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    2010年, 第30卷, 第1期 刊出日期:2010-01-20 上一期    下一期
    本期栏目: 论文 
    论文
    WEIGHTED ESTIMATES FOR COMMUTATORS OF OPERATORS CALDERÓN-ZYGMUNDWITH NON-DOUBLING MEASURES
    林海波, 孟岩, 杨大春
    数学物理学报(英文版). 2010 (1):  1-18.  DOI: 10.1016/S0252-9602(10)60017-3
    摘要 ( 1067 )   RICH HTML PDF(244KB) ( 1234 )   收藏

    Let μ be a nonnegative Radon measure on Rd, which only satisfies the polynomial growth condition. Under this assumption, the authors obtain some weighted weak-type estimates for the commutators generated by the multilinear Calder\'on-Zygmund operators and RBMO(μ) functions.

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    CYCLOTOMIC ELEMENTS IN K2F, REVISITED
    Jerzy Browkin
    数学物理学报(英文版). 2010 (1):  19-26.  DOI: 10.1016/S0252-9602(10)60018-5
    摘要 ( 595 )   RICH HTML PDF(157KB) ( 973 )   收藏

    Basing on results of Xu and Qin [10], and Guo [12] on cyclotomic elements in K2F for local fields F, we prove that every element in K2Q
    is a finite or infinite product of cyclotomic elements. Next, we extend this result to finite extensions of Q satisfying some additional conditions.

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    ADMISSIBILITY IN THE GENERAL GROWTH CURVE MODEL WITH RESPECT TO RESTRICTED |PARAMETER SETS UNDER MATRIX LOSS FUNCTION
    张尚立, 覃红
    数学物理学报(英文版). 2010 (1):  27-38.  DOI: 10.1016/S0252-9602(10)60019-7
    摘要 ( 692 )   RICH HTML PDF(175KB) ( 1044 )   收藏

    In this paper, we study the issue of admissibility in the growth curve model with respect to restricted parameter sets under matrix loss function. We obtain some necessary and sufficient conditions that the linear estimators of $KBL$ are admissible in the class of
    homogeneous linear estimators and in the class of  non-homogeneous linear estimators under the growth curve model with respect to
    restricted parameter sets, respectively.

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    PHASE RETRIEVAL OF TIME-LIMITED SIGNALS
    付应雄, 李落清
    数学物理学报(英文版). 2010 (1):  39-46.  DOI: 10.1016/S0252-9602(10)60020-3
    摘要 ( 820 )   RICH HTML PDF(159KB) ( 1051 )   收藏

    The problem of reconstructing a signal φ(x) from its magnitude |φ(x)| is of considerable interest to engineers and physicists. This article concerns the problem of determining a time-limited signal f with period 2π when |f(eix)| is known for x ∈[-π, π]. It is shown that the conditions |g(eix)|=|f(eix)| and |g(ei(x+b))-g(eix)|=|f(ei(x+b))-f(eix)|, b≠2π, together imply that either g=wf or g=vf, where both w and v have period b. Furthermore, if b/2π is irrational then the functions w and v reduce to some constants c1 and c2, respectively;  if b/2π is rational then  w takes the form w=eB1(eix}B2(eix) and v takes the form ei(x2πN/b+α)B1(eix)B2(eix), where B1 and B2 are Blaschke products.

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    DECAY RATES OF PLANAR VISCOUS RAREFACTION WAVE FOR MULTI-DIMENSIONAL SCALAR CONSERVATION LAW #br# WITH DEGENERATE VISCOSITY ON HALF SPACE
    刘艳红
    数学物理学报(英文版). 2010 (1):  47-54.  DOI: 10.1016/S0252-9602(10)60021-5
    摘要 ( 814 )   RICH HTML PDF(157KB) ( 1025 )   收藏

    We investigate the decay rates of the planar viscous rarefaction wave of the initial-boundary value problem to scalar conservation
    law with degenerate viscosity in several dimensions on the half-line space, where the corresponding one-dimensional problem
    admits the rarefaction wave as an asymptotic state. The analysis is based on the standard L2-energy method and L1-estimate.

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    INFINITELY MANY SOLUTIONS FOR ELLIPTIC SYSTEMS WITH STRONGLY INDEFINITE VARIATIONAL STRUCTURE
    刘朝霞
    数学物理学报(英文版). 2010 (1):  55-64.  DOI: 10.1016/S0252-9602(10)60022-7
    摘要 ( 812 )   RICH HTML PDF(160KB) ( 1074 )   收藏

    Based on the multiplicity results of Benci and Fortunato [4], we consider some elliptic systems with strongly indefinite quadratic part, and establish the existence of infinitely many nontrivial solutions in a suitable family of products of fractional Sobolev spaces.

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    CONVERGENCE ANALYSIS OF RUNGE-KUTTA METHODS FOR A CLASS OF RETARDED DIFFERENTIAL ALGEBRAIC SYSTEMS
    肖飞雁, 张诚坚
    数学物理学报(英文版). 2010 (1):  65-74.  DOI: 10.1016/S0252-9602(10)60023-9
    摘要 ( 856 )   RICH HTML PDF(172KB) ( 1226 )   收藏

    This article deals with a class of numerical methods for retarded differential algebraic systems with time-variable delay. The methods can be viewed as a combination of Runge-Kutta methods and  Lagrange interpolation. A new convergence concept, called $D_A$-convergence, is introduced. The DA-convergence result for the methods is derived. At the end, a numerical example is given to verify the computational effectiveness and the theoretical result.

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    SUBNORMAL SOLUTIONS OF DIFFERENTIAL EQUATIONS WITH PERIODIC COEFFICIENTS
    陈宗煊, 孙光镐
    数学物理学报(英文版). 2010 (1):  75-88.  DOI: 10.1016/S0252-9602(10)60024-0
    摘要 ( 653 )   RICH HTML PDF(199KB) ( 1313 )   收藏

    In this article, we apply the concept of hyper-order to higher order linear differential equations with periodic
    coefficients, investigate the existence and the form of its subnormal solution, and  estimate the growth of all other solutions, and answer the question raised by Gundersen and Steinbart for more general periodic differential equations.

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    BOCHNER TECHNIQUE ON STRONG KÄHLER-FINSLER MANIFOLDS
    肖金秀, 钟同德, 邱春晖
    数学物理学报(英文版). 2010 (1):  89-106.  DOI: 10.1016/S0252-9602(10)60025-2
    摘要 ( 737 )   RICH HTML PDF(236KB) ( 1223 )   收藏

    By using the Chern-Finsler connection and complex Finsler metric, the Bochner technique on strong Kähler-Finsler manifolds is studied. For a strong Kähler-Finsler manifold M, the authors first prove that there exists a system of local coordinate which is normalized at a point M=T1,0M \ o(M), and then the horizontal Laplace operator ΟH for differential forms on PTM is defined by the horizontal part of the Chern-Finsler connection and its curvature tensor, and the horizontal Laplace operator ?H on holomorphic vector bundle over PTM is also defined. Finally, we get a Bochner vanishing theorem for differential forms on PTM. Moreover, the Bochner vanishing theorem on a holomorphic line bundle over PTM is also obtained.

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    FINITENESS OF HIGHER CODIMENSIONAL DISJOINT MINIMAL GRAPHS
    东瑜昕, 嵇庆春, 张玮
    数学物理学报(英文版). 2010 (1):  107-112.  DOI: 10.1016/S0252-9602(10)60026-4
    摘要 ( 715 )   RICH HTML PDF(143KB) ( 876 )   收藏

    We estimate the number of disjoint open subsets in Rn, which can support area-decreasing minimal graphs. This result generalizes the related results of Li-Wang and Tkachev for minimal hypersurfaces to higher codimensional case.

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    MULTIPLE AND SIGN-CHANGING SOLUTIONS FOR NONLINEAR ELLIPTIC EQUATION WITH CRITICAL POTENTIAL AND CRITICAL PARAMETER
    王友军, 沈尧天
    数学物理学报(英文版). 2010 (1):  113-124.  DOI: 10.1016/S0252-9602(10)60027-6
    摘要 ( 690 )   RICH HTML PDF(200KB) ( 993 )   收藏

    Some embedding inequalities in Hardy-Sobolev space are proved. Furthermore, by the improved inequalities and the linking theorem, in a new k-order Sobolev-Hardy space, we obtain the existence of sign-changing solutions for the nonlinear elliptic equation
    \left\{\begin{array}{ll}
    \disp        -\Delta_{(k)}u:=-\Delta
    u-\frac{(N-2)^2}{4}\frac{u}{|x|^2}-\frac{1}{4}\sum\limits_{i=1}^{k-1}\frac{u}{|x|^2(\ln_{(i)}R/|x|)^2}
    =f(x,u),&\quad x\in\Omega, 
     u=0,&\quad x\in\partial\Omega,   \end{array}   \right.
    where 0\in \Omega \subset B_a(0)\subset {\Bbb R}^N, N\geq 3, \ln_{(i)}=\prod\limits_{j=1}^i\ln^{(j)},  and R=ae^{(k-1)}, where e^{(0)}=1,  e^{(j)}=e^{e^{(j-1)}} for j\geq 1, \ln^{(1)}=\ln,  \ln^{(j)}=\ln\ln^{(j-1)}  for j\geq 2. Besides, positive and negative solutions are obtained by a variant mountain pass theorem.

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    INEQUALITIES OF EIGENVALUES FOR BI-KOHN LAPLACIAN ON |HEISENBERG GROUP
    黄广月, 陈文艺
    数学物理学报(英文版). 2010 (1):  125-131.  DOI: 10.1016/S0252-9602(10)60028-8
    摘要 ( 695 )   RICH HTML PDF(139KB) ( 1098 )   收藏

    In this article, we consider the eigenvalue problem for the bi-Kohn Laplacian and obtain universal bounds on the
    (k+1)-th eigenvalue in terms of the first k eigenvalues independent of the domains.

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    ON MÜNTS FORMULA
    丁夏畦, 罗佩珠
    数学物理学报(英文版). 2010 (1):  132-136.  DOI: 10.1016/S0252-9602(10)60029-X
    摘要 ( 583 )   RICH HTML PDF(121KB) ( 845 )   收藏

    In the theory of Riemann Zeta-function, there is an important formula called M\"{u}nts formula. In this note we will give its general form.

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    EXISTENCE OF A COOPERATIVE ELLIPTIC SYSTEM INVOLVING PUCCI OPERATOR
    杨健夫, 余小辉
    数学物理学报(英文版). 2010 (1):  137-147.  DOI: 10.1016/S0252-9602(10)60030-6
    摘要 ( 747 )   RICH HTML PDF(181KB) ( 1005 )   收藏

    The authors study the existence of solutions for the nonlinear elliptic system

    {  -M\+λ, ∧(D2u)=f(u, v)   in  Ω,   

       -M\+λ, ∧(D2v)=f(u, v)   in  Ω,   

       u ≥ 0, v ≥ 0                    in  Ω,

       u=v=0                            on  ∂Ω,

    where Ω is a bounded convex domain in RN, N ≥ 2. It is shown that under some assumptions on f and g, the problem has at least one  positive solution (u,v).

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    AVERAGE ONESIDED WIDTHS OF SOBOLEV AND BESOV CLASSES
    杨柱元, 杨宗文, 刘永平
    数学物理学报(英文版). 2010 (1):  148-160.  DOI: 10.1016/S0252-9602(10)60031-8
    摘要 ( 571 )   RICH HTML PDF(200KB) ( 881 )   收藏

    The article concerns the average onesided widths of the  Sobolev and Besov classes and the classes of functions with bounded moduli of smoothness. The weak asymptotic results are obtained for the corresponding quantities.

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    ON LINEAR EXTENSION OF 1-LIPSCHITZ MAPPING FROM HILBERT SPACE INTO A NORMED SPACE
    王瑞东
    数学物理学报(英文版). 2010 (1):  161-165.  DOI: 10.1016/S0252-9602(10)60032-X
    摘要 ( 755 )   RICH HTML PDF(123KB) ( 1146 )   收藏

    In this article, we prove that an into 1-Lipschitz mapping from the unit sphere of a Hilbert space to the unit sphere of an arbitrary normed space, which under some conditions, can be extended to be a linear isometry on the whole
    space.

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    NORMALITY CRITERIA FOR FAMILIES OF MEROMORPHIC ALGEBROID FUNCTIONS
    孙道椿
    数学物理学报(英文版). 2010 (1):  166-172.  DOI: 10.1016/S0252-9602(10)60033-1
    摘要 ( 674 )   RICH HTML PDF(150KB) ( 1091 )   收藏

    By using the definition of Hausdorff distance, we prove some normality criteria for families of meromorphic algebroid functions. Some examples are given to complement the theory in this article.

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    A CLASS OF COMPOUND VECTOR-VALUED PROBLEM AND FACTORIZATION OF MATRIX FUNCTION
    郭国安, 杜金元
    数学物理学报(英文版). 2010 (1):  173-179.  DOI: 10.1016/S0252-9602(10)60034-3
    摘要 ( 729 )   RICH HTML PDF(143KB) ( 1179 )   收藏

    In this article, we consider a class of compound vector-valued problem on upper-half plane C+, which consists of vector Riemann problem along a closed contour in C+ with matrix coefficient in Hölder class and vector Hilbert problem on the real axis with essential bounded measurable matrix coefficient. Under appropriate assumption we obtain its solution by use of Corona theorem and factorization of matrix functions in decomposed Banach algebras.

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    APPLICATION OF MINIMUM PROJECTION UNIFORMITY CRITERION IN COMPLEMENTARY DESIGNS
    宋硕, 覃红
    数学物理学报(英文版). 2010 (1):  180-186.  DOI: 10.1016/S0252-9602(10)60035-5
    摘要 ( 700 )   RICH HTML PDF(150KB) ( 1180 )   收藏

    In this article, we consider the characterization problem in design theory. The objective is to characterize minimum
    projection uniformity for two-level designs in terms of their complementary designs. Here, the complementary design means a design in which all the Hamming distances of any two runs are the same, which generalizes the concept of a pair of complementary designs in the literature. Based on relationships of the uniformity pattern between a pair of complementary designs, we propose a minimum projection uniformity (MPU) rule to assess and compare two-level factorials.

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    VISCOSITY SOLUTIONS OF HJB EQUATIONS ARISING FROM THE VALUATION OF EUROPEAN PASSPORT OPTIONS
    边保军, 王杨, 张寄洲
    数学物理学报(英文版). 2010 (1):  187-202.  DOI: 10.1016/S0252-9602(10)60036-7
    摘要 ( 1109 )   RICH HTML PDF(214KB) ( 1409 )   收藏

    The passport option is a call option on the balance of a trading account. The option holder retains the gain from trading, while the issuer is liable for the net loss. In this article, the mathematical foundation for pricing the
    European passport option is established. The pricing equation which is a fully nonlinear equation is derived using the dynamic programming principle. The comparison principle, uniqueness and convexity preserving of the viscosity solutions of related HJB equation are proved. A relationship between the passport and lookback options is discussed.

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    FUNDAMENTAL GROUPS OF CLOSED POSITIVELY CURVED MANIFOLDS WITH ALMOST DISCRETE ABELIAN GROUP ACTIONS
    王雨生
    数学物理学报(英文版). 2010 (1):  203-207.  DOI: 10.1016/S0252-9602(10)60037-9
    摘要 ( 546 )   RICH HTML PDF(135KB) ( 1037 )   收藏

    Let M be a closed n-manifold of positive sectional curvature. Assume that $M$ admits an effective isometrical
    T1× Zpk-action with p prime. The main result of the article is that if k=1 for n=3 or k>n+1/4 for n ≥ 5, then there exists a positive constant $p(n)$, depending only on n, such that π1(M) is cyclic if p ≥ p(n).

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    LOCAL REGULARITY RESULT IN OBSTACLE PROBLEMS
    高红亚, 郭静, 左亚丽, 褚玉明
    数学物理学报(英文版). 2010 (1):  208-214.  DOI: 10.1016/S0252-9602(10)60038-0
    摘要 ( 787 )   RICH HTML PDF(156KB) ( 1062 )   收藏

    We obtain a local regularity result for solutions to Kψ,θ -obstacle problem of A-harmonic equation divA(x, u(x), ∨ u(x))=0, where A: Ω×R×R→ Rn is a Carath\'eodory function satisfying some coercivity and growth conditions with the natural exponent 1<p<n, the obstacle function ψ≥0$, and the boundary data θ W1, p(Ω).

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    SLANT SUBMANIFOLDS OF A RIEMANNIAN PRODUCT MANIFOLD
    Mehmet Atceken
    数学物理学报(英文版). 2010 (1):  215-224.  DOI: 10.1016/S0252-9602(10)60039-2
    摘要 ( 661 )   RICH HTML PDF(147KB) ( 1129 )   收藏

    In this article, the geometry of the slant submanifolds of a Riemannian product manifold is studied. Some necessary and sufficient conditions on slant, bi-slant and semi-slant submanifolds are given. We research fundamental properties of the distributions which are involved in definitions of semi- and bi-slant submanifolds
    in a Riemannian product manifold.

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    LIE SUPER-BIALGEBRA STRUCTURES |ON GENERALIZED SUPER-VIRASORO ALGEBRAS
    杨恒云, 苏育才
    数学物理学报(英文版). 2010 (1):  225-239.  DOI: 10.1016/S0252-9602(10)60040-9
    摘要 ( 674 )   RICH HTML PDF(206KB) ( 1101 )   收藏

    In this article, Lie super-bialgebra structures on generalized super-Virasoro algebras L are considered. It is proved that all such Lie super-bialgebras are coboundary triangular Lie super-bialgebras if and only if H1(LL{\cal L})=0.

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    ON WEAK MINIMUM ABERRATION AND NUMBER OF CLEAR TWO-FACTOR INTERACTION COMPONENTS IN sIVm-p DESIGNS
    杨贵军
    数学物理学报(英文版). 2010 (1):  240-246.  DOI: 10.1016/S0252-9602(10)60041-0
    摘要 ( 628 )   RICH HTML PDF(154KB) ( 864 )   收藏

    This article obtains some theoretical results on the number of clear two-factor interaction components and weak minimum aberration in an sIVm-p design, by considering the number of not clear two-factor interaction components of the design.

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    ON THE OPERATIONS OF ALGEBROID FUNCTIONS
    孙道椿, 高宗升
    数学物理学报(英文版). 2010 (1):  247-256.  DOI: 10.1016/S0252-9602(10)60042-2
    摘要 ( 782 )   RICH HTML PDF(162KB) ( 1150 )   收藏

    In this article, we first investigate the operational properties of algebroid functions. Then we prove two uniqueness theorems for algebroid functions.

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    WHITE NOISE APPROACH TO SCATTERING SOLUTION OF Φ44 WAVE EQUATION
    让光林
    数学物理学报(英文版). 2010 (1):  257-268.  DOI: 10.1016/S0252-9602(10)60043-4
    摘要 ( 810 )   RICH HTML PDF(206KB) ( 917 )   收藏

    Under the framework of white noise analysis, the existence of scattering solutions to the abstract dynamical φ44 wave equations in terms of generalized operators (see Section 3 below) is proven via a combination of the characterization for the symbol of generalized operators and the classical scattering results. In addition, some properties (Poincar\'{e} invariance and irreducibility) of the solutions are discussed.

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    AN EFFICIENT SEQUENTIAL DESIGN FOR SENSITIVITY EXPERIMENTS
    田玉斌, 房永飞
    数学物理学报(英文版). 2010 (1):  269-280.  DOI: 10.1016/S0252-9602(10)60044-6
    摘要 ( 629 )   RICH HTML PDF(197KB) ( 1046 )   收藏

    In sensitivity experiments, the response is binary and each experimental unit has a critical stimulus level that cannot be observed directly. It is often of interest to estimate extreme quantiles of the distribution of these
    critical stimulus levels over the tested products. For this purpose a new sequential scheme is proposed with some commonly used models. By using the bootstrap repeated-sampling principle, reasonable prior
    distributions based on a historic data set are specified. Then, a Bayesian strategy for the sequential procedure is provided and the estimator is given. Further, a high order approximation for such an estimator is explored and its consistency is proven. A simulation study shows that the proposed method gives superior performances over the existing methods.

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    GLOBAL SOLUTION TO THE CAUCHY PROBLEM ON A UNIVERSE FIREWORKS MODEL
    姜正禄, 田红炯
    数学物理学报(英文版). 2010 (1):  281-288.  DOI: 10.1016/S0252-9602(10)60045-8
    摘要 ( 798 )   RICH HTML PDF(157KB) ( 958 )   收藏

    We prove  existence and uniqueness of the global solution to the Cauchy problem on a universe fireworks model with finite total mass at the initial state when the ratio of the mass surviving the explosion, the probability of the explosion of fragments and the probability function of the velocity change of a surviving particle satisfy the corresponding physical conditions. Although the nonrelativistic Boltzmann-like equation modeling the universe
    fireworks is mathematically easy, this article leads rather theoretically to an understanding of how to construct contractive mappings in a Banach space for the proof of the existence and uniqueness of the solution  by means of methods taken from the famous work by DiPerna & Lions about the Boltzmann equation. We also show both the
    regularity and the time-asymptotic behavior of solution to the Cauchy problem.

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    MAXIMAL ATTRACTORS FOR THE COMPRESSIBLE NAVIER--STOKES EQUATIONS OF  VISCOUS AND HEAT CONDUCTIVE FLUID
    秦玉明, 宋锦萍
    数学物理学报(英文版). 2010 (1):  289-311.  DOI: 10.1016/S0252-9602(10)60046-X
    摘要 ( 717 )   RICH HTML PDF(259KB) ( 1029 )   收藏

    This article is concerned with the existence of maximal attractors in Hi (i=1,2,4) for the compressible Navier--Stokes equations for a polytropic viscous heat conductive ideal gas in bounded annular domains Ωn in Rn (n=2,3). One of the important features is that the metric spaces H(1), H(2), and H(4) we work with are three  incomplete
    metric spaces, as can be seen from the constraints θ >0 and u>0, with θ and u being absolute temperature and specific volume respectively. For any constants δ1δ2… δ8 verifying some conditions, a sequence of closed subspaces Hδ(i)    H(i) ;(i=1, 2, 4) is found, and the existence of maximal (universal) attractors in Hδ(i); (i=1, 2, 4) is
    established.

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    HOMOCLINIC ORBITS FOR A CLASS OF THE SECOND ORDER HAMILTONIAN SYSTEMS
    万莉莉, 唐春雷
    数学物理学报(英文版). 2010 (1):  312-318.  DOI: 10.1016/S0252-9602(10)60047-1
    摘要 ( 1217 )   RICH HTML PDF(146KB) ( 951 )   收藏

    The existence of homoclinic orbits is obtained by the variational approach for a class of second order Hamiltonian systems q(t)+  V(t, q(t))=0, where V(t, x)=-K(t,x)+W(t, x), K(t, x) is neither a quadratic form in x nor periodic in t and W(t, x) is superquadratic in x.

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    LIMITING BEHAVIOR OF RECURSIVE M-ESTIMATORS IN MULTIVARIATE LINEAR REGRESSION MODELS AND THEIR ASYMPTOTIC EFFICIENCIES
    缪柏其, 吴月华, 刘东海
    数学物理学报(英文版). 2010 (1):  319-329.  DOI: 10.1016/S0252-9602(10)60048-3
    摘要 ( 867 )   RICH HTML PDF(194KB) ( 1019 )   收藏

    Recursive algorithms are very useful for computing M-estimators of regression coefficients and scatter Parameters. In this article, it is shown that for a nondecreasing u1(t), under some mild conditions the recursive M-estimators of regression coefficients and scatter parameters are strongly consistent and the recursive M-estimator of the regression coefficients is also asymptotically normal distributed. Furthermore, optimal recursive M-estimators, asymptotic efficiencies of recursive M-estimators and asymptotic relative efficiencies between recursive M-estimators of regression coefficients are studied.

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    SOME POSTERIOR DISTRIBUTIONS FOR THE LAPLACE MEAN
    Saralees Nadarajah
    数学物理学报(英文版). 2010 (1):  330-340.  DOI: 10.1016/S0252-9602(10)60049-5
    摘要 ( 746 )   RICH HTML PDF(179KB) ( 988 )   收藏

    Two posterior distributions for the mean of the Laplace distribution are obtained by deriving the distributions of the product XY and the ratio X/Y when X and Y are Student's t and Laplace random variables distributed independently of each other. Tabulations of the associated percentage points are given along with computer programs for generating them.

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    THE POINCAR\'E-BERTRAND FORMULA ON THE BUILDING DOMAIN OF COMPLEX BIBALLS
    龚定东, 林良裕
    数学物理学报(英文版). 2010 (1):  341-349.  DOI: 10.1016/S0252-9602(10)60050-1
    摘要 ( 711 )   RICH HTML PDF(160KB) ( 1158 )   收藏

    The Poincaré-Bertrand formula takes an important position in the study of complex singular integral. The Poincaré-Bertrand formula on the complex sphere in the multidimensional complex Euclidian spaces was given by Sheng Gong. Using the method of solid angular coefficient, the authors extend the Poincaré-Bertrand formula on the complex sphere to the building domain of the complex biballs, and obtain a more general Poincaré-Bertrand formula with the solid angular coefficients.

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    MULTIPLE SOLUTIONS FOR NONAUTONOMOUS SECOND ORDER PERIODIC SYSTEMS
    Zdzislaw Denkowski, Leszek Gasinski, Nikolaos S. Papageorgiou
    数学物理学报(英文版). 2010 (1):  341-349.  DOI: 10.1016/S0252-9602(10)60051-3
    摘要 ( 726 )   RICH HTML PDF(167KB) ( 1208 )   收藏

    We study nonautonomonus second order periodic systems with a nonsmooth potential. Using the nonsmooth critical theory, we establish the existence of at least two nontrivial solutions. Our framework incorporates large classes of both subquadratic and superquadratic potentials at infinity.

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    INEQUALITIES OF THE QUERMASSINTEGRALS FOR THE Lp-PROJECTION BODY AND THE Lp-CENTROID BODY
    王卫东, 冷岗松
    数学物理学报(英文版). 2010 (1):  359-368.  DOI: 10.1016/S0252-9602(10)60052-5
    摘要 ( 653 )   RICH HTML PDF(160KB) ( 965 )   收藏

    Associated with the concepts of the Lp-mixed quermassintegrals, the Lp-mixed volume, and the Lp-dual mixed volume, we establish inequalities for the quermassintegrals of the Lp-projection body and the Lp-centroid body. Further, the general results for the Shephard problem of the Lp-projection body and the Lp-centroid body are obtained.

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