arXiv subjects

A. Soria-Lorente

Publications and source records attributed to A. Soria-Lorente.

5 recordsLinked to original sources

arXiv2022

On Polynomials Orthogonal with Respect to an Inner Product Involving Higher-Order Differences: The Meixner Case

In this contribution we consider sequences of monic polynomials orthogonal with respect to Sobolev-type inner product \[ \left\langle f,g\right\rangle= \langle {\bf u}^{\tt M},fg\rangle+λ\mathscr T^j f (α)\mathscr T^{j}g(α), \] where ${\bf u}^{\tt M}$ is the Meixner linear operator, $λ\in\mathbb{R}_{+}$, $j\in\mathbb{N}$, $α\leq 0$, and $\mathscr T$ is the forward difference operator $Δ$, or the backward difference operator $\nabla$. We derive an explicit representation for these polynomials. The ladder operators associated with these polynomials are obtained, and the linear difference equation of second order is also given. In addition, for these polynomials we derive a $(2j+3)$-term recurrence relation. Finally, we find the Mehler-Heine type formula for the $α\le 0$ case.

math.CA↗

arXiv2019

A steganographic approach based on the chaotic fractional map and in the DCT domain

A steganographic method based on the chaotic fractional map and in the DCT domain is proposed. This method embeds a secret message in some high frequency coefficients of the image using a 128-bit private key and a chaotic fractional map which generate a permutation indicating the positions where the secret bits will be embedded. An experimental work on the validation of the proposed method is also presented, showing performance in imperceptibility, quality, similarity and security analysis of the steganographic system. The proposed algorithm improved the level of imperceptibility and Cachin's security of stego-system analyzed through the values of Peak Signal-to-Noise Ratio (PSNR) and the Relative Entropy (RE).

cs.MM↗

arXiv2018

Analytic properties of some basic hypergeometric-Sobolev-type orthogonal polynomials

In this contribution we consider sequences of monic polynomials orthogonal with respect to a Sobolev-type inner product \[ \langle f,g \rangle _{S}:= \langle {\bf u}, f g\rangle +N (\mathscr D_q f)(α) (\mathscr D _{q}g)(α),\qquad α\in \mathbb R, \quad N\ge 0, \] where $\bf u$ is a $q$-classical linear functional and $\mathscr D _{q}$ is the $q$-derivative operator. We obtain some algebraic properties of these polynomials such as an explicit representation, a five-term recurrence relation as well as a second order linear $q$-difference holonomic equation fulfilled by such polynomials. We present an analysis of the behaviour of its zeros function of the mass $N$. In particular, we in the exact values of $N$ such that the smallest (respectively, the greatest) zero of the studied polynomials is located outside of the support of the measure. We conclude this work considering two examples.

math.CA↗

arXiv2012

First order non-homogeneous q-difference equation for Stieltjes function characterizing q-orthogonal polynomials

In this paper we give a characterization of some classical q-orthogonal polynomials in terms of a difference property of the associated Stieltjes function, i.e this function solves a first order non-homogeneous q-difference equation. The solutions of the aforementioned q-difference equation (given in terms of hypergeometric series) for some canonical cases, namely, q-Charlier, q-Kravchuk, q-Meixner and q-Hahn are worked out.

math.CA↗

arXiv2012

On new rational approximants to ζ(3)

New (infinitely many) rational approximants to ζ(3) proving its irrationality are given. The recurrence relations for the numerator and denominator of these approximants as well as their continued fraction expansions are obtained. A comparison of our approximants with Apéry's approximants to ζ(3) is shown.

math.CA↗