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SOME prOpErTIES OF LSQr FOr LArGE SpArSE LINEAr LEAST SQUArES prOBLEMS

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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.

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.

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

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.

THE GLOBAL ArTIFICIAL BOUNDArY CONDITIONS FOr NUMErICAL SIMULATIONS OF THE 3D FLOW ArOUND A SUBMErGED BODY

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Journal of Computational Mathematics 2003年第4期21卷 435-450页

作者： Hou-de Han Xin Wen (department of mathematical sciences, tsinghua university, beijing 100084, china) department of mathematical sciences Tsinghua University Beijing 100084 China

We consider the numerical approximations of the three-dimensional steady potential flow around a body moving in a liquid of finite constant depth at constant speed and distance below a free surface in a channel. One vertical side is introduced as the upstream artificial boundary and two vertical sides are introduced as the downstream artificial boundaries. On the artificial boundaries, a sequence of high-order global artificial boundary conditions are given. Then the original problem is reduced to a problem defined on a finite computational domain, which is equivalent to a variational problem. After solving the variational problem by the finite element method, we obtain the numerical approximation of the original problem. The numerical examples show that the artificial boundary conditions given in this paper are very effective.

关键词： Ship wave potential flow Global artificial boundary condition Finite element method.

Maximal regularity of second order delay equations in Banach spaces

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Science china Mathematics 2010年第1期53卷 51-62页

作者： BU ShangQuan ? & FANG Yi department of mathematical sciences, tsinghua university, beijing 100084, china department of mathematical sciences, tsinghua university, beijing 100084, china 1. department of mathematical sciences Tsinghua University Beijing 100084 China

We give necessary and sufficient conditions of Lp-maximal regularity(resp.B sp ,q-maximal regularity or F sp ,q-maximal regularity) for the second order delay equations:u″(t)=Au(t) + Gu't + F u t + f(t), t ∈ [0, 2π] with periodic boundary conditions u(0)=u(2π), u′(0)=u′(2π), where A is a closed operator in a Banach space X,F and G are delay operators on Lp([-2π, 0];X)(*** ,q([2π, 0];X) or Fsp,q([-2π, 0;X])).

关键词： maximal regularity second order delay equations Lebesgue-Bochner spaces Besov spaces Triebel-Lizorkin spaces

rEGULArIZATION OF SINGULAr SYSTEMS BY OUTpUTFEEDBACK

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Journal of Computational Mathematics 2000年第1期18卷 43-60页

作者： De-lin Chu Da-yong Cai(department of mathematical sciences, tsinghua university, beijing 100084, china) 清华大学北京 100084

presents a study which examined problem of regularization of a singular linear time-invariant system by derivative and proportional output feedback. reduced form for the system that can be computed using orthogonal tr... 详细信息

关键词： regularization singular systems output feedback

Modularity of Calabi-Yau varieties and conformal field theory

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Science china Mathematics 2008年第6期51卷 1135-1146页

作者： TAN FuCheng department of mathematical sciences,tsinghua university,beijing 100084,china department of mathematical sciences Tsinghua University Beijing 100084 China

We study the modularity problem of Calabi-Yau varieties from the conformal field theo- retic point of *** express the modular forms associated to all 1-dimensional Calabi-Yau orbifolds in terms of products of Dedekind eta functions,which is hoped to shed light on the modularity questions for higher dimensional Calabi-Yau varieties.

关键词： L-function Calabi-Yau variety Gepner model 53C80

Ar quivers,exceptional sequences and algorithms in derived Hall algebras

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Science china Mathematics 2010年第6期53卷 1609-1624页

作者： SHENG Jie department of mathematical sciences,tsinghua university,beijing 100084,china 1. department of mathematical sciences Tsinghua University Beijing 100084 China

Consider the canonical isomorphism between the positive part U+ of the quantum group Uq(g) and the Hall algebra H(Λ),where the semisimple Lie algebra g and the finite-dimensional hereditary algebra Λ share a Dynkin *** and Xiao have given two algorithms to decompose the root vectors into linear combinations of monomials of Chevalley generators of U+,respectively induced by the braid group action on the exceptional sequences of Λ-modules and the structure of the Auslander-reiten quiver of Λ.In this paper,we obtain the corresponding algorithms for the derived Hall algebra DH(Λ),which was introduced by *** show that both algorithms are applicable to the lattice algebra and Heisenberg double in the sense of *** the new recursive formulae have the same flavor with the quantum Serre relations.

关键词： derived Hall algebra exceptional sequence Ar quiver