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Journal of Systems Science & Complexity 2010年第4期23卷 815-821页

作者： Zhongxiao JIA department of mathematical sciences,Tsinghua University,Beijing 100084,china. department of mathematical sciences Tsinghua University

It is well-known that many Krylov solvers for linear systems,eigenvalue problems,andsingular value decomposition problems have very simple and elegant formulas for residual *** not only allow us to further understand the methods theoretically but also can be usedas cheap stopping criteria without forming approximate solutions and residuals at each step beforeconvergence takes *** for large sparse linear least squares problems is based on the Lanczosbidiagonalization process and is a Krylov ***,there has not yet been an analogouslyelegant formula for residual *** paper derives such kind of *** addition,the authorgets some other properties of LSQR and its mathematically equivalent CGLS.

关键词： CGLS krylov subspace lanczos bidiagonalization least squares lsqr normal equations.

Γ-CONVERGENCE OF INTEGRAL FUNCTIONALS DEPENDING ON VECTOR-VALUED FUNCTIONS OVER PARABOLIC DOMAINS

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Chinese Annals of Mathematics,Series B 2000年第2期21卷 249-258页

作者： JIAN HUAIYU(department of mathematical sciences, Tsinghua University, Beijing 100084, china.) department of mathematical sciences Tsinghua University Beijing 100084 China

This paper studies Γ-convergence for a sequence of parabolic functionals, where the integrand f is nonconvex, and periodic on the first variable. The author obtains the representation formula of the Γ-limit. The results in this paper support a conclusion which relates Γ-convergence of parabolic functionals to the associated gradiend flows and confirms one of De Giorgi’s conjectures partially.

关键词： Γ-convergence Parabolic-minima Nonconvex functionals Parabolic equations

MAXIMUM INFORMATION AND OPTIMUM ESTIMATING FUNCTION

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Chinese Annals of Mathematics,Series B 2003年第3期24卷 349-358页

作者： LIN Lu department of Statistics, School of mathematical sciences, Nankai University, Tianjin 300071, china. Nankai Univ Sch Math Sci Dept Stat Tianjin 300071 Peoples R China

In order to construct estimating functions in some parametric models, this paper introducestwo classes of information matrices. Some necessary and sufficient conditions for the informationmatrices achieving their upper bounds are given. For the problem of estimating the median,some optimum estimating functions based on the information matrices are acquired. Undersome regularity conditions, an approach to carrying out the best basis function is introduced. Innonlinear regression models, an optimum estimating function based on the information matricesis obtained. Some examples are given to illustrate the results. Finally, the concept of optimumestimating function and the methods of constructing optimum estimating function are developedin more general statistical models.

关键词： Quasi (pseudo) Fisher information Estimating function Quasi score Nonlinear regression model Median regression model

7th CIIE likely to prove solid growth platform for many companies

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china.Textile 2024年第4期 20-21页

作者： china.Daily

The robust demand of the Chinese market and the improving business environment in the country make china.a big growth opportunity for companies wishing to further expand their operations,said corporates that have registered to participate at this year's china.International Import *** 7th edition of the annual CIIE,to be held in Shanghai from Nov 5 to 10,started its 100-day countdown on Saturday.

关键词： companies likely operations

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SOBOLEV INEQUALITY ON RIEMANNIAN MANIFOLDS

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Chinese Annals of Mathematics,Series B 2005年第4期26卷 651-658页

作者： WANG MENG department of Mathematics, Zhejiang University, Hangzhou 310027, china.School of mathematical sciences, Pudan University, Shanghai 200433, china. department of Mathematics Zhejiang University Hangzhou 310027 China. School of mathematical sciences Fudan University Shanghai 200433 China

Let M be an n dimensional complete Riemannian manifold satisfying the doublingvolume property and an on-diagonal heat kernel estimate. The necessary-sufficientcondition for the Sobolev inequality ‖f‖q ≤ Cn,,v,p,q(... 详细信息

关键词： Sobolev inequality Complete manifold Riesz transform Potential Heat kernel

A MODIFIED LIKELIHOOD RATIO TEST FOR HOMOGENEITY IN BIVARIATE NORMAL MIXTURES OF TWO SAMPLES

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Journal of Systems Science & Complexity 2009年第3期22卷 460-468页

作者： Qingzhu LEI·Yongsong QINSchool of mathematical sciences,Guangxi Normal University,Guilin 541004,china. School of mathematical sciences Guangxi Normal University Guilin 541004 China

This paper investigates the asymptotic properties of a modified likelihood ratio statistic for testing homogeneity in bivariate normal mixture models of two samples. The asymptotic null distribution of the modified li... 详细信息

关键词： Asymptotic distribution mixture model likelihood ratio test.

TRIPLE　INTERACTIONS　OF　CONORMAL　WAVES　FOR　HIGHER　ORDER　SEMILINEAR　HYPERBOLIC　EQUMIONS

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Chinese Annals of Mathematics,Series B 1995年第1期16卷 23-32页

作者： FANG DAOYUAN (Center for mathematical sciences, Zhejiang University, Hangzhou 310027, china.) 浙江大学数学科学中心浙江杭州

The interaction of three conormal waves for semi-linear strictly hyperbolic equations of third order is considered. Let Σi, i = 1, 2, 3, be smooth characteristic surfaces for P= Da(D_t￣2 -△) intersecting transversally at the origin. Suppose that the solution u to Pu = f(t, x ,y)D u), ≤2 is conormal to Σi, i = 1, 2, 3, for t < 0. The author uses Bony's second microlocajization techniques and commutator arguments to conclude that the new singularities a short time after the triple interaction lie on the surface of the light cone Γ over the origin plus the surfaces obtained by flow-outs of the lines of intersection Γ ∩ Σi and Σi∩ Σj, i, j = 1, 2, 3.

关键词： Hyperbolic equation Conormal wave Interaction Characteristic surface.

Dimensions of a class of high-dimensional homogeneous Moran sets and Moran classes

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Progress in Natural Science:Materials International 2002年第9期12卷 17-22页

作者： YAN Ping(department of mathematical sciences, Tsinghua University, Beijing 100084, china. Tsing Hua Univ Dept Math Sci Beijing 100084 Peoples R China

A class of high-dimensional homogeneous Moran sets and Moran classes are introduced and some dimensional properties are studied. The Hausdorff dimension, modified lower box-counting dimension, lower and upper box-counting dimension, and packing dimension of high-dimensional homogeneous and partial homogeneous Cantor sets are determined. Moreover, a kind of fractal E is obtained, which is not regular but with the property Dimw(Ed) = dDimw(E), where w denotes any of the dimensions mentioned above.

关键词： Moran set Moran class homogeneous Cantor set partial homogeneous Cantor set dimension.

EXACT NONREFLECTING BOUNDARY CONDITIONS FOR AN ACOUSTIC PROBLEM IN THREE DIMENSIONS

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Journal of Computational Mathematics 2003年第1期21卷 15-24页

作者： Houde Han Chunxiong Zheng (department of mathematical sciences, Tsinghua University, Beijing 100084, china. department of mathematical sciences Tsinghua University 北京 100084

In this paper, nonreflecting artificial boundary conditions are considered for an acoustic problem in three dimensions. With the technique of Fourier decomposition under the orthogonal basis of spherical harmonics, three kinds of equivalent exact artificial boundary conditions are obtained on a spherical artificial boundary. A numerical test is presented to show the performance of the method.

关键词： Exterior problem Nonreflecting artificial boundary condition Acoustic equa-tion Three-dimensions.