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Cascade algorithm and multiresolution analysis on the Heisenberg group

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Progress in Natural Science:Materials International 2005年第7期15卷 602-608页

作者： LIU Heping, LIU Yu, PENG Lizhong and CHU Xiaoyong (lmam, school of mathematical sciences, {2., beijing 100871, China) lmam School of Mathematical Sciences Peking University Beijing 100871 China

In this paper we investigate the relationship between the convergence of cascade algorithm and orthogonal (or biorthogo-nal) multiresolution analysis on the Heisenberg group. It is proved that the (strong) convergence of cascade algorithm together with the perfect reconstruction condition induces an orthogonal multiresolution analysis and vice versa . Similar results are also proved for biorthogo-nal multiresolution analysis.

关键词： Heisenberg group cascade algorithm multiresolution analysis refinable functions.

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., 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 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, {2., 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.

Weight hierarchies of linear codes satisfying the Near-Chain condition

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Progress in Natural Science:Materials International 2005年第9期15卷 784-792页

作者： LIU Zihui1** and CHEN Wende2.1. school of mathematical sciences, peking university, {2., China 2. Laboratory of Systems and Control and Key State Laboratory of Information Security, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of sciences, beijing 100080, China) school of mathematical sciences Peking University Beijing 100871 China. Laboratory of Systems and Control and Key State Laboratory of Information Security Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China

The weight hierarchies of a linear [n,k;q] code C satisfying the Near-Chain condition are studied, almost all the weight hierarchies of such code are determined.

关键词： weight hierarchy Near-Chain condition difference sequence linear code.

Balanced multiple description subband coding based on multifilter banks

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Science China(Information sciences) 2011年第11期54卷 2359-2372页

作者： WANG Ning 1,LI BaoBin 2.& PENG LiZhong 1 1 lmam,school of mathematical sciences,{2.,beijing 100871,China 2.school of Information Science and Engineering,Graduate university of Chinese Academy of sciences,beijing 100190,China 1. lmam School of Mathematical Sciences Peking University Beijing 100871 China2. School of Information Science and Engineering Graduate University of Chinese Academy of Sciences Beijing 100190 China

Multiple description coding is one of the source coding techniques to alleviate the problems of packet loss in *** encoder generates several different descriptions of the source and the decoder can produce a useful reconstruction with any received subset of these *** of the earlier works concentrated on redundancy and the average distortion of the single-description reconstructions,which is insufficient to describe the *** this paper,a metric of the coding system,balance eccentric modulus,is defined to evaluate the difference in quality between the individual *** the discrete wavelet transform becomes trivial polyphase transform when setting the balance eccentric modulus at zero,we introduce a multiwavelet based scheme ***,a sufficient condition for balanced multiwavelet based multiple description coding is presented.

关键词： multiple description coding rate-distortion theory balance eccentric modulus balanced multiwavelet multifilter bank

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., beijing 100871, 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,peking university,{2.,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 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

Raising approximation order of refinable vector by increasing multiplicity

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Science China Mathematics 2006年第1期49卷 86-97页

作者： YANG Shouzhi & PENG Lizhong Department of Mathematics, Shantou university, Shantou 515063, China lmam, {2., peking university, beijing 100871, China Department of Mathematics Shantou University Shantou 515063 China lmam School of Mathematical Sciences Peking University Beijing 100871 China

An algorithm is presented for raising an approximation order of any given orthogonal multiscaling function with the dilation factor a. Let φ(x) = [φ1(x),φ2.x),…,φr(x)]T be an orthogonal multiscaling function with the dilation factor a and the approximation order m. We can construct a new orthogonal multiscaling function φnew(x) = [ φT(x). f3r+1(x),φr+2.x),…,φr+s(x)}T with the approximation order m + L(L ∈ Z+). In other words, we raise the approximation order of multiscaling function φ(x) by increasing its multiplicity. In addition, we discuss an especial setting. That is, if given an orthogonal multiscaling function φ(x) = [φ1 (x), φ2.x), …, φr(x)]T is symmetric, then the new orthogonal multiscaling function φnew(x) not only raise the approximation order but also preserve symmetry. Finally, some examples are given.

关键词： orthogonal, multiscaling functions, approximation order, symmetry.

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, {2., 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 2. × 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