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    2008年, 第28卷, 第4期 刊出日期:2008-10-20 上一期    下一期
    本期栏目: 论文 
    论文
    SOME REMARKS ON HOLOMORPHIC FUNCTIONS AND TAYLOR SERIES IN Cn
    余家荣
    数学物理学报(英文版). 2008 (4):  721-726.  DOI: 10.1016/S0252-9602(08)60073-9
    摘要 ( 932 )   RICH HTML PDF(137KB) ( 1450 )   收藏

    Some previous results on convergence of Taylor series in Cn [3] are improved by indicating outside the domain of convergence the points where the series diverges and simplifying some proofs. These results contain the Cauchy--Hadamard theorem in C. Some Cauchy integral formulas of a holomorphic function on a closed ball in Cn are constructed and the Taylor series expansion is deduced.

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    ZERO DISSIPATION LIMIT OF THE COMPRESSIBLE HEAT-CONDUCTING NAVIER-STOKES EQUATIONS IN THE PRESENCE OF THE SHOCK
    王益
    数学物理学报(英文版). 2008 (4):  727-748.  DOI: 10.1016/S0252-9602(08)60074-0
    摘要 ( 934 )   RICH HTML PDF(246KB) ( 1567 )   收藏

    The zero dissipation limit of the compressible heat-conducting Navier--Stokes equations in the presence of the shock is investigated. It is shown that when the heat conduction coefficient κ and the viscosity coefficient ε satisfy κ=O(ε), κ/ε ≥ c > 0, as ε → 0 (see (1.3)), if the solution of the corresponding Euler equations is piecewise smooth with shock wave satisfying the Lax entropy condition, then there exists a smooth solution to the Navier--Stokes equations, which converges to the piecewise smooth shock solution of the Euler equations away from the shock discontinuity at a rate of ε. The proof is given by a combination of the energy estimates and the matched asymptotic analysis introduced in [3].

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    LOWER BOUNDS FOR SUP+INF AND SUP*INF AND AN EXTENSION OF CHEN-LIN RESULT IN DIMENSION 3
    Samy Skander Bahoura
    数学物理学报(英文版). 2008 (4):  749-758.  DOI: 10.1016/S0252-9602(08)60075-2
    摘要 ( 932 )   RICH HTML PDF(180KB) ( 1295 )   收藏

    We give two results about Harnack type inequalities. First, on Riemannian surfaces, we have an estimate of type sup +inf. The second result concern the solutions of prescribed scalar curvature equation on the unit ball of Rn with Dirichlet condition.
    Next, we give an inequality of type (supKu)2s-1× inf

    Ωuc for positive solutions of △u=Vu5 on
    Ω ∈R3 , where K is a compact set of Ω and V is s-Hölderian, s ∈]-1/2,1] . For the case s=1/2 and Ω= S3, we prove that, if minΩu > m > 0 (for some particular constant m > 0), and the Hölderian constant A of V tends to 0 (in certain meaning), we have the uniform boundedness of the supremum of the solutions of the previous equation on any compact set of Ω.
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    THE NORMAL FAMILITY OF MERMORPHIC FUNCTIONS
    韩明华; 顾永兴
    数学物理学报(英文版). 2008 (4):  759-762.  DOI: 10.1016/S0252-9602(08)60076-4
    摘要 ( 883 )   RICH HTML PDF(121KB) ( 1344 )   收藏
    Let F be a family of mermorphic functions in a domain D, and let a, b, c be complex numbers, ab. If for each f F, the zeros of f-c are of multiplicity ≥ k+1, and Ef(k)(a) ∈Ef(a), Ef(k)(b) ∈ Ef(b), then F is normal in D.
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    AN OPERATORIAL APPROACH TO SINGULAR INTEGRAL EQUATIONS 0F A MODIFIED TYPE
    贺福利; 杜金元
    数学物理学报(英文版). 2008 (4):  763-769.  DOI: 10.1016/S0252-9602(08)60077-6
    摘要 ( 978 )   RICH HTML PDF(140KB) ( 903 )   收藏

    In this article, the authors discuss a kind of modified singular integral quations on a disjoint union of closed contours or a disjoint union of open arcs. The authors introduce some singular integral operators associated with this kind of singular integral equations, and obtain some useful properties for them. An operatorial approach is also given together with some illustrated examples.

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    A RELAXATION RESULT OF FUNCTIONALS IN THE SPACE SBD(Ω)
    吕中学; 杨孝平
    数学物理学报(英文版). 2008 (4):  770-778.  DOI: 10.1016/S0252-9602(08)60078-8
    摘要 ( 884 )   RICH HTML PDF(182KB) ( 899 )   收藏

    In this article, the authors obtain an integral representation for the relaxation of the functional F(x, u, Ω):={∫Ω f(x, u(x), εu(x))dx if u W1, 1(Ω, RN), +∞ otherwise,
    in the space of functions of bounded deformation, with respect to L1-convergence. Here εu represents the absolutely continuous part of the symmetrized distributional derivative εu.f(x, p, ξ) satisfying weak convexity assumption.

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    INTERSECTIONS AND POLAR FUNCTIONS OF FRACTIONAL BROWNIAN SHEETS
    陈振龙
    数学物理学报(英文版). 2008 (4):  779-796.  DOI: 10.1016/S0252-9602(08)60079-X
    摘要 ( 870 )   RICH HTML PDF(234KB) ( 1239 )   收藏

    Let BH={BH(t), t ∈ R+N} be a real-valued (N, d) fractional Brownian sheet with Hurst index H=(H1, …, HN). The characteristics of the polar functions for BH are discussed. The relationship between the class of continuous functions satisfying Lipschitz condition and the class of polar -functions of BH is obtained. The Hausdorff dimension about the fixed points and the inequality about the Kolmogorov’s entropy index for BH are presented. Furthermore, it is proved that any two independent fractional Brownian sheets are nonintersecting in some conditions. A problem proposed by LeGall about the existence of no-polar continuous functions satisfying the Hölder condition is also solved.

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    A SHORT NOTE ABOUT EXPOSED POINTS IN REAL BANACH SPACES
    Antonio Aizpuru; Francisco J Garc
    数学物理学报(英文版). 2008 (4):  797-800.  DOI: 10.1016/S0252-9602(08)60080-6
    摘要 ( 788 )   RICH HTML PDF(126KB) ( 1979 )   收藏

    We express the set of exposed points in terms of rotund points and non-smooth points. As long as we have Banach spaces each time "bigger", we consider sets of non-smooth points each time "smaller".

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    COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY, VACUUM AND GRAVITATIONAL FORCE IN THE CASE OF GENERAL PRESSURE
    姚磊; 汪文军
    数学物理学报(英文版). 2008 (4):  801-817.  DOI: 10.1016/S0252-9602(08)60081-8
    摘要 ( 1201 )   RICH HTML PDF(198KB) ( 1281 )   收藏

    This is a continuation of the article (Comm. Partial Differential Equations 26 (2001) 965). In this article, the authors consider the one-dimensional compressible isentropic Navier--Stokes equations with gravitational force, fixed boundary condition, a general pressure and the density-dependent viscosity coefficient when the viscous gas connects to vacuum state with a jump in density. Precisely, the viscosity coefficient μ is proportional to ρθ and 0 < θ < 1/2, where ρ is the density, and the pressure P=P(ρ) is a general pressure. The global existence and the uniqueness of weak solution are proved.

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    SUPPORTING AND SEPARATING SUBSETS FOR INVEX BODIES
    H.K. El-Sayied
    数学物理学报(英文版). 2008 (4):  818-822.  DOI: 10.1016/S0252-9602(08)60082-X
    摘要 ( 742 )   RICH HTML PDF(200KB) ( 996 )   收藏

    Invex bodies represent an important class of bodies which are considered as a generalization of convex bodies. In this article, the author studies the supporting for this class of bodies as well as the separating subsets of two bodies.

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    A NOTE ON KLEIN-GORDON-SCHRöDINGER EQUATIONS WITH HOMOGENEOUS DIRICHLET BOUNDARY CONDITION
    赵才地; 周盛凡; 李用声
    数学物理学报(英文版). 2008 (4):  823-833.  DOI: 10.1016/S0252-9602(08)60083-1
    摘要 ( 1033 )   RICH HTML PDF(175KB) ( 1288 )   收藏

    This note discusses the long time behavior of solutions for nonautonomous weakly dissipative Klein-Gordon-Schrödinger equations with homogeneous Dirichlet boundary condition. The authors prove the existence of compact kernel sections for the associated process by using a suitable decomposition of the equations.

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    A GLOBALLY UNIFORM ASYMPTOTIC EXPANSION OF THE HERMITE POLYNOMIALS
    史薇
    数学物理学报(英文版). 2008 (4):  834-842.  DOI: 10.1016/S0252-9602(08)60084-3
    摘要 ( 902 )   RICH HTML PDF(210KB) ( 1649 )   收藏

    In this article, the author extends the validity of a uniform asymptotic expansion of the Hermite polynomials Hn(2n+1α) to include all positive values of α. His method makes use of the rational functions introduced by Olde Daalhuis and Temme (SIAM J. Math. Anal., (1994), 25: 304-321). A new estimate for the remainder is given.

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    THE TANGENT CONES ON CONSTRAINT QUALIFICATIONS IN OPTIMIZATION PROBLEMS
    黄龙光
    数学物理学报(英文版). 2008 (4):  843-850.  DOI: 10.1016/S0252-9602(08)60085-5
    摘要 ( 830 )   RICH HTML PDF(141KB) ( 1866 )   收藏

    This article proposes a few tangent cones, which are relative to the constraint qualifications of optimization problems. With the upper and lower directional derivatives of an objective function, the characteristics of cones on the constraint qualifications are presented. The interrelations among the constraint qualifications, a few cones involved, and level sets of upper and lower directional derivatives are derived.

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    MULTIPLE POSITIVE SOLUTIONS BOUNDARY VALUE PROBLEMS FOR SUPERLINEAR SECOND ORDER SINGULAR WITH DERIVATIVE DEPENDENCE
    闫宝强
    数学物理学报(英文版). 2008 (4):  851-864.  DOI: 10.1016/S0252-9602(08)60086-7
    摘要 ( 911 )   RICH HTML PDF(191KB) ( 1084 )   收藏

    The existence of at least two positive solutions is presented for the singular second-order boundary value problem

    {(p(t)/1 (p(t)x’(t))′+Φ(t)f(t, x(t), p(t)x′(t))=0, 0 <t <1,

    limt→0 p(t)x′(t)=0, x(1)=0.
    by using the fixed point index, where f may be singular at x=0 and px’=0.

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    LIMIT CYCLES AND INVARIANT PARABOLA IN A KUKLES SYSTEM OF DEGREE THREE
    刘振海; E. Sáez; I. Szántó
    数学物理学报(英文版). 2008 (4):  865-869.  DOI: 10.1016/S0252-9602(08)60087-9
    摘要 ( 850 )   RICH HTML PDF(124KB) ( 1285 )   收藏

    In this article, the authors consider a class of Kukles planar polynomial differential system of degree three having an invariant parabola. For this class of second-order differential systems, it is shown that for certain values of the
    parameters the invariant parabola coexists with a center. For other values it can coexist with one, two or three small amplitude limit cycles which are constructed by Hopf bifurcation. This result gives an answer for the question given in [4], about the existence of limit cycles for such class of system.

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    SYMMETRIES IN YETTER-DRINFELD CATEGORIES OVER WEAK HOPF ALGEBRAS
    高楠
    数学物理学报(英文版). 2008 (4):  870-876.  DOI: 10.1016/S0252-9602(08)60088-0
    摘要 ( 824 )   RICH HTML PDF(137KB) ( 1115 )   收藏

    This article is devoted to the study of the symmetry in the Yetter-Drinfeld category of a finite-dimensional weak Hopf algebra.It generalizes the corresponding results in Hopf algebras.

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    PARTIAL REGULARITY FOR WEAK SOLUTIONS OF STATIONARY NAVIER-STOKES SYSTEMS
    陈淑红; 谭忠
    数学物理学报(英文版). 2008 (4):  877-894.  DOI: 10.1016/S0252-9602(08)60089-2
    摘要 ( 762 )   RICH HTML PDF(221KB) ( 1460 )   收藏

    This article is concerned with the partial regularity for the weak solutions
    of stationary Navier-Stokes system under the controllable growth condition. By A-harmonic approximation technique, the optimal regularity is obtained.

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    THE UNIFORMLY BOUNDEDNESS OF THE RIESZ TRANSFORMS ON THE CAYLEY HEISENBERG GROUPS
    栾静闻; 朱赋鎏
    数学物理学报(英文版). 2008 (4):  895-914.  DOI: 10.1016/S0252-9602(08)60090-9
    摘要 ( 931 )   RICH HTML PDF(221KB) ( 948 )   收藏

    In this article, the authors estimate some functions by using the explicit expression of the heat kernels for the Cayley Heisenberg groups, and then prove the uniform boundedness of the Riesz transforms on these nilpotent Lie groups.

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    VERSAL UNFOLDING OF EQUIVARIANT BIFURCATION PROBLEMS IN MORE GENERAL CASE UNDER TWO EQUIVALENT GROUPS
    李养成; 何伟
    数学物理学报(英文版). 2008 (4):  915-923.  DOI: 10.1016/S0252-9602(08)60091-0
    摘要 ( 752 )   RICH HTML PDF(164KB) ( 1350 )   收藏

    For the unfolding of equivariant bifurcation problems with two types of state
    variables in the presence of parameter symmetry, the versal unfolding theorem with respect to left-right equivalence is obtained by using the related methods and techniques in the singularity theory of smooth map-germs. The corresponding results in [4, 9] can be considered as its special cases. A relationship between the versal unfolding w.r.t. left-right equivalence and the
    versal deformation w.r.t. contact equivalence is established.

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    THE ASYMPTOTIC LIMIT FOR A COMBUSTION MODEL IN REGARD TO INFINITE REACTION RATE
    应隆安
    数学物理学报(英文版). 2008 (4):  924-932.  DOI: 10.1016/S0252-9602(08)60092-2
    摘要 ( 861 )   RICH HTML PDF(158KB) ( 910 )   收藏

    The Zeldovich-von Neumann-Doring model and the Chapman-Jouguet model for a simplified combustion model--Majda’s model is studied. The author proves a uniform maximum norm estimate, then proves that as the rate of chemical reaction tends to infinity the solutions to the Zeldovich-von Neumann-Doring model tend to that of the Chapman-Jouguet model. The type of combustion waves is studied. This result is compared with the result of the projection and finite difference method for the same model.

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    DERIVATIONS AND EXTENSIONS OF LIE COLOR ALGEBRA
    张庆成; 张永正
    数学物理学报(英文版). 2008 (4):  933-948.  DOI: 10.1016/S0252-9602(08)60093-4
    摘要 ( 765 )   RICH HTML PDF(200KB) ( 1621 )   收藏

    In this article, the authors obtain some results concerning derivations of finitely generated Lie color algebras and discuss the relation between skew derivation space SkDer(L) and central extension H2(L, F) on some Lie color algebras. Meanwhile, they generalize the notion of double extension to quadratic Lie color algebras, a sufficient condition for a quadratic Lie color algebra to be a double extension and further properties are given.

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    BOUND ON THE MAXIMUM NUMBER OF CLEAR TWO-FACTOR INTERACTIONS FOR 2n-(n-k) DESIGNS
    赵胜利; 张润楚
    数学物理学报(英文版). 2008 (4):  949-954.  DOI: 10.1016/S0252-9602(08)60094-6
    摘要 ( 840 )   RICH HTML PDF(151KB) ( 877 )   收藏

    Clear effects criterion is an important criterion for selecting fractional factorial designs [1]. Tang et al. [2] derived upper and lower bounds on the maximum number of clear two-factor interactions (2fi’s) in 2n-(n-k) designs of resolution III and IV by constructing 2n-(n-k) designs. But the method in [2] does not perform well sometimes when the resolution is III. This article modifies the construction method for 2n-(n-k) designs of resolution III in [2]. The modified method is a great improvement on that used in [2].

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    THE SUPERIORITY OF EMPIRICAL BAYES ESTIMATION OF PARAMETERS IN PARTITIONED NORMAL LINEAR MODEL
    张伟平; 韦来生
    数学物理学报(英文版). 2008 (4):  955-962.  DOI: 10.1016/S0252-9602(08)60095-8
    摘要 ( 714 )   RICH HTML PDF(151KB) ( 1530 )   收藏

    In this article, the empirical Bayes (EB) estimators are constructed for the estimable functions of the parameters in partitioned normal linear model. The superiorities of the EB estimators over ordinary least-squares (LS) estimator are investigated under mean square error matrix (MSEM) criterion.

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    HOMOGENIZATION OF A STATIONARY NAVIER-STOKES FLOW IN POROUS MEDIUM WITH THIN FILM
    姚正安; 赵红星
    数学物理学报(英文版). 2008 (4):  963-974.  DOI: 10.1016/S0252-9602(08)60096-X
    摘要 ( 936 )   RICH HTML PDF(181KB) ( 1401 )   收藏

    The article studies the homogenization of a stationary Navier-Stokes
    fluid in porous medium with thin film under Dirichlet boundary condition. At the end of the article, "Darcy’s law" is rigorously derived from this model as the parameter ε tends to zero, which is independent of the coordinates towards the thickness.

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    THE CONSTRUCTION OF DENUMERABLE q-PROCESSES IN RANDOM ENVIRONMENTS SATISFYING (F) OR (B)
    胡迪鹤; 胡晓予
    数学物理学报(英文版). 2008 (4):  975-988.  DOI: 10.1016/S0252-9602(08)60097-1
    摘要 ( 988 )   RICH HTML PDF(194KB) ( 1040 )   收藏

    This article is a continuation of [9]. Based on the discussion of random Kolmogorov forward (backward) equations, for any given q-matrix in random environment, Q(θ)=(q(θ; x, y), x, y∈ χ), an infinite class of q-processes in random environments satisfying the random Kolmogorov forward (backward) equation is constructed. Moreover, under some conditions, all the q-processes in random environments satisfying the random Kolmogorov forward (backward) equation are constructed.

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    EFFICIENT ESTIMATION OF FUNCTIONAL-COEFFICIENT REGRESSION MODELS WITH DIFFERENT SMOOTHING VARIABLES
    张日权; 李国英
    数学物理学报(英文版). 2008 (4):  989-997.  DOI: 10.1016/S0252-9602(08)60098-3
    摘要 ( 872 )   RICH HTML PDF(197KB) ( 1091 )   收藏

    In this article, a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined. First step, by the local linear technique and the averaged method, the initial estimates of the coefficient functions are given. Second step, based on the initial estimates, the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure. The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions. Two simulated examples show that the procedure is effective.

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    AN ORDER PRESERVING INEQUALITY FOR THREE OPERATORS VIA FURUTA INEQUALITY
    杨长森
    数学物理学报(英文版). 2008 (4):  998-002.  DOI: 10.1016/S0252-9602(08)60099-5
    摘要 ( 786 )   RICH HTML PDF(142KB) ( 896 )   收藏

    Furuta showed that if AB ≥0, then for each r≥0, f(p)=(Ar/2BpAr/2)t+r/p+r
    is decreasing for pt≥0. Using this result, the following inequality (Cr/2AB2A)δCr/2)p-1+r/4δ+rCp-1+r is obtained for 0<p≤1, r≥1, 1/4≤δ≤1 and three positive operators A, B, C satisfy (A1/2 B A1/2)p/2Ap, (B1/2 AB1/2)p/2Bp, (C1/2 AC1/2)p/2Cp, (A1/2 CA1/2)p/2Ap.

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