On Some Measure Convolution Operators in Neutron Transport Theory

We show how some fundamental spectral properties of neutron transport semigroups in L ^p spaces (1<p<+∞), such as stability of essential spectra or critical spectra and related results, can be inferred from the study of two measure convolution operators on  \(\mathbb{R}^{n}\) .     

Spectral Mapping Theorems for Neutron Transport, L1-Theory

This work deals with spectral mapping theorems for neutron transport semigroups in unbounded geometries and L¹ setting. The mathematical analysis relies on harmonic analysis of certain measure valued mappings related to Dyson-Phillips expansions and on some functional analytic results on the critical spectrum.     

Spectral Analysis for Adjacency Operators on Graphs

We put into evidence graphs with adjacency operator whose singular subspace is prescribed by the kernel of an auxiliary operator. In particular, for a family of graphs called admissible, the singular continuous spectrum is absent and there is at most an eigenvalue located at the origin. Among other examples, the one-dimensional XY model of solid-state physics is covered. The proofs rely on commutators methods. Submitted: July 15, 2006. Accepted: January 16, 2007.     

Spectral Decomposition of Cyclic Operators in Discrete Harmonic Analysis

For the operators of the discrete Fourier transform, the discrete Vilenkin–Christenson transform, and all linear transpositions of the discrete Walsh transform, we obtain their spectral decompositions and calculate the dimensions of eigenspaces. For complex operators, namely, the discrete Fourier transform and the Vilenkin–Christenson transform, we obtain real projectors on eigenspaces. For the discrete Walsh transform, we consider in detail the Paley and Walsh orderings and a new ordering in which the matrices of operators are symmetric. For operators of linear transpositions of the discrete Walsh transforms with nonsymmetric matrices, we obtain a spectral decomposition with complex projectors on eigenspaces. We also present the Parseval frame for eigenspaces of the discrete Walsh transform.     

Spectral Analysis of Operator Polynomials and Second-Order Differential Operators

Mathematical Notes - Studying spectral properties of operator polynomials is reduced to studying the corresponding spectral properties of operators defined by operator matrices. The results are...     

Spectral Analysis of Differential Operators with Involution and Operator Groups

We study the spectral properties of differential operators with involution of the following two types: operators with involution multiplying the potential and operators with involution multiplying the derivative. The similar operator method is used to obtain a refined asymptotics of the eigenvalues and eigenvectors of such operators. These asymptotics are used to derive asymptotic formulas for the operator groups generated by the operators in question. These operator groups can be used to describe mild solutions of the corresponding mixed problems.     

Spectral Analysis of Higher-Order Differential Operators II: Fourth-Order Equations

We investigate the location and nature of the spectrum of thefourth-order self-adjoint equation (p₀ y')'+(p₁ y')'+qy=zwy subject to certain asymptotic assumptions on the coefficients.The main tools are the theory of asymptotic integration andthe Titchmarsh–Weyl M-matrix. Asymptotic integration yieldsasymptotic formulae for the solutions of the differential equationwhich are then used to derive properties of the M-matrix. Thecharacterisation of spectral properties in terms of the boundarybehaviour of M leads to the desired results.     

Spectral Analysis of Abstract Parabolic Operators in Homogeneous Function Spaces

We use methods of harmonic analysis and group representation theory to study the spectral properties of the abstract parabolic operator \({\mathcal{L} = -{\rm d}/{\rm d}t + A}\) in homogeneous function spaces. We provide sufficient conditions for invertibility of such operators in terms of the spectral properties of the operator A and the semigroup generated by A. We introduce a homogeneous space of functions with absolutely summable spectrum and prove a generalization of the Gearhart–Prüss Theorem for such spaces. We use the results to prove existence and uniqueness of solutions of a certain class of non-linear equations.     

Spectral Doubling of Normal Operators and Connections with Antiunitary Operators

Equations such as AB = B ^T A have been studied in the finite dimensional setting in (Linear Algebra Appl 369:279–294, 2003). These equations have implications for the spectrum of B, when A is normal. Our aim is to generalize these results to an infinite dimensional setting. In this case it is natural to use JB*J for some conjugation operator J in place of B ^T . Our main result is a spectral pairing theorem for a bounded normal operator B which is applied to the study of the equation KB = B*K for K an antiunitary operator. In particular, using conjugation operators, we generalize the notion of Hamiltonian operator and skew-Hamiltonian operator in a natural way, derive some of their properties, and give a characterization of certain operators B for which AB = (JB*J)A and BA = A(JB*J) and also those B with KB = B*K for certain antiunitary operators K.     

Dynamics of Plane Strains in Heteromodular Isotropic Elastic Media

Journal of Applied and Industrial Mathematics - Under consideration are the features of nonlinear dynamics of a heteromodular elastic medium under the plane strain. Some mathematical model of the...     

非线性各向同性弹性材料热应力本构方程

在非线性各向同性弹性体张量形式的本构方程基础上,仅考虑温度初值和增值,按照表示定理,补充考虑温度影响的完备项,建立了非线性各向同性弹性材料完备的多项式形式的热应力本构方程和应变能函数．作为应用举例,利用MATLAB软件,将本构方程与现有文献中高温金属材料单向拉伸和压缩情况下弹性阶段的实验数据进行了拟合,结果表明实验值与所提出的理论模型的结果显示了良好的一致性．     

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??This article provides the readers with an introduction to thespectral theory of ergodic one dimensional Schrodinger operators. The theoremsdeveloped by the author are mainly discussed and their proofs are given in detail.     

各向同性弹性损伤本构方程的一般形式

直接从不可逆热力学基本定律出发,推导出弹性各向同性损伤材料本构方程的一般形式,克服了由应变等效假设建立的经典损伤本构方程的缺陷,并阐明了两种各向同性弹性损伤模型(单标量模型与双标量模型)之间的联系.研究表明,采用单标量描述的损伤模型,在材料损伤本构方程中含有两个“损伤效应函数”,反映损伤对于两个弹性常数的不同影响.应变等效假设给出的损伤本构方程,是该文方程的一个近似形式,常常不能满意地描述实际材料的损伤行为.     

Operators on Partial Inner Product Spaces: Towards a Spectral Analysis

Mediterranean Journal of Mathematics - Given a Lattice of Hilbert spaces V J and a symmetric operator A in V J , in the sense of partial inner product spaces, we define a generalized resolvent for...     

不同材料的两个各向同性弹性长条的焊接问题

利用复变方法和积分方程理论 ,讨论两个不同材料的各向同性弱性长条的焊接问题 ,在理论上 ,给出了弱性体应力分布封闭形式的解 .     

中子测井问题中非定常输运方程的谱流线扩散有限元耦合方法

针对中子测井问题,研究非定常Boltamann中子输运方程的确定型数值求解方法,给出了求解Boltzmann方程的球谐函数展开和流线扩散有限元耦合方法,证明了这种耦合方法的收敛性和误差估计。实际算例表明此方法是有效的。     

Spectral Analysis of Abstract Parabolic Operators in Homogeneous Function Spaces,II

We use methods of harmonic analysis and group representation theory to study the spectral properties of the abstract parabolic operator \(\mathscr {L}= -\mathrm{d}/\mathrm{d}t+A\) in homogeneous function spaces. We focus on the dependency between various invertibility states of such an operator. In particular, we prove that often, a generally weaker state of invertibility implies a stronger state for \(\mathscr {L}\) under mild additional conditions. For example, we show that if the operator \(\mathscr {L}\) is surjective and the imaginary axis is not contained in the interior of the spectrum of A, then \(\mathscr {L}\) is invertible.