id	sid	eid	entity	type
iajs-4071	1	1	363	CARDINAL
iajs-4071	1	2	2025	CARDINAL
iajs-4071	2	1	al-haitham	ORG
iajs-4071	2	2	university of baghdad	ORG
iajs-4071	3	1	4.0	CARDINAL
iajs-4071	3	2	nehmat k. ahmed 1	PERSON
iajs-4071	3	3	shaymaa m. mohammed	PERSON
iajs-4071	4	1	2	CARDINAL
iajs-4071	4	2	1,2	CARDINAL
iajs-4071	4	3	salahaddin university	ORG
iajs-4071	4	4	erbil	GPE
iajs-4071	4	5	iraq	GPE
iajs-4071	6	1	15	CARDINAL
iajs-4071	6	2	16 june 2025	DATE
iajs-4071	6	3	20 october 2025	DATE
iajs-4071	10	1	one	CARDINAL
iajs-4071	15	1	1	CARDINAL
iajs-4071	15	2	first	ORDINAL
iajs-4071	15	3	1	CARDINAL
iajs-4071	16	1	2011	DATE
iajs-4071	16	2	2	CARDINAL
iajs-4071	18	1	36	CARDINAL
iajs-4071	19	1	ahmad	PERSON
iajs-4071	19	2	b.	PERSON
iajs-4071	19	3	7	CARDINAL
iajs-4071	20	1	chen	PERSON
iajs-4071	21	1	das	GPE
iajs-4071	21	2	9	CARDINAL
iajs-4071	22	1	10	CARDINAL
iajs-4071	24	1	ihjpas	PERSON
iajs-4071	25	1	2025,38(4	TIME
iajs-4071	25	2	364	CARDINAL
iajs-4071	28	1	̃ ̃	ORG
iajs-4071	29	1	̃ ̃	ORG
iajs-4071	30	1	2.preliminaries 2.1	CARDINAL
iajs-4071	31	1	11	CARDINAL
iajs-4071	31	2	two	CARDINAL
iajs-4071	32	1	2.2	CARDINAL
iajs-4071	32	2	12	CARDINAL
iajs-4071	32	3	2.3	CARDINAL
iajs-4071	33	1	13	CARDINAL
iajs-4071	34	1	1	CARDINAL
iajs-4071	35	1	2.	CARDINAL
iajs-4071	36	1	3	CARDINAL
iajs-4071	36	2	2.4	CARDINAL
iajs-4071	37	1	13	CARDINAL
iajs-4071	37	2	1	CARDINAL
iajs-4071	39	1	2.	CARDINAL
iajs-4071	41	1	2.5	CARDINAL
iajs-4071	42	1	14	CARDINAL
iajs-4071	42	2	̃ ̃ ̃ ̃	ORG
iajs-4071	42	3	1	CARDINAL
iajs-4071	43	1	̃ ̃ ̃	ORG
iajs-4071	43	2	2	CARDINAL
iajs-4071	45	1	3	CARDINAL
iajs-4071	47	1	̃ ̃ ̃	ORG
iajs-4071	47	2	w	ORG
iajs-4071	49	1	2.6.	CARDINAL
iajs-4071	49	2	14	CARDINAL
iajs-4071	49	3	1	CARDINAL
iajs-4071	50	1	̃ ̃ ̃	ORG
iajs-4071	50	2	2	CARDINAL
iajs-4071	53	1	2.7.definition	CARDINAL
iajs-4071	57	1	ihjpas	PERSON
iajs-4071	58	1	2025,38(4	TIME
iajs-4071	59	1	2.8	CARDINAL
iajs-4071	64	1	2.9	CARDINAL
iajs-4071	64	2	15	CARDINAL
iajs-4071	72	1	2.10	CARDINAL
iajs-4071	72	2	13	CARDINAL
iajs-4071	72	3	14	CARDINAL
iajs-4071	72	4	15	CARDINAL
iajs-4071	72	5	16	CARDINAL
iajs-4071	72	6	17	CARDINAL
iajs-4071	73	1	̃ ̃ ̃) ̃ ̃	ORG
iajs-4071	73	2	̃ ̃	ORG
iajs-4071	73	3	̃ s.t. ̃ ) ̃	PERSON
iajs-4071	74	1	̃ ̃	ORG
iajs-4071	76	1	2.11	CARDINAL
iajs-4071	76	2	1	CARDINAL
iajs-4071	77	1	2	CARDINAL
iajs-4071	79	1	3	CARDINAL
iajs-4071	79	2	̃ ̃ ̃	ORG
iajs-4071	79	3	s.t ̃	PERSON
iajs-4071	81	1	2.12	CARDINAL
iajs-4071	81	2	15	CARDINAL
iajs-4071	86	1	2.13	CARDINAL
iajs-4071	87	1	14	CARDINAL
iajs-4071	87	2	̃ ̃	ORG
iajs-4071	90	1	1	CARDINAL
iajs-4071	91	1	2	CARDINAL
iajs-4071	96	1	ihjpas	PERSON
iajs-4071	97	1	2025,38(4	TIME
iajs-4071	98	1	366 2.14	CARDINAL
iajs-4071	99	1	15	CARDINAL
iajs-4071	99	2	̃ ̃	ORG
iajs-4071	100	1	̃ ̃	ORG
iajs-4071	101	1	2.15	CARDINAL
iajs-4071	101	2	18)a	CARDINAL
iajs-4071	101	3	̃ ̃	ORG
iajs-4071	101	4	1	CARDINAL
iajs-4071	103	1	2	CARDINAL
iajs-4071	104	1	3	CARDINAL
iajs-4071	106	1	4	CARDINAL
iajs-4071	108	1	5	CARDINAL
iajs-4071	109	1	6	CARDINAL
iajs-4071	111	1	8	CARDINAL
iajs-4071	115	1	10	CARDINAL
iajs-4071	117	1	2.16	CARDINAL
iajs-4071	118	1	16	CARDINAL
iajs-4071	119	1	2.17	CARDINAL
iajs-4071	120	1	16	CARDINAL
iajs-4071	121	1	2.18	CARDINAL
iajs-4071	121	2	19	CARDINAL
iajs-4071	121	3	1	CARDINAL
iajs-4071	122	1	2	CARDINAL
iajs-4071	123	1	2.19	CARDINAL
iajs-4071	124	1	10	CARDINAL
iajs-4071	125	1	2.20	CARDINAL
iajs-4071	125	2	14	CARDINAL
iajs-4071	125	3	̃ ̃	ORG
iajs-4071	125	4	iff ̃ ̃	ORG
iajs-4071	125	5	2.21	CARDINAL
iajs-4071	126	1	15	CARDINAL
iajs-4071	129	1	2.22	CARDINAL
iajs-4071	130	1	18	CARDINAL
iajs-4071	130	2	̃ ̃ )	ORG
iajs-4071	132	1	2.23	CARDINAL
iajs-4071	133	1	16	CARDINAL
iajs-4071	134	1	̃ ̃ ̃ ( ̃) )	ORG
iajs-4071	136	1	3.	CARDINAL
iajs-4071	139	1	3.1	CARDINAL
iajs-4071	141	1	̃ ̃ ̃	ORG
iajs-4071	142	1	3.2	CARDINAL
iajs-4071	146	1	3.1	CARDINAL
iajs-4071	146	2	ihjpas	PERSON
iajs-4071	147	1	2025,38(4	TIME
iajs-4071	147	2	367	CARDINAL
iajs-4071	147	3	1	CARDINAL
iajs-4071	148	1	2	CARDINAL
iajs-4071	148	2	3	CARDINAL
iajs-4071	148	3	4	CARDINAL
iajs-4071	149	1	two	CARDINAL
iajs-4071	160	1	two	CARDINAL
iajs-4071	161	1	1	CARDINAL
iajs-4071	161	2	̃ ̃ ̃ ̃	ORG
iajs-4071	161	3	2	CARDINAL
iajs-4071	161	4	3	CARDINAL
iajs-4071	161	5	̃ ̃ ̃ ̃	ORG
iajs-4071	162	1	4	CARDINAL
iajs-4071	163	1	3.3	CARDINAL
iajs-4071	164	1	1	CARDINAL
iajs-4071	166	1	2	CARDINAL
iajs-4071	169	1	3	CARDINAL
iajs-4071	171	1	4	CARDINAL
iajs-4071	173	1	5	CARDINAL
iajs-4071	175	1	6	CARDINAL
iajs-4071	177	1	7	CARDINAL
iajs-4071	179	1	8	CARDINAL
iajs-4071	181	1	9	CARDINAL
iajs-4071	183	1	ihjpas	PERSON
iajs-4071	184	1	2025,38(4	TIME
iajs-4071	185	1	368 10	DATE
iajs-4071	189	1	̃ ̃ ) ̃	ORG
iajs-4071	189	2	̃ ̃ ) ̃	ORG
iajs-4071	189	3	̃ ̃ ) ̃	ORG
iajs-4071	189	4	̃ ̃ ) ̃	ORG
iajs-4071	189	5	̃ ̃ )	ORG
iajs-4071	191	1	3.4.proposition	CARDINAL
iajs-4071	195	1	̃ ̃ ̃ ( ̃)then	ORG
iajs-4071	195	2	̃ ̃	ORG
iajs-4071	195	3	̃ ̃	ORG
iajs-4071	195	4	̃ ̃	ORG
iajs-4071	195	5	̃ ̃ ̃ ( ̃) ̃ ( ̃) ̃ ̃	ORG
iajs-4071	196	1	3.5	CARDINAL
iajs-4071	198	1	2.14	CARDINAL
iajs-4071	203	1	two	CARDINAL
iajs-4071	205	1	̃ ̃	ORG
iajs-4071	209	1	̃ ̃	ORG
iajs-4071	210	1	̃ ̃	ORG
iajs-4071	210	2	3.6	CARDINAL
iajs-4071	211	1	̃)is	CARDINAL
iajs-4071	211	2	two	CARDINAL
iajs-4071	214	1	̃ ̃	ORG
iajs-4071	220	1	s.t. ̃ ) ̃	PERSON
iajs-4071	225	1	3.7	CARDINAL
iajs-4071	234	1	2025,38(4	TIME
iajs-4071	235	1	369	CARDINAL
iajs-4071	237	1	̃ ̃	ORG
iajs-4071	240	1	̃ ̃	ORG
iajs-4071	241	1	3.8	CARDINAL
iajs-4071	242	1	3.9	CARDINAL
iajs-4071	243	1	1.	CARDINAL
iajs-4071	243	2	2	CARDINAL
iajs-4071	244	1	3.10	CARDINAL
iajs-4071	252	1	̃ ̃	ORG
iajs-4071	252	2	̃ ̃ ̃	ORG
iajs-4071	254	1	2.21	CARDINAL
iajs-4071	256	1	̃ ̃ ) ̃	ORG
iajs-4071	260	1	̃ ̃	ORG
iajs-4071	265	1	2.19	CARDINAL
iajs-4071	269	1	2.18(2	CARDINAL
iajs-4071	273	1	3.13.proposition	CARDINAL
iajs-4071	277	1	2.20	CARDINAL
iajs-4071	277	2	3.19	CARDINAL
iajs-4071	278	1	3.14	CARDINAL
iajs-4071	282	1	2.19	CARDINAL
iajs-4071	295	1	3.15	CARDINAL
iajs-4071	299	1	ihjpas	PERSON
iajs-4071	300	1	2025,38(4	TIME
iajs-4071	300	2	370	CARDINAL
iajs-4071	301	1	̃ ̃ ̃	ORG
iajs-4071	301	2	2.22	CARDINAL
iajs-4071	301	3	̃ ̃ ) ̃	ORG
iajs-4071	301	4	̃ ̃ ̃ ̃	ORG
iajs-4071	315	1	̃ ̃ ̃	ORG
iajs-4071	316	1	2.19	CARDINAL
iajs-4071	317	1	̃ ̃ ̃ ̃ ̃	ORG
iajs-4071	317	2	̃ ̃ ̃	ORG
iajs-4071	318	1	̃ ̃ ̃ ̃	ORG
iajs-4071	318	2	2.20	CARDINAL
iajs-4071	318	3	̃ ̃ ̃ ̃ ̃	ORG
iajs-4071	320	1	̃ ̃ ̃	ORG
iajs-4071	320	2	3.23	CARDINAL
iajs-4071	321	1	̃ ̃ ̃ ̃ ̃	ORG
iajs-4071	322	1	3.24	CARDINAL
iajs-4071	323	1	̃ ̃ ̃ ̃	ORG
iajs-4071	323	2	3.17	CARDINAL
iajs-4071	324	1	̃ ̃ ̃ ̃	ORG
iajs-4071	327	1	̃ ̃ ̃	ORG
iajs-4071	330	1	s.t.	PERSON
iajs-4071	331	1	̃ ̃ ̃	ORG
iajs-4071	331	2	3.26	CARDINAL
iajs-4071	332	1	3.24	CARDINAL
iajs-4071	334	1	̃ s.t.	PERSON
iajs-4071	335	1	̃ ̃ ̃ ̃	ORG
iajs-4071	335	2	̃ ̃ ̃ ( ̃	ORG
iajs-4071	339	1	̃ ̃ ̃ ̃	ORG
iajs-4071	339	2	ihjpas	PERSON
iajs-4071	340	1	2025,38(4	TIME
iajs-4071	340	2	371	CARDINAL
iajs-4071	341	1	̃ ̃ ̃	ORG
iajs-4071	341	2	2.19	CARDINAL
iajs-4071	341	3	̃ ̃ ̃ ̃	ORG
iajs-4071	342	1	̃ ̃ ̃ ( ̃	ORG
iajs-4071	345	1	3.23	CARDINAL
iajs-4071	346	1	̃ ̃ ̃ ( ̃	ORG
iajs-4071	347	1	̃ ̃ ̃ ̃	ORG
iajs-4071	348	1	4.	CARDINAL
iajs-4071	350	1	4.1.definition 4.1	CARDINAL
iajs-4071	352	1	s.t.	PERSON
iajs-4071	353	1	4.2	CARDINAL
iajs-4071	354	1	4.2	CARDINAL
iajs-4071	363	1	s.t.	PERSON
iajs-4071	367	1	̃ ̃ ̃	ORG
iajs-4071	370	1	s.t.	PERSON
iajs-4071	373	1	4.3	CARDINAL
iajs-4071	373	2	1	CARDINAL
iajs-4071	374	1	2	CARDINAL
iajs-4071	375	1	̃ ̃ ̃ c	ORG
iajs-4071	376	1	4.2	CARDINAL
iajs-4071	377	1	1	CARDINAL
iajs-4071	378	1	3.6	CARDINAL
iajs-4071	379	1	4.2	CARDINAL
iajs-4071	380	1	2	CARDINAL
iajs-4071	383	1	example 3.5	DATE
iajs-4071	385	1	1	CARDINAL
iajs-4071	385	2	example 3.5	DATE
iajs-4071	386	1	̃ ̃ ̃ c ̃	ORG
iajs-4071	387	1	o	DATE
iajs-4071	387	2	̃)but	PERSON
iajs-4071	387	3	̃ ̃ ̃ ̃ c ̃	ORG
iajs-4071	388	1	ihjpas	PERSON
iajs-4071	389	1	2025,38(4	TIME
iajs-4071	389	2	372 2	DATE
iajs-4071	390	1	example 3.5	DATE
iajs-4071	392	1	4.4.proposition	CARDINAL
iajs-4071	392	2	iff	ORG
iajs-4071	394	1	s.t	PERSON
iajs-4071	396	1	̃ ̃ ̃	ORG
iajs-4071	397	1	s.t.	PERSON
iajs-4071	400	1	s.t ̃	PERSON
iajs-4071	413	1	s.t.	PERSON
iajs-4071	415	1	4.2	CARDINAL
iajs-4071	416	1	4.5	CARDINAL
iajs-4071	416	2	̃ ̃	ORG
iajs-4071	417	1	1	CARDINAL
iajs-4071	418	1	2	CARDINAL
iajs-4071	419	1	3	CARDINAL
iajs-4071	420	1	3.8 4.6.proposition	CARDINAL
iajs-4071	421	1	̃ ̃	ORG
iajs-4071	422	1	4.2	CARDINAL
iajs-4071	422	2	3.18	CARDINAL
iajs-4071	423	1	4.8	CARDINAL
iajs-4071	423	2	̃ ̃	ORG
iajs-4071	425	1	4.2	CARDINAL
iajs-4071	425	2	3.14	CARDINAL
iajs-4071	427	1	1	CARDINAL
iajs-4071	428	1	2	CARDINAL
iajs-4071	429	1	3	CARDINAL
iajs-4071	430	1	3.15	CARDINAL
iajs-4071	432	1	̃ ̃	ORG
iajs-4071	433	1	1	CARDINAL
iajs-4071	433	2	iff	ORG
iajs-4071	434	1	2	CARDINAL
iajs-4071	434	2	iff	ORG
iajs-4071	435	1	1	CARDINAL
iajs-4071	435	2	2	CARDINAL
iajs-4071	435	3	3.16	CARDINAL
iajs-4071	435	4	4.2	CARDINAL
iajs-4071	436	1	ihjpas	PERSON
iajs-4071	437	1	2025,38(4	TIME
iajs-4071	437	2	373 5	DATE
iajs-4071	438	1	5.1.proposition	CARDINAL
iajs-4071	438	2	̃ ̃	ORG
iajs-4071	439	1	̃ ̃ ̃	ORG
iajs-4071	439	2	̃ ̃	ORG
iajs-4071	439	3	4.2	CARDINAL
iajs-4071	440	1	̃ ̃ ̃	ORG
iajs-4071	440	2	3.24	CARDINAL
iajs-4071	442	1	̃ ̃	ORG
iajs-4071	443	1	5.2.proposition	CARDINAL
iajs-4071	444	1	̃ ̃ ̃	ORG
iajs-4071	444	2	4.2	CARDINAL
iajs-4071	444	3	5.1	CARDINAL
iajs-4071	445	1	two	CARDINAL
iajs-4071	446	1	1	CARDINAL
iajs-4071	447	1	2	CARDINAL
iajs-4071	448	1	1	CARDINAL
iajs-4071	454	1	2	CARDINAL
iajs-4071	460	1	two	CARDINAL
iajs-4071	469	1	̃ ̃ ̃	ORG
iajs-4071	469	2	s.t.	PERSON
iajs-4071	471	1	s.t.	PERSON
iajs-4071	473	1	s.t	PERSON
iajs-4071	476	1	3.26	CARDINAL
iajs-4071	480	1	s.t	PERSON
iajs-4071	481	1	ihjpas	PERSON
iajs-4071	482	1	2025,38(4	TIME
iajs-4071	482	2	374	CARDINAL
iajs-4071	485	1	4.2	CARDINAL
iajs-4071	487	1	3.26	CARDINAL
iajs-4071	489	1	two	CARDINAL
iajs-4071	492	1	4.2	CARDINAL
iajs-4071	493	1	s.t.	PERSON
iajs-4071	499	1	̃ s.t.	PERSON
iajs-4071	503	1	3.26	CARDINAL
iajs-4071	503	2	two	CARDINAL
iajs-4071	504	1	4.2	CARDINAL
iajs-4071	505	1	5.8	CARDINAL
iajs-4071	507	1	̃ ̃ ̃	ORG
iajs-4071	509	1	̃ ̃	ORG
iajs-4071	509	2	s.t.	PERSON
iajs-4071	512	1	6	CARDINAL
iajs-4071	517	1	the university of salahaddin erbil	ORG
iajs-4071	518	1	ihjpas	PERSON
iajs-4071	519	1	2025,38(4	TIME
iajs-4071	519	2	375	CARDINAL
iajs-4071	520	1	1	CARDINAL
iajs-4071	521	1	molodtsov d. soft	PERSON
iajs-4071	521	2	first	ORDINAL
iajs-4071	523	1	1999;37:19–31	CARDINAL
iajs-4071	525	1	shabir m	PERSON
iajs-4071	525	2	naz m.	PERSON
iajs-4071	527	1	2011;61(7):1786–1799	CARDINAL
iajs-4071	528	1	3	CARDINAL
iajs-4071	529	1	al-shami	PERSON
iajs-4071	529	2	abu-gdairi r.	PERSON
iajs-4071	531	1	2023;11	CARDINAL
iajs-4071	531	2	840	CARDINAL
iajs-4071	532	1	math11040840 4	PERSON
iajs-4071	533	1	noori s	PERSON
iajs-4071	533	2	yousif yy	PERSON
iajs-4071	533	3	soft	PERSON
iajs-4071	534	1	iraqi journal of science	ORG
iajs-4071	535	1	2020;si(1):14	DATE
iajs-4071	536	1	5	CARDINAL
iajs-4071	537	1	yousif yy	PERSON
iajs-4071	537	2	hussain la	PERSON
iajs-4071	537	3	hussain ma	PERSON
iajs-4071	539	1	j interdiscip	PERSON
iajs-4071	540	1	2021;24:1925–1934	CARDINAL
iajs-4071	541	1	https.//doi.org/10.1080/09720502.2021.1966948 6	DATE
iajs-4071	542	1	al ghour s.	PERSON
iajs-4071	543	1	2023;29:317–328	CARDINAL
iajs-4071	544	1	ahmad b.	PERSON
iajs-4071	547	1	8	CARDINAL
iajs-4071	548	1	chen b.	PERSON
iajs-4071	549	1	mathematics & information sciences	ORG
iajs-4071	550	1	2013;7(1):287–294	CARDINAL
iajs-4071	550	2	9	CARDINAL
iajs-4071	550	3	das pk	PERSON
iajs-4071	551	1	j. 2014;54(2):221–236	PERSON
iajs-4071	552	1	yumak y	PERSON
iajs-4071	552	2	kaymakci ak	ORG
iajs-4071	554	1	2015;4:80–89	CARDINAL
iajs-4071	555	1	https.//arxiv.org/pdf/1312.6964 11	PRODUCT
iajs-4071	558	1	ibn alhaitham	ORG
iajs-4071	559	1	12	CARDINAL
iajs-4071	560	1	mohammad	PERSON
iajs-4071	560	2	r.	NORP
iajs-4071	561	1	ibn al-haitham	PERSON
iajs-4071	562	1	2020;33(4):122–136	CARDINAL
iajs-4071	563	1	13	CARDINAL
iajs-4071	564	1	mussa ys	PERSON
iajs-4071	564	2	khalaf ba	PERSON
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