id	sid	eid	entity	type
ejpam-460	1	1	5_460_zhichun.dvi	CARDINAL
ejpam-460	2	1	2	CARDINAL
ejpam-460	2	2	4, 2009	DATE
ejpam-460	2	3	532-543	CARDINAL
ejpam-460	2	4	1307-5543	CARDINAL
ejpam-460	2	5	extremal	GPE
ejpam-460	2	6	xie zhichun∗	PERSON
ejpam-460	2	7	huang xinzhong school	PERSON
ejpam-460	2	8	quanzhou	GPE
ejpam-460	2	9	fujian	GPE
ejpam-460	2	10	362021	DATE
ejpam-460	3	1	r. c.	PERSON
ejpam-460	5	1	3	CARDINAL
ejpam-460	5	2	extremal	GPE
ejpam-460	6	1	one	CARDINAL
ejpam-460	6	2	extremal	GPE
ejpam-460	7	1	2000	CARDINAL
ejpam-460	7	2	30c62	CARDINAL
ejpam-460	7	3	30c55	CARDINAL
ejpam-460	7	4	extremal	PERSON
ejpam-460	7	5	1	CARDINAL
ejpam-460	8	1	ω	ORDINAL
ejpam-460	8	2	ω′	CARDINAL
ejpam-460	8	3	⊂	GPE
ejpam-460	8	4	ω′	DATE
ejpam-460	8	5	ω	GPE
ejpam-460	8	6	1	CARDINAL
ejpam-460	8	7	acl	ORG
ejpam-460	8	8	ω	CARDINAL
ejpam-460	8	9	2	CARDINAL
ejpam-460	9	1	xiezhi	PERSON
ejpam-460	11	1	h. xinzhong	PERSON
ejpam-460	12	1	532	CARDINAL
ejpam-460	12	2	2009	DATE
ejpam-460	13	1	x. zhichun	PERSON
ejpam-460	13	2	h. xinzhong / eur	PERSON
ejpam-460	14	1	j. pure	PERSON
ejpam-460	14	2	2	CARDINAL
ejpam-460	14	3	2009	DATE
ejpam-460	14	4	532-543	CARDINAL
ejpam-460	14	5	533 fz̄(z	PERCENT
ejpam-460	14	6	µ(z	PERSON
ejpam-460	15	1	a.e.	GPE
ejpam-460	15	2	∈ ω	ORG
ejpam-460	16	1	1−k	CARDINAL
ejpam-460	17	1	ω	GPE
ejpam-460	18	1	fz|+|	CARDINAL
ejpam-460	18	2	fz|−|	CARDINAL
ejpam-460	19	1	extremal	GPE
ejpam-460	19	2	ω	GPE
ejpam-460	20	1	1	CARDINAL
ejpam-460	20	2	1	CARDINAL
ejpam-460	20	3	affine	ORG
ejpam-460	20	4	2	CARDINAL
ejpam-460	20	5	3	CARDINAL
ejpam-460	21	1	2	CARDINAL
ejpam-460	22	1	1	CARDINAL
ejpam-460	23	1	0	CARDINAL
ejpam-460	23	2	lim z→0	PERSON
ejpam-460	24	1	1 k	QUANTITY
ejpam-460	24	2	1	CARDINAL
ejpam-460	25	1	extremal	GPE
ejpam-460	25	2	1 k −1	QUANTITY
ejpam-460	26	1	0	CARDINAL
ejpam-460	26	2	extremal	GPE
ejpam-460	27	1	3	CARDINAL
ejpam-460	28	1	1	CARDINAL
ejpam-460	29	1	1 k ≤	QUANTITY
ejpam-460	29	2	1 k −1	QUANTITY
ejpam-460	29	3	1	CARDINAL
ejpam-460	30	1	1	CARDINAL
ejpam-460	32	1	1 k	QUANTITY
ejpam-460	32	2	k = k−1	PERSON
ejpam-460	32	3	k+1	DATE
ejpam-460	32	4	1	CARDINAL
ejpam-460	32	5	g(z	PERSON
ejpam-460	32	6	1 k ≤	QUANTITY
ejpam-460	33	1	1	CARDINAL
ejpam-460	33	2	h. xinzhong / eur	PERSON
ejpam-460	34	1	j. pure	PERSON
ejpam-460	34	2	2	CARDINAL
ejpam-460	34	3	2009	DATE
ejpam-460	34	4	532-543	CARDINAL
ejpam-460	34	5	534	CARDINAL
ejpam-460	35	1	3	CARDINAL
ejpam-460	35	2	extremal	GPE
ejpam-460	35	3	1 kmod(rr	QUANTITY
ejpam-460	35	4	1	CARDINAL
ejpam-460	35	5	1 k	QUANTITY
ejpam-460	36	1	1 kmod(rr	QUANTITY
ejpam-460	36	2	1	CARDINAL
ejpam-460	36	3	1	CARDINAL
ejpam-460	36	4	1	CARDINAL
ejpam-460	37	1	1 k	QUANTITY
ejpam-460	38	1	1 1 k 1 2π	QUANTITY
ejpam-460	38	2	1	CARDINAL
ejpam-460	40	1	3	CARDINAL
ejpam-460	42	1	one	CARDINAL
ejpam-460	42	2	extremal	GPE
ejpam-460	43	1	2	CARDINAL
ejpam-460	43	2	3	CARDINAL
ejpam-460	48	1	2	CARDINAL
ejpam-460	49	1	∈q	ORG
ejpam-460	51	1	1 k ei(θ+α	QUANTITY
ejpam-460	53	1	x. zhichun	PERSON
ejpam-460	53	2	h. xinzhong / eur	PERSON
ejpam-460	54	1	j. pure	PERSON
ejpam-460	54	2	2	CARDINAL
ejpam-460	54	3	2009	DATE
ejpam-460	54	4	532-543	CARDINAL
ejpam-460	54	5	535	CARDINAL
ejpam-460	55	1	4	CARDINAL
ejpam-460	55	2	1	CARDINAL
ejpam-460	55	3	1	CARDINAL
ejpam-460	55	4	1 k	QUANTITY
ejpam-460	57	1	1	CARDINAL
ejpam-460	57	2	1	CARDINAL
ejpam-460	58	1	1	CARDINAL
ejpam-460	58	2	1	CARDINAL
ejpam-460	60	1	1	CARDINAL
ejpam-460	60	2	1	CARDINAL
ejpam-460	60	3	1	CARDINAL
ejpam-460	60	4	1	CARDINAL
ejpam-460	61	1	lemma 1.3	ORG
ejpam-460	61	2	3	CARDINAL
ejpam-460	61	3	0≤	CARDINAL
ejpam-460	62	1	2π	CARDINAL
ejpam-460	64	1	1	CARDINAL
ejpam-460	64	2		NORP
ejpam-460	64	3	r′	DATE
ejpam-460	64	4	1	CARDINAL
ejpam-460	64	5	1	CARDINAL
ejpam-460	65	1	1	CARDINAL
ejpam-460	66	1	1 k eiϕ(r	PERSON
ejpam-460	67	1	ϕ(r	PERSON
ejpam-460	68	1	1 2	CARDINAL
ejpam-460	68	2	1 k	QUANTITY
ejpam-460	68	3	1	CARDINAL
ejpam-460	68	4	−ϕθ	ORG
ejpam-460	69	1	1 2	CARDINAL
ejpam-460	69	2	1	CARDINAL
ejpam-460	70	1	1 k −1	QUANTITY
ejpam-460	71	1	k − q.c.	PERSON
ejpam-460	71	2	2	CARDINAL
ejpam-460	72	1	1 k	QUANTITY
ejpam-460	72	2	1	CARDINAL
ejpam-460	74	1	1	CARDINAL
ejpam-460	76	1	x. zhichun	PERSON
ejpam-460	76	2	h. xinzhong / eur	PERSON
ejpam-460	77	1	j. pure	PERSON
ejpam-460	77	2	2	CARDINAL
ejpam-460	77	3	2009	DATE
ejpam-460	77	4	532-543	CARDINAL
ejpam-460	77	5	536	CARDINAL
ejpam-460	77	6	2	CARDINAL
ejpam-460	77	7	2	CARDINAL
ejpam-460	78	1	1)(ϕθ	CARDINAL
ejpam-460	79	1	1 k2	QUANTITY
ejpam-460	79	2	1	CARDINAL
ejpam-460	80	1	∈	ORG
ejpam-460	80	2	0	CARDINAL
ejpam-460	80	3	1	CARDINAL
ejpam-460	80	4	2π	CARDINAL
ejpam-460	81	1	ϕ(r	PERSON
ejpam-460	81	2	2π)−ϕ(r	CARDINAL
ejpam-460	82	1	2π	CARDINAL
ejpam-460	84	1	2π	CARDINAL
ejpam-460	85	1	2π	CARDINAL
ejpam-460	89	1	1	CARDINAL
ejpam-460	90	1	ψ(θ	GPE
ejpam-460	92	1	θ1,θ2	ORG
ejpam-460	92	2	0 ≤ θ1	MONEY
ejpam-460	92	3	1;θ1,θ2	DATE
ejpam-460	93	1	1;θ2,θ1+ 2π	DATE
ejpam-460	94	1	1	CARDINAL
ejpam-460	94	2	1;ψ(θ1),ψ(θ2	CARDINAL
ejpam-460	95	1	1	CARDINAL
ejpam-460	95	2	1;ψ(θ2),ψ(θ1	CARDINAL
ejpam-460	96	1	1 k	QUANTITY
ejpam-460	96	2	1 k mod(a2)≤mod	QUANTITY
ejpam-460	96	3	x. zhichun	PERSON
ejpam-460	96	4	h. xinzhong / eur	PERSON
ejpam-460	97	1	j. pure	PERSON
ejpam-460	97	2	2	CARDINAL
ejpam-460	97	3	2009	DATE
ejpam-460	97	4	532-543	CARDINAL
ejpam-460	97	5	537	CARDINAL
ejpam-460	97	6		NORP
ejpam-460	97	7	θ2−	PERSON
ejpam-460	99	1	0≤	CARDINAL
ejpam-460	102	1	1	CARDINAL
ejpam-460	102	2	ψ(θ	GPE
ejpam-460	105	1	1 k ei(θ+α	QUANTITY
ejpam-460	107	1	2	CARDINAL
ejpam-460	109	1	1 ≤	QUANTITY
ejpam-460	109	2	∈q	ORG
ejpam-460	110	1	ei(θ+α	PERSON
ejpam-460	111	1	3	CARDINAL
ejpam-460	112	1	x. zhichun	PERSON
ejpam-460	112	2	h. xinzhong / eur	PERSON
ejpam-460	113	1	j. pure	PERSON
ejpam-460	113	2	2	CARDINAL
ejpam-460	113	3	2009	DATE
ejpam-460	113	4	532-543	CARDINAL
ejpam-460	113	5	538	CARDINAL
ejpam-460	113	6	3	CARDINAL
ejpam-460	115	1	0	CARDINAL
ejpam-460	116	1	1 k	QUANTITY
ejpam-460	116	2	1 k	QUANTITY
ejpam-460	116	3	1 k	QUANTITY
ejpam-460	117	1	1	CARDINAL
ejpam-460	117	2	1	CARDINAL
ejpam-460	118	1	3	CARDINAL
ejpam-460	119	1	g(z	PERSON
ejpam-460	120	1	1 k	QUANTITY
ejpam-460	121	1	1 k	QUANTITY
ejpam-460	121	2	1 k	QUANTITY
ejpam-460	121	3	g(z	PERSON
ejpam-460	121	4	3	CARDINAL
ejpam-460	122	1	one	CARDINAL
ejpam-460	123	1	1	CARDINAL
ejpam-460	124	1	5	CARDINAL
ejpam-460	125	1	2	CARDINAL
ejpam-460	126	1	two	CARDINAL
ejpam-460	127	1	r∗ bounded	PERSON
ejpam-460	127	2	0 and b∗ 1	DATE
ejpam-460	129	1	3	CARDINAL
ejpam-460	130	1	0	CARDINAL
ejpam-460	130	2	2π	CARDINAL
ejpam-460	130	3	2π	CARDINAL
ejpam-460	130	4	4π2	CARDINAL
ejpam-460	130	5	2π	CARDINAL
ejpam-460	131	1	0	CARDINAL
ejpam-460	131	2	x. zhichun	PERSON
ejpam-460	131	3	h. xinzhong / eur	PERSON
ejpam-460	132	1	j. pure	PERSON
ejpam-460	132	2	2	CARDINAL
ejpam-460	132	3	2009	DATE
ejpam-460	132	4	532-543	CARDINAL
ejpam-460	132	5	539	CARDINAL
ejpam-460	133	1	2π	CARDINAL
ejpam-460	133	2	0	CARDINAL
ejpam-460	133	3	2π	CARDINAL
ejpam-460	134	1	1	CARDINAL
ejpam-460	135	1	2π	CARDINAL
ejpam-460	136	1	2π	CARDINAL
ejpam-460	136	2	4π2	CARDINAL
ejpam-460	136	3	2π	CARDINAL
ejpam-460	137	1	2π	CARDINAL
ejpam-460	137	2	0 1	QUANTITY
ejpam-460	137	3	2π	CARDINAL
ejpam-460	137	4	4π2	CARDINAL
ejpam-460	137	5	2π	CARDINAL
ejpam-460	141	1	0	CARDINAL
ejpam-460	142	1	3	CARDINAL
ejpam-460	143	1	4	CARDINAL
ejpam-460	143	2	1	CARDINAL
ejpam-460	143	3	two	CARDINAL
ejpam-460	143	4	0	CARDINAL
ejpam-460	143	5	2π	CARDINAL
ejpam-460	143	6	2π	CARDINAL
ejpam-460	147	1	|s1|hyp =	PERSON
ejpam-460	147	2	1	CARDINAL
ejpam-460	147	3	2π	CARDINAL
ejpam-460	147	4	r2 r1	PERSON
ejpam-460	147	5	1− r2)2 drdθ	TIME
ejpam-460	147	6	1 1−	TIME
ejpam-460	147	7	2	CARDINAL
ejpam-460	147	8	1	CARDINAL
ejpam-460	147	9	x. zhichun	PERSON
ejpam-460	147	10	h. xinzhong / eur	PERSON
ejpam-460	148	1	j. pure	PERSON
ejpam-460	148	2	2	CARDINAL
ejpam-460	148	3	2009	DATE
ejpam-460	148	4	532-543	CARDINAL
ejpam-460	148	5	540	CARDINAL
ejpam-460	149	1	1	CARDINAL
ejpam-460	149	2	1− |z|2)2	LAW
ejpam-460	149	3	2π	CARDINAL
ejpam-460	150	1	1− r2)2 drdθ	TIME
ejpam-460	150	2	1 2	CARDINAL
ejpam-460	150	3	2π	CARDINAL
ejpam-460	150	4	2(θ	CARDINAL
ejpam-460	150	5	1 1− r2 1	TIME
ejpam-460	150	6	1−	CARDINAL
ejpam-460	150	7	2	CARDINAL
ejpam-460	150	8	1 2	CARDINAL
ejpam-460	150	9	2π	CARDINAL
ejpam-460	152	1	3	CARDINAL
ejpam-460	152	2	1 1−	TIME
ejpam-460	152	3	2	CARDINAL
ejpam-460	152	4	1 2	CARDINAL
ejpam-460	152	5	2π	CARDINAL
ejpam-460	153	1	1 2	CARDINAL
ejpam-460	153	2	2π	CARDINAL
ejpam-460	155	1	1	CARDINAL
ejpam-460	155	2	1 1− r2	TIME
ejpam-460	155	3	2	CARDINAL
ejpam-460	155	4	1	CARDINAL
ejpam-460	155	5	2π	CARDINAL
ejpam-460	155	6	area(s1	GPE
ejpam-460	155	7	1 2	CARDINAL
ejpam-460	155	8	2π	CARDINAL
ejpam-460	156	1	2 dθ	QUANTITY
ejpam-460	156	2	∪∆r1	DATE
ejpam-460	156	3	area(s1	GPE
ejpam-460	156	4	lemma 2	ORG
ejpam-460	159	1	area(s1	GPE
ejpam-460	160	1	area(s1	GPE
ejpam-460	166	1	lemma 2	ORG
ejpam-460	166	2	x. zhichun	PERSON
ejpam-460	166	3	h. xinzhong / eur	PERSON
ejpam-460	167	1	j. pure	PERSON
ejpam-460	167	2	2	CARDINAL
ejpam-460	167	3	2009	DATE
ejpam-460	167	4	532-543	CARDINAL
ejpam-460	167	5	541	CARDINAL
ejpam-460	168	1	3	CARDINAL
ejpam-460	171	1	⇔ s1 = s2	PERSON
ejpam-460	173	1	3	CARDINAL
ejpam-460	173	2	2.1	CARDINAL
ejpam-460	174	1	5	CARDINAL
ejpam-460	176	1	0	DATE
ejpam-460	176	2	1	CARDINAL
ejpam-460	176	3	1	CARDINAL
ejpam-460	176	4	two	CARDINAL
ejpam-460	176	5	1	CARDINAL
ejpam-460	176	6	0 ≤	MONEY
ejpam-460	176	7	2π	CARDINAL
ejpam-460	177	1	s)|hyp	PERSON
ejpam-460	177	2	2	CARDINAL
ejpam-460	177	3	2	CARDINAL
ejpam-460	177	4	2	CARDINAL
ejpam-460	177	5	1− r2 1	DATE
ejpam-460	177	6	2−	CARDINAL
ejpam-460	177	7	1)(1−	CARDINAL
ejpam-460	177	8	2	CARDINAL
ejpam-460	177	9	1− r 2 k 1	PRODUCT
ejpam-460	178	1	1 k ei(θ+α	QUANTITY
ejpam-460	180	1	1	CARDINAL
ejpam-460	180	2	1	CARDINAL
ejpam-460	180	3	2	CARDINAL
ejpam-460	180	4	1	CARDINAL
ejpam-460	180	5	1−	CARDINAL
ejpam-460	180	6	1	CARDINAL
ejpam-460	181	1	2	CARDINAL
ejpam-460	181	2	2	CARDINAL
ejpam-460	181	3	2	CARDINAL
ejpam-460	181	4	1− r 2 k 2	PRODUCT
ejpam-460	181	5	1− r 2 k 1	PRODUCT
ejpam-460	182	1	s)|hyp	PERSON
ejpam-460	182	2	2	CARDINAL
ejpam-460	182	3	2	CARDINAL
ejpam-460	182	4	2	CARDINAL
ejpam-460	182	5	1− r2 1	DATE
ejpam-460	182	6	2−	CARDINAL
ejpam-460	182	7	1)(1−	CARDINAL
ejpam-460	182	8	2	CARDINAL
ejpam-460	182	9	1− r 2 k 1	PRODUCT
ejpam-460	182	10	x. zhichun	PERSON
ejpam-460	182	11	h. xinzhong / eur	PERSON
ejpam-460	183	1	j. pure	PERSON
ejpam-460	183	2	2	CARDINAL
ejpam-460	183	3	2009	DATE
ejpam-460	183	4	532-543	CARDINAL
ejpam-460	183	5	542	CARDINAL
ejpam-460	183	6	s)|hyp = |s|hyp	PERSON
ejpam-460	184	1	2	CARDINAL
ejpam-460	184	2	2	CARDINAL
ejpam-460	184	3	2	CARDINAL
ejpam-460	184	4	1− r2 1	DATE
ejpam-460	184	5	2	CARDINAL
ejpam-460	184	6	r2 1)(1−	ORG
ejpam-460	184	7	2	CARDINAL
ejpam-460	184	8	1− r 2 k 1	PRODUCT
ejpam-460	185	1	2	CARDINAL
ejpam-460	185	2	1	CARDINAL
ejpam-460	185	3	1−	CARDINAL
ejpam-460	185	4	1	CARDINAL
ejpam-460	186	1	2	CARDINAL
ejpam-460	186	2	2	CARDINAL
ejpam-460	186	3	2	CARDINAL
ejpam-460	186	4	1− r2 1	DATE
ejpam-460	186	5	2−	CARDINAL
ejpam-460	186	6	1)(1−	CARDINAL
ejpam-460	186	7	2	CARDINAL
ejpam-460	186	8	1− r 2 k 1	PRODUCT
ejpam-460	187	1	2	CARDINAL
ejpam-460	187	2	2	CARDINAL
ejpam-460	187	3	2	CARDINAL
ejpam-460	187	4	1− r 2 k 2	PRODUCT
ejpam-460	187	5	1− r 2 k 1	PRODUCT
ejpam-460	187	6	4	CARDINAL
ejpam-460	188	1	1	CARDINAL
ejpam-460	188	2	mod	PERSON
ejpam-460	189	1	1	CARDINAL
ejpam-460	189	2	4	CARDINAL
ejpam-460	190	1	1	CARDINAL
ejpam-460	190	2	1	CARDINAL
ejpam-460	191	1	2	CARDINAL
ejpam-460	192	1	1 k ei(θ+α	QUANTITY
ejpam-460	194	1	5	CARDINAL
ejpam-460	194	2	2	CARDINAL
ejpam-460	195	1	w|rk	DATE
ejpam-460	195	2	1 ≤ |w| ≤ rk 2	QUANTITY
ejpam-460	195	3	1	CARDINAL
ejpam-460	195	4	two	CARDINAL
ejpam-460	195	5	z||	PERSON
ejpam-460	195	6	2	CARDINAL
ejpam-460	196	1	r2 2 −	ORG
ejpam-460	198	1	1	CARDINAL
ejpam-460	199	1	1−	CARDINAL
ejpam-460	199	2	2	CARDINAL
ejpam-460	199	3	2	CARDINAL
ejpam-460	199	4	1	CARDINAL
ejpam-460	199	5	1−	CARDINAL
ejpam-460	199	6	1	CARDINAL
ejpam-460	199	7	543	CARDINAL
ejpam-460	201	1	ei(θ+α	PERSON
ejpam-460	203	1	the natural science foundation	ORG
ejpam-460	203	2	fujian province	GPE
ejpam-460	203	3	china	GPE
ejpam-460	203	4	2008j0195	CARDINAL
ejpam-460	204	1	1	CARDINAL
ejpam-460	204	2	new jersey	GPE
ejpam-460	204	3	d. van nostrandreinhold company,	PERSON
ejpam-460	204	4	princeton	PERSON
ejpam-460	204	5	1966	DATE
ejpam-460	205	1	2	CARDINAL
ejpam-460	205	2	zhu huacheng	PERSON
ejpam-460	205	3	zhou zemin	PERSON
ejpam-460	205	4	38(2	DATE
ejpam-460	205	5	1999	DATE
ejpam-460	205	6	205	CARDINAL
ejpam-460	206	1	3	CARDINAL
ejpam-460	206	2	liu lixin	PERSON
ejpam-460	206	3	zeng cuiping	PERSON
ejpam-460	206	4	chinese	NORP
ejpam-460	206	5	2007	DATE
ejpam-460	206	6	111120	DATE
ejpam-460	207	1	4	CARDINAL
ejpam-460	207	2	li zhong	PERSON
ejpam-460	207	3	beijing university press	ORG
ejpam-460	207	4	2005	DATE
ejpam-460	208	1	5	CARDINAL
ejpam-460	208	2	f. w.	PERSON
ejpam-460	208	3	väisälä jussi	PERSON
ejpam-460	210	1	helv	PERSON
ejpam-460	210	2	36	DATE
ejpam-460	210	3	1962	DATE
ejpam-460	210	4	19	CARDINAL