微结构固体中孤立波的演变及非光滑孤立波

给出了包含宏观应变和微形变的全部二次项以及宏观应变三次项的一种新的自由能函数.利用新自由能函数并根据Mindlin微结构理论，建立了描述微结构固体中纵波传播的一种新模型.利用近来发展的奇行波系统的动力系统理论，分析了系统的所有相图分支，并给出了周期波解、孤立波解、准孤立尖波解、孤立尖波解以及紧孤立波解.孤立尖波解和紧孤立波解的得到，有效地证明了在一定条件下，微结构固体中可以形成和存在孤立尖波和紧孤立波等非光滑孤立波.此结果进一步推广了微结构固体中只存在光滑孤立波的已有结论.     

具有连续时滞和功能性反应的非自治竞争系统的持续生存

本文利用Lyapunov-Razumikhin理论讨论了具有连续时滞和Ⅱ类功能性反应的非自治扩散竞争系统．此系统有两个种群n个斑块，其中一个种群可以在n个斑块中自由扩散，另一种群被限定在一斑块中不能扩散．当系数满足一定的条件时，证明了系统是持续生存的，此外，给出了该系统的一周期解全局吸引的充分条件．     

带有凹凸非线性项的Klein-Gordon-Maxwell系统解的存在性和多重性

研究一类Klein-Gordon-Maxwell系统解的存在性和多重性.当非线性项是凹凸非线性项时,利用变分方法获得了系统解的存在性和多重性结果,并完善了此系统解的存在性的已有结果.     

一类非线性对偶系统的渐近解及其可解性条件

利用渐近理论,讨论了一类非线性对偶系统.在适当的条件下,得出了这一类非线性系统解的存在性条件及其渐近解.将此结果用于二自由度陀螺系统,较简捷地得到了该系统的具有小而有限振幅的渐近解.     

二次微分系统的反射函数及其周期解

本文给出了二镒多项式微分系统具有满足特定关系式的反射函数和存在周期解的充要条件，以及在此条件下反射函数的具体表达式及周期解的稳定性态。     

验证形式可积系统解的完备性的机械化算法

在eid等人标准型概念的基础上，引进形式可积系统的概念，并给出验证形式可积系统解的完备性的机械化算法，并用此方法证明了各向同性弹性力学方程组的胡海昌解的完备性问题。     

某二阶微分方程周期解的存在性

本文研究非线性微分方程组周期解的存在性。此系统在许多振动问题中出现。系统(1)当(y)=y时周期解或极     

大型网络基于连通可靠度的最优可靠度分配

由于网络连通可靠度计算属于NP-hard问题,当系统可靠度无法显式表达时,基于连通可靠度的大型复杂网络优化通常只能采用启发式优化算法解决．通过对复杂网络连通可靠度算法结构的分析,给出了系统连通可靠度的Taylor方程．采用遗传算法,由系统连通可靠度的Taylor方程确定种群适应值,得到一个系统最优可靠度分配方案;将最优解带入改进Minty算法或递推分解算法中,计算该最优解的连通可靠度精确值和对应的连通可靠度的Taylor展开方程;再次采用遗传算法求最优解．当最优解对应的可靠度精确值和Taylor方程算得得近似值误差小于指定精度时,则此最优解为最终的系统最优可靠度分配方案A·D2将此优化过程称为迭代遗传算法．算例显示迭代遗传算法不仅可用于大型网络的连通可靠度最优分配,而且优化迭代过程中可以得到多组阶段最优解,这些解均落在最优解附近,构成了近似最优解群,在实际工程优化中拓展了选择面．     

非自治Volterra-Lotka竞争方程的渐进行为

研究了狀种群非自治Ｖｏｌｔｅｒｒａ Ｌｏｔｋａ竞争模型，这个模型中参数是与时间相关的，并且分别渐近接近于周期函数的，在某些条件下，证明了此模型的任意一个正解渐近接近于相应周期系统的唯一的严格正周期解     

一类人为错误可修复系统的指数稳定性分析

随着科学技术的发展,特别是电子产品和网络的运用,系统的可靠性分析变得日益重要.在Dhillon B S和Yang N F(1993)中通过增补变量的方法建立了这类系统的数学模型并进行研究.在此基础上进一步讨论系统解的渐进稳定性和指数稳定性,证明了系统算子在Bnacha空间中可以转化为C_0半群,0是系统算子的简单本征值,而且是系统在虚轴上唯一的谱点.此外本文还分析了在系统扰动前后系统算子解的基本谱,结果显示系统的动态解以指数稳定性趋向于系统的稳态解,通过maple作图发现系统稳定解有时候不一定趋向于系统的实际解,这对实际运用有重要的指导意义.     

A note on the Helmholz oscillator

The possible existence of a potentially chaotic soliton solution of an unperturbed classical oscillator is investigated. It is shown that in general the solution of the so-called “Helmholz oscillator” is a periodic solution. Special solutions are also found where a localized soliton solution or a decaying solution is obtained depending on the initial conditions.     

向量优化问题有效解的稳定性

运用标量化的方法,通过锥正定真有效解的上半连续性讨论了无限维赋范空间中锥有效解的部分上半连续性,证明了锥有效解的通有稳定性.在此基础上,进一步证明,在Baire纲的意义下,绝大多数的向量优化问题至少存在一个锥正定真有效解是本质的有效解,换句话说,绝大多数的向量优化问题锥有效解是几乎下半连续的.     

Making solutions invariant

In this paper a procedure is developed to modify a non-invariant solution in such a way that the resulting solution is invariant. Furthermore it is investigated which properties of the solution are inherited by the modified solution. Received: April 1995     

The Rayleigh–Stokes problem for an edge in a generalized Oldroyd-B fluid

The velocity field corresponding to the Rayleigh–Stokes problem for an edge, in an incompressible generalized Oldroyd-B fluid has been established by means of the double Fourier sine and Laplace transforms. The fractional calculus approach is used in the constitutive relationship of the fluid model. The obtained solution, written in terms of the generalized G-functions, is presented as a sum of the Newtonian solution and the corresponding non-Newtonian contribution. The solution for generalized Maxwell fluids, as well as those for ordinary Maxwell and Oldroyd-B fluids, performing the same motion, is obtained as a limiting case of the present solution. This solution can be also specialized to give the similar solution for generalized second grade fluids. However, for simplicity, a new and simpler exact solution is established for these fluids. For β → 1, this last solution reduces to a previous solution obtained by a different technique.     

Ginzburg-Landau equation with magnetic effect in a thin domain

We study the Ginzburg-Landau equation with magnetic effect in a thin domain in , where the thickness of the domain is controlled by a parameter . This equation is an Euler equation of a free energy functional and it has trivial solutions that are minimizers of the functional. In this article we look for a nontrivial stable solution to the equation, that is, a local minimizer of the energy functional. To prove the existence of such a stable solution in , we consider a reduced problem as and a nondegenerate stable solution to the reduced equation. Applying the standard variational argument, we show that there exists a stable solution in near the solution to the reduced equation if is sufficiently small. We also present a specific example of a domain which allows a stable vortex solution, that is, a stable solution with zeros. Received: 11 May 2001 / Accepted: 11 July 2001 /Published online: 19 October 2001     

The Rayleigh–Stokes problem for an edge in a generalized Oldroyd-B fluid

The velocity field corresponding to the Rayleigh–Stokes problem for an edge, in an incompressible generalized Oldroyd-B fluid has been established by means of the double Fourier sine and Laplace transforms. The fractional calculus approach is used in the constitutive relationship of the fluid model. The obtained solution, written in terms of the generalized G-functions, is presented as a sum of the Newtonian solution and the corresponding non-Newtonian contribution. The solution for generalized Maxwell fluids, as well as those for ordinary Maxwell and Oldroyd-B fluids, performing the same motion, is obtained as a limiting case of the present solution. This solution can be also specialized to give the similar solution for generalized second grade fluids. However, for simplicity, a new and simpler exact solution is established for these fluids. For β → 1, this last solution reduces to a previous solution obtained by a different technique.      

Numerical solution of a nonlinear reaction diffusion equation

In this paper, the authors propose a numerical method to compute the solution of a Cauchy problem with blow-up of the solution. The problem is split in two parts: a hyperbolic problem which is solved by using Hopf and Lax formula and a parabolic problem solved by a backward linearized Euler method in time and a finite element method in space. It is proved that the numerical solution blows up in a finite time as the exact solution and the support of the approximation of a self-similar solution remains bounded. The convergence of the scheme is obtained.     

On the theorem of T. Yamada and S. Watanabe

The well-known theorem of T. Yamada and S. Watanabe asserts that (weak) existence and pathwise uniqueness of the solution of a stochastic equation implies the existence of a strong solution. This is the most powerful tool for proving that a stochastic equation possesses a strong solution. However, pathwise uniqueness is far from being a necessary condition for this. Even if the solution is not unique in law it is also of interest to ask for strong solutions. In the present note, we will discuss in more detail the connection between pathwise uniqueness and the existence of a strong solution. We will state a condition which is not only sufficient but also necessary for the existence of a strong solution.     

An achievement rate approach to linear programming problems with an interval objective function

In this paper, we focus on a treatment of a linear programming problem with an interval objective function. From the viewpoint of the achievement rate, a new solution concept, the maximin achievement rate solution, is proposed. Nice properties of this solution are shown: a maximin achievement rate solution is necessarily optimal when a necessarily optimal solution exists, and if not, then it is still a possibly optimal solution. An algorithm for a maximin achievement rate solution is proposed based on a relaxation procedure together with a simplex method. A numerical example is given to demonstrate the proposed solution algorithm.     

On Torsion of Prismatic Bodies

The method of decaying residual solution is applied to obtain an approximate interior solution for the torsion of slender prismatic elastic bodies under different end conditions. The approximate solution is generally accurate up to terms that are exponentially small in the length-to-cross-sectional-width ratio. For stress end conditions, the result is identical to the classical Saint-Venant torsion solution. Similar types of simple solutions, not known previously, are obtained for different types of mixed end conditions. For displacement conditions at both ends, the corresponding Saint-Venant type result requires an accurate solution of a canonical problem for a semi-infinite prismatic body that is to be obtained once and for all. The solution of the canonical problem is elementary for a circular cross section. The approximate interior solution in that case is identical to the known exact interior solution.