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31.
Eckhard Steffen 《Discrete Mathematics》2004,280(1-3):191-214
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 ck 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 ζk 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. 相似文献
32.
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. 相似文献
33.
34.
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。 相似文献
35.
36.
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. 相似文献
37.
George Stoica 《Journal of Mathematical Analysis and Applications》2007,336(2):1489-1492
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. 相似文献
38.
汪巍 《数学的实践与认识》2004,34(3):103-109
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 . 相似文献
39.
New constructions of regular disjoint distinct difference sets (DDDS) are presented. In particular, multiplicative and additive DDDS are considered. 相似文献
40.
Philip T. Keenan 《Numerical Algorithms》1994,7(2):269-293
We describe a new family of discrete spaces suitable for use with mixed methods on certain quadrilateral and hexahedral meshes. The new spaces are natural in the sense of differential geometry, so all the usual mixed method theory, including the hybrid formulation, carries over to these new elements with proofs unchanged. Because transforming general quadrilaterals into squares introduces nonlinearity and because mixed methods involve the divergence operator, the new spaces are more complicated than either the corresponding Raviart-Thomas spaces for rectangles or corresponding finite element spaces for quadrilaterals. The new spaces are also limited to meshes obtained from a rectangular mesh through the application of a single global bilinear transformation. Despite this limitation, the new elements may be useful in certain topologically regular problems, where initially rectangular grids are deformed to match features of the physical region. They also illustrate the difficulties introduced into the theory of mixed methods by nonlinear transformations. 相似文献