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 21.7 days after submission; acceptance to publication is undertaken in 2.8 days (median values for papers published in this journal in the second 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.
Journal Cluster of Mathematics and Its Applications: AppliedMath, Axioms, Computation, Fractal and Fractional, Geometry, International Journal of Topology, Logics, Mathematics and Symmetry.

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

Imprint Information Journal Flyer Open Access ISSN: 2075-1680

Latest Articles

18 pages, 5296 KB

Open AccessArticle

Bending Fields for Dual Curves

by Marija S. Najdanović, Svetozar R. Rančić and Ljubica S. Velimirović

Axioms 2026, 15(2), 112; https://doi.org/10.3390/axioms15020112 - 3 Feb 2026

Abstract

This paper provides several new characterizations of the infinitesimal bending of dual curves, which is defined as an infinitesimal deformation preserving dual arc length (with appropriate precision). The main goal is to consider the infinitesimal deformations of ruled surfaces through the corresponding deformations of dual curves. Some useful properties of the infinitesimal bending of dual curves are obtained, and dual bending fields are determined. The Vekua-type characterization of the infinitesimal bending of dual curves is formulated in terms of the derivative of the dual arc length. Explicit formulas for dual infinitesimal bending fields of dual spherical curves are obtained using the Blaschke frame, considering both an arbitrary real parameter and the dual arc length. A necessary and sufficient condition for the infinitesimal bending of the dual curve to lie on the dual unit sphere is presented in terms of Blaschke and Frenet invariants. Several examples are illustrated graphically using our own software tool. Full article

(This article belongs to the Section Geometry and Topology)

19 pages, 335 KB

Open AccessArticle

A Note on Truncated Exponential-Based Appell Polynomials via Fractional Operators

by Waseem Ahmad Khan, Francesco Aldo Costabile, Khidir Shaib Mohamed, Alawia Adam and Shahid Ahmad Wani

Axioms 2026, 15(2), 111; https://doi.org/10.3390/axioms15020111 - 2 Feb 2026

Abstract

In this work, we construct a new class of Appell-type polynomials generated through extended truncated and truncated exponential kernels, and we analyze their core algebraic and operational features. In particular, we establish a suitable recurrence scheme and obtain the associated multiplicative and differential operators. By confirming the quasi-monomial structure, we further deduce the governing differential equation for the proposed family. In addition, we present both a series expansion and a determinant formulation, providing complementary representations that are useful for symbolic manipulation and computation. As special cases, we introduce and study subfamilies arising from this setting, namely, extended truncated exponential versions of the Bernoulli, Euler, and Genocchi polynomials, and discuss their structural identities and operational behavior. Overall, these developments broaden the theory of special polynomials and furnish tools relevant to problems in mathematical physics and differential equations. Full article

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

17 pages, 337 KB

Open AccessArticle

Polycyclic Codes and Their Application in Constructing AEAQECCs

by Juan Li, Yunbo Tian and Fanghui Ma

Axioms 2026, 15(2), 110; https://doi.org/10.3390/axioms15020110 - 2 Feb 2026

Abstract

In this article, we study polycyclic codes over the ring

R = F_{q} [v] / ⟨ v^{2} - 1 ⟩

, where

q = p^{m}

with p being an odd prime. First, we introduce polycyclic codes and sequential [...] Read more.

In this article, we study polycyclic codes over the ring

R = F_{q} [v] / ⟨ v^{2} - 1 ⟩

, where

q = p^{m}

with p being an odd prime. First, we introduce polycyclic codes and sequential codes over R, and characterize the structural properties of these polycyclic codes. Next, we analyze the Euclidean dual codes, annihilator dual codes, annihilator self-orthogonal codes, and annihilator linear complementary dual (LCD) codes associated with this family of codes. Finally, some asymmetric entanglement-assisted quantum error-correcting codes (AEAQECCs) are constructed from polycyclic codes over R. Moreover, the parameters of our AEAQECCs are new in the existing literature. Full article

(This article belongs to the Special Issue Advances in Applied Algebra and Related Topics)

21 pages, 1651 KB

Open AccessArticle

A Note on Chaos of a Modified Piecewise Linear Discontinuous System with Multiple-Well Potentials: Melnikov Approach with Simulations

by Tsvetelin Zaevski, Nikolay Kyurkchiev and Anton Iliev

Axioms 2026, 15(2), 109; https://doi.org/10.3390/axioms15020109 - 2 Feb 2026

Abstract

The topic of chaotic thresholds for piecewise linear discontinuous (PWLD) systems with multiple-well potentials is a persistent topic in the research of a number of authors. In this article we investigate the chaos of a modified piecewise linear discontinuous (MPWLD) system. The model, containing N free parameters, could be of interest to specialists working in this area. With a specially developed software product, we generate the Melnikov equation

M (t) = 0

and examine all its zeros. This opens up an opportunity for researchers to correctly understand and formulate the classical Melnikov criterion for the possible occurrence of chaos in dynamical systems. Several simulations are composed. We also demonstrate some specialized modules for investigating the dynamics of the proposed model. Intriguing and new generalizations made through probabilistic constructions are considered. Full article

(This article belongs to the Special Issue Complex Networks and Dynamical Systems)

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15 pages, 575 KB

Open AccessArticle

An Efficient Horvitz–Thompson-Type Estimator for Two Sensitive Means Using a Three-Stage Quantitative Randomized Response Under Complex Sampling

by Hamed Salemian, Eisa Mahmoudi and Osama Abdulaziz Alamri

Axioms 2026, 15(2), 108; https://doi.org/10.3390/axioms15020108 - 2 Feb 2026

Abstract

In many empirical studies, researchers face challenges when addressing sensitive topics as respondents may be reluctant to provide truthful answers due to privacy concerns. Traditional direct survey methods often yield biased or unreliable estimates in such contexts. The randomized response technique offers a robust alternative by improving data validity while protecting respondent confidentiality. This paper proposes a novel quantitative three-stage randomized response model, introducing a new Horvitz–Thompson (HT)-type estimator for estimating the means of two sensitive variables under a general sampling design. Simulation studies indicate that the proposed estimator can achieve lower bias and mean squared error (MSE) compared to other existing estimators in the literature. Additionally, an empirical investigation was conducted using data from Shahid Chamran University of Ahvaz to estimate the average rates of exam cheating and cigarette consumption among students under a simple random sampling scheme, further demonstrating the practical utility of the proposed approach. Full article

(This article belongs to the Section Mathematical Analysis)

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27 pages, 2743 KB

Open AccessArticle

A Natural Generalization of the XLindley Distribution and Its First-Order Autoregressive Process with Applications to Non-Gaussian Time Series

by Emrah Altun, Soheyla A. Ghomeishi and Hana N. Alqifari

Axioms 2026, 15(2), 107; https://doi.org/10.3390/axioms15020107 - 31 Jan 2026

Abstract

The natural generalization of the XLindley distribution is proposed. The mathematical properties of the generalized XLindley distribution are derived. The importance of the proposed model is evaluated on the first-order autoregressive process, and compared with its counterparts. Extensive simulation studies are carried out to demonstrate the suitability of the estimation methods. Empirical findings reveal that the first-order autoregressive process with generalized XLindley innovations produces better forecasting results than those of the gamma, weighted Lindley, and normal innovations. Additionally, a web-tool application of the proposed model is developed and deployed on a free server that is accessible for practitioners. Full article

(This article belongs to the Special Issue Advances in the Theory and Applications of Statistical Distributions)

14 pages, 288 KB

Open AccessArticle

Two-Sided Zero-Divisor Graphs of Order-Preserving and A-Decreasing Finite Transformation Semigroups

by Kemal Toker and Muhammet Uysal

Axioms 2026, 15(2), 106; https://doi.org/10.3390/axioms15020106 - 31 Jan 2026

Abstract

Let

O_{n} (A)

be the order-preserving and A-decreasing finite transformation semigroup on

X_{n} = {1, 2, \dots, n}

. It is known that

O_{n} (A)

has zero element if and only [...] Read more.

Let

O_{n} (A)

be the order-preserving and A-decreasing finite transformation semigroup on

X_{n} = {1, 2, \dots, n}

. It is known that

O_{n} (A)

has zero element if and only if

1 \in A

. In this paper, we investigate zero-divisor graphs of

O_{n} (A)

where

1 \in A

and

n \geq 4

. First, we determine the set of right, left, and two-sided zero-divisors of

O_{n} (A)

; and their cardinalities. Let

Γ (O_{n} (A))

be the undirected graph whose vertices are the two sided zero-divisors of

O_{n} (A)

excluding the zero element (

θ

) and distinct two vertices

α

and

β

joined by an edge if and only if

α β = θ = β α

. In this paper, we prove that

Γ (O_{n} (A))

is a connected graph and find its diameter, girth, domination number and degrees of all vertices in

Γ (O_{n} (A))

. Moreover, we prove that

Γ (O_{n} (A))

is a perfect graph and we calculate clique number and chromatic number of it. Full article

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

13 pages, 278 KB

Open AccessArticle

Existence and Uniqueness of Random Coupled Riemann–Liouville Fractional Differential Systems with Delays in Banach Spaces

by Abdeldjabar Bourega, Khelifa Daoudi, Mohammed Nour A. Rabih, Osman Abdalla Osman and Muntasir Suhail

Axioms 2026, 15(2), 105; https://doi.org/10.3390/axioms15020105 - 31 Jan 2026

Abstract

This paper investigates the existence and uniqueness of solutions for a class of Riemann–Liouville fractional differential systems with delays in Banach spaces that are randomly coupled. The analysis is carried out by constructing an appropriate operator under random conditions and applying Perov’s fixed-point [...] Read more.

(This article belongs to the Special Issue Fractional Differential Equations and Dynamical Systems, 2nd Edition)

16 pages, 1151 KB

Open AccessArticle

Bayesian Optimization of Non-Invariant Systems with Constraints Developed for Application to the ECR Ion Source VENUS

by Victor Watson, Christopher M. Campbell, Heather L. Crawford, Yue Shi Lai, Marco Salathe and Damon Todd

Axioms 2026, 15(2), 104; https://doi.org/10.3390/axioms15020104 - 31 Jan 2026

Abstract

In this work, we consider the optimization of non-invariant systems with both safety and control constraints. We present a new approach based on Bayesian optimization for the dynamic, safe and controlled optimization of such systems. Although there are other possible use cases, we focus on the application to the electron cyclotron resonance ion source VENUS. From experimental data, we have observed that VENUS behaves to first order as a non-invariant dynamic system with moving areas of instability. Our novel approach aims at providing a tool that can maintain system optimization in a safe way. This is accomplished by making sure the objective function, the beam current in the case of VENUS, does not fall under an operational minimum, while simultaneously requiring the optimization to avoid areas where VENUS is unstable. We compare the result of our approach on synthetic data modeled to mimic the behavior of VENUS with two methods from the literature, a standard Bayesian optimizer and a safe Bayesian optimizer, both adapted to deal with dynamic systems. A cross Student T-test is conducted to show the significance of the improvement given by the new method we introduce here, regarding the two preexisting methods we compared to. The results of the tests conducted on synthetic data show that the proposed method succeeds at maintaining the system optimized and obeys the predefined constraints better than the literature methods explored. Full article

(This article belongs to the Special Issue Applications of Bayesian Methods in Statistical Analysis)

17 pages, 310 KB

Open AccessArticle

Geometry of Lightlike Hypersurfaces in a Class of Almost (α,p)-Metallic Semi-Riemannian Manifold

by Rajinder Kaur, Vandana Gupta, Jasleen Kaur and Ibrahim Al-Dayel

Axioms 2026, 15(2), 103; https://doi.org/10.3390/axioms15020103 - 30 Jan 2026

Abstract

The aim of this paper is to investigate the geometry of lightlike hypersurfaces in an

(α, p)

-silver semi-Riemannian manifold. Our work analyzes the behavior of the structures induced on a lightlike hypersurface by the

(α, p)

[...] Read more.

The aim of this paper is to investigate the geometry of lightlike hypersurfaces in an

(α, p)

-silver semi-Riemannian manifold. Our work analyzes the behavior of the structures induced on a lightlike hypersurface by the

(α, p)

-silver semi-Riemannian framework. We define and introduce the geometry of invariant, anti-invariant, and screen semi-invariant lightlike hypersurfaces within an almost

(α, p)

-silver semi-Riemannian manifold. Furthermore, we develop results concerning parallelism and geodesicity of the associated distributions and illustrate these findings with suitable examples. Full article

(This article belongs to the Special Issue Advances in Differential Geometry and Singularity Theory, 2nd Edition)

14 pages, 323 KB

Open AccessArticle

Integral Representation and Non-Uniqueness of Solutions for Impulsive Right-Sided Riemann–Liouville Fractional-Order Systems

by Xu Lu, Qingmin Zhu and Xianmin Zhang

Axioms 2026, 15(2), 102; https://doi.org/10.3390/axioms15020102 - 30 Jan 2026

Abstract

This paper investigates the equivalent integral equations (EIEs) of two impulsive right-sided Riemann–Liouville fractional-order systems (IRRFOSs). The limit properties of one IRRFOS are employed to establish the linear additivity of impulsive effects. A computational approach based on fractional calculus for piecewise functions is then employed to construct the EIE corresponding to a single impulse. With the aid of this linear additivity, the EIE of the considered IRRFOS is obtained, and through the relationship between the two IRRFOSs, the EIE of the other IRRFOS is further derived. The results indicate that the solutions of both EIEs consist of linear combinations of

ϕ (t)

and

Φ_{j} (t)

(j = 1, 2, \dots, N)

containing an arbitrary constant, which implies the non-uniqueness of solutions to the two IRRFOSs. Finally, the computational procedure for deriving the EIEs of the two IRRFOSs is presented, and the non-uniqueness of solutions is illustrated through two numerical examples. Full article

25 pages, 4688 KB

Open AccessArticle

Spectrally Negative Lévy Risk Model Under Multi-Layer Ratcheting Dividend Strategy and Capital Injections

by Fuyun Sun and Yongxia Zhao

Axioms 2026, 15(2), 101; https://doi.org/10.3390/axioms15020101 - 30 Jan 2026

Abstract

In this study, we investigate the mixed n-layer ratcheting dividend and capital injection policies for a spectrally negative Lévy risk model, where dividend distributions are implemented continuously in a non-decreasing manner, and capital injections are conducted discretely at the jump instants of an independent Poisson process. We incorporate both terminal values and transaction costs into the analysis, making the model more in line with practical scenarios. The value function and the Laplace transform of the ruin time are derived by leveraging Lévy fluctuation theory, and all the obtained results are formulated in terms of scale functions. Furthermore, numerical examples based on the classic risk model are provided to illustrate the theoretical findings. Full article

15 pages, 272 KB

Open AccessArticle

Boundedness of Commutators Generated by the Rough Fractional Maximal Operator on Variable Exponent Central Morrey Spaces

by Yuhe Yang, Zhenzhen Yang and Suixin He

Axioms 2026, 15(2), 100; https://doi.org/10.3390/axioms15020100 - 30 Jan 2026

Abstract

In this paper, using harmonic analysis tools−including spherical harmonic decomposition of kernels, sharp maximal function estimates, and variable exponent space theory—we investigate the boundedness of the commutator

[b, M_{Ω, β}]

on variable exponent central Morrey spaces, under suitable [...] Read more.

[b, M_{Ω, β}]

on variable exponent central Morrey spaces, under suitable regularity conditions on the variable exponents. Here,

Ω \in L^{l} (S^{n - 1})

(

l \geq 1

) denotes a zero-degree homogeneous function on the unit sphere

S^{n - 1}

β

satisfies

0 \leq β < n

, and

b \in C B M O (R^{n})

. Full article

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

8 pages, 231 KB

Open AccessArticle

Representation of Solutions to a Two-Sided Matrix Delay Differential Equations

by Zhenyu Bai and Chuanzhi Bai

Axioms 2026, 15(2), 99; https://doi.org/10.3390/axioms15020099 - 30 Jan 2026

Abstract

In this paper, we investigate the representation of solution for the following linear matrix delayed differential equation [...] Read more.

In this paper, we investigate the representation of solution for the following linear matrix delayed differential equation

\dot{Y} (t) = A_{1} Y (t) + Y (t) A_{2} + B Y (t - τ) + Y (t - τ) C + F (t), t \in [0, \infty)

where t is an independent variable,

Y (t)

is an

n \times n

unknown variable matrix,

τ > 0

is a delay,

A_{1}, A_{2}, B

, and C are given

n \times n

constant matrices, and

F (t)

is a given

n \times n

variable matrix. Without requiring any commutativity condition between the coefficient matrices and

Φ

and F, we establish a formula for the initial problem

Y (t) = Φ (t)

t \in [- τ, 0]

, where

Φ (t)

is an

n \times n

variable matrix. The proof uses the vectorization technique and the method of steps. Our result settles Open Problems 1 and 2 posed by Diblík. Full article

(This article belongs to the Special Issue Recent Advances in Differential Equations and Related Topics)

15 pages, 286 KB

Open AccessArticle

Stability of Volume Inequalities Associated with L_p Zonoids

by Ai-Jun Li and Siyao Sun

Axioms 2026, 15(2), 98; https://doi.org/10.3390/axioms15020098 - 29 Jan 2026

Abstract

In this paper, we establish stability versions of the volume inequalities associated with

L_{p}

zonoids. These results, particularly for the case

1 \leq p \leq 2

, extend the case

p = 1

previously obtained by Brazitikos and Giannopoulos. As applications, we [...] Read more.

In this paper, we establish stability versions of the volume inequalities associated with

L_{p}

zonoids. These results, particularly for the case

1 \leq p \leq 2

, extend the case

p = 1

previously obtained by Brazitikos and Giannopoulos. As applications, we derive several stability inequalities for

L_{p}

isotropic convex bodies and for bodies with minimal p-mean width and minimal

L_{p}

surface area. Full article

(This article belongs to the Special Issue Advances in Functional Analysis and Banach Space)

11 pages, 335 KB

Open AccessArticle

Symmetry Group Analysis of the Unsteady Heat Transfer of Spherical Nanoparticles at a Small Reynolds Number Value

by Andriy A. Avramenko, Igor V. Shevchuk, Margarita M. Kovetskaya, Andrii S. Kobzar, Kyryl Fedortsev and Olesya Y. Stepanova

Axioms 2026, 15(2), 97; https://doi.org/10.3390/axioms15020097 - 29 Jan 2026

Abstract

The problem of unsteady heat transfer between the gaseous and solid phases in two-phase flows with solid nanoparticles is considered. Based on a symmetry analysis, a solution to the unsteady heat conduction equation in spherical coordinates is obtained. Dependencies for the temperature profile and the Nusselt number are derived. The time-dependent change in the Nusselt number during the interaction between the solid particle and the surrounding medium is demonstrated. Full article

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

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7 pages, 235 KB

Open AccessArticle

Singular Equivalences and ϕ-Dimensions

by Jinrui Yang and Yongyun Qin

Axioms 2026, 15(2), 96; https://doi.org/10.3390/axioms15020096 - 28 Jan 2026

Abstract

The

ϕ

-dimension of an algebra is a homological invariant arising from the Igusa–Todorov function. In this paper, we establish a new bound on the

ϕ

-dimensions of two algebras related by singular equivalences of the Morita-type with level. Full article

(This article belongs to the Special Issue Advances in Representation Theory of Algebras)

17 pages, 18117 KB

Open AccessArticle

The Dynamics of a Switched IPM Model with Predation-Induced Fear and Seasonal Birth in a Pest Population

by Xuemei Yang, Jianjun Jiao and Lin Wu

Axioms 2026, 15(2), 95; https://doi.org/10.3390/axioms15020095 - 28 Jan 2026

Abstract

IPM (Integrated Pest Management) strategies present a good theoretical framework for sustainably controlling pest populations. In this paper, we propose a switched IPM model with predation-induced fear and seasonally birth in a pest population. Employing theories of impulsive differential equations, we gain evidence [...] Read more.

(0, \bar{y (t)})

of the investigated system is GAS. The investigated system is also proven to be persistent. Our results provide new methods for IPM strategies. Full article

(This article belongs to the Section Mathematical Analysis)

11 pages, 256 KB

Open AccessArticle

A Novel Generalized Contraction in G-Metric Spaces and Its Fixed Point Theorem

by Nicola Fabiano, Zouaoui Bekri, Amir Baklouti and Abdullah Assiry

Axioms 2026, 15(2), 94; https://doi.org/10.3390/axioms15020094 - 28 Jan 2026

Abstract

We introduce a new hybrid contraction condition in the setting of G-metric spaces that unifies Banach-, Kannan-, and Chatterjea-type contractions applied to an iterate

T^{p}

of a self-map T. Under a natural coefficient constraint, we prove that such a map admits [...] Read more.

We introduce a new hybrid contraction condition in the setting of G-metric spaces that unifies Banach-, Kannan-, and Chatterjea-type contractions applied to an iterate

T^{p}

of a self-map T. Under a natural coefficient constraint, we prove that such a map admits a unique fixed point in a complete G-metric space. An illustrative example is provided to demonstrate the applicability of the result beyond classical contractions. Full article

(This article belongs to the Special Issue Advances in Functional Analysis and Banach Space)

12 pages, 333 KB

Open AccessArticle

Ordering Planar Graphs by Their Signless Laplacian Spectral Radii

by Ke Wang, Zhen Lin, Shumin Zhang and Chengfu Ye

Axioms 2026, 15(2), 93; https://doi.org/10.3390/axioms15020093 - 27 Jan 2026

Abstract

A graph is planar if it can be embedded in the plane such that its edges intersect only at their common endpoints. In this paper, we determine the graphs attaining the second and third largest signless Laplacian spectral radii among all planar graphs [...] Read more.

n \geq 398

. Furthermore, we apply this characterization to identify the planar graphs that achieve the first three largest values of the sum of the first and second largest signless Laplacian eigenvalues. Full article

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