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    25 July 2009, Volume 2009 Issue 4 Previous Issue    Next Issue
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    Survey on nullity of graphs
    SHU Jin-long ZHAI Ming-qing
    2009, 2009 (4):  1-9. 
    Abstract ( 3102 )   PDF (294KB) ( 1645 )   Save

    This paper gave a review of recent developments in the study of nullities of undirected simple graphs. The problem on nullity is very interesting in characterizing all kinds of properties of graphs as well as in determination of the stability of a molecule in chemistry. The results on bipartite graphs, trees, unicyclic graphs, bicyclic graphs, line graphs of trees were introduced. And the
    graphs with large nullities were discussed.

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    Some sharp lower bounds for energy
    <SPAN lang=EN-US style=
    2009, 2009 (4):  10-15. 
    Abstract ( 2884 )   PDF (156KB) ( 1489 )   Save
    The energy $\mathcal{E}(G)$ of a graph $G$ is the sum of the absolute values of
    all the eigenvalues of the adjacency matrix of $G$. It is used in chemistry to
    approximate the total $\pi$-electron energy of a molecule. This paper presented some new
    lower bounds for $\mathcal{E}(G)$, and characterized those graphs for which these bounds
    were attained.
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    Adjacent vertex-distinguishing edge partition of graphs
    BIAN Xi-yan; MIAO Lian-ying;SHANG Hua-hui DUAN Chun-yan; MA Guo-yi
    2009, 2009 (4):  16-20. 
    Abstract ( 2643 )   PDF (148KB) ( 1424 )   Save
    he minimum number of colors required to give a graph $G$ an adjacent
    vertex-distinguishing edge partition was studied. Based on the classification of the
    degree of a graph, this paper proved that every graph without $K_{2}$ of minimum degree
    at least 188 permits an adjacent vertex-distinguishing 3-edge partition. The result is
    more superior than previous ones.
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    Revised norm-preserving extension theorem
    FANG Mao-zhong{;}
    2009, 2009 (4):  21-25. 
    Abstract ( 2975 )   PDF (146KB) ( 1526 )   Save
    In this paper, the generalized inverse form solution of Davis, Kahan and
    Weinberger’s norm-preserving extension theorem was given. Consequently, Zheng’s result
    (1996) was proved in a more simple way.
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    Note on the convergence of AOR and 2PPJ iterative methods
    LIU Qing-bing$^{;}$; CHEN Guo-liang
    2009, 2009 (4):  26-34. 
    Abstract ( 2919 )   PDF (259KB) ( 1485 )   Save
    This paper analyzed the convergence of preconditioned AOR and 2PPJ iterative
    methods when the coefficient matrix is an $\emph{\textbf{M}}$-matrix, and pointed out
    some errors of known results and established correct convergence theorems. Meanwhile, by
    the $\emph{\textbf{H}}$-splitting theory, the convergence of the preconditioned AOR
    iterative method for the case of the coefficient matrix being an
    $\emph{\textbf{H}}$-matrix was discussed and the convergence interval of parameters was
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    Inverse eigenvalue problem for nonnegative matrices
    SHAN Song-ling
    2009, 2009 (4):  35-38. 
    Abstract ( 2717 )   PDF (199KB) ( 1479 )   Save
    For any given complex number $\lambda$, this paper proved that there exists a
    3 by 3 nonnegative matrix
    \textbf{\emph{A}} with at least 4 zero entries such that $\lambda$ is an eigenvalue of \textbf{\emph{A}}.
    The number 4 of zero entries here is the largest possible.
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    Algebraic method for least squares problems in quaternionic quantum theory
    LING Si-tao$^{;}$; JIANG Tong-song$^$; WEI Mu-sheng$^{;}
    2009, 2009 (4):  39-46. 
    Abstract ( 2824 )   PDF (172KB) ( 1480 )   Save
    This paper introduced concepts of norms of quaternion matrices by means of
    complex representation of a quaternion matrix, studied the quaternionic least squares
    (QLS) problem and derived an algebraic method of finding solutions of the QLS problem in
    quaternionic quantum theory. A numerical example verified the efficiency of the
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    Perturbation analysis for generalized indefinite least squares problems
    WANG Qian
    2009, 2009 (4):  47-53. 
    Abstract ( 2613 )   PDF (173KB) ( 1470 )   Save
    A new kind of weighted generalized inverse was defined to study indefinite
    least squares (ILS) problem and equality constrained indefinite least squares (ILSE)
    problem. By applying hyperbolic-QR factorization, the solutions to the two problems were
    obtained. Also the perturbation bounds of the solutions were derived.
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    Tests for functional-coefficient parts on semiparametric varying-coefficient partially linear models
    HUANG Zhen-sheng
    2009, 2009 (4):  54-61. 
    Abstract ( 2621 )   PDF (428KB) ( 1398 )   Save
    Based on the quasi-likelihood estimates obtained by the
    local linear method,~the generalized likelihood ratio tests for the
    models were established.~Under the null hypothesis the test
    statistic followed asymptotically the $\chi^{2}$-distribution with
    the scale constants and the degree of freedom being independent of
    the nuisance parameters and the nuisance functions,~which was called
    the Wilks phenomenon.~A simulated example was presented to
    illustrate the proposed methods.
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    Precise large deviation for sums of negatively associated \\[5pt]heavy-tailed random variables in $\mathcal{D}\cap\mathcal{L
    WANG Shi-jie $^{;}$;WANG Wen-sheng$^
    2009, 2009 (4):  62-68. 
    Abstract ( 2976 )   PDF (250KB) ( 1469 )   Save
    By using the characterization of heavy-tailed random variables in
    $\mathcal{D}\cap\mathcal{L}$, precise large
    deviations for sums (nonrandom sums and random sums) of negatively associated
    heavy-tailed random variables in $\mathcal{D}\cap\mathcal{L}$ were obtained, where the
    subclass $\mathcal{D}\cap\mathcal{L}$ strictly contains $\mathcal{C}$. Therefore, it
    firstly extends some existed precise large deviation results to some larger subclasses
    of heavy tailed distributions.
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    Robin problem for a class of semilinear singularly\\[5pt] perturbed ODE systems
    TONG Ai-hua
    2009, 2009 (4):  69-77. 
    Abstract ( 2984 )   PDF (272KB) ( 1201 )   Save
    The method of boundary function was used to construct uniformly valid
    asymptotic solutions of the Robin problem of a class of semilinear singularly perturbed
    equations, which are often used as models for chemical reactions. At the same time the
    existence and uniqueness of the solution and the estimation of the remainder for the
    problem were given.
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    Solutions to a linear wave equation with nonlinear\\[5pt] boundary conditions
    WANG Li-hua;
    2009, 2009 (4):  78-81. 
    Abstract ( 2569 )   PDF (208KB) ( 1327 )   Save

    This paper was concerned with a one-dimensional linear wave equation
    associated with nonlinear boundary conditions. The unique local solution to the wave
    equation was proved to exist. The result is that the nonlinearity at the boundary causes
    a finite time blow up of the solution, even for small initial data. And the upper bound
    to the blow up time is given in the paper

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    On cohomology of modular Lie superalgebras
    ZHENG Li-sun
    2009, 2009 (4):  82-91. 
    Abstract ( 2604 )   PDF (187KB) ( 1434 )   Save
    A result on vanishing cohomology for finite-dimensional modular Lie
    superalgebras was obtained, with aid of the approach provided by Dzhumadil’daev for
    modular Lie algebras. Some examples are given as demonstration of the vanishing result,
    as well as its applications.
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    Improved KMP algorithm
    YU Song;ZHENG Jun;HU Wenxin
    2009, 2009 (4):  92-97. 
    Abstract ( 3614 )   PDF (560KB) ( 1724 )   Save
    This paper established an improved KMPalgorithm for pattern matching in string. Tests proved that the algorithm has less comparison times and higher efficiency under the circumstances that the pattern first appears in the bottom half of a text string.
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    Evaluation scheme based on traffic flow forONU place in urban road WOBAN
    CHEN Lei;WANG Neng
    2009, 2009 (4):  98-106. 
    Abstract ( 2664 )   PDF (1399KB) ( 1382 )   Save
    A new idea to bring broadband service to vehicles by WOBAN (hybrid WirelessOptical BroadbandAccess Network) was presented and a working model of an urban road WOBAN was given. Considering traffic flow as a key factor for the optimal ONU (Optical Network Unit) placement in urban road WOBAN, a scheme to characterize urban road features based on traffic flow was proposed and four examined spot types were defined. Furthermore, we compared two place evaluation strategies. 
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    Fuzzy control based DCA algorithm
    ZHANG Hui;YI Fasheng
    2009, 2009 (4):  107-114. 
    Abstract ( 2412 )   PDF (957KB) ( 1426 )   Save
    TCP employs delaybased congestion avoidance (DCA) algorithms to improve the throughput of network system. However, there are many factors to affect the DCA algorithm efficiency. In order to solve these problems, a fuzzy control based DCA algorithms (FDCA) was proposed to reduce the influences of the factors. The simulations show that the algorithm provides more accurate and timely indication of network congestion, and increases network throughput.
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    Realization of lowcost true 3D volumetric display system
    TIAN Feng;;XU Jieming;LIU Jingao
    2009, 2009 (4):  115-123. 
    Abstract ( 2814 )   PDF (4815KB) ( 1631 )   Save
    By analysis of existed proposals for true 3D volumetric displays based on rotation, the visual voxel display technology was explained. In order to overcome limitations and shortcomings of current rotation proposals, a new highspeed display interface based on ARMCortexM3 was raised. Using its high speed bandwidth, equality of voxel volume and voxel brightness was realized. Finally horizontal 360°,vertical visual 180° visual angle range and high brightness display effect is obtained.
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    Electrical conductivity of polyphenylacetylene doped by bromine vapor
    LIANG Dan;HAN Feifei;WANG Hongmin;TANG Guoqiang YE Jing;WU Lingjuan;XU Xuecheng
    2009, 2009 (4):  124-130. 
    Abstract ( 2948 )   PDF (1383KB) ( 1830 )   Save
    Through absorption of bromine vapor, the electrical conductivity of Polyphenylacetylene (PPA) enhanced by 1012 times. After pressing the bromine doped powder sample into pellet, we found that the conductivity of the samples increased with time. UVVis spectra, IR, and XPS spectra indicated that strong conjugation effect exists between PPA and bromine, and Charge Transfer Complex (CTC) is formed in PPA after doping; bromine doping increases the conjugation of PPA and improves its conductivity; the pressure can promote the doping effect of bromine on PPA.
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    Structure and magnetic properties of (Fe1-x Nx)4Nfrom First Principles
    BAO Mingli;XIE Wenhui;ZHAO Zhenjie
    2009, 2009 (4):  131-136. 
    Abstract ( 2607 )   PDF (651KB) ( 1515 )   Save
    The structural and magnetic properties of the antiperovskite (Fe1-x Nx)4N compounds were investigated by employing a full potential linearized augmented plane wave method (FPLAPW).The dependence of lattice constants on the content of Ni was calculated.The calculated results of total energy imply that Ni prefers to occupy the corner sites rather than the facecenter sites.The investigation of the dependence of the binding energy of (Fe1-x Nx)4N on the Ni content indicates that the stabilization of ( (Fe1-x Nx)4N increases firstly and then decreases. The compound reaches the most stabilization at x=0.25.After x>0.75, it becomes unstable, which is agreed with the result of experiment very well.The effects of different exchange correlation potentials on the magnetic moment were discussed.
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