查询词典 bifurcation point

In chapter three, the new concepts of the bifurcation point and asymptotic bifurcation point of compact continuous operators in Menger PN-spaces are introduced. Some sufficient conditions for the existence of the bifurcation point and asymptotic bifurcation point are obtained. And the problems on the intrinsic value and intrinsic element of compact continuous operators are studied in Menger PN-spaces. A series of theorems on the existence of the intrinsic value and intrinsic element are obtained.

第三章，在概率赋范线性空间中提出非线性算子的歧点和渐近歧点的新概念，获得了非线性算子存在歧点和渐近歧点的充分条件；讨论了Menger概率赋范线性空间中非线性算子的固有值和固有元问题，得到了非线性算子存在固有值和固有元的一系列充分条件。

From 1 to 8, this one is the main line; 4/16/34 is the main line of the first bifurcation point; 5/11/15 is the last main line of a bifurcation point; turn bar and so on.

从1到8，这一条就是主线；4/16/34是主线上第一个分叉点；5/11/15是主线上最后一个分叉点；依次类推吧。

And both symmetry-breaking bifurcation point and symmetry-recovering bifurcation point were calculated.

并计算了系统发生对称性破缺分岔点和对称性恢复点。

In chapter 3,the bifurcation theory of topological current is established inthe neighborhoods of limit point,bifurcation point and higher degeneratedpoint respectively.

第三章讨论和建立了拓扑流在极限点，分岔点和高阶退化点的分歧理论。

The formulas for calculating the bifurcation ratios and the way to determine the location of bifurcation point were presented.

进行血液动力学模拟和血液传热计算需要先建立血管网络，为此，借鉴强制结构优化方法，提出了基于分支法则、Poiseuille＇s law及质量守恒原则，直接在模拟区域上生成动脉血管树的新方法及相应的半径比计算公式和分支点确定步骤。

The results show that it is a supercritical bifurcation point, or saddle node bifurcation point under some parameters ranges.

这表示参数经过一个临界值后，由原来再生一个细胞变成再生两个细胞

Numerical simulations performed on other typical reaction-diffusion models confirm this analysis and suggest that our findings are robust and independent of the type of bifurcation, and even whether the system is close to or far from the bifurcation point.

这些结果，不但与具体的模型没有关系，而且也不依赖于系统所经历的Hopf分岔的类型，甚至系统是否远离分岔点。

The main advantages of the methodare that(1)this method is valid for all kinds of bifurcation pointswith the codimension ≤3;(2)it does not use any informations forsecond order derivatives and does not need the bifurcation point to beknown accurately in implementation;(3)it is sufficient to implementthe method that a standard continuation procedure is only used;and(4)derivation of the method is independent on the asymptotic expan-sions of the bifurcation solutions.

这种方法的主要优点是：(1)适应于一切余维数不超过3的分支点；(2)不需要任何二阶导数的信息，也不必精确地知道分支点的位置；(3)只需使用标准延拓软件就可以实现；(4)方法不依赖于分支解的渐近展式。

In condensed matter physics,we present an analyticaltopological current theory of point defects which unifies the topologicalquantization,homotopic classification and evolution of defects in oneframework.The number of possible branch lines is shown to be 2s once atmost at the bifurcation point of order parameter with degeneracy s and thetopological charge is conserved during bifurcation processes.

论文在凝聚态物理中给出了缺陷解析的拓扑流理论，将缺陷的拓扑量子化，同伦分类和演化统一在一个框架之内，并证明了在序参量退化度为s的分岔点，缺陷分岔数目最多为2的s次方，而且在分岔过程中拓扑荷是守恒的。

The cavitated bifurcation equation that describes cavity formation and growth in the interior of the sphere is obtained. It is proved that there exists a unique bifurcation point on the trivial solution of the cavitated bifurcation equation.

本文利用分岔理论和动力学理论中的基本观点、方法和结论，对具有缺陷的超弹性材科组成的球体内部的空穴生成和增长的拟静态问题以及空穴生成后随时间的运动规律等方面进行了系统的研究，得到了一些新的结论，同时给出了相应的数值分析。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失