网络安全产品研究

本文在研究了网络安全的国内外有关情况后对网络安全技术进行了探讨 ,介绍了一种简单而实用的网络安全产品 ,添补了这方面的空白 ,而且本文介绍的产品已经应用到了许多部门 ,为网络安全做出了贡献     

高阶数值微分的积分方法

本文研究了高阶数值微分问题,利用Groetsch的思想,获得了可以稳定逼近近似已知函数的任意阶导数的积分方法,并在一定条件下,给出了收敛率.给出了二阶、三阶和四阶数值微分问题的数值实验,实验结果表明了方法的有效性.     

秩为1矩阵的性质及应用

给出了秩1矩阵的结构,讨论了这类矩阵在矩阵运算、对角化、标准型等方面的性质,推广和改进了文[1]的一些相关结果,并指出了它的若干应用,重点讨论了一类矩阵,得到了有关结论和方法.     

老歪的礼物

放暑假了,庄库欢天喜地地和爸爸妈妈旅游去了,贝卡在Q岛上乐不思蜀,卡卡西被她朋友拉去逛街,正好遂了她的意,柯西探长视休息为无聊。只有老歪,学生不用上课了,看着空荡荡的教室和空荡荡的校园,他突然不知道该干啥了。     

具有时延和乱序网络化系统的动态矩阵控制北大核心CSCD

研究了具有时延和数据包乱序的网络化系统的动态矩阵控制问题.首先,通过时序分析,给出了控制器端和执行器端处理乱序的方法,建立了包含时延和乱序的网络化系统模型.然后,针对所建立的模型,提出了改进的动态矩阵控制算法,给出了控制器的设计方法.进一步,通过对系统的稳定性分析,导出了保证闭环系统稳定的充分条件.最后,通过仿真验证了所提方法的有效性.     

基于概率论的防空武器系统对集群敌机的服务效能研究

论述了防空武器系统服务效能的概念,提出了服务效能的评估指标,做出了符合防空作战一般规律的假设,据此,通过概率论的方法分析了对抗系统的各种状态,论证了系统统计平衡状态的存在,进而建立了数学解析模型,最后得出了对防空武器系统服务效能的定量评估指标.     

分层教学的Bayes分析

对学校分层教学进行了初步探索 ,提出了分层分班的 Bayes决策 ,介绍了分层分班方法 ,获得了一些结论 ,并完成了对这些结论的证明 ,从理论上论述了分层教学是实施“因材施教”教育原则和素质教育的有效途径 ,给出了应用实例 .     

区间数的绝对值与区间值函数的极限

研究了区间数的绝对值和区间值函数的极限问题.首先,讨论了区间数的H-差的性质,得到了H-差的两个运算法则;然后,给出了区间数的绝对值概念,并讨论了区间数绝对值的性质;最后,借助区间数的H-差和绝对值的概念,建立了区间值函数极限概念的一种新的表达方式,给出了极限存在的充分必要条件,证明了极限值的唯一性及对加法运算和数乘运算的封闭性.     

轴向弹塑性应力波作用下直杆中的分叉问题

考虑了一个弹塑性直杆的动力屈曲问题,将其归结为轴向阶跃应力波的传播导致的分叉问题,分析了横向惯性效应的影响,并考虑了应力波反射的作用,给出了相应的屈曲条件,最后进行了数值分析,从中得到了一些有益的结论·     

赏析2011年湖北高考理科立几题

2011年高考已经落幕,笔者有意关注了湖北数学试卷,解读理科数学试卷,两道立体几何试题给我留下了很深的印象.小题的背景和问题设置让人耳目一新;大题的解法入口宽,方法多,涉及的知识面广,打破了单纯考查立体几何的常规,建立了立体几何与函数、三角、向量、解几的密切联系.这两道试题充分体现了源于教材,略高于教     

On Birman's sequence of Hardy–Rellich-type inequalities

In 1961, Birman proved a sequence of inequalities $\{I_n\}$, for $n\in \mathbb{N}$, valid for functions in $C_0^n((0,\infty ))?L^2((0,\infty ))$. In particular, $I_1$ is the classical (integral) Hardy inequality and $I_2$ is the well-known Rellich inequality. In this paper, we give a proof of this sequence of inequalities valid on a certain Hilbert space $H_n([0,\infty ))$ of functions defined on $[0,\infty )$. Moreover, $f\in H_n([0,\infty ))$ implies $f^{\prime }\in H_{n?1}([0,\infty ))$; as a consequence of this inclusion, we see that the classical Hardy inequality implies each of the inequalities in Birman's sequence. We also show that for any finite $b>0$, these inequalities hold on the standard Sobolev space $H_0^n((0,b))$. Furthermore, in all cases, the Birman constants ${[(2n?1)!!]}^2/2^{2n}$ in these inequalities are sharp and the only function that gives equality in any of these inequalities is the trivial function in $L^2((0,\infty ))$ (resp., $L^2((0,b))$). We also show that these Birman constants are related to the norm of a generalized continuous Cesàro averaging operator whose spectral properties we determine in detail.     

Some multicolor bipartite Ramsey numbers involving cycles and a small number of colors

For bipartite graphs $G_1,G_2,\dots ,G_k$, the bipartite Ramsey number $b(G_1,G_2,\dots ,G_k)$ is the least positive integer $b$ so that any coloring of the edges of $K_{b,b}$ with $k$ colors will result in a copy of $G_i$ in the $i$th color for some $i$. In this paper, our main focus will be to bound the following numbers: $b(C_{2t_1},C_{2t_2})$ and $b(C_{2t_1},C_{2t_2},C_{2t_3})$ for all $t_i\ge 3,$$b(C_{2t_1},C_{2t_2},C_{2t_3},C_{2t_4})$ for $3\le t_i\le 9,$ and $b(C_{2t_1},C_{2t_2},C_{2t_3},C_{2t_4},C_{2t_5})$ for $3\le t_i\le 5.$ Furthermore, we will also show that these mentioned bounds are generally better than the bounds obtained by using the best known Zarankiewicz-type result.     

Multiplicity of positive solutions for a class of concave-convex elliptic equations with critical growth

In this article, the following concave and convex nonlinearities elliptic equations involving critical growth is considered,{-△u=g(x)|u|2*-2u+λf(x)|u|q-2u,x∈Ω,u=0,x∈■Ω where Ω■R~N(N≥3) is an open bounded domain with smooth boundary, 1 q 2, λ 0.2*=2 N/(N-2)is the critical Sobolev exponent,f∈L2~*/(2~*-q)(Ω)is nonzero and nonnegative,and g ∈ C(■) is a positive function with k local maximum points. By the Nehari method and variational method,k+1 positive solutions are obtained. Our results complement and optimize the previous work by Lin [MR2870946, Nonlinear Anal. 75(2012) 2660-2671].     

A semilinear elliptic equation with a mild singularity at u = 0: Existence and homogenization

In this paper we consider singular semilinear elliptic equations whose prototype is the following

$\{\begin{array}{cc}?divA(x)Du=f(x)g(u)+l(x)\hfill & \text{in}\mathrm{\Omega },\hfill \\ u=0\hfill & \text{on}?\mathrm{\Omega },\hfill \end{array}$

where Ω is an open bounded set of ${\mathbb{R}}^N,N\ge 1$, $A\in L^{\infty }{(\mathrm{\Omega })}^{N\times N}$ is a coercive matrix, $g:[0,+\infty [\to [0,+\infty ]$ is continuous, and $0\le g(s)\le \frac{1}{s^{\gamma }}+1$ for every $s>0$, with $0<\gamma \le 1$ and $f,l\in L^r(\mathrm{\Omega })$, $r=\frac{2N}{N+2}$ if $N\ge 3$, $r>1$ if $N=2$, $r=1$ if $N=1$, $f(x),l(x)\ge 0$ a.e. $x\in \mathrm{\Omega }$.We prove the existence of at least one nonnegative solution as well as a stability result; we also prove uniqueness if $g(s)$ is nonincreasing or “almost nonincreasing”.Finally, we study the homogenization of these equations posed in a sequence of domains ${\mathrm{\Omega }}^{\epsilon }$ obtained by removing many small holes from a fixed domain Ω.     

Extremal problems on the Hamiltonicity of claw-free graphs

In 1962, Erd?s proved that if a graph $G$ with $n$ vertices satisfies

$e\left(G\right)>max\left\{\left(\genfrac{}{}{0ex}{}{n?k}{2}\right)+k^2,\left(\genfrac{}{}{0ex}{}{?(n+1)∕2?}{2}\right)+{?\frac{n?1}{2}?}^2\right\},$

where the minimum degree $\delta \left(G\right)\ge k$ and $1\le k\le (n?1)∕2$, then it is Hamiltonian. For $n\ge 2k+1$, let $E_n^k=K_k\vee (k{K}_1+K_{n?2k})$, where “$\vee$” is the “join” operation. One can observe $e\left(E_n^k\right)=\left(\genfrac{}{}{0ex}{}{n?k}{2}\right)+k^2$ and $E_n^k$ is not Hamiltonian. As $E_n^k$ contains induced claws for $k\ge 2$, a natural question is to characterize all 2-connected claw-free non-Hamiltonian graphs with the largest possible number of edges. We answer this question completely by proving a claw-free analog of Erd?s’ theorem. Moreover, as byproducts, we establish several tight spectral conditions for a 2-connected claw-free graph to be Hamiltonian. Similar results for the traceability of connected claw-free graphs are also obtained. Our tools include Ryjá?ek’s claw-free closure theory and Brousek’s characterization of minimal 2-connected claw-free non-Hamiltonian graphs.     

Global existence and boundedness for a class of second-order nonlinear differential equations

In this paper we obtain new conditions for the global existence and boundedness of solutions for nonlinear second-order equations of the form ${\left(r\left(t\right){\left|u^{\prime }\right|}^{p?2}{u}^{\prime }\right)}^{\prime }+g(t,u,u^{\prime })u^{\prime }+a\left(t\right)f\left(u\right)=e\left(t\right)\text{,}$ where $p>1$ is a real constant. The results are applicable to well-known Emden–Fowler and Lienard type equations. An illustrative example is also provided.