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DIMENSIONS OF SELF-AFFINE SETS WITH OVErLAPS

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Chinese Annals of mathematics,Series B 2003年第3期24卷 275-284页

作者： huA Su Department of mathematics, tsinghua university, beijing 100084, china. Tsing hua Univ Dept Math Beijing 100084 Peoples R China

The authora develop an algorithm to show that a class of self-affine sets with overlaps can be viewed as sofic affine-invariant sets without overlaps,thus by using the results of [11] and [10],the hausdorff and minkow... 详细信息

关键词： self-affine set overlap hausdorff dimension minkowski dimension

rEDUCTIONS OF ADJOINT rEPrESENTATIONS TO LAX rEPrESENTATIONS FOr CONSTrAINED FLOWS

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Chinese Annals of mathematics,Series B 1996年第2期17卷 187-198页

作者： ZENG YUNBO Department of Applied mathematics, tsinghua university, beijing 100084, china. TSING huA UNIV DEPT APPL MATHBEIJING 100084PEOPLES R CHINA

Within framework of zero-curvature representation theory, the Lax representations for x- andtn-constrained flows of soliton hierarchy are obtained from reductions of adjoint representationsof the auxiliary linear problems. This method is applied to the third order spectral problem bytaking modified Boussinesq hierarchy as an illustrative example.

关键词： Constrained flow Lax representation Adjoint representation Soliton hierarchy

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.

rECOGNITION AND CLASSIFICATION FOr O(n)-EQUIVArIANT BIFUrCATIONS WITH O(n)-CODIMENSION LESS THAN 5

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Chinese Annals of mathematics,Series B 1998年第4期19卷 391-400页

作者： WANG XIAOFENG (Department of Applied mathematics, tsinghua university, beijing 100084, china.)TANG YUN (Department of Applied mathematics, tsinghua university, beijing 100084, china.)WANG DUO (School of Mathematical Science, Peking universityl Beliing 10 Tsing hua Univ Dept Appl Math Beijing 100084 Peoples R China Peking Univ Sch Math Sci Beijing 100080 Peoples R China

Bifurcation problems equivariant under the standard action of the orthogonal group O(n) up to O(n)-codimension 4 are classified into 19 classes. For each class the normal form and one universal unfolding are calculate... 详细信息

关键词： O(n)-equivariant bifurcation Normal form Universal unfolding recognition problem

Moran sets and Moran classes

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Chinese Science Bulletin 2001年第22期46卷 1849-1856页

作者： WEN ZhiyingDepartment of mathematics, tsinghua university, beijing 100084, china Department of mathematics Tsinghua University Beijing China

The purpose of this survey is to present Moran sets and Moran classes which generalize the classical self-similar sets from the following points: (i) The placements of the basic sets at each step of the constructions can be arbitrary; (ii) the contraction ratios may be different at each step; and (iii) the lower limit of the contraction ratios permits zero. In this discussion we will present geometrical properties and results of dimensions of these sets and classes, and discuss conformal Moran sets and random Moran sets as well.

关键词： Moran set Moran classes dimension.

Median cross-validation criterion

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Chinese Science Bulletin 1997年第23期42卷 1956-1959页

作者： YANG YingDepartment of Applied mathematics, tsinghua university, beijing 100084, china Department of Applied mathematics Tsinghua University Beijing China

CONSIDEr the nonparametric median regression model Yni = g (xni) + εni, 1≤i≤n （1）where g: [0, 1]|→r is an unknown function of interest; {xni, 1≤i≤n} is the fixed design pointsin the interval [0, 1]; {εni, 1≤i≤n} is a triangular array of row iid random variables having medi-an zero, and {Yni, 1≤i≤n} is the observation. For each x∈[0, 1], n≥1, let Dnj（x） denotethe jth nearest neighber of x, j=1, 2,…, n, i. e. {Dn1（x）, Dn2（x）,…, Dnn（x）} is a trans-position of {xn1, xn2,…, xnn} satisfying |Dn1（x）-x|≤|Dn2（x）-x|≤…≤|Dnn（x）-x|.The tie is broken by the chronological order. The

关键词： median cross validation Bahadur’s representation asymptotic oplimality.

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

MULTISTEP DISCrETIZATION OF INDEX 3 DAES

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Journal of Computational mathematics 2000年第3期18卷 325-336页

作者： Yang Cao Qing-yang Li (Department of mathematics, tsinghua university, beijing 100084, china. 清华大学北京 100084

Studies the different types of multistep discretization of index 3 differential-algebraic equations in Hessenberg form. Existense, uniqueness and influence of perturbations; Local convergence of multistep discretizati... 详细信息

关键词： multistep methods Adams method BDF DAEs Index 3

THE APPrOXIMATIONS OF THE EXACT BOUNDArY CONDITION AT AN ArTIFICIAL BOUNDArY FOr LINEArIZED INCOMPrESSIBLE VISCOUS FLOWS

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Journal of Computational mathematics 1998年第3期16卷 239-256页

作者： Wei-zhu Bao (Department of Applied mathematics, tsinghua university, beijing 100084, P.r. china. 清华大学应用数学系北京

We consider the linearized incompressible Navier-Stokes (Oseen) equations in a flat channel. A sequence of approximations to the exact boundary condition at an artificial boundary is derived. Then the original problem is reduced to a boundary value problem in a bounded domain, which is well-posed. A finite element approximation on the bounded domain is given, furthermore the error estimate of the finite element approximation is obtained. Numerical example shows that our artificial boundary conditions are very effective.

关键词： Oseen equations artificial boundary artificial boundary condition finite element approximation error estimate