Axioms

15 pages, 265 KB

Open AccessArticle

Algorithms for Solving the Resolvent of the Sum of Two Maximal Monotone Operators with a Finite Family of Nonexpansive Operators

by Ali Berrailes and Abdallah Beddani

Axioms 2025, 14(11), 783; https://doi.org/10.3390/axioms14110783 (registering DOI) - 25 Oct 2025

Abstract

In this paper, we address a variational problem involving the sum of two maximal monotone operators combined with a finite family of nonexpansive operators. To solve this problem, we propose iterative algorithms based on single-valued mappings. First, we examine cases involving two or [...] Read more.

In this paper, we address a variational problem involving the sum of two maximal monotone operators combined with a finite family of nonexpansive operators. To solve this problem, we propose iterative algorithms based on single-valued mappings. First, we examine cases involving two or three maximal monotone operators, introducing novel algorithms to obtain their solutions. Secondly, we extend our analysis by applying the Ishikawa iterative scheme within the framework of fixed-point theory. This allows us to establish strong convergence results. Finally, we provide an illustrative example to demonstrate the effectiveness and applicability of the proposed methods. Full article

(This article belongs to the Special Issue Modern Problems of Analysis, Optimization, Approximation and Their Applications)

21 pages, 1805 KB

Open AccessArticle

Assessment of Compliance with Integral Conservation Principles in Chemically Reactive Flows Using rhoCentralRfFoam

by Marcelo Frias, Luis Gutiérrez Marcantoni and Sergio Elaskar

Axioms 2025, 14(11), 782; https://doi.org/10.3390/axioms14110782 (registering DOI) - 25 Oct 2025

Abstract

Reliable simulations of any flow require proper preservation of the fundamental principles governing the mechanics of its motion, whether in differential or integral form. When these principles are solved in differential form, discretization schemes introduce errors by transforming the continuous physical domain into [...] Read more.

Reliable simulations of any flow require proper preservation of the fundamental principles governing the mechanics of its motion, whether in differential or integral form. When these principles are solved in differential form, discretization schemes introduce errors by transforming the continuous physical domain into a discrete representation that only approximates it. This paper analyzes the numerical performance of the solver for supersonic chemically active flows, rhoCentralRfFoam, using integral conservation principles of mass, momentum, energy, and chemical species as a validation tool in a classical test case with a highly refined mesh under nonlinear pre-established reference conditions. The analysis is conducted on this specific test case; however, the methodology presented here can be applied to any problem under study. It may serve as an a posteriori verification tool or be integrated into the solver’s workflow, enabling automatic verification of conservation at each time step. The resulting deviations are evaluated, and it is observed that the numerical errors remain below

0.25 %

, even in cases with a high degree of nonlinearity. These results provide preliminary validation of the solver’s accuracy, as well as its ability to capture physically consistent solutions using only information generated internally by the solver for validation. This represents a significant advantage over validation methods that require external comparison with reference solutions, numerical benchmarks, or exact solutions. Full article

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

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16 pages, 702 KB

Open AccessArticle

Total Decoupling of 2D Lattice Vibration

by Nan Jiang, Qizhi Zhang and Jianwei Wang

Axioms 2025, 14(11), 781; https://doi.org/10.3390/axioms14110781 (registering DOI) - 24 Oct 2025

Abstract

Lattice structures find broad application in aerospace, automotive, biomedical, and energy systems owing to their exceptional structural stability. These systems typically exhibit complex internal couplings that facilitate vibration propagation across the entire network. The primary objective of this study is to achieve total [...] Read more.

Lattice structures find broad application in aerospace, automotive, biomedical, and energy systems owing to their exceptional structural stability. These systems typically exhibit complex internal couplings that facilitate vibration propagation across the entire network. The primary objective of this study is to achieve total decoupling of 2D lattice vibration system, which involves eliminating all inter-subsystem interactions while preserving spectrum. Building upon prior research, we develop structure-preserving isospectral transformation flow (SPITF) framework to address this challenge. Two principle results are established: first, the equations of motion are systematically derived for lattice vibration systems; second, total decoupling is successfully realized for such systems. Numerical experiments validate the decoupling capability of lattice vibration systems. Full article

(This article belongs to the Special Issue Nonlinear Dynamical System and Its Applications)

17 pages, 248 KB

Open AccessArticle

Lie Derivations on Generalized Matrix Algebras by Local Actions

by Jinhong Zhuang, Yanping Chen and Yijia Tan

Axioms 2025, 14(11), 780; https://doi.org/10.3390/axioms14110780 (registering DOI) - 24 Oct 2025

Abstract

Let

G = G (A, B, M, N)

be a generalized matrix algebra. A linear map

Δ : G \to G

is called a Lie derivation at

E \in G

if [...] Read more.

Let

G = G (A, B, M, N)

be a generalized matrix algebra. A linear map

Δ : G \to G

is called a Lie derivation at

E \in G

if

Δ ([U, V]) = [Δ (U), V] + [U, Δ (V)]

for all pairs

U, V \in G

such that

U V = E

. In this paper, we use techniques of matrix decomposition and algebraic identity analysis to fully characterize the general form of Lie derivations at

E = (\begin{matrix} e_{0} & 0 \\ 0 & 0 \end{matrix})

, where

e_{0}

is an arbitrary fixed element in

A

. Our main result establishes a necessary and sufficient condition for a Lie derivation at

E = (\begin{matrix} e_{0} & 0 \\ 0 & 0 \end{matrix})

to be decomposable into the sum of a derivation of

G

and a center-valued linear map. This characterization significantly extends the classical results concerning global Lie derivations and provides a deeper insight into the local Lie-type behavior in operator algebras. Full article

28 pages, 12538 KB

Open AccessArticle

Embedding Vacuum Fluctuations in the Dirac Equation: On the Neutrino Electric Millicharge and Magnetic Moment

by Hector Eduardo Roman

Axioms 2025, 14(11), 779; https://doi.org/10.3390/axioms14110779 - 23 Oct 2025

Abstract

An extension of the Dirac equation for an initially massless particle carrying an electric charge, assumed to be embedded via minimal coupling into an external fluctuating electromagnetic four-potential of the vacuum, is suggested. We conjecture that appropriate averages of the four-vector can lead [...] Read more.

An extension of the Dirac equation for an initially massless particle carrying an electric charge, assumed to be embedded via minimal coupling into an external fluctuating electromagnetic four-potential of the vacuum, is suggested. We conjecture that appropriate averages of the four-vector can lead to observable quantities, such as a particle mass in its rest frame. The conditions on the potential mean values to become gauge-invariant are obtained. The mass is found to be proportional to the magnitude of the charge times the associated mean Lorentz scalar of the four-potential, and the relation holds for both spacelike and timelike types of four-vectors. For the latter, the extended Dirac equation violates Lorentz covariance, but the violation can be argued to occur within a time scale allowed by the uncertainty principle. For larger times, the particle has acquired a mass and Lorentz covariance is restored. This mathematical scenario is applied to acquire estimates of the neutrino millicharge and magnetic moment, in good agreement with the present upper bounds obtained experimentally. The issue of unstable particle decay is considered by focusing, for illustration, on the main decay channels of the selected particles. From the lifetime of the

τ

lepton, a lower bound of the effective neutrino mass is predicted, which can be tested in future experiments. Full article

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

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19 pages, 294 KB

Open AccessArticle

Ore Extensions of Multiplier Hopf Coquasigroups

by Rui Zhang, Na Zhang, Yapeng Zeng and Tao Yang

Axioms 2025, 14(11), 778; https://doi.org/10.3390/axioms14110778 - 23 Oct 2025

Abstract

This paper introduces and investigates Ore extensions in the context of multiplier Hopf coquasigroups, a structure that generalizes both multiplier Hopf algebras and Hopf coquasigroups. We establish necessary and sufficient conditions under which an Ore extension of a regular multiplier Hopf coquasigroup itself [...] Read more.

This paper introduces and investigates Ore extensions in the context of multiplier Hopf coquasigroups, a structure that generalizes both multiplier Hopf algebras and Hopf coquasigroups. We establish necessary and sufficient conditions under which an Ore extension of a regular multiplier Hopf coquasigroup itself forms a regular multiplier Hopf coquasigroup. Furthermore, we explore the isomorphism problem for such Ore extensions, providing criteria for the equivalence of two extensions. The case of multiplier Hopf coquasigroups is also analyzed, with conditions derived for the Ore extension to inherit the structure. Our results unify and extend prior work on Ore extensions in the settings of Hopf algebras, multiplier Hopf algebras, and Hopf coquasigroups. Full article

(This article belongs to the Special Issue Advances in Hopf Algebras, Tensor Categories and Related Topics)

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30 pages, 3321 KB

Open AccessArticle

An Efficient Temporal Two-Mesh Compact ADI Method for Nonlinear Schrödinger Equations with Error Analysis

by Siriguleng He, Eerdun Buhe and Chelimuge Bai

Axioms 2025, 14(11), 777; https://doi.org/10.3390/axioms14110777 - 23 Oct 2025

Abstract

In this article, we present an efficient numerical strategy for the two-dimensional nonlinear Schrödinger equation, focusing on its development and analysis. Our approach begins with proposing a nonlinear, energy-conservative, fourth-order, compact, alternating-direction, implicit (ADI) scheme. To boost efficiency when solving the associated nonlinear [...] Read more.

In this article, we present an efficient numerical strategy for the two-dimensional nonlinear Schrödinger equation, focusing on its development and analysis. Our approach begins with proposing a nonlinear, energy-conservative, fourth-order, compact, alternating-direction, implicit (ADI) scheme. To boost efficiency when solving the associated nonlinear system, we then implement this scheme using a temporal two-mesh (TTM) algorithm. Under discretization with coarse time step

τ_{_{C}}

, fine time step

τ_{_{F}}

, and spatial mesh size h, the numerical scheme exhibits a convergence rate of order

O (τ_{_{C}}^{4} + τ_{_{F}}^{2} + h^{4})

in both the discrete

L_{2}

-norm and

H_{1}

-norm. To facilitate the convergence analysis under fine time discretization, we propose a novel technique along with several supporting lemmas that enable the estimation of the discrete

L_{4}

-norm error term over the temporal coarse mesh. Numerical experiments are then performed to validate the theoretical results and demonstrate the effectiveness of the proposed algorithm. The numerical results show that the new algorithm produces highly accurate results and preserves the conservation laws of mass and energy. Compared with the fully nonlinear compact ADI scheme, it reduces computational time while maintaining accuracy. Full article

29 pages, 385 KB

Open AccessArticle

Harmonic Series of Convergence Ratio “1/4" with Cubic Central Binomial Coefficients

by Chunli Li and Wenchang Chu

Axioms 2025, 14(11), 776; https://doi.org/10.3390/axioms14110776 - 23 Oct 2025

Abstract

We examine a useful hypergeometric transformation formula by means of the coefficient extraction method. A large class of “binomial/harmonic series” (of convergence ratio “

1 / 4

”) containing the cubic central binomial coefficients and harmonic numbers is systematically investigated. Numerous closed summation [...] Read more.

We examine a useful hypergeometric transformation formula by means of the coefficient extraction method. A large class of “binomial/harmonic series” (of convergence ratio “

1 / 4

”) containing the cubic central binomial coefficients and harmonic numbers is systematically investigated. Numerous closed summation formulae are established, including a remarkable series about harmonic numbers of the third order. Full article

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

28 pages, 1946 KB

Open AccessArticle

Efficient Analysis of the Gompertz–Makeham Theory in Unitary Mode and Its Applications in Petroleum and Mechanical Engineering

by Refah Alotaibi, Hoda Rezk and Ahmed Elshahhat

Axioms 2025, 14(11), 775; https://doi.org/10.3390/axioms14110775 - 22 Oct 2025

Viewed by 72

Abstract

This paper introduces a novel three-parameter probability model, the unit-Gompertz–Makeham (UGM) distribution, designed for modeling bounded data on the unit interval (0,1). By transforming the classical Gompertz–Makeham distribution, we derive a unit-support distribution that flexibly accommodates a wide range of shapes in both [...] Read more.

This paper introduces a novel three-parameter probability model, the unit-Gompertz–Makeham (UGM) distribution, designed for modeling bounded data on the unit interval (0,1). By transforming the classical Gompertz–Makeham distribution, we derive a unit-support distribution that flexibly accommodates a wide range of shapes in both the density and hazard rate functions, including increasing, decreasing, bathtub, and inverted-bathtub forms. The UGM density exhibits rich patterns such as symmetric, unimodal, U-shaped, J-shaped, and uniform-like forms, enhancing its ability to fit real-world bounded data more effectively than many existing models. We provide a thorough mathematical treatment of the UGM distribution, deriving explicit expressions for its quantile function, mode, central and non-central moments, mean residual life, moment-generating function, and order statistics. To facilitate parameter estimation, eight classical techniques, including maximum likelihood, least squares, and Cramér–von Mises methods, are developed and compared via a detailed simulation study assessing their accuracy and robustness under varying sample sizes and parameter settings. The practical relevance and superior performance of the UGM distribution are demonstrated using two real-world engineering datasets, where it outperforms existing bounded models, such as beta, Kumaraswamy, unit-Weibull, unit-gamma, and unit-Birnbaum–Saunders. These results highlight the UGM distribution’s potential as a versatile and powerful tool for modeling bounded data in reliability engineering, quality control, and related fields. Full article

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

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Axioms, Volume 14, Issue 11 (November 2025) – 9 articles

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