id	sid	eid	entity	type
cana-756	1	1	1074	CARDINAL
cana-756	2	1	3s	CARDINAL
cana-756	2	2	2024	CARDINAL
cana-756	2	3	156	CARDINAL
cana-756	3	1	krishna murty1	PERSON
cana-756	3	2	k.chennakesavulu2	GPE
cana-756	3	3	c. jaya subba	PERSON
cana-756	3	4	reddy3 krishnamurty.vadrevu@gmail.com1	PERSON
cana-756	3	5	intell.chenna@gmail.com2	ORG
cana-756	3	6	1research	CARDINAL
cana-756	3	7	tirupati	GPE
cana-756	3	8	andhra pradesh	ORG
cana-756	3	9	india	GPE
cana-756	4	1	2professor	CARDINAL
cana-756	4	2	anantapur	GPE
cana-756	4	3	andhra pradesh	ORG
cana-756	4	4	india	GPE
cana-756	5	1	3professor	CARDINAL
cana-756	5	2	s. v. university, tirupati	ORG
cana-756	5	3	andhra pradesh	ORG
cana-756	5	4	india	GPE
cana-756	6	1	05-04-2024	CARDINAL
cana-756	6	2	25	CARDINAL
cana-756	6	3	10-06-2024	CARDINAL
cana-756	7	1	𝜎	ORG
cana-756	7	2	r.	NORP
cana-756	7	3	𝐷2	ORG
cana-756	7	4	two	CARDINAL
cana-756	7	5	𝐷1	DATE
cana-756	7	6	𝐷2	CARDINAL
cana-756	8	1	two	CARDINAL
cana-756	8	2	r. keywords	PERSON
cana-756	9	1	1.	CARDINAL
cana-756	9	2	m. bresar	PERSON
cana-756	9	3	j. vukman	PERSON
cana-756	10	1	14	CARDINAL
cana-756	11	1	posner	ORG
cana-756	11	2	first	ORDINAL
cana-756	12	1	9	CARDINAL
cana-756	13	1	m. ashraf	PERSON
cana-756	14	1	13	CARDINAL
cana-756	14	2	k. kaya et al	PERSON
cana-756	15	1	12	CARDINAL
cana-756	16	1	j.c. chang	PERSON
cana-756	17	1	11	CARDINAL
cana-756	18	1	argac et al	PERSON
cana-756	19	1	17	CARDINAL
cana-756	20	1	n. aydin	PERSON
cana-756	20	2	18	CARDINAL
cana-756	20	3	argac	ORG
cana-756	21	1	10	CARDINAL
cana-756	22	1	m.n.	GPE
cana-756	23	1	15	CARDINAL
cana-756	23	2	c. jaya subba reddy et al	FAC
cana-756	24	1	2,4	CARDINAL
cana-756	26	1	1	CARDINAL
cana-756	27	1	16	CARDINAL
cana-756	27	2	3,6	CARDINAL
cana-756	28	1	c. jaya subba reddy et al	FAC
cana-756	29	1	7	CARDINAL
cana-756	29	2	bi-(𝜎,𝜏)derivations	ORG
cana-756	30	1	bi(𝜎	PERSON
cana-756	30	2	6	CARDINAL
cana-756	31	1	1074	CARDINAL
cana-756	32	1	3s	CARDINAL
cana-756	32	2	2024	CARDINAL
cana-756	32	3	157	CARDINAL
cana-756	32	4	2	CARDINAL
cana-756	33	1	𝑢𝑅𝑢	NORP
cana-756	33	2	0	CARDINAL
cana-756	33	3	0	CARDINAL
cana-756	33	4	2-torsion	QUANTITY
cana-756	33	5	2𝑢	CARDINAL
cana-756	34	1	0	CARDINAL
cana-756	34	2	0	CARDINAL
cana-756	34	3	𝜎	ORG
cana-756	34	4	r.	NORP
cana-756	34	5	𝑑(𝑣)𝜎(𝑢	GPE
cana-756	34	6	+ 𝜏(𝑣)𝑑(𝑢	GPE
cana-756	37	1	𝜏)derivation	ORG
cana-756	39	1	+ 𝜏(𝑣)𝑑(𝑢	GPE
cana-756	40	1	d1(u	PERSON
cana-756	41	1	ud1(v	NORP
cana-756	41	2	w	GPE
cana-756	41	3	+ d1(u	PERSON
cana-756	41	4	w)v	GPE
cana-756	41	5	∀ u	GPE
cana-756	41	6	w ∈ r.	PERSON
cana-756	42	1	w	ORG
cana-756	43	1	w	GPE
cana-756	43	2	∀ u	GPE
cana-756	43	3	w ∈ r.	PERSON
cana-756	43	4	1	CARDINAL
cana-756	44	1	w)v + ud1(v	PERSON
cana-756	44	2	δ1(v	ORG
cana-756	44	3	+ vd1(u	DATE
cana-756	44	4	w	GPE
cana-756	44	5	∀ u	PERSON
cana-756	44	6	w ∈ r.	PERSON
cana-756	44	7	w	ORG
cana-756	44	8	δ1(v	ORG
cana-756	44	9	+ τ(v)d1(u	GPE
cana-756	44	10	w	GPE
cana-756	44	11	∀ u	GPE
cana-756	44	12	w ∈ r.	PERSON
cana-756	44	13	two	CARDINAL
cana-756	44	14	w	GPE
cana-756	44	15	0	CARDINAL
cana-756	44	16	w ∈ r.	PERSON
cana-756	44	17	two	CARDINAL
cana-756	44	18	v)rδ2(v	ORG
cana-756	44	19	w	ORG
cana-756	44	20	0	CARDINAL
cana-756	44	21	w ∈ r.	PERSON
cana-756	44	22	2-torsion-free	QUANTITY
cana-756	44	23	σ	ORG
cana-756	44	24	r.	NORP
cana-756	46	1	two	CARDINAL
cana-756	46	2	σδ2 = δ2σ	PERSON
cana-756	47	1	1	CARDINAL
cana-756	48	1	2	CARDINAL
cana-756	48	2	1074	CARDINAL
cana-756	49	1	3s	CARDINAL
cana-756	49	2	2024	CARDINAL
cana-756	49	3	158	CARDINAL
cana-756	49	4	0	CARDINAL
cana-756	49	5	0	CARDINAL
cana-756	49	6	𝑢𝑟𝑣 + 𝑣𝑟𝑢	LOC
cana-756	49	7	0	CARDINAL
cana-756	49	8	0	CARDINAL
cana-756	50	1	2	CARDINAL
cana-756	50	2	2	CARDINAL
cana-756	50	3	5	CARDINAL
cana-756	51	1	two	CARDINAL
cana-756	51	2	0	CARDINAL
cana-756	51	3	∀ u	PERSON
cana-756	51	4	∈	ORG
cana-756	51	5	w	GPE
cana-756	51	6	0	CARDINAL
cana-756	51	7	∀ u	PERSON
cana-756	51	8	w ∈ r. lemma 3	PERSON
cana-756	52	1	1	CARDINAL
cana-756	52	2	2	CARDINAL
cana-756	53	1	1.two	CARDINAL
cana-756	54	1	2.d1(u	CARDINAL
cana-756	55	1	0	CARDINAL
cana-756	55	2	∀ u	GPE
cana-756	55	3	w ∈ r. lemma 4	PERSON
cana-756	55	4	2	CARDINAL
cana-756	56	1	two	CARDINAL
cana-756	56	2	0	CARDINAL
cana-756	57	1	𝐷2	ORG
cana-756	58	1	𝐷1	DATE
cana-756	58	2	𝐷2	ORG
cana-756	58	3	𝐷1(𝑢	NORP
cana-756	58	4	𝑣)𝑟𝐷2(𝑣	GPE
cana-756	58	5	0	CARDINAL
cana-756	58	6	∈ 𝑅 𝐷1(𝐷1(𝑢	ORG
cana-756	58	7	0	CARDINAL
cana-756	58	8	𝑣)	ORG
cana-756	59	1	𝑤))𝐷1(𝑟	ORG
cana-756	60	1	𝐷1(𝐷1(𝑢	DATE
cana-756	60	2	𝜎𝐷1	ORDINAL
cana-756	60	3	𝜏𝐷2 = 𝐷2𝜏	PERSON
cana-756	60	4	𝜎	ORG
cana-756	60	5	𝐷1(𝐷2(𝑣	GPE
cana-756	61	1	𝐷1(𝑟	WORK_OF_ART
cana-756	61	2	𝐷1(𝐷1(𝑢	DATE
cana-756	62	1	𝐷2	ORG
cana-756	62	2	𝐷1𝐷2(𝑣	GPE
cana-756	63	1	𝐷1𝐷2(𝑣	ORG
cana-756	63	2	0 𝐷1𝐷2(𝑣	PERCENT
cana-756	63	3	𝑤)𝑟𝐷1𝐷2(𝑣	ORG
cana-756	63	4	0 𝐷1𝐷2(𝑣	PERCENT
cana-756	64	1	r.	NORP
cana-756	64	2	0	CARDINAL
cana-756	65	1	𝐷2	ORG
cana-756	65	2	two	CARDINAL
cana-756	65	3	0	CARDINAL
cana-756	67	1	𝐷2(𝑢	GPE
cana-756	67	2	1074	CARDINAL
cana-756	68	1	3s	CARDINAL
cana-756	68	2	2024	CARDINAL
cana-756	68	3	159	CARDINAL
cana-756	69	1	𝑚)𝜎(𝐷2(𝑣	ORG
cana-756	70	1	+ 𝜏(𝜎(𝑢))𝐷1(𝐷2(𝑣	DATE
cana-756	72	1	𝜎𝐷2	ORG
cana-756	72	2	𝜏𝐷2 = 𝐷2𝜏	PERSON
cana-756	72	3	𝜎	ORG
cana-756	72	4	𝐷2	CARDINAL
cana-756	72	5	𝐷2(𝑢	GPE
cana-756	72	6	𝑤)𝐷1(𝑣	GPE
cana-756	73	1	𝐷2	CARDINAL
cana-756	73	2	𝐷2(𝑢	GPE
cana-756	73	3	𝑤)𝐷1(𝑣	GPE
cana-756	74	1	0	CARDINAL
cana-756	74	2	3	CARDINAL
cana-756	74	3	𝐷2	ORG
cana-756	75	1	3	CARDINAL
cana-756	75	2	1	CARDINAL
cana-756	75	3	two	CARDINAL
cana-756	76	1	δ1(v	ORG
cana-756	76	2	w	GPE
cana-756	76	3	0	CARDINAL
cana-756	76	4	∀ u	GPE
cana-756	76	5	w	GPE
cana-756	76	6	∈	ORG
cana-756	76	7	δ1(v	ORG
cana-756	76	8	w	GPE
cana-756	76	9	0	CARDINAL
cana-756	76	10	∀ u	GPE
cana-756	76	11	w	GPE
cana-756	76	12	∈	ORG
cana-756	76	13	r.	NORP
cana-756	76	14	r.	NORP
cana-756	76	15	v)rδ2(v	ORG
cana-756	76	16	w	ORG
cana-756	77	1	v)rδ1(v	PERSON
cana-756	77	2	w	GPE
cana-756	77	3	3.1	CARDINAL
cana-756	78	1	1	CARDINAL
cana-756	78	2	3.2	CARDINAL
cana-756	79	1	0	CARDINAL
cana-756	82	1	0	CARDINAL
cana-756	83	1	3.2	CARDINAL
cana-756	83	2	∈	ORG
cana-756	83	3	3.2	CARDINAL
cana-756	84	1	0	CARDINAL
cana-756	85	1	σ	ORG
cana-756	86	1	0	CARDINAL
cana-756	86	2	∀ u	GPE
cana-756	86	3	w ∈ r.	PERSON
cana-756	86	4	3.1	CARDINAL
cana-756	86	5	0	CARDINAL
cana-756	86	6	∀ u	GPE
cana-756	86	7	w ∈ r.	PERSON
cana-756	86	8	1074	CARDINAL
cana-756	87	1	3s	CARDINAL
cana-756	87	2	2024	CARDINAL
cana-756	87	3	160	CARDINAL
cana-756	87	4	0	CARDINAL
cana-756	87	5	3.3	CARDINAL
cana-756	87	6	∈	ORG
cana-756	87	7	3.3	CARDINAL
cana-756	89	1	0	CARDINAL
cana-756	90	1	3.3	CARDINAL
cana-756	90	2	σ	ORG
cana-756	90	3	0	CARDINAL
cana-756	90	4	∀ u	GPE
cana-756	91	1	1	CARDINAL
cana-756	91	2	w	ORG
cana-756	91	3	3.4	CARDINAL
cana-756	91	4	w)d1(u	ORG
cana-756	92	1	3.5	CARDINAL
cana-756	92	2	v)rδ2(v	ORG
cana-756	92	3	w	ORG
cana-756	93	1	v)rδ1(v	PERSON
cana-756	93	2	w	GPE
cana-756	93	3	w ∈ r.	PERSON
cana-756	93	4	3.6	CARDINAL
cana-756	93	5	lemma	ORG
cana-756	93	6	1	CARDINAL
cana-756	94	1	0	CARDINAL
cana-756	94	2	∀ u	PERSON
cana-756	95	1	3.7	CARDINAL
cana-756	95	2	∈	ORG
cana-756	95	3	3.7	CARDINAL
cana-756	95	4	3.6	CARDINAL
cana-756	95	5	v)δ1(v	PERSON
cana-756	95	6	0	CARDINAL
cana-756	95	7	∀ u	GPE
cana-756	95	8	w	GPE
cana-756	95	9	∈	ORG
cana-756	95	10	v)δ1(v	PERSON
cana-756	95	11	v)δ1(v	PERSON
cana-756	96	1	0	CARDINAL
cana-756	97	1	3.8	CARDINAL
cana-756	97	2	3.8	CARDINAL
cana-756	97	3	3.8	CARDINAL
cana-756	97	4	0	CARDINAL
cana-756	97	5	w	GPE
cana-756	97	6	r. d2(u	PERSON
cana-756	97	7	0	CARDINAL
cana-756	98	1	σ	ORG
cana-756	99	1	δ1(v	ORG
cana-756	99	2	w	GPE
cana-756	99	3	∀ u	PERSON
cana-756	99	4	w	GPE
cana-756	99	5	∈	ORG
cana-756	99	6	3.9	CARDINAL
cana-756	99	7	1	CARDINAL
cana-756	99	8	d2(u	GPE
cana-756	99	9	v)δ1(v	PERSON
cana-756	99	10	δ1(v	ORG
cana-756	99	11	w)d2(u	DATE
cana-756	99	12	w ∈ r.	PERSON
cana-756	99	13	3.10	CARDINAL
cana-756	99	14	3.5	CARDINAL
cana-756	99	15	3.10	CARDINAL
cana-756	100	1	v)δ1(v	PERSON
cana-756	101	1	0	CARDINAL
cana-756	103	1	v)δ2	PERSON
cana-756	103	2	δ1(v	ORG
cana-756	103	3	w	GPE
cana-756	103	4	3.11	CARDINAL
cana-756	103	5	v)δ2	PERSON
cana-756	103	6	δ1(v	ORG
cana-756	103	7	w	GPE
cana-756	103	8	0	CARDINAL
cana-756	104	1	3.12	CARDINAL
cana-756	104	2	r.	NORP
cana-756	104	3	∈	ORG
cana-756	104	4	3.11	CARDINAL
cana-756	104	5	3.12	CARDINAL
cana-756	104	6	1074	CARDINAL
cana-756	105	1	3s	CARDINAL
cana-756	105	2	2024	CARDINAL
cana-756	105	3	w	GPE
cana-756	105	4	0	CARDINAL
cana-756	105	5	w	GPE
cana-756	105	6	∈	ORG
cana-756	105	7	σ	ORG
cana-756	105	8	v)rδ2	PERSON
cana-756	105	9	v)rδ1(v	PERSON
cana-756	105	10	0	CARDINAL
cana-756	105	11	w	GPE
cana-756	105	12	∈	ORG
cana-756	105	13	lemma 1	ORG
cana-756	106	1	2	CARDINAL
cana-756	106	2	two	CARDINAL
cana-756	106	3	v)δ2	PERSON
cana-756	107	1	w	ORG
cana-756	108	1	r.	NORP
cana-756	108	2	v)rδ2(v	ORG
cana-756	108	3	w	ORG
cana-756	108	4	0	CARDINAL
cana-756	109	1	v)rδ2(v	ORG
cana-756	109	2	w	ORG
cana-756	111	1	0	CARDINAL
cana-756	111	2	w ∈ r.	PERSON
cana-756	111	3	lemma1	ORG
cana-756	111	4	3.13	CARDINAL
cana-756	111	5	3.5	CARDINAL
cana-756	111	6	1	CARDINAL
cana-756	112	1	0	CARDINAL
cana-756	114	1	w ∈ r. conversely	PERSON
cana-756	114	2	v)δ2	PERSON
cana-756	114	3	0	CARDINAL
cana-756	114	4	w ∈ r.	PERSON
cana-756	114	5	3.14	CARDINAL
cana-756	114	6	v)δ2	PERSON
cana-756	115	1	0	CARDINAL
cana-756	116	1	3.14	CARDINAL
cana-756	116	2	3.15	CARDINAL
cana-756	116	3	3.15	CARDINAL
cana-756	116	4	3.14	CARDINAL
cana-756	117	1	0	CARDINAL
cana-756	118	1	σ	ORG
cana-756	118	2	w	ORG
cana-756	118	3	0	CARDINAL
cana-756	118	4	w	GPE
cana-756	118	5	∈	ORG
cana-756	119	1	3	CARDINAL
cana-756	119	2	two	CARDINAL
cana-756	119	3	v)δ2	PERSON
cana-756	120	1	r.	NORP
cana-756	120	2	v)rδ2(v	ORG
cana-756	120	3	w	ORG
cana-756	120	4	0 and so δ1(u	DATE
cana-756	120	5	0	CARDINAL
cana-756	121	1	1	CARDINAL
cana-756	121	2	0	CARDINAL
cana-756	121	3	3.4	CARDINAL
cana-756	121	4	theorem1	ORG
cana-756	121	5	1074	CARDINAL
cana-756	122	1	3s	CARDINAL
cana-756	122	2	2024	CARDINAL
cana-756	122	3	162	CARDINAL
cana-756	123	1	w	GPE
cana-756	124	1	w	GPE
cana-756	124	2	δ1(d1(u	ORG
cana-756	124	3	+ τ(d1(u	GPE
cana-756	125	1	w	GPE
cana-756	126	1	σδ2 = δ2σ	PERSON
cana-756	126	2	σ	ORG
cana-756	126	3	δ1(d1(u	ORG
cana-756	126	4	w	GPE
cana-756	128	1	+ rd1(u	GPE
cana-756	128	2	w	GPE
cana-756	128	3	0	CARDINAL
cana-756	129	1	3.16	CARDINAL
cana-756	129	2	δ1(d1(u	ORG
cana-756	129	3	w	ORG
cana-756	129	4	2	CARDINAL
cana-756	129	5	0	CARDINAL
cana-756	129	6	w	GPE
cana-756	129	7	∈	ORG
cana-756	129	8	3.16	CARDINAL
cana-756	129	9	w	GPE
cana-756	130	1	0	CARDINAL
cana-756	130	2	w ∈ r.	PERSON
cana-756	130	3	w	GPE
cana-756	130	4	w	GPE
cana-756	130	5	w	ORG
cana-756	130	6	0	CARDINAL
cana-756	131	1	3.17	CARDINAL
cana-756	131	2	uδ2(v	GPE
cana-756	131	3	w	GPE
cana-756	131	4	3.17	CARDINAL
cana-756	131	5	d1(δ2(v	ORG
cana-756	131	6	w	GPE
cana-756	131	7	+ τ(δ2(v	GPE
cana-756	131	8	w	GPE
cana-756	132	1	d1(u	PERSON
cana-756	132	2	w	ORG
cana-756	132	3	0	CARDINAL
cana-756	133	1	3.17	CARDINAL
cana-756	133	2	σ	ORG
cana-756	133	3	d1(δ2(v	ORG
cana-756	133	4	w	GPE
cana-756	133	5	w	ORG
cana-756	133	6	0	CARDINAL
cana-756	133	7	w ∈	ORG
cana-756	133	8	d1δ2(v	ORG
cana-756	133	9	w	GPE
cana-756	133	10	d1δ2(v	ORG
cana-756	133	11	d1δ2(v	ORG
cana-756	133	12	w	GPE
cana-756	133	13	0	CARDINAL
cana-756	134	1	the semiprime ness of r	ORG
cana-756	135	1	two	CARDINAL
cana-756	135	2	first	ORDINAL
cana-756	136	1	v)rδ2(v	ORG
cana-756	136	2	w	ORG
cana-756	136	3	0	CARDINAL
cana-756	136	4	w ∈ r.	PERSON
cana-756	136	5	lemma 1	ORG
cana-756	136	6	0	CARDINAL
cana-756	137	1	3.18	CARDINAL
cana-756	137	2	∈	ORG
cana-756	137	3	3.18	CARDINAL
cana-756	137	4	w	GPE
cana-756	137	5	0	CARDINAL
cana-756	137	6	w	GPE
cana-756	137	7	∈	ORG
cana-756	137	8	σ	ORG
cana-756	137	9	v)r δ2(v	ORG
cana-756	137	10	w	ORG
cana-756	137	11	0	CARDINAL
cana-756	137	12	w	GPE
cana-756	137	13	∈	ORG
cana-756	137	14	3.19	CARDINAL
cana-756	137	15	∈	ORG
cana-756	137	16	3.19	CARDINAL
cana-756	137	17	σ	ORG
cana-756	137	18	1074	CARDINAL
cana-756	138	1	3s	CARDINAL
cana-756	138	2	2024	CARDINAL
cana-756	138	3	163	CARDINAL
cana-756	138	4	v)r δ2(v	ORG
cana-756	138	5	0	CARDINAL
cana-756	139	1	3.9	CARDINAL
cana-756	139	2	2	CARDINAL
cana-756	139	3	2	CARDINAL
cana-756	139	4	first	ORDINAL
cana-756	139	5	three	CARDINAL
cana-756	139	6	zero	CARDINAL
cana-756	140	1	0	CARDINAL
cana-756	140	2	∈	ORG
cana-756	140	3	0	CARDINAL
cana-756	141	1	d1(u	PERSON
cana-756	141	2	wd2(v	DATE
cana-756	141	3	wd2(u	DATE
cana-756	141	4	wd2(v	DATE
cana-756	141	5	w	GPE
cana-756	142	1	0	CARDINAL
cana-756	142	2	lemma 2	ORG
cana-756	143	1	lemma 4	ORG
cana-756	144	1	two	CARDINAL
cana-756	145	1	v)δ2	PERSON
cana-756	147	1	3.20	CARDINAL
cana-756	147	2	0	CARDINAL
cana-756	148	1	d1δ2(uv	ORG
cana-756	148	2	w	GPE
cana-756	148	3	d1(δ2(uv	ORG
cana-756	148	4	w	GPE
cana-756	148	5	w	GPE
cana-756	148	6	∈	ORG
cana-756	148	7	w	GPE
cana-756	149	1	σ	ORG
cana-756	150	1	+ vd2(u	DATE
cana-756	150	2	w	GPE
cana-756	150	3	=d1(u	PERSON
cana-756	150	4	w	GPE
cana-756	151	1	w	ORG
cana-756	151	2	w	GPE
cana-756	151	3	+ τ(d2(u	DATE
cana-756	151	4	w	GPE
cana-756	151	5	∈	ORG
cana-756	151	6	σ	ORG
cana-756	152	1	=d1(u	PERSON
cana-756	152	2	+ ud1(δ2(v	GPE
cana-756	152	3	w	GPE
cana-756	153	1	w	GPE
cana-756	154	1	w	ORG
cana-756	154	2	+ d2(u	GPE
cana-756	154	3	∀ u	PERSON
cana-756	154	4	w	GPE
cana-756	154	5	∈	ORG
cana-756	154	6	3.21	CARDINAL
cana-756	155	1	lemma 4	ORG
cana-756	155	2	0	CARDINAL
cana-756	156	1	0	CARDINAL
cana-756	156	2	∀ u	GPE
cana-756	156	3	w	GPE
cana-756	156	4	∈ r. therefore	PERSON
cana-756	156	5	3.21	CARDINAL
cana-756	156	6	w	GPE
cana-756	156	7	w	GPE
cana-756	156	8	w	GPE
cana-756	156	9	∈	ORG
cana-756	158	1	3.22	CARDINAL
cana-756	158	2	1074	CARDINAL
cana-756	159	1	3s	CARDINAL
cana-756	159	2	2024	CARDINAL
cana-756	159	3	164	CARDINAL
cana-756	159	4	∈	ORG
cana-756	159	5	3.22	CARDINAL
cana-756	159	6	σ	ORG
cana-756	159	7	w	ORG
cana-756	160	1	0	CARDINAL
cana-756	161	1	3.22	CARDINAL
cana-756	161	2	∀ u	GPE
cana-756	161	3	∈	ORG
cana-756	161	4	1	CARDINAL
cana-756	161	5	δ2(v1	PERSON
cana-756	161	6	w)d1(u	ORG
cana-756	162	1	d1(u	PERSON
cana-756	162	2	d1(u	PERSON
cana-756	163	1	3.23	CARDINAL
cana-756	163	2	3.20	CARDINAL
cana-756	163	3	3.23	CARDINAL
cana-756	163	4	w	ORG
cana-756	164	1	2	CARDINAL
cana-756	165	1	4	CARDINAL
cana-756	165	2	two	CARDINAL
cana-756	167	1	1	CARDINAL
cana-756	167	2	2	CARDINAL
cana-756	167	3	1	CARDINAL
cana-756	167	4	0	CARDINAL
cana-756	168	1	two	CARDINAL
cana-756	168	2	r.	NORP
cana-756	168	3	v)rδ2	PERSON
cana-756	168	4	0	CARDINAL
cana-756	168	5	∀ u	GPE
cana-756	168	6	w	GPE
cana-756	168	7	∈	ORG
cana-756	168	8	lemma 1	ORG
cana-756	168	9	0	CARDINAL
cana-756	168	10	∈	ORG
cana-756	168	11	v)δ2	PERSON
cana-756	168	12	v)δ2	ORG
cana-756	169	1	0	CARDINAL
cana-756	170	1	3.24	CARDINAL
cana-756	170	2	∈	ORG
cana-756	170	3	3.24	CARDINAL
cana-756	170	4	0 δ1(u	DATE
cana-756	170	5	v)δ2	ORG
cana-756	170	6	0	CARDINAL
cana-756	170	7	∀ u	GPE
cana-756	170	8	w	GPE
cana-756	170	9	∈	ORG
cana-756	170	10	3.25	CARDINAL
cana-756	170	11	σ	ORG
cana-756	170	12	3.1	CARDINAL
cana-756	170	13	3.9	CARDINAL
cana-756	170	14	3.5	CARDINAL
cana-756	170	15	first	ORDINAL
cana-756	170	16	three	CARDINAL
cana-756	170	17	zero	CARDINAL
cana-756	170	18	3.25	CARDINAL
cana-756	170	19	0	CARDINAL
cana-756	170	20	∀ u	GPE
cana-756	170	21	w	GPE
cana-756	170	22	∈	ORG
cana-756	170	23	r)ud1(r	ORG
cana-756	170	24	0	CARDINAL
cana-756	170	25	∀ u	GPE
cana-756	170	26	w	GPE
cana-756	170	27	∈	ORG
cana-756	171	1	0	CARDINAL
cana-756	171	2	0	CARDINAL
cana-756	171	3	2	CARDINAL
cana-756	171	4	0	CARDINAL
cana-756	171	5	∀ u	GPE
cana-756	171	6	w	GPE
cana-756	171	7	∈	ORG
cana-756	171	8	lemma1	PERSON
cana-756	172	1	0	CARDINAL
cana-756	172	2	∀ u	GPE
cana-756	172	3	∈	ORG
cana-756	172	4	3.26	CARDINAL
cana-756	173	1	1074	CARDINAL
cana-756	174	1	3s	CARDINAL
cana-756	174	2	2024	CARDINAL
cana-756	174	3	165	CARDINAL
cana-756	174	4	two	CARDINAL
cana-756	174	5	r.	NORP
cana-756	174	6	3.4	CARDINAL
cana-756	174	7	1	CARDINAL
cana-756	175	1	0	CARDINAL
cana-756	175	2	∀ u	GPE
cana-756	175	3	w	GPE
cana-756	175	4	∈	ORG
cana-756	176	1	0	CARDINAL
cana-756	176	2	∀ u	GPE
cana-756	176	3	w	GPE
cana-756	176	4	∈	ORG
cana-756	176	5	w	GPE
cana-756	178	1	w	GPE
cana-756	178	2	0 δ2(d1(u	PERSON
cana-756	178	3	w	GPE
cana-756	179	1	+ τ(d1(u	GPE
cana-756	179	2	w	GPE
cana-756	180	1	v)d2	ORG
cana-756	180	2	w	GPE
cana-756	181	1	0	CARDINAL
cana-756	182	1	σ	ORG
cana-756	182	2	δ2(d1(u	PERSON
cana-756	182	3	m)r δ2(v	ORG
cana-756	182	4	0	CARDINAL
cana-756	182	5	∀ u	GPE
cana-756	182	6	w	GPE
cana-756	182	7	∈	ORG
cana-756	182	8	w	ORG
cana-756	183	1	0	CARDINAL
cana-756	183	2	wδ2(v	ORG
cana-756	183	3	w	GPE
cana-756	183	4	v)r δ2(d1(u	GPE
cana-756	184	1	v)r d1(u	PERSON
cana-756	185	1	0	CARDINAL
cana-756	186	1	v)r δ2d1(u	LOC
cana-756	186	2	0	CARDINAL
cana-756	186	3	∀ u	GPE
cana-756	186	4	w	GPE
cana-756	186	5	∈	ORG
cana-756	186	6	v)r δ2d1(u	FAC
cana-756	186	7	v)r δ2d1(u	LOC
cana-756	187	1	0	CARDINAL
cana-756	191	1	0	CARDINAL
cana-756	192	1	3.9	CARDINAL
cana-756	192	2	1	CARDINAL
cana-756	192	3	δ1(v	ORG
cana-756	192	4	w	GPE
cana-756	192	5	0	CARDINAL
cana-756	192	6	∀ u	GPE
cana-756	192	7	w	GPE
cana-756	192	8	∈	ORG
cana-756	192	9	w)rd2(u	DATE
cana-756	192	10	0	CARDINAL
cana-756	192	11	∀ u	GPE
cana-756	192	12	w	GPE
cana-756	192	13	∈	ORG
cana-756	192	14	δ1(rd2(u	PERSON
cana-756	192	15	m)σ(δ1(v	ORG
cana-756	192	16	w	GPE
cana-756	194	1	w	PERSON
cana-756	194	2	δ1(d2(u	PERSON
cana-756	194	3	w	GPE
cana-756	195	1	+ τ(d2(u	DATE
cana-756	195	2	m)σ(δ1(v	ORG
cana-756	195	3	w	GPE
cana-756	196	1	w	PERSON
cana-756	196	2	0	CARDINAL
cana-756	196	3	∀ u	GPE
cana-756	196	4	w	GPE
cana-756	196	5	∈	ORG
cana-756	196	6	τd2 =	PERSON
cana-756	196	7	σ	ORG
cana-756	196	8	δ1(d2(u	PERSON
cana-756	196	9	+ d2(u	GPE
cana-756	196	10	w	PERSON
cana-756	197	1	w	GPE
cana-756	197	2	0	CARDINAL
cana-756	197	3	∀ u	GPE
cana-756	197	4	w	GPE
cana-756	197	5	∈	ORG
cana-756	197	6	3.26	CARDINAL
cana-756	197	7	δ1(d2(u	PERSON
cana-756	197	8	0	CARDINAL
cana-756	197	9	1074	CARDINAL
cana-756	198	1	3s	CARDINAL
cana-756	198	2	2024	CARDINAL
cana-756	198	3	166	CARDINAL
cana-756	198	4	δ1d2(u	PERSON
cana-756	198	5	v)rδ1(v	PERSON
cana-756	198	6	w	GPE
cana-756	198	7	0	CARDINAL
cana-756	198	8	∀ u	GPE
cana-756	198	9	w	GPE
cana-756	198	10	∈	ORG
cana-756	198	11	w	ORG
cana-756	198	12	wd2(u	DATE
cana-756	198	13	σ	ORG
cana-756	198	14	δ1d2(u	PERSON
cana-756	198	15	v)rδ1(v	PERSON
cana-756	198	16	d2(u	GPE
cana-756	198	17	v))w	PRODUCT
cana-756	199	1	v)rd2(u	PERSON
cana-756	199	2	1	CARDINAL
cana-756	199	3	0	CARDINAL
cana-756	199	4	∀ u	GPE
cana-756	199	5	w	GPE
cana-756	199	6	∈	ORG
cana-756	199	7	3.26	CARDINAL
cana-756	199	8	δ1d2(u	PERSON
cana-756	199	9	v)rδ1(v	PERSON
cana-756	199	10	d2(u	GPE
cana-756	199	11	v))w	PRODUCT
cana-756	199	12	0	CARDINAL
cana-756	199	13	δ1d2(u	PERSON
cana-756	199	14	v)rδ1(v	PERSON
cana-756	199	15	d2(u	GPE
cana-756	199	16	v)rδ1(v	PERSON
cana-756	199	17	d2(u	GPE
cana-756	200	1	0	CARDINAL
cana-756	200	2	δ1d2(u	PERSON
cana-756	200	3	v)rδ1(v	PERSON
cana-756	200	4	d2(u	GPE
cana-756	201	1	v)rδ1(d2(u	PERSON
cana-756	201	2	δ1d2(u	PERSON
cana-756	201	3	0	CARDINAL
cana-756	201	4	0	CARDINAL
cana-756	202	1	1	CARDINAL
cana-756	202	2	two	CARDINAL
cana-756	202	3	r.	NORP
cana-756	202	4	3.9	CARDINAL
cana-756	202	5	1	CARDINAL
cana-756	202	6	δ1(v	ORG
cana-756	202	7	w	GPE
cana-756	202	8	w	PERSON
cana-756	203	1	σ	ORG
cana-756	203	2	+ d2(u	GPE
cana-756	203	3	w	PERSON
cana-756	204	1	0	CARDINAL
cana-756	205	1	3.1	CARDINAL
cana-756	205	2	3.10	CARDINAL
cana-756	205	3	first	ORDINAL
cana-756	205	4	two	CARDINAL
cana-756	205	5	zero	CARDINAL
cana-756	206	1	0 d2(u	PERCENT
cana-756	206	2	w)rd2(u	DATE
cana-756	206	3	0	CARDINAL
cana-756	206	4	∀ u	GPE
cana-756	206	5	w	GPE
cana-756	206	6	∈	ORG
cana-756	207	1	w ∈ r.	PERSON
cana-756	207	2	3.27	CARDINAL
cana-756	207	3	w))d2δ1(v	PERSON
cana-756	207	4	w	GPE
cana-756	207	5	w	ORG
cana-756	207	6	w)d2(u	DATE
cana-756	208	1	0	CARDINAL
cana-756	209	1	3.27	CARDINAL
cana-756	209	2	w	GPE
cana-756	209	3	w	ORG
cana-756	210	1	0	CARDINAL
cana-756	210	2	w	ORG
cana-756	210	3	0	CARDINAL
cana-756	210	4	w ∈ r. hence	PERSON
cana-756	210	5	1	CARDINAL
cana-756	210	6	0	CARDINAL
cana-756	211	1	2	CARDINAL
cana-756	211	2	1074	CARDINAL
cana-756	212	1	3s	CARDINAL
cana-756	212	2	2024	CARDINAL
cana-756	212	3	167	CARDINAL
cana-756	212	4	w	ORG
cana-756	212	5	0	CARDINAL
cana-756	212	6	∀ u	GPE
cana-756	212	7	w	GPE
cana-756	212	8	∈	ORG
cana-756	212	9	w	GPE
cana-756	213	1	0	CARDINAL
cana-756	213	2	∀ u	GPE
cana-756	213	3	w	GPE
cana-756	213	4	∈	ORG
cana-756	213	5	δ1(δ2(v	ORG
cana-756	213	6	w	ORG
cana-756	213	7	+ τ(δ2(v	GPE
cana-756	213	8	w))d1(r,	ORG
cana-756	213	9	1	CARDINAL
cana-756	214	1	w	GPE
cana-756	214	2	0	CARDINAL
cana-756	214	3	σ	ORG
cana-756	214	4	r. δ1(δ2(v	PERSON
cana-756	214	5	w	ORG
cana-756	214	6	+ rδ2(v	DATE
cana-756	214	7	w	GPE
cana-756	215	1	3.5	CARDINAL
cana-756	215	2	1	CARDINAL
cana-756	215	3	two	CARDINAL
cana-756	215	4	zero	CARDINAL
cana-756	216	1	0	CARDINAL
cana-756	217	1	w	ORG
cana-756	217	2	w	GPE
cana-756	217	3	w	ORG
cana-756	217	4	w	GPE
cana-756	218	1	r.	NORP
cana-756	219	1	0	CARDINAL
cana-756	220	1	1	CARDINAL
cana-756	220	2	0	CARDINAL
cana-756	220	3	∀ u	GPE
cana-756	220	4	w	GPE
cana-756	220	5	∈	ORG
cana-756	220	6	δ2(δ2(u	ORG
cana-756	220	7	w	PERSON
cana-756	221	1	0	CARDINAL
cana-756	221	2	∀ u	GPE
cana-756	221	3	w	GPE
cana-756	221	4	∈ r.	PERSON
cana-756	222	1	4	CARDINAL
cana-756	226	1	w	GPE
cana-756	227	1	two	CARDINAL
cana-756	227	2	σ	ORG
cana-756	228	1	two	CARDINAL
cana-756	228	2	δ1,d1	NORP
cana-756	228	3	𝐷2	ORG
cana-756	228	4	two	CARDINAL
cana-756	233	1	1074	CARDINAL
cana-756	234	1	3s	CARDINAL
cana-756	234	2	2024	CARDINAL
cana-756	234	3	168	CARDINAL
cana-756	235	1	one	CARDINAL
cana-756	237	1	5	CARDINAL
cana-756	240	1	1	CARDINAL
cana-756	240	2	a. ali	PERSON
cana-756	240	3	d. filippis	PERSON
cana-756	240	4	f. shujat	PERSON
cana-756	240	5	mathematical bechak	PERSON
cana-756	240	6	66(4	CARDINAL
cana-756	240	7	2014	DATE
cana-756	240	8	410–417	CARDINAL
cana-756	241	1	2	CARDINAL
cana-756	241	2	c. jaya subba reddy	FAC
cana-756	241	3	7(2	CARDINAL
cana-756	241	4	2019),117–120	CARDINAL
cana-756	242	1	3	CARDINAL
cana-756	242	2	c. jaya subba reddy	FAC
cana-756	242	3	2016),423–428	CARDINAL
cana-756	243	1	4	CARDINAL
cana-756	243	2	c. jaya subba reddy	FAC
cana-756	243	3	b. ramoorthy reddy	PERSON
cana-756	243	4	4(1)(2017	CARDINAL
cana-756	243	5	21–27	CARDINAL
cana-756	244	1	5	CARDINAL
cana-756	244	2	c.jaya subba reddy	PERSON
cana-756	244	3	2016	CARDINAL
cana-756	244	4	22	CARDINAL
cana-756	245	1	6	CARDINAL
cana-756	245	2	c.jaya subba reddy	PERSON
cana-756	245	3	reddy	ORG
cana-756	245	4	σ	ORG
cana-756	245	5	8(6	CARDINAL
cana-756	245	6	2018	DATE
cana-756	245	7	45	CARDINAL
cana-756	246	1	7	CARDINAL
cana-756	246	2	c.jaya subba reddy	PERSON
cana-756	246	3	2024	CARDINAL
cana-756	246	4	5133-5138	DATE
cana-756	247	1	8	CARDINAL
cana-756	247	2	c.jaya subba reddy	PERSON
cana-756	248	1	krishna murty	PERSON
cana-756	248	2	15	CARDINAL
cana-756	248	3	4)1,(2024),2028	CARDINAL
cana-756	249	1	9	CARDINAL
cana-756	249	2	proc.amer.mth.soc.	GPE
cana-756	249	3	1093-1100	CARDINAL
cana-756	250	1	10	CARDINAL
cana-756	250	2	e. koc	PERSON
cana-756	250	3	σ	ORG
cana-756	250	4	east asian	NORP
cana-756	250	5	mathematical journal	ORG
cana-756	250	6	24(4	CARDINAL
cana-756	250	7	2008	DATE
cana-756	250	8	389–398	CARDINAL
cana-756	251	1	11	CARDINAL
cana-756	252	1	taiwanese	NORP
cana-756	252	2	j. math.7(1)(2003),103-113	PERSON
cana-756	253	1	12	CARDINAL
cana-756	253	2	k. kaya	PERSON
cana-756	253	3	e. guven	PERSON
cana-756	253	4	m. soyturk	PERSON
cana-756	253	5	mathematics,13(3	PERSON
cana-756	253	6	2006	DATE
cana-756	253	7	189–195	CARDINAL
cana-756	254	1	13	CARDINAL
cana-756	254	2	m. ashraf	PERSON
cana-756	254	3	archivum mathematicum	PERSON
cana-756	254	4	38(4	CARDINAL
cana-756	254	5	2002	DATE
cana-756	254	6	259–264	CARDINAL
cana-756	255	1	14	CARDINAL
cana-756	255	2	m. bresar	PERSON
cana-756	255	3	posner	ORG
cana-756	255	4	radovi mathematicki	PERSON
cana-756	255	5	5	CARDINAL
cana-756	255	6	237	CARDINAL
cana-756	256	1	15	CARDINAL
cana-756	256	2	m. n. daif	PERSON
cana-756	256	3	m. t. el-sayiad	PERSON
cana-756	256	4	jmi international journal of mathematical sciences	ORG
cana-756	256	5	1(1	CARDINAL
cana-756	256	6	2010	DATE
cana-756	256	7	23–34	CARDINAL
cana-756	257	1	16	CARDINAL
cana-756	257	2	m. n. daif	PERSON
cana-756	257	3	m. s. t. el-sayiad	PERSON
cana-756	257	4	jordan	GPE
cana-756	257	5	oriental journal	ORG
cana-756	257	6	2(2	CARDINAL
cana-756	257	7	2010	DATE
cana-756	258	1	17	CARDINAL
cana-756	258	2	a. nakajima	PERSON
cana-756	258	3	e. albaş	PERSON
cana-756	258	4	turkish	NORP
cana-756	258	5	28(2	GPE
cana-756	258	6	2004	DATE
cana-756	259	1	185–194	CARDINAL
cana-756	260	1	18	CARDINAL
cana-756	260	2	o. golbaşi	PERSON
cana-756	260	3	n. aydin	PERSON
cana-756	260	4	σ	ORG
cana-756	260	5	siberian mathematical journal	ORG
cana-756	260	6	2007	DATE
cana-756	260	7	979	CARDINAL