Related papers: Colombeau Algebra: A pedagogical introduction
Algebras of ultradifferentiable generalized functions are introduced. We give a microlocal analysis within these algebras related to the regularity type and the ultradifferentiable property.
The concept of monogenic functions over real alternative $\ast$-algebras has recently been introduced to unify several classical monogenic (or regular) functions theories in hypercomplex analysis, including quaternionic, octonionic, and…
We introduce Riemannian Lie algebroids as a generalization of Riemannian manifolds and we show that most of the classical tools and results known in Riemannian geometry can be stated in this setting. We give also some new results on the…
These notes are a self-contained introduction to Galois theory, designed for the student who has done a first course in abstract algebra.
We consider a class of generalized binomials emerging in fractional calculus. After establishing some general properties, we focus on a particular yet relevant case, for which we provide several ready-for-use combinatorial identities,…
In this paper, we introduce new classes of functions that extend the known classes of functions of complex variable, such as entire functions, meromorphic functions, rational functions and polynomial functions and take values in the set of…
Gendo-Frobenius algebras are a common generalisation of Frobenius algebras and of gendo-symmetric algebras. A comultiplication is constructed for gendo-Frobenius algebras, which specialises to the known comultiplications on Frobenius and on…
A field algebra is a ``non-commutative'' generalization of a vertex algebra. In this paper we develop foundations of the theory of field algebras.
In this paper, a $k$-th generalized modulus of smoothness is defined based on an asymmetric operator of generalized translation and a theorem is proved about the coincidence of class of functions defined by this modulus and a class of…
Leibniz algebras are certain generalization of Lie algebras. It is natural to generalize concepts in Lie algebras to Leibniz algebras and investigate whether the corresponding results still hold. In this paper we introduce the notion of…
Some notions of algebraic geometry can be defined for arbitrary varieties of algebras. This leads to universal algebraic geometry. The main idea of the presented theory is to consider interactions between algebra, logic and geometry in…
We introduce an asymmetric operator of generalised translation, define the generalised modulus of smoothness by its means, and obtain the direct and inverse theorems in approximation theory for it.
Combining the derivative operator with a binomial sum from the telescoping method, we establish a family of summation formulas involving generalized harmonic numbers.
The method of exhaustion is generalized to a simple formula that can be used to integrate functions under very general conditions, provided that the integral exists. Both a geometric proof (following the usual procedure for the method of…
Generalized numberings are an extension of Ershov's notion of numbering, based on partial combinatory algebra (pca) instead of the natural numbers. We study various algebraic properties of generalized numberings, relating properties of the…
Colombeau's generalized functions are used to adapt the distributional approach to singular hypersurfaces in general relativity with signature change. Equations governing the dynamics of singular hypersurface is obtained and it is shown…
This book is an introductory course to basic commutative algebra with a particular emphasis on finitely generated projective modules. We adopt the constructive point of view, with which all existence theorems have an explicit algorithmic…
This is a pedagogical review on polarized structure functions .
The aim of this paper is to show that even if the natural algebraic semantic for modal (normal) logic is modal algebra, the more general class of subordination algebras (roughly speaking, the non symmetric contact algebras) is adequate too…
We present a simple short proof of the Fundamental Theorem of Algebra, without complex analysis and with a minimal use of topology. It can be taught in a first year calculus class.