A New Family of Cyclic Difference Sets with Singer Parameters in Characteristic Three

We construct a new family of cyclic difference sets with parameters ((3 ^d – 1)/2, (3 ^{d – 1} – 1)/2, (3 ^{d – 2} – 1)/2) for each odd d. The difference sets are constructed with certain maps that form Jacobi sums. These new difference sets are similar to Maschietti's hyperoval difference sets, of the Segre type, in characteristic two. We conclude by calculating the 3-ranks of the new difference sets.     

Measurements of edge-uncolorability

Cubic bridgeless graphs with chromatic index four are called uncolorable. We introduce parameters measuring the uncolorability of those graphs and relate them to each other. For k=2,3, let c_k be the maximum size of a k-colorable subgraph of a cubic graph G=(V,E). We consider r₃=|E|−c₃ and . We show that on one side r₃ and r₂ bound each other, but on the other side that the difference between them can be arbitrarily large. We also compare them to the oddness ω of G, the smallest possible number of odd circuits in a 2-factor of G. We construct cyclically 5-edge connected cubic graphs where r₃ and ω are arbitrarily far apart, and show that for each 1c<2 there is a cubic graph such that ωcr₃. For k=2,3, let ζ_k denote the largest fraction of edges that can be k-colored. We give best possible bounds for these parameters, and relate them to each other.     

Viscosity solutions of fully nonlinear parabolic systems

In this paper, we discuss the viscosity solutions of the weakly coupled systems of fully nonlinear second-order degenerate parabolic equations and their Cauchy-Dirichlet problem. We prove the existence, uniqueness and continuity of viscosity solution by combining Perron's method with the technique of coupled solutions. The results here generalize those in Proc. London Math. Soc. 63 (1991) 212-240 and Comm. Partial Differential Equations 16 (1991) 1095-1128.     

Concerning seven and eight mutually orthogonal Latin squares

In this paper, three new direct Mutually Orthogonal Latin Squares (MOLS) constructions are presented for 7 MOLS(24), 7 MOLS(75) and 8 MOLS(36); then using recursive methods, several new constructions for 7 and 8 MOLS are obtained. These reduce the largest value for which 7 MOLS are unknown from 780 to 570, and the largest odd value for which 8 MOLS are unknown from 1935 to 419. © 2003 Wiley Periodicals, Inc.     

高阶非线性时滞差分方程解的渐近性

研究如下的具强迫项的高阶非线性时滞差分方程△^my(n) u(n)l↑∑i=1 gi(y(n-τ))=v(n)其中，m≥1，u,v：N→R，gi：R→R且τ∈{0，1，2，3，…)，i=1，2，…，l，得到了使该方程的解具有某种渐近性态的充分条件。     

用数值方法分析微孔激光器出射光的近场特性

微孔激光器作为应用于近场光信息存储系统中的一种新型光源，它的出射光斑的近场特性对于近场光存储是十分重要的。针对纳米孔径运用角谱进行Fox-Li数值迭代，得到不同孔径微孔激光器的基模光强分布，然后运用二维非线性时域有限差分法分析微孔激光器出射端即微孔金属膜的近场光学性质，模拟计算了不同孔径和厚度的微孔金属膜的光强近场分布，从应用于近场光存储的角度，给出反映其近场光学特性的相关数据。发现由于TM模式下金属存在局域表面等离子增强效应，使得其出射强度比TE模式高一个数量级，从而更适于作为实际中近场光存储系统和原理试验的光学头。     

三阶非线性时滞差分方程解的渐近性

研究了一类三阶非线性变滞量差分方程解的渐近性,给出了该类方程的非振动解当n→+∞时渐近趋于零或趋于某有限数值的几个充分条件.     

Oscillation of certain partial difference equations

In this paper we consider a class of nonlinear delay partial difference equations and a class of linear delay partial difference equations with variable coefficients, which may change sign. We obtain oscillation criteria for these equations. There are no results for the oscillation of these equations up to now.     

Baum-Katz-Nagaev type results for martingales

We obtain a Baum-Katz-Nagaev type theorem for bounded martingale difference sequences that have more than a second moment, and prove that the celebrated Hsu-Robbins-Erd?s theorem fails for martingales.     

差分系统基于两种度量的极端稳定性

首先引入了差分系统基于两种度量的极端稳定性概念 ,然后建立了一些关于差分系统 ( h0 ,h)极端稳定性 (极端一致稳定性 ,极端渐近稳定性 ,极端一致渐近稳定性 )的判定准则 .在所得到的定理中 ,对△ V的限制较弱 ,特别地 ,△V甚至可以恒为正 ,从而便于实际应用 .