You seem to have javascript disabled. Please note that many of the page functionalities won't work as expected without javascript enabled.

Search for Articles:

Title / Keyword

Author / Affiliation / Email

Journal

Article Type

Advanced Search

Section

Special Issue

Volume

Issue

Number

Page

Logical OperatorOperator

Search Text

Search Type

Journal Description

Axioms

Axioms is an international, peer-reviewed, open access journal of mathematics, mathematical logic and mathematical physics, published monthly online by MDPI. The European Society for Fuzzy Logic and Technology (EUSFLAT), International Fuzzy Systems Association (IFSA), Union of Slovak Mathematicians and Physicists (JSMF) and Eurekas Community are affiliated with Axioms and their members receive discounts on the article processing charges.

Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
High visibility: indexed within SCIE (Web of Science), dblp, and other databases.
Journal Rank: JCR - Q2 (Mathematics, Applied)
Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 21.6 days after submission; acceptance to publication is undertaken in 2.8 days (median values for papers published in this journal in the first half of 2025).
Recognition of Reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.
Companion journal: Logics.

Impact Factor: 1.6 (2024); 5-Year Impact Factor: 1.5 (2024)

Imprint Information Journal Flyer Open Access ISSN: 2075-1680

Latest Articles

22 pages, 481 KiB

Open AccessArticle

Fuzzy Signature from Computational Diffie–Hellman Assumption in the Standard Model

by Yunhua Wen, Tianlong Jin and Wei Li

Axioms 2025, 14(8), 613; https://doi.org/10.3390/axioms14080613 (registering DOI) - 6 Aug 2025

Fuzzy signature (

{SIG}_{F}

) is a type of digital signature that preserves the core functionalities of traditional signatures, while accommodating variations and non-uniformity in the signing key. This property enables the direct use of high-entropy fuzzy data, such as biometric information, [...] Read more.

Fuzzy signature (

{SIG}_{F}

) is a type of digital signature that preserves the core functionalities of traditional signatures, while accommodating variations and non-uniformity in the signing key. This property enables the direct use of high-entropy fuzzy data, such as biometric information, as the signing key. In this paper, we define the m-existentially unforgeable under chosen message attack (

m {- EUF - CMA}^{*}

) security of fuzzy signature. Furthermore, we propose a generic construction of fuzzy signature, which is composed of a homomorphic secure sketch (

SS

) with an error-recoverable property, a homomorphic average-case strong extractor (

Ext

), and a homomorphic and key-shift* secure signature scheme (

SIG

). By instantiating the foundational components, we present a

m {- EUF - CMA}^{*}

secure fuzzy signature instantiation based on the Computational Diffie–Hellman (CDH) assumption over bilinear groups in the standard model. Full article

► Show Figures

Figure 1

20 pages, 360 KiB

Open AccessArticle

Parabolic and Linear Rotational Motions on Cones and Hyperboloids

by Harun Barış Çolakoğlu, Mehmet Duru and Ayşe Yılmaz Ceylan

Axioms 2025, 14(8), 612; https://doi.org/10.3390/axioms14080612 (registering DOI) - 6 Aug 2025

In this study, we consider the Lorentzian rotation about a lightlike axis. First, we introduce a geometric characterization for the rotation angle between two vectors that can overlap each other under a Lorentzian rotation about a lightlike axis. Then, we give a definition [...] Read more.

In this study, we consider the Lorentzian rotation about a lightlike axis. First, we introduce a geometric characterization for the rotation angle between two vectors that can overlap each other under a Lorentzian rotation about a lightlike axis. Then, we give a definition for the angle measurement between two spacelike vectors whose vector product is lightlike. Later, we generalize the Lorentzian rotation about a lightlike axis, and determine matrices of these transformations using the Cartan frame and the well-known Rodrigues formula, then using the Cayley map, and finally using the generalized split quaternions. We see that such transformations give parabolic rotational motions on general cones or general hyperboloids of one or two sheets, while they also give linear rotational motions on general hyperboloids of one sheet. Full article

(This article belongs to the Section Geometry and Topology)

23 pages, 311 KiB

Open AccessArticle

Some Results on Maxima and Minima of Real Functions of Vector Variables: A New Perspective

by Bibiano Martin Cerna Maguiña, Dik Dani Lujerio Garcia, Victor Pocoy Yauri, Vladimir Giovanni Rodriguez Sabino and Ruben Mario Leiva Bernuy

Axioms 2025, 14(8), 611; https://doi.org/10.3390/axioms14080611 - 6 Aug 2025

This article presents a method for proving several theorems that enable the determination of the maxima and minima of certain classes of real-valued functions with vector variables, without relying on the classical theory based on partial derivatives. However, the main objective of this [...] Read more.

This article presents a method for proving several theorems that enable the determination of the maxima and minima of certain classes of real-valued functions with vector variables, without relying on the classical theory based on partial derivatives. However, the main objective of this work is not to compare this approach with existing methods but, rather, to extend the study of extrema in real functions of vector variables that are not differentiable, as illustrated in Example 1. Each theorem is accompanied by various examples that demonstrate its applicability. The results are based on Theorems 1 and 2, as well as the selection of an appropriate connection between Theorem 2 and the functions to be optimized. Additionally, definitions related to the hierarchy between variables within a given domain are introduced, providing the theoretical framework necessary for the development of the proposed results. Full article

25 pages, 4865 KiB

Open AccessArticle

Mathematical Modeling, Bifurcation Theory, and Chaos in a Dusty Plasma System with Generalized (r^⋆, q^⋆) Distributions

by Beenish, Maria Samreen and Fehaid Salem Alshammari

Axioms 2025, 14(8), 610; https://doi.org/10.3390/axioms14080610 - 5 Aug 2025

This study investigates the dynamics of dust acoustic periodic waves in a three-component, unmagnetized dusty plasma system using generalized

(r^{⋆}, q^{⋆})

distributions. First, boundary conditions are applied to reduce the model to a second-order nonlinear ordinary differential equation. [...] Read more.

This study investigates the dynamics of dust acoustic periodic waves in a three-component, unmagnetized dusty plasma system using generalized

(r^{⋆}, q^{⋆})

distributions. First, boundary conditions are applied to reduce the model to a second-order nonlinear ordinary differential equation. The Galilean transformation is subsequently applied to reformulate the second-order ordinary differential equation into an unperturbed dynamical system. Next, phase portraits of the system are examined under all possible conditions of the discriminant of the associated cubic polynomial, identifying regions of stability and instability. The Runge–Kutta method is employed to construct the phase portraits of the system. The Hamiltonian function of the unperturbed system is subsequently derived and used to analyze energy levels and verify the phase portraits. Under the influence of an external periodic perturbation, the quasi-periodic and chaotic dynamics of dust ion acoustic waves are explored. Chaos detection tools confirm the presence of quasi-periodic and chaotic patterns using Basin of attraction, Lyapunov exponents, Fractal Dimension, Bifurcation diagram, Poincaré map, Time analysis, Multi-stability analysis, Chaotic attractor, Return map, Power spectrum, and 3D and 2D phase portraits. In addition, the model’s response to different initial conditions was examined through sensitivity analysis. Full article

(This article belongs to the Special Issue Trends in Dynamical Systems and Applied Mathematics)

► Show Figures

Figure 1

16 pages, 343 KiB

Open AccessArticle

Structured Distance to Normality of Dirichlet–Neumann Tridiagonal Toeplitz Matrices

by Zhaolin Jiang, Hongxiao Chu, Qiaoyun Miao and Ziwu Jiang

Axioms 2025, 14(8), 609; https://doi.org/10.3390/axioms14080609 - 5 Aug 2025

This paper conducts a rigorous study on the spectral properties and operator-space distances of perturbed Dirichlet–Neumann tridiagonal (PDNT) Toeplitz matrices, with emphasis on their asymptotic behaviors. We establish explicit closed-form solutions for the eigenvalues and associated eigenvectors, highlighting their fundamental importance for characterizing [...] Read more.

This paper conducts a rigorous study on the spectral properties and operator-space distances of perturbed Dirichlet–Neumann tridiagonal (PDNT) Toeplitz matrices, with emphasis on their asymptotic behaviors. We establish explicit closed-form solutions for the eigenvalues and associated eigenvectors, highlighting their fundamental importance for characterizing matrix stability in the presence of perturbations. By exploiting the structural characteristics of PDNT Toeplitz matrices, we obtain closed-form expressions quantifying the distance to normality, the deviation from normality. Full article

► Show Figures

Figure 1

19 pages, 317 KiB

Open AccessFeature PaperArticle

New Class of Specific Functions with Fractional Derivatives

by Hatun Özlem Güney and Shigeyoshi Owa

Axioms 2025, 14(8), 608; https://doi.org/10.3390/axioms14080608 - 5 Aug 2025

Let

A_{n}

be the class of specific analytic functions [...] Read more.

Let

A_{n}

be the class of specific analytic functions

f (z) = z + \sum_{k = 1}^{\infty} a_{1 + \frac{k}{n}} z^{1 + \frac{k}{n}} (n \in N = {1, 2, 3, \dots})

in the open unit disk

U .

For

f (z) \in A_{n},

fractional derivatives

D_{z}^{λ} f (z)

and

D_{z}^{j + λ} f (z)

(0 \leq λ < 1, j \in N)

are defined by using Gamma functions. Applying such fractional derivatives, we introduce a new subclass

A_{n} (j, λ, α, β)

of

A_{n} .

In this paper, we establish sufficient conditions for

f (z)

for

A_{n} (j, λ, α, β),

coefficient inequalities for

| a_{1 + \frac{1}{n}} |

and

| a_{1 + \frac{k}{n}} |

(k = 2, 3, 4, \dots)

of

f (z) \in A_{n} (j, λ, α, β),

and some interesting argument properties of fractional derivatives for

f (z) \in A_{n}

through an example. Full article

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

24 pages, 362 KiB

Open AccessArticle

Critical Sets and Unavoidable Sets of Strictly Concentric Magic Squares of Odd Order and Their Application to Prime Strictly Concentric Magic Squares of Order 5

by Anna Louise Skelt, Stephanie Perkins and Paul Alun Roach

Axioms 2025, 14(8), 607; https://doi.org/10.3390/axioms14080607 - 4 Aug 2025

There has been much interest in the mathematical investigation of critical sets and unavoidable sets in Latin Squares, Sudoku, and their applications to practical problems in areas such as agriculture and cryptology. This paper considers the associated structures of Strictly Concentric Magic Squares [...] Read more.

There has been much interest in the mathematical investigation of critical sets and unavoidable sets in Latin Squares, Sudoku, and their applications to practical problems in areas such as agriculture and cryptology. This paper considers the associated structures of Strictly Concentric Magic Squares (SCMSs) and Prime Strictly Concentric Magic Squares (PSCMSs). A framework of formal definitions is given that leads to the definitions of critical sets and unavoidable sets. Minimal critical sets are of interest in Latin Squares, and in this article, the cardinality of minimal critical sets of SCMS is given for all n, n odd. Two families of unavoidable sets are established for SCMS, leading to a complete classification of unavoidable sets of minimum PSCMS of order 5. Full article

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

► Show Figures

Figure 1

20 pages, 390 KiB

Open AccessArticle

Injective Hulls of Infinite Totally Split-Decomposable Metric Spaces

by Maël Pavón

Axioms 2025, 14(8), 606; https://doi.org/10.3390/axioms14080606 - 4 Aug 2025

We extend the theory of splits in finite metric spaces to infinite ones. Within this more general framework, we investigate the class of spaces having metrics that are integer-valued and totally split-decomposable, as well as the polyhedral complex structure of their injective hulls. [...] Read more.

We extend the theory of splits in finite metric spaces to infinite ones. Within this more general framework, we investigate the class of spaces having metrics that are integer-valued and totally split-decomposable, as well as the polyhedral complex structure of their injective hulls. For this class, we provide a characterization for the injective hull to be combinatorially equivalent to a CAT(0) cube complex. Intermediate results include the generalization of the decomposition theory introduced by Bandelt and Dress in 1992 as well as results on the tight span of totally split-decomposable metric spaces proved by Huber, Koolen, and Moulton in 2006. Next, using results of Lang from 2013, we obtain proper actions on CAT(0) cube complexes for finitely generated groups endowed with a totally split-decomposable word metric and for which the associated splits satisfy a simple combinatorial property. In the case of Gromov hyperbolic groups, the obtained action is both proper aand co-compact. Finally, we obtain as an application that injective hulls of odd cycles are cell complexes isomorphic to CAT(0) cube complexes. Full article

(This article belongs to the Section Geometry and Topology)

► Show Figures

Graphical abstract

17 pages, 2693 KiB

Open AccessArticle

Mitigating the Drawbacks of the L₀ Norm and the Total Variation Norm

by Gengsheng L. Zeng

Axioms 2025, 14(8), 605; https://doi.org/10.3390/axioms14080605 - 4 Aug 2025

In compressed sensing, it is believed that the L₀ norm minimization is the best way to enforce a sparse solution. However, the L₀ norm is difficult to implement in a gradient-based iterative image reconstruction algorithm. The total variation (TV) norm minimization [...] Read more.

In compressed sensing, it is believed that the L₀ norm minimization is the best way to enforce a sparse solution. However, the L₀ norm is difficult to implement in a gradient-based iterative image reconstruction algorithm. The total variation (TV) norm minimization is considered a proper substitute for the L₀ norm minimization. This paper points out that the TV norm is not powerful enough to enforce a piecewise-constant image. This paper uses the limited-angle tomography to illustrate the possibility of using the L₀ norm to encourage a piecewise-constant image. However, one of the drawbacks of the L₀ norm is that its derivative is zero almost everywhere, making a gradient-based algorithm useless. Our novel idea is to replace the zero value of the L₀ norm derivative with a zero-mean random variable. Computer simulations show that the proposed L₀ norm minimization outperforms the TV minimization. The novelty of this paper is the introduction of some randomness in the gradient of the objective function when the gradient is zero. The quantitative evaluations indicate the improvements of the proposed method in terms of the structural similarity (SSIM) and the peak signal-to-noise ratio (PSNR). Full article

(This article belongs to the Special Issue Advances in Mathematical Methods in Signal Processing and Its Applications)

► Show Figures

Figure 1

14 pages, 403 KiB

Open AccessArticle

An Inexact Nonsmooth Quadratic Regularization Algorithm

by Anliang Wang, Xiangmei Wang and Chunfang Liao

Axioms 2025, 14(8), 604; https://doi.org/10.3390/axioms14080604 - 4 Aug 2025

The quadratic regularization technique is widely used in the literature for constructing efficient algorithms, particularly for solving nonsmooth optimization problems. We propose an inexact nonsmooth quadratic regularization algorithm for solving large-scale optimization, which involves a large-scale smooth separable item and a nonsmooth one. [...] Read more.

The quadratic regularization technique is widely used in the literature for constructing efficient algorithms, particularly for solving nonsmooth optimization problems. We propose an inexact nonsmooth quadratic regularization algorithm for solving large-scale optimization, which involves a large-scale smooth separable item and a nonsmooth one. The main difference between our algorithm and the (exact) quadratic regularization algorithm is that it employs inexact gradients instead of the full gradients of the smooth item. Also, a slightly different update rule for the regularization parameters is adopted for easier implementation. Under certain assumptions, it is proved that the algorithm achieves a first-order approximate critical point of the problem, and the iteration complexity of the algorithm is

O (ε^{- 2})

. In the end, we apply the algorithm to solve LASSO problems. The numerical results show that the inexact algorithm is more efficient than the corresponding exact one in large-scale cases. Full article

► Show Figures

Figure 1

16 pages, 281 KiB

Open AccessArticle

Existence and Uniqueness of Solutions for Impulsive Stochastic Differential Variational Inequalities with Applications

by Wei Liu and Kui Liu

Axioms 2025, 14(8), 603; https://doi.org/10.3390/axioms14080603 - 3 Aug 2025

This paper focuses on exploring an impulsive stochastic differential variational inequality (ISDVI), which combines an impulsive stochastic differential equation and a stochastic variational inequality. Innovatively, our work incorporates two key aspects: first, our stochastic differential equation contains an impulsive term, enabling better handling [...] Read more.

This paper focuses on exploring an impulsive stochastic differential variational inequality (ISDVI), which combines an impulsive stochastic differential equation and a stochastic variational inequality. Innovatively, our work incorporates two key aspects: first, our stochastic differential equation contains an impulsive term, enabling better handling of sudden event impacts; second, we utilize a non-local condition

z (0) = χ_{0} + ϑ (z)

that integrates measurements from multiple locations to construct superior models. Methodologically, we commence our analysis by using the projection method, which ensures the existence and uniqueness of the solution to ISDVI. Subsequently, we showcase the practical applicability of our theoretical findings by implementing them in the investigation of a stochastic consumption process and electrical circuit model. Full article

► Show Figures

Figure 1

22 pages, 463 KiB

Open AccessArticle

Improved Bounds for Integral Jensen’s Inequality Through Fifth-Order Differentiable Convex Functions and Applications

by Sidra Nisar, Fiza Zafar and Hind Alamri

Axioms 2025, 14(8), 602; https://doi.org/10.3390/axioms14080602 - 2 Aug 2025

The main objective of this research is to obtain interesting estimates for Jensen’s gap in the integral sense, along with their applications. The convexity of a fifth-order absolute function is used to established proposed estimates of Jensen’s gap. We performed numerical computations to [...] Read more.

The main objective of this research is to obtain interesting estimates for Jensen’s gap in the integral sense, along with their applications. The convexity of a fifth-order absolute function is used to established proposed estimates of Jensen’s gap. We performed numerical computations to compare our estimates with previous findings. With the use of the primary findings, we are able to obtain improvements of the Hölder inequality and Hermite–Hadamard inequality. Furthermore, the primary results lead to some inequalities for power means and quasi-arithmetic means. We conclude by outlining the information theory applications of our primary inequalities. Full article

(This article belongs to the Special Issue Theory and Application of Integral Inequalities, 2nd Edition)

► Show Figures

Figure 1

23 pages, 1480 KiB

Open AccessArticle

Operator Newton Method for Large-Scale Coupled Riccati Equations Arising from Jump Systems

by Bo Yu, Yiwen Liu and Ning Dong

Axioms 2025, 14(8), 601; https://doi.org/10.3390/axioms14080601 - 1 Aug 2025

Consider a class of coupled discrete-time Riccati equations arising from jump systems. To compute their solutions when systems reach a steady state, we propose an operator Newton method and correspondingly establish its quadratic convergence under suitable assumptions. The advantage of the proposed method [...] Read more.

Consider a class of coupled discrete-time Riccati equations arising from jump systems. To compute their solutions when systems reach a steady state, we propose an operator Newton method and correspondingly establish its quadratic convergence under suitable assumptions. The advantage of the proposed method lies in the fact that its subproblems are solved using the operator Smith method, which allows it to maintain quadratic convergence in both the inner and outer iterations. Moreover, it does not require the constant term matrix of the equation to be invertible, making it more broadly applicable than existing inverse-free iterative methods. For large-scale problems, we develop a low-rank variant by incorporating truncation and compression techniques into the operator Newton framework. A complexity analysis is also provided to assess its scalability. Numerical experiments demonstrate that the presented low-rank operator Newton method is highly effective in approximating solutions to large-scale structured coupled Riccati equations. Full article

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

► Show Figures

Figure 1

15 pages, 322 KiB

Open AccessArticle

Characterization of the Best Approximation and Establishment of the Best Proximity Point Theorems in Lorentz Spaces

by Dezhou Kong, Zhihao Xu, Yun Wang and Li Sun

Axioms 2025, 14(8), 600; https://doi.org/10.3390/axioms14080600 - 1 Aug 2025

Since the monotonicity of the best approximant is crucial to establish partial ordering methods, in this paper, we, respectively, characterize the best approximants in Banach function spaces and Lorentz spaces

Γ_{p, w}

, in which we especially focus on the monotonicity [...] Read more.

Since the monotonicity of the best approximant is crucial to establish partial ordering methods, in this paper, we, respectively, characterize the best approximants in Banach function spaces and Lorentz spaces

Γ_{p, w}

, in which we especially focus on the monotonicity characterizations. We first study monotonicity characterizations of the metric projection operator onto sublattices in general Banach function spaces by the property

H_{g}

. The sufficient and necessary conditions for monotonicity of the metric projection onto cones and sublattices are then, respectively, established in

Γ_{p, w}

. The Lorentz spaces

Γ_{p, w}

are also shown to be reflexive under the condition

R B_{p}

, which is the basis for the existence of the best approximant. As applications, by establishing the partial ordering methods based on the obtained monotonicity characterizations, the solvability and approximation theorems for best proximity points are deduced without imposing any contractive and compact conditions in

Γ_{p, w}

. Our results extend and improve many previous results in the field of the approximation and partial ordering theory. Full article

(This article belongs to the Section Mathematical Analysis)

40 pages, 1868 KiB

Open AccessArticle

A Logifold Structure for Measure Space

by Inkee Jung and Siu-Cheong Lau

Axioms 2025, 14(8), 599; https://doi.org/10.3390/axioms14080599 - 1 Aug 2025

In this paper, we develop a geometric formulation of datasets. The key novel idea is to formulate a dataset to be a fuzzy topological measure space as a global object and equip the space with an atlas of local charts using graphs of [...] Read more.

In this paper, we develop a geometric formulation of datasets. The key novel idea is to formulate a dataset to be a fuzzy topological measure space as a global object and equip the space with an atlas of local charts using graphs of fuzzy linear logical functions. We call such a space a logifold. In applications, the charts are constructed by machine learning with neural network models. We implement the logifold formulation to find fuzzy domains of a dataset and to improve accuracy in data classification problems. Full article

(This article belongs to the Special Issue Recent Advances in Function Spaces and Their Applications)

► Show Figures

Figure 1

12 pages, 2519 KiB

Open AccessArticle

Mathematical Formulation of Causal Propagation in Relativistic Ideal Fluids

by Dominique Brun-Battistini, Alfredo Sandoval-Villalbazo and Hernando Efrain Caicedo-Ortiz

Axioms 2025, 14(8), 598; https://doi.org/10.3390/axioms14080598 - 1 Aug 2025

We establish a rigorous kinetic-theoretical framework to analyze causal propagation in thermal transport phenomena within relativistic ideal fluids, building a more rigorous framework based on the kinetic theory of gases. Specifically, we provide a refined derivation of the wave equation governing thermal and [...] Read more.

We establish a rigorous kinetic-theoretical framework to analyze causal propagation in thermal transport phenomena within relativistic ideal fluids, building a more rigorous framework based on the kinetic theory of gases. Specifically, we provide a refined derivation of the wave equation governing thermal and density fluctuations, clarifying its hyperbolic nature and the associated characteristic propagation speeds. The analysis confirms that thermal fluctuations in a simple non-degenerate relativistic fluid satisfy a causal wave equation in the Euler regime, and it recovers the classical expression for the speed of sound in the non-relativistic limit. This work offers enhanced mathematical and physical insights, reinforcing the validity of the hyperbolic description and suggesting a foundation for future studies in dissipative relativistic hydrodynamics. Full article

(This article belongs to the Section Mathematical Physics)

► Show Figures

Figure 1

43 pages, 2466 KiB

Open AccessArticle

Adaptive Ensemble Learning for Financial Time-Series Forecasting: A Hypernetwork-Enhanced Reservoir Computing Framework with Multi-Scale Temporal Modeling

by Yinuo Sun, Zhaoen Qu, Tingwei Zhang and Xiangyu Li

Axioms 2025, 14(8), 597; https://doi.org/10.3390/axioms14080597 - 1 Aug 2025

Financial market forecasting remains challenging due to complex nonlinear dynamics and regime-dependent behaviors that traditional models struggle to capture effectively. This research introduces the Adaptive Financial Reservoir Network with Hypernetwork Flow (AFRN–HyperFlow) framework, a novel ensemble architecture integrating Echo State Networks, temporal convolutional [...] Read more.

Financial market forecasting remains challenging due to complex nonlinear dynamics and regime-dependent behaviors that traditional models struggle to capture effectively. This research introduces the Adaptive Financial Reservoir Network with Hypernetwork Flow (AFRN–HyperFlow) framework, a novel ensemble architecture integrating Echo State Networks, temporal convolutional networks, mixture density networks, adaptive Hypernetworks, and deep state-space models for enhanced financial time-series prediction. Through comprehensive feature engineering incorporating technical indicators, spectral decomposition, reservoir-based representations, and flow dynamics characteristics, the framework achieves superior forecasting performance across diverse market conditions. Experimental validation on 26,817 balanced samples demonstrates exceptional results with an F1-score of 0.8947, representing a 12.3% improvement over State-of-the-Art baseline methods, while maintaining robust performance across asset classes from equities to cryptocurrencies. The adaptive Hypernetwork mechanism enables real-time regime-change detection with 2.3 days average lag and 95% accuracy, while systematic SHAP analysis provides comprehensive interpretability essential for regulatory compliance. Ablation studies reveal Echo State Networks contribute 9.47% performance improvement, validating the architectural design. The AFRN–HyperFlow framework addresses critical limitations in uncertainty quantification, regime adaptability, and interpretability, offering promising directions for next-generation financial forecasting systems incorporating quantum computing and federated learning approaches. Full article

(This article belongs to the Special Issue Financial Mathematics and Econophysics)

► Show Figures

Figure 1

24 pages, 440 KiB

Open AccessArticle

New Applications and Improvements of Sinc Functions for Solving a System of Fredholm Integral Equations

by Saeed Althubiti and Abdelaziz Mennouni

Axioms 2025, 14(8), 596; https://doi.org/10.3390/axioms14080596 - 1 Aug 2025

This study introduces two novel methodologies for solving systems of Fredholm integral equations, with particular emphasis on second-kind equations. The first method integrates the Sinc-collocation technique with a newly developed singular exponential transformation, enhancing convergence behavior and numerical stability. A comprehensive convergence analysis [...] Read more.

This study introduces two novel methodologies for solving systems of Fredholm integral equations, with particular emphasis on second-kind equations. The first method integrates the Sinc-collocation technique with a newly developed singular exponential transformation, enhancing convergence behavior and numerical stability. A comprehensive convergence analysis is conducted to support this approach. The second method employs a double exponential transformation, leading to a pair of linear equations whose solvability is established using the double projection method. Rigorous theoretical analysis is presented, including convergence theorems and newly derived error bounds. A system of two Fredholm integral equations is treated as a practical case study. Numerical examples are provided to illustrate the effectiveness and accuracy of the proposed methods, substantiating the theoretical results. Full article

(This article belongs to the Special Issue Recent Trends in Numerical Methods for Functional Equations)

► Show Figures

Figure 1

36 pages, 2272 KiB

Open AccessArticle

Failure Cause Analysis Under Progressive Type-II Censoring Using Generalized Linear Exponential Competing Risks Model with Medical and Industrial Applications

by Shafya Alhidairah, Farouq Mohammad A. Alam and Mazen Nassar

Axioms 2025, 14(8), 595; https://doi.org/10.3390/axioms14080595 - 1 Aug 2025

This study focuses on analyzing progressive Type-II right censoring competing risks datasets. The latent causes of failures are assumed to follow independent generalized linear exponential distributions. The maximum likelihood and maximum product of spacing methods are employed to estimate the unknown parameters and [...] Read more.

This study focuses on analyzing progressive Type-II right censoring competing risks datasets. The latent causes of failures are assumed to follow independent generalized linear exponential distributions. The maximum likelihood and maximum product of spacing methods are employed to estimate the unknown parameters and survival indices. Furthermore, approximate confidence intervals are derived using the asymptotic normality of the maximum likelihood and the maximum product of spacing estimators. Additionally, bootstrap methods are employed to construct confidence intervals. A comprehensive simulation study is carried out to evaluate the effectiveness of these estimation approaches. Finally, real-world datasets are analyzed to illustrate the practical applicability of the proposed model. Full article

(This article belongs to the Special Issue Reliability and Risk of Complex Systems: Modelling, Analysis and Optimization, 2nd Edition)

► Show Figures

Figure 1

13 pages, 268 KiB

Open AccessFeature PaperArticle

A 4 × 4 Matrix Spectral Problem Involving Four Potentials and Its Combined Integrable Hierarchy

by Wen-Xiu Ma and Ya-Dong Zhong

Axioms 2025, 14(8), 594; https://doi.org/10.3390/axioms14080594 - 1 Aug 2025

This paper introduces a specific matrix spectral problem involving four potentials and derives an associated soliton hierarchy using the zero-curvature formulation. The bi-Hamiltonian formulation is derived via the trace identity, thereby establishing the hierarchy’s Liouville integrability. This is exemplified through two systems: generalized [...] Read more.

This paper introduces a specific matrix spectral problem involving four potentials and derives an associated soliton hierarchy using the zero-curvature formulation. The bi-Hamiltonian formulation is derived via the trace identity, thereby establishing the hierarchy’s Liouville integrability. This is exemplified through two systems: generalized combined NLS-type equations and modified KdV-type equations. Owing to Liouville integrability, each member of the hierarchy admits a bi-Hamiltonian structure and, consequently, possesses infinitely many symmetries and conservation laws. Full article

More Articles...

Submit to Axioms Review for Axioms

Journal Menu

Journal Browser

► Journal Browser

Highly Accessed Articles

View More...

Latest Books

More Books and Reprints...

E-Mail Alert

News

31 July 2025
MDPI INSIGHTS: The CEO's Letter #25 - 8,000 Staff Worldwide, Korea Visit, 100,000 Preprints, Malaysia Roundtable, Canada Consortium Deal

23 July 2025
Join Us at the 2^nd Physical & Mathematical Sciences Summit—Quantum Artificial Intelligence, 22–24 August 2025, Haikou, China

8 July 2025
Axioms | Title Story Articles for the Second Half of 2024

More News & Announcements...

Topics

Propose a Topic

Topic in AppliedMath, Axioms, Fractal Fract, Mathematics, Symmetry

Fixed Point Theory and Measure Theory Topic Editors: Safeer Hussain Khan, Lateef Olakunle Jolaoso, Olaniyi S. Iyiola
Deadline: 30 November 2025

Topic in AppliedMath, Axioms, Fractal Fract, MCA, Mathematics, Symmetry

Fractional Calculus, Symmetry Phenomenon and Probability Theory for PDEs, and ODEs Topic Editors: Renhai Wang, Junesang Choi
Deadline: 31 December 2025

Topic in AppliedMath, Axioms, Computation, Mathematics, Symmetry

A Real-World Application of Chaos Theory Topic Editors: Adil Jhangeer, Mudassar Imran
Deadline: 28 February 2026

Topic in Axioms, Computation, Fractal Fract, Mathematics, Symmetry

Fractional Calculus: Theory and Applications, 2nd Edition Topic Editors: António Lopes, Liping Chen, Sergio Adriani David, Alireza Alfi
Deadline: 30 May 2026

More Topics

Conferences

Announce Your Conference

13–15 April 2026 The 1st International Online Conference on Fractal and Fractional: Theoretical Foundations and Interdisciplinary Applications

25–30 January 2026 The Eighteenth International Conference on Fuzzy Set Theory and Applications, FSTA 2026

More Conferences...

Special Issues

Propose a Special Issue

Special Issue in Axioms

Mathematical Modeling and Control: Theory and Applications Guest Editors: Guangying Lv, Jian Wang
Deadline: 29 August 2025

Special Issue in Axioms

Differential Equations and Related Topics, 2nd Edition Guest Editors: Daniela Marian, Ali Shokri, Daniela Inoan
Deadline: 29 August 2025

Special Issue in Axioms

Difference, Functional, and Related Equations, 2nd Edition Guest Editors: Ravi Shankar, Qun Liu
Deadline: 29 August 2025

Special Issue in Axioms

Advances in Mathematical Models and Applications Guest Editors: Juan Pablo Gutiérrez-Jara, Fernando Córdova-Lepe
Deadline: 30 August 2025

More Special Issues

Back to TopTop