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Symmetry
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Singular Distributions With Special Structures and Symmetries
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Singular Distributions With Special Structures and Symmetries

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

Deadline for manuscript submissions: closed (30 November 2023) | Viewed by 5532

Special Issue Editor

Prof. Dr. Paul Popescu

E-Mail Website
Guest Editor
Department of Applied Mathematics, University of Craiova, 200585 Craiova, Romania
Interests: mathematics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The aim of our Special Issue, titled “Singular Distributions with Special Structures and Symmetries”, is to bring together outstanding theoretical contributions to singular geometric distributions, adapting special structures and symmetries from various mathematical and physical research areas, but with real-world applications. Some of the topics of interest include:

  • Special structures specific to all mathematical or physical areas, which can offer outstanding examples to motivate general notions. They have specific symmetries that sometimes determine their theoretical force;
  • Singular geometric distributions, which are involved in many concrete applications, mostly in mechanics and control, but also elsewhere;
  • Lagrangians and Hamiltonians, whose use is adapted to singular geometric distributions, such as singular foliations, and which can be performed as in some classical cases;
  • The anchored approach used for singular geometric distributions, which can provide general structures and symmetries in an analogous way to classical cases; 
  • Classical generalizations using different types of algebroids or groupoids, which can be transferred to the study of singular structures and symmetries using classical methods for regular structures.

Our belief is that certain methods of discretization, such that the Veselov type of tangent spaces, can be extended to more general cases. The investigation of their properties, including symmetries, is therefore of extreme importance.

Prof. Dr. Paul Popescu
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

  • singular geometric distribution
  • anchored bundle
  • almost Lie algebroid
  • Lie algebroid
  • symmetry
  • discretization
  • foliation

Published Papers (5 papers)

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Research

16 pages, 392 KiB  
Article
Jacobi Stability for T-System
by Florian Munteanu
Symmetry 2024, 16(1), 84; https://doi.org/10.3390/sym16010084 - 09 Jan 2024
Viewed by 1065
Abstract
In this paper will be considered a three-dimensional autonomous quadratic polynomial system of first-order differential equations with three real parameters, the so-called T-system. This system is symmetric relative to the Oz-axis and represents a special type of the generalized Lorenz system. [...] Read more.
In this paper will be considered a three-dimensional autonomous quadratic polynomial system of first-order differential equations with three real parameters, the so-called T-system. This system is symmetric relative to the Oz-axis and represents a special type of the generalized Lorenz system. The approach of this work will consist of the study of the nonlinear dynamics of this system through the Kosambi–Cartan–Chern (KCC) geometric theory. More exactly, we will focus on the associated system of second-order differential equations (SODE) from the point of view of Jacobi stability by determining the five invariants of the KCC theory. These invariants determine the internal geometrical characteristics of the system, and particularly, the deviation curvature tensor is decisive for Jacobi stability. Furthermore, we will look for necessary and sufficient conditions that the system parameters must satisfy in order to have Jacobi stability for every equilibrium point. Full article
(This article belongs to the Special Issue Singular Distributions With Special Structures and Symmetries)
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18 pages, 325 KiB  
Article
A Generalization of Secondary Characteristic Classes on Lie Pseudoalgebras
by Bogdan Balcerzak
Symmetry 2024, 16(1), 24; https://doi.org/10.3390/sym16010024 - 24 Dec 2023
Viewed by 691
Abstract
The aim of the paper is to construct a secondary characteristic homomorphism for Lie pseudoalgebras. The case of inner product modules is under consideration. Full article
(This article belongs to the Special Issue Singular Distributions With Special Structures and Symmetries)
16 pages, 5209 KiB  
Article
Multiple Soliton Solutions for Coupled Modified Korteweg–de Vries (mkdV) with a Time-Dependent Variable Coefficient
by Haroon D. S. Adam, Khalid I. A. Ahmed, Mukhtar Yagoub Youssif and Marin Marin
Symmetry 2023, 15(11), 1972; https://doi.org/10.3390/sym15111972 - 25 Oct 2023
Viewed by 812
Abstract
In this manuscript, we implement analytical multiple soliton wave and singular soliton wave solutions for coupled mKdV with a time-dependent variable coefficient. Based on the similarity transformation and Hirota bilinear technique, we construct both multiple wave kink and wave singular kink solutions for [...] Read more.
In this manuscript, we implement analytical multiple soliton wave and singular soliton wave solutions for coupled mKdV with a time-dependent variable coefficient. Based on the similarity transformation and Hirota bilinear technique, we construct both multiple wave kink and wave singular kink solutions for coupled mKdV with a time-dependent variable coefficient. We implement the Hirota bilinear technique to compute analytical solutions for the coupled mKdV system. Such calculations are made by using a software with symbolic computation software, for instance, Maple. Recently some researchers used Maple in order to show that the bilinear method of Hirota is a straightforward technique which can be used in the approach of differential, nonlinear models. We analyzed whether the experiments proved that the procedure is effective and can be successfully used for many other mathematical models used in physics and engineering. The results of this study display that the profiles of multiple-kink and singular-kink soliton types can be efficiently controlled by selecting the particular form of a similar time variable. The changes in the solitons based on the changes in the arbitrary function of time allows for more applications of them in applied sciences. Full article
(This article belongs to the Special Issue Singular Distributions With Special Structures and Symmetries)
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11 pages, 262 KiB  
Article
Extended Curvatures and Lie Algebroids
by Marcela Popescu and Paul Popescu
Symmetry 2022, 14(7), 1375; https://doi.org/10.3390/sym14071375 - 04 Jul 2022
Cited by 2 | Viewed by 900
Abstract
The aim of the paper is to find conditions in which the derived almost Lie vector bundle E1 of an almost Lie vector bundle E is a Lie algebroid. The conditions are that some extended curvatures on E, considered in the [...] Read more.
The aim of the paper is to find conditions in which the derived almost Lie vector bundle E1 of an almost Lie vector bundle E is a Lie algebroid. The conditions are that some extended curvatures on E, considered in the paper, are vanishing. Two non-trivial examples are given. One example is when E0 is a skew symmetric algebroid; the other one is when E1 is not a skew symmetric algebroid. Full article
(This article belongs to the Special Issue Singular Distributions With Special Structures and Symmetries)
12 pages, 286 KiB  
Article
Analyzing the Jacobi Stability of Lü’s Circuit System
by Florian Munteanu
Symmetry 2022, 14(6), 1248; https://doi.org/10.3390/sym14061248 - 16 Jun 2022
Cited by 4 | Viewed by 1179
Abstract
By reformulating the circuit system of Lü as a set of two second order differential equations, we investigate the nonlinear dynamics of Lü’s circuit system from the Jacobi stability point of view, using Kosambi–Cartan–Chern geometric theory. We will determine the five KCC invariants, [...] Read more.
By reformulating the circuit system of Lü as a set of two second order differential equations, we investigate the nonlinear dynamics of Lü’s circuit system from the Jacobi stability point of view, using Kosambi–Cartan–Chern geometric theory. We will determine the five KCC invariants, which express the intrinsic geometric properties of the system, including the deviation curvature tensor. Finally, we will obtain necessary and sufficient conditions on the parameters of the system to have the Jacobi stability near the equilibrium points. Full article
(This article belongs to the Special Issue Singular Distributions With Special Structures and Symmetries)
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