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Symmetry
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Symmetry in Numerical Analysis and Applied Mathematics
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Symmetry in Numerical Analysis and Applied Mathematics

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

Deadline for manuscript submissions: 30 June 2025 | Viewed by 4364

Special Issue Editors

Dr. Mariusz Pleszczyński

E-Mail Website
Guest Editor
Institute of Mathematics, Silesian University of Technology, 44-100 Gliwice, Poland
Interests: numerical methods; programming; applied mathematics
Dr. Rafal Brociek

E-Mail Website
Guest Editor
Department of Artificial Intelligence Modelling, Faculty of Applied Mathematics, Silesian University of Technology, 44-100 Gliwice, Poland
Interests: heat conduction; inverse problem; fractional derivative; intelligent algorithms
Special Issues, Collections and Topics in MDPI journals
Dr. Giacomo Capizzi

E-Mail Website
Guest Editor
Associate Professor, Department of Electrical, Electronics and Informatics Engineering, University of Catania, Viale Andrea Doria 6, 95125 Catania, Italy
Interests: wavelet theory; neural networks; statistical pattern recognition; bayesian networks; theory and design of linear and nonlinear digital/analog filters; integrated generation systems; renewable energy sources; and battery storage modeling and simulation
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The world is mathematical. Symmetry and asymmetry play an important role in it. Many issues in technology, engineering, physics, electronics, mechanics, and even economic sciences or biology can be described with more or less complex mathematical models. This is why it is so important to constantly expand our knowledge in this field.

The aim of this Special Issue is to provide a series of articles presenting the broadly understood application of mathematics to solve problems occurring in mathematical modeling, engineering, technology, computer science, and other branches of study. In particular, we welcome submissions on methods for solving differential and integral equations (including fractional-order equations), functional equations, integral approximations, and applications of mathematics bordering on computer science, e.g., word combinatorics, heuristic algorithms, and artificial intelligence methods.

We look forward to receiving your contributions.

Dr. Mariusz Pleszczyński
Dr. Rafal Brociek
Prof. Dr. Giacomo Capizzi
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

  • artificial intelligence methods
  • heuristic algorithms
  • computer mathematics
  • numerical analysis
  • mathematical modeling
  • numerical methods
  • differential, integral, and functional equations

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

Published Papers (6 papers)

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Research

21 pages, 1371 KiB  
Article
Developing a New Approach for Assessing and Improving Business Excellence: Integrating Fuzzy Analytic Hierarchical Process and Constraint Programming Model
by Tijana Petrović, Danijela Tadić, Dragan Marinković, Goran Đurić and Nikola Komatina
Symmetry 2025, 17(4), 607; https://doi.org/10.3390/sym17040607 - 16 Apr 2025
Viewed by 180
Abstract
This study introduces a novel two-stage model for assessing and enhancing business excellence based on the EFQM framework. The Fuzzy Analytic Hierarchy Process (FAHP) is used in the first stage to calculate the weight vectors of criteria and sub-criteria, incorporating uncertainty through triangular [...] Read more.
This study introduces a novel two-stage model for assessing and enhancing business excellence based on the EFQM framework. The Fuzzy Analytic Hierarchy Process (FAHP) is used in the first stage to calculate the weight vectors of criteria and sub-criteria, incorporating uncertainty through triangular fuzzy numbers (TFNs). In the second stage, the OR-Tools CP-SAT solver is used to solve the selection and improvement of sub-criteria as a multidimensional knapsack problem with mixed min/max constraints. In this way, a new and enhanced model for evaluating business excellence is presented—one that takes into account the company’s current capabilities and circumstances while also providing management with a starting point for enhancing business performance. The model is validated using data from a manufacturing company in central Serbia. The findings suggest that improvement efforts should not be symmetrically distributed across all EFQM criteria and sub-criteria. Instead, an asymmetric approach provides efficient resource allocation while maximizing business excellence improvements. This study emphasizes the balance or symmetry between subjective decision-makers’ assessments and mathematically based optimization, demonstrating the practical applicability of the proposed method in strategic decision-making under resource constraints. Full article
(This article belongs to the Special Issue Symmetry in Numerical Analysis and Applied Mathematics)
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9 pages, 240 KiB  
Article
Roots of Binary Shuffle Squares
by Dominika Datko and Bartłomiej Pawlik
Symmetry 2025, 17(2), 305; https://doi.org/10.3390/sym17020305 - 17 Feb 2025
Viewed by 351
Abstract
A square is a word of the form XX, where X is any finite non-empty word. For example, couscous is a square. A shuffle square is a finite word that can be formed by self-shuffling a word; for instance, the Spanish [...] Read more.
A square is a word of the form XX, where X is any finite non-empty word. For example, couscous is a square. A shuffle square is a finite word that can be formed by self-shuffling a word; for instance, the Spanish word acaece is a shuffle square but not a square. We discuss both known and novel enumerative problems related to shuffle squares, with a focus on the number of distinct roots of binary shuffle squares. We introduce the term explicit shuffle squares, propose several conjectures, and present some preliminary results towards their resolution. Our discussion is supported by computational experiments. In particular, we determine the exact number of distinct roots of binary shuffle squares with a length of up to 24. On the other hand, we show that every non-constant binary word of length n generates at least n different shuffle squares. Full article
(This article belongs to the Special Issue Symmetry in Numerical Analysis and Applied Mathematics)
17 pages, 319 KiB  
Article
Asymptotics of Riemann Sums for Uniform Partitions of Intervals of Integration
by Marcin Adam, Jakub Jan Ludew, Michał Różański, Adrian Smuda and Roman Wituła
Symmetry 2025, 17(2), 226; https://doi.org/10.3390/sym17020226 - 4 Feb 2025
Viewed by 586
Abstract
Our goal is to prove the Euler–Maclaurin summation formula using only the Taylor formula. Furthermore, the Euler–Maclaurin summation formula will be considered for the case of functions of the class C2k([a,b]). A stronger [...] Read more.
Our goal is to prove the Euler–Maclaurin summation formula using only the Taylor formula. Furthermore, the Euler–Maclaurin summation formula will be considered for the case of functions of the class C2k([a,b]). A stronger version of the estimation of the rest for functions of class Cn([a,b]) is given. We will also present the application of the obtained Euler–Maclaurin summation formulas to determine the asymptotics of Riemann sums for uniform partitions of intervals of integration. This paper also introduces the concepts of the asymptotic smoothing of the graph of a given function, as well as the asymptotic uniform distribution of the positive and negative values of the given function (generalizing the concept of the symmetric distribution of these values with respect to the x-axis, as in the case of the Peano–Jordan measure). Full article
(This article belongs to the Special Issue Symmetry in Numerical Analysis and Applied Mathematics)
11 pages, 375 KiB  
Article
A New Proof of Ramsey’s Theorem
by Jakub Jan Ludew, Bogdana Oliynyk, Michał Różański, Alicja Samulewicz, Adrian Smuda, Monika Szymura and Roman Wituła
Symmetry 2024, 16(12), 1660; https://doi.org/10.3390/sym16121660 - 16 Dec 2024
Viewed by 884
Abstract
Ramsey’s theorem states that for any natural numbers n, m there exists a natural number N such that any red–blue coloring of the graph KN contains either a red Kn or blue Km as a subgraph. The smallest such [...] Read more.
Ramsey’s theorem states that for any natural numbers n, m there exists a natural number N such that any red–blue coloring of the graph KN contains either a red Kn or blue Km as a subgraph. The smallest such N is called the Ramsey number, denoted as R(n,m). In this paper, we reformulate this theorem and present a proof of Ramsey’s theorem that is novel as far as we are aware. Full article
(This article belongs to the Special Issue Symmetry in Numerical Analysis and Applied Mathematics)
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14 pages, 271 KiB  
Article
Improper Integrals of Type II—A New Look and Some Surprising Facts
by Jakub Jan Ludew, Michał Różański, Wiktor Tomiczek, Adrian Smuda and Roman Wituła
Symmetry 2024, 16(12), 1637; https://doi.org/10.3390/sym16121637 - 11 Dec 2024
Viewed by 848
Abstract
The goal of this work is to present a new theoretical and simultaneously practical approach to the conception of improper integrals of type II and, consequently, to improper integrals of type I. Seven distinct definitions of improper integrals of type II are presented, [...] Read more.
The goal of this work is to present a new theoretical and simultaneously practical approach to the conception of improper integrals of type II and, consequently, to improper integrals of type I. Seven distinct definitions of improper integrals of type II are presented, each illustrated by suitable examples. Among them, particularly important are those defined on nets composed of sets symmetric with respect to points belonging to a given finite family of points. Connections between improper integrals of type II defined here are described in two main theorems. It should be emphasized that all definitions of improper integrals presented here are special cases of a very general definition of improper integrals on non-compact sets, which is presented at the end of this work. This definition is inspired by a concept introduced by Maurin. Full article
(This article belongs to the Special Issue Symmetry in Numerical Analysis and Applied Mathematics)
20 pages, 1332 KiB  
Article
Differential Transform Method (DTM) and Physics-Informed Neural Networks (PINNs) in Solving Integral–Algebraic Equation Systems
by Rafał Brociek and Mariusz Pleszczyński
Symmetry 2024, 16(12), 1619; https://doi.org/10.3390/sym16121619 - 6 Dec 2024
Viewed by 921
Abstract
Integral–algebraic equations and their systems are a common description of many technical and engineering problems. Often, such models also describe certain dependencies occurring in nature (e.g., ecosystem behaviors). The integral equations occurring in this problem may have two types of domains—symmetric or asymmetric. [...] Read more.
Integral–algebraic equations and their systems are a common description of many technical and engineering problems. Often, such models also describe certain dependencies occurring in nature (e.g., ecosystem behaviors). The integral equations occurring in this problem may have two types of domains—symmetric or asymmetric. Depending on whether such symmetry exists in the system describing a given problem, we must choose the appropriate method to solve this system. In this task, the absence of symmetry is more advantageous, but the presented examples demonstrate how one can approach cases where symmetry is present. In this paper, we present the application of two methods for solving such tasks: the analytical Differential Transform Method (DTM) and Physics-informed Neural Networks (PINNs). We consider a wide class of these types of equation systems, including Volterra and Fredholm integrals (which are also in a single model). We demonstrate that despite the complex nature of the problem, both methods are capable of handling such tasks, and thus, they can be successfully applied to the issues discussed in this article. Full article
(This article belongs to the Special Issue Symmetry in Numerical Analysis and Applied Mathematics)
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