Roger, Claude
Published in
Advances in Pure and Applied Mathematics

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 ...

Baklouti, Ali
Published in
Advances in Pure and Applied Mathematics

Dammak, Jamel Salem, Rahma
Published in
Advances in Pure and Applied Mathematics

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 i...

Abdelmoula, Lobna Baklouti, Ali Bouaziz, Yasmine
Published in
Advances in Pure and Applied Mathematics

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 ...

Deleaval, Luc
Published in
Advances in Pure and Applied Mathematics

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.

da Silva, Daniel Oliveira
Published in
Advances in Pure and Applied Mathematics

We consider the Cauchy problem for the Thirring model in the Gevrey spaces G σ , s {G^{\sigma,s}} . In particular, we prove that the analyticity of solutions persists for a short time. In addition, we derive a sufficient condition to ensure that solutions will continue to be analytic for all time.

Esmaeili, Hamid Erfanifar, Raziyeh Rashidi, Mahdis
Published in
Advances in Pure and Applied Mathematics

A new Schulz-type method to compute the Moore–Penrose inverse of a matrix is proposed. Every iteration of the method involves four matrix multiplications. It is proved that this method always converge with fourth-order. A wide set of numerical comparisons of the proposed method with nine higher order methods shows that the average number of matrix ...

Shojaee, Neda Rezaii, Morteza Mirmohammad
Published in
Advances in Pure and Applied Mathematics

In the present work, the harmonic vector field is defined on closed Finsler measure spaces through different approaches. At first, the weighted harmonic vector field is obtained as the solution space of a PDE system. Then a suitable Dirichlet energy functional is introduced. A σ-harmonic vector field is considered as the critical point of related a...

Gallardo, Léonard Rejeb, Chaabane Sifi, Mohamed
Published in
Advances in Pure and Applied Mathematics

For a root system R on ℝ d {\mathbb{R}^{d}} and a nonnegative multiplicity function k on R, we consider the heat kernel p k ( t , x , y ) {p_{k}(t,x,y)} associated to the Dunkl Laplacian operator Δ k {\Delta_{k}} . For β ∈ ] 0 , d + 2 γ [ {\beta\in{]0,d+2\gamma[}} , where γ = 1 2 ∑ α ∈ R k ( α ) {\gamma=\frac{1}{2}\sum_{\alpha\in R}k(\alpha)}...

Mustafa, Muhammad I.
Published in
Advances in Pure and Applied Mathematics

In this paper we consider a plate equation with infinite memory in the presence of nonlinear feedbacks with and without delay. Under suitable condition on the weight of the delayed feedback compared with the weight of the non-delayed feedback, we use the energy method to establish an explicit and general decay rate result without imposing restricti...