Axioms

10 pages, 258 KB

Open AccessArticle

Three Problems for Decision Rule Systems from Closed Classes

by Kerven Durdymyradov and Mikhail Moshkov

Axioms 2025, 14(8), 648; https://doi.org/10.3390/axioms14080648 - 21 Aug 2025

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The study of the relationships between DRSs (Decision Rule Systems) and DTs (Decision Trees) is of considerable interest in computer science. In this paper, we consider classes of DRSs that are closed under specific operations. First, we examine classes that are closed under [...] Read more.

The study of the relationships between DRSs (Decision Rule Systems) and DTs (Decision Trees) is of considerable interest in computer science. In this paper, we consider classes of DRSs that are closed under specific operations. First, we examine classes that are closed under the operation of the removal of features and analyze the functions characterizing the worst-case dependence of the minimum depth of DDTs (Deterministic Decision Trees) and NDTs (Nondeterministic Decision Trees), solving the task of finding all true DRs in a DRS on the number of different features in the system. Second, we extend our analysis to classes that are closed under the removal of features and rules, studying the worst-case behavior of the minimum DT depth for the task of finding at least one true DR. Third, we investigate classes closed under the removal of features and rules in the context of finding all right-hand sides of true DRs. We prove that, in all three cases, the corresponding functions characterizing the worst-case minimum depth of DTs are either bounded from above by a constant or grow linearly. Full article

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27 pages, 4595 KB

Open AccessArticle

The Unit Inverse Maxwell–Boltzmann Distribution: A Novel Single-Parameter Model for Unit-Interval Data

by Murat Genç and Ömer Özbilen

Axioms 2025, 14(8), 647; https://doi.org/10.3390/axioms14080647 - 21 Aug 2025

Viewed by 274

Abstract

The Unit Inverse Maxwell–Boltzmann (UIMB) distribution is introduced as a novel single-parameter model for data constrained within the unit interval (

0, 1

), derived through an exponential transformation of the Inverse Maxwell–Boltzmann distribution. Designed to address the limitations of traditional unit-interval [...] Read more.

The Unit Inverse Maxwell–Boltzmann (UIMB) distribution is introduced as a novel single-parameter model for data constrained within the unit interval (

0, 1

), derived through an exponential transformation of the Inverse Maxwell–Boltzmann distribution. Designed to address the limitations of traditional unit-interval distributions, the UIMB model exhibits flexible density shapes and hazard rate behaviors, including right-skewed, left-skewed, unimodal, and bathtub-shaped patterns, making it suitable for applications in reliability engineering, environmental science, and health studies. This study derives the statistical properties of the UIMB distribution, including moments, quantiles, survival, and hazard functions, as well as stochastic ordering, entropy measures, and the moment-generating function, and evaluates its performance through simulation studies and real-data applications. Various estimation methods, including maximum likelihood, Anderson–Darling, maximum product spacing, least-squares, and Cramér–von Mises, are assessed, with maximum likelihood demonstrating superior accuracy. Simulation studies confirm the model’s robustness under normal and outlier-contaminated scenarios, with MLE showing resilience across varying skewness levels. Applications to manufacturing and environmental datasets reveal the UIMB distribution’s exceptional fit compared to competing models, as evidenced by lower information criteria and goodness-of-fit statistics. The UIMB distribution’s computational efficiency and adaptability position it as a robust tool for modeling complex unit-interval data, with potential for further extensions in diverse domains. Full article

(This article belongs to the Section Mathematical Analysis)

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19 pages, 9081 KB

Open AccessArticle

High-Order Time–Space Compact Difference Methods for Semi-Linear Sobolev Equations

by Bo Hou, Tianhua Wang, Guoqu Deng and Zhi Wang

Axioms 2025, 14(8), 646; https://doi.org/10.3390/axioms14080646 - 21 Aug 2025

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Abstract

In this paper, high-order compact difference methods (HOCDMs) are proposed to solve the semi-linear Sobolev equations (SLSEs), which arise in various physical models, such as porous media flow and heat conduction. First, a two-level numerical method is given by applying the Crank–Nicolson (C-N) [...] Read more.

In this paper, high-order compact difference methods (HOCDMs) are proposed to solve the semi-linear Sobolev equations (SLSEs), which arise in various physical models, such as porous media flow and heat conduction. First, a two-level numerical method is given by applying the Crank–Nicolson (C-N) method in time and the fourth-order compact difference method in space. This method is shown to achieve second-order accuracy in time and fourth-order accuracy in space. Subsequently, we introduce the Richardson extrapolation technique to improve the temporal accuracy of the two-level method from second order to fourth order. Furthermore, we devise a fully fourth-order method in both time and space by applying the fourth-order difference method to discretize both temporal and spatial derivatives, and we provide a proof of its convergence. Finally, a series of numerical experiments is conducted to verify the effectiveness of the proposed methods. Full article

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16 pages, 1415 KB

Open AccessArticle

Approximation by Power Series of Functions

by Andrej Liptaj

Axioms 2025, 14(8), 645; https://doi.org/10.3390/axioms14080645 - 21 Aug 2025

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Abstract

Derivative-matching approximations are constructed as power series built from functions. The method assumes knowledge of the special values of the Bell polynomials of the second kind, for which we refer to the literature. The presented ideas may have applications in numerical mathematics. Full article

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

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20 pages, 331 KB

Open AccessArticle

Discrete Limit Bohr–Jessen Type Theorem for the Epstein Zeta-Function in Short Intervals

by Antanas Laurinčikas and Renata Macaitienė

Axioms 2025, 14(8), 644; https://doi.org/10.3390/axioms14080644 - 19 Aug 2025

Viewed by 254

Abstract

We prove a probabilistic limit theorem for the Epstein zeta-function

ζ (s; Q)

in the interval

[N, N + M]

as

N \to \infty

, using discrete shifts [...] Read more.

We prove a probabilistic limit theorem for the Epstein zeta-function

ζ (s; Q)

in the interval

[N, N + M]

as

N \to \infty

, using discrete shifts

ζ (σ + i k h; Q)

, where

h > 0

and

σ > \frac{n - 1}{2}

are fixed. Here, Q is a positive-definite

n \times n

matrix, and the interval length M satisfies

h^{- 1} {(N h)}^{27 / 82} ⩽ M ⩽ h^{- 1} {(N h)}^{1 / 2}

. The limit measure is given explicitly. This theorem is the first result in short intervals for

ζ (s; Q)

. The obtained theorem improves the known results established for the interval of length N. Since the considered probability measures are defined in terms of frequency, theorems in short intervals have a certain advantage in the detection of

ζ (σ + i k h; Q)

with a given property, as well as in the characterization of the asymptotic behaviour of

ζ (s; Q)

in general. Full article

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

25 pages, 4032 KB

Open AccessArticle

New Logistic Family of Distributions: Applications to Reliability Engineering

by Laxmi Prasad Sapkota, Nirajan Bam, Pankaj Kumar and Vijay Kumar

Axioms 2025, 14(8), 643; https://doi.org/10.3390/axioms14080643 - 19 Aug 2025

Viewed by 500

Abstract

This study introduces a novel family of probability distributions, termed the Pi-Power Logistic-G family, constructed through the application of the Pi-power transformation technique. By employing the Weibull distribution as the baseline generator, a new and flexible model, the Pi-Power Logistic Weibull distribution, is [...] Read more.

This study introduces a novel family of probability distributions, termed the Pi-Power Logistic-G family, constructed through the application of the Pi-power transformation technique. By employing the Weibull distribution as the baseline generator, a new and flexible model, the Pi-Power Logistic Weibull distribution, is formulated. Particular emphasis is given to this specific member of the family, which demonstrates a rich variety of hazard rate shapes, including J-shaped, reverse J-shaped, and monotonic increasing patterns, thereby highlighting its adaptability in modeling diverse types of lifetime data. The paper examines the fundamental properties of this distribution and applies the method of maximum likelihood estimation (MLE) to determine its parameters. A Monte Carlo simulation was performed to assess the performance of the estimation method, demonstrating that both Bias and mean square error decline as the sample size increases. The utility of the proposed distribution is further highlighted through its application to real-world engineering datasets. Using model selection metrics and goodness-of-fit tests, the results demonstrate that the proposed model outperforms existing alternatives. In addition, a Bayesian approach was used to estimate the parameters of both datasets, further extending the model’s applicability. The findings of this study have significant implications for the fields of reliability modeling, survival analysis, and distribution theory, enhancing methodologies and offering valuable theoretical insights. Full article

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12 pages, 257 KB

Open AccessArticle

Global Weak Solution in a p-Laplacian Attraction–Repulsion Chemotaxis System with Nonlinear Sensitivity and Signal Production

by Hengyu Ren and Zhe Jia

Axioms 2025, 14(8), 642; https://doi.org/10.3390/axioms14080642 - 18 Aug 2025

Viewed by 232

Abstract

This paper is devoted to a p-Laplacian attraction–repulsion chemotaxis system with nonlinear sensitivity and signal production. We obtain the global existence and boundedness of weak solutions by means of energy estimates, the Aubin–Lions lemma, and parabolic and elliptic regularity estimates. Full article

(This article belongs to the Special Issue Differential Equations and Its Application)

15 pages, 247 KB

Open AccessArticle

A Hyper-Dual Number Approach to Higher-Order Derivative Computation

by Ji Eun Kim

Axioms 2025, 14(8), 641; https://doi.org/10.3390/axioms14080641 - 18 Aug 2025

Viewed by 346

Abstract

This paper develops a theoretical framework for the computation of higher-order derivatives based on the algebra of hyper-dual numbers. Extending the classical dual number system, hyper-dual numbers provide a natural and rigorous mechanism for encoding and propagating derivative information through function composition and [...] Read more.

This paper develops a theoretical framework for the computation of higher-order derivatives based on the algebra of hyper-dual numbers. Extending the classical dual number system, hyper-dual numbers provide a natural and rigorous mechanism for encoding and propagating derivative information through function composition and arithmetic operations. We formalize the underlying algebraic structure, define generalized hyper-dual extensions of scalar functions via multidimensional Taylor expansions, and establish consistency with standard differential calculus. The proposed approach enables exact computation of partial derivatives and mixed higher-order derivatives without resorting to symbolic manipulation or approximation schemes. We further investigate the algebraic properties and closure under differentiable operations, illustrating the method’s potential for unifying aspects of automatic differentiation with multivariable calculus. This study contributes to the theoretical foundation of algorithmic differentiation and highlights hyper-dual numbers as a precise and elegant tool in computational differential analysis. Full article

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

13 pages, 364 KB

Open AccessArticle

Two Reducts of Basic Algebras

by Wenjing Zhang and Jing Wang

Axioms 2025, 14(8), 640; https://doi.org/10.3390/axioms14080640 - 16 Aug 2025

Viewed by 284

Abstract

This paper investigates the relationship between implication reducts and Sheffer stroke reducts in basic algebras. The study establishes a one-to-one correspondence between bounded Sheffer stroke basic algebras and strong implication basic algebras. Furthermore, it examines several key properties of compatible filters in Sheffer [...] Read more.

This paper investigates the relationship between implication reducts and Sheffer stroke reducts in basic algebras. The study establishes a one-to-one correspondence between bounded Sheffer stroke basic algebras and strong implication basic algebras. Furthermore, it examines several key properties of compatible filters in Sheffer stroke basic algebras. Full article

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23 pages, 3747 KB

Open AccessArticle

Mathematical Modeling of the Impact of Desert Dust on Asthma Dynamics

by Zakaria S. Al Ajlan and Moustafa El-Shahed

Axioms 2025, 14(8), 639; https://doi.org/10.3390/axioms14080639 - 16 Aug 2025

Viewed by 278

Abstract

This study presents a mathematical model to describe the transmission dynamics of asthma, explicitly accounting for the impact of dust waves and airborne particulate matter in the environment, recognized as key triggers of asthma exacerbations. The model incorporates a single endemic equilibrium point, [...] Read more.

This study presents a mathematical model to describe the transmission dynamics of asthma, explicitly accounting for the impact of dust waves and airborne particulate matter in the environment, recognized as key triggers of asthma exacerbations. The model incorporates a single endemic equilibrium point, which is shown to be locally asymptotically stable. To mitigate the burden of asthma, we employed the Pontryagin Maximum Principle within an optimal control framework, incorporating three time-dependent intervention strategies: vaccination, treatment, and avoidance of environmental triggers such as dust exposure. The model was numerically solved using the fourth-order Runge–Kutta method in conjunction with a forward–backward sweep algorithm to investigate the effects of various control combinations on the prevalence of asthma. Additionally, a comprehensive cost-effectiveness analysis was conducted to evaluate the economic viability of each strategy. The results indicate that the combined application of vaccination and treatment is the most cost-effective approach among the strategies analyzed, significantly reducing the number of asthma cases at minimal cost. All simulations and numerical experiments were performed to validate the theoretical findings and quantify the effectiveness of the proposed interventions under realistic environmental conditions driven by dust activity. The model highlights the importance of integrated medical and environmental control policies in mitigating asthma outbreaks, particularly in regions frequently exposed to dust storms. Full article

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37 pages, 45303 KB

Open AccessArticle

Dynamic Analysis and Application of 6D Multistable Memristive Chaotic System with Wide Range of Hyperchaotic States

by Fei Yu, Yumba Musoya Gracia, Rongyao Guo, Zhijie Ying, Jiarong Xu, Wei Yao, Jie Jin and Hairong Lin

Axioms 2025, 14(8), 638; https://doi.org/10.3390/axioms14080638 - 15 Aug 2025

Cited by 1 | Viewed by 375

Abstract

In this study, we present a novel, six-dimensional, multistable, memristive, hyperchaotic system model demonstrating two positive Lyapunov exponents. With the maximum Lyapunov exponents surpassing 21, the developed system shows pronounced hyperchaotic behavior. The dynamical behavior was analyzed through phase portraits, bifurcation diagrams, and [...] Read more.

In this study, we present a novel, six-dimensional, multistable, memristive, hyperchaotic system model demonstrating two positive Lyapunov exponents. With the maximum Lyapunov exponents surpassing 21, the developed system shows pronounced hyperchaotic behavior. The dynamical behavior was analyzed through phase portraits, bifurcation diagrams, and Lyapunov exponent spectra. Parameter b was a key factor in regulating the dynamical behavior of the system, mainly affecting the strength and direction of the influence of

z_{1}

on

z_{2}

. It was found that when the system parameter b was within a wide range of

[13, 300]

, the system remained hyperchaotic throughout. Analytical establishment of multistability mechanisms was achieved through invariance analysis of the state variables under specific coordinate transformations. Furthermore, offset boosting control was realized by strategically modulating the fifth state variable,

z_{5}

. The FPGA-based experimental results demonstrated that attractors observed via an oscilloscope were in close agreement with numerical simulations. To validate the system’s reliability for cybersecurity applications, we designed a novel image encryption method utilizing this hyperchaotic model. The information entropy of the proposed encryption algorithm was closer to the theoretical maximum value of 8. This indicated that the system can effectively disrupt statistical patterns. Experimental outcomes confirmed that the proposed image encryption method based on the hyperchaotic system exhibits both efficiency and reliability. Full article

(This article belongs to the Special Issue Nonlinear Dynamical System and Its Applications)

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28 pages, 604 KB

Open AccessArticle

A Study of Global Dynamics and Oscillatory Behavior of Rational-Type Nonlinear Fuzzy Difference Equations with Exponential Decay

by Sara Saud, Carlo Cattani, Muhammad Tanveer, Muhammad Usman and Asifa Tassaddiq

Axioms 2025, 14(8), 637; https://doi.org/10.3390/axioms14080637 - 15 Aug 2025

Viewed by 426

Abstract

The concept of fuzzy modeling and fuzzy system design has opened new horizons of research in functional analysis, having a significant impact on major fields such as data science, machine learning, and so on. In this research, we use fuzzy set theory to [...] Read more.

The concept of fuzzy modeling and fuzzy system design has opened new horizons of research in functional analysis, having a significant impact on major fields such as data science, machine learning, and so on. In this research, we use fuzzy set theory to analyze the global dynamics and oscillatory behavior of nonlinear fuzzy difference equations with exponential decay. We discuss the stability, oscillatory patterns, and convergence of solutions under different initial conditions. The exponential structure simplifies the analysis while providing a clear understanding of the system’s behavior over time. The study reveals how fuzzy parameters influence growth or decay trends, emphasizing the method’s effectiveness in handling uncertainty. Our findings advance the understanding of higher-order fuzzy difference equations and their potential applications in modeling systems with imprecise data. Using the characterization theorem, we convert a fuzzy difference equation into two crisp difference equations. The g-division technique was used to investigate local and global stability and boundedness in dynamics. We validate our theoretical results using numerical simulations. Full article

(This article belongs to the Special Issue New Perspectives in Operator Theory and Functional Analysis)

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22 pages, 2344 KB

Open AccessArticle

Relativistic Algebra over Finite Ring Continuum

by Yosef Akhtman

Axioms 2025, 14(8), 636; https://doi.org/10.3390/axioms14080636 - 14 Aug 2025

Viewed by 605

Abstract

We present a formal reconstruction of the conventional number systems, including integers, rationals, reals, and complex numbers, based on the principle of relational finitude over a finite field

F_{p}

. Rather than assuming actual infinity, we define arithmetic and algebra as observer-dependent [...] Read more.

We present a formal reconstruction of the conventional number systems, including integers, rationals, reals, and complex numbers, based on the principle of relational finitude over a finite field

F_{p}

. Rather than assuming actual infinity, we define arithmetic and algebra as observer-dependent constructs grounded in finite field symmetries. Consequently, we formulate relational analogues of the conventional number classes, expressed relationally with respect to a chosen reference frame. We define explicit mappings for each number class, preserving their algebraic and computational properties while eliminating ontological dependence on infinite structures. For example, relationally framed rational numbers emerge from dense grids generated by primitive roots of a finite field, enabling proportional reasoning without infinity, while scale-periodicity ensures invariance under zoom operations, approximating continuity in a bounded structure. The resultant framework—that we denote as Finite Ring Continuum—aims to establish a coherent foundation for mathematics, physics and formal logic in an ontologically finite paradox-free informational universe. Full article

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

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25 pages, 347 KB

Open AccessArticle

Fixed-Point Theorems in Branciari Distance Spaces

by Seong-Hoon Cho

Axioms 2025, 14(8), 635; https://doi.org/10.3390/axioms14080635 - 14 Aug 2025

Viewed by 270

Abstract

In this study, the concepts of

σ

-Caristi maps and generalized

σ

-contraction maps are introduced, and fixed-point theorems for such maps are established. A generalization of Caristi’s fixed-point theorem and Banach’s contraction principle is proved. The relationships among the various contraction conditions [...] Read more.

In this study, the concepts of

σ

-Caristi maps and generalized

σ

-contraction maps are introduced, and fixed-point theorems for such maps are established. A generalization of Caristi’s fixed-point theorem and Banach’s contraction principle is proved. The relationships among the various contraction conditions introduced in this paper are examined. Examples are provided to elucidate the main theorem, and applications to integral and differential equations are also discussed. Full article

(This article belongs to the Special Issue Trends in Fixed Point Theory and Fractional Calculus)

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15 pages, 285 KB

Open AccessArticle

Applications of Variational Analysis to Strong Nash Equilibria

by Glenn Harris and Sien Deng

Axioms 2025, 14(8), 634; https://doi.org/10.3390/axioms14080634 - 14 Aug 2025

Viewed by 249

Abstract

Game theory problems have a wide array of applications and intricate structures. Because of this, there are different types of solution concepts available in the literature. In this work, strong Nash equilibria (a type of solution to game theoretic problems that extends Nash [...] Read more.

Game theory problems have a wide array of applications and intricate structures. Because of this, there are different types of solution concepts available in the literature. In this work, strong Nash equilibria (a type of solution to game theoretic problems that extends Nash equilibria) are explored. Some new sufficient conditions for the existence of said solutions are put forth. An algorithm is also provided that, when convergent, will lead to a strong Nash equilibrium. Some tests to determine the practical efficiency of the algorithm are included. Full article

(This article belongs to the Special Issue Mathematical Methods in the Applied Sciences, 2nd Edition)

17 pages, 338 KB

Open AccessArticle

Evaluations of Some General Classes of Mordell Integrals by Applying the Mellin-Barnes-Type Contour Integration

by Hari Mohan Srivastava, Mohd Idris Qureshi, Mohd Shahid Baboo and Bhawna Gupta

Axioms 2025, 14(8), 633; https://doi.org/10.3390/axioms14080633 - 14 Aug 2025

Viewed by 281

Abstract

In this paper, motivated by the contributions of several researchers, including (for example) Riemann, Kronecker, Lerch, Ramanujan, and Glaisher on some special integrals known as Mordell’s integrals, we consider the problem of the evaluation of some generalized Mordell integrals by applying the Mellin-Barnes-type [...] Read more.

In this paper, motivated by the contributions of several researchers, including (for example) Riemann, Kronecker, Lerch, Ramanujan, and Glaisher on some special integrals known as Mordell’s integrals, we consider the problem of the evaluation of some generalized Mordell integrals by applying the Mellin-Barnes-type contour integration. In particular, we have evaluated the following integrals:

I_{1} : = \int_{0}^{\infty} \frac{e^{- a t^{2} + b t}}{e^{c t} + g} d t and I_{2} : = \int_{- \infty}^{\infty} \frac{e^{- a t^{2} + b t}}{e^{c t} + g} d t

for real or complex parameters

a, b, c

, and g with

ℜ (a) > 0

in terms of Meijer’s G-function and the generalized hypergeometric function _pF_q. Full article

(This article belongs to the Special Issue Theory of Functions and Applications, 3rd Edition)

29 pages, 564 KB

Open AccessArticle

Edgeworth Coefficients for Standard Multivariate Estimates

by Christopher Stroude Withers

Axioms 2025, 14(8), 632; https://doi.org/10.3390/axioms14080632 - 13 Aug 2025

Viewed by 212

Abstract

I give for the first time explicit formulas for the coefficients needed for the fourth-order Edgeworth expansions of a multivariate standard estimate. I call these the Edgeworth coefficients. They are Bell polynomials in the cumulant coefficients. Standard estimates include most estimates of [...] Read more.

I give for the first time explicit formulas for the coefficients needed for the fourth-order Edgeworth expansions of a multivariate standard estimate. I call these the Edgeworth coefficients. They are Bell polynomials in the cumulant coefficients. Standard estimates include most estimates of interest, including smooth functions of sample means and other empirical estimates. I also give applications to ellipsoidal and hyperrectangular sets. Full article

(This article belongs to the Special Issue New Perspectives in Mathematical Statistics, 2nd Edition)

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13 pages, 274 KB

Open AccessArticle

Extremely Exceptional Sets on Run-Length Function for Reals in Beta-Dynamical System

by Lixuan Zheng, Ziying Wu and Na Yuan

Axioms 2025, 14(8), 631; https://doi.org/10.3390/axioms14080631 - 12 Aug 2025

Viewed by 273

Abstract

The extremely exceptional set for the run-length function in the beta-dynamical system is investigated in this study. For any real x in

(0, 1]

, the run-length function related to x that measures the maximal length of the initial digit [...] Read more.

The extremely exceptional set for the run-length function in the beta-dynamical system is investigated in this study. For any real x in

(0, 1]

, the run-length function related to x that measures the maximal length of the initial digit sequence of the

β

-expansion of x appears consecutively among the first n digits of the

β

-expansion of another real number y in

(0, 1]

. The extremely exceptional set consists of all real numbers y with run-length exhibiting extreme oscillatory behavior: the limit inferior of the ratio of the run-length function to the logarithm base

β

of n is zero, while the limit superior of this same ratio is infinity. We prove that the Hausdorff dimension of this set is either 0 or 1, determined solely by the asymptotic scaling of the basic intervals containing x. Crucially, for all x belonging to

(0, 1]

, the set is residual in

[0, 1]

, which implies that its boxing dimension is 1, which generalizes some known results. Full article

23 pages, 833 KB

Open AccessArticle

Gaussian–Versoria Mixed Kernel Correntropy-Based Robust Parameter and State Estimation for Bilinear State–Space Systems with Non-Gaussian Process and Measurement Noises

by Xuehai Wang and Yijuan Duan

Axioms 2025, 14(8), 630; https://doi.org/10.3390/axioms14080630 - 12 Aug 2025

Viewed by 250

Abstract

This paper investigates the joint state and parameter estimation issue of the bilinear state–space system with non-Gaussian process noise and non-Gaussian measurement noise. Tackling such an issue is challenging because either of these noises may seriously degrade the estimation performance. To significantly counteract [...] Read more.

This paper investigates the joint state and parameter estimation issue of the bilinear state–space system with non-Gaussian process noise and non-Gaussian measurement noise. Tackling such an issue is challenging because either of these noises may seriously degrade the estimation performance. To significantly counteract the negative effect of these non-Gaussian noises, a Gaussian–Versoria mixed kernel correntropy (GVMKC)-based cost function is introduced by integrating two different types of kernel functions into a mixed kernel. Subsequently, a GVMKC-based Kalman filtering and a GVMKC-based robust recursive least squares method are derived for estimating the system states and parameters, respectively. Thus, a robust joint parameter and state estimation method is developed by implementing the interactive computation. The effectiveness of the proposed method is confirmed by simulation examples. Full article

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12 pages, 268 KB

Open AccessArticle

Analysis of Delay-Type Integro-Differential Systems Described by the Φ-Hilfer Fractional Derivative

by Ravichandran Vivek, Waleed Mohammed Abdelfattah and Elsayed Mohamed Elsayed

Axioms 2025, 14(8), 629; https://doi.org/10.3390/axioms14080629 - 11 Aug 2025

Viewed by 382

Abstract

In this article, a novel type of equation, namely the

Φ

-Hilfer fractional-order integro-differential delay system (

Φ

-HFOIDDS), is proposed. Here, we study the existence and Hyers–Ulam–Mittag–Leffler (H-U-M-L) stability of the aforementioned equation which are obtained by using the multivariate Mittag–Leffler function, [...] Read more.

In this article, a novel type of equation, namely the

Φ

-Hilfer fractional-order integro-differential delay system (

Φ

-HFOIDDS), is proposed. Here, we study the existence and Hyers–Ulam–Mittag–Leffler (H-U-M-L) stability of the aforementioned equation which are obtained by using the multivariate Mittag–Leffler function, Banach contraction principle, and Picard operator method as well as generalized Gronwall inequality. Finally, we conclude this paper by constructing a suitable example to illustrate the applicability of the principal outcomes. Full article

(This article belongs to the Special Issue Dynamics, Stability, Chaos, Control and Applications of Dynamical Systems)

13 pages, 236 KB

Open AccessArticle

Perturbation for the Group Inverse in a Banach Algebra

by Dayong Liu, Tugce Pekacar Calci, Handan Kose and Huanyin Chen

Axioms 2025, 14(8), 628; https://doi.org/10.3390/axioms14080628 - 11 Aug 2025

Viewed by 278

Abstract

We present new additive results for the group inverse in a Banach algebra under certain perturbations. The upper bound of

{∥ (a + b)}^{#} - a^{d} ∥

is thereby given. These results extend the main results presented by Liu, [...] Read more.

We present new additive results for the group inverse in a Banach algebra under certain perturbations. The upper bound of

{∥ (a + b)}^{#} - a^{d} ∥

is thereby given. These results extend the main results presented by Liu, Qin, and Wei. We then apply them to establish the representation of the group inverse of

a + b

under a kind of commutative perturbation condition. Finally, some numerical examples are given to demonstrate the main results. Full article

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

38 pages, 1897 KB

Open AccessArticle

Applied Statistical Modeling Using the Truncated Perk Distribution: Estimation Methods and Multidisciplinary Real-Data Applications

by Ahmed Mohamed El Gazar, Mahmoud M. Abdelwahab, Mustafa M. Hasaballah and Dina A. Ramadan

Axioms 2025, 14(8), 627; https://doi.org/10.3390/axioms14080627 - 11 Aug 2025

Viewed by 365

Abstract

In this paper, we propose a new version of the Perk distribution, called the truncated Perk distribution. Fundamental properties of the new distribution are discussed, including moments, the moment generating function, the probability-weighted function, the quantile function, order statistics, Rényi entropy, and Tsallis [...] Read more.

In this paper, we propose a new version of the Perk distribution, called the truncated Perk distribution. Fundamental properties of the new distribution are discussed, including moments, the moment generating function, the probability-weighted function, the quantile function, order statistics, Rényi entropy, and Tsallis entropy. In practice, for the estimation of the model parameters, we use seven traditional estimation methods. A simulation study was performed to demonstrate the practical utility of the proposed distribution. In this study, two common estimation methods, MLE and Bayesian estimation, are compared to determine which method provides more accurate and reliable parameter estimates. The potential utility of the truncated Perk model is exhibited through its use on three real datasets. The applications indicate that the truncated Perk distribution can give better fits than some other corresponding distributions. Full article

(This article belongs to the Special Issue Methods and Applications of Advanced Statistical Analysis, 2nd Edition)

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15 pages, 358 KB

Open AccessFeature PaperArticle

Multi-Task CNN-LSTM Modeling of Zero-Inflated Count and Time-to-Event Outcomes for Causal Inference with Functional Representation of Features

by Jong-Min Kim

Axioms 2025, 14(8), 626; https://doi.org/10.3390/axioms14080626 - 11 Aug 2025

Viewed by 559

Abstract

We propose a novel deep learning framework for counterfactual inference on the COMPAS dataset, utilizing a multi-task CNN-LSTM architecture. The model jointly predicts multiple outcome types: (i) count outcomes with zero inflation, modeled using zero-inflated Poisson (ZIP), zero-inflated negative binomial (ZINB), and negative [...] Read more.

We propose a novel deep learning framework for counterfactual inference on the COMPAS dataset, utilizing a multi-task CNN-LSTM architecture. The model jointly predicts multiple outcome types: (i) count outcomes with zero inflation, modeled using zero-inflated Poisson (ZIP), zero-inflated negative binomial (ZINB), and negative binomial (NB) distributions; (ii) time-to-event outcomes, modeled via the Cox proportional hazards model. To effectively leverage the structure in high-dimensional tabular data, we integrate functional data analysis (FDA) techniques by transforming covariates into smooth functional representations using B-spline basis expansions. Specifically, we construct a pseudo-temporal index over predictor variables and fit basis expansions to each subject’s feature vector, yielding a low-dimensional set of coefficients that preserve smooth variation while reducing noise. This functional representation enables the CNN-LSTM model to capture both local and global temporal patterns in the data, including treatment-covariate interactions. Our approach estimates both population-average and individual-level treatment effects (ATE and CATE) for each outcome and evaluates predictive performance using metrics such as Poisson deviance, root mean squared error (RMSE), and the concordance index (C-index). Statistical inference on treatment effects is supported via bootstrap-based confidence intervals and hypothesis testing. Overall, this comprehensive framework facilitates flexible modeling of heterogeneous treatment effects in structured, high-dimensional data, advancing causal inference methodologies in criminal justice and related domains. Full article

(This article belongs to the Special Issue Functional Data Analysis and Its Application)

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14 pages, 653 KB

Open AccessArticle

Bipartite Synchronization of Cooperation–Competition Neural Networks Using Asynchronous Sampling Scheme

by Shuxian Fan, Yongjie Shi and Zhongliang Wei

Axioms 2025, 14(8), 625; https://doi.org/10.3390/axioms14080625 - 11 Aug 2025

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Abstract

This paper investigates the bipartite synchronization problem for cooperation–competition neural networks (CCNNs) under asynchronous sampling control. First, using signed graph theory to characterize the interrelationships between cooperation and competition, a mathematical model for cooperative–competitive neural networks is established. To formulate the error systems [...] Read more.

This paper investigates the bipartite synchronization problem for cooperation–competition neural networks (CCNNs) under asynchronous sampling control. First, using signed graph theory to characterize the interrelationships between cooperation and competition, a mathematical model for cooperative–competitive neural networks is established. To formulate the error systems of such networks, a Laplacian matrix with zero row sum is derived through coordinate transformation techniques. Considering network complexity and deception attack impacts, an asynchronous sampling-based secure control scheme is designed while preserving performance guarantees. By relaxing positive definiteness constraints, a class of looped functionals is introduced. State norm estimations are utilized to derive criteria for achieving bipartite synchronization. The feedback gain matrices of the asynchronous sampling controller are obtained by solving linear matrix inequalities. Finally, numerical simulations validate the effectiveness of the proposed method. Full article

(This article belongs to the Section Mathematical Analysis)

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17 pages, 310 KB

Open AccessArticle

Analytical Solutions for Generalized Stochastic HSC-KdV Equations with Variable Coefficients Using Hermite Transform and F-Expansion Method

by Mohammed Zakarya, Nadiah Zafer Al-Shehri, Hegagi M. Ali, Mahmoud A. Abd-Rabo and Haytham M. Rezk

Axioms 2025, 14(8), 624; https://doi.org/10.3390/axioms14080624 - 10 Aug 2025

Viewed by 327

Abstract

This study focuses on analyzing the generalized HSC-KdV equations characterized by variable coefficients and Wick-type stochastic (Wt.S) elements. To derive white noise functional (WNF) solutions, we employ the Hermite transform, the homogeneous balance principle, and the

F_{e}

(F-expansion) technique. Leveraging the inherent [...] Read more.

This study focuses on analyzing the generalized HSC-KdV equations characterized by variable coefficients and Wick-type stochastic (Wt.S) elements. To derive white noise functional (WNF) solutions, we employ the Hermite transform, the homogeneous balance principle, and the

F_{e}

(F-expansion) technique. Leveraging the inherent connection between hypercomplex system (HCS) theory and white noise (WN) analysis, we establish a comprehensive framework for exploring stochastic partial differential equations (PDEs) involving non-Gaussian parameters (N-GP). As a result, exact solutions expressed through Jacobi elliptic functions (JEFs) and trigonometric and hyperbolic forms are obtained for both the variable coefficients and stochastic forms of the generalized HSC-KdV equations. An illustrative example is included to validate the theoretical findings. Full article

22 pages, 374 KB

Open AccessArticle

On the Definability Problem of First-Order Sentences by Propositional Intuitionistic Formulas

by Grigor Kolev and Tinko Tinchev

Axioms 2025, 14(8), 623; https://doi.org/10.3390/axioms14080623 - 8 Aug 2025

Viewed by 360

Abstract

We consider restricted forms of the algorithmic problem of definability of first-order sentences by propositional formulas with intuitionistic Kripke frames semantics. We demonstrate positive resolutions for classes of intuitionistic Kripke frames based on linear orders and conversely show that a few natural first-order [...] Read more.

We consider restricted forms of the algorithmic problem of definability of first-order sentences by propositional formulas with intuitionistic Kripke frames semantics. We demonstrate positive resolutions for classes of intuitionistic Kripke frames based on linear orders and conversely show that a few natural first-order definable classes give rise to undecidable definability problems by applying the model-theoretic in the nature technique of stable classes of Kripke frames. Full article

(This article belongs to the Section Logic)

37 pages, 5079 KB

Open AccessArticle

The Complexity of Classes of Pyramid Graphs Based on the Fritsch Graph and Its Related Graphs

by Ahmad Asiri and Salama Nagy Daoud

Axioms 2025, 14(8), 622; https://doi.org/10.3390/axioms14080622 - 8 Aug 2025

Viewed by 283

Abstract

A quantitative study of the complicated three-dimensional structures of artificial atoms in the field of intense matter physics requires a collaborative method that combines a statistical analysis of unusual graph features related to atom topology. Simplified circuits can also be produced by using [...] Read more.

A quantitative study of the complicated three-dimensional structures of artificial atoms in the field of intense matter physics requires a collaborative method that combines a statistical analysis of unusual graph features related to atom topology. Simplified circuits can also be produced by using similar transformations to streamline complex circuits that need laborious mathematical calculations during analysis. These modifications can also be used to determine the number of spanning trees required for specific graph families. The explicit derivation of formulas to determine the number of spanning trees for novel pyramid graph types based on the Fritsch graph, which is one of only six graphs in which every neighborhood is a 4- or 5-vertex cycle, is the focus of our study. We conduct this by utilizing our understanding of difference equations, weighted generating function rules, and the strength of analogous transformations found in electrical circuits. Full article

(This article belongs to the Special Issue Graph Theory and Combinatorics: Theory and Applications)

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30 pages, 2112 KB

Open AccessArticle

Numerical Treatment of Hyperbolic-Type Problems with Single and Double Interfaces via Meshless Method

by Muhammad Asif, Naveed Akhtar, Farhan Khan, Faisal Bilal and Ioan-Lucian Popa

Axioms 2025, 14(8), 621; https://doi.org/10.3390/axioms14080621 - 8 Aug 2025

Viewed by 291

Abstract

Hyperbolic interface problems frequently arise in a wide range of scientific and engineering applications, particularly in scenarios involving wave propagation or transport phenomena across media with discontinuous properties. These problems are characterized by abrupt changes in material coefficients or domain features, which pose [...] Read more.

Hyperbolic interface problems frequently arise in a wide range of scientific and engineering applications, particularly in scenarios involving wave propagation or transport phenomena across media with discontinuous properties. These problems are characterized by abrupt changes in material coefficients or domain features, which pose significant challenges for numerical approximation. In this study, we propose an efficient and robust computational framework for solving one-dimensional hyperbolic interface problems with both single and double interfaces. The methodology combines the finite difference method (FDM) for time discretization with meshless radial basis functions (RBFs) for spatial approximation, enabling accurate resolution of interface discontinuities. This hybrid approach is adaptable to both linear and nonlinear models and is capable of handling constant as well as variable coefficients. Linear systems are solved using Gaussian elimination, while nonlinear systems are addressed through a quasi-Newton linearization method. To validate the performance of the proposed method, we compute the maximum absolute errors (MAEs) and root mean square errors (RMSEs) over various spatial and temporal discretizations. Numerical experiments demonstrate that the approach exhibits fast convergence, excellent accuracy, and ease of implementation, making it a practical tool for solving complex hyperbolic problems with interface conditions. Overall, the method provides a reliable and scalable solution for a class of problems where traditional numerical techniques often discontinuties. Full article

(This article belongs to the Special Issue Advanced Approximation Techniques and Their Applications, 2nd Edition)

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18 pages, 3211 KB

Open AccessArticle

Sharp Results and Fluid Flow Applications for a Specific Class of Meromorphic Functions Introduced by a New Operator

by Aya F. Elkhatib, Atef F. Hashem, Adela O. Mostafa and Mohammed M. Tharwat

Axioms 2025, 14(8), 620; https://doi.org/10.3390/axioms14080620 - 8 Aug 2025

Viewed by 341

Abstract

In this investigation, we introduce a new meromorphic operator defined by meromorphic univalent functions. A new class of meromorphic functions is introduced by this operator, which can generate several distinct subclasses depending on the values of its parameters. Within the framework of this [...] Read more.

In this investigation, we introduce a new meromorphic operator defined by meromorphic univalent functions. A new class of meromorphic functions is introduced by this operator, which can generate several distinct subclasses depending on the values of its parameters. Within the framework of this class of functions, we obtain several significant algebraic and geometric properties, including coefficient estimates, distortion theorems, the radius of starlikeness, convex combination closure, extreme point characterization, and neighborhood structure. Our findings are sharp, offering accurate and significant insights into the mathematical structure and behavior of these functions. In addition, we present several applications of these results in fluid mechanics, like identifying stagnation points in vortex flows, predicting velocity decline in source/sink systems, and determining stability thresholds that protect crucial streamlines from perturbations, which demonstrates that the introduced operator and class characterize critical properties of 2D potential flows. Full article

(This article belongs to the Special Issue New Developments in Geometric Function Theory, 3rd Edition)

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23 pages, 4761 KB

Open AccessArticle

Inference for Maximum Ranked Set Sampling with Unequal Samples from the Burr Type-III Model with Cycle Effects

by Zirui Chu, Liang Wang, Yogesh Mani Tripathi and Yuhlong Lio

Axioms 2025, 14(8), 619; https://doi.org/10.3390/axioms14080619 - 8 Aug 2025

Viewed by 273

Abstract

This paper explores statistical inferences for the maximum ranked set sampling with unequal samples (MaxRSSU) from the Burr Type-III distribution. Under the assumption that the differences between different multiple MaxRSSU cycles are non-ignorable, classical likelihood and Bayesian approaches are employed for estimation of [...] Read more.

This paper explores statistical inferences for the maximum ranked set sampling with unequal samples (MaxRSSU) from the Burr Type-III distribution. Under the assumption that the differences between different multiple MaxRSSU cycles are non-ignorable, classical likelihood and Bayesian approaches are employed for estimation of the model parameters and reliability indices. By taking into account the multiple-cycle effect, the maximum likelihood estimators for the parameters of the Burr Type-III distribution are established, along with an analysis of their existence and uniqueness. Furthermore, approximate confidence intervals are constructed based on asymptotic theory. In addition, a hierarchical Bayesian framework is conducted for analysis, and a Monte Carlo sampling method is proposed for complex posterior computation. Extensive simulation studies are carried out for evaluating the performance of the proposed methods, and a further two real-data examples are also provided for illustration. The numerical results indicate that the proposed methods work satisfactorily and the hierarchical Bayesian approach appears more appealing when the uncertainty cycle effect is involved. Full article

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Axioms, Volume 14, Issue 8 (August 2025) – 103 articles

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