Advances in Pure and Applied Mathematics

Published by De Gruyter

Volume 9 Issue 4 - Special Issue: Proceedings of the 22nd Meeting of the Tunisian Mathematical Society, Mahdia, Tunisia, 2017

Issue of Advances in Pure and Applied Mathematics

Contents
Journal Overview

Publicly Available October 1, 2018

Frontmatter

Page range: i-iv

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Publicly Available August 7, 2018

Proceedings of the 22nd Meeting of the Tunisian Mathematical Society

Ali Baklouti

Page range: 235-236

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February 11, 2018

A note on the behavior of the Dunkl maximal operator

Luc Deleaval

Page range: 237-246

Abstract

This note is a contribution to the Proceedings of the Conference of the Tunisian Mathematical Society CSMT 2017. After briefly revisiting the case of the standard Hardy–Littlewood maximal operator, we will discuss the behavior of the Dunkl maximal operator in both the scalar and vector-valued cases.

February 17, 2018

On the generalized moment separability theorem for type 1 solvable Lie groups

Lobna Abdelmoula, Ali Baklouti, Yasmine Bouaziz

Page range: 247-277

Abstract

Let G be a type 1 connected and simply connected solvable Lie group. The generalized moment map for π in G^{\widehat{G}}, the unitary dual of G , sends smooth vectors of the representation space of π to 𝒰⁢(𝔤)*{{\mathcal{U}(\mathfrak{g})}^{*}}, the dual vector space of 𝒰⁢(𝔤){\mathcal{U}(\mathfrak{g})}. The convex hull of the image of the generalized moment map for π is called its generalized moment set , denoted by J⁢(π){J(\pi)}. We say that G^{\widehat{G}} is generalized moment separable when the generalized moment sets differ for any pair of distinct irreducible unitary representations. Our main result in this paper provides a second proof of the generalized moment separability theorem for G .

March 17, 2018

Graphic topology on tournaments

Jamel Dammak, Rahma Salem

Page range: 279-285

Abstract

Alexandroff spaces are the topological spaces in which the intersection of arbitrary many open sets is open. Let T be an indecomposable tournament. In this paper, first, we associate a trivial topology to T . Then we define another topology on T , called the graphic topology of T , and we show that it is an Alexandroff topology. Our motivation is to investigate some properties of this topology.

September 10, 2018

The even, the odd, the superalgebras and their derivations

Claude Roger

Page range: 287-294

Abstract

We give an introduction to superalgebra, founded on the difference between even (commuting) and odd (anti-commuting) variables. We give a sketch of Graßmann’s work, and show how derivations of those structures induce various superalgebra structures, Lie superalgebras of Cartan type being obtained with even derivations, while odd derivations induce Jordan-type superalgebras.

About this journal

Advances in Pure and Applied Mathematics is now published by ISTE.