首页期刊导航|中国科学：数学（英文版）
期刊信息/Journal information
中国科学：数学（英文版）
中国科学：数学（英文版）

周光召

月刊

1674-7283

sales@scichina.org

010-64019820

100717

北京东黄城根北街16号

中国科学：数学（英文版）/Journal Science China(Mathematics)CSCDCSTPCDSCI
查看更多>>《中国科学》是中国科学院主办、中国科学杂志社出版的自然科学专业性学术刊物。《中国科学》任务是反映中国自然科学各学科中的最新科研成果，以促进国内外的学术交流。《中国科学》以论文形式报道中国基础研究和应用研究方面具有创造性的、高水平的和有重要意义的科研成果。在国际学术界，《中国科学》作为代表中国最高水平的学术刊物也受到高度重视。国际上最具有权威的检索刊物SCI，多年来一直收录《中国科学》的论文。1999年《中国科学》夺得国家期刊奖的第一名。
正式出版
收录年代

    Positive definiteness of real quadratic forms resulting from the variable-step L1-type approximations of convolution operators

    Hong-Lin LiaoTao TangTao Zhou
    237-252页
    查看更多>>摘要：The positive definiteness of real quadratic forms with convolution structures plays an important role in stability analysis for time-stepping schemes for nonlocal operators.In this work,we present a novel analysis tool to handle discrete convolution kernels resulting from variable-step approximations for convolution operators.More precisely,for a class of discrete convolution kernels relevant to variable-step L1-type time discretizations,we show that the associated quadratic form is positive definite under some easy-to-check algebraic conditions.Our proof is based on an elementary constructing strategy by using the properties of discrete orthogonal convolution kernels and discrete complementary convolution kernels.To our knowledge,this is the first general result on simple algebraic conditions for the positive definiteness of variable-step discrete convolution kernels.Using the unified theory,we obtain the stability for some simple nonuniform time-stepping schemes straightforwardly.
      原文链接:
    • 万方数据
    • 维普

    On asymptotic stability of the 3D Boussinesq equations without heat conduction

    Lihua DongYongzhong Sun
    253-280页
    查看更多>>摘要：We investigate the asymptotic stability of the solutions to Boussinesq equations without heat conduction with the initial data near a specific stationary solution in the three-dimensional domain Ω=R2 ×(0,1).It is shown that the solution starting from a small perturbation to the stationary solution converges to it with explicit algebraic rates as time tends to infinity.
      原文链接:
    • 万方数据
    • 维普

    One-dimensional monotone nonautonomous dynamical systems

    David Cheban
    281-314页
    查看更多>>摘要：This work is devoted to the study of the dynamics of one-dimensional monotone nonautonomous(cocycle)dynamical systems.A description of the structures of their invariant sets,omega limit sets,Bohr/Levitan almost periodic and almost automorphic motions,global attractors,and pinched and minimal sets is given.An application of our general results is given to scalar differential and difference equations.
      原文链接:
    • 万方数据
    • 维普

    A new class of generalized quasi-variational inequalities with applications to Oseen problems under nonsmooth boundary conditions

    Shengda ZengAkhtar A.KhanStanis?aw Migórski
    315-338页
    查看更多>>摘要：In this paper,we study a generalized quasi-variational inequality(GQVI for short)with two multivalued operators and two bifunctions in a Banach space setting.A coupling of the Tychonov fixed point principle and the Katutani-Ky Fan theorem for multivalued maps is employed to prove a new existence theorem for the GQVI.We also study a nonlinear optimal control problem driven by the GQVI and give sufficient conditions ensuring the existence of an optimal control.Finally,we illustrate the applicability of the theoretical results in the study of a complicated Oseen problem for non-Newtonian fluids with a nonmonotone and multivalued slip boundary condition(i.e.,a generalized friction constitutive law),a generalized leak boundary condition,a unilateral contact condition of Signorini's type and an implicit obstacle effect,in which the multivalued slip boundary condition is described by the generalized Clarke subgradient,and the leak boundary condition is formulated by the convex subdifferential operator for a convex superpotential.
      原文链接:
    • 万方数据
    • 维普

    On hypersurfaces of H2 × H2

    Dong GaoHui MaZeke Yao
    339-366页
    查看更多>>摘要：In this paper,we study hypersurfaces of H2 × H2.We first classify the hypersurfaces with constant principal curvatures and constant product angle functions.Then we classify homogeneous hypersurfaces and isoparametric hypersurfaces,respectively.Finally,we classify the hypersurfaces with at most two distinct constant principal curvatures,as well as those with three distinct constant principal curvatures under some additional conditions.
      原文链接:
    • 万方数据

    A level line of the Gaussian free field with measure-valued boundary conditions

    Titus LupuHao Wu
    367-404页
    查看更多>>摘要：In this article,we construct samples of Schramm-Loewner-evolution-like curves out of samples of the conformal loop ensemble and Poisson point processes of Brownian excursions.We show that the laws of these curves depend continuously on the intensity measure of the Brownian excursions.Using such a construction of curves,we extend the notion of level lines of the Gaussian free field to the case where the boundary condition is measure-valued.
      原文链接:
    • 万方数据
    • 维普

    Optimal decorrelated score subsampling for generalized linear models with massive data

    Junzhuo GaoLei WangHeng Lian
    405-430页
    查看更多>>摘要：In this paper,we consider the unified optimal subsampling estimation and inference on the low-dimensional parameter of main interest in the presence of the nuisance parameter for low/high-dimensional generalized linear models(GLMs)with massive data.We first present a general subsampling decorrelated score function to reduce the influence of the less accurate nuisance parameter estimation with the slow convergence rate.The consistency and asymptotic normality of the resultant subsample estimator from a general decorrelated score subsampling algorithm are established,and two optimal subsampling probabilities are derived under the A-and L-optimality criteria to downsize the data volume and reduce the computational burden.The proposed optimal subsampling probabilities provably improve the asymptotic efficiency of the subsampling schemes in the low-dimensional GLMs and perform better than the uniform subsampling scheme in the high-dimensional GLMs.A two-step algorithm is further proposed to implement,and the asymptotic properties of the corresponding estimators are also given.Simulations show satisfactory performance of the proposed estimators,and two applications to census income and Fashion-MNIST datasets also demonstrate its practical applicability.
      原文链接:
    • 万方数据
    • 维普

    An oscillation-free Hermite WENO scheme for hyperbolic conservation laws

    Zhuang ZhaoJianxian Qiu
    431-454页
    查看更多>>摘要：In this paper,the sixth-order oscillation-free Hermite weighted essentially non-oscillatory(OF-HWENO)scheme is proposed for hyperbolic conservation laws on structured meshes,where the zeroth-and first-order moments are the variables for the governing equations.The main difference from other HWENO schemes existing in the literature is that we add high-order numerical damping terms in the first-order moment equations to control spurious oscillations for the OF-HWENO scheme.The OF-HWENO scheme not only can achieve the designed optimal numerical order,but also can be easily implemented as we use only one set of stencils in the reconstruction procedure and the same reconstructed polynomials are applied for the zeroth-and first-order moment equations.In order to obtain the adaptive order resolution when facing discontinuities,a transition polynomial is added in the reconstruction,where the associated linear weights can also be any positive numbers as long as their summation equals one.In addition,the OF-HWENO scheme still keeps compactness as only immediate neighbor values are needed in the space discretization.Some benchmark numerical tests are performed to illustrate the high-order accuracy,high resolution and robustness of the proposed scheme.
      原文链接:
    • 万方数据
    • 维普

    A product version of the Hilton-Milner-Frankl theorem

    Peter FranklJian Wang
    455-474页
    查看更多>>摘要：Two families F and G of k-subsets of {1,2,...,n} are called non-trivial cross t-intersecting if|F ∩ G|≥t for all F ∈ F,G ∈ G and | ∩ {F:F ∈ F}|＜t,| ∩ {G:G ∈ G}|＜t.In the present paper,we determine the maximum product of the sizes of two non-trivial cross t-intersecting families of k-subsets of{1,2,...,n} for n ≥ 4(t+2)2k2,k ≥ 5,which is a product version of the Hilton-Milner-Frankl theorem.
      原文链接:
    • 万方数据
    • 维普

    Information for authors

    封3页
      原文链接:
    • 万方数据