查询词典 Morse theory

These results belong to the category of"local Morse theory".

这些结果属于局部Morse理论的范畴。

The main tool used here is Morse theory.

这里利用的工具是Morse理论。

The existence of multiple periodic solutions of the equations is gotten by using convex Hamiltonian theory and Morse index theory.

讨论了一类扰动时滞微分方程的多重周期解的存在性问题，运用凸Hamilton系统理论和Morse指标理论得到了这类方程多重周期解的存在性。

We mainly give a simple brief introduction to Morse theory and Morse function, and introduce a two-dimensional manifolds on the Morse-Smale complex.

在此基础上，提出了一种对二维流形上的Morse-Smale复形顶点进行优化从而达到优化四边形形状的算法。

In the rest of this dissertation, we apply our above abstract results,"global Morse theory"and other critical point theorems to some semilinear resonant elliptic boundary value problems as well as some asymptotically"linear"or super"linear"p-Laplacian equations, and obtain the existence or multiplicity of solutions.

在后半部分，我们运用上面的抽象结果，以及大范围Morse理论和其他临界点理论，研究一些半线性椭圆共振问题的多重解的存在性，以及一些渐近线性或超线性p-Laplacian方程的解的存在性或多重性。

In this paper, we study the existence of sign-changing and multiple nontrivial solutions for a kind of quasilinear elliptic equations with Dirichlet boundary value by applying minimax methods and Morse theory.

本文我们将应用极大极小方法和Morse理论研究一类拟线性椭圆方程Dirichlet边值问题多解的存在性和解的变号性质。设Ω是R~N(N≥1)中的有界区域，具有光滑边界？

It can be divided into two chapters.In chapter one ,we state a few usual notations,definitions and basic results.In chapter two, we first establish a Morse index theory for 2p-order linear Hamiltonian systems.Then as applications of the index theory ,we discuss nontrivial solutions for nonlinear Hamiltonian systems by making use of Leray-Schauder degree theory and Morse theory.

全文分为两章：第一章中给出了本文所要用到的一些基础知识和一些常用的记号；第二章先建立了线性2p-阶Hamiltonian系统的指标；作为此分类指标的应用，结合Leray-Schauder度理论及Morse 理论，讨论了渐近线性系统的非平凡解的存在性。

By constructing Morse-Smale complex over the physically less important subregions and proceeding by repeatedly removing a pair of critical points from the complex,the topological feature is simplified and smoothed,this method is based on the morse theory.

结合Morse理论在次要物理特征所在区域构造Morse-Smale复形，并通过对复形上一系列临界点对的删除，达到简化和平滑函数拓扑特征的目的。

Given a mesh, we first solve a Poisson equation to construct a scalar field and use it to generate some critical points. The cutting paths between the critical points and the boundaries are solved in the Poisson scalar field using the deepest descent method. For meshes with nonzero-genus, we construct a Harmonic scalar field, and connect the saddle points with the boundaries based on the Morse theory.

对于给定的任意网格，通过求解泊松方程构造标量场来选取临界点，并采用最速下降法给出临界点到边界或者初始点的切割路径；对于亏格不为零的网格，基于Morse理论，通过构造一个调和标量场来得到鞍点，并将它们连接到边界。

Delay differential equations; variational structure; Minimax theory; Morse theory; multiple periodic solutions; subharmonic solutions; Z_p geometrical index

基础科学，数学，数学分析时滞微分方程；变分结构；极小极大理论； Morse理论；多重周期解；次调和解；广义Z_p几何指标

Lugalbanda was a god and shepherd king of Uruk where he was worshipped for over a thousand years.

Lugalbanda 是神和被崇拜了一千年多 Uruk古埃及喜克索王朝国王。

I am coming just now,' and went on perfuming himself with Hunut, then he came and sat.

我来只是现在，'歼灭战perfuming自己与胡努特，那麼，他来到和SAT 。