Inner bounds for the spectrum of quasinormal operators

A linear operator in a separable Hilbert space is called a quasinormal one if it is a sum of a normal operator and a compact one. In the paper, bounds for the spectrum of quasinormal operators are established. In addition, the lower estimate for the spectral radius is derived. Under some restrictions, that estimate improves the well-known results. Applications to integral operators and matrices are discussed. Our results are new even in the finite-dimensional case.

     

On the spectral sequence constructors of Guichardet and Stefan

The concept of a spectral sequence constructor is generalised to Hopf Galois extensions. The spectral sequence constructions that are given by Guichardet for crossed product algebras are also generalised and shown to provide examples. It is shown that all spectral sequence constructors for Hopf Galois extensions construct the same spectral sequence.     

Spectral and Pseudospectral Approximations Using Hermite Functions: Application to the Dirac Equation

We consider in this paper spectral and pseudospectral approximations using Hermite functions for PDEs on the whole line. We first develop some basic approximation results associated with the projections and interpolations in the spaces spanned by Hermite functions. These results play important roles in the analysis of the related spectral and pseudospectral methods. We then consider, as an example of applications, spectral and pseudospectral approximations of the Dirac equation using Hermite functions. In particular, these schemes preserve the essential conservation property of the Dirac equation. We also present some numerical results which illustrate the effectiveness of these methods.     

Comment on “A Hierarchy of Integrable Nonlinear Lattice Equations and New Integrable Symplectic Map“

Comment on a recent paper on Commun. Theor. Phys. (Beijing, China) 38 (2002) pp. 523-528.     

An inverse spectral problem for a nonsymmetric differential operator: Reconstruction of eigenvalue problem

In this paper, an algorithm is established to reconstruct an eigenvalue problem from the given data satisfying certain conditions. These conditions are proved to be not only necessary but also sufficient for the given data to coincide with the spectral characteristics corresponding to the reconstructed eigenvalue problem.     

类型γ射线能谱指纹的识别机理

放射源的辐射指纹能起到标识和鉴别放射性物体的作用.在涉及核弹头不可逆销毁过程的深度核裁军核查中,核弹头的辐射指纹对标识和鉴别裁减下来的核弹头将起到关键作用.预先研究辐射指纹的有关技术,如识别机理的研究,将有助于深度核裁军的核弹头核查技术发展.以实验室放射源为研究对象,探索了类型γ射线能谱指纹的同一性识别机理.类型γ射线指纹识别机理的研究,就是要找出一种合适的方法,以较高的置信度,描述两个正在进行比较的γ射线指纹是否为同一放射源的指纹.采用了谱形比较法,并用谱相似度概念来描述两个指纹的相似程度.在谱形比较思想的指导下,编制了放射源类型指纹识别软件,并通过放射源同一性的识别实验验证了软件的有效性,同时研究了谱相似度随统计涨落和测量条件,如时间、源强和本底等因素的变化情况.研究结果表明:1)用相似度概念来描述两个指纹的相似程度,回答两个待比较的γ射线能谱是否代表同一类型放射源,是切实可行的;2)该识别机理只具备识别放射源类型的能力,而对同一类型、差异甚微的放射源个体还不能识别 关键词： γ射线能谱指纹 辐射指纹 识别机理 核查技术     

Slutsky定理在样本分位数的极限分布证明上的应用

为了更好地理解和应用样本分位数的极限分布,利用Slutsky定理,推导了样本分位数的极限分布.     

Families of Line-Graphs and Their Quantization

Any directed graph G with N vertices and J edges has an associated line-graph L(G) where the J edges form the vertices of L(G). We show that the non-zero eigenvalues of the adjacency matrices are the same for all graphs of such a family L ⁿ (G). We give necessary and sufficient conditions for a line-graph to be quantisable and demonstrate that the spectra of associated quantum propagators follow the predictions of random matrices under very general conditions. Line-graphs may therefore serve as models to study the semiclassical limit (of large matrix size) of a quantum dynamics on graphs with fixed classical behaviour.     

用光学多通道分析仪系统作高分辨光谱测量的技术

通常的光多通道分析仪(OMA)存在着同时谱宽与分辨率的矛盾.本文所述方法,在不减小谱宽的前提下,可将该分析仪光谱分辨率提高1～2量级,使之可适用于高分辨率谱研究.     

含铒碲酸盐玻璃的上转换荧光性质研究

在室温下,用804nm波长的半导体激光器作激发源,在TeO_2-PbO基掺铒碲酸盐玻璃中实现了中心波长分别为525nm,550nm和660nm的上转换发射.荧光强度与激发功率呈非线性关系.估测了PbO含量对上转换荧光相对强度的影响.