id	sid	eid	entity	type
ejpam-6140	1	1	european journal	ORG
ejpam-6140	1	2	2025	DATE
ejpam-6140	1	3	18	CARDINAL
ejpam-6140	1	4	3	CARDINAL
ejpam-6140	1	5	6140	CARDINAL
ejpam-6140	1	6	1307-5543	DATE
ejpam-6140	1	7	new york	GPE
ejpam-6140	1	8	one	CARDINAL
ejpam-6140	1	9	i. khalil1,2,∗	PERSON
ejpam-6140	1	10	ishak hashim1	PERSON
ejpam-6140	1	11	maan a. rasheed3	PERSON
ejpam-6140	1	12	momani4 1	ORG
ejpam-6140	1	13	universiti kebangsaan malaysia	PERSON
ejpam-6140	1	14	43600	DATE
ejpam-6140	1	15	ukm bangi	PERSON
ejpam-6140	1	16	selangor	GPE
ejpam-6140	1	17	malaysia 2	ORG
ejpam-6140	1	18	tikrit university	ORG
ejpam-6140	1	19	tikrit	GPE
ejpam-6140	1	20	iraq	GPE
ejpam-6140	1	21	3	CARDINAL
ejpam-6140	1	22	university of baghdad	ORG
ejpam-6140	1	23	baghdad	GPE
ejpam-6140	1	24	iraq	GPE
ejpam-6140	1	25	4	CARDINAL
ejpam-6140	1	26	ajman university	ORG
ejpam-6140	1	27	ajman	GPE
ejpam-6140	1	28	united arab	GPE
ejpam-6140	1	29	emirates	GPE
ejpam-6140	2	1	one	CARDINAL
ejpam-6140	2	2	parabolic systems	ORG
ejpam-6140	3	1	firstly	ORDINAL
ejpam-6140	5	1	secondly	ORDINAL
ejpam-6140	5	2	two	CARDINAL
ejpam-6140	8	1	second	ORDINAL
ejpam-6140	13	1	2020	DATE
ejpam-6140	13	2	35k57	CARDINAL
ejpam-6140	13	3	65m06	CARDINAL
ejpam-6140	13	4	65m12	CARDINAL
ejpam-6140	13	5	35b44	CARDINAL
ejpam-6140	13	6	1	CARDINAL
ejpam-6140	14	1	recent decades	DATE
ejpam-6140	14	2	1	CARDINAL
ejpam-6140	14	3	3	CARDINAL
ejpam-6140	16	1	m. i. khalil	PERSON
ejpam-6140	17	1	1	CARDINAL
ejpam-6140	17	2	2025	CARDINAL
ejpam-6140	18	1	m. i. khalil et al	PERSON
ejpam-6140	19	1	j. pure	PERSON
ejpam-6140	19	2	18	CARDINAL
ejpam-6140	19	3	3	CARDINAL
ejpam-6140	19	4	2025	CARDINAL
ejpam-6140	19	5	6140 2	DATE
ejpam-6140	19	6	17	CARDINAL
ejpam-6140	22	1	9	CARDINAL
ejpam-6140	22	2	11	CARDINAL
ejpam-6140	23	1	10	CARDINAL
ejpam-6140	23	2	0	CARDINAL
ejpam-6140	26	1	0	CARDINAL
ejpam-6140	28	1	+ f(v	PERSON
ejpam-6140	28	2	0	CARDINAL
ejpam-6140	28	3	1)×	DATE
ejpam-6140	28	4	0	CARDINAL
ejpam-6140	30	1	v(0	PERSON
ejpam-6140	31	1	0	CARDINAL
ejpam-6140	31	2	0	CARDINAL
ejpam-6140	31	3	0	CARDINAL
ejpam-6140	31	4	1	CARDINAL
ejpam-6140	33	1	0	CARDINAL
ejpam-6140	33	2	∈	ORG
ejpam-6140	34	1	12	CARDINAL
ejpam-6140	35	1	time[9	ORG
ejpam-6140	36	1	1	CARDINAL
ejpam-6140	37	1	1	CARDINAL
ejpam-6140	37	2	13–19	CARDINAL
ejpam-6140	38	1	15	CARDINAL
ejpam-6140	39	1	two	CARDINAL
ejpam-6140	39	2	9	CARDINAL
ejpam-6140	39	3	13	DATE
ejpam-6140	39	4	15	CARDINAL
ejpam-6140	39	5	g(u	PRODUCT
ejpam-6140	39	6	1 f(v	QUANTITY
ejpam-6140	40	1	g(u	PRODUCT
ejpam-6140	40	2	0	CARDINAL
ejpam-6140	41	1	the last decades	DATE
ejpam-6140	41	2	20–26	CARDINAL
ejpam-6140	42	1	25	CARDINAL
ejpam-6140	42	2	1	CARDINAL
ejpam-6140	42	3	m. i. khalil et al	PERSON
ejpam-6140	43	1	j. pure	PERSON
ejpam-6140	43	2	18	CARDINAL
ejpam-6140	43	3	3	CARDINAL
ejpam-6140	43	4	2025	CARDINAL
ejpam-6140	43	5	6140 3	DATE
ejpam-6140	43	6	17	CARDINAL
ejpam-6140	48	1	26	CARDINAL
ejpam-6140	48	2	1	CARDINAL
ejpam-6140	49	1	nbus	ORG
ejpam-6140	49	2	1	CARDINAL
ejpam-6140	52	1	1	CARDINAL
ejpam-6140	53	1	c.n.	GPE
ejpam-6140	54	1	six	CARDINAL
ejpam-6140	55	1	second	ORDINAL
ejpam-6140	55	2	1	CARDINAL
ejpam-6140	56	1	1	CARDINAL
ejpam-6140	56	2	section three	LAW
ejpam-6140	57	1	fourth	ORDINAL
ejpam-6140	58	1	two	CARDINAL
ejpam-6140	60	1	1.1	CARDINAL
ejpam-6140	61	1	0 ≤	MONEY
ejpam-6140	63	1	1	CARDINAL
ejpam-6140	69	1	2	CARDINAL
ejpam-6140	69	2	second	ORDINAL
ejpam-6140	69	3	1	CARDINAL
ejpam-6140	69	4	the standard secondorder central	ORG
ejpam-6140	70	1	27	CARDINAL
ejpam-6140	71	1	− 2ui	PERSON
ejpam-6140	72	1	3	CARDINAL
ejpam-6140	72	2	2vi	ORDINAL
ejpam-6140	73	1	4	CARDINAL
ejpam-6140	73	2	0	CARDINAL
ejpam-6140	73	3	5	CARDINAL
ejpam-6140	73	4	0 ≤	MONEY
ejpam-6140	73	5	6	CARDINAL
ejpam-6140	73	6	1	CARDINAL
ejpam-6140	74	1	26	CARDINAL
ejpam-6140	75	1	m. i. khalil et al	PERSON
ejpam-6140	76	1	j. pure	PERSON
ejpam-6140	76	2	18	CARDINAL
ejpam-6140	76	3	3	CARDINAL
ejpam-6140	76	4	2025	CARDINAL
ejpam-6140	76	5	6140 4 of 17	DATE
ejpam-6140	78	1	0	CARDINAL
ejpam-6140	78	2	7	CARDINAL
ejpam-6140	79	1	1	CARDINAL
ejpam-6140	80	1	26	CARDINAL
ejpam-6140	80	2	0	CARDINAL
ejpam-6140	82	1	1	CARDINAL
ejpam-6140	83	1	26	CARDINAL
ejpam-6140	83	2	1	CARDINAL
ejpam-6140	87	1	∞ ∥u0∥ ds g1(s	PERSON
ejpam-6140	87	2	9	CARDINAL
ejpam-6140	88	1	1	CARDINAL
ejpam-6140	88	2	1)c0	CARDINAL
ejpam-6140	88	3	10	CARDINAL
ejpam-6140	90	1	+ 1 p+	DATE
ejpam-6140	90	2	11	CARDINAL
ejpam-6140	90	3	1	CARDINAL
ejpam-6140	90	4	0	CARDINAL
ejpam-6140	90	5	1	CARDINAL
ejpam-6140	90	6	1	CARDINAL
ejpam-6140	90	7	0	CARDINAL
ejpam-6140	91	1	12	CARDINAL
ejpam-6140	91	2	2	CARDINAL
ejpam-6140	92	1	26	CARDINAL
ejpam-6140	92	2	∈	ORG
ejpam-6140	92	3	′′	ORG
ejpam-6140	92	4	g′′	PERSON
ejpam-6140	92	5	0	DATE
ejpam-6140	92	6	0	CARDINAL
ejpam-6140	93	1	0,∞	DATE
ejpam-6140	93	2	∀ε	PERSON
ejpam-6140	93	3	0	CARDINAL
ejpam-6140	94	1	13	CARDINAL
ejpam-6140	95	1	limz→∞	PRODUCT
ejpam-6140	96	1	0	CARDINAL
ejpam-6140	96	2	lim z→∞	PERSON
ejpam-6140	98	1	14	CARDINAL
ejpam-6140	99	1	0	CARDINAL
ejpam-6140	99	2	0	CARDINAL
ejpam-6140	99	3	15	CARDINAL
ejpam-6140	99	4	i=1 hui(t)υi	GPE
ejpam-6140	99	5	i=1 hvi(t),υi	PERSON
ejpam-6140	99	6	16	CARDINAL
ejpam-6140	99	7	m. i. khalil et al	PERSON
ejpam-6140	100	1	j. pure	PERSON
ejpam-6140	100	2	18	CARDINAL
ejpam-6140	100	3	3	CARDINAL
ejpam-6140	100	4	2025	CARDINAL
ejpam-6140	100	5	6140 5	DATE
ejpam-6140	100	6	17	CARDINAL
ejpam-6140	100	7	−δ2υi	CARDINAL
ejpam-6140	100	8	1	CARDINAL
ejpam-6140	100	9	2	DATE
ejpam-6140	102	1	1	CARDINAL
ejpam-6140	102	2	0	CARDINAL
ejpam-6140	102	3	4	CARDINAL
ejpam-6140	102	4	sin2	DATE
ejpam-6140	102	5	2	CARDINAL
ejpam-6140	103	1	17	CARDINAL
ejpam-6140	104	1	∈	ORG
ejpam-6140	104	2	18	CARDINAL
ejpam-6140	104	3	λnz2	LOC
ejpam-6140	106	1	19	CARDINAL
ejpam-6140	106	2	3	CARDINAL
ejpam-6140	107	1	26	CARDINAL
ejpam-6140	107	2	∈	ORG
ejpam-6140	107	3	1	CARDINAL
ejpam-6140	107	4	1]×	CARDINAL
ejpam-6140	108	1	0	CARDINAL
ejpam-6140	109	1	0	CARDINAL
ejpam-6140	110	1	0	CARDINAL
ejpam-6140	110	2	20	CARDINAL
ejpam-6140	110	3	1	CARDINAL
ejpam-6140	110	4	∈	PRODUCT
ejpam-6140	110	5	∥uh(t)−	ORG
ejpam-6140	111	1	o	DATE
ejpam-6140	111	2	∥e(0)∥∞ + h2	PRODUCT
ejpam-6140	111	3	∥vh(t)−	ORG
ejpam-6140	111	4	o	DATE
ejpam-6140	111	5	∥e(0)∥∞ + h2	PRODUCT
ejpam-6140	111	6	0	CARDINAL
ejpam-6140	111	7	21	CARDINAL
ejpam-6140	112	1	∥e(0)∥∞ = max {∥∥u0	PERSON
ejpam-6140	112	2	4	CARDINAL
ejpam-6140	113	1	26	CARDINAL
ejpam-6140	113	2	∈	ORG
ejpam-6140	113	3	f(z	DATE
ejpam-6140	113	4	g(z	PERSON
ejpam-6140	113	5	0	CARDINAL
ejpam-6140	115	1	0	DATE
ejpam-6140	115	2	•	CARDINAL
ejpam-6140	117	1	limz→∞	PRODUCT
ejpam-6140	117	2	0	CARDINAL
ejpam-6140	117	3	limz→∞	PRODUCT
ejpam-6140	118	1	0 • f(z̄)− π2z̄	CARDINAL
ejpam-6140	118	2	0	CARDINAL
ejpam-6140	119	1	∈	ORG
ejpam-6140	119	2	1]×	CARDINAL
ejpam-6140	120	1	0	CARDINAL
ejpam-6140	121	1	lim t→t	PERSON
ejpam-6140	121	2	1	CARDINAL
ejpam-6140	122	1	1	CARDINAL
ejpam-6140	122	2	22	CARDINAL
ejpam-6140	122	3	m. i. khalil et al	PERSON
ejpam-6140	123	1	j. pure	PERSON
ejpam-6140	123	2	18	CARDINAL
ejpam-6140	123	3	3	CARDINAL
ejpam-6140	123	4	2025	CARDINAL
ejpam-6140	123	5	6140 6	DATE
ejpam-6140	123	6	17	CARDINAL
ejpam-6140	123	7	0(1	CARDINAL
ejpam-6140	123	8	0	CARDINAL
ejpam-6140	123	9	lim	PERSON
ejpam-6140	123	10	2	CARDINAL
ejpam-6140	123	11	crank-nicolson	ORG
ejpam-6140	123	12	0 ≤	MONEY
ejpam-6140	125	1	+ kn	PERSON
ejpam-6140	126	1	un	ORG
ejpam-6140	127	1	un 1	ORG
ejpam-6140	127	2	u n 2	FAC
ejpam-6140	128	1	un i−1	PERSON
ejpam-6140	130	1	un	ORG
ejpam-6140	130	2	2	CARDINAL
ejpam-6140	131	1	1	CARDINAL
ejpam-6140	132	1	3),(4	CARDINAL
ejpam-6140	132	2	1 2	CARDINAL
ejpam-6140	133	1	firstly	ORDINAL
ejpam-6140	133	2	1s	CARDINAL
ejpam-6140	134	1	kn	PERSON
ejpam-6140	135	1	∂v ∂t	GPE
ejpam-6140	136	1	kn	PERSON
ejpam-6140	136	2	1 2	CARDINAL
ejpam-6140	137	1	1 2	CARDINAL
ejpam-6140	139	1	1 2h2	CARDINAL
ejpam-6140	140	1	un	ORG
ejpam-6140	145	1	1 2h2	CARDINAL
ejpam-6140	148	1	2v	CARDINAL
ejpam-6140	151	1	kn	PERSON
ejpam-6140	152	1	un	ORG
ejpam-6140	153	1	3),(4	CARDINAL
ejpam-6140	154	1	1 2h2	CARDINAL
ejpam-6140	155	1	un	ORG
ejpam-6140	161	1	1 2h2	CARDINAL
ejpam-6140	164	1	2v	CARDINAL
ejpam-6140	166	1	un	ORG
ejpam-6140	167	1	m. i. khalil et al	PERSON
ejpam-6140	168	1	j. pure	PERSON
ejpam-6140	168	2	18	CARDINAL
ejpam-6140	168	3	3	CARDINAL
ejpam-6140	168	4	2025	CARDINAL
ejpam-6140	168	5	6140 7	DATE
ejpam-6140	168	6	17	CARDINAL
ejpam-6140	168	7	1 + rn)u	QUANTITY
ejpam-6140	170	1	1− rn)u n	EVENT
ejpam-6140	171	1	un i+1 + un	ORG
ejpam-6140	172	1	+ knf	QUANTITY
ejpam-6140	172	2	23	CARDINAL
ejpam-6140	172	3	1 +	CARDINAL
ejpam-6140	173	1	1− rn)v	EVENT
ejpam-6140	175	1	24	CARDINAL
ejpam-6140	176	1	hα∥∥un	PERSON
ejpam-6140	177	1	1 ≤	QUANTITY
ejpam-6140	178	1	25	CARDINAL
ejpam-6140	178	2	1	CARDINAL
ejpam-6140	180	1	un	ORG
ejpam-6140	181	1	26	CARDINAL
ejpam-6140	182	1	27	CARDINAL
ejpam-6140	182	2	2	CARDINAL
ejpam-6140	183	1	−1 2	MONEY
ejpam-6140	183	2	0 .	PERCENT
ejpam-6140	186	1	−1 2	MONEY
ejpam-6140	191	1	1	CARDINAL
ejpam-6140	193	1	0	CARDINAL
ejpam-6140	196	1	ṽ	ORG
ejpam-6140	196	2	∣∣∣ ≤	MONEY
ejpam-6140	199	1	∣∣∣	CARDINAL
ejpam-6140	199	2	28)∣∣∣g	CARDINAL
ejpam-6140	199	3	un	ORG
ejpam-6140	200	1	∣∣∣ ≤	MONEY
ejpam-6140	200	2	∣∣∣	CARDINAL
ejpam-6140	200	3	29	CARDINAL
ejpam-6140	200	4	un	ORG
ejpam-6140	201	1	ṽ	ORG
ejpam-6140	201	2	0	CARDINAL
ejpam-6140	201	3	1	DATE
ejpam-6140	201	4	2	CARDINAL
ejpam-6140	205	1	ṽ	ORG
ejpam-6140	205	2	∣∣∣v n	PERSON
ejpam-6140	205	3	30	CARDINAL
ejpam-6140	205	4	ṽ	ORG
ejpam-6140	206	1	n h	ORG
ejpam-6140	206	2	ṽ	ORG
ejpam-6140	206	3	0	CARDINAL
ejpam-6140	209	1	28	CARDINAL
ejpam-6140	210	1	29	CARDINAL
ejpam-6140	211	1	m. i. khalil et al	PERSON
ejpam-6140	212	1	j. pure	PERSON
ejpam-6140	212	2	18	CARDINAL
ejpam-6140	212	3	3	CARDINAL
ejpam-6140	212	4	2025	CARDINAL
ejpam-6140	212	5	6140 8	DATE
ejpam-6140	212	6	17 2.1	CARDINAL
ejpam-6140	213	1	u0 h	ORG
ejpam-6140	213	2	0	CARDINAL
ejpam-6140	213	3	kn	PERSON
ejpam-6140	213	4	25	CARDINAL
ejpam-6140	214	1	26	CARDINAL
ejpam-6140	214	2	27	CARDINAL
ejpam-6140	215	1	1	CARDINAL
ejpam-6140	215	2	2	DATE
ejpam-6140	216	1	3,4	CARDINAL
ejpam-6140	216	2	1015	CARDINAL
ejpam-6140	216	3	∥v	DATE
ejpam-6140	216	4	n h ∥∞ ≥ 1015 (vi	ORG
ejpam-6140	216	5	n=0 kn	PERSON
ejpam-6140	217	1	3.	CARDINAL
ejpam-6140	217	2	three	CARDINAL
ejpam-6140	218	1	first	ORDINAL
ejpam-6140	220	1	5	CARDINAL
ejpam-6140	221	1	1 2	CARDINAL
ejpam-6140	222	1	2	CARDINAL
ejpam-6140	222	2	∣∣∣∣tn+ 1	DATE
ejpam-6140	222	3	2	CARDINAL
ejpam-6140	222	4	c3	PERSON
ejpam-6140	222	5	0	CARDINAL
ejpam-6140	224	1	1 2	CARDINAL
ejpam-6140	224	2	1 2	CARDINAL
ejpam-6140	228	1	2uni +	DATE
ejpam-6140	229	1	1 2	CARDINAL
ejpam-6140	229	2	1 2	CARDINAL
ejpam-6140	232	1	+o	DATE
ejpam-6140	233	1	1 2	CARDINAL
ejpam-6140	235	1	0	CARDINAL
ejpam-6140	236	1	1 2	CARDINAL
ejpam-6140	236	2	k = max n∈n kn	PERSON
ejpam-6140	236	3	m. i. khalil et al	PERSON
ejpam-6140	237	1	j. pure	PERSON
ejpam-6140	237	2	18	CARDINAL
ejpam-6140	237	3	3	CARDINAL
ejpam-6140	237	4	2025	CARDINAL
ejpam-6140	237	5	6140 9	DATE
ejpam-6140	237	6	∣∣∣∣tn+	PRODUCT
ejpam-6140	237	7	1 2	CARDINAL
ejpam-6140	237	8	1 2	CARDINAL
ejpam-6140	237	9	zero	CARDINAL
ejpam-6140	237	10	zero	CARDINAL
ejpam-6140	238	1	c.n.	GPE
ejpam-6140	239	1	6	CARDINAL
ejpam-6140	240	1	1−	LANGUAGE
ejpam-6140	240	2	maxn∈n kn	PERSON
ejpam-6140	241	1	1	CARDINAL
ejpam-6140	241	2	2	DATE
ejpam-6140	243	1	1	CARDINAL
ejpam-6140	243	2	2	DATE
ejpam-6140	246	1	vni −v n	PERSON
ejpam-6140	247	1	1	CARDINAL
ejpam-6140	247	2	1	CARDINAL
ejpam-6140	248	1	∣∣e1ui∣∣ = ∣∣∣e1uj∣∣∣	PERSON
ejpam-6140	248	2	∣∣e1vi∣∣.	PERSON
ejpam-6140	248	3	1 +	CARDINAL
ejpam-6140	248	4	r0 2	ORG
ejpam-6140	248	5	2	CARDINAL
ejpam-6140	248	6	∣∣∣	CARDINAL
ejpam-6140	248	7	∣∣∣(1−	CARDINAL
ejpam-6140	249	1	2	CARDINAL
ejpam-6140	251	1	∣∣∣	CARDINAL
ejpam-6140	252	1	1− rn	PRODUCT
ejpam-6140	252	2	0	CARDINAL
ejpam-6140	252	3	1− r0	PRODUCT
ejpam-6140	252	4	u ∥∥+ r0	PERSON
ejpam-6140	252	5	0	CARDINAL
ejpam-6140	252	6	∥∥ ≤	MONEY
ejpam-6140	252	7	1 +	CARDINAL
ejpam-6140	253	1	1 +	CARDINAL
ejpam-6140	253	2	1	CARDINAL
ejpam-6140	253	3	2	DATE
ejpam-6140	253	4	3	DATE
ejpam-6140	255	1	1	CARDINAL
ejpam-6140	255	2	2	DATE
ejpam-6140	255	3	3	DATE
ejpam-6140	257	1	1	CARDINAL
ejpam-6140	257	2	∣∣∣	CARDINAL
ejpam-6140	257	3	∣∣∣ m. i. khalil et al	ORG
ejpam-6140	258	1	j. pure	PERSON
ejpam-6140	258	2	18	CARDINAL
ejpam-6140	258	3	3	CARDINAL
ejpam-6140	258	4	2025	CARDINAL
ejpam-6140	258	5	6140 10	DATE
ejpam-6140	258	6	∣∣∣	CARDINAL
ejpam-6140	258	7	1 + rn	QUANTITY
ejpam-6140	258	8	∣∣∣) ≤	MONEY
ejpam-6140	258	9	r0 2 (	ORG
ejpam-6140	258	10	− rn 2 ( en+1	ORG
ejpam-6140	258	11	+ en+1 uj−1	ORG
ejpam-6140	258	12	∣∣∣	CARDINAL
ejpam-6140	258	13	∣∣∣(1−	CARDINAL
ejpam-6140	259	1	+ kn	PERSON
ejpam-6140	260	1	∣∣∣	CARDINAL
ejpam-6140	261	1	1− rn	PRODUCT
ejpam-6140	261	2	0	CARDINAL
ejpam-6140	261	3	that∥∥en+1	CARDINAL
ejpam-6140	261	4	1− rn	PRODUCT
ejpam-6140	262	1	∣∣vnj − v n j ∣∣∥∥en+1 u	PERSON
ejpam-6140	262	2	1 +	CARDINAL
ejpam-6140	262	3	1)kl)max	CARDINAL
ejpam-6140	262	4	∥∥ ≤ exp	MONEY
ejpam-6140	263	1	that∥∥en+1 v ∥∥ ≤ exp	QUANTITY
ejpam-6140	264	1	22	CARDINAL
ejpam-6140	264	2	7	CARDINAL
ejpam-6140	265	1	2	CARDINAL
ejpam-6140	267	1	maxn∈n kn	PERSON
ejpam-6140	268	1	1	CARDINAL
ejpam-6140	268	2	2	DATE
ejpam-6140	270	1	1	CARDINAL
ejpam-6140	270	2	2	DATE
ejpam-6140	274	1	− un	PERSON
ejpam-6140	274	2	− v n	PERSON
ejpam-6140	275	1	1	CARDINAL
ejpam-6140	275	2	0	CARDINAL
ejpam-6140	275	3	0	CARDINAL
ejpam-6140	275	4	1	CARDINAL
ejpam-6140	276	1	en+1	ORG
ejpam-6140	277	1	0	CARDINAL
ejpam-6140	277	2	1	CARDINAL
ejpam-6140	278	1	1	CARDINAL
ejpam-6140	278	2	∣∣∣e1uj∣∣∣	DATE
ejpam-6140	278	3	∣∣e1ui∣∣.	GPE
ejpam-6140	278	4	1 +	CARDINAL
ejpam-6140	278	5	r0 2	ORG
ejpam-6140	278	6	2	CARDINAL
ejpam-6140	278	7	∣∣∣	CARDINAL
ejpam-6140	278	8	∣∣∣(1−	CARDINAL
ejpam-6140	279	1	2	CARDINAL
ejpam-6140	282	1	∣∣∣	CARDINAL
ejpam-6140	283	1	m. i. khalil et al	PERSON
ejpam-6140	284	1	j. pure	PERSON
ejpam-6140	284	2	18	CARDINAL
ejpam-6140	284	3	3	CARDINAL
ejpam-6140	284	4	2025	CARDINAL
ejpam-6140	284	5	6140 11	DATE
ejpam-6140	284	6	17	CARDINAL
ejpam-6140	284	7	∣∣∣e1uj∣∣∣ ≤ lk ∣∣∣e0uj∣∣∣+	QUANTITY
ejpam-6140	284	8	0	CARDINAL
ejpam-6140	284	9	0	CARDINAL
ejpam-6140	286	1	∣∣∣e1uj∣∣∣ ≤ c1	MONEY
ejpam-6140	286	2	0	CARDINAL
ejpam-6140	286	3	1	CARDINAL
ejpam-6140	288	1	c1 = c.	PERSON
ejpam-6140	289	1	0	CARDINAL
ejpam-6140	289	2	1	CARDINAL
ejpam-6140	289	3	2	CARDINAL
ejpam-6140	290	1	0	CARDINAL
ejpam-6140	291	1	1	CARDINAL
ejpam-6140	291	2	∣∣∣	CARDINAL
ejpam-6140	291	3	∣∣∣	CARDINAL
ejpam-6140	291	4	1 + rn	QUANTITY
ejpam-6140	292	1	∣∣∣) ≤	MONEY
ejpam-6140	292	2	1 + rn	QUANTITY
ejpam-6140	292	3	− rn 2 ( en+1	ORG
ejpam-6140	292	4	+ en+1 uj−1	ORG
ejpam-6140	292	5	∣∣∣	CARDINAL
ejpam-6140	292	6	∣∣∣(1−	CARDINAL
ejpam-6140	294	1	+ kn	PERSON
ejpam-6140	296	1	∣∣∣	CARDINAL
ejpam-6140	297	1	1− rn	PRODUCT
ejpam-6140	297	2	0	CARDINAL
ejpam-6140	297	3	that∥∥en+1	CARDINAL
ejpam-6140	297	4	1− rn	PRODUCT
ejpam-6140	298	1	∣∣vnj − v	PERSON
ejpam-6140	298	2	n j ∣∣+ ∣∣∣tn+1/2 ui	ORG
ejpam-6140	298	3	∣∣∣ ≤	MONEY
ejpam-6140	300	1	+ klcn	PERSON
ejpam-6140	301	1	1 + kl)cn	CARDINAL
ejpam-6140	304	1	1 + kl)cn	MONEY
ejpam-6140	306	1	0	CARDINAL
ejpam-6140	306	2	1	CARDINAL
ejpam-6140	308	1	0	CARDINAL
ejpam-6140	308	2	1	CARDINAL
ejpam-6140	309	1	•	CARDINAL
ejpam-6140	310	1	26	CARDINAL
ejpam-6140	310	2	27	CARDINAL
ejpam-6140	310	3	28	CARDINAL
ejpam-6140	310	4	•	CARDINAL
ejpam-6140	311	1	3	CARDINAL
ejpam-6140	312	1	maxn kn	PERSON
ejpam-6140	312	2	25	CARDINAL
ejpam-6140	312	3	zero	CARDINAL
ejpam-6140	312	4	1 ≤ α ≤ 2	QUANTITY
ejpam-6140	314	1	m. i. khalil et al	PERSON
ejpam-6140	315	1	j. pure	PERSON
ejpam-6140	315	2	18	CARDINAL
ejpam-6140	315	3	3	CARDINAL
ejpam-6140	315	4	2025	CARDINAL
ejpam-6140	315	5	6140 12	DATE
ejpam-6140	315	6	two	CARDINAL
ejpam-6140	316	1	20, 40,	DATE
ejpam-6140	316	2	80	DATE
ejpam-6140	316	3	160	CARDINAL
ejpam-6140	316	4	320	CARDINAL
ejpam-6140	316	5	1	CARDINAL
ejpam-6140	316	6	2	CARDINAL
ejpam-6140	319	1	•	CARDINAL
ejpam-6140	319	2	first	ORDINAL
ejpam-6140	319	3	∈	ORG
ejpam-6140	320	1	1015 and ∥v	DATE
ejpam-6140	320	2	1015	CARDINAL
ejpam-6140	322	1	•	CARDINAL
ejpam-6140	323	1	•	CARDINAL
ejpam-6140	323	2	2	CARDINAL
ejpam-6140	323	3	•	CARDINAL
ejpam-6140	324	1	seconds	TIME
ejpam-6140	325	1	4.1	TIME
ejpam-6140	325	2	1	CARDINAL
ejpam-6140	325	3	ut = uxx	PERSON
ejpam-6140	326	1	0	CARDINAL
ejpam-6140	326	2	1	CARDINAL
ejpam-6140	326	3	0	CARDINAL
ejpam-6140	328	1	v(0	PERSON
ejpam-6140	329	1	0	CARDINAL
ejpam-6140	329	2	0	CARDINAL
ejpam-6140	330	1	70	CARDINAL
ejpam-6140	330	2	80	CARDINAL
ejpam-6140	330	3	0	CARDINAL
ejpam-6140	330	4	1	CARDINAL
ejpam-6140	330	5	31	CARDINAL
ejpam-6140	331	1	2	CARDINAL
ejpam-6140	331	2	ut = uxx + v6	PERSON
ejpam-6140	332	1	0	CARDINAL
ejpam-6140	332	2	1	CARDINAL
ejpam-6140	332	3	0	CARDINAL
ejpam-6140	333	1	v(0	PERSON
ejpam-6140	334	1	0	CARDINAL
ejpam-6140	334	2	0	CARDINAL
ejpam-6140	335	1	60	CARDINAL
ejpam-6140	335	2	1−	CARDINAL
ejpam-6140	335	3	2−x	CARDINAL
ejpam-6140	335	4	70	CARDINAL
ejpam-6140	335	5	1−	ORDINAL
ejpam-6140	335	6	2−x	CARDINAL
ejpam-6140	335	7	0	CARDINAL
ejpam-6140	335	8	1	CARDINAL
ejpam-6140	335	9	32	CARDINAL
ejpam-6140	335	10	m. i. khalil et al	PERSON
ejpam-6140	336	1	j. pure	PERSON
ejpam-6140	336	2	18	CARDINAL
ejpam-6140	336	3	3	CARDINAL
ejpam-6140	336	4	2025	CARDINAL
ejpam-6140	336	5	6140 13	DATE
ejpam-6140	336	6	17	CARDINAL
ejpam-6140	336	7	1	CARDINAL
ejpam-6140	336	8	1	CARDINAL
ejpam-6140	336	9	c.n.	GPE
ejpam-6140	337	1	1	CARDINAL
ejpam-6140	337	2	1/20	CARDINAL
ejpam-6140	338	1	1/40	CARDINAL
ejpam-6140	338	2	4 2.0966e-04	MONEY
ejpam-6140	339	1	1/80	CARDINAL
ejpam-6140	339	2	0.346336	CARDINAL
ejpam-6140	339	3	1.8383	CARDINAL
ejpam-6140	339	4	2.0205	MONEY
ejpam-6140	339	5	4	CARDINAL
ejpam-6140	339	6	2.608468	ORG
ejpam-6140	339	7	2.0716	ORG
ejpam-6140	339	8	2	CARDINAL
ejpam-6140	339	9	1	CARDINAL
ejpam-6140	339	10	c.n.	GPE
ejpam-6140	339	11	2	CARDINAL
ejpam-6140	339	12	1/20	CARDINAL
ejpam-6140	339	13	0.230858	CARDINAL
ejpam-6140	340	1	1/40	CARDINAL
ejpam-6140	340	2	7.6677e-06	CARDINAL
ejpam-6140	341	1	1/80	CARDINAL
ejpam-6140	341	2	2.1630	CARDINAL
ejpam-6140	341	3	3	CARDINAL
ejpam-6140	341	4	2	CARDINAL
ejpam-6140	341	5	c.n.	GPE
ejpam-6140	341	6	1	CARDINAL
ejpam-6140	341	7	1/20 3	DATE
ejpam-6140	342	1	1/40	CARDINAL
ejpam-6140	342	2	2.0886e-04	CARDINAL
ejpam-6140	343	1	1/80	CARDINAL
ejpam-6140	343	2	5.2830e-05	CARDINAL
ejpam-6140	343	3	3.8765e-05	CARDINAL
ejpam-6140	343	4	2.653295	ORG
ejpam-6140	343	5	2.0450	CARDINAL
ejpam-6140	343	6	m. i. khalil et al	PERSON
ejpam-6140	344	1	j. pure	PERSON
ejpam-6140	344	2	18	CARDINAL
ejpam-6140	344	3	3	CARDINAL
ejpam-6140	344	4	2025	CARDINAL
ejpam-6140	344	5	6140 14	DATE
ejpam-6140	344	6	17	CARDINAL
ejpam-6140	344	7	4	CARDINAL
ejpam-6140	344	8	2	CARDINAL
ejpam-6140	344	9	c.n.	GPE
ejpam-6140	344	10	2	CARDINAL
ejpam-6140	344	11	1/20 4	DATE
ejpam-6140	344	12	0.223913	CARDINAL
ejpam-6140	345	1	1/40	CARDINAL
ejpam-6140	345	2	3.9994e-05	MONEY
ejpam-6140	346	1	1/80	CARDINAL
ejpam-6140	346	2	5	CARDINAL
ejpam-6140	346	3	1.044031	CARDINAL
ejpam-6140	346	4	1.3396e-06	CARDINAL
ejpam-6140	346	5	1.7424e-07	CARDINAL
ejpam-6140	346	6	2.458527 2.7496e-07	PRODUCT
ejpam-6140	346	7	2.2845	MONEY
ejpam-6140	346	8	1	CARDINAL
ejpam-6140	346	9	example 1	DATE
ejpam-6140	346	10	c.n.	GPE
ejpam-6140	346	11	320	CARDINAL
ejpam-6140	346	12	2	CARDINAL
ejpam-6140	346	13	2	CARDINAL
ejpam-6140	346	14	2	CARDINAL
ejpam-6140	346	15	c.n.	GPE
ejpam-6140	346	16	320	CARDINAL
ejpam-6140	346	17	2	CARDINAL
ejpam-6140	346	18	4.2	CARDINAL
ejpam-6140	346	19	1-4	CARDINAL
ejpam-6140	346	20	1-2	CARDINAL
ejpam-6140	346	21	firstly	ORDINAL
ejpam-6140	346	22	0.5	CARDINAL
ejpam-6140	346	23	1	CARDINAL
ejpam-6140	346	24	15	CARDINAL
ejpam-6140	348	1	close to zero	CARDINAL
ejpam-6140	349	1	0.also	CARDINAL
ejpam-6140	351	1	m. i. khalil et al	PERSON
ejpam-6140	352	1	j. pure	PERSON
ejpam-6140	352	2	18	CARDINAL
ejpam-6140	352	3	3	CARDINAL
ejpam-6140	352	4	2025	CARDINAL
ejpam-6140	352	5	6140 15 of 17 5	DATE
ejpam-6140	353	1	two	CARDINAL
ejpam-6140	355	1	two	CARDINAL
ejpam-6140	357	1	second	ORDINAL
ejpam-6140	358	1	1	CARDINAL
ejpam-6140	358	2	sean laverty	ORG
ejpam-6140	358	3	brittany bannish	PERSON
ejpam-6140	360	1	aip	ORG
ejpam-6140	360	2	2096	CARDINAL
ejpam-6140	361	1	aip	ORG
ejpam-6140	361	2	2019	DATE
ejpam-6140	362	1	2	CARDINAL
ejpam-6140	362	2	zinah khalid	PERSON
ejpam-6140	362	3	el jai.	PERSON
ejpam-6140	363	1	γ* agfo	ORG
ejpam-6140	364	1	1664	CARDINAL
ejpam-6140	364	2	012061	DATE
ejpam-6140	365	1	iop publishing	ORG
ejpam-6140	365	2	2020	DATE
ejpam-6140	366	1	3	CARDINAL
ejpam-6140	366	2	samir benhadid	PERSON
ejpam-6140	368	1	baghdad science journal	ORG
ejpam-6140	368	2	2022	CARDINAL
ejpam-6140	369	1	4	CARDINAL
ejpam-6140	369	2	avner friedman	PERSON
ejpam-6140	369	3	bryce mcleod	PERSON
ejpam-6140	371	1	indiana university mathematics journal	ORG
ejpam-6140	371	2	34(2):425–447	CARDINAL
ejpam-6140	371	3	1985	DATE
ejpam-6140	372	1	5	CARDINAL
ejpam-6140	372	2	stanley kaplan	PERSON
ejpam-6140	374	1	16(3):305–330	DATE
ejpam-6140	374	2	1963	DATE
ejpam-6140	375	1	6	CARDINAL
ejpam-6140	376	1	474(1):513	CARDINAL
ejpam-6140	376	2	517	CARDINAL
ejpam-6140	376	3	2019	DATE
ejpam-6140	377	1	raad awad hameed	PERSON
ejpam-6140	377	2	amal nouman khalaf	PERSON
ejpam-6140	377	3	hiba ali kareem	PERSON
ejpam-6140	379	1	j. appl	PERSON
ejpam-6140	380	1	43(1):123–137	DATE
ejpam-6140	380	2	2025	DATE
ejpam-6140	381	1	8	CARDINAL
ejpam-6140	381	2	manar khalil	PERSON
ejpam-6140	381	3	ishak hashim	PERSON
ejpam-6140	381	4	maan rasheed	PERSON
ejpam-6140	382	1	european	NORP
ejpam-6140	382	2	17(3):1516–1538	CARDINAL
ejpam-6140	382	3	2024	DATE
ejpam-6140	383	1	9	CARDINAL
ejpam-6140	384	1	iraqi	NORP
ejpam-6140	384	2	3052–3060	CARDINAL
ejpam-6140	384	3	2021	CARDINAL
ejpam-6140	385	1	10	CARDINAL
ejpam-6140	387	1	baghdad science journal	ORG
ejpam-6140	387	2	18(2):315–321	CARDINAL
ejpam-6140	387	3	2021	DATE
ejpam-6140	388	1	m. i. khalil et al	PERSON
ejpam-6140	389	1	j. pure	PERSON
ejpam-6140	389	2	18	CARDINAL
ejpam-6140	389	3	3	CARDINAL
ejpam-6140	389	4	2025	CARDINAL
ejpam-6140	389	5	6140 16	DATE
ejpam-6140	389	6	11	CARDINAL
ejpam-6140	391	1	1998	DATE
ejpam-6140	392	1	12	CARDINAL
ejpam-6140	392	2	nina n ural’ceva.	NORP
ejpam-6140	393	1	linear	ORG
ejpam-6140	393	2	23	CARDINAL
ejpam-6140	394	1	american	NORP
ejpam-6140	394	2	1988	DATE
ejpam-6140	395	1	13	CARDINAL
ejpam-6140	395	2	keng deng	PERSON
ejpam-6140	397	1	zeitschrift für	ORG
ejpam-6140	397	2	angewandte mathematik	ORG
ejpam-6140	397	3	und physik zamp	PERSON
ejpam-6140	397	4	47:132–143	CARDINAL
ejpam-6140	397	5	1996	DATE
ejpam-6140	398	1	14	CARDINAL
ejpam-6140	398	2	monica marras	PERSON
ejpam-6140	398	3	s vernier-piro	PERSON
ejpam-6140	398	4	giuseppe	PERSON
ejpam-6140	401	1	j. pure	PERSON
ejpam-6140	401	2	93(2):297–306	GPE
ejpam-6140	401	3	2014	DATE
ejpam-6140	402	1	15	CARDINAL
ejpam-6140	402	2	avner friedman	PERSON
ejpam-6140	402	3	yoshikazu giga	PERSON
ejpam-6140	403	1	semilinear parabolic systems	ORG
ejpam-6140	404	1	j. fac	PERSON
ejpam-6140	405	1	sci.	ORG
ejpam-6140	405	2	univ	NORP
ejpam-6140	406	1	tokyo	GPE
ejpam-6140	407	1	ia	GPE
ejpam-6140	407	2	1987	DATE
ejpam-6140	408	1	16	CARDINAL
ejpam-6140	409	1	parabolic system of	ORG
ejpam-6140	410	1	i. differential equat	PERSON
ejpam-6140	410	2	1984	DATE
ejpam-6140	411	1	17	CARDINAL
ejpam-6140	411	2	zg lin	PERSON
ejpam-6140	411	3	ch xie	PERSON
ejpam-6140	411	4	mx wang	PERSON
ejpam-6140	415	1	j	PERSON
ejpam-6140	415	2	13:327–378, 1997	DATE
ejpam-6140	416	1	18	CARDINAL
ejpam-6140	418	1	the european mathematical society	ORG
ejpam-6140	418	2	11(1):169–188	DATE
ejpam-6140	418	3	2009	DATE
ejpam-6140	419	1	19	CARDINAL
ejpam-6140	419	2	zheng	PERSON
ejpam-6140	419	3	lizhong zhao	PERSON
ejpam-6140	419	4	feng chen	PERSON
ejpam-6140	421	1	51(4):663–672, 2002	DATE
ejpam-6140	422	1	20	CARDINAL
ejpam-6140	422	2	luis m abia	PERSON
ejpam-6140	422	3	jc lopez-marcos	PERSON
ejpam-6140	424	1	20(1-2):145	CARDINAL
ejpam-6140	424	2	156, 1996	DATE
ejpam-6140	425	1	21	CARDINAL
ejpam-6140	427	1	italian	NORP
ejpam-6140	427	2	44:805–813	CARDINAL
ejpam-6140	427	3	2020	DATE
ejpam-6140	428	1	22	CARDINAL
ejpam-6140	428	2	raad awad hameed	PERSON
ejpam-6140	428	3	amal nouman khalaf	PERSON
ejpam-6140	429	1	one	CARDINAL
ejpam-6140	430	1	iraqi	NORP
ejpam-6140	430	2	354–364	CARDINAL
ejpam-6140	430	3	2023	CARDINAL
ejpam-6140	431	1	23	CARDINAL
ejpam-6140	431	2	weizhang huang	PERSON
ejpam-6140	431	3	jingtang ma	PERSON
ejpam-6140	431	4	robert d russell	PERSON
ejpam-6140	433	1	227(13):6532–6552, 2008	DATE
ejpam-6140	434	1	24	CARDINAL
ejpam-6140	434	2	chien-hong cho	PERSON
ejpam-6140	434	3	hisashi okamoto	ORG
ejpam-6140	436	1	52(2):391–415	DATE
ejpam-6140	436	2	2020	DATE
ejpam-6140	437	1	25	CARDINAL
ejpam-6140	437	2	chien-hong cho	PERSON
ejpam-6140	437	3	ying-jung lu	PERSON
ejpam-6140	439	1	6(11):11749–11777	CARDINAL
ejpam-6140	439	2	2021	DATE
ejpam-6140	440	1	26	CARDINAL
ejpam-6140	440	2	manar ismael	PERSON
ejpam-6140	440	3	ishak hashim	PERSON
ejpam-6140	440	4	maan rasheed	PERSON
ejpam-6140	440	5	eddie ismail	PERSON
ejpam-6140	442	1	32:387–407	DATE
ejpam-6140	442	2	11 2023	CARDINAL
ejpam-6140	443	1	27	CARDINAL
ejpam-6140	445	1	oxford university press	ORG
ejpam-6140	445	2	1985	DATE
ejpam-6140	446	1	m. i. khalil et al	PERSON
ejpam-6140	447	1	j. pure	PERSON
ejpam-6140	447	2	18	CARDINAL
ejpam-6140	447	3	3	CARDINAL
ejpam-6140	447	4	2025	CARDINAL
ejpam-6140	447	5	6140 17	DATE
ejpam-6140	447	6	17	CARDINAL
ejpam-6140	447	7	28	CARDINAL
ejpam-6140	447	8	richard varga	PERSON
ejpam-6140	448	1	s. 1962	PERSON
ejpam-6140	449	1	englewood cliffs: prenticeflall	FAC
ejpam-6140	449	2	1962	DATE