查询词典 codimension

Finally we study universal unfoldings correspondingto normal forms for the degenerate bifurcations of codimension two,codimension threeand codimension four.

最后研究了余维2退化、余维3退化和余维4退化分岔情况下相应规范形的普适开折。

For example, Keyfitz made the classification of the bifurcations in one state variable, without symmetry up to codimension 7; Golubitsky and Schaeffer obtained the classification of the bifurcation problems in one state variable with Z_2 symmetry, in one parameter up to codimension 3; Golubitsky and Roberts studied the classification of degenerate Hopf bifurcation in two state variables with dihedron D_4 symmetry, in one parameter up to topological codimension 2; Melbourne obtained the classification of bifurcations in three state variables with octahedral symmetry, in one parameter, up to

需要指出的是以上研究均没有考虑分歧参数的对称性，Futer，Sitta和Stewart的工作虽然考虑了分歧参数的对称性，但仅限于分歧参数与状态变量具有相同的对称性，他们得到了状态变量与分歧参数均关于二面体群D_4对称，拓扑余维数不大于1的分歧问题的分类。高守平和李养成则讨论状态变量和分歧参数均具有对称性且对称性可以不同的分歧问题，并给出了状态(来源：A770707BC论文网www.abclunwen.com)变量关于二面体群D_4对称，分歧参数关于S~1对称，拓扑余维不超过1的分歧问题的分类。本文第一章讨论两个状态变量关于二面体群D_3对称，两个分歧参数关于O(2)对称的分歧问题，给出了该类分歧问题在非退化条件q(0)≠0下所有情形的分类与相应的识别条来源：AdadaBC论文网www.abclunwen.com

For the first time, we have applied this method to study the problem of bifurcations of map, including codimension one, codimension two and flip bifurcations.

本文将该方法推广至映射分叉问题的研究，包括余维一、余维二分叉和倍化分叉。

When and we show that system (1) has the cusp bifurcation of codimension 2(ie,Bogdanov-Takens bifurcation); when ,we show that this system has the cusp bifurcation with codimension at least S.

而且我们选择了系统的原参数中的二个作为分支参数，可以使系统(1)进行Bogdanov-Takens余维2普适开折，从而证明系统(1)同宿轨的存在性。

For higher codimension, the situation becomes more complicated. Due to the counterexample of Lawson-Osserman [31], the higher codimension Bernstein type result is not expected to be true in the most generality.

在余维数为1的情况，这个结果以被推广到(n+1)-维欧氏空间中(n≤7)，以及在某种增长性限制下，这个结果被推广到任意维数欧氏空间中，这些结果可以参考[17]及其参考文献中所提到的文献。

If a n-dimensional unoriented cobordism class α_n containing a representative that admits a (Z_2)~k-action with fixed point set of constant codimension r,we may say that α∈is an ideal of the unoricnted cobordism ring MO_*=.

若n维未定向协边类α_n的一个代表元M~n上有不动点集为常余维数r的(Z_2)~k光滑作用，则记α_n∈J_~r.J_~=∑_n≥r_J_(n，k~r是未定向上协边环MO_+=∑_(n≥0)MO_n的理想。

The normal forms for codimension two bifurcation of map are also discussed in this dissertation.

本文还研究了映射余维二分叉的范式。

We treat the codimension two bifurcation of impact vibration system.

本文研究碰撞振动系统的余维二分叉问题。

By means of singularities theory,four kinds of transition set s and diagrams of codimension five are acquired.

应用奇异性理论分析方法对系统主参数共振的分岔方程进行了奇异性分析，得到了余维5四种不同情况的转迁集与分岔图。

Finally,we demonstrate the rich dynamics of codimension two bifurcations with numerical simulations.

并通过数值模拟解验证了余维2分岔丰富的动力学性质。

In contrast to the ubiquitous rising-sun-with-rays military flag of the Japanese, Chinese banners and ensigns feature a range of designs.

与遍地都是的太阳军旗不同，中国人的旗帜和徽章设计得各式各样。

From their small corner of Feng's Guangzhou headquarters -- a jumble of pink leashes, squeezable rubber steaks, and plastic doggy Santas for Fido's stocking -- Soleil's designers come up with at least five new products a month.

从Feng 设在广州总部的产品展示柜台上可以看到，Soleil的设计师每月至少设计出5件新产品。