Axioms

19 pages, 718 KiB

Open AccessArticle

A Totally Relaxed, Self-Adaptive Tseng Extragradient Method for Monotone Variational Inequalities

by Olufemi Johnson Ogunsola, Olawale Kazeem Oyewole, Seithuti Philemon Moshokoa and Hammed Anuoluwapo Abass

Axioms 2025, 14(5), 354; https://doi.org/10.3390/axioms14050354 - 7 May 2025

Abstract

In this work, we study a class of variational inequality problems defined over the intersection of sub-level sets of a countable family of convex functions. We propose a new iterative method for approximating the solution within the framework of Hilbert spaces. The method [...] Read more.

In this work, we study a class of variational inequality problems defined over the intersection of sub-level sets of a countable family of convex functions. We propose a new iterative method for approximating the solution within the framework of Hilbert spaces. The method incorporates several strategies, including inertial effects, a self-adaptive step size, and a relaxation technique, to enhance convergence properties. Notably, it requires computing only a single projection onto a half space. Using some mild conditions, we prove that the sequence generated by our proposed method is strongly convergent to a minimum-norm solution to the problem. Finally, we present some numerical results that validate the applicability of our proposed method. Full article

(This article belongs to the Section Mathematical Analysis)

► Show Figures

Figure 1

13 pages, 345 KiB

Open AccessArticle

Slant Helices and Darboux Helices in Myller Configuration

by Yanlin Li, Akın Alkan, Mehmet Önder and Yuquan Xie

Axioms 2025, 14(5), 353; https://doi.org/10.3390/axioms14050353 - 5 May 2025

Viewed by 52

Abstract

In this paper, we study slant helices (or

{\overline{ξ}}_{2}

-helices) and Darboux helices in the Myller configuration M. We demonstrate that a curve in M is a slant helix if and only if it is a Darboux helix. We present [...] Read more.

In this paper, we study slant helices (or

{\overline{ξ}}_{2}

-helices) and Darboux helices in the Myller configuration M. We demonstrate that a curve in M is a slant helix if and only if it is a Darboux helix. We present the alternative frame for a curve in M. Furthermore, we derive the differential equations that characterize the curves in M using both the Frenet-type frame and the alternative frame. Full article

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

► Show Figures

Figure 1

14 pages, 280 KiB

Open AccessArticle

Essential Norm of Products of Volterra-Type Operators and Composition Operators on Iterated Banach-Type Spaces

by Rabab Alyusof, Shams Alyusof and Nacir Hmidouch

Axioms 2025, 14(5), 352; https://doi.org/10.3390/axioms14050352 - 4 May 2025

Viewed by 119

Abstract

Let

H (D)

be the set of analytic functions on the open unit disk

D

. For

n \in N_{0} : = N \cup {0}

, define the iterated weighted-type Banach space [...] Read more.

Let

H (D)

be the set of analytic functions on the open unit disk

D

. For

n \in N_{0} : = N \cup {0}

, define the iterated weighted-type Banach space

V_{n} : = \{f \in H (D) : {sup}_{z \in D} {(1 - | z |}^{2}) | f^{(n)} (z) | < \infty\} .

In this work, we study the boundedness and the essential norm of products of Volterra-type operators and composition operators on iterated weighted-type Banach spaces. Full article

22 pages, 827 KiB

Open AccessArticle

Fuzzy Clustering Based on Activity Sequence and Cycle Time in Process Mining

by Onur Dogan and Hunaıda Avvad

Axioms 2025, 14(5), 351; https://doi.org/10.3390/axioms14050351 - 4 May 2025

Viewed by 115

Abstract

Clustering plays a vital role in process mining as it organizes complex event logs into meaningful groups, helping to identify common patterns, outliers, and inefficiencies. This simplification enables organizations to detect bottlenecks and optimize workflows by uncovering trends and variations that might otherwise [...] Read more.

Clustering plays a vital role in process mining as it organizes complex event logs into meaningful groups, helping to identify common patterns, outliers, and inefficiencies. This simplification enables organizations to detect bottlenecks and optimize workflows by uncovering trends and variations that might otherwise remain hidden. Fuzzy clustering addresses the challenge of overlapping behaviors, providing actionable insights for targeted improvements and enhanced operational efficiency. Nevertheless, conventional clustering algorithms for process mining focus either on activity sequences or cycle times, resulting in incomplete insights due to the neglect of temporal or structural variations. This work introduces a new fuzzy clustering methodology that incorporates both activity sequences and cycle times through a weighted distance metric. The proposed approach balances the weights of similarity in sequences as well as time variation flexibly using the parameter

α

, enabling clusters to represent both structural as well as performance-based process attributes. Through using fuzzy C-means clustering, the method allows cases to have multiple memberships with different membership degrees, providing flexibility regarding overlapping process behavior. An experimental evaluation using real-life event logs demonstrates the effectiveness of the method in discerning process variants. It yields superior results compared to conventional methods that account for only sequence-based clustering scenarios, as well as time-based clustering methods. The results describe the significant importance of optimizing clustering results by varying

α

, where a balanced weighting (

α = 0.5

) gives more meaningful clusters. Ultimately, the framework enhances process mining by offering detailed insights for analyzing operational inefficiencies, bottlenecks, and resource allocation mismatches, providing substantial real-world benefits for industries that demand effective process improvement. Full article

(This article belongs to the Special Issue Recent Advances in Fuzzy Theory Applications)

► Show Figures

Figure 1

25 pages, 321 KiB

Open AccessArticle

Analytical and Geometric Foundations and Modern Applications of Kinetic Equations and Optimal Transport

by Cécile Barbachoux and Joseph Kouneiher

Axioms 2025, 14(5), 350; https://doi.org/10.3390/axioms14050350 - 4 May 2025

Viewed by 159

Abstract

We develop a unified analytical framework that systematically connects kinetic theory, optimal transport, and entropy dissipation through the novel integration of hypocoercivity methods with geometric structures. Building upon but distinctly extending classical hypocoercivity approaches, we demonstrate how geometric control, via commutators and curvature-like [...] Read more.

We develop a unified analytical framework that systematically connects kinetic theory, optimal transport, and entropy dissipation through the novel integration of hypocoercivity methods with geometric structures. Building upon but distinctly extending classical hypocoercivity approaches, we demonstrate how geometric control, via commutators and curvature-like structures in probability spaces, resolves degeneracies inherent in kinetic operators. Centered around the Boltzmann and Fokker–Planck equations, we derive sharp exponential convergence estimates under minimal regularity assumptions, improving on prior methods by incorporating Wasserstein gradient flow techniques. Our framework is further applied to the study of hydrodynamic limits, collisional relaxation in magnetized plasmas, the Vlasov–Poisson system, and modern data-driven algorithms, highlighting the central role of entropy as both a physical and variational tool across disciplines. By bridging entropy dissipation, optimal transport, and geometric analysis, our work offers a new perspective on stability, convergence, and structure in high-dimensional kinetic models and applications. Full article

(This article belongs to the Special Issue Mathematical and Statistical Methods and Their Applications, 2nd Edition)

► Show Figures

Graphical abstract

11 pages, 586 KiB

Open AccessArticle

Theoretical Proof of and Proposed Experimental Search for the Ground Triplet State of a Wigner-Regime Two-Electron ‘Artificial Atom’ in a Magnetic Field

by Marlina Slamet and Viraht Sahni

Axioms 2025, 14(5), 349; https://doi.org/10.3390/axioms14050349 - 3 May 2025

Viewed by 169

Abstract

It is experimentally established that there is no ground triplet state of the natural

H e

atom. There is also no exact analytical solution to the Schrödinger equation corresponding to this state. For a two-dimensional two-electron ‘artificial atom’ or a semiconductor quantum dot [...] Read more.

It is experimentally established that there is no ground triplet state of the natural

H e

atom. There is also no exact analytical solution to the Schrödinger equation corresponding to this state. For a two-dimensional two-electron ‘artificial atom’ or a semiconductor quantum dot in a magnetic field, as described by the Schrödinger–Pauli equation, we provide theoretical proof of the existence of a ground triplet state by deriving an exact analytical correlated wave function solution to the equation. The state exists in the Wigner high-electron-correlation regime. We further explain that the solution satisfies all requisite symmetry and electron coalescence constraints of a triplet state. Since, due to technological advances, such a Wigner crystal quantum dot can be created, we propose an experimental search for the theoretically predicted ground triplet-state spectral line. We note that there exists an analytical solution to the Schrödinger–Pauli equation for a ground singlet state in the Wigner regime for the same value of the magnetic field. The significance to quantum mechanics of the probable experimental observation of the ground triplet state for an ‘artificial atom’ is discussed. Full article

(This article belongs to the Special Issue Recent Advances in Quantum Mechanics and Mathematical Physics)

► Show Figures

Figure 1

17 pages, 345 KiB

Open AccessArticle

A Partitioning-Based Approach to Variable Selection in WLW Model for Multivariate Survival Data

by Wenjian Tian and Wenquan Cui

Axioms 2025, 14(5), 348; https://doi.org/10.3390/axioms14050348 - 30 Apr 2025

Viewed by 99

Abstract

In this paper, we propose a new variable selection method using a partitioning-based estimating equation for multivariate survival data to simultaneously perform variable selection and parameter estimation. The main idea of the partitioning-based estimating equation is to partition the score function into small [...] Read more.

In this paper, we propose a new variable selection method using a partitioning-based estimating equation for multivariate survival data to simultaneously perform variable selection and parameter estimation. The main idea of the partitioning-based estimating equation is to partition the score function into small blocks. We construct our method using the SCAD penalty function and achieve the purpose of directly selecting variables through the estimating equation. We further establish asymptotic normality and prove that our method achieves the oracle property. Moreover, we use a simple approximation of the penalty function such that our method can be implemented algorithmically. We conducted simulation studies to validate the performance of our method and analyzed the dataset from the Colon Cancer Study. Full article

► Show Figures

Figure 1

16 pages, 274 KiB

Open AccessArticle

A New Perspective on Intuitionistic Fuzzy Structures in Sheffer Stroke BCK-Algebras

by Ravi Kumar Bandaru, Rajesh Neelamegarajan, Tahsin Oner and Amal S. Alali

Axioms 2025, 14(5), 347; https://doi.org/10.3390/axioms14050347 - 30 Apr 2025

Viewed by 118

Abstract

This study introduces the concept of an intuitionistic fuzzy SBCK-subalgebra (SBCK-ideal) and explores the level set of an intuitionistic fuzzy set within the context of Sheffer stroke BCK-algebras. These newly defined concepts are crucial for understanding the interaction between intuitionistic logic and Sheffer [...] Read more.

This study introduces the concept of an intuitionistic fuzzy SBCK-subalgebra (SBCK-ideal) and explores the level set of an intuitionistic fuzzy set within the context of Sheffer stroke BCK-algebras. These newly defined concepts are crucial for understanding the interaction between intuitionistic logic and Sheffer stroke BCK-algebras. The paper establishes a connection between subalgebras and level sets in the framework of Sheffer stroke BCK-algebras, demonstrating that the level set of intuitionistic fuzzy SBCK-subalgebras corresponds precisely to their subalgebras, and conversely. Additionally, the study provides novel results regarding the structural properties of Sheffer stroke BCK-algebras under intuitionistic fuzzy logic, specifically focusing on the conditions under which fuzzy sets become SBCK-subalgebras or SBCK-ideals. This work contributes to the theoretical foundations of fuzzy logic in algebraic structures, offering a deeper understanding of the interplay between intuitionistic fuzzy sets and the algebraic operations within Sheffer stroke BCK-algebras. Full article

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

28 pages, 388 KiB

Open AccessArticle

Boundary Concentrated Solutions for an Elliptic Equation with Subcritical Nonlinearity

by Sadeem Al-Harbi and Mohamed Ben Ayed

Axioms 2025, 14(5), 346; https://doi.org/10.3390/axioms14050346 - 30 Apr 2025

Viewed by 90

Abstract

In this paper, we consider the nonlinear Neumann problem

(Q_{ε}) : - Δ u + V (x) u = u^{\frac{n + 2}{n - 2} - ε}

, with

u > 0

in

Ω

and [...] Read more.

In this paper, we consider the nonlinear Neumann problem

(Q_{ε}) : - Δ u + V (x) u = u^{\frac{n + 2}{n - 2} - ε}

, with

u > 0

in

Ω

and

\partial u / \partial ν = 0

on

\partial Ω

, where

Ω

is a bounded regular domain in

R^{n}

, with

n \geq 4

,

ε

is a small positive parameter, and V is a non-constant smooth positive function on

\bar{Ω}

. Assuming the flatness of the boundary near the critical points of the restriction of the function V on the boundary, we construct boundary peak solutions with isolated bubbles, leading to a multiplicity result for

(Q_{ε})

. The proof of our results relies on expanding the gradient of the associated functional and testing the equation with the appropriate vector fields, which yields constraints for the concentration points and blow-up rates. A thorough analysis of these constraints leads to our results. Full article

18 pages, 357 KiB

Open AccessArticle

Multiple Solutions of Fractional Kazdan–Warner Equation for Negative Case on Finite Graphs

by Liang Shan and Yang Liu

Axioms 2025, 14(5), 345; https://doi.org/10.3390/axioms14050345 - 30 Apr 2025

Viewed by 148

Abstract

This work establishes the multiplicity of solutions for the fractional Kazdan–Warner equation on finite graphs for the negative case. Our main focus lies in analyzing the nonlinear equation defined on a finite graph

(V, E, μ, w)

: [...] Read more.

This work establishes the multiplicity of solutions for the fractional Kazdan–Warner equation on finite graphs for the negative case. Our main focus lies in analyzing the nonlinear equation defined on a finite graph

(V, E, μ, w)

:

{(- Δ)}^{s} u = (K + λ) e^{2 u} - κ in V,

where the fraction

s \in (0, 1)

and real parameter

λ

are given, and the graph functions K and

κ

satisfy

\max_{x \in V} K (x) = 0

,

K ≢ 0

and

\int_{V} κ d μ < 0

. We derive the solvability characteristics of the above equation with the help of variational theory and the upper and lower solutions method. Full article

(This article belongs to the Section Mathematical Physics)

► Show Figures

Figure 1

18 pages, 266 KiB

Open AccessArticle

The Reverse Order Law for the {1,3M,4N}—The Inverse of Two Matrix Products

by Yingying Qin, Baifeng Qiu and Zhiping Xiong

Axioms 2025, 14(5), 344; https://doi.org/10.3390/axioms14050344 - 30 Apr 2025

Viewed by 106

Abstract

By using the maximal and minimal ranks of some generalized Schur complement, the equivalent conditions for the reverse order law

(A B) {1, 3 M, 4 K} = B {1, 3 N, 4 K} A {1, 3 M, 4 N}

are presented. Full article

(This article belongs to the Special Issue Advances in Linear Algebra with Applications, 2nd Edition)

19 pages, 12884 KiB

Open AccessArticle

Evolutionary Search for Polynomial Lyapunov Functions: A Genetic Programming Method for Exponential Stability Certification

by Roman Pykhnivskyi, Anton Ryzhov, Andrii Sobchuk and Yurii Kravchenko

Axioms 2025, 14(5), 343; https://doi.org/10.3390/axioms14050343 - 30 Apr 2025

Viewed by 211

Abstract

This paper presents a method for constructing polynomial Lyapunov functions to analyze the stability of nonlinear dynamical systems. The approach is based on genetic programming, a variant of genetic algorithms where the search space consists of hierarchical tree structures. In our formulation, these [...] Read more.

This paper presents a method for constructing polynomial Lyapunov functions to analyze the stability of nonlinear dynamical systems. The approach is based on genetic programming, a variant of genetic algorithms where the search space consists of hierarchical tree structures. In our formulation, these polynomial functions are represented as binary trees. The Lyapunov conditions for exponential stability are interpreted as a minimax optimization problem, using a carefully designed fitness metric to ensure positivity and dissipation within a chosen domain. The genetic algorithm then evolves candidate polynomial trees, minimizing constraint violations and continuously refining stability guarantees. Numerical examples illustrate that this methodology can effectively identify and optimize Lyapunov functions for a wide range of systems, indicating a promising direction for automated stability proofs in engineering applications. Full article

(This article belongs to the Special Issue Modern Trends and Application of Decision-Making Theory, Stability and Control)

► Show Figures

Figure 1

21 pages, 331 KiB

Open AccessArticle

Optimality Conditions and Stability Analysis for the Second-Order Cone Constrained Variational Inequalities

by Li Wang, Yining Sun, Juhe Sun, Yanhong Yuan and Bin Wang

Axioms 2025, 14(5), 342; https://doi.org/10.3390/axioms14050342 - 29 Apr 2025

Viewed by 109

Abstract

In this paper, we study the optimality conditions and perform a stability analysis for the second-order cone constrained variational inequalities (SOCCVI) problem. The Lagrange function and Karush–Kuhn–Tucker (KKT) condition of the SOCCVI problem is given, and the optimality conditions for the SOCCVI problem [...] Read more.

In this paper, we study the optimality conditions and perform a stability analysis for the second-order cone constrained variational inequalities (SOCCVI) problem. The Lagrange function and Karush–Kuhn–Tucker (KKT) condition of the SOCCVI problem is given, and the optimality conditions for the SOCCVI problem are studied. Then, the second-order sufficient condition satisfying the constrained nondegenerate condition is proved. The strong second-order sufficient condition is defined. And the nonsingularity of Clarke’s generalized Jacobian of the KKT point, the strong regularity of the KKT point, the uniform second-order growth condition, the strong stability of the KKT point, and the local Lipschtiz homeomorphism of the KKT point for the SOCCVI problem are proved to be equivalent to each other. Then, the stability theorem of the SOCCVI problem is obtained. Full article

(This article belongs to the Section Mathematical Analysis)

21 pages, 678 KiB

Open AccessArticle

On the Bivariate Vector-Valued Rational Interpolation and Recovery Problems

by Lixia Xiao, Peng Xia and Shugong Zhang

Axioms 2025, 14(5), 341; https://doi.org/10.3390/axioms14050341 - 29 Apr 2025

Viewed by 133

Abstract

This paper investigates bivariate vector-valued rational interpolation and recovery problems with common divisors in their denominators. By leveraging these shared divisors and employing a component-wise rational interpolation approach, we reduce the degree of the interpolation problem. Furthermore, a new algorithm for recovering bivariate [...] Read more.

This paper investigates bivariate vector-valued rational interpolation and recovery problems with common divisors in their denominators. By leveraging these shared divisors and employing a component-wise rational interpolation approach, we reduce the degree of the interpolation problem. Furthermore, a new algorithm for recovering bivariate vector-valued rational functions is proposed. Experimental results demonstrate that, compared to classical algorithms, our method achieves faster computation speed without compromising accuracy. This advantage is particularly evident in the recovery of bivariate vector-valued rational functions. Full article

► Show Figures

Figure 1

19 pages, 324 KiB

Open AccessArticle

Sparse Robust Weighted Expectile Screening for Ultra-High-Dimensional Data

by Xianjun Wu, Pingping Han and Mingqiu Wang

Axioms 2025, 14(5), 340; https://doi.org/10.3390/axioms14050340 - 28 Apr 2025

Viewed by 111

Abstract

This paper investigates robust feature screening for ultra-high dimensional data in the presence of outliers and heterogeneity. Considering the susceptibility of likelihood methods to outliers, we propose a Sparse Robust Weighted Expectile Regression (SRoWER) method that combines the

L_{2} E

criterion with [...] Read more.

This paper investigates robust feature screening for ultra-high dimensional data in the presence of outliers and heterogeneity. Considering the susceptibility of likelihood methods to outliers, we propose a Sparse Robust Weighted Expectile Regression (SRoWER) method that combines the

L_{2} E

criterion with expectile regression. By utilizing the IHT algorithm, our method effectively incorporates correlations of covariates and enables joint feature screening. The proposed approach demonstrates robustness against heavy-tailed errors and outliers in data. Simulation studies and a real data analysis are provided to demonstrate the superior performance of the SRoWER method when dealing with outlier-contaminated explanatory variables and/or heavy-tailed error distributions. Full article

(This article belongs to the Section Mathematical Physics)

12 pages, 1106 KiB

Open AccessArticle

A Penalized Orthogonal Kriging Method for Selecting a Global Trend

by Xituo Zhang, Guoxing Gao, Jianxin Zhao and Xinmin Li

Axioms 2025, 14(5), 339; https://doi.org/10.3390/axioms14050339 - 28 Apr 2025

Viewed by 134

Abstract

A kriging regression model is a popular and effective type of surrogate model in computer experiments. A significant challenge arises when the mean function of the model includes polynomial terms with unknown coefficients, leading to identifiability problems and potentially unreliable results. To overcome [...] Read more.

A kriging regression model is a popular and effective type of surrogate model in computer experiments. A significant challenge arises when the mean function of the model includes polynomial terms with unknown coefficients, leading to identifiability problems and potentially unreliable results. To overcome this problem, Plumlee and Joseph (2018) introduced an orthogonal kriging model. Variable selection for kriging models has been widely considered by researchers in computer experiments. In this paper, we introduce a new method for combining orthogonal kriging with penalized variable selection. Furthermore, an efficient algorithm is given to select the correct mean function. The simulation results and an example study with real data show that the proposed method is superior to others in variable recognition rate and prediction accuracy. Full article

► Show Figures

Figure 1

22 pages, 307 KiB

Open AccessArticle

An Investigation into Bipolar Fuzzy Hoop Algebras and Their Applications

by Tahsin Oner, Rajesh Neelamegarajan, Ravi Kumar Bandaru and Hashem Bordbar

Axioms 2025, 14(5), 338; https://doi.org/10.3390/axioms14050338 - 28 Apr 2025

Viewed by 115

Abstract

This paper introduces bipolar fuzzy sub-hoops and bipolar fuzzy filters within hoop algebras, extending fuzzy logic to incorporate both positive and negative membership degrees. We define these structures, explore their algebraic properties, and establish their interplay through rigorous theorems. Key results include characterizations [...] Read more.

This paper introduces bipolar fuzzy sub-hoops and bipolar fuzzy filters within hoop algebras, extending fuzzy logic to incorporate both positive and negative membership degrees. We define these structures, explore their algebraic properties, and establish their interplay through rigorous theorems. Key results include characterizations of bipolar fuzzy filters via level sets and conditions under which they become implicative filters. These findings enhance the theoretical framework of many-valued logic and offer practical applications in decision-making, image processing, and spatial reasoning under uncertainty. Our work provides a foundation for advanced fuzzy systems handling complex, contradictory information. Full article

(This article belongs to the Special Issue Computational Algebra, Coding Theory and Cryptography: Theory and Applications, 2nd Edition)

21 pages, 929 KiB

Open AccessArticle

Involute Partner-Ruled Surfaces Formed by Involutes of Spacelike Curves in Minkowski Three-Space

by Özgür Boyacıoğlu Kalkan, Süleyman Şenyurt, Davut Canlı and Luca Grilli

Axioms 2025, 14(5), 337; https://doi.org/10.3390/axioms14050337 - 28 Apr 2025

Viewed by 229

Abstract

We introduced the concept of involute partner-ruled surfaces, which are formed by the involutes of spacelike curves and additional conditions ensuring the presence of definite surface normals in Minkowski three-space. First, we provided the criteria for each couple of involute partner-ruled surfaces to [...] Read more.

We introduced the concept of involute partner-ruled surfaces, which are formed by the involutes of spacelike curves and additional conditions ensuring the presence of definite surface normals in Minkowski three-space. First, we provided the criteria for each couple of involute partner-ruled surfaces to be simultaneously developable and minimal. Then, we established the requirements for the coordinate curves lying on these surfaces to be geodesic, asymptotic, and lines of curvature. We also expanded this paper with an example by providing graphical illustrations of the involute partner-ruled surfaces. Full article

(This article belongs to the Section Geometry and Topology)

► Show Figures

Figure 1

13 pages, 280 KiB

Open AccessArticle

Exploring Geometrical Properties of Annihilator Intersection Graph of Commutative Rings

by Ali Al Khabyah and Moin A. Ansari

Axioms 2025, 14(5), 336; https://doi.org/10.3390/axioms14050336 - 27 Apr 2025

Viewed by 161

Abstract

Let

Λ

denote a commutative ring with unity and

D (Λ)

denote a collection of all annihilating ideals from

Λ

. An annihilator intersection graph of

Λ

is represented by the notation

AIG (Λ)

. This graph is not [...] Read more.

Let

Λ

denote a commutative ring with unity and

D (Λ)

denote a collection of all annihilating ideals from

Λ

. An annihilator intersection graph of

Λ

is represented by the notation

AIG (Λ)

. This graph is not directed in nature, where the vertex set is represented by

D {(Λ)}^{*}

. There is a connection in the form of an edge between two distinct vertices

ς

and

ϱ

in

AIG (Λ)

iff

A n n (ς ϱ) \neq A n n (ς) \cap A n n (ϱ)

. In this work, we begin by categorizing commutative rings

Λ

, which are finite in structure, so that

AIG (Λ)

forms a star graph/2-outerplanar graph, and we identify the inner vertex number of

AIG (Λ)

. In addition, a classification of the finite rings where the genus of

AIG (Λ)

is 2, meaning

AIG (Λ)

is a double-toroidal graph, is also investigated. Further, we determine

Λ

, having a crosscap 1 of

AIG (Λ),

indicating that

AIG (Λ)

is a projective plane. Finally, we examine the domination number for the annihilator intersection graph and demonstrate that it is at maximum, two. Full article

► Show Figures

Figure 1

11 pages, 278 KiB

Open AccessArticle

On the Action of a Subgroup of the Modular Group on Imaginary Quadratic Number Fields

by Abdulaziz Deajim

Axioms 2025, 14(5), 335; https://doi.org/10.3390/axioms14050335 - 27 Apr 2025

Viewed by 128

Abstract

Consider the modular group

PSL (2, Z) = ⟨ x, y | x^{2} = y^{3} = 1 ⟩

generated by the transformations

x : z \mapsto - 1 / z

and [...] Read more.

Consider the modular group

PSL (2, Z) = ⟨ x, y | x^{2} = y^{3} = 1 ⟩

generated by the transformations

x : z \mapsto - 1 / z

and

y : z \mapsto (z - 1) / z

. Let H be the proper subgroup

⟨ y, v | y^{3} = v^{3} = 1 ⟩

of

PSL (2, Z)

, where

v = x y x

. For a positive square-free integer n, this article studies the action of H on the subset

{\frac{a + \sqrt{- n}}{c} | a, b = \frac{a^{2} + n}{c}, c \in Z, c \neq 0}

of the imaginary quadratic number field

Q (\sqrt{- n})

where, in particular, the accurate estimate of the number of orbits arising from this action is given, correcting the estimate given in some of the relevant literature. Full article

(This article belongs to the Special Issue Elliptic Curves, Modular Forms, L-Functions and Applications)

17 pages, 524 KiB

Open AccessArticle

Closed-Form Meromorphic Solutions of High-Order and High-Dimensional Differential Equations

by Hongqiang Tu and Yongyi Gu

Axioms 2025, 14(5), 334; https://doi.org/10.3390/axioms14050334 - 27 Apr 2025

Viewed by 100

Abstract

In this paper, we investigate closed-form meromorphic solutions of the fifth-order Sawada-Kotera (fSK) equation and (3+1)-dimensional generalized shallow water (gSW) equation. The study of high-order and high-dimensional differential equations is pivotal for modeling complex nonlinear phenomena in physics and engineering, where higher-order dispersion, [...] Read more.

In this paper, we investigate closed-form meromorphic solutions of the fifth-order Sawada-Kotera (fSK) equation and (3+1)-dimensional generalized shallow water (gSW) equation. The study of high-order and high-dimensional differential equations is pivotal for modeling complex nonlinear phenomena in physics and engineering, where higher-order dispersion, dissipation, and multidimensional dynamics govern system behavior. Constructing explicit solutions is of great significance for the study of these equations. The elliptic, hyperbolic, rational, and exponential function solutions for these high-order and high-dimensional differential equations are achieved by proposing the extended complex method. The planar dynamics behavior of the (3+1)-dimensional gSW equation and its phase portraits are analyzed. Using computational simulation, the chaos behaviors of the high-dimensional differential equation under noise perturbations are examined. The dynamic structures of some obtained solutions are revealed via some 2D and 3D graphs. The results show that the extended complex method is an efficient and straightforward approach to solving diverse differential equations in mathematical physics. Full article

(This article belongs to the Special Issue Recent Advances in Complex Analysis and Related Topics)

► Show Figures

Figure 1

21 pages, 382 KiB

Open AccessArticle

Idealizing Rough Topological Structures Generated by Several Types of Maximal Neighborhoods and Exploring Their Applications

by Mona Hosny

Axioms 2025, 14(5), 333; https://doi.org/10.3390/axioms14050333 - 27 Apr 2025

Viewed by 116

Abstract

Several different topologies utilizing ideals are created and compared with previous topologies. The results show that the previous ones are weaker than the current ones and that the current ones are stronger. The merits of these topologies are proposed, and the smallest and [...] Read more.

Several different topologies utilizing ideals are created and compared with previous topologies. The results show that the previous ones are weaker than the current ones and that the current ones are stronger. The merits of these topologies are proposed, and the smallest and largest among them are identified; this merit distinguishes the present study from previous ones. Afterwards, these topologies are employed to conduct more in-depth investigations on broadened rough sets. The proposed approximate models are particularly significant as applied to rough sets because they diminish vagueness and uncertainty compared to prior models. Moreover, the proposed models stand out from their predecessors because they can compare all types of approximations, display all the features described by Pawlak, and possess the property of monotonicity across any relations. Furthermore, a medical application is showcased to emphasize the significance of the current findings. Additionally, the advantages of the adopted approach are examined, alongside an evaluation of its limitations. The paper wraps up with the essential features of the proposed manner and recommend avenues for future research. Full article

(This article belongs to the Special Issue Topics in General Topology and Applications)

16 pages, 416 KiB

Open AccessArticle

Compositional Scheduling in Industry 4.0 Cyber-Physical Systems

by Fernando Tohmé and Daniel Rossit

Axioms 2025, 14(5), 332; https://doi.org/10.3390/axioms14050332 - 27 Apr 2025

Viewed by 195

Abstract

Cyber-physical systems (CPSs) are fundamental components of Industry 4.0 production environments. Their interconnection is crucial for the successful implementation of distributed and autonomous production plans. A particularly relevant challenge is the optimal scheduling of tasks that require the collaboration of multiple CPSs. To [...] Read more.

Cyber-physical systems (CPSs) are fundamental components of Industry 4.0 production environments. Their interconnection is crucial for the successful implementation of distributed and autonomous production plans. A particularly relevant challenge is the optimal scheduling of tasks that require the collaboration of multiple CPSs. To ensure the feasibility of optimal schedules, two primary issues must be addressed: (1) The design of global systems emerging from the interconnection of CPSs; (2) The development of a scheduling formalism tailored to interconnected Industry 4.0 settings. Our approach is based on a Category Theory formalization of interconnections as compositions. This framework aims to guarantee that the emergent behaviors align with the intended outcomes. Building upon this foundation, we introduce a formalism that captures the assignment of operations to cyber-physical systems. Full article

► Show Figures

Figure 1

28 pages, 333 KiB

Open AccessArticle

Bipolar Fuzzy Sheffer Stroke in BCK-Algebras

by Tahsin Oner, Rajesh Neelamegarajan, Ravi Kumar Bandaru and Amal S. Alali

Axioms 2025, 14(5), 331; https://doi.org/10.3390/axioms14050331 - 26 Apr 2025

Viewed by 152

Abstract

In this study, we examine bipolar fuzzy SBCK-subalgebras and their corresponding level sets of bipolar fuzzy sets in the setting of Sheffer stroke BCK-algebras. These concepts contribute significantly to the analysis of bipolar logical structures within this algebraic context. We demonstrate a bidirectional [...] Read more.

In this study, we examine bipolar fuzzy SBCK-subalgebras and their corresponding level sets of bipolar fuzzy sets in the setting of Sheffer stroke BCK-algebras. These concepts contribute significantly to the analysis of bipolar logical structures within this algebraic context. We demonstrate a bidirectional relationship between SBCK-subalgebras and their level sets, proving that each level set derived from a bipolar fuzzy SBCK-subalgebra constitutes a subalgebra, and, conversely, each such subalgebra defines an associated level set. This duality emphasizes the structural interplay between bipolar fuzzy logic and the Sheffer stroke operation in BCK-algebras. Full article

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

30 pages, 515 KiB

Open AccessArticle

Parameter Estimation of the Lomax Lifetime Distribution Based on Middle-Censored Data: Methodology, Applications, and Comparative Analysis

by Peiyao Ren, Wenhao Gui and Shan Liang

Axioms 2025, 14(5), 330; https://doi.org/10.3390/axioms14050330 - 26 Apr 2025

Viewed by 246

Abstract

The Lomax distribution has important applications in survival analysis, reliability engineering, insurance, finance, and other fields. Middle-censoring is an important censoring scheme, and data with middle-censoring will produce censoring in random intervals. This paper studies the parameter estimation of the Lomax distribution based [...] Read more.

The Lomax distribution has important applications in survival analysis, reliability engineering, insurance, finance, and other fields. Middle-censoring is an important censoring scheme, and data with middle-censoring will produce censoring in random intervals. This paper studies the parameter estimation of the Lomax distribution based on middle-censored data. The expectation–maximization algorithm is employed to compute the maximum likelihood estimates of the two unknown parameters of the Lomax distribution. After processing the data using the midpoint approach estimation, the parameter estimates are obtained by two computational methods: the Newton–Raphson iteration method and the fixed-point method. Moreover, the calculation methods for the asymptotic confidence intervals of the two parameters are provided, with the confidence interval coverage rate serving as one of the criteria for evaluating the estimation performance. In the Bayesian estimation aspect, the shape parameter is estimated using a Gamma prior distribution, and the Gibbs sampling method is employed for the solution. Finally, both simulation data and real data are used to compare the accuracy of the various estimation methods. Full article

(This article belongs to the Special Issue Computational Statistics and Its Applications)

► Show Figures

Figure 1

18 pages, 293 KiB

Open AccessArticle

Existence and Controls for Fractional Evolution Equations

by Ying Chen and Yong Zhou

Axioms 2025, 14(5), 329; https://doi.org/10.3390/axioms14050329 - 24 Apr 2025

Viewed by 165

Abstract

In this paper, we investigate the existence and uniqueness of mild solutions for non-autonomous fractional evolution equations (NFEEs) using the technique of non-compactness measure, focusing on scenarios where the semigroup is non-compact. Furthermore, the optimal control of nonlinear NFEEs with integral index functionals [...] Read more.

In this paper, we investigate the existence and uniqueness of mild solutions for non-autonomous fractional evolution equations (NFEEs) using the technique of non-compactness measure, focusing on scenarios where the semigroup is non-compact. Furthermore, the optimal control of nonlinear NFEEs with integral index functionals is studied, and the existence of optimal control pairs is proven. Finally, by constructing a corresponding Gramian controllability operator using the solution operator, a sufficient condition is provided for the existence of approximate controllability of the corresponding problem. Full article

(This article belongs to the Special Issue Nonlinear Fractional Differential Equations: Theory and Applications)

16 pages, 2342 KiB

Open AccessArticle

Improving Safety Awareness Campaigns Through the Use of Graph Neural Networks

by Jose D. Hernández Guillén and Angel Martín del Rey

Axioms 2025, 14(5), 328; https://doi.org/10.3390/axioms14050328 - 24 Apr 2025

Viewed by 159

Abstract

Phishing is one of the main threats against companies where the main weakness against this type of threat is the worker. For this reason, it is essential that workers have a high security awareness for which it is fundamental to carry out a [...] Read more.

Phishing is one of the main threats against companies where the main weakness against this type of threat is the worker. For this reason, it is essential that workers have a high security awareness for which it is fundamental to carry out a good safety-awareness campaign. However, as far as we are concerned, a mathematical study of the evolution of security awareness taking into account interactions with other people has not been considered. In this paper, we study how security awareness evolves through two belief-propagation models and Graph Neural Networks. Since this approach is new, the two most basic models were chosen to simulate propagation of beliefs: Sznajd model variant and Hegselmann–Krause model. On the other hand, because Graph Neural Networks are a current and very powerful tool, it was decided to use them to analyze the evolution of beliefs. We consider that with them information-awareness campaigns can be improved. As an example, we propose different awareness measures according to future beliefs and social influence. Full article

(This article belongs to the Section Mathematical Analysis)

► Show Figures

Figure A1

19 pages, 329 KiB

Open AccessArticle

Symbol-Pair Distances of a Class of Repeated-Root Constacyclic Codes of Length np^s over

F_{p^{m}}

and over

F_{p^{m}} + u F_{p^{m}}

by Wei Zhao, Weixian Li and Hui Chen

Axioms 2025, 14(5), 327; https://doi.org/10.3390/axioms14050327 - 24 Apr 2025

Viewed by 218

Abstract

Symbol-pair codes are a class of block codes with symbol-pair metrics designed to protect against pair errors that may occur in high-density data storage systems. Maximum distance separable (MDS) symbol-pair codes are optimal in the sense that they can attain the highest pair-error [...] Read more.

Symbol-pair codes are a class of block codes with symbol-pair metrics designed to protect against pair errors that may occur in high-density data storage systems. Maximum distance separable (MDS) symbol-pair codes are optimal in the sense that they can attain the highest pair-error correctability within the same code length and code size. Constructing MDS symbol-pair codes is one of the main topics in symbol-pair code research. In this paper, we investigate and characterize the symbol-pair distances of constacyclic codes of arbitrary lengths over finite fields and finite chain rings. Using the characterization of the symbol-pair distance, we present three new classes of MDS symbol-pair constacyclic codes that exhibit large minimum distances. Full article

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

3 pages, 123 KiB

Open AccessEditorial

Advances in Dynamical Systems and Control

by Selene Lilette Cardenas-Maciel, Jorge Antonio Lopez-Renteria and Nohe Ramon Cazarez-Castro

Axioms 2025, 14(5), 326; https://doi.org/10.3390/axioms14050326 - 23 Apr 2025

Viewed by 125

Abstract

In this Editorial, we present “Advances in Dynamical Systems and Control”, a Special Issue of Axioms [...] Full article

(This article belongs to the Special Issue Advances in Dynamical Systems and Control)

13 pages, 254 KiB

Open AccessArticle

Ricci Solitons on Riemannian Hypersurfaces Generated by Torse-Forming Vector Fields in Riemannian and Lorentzian Manifolds

by Norah Alshehri and Mohammed Guediri

Axioms 2025, 14(5), 325; https://doi.org/10.3390/axioms14050325 - 23 Apr 2025

Viewed by 132

Abstract

In this paper, we examine torse-forming vector fields to characterize extrinsic spheres (that is, totally umbilical hypersurfaces with nonzero constant mean curvatures) in Riemannian and Lorentzian manifolds. First, we analyze the properties of these vector fields on Riemannian manifolds. Next, we focus on [...] Read more.

In this paper, we examine torse-forming vector fields to characterize extrinsic spheres (that is, totally umbilical hypersurfaces with nonzero constant mean curvatures) in Riemannian and Lorentzian manifolds. First, we analyze the properties of these vector fields on Riemannian manifolds. Next, we focus on Ricci solitons on Riemannian hypersurfaces induced by torse-forming vector fields of Riemannian or Lorentzian manifolds. Specifically, we show that such a hypersurface in the manifold with constant sectional curvature is either totally geodesic or an extrinsic sphere. Full article

Journal Menu

Journal Browser

Axioms, Volume 14, Issue 5 (May 2025) – 32 articles

Further Information

Guidelines

MDPI Initiatives

Follow MDPI