Axioms

14 pages, 296 KB

Open AccessArticle

A Rigidity Theorem on Spacelike Hypersurfaces in Generalized Robertson–Walker Spacetimes

by Ning Zhang

Axioms 2026, 15(3), 241; https://doi.org/10.3390/axioms15030241 - 23 Mar 2026

Viewed by 160

We study the properties of complete parabolic constant mean curvature spacelike hypersurfaces in generalized Robertson–Walker (GRW) spacetimes

I \times_{φ} P^{n}

whose warping function

φ

fulfills a certain convexity criterion such that

- φ

is convex, and whose Ricci curvature of the [...] Read more.

We study the properties of complete parabolic constant mean curvature spacelike hypersurfaces in generalized Robertson–Walker (GRW) spacetimes

I \times_{φ} P^{n}

whose warping function

φ

fulfills a certain convexity criterion such that

- φ

is convex, and whose Ricci curvature of the fiber

P^{n}

is non-negative. Our approach is based on calculating the Laplacian of an appropriate function. Under appropriate conditions on the constant mean curvature, by using the parabolicity, we obtain a rigidity theorem and some corollaries of spacelike hypersurfaces. As a consequence, we solve new corresponding Calabi–Bernstein-type problems. Full article

(This article belongs to the Special Issue Recent Developments in Differential Geometry and Its Applications)

16 pages, 940 KB

Open AccessArticle

Leader-Following Consensus of One-Sided Lipschitz Multi-Agent Systems with Delay and Stochastic Perturbation

by Tuo Zhou

Axioms 2026, 15(3), 240; https://doi.org/10.3390/axioms15030240 - 23 Mar 2026

Viewed by 181

Abstract

This paper is concerned with the leader-following consensus of time-delay multi-agent systems (MASs) with stochastic perturbation over a directed network. Different from existing literature subject to the conventional Lipschitz condition, the one-sided Lipschitz nonlinear MASs with delay are discussed. First, to address the [...] Read more.

This paper is concerned with the leader-following consensus of time-delay multi-agent systems (MASs) with stochastic perturbation over a directed network. Different from existing literature subject to the conventional Lipschitz condition, the one-sided Lipschitz nonlinear MASs with delay are discussed. First, to address the challenge, in combination with current and delay information, the composite control law is constructed. By employing the Lyapunov function and using the Itô formula, this proves that the followers can eventually track the leader. Second, in the presence of external disturbance, sufficient conditions are established for the H-infinity leader-following consensus of one-sided Lipschitz nonlinear stochastic MASs. Further, the method to handle the one-sided Lipschitz nonlinearities is directly applicable to the stochastic MASs with conventional Lipschitz nonlinear dynamics, and the corresponding results are easily obtained. Finally, the relationship between one-sided Lipschitz scalars and time-delay parameters are presented, and the simulation results are given to verify the theoretical algorithms. Full article

(This article belongs to the Section Mathematical Analysis)

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18 pages, 289 KB

Open AccessFeature PaperArticle

The New Bipolar Intuitionistic Fuzzy Metric Space (NBIFM-Space) with Applications

by Bratislav Iričanin, Tatjana Došenović, Nebojša M. Ralević and Biljana Carić

Axioms 2026, 15(3), 239; https://doi.org/10.3390/axioms15030239 - 23 Mar 2026

Viewed by 237

Abstract

This paper introduces the New Bipolar Intuitionistic Fuzzy Metric Space (NBIFM-space)—a mathematical framework that extends intuitionistic and previously proposed bipolar intuitionistic structures by providing a complete three-component formulation based on positive similarity, negative similarity, and indeterminacy. Unlike earlier bipolar intuitionistic models, [...] Read more.

This paper introduces the New Bipolar Intuitionistic Fuzzy Metric Space (NBIFM-space)—a mathematical framework that extends intuitionistic and previously proposed bipolar intuitionistic structures by providing a complete three-component formulation based on positive similarity, negative similarity, and indeterminacy. Unlike earlier bipolar intuitionistic models, the NBIFM-space employs normalized metric components and coordinated triangular norms denoted by t-norm/t-conorm interactions, yielding a fully consistent topological and analytic setting. We have developed the basic properties of this structure and have demonstrated its effectiveness in image processing, where the explicit separation of attraction, repulsion, and uncertainty leads to robust edge-preserving filtering. Furthermore, a Banach-type fixed point theorem is established in the full NBIFM framework. Full article

(This article belongs to the Special Issue Advances in Fuzzy Logic with Applications)

18 pages, 331 KB

Open AccessArticle

Some Distributional Properties of the Matrix-Variate Generalized Gamma Model

by Arak M. Mathai and Serge B. Provost

Axioms 2026, 15(3), 238; https://doi.org/10.3390/axioms15030238 - 23 Mar 2026

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Abstract

This paper employs Jacobians of matrix transformations to derive the density function of a matrix-variate generalized gamma distribution, together with its normalizing constant. By applying the inverse Mellin transform, explicit expressions for the density functions of the determinant and the trace are obtained [...] Read more.

This paper employs Jacobians of matrix transformations to derive the density function of a matrix-variate generalized gamma distribution, together with its normalizing constant. By applying the inverse Mellin transform, explicit expressions for the density functions of the determinant and the trace are obtained in terms of generalized hypergeometric functions. The characteristic function and the first two moments follow from an associated density generator. Both the real and complex cases are treated, and several important special cases are identified. A simulation study reveals that the proposed model provides a more accurate fit than other distributions that are also defined on the cone of positive definite matrices. Moreover, it is shown to exhibit superior performance when applied to two empirical data sets. Applications involving the modeling of scatter matrices arising in financial studies, biostatistics, and reliability analysis are also discussed. Full article

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

29 pages, 426 KB

Open AccessArticle

Umbral Theory and the Algebra of Formal Power Series

by Roberto Ricci

Axioms 2026, 15(3), 237; https://doi.org/10.3390/axioms15030237 - 21 Mar 2026

Viewed by 157

Abstract

Umbral theory, formulated in its modern version by S. Roman and G. C. Rota, has been reconsidered in more recent times by G. Dattoli and collaborators with the aim of devising a working computational tool in the framework of special function theory. Concepts [...] Read more.

Umbral theory, formulated in its modern version by S. Roman and G. C. Rota, has been reconsidered in more recent times by G. Dattoli and collaborators with the aim of devising a working computational tool in the framework of special function theory. Concepts like the umbral image and umbral vacuum have been introduced as pivotal elements of the discussion which, albeit effective, lack generality. This article is directed towards endowing the formalism with a rigorous formulation within the context of formal power series with complex coefficients

(C ⟦ t ⟧, \partial)

. The new formulation is founded on the definition of the umbral operator

u

as a functional in the “umbral ground state” subalgebra of analytically convergent formal series

φ \in C {t}

. We consider in detail some specific classes of umbral ground states

φ

and analyse the conditions for analytic convergence of the corresponding umbral identities, defined as formal series resulting from the action on

φ

of operators of the form

f (ζ u^{μ})

with

f \in C {t}

and

μ, ζ \in C

. For these umbral states, we exploit the Gevrey classification of formal power series to establish a connection with the theory of Borel–Laplace resummation, allowing us to make rigorous sense of a large class of—even divergent—umbral identities. As an application of the proposed theoretical framework, we introduce and investigate the properties of new umbral images for the Gaussian trigonometric functions, which emphasise the trigonometric-like nature of these functions and enable defining the concept of a “Gaussian Fourier transform”, a potentially powerful tool for applications. Full article

(This article belongs to the Special Issue Applications in Functional Analysis)

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36 pages, 4052 KB

Open AccessArticle

Data-Driven Prediction of Surface Transport Quantities in Williamson Nanofluid Flow via Hybrid Numerical Neural Approach

by Yasir Nawaz, Nabil Kerdid, Muhammad Shoaib Arif and Mairaj Bibi

Axioms 2026, 15(3), 236; https://doi.org/10.3390/axioms15030236 - 20 Mar 2026

Viewed by 183

Abstract

This study introduces an efficient and accurate two-stage explicit computational scheme for solving partial differential equations (PDEs) containing first-order time derivatives. The suggested method is a modification of the classical Runge–Kutta scheme that introduces a new first-stage formulation. This minimizes numerical error with [...] Read more.

This study introduces an efficient and accurate two-stage explicit computational scheme for solving partial differential equations (PDEs) containing first-order time derivatives. The suggested method is a modification of the classical Runge–Kutta scheme that introduces a new first-stage formulation. This minimizes numerical error with moderate step sizes while preserving the stability region of the classical method. Spatial discretization is performed using a sixth-order compact finite-difference scheme to obtain high-resolution solutions. The analysis of stability and convergence is strictly determined for both scalar and system forms of convection–diffusion-type equations. To illustrate the suitability of the method, a dimensionless mathematical model of the unsteady, incompressible, laminar flow of a Prandtl-type non-Newtonian nanofluid over a Riga plate is considered, accounting for viscous dissipation, thermophoresis, Brownian motion, and a magnetic field. Here, the Prandtl ternary nanofluid is defined as a non-Newtonian nanofluid that follows the Prandtl rheological model, and it exhibits three critical transport phenomena: heat conduction, viscous dissipation, and nanoparticle diffusion. Representative values of the Prandtl number

P_{r} = 3

and Reynolds number

R_{e} = 5

are used to perform the simulation, and other parameters, including but not limited to the Hartmann number

H_{a}

, Williamson number

W_{e}

, thermophoresis

N_{t}

and Brownian motion

N_{b}

, are varied to evaluate the flow behavior. Moreover, an artificial neural network (ANN)-developed surrogate model is used to calculate the skin friction coefficient and the local Sherwood number, using five input parameters: the Reynolds number, Prandtl number, Schmidt number, Brownian motion parameter, and thermophoresis parameter. The governing partial differential equations yield high-fidelity numerical data used to train the surrogate model. The data is split into 80% for training, 10% for validation, and 10% for testing. The ANN is tested using regression analysis and error histograms, which demonstrate high accuracy and generalization capacity. Numerical simulation combined with AI-based prediction is a cost-efficient method for real-time estimation of complex non-Newtonian nanofluid systems. Full article

(This article belongs to the Special Issue Recent Developments in Mathematical Fluid Dynamics)

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15 pages, 1153 KB

Open AccessArticle

Structured Over-Relaxed Monotone FISTA for Linear Inverse Problems in Image Restoration

by Zixuan Chen and Xinzhu Zhao

Axioms 2026, 15(3), 235; https://doi.org/10.3390/axioms15030235 - 20 Mar 2026

Viewed by 153

Abstract

In this paper, we propose an efficient numerical algorithm for solving large-scale ill-posed linear inverse problems encountered in image restoration. To boost computational efficiency, we extend the structured fast iterative shrinkage-thresholding algorithm (sFISTA) for addressing the corresponding

l_{1}

-regularized minimization problem, and [...] Read more.

In this paper, we propose an efficient numerical algorithm for solving large-scale ill-posed linear inverse problems encountered in image restoration. To boost computational efficiency, we extend the structured fast iterative shrinkage-thresholding algorithm (sFISTA) for addressing the corresponding

l_{1}

-regularized minimization problem, and further introduce the over-relaxation technique to accelerate the algorithm. The proposed algorithm is termed structured over-relaxed monotone FISTA (sOMFISTA). The convergence analysis of sOMFISTA is also conducted. The algorithmic framework of sOMFISTA is universally applicable to any non-smooth convex regularization term, exhibiting remarkable flexibility. Extensive numerical experiments are carried out to systematically validate the superiority in efficiency and performance of the proposed sOMFISTA. Full article

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11 pages, 243 KB

Open AccessArticle

Spatial Asymptotics and Polynomial Decay for Nonlinear Parabolic Equations in

R^{3}

Exterior Region

by Jincheng Shi and Yiwu Lin

Axioms 2026, 15(3), 234; https://doi.org/10.3390/axioms15030234 - 20 Mar 2026

Viewed by 172

Abstract

This paper investigates the spatial asymptotic behavior of solutions to a class of nonlinear parabolic equations defined on an exterior region in

R^{3}

. By constructing a suitable weighted energy functional and employing a fractional-order differential inequality technique, we establish a sharp [...] Read more.

This paper investigates the spatial asymptotic behavior of solutions to a class of nonlinear parabolic equations defined on an exterior region in

R^{3}

. By constructing a suitable weighted energy functional and employing a fractional-order differential inequality technique, we establish a sharp Phragmén–Lindelöf type alternative: the solution either ceases to exist at a finite radial distance or decays to zero as the radial variable

r \to \infty

when the power

p > 2

. In the decay case, we derive explicit polynomial type decay estimates. The analysis is conducted in unbounded exterior domains where traditional compactness arguments are not applicable, extending previous studies on semi-infinite cylinders to more complex geometric settings. Our results reveal distinct spatial behaviors compared to those observed in linear or differently nonlinear parabolic problems and can be seen as a version of Saint-Venant principle in exterior regions. Full article

15 pages, 311 KB

Open AccessArticle

IB-TOT: Identity-Based Traceable Oblivious Transfer and Its Applications

by Weiwei Liu, Yankang Zhang and Kunhao Yang

Axioms 2026, 15(3), 233; https://doi.org/10.3390/axioms15030233 - 20 Mar 2026

Viewed by 147

Abstract

Oblivious Transfer (OT) is a fundamental cryptographic primitive for privacy-preserving data exchange. While traditional OT protocols guarantee unconditional receiver anonymity, they inherently lack the mechanisms to prevent abusive mass data harvesting. Traceable Oblivious Transfer (TOT) addresses this by introducing “conditional anonymity,” revoking the [...] Read more.

Oblivious Transfer (OT) is a fundamental cryptographic primitive for privacy-preserving data exchange. While traditional OT protocols guarantee unconditional receiver anonymity, they inherently lack the mechanisms to prevent abusive mass data harvesting. Traceable Oblivious Transfer (TOT) addresses this by introducing “conditional anonymity,” revoking the privacy of malicious users. However, existing TOT mechanisms either rely on computationally expensive dynamic assumptions or require continuous interaction with a Trusted Third Party (TTP) to manage credentials. To overcome these limitations, we present an Identity-Based Traceable Oblivious Transfer (IB-TOT) protocol. By synergizing polynomial-based secret sharing with Blind Identity-Based Encryption (Blind IBE), our scheme completely eliminates the TTP during the data transfer stage. The Blind IBE extraction algorithm serves as the primary oblivious channel, utilizing data indices as user identities. We strictly bound the receiver’s query quota by embedding a degree-k tracing polynomial directly into the key issuance phase. Honest clients enjoy fully protected retrieval of up to k items, whereas any attempt to exceed this quota deterministically exposes the violator’s identity. Comprehensive security proofs demonstrate that IB-TOT satisfies sender privacy, receiver privacy, and strict accountability under standard static assumptions (DBDH and DL). Full article

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19 pages, 446 KB

Open AccessArticle

Convergence Analysis of Wang–Zheng-Type Iterative Methods for the Simultaneous Approximation of Multiple Zeros

by Maria T. Vasileva and Slav I. Cholakov

Axioms 2026, 15(3), 232; https://doi.org/10.3390/axioms15030232 - 20 Mar 2026

Viewed by 246

Abstract

This paper studies a new family of iterative methods for the simultaneous approximation of polynomial zeros with known multiplicities. The methods are obtained by combining the Wang–Zheng iteration function with an arbitrary iteration function. This approach leads to a class of methods referred [...] Read more.

This paper studies a new family of iterative methods for the simultaneous approximation of polynomial zeros with known multiplicities. The methods are obtained by combining the Wang–Zheng iteration function with an arbitrary iteration function. This approach leads to a class of methods referred to as Wang–Zheng-type methods with correction for multiple zeros. A local convergence analysis is developed for a wide class of iteration functions. The analysis describes the conditions under which the proposed methods converge locally. Several known iterative methods are examined as special cases of the general results. In particular, the family constructed by Kyurkchiev and Andreev (1990) is included. For every positive integer N, the N-th method of this family has convergence order

3 N + 1

. The main local convergence theorem extends, complements and improves earlier results by Wang and Wu (1987) and by Kyurkchiev and Andreev (1990). Full article

(This article belongs to the Section Mathematical Analysis)

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19 pages, 331 KB

Open AccessArticle

Symmetry Transformations of a Nonlinear Model of Optical Wave Transmission

by Jean-Claude Ndogmo, Emmanuel Mayombo Mbala and Mensah Kekeli Folly-Gbetoula

Axioms 2026, 15(3), 231; https://doi.org/10.3390/axioms15030231 - 20 Mar 2026

Viewed by 235

Abstract

The full symmetry group is found for a system of nonlinear schrödinger equations describing the propagation of optical pulses in an isotropic media. It is shown, in particular, that the six-dimensional symmetry group found is composed of a scaling transformation and a rotation [...] Read more.

The full symmetry group is found for a system of nonlinear schrödinger equations describing the propagation of optical pulses in an isotropic media. It is shown, in particular, that the six-dimensional symmetry group found is composed of a scaling transformation and a rotation of the four-dimensional space, thereby proving that the symmetry group preserves the shape of solutions. A symmetry classification of one-dimensional subalgebras of the Lie algebra is performed and yields, in particular, the symmetry reduction to the most general system of equations satisfied by the solitary waves of the equation. Explicit soliton solutions of the equation are found by largely autonomous technics. The found solitons are used to recursively generate two new ones by means of two iterations using the symmetry group. Other properties of the system are also highlighted, as well as the possible connections between the theories of symmetry groups and Darboux transformations inspired by this study. Full article

(This article belongs to the Section Mathematical Analysis)

23 pages, 353 KB

Open AccessArticle

Well-Posedness of the Nonhomogeneous Initial-Boundary Value Problem for the Coupled Hirota Equation

by Shu Wang and Huifeng Wang

Axioms 2026, 15(3), 230; https://doi.org/10.3390/axioms15030230 - 20 Mar 2026

Viewed by 170

Abstract

In this work, we address the nonhomogeneous initial-boundary value problem for the coupled Hirota equation posed on the finite interval

[0, L]

. To investigate the well-posedness of this problem, we first adopt an appropriate transformation, namely the Laplace transform, [...] Read more.

In this work, we address the nonhomogeneous initial-boundary value problem for the coupled Hirota equation posed on the finite interval

[0, L]

. To investigate the well-posedness of this problem, we first adopt an appropriate transformation, namely the Laplace transform, which is tailored to the specific characteristics of the problem, and further obtain an explicit solution formula for the linear inhomogeneous coupled system. Subsequently, the local well-posedness of the original nonhomogeneous initial-boundary value problem in

X_{s, T} \times X_{s, T} (X_{s, T} = C (0, T; H^{s} (0, 1)) \cap L^{2} (0, T; H^{s + 1} (0, 1)))

is rigorously established through the combination of this explicit formula, the contraction mapping principle and energy estimates. Full article

15 pages, 1117 KB

Open AccessArticle

Application of Impulsive SIRQ Models for the Development of Forecasting and Cyberattack Mitigation Scenarios

by Valentyn Sobchuk, Vitalii Savchenko, Bohdan Stepanchenko and Halyna Haidur

Axioms 2026, 15(3), 229; https://doi.org/10.3390/axioms15030229 - 19 Mar 2026

Viewed by 242

Abstract

This paper proposes an impulsive SIRQ model for the analysis of computer network resilience against malware propagation and distributed denial-of-service (DDoS) attacks. The model extends classical epidemic frameworks by combining the continuous-time dynamics of malicious object spreading with discrete control actions corresponding to [...] Read more.

This paper proposes an impulsive SIRQ model for the analysis of computer network resilience against malware propagation and distributed denial-of-service (DDoS) attacks. The model extends classical epidemic frameworks by combining the continuous-time dynamics of malicious object spreading with discrete control actions corresponding to mass updates, node isolation, and access control policies. A qualitative analysis of the resulting system of impulsive differential equations is performed. The basic reproduction number

R_{0}

, identified as a threshold parameter characterizing the intensity of attack propagation, and sufficient conditions for the global asymptotic stability of the infection-free state are established. It is shown that, under periodic impulsive control, the infection-free state can be stabilized with respect to the target population coordinates even when

R_{0} > 1

. An exponential decay estimate for the total active threat is derived, guaranteeing the asymptotic extinction of the infected and quarantined node populations. The proposed approach provides quantitative criteria for the effectiveness of impulsive cyber defense strategies and offers a theoretical foundation for the design of adaptive multi-layer protection systems for critical information infrastructures. Practical interpretation of the results illustrates the dependence of the critical impulsive control period on the model parameters and demonstrates the applicability of the approach to cybersecurity strategy design. Full article

(This article belongs to the Special Issue Modern Trends and Application of Decision-Making Theory, Stability and Control, 2nd Edition)

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18 pages, 425 KB

Open AccessArticle

ARIMA Model Selection and Prediction Intervals

by W. A. Dhanushka M. Welagedara, Mulubrhan G. Haile and David J. Olive

Axioms 2026, 15(3), 228; https://doi.org/10.3390/axioms15030228 - 19 Mar 2026

Viewed by 240

Abstract

Inference after model selection is a very important problem. Model selection algorithms for ARIMA time series, with criteria such as AIC and BIC, tend to select an inconsistent model with positive probability, making data-splitting inference for testing and confidence intervals unreliable. One technique [...] Read more.

Inference after model selection is a very important problem. Model selection algorithms for ARIMA time series, with criteria such as AIC and BIC, tend to select an inconsistent model with positive probability, making data-splitting inference for testing and confidence intervals unreliable. One technique was fairly reliable for sample sizes greater than 600, and a modification also worked. Model selection is often useful for prediction, since the selected submodel tends to have fitted values and residuals that are highly correlated with those of the full model. A few prediction intervals perform fairly well even after model selection. A useful technique for handling outliers is to replace the outliers with missing values. Full article

(This article belongs to the Special Issue Probability Theory and Stochastic Processes: Theory and Applications)

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14 pages, 309 KB

Open AccessFeature PaperArticle

Standardized Coefficients of Multiple Regression Beyond One and Multicollinearity Diagnostics

by Stan Lipovetsky

Axioms 2026, 15(3), 227; https://doi.org/10.3390/axioms15030227 - 18 Mar 2026

Viewed by 300

Abstract

Standardized coefficients of multiple regression, also known as beta coefficients, by absolute value are usually smaller than one, but sometimes they can exceed one. This effect had been studied mostly for models with two predictors, where it was explained by the high collinearity [...] Read more.

Standardized coefficients of multiple regression, also known as beta coefficients, by absolute value are usually smaller than one, but sometimes they can exceed one. This effect had been studied mostly for models with two predictors, where it was explained by the high collinearity between them. The current paper considers multiple linear regression and defines the necessary and sufficient conditions for beta coefficients to exceed one. These conditions determine a measure of each predictor’s connection to the dependent variable in the model relative to the connection with other predictors. This criterion presents a new measure for diagnostics of the multicollinearity, which can be employed additionally to the commonly used variance inflation factor. A new interpretation is given to the meaning of the squared beta coefficients themselves. Numerical examples demonstrate these novel features. The obtained results are useful in applied regression analysis, helping practitioners and educators to understand and to explain the outcomes of regression modeling. Full article

15 pages, 333 KB

Open AccessArticle

Relational Generalized Nonlinear Contractions of Pant Type with an Application to Nonlinear Integral Equations

by Doaa Filali, Mohammed Zayed Alruwaytie, Abdulaziz Abbas Alshammari, Faizan Ahmad Khan, Bassam Z. Albalawi and Adel Alatawi

Axioms 2026, 15(3), 226; https://doi.org/10.3390/axioms15030226 - 17 Mar 2026

Viewed by 205

Abstract

The objective of this paper is to propose some fixed-point findings under a relational contraction of Pant type employing a pair of auxiliary functions and through a generalized class of transitive binary relations. Our outcomes extend, sharpen, modify and enrich many existing findings. [...] Read more.

The objective of this paper is to propose some fixed-point findings under a relational contraction of Pant type employing a pair of auxiliary functions and through a generalized class of transitive binary relations. Our outcomes extend, sharpen, modify and enrich many existing findings. To facilitate our research, we create a few instances that convey our findings. Through the use of our outcomes, we demonstrate the existence and uniqueness of solutions for a nonlinear integral equation. Full article

(This article belongs to the Special Issue Advances in Fixed Point Theory with Applications)

15 pages, 275 KB

Open AccessArticle

A General Coefficient Theorem for Univalent Functions: Generalization of the Bieberbach and Zalcman Conjectures

by Samuel L. Krushkal

Axioms 2026, 15(3), 225; https://doi.org/10.3390/axioms15030225 - 17 Mar 2026

Viewed by 266

Abstract

The main result of this paper is that any rotationally homogeneous polynomial functional [...] Read more.

The main result of this paper is that any rotationally homogeneous polynomial functional

J (f) = \sum_{| α | = n_{0}}^{N} C_{m_{1}, \dots, m_{s}} a_{m_{1}}^{α_{m_{1}}} \dots a_{m_{s}}^{α_{m_{s}}}

with

| α | = α_{m_{1}} + \dots + α_{m_{s}} \geq 3, 2 < a_{m_{1}} < \dots < a_{m_{s}} < \infty

, depending on the distinguished finitely many coefficients

a_{m_{j}}

, is maximized on S by Koebe’s function

κ_{θ} (z) = z / {(1 - e^{i θ} z)}^{2}

with

θ \in [- π, π]

. This includes, in particular, the well-known Bieberbach and Zalcman conjectures and covers many other coefficient estimates for univalent functions. As an application, the main theorem provides the solution of the generalized Zalcman conjecture posed by Ma. Full article

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

87 pages, 61280 KB

Open AccessFeature PaperReview

Differential Topology and Matrix Analysis: An Overview

by Petko H. Petkov

Axioms 2026, 15(3), 224; https://doi.org/10.3390/axioms15030224 - 16 Mar 2026

Viewed by 255

Abstract

This overview illustrates the application of methods from differential topology to several important problems in matrix analysis. In particular, it focuses on the use of smooth manifolds and smooth mappings to study fundamental issues such as the determination of matrix rank and the [...] Read more.

This overview illustrates the application of methods from differential topology to several important problems in matrix analysis. In particular, it focuses on the use of smooth manifolds and smooth mappings to study fundamental issues such as the determination of matrix rank and the computation of the Jordan form in the presence of uncertainties. Various aspects of numerical matrix analysis are discussed, including the genericity of matrix problems, characterization of singular sets in the parameter space, the distance to ill-posedness and its relation to problem conditioning. The conditioning of matrix problems is considered in both deterministic and probabilistic settings. The paper also addresses the regularization of ill-posed matrix problems in the presence of errors. Several examples are provided to illustrate these concepts and their practical relevance. The overview is intended for specialists from different fields who use matrix analysis in their work and do not have a strong background in differential topology. Full article

(This article belongs to the Special Issue New Advances in Numerical Linear Algebra and Its Applications)

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16 pages, 5900 KB

Open AccessArticle

A New Model Dimension Reduction Technique Based on Finite Volume Element and Proper Orthogonal Decomposition for Solving the 2D Hyperbolic Equation

by Yuejie Li, Jing Yang and Zhendong Luo

Axioms 2026, 15(3), 223; https://doi.org/10.3390/axioms15030223 - 16 Mar 2026

Viewed by 173

Abstract

This article mainly researches the model dimension reduction in the finite volume element (FVE) method based on proper orthogonal decomposition (POD) for the two-dimensional (2D) hyperbolic equation. For this objective, an FVE method with unconditional stability and second-order temporal accuracy, and the existence, [...] Read more.

This article mainly researches the model dimension reduction in the finite volume element (FVE) method based on proper orthogonal decomposition (POD) for the two-dimensional (2D) hyperbolic equation. For this objective, an FVE method with unconditional stability and second-order temporal accuracy, and the existence, stability, and error estimates of the FVE solutions are first reviewed. Thereafter, most importantly, a new FVF model dimension reduction (FVEMDR) formulation is established by applying POD technology to lower the dimension of the vectors composed of unknown coefficients for the FVE solutions. The greatest contribution of this article is the theoretical analysis of the existence, unconditional stability, and error estimations for the FVEMDR solutions. Moreover, in computation, two sets of numerical simulations are provided to confirm the validity of the theoretical results and show the effectiveness of the FVEMRD formulation. Full article

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36 pages, 4478 KB

Open AccessArticle

CBAM-BiLSTM-DDQN: A Novel Adaptive Quantitative Trading Model for Financial Data Analysis

by Yan Zhang, Mingxuan Zhou, Feng Sun and Yuehua Wu

Axioms 2026, 15(3), 222; https://doi.org/10.3390/axioms15030222 - 16 Mar 2026

Viewed by 496

Abstract

Financial data analysis remains a significant challenge due to the inherent stochasticity, non-stationarity, and low signal-to-noise ratio of market data. Conventional methods often struggle to disentangle intrinsic trends from noise and frequently overlook the critical influence of investor sentiment on price dynamics. To [...] Read more.

Financial data analysis remains a significant challenge due to the inherent stochasticity, non-stationarity, and low signal-to-noise ratio of market data. Conventional methods often struggle to disentangle intrinsic trends from noise and frequently overlook the critical influence of investor sentiment on price dynamics. To address these issues, we propose an adaptive trading model named CBAM-BiLSTM-DDQN, which integrates signal decomposition, multi-source feature fusion, and deep reinforcement learning. First, we construct a comprehensive heterogeneous feature set by combining price signals decomposed via Variational Mode Decomposition (VMD) and investor sentiment indices extracted from financial texts. Subsequently, a Genetic Algorithm (GA) is employed to identify the most significant feature subset, effectively reducing dimensionality and redundancy. Finally, these optimized features are input into a Double Deep Q-Network (DDQN) agent equipped with a Convolutional Block Attention Module (CBAM) and a Bidirectional Long Short-Term Memory (BiLSTM) network to capture complex spatiotemporal dependencies. We evaluated this approach through simulated trading on three major Chinese stock indices—the Shanghai Stock Exchange Composite (SSEC), the Shenzhen Stock Exchange Component (SZSE), and the China Securities 300 (CSI 300). Experimental results demonstrate the superiority of our method over traditional strategies and standard baselines; specifically, the trading agent achieved robust cumulative returns across the SSEC and CSI 300 indices, confirming the model’s exceptional capability in balancing profitability and risk aversion in complex financial environments. Furthermore, additional experiments on individual stocks in the Chinese A-share market reinforce the robustness and generalization ability of our proposed model, validating its practical potential for diverse trading scenarios. Furthermore, additional experiments on individual stocks in the Chinese A-share market reinforce the robustness and generalization ability of our proposed model, validating its practical potential for diverse trading scenarios. Full article

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

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25 pages, 372 KB

Open AccessArticle

Interval-Valued Intuitionistic Fuzzy n-Fold Implicative Filters in Hoop Algebra

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

Axioms 2026, 15(3), 221; https://doi.org/10.3390/axioms15030221 - 16 Mar 2026

Viewed by 202

Abstract

This paper introduces the concept of interval-valued intuitionistic fuzzy n-fold implicative filters in hoop algebras and explores their fundamental properties. We establish several new and equivalent characterizations, investigate their closure properties, and provide explicit algorithms for their construction and verification. Furthermore, we [...] Read more.

This paper introduces the concept of interval-valued intuitionistic fuzzy n-fold implicative filters in hoop algebras and explores their fundamental properties. We establish several new and equivalent characterizations, investigate their closure properties, and provide explicit algorithms for their construction and verification. Furthermore, we examine the relationships between interval-valued intuitionistic fuzzy n-fold implicative filters, interval-valued intuitionistic fuzzy filters, and classical n-fold implicative filters. The results presented here extend beyond straightforward generalizations, offering both practical tools and theoretical insights that are not previously available in the literature. The results presented here build upon earlier studies by systematically characterizing interval-valued intuitionistic fuzzy n-fold implicative filters in hoop algebras. Several new equivalent conditions and computational methods are introduced, and relationships with existing filter concepts are clarified. Full article

(This article belongs to the Special Issue New Perspectives in Fuzzy Sets and Their Applications, 2nd Edition)

15 pages, 308 KB

Open AccessArticle

Boundedness and Applications of Fractional Integral Operators in Nonlocal Problems with Fractional Laplacians

by Saba Mehmood, Dušan J. Simjanović and Branislav M. Randjelović

Axioms 2026, 15(3), 220; https://doi.org/10.3390/axioms15030220 - 16 Mar 2026

Viewed by 284

Abstract

In this paper, we investigate the properties of the boundedness of fractional integral operators

K_{α}

defined on general measure metric spaces. We study their action in Lebesgue spaces

L^{p} (Y)

, Morrey spaces

L_{φ}^{p} (Y)

[...] Read more.

In this paper, we investigate the properties of the boundedness of fractional integral operators

K_{α}

defined on general measure metric spaces. We study their action in Lebesgue spaces

L^{p} (Y)

, Morrey spaces

L_{φ}^{p} (Y)

, and extend our analysis to fractional Sobolev spaces

W^{α, p} (Y)

. Using classical dyadic decomposition and the Hardy–Littlewood maximal operator, we establish sharp bounds for

K_{α}

in terms of kernel parameters and the geometric structure of the space. A significant contribution of this work is the proof that

K_{α}

is bounded from

W^{α, p} (Y)

to

L^{q} (Y)

, where thus linking our operator-theoretic framework with the theory of nonlocal and fractional partial differential equations. These results provide valuable tools for studying regularity, a priori estimates, and solution mappings in nonlocal problems involving the fractional Laplacian and related operators on irregular or non- Euclidean domains. Full article

(This article belongs to the Special Issue Advancements in Applied Mathematics and Computational Physics, 2nd Edition)

21 pages, 11307 KB

Open AccessArticle

A Symmetry-Preserving Extrapolated Primal-Dual Hybrid Gradient Method for Saddle-Point Problems

by Xiayang Zhang, Wenzhuo Li, Bowen Chang, Wei Liu and Shiyu Zhang

Axioms 2026, 15(3), 219; https://doi.org/10.3390/axioms15030219 - 16 Mar 2026

Viewed by 249

Abstract

The primal-dual hybrid gradient (PDHG) method is widely used for convex–concave saddle-point problems, yet its extrapolated variants are typically asymmetric because only one side is extrapolated. We propose a symmetry-preserving refinement, E-PDHG, which performs dual-side extrapolation followed by an explicit correction step. Under [...] Read more.

The primal-dual hybrid gradient (PDHG) method is widely used for convex–concave saddle-point problems, yet its extrapolated variants are typically asymmetric because only one side is extrapolated. We propose a symmetry-preserving refinement, E-PDHG, which performs dual-side extrapolation followed by an explicit correction step. Under standard step-size conditions, we establish global convergence for all

η \in (- 1, 1)

and derive a pointwise (non-ergodic)

O (1 / \sqrt{t})

rate for the last iterate. The method does not improve the asymptotic complexity order of PDHG; instead, it enlarges the practically stable parameter region while retaining the same per-iteration cost. Numerical experiments on image deblurring/inpainting and additional machine learning benchmarks (logistic regression and LASSO) demonstrate improved finite-iteration stability and efficiency. Full article

(This article belongs to the Section Mathematical Analysis)

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39 pages, 8656 KB

Open AccessArticle

The Unit Arcsine–Exponential Distribution and Its Statistical Properties with Inference and Application to Reliability Data

by Asmaa S. Al-Moisheer, Khalaf S. Sultan, Moustafa N. Mousa and Mahmoud M. M. Mansour

Axioms 2026, 15(3), 218; https://doi.org/10.3390/axioms15030218 - 15 Mar 2026

Viewed by 276

Abstract

This paper presents a new continuous data model, the Unit Arcsine–Exponential distribution (UASED), a flexible data model on the unit interval. It is built up by an exponential-based arcsine-type transformation to allow it to represent a very wide range of shapes that can [...] Read more.

This paper presents a new continuous data model, the Unit Arcsine–Exponential distribution (UASED), a flexible data model on the unit interval. It is built up by an exponential-based arcsine-type transformation to allow it to represent a very wide range of shapes that can be used to model proportions and rates. A number of basic properties are obtained, such as closed-form formulas of the quantile function, moments, and entropy measures. Maximum likelihood and maximum product of spacings methods are developed to estimate parameters, and their performance is determined by Monte Carlo simulation, which shows that these methods can reasonably estimate the parameters and be stable over a variety of different parameter settings. To demonstrate that a model is practically useful, an application to real-world data on the reliability of devices in terms of failure time is discussed. The findings indicate that the UASED is a good fit to the data, in the sense that it is effective in terms of skewness and tail behavior and compares well or competes favorably with current unit distributions. All in all, the suggested model is a sparse alternative to model bounded data with sound inferential characteristics and high practical utility. Full article

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13 pages, 305 KB

Open AccessArticle

Stronger Versions of Stein–Weiss Inequalities

by Youjiang Lin, Jinghong Zhou and Jiaming Lan

Axioms 2026, 15(3), 217; https://doi.org/10.3390/axioms15030217 - 13 Mar 2026

Viewed by 202

Abstract

In this paper, stronger versions of Stein–Weiss inequalities and reverse Stein–Weiss inequalities are established. Full article

23 pages, 831 KB

Open AccessArticle

Periodic Asymmetric LogGARCH Stochastic Volatility Models: Structure and Application

by Omar Alzeley and Ahmed Ghezal

Axioms 2026, 15(3), 216; https://doi.org/10.3390/axioms15030216 - 13 Mar 2026

Viewed by 184

Abstract

This paper introduces a new class of periodic volatility models, namely, the Stochastic Volatility Periodic Logarithmic Asymmetric GARCH (PlogAG-SV) model. The proposed framework extends periodic logGARCH models by incorporating a stochastic volatility component combined with a distinctive threshold mechanism, thereby significantly enhancing their [...] Read more.

This paper introduces a new class of periodic volatility models, namely, the Stochastic Volatility Periodic Logarithmic Asymmetric GARCH (PlogAG-SV) model. The proposed framework extends periodic logGARCH models by incorporating a stochastic volatility component combined with a distinctive threshold mechanism, thereby significantly enhancing their ability to capture asymmetric and time-varying volatility dynamics. Sufficient conditions for strict stationarity, second-order stationarity, and the existence of higher-order moments are rigorously established, providing a comprehensive characterization of the model’s probabilistic properties. Parameter estimation is conducted via extensive Monte Carlo simulations, demonstrating the robustness and reliability of the proposed estimation procedure across a wide range of scenarios. Furthermore, the empirical relevance of the PlogAG-SV model is illustrated through an application to the Algerian dinar–euro exchange rate, highlighting its effectiveness in modeling real-world financial volatility. Full article

(This article belongs to the Special Issue Methods and Applications of Advanced Statistical Analysis, 3rd Edition)

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16 pages, 313 KB

Open AccessArticle

Biharmonic Conformal Immersions into a 3-Dimensional Conformally Flat Space

by Ze-Ping Wang and Xue-Yi Chen

Axioms 2026, 15(3), 215; https://doi.org/10.3390/axioms15030215 - 13 Mar 2026

Viewed by 215

Abstract

This paper investigates biharmonic conformal immersions of surfaces into a conformally flat 3-space. We first establish a characterization of such immersions of totally umbilical surfaces into a generic 3-manifold. It is then proved that any biharmonic conformal immersion of a totally umbilical surface [...] Read more.

This paper investigates biharmonic conformal immersions of surfaces into a conformally flat 3-space. We first establish a characterization of such immersions of totally umbilical surfaces into a generic 3-manifold. It is then proved that any biharmonic conformal immersion of a totally umbilical surface into a nonpositively curved 3-manifold is necessarily a conformal minimal immersion. We further examine the biharmonicity of conformal immersions of totally umbilical planes into a conformally flat 3-space and construct explicit examples of such immersions from a 2-sphere (minus a point) into a conformally flat 3-sphere. Finally, the study is extended to biharmonic conformal immersions of Hopf cylinders associated with a Riemannian submersion. Full article

(This article belongs to the Section Geometry and Topology)

30 pages, 954 KB

Open AccessArticle

Poisson Mixed-Effects Count Regression Model Based on Double SCAD Penalty and Its Simulation Study

by Keqian Li, Xueni Ren, Hanfang Li and Youxi Luo

Axioms 2026, 15(3), 214; https://doi.org/10.3390/axioms15030214 - 12 Mar 2026

Viewed by 174

Abstract

This paper focuses on variable selection and parameter estimation for mixed-effects Poisson count regression models. To simultaneously select important variables in both fixed effects and random effects, we propose a double-penalized Poisson count regression model with the Smoothly Clipped Absolute Deviation (SCAD) penalty [...] Read more.

This paper focuses on variable selection and parameter estimation for mixed-effects Poisson count regression models. To simultaneously select important variables in both fixed effects and random effects, we propose a double-penalized Poisson count regression model with the Smoothly Clipped Absolute Deviation (SCAD) penalty imposed on both components. To estimate the unknown parameters, we develop a new iterative algorithm called the Double SCAD–Local Quadratic Approximation (DSCAD-LQA) algorithm. Under regularity conditions, the consistency and Oracle property of the proposed estimator are established. Simulation studies are conducted under two types of penalty parameter selection criteria: the Schwarz Information Criterion (SIC) and the Generalized Approximate Cross-Validation (GACV). We evaluate the performance of the proposed method under different levels of correlation among explanatory variables and different covariance structures of random effects. Comparisons are also carried out with the non-penalized model, the single-penalized model, and the double LASSO-penalized model. The results demonstrate that the proposed double SCAD penalty method performs better than the other three methods in terms of important variable selection and coefficient estimation, and is especially effective for sparse models. Full article

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30 pages, 1036 KB

Open AccessArticle

Classical and Bayesian Inference for the Two-Parameter Chen Distribution with Random Censored Data

by Zihan Zhao, Wenhao Gui, Minghui Liu and Lanxi Zhang

Axioms 2026, 15(3), 213; https://doi.org/10.3390/axioms15030213 - 12 Mar 2026

Viewed by 268

Abstract

This study explores classical and Bayesian estimation for the two-parameter Chen distribution with randomly censored data, where censoring times follow an independent two-parameter Chen distribution with separate shape and scale parameters. We first derive the maximum likelihood estimators of the unknown parameters, together [...] Read more.

This study explores classical and Bayesian estimation for the two-parameter Chen distribution with randomly censored data, where censoring times follow an independent two-parameter Chen distribution with separate shape and scale parameters. We first derive the maximum likelihood estimators of the unknown parameters, together with their asymptotic variances and credible intervals, and further adopt the method of moments, L-moments and least squares methods for classical estimation. Under the generalized entropy loss function and inverse gamma priors, Bayesian estimation is implemented via Gibbs sampling, with the highest posterior density credible intervals of parameters constructed accordingly. We also investigate the estimation of key reliability and lifetime characteristics of the distribution, and conduct Monte Carlo simulations to compare the performance of all aforementioned estimation methods. Finally, two real-world CMAPSS jet engine lifetime datasets from NASA are applied to validate the practical effectiveness of the proposed estimation approaches, demonstrating the enhanced flexibility of the Chen distribution compared to the exponential distribution in fitting aerospace-related censored data, given the marginal p-values in the K-S tests. Full article

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

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21 pages, 2286 KB

Open AccessArticle

Command-Filtered Fuzzy Adaptive Output Feedback Control for Nonlinear Power Systems with Actuator Faults

by Sen Wang, Junzhe Yan, Chenxuan Sheng, Huai Liu and Guobao Liu

Axioms 2026, 15(3), 212; https://doi.org/10.3390/axioms15030212 - 12 Mar 2026

Viewed by 354

Abstract

This study presents a command-filtered fuzzy adaptive control method for nonlinear thyristor controlled series compensation (TCSC) systems subject to actuator faults, unknown nonlinearities, and unmeasurable states. To enhance applicability, the TCSC-based single-machine infinite-bus (SMIB) system is first transformed into a nonlinear form preserving [...] Read more.

This study presents a command-filtered fuzzy adaptive control method for nonlinear thyristor controlled series compensation (TCSC) systems subject to actuator faults, unknown nonlinearities, and unmeasurable states. To enhance applicability, the TCSC-based single-machine infinite-bus (SMIB) system is first transformed into a nonlinear form preserving the inherent nonlinear characteristics of the power system. A state observer is then designed to estimate the unmeasurable states. Using these estimated states, a fuzzy control algorithm approximates the uncertain nonlinearities. By integrating command filtering techniques, an adaptive output feedback controller is developed, which ensures system stability and avoids the “explosion of complexity” issue. Simulation results verify the effectiveness of the proposed control approach. Full article

(This article belongs to the Topic Modeling, Stability, and Control of Dynamic Systems and Their Applications)

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Axioms, Volume 15, Issue 3 (March 2026) – 85 articles

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