Submit to Special Issue Submit Abstract to Special Issue Review for Symmetry Propose a Special Issue

Journal Menu

Journal Browser

► Journal Browser

Special Issue "Theory and Applications of Special Functions II"

Print Special Issue Flyer
Special Issue Editors
Special Issue Information
Published Papers

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Physics".

Deadline for manuscript submissions: 30 November 2023 | Viewed by 5108

Share This Special Issue

Special Issue Editor

Dr. Diego Caratelli

E-Mail Website
Guest Editor

Department of Electrical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands
Interests: electronic engineering; antennas and propagation; wireless communications; RF engineering
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Different applications of modern engineering and physical sciences require thorough knowledge of applied mathematics, particularly special functions. These are frequently adopted in acoustics, thermodynamics, electromagnetics, and optics, to express the approximate or exact analytical solution of complex problems, thus providing a better understanding of and meaningful insight into underlying properties and mechanisms.

In this Special Issue, we focus on the application of classical and higher-order special functions to advanced problems of mathematical physics that are characterized by specific (i.e., rectangular, cylindrical, and spherical) symmetry or, conversely, rely on more unconventional models. Attention is given, also, to the illustration of properties of novel special functions, with particular attention paid to the relevant governing differential equation; recurrence formulae; as well as efficient computational algorithms, such as those based on uniform asymptotic representations for small and large arguments.

We look forward to your contributions to review- and original-research articles dealing with the recent advances in the theory and applications of special functions.

Dr. Diego Caratelli
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (6 papers)

Download All Papers

Order results

Result details

Show export options Show export options

Select all

Export citation of selected articles as:

Research

Open AccessArticle

A Note on the Lambert W Function: Bernstein and Stieltjes Properties for a Creep Model in Linear Viscoelasticity

Francesco Mainardi

Enrico Masina

and

Juan Luis González-Santander

Symmetry 2023, 15(9), 1654; https://doi.org/10.3390/sym15091654 - 26 Aug 2023

Viewed by 348

Abstract

The purpose of this note is to propose an application of the Lambert W function in linear viscoelasticity based on the Bernstein and Stieltjes properties of this function. In particular, we recognize the role of its main branch,

W_{0} (t)

[...] Read more.

W_{0} (t)

, in a peculiar model of creep with two spectral functions in frequency that completely characterize the creep model. In order to calculate these spectral functions, it turns out that the conjugate symmetry property of the Lambert W function along its branch cut on the negative real axis is essential. We supplement our analysis by computing the corresponding relaxation function and providing the plots of all computed functions. Full article

(This article belongs to the Special Issue Theory and Applications of Special Functions II)

► Show Figures

Figure 1

Open AccessArticle

Monomiality and a New Family of Hermite Polynomials

Giuseppe Dattoli

and

Silvia Licciardi

Symmetry 2023, 15(6), 1254; https://doi.org/10.3390/sym15061254 - 13 Jun 2023

Viewed by 416

Abstract

The monomiality principle is based on an abstract definition of the concept of derivative and multiplicative operators. This allows to treat different families of special polynomials as ordinary monomials. The procedure underlines a generalization of the Heisenberg–Weyl group, along with the relevant technicalities and symmetry properties. In this article, we go deeply into the formulation and meaning of the monomiality principle and employ it to study the properties of a set of polynomials, which, asymptotically, reduce to the ordinary two-variable Kampè dè Fèrièt family. We derive the relevant differential equations and discuss the associated orthogonality properties, along with the relevant generalized forms. Full article

(This article belongs to the Special Issue Theory and Applications of Special Functions II)

► Show Figures

Figure 1

Open AccessArticle

Poly-Cauchy Numbers with Higher Level

Takao Komatsu

and

Víctor F. Sirvent

Symmetry 2023, 15(2), 354; https://doi.org/10.3390/sym15020354 - 28 Jan 2023

Cited by 1 | Viewed by 519

Abstract

In this article, mainly from the analytical aspect, we introduce poly-Cauchy numbers with higher levels (level s) as a kind of extensions of poly-Cauchy numbers with level 2 and the original poly-Cauchy numbers and investigate their properties. Such poly-Cauchy numbers with higher levels are yielded from the inverse relationship with an s-step function of the exponential function. We show such a function with recurrence relations and give the expressions of poly-Cauchy numbers with higher levels. Poly-Cauchy numbers with higher levels can be also expressed in terms of iterated integrals and a combinatorial summation. Poly-Cauchy numbers with higher levels for negative indices have a double summation formula. In addition, Cauchy numbers with higher levels can be also expressed in terms of determinants. Full article

(This article belongs to the Special Issue Theory and Applications of Special Functions II)

Open AccessFeature PaperArticle

Bell’s Polynomials and Laplace Transform of Higher Order Nested Functions

Diego Caratelli

and

Paolo Emilio Ricci

Symmetry 2022, 14(10), 2139; https://doi.org/10.3390/sym14102139 - 13 Oct 2022

Cited by 1 | Viewed by 752

Abstract

Using Bell’s polynomials it is possible to approximate the Laplace Transform of composite functions. The same methodology can be adopted for the evaluation of the Laplace Transform of higher-order nested functions. In this case, a suitable extension of Bell’s polynomials, as previously introduced in the scientific literature, is used, namely higher order Bell’s polynomials used in the representation of the derivatives of multiple nested functions. Some worked examples are shown, and some of the polynomials used are reported in the Appendices. Full article

(This article belongs to the Special Issue Theory and Applications of Special Functions II)

► Show Figures

Figure 1

Open AccessArticle

Implementation of Two-Mode Gaussian States Whose Covariance Matrix Has the Standard Form

Gianfranco Cariolaro

and

Roberto Corvaja

Symmetry 2022, 14(7), 1485; https://doi.org/10.3390/sym14071485 - 20 Jul 2022

Cited by 1 | Viewed by 1444

Abstract

This paper deals with the covariance matrix (CM) of two-mode Gaussian states, which, together with the mean vector, fully describes these states. In the two-mode states, the (ordinary) CM is a real symmetric matrix of order 4; therefore, it depends on 10 real variables. However, there is a very efficient representation of the CM called the standard form (SF) that reduces the degrees of freedom to four real variables, while preserving all the relevant information on the state. The SF can be easily evaluated using a set of symplectic invariants. The paper starts from the SF, introducing an architecture that implements with primitive components the given two-mode Gaussian state having the CM with the SF. The architecture consists of a beam splitter, followed by the parallel set of two single–mode real squeezers, followed by another beam splitter. The advantage of this architecture is that it gives a precise non-redundant physical meaning of the generation of the Gaussian state. Essentially, all the relevant information is contained in this simple architecture. Full article

(This article belongs to the Special Issue Theory and Applications of Special Functions II)

► Show Figures

Figure 1

Open AccessArticle

Gaussian States: Evaluation of the Covariance Matrix from the Implementation with Primitive Component

Gianfranco Cariolaro

Roberto Corvaja

and

Filippo Miatto

Symmetry 2022, 14(7), 1286; https://doi.org/10.3390/sym14071286 - 21 Jun 2022

Cited by 1 | Viewed by 1019

Abstract

Quantum Gaussian states play a fundamental role in quantum communications and in quantum information. This paper deals with the implementation of multimode, and particularly of two-mode Gaussian unitaries and Gaussian states with primitive components (phase shifters, single-mode real squeezers, displacements, and beam splitters). The architecture thus obtained allows one to obtain an insight into the physical meaning of each variable involved. Moreover, following the implementation architecture, it is possible to formulate an easy algebra (radical free) for the main operations and transformations of Gaussian states. Full article

(This article belongs to the Special Issue Theory and Applications of Special Functions II)

► Show Figures

Journal Menu

Journal Browser

Special Issue "Theory and Applications of Special Functions II"

Share This Special Issue

Special Issue Editor

Special Issue Information

Published Papers (6 papers)

Research

Further Information

Guidelines

MDPI Initiatives

Follow MDPI