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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,{3., Beijing {4., 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,{3., Beijing {4., china LMAM School of Mathematical Sciences Peking University Beijing 100871 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,{3., Beijing {4., 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.

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,{3. {4.,Beijing 100871,china 1. school of mathematical sciences Peking University Beijing 100871 China

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 *** 193.,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

Uniqueness and local stability for the inverse scattering problem of determining the cavity

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Science china Mathematics 2005年第8期48卷 1113-1123页

作者： FENG Lixin & MA Fuming LMAM, school of mathematical sciences,{3., Beijing {4., china school of mathematical sciences, Heilongjiang university, Harbin 150080, china school of mathematical sciences, Jilin university, Changchun 13.012, china 1. LMAM School of Mathematical Sciences Peking University 100871 Beijing China 2. school of mathematical sciences Heilongjiang University 150080 Harbin China 3. school of mathematical sciences Jilin University 130012 Changchun China

Considering a time-harmonic electromagnetic plane wave incident on an arbitrarily shaped open cavity embedded in infinite ground plane, the physical process is modelled by Maxwell's equations. We investigate the inverse problem of determining the shape of the open cavity from the information of the measured scattered field. Results on the uniqueness and the local stability of the inverse problem in the 2-dimensional TM (transverse magnetic) polarization are proved in this paper.

关键词： uniqueness, stability, Maxwell's equations, inverse scattering problem.

The regular representation and regular covariant representation of crossed products of Woronowicz C^(*)-algebras

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Science china Mathematics 2005年第9期48卷 1245-1259页

作者： ZHANG Xiaoxia~(1,2) & GUO Maozheng~(1,3. 1. school of mathematical sciences,{3. {4.,Beijing 100871,china 2. Department of Mathematics,Yantai {4.,Yantai 264.05,china 3. LMAM,{3. {4.,Beijing 100871,china 1. school of mathematical sciences Peking University 100871 Beijing China 2. Department of Mathematics Yantai University 264005 Yantai China 3. LMAM Peking University 100871 Beijing China

In this paper,it is shown that the regular representation and regular covariant representation of the crossed products A×α G correspond to the twisted multiplicative unitary operators,where A is a Woronowicz C~*-algebra acted upon by a discrete group ***,it is also shown that the regular covariant C~*-algebra is the Woronowicz C~*-algebra which corresponds to a multiplicative ***,an explicit description of the multiplicative unitary operator for C(SU_q(2) )×α (?) is given in terms of those of the Woronowicz C~*-algebra C(SU_q(2) ) and the discrete group G.

关键词： multiplicative unitary operator, Woronowicz C*-algebra, crossed product.

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 {3. {4. Beijing 100871 china 1. LMAM and school of mathematical sciences Peking University Beijing 100871 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 14.20 14.24

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,{3., Beijing {4., 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

Wavelets associated with Hankel transform and their Weyl transforms

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Science china Mathematics 2004年第3期47卷 393-400页

作者： PENG Lizhong MA Ruiqin LMAM, school of mathematical sciences,{3., Beijing {4., china 1. LMAM School of Mathematical Sciences Peking University 100871 Beijing China

The Hankel transform is an important transform. In this paper, westudy the wavelets associated with the Hankel transform, thendefine the Weyl transform of the wavelets. We give criteria of itsboundedness and compactne... 详细信息

关键词： Bessel function, Hankel transform, wavelets, Weyltransform, boundedness, compactness.