同调群

本文讨论了拓扑流形上Fb的整系数同调群和F的拓扑临界点的不变量间的关系。

In this paper we discuss the relation between the integer homology group of F_b on topological manifold and the invariants of topologically critical point of F.

其次介绍了张量积的基本性质，复形和Hochschild同调群的定义，余代数的定义并且举出一些余代数的例子。

Secondly , we introduce the basic properties of tensor product , and the definitions of complex and Hochschild homology group , the definition of coalgebra and some examples .

Loop代数的上同调群

Cohomology Groups of the Loop Algebra

Banach代数的n-维上同调群与n-扩张

N-dimensional cohomology groups of Banach Algebras and n-extensions

CP~n（Q）的加权blowup及陈-阮上同调群

Weighted Blowup of CP ~ n ( Q ) and Chen-Ruan Cohomology Group

关于紧Riemann曲面上同调群的一些性质

Some Properties of Cohomology Group on Compact Riemann Surface

系数在不可约模中Witt代数的限制上同调群

The Restricted Cohomology of Witt Algebras with Coefficients in an Irreducible Module

Virasoro代数的上同调群成零条件

On the Vanishing of Cohomology Groups of the Virasoro Algebra

对于函子AHom~C、AHOM和coC，我们分别研究了它们的右导来函子并对其上同调群进行了讨论，得出这几个右导来函子之间的联系。

For the functors _AHom ~ C , _AHOM and coC , we study their right derived functors and discuss the relations between them .

第四章中，我们主要研究具有三个点的且不带方向圈的有向箭图的路代数上的完备例外序列的自同态代数的Hochschild上同调群。

Especially , we compute the Hochschild cohomology of endomorphism algebras of complete exceptional sequence of the path algebra whose quiver has 3 vertices and has no orientation .

该方法利用扩展等面积准则（EEAC）稳定性理论中的主导模式概念，识别所有可能出现的暂态功角失稳模式，并据此将所有的发电机节点划分为不同的同调群。

All potentially critical-modes for transient angle stability are identified by extended equal area criterion ( EEAC ), and then a PMU is assigned to one of the power plants in each critical cluster .

本文在假定势能函数是Morse函数的情况下，通过计算位形空间的同调群并利用Morse不等式来估计某些质点系的平衡位置的个数。

In the paper the potential functions are assumed to be Morse functions and the number of equilibrium positions of certain systems of n mass points is estimated by calculating of the homology groups of configuration spaces of the systems and Morse inequalities .

并说明了对于有序Morse函数而言，谱序列算同调群的方法与下Witten复合形算法是一致的；而对于一般的Morse函数，这两种算法在形式上是不一致的。

They also indicate that for order Morse functions , it can be computed out the same homological groups by method of spectral sequences , as by Witten complex , although they are very different in form for general Morse functions .

自从Hochschild在1942年研究结合代数的同调群时提出Hochschild同调群的概念和理论以来，它在数学的许多分支均有广泛应用。

Since Hochschild proposed the concept and theory of Hochschild homology group while researching the homology group of associative algebra in 1942 , it is widely used in many branches of mathematics .

平面上紧致子集的同调群及不动点性质

On homology and fixed point properties of compact plane sets

关于整同调群结构的进一步刻画

The further description on the structure of homology group with integral coefficients

关于代数几何中几个同调群的计算

About the calculation of several homology groups in algebraic geometry

单纯同调群不变性的一个充要条件及其应用

A Sufficient and necessary condition of unchangeability about Simplicial homology group and application

上三角矩阵代数的交叉模和三阶上同调群

Crossed Modules and Third Cohomology of Triangular Lie Algebras

量子群上同调群的合成因子

Composition factors of cohomology groups for quantum groups

同伦群和上同调群的上乘积

Homotopy Groups and cup product of cohomology groups

原Heisenberg&Virasoro代数的二上同调群

Second Cohomology Groups of the Original Heisenberg-Virasoro Algebra

本文研究了图的邻域复形同调群的性质。

In this paper we study some properties of homology group of neighborhood complexes of graphs .

在特征数0的代数闭域上半单纯代数群的上同调群

The Cohomology of Semi - simple Algebraic Groups Over an Algebraically Closed Field of Characteristic O

群中心扩张与二维上同调群通用系数定理

Central extensions of a group and the universal coefficient theorem in the cohomology groups of dimension 2

从同调群的定义和要点、同调群的识别、等值模型及参数的确定等方面评述动态等值的研究和应用现状。

Researches and applications on dynamic equivalences are reviewed from aspects of coherency definitions , coherency identifications , equivalent models and parameters .

最后我们通过一些已知代数的同调群，计算得到了这类李代数的双代数结构。

Finally , we calculate and get its bialgebra structure through a convenient method using some Known cohomology group of some related algebra .

强调只有直接从完整的受扰轨迹中挖掘深层信息，才能可靠识别非自治非线性系统中的同调群。

Only if stability information is excavated out directly from the whole disturbed trajectories , coherency can be identified from non-autonomous and nonlinear system .

利用胞腔模和单模的上同调群，得到了几个关于胞腔代数半单性的评判准则；

By using the cohomology groups of cell modules and simple modules , we then give some new criteria for the semi-simplicity of cellular algebras .

本文利用任意n维平直空间（平移群流形）到n维球S~n的Kronccker映象，给出平移群的任意高阶同调群上闭链的明显表达式。

An explicit expression for any higher cocycles in translation group is given by means of Kronecker mapping from the n-dimensional flat space ( translation group manifold ) to the n-dimensional sphere .