id	sid	eid	entity	type
ejpam-5844	1	1	european journal	ORG
ejpam-5844	1	2	2025	DATE
ejpam-5844	1	3	18	CARDINAL
ejpam-5844	1	4	2	CARDINAL
ejpam-5844	1	5	5844	CARDINAL
ejpam-5844	1	6	new york	GPE
ejpam-5844	1	7	ahmad al-natoor1,∗	PERSON
ejpam-5844	1	8	rawan al-smadi2	PERSON
ejpam-5844	1	9	burqan2 1	ORG
ejpam-5844	1	10	isra university	ORG
ejpam-5844	1	11	amman	GPE
ejpam-5844	1	12	jordan 2	ORG
ejpam-5844	1	13	zarqa university	ORG
ejpam-5844	1	14	13110	DATE
ejpam-5844	1	15	jordan	PERSON
ejpam-5844	4	1	2020	DATE
ejpam-5844	4	2	15a60 15a42	DATE
ejpam-5844	4	3	15a16	CARDINAL
ejpam-5844	4	4	1	CARDINAL
ejpam-5844	5	1	n × n	LOC
ejpam-5844	6	1	∈	ORG
ejpam-5844	7	1	∈	ORG
ejpam-5844	8	1	1	CARDINAL
ejpam-5844	8	2	2	CARDINAL
ejpam-5844	8	3	y ∈ mn	PERSON
ejpam-5844	8	4	1	CARDINAL
ejpam-5844	8	5	1	CARDINAL
ejpam-5844	8	6	2	DATE
ejpam-5844	9	1	1	CARDINAL
ejpam-5844	10	1	2	CARDINAL
ejpam-5844	10	2	2	CARDINAL
ejpam-5844	11	1	3	CARDINAL
ejpam-5844	11	2	4	CARDINAL
ejpam-5844	11	3	5	CARDINAL
ejpam-5844	11	4	6	CARDINAL
ejpam-5844	13	1	ahmad.alnatoor@iu.edu.jo	PERSON
ejpam-5844	13	2	a. al-natoor	PERSON
ejpam-5844	13	3	r. al-smadi	PERSON
ejpam-5844	13	4	a. burqan	PERSON
ejpam-5844	14	1	1	CARDINAL
ejpam-5844	14	2	2025	CARDINAL
ejpam-5844	15	1	a. al-natoor	PERSON
ejpam-5844	15	2	r. al-smadi	PERSON
ejpam-5844	15	3	a. burqan	PERSON
ejpam-5844	16	1	j. pure	PERSON
ejpam-5844	16	2	18	CARDINAL
ejpam-5844	16	3	2	CARDINAL
ejpam-5844	16	4	2025	CARDINAL
ejpam-5844	16	5	5844 2	DATE
ejpam-5844	16	6	10 2	CARDINAL
ejpam-5844	16	7	sj(b	NORP
ejpam-5844	16	8	3	CARDINAL
ejpam-5844	16	9	1	CARDINAL
ejpam-5844	16	10	2n	CARDINAL
ejpam-5844	17	1	1	CARDINAL
ejpam-5844	19	1	j = 1	WORK_OF_ART
ejpam-5844	19	2	2n	CARDINAL
ejpam-5844	20	1	max	PERSON
ejpam-5844	20	2	y ⊕	PERSON
ejpam-5844	21	1	y ⊕	PERSON
ejpam-5844	22	1	1	CARDINAL
ejpam-5844	23	1	∈	ORG
ejpam-5844	23	2	g(t	NORP
ejpam-5844	25	1	j = 1	WORK_OF_ART
ejpam-5844	25	2	2n	CARDINAL
ejpam-5844	30	1	0	CARDINAL
ejpam-5844	34	1	0	CARDINAL
ejpam-5844	36	1	a)a2	PRODUCT
ejpam-5844	36	2	b)b2	ORG
ejpam-5844	38	1	b)b2	ORG
ejpam-5844	39	1	0	CARDINAL
ejpam-5844	44	1	0	CARDINAL
ejpam-5844	46	1	4	CARDINAL
ejpam-5844	46	2	1	CARDINAL
ejpam-5844	47	1	a. al-natoor	PERSON
ejpam-5844	47	2	r. al-smadi	PERSON
ejpam-5844	47	3	a. burqan	PERSON
ejpam-5844	48	1	j. pure	PERSON
ejpam-5844	48	2	18	CARDINAL
ejpam-5844	48	3	2	CARDINAL
ejpam-5844	48	4	2025	CARDINAL
ejpam-5844	48	5	5844 3	DATE
ejpam-5844	49	1	0	CARDINAL
ejpam-5844	51	1	0	CARDINAL
ejpam-5844	52	1	ab ba	PERSON
ejpam-5844	53	1	0	CARDINAL
ejpam-5844	53	2	max	PERSON
ejpam-5844	56	1	∈	ORG
ejpam-5844	56	2	0	CARDINAL
ejpam-5844	57	1	0	CARDINAL
ejpam-5844	57	2	0	CARDINAL
ejpam-5844	63	1	5	CARDINAL
ejpam-5844	63	2	3	CARDINAL
ejpam-5844	63	3	4	CARDINAL
ejpam-5844	63	4	5	CARDINAL
ejpam-5844	64	1	2	CARDINAL
ejpam-5844	65	1	8]let	CARDINAL
ejpam-5844	66	1	j = 1	WORK_OF_ART
ejpam-5844	66	2	2n	CARDINAL
ejpam-5844	68	1	a. al-natoor	PERSON
ejpam-5844	68	2	r. al-smadi	PERSON
ejpam-5844	68	3	a. burqan	PERSON
ejpam-5844	69	1	j. pure	PERSON
ejpam-5844	69	2	18	CARDINAL
ejpam-5844	69	3	2	CARDINAL
ejpam-5844	69	4	2025	CARDINAL
ejpam-5844	69	5	5844 4	DATE
ejpam-5844	69	6	10	CARDINAL
ejpam-5844	70	1	∈	ORG
ejpam-5844	70	2	g(t	NORP
ejpam-5844	72	1	j = 1	WORK_OF_ART
ejpam-5844	72	2	2n	CARDINAL
ejpam-5844	73	1	max	PERSON
ejpam-5844	75	1	6	CARDINAL
ejpam-5844	76	1	1	CARDINAL
ejpam-5844	76	2	4	CARDINAL
ejpam-5844	78	1	0	CARDINAL
ejpam-5844	78	2	lemma 2	ORG
ejpam-5844	78	3	max	PERSON
ejpam-5844	79	1	⊕	GPE
ejpam-5844	80	1	max	PERSON
ejpam-5844	80	2	ab ba	ORG
ejpam-5844	81	1	7	CARDINAL
ejpam-5844	81	2	3	CARDINAL
ejpam-5844	81	3	7	CARDINAL
ejpam-5844	82	1	6	CARDINAL
ejpam-5844	82	2	2	CARDINAL
ejpam-5844	83	1	1	CARDINAL
ejpam-5844	83	2	2	CARDINAL
ejpam-5844	83	3	2	CARDINAL
ejpam-5844	84	1	2	CARDINAL
ejpam-5844	85	1	3	CARDINAL
ejpam-5844	86	1	9]let	CARDINAL
ejpam-5844	86	2	∈	ORG
ejpam-5844	87	1	j = 1	WORK_OF_ART
ejpam-5844	87	2	2n	CARDINAL
ejpam-5844	89	1	1	CARDINAL
ejpam-5844	91	1	j = 1	WORK_OF_ART
ejpam-5844	91	2	2n	CARDINAL
ejpam-5844	92	1	0	CARDINAL
ejpam-5844	92	2	max	PERSON
ejpam-5844	93	1	+ 1 2 ∥∥a2	QUANTITY
ejpam-5844	94	1	a. al-natoor	PERSON
ejpam-5844	94	2	r. al-smadi	PERSON
ejpam-5844	94	3	a. burqan	PERSON
ejpam-5844	95	1	j. pure	PERSON
ejpam-5844	95	2	18	CARDINAL
ejpam-5844	95	3	2	CARDINAL
ejpam-5844	95	4	2025	CARDINAL
ejpam-5844	95	5	5844 5	DATE
ejpam-5844	95	6	10	CARDINAL
ejpam-5844	96	1	6	CARDINAL
ejpam-5844	97	1	0	CARDINAL
ejpam-5844	97	2	max	PERSON
ejpam-5844	97	3	max	PERSON
ejpam-5844	97	4	0	CARDINAL
ejpam-5844	98	1	max	PERSON
ejpam-5844	98	2	0	CARDINAL
ejpam-5844	99	1	0	CARDINAL
ejpam-5844	100	1	3	CARDINAL
ejpam-5844	100	2	max	PERSON
ejpam-5844	100	3	0	CARDINAL
ejpam-5844	101	1	max	PERSON
ejpam-5844	102	1	+ 1 2 ∥∥a2	QUANTITY
ejpam-5844	103	1	3	CARDINAL
ejpam-5844	104	1	∈	ORG
ejpam-5844	104	2	g(t	NORP
ejpam-5844	106	1	j = 1	WORK_OF_ART
ejpam-5844	106	2	2	DATE
ejpam-5844	106	3	2n	CARDINAL
ejpam-5844	109	1	j = 1	PERSON
ejpam-5844	112	1	1	CARDINAL
ejpam-5844	112	2	4	CARDINAL
ejpam-5844	114	1	−q2	ORG
ejpam-5844	115	1	−q2∥ a. al-natoor	PERSON
ejpam-5844	115	2	r. al-smadi	PERSON
ejpam-5844	115	3	a. burqan	PERSON
ejpam-5844	116	1	j. pure	PERSON
ejpam-5844	116	2	18	CARDINAL
ejpam-5844	116	3	2	CARDINAL
ejpam-5844	116	4	2025	CARDINAL
ejpam-5844	116	5	5844 6	DATE
ejpam-5844	116	6	3	CARDINAL
ejpam-5844	117	1	a)a2	PRODUCT
ejpam-5844	117	2	b)b2	ORG
ejpam-5844	118	1	+ 1 2	DATE
ejpam-5844	118	2	0	CARDINAL
ejpam-5844	120	1	⊕	PERSON
ejpam-5844	120	2	a)a2	PRODUCT
ejpam-5844	123	1	a)a2	PRODUCT
ejpam-5844	123	2	b)b2	ORG
ejpam-5844	124	1	+ 1 2	DATE
ejpam-5844	129	1	a)a2	PRODUCT
ejpam-5844	129	2	b)b2	ORG
ejpam-5844	130	1	+ 1 2	DATE
ejpam-5844	132	1	9	CARDINAL
ejpam-5844	132	2	3	CARDINAL
ejpam-5844	132	3	9	CARDINAL
ejpam-5844	133	1	4	CARDINAL
ejpam-5844	134	1	10]let	CARDINAL
ejpam-5844	136	1	2	CARDINAL
ejpam-5844	138	1	j = 1	WORK_OF_ART
ejpam-5844	138	2	2n	CARDINAL
ejpam-5844	140	1	g(t	NORP
ejpam-5844	142	1	⊕ 0	GPE
ejpam-5844	142	2	ab3 ba3	PERSON
ejpam-5844	143	1	ab3 ba3	PERSON
ejpam-5844	145	1	a. al-natoor	PERSON
ejpam-5844	145	2	r. al-smadi	PERSON
ejpam-5844	145	3	a. burqan	PERSON
ejpam-5844	146	1	j. pure	PERSON
ejpam-5844	146	2	18	CARDINAL
ejpam-5844	146	3	2	CARDINAL
ejpam-5844	146	4	2025	CARDINAL
ejpam-5844	146	5	5844 7	DATE
ejpam-5844	147	1	lemma 4	ORG
ejpam-5844	148	1	11	CARDINAL
ejpam-5844	148	2	10	CARDINAL
ejpam-5844	148	3	1	CARDINAL
ejpam-5844	148	4	2	DATE
ejpam-5844	149	1	5	CARDINAL
ejpam-5844	151	1	a∗a	ORG
ejpam-5844	151	2	∥b∥2	CARDINAL
ejpam-5844	151	3	11	CARDINAL
ejpam-5844	151	4	1	CARDINAL
ejpam-5844	152	1	10	CARDINAL
ejpam-5844	152	2	√ ∥b∥	PERSON
ejpam-5844	152	3	√	PERSON
ejpam-5844	153	1	1 2	CARDINAL
ejpam-5844	153	2	a∗a	ORG
ejpam-5844	153	3	∥b∥2	CARDINAL
ejpam-5844	154	1	4	CARDINAL
ejpam-5844	157	1	j = 1	WORK_OF_ART
ejpam-5844	157	2	2n	CARDINAL
ejpam-5844	157	3	max	PERSON
ejpam-5844	157	4	2 √ k1k2	QUANTITY
ejpam-5844	158	1	k1e ∗e	PERSON
ejpam-5844	159	1	k1f ∗e k2b	PERSON
ejpam-5844	160	1	12	CARDINAL
ejpam-5844	161	1	+bb∗∥	PERCENT
ejpam-5844	164	1	t3	ORG
ejpam-5844	167	1	√ k1	PERSON
ejpam-5844	167	2	k2 a. al-natoor	PERSON
ejpam-5844	167	3	r. al-smadi	PERSON
ejpam-5844	167	4	a. burqan	PERSON
ejpam-5844	168	1	j. pure	PERSON
ejpam-5844	168	2	18	CARDINAL
ejpam-5844	168	3	2	CARDINAL
ejpam-5844	168	4	2025	CARDINAL
ejpam-5844	168	5	5844 8 of 10	DATE
ejpam-5844	170	1	t ∗ 3	DATE
ejpam-5844	170	2	∥t2∥	PERSON
ejpam-5844	170	3	t ∗ 1	DATE
ejpam-5844	172	1	t3	ORG
ejpam-5844	173	1	1 2 √ k1k2max	QUANTITY
ejpam-5844	173	2	a∗a	ORG
ejpam-5844	173	3	b∗a bb	PERSON
ejpam-5844	174	1	1 2 √ k1k2max	QUANTITY
ejpam-5844	174	2	a∗a	ORG
ejpam-5844	174	3	b∗a b∗b	PERSON
ejpam-5844	174	4	k1k2	NORP
ejpam-5844	174	5	max	PERSON
ejpam-5844	176	1	k1k2	NORP
ejpam-5844	177	1	k1e ∗e	PERSON
ejpam-5844	178	1	k1f ∗e k2b	PERSON
ejpam-5844	180	1	3	CARDINAL
ejpam-5844	183	1	j = 1	WORK_OF_ART
ejpam-5844	183	2	2n	CARDINAL
ejpam-5844	183	3	max	PERSON
ejpam-5844	183	4	2	CARDINAL
ejpam-5844	185	1	∗ 2	DATE
ejpam-5844	188	1	12	CARDINAL
ejpam-5844	188	2	max	PERSON
ejpam-5844	189	1	k1b ∗b k1a	PERSON
ejpam-5844	190	1	max	PERSON
ejpam-5844	190	2	2	CARDINAL
ejpam-5844	190	3	a. al-natoor	PERSON
ejpam-5844	190	4	r. al-smadi	PERSON
ejpam-5844	190	5	a. burqan	PERSON
ejpam-5844	191	1	j. pure	PERSON
ejpam-5844	191	2	18	CARDINAL
ejpam-5844	191	3	2	CARDINAL
ejpam-5844	191	4	2025	CARDINAL
ejpam-5844	191	5	5844 9	DATE
ejpam-5844	191	6	10	CARDINAL
ejpam-5844	191	7	max	PERSON
ejpam-5844	191	8	2	CARDINAL
ejpam-5844	192	1	max	PERSON
ejpam-5844	192	2	2	CARDINAL
ejpam-5844	193	1	max	PERSON
ejpam-5844	193	2	2	CARDINAL
ejpam-5844	193	3	max	PERSON
ejpam-5844	193	4	2	CARDINAL
ejpam-5844	194	1	6	CARDINAL
ejpam-5844	195	1	12]let	CARDINAL
ejpam-5844	196	1	j = 1	WORK_OF_ART
ejpam-5844	196	2	13	CARDINAL
ejpam-5844	197	1	14	CARDINAL
ejpam-5844	197	2	5	CARDINAL
ejpam-5844	199	1	0	CARDINAL
ejpam-5844	200	1	15	CARDINAL
ejpam-5844	202	1	16	CARDINAL
ejpam-5844	205	1	13	CARDINAL
ejpam-5844	207	1	1/2	CARDINAL
ejpam-5844	208	1	1/2	CARDINAL
ejpam-5844	211	1	a. al-natoor	PERSON
ejpam-5844	211	2	r. al-smadi	PERSON
ejpam-5844	211	3	a. burqan	PERSON
ejpam-5844	212	1	j. pure	PERSON
ejpam-5844	212	2	18	CARDINAL
ejpam-5844	212	3	2	CARDINAL
ejpam-5844	212	4	2025	CARDINAL
ejpam-5844	212	5	5844 10	DATE
ejpam-5844	215	1	0	CARDINAL
ejpam-5844	215	2	sn	ORG
ejpam-5844	216	1	0	CARDINAL
ejpam-5844	216	2	√	CARDINAL
ejpam-5844	216	3	sn	ORG
ejpam-5844	218	1	15	CARDINAL
ejpam-5844	219	1	16	CARDINAL
ejpam-5844	219	2	14	CARDINAL
ejpam-5844	219	3	15	CARDINAL
ejpam-5844	220	1	1	CARDINAL
ejpam-5844	220	2	y. tao	PERSON
ejpam-5844	222	1	416(2	CARDINAL
ejpam-5844	222	2	2006	DATE
ejpam-5844	223	1	2	CARDINAL
ejpam-5844	223	2	a. al-natoor	PERSON
ejpam-5844	223	3	o. hirzallah	PERSON
ejpam-5844	223	4	f. kittaneh	PERSON
ejpam-5844	225	1	14(1):7	CARDINAL
ejpam-5844	225	2	2023	CARDINAL
ejpam-5844	226	1	3	CARDINAL
ejpam-5844	226	2	a. al-natoor	PERSON
ejpam-5844	226	3	f. alrimawi	PERSON
ejpam-5844	228	1	european journal	ORG
ejpam-5844	228	2	18(1):558–578	CARDINAL
ejpam-5844	228	3	2025	DATE
ejpam-5844	229	1	4	CARDINAL
ejpam-5844	229	2	a. al-natoor	PERSON
ejpam-5844	229	3	m. a. amleh	PERSON
ejpam-5844	229	4	a. burqan	PERSON
ejpam-5844	231	1	17(2):581–589	DATE
ejpam-5844	231	2	2023	CARDINAL
ejpam-5844	232	1	5	CARDINAL
ejpam-5844	232	2	a. al-natoor	PERSON
ejpam-5844	232	3	a. burqan	PERSON
ejpam-5844	232	4	m. a. amleh	PERSON
ejpam-5844	232	5	c. conde	PERSON
ejpam-5844	234	1	18(3):911–919	CARDINAL
ejpam-5844	234	2	2024	DATE
ejpam-5844	235	1	6	CARDINAL
ejpam-5844	235	2	f. kittaneh	PERSON
ejpam-5844	236	1	2	CARDINAL
ejpam-5844	237	1	journal of linear	ORG
ejpam-5844	237	2	32:116–124	CARDINAL
ejpam-5844	237	3	2017	DATE
ejpam-5844	238	1	7	CARDINAL
ejpam-5844	238	2	f. kittaneh	PERSON
ejpam-5844	238	3	h. r. moradi	PERSON
ejpam-5844	238	4	m. sababheh	PERSON
ejpam-5844	240	1	mathematical inequalities & applications	ORG
ejpam-5844	240	2	27(3):759–774	ORG
ejpam-5844	240	3	2024	DATE
ejpam-5844	241	1	8	CARDINAL
ejpam-5844	241	2	a. al-natoor	PERSON
ejpam-5844	241	3	f. kittaneh	PERSON
ejpam-5844	243	1	linear	ORG
ejpam-5844	243	2	multilinear	ORG
ejpam-5844	243	3	70(21):4498–4509	CARDINAL
ejpam-5844	243	4	2022	CARDINAL
ejpam-5844	244	1	9	CARDINAL
ejpam-5844	244	2	a. al-natoor	PERSON
ejpam-5844	244	3	o. hirzallah	PERSON
ejpam-5844	244	4	f. kittaneh	PERSON
ejpam-5844	246	1	2024	DATE
ejpam-5844	247	1	10	CARDINAL
ejpam-5844	247	2	r. bhatia	PERSON
ejpam-5844	247	3	f. kittaneh	PERSON
ejpam-5844	249	1	428(8-9):2177–2191, 2008	ORG
ejpam-5844	250	1	11	CARDINAL
ejpam-5844	250	2	h. albadawi	PERSON
ejpam-5844	252	1	3(2):10–18	CARDINAL
ejpam-5844	252	2	2012	DATE
ejpam-5844	253	1	12	CARDINAL
ejpam-5844	253	2	f. zhang	PERSON
ejpam-5844	254	1	new york	GPE
ejpam-5844	254	2	2 edition	QUANTITY
ejpam-5844	254	3	2011	DATE