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This paper deals with some results concerning finitely generated coreduced comultiplication modules over a commutative ring.
Aspects of compatibility of topologies of parallel computing systems and tasks are investigated. The introduction of appropriate indexes based on the original topological model of parallel computations and on the nontraditional description…
In this work we develop some categorical aspects of the double structure of a module.
In this text we expose basic cases of some fundamental ideas and methods of topology. Namely, of homotopy, degree, fundamental group, covering, Whitehead invariant, etc. This is done by considering the elementary example: closed polygonal…
This work presents the mathematical foundations for the generation of integrable cross-field on 2D manifolds based on user-imposed singularity configuration. In this paper, we either use singularities that appear naturally, e.g., by solving…
The theory of representations of a crossed module is a direct generalization of the theory of representations of groups. For a finite group G, the Drinfeld quantum double of the group G is a Hopf algebra that represents a special case of…
In this paper, we develop a method to compute the Morse homology of a manifold when descending manifolds and ascending manifolds intersect cleanly, but not necessarily transversely. While obstruction bundle gluing defined by Hutchings and…
Recently, sub-indices and sub-factors of groups with connections to number theory, additive combinatorics, and factorization of groups have been introduced and studied. Since all group subsets are considered in the theory and there are many…
In this paper we present a new approach to computing homology (with field coefficients) and persistent homology. We use concepts from discrete Morse theory, to provide an algorithm which can be expressed solely in terms of simple graph…
We classify two-qubit commuting Hamiltonians in terms of their computational complexity. Suppose one has a two-qubit commuting Hamiltonian H which one can apply to any pair of qubits, starting in a computational basis state. We prove a…
We propose and analyze a mathematical model of Modulated Luminescent Tomography. We show that when single X-rays or focused X-rays are used as an excitation, the problem is similar to the inversion of weighted X-ray transforms. In…
Cellular automata are investigated towards their ability to compute transductions, that is, to transform inputs into outputs. The families of transductions computed are classified with regard to the time allowed to process the input and to…
We discuss computability and computational complexity of conformal mappings and their boundary extensions. As applications, we review the state of the art regarding computability and complexity of Julia sets, their invariant measures and…
The majority of model-based clustering techniques is based on multivariate Normal models and their variants. In this paper copulas are used for the construction of flexible families of models for clustering applications. The use of copulas…
In this paper, we introduce the concept of crossed module for Hom-Leibniz-Rinehart algebras. We study the cohomology and extension theory of Hom-Leibniz-Rinehart algebras. It is proved that there is one-to-one correspondence between…
We consider the categorical equivalence between crossed modules over groupoids and double groupoids with thin structures; and by this equivalence, we prove how normality and quotient concepts are related in these two categories and give…
In this paper, we will construct the injective resolution of any $\cR$-2-module, define the right derived 2-functor, and give some related properties of the derived 2-functor in ($\cR$-2-Mod).
We introduce a "deformation" of plumbing. We also define a structure of data used in a calculation by computer aid of the crosscap numbers of alternating knots.
We present an understandable, efficient, and streamlined proof of the Holonomy Decomposition for finite transformation semigroups and automata. This constructive proof closely follows the existing computational implementation. Its novelty…
The paper is devoted to study the behavior of quasitopological homotopy groups on inverse limit spaces. More precisely, we present some conditions under which the quasitopological homotopy group of an inverse limit space and especially a…