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

23 pages, 557 KB

Open AccessArticle

A Multi-Stage Decomposition and Hybrid Statistical Framework for Time Series Forecasting

by Swera Zeb Abbasi, Mahmoud M. Abdelwahab, Imam Hussain, Moiz Qureshi, Moeeba Rind, Paulo Canas Rodrigues, Ijaz Hussain and Mohamed A. Abdelkawy

Axioms 2026, 15(4), 273; https://doi.org/10.3390/axioms15040273 - 9 Apr 2026

Abstract

Modeling and forecasting nonstationary and nonlinear economic time series remain fundamentally challenging due to structural breaks, volatility clustering, and noise contamination that distort the intrinsic stochastic structure. To address these limitations, this study proposes a novel three-stage hybrid statistical framework that systematically integrates multi-level signal decomposition with structured parametric modeling to enhance predictive accuracy. The proposed hybrid architectures—EMD–EEMD–ARIMA, EMD–EEMD–GMDH, and EMD–EEMD–ETS—employ a hierarchical decomposition–reconstruction strategy before forecasting. In the first stage, Empirical Mode Decomposition (EMD) decomposes the observed series into intrinsic mode functions (IMFs) and a residual component. In the second stage, Ensemble Empirical Mode Decomposition (EEMD) is applied to further refine the extracted components, mitigating mode mixing and improving signal separability. In the final stage, each reconstructed component is modeled using ARIMA, Exponential Smoothing State Space (ETS), and Group Method of Data Handling (GMDH) frameworks, and the individual forecasts are aggregated to obtain the final prediction. Empirical evaluation based on a recursive one-step-ahead forecasting scheme demonstrates consistent numerical improvements across all standard accuracy measures. In particular, the proposed EMD–EEMD–ARIMA model achieves the lowest forecasting error, reducing the root-mean-square error (RMSE) by approximately 6–7% relative to the best-performing single-stage model and by about 3–4% relative to the two-stage EMD-based hybrids. Similar improvements are observed in mean squared error (MSE), mean absolute error (MAE), and mean absolute percentage error (MAPE), indicating enhanced stability and robustness of the three-stage architecture. The results provide strong numerical evidence that multi-level decomposition combined with structured statistical modeling yields superior predictive performance for complex nonlinear and nonstationary time series. The proposed framework offers a mathematically coherent, computationally tractable, and systematically structured hybrid modeling strategy that effectively integrates noise-assisted decomposition with parametric and data-driven forecasting techniques. Full article

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

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15 pages, 305 KB

Open AccessArticle

On the Bounding Function of Cogirth and Supereulerian Regular Matroids

by Xiaoxiao Qin, Fulong Ye and Bofeng Huo

Axioms 2026, 15(4), 272; https://doi.org/10.3390/axioms15040272 - 9 Apr 2026

Abstract

Following Bauer’s 1985 question on how a graph’s minimum degree relates to it being supereulerian, Catlin solved the problem for graphs with a minimum degree of at least

\frac{n}{5}

. Subsequently, Lai solved it for the case where the minimum degree is [...] Read more.

Following Bauer’s 1985 question on how a graph’s minimum degree relates to it being supereulerian, Catlin solved the problem for graphs with a minimum degree of at least

\frac{n}{5}

. Subsequently, Lai solved it for the case where the minimum degree is at least

\frac{n}{10}

. Projecting this problem into the setting of matroids leads to the question of the relationship between a matroid being supereulerian and its cogirth. In 2025, Qin et al. showed that a connected simple regular matroid M with cogirth at

\max {\frac{r (M) + 1}{15}, 9}

is supereulerian. In this paper, we prove that for any real number c with

15 < c < 20

, there exists a smallest integer

f (c)

such that every connected simple regular matroid M with cogirth at least

\max {\frac{r (M) + 1}{c}, f (c)}

has a spanning Eulerian subset. Full article

12 pages, 277 KB

Open AccessArticle

Product Inequalities and Log-Convexity Results for Struve Functions and Their First Derivative

by Dimitris A. Frantzis and Eugenia N. Petropoulou

Axioms 2026, 15(4), 271; https://doi.org/10.3390/axioms15040271 - 9 Apr 2026

Abstract

Some inequalities for products of Struve functions

H_{ν} (x)

when

| ν | \leq \frac{1}{2}

are established using their infinite product formula as well as the arithmetic–geometric mean inequality. When these results are combined with some previously established results [...] Read more.

Some inequalities for products of Struve functions

H_{ν} (x)

when

| ν | \leq \frac{1}{2}

are established using their infinite product formula as well as the arithmetic–geometric mean inequality. When these results are combined with some previously established results in the literature, they lead to interesting inequalities between

H_{ν} (x)

and

J_{ν} (x)

, where

J_{ν} (x)

is the Bessel function of the first kind. Analogous results are also derived for

H_{ν}^{'} (x)

when

0 \leq ν \leq \frac{1}{2}

. Moreover, results concerning the log-convexity or log-concavity of certain functions involving

H_{ν}^{(m)} (x)

m = 0, 1

are also established. Full article

(This article belongs to the Section Mathematical Analysis)

12 pages, 259 KB

Open AccessArticle

From Dedekind’s Level 12 Identities to Combinatorial Structures of Colored Partitions

by Fatemah Mofarreh, Arooj Fatima and Ahmer Ali

Axioms 2026, 15(4), 270; https://doi.org/10.3390/axioms15040270 - 8 Apr 2026

Abstract

The Dedekind

η

-function plays an important role in number theory, particularly in the study of modular forms, q-series, and partition identities. In this paper, we investigate several level-12

η

-function identities and examine their combinatorial implications. These identities are obtained from [...] Read more.

The Dedekind

η

-function plays an important role in number theory, particularly in the study of modular forms, q-series, and partition identities. In this paper, we investigate several level-12

η

-function identities and examine their combinatorial implications. These identities are obtained from algebraic transformations of known expansions involving mock theta functions, which were originally introduced by Srinivasa Ramanujan. By employing classical q-series techniques and modular transformations, we derive identities that reveal interesting relationships among

η

-functions. We further interpret these identities combinatorially to establish correspondences between specific classes of colored partitions with prescribed color restrictions. These results provide new insights into the structure of colored partition functions and highlight the interplay between mock theta functions, Dedekind

η

-function identities, and combinatorial partition theory. Our findings contribute to a deeper understanding of the connections between modular forms and colored partitions and suggest further directions for research in number theory and combinatorics. Full article

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

29 pages, 5917 KB

Open AccessArticle

Deferred Cesàro Summability and Korovkin-Type Approximation Theorems for Double Sequences on Time Scales

by Hari M. Srivastava, Bidu Bhusan Jena and Susanta Kumar Paikray

Axioms 2026, 15(4), 269; https://doi.org/10.3390/axioms15040269 - 8 Apr 2026

Abstract

This paper investigates fundamental concepts of statistical convergence for double sequences of time-scale functions via the deferred Cesàro summability mean. Several limit properties and inclusion relations between the newly-introduced convergence notions are established. Based on these concepts, a number of Korovkin-type approximation theorems are proved for time-scale functions of two variables by using suitable algebraic test functions. Illustrative examples involving a positive linear operator associated with bivariate Bernstein polynomials are presented to demonstrate the applicability of the theoretical results. In addition, the rate of statistical convergence with respect to the deferred Cesàro summability method is studied and estimated. Full article

(This article belongs to the Section Mathematical Analysis)

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17 pages, 511 KB

Open AccessArticle

Homogeneity Test and Sample Size of Relative Risk Ratios for Complex Paired Data Under Dalla’s Model

by Shuman Sun and Zhiming Li

Axioms 2026, 15(4), 268; https://doi.org/10.3390/axioms15040268 - 7 Apr 2026

Abstract

In clinical research, unilateral data and bilateral data are commonly collected when paired organs or body parts of people receive treatment. Existing models are often inadequate for the research of combined unilateral and bilateral data. Considering population heterogeneity, this paper proposes three statistical tests and sample size estimation methods for the relative risk ratio in stratified unilateral and bilateral data under Dallal’s model. We derive test statistics (i.e., likelihood ratio, Wald-type, and score statistics) and evaluate their performance in terms of type I error rates and powers. Then, sample size determination is performed using an iterative algorithm. Monte Carlo simulations demonstrate that the score test performs well across various parameter configurations. Moreover, the estimated powers for determining sample size based on the score test are closer to the actual empirical powers. Two real examples of otolaryngology and myopathy are provided to illustrate the effectiveness of the proposed methods. Full article

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33 pages, 431 KB

Open AccessArticle

The Yamabe Flow Under the Rotational Ansatz of Noncompact (Pseudo-Riemannian) Solitons: Schwarzschild and Generalized-Schwarzschild Solitons

by Orchidea Maria Lecian

Axioms 2026, 15(4), 267; https://doi.org/10.3390/axioms15040267 - 7 Apr 2026

Abstract

The present paper is aimed at studying the convergence of the Yamabe flow in the case of noncompact solitons. The more specified example of locally conformally flat noncompact solitons is addressed with the aim to newly analyse the qualities of the Ricci scalar. The particular case of noncompact pseudo-Riemannian solitons is studied; moreover, in the instances of Schwarzschild and Generalized-Schwarzschild geometries, rescalings of spherically symmetric weights are performed. For this purpose, new results are achieved as far as the considered structures are concerned. The Myers Theorem is upgraded as the new Myers paradigm of spacetime-dimensional manifolds, where the Einstein Field Equations can now be taken into account. In particular, the Myers Theorems are studied here as far as their new implementation in General Relativity Theory is concerned. As a first important result, the Myers mean curvature is found to coincide with the Ricci scalar in General Relativity Theory, where the 4-position of the observer, from which the 4-velocity 4-vector is calculated from, is taken as that of the observer solidal with the reference frame of the photon. The following results are also of relevance. In more detail, the umbilicity conditions are applied. At a further step, the role of the umbilicity conditions in GR after the Myers Theorems are studied for weighted manifolds and specific new implications of weighted manifolds are developed. The description of the weighted Schwarzschild manifolds and that of the weighted Generalized-Schwarzschild manifolds are newly studied as follows: as a new finding, the Birkhoff Theorem is newly reconciled with the rotational ansatz of the metrised solitons, and the comparison with the previous results about the Brendle non-metrised solitons is accomplished with the outcome stressing the new roles of the new rescalings of the metric tensor with respect to the previous known results of the scaling of the metric tensor of the non-metrised solitons. In the present framework, these procedures allow one to prove the reconciliation of the EFEs with the Yamabe flow. The flow on the tipping lightcones is newly written. The umbilicity condition is studied in General Relativity after the upgrade of the Myers Theorems as far as the sectional curvatures are concerned; as a result, the Calabi–Bernstein description is implemented in General Relativity, as well as the Chen–Yau requirements, and the cases of weighted manifolds are taken into account. More specifically, the equal-time 2-dimensional space surfaces are studied analytically, onto which the weighted General-Relativistic solitons which satisfy the Einstein field equations after the Yamabe flow are projected due to the rotational ansatz. As an accessory introductory result, the class of Wu non-metrised solitons are proven to be discarded in several aspects of the Wu description as the conditions provided after the work of Wu are not compatible with metrisation. Full article

(This article belongs to the Section Hilbert’s Sixth Problem)

14 pages, 266 KB

Open AccessArticle

On Sawyer Duality in One and Higher Dimensions

by Alberto Fiorenza, Pankaj Jain and Saujanya Mohanty

Axioms 2026, 15(4), 266; https://doi.org/10.3390/axioms15040266 - 7 Apr 2026

Abstract

We develop the Sawyer duality principle for non-increasing functions where, in the denominator, the function g is replaced by

\int_{x}^{\infty} \frac{g (t)}{t} d t

. This result complements Stepanov’s result in which g was replaced by [...] Read more.

We develop the Sawyer duality principle for non-increasing functions where, in the denominator, the function g is replaced by

\int_{x}^{\infty} \frac{g (t)}{t} d t

. This result complements Stepanov’s result in which g was replaced by

\frac{1}{x} \int_{0}^{x} g (t) d t

. We use our result and obtain Stepanov’s result for non-decreasing functions and similarly use Stepanov’s result in proving our result for non-decreasing functions. These results have also been obtained in

R^{n}

. Full article

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

23 pages, 393 KB

Open AccessArticle

Curvature–Cohomology Criterion for Projectivity: A Synthesis of Classical Results in Hodge Theory

by Ghaliah Alhamzi, Mona Bin-Asfour, Emad Solouma, Abdullah Alahmari, Mansoor Alsulami and Sayed Saber

Axioms 2026, 15(4), 265; https://doi.org/10.3390/axioms15040265 - 6 Apr 2026

Abstract

This paper synthesizes classical results in Hodge theory, curvature positivity, and vanishing theorems to give a concise curvature–cohomology criterion for the projectivity of compact Kähler manifolds. While each analytic component—Yau’s solution of the Calabi conjecture, the Bochner–Kodaira–Nakano identity, and Kodaira’s embedding theorem—is well-known, [...] Read more.

c_{1} (M)

admits a semi-positive real

(1, 1)

representative that is strictly positive at some point (or equivalently has a maximal rank n somewhere), then M is projective. Beyond the maximal rank case, we refine Girbau’s classical vanishing theorem to obtain an optimal rank-sensitive bound: if

2 π c_{1} (M)

has a semi-positive representative whose pointwise rank is k somewhere, then

H^{p, 0} (M) = 0

for all

p > n - k

. This sharpens the classical Girbau–Griffiths–Harris vanishing theorem and quantifies how partial positivity of a Ricci representative constrains Hodge cohomology. We situate these criteria alongside classical tests (Kodaira integrality and Moishezon) and numerical descriptions of the Kähler cone (Demailly–Paun), discuss deformation-invariance properties, and relate them to RC positivity and Campana–Peternell-type statements. Examples illustrate the sharpness of the hypotheses, and we survey the effective bounds—ranging from rigorous uniform high ampleness results to conjectural optimal constants—with clear distinction between proven theorems, refinements of classical results, and open problems. The contribution of this work lies not in new analytic techniques but in (1) isolating a sharp curvature condition at the level of

c_{1} (M)

; (2) organizing classical tools into a direct projectivity criterion; and (3) clarifying the rank-dependent vanishing behavior that follows from partial positivity. Full article

(This article belongs to the Special Issue Recent Advances in Complex Analysis and Applications, 2nd Edition)

28 pages, 13837 KB

Open AccessReview

Spacetime Metrics with Spherical Symmetry: A Short Review on the Riemann Tensors and Kretschmann Scalars

by Hector Eduardo Roman

Axioms 2026, 15(4), 264; https://doi.org/10.3390/axioms15040264 - 5 Apr 2026

Abstract

While the standard Schwarzschild metric is overwhelmingly employed in general relativity (GR) as the starting point for various spherical spacetime metric calculations, its isotropic (ISO) form is mentioned in more specialized contexts and its derivation is barely discussed in published GR literature. In this work, we review the isotropic metric, stressing that it stands out as a useful spherically symmetric metric to be employed also in traditional GR problems. We start by deriving the ISO metric through solving the vacuum field equations in Cartesian coordinates, thereby obtaining the Ricci tensor also in spherical coordinates. We then analytically calculate the Riemann tensor in Cartesian coordinates, proving its consistency with the Ricci tensor calculation for pedagogical reasons. Finally, from the Riemann tensor we exactly evaluate the Kretschmann scalar, which lacks metric singularities, a result consistent with the known singular behavior of the standard Schwarzschild metric. We conclude that the isotropic metric naturally emerges as a suitable candidate for modeling static neutron stars and regular black holes, thereby complementing the present attempts to understand these rapidly evolving research fields. Full article

(This article belongs to the Special Issue Special Functions and Related Topics, 2nd Edition)

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12 pages, 262 KB

Open AccessArticle

Stochastic Stability Analysis for Neutral Systems with Hadamard Fractional Derivatives

by Sahar Mohammad A. Abusalim, Abdellatif Ben Makhlouf and Raouf Fakhfakh

Axioms 2026, 15(4), 263; https://doi.org/10.3390/axioms15040263 - 5 Apr 2026

Abstract

This work investigates stability under Hyers–Ulam criteria for a class of Hadamard Neutral fractional stochastic differential equations (HNFSDE). The analysis applies a fixed-point theorem (FPT) combined with principles of stochastic integration. To illustrate the applicability of the derived theoretical results, two demonstrative cases [...] Read more.

(This article belongs to the Special Issue Fractional Differential Equation and Its Applications)

28 pages, 621 KB

Open AccessArticle

Averaging Principle for Itô–Doob Fractional Stochastic Systems in mth Moment

by Muhammad Imran Liaqat and Ramy M. Hafez

Axioms 2026, 15(4), 262; https://doi.org/10.3390/axioms15040262 - 4 Apr 2026

Abstract

This study presents results on the well-posedness, Ulam–Hyers stability, and

m

th moment averaging principle for the Itô–Doob fractional stochastic system within the framework of

η

-Caputo fractional derivatives. We demonstrate well-posedness using the fixed-point approach. A generalized Grönwall inequality is employed to [...] Read more.

This study presents results on the well-posedness, Ulam–Hyers stability, and

m

th moment averaging principle for the Itô–Doob fractional stochastic system within the framework of

η

-Caputo fractional derivatives. We demonstrate well-posedness using the fixed-point approach. A generalized Grönwall inequality is employed to establish sufficient conditions for Ulam–Hyers stability. Furthermore, we establish the averaging principle that facilitates obtaining a simplified averaged system from the original complex, multiple time-scale system. Finally, numerical simulations using the Euler–Maruyama method are provided to support the theoretical findings. Full article

(This article belongs to the Special Issue Numerical Analysis, Approximation Theory and Related Topics)

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14 pages, 915 KB

Open AccessArticle

Stability of Self-Gravitating Bosonic Configurations

by Gilbert Reinisch and José Antonio de Freitas Pacheco

Axioms 2026, 15(4), 261; https://doi.org/10.3390/axioms15040261 - 3 Apr 2026

Abstract

We study equilibrium and stability properties of self-gravitating bosonic configurations in the nonrelativistic regime by numerically solving the nonlinear Gross–Pitaevskii–Poisson (GPP) equations system. Using an appropriate coordinate transformation, the equations are written in a dimensionless form independent of the physical model parameters, so that each configuration is determined only by the central value of the wave function. We compute sequences of stationary solutions including ground and radially excited states and identify bifurcation points between them. The virial relation is used as a diagnostic condition for equilibrium, leading to the determination of a critical central density and a maximum particle number above which no stationary solutions are found. Excited configurations satisfying the virial relation are expected to be metastable since they violate stability conditions resulting from radial perturbation analyses. From the critical particle number, we estimate the maximum stable mass and radius. For axion-like bosons with mass

10^{- 5}

eV, the resulting configurations have masses of the order of tens of Earth masses and meter-scale radii. Full article

(This article belongs to the Special Issue Mathematical Cosmology)

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22 pages, 304 KB

Open AccessArticle

A Banach–Lie Approach to Ternary Symmetries in Nest Algebras

by Amal S. Alali, Nazim and Junaid Nisar

Axioms 2026, 15(4), 260; https://doi.org/10.3390/axioms15040260 - 2 Apr 2026

Abstract

Let

N

be a nest on a Banach space, and let

Alg (N)

denote the associated nest algebra equipped with the operator norm. In this paper, we develop a Banach–Lie framework for bounded triple derivations and triple automorphisms on [...] Read more.

Let

N

be a nest on a Banach space, and let

Alg (N)

denote the associated nest algebra equipped with the operator norm. In this paper, we develop a Banach–Lie framework for bounded triple derivations and triple automorphisms on

Alg (N)

. We prove that the space of bounded triple derivations is closed under the commutator bracket and hence forms a Lie algebra, while the set of triple automorphisms forms a norm-closed subgroup of

GL (Alg (N))

. We further establish an exponential–differential correspondence between these two classes: the exponential of a bounded triple derivation yields a one-parameter group of triple automorphisms, and conversely, the tangent space at the identity of the triple automorphism group is identified with the Lie algebra of bounded triple derivations. We also relate these objects to derivations and automorphisms of the standard embedding Lie algebra associated with the Lie triple system naturally induced by

Alg (N)

. To illustrate the general theory, we finally determine explicit forms of triple derivations and triple automorphisms for the eight non-perfect three-dimensional real Lie algebras. Full article

10 pages, 254 KB

Open AccessArticle

On the Monogenity of Totally Complex Pure Octic Fields

by István Gaál

Axioms 2026, 15(4), 259; https://doi.org/10.3390/axioms15040259 - 2 Apr 2026

Abstract

Let

0, 1 \neq m \in Z

and

α = \sqrt[8]{m}

. According to the results of Gaál and El Fadil,

α

generates a power integral basis in

K = Q (α)

, if and only if m is [...] Read more.

Let

0, 1 \neq m \in Z

and

α = \sqrt[8]{m}

. According to the results of Gaál and El Fadil,

α

generates a power integral basis in

K = Q (α)

, if and only if m is square-free and

m ≢ 1 (\mod 4)

. In the present paper, we consider totally complex pure octic fields, as in the case

m < 0

, with m satisfying the above property. In this case,

(1, α, α^{2}, \dots, α^{7})

is an integral basis. Our purpose is to investigate whether K admits any other generators of power integral bases, inequivalent to

α

. We present an efficient method to calculate generators of power integral bases in this type of fields with coefficients

< 10^{200}

in the above integral basis. We report on the results of our calculation for this type of field with

0 > m > - 5000

, which yields 2024 fields. Full article

20 pages, 287 KB

Open AccessArticle

Nonlinear Mixed Skew Jordan-Type Higher Derivations on ∗-Algebras

by Yimeng Yue, Liang Kong, Fenhong Li and Fugang Chao

Axioms 2026, 15(4), 258; https://doi.org/10.3390/axioms15040258 - 2 Apr 2026

Abstract

Let

A

be a unital ∗-algebra containing a nontrivial projection P. In this paper, we introduce the notion of a nonlinear mixed skew Jordan-type derivation (that is, [...] Read more.

Let

A

be a unital ∗-algebra containing a nontrivial projection P. In this paper, we introduce the notion of a nonlinear mixed skew Jordan-type derivation (that is,

p_{n} (S_{1}, S_{2}, S_{3}, \dots, S_{n}) = S_{1} ⋄ S_{2} • S_{3} • \dots • S_{n}

, where

S ⋄ K = S^{*} K + K^{*} S

and

S • K = S K + K S^{*}

for all

S, K \in A

) and show that if a map

Φ

A \to A

satisfies

Φ (p_{n} (S_{1}, S_{2}, \dots, S_{n})) = \sum_{k = 1}^{n} p_{n} (S_{1}, S_{2}, \dots S_{k - 1}, Φ (S_{k}), S_{k + 1}, \dots, S_{n})

, for all

S_{1}, S_{2}, \dots, S_{n} \in A

and all

n \geq 3

, then

Φ

is an additive ∗-derivation. Furthermore, we generalize this result to higher derivable maps on

A

. As applications, the above result is applied to several special classes of unital ∗-algebras such as prime ∗-algebras, factor von Neumann algebras and standard operator algebras. Full article

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

21 pages, 6457 KB

Open AccessArticle

Estimator-Based Time-Varying Feedback Control for Uncertain, Anti-Stable Heat Equation in a Prescribed Finite Time

by Chengzhou Wei

Axioms 2026, 15(4), 257; https://doi.org/10.3390/axioms15040257 - 1 Apr 2026

Abstract

This paper studies prescribed-time (PT) stabilization for a heat equation with an unstable term at the uncontrolled boundary, subject to external disturbances and internal unknown mode uncertainties at the controlled boundary. A boundary time-varying output feedback control scheme based on disturbance estimation is developed, where the convergence time is independent of the initial condition and can be specified a priori. A disturbance estimator using boundary measurements and a time-varying tuning function enables prescribed-time estimation of both the disturbance and the system state. By integrating active disturbance rejection control with the backstepping technique, a boundary output feedback controller is derived. A simulation example from the burning process of a solid propellant rocket demonstrates the effectiveness of the proposed approach. Full article

(This article belongs to the Section Mathematical Physics)

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20 pages, 701 KB

Open AccessArticle

A Hybrid Numerical Method Combining Legendre Polynomials and Improved Block-Pulse Functions for Solving Linear Systems of Fredholm Integral Equations

by Mohammed Z. Alqarni, Mohamed A. Ramadan and Heba S. Osheba

Axioms 2026, 15(4), 256; https://doi.org/10.3390/axioms15040256 - 1 Apr 2026

Abstract

In order to solve linear systems of Fredholm integral equations, this paper proposes a novel hybrid numerical method that combines improved block-pulse functions with Legendre polynomials. By utilizing the orthogonality and strong approximation properties of Legendre polynomials along with the computational simplicity of improved block-pulse functions, the suggested method converts the integral system into an equivalent system of algebraic equations. The approach outperforms a number of conventional numerical methods in terms of accuracy and convergence speed. The robustness, efficiency, and stability of the suggested scheme are validated by several numerical remarks, which also show how well it works for solving complex Fredholm integral systems that arise in scientific and engineering applications. Full article

(This article belongs to the Section Mathematical Analysis)

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5 pages, 185 KB

Open AccessArticle

Log-Convexity and Fixed Points of Permutations

by Miklós Bóna

Axioms 2026, 15(4), 255; https://doi.org/10.3390/axioms15040255 - 1 Apr 2026

Abstract

We provide a combinatorial proof for the fact that the numbers of derangements of length n form a log-convex sequence for

n \geq 3

. A minor modification of our proof yields the same result for permutations of length

n \geq 4

that [...] Read more.

We provide a combinatorial proof for the fact that the numbers of derangements of length n form a log-convex sequence for

n \geq 3

. A minor modification of our proof yields the same result for permutations of length

n \geq 4

that have exactly one fixed point. We explain why these statements do not generalize for permutations with exactly k fixed points where

k \geq 3

. Full article

(This article belongs to the Special Issue Permutation Patterns)

15 pages, 1089 KB

Open AccessArticle

Application of Lie Group Transformation to Laminar Magnetohydrodynamic Flow Between Two Infinite Parallel Plates Under Uniform Magnetic Field

by Anood M. Hanafy, Mina B. Abd-el-Malek and Nagwa A. Badran

Axioms 2026, 15(4), 254; https://doi.org/10.3390/axioms15040254 - 31 Mar 2026

Abstract

This study aims to advance the understanding of laminar magnetohydrodynamic (MHD) fluid flow between two parallel plates subjected to a uniform transverse magnetic field, motivated by its significant applications in engineering and industrial systems such as nuclear reactor cooling, MHD generators, and electromagnetic pumping devices. The governing equations are simplified using a one-parameter Lie group symmetry transformation, which exploits the inherent symmetry properties of the system to reduce the original unsteady partial differential equations to a system of ordinary differential equations. The reduced equations are solved exactly under appropriate boundary and initial conditions, ensuring mathematically consistent and physically realistic solutions. A comprehensive analysis is conducted to examine the influence of key physical parameters, along with the applied magnetic field, on the velocity, temperature, and concentration profiles. The selected parameter ranges encompass a broad spectrum of physically relevant cases, enabling a detailed assessment of their effects. The results indicate that the transverse magnetic field exerts a damping effect on the flow, reducing the velocity profile due to the Lorentz force. Moreover, an increase in the Schmidt number accelerates the achievement of a steady-state concentration, while higher Prandtl numbers reduce the temperature profile. In contrast, the radiation parameter enhances the temperature distribution. In addition, the skin-friction coefficient is presented graphically, and the Nusselt number is evaluated to characterize the heat transfer performance. Overall, the findings provide valuable insight into the effects of magnetic, thermal, and solutal parameters on laminar MHD flow between parallel plates. Full article

(This article belongs to the Section Mathematical Analysis)

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