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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,{2.,beijing 100871,China 2. Department of Mathematics,Yantai university,Yantai 2.4005.China 3. LMAM,{2.,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.

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 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, {2., 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.

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 5.0}02., China 2. {5. of {2. Sciences, peking university, 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.

Density-functional formula for strongly correlated systems

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Progress in Natural Science:Materials International 2005年第5期15卷 395-401页

作者： WANG Huaiyu1*, HAN Rushan2.and CHEN Nanxian1(1. Department of Physics, Tsinghua university, beijing 100084, China 2. Department of Physics, {2., {5., China) Department of Physics Tsinghua University Beijing 100084 China Department of Physics Peking University Beijing 100871 China

Density functional method is applied for strongly correlated systems. Based on the assumption that the systems are composed of electrons in singly-occupied orbitals and those in doubly-occupied orbitals, a set of self-consistent equations are obtained by standard variation procedure. The equations consist of two parts. One part is to solve the wave functions of the electrons in singly-occupied orbitals and the other is to solve the wave functions of the electrons in doubly-occupied orbitals. The physical meanings of the terms appearing in the equations are discussed.

关键词： density-functional theory strongly correlated systems doubly-occupied orbital two-particle wave function self-consistent equations.

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,{2.,beijing 100871,China 1. school of mathematical Sciences Peking University Beijing 100871 China

In 195.,Hadwiger made a conjecture that every n-dimensional convex body can be covered by 2. 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

An eSnake model for medical image segmentation

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Progress in Natural Science:Materials International 2005年第5期15卷 424-429页

作者： Lv Hongyu1, YUAN Kehong2. BAO Shanglian1, ZU Donglin1 and DUAN Chaijie1*(1. The Research Center for Tumor Diagnosis and Therapeutical Physics & beijing Key Laboratory of Medical Physics and Engineering, beijing 100871, China 2. Key Laboratory of Pure and Applied Mathematics, {2. of {5. Sciences, peking university, beijing 100871, China) The Research Center for Tumor Diagnosis and Therapeutical Physics & beijing Key Laboratory of Medical Physics and Engineering Beijing 100871 China Key Laboratory of Pure and Applied Mathematics School of Mathematical Sciences Peking University Beijing 100871 China

A novel scheme of external force for detecting the object boundary of medical image based on Snakes (active contours) is introduced in the paper. In our new method, an electrostatic field on a template plane above the original image plane is designed to form the map of the external force. Compared with the method of Gradient Vector Flow (GVF), our approach has clear physical meanings. It has stronger ability to conform to boundary concavities, is simple to implement, and reliable for shape segmenting. Additionally, our method has larger capture range for the external force and is useful for medical image preprocessing in various applications. Finally, by adding the balloon force to the electrostatic field model, our Snake is able to represent long tube-like shapes or shapes with significant protrusions or bifurcations, and it has the specialty to prevent Snake leaking from large gaps on image edge by using a two-stage segmentation technique introduced in this paper. The test of our models proves that our methods are robust, precise in medical image segmentation.

关键词： image segmentation eSnake external force electrostatic field balloon force.

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.

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,school of {2. Sciences,{5.,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.