Axioms

20 pages, 391 KiB

Open AccessArticle

Second-Order Implicit–Explicit Difference Scheme for Pseudoparabolic Equations with Nonlinear Flux

by Miglena N. Koleva and Lubin G. Vulkov

Axioms 2025, 14(7), 545; https://doi.org/10.3390/axioms14070545 - 21 Jul 2025

Viewed by 319

In this work we propose a new second-order implicit–explicit difference scheme for a pseudoparabolic equation with a nonlinear flux term. The proposed method is evaluated in comparison with two known numerical approaches. The significance of this study stems from its relevance to physical [...] Read more.

In this work we propose a new second-order implicit–explicit difference scheme for a pseudoparabolic equation with a nonlinear flux term. The proposed method is evaluated in comparison with two known numerical approaches. The significance of this study stems from its relevance to physical and mechanical models, including the Benjamin–Bona–Mahony (–Burgers) equations, which arise as specific instances of the considered equation. A stability analysis of the constructed scheme is conducted. Furthermore, the method is generalized to address a two-dimensional case. Several numerical experiments are carried out to assess the accuracy and efficiency of the proposed scheme. Full article

(This article belongs to the Special Issue Numerical Computation, Approximation of Functions and Applied Mathematics, 2nd Edition)

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23 pages, 752 KiB

Open AccessArticle

On Joint Progressively Censored Gumbel Type-II Distributions: (Non-) Bayesian Estimation with an Application to Physical Data

by Mustafa M. Hasaballah, Mahmoud E. Bakr, Oluwafemi Samson Balogun and Arwa M. Alshangiti

Axioms 2025, 14(7), 544; https://doi.org/10.3390/axioms14070544 - 20 Jul 2025

Viewed by 263

Abstract

This paper presents a comprehensive statistical analysis of the Gumbel Type-II distribution based on joint progressive Type-II censoring. It derives the maximum likelihood estimators for the distribution parameters and constructs their asymptotic confidence intervals. It investigates Bayesian estimation using non-informative and informative priors [...] Read more.

This paper presents a comprehensive statistical analysis of the Gumbel Type-II distribution based on joint progressive Type-II censoring. It derives the maximum likelihood estimators for the distribution parameters and constructs their asymptotic confidence intervals. It investigates Bayesian estimation using non-informative and informative priors under the squared error loss function and the LINEX loss function, applying Markov Chain Monte Carlo methods. A detailed simulation study evaluates the estimators’ performance in terms of average estimates, mean squared errors, and average confidence interval lengths. Results show that Bayesian estimators can outperform maximum likelihood estimators, especially with informative priors. A real data example demonstrates the practical use of the proposed methods. The analysis confirms that the Gumbel Type-II distribution with joint progressive censoring provides a flexible and effective model for lifetime data, enabling more accurate reliability assessment and risk analysis in engineering and survival studies. Full article

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19 pages, 946 KiB

Open AccessArticle

Enhanced Fast Fractional Fourier Transform (FRFT) Scheme Based on Closed Newton-Cotes Rules

by Aubain Nzokem, Daniel Maposa and Anna M. Seimela

Axioms 2025, 14(7), 543; https://doi.org/10.3390/axioms14070543 - 20 Jul 2025

Viewed by 311

Abstract

The paper presents an enhanced numerical framework for computing the one-dimensional fast Fractional Fourier Transform (FRFT) by integrating closed-form Composite Newton-Cotes quadrature rules. We show that a FRFT of a

Q N

-length weighted sequence can be decomposed analytically into two mathematically [...] Read more.

The paper presents an enhanced numerical framework for computing the one-dimensional fast Fractional Fourier Transform (FRFT) by integrating closed-form Composite Newton-Cotes quadrature rules. We show that a FRFT of a

Q N

-length weighted sequence can be decomposed analytically into two mathematically commutative compositions: one involving the composition of a FRFT of an N-length sequence and a FRFT of a Q-length weighted sequence, and the other in reverse order. The composite FRFT approach is applied to the inversion of Fourier and Laplace transforms, with a focus on estimating probability densities for distributions with complex-valued characteristic functions. Numerical experiments on the Variance-Gamma (VG) and Generalized Tempered Stable (GTS) models show that the proposed scheme significantly improves accuracy over standard (non-weighted) fast FRFT and classical Newton-Cotes quadrature, while preserving computational efficiency. The findings suggest that the composite FRFT framework offers a robust and mathematically sound tool for transform-based numerical approximations, particularly in applications involving oscillatory integrals and complex-valued characteristic functions. Full article

(This article belongs to the Special Issue Numerical Analysis and Applied Mathematics)

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16 pages, 343 KiB

Open AccessArticle

Tame Secant Varieties and Group Actions

by Edoardo Ballico

Axioms 2025, 14(7), 542; https://doi.org/10.3390/axioms14070542 - 20 Jul 2025

Viewed by 231

Abstract

Let X be a complex projective variety embedded in a complex projective space. The dimensions of the secant varieties of X have an expected value, and it is important to know if they are equal or at least near to this expected value. [...] Read more.

Let X be a complex projective variety embedded in a complex projective space. The dimensions of the secant varieties of X have an expected value, and it is important to know if they are equal or at least near to this expected value. Blomenhofer and Casarotti proved important results on the embeddings of G-varieties, G being an algebraic group, embedded in the projectivations of an irreducible G-representation, proving that no proper secant variety is a cone. In this paper, we give other conditions which assure that no proper secant varieties of X are a cone, e.g., that X is G-homogeneous. We consider the Segre product of two varieties with the product action and the case of toric varieties. We present conceptual tests for it, and discuss the information we obtained from certain linear projections of X. For the Segre–Veronese embeddings of

P^{n} \times P^{n}

with respect to forms of bidegree

(1, d)

, our results are related to the simultaneous rank of degree d forms in

n + 1

variables. Full article

20 pages, 300 KiB

Open AccessArticle

Categories of L-Primals, L-Pre-Proximities, and L-Topologies

by Ahmed A. Ramadan and Anwar J. Fawakhreh

Axioms 2025, 14(7), 541; https://doi.org/10.3390/axioms14070541 - 18 Jul 2025

Viewed by 281

Abstract

This paper introduces and investigates the fundamental properties of L-primals, a generalization of the primal concept within the framework of L-fuzzy sets and complete lattices. Building upon the established theories of L-topological spaces and L-pre-proximity spaces, this research explores [...] Read more.

This paper introduces and investigates the fundamental properties of L-primals, a generalization of the primal concept within the framework of L-fuzzy sets and complete lattices. Building upon the established theories of L-topological spaces and L-pre-proximity spaces, this research explores the interrelations among these three generalized topological structures. The study establishes novel categorical links, demonstrating the existence of concrete functors between categories of L-primal spaces and L-pre-proximity spaces, as well as between categories of L-pre-proximity spaces and stratified L-primal spaces. Furthermore, the paper clarifies the existence of a concrete functor between the category of stratified L-primal spaces and the category of L-topological spaces, and vice versa, thereby establishing Galois correspondences between these categories. Theoretical findings are supported by illustrative examples, including applications within the contexts of information systems and medicine, demonstrating the practical aspects of the developed theory. Full article

(This article belongs to the Topic Fuzzy Sets Theory and Its Applications)

14 pages, 2182 KiB

Open AccessFeature PaperArticle

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 - 17 Jul 2025

Viewed by 216

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

Open AccessArticle

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 - 17 Jul 2025

Viewed by 191

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

Open AccessArticle

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 - 17 Jul 2025

Viewed by 320

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

Open AccessArticle

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

Viewed by 222

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

L^{1}

-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

L^{1}

-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

Open AccessArticle

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

Viewed by 193

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

20 pages, 7720 KiB

Open AccessArticle

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 252

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

Open AccessArticle

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 222

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

Open AccessFeature PaperArticle

Clifford Distributions Revisited

by Fred Brackx

Axioms 2025, 14(7), 533; https://doi.org/10.3390/axioms14070533 - 14 Jul 2025

Viewed by 209

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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Graphical abstract

21 pages, 330 KiB

Open AccessArticle

Distribution Modulo One of αp^γ + 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 309

Abstract

Let

α, β \in R

with

α \neq 0

, and let

γ \in (0, 5 / 6)

. Define the set

M_{1}

to consist of primes p such that

p + 2

is almost prime, and let [...] Read more.

Let

α, β \in R

with

α \neq 0

, and let

γ \in (0, 5 / 6)

. Define the set

M_{1}

to consist of primes p such that

p + 2

is almost prime, and let

M_{2}

be the set of primes of the form

p = a^{2} + b^{2} + 1

. We study the distribution of

α p^{γ} + β

modulo one, as p ranges over the sets

M_{1}

and

M_{2}

, respectively. Full article

(This article belongs to the Special Issue Mathematical Analysis and Applications IV)

20 pages, 2678 KiB

Open AccessArticle

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 275

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, 389 KiB

Open AccessArticle

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 217

Abstract

This paper mainly studies the existence of sign-changing solutions for the following

p (x)

-biharmonic Kirchhoff-type equations: [...] Read more.

This paper mainly studies the existence of sign-changing solutions for the following

p (x)

-biharmonic Kirchhoff-type equations:

- (a + b \int_{R^{N}} \frac{1}{p (x)} {| Δ u |}^{p (x)} d x) Δ_{p (x)}^{2} u + V (x) {| u |}^{p (x) - 2} u

=

K (x) f (u), x \in R^{N}

, where

Δ_{p (x)}^{2} u = Δ ({| Δ u |}^{p (x) - 2} Δ u)

is the

p (x)

biharmonic operator,

a, b > 0

are constants,

N \geq 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

u_{b}

. In addition, the convergence property of

u_{b}

as

b \to 0

is also established. Full article

17 pages, 255 KiB

Open AccessArticle

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 255

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, 1871 KiB

Open AccessArticle

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 650

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

Open AccessArticle

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 342

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

Open AccessArticle

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 298

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 \leq 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

Open AccessArticle

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 403

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

Open AccessArticle

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 266

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, 307 KiB

Open AccessArticle

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 297

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

Open AccessArticle

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 529

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

Open AccessArticle

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 268

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

Open AccessArticle

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 315

Abstract

This study explores the dynamics of particle motion in pseudo-Galilean

3 -

space

G_{3}^{1}

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

G_{3}^{1}

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

G_{3}^{1}

. 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

G_{3}^{1}

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

Open AccessArticle

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 277

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

Open AccessArticle

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 310

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

Open AccessArticle

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 243

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

Open AccessArticle

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 263

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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Axioms, Volume 14, Issue 7 (July 2025) – 67 articles

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