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Second-order error analysis of the averaged L1 scheme L1 for time-fractional initial-value and subdiffusion problems

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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

The joint Laplace transforms for killed diffusion occupation times

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Applied mathematics(A Journal of Chinese Universities) 2024年第3期39卷 398-415页

作者： LI Ying-qiu CHEN Ye school of mathematics and Statistics Changsha University of Science and TechnologyChangsha 410114China College of mathematics and computational science Hunan University of Arts and ScienceChangde 415000China

The approach of Li and Zhou(2014)is adopted to find the Laplace transform of occupation time over interval(0,a)and joint occupation times over semi-infinite intervals(-∞,a)and(b,∞)for a time-homogeneous diffusion pr... 详细信息

关键词： time-homogeneous diffusion process occupation time joint occupation time Laplace transform Brownian motion with drift

Solitary,periodic,kink wave solutions of a perturbed high-order nonlinear Schrödinger equation via bifurcation theory

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Propulsion and Power Research 2024年第3期13卷 433-444页

作者： Qiancheng Ouyang Zaiyun Zhang Qiong Wang Wenjing Ling Pengcheng Zou Xinping Li school of mathematics Hunan Institute of Science and TechnologyYueyangHunan 414006China school of mathematics and computational science Hunan University of Science and TechnologyXiangtanHunan 411201China

In this paper,by using the bifurcation theory for dynamical system,we construct traveling wave solutions of a high-order nonlinear Schrödinger equation with a quintic ***,based on wave variables,the equation is transformed into an ordinary differential ***,under the parameter conditions,we obtain the Hamiltonian system and phase ***,traveling wave solutions which contains solitary,periodic and kink wave so-lutions are constructed by integrating along the homoclinic or heteroclinic *** addition,by choosing appropriate values to parameters,different types of structures of solutions can be displayed ***,the computational work and it’sfigures show that this tech-nique is influential and efficient.

关键词： Traveling wave solution High-order nonlinear Schrödinger equation Bifurcation theory Dynamical system Hamiltonian system

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

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

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

A FINITE DIFFERENCE METHOD FOR TWO DIMENSIONAL ELLIPTIC INTERFACE PROBLEMS WITH IMPERFECT CONTACT

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Journal of computational mathematics 2024年第5期42卷 1328-1355页

作者： Fujun Cao Dongfang Yuan Dongxu Jia Guangwei Yuan school of science Inner Mongolia University of Science and TechnologyBaotou 014010Inner MongoliaChina school of science Tianjin University of TechnologyTianjin 300384China Laboratory of computational Physics Institute of Applied Physics and Computational MathematicsP.O.Box 8009Beijing 100088China

In this paper two dimensional elliptic interface problem with imperfect contact is considered,which is featured by the implicit jump condition imposed on the imperfect contact interface,and the jumping quantity of the unknown is related to the flux across the interface.A finite difference method is constructed for the 2D elliptic interface problems with straight and curve interface ***,the stability and convergence analysis are given for the constructed ***,in particular case,it is proved to be *** examples for elliptic interface problems with straight and curve interface shapes are tested to verify the performance of the *** numerical results demonstrate that it obtains approximately second-order accuracy for elliptic interface equations with implicit jump condition.

关键词： Finite difference method Elliptic interface problem Imperfect contact

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