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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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    One-cycles on Gushel-Mukai fourfolds and the Beauville-Voisin filtration

    Ruxuan Zhang
    713-732页
    查看更多>>摘要：We prove that the invariant locus of the involution associated with a general double Eisenbud-Popescu-Walter(EPW)sextic is a constant cycle surface and introduce a filtration on CH1 of a Gushel-Mukai fourfold.We verify the sheaf/cycle correspondence for sheaves supported on low-degree rational curves,parallel to the case of cubic fourfolds of Shen-Yin's work.
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    Homological dimensions of gentle algebras via geometric models

    Yu-Zhe LiuHanpeng GaoZhaoyong Huang
    733-766页
    查看更多>>摘要：Let A=kQ/I be a finite-dimensional basic algebra over an algebraically closed field k,which is a gentle algebra with the marked ribbon surface(SA,M A,ГA).It is known that SA can be divided into some elementary polygons {Δi | 1 ≤ i ≤ d} by ГA,which has exactly one side in the boundary of SA.Let (c)(Δi)be the number of sides of Δi belonging to ГA if the unmarked boundary component of SA is not a side of Δi;otherwise,(c)(Δi)=∞,and let f-Δ be the set of all the non-∞-elementary polygons and FA(resp.f-FA)be the set of all the forbidden threads(resp.of finite length).Then we have(1)the global dimension of A is max1≤i≤d(c)(Δi)—1=maxп∈FA l(Π),where l(Π)is the length of Π;(2)the left and right self-injective dimensions of A are{0,if Q is either a point or an oriented cycle with full relations,maxΔi∈f-Δ{1,(c)(Δi)-1}=maxΠ∈f-FA l(Π),otherwise.As a consequence,we get that the finiteness of the global dimension of gentle algebras is invariant under Avella-Geiss(AG)-equivalence.In addition,we get that the number of indecomposable non-projective Gorenstein projective modules over gentle algebras is also invariant under AG-equivalence.
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    Some properties of Melnikov functions near a cuspidal loop

    Junmin YangMaoan Han
    767-786页
    查看更多>>摘要：In this paper,we consider the first-order Melnikov functions and limit cycle bifurcations of a near-Hamiltonian system near a cuspidal loop.By establishing relations between the coefficients in the expansions of the two Melnikov functions,we give a general method to obtain the number of limit cycles near the cuspidal loop.As an application,we consider a kind of Liénard systems and obtain a new estimation on the lower bound of the maximum number of limit cycles.
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    The low Mach number limit of non-isentropic magnetohydrodynamic equations with large temperature variations in bounded domains

    Min LiangYaobin Ou
    787-818页
    查看更多>>摘要：This paper verifies the low Mach number limit of the non-isentropic compressible magnetohydrody-namic(MHD)equations with or without the magnetic diffusion in a three-dimensional bounded domain when the temperature variation is large but finite.The uniform estimates of strong solutions are established in a short time interval independent of the Mach number,provided that the slip boundary condition for the velocity and the Neumann boundary condition for the temperature are imposed and the initial data is well-prepared.
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    On Leray's problem in an infinitely long pipe with the Navier-slip boundary condition

    Zijin LiXinghong PanJiaqi Yang
    819-854页
    查看更多>>摘要：The original Leray's problem concerns the well-posedness of weak solutions to the steady incompressible Navier-Stokes equations in a distorted pipe,which approach the Poiseuille flow subject to the no-slip boundary condition at spatial infinity.In this paper,the same problem with the Navier-slip boundary condition instead of the no-slip boundary condition,is addressed.Due to the complexity of the boundary condition,some new ideas,presented as follows,are introduced to handle the extra difficulties caused by boundary terms.First,the Poiseuille flow in the semi-infinite straight pipe with the Navier-slip boundary condition will be introduced,which will serve as the asymptotic profile of the solution to the generalized Leray's problem at spatial infinity.Second,a solenoidal vector function defined in the whole pipe,satisfying the Navier-slip boundary condition,having the designated flux and equalling the Poiseuille flow at a large distance,will be carefully constructed.This plays an important role in reformulating our problem.Third,the energy estimates depend on a combined L2-estimate of the gradient and the stress tensor of the velocity.
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    Rigidity of non-renormalizable Newton maps

    Pascale RoeschYongcheng YinJinsong Zeng
    855-872页
    查看更多>>摘要：Non-renormalizable Newton maps are rigid.More precisely,we prove that their Julia sets carry no invariant line fields and that a topological conjugacy between them is equivalent to a quasiconformal conjugacy.
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    Classification of complete 3-dimensional self-shrinkers in the Euclidean space R4

    Qing-Ming ChengZhi LiGuoxin Wei
    873-882页
    查看更多>>摘要：In this paper,we completely classify 3-dimensional complete self-shrinkers with the constant norm S of the second fundamental form and the constant f3 in the Euclidean space R4,where hij's are components of the second fundamental form,S=Σi,jh2ij and f3=Σi,j,khijhjkhki.
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    A new quantity in Finsler geometry

    Xiaohuan MoXiaoyang Wang
    883-890页
    查看更多>>摘要：In this paper,we study a new Finslerian quantity(T)defined by the T-curvature and the angular metric tensor.We show that the(T)-curvature not only gives a measure of the failure of a Finsler metric to be of scalar flag curvature but also has a vanishing trace.We find that the T-curvature is closely related to the Riemann curvature,the Matsumoto torsion and the(Θ)-curvature.We solve Z.Shen's open problem in terms of the(T)-curvature.Finally,we give a global rigidity result for Finsler metrics of negative Ricci curvature on a compact manifold via the(T)-curvature,generalizing a theorem previously only known in the case of negatively curved Finsler metrics of scalar flag curvature.
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    High-dimensional robust inference for censored linear models

    Jiayu HuangYuanshan Wu
    891-918页
    查看更多>>摘要：Due to the direct statistical interpretation,censored linear regression offers a valuable complement to the Cox proportional hazards regression in survival analysis.We propose a rank-based high-dimensional inference for censored linear regression without imposing any moment condition on the model error.We develop a theory of the high-dimensional U-statistic,circumvent challenges stemming from the non-smoothness of the loss function,and establish the convergence rate of the regularized estimator and the asymptotic normality of the resulting de-biased estimator as well as the consistency of the asymptotic variance estimation.As censoring can be viewed as a way of trimming,it strengthens the robustness of the rank-based high-dimensional inference,particularly for the heavy-tailed model error or the outlier in the presence of the response.We evaluate the finite-sample performance of the proposed method via extensive simulation studies and demonstrate its utility by applying it to a subcohort study from The Cancer Genome Atlas(TCGA).
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    The fast method and convergence analysis of the fractional magnetohydrodynamic coupled flow and heat transfer model for the generalized second-grade fluid

    Xiaoqing ChiHui ZhangXiaoyun Jiang
    919-950页
    查看更多>>摘要：In this paper,we first establish a new fractional magnetohydrodynamic(MHD)coupled flow and heat transfer model for a generalized second-grade fluid.This coupled model consists of a fractional momentum equation and a heat conduction equation with a generalized form of Fourier law.The second-order fractional backward difference formula is applied to the temporal discretization and the Legendre spectral method is used for the spatial discretization.The fully discrete scheme is proved to be stable and convergent with an accuracy of O((τ)2+N-r),where(τ) is the time step-size and N is the polynomial degree.To reduce the memory requirements and computational cost,a fast method is developed,which is based on a globally uniform approximation of the trapezoidal rule for integrals on the real line.The strict convergence of the numerical scheme with this fast method is proved.We present the results of several numerical experiments to verify the effectiveness of the proposed method.Finally,we simulate the unsteady fractional MHD flow and heat transfer of the generalized second-grade fluid through a porous medium.The effects of the relevant parameters on the velocity and temperature are presented and analyzed in detail.
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