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    A NOTE ON SINGULAR VALUE DECOMPOSITION FOR RADON TRANSFORM IN R^N
    WANG Jin-Ping, DU Jin-Yuan
    Acta mathematica scientia,Series B    2002, 22 (3): 311-318.  
    Abstract656)      PDF(pc) (128KB)(7672)       Save

    The singular value decomposition is derived when the Radon transform is restricted to functions which are square integrable on the unit ball in Rn with respect to the weight W(x). It fulfilles mainly by means of the projection-slice theorem.The range of the Radon transform is spanned by products of Gegenbauer polynomials and spherical harmonics. The inverse transform of the those basis functions are given. This immediately
    leads to an inversion formula by series expansion and range characterizations.

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    EXISTENCE OF SOLUTION FOR A BOUNDARY VALUE PROBLEM OF FRACTIONAL ORDER
    Zhang Shuqin
    Acta mathematica scientia,Series B    DOI: 10.1016/S0252-9602(06)60044-1
    MULTI-DIMENSIONAL GEOMETRIC BROWNIAN MOTIONS, ONSAGER-MACHLUP FUNCTIONS, AND APPLICATIONS TO MATHEMATICAL FINANCE
    胡耀忠
    Acta mathematica scientia,Series B    2000, 20 (3): 341-358.  
    Abstract930)      PDF(pc) (185KB)(3623)       Save

    The solutions of the following bilinear stochastic differential equation are stud-
    ied
    dxt =
    Xm
    k=1
    Ak
    t xtdwk(t) + Btxtdt
    where Ak
    t , Bt are (deterministic) continuous matrix-valued functions of t and w1(t), · · ·,
    wm(t) are m independent standard Brownian motions. Conditions are given such that the
    solution is positive if the initial condition is positive. The equation the most probable path
    must satisfy is also derived and applied to a mathematical finance problem.

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    RIESZ IDEMPOTENT AND BROWDER´S THEOREM FOR ABSOLUTE-(p, r)-PARANORMAL OPERATORS
    Salah Mecheri
    Acta mathematica scientia,Series B    2012, 32 (6): 2259-2264.   DOI: 10.1016/S0252-9602(12)60175-1
    Abstract542)      PDF(pc) (156KB)(3556)       Save

    An operator T is said to be paranormal if ||T2x|| ≥ ||Tx||2 holds for every unit vector x. Several extensions of paranormal operators are considered until now, for example absolute-k-paranormal and p-paranormal introduced in [10], [14], respectively. Yamazaki and Yanagida [38] introduced the class of absolute-(p, r)-paranormal operators as a further generalization of the classes of both absolute-k-paranormal and p-paranormal operators. An operator T ∈B(H) is called absolute-(p, r)-paranormal operator if |||T|p|T*|rx||r ≥ |||T*|rx||p+r for every unit vector x ∈ H and for positive real numbers p > 0 and r > 0. The famous result of Browder, that self adjoint operators satisfy Browder´s theorem, is extended to several classes of operators. In this paper we show that for any absolute-(p, r)-paranormal operator T, T satisfies Browder´s theorem and a-Browder´s theorem. It is also shown that if E is the Riesz idempotent for a nonzero isolated point μ of the spectrum of a absolute-(p, r)-paranormal operator T, then E is self-adjoint if and only if the null space of T μ, N(Tμ)  N(T* − μ).

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    INTERSECTION OF PRIME SUBMODULES AND DIMENSION OF MODULES
    A. Azizi
    Acta mathematica scientia,Series B    2005, 25 (3): 385-394.  
    Abstract799)      PDF(pc) (178KB)(3536)       Save

    The aim of this paper is to study the conditions by which a P-prime sub-
    module can be expressed as a ¯nite intersection or union of P-prime submodules. Also
    corresponding to dimension and rank of modules, some equivalent conditions for a ring to
    be a Dedekind domain are given.

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    GLOBAL DYNAMICS OF AN SEIR EPIDEMIC MODEL WITH IMMIGRATION OF DIFFERENT COMPARTMENTS
    Zhang Juan; Li Jianquan; Ma Zhien
    Acta mathematica scientia,Series B    DOI: 10.1016/S0252-9602(06)60081-7
    FORMATION OF NECROTIC CORES IN THE GROWTH OF TUMORS: ANALYTIC RESULTS
    Cui Shangbin
    Acta mathematica scientia,Series B    DOI: 10.1016/S0252-9602(06)60104-5
    SOLVING SECOND ORDER DIFFERENTIAL EQUATIONS IN QUANTUM MECHANICS BY ORDER REDUCTION
    C. Ted Chen
    Acta mathematica scientia,Series B    2003, 23 (2): 274-.  
    Abstract853)      PDF(pc) (156KB)(2893)       Save

    t Solving the famous Hermite, Legendre, Laguerre and Chebyshev equations
    requires different techniques of unique character for each equation. By reducing these
    differential equations of second order to a common solvable differential equation of first
    order, a simple common solution is provided to cover all the existing standard solutions
    of these named equations. It is easier than the method of generating functions and more
    powerful than the Frobenius method of power series.

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    GLOBAL STABILITY OF AN SIRS EPIDEMIC MODEL WITH DELAYS
    Zhen Jin; Ma Zhien; Han Maoan
    Acta mathematica scientia,Series B    DOI: 10.1016/S0252-9602(06)60051-9
    CONE--DIRECTED CONTINGENT DERIVATIVES AND GENERALIZED PREINVEX SET-VALUED OPTIMIZATION
    Qiu Jinghui
    Acta mathematica scientia,Series B    DOI: 10.1016/S0252-9602(07)60019-8
    COMPRESSIBLE NAVIER-STOKES-POISSON EQUATIONS
    XIAO Ling, LI Hai-Liang
    Acta mathematica scientia,Series B    2010, 30 (6): 1937-1948.   DOI: 10.1016/S0252-9602(10)60184-1
    Abstract1093)      PDF(pc) (192KB)(2578)       Save

    This is a survey paper on the study of compressible Navier-Stokes-Poisson equations. The emphasis is on the long time behavior of global solutions to multi-dimensional compressible Navier-Stokes-Poisson equations, and the optimal decay rates for both unipolar and bipolar compressible Navier-Stokes-Poisson equations are discussed.

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    ON MULTIPLICATION AND COMULTIPLICATION MODULES
    H. Ansari-Toroghy, F. Farshadifar
    Acta mathematica scientia,Series B    2011, 31 (2): 694-700.   DOI: 10.1016/S0252-9602(11)60269-5
    Abstract668)      PDF(pc) (137KB)(2480)       Save

    This article deals with some results concerning multiplication and comultiplication modules over a commutative ring.

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    SOME EULER SPACES OF DIFFERENCE SEQUENCES OF ORDER m
    Harun Polat; Feyzi Basar
    Acta mathematica scientia,Series B    DOI: 10.1016/S0252-9602(07)60024-1
    NONLINEAR EVOLUTION SYSTEMS AND GREEN'S FUNCTION
    WANG Wei-Ke
    Acta mathematica scientia,Series B    2010, 30 (6): 2051-2063.   DOI: 10.1016/S0252-9602(10)60190-7
    Abstract731)      PDF(pc) (202KB)(2390)       Save

    In this paper, we will introduce how to apply Green's function method to get the pointwise estimates for the solutions of Cauchy problem of nonlinear evolution equations with dissipative  structure. First of all, we introduce the pointwise estimates of the time-asymptotic shape of the solutions of the isentropic Navier-Stokes equations and show to exhibit the generalized Huygen's principle. Then, for other nonlinear
    dissipative evolution equations, we will only introduce the result and give some brief explanations. Our approach is based on the detailed analysis of the Green's function of the linearized system and micro-local analysis, such as frequency decomposition and so on.

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    RECURSIVE FORMULA FOR CALCULATING THE
    CHROMATIC POLYNOMIAL OF A GRAPH BY
    VERTEX DELETION
    HU Jin
    Acta mathematica scientia,Series B    2004, 24 (4): 577-582.  
    Abstract608)      PDF(pc) (116KB)(2382)       Save

    new recursive vertex-deleting formula for the computation of the chromatic
    polynomial of a graph is obtained in this paper. This algorithm is not only a good tool for
    further studying chromatic polynomials but also the fastest among all the algorithms for
    the computation of chromatic polynomials.

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    A CHARACTERIZATION OF LOCALLY COMPACT INNER AMENABLE GROUPS
    Ali Ghaffari
    Acta mathematica scientia,Series B    DOI: 10.1016/S0252-9602(08)60061-2
    ON ALMOST PRIME SUBMODULES
    Hani A. Khashan
    Acta mathematica scientia,Series B    2012, 32 (2): 645-651.   DOI: 10.1016/S0252-9602(12)60045-9
    Abstract524)      PDF(pc) (133KB)(2342)       Save

    In this article, we define almost prime submodules as a new generalization of prime and weakly prime submodules of unitary modules over a commutative ring with identity. We study some basic properties of almost prime submodules and give some char-acterizations of them, especially for (finitely generated faithful) multiplication modules.

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    VARIOUS NOTIONS OF ORTHOGONALITY IN NORMED SPACES
    N.B. OKELO, J.O. AGURE, P.O. OLECHE
    Acta mathematica scientia,Series B    2013, 33 (5): 1387-1397.   DOI: 10.1016/S0252-9602(13)60090-9
    Abstract221)      PDF(pc) (191KB)(2331)       Save

    In this paper, we present various notions and aspects of orthogonality in normed spaces. Characterizations and generalizations of orthogonality are also consid-ered. Results on orthogonality of the range and the kernel of elementary operators and the operators implementing them also are given.

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    THE CARBUNCLE PHENOMENON IS INCURABLE
    Volker Elling
    Acta mathematica scientia,Series B    2009, 29 (6): 1647-1656.   DOI: 10.1016/S0252-9602(10)60007-0
    Abstract769)      PDF(pc) (363KB)(2305)       Save

    Numerical approximations of multi-dimensional shock waves sometimes exhibit an instability called the  carbuncle phenomenon.
    Techniques for suppressing carbuncles are trial-and-error and lack in reliability and generality, partly because theoretical knowledge about carbuncles is equally unsatisfactory. It is not known which numerical schemes are affected in which circumstances, what causes carbuncles to appear and whether carbuncles are purely numerical artifacts or rather features of a continuum equation or model.

    This article presents evidence towards the latter: we propose that carbuncles are a special class of entropy solutions which can be physically correct in some circumstances. Using "filaments'', we trigger a single carbuncle in a new and more reliable way, and compute the structure in detail in similarity coordinates. We argue that carbuncles can, in some circumstances, be valid vanishing viscosity limits.
    Trying to suppress them is making a physical assumption that may be false.

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    A COMPARISON OF FORECASTING MODELS OF THE VOLATILITY IN SHENZHEN STOCK MARKET
    Pang Sulin; Deng Feiqi; Wang Yanming
    Acta mathematica scientia,Series B    DOI: 10.1016/S0252-9602(07)60011-3