微分流形

本文讨论基于微分流形框架随机神经网络学习算法，称为em学习算法；

In this paper , a learning algorithm for stochastic neural networks , the em algorithm , is proposed based on differential manifold frameworks .

本文给出了一种不利用李群论，而仅凭微分流形和矩阵论的一些基本知识便能算出dim（O（n；R））的方法。

This paper gives a method by which we can calculate the dim ( O ( n ; R )) . The method is obtained only by using basic knowledge of differential manifold and matrix theory , but without using Lie group Theory .

微分流形上r阶联络到其丛空间的水平提升及相应的曲率与挠率张量

Horizontal lift of connection of order r on manifolds to the bundle spaces and the curvature & torsion tensors

利用谱序列方法证明了对于紧致微分流形上一般的Morse函数而言，Morse不等式均成立。

The authors use method of spectral sequences to prove that Morse inequalities are hold on differential compact manifolds for general Morse functions .

对于多层随机神经网络模型，我们从微分流形的角度分析它的对偶平坦流形结构，描述em算法对于多层前馈随机神经网络模型学习算法实现和加速技术。

At first , we analyze the dual flat manifold structure of stochastic neural networks , and then give the em algorithm implementation for 3 layers of stochastic perceptrons . A speeding theory of the em algorithm is shown .

定向微分流形上Stiefel-Whitney示性类的积分公式

The Integral Formulas of Stiefel-Whitney Classes on an Oriented Differentiable Manifold

机器人操作性能的微分流形理论与方法研究

Theory and Methodology of the Robot Manipulability based on Differential Manifolds

微分流形上切向量定义的新几何解释

New Geometrical Explanation of the Definition of Tangent Vector on Differential Manifolds

基于微分流形的动力系统理论方法；

The theory and method of dynamic system based on the differential manifold ;

微分流形上的C~∞同伦映射

The C ~ ∞ Homotopic Mapping on Differentiable Manifolds

微分流形及其应用的某些注释（英文）

Some remarks on differential manifolds and their applications ;

微分流形与调和映射发展简况

Recent Developments of Differential Manifolds and Harmonic Maps

微分流形及其在测绘科学中的应用初探

A Tentative Investigation on Differentiable Manifold and It 's Application to Surveying and Mapping

微分流形上的变换群

Transformation s group on the Differentiable Manifolds

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 .

递归神经网络微分流形方法。

Differentiable manifolds methods in RNN .

基于微分流形的神经计算

Neural Computing Based on Differential Manifold

它的研究对象是人工神经网络，即由大量神经元组成的非线性动力系统。本文介绍用微分流形研究神经信息处理的重要概念.讨论研究机理和方法。

This paper introduces the important concepts on neural information processing based on differential manifold The research mechanism and approaches are also discussed here .

对于具有简单拓扑结构，存在着一致的全局参数化的控制网格，我们将把控制网格直接映射到微分流形上，因此可以很容易地对曲面进行构造和控制。

For a control mesh with consistent parameterization , the surface can be easily constructed because it can be mapped to differential manifold directly .

该模型以几何的改变为视角，应用几何.拓扑的方法建立结构钢韧性损伤微分流形，并讨论一般流形中含韧性损伤结构钢的力学状态。

This model has established differential manifold of ductile damage with view of geometry , and discussed the mechanical state of structural steel in the manifold .

基于信息几何建立股票收益率满足的概率分布族所构成的微分流形，给出流形的几何结构。

Constructs the differential manifold of stock return process based on information geometry , and gives its geometric structure such as the Fisher metric matrix and α - connection coefficients .

数控设备应适应不同技能层次的操作者，这是企业对设备操作性能的需求。机器人操作性能的微分流形理论与方法研究

In serviceability , the numerical control equipments should adapt to different level of skilled operators , so to satisfy the equipment buyers . Theory and Methodology of the Robot Manipulability based on Differential Manifolds

按照微分流形、向量场、李导数、分布这一顺序，由浅入深地简述了非线性系统微分几何控制理论赖以发展的最基本的数学基础。

The basic mathematical concepts : differential manifolds , vector fields , Lie derivatives and distributions are explained successively , which are the foundation for developing the differential geometric control theory of nonlinear control systems .

以微分流形的分布为工具，得到了一类非线性系统可通过对角状态反馈变换实现系统的解耦及线性化的充要条件。

Based on the tool of distribution of differential manifold , this paper gives the sufficient and necessary conditions of decoupling and linearization of multivariate nonlinear system by using the transformation of diagonal state feedback .

广义有理参数曲线曲面定义在与控制网格拓扑同胚的微分流形上，以高度一般的势函数为基函数，其控制网格可以是任意的一维拓扑流形和二维可定向拓扑流形。

In the framework , a control mesh may be arbitrary one-dimensional or two-dimensional orientated topological manifold , and the curve or surface is defined on differential manifold homeomorphic to the control mesh with a potential function as its basis functions .

第六章讨论了亚椭圆微分形式与流形的第一Betti数之间的关系。

Chapter six discusses the connection about the hypoelliptic form with the first Betti number of manifold .

微分方程及其中心流形方法的自动化简

On Simplification Automatically of Differential Equation and the Central Manifold Method

变系数微分方程的积分流形血流变系统粘度的积分算法

Integral Manifolds of Differential Systems with Variable Coefficients The integral arithmetic of viscosity for the rheogeniometer

本文从近代微分几何及其核心概念微分流形着手，阐释了流形及相关问题与时空结构的关系；

Based on differential geometry and its fundamental concept & differential manifold , the space-time background is pointed out in this paper , its structure is analyzed and discussed further .

介绍了一种非线性系统精确线性化的新方法&微分几何法，它是采用微分流形的概念，通过状态空间的微分同胚变换和状态反馈控制使得非线性系统线性化。

This paper introduces briefly differential geometric approach for exact linearization of nonlinear systems . The method based on the concept of differential manifold linearizes nonlinear systems by diffeomorphisms and feedback transformations of state space .