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中国科学：数学（英文版）
中国科学：数学（英文版）

周光召

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1674-7283

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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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    Nadel-type multiplier ideal sheaves on complex spaces with singularities

    Zhenqian Li
    951-974页
    查看更多>>摘要：In this article,we introduce multiplier ideal sheaves on complex spaces with singularities(not necessarily normal)via Ohsawa's extension measure,as a special case of which,it turns out to be the so-called Mather-Jacobian multiplier ideals in the algebro-geometric setting.Inspired by Nadel's coherence and Guan-Zhou's strong openness properties of the multiplier ideal sheaves,we discuss similar properties for the generalized multiplier ideal sheaves.As applications,we obtain a reasonable generalization of(algebraic)adjoint ideal sheaves to the analytic setting and establish some extension theorems on Kähler manifolds from singular hypersurfaces.Relying on our multiplier and adjoint ideals,we also give characterizations for several important classes of singularities of pairs associated with plurisubharmonic functions.
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    • 维普

    The spectrum and stability of travelling pulses in a coupled FitzHugh-Nagumo equation

    Qi QiaoXiang Zhang
    975-1010页
    查看更多>>摘要：For a coupled slow-fast FitzHugh-Nagumo(FHN)equation derived from a reaction-diffusion-mechanics(RDM)model,Holzer et al.(2013)studied the existence and stability of the travelling pulse,which consists of two fast orbit arcs and two slow ones,where one fast segment passes the unique fold point with algebraic decreasing and two slow ones follow normally hyperbolic critical curve segments.Shen and Zhang(2021)obtained the existence of the travelling pulse,whose two fast orbit arcs both exponentially decrease,and one of the slow orbit arcs could be normally hyperbolic or not at the origin.Here,we characterize both the nonlinear and spectral stability of this travelling pulse.
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    Quantitative Green's function estimates for lattice quasi-periodic Schr?dinger operators

    Hongyi CaoYunfeng ShiZhifei Zhang
    1011-1058页
    查看更多>>摘要：In this paper,we establish quantitative Green's function estimates for some higher-dimensional lattice quasi-periodic(QP)Schrödinger operators.The resonances in the estimates can be described via a pair of symmetric zeros of certain functions,and the estimates apply to the sub-exponential-type non-resonance conditions.As the application of quantitative Green's function estimates,we prove both the arithmetic version of Anderson localization and the finite volume version of(1/2-)-Hölder continuity of the integrated density of states(IDS)for such QP Schrödinger operators.This gives an affirmative answer to Bourgain's problem in Bourgain(2000).
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    Space-time estimates of the 3D bipolar compressible Navier-Stokes-Poisson system with unequal viscosities

    Zhigang WuWeike Wang
    1059-1084页
    查看更多>>摘要：The space-time behavior for the Cauchy problem of the 3D compressible bipolar Navier-Stokes-Poisson(BNSP)system with unequal viscosities is given.The space-time estimate of the electric field▽ø=▽(-△)-1(n-Zρ)is the most important in deducing generalized Huygens'principle for the BNSP system and it requires proving that the space-time estimate of n-Zρ only contains the diffusion wave due to the singularity of the operator ▽(-△)-1.A suitable linear combination of unknowns reformulating the original system into two small subsystems for the special case(with equal viscosities)in Wu and Wang(2017)is crucial for both linear analysis and nonlinear estimates,especially for the space-time estimate of ▽φ.However,the benefits from this reformulation will no longer exist in general cases.Here,we study an 8 x 8 Green's matrix directly.More importantly,each entry in Green's matrix contains wave operators in the low-frequency part,which will generally produce Huygens'wave;as a result,one cannot achieve the space-time estimate of n-Zρthat only contains the diffusion wave as before.We overcome this difficulty by taking a more detailed spectral analysis and developing new estimates arising from subtle cancellations in Green's function.
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    The twisted conical K?hler-Ricci solitons on Fano manifolds

    Xishen JinJiawei Liu
    1085-1102页
    查看更多>>摘要：In this paper,we show the relation between the existence of twisted conical Kähler-Ricci solitons and the greatest log Bakry-Emery-Ricci lower bound on Fano manifolds.This is based on our proofs of some openness theorems on the existence of twisted conical Kähler-Ricci solitons,which generalize Donaldson's existence conjecture and the openness theorem of the conical Kähler-Einstein metrics to the conical soliton case.
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    Spectral flow,Llarull's rigidity theorem in odd dimensions and its generalization

    Yihan LiGuangxiang SuXiangsheng Wang
    1103-1114页
    查看更多>>摘要：For a compact spin Riemannian manifold(M,gTM)of dimension n such that the associated scalar curvature kTM verifies that kTM≥n(n-1),Llarull's rigidity theorem says that any area-decreasing smooth map f from M to the unit sphere Sn of nonzero degree is an isometry.In this paper,we present a new proof of Llarull's rigidity theorem in odd dimensions via a spectral flow argument.This approach also works for a generalization of Llarull's theorem when the sphere Sn is replaced by an arbitrary smooth strictly convex closed hypersurface inRn+1.The results answer two questions by Gromov(2023).
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    A GMM approach in coupling internal data and external summary information with heterogeneous data populations

    Jun ShaoJinyi WangLei Wang
    1115-1132页
    查看更多>>摘要：Because of advances in data collection and storage,statistical analysis in modern scientific research and practice now has opportunities to utilize external information such as summary statistics from similar studies.A likelihood approach based on a parametric model assumption has been developed in the literature to utilize external summary information when the populations for external and main internal data are assumed to be the same.In this article,we instead consider the generalized estimation equation(GEE)approach for statistical inference,which is semiparametric or nonparametric,and show how to utilize external summary information even when internal and external data populations are not the same.Our approach is coupling the internal data and external summary information to form additional estimation equations and then applying the generalized method of moments(GMM).We show that the proposed GMM estimator is asymptotically normal and,under some conditions,is more efficient than the GEE estimator without using external summary information.Estimators of the asymptotic covariance matrix of the GMM estimators are also proposed.Simulation results are obtained to confirm our theory and quantify the improvements by utilizing external data.An example is also included for illustration.
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    Analysis of a class of globally divergence-free HDG methods for stationary Navier-Stokes equations

    Gang ChenXiaoping Xie
    1133-1158页
    查看更多>>摘要：In this paper,we analyze a class of globally divergence-free(and therefore pressure-robust)hybridizable discontinuous Galerkin(HDG)finite element methods for stationary Navier-Stokes equations.The methods use the Pk/Pk-1(k≥1)discontinuous finite element combination for the velocity and pressure approximations in the interior of elements,piecewise Pm(m=k,k-1)for the velocity gradient approximation in the interior of elements,and piecewise Pk/Pk for the trace approximations of the velocity and pressure on the inter-element boundaries.We show that the uniqueness condition for the discrete solution is guaranteed by that for the continuous solution together with a sufficiently small mesh size.Based on the derived discrete HDG Sobolev embedding properties,optimal error estimates are obtained.Numerical experiments are performed to verify the theoretical analysis.
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    Mean field game of optimal relative investment with jump risk

    Lijun BoShihua WangXiang Yu
    1159-1188页
    查看更多>>摘要：In this paper,we study the n-player game and the mean field game under the constant relative risk aversion relative performance on terminal wealth,in which the interaction occurs by peer competition.In the model with n agents,the price dynamics of underlying risky assets depend on a common noise and contagious jump risk modeled by a multi-dimensional nonlinear Hawkes process.With a continuum of agents,we formulate the mean field game problem and characterize a deterministic mean field equilibrium in an analytical form under some conditions,allowing us to investigate some impacts of model parameters in the limiting model and discuss some financial implications.Moreover,based on the mean field equilibrium,we construct an approximate Nash equilibrium for the n-player game when n is sufficiently large.The explicit order of the approximation error is also derived.
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