arXiv subjects

Jayme Vaz

Publications and source records attributed to Jayme Vaz.

7 recordsLinked to original sources

arXiv2026

A Generalization of the Fox H-function

In this paper we present a generalization of the Fox H-function called Fox-Barnes J-function. Like the Fox H-function, it is defined as a contour integral in the complex plane, but instead of an integrand given by a ratio of products of gamma functions involving several parameters, we use a ratio of products of double gamma functions. We study the conditions for its existence and how to choose a contour of integration based on the involved parameters. We discuss how the Fox H-function appears as a particular case and prove some properties of the Fox-Barnes J-function. As an application, we show how the Laplace transform of the Kilbas-Saigo function can be conveniently written in terms of the Fox-Barnes J-function, even in cases where the usual series representation is not convergent.

math.GM↗

arXiv2025

Relaxation equations with stretched non-local operators: renewal and time-changed processes

We introduce and study renewal processes defined by means of extensions of the standard relaxation equation through ``stretched" non-local operators (of order $α$ and with parameter $γ$). In a first case we obtain a generalization of the fractional Poisson process, which displays either infinite or finite expected waiting times between arrivals, depending on the parameter $γ$. Therefore, the introduction in the operator of the non-homogeneous term driven by $γ$ allows us to regulate the transition between different regimes of our renewal process. We then consider a second-order relaxation-type equation involving the same operator, under different sets of conditions on the constants involved; for a particular choice of these constants, we prove that the corresponding renewal process is linked to the first one by convex combination of its distributions. We also discuss alternative models related to the same equations and their time-changed representation, in terms of the inverse of a non-decreasing process which generalizes the $α$-stable Lévy subordinator.

math.PR↗

arXiv2025

Stretched non-local Pearson diffusions

We define a novel class of time changed Pearson diffusions, termed stretched non local Pearson diffusions, where the stochastic time change model has the Kilbas Saigo function as its Laplace transform. Moreover, we introduce a stretched variant of the Caputo fractional derivative and prove that its eigenfunction is, in fact, the Kilbas Saigo function. Furthermore, we solve fractional Cauchy problems involving the generator of the Pearson diffusion and the Fokker Planck operator, providing both analytic and stochastic solutions, which connect the newly defined process and fractional operator with the Kilbas Saigo function. We also prove that stretched non local Pearson diffusions share the same limiting distributions as their standard counterparts. Finally, we investigate fractional hyperbolic Cauchy problems for Pearson diffusions, which resemble time fractional telegraph equations, and provide both analytical and stochastic solutions. As a byproduct of our analysis, we derive a novel representation and an asymptotic formula for the Kilbas Saigo function with complex argument, which, to the best of our knowledge, are not currently available in the existing literature.

math.PR↗

arXiv2023

On Fractional Spherically Restricted Hyperbolic Diffusion Random Field

The paper investigates solutions of the fractional hyperbolic diffusion equation in its most general form with two fractional derivatives of distinct orders. The solutions are given as spatial-temporal homogeneous and isotropic random fields and their spherical restrictions are studied. The spectral representations of these fields are derived and the associated angular spectrum is analysed. The obtained mathematical results are illustrated by numerical examples. In addition, the numerical investigations assess the dependence of the covariance structure and other properties of these fields on the orders of fractional derivatives.

math.PR↗

arXiv2005

Twistors, Generalizations and Exceptional Structures

This paper is intended to describe twistors via the paravector model of Clifford algebras and to relate such description to conformal maps in the Clifford algebra over R(4,1), besides pointing out some applications of the pure spinor formalism. We construct twistors in Minkowski spacetime as algebraic spinors associated with the Dirac-Clifford algebra, using one lower spacetime dimension than standard Clifford algebra formulations, since for this purpose the Clifford algebra over R{4,1} is also used to describe conformal maps, instead of R{2,4}. It is possible to identify the twistor fiber in four, six and eight dimensions, respectively, with the coset spaces SO(4)/(SU(2) x U(1)/Z_2) = CP1, SO(6)/(SU(3)x U(1)/Z_2) = CP3 and SO(8)/(Spin(6)x Spin(2)/Z_2). The last homogeneous space is closely related to the SO(8) spinor decomposition reserving SO(8) symmetry in type IIB superstring theory. Indeed, aside the IIB theory, there is no SO(8) spinor decomposition preserving SO(8) symmetry and, in this case, one can introduce distinct coordinates and conjugate momenta only if the Spin(8) symmetry is broken by a Spin(6) x Spin(2) subgroup of Spin(8). Also, it is reviewed how to generalize the Penrose flagpole, constructing a flagpole that is more general than the Penrose one, which arises in a particular case (Benn & Tucker description). We investigate the well-known relation between this flagpole and the SO(2n)/U(n) twistorial structure, which emerges when one considers the set X of all totally isotropic subspaces of C{2n}, and an isomorphism from the set of pure spinors to X. Finally we point out some relations between twistors fibrations and the classification of compact homogeneous quaternionic-Kahler manifolds (the so-called Wolf spaces), and exceptional Lie structures.

math-ph↗

arXiv1998

About Zitterbewegung and electron structure

We start from the spinning electron theory by Barut and Zanghi, which has been recently translated into the Clifford algebra language. We "complete" such a translation, first of all, by expressing in the Clifford formalism a particular Barut-Zanghi (BZ) solution, which refers (at the classical limit) to an internal helical motion with a time-like speed [and is here shown to originate from the superposition of positive and negative frequency solutions of the Dirac equation]. Then, we show how to construct solutions of the Dirac equation describing helical motions with light-like speed, which meet very well the standard interpretation of the velocity operator in the Dirac equation theory (and agree with the solution proposed by Hestenes, on the basis --however-- of ad-hoc assumptions that are unnecessary in the present approach). The above results appear to support the conjecture that the Zitterbewegung motion (a helical motion, at the classical limit) is responsible for the electron spin.

quant-ph↗

arXiv1998

Generalization of Dirac Non-Linear Electrodynamics, and Spinning Charged Particles

In this note we generalized the Dirac non-linear electrodynamics, by introducing two potentials (namely, the vector potential A and the pseudo-vector potential gamma^5 B of the electromagnetic theory with charges and magnetic monopoles) and by imposing the pseudoscalar part of the product omega.omega* to be zero, with omega = A + gamma^5 B. We show that the field equations of such a theory possess a soliton-like solution which can represent a priori a "charged particle", since it is endowed with a Coulomb field plus the field of a magnetic dipole. The rest energy of the soliton is finite, and the angular momentum stored in its electromagnetic field can be identified --for suitable choices of the parameters-- with the spin of the charged particle. Thus this approach seems to yield a classical model for the charged (spinning) particle, which does not meet the problems met by earlier attempts in the same direction.

quant-ph↗