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Volume 14
Issue 4
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Axioms, Volume 14, Issue 4 (April 2025) – 93 articles

Cover Story (view full-size image): This contribution to the Mathematical Theory of Contact Mechanics models analyses and simulates the motion of a mass–spring–damper system with friction. The focus is on the propagation of detachment or slip waves as the system transits from a stick state to a slip motion. Inclusion of friction makes it a system of differential set-valued inclusions. The solutions are non-smooth, so a numerical regularization method is employed. The numerical simulations support the theoretical analysis of slip initiation, reachability, and energy balance. In subsequent work, we will provide mathematical and numerical analyses of a system of n masses and its continuous limit, as well as investigate the formation of detachment waves in thin solids. This also serves as a ‘simple’ example of how abstract theoretical results find practical applications. View this paper
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22 pages, 5414 KiB  
Article
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
Viewed by 173
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  
Article
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
Viewed by 104
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  
Article
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
Viewed by 90
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  
Article
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
Viewed by 152
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  
Article
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
Viewed by 79
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  
Article
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
Viewed by 90
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  
Article
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
Viewed by 143
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  
Article
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
Viewed by 135
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  
Article
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
Viewed by 127
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  
Article
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
Viewed by 134
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  
Article
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
Viewed by 119
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  
Article
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
Viewed by 151
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  
Article
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
Viewed by 126
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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24 pages, 2849 KiB  
Article
Optimization Decisions with Bounded Rationality in Customer-Intensive Services Under Gumbel Distributions
by Gang Fu, Minghui Jiang and Wentao Zhan
Axioms 2025, 14(4), 309; https://doi.org/10.3390/axioms14040309 - 17 Apr 2025
Viewed by 215
Abstract
Customers’ bounded rationality significantly influences the effectiveness of advertising and related decision-making in customer-intensive services. This paper, based on the M/M/1 queuing model and incorporating the characteristics of customers’ bounded rationality, conducts an optimization analysis of the decision-making of customer-intensive service providers. In [...] Read more.
Customers’ bounded rationality significantly influences the effectiveness of advertising and related decision-making in customer-intensive services. This paper, based on the M/M/1 queuing model and incorporating the characteristics of customers’ bounded rationality, conducts an optimization analysis of the decision-making of customer-intensive service providers. In this optimization process, we use the Gumbel distribution to model the random noise in customers’ bounded rationality, where the scale parameter characterizes the degree of bounded rationality, and customers’ choices follow a multinomial logit (MNL) choice model. We adopt the symmetric Nash equilibrium to prove the uniqueness of equilibrium in the duopoly market. Furthermore, we derive the optimal service rate and corresponding advertising expenditure levels for both monopoly and duopoly markets through optimization analysis. Our findings indicate that, regardless of market structure, an increase in the scale parameter of the Gumbel distribution, which captures customers’ bounded rationality, leads service providers to adopt a lower service rate to attract customers and reduce advertising expenditures. Notably, this strategy paradoxically results in higher profits for service providers. Additionally, we mathematically prove that, in both monopoly and duopoly markets, the proportion of customers choosing to enter the system follows a unimodal function of the service rate, and a unique and stable Nash equilibrium exists. Furthermore, we find that in the duopoly market, service providers, as a competitive strategy, set a lower service rate compared to the monopoly market. However, in the duopoly market, the proportion of customers attracted by each service provider is lower than in the monopoly market. We also confirmed the results through numerical simulation analysis. Full article
(This article belongs to the Special Issue Mathematical Modeling, Simulations and Applications)
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15 pages, 276 KiB  
Article
Irresolute Homotopy and Covering Theory in Irresolute Topological Groups
by Kadriye Başar and Hürmet Fulya Akız
Axioms 2025, 14(4), 308; https://doi.org/10.3390/axioms14040308 - 17 Apr 2025
Viewed by 123
Abstract
In this paper, we explore certain properties related to connectedness and introduce the definition of irresolute paths. Subsequently, we define the concepts of semi-path connectedness, locally semi-path connectedness, and semi-locally s-simply connected spaces. Additionally, we introduce the concept of irresolute homotopy and reconstruct [...] Read more.
In this paper, we explore certain properties related to connectedness and introduce the definition of irresolute paths. Subsequently, we define the concepts of semi-path connectedness, locally semi-path connectedness, and semi-locally s-simply connected spaces. Additionally, we introduce the concept of irresolute homotopy and reconstruct the fundamental group based on this framework. Furthermore, we prove that the structure of an irresolute topological group with a universal irresolute covering can be lifted to its irresolute covering space. Full article
(This article belongs to the Special Issue Trends in Differential Geometry and Algebraic Topology)
13 pages, 547 KiB  
Article
When Every Total Program Is a Finite Tree-Program: A Study of Program-Saturated Classes of Structures
by Mikhail Moshkov
Axioms 2025, 14(4), 307; https://doi.org/10.3390/axioms14040307 - 17 Apr 2025
Viewed by 125
Abstract
This paper investigates classes of structures and individual structures where programs implementing functions defined everywhere (total programs) are equivalent to finite tree-programs. The programs considered may include cycles and contain at most countably many nodes. The analysis begins with programs where arbitrary terms [...] Read more.
This paper investigates classes of structures and individual structures where programs implementing functions defined everywhere (total programs) are equivalent to finite tree-programs. The programs considered may include cycles and contain at most countably many nodes. The analysis begins with programs where arbitrary terms of a given signature are used in function nodes, and arbitrary formulas of this signature are used in predicate nodes. The results are then extended to programs that closely resemble computation trees: if such a program is a finite tree-program, it can be classified as an ordinary computation tree. Full article
(This article belongs to the Special Issue Advances in Graph Theory with Its Applications)
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14 pages, 605 KiB  
Article
Three Kinds of Denting Points and Their Further Applications in Banach Spaces
by Xiaoxia Wang, Yunan Cui and Yaoming Niu
Axioms 2025, 14(4), 306; https://doi.org/10.3390/axioms14040306 - 16 Apr 2025
Viewed by 135
Abstract
In this paper, we study three kinds of dentabilities and present their important applications in the geometric theory of Banach spaces. First, the relations between weak-denting points and extreme points are established. Moreover, we characterize strong convex spaces and weakly locally uniformly smooth [...] Read more.
In this paper, we study three kinds of dentabilities and present their important applications in the geometric theory of Banach spaces. First, the relations between weak-denting points and extreme points are established. Moreover, we characterize strong convex spaces and weakly locally uniformly smooth spaces by using weakly locally uniform dentability. Finally, we provide some important applications of strong∗ dentability in Fréchet-smooth Banach spaces while investigating the density of strong∗ points in dual Banach spaces. Full article
3 pages, 142 KiB  
Editorial
Numerical Analysis and Optimization
by Milena J. Petrović, Predrag S. Stanimirović and Gradimir V. Milovanović
Axioms 2025, 14(4), 305; https://doi.org/10.3390/axioms14040305 - 16 Apr 2025
Viewed by 138
Abstract
This Editorial introduces this Special Issue of Axioms, which collates 10 articles showcasing the latest research related to problems in the two major scientific fields named in its title: “Numerical Analysis and Optimization” [...] Full article
(This article belongs to the Special Issue Numerical Analysis and Optimization)
16 pages, 283 KiB  
Article
Existence Results for Singular p-Biharmonic Problem with HARDY Potential and Critical Hardy-Sobolev Exponent
by Gurpreet Singh
Axioms 2025, 14(4), 304; https://doi.org/10.3390/axioms14040304 - 16 Apr 2025
Viewed by 156
Abstract
In this article, we consider the singular p-biharmonic problem involving Hardy potential and critical Hardy–Sobolev exponent. Firstly, we study the existence of ground state solutions by using the minimization method on the associated Nehari manifold. Then, we investigate the least-energy sign-changing solutions [...] Read more.
In this article, we consider the singular p-biharmonic problem involving Hardy potential and critical Hardy–Sobolev exponent. Firstly, we study the existence of ground state solutions by using the minimization method on the associated Nehari manifold. Then, we investigate the least-energy sign-changing solutions by considering the Nehari nodal set. In both cases, the critical Sobolev exponent is of great importance as the solutions exists only if we are below the critical Sobolev exponent. Full article
(This article belongs to the Special Issue Advances in Partial Differential Equations: Qualitative Analysis and Numerical Methods)
13 pages, 273 KiB  
Article
Filtered Products of Copies of Injective Modules
by Driss Bennis, Juan Ramón García Rozas, Maroua Mbarki and Luis Oyonarte
Axioms 2025, 14(4), 303; https://doi.org/10.3390/axioms14040303 - 16 Apr 2025
Viewed by 110
Abstract
We study the transfer of injectivity to filtered products of copies of an injective module. This leads to the introduction of a generalized Noetherian condition, the so-called (ℵ,M)-Noetherian rings. We prove that M is F-injective for [...] Read more.
We study the transfer of injectivity to filtered products of copies of an injective module. This leads to the introduction of a generalized Noetherian condition, the so-called (ℵ,M)-Noetherian rings. We prove that M is F-injective for every filter F with cpl(F)≥ℵ if and only if R is (ℵ,M)-Noetherian. We also examine the behavior of filtered products of τ-injective torsion-free modules, establishing preservation results under suitable conditions. Full article
(This article belongs to the Special Issue Trends in Differential Geometry and Algebraic Topology)
25 pages, 420 KiB  
Article
An Axiomatic Approach to Mild Distributions
by Hans G. Feichtinger
Axioms 2025, 14(4), 302; https://doi.org/10.3390/axioms14040302 - 16 Apr 2025
Viewed by 199
Abstract
The Banach Gelfand Triple (S0,L2,S0′) consists of the Feichtinger algebra S0(Rd) as a space of test functions, the dual space S0′(Rd), [...] Read more.
The Banach Gelfand Triple (S0,L2,S0′) consists of the Feichtinger algebra S0(Rd) as a space of test functions, the dual space S0′(Rd), known as the space of mild distributions, and the intermediate Hilbert space L2(Rd). This Gelfand Triple is very useful for the description of mathematical problems in the area of time-frequency analysis, but also for classical Fourier analysis and engineering applications. Because the involved spaces are Banach spaces, we speak of a Banach Gelfand Triple, in contrast to the widespread concept of rigged Hilbert spaces, which usually involve nuclear Frechet spaces. Still, both concepts serve very similar purposes. Based on the manifold properties of S0(Rd), it has found applications in the derivation of mathematical statements related to Gabor Analysis but also in providing an alternative and more lucid description of classical results, such as the Shannon sampling theory, with a potential to renew the way how Fourier and time-frequency analysis, but also signal processing courses for engineers (or physicists and mathematicians) could be taught in the future. In the present study, we will demonstrate that one could choose a relatively large variety of similar Banach Gelfand Triples, even if one wants to include key properties such as Fourier invariance (an extended version of Plancherel’s Theorem). Some of them appeared naturally in the literature. It turns out, that S0(Rd) is the smallest member of this family. Consequently S0′(Rd) is the largest dual space among all these spaces, which may be one of the reasons for its universal usefulness. This article provides a study of the basic properties following from a short list of relatively simple assumptions and gives a list of non-trivial examples satisfying these basic axioms. Full article
(This article belongs to the Section Mathematical Analysis)
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19 pages, 929 KiB  
Article
Simulation-Based Evaluation of Robust Transformation Techniques for Median Estimation Under Simple Random Sampling
by Fatimah A. Almulhim and Abdulaziz S. Alghamdi
Axioms 2025, 14(4), 301; https://doi.org/10.3390/axioms14040301 - 16 Apr 2025
Viewed by 149
Abstract
An efficient estimator can reduce both bias and mean squared error to provide more accurate results by using the transformation strategy. In this paper, an enhanced class of ratio–product types of estimators is introduced, which employs the transformation technique by linearly combining two [...] Read more.
An efficient estimator can reduce both bias and mean squared error to provide more accurate results by using the transformation strategy. In this paper, an enhanced class of ratio–product types of estimators is introduced, which employs the transformation technique by linearly combining two robust measures, the trimean and decile mean, and five non-conventional measures, the range, inter-quartile range, mid-range, quartile average, and quartile deviation, on auxiliary variables with a simple random sampling method to estimate the finite population median. This transformation approach improves efficiency and enables estimators to manage data variability better. Using these estimators, we investigate their bias and mean squared error up to the first order of approximation. A comparison of the proposed estimators and existing methods is conducted through five simulated populations generated through different suitable distributions and three real datasets. By improving the precision and efficiency of median estimation, the proposed estimators ensure accurate and reliable results. Comparing the new estimators to traditional estimators, the findings show superior performance for new estimators in terms of mean squared errors (MSEs). Full article
(This article belongs to the Special Issue Probability, Statistics and Estimations, 2nd Edition)
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25 pages, 985 KiB  
Article
Construction of Topic Hierarchy with Subtree Representation for Knowledge Graphs
by Yujia Zhang, Wenjie Xu, Zheng Yu and Marek Z. Reformat
Axioms 2025, 14(4), 300; https://doi.org/10.3390/axioms14040300 - 15 Apr 2025
Viewed by 137
Abstract
Hierarchy analysis of the knowledge graphs aims to discover the latent structure inherent in knowledge base data. Drawing inspiration from topic modeling, which identifies latent themes and content patterns in text corpora, our research seeks to adapt these analytical frameworks to the hierarchical [...] Read more.
Hierarchy analysis of the knowledge graphs aims to discover the latent structure inherent in knowledge base data. Drawing inspiration from topic modeling, which identifies latent themes and content patterns in text corpora, our research seeks to adapt these analytical frameworks to the hierarchical exploration of knowledge graphs. Specifically, we adopt a non-parametric probabilistic model, the nested hierarchical Dirichlet process, to the field of knowledge graphs. This model discovers latent subject-specific distributions along paths within the tree. Consequently, the global tree can be viewed as a collection of local subtrees for each subject, allowing us to represent subtrees for each subject and reveal cross-thematic topics. We assess the efficacy of this model in analyzing the topics and word distributions that form the hierarchical structure of complex knowledge graphs. We quantitatively evaluate our model using four common datasets: Freebase, Wikidata, DBpedia, and WebRED, demonstrating that it outperforms the latest neural hierarchical clustering techniques such as TraCo, SawETM, and HyperMiner. Additionally, we provide a qualitative assessment of the induced subtree for a single subject. Full article
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22 pages, 1304 KiB  
Article
Detachment Waves in Frictional Contact II: Analysis and Simulations of a Three-Mass System
by Jeongho Ahn and Meir Shillor
Axioms 2025, 14(4), 299; https://doi.org/10.3390/axioms14040299 - 15 Apr 2025
Viewed by 122
Abstract
This work continues the study of a mathematical model for the motion of a mass–spring–damper system with friction. There, a two-mass model was constructed, its solvability established, the steady states investigated, and numerical simulations presented. The main interest here is in the modeling, [...] Read more.
This work continues the study of a mathematical model for the motion of a mass–spring–damper system with friction. There, a two-mass model was constructed, its solvability established, the steady states investigated, and numerical simulations presented. The main interest here is in the modeling, analysis of the steady states, and simulation of a three-mass system—in particular, in the propagation of detachment or slip waves, which happen when the system transits from a stick state to a slip motion. The introduction of friction changes the problem into systems of three differential set-valued inclusions, which are mathematically and computationally very challenging. The analysis of the steady states shows the regions of stick, where there is enough frictional resistance that prevents motion. The proposed numerical methods are implemented, and the simulations show some representative types of system behavior, especially the cases of detachment waves. Some of the numerical simulations specifically support the theoretical analysis of slip initiation, reachability, and energy balance. Full article
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15 pages, 4808 KiB  
Article
Unveiling the Transformative Power: Exploring the Nonlocal Potential Approach in the (3 + 1)-Dimensional Yu–Toda–Sasa–Fukuyama Equation
by Enas Y. Abu El Seoud, Ahmed S. Rashed and Samah M. Mabrouk
Axioms 2025, 14(4), 298; https://doi.org/10.3390/axioms14040298 - 15 Apr 2025
Viewed by 150
Abstract
This paper focuses on the investigation of the Yu–Toda–Sasa–Fukuyama (YTSF) equation in its three-dimensional form. Based on the well-known Euler operator, a set of seven non-singular local multipliers is explored. Using these seven non-singular multipliers, the corresponding local conservation laws are derived. Additionally, [...] Read more.
This paper focuses on the investigation of the Yu–Toda–Sasa–Fukuyama (YTSF) equation in its three-dimensional form. Based on the well-known Euler operator, a set of seven non-singular local multipliers is explored. Using these seven non-singular multipliers, the corresponding local conservation laws are derived. Additionally, an auxiliary potential-related system of partial differential equations (PDEs) is constructed. This study delves into nonlocal systems, which reveal numerous intriguing exact solutions of the YTSF equation. The nonlinear systems exhibit stable structures such as kink solitons, representing transitions, and breather or multi-solitons, modeling localized energy packets and complex interactions. These are employed in materials science, optics, communications, and plasma. Additionally, patterns such as parabolic backgrounds with ripples inform designs involving structured or varying media such as waveguides. Full article
(This article belongs to the Special Issue Difference, Functional, and Related Equations, 2nd Edition)
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18 pages, 1701 KiB  
Article
Furstenberg Topology and Collatz Problem
by Edward Tutaj and Halszka Tutaj-Gasinska
Axioms 2025, 14(4), 297; https://doi.org/10.3390/axioms14040297 - 15 Apr 2025
Viewed by 160
Abstract
The aims of this paper are two-fold. First, we present the result of the decomposition on the iterations of a Collatz transform into arithmetic sequences. With this, we prove that in Furstenberg topology, the set of (odd) integers with an infinite stopping time [...] Read more.
The aims of this paper are two-fold. First, we present the result of the decomposition on the iterations of a Collatz transform into arithmetic sequences. With this, we prove that in Furstenberg topology, the set of (odd) integers with an infinite stopping time is closed and nowhere dense. Then, we move our considerations to some monoids L in N, where we define a suitably modified Collatz transform, and we present some results of numerical investigations on the behaviour of these modified transforms. Full article
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14 pages, 293 KiB  
Article
A Class of Local Non-Chain Rings of Order p5m
by Alhanouf Ali Alhomaidhi, Badriyah Rashed Alshahrani and Sami Alabiad
Axioms 2025, 14(4), 296; https://doi.org/10.3390/axioms14040296 - 15 Apr 2025
Viewed by 173
Abstract
This study investigates finite commutative local non-chain rings characterized by the well-established invariants p, n, m, l, and k, where p denotes a prime number. We specifically focus on Frobenius local rings with length [...] Read more.
This study investigates finite commutative local non-chain rings characterized by the well-established invariants p, n, m, l, and k, where p denotes a prime number. We specifically focus on Frobenius local rings with length l=5 and an index of nilpotency t=4. The significance of Frobenius rings in coding theory arises when specific results of linear codes are applicable to both finite fields and finite Frobenius rings. In light of this, we provide a comprehensive classification and enumeration of Frobenius local rings of order p5m with t=4, highlighting their distinctive properties in relation to varying values of n. This research advances our understanding of the structural features of Frobenius rings and their applications in coding theory. Full article
12 pages, 273 KiB  
Article
Resolvents for Convex Functions on Geodesic Spaces and Their Nonspreadingness
by Takuto Kajimura, Yasunori Kimura and Fumiaki Kohsaka
Axioms 2025, 14(4), 295; https://doi.org/10.3390/axioms14040295 - 14 Apr 2025
Viewed by 130
Abstract
The convex optimization problems have been considered by many researchers on geodesic spaces. In these problems, the resolvent operators play an important role. In this paper, we propose new resolvents on geodesic spaces, and we show that they have better properties than other [...] Read more.
The convex optimization problems have been considered by many researchers on geodesic spaces. In these problems, the resolvent operators play an important role. In this paper, we propose new resolvents on geodesic spaces, and we show that they have better properties than other known resolvent operators. Full article
(This article belongs to the Special Issue New Theory and Applications of Nonlinear Analysis, Fractional Calculus and Optimization, 2nd Edition)
17 pages, 346 KiB  
Article
A New Class of Interval-Valued Discrete Sugeno-like Integrals
by Nícolas Jacobino, Nicolás Zumelzu, Claudio Callejas, Eduardo Palmeira and Benjamín Bedregal
Axioms 2025, 14(4), 294; https://doi.org/10.3390/axioms14040294 - 14 Apr 2025
Viewed by 186
Abstract
Discrete Sugeno integrals form a significant family of aggregation functions. Several variants of these integrals have been proposed, most of which replace the minimum operation with alternative operations, such as product, overlap functions, and t-norms. Notably, the associativity of t-norms in discrete Sugeno [...] Read more.
Discrete Sugeno integrals form a significant family of aggregation functions. Several variants of these integrals have been proposed, most of which replace the minimum operation with alternative operations, such as product, overlap functions, and t-norms. Notably, the associativity of t-norms in discrete Sugeno integrals has no significant consequences, leading us to relinquish this property and introduce the concept of partial t-norms. Although interval-valued versions of the discrete Sugeno integral or its variants have been limited, this paper presents a novel approach based on interval-valued partial t-norms, admissible orders, and interval-valued fuzzy measures. We provide rigorous proofs of the properties of this operator class. Full article
(This article belongs to the Special Issue Advances in Fuzzy Logic and Computational Intelligence)
12 pages, 282 KiB  
Article
Partitioning Planar Graphs Without Specific Cycles into a Forest and a Disjoint Union of Paths
by Pongpat Sittitrai, Keaitsuda Maneeruk Nakprasit and Kittikorn Nakprasit
Axioms 2025, 14(4), 293; https://doi.org/10.3390/axioms14040293 - 14 Apr 2025
Viewed by 132
Abstract
In this paper, we show that if a planar graph G satisfies the following conditions: (i) none of its 3-faces is adjacent to a 6−-face, and (ii) none of its 4-faces is adjacent to a 5−-face, then [...] Read more.
In this paper, we show that if a planar graph G satisfies the following conditions: (i) none of its 3-faces is adjacent to a 6−-face, and (ii) none of its 4-faces is adjacent to a 5−-face, then V(G) can be partitioned into two subsets, each induces a forest, while one of the forests has maximum degree of at most 2. This result implies that every planar graph (i) with no chordal 7−-cycles, or (ii) with neither 4- nor 6-cycles, also admits such a partition. Full article
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