Lambda-fold 2-perfect 6-cycle systems in equipartite graphs

A 6-cycle system of a graph G is an edge-disjoint decomposition of G into 6-cycles. Graphs G, for which necessary and sufficient conditions for existence of a 6-cycle system have been found, include complete graphs and complete equipartite graphs. A 6-cycle system of G is said to be 2-perfect if the graph formed by joining all vertices distance 2 apart in the 6-cycles is again an edge-disjoint decomposition of G, this time into 3-cycles, since the distance 2 graph in any 6-cycle is a pair of disjoint 3-cycles.Necessary and sufficient conditions for existence of 2-perfect 6-cycle systems of both complete graphs and complete equipartite graphs are known, and also of λ-fold complete graphs. In this paper, we complete the problem, giving necessary and sufficient conditions for existence of λ-fold 2-perfect 6-cycle systems of complete equipartite graphs.     

一类广义Sierpinski地毯的Huasdorff维数

通过在任意给定的凸四边形和三角形上构造一个不同于通常欧氏度量的度量,证明了如果把构造经典Sierpinski地毯的初始图形正方形换成任意一个凸四边形或者三角形,则得到的广义Sierpinski地毯与经典的Sierpinski地毯具有相同的Haus-dorff维数.     

Complete photonic band gaps in one-dimensional ternary photonic crystals containing single negative materials

Complete photonic band gaps (PBGs) are found in one-dimensional ternary photonic crystals (1D TPCs) composed of an ordinary dielectric and single negative metamaterials. The proposed TPC gives omni directional PBG completely independent of polarizations dependent weekly on angle of incidence. Here the choice of different parameters of TPC is done in such a way so that it eliminates the Brewster's-angle transmission resonance, thus allowing a complete 3D PBG. It exhibits a photonic band or gap near frequencies where either the magnetic permeability or the electric permittivity of the metamaterial changes sign, whose width increases with the increasing angle of incidence. These result from the dispersive properties of the metamaterials and disappear for the particular case of propagation along the stratification direction. The results are discussed in terms of incident angle, layer thickness, dielectric constant of the dielectric material for TE and TM polarizations.     

完全收敛性中的Paley不等式

本文研究了完全收敛性中的Paley不等式,得到了Hsu-Robbins-Erds大数定律的更加精确的下界和上界,讨论了文[1]中提出的问题,同时在更加广泛的大数定律的意义下推广了[1]的结果,得到了比文[2,3]更加精确的结论。     

Unbalanced bipartite factorizations of complete bipartite graphs

We construct a new infinite family of factorizations of complete bipartite graphs by factors all of whose components are copies of a (fixed) complete bipartite graph K_p,q. There are simple necessary conditions for such factorizations to exist. The family constructed here demonstrates sufficiency in many new cases. In particular, the conditions are always sufficient when q=p+1.     

Pseudo Availability of Repairable System

Availability is a very basic characteristic of a system for measuring its performance. Various traditional availabilities have been defined in the literature. This article considers repairable system, the failure of which can be detected only by inspection, and incorporates both inspection and repair into consideration. The concept of pseudo availability is introduced and studied. Pseudo availability differs from the traditional availabilities in that once the system is in ‘up’ state it will remain there forever without change. The expression and/or its Laplace transform are derived. The limiting behavior of pseudo availability is also studied. AMS 2000 Subject Classification Primary 60K10, Secondary 60E10     

4维完备Einstein流形的一些注释

本文给出了在开的定向的4维流形上存在有界曲率的完备Einstein度量的障碍．     

一维光子晶体的有效折射率及色散特性

对有限长度一维光子晶体引入了复有效折射率的概念.它的实部描述了一维光子晶体的色散特性, 虚部反映了光在光子禁带被损耗衰减而消失的特征.从具体计算λ/4 波片堆组成的一维光子晶体的复有效折射率的结果可以看到,它的实部受到光子带结构的调制,在光子禁带及透射带中的一部分出现反常色散现象.在很大的频率范围内,有效折射率变得小于1.     

Separation properties of induced I(L)-topological spaces

The concept of induced I(L)-topological spaces has been introduced by Kubiak (Ph.D. Thesis, UAM, Poznan, 1985) and independently by Wang (Kexue Tongbao 34 (5) (1989) 333). In this paper, the separation properties in the sense of Hutton–Reilly of induced I(L)-topological spaces are investigated. The main result of the paper is a characterization of L-topological spaces by means of the appropriate Hutton–Reilly separation properties of its induced I(L)-topological space.