Special Issue "Polynomials: Theory and Applications"

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: 29 February 2020.

Special Issue Editor

Prof. Dr. Cheon-Seoung Ryoo
E-Mail Website
Guest Editor
Department of Mathematics, Hannam University, Daejeon 34430, Korea
Interests: numerical analysis; scientific computing; error analysis and interval analysis; partial differential equations; boundary value problems; sequences and sets; numbers; polynomials; Zeta and L-functions: analytic theory; p-adic functional analysis

Special Issue Information

Dear Colleagues,

The importance of polynomials in the interdisciplinary field of mathematics, engineering, and science is well known. Over the past several decades, research on polynomials has been conducted extensively in many disciplines.

This Special Issue welcomes all research papers related to polynomials in mathematics, science, and industry.

Potential topics include but are not limited to the following:

  • The modern umbral calculus (binomial, Appell, and Sheffer polynomial sequences)
  • Orthogonal polynomials, matrix orthogonal polynomials, multiple orthogonal polynomials
  • Matrix and determinant approach to special polynomial sequences
  • Applications of special polynomial sequences
  • Number theory and special functions
  • Asymptotic methods in orthogonal polynomials
  • Fractional calculus and special functions
  • Symbolic computations and special functions
  • Applications of special functions to statistics, physical sciences, and engineering

Prof. Dr. Cheon-Seoung Ryoo
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 papers will be 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. Mathematics 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 1200 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

  • umbral calculus
  • orthogonal polynomials, matrix orthogonal polynomials
  • special polynomial sequences
  • applications of special polynomial sequences
  • number theory and special functions
  • fractional calculus and special functions
  • symbolic computations and special functions
  • applications of special functions to statistics, physical sciences, and engineering

Published Papers (7 papers)

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Research

Open AccessFeature PaperArticle
Iterating the Sum of Möbius Divisor Function and Euler Totient Function
Mathematics 2019, 7(11), 1083; https://doi.org/10.3390/math7111083 - 09 Nov 2019
Abstract
In this paper, according to some numerical computational evidence, we investigate and prove certain identities and properties on the absolute Möbius divisor functions and Euler totient function when they are iterated. Subsequently, the relationship between the absolute Möbius divisor function with Fermat primes [...] Read more.
In this paper, according to some numerical computational evidence, we investigate and prove certain identities and properties on the absolute Möbius divisor functions and Euler totient function when they are iterated. Subsequently, the relationship between the absolute Möbius divisor function with Fermat primes has been researched and some results have been obtained. Full article
(This article belongs to the Special Issue Polynomials: Theory and Applications)
Open AccessArticle
Differential Equations Arising from the Generating Function of the (r, β)-Bell Polynomials and Distribution of Zeros of Equations
Mathematics 2019, 7(8), 736; https://doi.org/10.3390/math7080736 - 12 Aug 2019
Abstract
In this paper, we study differential equations arising from the generating function of the ( r , β ) -Bell polynomials. We give explicit identities for the ( r , β ) -Bell polynomials. Finally, we find the zeros of the ( r [...] Read more.
In this paper, we study differential equations arising from the generating function of the ( r , β ) -Bell polynomials. We give explicit identities for the ( r , β ) -Bell polynomials. Finally, we find the zeros of the ( r , β ) -Bell equations with numerical experiments. Full article
(This article belongs to the Special Issue Polynomials: Theory and Applications)
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Open AccessArticle
Truncated Fubini Polynomials
Mathematics 2019, 7(5), 431; https://doi.org/10.3390/math7050431 - 15 May 2019
Abstract
In this paper, we introduce the two-variable truncated Fubini polynomials and numbers and then investigate many relations and formulas for these polynomials and numbers, including summation formulas, recurrence relations, and the derivative property. We also give some formulas related to the truncated Stirling [...] Read more.
In this paper, we introduce the two-variable truncated Fubini polynomials and numbers and then investigate many relations and formulas for these polynomials and numbers, including summation formulas, recurrence relations, and the derivative property. We also give some formulas related to the truncated Stirling numbers of the second kind and Apostol-type Stirling numbers of the second kind. Moreover, we derive multifarious correlations associated with the truncated Euler polynomials and truncated Bernoulli polynomials. Full article
(This article belongs to the Special Issue Polynomials: Theory and Applications)
Open AccessFeature PaperArticle
On Positive Quadratic Hyponormality of a Unilateral Weighted Shift with Recursively Generated by Five Weights
Mathematics 2019, 7(2), 212; https://doi.org/10.3390/math7020212 - 25 Feb 2019
Abstract
Let 1 < a < b < c < d and α ^ 5 : = 1 , a , b , c , d be a weighted sequence that is recursively generated by five weights 1 , a , b , [...] Read more.
Let 1 < a < b < c < d and α ^ 5 : = 1 , a , b , c , d be a weighted sequence that is recursively generated by five weights 1 , a , b , c , d . In this paper, we give sufficient conditions for the positive quadratic hyponormalities of W α x and W α y , x , with α x : x , α ^ 5 and α y , x : y , x , α ^ 5 . Full article
(This article belongs to the Special Issue Polynomials: Theory and Applications)
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Open AccessArticle
Ground State Solutions for Fractional Choquard Equations with Potential Vanishing at Infinity
Mathematics 2019, 7(2), 151; https://doi.org/10.3390/math7020151 - 05 Feb 2019
Abstract
In this paper, we study a class of nonlinear Choquard equation driven by the fractional Laplacian. When the potential function vanishes at infinity, we obtain the existence of a ground state solution for the fractional Choquard equation by using a non-Nehari manifold method. [...] Read more.
In this paper, we study a class of nonlinear Choquard equation driven by the fractional Laplacian. When the potential function vanishes at infinity, we obtain the existence of a ground state solution for the fractional Choquard equation by using a non-Nehari manifold method. Moreover, in the zero mass case, we obtain a nontrivial solution by using a perturbation method. The results improve upon those in Alves, Figueiredo, and Yang (2015) and Shen, Gao, and Yang (2016). Full article
(This article belongs to the Special Issue Polynomials: Theory and Applications)
Open AccessArticle
Some Identities on Degenerate Bernstein and Degenerate Euler Polynomials
Mathematics 2019, 7(1), 47; https://doi.org/10.3390/math7010047 - 04 Jan 2019
Cited by 4
Abstract
In recent years, intensive studies on degenerate versions of various special numbers and polynomials have been done by means of generating functions, combinatorial methods, umbral calculus, p-adic analysis and differential equations. The degenerate Bernstein polynomials and operators were recently introduced as degenerate [...] Read more.
In recent years, intensive studies on degenerate versions of various special numbers and polynomials have been done by means of generating functions, combinatorial methods, umbral calculus, p-adic analysis and differential equations. The degenerate Bernstein polynomials and operators were recently introduced as degenerate versions of the classical Bernstein polynomials and operators. Herein, we firstly derive some of their basic properties. Secondly, we explore some properties of the degenerate Euler numbers and polynomials and also their relations with the degenerate Bernstein polynomials. Full article
(This article belongs to the Special Issue Polynomials: Theory and Applications)
Open AccessArticle
Some Identities Involving Hermite Kampé de Fériet Polynomials Arising from Differential Equations and Location of Their Zeros
Mathematics 2019, 7(1), 23; https://doi.org/10.3390/math7010023 - 26 Dec 2018
Abstract
In this paper, we study differential equations arising from the generating functions of Hermit Kamp e ´ de F e ´ riet polynomials. Use this differential equation to give explicit identities for Hermite Kamp e ´ de F e ´ riet polynomials. Finally, [...] Read more.
In this paper, we study differential equations arising from the generating functions of Hermit Kamp e ´ de F e ´ riet polynomials. Use this differential equation to give explicit identities for Hermite Kamp e ´ de F e ´ riet polynomials. Finally, use the computer to view the location of the zeros of Hermite Kamp e ´ de F e ´ riet polynomials. Full article
(This article belongs to the Special Issue Polynomials: Theory and Applications)
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