同分布的NA序列加权和的强大数律

讨论了同分布NA随机变量序列加权和的强大数律,所得结果推广了Z．D．Bai和P．E．Cheng及S．H．Sung的结果．     

具有立方对称性及两个弛豫时间的微极热弹性介质中调和时间源引起的变形

研究了具有立方对称性及两个弛豫时间的微极热弹性介质在调和时间源中的响应．采用了Fourier变换以及数值逆变换技术．在物理域中,得到了位移、应力、微转动和温度分布的数值结果．将微极立方晶体法向位移、法向力应力、切向耦合应力和温度分布的计算结果,与微极各向同性固体的结果进行比较．绘制了指定材料的数值结果图形．还推断了某些特殊情况的结果．     

三角Hopf代数表示范畴上的Lie余代数

本文在三角Ｈｏｐｆ代数表示范畴上系统地研究了Ｌｉｅ余代数,在此范畴上 的Ｌｉｅ余代数与Ｈｏｐｆ代数之间建立了重要的联系．主要给出了Ｌｉｅ余代数的余包络 余代数的结构．所得结果自然是关于Ｌｉｅ代数的对偶结果,推广了 Ｓｗｅｅｄｌｅｒ Ｍ． Ｅ．, Ｇｕｒｅｖｉｃｈ Ｄ．Ｉ．, Ｍｉｃｈａｅｌｉｓ Ｗ．和 Ｍａｉｉｄ Ｓ．等人的结果．     

三角Hopf代数表示范畴上的Lie余代数

本文在三角Ｈｏｐｆ代数表示范畴上系统地研究了Ｌｉｅ余代数,在此范畴上 的Ｌｉｅ余代数与Ｈｏｐｆ代数之间建立了重要的联系．主要给出了Ｌｉｅ余代数的余包络 余代数的结构．所得结果自然是关于Ｌｉｅ代数的对偶结果,推广了 Ｓｗｅｅｄｌｅｒ Ｍ． Ｅ．, Ｇｕｒｅｖｉｃｈ Ｄ．Ｉ．, Ｍｉｃｈａｅｌｉｓ Ｗ．和 Ｍａｉｉｄ Ｓ．等人的结果．     

Elman网络梯度学习法的收敛性

考虑有限样本集上Elman网络梯度学习法的确定性收敛性．证明了误差函数的单调递减性．给出了一个弱收敛性结果和一个强收敛结果,表明误差函数的梯度收敛于0,权值序列收敛于固定点．通过数值例子验证了理论结果的正确性．     

新的不动点定理及应用

本文获得了几个压缩型映射的不动点定理,改进了相应文献的结果．应用该定理,给出了一类时滞积分方程的正概周期解的存在性结果．推广了已有的结果．     

Banach空间中线性算子的Drazin广义逆的表示

1981年,1985年,2000年,乔三正、蔡东汉、魏益民分别给出Drazin广义逆不同形式的表示．本文将对上述结果进行推广,给出Drazin广义逆的统一表示,使上述三个结果均成为本文主要结果的特例．在本文主要结果的基础上,利用算子谱理论,给出Drazin广义逆的一种逼近形式的表示,同时给出逼近解的估计．此结果推广了蔡东汉、魏益民的相应结果．     

Clifford分析中双曲调和函数的一种边值问题

本文讨论Ｃｌｉｆｆｏｒｄ分析中双曲调和函数的积分表达式及其一种边值问题解的存在性．所得结果推广了１９９２年Ｈ．Ｌｅｕｔｗｉｌｅｒ［１］的结果．     

Kloosterman和的角度

有限域 Ｆｑ（ｑ为奇）上的 Ｋｌｏｏｓｔｅｒｍａｎ和是两个模为 ｑ１／２的共轭复数之和．这个复数的角度就称为相应的Ｋｌｏｏｓｔｅｒｍａｎ和的角度．我们在本文给出了Ｋｌｏｏｓｔｅｒｍａｎ和的角度的一些结果,改进了Ｋａｔｚ Ｎ．［１］的一些结果,也改进和推广了Ｃｏｎｒｅｙ　Ｊ．和Ｉｗａｎｉｅ Ｈ．［２］的结果．     

关于集值非线性混合变分不等式问题

本文研究一类广义集值非线性混合变分不等式问题,建立了其解的存在性定理．我们的工作是zhang工作的修正．我们的结果是Cho etc．和Verma的相应结果的改进和发展．     

两类带有确定潜伏期的SEIS传染病模型的分析

通过研究两类带有确定潜伏期的SEIS传染病模型,发现对种群的常数输入和指数输入会使疾病的传播过程产生本质的差异．对于带有常数输入的情形,找到了地方病平衡点存在及局部渐近稳定的阈值,证明了地方病平衡点存在时一定局部渐近稳定,并且疾病一致持续存在．对于带有指数输入的情形,发现地方病平衡点当潜伏期充分小时是局部渐近稳定的,当潜伏期充分大时是不稳定的．     

Polynomial-time algorithms for regular set-covering and threshold synthesis

A set-covering problem is called regular if a cover always remains a cover when any column in it is replaced by an earlier column. From the input of the problem - the coefficient matrix of the set-covering inequalities - it is possible to check in polynomial time whether the problem is regular or can be made regular by permuting the columns. If it is, then all the minimal covers are generated in polynomial time, and one of them is an optimal solution. The algorithm also yields an explicit bound for the number of minimal covers. These results can be used to check in polynomial time whether a given set-covering problem is equivalent to some knapsack problem without additional variables, or equivalently to recognize positive threshold functions in polynomial time. However, the problem of recognizing when an arbitrary Boolean function is threshold is NP-complete. It is also shown that the list of maximal non-covers is essentially the most compact input possible, even if it is known in advance that the problem is regular.     

一类具有垂直传染和预防接种的SEIR传染病模型的定性分析

建立并分析了一类对出生时没有被染病母体垂直传染的染病者的新生儿进行免疫接种的SEIR传染病模型.得到了疾病是否灭绝的阈值R0,当R0<1时,无病平衡点全局渐近稳定的.当R0>1时,地方病平衡点局部渐近稳定的,且疾病一致持续生存.     

Milnor方图中的w-凝聚性

整环R称为ω-凝聚整环,是指R的每个有限型理想是有限表现型的.本文证明了ω-凝聚整环是v-凝聚整环,且若(RDTF,M)是Milnor方图,则在Ⅰ型情形,R是ω-凝聚整环当且仅当D和T都是ω-整环,且T_M是赋值环;对于Ⅱ-型情形,R是ω-凝聚整环当且仅当D是域,[F:D]<∞,M是R的有限型理想,T是ω-凝聚整环,且R_M是凝聚整环.     

覆盖下近似算子的拓扑性质

在不限制U为有限论域的情况下,研究了覆盖下近似算子XL和CL的拓扑性质。证明了覆盖下近似算子XL是内部算子,而且由XL生成的拓扑TXL为包含由覆盖C本身作为子基生成的拓扑TC的最小Alexandrov拓扑。特别地,当U为有限论域时,TXL=TC.然而,覆盖下近似算子CL不是内部算子。当覆盖C为某拓扑的基时,CL是内部算子,且此时由CL生成的拓扑TCL与TC是同一个拓扑。若进一步要求U为有限论域,则TCL=TXL=TC,进而CL=XL.     

带有反馈的因果模型中的独立性识别

在本文中,直接利用计算要概率分布的办法证明了在史包含离散变量４ 反馈系统产生的因果图中的条件独立关系可以由ｄ－分离识别出．     

On the density of the minimal subspaces generated by discrete linear Hamiltonian systems

This paper focuses on the density of the minimal subspaces generated by a class of discrete linear Hamiltonian systems. It is shown that the minimal subspace is densely defined if and only if the maximal subspace is an operator; that is, it is single valued. In addition, it is shown that, if the interval on which the systems are defined is bounded from below or above, then the minimal subspace is non-densely defined in any non-trivial case.     

The Cauchy problem for a generalized Camassa–Holm equation

In this paper, we are concerned with the Cauchy problem of the generalized Camassa–Holm equation. Using a Galerkin-type approximation scheme, it is shown that this equation is well-posed in Sobolev spaces $H^s$, $s>3/2$ for both the periodic and the nonperiodic case in the sense of Hadamard. That is, the data-to-solution map is continuous. Furthermore, it is proved that this dependence is sharp by showing that the solution map is not uniformly continuous. The nonuniform dependence is proved using the method of approximate solutions and well-posedness estimates. Moreover, it is shown that the solution map for the generalized Camassa–Holm equation is Hölder continuous in $H^r$-topology. Finally, with analytic initial data, we show that its solutions are analytic in both variables, globally in space and locally in time.     

递推阻尼最小二乘法的收敛性与稳定性

递推最小二乘法是参数辨识中最常用的方法,但容易产生参数爆发现象.因此对一种更稳定的辨识方法——递推阻尼最小二乘法进行了收敛特性的分析.在使用算法之前先归一化测量向量,结果表明,参数化距离收敛于一个零均值随机变量,并且在持续激励条件下,适应增益矩阵的条件数有界.参数化距离的方差有界.     

An Improved Branch & Bound Method for the Uncapacitated Competitive Location Problem

In this paper, the problem of locating new facilities in a competitive environment is considered. The problem is formulated as the firm expected profit maximization and a set of nodes is selected in a graph representing the geographical zone. Profit depends on fixed and deterministic location costs and, since customers are independent decision-makers, on the expected market share. The problem is an instance of nonlinear integer programming, because the objective function is concave and submodular. Due to this complexity a branch & bound method is developed for solving small size problems (that is, when the number of nodes is less than 50), while a heuristic is necessary for larger problems. The branch & bound is called data-correcting method, while the approximate solutions are obtained using the heuristic-concentration method.