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Juan Bory Reyes

Publications and source records attributed to Juan Bory Reyes.

13 recordsLinked to original sources
arXiv2026

Lesche stability of the Shannon strong hyperbolic entropy and some hyperbolic extensions

In recent decades, several definitions of new entropy measures have been proposed, which expands the range of applications for this important tool. The present work focuses on the extension of the classical Shannon entropy to the hyperbolic number plane $\mathbb{D}$ with the notion of valued hyperbolic probability. It is shown that the Shannon strong hyperbolic entropy over a discrete hyperbolic probability distribution $(ρ_{1}, \ldots,ρ_{N})$ can be established by the action of the hyperbolic derivative on the generating function $\sum_{s=1}^{N}ρ_{s}^{-ξ}$ with respect to the hyperbolic variable $ξ$ and then we tend $ξ$ to $-1_{\mathbb{D}}$. Furthermore, we prove that this hyperbolic extension possesses the Lesche stability property, also known as experimental robustness. Finally, we present some results on the hyperbolic extension of the Rényi entropy and hyperbolic extropy.

math.DS↗
arXiv2026

Revisiting Fischer decompositions by inframonogenic functions

We explore Fischer decompositions from the perspective of inframonogenic functions in Clifford analysis, a non-commutative version of harmonic functions in Euclidean spaces. We study decomposition formulas for polynomial spaces involving inframonogenic and harmonic components, providing fresh insights into their algebraic structures and further important applications.

math.CV↗
arXiv2023

Magnetic Schrödinger operator with the potential supported in a curved two-dimensional strip

We consider the magnetic Schrödinger operator $H=(i \nabla +A)^2- V$ with a non-negative potential $V$ supported over a strip which is a local deformation of a straight one, and the magnetic field $B:=\mathrm{rot}(A)$ is assumed to be nonzero and local. We show that the magnetic field does not change the essential spectrum of this system, and investigate a sufficient condition for the discrete spectrum of $H$ to be empty.

math.SP↗
arXiv2023

A higher Dimensional Marcinkiewicz Exponent and the Riemann Boundary Value Problems for Polymonogenic Functions on Fractals Domains

We use a high-dimensional version of the Marcinkiewicz exponent, a metric characteristic for non-rectifiable plane curves, to present a direct application to the solution of some kind of Riemann boundary value problems on fractal domains of Euclidean space $\mathbb{R}^{n+1}, n\geq2$ for Clifford algebra-valued polymonogenic functions with boundary data in classes of higher order Lipschitz functions. Sufficient conditions to guarantee the existence and uniqueness of solution to the problems are proved. To illustrate the delicate nature of this theory we described a class of hypersurfaces where the results are more refined than those that exist in literature.

math.CV↗
arXiv2023

On the Notion of a Function of Bounded Variation and of Riemann-Stieltjes Integral with Strong Partitions on Hyperbolic Intervals

In this paper we provided a classification for partitions of intervals on the hyperbolic plane. Given a partition, to be named strong, we define a notion of a hyperbolic-valued functions of bounded variation and a kind of Riemann-Stieltjes integral. A condition relating to both concepts appears to be natural for the existence of the integral, as it occurs in real analysis.

math.CV↗
arXiv2021

Generalized Laplacian decomposition of vector fields on fractal surfaces

We consider the behavior of generalized Laplacian vector fields on a Jordan domain of $\mathbb{R}^{3}$ with fractal boundary. Our approach is based on properties of the Teodorescu transform and suitable extension of the vector fields. Specifically, the present article addresses the decomposition problem of a Hölder continuous vector field on the boundary (also called reconstruction problem) into the sum of two generalized Laplacian vector fields in the domain and in the complement of its closure, respectively. In addition, conditions on a Hölder continuous vector field on the boundary to be the trace of a generalized Laplacian vector field in the domain are also established.

math.CV↗
arXiv2020

Condición de Lorentz y ecuaciones de ondas electromagnéticas como propiedades emergentes del sistema de Maxwell

This article deals with the study of electromagnetic waves equations and the Lorentz condition, as emergent properties of Maxwell's system in the context of systems theory. To do this, the wave equations and the Helmholtz equation are first deduced. Using the displaced Dirac operator, which is closely related to the main vector calculation operators, it is possible to establish a direct connection between the solutions of the Maxwell time-harmonic system and two quaternion equations. Also, the application of the Lorentz condition to transform the time-harmonic Maxwell system into a simple quaternion equation based on the scalar and vector potentials is exposed.

physics.class-ph↗
arXiv2020

On a Riemann-Hilbert boundary value problem for $(φ,ψ)$-harmonic functions in $\mathbb{R}^m$

The purpose of this paper is to solve a kind of Riemann-Hilbert boundary value problem for $(φ,ψ)$-harmonic functions, which are linked with the use of two orthogonal basis of the Euclidean space $\mathbb{R}^m$. We approach this problem using the language of Clifford analysis for obtaining the explicit expression of the solution of the problem in a Jordan domain $Ω\subset\mathbb{R}^m$ with fractal boundary. One of the remarkable feature in this study is that the boundary data involves higher order Lipschitz class of functions.

math.AP↗
arXiv2018

Bochner-Martinelli formula in superspace

In a series of recent papers, a harmonic and hypercomplex function theory in superspace has been established and amply developed. In this paper, we address the problem of establishing Cauchy integral formulae in the framework of Hermitian Clifford analysis in superspace. This allows us to obtain a successful extension of the classical Bochner-Martinelli formula to superspace by means of the corresponding projections on the space of spinor-valued superfunctions.

math.CV↗