Basic differential forms for actions of Lie groups

A section of a Riemannian -manifold is a closed submanifold which meets each orbit orthogonally. It is shown that the algebra of -invariant differential forms on which are horizontal in the sense that they kill every vector which is tangent to some orbit, is isomorphic to the algebra of those differential forms on which are invariant with respect to the generalized Weyl group of , under some condition.

     

指数型二分性,Melnikov函数和异宿轨道

本文用不同于Ｐａｌｍｅｒ＾［２］的方法，讨论了非自治微分方程存在异宿轨道的条件。得到了已知文献中不同的一个Ｍｅｌｍｉｋｏｖ型的函数。     

The action of the group of bundle-automorphisms on the space of connections and the geometry of gauge theories

Some aspects of the geometry of gauge theories are sketched in this review. We deal essentially with Yang-Mills theory, discussing the structure of the space of gauge orbits and the geometrical interpretation of ghosts and anomalies. Occasionally we deal also with classical gauge theories of gravitation and in particular we study the action of the group of diffeomorphisms on the space of linear connections. Finally we comment on the mathematical interpretation of anomalies in field theories.     

塞来昔布的密度泛函理论计算及光谱分析

塞来昔布(Celecoxib, CXB)是COX-2的高选择性抑制剂,经过20年的发展已经成为世界范围内使用最为广泛的一类处方药.本文基于密度泛函理论,使用B3LYP泛函,6-311++G(d, p)基组进行结构优化.在此工作上对该药物分子的结构、红外光谱、拉曼光谱、分子前线轨道、静电势和激发态性质做了一系列的研究.结果表明：CXB分子是一个稳定的非平面扭曲结构,此结构使得该药物分子在COX-2上的疏水通道中可以迅速通过,从而形成了一个可与苯磺酰胺片段结合的结合腔.对化合物进行频率计算,分别得到红外光谱和拉曼光谱,与实验采集的数据进行对比,呈现出较好的一致性.对分子的基态进行前线轨道和静电势的分析,磺酰胺基与COX-2易形成氢键作用.在CXB分子的激发态研究中发现,CXB分子的激发态性质主要由第1激发态、第3激发态和第6激发态共同决定.这为理解CXB的作用机理提供了重要的信息,也为后期扩展CXB衍生物提供了理论基础.     

Orbits in symmetric spaces

We characterize those elements in fully symmetric spaces on the interval (0,1) or on the semi-axis (0,∞) whose orbits are the norm-closed convex hull of their extreme points.     

Minimal orbits of metrics

The group of diffeomorphisms of a compact manifold acts isometrically on the space of Riemannian metrics with its L² metric. Following Arnaudon and Paycha (1995) and Maeda, Rosenberg and Tondeur (1993), we define minimal orbits for this action by a zeta function regularization. We show that odd dimensional isotropy irreducible homogeneous spaces give rise to minimal orbits, the first known examples of minimal submanifolds of infinite dimension and codimension. We also find a flat 2-torus giving a stable minimal orbit. We prove that isolated orbits are minimal, as in finite dimensions.     

Zakharov方程组与Hirota方程的同宿轨道

利用Hirota方法得到Zakharov方程组和Hirota方程同宿轨道的解析表达式.     

Infinitesimal orbit type theorem for normalizable actions

Let α:G×M→M$\alpha :G\times M\to M$ be a differentiable action of a Lie group G$G$ on a connected differentiable manifold M$M$. Assume that the local tube theorem holds at every x∈M$x\in M$. Then the following is proved: there is a maximal infinitesimal orbit type, called the principal, such that the union of the orbits belonging to this infinitesimal type is an open and dense set in M$M$.