提出了一个非流形结构的表示方法——粘合边结构，其数学基础是代数拓扑中的复形理论。
An identification edge structure is put forward to represent non manifold modeling, which is built on the concepts and methods of the complex and CW complex in algebraic topology.
实际建模过程中，经常会遇到非流形的多边形表面，但很多现有的图形学算法都是基于流形结构的。
In the progress of modeling, We often meet Non-Manifold polygonal surfaces, but a lot of graphical algorithms that operate exclusively on a Manifold polygonal surfaces.
佩雷尔曼的成就在于他实现了理查德·汉密尔顿的计划，从而揭示出三维流形空间的深邃的结构。
What Perelman has achieved is the fulfillment of Richard Hamilton's program, thus revealing a profound structure in the space of 3-manifolds.
研究量子统计中曲指数族子流形的不同度量的对偶结构。
Quantum version of the curved exponential family is studied where its dual structure with different metrics.
这理论表明，本构方程完全确定物质流形的几何结构。
This theory shows that the constitutive equations determine entirely the geometric structure of the material manifold.
流形学习有助于发现数据的内在分布和几何结构。
Manifold learning is helpful to the discovery of the intrinsic distribution and geometry structure of data.
与现有的非线性时间序列消噪算法不同，基于主流形的消噪算法更强调时间序列的整体结构。
Different from the existent noise reduction methods in nonlinear time series, the method based on principal manifold learning emphasized more on the global structure of time series.
流形学习旨在获得非线性分布数据的内在结构，可以用于非线性降维。
Manifold learning attempts to obtain the intrinsic structure of non-linearly distributed data, which can be used in non-linear dimensionality reduction(NLDR).
讨论了交通流形成自组织的条件，建立了交通流耗散结构模型，并与ITS进行比较分析。
This paper discusses the condition of the traffic flow self-organized. A dissipative Structure model is established and compare with ITS.
然后，我们将看到微分同胚群作用下的辛商为特殊子流形模空间上的以环面为结构群的丛。
And then we will see that in the framework of diffeomorphism group the symplectic quotient is torus bundle over the moduli space of special submanifold.
本文引入并研究了叶层结构的定向性，作为应用，讨论了李群在流形上的自由作用，给出了存在李群自由作用的一个必要条件。
In this paper, the orientability of foliations was investigated, and an application to the free action of Lie groups on manifolds was given as well.
本文提出了用流形无法和子域奇异边界元法相结合模拟结构地震响应及地震破坏的方法。
In this paper, a method based on the combination of Manifold and Singular Boundary Element method to simulate seismic responses and failure processes of structures is presented.
通过非流形造型与基于物理的造型相结合，从拓扑结构和几何信息两个方面扩大了模型的表示范围。
Representing objects by combining non manifold modeling and physically based modeling enlarges the representing domain for both topology and geometry.
李群机器学习(LML)既继承了流形学习的优点，又充分利用了李群的代数结构和几何结构的数学本质，自提出以来就引起了许多研究者的关注。
Lie group Machine learning (LML) inherit the advantages of manifold learning method and make full use of the Lie group's structure of algebraic and geometry in mathematics.
讨论特殊半对称联络的黎曼流形，给出了该流形曲率张量的一个代数结构。
In the present paper, the algebra property of Riemannian manifold which is contained some special semi symmetric connection is given.
通过对给定共形紧致流形上的L2调和1形式空间的研究，确定了共形紧致流形的结构。
The main purpose of our paper is to understand the structure of conformally compact manifolds by studying the space of L2 harmonic 1-forms on it.
本文提出并采用微分流形理论证明智能机器人体系结构可分解性定理。
In this paper, a decomposability theorem is presented and proved by differentiable manifolds theories.
然而，当高维数据所逼近或近似的一个低维流形自相交时，欧氏距离意义上的邻域不能完全反映低维点的相邻关系，往往难以体现真实的局部线性结构。
However, when the underlying lower-dimensional manifold is self-intersecting at some points, it's difficult to obtain local lower-dimensional structure from the Euclidean neighborhoods.
实验圆阵的实测阵列流形和理论阵列流形存在较大误差，这表明该文采用的可适用于任意结构阵列的宽带恒定束宽波束形成方法具有良好的宽容性。
The big difference between measured and theoretic manifold of the circular array showed that the broadband constant beamwidth beamforming method used in the paper has good tolerance.
黎曼流形上的幂零结构指什么？
地质结构往往由于断层等的存在经常呈现出非流形的情况，使得对复杂地质结构建模相对困难。
Geology structure often presents non-manifold situation due to faults, resulting in relatively difficulties on complex geological structure modeling.
学者们提出剩下的六维卷藏在奇 妙的结构里，这就是著名的卡拉比-丘流形。
According to theorists, the missing six are curled up in bizarre structures known as Calabi-Yau manifolds.
由于经典渗流力学是建立在均匀性假说基础上，因此不能考虑孔隙介质细观结构对渗流形貌的影响。
The classical seepage mechanics can not be used to investigate the effect of mesostructure of porous media on the shape of seepage because it is based on the assumption of homogenous media.
本文摘要叙述有关三维紧致光滑流形上结构稳定的微分同胚的一个特征性定理的证明。
This note takes a sketch of a proof of a characterization theorem for diffeomorphisms oa a compact 3-dimensional smooth manifold to be structurally stable.
借助于Gauss过程，就可以从这个流形坐标推理出人体的姿态结构和外轮廓。
The intrinsic pose structure and silhouette are then deduced from these coordinates using a Gaussian process.
垂直流洁净工作台采用垂直单向流净化原理的气流形式，将低噪音离心风机、静压箱、滤器结合成单独一体的单元式结构。
Vertical flow clean bench vertical form of a one-way flow of gas purifying, low noise centrifugal fan, static bins Filter modules combined into a single integrated structure.
垂直流洁净工作台采用垂直单向流净化原理的气流形式，将低噪音离心风机、静压箱、滤器结合成单独一体的单元式结构。
Vertical flow clean bench vertical form of a one-way flow of gas purifying, low noise centrifugal fan, static bins Filter modules combined into a single integrated structure.
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