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Symmetry
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Symmetry in Abstract Differential Equations
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Symmetry in Abstract Differential Equations

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

Deadline for manuscript submissions: closed (15 June 2022) | Viewed by 6438

Special Issue Editor

Prof. Dr. Angelo Favini

E-Mail Website
Guest Editor
Department of Mathematics, University of Bologna, 40126 Bologna, Italy
Interests: mathematics; computer science; engineering; decision sciences; agricultural and biological sciences; environmental science; physics and astronomy

Special Issue Information

Dear Colleagues,

We welcome interdisciplinary interaction between different fields of science, and we intend to follow in the footsteps of Hermann Weyl, a great researcher responsible for important progress in the field of symmetry in math and physics. He expressed great interest in symmetry in many additional fields of science, as explored in his eye-opening book, Symmetry. As expressed by Weyl, symmetry is a fundamental phenomenon in nature and all sciences. This Special Issue of Symmetry aims to promote the discussion and exchange of cutting-edge knowledge and ideas of symmetry in a variety of subjects ranging from physics, chemistry, mathematics, and computer science, to biology. In particular, results on:

- Symmetry groups;

- Reflection groups;

- Classification of symmetry;

- Symmetry and degenerate differential equations;

- Dynamic inequalities;

- Nonlinear optimization;

- Gronwall–Bellman type inequalities;

are welcome.

Submit your paper and select the Journal “Symmetry” and the Special Issue “Symmetry in Abstract Differential Equations” via: MDPI submission system. Our papers will be published on a rolling basis and we will be pleased to receive your submission once you have finished it.

Prof. Dr. Angelo Favini
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

  • Symmetry groups
  • Reflection groups
  • Classification of symmetry
  • Symmetry and degenerate differential equations
  • Dynamic inequalities
  • Nonlinear optimization
  • Gronwall–Bellman type inequalities

Published Papers (4 papers)

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Research

18 pages, 286 KiB  
Article
Equivalent Conditions of the Reverse Hardy-Type Integral Inequalities
by Michael Th. Rassias, Bicheng Yang and Andrei Raigorodskii
Symmetry 2023, 15(2), 463; https://0-doi-org.brum.beds.ac.uk/10.3390/sym15020463 - 09 Feb 2023
Viewed by 884
Abstract
Hardy-type integral inequalities play a prominent role in the study of analytic inequalities, which are essential in mathematical analysis and its various applications, such as in the study of symmetry and asymmetry phenomena. In this paper, employing methods of real analysis and using [...] Read more.
Hardy-type integral inequalities play a prominent role in the study of analytic inequalities, which are essential in mathematical analysis and its various applications, such as in the study of symmetry and asymmetry phenomena. In this paper, employing methods of real analysis and using weight functions, we investigate some equivalent conditions of two kinds of reverse Hardy-type integral inequalities with a particular non-homogeneous kernel. A few equivalent conditions of two kinds of reverse Hardy-type integral inequalities with a particular homogeneous kernel are deduced in the form of applications. Full article
(This article belongs to the Special Issue Symmetry in Abstract Differential Equations)
20 pages, 343 KiB  
Article
An Inexact Optimal Hybrid Conjugate Gradient Method for Solving Symmetric Nonlinear Equations
by Jamilu Sabi’u, Kanikar Muangchoo, Abdullah Shah, Auwal Bala Abubakar and Kazeem Olalekan Aremu
Symmetry 2021, 13(10), 1829; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13101829 - 01 Oct 2021
Cited by 6 | Viewed by 1648
Abstract
This article presents an inexact optimal hybrid conjugate gradient (CG) method for solving symmetric nonlinear systems. The method is a convex combination of the optimal Dai–Liao (DL) and the extended three-term Polak–Ribiére–Polyak (PRP) CG methods. However, two different formulas for selecting the convex [...] Read more.
This article presents an inexact optimal hybrid conjugate gradient (CG) method for solving symmetric nonlinear systems. The method is a convex combination of the optimal Dai–Liao (DL) and the extended three-term Polak–Ribiére–Polyak (PRP) CG methods. However, two different formulas for selecting the convex parameter are derived by using the conjugacy condition and also by combining the proposed direction with the default Newton direction. The proposed method is again derivative-free, therefore the Jacobian information is not required throughout the iteration process. Furthermore, the global convergence of the proposed method is shown using some appropriate assumptions. Finally, the numerical performance of the method is demonstrated by solving some examples of symmetric nonlinear problems and comparing them with some existing symmetric nonlinear equations CG solvers. Full article
(This article belongs to the Special Issue Symmetry in Abstract Differential Equations)
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18 pages, 314 KiB  
Article
Surfaces and Curves Induced by Nonlinear Schrödinger-Type Equations and Their Spin Systems
by Akbota Myrzakul, Gulgassyl Nugmanova, Nurzhan Serikbayev and Ratbay Myrzakulov
Symmetry 2021, 13(10), 1827; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13101827 - 30 Sep 2021
Cited by 5 | Viewed by 1187
Abstract
In recent years, symmetry in abstract partial differential equations has found wide application in the field of nonlinear integrable equations. The symmetries of the corresponding transformation groups for such equations make it possible to significantly simplify the procedure for establishing equivalence between nonlinear [...] Read more.
In recent years, symmetry in abstract partial differential equations has found wide application in the field of nonlinear integrable equations. The symmetries of the corresponding transformation groups for such equations make it possible to significantly simplify the procedure for establishing equivalence between nonlinear integrable equations from different areas of physics, which in turn open up opportunities to easily find their solutions. In this paper, we study the symmetry between differential geometry of surfaces/curves and some integrable generalized spin systems. In particular, we investigate the gauge and geometrical equivalence between the local/nonlocal nonlinear Schrödinger type equations (NLSE) and the extended continuous Heisenberg ferromagnet equation (HFE) to investigate how nonlocality properties of one system are inherited by the other. First, we consider the space curves induced by the nonlinear Schrödinger-type equations and its equivalent spin systems. Such space curves are governed by the Serret–Frenet equation (SFE) for three basis vectors. We also show that the equation for the third of the basis vectors coincides with the well-known integrable HFE and its generalization. Two other equations for the remaining two vectors give new integrable spin systems. Finally, we investigated the relation between the differential geometry of surfaces and integrable spin systems for the three basis vectors. Full article
(This article belongs to the Special Issue Symmetry in Abstract Differential Equations)
15 pages, 300 KiB  
Article
Some Gronwall–Bellman Inequalities on Time Scales and Their Continuous Forms: A Survey
by Francesca Barich
Symmetry 2021, 13(2), 198; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13020198 - 26 Jan 2021
Cited by 2 | Viewed by 1726
Abstract
Some generalizations of the Gronwall–Bellman (G–B) inequality are presented in this paper in continuous form and on time scales. After S. Hilger introduced the time scales theory in 1988, over the years many mathematicians have studied new versions of this inequality according to [...] Read more.
Some generalizations of the Gronwall–Bellman (G–B) inequality are presented in this paper in continuous form and on time scales. After S. Hilger introduced the time scales theory in 1988, over the years many mathematicians have studied new versions of this inequality according to new results; the purpose of this paper is to present some of them. Therefore, in the Introduction, some generalizations of G–B inequality in continuous forms, linear and nonlinear are presented. In the second section, some important and interesting results on time scales theory are given. In the third and main part of our paper, G–B inequalities on time scales and their possible connection with G–B inequalities presented in the introduction are investigated. In particular, in the third section of this work, more attention is given to G–B type inequalities on time scales discussed in the last four years. Full article
(This article belongs to the Special Issue Symmetry in Abstract Differential Equations)
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