奇点理论

Z2对称奇点理论的一点推广

Some Generalization of Singularity Theory with Z_2-Symmetry

SINGULAR是个值得一试的系统，如果您对奇点理论感兴趣则尤其如此。

SINGULAR is a worthwhile system to try out , especially if you 're interested in singularity theory .

对于交换代数、代数几何和奇点理论，SINGULAR计算机代数系统在软件包内核以及共享库中提供了大量的算法。

For commutative algebra , algebraic geometry , and singularity theory , the SINGULAR computer algebra system provides a large variety of algorithms in the package kernel as well as shared libraries .

MorseLemma是奇点理论中一个极为重要的结论。[1]的作者称其文中的定理1和定理2是MorseLemma的推广。

We find that : the Theorems 1 and 2 , called " the generalization of Morse Lemma " in [ 1 ] , are just a copy of a well known result in Singularity Theory , and the conclusion of Theorem 2 is not true .

用奇点理论研究两类非线性边值问题的分支解

On the Bifurcation Solutions of Some Nonlinear BVPs : Using Singularity Theory

长方体ΔT场及其梯度场无解析奇点理论表达式

Cuboid δτ and its gradient forward theoretical expressions without analytic odd points

等变奇点理论中的&类有限生成模

Some of Finitely Generated Modules in Equivariant Singularity Theory

所谓的突变理论就是一门应用奇点理论的学科。

The so-called catastrophe theory is one of the applications of the singularity theory .

本文讨论奇点理论在分问题中的应用。

The aim of this paper is discussing the applications of singularities to bifurcation problems .

可微映射的奇点理论

Theory of singularities of differentiable mappings

利用奇点理论的思想和方法研究了具有平凡解的分支问题。

The bifurcation problems with trivial solution is discussed by using the methods in singularity theory .

借助于奇点理论中的有限决定性可以将无限维识别问题转化为有限维的情形来处理。

The use of the finite determinacy in singularity theory can transfer infinitely dimensional recognition to finitely dimensional recognition .

第二.分歧问题及其开折的稳定性.对光滑映射芽的各种稳定性的讨论是奇点理论的一个重要部分。

The discussion of various stabilities of smooth map-germs is an important part of the study of singularity theory .

利用奇点理论给出了空穴分岔方程在分岔点的等价正规形。

Equivalent normal forms of the cavitated bifurcation equation at the bifurcation point were presented by using singularity theory .

由相平面的奇点理论，得到了判别力学系统稳定性的几何表示&稳定域。

From singularity theory of phase plane the geometry expressiron ~ stable region to decide the stability of mechanics system bas been obtained .

借助于奇点理论中的一个基本概念（有限决定性），这一问题常常可以转化为有限维的情形来处理。

This problem can often be reduced to one of finite dimensions by using a key idea the finite determinacy in singularity theory .

因此本文提出了点元法全空间无解析奇点理论表达式。

So the forward theoretical expressions without analytic odd points in whole spaces of gravity and magnetic forward is brought forward in this text .

研究分歧问题主要是如何将光滑映射奇点理论中的相关概念和技巧适当地引到分歧问题中来。

The study of bifurcation problems is mainly about how to imply the related concepts and techniques in singularity theory of smooth map germs to bifurcation problems .

本文主要研究奇点理论在医学图像特征提取中的应用，从而为医学图像分割打下基础。

This paper mainly studied the application of singularity theory used in medical image feature extraction , and then we can continue the study of the image cut .

本文应用该定理讨论出现在等变奇点理论及等变分歧理论中的有限生成模与向量子空间，将已知的一些结果推广到更一般情形。

Applying the theorem above , it is dealt with finitely generated modules and vector subspaces arisen from the study of equivariant singularity theory and equivariant bifurcation theory .

用奇点理论方法证明了空穴分岔方程等价于一类具有单边约束条件的正规形；

It is shown that the cavitated bifurcation equation is equivalent to a class of normal forms with single-sided constraint conditions at the critical point by using singularity theory .

用奇点理论中横截开折的理论对相对映射芽的强有限决定性与通用开折之间的关系进行了研究。

In this paper , we make use of relative transverality unfolding to study the relation of strong relative AS , T finite determinacy of map germs with relative versal unfolding .

本文详细推导了全空间无解析奇点理论表达式，在此基础上进行了相应的软件开发及模型试算，均取得很好的效果。

This text deduced the forward theoretical expressions without analytic odd points in whole spaces of gravity and magnetic forward , going forward to go to correspond with this foundation of the software develop and the model try to calculate , all obtaining good result .

在两端受力矩单独作用的条件下，杆的平衡微分方程可转换为用欧拉角表述的一阶自治系统，并有可能利用相平面的奇点理论分析弹性细杆平衡状态的稳定性。

The differential equation of equilibrium of the rod subjected to torques on both ends can be transformed to an autonomous system of Eulerian angles . The stability and bifurcation of the equilibrium states of the rod are analysed by using the singularity theory of phase plane .

奇点定性理论中的V函数微分法

On the Differential Calculus of Liapunov Functions in the Qualitative Theory of Singular Points

T场及其梯度场在上半无源空间无解析奇点的理论表达式。

T and its gradients'forward theoretical expressions without analytic odd points .

奇点共轭理论与0～°渐开线包络蜗杆传动的原理与技术

The Theory of Singular Conjugation and the Principle and Technology of 0 ~° Involute & Enveloping Worm Gear Drive

运用奇点量理论和计算方法求出了一类三次系统原点的最高阶奇点量并证明为5阶；

According the theory of the singular point value and the calculating method , the highest singular point of the origin - 5th degree is obtained and proved for a class of cubic system .

本文系统地论述了奇点（含突变）理论形成的历史背景以及与系统科学的关系，翔实地证明了奇点理论是系统科学的数学支柱之一。

In this paper , we detail relations between singularity theory and systems engineering , and have proved singularity theory is one of the mathematical support of systems engineering .