id	sid	eid	entity	type
ejpam-4830	1	1	european journal	ORG
ejpam-4830	2	1	16	CARDINAL
ejpam-4830	2	2	3	CARDINAL
ejpam-4830	2	3	2023	CARDINAL
ejpam-4830	2	4	1830-1847	DATE
ejpam-4830	2	5	1307-5543	DATE
ejpam-4830	2	6	new york	GPE
ejpam-4830	2	7	british	NORP
ejpam-4830	2	8	r. sumalpong	PERSON
ejpam-4830	2	9	jr.1,∗	GPE
ejpam-4830	2	10	michael b. frondoza1	PERSON
ejpam-4830	2	11	noel lito b. sayson3	PERSON
ejpam-4830	3	1	mindanao	GPE
ejpam-4830	3	2	university iligan institute of technology	ORG
ejpam-4830	3	3	iligan city	GPE
ejpam-4830	3	4	philippines 2 department of physics	ORG
ejpam-4830	3	5	mindanao	GPE
ejpam-4830	3	6	university iligan institute of technology	ORG
ejpam-4830	3	7	iligan city	GPE
ejpam-4830	3	8	philippines	GPE
ejpam-4830	5	1	european	NORP
ejpam-4830	5	2	american	NORP
ejpam-4830	6	1	british	NORP
ejpam-4830	6	2	american	NORP
ejpam-4830	6	3	european	NORP
ejpam-4830	7	1	british	NORP
ejpam-4830	8	1	pde	ORG
ejpam-4830	10	1	2020	DATE
ejpam-4830	10	2	62p05	CARDINAL
ejpam-4830	10	3	97m30	CARDINAL
ejpam-4830	10	4	british	NORP
ejpam-4830	10	5	american	NORP
ejpam-4830	10	6	european	NORP
ejpam-4830	10	7	1	CARDINAL
ejpam-4830	11	1	european	NORP
ejpam-4830	11	2	american	NORP
ejpam-4830	13	1	european	NORP
ejpam-4830	13	2	american	NORP
ejpam-4830	14	1	∗corresponding	PERSON
ejpam-4830	15	1	felipejr.sumalpong@g.msuiit.edu.ph	ORG
ejpam-4830	15	2	sumalpong	PERSON
ejpam-4830	15	3	michael.frondoza@g.msuiit.edu.ph	GPE
ejpam-4830	15	4	m. frondoza	PERSON
ejpam-4830	15	5	noellito.sayson@g.msuiit.edu.ph	ORG
ejpam-4830	15	6	b. sayson	PERSON
ejpam-4830	15	7	1830	DATE
ejpam-4830	16	1	2023	CARDINAL
ejpam-4830	17	1	f. sumalpong	PERSON
ejpam-4830	17	2	m. frondoza	PERSON
ejpam-4830	17	3	n.l. sayson	GPE
ejpam-4830	18	1	j. pure	PERSON
ejpam-4830	18	2	16	CARDINAL
ejpam-4830	18	3	3	CARDINAL
ejpam-4830	18	4	2023	CARDINAL
ejpam-4830	18	5	1830-1847	DATE
ejpam-4830	18	6	1831	DATE
ejpam-4830	18	7	european	NORP
ejpam-4830	21	1	5	CARDINAL
ejpam-4830	21	2	british	NORP
ejpam-4830	21	3	american	NORP
ejpam-4830	21	4	european	NORP
ejpam-4830	23	1	5	CARDINAL
ejpam-4830	24	1	british	NORP
ejpam-4830	24	2	5	CARDINAL
ejpam-4830	25	1	2	CARDINAL
ejpam-4830	25	2	zhang	PERSON
ejpam-4830	25	3	zhou	PERSON
ejpam-4830	25	4	european	NORP
ejpam-4830	26	1	5	CARDINAL
ejpam-4830	28	1	section 2	LAW
ejpam-4830	28	2	british	NORP
ejpam-4830	28	3	5	CARDINAL
ejpam-4830	29	1	section 3	LAW
ejpam-4830	29	2	two	CARDINAL
ejpam-4830	31	1	2	CARDINAL
ejpam-4830	31	2	1	CARDINAL
ejpam-4830	31	3	2	DATE
ejpam-4830	33	1	0,∞	DATE
ejpam-4830	35	1	x0	ORG
ejpam-4830	35	2	0	CARDINAL
ejpam-4830	35	3	1	CARDINAL
ejpam-4830	35	4	∈	ORG
ejpam-4830	35	5	ω	ORDINAL
ejpam-4830	36	1	w	ORG
ejpam-4830	37	1	w	ORG
ejpam-4830	38	1	british	NORP
ejpam-4830	39	1	british	NORP
ejpam-4830	39	2	years	DATE
ejpam-4830	39	3	5	CARDINAL
ejpam-4830	39	4	1	CARDINAL
ejpam-4830	40	1	5	CARDINAL
ejpam-4830	40	2	british	NORP
ejpam-4830	40	3	european	NORP
ejpam-4830	40	4	f. sumalpong	PERSON
ejpam-4830	40	5	m. frondoza	PERSON
ejpam-4830	40	6	n.l. sayson	GPE
ejpam-4830	41	1	j. pure	PERSON
ejpam-4830	41	2	16	CARDINAL
ejpam-4830	41	3	3	CARDINAL
ejpam-4830	41	4	2023	CARDINAL
ejpam-4830	41	5	1830-1847	DATE
ejpam-4830	41	6	1832	DATE
ejpam-4830	42	1	5	CARDINAL
ejpam-4830	42	2	british	NORP
ejpam-4830	43	1	0	CARDINAL
ejpam-4830	44	1	5	CARDINAL
ejpam-4830	45	1	0 ≤	MONEY
ejpam-4830	46	1	2	CARDINAL
ejpam-4830	46	2	̸=	ORG
ejpam-4830	46	3	dpµc	PERSON
ejpam-4830	46	4	3	CARDINAL
ejpam-4830	46	5	∫	ORG
ejpam-4830	46	6	4	CARDINAL
ejpam-4830	46	7	1	CARDINAL
ejpam-4830	46	8	0 ≤	MONEY
ejpam-4830	48	1	5	CARDINAL
ejpam-4830	49	1	lemma 1	ORG
ejpam-4830	49	2	2	CARDINAL
ejpam-4830	50	1	− ∫	ORG
ejpam-4830	50	2	6	CARDINAL
ejpam-4830	51	1	1	CARDINAL
ejpam-4830	52	1	σ(αt)xtdw	LOC
ejpam-4830	53	1	0 ≤	MONEY
ejpam-4830	53	2	x0	ORG
ejpam-4830	53	3	∈	ORG
ejpam-4830	53	4	0,∞	DATE
ejpam-4830	54	1	3	CARDINAL
ejpam-4830	55	1	british	NORP
ejpam-4830	55	2	k −xt	PERSON
ejpam-4830	56	1	7	CARDINAL
ejpam-4830	56	2	∈	ORG
ejpam-4830	56	3	0,∞	DATE
ejpam-4830	57	1	british	NORP
ejpam-4830	59	1	f. sumalpong	PERSON
ejpam-4830	59	2	m. frondoza	PERSON
ejpam-4830	59	3	n.l. sayson	GPE
ejpam-4830	60	1	j. pure	PERSON
ejpam-4830	60	2	16	CARDINAL
ejpam-4830	60	3	3	CARDINAL
ejpam-4830	60	4	2023	CARDINAL
ejpam-4830	60	5	1830-1847	DATE
ejpam-4830	60	6	1833	DATE
ejpam-4830	60	7	5	CARDINAL
ejpam-4830	60	8	9	CARDINAL
ejpam-4830	60	9	7	CARDINAL
ejpam-4830	60	10	s	GPE
ejpam-4830	60	11	10	CARDINAL
ejpam-4830	60	12	0 ≤	MONEY
ejpam-4830	60	13	zµc s	ORG
ejpam-4830	60	14	2	CARDINAL
ejpam-4830	63	1	11	CARDINAL
ejpam-4830	63	2	k −xτz	PERSON
ejpam-4830	65	1	12	CARDINAL
ejpam-4830	66	1	british	NORP
ejpam-4830	66	2	0	CARDINAL
ejpam-4830	66	3	x0	ORG
ejpam-4830	66	4	0≤τ≤t	CARDINAL
ejpam-4830	67	1	13	CARDINAL
ejpam-4830	67	2	0≤τ≤t	CARDINAL
ejpam-4830	69	1	supremum	ORG
ejpam-4830	69	2	0	CARDINAL
ejpam-4830	69	3	ẽ	ORG
ejpam-4830	70	1	0	CARDINAL
ejpam-4830	71	1	british	NORP
ejpam-4830	72	1	0	CARDINAL
ejpam-4830	75	1	14	CARDINAL
ejpam-4830	76	1	0	CARDINAL
ejpam-4830	76	2	11	CARDINAL
ejpam-4830	77	1	british	NORP
ejpam-4830	78	1	0	CARDINAL
ejpam-4830	78	2	13	CARDINAL
ejpam-4830	78	3	0≤τ≤t−t ẽt	CARDINAL
ejpam-4830	78	4	xt+τ	PERSON
ejpam-4830	80	1	15	CARDINAL
ejpam-4830	80	2	supremum	ORG
ejpam-4830	81	1	0	CARDINAL
ejpam-4830	81	2	t−t	GPE
ejpam-4830	82	1	∈	ORG
ejpam-4830	83	1	2	CARDINAL
ejpam-4830	83	2	7	CARDINAL
ejpam-4830	83	3	11	CARDINAL
ejpam-4830	83	4	zr t	PERSON
ejpam-4830	83	5	zr 0,τ	GPE
ejpam-4830	83	6	15	CARDINAL
ejpam-4830	83	7	f. sumalpong	PERSON
ejpam-4830	83	8	m. frondoza	PERSON
ejpam-4830	83	9	n.l. sayson	GPE
ejpam-4830	84	1	j. pure	PERSON
ejpam-4830	84	2	16	CARDINAL
ejpam-4830	84	3	3	CARDINAL
ejpam-4830	84	4	2023	CARDINAL
ejpam-4830	84	5	1830-1847	DATE
ejpam-4830	84	6	1834	DATE
ejpam-4830	85	1	0≤τ≤t−t	CARDINAL
ejpam-4830	85	2	16	CARDINAL
ejpam-4830	85	3	x(r	PERSON
ejpam-4830	86	1	σ(αt)xtdw	LOC
ejpam-4830	86	2	x0	ORG
ejpam-4830	87	1	1	CARDINAL
ejpam-4830	87	2	1	CARDINAL
ejpam-4830	89	1	0	CARDINAL
ejpam-4830	89	2	17	CARDINAL
ejpam-4830	91	1	0 ≤	QUANTITY
ejpam-4830	93	1	1− λ)x3	WORK_OF_ART
ejpam-4830	93	2	0,∞	DATE
ejpam-4830	94	1	1− λ)x3	PRODUCT
ejpam-4830	96	1	1− λ)x3z	PRODUCT
ejpam-4830	99	1	1− λ)x3z	PRODUCT
ejpam-4830	108	1	17	CARDINAL
ejpam-4830	109	1	k −xt	PERSON
ejpam-4830	110	1	0	DATE
ejpam-4830	113	1	15	CARDINAL
ejpam-4830	113	2	7→	CARDINAL
ejpam-4830	113	3	18	CARDINAL
ejpam-4830	114	1	0	CARDINAL
ejpam-4830	114	2	∈	ORG
ejpam-4830	115	1	k − xt	PERSON
ejpam-4830	116	1	0	DATE
ejpam-4830	119	1	17	CARDINAL
ejpam-4830	119	2	18	CARDINAL
ejpam-4830	120	1	0	CARDINAL
ejpam-4830	120	2	∈	ORG
ejpam-4830	122	1	0	CARDINAL
ejpam-4830	123	1	19	CARDINAL
ejpam-4830	123	2	f. sumalpong	PERSON
ejpam-4830	123	3	m. frondoza	PERSON
ejpam-4830	123	4	n.l. sayson	GPE
ejpam-4830	124	1	j. pure	PERSON
ejpam-4830	124	2	16	CARDINAL
ejpam-4830	124	3	3	CARDINAL
ejpam-4830	124	4	2023	CARDINAL
ejpam-4830	124	5	1830-1847 1835	DATE
ejpam-4830	126	1	k −xt	PERSON
ejpam-4830	128	1	20	CARDINAL
ejpam-4830	128	2	⊂	GPE
ejpam-4830	129	1	15	CARDINAL
ejpam-4830	129	2	τ ∈	PERSON
ejpam-4830	131	1	2.9	CARDINAL
ejpam-4830	131	2	46	CARDINAL
ejpam-4830	132	1	6	CARDINAL
ejpam-4830	133	1	0	CARDINAL
ejpam-4830	134	1	21	CARDINAL
ejpam-4830	134	2	0,∞	DATE
ejpam-4830	134	3	15	CARDINAL
ejpam-4830	134	4	7→	CARDINAL
ejpam-4830	136	1	0	CARDINAL
ejpam-4830	136	2	j ∈ m.	PERSON
ejpam-4830	136	3	46	CARDINAL
ejpam-4830	136	4	2	CARDINAL
ejpam-4830	136	5	0	CARDINAL
ejpam-4830	136	6	22	CARDINAL
ejpam-4830	136	7	bd(t	ORG
ejpam-4830	136	8	44	DATE
ejpam-4830	137	1	24	CARDINAL
ejpam-4830	138	1	1	CARDINAL
ejpam-4830	139	1	7→ gµc(t	QUANTITY
ejpam-4830	139	2	0	CARDINAL
ejpam-4830	141	1	∈	ORG
ejpam-4830	141	2	0,∞	DATE
ejpam-4830	142	1	0	CARDINAL
ejpam-4830	145	1	0,∞	DATE
ejpam-4830	145	2	0 ≤	MONEY
ejpam-4830	147	1	0 ≤	QUANTITY
ejpam-4830	148	1	t2,t	GPE
ejpam-4830	149	1	k − xzµc	ORG
ejpam-4830	152	1	t1,t − zµc	ORG
ejpam-4830	152	2	t2,t	GPE
ejpam-4830	152	3	ft2	CARDINAL
ejpam-4830	154	1	∣∣∣∣∣zµc t1,t	PERSON
ejpam-4830	154	2	1− zµc t2,t zµc	MONEY
ejpam-4830	154	3	ft2	CARDINAL
ejpam-4830	154	4	xeµc ∣∣∣∣∣zµc t1,t	PERSON
ejpam-4830	154	5	1−	ORDINAL
ejpam-4830	154	6	2	CARDINAL
ejpam-4830	154	7	ft2	CARDINAL
ejpam-4830	155	1	0	DATE
ejpam-4830	157	1	f. sumalpong	PERSON
ejpam-4830	157	2	m. frondoza	PERSON
ejpam-4830	157	3	n.l. sayson	GPE
ejpam-4830	158	1	j. pure	PERSON
ejpam-4830	158	2	16	CARDINAL
ejpam-4830	158	3	3	CARDINAL
ejpam-4830	158	4	2023	CARDINAL
ejpam-4830	158	5	1830-1847	DATE
ejpam-4830	158	6	1836	DATE
ejpam-4830	158	7	2	CARDINAL
ejpam-4830	159	1	7→	CARDINAL
ejpam-4830	159	2	0	CARDINAL
ejpam-4830	161	1	7→	CARDINAL
ejpam-4830	161	2	∈	ORG
ejpam-4830	161	3	0,∞	DATE
ejpam-4830	162	1	0	CARDINAL
ejpam-4830	163	1	∈	ORG
ejpam-4830	163	2	0,∞	DATE
ejpam-4830	164	1	0 ≤	MONEY
ejpam-4830	165	1	15	CARDINAL
ejpam-4830	166	1	0 ≤ ∣∣∣v	MONEY
ejpam-4830	166	2	i)−	PERSON
ejpam-4830	166	3	∣∣∣ ≤	MONEY
ejpam-4830	168	1	xt1+τ1	GPE
ejpam-4830	168	2	xt2+τ2	ORG
ejpam-4830	168	3	ft2	CARDINAL
ejpam-4830	168	4	∣∣∣ ≤ ∣∣∣e	MONEY
ejpam-4830	169	1	xt1+τ1 , j	ORG
ejpam-4830	169	2	xt2+τ2	ORG
ejpam-4830	169	3	ft2	CARDINAL
ejpam-4830	169	4	∣∣∣ ≤ ∣∣∣e	MONEY
ejpam-4830	170	1	xt1+τ1	GPE
ejpam-4830	170	2	xt2+τ2	ORG
ejpam-4830	170	3	ft2	CARDINAL
ejpam-4830	170	4	∣∣gµc(t1 + τ1	DATE
ejpam-4830	170	5	xt1+τ1	GPE
ejpam-4830	170	6	xt2+τ2	ORG
ejpam-4830	170	7	∣∣∣ ft2	CARDINAL
ejpam-4830	171	1	1	CARDINAL
ejpam-4830	171	2	0	CARDINAL
ejpam-4830	172	1	3	CARDINAL
ejpam-4830	173	1	j)−g(t	PERSON
ejpam-4830	173	2	0	CARDINAL
ejpam-4830	173	3	23	CARDINAL
ejpam-4830	174	1	0	CARDINAL
ejpam-4830	174	2	0,∞	DATE
ejpam-4830	175	1	0	CARDINAL
ejpam-4830	176	1	24	CARDINAL
ejpam-4830	176	2	7→	CARDINAL
ejpam-4830	176	3	7→ gµc(t	QUANTITY
ejpam-4830	176	4	0	CARDINAL
ejpam-4830	178	1	0	CARDINAL
ejpam-4830	178	2	0	CARDINAL
ejpam-4830	178	3	25	CARDINAL
ejpam-4830	179	1	3	CARDINAL
ejpam-4830	181	1	lim	PERSON
ejpam-4830	183	1	26	CARDINAL
ejpam-4830	183	2	f. sumalpong	PERSON
ejpam-4830	183	3	m. frondoza	PERSON
ejpam-4830	183	4	n.l. sayson	GPE
ejpam-4830	184	1	j. pure	PERSON
ejpam-4830	184	2	16	CARDINAL
ejpam-4830	184	3	3	CARDINAL
ejpam-4830	184	4	2023	CARDINAL
ejpam-4830	184	5	1830-1847	DATE
ejpam-4830	185	1	0,∞	DATE
ejpam-4830	185	2	0	CARDINAL
ejpam-4830	186	1	0	CARDINAL
ejpam-4830	186	2	27	CARDINAL
ejpam-4830	186	3	21	CARDINAL
ejpam-4830	187	1	0≤τ≤t−t	CARDINAL
ejpam-4830	187	2	xt+τ	PERSON
ejpam-4830	188	1	e−rτ+ϵ	NORP
ejpam-4830	188	2	τ+ϵ	GPE
ejpam-4830	188	3	xt+τ+ϵ , j	ORG
ejpam-4830	189	1	28	CARDINAL
ejpam-4830	189	2	first	ORDINAL
ejpam-4830	189	3	0 as ϵ	PERCENT
ejpam-4830	190	1	29	CARDINAL
ejpam-4830	191	1	0	CARDINAL
ejpam-4830	192	1	0	CARDINAL
ejpam-4830	192	2	0≤s≤t−t	DATE
ejpam-4830	192	3	k −	ORG
ejpam-4830	192	4	ϵ)xsz	PERSON
ejpam-4830	192	5	t+s	GPE
ejpam-4830	194	1	ϵ)xsz	PERSON
ejpam-4830	194	2	t+s	GPE
ejpam-4830	196	1	0	CARDINAL
ejpam-4830	196	2	0≤s≤t−t	DATE
ejpam-4830	196	3	k − xxsz µc	PERSON
ejpam-4830	196	4	t+s	GPE
ejpam-4830	198	1	ϵ)xsz	PERSON
ejpam-4830	198	2	t+s	GPE
ejpam-4830	200	1	0	CARDINAL
ejpam-4830	200	2	0≤s≤t−t	DATE
ejpam-4830	200	3	k − xxsz µc	PERSON
ejpam-4830	200	4	t+s	GPE
ejpam-4830	202	1	1 2	CARDINAL
ejpam-4830	202	2	k − xzµc	ORG
ejpam-4830	202	3	t+s	DATE
ejpam-4830	202	4	− ϵzµc t+s	ORG
ejpam-4830	202	5	− xzµc	ORG
ejpam-4830	202	6	t+s	DATE
ejpam-4830	202	7	− ϵzµc t+s	ORG
ejpam-4830	202	8	lim	PERSON
ejpam-4830	203	1	0	CARDINAL
ejpam-4830	203	2	0≤s≤t−t	DATE
ejpam-4830	203	3	k − xxsz µc	PERSON
ejpam-4830	203	4	t+s	GPE
ejpam-4830	205	1	1 2	CARDINAL
ejpam-4830	205	2	k − xzµc	ORG
ejpam-4830	205	3	t+s	DATE
ejpam-4830	205	4	− ϵzµc t+s	ORG
ejpam-4830	205	5	− xzµc	ORG
ejpam-4830	205	6	t+s	DATE
ejpam-4830	205	7	− ϵzµc t+s	ORG
ejpam-4830	206	1	0	CARDINAL
ejpam-4830	206	2	0≤s≤t−t	DATE
ejpam-4830	206	3	k − xxsz µc	PERSON
ejpam-4830	206	4	t+s	GPE
ejpam-4830	208	1	1 2	CARDINAL
ejpam-4830	208	2	k − xzµc	ORG
ejpam-4830	208	3	t+s,	GPE
ejpam-4830	208	4	− xzµc	ORG
ejpam-4830	208	5	t+s	DATE
ejpam-4830	208	6	f. sumalpong	PERSON
ejpam-4830	208	7	m. frondoza	PERSON
ejpam-4830	208	8	n.l. sayson	GPE
ejpam-4830	209	1	j. pure	PERSON
ejpam-4830	209	2	16	CARDINAL
ejpam-4830	209	3	3	CARDINAL
ejpam-4830	209	4	2023	CARDINAL
ejpam-4830	209	5	1830-1847 1838	DATE
ejpam-4830	210	1	0	CARDINAL
ejpam-4830	210	2	0≤s≤t−t	DATE
ejpam-4830	210	3	k − xxsz µc	PERSON
ejpam-4830	210	4	t+s	GPE
ejpam-4830	212	1	k − xxsz µc	PERSON
ejpam-4830	212	2	t+s	GPE
ejpam-4830	214	1	0	CARDINAL
ejpam-4830	214	2	0≤s≤t−t	DATE
ejpam-4830	214	3	k − xxsz µc	PERSON
ejpam-4830	214	4	t+s	GPE
ejpam-4830	216	1	k − xxsz µc	PERSON
ejpam-4830	216	2	t+s	GPE
ejpam-4830	216	3	0	CARDINAL
ejpam-4830	217	1	0	CARDINAL
ejpam-4830	217	2	26	CARDINAL
ejpam-4830	217	3	28	CARDINAL
ejpam-4830	218	1	lim	PERSON
ejpam-4830	221	1	0≤τ≤t−t	CARDINAL
ejpam-4830	223	1	30	CARDINAL
ejpam-4830	223	2	26	CARDINAL
ejpam-4830	224	1	3	CARDINAL
ejpam-4830	226	1	4	CARDINAL
ejpam-4830	228	1	0	CARDINAL
ejpam-4830	228	2	j ∈ m. proof	PERSON
ejpam-4830	229	1	0,∞	DATE
ejpam-4830	230	1	0,∞	DATE
ejpam-4830	231	1	0	CARDINAL
ejpam-4830	231	2	0	CARDINAL
ejpam-4830	233	1	f. sumalpong	PERSON
ejpam-4830	233	2	m. frondoza	PERSON
ejpam-4830	233	3	n.l. sayson	GPE
ejpam-4830	234	1	j. pure	PERSON
ejpam-4830	234	2	16	CARDINAL
ejpam-4830	234	3	3	CARDINAL
ejpam-4830	234	4	2023	CARDINAL
ejpam-4830	234	5	1830-1847	DATE
ejpam-4830	234	6	31	CARDINAL
ejpam-4830	234	7	becomes∣∣∣∣∣∂v∂x	ORG
ejpam-4830	235	1	2	CARDINAL
ejpam-4830	236	1	32	CARDINAL
ejpam-4830	238	1	0	CARDINAL
ejpam-4830	238	2	0,∞	DATE
ejpam-4830	240	1	2	CARDINAL
ejpam-4830	241	1	33	CARDINAL
ejpam-4830	241	2	32	CARDINAL
ejpam-4830	241	3	33	CARDINAL
ejpam-4830	243	1	0	CARDINAL
ejpam-4830	244	1	6	CARDINAL
ejpam-4830	244	2	24	CARDINAL
ejpam-4830	247	1	j)−gµc(t	GPE
ejpam-4830	249	1	0,∞	DATE
ejpam-4830	254	1	+ 1 2	DATE
ejpam-4830	254	2	2	CARDINAL
ejpam-4830	254	3	f(s	DATE
ejpam-4830	256	1	34	CARDINAL
ejpam-4830	256	2	f. sumalpong	PERSON
ejpam-4830	256	3	m. frondoza	PERSON
ejpam-4830	256	4	n.l. sayson	GPE
ejpam-4830	257	1	j. pure	PERSON
ejpam-4830	257	2	16	CARDINAL
ejpam-4830	257	3	3	CARDINAL
ejpam-4830	257	4	2023	CARDINAL
ejpam-4830	257	5	1830-1847	DATE
ejpam-4830	258	1	0	CARDINAL
ejpam-4830	259	1	5	CARDINAL
ejpam-4830	261	1	0	CARDINAL
ejpam-4830	261	2	35	CARDINAL
ejpam-4830	262	1	14	CARDINAL
ejpam-4830	264	1	k −xt	PERSON
ejpam-4830	265	1	∈	ORG
ejpam-4830	266	1	7	CARDINAL
ejpam-4830	266	2	i=1 qjig µc(t	ORG
ejpam-4830	266	3	+ σ(j)x	DATE
ejpam-4830	269	1	i=1 qjig µc(t	ORG
ejpam-4830	270	1	0	CARDINAL
ejpam-4830	271	1	36	CARDINAL
ejpam-4830	271	2	36	CARDINAL
ejpam-4830	271	3	34	CARDINAL
ejpam-4830	273	1	37	CARDINAL
ejpam-4830	273	2	∈	ORG
ejpam-4830	273	3	0,∞	DATE
ejpam-4830	276	1	6	CARDINAL
ejpam-4830	278	1	38	CARDINAL
ejpam-4830	279	1	xb = bd(t	ORG
ejpam-4830	282	1	7→	CARDINAL
ejpam-4830	282	2	f. sumalpong	PERSON
ejpam-4830	282	3	m. frondoza	PERSON
ejpam-4830	282	4	n.l. sayson	GPE
ejpam-4830	283	1	j. pure	PERSON
ejpam-4830	283	2	16	CARDINAL
ejpam-4830	283	3	3	CARDINAL
ejpam-4830	283	4	2023	CARDINAL
ejpam-4830	283	5	1830-1847 1841	DATE
ejpam-4830	283	6	lemma 2	ORG
ejpam-4830	283	7	at least one	CARDINAL
ejpam-4830	283	8	∈	ORG
ejpam-4830	288	1	7	CARDINAL
ejpam-4830	289	1	⊂	GPE
ejpam-4830	291	1	39	CARDINAL
ejpam-4830	292	1	0	CARDINAL
ejpam-4830	293	1	27	CARDINAL
ejpam-4830	294	1	29	CARDINAL
ejpam-4830	294	2	30	CARDINAL
ejpam-4830	297	1	lim inf	PERSON
ejpam-4830	301	1	40	CARDINAL
ejpam-4830	301	2	8	CARDINAL
ejpam-4830	303	1	0	CARDINAL
ejpam-4830	304	1	f. sumalpong	PERSON
ejpam-4830	304	2	m. frondoza	PERSON
ejpam-4830	304	3	n.l. sayson	GPE
ejpam-4830	305	1	j. pure	PERSON
ejpam-4830	305	2	16	CARDINAL
ejpam-4830	305	3	3	CARDINAL
ejpam-4830	305	4	2023	CARDINAL
ejpam-4830	305	5	1830-1847	DATE
ejpam-4830	307	1	0	CARDINAL
ejpam-4830	307	2	0	CARDINAL
ejpam-4830	308	1	lemma 1	ORG
ejpam-4830	308	2	2	CARDINAL
ejpam-4830	308	3	e−rsgµc(t+ s	ORG
ejpam-4830	308	4	αt+s	GPE
ejpam-4830	310	1	e−rulgµc(u	GPE
ejpam-4830	310	2	xu, αu)du+ms	GPE
ejpam-4830	310	3	41	CARDINAL
ejpam-4830	310	4	t+s t	GPE
ejpam-4830	310	5	xu	PERSON
ejpam-4830	311	1	0	CARDINAL
ejpam-4830	311	2	t−t	GPE
ejpam-4830	312	1	0	CARDINAL
ejpam-4830	313	1	lemma	ORG
ejpam-4830	313	2	1	CARDINAL
ejpam-4830	313	3	4	CARDINAL
ejpam-4830	313	4	37	CARDINAL
ejpam-4830	314	1	0	CARDINAL
ejpam-4830	316	1	0	CARDINAL
ejpam-4830	323	1	41	CARDINAL
ejpam-4830	326	1	e−rulgµc(u	GPE
ejpam-4830	326	2	xu	GPE
ejpam-4830	326	3	αu)du	DATE
ejpam-4830	327	1	42	CARDINAL
ejpam-4830	327	2	xu	PERSON
ejpam-4830	328	1	42	CARDINAL
ejpam-4830	328	2	15	CARDINAL
ejpam-4830	333	1	0	CARDINAL
ejpam-4830	333	2	37	CARDINAL
ejpam-4830	333	3	42	CARDINAL
ejpam-4830	334	1	0	CARDINAL
ejpam-4830	334	2	37	CARDINAL
ejpam-4830	334	3	0	CARDINAL
ejpam-4830	335	1	43	CARDINAL
ejpam-4830	337	1	0	CARDINAL
ejpam-4830	338	1	42	CARDINAL
ejpam-4830	339	1	0	CARDINAL
ejpam-4830	339	2	t−t	GPE
ejpam-4830	340	1	0	CARDINAL
ejpam-4830	341	1	bd(t	ORG
ejpam-4830	342	1	0,∞	DATE
ejpam-4830	343	1	44	CARDINAL
ejpam-4830	343	2	f. sumalpong	PERSON
ejpam-4830	343	3	m. frondoza	PERSON
ejpam-4830	343	4	n.l. sayson	GPE
ejpam-4830	344	1	j. pure	PERSON
ejpam-4830	344	2	16	CARDINAL
ejpam-4830	344	3	3	CARDINAL
ejpam-4830	344	4	2023	CARDINAL
ejpam-4830	344	5	1830-1847 1843	DATE
ejpam-4830	344	6	24	CARDINAL
ejpam-4830	345	1	2	CARDINAL
ejpam-4830	347	1	0	CARDINAL
ejpam-4830	348	1	x]× {j} ⊂	PERSON
ejpam-4830	349	1	45	CARDINAL
ejpam-4830	350	1	0	CARDINAL
ejpam-4830	351	1	46	DATE
ejpam-4830	352	1	x]× {j	PERSON
ejpam-4830	354	1	0,∞	DATE
ejpam-4830	356	1	j)−gµc(t	GPE
ejpam-4830	357	1	3	CARDINAL
ejpam-4830	357	2	45	CARDINAL
ejpam-4830	358	1	44	CARDINAL
ejpam-4830	359	1	x]× {j} ⊂	PERSON
ejpam-4830	361	1	9	CARDINAL
ejpam-4830	362	1	47	CARDINAL
ejpam-4830	363	1	0	CARDINAL
ejpam-4830	366	1	0	CARDINAL
ejpam-4830	367	1	0	CARDINAL
ejpam-4830	368	1	23	CARDINAL
ejpam-4830	368	2	42	CARDINAL
ejpam-4830	368	3	j)−gµc(s2	PERSON
ejpam-4830	371	1	∫ s2+τs2 s2 e−rulgµc(u	ORG
ejpam-4830	371	2	xu	GPE
ejpam-4830	371	3	αu)du	DATE
ejpam-4830	373	1	xs2+u	ORG
ejpam-4830	374	1	48	CARDINAL
ejpam-4830	374	2	48	CARDINAL
ejpam-4830	374	3	49	CARDINAL
ejpam-4830	374	4	j)−gµc(s1	PERSON
ejpam-4830	374	5	f. sumalpong	PERSON
ejpam-4830	374	6	m. frondoza	PERSON
ejpam-4830	374	7	n.l. sayson	GPE
ejpam-4830	375	1	j. pure	PERSON
ejpam-4830	375	2	16	CARDINAL
ejpam-4830	375	3	3	CARDINAL
ejpam-4830	375	4	2023	CARDINAL
ejpam-4830	375	5	1830-1847 1844	DATE
ejpam-4830	377	1	e−rulgµc(u	GPE
ejpam-4830	377	2	xu	GPE
ejpam-4830	377	3	αu)du	CARDINAL
ejpam-4830	378	1	0	CARDINAL
ejpam-4830	378	2	49	CARDINAL
ejpam-4830	380	1	xs2+u	ORG
ejpam-4830	381	1	0	CARDINAL
ejpam-4830	382	1	xs2+u	ORG
ejpam-4830	382	2	αs2+u)du− lgµc(s1 + u	ORG
ejpam-4830	383	1	37	CARDINAL
ejpam-4830	383	2	0	CARDINAL
ejpam-4830	384	1	0	CARDINAL
ejpam-4830	385	1	3	CARDINAL
ejpam-4830	387	1	0	CARDINAL
ejpam-4830	389	1	first	ORDINAL
ejpam-4830	391	1	1	CARDINAL
ejpam-4830	392	1	bd(t0	ORG
ejpam-4830	392	2	x′	DATE
ejpam-4830	392	3	0	CARDINAL
ejpam-4830	392	4	bd(t0	ORG
ejpam-4830	392	5	t′	CARDINAL
ejpam-4830	392	6	t′	CARDINAL
ejpam-4830	392	7	↑	ORG
ejpam-4830	393	1	lemma 4	ORG
ejpam-4830	393	2	7→	CARDINAL
ejpam-4830	393	3	7→	CARDINAL
ejpam-4830	395	1	newton-leibniz	ORG
ejpam-4830	395	2	6	CARDINAL
ejpam-4830	395	3	x′	DATE
ejpam-4830	396	1	t′	ORDINAL
ejpam-4830	396	2	u, j	ORG
ejpam-4830	397	1	x′	DATE
ejpam-4830	397	2	t′,	DATE
ejpam-4830	397	3	x′	DATE
ejpam-4830	398	1	x′	DATE
ejpam-4830	399	1	2	CARDINAL
ejpam-4830	401	1	bd(t0	GPE
ejpam-4830	401	2	j) f. sumalpong	PERSON
ejpam-4830	401	3	m. frondoza	PERSON
ejpam-4830	401	4	n.l. sayson	GPE
ejpam-4830	402	1	j. pure	PERSON
ejpam-4830	402	2	16	CARDINAL
ejpam-4830	402	3	3	CARDINAL
ejpam-4830	402	4	2023	CARDINAL
ejpam-4830	402	5	1830-1847	DATE
ejpam-4830	402	6	0	CARDINAL
ejpam-4830	402	7	bd(t0	ORG
ejpam-4830	403	1	40	CARDINAL
ejpam-4830	403	2	∗	CARDINAL
ejpam-4830	403	3	newton-leibniz	ORG
ejpam-4830	403	4	0	CARDINAL
ejpam-4830	405	1	∗	CARDINAL
ejpam-4830	406	1	j	PERSON
ejpam-4830	407	1	∗	CARDINAL
ejpam-4830	408	1	bd(t0	GPE
ejpam-4830	410	1	bd	PERSON
ejpam-4830	412	1	4	CARDINAL
ejpam-4830	414	1	t t j(t	ORG
ejpam-4830	414	2	bd(t	ORG
ejpam-4830	414	3	αu)du	CARDINAL
ejpam-4830	414	4	50	CARDINAL
ejpam-4830	414	5	0 ≤	MONEY
ejpam-4830	414	6	k −xt	PERSON
ejpam-4830	416	1	51	CARDINAL
ejpam-4830	416	2	j(t	PERSON
ejpam-4830	416	3	xu	PERSON
ejpam-4830	416	4	j)i(xu	PERSON
ejpam-4830	418	1	52	CARDINAL
ejpam-4830	418	2	0 ≤	MONEY
ejpam-4830	418	3	0,∞	DATE
ejpam-4830	420	1	16	CARDINAL
ejpam-4830	422	1	0	CARDINAL
ejpam-4830	423	1	0	CARDINAL
ejpam-4830	425	1	21	CARDINAL
ejpam-4830	425	2	16	CARDINAL
ejpam-4830	426	1	∣∣∣	CARDINAL
ejpam-4830	429	1	0	CARDINAL
ejpam-4830	431	1	53	CARDINAL
ejpam-4830	431	2	4	CARDINAL
ejpam-4830	431	3	f. sumalpong	PERSON
ejpam-4830	431	4	m. frondoza	PERSON
ejpam-4830	431	5	n.l. sayson	GPE
ejpam-4830	432	1	j. pure	PERSON
ejpam-4830	432	2	16	CARDINAL
ejpam-4830	432	3	3	CARDINAL
ejpam-4830	432	4	2023	CARDINAL
ejpam-4830	432	5	1830-1847 1846	DATE
ejpam-4830	432	6	k −xt	PERSON
ejpam-4830	437	1	xu	PERSON
ejpam-4830	437	2	̸= bd(u	PERSON
ejpam-4830	440	1	xu−	PERSON
ejpam-4830	440	2	i(xu	CARDINAL
ejpam-4830	440	3	54	CARDINAL
ejpam-4830	440	4	wherem	PERSON
ejpam-4830	440	5	xu)t≤u≤t	PRODUCT
ejpam-4830	440	6	7→	CARDINAL
ejpam-4830	441	1	−p(x ≤ k	PERSON
ejpam-4830	444	1	0	CARDINAL
ejpam-4830	444	2	4.4	CARDINAL
ejpam-4830	444	3	45	CARDINAL
ejpam-4830	444	4	1	CARDINAL
ejpam-4830	445	1	0	CARDINAL
ejpam-4830	446	1	7	CARDINAL
ejpam-4830	446	2	two	CARDINAL
ejpam-4830	446	3	54	CARDINAL
ejpam-4830	447	1	53	CARDINAL
ejpam-4830	447	2	54	CARDINAL
ejpam-4830	447	3	k −xt	PERSON
ejpam-4830	448	1	xu	PERSON
ejpam-4830	451	1	55	CARDINAL
ejpam-4830	451	2	k −xt	PERSON
ejpam-4830	453	1	xu	PERSON
ejpam-4830	455	1	t t j(t	ORG
ejpam-4830	455	2	bd(t	ORG
ejpam-4830	456	1	4.	CARDINAL
ejpam-4830	456	2	british	NORP
ejpam-4830	456	3	f. samee (	PERSON
ejpam-4830	456	4	2011	DATE
ejpam-4830	457	1	british	NORP
ejpam-4830	458	1	british	NORP
ejpam-4830	459	1	1847	DATE
ejpam-4830	460	1	1	CARDINAL
ejpam-4830	462	1	oxford university press	ORG
ejpam-4830	462	2	new york	GPE
ejpam-4830	462	3	2009	DATE
ejpam-4830	463	1	2	CARDINAL
ejpam-4830	463	2	y zhou	PERSON
ejpam-4830	464	1	european	NORP
ejpam-4830	465	1	94:281–300, 2006	DATE
ejpam-4830	466	1	3	CARDINAL
ejpam-4830	467	1	2nd	ORDINAL
ejpam-4830	468	1	john wiley	PERSON
ejpam-4830	468	2	new york	GPE
ejpam-4830	468	3	2003	DATE
ejpam-4830	469	1	4	CARDINAL
ejpam-4830	471	1	3:499–535, 2005	DATE
ejpam-4830	472	1	5	CARDINAL
ejpam-4830	473	1	british	NORP
ejpam-4830	474	1	6:537–563	CARDINAL
ejpam-4830	474	2	2011	DATE
ejpam-4830	475	1	6	CARDINAL
ejpam-4830	476	1	zürich	WORK_OF_ART
ejpam-4830	476	2	birkhäuser verlag	PERSON
ejpam-4830	476	3	2006	DATE