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On solving equations of algebraic sum of equal powers

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Science China mathematics 2006年第9期49卷 1153-1157页

作者： WANG Xinghua & YANG Shijun department of mathematics, {2. {3., hangzhou 3.002., China department of mathematics, hangzhou Normal College, hangzhou 3.003., China department of mathematics Zhejiang University Hangzhou 310028 China department of mathematics Hangzhou Normal College Hangzhou 310036 China

It is well known that a system of equations of sum of equal powers can be converted to an algebraic equation of higher degree via Newton's identities. This is the Viete-Newton theorem. This work reports the generalizations of the Viete-Newton theorem to a system of equations of algebraic sum of equal powers. By exploiting some facts from algebra and combinatorics,it is shown that a system of equations of algebraic sum of equal powers can be converted in a closed form to two algebraic equations, whose degree sum equals the number of unknowns of the system of equations of algebraic sum of equal powers.

关键词： algebraic sum of equal powers, Newton's identities, system of equations,roots of a polynomial.

Time-periodic solutions of the Einstein's field equations II:geometric singularities

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Science China mathematics 2010年第6期53卷 1507-1520页

作者： KONG DeXing1,LIU KeFeng2.& SHEN Ming3.1department of mathematics,{2. {3.,hangzhou 3.002.,China 2.0} of mathematics,{3. of California at Los Angeles,CA 90095,USA 3.enter of Mathematical Sciences,{2. {3.,hangzhou 3.002.,China 1. department of mathematics Zhejiang University Hangzhou 310027 China2. Department of Mathematics University of California at Los Angeles Los Angeles CA 90095 USA3. Center of Mathematical Sciences Zhejiang University Hangzhou 310027 China

In this paper,we construct several kinds of new time-periodic solutions of the vacuum Einstein's field equations whose Riemann curvature tensors vanish,keep finite or take the infinity at some points in these space-times,*** singularities of these new time-periodic solutions are investigated and some new physical phenomena are discovered.

关键词： Einstein’s field equations time-periodic solution Riemann curvature tensor singularity event horizon

On Holomorphic Automorphisms of a Class of Non-homogeneous Rigid Hypersurfaces in C^(N+1)

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Chinese Annals of mathematics,Series B 2010年第2期31卷 201-210页

作者： Qingyan WU department of mathematics,Linyi Normal {2.,Linyi 2.6005,Shandong,China department of mathematics,zhejiang {2.,hangzhou 3.002.,China department of mathematics Linyi Normal University Linyi 276005 Shandong China department of mathematics Zhejiang University Hangzhou 310027 China

The author determines the real-analytic infinitesimal CR automorphisms of a class of non-homogeneous rigid hypersurfaces in CN+1 near the origin,and the connected component containing the identity transformation of al... 详细信息

关键词： Real-analytic infinitesimal CR automorphisms Rigid hypersurfaces Holomorphic automorphisms

SOME FUNCTIONAL LIMIT THEOREMS FOR THE INFINITE SERIES OF OU PROCESSES

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Chinese Annals of mathematics,Series B 2003年第2期24卷 249-260页

作者： WANG WENSHENG LIN ZHENGYAN department of mathematics, {2. {3., hangzhou 3.002., China. department of mathematics, hangzhou Teacher’s College, hangzhou 3.0012. China. E-mail: wswang@*** department of mathematics, {2. {3., hangzhou 3.002., China. zhejiang Univ Dept Math Hangzhou 310028 Peoples R China hangzhou Teachers Coll Dept Math Hangzhou 310012 Peoples R China

This paper obtains functional modulus of continuity and Strassen's functional LIL of theinfinite series of independent Ornstein-Uhlenbeck processes, which also imply the Levy's exactmodulus of continuity and LIL of th... 详细信息

关键词： Ornstein-Uhlenbeck processes Stationary Gaussian processes Modulus of continuity Law of the iterated logarithm

Almost sure central limit theorems for random functions

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Science China mathematics 2006年第12期49卷 1788-1799页

作者： LU Chuanrong, QIU Jin & XU Jianjun School of mathematics and Statistics, zhejiang {2. of Finance and Economics, {3. 3.0018, China department of mathematics, zhejiang {2., {3. 3.002., China 1. School of mathematics and Statistics Zhejiang University of Finance and Economics Hangzhou 310018 China 2. department of mathematics Zhejiang University Hangzhou 310028 China

Let {Xn,-∞< n <∞} be a sequence of independent identically distributed random variables with EX1 = 0, EX12.= 1 and let Sn =∑k=1∞Xk, and Tn = Tn(X1,…,Xn) be a random function such that Tn = ASn + Rn, where supn E|... 详细信息

Let {Xn,-∞2.= 1 and let Sn =∑k=1∞Xk, and Tn = Tn(X1,…,Xn) be a random function such that Tn = ASn + Rn, where supn E|Rn| 2.) a.s., or Rn = O(n1/2.2.) a.s., 0 <γ< 1/8. In this paper, we prove the almost sure central limit theorem (ASCLT) and the function-typed almost sure central limit theorem (FASCLT) for the random function Tn. As a consequence, it can be shown that ASCLT and FASCLT also hold for U-statistics, Von-Mises statistics, linear processes, moving average processes, error variance estimates in linear models, power sums, product-limit estimators of a continuous distribution, product-limit estimators of a quantile function, etc.

关键词： statistics,random function,almost sure central limit theorem,logarithm average.

ON CONVERGENCE OF NOUREIN ITERATIONS FOR SIMULTANEOUS FINDING ALL ZEROS OF A POLYNOMIAL

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Journal of Computational mathematics 2000年第2期18卷 113-122页

作者： Shi-mingZheng Zheng-da Huang (department of mathematics, Xixi Campus, {2. {3., hangzhou 3.002., China) 浙江大学浙江杭州 310028

Presents the first estimation conditions for Nourein iterations for simultaneous finding all zeros of a polynomial under which the iteration processes are guaranteed to converge. Computational formulas; Theorems and p... 详细信息

关键词： polynomial zeros parallel iteration Nourein iterations point estimation convergence

ON THE CONVERGENCE OF KING-WERNER ITERATIONMETHOD IN BANACH SPACEON THE CONVERGENCE OF KING-WERNER ITERATIONMETHOD IN BANACH SPACE

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Journal of Computational mathematics 2000年第5期18卷 457-466页

作者： Zheng-da Huang (department of mathematics, XiXi Campus, {2. {3., hangzhou 3.002., China) department of mathematics XiXi Campus Zhejiang University Hangzhou 310028 China

In this paper. a Kantorovitch- Ostrowski type convergence theorem and an error estimate of using the information of higher derivatives at the center between initial points for King-Werner iteration method in Banach ... 详细信息

关键词： Information at the center between initial points King-Werner iteration method Convergence Error estimate.

Constructing a quasi-Legendre basis based on the C-Bézier basis

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Progress in Natural Science:Materials International 2005年第6期15卷 559-563页

作者： HUANG Yu* and WANG Guozhao(department of mathematics, {2. {3., hangzhou 3.002., China) department of mathematics Zhejiang University Hangzhou 310027 China

In the space Γ_n=span｛sint,cost,1,t,t2.…,t n-2.｝, a C-Bézier basis is constructed by an integral approach. However, the C-Bézier basis is not orthogonal. For some applications, we construct an orthogonal basis based on the C-Bézier basis, which has remarkable properties similar to that of the Legendre basis. Then we derive the transformation matrices that convert the C-Bézier basis and the orthogonal basis into each other. As an example of application, we apply this orthogonal basis to the degree reduction approximation of the C-Bézier curves.

关键词： C-Bézier basis orthogonal basis basis transformations degree reduction.

GLOBAL EXISTENCE AND ASYMPTOTICS BEHAVIOR OF SOLUTIONS FOR A RESONANT KLEIN-GORDON SYSTEM IN TWO SPACE DIMENSIONS

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Chinese Annals of mathematics,Series B 2005年第1期26卷 89-104页

作者： XUERUYING FANGDAOYUAN departmentofmathematics ZhejiangUniversityHangzhou310027China departmentofmathematics ZhejiangUniversityHangzhou310027China

The authors study a resonant Klein-Gordon system with convenient nonlinearities in two space dimensions, prove that such a system has global solutions for small, smooth,compactly supported Cauchy data, and find that t... 详细信息

关键词： Klein-Gordon equation Asymptotic behavior Global existence