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In this paper we propose an algebraic formalization of connectors in the quantitative setting, in order to address their non-functional features in architectures of component-based systems. We firstly present a weighted Algebra of…
We discuss several seemingly assorted objects: the umbral calculus, generalised translations and associated transmutations, symbolic calculus of operators. The common framework for them is representations of the Weyl algebra of the…
Borchers and Wiesbrock have demonstrated certain results concerning the one-parameter semigroups of endomorphisms of von Neumann algebras that appear as lightlike translations in the theory of algebras of local observables. These results…
Pre-trained large language models (LLM) are starting to be widely used in many applications. In this work, we explore the use of these models in interactive machine translation (IMT) environments. In particular, we have chosen mBART…
This paper is based on three hours of lectures given by the first author in the "Focus Program on Analytic Function Spaces and their Applications" July 1 -- December 31, 2021, organized by the Fields Institute for Research in Mathematical…
Centered weighted composition operators on $L^2$-spaces are characterized. The characterization is obtained without the assumption that the operator is a product of a multiplication and a composition operator. The concept of spectrally…
We introduce the notion of a weighted $\delta$-vector of a lattice polytope. Although the definition is motivated by motivic integration, we study weighted $\delta$-vectors from a combinatorial perspective. We present a version of Ehrhart…
The aim of the present paper is, firstly we study the concepts of (m, (q_1, ..., q_d))- partial isometries on a Hilbert space, secondly, we introduce the notion of m- invertibility of tuples of operators as a natural generalization of the…
In this paper, among other things, we study those conditions under which the weighted semigroup algebra $\ell^1(S,\omega)$ is a dual Banach algebra with respect to predual $c_0(S)$. Some useful examples, illustrating the results, are also…
We study Sobolev spaces with weights in the half-space $\mathbb{R}^{N+1}_+=\{(x,y): x \in \mathbb{R}^N, y>0\}$, adapted to the singular elliptic operators \begin{equation*} \mathcal L =y^{\alpha_1}\Delta_{x}…
Let $\mathcal{X}$ be a real separable Hilbert space. Let $Q$ be a linear, self-adjoint, positive, trace class operator on $\mathcal{X}$, let $F:\mathcal{X}\rightarrow\mathcal{X}$ be a (smooth enough) function and let $\{W(t)\}_{t\geq 0}$ be…
Using {\it weighted traces} which are linear functionals of the type $$A\to tr^Q(A):=(tr(A Q^{-z})-z^{-1} tr(A Q^{-z}))_{z=0}$$ defined on the whole algebra of (classical) pseudo-differential operators (P.D.O.s) and where $Q$ is some…
The concept of a k-translatable groupoid is explored in depth. Some properties of idempotent k-translatable groupoids, left cancellative k-translatable groupoids and left unitary k-translatable groupoids are proved. Necessary and sufficient…
It is well-known that the theories of semi-vector spaces and semi-algebras -- which were not much studied over time -- are utilized/applied in Fuzzy Set Theory in order to obtain extensions of the concept of fuzzy numbers as well as to…
The purpose of this work is to transport the information from multiple randomized controlled trials to the target population where we only have the control group data. Previous works rely critically on the mean exchangeability assumption.…
We study the weak limit semigroup of an operator $T$, i.e., the set of all operators being weak limit points of the powers of $T$, in three different but related contexts: Koopman operators of measure-preserving transformations,…
In this paper we study the boundedness in weighted variable Lebesgue spaces of operators associated with the semigroup generated by the time-independent Schr\"odinger operator $\mathcal{L}=-\Delta+V$ in $\mathbb{R}^d$, where $d>2$ and the…
In this article we will study semigroupoids, and more specifically inverse semigroupoids. These are a common generalization to both inverse semigroups and groupoids, and provide a natural language on which several types of dynamical…
In this paper we study the analytic torsion and the $L^2$-torsion of compact locally symmetric manifolds. We consider the analytic torsion with respect to representations of the fundamental group which are obtained by restriction of…
We will prove that there is a direct relationship between the Poincare subgroup of translations, and the group of tetrad transformations LB1 introduced in a previous manuscript. LB1 is the group composed by SO(1; 1) plus two kinds of…