Axioms

3 pages, 143 KB

Open AccessEditorial

Axioms and Methods for Handling Differential Equations and Inverse Problems

by Zoltán Vizvári, Mihály Klincsik, Róbert Kersner, Péter Odry, Zoltán Sári and Vladimir Tadić

Axioms 2025, 14(9), 692; https://doi.org/10.3390/axioms14090692 - 12 Sep 2025

Modeling real-life problems requires a variety of differential equations that often cause significant challenges for researchers [...] Full article

(This article belongs to the Special Issue Axioms and Methods for Handling Differential Equations and Inverse Problems)

19 pages, 643 KB

Open AccessArticle

MaxSum Spanning Tree Interdiction and Improvement Problems Under Weighted l_∞ Norm⁺

by Qiao Zhang, Junhua Jia and Xiao Li

Axioms 2025, 14(9), 691; https://doi.org/10.3390/axioms14090691 - 11 Sep 2025

Abstract

The Max+Sum Spanning Tree (MSST) problem, with applications in secure communication systems, seeks a spanning tree T minimizing

{max}_{e \in T} w (e) + \sum_{e \in T} c (e)

on a given edge-weighted undirected network [...] Read more.

The Max+Sum Spanning Tree (MSST) problem, with applications in secure communication systems, seeks a spanning tree T minimizing

{max}_{e \in T} w (e) + \sum_{e \in T} c (e)

on a given edge-weighted undirected network

G (V, E, c, w)

, where the sets V and E are the sets of vertices and edges, respectively. The functions c and w are defined on the edge set, representing transmission cost and verification delay in secure communication systems, respectively. This problem can be solved within

O (| E | log | V |)

time. We investigate its interdiction (MSSTID) and improvement (MSSTIP) problems under the weighted

l_{\infty}

norm. MSSTID seeks minimal edge weight adjustments (to either c or w) to degrade network performance by ensuring the optimal MSST’s weight is at least K, while MSSTIP similarly aims to enhance performance by making the optimal MSST’s weight at most K through minimal weight modifications. These problems naturally arise in adversarial and proactive performance enhancement scenarios, respectively, where network robustness or efficiency must be guaranteed through constrained resource allocation. We first establish their mathematical models. Subsequently, we analyze the properties of the optimal value to determine the relationship between the magnitude of a given number and the optimal value. Then, utilizing binary search methods and greedy techniques, we design four algorithms with time complexity

O (| E |^{2} log | V |)

to solve the above problems by modifying w or c. Finally, numerical experiments are conducted to demonstrate the effectiveness of the algorithms. Full article

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

21 pages, 1502 KB

Open AccessArticle

Max–Min Transitive Closure of Randomly Generated Fuzzy Matrix: Bernoulli and Classical Probabilistic Models

by Nan Li, Xianfeng Yu and Wuniu Liu

Axioms 2025, 14(9), 690; https://doi.org/10.3390/axioms14090690 - 11 Sep 2025

Abstract

A randomly generated fuzzy matrix refers to a fuzzy matrix in which the values of elements belong to the sample space of a [0,1]-random variable that follows a certain probability distribution. This paper studies the max–min transitive closure of two-type randomly generated fuzzy [...] Read more.

A randomly generated fuzzy matrix refers to a fuzzy matrix in which the values of elements belong to the sample space of a [0,1]-random variable that follows a certain probability distribution. This paper studies the max–min transitive closure of two-type randomly generated fuzzy matrices: Bernoulli and classical probabilistic models. By introducing the concept of superposed fuzzy matrices, we investigate the probability distribution of the transitive closure of randomly generated fuzzy matrices for two probabilistic models. First, we presented the arithmetic operation rules for the superposed fuzzy relations. The expected value of the randomly generated Bernoulli fuzzy matrix transition closure was studied. A direct calculation method for the randomly generated fuzzy matrix transitive closure of the classical probability model was provided. Finally, the errors between the direct calculation method and the traditional transitive closure calculation method were compared. Full article

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18 pages, 796 KB

Open AccessArticle

Hybrid Beamforming via Fourth-Order Tucker Decomposition for Multiuser Millimeter-Wave Massive MIMO Systems

by Haiyang Dong and Zheng Dou

Axioms 2025, 14(9), 689; https://doi.org/10.3390/axioms14090689 - 9 Sep 2025

Viewed by 416

Abstract

To enhance the spectral efficiency of hybrid beamforming in millimeter-wave massive MIMO systems, the problem is formulated as a high-dimensional non-convex optimization under constant modulus constraints. A novel algorithm based on fourth-order tensor Tucker decomposition is proposed. Specifically, the frequency-domain channel matrices are [...] Read more.

To enhance the spectral efficiency of hybrid beamforming in millimeter-wave massive MIMO systems, the problem is formulated as a high-dimensional non-convex optimization under constant modulus constraints. A novel algorithm based on fourth-order tensor Tucker decomposition is proposed. Specifically, the frequency-domain channel matrices are structured into a fourth-order tensor to explicitly capture the couplings across the spatial, frequency, and user domains. To tackle the non-convexity induced by constant modulus constraints, the analog precoder and combiner are derived by solving a truncated-rank Tucker decomposition problem through the Alternating Direction Method of Multipliers and Alternating Least Squares schemes. Subsequently, in the digital domain, the Regularized Block Diagonalization algorithm is integrated with the subcarrier and user factor matrices—obtained from the tensor decomposition—along with the water-filling strategy to design the digital precoder and combiner, thereby achieving a balance between multi-user interference suppression and noise enhancement. The proposed tensor-based algorithm is demonstrated through simulations to outperform existing state-of-the-art schemes. This work provides an efficient and mathematically sound solution for hybrid beamforming in dense multi-user scenarios envisioned for sixth-generation mobile communications. Full article

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19 pages, 1123 KB

Open AccessArticle

Partitioning AG(2,q), q≡7 Mod 12, into MöbiusKantor Configurations and One Point

by Stefano Innamorati

Axioms 2025, 14(9), 688; https://doi.org/10.3390/axioms14090688 - 9 Sep 2025

Viewed by 101

Abstract

By the cyclic structure of the affine plane AG(2,q), q≡7 mod 12, a mixed partition into a set of Möbius–Kantor configurations and a one-point set is provided. This generalizes a 2006 result of L. Berardi and T. Masini, who partitioned [...] Read more.

By the cyclic structure of the affine plane AG(2,q), q≡7 mod 12, a mixed partition into a set of Möbius–Kantor configurations and a one-point set is provided. This generalizes a 2006 result of L. Berardi and T. Masini, who partitioned the affine plane of order 7 into a set of Möbius–Kantor configurations and a one-point set. Full article

(This article belongs to the Section Geometry and Topology)

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21 pages, 347 KB

Open AccessArticle

Fixed-Point Theorems in Sequential G-Metric Spaces and Their Application to the Solvability of a System of Integral Equations

by Robab Abdi, Hasan Hosseinzadeh, Vahid Parvaneh, Monica Bota and Jamal Rezaei Roshan

Axioms 2025, 14(9), 687; https://doi.org/10.3390/axioms14090687 - 8 Sep 2025

Viewed by 109

Abstract

The goal of this work is to demonstrate some fixed-point theorems for

J S

-contractions over sequential G-metric spaces that are not necessarily continuous in any variable and do not enjoy the triangle inequality. This new space is a generalization of standard [...] Read more.

The goal of this work is to demonstrate some fixed-point theorems for

J S

-contractions over sequential G-metric spaces that are not necessarily continuous in any variable and do not enjoy the triangle inequality. This new space is a generalization of standard G-metric spaces and

G_{b}

-metric spaces. Additionally, a related application and an illustrated example are included to verify the accuracy of the findings. Full article

(This article belongs to the Section Mathematical Analysis)

8 pages, 248 KB

Open AccessArticle

On the Positive Definite Lattice with Determinant 5

by Libo Zhao, Yangming Li, Lü Gong and Huilong Gu

Axioms 2025, 14(9), 686; https://doi.org/10.3390/axioms14090686 - 8 Sep 2025

Viewed by 160

Abstract

This paper is devoted to providing a classification of positive definite lattices with determinant 5 and a rank less than or equal to 6. Full article

22 pages, 350 KB

Open AccessArticle

Coupled System of (k, ψ)-Hilfer and (k, ψ)-Caputo Sequential Fractional Differential Equations with Non-Separated Boundary Conditions

by Furkan Erkan, Nuket Aykut Hamal, Sotiris K. Ntouyas, Jessada Tariboon and Phollakrit Wongsantisuk

Axioms 2025, 14(9), 685; https://doi.org/10.3390/axioms14090685 - 7 Sep 2025

Viewed by 213

Abstract

This paper is concerned with the existence and uniqueness of solutions for a coupled system of

(k, ψ)

-Hilfer and

(k, ψ)

-Caputo sequential fractional differential equations with non-separated boundary conditions. We make use of the Banach [...] Read more.

This paper is concerned with the existence and uniqueness of solutions for a coupled system of

(k, ψ)

-Hilfer and

(k, ψ)

-Caputo sequential fractional differential equations with non-separated boundary conditions. We make use of the Banach contraction mapping principle to obtain the uniqueness result, while two existence results are proved by using Leray–Schauder nonlinear alternative and Krasnosel’skiĭ’s fixed point theorem. The obtained results are illustrated by numerical examples. Full article

(This article belongs to the Special Issue Advances in Nonlinear Analysis and Boundary Value Problems)

19 pages, 2685 KB

Open AccessArticle

Sharp Bounds and Electromagnetic Field Applications for a Class of Meromorphic Functions Introduced by a New Operator

by Abdelrahman M. Yehia, Atef F. Hashem, Samar M. Madian and Mohammed M. Tharwat

Axioms 2025, 14(9), 684; https://doi.org/10.3390/axioms14090684 - 5 Sep 2025

Viewed by 255

Abstract

In this paper, we present a new integral operator that acts on a class of meromorphic functions on the punctured unit disc

U^{*}

. This operator enables the definition of a new subclass of meromorphic univalent functions. We obtain sharp bounds for [...] Read more.

In this paper, we present a new integral operator that acts on a class of meromorphic functions on the punctured unit disc

U^{*}

. This operator enables the definition of a new subclass of meromorphic univalent functions. We obtain sharp bounds for the Fekete–Szegö inequality and the second Hankel determinant for this class. The theoretical approach is based on differential subordination. Furthermore, we link these theoretical insights to applications in 2D electromagnetic field theory by outlining a physical framework in which the operator functions as a field transformation kernel. We show that the operator’s parameters correspond to physical analogs of field regularization and spectral redistribution, and we use subordination theory to simulate the design of vortex-free fields. The findings provide new insights into the interaction between geometric function theory and physical field modeling. Full article

(This article belongs to the Special Issue New Developments in Geometric Function Theory, 4th Edition)

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13 pages, 265 KB

Open AccessArticle

Multidual Complex Numbers and the Hyperholomorphicity of Multidual Complex-Valued Functions

by Ji Eun Kim

Axioms 2025, 14(9), 683; https://doi.org/10.3390/axioms14090683 - 5 Sep 2025

Viewed by 240

Abstract

We develop a rigorous algebraic–analytic framework for multidual complex numbers

{DC}_{n}

within the setting of Clifford analysis and establish a comprehensive theory of hyperholomorphic multidual complex-valued functions. Our main contributions are (i) a fully coupled multidual Cauchy–Riemann system derived from the Dirac [...] Read more.

We develop a rigorous algebraic–analytic framework for multidual complex numbers

{DC}_{n}

within the setting of Clifford analysis and establish a comprehensive theory of hyperholomorphic multidual complex-valued functions. Our main contributions are (i) a fully coupled multidual Cauchy–Riemann system derived from the Dirac operator, yielding precise differentiability criteria; (ii) generalized conjugation laws and the associated norms that clarify metric and geometric structure; and (iii) explicit operator and kernel constructions—including generalized Cauchy kernels and Borel–Pompeiu-type formulas—that produce new representation theorems and regularity results. We further provide matrix–exponential and functional calculus representations tailored to

{DC}_{n}

, which unify algebraic and analytic viewpoints and facilitate computation. The theory is illustrated through a portfolio of examples (polynomials, rational maps on invertible sets, exponentials, and compositions) and a solvable multidual boundary value problem. Connections to applications are made explicit via higher-order automatic differentiation (using nilpotent infinitesimals) and links to kinematics and screw theory, highlighting how multidual analysis expands classical holomorphic paradigms to richer, nilpotent-augmented coordinate systems. Our results refine and extend prior work on dual/multidual numbers and situate multidual hyperholomorphicity within modern Clifford analysis. We close with a concise summary of notation and a set of concrete open problems to guide further development. Full article

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

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16 pages, 298 KB

Open AccessArticle

Interior Approximate Controllability of a Class of Nonlinear Thermoelastic Plate Equations

by Cosme Duque, Hugo Leiva and Zoraida Sivoli

Axioms 2025, 14(9), 682; https://doi.org/10.3390/axioms14090682 - 4 Sep 2025

Viewed by 183

Abstract

This article introduces new sufficient conditions ensuring the interior approximate controllability of semilinear thermoelastic plate equations subject to Dirichlet boundary conditions. The analysis is carried out by reformulating the system as an abstract evolution equation on a suitable Banach space. A key role [...] Read more.

This article introduces new sufficient conditions ensuring the interior approximate controllability of semilinear thermoelastic plate equations subject to Dirichlet boundary conditions. The analysis is carried out by reformulating the system as an abstract evolution equation on a suitable Banach space. A key role is played by the compactness of the semigroup generated by the linear operator, which allows us to treat the nonlinear components effectively. To establish controllability, we apply Rothe’s fixed-point theorem, which provides the necessary framework for handling nonlinear perturbations. The results obtained contribute to the existing literature, since the controllability of the specific semilinear thermoelastic system considered here has not been previously investigated. Full article

(This article belongs to the Special Issue Modern Problems of Analysis, Optimization, Approximation and Their Applications)

22 pages, 981 KB

Open AccessArticle

Analysis of the Dynamic Properties of a Discrete Epidemic Model Affected by Media Coverage

by Yanfang Liang and Wenlong Wang

Axioms 2025, 14(9), 681; https://doi.org/10.3390/axioms14090681 - 4 Sep 2025

Viewed by 324

Abstract

This study investigates the dynamic behaviors of the discrete epidemic model influenced by media coverage through integrated analytical and numerical approaches. The primary objective is to quantitatively assess the impact of media coverage on disease outbreak patterns using mathematical modeling. Firstly, the Euler [...] Read more.

This study investigates the dynamic behaviors of the discrete epidemic model influenced by media coverage through integrated analytical and numerical approaches. The primary objective is to quantitatively assess the impact of media coverage on disease outbreak patterns using mathematical modeling. Firstly, the Euler method is used to discretize the model (2), and the periodic solution is strictly analyzed. Secondly, the coefficients and conditions of restricted flip and Neimark–Sacker bifurcation are studied by using the center manifold theorem and bifurcation theory. By calculating the largest Lyapunov exponent near the critical bifurcation point, the occurrence of chaos and limit cycles is proved. On this basis, the chaotic control of the system is carried out by using state feedback and hybrid control. Under certain conditions, the chaos and bifurcation of the system can be stabilized by control strategies. Numerical simulations further reveal bifurcation dynamics, chaotic behaviors, and control technologies. Our results show that media coverage is a key factor in regulating the intensity of disease transmission and chaos. The control technology can effectively prevent the large-scale outbreak of epidemic diseases. Importantly, enhanced media coverage can effectively promote public awareness and defensive behaviors, thereby contributing to the mitigation of disease transmission. Full article

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

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25 pages, 5594 KB

Open AccessArticle

Analysis of Bifurcation and Stability in an Epidemic Model of HPV Infection and Cervical Cancer with Two Time Delays

by Mengyuan Hua and Tiansi Zhang

Axioms 2025, 14(9), 680; https://doi.org/10.3390/axioms14090680 - 3 Sep 2025

Viewed by 209

Abstract

Cervical cancer (CC), which continues to be a major public health concern that causes cancer deaths among women worldwide, is mostly caused by persistent human papillomavirus (HPV) infection. This study suggests a dual-delay model of HPV-C infection dynamics that takes into account both [...] Read more.

Cervical cancer (CC), which continues to be a major public health concern that causes cancer deaths among women worldwide, is mostly caused by persistent human papillomavirus (HPV) infection. This study suggests a dual-delay model of HPV-C infection dynamics that takes into account both cancerous delay and the immune response delay. We identify disease-free and diseased equilibria, investigate their local asymptotic stability, and show that the system is non-negative and bounded. We prove the global asymptotic stability of the equilibria by building Lyapunov functions and using the basic reproduction number

R_{0}

, and look into the existence of Hopf bifurcations. Additionally, we use forward sensitivity analysis to determine important control parameters. Lastly, the theoretical results were confirmed by numerical simulations. The study demonstrates that time delays play a crucial role in viral transmission and carcinogenesis. The process from HPV infection to the formation of cervical cancer is more correctly simulated by this model, which offers a theoretical mathematical basis for researching the pathophysiology of cervical cancer and developing clinical prevention and control measures. Full article

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14 pages, 292 KB

Open AccessArticle

Oettli-Théra Theorem and Ekeland Variational Principle in Fuzzy b-Metric Spaces

by Xuan Liu, Fei He and Ning Lu

Axioms 2025, 14(9), 679; https://doi.org/10.3390/axioms14090679 - 3 Sep 2025

Viewed by 228

Abstract

The purpose of this paper is to establish the Oettli–Th

\overset{´}{e}

ra theorem in the setting of KM-type fuzzy b-metric spaces. To achieve this, we first prove a lemma that removes the constraints on the space coefficients, which significantly simplifies the [...] Read more.

The purpose of this paper is to establish the Oettli–Th

\overset{´}{e}

ra theorem in the setting of KM-type fuzzy b-metric spaces. To achieve this, we first prove a lemma that removes the constraints on the space coefficients, which significantly simplifies the proof process. Based on the Oettli–Th

\overset{´}{e}

ra theorem, we further demonstrate the equivalence of Ekeland variational principle, Caristi’s fixed point theorem, and Takahashi’s nonconvex minimization theorem in fuzzy b-metric spaces. Notably, the results obtained in this paper are consistent with the conditions of the corresponding theorems in classical fuzzy metric spaces, thereby extending the existing theories to the broader framework of fuzzy b-metric spaces. Full article

(This article belongs to the Section Mathematical Analysis)

20 pages, 1369 KB

Open AccessArticle

Bin-3-Way-PARAFAC-PLS: A 3-Way Partial Least Squares for Binary Response

by Elisa Frutos-Bernal, Laura Vicente-González and Ana Elizabeth Sipols

Axioms 2025, 14(9), 678; https://doi.org/10.3390/axioms14090678 - 3 Sep 2025

Viewed by 302

Abstract

In various research domains, researchers frequently encounter multiple datasets pertaining to the same subjects, with one dataset providing explanatory variables for the others. To address this structure, we introduce the Binary 3-way PARAFAC Partial Least Squares (Bin-3-Way-PARAFAC-PLS), a novel multiway regression method. This [...] Read more.

In various research domains, researchers frequently encounter multiple datasets pertaining to the same subjects, with one dataset providing explanatory variables for the others. To address this structure, we introduce the Binary 3-way PARAFAC Partial Least Squares (Bin-3-Way-PARAFAC-PLS), a novel multiway regression method. This method is specifically engineered for scenarios involving a three-way real-valued explanatory data array and a matrix of binary response data. We detail the algorithm’s implementation and illustrate its practical application. Furthermore, we describe biplot representations to aid in result interpretation. The accompanying software necessary for implementing the method is also provided. Finally, the proposed method’s utility in real-world problem-solving is demonstrated through its application to a psychological dataset. Full article

(This article belongs to the Special Issue Probability, Statistics and Estimations, 2nd Edition)

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24 pages, 7058 KB

Open AccessArticle

Dynamical Analysis of a Caputo Fractional-Order Modified Brusselator Model: Stability, Chaos, and 0-1 Test

by Messaoud Berkal and Mohammed Bakheet Almatrafi

Axioms 2025, 14(9), 677; https://doi.org/10.3390/axioms14090677 - 2 Sep 2025

Viewed by 400

Abstract

Differential equations have demonstrated significant practical effectiveness across diverse fields, including physics, chemistry, biological engineering, computer science, electrical power systems, and security cryptography. This study investigates the dynamics of a Caputo fractional discrete-time modified Brusselator model. Conditions for the existence and local stability [...] Read more.

Differential equations have demonstrated significant practical effectiveness across diverse fields, including physics, chemistry, biological engineering, computer science, electrical power systems, and security cryptography. This study investigates the dynamics of a Caputo fractional discrete-time modified Brusselator model. Conditions for the existence and local stability of the fixed point

F P

are established. Using bifurcation theory, the occurrence of both period-doubling and Neimark–-Sacker bifurcations is analyzed, revealing that these bifurcations occur at specific values of the bifurcation parameter. Maximum Lyapunov characteristic exponents are computed to assess system sensitivity. Two-dimensional diagrams are presented to illustrate phase portraits, local stability regions, closed invariant curves, bifurcation types, and Lyapunov exponents, while the 0-1 test confirms the presence of chaos in the model. Finally, MATLAB simulations validate the theoretical results. Full article

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

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37 pages, 2075 KB

Open AccessArticle

Malliavin Differentiability and Density Smoothness for Non-Lipschitz Stochastic Differential Equations

by Zhaoen Qu, Yinuo Sun and Lei Zhang

Axioms 2025, 14(9), 676; https://doi.org/10.3390/axioms14090676 - 2 Sep 2025

Viewed by 328

Abstract

In this paper, we investigate the Malliavin differentiability and density smoothness of solutions to stochastic differential equations (SDEs) with non-Lipschitz coefficients. Specifically, we consider equations of the form [...] Read more.

In this paper, we investigate the Malliavin differentiability and density smoothness of solutions to stochastic differential equations (SDEs) with non-Lipschitz coefficients. Specifically, we consider equations of the form

d X_{t} = b (X_{t}) d t + σ (X_{t}) d W_{t}, X_{0} = x_{0}

where the drift b(·) and diffusion σ(·) may violate the global Lipschitz condition but satisfy weaker assumptions such as Hölder continuity, linear growth, and non-degeneracy. By employing Malliavin calculus theory, large deviation principles, and Fokker–Planck equations, we establish comprehensive results concerning the existence and uniqueness of solutions, their Malliavin differentiability, and the smoothness properties of density functions. Our main contributions include (1) proving the Malliavin differentiability of solutions under the standard linear growth condition combined with Hölder continuity; (2) establishing the existence and smoothness of density functions using Norris lemma and the Bismut–Elworthy–Li formula; and (3) providing optimal estimates for density functions through large deviation theory. These results have significant applications in financial mathematics (e.g., CIR, CEV, and Heston models), biological system modeling (e.g., stochastic population dynamics and neuronal and epidemiological models), and other scientific domains. Full article

(This article belongs to the Special Issue Stochastic and Statistical Analyses in Natural Sciences, Second Edition)

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30 pages, 403 KB

Open AccessArticle

The Numerical Solution of Volterra Integral Equations

by Peter Junghanns

Axioms 2025, 14(9), 675; https://doi.org/10.3390/axioms14090675 - 1 Sep 2025

Viewed by 281

Abstract

Recently we studied a collocation–quadrature method in weighted

L^{2}

spaces as well as in the space of continuous functions for a Volterra-like integral equation of the form [...] Read more.

Recently we studied a collocation–quadrature method in weighted

L^{2}

spaces as well as in the space of continuous functions for a Volterra-like integral equation of the form

u (x) - \int_{α x}^{1} h (x - α y) u (y) d y = f (x), 0 < x < 1,

where

h (x)

(with a possible singularity at

x = 0

) and

f (x)

are given (in general complex-valued) functions, and

α \in (0, 1)

is a fixed parameter. Here, we want to investigate the same method for the case when

α = 1 .

More precisely, we consider (in general weakly singular) Volterra integral equations of the form

u (x) - \int_{0}^{x} h (x, y) {(x - y)}^{κ} u (y) d y = f (x), 0 < x < 1,

where

κ > - 1

, and

h : D ⟶ C

is a continuous function,

D = \{(x, y) \in R^{2} : 0 < y < x < 1\} .

The passage from

0 < α < 1

to

α = 1

and the consideration of more general kernel functions

h (x, y)

make the studies more involved. Moreover, we enhance the family of interpolation operators defining the approximating operators, and, finally, we ask if, in comparison to collocation–quadrature methods, the application of the Nyström method together with the theory of collectively compact operator sequences is possible. Full article

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

14 pages, 288 KB

Open AccessArticle

Geometric Perspective of Relativistic Bulk Viscous Fluid String Spacetime

by Mohd Danish Siddiqi and Ibrahim Al-Dayel

Axioms 2025, 14(9), 674; https://doi.org/10.3390/axioms14090674 - 1 Sep 2025

Viewed by 315

Abstract

The goal of the article is to examine the behavior of bulk viscous fluid string spacetime with a fluid density of the bulk viscous fluid string

ρ

and a tension of the bulk viscous fluid string

λ

. This is known as relativistic [...] Read more.

The goal of the article is to examine the behavior of bulk viscous fluid string spacetime with a fluid density of the bulk viscous fluid string

ρ

and a tension of the bulk viscous fluid string

λ

. This is known as relativistic bulk viscous fluid string spacetime. We derive some conclusions for bulk viscous fluid string with a vanishing space–matter tensor and a divergence-free matter tensor. We then focus on certain curvature properties for bulk viscous fluid string spacetime, including conformally flat, Ricci recurrent, Ricci semi-symmetric, and pseudo-Ricci-symmetric. Some physical results that align with the equation of state of Ricci semi-symmetric bulk viscous fluid string spacetime are also obtained. Full article

(This article belongs to the Special Issue Differential Geometry and Its Application, 3rd Edition)

9 pages, 268 KB

Open AccessArticle

A Note on Finite-to-Infinite Extensions and Homotopy Invariance of Digraph Brown Functors

by Hsuan-Yi Liao and Byungdo Park

Axioms 2025, 14(9), 673; https://doi.org/10.3390/axioms14090673 - 1 Sep 2025

Viewed by 229

Abstract

This paper develops extension theory for Brown functors in directed graph homotopy theory. We establish a systematic method for extending Brown functors from finite directed graphs to arbitrary directed graphs using inverse limits over finite subdigraphs. We prove that this extension is well-defined [...] Read more.

This paper develops extension theory for Brown functors in directed graph homotopy theory. We establish a systematic method for extending Brown functors from finite directed graphs to arbitrary directed graphs using inverse limits over finite subdigraphs. We prove that this extension is well-defined and preserves essential functorial properties. Additionally, we provide an alternative characterization of this extension through the Yoneda lemma, demonstrating how extended Brown functors can be naturally identified with sets of natural transformations from representable functors. This categorical perspective offers deeper theoretical insight into the structure of extended Brown functors and establishes important connections with classical representability theory, providing the technical foundation for Brown representability in directed graph theory. Full article

(This article belongs to the Special Issue Trends in Differential Geometry and Algebraic Topology)

14 pages, 289 KB

Open AccessArticle

Impact of Measurement Error on Residual Extropy Estimation

by Radhakumari Maya, Muhammed Rasheed Irshad, Febin Sulthana and Maria Longobardi

Axioms 2025, 14(9), 672; https://doi.org/10.3390/axioms14090672 - 31 Aug 2025

Viewed by 277

Abstract

In scientific analyses, measurement errors in data can significantly impact statistical inferences, and ignoring them may lead to biased and invalid results. This study focuses on the estimation of the residual extropy function, in the presence of measurement errors. We developed an estimator [...] Read more.

In scientific analyses, measurement errors in data can significantly impact statistical inferences, and ignoring them may lead to biased and invalid results. This study focuses on the estimation of the residual extropy function, in the presence of measurement errors. We developed an estimator for the extropy function and established its asymptotic properties. A comprehensive simulation study evaluates the performance of the proposed estimators under various error scenarios, while their practical utility and precision are demonstrated through an application to a real-world data set. Full article

10 pages, 219 KB

Open AccessArticle

Images of Generalized Multilinear Polynomials on Upper Triangular Matrix Algebras

by Qian Chen and Yu Wang

Axioms 2025, 14(9), 671; https://doi.org/10.3390/axioms14090671 - 30 Aug 2025

Viewed by 288

Abstract

A polynomial is called a generalized multilinear polynomial if it is a sum of some multilinear polynomials over a field. The goal of this paper is to give a description of the images of generalized multilinear polynomials on upper triangular matrix algebras, generalizing [...] Read more.

A polynomial is called a generalized multilinear polynomial if it is a sum of some multilinear polynomials over a field. The goal of this paper is to give a description of the images of generalized multilinear polynomials on upper triangular matrix algebras, generalizing all results of the Fagundes–Mello conjecture proposed by Fagundes and Mello in 2019. Full article

20 pages, 1534 KB

Open AccessArticle

Numerical Solutions for Fractional Fixation Times in Evolutionary Models

by Somayeh Mashayekhi

Axioms 2025, 14(9), 670; https://doi.org/10.3390/axioms14090670 - 29 Aug 2025

Viewed by 268

Abstract

The fixation time of alleles is a fundamental concept in population genetics, traditionally studied using the Wright–Fisher model and classical coalescent theory. However, these models often assume homogeneous environments and equal reproductive success among individuals, limiting their applicability to real-world populations where environmental [...] Read more.

The fixation time of alleles is a fundamental concept in population genetics, traditionally studied using the Wright–Fisher model and classical coalescent theory. However, these models often assume homogeneous environments and equal reproductive success among individuals, limiting their applicability to real-world populations where environmental heterogeneity plays a significant role. In this paper, we introduce a new forward-time model for estimating fixation time that incorporates environmental heterogeneity through the use of fractional calculus. By introducing a fractional parameter α, we capture the effects of heterogeneous environments on offspring production. To solve the resulting fractional differential equations, we develop a novel spectral method based on Eta-based functions, which are well-suited for approximating solutions to complex, high-variation systems. The proposed method reduces the problem to an optimization framework via the operational matrix of fractional derivatives. We demonstrate the effectiveness and accuracy of this approach through numerical examples and show that it consistently captures fixation dynamics across various scenarios. This work offers a robust and flexible framework for modeling evolutionary processes in heterogeneous environments. Full article

(This article belongs to the Special Issue Fractional Differential Equations and Dynamical Systems)

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16 pages, 448 KB

Open AccessArticle

On Structural Characterization and Computation of the Diameter and Girth of Bipartite Gap Poset Graphs with Python Application

by Maria Mehtab, Muhammad Ahsan Binyamin, Syed Sheraz Asghar, Amal S. Alali and Khawar Mehmood

Axioms 2025, 14(9), 669; https://doi.org/10.3390/axioms14090669 - 29 Aug 2025

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Abstract

In this article, a correspondence between some important classes of numerical semigroups and well-known families of bipartite graphs has been established. Also, it has been demonstrated that, if

m (S)

is the multiplicity of a numerical semigroup

S

, then the [...] Read more.

In this article, a correspondence between some important classes of numerical semigroups and well-known families of bipartite graphs has been established. Also, it has been demonstrated that, if

m (S)

is the multiplicity of a numerical semigroup

S

, then the diameter and the girth of bipartite gap poset graphs are bounded by the numbers

2 m (S) - 3

and

m (S) - 1

, respectively. Moreover, the Python code to compute the diameter and girth of gap poset graphs has been implemented. Full article

(This article belongs to the Special Issue Graph Invariants and Their Applications)

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41 pages, 1229 KB

Open AccessArticle

The Classical Origin of Spin: Vectors Versus Bivectors

by Bryan Sanctuary

Axioms 2025, 14(9), 668; https://doi.org/10.3390/axioms14090668 - 29 Aug 2025

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Abstract

There are two ways of linearizing the Klein–Gordon equation: Dirac’s choice, which introduces a matter–antimatter pair, and a second approach using a bivector, which Dirac did not consider. In this paper, we show that a bivector provides the classical origin of quantum spin. [...] Read more.

There are two ways of linearizing the Klein–Gordon equation: Dirac’s choice, which introduces a matter–antimatter pair, and a second approach using a bivector, which Dirac did not consider. In this paper, we show that a bivector provides the classical origin of quantum spin. At high precessional frequencies, a symmetry transformation occurs in which classical reflection becomes quantum parity. We identify a classical spin-1 boson and demonstrate how bosons deliver energy, matter, and torque to a surface. The correspondence between classical and quantum domains allows spin to be identified as a quantum bivector,

i σ

. Using geometric algebra, we show that a classical boson has two blades, corresponding to magnetic quantum number states

m = \pm 1

. We conclude that fermions are the blades of bosons, thereby unifying both into a single particle theory. We compare and contrast the Standard Model, which uses chiral vectors as fundamental, with the Bivector Standard Model, which uses bivectors, with two hands, as fundamental. Full article

(This article belongs to the Special Issue Mathematical Aspects of Quantum Field Theory and Quantization)

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22 pages, 3799 KB

Open AccessArticle

Privacy-Preserving Statistical Inference for Stochastic Frontier Analysis

by Mengxiang Quan, Yunquan Song and Xinmin Wang

Axioms 2025, 14(9), 667; https://doi.org/10.3390/axioms14090667 - 29 Aug 2025

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Abstract

We present the first differentially private framework for stochastic frontier analysis (SFA), addressing the challenge of non-convex objectives in privacy-preserving efficiency estimation. We construct a bounded parameter space to control gradient sensitivity and adapt the Frank–Wolfe algorithm with calibrated linear oracle noise to [...] Read more.

We present the first differentially private framework for stochastic frontier analysis (SFA), addressing the challenge of non-convex objectives in privacy-preserving efficiency estimation. We construct a bounded parameter space to control gradient sensitivity and adapt the Frank–Wolfe algorithm with calibrated linear oracle noise to mitigate cumulative perturbation. Incorporating

l_{1}

-regularization facilitates sparse and interpretable variable selection under strict

(ϵ, δ)

-differential privacy. Experiments demonstrate 15–35% MAE reduction under

ϵ = 0.1

, along with strong scalability and estimation accuracy compared to prior DP methods for non-convex models. Full article

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

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17 pages, 1942 KB

Open AccessArticle

On the Combination of the Laplace Transform and Integral Equation Method to Solve the 3D Parabolic Initial Boundary Value Problem

by Roman Chapko and Svyatoslav Lavryk

Axioms 2025, 14(9), 666; https://doi.org/10.3390/axioms14090666 - 29 Aug 2025

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Abstract

We consider a two-step numerical approach for solving parabolic initial boundary value problems in 3D simply connected smooth regions. The method uses the Laplace transform in time, reducing the problem to a set of independent stationary boundary value problems for the Helmholtz equation [...] Read more.

We consider a two-step numerical approach for solving parabolic initial boundary value problems in 3D simply connected smooth regions. The method uses the Laplace transform in time, reducing the problem to a set of independent stationary boundary value problems for the Helmholtz equation with complex parameters. The inverse Laplace transform is computed using a sinc quadrature along a suitably chosen contour in the complex plane. We show that due to a symmetry of the quadrature nodes, the number of stationary problems can be decreased by almost a factor of two. The influence of the integration contour parameters on the approximation error is also researched. Stationary problems are numerically solved using a boundary integral equation approach applying the Nyström method, based on the quadratures for smooth surface integrals. Numerical experiments support the expectations. Full article

(This article belongs to the Topic Numerical Methods for Partial Differential Equations)

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22 pages, 375 KB

Open AccessArticle

Spatial Generalized Octonionic Curves

by Mücahit Akbıyık, Jeta Alo and Seda Yamaç Akbıyık

Axioms 2025, 14(9), 665; https://doi.org/10.3390/axioms14090665 - 29 Aug 2025

Viewed by 261

Abstract

This study investigates curves in a 7-dimensional space, represented by spatial generalized octonion-valued functions of a single variable, where the general octonions include real, split, semi, split semi, quasi, split quasi, and para octonions. We begin by constructing a new frame, referred to [...] Read more.

This study investigates curves in a 7-dimensional space, represented by spatial generalized octonion-valued functions of a single variable, where the general octonions include real, split, semi, split semi, quasi, split quasi, and para octonions. We begin by constructing a new frame, referred to as the

G_{2}

-frame, for spatial generalized octonionic curves, and subsequently derive the corresponding derivative formulas. We also present the connection between the

G_{2}

-frame and the standard orthonormal basis of spatial generalized octonions. Moreover, we verify that Frenet–Serret formulas hold for spatial generalized octonionic curves. We establish the

G_{2}

-congruence of two spatial generalized octonionic curves and present the correspondence between the Frenet–Serret frame and the

G_{2}

-frame. A key advantage of the

G_{2}

-frame is that the associated frame equations involve lower-order derivatives. This method is both time-efficient and computationally efficient. To demonstrate the theory, we present an example of a unit-speed spatial generalized octonionic curve and compute its

G_{2}

-frame and invariants using MATLAB. Full article

(This article belongs to the Special Issue Advances in Mathematics and Its Applications, 2nd Edition)

20 pages, 1534 KB

Open AccessArticle

Custom Score Function: Projection of Structural Attention in Stochastic Structures

by Mine Doğan and Mehmet Gürcan

Axioms 2025, 14(9), 664; https://doi.org/10.3390/axioms14090664 - 29 Aug 2025

Viewed by 277

Abstract

This study introduces a novel approach to correlation-based feature selection and dimensionality reduction in high-dimensional data structures. To this end, a customized scoring function is proposed, designed as a dual-objective structure that simultaneously maximizes the correlation with the target variable while penalizing redundant [...] Read more.

This study introduces a novel approach to correlation-based feature selection and dimensionality reduction in high-dimensional data structures. To this end, a customized scoring function is proposed, designed as a dual-objective structure that simultaneously maximizes the correlation with the target variable while penalizing redundant information among features. The method is built upon three main components: correlation-based preliminary assessment, feature selection via the tailored scoring function, and integration of the selection results into a t-SNE visualization guided by Rel/Red ratios. Initially, features are ranked according to their Pearson correlation with the target, and then redundancy is assessed through pairwise correlations among features. A priority scheme is defined using a scoring function composed of relevance and redundancy components. To enhance the selection process, an optimization framework based on stochastic differential equations (SDEs) is introduced. Throughout this process, feature weights are updated using both gradient information and diffusion dynamics, enabling the identification of subsets that maximize overall correlation. In the final stage, the t-SNE dimensionality reduction technique is applied with weights derived from the Rel/Red scores. In conclusion, this study redefines the feature selection process by integrating correlation-maximizing objectives with stochastic modeling. The proposed approach offers a more comprehensive and effective alternative to conventional methods, particularly in terms of explainability, interpretability, and generalizability. The method demonstrates strong potential for application in advanced machine learning systems, such as credit scoring, and in broader dimensionality reduction tasks. Full article

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20 pages, 358 KB

Open AccessArticle

Ideal (I₂) Convergence in Fuzzy Paranormed Spaces for Practical Stability of Discrete-Time Fuzzy Control Systems Under Lacunary Measurements

by Muhammed Recai Türkmen and Hasan Öğünmez

Axioms 2025, 14(9), 663; https://doi.org/10.3390/axioms14090663 - 29 Aug 2025

Viewed by 351

Abstract

We investigate the stability of linear discrete-time control systems with a fuzzy logic feedback under sporadic sensor data loss. In our framework, each state measurement is a fuzzy number, and occasional “packet dropouts” are modeled by a lacunary subsequence of missing readings. We [...] Read more.

We investigate the stability of linear discrete-time control systems with a fuzzy logic feedback under sporadic sensor data loss. In our framework, each state measurement is a fuzzy number, and occasional “packet dropouts” are modeled by a lacunary subsequence of missing readings. We introduce a novel mathematical approach using lacunary statistical convergence in fuzzy paranormed spaces to analyze such systems. Specifically, we treat the sequence of fuzzy measurements as a double sequence (indexed by time and state component) and consider an admissible ideal of “negligible” index sets that includes the missing–data pattern. Using the concept of ideal fuzzy—paranorm convergence (I-fp convergence), we formalize a lacunary statistical consistency condition on the fuzzy measurements. We prove that if the closed-loop matrix

A - B K

is Schur stable (i.e.,

∥ A - B K ∥ < 1

) in the absence of dropouts, then under the lacunary statistical consistency condition, the controlled system is practically stable despite intermittent measurement losses. In other words, for any desired tolerance, the state eventually remains within that bound (though not necessarily converging to zero). Our result yields an explicit, non-probabilistic (distribution-free) analytical criterion for robustness to sensor dropouts, without requiring packet-loss probabilities or Markov transition parameters. This work merges abstract convergence theory with control application: it extends statistical and ideal convergence to double sequences in fuzzy normed spaces and applies it to ensure stability of a networked fuzzy control system. Full article

(This article belongs to the Special Issue Mathematical Modeling and Control: Theory and Applications)

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Axioms, Volume 14, Issue 9 (September 2025) – 44 articles

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