上三角无穷维Hamilton算子特征值的代数指标

无穷维Hamilton算子特征函数系是否完备与其代数指标有关,研究了上三角无穷维Hamilton算子特征值的代数指标问题,基于主对角元的特征值和特征向量的某些性质,得到上三角无穷维Hamilton算子的几何重数和代数重数.     

弹性理论中上三角无穷维Hamilton算子根向量组的完备性

考虑弹性力学中一类上三角无穷维 Hamilton 算子．首先,给出此类Hamilton算子特征值的几何重数和代数指标,进而得到代数重数．其次,根据Hamilton算子特征值的代数重数确定其特征(根)向量组完备的形式,得到此类Hamilton算子特征(根)向量组的完备性是由内部算子特征向量组决定．最后,将所得结果应用到弹性力学问题中．     

一类算子矩阵特征值的代数指标和代数重数

自伴算子特征值的几何重数与代数重数相等,但对于非自伴算子不一定成立,这主要是特征值的代数指标起着决定性的作用.讨论了一类非自伴算子矩阵特征值的几何重数,代数指标与代数重数.     

一类Hamilton算子的重数和完备性及其应用

对于一类Hamilton算子,考虑其特征值的重数,以及特征向量组和根向量组的完备性.首先给出了特征值的几何重数、代数指标和代数重数,再结合特征向量和根向量的辛正交性得到了特征向量组和根向量组完备的充分必要条件,最后将上述结果应用于板弯曲方程、平面弹性问题和Stokes流等问题中.     

一类无穷维Hamilton算子根向量组的完备性

本文研究主对角元为常数的无穷维Hamilton算子的特征值问题.基于次对角元乘积的特征值和特征向量的某些性质,刻画此类Hamilton算子特征值分布、特征值的代数指标、特征向量(或一阶根向量)的辛正交关系及特征向量组和根向量组在辛Hilbert空间中完备的充要条件.     

两部件并联维修系统算子的性质

研究了两部件并联维修系统算子的性质,通过选取空间和定义算子将模型方程转化成了抽象柯西问题,证明了系统算子是定义域稠的预解正算子,0是系统算子的几何重数为1的本征值.讨论了系统算子的共轭算子及其定义域,证明了0是共轭算子的代数重数为1的特征值.     

一类具有转移条件的向量Sturm-Liouville问题的特征值

考虑了一类具有转移条件的向量Sturm-Liouville问题的特征值及其重数问题.首先构造了与问题相关的新内积和基本解,得到特征值的充要条件.在此基础上证明了二维情况下,问题特征值的代数重数与几何重数相等.     

基于二次算子族的无界Hamilton算子根向量组的基性质

利用无界Hamilton算子导出的二次算子族,本文研究了一类无界Hamilton算子根向量组的Schauder基性质.首先,建立了无界Hamilton算子的根向量与相应的二次算子族的根向量之间的关系.其次,借助二次算子族谱的相关性质,刻画了无界Hamilton算子的本征值分布以及本征值的代数指标,并得到了无界Hamilton算子的根向量组是某个Hilbert空间的一个块状Schauder基的充要条件.最后,将所得结果应用于矩形薄板弯曲问题.     

两同型部件温贮备可修系统解的指数渐近稳定性

运用强连续半群理论研究两同型部件温贮备可修系统解的指数渐近性质,首先证明系统所生成的C0半群T(t)是拟紧的.其次证明0是对应于系统的主算子及其共轭算子的几何重数和代数重数为1的特征值,推出在右半平面和虚轴上除0以外其他所有点都属于该算子的豫解集,由此推出该系统的时间依赖解当时刻趋向于无穷时强收敛于系统的稳态解.     

带特殊重试时间的M/M/1重试排队模型的一个特征值

证明0是对应于带特殊重试时间的M/M/1重试排队模型主算子的几何重数为1的特征值,0是此主算子的共轭算子的特征值.     

The algebraic multiplicity of the complex eigenvalues of population operator and its application

In this paper we discuss the algebraic multiplicity of the complex eigenvalue of population operator. Under certain condition we first prove that all the complex eigenvalues of this operator, except at most finitely many ones, are of algebraic multiplicity 1,and then, as an application of this result, we obtain the asymptotic expansion of the solution of corresponding population system.     

Triangular strictly cyclic operators

The title refers to an empty class of operators. Moreover, if T is a triangular Banach space operator, then either T is algebraic and the double commutant has infinite strict multiplicity, or T is not algebraic and the commutant has infinite strict multiplicity. A rationally strictly cyclic, but not strictly cyclic, operator cannot have finite strict multiplicity.This research was partially supported by a Grant of the National Science Foundation.     

Hyperbolicity of periodic solutions of functional differential equations with several delays

We study conditions for the hyperbolicity of periodic solutions to nonlinear functional differential equations in terms of the eigenvalues of the monodromy operator. The eigenvalue problem for the monodromy operator is reduced to a boundary value problem for a system of ordinary differential equations with a spectral parameter. This makes it possible to construct a characteristic function. We prove that the zeros of this function coincide with the eigenvalues of the monodromy operator and, under certain additional conditions, the multiplicity of a zero of the characteristic function coincides with the algebraic multiplicity of the corresponding eigenvalue.     

Existence,nonexistence and multiplicity results for nonlocal Dirichlet problems

In this paper we establish various existence, nonexistence and multiplicity results for fully nonlinear Dirichlet problems associated to nonlocal Hamilton–Jacobi equations. This study is accomplished by a careful analysis of the principal eigenvalues of the elliptic operator. Resonance phenomena and anti maximum principles are also established.     

Spectral properties of a nonlocal second-order difference operator

We consider a spectral problem for a nonlocal difference operator of second derivative with variable coefficients and with a complex parameter in the boundary condition. We study the algebraic and geometric multiplicity of the eigenvalues and the sign of their real part. We obtain conditions on the parameter which ensure that the entire spectrum of the operator lies in the right complex half-plane.     

板几何中一类具抽象边界条件迁移算子的谱

在LP（1≤P〈∞）空间上，研究了板几何中一类具抽象边界条件下各向异性、连续能量、非均匀介质的迁移方程，证明了这类方程相应的迁移算子的谱在右半平面中仅由有限个具有限代数重数的离散本征值组成等结果．     

人口算子的谱性质

本文讨论人口算子的谱性质,得到了人口算子本征值除可能有限个外均是代数单的,人口算子本征值新的分布性质,人口算子广义本征函数不构成基序列,Ｌ２［０,ｒ２］上的人口算子根子空间完整等．