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Symmetry
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Current Trends in Symmetric Polynomials with Their Applications Ⅲ
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Current Trends in Symmetric Polynomials with Their Applications Ⅲ

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

Deadline for manuscript submissions: closed (1 October 2021) | Viewed by 11832

Special Issue Editor

Prof. Taekyun Kim

E-Mail Website
Guest Editor
Department of Mathematics, College of Natural Science, Kwangwoon University, Seoul 139-704, Republic of Korea
Interests: number theory; analysis and applications; stochastic process
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The symmetric polynomials have various applications in many branches of mathematics and mathematical physics. These polynomials are defined by linear polynomials (differential relations), globally referred to as functional equations that arise in well-defined combinatorial contexts, and they lead systematically to well-defined classes of functions. The symmetric functions for the sequence of polynomials are used in analyzing sequences of functions, in finding a closed formula for a sequence, in finding recurrence relations and differential equations, in relationships between sequences, in asymptotic behavior of sequences, and in proving identities involving sequences.

We aim to design this special issue for researchers with an interest in pure and applied Mathematics. This special issue aims to present theory, methods, and applications of recent/current symmetric polynomials.

Each paper that will be published in this special issue aims at enriching the understanding of current research problems, theories, and applications on the chosen topics. The emphasis will be to present the basic developments concerning an idea in full detail, and also contain the most recent advances made in the area of symmetric functions and polynomials.

Advanced research on symmetric functions and polynomials is essential to study and model various changes in their natures. We will attempt to include some carefully selected papers in these areas of research that have significant applications. Much applicable mathematics cannot be investigated further or used without the applications of symmetric special functions and polynomials.

Thus, this special issue is expected to be beneficial for researchers who are interested in mathematics that has applications in pure and applied mathematics and uses tools mainly from the broad mathematical grouping.

Prof. Taekyun Kim
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.

Keywords

  • Symmetric polynomials
  • Special Functions
  • Special polynomials
  • Inequalities
  • Integral Equations
  • Mathematical Physics
  • Bosonic p-adic integral
  • Fermionic p-adic integral

Published Papers (6 papers)

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Research

35 pages, 445 KiB  
Article
Rational Interpolation: Jacobi’s Approach Reminiscence
by Alexei Uteshev, Ivan Baravy and Elizaveta Kalinina
Symmetry 2021, 13(8), 1401; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13081401 - 01 Aug 2021
Cited by 2 | Viewed by 2239
Abstract
We treat the interpolation problem {f(xj)=yj}j=1N for polynomial and rational functions. Developing the approach originated by C. Jacobi, we represent the interpolants by virtue of the Hankel polynomials generated by [...] Read more.
We treat the interpolation problem {f(xj)=yj}j=1N for polynomial and rational functions. Developing the approach originated by C. Jacobi, we represent the interpolants by virtue of the Hankel polynomials generated by the sequences of special symmetric functions of the data set like {∑j=1Nxjkyj/W′(xj)}k∈N and {∑j=1Nxjk/(yjW′(xj))}k∈N; here, W(x)=∏j=1N(x−xj). We also review the results by Jacobi, Joachimsthal, Kronecker and Frobenius on the recursive procedure for computation of the sequence of Hankel polynomials. The problem of evaluation of the resultant of polynomials p(x) and q(x) given a set of values {p(xj)/q(xj)}j=1N is also tackled within the framework of this approach. An effective procedure is suggested for recomputation of rational interpolants in case of extension of the data set by an extra point. Full article
(This article belongs to the Special Issue Current Trends in Symmetric Polynomials with Their Applications Ⅲ)
16 pages, 9168 KiB  
Article
An Improved Estimation Method of Mutual Inductance Angle for a Two-Dimensional Wireless Power Transfer System
by Sangyong Lee, Jeonho Lee, Jongkyum Kwon and Se-Kyo Chung
Symmetry 2021, 13(3), 448; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13030448 - 10 Mar 2021
Viewed by 1757
Abstract
The improvement of power transmission efficiency (PTE) is an important issue in the design of a wireless power transfer (WPT) system. The WPT system with multiple transmitting (Tx) or receiving (Rx) coils is a way to improve the PTE. This paper deals with [...] Read more.
The improvement of power transmission efficiency (PTE) is an important issue in the design of a wireless power transfer (WPT) system. The WPT system with multiple transmitting (Tx) or receiving (Rx) coils is a way to improve the PTE. This paper deals with the estimation of the mutual inductance angle for a two-dimensional (2D) WPT system with two Tx coils and one Rx coil. The mutual inductance angle is one of the most important parameters to determine the PTE in the 2D WPT system. The condition for the maximum PTE is investigated and the mutual inductance angle is defined for the 2D WPT system. An improved estimation method of the mutual inductance angle is proposed based on the phase-locked loop (PLL) technique using the voltages and currents of the Tx coils. The simulation and experimental results are provided to validate the effectiveness of the proposed method. Full article
(This article belongs to the Special Issue Current Trends in Symmetric Polynomials with Their Applications Ⅲ)
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18 pages, 301 KiB  
Article
On Weak Limiting Distributions for Random Walks on a Spider
by Youngsoo Seol
Symmetry 2020, 12(12), 2000; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12122000 - 04 Dec 2020
Cited by 1 | Viewed by 1040
Abstract
In this article, we study random walks on a spider that can be established from the classical case of simple symmetric random walks. The primary purpose of this article is to establish a functional central limit theorem for random walks on a spider [...] Read more.
In this article, we study random walks on a spider that can be established from the classical case of simple symmetric random walks. The primary purpose of this article is to establish a functional central limit theorem for random walks on a spider and to define Brownian spider as the resulting weak limit. In special case, random walks on a spider can be characterized as skew random walks. It is well known for skew Brownian motion as the resulting weak limit of skew random walks. We first will study the tightness and then it will be shown for the convergence of finite dimensional distribution for random walks on a spider. Full article
(This article belongs to the Special Issue Current Trends in Symmetric Polynomials with Their Applications Ⅲ)
10 pages, 248 KiB  
Article
Note on the Type 2 Degenerate Multi-Poly-Euler Polynomials
by Waseem Ahmad Khan, Mehmet Acikgoz and Ugur Duran
Symmetry 2020, 12(10), 1691; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12101691 - 15 Oct 2020
Cited by 23 | Viewed by 1773
Abstract
Kim and Kim (Russ. J. Math. Phys. 26, 2019, 40-49) introduced polyexponential function as an inverse to the polylogarithm function and by this, constructed a new type poly-Bernoulli polynomials. Recently, by using the polyexponential function, a number of generalizations of some polynomials and [...] Read more.
Kim and Kim (Russ. J. Math. Phys. 26, 2019, 40-49) introduced polyexponential function as an inverse to the polylogarithm function and by this, constructed a new type poly-Bernoulli polynomials. Recently, by using the polyexponential function, a number of generalizations of some polynomials and numbers have been presented and investigated. Motivated by these researches, in this paper, multi-poly-Euler polynomials are considered utilizing the degenerate multiple polyexponential functions and then, their properties and relations are investigated and studied. That the type 2 degenerate multi-poly-Euler polynomials equal a linear combination of the degenerate Euler polynomials of higher order and the degenerate Stirling numbers of the first kind is proved. Moreover, an addition formula and a derivative formula are derived. Furthermore, in a special case, a correlation between the type 2 degenerate multi-poly-Euler polynomials and degenerate Whitney numbers is shown. Full article
(This article belongs to the Special Issue Current Trends in Symmetric Polynomials with Their Applications Ⅲ)
16 pages, 422 KiB  
Article
Efficiency of Cluster Validity Indexes in Fuzzy Clusterwise Generalized Structured Component Analysis
by Ji Hoon Ryoo, Seohee Park, Seongeun Kim and Hyun Suk Ryoo
Symmetry 2020, 12(9), 1514; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12091514 - 14 Sep 2020
Cited by 6 | Viewed by 2030
Abstract
Fuzzy clustering has been broadly applied to classify data into K clusters by assigning membership probabilities of each data point close to K centroids. Such a function has been applied into characterizing the clusters associated with a statistical model such as structural equation [...] Read more.
Fuzzy clustering has been broadly applied to classify data into K clusters by assigning membership probabilities of each data point close to K centroids. Such a function has been applied into characterizing the clusters associated with a statistical model such as structural equation modeling. The characteristics identified by the statistical model further define the clusters as heterogeneous groups selected from a population. Recently, such statistical model has been formulated as fuzzy clusterwise generalized structured component analysis (fuzzy clusterwise GSCA). The same as in fuzzy clustering, the clusters are enumerated to infer the population and its parameters within the fuzzy clusterwise GSCA. However, the identification of clusters in fuzzy clustering is a difficult task because of the data-dependence of classification indexes, which is known as a cluster validity problem. We examined the cluster validity problem within the fuzzy clusterwise GSCA framework and proposed a new criterion for selecting the most optimal number of clusters using both fit indexes of the GSCA and the fuzzy validity indexes in fuzzy clustering. The criterion, named the FIT-FHV method combining a fit index, FIT, from GSCA and a cluster validation measure, FHV, from fuzzy clustering, performed better than any other indices used in fuzzy clusterwise GSCA. Full article
(This article belongs to the Special Issue Current Trends in Symmetric Polynomials with Their Applications Ⅲ)
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11 pages, 817 KiB  
Article
Note on the Hurwitz–Lerch Zeta Function of Two Variables
by Junesang Choi, Recep Şahin, Oğuz Yağcı and Dojin Kim
Symmetry 2020, 12(9), 1431; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12091431 - 28 Aug 2020
Cited by 4 | Viewed by 2010
Abstract
A number of generalized Hurwitz–Lerch zeta functions have been presented and investigated. In this study, by choosing a known extended Hurwitz–Lerch zeta function of two variables, which has been very recently presented, in a systematic way, we propose to establish certain formulas and [...] Read more.
A number of generalized Hurwitz–Lerch zeta functions have been presented and investigated. In this study, by choosing a known extended Hurwitz–Lerch zeta function of two variables, which has been very recently presented, in a systematic way, we propose to establish certain formulas and representations for this extended Hurwitz–Lerch zeta function such as integral representations, generating functions, derivative formulas and recurrence relations. We also point out that the results presented here can be reduced to yield corresponding results for several less generalized Hurwitz–Lerch zeta functions than the extended Hurwitz–Lerch zeta function considered here. For further investigation, among possibly various more generalized Hurwitz–Lerch zeta functions than the one considered here, two more generalized settings are provided. Full article
(This article belongs to the Special Issue Current Trends in Symmetric Polynomials with Their Applications Ⅲ)
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