查询词典 manifolds

According to differentiable manifolds theory, the paper discusses tile Legendre transformation of the Pfaffian form, introdues the operator of the Legendre transformation, derives the relation between the Legendre transformation and the partial differentiation and proves three law s.

从微分流形理论出发，讨论了Pfaff形式的勒让德变换；引入了勒让德变换算子；给出了勒让德变换与偏微商的关系；证明了两个定理和一个引理。

This paper presents a method of localized linear manifold self-organizing map, which is able to learn a set of ordered low-dimensional linear manifolds in the high-dimensional vector space.

摘要提出一种局部化的线性流形自组织映射方法，可自主学习高维向量空间中的一组有序的低维线性流形。

In this project, we have mainly researched the complex-anlyticity,constancy and stability of pluriharmonic maps to complex grassmannian manifolds;the characterization and isotropicity of pluriharmonic maps with finite uniton number;the regularity, singularty and Liouville theorem of harmonic maps.

本课题着重研究到复Grassmann流形多重调和映照的复分析、常值性及稳定性之间的关系；具有有限uniton数的多重调和映照的特征与迷向性；调和映照的正则性、奇异性及Liouville定理。

Locally projectively flat manifolds;equiaffine differential geometry;projective Blaschke manifold

局部射影平坦流形；等仿射微分几何；射影Blaschke流形

For the interpolation problems in which the nodes are on one or more algebraic manifolds, we pointed out the interpolation bases of the lowest degree w.r.t.a graded term order and gave a new algorithm. We also gave a estimation for the degree of the interpolation polynomial.

我们针对插值节点位于一个或几个代数流形上的插值问题，从理论上指出了插值问题在某一分次序下最低次的插值基并给出了新的算法，同时也对插值多项式的次数作了估计。

One of its main goals is to classify topologically, or even metrically, manifolds with certain geometry conditions on, say, curvature, volume, diameter.

二十世纪三四十年代发展起来的整体微分几何，其中的一个重要部分是讨论流形的曲率是如何影响流形的拓扑乃至度量性质。

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。

Invariant manifolds are important for the study of dynamic systems. Since they are hard to he computed h analytical expression, the numerical method for approximating invariant manifold is an important mean.

不变流形在动力学研究的许多方面都有重要意义，由于不变流形很难通过解析表达式求解，对其做近似计算就成为重要的手段。

After the completion of DAE with removal of singular points, a DAE system may be transformed into ordinary differential equations on manifolds; it is also possible to transform DAE to a singular perturbed system as ODE.

通过将DAE完备化并去掉奇异部分，可以把DAE化为流形上的常微系统；也可以将DAE化为奇异摄动系统而得到ODE。

This is because the manifolds are actually in phase space which includes both position and velocity.

这是因为流形在相空间内包括了位置和速度实际。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。