微分拓扑

This work opened up the new field of differential topology .

这工作开放微分拓扑结构新领域。

This course is meant to bring graduate students who will be using ideas from differential topology and differential geometry up to speed on these topics.

本课程的目的是让需要使用微分拓扑和微分几何的研究生能在这个方向上尽快入门。

Contemporary geometric topology and differential topology , and particular subfields such as Morse theory , would be counted by most mathematicians as part of geometry.

现代微分几何拓扑和拓扑结构，特别是分支如莫尔斯理论，将计算的大多数数学家的一部分几何。

Topology is traditionally decomposed into three parts: General topology, Algebraic topology and Differential topology.

习惯上拓扑学被分成点集拓扑、代数拓扑和微分拓扑三部分。

Furthermore,this course is benefitial to study differential topology, Riemannian Geometry, Lie group and Nonlinear Analysis etc.

为进一步学习微分几何、微分拓扑、几何分析、黎曼几何、李群、低维拓扑和非线性分析等相关课程奠定良好的基础，并为阅读当代数学文献创造条件。

The VCO core uses a differential topology to provide a stable frequen- cy versus supply voltage and improve the immunity to load variations.

VCO的内核采用了微分拓扑提供一个稳定的同步周期- cy的改善与电源电压和负载变化的免疫力。

For this reason, the project creates the mathematical model and numerical method of backcalculation of layer moduli in asphalt pavement based on homotopy method in accordance with the theories of differential topology and optimization. Through selecting the rational objective functions of backcalculation of moduli, a large number of deflection basins of asphalt pavement with FWD are made the backcalculation of moduli to solve effectively the present problems and ensure the reliability of backcalculation of layer moduli in asphalt pavement.

为此，本项目根据微分拓扑和最优化理论，建立了基于同伦方法的沥青路面模量反算的数学模型和计算方法，并通过选取合理的模量反算目标函数，对大量FWD实测的沥青路面弯沉盆进行了模量反算，从而有效地解决了目前存在的问题，保证了沥青路面模量反算的可靠性。

Based on theanalysis of topology structure of parallel mechanisms and using differential topology anddifferential manifolds as mathematical tools, we propose a new classification method. Thismethod classifies singularities of parallel mechanisms into two basic types, i.e. topologysingularity and parameterization singularity. This kind of classification has clear physical andmathematical meaning and fully reveals the characteristic of configuration space of parallelmechanisms.

采用微分拓扑和微分流形等现代数学工具，在对并联机构位形空间的拓扑结构进行分析的基础上，提出了一种新的奇异位形的分类方法，即把奇异位形分为拓扑奇异位形、参数化奇异位形两种类型，这种分类方法充分体现了并联机构位形空间的特点，具有十分明确的物理和数学意义。

This book is intended to provide a working knowledge of those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles, and Chern forms that are essential for a deeper understanding of both classical and modern physics and engineering.

本书试图提供外微分形式、微分几何、代数拓扑、微分拓扑、李群、向量丛、Chern公式等前沿知识，它们对于深入理解经典物理、现代物理以及工程都是必需的。

The existence of solutions for two-point boundary value problem subject to nonlinear second order differential equation with mixed boundary conditions is studied by using topological transversality theorem, and some known results are improved.

现利用拓扑横截定理，考虑了二阶常微分方程两点边值问题在组合边界条件下的解的存在性，对二阶常微分方程两点边值问题所对应的辅助问题作先验界估计，并利用拓扑横截定理，得到了边值问题解的存在性，推广了一些已有结果。

And Satan entered into Judas who was called Iscariot and was of the number of the twelve.

22：3 这时，撒但进了那称为加略人的犹大里面，他本是十二数中的一个。

Teachers to consciously reflect on the study of theory and practice, constantly adjust and perfect their knowledge structure, in understanding the future of education, and social life on the basis of a correct conception of modern education bioethics.

教师在自觉进行理论学习和实践反思，不断调整和完美自己的知识结构，在认识生物教育的未来性，生命性和社会性的基础上形成正确的现代教育生命伦理观。