Symmetry in Mathematical and Statistical Sciences: Theory, Methods, and Applications

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

Deadline for manuscript submissions: 31 January 2027 | Viewed by 1170

Editors


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Guest Editor
Department of Mathematics, Faculty of Science, Mahasarakham University, Mahasarakham, Thailand
Interests: topology; multifunctions; continuity theory

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Guest Editor
Department of Mathematics, Faculty of Science, Mahasarakham University, Mahasarakham, Thailand
Interests: sampling theory; statistical modelling; statisitics; sampling design

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Guest Editor
Department of Mathematics, Faculty of Science, Mahasarakham University, Mahasarakham, Thailand
Interests: mathematical models; mathematical modelling

Special Issue Information

Dear Colleagues,

This Special Issue aims to provide an interdisciplinary forum for frontier research in mathematical and statistical sciences, emphasizing symmetry as a fundamental organizing principle in theoretical development, methodological innovation, and interdisciplinary applications. This Special Issue will highlight the complementary roles of mathematics and statistics in advancing scientific understanding and addressing complex problems across diverse domains. In this context, this Special Issue will focus on the development, refinement, and rigorous analysis of fundamental concepts in mathematics and statistics, where symmetry serves as a unifying theoretical framework across disciplines. Contributions may address topics such as topological structures and properties, differential equations, nonlinear and dynamical systems, or the theoretical foundations of statistical modeling, statistical inference, sampling theory, and asymptotic analysis.

From a methodological and applied perspective, this Special Issue welcomes studies that apply mathematical theory and statistical methodologies to real-world and interdisciplinary problems, with particular emphasis on symmetry, invariance, and balanced structures in model formulation and analysis. Relevant contributions include, but are not limited to, mathematical and dynamical modeling, symmetry-aware differential equation-based approaches, statistical inference under uncertainty that exploits symmetric dependence or correlation structures, advanced and adaptive sampling methods with balanced or symmetry-driven designs, and computational and data-driven techniques that leverage symmetry to support robust analysis, prediction, and informed decision-making.

Overall, this Special Issue seeks to foster collaboration between mathematicians, statisticians, and applied researchers and to showcase innovative theoretical insights and practical methodologies that leverage symmetry, invariance, and structural balance to contribute to the continued development of mathematical and statistical sciences.

Topics of Interest, include but not limited to, the following:

  • Mathematical modeling of biological and epidemiological systems.
  • Dynamical systems and stability analysis.
  • Ordinary and partial differential equations and symmetry-based solution methods.
  • Nonlinear analysis and asymptotic methods.
  • General topology and its applications:
    • Hyperconnectedness;
    • Extremal disconnectedness;
    • Submaximality and expandability;
    • Continuity for multifunctions.
  • Statistical modeling and statistical inference under symmetric dependence structures.
  • Sampling methods and asymptotic analysis.
  • Computational and applied statistics exploiting symmetry and invariance principles.

Dr. Chawalit Boonpok
Dr. Nipaporn Chutiman
Dr. Inthira Chaiya
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 250 words) can be sent to the Editorial Office for assessment.

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-anonymized 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

  • mathematical modeling
  • dynamical systems
  • differential equations
  • nonlinear analysis
  • symmetry and invariance
  • epidemiological and biological modeling
  • general topology
  • hyperconnectedness
  • extremal disconnectedness
  • submaximality
  • expandability
  • continuity for multifunctions
  • statistical modeling
  • statistical inference
  • asymptotic analysis
  • sampling methods
  • computational statistics

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Published Papers (2 papers)

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16 pages, 34018 KB  
Article
On Some Incommensurate Fractional-Order Reaction–Diffusion Systems: The Degn–Harrison and Its Stability
by Omar Kahouli, Amel Hioual, Adel Ouannas, Waleed Mohammed Abdelfattah, Younès Bahou, Ilyes Abidi, Sameir Hamed, Mohamed Chaabane and Sarra Elgharbi
Symmetry 2026, 18(5), 862; https://doi.org/10.3390/sym18050862 - 19 May 2026
Viewed by 209
Abstract
In this paper, we consider a reaction–diffusion system governed by incommensurate fractional time derivatives based on the Degn–Harrison model. Its formulation incorporates various memory effects on axial position through Caputo derivatives of variable orders, producing a more realistic modeling of the temporal dynamics. [...] Read more.
In this paper, we consider a reaction–diffusion system governed by incommensurate fractional time derivatives based on the Degn–Harrison model. Its formulation incorporates various memory effects on axial position through Caputo derivatives of variable orders, producing a more realistic modeling of the temporal dynamics. This paper starts with a study of the spatially homogeneous system and establishes conditions for local stability by using the Matignon criterion. The spectral decomposition method under Neumann boundary condition is then applied to study the complete reaction–diffusion system and describe diffusion-induced instabilities. Our results indicate that the noninteger fractional orders lead to significant changes in stability regions, as well as the initiation of pattern formation. Specifically, the orders of fractions induced as a control variable are regarded to be effective in controlling the stability of the system, thus they are global (or positive) control variables when their values achieved at some levels apply to the entire saturation, etc. Our numerical simulations are in excellent agreement with the theoretical predictions and show that memory asymmetry induces complex spatiotemporal dynamics not seen for classical integer-order systems. Full article
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21 pages, 550 KB  
Article
Sheffer-Type General-λ-Matrix Polynomials and Their Structural Properties
by Ghazala Yasmin, Aditi Sharma, Georgia Irina Oros and Shahid Ahmad Wani
Symmetry 2026, 18(5), 760; https://doi.org/10.3390/sym18050760 - 28 Apr 2026
Cited by 1 | Viewed by 382
Abstract
In this paper, a new class of special polynomials, called the Sheffer-type general-λ-matrix polynomials, is introduced within the framework of the monomiality principle. This family is obtained by combining the structure of Sheffer sequences with the theory of general-λ matrix [...] Read more.
In this paper, a new class of special polynomials, called the Sheffer-type general-λ-matrix polynomials, is introduced within the framework of the monomiality principle. This family is obtained by combining the structure of Sheffer sequences with the theory of general-λ matrix polynomials, which leads to a unified formulation encompassing several polynomial families. Fundamental properties of the proposed polynomials are established, including their generating function, explicit series representation, summation formulas, quasi-monomial structure, differential relations, and determinant representation. The proposed framework addresses an important problem in the theory of special functions: the systematic construction of matrix-valued polynomial families that simultaneously generalize both classical scalar polynomials and existing matrix polynomial hierarchies. Such a unified structure is of broad significance, with applications in quantum mechanics (wave function expansions), mathematical physics (matrix differential equations and spectral problems), approximation theory, and the study of special functions in the matrix domain. Several hybrid forms of the proposed family are derived through appropriate choices of the defining functions, which yield polynomial subclasses related to classical families such as Hermite, Laguerre, Bessel, and Poisson–Charlier polynomials. These subclasses illustrate how the proposed framework provides a systematic approach for constructing and studying generalized polynomial structures. In each case, the matrix parameter L introduces a new layer of structural richness not present in the scalar setting, enabling the modelling of phenomena governed by matrix-valued spectral data. Furthermore, a numerical and graphical investigation of selected hybrid forms is carried out using Mathematica (version 14.3, 2025; Wolfram Research, Inc.). Surface plots, distributions of complex zeros, and real-zero patterns are presented for different parameter values, highlighting the influence of the parameters on the behavior and structural characteristics of the polynomials. Full article
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