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science China mathematics 2024年第7期67卷 1641-1664页

作者： Jinye Shen Fanhai Zeng Martin Stynes school of mathematics Southwestern University of Finance and EconomicsChengdu611130China school of mathematics Shandong UniversityJinan250100China Applied and computational mathematics Division Beijing Computational Science Research CenterBeijing100193China

Fractional initial-value problems(IVPs) and time-fractional initial-boundary value problems(IBVPs), each with a Caputo temporal derivative of order α ∈(0, 1), are considered. An averaged variant of the well-known L1 scheme is proved to be O(N^(-2)) convergent for IVPs on suitably graded meshes with N points, thereby improving the O(N^(-(2-α))) convergence rate of the standard L1 scheme. The analysis relies on a delicate decomposition of the temporal truncation error that yields a sharp dependence of the order of convergence on the degree of mesh grading used. This averaged L1 scheme can be combined with a finite difference or piecewise linear finite element discretization in space for IBVPs, and under a restriction on the temporal mesh width, one gets again O(N^(-2)) convergence in time, together with O(h^(2)) convergence in space,where h is the spatial mesh width. Numerical experiments support our results.

关键词： time-fractional subdiffusion averaged L1 scheme

GENERALIZED FORELLI-RUDIN TYPE OPERATORS BETWEEN SEVERAL FUNCTION SPACES ON THE UNIT BALL OF C^(N)

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Acta Mathematica Scientia 2024年第4期44卷 1301-1326页

作者： Xuejun ZHANG Yuting GUO Hongxin CHEN Pengcheng TANG College of mathematics and Statistics Hunan Normal University.Changsha 410081China school of mathematics Hunan UniversityChangsha 410082China school of mathematics and computational science Hunan University of Science and TechnologyXiangtan 411201China

In this paper,we investigate sufficient and necessary conditions such that generalized Forelli-Rudin type operators T_(λ,τ,k),S_(λ,τ,k),Q_(λ,τ,k)and R_(λ,τ,k)are bounded between Lebesgue type *** order to prov... 详细信息

关键词： Forelli-Rudin type operator L^(p q s k)(B_(n))space boundedness unit ball

CONVERGENCE ANALYSIS OF SOME FINITE ELEMENT PARALLEL ALGORITHMS FOR THE STATIONARY INCOMPRESSIBLE MHD EQUATIONS

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Journal of computational mathematics 2024年第1期42卷 49-70页

作者： Xiaojing Dong Yinnian He Hunan Key Laboratory for Computation and Simulation in science and Engineering Key Laboratory of Intelligent Computing&Information Processing of Ministry of EducationSchool of Mathematics and Computational ScienceXiangtan UniversityXiangtan 411105China Institute of Applied Physics and computational mathematics Beijing 100088China school of mathematics and Statistics Xi'an Jiaotong UniversityXi'an 710049China

By combination of iteration methods with the partition of unity method(PUM),some finite element parallel algorithms for the stationary incompressible magnetohydrodynamics(MHD)with different physical parameters are presented and *** algorithms are highly *** first,a global solution is obtained on a coarse grid for all approaches by one of the iteration *** parallelized residual schemes,local corrected solutions are calculated on finer meshes with overlapping *** subdomains can be achieved flexibly by a class of *** proposed algorithm is proved to be uniformly stable and ***,one numerical example is presented to confirm the theoretical findings.

关键词： Partition of unity method Local and parallel algorithm Finite element method Iteration methods Magnetohydrodynamics

On weighted compactness of commutators of bilinear vector-valued singular integral operators and applications

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Acta Mathematica Sinica,English Series 2024年

作者： Zheng Yang LI Liu LU Fang Hui LIAO Qing Ying XUE school of mathematics & computational science Hunan University of Science and Technology school of mathematics & computational science Xiangtan University school of Mathematical sciences Laboratory of Mathematics and Complex Systems Ministry of Education Beijing Normal University

Let T be a bilinear vector-valued singular integral operator satisfies some mild regularity conditions,which may not fall under the scope of the theory of standard Calderón-Zygmund *** any b=(b1,b2) ∈(CMO(Rn))2,let [T,bj]ej(j=1,2),[T,■]_α be the commutators in the j-th entry and the iterated commutators of T,*** this paper,for all p0> 1,p0/2

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Nadel-type multiplier ideal sheaves on complex spaces with singularities

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science China mathematics 2024年第5期67卷 951-974页

作者： Zhenqian Li school of mathematics and computational science Xiangtan UniversityXiangtan 411105China Siwuge Technology Co.Ltd. Chengdu 610093China

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 socalled Mather-Jacobian multiplier ideals in the algebro-geometric *** 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 *** applications,we obtain a reasonable generalization of(algebraic)adjoint ideal sheaves to the analytic setting and establish some extension theorems on K?hler manifolds from singular *** on our multiplier and adjoint ideals,we also give characterizations for several important classes of singularities of pairs associated with plurisubharmonic functions.

关键词： multiplier ideal sheaves plurisubharmonic functions Ohsawa-Takegoshi Luextension theorem rational singularities

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Fuzzy Quasi-Pseudo-b-Metrics on Algebraic Structures

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Journal of Mathematical Research with Applications 2024年第3期44卷 397-407页

作者： Jiancai WEI Yeqing SHENG Lihong XIE Piyu LI school of mathematics and computational science Wuyi University school of mathematics and Statistics Xuzhou Institute of Technology

In this paper, we mainly study fuzzy (quasi-)pseudo-b-metrics on algebraic *** mainly establish the following results:(1) If a group G with a topologyτ, which is induced by a left invariant fuzzy quasi-pseudo-b-metric (resp., pseudo-b-metric) on the G, is a right topological group, then G with the topologyτis a paratopological group (resp., a topological group) and (2) If a semigroup S with a topologyτis induced by an invariant fuzzy quasi-pseudob-metric, then S with the topologyτis a topological semigroup.

关键词： left topological group right topological group semitopological group paratopological group topological group topological semigroup fuzzy quasi-pseudo-b-metric invariant fuzzy (quasi-)pseudo-b-metric

Asymptotic Inference in the Random Coefficient Autoregressive Model with Time-functional Variance Noises

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Acta Mathematicae Applicatae Sinica 2024年第2期40卷 320-346页

作者： En-wen ZHU Zi-wei DENG Han-jun ZHANG Jun CAO Xiao-hui LIU Department of mathematics and Statistics Changsha University of Science and TechnologyChangsha 410114China school of mathematics and computational science Xiangtan UniversityXiangtan 411105China school of Statistics and Data science and Key Laboratory of Data Science in Finance and EconomicsJiangxi University of Finance and EconomicsNanchang 330013China

This paper considers the random coefficient autoregressive model with time-functional variance noises,hereafter the RCA-TFV *** first establish the consistency and asymptotic normality of the conditional least squares estimator for the constant *** semiparametric least squares estimator for the variance of the random coefficient and the nonparametric estimator for the variance function are constructed,and their asymptotic results are reported.A simulation study is presented along with an analysis of real data to assess the performance of our method in finite samples.

关键词： random coefficient autoregressive model time-functional variance conditional least squares semiparametric least squares

A Deep Learning Method for Computing Eigenvalues of the Fractional Schrödinger Operator

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Journal of Systems science & Complexity 2024年第2期37卷 391-412页

作者： GUO Yixiao MING Pingbing LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China school of Mathematical sciences University of Chinese Academy of SciencesBeijing 100049China

The authors present a novel deep learning method for computing eigenvalues of the fractional Schrödinger *** proposed approach combines a newly developed loss function with an innovative neural network architecture that incorporates prior knowledge of the *** improvements enable the proposed method to handle both high-dimensional problems and problems posed on irregular bounded *** authors successfully compute up to the first 30 eigenvalues for various fractional Schrödinger *** an application,the authors share a conjecture to the fractional order isospectral problem that has not yet been studied.

关键词： Eigenvalue problem deep learning fractional Schrödinger operator isospectral problem

Prescribed-time stabilization and inverse optimal control of stochastic high-order nonlinear systems

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science China(Information sciences) 2024年第2期67卷 144-156页

作者： Ran LIU Hui WANG Wuquan LI school of mathematics and Statistics science Ludong University

This paper investigates the prescribed-time state-feedback stabilization and prescribed-time inverse optimality problems for stochastic high-order nonlinear systems. First, a time-varying controller is designed by developing scaled quartic Lyapunov functions, which can guarantee that the system has a unique strong solution almost surely on the prescribed interval for any system initial conditions and that the states and the control converge to the origin in a mean-square form within the prescribed time. Then, the controller is redesigned to address the problem of prescribed-time inverse optimal mean-square stabilization. Finally,a concrete example is provided to confirm the efficiency of the proposed design schemes.

关键词： stochastic high-order nonlinear systems prescribed-time stabilization the scaled design inverse optimality

Nonlinear Seebeck and Peltier effects in a Majorana nanowire coupled to leads

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Chinese Physics B 2024年第7期33卷 547-552页

作者：迟锋刘佳付振国刘黎明易子川 school of Electronic and Information Engineering UESTC of ChinaZhongshan InstituteZhongshan 528400China school of science Inner Mongolia University of Science and TechnologyBaotou 014010China Institute of Applied Physics and computational mathematics Beijing 100088China

We theoretically study nonlinear thermoelectric transport through a topological superconductor nanowire hosting Majorana bound states(MBSs) at its two ends, a system named as Majorana nanowire(MNW). We consider that the MNW is coupled to the left and right normal metallic leads subjected to either bias voltage or temperature gradient. We focus our attention on the sign change of nonlinear Seebeck and Peltier coefficients induced by mechanisms related to the MBSs, by which the possible existence of MBSs might be proved. Our results show that for a fixed temperature difference between the two leads, the sign of the nonlinear Seebeck coefficient(thermopower) can be reversed by changing the overlap amplitude between the MBSs or the system equilibrium temperature, which are similar to the cases in linear response regime. By optimizing the MBS–MBS interaction amplitude and system equilibrium temperature, we find that the temperature difference may also induce sign change of the nonlinear thermopower. For zero temperature difference and finite bias voltage, both the sign and magnitude of nonlinear Peltier coefficient can be adjusted by changing the bias voltage or overlap amplitude between the MBSs. In the presence of both bias voltage and temperature difference, we show that the electrical current at zero Fermi level and the states induced by overlap between the MBSs keep unchanged, regardless of the amplitude of temperature difference. We also find that the direction of the heat current driven by bias voltage may be changed by weak temperature difference.

关键词： quantum dot nonlinear Seebeck coefficient Peltier coefficient Majorana bound states sign change