id	sid	eid	entity	type
ejpam-3209	1	1	european journal	ORG
ejpam-3209	2	1	11	CARDINAL
ejpam-3209	2	2	2, 2018	DATE
ejpam-3209	2	3	375	CARDINAL
ejpam-3209	2	4	new york	GPE
ejpam-3209	2	5	e. d. j. owusu-ansah1	PERSON
ejpam-3209	2	6	s. k. amponsah1	PERSON
ejpam-3209	2	7	c. sebil1	PERSON
ejpam-3209	3	1	1	CARDINAL
ejpam-3209	3	2	kwame nkrumah university of science and technology	ORG
ejpam-3209	3	3	kumasi	GPE
ejpam-3209	3	4	ghana	GPE
ejpam-3209	4	1	‖v‖	ORG
ejpam-3209	5	1	0	CARDINAL
ejpam-3209	5	2	2	CARDINAL
ejpam-3209	5	3	‖v‖	ORG
ejpam-3209	5	4	2,∞	CARDINAL
ejpam-3209	6	1	first	ORDINAL
ejpam-3209	7	1	0	CARDINAL
ejpam-3209	7	2	1	CARDINAL
ejpam-3209	9	1	2010	DATE
ejpam-3209	9	2	44b45	CARDINAL
ejpam-3209	9	3	44b46	CARDINAL
ejpam-3209	9	4	first	ORDINAL
ejpam-3209	9	5	second	ORDINAL
ejpam-3209	9	6	1	CARDINAL
ejpam-3209	12	1	first	ORDINAL
ejpam-3209	12	2	1	CARDINAL
ejpam-3209	14	1	2	CARDINAL
ejpam-3209	15	1	agm	ORG
ejpam-3209	15	2	i=1 xi	PERSON
ejpam-3209	15	3	1 n ≤ 1 n	QUANTITY
ejpam-3209	15	4	n ∈ n	PRODUCT
ejpam-3209	15	5	∈	ORG
ejpam-3209	18	1	two	CARDINAL
ejpam-3209	18	2	agm	ORG
ejpam-3209	18	3	ab ≤	ORG
ejpam-3209	18	4	2	CARDINAL
ejpam-3209	18	5	2	CARDINAL
ejpam-3209	19	1	e. d. j. owusu-ansah	PERSON
ejpam-3209	19	2	skamponsah@knust.edu.gh	DATE
ejpam-3209	19	3	s. k. amponsah	PERSON
ejpam-3209	21	1	375	CARDINAL
ejpam-3209	21	2	2018	DATE
ejpam-3209	22	1	barnes et al	PERSON
ejpam-3209	23	1	j. pure	PERSON
ejpam-3209	23	2	11	CARDINAL
ejpam-3209	23	3	2	CARDINAL
ejpam-3209	23	4	2018	DATE
ejpam-3209	23	5	375	CARDINAL
ejpam-3209	23	6	3	CARDINAL
ejpam-3209	24	1	agm	ORG
ejpam-3209	24	2	4	CARDINAL
ejpam-3209	24	3	5	CARDINAL
ejpam-3209	25	1	6	CARDINAL
ejpam-3209	25	2	one	CARDINAL
ejpam-3209	25	3	one	CARDINAL
ejpam-3209	25	4	1	CARDINAL
ejpam-3209	27	1	agm	ORG
ejpam-3209	28	1	7	CARDINAL
ejpam-3209	29	1	two	CARDINAL
ejpam-3209	30	1	newton	ORG
ejpam-3209	30	2	first	ORDINAL
ejpam-3209	30	3	third	ORDINAL
ejpam-3209	31	1	2	CARDINAL
ejpam-3209	31	2	1 ≤	QUANTITY
ejpam-3209	31	3	8	CARDINAL
ejpam-3209	32	1	9	CARDINAL
ejpam-3209	32	2	agm	ORG
ejpam-3209	33	1	10	CARDINAL
ejpam-3209	33	2	weierstrass	GPE
ejpam-3209	34	1	the 21st century	DATE
ejpam-3209	35	1	jordan	PERSON
ejpam-3209	35	2	11	CARDINAL
ejpam-3209	35	3	2	CARDINAL
ejpam-3209	35	4	1	CARDINAL
ejpam-3209	35	5	2	CARDINAL
ejpam-3209	36	1	hilbert	PERSON
ejpam-3209	36	2	1 2	CARDINAL
ejpam-3209	36	3	1 2	CARDINAL
ejpam-3209	36	4	12	CARDINAL
ejpam-3209	37	1	agm	ORG
ejpam-3209	37	2	two	CARDINAL
ejpam-3209	38	1	two	CARDINAL
ejpam-3209	38	2	0,∞	TIME
ejpam-3209	38	3	first	ORDINAL
ejpam-3209	39	1	0	CARDINAL
ejpam-3209	39	2	2	CARDINAL
ejpam-3209	39	3	second	ORDINAL
ejpam-3209	39	4	‖v‖	ORG
ejpam-3209	39	5	2,∞	CARDINAL
ejpam-3209	41	1	section 1	LAW
ejpam-3209	42	1	section 2	LAW
ejpam-3209	42	2	first	ORDINAL
ejpam-3209	42	3	generalized linear	ORG
ejpam-3209	42	4	second	ORDINAL
ejpam-3209	43	1	section 3	LAW
ejpam-3209	43	2	first	ORDINAL
ejpam-3209	44	1	second	ORDINAL
ejpam-3209	44	2	section 4	LAW
ejpam-3209	45	1	section 5	LAW
ejpam-3209	45	2	section 6	DATE
ejpam-3209	46	1	barnes et al	PERSON
ejpam-3209	47	1	j. pure	PERSON
ejpam-3209	47	2	11	CARDINAL
ejpam-3209	47	3	2	CARDINAL
ejpam-3209	47	4	2018	DATE
ejpam-3209	47	5	375	CARDINAL
ejpam-3209	47	6	two	CARDINAL
ejpam-3209	47	7	first	ORDINAL
ejpam-3209	47	8	‖v‖	ORG
ejpam-3209	47	9	∀ u	PERSON
ejpam-3209	48	1	0	CARDINAL
ejpam-3209	48	2	2	CARDINAL
ejpam-3209	48	3	1	CARDINAL
ejpam-3209	48	4	second	ORDINAL
ejpam-3209	48	5	‖v‖	ORG
ejpam-3209	48	6	∀ u	PERSON
ejpam-3209	49	1	0	CARDINAL
ejpam-3209	49	2	2	CARDINAL
ejpam-3209	50	1	2	CARDINAL
ejpam-3209	51	1	1	CARDINAL
ejpam-3209	52	1	r.	NORP
ejpam-3209	53	1	0	CARDINAL
ejpam-3209	54	1	0	CARDINAL
ejpam-3209	54	2	∀ u	PERSON
ejpam-3209	54	3	∈	ORG
ejpam-3209	54	4	α(u1	CARDINAL
ejpam-3209	54	5	+ β(u2	GPE
ejpam-3209	54	6	∀ α	PERSON
ejpam-3209	54	7	∈	ORG
ejpam-3209	54	8	13	CARDINAL
ejpam-3209	55	1	2	CARDINAL
ejpam-3209	56	1	0,∞	TIME
ejpam-3209	56	2	∈	ORG
ejpam-3209	56	3	0	DATE
ejpam-3209	56	4	0	CARDINAL
ejpam-3209	56	5	∈	ORG
ejpam-3209	56	6	∈	ORG
ejpam-3209	56	7	‖v‖	ORG
ejpam-3209	56	8	∀ u	PERSON
ejpam-3209	59	1	14	CARDINAL
ejpam-3209	60	1	3	CARDINAL
ejpam-3209	62	1	y ∈	PERSON
ejpam-3209	63	1	15	CARDINAL
ejpam-3209	64	1	barnes et al	PERSON
ejpam-3209	65	1	j. pure	PERSON
ejpam-3209	65	2	11	CARDINAL
ejpam-3209	65	3	2	CARDINAL
ejpam-3209	65	4	2018	DATE
ejpam-3209	65	5	375	CARDINAL
ejpam-3209	65	6	4	CARDINAL
ejpam-3209	67	1	‖tx‖ ≤ k‖x‖	FAC
ejpam-3209	67	2	∈	ORG
ejpam-3209	69	1	16	CARDINAL
ejpam-3209	69	2	5	CARDINAL
ejpam-3209	70	1	f(x	ORG
ejpam-3209	71	1	∀ f	ORG
ejpam-3209	71	2	g ∈ e.	PERSON
ejpam-3209	72	1	17	CARDINAL
ejpam-3209	73	1	2.1	CARDINAL
ejpam-3209	74	1	first	ORDINAL
ejpam-3209	75	1	firstly	ORDINAL
ejpam-3209	75	2	2	CARDINAL
ejpam-3209	76	1	0	CARDINAL
ejpam-3209	76	2	u	NORP
ejpam-3209	76	3	+ 2(u	DATE
ejpam-3209	76	4	u	NORP
ejpam-3209	78	1	+ 2(u	DATE
ejpam-3209	78	2	−2(u	PERSON
ejpam-3209	78	3	1 2	CARDINAL
ejpam-3209	78	4	u)(v	PERSON
ejpam-3209	78	5	u)(u	ORG
ejpam-3209	78	6	+ 4(u	CARDINAL
ejpam-3209	79	1	u)(v	PERSON
ejpam-3209	79	2	u)(u	ORG
ejpam-3209	79	3	+ 6(u	DATE
ejpam-3209	79	4	u)(v	NORP
ejpam-3209	80	1	+ 4(u	CARDINAL
ejpam-3209	80	2	u)(v	PERSON
ejpam-3209	81	1	1 6	CARDINAL
ejpam-3209	81	2	u)(v	PERSON
ejpam-3209	81	3	u+ v)4 −{(u	ORG
ejpam-3209	81	4	u)(v	NORP
ejpam-3209	81	5	u+ v)4 barnes et al	ORG
ejpam-3209	82	1	j. pure	PERSON
ejpam-3209	82	2	11	CARDINAL
ejpam-3209	82	3	2	CARDINAL
ejpam-3209	82	4	2018	DATE
ejpam-3209	82	5	375	CARDINAL
ejpam-3209	82	6	389 379	CARDINAL
ejpam-3209	82	7	u)(v	PERSON
ejpam-3209	82	8	first	ORDINAL
ejpam-3209	83	1	nc4(u	GPE
ejpam-3209	83	2	v)2 +n	ORG
ejpam-3209	83	3	u) n−6 2	ORG
ejpam-3209	83	4	+ nc7(u	PERSON
ejpam-3209	83	5	2	CARDINAL
ejpam-3209	84	1	2	CARDINAL
ejpam-3209	85	1	u, u	ORG
ejpam-3209	85	2	2	CARDINAL
ejpam-3209	85	3	0	CARDINAL
ejpam-3209	85	4	2	CARDINAL
ejpam-3209	85	5	u	NORP
ejpam-3209	85	6	nc3(u	MONEY
ejpam-3209	85	7	u) n−4 2	ORG
ejpam-3209	85	8	u) n−4 2	ORG
ejpam-3209	85	9	v)2 +n	ORG
ejpam-3209	85	10	u) n−6 2	ORG
ejpam-3209	85	11	2	CARDINAL
ejpam-3209	86	1	u, u	ORG
ejpam-3209	86	2	2	CARDINAL
ejpam-3209	86	3	u	NORP
ejpam-3209	87	1	nc3(u	MONEY
ejpam-3209	87	2	u) n−4 2	ORG
ejpam-3209	87	3	u) n−4 2	ORG
ejpam-3209	87	4	v)2 +n	ORG
ejpam-3209	87	5	u) n−6 2	ORG
ejpam-3209	87	6	2	CARDINAL
ejpam-3209	88	1	2	CARDINAL
ejpam-3209	89	1	u, u	ORG
ejpam-3209	89	2	2	CARDINAL
ejpam-3209	89	3	2	CARDINAL
ejpam-3209	89	4	v)‖n ⇒ ‖u‖‖v‖ ≤ ‖u‖+	PERSON
ejpam-3209	89	5	‖v‖	ORG
ejpam-3209	89	6	∀ u	PERSON
ejpam-3209	90	1	0	CARDINAL
ejpam-3209	90	2	2	CARDINAL
ejpam-3209	91	1	3	CARDINAL
ejpam-3209	91	2	2.2	CARDINAL
ejpam-3209	92	1	second	ORDINAL
ejpam-3209	92	2	two	CARDINAL
ejpam-3209	93	1	2	CARDINAL
ejpam-3209	93	2	0	CARDINAL
ejpam-3209	93	3	u	NORP
ejpam-3209	93	4	+ 2(u	DATE
ejpam-3209	94	1	+ 2(u	DATE
ejpam-3209	94	2	+ 2(u	DATE
ejpam-3209	95	1	1 2	CARDINAL
ejpam-3209	95	2	v)‖2 barnes et al	PERSON
ejpam-3209	96	1	j. pure	PERSON
ejpam-3209	96	2	11	CARDINAL
ejpam-3209	96	3	2	CARDINAL
ejpam-3209	96	4	2018	DATE
ejpam-3209	96	5	375	CARDINAL
ejpam-3209	96	6	‖v‖	ORG
ejpam-3209	96	7	u)(u	ORG
ejpam-3209	97	1	+ 4(u	CARDINAL
ejpam-3209	97	2	u)(v	NORP
ejpam-3209	97	3	u)(u	ORG
ejpam-3209	97	4	+ 6(u	DATE
ejpam-3209	97	5	u)(v	NORP
ejpam-3209	97	6	+ 4(u	CARDINAL
ejpam-3209	97	7	u)(v	NORP
ejpam-3209	97	8	u)(v	NORP
ejpam-3209	98	1	1 6	CARDINAL
ejpam-3209	98	2	u)(v	PERSON
ejpam-3209	98	3	u)(v	PERSON
ejpam-3209	98	4	u)(v	NORP
ejpam-3209	98	5	‖v‖	ORG
ejpam-3209	98	6	second	ORDINAL
ejpam-3209	98	7	nc4(u	GPE
ejpam-3209	98	8	v)2 +n	ORG
ejpam-3209	98	9	u) n−6 2	ORG
ejpam-3209	98	10	+ nc7(u	PERSON
ejpam-3209	98	11	2	CARDINAL
ejpam-3209	99	1	2	CARDINAL
ejpam-3209	100	1	u, u	ORG
ejpam-3209	100	2	2	CARDINAL
ejpam-3209	100	3	0	CARDINAL
ejpam-3209	100	4	nc3(u	MONEY
ejpam-3209	100	5	u) n−4 2	ORG
ejpam-3209	100	6	u) n−4 2	ORG
ejpam-3209	100	7	v)2 +n	ORG
ejpam-3209	100	8	u) n−6 2	ORG
ejpam-3209	100	9	2	CARDINAL
ejpam-3209	101	1	u, u	ORG
ejpam-3209	101	2	u	NORP
ejpam-3209	101	3	nc3(u	MONEY
ejpam-3209	101	4	u) n−4 2	ORG
ejpam-3209	101	5	u) n−4 2	ORG
ejpam-3209	101	6	v)2 +n	ORG
ejpam-3209	101	7	u) n−6 2	ORG
ejpam-3209	101	8	2	CARDINAL
ejpam-3209	102	1	2	CARDINAL
ejpam-3209	103	1	u, u	ORG
ejpam-3209	103	2	4	CARDINAL
ejpam-3209	103	3	2	CARDINAL
ejpam-3209	103	4	2	CARDINAL
ejpam-3209	103	5	‖u‖‖v‖}n	LOC
ejpam-3209	103	6	‖v‖	ORG
ejpam-3209	103	7	∀ u	PERSON
ejpam-3209	103	8	2,∞	CARDINAL
ejpam-3209	104	1	4	CARDINAL
ejpam-3209	104	2	3	CARDINAL
ejpam-3209	104	3	first	ORDINAL
ejpam-3209	104	4	first	ORDINAL
ejpam-3209	106	1	j. pure	PERSON
ejpam-3209	106	2	11	CARDINAL
ejpam-3209	106	3	2	CARDINAL
ejpam-3209	106	4	2018	DATE
ejpam-3209	106	5	375	CARDINAL
ejpam-3209	106	6	first	ORDINAL
ejpam-3209	107	1	3.1	CARDINAL
ejpam-3209	107	2	first	ORDINAL
ejpam-3209	107	3	firstly	ORDINAL
ejpam-3209	107	4	first	ORDINAL
ejpam-3209	107	5	1	CARDINAL
ejpam-3209	107	6	two	CARDINAL
ejpam-3209	108	1	0	CARDINAL
ejpam-3209	108	2	2	CARDINAL
ejpam-3209	110	1	1	CARDINAL
ejpam-3209	110	2	5 6	DATE
ejpam-3209	110	3	13 18	DATE
ejpam-3209	110	4	6 ∥∥∥∥∥∥13 18 ∥∥∥ ≤	MONEY
ejpam-3209	110	5	6 ∥∥∥+	QUANTITY
ejpam-3209	110	6	18	CARDINAL
ejpam-3209	110	7	65 108	QUANTITY
ejpam-3209	110	8	28 18	DATE
ejpam-3209	111	1	2	CARDINAL
ejpam-3209	111	2	2	MONEY
ejpam-3209	111	3	5	CARDINAL
ejpam-3209	111	4	2 ∥∥∥+	QUANTITY
ejpam-3209	111	5	5	CARDINAL
ejpam-3209	112	1	3	CARDINAL
ejpam-3209	112	2	19 10	DATE
ejpam-3209	112	3	9 5	DATE
ejpam-3209	112	4	10	CARDINAL
ejpam-3209	112	5	37 10	CARDINAL
ejpam-3209	113	1	3.2	CARDINAL
ejpam-3209	113	2	first	ORDINAL
ejpam-3209	113	3	first	ORDINAL
ejpam-3209	114	1	three	CARDINAL
ejpam-3209	114	2	1− norm,	TIME
ejpam-3209	115	1	4	CARDINAL
ejpam-3209	116	1	1 2	CARDINAL
ejpam-3209	116	2	4 5	CARDINAL
ejpam-3209	116	3	4 5	CARDINAL
ejpam-3209	116	4	1 ≤ ∥∥∥	QUANTITY
ejpam-3209	116	5	1 + ∥∥∥	QUANTITY
ejpam-3209	116	6	4 5	CARDINAL
ejpam-3209	116	7	1	CARDINAL
ejpam-3209	116	8	69 30	CARDINAL
ejpam-3209	117	1	5	CARDINAL
ejpam-3209	118	1	1 2	CARDINAL
ejpam-3209	118	2	4 5	CARDINAL
ejpam-3209	118	3	2 ∥∥∥	QUANTITY
ejpam-3209	118	4	4 5	CARDINAL
ejpam-3209	118	5	2 ≤ ∥∥∥	QUANTITY
ejpam-3209	118	6	2 + ∥∥∥	QUANTITY
ejpam-3209	118	7	4 5	CARDINAL
ejpam-3209	118	8	2 ⇒	PERCENT
ejpam-3209	119	1	barnes et al	PERSON
ejpam-3209	120	1	j. pure	PERSON
ejpam-3209	120	2	11	CARDINAL
ejpam-3209	120	3	2	CARDINAL
ejpam-3209	120	4	2018	DATE
ejpam-3209	121	1	375	CARDINAL
ejpam-3209	121	2	389 382	CARDINAL
ejpam-3209	121	3	6	CARDINAL
ejpam-3209	122	1	1 2	CARDINAL
ejpam-3209	122	2	4 5	CARDINAL
ejpam-3209	122	3	4 5	CARDINAL
ejpam-3209	122	4	∞ ≤ ∥∥∥	QUANTITY
ejpam-3209	122	5	∞ + ∥∥∥	PERSON
ejpam-3209	122	6	4 5	CARDINAL
ejpam-3209	123	1	3.3	CARDINAL
ejpam-3209	124	1	first	ORDINAL
ejpam-3209	127	1	0	CARDINAL
ejpam-3209	128	1	0	CARDINAL
ejpam-3209	129	1	|〈sin(θ	PERSON
ejpam-3209	130	1	0	CARDINAL
ejpam-3209	131	1	5	CARDINAL
ejpam-3209	131	2	first	ORDINAL
ejpam-3209	131	3	5	CARDINAL
ejpam-3209	131	4	0 ≤	MONEY
ejpam-3209	131	5	sin(θ)‖+ ‖	ORG
ejpam-3209	132	1	0	CARDINAL
ejpam-3209	133	1	1 + 1)0	DATE
ejpam-3209	133	2	0	CARDINAL
ejpam-3209	134	1	20	CARDINAL
ejpam-3209	134	2	1	CARDINAL
ejpam-3209	134	3	|〈sin(θ	PERSON
ejpam-3209	134	4	1 ≤	MONEY
ejpam-3209	134	5	1	CARDINAL
ejpam-3209	135	1	6	CARDINAL
ejpam-3209	136	1	j. pure	PERSON
ejpam-3209	136	2	11	CARDINAL
ejpam-3209	136	3	2	CARDINAL
ejpam-3209	136	4	2018	DATE
ejpam-3209	136	5	375	CARDINAL
ejpam-3209	136	6	389 383	CARDINAL
ejpam-3209	136	7	first	ORDINAL
ejpam-3209	136	8	6	CARDINAL
ejpam-3209	136	9	1 ≤	MONEY
ejpam-3209	136	10	sin(θ)‖+ ‖ cos(θ)‖	ORG
ejpam-3209	136	11	1	CARDINAL
ejpam-3209	137	1	1	CARDINAL
ejpam-3209	137	2	1 + 1)1	CARDINAL
ejpam-3209	137	3	1	CARDINAL
ejpam-3209	137	4	2	CARDINAL
ejpam-3209	138	1	2	CARDINAL
ejpam-3209	138	2	|〈sin(θ	PERSON
ejpam-3209	138	3	2 ≤	MONEY
ejpam-3209	138	4	2	CARDINAL
ejpam-3209	138	5	7	CARDINAL
ejpam-3209	138	6	first	ORDINAL
ejpam-3209	138	7	7	CARDINAL
ejpam-3209	138	8	2 ≤	MONEY
ejpam-3209	138	9	sin(θ)‖+ ‖ cos(θ)‖	ORG
ejpam-3209	138	10	2	CARDINAL
ejpam-3209	138	11	2	CARDINAL
ejpam-3209	138	12	1 + 1)2	DATE
ejpam-3209	138	13	2	CARDINAL
ejpam-3209	138	14	22	CARDINAL
ejpam-3209	141	1	|〈sin(θ	PERSON
ejpam-3209	144	1	8)	CARDINAL
ejpam-3209	144	2	first	ORDINAL
ejpam-3209	144	3	6	CARDINAL
ejpam-3209	144	4	sin(θ)‖+ ‖ cos(θ)‖ )	ORG
ejpam-3209	146	1	1 + 1)n	DATE
ejpam-3209	148	1	9	CARDINAL
ejpam-3209	148	2	first	ORDINAL
ejpam-3209	149	1	1	CARDINAL
ejpam-3209	150	1	0	CARDINAL
ejpam-3209	150	2	2	CARDINAL
ejpam-3209	151	1	0	CARDINAL
ejpam-3209	151	2	1	CARDINAL
ejpam-3209	151	3	‖ex‖‖	PERSON
ejpam-3209	152	1	j. pure	PERSON
ejpam-3209	152	2	11	CARDINAL
ejpam-3209	152	3	2	CARDINAL
ejpam-3209	152	4	2018	DATE
ejpam-3209	152	5	375	CARDINAL
ejpam-3209	156	1	6	CARDINAL
ejpam-3209	157	1	two	CARDINAL
ejpam-3209	157	2	‖v‖	ORG
ejpam-3209	157	3	17	CARDINAL
ejpam-3209	158	1	first	ORDINAL
ejpam-3209	158	2	2	CARDINAL
ejpam-3209	160	1	10	CARDINAL
ejpam-3209	160	2	‖v‖	ORG
ejpam-3209	160	3	‖v‖	ORG
ejpam-3209	160	4	∣∣∣p ⇒	PERSON
ejpam-3209	163	1	3	CARDINAL
ejpam-3209	163	2	10	CARDINAL
ejpam-3209	163	3	|‖u‖‖v‖|p	ORG
ejpam-3209	164	1	2p{|u|p + |v|p	QUANTITY
ejpam-3209	164	2	∀ u	PERSON
ejpam-3209	165	1	0	CARDINAL
ejpam-3209	165	2	2	CARDINAL
ejpam-3209	165	3	3	CARDINAL
ejpam-3209	166	1	two	CARDINAL
ejpam-3209	166	2	∀ ‖u‖	GPE
ejpam-3209	166	3	‖v‖ ∈	ORG
ejpam-3209	167	1	0	CARDINAL
ejpam-3209	167	2	2	CARDINAL
ejpam-3209	168	1	3	CARDINAL
ejpam-3209	168	2	2	CARDINAL
ejpam-3209	169	1	barnes et al	PERSON
ejpam-3209	170	1	j. pure	PERSON
ejpam-3209	170	2	11	CARDINAL
ejpam-3209	170	3	2	CARDINAL
ejpam-3209	170	4	2018	DATE
ejpam-3209	170	5	375	CARDINAL
ejpam-3209	170	6	4	CARDINAL
ejpam-3209	170	7	at least one	CARDINAL
ejpam-3209	171	1	0	CARDINAL
ejpam-3209	171	2	1	CARDINAL
ejpam-3209	172	1	∣∣∣ ∫ ω	ORG
ejpam-3209	172	2	∣∣∣p ≤ ∫ ω	ORG
ejpam-3209	172	3	first	ORDINAL
ejpam-3209	172	4	obtain∣∣∣ ∫ ω	ORG
ejpam-3209	172	5	∣∣∣p ≤ ∫ ω	ORG
ejpam-3209	172	6	∣∣∣ ∫ ω	ORG
ejpam-3209	172	7	∣∣∣p	GPE
ejpam-3209	172	8	1	CARDINAL
ejpam-3209	172	9	∫ ω ∣∣∣f(x)|pdx+ ∫ ω	ORG
ejpam-3209	172	10	1	CARDINAL
ejpam-3209	172	11	∣∣∣ ∫ ω	ORG
ejpam-3209	172	12	∣∣∣p	GPE
ejpam-3209	172	13	1	CARDINAL
ejpam-3209	172	14	∫ ω ∣∣∣f(x)|pdx	ORG
ejpam-3209	173	1	1	CARDINAL
ejpam-3209	173	2	∫ ω	ORG
ejpam-3209	173	3	1	CARDINAL
ejpam-3209	174	1	11	CARDINAL
ejpam-3209	175	1	12	CARDINAL
ejpam-3209	175	2	11	CARDINAL
ejpam-3209	175	3	12	CARDINAL
ejpam-3209	176	1	4	CARDINAL
ejpam-3209	176	2	two	CARDINAL
ejpam-3209	177	1	5	CARDINAL
ejpam-3209	177	2	f(x	ORG
ejpam-3209	179	1	0	CARDINAL
ejpam-3209	179	2	1	CARDINAL
ejpam-3209	179	3	0	CARDINAL
ejpam-3209	179	4	1	CARDINAL
ejpam-3209	180	1	∣∣∣ ≤ 2(b−	MONEY
ejpam-3209	181	1	barnes et al	PERSON
ejpam-3209	182	1	j. pure	PERSON
ejpam-3209	182	2	11	CARDINAL
ejpam-3209	182	3	2	CARDINAL
ejpam-3209	182	4	2018	DATE
ejpam-3209	182	5	375	CARDINAL
ejpam-3209	182	6	∣∣∣	CARDINAL
ejpam-3209	185	1	∣∣∣	CARDINAL
ejpam-3209	186	1	first	ORDINAL
ejpam-3209	187	1	∣∣∣	CARDINAL
ejpam-3209	187	2	∣∣∣ sin(nx	MONEY
ejpam-3209	187	3	∣∣∣}dx	DATE
ejpam-3209	187	4	∣∣∣	CARDINAL
ejpam-3209	191	1	1dx+	CARDINAL
ejpam-3209	191	2	1dx ⇒ ∣∣∣	ORG
ejpam-3209	195	1	∣∣∣ ≤ 2(b−	MONEY
ejpam-3209	196	1	4	CARDINAL
ejpam-3209	196	2	second	ORDINAL
ejpam-3209	196	3	second	ORDINAL
ejpam-3209	197	1	6	CARDINAL
ejpam-3209	198	1	two	CARDINAL
ejpam-3209	198	2	∀ u	PERSON
ejpam-3209	199	1	2,∞	CARDINAL
ejpam-3209	199	2	‖v‖	ORG
ejpam-3209	199	3	‖v‖	ORG
ejpam-3209	200	1	13	CARDINAL
ejpam-3209	200	2	‖v‖	ORG
ejpam-3209	201	1	14	CARDINAL
ejpam-3209	201	2	13	CARDINAL
ejpam-3209	201	3	14	CARDINAL
ejpam-3209	202	1	barnes et al	PERSON
ejpam-3209	203	1	j. pure	PERSON
ejpam-3209	203	2	11	CARDINAL
ejpam-3209	203	3	2	CARDINAL
ejpam-3209	203	4	2018	DATE
ejpam-3209	203	5	375	CARDINAL
ejpam-3209	203	6	7	CARDINAL
ejpam-3209	204	1	∣∣∣ ∫ ω	ORG
ejpam-3209	204	2	∣∣∣p ≤ ∫ ω	ORG
ejpam-3209	204	3	second	ORDINAL
ejpam-3209	205	1	∫ ω |f(x)g(x)|dx ⇒ ∫ ω	ORG
ejpam-3209	205	2	∫ ω	ORG
ejpam-3209	206	1	15	CARDINAL
ejpam-3209	208	1	16	CARDINAL
ejpam-3209	208	2	15	CARDINAL
ejpam-3209	208	3	16	CARDINAL
ejpam-3209	209	1	⇒ ∫ ω |f(x)|p + |g(x)|pdx = ∫ ω	ORG
ejpam-3209	209	2	∫ ω |f(x)|p + |g(x)|pdx ) 1	ORG
ejpam-3209	209	3	∫ ω |f(x)|p|g(x)|pdx	ORG
ejpam-3209	209	4	1	CARDINAL
ejpam-3209	209	5	∫ ω |f(x)|pdx	ORG
ejpam-3209	209	6	1	CARDINAL
ejpam-3209	210	1	1	CARDINAL
ejpam-3209	210	2	∫ ω |f(x)|pdx	ORG
ejpam-3209	210	3	1	CARDINAL
ejpam-3209	210	4	1	CARDINAL
ejpam-3209	212	1	5	CARDINAL
ejpam-3209	212	2	9	CARDINAL
ejpam-3209	212	3	first	ORDINAL
ejpam-3209	212	4	1 ≤ 2n	CARDINAL
ejpam-3209	212	5	0	CARDINAL
ejpam-3209	212	6	1	DATE
ejpam-3209	212	7	2	CARDINAL
ejpam-3209	215	1	first	ORDINAL
ejpam-3209	215	2	second	ORDINAL
ejpam-3209	216	1	one	CARDINAL
ejpam-3209	217	1	388 6	CARDINAL
ejpam-3209	217	2	first	ORDINAL
ejpam-3209	217	3	two	CARDINAL
ejpam-3209	218	1	second	ORDINAL
ejpam-3209	218	2	two	CARDINAL
ejpam-3209	219	1	first	ORDINAL
ejpam-3209	220	1	0	CARDINAL
ejpam-3209	220	2	1	CARDINAL
ejpam-3209	224	1	first	ORDINAL
ejpam-3209	224	2	1	CARDINAL
ejpam-3209	225	1	1	CARDINAL
ejpam-3209	225	2	a. m. fink	PERSON
ejpam-3209	225	3	249	CARDINAL
ejpam-3209	225	4	2000).pp	CARDINAL
ejpam-3209	225	5	118	CARDINAL
ejpam-3209	226	1	2	CARDINAL
ejpam-3209	226	2	b. barnes	PERSON
ejpam-3209	226	3	e. d. j. owusu-ansah	PERSON
ejpam-3209	226	4	s. k. amponsah	PERSON
ejpam-3209	226	5	i. a. adjei	PERSON
ejpam-3209	226	6	european journal	ORG
ejpam-3209	226	7	2018	DATE
ejpam-3209	228	1	352-361	CARDINAL
ejpam-3209	229	1	3	CARDINAL
ejpam-3209	229	2	d. s. mitrinović	ORG
ejpam-3209	229	3	new york	GPE
ejpam-3209	229	4	1961	DATE
ejpam-3209	230	1	4	CARDINAL
ejpam-3209	231	1	13	CARDINAL
ejpam-3209	231	2	1	CARDINAL
ejpam-3209	233	1	49-54	CARDINAL
ejpam-3209	234	1	5	CARDINAL
ejpam-3209	234	2	g. h. hardy	PERSON
ejpam-3209	234	3	j. e. littlewood	PERSON
ejpam-3209	234	4	g. polya	PERSON
ejpam-3209	235	1	london	GPE
ejpam-3209	235	2	new york	GPE
ejpam-3209	235	3	cambridge university press	ORG
ejpam-3209	235	4	1978	DATE
ejpam-3209	236	1	6	CARDINAL
ejpam-3209	236	2	d. s. mitrinović	PERSON
ejpam-3209	236	3	j. e. pec̆arić	PERSON
ejpam-3209	236	4	a. m. fink	PERSON
ejpam-3209	236	5	kluwer	ORG
ejpam-3209	236	6	dordrecht	ORG
ejpam-3209	236	7	1993).pp	CARDINAL
ejpam-3209	236	8	69	CARDINAL
ejpam-3209	237	1	7	CARDINAL
ejpam-3209	237	2	s. alan	PERSON
ejpam-3209	237	3	courant institute of mathematical sciences	ORG
ejpam-3209	237	4	new york university	ORG
ejpam-3209	237	5	2013	DATE
ejpam-3209	239	1	8	CARDINAL
ejpam-3209	239	2	j. v. grabiner	PERSON
ejpam-3209	239	3	newton	GPE
ejpam-3209	240	1	american	NORP
ejpam-3209	240	2	monthly	DATE
ejpam-3209	240	3	104	ORG
ejpam-3209	240	4	1997).pp	CARDINAL
ejpam-3209	240	5	393	CARDINAL
ejpam-3209	241	1	9	CARDINAL
ejpam-3209	241	2	s. wu	PERSON
ejpam-3209	241	3	308	CARDINAL
ejpam-3209	241	4	2005).pp	CARDINAL
ejpam-3209	241	5	689-702	CARDINAL
ejpam-3209	242	1	10	CARDINAL
ejpam-3209	242	2	m. s. klamkin	PERSON
ejpam-3209	242	3	amer	PERSON
ejpam-3209	242	4	82	DATE
ejpam-3209	242	5	1975).pp	CARDINAL
ejpam-3209	243	1	741	CARDINAL
ejpam-3209	244	1	11	CARDINAL
ejpam-3209	244	2	d. s. mitrinović	ORG
ejpam-3209	244	3	p. m. vasić	PERSON
ejpam-3209	244	4	new york	GPE
ejpam-3209	244	5	1970	DATE
ejpam-3209	244	6	389	CARDINAL
ejpam-3209	244	7	12	CARDINAL
ejpam-3209	244	8	i. schur	PERSON
ejpam-3209	244	9	bemerkungen zur theorie de beschränkten bilinearformen mit unendlich vielen veränderlichen	PERSON
ejpam-3209	244	10	140	CARDINAL
ejpam-3209	244	11	1911).pp	CARDINAL
ejpam-3209	245	1	1-28	CARDINAL
ejpam-3209	246	1	13	CARDINAL
ejpam-3209	246	2	b. kolman	PERSON
ejpam-3209	246	3	d. r. hill	PERSON
ejpam-3209	246	4	prentice-hall, inc	ORG
ejpam-3209	246	5	new jersey	GPE
ejpam-3209	246	6	2000	DATE
ejpam-3209	247	1	14	CARDINAL
ejpam-3209	247	2	j. t. scheick	PERSON
ejpam-3209	247	3	prentice-hall, inc	ORG
ejpam-3209	247	4	new york	GPE
ejpam-3209	247	5	1997	DATE
ejpam-3209	248	1	15	CARDINAL
ejpam-3209	248	2	j. t. oden	PERSON
ejpam-3209	248	3	first	ORDINAL
ejpam-3209	248	4	prentice-hall, inc	ORG
ejpam-3209	248	5	new jersey	GPE
ejpam-3209	248	6	1979	DATE
ejpam-3209	249	1	16	CARDINAL
ejpam-3209	249	2	c. e. chidume	PERSON
ejpam-3209	249	3	longman	ORG
ejpam-3209	249	4	nigeria	GPE
ejpam-3209	249	5	1989	DATE
ejpam-3209	250	1	17	CARDINAL
ejpam-3209	251	1	pearson education, inc	ORG
ejpam-3209	251	2	4th	ORDINAL
ejpam-3209	251	3	2010	DATE