A simple proof of the spectral excess theorem for distance-regular graphs

The spectral excess theorem provides a quasi-spectral characterization for a (regular) graph Γ with d+1 distinct eigenvalues to be distance-regular graph, in terms of the excess (number of vertices at distance d) of each of its vertices. The original approach, due to Fiol and Garriga in 1997, was obtained by using a local approach, so giving a characterization of the so-called pseudo-distance-regularity around a vertex. In this paper we present a new simple projection method based in a global point of view, and where the mean excess plays an essential role.     

Deleting Vertices and Interlacing Laplacian Eigenvalues

The authors obtain an interlacing relation between the Laplacian spectra of a graph G and its subgraph G - U, which is obtained from G by deleting all the vertices in the vertex subset U together with their incident edges. Also, some applications of this interlacing property are explored and this interlacing property is extended to the edge weighted graphs.     

Spectrum of a homogeneous graph

We describe the spectrum of the Laplacian for a homogeneous graph acted on by a discrete group. This follows from a more general result which describes the spectrum of a convolution operator on a homogeneous space of a locally compact group. We also prove a version of Harnack inequality for a Schrödinger operator on an invariant homogeneous graph.     

Scaling spectra and return times of dynamical systems

The grand canonical version of the spectrum of singularities formalism is presented, relying naturally upon certain Markov transition graphs. The structure of a graph is simply determined by the close return times of the dynamical system described. Thus, an intimate connection exists between the shape of the singularity curve and a small but interesting set of dynamical properties.     

HER磁镜装置中Hα测量及结果

本文描述HER磁镜中Ha面发光度时空分布的测量,发现等离子体发光,扰动,工作模式等呈环状结构;一个良好的热电子环可以抑制扰动环区的低频扰动。     

希尔伯特空间有限区域成像积分算子的谱

本文讨论了希尔伯特空间中有限区域成像积分算子的本征值和本征函数,研究了非对称核的情形,并用微扰和有限秩方法计算了衍射受限和离焦情况下的本征值和本征函数。     

微波强场中的光谱激发现象

本文报道了元素，化合物和放电灯在微波强场产生的激发现象。介绍了一种在微波强场中产生原子发射光谱的新方法。采用作者自行改制的微波激发装置，即可使固态的元素和化合物产生光谱辐射，也可使各种放电灯和气体光谱管得以激发，用一种装置实现了几种装置的功能，对于该方法存在的问题，文中也作了一定的说明。     

Spectrum planning and performance evaluation between heterogeneous satellite networks

A new network has been recently proposed for the provision of fixed broadband services via high altitude platform stations (HAPS) in the 48/47 GHz band. One of the critical issues of this technology is spectrum sharing with the fixed satellite service. This paper examines the effect of Earth-to-stratosphere co-channel interference produced by ground stations of HAPS network to geostationary orbit (GEO) satellite receivers and proposes an interference-to-noise (I/N) calculation model for the evaluation of the current HAPS ground stations power characteristics set by ITU-R. Analytical and simulation results for archetypal systems in realistic scenarios indicate that efficient use of the spectrum shared between heterogeneous HAPS and Fixed Satellite Networks is feasible. Certain consideration is needed prior to the HAPS network development in suburban areas for latitudes from 55° to 65°, and in rural areas for latitudes from 60° to 75°.     

A unification of some matrix factorization results

A unification of some factorization results regarding products of positive-definite matrices, commutators, and products of involutions is presented. This topic was first presented by Sourour for fields with, in the latter two classes, sufficiently many elements in terms of the order of the matrix being factored. The current presentation is valid for matrices over any field with at least four elements, and is independent of the order of the matrix being factored.