Related papers: Galois Connections for Generalized Functions and R…
In this paper, we introduce a way to generalize the Euler's gamma function as well as some related special functions. With a given polynomial in one variable $f(t)\ge 0$, we can associate a function, so-called "gamma function associated…
For a restricted class of potentials (harmonic+Gaussian potentials), we express the resolvent integral for the correlation functions of simple traces of powers of complex matrices of size $N$, in term of a determinant; this determinant is…
To generalize the notion of Galois closure for separable field extensions, we devise a notion of $G$-closure for algebras of commutative rings $R\to A$, where $A$ is locally free of rank $n$ as an $R$-module and $G$ is a subgroup of…
Starting from the Colombeau's full generalized functions, the sharp topologies and the notion of generalized points, we introduce a new kind differential calculus (for functions between totally disconnected spaces). We study generalized…
A previously established correspondence between definite-parity real functions and inner analytic functions is generalized to real functions without definite parity properties. The set of inner analytic functions that corresponds to the set…
Garret Birkhoff observed that any binary relation between two sets determines a Galois connection between the powersets, or equivalently, closure operators on the powersets, or equivalently, complete lattices of subsets that are dually…
Starting from a description of various generalized function algebras based on sequence spaces, we develop the general framework for considering linear problems with singular coefficients or non linear problems. Therefore, we prove…
Plateaued functions as an extension of bent functions play a significant role in cryptography, coding theory, sequences and combinatorics. In \cite{Mesnager9}, Mesnager \emph{et al.} introduced generalized plateaued functions in order to…
In this paper we define operations of preradicals of any abelian category. We define idempotent preradicals and radicals. We prove that every adjoint pair between abelian categories induces a Galois connection between the corresponding…
We investigate regularity properties of generalized conjugate functions induced by a general coupling function and the associated generalized proximal mapping. Our main results provide verifiable conditions ensuring local single-valuedness,…
We explore \emph{semibounded} expansions of arbitrary ordered groups; namely, expansions that do not define a field on the whole universe. We introduce the notion of a \emph{semibounded} expansion of an arbitrary ordered group, extending…
A generalised Paley map is a Cayley map for the additive group of a finite field F, with a subgroup S=-S of the multiplicative group as generating set, cyclically ordered by powers of a generator of S. We characterise these as the…
We introduce the notion of generalized function taking values in a smooth manifold into the setting of full Colombeau algebras. After deriving a number of characterization results we also introduce a corresponding concept of generalized…
For a finite group $G$ and a sufficiently large (but fixed) prime power $q$ coprime to $G$ we obtain asymptotics for the number of regular Galois extensions $L/ \mathbb{F}_q(t)$, with $\mathrm{Gal}(L/\mathbb{F}_q(t)) \cong G$, ramified at a…
We introduce a new approach to the description of multi-sorted clones (sets of $k$-tuples of operations of the same arity, closed under coordinatewise composition and containing all projection tuples) on a two-element domain. Leveraging the…
Given a finite category T, we consider the functor category [T,A], where A can in particular be any quasi-abelian category. Examples of quasi-abelian categories are given by any abelian category but also by non-exact additive categories as…
Given a densely defined and closed operator $A$ acting on a complex Hilbert space $\mathcal{H}$, we establish a one-to-one correspondence between its closed extensions and subspaces $\mathfrak{M}\subset\mathcal{D}(A^*)$, that are closed…
The present article is devoted to the generalized Salem functions, the generailed shift operator, and certain related problems. A description of further investigations of the author of this article is given.These investigations (in terms of…
By discussing several examples, the theory of generalized functional models is shown to be very natural for modeling some situations of reasoning under uncertainty. A generalized functional model is a pair (f, P) where f is a function…
For an odd prime $p$ and polynomial $P(T)$, we consider the extension $F$ of $k={\mathbb F}_p(T)$ defined by adjoining a root of $x^p+Tx-P(T)$. Such a field is a function field analogue of the number field ${\mathbb Q}(\sqrt[p]{n})$. We…