id	sid	eid	entity	type
ejpam-6447	1	1	european journal	ORG
ejpam-6447	1	2	2025	DATE
ejpam-6447	1	3	18	CARDINAL
ejpam-6447	1	4	3	CARDINAL
ejpam-6447	1	5	6447	CARDINAL
ejpam-6447	1	6	new york	GPE
ejpam-6447	1	7	samia bushnaq1	PERSON
ejpam-6447	1	8	sameera bano2	PERSON
ejpam-6447	1	9	anwar zeb2,∗ 1	ORG
ejpam-6447	1	10	jordan 2	ORG
ejpam-6447	1	11	mathematics comsats university	ORG
ejpam-6447	1	12	islamabad	GPE
ejpam-6447	1	13	abbottabad	GPE
ejpam-6447	1	14	kpk	GPE
ejpam-6447	1	15	pakistan	GPE
ejpam-6447	6	1	fourth	ORDINAL
ejpam-6447	6	2	kutta	ORG
ejpam-6447	8	1	2020	DATE
ejpam-6447	8	2	92d30	CARDINAL
ejpam-6447	8	3	37n25	CARDINAL
ejpam-6447	8	4	1	CARDINAL
ejpam-6447	10	1	covid-19	DATE
ejpam-6447	10	2	1–4	CARDINAL
ejpam-6447	12	1	8	CARDINAL
ejpam-6447	13	1	recent years	DATE
ejpam-6447	16	1	american	NORP
ejpam-6447	17	1	10–12	CARDINAL
ejpam-6447	20	1	s. bushnaq	PERSON
ejpam-6447	20	2	s. bano	PERSON
ejpam-6447	20	3	a. zeb	PERSON
ejpam-6447	20	4	1	CARDINAL
ejpam-6447	20	5	2025	CARDINAL
ejpam-6447	21	1	s. bushnaq	PERSON
ejpam-6447	21	2	s. bano	PERSON
ejpam-6447	21	3	a. zeb	PERSON
ejpam-6447	22	1	j. pure	PERSON
ejpam-6447	22	2	18	CARDINAL
ejpam-6447	22	3	3	CARDINAL
ejpam-6447	22	4	2025	CARDINAL
ejpam-6447	22	5	6447 2	DATE
ejpam-6447	22	6	12	CARDINAL
ejpam-6447	22	7	fourteen-fold	CARDINAL
ejpam-6447	22	8	13–15	CARDINAL
ejpam-6447	24	1	16–20	CARDINAL
ejpam-6447	25	1	21	CARDINAL
ejpam-6447	25	2	22	CARDINAL
ejpam-6447	26	1	23	CARDINAL
ejpam-6447	26	2	24	CARDINAL
ejpam-6447	31	1	first	ORDINAL
ejpam-6447	34	1	fourth	ORDINAL
ejpam-6447	34	2	kutta	ORG
ejpam-6447	36	1	section 2	LAW
ejpam-6447	37	1	section 3	LAW
ejpam-6447	38	1	section 4	LAW
ejpam-6447	39	1	section 5	LAW
ejpam-6447	40	1	section 6	LAW
ejpam-6447	41	1	2	CARDINAL
ejpam-6447	42	1	four	CARDINAL
ejpam-6447	43	1	λ− β(a	PERSON
ejpam-6447	44	1	1	CARDINAL
ejpam-6447	44	2	σ	ORG
ejpam-6447	44	3	β(a	GPE
ejpam-6447	44	4	seasonally	DATE
ejpam-6447	44	5	s. bushnaq	PERSON
ejpam-6447	44	6	s. bano	PERSON
ejpam-6447	44	7	a. zeb	PERSON
ejpam-6447	45	1	j. pure	PERSON
ejpam-6447	45	2	18	CARDINAL
ejpam-6447	45	3	3	CARDINAL
ejpam-6447	45	4	2025	CARDINAL
ejpam-6447	45	5	6447 3	DATE
ejpam-6447	46	1	2πt	ORDINAL
ejpam-6447	47	1	1-4	CARDINAL
ejpam-6447	47	2	1	CARDINAL
ejpam-6447	47	3	1	CARDINAL
ejpam-6447	49	1	3	CARDINAL
ejpam-6447	49	2	zero	CARDINAL
ejpam-6447	50	1	di	ORG
ejpam-6447	50	2	0	CARDINAL
ejpam-6447	51	1	0	CARDINAL
ejpam-6447	51	2	β(a	GPE
ejpam-6447	51	3	0	CARDINAL
ejpam-6447	51	4	0	CARDINAL
ejpam-6447	52	1	e0	GPE
ejpam-6447	52	2	i0	GPE
ejpam-6447	53	1	s. bushnaq	PERSON
ejpam-6447	53	2	s. bano	PERSON
ejpam-6447	53	3	a. zeb	PERSON
ejpam-6447	54	1	j. pure	PERSON
ejpam-6447	54	2	18	CARDINAL
ejpam-6447	54	3	3	CARDINAL
ejpam-6447	54	4	2025	CARDINAL
ejpam-6447	54	5	6447 4	DATE
ejpam-6447	54	6	12	DATE
ejpam-6447	55	1	0	CARDINAL
ejpam-6447	57	1	d∗(s ∗	ORG
ejpam-6447	57	2	e∗	GPE
ejpam-6447	57	3	r∗	PERSON
ejpam-6447	57	4	e∗	ORG
ejpam-6447	58	1	1	CARDINAL
ejpam-6447	58	2	1	CARDINAL
ejpam-6447	58	3	1	CARDINAL
ejpam-6447	59	1	1	CARDINAL
ejpam-6447	59	2	0	CARDINAL
ejpam-6447	59	3	3.1	CARDINAL
ejpam-6447	61	1	3.2	CARDINAL
ejpam-6447	62	1	1	CARDINAL
ejpam-6447	63	1	sfe	ORG
ejpam-6447	63	2	e0	ORG
ejpam-6447	63	3	i0	GPE
ejpam-6447	63	4	λµ	ORG
ejpam-6447	63	5	0	DATE
ejpam-6447	63	6	0	DATE
ejpam-6447	63	7	0	DATE
ejpam-6447	64	1	jacobian	NORP
ejpam-6447	64	2	sfe	ORG
ejpam-6447	64	3	0	CARDINAL
ejpam-6447	66	1	0	CARDINAL
ejpam-6447	66	2	0 γ −µ 	ORG
ejpam-6447	67	1	2	CARDINAL
ejpam-6447	67	2	− λ′i|	PERSON
ejpam-6447	68	1	− λ′i|	PERSON
ejpam-6447	70	1	0	CARDINAL
ejpam-6447	71	1	c1	PERSON
ejpam-6447	72	1	0	CARDINAL
ejpam-6447	75	1	0	CARDINAL
ejpam-6447	75	2	s. bushnaq	PERSON
ejpam-6447	75	3	s. bano	PERSON
ejpam-6447	75	4	a. zeb	PERSON
ejpam-6447	76	1	j. pure	PERSON
ejpam-6447	76	2	18	CARDINAL
ejpam-6447	76	3	3	CARDINAL
ejpam-6447	76	4	2025	CARDINAL
ejpam-6447	76	5	6447 5	DATE
ejpam-6447	76	6	12	CARDINAL
ejpam-6447	78	1	0	CARDINAL
ejpam-6447	82	1	routh-hurwitz	ORG
ejpam-6447	82	2	1	CARDINAL
ejpam-6447	82	3	jacobian	NORP
ejpam-6447	83	1	2	CARDINAL
ejpam-6447	84	1	1	CARDINAL
ejpam-6447	86	1	e∗	ORG
ejpam-6447	87	1	1	CARDINAL
ejpam-6447	87	2	1	CARDINAL
ejpam-6447	87	3	1	CARDINAL
ejpam-6447	88	1	jacobian	NORP
ejpam-6447	88	2	0	CARDINAL
ejpam-6447	88	3	0	CARDINAL
ejpam-6447	89	1	0	CARDINAL
ejpam-6447	89	2	0 γ −µ 	ORG
ejpam-6447	91	1	− λ′i|	PERSON
ejpam-6447	91	2	− λ′i|	PERSON
ejpam-6447	92	1	0	CARDINAL
ejpam-6447	92	2	0	CARDINAL
ejpam-6447	93	1	0	CARDINAL
ejpam-6447	94	1	fourth	ORDINAL
ejpam-6447	96	1	0	CARDINAL
ejpam-6447	97	1	0	CARDINAL
ejpam-6447	98	1	one	CARDINAL
ejpam-6447	98	2	first	ORDINAL
ejpam-6447	98	3	− µ− λ′)(((σ +	GPE
ejpam-6447	99	1	βσs∗	GPE
ejpam-6447	100	1	0	CARDINAL
ejpam-6447	100	2	s. bushnaq	PERSON
ejpam-6447	100	3	s. bano	PERSON
ejpam-6447	100	4	a. zeb	PERSON
ejpam-6447	101	1	j. pure	PERSON
ejpam-6447	101	2	18	CARDINAL
ejpam-6447	101	3	3	CARDINAL
ejpam-6447	101	4	2025	CARDINAL
ejpam-6447	101	5	6447 6	DATE
ejpam-6447	103	1	0	CARDINAL
ejpam-6447	105	1	0	CARDINAL
ejpam-6447	108	1	0	CARDINAL
ejpam-6447	108	2	1	CARDINAL
ejpam-6447	108	3	1	CARDINAL
ejpam-6447	109	1	forr0	PRODUCT
ejpam-6447	109	2	1	CARDINAL
ejpam-6447	109	3	routh	ORG
ejpam-6447	109	4	hurwitz	PERSON
ejpam-6447	112	1	4	CARDINAL
ejpam-6447	112	2	4.1	CARDINAL
ejpam-6447	113	1	3	CARDINAL
ejpam-6447	115	1	0	CARDINAL
ejpam-6447	116	1	2	CARDINAL
ejpam-6447	117	1	3	CARDINAL
ejpam-6447	117	2	1	CARDINAL
ejpam-6447	117	3	0	CARDINAL
ejpam-6447	117	4	0	CARDINAL
ejpam-6447	117	5	2	CARDINAL
ejpam-6447	117	6	zero	CARDINAL
ejpam-6447	118	1	0	CARDINAL
ejpam-6447	118	2	3	CARDINAL
ejpam-6447	119	1	0	CARDINAL
ejpam-6447	121	1	1	CARDINAL
ejpam-6447	122	1	0	CARDINAL
ejpam-6447	128	1	0	CARDINAL
ejpam-6447	130	1	s. bushnaq	PERSON
ejpam-6447	130	2	s. bano	PERSON
ejpam-6447	130	3	a. zeb	PERSON
ejpam-6447	131	1	j. pure	PERSON
ejpam-6447	131	2	18	CARDINAL
ejpam-6447	131	3	3	CARDINAL
ejpam-6447	131	4	2025	CARDINAL
ejpam-6447	131	5	6447 7 of 12	DATE
ejpam-6447	132	1	2 +	CARDINAL
ejpam-6447	132	2	2	CARDINAL
ejpam-6447	135	1	2ϵ2	CARDINAL
ejpam-6447	136	1	2 2	DATE
ejpam-6447	137	1	0	CARDINAL
ejpam-6447	139	1	2ϵ2	CARDINAL
ejpam-6447	141	1	0	CARDINAL
ejpam-6447	141	2	2	CARDINAL
ejpam-6447	141	3	2ϵ2	CARDINAL
ejpam-6447	141	4	2	CARDINAL
ejpam-6447	141	5	0 λ2s2 2ϵ1 da	TIME
ejpam-6447	142	1	i(t	ORG
ejpam-6447	142	2	0	CARDINAL
ejpam-6447	143	1	σ −	ORG
ejpam-6447	143	2	2	CARDINAL
ejpam-6447	143	3	2ϵ2	CARDINAL
ejpam-6447	143	4	0	CARDINAL
ejpam-6447	144	1	γ −	ORG
ejpam-6447	144	2	2	CARDINAL
ejpam-6447	144	3	0	CARDINAL
ejpam-6447	145	1	0	CARDINAL
ejpam-6447	146	1	lasalle	GPE
ejpam-6447	147	1	4.2	CARDINAL
ejpam-6447	148	1	4	CARDINAL
ejpam-6447	150	1	1 2	CARDINAL
ejpam-6447	150	2	− e∗	PERSON
ejpam-6447	153	1	1	CARDINAL
ejpam-6447	154	1	− e∗	PERSON
ejpam-6447	156	1	− e∗	PERSON
ejpam-6447	157	1	s. bushnaq	PERSON
ejpam-6447	157	2	s. bano	PERSON
ejpam-6447	157	3	a. zeb	PERSON
ejpam-6447	158	1	j. pure	PERSON
ejpam-6447	158	2	18	CARDINAL
ejpam-6447	158	3	3	CARDINAL
ejpam-6447	158	4	2025	CARDINAL
ejpam-6447	158	5	6447 8	DATE
ejpam-6447	160	1	− e∗)−	PERSON
ejpam-6447	162	1	− e∗	PERSON
ejpam-6447	164	1	1 2ϵ	CARDINAL
ejpam-6447	167	1	dv	ORG
ejpam-6447	169	1	+σ 2	MONEY
ejpam-6447	170	1	− (γ + µ−	ORG
ejpam-6447	170	2	2	CARDINAL
ejpam-6447	171	1	2	CARDINAL
ejpam-6447	173	1	s. bushnaq	PERSON
ejpam-6447	173	2	s. bano	PERSON
ejpam-6447	173	3	a. zeb	PERSON
ejpam-6447	174	1	j. pure	PERSON
ejpam-6447	174	2	18	CARDINAL
ejpam-6447	174	3	3	CARDINAL
ejpam-6447	174	4	2025	CARDINAL
ejpam-6447	174	5	6447 9	DATE
ejpam-6447	174	6	euler	PERSON
ejpam-6447	174	7	β(a	GPE
ejpam-6447	176	1	e(0)=50	GPE
ejpam-6447	176	2	i(0)=30	ORG
ejpam-6447	176	3	r(0)=20 and p(0)=n-e(0)-i(0)-r(0	GPE
ejpam-6447	177	1	10.25	CARDINAL
ejpam-6447	177	2	0.005	CARDINAL
ejpam-6447	177	3	0.1	CARDINAL
ejpam-6447	177	4	0.03	CARDINAL
ejpam-6447	177	5	250	CARDINAL
ejpam-6447	177	6	1	CARDINAL
ejpam-6447	177	7	euler	PERSON
ejpam-6447	177	8	euler	PERSON
ejpam-6447	177	9	euler	PERSON
ejpam-6447	177	10	euler	PERSON
ejpam-6447	177	11	2	CARDINAL
ejpam-6447	177	12	euler	PERSON
ejpam-6447	178	1	euler	PERSON
ejpam-6447	179	1	euler	PERSON
ejpam-6447	180	1	euler	PERSON
ejpam-6447	181	1	euler	PERSON
ejpam-6447	183	1	euler	PERSON
ejpam-6447	184	1	s. bushnaq	PERSON
ejpam-6447	184	2	s. bano	PERSON
ejpam-6447	184	3	a. zeb	PERSON
ejpam-6447	185	1	j. pure	PERSON
ejpam-6447	185	2	18	CARDINAL
ejpam-6447	185	3	3	CARDINAL
ejpam-6447	185	4	2025	CARDINAL
ejpam-6447	185	5	6447 10	DATE
ejpam-6447	185	6	β(a	GPE
ejpam-6447	185	7	β(a	GPE
ejpam-6447	185	8	β(a	GPE
ejpam-6447	185	9	β(a	GPE
ejpam-6447	185	10	β(a	GPE
ejpam-6447	185	11	β(a	GPE
ejpam-6447	185	12	β(a	GPE
ejpam-6447	185	13	β(a	GPE
ejpam-6447	185	14	β(a	GPE
ejpam-6447	185	15	β(a	GPE
ejpam-6447	185	16	β(a	GPE
ejpam-6447	185	17	β(a	GPE
ejpam-6447	185	18	3	CARDINAL
ejpam-6447	185	19	β(a	GPE
ejpam-6447	186	1	β(a	GPE
ejpam-6447	187	1	β(a	GPE
ejpam-6447	187	2	β(a	GPE
ejpam-6447	188	1	euler	PERSON
ejpam-6447	188	2	β(a	GPE
ejpam-6447	189	1	euler	PERSON
ejpam-6447	189	2	β(a	GPE
ejpam-6447	190	1	euler	PERSON
ejpam-6447	190	2	β(a	GPE
ejpam-6447	191	1	euler	PERSON
ejpam-6447	191	2	β(a	GPE
ejpam-6447	192	1	β(a	GPE
ejpam-6447	192	2	β(a	GPE
ejpam-6447	193	1	β(a	ORG
ejpam-6447	193	2	β(a	GPE
ejpam-6447	194	1	6	CARDINAL
ejpam-6447	198	1	s. bushnaq	PERSON
ejpam-6447	198	2	s. bano	PERSON
ejpam-6447	198	3	a. zeb	PERSON
ejpam-6447	199	1	j. pure	PERSON
ejpam-6447	199	2	18	CARDINAL
ejpam-6447	199	3	3	CARDINAL
ejpam-6447	199	4	2025	CARDINAL
ejpam-6447	199	5	6447 11	DATE
ejpam-6447	199	6	12	CARDINAL
ejpam-6447	204	1	one	CARDINAL
ejpam-6447	208	1	1	CARDINAL
ejpam-6447	208	2	r. m. anderson	PERSON
ejpam-6447	208	3	r. m.	PERSON
ejpam-6447	210	1	oxford university press	ORG
ejpam-6447	210	2	1991	DATE
ejpam-6447	211	1	2	CARDINAL
ejpam-6447	211	2	h. w. hethcote	PERSON
ejpam-6447	213	1	siam	GPE
ejpam-6447	213	2	42(4):599–653	ORG
ejpam-6447	213	3	2000	DATE
ejpam-6447	214	1	3	CARDINAL
ejpam-6447	214	2	f. brauer	PERSON
ejpam-6447	214	3	c. castillo-chavez	PERSON
ejpam-6447	214	4	z. feng	PERSON
ejpam-6447	216	1	2019	DATE
ejpam-6447	217	1	4	CARDINAL
ejpam-6447	217	2	j. a. p. heesterbeek	PERSON
ejpam-6447	217	3	t. britton	PERSON
ejpam-6447	219	1	princeton university press	ORG
ejpam-6447	219	2	2013	DATE
ejpam-6447	220	1	5	CARDINAL
ejpam-6447	220	2	l. g. de pillis	PERSON
ejpam-6447	220	3	a. e. radunskaya	PERSON
ejpam-6447	222	1	238(4):841	CARDINAL
ejpam-6447	222	2	862, 2006	DATE
ejpam-6447	223	1	6	CARDINAL
ejpam-6447	223	2	m. gümüs	PERSON
ejpam-6447	223	3	ö. öcalan	NORP
ejpam-6447	225	1	2014	DATE
ejpam-6447	225	2	article id 395954	LAW
ejpam-6447	225	3	5	CARDINAL
ejpam-6447	225	4	2014	DATE
ejpam-6447	226	1	7	CARDINAL
ejpam-6447	226	2	m. y. li	PERSON
ejpam-6447	226	3	j. s. muldowney	PERSON
ejpam-6447	228	1	125(2):155–164, 1995	DATE
ejpam-6447	229	1	8	CARDINAL
ejpam-6447	229	2	j. wang	PERSON
ejpam-6447	229	3	m. zhang	PERSON
ejpam-6447	229	4	w. yang	PERSON
ejpam-6447	230	1	313:1–34	CARDINAL
ejpam-6447	230	2	2022	CARDINAL
ejpam-6447	231	1	9	CARDINAL
ejpam-6447	231	2	c. liu	PERSON
ejpam-6447	231	3	j. shi	PERSON
ejpam-6447	232	1	two	CARDINAL
ejpam-6447	233	1	65:103434	CARDINAL
ejpam-6447	233	2	2022	CARDINAL
ejpam-6447	234	1	10	CARDINAL
ejpam-6447	234	2	e. alzahrani	PERSON
ejpam-6447	234	3	a. zeb	PERSON
ejpam-6447	236	1	2020:1–13	GPE
ejpam-6447	236	2	2020	DATE
ejpam-6447	237	1	11	CARDINAL
ejpam-6447	237	2	a. zeb	PERSON
ejpam-6447	237	3	s. kumar	PERSON
ejpam-6447	237	4	a. tesfay	PERSON
ejpam-6447	237	5	a. kumar	PERSON
ejpam-6447	239	1	32(3):915–930	DATE
ejpam-6447	239	2	2022	CARDINAL
ejpam-6447	240	1	12	CARDINAL
ejpam-6447	240	2	s. m. lestari	PERSON
ejpam-6447	240	3	y. yulida	PERSON
ejpam-6447	240	4	a. s. lestia	PERSON
ejpam-6447	240	5	m. a. karim	PERSON
ejpam-6447	242	1	2106(1):012025	CARDINAL
ejpam-6447	242	2	2021	DATE
ejpam-6447	243	1	13	CARDINAL
ejpam-6447	243	2	a. m. pulecio-montoya	PERSON
ejpam-6447	243	3	l. e. lópez-montenegro	PERSON
ejpam-6447	243	4	l. m. benavides	PERSON
ejpam-6447	245	1	12(3):117–129, 2019	DATE
ejpam-6447	246	1	14	CARDINAL
ejpam-6447	246	2	z. alkhudari	PERSON
ejpam-6447	246	3	s. al-sheikh	PERSON
ejpam-6447	246	4	s. al-tuwairqi	PERSON
ejpam-6447	248	1	9(25):1207–1222	DATE
ejpam-6447	248	2	2014	DATE
ejpam-6447	249	1	s. bushnaq	PERSON
ejpam-6447	249	2	s. bano	PERSON
ejpam-6447	249	3	a. zeb	PERSON
ejpam-6447	250	1	j. pure	PERSON
ejpam-6447	250	2	18	CARDINAL
ejpam-6447	250	3	3	CARDINAL
ejpam-6447	250	4	2025	CARDINAL
ejpam-6447	250	5	6447 12	DATE
ejpam-6447	250	6	12	CARDINAL
ejpam-6447	251	1	15	CARDINAL
ejpam-6447	251	2	g. zaman	PERSON
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ejpam-6447	253	1	malaysian	NORP
ejpam-6447	254	1	second	ORDINAL
ejpam-6447	254	2	34(2):403–415, 2011	DATE
ejpam-6447	255	1	16	CARDINAL
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ejpam-6447	255	3	s. al-sheikh	PERSON
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ejpam-6447	257	1	2014(1):847075	CARDINAL
ejpam-6447	257	2	2014	DATE
ejpam-6447	258	1	17	CARDINAL
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ejpam-6447	260	1	37(7):5326–5334, 2013	DATE
ejpam-6447	261	1	18	CARDINAL
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ejpam-6447	261	3	a. bano	PERSON
ejpam-6447	261	4	e. alzahrani	PERSON
ejpam-6447	261	5	g. zaman	PERSON
ejpam-6447	263	1	aip advances	ORG
ejpam-6447	263	2	8(4	CARDINAL
ejpam-6447	263	3	2018	DATE
ejpam-6447	264	1	19	CARDINAL
ejpam-6447	264	2	y. s. tan	PERSON
ejpam-6447	264	3	x. li	PERSON
ejpam-6447	264	4	j. yang	PERSON
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ejpam-6447	267	5	g. zaman	PERSON
ejpam-6447	269	1	mediterranean journal of mathematics	ORG
ejpam-6447	269	2	15:1–11	CARDINAL
ejpam-6447	269	3	2018	DATE
ejpam-6447	270	1	21	CARDINAL
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ejpam-6447	273	4	a. zeb	PERSON
ejpam-6447	273	5	s. saeed	PERSON
ejpam-6447	273	6	t. tareq	PERSON
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ejpam-6447	276	1	23	CARDINAL
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ejpam-6447	276	4	d. kiouach	PERSON
ejpam-6447	276	5	a. belmaâti	PERSON
ejpam-6447	278	1	statistics & probability	ORG
ejpam-6447	278	2	81(8):1276–1284, 2011	DATE
ejpam-6447	279	1	24	CARDINAL
ejpam-6447	279	2	a. zeb	PERSON
ejpam-6447	279	3	g. zaman	PERSON
ejpam-6447	279	4	i. h. jung	PERSON
ejpam-6447	279	5	m. khan	PERSON
ejpam-6447	281	1	zeitschrift für	ORG
ejpam-6447	281	2	69(5	CARDINAL
ejpam-6447	281	3	2014	DATE
