Juan Bory-Reyes

• Ph.D. (1988), Dr.Sc. (2008)
• Professor (Full) at National Polytechnic Institute

The paper deals with two second order elliptic systems of partial differential equations in Clifford analysis. They are of the form \({^\phi \!\underline{\partial }}f{^\psi \!\underline{\partial }}=0\) and \(f{^\phi \!\underline{\partial }}{^\psi \!\underline{\partial }}=0\), where \({^\phi \!\underline{\partial }}\) stands for the Dirac operator r...

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 i...

Clifford analysis offers suited framework for a unified treatment of higher-dimensional phenomena. This paper is concerned with boundary value problems for higher order Dirac operators, which are directly related to the Lamé-Navier and iterated Laplace operators. The conditioning of the problems upon the boundaries of the considered domains ensures...

El análisis de Clifford tiene muchas aplicaciones inesperadas en geometría diferencial y análisis global. Es el caso del tratamiento efectivo de las rotaciones en espacios euclidianos de alta dimensión mediante los grupos espinoriales, uno de los cuales es el grupo de Lorentz de la relatividad especial. En el presente estudio se aborda la reconstru...

This paper introduce a fractional-fractal $\psi$-Fueter operator in the quaternionic context inspired in the concepts of proportional fractional derivative and Hausdorff derivative of a function with respect to a fractal measure. Moreover, we establish the corresponding Stokes and Borel-Pompeiu formulas associated to this generalized fractional-fra...

The study of ψ−hyperholomorphic functions defined on domains in R4 with values in H, namely null-solutions of the ψ−Fueter operator, is a topic which captured great interest in quaternionic analysis. In the setting of (q,q′)−calculus, also known as post quantum calculus, we introduce a deformation of the ψ−Fueter operator written in terms of suitab...

Based on the Riemann-Liouville derivatives with respect to functions taking values in the set of hyperbolic numbers, we consider a new bicomplex proportional fractional (ϑ, φ)-weighted Cauchy-Riemann operator, involving orthogonal bicomplex functions as weights, and its associated fractional Borel-Pompeiu formula is proved as the main result.

The goal of the talk is to present a brief review of results on the homogeneous Riemann boundary value problem for analytic functions with very general boundary data

This work presents the basic elements and results of a Clifford algebra valued fractional slice monogenic functions theory defined from the null-solutions of a suitably fractional Cauchy-Riemann operator in the Riemann-Liouville and Caputo sense with respect to a pair of real valued functions on certain domains of Euclidean spaces.

The transition toward the new technological paradigm in production systems resulting from Industry 4.0 (hereinafter I4.0) pursues, among its main objectives, greater operational efficiency and productivity, a greater scope of automation, customization, and flexibility in production, an increase in man–machine interaction, and the creation of more c...

The purpose of this paper is to combine the (q,q′)$$ \left(q,{q}^{\prime}\right) $$‐calculus in the quaternionic context, which is proposed via two kinds of (q,q′)$$ \left(q,{q}^{\prime}\right) $$‐operators, with the theory of slice regular functions. Specifically, we shall work in suitable subclasses of slice regular functions in which the (q,q′)$...

In this paper we derive Lieb-Thirring estimates for eigenvalues of Dirichlet Laplacians below the threshold of the essential spectrum on asymptotically Archimedean spiral-shaped regions.

We consider the magnetic Schrödinger operator H=(i∇+A)2-V\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H=(i \nabla +A)^2- V$$\end{document} with a non-negative potent...

The accelerated evolution of technology in the last decade has enabled breakthroughs in fields of science such as medicine, robotics, bionics and rehabilitation by integrating knowledge and techniques from these areas. Rehabilitation exoskeletons are examples of multidisciplinary integration in the development of physiotherapeutic intervention tool...

Clifford analysis, using Clifford algebras named after the British mathematician and philosopher William Kingdon Clifford (4 May 1845 – 3 March 1879), is the study of Dirac operators in analysis and geometry, together with their applications. This intrinsically multidimensional function theory, constitutes a generalization of the theory of holomorp...

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...

In this paper, we study existence of solutions to the scalar additive Jump problem and the Riemann boundary value problems in the context of vectorial Clifford analysis on domains with fractal boundaries. A reduction procedure is applied with great effectiveness to find the solution of the problems.

Several new network information dimension definitions have been proposed in recent decades, expanding the scope of applicability of this seminal tool. This paper proposes a new definition based on Deng entropy and d-summability (a concept from geometric measure theory). We will prove to what extent the new formulation will be useful in the theoreti...

The study of $\psi-$hyperholomorphic functions defined on domains in $\mathbb R^4$ with values in $\mathbb H$, namely null-solutions of the $\psi-$Fueter operator, where $\psi$ denotes a structural set, is a topic which captured great interest in quaternionic analysis. This class of functions is more general than that of Fueter regular functions. A...

The study of ψ−hyperholomorphic functions defined on domains in R 4 with values in H, namely null-solutions of the ψ−Fueter operator, is a topic which captured great interest in quaternionic analysis. This class of functions is more general than that of Fueter regular functions. In the setting of (q, q ′)−calculus, also known as post quantum calcul...

Clifford analysis offers suited framework for a unified treatment of higher-dimensional phenomena. This paper is concerned with boundary value problems for higher order Dirac operators, which are directly related to the Lamé-Navier and iterated Laplace operators. The conditioning of the problems upon the boundaries of the considered domains ensures...

In this paper, we study the existence of solutions to the scalar additive Jump problem and the Riemann boundary value problems in the context of vectorial Clifford analysis on domains with fractal boundaries. A reduction procedure is applied with great effectiveness to find the solution of the problems.

The theory of slice regular functions of a quaternionic variable on the unit ball of the quaternions was introduced by Gentili and Struppa in 2006 and nowadays it is a well established function theory, especially in view of its applications to operator theory. In this paper, we introduce the notion of fractional slice regular functions of a quatern...

The main goal of this paper is to construct a proportional analogues of the quaternionic fractional Fueter-type operator recently introduced in the literature. We start by establishing a quaternionic version of the well-known proportional fractional integral and derivative with respect to a real-valued function via the Riemann-Liouville fractional...

The transition toward the new technological paradigm in production systems resulting from Industry 4.0 (hereinafter I4.0) pursues, among its main objectives, greater operational efficiency and productivity, a greater scope of automation, customization, and flexibility in production, an increase in man-machine interaction, and the creation of more c...

This article introduces a new fractional approach to the concept of information dimensions in complex networks based on the (q,q′)-entropy proposed in the literature. The q parameter measures how far the number of sub-systems (for a given size ε) is from the mean number of overall sizes, whereas q′ (the interaction index) measures when the interact...

This article introduces a new fractional approach to the concept of information dimension of complex networks, based on a (q,q′)-entropy proposed in the literature. The q parameter measures how far is the number of subsystems (for a given size ε) from the mean number of overall sizes. The q′ (interaction index) measures when the interactions betwee...

En esta presentación se exponen los resultados obtenidos del estudio de problemas de frontera, bien planteados en el sentido de Hadamard, para el operador sándwich en el Análisis de Clifford. Además, se muestra cómo dichos problemas se comportan mal planteados si consideramos operadores de Dirac construidos con bases ortonormales distintas a la est...

Several new network information dimension definitions have been proposed in recent decades, expanding the scope of applicability of this seminal tool. This paper proposes a new definition based on Deng entropy and d-summability (a concept from geometric measure theory). We will prove to what extent the new formulation will be useful in the theoreti...

Based on the Riemann-Liouville derivatives with respect to functions taking values in the set of hyperbolic numbers, we consider a novel bicomplex proportional fractional (ϑ, ϕ)−weighted Cauchy-Riemann operator, involving weights hyperbolic orthogonal bicomplex functions. This operator is defined for the first time here, and its associated fraction...

We consider the magnetic Schrödinger operator H = (i∇ + 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 := 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 suffic...

We prove an analog of the quaternionic Borel-Pompieu formula in the sense of proportional fractional ψ-Cauchy-Riemann operators via Riemann-Liouville derivative with respect to another function.

We prove an analog of the quaternionic Borel-Pompieu formula in the sense of proportional fractional $\psi$-Cauchy-Riemann operators via Riemann-Liouville derivative with respect to another function.

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...

The theory of slice regular functions of a quaternionic variable on the unit ball of the quaternions was introduced by Gentili and Struppa in 2006 and nowadays it is a well established function theory, especially in view of its applications to operator theory. In this paper, we introduce the notion of fractional slice regular functions of a quatern...

Let $\Omega\subset\R^m$ be a bounded regular domain, let $\pux$ the standard Dirac operator in $\R^m$ and let $\R_{0,m}$ be the Clifford algebra constructed over the quadratic space $\R^{0,m}$. For $k\in \{1,\dots, m\}$ fixed, $\R^{(k)}_{0,m}$ denotes the space of $k-$vectors in $\R_{0,m}$. In the framework of Clifford analysis we consider two bo...

The purpose of this paper is to establish a Borel-Pompeiu type formula induced from a fractional bicomplex $(\vartheta,\varphi)-$weighted Cauchy-Riemann operator, where the weights are two hyperbolic orthogonal bicomplex functions and the fractionality is understand in the sense of Riemann-Liouville and Caputo approaches.

Se hace un breve recorrido por la trayectoria de vida de un matemático cubano

In this paper we provided a classification for partitions of intervals on the hyper-bolic 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 i...

Quaternionic analysis is a branch of classical analysis referring to different generalizations of the Cauchy-Riemann equations to the quaternion skew field H context. In this work we deals with H-valued (θ,u)-hyperholomorphic functions related to elements of the kernel of the Helmholtz operator with a parameter u∈H, just in the same way as the usua...

We first prove a Cauchy’s integral theorem and a Cauchy-type formula for certain inhomogeneous Cimmino system from quaternionic analysis perspective. The second part of the paper directs the attention towards some applications of the mentioned results, dealing in particular with four kinds of weighted Bergman spaces, reproducing kernels, projection...

In this paper, we combine the fractional 𝜓−hyperholomorphic function theory with the fractional calculus with respect to another function. As amain result, a fractional Borel–Pompeiu type formula related to a fractional 𝜓−Fueter operator with respect to a vector-valued function is proved.

We give some characterizations of Lipschitz type spaces of slice regular functions in the unit ball of the skew field of quaternions with prescribed modulus of continuity.

We give some characterizations of Lipschitz type spaces of slice regular functions in the unit ball of the skew field of quaternions with prescribed modulus of continuity.

We first prove a Cauchy's integral theorem and Cauchy type formula for certain inhomogeneous Cimmino system from quaternionic analysis perspective. The second part of the paper directs the attention towards some applications of the mentioned results, dealing in particular with four kinds of weighted Bergman spaces, reproducing kernels, projection a...

The quantification of learning acquisition in a blended and online course is still slightly explored from the complex systems lens. The fractional online learning rate (fOLR) using fractional integrals is introduced. The notion of fOLR is based on the nonlinearity of the individual students learning pathway network, built from Learning Management S...

The purpose of this paper is to establish a Borel-Pompeiu type formula induced from a fractional bicomplex $(\vartheta,\varphi)-$weighted Cauchy-Riemann operator, where the weights are two hyperbolic orthogonal bicomplex functions and the fractionality is understand in the Riemann-Liouville sense.

In this paper we combine the fractional $\psi-$hyperholomorphic function theory with the fractional calculus with respect to another function. As a main result, a fractional Borel-Pompeiu type formula related to a fractional $\psi-$Fueter operator with respect to a vector-valued function, is proved.

The purpose of this paper is to solve a kind of the Riemann–Hilbert boundary value problem for ( φ , ψ ) {(\varphi,\psi)} -harmonic functions, which are linked with the use of two orthogonal bases of the Euclidean space ℝ m {\mathbb{R}^{m}} . We approach this problem using the language of Clifford analysis for obtaining an explicit expression of th...

This paper is a continuation of our work [J. O. González Cervantes and J. Bory Reyes, A quaternionic fractional Borel–Pompeiu type formula, Fractal 30(1) (2022) 2250013], where we introduced a fractional operator calculus related to a fractional [Formula: see text]-Fueter operator in the one-dimensional Riemann–Liouville derivative sense in each di...

En esta plática se habla de la extensión de sistemas de funciones iteradas a espacios métricos hiperbólico valuados, así como su aplicación sobre una versión del juego del caos con probabilidades sobre el plano hiperbólico.

In this paper we present a hyperholomorphic (associated to the Helmholtz equation) approach to the Riemann-Hilbert boundary value problem (RHBVP for short) in domains of ${\mathbb R}^2$ with h-summable boundaries. We apply our results to Maxwell’s system and study an electromagnetic RHBVP for the case time-harmonic. The study is based on a reformul...

Decision trees are decision support data mining tools that create, as the name suggests, a tree-like model. The classical C4.5 decision tree, based on the Shannon entropy, is a simple algorithm to calculate the gain ratio and then split the attributes based on this entropy measure. Tsallis and Renyi entropies (instead of Shannon) can be employed to...

In theoretical setting, associated with a fractional $\psi-$Fueter operator that depends on an additional vector of complex parameters with fractional real parts, this paper establishes a fractional analogue of Borel-Pompeiu formula as a first step to develop a fractional $\psi-$hyperholomorphic function theory and the related operator calculus.

In this work, we introduce a fractional generalization of the classical Moisil-Teodorescu operator that provides a concise notation for presenting a mathematical formulation of physical systems in fractional space from various branches of science and engineering. The method used in this article, called the Stillinger’s formalism, is combined in a n...

Euclidean Clifford analysis has become a well-established theory of monogenic functions in higher-dimensional Euclidean space with a variety of applications both inside and outside of mathematics. Noncommutativity of the geometric product in Clifford algebras leads to what are now known as inframonogenic functions, which are characterized by certai...

The history of Bergman spaces goes back to the book [4] in the early fifties by S. Bergman, where the first systematic treatment of the subject was given, and since then there have been a lot of papers devoted to this area. Some standard works here are [5], [8], [16], [29] and the references therein, which contain a broad summary and historical not...

RESUMEN En el presente artículo se estudian las ecuaciones de ondas electromagnéticas y la condición de Lorentz, como propiedades emergentes del sistema de Maxwell en el contexto de la Teoría de Sistemas. Para este fin, se deducen las ecuaciones de ondas y la ecuación de Helmholtz. Haciendo uso del operador de Dirac desplazado y su estrecha relació...

In this note we establish a necessary and sufficient condition for solvability of the homogeneous Riemann boundary problem with infinity index on a rectifiable open curve. The index of the problem we deal with considers the influence of the requirement of the solutions of the problem, the degree of non-smoothness of the curve at the endpoints as we...

The current COVID-19 pandemic mainly affects the upper respiratory tract. People with COVID-19 report a wide range of symptoms, some of which are similar to those of common flu, such as sore throat and rhinorrhea. Additionally, COVID-19 share many clinical symptoms with severe pneumonia, including fever, fatigue, dry cough, and respiratory distress...

We present a brief review of results on the homogeneous Riemann boundary value problem for analytic functions with very general boundary data.

SEMINARIO ABIERTO ESIME ZACATENCO

In this paper, we aim to discuss the Noether property of the Riemann boundary value problems in a Banach algebra of continuous functions over simple closed curves and its direct approximate solution through approximation of the principal coefficient, establishing a bound for the error of approximate solution of the problem to the exact solution.

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 operator...

In this paper, we define two types of partitions of an hyperbolic interval: weak and strong. Strong partitions enables us to define, in a natural way, a notion of hyperbolic valued functions of bounded variation and hyperbolic analogue of Riemann-Stieltjes integral. We prove a deep relation between both concepts like it occurs in the context of rea...

Quaternionic analysis offers a function theory focused on the concept of $\psi-$hyperholomorphic functions defined as null solutions of the $\psi-$Fueter operator, where $\psi$ is an arbitrary orthogonal base (called structural set) of $\mathbb H^4$. The main goal of the present paper is to extend the results given in \cite{BG2}, where a fractional...

The present paper is a continuation of our work [11], where we introduced a fractional operator calculus related to a fractional ${\psi}-$Fueter operator in the one-dimensional Riemann-Liouville derivative sense in each direction of the quaternionic structure, that depends on an additional vector of complex parameters with fractional real parts. Th...

Quaternionic analysis is regarded as a broadly accepted branch of classical analysis referring to many different types of extensions of the Cauchy-Riemann equations to the quaternion skew field $\mathbb H$. In this work we deals with a well-known $(\theta, u)-$hyperholomorphic $\mathbb H-$valued functions class related to elements of the kernel of...

Quaternionic analysis relies heavily on results on functions defined on domains in $\mathbb R^4$ (or $\mathbb R^3$) with values in $\mathbb H$. This theory is centered around the concept of $\psi-$hyperholomorphic functions i.e., null-solutions of the $\psi-$Fueter operator related to a so-called structural set $\psi$ of $\mathbb H^4$. Fractional c...

This paper aims at proving the boundedness property of multidimensional singular integral operators associated with \((\varphi ,\psi )\)-harmonic functions, which are connected by the use of two orthogonal basis of the Euclidean space \({{\mathbb {R}}}^m\). Besides, necessary and sufficient conditions for the solvability of the \({\overline{\partia...

We consider the behavior of generalized Laplacian vector fields on a Jordan domain of R3 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 c...

In this paper, based on a proposed notion of generalized conjugate harmonic pairs in the framework of complex Clifford analysis, necessary and sufficient conditions for the solvability of inhomogeneous perturbed generalized Moisil–Teodorescu systems in higher dimensional Euclidean spaces are proved. As an application, we derive corresponding solvab...

In the present work we obtain some analogues of the Hilbert formulas on the unit circle for iterated Cauchy-Riemann operator in one-dimensional complex analysis involving higher order Lipschitz classes. Furthermore, a Poincaré-Bertrand formula related to the corresponding singular iterated Cauchy integral over the boundary of a smoothly bounded dom...

A two-parameter (namely, \vec{\alpha} and \vec{\beta}) fractional Tsallis information dimensions of complex networks based on q−logarithm is introduced. The meanings assigned to such parameters are the quantification of the interaction among the elements (nodes) that are part of the same sub-system (sub-network) and the interaction among the sub-sy...

In this paper, we mainly consider the Riemann boundary value problems for lower dimensional non-commutative Clifford algebras valued monogenic functions. The solutions are given in an explicit way and concrete examples are presented to illustrate the results.

In this paper, we shall be interested in solving Dirichlet-type problems for solutions of certain classes of Beltrami equations, to be called β-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-...

It is generally well understood the legitimate action of the Moisil-Theodoresco operator, over a quaternionic valued function defined on $\mathbb{R}^3$ (sum of a scalar and a vector field) in Cartesian coordinates, but it does not so in any orthogonal curvilinear coordinate system. This paper sheds some new light on the technical aspect of the subj...

In this article, a new algorithm to select the relevant nodes —those that maintain the cohesion of the network— of the complex network is presented. The result shows that the proposed approach outperforms degree, PageRank and betweenness in most of the several real complex networks. The rationale of the algorithm is to discover the self-similarity...

In this paper, we provide extensions to hyperbolic numbers plane of the classical Chaos game algorithm and the Shannon entropy. Both notions connected with that of probability with values in hyperbolic number, introduced by Alpay et al. [Kolmogorov’s axioms for probabilities with values in hyperbolic numbers, Adv. Appl. Clifford Algebras 27(2) (201...

The paper provides integral representations for solutions to a certain first order partial differential equation natural arising in the factorization of the Lame-Navier system with the help of Clifford analysis techniques. These representations look like in spirit to the Borel–Pompeiu and Cauchy integral formulas both in three and higher dimensiona...

In this article, new information dimensions of complex networks are introduced underpinned by fractional order entropies proposed in the literature. This fractional approach of the concept of information dimension is applied to several real and synthetic complex networks, and the achieved results are analyzed and compared with the corresponding one...

The classical and modified equations of Kolmogorov-Johnson-Mehl-Avrami are compared with the equations of conventional Gompertz and Montijano-Bergues-Bory-Gompertz, in the frame of growth kinetics of tumors. For this, different analytical and numerical criteria are used to demonstrate the similarity between them, in particular the distance of Hausd...

In the present work we obtain some analogues of the Hilbert formulas on the unit circle and on the upper half-plane for the theory of solutions of a special case of the Beltrami equation in C to be referred as β-analytic functions. Furthermore, a Poincaré–Bertrand formula related to the β-Cauchy singular integral over a closed Jordan curve is deriv...

The Moisil‐Teodorescu operator is considered to be a good analogue of the usual Cauchy–Riemann operator of complex analysis in the framework of quaternionic analysis and it is a square root of the scalar Laplace operator in $\mathbb{R}^3$. In the present work, a general quaternionic structure is developed for the local fractional Moisil–Teodorescu...

We construct new examples of parametric iterated function systems converging to some fractal shapes. The main goal is the study of the continuous growth and the rate of change of the attractor of the corresponding parametrization.

The purpose of this paper is to solve a kind of Riemann-Hilbert boundary value problem for $(\varphi,\psi)$-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 pro...

In this paper, general quaternionic structure are developed for the local fractional Moisil-Teodorescu operator in Cantor-type cylindrical and spherical coordinate systems. Two examples for the Helmholtz equation with local fractional derivatives on the Cantor sets are shown by making use of this local fractional Moisil-Teodorescu operator.

In this paper we derive a Cauchy integral representation formula for the solutions of the iterated sandwich equation \(\partial _{{\underline{x}}}^{2k-1}f\partial _{{\underline{x}}}=0\), where k is a positive integer and \(\partial _{{\underline{x}}}\) stands for the Dirac operator in the Euclidean space \({{\mathbb {R}}}^m\). We call these solutio...

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 H\"older continuous vector field on the...

We investigate an electromagnetic Dirichlet type problem for the 2D quaternionic time-harmonic Maxwell system over a great generality of fractal closed type curves, which bound Jordan domains in R2. The study deals with a novel approach of h-summability condition for the curves, which would be extremely irregular and deserve to be considered fracta...

In this paper we consider the problem of reconstructing solutions to a generalized Moisil–Teodorescu system in Jordan domains of R3 with rectifiable boundary. In order to determine conditions for existence of solutions to the problem we embed the system in an appropriate generalized quaternionic setting.

In this paper we consider the problem of reconstructing solutions to a generalized Moisil–Teodorescu system in Jordan domains of R3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{...

In this work, we propose a biquaternionic reformulation of a fractional monochromatic Maxwell system. Additionally, some examples are given to illustrate how the quaternionic fractional approach emerges in linear hydrodynamics and elasticity.

In this article, a box-covering Tsallis information dimension is introduced, and the physical interpretation of this new dimension has been assigned. Moreover, based on the introduced parameter q , a characterization of non-extensive networks is stated, allowing the classification according to super-extensive (q ≺ 1), sub-extensive (q 1) or extensi...

In this paper, based on a proposed notion of generalized conjugate harmonic pairs in the framework of complex Clifford analysis, necessary and sufficient conditions for the solvability of inhomogeneous perturbed generalized Moisil-Teodorescu systems in higher dimensional Euclidean spaces are proved. As an application, we derive corresponding solvab...