Axioms

16 pages, 2342 KiB

Open AccessArticle

Improving Safety Awareness Campaigns Through the Use of Graph Neural Networks

by Jose D. Hernández Guillén and Angel Martín del Rey

Axioms 2025, 14(5), 328; https://doi.org/10.3390/axioms14050328 - 24 Apr 2025

Phishing is one of the main threats against companies where the main weakness against this type of threat is the worker. For this reason, it is essential that workers have a high security awareness for which it is fundamental to carry out a [...] Read more.

Phishing is one of the main threats against companies where the main weakness against this type of threat is the worker. For this reason, it is essential that workers have a high security awareness for which it is fundamental to carry out a good safety-awareness campaign. However, as far as we are concerned, a mathematical study of the evolution of security awareness taking into account interactions with other people has not been considered. In this paper, we study how security awareness evolves through two belief-propagation models and Graph Neural Networks. Since this approach is new, the two most basic models were chosen to simulate propagation of beliefs: Sznajd model variant and Hegselmann–Krause model. On the other hand, because Graph Neural Networks are a current and very powerful tool, it was decided to use them to analyze the evolution of beliefs. We consider that with them information-awareness campaigns can be improved. As an example, we propose different awareness measures according to future beliefs and social influence. Full article

(This article belongs to the Section Mathematical Analysis)

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19 pages, 329 KiB

Open AccessArticle

Symbol-Pair Distances of a Class of Repeated-Root Constacyclic Codes of Length np^s over

F_{p^{m}}

and over

F_{p^{m}} + u F_{p^{m}}

by Wei Zhao, Weixian Li and Hui Chen

Axioms 2025, 14(5), 327; https://doi.org/10.3390/axioms14050327 - 24 Apr 2025

Abstract

Symbol-pair codes are a class of block codes with symbol-pair metrics designed to protect against pair errors that may occur in high-density data storage systems. Maximum distance separable (MDS) symbol-pair codes are optimal in the sense that they can attain the highest pair-error [...] Read more.

Symbol-pair codes are a class of block codes with symbol-pair metrics designed to protect against pair errors that may occur in high-density data storage systems. Maximum distance separable (MDS) symbol-pair codes are optimal in the sense that they can attain the highest pair-error correctability within the same code length and code size. Constructing MDS symbol-pair codes is one of the main topics in symbol-pair code research. In this paper, we investigate and characterize the symbol-pair distances of constacyclic codes of arbitrary lengths over finite fields and finite chain rings. Using the characterization of the symbol-pair distance, we present three new classes of MDS symbol-pair constacyclic codes that exhibit large minimum distances. Full article

(This article belongs to the Section Algebra and Number Theory)

3 pages, 123 KiB

Open AccessEditorial

Advances in Dynamical Systems and Control

by Selene Lilette Cardenas-Maciel, Jorge Antonio Lopez-Renteria and Nohe Ramon Cazarez-Castro

Axioms 2025, 14(5), 326; https://doi.org/10.3390/axioms14050326 - 23 Apr 2025

Abstract

In this Editorial, we present “Advances in Dynamical Systems and Control”, a Special Issue of Axioms [...] Full article

(This article belongs to the Special Issue Advances in Dynamical Systems and Control)

13 pages, 254 KiB

Open AccessArticle

Ricci Solitons on Riemannian Hypersurfaces Generated by Torse-Forming Vector Fields in Riemannian and Lorentzian Manifolds

by Norah Alshehri and Mohammed Guediri

Axioms 2025, 14(5), 325; https://doi.org/10.3390/axioms14050325 - 23 Apr 2025

Abstract

In this paper, we examine torse-forming vector fields to characterize extrinsic spheres (that is, totally umbilical hypersurfaces with nonzero constant mean curvatures) in Riemannian and Lorentzian manifolds. First, we analyze the properties of these vector fields on Riemannian manifolds. Next, we focus on [...] Read more.

In this paper, we examine torse-forming vector fields to characterize extrinsic spheres (that is, totally umbilical hypersurfaces with nonzero constant mean curvatures) in Riemannian and Lorentzian manifolds. First, we analyze the properties of these vector fields on Riemannian manifolds. Next, we focus on Ricci solitons on Riemannian hypersurfaces induced by torse-forming vector fields of Riemannian or Lorentzian manifolds. Specifically, we show that such a hypersurface in the manifold with constant sectional curvature is either totally geodesic or an extrinsic sphere. Full article

16 pages, 1695 KiB

Open AccessArticle

Iterative Learning Control with Adaptive Kalman Filtering for Trajectory Tracking in Non-Repetitive Time-Varying Systems

by Lei Wang, Shunjie Zhu, Menghan Wei, Xiaoxiao Wang, Ziwei Huangfu and Yiyang Chen

Axioms 2025, 14(5), 324; https://doi.org/10.3390/axioms14050324 - 23 Apr 2025

Abstract

This paper presents an adaptive Kalman filter (AKF)-enhanced iterative learning control (ILC) scheme to improve trajectory tracking in non-repetitive time-varying systems (NTVSs), particularly in industrial applications. Unlike traditional ILC methods that assume fixed system dynamics, gradual parameter variations in NTVSs require adaptive approaches [...] Read more.

This paper presents an adaptive Kalman filter (AKF)-enhanced iterative learning control (ILC) scheme to improve trajectory tracking in non-repetitive time-varying systems (NTVSs), particularly in industrial applications. Unlike traditional ILC methods that assume fixed system dynamics, gradual parameter variations in NTVSs require adaptive approaches to address factors such as tool wear and sensor drift, which significantly affect tracking accuracy. By integrating AKF, the proposed method continuously estimates time-varying parameters and uncertainties in real time, thus improving the robustness and adaptability of trajectory tracking. Theoretical analysis is conducted to confirm the robust convergence and stability of the AKF-enhanced ILC scheme under uncertain and time-varying conditions. Experimental results demonstrate that the proposed approach significantly outperforms conventional ILC methods, ensuring precise and reliable tracking performance in dynamic industrial scenarios. Full article

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11 pages, 240 KiB

Open AccessArticle

A Note on the Soft Group Category

by Nazmiye Alemdar and Hasan Arslan

Axioms 2025, 14(5), 323; https://doi.org/10.3390/axioms14050323 - 22 Apr 2025

Abstract

The main purpose of this paper is to introduce the structure of the soft group category. In this category, we determine some special objects and morphisms having a universal structure such as the final object and a product. Therefore, the category of soft [...] Read more.

The main purpose of this paper is to introduce the structure of the soft group category. In this category, we determine some special objects and morphisms having a universal structure such as the final object and a product. Therefore, the category of soft groups is a symmetric monodial category. Full article

22 pages, 5414 KiB

Open AccessArticle

Generation of Julia Sets for a Novel Class of Generalized Rational Functions via Generalized Viscosity Iterative Method

by Iqbal Ahmad and Ahmad Almutlg

Axioms 2025, 14(4), 322; https://doi.org/10.3390/axioms14040322 - 21 Apr 2025

Abstract

This article investigates and analyzes the diverse patterns of Julia sets generated by new classes of generalized exponential and sine rational functions. Using a generalized viscosity approximation-type iterative method, we derive escape criteria to visualize the Julia sets of these functions. This approach [...] Read more.

This article investigates and analyzes the diverse patterns of Julia sets generated by new classes of generalized exponential and sine rational functions. Using a generalized viscosity approximation-type iterative method, we derive escape criteria to visualize the Julia sets of these functions. This approach enhances existing algorithms, enabling the visualization of intricate fractal patterns as Julia sets. We graphically illustrate the variations in size and shape of the images as the iteration parameters change. The new fractals obtained are visually appealing and attractive. Moreover, we observe fascinating behavior in Julia sets when certain input parameters are fixed, while the values of n and m vary. We believe the conclusions of this study will inspire and motivate researchers and enthusiasts with a strong interest in fractal geometry. Full article

(This article belongs to the Topic Fractal and Design of Multipoint Iterative Methods for Nonlinear Problems)

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13 pages, 347 KiB

Open AccessFeature PaperArticle

On the Dynamics of a Modified van der Pol–Duffing Oscillator

by Oscar A. R. Cespedes and Jaume Llibre

Axioms 2025, 14(4), 321; https://doi.org/10.3390/axioms14040321 - 21 Apr 2025

Abstract

The 3-dimensional modified van der Pol–Duffing oscillator has been studied by several authors. We complete its study, first characterizing its zero-Hopf equilibria and then its zero-Hopf bifurcations—i.e., we provide sufficient conditions for the existence of three, two or one periodic solutions, bifurcating from [...] Read more.

The 3-dimensional modified van der Pol–Duffing oscillator has been studied by several authors. We complete its study, first characterizing its zero-Hopf equilibria and then its zero-Hopf bifurcations—i.e., we provide sufficient conditions for the existence of three, two or one periodic solutions, bifurcating from the zero-Hopf equilibrium localized at the origin of coordinates. Recall that an equilibrium point of a 3-dimensional differential system whose eigenvalues are zero and a pair of purely imaginary eigenvalues is a zero-Hopf equilibrium. Finally, we determine the dynamics of this system near infinity, i.e., we control the orbits that escape to or come from the infinity. Full article

(This article belongs to the Special Issue Advances in Mathematical Modeling and Related Topics)

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15 pages, 1322 KiB

Open AccessArticle

Enhancing Efficient Data Transmission in IBM WebSphere Using Relational Data eXchange (RDX) Mechanism and Tandem Queue

by Suthanthira Raj Devi Latha, Subramani Palani Niranjan, Sorin Vlase and Maria Luminita Scutaru

Axioms 2025, 14(4), 320; https://doi.org/10.3390/axioms14040320 - 21 Apr 2025

Abstract

This study investigates tandem queues with two service nodes. The consumer needs to obtain services at the following two nodes in this system: the IBM online sphere for artificial intelligence (AI) and the complex RDX mechanism. Before the second essential service (SES), by [...] Read more.

This study investigates tandem queues with two service nodes. The consumer needs to obtain services at the following two nodes in this system: the IBM online sphere for artificial intelligence (AI) and the complex RDX mechanism. Before the second essential service (SES), by utilizing AI to validate the data in IBM WebSphere and insight, the first essential service (FES) begins with the RDX mechanism. If there are fewer customers than “a” after a service at node 1 is finished, the server departs for a subsequent assignment. As soon as the vacation value reached the threshold, the service began. After the service concludes at node 1, it moves on to node 2. In this study, the supplemental variable technique is used to determine the probability-generating function (PGF) at any given time. A numerical solution also yields certain features of the queueing system. Full article

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16 pages, 1520 KiB

Open AccessArticle

High-Order Approximations for a Pseudoparabolic Equation of Turbulent Mass-Transfer Diffusion

by Miglena N. Koleva and Lubin G. Vulkov

Axioms 2025, 14(4), 319; https://doi.org/10.3390/axioms14040319 - 21 Apr 2025

Abstract

Numerical solutions of turbulent mass-transfer diffusion present challenges due to the nonlinearity of the elliptic–parabolic degeneracy of the mathematical models. Our main result in this paper concerns the development and implementation of an efficient high-order numerical method that is fourth-order accurate in space [...] Read more.

Numerical solutions of turbulent mass-transfer diffusion present challenges due to the nonlinearity of the elliptic–parabolic degeneracy of the mathematical models. Our main result in this paper concerns the development and implementation of an efficient high-order numerical method that is fourth-order accurate in space and second-order accurate in time for computing both the solution and its gradient for a Barenblatt-type equation. First, we reduce the original Neumann boundary value problem to a Dirichlet problem for the equation of the solution gradient. This problem is then solved by a compact fourth-order spatial approximation. To implement the numerical discretization, we employ Newton’s iterative method. Then, we compute the original solution while preserving the order of convergence. Numerical test results confirm the efficiency and accuracy of the proposed numerical scheme. Full article

(This article belongs to the Special Issue Advances in Nonlinear Analysis and Numerical Modeling)

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18 pages, 338 KiB

Open AccessArticle

Existence of Solutions for Caputo-Type Fractional (p,q)-Difference Equations Under Robin Boundary Conditions

by Hailong Ma and Hongyu Li

Axioms 2025, 14(4), 318; https://doi.org/10.3390/axioms14040318 - 21 Apr 2025

Abstract

In this paper, we investigate the existence results of solutions for Caputo-type fractional

(p, q)

-difference equations. Using Banach’s fixed-point theorem, we obtain the existence and uniqueness results. Meanwhile, by applying Krasnoselskii’s fixed-point theorem and Leray-Schauder’s nonlinear alternative, we also [...] Read more.

In this paper, we investigate the existence results of solutions for Caputo-type fractional

(p, q)

-difference equations. Using Banach’s fixed-point theorem, we obtain the existence and uniqueness results. Meanwhile, by applying Krasnoselskii’s fixed-point theorem and Leray-Schauder’s nonlinear alternative, we also obtain the existence results of non-trivial solutions. Finally, we provide examples to verify the correctness of the given results. Moreover, relevant applications are presented through specific examples. Full article

(This article belongs to the Special Issue Fractional Calculus—Theory and Applications, 3rd Edition)

26 pages, 437 KiB

Open AccessFeature PaperArticle

Multivariate Polynomial Interpolation for Cubical Zero-Dimensional Schemes

by Edoardo Ballico

Axioms 2025, 14(4), 317; https://doi.org/10.3390/axioms14040317 - 21 Apr 2025

Abstract

We compute the multigraded Hilbert function of general unions of certain degree-8 zero-dimensional schemes, called 2cubes, for the Segre 3-folds and the three-dimensional smooth quadric hypersurface. On the Segre 3-folds, we handle the evaluation at the zero-dimensional scheme of all multigraded addenda of [...] Read more.

We compute the multigraded Hilbert function of general unions of certain degree-8 zero-dimensional schemes, called 2cubes, for the Segre 3-folds and the three-dimensional smooth quadric hypersurface. On the Segre 3-folds, we handle the evaluation at the zero-dimensional scheme of all multigraded addenda of their ring, not just the one associated to the Segre embedding. We discuss the Hilbert function and the index of regularity of the unions of several other low-degree zero-dimensional schemes. Full article

(This article belongs to the Section Algebra and Number Theory)

14 pages, 265 KiB

Open AccessArticle

Existence Results for Some Classes of Weighted Equilibrium Problems

by Miruna-Mihaela Beldiman and Andrei-Dan Halanay

Axioms 2025, 14(4), 316; https://doi.org/10.3390/axioms14040316 - 21 Apr 2025

Abstract

Starting from some systems of vector equilibrium problems, we obtain the existence of the solution for a class of weighted equilibrium problems, under different types of generalized pseudo-monotonicity assumptions. We present both new and previous results, making a connection between them and giving [...] Read more.

Starting from some systems of vector equilibrium problems, we obtain the existence of the solution for a class of weighted equilibrium problems, under different types of generalized pseudo-monotonicity assumptions. We present both new and previous results, making a connection between them and giving a few examples. Using the main theorem, we derive the solution existence for the initial systems and discuss a corresponding set-valued problem. Finally, we consider the case of a real normed space. We extend some previously obtained results from the literature about weighted variational inequalities, and we also give proofs for some results we previously announced. We give some relevant examples for our notions. Full article

13 pages, 257 KiB

Open AccessArticle

Investigating the Hyers–Ulam Stability of the Generalized Drygas Functional Equation: New Results and Methods

by Gang Lyu, Yang Liu, Yuanfeng Jin and Yingxiu Jiang

Axioms 2025, 14(4), 315; https://doi.org/10.3390/axioms14040315 - 21 Apr 2025

Abstract

In this paper, we explore the Hyers–Ulam stability of a generalized Drygas functional equation, which extends the classical Drygas equation by incorporating additional parameters and conditions. Our investigation focuses on mappings from a real vector space into a Banach space and employs the [...] Read more.

In this paper, we explore the Hyers–Ulam stability of a generalized Drygas functional equation, which extends the classical Drygas equation by incorporating additional parameters and conditions. Our investigation focuses on mappings from a real vector space into a Banach space and employs the fixed-point method to establish stability criteria. Our findings provide new insights into the conditions under which the generalized Drygas equation maintains stability, contributing to the broader understanding of functional equations in mathematical analysis. The results have implications for the study of functional equations and their applications in various mathematical contexts. Full article

(This article belongs to the Special Issue Theory and Application of Integral Inequalities, 2nd Edition)

23 pages, 543 KiB

Open AccessArticle

Numerical Solutions for Nonlinear Ordinary and Fractional Duffing Equations Using Combined Fibonacci–Lucas Polynomials

by Waleed Mohamed Abd-Elhameed, Omar Mazen Alqubori, Amr Kamel Amin and Ahmed Gamal Atta

Axioms 2025, 14(4), 314; https://doi.org/10.3390/axioms14040314 - 19 Apr 2025

Abstract

Two nonlinear Duffing equations are numerically treated in this article. The nonlinear fractional-order Duffing equations and the second-order nonlinear Duffing equations are handled. Based on the collocation technique, we provide two numerical algorithms. To achieve this goal, a new family of basis functions [...] Read more.

Two nonlinear Duffing equations are numerically treated in this article. The nonlinear fractional-order Duffing equations and the second-order nonlinear Duffing equations are handled. Based on the collocation technique, we provide two numerical algorithms. To achieve this goal, a new family of basis functions is built by combining the sets of Fibonacci and Lucas polynomials. Several new formulae for these polynomials are developed. The operational matrices of integer and fractional derivatives of these polynomials, as well as some new theoretical results of these polynomials, are presented and used in conjunction with the collocation method to convert nonlinear Duffing equations into algebraic systems of equations by forcing the equation to hold at certain collocation points. To numerically handle the resultant nonlinear systems, one can use symbolic algebra solvers or Newton’s approach. Some particular inequalities are proved to investigate the convergence analysis. Some numerical examples show that our suggested strategy is effective and accurate. The numerical results demonstrate that the suggested collocation approach yields accurate solutions by utilizing Fibonacci–Lucas polynomials as basis functions. Full article

(This article belongs to the Special Issue Fractional Calculus and Its Applications: Historical and Recent Developments)

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36 pages, 3502 KiB

Open AccessArticle

Hopf Bifurcation and Optimal Control in an Ebola Epidemic Model with Immunity Loss and Multiple Delays

by Halet Ismail, Lingeshwaran Shangerganesh, Ahmed Hussein Msmali, Said Bourazza and Mutum Zico Meetei

Axioms 2025, 14(4), 313; https://doi.org/10.3390/axioms14040313 - 19 Apr 2025

Abstract

This paper studies the effects of resource limitations, immunity decay, and delays on an Ebola epidemic model and an optimal control strategy. The model includes two types of delays: a delay in the incubation period of infected individuals and a delay in treatment. [...] Read more.

This paper studies the effects of resource limitations, immunity decay, and delays on an Ebola epidemic model and an optimal control strategy. The model includes two types of delays: a delay in the incubation period of infected individuals and a delay in treatment. Conditions for a Hopf bifurcation at the endemic equilibrium are verified, with its direction and stability analyzed via normal form theory and the center manifold theorem. We also studied the optimal control problem for the SIRD delay model using educational campaigns and Ebola survivors’ immunity as control variables. Furthermore, we formulate an optimization problem based on Pontryagin’s maximum principle. This problem uses a modified Runge-Kutta approach with delays to discover the best control strategy to reduce infections and intervention costs. Finally, simulation results confirm analytical conclusions and show the practical implications of the optimum Ebola control plan using the dde23 MATLAB R2024a built-in solver and DDE-Biftool. Full article

(This article belongs to the Section Mathematical Analysis)

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17 pages, 430 KiB

Open AccessArticle

Young and Inverse Young Inequalities on Euclidean Jordan Algebra

by Chien-Hao Huang

Axioms 2025, 14(4), 312; https://doi.org/10.3390/axioms14040312 - 18 Apr 2025

Abstract

This paper mainly focuses on in-depth research on inequalities on symmetric cones. We will further analyze and discuss the inequalities we developed on the second-order cone and develop more inequalities. According to our past research in dealing with second-order cone inequalities, we derive [...] Read more.

This paper mainly focuses on in-depth research on inequalities on symmetric cones. We will further analyze and discuss the inequalities we developed on the second-order cone and develop more inequalities. According to our past research in dealing with second-order cone inequalities, we derive more inequalities concerning the eigenvalue version of Young’s inequality and trace a version of an inverse Young inequality and its applications. These conclusions align with the results established for the positive semidefinite cone, which is also a symmetric cone. It is of considerable help to the establishment of inequalities on symmetric cones and the analysis of their derivative algorithms. Full article

(This article belongs to the Special Issue New Theory and Applications of Nonlinear Analysis, Fractional Calculus and Optimization, 2nd Edition)

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17 pages, 7948 KiB

Open AccessArticle

Evolutionary Dynamics of Stochastic Q Learning in Multi-Agent Systems

by Luping Liu and Gang Sun

Axioms 2025, 14(4), 311; https://doi.org/10.3390/axioms14040311 - 18 Apr 2025

Abstract

Since high complexity and uncertainty is inherent in real-world environments that can influence the strategies choices of agents, we introduce a stochastic perturbation term to characterize the interference caused by uncertain factors on multi-agent systems (MASs). Firstly, the stochastic Q learning is designed [...] Read more.

Since high complexity and uncertainty is inherent in real-world environments that can influence the strategies choices of agents, we introduce a stochastic perturbation term to characterize the interference caused by uncertain factors on multi-agent systems (MASs). Firstly, the stochastic Q learning is designed by introducing stochastic perturbation term into Q learning, and the corresponding replicator dynamic equations of stochastic Q learning are derived. Secondly, we focus on two-agent games with two and three action scenarios, analyzing the impact of learning parameters on agents’ strategy selection and demonstrating how the learning process converges to its Nash equilibria. Finally, we also conduct a sensitivity analysis on exploration parameters, demonstrating how exploration rates affect the convergence process in potential games. The analysis and numerical experiments offer insights into the effectiveness of different exploration parameters in scenarios involving uncertainty. Full article

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20 pages, 5488 KiB

Open AccessArticle

Circuit Design and Implementation of a Time-Varying Fractional-Order Chaotic System

by Burak Arıcıoğlu

Axioms 2025, 14(4), 310; https://doi.org/10.3390/axioms14040310 - 17 Apr 2025

Abstract

This paper presents a circuit design methodology for the analog realization of time-varying fractional-order chaotic systems. While most existing studies implement such systems by switching between two or more constant fractional orders, these approaches become impractical when the fractional order changes smoothly over [...] Read more.

This paper presents a circuit design methodology for the analog realization of time-varying fractional-order chaotic systems. While most existing studies implement such systems by switching between two or more constant fractional orders, these approaches become impractical when the fractional order changes smoothly over time. To overcome this limitation, the proposed method introduces a transfer function approximation specifically designed for variable fractional-order integrators. The formulation relies on a linear and time-invariant definition of the fractional-order operator, ensuring compatibility with Laplace-domain analysis. Under the condition that the fractional-order function is Laplace-transformable and its Bode plot slope lies between

- 20

dB/decade and 0 dB/decade, the system is realized using op-amps and standard RC components. The Grünwald–Letnikov method is employed for numerical calculation of phase portraits, which are then compared with simulation and experimental results. The strong agreement among these results confirms the effectiveness of the proposed method. Full article

(This article belongs to the Special Issue Fractional Differential Equation and Its Applications)

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