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Symmetry
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Symmetry in Methods of Numerical Analysis and Its Application in...
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Symmetry in Methods of Numerical Analysis and Its Application in Engineering

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

Deadline for manuscript submissions: closed (31 October 2024) | Viewed by 3947

Special Issue Editors

Prof. Dr. Sandra Pinelas

E-Mail Website
Guest Editor
Departamento De Ciencias Exatas E Engenharia Academia Militar, Av. Conde Castro Guimaraes, 2720-113 Amadora, Portugal
Interests: differential equations; difference equations; oscillatory behavior; asymptotic behavior
Special Issues, Collections and Topics in MDPI journals
Dr. Ivan Dražić

E-Mail Website
Co-Guest Editor
Department of Applied Mathematics, Faculty of Engineering, University of Rijeka, Vukovarska 58, 51000 Rijeka, Croatia
Interests: partial differential; equationsmicropolar; fluidsnumerical analysis
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Symmetries have important roles in solving differential equations. The aim of this Special Issue is to introduce recent research results in numerical analysis and its applications in engineering.

Papers in all areas of numerical analysis and applications are welcome. More specifically, we welcome papers that concern topics including, but not limited to, the following:

  • Ordinary differential equations;
  • Partial differential equations;
  • Stochastic differential equations;
  • Approximation theory;
  • Numerical linear algebra;
  • Numerical integral equations;
  • Numerical problems in dynamical systems;
  • Applications to the sciences (computational physics, computational statistics, computational chemistry, computational engineering, etc.).

Prof. Dr. Sandra Pinelas
Dr. Ivan Dražić
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

  • numerical methods
  • difference equations
  • differential equations
  • applications

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Further information on MDPI's Special Issue polices can be found here.

Published Papers (3 papers)

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Research

9 pages, 466 KiB  
Article
A New Approach to Circular Inversion in l1-Normed Spaces
by Temel Ermiş, Ali Osman Şen and Johan Gielis
Symmetry 2024, 16(7), 874; https://doi.org/10.3390/sym16070874 - 10 Jul 2024
Viewed by 546
Abstract
While there are well-known synthetic methods in the literature for finding the image of a point under circular inversion in l2-normed geometry (Euclidean geometry), there is no similar synthetic method in Minkowski geometry, also known as the geometry of finite-dimensional Banach [...] Read more.
While there are well-known synthetic methods in the literature for finding the image of a point under circular inversion in l2-normed geometry (Euclidean geometry), there is no similar synthetic method in Minkowski geometry, also known as the geometry of finite-dimensional Banach spaces. In this study, we have succeeded in creating a synthetic construction of the circular inversion in l1-normed spaces, which is one of the most fundamental examples of Minkowski geometry. Moreover, this synthetic construction has been given using the Euclidean circle, independently of the l1-norm. Full article
(This article belongs to the Special Issue Symmetry in Methods of Numerical Analysis and Its Application in Engineering)
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14 pages, 258 KiB  
Article
2D Discrete Yang–Mills Equations on the Torus
by Volodymyr Sushch
Symmetry 2024, 16(7), 823; https://doi.org/10.3390/sym16070823 - 1 Jul 2024
Viewed by 836
Abstract
In this paper, we introduce a discretization scheme for the Yang–Mills equations in the two-dimensional case using a framework based on discrete exterior calculus. Within this framework, we define discrete versions of the exterior covariant derivative operator and its adjoint, which capture essential [...] Read more.
In this paper, we introduce a discretization scheme for the Yang–Mills equations in the two-dimensional case using a framework based on discrete exterior calculus. Within this framework, we define discrete versions of the exterior covariant derivative operator and its adjoint, which capture essential geometric features similar to their continuous counterparts. Our focus is on discrete models defined on a combinatorial torus, where the discrete Yang–Mills equations are presented in the form of both a system of difference equations and a matrix form. Full article
(This article belongs to the Special Issue Symmetry in Methods of Numerical Analysis and Its Application in Engineering)
17 pages, 316 KiB  
Article
Uncertainty Principles for the Two-Sided Quaternion Windowed Quadratic-Phase Fourier Transform
by Mohammad Younus Bhat, Aamir Hamid Dar, Irfan Nurhidayat and Sandra Pinelas
Symmetry 2022, 14(12), 2650; https://doi.org/10.3390/sym14122650 - 15 Dec 2022
Cited by 10 | Viewed by 1555
Abstract
A recent addition to the class of integral transforms is the quaternion quadratic-phase Fourier transform (Q-QPFT), which generalizes various signal and image processing tools. However, this transform is insufficient for addressing the quadratic-phase spectrum of non-stationary signals in the quaternion domain. To address [...] Read more.
A recent addition to the class of integral transforms is the quaternion quadratic-phase Fourier transform (Q-QPFT), which generalizes various signal and image processing tools. However, this transform is insufficient for addressing the quadratic-phase spectrum of non-stationary signals in the quaternion domain. To address this problem, we, in this paper, study the (two sided) quaternion windowed quadratic-phase Fourier transform (QWQPFT) and investigate the uncertainty principles associated with the QWQPFT. We first propose the definition of QWQPFT and establish its relation with quaternion Fourier transform (QFT); then, we investigate several properties of QWQPFT which includes inversion and the Plancherel theorem. Moreover, we study different kinds of uncertainty principles for QWQPFT such as Hardy’s uncertainty principle, Beurling’s uncertainty principle, Donoho–Stark’s uncertainty principle, the logarithmic uncertainty principle, the local uncertainty principle, and Pitt’s inequality. Full article
(This article belongs to the Special Issue Symmetry in Methods of Numerical Analysis and Its Application in Engineering)
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