Related papers: The Fundamental Theorems in the framework of Bicom…
Tate cohomology has been generalised by several authors using different constructions that have applications in group theory, ring theory and homotopical algebra. Therefore, there is a need for a uniform account that explains why their…
This paper begins the study of infinite-dimensional modules defined on bicomplex numbers. It generalizes a number of results obtained with finite-dimensional bicomplex modules. The central concept introduced is the one of a bicomplex…
The module theorem by Janhunen et al. demonstrates how to provide a modular structure in answer set programming, where each module has a well-defined input/output interface which can be used to establish the compositionality of answer sets.…
In this paper we study codes where the alphabet is a finite Frobenius bimodule over a finite ring. We discuss the extension property for various weight functions. Employing an entirely character-theoretic approach and a duality theory for…
Let $H$ be a Hopf group coalgebra with a bijective antipode and $A$ an $H$-comodule Poisson algebra. In this paper, we mainly generalize the fundamental theorem of Poisson Hopf modules to the case of Hopf group coalgebras.
This paper introduces semiopen and semiclosed soft sets in soft topological spaces. The notions of interior and closure are generalized using these sets. A detail study is carried out on properties of semiopen, semiclosed soft sets, semi…
We study the $2$-categories BIon, of (generalized) bounded ionads, and $\text{Acc}_\omega$, of accessible categories with directed colimits, as an abstract framework to approach formal model theory. We relate them to topoi and (lex)…
This paper introduces a novel approach to multi-parameter persistence using 2-categorical structures. We develop a framework that captures hierarchical interactions between filter parameters, overcoming fundamental limitations of…
We present an application of the basic mathematical concept of complex functions as topological solitons, a most interesting area of research in physics. Such application of complex theory is virtually unknown outside the community of…
This article is meant as a gentle introduction to the "topological terms" that often play a decisive role in effective theories describing topological quantum effects in condensed matter systems. We first take up several prominent examples,…
The purpose of this paper is to introduce basic concepts that are fundamental in the examination of composite moduli, while avoiding the notoriously difficult problem of prime-factorization. We introduce a new class of numbers, called…
Following Eilenberg-Steenrod axiomatic approach we construct the universal ordinary homology theory for any homological structure on a given category by representing ordinary theories with values in abelian categories. For a convenient…
We study the parametrizations of simple modules provided by the theory of basic sets for all finite Weyl groups. In the case of type B, we show the existence of basic sets for the matrices of constructible representations. Then we study…
An algebraic deformation theory of module-algebras over a bialgebra is constructed. The cases of module-coalgebras, comodule-algebras, and comodule-coalgebras are also considered.
Evaluation of basic integrals over Gaussian functions, traditionally utilized for electronic structure computations on molecules and solids, is discussed in a pedagogical form.
We give some functorial characterizations of flat strict Mittag-Leffler modules. We characterize reflexive functors of modules with similar tools, definitions and theorems.
We establish some cohomological bounds in D-module theory that are known in the holonomic case and folklore in general. The method rests on a generalization of the b-function lemma for non-holonomic D-modules.
Functional integrals are defined in terms of locally compact topological groups and their associated Banach-valued Haar integrals. This approach generalizes the functional integral scheme of Cartier and DeWitt-Morette. The definition allows…
Basic pairs and their morphisms are the most elementary framework in which standard topological notions can be defined. We present here a new interpretation of topological concepts as those which can be communicated faithfully between the…
A complex-analytic structure within the unit disk of the complex plane is presented. It can be used to represent and analyze a large class of real functions. It is shown that any integrable real function can be obtained by means of the…