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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, {2., beijing 100871, China lmam School of Mathematical Sciences Peking University Beijing 100871 China

Let f(z) = e2.iθz(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 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 {2. 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 14E2. 14F2.

Oblique derivative problem for general Chaplygin-Rassias equations

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Science China Mathematics 2008年第1期51卷 5-36页

作者： WEN GuoChun lmam, school of mathematical sciences, {2., beijing 100871, China lmam School of Mathematical Sciences Peking University Beijing 100871 China

The present paper deals with the oblique derivative problem for general second order equations of mixed (elliptic-hyperbolic) type with the nonsmooth parabolic degenerate line $$K_1 (y)u_{xx} + \left| {K_2.(x)} \right|u_{yy} + a(x,y)u_x + b(x,y)u_y + c(x,y)u = - d(x,y)$$ in any plane domain D with the boundary ?D=Γ ∪ L 1 ∪ L 2.∪ L 3 ∪ L 4, where Γ(? {y > 0}) ∈ C μ 2.(0 2. L 3, L 4 are four characteristics with the slopes ?H 2.x)/H 1(y), H 2.x)/H 1(y),?H 2.x)/H 1(y),H 2.x)/H 1(y) (H 1(y) = √|K 1(y)|, H 2.x) = √|K 2.x)| in {y 2.{2.\frac{{\partial u}}{{\partial \nu }} = \frac2.{{H(x,y)}}\operatorname{Re} \left[ {\overline {\lambda (z)} u_{\tilde z} } \right] = r(z), z \in \Gamma \cup L_1 \cup L_4 , \operatorname{Im} \left[ {\overline {\lambda (z)} u_{\tilde z} } \right]\left| {_{z = z_l } } \right. = b_l ,l = 1,2. u( - 1) = b_0 ,u(1) = b_3 ,$$ in which z 1, z 2.are the intersection points of L 1, L 2. L 3, L 4 respectively. The above equations can be called the general Chaplygin-Rassias equations, which include the Chaplygin-Rassias equations $$K_1 (y)(M_2.(x)u_x )_x + M_1 (x)(K_2.(y)u_y )_y + r(x,y)u = f(x,y), in D$$ as their special case. The above boundary value problem includes the Tricomi problem of the Chaplygin equation: K(y)u xx+u yy = 0 with the boundary condition u(z) = ?(z) on Γ ∪ L 1 ∪ L 4 as a special case. Firstly some estimates and the existence of solutions of the corresponding boundary value problems for the degenerate elliptic and hyperbolic equations of second order are discussed. Secondly, the solvability of the Tricomi problem, the oblique derivative problem and Frankl problem for the general Chaplygin-Rassias equations are proved. The used method in this paper is different from those in other papers, because the new notations W(z) = W(x + iy) = $u_{\tilde z} $ = [H

关键词： oblique derivative problem equations of mixed type nonsmooth degenerate line 35J70 35L80 35N99

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, {2., 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

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, {2., beijing 100871, 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.

Pole assignment in descriptor periodic systems

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Science China Mathematics 2005年第10期48卷 1309-1332页

作者： FAN Hung-Yuan~1 LIN Wen-Wei~1 & XU Shufang~2.1. Department of Mathematics,Tsing Hua university,Hsinchu 30043,China 2. lmam,{2.,peking university,beijing 100871,China 1. Department of Mathematics Tsing Hua University 30043 Hsinchu China 2. lmam School of Mathematical Sciences Peking University 100871 Beijing China

In this paper a pole assignment problem is considered for the descriptor linear discrete-time periodic systems, which is using the periodic proportional-derivative feedback to modify a given system such that the closed loop system has a specified selfconjugate set of eigenvalues. It is shown that the complete reachability of an open loop periodic system is equivalent to the possibility of assigning an arbitrary set of the eigenvalues to the system by choosing the suitable periodic proportional-derivative feedback.A computational approach is also proposed to solve the problem, which uses the reliable numerical techniques based on the orthogonal transformations. Numerical examples are presented to illustrate the effectiveness of the proposed approach.

关键词： descriptor linear periodic system, pole assignment, proportional and derivative feedback, numerical method, periodic Schur decomposition.

The lifting scheme of 4-channel orthogonal wavelet transforms

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Progress in Natural Science:Materials International 2006年第1期16卷 100-104页

作者： PENG Lizhong and CHU Xiaoyong (lmam, school of mathematical sciences, {2., beijing 100871, China) [a]peking Universiy LMAM School of Mathematical Sciences Beijing China

The 4-channel smooth wavelets with linear phase and orthogonality are designed from the 2.channel orthogonal wavelets with high transfer vanishing moments. Reversely, for simple lifting scheme of such 4-channel orthogonal wavelet transforms, a new 2.channel orthogonal wavelet associated with this 4-channel wavelet is constructed. The new 2.channel wavelet has at least the same number of vanishing moments as the associated 4-channel one. Finally, by combining the two such 2.channel wavelet systems, the lifting scheme of 4-channel orthogonal wavelet transform, which has simple structure and is easy to apply, is presented.

关键词： lifting scheme 4-channel orthogonal wavelet 2.channel orthogonal wavelet vanishing moment transfer vanishing moment linear phase.

Real solution isolation with multiplicity of zero-dimensional triangular systems

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Science China(Information sciences) 2011年第1期54卷 60-69页

作者： ZHANG ZhiHai,FANG Tian & XIA BiCan lmam,school of mathematical sciences,{2.,beijing 100871,China 1. lmam School of Mathematical Sciences Peking University Beijing 100871 China

Existing algorithms for isolating real solutions of zero-dimensional polynomial systems do not compute the multiplicities of the *** this paper,we define in a natural way the multiplicity of solutions of zero-dimensional triangular polynomial systems and prove that our definition is equivalent to the classical definition of local(intersection)*** we present an effective and complete algorithm for isolating real solutions with multiplicities of zero-dimensional triangular polynomial systems using our definition. The algorithm is based on interval arithmetic and square-free factorization of polynomials with real algebraic *** computational results on some examples from the literature are presented.

关键词： real solution isolation local multiplicity local ring polynomial system solving

Two applications of generalized Carleson measures to meromorphic Besov-type spaces

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Chinese Science Bulletin 1998年第15期43卷 1260-1264页

作者： TAN Haiou 1 and XIAO Jie 2.1. Department of Mathematics, Wuyi university, Jiangmen 52.02., China 2. school of mathematical sciences, {2., beijing 100871, China Department of Mathematics Wuyi University Jiangmen China school of mathematical sciences Peking University Beijing China

The generalized Carleson measures are used to characterize the meromorphic Besov_type spaces and to explore some inclusions between these spaces.

关键词： generalized Carleson measures meromorphic Besov_type spaces.