Special Issue "Applications of Symmetric Functions Theory to Certain Fields"

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics and Symmetry/Asymmetry".

Deadline for manuscript submissions: 15 September 2022 | Viewed by 4092

Special Issue Editors

Dr. Serkan Araci
E-Mail Website
Guest Editor
Department of Economics, Faculty of Economics, Administrative and Social Sciences, Hasan Kalyoncu University, TR-27410 Gaziantep, Turkey
Interests: q-special functions and q-special polynomials; q-series; analytic number theory; umbral theory; p-adic q-analysis; fractional calculus and its applications
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Ayhan Esi
E-Mail Website
Guest Editor
Department of Basic Engineering Sciences, Engineering Faculty, Malatya Turgut Ozal University, 44040, Malatya, Turkey
Interests: summability theory; sequence and series; function spaces

Special Issue Information

Dear Colleagues,

Symmetric polynomials and symmetric functions are ubiquitous in mathematics and mathematical physics. For example, they appear in elementary algebra representation theories of symmetric groups and general linear groups over the complex field or finite fields. The theory of symmetric functions has also many applications to enumerative combinatorics, as well as to such other branches of mathematics as group theory, Lie algebras, and algebraic geometry. Indeed, the Frobenius map and its extensions provide a bridge translating representation theory problems to symmetric function problems and ultimately to combinatorial problems. They have also played a central role in random matrix theory in the computation of quantities such as joint moments of traces and joint moments of characteristic polynomials of matrices.

This Special Issue will reflect the diversity of the topics in the applications of symmetric functions, symmetric function spaces and symmetries.

Potential topics include but are not limited to the following:

  • Combinatorial applications of symmetric function theory;
  • Applications of symmetric function theory to certain function spaces;
  • Application of symmetric functions in some applied science problems;
  • Symmetric functions over finite fields.

Dr. Serkan Araci
Prof. Dr. Ayhan Esi
Guest Editors

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 1800 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 (5 papers)

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Research

Article
Radius of k-Parabolic Starlikeness for Some Entire Functions
Symmetry 2022, 14(4), 637; https://doi.org/10.3390/sym14040637 - 22 Mar 2022
Viewed by 348
Abstract
This article considers three types of analytic functions based on their infinite product representation. The radius of the k-parabolic starlikeness of the functions of these classes is studied. The optimal parameter values for k-parabolic starlike functions are determined in the unit [...] Read more.
This article considers three types of analytic functions based on their infinite product representation. The radius of the k-parabolic starlikeness of the functions of these classes is studied. The optimal parameter values for k-parabolic starlike functions are determined in the unit disk. Several examples are provided that include special functions such as Bessel, Struve, Lommel, and q-Bessel functions. Full article
(This article belongs to the Special Issue Applications of Symmetric Functions Theory to Certain Fields)
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Article
Solving the Economic Growth Acceleration Model with Memory Effects: An Application of Combined Theorem of Adomian Decomposition Methods and Kashuri–Fundo Transformation Methods
Symmetry 2022, 14(2), 192; https://doi.org/10.3390/sym14020192 - 19 Jan 2022
Viewed by 347
Abstract
The primary purpose of this study is to solve the economic growth acceleration model with memory effects for the quadratic cost function (Riccati fractional differential equation), using Combined Theorem of Adomian Polynomial Decomposition and Kashuri–Fundo Transformation methods. The economic growth model (EGM) with [...] Read more.
The primary purpose of this study is to solve the economic growth acceleration model with memory effects for the quadratic cost function (Riccati fractional differential equation), using Combined Theorem of Adomian Polynomial Decomposition and Kashuri–Fundo Transformation methods. The economic growth model (EGM) with memory effects for the quadratic cost function is analysed by modifying the linear fractional differential equation. The study’s significant contribution is to develop a linear cost function in the EGM for a quadratic non-linear cost function and determine the specific conditions of the Riccati fractional differential equation (RFDEs) in the EGM with memory effects. The study results showed that RFDEs in the EGM involving the memory effect have a solution and singularity. Additionally, this study presents a comparison of exact solutions using Lie symmetry, Combined Theorem of Adomian Polynomial Decomposition, and Kashuri–Fundo Transformation methods. The results showed that the three methods have the same solution. Furthermore, this study provides a numerical solution to the RFDEs on the EGM with memory effects. The numerical simulation results showed that the output value of Y(t) for the quadratic cost function in the economic growth model is significantly affected by the memory effect. Full article
(This article belongs to the Special Issue Applications of Symmetric Functions Theory to Certain Fields)
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Article
A Quadruple Integral Involving Chebyshev Polynomials Tn(x): Derivation and Evaluation
Symmetry 2022, 14(1), 100; https://doi.org/10.3390/sym14010100 - 07 Jan 2022
Cited by 1 | Viewed by 224
Abstract
The aim of the current document is to evaluate a quadruple integral involving the Chebyshev polynomial of the first kind Tn(x) and derive in terms of the Hurwitz-Lerch zeta function. Special cases are evaluated in terms of fundamental constants. [...] Read more.
The aim of the current document is to evaluate a quadruple integral involving the Chebyshev polynomial of the first kind Tn(x) and derive in terms of the Hurwitz-Lerch zeta function. Special cases are evaluated in terms of fundamental constants. The zero distribution of almost all Hurwitz-Lerch zeta functions is asymmetrical. All the results in this work are new. Full article
(This article belongs to the Special Issue Applications of Symmetric Functions Theory to Certain Fields)
Article
Coefficient Estimates for a Subclass of Meromorphic Multivalent q-Close-to-Convex Functions
Symmetry 2021, 13(10), 1840; https://doi.org/10.3390/sym13101840 - 01 Oct 2021
Cited by 8 | Viewed by 645
Abstract
By making use of the concept of basic (or q-) calculus, many subclasses of analytic and symmetric q-starlike functions have been defined and studied from different viewpoints and perspectives. In this article, we introduce a new class of meromorphic multivalent close-to-convex [...] Read more.
By making use of the concept of basic (or q-) calculus, many subclasses of analytic and symmetric q-starlike functions have been defined and studied from different viewpoints and perspectives. In this article, we introduce a new class of meromorphic multivalent close-to-convex functions with the help of a q-differential operator. Furthermore, we investigate some useful properties such as sufficiency criteria, coefficient estimates, distortion theorem, growth theorem, radius of starlikeness, and radius of convexity for this new subclass. Full article
(This article belongs to the Special Issue Applications of Symmetric Functions Theory to Certain Fields)
Article
Two New Bailey Lattices and Their Applications
Symmetry 2021, 13(6), 958; https://doi.org/10.3390/sym13060958 - 28 May 2021
Cited by 3 | Viewed by 796
Abstract
In our present investigation, we develop two new Bailey lattices. We describe a number of q-multisums new forms with multiple variables for the basic hypergeometric series which arise as consequences of these two new Bailey lattices. As applications, two new transformations for [...] Read more.
In our present investigation, we develop two new Bailey lattices. We describe a number of q-multisums new forms with multiple variables for the basic hypergeometric series which arise as consequences of these two new Bailey lattices. As applications, two new transformations for basic hypergeometric by using the unit Bailey pair are derived. Besides it, we use this Bailey lattice to get some kind of mock theta functions. Our results are shown to be connected with several earlier works related to the field of our present investigation. Full article
(This article belongs to the Special Issue Applications of Symmetric Functions Theory to Certain Fields)
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