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Symmetry
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Algebraic Systems, Models and Applications
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Algebraic Systems, Models and Applications

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

Deadline for manuscript submissions: 28 February 2025 | Viewed by 6302

Special Issue Editors

Prof. Dr. Ioan Rașa

E-Mail
Guest Editor
Department of Mathematics, Technical University of Cluj-Napoca, Cluj-Napoca, Romania
Interests: ulam stability of operators; functional equations; functional analysis; approximation theory; inequalities
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Stefano De Marchi

E-Mail Website
Guest Editor
Department of Mathematics“Tullio Levi-Civita”, University of Padova, Padova, Italy
Interests: multivariate polynomial approximation; kernel-based approximation; image analysis

Special Issue Information

Dear Colleagues,

This Special Issue is devoted to the study of algebraic systems with applications to real-world problems. The existence, uniqueness, and non-uniqueness of solutions are important topics for investigations. Numerical methods for approximating the solutions will be considered with priority. Of course, fixed point theorems and iterative methods are essential tools in these studies. In particular, special attention will be paid to systems with positive coefficients and positive solutions. It is known that such systems appear in several applications and we will be interested in enlarging the list of these applications.

In our intention, this Special Issue should report new results on algebraic systems and their applications to various fields of natural sciences and engineering, as well as facilitate interactions among researchers, discuss important research problems and directions, and promote these methods in various research areas. We look forward to receiving and editorially processing your contributions to this Special Issue.

With kind regards and thanks in advance for your contributions.

Prof. Dr. Ioan Rașa
Prof. Dr. Stefano De Marchi
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

  • algebraic systems
  • positive solutions
  • existence, uniqueness
  • fixed point theorems
  • iterative methods
  • approximate solutions
  • numerical methods
  • applications to boundary value problems
  • dirichlet problems
  • difference equations
  • image analysis
  • collocation
  • kernel-based approximation

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

Published Papers (5 papers)

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Research

24 pages, 15074 KiB  
Article
A Symmetric Reversible Audio Information Hiding Algorithm Using Matrix Embedding Within Image Carriers
by Yongqiang Tuo, Guodong Li and Kaiyue Hou
Symmetry 2024, 16(12), 1586; https://doi.org/10.3390/sym16121586 - 27 Nov 2024
Viewed by 516
Abstract
To address the vulnerability of existing hiding algorithms to differential attacks and the limitations of single chaotic systems, such as small key space and low security, a novel algorithm combining audio encryption with information hiding is proposed. First, the original audio is divided [...] Read more.
To address the vulnerability of existing hiding algorithms to differential attacks and the limitations of single chaotic systems, such as small key space and low security, a novel algorithm combining audio encryption with information hiding is proposed. First, the original audio is divided into blocks to enhance efficiency. A “one-time pad” mechanism is achieved by associating the key with the plaintext, and a new multidimensional sine-coupled chaotic map is designed, which, in conjunction with multiple chaotic systems, generates the key stream. Next, the block-processed audio signals are matrix-converted and then encrypted using cyclic remainder scrambling, an improved Josephus scrambling, XOR diffusion, and bit diffusion. This results in an encrypted audio information matrix. Finally, the GHM multiwavelet transform is used to select embedding channels, and the least significant bit (LSB) method is employed to hide the information within the carrier image. The algorithm is symmetric, and decryption involves simply reversing the encryption process on the stego image. Experimental results demonstrate that the Structural Similarity Index (SSIM) between the carrier image and the stego image is 0.992540, the Peak Signal-to-Noise Ratio (PSNR) is 49.659404 dB, and the Mean Squared Error (MSE) is 0.708044. These metrics indicate high statistical similarity and indistinguishability in visual appearance. The key space of the encryption algorithm is approximately 2850, which effectively resists brute-force attacks. The energy distribution of the encrypted audio approximates noise, with information entropy close to 8, uniform histograms, high scrambling degree, strong resistance to differential attacks, and robustness against noise and cropping attacks. Full article
(This article belongs to the Special Issue Algebraic Systems, Models and Applications)
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20 pages, 2672 KiB  
Article
Persistence Symmetric Kernels for Classification: A Comparative Study
by Cinzia Bandiziol and Stefano De Marchi
Symmetry 2024, 16(9), 1236; https://doi.org/10.3390/sym16091236 - 20 Sep 2024
Viewed by 961
Abstract
The aim of the present work is a comparative study of different persistence kernels applied to various classification problems. After some necessary preliminaries on homology and persistence diagrams, we introduce five different kernels that are then used to compare their performances of classification [...] Read more.
The aim of the present work is a comparative study of different persistence kernels applied to various classification problems. After some necessary preliminaries on homology and persistence diagrams, we introduce five different kernels that are then used to compare their performances of classification on various datasets. We also provide the Python codes for the reproducibility of results and, thanks to the symmetry of kernels, we can reduce the computational costs of the Gram matrices. Full article
(This article belongs to the Special Issue Algebraic Systems, Models and Applications)
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13 pages, 297 KiB  
Article
On Centralizers of Idempotents with Restricted Range
by Dilawar J. Mir and Amal S. Alali
Symmetry 2024, 16(6), 769; https://doi.org/10.3390/sym16060769 - 19 Jun 2024
Viewed by 924
Abstract
This study delves into the structure and properties of left inverse zero divisor bands within semigroups, identifying their maximal forms and broadening the theoretical landscape of semigroup analysis. A significant focus is placed on the automorphisms of a semigroup S of centralizers of [...] Read more.
This study delves into the structure and properties of left inverse zero divisor bands within semigroups, identifying their maximal forms and broadening the theoretical landscape of semigroup analysis. A significant focus is placed on the automorphisms of a semigroup S of centralizers of idempotent transformations with restricted range, revealing that these automorphisms are inner ones and induced by the units of S. Additionally, we establish that the automorphism group Aut(S) is isomorphic to US, the group of units of S. These findings extend previous results on semigroups of transformations, enhancing their applicability and providing a more unified theory. The practical implications of this work span multiple fields, including automata theory, coding theory, cryptography, and graph theory, offering tools for more efficient algorithms and models. By simplifying complex concepts and providing a solid foundation for future research, this study makes significant contributions to both theoretical and applied mathematics. Full article
(This article belongs to the Special Issue Algebraic Systems, Models and Applications)
21 pages, 5341 KiB  
Article
A Novel Quintic B-Spline Technique for Numerical Solutions of the Fourth-Order Singular Singularly-Perturbed Problems
by Muhammad Zain Yousaf, Hari Mohan Srivastava, Muhammad Abbas, Tahir Nazir, Pshtiwan Othman Mohammed, Miguel Vivas-Cortez and Nejmeddine Chorfi
Symmetry 2023, 15(10), 1929; https://doi.org/10.3390/sym15101929 - 18 Oct 2023
Cited by 4 | Viewed by 1715
Abstract
Singular singularly-perturbed problems (SSPPs) are a powerful mathematical tool for modelling a variety of real phenomena, such as nuclear reactions, heat explosions, mechanics, and hydrodynamics. In this paper, the numerical solutions to fourth-order singular singularly-perturbed boundary and initial value problems are presented using [...] Read more.
Singular singularly-perturbed problems (SSPPs) are a powerful mathematical tool for modelling a variety of real phenomena, such as nuclear reactions, heat explosions, mechanics, and hydrodynamics. In this paper, the numerical solutions to fourth-order singular singularly-perturbed boundary and initial value problems are presented using a novel quintic B-spline (QBS) approximation approach. This method uses a quasi-linearization approach to solve SSPNL initial/boundary value problems. And the non-linear problems are transformed into a sequence of linear problems by applying the quasi-linearization approach. The QBS functions produce more accurate results when compared to other existing approaches because of their local support, symmetry, and partition of unity features. This method can be applied to immediately solve the SSPPs without reducing the order in which they are presented. It has been demonstrated that the suggested numerical approach converges uniformly over the whole domain. The proposed approach is implemented on a few problems to validate the scheme. The computational results are compared, and they illustrate that the proposed approach performs better. Full article
(This article belongs to the Special Issue Algebraic Systems, Models and Applications)
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12 pages, 1187 KiB  
Article
Intelligent Separation and Identification of Sub-Information Based on Dynamic Mathematical Model
by Xiuquan Zhang and Lin Shen
Symmetry 2023, 15(2), 477; https://doi.org/10.3390/sym15020477 - 10 Feb 2023
Cited by 1 | Viewed by 943
Abstract
P-sets (P stands for Packet), a set pair with dynamic and law characteristics, are made up of an internal and an outer P-set, which is obtained by introducing dynamic characteristics into the Cantor set and improving the Cantor set. The concepts of [...] Read more.
P-sets (P stands for Packet), a set pair with dynamic and law characteristics, are made up of an internal and an outer P-set, which is obtained by introducing dynamic characteristics into the Cantor set and improving the Cantor set. The concepts of αF-sub-information, αF¯-sub-information, and (αF,αF¯)-sub-information are presented in this paper based on P-sets, and it is then suggested that the relationship between the generation of sub-information and its attribute, the process of attribute reasoning, reasoning structure, and sub-information intelligent separation-acquisition be explored. These findings were used to design a sub-information intelligent separation-identification algorithm. By using these results, the application of intelligent separation and the identification of case information are given. Full article
(This article belongs to the Special Issue Algebraic Systems, Models and Applications)
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