检索结果-南通市图书馆

Journal of Computational Mathematics 2024年第1期42卷 71-110页

作者： Shipeng Mao Jiaao Sun Wendong Xue NCMIS LSECInstitute of Computational Mathematics and Scientific/Enginnering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China

In this paper,we consider the initial-boundary value problem(IBVP)for the micropolar Naviers-Stokes equations(MNSE)and analyze a first order fully discrete mixed finite element scheme.We first establish some regularity results for the solution of MNSE,which seem to be not available in the literature.Next,we study a semi-implicit time-discrete scheme for the MNSE and prove L2-H1 error estimates for the time discrete solution.Furthermore,certain regularity results for the time discrete solution are establishes rigorously.Based on these regularity results,we prove the unconditional L2-H1 error estimates for the finite element solution of MNSE.Finally,some numerical examples are carried out to demonstrate both accuracy and efficiency of the fully discrete finite element scheme.

关键词： Micropolar fluids Regularity estimates Euler semi-implicit scheme Mixed finite element methods Unconditional convergence

Positive definiteness of real quadratic forms resulting from the variable-step L1-type approximations of convolution operators

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Science China Mathematics 2024年第2期67卷 237-252页

作者： Hong-Lin Liao Tao Tang Tao Zhou School of Mathematics Nanjing University of Aeronautics and AstronauticsNanjing 211106China Division of Science and Technology BNU-HKBU United International CollegeZhuhai 519087China SUSTech International Center for Mathematics Shenzhen 518055China NCMIS&LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

The positive definiteness of real quadratic forms with convolution structures plays an important rolein stability analysis for time-stepping schemes for nonlocal operators. In this work, we present a novel analysistool to handle discrete convolution kernels resulting from variable-step approximations for convolution operators.More precisely, for a class of discrete convolution kernels relevant to variable-step L1-type time discretizations, weshow that the associated quadratic form is positive definite under some easy-to-check algebraic conditions. Ourproof is based on an elementary constructing strategy by using the properties of discrete orthogonal convolutionkernels and discrete complementary convolution kernels. To our knowledge, this is the first general result onsimple algebraic conditions for the positive definiteness of variable-step discrete convolution kernels. Using theunified theory, we obtain the stability for some simple nonuniform time-stepping schemes straightforwardly.

关键词： discrete convolution kernels positive definiteness variable time-stepping orthogonal convolution kernels complementary convolution kernels

On Some Computational Problems in Local Fields

在线全文

学校读者我要写书评

暂无评论

Journal of Systems Science & Complexity 2022年第3期35卷 1191-1200页

作者： DENG Yingpu LUO Lixia PAN Yanbin XIAO Guanju Key Laboratory of Mathematics Mechanization NCMISAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China

Lattices in Euclidean spaces are important research objects in geometric number theory,and they have important applications in many areas,such as cryptology.The shortest vector problem(SVP)and the closest vector problem(CVP)are two famous computational problems about lattices.In this paper,we consider p-adic lattices in local fields,and define the p-adic analogues of SVP and CVP in local fields.The authors find that,in contrast with lattices in Euclidean spaces,the situation is different and interesting.The SVP in Euclidean spaces corresponds to the Longest Vector Problem(LVP)in local fields.The authors develop relevant algorithms,indicating that these problems are computable.

关键词： CVP lattice LVP local field SVP

Null-free False Discovery Rate Control Using Decoy Permutations

在线全文

学校读者我要写书评

暂无评论

Acta Mathematicae Applicatae Sinica 2022年第2期38卷 235-253页

作者： Kun He Mengjie Li Yan Fu Fuzhou Gong Xiaoming Sun Institute of Computing Technology Chinese Academy of SciencesBeijing 100190China CEMS NCMISRCSDSAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China University of Chinese Academy of Sciences Beijing 100049China

The traditional approaches to false discovery rate(FDR)control in multiple hypothesis testing are usually based on the null distribution of a test statistic.However,all types of null distributions,including the theoretical,permutation-based and empirical ones,have some inherent drawbacks.For example,the theoretical null might fail because of improper assumptions on the sample distribution.Here,we propose a null distributionfree approach to FDR control for multiple hypothesis testing in the case-control study.This approach,named target-decoy procedure,simply builds on the ordering of tests by some statistic or score,the null distribution of which is not required to be known.Competitive decoy tests are constructed from permutations of original samples and are used to estimate the false target discoveries.We prove that this approach controls the FDR when the score function is symmetric and the scores are independent between different tests.Simulation demonstrates that it is more stable and powerful than two popular traditional approaches,even in the existence of dependency.Evaluation is also made on two real datasets,including an arabidopsis genomics dataset and a COVID-19 proteomics dataset.

关键词： multiple testing false discovery rate null distribution-free p-value-free decoy permutations knockoff filter

On the reinforcement learning extended state observer for a class of uncertain sampled-data control systems

在线全文

学校读者我要写书评

暂无评论

Science China(Information Sciences) 2023年第7期66卷 73-74页

作者： Guojie TANG Wenchao XUE Haitao FANG Kun ZHANG LSC NCMIS Academy of Mathematics and Systems Science Chinese Academy of Sciences School of Mathematical Sciences University of Chinese Academy of Sciences School of Astronautics Beihang University

In the last few decades, the extended state observer(ESO) [1] has been demonstrated to be an effective tool for dealing with uncertain control systems and many modified ESOs have been proposed to get the desired estimation performance [2–4]. Nevertheless, most of these methods assume that part of the model information is already known.Therefore, a data-driven tuning law for ESO without assuming model information for disturbances and noise seems to be a significant open issue.

关键词： DISTURBANCE REJECTION

A POSITIVITY-PRESERVING FINITE ELEMENT METHOD FOR QUANTUM DRIFT-DIFFUSION MODEL

在线全文

同方期刊数据库

学校读者我要写书评

暂无评论

Journal of Computational Mathematics 2023年第5期41卷 909-932页

作者： Pengcong Mu Weiying Zheng School of Mathematical Science University of Chinese Academy of SciencesBeijing 100049China LSEC NCMISInstitute of Computational Mathematics and Scientific ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

In this paper,we propose a positivity-preserving finite element method for solving the three-dimensional quantum drift-diffusion model.The model consists of five nonlinear elliptic equations,and two of them describe quantum corrections for quasi-Fermi levels.We propose an interpolated-exponential finite element(IEFE)method for solving the two quantum-correction equations.The IEFE method always yields positive carrier densities and preserves the positivity of second-order differential operators in the Newton linearization of quantum-correction equations.Moreover,we solve the two continuity equations with the edge-averaged finite element(EAFE)method to reduce numerical oscillations of quasi-Fermi levels.The Poisson equation of electrical potential is solved with standard Lagrangian finite elements.We prove the existence of solution to the nonlinear discrete problem by using a fixed-point iteration and solving the minimum problem of a new discrete functional.A Newton method is proposed to solve the nonlinear discrete problem.Numerical experiments for a three-dimensional nano-scale FinFET device show that the Newton method is robust for source-to-gate bias voltages up to 9V and source-to-drain bias voltages up to 10V.

关键词： Quantum drift-diffusion model Positivity-preserving finite element method Newton method FinFET device High bias voltage

A VARIATIONAL ANALYSIS FOR THE MOVING FINITE ELEMENT METHOD FOR GRADIENTFLOWS

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Journal of Computational Mathematics 2023年第2期41卷 191-210页

作者： Xianmin Xu LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingNCMISAMSSChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China

By using the Onsager principle as an approximation tool,we give a novel derivation for the moving finite element method for gradient flow equations.We show that the discretized problem has the same energy dissipation structure as the continuous one.This enables us to do numerical analysis for the stationary solution of a nonlinear reaction diffusion equation using the approximation theory of free-knot piecewise polynomials.We show that under certain conditions the solution obtained by the moving finite element method converges to a local minimizer of the total energy when time goes to infinity.The global minimizer,once it is detected by the discrete scheme,approximates the continuous stationary solution in optimal order.Numerical examples for a linear diffusion equation and a nonlinear Allen-Cahn equation are given to verify the analytical results.

关键词： Moving finite element method Convergence analysis Onsager principle

Operations Research in the Blockchain Technology

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Journal of the Operations Research Society of China 2022年第2期10卷 401-422页

作者： Xu Wang Ling-Yun Wu IAM MADISNCMISAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China Department of Industrial Engineering Tsinghua UniversityBeijing 100084China

In the past decade,as a decentralized distributed database technology blockchain has developed rapidly at an unprecedented speed and been applied to a wide range of scenarios far beyond cryptocurrencies,for example,insurance,energy,risk management,and Internet of things(IoT).The blockchain technology combines the achievements from cryptography,computer science,economics,and operations research and has increasingly attracted attention from both academia and industry.Though the operations research has been widely adopted in the blockchain technology,there is a lack of comprehensive survey on the operations research in blockchain-related issues.In order to fill the gap,we analyze the blockchain technology through the perspective of operations research and present a comprehensive review of the operations research problems from the aspects of security and stability,efficiency and performance,and resource allocation.This paper aimed to help the relevant readers in the field of operations research find their own points of interest and conduct in-depth research on the blockchain technology,hoping to promote the rapid development and wider application of the blockchain technology in the near future.

关键词： Blockchain Operations research Security Efficiency Resource allocation

RESULTS ON PERMUTATION SYMMETRIC BOOLEAN FUNCTIONS

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Journal of Systems Science & Complexity 2013年第2期26卷 302-312页

作者： ZHANG Yanjuan DENG Yingpu Key Laboratory of Mathematics Mechanization NCMISAcademy of Mathematics and Systems ScienceChinese Academy of Sciences

This paper provides a systematic method on the enumeration of various permutation symmetric Boolean functions.The results play a crucial role on the search of permutation symmetric Boolean functions with good cryptographic properties.The proposed method is algebraic in nature.As a by-product,the authors correct and generalize the corresponding results of Stanica and Maitra(2008).Further,the authors give a complete classification of block-symmetric bent functions based on the results of Zhao and Li(2006),and the result is the only one classification of a certain class of permutation symmetric bent functions after the classification of symmetric bent functions proposed by Savicky(1994).

关键词：对称弯曲布尔函数排列功能分类代数性质一类分类副产品 NIC

Transition pathways in Cylinder-Gyroid interface

在线全文

学校读者我要写书评

暂无评论

Communications in Computational Physics 2022年第8期32卷 810-828页

作者： Xiaomei Yao Jie Xu Lei Zhang Beijing International Center for Mathematical Research Peking UniversityBeijing 100871China LSEC&NCMIS Institute of Computational Mathematics and Scientific/Engineering Computing(ICMSEC)Academy of Mathematics and Systems Science(AMSS)Chinese Academy of SciencesBeijingChina

When two distinct ordered phases contact,the interface may exhibit rich and fascinating structures.Focusing on the Cylinder-Gyroid interface system,transition pathways connecting various interface morphologies are studied armed with the Landau–Brazovskii model.Specifically,minimum energy paths are obtained by computing transition states with the saddle dynamics.We present four primary transition pathways connecting different local minima,representing four different mechanisms of the formation of the Cylinder-Gyroid interface.The connection of Cylinder and Gyroid can be either direct or indirect via Fddd with three different orientations.Under different displacements,each of the four pathways may have the lowest energy.

关键词： Landau-Brazovskii model Cylinder-Gyroid interface saddle dynamics transition state transition pathway