Related papers: On analysis in algebras and modules
We extend the framework of abstract algebraic logic to weak logics, namely logical systems which are not necessarily closed under uniform substitution. We interpret weak logics by algebras expanded with an additional predicate and we…
A method of solving Maxwell equations in a vicinity of a multipole particle (moving along an arbitrary trajectory) is proposed. The method is based on a geometric construction of a trajectory-adapted coordinate system, which simplifies…
This is a survey on recent progress in algebraic deformation theory and the application of algebraic operads to its study. We review the classical homotopical tools in the theory of algebraic operads, namely Koszul duality. We give concrete…
We show that the general method of Lie algebra expansions can be applied to re-construct several algebras and related actions for non-relativistic gravity that have occurred in the recent literature. We explain the method and illustrate its…
We consider Hilbert algebras with a supplementary Fr\'echet topology and get various extensions of the algebraic structure by using duality techniques. In particular we obtain optimal multiplier-type involutive algebras, which in…
This paper gives an overview of some basic properties of Leibniz algebras. Some of the results were known earlier, but in the article they are accompanied by new simple proofs. Some of the results are new. The article can be viewed as a…
In this paper we aim to generalize results obtained in the framework of fractional calculus by the way of reformulating them in terms of operator theory. In its own turn, the achieved generalization allows us to spread the obtained…
The purpose of this article is to discuss recent advances in the growing field of phase retrieval, and to publicize open problems that we believe will be of interest to mathematicians in general, and algebraists in particular.
Fundamentals on Lie group methods and applications to differential equations are surveyed. Many examples are included to elucidate their extensive applicability for analytically solving both ordinary and partial differential equations.
Extended formulations are an important tool to obtain small (even compact) formulations of polytopes by representing them as projections of higher dimensional ones. It is an important question whether a polytope admits a small extended…
We present a restricted version of some affine Jacobi's residue formula (on an affine algebraic variety) with applications to higher dimensional (and affine) analogues of Wood's (or Reiss's) relations about the interpolation of pieces of…
In this paper, an open problem in the multidimensional complex analysis is pesented that arises in the investigation of the regularity properties of Fourier integral operators and in the regularity theory for hyperbolic partial differential…
An extended summary of the lecture course given at the V School on Geometry and Physics, Bia\l owe\.za 2016, in which an algebraic approach to differentiation and integration that is characteristic for non-commutative geometry is described.
This work proposes an algebraic model for classical information theory. We first give an algebraic model of probability theory. Information theoretic constructs are based on this model. In addition to theoretical insights provided by our…
This paper is meant to be a short review and summary of recent results on the structure of finite and affine classical W-algebras, and the application of the latter to the theory of generalized Drinfeld-Sokolov hierarchies.
We discuss the general method of Grushin problems, closely related to Shur complements, Feshbach projections and effective Hamiltonians, and describe various appearances in spectral theory, pdes, mathematical physics and numerical problems.
We Study versions of Cauchy formula in more general algebras than the complex case.
We provide a mathematical theory and methodology for synthesising equational logics from algebraic metatheories. We illustrate our methodology by means of two applications: a rational reconstruction of Birkhoff's Equational Logic and a new…
The aim of this text is to provide a linguistically accessible, but comprehensive introduction into a variety of topics in dynamical systems and its applications. Whilst preliminary knowledge of dynamical systems is useful, it is not…
This book deals with the theory of generalized algebraic transformations, which is elaborated with the aim to provide a relatively simple theoretical tool that enables an exact treatment of diverse more complex lattice-statistical models.…