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normal Functions and α-normal Functions

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Acta Mathematica Sinica,English Series 2000年第3期16卷 399-404页

作者： Yan Xu department of Mathematics,nanjing normal {3.,nanjing 210097 P.R.china department of Mathematics Nanjing Normal University Nanjing 210097 P. R. China

This paper has studied two open questions about normal functions due to Lappan,and obtained two corresponding results for α-normal functions.

关键词： Spherical derivative normal function α-normal function

ON TWO CONJECTURES OF THE QUADRATIC DIFFERENTIAL SYSTEMS

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Chinese Annals of Mathematics,Series B 1997年第4期18卷 429-434页

作者： ZHANG XIANG Institute of Mathematics,nanjing normal university,nanjing 210097,china 南京师范大学数学所江苏南京

Two conjectures in the qualitative theory of quadratic differential systems are proved under certain conditions.

关键词： Quadratic system Limit cycle Dulac function

Completely regular paracompact reflection of locales

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Science china Mathematics 2006年第6期49卷 820-826页

作者： HE Wei & LUO Maokang department of Mathematics, nanjing normal university, nanjing 210097,{3. department of Mathematics, Sichuan university, Chengdu 610064,{3. department of Mathematics Nanjing Normal University Nanjing 210097 China department of Mathematics Sichuan University Chengdu 610064 China

We give an explicit construction of the completely regular paracompact reflection pL of a completely regular locale L described as a sublocale of the Stone-tech compactification βL of L.

关键词： completely regular paracompact locale, nucleus.

Regular n-simplices in R^n with vertices in Z^(n)

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Science china Mathematics 2004年第1期47卷 104-113页

作者： XIA Jianguo & QIN Hourongdepartment of Mathematics, nanjing normal university, nanjing 210097,{3. (email: jgxia@***) department of Mathematics, nanjing university, nanjing 210093.{3. Dept. of Math. Nanjing Normal Univ. Nanjing 210097 China Dept. of Math. Nanjing Univ. Nanjing 210093 China

In this paper the Ⅰ and Ⅱ regular n-simplices are introduced. We prove that the sufficient and necessary conditions for existence of an Ⅰ regular n-simplex in Rn are that if n is even then n = 4m(m + 1), and if n is odd then n = 4m + 1 with that n + 1 can be expressed as a sum of two integral squares or n = 4m - 1, and that the sufficient and necessary condition for existence of a Ⅱ regular n-simplex in Rn is n = 2m2 - 1 or n = 4m(m+1)(m 6 N). The connection between regulars-simplex in Rn and combinational design is given.

关键词： regular n-simplex in Rn, quadratic form.

The pointwise dimension of self-similar measures

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Chinese Science Bulletin 1999年第23期44卷 2136-2140页

作者： CHEN Ercai and XIONG Jincheng department of Mathematics , nanjing normal university , nanjing 210097,{3. department of Mathematics , South{3. normal university, Guangzhou 51063. ,{3. department of Mathematics Nanjing Normal University Nanjing China department of Mathematics South China Normal University Guangzhou China

The problem about the existence of pointwise dimension of self-similar measure has been discussed. The Hausdorff dimension of the set of those points for which the pointwise dimension does not exist equals the dimenti... 详细信息

关键词： self-similar measure point wise dimension Hausdorff dimension multifractal symbolic space.

Study on lithogeochemistry of Middle Jurassic basalts from southern china represented by the Fankeng basalts from Yongding of Fujian Province

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Science china Earth Sciences 2006年第10期49卷 1020-1031页

作者： ZHOU Jincheng1,2, JIANG Shaoyong1,2, WANG Xiaolei1,2, YANG Jinghong 1,2 & ZHANG Mengqun 3.1. State Key Laboratory of Mineral Deposit Research, nanjing university, nanjing 210093.{3. 2. department of Earth Sciences, nanjing university, nanjing 210093.{3. 3. Modern Analysis Center, nanjing university, nanjing 210093.{3. 1. State Key Laboratory of Mineral Deposit Research Nanjing University Nanjing 210093 China 2. department of Earth Sciences Nanjing University Nanjing 210093 China 3. Modern Analysis Center Nanjing University Nanjing 210093 China

There exists an E-W trending Middle Jurassic volcanic zone in southern china. The Fankeng basalts in the Yongding basin of Fujian Province are considered to be a typical example. The Fankeng basalts have TiO2 contents in the range of 1.92%-3.21%. They are classified as high-Ti basalts. They also have higher total Fe (averaging FeO* = 11.09%). The Middle Jurassic Fankeng basalts from southwestern Fujian have obvious distinctive lithogeochemical features from early Cre- taceous basalts from southeastern coast of china. They have higher HFSE, such as Th, Nb, Ta, Zr and Ti. Their element ratios related with HFSE, such as Zr/Ba, La/Nb, La/Ta ,Zr/Y, Ti/Y, Ba/Nb, K/Ti and Rb/Zr are similar to those of OIB. The most samples have ε Nd(T) of-0.70-0.24, which are near chondrite. Some samples have higher ε Nd(T) of ***, these basaltic magmas might be derived from depleted asthenospheric mantle. The lithogeochemical characteristics of the Fankeng basalts may be caused by interaction between asthenosphere and lithosphere at the time. The (Early-) Middle Jurassic basalts and gabbros from southeastern Hunan, southern Jiangxi and northern Guangdong provinces show similar geochemical features to those of the Fankeng basalts from the Yongding of Fujian. Occurrence of these OIB-type basalts in the area may be regarded as the petrological mark of upwelling of asthenosphere at the time. Upwelling of asthenosphere has led to tectonic extension and the formation of rifted basin in the area.

关键词： interaction between asthenosphere and lithosphere, lithogeochemistry, basalts, Middle Jurassic, southern china.

Time of impact of fragment P2 of comet SL 9 on Jupiter

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Chinese Science Bulletin 1997年第5期42卷 396-398页

作者： ZHOU Hongnan,QIAN Bochen, HUANG Keliang and LI Qibin1. department of Astronomy, nanjing university, nanjing 210093. china 2. Shanghai Observatory, Chinese Academy of Sciences, Shanghai 20003., china 3. Physics department, nanjing normal university, nanjing 210097, china 4. Beijing Astronomical Observatory, Chinese Academy of Sciences, Beijing 100080, china department of Astronomy Nanjing University Nanjing China Shanghai Observatory Chinese Academy of Sciences Shanghai China Physics department Nanjing Normal University Nanjing China Beijing Astronomical Observatory Chinese Academy of Sciences Behijing China

FROM 1994-07-16 to 1994-07-22, 21 fragments of comet SL 9 impacted against Jupiter in succession. During the impact period the impact of fragments D, E, K, N, P2 and S was observed in china. We used a 1.56-m telescope with the CCD camera of Shanghai Observatory to monitor Jupiter and its Galilean Satellites, obtaining 1000 high-quality images at B, V, I wave bands. Our data on optical wave bands are rather complete and valuable in the world. Specially, we got some images of Jupiter, Io and Europa in the impact time of fragment P2 impacting against Jupiter. This will help us understand the precise time, position, depth and energy of the P2’s collision. In this note, we report the impact time of fragment P2 of comet SL 9 and Jupiter. Since the impact of comet SL 9 was expected to take place on the side of Jupiter

关键词： comet comet Shoemaker-Levy 9 impacting against Jupiter impact time.

A specific family of cyclotomic polynomials of order three

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Science china Mathematics 2010年第9期53卷 2269-2274页

作者： JI ChunGang School of Mathematical Sciences,nanjing normal university,nanjing 210097,china 1. School of Mathematical Sciences Nanjing Normal University Nanjing 210097 China

Let A(n) be the largest absolute value of any coefficient of n-th cyclotomic polynomial Φn(x).We say Φn(x) is flat if A(n) = *** this paper,for odd primes p < q < r and 2r ≡±1(mod pq),we prove that Φpqr(x) is fla... 详细信息

Let A(n) be the largest absolute value of any coefficient of n-th cyclotomic polynomial Φn(x).We say Φn(x) is flat if A(n) = *** this paper,for odd primes p 3.and q ≡ 1(mod 3..

关键词： cyclotomic polynomial flat cyclotomic polynomial ternary cyclotomic polynomial

Characteristics of fMRI BOLD signal and its neurophysiological mechanism

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Progress in Natural Science:Materials International 2007年第6期17卷 630-638页

作者： Zhao Xiaohu1,2, Wu Yigen3.and Guo Shengli3.1. College of Life Sciences, Zhejiang university, Hangzhou 3.0058, china 2. Imaging department of Tongji Hospital of Tongji university, Shanghai 200065, china 3. College of Mathematics and Physics, nanjing university of Information Science and Technology, nanjing 210044, china) College of Life Sciences Zhejiang University Hangzhou 310058 China Imaging department Tongji Hospital Tongji University Shanghai 200065 China College of Mathematics and Physics Nanjing University of Information Science and Technology Nanjing 210044 China

The functional magnetic resonance imaging (fMRI) based on blood oxygen level dependent (BOLD) contrast has emerged as one of the most potent noninvasive tools for mapping brain function and has been widely used to explore physiological, pathological changes and mental activity in the brain. Exploring the nature and property of BOLD signal has recently attracted more attentions. Despite that great progress has been made in investigation of the characteristics and neurophysiological basis, the exact nature of BOLD signal remains unclear. In this paper we discuss the characteristics of BOLD signals, the nonlinear BOLD response to external stimuli and the relation between BOLD signals and neural electrophysiological recordings. Furthermore, we develop our new opinions regarding nonlinear BOLD response and make some perspectives on future study.

关键词： functional magnetic resonance imaging blood oxygen level dependent nonlinear response neural electrophysiological activity.