一个阿贝尔积分根的数目的下界

霍尔普夫分支是动力系统分支理论中一个重要的部分,几乎所有的问题都和非退化中心附近的极限环的数目以及扰动相关. 本文研究了一个近哈密尔顿系统. 通过利用霍尔普夫极限环分支理论,得到相应的阿贝尔积分孤立零点的最大个数的下界,由此给出了最大数目极限环的下界.     

Canonical Differential Calculi for Finitely Generated Abelian Groups and Their Fermionic Representations

Canonical differential calculi are defined for finitely generated Abelian groups with involutions existing consistemtly.Two such the canonical calculi are presented.Fermionic representations for canonical calculi are defined based on quantized calculi.Fermionic representations for aforementioned two canonical calculi are searched out.     

Hausdorff operators on compact abelian groups

Necessary and sufficient conditions are given for the boundedness of Hausdorff operators on the generalized Hardy spaces $H_E^p(G)$, real Hardy space $H_{\mathbb{R}}^1(G)$, $\text{BMO}(G)$, and $\text{BMOA}(G)$ for compact Abelian group G. Surprisingly, these conditions turned out to be the same for all groups and spaces under consideration. Applications to Dirichlet series are given. The case of the space of continuous functions on G and examples are also considered.     

Geometric partial comodules over flat coalgebras in Abelian categories are globalizable

The aim of this paper is to prove the statement in the title. As a by-product, we obtain new globalization results in cases never considered before, such as partial corepresentations of Hopf algebras. Moreover, we show that for partial representations of groups and Hopf algebras, our globalization coincides with those described earlier in literature. Finally, we introduce Hopf partial comodules over a bialgebra as geometric partial comodules in the monoidal category of (global) modules. By applying our globalization theorem we obtain an analogue of the fundamental theorem for Hopf modules in this partial setting.