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Weighted moments for a supercritical branching process in a varying or random environment

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science China mathematics 2011年第7期54卷 1437-1444页

作者： LI YingQiu1,2, HU YangLi1,2 & LIU QuanSheng1,3, 1college of mathematics and Computing sciences, Changsha University of science and Technology, Changsha 410004, China 2college of mathematics and computer sciences, Hunan Normal University, Changsha 410081, China 3LMAM, University of Bretgne-Sud, BP573, 56017 Vannes, France 1. college of mathematics and Computing sciences Changsha University of Science and Technology Changsha 410004 China2. College of Mathematics and Computer Sciences Hunan Normal University Changsha 410081 China3. LMAM University of Bretgne-Sud BP573 56017 Vannes France

Let W be the limit of the normalized population size of a supercritical branching process in a varying or random environment. By an elementary method, we find sufficient conditions under which W has finite weighted mo... 详细信息

关键词： branching process varying environment random environment moment martingale

A centrality measure based on spectral optimization of modularity density

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science China(Information sciences) 2010年第9期53卷 1727-1737页

作者： FU LiDong1,2*,GAO Lin1 & MA XiaoKe1 1School of computer science and Engineering,Xidian University,Xi'an 710071,China 2college of computer,Xi'an University of science and Technology,Xi'an 710054,China 1. School of computer science and Engineering Xidian University Xi’an 710071 China2. College of Computer Xi’an University of Science and Technology Xi’an 710054 China

Centrality analysis has been shown to be a valuable method for the structural analysis of complex *** is used to identify key elements within networks and to rank network elements such that experiments can be tailored to interesting *** this paper,we show that the optimization process of modularity density can be written in terms of the eigenspectrum of kernel *** on the eigenvectors belonging to the largest eigenvalue of kernel matrix,we present a new centrality measure that characterizes the contribution of each node to its assigned community in a network,called modularity density *** measure is illustrated and compared with the standard centrality measures by using respectively an artificial example and a classic network data *** statistical distribution of modularity density centrality is investigated by considering large computer generated graphs and two large networks from the real *** results show the significance of the proposed approach.

关键词： centrality modularity density centrality kernel matrix eigenspectrum

Minimal regular 2-graphs and applications

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science China mathematics 2006年第2期49卷 158-172页

作者： FAN Hongbing, LIU Guizhen & LIU Jiping Department of Physics and computer science, Wilfrid Laurier University, Waterloo, ON., N2L 3C5 Canada School of mathematics and System science, Shandong University, Jinan 250100, China Department of mathematics and computer science, University of Lethbridge, Lethbridge, AB., T1K 3M4, Canada 1. Department of Physics and computer science Wilfrid Laurier University Waterloo ON. N2L 3C5 Canada 2. School of mathematics and System science Shandong University Jinan 250100 China 3. Department of mathematics and computer science University of Lethbridge Lethbridge AB. T1K 3M4 Canada

A 2-graph is a hypergraph with edge sizes of at most two. A regular 2-graph is said to be minimal if it does not contain a proper regular factor. Let f2(n) be the maximum value of degrees over all minimal regular 2-graphs of n vertices. In this paper, we provide a structure property of minimal regular 2-graphs, and consequently, prove that f2(n) = n+3-i/3, where 1 ≤ i ≤ 6, i ≡ n (mod 6) and n ≥ 7, which solves a conjecture posed by Fan, Liu, Wu and Wong. As applications in graph theory, we are able to characterize unfactorable regular graphs and provide the best possible factor existence theorem on degree conditions. Moreover, fa(n) and the minimal 2-graphs can be used in the universal switch box designs, which originally motivated this study.

关键词： graph regular factor 2-graph switch box design.

Adaptive bidirectional diffusion for image restoration

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science China(Information sciences) 2010年第12期53卷 2452-2460页

作者： FU ShuJun 1,2 & ZHANG CaiMing 1 1 School of computer science and Technology, Shandong University, Jinan 250101, China 2 School of mathematics, Shandong University, Jinan 250100, China 1. School of computer science and Technology Shandong University Jinan 250101 China2. School of Mathematics Shandong University Jinan 250100 China

A large number of applications in image processing and computer vision depend on image quality. In this paper, combining the forward diffusion with the backward diffusion by different weights, we present an adaptive bidirectional diffusion method for image denoising and deblurring simultaneously. Further, we introduce a gradient factor into the data fidelity term, which forms a spatially varying constraint and allows a better restoration of image edges and fine details. In order to obtain a stable solution, we develop a numerically stable scheme and give its theoretical analysis. Finally, we show advantages of this method in deblurring edges, denoising and restoring fine details of image compared with other related methods in experiments.

关键词： image restoration bidirectional diffusion inverse diffusion anisotropic diffusion stabilizing scheme spatially varying constraint

Large Solutions to Complex Monge-Ampère Equations: Existence, Uniqueness and Asymptotics

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Chinese Annals of mathematics,Series B 2011年第4期32卷 569-580页

作者： Ni XIANG Xiaoping YANG Faculty of mathematics and computer science Hubei University Wuhan 430000 China School of science Nanjing University of Science and Technology Nanjing 210094 China

The authors consider the complex Monge-Ampere equation det（uij） = ψ（z, u, △↓u） in bounded strictly pseudoconvex domains Ω, subject to the singular boundary condition u =∞ on δΩ. Under suitable conditions on ψ, the existence, uniqueness and the exact asymptotic behavior of solutions Monge-Ampere equations are established to boundary blow-up problems for the complex

关键词： Complex Monge-Ampere equation Boundary blow-up Plurisubharmonic Pseudoconvex Asymptotics

Clustering-based hyperspectral band selection using sparse nonnegative matrix factorization

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Journal of Zhejiang University-science C(computers and Electronics) 2011年第7期12卷 542-549页

作者： Ji-ming LI 1,2,Yun-tao QIAN 1 (1 School of computer science and Technology,Zhejiang University,Hangzhou 310027,China) (2 Zhejiang Police college,Hangzhou 310053,China) School of computer science and Technology Zhejiang University Zhejiang Police college

Hyperspectral imagery generally contains a very large amount of data due to hundreds of spectral *** selection is often applied firstly to reduce computational cost and facilitate subsequent tasks such as land-cover classification and higher level image *** this paper,we propose a new band selection algorithm using sparse nonnegative matrix factorization (sparse NMF).Though acting as a clustering method for band selection,sparse NMF need not consider the distance metric between different spectral bands,which is often the key step for most common clustering-based band selection *** imposing sparsity on the coefficient matrix,the bands' clustering assignments can be easily indicated through the largest entry in each column of the *** results showed that sparse NMF provides considerable insight into the clustering-based band selection problem and the selected bands are good for land-cover classification.

关键词： Hyperspectral Band selection Clustering Sparse nonnegative matrix factorization

Some Properties of Cauchy-Type Singular Integrals in Clifford Analysis

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Journal of Mathematical Research with Applications 2012年第2期32卷 189-200页

作者： Heju YANG 1,2,Yuying QIAO 1,Sha HUANG 1 1.college of mathematics and Information science,Hebei Normal University,Hebei 050016,P.R.China 2.college of science,Hebei University of science and Technology,Hebei 050018,P.R.China college of mathematics and Information science Hebei Normal University Hebei 050016

First,we give a module estimation of the singular integral with a differential *** by proving the existences of Cauchy principal value we obtain the transformation formula of the Cauchy-type singular integrals with a ... 详细信息

关键词： Clifford analysis Cauchy principal value Cauchy-type singular integral with a parameter transformation formula.

Complex variable method for plane elasticity of icosahedral quasicrystals and elliptic notch problem

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science China(Physics,Mechanics & Astronomy) 2008年第7期51卷 773-780页

作者： LI LianHe1,2 & FAN TianYou1 1 Department of Physics, Beijing Institute of Technology, Beijing 100081, China 2.college of mathematics science, Inner Mongolia Normal University, Hohhot 010022, China Department of Physics Beijing Institute of Technology Beijing 100081 China college of mathematics science Inner Mongolia Normal University Hohhot 010022 China

The complex variable method for the plane elasticity theory of icosahedral quasicrystals is developed. Based on the general solution obtained previously, complex representations of stress and displacement components of phonon and phason fields in the quasicrystals are given. With the help of conformal transformation, an analytic solution for the elliptic notch problem of the material is presented. The solution of the Griffith crack problem can be observed as a special case of the results. The stress intensity factor and energy release rate of the crack are also obtained.

关键词： icosahedral quasicrystals plane elasticity elliptic notch complex variable method

Finite automata based on quantum logic and monadic second-order quantum logic

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science China(Information sciences) 2010年第1期53卷 101-114页

作者： LI YongMing college of computer science, Shaanxi Normal University, Xi’an 710062, China 1. college of computer science Shaanxi Normal University Xi’an 710062 China

We introduce monadic second-order quantum logic and prove that the behaviors of finite automata based on quantum logic are precisely the quantum languages definable with sentences of our monadic secondorder quantum logic. This generalizes Büchi’s and Elgot’s fundamental theorems to quantum logic setting. We also consider first-order quantum logic and show that star-free quantum languages and aperiodic quantum languages introduced here coincide with the first-order quantum definable ones. This generalizes Schützenberger’s fundamental theorems to quantum logic setting. The determinazation of finite automata based on quantum logic is studied by introducing the generalized subset construction method. Then the Kleene theorem in the frame of quantum logic is presented here.

关键词： quantum logic finite automaton monadic second quantum logic quantum language quantum computation Kleene theorem