Mathematics > Home > Advances in Pure and Applied Mathematics > Issue

Mehdi Rezaei,
Mehdi Alaeiyan

Let $$$G$$$ be a permutation group on a set $$$\Omega$$$ with no fixed points in $$$\Omega$$$, and let $$$m$$$ be a positive integer. If for each subset $$$\Gamma$$$ of $$$\Omega$$$ the size $$$\Gamma^{g}-\Gamma|$$$ is bounded, for $$$g\in G$$$, the movement of $$$g$$$ is defined as move $$$(g):=\max{|\Gamma^{g}-\Gamma|}$$$ over all subsets $$$\Gamma$$$ of $$$\Omega$$$, and move $$$(G)$$$ is defined as the maximum of move $$$(g)$$$ over all non-identity elements of $$$g\in G$$$. Suppose that $$$G$$$ is not a 2-group. It was shown by Praeger that $$$|\Omega|\leqslant\lceil\frac{2mp}{p-1}\rceil+t-1$$$, where $$$t$$$ is the number of $$$G$$$-orbits on $$$\Omega$$$ and $$$p$$$ is the least odd prime dividing $$$|G|$$$. In this paper, we classify all permutation groups with maximum possible degree $$$|\Omega|=\lceil\frac{2mp}{p-1}\rceil+t-1$$$ for $$$t=2$$$, in which every non-identity element has constant movement $$$m$$$.

[FORTHCOMING] Algebraic properties of subspace topologies

Noômen Jarboui,
Bana Al Subaiei

It is shown that the collection of all topologies on a given set $$$X$$$ coincide with the set of subsemirings of the power set $$$\mathcal{P}(X)$$$ (equipped with union and intersection) if and only if $$$X$$$ is finite. Furthermore, given a topological space $$$(X, \mathcal{T})$$$ and a subset $$$A$$$ of $$$X$$$, we characterize when the subspace topology $$$\mathcal{T}_A$$$ is a maximal (resp., a prime) ideal of the semiring $$$\mathcal{T}$$$. As applications, we provide an algebraic characterization of the one-point compactification of a noncompact, Tychonoff space. Moreover, we describe explicitly the semiring homomorphisms from $$$\mathcal{P}(X)$$$ into $$$\mathcal{P}(Y)$$$ in case $$$X$$$ is a finite set and $$$Y$$$ is an arbitrary nonempty set.

[FORTHCOMING] Kan extendable subcategories and fibrewise topology

Moncef Ghazel

We use pointwise Kan extensions to generate new subcategories out of old ones. We investigate the properties of these newly produced categories and give sufficient conditions for their cartesian closedness to hold. Our methods are of general use. Here we apply them particularly to the study of the properties of certain categories of fibrewise topological spaces. In particular, we prove that the categories of fibrewise compactly generated spaces, fibrewise sequential spaces and fibrewise Alexandroff spaces are cartesian closed provided that the base space satisfies the right separation axiom.

[FORTHCOMING] Morphology of the connected components of the boolean sum of two digraphs (≤ 5)-hypomorphic up to complementation

Aymen Ben Amira,
Jamel Dammak,
Hamza Si Kaddour

Let $$$G=(V,E)$$$ and $$$G'=(V,E')$$$ be two digraphs, $$$(\leq 5)$$$-hypomorphic up to complementation, and $$$U:=G\dot{+} G'$$$ be the boolean sum of $$$G$$$ and $$$G'$$$. The case where $$$U$$$ and $$$\overline U$$$ are both connected was studied by the authors and B.Chaari giving the form of the pair$$$\{G, G'\}$$$. In this paper we study the case where $$$U$$$ is not connected and give the morphology of the pair $$$\{G_{\restriction {V({\mathcal C})}},G'_{\restriction {V({\mathcal C})}}\}$$$ whenever $$$C$$$ is a connected component of $$$U$$$.

[FORTHCOMING] Compatibility of a Jacobi structure and a Riemannian structure on a Lie algebroid

Yacine Aït Amrane,
Ahmed Zeglaoui

In a preceding paper we introduced a notion of compatibility between a Jacobi structure and a Riemannian structure on a smooth manifold. We proved that in the case of fundamental examples of Jacobi structures : Poisson structures, contact structures and locally conformally symplectic structures, we get respectively Riemann-Poisson structures in the sense of M. Boucetta, (1/2)-Kenmotsu structures and locally conformally Kähler structures. In this paper we are generalizing this work to the framework of Lie algebroids.

2024

Volume 24- 15

Issue 1 (January 2024)Issue 2 (Special CSMT 2023)

Issue 3 (June 2024)

2023

Volume 23- 14

Issue 1 (January 2023)Issue 2 (Special CSMT 2022)

Issue 3 (June 2023)

Issue 4 (September 2023)

2022

Volume 22- 13

Issue 1 (January 2022)Issue 2 (March 2022)

Issue 3 (June 2022)

Issue 4 (September 2022)

2021

Volume 21- 12

Issue 1 (January 2021)Issue 2 (May 2021)

Issue 3 (Special AUS-ICMS 2020)

Issue 4 (September 2021)

2020

Volume 20- 11

Issue 1 (May 2020)Issue 2 (September 2020)