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Volume 14
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Axioms, Volume 14, Issue 7 (July 2025) – 62 articles

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14 pages, 2182 KiB  
Article
Stability Analysis of a Master–Slave Cournot Triopoly Model: The Effects of Cross-Diffusion
by Maria Francesca Carfora and Isabella Torcicollo
Axioms 2025, 14(7), 540; https://doi.org/10.3390/axioms14070540 (registering DOI) - 17 Jul 2025
Abstract
A Cournot triopoly is a type of oligopoly market involving three firms that produce and sell homogeneous or similar products without cooperating with one another. In Cournot models, firms’ decisions about production levels play a crucial role in determining overall market output. Compared [...] Read more.
A Cournot triopoly is a type of oligopoly market involving three firms that produce and sell homogeneous or similar products without cooperating with one another. In Cournot models, firms’ decisions about production levels play a crucial role in determining overall market output. Compared to duopoly models, oligopolies with more than two firms have received relatively less attention in the literature. Nevertheless, triopoly models are more reflective of real-world market conditions, even though analyzing their dynamics remains a complex challenge. A reaction–diffusion system of PDEs generalizing a nonlinear triopoly model describing a master–slave Cournot game is introduced. The effect of diffusion on the stability of Nash equilibrium is investigated. Self-diffusion alone cannot induce Turing pattern formation. In fact, linear stability analysis shows that cross-diffusion is the key mechanism for the formation of spatial patterns. The conditions for the onset of cross-diffusion-driven instability are obtained via linear stability analysis, and the formation of several Turing patterns is investigated through numerical simulations. Full article
(This article belongs to the Special Issue New Perspectives in Applied Mathematics with Nonlinear Equations and Dynamical Systems)
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9 pages, 252 KiB  
Article
On Extended d-D Kappa Distribution
by Arak M. Mathai and Hans J. Haubold
Axioms 2025, 14(7), 539; https://doi.org/10.3390/axioms14070539 (registering DOI) - 17 Jul 2025
Abstract
The thermal Doppler broadening of spectral profiles for particle populations in the absence or presence of potential fields can be described by kappa distributions. The kappa distribution provides a replacement for the Maxwell–Boltzmann distribution, which can be considered as a generalization for describing [...] Read more.
The thermal Doppler broadening of spectral profiles for particle populations in the absence or presence of potential fields can be described by kappa distributions. The kappa distribution provides a replacement for the Maxwell–Boltzmann distribution, which can be considered as a generalization for describing systems characterized by local correlations among their particles, as found in space and astrophysical plasmas. This paper presents all special cases of kappa distributions as members of a general pathway family of densities introduced by Mathai. The aim of the present paper is to bring to attention the application of various forms of the kappa distribution, its various special cases and its generalizations, which, in scalar-variable and multivariate situations, belong to a general family of distributions known as Mathai’s pathway models, comprising three different families of functions, namely the generalized type-1 beta, type-2 beta and gamma families. Through one parameter, known as the pathway parameter, one will be able to reach all the three families of functions and the stages of transitioning from one family to another. After pointing out the connection of multivariate (vector-variate) kappa distributions to the multivariate pathway model, the multivariate kappa distribution is extended to the real matrix-variate case by working out the various forms and by evaluating the normalizing constants of the various forms of the matrix-variate case explicitly. It is also pointed out that the pathway models are available for the scalar, vector and rectangular matrix-variate cases in the real domain as well as in the complex domain. Full article
14 pages, 555 KiB  
Article
A Novel Hyper-Heuristic Algorithm for Bayesian Network Structure Learning Based on Feature Selection
by Yinglong Dang, Xiaoguang Gao and Zidong Wang
Axioms 2025, 14(7), 538; https://doi.org/10.3390/axioms14070538 (registering DOI) - 17 Jul 2025
Abstract
Bayesian networks (BNs) are effective and universal tools for addressing uncertain knowledge. BN learning includes structure learning and parameter learning, and structure learning is its core. The topology of a BN can be determined by expert domain knowledge or obtained through data analysis. [...] Read more.
Bayesian networks (BNs) are effective and universal tools for addressing uncertain knowledge. BN learning includes structure learning and parameter learning, and structure learning is its core. The topology of a BN can be determined by expert domain knowledge or obtained through data analysis. However, when many variables exist in a BN, relying only on expert knowledge is difficult and infeasible. Therefore, the current research focus is to build a BN via data analysis. However, current data learning methods have certain limitations. In this work, we consider a combination of expert knowledge and data learning methods. In our algorithm, the hard constraints are derived from highly reliable expert knowledge, and some conditional independent information is mined by feature selection as a soft constraint. These structural constraints are reasonably integrated into an exponential Monte Carlo with counter (EMCQ) hyper-heuristic algorithm. A comprehensive experimental study demonstrates that our proposed method exhibits more robustness and accuracy compared to alternative algorithms. Full article
(This article belongs to the Special Issue Advances in Mathematical Optimization Algorithms and Its Applications)
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21 pages, 962 KiB  
Article
Modal Regression Estimation by Local Linear Approach in High-Dimensional Data Case
by Fatimah A. Almulhim, Mohammed B. Alamari, Ali Laksaci and Zoulikha Kaid
Axioms 2025, 14(7), 537; https://doi.org/10.3390/axioms14070537 - 16 Jul 2025
Abstract
This paper introduces a new nonparametric estimator for detecting the conditional mode in the functional input variable setting. The estimator integrates a local linear approach with an L1-robust algorithm and treats the modal regression as the minimizer of the quantile derivative. [...] Read more.
This paper introduces a new nonparametric estimator for detecting the conditional mode in the functional input variable setting. The estimator integrates a local linear approach with an L1-robust algorithm and treats the modal regression as the minimizer of the quantile derivative. As an asymptotic result, we derive the theoretical properties of the estimator by analyzing its convergence rate under the almost complete consistency framework. The result is stated under standard conditions, characterizing both the functional structure of the data and the local linear approximation properties of the model. Moreover, the expression of the convergence rate retains the usual form of the stochastic convergence rate in functional statistics. Simulations and real-data applications demonstrate the algorithm’s effectiveness, showing its advantage over existing methods in high-dimensional prediction tasks. Full article
(This article belongs to the Special Issue Advances in Statistical Simulation and Computing)
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13 pages, 295 KiB  
Article
On Subprojectivity of Goldie Torsion Modules
by Hashem Bordbar, Yılmaz Durğun, Yara Şihkayad and Ergül Türkmen
Axioms 2025, 14(7), 536; https://doi.org/10.3390/axioms14070536 - 16 Jul 2025
Abstract
Recently, the concept of subprojectivity domains for modules has been introduced as a means of quantifying the level of projectivity exhibited by a module. In this research article, we focus on the subprojectivity domain of Goldie torsion modules. In particular, we establish that [...] Read more.
Recently, the concept of subprojectivity domains for modules has been introduced as a means of quantifying the level of projectivity exhibited by a module. In this research article, we focus on the subprojectivity domain of Goldie torsion modules. In particular, we establish that a ring denoted as R is classified as right nonsingular if and only if the subprojectivity domain of each Goldie torsion module is closed under submodules. In addition, we demonstrate that a right C-ring is a right nonsingular ring if and only if every module possesses an epic ecf-flat envelope, which is further equivalent to each Goldie torsion module having an epic projective envelope. Full article
21 pages, 7720 KiB  
Article
Dynamical Behaviors of a Stochastic Semi-Parametric SEIR Model with Infectivity in the Incubation Period
by Mei Li and Jing Zhang
Axioms 2025, 14(7), 535; https://doi.org/10.3390/axioms14070535 - 15 Jul 2025
Viewed by 51
Abstract
This paper investigates a stochastic semi-parametric SEIR model characterized by infectivity during the incubation period and influenced by white noise perturbations. First, based on the theory of stochastic persistence, we derive the conditions required for the disease to persist within the model. Under [...] Read more.
This paper investigates a stochastic semi-parametric SEIR model characterized by infectivity during the incubation period and influenced by white noise perturbations. First, based on the theory of stochastic persistence, we derive the conditions required for the disease to persist within the model. Under these conditions, we apply Khasminskii’s ergodic theorem and Lyapunov functions to establish that the model possesses a unique ergodic stationary distribution. Finally, we utilize Khasminskii’s periodic theorem to examine the corresponding stochastic periodic SEIR model derived from the stochastic semi-parametric SEIR model, identifying sufficient conditions for the existence of non-trivial periodic solutions. Our theoretical results are further validated through numerical simulations. Full article
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16 pages, 1998 KiB  
Article
Marginal Design of a Pneumatic Stage Position Using Filtered Right Coprime Factorization and PPC-SMC
by Tomoya Hoshina, Yusaku Tanabata and Mingcong Deng
Axioms 2025, 14(7), 534; https://doi.org/10.3390/axioms14070534 - 15 Jul 2025
Viewed by 58
Abstract
In recent years, pneumatic stages have attracted attention as stages for semiconductor manufacturing equipment due to their low cost and minimal maintenance requirements. However, pneumatic stages include nonlinear elements such as friction and air compressibility, making precise control challenging. To address this issue, [...] Read more.
In recent years, pneumatic stages have attracted attention as stages for semiconductor manufacturing equipment due to their low cost and minimal maintenance requirements. However, pneumatic stages include nonlinear elements such as friction and air compressibility, making precise control challenging. To address this issue, this paper aims to achieve high-precision positioning by applying a nonlinear position control method to pneumatic stages. To achieve this, we propose a control method that combines filtered right coprime factorization and Prescribed Performance Control–Sliding Mode Control (PPC-SMC). Filtered right coprime factorization not only stabilizes and simplifies the plant but also reduces noise. Furthermore, PPC-SMC enables safer and faster control by constraining the system state within a switching surface that imposes limits on the error range. Through experiments on the actual system, it was confirmed that the proposed method achieves dramatically higher precision and faster tracking compared to conventional methods. Full article
(This article belongs to the Special Issue New Perspectives in Control Theory)
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90 pages, 673 KiB  
Article
Clifford Distributions Revisited
by Fred Brackx
Axioms 2025, 14(7), 533; https://doi.org/10.3390/axioms14070533 - 14 Jul 2025
Viewed by 56
Abstract
In the framework of harmonic and Clifford analysis, specific distributions in Euclidean space of arbitrary dimension, which are of particular importance for theoretical physics, are once more thoroughly studied. Indeed, actions involving spherical coordinates, such as the radial derivative and multiplication and division [...] Read more.
In the framework of harmonic and Clifford analysis, specific distributions in Euclidean space of arbitrary dimension, which are of particular importance for theoretical physics, are once more thoroughly studied. Indeed, actions involving spherical coordinates, such as the radial derivative and multiplication and division by the radial distance, only make sense when considering so-called signumdistributions, that is, bounded linear functionals on a space of test functions showing a singularity at the origin. Introducing these signumdistributions, the actions of a whole series of scalar and vectorial differential operators on the distributions under consideration, lead to a number of surprising results, as illustrated by some examples in three-dimensional mathematical physics. Full article
(This article belongs to the Special Issue Recent Advances in Complex Analysis and Related Topics)
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21 pages, 330 KiB  
Article
Distribution Modulo One of αpγ + β for Special Classes of Primes
by Atanaska Georgieva and Tatiana L. Todorova
Axioms 2025, 14(7), 532; https://doi.org/10.3390/axioms14070532 - 12 Jul 2025
Viewed by 168
Abstract
Let α,β∈R with α≠0, and let γ∈(0,5/6). Define the set M1 to consist of primes p such that p+2 is almost prime, and let [...] Read more.
Let α,β∈R with α≠0, and let γ∈(0,5/6). Define the set M1 to consist of primes p such that p+2 is almost prime, and let M2 be the set of primes of the form p=a2+b2+1. We study the distribution of αpγ + β modulo one, as p ranges over the sets M1 and M2, respectively. Full article
(This article belongs to the Special Issue Mathematical Analysis and Applications IV)
20 pages, 2681 KiB  
Article
The Effects of the Weak Allee Effect and Disease on the Dynamics of a Predator–Prey System: Stability and Bifurcation Properties
by Yurong Dong, Hua Liu, Jianhua Ye, Gang Ma and Yumei Wei
Axioms 2025, 14(7), 531; https://doi.org/10.3390/axioms14070531 - 12 Jul 2025
Viewed by 104
Abstract
In this paper, an eco-epidemiological model with a weak Allee effect and prey disease dynamics is discussed. Mathematical features such as non-negativity, boundedness of solutions, and local stability of the feasible equilibria are discussed. Additionally, the transcritical bifurcation, saddle-node bifurcation, and Hopf bifurcation [...] Read more.
In this paper, an eco-epidemiological model with a weak Allee effect and prey disease dynamics is discussed. Mathematical features such as non-negativity, boundedness of solutions, and local stability of the feasible equilibria are discussed. Additionally, the transcritical bifurcation, saddle-node bifurcation, and Hopf bifurcation are proven using Sotomayor’s theorem and Poincare–Andronov–Hopf theorems. In addition, the correctness of the theoretical analysis is verified by numerical simulation. The numerical simulation results show that the eco-epidemiological model with a weak Allee effect has complex dynamics. If the prey population is not affected by disease, the predator becomes extinct due to a lack of food. Under low infection rates, all populations are maintained in a coexistent state. The Allee effect does not influence this coexistence. At high infection rates, if the prey population is not affected by the Allee effect, the infected prey is found to coexist in an oscillatory state. The predator population and the susceptible prey population will be extinct. If the prey population is affected by the Allee effect, all species will be extinct. Full article
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27 pages, 388 KiB  
Article
Existence of Sign-Changing Solutions for a Class of p(x)-Biharmonic Kirchhoff-Type Equations
by Rui Deng and Qing Miao
Axioms 2025, 14(7), 530; https://doi.org/10.3390/axioms14070530 - 12 Jul 2025
Viewed by 84
Abstract
This paper mainly studies the existence of sign-changing solutions for the following px-biharmonic Kirchhoff-type equations: [...] Read more.
This paper mainly studies the existence of sign-changing solutions for the following px-biharmonic Kirchhoff-type equations: −a+b∫RN1p(x)|Δu|p(x)dxΔp(x)2u+V(x)|u|p(x)−2u = Kxf(u),x∈RN where Δp(x)2u=Δ|Δu|p(x)−2Δu is the p(x) biharmonic operator, a,b>0 are constants, N≥2, V(x),K(x) are positive continuous functions which vanish at infinity, and the nonlinearity f has subcritical growth. Using the Nehari manifold method, deformation lemma, and other techniques of analysis, it is demonstrated that there are precisely two nodal domains in the problem’s least energy sign-changing solution ub. In addition, the convergence property of ub as b→0 is also established. Full article
17 pages, 255 KiB  
Article
Wrapping Generalized Laplace and Generalized Discrete Laplace Distributions
by Barry C. Arnold and Ashis SenGupta
Axioms 2025, 14(7), 529; https://doi.org/10.3390/axioms14070529 - 11 Jul 2025
Viewed by 94
Abstract
Generalized Laplace and discrete generalized Laplace models are described and some of their properties are reviewed. For the analysis of directional data, it is natural to consider wrapped versions of these models. A well-known result for the circular and, more recently, for multivariate [...] Read more.
Generalized Laplace and discrete generalized Laplace models are described and some of their properties are reviewed. For the analysis of directional data, it is natural to consider wrapped versions of these models. A well-known result for the circular and, more recently, for multivariate circular distributions that mixing and wrapping commute, allows us to readily determine the nature of these wrapped models. Some bivariate extensions of these models are discussed, together with some consideration of the feasibility of wrapping such models. Multivariate versions of the models can be envisioned. Full article
21 pages, 1847 KiB  
Article
Fusion of Recurrence Plots and Gramian Angular Fields with Bayesian Optimization for Enhanced Time-Series Classification
by Maria Mariani, Prince Appiah and Osei Tweneboah
Axioms 2025, 14(7), 528; https://doi.org/10.3390/axioms14070528 - 10 Jul 2025
Viewed by 254
Abstract
Time-series classification remains a critical task across various domains, demanding models that effectively capture both local recurrence structures and global temporal dependencies. We introduce a novel framework that transforms time series into image representations by fusing recurrence plots (RPs) with both Gramian Angular [...] Read more.
Time-series classification remains a critical task across various domains, demanding models that effectively capture both local recurrence structures and global temporal dependencies. We introduce a novel framework that transforms time series into image representations by fusing recurrence plots (RPs) with both Gramian Angular Summation Fields (GASFs) and Gramian Angular Difference Fields (GADFs). This fusion enriches the structural encoding of temporal dynamics. To ensure optimal performance, Bayesian Optimization is employed to automatically select the ideal image resolution, eliminating the need for manual tuning. Unlike prior methods that rely on individual transformations, our approach concatenates RP, GASF, and GADF into a unified representation and generalizes to multivariate data by stacking transformation channels across sensor dimensions. Experiments on seven univariate datasets show that our method significantly outperforms traditional classifiers such as one-nearest neighbor with Dynamic Time Warping, Shapelet Transform, and RP-based convolutional neural networks. For multivariate tasks, the proposed fusion model achieves macro F1 scores of 91.55% on the UCI Human Activity Recognition dataset and 98.95% on the UCI Room Occupancy Estimation dataset, outperforming standard deep learning baselines. These results demonstrate the robustness and generalizability of our framework, establishing a new benchmark for image-based time-series classification through principled fusion and adaptive optimization. Full article
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26 pages, 1556 KiB  
Article
Modified Two-Parameter Ridge Estimators for Enhanced Regression Performance in the Presence of Multicollinearity: Simulations and Medical Data Applications
by Muteb Faraj Alharthi and Nadeem Akhtar
Axioms 2025, 14(7), 527; https://doi.org/10.3390/axioms14070527 - 10 Jul 2025
Viewed by 143
Abstract
Predictive regression models often face a common challenge known as multicollinearity. This phenomenon can distort the results, causing models to overfit and produce unreliable coefficient estimates. Ridge regression is a widely used approach that incorporates a regularization term to stabilize parameter estimates and [...] Read more.
Predictive regression models often face a common challenge known as multicollinearity. This phenomenon can distort the results, causing models to overfit and produce unreliable coefficient estimates. Ridge regression is a widely used approach that incorporates a regularization term to stabilize parameter estimates and improve the prediction accuracy. In this study, we introduce four newly modified ridge estimators, referred to as RIRE1, RIRE2, RIRE3, and RIRE4, that are aimed at tackling severe multicollinearity more effectively than ordinary least squares (OLS) and other existing estimators under both normal and non-normal error distributions. The ridge estimators are biased, so their efficiency cannot be judged by variance alone; instead, we use the mean squared error (MSE) to compare their performance. Each new estimator depends on two shrinkage parameters, k and d, making the theoretical analysis complex. To address this, we employ Monte Carlo simulations to rigorously evaluate and compare these new estimators with OLS and other existing ridge estimators. Our simulations show that the proposed estimators consistently minimize the MSE better than OLS and other ridge estimators, particularly in datasets with strong multicollinearity and large error variances. We further validate their practical value through applications using two real-world datasets, demonstrating both their robustness and theoretical alignment. Full article
(This article belongs to the Special Issue Applied Mathematics and Mathematical Modeling)
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18 pages, 300 KiB  
Article
Applications of Complex Uncertain Sequences via Lacunary Almost Statistical Convergence
by Xiu-Liang Qiu, Kuldip Raj, Sanjeev Verma, Samrati Gorka, Shixiao Xiao and Qing-Bo Cai
Axioms 2025, 14(7), 526; https://doi.org/10.3390/axioms14070526 - 10 Jul 2025
Viewed by 147
Abstract
We explore the realm of uncertainty theory by investigating diverse notions of convergence and statistical convergence concerning complex uncertain sequences. Complex uncertain variables can be described as measurable functions mapping from an uncertainty space to the set of complex numbers. They are employed [...] Read more.
We explore the realm of uncertainty theory by investigating diverse notions of convergence and statistical convergence concerning complex uncertain sequences. Complex uncertain variables can be described as measurable functions mapping from an uncertainty space to the set of complex numbers. They are employed to represent and model complex uncertain quantities. We introduce the concept of lacunary almost statistical convergence of order α(0<α≤1) for complex uncertain sequences, examining various aspects of uncertainty such as distribution, mean, measure, uniformly almost sure convergence and almost sure convergence. Additionally, we establish connections between the constructed sequence spaces by providing illustrative instances. Importantly, lacunary almost statistical convergence provides a flexible framework for handling sequences with irregular behavior, which often arise in uncertain environments with imprecise data. This makes our approach particularly useful in practical fields such as engineering, data modeling and decision-making, where traditional deterministic methods are not always applicable. Our approach offers a more flexible and realistic framework for approximating functions in uncertain environments where classical convergence may not apply. Thus, this study contributes to approximation theory by extending its tools to settings involving imprecise or noisy data. Full article
(This article belongs to the Special Issue Numerical Computation, Approximation of Functions and Applied Mathematics, 2nd Edition)
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19 pages, 528 KiB  
Article
Quantum-Inspired Attention-Based Semantic Dependency Fusion Model for Aspect-Based Sentiment Analysis
by Chenyang Xu, Xihan Wang, Jiacheng Tang, Yihang Wang, Lianhe Shao and Quanli Gao
Axioms 2025, 14(7), 525; https://doi.org/10.3390/axioms14070525 - 9 Jul 2025
Viewed by 209
Abstract
Aspect-Based Sentiment Analysis (ABSA) has gained significant popularity in recent years, which emphasizes the aspect-level sentiment representation of sentences. Current methods for ABSA often use pre-trained models and graph convolution to represent word dependencies. However, they struggle with long-range dependency issues in lengthy [...] Read more.
Aspect-Based Sentiment Analysis (ABSA) has gained significant popularity in recent years, which emphasizes the aspect-level sentiment representation of sentences. Current methods for ABSA often use pre-trained models and graph convolution to represent word dependencies. However, they struggle with long-range dependency issues in lengthy texts, resulting in averaging and loss of contextual semantic information. In this paper, we explore how richer semantic relationships can be encoded more efficiently. Inspired by quantum theory, we construct superposition states from text sequences and utilize them with quantum measurements to explicitly capture complex semantic relationships within word sequences. Specifically, we propose an attention-based semantic dependency fusion method for ABSA, which employs a quantum embedding module to create a superposition state of real-valued word sequence features in a complex-valued Hilbert space. This approach yields a word sequence density matrix representation that enhances the handling of long-range dependencies. Furthermore, we introduce a quantum cross-attention mechanism to integrate sequence features with dependency relationships between specific word pairs, aiming to capture the associations between particular aspects and comments more comprehensively. Our experiments on the SemEval-2014 and Twitter datasets demonstrate the effectiveness of the quantum-inspired attention-based semantic dependency fusion model for the ABSA task. Full article
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30 pages, 956 KiB  
Article
Stochastic Production Planning with Regime-Switching: Sensitivity Analysis, Optimal Control, and Numerical Implementation
by Dragos-Patru Covei
Axioms 2025, 14(7), 524; https://doi.org/10.3390/axioms14070524 - 8 Jul 2025
Viewed by 133
Abstract
This study investigates a stochastic production planning problem with regime-switching parameters, inspired by economic cycles impacting production and inventory costs. The model considers types of goods and employs a Markov chain to capture probabilistic regime transitions, coupled with a multidimensional Brownian motion representing [...] Read more.
This study investigates a stochastic production planning problem with regime-switching parameters, inspired by economic cycles impacting production and inventory costs. The model considers types of goods and employs a Markov chain to capture probabilistic regime transitions, coupled with a multidimensional Brownian motion representing stochastic demand dynamics. The production and inventory cost optimization problem is formulated as a quadratic cost functional, with the solution characterized by a regime-dependent system of elliptic partial differential equations (PDEs). Numerical solutions to the PDE system are computed using a monotone iteration algorithm, enabling quantitative analysis. Sensitivity analysis and model risk evaluation illustrate the effects of regime-dependent volatility, holding costs, and discount factors, revealing the conservative bias of regime-switching models when compared to static alternatives. Practical implications include optimizing production strategies under fluctuating economic conditions and exploring future extensions such as correlated Brownian dynamics, non-quadratic cost functions, and geometric inventory frameworks. In contrast to earlier studies that imposed static or overly simplified regime-switching assumptions, our work presents a fully integrated framework—combining optimal control theory, a regime-dependent system of elliptic PDEs, and comprehensive numerical and sensitivity analyses—to more accurately capture the complex stochastic dynamics of production planning and thereby deliver enhanced, actionable insights for modern manufacturing environments. Full article
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15 pages, 298 KiB  
Article
Fuzzy Treatment for Meromorphic Classes of Admissible Functions Connected to Hurwitz–Lerch Zeta Function
by Ekram E. Ali, Rabha M. El-Ashwah, Abeer M. Albalahi and Rabab Sidaoui
Axioms 2025, 14(7), 523; https://doi.org/10.3390/axioms14070523 - 8 Jul 2025
Viewed by 200
Abstract
Fuzzy differential subordinations, a notion taken from fuzzy set theory and used in complex analysis, are the subject of this paper. In this work, we provide an operator and examine the characteristics of meromorphic functions in the punctured open unit disk that are [...] Read more.
Fuzzy differential subordinations, a notion taken from fuzzy set theory and used in complex analysis, are the subject of this paper. In this work, we provide an operator and examine the characteristics of meromorphic functions in the punctured open unit disk that are related to a class of complex parameter operators. Complex analysis ideas from geometric function theory are used to derive fuzzy differential subordination conclusions. Due to the compositional structure of the operator, some pertinent classes of admissible functions are studied through the application of fuzzy differential subordination. Full article
(This article belongs to the Special Issue New Developments in Geometric Function Theory, 3rd Edition)
31 pages, 2227 KiB  
Article
Observer-Linked Branching (OLB)—A Proposed Quantum-Theoretic Framework for Macroscopic Reality Selection
by Călin Gheorghe Buzea, Florin Nedeff, Valentin Nedeff, Dragos-Ioan Rusu, Maricel Agop and Decebal Vasincu
Axioms 2025, 14(7), 522; https://doi.org/10.3390/axioms14070522 - 8 Jul 2025
Viewed by 247
Abstract
We propose Observer-Linked Branching (OLB), a mathematically rigorous extension of quantum theory in which an observer’s cognitive commitment actively modulates collapse dynamics at macroscopic scales. The OLB framework rests on four axioms, employing a norm-preserving nonlinear Schrödinger evolution and Lüders-type projection triggered by [...] Read more.
We propose Observer-Linked Branching (OLB), a mathematically rigorous extension of quantum theory in which an observer’s cognitive commitment actively modulates collapse dynamics at macroscopic scales. The OLB framework rests on four axioms, employing a norm-preserving nonlinear Schrödinger evolution and Lüders-type projection triggered by crossing a cognitive commitment threshold. Our expanded formalism provides five main contributions: (1) deriving Lie symmetries of the observer–environment interaction Hamiltonian; (2) embedding OLB into the Consistent Histories and path-integral formalisms; (3) multi-agent network simulations demonstrating intentional synchronisation toward shared macroscopic outcomes; (4) detailed statistical power analyses predicting measurable biases (up to ~5%) in practical experiments involving traffic delays, quantum random number generators, and financial market sentiment; and (5) examining the conceptual, ethical, and neuromorphic implications of intent-driven reality selection. Full reproducibility is ensured via the provided code notebooks and raw data tables in the appendices. While the theoretical predictions are precisely formulated, empirical validation is ongoing, and no definitive field results are claimed at this stage. OLB thus offers a rigorous, norm-preserving and falsifiable framework to empirically test whether cognitive engagement modulates macroscopic quantum outcomes in ways consistent with—but extending—standard quantum predictions. Full article
(This article belongs to the Special Issue A Century of Quantum Mechanics: Mathematical Foundations and Computational Applications)
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25 pages, 8764 KiB  
Article
A Comprehensive Study on the Applications of NTIM and OAFM in Analyzing Fractional Navier–Stokes Equations
by Siddiq Ur Rehman, Rashid Nawaz, Faisal Zia and Nick Fewster-Young
Axioms 2025, 14(7), 521; https://doi.org/10.3390/axioms14070521 - 7 Jul 2025
Viewed by 141
Abstract
This article introduces two enhanced techniques: the Natural Transform Iterative Method (NTIM) and the Optimal Auxiliary Function Method (OAFM). These approaches provide a close approximation for solving fractional-order Navier–Stokes equations, which are widely employed in domains such as biology, ecology, and applied sciences. [...] Read more.
This article introduces two enhanced techniques: the Natural Transform Iterative Method (NTIM) and the Optimal Auxiliary Function Method (OAFM). These approaches provide a close approximation for solving fractional-order Navier–Stokes equations, which are widely employed in domains such as biology, ecology, and applied sciences. By comparing the solutions derived from these methods to exact solutions, it is clear that they provide accurate and efficient outcomes. These findings highlight the straightforward yet effective use of these methodologies in modeling engineering systems. Navier–Stokes equations have numerous practical uses, including analyzing fluid flow in pipelines and channels, predicting weather patterns, and constructing aircraft and vehicles. Full article
(This article belongs to the Special Issue Nonlinear Fractional Differential Equations: Theory and Applications)
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10 pages, 456 KiB  
Article
A Geometric Variational Problem for Pseudo-Galilean Particles
by Ayşe Yılmaz Ceylan, Tunahan Turhan and Gözde Özkan Tükel
Axioms 2025, 14(7), 520; https://doi.org/10.3390/axioms14070520 - 7 Jul 2025
Viewed by 224
Abstract
This study explores the dynamics of particle motion in pseudo-Galilean 3−space G31 by considering actions that incorporate both curvature and torsion of trajectories. We consider a general energy functional and formulate Euler–Lagrange equations corresponding to this functional under some [...] Read more.
This study explores the dynamics of particle motion in pseudo-Galilean 3−space G31 by considering actions that incorporate both curvature and torsion of trajectories. We consider a general energy functional and formulate Euler–Lagrange equations corresponding to this functional under some boundary conditions in G31. By adapting the geometric tools of the Frenet frame to this setting, we analyze the resulting variational equations and provide illustrative solutions that highlight their structural properties. In particular, we examine examples derived from natural Hamiltonian trajectories in G31 and extend them to reflect the distinctive geometric features of pseudo-Galilean spaces, offering insight into their foundational behavior and theoretical implications. Full article
(This article belongs to the Section Geometry and Topology)
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11 pages, 438 KiB  
Article
Stability Analysis of Fixed-Wing UAV Swarms Under Time-Delayed Tracking Control Law
by Ana-Maria Bordei and Andrei Halanay
Axioms 2025, 14(7), 519; https://doi.org/10.3390/axioms14070519 - 6 Jul 2025
Viewed by 163
Abstract
This paper analyzes the stability of trajectory tracking in fixed-wing UAV swarms subject to time-delayed feedback control. A delay-dependent stability criterion is established using a combination of Routh–Hurwitz analysis and a transcendental characteristic equation method. The study identifies a critical delay threshold beyond [...] Read more.
This paper analyzes the stability of trajectory tracking in fixed-wing UAV swarms subject to time-delayed feedback control. A delay-dependent stability criterion is established using a combination of Routh–Hurwitz analysis and a transcendental characteristic equation method. The study identifies a critical delay threshold beyond which the tracking objective becomes unstable. The influence of delayed feedback on the system dynamics is analyzed, showing how time delays affect the swarm’s ability to maintain formation. Numerical simulations confirm the theoretical predictions and illustrate the loss of stability as the delay increases. The findings underline the importance of accounting for delays when evaluating control performance in UAV swarm coordination. Full article
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17 pages, 343 KiB  
Article
On the Conflation of Poisson and Logarithmic Distributions with Applications
by Abdulhamid A. Alzaid, Anfal A. Alqefari and Najla Qarmalah
Axioms 2025, 14(7), 518; https://doi.org/10.3390/axioms14070518 - 6 Jul 2025
Viewed by 179
Abstract
It is frequent for real-life count data to show inflation in lower values; however, most of the well-known count distributions cannot capture such a feature. The present paper introduces a new distribution for modeling inflated count data in small values based on a [...] Read more.
It is frequent for real-life count data to show inflation in lower values; however, most of the well-known count distributions cannot capture such a feature. The present paper introduces a new distribution for modeling inflated count data in small values based on a conflation of distributions approach. The new distribution inherits some properties from Poisson distribution (PD) and logarithmic distribution (LD), making it a powerful modeling tool. It can serve as an alternative to PD, LD, and zero-truncated distributions. The new distribution is worth considering theoretically, as it belongs to the weighted PD family. With zero as a support point, two additional models are suggested for the new distribution. These modifications yield distributions that demonstrate overdispersion models comparable to the negative binomial distribution (NBD) while retaining essential PD properties, making them suitable for accurately representing count data with frequent events of low frequency and high variance. Furthermore, we discuss the superior performance of three new distributions in modeling real count data compared to traditional count distributions such as PD and NBD, as well as other discrete distributions. This paper examines the key statistical properties of the proposed distributions. A comparison of the novel and other distributions in the literature is shown employing real-life data from some domains. All of the computations shown in this study are generated using the R programming language. Full article
(This article belongs to the Special Issue Advances in the Theory and Applications of Statistical Distributions)
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12 pages, 265 KiB  
Article
Existence of Weakly Pareto–Nash Equilibrium for Multiobjective Games with Infinitely Many Players
by Huaxin Chen and Wensheng Jia
Axioms 2025, 14(7), 517; https://doi.org/10.3390/axioms14070517 - 4 Jul 2025
Viewed by 150
Abstract
Our work proves the existence of weakly Pareto–Nash equilibrium (PNE) in multiobjective games (MGs) with infinitely many players. First, we demonstrate the existence of weakly PNE under compactness assumptions by using the intersection theorem. Then, we extend the intersection theorem to the non-compact [...] Read more.
Our work proves the existence of weakly Pareto–Nash equilibrium (PNE) in multiobjective games (MGs) with infinitely many players. First, we demonstrate the existence of weakly PNE under compactness assumptions by using the intersection theorem. Then, we extend the intersection theorem to the non-compact case and obtain a new intersection theorem. Finally, we prove the existence of weakly PNE in MGs with infinitely many players without compactness assumptions. Full article
(This article belongs to the Special Issue Mathematical Optimizations and Operations Research)
25 pages, 646 KiB  
Article
Exponential Squared Loss-Based Robust Variable Selection with Prior Information in Linear Regression Models
by Hejun Wei, Tian Jin and Yunquan Song
Axioms 2025, 14(7), 516; https://doi.org/10.3390/axioms14070516 - 4 Jul 2025
Viewed by 151
Abstract
This paper proposes a robust variable selection method that incorporates prior information through linear constraints. For more than a decade, penalized likelihood frameworks have been the predominant approach for variable selection, where appropriate loss and penalty functions are selected to formulate unconstrained optimization [...] Read more.
This paper proposes a robust variable selection method that incorporates prior information through linear constraints. For more than a decade, penalized likelihood frameworks have been the predominant approach for variable selection, where appropriate loss and penalty functions are selected to formulate unconstrained optimization problems. However, in many specific applications, some prior information can be obtained. In this paper, we reformulate variable selection by incorporating prior knowledge as linear constraints. In addition, the loss function adopted in this paper is a robust exponential squared loss function, which ensures that the estimation of model parameter coefficient will not have a great impact when there are a few outliers in the dataset. This paper uses the designed solution algorithm to calculate the estimated values of coefficients and some other parameters, and finally conducts numerical simulations and a real-data experiment. Experimental results demonstrate that our model significantly improves estimation robustness compared to existing methods, even in outlier-contaminated scenarios. Full article
(This article belongs to the Special Issue Computational Statistics and Its Applications, 2nd Edition)
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21 pages, 1556 KiB  
Article
Hexic-Chebyshev Collocation Method for Solving Distributed-Order Time-Space Fractional Diffusion Equations
by Afshin Babaei, Sedigheh Banihashemi, Behrouz Parsa Moghaddam and Arman Dabiri
Axioms 2025, 14(7), 515; https://doi.org/10.3390/axioms14070515 - 3 Jul 2025
Viewed by 290
Abstract
This paper presents a spectral method to solve nonlinear distributed-order diffusion equations with both time-distributed-order and two-sided space-fractional terms. These are highly challenging to solve analytically due to the interplay between nonlinearity and the fractional distributed-order nature of the time and space derivatives. [...] Read more.
This paper presents a spectral method to solve nonlinear distributed-order diffusion equations with both time-distributed-order and two-sided space-fractional terms. These are highly challenging to solve analytically due to the interplay between nonlinearity and the fractional distributed-order nature of the time and space derivatives. For this purpose, Hexic-kind Chebyshev polynomials (HCPs) are used as the backbone of the method to transform the primary problem into a set of nonlinear algebraic equations, which can be efficiently solved using numerical solvers, such as the Newton–Raphson method. The primary reason of choosing HCPs is due to their remarkable recurrence relations, facilitating their efficient computation and manipulation in mathematical analyses. A comprehensive convergence analysis was conducted to validate the robustness of the proposed method, with an error bound derived to provide theoretical guarantees for the solution’s accuracy. The method’s effectiveness is further demonstrated through two test examples, where the numerical results are compared with existing solutions, confirming the approach’s accuracy and reliability. Full article
(This article belongs to the Special Issue Recent Advances in Fractional Differential Equations and Inequalities)
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22 pages, 753 KiB  
Article
Existence and Global Exponential Stability of Equilibrium for an Epidemic Model with Piecewise Constant Argument of Generalized Type
by Kuo-Shou Chiu and Fernando Córdova-Lepe
Axioms 2025, 14(7), 514; https://doi.org/10.3390/axioms14070514 - 3 Jul 2025
Viewed by 285
Abstract
The authors investigate an epidemic model described by a differential equation, which includes a piecewise constant argument of the generalized type (DEPCAG). In this work, the main goal is to find an invariant region for the system and prove the existence and uniqueness [...] Read more.
The authors investigate an epidemic model described by a differential equation, which includes a piecewise constant argument of the generalized type (DEPCAG). In this work, the main goal is to find an invariant region for the system and prove the existence and uniqueness of solutions with the defined conditions using integral equations. On top of that, an auxiliary result is established, outlining the relationship between the unknown function values in the deviation argument and the time parameter. The stability analysis is conducted using the Lyapunov–Razumikhin method, adapted for differential equations with a piecewise constant argument of the generalized type. The trivial equilibrium’s stability is examined, and the stability of the positive equilibrium is assessed by transforming it into a trivial form. Finally, sufficient conditions for the uniform asymptotic stability of both the trivial and positive equilibria are established. Full article
(This article belongs to the Section Mathematical Analysis)
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17 pages, 3336 KiB  
Article
Modeling and Exploration of Localized Wave Phenomena in Optical Fibers Using the Generalized Kundu–Eckhaus Equation for Femtosecond Pulse Transmission
by Ejaz Hussain, Ali H. Tedjani, Khizar Farooq and Beenish
Axioms 2025, 14(7), 513; https://doi.org/10.3390/axioms14070513 - 3 Jul 2025
Viewed by 160
Abstract
This manuscript aims to explore localized waves for the nonlinear partial differential equation referred to as the (1+1)-dimensional generalized Kundu–Eckhaus equation with an additional dispersion term that describes the propagation of the ultra-short femtosecond pulses in an optical [...] Read more.
This manuscript aims to explore localized waves for the nonlinear partial differential equation referred to as the (1+1)-dimensional generalized Kundu–Eckhaus equation with an additional dispersion term that describes the propagation of the ultra-short femtosecond pulses in an optical fiber. This research delves deep into the characteristics, behaviors, and localized waves of the (1+1)-dimensional generalized Kundu–Eckhaus equation. We utilize the multivariate generalized exponential rational integral function method (MGERIFM) to derive localized waves, examining their properties, including propagation behaviors and interactions. Motivated by the generalized exponential rational integral function method, it proves to be a powerful tool for finding solutions involving the exponential, trigonometric, and hyperbolic functions. The solutions we found using the MGERIF method have important applications in different scientific domains, including nonlinear optics, plasma physics, fluid dynamics, mathematical physics, and condensed matter physics. We apply the three-dimensional (3D) and contour plots to illuminate the physical significance of the derived solution, exploring the various parameter choices. The proposed approaches are significant and applicable to various nonlinear evolutionary equations used to model nonlinear physical systems in the field of nonlinear sciences. Full article
(This article belongs to the Special Issue Applied Nonlinear Dynamical Systems in Mathematical Physics)
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11 pages, 260 KiB  
Article
Averaging of Linear Quadratic Parabolic Optimal Control Problem
by Olena Kapustian, Oleksandr Laptiev and Adalbert Makarovych
Axioms 2025, 14(7), 512; https://doi.org/10.3390/axioms14070512 - 2 Jul 2025
Viewed by 164
Abstract
This paper studies an averaged Linear Quadratic Regulator (LQR) problem for a parabolic partial differential equation (PDE), where the system dynamics are affected by uncertain parameters. Instead of assuming a deterministic operator, we model the uncertainty using a probability distribution over a set [...] Read more.
This paper studies an averaged Linear Quadratic Regulator (LQR) problem for a parabolic partial differential equation (PDE), where the system dynamics are affected by uncertain parameters. Instead of assuming a deterministic operator, we model the uncertainty using a probability distribution over a set of possible system dynamics. This approach extends classical optimal control theory by incorporating an averaging framework to account for parameter uncertainty. We establish the existence and uniqueness of the optimal control solution and analyze its convergence as the probability distribution governing the system parameters changes. These results provide a rigorous foundation for solving optimal control problems in the presence of parameter uncertainty. Our findings lay the groundwork for further studies on optimal control in dynamic systems with uncertainty. Full article
(This article belongs to the Special Issue Modern Trends and Application of Decision-Making Theory, Stability and Control)
20 pages, 1115 KiB  
Article
A Novel Computational Framework for Time-Fractional Higher-Order KdV Models: CLADM-Based Solutions and Comparative Analysis
by Priti V. Tandel, Anant Patel and Trushitkumar Patel
Axioms 2025, 14(7), 511; https://doi.org/10.3390/axioms14070511 - 1 Jul 2025
Viewed by 173
Abstract
This study applies the Conformable Laplace Adomian Decomposition Method (CLADM) to solve generalized time-fractional Korteweg–de Vries (KdV) models, including seventh- and fifth-order models. CLADM combines the conformable fractional derivative and Laplace transform with the Adomian decomposition technique, offering analytic approximate solutions. Numerical and [...] Read more.
This study applies the Conformable Laplace Adomian Decomposition Method (CLADM) to solve generalized time-fractional Korteweg–de Vries (KdV) models, including seventh- and fifth-order models. CLADM combines the conformable fractional derivative and Laplace transform with the Adomian decomposition technique, offering analytic approximate solutions. Numerical and graphical results, generated using MATLAB R2020a 9.8.0.1323502, validate the method’s efficiency and precision in capturing fractional-order dynamics. Fractional parameters ϱ significantly influence wave behavior, with higher orders yielding smoother profiles and reduced oscillations. Comparative analysis confirms CLADM’s superiority over existing methods in minimizing errors. The versatility of CLADM highlights its potential for studying nonlinear wave phenomena in diverse applications. Full article
(This article belongs to the Special Issue Fractional Calculus and Applied Analysis, 2nd Edition)
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