查询词典 combinatorial manifold

Estimate shows the resonant gaps between KAM tori can be as large as of order 〓, while the transversality which can be obtained by Poincaré-Melnikov method in the stable manifold and the unstable manifold, as best as we can hope, is only order 〓.

但在通有的摄动下，部分双曲环面会破裂，仅用Poincaré-Melnikov方法无法构造出足够长的"传递链"。

According to Shilnikov Theorem, on the condition that satisfies the basic characteristics of heteroclinic orbit, Shilnikov inequality and the eigenvalue equation, by finding a heteroclinic orbit consist of three geometric invariant sets, namely unstable manifold, heteroclinic point, and stable manifold, a set of real parameters accordance with the condition of existing heteroclnic orbit is obtained in this chaotic system.

根据Shilnikov定理，在满足异宿轨道基本特性、Shilnikov不等式和特征方程条件下，通过寻找该系统中一条由不稳定流形、异宿点和稳定流形三个几何不变集构成的异宿轨道，在分段Sprott系统中导出了存在异宿轨道时该系统中各个参数应符合的条件，并找到了一组对应的实参数，由此证明了异宿轨道的存在性。

Automation Box Packaging machine is Set Unwrap box,Loading stuff,box hem, Spray Glue,Closed box,integration machinery,apply manifold Variety manifold specification The carton packaging, with the most advanced high-speed automatic two-sol-Lance heat from the PLC microcomputer control, automatic alarm, fault tips,step motor automatic adjustment into the carton size.

全自动纸盒封装机是集开盒、装料、折盒、喷胶、封盒一体机，适用于多品种，多规格的纸盒包装，配有国内最先进的全自动的高速双喷枪热溶胶机，由PLC微电脑控制，自动报警，故障提示。步进电机自动调节纸盒大小。

Structure-Based Approximation Learning Theory: Under the description of manifold and topological architecture of neural field, we have proposed a learning frameworks of neural networks based on global architecture approximation theory borrowed from the concept of topology and manifold to solve the optimal problems of learning in non-nonlinear and non-Euclidean space, and discussed a few basic components of the learning theory, learning mechanism and learning algorithm in the term of structure-based approximation and global structure analysis.

基于结构的逼近学习理论：通过人工神经网络模型神经场的流形结构和拓扑结构描述，我们提出了在非线性和非欧氏空间中基于整体结构逼近的神经场学习理论框架；用对偶流形理论和拓扑概念作为工具，讨论了神经网络的学习理论、学习机理、学习算法和算法的具体实现。

And then, by regarding the curve and surface as a map from differential manifold to topological manifold, we present the framework of GRPCS and discussed its basic properties in detail. GRPCS provides a unified framework for parametric curve and surface.

然后通过势函数来构造微分流形上的单位分解，将曲线曲面看作微分流形到拓扑流形的映射，给出了广义有理参数曲线曲面的整体理论框架，并对广义有理参数曲线曲面的基本性质进行了讨论。

A method of the surface combination based on classification or Euler Operation and the computation of the surface boundaries of a surface is offered to finish the geometry mapping of surfaces between half-edge model and the closed_shell branch of manifold surface model. Moreover, the concepts of conformal-shape geometrical mapping and topological mapping are given. The bi-directional conformal-shape topological mapping between half-edge model and the closed_shell branch of manifold surface model is proved.

提出了一种基于等价分类和欧拉操作的面片合成和曲面边界计算方法，完成了半边模型到流形曲面模型closed shell枝的曲面几何映射；给出了保形几何和保形拓扑映射概念，证明了半边模型到流形曲面模型的closed_shell分枝的双向保形拓扑映射。

The last three chapters is partⅡ:Our main goal is to study dipolarizations and〓 manifolds.Let M be a symplectic manifold,if M admits two smoothtransversal Lagrangian foliations,then M is called a〓manifold.

后三章为第二部分，主要讨论双极化与仿凯勒流形，设M是一个辛流形，如果在M上存在两个横截的拉格朗日叶状结构，则称M为一个仿凯勒流形。

Without amusements it is wearisome, like a long journey where there are no inns: manifold knowledge gives manifold leasure.

没有乐趣的人生是乏味的，就像连小酒馆都没有的长途旅行：惟有博闻才能富享从容。

Without amusements it is wearisome, like a long journey where there are no inns: manifold knowl edge gives manifold leasure.

没有娱乐的生活是可怕的，就象漫漫旅途中没有了歇脚的小酒馆，丰富的知识提供了多彩的生活。

Without amusements it is wearisome, like a long journey where there are no inns: manifold knowledge gives manifold leasure.

但是我们在吃过程之中要知道享受快乐，就好比我们进行一次长途的跋涉，但是我们自始至终没有休息过，多元化的知识给我们提供了帮助

Diabetes is a social disease that affects several million people worldwide.

糖尿病是一个社会性疾病，全世界有数百万人罹患此病。

I'll call you on Friday to see if we can reschedule our luncheon meeting at your convenience.

我星期五会给您打电话在您方便的时候我们重新安排我们的午餐约会。