微分拓扑

One of the goals of this thesis is to devote ourselves to the differential equations which permit singularities and impulsive in abstract space.

本文中，我们利用拓扑度理论和有关非紧性测度的理论，在相对广泛的条件下，研究了抽象空间中几类微分方程正解及多解的存在性。

They are studied for their global properties by the methods of algebra and algebraic topology and form a natural domain for the global analysis of differential equations.

它们的整体性质用代数和代数拓扑的方法进行研究，并且形成微分方程式的整体分析的一个自然的领域。

They are studied for their global properties by the methods of algebra and algebraic topology and form a natural domain for the global analysis of differ tial equations.

它们的整体性质用代数和代数拓扑的方法进行研究，并且形成微分方程式的整体分析的一个自然的领域。

The existence of periodic solutions to the second order ordinary differential equation in Banach space is discussed.

本文利用半序理论，非紧性测度，凝聚映射的拓扑度，不动点定理及锥上不动点指数理论，讨论了Banach空间E中二阶常微分方程周期边值问题解的存在性，主要结果有一。

The surface representation in discrete form and its differential computation are important issues in computer graphics and geometric design.

0引言一般来说，曲面的一阶微分量是指曲面的切平面方向和法向量，二阶微分量是指曲面的曲率等有关量·它们作为重要的曲面信息度量指标，在计算机图形学，机器人视觉和计算机辅助设计等领域发挥了重要的作用·传统的曲面是连续形式的参数曲面和隐式曲面，其微分量的计算已经有了较完备的方法·随着激光测距扫描等三维数据采样技术和硬件设备的长足进步，以及图形工业对任意拓扑结构光滑曲面造型的需求日益迫切，离散形式的曲面———细分曲面、网格曲面和点云曲面正在逐渐成为计算机图形学和几何设计领域的新宠·于是，对这种离散形式的曲面如何估

By dropping this assumption of fixed topology and metric, one can investigate alternative theories within differential geometry that yield an appropriately changing topological structure, and search for and check its testable consequences.

通过抛弃这一拓扑与量度确定不变的假设，在一个能生成一种适当的变化性拓扑架构的微分几何学之中，我们就可以探究其他的理论并寻找与检验其可检验的结果。

On the other hand , illuminated by close relation between harmonic maps and sumanifold theory, we have also researched in-depth about some relative problems in submanifolds theory which include: the estimate of heat kernel and eigenvalue and it geometric application of submanifolds with or without boundary; many kinds of pinching problem of submanifolds which include the rigidity theorem, topological sphere theorem, differential sphere theorem and topological finite theorem.

另外，鉴于调和映照与子流形之间的密切关系，我们还要深入研究子流形几何中与之相关的一些问题，主要包括：带边与不带边子流形的热核与特征值估计及其几何应用；子流形的刚性定理、拓扑球定理、微分球面定理、拓扑有限性定理等各类Pinching问题。

Fundamental concepts in power system differential-algebraic equations model, like singular point and multiple energy function sheets defined on constraint manifolds, are studied.

所得研究成果揭示了微分代数模型与奇异扰动模型的本质区别、奇异性与系统模型和系统负载的联系、结构保持能量函数法可能具有的内在保守性等，这对深入理解电力系统微分代数方程模型的拓扑结构、结构保持能量函数法和暂态电压稳定及其与功角稳定的关系具有一定的价值。

Meanwhile, we have gotten stability for the subdifferential of cone efficient point sets and cone weakly efficient point sets of multiobjective programming with respect to perturbation of cone respectively.

对于局部凸拓扑向量空间的多目标规划问题，本文研究并得到当确定空间序的控制锥受扰动，它们的锥有效点集和锥弱有效点集分别在锥次微分和锥弱次微分意义下的稳定性结果。

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。

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。