The Hahn–Banach Theorem for Partially Ordered Totally Convex, Positively Convex and Superconvex Modules

The Hahn–Banach Theorem for partially ordered totally convex modules [3] and a necessary and sufficient condition for the existence of an extension of a morphism from a submodule C ₀ of a partially ordered totally convex module C (with the ordered unit ball of the reals as codomain) to C, are proved. Moreover, the categories of partially ordered positively convex and superconvex modules are introduced and for both categories the Hahn–Banach Theorem is proved.     

平面分拆的矢量控制方法：列严格梯形平面分拆

作为移位平面分拆的自然拓广,本文引入了梯形平面分拆的概念.应用矢量控制技巧,建立了给定形状和行(列)分部约束的列严格梯形平面分拆集合之枚举函数的初等对称函数行列式表达式.其中之一的重要特例构成了关于循环对称平面分拆的Macdonald猜想的证明基础.     

Extensions of Modules over Schur Algebras, Symmetric Groups and Hecke Algebras

We study the relation between the cohomology of general linear and symmetric groups and their respective quantizations, using Schur algebras and standard homological techniques to build appropriate spectral sequences. As our methods fit inside a much more general context within the theory of finite-dimensional algebras, we develop our results first in that general setting, and then specialize to the above situations. From this we obtain new proofs of several known results in modular representation theory of symmetric groups. Moreover, we reduce certain questions about computing extensions for symmetric groups and Hecke algebras to questions about extensions for general linear groups and their quantizations.     

M.Riesz定理的注记

设u(z)是单位圆内的实值调和函数 ,若 p_平均Mp(r ,u) =12π∫2π0｜u(reiθ) ｜pdθ1 p <∞ ,则称u(z) ∈hp( 1

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