Numerical detection of symmetry breaking bifurcation points with nonlinear degeneracies

A numerical tool for the detection of degenerated symmetry breaking bifurcation points is presented. The degeneracies are classified and numerically processed on -D restrictions of the bifurcation equation. The test functions that characterise each of the equivalence classes are constructed by means of an equivariant numerical version of the Liapunov-Schmidt reduction. The classification supplies limited qualitative information concerning the imperfect bifurcation diagrams of the detected bifurcation points.

     

Existence and Limiting Behavior of Trajectories Associated with P0-equations

Given a continuous P₀-function F : Rⁿ Rⁿ, we describe a method of constructing trajectories associated with the P₀-equation F(x) = 0. Various well known equation-based reformulations of the nonlinear complementarity problem and the box variational inequality problem corresponding to a continuous P₀-function lead to P₀-equations. In particular, reformulations via (a) the Fischer function for the NCP, (b) the min function for the NCP, (c) the fixed point map for a BVI, and (d) the normal map for a BVI give raise to P₀-equations when the underlying function is P₀. To generate the trajectories, we perturb the given P₀-function F to a P-function F(x, ); unique solutions of F(x, ) = 0 as varies over an interval in (0, ) then define the trajectory. We prove general results on the existence and limiting behavior of such trajectories. As special cases we study the interior point trajectory, trajectories based on the fixed point map of a BVI, trajectories based on the normal map of a BVI, and a trajectory based on the aggregate function of a vertical nonlinear complementarity problem.     

确定论动力学系统的内在随机性

论述了物理学中确定论自然观的局限性,分析研究了导致一切动力学现象复杂性根源,指出了混沌存在的普遍性和混沌动力学在现代科学中的重大影响.     

钢筋混凝土受弯构件的优化设计—一类离散型非线性规划

研究钢筋混凝土受弯构件的优化设计问题，建立了新的数学模型—一类离散型非线性规划，给出了计算步骤与若干算例．提出的算法容易在微机上实现，所有可行解都是整数解，而且所得最优值在一定条件下是总体最优值．     

Extended Hyperbola Function Method and Its Application to Nonlinear Equations

An extended hyperbola function method is proposed to construct exact solitary wave solutions to nonlinear wave equation based upon a coupled Riccati equation. It is shown that more new solitary wave solutions can be found by this new method, which include kink-shaped soliton solutions, bell-shaped soliton solutions and new solitary wave.The new method can be applied to other nonlinear equations in mathematical physics.     

Infinite-dimensional gauge groups and special nonlinear gravitons

A gauge theory in flat space—time, in which the gauge algebra is the (infinite-dimensional) algebra of vector fields on a surface, determines a curved space—time metric. This note deals with some completely integrable examples, concentrating on the N → ∞ limit of the Euler—Arnol'd equations [geodesics on SO(N)]. In this case, the metric turns out to be flat, which points the way to a coordinate transformation that solves the original equations.     

Local convergence of quasi-Newton methods for B-differentiable equations

We study local convergence of quasi-Newton methods for solving systems of nonlinear equations defined by B-differentiable functions. We extend the classical linear and superlinear convergence results for general quasi-Newton methods as well as for Broyden's method. We also show how Broyden's method may be applied to nonlinear complementarity problems and illustrate its computational performance on two small examples.     

基于神经网络模型偶的投入产出建模（英文）

基于投入产出中使用和投入两个方向的非线性关系，本文利用神经网络技术建立了一种新的投入产出模型，并讨论了该模型在投入系数综合预测中的应用。文中报导了神经网络模型偶的修正了的反传训练公式。最后，中国广东省的仿真例子表明了所给算法的有效性和该建模方法的特点     

Limit Gaussian Behavior of the Solutions of the Multidimensional Burger'; Equation with Weak-Dependent Initial Conditions

Asymptotic normality of the solutions of the initial-value problems for multidimensional Burgers' equation with weakly dependent possible non-Gaussian initial condition is proved.     

逆系统方法及其应用

本文提出了一种设计非线性反馈控制系统的方法，称作过系统方法．这种方法的要点，就是用对象的逆系统构造出一种可用反馈结构实现的“α──阶积分逆系统”，将原对象补偿为具有线性传递关系的系统，即α阶伪线性系统，然后用线性系统的理论来解决这种系统的综合问题。同时，本文还将逆系统方法用于机械手控制系统的设计，从所给出的仿真来看，结果是令人满意的。