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Selected Papers of International Conference on Mathematical and Statistical Sciences: A Selçuk Meeting (Dedicated to Victims of Türkiye Earthquakes)

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

Deadline for manuscript submissions: closed (30 September 2023) | Viewed by 2901

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Special Issue Editors

Dr. Tuncer Acar

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Guest Editor

Department of Mathematics, Salcuk University, Konya, Turkey
Interests: approximation theory; sequence spaces; quantum calculus; special functions; functional analysis

Prof. Dr. Ali Aral

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Guest Editor

Department of Mathematics, Salcuk University, Konya, Turkey
Interests: approximation theory; quantum calculus

Special Issue Information

Dear Colleagues,

The Special Issue is dedicated to selected papers presented at the online conference Internatoinal E-Conference on Mathematical and Statistical Sciences: A selçuk Meetin, which is dedicated to victims of Türkiye earthquakes (https://icomss23.selcuk.edu.tr/).

The conference has sessions on Algebra, Analysis, Applied Mathematics, Geometry and Topology. Hence, papers from this field related to symmetry can be submitted to this Special Issue.

Dr. Tuncer Acar
Prof. Dr. Ali Aral
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

symmetry in analysis
algebra
applied mathematics
topology
geometry

Published Papers (2 papers)

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Research

14 pages, 289 KiB

Open AccessArticle

Artificial Neural Networks Using Quiver Representations of Finite Cyclic Groups

by Lucky Cahya Wanditra, Intan Muchtadi-Alamsyah and Dellavitha Nasution

Symmetry 2023, 15(12), 2110; https://doi.org/10.3390/sym15122110 - 24 Nov 2023

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Abstract

In this paper, we propose using quiver representations as a tool for understanding artificial neural network algorithms. Specifically, we construct these algorithms by utilizing the group algebra of a finite cyclic group as vertices and convolution transformations as maps. We will demonstrate the neural network using convolution operation in the group algebra. The convolution operation in the group algebra that is formed by a finite cyclic group can be seen as a circulant matrix. We will represent a circulant matrix as a map from a cycle permutation matrix to a polynomial function. Using the permutation matrix, we will see some properties of the circulant matrix. Furthermore, we will examine some properties of circulant matrices using representations of finite symmetric groups as permutation matrices. Using the properties, we also examine the properties of moduli spaces formed by the actions of the change of basis group on the set of quiver representations. Through this analysis, we can compute the dimension of the moduli spaces. Full article

(This article belongs to the Special Issue Selected Papers of International Conference on Mathematical and Statistical Sciences: A Selçuk Meeting (Dedicated to Victims of Türkiye Earthquakes))

19 pages, 478 KiB

Open AccessArticle

Representations of Flat Virtual Braids by Automorphisms of Free Group

by Bogdan Chuzhinov and Andrey Vesnin

Symmetry 2023, 15(8), 1538; https://doi.org/10.3390/sym15081538 - 3 Aug 2023

Cited by 1 | Viewed by 1078

Abstract

Representations of braid group

B_{n}

n \geq 2

strands by automorphisms of a free group of rank n go back to Artin. In 1991, Kauffman introduced a theory of virtual braids, virtual knots, and links. The virtual braid group [...] Read more.

Representations of braid group

B_{n}

n \geq 2

strands by automorphisms of a free group of rank n go back to Artin. In 1991, Kauffman introduced a theory of virtual braids, virtual knots, and links. The virtual braid group

V B_{n}

n \geq 2

strands is an extension of the classical braid group

B_{n}

by the symmetric group

S_{n}

. In this paper, we consider flat virtual braid groups

F V B_{n}

n \geq 2

strands and construct a family of representations of

F V B_{n}

by automorphisms of free groups of rank

2 n

. It has been established that these representations do not preserve the forbidden relations between classical and virtual generators. We investigated some algebraic properties of the constructed representations. In particular, we established conditions of faithfulness in case