树图对完全图的多色Ramsey数

首先证明了关于一般图的多色Ramsey数的一个下界,该下界是一类星图对完全图的多色Ramsey数的精确下界;其次证明了关于星图对完全图的多色Ramsey数的上界,该上界是一类星图对完全图的多色RamSey数的精确上界;最后证明关于树图对完全图的多色Ramsey数的上界.     

代数构造及在Ramsey理论中的应用

这篇文章在伽罗瓦域上的代数构造和关于一些特定类型图的Ramsey数之间建立了一个关系. 研究了关于伽罗瓦域上的代数构造的方程及方程组的解. 我们得到了一些关于二部图的Ramsey数的新的下界和上界.     

Ramsey数的性质研究

本文得出了若干有关Ramsey数性质的结论,这些结论可直接用来推导Ram-sey数的下界公式,也可用来改进已有的Ramsey数的下界结果,本文中定理的证明思路,还能用于研究其它的图论和组合数学问题。     

关于Ramsey数下界的部分结果

本文得到 Ramsey数下界的一个计算公式 :R( l,s+ t-2 )≥ R( l,s) + R( l,t) -1 ,(式中 l、s、t≥ 3) .用此公式算得的 Ramsey数的下界比用其它公式算得的下界好 .     

确定Ramsey数下界值的随机算法

文[1—2]借助于计算机得到了几个Ramsey数的下界值,但由于计算机确定Ramsey数的下界值往往需要判断多达指数级的各种情况,因此所需的计算时间常使人难以接受.本文提出了一种确定Ramsey数r(k,l)下界值的随机算法,该算法试图随机而有针对性地构造一个有n个顶点的简单图G,使G中既无k个顶点的团又无l个顶点的独立集,从而确定n+1是r     

Ramsey数R(K_3,K_(16)-e)的一个下界

图论方法是研究Ramsey理论中最常用的方法,80多年的研究产生了大量的成果.Ramsey数R(G,H)是这样的最小正整数n,使得完全图K_n的边的任何一种红、蓝染色都会有一个红色边子图G,或者有一个蓝色边子图H.本文找到Ramsey数R(K_3,K_(16-e))的一个下界.     

9个经典Ramsey数R(3,t)的新下界

本文研究了经典Ramsey数R(3,t)的下界问题.利用素数阶循环图的性质改进一般阶循环图团数的计算方法,获得了9个经典Ramsey数R(3,t)的新下界:R(3,29)≥183,R(3,30)≥189,R(3,32)≥213,R(3,33)≥218,R(3,34)≥226,R(3,35)≥231,R(3,36)≥239,R(3,37)≥244,R(3,38)≥256,其中前三个结果分别改进了迄今已知的最好的下界,后6个结果是本文首次报道的.     

素数阶循环图和经典Ramsey数R（4，n）的三个新下界

研究了素数阶循环圈的基本性质，提出了寻求有效参数构造正则循环圈的新方法，得到了3个经典Ramsey数的新下界：R（4，17）≥164，R（4，18）≥182，R（4，22）≥282．这前2个结果填补了关于Ramsey数综述[2]的上下界表中的2个空白，第3个结果超过了目前已知的最好下界R（4，22）≥258，     

Ramsey数的若干新性质

Ramsey数N(q_1,q_2,…,q_n;t)是组合数学中很有意义的一类数.经过研究,作者得到了以下结果,利用这些结果能导出一些Ramsey数的新下界. 本文所用代表数的符号均表示任意正整数. 定理1 若q_0、q_1、…、qn≥t≥2,则N(q_0+q_1-1,q_2,q_3,…,q_n;t)≥N(q_0.q_2,q_3…,q_n;t)+N(q_1,q_2,…,q_n;t)-1.     

关于SCHUR定理

Schur定理是关于Ramsey数在应用方面的一个定理。本文推广了Schur定理,使之成为广义的Ramseg数在应用方面更一般的一个定理,本文还对“Schur解”的个数的下界进行了研究。     

J—自共轭微分算子谱的定性分析

本文对J－自共轭微分算子谱理论研究情况做一些概要性的介绍,第一部分简要回顾了J－自共轭微分算子理论研究的发展过程,第二,三部分介绍了J－自共轭微分算子的本质谱和离散谱定性分析的主要方法和结论;第四部分扼要叙述J－自共轭微分算子其它方面的一些工作,以及J－自共轭微分算子谱理论研究中尚待解决的问题。     

一类单位圆上的Chebyshev权的Cauchy型求积公式

在本文中,我们首先给出一些基本的结果和一些概念,然后给出单位圆上带Cheby shev权的一些Cauchy主值积分的求积公式,最后给出了它们的误差估计.     

Bifurcation analysis and feedback control of a 3D chaotic system

In this paper, we analyze a three-dimensional differential system derived from the Chen system based on the first Lyapunov coefficient, and apply it to investigate the local bifurcation. And we present some insights on bifurcation and stability, also obtain some conditions for subcritical and supercritical. Finally, we give some numerical simulation studies of system in order to verify analytic results.     

Modular invariance and anomaly cancellation formulas

By studying modular invariance properties of some characteristic forms, we get some new anomaly cancellation formulas. As an application, we derive some results on divisibilities on spin manifolds and congruences on spin ^c manifolds.     

Shape optimization of stationary Navier-Stokes equation over classes of convex domains

In this work, we obtain some properties for the family of some convex domains. Based on these, we prove the existence of solutions of some shape optimization for stationary Navier-Stokes equations.     

Busemann Functions and Barrier Functions

On a smooth, non-compact, complete, boundaryless, connected Riemannian manifold there are two kinds of functions: Busemann functions with respect to rays and barrier functions with respect to lines (if there exists at least one). In this paper we collect some known properties on Busemann functions and introduce some new fundamental properties on barrier functions. Based on these properties of barrier functions, we could define some relations on the set of lines and thus classify them. With the equivalence relation we introduced, we present a generalization of a rigidity conjecture.     

Notes on the Dai-Yuan-Yuan modified spectral gradient method

In this paper, we give some notes on the two modified spectral gradient methods which were developed in [10]. These notes present the relationship between their stepsize formulae and some new secant equations in the quasi-Newton method. In particular, we also introduce another two new choices of stepsize. By using an efficient nonmonotone line search technique, we propose some new spectral gradient methods. Under some mild conditions, we show that these proposed methods are globally convergent. Numerical experiments on a large number of test problems from the CUTEr library are also reported, which show that the efficiency of these proposed methods.     

On the entropy conditions for some flux limited diffusion equations

In this paper we give a characterization of the notion of entropy solutions of some flux limited diffusion equations for which we can prove that the solution is a function of bounded variation in space and time. This includes the case of the so-called relativistic heat equation and some generalizations. For them we prove that the jump set consists of fronts that propagate at the speed given by Rankine-Hugoniot condition and we give on it a geometric characterization of the entropy conditions. Since entropy solutions are functions of bounded variation in space once the initial condition is, to complete the program we study the time regularity of solutions of the relativistic heat equation under some conditions on the initial datum. An analogous result holds for some other related equations without additional assumptions on the initial condition.     

Key-Dependent S-Boxes and Differential Cryptanalysis

Key-dependent S-boxes gained some prominence in block cipher design when Twofish became an AES finalist. In this paper we make some observations on how the cryptanalyst might work with key-dependent S-boxes, we begin to develop a framework for the differential cryptanalysis of key-dependent S-boxes, and we introduce some basic techniques that were used in an analysis of reduced-round Twofish.     

关于p-幂零限制李超代数

我们讨论了p-幂零限制李超代数的一些性质，分别给出了p-幂零和幂零限制李超代数的几个充分必要条件，并讨论了幂零与p-幂零之间的关系．最后，证明了幂零限制李超代数的一些性质．