id	sid	eid	entity	type
ejpam-5569	1	1	european journal	ORG
ejpam-5569	1	2	2025	DATE
ejpam-5569	1	3	18	CARDINAL
ejpam-5569	1	4	2	CARDINAL
ejpam-5569	1	5	5569	CARDINAL
ejpam-5569	1	6	1307-5543	DATE
ejpam-5569	1	7	new york	GPE
ejpam-5569	1	8	nawal m. noureldeen1,2	PERSON
ejpam-5569	1	9	elsayed badr3,4,5,hanan m. shabana6,∗	PERSON
ejpam-5569	1	10	m. e. abdel-aal7	PERSON
ejpam-5569	1	11	1	CARDINAL
ejpam-5569	1	12	saudi arabia	GPE
ejpam-5569	1	13	2	CARDINAL
ejpam-5569	1	14	ain shams university	ORG
ejpam-5569	1	15	egypt 3	ORG
ejpam-5569	1	16	misr university for science and technology	ORG
ejpam-5569	1	17	p.o.	ORG
ejpam-5569	1	18	77	DATE
ejpam-5569	1	19	giza	PERSON
ejpam-5569	1	20	egypt 4	ORG
ejpam-5569	1	21	egypt	GPE
ejpam-5569	1	22	5	CARDINAL
ejpam-5569	1	23	egyptian	NORP
ejpam-5569	1	24	egypt 6	ORG
ejpam-5569	1	25	menoufia university	ORG
ejpam-5569	1	26	menouf	GPE
ejpam-5569	1	27	32952	DATE
ejpam-5569	1	28	egypt 7	ORG
ejpam-5569	1	29	13518	DATE
ejpam-5569	1	30	egypt	GPE
ejpam-5569	10	1	1-4	CARDINAL
ejpam-5569	11	1	2020	DATE
ejpam-5569	11	2	05c78	CARDINAL
ejpam-5569	11	3	05c15	CARDINAL
ejpam-5569	12	1	n. m. noureldeen	PERSON
ejpam-5569	12	2	e. badr	PERSON
ejpam-5569	12	3	h. m. shabana	PERSON
ejpam-5569	12	4	mohamed.abdelghani@fsc.bu.edu.eg	PERSON
ejpam-5569	12	5	m. e. abdel-aal	PERSON
ejpam-5569	12	6	1	CARDINAL
ejpam-5569	13	1	2025	CARDINAL
ejpam-5569	14	1	n. m. noureldeen et al	PERSON
ejpam-5569	15	1	j. pure	PERSON
ejpam-5569	15	2	18	CARDINAL
ejpam-5569	15	3	2	CARDINAL
ejpam-5569	15	4	2025	CARDINAL
ejpam-5569	15	5	5569 2	DATE
ejpam-5569	15	6	25	CARDINAL
ejpam-5569	15	7	integer linear	ORG
ejpam-5569	16	1	1	CARDINAL
ejpam-5569	16	2	1	CARDINAL
ejpam-5569	17	1	two	CARDINAL
ejpam-5569	18	1	diam	PERSON
ejpam-5569	20	1	model 1	DATE
ejpam-5569	34	1	two	CARDINAL
ejpam-5569	35	1	j. pure	PERSON
ejpam-5569	35	2	18	CARDINAL
ejpam-5569	35	3	2	CARDINAL
ejpam-5569	35	4	2025	CARDINAL
ejpam-5569	35	5	5569 3	DATE
ejpam-5569	35	6	25	CARDINAL
ejpam-5569	37	1	1	CARDINAL
ejpam-5569	38	1	2	CARDINAL
ejpam-5569	39	1	griggs	PERSON
ejpam-5569	39	2	yeh	PERSON
ejpam-5569	40	1	3	CARDINAL
ejpam-5569	40	2	first	ORDINAL
ejpam-5569	40	3	l(2	ORG
ejpam-5569	40	4	1	CARDINAL
ejpam-5569	40	5	two	CARDINAL
ejpam-5569	41	1	l(2	ORG
ejpam-5569	41	2	1	CARDINAL
ejpam-5569	42	1	0	CARDINAL
ejpam-5569	42	2	two	CARDINAL
ejpam-5569	42	3	1	CARDINAL
ejpam-5569	43	1	2	CARDINAL
ejpam-5569	43	2	2	CARDINAL
ejpam-5569	45	1	chartrand et al	ORG
ejpam-5569	46	1	4	CARDINAL
ejpam-5569	48	1	∈	ORG
ejpam-5569	49	1	two	CARDINAL
ejpam-5569	49	2	diam	PERSON
ejpam-5569	50	1	max	PERSON
ejpam-5569	50	2	∈	ORG
ejpam-5569	51	1	0	CARDINAL
ejpam-5569	51	2	1	DATE
ejpam-5569	51	3	2	DATE
ejpam-5569	51	4	3	DATE
ejpam-5569	55	1	∈	ORG
ejpam-5569	56	1	max	PERSON
ejpam-5569	57	1	∈	ORG
ejpam-5569	59	1	2.	CARDINAL
ejpam-5569	59	2	5	CARDINAL
ejpam-5569	60	1	saha	PERSON
ejpam-5569	60	2	panigrahi	PERSON
ejpam-5569	60	3	6	CARDINAL
ejpam-5569	60	4	moussa	PERSON
ejpam-5569	60	5	one	CARDINAL
ejpam-5569	60	6	6	CARDINAL
ejpam-5569	63	1	8	CARDINAL
ejpam-5569	64	1	n. m.	PERSON
ejpam-5569	66	1	j. pure	PERSON
ejpam-5569	66	2	18	CARDINAL
ejpam-5569	66	3	2	CARDINAL
ejpam-5569	66	4	2025	CARDINAL
ejpam-5569	66	5	5569 4	DATE
ejpam-5569	66	6	25	CARDINAL
ejpam-5569	66	7	9	CARDINAL
ejpam-5569	72	1	integer linear	ORG
ejpam-5569	76	1	section 3	LAW
ejpam-5569	77	1	integer linear	ORG
ejpam-5569	77	2	section 4	LAW
ejpam-5569	77	3	section 5	LAW
ejpam-5569	78	1	section 6	DATE
ejpam-5569	79	1	section 7.	LAW
ejpam-5569	79	2	3	CARDINAL
ejpam-5569	80	1	1	CARDINAL
ejpam-5569	82	1	two	CARDINAL
ejpam-5569	82	2	first	ORDINAL
ejpam-5569	82	3	second	ORDINAL
ejpam-5569	82	4	1	CARDINAL
ejpam-5569	83	1	1	CARDINAL
ejpam-5569	85	1	vi	PERSON
ejpam-5569	85	2	1 ≤ i ≤ n	QUANTITY
ejpam-5569	85	3	n. m. noureldeen	PERSON
ejpam-5569	86	1	j. pure	PERSON
ejpam-5569	86	2	18	CARDINAL
ejpam-5569	86	3	2	CARDINAL
ejpam-5569	86	4	2025	CARDINAL
ejpam-5569	86	5	5569 5	DATE
ejpam-5569	86	6	25	DATE
ejpam-5569	87	1	1 ≤	QUANTITY
ejpam-5569	87	2	1	CARDINAL
ejpam-5569	87	3	uivi+1	LOC
ejpam-5569	87	4	1 ≤	QUANTITY
ejpam-5569	87	5	1	CARDINAL
ejpam-5569	88	1	two	CARDINAL
ejpam-5569	89	1	1 ≤ i ≤ n	QUANTITY
ejpam-5569	89	2	1 ≤ i ≤ n	QUANTITY
ejpam-5569	90	1	2n	CARDINAL
ejpam-5569	90	2	1	CARDINAL
ejpam-5569	90	3	2	CARDINAL
ejpam-5569	92	1	1	CARDINAL
ejpam-5569	93	1	2	CARDINAL
ejpam-5569	95	1	f(u2	GPE
ejpam-5569	95	2	f(v1	DATE
ejpam-5569	96	1	0	CARDINAL
ejpam-5569	96	2	3	DATE
ejpam-5569	96	3	1	DATE
ejpam-5569	96	4	4	CARDINAL
ejpam-5569	97	1	2	CARDINAL
ejpam-5569	98	1	3	CARDINAL
ejpam-5569	100	1	f(u2	ORG
ejpam-5569	100	2	f(v1	DATE
ejpam-5569	100	3	f(v3	ORG
ejpam-5569	101	1	0	CARDINAL
ejpam-5569	101	2	5	DATE
ejpam-5569	101	3	1	DATE
ejpam-5569	101	4	2	DATE
ejpam-5569	101	5	6	DATE
ejpam-5569	101	6	3	CARDINAL
ejpam-5569	102	1	3	CARDINAL
ejpam-5569	103	1	4	CARDINAL
ejpam-5569	104	1	f(u2	ORG
ejpam-5569	104	2	f(u4	ORG
ejpam-5569	105	1	0	CARDINAL
ejpam-5569	105	2	5	DATE
ejpam-5569	105	3	10	DATE
ejpam-5569	105	4	1	DATE
ejpam-5569	105	5	2	DATE
ejpam-5569	105	6	7	DATE
ejpam-5569	105	7	12	DATE
ejpam-5569	105	8	3	CARDINAL
ejpam-5569	106	1	4	CARDINAL
ejpam-5569	107	1	5	CARDINAL
ejpam-5569	109	1	5	CARDINAL
ejpam-5569	109	2	f(u2	ORG
ejpam-5569	109	3	f(u4	ORG
ejpam-5569	109	4	f(u5	ORG
ejpam-5569	109	5	f(v1	DATE
ejpam-5569	110	1	6, 13	DATE
ejpam-5569	110	2	0	CARDINAL
ejpam-5569	110	3	16	DATE
ejpam-5569	110	4	7	DATE
ejpam-5569	110	5	9	DATE
ejpam-5569	110	6	19	DATE
ejpam-5569	110	7	3	DATE
ejpam-5569	110	8	22	DATE
ejpam-5569	110	9	10	CARDINAL
ejpam-5569	110	10	n ≥ 6	DATE
ejpam-5569	111	1	1	CARDINAL
ejpam-5569	112	1	n ≡ 2(mod4	ORG
ejpam-5569	116	1	k ≥ 1	ORG
ejpam-5569	116	2	n ≡ 2(mod4	ORG
ejpam-5569	116	3	2n+	CARDINAL
ejpam-5569	117	1	1 ≤	QUANTITY
ejpam-5569	119	1	3n− 5)(j	CARDINAL
ejpam-5569	119	2	1	CARDINAL
ejpam-5569	120	1	1)(j	CARDINAL
ejpam-5569	120	2	2	CARDINAL
ejpam-5569	120	3	k + 2 ≤ i ≤ 2k + 1	ORG
ejpam-5569	120	4	1 ≤	QUANTITY
ejpam-5569	123	1	6k + 1)−	DATE
ejpam-5569	123	2	1	CARDINAL
ejpam-5569	123	3	2k + 2 ≤	MONEY
ejpam-5569	124	1	1 ≤ j ≤ k	QUANTITY
ejpam-5569	124	2	3k	CARDINAL
ejpam-5569	124	3	j f(uj	PERSON
ejpam-5569	125	1	1	CARDINAL
ejpam-5569	125	2	3k + 2 ≤	MONEY
ejpam-5569	125	3	1 ≤ j ≤ k	QUANTITY
ejpam-5569	126	1	j n. m. noureldeen	PERSON
ejpam-5569	128	1	j. pure	PERSON
ejpam-5569	128	2	18	CARDINAL
ejpam-5569	128	3	2	CARDINAL
ejpam-5569	128	4	2025	CARDINAL
ejpam-5569	128	5	5569 6	DATE
ejpam-5569	128	6	25	DATE
ejpam-5569	128	7	2	CARDINAL
ejpam-5569	129	1	2n+	CARDINAL
ejpam-5569	130	1	1 ≤	QUANTITY
ejpam-5569	130	2	1)(j	CARDINAL
ejpam-5569	130	3	1	CARDINAL
ejpam-5569	130	4	1)(j	CARDINAL
ejpam-5569	130	5	2	CARDINAL
ejpam-5569	130	6	k + 1 ≤ i ≤ 2k + 1	FAC
ejpam-5569	130	7	1 ≤ j ≤	QUANTITY
ejpam-5569	132	1	andi = k	PERSON
ejpam-5569	134	1	2k + 1	DATE
ejpam-5569	135	1	1	CARDINAL
ejpam-5569	135	2	2k + 2 ≤	MONEY
ejpam-5569	135	3	1 ≤ j ≤	QUANTITY
ejpam-5569	138	1	3k	CARDINAL
ejpam-5569	140	1	3k + 3 ≤	QUANTITY
ejpam-5569	141	1	1 ≤ j ≤ k	QUANTITY
ejpam-5569	144	1	two	CARDINAL
ejpam-5569	145	1	1 x	QUANTITY
ejpam-5569	146	1	un	ORG
ejpam-5569	149	1	1	CARDINAL
ejpam-5569	150	1	d(x	ORG
ejpam-5569	150	2	1	CARDINAL
ejpam-5569	150	3	2	CARDINAL
ejpam-5569	152	1	2n+	CARDINAL
ejpam-5569	153	1	1)]|	CARDINAL
ejpam-5569	155	1	2n+	CARDINAL
ejpam-5569	157	1	1)]|	CARDINAL
ejpam-5569	157	2	2n+	CARDINAL
ejpam-5569	159	1	d(x	ORG
ejpam-5569	159	2	3	CARDINAL
ejpam-5569	159	3	d(x	ORG
ejpam-5569	160	1	2k	CARDINAL
ejpam-5569	161	1	f(u2k+1)|	CARDINAL
ejpam-5569	162	1	3n− 5)(k	CARDINAL
ejpam-5569	162	2	1	CARDINAL
ejpam-5569	163	1	1)(k	CARDINAL
ejpam-5569	163	2	2)]|	CARDINAL
ejpam-5569	163	3	2n− 1)−	DATE
ejpam-5569	163	4	3n− 5)(k	CARDINAL
ejpam-5569	163	5	1	CARDINAL
ejpam-5569	163	6	1)(k	CARDINAL
ejpam-5569	166	1	2n− 1)−	DATE
ejpam-5569	166	2	3n− 5)(k	CARDINAL
ejpam-5569	166	3	1	CARDINAL
ejpam-5569	166	4	1)(k	CARDINAL
ejpam-5569	166	5	2k	CARDINAL
ejpam-5569	166	6	4	CARDINAL
ejpam-5569	166	7	d(x	ORG
ejpam-5569	167	1	3k	CARDINAL
ejpam-5569	169	1	6k + 1)]|	CARDINAL
ejpam-5569	170	1	6k + 1)| n. m. noureldeen	QUANTITY
ejpam-5569	171	1	j. pure	PERSON
ejpam-5569	171	2	18	CARDINAL
ejpam-5569	171	3	2	CARDINAL
ejpam-5569	171	4	2025	CARDINAL
ejpam-5569	171	5	5569 7	DATE
ejpam-5569	171	6	25	CARDINAL
ejpam-5569	171	7	1	CARDINAL
ejpam-5569	171	8	6k + 1)|	CARDINAL
ejpam-5569	171	9	3)(k	CARDINAL
ejpam-5569	173	1	1	CARDINAL
ejpam-5569	173	2	6k + 1)|	CARDINAL
ejpam-5569	173	3	3k	CARDINAL
ejpam-5569	173	4	5 x	QUANTITY
ejpam-5569	176	1	1]|	CARDINAL
ejpam-5569	176	2	1	CARDINAL
ejpam-5569	177	1	d(x	ORG
ejpam-5569	177	2	1	CARDINAL
ejpam-5569	177	3	6	CARDINAL
ejpam-5569	179	1	2)−	CARDINAL
ejpam-5569	179	2	2	CARDINAL
ejpam-5569	179	3	2n+	CARDINAL
ejpam-5569	179	4	1	CARDINAL
ejpam-5569	179	5	1)(k	CARDINAL
ejpam-5569	179	6	2)]|	CARDINAL
ejpam-5569	180	1	1	CARDINAL
ejpam-5569	180	2	1)(k	CARDINAL
ejpam-5569	181	1	7	CARDINAL
ejpam-5569	183	1	2)−	CARDINAL
ejpam-5569	183	2	2	CARDINAL
ejpam-5569	183	3	2n+	CARDINAL
ejpam-5569	183	4	1	CARDINAL
ejpam-5569	183	5	1)(k	CARDINAL
ejpam-5569	183	6	2)+	CARDINAL
ejpam-5569	183	7	1)]|	CARDINAL
ejpam-5569	184	1	1	CARDINAL
ejpam-5569	184	2	1)(k	CARDINAL
ejpam-5569	184	3	2	CARDINAL
ejpam-5569	184	4	1)|	CARDINAL
ejpam-5569	184	5	d(x	ORG
ejpam-5569	184	6	1	CARDINAL
ejpam-5569	185	1	8	CARDINAL
ejpam-5569	188	1	2k	CARDINAL
ejpam-5569	188	2	2k	CARDINAL
ejpam-5569	188	3	2)−	CARDINAL
ejpam-5569	189	1	2	CARDINAL
ejpam-5569	189	2	2n+	CARDINAL
ejpam-5569	189	3	1	CARDINAL
ejpam-5569	189	4	1)(k	CARDINAL
ejpam-5569	189	5	2)+	CARDINAL
ejpam-5569	190	1	2k	CARDINAL
ejpam-5569	191	1	1	CARDINAL
ejpam-5569	191	2	1)(k	CARDINAL
ejpam-5569	191	3	2	CARDINAL
ejpam-5569	191	4	2k + 1)|	CARDINAL
ejpam-5569	191	5	3k + 1	DATE
ejpam-5569	191	6	d(x	ORG
ejpam-5569	192	1	3k	CARDINAL
ejpam-5569	193	1	9	CARDINAL
ejpam-5569	193	2	1 ≤	CARDINAL
ejpam-5569	193	3	n. m.	PERSON
ejpam-5569	195	1	j. pure	PERSON
ejpam-5569	195	2	18	CARDINAL
ejpam-5569	195	3	2	CARDINAL
ejpam-5569	195	4	2025	CARDINAL
ejpam-5569	195	5	5569 8	DATE
ejpam-5569	195	6	25	CARDINAL
ejpam-5569	195	7	9.1	CARDINAL
ejpam-5569	195	8	1	CARDINAL
ejpam-5569	197	1	|0−	PERSON
ejpam-5569	197	2	2	CARDINAL
ejpam-5569	197	3	2n+	CARDINAL
ejpam-5569	197	4	1	CARDINAL
ejpam-5569	198	1	1)(k	CARDINAL
ejpam-5569	198	2	2)]|	CARDINAL
ejpam-5569	198	3	2	CARDINAL
ejpam-5569	198	4	2n+	CARDINAL
ejpam-5569	198	5	1	CARDINAL
ejpam-5569	198	6	1)(k	CARDINAL
ejpam-5569	198	7	d(x	ORG
ejpam-5569	199	1	1	CARDINAL
ejpam-5569	201	1	9.2	CARDINAL
ejpam-5569	201	2	1 ≤	QUANTITY
ejpam-5569	204	1	1 ≤ j ≤ k	QUANTITY
ejpam-5569	207	1	1)(j	CARDINAL
ejpam-5569	208	1	1)(j	CARDINAL
ejpam-5569	208	2	2)]|	CARDINAL
ejpam-5569	211	1	2	CARDINAL
ejpam-5569	211	2	2n+	CARDINAL
ejpam-5569	211	3	1)+	CARDINAL
ejpam-5569	213	1	1)(k	CARDINAL
ejpam-5569	213	2	2	CARDINAL
ejpam-5569	213	3	1)(j	CARDINAL
ejpam-5569	213	4	1	CARDINAL
ejpam-5569	213	5	1)(j	CARDINAL
ejpam-5569	213	6	2)]|	CARDINAL
ejpam-5569	214	1	1	CARDINAL
ejpam-5569	216	1	1	CARDINAL
ejpam-5569	216	2	1 ≤ j ≤	QUANTITY
ejpam-5569	217	1	1)(j	CARDINAL
ejpam-5569	217	2	1	CARDINAL
ejpam-5569	217	3	1)(j	CARDINAL
ejpam-5569	217	4	2)]|	CARDINAL
ejpam-5569	219	1	2	CARDINAL
ejpam-5569	219	2	2n+	CARDINAL
ejpam-5569	219	3	1	CARDINAL
ejpam-5569	219	4	1)(k	CARDINAL
ejpam-5569	219	5	2	CARDINAL
ejpam-5569	219	6	2n+ 1)|	CARDINAL
ejpam-5569	219	7	2	CARDINAL
ejpam-5569	219	8	2n+	CARDINAL
ejpam-5569	219	9	1	CARDINAL
ejpam-5569	220	1	1)(k	CARDINAL
ejpam-5569	220	2	2	CARDINAL
ejpam-5569	220	3	2n+ 1)|	CARDINAL
ejpam-5569	220	4	d(x	ORG
ejpam-5569	220	5	1	CARDINAL
ejpam-5569	222	1	9.3	CARDINAL
ejpam-5569	223	1	1 ≤	QUANTITY
ejpam-5569	227	1	1	CARDINAL
ejpam-5569	228	1	3k	CARDINAL
ejpam-5569	229	1	1	CARDINAL
ejpam-5569	230	1	|f(ui)−	NORP
ejpam-5569	230	2	|0−	PERSON
ejpam-5569	230	3	2	CARDINAL
ejpam-5569	230	4	2n+	CARDINAL
ejpam-5569	230	5	1	CARDINAL
ejpam-5569	230	6	1)(k	CARDINAL
ejpam-5569	230	7	2	CARDINAL
ejpam-5569	230	8	d(x	ORG
ejpam-5569	230	9	1	CARDINAL
ejpam-5569	232	1	2	CARDINAL
ejpam-5569	232	2	1	CARDINAL
ejpam-5569	232	3	n. m.	PERSON
ejpam-5569	234	1	j. pure	PERSON
ejpam-5569	234	2	18	CARDINAL
ejpam-5569	234	3	2	CARDINAL
ejpam-5569	234	4	2025	CARDINAL
ejpam-5569	234	5	5569 9	DATE
ejpam-5569	234	6	25	CARDINAL
ejpam-5569	234	7	2	CARDINAL
ejpam-5569	234	8	1	CARDINAL
ejpam-5569	234	9	2	CARDINAL
ejpam-5569	235	1	6	CARDINAL
ejpam-5569	235	2	n ≡ 3(mod4	ORG
ejpam-5569	237	1	3	CARDINAL
ejpam-5569	238	1	4k+3	DATE
ejpam-5569	240	1	2n+	CARDINAL
ejpam-5569	240	2	+ 2(i−	DATE
ejpam-5569	240	3	1 ≤	QUANTITY
ejpam-5569	242	1	2)−	CARDINAL
ejpam-5569	242	2	3n−	CARDINAL
ejpam-5569	242	3	1	CARDINAL
ejpam-5569	243	1	1)(j	CARDINAL
ejpam-5569	243	2	2	CARDINAL
ejpam-5569	243	3	k + 2 ≤ i ≤ 2k + 1	ORG
ejpam-5569	243	4	1 ≤ j ≤ k	QUANTITY
ejpam-5569	245	1	1	CARDINAL
ejpam-5569	245	2	2k	CARDINAL
ejpam-5569	246	1	1	CARDINAL
ejpam-5569	246	2	2k + 3 ≤	QUANTITY
ejpam-5569	247	1	1 ≤ j ≤ k	QUANTITY
ejpam-5569	248	1	3k	CARDINAL
ejpam-5569	249	1	j) f(uj	ORG
ejpam-5569	250	1	1	CARDINAL
ejpam-5569	250	2	3k + 3 ≤	QUANTITY
ejpam-5569	251	1	1 ≤	QUANTITY
ejpam-5569	253	1	4k	CARDINAL
ejpam-5569	253	2	+ 4− j	PERSON
ejpam-5569	254	1	3	CARDINAL
ejpam-5569	254	2	2n+	CARDINAL
ejpam-5569	254	3	1 ≤	QUANTITY
ejpam-5569	254	4	k f(vk	PERSON
ejpam-5569	254	5	1	CARDINAL
ejpam-5569	254	6	1	CARDINAL
ejpam-5569	254	7	1)(j	CARDINAL
ejpam-5569	254	8	2	CARDINAL
ejpam-5569	254	9	k + 1 ≤ i ≤ 2k + 1,where	FAC
ejpam-5569	254	10	1 ≤ j ≤	QUANTITY
ejpam-5569	257	1	3	CARDINAL
ejpam-5569	257	2	2k + 2 f(vk+j	QUANTITY
ejpam-5569	258	1	2k + 1	DATE
ejpam-5569	259	1	1	CARDINAL
ejpam-5569	259	2	2k + 3 ≤	QUANTITY
ejpam-5569	259	3	1 ≤	QUANTITY
ejpam-5569	261	1	3k	CARDINAL
ejpam-5569	261	2	j f(vn+1−j	PERSON
ejpam-5569	262	1	f(vj)−	DATE
ejpam-5569	262	2	2j	CARDINAL
ejpam-5569	262	3	3k + 4 ≤	MONEY
ejpam-5569	262	4	1 ≤ j ≤ k	QUANTITY
ejpam-5569	262	5	4k	CARDINAL
ejpam-5569	263	1	+	NORP
ejpam-5569	265	1	n ≥ 6	DATE
ejpam-5569	267	1	two	CARDINAL
ejpam-5569	268	1	1 x	QUANTITY
ejpam-5569	269	1	un	ORG
ejpam-5569	272	1	1	CARDINAL
ejpam-5569	273	1	d(x	ORG
ejpam-5569	274	1	1	CARDINAL
ejpam-5569	275	1	n. m. noureldeen et al	PERSON
ejpam-5569	276	1	j. pure	PERSON
ejpam-5569	276	2	18	CARDINAL
ejpam-5569	276	3	2	CARDINAL
ejpam-5569	276	4	2025	CARDINAL
ejpam-5569	276	5	5569 10	DATE
ejpam-5569	276	6	25	CARDINAL
ejpam-5569	276	7	2	CARDINAL
ejpam-5569	279	1	2n+	CARDINAL
ejpam-5569	280	1	1)]|	CARDINAL
ejpam-5569	282	1	2n+	CARDINAL
ejpam-5569	284	1	1)]|	CARDINAL
ejpam-5569	284	2	2n+	CARDINAL
ejpam-5569	285	1	1	CARDINAL
ejpam-5569	286	1	3	CARDINAL
ejpam-5569	287	1	f(u2k+1)|	CARDINAL
ejpam-5569	288	1	2)−	CARDINAL
ejpam-5569	288	2	3n− 6)(k	CARDINAL
ejpam-5569	288	3	1	CARDINAL
ejpam-5569	289	1	1)(k	CARDINAL
ejpam-5569	289	2	2)]|	CARDINAL
ejpam-5569	289	3	2)−	CARDINAL
ejpam-5569	289	4	3n− 6)(k	CARDINAL
ejpam-5569	289	5	1	CARDINAL
ejpam-5569	290	1	1)(k	CARDINAL
ejpam-5569	293	1	2)−	CARDINAL
ejpam-5569	293	2	3n− 6)(k	CARDINAL
ejpam-5569	293	3	1	CARDINAL
ejpam-5569	293	4	1)(k	CARDINAL
ejpam-5569	293	5	2k	CARDINAL
ejpam-5569	294	1	4	CARDINAL
ejpam-5569	296	1	1]|	CARDINAL
ejpam-5569	296	2	|n2	DATE
ejpam-5569	296	3	− n−	PERSON
ejpam-5569	296	4	1| ≥ n	DATE
ejpam-5569	297	1	5	CARDINAL
ejpam-5569	299	1	f(uk+2	GPE
ejpam-5569	299	2	6k + 2)]|	QUANTITY
ejpam-5569	300	1	6k + 2)|	QUANTITY
ejpam-5569	300	2	− n−	PERSON
ejpam-5569	300	3	1	CARDINAL
ejpam-5569	300	4	6k + 2)|	QUANTITY
ejpam-5569	301	1	6 x	QUANTITY
ejpam-5569	304	1	2]|	CARDINAL
ejpam-5569	304	2	2	CARDINAL
ejpam-5569	305	1	d(x	ORG
ejpam-5569	306	1	1	CARDINAL
ejpam-5569	307	1	n. m. noureldeen et al	PERSON
ejpam-5569	308	1	j. pure	PERSON
ejpam-5569	308	2	18	CARDINAL
ejpam-5569	308	3	2	CARDINAL
ejpam-5569	308	4	2025	CARDINAL
ejpam-5569	308	5	5569 11	DATE
ejpam-5569	308	6	25	CARDINAL
ejpam-5569	308	7	7	CARDINAL
ejpam-5569	309	1	3)−	CARDINAL
ejpam-5569	309	2	3	CARDINAL
ejpam-5569	309	3	2n+	CARDINAL
ejpam-5569	309	4	1	CARDINAL
ejpam-5569	309	5	1)(k	CARDINAL
ejpam-5569	309	6	2)]|	CARDINAL
ejpam-5569	310	1	1	CARDINAL
ejpam-5569	310	2	1)(k	CARDINAL
ejpam-5569	310	3	+ 3	DATE
ejpam-5569	310	4	d(x	ORG
ejpam-5569	310	5	1	CARDINAL
ejpam-5569	311	1	8	CARDINAL
ejpam-5569	313	1	3)−	CARDINAL
ejpam-5569	314	1	3	CARDINAL
ejpam-5569	314	2	2n+	CARDINAL
ejpam-5569	314	3	1	CARDINAL
ejpam-5569	314	4	1)(k	CARDINAL
ejpam-5569	314	5	2)+	CARDINAL
ejpam-5569	315	1	1	CARDINAL
ejpam-5569	315	2	1)]|	CARDINAL
ejpam-5569	316	1	1	CARDINAL
ejpam-5569	316	2	1)(k	CARDINAL
ejpam-5569	316	3	2	CARDINAL
ejpam-5569	316	4	1	CARDINAL
ejpam-5569	317	1	1)|	CARDINAL
ejpam-5569	317	2	+ 3	DATE
ejpam-5569	317	3	d(x	ORG
ejpam-5569	317	4	1	CARDINAL
ejpam-5569	318	1	9	CARDINAL
ejpam-5569	321	1	3]|	CARDINAL
ejpam-5569	321	2	3|	ORDINAL
ejpam-5569	322	1	10	CARDINAL
ejpam-5569	326	1	2k	CARDINAL
ejpam-5569	326	2	1	CARDINAL
ejpam-5569	326	3	2k	CARDINAL
ejpam-5569	326	4	2)−	CARDINAL
ejpam-5569	327	1	3	CARDINAL
ejpam-5569	327	2	2n+	CARDINAL
ejpam-5569	327	3	1	CARDINAL
ejpam-5569	327	4	1)(k	CARDINAL
ejpam-5569	327	5	2	CARDINAL
ejpam-5569	327	6	2n+ 1)+ +	DATE
ejpam-5569	327	7	2k	CARDINAL
ejpam-5569	329	1	1	CARDINAL
ejpam-5569	329	2	1)(k	CARDINAL
ejpam-5569	329	3	2	CARDINAL
ejpam-5569	329	4	2k + 1	DATE
ejpam-5569	330	1	11	CARDINAL
ejpam-5569	330	2	1 ≤	CARDINAL
ejpam-5569	330	3	11.1	CARDINAL
ejpam-5569	331	1	1 ≤	QUANTITY
ejpam-5569	331	2	k n. m. noureldeen	PERSON
ejpam-5569	332	1	j. pure	PERSON
ejpam-5569	332	2	18	CARDINAL
ejpam-5569	332	3	2	CARDINAL
ejpam-5569	332	4	2025	CARDINAL
ejpam-5569	332	5	5569 12	DATE
ejpam-5569	332	6	25	CARDINAL
ejpam-5569	334	1	3	CARDINAL
ejpam-5569	334	2	2n+ 7)(i− 1)+ + 2(i−	DATE
ejpam-5569	334	3	2)]|	CARDINAL
ejpam-5569	336	1	3	CARDINAL
ejpam-5569	336	2	4)(i−	CARDINAL
ejpam-5569	336	3	3	CARDINAL
ejpam-5569	336	4	4)(i− 1)|	CARDINAL
ejpam-5569	339	1	11.2	CARDINAL
ejpam-5569	340	1	2k	CARDINAL
ejpam-5569	340	2	2k	CARDINAL
ejpam-5569	340	3	|n2	DATE
ejpam-5569	340	4	− n−	PERSON
ejpam-5569	340	5	1−	TIME
ejpam-5569	341	1	3]|	CARDINAL
ejpam-5569	343	1	2)]|	CARDINAL
ejpam-5569	343	2	2	CARDINAL
ejpam-5569	345	1	11.3	CARDINAL
ejpam-5569	346	1	3k + 4 ≤	QUANTITY
ejpam-5569	346	2	3k + 4 ≤	MONEY
ejpam-5569	347	1	+ 2j	CARDINAL
ejpam-5569	348	1	f(vj)−	CARDINAL
ejpam-5569	348	2	1 ≤	QUANTITY
ejpam-5569	350	1	|f(uj)−	DATE
ejpam-5569	351	1	+ 4j	CARDINAL
ejpam-5569	351	2	1|	CARDINAL
ejpam-5569	351	3	1 ≤	QUANTITY
ejpam-5569	351	4	j ≤ k ≥ diam(d2(pn	PERSON
ejpam-5569	353	1	11.4	CARDINAL
ejpam-5569	353	2	1 ≤	QUANTITY
ejpam-5569	357	1	1 ≤ j ≤ k	QUANTITY
ejpam-5569	361	1	2n− 1)+	DATE
ejpam-5569	362	1	1	CARDINAL
ejpam-5569	362	2	1)(j	CARDINAL
ejpam-5569	362	3	2)]|	CARDINAL
ejpam-5569	365	1	3	CARDINAL
ejpam-5569	365	2	2n+	CARDINAL
ejpam-5569	365	3	1)+	CARDINAL
ejpam-5569	367	1	1)(k	CARDINAL
ejpam-5569	367	2	2	CARDINAL
ejpam-5569	367	3	1	CARDINAL
ejpam-5569	367	4	1	CARDINAL
ejpam-5569	367	5	1)(j	CARDINAL
ejpam-5569	367	6	2)]|	CARDINAL
ejpam-5569	367	7	1	CARDINAL
ejpam-5569	367	8	2k + 1	DATE
ejpam-5569	370	1	|0−	PERSON
ejpam-5569	370	2	1	CARDINAL
ejpam-5569	370	3	1	CARDINAL
ejpam-5569	370	4	1)(j	CARDINAL
ejpam-5569	370	5	2)]|	CARDINAL
ejpam-5569	370	6	3	CARDINAL
ejpam-5569	370	7	2n+	CARDINAL
ejpam-5569	370	8	1	CARDINAL
ejpam-5569	371	1	1)(k	CARDINAL
ejpam-5569	371	2	2)+	CARDINAL
ejpam-5569	371	3	3	CARDINAL
ejpam-5569	371	4	2n+	CARDINAL
ejpam-5569	371	5	1	CARDINAL
ejpam-5569	372	1	1)(k	CARDINAL
ejpam-5569	372	2	2)+	CARDINAL
ejpam-5569	373	1	1	CARDINAL
ejpam-5569	373	2	1)|	CARDINAL
ejpam-5569	373	3	n. m. noureldeen et al	PERSON
ejpam-5569	374	1	j. pure	PERSON
ejpam-5569	374	2	18	CARDINAL
ejpam-5569	374	3	2	CARDINAL
ejpam-5569	374	4	2025	CARDINAL
ejpam-5569	374	5	5569 13	DATE
ejpam-5569	374	6	25	CARDINAL
ejpam-5569	374	7	+ 3	DATE
ejpam-5569	374	8	d(x	ORG
ejpam-5569	374	9	1	CARDINAL
ejpam-5569	376	1	4k + 3	DATE
ejpam-5569	378	1	+ 1−	TIME
ejpam-5569	378	2	3]|	CARDINAL
ejpam-5569	380	1	3− 1]|	DATE
ejpam-5569	381	1	− 4| ≥ n	PERSON
ejpam-5569	381	2	+ 3	DATE
ejpam-5569	381	3	1	CARDINAL
ejpam-5569	381	4	d(x	ORG
ejpam-5569	381	5	1	CARDINAL
ejpam-5569	385	1	3	CARDINAL
ejpam-5569	385	2	2	CARDINAL
ejpam-5569	385	3	3	CARDINAL
ejpam-5569	385	4	d2(p15	GPE
ejpam-5569	385	5	2	CARDINAL
ejpam-5569	385	6	3	CARDINAL
ejpam-5569	386	1	6	CARDINAL
ejpam-5569	390	1	integer n ≡	PRODUCT
ejpam-5569	390	2	2	CARDINAL
ejpam-5569	391	1	2n+	CARDINAL
ejpam-5569	391	2	+ 2(i−	DATE
ejpam-5569	391	3	1 ≤	QUANTITY
ejpam-5569	391	4	3	CARDINAL
ejpam-5569	392	1	1	CARDINAL
ejpam-5569	392	2	1)(j	CARDINAL
ejpam-5569	392	3	2	CARDINAL
ejpam-5569	392	4	k + 2 ≤ i ≤ 2k	ORG
ejpam-5569	392	5	1 ≤ j ≤ k	QUANTITY
ejpam-5569	393	1	1	CARDINAL
ejpam-5569	396	1	6k	CARDINAL
ejpam-5569	396	2	3)−	CARDINAL
ejpam-5569	396	3	1	CARDINAL
ejpam-5569	396	4	2k + 1 ≤	QUANTITY
ejpam-5569	397	1	1	CARDINAL
ejpam-5569	398	1	1 ≤	QUANTITY
ejpam-5569	400	1	1	CARDINAL
ejpam-5569	401	1	3k	CARDINAL
ejpam-5569	401	2	− j f(uj	PERSON
ejpam-5569	402	1	1	CARDINAL
ejpam-5569	402	2	3k ≤	MONEY
ejpam-5569	403	1	1 ≤ j ≤	QUANTITY
ejpam-5569	406	1	j n. m. noureldeen	PERSON
ejpam-5569	407	1	j. pure	PERSON
ejpam-5569	407	2	18	CARDINAL
ejpam-5569	407	3	2	CARDINAL
ejpam-5569	407	4	2025	CARDINAL
ejpam-5569	407	5	5569 14 of 25	DATE
ejpam-5569	407	6	2	CARDINAL
ejpam-5569	407	7	2n+	CARDINAL
ejpam-5569	407	8	1 ≤	QUANTITY
ejpam-5569	408	1	1	CARDINAL
ejpam-5569	409	1	k f(vk	PERSON
ejpam-5569	409	2	3)(j	CARDINAL
ejpam-5569	409	3	1	CARDINAL
ejpam-5569	410	1	1)(j	CARDINAL
ejpam-5569	410	2	2	CARDINAL
ejpam-5569	411	1	1 ≤ j ≤ k	QUANTITY
ejpam-5569	412	1	2k	CARDINAL
ejpam-5569	412	2	1	CARDINAL
ejpam-5569	413	1	1	CARDINAL
ejpam-5569	413	2	2k + 1 ≤	QUANTITY
ejpam-5569	414	1	1 ≤	QUANTITY
ejpam-5569	417	1	3k	CARDINAL
ejpam-5569	417	2	2j	CARDINAL
ejpam-5569	417	3	1	CARDINAL
ejpam-5569	417	4	3k + 2 ≤	MONEY
ejpam-5569	417	5	1 ≤ j ≤	QUANTITY
ejpam-5569	419	1	1	CARDINAL
ejpam-5569	419	2	two	CARDINAL
ejpam-5569	419	3	k ≥ 2.	ORG
ejpam-5569	419	4	1 x	QUANTITY
ejpam-5569	420	1	un	ORG
ejpam-5569	423	1	1	CARDINAL
ejpam-5569	424	1	d(x	ORG
ejpam-5569	424	2	1	CARDINAL
ejpam-5569	424	3	2	CARDINAL
ejpam-5569	426	1	2n+	CARDINAL
ejpam-5569	426	2	1	CARDINAL
ejpam-5569	427	1	1)(k	CARDINAL
ejpam-5569	427	2	2)]|	CARDINAL
ejpam-5569	429	1	2n+	CARDINAL
ejpam-5569	429	2	1	CARDINAL
ejpam-5569	430	1	1)(k	CARDINAL
ejpam-5569	430	2	2)]|	CARDINAL
ejpam-5569	430	3	2n+	CARDINAL
ejpam-5569	430	4	1	CARDINAL
ejpam-5569	430	5	1)(k	CARDINAL
ejpam-5569	430	6	2	CARDINAL
ejpam-5569	430	7	4k	CARDINAL
ejpam-5569	431	1	3	CARDINAL
ejpam-5569	434	1	3]|	CARDINAL
ejpam-5569	436	1	3]|	CARDINAL
ejpam-5569	436	2	3)(k	CARDINAL
ejpam-5569	436	3	1	CARDINAL
ejpam-5569	436	4	1)(k	CARDINAL
ejpam-5569	436	5	2	CARDINAL
ejpam-5569	437	1	3|	DATE
ejpam-5569	437	2	4k	CARDINAL
ejpam-5569	437	3	d(x	ORG
ejpam-5569	437	4	1	CARDINAL
ejpam-5569	438	1	4	CARDINAL
ejpam-5569	440	1	2n+ 2−	DATE
ejpam-5569	440	2	3n−	CARDINAL
ejpam-5569	440	3	2	CARDINAL
ejpam-5569	441	1	2)(k	CARDINAL
ejpam-5569	442	1	3)]|	CARDINAL
ejpam-5569	442	2	2n+ 2−	CARDINAL
ejpam-5569	442	3	3n−	CARDINAL
ejpam-5569	442	4	2	CARDINAL
ejpam-5569	443	1	2)(k	CARDINAL
ejpam-5569	444	1	3)|	CARDINAL
ejpam-5569	446	1	3)(k	CARDINAL
ejpam-5569	446	2	1	CARDINAL
ejpam-5569	448	1	1)(k	CARDINAL
ejpam-5569	448	2	3n−	CARDINAL
ejpam-5569	448	3	2)+	CARDINAL
ejpam-5569	448	4	n. m. noureldeen et al	PERSON
ejpam-5569	449	1	j. pure	PERSON
ejpam-5569	449	2	18	CARDINAL
ejpam-5569	449	3	2	CARDINAL
ejpam-5569	449	4	2025	CARDINAL
ejpam-5569	449	5	5569 15	DATE
ejpam-5569	450	1	2)(k	CARDINAL
ejpam-5569	450	2	3)|	CARDINAL
ejpam-5569	450	3	4k	CARDINAL
ejpam-5569	450	4	d(x	ORG
ejpam-5569	450	5	1	CARDINAL
ejpam-5569	451	1	5	CARDINAL
ejpam-5569	453	1	6k	CARDINAL
ejpam-5569	453	2	3)]|	CARDINAL
ejpam-5569	454	1	6k	CARDINAL
ejpam-5569	454	2	3)|	CARDINAL
ejpam-5569	454	3	2n+	CARDINAL
ejpam-5569	454	4	6k	CARDINAL
ejpam-5569	454	5	3)|	CARDINAL
ejpam-5569	455	1	3)(k	CARDINAL
ejpam-5569	455	2	1	CARDINAL
ejpam-5569	457	1	1)(k	CARDINAL
ejpam-5569	457	2	2)−	CARDINAL
ejpam-5569	457	3	6k	CARDINAL
ejpam-5569	457	4	3)|	CARDINAL
ejpam-5569	457	5	4k	CARDINAL
ejpam-5569	457	6	d(x	ORG
ejpam-5569	457	7	1	CARDINAL
ejpam-5569	458	1	6 x	QUANTITY
ejpam-5569	461	1	1]|	CARDINAL
ejpam-5569	461	2	1	CARDINAL
ejpam-5569	462	1	d(x	ORG
ejpam-5569	462	2	1	CARDINAL
ejpam-5569	462	3	7	CARDINAL
ejpam-5569	463	1	2)−	CARDINAL
ejpam-5569	463	2	2	CARDINAL
ejpam-5569	463	3	2n+	CARDINAL
ejpam-5569	463	4	2	CARDINAL
ejpam-5569	463	5	2)(k	CARDINAL
ejpam-5569	464	1	3)]|	CARDINAL
ejpam-5569	465	1	2	CARDINAL
ejpam-5569	466	1	2)(k	CARDINAL
ejpam-5569	466	2	3)|	CARDINAL
ejpam-5569	466	3	4k	CARDINAL
ejpam-5569	468	1	8	CARDINAL
ejpam-5569	470	1	2)−	CARDINAL
ejpam-5569	471	1	2	CARDINAL
ejpam-5569	471	2	2n+	CARDINAL
ejpam-5569	471	3	2	CARDINAL
ejpam-5569	472	1	2)(k	CARDINAL
ejpam-5569	472	2	1)(k	CARDINAL
ejpam-5569	472	3	1	CARDINAL
ejpam-5569	473	1	1)(k	CARDINAL
ejpam-5569	473	2	2)]|	CARDINAL
ejpam-5569	474	1	1	CARDINAL
ejpam-5569	474	2	2)(k	CARDINAL
ejpam-5569	474	3	3	CARDINAL
ejpam-5569	474	4	1)(k	CARDINAL
ejpam-5569	474	5	1)+	ORDINAL
ejpam-5569	476	1	1)(k	CARDINAL
ejpam-5569	476	2	4k	CARDINAL
ejpam-5569	476	3	d(x	ORG
ejpam-5569	476	4	1	CARDINAL
ejpam-5569	477	1	n. m.	PERSON
ejpam-5569	479	1	j. pure	PERSON
ejpam-5569	479	2	18	CARDINAL
ejpam-5569	479	3	2	CARDINAL
ejpam-5569	479	4	2025	CARDINAL
ejpam-5569	479	5	5569 16	DATE
ejpam-5569	479	6	25	CARDINAL
ejpam-5569	480	1	2k	CARDINAL
ejpam-5569	480	2	1)]|	CARDINAL
ejpam-5569	480	3	f(vk−1	ORG
ejpam-5569	480	4	2k	CARDINAL
ejpam-5569	480	5	1)]|	CARDINAL
ejpam-5569	480	6	2)−	CARDINAL
ejpam-5569	480	7	2	CARDINAL
ejpam-5569	480	8	2n+	CARDINAL
ejpam-5569	480	9	2	CARDINAL
ejpam-5569	480	10	2)(k	CARDINAL
ejpam-5569	480	11	3	CARDINAL
ejpam-5569	480	12	2n+ 1)+ +	DATE
ejpam-5569	480	13	2k	CARDINAL
ejpam-5569	480	14	1)]|	CARDINAL
ejpam-5569	481	1	2	CARDINAL
ejpam-5569	482	1	2)(k	CARDINAL
ejpam-5569	482	2	3	CARDINAL
ejpam-5569	482	3	2k	CARDINAL
ejpam-5569	482	4	4k	CARDINAL
ejpam-5569	482	5	d(x	ORG
ejpam-5569	482	6	1	CARDINAL
ejpam-5569	483	1	10 x ∈	QUANTITY
ejpam-5569	483	2	1 ≤	CARDINAL
ejpam-5569	483	3	10.1	CARDINAL
ejpam-5569	483	4	1	CARDINAL
ejpam-5569	485	1	1	CARDINAL
ejpam-5569	487	1	|0−	PERSON
ejpam-5569	487	2	2	CARDINAL
ejpam-5569	487	3	2n+	CARDINAL
ejpam-5569	487	4	2	CARDINAL
ejpam-5569	488	1	2)(k	CARDINAL
ejpam-5569	488	2	3)]|	CARDINAL
ejpam-5569	488	3	2	CARDINAL
ejpam-5569	488	4	2n+	CARDINAL
ejpam-5569	488	5	2	CARDINAL
ejpam-5569	489	1	2)(k	CARDINAL
ejpam-5569	489	2	3)|	CARDINAL
ejpam-5569	489	3	4k	CARDINAL
ejpam-5569	489	4	d(x	ORG
ejpam-5569	489	5	1	CARDINAL
ejpam-5569	491	1	10.2	CARDINAL
ejpam-5569	492	1	1 ≤	QUANTITY
ejpam-5569	493	1	k ≤ l ≤ 2k	FAC
ejpam-5569	493	2	1	CARDINAL
ejpam-5569	493	3	1 ≤ j ≤	QUANTITY
ejpam-5569	494	1	1	CARDINAL
ejpam-5569	497	1	f(vk−1	ORG
ejpam-5569	497	2	1)(j	CARDINAL
ejpam-5569	498	1	1)(j	CARDINAL
ejpam-5569	498	2	2)]|	CARDINAL
ejpam-5569	501	1	2	CARDINAL
ejpam-5569	501	2	2n+	CARDINAL
ejpam-5569	501	3	2)+	CARDINAL
ejpam-5569	501	4	2)(k	CARDINAL
ejpam-5569	501	5	3	CARDINAL
ejpam-5569	501	6	1)(j	CARDINAL
ejpam-5569	501	7	1	CARDINAL
ejpam-5569	501	8	1)(j	CARDINAL
ejpam-5569	501	9	2)]|	CARDINAL
ejpam-5569	501	10	10.3	CARDINAL
ejpam-5569	502	1	1	CARDINAL
ejpam-5569	502	2	1	CARDINAL
ejpam-5569	502	3	1 ≤ j ≤	QUANTITY
ejpam-5569	504	1	1	CARDINAL
ejpam-5569	504	2	f(vk−1	ORG
ejpam-5569	504	3	1)(j	CARDINAL
ejpam-5569	504	4	1	CARDINAL
ejpam-5569	504	5	1)(j	CARDINAL
ejpam-5569	504	6	2)]|	CARDINAL
ejpam-5569	504	7	2	CARDINAL
ejpam-5569	504	8	2n+	CARDINAL
ejpam-5569	504	9	2	CARDINAL
ejpam-5569	504	10	2)(k	CARDINAL
ejpam-5569	504	11	3	CARDINAL
ejpam-5569	504	12	2n+ 1)|	CARDINAL
ejpam-5569	504	13	2	CARDINAL
ejpam-5569	504	14	2n+	CARDINAL
ejpam-5569	504	15	2	CARDINAL
ejpam-5569	505	1	2)(k	CARDINAL
ejpam-5569	505	2	3	CARDINAL
ejpam-5569	505	3	2n+ 1)|	CARDINAL
ejpam-5569	505	4	4k	CARDINAL
ejpam-5569	505	5	d(x	ORG
ejpam-5569	505	6	1	CARDINAL
ejpam-5569	507	1	10.4	CARDINAL
ejpam-5569	508	1	1 ≤	QUANTITY
ejpam-5569	509	1	2k ≤ l ≤	QUANTITY
ejpam-5569	510	1	1	CARDINAL
ejpam-5569	510	2	n. m.	PERSON
ejpam-5569	512	1	j. pure	PERSON
ejpam-5569	512	2	18	CARDINAL
ejpam-5569	512	3	2	CARDINAL
ejpam-5569	512	4	2025	CARDINAL
ejpam-5569	512	5	5569 17	DATE
ejpam-5569	512	6	25	CARDINAL
ejpam-5569	512	7	f(vn−(k+j−2))|	GPE
ejpam-5569	512	8	1 ≤ j ≤ k. subcase	QUANTITY
ejpam-5569	512	9	10.5	CARDINAL
ejpam-5569	513	1	1	CARDINAL
ejpam-5569	513	2	3k	CARDINAL
ejpam-5569	514	1	1	CARDINAL
ejpam-5569	514	2	1	CARDINAL
ejpam-5569	515	1	f(vn−k−1)|	CARDINAL
ejpam-5569	515	2	|0− f(vk	PERSON
ejpam-5569	515	3	1|	CARDINAL
ejpam-5569	516	1	2	CARDINAL
ejpam-5569	517	1	2n+	CARDINAL
ejpam-5569	517	2	2	CARDINAL
ejpam-5569	518	1	2)(k	CARDINAL
ejpam-5569	518	2	3	CARDINAL
ejpam-5569	518	3	4k	CARDINAL
ejpam-5569	518	4	d(x	ORG
ejpam-5569	518	5	1	CARDINAL
ejpam-5569	519	1	|f(x)−f(y)|	DATE
ejpam-5569	520	1	4	CARDINAL
ejpam-5569	520	2	3	CARDINAL
ejpam-5569	520	3	4	CARDINAL
ejpam-5569	520	4	3	CARDINAL
ejpam-5569	520	5	4	CARDINAL
ejpam-5569	521	1	6	CARDINAL
ejpam-5569	521	2	n ≡ 1(mod4	ORG
ejpam-5569	523	1	2	CARDINAL
ejpam-5569	524	1	integer n ≡ 1(mod4	PRODUCT
ejpam-5569	524	2	+ 1	DATE
ejpam-5569	524	3	k ≥ 2	ORG
ejpam-5569	525	1	2n+	CARDINAL
ejpam-5569	525	2	+ 2(i−	DATE
ejpam-5569	525	3	1 ≤	QUANTITY
ejpam-5569	525	4	3	CARDINAL
ejpam-5569	526	1	2n−	CARDINAL
ejpam-5569	526	2	3)−	CARDINAL
ejpam-5569	526	3	1	CARDINAL
ejpam-5569	526	4	1)(j	CARDINAL
ejpam-5569	526	5	2	CARDINAL
ejpam-5569	526	6	k + 2 ≤ i ≤ 2k	ORG
ejpam-5569	526	7	1 ≤ j ≤ k	QUANTITY
ejpam-5569	527	1	1	CARDINAL
ejpam-5569	529	1	2	CARDINAL
ejpam-5569	529	2	2k	CARDINAL
ejpam-5569	530	1	6k	CARDINAL
ejpam-5569	530	2	2)−	CARDINAL
ejpam-5569	530	3	1	CARDINAL
ejpam-5569	530	4	2k + 2 ≤	MONEY
ejpam-5569	530	5	1 ≤ j ≤	QUANTITY
ejpam-5569	532	1	1	CARDINAL
ejpam-5569	533	1	3k	CARDINAL
ejpam-5569	534	1	1	CARDINAL
ejpam-5569	534	2	3k + 1 ≤	QUANTITY
ejpam-5569	534	3	1 ≤	QUANTITY
ejpam-5569	535	1	+ 2− j	CARDINAL
ejpam-5569	535	2	n. m. noureldeen	PERSON
ejpam-5569	537	1	j. pure	PERSON
ejpam-5569	537	2	18	CARDINAL
ejpam-5569	537	3	2	CARDINAL
ejpam-5569	537	4	2025	CARDINAL
ejpam-5569	537	5	5569 18	DATE
ejpam-5569	537	6	3	CARDINAL
ejpam-5569	537	7	2n+	CARDINAL
ejpam-5569	538	1	1 ≤	QUANTITY
ejpam-5569	539	1	1	CARDINAL
ejpam-5569	540	1	2	DATE
ejpam-5569	540	2	k f(vk	PERSON
ejpam-5569	540	3	2n	CARDINAL
ejpam-5569	540	4	2)(j	CARDINAL
ejpam-5569	540	5	1	CARDINAL
ejpam-5569	541	1	1)(j	CARDINAL
ejpam-5569	541	2	2	CARDINAL
ejpam-5569	541	3	k + 1 ≤ i ≤ 2k	FAC
ejpam-5569	541	4	1 ≤ j ≤ k	QUANTITY
ejpam-5569	542	1	2	CARDINAL
ejpam-5569	542	2	2k + 1 f(vk−1+j	MONEY
ejpam-5569	542	3	2k + 1	DATE
ejpam-5569	542	4	1	CARDINAL
ejpam-5569	542	5	2k + 2 ≤	MONEY
ejpam-5569	543	1	1 ≤ j ≤ k	QUANTITY
ejpam-5569	545	1	3k	CARDINAL
ejpam-5569	546	1	2j	CARDINAL
ejpam-5569	546	2	3k + 3 ≤	QUANTITY
ejpam-5569	547	1	1 ≤ j ≤	QUANTITY
ejpam-5569	549	1	1	CARDINAL
ejpam-5569	549	2	+ 2−	CARDINAL
ejpam-5569	550	1	5	CARDINAL
ejpam-5569	550	2	4	CARDINAL
ejpam-5569	550	3	n ≡ 1	ORG
ejpam-5569	550	4	4k	CARDINAL
ejpam-5569	550	5	+ 1	DATE
ejpam-5569	550	6	3	CARDINAL
ejpam-5569	550	7	5	CARDINAL
ejpam-5569	550	8	4	CARDINAL
ejpam-5569	550	9	4	CARDINAL
ejpam-5569	551	1	integer linear	ORG
ejpam-5569	552	1	18–20	CARDINAL
ejpam-5569	557	1	1 ≤	CARDINAL
ejpam-5569	558	1	1 ≤ i ≤ n	QUANTITY
ejpam-5569	561	1	1 ≤	QUANTITY
ejpam-5569	562	1	1	CARDINAL
ejpam-5569	562	2	2 ≤	MONEY
ejpam-5569	564	1	5	CARDINAL
ejpam-5569	564	2	6	CARDINAL
ejpam-5569	564	3	1-4	CARDINAL
ejpam-5569	565	1	section 4	LAW
ejpam-5569	567	1	j. pure	PERSON
ejpam-5569	567	2	18	CARDINAL
ejpam-5569	567	3	2	CARDINAL
ejpam-5569	567	4	2025	CARDINAL
ejpam-5569	567	5	5569 19	DATE
ejpam-5569	567	6	25	CARDINAL
ejpam-5569	567	7	2.8 ghz	QUANTITY
ejpam-5569	567	8	8	CARDINAL
ejpam-5569	568	1	7	CARDINAL
ejpam-5569	569	1	2	CARDINAL
ejpam-5569	569	2	4	CARDINAL
ejpam-5569	569	3	6	CARDINAL
ejpam-5569	569	4	5	CARDINAL
ejpam-5569	569	5	2	CARDINAL
ejpam-5569	569	6	3	DATE
ejpam-5569	569	7	4	CARDINAL
ejpam-5569	570	1	1	CARDINAL
ejpam-5569	570	2	2	DATE
ejpam-5569	570	3	3	DATE
ejpam-5569	570	4	4	CARDINAL
ejpam-5569	570	5	2	CARDINAL
ejpam-5569	570	6	1	CARDINAL
ejpam-5569	570	7	2	DATE
ejpam-5569	570	8	3	DATE
ejpam-5569	570	9	4	CARDINAL
ejpam-5569	570	10	6	CARDINAL
ejpam-5569	571	1	2	CARDINAL
ejpam-5569	572	1	6	CARDINAL
ejpam-5569	573	1	2	CARDINAL
ejpam-5569	573	2	3	DATE
ejpam-5569	573	3	4	DATE
ejpam-5569	573	4	5	DATE
ejpam-5569	574	1	2n	CARDINAL
ejpam-5569	574	2	1,2,3,4	CARDINAL
ejpam-5569	574	3	6	CARDINAL
ejpam-5569	575	1	2 4 4 o(1	TIME
ejpam-5569	575	2	4	CARDINAL
ejpam-5569	575	3	6	CARDINAL
ejpam-5569	575	4	12	CARDINAL
ejpam-5569	575	5	23	CARDINAL
ejpam-5569	575	6	3	CARDINAL
ejpam-5569	575	7	1	CARDINAL
ejpam-5569	576	1	6	CARDINAL
ejpam-5569	577	1	4	CARDINAL
ejpam-5569	578	1	2n	CARDINAL
ejpam-5569	578	2	1	CARDINAL
ejpam-5569	579	1	6	CARDINAL
ejpam-5569	580	1	6 12 33	TIME
ejpam-5569	580	2	33	CARDINAL
ejpam-5569	580	3	95	CARDINAL
ejpam-5569	580	4	189	CARDINAL
ejpam-5569	580	5	315	CARDINAL
ejpam-5569	580	6	473	CARDINAL
ejpam-5569	580	7	473	CARDINAL
ejpam-5569	580	8	663	CARDINAL
ejpam-5569	580	9	60 885	QUANTITY
ejpam-5569	580	10	885 0.083501	CARDINAL
ejpam-5569	580	11	34 68 1139	DATE
ejpam-5569	580	12	1425	CARDINAL
ejpam-5569	580	13	1743	CARDINAL
ejpam-5569	580	14	2093	CARDINAL
ejpam-5569	580	15	2475 0.121298	PERCENT
ejpam-5569	580	16	4803	DATE
ejpam-5569	580	17	0.301669 54 108 2889	MONEY
ejpam-5569	580	18	2889	CARDINAL
ejpam-5569	580	19	3335	PRODUCT
ejpam-5569	580	20	3335	CARDINAL
ejpam-5569	580	21	3813	CARDINAL
ejpam-5569	580	22	7443	DATE
ejpam-5569	580	23	4064	DATE
ejpam-5569	580	24	4064	DATE
ejpam-5569	580	25	7939	DATE
ejpam-5569	580	26	0.527846 68	MONEY
ejpam-5569	580	27	4590	PRODUCT
ejpam-5569	580	28	4590	CARDINAL
ejpam-5569	580	29	5148	DATE
ejpam-5569	580	30	5738	DATE
ejpam-5569	580	31	11251	DATE
ejpam-5569	580	32	0.875030 80	MONEY
ejpam-5569	580	33	6360	CARDINAL
ejpam-5569	580	34	6360	CARDINAL
ejpam-5569	580	35	4	DATE
ejpam-5569	580	36	3	CARDINAL
ejpam-5569	580	37	6	CARDINAL
ejpam-5569	580	38	1 coincide	TIME
ejpam-5569	580	39	6	CARDINAL
ejpam-5569	581	1	1	CARDINAL
ejpam-5569	581	2	3	CARDINAL
ejpam-5569	581	3	1	CARDINAL
ejpam-5569	581	4	n. m.	PERSON
ejpam-5569	583	1	j. pure	PERSON
ejpam-5569	583	2	18	CARDINAL
ejpam-5569	583	3	2	CARDINAL
ejpam-5569	583	4	2025	CARDINAL
ejpam-5569	583	5	5569 20	DATE
ejpam-5569	583	6	25	CARDINAL
ejpam-5569	583	7	6	CARDINAL
ejpam-5569	584	1	1	CARDINAL
ejpam-5569	584	2	7	CARDINAL
ejpam-5569	585	1	6	CARDINAL
ejpam-5569	585	2	1	CARDINAL
ejpam-5569	586	1	6	CARDINAL
ejpam-5569	587	1	4	CARDINAL
ejpam-5569	587	2	4	CARDINAL
ejpam-5569	587	3	2	CARDINAL
ejpam-5569	588	1	6	CARDINAL
ejpam-5569	589	1	3(mod)4	CARDINAL
ejpam-5569	590	1	2n	CARDINAL
ejpam-5569	590	2	2	CARDINAL
ejpam-5569	591	1	6	CARDINAL
ejpam-5569	592	1	7 14 46	TIME
ejpam-5569	592	2	46	DATE
ejpam-5569	592	3	118	CARDINAL
ejpam-5569	592	4	118	CARDINAL
ejpam-5569	592	5	222	CARDINAL
ejpam-5569	592	6	222	CARDINAL
ejpam-5569	592	7	358	CARDINAL
ejpam-5569	592	8	649	CARDINAL
ejpam-5569	592	9	526	CARDINAL
ejpam-5569	592	10	0.051813	ORG
ejpam-5569	592	11	54 726	QUANTITY
ejpam-5569	592	12	726 0.081522	CARDINAL
ejpam-5569	592	13	958	CARDINAL
ejpam-5569	592	14	1222	DATE
ejpam-5569	592	15	0.092306 2313 0.266207	MONEY
ejpam-5569	592	16	1518	CARDINAL
ejpam-5569	592	17	1518	CARDINAL
ejpam-5569	592	18	43 86	DATE
ejpam-5569	592	19	1846	DATE
ejpam-5569	592	20	1846	DATE
ejpam-5569	592	21	94 2206	TIME
ejpam-5569	592	22	2206	CARDINAL
ejpam-5569	592	23	4233	DATE
ejpam-5569	592	24	0.486650 51 102 2598	MONEY
ejpam-5569	592	25	2598	CARDINAL
ejpam-5569	592	26	3022	CARDINAL
ejpam-5569	592	27	5833	DATE
ejpam-5569	592	28	3478	CARDINAL
ejpam-5569	593	1	3966	CARDINAL
ejpam-5569	593	2	4486	PRODUCT
ejpam-5569	593	3	4486	DATE
ejpam-5569	593	4	0.829255 75	MONEY
ejpam-5569	593	5	5622	DATE
ejpam-5569	593	6	10953	DATE
ejpam-5569	593	7	83 166 6886	DATE
ejpam-5569	593	8	6886	DATE
ejpam-5569	593	9	13449	DATE
ejpam-5569	593	10	87	CARDINAL
ejpam-5569	593	11	7566	DATE
ejpam-5569	593	12	7566	DATE
ejpam-5569	593	13	1.293168 n. m. noureldeen et al	QUANTITY
ejpam-5569	594	1	j. pure	PERSON
ejpam-5569	594	2	18	CARDINAL
ejpam-5569	594	3	2	CARDINAL
ejpam-5569	594	4	2025	CARDINAL
ejpam-5569	594	5	5569 21	DATE
ejpam-5569	594	6	25	CARDINAL
ejpam-5569	594	7	4	CARDINAL
ejpam-5569	594	8	7	CARDINAL
ejpam-5569	594	9	2	CARDINAL
ejpam-5569	594	10	6	CARDINAL
ejpam-5569	594	11	4	CARDINAL
ejpam-5569	595	1	2	CARDINAL
ejpam-5569	595	2	4	CARDINAL
ejpam-5569	595	3	2	CARDINAL
ejpam-5569	595	4	6	CARDINAL
ejpam-5569	596	1	2	CARDINAL
ejpam-5569	596	2	7	CARDINAL
ejpam-5569	597	1	7	CARDINAL
ejpam-5569	597	2	2	CARDINAL
ejpam-5569	598	1	6	CARDINAL
ejpam-5569	599	1	3(mod)4	CARDINAL
ejpam-5569	599	2	8	CARDINAL
ejpam-5569	599	3	3	CARDINAL
ejpam-5569	600	1	6	CARDINAL
ejpam-5569	601	1	5	CARDINAL
ejpam-5569	601	2	8	CARDINAL
ejpam-5569	601	3	3	CARDINAL
ejpam-5569	601	4	6	CARDINAL
ejpam-5569	601	5	4	CARDINAL
ejpam-5569	602	1	3	CARDINAL
ejpam-5569	602	2	5	CARDINAL
ejpam-5569	602	3	3	CARDINAL
ejpam-5569	602	4	6	CARDINAL
ejpam-5569	603	1	3	CARDINAL
ejpam-5569	603	2	7	CARDINAL
ejpam-5569	604	1	n. m. noureldeen et al	PERSON
ejpam-5569	605	1	j. pure	PERSON
ejpam-5569	605	2	18	CARDINAL
ejpam-5569	605	3	2	CARDINAL
ejpam-5569	605	4	2025	CARDINAL
ejpam-5569	605	5	5569 22	DATE
ejpam-5569	605	6	25	CARDINAL
ejpam-5569	605	7	5	CARDINAL
ejpam-5569	605	8	3	CARDINAL
ejpam-5569	607	1	2n	CARDINAL
ejpam-5569	607	2	3	CARDINAL
ejpam-5569	608	1	6	CARDINAL
ejpam-5569	609	1	8 16 60	QUANTITY
ejpam-5569	609	2	60	CARDINAL
ejpam-5569	609	3	138	CARDINAL
ejpam-5569	609	4	248	CARDINAL
ejpam-5569	609	5	248	CARDINAL
ejpam-5569	609	6	390	CARDINAL
ejpam-5569	609	7	0.053037 723	MONEY
ejpam-5569	609	8	564	CARDINAL
ejpam-5569	609	9	770	CARDINAL
ejpam-5569	609	10	64 1008	DATE
ejpam-5569	609	11	1008	DATE
ejpam-5569	609	12	1278	CARDINAL
ejpam-5569	609	13	1278	CARDINAL
ejpam-5569	609	14	1580	CARDINAL
ejpam-5569	609	15	88 1914	DATE
ejpam-5569	609	16	1914	DATE
ejpam-5569	609	17	2280	CARDINAL
ejpam-5569	609	18	4419	DATE
ejpam-5569	609	19	0.287511 52	MONEY
ejpam-5569	609	20	104 2678 o(1	LAW
ejpam-5569	609	21	2678	CARDINAL
ejpam-5569	609	22	0.451393 56 112	MONEY
ejpam-5569	609	23	3108	DATE
ejpam-5569	609	24	3570	CARDINAL
ejpam-5569	609	25	4064	DATE
ejpam-5569	609	26	4064	DATE
ejpam-5569	609	27	7939	DATE
ejpam-5569	609	28	0.527846 68	MONEY
ejpam-5569	609	29	4590	PRODUCT
ejpam-5569	609	30	4590	CARDINAL
ejpam-5569	609	31	5148	DATE
ejpam-5569	609	32	10083	DATE
ejpam-5569	609	33	5738	DATE
ejpam-5569	609	34	11251	DATE
ejpam-5569	609	35	0.983264 80	MONEY
ejpam-5569	609	36	6360	CARDINAL
ejpam-5569	609	37	6360	CARDINAL
ejpam-5569	609	38	7014	DATE
ejpam-5569	610	1	13779	DATE
ejpam-5569	610	2	1.034510	CARDINAL
ejpam-5569	610	3	9	CARDINAL
ejpam-5569	610	4	4	CARDINAL
ejpam-5569	611	1	6	CARDINAL
ejpam-5569	612	1	1(mod)4	CARDINAL
ejpam-5569	612	2	6	CARDINAL
ejpam-5569	612	3	9	CARDINAL
ejpam-5569	612	4	4	CARDINAL
ejpam-5569	612	5	6	CARDINAL
ejpam-5569	612	6	4	CARDINAL
ejpam-5569	613	1	4	CARDINAL
ejpam-5569	613	2	6	CARDINAL
ejpam-5569	613	3	4	CARDINAL
ejpam-5569	613	4	6	CARDINAL
ejpam-5569	613	5	n. m. noureldeen et al	PERSON
ejpam-5569	614	1	j. pure	PERSON
ejpam-5569	614	2	18	CARDINAL
ejpam-5569	614	3	2	CARDINAL
ejpam-5569	614	4	2025	CARDINAL
ejpam-5569	614	5	5569 23	DATE
ejpam-5569	614	6	25	DATE
ejpam-5569	615	1	4	CARDINAL
ejpam-5569	615	2	7	CARDINAL
ejpam-5569	616	1	6	CARDINAL
ejpam-5569	616	2	4	CARDINAL
ejpam-5569	617	1	6	CARDINAL
ejpam-5569	618	1	1(mod)4	CARDINAL
ejpam-5569	619	1	2n	CARDINAL
ejpam-5569	619	2	4	CARDINAL
ejpam-5569	619	3	6	CARDINAL
ejpam-5569	620	1	9 18 79	QUANTITY
ejpam-5569	620	2	79	CARDINAL
ejpam-5569	620	3	167	CARDINAL
ejpam-5569	620	4	287	CARDINAL
ejpam-5569	620	5	287	CARDINAL
ejpam-5569	620	6	0.04728 513 0.134112	MONEY
ejpam-5569	620	7	439	CARDINAL
ejpam-5569	620	8	439 0.049498	CARDINAL
ejpam-5569	620	9	623	CARDINAL
ejpam-5569	620	10	58 839	QUANTITY
ejpam-5569	620	11	839	CARDINAL
ejpam-5569	620	12	1087	CARDINAL
ejpam-5569	620	13	74 1367	TIME
ejpam-5569	620	14	1367	DATE
ejpam-5569	620	15	1679	CARDINAL
ejpam-5569	620	16	45	MONEY
ejpam-5569	620	17	2023	CARDINAL
ejpam-5569	620	18	2399 0.114788	CARDINAL
ejpam-5569	620	19	2807	CARDINAL
ejpam-5569	620	20	0.451393 57	MONEY
ejpam-5569	620	21	3247	CARDINAL
ejpam-5569	620	22	3719	CARDINAL
ejpam-5569	620	23	0.166031	ORG
ejpam-5569	620	24	4223	CARDINAL
ejpam-5569	620	25	4759	DATE
ejpam-5569	620	26	4759	DATE
ejpam-5569	621	1	10369	DATE
ejpam-5569	621	2	5927	DATE
ejpam-5569	621	3	162 6559	DATE
ejpam-5569	621	4	6559	DATE
ejpam-5569	621	5	12801	DATE
ejpam-5569	621	6	7223	DATE
ejpam-5569	621	7	14113	DATE
ejpam-5569	633	1	n. m. noureldeen et al	PERSON
ejpam-5569	634	1	j. pure	PERSON
ejpam-5569	634	2	18	CARDINAL
ejpam-5569	634	3	2	CARDINAL
ejpam-5569	634	4	2025	CARDINAL
ejpam-5569	634	5	5569	DATE
ejpam-5569	634	6	25 7	DATE
ejpam-5569	640	1	two	CARDINAL
ejpam-5569	650	1	1	CARDINAL
ejpam-5569	650	2	w. k. hale	PERSON
ejpam-5569	653	1	68(12):1497–1514, 1980	DATE
ejpam-5569	654	1	2	CARDINAL
ejpam-5569	654	2	j. a. a. gallian	PERSON
ejpam-5569	656	1	combinatorics	ORG
ejpam-5569	656	2	24	CARDINAL
ejpam-5569	656	3	2021	DATE
ejpam-5569	657	1	3	CARDINAL
ejpam-5569	657	2	j. griggs	PERSON
ejpam-5569	657	3	r. yeh	PERSON
ejpam-5569	658	1	2	CARDINAL
ejpam-5569	658	2	siam journal	ORG
ejpam-5569	658	3	5(4):586–595, 1992	DATE
ejpam-5569	659	1	4	CARDINAL
ejpam-5569	659	2	g. chartrand	PERSON
ejpam-5569	659	3	d. erwin	PERSON
ejpam-5569	659	4	p. zhang	PERSON
ejpam-5569	659	5	f. harary	PERSON
ejpam-5569	661	1	the institute of combinatorics	ORG
ejpam-5569	661	2	33:77–85, 2001	DATE
ejpam-5569	662	1	5	CARDINAL
ejpam-5569	662	2	m. kehikech	PERSON
ejpam-5569	662	3	r. khemoufa	PERSON
ejpam-5569	663	1	linear	ORG
ejpam-5569	664	1	27(1):105–123	GPE
ejpam-5569	664	2	2007	DATE
ejpam-5569	665	1	6	CARDINAL
ejpam-5569	665	2	p. panigrahi	PERSON
ejpam-5569	667	1	7643	DATE
ejpam-5569	667	2	125–129,	DATE
ejpam-5569	667	3	2012	DATE
ejpam-5569	668	1	7	CARDINAL
ejpam-5569	668	2	e. m. badr	PERSON
ejpam-5569	668	3	m. i. moussa	PERSON
ejpam-5569	670	1	26(7):4955–4964	CARDINAL
ejpam-5569	670	2	2020	DATE
ejpam-5569	671	1	n. m. noureldeen et al	PERSON
ejpam-5569	672	1	j. pure	PERSON
ejpam-5569	672	2	18	CARDINAL
ejpam-5569	672	3	2	CARDINAL
ejpam-5569	672	4	2025	CARDINAL
ejpam-5569	672	5	5569 25	DATE
ejpam-5569	672	6	25	CARDINAL
ejpam-5569	673	1	8	CARDINAL
ejpam-5569	673	2	s. gomathi	PERSON
ejpam-5569	673	3	p. venugopal	PERSON
ejpam-5569	675	1	12(3):665–676	CARDINAL
ejpam-5569	675	2	2021	DATE
ejpam-5569	676	1	9	CARDINAL
ejpam-5569	676	2	r. mahapatra	PERSON
ejpam-5569	676	3	s. samanta	PERSON
ejpam-5569	676	4	t. allahviranloo	GPE
ejpam-5569	676	5	m. pal	PERSON
ejpam-5569	678	1	38:1–20	DATE
ejpam-5569	678	2	2019	DATE
ejpam-5569	679	1	10	CARDINAL
ejpam-5569	679	2	x. li	PERSON
ejpam-5569	679	3	v. mak	PERSON
ejpam-5569	679	4	s. zhou	PERSON
ejpam-5569	681	1	158:507–515,	DATE
ejpam-5569	681	2	2010	DATE
ejpam-5569	682	1	11	CARDINAL
ejpam-5569	683	1	liu	PERSON
ejpam-5569	684	1	308:1153–1164, 2008	DATE
ejpam-5569	685	1	12	CARDINAL
ejpam-5569	687	1	s. r. kola	PERSON
ejpam-5569	690	1	j. graphs	PERSON
ejpam-5569	690	2	17(1):269–275, 2020	DATE
ejpam-5569	691	1	13	CARDINAL
ejpam-5569	692	1	liu	PERSON
ejpam-5569	692	2	m. xie	PERSON
ejpam-5569	694	1	90:307–319	CARDINAL
ejpam-5569	694	2	2009	DATE
ejpam-5569	695	1	14	CARDINAL
ejpam-5569	696	1	liu	PERSON
ejpam-5569	698	1	j. discrete	PERSON
ejpam-5569	698	2	19:610–621, 2005	DATE
ejpam-5569	699	1	15	CARDINAL
ejpam-5569	699	2	h. qi	PERSON
ejpam-5569	699	3	s. nazeer	PERSON
ejpam-5569	699	4	i. kousar	PERSON
ejpam-5569	699	5	m. a. umar	PERSON
ejpam-5569	699	6	n. a. shah	PERSON
ejpam-5569	700	1	ieee access,	PERSON
ejpam-5569	700	2	8:109801–109806	CARDINAL
ejpam-5569	700	3	2020	DATE
ejpam-5569	701	1	16	CARDINAL
ejpam-5569	701	2	m. morris-rivera	PERSON
ejpam-5569	701	3	m. tomova	PERSON
ejpam-5569	701	4	y. yeager	PERSON
ejpam-5569	702	1	103:81–96, 2012	DATE
ejpam-5569	703	1	17	CARDINAL
ejpam-5569	703	2	j. p. ortiz	PERSON
ejpam-5569	703	3	p. martinez	PERSON
ejpam-5569	703	4	m. tomova	PERSON
ejpam-5569	707	1	311:45–62, 2011	DATE
ejpam-5569	708	1	18	CARDINAL
ejpam-5569	708	2	v. s. reddy	PERSON
ejpam-5569	708	3	v. k. iyer	PERSON
ejpam-5569	712	1	71(2):207–215, 2011	DATE
ejpam-5569	713	1	19	CARDINAL
ejpam-5569	713	2	p. panigrahi	PERSON
ejpam-5569	715	1	australian	NORP
ejpam-5569	715	2	j. combin	PERSON
ejpam-5569	715	3	55:273–288,	DATE
ejpam-5569	715	4	2013	DATE
ejpam-5569	716	1	20	CARDINAL
ejpam-5569	716	2	p. panigrahi	PERSON
ejpam-5569	718	1	192:87–100	DATE
ejpam-5569	718	2	2015	DATE
ejpam-5569	719	1	21	CARDINAL
ejpam-5569	719	2	p. zhang	PERSON
ejpam-5569	721	1	2002	DATE
ejpam-5569	722	1	22	CARDINAL
ejpam-5569	722	2	a. h. alkasasbeh	PERSON
ejpam-5569	722	3	e. badr	PERSON
ejpam-5569	722	4	h. attiya	PERSON
ejpam-5569	722	5	h. m. shabana	PERSON
ejpam-5569	724	1	2023	CARDINAL
ejpam-5569	725	1	23	CARDINAL
ejpam-5569	725	2	e. badr	PERSON
ejpam-5569	725	3	s. nada	PERSON
ejpam-5569	725	4	m. m. a. al-shamiri	PERSON
ejpam-5569	725	5	a. abdel-hay	PERSON
ejpam-5569	725	6	a. elrokh	PERSON
ejpam-5569	727	1	j. math	PERSON
ejpam-5569	727	2	3303	CARDINAL
ejpam-5569	727	3	2022	CARDINAL
ejpam-5569	728	1	24	CARDINAL
ejpam-5569	728	2	n. m. noureldeen	PERSON
ejpam-5569	728	3	e. badr	PERSON
ejpam-5569	728	4	i. m. hagag	PERSON
ejpam-5569	728	5	h. shabana	PERSON
ejpam-5569	731	1	j. pure	PERSON
ejpam-5569	731	2	18(1):5614	ORG
ejpam-5569	731	3	2025	DATE
ejpam-5569	732	1	25	CARDINAL
ejpam-5569	732	2	k. n. meera	PERSON
ejpam-5569	733	1	journal of intelligent &	ORG
ejpam-5569	733	2	44(2):1691–1702	CARDINAL
ejpam-5569	733	3	2023	CARDINAL
ejpam-5569	734	1	26	CARDINAL
ejpam-5569	734	2	k. n. meera	PERSON
ejpam-5569	736	1	2021	CARDINAL
ejpam-5569	736	2	2nd	ORDINAL
ejpam-5569	736	3	4.0	CARDINAL
ejpam-5569	736	4	1–3	CARDINAL
ejpam-5569	736	5	bangalore	GPE
ejpam-5569	736	6	india	GPE
ejpam-5569	736	7	2021	DATE