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INFINITE ELEMENT METHOD FOR THE EXTERIOR PROBLEMS OF THE HELMHOLTZ EQUATIONS

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Journal of Computational mathematics 2000年第6期18卷 657-672页

作者： Lung-an Ying (school of mathematical sciences, peking university, beijing 100871, china) 北京大学北京 100871

There are two cases of the exterior problems of the Helmholtz equation. If λ ≥ 0 the bilinear form is coercive, and if λ < 0 it is the scattering problem. We give a new approach of the infinite element method, which enables us to solve these exterior problems as well as corner problems. A numerical example of the scattering problem is given. [ABSTRACT FROM AUTHOR]

关键词： Helmholtz equation exterior problem infinite element method

Hausdorff dimension of Julia set of a polynomial with a Siegel disk

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Science china mathematics 2006年第9期49卷 1284-1296页

作者： SHEN Liang LMAM, school of mathematical sciences, peking university, beijing 100871, china LMAM School of Mathematical Sciences Peking University Beijing China

Let f(z) = e2πiθz(1+z/d)d,θ∈R\Q be a polynomial. Ifθis an irrational number of bounded type, it is easy to see that f(z) has a Siegel disk centered at 0. In this paper, we will show that the Hausdorff dimension o... 详细信息

关键词： Hausdorff dimension Siegel disk porous set

On Riemann-Finsler geometry

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Chinese Science Bulletin 1998年第6期43卷 447-450页

作者： MO Xiaohuan school of mathematical sciences, peking university, beijing 100871, china school of mathematical sciences Peking University Beijing China

The history of Finsler geometry is reviewed and briefly recent development in Finsler geometry and its application is completed systematically. Furthermore, an interesting open problem has been proposed in this field.

关键词： Finsler space Chern connection Hilbert form Minkowski potential projective sphere bundle.

ON THE CENTRAL RELAXING SCHEME Ⅱ: SYSTEMS OF HYPERBOLIC CONSERVATION LAWS

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Journal of Computational mathematics 2001年第6期19卷 571-582页

作者： Hua-zhong Tang (school of mathematical sciences, peking university, beijing 100871, china) (LSEC,ICMSEC Academy of mathematics and Systems sciences, Chinese Academy of sciences, beijing 100080, china) school of mathematical sciences Peking University Beijing 100871 China

This paper continues to study the central relaxing schemes for system of hyperbolic conservation laws, based on the local relaxation approximation. Two classes of relaxing systems with stiff source term are introduced to approximate system of conservation laws in curvilinear coordinates. Based on them, the semi-implicit relaxing schemes are con- structed as in [6, 12] without using any linear or nonlinear Riemann solvers. Numerical experiments for one-dimensional and two-dimensional problems are presented to demon- strate the performance and resolution of the current schemes.

关键词： Hyperbolic conservation laws The relaxing system The central relaxing schemes The Euler equations.

CONVERGENCE OF VORTEX METHODS FOR 3-D EULER EQUATIONS

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Journal of Computational mathematics 2000年第3期18卷 239-250页

作者： Jia-fu Lin (Institute of System Science, Academy of mathematics and System sciences, Chinese Academy of sciences, beijing, 100080, china school of mathematical sciences, peking university, beijing 100871, china) 中科院系统科学所北京 100080

Presents a study on the convergence of vortex methods for the three-dimensional Euler equations in bounded domains. Related studies on the convergence of vortex methods; Formulation of vortex methods; Convergence for ... 详细信息

关键词： Euler equations vortex methods convergence initial-boundary value problem

A quantitative program for Hadwiger's covering conjecture

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Science china mathematics 2010年第9期53卷 2551-2560页

作者： ZONG Chuanming school of mathematical sciences,peking university,beijing 100871,china school of mathematical sciences Peking University

In 1957,Hadwiger made a conjecture that every n-dimensional convex body can be covered by 2n translates of its *** to now,this conjecture is still open for all n *** 1933,Borsuk made a conjecture that every n-dimensional bounded set can be divided into n + 1 subsets of smaller *** to now,this conjecture is open for 4 n *** this article we encode the two conjectures into continuous functions defined on the spaces of convex bodies,propose a four-step program to attack them,and obtain some partial results.

关键词： convex body Hadwiger’s conjecture Banach-Mazur metric β-net Borsuk’s conjecture

BRILL-NOETHER MATRIX FOR RANK TWO VECTOR BUNDLES

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Chinese Annals of mathematics,Series B 2002年第4期23卷 531-538页

作者： TAN XIAOJIANGschool of mathematical sciences, peking university, beijing 100871, china school of mathematical sciences Peking University Beijing 100871 China

Let X be an arbitrary smooth irreducible complex projective curve, E (?)X a rank two vector bundle generated by its sections. The author first represents ?as a triple {D1,D2,f}, where D1 , D2 are two effective divisors with d = deg(D1) + deg(D2), and f ∈ H?X, [D1] |D2) is a. collection of polynomials. E is the extension of [D2] by [D1] which is determined by f. By using / and the Brill-Noether matrix of D1+D2, the author constructs a 2g × d matrix WE whose zero space gives Im{H0(X,[D1]) (?) H0(X, [D1] |D1)}(?) Im{H?X, E) (?) H0(X,[D2]) (?) H0(X, [D2]|D2)} From this and H0(X,E) = H0(X,[D1]) (?)Im{H0(X,E) (?) H0(X, [D2])}, it is got in particular that dimH0(X, E) = deg(E) - rank(WE) + 2.

关键词： Brill-Noether matrix Vector bundle Effective divisor

On multiply of sections of line bundles on compact Riemann surfaces

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Science china mathematics 2008年第4期51卷 721-727页

作者： TAN XiaoJiang LMAM and school of mathematical sciences peking university beijing 100871 china LMAM and school of mathematical sciences Peking University Beijing China

In this paper,we give some conditions on the surjective of multiply maps H^0(R,L)×H^0(R,K)→H^0(R,L(?)K).Here R is a compact Riemann surface,L a line bundle on R and K is the canonical line bundle.

关键词： compact Riemann surfaces line bundles 14E20 14F24

Theory of optimal blocking for fractional factorial split-plot designs

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Science china mathematics 2005年第5期48卷 649-656页

作者： Al Mingyao & HE Shuyuan Key Laborartory of Pure and Applied mathematics, school of mathematical sciences, peking university, beijing 100871, china Key Laborartory of Pure and Applied mathematics School of Mathematical Sciences Peking University Beijing China

The issue of optimal blocking for fractional factorial split-plot (FFSP) designs is considered under the two criteria of minimum aberration and maximum estimation capacity. The criteria of minimum secondary aberration (MSA) and maximum secondary estimation capacity (MSEC) are developed for discriminating among rival nonisomorphic blcoked FFSP designs. A general rule for identifying MSA or MSEC blocked FFSP designs through their blocked consulting designs is established.

关键词： blocking consulting design estimation capacity minimum secondary aberration fractional factorial split-plot design.