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    2006年, 第26卷, 第4期 刊出日期:2006-10-20 上一期    下一期
    本期栏目: 论文 
    论文
    INDEPENDENT-SET-DELETABLE FACTOR-CRITICAL POWER GRAPHS
    原晋江
    数学物理学报(英文版). 2006 (4):  577-584.  DOI: 10.1016/S0252-9602(06)60083-0
    摘要 ( 1662 )   RICH HTML PDF(135KB) ( 1619 )   收藏

    It is said that a graph G is independent-set-deletable factor-critical (in short, ID-factor-critical), if, for every independent set I which has the same parity as |V(G)|, G-I has a perfect matching. A graph G is strongly IM-extendable, if for every spanning supergraph H of G, every induced matching of H is included in a perfect matching of H. The k-th power of G, denoted by Gk, is the graph with vertex set V(G) in which two vertices are adjacent if and only if they have distance at most k in G. ID-factor-criticality and IM-extendability of power graphs are discussed
    in this article. The author shows that, if G is a connected graph, then G3 and T(G) (the total graph of G) are ID-factor-critical, and G4 (when |V(G)| is even) is strongly IM-extendable; if G is 2-connected, then D2 is ID-factor-critical.

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    A KERNEL-TYPE ESTIMATOR OF A QUANTILE FUNCTION UNDER RANDOMLY#br# TRUNCATED DATA
    周勇; 吴国富; 李道纪
    数学物理学报(英文版). 2006 (4):  585-594.  DOI: 10.1016/S0252-9602(06)60084-2
    摘要 ( 1642 )   RICH HTML PDF(153KB) ( 1907 )   收藏

    A kernel-type estimator of the quantile function Q(p)=inf{t:F(t)≥p}, 0≤p≤1, is proposed based on the kernel smoother when the data are subjected to random truncation. The Bahadur-type representations of the kernel smooth estimator are established, and from Bahadur representations the authors can show that this estimator is strongly consistent, asymptotically normal, and weakly convergent.

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    A CASE STUDY IN THE APPLICATION OF SUPERSATURATED DESIGNS TO COMPUTER EXPERIMENTS
    刘民千; 方开泰
    数学物理学报(英文版). 2006 (4):  595-602.  DOI: 10.1016/S0252-9602(06)60085-4
    摘要 ( 1989 )   RICH HTML PDF(164KB) ( 2076 )   收藏

    Supersaturated design is essentially a fractional factorial design in which the number of potential effects is greater than the number of runs. In this article, the supersaturated design is applied to a computer experiment through an example of steady current circuit model problem. A uniform mixed-level supersaturated design and the centered quadratic regression model are used.
    This example shows that supersaturated design and quadratic regression modeling method are very effective for screening effects and building the predictor. They are not only useful in computer experiments but also in industrial and other scientific experiments.

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    THE ASYMPTOTIC PROPERTIES OF SUPERCRITICAL BISEXUAL GALTON-WATSON BRANCHING PROCESSES WITH IMMIGRATION OF MATING UNITS
    马世霞; 邢永胜
    数学物理学报(英文版). 2006 (4):  603-609.  DOI: 10.1016/S0252-9602(06)60086-6
    摘要 ( 1594 )   RICH HTML PDF(129KB) ( 1793 )   收藏

    In this article the supercritical bisexual Galton--Watson branching processes with the immigration of mating units is considered. A necessary condition for the almost sure convergence, and a sufficient condition for the L1 convergence are given for the process with the suitably normed condition.

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    ON THE ESTIMATION OF GENERALIZED LEBESGUE CONSTANT AND MODULUS OF GENERALIZED SINGULAR QUADRATURE FORMULAS AND ITS APPLICATION
    蔡好涛; 杜金元
    数学物理学报(英文版). 2006 (4):  610-614.  DOI: 10.1016/S0252-9602(06)60087-8
    摘要 ( 1216 )   RICH HTML PDF(120KB) ( 945 )   收藏

    This article, first gives the estimaties of two modulus, namely, generalized Lebesgue constant and modulus of generalized singular integral quadrature formulas, then applies them to obtain the error bounds of the operator BLmp to the operator B.

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    THE DIMENSIONS OF THE RANGE OF RANDOM WALKS IN TIME-RANDOM ENVIRONMENTS
    张晓敏; 胡迪鹤
    数学物理学报(英文版). 2006 (4):  615-628.  DOI: 10.1016/S0252-9602(06)60088-X
    摘要 ( 1552 )   RICH HTML PDF(190KB) ( 964 )   收藏

    Suppose {Xn} is a random walk in time-random environment with state space Zd, |Xn| approaches infinity, then under some reasonable conditions of stability, the upper bound of the discrete Packing dimension of the range of {Xn} is any stability index α. Moreover, if the environment is stationary, a similar result for the lower bound of the discrete Hausdorff dimension is derived. Thus, the range is a fractal set for almost every environment.

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    LOWER HEDGING OF CONTINGENT CLAIMS IN RANDOMLY CONSTRAINED MARKETS
    陈典发; 冯建芬
    数学物理学报(英文版). 2006 (4):  629-638.  DOI: 10.1016/S0252-9602(06)60089-1
    摘要 ( 1066 )   RICH HTML PDF(149KB) ( 911 )   收藏

    This article studies European contingent claims in a randomly constrained market and derives their lower-hedging costs by means of a family of auxiliary risk premiums.

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    AN ESTIMATE ON THE DISTRIBUTION AND MOMENTS OF THE LAST EXIT TIME OF AN ELLIPTIC DIFFUSION PROCESS
    李波; 刘禄勤
    数学物理学报(英文版). 2006 (4):  639-645.  DOI: 10.1016/S0252-9602(06)60090-8
    摘要 ( 1212 )   RICH HTML PDF(132KB) ( 1784 )   收藏

    Let LB be the last exit time from a compact set B of an elliptic diffusion process X. A moderate estimate for the distribution of LB is obtained, and the sufficient and necessary condition for Ex (LBk)<[infinty] is proved.

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    GEOMETRIC OPTICS FOR 3D-HARTREE-TYPE EQUATION WITH COULOMB POTENTIAL
    陈琼蕾; 章志飞
    数学物理学报(英文版). 2006 (4):  646-654.  DOI: 10.1016/S0252-9602(06)60091-X
    摘要 ( 1253 )   RICH HTML PDF(150KB) ( 1000 )   收藏

    This article considers a family of 3D-Hartree-type equation with Coulomb potential |x|-1, whose initial data oscillates so that a caustic appears. In the linear geometric optics case, by using the Lagrangian integrals, a uniform description of the solution outside the caustic, and near the caustic are obtained.

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    DISRUPTION MANAGEMENT FOR SUPPLY CHAIN COORDINATION WITH EXPONENTIAL DEMAND FUNCTION
    黄崇超; 于刚; 汪嵩; 王先甲
    数学物理学报(英文版). 2006 (4):  655-669.  DOI: 10.1016/S0252-9602(06)60092-1
    摘要 ( 1143 )   RICH HTML PDF(175KB) ( 2146 )   收藏

    The coordination problem of a supply chain comprising one supplier and one retailer under market demand disruption is studied in this article. A novel exponential demand function is adopted, and the penalty cost is introduced explicitly to capture the deviation production cost caused by the market demand disruption. The optimal strategies are obtained for different disruption scale under the centralized mode. For the decentralized mode, it is proved that the supply chain can be fully coordinated by adjusting the price discount policy appropriately when disruption occurs. Furthermore, the authors point out that similar results can be established for more general demand functions that represent different market circumstances if certain
    assumptions are satisfied.

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    POSITIVE EQUILIBRIUM SOLUTIONS OF SEMILINEAR PARABOLIC EQUATIONS
    娄本东
    数学物理学报(英文版). 2006 (4):  670-678.  DOI: 10.1016/S0252-9602(06)60093-3
    摘要 ( 1477 )   RICH HTML PDF(191KB) ( 1095 )   收藏

    The author studies semilinear parabolic equations with initial and periodic boundary value conditions. In the presence of non-well-ordered sub- and
    super-solutions: ``subsolution ≮ supersolution", the existence and stability/instability of equilibrium solutions are obtained.

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    THE PERMUTATION FORMULA OF SINGULAR INTEGRALS WITH BOCHNER-MARTINELLI KERNEL ON STEIN MANIFOLDS
    钟同德; 陈吕萍
    数学物理学报(英文版). 2006 (4):  679-690.  DOI: 10.1016/S0252-9602(06)60094-5
    摘要 ( 1512 )   RICH HTML PDF(160KB) ( 1336 )   收藏

    Using the method of localization, the authors obtain the permutation formula of singular integrals with Bochner-Martinelli kernel for a relative compact domain with C(1) smooth boundary on a Stein manifold. As an application the authors discuss the regularization problem for linear singular integral equations with Bochner--Martinelli kernel and variable coefficients; using permutation formula, the singular integral equation can be reduced to a fredholm equation.

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    MODERATE DEVIATIONS FROM HYDRODYNAMIC LIMIT OF A GINZBURG-LANDAU MODEL
    王霞; 高付清
    数学物理学报(英文版). 2006 (4):  691-701.  DOI: 10.1016/S0252-9602(06)60095-7
    摘要 ( 1114 )   RICH HTML PDF(159KB) ( 1058 )   收藏

    The authors consider the moderate deviations of hydrodynamic limit for
    Ginzburg-Landau models. The moderate deviation principle of hydrodynamic limit for a specific Ginzburg--Landau model is obtained and an explicit formula of the rate function is derived.

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    ON THE SINGULAR DIRECTIONS OF VALUE DISTRIBUTION OF HOLOMORPHIC CURVES IN Pn(C)
    涂振汉; 李平丽
    数学物理学报(英文版). 2006 (4):  702-710.  DOI: 10.1016/S0252-9602(06)60096-9
    摘要 ( 1257 )   RICH HTML PDF(147KB) ( 1148 )   收藏

    This article proves the existence of singular directions of value distribution theory for some transcendental holomorphic curves in the n-dimensional complex projective space Pn(C). An example is given to complement these results.

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    THE HOMOTHETIC MOTIONS IN THE LORENTZ 3-SPACE
    M. Tosun; A. Kucuk; M.A. Gungor
    数学物理学报(英文版). 2006 (4):  711-719.  DOI: 10.1016/S0252-9602(06)60097-0
    摘要 ( 1346 )   RICH HTML PDF(137KB) ( 1898 )   收藏

    In this article, the properties of the homothetic motions in three-dimensional Lorentz space are investigated. Also, some geometric results between velocity and acceleration vectors of a point in a spatial motion are obtained.

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    RELATIVE WIDTH OF SMOOTH CLASSES OF MULTIVARIATE PERIODIC FUNCTIONS WITH RESTRICTIONS ON ITERATED LAPLACE DERIVATIVES IN THE L2-METRIC
    刘永平; 杨连红
    数学物理学报(英文版). 2006 (4):  720-728.  DOI: 10.1016/S0252-9602(06)60098-2
    摘要 ( 1014 )   RICH HTML PDF(162KB) ( 1258 )   收藏

    For two subsets W and V of a Banach space X, let Kn(W,V,X) denote the relative Kolmogorov n-width of W relative to V defined by

    Kn(W,V,X):= infLn supf∈W inf g∈ V∩ Ln || f-g||X,
    where the infimum is taken over all n-dimensional linear subspaces Ln of X. Let W2(△r) denote the class of 2π-periodic functions f with d-variables satisfying
    [-π,π]d |△r f(x)|2,dx≤ 1,
    while △r is the r-iterate of Laplace operator △. This article discusses the relative Kolmogorov n-width of W2(△r)$ relative to W2(△r) in Lq([-π,π]d),(1≤ q≤∞), and obtain its weak asymptotic result.

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    SECOND-ORDER OPTIMALITY CONDITIONS FOR OPTIMAL CONTROL PROBLEMS GOVERNED BY 3-DIMENSIONAL NEVIER--STOKES EQUATIONS
    王丽娟; 何培杰
    数学物理学报(英文版). 2006 (4):  729-734.  DOI: 10.1016/S0252-9602(06)60099-4
    摘要 ( 1198 )   RICH HTML PDF(121KB) ( 1265 )   收藏

    This article is concerned with second-order necessary and sufficient optimality conditions for optimal control problems governed by 3-dimensional Navier--Stokes equations. The periodic state constraint is considered.

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    QUANTUM COHOMOLOGY OF BLOWUPS OF SURFACES AND ITS FUNCTORIALITY PROPERTY
    胡建勋
    数学物理学报(英文版). 2006 (4):  735-743.  DOI: 10.1016/S0252-9602(06)60100-8
    摘要 ( 1021 )   RICH HTML PDF(162KB) ( 1244 )   收藏

    In this article, using the WDVV equation, the author first proves that all
    Gromov-Witten invariants of blowups of surfaces can be computed from the Gromov--Witten invariants of itself by some recursive relations. Furthermore, it may determine the quantum product on blowups. It also proves that there is some degree of functoriality of the big quantum cohomology for a blowup.

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    MATHEMATICAL RESULTS RELATED TO A TWO-DIMENSIONAL MAGNETO-HYDRODYNAMIC EQUATIONS
    酒全森; 牛冬娟
    数学物理学报(英文版). 2006 (4):  744-756.  DOI: 10.1016/S0252-9602(06)60101-X
    摘要 ( 1582 )   RICH HTML PDF(170KB) ( 1887 )   收藏

    The two-dimensional magneto-hydrodynamic (MHD) equations are considered in this article. Viscous approximations are used to obtain the local existence and uniqueness of the classical solution. When the viscous term vanishes, the convergence rates, a main problem in turbulence, are also discussed. Moreover, a blow-up criterion for our classical solution is established in terms of the magnetic fields.

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    AN IMPROVED SEARCH-EXTENTION METHOD FOR SOLVING SEMILINEAR PDES
    谢资清; 陈传淼; 徐云
    数学物理学报(英文版). 2006 (4):  757-766.  DOI: 10.1016/S0252-9602(06)60102-1
    摘要 ( 1390 )   RICH HTML PDF(475KB) ( 1364 )   收藏

    This article will combine the finite element method, the interpolated coefficient finite element method, the eigenfunction expansion method, and the search-extension method to obtain the multiple solutions for semilinear elliptic equations. This strategy not only grently reduces the expensive computation,
    but also is successfully implemented to obtain multiple solutions for a class of semilinear elliptic boundary value problems with non-odd nonlinearity on some convex or nonconvex domains. Numerical solutions illustrated by their graphics for visualization will show the efficiency of the approach.

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    SOME RESULTS ON HYPERBOLIC SYSTEMS WITH RELAXATION
    伍锦棠; 郑永树
    数学物理学报(英文版). 2006 (4):  767-780.  DOI: 10.1016/S0252-9602(06)60103-3
    摘要 ( 1211 )   RICH HTML PDF(181KB) ( 1278 )   收藏

    In this article, first, the authors prove that there exists a unique global smooth solution for the Cauthy problem to the hyperbolic conservation laws systems with relaxation; second, in the large time station, they prove that the global smooth solutions of the hyperbolic conservation laws systems with relaxation converge to rarefaction waves solution at a determined Lp (p[gteq]2) decay rate.

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    FORMATION OF NECROTIC CORES IN THE GROWTH OF TUMORS: ANALYTIC RESULTS
    崔尚斌
    数学物理学报(英文版). 2006 (4):  781-796.  DOI: 10.1016/S0252-9602(06)60104-5
    摘要 ( 1481 )   RICH HTML PDF(179KB) ( 3239 )   收藏

    In this article, the author studies the mechanism of formation of necrotic cores in the growth of tumors by using rigorous analysis of a mathematical model.
    The model modifies a corresponding tumor growth model proposed by Byrne
    and Chaplain in 1996, in the case where no inhibitors exist. The modification is made such that both necrotic tumors and nonnecrotic tumors can be nonsidered in a joint way. It is proved that if the nutrient supply is below a threshold value, then there is not dormant tumor, and all evolutionary tumors will finally vanish. If instead the nutrient supply is above this threshold value then there is a unique dormant tumor which can either be necrotic or nonnecrotic, depending on the level of the nutrient supply and the level of dead-cell dissolution rate, and all evolutionary tumors will converge to this dormant tumor. It is also proved that, in the second case, if the dormant tumor is necrotic then an evolutionary tumor will form a necrotic core at a finite time, and if the dormant tumor is nonnecrotic then an evolutionary tumor will also be nonnecrotic from a finite time.

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