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中国科学：数学（英文版）
中国科学：数学（英文版）

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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。
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    On n-universal quadratic forms over dyadic local fields

    Zilong HeYong Hu
    1481-1506页
    查看更多>>摘要：Let n≥2 be an integer.We give necessary and sufficient conditions for an integral quadratic form over dyadic local fields to be n-universal by using invariants from Beli's theory of bases of norm generators.Also,we provide a minimal set for testing n-universal quadratic forms over dyadic local fields,as an analogue of Bhargava and Hanke's 290-theorem(or Conway and Schneeberger's 15-theorem)on universal quadratic forms with integer coefficients.
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    Conics on Barth-Bauer octics

    Alex Degtyarev
    1507-1524页
    查看更多>>摘要：We analyze the configurations of conics and lines on a special class of Kummer octic surfaces.In particular,we bound the number of conics by 176 and show that there is a unique surface with 176 conics,all irreducible:it admits a faithful action of one of the Mukai groups.Therefore,we also discuss conics and lines on Mukai surfaces:we discover a double plane(ramified at a smooth sextic curve)that contains 8,910 smooth conics.
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    Partial regularity and nonlinear potential estimates for Stokes systems with super-quadratic growth

    Lingwei MaZhenqiu Zhang
    1525-1554页
    查看更多>>摘要：This paper builds a bridge between partial regularity theory and nonlinear potential theory for the following generalized stationary Stokes system with super-quadratic growth and continuous coefficients:-div A(x,Du)+▽π=f,divu=0,where Du is the symmetric part of the gradient ▽u.We first establish an e-regularity criterion involving both the excess functional of the symmetric gradient Du and Wolff potentials of the nonhomogeneous term f to guarantee the local vanishing mean oscillation(VMO)-regularity of Du in an open subset Ωu of Ω with full measure.Such an e-regularity criterion leads to a pointwise Wolff potential estimate of Du,which immediately infers that Du is partially C0-regular under appropriate assumptions.Finally,we give a local continuous modulus estimate of Du.
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    Concentration breaking on two optimization problems

    Yong HuangQinfeng LiQiuqi Li
    1555-1570页
    查看更多>>摘要：In the present paper,we study the boundary concentration-breaking phenomena on two thermal insulation problems considered on Lipschitz domains,based on Serrin's overdetermined result,the perturbation argument,and a comparison of Laplacian eigenvalues with different boundary conditions.Since neither of the functionals in the two problems is C1,another key ingredient is to obtain the global Hölder regularity of minimizers of both problems on Lipschitz domains.Also,the exact dependence on the domain of breaking thresholds is given in the first problem,and the breaking values are obtained in the second problem on ball domains,which are related to 2π in dimension 2.
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    Composition operators on weighted Bergman spaces induced by doubling weights

    Xin GuoMaofa Wang
    1571-1598页
    查看更多>>摘要：Given a doubling weight ω on the unit disk D,let Apω be the space of all the holomorphic functions f,where‖f‖Aωp:=(∫D|f(z)|pω(z)dA(z)1/p＜∞.We completely characterize the topological connectedness of the set of composition operators on Aωp.As an application,we construct an interesting example which reveals that two composition operators on Aαp in the same path component may fail to have a compact difference and give a negative answer to the Shapiro-Sundberg question in the(standard)weighted Bergman space.In addition,we completely describe the central compactness of any finite linear combinations of composition operators on Aωp in three terms:a Julia-Carathéodory-type function-theoretic characterization,a power-type characterization,and a Carleson-type measure-theoretic characterization.
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    Weak type(1,1)of the Riesz transform on some direct product manifolds with exponential volume growth

    Hong-Quan LiJie-Xiang Zhu
    1599-1622页
    查看更多>>摘要：In this paper,we are concerned with the Riesz transform on the direct product manifold Hn × M,where Hn is the n-dimensional real hyperbolic space,and M is a connected complete non-compact Riemannian manifold satisfying the volume doubling property and generalized Gaussian or sub-Gaussian upper estimates for the heat kernel.We establish its weak type(1,1)property.In addition,we obtain the weak type(1,1)of the heat maximal operator in the same setting.Our arguments also work for a large class of direct product manifolds with exponential volume growth.Particularly,we provide a simpler proof of weak type(1,1)boundedness of some operators considered in the work of Li et al.(2016).
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    The character of Thurston's circle packings

    Huabin GeAijin Lin
    1623-1640页
    查看更多>>摘要：We introduce the character of Thurston's circle packings in the hyperbolic background geometry.Consequently,some quite simple criteria are obtained for the existence of hyperbolic circle packings.For example,if a closed surface X admits a circle packing with all the vertex degrees di≥7,then it admits a unique complete hyperbolic metric so that the triangulation graph of the circle packing is isotopic to a geometric decomposition of X.This criterion is sharp due to the fact that any closed hyperbolic surface admits no triangulations with all d i≤6.As a corollary,we obtain a new proof of the uniformization theorem for closed surfaces with genus g≥2;moreover,any hyperbolic closed surface has a geometric decomposition.To obtain our results,we use Chow-Luo's combinatorial Ricci flow as a fundamental tool.
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    Second-order error analysis of the averaged L1 scheme (L1) for time-fractional initial-value and sub diffusion problems

    Jinye ShenFanhai ZengMartin Stynes
    1641-1664页
    查看更多>>摘要：Fractional initial-value problems(IVPs)and time-fractional initial-boundary value problems(IBVPs),each with a Caputo temporal derivative of order α ∈(0,1),are considered.An averaged variant of the well-known L1 scheme is proved to be O(N-2)convergent for IVPs on suitably graded meshes with N points,thereby improving the O(N-(2-α))convergence rate of the standard L1 scheme.The analysis relies on a delicate decomposition of the temporal truncation error that yields a sharp dependence of the order of convergence on the degree of mesh grading used.This averaged L1 scheme can be combined with a finite difference or piecewise linear finite element discretization in space for IBVPs,and under a restriction on the temporal mesh width,one gets again O(N-2)convergence in time,together with O(h2)convergence in space,where h is the spatial mesh width.Numerical experiments support our results.
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    Boundary points,minimal L2 integrals and concavity property Ⅱ:Weakly pseudoconvex K?hler manifolds

    Qi'an GuanZhitong MiZheng Yuan
    1665-1718页
    查看更多>>摘要：In this paper,we consider minimal L2 integrals on the sublevel sets of plurisubharmonic functions on weakly pseudoconvex Kähler manifolds with Lebesgue measurable gain related to modules at boundary points of the sublevel sets,and establish a concavity property of the minimal L2 integrals.As applications,we present a necessary condition for the concavity degenerating to linearity,a concavity property related to modules at inner points of the sublevel sets,an optimal support function related to modules,a strong openness property of modules and a twisted version,and an effectiveness result of the strong openness property of modules.
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