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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 the inviscid limit of the compressible Navier-Stokes equations near Onsager's regularity in bounded domains

    Robin Ming ChenZhilei LiangDehua WangRunzhang Xu...
    1-22页
    查看更多>>摘要：The viscous dissipation limit of weak solutions is considered for the Navier-Stokes equations of compressible isentropic flows confined in a bounded domain.We establish a Kato-type criterion for the validity of the inviscid limit for the weak solutions of the Navier-Stokes equations in a function space with the regularity index close to Onsager's critical threshold.In particular,we prove that under such a regularity assumption,if the viscous energy dissipation rate vanishes in a boundary layer of thickness in the order of the viscosity,then the weak solutions of the Navier-Stokes equations converge to a weak admissible solution of the Euler equations.Our approach is based on the commutator estimates and a subtle foliation technique near the boundary of the domain.
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    Cα regularity of weak solutions of non-homogeneous ultraparabolic equations with drift terms

    Wendong WangLiqun Zhang
    23-44页
    查看更多>>摘要：We consider a class of non-homogeneous ultraparabolic differential equations with singular drift terms arising from some physical models,and prove that weak solutions are Hölder continuous,which are sharp in some sense and also generalize the well-known De Giorgi-Nash-Moser theory to degenerate parabolic equations satisfying the Hörmander hypoellipticity condition.The new ingredients are manifested in two aspects:on the one hand,for lower-order terms,we exploit a new Sobolev inequality suitable for the Moser iteration by improving the result of Pascucci and Polidoro(2004);on the other hand,we explore the G-function from an early idea of Kruzhkov(1964)and an approximate weak Poincaré inequality for non-negative weak sub-solutions to prove the Hölder regularity.
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    On self-affine tiles that are homeomorphic to a ball

    J?rg M.ThuswaldnerShu-Qin Zhang
    45-76页
    查看更多>>摘要：Let M be a 3 × 3 integer matrix which is expanding in the sense that each of its eigenvalues is greater than 1 in modulus and let D C Z3 be a digit set containing |det M| elements.Then the unique nonempty compact set T=T(M,D)defined by the set equation MT=T+D is called an integral self-affine tile if its interior is nonempty.If D is of the form D={0,v,...,(|det M|-1)v},we say that T has a collinear digit set.The present paper is devoted to the topology of integral self-affine tiles with collinear digit sets.In particular,we prove that a large class of these tiles is homeomorphic to a closed 3-dimensional ball.Moreover,we show that in this case,T carries a natural CW complex structure that is defined in terms of the intersections of T with its neighbors in the lattice tiling {T+z:z ∈ Z3} induced by T.This CW complex structure is isomorphic to the CW complex defined by the truncated octahedron.
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    On the core entropy of Newton maps

    Yan Gao
    77-128页
    查看更多>>摘要：In this paper,we define the core entropy for postcritically-finite Newton maps and study its continuity within this family.We show that the entropy function is not continuous in this family,which is different from the polynomial case,and describe completely the continuity of the entropy function at the generic parameters.
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    The symmetric space,strong isotropy irreducibility and equigeodesic properties

    Ming XuJu Tan
    129-148页
    查看更多>>摘要：A smooth curve on a homogeneous manifold G/H is called a Riemannian equigeodesic if it is a homogeneous geodesic for any G-invariant Riemannian metric.The homogeneous manifold G/H is called Riemannian equigeodesic,if for any x ∈ G/H and any nonzero y ∈ Tx(G/H),there exists a Riemannian equigeodesic c(t)with c(0)=x and (c)(0)=y.These two notions can be naturally transferred to the Finsler setting,which provides the definitions for Finsler equigeodesics and Finsler equigeodesic spaces.We prove two classification theorems for Riemannian equigeodesic spaces and Finsler equigeodesic spaces,respectively.Firstly,a homogeneous manifold G/H with a connected simply connected quasi compact G and a connected H is Riemannian equigeodesic if and only if it can be decomposed as a product of Euclidean factors and compact strongly isotropy irreducible factors.Secondly,a homogeneous manifold G/H with a compact semisimple G is Finsler equigeodesic if and only if it can be locally decomposed as a product,in which each factor is Spin(7)/G2,G2/SU(3) or a symmetric space of compact type.These results imply that the symmetric space and the strongly isotropy irreducible space of compact type can be interpreted by equigeodesic properties.As an application,we classify the homogeneous manifold G/H with a compact semisimple G such that all the G-invariant Finsler metrics on G/H are Berwald.It suggests a new project in homogeneous Finsler geometry,i.e.,to systematically study the homogeneous manifold G/H on which all the G-invariant Finsler metrics satisfy a certain geometric property.
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    An infinite-dimensional representation of the Ray-Knight theorems

    Elie A?dékonYueyun HuZhan Shi
    149-162页
    查看更多>>摘要：The classical Ray-Knight theorems for the Brownian motion determine the law of its local time process either at the first hitting time of a given value a by the local time at the origin,or at the first hitting time of a given position b by the Brownian motion.We extend these results by describing the local time process jointly for all a and b,by means of the stochastic integral with respect to an appropriate white noise.Our result applies to μ-processes,and has an immediate application:a μ-process is the height process of a Feller continuous-state branching process(CSBP)with immigration(Lambert(2002)),whereas a Feller CSBP with immigration satisfies a stochastic differential equation(SDE)driven by a white noise(Dawson and Li(2012));our result gives an explicit relation between these two descriptions and shows that the SDE in question is a reformulation of Tanaka's formula.
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    Asymptotics for the joint tail probability of bidimensional randomly weighted sums with applications to insurance

    Yang YangShaoying ChenKam Chuen Yuen
    163-186页
    查看更多>>摘要：This paper studies the joint tail behavior of two randomly weighted sums ∑mi=1ΘiXi and ∑nj=1 θjYj for some m,n ∈ N∪ {∞},in which the primary random variables {Xi;i ∈ N} and {Yi;i ∈ N},respectively,are real-valued,dependent and heavy-tailed,while the random weights {Θi,θi;i∈ N} are nonnegative and arbitrarily dependent,but the three sequences {Xi;i ∈ N},{Yi;i ∈ N} and{Θi,θi;i∈ N} are mutually independent.Under two types of weak dependence assumptions on the heavy-tailed primary random variables and some mild moment conditions on the random weights,we establish some(uniformly)asymptotic formulas for the joint tail probability of the two randomly weighted sums,expressing the insensitivity with respect to the underlying weak dependence structures.As applications,we consider both discrete-time and continuous-time insurance risk models,and obtain some asymptotic results for ruin probabilities.
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    Double stabilizations and convergence analysis of a second-order linear numerical scheme for the nonlocal Cahn-Hilliard equation

    Xiao LiZhonghua QiaoCheng Wang
    187-210页
    查看更多>>摘要：In this paper,we study a second-order accurate and linear numerical scheme for the nonlocal Cahn-Hilliard equation,The scheme is established by combining a modified Crank-Nicolson approximation and the Adams-Bashforth extrapolation for the temporal discretization,and by applying the Fourier spectral collocation to the spatial discretization.In addition,two stabilization terms in different forms are added for the sake of the numerical stability.We conduct a complete convergence analysis by using the higher-order consistency estimate for the numerical scheme,combined with the rough error estimate and the refined estimate.By regarding the numerical solution as a small perturbation of the exact solution,we are able to justify the discrete l∞ bound of the numerical solution,as a result of the rough error estimate.Subsequently,the refined error estimate is derived to obtain the optimal rate of convergence,following the established l∞ bound of the numerical solution.Moreover,the energy stability is also rigorously proved with respect to a modified energy.The proposed scheme can be viewed as the generalization of the second-order scheme presented in an earlier work,and the energy stability estimate has greatly improved the corresponding result therein.
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    Time-inconsistent stochastic linear-quadratic control problem with indefinite control weight costs

    Qi LüBowen Ma
    211-236页
    查看更多>>摘要：A time-inconsistent linear-quadratic optimal control problem for stochastic differential equations is studied.We introduce conditions where the control cost weighting matrix is possibly singular.Under such conditions,we obtain a family of closed-loop equilibrium strategies via multi-person differential games.This result extends Yong's work(2017)in the case of stochastic differential equations,where a unique closed-loop equilibrium strategy can be derived under standard conditions(namely,the control cost weighting matrix is uniformly positive definite,and the other weighting coefficients are positive semidefinite).
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