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In this paper, we generalize the arithmetic functions $\tau$ and $\tau^{\left(e\right)}$ in algebraic number fields and we find some properties of these functions.
Discrete convex functions are used in many areas, including operations research, discrete-event systems, game theory, and economics. The objective of this paper is to offer a survey on fundamental operations for various kinds of discrete…
This paper is devoted to conditions defined in terms of the generalized shift operator for a rational number to be representable by certain positive generalizations of $q$-ary expansions.
We consider functional equations (Cauchy's, Abel's and some other functional equations) and show that to find general solution of these equations is equivalent to establish that a space-transformation of a Brownian Motion by suitable…
We introduce a natural generalization of a well studied integration operator acting on the family of Hardy spaces in the unit disc. We study the boundedness and compactness properties of the operator and finally we use these results to give…
An elementary introduction to functional methods and the Schwinger-Dyson equations is presented. Emphasis is placed on practical topics not normally covered in textbooks, such as a diagrammatic method for generating equations at high order,…
We present a detailed synthetic overview of the utilisation of categorical techniques in the study of order structures together with their applications in operational quantum theory. First, after reviewing the notion of residuation and its…
In this paper we presents further developments regarding the enrichment of the basic Theory of Order Completion. In particular, spaces of generalized functions are constructed that contain generalized solutions to all systems of continuous,…
New perspectives, proofs, and some extensions of known results are presented concerning the behavior of the Fitzpatrick function of a monotone type operator in the general context of a locally convex space.
This article is meant to give a lucid and widely accessible, self-contained account of a novel way of performing arithmetic operations on fuzzy intervals. Based on two formulae of generalized inversion (the first in close analogy to the…
We will generalize the concept of aggregation function for mathematical structures as a certain function between quantales. In fact, these functions turn to be exactly the lax morphism of quantales. This provides a global framework for the…
We model generalized harmonic functions on rings of differential operators and complex function spaces. The differential operators in the second Weyl-algebra that commute with rotations are described and leads to a natural notion for such…
The main aim of this paper is to describe the most adequate generalization of the Cauchy-Riemann system fixing properties of classical functions in octonionic case. An octonionic generalization of the Laplace transform is introduced.…
We develop elements of a general dilation theory for operator-valued measures and bounded linear maps between operator algebras that are not necessarily completely-bounded. We prove our main results by extending and generalizing some known…
A general type of ray class fields of global function fields is investigated. The systematic computation of their genera leads to new examples of curves over finite fields with comparatively many rational points.
In this paper we first introduce the Heron and Heinz means of two convex functionals. Afterwards, some inequalities involving these functional means are investigated. The operator versions of our theoretical functional results are…
Some solutions of the Heavenly equations and their generalizations are considered
We investigate extended processes given by last-passage times in directed models defined using exponential variables with decaying mean. In certain cases we find the universal Airy process, but other cases lead to non-universal and trivial…
This tutorial paper presents a survey of results, both classical and new, linking inner functions and operator theory. Topics discussed include invariant subspaces, universal operators, Hankel and Toeplitz operators, model spaces, truncated…
We present several aspects of the "topology of meromorphic functions", which we conceive as a general theory which includes the topology of holomorphic functions, the topology of pencils on quasi-projective spaces and the topology of…