Maschke-type theorem and Morita context over weak Hopf algebras

This paper gives a Maschke-type theorem over semisimple weak Hopf algebras, extends the well-known Maschke-type theorem given by Cohen and Fishman and constructs a Morita context over weak Hopf algebras.     

分次环，A，Aｅ和Smash积A＃G*是亚直既约环的条件

讨论了分次环Ａ，Ａ_ｅ和Ａ＃Ｇ^*的相关性质，在Ａ是分次忠实时，Ａ＃Ｇ^*是亚直既约环当且仅当Ａ_ｅ是亚直既约环；在Ａ是分次非退化时，Ａ＃Ｇ^*是Ｇ亚直既约环当且仅当Ａ是分次亚直既约环．     

Commuting Homotopy Limits and Smash Products

In general the processes of taking a homotopy inverse limit of a diagram of spectra and smashing spectra with a fixed space do not commute. In this paper we investigate under what additional assumptions these two processes do commute. In fact we deal with an equivariant generalization that involves spectra and smash products over the orbit category of a discrete group. Such a situation naturally occurs if one studies the equivariant homology theory associated to topological cyclic homology. The main theorem of this paper will play a role in the generalization of the results obtained by Bökstedt, Hsiang and Madsen about the algebraic K-theory Novikov Conjecture to the assembly map for the family of virtually cyclic subgroups.     

代数A在子代数A^H上投射的若干充分条件

假设Ｈ是域ｋ上的有限维Ｈｏｐｆ代数,Ａ是Ｈ－模代数,本文刻画了Ａ＾ＨＡ的投射性并给出了Ａ＾ＨＡ是投射的若干充分条件,其中Ａ＾Ｈ是Ａ的Ｈ－不变子代数。     

群分次环和Morita等价

设Ｒ是Ｇ－分次环，Ｈ是Ｇ的子群，本文通过构造两个Ｍｏｒｉｔａｃｏｎｔｅｘｔ，给出了环Ｂ｛Ｈ｝Ｍｏｒｉｔａ等价于Ｒ＿Ｈ，Ｒ＃Ｇ￣＊Ｍｏｒｉｔａ等价于Ｒ＿Ｈ＃Ｈ￣＊的充分必要条件．     

L-R smash products for multiplier Hopf algebras

The theory of L-R smash product is extended to multiplier Hopf algebras and a sufficient condition for L-R smash product to be regular multiplier Hopf algebras is given. In particular, the result of the paper implies Delvaux＇s main theorem in the case of smash products.     

基于SOM和RBF网络的软测量方法研究

针对氢粉碎过程中钕铁硼粉碎状态不可知,为有效预测合金的反应状态,提出了一种基于自组织特征映射(SOM)神经网络和径向基函数(RBF)神经网络结合构建的网络模型。在该模型中,SOM神经网络作为聚类网络,采用无教师学习算法对输入样本进行自组织分类,并将分类中心及其对应的权值向量传递给RBF神经网络,作为径向基函数的中心;RBF神经网络作为基础网络,采用高斯函数作为径向基函数实现从输入到隐含层的非线性映射,输出层则采用有教师学习算法训练网络的权值,从而实现输入层到输出层的线性映射。并以钕铁硼氢粉碎过程合金中氢含量为检测对象,运用上述方法在MATLAB平台上建立了合金中氢含量预测模型,并完成了仿真验证。     

弱Hopf代数作用与冲积

本文研究了弱Hopf代数上的冲积并讨论了它约性质．设H是弱Hopf代数,A是左H-摸代数．我们给出了冲积A#H是弱双代数的一个充分条件以及A#H是A可分扩张的一个判定条件．另外,利用积分理论研究了Hopf模代数的有限性条件．     

Weyl型代数的环论性质

设A是代数闭域k上有单位元1的交换结合代数，D是A的交换κ-导子组成的非零k-向量空间，苏育才与赵开明引进Weyl型代数A[D]并且证明了结合代数A[D]是单代数当且仅当A是D-单的且k1[D]在A上的作用为忠实的,通过证明A[D]与smash product A#U(D)同构，我们给出了这一结果的一个纯环论的证明，同时给出了A[D]的一个Ore扩张实现。