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The 32th Congress of The Jangjeon Mathematical Society (ICJMS2019) will...
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The 32th Congress of The Jangjeon Mathematical Society (ICJMS2019) will be Held at Far Eastern Federal Universit, Vladivostok Russia

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

Deadline for manuscript submissions: closed (31 July 2020) | Viewed by 42262

Special Issue Editors

Prof. Dr. Taekyun Kim

E-Mail Website1 Website2
Guest Editor
Department of Mathematics, Kwangwoon University, Seoul 139-701, Korea
Interests: q-Calculus; p-adic Analysis; Analytic Number Theory; Complex Analysis
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Yilmaz Simsek

E-Mail Website1 Website2
Guest Editor
Akdeniz University
Interests: q-calculus; p-adic analysis; analytic number theory; complex analysis
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Dmitry V. Dolgy

E-Mail Website
Guest Editor
1. Education Glocal Center, Kwangwoon University, Seoul 01897, Republic of Korea
2. Mathematical Methods in Economy, School of Natural Sciences, Far Eastern Federal University, 690091 Vladivostok, Russia
Interests: q-calculus; p-adic analysis; analytic number theory; complex analysis

Special Issue Information

Dear Colleagues,

We would like to announce that in 2019 the Journal Symmetry will publish an additional Special Issue for the 32th Congress of the Jangjeon Mathematical Society (ICJMS2019), which will be held at Far Eastern Federal Universit, Vladivostok, Russia. The papers presented at this conference will be considered for publication in this Issue by the special Guest Editors. We would like to invite all the authors to this conference and to contribute to this Special Issue by submitting their work to Symmetry on the following subjects: pure and computational and applied mathematics and statistics, and mathematical physics (related to p-adic analysis, umbral algebra, and their applications)

Prof. Dr. Taekyun Kim
Prof. Dr. Yilmaz Simsek
Prof. Dr. Dmitry V Dolgy
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 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

  • Analysis
  • Algebra
  • Linear and multilinear algebra
  • Clifford algebras and applications
  • Real and complex functions
  • Orthogonal polynomials
  • Special numbers and functions
  • Fractional Calculus and q-theory
  • Number theory and combinatorics
  • Approximation theory and optimization
  • Integral transformations, equations, and operational calculus
  • Partial differential equations
  • Geometry and its applications
  • Numerical methods and algorithms
  • Probability and statistics and their applications
  • Scientific computation
  • Mathematical methods in physics and in engineering
  • Mathematical geosciences

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Published Papers (16 papers)

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16 pages, 298 KiB  
Article
A New Class of Symmetric Beta Type Distributions Constructed by Means of Symmetric Bernstein Type Basis Functions
by Fusun Yalcin and Yilmaz Simsek
Symmetry 2020, 12(5), 779; https://doi.org/10.3390/sym12050779 - 7 May 2020
Cited by 7 | Viewed by 2860 | Correction
Abstract
The main aim of this paper is to define and investigate a new class of symmetric beta type distributions with the help of the symmetric Bernstein-type basis functions. We give symmetry property of these distributions and the Bernstein-type basis functions. Using the Bernstein-type [...] Read more.
The main aim of this paper is to define and investigate a new class of symmetric beta type distributions with the help of the symmetric Bernstein-type basis functions. We give symmetry property of these distributions and the Bernstein-type basis functions. Using the Bernstein-type basis functions and binomial series, we give some series and integral representations including moment generating function for these distributions. Using generating functions and their functional equations, we also give many new identities related to the moments, the polygamma function, the digamma function, the harmonic numbers, the Stirling numbers, generalized harmonic numbers, the Lah numbers, the Bernstein-type basis functions, the array polynomials, and the Apostol–Bernoulli polynomials. Moreover, some numerical values of the expected values for the logarithm of random variable are given. Full article
(This article belongs to the Special Issue The 32th Congress of The Jangjeon Mathematical Society (ICJMS2019) will be Held at Far Eastern Federal Universit, Vladivostok Russia)
9 pages, 877 KiB  
Article
Euler–Catalan’s Number Triangle and Its Application
by Yuriy Shablya and Dmitry Kruchinin
Symmetry 2020, 12(4), 600; https://doi.org/10.3390/sym12040600 - 10 Apr 2020
Cited by 4 | Viewed by 3286
Abstract
In this paper, we study such combinatorial objects as labeled binary trees of size n with m ascents on the left branch and labeled Dyck n-paths with m ascents on return steps. For these combinatorial objects, we present the relation of the [...] Read more.
In this paper, we study such combinatorial objects as labeled binary trees of size n with m ascents on the left branch and labeled Dyck n-paths with m ascents on return steps. For these combinatorial objects, we present the relation of the generated number triangle to Catalan’s and Euler’s triangles. On the basis of properties of Catalan’s and Euler’s triangles, we obtain an explicit formula that counts the total number of such combinatorial objects and a bivariate generating function. Combining the properties of these two number triangles allows us to obtain different combinatorial objects that may have a symmetry, for example, in their form or in their formulas. Full article
(This article belongs to the Special Issue The 32th Congress of The Jangjeon Mathematical Society (ICJMS2019) will be Held at Far Eastern Federal Universit, Vladivostok Russia)
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8 pages, 737 KiB  
Article
The Quadratic Residues and Some of Their New Distribution Properties
by Tingting Wang and Xingxing Lv
Symmetry 2020, 12(3), 421; https://doi.org/10.3390/sym12030421 - 5 Mar 2020
Cited by 9 | Viewed by 3156
Abstract
In this paper, we give some interesting identities and asymptotic formulas for one kind of counting function, by studying the computational problems involving the symmetry sums of one kind quadratic residues and quadratic non-residues mod   p . The main methods we used [...] Read more.
In this paper, we give some interesting identities and asymptotic formulas for one kind of counting function, by studying the computational problems involving the symmetry sums of one kind quadratic residues and quadratic non-residues mod   p . The main methods we used are the properties of the Legendre’s symbol mod   p , and the estimate for character sums. As application, we solve two open problems proposed by Zhiwei Sun. Full article
(This article belongs to the Special Issue The 32th Congress of The Jangjeon Mathematical Society (ICJMS2019) will be Held at Far Eastern Federal Universit, Vladivostok Russia)
13 pages, 295 KiB  
Article
A Note on Weakly S-Noetherian Rings
by Dong Kyu Kim and Jung Wook Lim
Symmetry 2020, 12(3), 419; https://doi.org/10.3390/sym12030419 - 5 Mar 2020
Cited by 3 | Viewed by 2669
Abstract
Let R be a commutative ring with identity and S a (not necessarily saturated) multiplicative subset of R. We call the ring R to be a weakly S-Noetherian ring if every S-finite proper ideal of R is an S-Noetherian [...] Read more.
Let R be a commutative ring with identity and S a (not necessarily saturated) multiplicative subset of R. We call the ring R to be a weakly S-Noetherian ring if every S-finite proper ideal of R is an S-Noetherian R-module. In this article, we study some properties of weakly S-Noetherian rings. In particular, we give some conditions for the Nagata’s idealization and the amalgamated algebra to be weakly S-Noetherian rings. Full article
(This article belongs to the Special Issue The 32th Congress of The Jangjeon Mathematical Society (ICJMS2019) will be Held at Far Eastern Federal Universit, Vladivostok Russia)
13 pages, 306 KiB  
Article
Some New Families of Special Polynomials and Numbers Associated with Finite Operators
by Yilmaz Simsek
Symmetry 2020, 12(2), 237; https://doi.org/10.3390/sym12020237 - 4 Feb 2020
Cited by 9 | Viewed by 1988
Abstract
The aim of this study was to define a new operator. This operator unify and modify many known operators, some of which were introduced by the author. Many properties of this operator are given. Using this operator, two new classes of special polynomials [...] Read more.
The aim of this study was to define a new operator. This operator unify and modify many known operators, some of which were introduced by the author. Many properties of this operator are given. Using this operator, two new classes of special polynomials and numbers are defined. Many identities and relationships are derived, including these new numbers and polynomials, combinatorial sums, the Bernoulli numbers, the Euler numbers, the Stirling numbers, the Daehee numbers, and the Changhee numbers. By applying the derivative operator to these new polynomials, derivative formulas are found. Integral representations, including the Volkenborn integral, the fermionic p-adic integral, and the Riemann integral, are given for these new polynomials. Full article
(This article belongs to the Special Issue The 32th Congress of The Jangjeon Mathematical Society (ICJMS2019) will be Held at Far Eastern Federal Universit, Vladivostok Russia)
11 pages, 291 KiB  
Article
Properties of Partially Degenerate Complex Appell Polynomials
by Dojin Kim and Sangil Kim
Symmetry 2019, 11(12), 1508; https://doi.org/10.3390/sym11121508 - 11 Dec 2019
Viewed by 1974
Abstract
Degenerate versions of polynomial sequences have been recently studied to obtain useful properties such as symmetric identities by introducing degenerate exponential-type generating functions. As part of our continued work in degenerate versions of generating functions, we subsequently present our study on degenerate complex [...] Read more.
Degenerate versions of polynomial sequences have been recently studied to obtain useful properties such as symmetric identities by introducing degenerate exponential-type generating functions. As part of our continued work in degenerate versions of generating functions, we subsequently present our study on degenerate complex Appell polynomials by considering a partially degenerate version of the generating functions of ordinary complex Appell polynomials in this paper. We only consider partially degenerate generating functions to retain the crucial properties of the Appell sequence, and we present useful identities and general properties by splitting complex values into their real and imaginary parts; moreover, we provide several explicit examples. Additionally, the differential equations satisfied by degenerate complex Bernoulli and Euler polynomials are derived by the quasi-monomiality principle using Appell-type polynomials. Full article
(This article belongs to the Special Issue The 32th Congress of The Jangjeon Mathematical Society (ICJMS2019) will be Held at Far Eastern Federal Universit, Vladivostok Russia)
7 pages, 210 KiB  
Article
Some New Identities of Second Order Linear Recurrence Sequences
by Yanyan Liu and Xingxing Lv
Symmetry 2019, 11(12), 1496; https://doi.org/10.3390/sym11121496 - 10 Dec 2019
Cited by 6 | Viewed by 2253
Abstract
The main purpose of this paper is using the combinatorial method, the properties of the power series and characteristic roots to study the computational problem of the symmetric sums of a certain second-order linear recurrence sequences, and obtain some new and interesting identities. [...] Read more.
The main purpose of this paper is using the combinatorial method, the properties of the power series and characteristic roots to study the computational problem of the symmetric sums of a certain second-order linear recurrence sequences, and obtain some new and interesting identities. These results not only improve on some of the existing results, but are also simpler and more beautiful. Of course, these identities profoundly reveal the regularity of the second-order linear recursive sequence, which can greatly facilitate the calculation of the symmetric sums of the sequences in practice. Full article
(This article belongs to the Special Issue The 32th Congress of The Jangjeon Mathematical Society (ICJMS2019) will be Held at Far Eastern Federal Universit, Vladivostok Russia)
8 pages, 252 KiB  
Article
Identities Involving the Fourth-Order Linear Recurrence Sequence
by Lan Qi and Zhuoyu Chen
Symmetry 2019, 11(12), 1476; https://doi.org/10.3390/sym11121476 - 4 Dec 2019
Cited by 1 | Viewed by 2234
Abstract
In this paper, we introduce the fourth-order linear recurrence sequence and its generating function and obtain the exact coefficient expression of the power series expansion using elementary methods and symmetric properties of the summation processes. At the same time, we establish some relations [...] Read more.
In this paper, we introduce the fourth-order linear recurrence sequence and its generating function and obtain the exact coefficient expression of the power series expansion using elementary methods and symmetric properties of the summation processes. At the same time, we establish some relations involving Tetranacci numbers and give some interesting identities. Full article
(This article belongs to the Special Issue The 32th Congress of The Jangjeon Mathematical Society (ICJMS2019) will be Held at Far Eastern Federal Universit, Vladivostok Russia)
10 pages, 318 KiB  
Article
Signed Domination Number of the Directed Cylinder
by Haichao Wang and Hye Kyung Kim
Symmetry 2019, 11(12), 1443; https://doi.org/10.3390/sym11121443 - 23 Nov 2019
Cited by 3 | Viewed by 2256
Abstract
In a digraph D = ( V ( D ) , A ( D ) ) , a two-valued function f : V ( D ) → { − 1 , 1 } defined on the vertices of D is called a signed [...] Read more.
In a digraph D = ( V ( D ) , A ( D ) ) , a two-valued function f : V ( D ) → { − 1 , 1 } defined on the vertices of D is called a signed dominating function if f ( N − [ v ] ) ≥ 1 for every v in D. The weight of a signed dominating function is f ( V ( D ) ) = ∑ v ∈ V ( D ) f ( v ) . The signed domination number γ s ( D ) is the minimum weight among all signed dominating functions of D. Let P m × C n be the Cartesian product of directed path P m and directed cycle C n . In this paper, the exact value of γ s ( P m × C n ) is determined for any positive integers m and n. Full article
(This article belongs to the Special Issue The 32th Congress of The Jangjeon Mathematical Society (ICJMS2019) will be Held at Far Eastern Federal Universit, Vladivostok Russia)
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14 pages, 292 KiB  
Article
Bounds for the Coefficient of Faber Polynomial of Meromorphic Starlike and Convex Functions
by Oh Sang Kwon, Shahid Khan, Young Jae Sim and Saqib Hussain
Symmetry 2019, 11(11), 1368; https://doi.org/10.3390/sym11111368 - 4 Nov 2019
Cited by 5 | Viewed by 1860
Abstract
Let Σ be the class of meromorphic functions f of the form f ( ζ ) = ζ + ∑ n = 0 ∞ a n ζ − n which are analytic in [...] Read more.
Let Σ be the class of meromorphic functions f of the form f ( ζ ) = ζ + ∑ n = 0 ∞ a n ζ − n which are analytic in Δ : = { ζ ∈ C : | ζ | > 1 } . For n ∈ N 0 : = N ∪ { 0 } , the nth Faber polynomial Φ n ( w ) of f ∈ Σ is a monic polynomial of degree n that is generated by a function ζ f ′ ( ζ ) / ( f ( ζ ) − w ) . For given f ∈ Σ , by F n , i ( f ) , we denote the ith coefficient of Φ n ( w ) . For given 0 ≤ α < 1 and 0 < β ≤ 1 , let us consider domains H α and S β ⊂ C defined by H α = { w ∈ C : Re ( w ) > α } and S β = { w ∈ C : | arg ( w ) | < β } , which are symmetric with respect to the real axis. A function f ∈ Σ is called meromorphic starlike of order α if ζ f ′ ( ζ ) / f ( ζ ) ∈ H α for all ζ ∈ Δ . Another function f ∈ Σ is called meromorphic strongly starlike of order β if ζ f ′ ( ζ ) / f ( ζ ) ∈ S β for all ζ ∈ Δ . In this paper we investigate the sharp bounds of F n , n − i ( f ) , n ∈ N 0 , i ∈ { 2 , 3 , 4 } , for meromorphic starlike functions of order α and meromorphic strongly starlike of order β . Similar estimates for meromorphic convex functions of order α ( 0 ≤ α < 1 ) and meromorphic strongly convex of order β ( 0 < β ≤ 1 ) are also discussed. Full article
(This article belongs to the Special Issue The 32th Congress of The Jangjeon Mathematical Society (ICJMS2019) will be Held at Far Eastern Federal Universit, Vladivostok Russia)
14 pages, 251 KiB  
Article
A Note on the Degenerate Type of Complex Appell Polynomials
by Dojin Kim
Symmetry 2019, 11(11), 1339; https://doi.org/10.3390/sym11111339 - 31 Oct 2019
Cited by 19 | Viewed by 2668
Abstract
In this paper, complex Appell polynomials and their degenerate-type polynomials are considered as an extension of real-valued polynomials. By treating the real value part and imaginary part separately, we obtained useful identities and general properties by convolution of sequences. To justify the obtained [...] Read more.
In this paper, complex Appell polynomials and their degenerate-type polynomials are considered as an extension of real-valued polynomials. By treating the real value part and imaginary part separately, we obtained useful identities and general properties by convolution of sequences. To justify the obtained results, we show several examples based on famous Appell sequences such as Euler polynomials and Bernoulli polynomials. Further, we show that the degenerate types of the complex Appell polynomials are represented in terms of the Stirling numbers of the first kind. Full article
(This article belongs to the Special Issue The 32th Congress of The Jangjeon Mathematical Society (ICJMS2019) will be Held at Far Eastern Federal Universit, Vladivostok Russia)
7 pages, 209 KiB  
Article
Tribonacci Numbers and Some Related Interesting Identities
by Shujie Zhou and Li Chen
Symmetry 2019, 11(10), 1195; https://doi.org/10.3390/sym11101195 - 24 Sep 2019
Cited by 5 | Viewed by 3094
Abstract
The main purpose of this paper is, by using elementary methods and symmetry properties of the summation procedures, to study the computational problem of a certain power series related to the Tribonacci numbers, and to give some interesting identities for these numbers. Full article
(This article belongs to the Special Issue The 32th Congress of The Jangjeon Mathematical Society (ICJMS2019) will be Held at Far Eastern Federal Universit, Vladivostok Russia)
16 pages, 270 KiB  
Article
A Note on Degenerate Euler and Bernoulli Polynomials of Complex Variable
by Dae San Kim, Taekyun Kim and Hyunseok Lee
Symmetry 2019, 11(9), 1168; https://doi.org/10.3390/sym11091168 - 16 Sep 2019
Cited by 31 | Viewed by 3216
Abstract
Recently, the so-called new type Euler polynomials have been studied without considering Euler polynomials of a complex variable. Here we study degenerate versions of these new type Euler polynomials. This has been done by considering the degenerate Euler polynomials of a complex variable. [...] Read more.
Recently, the so-called new type Euler polynomials have been studied without considering Euler polynomials of a complex variable. Here we study degenerate versions of these new type Euler polynomials. This has been done by considering the degenerate Euler polynomials of a complex variable. We also investigate corresponding ones for Bernoulli polynomials in the same manner. We derive some properties and identities for those new polynomials. Here we note that our result gives an affirmative answer to the question raised by the reviewer of the paper. Full article
(This article belongs to the Special Issue The 32th Congress of The Jangjeon Mathematical Society (ICJMS2019) will be Held at Far Eastern Federal Universit, Vladivostok Russia)
19 pages, 282 KiB  
Article
Two Parametric Kinds of Eulerian-Type Polynomials Associated with Euler’s Formula
by Neslihan Kilar and Yilmaz Simsek
Symmetry 2019, 11(9), 1097; https://doi.org/10.3390/sym11091097 - 2 Sep 2019
Cited by 15 | Viewed by 2464
Abstract
The purpose of this article is to construct generating functions for new families of special polynomials including two parametric kinds of Eulerian-type polynomials. Some fundamental properties of these functions are given. By using these generating functions and the Euler’s formula, some identities and [...] Read more.
The purpose of this article is to construct generating functions for new families of special polynomials including two parametric kinds of Eulerian-type polynomials. Some fundamental properties of these functions are given. By using these generating functions and the Euler’s formula, some identities and relations among trigonometric functions, two parametric kinds of Eulerian-type polynomials, Apostol-type polynomials, the Stirling numbers and Fubini-type polynomials are presented. Computational formulae for these polynomials are obtained. Applying a partial derivative operator to these generating functions, some derivative formulae and finite combinatorial sums involving the aforementioned polynomials and numbers are also obtained. In addition, some remarks and observations on these polynomials are given. Full article
(This article belongs to the Special Issue The 32th Congress of The Jangjeon Mathematical Society (ICJMS2019) will be Held at Far Eastern Federal Universit, Vladivostok Russia)
11 pages, 236 KiB  
Article
Degenerate Stirling Polynomials of the Second Kind and Some Applications
by Taekyun Kim, Dae San Kim, Han Young Kim and Jongkyum Kwon
Symmetry 2019, 11(8), 1046; https://doi.org/10.3390/sym11081046 - 14 Aug 2019
Cited by 34 | Viewed by 3545
Abstract
Recently, the degenerate λ -Stirling polynomials of the second kind were introduced and investigated for their properties and relations. In this paper, we continue to study the degenerate λ -Stirling polynomials as well as the r-truncated degenerate λ -Stirling polynomials of the [...] Read more.
Recently, the degenerate λ -Stirling polynomials of the second kind were introduced and investigated for their properties and relations. In this paper, we continue to study the degenerate λ -Stirling polynomials as well as the r-truncated degenerate λ -Stirling polynomials of the second kind which are derived from generating functions and Newton’s formula. We derive recurrence relations and various expressions for them. Regarding applications, we show that both the degenerate λ -Stirling polynomials of the second and the r-truncated degenerate λ -Stirling polynomials of the second kind appear in the expressions of the probability distributions of appropriate random variables. Full article
(This article belongs to the Special Issue The 32th Congress of The Jangjeon Mathematical Society (ICJMS2019) will be Held at Far Eastern Federal Universit, Vladivostok Russia)

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3 pages, 191 KiB  
Erratum
Kim, T. et al. Degenerate Stirling Polynomials of the Second Kind and Some Applications. Symmetry, 2019, 11(8), 1046
by Taekyun Kim, Dae San Kim, Han Young Kim and Jongkyum Kwon
Symmetry 2019, 11(12), 1530; https://doi.org/10.3390/sym11121530 - 17 Dec 2019
Cited by 1 | Viewed by 1742
Abstract
The authors wish to make the following corrections to the published paper [...] Full article
(This article belongs to the Special Issue The 32th Congress of The Jangjeon Mathematical Society (ICJMS2019) will be Held at Far Eastern Federal Universit, Vladivostok Russia)
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