检索结果-南通市图书馆

Acta Mathematica Scientia 2025年第1期45卷 143-152页

作者： Andrea COLESANTI Dipartimento di Matematica&Informdtica‘U.Dini’ Universitàdegli Studi di FirenzeViale Morgagni 67/A-50134FirenzeItaly

Given an open bounded subsetΩofℝn we consider the eigenvalue problem{Δu-(■u,■V)=-λvu,u>0inΩ,u=0 onδΩ,where V is a given function defined inΩandλV is the relevant *** determine sufficient conditions on V such that ifΩis convex,the solution u is *** also determine sufficient conditions ensuring thatλV,as a function of the setΩ,verifies a convexity inequality with respect to the Minkowski addition of sets.

关键词： eigenvalue log-concavity elliptic operator Brunn-Minkowski inequality convex body

eigenvalue estimate on a compact Riemann manifold

在线全文

学校读者我要写书评

暂无评论

Science China Mathematics 1999年第9期42卷 897-904页

作者：赵迪 1. Institute of Mathematics Chinese Academy of Sciences 100080 Beijing China

LetM be a compact Riemann manifold with the Ricci curvature ? - R(R = const. > 0) . Denote by d the diameter ofM. Then the first eigenvalue λ1 ofM satisfies $\lambda _1 \geqslant \frac{{\pi ^2 }}{{d^2 }} - 0.52R$ . Moreover if $R \leqslant \frac{{5\pi ^2 }}{{3d^2 }}$ , then $\lambda _1 \geqslant \frac{{\pi ^2 }}{{d^2 }} - \frac{R}{2}$

关键词： Riemann manifold eigenvalue Ricci curvature.

eigenvalue problem of a class of fourth-order Hamiltonian operators

在线全文

学校读者我要写书评

暂无评论

Applied Mathematics(A Journal of Chinese Universities) 2013年第1期28卷 101-115页

作者： WANG Hua HUANG Jun-jie Alatancang College of Sciences Inner Mongolia University of Technology School of Mathematical Sciences Inner Mongolia University

The eigenvalue problem of a class of fourth-order Hamiltonian operators is studied. We first obtain the geometric multiplicity, the algebraic index and the algebraic multiplicity of each eigenvalue of the Hamiltonian operators. Then, some necessary and sufficient conditions for the completeness of the eigen or root vector system of the Hamiltonian operators are given, which is characterized by that of the vector system consisting of the first components of all eigenvectors. Moreover, the results are applied to the plate bending problem.

关键词： Hamiltonian operator eigenvalue multiplicity completeness.

eigenvalue PROBLEM OF A LARGE SCALE INDEFINITE GYROSCOPIC DYNAMIC SYSTEM

在线全文

学校读者我要写书评

暂无评论

Applied Mathematics and Mechanics(English Edition) 2006年第1期27卷 15-22页

作者：隋永枫钟万勰 State Key Laboratory of Structural Analysis of Industrial Equipment

Gyroscopic dynamic system can be introduced to Hamiltonian system. Based on an adjoint symplectic subspace iteration method of Hamiltonian gyroscopic system, an adjoint symplectic subspace iteration method of indefinite Hamiltonian function gyroscopic system was proposed to solve the eigenvalue problem of indefinite Hamiltonian function gyroscopic system. The character that the eigenvalues of Hamiltonian gyroscopic system are only pure imaginary or zero was used. The eigenvalues that Hamiltonian function is negative can be separated so that the eigenvalue problem of positive definite Hamiltonian function system was presented, and an adjoint symplectic subspace iteration method of positive definite Hamiltonian function system was used to solve the separated eigenvalue problem. Therefore, the eigenvalue problem of indefinite Hamiltonian function gyroscopic system was solved, and two numerical examples were given to demonstrate that the eigensolutions converge exactly.

关键词： gyroscopic system Hamiltonian function symplectic eigenvalue

eigenvalue Analysis of Thin Plate with Complicated Shapes By a Novel Infinite Element Method

在线全文

学校读者我要写书评

暂无评论

Computer Modeling in Engineering & Sciences 2019年第8期120卷 273-292页

作者： Deshin Liu Yuwei Chen Department of Mechanical Engineering and Advanced Institute of Manufacturing with High-Tech Innovations National Chung-Cheng UniversityMinhsiungChiayi 62102Taiwan

A novel infinite element method(IEM)is presented for solving plate vibration problems in this *** the proposed IEM,the substructure domain is partitioned into multiple layers of geometrically similar finite elements which use only the data of the boundary nodes.A convergence criterion based on the trace of the mass matrix is used to determine the number of layers in the IE model partitioning ***,in implementing the Craig-Bampton(CB)reduction method,the inversion of the global stiffness matrix is calculated using only the stiffness matrix of the first element *** validity and performance of the proposed method are investigated by means of four illustrative *** first example considers the case of a simple clamped rectangular *** is observed that the IEM results are consistent with the theoretical results for first six natural *** second example considers the frequency response of a clamped rectangular plate with a *** main feature of IEM is that a very fine and good quality virtual mesh can be created around the crack *** third and fourth examples consider the natural frequency of a multiple point supported plate and a perforated plate,*** results are obtained just need to adjust the reference point or boundary *** parametric analyses for various geometric profiles are easy to be conducted using these numerical *** general,the results presented in this study have shown that the proposed method provides a direct,convenient and accurate tool for eigenvalue analysis of thin plate structure with complicated shapes.

关键词： Infinite element method Craig-Bampton method plate vibration eigenvalue problem

eigenvalue PROBLEM FOR FIELD EQUATION INVOLVING LIMITING NONLINEARITY

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Acta Mathematica Scientia 1990年第4期10卷 432-447页

作者：严树森李工宝 ACAD SINICA INST MATH SCIWUHANPEOPLES R CHINA

In this paper, we study the following eigenvalue problem involving limiting nonlinearity [GRAPHICS] by a new way of using the concentration-compactness principle. Even in the nonlimiting situation, we improve the know... 详细信息

关键词： eigenvalue nontrivial compactness seeking nonlinearity limiting holds belongs compl minimizing

Uncertain eigenvalue analysis of the dielectric-filled waveguide by an interval vector finite element method

在线全文

学校读者我要写书评

暂无评论

Science China(Technological Sciences) 2022年第2期65卷 336-346页

作者： WANG ZhongHua JIANG Chao NI BingYu LI JinWu ZHENG Jing YAO ZhongYang State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body College of Mechanical and Vehicle EngineeringHunan UniversityChangsha 410082China

eigenvalues of the dielectric-filled waveguide are of great importance to its transmission characteristic analysis and optimization design, which could be easily affected by spatially uncertain dielectric parameters. For the sake of quantifying their influence on eigenvalues of the dielectric-filled waveguide and overcoming the limitation of less samples, an interval vector finite element method(IVFEM) is proposed to acquire the lower and upper bounds of the eigenvalues with spatial uncertainty of the medium parameters. Firstly, the uncertain dielectric material properties are described by the interval field model and the corresponding interval Karhunen-Loève(K-L) approximate method. Secondly, by inserting the interval uncertainties into the constitutive relationship of the standard generalized eigenvalue equations of the dielectric-filled waveguide, an interval standard generalized eigenvalue equation is then formulated. At last, the lower and upper bounds of the eigenvalues are calculated according to the first-order perturbation method, which can be used to estimate the transmission properties of the waveguide efficiently. Three kinds of the dielectric-filled waveguides are analyzed by the proposed IVFEM and verified by Monte Carlo simulation method.

关键词： dielectric-filled waveguide eigenvalue spatial uncertainty interval vector finite element method

eigenvalue approximation from below using non-conforming finite elements

在线全文

学校读者我要写书评

暂无评论

Science China Mathematics 2010年第1期53卷 137-150页

作者： YANG YiDu 1 ,ZHANG ZhiMin 2 & LIN FuBiao 11 School of Mathematics and Computer Science,Guizhou Normal University,Guiyang 550001,China 2 Department of Mathematics,Wayne State University,Detroit,MI 48202,USA 1. School of Mathematics and Computer Science Guizhou Normal University Guiyang 550001 China2. Department of Mathematics Wayne State University Detroit MI 48202 USA

This is a survey article about using non-conforming finite elements in solving eigenvalue problems of elliptic operators,with emphasis on obtaining lower bounds. In addition,this article also contains some new materials for eigenvalue approximations of the Laplace operator,which include:1) the proof of the fact that the non-conforming Crouzeix-Raviart element approximates eigenvalues associated with smooth eigenfunctions from below;2) the proof of the fact that the non-conforming EQ rot1 element approximates eigenvalues from below on polygonal domains that can be decomposed into rectangular elements;3) the explanation of the phenomena that numerical eigenvalues λ 1,h and λ 3,h of the non-conforming Q rot1 element approximate the true eigenvalues from below for the L-shaped domain. Finally,we list several unsolved problems.

关键词： non-conforming element eigenvalue lower bound

Limit Set Problem of Multi-Agent Systems with Finite States: An eigenvalue-Based Approach

在线全文

学校读者我要写书评

暂无评论

Journal of Systems Science & Complexity 2015年第3期28卷 570-579页

作者： WANG Lin WANG Xiaofan WANG Jinhuan Department of Automation Shanghai Jiao Tong University and Key Laboratory of System Control and Information Processing Ministry of Education School of Sciences Hebei University of Technology

This paper studies the limit set of multi-agent system with finite states, in which the system is converted into a linear system through an expansion of space. Then, the structure properties of the system matrix are investigated, and the relationships between the eigenvalues and the limit set are developed. As an application, the nilpotent problem of elementary cellular automata(ECA) known as algorithmically undecidable is considered, and all the nilpotent ECA are found out which consists of rules 0, 8, 64, 239, 253, 255.

关键词： Cellular automata eigenvalue finite states limit set multi-agent system nilpotent.

PRECONDITIONING BLOCK LANCZOS ALGORITHM FOR SOLVING SYMMETRIC eigenvalue PROBLEMS

在线全文

学校读者我要写书评

暂无评论

Journal of Computational Mathematics 2000年第4期18卷 365-374页

作者： Hua Dai Peter Lancaster Nanjing University of Aeronautics and Astronautics Naming210018China University of Calgary CalgaryCanada

A preconditioned iterative method for computing a few eigenpairs of large sparse symmetric matrices is presented in this paper. The proposed method which combines the preconditioning techniques with the efficiency of block Lanczos algorithm is suitable for determination of the extreme eigenvalues as well as their multiplicities. The global convergence and the asymptotically quadratic convergence of the new method are also demonstrated. [ABSTRACT FROM AUTHOR]

关键词： eigenvalue eigenvector sparse matrices Lanczos method preconditioning