关于运输问题最优解的进一步讨论

首先给出了运输问题最优解的相关概念,将最优解扩展到广义范畴,提出狭义多重最优解和广义多重最优解的概念及其区别.然后给出了惟一最优解、多重最优解、广义有限多重最优解、广义无限多重最优解的判定定理及其证明过程.最后推导出了狭义有限多重最优解个数下限和广义有限多重最优解个数上限的计算公式,并举例验证了结论的正确性.     

Benjamin-Ono方程的广义解

讨论了Benjamin-Ono方程在Colombeau意义下的广义解的存在性，唯一性及在经典解存在的情况下与经典解的关系．     

矩阵方程AX=B的中心对称定秩解及其最佳逼近

本文研究了矩阵方程AX=B的中心对称解.利用矩阵对的广义奇异值分解和广义逆矩阵,获得了该方程有中心对称解的充要条件以及有解时,最大秩解、最小秩解的一般表达式,并讨论了中心对称最小秩解集合中与给定矩阵的最佳逼近解.     

多目标决策问题的广义折衷解研究

引进决策偏好参数，提出了多目标决策问题的广义折衷解概念，然后探讨了广义折衷解的性质，最后也给出其数学规划的求解方法。     

广义WBK型耗散方程的衰减振荡解及其误差估计

对广义WBK型耗散方程作了定性分析,研究了方程行波解的性态与耗散系数r之间的关系.并利用假设待定法,求出了广义WBK型耗散方程的衰减振荡解的近似解.最后,证明了用方法得到的广义WBK型耗散方程衰减振荡解的近似解与其精确解间的误差是以指数形式速降的无穷小量.     

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.     

关于矩阵方程XB=C的结构解

很多应用中导出矩阵方程XB=G,本文考虑此方程的结构解.首先考虑自伴矩阵解及反自伴矩阵解,接下来考虑广义对称解及广义反对称解,最后讨论更广泛的矩阵方程AXB=C的酉矩阵解.所得结果推广了Sun,Tisseur,Trench等人的-些结果.     

n维广义IMBq方程的初边值问题

本文研究广义IMBq方程utt-2utt-2tu=2g(u)的初边值问题局部广义解和古典解的存在性、唯一性,并给出解爆破的充分条件.     

广义超弹性杆方程关于Neumann问题解的存在性

通过对广义超弹性杆方程的Neumann边界条件及初始条件的研究,得到了广义超弹性杆方程在Neumann边界条件下局部解和整体解的存在.     

赋范线性空间多目标规划的 广义KT-真有效解

对于赋范线性空间中的多目标规划问题,引进了广义KT-真有效解的概念.在一定条件下,得到了广义KT-真有效解和广义H-局部真有效解之间的关系.     

Bifurcations and exact traveling wave solutions of the equivalent complex short-pulse equations

In this paper, we study the traveling wave solutions for a complex short-pulse equation of both focusing and defocusing types, which governs the propagation of ultrashort pulses in nonlinear optical fibers. It can be viewed as an analog of the nonlinear Schrodinger (NLS) equation in the ultrashort-pulse regime. The corresponding traveling wave systems of the equivalent complex short-pulse equations are two singular planar dynamical systems with four singular straight lines. By using the method of dynamical systems, bifurcation diagrams and explicit exact parametric representations of the solutions are given, including solitary wave solution, periodic wave solution, peakon solution, periodic peakon solution and compacton solution under different parameter conditions.     

多目标规划的r—有效解和r—最优

本文引入有限维向量空间的r-序类概念,讨论了它们的基本性质。在此基础上,定义了多目标规划的r-有效解和r-最优解,研究了它们与其它有关解之间的关系。     

A class of discrete time generalized Riccati equations

In this paper, a class of discrete-time backward non-linear equations defined on some ordered Hilbert spaces of symmetric matrices is considered. The problem of the existence of some global solutions is investigated. The class of considered discrete-time non-linear equations contains, as special cases, a great number of difference Riccati equations both from the deterministic and the stochastic framework. The results proved in the paper provide the sets of necessary and sufficient conditions that guarantee the existence of some special solutions of the considered equations as: the maximal solution, the stabilizing solution and the minimal positive semi-definite solution. These conditions are expressed in terms of the feasibility of some suitable systems of linear matrix inequalities (LMI). One shows that in the case of the equations with periodic coefficients to verify the conditions that guarantee the existence of the maximal or the stabilizing solution, we have to check the solvability of some systems of LMI with a finite number of inequations. The proofs are based on some suitable properties of discrete-time linear equations defined by the positive operators on some ordered Hilbert spaces chosen adequately. The results derived in this paper provide useful conditions that guarantee the existence of the maximal solution or the stabilizing solution for different classes of difference matrix Riccati equations involved in many problems of robust control both in the deterministic and the stochastic framework. The proofs are deterministic and are accessible to the readers less familiarized with the stochastic reasonings.     

渐近线性算子方程的四种类型的解

利用拓扑度理论及不动点指数理论,讨论了渐近线性算子方程的四种类型的解(即零解、正解、负解和变号解)的存在性,并将这一抽象结果应用于微分方程两点边值问题.     

Dynamical Behavior and Exact Traveling Wave Solutions for Three Special Variants of the Generalized Tzitzeica Equation

The dynamics and bifurcations of traveling wave solutions are studied for three nonlinear wave equations. A new phenomenon, such as a composed orbit, which consists of two or three heteroclinic orbits, may correspond to a solitary wave solution, a periodic wave solution or a peakon solution, is found for the equations. Some previous results are extended.     

一类非线性积分微分方程解及其构造

本文讨论了核反应堆动力学中一类具缓发中子的非线性积分微分方程．在一定的条件下证明了该方程在p空间中Mild解、强解、局部解的存在唯一性，以及用迭代法求解的合理性，并估计了收敛速度．     

二粒子Boltzmann方程组的奇异扰动解法

讨论了二粒子Boltzmann方程组的边界层解.为此我们先对未知变量进行了Fourier变换,然后运用前人的方法对变换后的函数进行展开.通过对未知变量做一些特殊的函数展开,得到了二粒子Boltzmann方程组的正规解和边界层解,并得到了边界层解的初级和高级近似.     

含参广义集值向量均衡问题有效解映射下半连续的最优条件

在实Hausdorff拓扑向量空间中研究一类含参广义集值向量均衡问题弱有效解与有效解映射的下半连续性. 在近似锥-次类凸的条件下, 运用标量化的方法得到弱有效解的标量化结果. 在适当条件下, 得到含参广义集值向量均衡问题弱有效解与有效解映射下半连续性定理.     

An axiomatization of the egalitarian solutions

The egalitarian solutions for general cooperative games which were defined and axiomatized by Kalai and Samet, are compared to the Harsanyi solution. It is shown that axioms used by Hart to characterize the Harsanyi solution can be used to characterize the (symmetric) egalitarian solution. The only changes needed are the omission of the scale covariance axiom and the inclusion, in the domain of the solution, of games which lack a certain smoothness requirement.     

Mathematical studies of the solution of Burgers' equations by Adomian decomposition method

In this paper, a novel Adomian decomposition method (ADM) is developed for the solution of Burgers' equation. While high level of this method for differential equations are found in the literature, this work covers most of the necessary details required to apply ADM for partial differential equations. The present ADM has the capability to produce three different types of solutions, namely, explicit exact solution, analytic solution, and semi-analytic solution. In the best cases, when a closed-form solution exists, ADM is able to capture this exact solution, while most of the numerical methods can only provide an approximation solution. The proposed ADM is validated using different test cases dealing with inviscid and viscous Burgers' equations. Satisfactory results are obtained for all test cases, and, particularly, results reported in this paper agree well with those reported by other researchers.