用Lebesgue-Stieltjes积分定义的间断解的存在唯一性

在Lebesgue-Stieltjies积分定义的广义解的意义下,证明了一个双曲型方程组Cauchy问题整体广义解的存在性和唯一性.作为经典广义解的自然推广,文中的广义解可以包含某些具奇性的双曲波如δ-波.也适用更一般的方程组.     

一个广义Boussinesq方程解的存在性与衰减性

文章研究一个广义Boussinesq方程的Cauchy问题.利用长短波分解、Green函数办法和能量方法,证明全局解的存在性,并且给出解的Lp衰减估计.     

一类脉冲分数阶微分方程广义反周期边值问题解的存在性（英文）

本文研究一类脉冲分数阶微分方程广义反周期边值问题解的存在性,利用不动点理论得到一些解的存在性结论,推广和补充了已有的一些结论.此外给出一个实例说明论文的主要结果的可行性.     

广义强非线性拟补问题*

利用本文中的算法,我们证明了广义强非线性拟补问题解的存在性及由算法产生的迭代序列的收敛性,改进和发展了Noor,Chang-Huang等人的结果.此外,也给出了求广义强非线性拟补问题的近似解的另一更一般的迭代算法并证明了由此迭代格式获得的近似解收敛于此补问题的精确解.     

广义分布半群与退化发展方程的分布解

在Banach空间中引进了由有界线性算子引导的广义分布半群的新概念,并讨论了它的有关性质.在我们的方法中,广义分布半群的生成元可以不是稠定的.此外,还引进了退化发展方程在Laplace变换意义下的分布解,应用广义分布半群给出了退化发展方程分布解的构造性表达式.     

Clifford分析中广义超正则函数的一个非线性边值问题

讨论了Cliffrd分析中广义超正则函数的一个非线性边值问题.首先将广义超正则函数分解为两个奇异积分算子,然后给出了广义超正则函数的Plemelj公式及相关奇异积分算子的性质,最后利用Schauder不动点原理证明了广义超正则函数的一个非线性边值问题的解的存在性及积分表达式.     

一类广义Li\'enard方程周期正解的存在性

本文证明一类广义Li\''enard方程周期正解的存在性及渐近稳定性. 我们讨论的非自治函数可满足超线性条件,克服了连续定理讨论超线性条件的困难. 文章的最后,我们给出两个例子和数值解以及对应的相图和时间序列图来验证我们的结论.     

广义绝对值方程组唯一可行解注记

该文主要考虑广义绝对值方程组唯一可行解的存在性.基于区间矩阵的正则性及矩阵的2-范数,给出一些新的有用的结果可用于确定广义绝对值方程组的唯一可行解.     

Jordan标准形过渡矩阵的一种算法

给出Jordan定理的一个证明,以及Jordan标准形过渡矩阵的一种算法:求出一线性方程组解空间的基,解空间即是矩阵关于某特征值的特征向量、广义特征向量所张成的子空间,在该解空间中依次找出各特征向量及所对应的广义特征向量.一个8阶矩阵的计算实例表明算法简便实用.     

指数型增广拉格朗日函数在广义半无限规划中的应用

本文利用指数型增广拉格朗日函数将一类广义半无限极大极小问题在一定条件下转化为标准的半无限极大极小问题,使它们具有相同的局部与全局最优解.我们给出了两个转化条件:一个是充分与必要条件,另一个是在实际中易于验证的充分条件.通过这种转化,我们给出了广义半无限极大极小问题的一个新的一阶最优性条件.     

Metric regularity of a positive order for generalized equations

This paper focuses on the metric regularity of a positive order for generalized equations. More concretely, we establish verifiable sufficient conditions for a generalized equation to achieve the metric regularity of a positive order at its a given solution. The provided conditions are expressed in terms of the Fréchet coderivative/or the Mordukhovich coderivative/or the Clarke one of the corresponding multifunction formulated the generalized equation. In addition, we show that such sufficient conditions turn out to be also necessary for the metric regularity of a positive order of the generalized equation in the case where the multifunction established the generalized equation is closed and convex.     

Solutions of nonlinear differential equations

We consider an ordinary nonlinear differential equation with generalized coefficients as an equation in differentials in the algebra of new generalized functions. The solution of such an equation is a new generalized function. In this article we formulate necessary and sufficient conditions for when the solution of the given equation in the algebra of new generalized functions is associated with an ordinary function. Moreover, a class of all possible associated functions is described.     

模糊网络最大流算法研究

将模糊数差值B~-A~视为模糊方程X~+A~=B~的解,进而探讨了模糊方程的求解问题,并基于目的规划理论,给出了模糊方程的广义解定义.运用目的规划的单纯型方法,得到了模糊方程广义解的计算公式及模糊方程广义解的若干性质.由模糊方程的广义解引申出了模糊数差值的定义.运用该定义将传统的网络最大流算法推广到模糊环境.结果表明,模糊数差值定义,克服了基于扩展原理意义下的模糊运算所产生的各种问题,解决了这些传统理论方法的拓展问题.     

Optimal control of the viscous generalized Camassa–Holm equation

In this paper, we study the optimal control problem for the viscous generalized Camassa–Holm equation. We deduce the existence and uniqueness of weak solution to the viscous generalized Camassa–Holm equation in a short interval by using Galerkin method. Then, by using optimal control theories and distributed parameter system control theories, the optimal control of the viscous generalized Camassa–Holm equation under boundary condition is given and the existence of optimal solution to the viscous generalized Camassa–Holm equation is proved.     

Teaching the computer how to discover(!) and then prove(!!) (all by itself(!!!)) analogues of Collatz's notorious 3x + 1 conjecture

In this paper, we study the global attractivity for a class of periodic difference equation with delay which has a generalized form of Pielou's difference equation. The global dynamics of the equation is characterized by using a relation between the upper limit and lower limit of the solution. There are two possible global dynamics: zero solution is globally attractive or there exists a periodic solution which is globally attractive. Recent results by Camouzis and Ladas [Periodically forced Pielou's equation, J. Math. Anal. Appl. 333 (1) (2007) 117–127] are generalized. Two examples are given to illustrate our results.     

一类Riccati矩阵方程广义自反解的双迭代算法

本文研究了一类Riccati矩阵方程广义自反解的数值计算问题.利用牛顿算法将Riccati矩阵方程的广义自反解问题转化为线性矩阵方程的广义自反解或者广义自反最小二乘解问题,再利用修正共轭梯度法计算后一问题,获得了求Riccati矩阵方程的广义自反解的双迭代算法.拓宽了求解非线性矩阵方程的迭代算法.数值算例表明双迭代算法是有效的.     

Generalized inverses and Douglas equations

In this paper we study the general concept of reduced solution for a Douglas type equation and we parametrize these solutions using generalized inverses. On the other hand, we characterize different sorts of generalized inverses by means of solutions of Douglas type equations.

     

随机Volterra积分方程的广义样本解

本文研究了随机积分方程的广义样本解.利用随机微分方程转换为带参数常微分方程的方法,给出了一类随机Volterra积分方程的广义样本解,这类方程在许多应用领域是常见的.     

Nonlocal representation of the sl(2, R) algebra for the Chazy equation

A demonstration of how the point symmetries of the Chazy equation become nonlocal symmetries for the reduced equation is discussed. Moreover we construct an equivalent third-order differential equation which is related to the Chazy equation under a generalized transformation, and find the point symmetries of the Chazy equation are generalized symmetries for the new equation. With the use of singularity analysis and a simple coordinate transformation we construct a solution for the Chazy equation which is given by a right Painlevé series. The singularity analysis is applied to the new third-order equation and we find that it admits two solutions, one given by a left Painlevé series and one given by a right Painlevé series where the leading-order behaviors and the resonances are explicitly those of the Chazy equation.     

广义四元数的一次代数方程

本文运用广义四元数代数的矩阵表示讨论了两类广义四元数的一次代数方程的解问题，并得到了这两类代数方程有唯一解、无穷多解，无解的判别条件。