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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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    Pseudoeffective thresholds and cohomology of twisted symmetric tensor fields on irreducible Hermitian symmetric spaces

    Feng Shao
    2433-2452页
    查看更多>>摘要：Let X be an irreducible Hermitian symmetric space of compact type(IHSS for short).In this paper,we give the irreducible decomposition of SymrTx.As a by-product,we give a cohomological characterization of the rank of X.Moreover,we introduce pseudoeffective thresholds to measure the bigness of tangent bundles of smooth complex projective varieties precisely and calculate them for irreducible Hermitian symmetric spaces of compact type.
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    Gorenstein projective modules over rings of Morita contexts

    Qianqian GuoChangchang Xi
    2453-2484页
    查看更多>>摘要：Under semi-weak and weak compatibility conditions of bimodules,we establish necessary and sufficient conditions of Gorenstein-projective modules over rings of Morita contexts with one bimodule homomorphism zero.This extends greatly the results on triangular matrix Artin algebras and on Artin algebras of Morita contexts with two bimodule homomorphisms zero in the literature,where only sufficient conditions are given under a strong assumption of compatibility of bimodules.An application is provided to describe Gorenstein-projective modules over noncommutative tensor products arising from Morita contexts.Our results are proved under a general setting of noetherian rings and modules instead of Artin algebras and modules.
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    Global classical solutions for 3D compressible magneto-micropolar fluids without resistivity and spin viscosity in a strip domain

    Zefu FengGuangyi HongChangjiang Zhu
    2485-2514页
    查看更多>>摘要：In this paper,we consider 3D compressible magneto-micropolar fluids without resistivity and spin viscosity in a strip domain.The prominent character of the governing model is the presence of the microstructure,a linear coupling structure involving derivatives of the velocity fields,which along with the lack of spin viscosity brings several challenges to the analysis.By exploiting the two-tier energy method developed in Guo and Tice(Arch Ration Mech Anal,2013),we prove the global existence of classical solutions to the governing model around a uniform magnetic field that is non-parallel to the horizontal boundary.Moreover,we show that the solution converges to the steady state at an almost exponential rate as time goes to infinity.One of the main ingredients in our analysis,compared with previous works on micropolar fluids,is that we deal with the microstructure by establishing some delicate estimates based on the analysis of the div-curl decomposition,and the coupling between the fluid velocity and the vorticity of angular velocity.
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    Point defects in 2-D liquid crystals with a singular potential:Profiles and stability

    Zhiyuan GengWei Wang
    2515-2540页
    查看更多>>摘要：We study radial symmetric point defects with degree k/2 in the 2-D disk or R2 in the Q-tensor framework with a singular bulk energy,which is defined by Bingham closure.First,we obtain the existence of solutions for the profiles of radial symmetric point defects with degree k/2 in the 2-D disk or R2.Then,we prove that the solution is stable for|k|=1 and unstable for|k|＞1.Some identities are derived and utilized throughout the proof of existence and stability/instability.
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    Aubry-Mather theory for contact Hamiltonian systems Ⅲ

    Panrui NiLin Wang
    2541-2570页
    查看更多>>摘要：By exploiting the contact Hamiltonian dynamics(T*M × R,Φt)around the Aubry set of contact Hamiltonian systems,we provide a relation among the Mather set,the Φt-recurrent set,the strongly static set,the Aubry set,the Mané set,and the Φt-non-wandering set.Moreover,we consider the strongly static set,as a new flow-invariant set between the Mather set and the Aubry set in the strictly increasing case.We show that this set plays an essential role in the representation of certain minimal forward weak Kolmogorov-Arnold-Moser(KAM)solutions and the existence of transitive orbits around the Aubry set.
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    Jackson-type inequalities on high-dimensional spheres

    Yeli NiuFeng Dai
    2571-2586页
    查看更多>>摘要：We study Jackson's inequality on high-dimensional spheres with respect to the modulus of smoothness defined via the rotation group.We obtain a version of Jackson's inequality with a dimension-free constant,extending Newman and Shapiro's well-known results in 1964 from the case of r=1 and p=∞ to more general cases.Our results partially overcome the curse of dimensionality.We also establish similar results on the equivalence of the K-functional and modulus of smoothness.
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    Optimal control of differential quasivariational-hemivariational inequalities with applications

    Dong-ling CaiStanisław MigórskiYi-bin Xiao
    2587-2606页
    查看更多>>摘要：In this paper,we study a new class of differential quasivariational-hemivariational inequalities of the elliptic type.The problem consists of a system coupling the Cauchy problem for an ordinary differential equation with the variational-hemivariational inequalities,unilateral constraints,and history-dependent operators.First,based on the Minty formulation and the continuity of the solution map of a parametrized quasivariational-hemivariational inequality,and a fixed point theorem for a history-dependent operator,we prove a result on the well-posedness.Next,we examine optimal control problems for differential quasivariational-hemivariational inequalities,including a time-optimal control problem and a maximum stay control problem,for which we show the existence of solutions.In all the optimal control problems,the system is controlled through a distributed and boundary control,a control in initial conditions,and a control that appears in history-dependent operators.Finally,we illustrate the results by considering a nonlinear controlled system for a time-dependent elliptic equation with unilateral constraints.
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    Minimal Legendrian surfaces in the tangent sphere bundle of R3

    Mingyan LiGuofang Wang
    2607-2628页
    查看更多>>摘要：In this paper,we study minimal Legendrian surfaces ∑ immersed in the tangent sphere bundle T1R3.We classify(1)totally geodesic Legendrian surfaces,(2)closed minimal Legendrian surfaces of genus smaller than or equal to 1 and complete minimal Legendrian surfaces with the non-negative Gauss curvature,and(3)complete stable minimal Legendrian surfaces.
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    Berry-Esseen bounds for self-normalized sums of locally dependent random variables

    Zhuo-Song Zhang
    2629-2652页
    查看更多>>摘要：The Berry-Esseen bound provides an upper bound on the Kolmogorov distance between a random variable and the normal distribution.In this paper,we establish Berry-Esseen bounds with optimal rates for self-normalized sums of locally dependent random variables,assuming only a second-moment condition.Our proof leverages Stein's method and introduces a novel randomized concentration inequality,which may also be of independent interest for other applications.Our main results have applied to self-normalized sums of m-dependent random variables and graph dependency models.
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    A fiducial approach to the nonparametric deconvolution problem:The discrete case

    Yifan CuiJan Hannig
    2653-2670页
    查看更多>>摘要：Fiducial inference is applied to nonparametric g-modeling in the discrete case.We propose a computationally efficient algorithm to sample from the fiducial distribution and use the generated samples to construct point estimates and confidence intervals.We study the theoretical properties of the fiducial distribution and perform extensive simulations in various scenarios.The proposed approach gives rise to good statistical performance in terms of the mean squared error of point estimators and coverage of confidence intervals.Furthermore,we apply the proposed fiducial method to estimate the probability of each satellite site being malignant using gastric adenocarcinoma data with 844 patients.
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