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Complete solving of explicit evaluation of Gauss sums in the index 2 case

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Science china Mathematics 2010年第9期53卷 2525-2542页

作者： YANG Jing1,2 & XIA LingLi3,1Department of mathematical sciences,Tsinghua university,Beijing 100084,china 2Division of mathematical sciences,school of Physical and mathematical sciences,Nanyang Technological university,637371,Singapore 3Basic Courses Department,Beijing Union university,Beijing 100101,china 1. Department of mathematical sciences Tsinghua University Beijing 100084 China2. Division of Mathematical Sciences School of Physical and Mathematical Sciences Nanyang Technological University 637371 Nanyang Singapore3. Basic Courses Department Beijing Union University Beijing 100101 China

Let p be a prime number,N be a positive integer such that gcd(N,p) = 1,q = pf where f is the multiplicative order of p modulo *** χ be a primitive multiplicative character of order N over finite field *** paper studies the problem of explicit evaluation of Gauss sums G(χ) in the "index 2 case"(i.e.[(Z/NZ):] = 2).Firstly,the classification of the Gauss sums in the index 2 case is ***,the explicit evaluation of Gauss sums G(χλ)(1 λ N-1) in the index 2 case with order N being general even integer(i.e.N = 2r·N0,where r,N0 are positive integers and N0 3 is odd) is ***,combining with the researches before,the problem of explicit evaluation of Gauss sums in the index 2 case is completely solved.

关键词： Gauss sum Stickelberger’s theorem Stickelberger congruence Davenport-Hasse lifting formula Davenport-Hasse product formula

Conformal isoparametric hypersurfaces with two distinct conformal principal curvatures in conformal space

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Science china Mathematics 2010年第4期53卷 953-965页

作者： NIE ChangXiong 1,2,LI TongZhu 3,HE YiJun 4 & WU ChuanXi 5 1 Faculty of Mathematics and Computer sciences,Hubei university,Wuhan 430062,china 2 school of mathematical sciences,Peking university,Beijing 100871,china 3 Faculty of sciences,Beijing Institute of Technology,Beijing 100081,china 4 school of mathematical sciences,Shanxi university,Taiyuan 030006,china 5 Institute of Mathematics,Hubei university,Wuhan 430062,china 1. Faculty of Mathematics and Computer sciences Hubei University Wuhan 430062 China2. School of Mathematical Sciences Peking University Beijing 100871 China3. Faculty of Sciences Beijing Institute of Technology Beijing 100081 China4. School of Mathematical Sciences Shanxi University Taiyuan 030006 China5. Institute of Mathematics Hubei University Wuhan 430062 China

The conformal geometry of regular hypersurfaces in the conformal space is *** classify all the conformal isoparametric hypersurfaces with two distinct conformal principal curvatures in the conformal space up to confor... 详细信息

关键词： Lorentz conformal geometry conformal invariants conformal isoparametric hypersurfaces

Study of D^0-D^0 mixing at a giga-Z linear collider

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Science china(Physics,Mechanics & Astronomy) 2010年第11期53卷 1953-1956页

作者： LI HaiBo 1 & YANG MaoZhi 2 1 Institute of High Energy Physics,P.O.Box 918,Beijing 100049,china 2 school of Physics,nankai university,tianjin 300071,china Institute of High Energy Physics Beijing China school of Physics Nankai University Tianjin China

The possibility of studying D 0-D 0 mixing at a giga-Z linear collider "Z factory" where 10 9 hadronic Z 0 decays can be accumulated is *** discuss the sensitivity for the measurements of neutral D mixing *** results are compared to those attainable at B *** find that the typical decay length of the neutral D mesons at Z factory is about 10 times larger than that at B *** addition,the resolution of the vertex detector of a giga-Z factory is 2-3 times better than that of B *** proper time resolution at Z factory is about 20-30 times better than that at B *** the determination of the mixing parameters at a giga-Z factory is more precise.

关键词： Z factory D0 mesons mixing B factory

Local 3-cocycles of von Neumann algebras

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Science china Mathematics 2007年第9期50卷 1240-1250页

作者： Cheng-jun HOU~(1+) Ben-yin FU~2 1 school of mathematical sciences,Qufu Normal university,Qufu 273165,china 2 school of mathematical sciences,Fudan university,Shanghai 200433,china 1. school of mathematical sciences Qufu Normal University Qufu 273165 China 2. school of mathematical sciences Fudan University Shanghai 200433 China

We show that every local 3-cocycle of a von Neumann algebra $\mathcal{R}$ into an arbitrary unital dual $\mathcal{R}$ -bimodule $\mathcal{S}$ is a 3-cocycle.

关键词： von Neumann algebra dual bimodule local 3-cocycle 3-cocycle 46L10

Optimal variational principle for backward stochastic control systems associated with Lévy processes

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Science china Mathematics 2012年第4期55卷 745-761页

作者： TANG MaoNing 1 & ZHANG Qi 2,1 Department of mathematical sciences,Huzhou university,Huzhou 313000,china 2 school of mathematical sciences,Fudan university,Shanghai 200433,china 1. Department of mathematical sciences Huzhou University Huzhou 313000 China2. School of Mathematical Sciences Fudan University Shanghai 200433 China

The paper is concerned with optimal control of backward stochastic differentiM equation （BSDE） driven by Teugel＇s martingales and an independent multi-dimensional Brownian motion, where Teugel＇s martingales are a family of pairwise strongly orthonormal martingales associated with L6vy processes （see e.g., Nualart and Schoutens＇ paper in 2000）. We derive the necessary and sufficient conditions for the existence of the optimal control by means of convex variation methods and duality techniques. As an application, the optimal control problem of linear backward stochastic differential equation with a quadratic cost criteria （or backward linear-quadratic problem, or BLQ problem for short） is discussed and characterized by a stochastic Hamilton system.

关键词： stochastic control stochastic maximum principle Ldvy processes Teugel's martingales backwardstochastic differential equations

Real solution isolation with multiplicity of zero-dimensional triangular systems

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Science china(Information sciences) 2011年第1期54卷 60-69页

作者： ZHANG ZhiHai,FANG Tian & XIA BiCan LMAM,school of mathematical sciences,Peking university,Beijing 100871,china 1. LMAM School of Mathematical Sciences Peking University Beijing 100871 China

Existing algorithms for isolating real solutions of zero-dimensional polynomial systems do not compute the multiplicities of the *** this paper,we define in a natural way the multiplicity of solutions of zero-dimensional triangular polynomial systems and prove that our definition is equivalent to the classical definition of local(intersection)*** we present an effective and complete algorithm for isolating real solutions with multiplicities of zero-dimensional triangular polynomial systems using our definition. The algorithm is based on interval arithmetic and square-free factorization of polynomials with real algebraic *** computational results on some examples from the literature are presented.

关键词： real solution isolation local multiplicity local ring polynomial system solving

The Koppelman-Leray formula on complex Finsler manifolds

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Science china Mathematics 2005年第6期48卷 847-863页

作者： QIU Chunhui & ZHONG Tongde school of mathematical sciences, Xiamen university, Xiamen 361005, china Academy of Mathematics and System sciences, Chinese Academy of sciences, Beijing 100080, china 1. school of mathematical sciences Xiamen University 361005 Xiamen China 2. Academy of Mathematics and System sciences Chinese Academy of Sciences 100080 Beijing China

By means of the invariant integral kernel (the Berndtsson kernel), the complex Finsler metric and the non-linear connection associated with the Chern-Finsler connection to research into the integral representation theory on complex Finsler manifolds, theKoppelman and Koppelman-Leray formulas are obtained, and the - -equations are solved.

关键词： complex Finsler manifold, Chern-Finsler connection, invariant integral kernel, Koppelman-Lerayformulas, - -equation.

Hereditary C~*-subalgebras and comparison of positive elements

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Science china Mathematics 2010年第6期53卷 1565-1570页

作者： WEI ChangGuo1,& WANG LiGuang2 1school of mathematical sciences,Ocean university of china,Qingdao 266071,china 2school of mathematical sciences,Qufu Normal university,Qufu 273165,china 1. school of mathematical sciences Ocean University of China Qingdao 266071 China2. School of Mathematical Sciences Qufu Normal University Qufu 273165 China

Characterizations of hereditary subalgebras generated by subsets of a C*-algebra are given through open *** these results,we give some equivalent conditions of comparison of positive elements.

关键词： hereditary subalgebra open projection positive element

Sharpness on the Lower Bound of the Lifespan of Solutions to Nonlinear Wave Equations

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Chinese Annals of Mathematics,Series B 2011年第4期32卷 521-526页

作者： Yi ZHOU 1 Wei HAN 2 1 Nonlinear mathematical Modeling and Methods Laboratory Shanghai Key Laboratory for Contem- porary Applied Mathematics school of mathematical sciences, Fudan university, Shanghai 200433, china. 2 school of mathematical sciences, Fudan university, Shanghai 200433, china Department of Mathematics, North university of china, Taiyuan 030051, china. Nonlinear mathematical Modeling and Methods Laboratory Shanghai Key Laboratory for Contemporary Applied Mathematics School of Mathematical Sciences Fudan University Shanghai 200433 China

This paper is devoted to proving the sharpness on the lower bound of the lifespan of classical solutions to general nonlinear wave equations with small initial data in the case n = 2 and cubic nonlinearity （see the results of T. T. Li and Y. M. Chen in 1992）. For this purpose, the authors consider the following Cauchy problem： { where □=δt^2-∑i=1n δx^^2 is the wave operator, g（x）（≡/） 0 is a smooth non-negative function with compact support, and ε 〉 0 is a small parameter. It is shown that the solution blows up in a finite time, and the lifespan T（ε） of solutions has an upper bound T（ε） ≤ exp（Aε-2） with a positive constant A independent of ε, which belongs to the same kind of the lower bound of the lifespan.

关键词： Nonlinear wave equation Cauchy problem Lifespan