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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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    Eventually homological isomorphisms and Gorenstein projective modules

    Yongyun QinDawei Shen
    1719-1734页
    查看更多>>摘要：We prove that a certain eventually homological isomorphism between module categories induces triangle equivalences between their singularity categories,Gorenstein defect categories and stable categories of Gorenstein projective modules.Furthermore,we show that the Auslander-Reiten conjecture and the Gorenstein symmetry conjecture can be reduced by eventually homological isomorphisms.Applying these results to arrow removal and vertex removal,we describe the Gorenstein projective modules over some non-monomial algebras and verify the Auslander-Reiten conjecture for certain algebras.
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    Semi-derived Ringel-Hall algebras and Hall algebras of odd-periodic relative derived categories

    Ji LinLiangang Peng
    1735-1760页
    查看更多>>摘要：Let t be a positive integer and A be a hereditary abelian category satisfying some finiteness conditions.We define the semi-derived Ringel-Hall algebra of A from the category Cz/t(A)of Z/t-graded complexes and obtain a natural basis of the semi-derived Ringel-Hall algebra.Moreover,we describe the semi-derived Ringel-Hall algebra by the generators and defining relations.In particular,if t is an odd integer,we show an embedding of the derived Hall algebra of the odd-periodic relative derived category in the extended semi-derived Ringel-Hall algebra.
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    Long-wave instabilities

    Dongfen BianEmmanuel Grenier
    1761-1776页
    查看更多>>摘要：This paper aims to give a detailed presentation of long-wave instabilities of shear layers for Navier-Stokes equations,and in particular to give a simple and easy-to-read presentation of the study of the Orr-Sommerfeld equation and to detail the analysis of its adjoint.Using these analyses,we prove the existence of long-wave instabilities in the cases of slowly rotating fluids,slightly compressible fluids,or fluids with Navier boundary conditions,under smallness conditions.
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    H?lder continuous weak solutions of the 2D Boussinesq equation with thermal diffusion

    Tianwen LuoTao TaoLiqun Zhang
    1777-1806页
    查看更多>>摘要：We show the existence of Holder continuous periodic weak solutions of the 2D Boussinesq equation with thermal diffusion which satisfy the prescribed kinetic energy.More precisely,for any smooth e(t):[0,1]→ R+and ε ∈(0,1/10),there exist v ∈ C1/10-ε([0,1]× T2)and θ ∈ C1,1/20-ε/2tC2,1/10-εx([0,1]× T2),which satisfy(1.1)in the sense of distribution and e(t)=∫T2|v(t,x)|2dx,(v)t ∈[0,1].
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    Non-symmetric differentially subordinate martingales and sharp weak-type bounds for Fourier multipliers

    Meryem AkboudjYong JiaoAdam Osękowski
    1807-1826页
    查看更多>>摘要：Let p＞2 be a given exponent.In this paper,we prove,with the best constant,the weak-type(p,p)inequality||Tmf||Lp,∞(Rd)≤ Cp||f||Lp(Rd)for a large class of non-symmetric Fourier multipliers Tm obtained via modulation of jumps of certain Lévy processes.In particular,the estimate holds for appropriate linear combinations of second-order Riesz transforms and skew versions of the Beurling-Ahlfors operator on the complex plane.The proof rests on a novel probabilistic bound for Hilbert-space-valued martingales satisfying a certain non-symmetric subordination principle.Further applications to harmonic functions and Riesz systems on Euclidean domains are indicated.
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    Geometry of holomorphic invariant strongly pseudoconvex complex Finsler metrics on the classical domains

    Xiaoshu GeChunping Zhong
    1827-1864页
    查看更多>>摘要：In this paper,a class of holomorphic invariant metrics is introduced on the irreducible classical domains of types Ⅰ-Ⅳ,which are strongly pseudoconvex complex Finsler metrics in the strict sense of Abate and Patrizio(1994).These metrics are of particular interest in several complex variables since they are holomorphic invariant complex Finsler metrics found in the literature which enjoy good regularity as well as strong pseudoconvexity and can be explicitly expressed to admit differential geometry studies.They are,however,not necessarily Hermitian quadratic as the Bergman metrics.These metrics are explicitly constructed via deformation of the corresponding Bergman metric on the irreducible classical domains of types Ⅰ-Ⅳ,respectively,and they are all proved to be complete Kähler-Berwald metrics.They enjoy very similar curvature properties as those of the Bergman metric on the irreducible classical domains,i.e.,their holomorphic sectional curvatures are bounded between two negative constants and their holomorphic bisectional curvatures are always nonpositive and bounded below by negative constants,respectively.From the viewpoint of complex analysis,these metrics are analogs of Bergman metrics in complex Finsler geometry which do not necessarily have Hermitian quadratic restrictions in the sense of Chern(1996).
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    Normalized and self-normalized Cramér-type moderate deviations for the Euler-Maruyama scheme for the SDE

    Xiequan FanHaijuan HuLihu Xu
    1865-1880页
    查看更多>>摘要：In this paper,we establish normalized and self-normalized Cramér-type moderate deviations for the Euler-Maruyama scheme for SDE.Due to our results,Berry-Esseen's bounds and moderate deviation principles are also obtained.Our normalized Cramér-type moderate deviations refine the recent work of Lu et al.(2022).
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    Flexible,efficient,and accurate tests for epidemics

    Linjiajie FangBing-Yi JingShen LingQiyue Wang...
    1881-1898页
    查看更多>>摘要：Group testing involves discovering a small subset of distinguished subjects from a large population while efficiently reducing the total number of tests.It has been widely used for industrial testing,information technology,and biology,especially epidemic screening.Tests,in reality,are noisy for the presence of false outcomes.Some tests are accurate but time-consuming,while others are cheaper but less accurate.Exactly which test to use is constrained by various considerations,such as availability,cost,accuracy,and efficiency.In this paper,we propose flexible,efficient,and accurate tests(FEATs).FEATs are based on group testing with simple but careful designs by incorporating ideas such as close contact cliques and repeated tests.FEATs could dramatically improve the efficiency or accuracy of existing tests.For example,for accurate but slow tests,the FEAT can improve efficiency multiple times without compromising accuracy.On the other hand,for fast but inaccurate tests,the FEAT can sharply reduce the false-negative rate(FNR)and significantly increase efficiency.Theoretical justifications are provided.We point out some scenarios where the FEAT can be effectively employed.
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    On the superconvergence of a WG method for the elliptic problem with variable coefficients

    Junping WangXiaoshen WangXiu YeShangyou Zhang...
    1899-1910页
    查看更多>>摘要：This article extends a recently developed superconvergence result for weak Galerkin(WG)approximations for modeling partial differential equations from constant coefficients to variable coefficients.This superconvergence features a rate that is two orders higher than the optimal-order error estimates in the usual energy and L2 norms.The extension from constant to variable coefficients for the modeling equations is highly non-trivial.The underlying technical analysis is based on a sequence of projections and decompositions.Numerical results confirm the superconvergence theory for second-order elliptic problems with variable coefficients.
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    Parametric"non-nested"discriminants for multiplicities of univariate polynomials

    Hoon HongJing Yang
    1911-1932页
    查看更多>>摘要：We consider the problem of complex root classification,i.e.,finding the conditions on the coefficients of a univariate polynomial for all possible multiplicity structures on its complex roots.It is well known that such conditions can be written as conjunctions of several polynomial equalities and one inequality in the coefficients.Those polynomials in the coefficients are called discriminants for multiplicities.It is also known that discriminants can be obtained using repeated parametric greatest common divisors.The resulting discriminants are usually nested determinants,i.e.,determinants of matrices whose entries are determinants,and so on.In this paper,we give a new type of discriminant that is not based on repeated greatest common divisors.The new discriminants are simpler in the sense that they are non-nested determinants and have smaller maximum degrees.
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