576	1	4	3	CARDINAL
ejpam-6576	1	5	6576	CARDINAL
ejpam-6576	1	6	1307-5543	DATE
ejpam-6576	1	7	new york	GPE
ejpam-6576	1	8	j. lakshminarayana1,∗	PERSON
ejpam-6576	1	9	v.b.v.n	PERSON
ejpam-6576	1	10	prasad1	PERSON
ejpam-6576	1	11	srinivasa rao ravi2	PERSON
ejpam-6576	1	12	prasad korrapati2	ORG
ejpam-6576	2	1	1	CARDINAL
ejpam-6576	2	2	koneru lakshmaiah education foundation	ORG
ejpam-6576	2	3	vaddeswaram-522502	DATE
ejpam-6576	2	4	guntur	PERSON
ejpam-6576	2	5	dist	NORP
ejpam-6576	3	1	andhra pradesh	ORG
ejpam-6576	3	2	india 2 department of mathematics university college of sciences	ORG
ejpam-6576	3	3	acharya nagarjuna university	ORG
ejpam-6576	4	1	guntur	PERSON
ejpam-6576	4	2	dist	NORP
ejpam-6576	4	3	andhra pradesh	ORG
ejpam-6576	4	4	india 3	ORG
ejpam-6576	4	5	j.c college	ORG
ejpam-6576	4	6	chowdavaram-522019	PERSON
ejpam-6576	4	7	guntur	PERSON
ejpam-6576	4	8	dist.),andhra	GPE
ejpam-6576	4	9	india	GPE
ejpam-6576	5	1	two	CARDINAL
ejpam-6576	6	1	first	ORDINAL
ejpam-6576	6	2	second	ORDINAL
ejpam-6576	10	1	type-r(1	ORG
ejpam-6576	11	1	type-r(1	ORG
ejpam-6576	12	1	2020	DATE
ejpam-6576	12	2	16y30	CARDINAL
ejpam-6576	12	3	n -group	ORG
ejpam-6576	12	4	r(1	ORG
ejpam-6576	12	5	r(1	ORG
ejpam-6576	12	6	1	CARDINAL
ejpam-6576	13	1	zero	CARDINAL
ejpam-6576	14	1	n. j. groenewald	PERSON
ejpam-6576	15	1	1	CARDINAL
ejpam-6576	18	1	2002511005@kluniversity.in	CARDINAL
ejpam-6576	18	2	j. lakshminarayana	PERSON
ejpam-6576	18	3	vbvnprasad@kluniversity.in	PERSON
ejpam-6576	18	4	v.b.v.n	ORG
ejpam-6576	18	5	prasad	ORG
ejpam-6576	18	6	dr rsrao@yahoo.com	PERSON
ejpam-6576	18	7	s. rao ravi	ORG
ejpam-6576	18	8	s. p. korrapati	PERSON
ejpam-6576	18	9	a. v. ramakrishna	PERSON
ejpam-6576	18	10	1	CARDINAL
ejpam-6576	19	1	2025	CARDINAL
ejpam-6576	22	1	j. pure	PERSON
ejpam-6576	22	2	18	CARDINAL
ejpam-6576	22	3	3	CARDINAL
ejpam-6576	22	4	2025	CARDINAL
ejpam-6576	22	5	6576 2	DATE
ejpam-6576	22	6	7	CARDINAL
ejpam-6576	22	7	2	CARDINAL
ejpam-6576	24	1	3	CARDINAL
ejpam-6576	25	1	4	CARDINAL
ejpam-6576	26	1	5	CARDINAL
ejpam-6576	27	1	6	CARDINAL
ejpam-6576	28	1	8	CARDINAL
ejpam-6576	31	1	t,+	ORG
ejpam-6576	32	1	∈	ORG
ejpam-6576	37	1	∈	ORG
ejpam-6576	38	1	2	CARDINAL
ejpam-6576	38	2	r(1	ORG
ejpam-6576	38	3	zero	CARDINAL
ejpam-6576	39	1	1	CARDINAL
ejpam-6576	40	1	0	CARDINAL
ejpam-6576	40	2	0	CARDINAL
ejpam-6576	40	3	r(1	ORG
ejpam-6576	41	1	0	CARDINAL
ejpam-6576	41	2	0	CARDINAL
ejpam-6576	41	3	∈	ORG
ejpam-6576	41	4	r.	NORP
ejpam-6576	41	5	1	CARDINAL
ejpam-6576	43	1	r(1	ORG
ejpam-6576	44	1	1	CARDINAL
ejpam-6576	46	1	r(1	ORG
ejpam-6576	51	1	j. pure	PERSON
ejpam-6576	51	2	18	CARDINAL
ejpam-6576	51	3	3	CARDINAL
ejpam-6576	51	4	2025	CARDINAL
ejpam-6576	51	5	6576 3	DATE
ejpam-6576	51	6	7	CARDINAL
ejpam-6576	52	1	gn ̸=	ORG
ejpam-6576	53	1	r(1	ORG
ejpam-6576	54	1	0	CARDINAL
ejpam-6576	56	1	r(1	ORG
ejpam-6576	57	1	∈	ORG
ejpam-6576	58	1	r(1	ORG
ejpam-6576	58	2	0	CARDINAL
ejpam-6576	59	1	0	CARDINAL
ejpam-6576	59	2	⊆	CARDINAL
ejpam-6576	59	3	0	CARDINAL
ejpam-6576	60	1	0	CARDINAL
ejpam-6576	60	2	⊆	CARDINAL
ejpam-6576	60	3	0	CARDINAL
ejpam-6576	60	4	0	CARDINAL
ejpam-6576	61	1	0	CARDINAL
ejpam-6576	61	2	∈	ORG
ejpam-6576	61	3	0	CARDINAL
ejpam-6576	62	1	0	CARDINAL
ejpam-6576	63	1	r(1	ORG
ejpam-6576	64	1	2	CARDINAL
ejpam-6576	65	1	r(1	ORG
ejpam-6576	67	1	r(1	ORG
ejpam-6576	70	1	3	CARDINAL
ejpam-6576	71	1	r(1	ORG
ejpam-6576	76	1	r(1	ORG
ejpam-6576	78	1	r(1	ORG
ejpam-6576	80	1	g0	ORG
ejpam-6576	81	1	g1	ORG
ejpam-6576	81	2	g1	ORG
ejpam-6576	82	1	g1 − g2 =	ORG
ejpam-6576	83	1	g,+	GPE
ejpam-6576	84	1	⊆	CARDINAL
ejpam-6576	84	2	g0n	GPE
ejpam-6576	84	3	gx	ORG
ejpam-6576	84	4	g ∈ g0n	PERSON
ejpam-6576	84	5	∈	ORG
ejpam-6576	85	1	i.	PERSON
ejpam-6576	85	2	i. gx	PERSON
ejpam-6576	103	1	r(1	ORG
ejpam-6576	104	1	5	CARDINAL
ejpam-6576	107	1	r(1	ORG
ejpam-6576	108	1	r(1	ORG
ejpam-6576	110	1	r(1	ORG
ejpam-6576	111	1	gx	ORG
ejpam-6576	115	1	j. lakshminarayana et al	PERSON
ejpam-6576	116	1	j. pure	PERSON
ejpam-6576	116	2	18	CARDINAL
ejpam-6576	116	3	3	CARDINAL
ejpam-6576	116	4	2025	CARDINAL
ejpam-6576	116	5	6576 4 of 7	DATE
ejpam-6576	136	1	6	CARDINAL
ejpam-6576	137	1	1	CARDINAL
ejpam-6576	138	1	0	CARDINAL
ejpam-6576	140	1	0	CARDINAL
ejpam-6576	141	1	0	CARDINAL
ejpam-6576	142	1	zero	CARDINAL
ejpam-6576	142	2	g0	ORG
ejpam-6576	143	1	0	CARDINAL
ejpam-6576	144	1	0	CARDINAL
ejpam-6576	146	1	0	CARDINAL
ejpam-6576	150	1	⊆	CARDINAL
ejpam-6576	150	2	g0	ORG
ejpam-6576	150	3	0	CARDINAL
ejpam-6576	150	4	0	CARDINAL
ejpam-6576	151	1	0	CARDINAL
ejpam-6576	152	1	0	CARDINAL
ejpam-6576	152	2	0	CARDINAL
ejpam-6576	153	1	2	CARDINAL
ejpam-6576	154	1	1	CARDINAL
ejpam-6576	154	2	0	CARDINAL
ejpam-6576	155	1	r(1	ORG
ejpam-6576	156	1	3	CARDINAL
ejpam-6576	157	1	r(1	ORG
ejpam-6576	157	2	zero	CARDINAL
ejpam-6576	157	3	r(1	ORG
ejpam-6576	158	1	1	CARDINAL
ejpam-6576	159	1	r(1	ORG
ejpam-6576	160	1	r(1	ORG
ejpam-6576	162	1	r(1	ORG
ejpam-6576	162	2	r(1	ORG
ejpam-6576	162	3	0	CARDINAL
ejpam-6576	163	1	4	CARDINAL
ejpam-6576	163	2	r(1	ORG
ejpam-6576	163	3	∈	ORG
ejpam-6576	167	1	zero	CARDINAL
ejpam-6576	168	1	r(1	ORG
ejpam-6576	169	1	r(1	ORG
ejpam-6576	170	1	2	CARDINAL
ejpam-6576	171	1	n and n	ORG
ejpam-6576	171	2	r(1	ORG
ejpam-6576	172	1	r(1	ORG
ejpam-6576	174	1	r(1	ORG
ejpam-6576	175	1	zero	CARDINAL
ejpam-6576	175	2	r(1	ORG
ejpam-6576	175	3	zero	CARDINAL
ejpam-6576	175	4	n/p	ORG
ejpam-6576	176	1	5	CARDINAL
ejpam-6576	176	2	r(1	ORG
ejpam-6576	176	3	gx	ORG
ejpam-6576	178	1	r(1	ORG
ejpam-6576	182	1	j. pure	PERSON
ejpam-6576	182	2	18	CARDINAL
ejpam-6576	182	3	3	CARDINAL
ejpam-6576	182	4	2025	CARDINAL
ejpam-6576	182	5	6576 5	DATE
ejpam-6576	182	6	4	DATE
ejpam-6576	186	1	r(1	ORG
ejpam-6576	187	1	r(1	ORG
ejpam-6576	189	1	r(1	ORG
ejpam-6576	190	1	zero	CARDINAL
ejpam-6576	190	2	r(1	ORG
ejpam-6576	193	1	zero	CARDINAL
ejpam-6576	193	2	r(1	ORG
ejpam-6576	195	1	n and n/j	ORG
ejpam-6576	195	2	∈	ORG
ejpam-6576	196	1	zero	CARDINAL
ejpam-6576	196	2	r(1	ORG
ejpam-6576	197	1	1	CARDINAL
ejpam-6576	197	2	2	DATE
ejpam-6576	198	1	zero	CARDINAL
ejpam-6576	198	2	r(1	ORG
ejpam-6576	199	1	1	CARDINAL
ejpam-6576	200	1	1	CARDINAL
ejpam-6576	203	1	1	CARDINAL
ejpam-6576	210	1	y ∈ n	PERSON
ejpam-6576	212	1	⊆	CARDINAL
ejpam-6576	212	2	0 ̸= g1	WORK_OF_ART
ejpam-6576	212	3	g1	ORG
ejpam-6576	213	1	g1	ORG
ejpam-6576	214	1	i. lemma 2	PERSON
ejpam-6576	216	1	1	CARDINAL
ejpam-6576	218	1	r(1	ORG
ejpam-6576	218	2	g0	ORG
ejpam-6576	221	1	∈	ORG
ejpam-6576	229	1	hn ̸=	ORG
ejpam-6576	233	1	y ∈ n	PERSON
ejpam-6576	242	1	r(1	ORG
ejpam-6576	247	1	i. k.	PERSON
ejpam-6576	248	1	j. lakshminarayana et	PERSON
ejpam-6576	250	1	j. pure	PERSON
ejpam-6576	250	2	18	CARDINAL
ejpam-6576	250	3	3	CARDINAL
ejpam-6576	250	4	2025	CARDINAL
ejpam-6576	250	5	6576 6	DATE
ejpam-6576	250	6	7	CARDINAL
ejpam-6576	250	7	1	CARDINAL
ejpam-6576	254	1	j ⊆	LAW
ejpam-6576	255	1	j ̸⊆	LAW
ejpam-6576	257	1	r(1	ORG
ejpam-6576	257	2	0	CARDINAL
ejpam-6576	258	1	lemma 1	ORG
ejpam-6576	258	2	r(1	ORG
ejpam-6576	261	1	j ⊆	LAW
ejpam-6576	263	1	2	CARDINAL
ejpam-6576	266	1	1	CARDINAL
ejpam-6576	266	2	lemma 2	ORG
ejpam-6576	266	3	r(1	ORG
ejpam-6576	266	4	0)j	CARDINAL
ejpam-6576	267	1	0)j	CARDINAL
ejpam-6576	269	1	3	CARDINAL
ejpam-6576	273	1	2	CARDINAL
ejpam-6576	277	1	7	CARDINAL
ejpam-6576	277	2	3	CARDINAL
ejpam-6576	277	3	4	CARDINAL
ejpam-6576	280	1	7	CARDINAL
ejpam-6576	281	1	3	CARDINAL
ejpam-6576	283	1	6	CARDINAL
ejpam-6576	283	2	5	CARDINAL
ejpam-6576	283	3	8	CARDINAL
ejpam-6576	284	1	6	CARDINAL
ejpam-6576	285	1	5	CARDINAL
ejpam-6576	286	1	8	CARDINAL
ejpam-6576	291	1	j. pure	PERSON
ejpam-6576	291	2	18	CARDINAL
ejpam-6576	291	3	3	CARDINAL
ejpam-6576	291	4	2025	CARDINAL
ejpam-6576	291	5	6576 7	DATE
ejpam-6576	291	6	7	CARDINAL
ejpam-6576	291	7	1	CARDINAL
ejpam-6576	291	8	n. j. groenewald	PERSON
ejpam-6576	293	1	north-	NORP
ejpam-6576	293	2	137:97–100, 1987	DATE
ejpam-6576	294	1	2	CARDINAL
ejpam-6576	294	2	g. l. booth	PERSON
ejpam-6576	294	3	n. j. groenewald	PERSON
ejpam-6576	296	1	8:25–38, 1992	DATE
ejpam-6576	297	1	3	CARDINAL
ejpam-6576	297	2	n. j. groenewald	PERSON
ejpam-6576	299	1	137:1–14	CARDINAL
ejpam-6576	299	2	2013	DATE
ejpam-6576	300	1	4	CARDINAL
ejpam-6576	300	2	s. juglal	PERSON
ejpam-6576	300	3	n.j	GPE
ejpam-6576	302	1	17(1):887–904, 2010	DATE
ejpam-6576	303	1	5	CARDINAL
ejpam-6576	303	2	r. srinivasa rao	PERSON
ejpam-6576	303	3	s. veldsman	PERSON
ejpam-6576	305	1	30(1	CARDINAL
ejpam-6576	305	2	2019	DATE
ejpam-6576	306	1	6	CARDINAL
ejpam-6576	306	2	r. srinivasa	PERSON
ejpam-6576	306	3	rao kilaru	PERSON
ejpam-6576	306	4	j. lakshminarayana	PERSON
ejpam-6576	307	1	a. v. ramakrishna	PERSON
ejpam-6576	310	1	geom	PERSON
ejpam-6576	310	2	59(1):51–60	DATE
ejpam-6576	310	3	2018	DATE
ejpam-6576	311	1	7	CARDINAL
ejpam-6576	311	2	k. siva prasad r. srinivasa rao	PERSON
ejpam-6576	311	3	k. naga	PERSON
ejpam-6576	311	4	koteswara rao	PERSON
ejpam-6576	311	5	k jaya lakshmi narayana	ORG
ejpam-6576	313	1	32:1333–1339	CARDINAL
ejpam-6576	313	2	2021	DATE
ejpam-6576	314	1	8	CARDINAL
ejpam-6576	314	2	r. srinivasa	PERSON
ejpam-6576	314	3	rao kilaru	PERSON
ejpam-6576	314	4	j. lakshminarayana	PERSON
ejpam-6576	315	1	a. v. ramakrishna	PERSON
ejpam-6576	317	1	european journal	ORG
ejpam-6576	317	2	2024	DATE