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eigenvalues for the Clamped Plate Problem of L_(ν)^(2) Operator on Complete Riemannian Manifolds

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Acta Mathematica Sinica,English Series 2024年第9期40卷 2223-2243页

作者： Ling Zhong ZENG Jiangxi Provincial Center for Applied Mathematics&School of Mathematics and Statistics Jiangxi Normal UniversityNanchang 330022P.R.China

L_(ν) operator is an important extrinsic differential operator of divergence type and has profound geometric *** this paper,we consider the clamped plate problem of L_(ν)^(2)operator on a bounded domain of the complete Riemannian manifolds.A general formula of eigenvalues of L_(ν)^(2) operator is *** this general formula,we obtain some estimates for the eigenvalues with higher order on the complete Riemannian *** several fascinating applications,we discuss this eigenvalue problem on the complete translating solitons,minimal submanifolds on the Euclidean space,submanifolds on the unit sphere and projective *** particular,we get a universal inequality with respect to the L_(II) operator on the translating ***,it is very difficult to get universal inequalities for weighted Laplacian and even Laplacian on the complete Riemannian ***,this work can be viewed as a new contribution to universal estimate.

关键词： Mean curvature flows L_(ν)^(2)operator clamped plate problem eigenvalues Riemannian manifolds translating solitons

eigenvalues of the Manifold Sp（n）/U（n）

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Acta Mathematica Sinica,English Series 2011年第11期27卷 2269-2274页

作者： Yi HONG Wen Ge CHEN Department of Mathematics South China University of Technology Guangzhou 510640 P. R. China

In this paper, we give the eigenvalues of the manifold Sp（n）/U（n）. We prove that an eigenvalue λs（f1,f2,...,fn） of the Lie group Sp（n）, corresponding to the representation with label （f1, f2,..., fn）, is an... 详细信息

关键词： Manifold eigenvalues group representation theory

An Alternative Method for Calculating Bound-State of Energy eigenvalues of Klein-Gordon for Quasi-exactly Solvable Potentials

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Chinese Physics Letters 2009年第2期26卷 13-16页

作者： Eser Olgar Department of Physics and Engineering University of Gaziantep Gaziantep Turkey

We obtain the bound-state energy of the Klein-Gordon equation for some examples of quasi-exactly solvable potentials within the framework of asymptotic iteration method （AIM）. The eigenvalues are calculated for type- 1 solutions. The whole quasi-exactly solvable potentials are generated from the defined relation between the vector and scalar potentials.

关键词： BOUND states (Quantum mechanics) eigenvalues KLEIN-Gordon equation ITERATIVE methods (Mathematics) MATHEMATICAL physics -- Asymptotic theory NUMERICAL analysis

eigenvalues of Elliptic Systems for the Mixed Problem in Perturbations of Lipschitz Domains with Nonhomogeneous Neumann Boundary Conditions

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Journal of Partial Differential Equations 2020年第1期33卷 48-63页

作者： MIYAZAKI Kohei TAYLOR Justin L. Department of Mathematics&Statistics Murray State UniversityMurrayKentuckyU.S.A

We study eigenvalues of an elliptic operator with mixed boundary conditions on very general decompositions of the *** impose nonhomogeneous conditions on the part of the boundary where the Neumann term lies in a certain Sobolev or Lp *** work compares the behavior of and gives a relationship between the eigenvalues and eigenfunctions on the unperturbed and perturbed domains,respectively.

关键词： eigenvalues elliptic systems mixed problem perturbed domains

Berry-Esseen bounds and Cramér type large deviations for eigenvalues of random matrices.

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Science China Mathematics 2015年第9期58卷 1959-1980页

作者： CHEN Lei GAO FuQing WANG ShaoChen School of Mathematics and Statistics Wuhan University School of Mathematics and Statistics Jiangsu Normal University

We establish Berry-Esseen bounds and Cramér type large deviations for the eigenvalues of Wigner Hermitian matrices in the bulk and at the edge cases. Similar results are also obtained for covariance matrices.

关键词： random matrices eigenvalues Berry-Esseen bounds Cramér type large deviations

Analysis of eigenvalues for Molecular Structures

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Computers, Materials & Continua 2022年第10期73卷 1225-1236页

作者： Muhammad Haroon Aftab Kamel Jebreen Mohammad Issa Sowaity Muhammad Hussain Department of Mathematics and Statistics The University of LahoreLahore54000Pakistan Department of Mathematics An-Najah National UniversityNablusP400Palestine Department of Mathematics Palestince Polytechnic UniversityHebronP766Palestine Department of Mathematics Comsats University IslamabadLahore CampusLahore54000Pakistan

In this article,we study different molecular structures such as Polythiophene network,PLY(n)for n=1,2,and 3,Orthosilicate(Nesosilicate)SiO4,Pyrosilicates(Sorosilicates)Si2O7,Chain silicates(Pyroxenes)(SiO3)n,and Cyclic silicates(Ring Silicates)Si3O9 for their cardinalities,chromatic numbers,graph variations,eigenvalues obtained from the adjacency matrices which are square matrices in order and their corresponding characteristics *** convert the general structures of these chemical networks in to mathematical graphical *** transform the molecular structures of these chemical networks which are mentioned above,into a simple and undirected planar graph and sketch them with various techniques of *** matrices obtained from these simple undirected graphs are *** also label the molecular structures by assigning different *** graphs have also been studied for *** a connected graph,the eigenvalue that shows its peak point(largest value)obtained from the adjacency matrix has multiplicity ***,the gap between the largest and its smallest eigenvalues is interlinked with some form of“connectivity measurement of the structural graph”.We also note that the chemical structures,Orthosilicate(Nesosilicate)SiO4,Pyrosilicates(Sorosilicates)Si2O7,Chain silicates(Pyroxenes)(SiO3)n,and Cyclic silicates(Ring Silicates)Si3O9 generally have two same *** matrices have great importance in the field of computer science.

关键词： Vertex degree edges eigenvalues characteristics polynomials adjacency matrices graphical model genetics polythiophene silicates

Transmission eigenvalues and the Riemann Zeta Function in Scattering Theory for Automorphic Forms on Fuchsian Groups of Type Ⅰ

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Acta Mathematica Sinica,English Series 2019年第6期35卷 987-1010页

作者： Fioralba CAKONI Sagun CHANILLO Department of Mathematics Rutgers University

We introduce the concept of transmission eigenvalues in scattering theory for automorphic forms on fundamental domains generated by discrete groups acting on the hyperbolic upper half complex plane. In particular, we consider Fuchsian groups of Type Ⅰ. Transmission eigenvalues are related to those eigen-parameters for which one can send an incident wave that produces no scattering. The notion of transmission eigenvalues, or non-scattering energies, is well studied in the Euclidean geometry, where in some cases these eigenvalues appear as zeros of the scattering matrix. As opposed to scattering poles,in hyperbolic geometry such a connection between zeros of the scattering matrix and non-scattering energies is not studied, and the goal of this paper is to do just this for particular arithmetic *** such groups, using existing deep results from analytic number theory, we reveal that the zeros of the scattering matrix, consequently non-scattering energies, are directly expressed in terms of the zeros of the Riemann zeta function. Weyl's asymptotic laws are provided for the eigenvalues in those cases along with estimates on their location in the complex plane.

关键词： Transmission eigenvalues Fuchsian groups Riemann zeta function scattering theory

Absence of eigenvalues for quasiperiodic Schrodinger type operators

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Frontiers of Mathematics in China 2019年第3期14卷 645-659页

作者： Jiahao XU Xin ZHAO Department of Mathematical Sciences Nanjing University Nanjing 210093 China

We obtain the matrix-valued Schrodinger-type operators [Hα,θ] with Lipschitz potentials having no eigenvalues on the set {E : L ( E )<δ)C,d(α,θ),where δ is an explicit function depending on the sampling function... 详细信息

关键词： Quasiperiodic Schrodinger type operators absence of eigenvalues singular continuous spectrum

Asymptotic of eigenvalues and Lattice Points

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Acta Mathematica Sinica,English Series 2006年第6期22卷 1645-1650页

作者： Juan Pablo PINASCO Instituto de Ciencias Universidad Nacional de General Sarmiento

dimension. elementary domains of In this work we study the spectral counting function for the p-Laplace operator in one We show the existence of a two-term Weyl-type asymptote. The method of proof is rather based on ... 详细信息

关键词： p-Laplacian eigenvalues lattice points