ρ-(h,φ)-弱预不变凸函数及其性质

利用BEN-TAL广义代数运算对强预不变凸函数和(h,φ)-η-预不变凸函数进行推广,定义了一类新的广义(h,φ)-凸函数-ρ-(h,φ)-弱预不变凸函数,给出并证明了它的一些性质。

弱广义对角交叉积的表示范畴

引入弱(H,A)-Yetter Drinfeld模和弱广义对角交叉积代数,证明了弱广义对角交叉积的表示范畴同构于弱(H,A)-Yetter Drinfeld模范畴.

Morita context of weak Hopf group coalgebras

The concept of weak Hopf group coalgebras is a natural generalization of the notions of both weak Hopf algebras（quantum groupoids） and Hopf group coalgebras.Let π be a group.The Morita context is considered in the sense of weak Hopf π-coalgebras.Let H be a finite type weak Hopf π-coalgebra,and A a weak right π-H-comodule algebra.It is constructed that a Morita context connects A#H＊ which is a weak smash product and the ring of coinvariants AcoH.This result is the generalization of that of Wang＇s in the paper ＂Morita contexts,π-Galois extensions for Hopf π-coalgebras＂ in 2006.Furthermore,the result is important for constructing weak π-Galois extensions.

(h,φ)-方向导数与(h,φ)-次梯度

首先根据Ben-Tal广义代数运算定义了一类(h,φ)-方向导数并得到了它的一些基本性质,然后在(h,φ)-方向导数概念的基础上定义了(h,φ)-次梯度与正则弱(h,φ)-Lipschitz函数,讨论了它们的一些相关性质。从得到的结果可以看出:(h,)φ-方向导数与(h,φ)-次梯度推广了以往的广义方向导数与次梯度的概念,且能够互相刻画彼此的性质;对于某些函数无法用Clarke广义梯度研究时,可以用(h,)φ-次梯度来研究;正则弱(h,)φ-Lipschitz函数的概念推广了可微函数与凸函数概念。

On the Structure of the B-cocleft Module Coalgebra

In this paper we develope the notions of crossed coproduct of Hopf algebras and study an equivalent theorem of generalized crossed coproduct of H weakly comodule coalgebras and H module coalgebras. The main result is to prove a structure theorem about B cocleft H module coalgebras.

Banach空间上范数的K超光滑性

提出了Bandch空间上范数的K超光滑性的概念,探讨了它和KVS、KSS以及RNP的关系,并讨论了K超光滑的一些等价条件。

Crossed Products over Weak Hopf Algebras Related to Cleft Extensions and Cohomology

The authors present the general theory of cleft extensions for a cocommutative weak Hopf algebra H. For a right H-comodule algebra, they obtain a bijective corre- spondence between the isomorphisms classes of H-cleft extensions AH → A, where AH is the subalgebra of coinvariants, and the equivalence classes of crossed systems for H over AH. Finally, they establish a bijection between the set of equivalence classes of crossed systems with a fixed weak H-module algebra structure and the second cohomology group H2φZ（AH） （H, Z（AH））, where Z（AH） is the center of AH.