id	sid	eid	entity	type
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m-1155	1	2	2992-4421	DATE
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m-1155	15	3	5	DATE
m-1155	15	4	6,7,8	CARDINAL
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m-1155	15	6	sunday	DATE
m-1155	15	7	ubong dominic department	ORG
m-1155	15	8	aksu uwakwe	PERSON
m-1155	15	9	ikoku university of education	ORG
m-1155	15	10	akwaibom state university	ORG
m-1155	15	11	akwaibom state	ORG
m-1155	15	12	nigeria ijo	ORG
m-1155	15	13	08	CARDINAL
m-1155	16	1	09 |	DATE
m-1155	16	2	september 2025	DATE
m-1155	17	1	38	CARDINAL
m-1155	17	2	ijo international journal of mathematics	ORG
m-1155	17	3	2992-4421	DATE
m-1155	18	1	thomas	PERSON
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m-1155	18	6	2025 ||	QUANTITY
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m-1155	19	3	6,7,8	CARDINAL
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m-1155	21	1	recent time	DATE
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m-1155	30	2	1	CARDINAL
m-1155	31	1	0-1 year	DATE
m-1155	31	2	2	CARDINAL
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m-1155	33	2	4	CARDINAL
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m-1155	35	1	09 |	DATE
m-1155	35	2	september 2025	DATE
m-1155	36	1	39	CARDINAL
m-1155	36	2	ijo international journal of mathematics	ORG
m-1155	36	3	2992-4421	DATE
m-1155	36	4	thomas	PERSON
m-1155	36	5	henry sylvester * https://ijojournals.com/	PERSON
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m-1155	36	7	09	CARDINAL
m-1155	36	8	september	DATE
m-1155	36	9	2025 ||	QUANTITY
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m-1155	41	2	1	CARDINAL
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m-1155	42	1	09 |	DATE
m-1155	42	2	september 2025	DATE
m-1155	43	1	40	CARDINAL
m-1155	43	2	ijo international journal of mathematics	ORG
m-1155	43	3	2992-4421	DATE
m-1155	43	4	thomas	PERSON
m-1155	43	5	henry sylvester * https://ijojournals.com/	PERSON
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m-1155	43	7	09	CARDINAL
m-1155	43	8	september	DATE
m-1155	43	9	2025 ||	QUANTITY
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m-1155	44	3	09	CARDINAL
m-1155	45	1	september 2025	DATE
m-1155	46	1	41	CARDINAL
m-1155	46	2	ijo international journal of mathematics	ORG
m-1155	46	3	2992-4421	DATE
m-1155	46	4	thomas	PERSON
m-1155	46	5	henry sylvester * https://ijojournals.com/	PERSON
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m-1155	46	7	09	CARDINAL
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m-1155	46	9	2025 ||	QUANTITY
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m-1155	47	12	2�2	QUANTITY
m-1155	47	13	2.6	CARDINAL
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m-1155	47	15	2	CARDINAL
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m-1155	47	23	3.3	CARDINAL
m-1155	47	24	08	CARDINAL
m-1155	48	1	09 |	DATE
m-1155	48	2	september 2025	DATE
m-1155	49	1	42	CARDINAL
m-1155	49	2	ijo international journal of mathematics	ORG
m-1155	49	3	2992-4421	DATE
m-1155	49	4	thomas	PERSON
m-1155	49	5	henry sylvester * https://ijojournals.com/	PERSON
m-1155	49	6	08	CARDINAL
m-1155	49	7	09	CARDINAL
m-1155	49	8	september	DATE
m-1155	49	9	2025 ||	QUANTITY
m-1155	50	1	1	CARDINAL
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m-1155	50	3	3.5	CARDINAL
m-1155	50	4	1	CARDINAL
m-1155	50	5	3.6	CARDINAL
m-1155	50	6	3.7	CARDINAL
m-1155	50	7	3.8	CARDINAL
m-1155	50	8	1	CARDINAL
m-1155	50	9	0	CARDINAL
m-1155	50	10	1	CARDINAL
m-1155	50	11	3.0	CARDINAL
m-1155	50	12	3.1	CARDINAL
m-1155	50	13	3.1	CARDINAL
m-1155	50	14	3.8	CARDINAL
m-1155	50	15	3.9	CARDINAL
m-1155	51	1	0	CARDINAL
m-1155	51	2	08	CARDINAL
m-1155	52	1	09 |	DATE
m-1155	52	2	september 2025	DATE
m-1155	53	1	43	CARDINAL
m-1155	53	2	ijo international journal of mathematics	ORG
m-1155	53	3	2992-4421	DATE
m-1155	53	4	thomas	PERSON
m-1155	53	5	henry sylvester * https://ijojournals.com/	PERSON
m-1155	53	6	08	CARDINAL
m-1155	53	7	09	CARDINAL
m-1155	53	8	september	DATE
m-1155	53	9	2025 ||	QUANTITY
m-1155	54	1	⎜ ⎜ ⎜ ⎜ ⎜	PERSON
m-1155	54	2	ℒ2 ℒ3	QUANTITY
m-1155	54	3	ℒ5	CARDINAL
m-1155	54	4	ℒ6	CARDINAL
m-1155	54	5	ℒ8 ⎠ ⎟ ⎟ ⎟ ⎟ ⎟	QUANTITY
m-1155	54	6	⎜ ⎜ ⎜ ⎜	PERSON
m-1155	54	7	⎜ ⎜ ⎜	PERSON
m-1155	54	8	1	CARDINAL
m-1155	54	9	1	CARDINAL
m-1155	54	10	3.10	CARDINAL
m-1155	54	11	20	CARDINAL
m-1155	54	12	0	CARDINAL
m-1155	54	13	second	ORDINAL
m-1155	54	14	0	CARDINAL
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m-1155	54	16	3.1	CARDINAL
m-1155	54	17	3.8)is	CARDINAL
m-1155	54	18	3.1	CARDINAL
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m-1155	55	2	0	CARDINAL
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m-1155	55	6	2	CARDINAL
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m-1155	57	2	2	CARDINAL
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m-1155	58	1	09 |	DATE
m-1155	58	2	september 2025	DATE
m-1155	59	1	44	CARDINAL
m-1155	59	2	ijo international journal of mathematics	ORG
m-1155	59	3	2992-4421	DATE
m-1155	60	1	thomas	PERSON
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m-1155	60	4	09	CARDINAL
m-1155	60	5	september	DATE
m-1155	60	6	2025 ||	QUANTITY
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m-1155	61	3	2	CARDINAL
m-1155	61	4	∈	ORG
m-1155	61	5	0	CARDINAL
m-1155	61	6	0	CARDINAL
m-1155	61	7	‖. ‖	ORG
m-1155	62	1	0	CARDINAL
m-1155	62	2	0	CARDINAL
m-1155	62	3	3.9	CARDINAL
m-1155	64	1	2	CARDINAL
m-1155	64	2	2	CARDINAL
m-1155	64	3	− k[℘](�)‖	PERSON
m-1155	65	1	2	CARDINAL
m-1155	66	1	2	CARDINAL
m-1155	66	2	2	CARDINAL
m-1155	67	1	2	CARDINAL
m-1155	67	2	− k[℘](�)‖	PERSON
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m-1155	67	4	2	CARDINAL
m-1155	67	5	1	CARDINAL
m-1155	67	6	2	CARDINAL
m-1155	67	7	08	CARDINAL
m-1155	68	1	09 |	DATE
m-1155	68	2	september 2025	DATE
m-1155	69	1	45	CARDINAL
m-1155	69	2	ijo international journal of mathematics	ORG
m-1155	69	3	2992-4421	DATE
m-1155	69	4	thomas	PERSON
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m-1155	70	3	09	CARDINAL
m-1155	70	4	september	DATE
m-1155	70	5	2025 ||	QUANTITY
m-1155	71	1	2	CARDINAL
m-1155	71	2	2	CARDINAL
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m-1155	71	4	ℒsatisfies	PERSON
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m-1155	72	1	+ 2	TIME
m-1155	72	2	2	CARDINAL
m-1155	73	1	− k[℘](�)‖	PERSON
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m-1155	74	2	2	CARDINAL
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m-1155	75	2	2	CARDINAL
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m-1155	76	2	3.1)-(3.8	DATE
m-1155	77	1	08	CARDINAL
m-1155	78	1	09 |	DATE
m-1155	78	2	september 2025	DATE
m-1155	79	1	46	CARDINAL
m-1155	79	2	ijo international journal of mathematics	ORG
m-1155	79	3	2992-4421	DATE
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m-1155	80	5	2025 ||	QUANTITY
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m-1155	85	1	φ ∈ s	PERSON
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m-1155	85	7	3	DATE
m-1155	85	8	8	CARDINAL
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m-1155	87	3	2	DATE
m-1155	87	4	3	DATE
m-1155	87	5	8	CARDINAL
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m-1155	87	7	08	CARDINAL
m-1155	88	1	09 |	DATE
m-1155	88	2	september 2025	DATE
m-1155	89	1	47	CARDINAL
m-1155	89	2	ijo international journal of mathematics	ORG
m-1155	89	3	2992-4421	DATE
m-1155	89	4	thomas	PERSON
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m-1155	89	7	09	CARDINAL
m-1155	89	8	september	DATE
m-1155	89	9	2025 ||	QUANTITY
m-1155	90	1	3.4	CARDINAL
m-1155	91	1	φ ∈	PERSON
m-1155	91	2	3.17	CARDINAL
m-1155	91	3	2(1	CARDINAL
m-1155	91	4	2	CARDINAL
m-1155	91	5	2	CARDINAL
m-1155	91	6	2(1	CARDINAL
m-1155	91	7	2	CARDINAL
m-1155	91	8	2	CARDINAL
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m-1155	91	11	2	CARDINAL
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m-1155	92	1	2(1	CARDINAL
m-1155	92	2	2	CARDINAL
m-1155	92	3	2	CARDINAL
m-1155	92	4	2	CARDINAL
m-1155	92	5	2	CARDINAL
m-1155	92	6	2	CARDINAL
m-1155	92	7	3.5	CARDINAL
m-1155	93	1	0	CARDINAL
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m-1155	94	2	∈s	ORG
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m-1155	95	2	08	CARDINAL
m-1155	96	1	09 |	DATE
m-1155	96	2	september 2025	DATE
m-1155	97	1	48	CARDINAL
m-1155	97	2	ijo international journal of mathematics	ORG
m-1155	97	3	2992-4421	DATE
m-1155	97	4	thomas	PERSON
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m-1155	98	2	08	CARDINAL
m-1155	98	3	09	CARDINAL
m-1155	98	4	september	DATE
m-1155	98	5	2025 ||	QUANTITY
m-1155	99	1	2(1	CARDINAL
m-1155	99	2	2	CARDINAL
m-1155	99	3	2	CARDINAL
m-1155	99	4	2	CARDINAL
m-1155	99	5	2(1	CARDINAL
m-1155	99	6	2	CARDINAL
m-1155	99	7	2	CARDINAL
m-1155	99	8	2	CARDINAL
m-1155	99	9	2(1	CARDINAL
m-1155	99	10	2	CARDINAL
m-1155	99	11	2(1	CARDINAL
m-1155	99	12	2	CARDINAL
m-1155	99	13	2	CARDINAL
m-1155	99	14	2(1	CARDINAL
m-1155	99	15	2	CARDINAL
m-1155	99	16	2	CARDINAL
m-1155	99	17	2	CARDINAL
m-1155	99	18	2	CARDINAL
m-1155	99	19	2	CARDINAL
m-1155	99	20	4.0	CARDINAL
m-1155	100	1	08	CARDINAL
m-1155	101	1	09 |	DATE
m-1155	101	2	september 2025	DATE
m-1155	102	1	49	CARDINAL
m-1155	102	2	ijo international journal of mathematics	ORG
m-1155	102	3	2992-4421	DATE
m-1155	102	4	thomas	PERSON
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m-1155	102	6	08	CARDINAL
m-1155	102	7	09	CARDINAL
m-1155	102	8	september	DATE
m-1155	102	9	2025 ||	QUANTITY
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m-1155	104	2	3.8	CARDINAL
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m-1155	107	2	4.1.1	CARDINAL
m-1155	107	3	4.1.2	CARDINAL
m-1155	107	4	4.1.3	CARDINAL
m-1155	107	5	1	CARDINAL
m-1155	107	6	4.1.5	CARDINAL
m-1155	107	7	4.1.7	CARDINAL
m-1155	107	8	08	CARDINAL
m-1155	108	1	09 |	DATE
m-1155	108	2	september 2025	DATE
m-1155	109	1	50	CARDINAL
m-1155	109	2	ijo international journal of mathematics	ORG
m-1155	109	3	2992-4421	DATE
m-1155	109	4	thomas	PERSON
m-1155	109	5	henry sylvester * https://ijojournals.com/	PERSON
m-1155	109	6	08	CARDINAL
m-1155	109	7	09	CARDINAL
m-1155	109	8	september	DATE
m-1155	109	9	2025 ||	QUANTITY
m-1155	111	1	2	CARDINAL
m-1155	111	2	2	CARDINAL
m-1155	111	3	1	CARDINAL
m-1155	111	4	1(0	CARDINAL
m-1155	111	5	1	CARDINAL
m-1155	111	6	2(0	CARDINAL
m-1155	111	7	1	CARDINAL
m-1155	111	8	2 ��1�1 +	QUANTITY
m-1155	111	9	2	CARDINAL
m-1155	111	10	2	CARDINAL
m-1155	111	11	4.2.2	CARDINAL
m-1155	111	12	1	CARDINAL
m-1155	111	13	4.2.3	DATE
m-1155	111	14	1	CARDINAL
m-1155	111	15	2	CARDINAL
m-1155	111	16	2	CARDINAL
m-1155	111	17	1	CARDINAL
m-1155	111	18	2(1	CARDINAL
m-1155	112	1	1(0	CARDINAL
m-1155	112	2	1	CARDINAL
m-1155	112	3	4.2.5	CARDINAL
m-1155	112	4	2(0	CARDINAL
m-1155	112	5	1	CARDINAL
m-1155	112	6	2(1	CARDINAL
m-1155	112	7	2	CARDINAL
m-1155	112	8	2�2	QUANTITY
m-1155	112	9	1	CARDINAL
m-1155	112	10	2	CARDINAL
m-1155	112	11	3	CARDINAL
m-1155	112	12	4,2.7	CARDINAL
m-1155	112	13	08	CARDINAL
m-1155	113	1	09 |	DATE
m-1155	113	2	september 2025	DATE
m-1155	114	1	51	CARDINAL
m-1155	114	2	ijo international journal of mathematics	ORG
m-1155	114	3	2992-4421	DATE
m-1155	114	4	thomas	PERSON
m-1155	114	5	henry sylvester * https://ijojournals.com/	PERSON
m-1155	114	6	08	CARDINAL
m-1155	114	7	09	CARDINAL
m-1155	114	8	september	DATE
m-1155	114	9	2025 ||	QUANTITY
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m-1155	115	5	8)	CARDINAL
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m-1155	115	12	2 ��1�1 +	QUANTITY
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m-1155	115	32	7	CARDINAL
m-1155	115	33	1	CARDINAL
m-1155	115	34	2	CARDINAL
m-1155	115	35	3	CARDINAL
m-1155	115	36	08	CARDINAL
m-1155	116	1	09 |	DATE
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m-1155	121	5	1	CARDINAL
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m-1155	122	1	1 �2 ∑	QUANTITY
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m-1155	124	1	09 |	DATE
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m-1155	127	1	09 |	DATE
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m-1155	130	1	09 |	DATE
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m-1155	131	2	ijo international journal of mathematics	ORG
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m-1155	132	5	2025 ||	QUANTITY
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m-1155	135	1	09 |	DATE
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m-1155	137	5	september	DATE
m-1155	137	6	2025 ||	QUANTITY
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m-1155	139	1	09 |	DATE
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m-1155	140	5	2025 ||	QUANTITY
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m-1155	143	5	2025 ||	QUANTITY
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m-1155	154	1	09 |	DATE
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m-1155	157	7	1)}{1	CARDINAL
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m-1155	157	10	1	CARDINAL
m-1155	157	11	1)}{1	CARDINAL
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m-1155	158	1	09 |	DATE
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m-1155	158	3	62	CARDINAL
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m-1155	159	5	2025 ||	QUANTITY
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m-1155	187	1	2023	CARDINAL
m-1155	187	2	10	CARDINAL
m-1155	187	3	20499361231161936	DATE
m-1155	187	4	2023 march 28	DATE
m-1155	188	1	10.1177/20499361231161936 3	CARDINAL
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m-1155	190	3	2020	DATE
m-1155	191	1	bmc infect dis 2022	ORG
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m-1155	191	3	46	CARDINAL
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m-1155	196	6	3	CARDINAL
m-1155	196	7	2024	DATE
m-1155	196	8	391-404 8	CARDINAL
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m-1155	197	2	j. i. uwakwe	PERSON
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m-1155	199	2	sunday	DATE
m-1155	199	3	2015	DATE
m-1155	199	4	08	CARDINAL
m-1155	199	5	09 |	DATE
m-1155	199	6	september 2025	DATE
m-1155	199	7	64 https://www.ncbi.nlm.nih.gov/pmc/articles/pmc7312233/ https://www.ncbi.nlm.nih.gov/pmc/articles/pmc7312233/	QUANTITY
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m-1155	200	1	https://scholar.google.com/scholar_lookup?journal=bmc+infect+dis&title=diphtheria+resurgence+in+sada%e2%80%99a-yemen,+2017%e2%80%932020&author=aa+al-dar&author=m+al-qassimi&author=fh+ezzadeen&volume=22&publication_year=2022&pages=46&pmid=35016630& https://www.cdc.gov/diphtheria	ORG
m-1155	200	2	ijo international journal of mathematics	ORG
m-1155	200	3	2992-4421	DATE
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m-1155	201	4	09	CARDINAL
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m-1155	201	6	2025 ||	QUANTITY
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m-1155	208	3	8	CARDINAL
m-1155	208	4	8, august	DATE
m-1155	208	5	2023	CARDINAL
m-1155	208	6	2165	DATE
m-1155	208	7	11	CARDINAL
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m-1155	209	2	sunday	DATE
m-1155	210	1	sci. &engg	ORG
m-1155	211	1	appls	PERSON
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m-1155	214	1	september, 2014	DATE
m-1155	215	1	217	CARDINAL
m-1155	216	1	sunday	DATE
m-1155	216	2	inyama simeon chioma	PERSON
m-1155	216	3	2012	DATE
m-1155	216	4	mathematics and statistics 8 (	ORG
m-1155	216	5	2	CARDINAL
m-1155	216	6	248	CARDINAL
m-1155	216	7	2012	DATE
m-1155	216	8	13	CARDINAL
m-1155	217	1	sunday	DATE
m-1155	217	2	inyama	ORG
m-1155	217	3	first	ORDINAL
m-1155	217	4	the nigerian association of mathematical physics	ORG
m-1155	217	5	24	CARDINAL
m-1155	217	6	2013	DATE
m-1155	217	7	257-260	QUANTITY
m-1155	217	8	14	CARDINAL
m-1155	218	1	sunday	DATE
m-1155	218	2	sampson	GPE
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m-1155	218	4	2278-5728	ORG
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