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Let $M$ be a closed, oriented, simply connected 6-manifold. After localization away from 2, we give a homotopy decomposition of $\Sigma M$ in terms of spheres, Moore spaces and other recognizable spaces. As applications we calculate…

This paper is a compressed summary of some principal definitions and concepts in the approach to the black box algebra being developed by the authors. We suggest that black box algebra could be useful in cryptanalysis of homomorphic…

In this paper, we give an introduction for rough groups and rough homomorphisms. Then we present some properties related to topological rough subgroups and rough subsets. We construct the product of topological rough groups and give an…

We explore the connection between ring homomorphisms and semigroup homomorphisms on matrix algebras over rings or $C^*$-algebras.

This note reviews some of the recent work on biharmonic conformal maps (see \cite{OC}, Chapter 11, for a detailed survey). It will be focused on biharmonic conformal immersions and biharmonic conformal maps between manifolds of the same…

Several problems in number theory when reformulated in terms of homogenous dynamics involve study of limiting distributions of translates of algebraically defined measures on orbits of reductive groups. The general non-divergence and…

The aim of this paper is to extend Gerstenhaber formal deformations of algebras to the case of Hom-Alternative and Hom-Malcev algebras. We construct deformation cohomology groups in low dimensions. Using a composition construction, we give…

This paper aims to examine the version of the topological group structure in proximity and especially descriptive proximity spaces, that is, the concepts of proximal group and descriptive proximal group are introduced. In addition, the…

This paper studies the formal deformations of differential algebra morphisms. As a consequence, we develop a cohomology theory of differential algebra morphisms to interpret the lower degree cohomology groups as formal deformations. Then,…

In this paper we examine various properties/constructions which are known for reductive groups and we do some experiments to see to what extent they generalize to symmetric spaces.

The group ring of the automorphism group of a p-group is studied using the automorphism groups of subgroups and quotient groups of P.

A neighborhood homotopy is an equivalence relation on spatial graphs which is generated by crossing changes on the same component and neighborhood equivalence. We give a complete classification of all 2-component spatial graphs up to…

We survey several mathematical developments in the holonomy approach to gauge theory. A cornerstone of this approach is the introduction of group structures on spaces of based loops on a smooth manifold, relying on certain homotopy…

We show that a rank reduction technique for string C-group representations first used for the symmetric groups generalizes to arbitrary settings. The technique permits us, among other things, to prove that orthogonal groups defined on…

In this text, we are concerned with ring epimorphisms, and more specifically universal localisations, from path algebras to matrix algebras. We are mainly focused on constructing ring epimorphisms and universal localisations by extending…

Despite a blossoming of research activity on racks and their homology for over two decades, with a record of diverse applications to central parts of contemporary mathematics, there are still very few examples of racks whose homology has…

Lie-symmetry methods are used to determine the symmetry group of reduced magnetohydrodynamics. This group allows for arbitrary, continuous transformations of the fields themselves, along with space-time transformations. The derivation…

A network can be analyzed at different topological scales, ranging from single nodes to motifs, communities, up to the complete structure. We propose a novel intermediate-level topological analysis that considers non-overlapping subgraphs…

In the branch of mathematics known as graph theory, graphs are considered as a set of points, called vertices, with connections between these points, called edges. The purpose of this paper is to study mappings between two graphs that have…

We investigate geometric properties of homogeneous parabolic geometries with generalized symmetries. We show that they can be reduced to a simpler geometric structures and interpret them explicitly. For specific types of parabolic…